LIBRARY University of California. Class THE PRACTICE OF NAVIGATION AND NAUTICAL ASTRONOMY. THE PEAGTICE OF NAVIGATION NAUTICAL ASTEONOMY. HENRY RAPER, Lieut. R.N., F.R.A.S., F.R.G.S NINETEENTH EDITION. REVISED AND ENLARGED. Uonlfon : PUBLISHED BY J. D. POTTER, Admiralty Agent far Cliarls 145 MINORIES, E. 1908 ^.f^ REAR-ADMIRAL SIR FRANCIS BEAUFORT, K C.B. HYDROGRAPHER TO THE ADMIRALTY SIR, The eminent station which you occupy in tlie naval scientific world renders it highly gratifying to me to dedicate the following Work to you as a testimony of my regard and esteem ; while the general accordance of my views on the subject with those of your more experienced judgment, gives me the greater confidence in laying my labours before the Public. 1 have the honour to be, SlT; Your obedient Servant, HENRY RAPER. 225301 PREFACE FIRST EDITION. Tdis Wcrk is intended for the use of all persons concerned either with the navigation of ships or with the determination of latitude and longitude on shore. The present volume, which is devoted exclusively to tlie prac- tice, contains all the rules and tables necessary in navigation, and for the determination of latitude and longitude by means of the sextant or reflecting circle. The study of its contents demands no |>revious attainments beyond the knowledge of the elements of arithmetic. Every endeavour has been made to render the whole easy of reference, and to adapt it to the use of those who may desire to instruct themselves. Rules which admit of more cases than one, as, for example, that for applying the equation of equal altitudes, are given in the form o( tables ; so that the several con- ditions involved, and their mutual connexion, being exhibited to the eye, the computer is relieved from the sense of complication, and the cliance of a mistake is materially diminished. An ample alpha- betical index is annexed, by whicli tlie reader is at once referred to all the inforiuation which the volimie can afford him. Those who have been brought u]) to the sea, and who have experienced the distaste for long calculations which that kind of life inspires, will not hesitate to admit that the only means of inducing seamen generally to profit by the numerous occasions •A-hich offer themselves for finding the place of the ship is extreme VI PREFACE TO THE FIRST EDITION. breviiy of solution. It is not, however, merely as a concession to indolence, that rules should be made as easy and simple as possible; the nature of a sea life demands that every exertion should be made to ? bridge computation, which has often to be conducted in circum- stances of danger, anxiety, or fatigue, and so to separate the several points, that the seaman may be referred directly to what concerns his case, to the exclusion of all other matter. These considerations have lieen carefully kept in view in the rules, in the examples, and in the form and order of the tables. Two kinds of solutions are employed, and, in general, two only; naicely, an approximate method, and a complete, or, as it is called, rigorous, method. The former may often serve in cases of haste, or when precision is not necessary, and will also afford a conve- nient check against the effects of a mistake in the more elaborate metiiod. All the computations are effected by the well-known methods of inspection and logarithms; and as the former, it is presumed, leave but little to be desired in point of expedition, Gunter's scale, or other mechanical methods, are not employed. Sailing on a Great Circle is, in this work, reduced, like Plane Sailing, to Inspection, by means of the Spherical Travebsk Taulr. Convenient rules are given for finding the distance of the land by its change of bearing, and by its altitude observed above the sea-horizon. The seaman will find every necessary information on the subject of local magnetic deviation. The highly useful problem of determining the latitude at sea, by the reduction of an altitude to the meridian, will be found greatly abridged ; and a table is added for the purpose of shewing the limits within which the result may be depended upon when the time at shi|) is in error. This table will bo found, it is presumed, of considerable utility, as it is perhaps from the want of some specific information as to the degree of confidence which it is safe to place in the result, no less than of a short and easy rule, that this excellent observation is almost entirely neglected ; and, in conse- tjiienee, the latitude, when the meridian altitude is not exactly obtained, is too often lost for the day. The approximate solution of the double altitude, as a questioL of Time, will be found, it is hoped, well adapted to general use: since unless tLe latitude by account is very much in error this PREFACE TO THE FIRST EDITION. VU aietnud determines both the true latitiiJe anil tlie time at ship; and the computation of the time is one with which seamen are familiar in the next degree to tnat of the latitude by meridian altitude. The principle is not new, but rules have not hitherto been given for computing directly the error of the latitude by account. The first approximate method of clearing the lunar distance ia new, being effected, like many other problems, by the Siiherical Traverse Table. The rigorous method is a modification of Borda's, and employs five logarithms, of which two only are taken out to seconds. In a work in which many of the methods are new, I have felt it would be more satisfactory to the professional reader to find them illustrated by observations actually taken at sea. The examples are accordingly selected from the journals of Captain W. F. W. Owen, who kindly lent them to me for the purpose; though, neces- sarily, in proceeding by fixed rules, I could not introduce the solutions employed by that distinguished navigator. The remaining observations have been furnished to me by the Rev. G. Fisher, astronomer to Sir Edward Parry's expedition to the Polar Seas. In order to enable the computer to judge of the degree of pre- cision to which he attains, the degree of dependance to be placed on tiie result, or the limit of probable error, is indicated. This is the more important, as very indistinct and erroneous notions prevail among practical persons on the subject of accuracy of com])utation ; and much time is, in consequence, often lost in computing to a degree of precision wholly inconsistent with that of the elements themselves. The mere habit of working invariably to a useless precision, while it can never advance the computer's knowledge of the subject, has the unfavourable tendency of deceiving those who are not aware of the true nature of such questions into the per- suasion that a result is always as correct as the cop puter chooses to make it; and tlius leads them to place the same confidence in all observations, provided only they arc ivorhtd to the same degree of accuracy. By habitually following the short precepts laid down on this point, tlie computer will learn insensibly to estimate the value of liis results ; of which, since the limit of error is the sole ciiterion of the accuracy of any determination, he cannot otherwise be a judge. The degree of precision to which it is proper to carry the work in any case is observed, in general, in the examples. In the Tables every endeavour has been made to repde"- the Vm PREFACE TO THE FIRST EDITION. collection complete for the purposes required, and to compress the whole into small compass. For the sake of clearness, a different figure has beei) adopted for the argument and for the numbers in the body of each table. In the logarithms six places of figures only are employed, because a single result in which six places are necessary cannot be depended upon to the degree of precision obtained. On the same principle, some of the logaritlims are given to three places only. The log. sine square of half the arc, Table 61, universally familiar to seamen in finding the time, is given, for the convenience of this constant computation, to every second of the 12 hours. By means of this term tables of versed sines are dispensed with, all our solutions being either numeral or purely logarithmic. I have not, either in the Rules or the Tables, aimed to make that additive which is in the nature of things subtractive. The precept subtract is as easy as the precept add; and when the student has the natural process before him he may be led to dis- cover the reason of it; and must thus, by attention, always advance in knowledge of the subject. But an artificial process obstructs the exercise of the faculties, or leads the student, who reflects on what he does, to false conclusions. The composition of the Table of Maritime Positions has been a very laborious task, and has caused great delay in the appearance of the Work. The numerous chronometric measures furnished of late years liave rendered it necessary to deduce longitudes in a more systematic and accurate manner than that hitherto followed, which has cliiefly consisted in modifying former determinations by means of those succeeding them. Absolute, or astronomical positions, and relative positions, being distinct things, and the latter being by far of the greater consequence to navigation, it is necessary, preparatory to a complete and final arrangement, to separate these two kinds of determinations. Accoi'dingly, in a series of papers, some of which have been already published in the Nautical Magazine,* I have endeavoured to arrange the chronometric differences of longitude with reference to certain fixed points, convenient for the purpose, which it is proposed to call Secondary Meridians. These standard • The data or evidence for the several positions being given in these papers, the ralue of each determination is easily appreciated ; and accordingly, individuals in pos- session of one or more good watches may, by correcting defective measures, or by establisliing new linlcs of connexion, render material service to maritime geography. See Nautical Maijazine, 1839, and followin;^ years. rUEFACE TO THE FIRST EDITION. IX Iiositioiis, of which the number assumed is eighteen, being con- siderably distant from each other, are determined nearly enough for present purposes, and would, according to the system proposed, be finally settled by long series of astronomical observations. An account of the principles adopted in this arrangement, and of the several voyages and surveys from which the materials have been taken, will be found, together with some suggestions for the advancement of the subject, in the Nautical Magazine. But it is necessary to state here, that the late determinations of the longitude of Madras have, from the importance of that position, occasioned a long and intricate discussion. Mr. Riddle and Mr. Maclear have compared observations of moon culminating stars made at Madias, with like observations made in Great Britain and at the Cape of Good Hope respectively. According to their computations, which agree very nearly, the received longitude, 80" 17' 21", is about 3' "21" too great. The number and superior character of these observa- tions, and the agreement of the results, liave led me to adopt, with- out hesitation, 80° 14' 0" ; while the magnitude of the correction has rendered it indispensable to trace its effects on the longitudes of the Eastern Seas.* Precision in the Maritime Positions, especially in the longitudes, becomes, as navigation advances to perfection, a matter of increasing importance; because, where longitudes are well determined, the error of a chronometer may be ascertained on every occasion of making the land. It will not be out of place to remark here that it is high time the chronometer should be found, like the compass, among the stores of every vessel beyond a mere coaster. It would be superfluous to attempt to prove that the hardships and privations consequent on missing a port, the losses of ships from being out in their reckonings, and the evils incident to navigation generally from the want of a ready means of checking the enormous errors to which the dead reckoning is liable, would, in numy cases, have been prevented by a chronometer. In urging tiiis recommendation, it is, of course, taken for granted tliat they to whose hands the chronometer is entrusted are qualified to make a ])roper use of it. Employed merely as a check, a single chronometer cannot fail to prove of great service ; but too firm a reliance on such an instrument would lead to the dangerous error • The accepted LnngituJe of Madras, India TrigonoiDetiical Survey, 1878 (sea pnge ?94), is 80° 14' S« ' E K PREFACE TO THE FIRST EDHION. i»f relaxing that vigilance which tlie known uncertaintj of the dead re-jkonuig keeps perpetuallv alive. A list of times of high water, or, as they are now called, Esta- blishments of Ports, is not given. The researches on tlie tides made of late years by Mr. Lubbock and the Rev. W. Wheweil, iiave proved that the establishment cannot be truly deduced but from numerous observations, and consequently that a sim])le recorded time of high water is altogether insufficient. Moreover, if the esta- blishment were correctly known, the time of high water, as also the height of the tide, cannot be determined without other elements, which, except in comparatively few places, are not afforded. But in navigation it is not the true instant of high or low water that is required so much as the time at which the flood or ebb stream turns, oecause tliis last affects every vessel when near the shore ; and the proper place for information of this kind is, obviously, the Sailing Directions. Although some results of the kind might be advantageously placed in a general work on navigation, yet the uncertainty of almost all that has been published, and the difficulty of collecting better materials, will, it is hoped, excuse the omission, at least for the present. It may, however, be remarked, that under whatever form it maj hereafter be found advisable to publish particulars of the tides, the observations required are so numerous, the discussions so tedious, and the whole subject so complicated, that no individual could undertake successfully to treat this branch of navigation unless ia a work devoted exclusively to its consideration. The subject of Maritime Surveying, usually treated in works of this kind, has been omitted. Surveying is no part of the navigation of a ship, and a survey having any pretensions to authority can scarcely be made by a person whose qualifications for the task are confined to the slender information contained in a few pages. A survey is a matter of too great consequence to the security of navi- gation to be received from incompetent hands ; and the seaman who desires to acquire a knowledge of surveying should study works treating expressly of this branch of science. The customary chapter on the Winds has likewise been omitted. The subject, generally, does not belong to tfie navigation of a ship,* and, even if it did, the general information contained in a few pages, thougli interesting as a branch of natural philosophy, is PH.KTACE TO THE FIRST EDITION. xl neoessarilv too vague to be effective in shaping tlie course. The same applies to Currents, and also to the Marine Baronietc r ; which, though matters of important consideration in sea-voyages, are not concerned in the practice of navigation, since this term, in btrictness, comprehends only tlie consideration of the place of tlic ship when her circumstances and destination are given. Tlie space gained by the omission of these collateral subjects, and other matters sometimes introduced, is appropriated to the numerous practical details of the proper subjects of such a treatise. The Work will be completed by another volume, wliicli will be entitled the Theory of Navigation, and will contain the construc- tion of the rules and tables, for the advantage of those who desiie to confirm their practical knowledge by matliematical investigation. It will contain, likewise, those methods in which the transit and azimuth instruments are employed. The present volume being thus, in tlie ordinary practice of navigation, indepentlent of the second, no notice of anotlier volume appears in the title-page. By the term Theory is commonly understood, in this particular :nibject at least, the scientific principles on which the rules are formed. Considerations of this kind are thus altogether excluded from the present volume; but, on tiie other hand, that rationale, or process of reasoning, which, in considering the nature of the case, is obvious to common sense or apprehension, is, in raost cases, intro- duced, as necessary to a clear understanding of important points. The theory and the practice are thus kept purposely distinct. The former is not always necessary to successful practice; and rules constructed for ready and general application approacli to perfec- tion in proportion as they leave less to individual judgment or skill. It is the custom, generally, to teach the theory first ; the impression forced upon me is, on the contrary, that the practice is itself the best foundation for sound and rapid advancement in the theory. For he who has acquired the practice knows the nature and extent of the subject; and in proceeding to the theory he has a distinct pev^cption of the object to be attained. This is not the place for a discussion on these points; but it was incumbent on me to state, in a few words, the grounds of the arrangement adopted. It is manifestly the duty of a writer, who undertakes to treat a subject in a thoroughly practical manner, not only to discuss every point which ])resents itself, but also to pronounce a decided (>)iiiiii)n in every case. It is proper to bring this point under tlic notiru nl Xli PREFACE TO THE 1-IRST EDITION the reader, who, especially if he has more experience in these inattprs than myself, might otherwise be disposed to consider many things In this volume as laid down too positively. I cannot close the preface to a work which has been some years in preparation, and in which I have endeavoured to reduce to a practical form every useful consideration which has been suggested by my own experience or by intercourse with eminent officers and men of science, without soliciting the indulgence of the reader to errors and to deficiencies. Absolute correctness, especially in tables, is scarcely attainable ; and in a treatise which contains much that has not appeared before, I cannot reasonably fiatter myself that, notwithstanding every care and attention, some small inaccuracies may not be found. H. B Saptemhkr 1 6'}0 ADVERTISEMENT THIRD EDITION. In tlie Advertisement to tlie Second Edition Iliad the satisfaction of being able to state that the Eoyal Geographical Society had conferred the flattering distinction of their gold medal on the first edition, and that the Lords Commissioners of the Admiralty had honoured my work by ordering it to be supplied to Her Majesty's Navy as ship's stores. The present edition has been greatly augmented. Much of the -work has been rewritten. Two approximate methods of determining the time, though of inferior value, are introduced, since a work aiming to be complete for practice should contain provision for extreme cases. Nos. 789, 791. The introductory portion, it had often been suggested, was in- sufficient for the purposes of elementary instruction. It is easier to allege this, than to lay down a condition which is to determine the extent of such preliminary matter. An attempt, however, has been made to fix a limit, on the following grounds : — The most general defect, perhaps, in the education of seamen, as regards the present subject, is an insufficient knowledge of iiiitlimetic; by which I mean, not of the more advanced rules, but of the elements, and especially of proportion. Now all ques- tions to which arithmetical processes are applied involve some proportion, which the operation is to bring out, or distinctly assign ; and it appears, accordingly, a great omission in our education that we are not more exercised on this point, which is tbe sole object or end of the processes which we learn to practise mechanically! KIV ADVKRTl&EMKiNT TO THR THIRD KUITION. Again, in geometry, it is not tlie variety of problems wliicb benefits the practical man, but a v^ell-grouiided and familiar know- ledge of a few comprehciibive propositions, which he applies readily, and with confidence; and the geometrical knowledge which appears to me to suffice to our present purpose is comprised in, — 1, the property of the square of the hypothenuse; 2, the measure of an nngle at the cir^'iuiference ; 3, the similarity of pl-ine triangles The first is of general importance; the second includea the problem of fixing a station by means of two angles subtended by three objects; and the third is the basis of trigonometry. In this edition, therefore, proportions and fractions are treated at some length, and illustrated by numerous examples which afford tlie student abundant exercise ; and a short course of geometry is given, after the manner of Euclid, sufficient to establish the above important theorems. These limitations, the reader will bear in mind, are intended to apply only to that particular quantity of elementary matter which is assumed to be necessary and sufficient for the scale of attain- ment contemplated in the present volume. In the Table of Positions many points of information of con- sequence to seamen are expressed by means of a new system of Symbols. In these days little apology is required for introducing a scheme which a few years ago would have been deemed a rash innovation. But a growing tendency to the use of symbols mani- fests itself on all sides. Efforts have been made to represent, as far as possible, all matters of instruction under a form addressed to the eye ;* and symbols effect this object in an eminent degree, for their distinct and cons])icuous forms, contrasting with the mono- tonous aspect of alphabetic writing, arrest and fix the attention, while their extreme conciseness admits the insertion of matters to which, for want of room, no allusion could otherwise be made. The employment of symbols, therefore, on a more extensive scale than we have yet been used to, and that at no distant period, may be considered inevitable ; and the present system, which bos occupied my attention for several years, is proposed as so far deserving consideration that it is constructed with rigid adherence to principles.f The number of sigus which I have ventured to • The Physical Atlas Is an example. f The necessity for a uniformity in hydrographic sym'iols has already shewn its.Mf. Symbols similar in character denote, on the French charts, rocks 'ibuce the water, <>ui1 oil the Kussian charts rocks below the water. ATJVF.RTISl'.MKNT TO TlIK THIRD EDITION, \\ iiifrodiipe is small, since, in matters waiting tlie sanction of experi- (Mice. it is better to move too slow than too fast. The introduction of symbols has necessarily modified the original design of the work, as described in the preface, and has justified allu- sion to many matters which otherwise would not have found a place •n it. The chief labour of this eaition tas, indeea, ofthe two former) has been tlie Table of Positions, which, in consequence of the nu- nierous references made to my labours in this country and abroad, I was desirou3 to extend. The list now contains 8,800 places; and as the degree of accuracy is indicated wherever I have found the means of forming a judgment, and as many physical details are supplied, — such as the dimensions of islands, heights, and the depths of shoals, — the table may be considered as representing the state of maritime geography at this day. The number of voyages, charts, and surveys, which it has been necessary to consult, — the labour of digesting and comparing the mass of materials collected, and the introduction, by a new method, of numerous details im- portant to navigation, — will, it is hoped, excuse tlie long delay in the appearance of this edition, and account for the work having remained out of print for nearly three years. In conclusion, I gladly express my obligation to the draftsmen and other gentlemen of the Hydrographic Office, whose patience during many years I have sorely taxed in the inspection and re- examination of thousands of documents, and without whose active and disinterested assistance I must have left much in a very unsa- tisfactory state. ADVERTISEMENT TO THE NINETEENTH EDITION The revision and enlargement of this edition of the « Practice ol Navigation and Nautical Astronomy » was undertaken with con- siderable diffidence, it being felt, that while it was possible to spoil little could be done to improve, this best of practical works ^^ Criptrir Sr golden age of practical Navigation and v.,.+iP.l Survevin- by an officer in constant communication with Ltor aTd HorsbLgh, and the Captains and Masters who served under these distinguished chiefs in England and India LTutliant Eaper's labours are founded u^^n a t^^-o^f P-"^ experience, and may be looked upon as the work of a Sailor for the use and benefit of Sailors at Sea. , One chapter alone required to be re-written. The use of iron in modern Lpbuildhig, by its natural effect on the Mariners Compass, having greatly increased the difficul les of navi^^a.^n at sea some additions have therefore been made to what Eaper Lad Lady written upon this important subject. This chaptei^ as well as^U parts of the book referring to the variation and LTation of the'compass, has been re-written by Captain W. Mayes, R N late Superintendent of Compasses at the Admiralty. _ ■ Captain Mayes has also assisted in making a careful examina- tion of the whole work, which is sufficient guarantee for its having nrs^utfytwedhowwell and earnestly Eaper had c^^^^^^^^ out the intention expressed in the Preface to his First Edition (sTe p. V) of" inducing seamen to profit by the numerous occasions ' Sailors are earnestly requested to read til? Trefoct ADVEKTISKMKNT TO TIIIC NINETKICNTII KUITION. XVU (vbicb offer themselves for finding the place of the ship ; " by laying before them methods whose " extreme brevity of solution abridged computation." These short rules aid the prompt decision upon which the safety and success of a ship at sea so often depend. A brief study of the comprehensive index will call attention to " the numerous occasions " alluded to. The key to most of the modern short methods for fixing the position of the ship will be found in Raper's " Practice of Navi- gation." Under the head of " Degree of Dependance " is placed before the navigator the amount of possible error, a thought which should never be absent from bis mind in considering the estimated position of a ship, with the view of determining his future proceedings. The sailor's attention is earnestly called to the chapter entitled " Navigating the Ship," which contains what John Davis, the navigator, writing in 1607, aptly termed the " Seaman's Secrets." In this, the concluding chapter of the work, Raper shows clearly the never ceasing watchfulness that is required, in both fair and foul weather, in obtaining the observations, terrestrial as well as celestial, necessary to conduct a vessel in safety from one port to another. The simplicity of its mathematical theory makes Navigation appear an easy matter to men teaching or using it on shore ; but Pilotage, common and proper, is a very different business when practised by sailors in a gale of wind, at night, or in hazy weather, on board a ship at sea. Proficiency in the science can never compensate for a lack of experience in the handicraft of naviga- tion. This experience can be attained only by incessant practice at sea; by a capacity for taking trouble, unceasing caution, and a desire to do well. In such labours the sailor will find no better friend and assistant than Raper's " Practice of Navigation." No changes in the numbering of the paragraphs have been made, and great care has been taken to leave the book in the style in which it was originally written, so that old students will have no difficulty in finding the various methods with which they are familiar. Some slight changes have been made in the Tables. Con- siderinrr tlie great increase of speed attained by modern steam- ships, Table 1, formerly Table 2, has been enlarged from 300 to GOO miles of distance. The Table giving the Diff. lat. and Departure for every quarter point has been withdrawn. Xviii ADVERTISEMENT TO THE NINETEENTH EDITION. Table 10, of Maritime Positions, upon which Eaper bestowed a very large amount of labour, has been revised with great care from the latest Admiralty Charts, so that it may still " be considered as representing the maritime geography of this day " (see p. xv). These; positions mainly deiJend on the Table of Longitudes accepted for Secondary Meridians, amended from telegraphic observations to 1887, published in the Admiralty " Instructions to Hydrographic Surveyors." This Table of Secondary Meridians has been inserted in the Explanation of Table 10. Steam having in a great measure rendered Table 12 obsolete, it has been replaced by a Table of the navigable Mercatorial Dis- tances between the principal ports and points of the world. Tables 11 and 13 (Approximate Variation of the Compass, and Tide-hours, or Establishment of the Ports) have been taken out, as the Admiralty Charts, and Admiralty and Indian Tide Tables, published yearly; with the Chart of Curves of Equal Magnetic Variation (No. 2598), corrected up to date; always give the latest information. These tables have been replaced by others showing first: where docks &c. may be found and coals obtained ; and second, the position and nature of the Time signals, in all parts of the world, for the correction and rating of chronometers. Table 65, of natm-al sines, taiigents, &c., to assist magnetic computations, has been inserted in lieu of that of log. sines, tangents, &c., to quarter points. With these few exceptions the Tables retain the same numbers they held in former editions. In conclusion, thanks are due to Captain John C. Almond, Nautical Inspector of the P. and 0. Company, for his many valuable suggestions. THOMAS A. HULL. ilAMEE, Honor Oak : December 21, 1810. In this reprint of the Nineteenth Editiof., the Sun's declination, the Sidereal Time, and the Equation of Time have been given for the years 1901, 1902, 1903 and 1904, in Tables 60, 61, and 62. Table 60a, correction of Sun's declination in Table 60 to 1928, has been restored. Tables 10, 12, and 13 have been brought up to date. Table 38, Corrections of Altitudes of Sun and Stars, has been extended, and the gross corrections are given for ' Height of the eye ' up to 60 feet. Table 47, Limits of the Reduction to the Meridian at Sea, has been recast. Table 70, Logarithms for computing the Reduction to the Meridian at Sea, has been extended to 35' of declination. Tables 41 and .52 have also been recast. CONTENTS. INTRODUCTION. I. Fractions 1 II. PnoPOETlON 10 III. LOOARITHMS 18 IV. Peactical Geomethy 21 V. Geometet and Plane Tkioonometbv 32 VI. MtrTHons of Solution fiO VII. Spueeical Teigonometey 65a NAVIGATION, p I. PFFiNmoNS 55 II. ISSTBUMENTS OF NAVIGATION 63 I. The Compass 63 „ „ Variation of 70 „ „ Deviation of 73 „ „ Adjustment of 81 Magnetic Maps 82 II. The Log and Glasses 104 Sextant, Peotractoe, and Station-Pointer 143 & 178 III. TnE Sailings 106 I. Plane Sailing, with Teaveese, Ccebent, and Windward Sailings 106 II. Parallel Sailing, with Middle Latitude, and Mercatdr's Sailings 119 III. Great Circle Sailing 129 IV. Taking Departdres 137 I. By a Single Bearing and Distance 137 II. Determination of Distance 137 III. Methods by the Chart 143 V. Charts 145 I. Use ok Meecator's Chaet 116 „ Projection of a Geeat Circle U7 II. Oon.itruction of Mercatok's Chart M!) III. Properties of certain Peojections 149 VI. BOLNDINO l.'>l CONTENTS. rxoF The Ship's Journal 154 I. Keeping the Ship's .Tocbnal .. l-'yi IL The Day's Work l-"^" NAUTICAL ASTRONOMY. Definitions 16] II. Instruments of Nautical Astronomy 1-78 I. The REtxECTiNO Instruments, Sextant I'S II. The Aetificiai. Hohizon 188 III. The Cheonometeh 191 III. Taking Observations 1^3 I. Observing Altitudes 193 II. Observations ttith and without Assistants ... 201 III. Employment of the Hack Watch 202 IV. Finding the Stars 203 IV. Subordinate Computations 205 I. The Greenwich Date 206 n. Reduction of the Elements in the Nautical Almanac 207 III. Conversion of Times 216 IV. Houh-Angles 218 V. Times of certain Phenomena 224 VI. Altitudes 230 VII. Azimuths 240 v. Finding the Latitude 243 I. By the Meridian Altitude 243 II. By the Reduction to the Meridian 249 III. By Double Altitude of the same Body 255 IV. By Double Altitude of different Bodies 270 V. lir the Altitdde of the Pole Star 277 VI. Finding tee Tim r, • I. By a Single Altitdde 278 II. By Diffeeence of Altitude near the Meeidlah 285 III. By Equal Altitudes 287 IV. Rating the Cheo.nometeb 233 PAOM VII. PlNDINQ THK LONGITUDE 2t>7 I. By the Cueonometbb 297 II. B» THB Lunar Obseetation 301 m. By the Moon's Altitudb 319 IV. By a» Occhltation 322 V. By Eclipses of Jupiteb's Satellites 3?,fi VUl. Finding the Vabution op the Compass 326 L By THB Amputudh 326 II. By the AzraoTK 328 III. By Asthonomical Bearings 331 IV. By Tkrhestelil Beabings 333 IX. The Tides 335 I. Phenomena of the Tides 33S II. Edles for Finding thb Timb of High Wateb... 341 III. TiDB Obsebvations 345 NAVIGATING THE SHIP. 1. Shaping the Couhse 347 II. Place of thb Ship 3S1 in. Deisemining the Coerent 364 IV. Making thb Land 365 Ekplakation or the Tables 377 TABLES. N^.VIGATIOK Tnii Sailings :— TABLE PAGE P&na 1. Ti-averse Table to Degrees 432 Explanation 377 3. Departiire and Corresponding Difference ofLongitnde 622 „ 381 4. Difference of Longitude and Correspond- ing Departure 523 „ 381 5. Spherical Traverse Table 524 ,, 382 6. Meridional Parts 533 „ 385 Departures : — 7. For finding the Distance of an Object, by Two Bearings and the Distance run between them 538 „ 386 8. True Depression or Distance of the Sea Horizon 539 „ 386 9. Number of Feet subtending an Angle of 1' at different Distances 539 „ 387 10. Maritime Positions • 540 „ 387 11. Places at which Docks may be found, Coals obtained, &c 634 „ 406 12. Navigable Mercatorial Distances 635 „ 406 13. Time Signals 644 „ 407 Tides : — 14. Epacts 646 „ 407 15. Semimenstrnal Inequality 046 „ 407 16. Approximate Rise and Fall of the Tide 646 ,. 407 NAUTICAL ASTEONOMY. Repuctiok of the Elements in the Nautical Almanac:— 17. For converting Arc into Time 647 „ 408 18. For converting Time into Arc 617 „ 408 19. Correction of the Sun's Declination, at Sea 648 „ 408 • Tallin of Longitudes accepted for Secondary Meridians, 392. CONTENTS. XX HI TARLK riOg Ff.r.ti 20. Correction of the Equation of Time, at Sea G48 Explanation 408 21. For reducing Daily and Twelve-hourly Variations 649 „ 408 21a. Logarithms for reducing Daily Varia- tions G5.5 „ 409 22. For reducing the Moon's Declination ... Git? „ 409 2.3. Acceleration 650 „ 409 24. Retardation 659 „ 409 25. For finding the Equation of Second Dif- ferences 060 „ 409 Times or certain Phenomena: — 26. Apparent Time of the Sun's Rising and Setting 661 „ 410 27. Approximate Apparent Times of the Meridian Passages of the principal Fixed Stars 664 „ 410 27A.Correction of the Times in Table 27 ... 665 „ 410 28. Correction of the Time of the Moon's Meridian Passage 665 „ 410 29. Hour-angle and Altitude of a Body upon the Prime Vertical 666 „ 41J A.UITCDE : — 30. Apparent Dip of the Sea Horizon 671 „ 411 31. Mean Astronomical Refraction 671 „ 412 32. Correction of the Mean Refraction for the Height of the Thermometer 672 „ 412 33. Correction of the Mean Refraction for the Height of the Barometer 673 „ 412 34. The Sun's Parallax in Altitude, and Semidiameter 673 „ 413 35. Dip of the Shore Horizon 673 „ 413 36. Corresponding Thermometers 674 „ 413 37. Corresponding French and English Measures 674 „ 413 38. Corrections of Altitude of the Sun and Stars 675 „ 41i 39. Correction of the Moon's apparent Alti- tude 676 „ 414 40. Corresponding Horizontal Parallax and Semidiameter of the Moon 685 „ 414 b 41. Correction of the Moon's Equatorial Parallax for the Figure of the Earth . 685 42. Augmentation of the Moon's Semi- diameter , 685 43. Correction for reducing the true Alti- tude of the Sun or a Star to the appa- rent Altitude 086 44. Correction for reducing the true Alti- titude of the Moon to the apparent Altitude GSG 45. Parallax in Altitude of a Planet 6SG 46. Azimuth and corresponding Change of Altitude in One Minute of Time 687 LatITUL'K : — 47. Limits of the Rtxluction to the Meridian at Sea 688 48. Value of the Reduction at which the Second Reduction amounts to 1' G88 49. For computing the Reduction to the Meridian in Seconds 689 50. For computing the Second Reduction in Seconds 691 51. Correction of the Altitude of the Pole Star 692 52. Reduction of Latitude 693 liONOnUBE: — 53. Correction of the Lunar Distance for the Contraction of the Vertical Semidiameter 693 54. Error of Observation arising from an Error of the Parallelism of the Line of Sight 693 55. For correcting the Lunar Distance for the Spheroidal Figure of the Earth... 693 5C. For computing the Moon's Second Cor- rection of Distance 694 - 57. Correction of the Greenwich Mean Time for the Second Difference of the Lunar Distance 695 B8. Error of the Ship's Place in Nautical Miles, and of the Longitude in Time, corresponding to an Error of 1' in the Lunar Distance t'>95 Explanation 414 » 415 415 415 415 415 41 C 416 416 417 417 418 418 418 CONTENTS. XXV Variation of tub Compass: — 59. Amplitades 690-7 Explanation 419 59a. Correction of the Amplitude observed on the Horizon, for the Effect of Re- fraction 690-7 „ 420 To Supply the Place of tub Nautical Almanac : — 60. Declination of the Sun 698 „ 420 60a. Correction of the Sun's Declination 700 „ 420 01. Sidereal Time and Riglit Ascension of the Sun 701 „ 421 62. The Equation of Time 703 „ 421 6:{. Mean Places of Stars 705 „ 421 LodAKI THM.'' : — 64. Logarithms of Numbers 706 „ 422 64a. Spheroidal Tables 724 „ 423 65. Natural Sines, Cosines, Tangents, Co- tangents, Secants, and Cosecants 725 „ 4?3 66. Log. Sines of small Arcs to each Second 726 ,, 423 67. Log. Sines of small Arcs to Ten Seconds 735 „ 424 68. Log. Sines,Cosines, Tangents, Cotangents, Secants, and Cosecants 738 „ 424 69. Logarithm of the Square of the Sine of HalftheArc 828 „ 426 70. Logarithms for computing the Reduction to the Meridian, at Sea 803 ,, 427 71. Logarithms for computing the Correction of the Latitude bj Account 897 „ 423 72. Logarithms for computing the Equation of Equal Altitudes 899 „ 428 73. The Logarithmic Difference 900 „ 428 74. Proportional Logarithms 909 „ 129 Aur.RKviATiONS adopted on Admiralty Charts, WITH Explanatory Noif.s 9?li Gknkral Indlx 927 Maps of botu IIemispueuls To be ^'laced between pages S2 mni 83 DlA'lBAM TO ILLUSTRATE SUMNEU's METHOD FOR FINDINO THE Posnioy OK A Ship at Sea Tofacepaye 363 INTRODUCTION. r. KitACTiONS. II. Proportion. III. Logarithms. IV. Prao- TiCAL Geometry. V. Eaising the Trigonometrical Canos. VI. Methods of Solution. 1. Vulgar Fractione. 1. A NUMBER which is a portion of 1, or unity, is properly- called a fraction ; thus, if we divide a foot into 3 equal parts, each of such parts is the fraction called a third, and written ^. These numbers arise, in arithmetical operations, in division, when the dividend is not divisible by the divisor in whole numbers, or, as they are called, integers; thus, if we divide 10 feet into 3 equal parts, each will measure 3 ft. and one-third, or 10 divided by 3 gives the quotient 3, and 1 over — that is, 1 not divided like the rest ; but proceeding now to divide this 1 by 3, we call the result or quotient ^ ; that is, 1 divided uy S. 2. If we divide 1 into four equal parts, each is one-fourth, written ^ ; if into 5 equal parts, each is vue-fftii, written ^; thus, the name of the fraction is that of the number of parts into which the unity or entire quantity is divided ; and this number is hence called the denominator of the fraction. 3. If we take two of thi-ee equal parts of subdivision, or two- thirds, we write § ; if we take three of four equal subdivisions, we write I ; if we take three of seven equal subdivisions, we write ^ ; and 80 on : the number 2, 3, in these examples, which shews or enumerates the number of fractional parts taken, is hence called the numerator. The term fraction is thus used to denote not only one part or subdivision, but any number of such. 4. In enumerating fractional parts we may go on, for example, s' l> 5> I' I' 5' 5' '^''- Here f represents the whole, or entire quantity, since it enumerates as many parts as the whole is divided into; the fractions (so called) beyond this, as 9,, i, are all greater tlian 1, and are termed mixed or improper fractions. 5. The fractions to the left of f are less than 1, and are proper fractions; hence, when the numerator is less than the denominator, the fraction is less than 1 ; when equal, the fraction represents 1 ; and when greater, it is greater than 1, and is capable of being resolved into a whole number witl or without a fraction. INTRODUCTIO>f. Hence aUci, the greater the denominator the smal.er the fractioa, and the smaller the denominator the larger the fraction. 6. If we take a line AB, and divide it into 3 equal parts by tiie points K, l; and another line BC equal to it, and divided similarly Rt M, N, then Al is « of AB, or of i. Then the parts being all equal, Ak and kl, are equal to lB and Bm, and these to mn and nC; therefoie Ak and kl are J of AC, that 18, of 2. Hence Al is | of 1, and ^ of 2 ; or, ^ of 2, and | of 1 are the same thing. If AB is 1 yard, it is evident at once, since 2 ft. or I of 1 yard are | of 6 feet, or 2 yards. 7. The value of a fraction is not changed by multiplying the numerator and denominator by the same number. The term one-half is equivalent to two-quarters, to four-eighths, and so on ; that is ^, f , J, &c. are all equal ; since it is evident that the result is the same if we divide the whole into twice the number of parts, and take twice the number, or into 3 times the number of parts, and take 3 times as many of them. The above fractions are ^, the numerator and denominator being both multiplied successively by 2. Again, take f, multiply both numerator and denominator by 3, it becomes -j*^^ : if now we take a line and divide it into 5 equal parts, and 15 equal parts, it will be the same thing whether we take two OJ the larger parts, or six of the smaller, wliich are J the size. 8. The value of a fraction is not changed by dividing the nume- rator and denominator by the same number. This appears in exactly the same way as the above, in any case ; thus, -/j, dividing both im- merator and denominator by 3, gives |. The process is equivaleiii to dividing the unit into larger portions, and taking fewer of them in proportion Fractions are tlius often simplified : example, -f^j is evidently re- ducible to iVs ; tVjs to Jj.* • A fraction is reduced to its simplest terms by finding tlieit greatest common meayi.-'e, thit is, the largest number which will divide them ba"j without a remainder. To find tif greatest common measure of two numbers, Divide the greater by the less. Consider the remainder as a new divisor to the former divisor as a dividend, and find the next remainder. Consider the last remainder as a ne.v divisor, and find the next remainder, and so on. The last divisor is the number required. If the last divisor is 1, the numbers have no common measure but 1, that is, arc not further reducible. Ex. I. Find the greatest sate of 24 and 124. 24)124(5 J 3 [1] Reduflion to a Cmnmon JJmnmJnatnr. 9. Suppose it is required to add togetlier 5 and |; if wc could p.i once express tliirds in fifths, or fiftlis in thirds, we siiould then merely enumerate tiie number of parts ; but as one of these fractions is no exact number of times g;reatcr than the other, (as may be seen by dividing a line into 5 parts and 3 parts), we cannot do this. But by multiplying the numerator and denominator of one by some number, and of the other by some oilier number, (which leaves the fractions unchanged in value. No. 6) we may select such multipliers as will produce the same number in the denominator; thus, multiplying the numerator and denominator of f by 5, gives ^-y, and muitiplying the numerator and denominator of | by 3 gives ^, and the fracuoi.a f and f are thus reduced to 15ths. Again, to reduce -^^ and ^^ to the same denominator, multiply the numerator and denominator of j'j by 11, which gives ^^^^, and -,', by 12, which gives ^^.*j. These reductions are effected by multiplying each numerator by the other denominator, and the two denominators together ; and the same ajjplies to three or more fractions taken in succession. Hence the Rule: Multiply the numerator of each fraction by every deno- minator, except its own. for the new numerator, and multiply all the dtiiominators together for the new denominator. &.. I. Reduce -, -'-, and -. 3 >5 7 2«.,«7 iM"? .MX'5 „"o »i il 3x15x7 3x15x7 3x15x7 315'3'5'3'S" RI.2, Reduce ii, I. and i. 11x1x7 1x17x7 4x17x2 154 1,9 ,36 17 X a X 7' 17 X 2 X 7' 17 X 2 X 7' 238' 238' 237 SX.S. Reduce-.and-;. iM 175 360 420' 4S0' 4»o' 10. The process of reduction to a common denominator is often necessary in the comparison of two fractions, to find which of the two is the greater ; thus, to compare j'^ and ^, these become ^^| and ^-^ hence -j'f is the greater. 1 1 . Whole numbers are written in the fractional form by em- ploying 1 as the denominator ; thus 3 is written ^, the 1 is in the place of the unit divided into 1 part (No. 2), that is, left entire, and the 3 denotes that 3 such jiarts are taken (No. 3). 12. By means of this last notation whole numbers are reduced to fractions w ith the same denominator, by the rule No. 9. Thus 1 1 and I, or '-' and { hcconie V *"<^ l- 13. Reduce the fractions to a common denominator, add the numes rators (No. 9), and under the sum place the common denominator. Ex. 1. Add tugeUier -'- «d -. These bea,ite ^-^^ = -2, ,.nd ^^^ =■ ^■, ihcs ,m 17 3 17x3 51 3x17 c. r>f.. I. ;-..:. *2 INTEODUCTION. Add together -, -, and -. Ane, Add — , -, and . Ans. • 3 ^ , ' A 364- -^, --, and -. Ans. ^-r^ : 10' 16 3 4S0 [3.] Subtraction. 14. Kule: Reduce the fractions to a common denominator, and subtract the lesser numerator from the greater for a numerator. TiiU!^, suppose it required to subtract J from i, these become Jj, and ■/j, and fg from -3^ leaves Jj, tlie remainder required. Hence it appears that the ditFerence between ]- part and I j)arl )s -\, of the whole. Fhid tl.e difference between ^ and -. These become 1^ a udii 35 35' Subtract -L fro. i-. An. ^. Subtract— from — . Ans. ^ = .^. 13 5 65 6s [4.] Jitultlplicatluii, 15. To multiply a fraction by a whole number is to repeat tiiu fraction a given number of times ; that is, to multiply \ by 3, or to take \ three times, gives \. Hence to multiply a fraction by a whole number is to multiply the numerator. Hence a number multiplied by a (proper) fraction is diminished; thus, 3 multiplied by i, which is ^, is less ttian 3. 16. To multiply a fraction by a fraction, as for example ^ bv |. Since I is the same as twice one-fifth, we have to take J of |, and double the result. To take \ of 4 is to divide } into 5 parts and take one of them; now } is 3 X J^ (by No. 6), and dividing 4 into 5 equal parts gives j,'^-, since 5 such parts repeated 7 times make up 1. Hence 3 of these parts (or 4 divided into 5 parts) is /y, which is therefore -^ of 4- and -Jj doubled, or ^3^, is j of 4. Now, the numerator 6 is the product of the two given numerators, 2 and 3 (as apj)ears by the process) ; and the denominator 35 is the product of the denominators 7 and 5. If we had to multiply this re- sult by a third fraction, the process would be the same ; hence the Kule. Multiply all the numerators together for a new numerator, and all the denominators for a new denominator. El. 1. Multiply i, -, and -. Ans. -ii. Ex.2. Multiply |-", bv -. Am. -^ 3 5 7 105 ' • 63 ■ 7 44' Ex. 3. Multiply ij- -. i'nd -. Ans.—. ' ' j6 3 5 S40 17. If we multiply j by itself, we liave *, tbis again by \ gives /^i cow /^ diH'crs little iVoni -^^, and /j is otiual to *, \\'\nci\ is very FRACTIONS. 5 Qiiitli loss tliaii 5. Again, \ multiplied by itself is ,'j, ami tiiis niultiplicd again by 4 's ^^. Hence a proper fraction is diminislied by continually multiplying It by itself. [b.] Dinsion. 18. To divide a fraction, as J, by a whole number, as 4, is to find a new fraction which, repeated 4 times, shall produce ^ : that is, «e have to divide a third into 4 equal parts. It will be at once seen, on dividing a line into 3 equal parts, that to divide each third into 4 equal j)arts, is to divide tiie whole line mto 12 equal parts, and since 4 of such parts, or twelfths, constitute a third, j'j is the required fraction. Hence, as similar reasoning applies to any other traction or whole number, the most general rule for dividing a fraction by a whole number is to multiply the denomi- nator by the given whole number; but if the numerator be a multiple of the divisor, it is better to divide the numerator as it leaves the result in a more reduced state. 19. To divide a whole number, as 3, by a fraction, as -J. Dividing 3 by 1, that is, finding how often 1 is contained in 3, gives 3. Now, it is easily seen, since -J is 4 times smaller than 1, that it must be contained in 3, four times oftener, that is 12 times; and 12 is the product of 3 by the denominator 4. To divide 3 by |. Since | is twice ^, we have to divide 3 by j, and take half the quotient; and we know that to divide by the product of two numbers, 2 x ^, is the same thing as to divide by theiu separately, that is, 3 divided by f is 3 multiplied by 6 (No. 181, and divided by 2 ; or 3-i-| is the same as 3 x f , or ^. Here f is the fraction | inverted. As similar reasoning applies to any numbers and fractions. Me have the Rule. To divide by a fraction, invert the fractional divisor, and proceed as in multiplication. 20. To divide a fraction by a fraction. We have evidently io treat the dividend as a whole "number, and apply to the divisor the rule above. Ex 1, DinJc-^by-. J-^l = - = l. Ex.2. Divide Uy - Aris-ii. Ex. 3. Divide * by -5-. Ans. ". Hence it appears tliat the smaller the fractional divisor tb^ greater is the quotient. 21. When a quantity is both multiplied and divided by the saiue number, it remains unchanged. Hence when the same number occurs in the numerator and denominator of a fraction, or of two or more fractions multiplied together, we simply omit or erase it ; a.s, m^, '.1-' '♦k'kZ -1 ' ' ' ± (, I IKTBOD'JCnOK. II. Decimal Fractions. '12. Tenths, hundredths (which are tenths of tenths), and so oii, are called Decimal Fractions, and may be written as fractions, havina: for denominators 10, 100, &c., thus, one-tenth, J^ ; three hundredtlis, j-g-^, &c. But as these quantities are counted by tens, like common numbers, it is simpler and more concise to write them in continuation with the common numbers, only taking care to put a dot, called the decimal point, where the whole number ends and the fraction begins; that is, between the unit and the tenth : thus, '21*3"i signifies 21 and 3-tenths and 2-hundredths ; 432-9 signifies 432 and 9-tentlis ; 33-05 signifies 33, no tenths, 5 hundredths. 23. In the fractional part beyond the dot, each figure may be read in its separate denomination, or the whole may be read in the deno- mination of the last: thus, -32 is read either as 3-tenths and 2 hun- dredths, or as 32-hundredths; just as 32 is road either as 3 tens and 2 units, or as 32 units. 24. As-5, (or5-tentlis)isthehalfof l,so-05 is the half of 0-1, or 5 hundredth-parts are the half of one-tenth ; 5 thousandth-parts are the half of a hundredth-part. The half of 5 tenths is 2 tenths and half a tenth, that is, 2 tenths and 5 hundredths, or 025. Hence the fractions, quarter, half, and three-quarters are written in decimals, 0-25, 0-5, and 0-75. All the preceding rules apply equally to decimal fractions , but R8 these last, from their denominators being multiplied by 10, are o/ a uniform kind, special rules have been made for them, relating, however, almost entirely to the placing of the decimal point. [1.] Addition and Subtraction, 25. Place the quantities so that their decimal points shall be it the same vertical line ; for then the quantities of the same denominn- tion will stand together. Then proceed as in the addition or subtraction of whole numbers. n 3rS subtract ii-6i. Add together 0-35, 47-4, and Ex. 0-35 47-4 Sura 56-87 Add together 71-99, 4-1, aud Ex. 72-99 4"i . 5 -'3' Snm 129-40 [2] Mult iplication. From 423-5 subtract 97-9. 4-3-5 97-9 26. Multiiily the numbers together as whole r.uLnbers, and poii.i ofJ'aa many decimal places in the ])roduct (beginning at the right) as there are decimal places in the multiplier and nmltiplicand together. WIiP!! tlie Jeciuiiil places to be pointed off are more 'ii nuinhei tliiin the figures of tfie product, make up the proper iimiil)cr by prefixing ciphers to the product. Ei. 1. Multiply 34- 1 by 3-71- 34-11 3"72 68z2 »3*77 Multiply '20 1 by "06 The profluct of 201 by 6 is 1206 ; in soi are three decimals, in 06 are two ; to inak.-! up five decimals, a cipher is prefixed £0 1206. In 34-11 are two decimals; in 3-72 are ^co ; therefore four decimal places are pointed 3lT. Ex. 3. Multiply 9001 by 0.034. Ans. 3-06034. ■Rx. 4. Multiply together 1-3, 1-2, and 0-09. Ans. 0-1404. [3.] Division. 27. Divide as in whole niinibers. The rule for placing the deci- mal point is, that the quotient and divisor together must contain as many decimals as the dividend.* Ex. 3. Divide 2-392 by 4-6. 4-6)2-392(52 230 92 9» Here 2-392 contains three decimak, .ind 4-6 one, the remaining tw-o required must therefore be obtained by pointing of! botli figures of 52 thus, -52. Ex. i. Divide 338-4 by 9-4. 9-4)35S-4(36 282 564 Here the dividend has one decimaJ, and the divisor also one, or as many, and the quotient is therefore an integer. 28. When llie dividend has no decimals, ciphers must he annexed, preceded by the decimal point. Ex. 1. Divide 19 by -04. Ex. 2. Divide 132 by 0-7. Annexing two ciphers to 19, gives the Annexing five ciphers (decimals) gi\es COmplele quotient 475. quotient 1885714. Then the n-amher wnirh Ided to one decimal in 0-7 to make up fiv3, four. Ans. 188-5714. 29. AVhen the number of figures in the quotient is not siifHcient to make up the required nuinher of decimals, cijihers must be pre- fi.xed. Divide 17-34 by 3-4. 3'4)"7'34(5' e 17-34 contains two decimals, 3-4 1 only one ; therefore 5 1 must contain aining one required, and be written i?:t. 2. Divide 541-2 by 66. 66)541-2(82 528 132 132 Here 54 J -2 contains one decimal, 66 none ; ice ^2mii8tcontain one, and be written 8-2. • It is always caay to verify the itakes \ thuii, 17-34 divided by 3 1 will be near 17 diviilcd by 3; that is, less than G (as 5 1 i^^ ^gain, 2-392 dividsd bv 4 6, i« not frj fron 7 diviaed bv 4, (,r » hilf (which is marly -52) El. 1. Divide •1734 by 3'4.. 1 Ki. 2. Diride 2-391 oy 46. Here •1734 lontains four decimal!, and [ Here 2*39i contains three decimals, and |. one; the quotient 51 (Ex. i, above) j 46 none; the quotient (52) must contain ; only two figures, and three are re- three, and becomes o'052. juired , hence 51 must be written 0-051. | Ex.3. Divide 27-9 by 002. Annexing one cipher, the quotient is 1395. Ex. 4. Divide 0-0296 by 5-2. Annexing two ciphers gives quotient 569, which is 0-00569, lince the five in this added to one in 5-2 make up six. 30. Tlie division may always be carried to any degree of accuracy by annexing cipliers to the dividend, as is seen in E.\. 2, No. '28. 31. The decimal point maybe removed altogether from both the divisor and dividend, by continually multiplying each by 10; for the ([uotient will thus remain unaltered. No. 7. The first decimal in the quotient will then appear only with the first cipher annexed to carry on the division. Ex. Divide 27-9 by 0-02. Multiplied by 10 they become 279 and 0-2 ; multiplied again Uity become 2790 and 2, the quotient of which is 1395. This easy process furnishes a complete security against wrongly placing the decimal point in the quotient. [4.] Reduction. 32. The great convenience of aeciraals makes it often desirable :o reduce vulgar fractions to the decimal form. To reduce a Vulgar Fraction to a Decimal Fraction. Divide the numerator by the denominator, adding ciphers bjs required. The quotient is the decimal required. Ex. 1. Reduce - to a decimal fraction. Dividing 10 by 5 (the cipher being added") we find -is 0-2. 5 Ex. 2 Reduce - to a decimal fraction. Dividing 10 by 3 gives 3; the next cipher added gives another 3, and so on continuilly. The fraction required is therefore 0-333, *c. Ek. 3. Find what decimal of i (nautical) mile is 700 feet. niere are 6080 feet, nearly, in i such mile ; hence i foot is of i mile, and 700 f-Vit 700 ftm T-T" of 1 miie, which gives 0-115 of i ""il^t nearly Ex. 4. Find what decimal of i minute is 42 seconds. I second is — of i minute, hence 4: seconds are — or 0-7 of a minute ; or, as it may be Ex.5. Find what decii nalof I foot i 8* inches First, J fcence 875 is 0-75 inches of I inch are *'", , hence Scinches are 8-7 or 0-729, of J foot. Ex.6. Find what decimal of I degre is 8' 37". 37" are r>f ',oro-6 of 1' them '^ro"f'^ Kx. 7. Find what decimal of i day i ^.2"' are ^ o'' i*", or o''.y ; and i' I*- 154106, Sic. 33, Or, reduce tlie given quantity to tiie lowest of its denoiuinatioii-) when tliere ;iro more than one, Jiiui also the integer to which it is referred, to the same dcnoininatii)n ; then divide the given quantity by the integer thus reduced. Ex. 1. (Ex. 3, above.) The given qu.intity, 700 feet, being all in one dfnorainatlon, requires no further reduction. The integer I mile, reduced to the same denomination, is 6080 feet ; then 700 divided by 5o8o gives 0-115. El. 2 (Ex. 5, above.) S inches and 3 quarters are 35 quarters ; and i foot reduced to the same denomination, is 48 quarters ; tlien 35 divided by 48 gives 0-729 34. To reduce a Decimal Fraction to a Vulgar Fraction. Note the number of parts which the unit or integer of the given quantity contains of the ne.xt inferior denomination, and multij)ly the given decimal by this number ; the product is the given quantity expressed in that denomination If this product have a decimal part, multiply this decimal by the number of parts which the unit of the present denomination contains of the next inferior denomination to that just before employed: this product is the quantity which the given decimal contains of that next denomination. Proceed (if there till be decimals), m like manner, to the lowest denomination in which the decimal is required to be expressed Kk. 1. Find the number of feet in o-i i c of i mile. The next inferior den is here feet, of \ Ans. (in the lowest denomination required) 6994 feet. Ex. 2. Find the number of seconds in 0-7 of i minute. The next inferior denomination to that of minutes | ° J is seconds, of which the number in i minute is) — Ans. 42-0 Beconda, the number of inches and eighths in 0-48 of i foot. 0-48 Tlie next inferior denomination to that of feet ) is inches, of which the number in i foot is) '--^ The next proposed inferior denomination to inches ) ' ^„ ''"'''^'* is eighths, of which the number in i inch is) Ans. 5 inches and 6-08 eighths, or - nearly. Find the number of minutes and seconds in o'-- 6-(j8 eighti^ Tlie next inferior denomination to that of degrees! °'^'J is minutes, of which the number in 1" is) ••■•• E^ The next inferior denomination to minutes 1 *+ '°+° nds, of which the Ans. 44' 2"-4. J. ^00 Find the number of hours and minutes in 0-37 of a day. The next inferior denomination to days is) °'" hours, of which the number in i d.iB24j i* 71ie next inferior denominntion to houn u{ »-88 hours minatea, of which the number in 1'' ii 60 ) Ant. 8'' si^-g. jiSo 10 INTRODUCTION. 35. When we propose to use tlie nearest whole nmiiber, rejecting tlie decimals, ii'the decimal is less tliaii '5, we omit it, if greater than •5, we count it as a unit. For example, if we propose to take 31'3 as a whole number, we call it 31 ; if we propose to take 31-7 as a whole number, we call it 32. The reason is, obviously, that 31-3 is nearer to 31 than it is to 32, whereas 31'7 is nearer to 32 than it is to 31. In like manner, we may abridge the decimals themselves when accuracy is not required: thus, for ex. 11 '567 may, when two places only are required, be written 11-57, or when one place only, 116* II. Proportion. 36. By the term ratio we commonly understand the relative niangnitude or quantity of two things of the same kind ; thus, when we speak of the ratio of two numbers, 12 and 4, we mean their relative magnitude, or the result of comparing them together in respect of quantity. 37. The most distinct and intelligible notion which we can form of the degree in which one quantity or magnitude is greater than another, is the number of times one contains the other; that is, the quotient of one by the other is the measure of the ratio. Thus, to compare 12 and 4, we find that 12 contains 4 three times, or the quotient i^-, or the number 3, is the measure of the ratio of 12 to 4.+ (1.) The sign + , caWei plus (which is the Latin for more), signifies adiilive, or to be the Latin for less), signifies stilili-aclive, or t<- Ex. + 3 signifies 3 to be added, —3 signifies 3 to be mbtracteii (3.) The sign x signifies multiplied by. Ex. 7x5 signifies 7 multiplied by 5. (4.) The sign -i- signifies divided by. The operation of division is also indicated by writing the divisor under the dividend, with a line between them. Ex. 14 -r 2 signifies 14 divided by 2 ; which is as frequently denoted thus, — . (.'p.) The sign = signifies equal to (or amounting to). Examples of the preceding, with the results in each case, will stand thus : — (1.) 14 and 3 = 17, or 14+ 3 = 17. (2.) 10 - 3 = 7. (3.) 7 "5 = 35- (•<•) .4-^ = 7, or^=,. These processes appear much more conspicuous to tlie eye than wiien written out in words at length. + But, instead of saying that the absolute number 3 is tlie msseure of the ratio 12 : 4, it is more correct to say that the measure is itself the ratio of 3 : 1 ; because, in all cases of measure, we employ a convenient quantity of the same kind as a unit, as 1 foot, or 1 mile. for length, 1 second for time, &c. ; so the measure of ratio is itself a ratio, but of the limpU-st form that can l)e found PROrOUTION. 11 The ratio or proportion (for tlie teniis are often used indifferently) of two numbers, as 12 and 4, is written thus, 12 : 4, or, as above, >/. 38. Suppose it recpiired to find the ratio of 12 to 5. 12 contains 5 more tiian twice, but not three times. By actual division, ^ gives 25 ; but this, instead of being simpler, is more coinph.x than y. Hence, as we cannot snn]ilify this fraction (12 and 5 having no common measure but 1), it remains as the measure, or represents the ratio of 12 : 5 39. In the same manner is represented tlie ratio of 4 to 12, in which the smaller term is taken first; for though 4 does not contain 12, yet it contains the third part of 12, so that there is still an exaci relation between the numbers in this order : in other words, the ratio of 4 to 12 is the same as the ratio of + to 1 ; but the ratio of J to 1, or a third to the whole, is the same as that of 1 to 3, since each contains the other three times. Hence, 4 : 12, or a : 1, is the same as 1 : 3, or ^ the same as ^, which is the measure of j%. 40. There is an employment of ratio or fractions which is often embarrasiing to unpractised arithmeticians. If we increase 6 to 7, we add [sixth, for 1 is -^ of 6, and 6 + 1 make 7 ; but, if we now diminish 7 to (5, we take away \-seventh, for 4 of 7 is 1, and 7— 1 is 6. In the first case, we take a fraction of 6, in the second, a fraction of 7 ; and it is obvious that the same quantity cannot be the same fraction of two different numbers. In like manner 3 increased by -J of itself becomes 4; but to pass back again from 4 to 3, we must take away ^^ of 4. 41. It may be convenient to express the change of a quantity in any ratio, by means of the increase or diminution it undergoes, measured by a fraction of itself. To increase a number in the ratio of f . | is composed of | and *, or 1 and f ; hence the number is to be increased by ■§ of itself. To diminisii a immber in the ratio of }. t is equivalent to f, deducting |, or to 1— y; hence the number is to be diminished by ^ of itself. Ex. 1 . A number is increased in the ratio of — , by wliut fraction of itself is it increased ? Answer I^ " '55' Ex 2. A number is diminished in the ratio of—, by what fraction of itself is it diminished ? Answei, — . 5' 42. The first of two terms taken in order is called the antecedent, Hud the second the consequent: thus, in 12 : 4, 12 is the antecedent, and 4 tlie consequent; in 4 : 12, 4 is the antecedent. 1. Direct Proportion. 43. When two pairs of terms occur, each antecedent having ths Bame ratio to its consequent, the four terms corstitutc an analogy, or proporti()n, as it is also called : thus, 18 and 6, 12 and 4, each pair 12 INTRODUCTION. Iiaviiig for its measure the ratio |. form tliis proportion — 18 is to 6 as 12 is to 4 ; or, as it is written for abbreviation, 18:6:: 12:4. The same is also written thus: 'g" = '^, anil read " the ratio of IS 10 C) is equal to the ratio of 12 to 4."* 44. In every proportion tlie product of the two extreme terms is equal to the product of the two mean (or middle) terms: thus, in 18 : 6 : : 12 : 4, 18x4 = 6x 12 = 72.t This property affords the test by which we learn the various alterations that may be made in a proportion, the original proportionality being still preserved. 45. The following- variations in the order of tiie four terms of a pro)3ortion occur the most frequently : — Given form, 18 ; 6 ;; 12 ; 4 / 4. ; 6 :; 12 C i5 Alternately, 18 : 12 ;; 6 ; 4 , ... 6 ; 4 :; 18 : 12 Ueversing, 6 : ,8 :; 4 ; ,1 I" l.ke manner, „_ . ,^ . . ^ . g • Or, 4 : 12 :; 6 ; 18 ' 12 : 4 ;: i8 : 6 4ti. In a ])roportion, either of the mean terms is equal to the pioduct of the extremes divided by the other mean. Also, either of the extremes is equal to the product of the means divided by tiie other extreme; as in Hence, if any tliree terms of a proportion be given, the fourth may be found. 47. It is often required to increase or diminish a quantity in a certain ratio, or proportion. For e.xample, to increase the number 12 in the ratio of 3 to 1, is to multiply by 3. For the increased (|uantity (which, being yet unknown, we will call .t) is to be to tlie given quantity 12, as"3 to 1, or .t : 12 : : 3 : 1. Whence (No. 44) lxa:=I2x3. Again, to reduce a number, as 13, in the ratio of •5 to 7, is to multi])ly it by 5 and then divide by 7, for the required number (.r) is to be to the given number (13) as 5 is to 7, whence 13x5 ^ = -T-- For example, if certain provisions last 122 men a given time, it is evident that, in order to last 146 men the same time, they must be increased in the ratio ol 146 : 122; tluit is, multiplied by 146, and then divideil by 122. Again, if certain provisions suffice 106 men, and they are required to serve only 74 men, they may be diminished in the ratio of 74 to 106 ; that is, x 74-;- 106. * Hence proportion is also desmbed as being the equality of ratio. t Hence, also, when the products of two pairs of numbers are equal, the four numbers may be written as a proportion. Ex. 22 x 66 = 4 x 363 ; hence 22 : 4 \\ 363 : 60. Csre must be taken in tlie order of the terms, which, though indifferent in a product \s every tiling in a proportioa. 'I PROPORTION. la [1.] Rule Iff Three, Direel. 48. Numerous arithmetical questions occur in a form more or less like this : if 5 men do 20 yards of work, how many yards will 1 1 ineji do, in the same time, and under the same circum- stances.* (1.) The most obvious and natural method of solving such ques lions is the Method of Unity. Tlius, if o men do 20 yards, 1 uian alone will do 4 yards, and therefore 1 1 men will do 1 1 times 4 yards. (2.) The General Method is to arrange the terms in the manner of a proportion, and then to find the unknown term from the other three, (No. 46). Thus, it is obvious that a constant proportion obtaining between the men and their work, we have 5 men ; 20 yards : : 11 men : number of yards required. This process is called the Rule of Three. (3.) They, however, who are practically familiar with ratio, 01 proportion, perceive, on considering the question, the ratio in which one of the given terms is to be changed, so as to suit the conditions ; and thus the solution is effected at a single step. Thus, in the above ([uestion, it is evident that the given number of yards, 20, is to be increased in the ratio of 1 1 : 5 ; that is, in exactly tiie same ratio as the number of men is increased. The solution, therefore, is com- prised in these figures, 20 x V, which gives 44. 49. Various precepts have been suggested for ensuring a correct order in the arrangement of the terms, or the statement of the question, as it is called ; and one of sucii, which is often useful, is t. consider the terms given as standing to each other in tlie relation of cause or agent, and effect (as, for instance, tlie men in the above example and their work). By this supposition (which, however, is arbitrary and unsatisfactory enough in many cases), the four terms are rightly paired, or the antecedents and consequents rightly taken. But the fact is, tliat no mechanical rules can so completely supersede the notion of proportionality as to absolve the mind from all neces- sity for estimating it; and, consequently, the student, if he clearly understands proportion, depends upon it alone; and if he does not, he cannot, from any number of precepts, feel the least confidence in the soundness of his result. As a right apprehension of proportion is most essential to every one who has any thing to do with calculation, we have, for the sake of exercise, solved several examples in each of the above tliree forms. E«. 1. A steam-vessel consumes 13 tons of coal in ij days ; how long will 98 tons last ? (1.) Method of Unity : 13 tons in i}d. or Jd.,is i ton in or ^jd., and 98 ton» ii 4x13 98 X |j or 135'j days, or 13d. fh. nearly. * In the application of the njeg which follow, the circumstances are supposed to remain the same, that is, the change of the n\irabeia does not imply any othei change If. for rJiample, the increased number of men should be in each other's way, so a» to interfere with their Uboui, tUij inujt be made a feiMralr contideration. It 1-1 INTRODUCTION. (2.) General Method: 13 ; ijd. :: 98 I d. req. = 175 x 98+ 13 =• i3-i dayt. (3.) By Ratio : Here ij (diys) is to be increased in the ratio of 98 to 13. r75X98-M3 = i3-2. Kx 2 If 13 men make 420 yards in 20 days ; how much will they make in 11 days? Note. — The number of men remaining the same, while the time and tlie *rort change, need not be noticed. (1.) 420 yds. in 20 d. is 21 yds. in i d., and 11x21, or 231 yds. in 11 days. (2.) 420 yds. ; 20 d. :: yds. req. : 11 yds. req. = 11 x 420-=-20 = 23i yds. (3.) Here 420 is to be diminished in the ratio of 1 1 to 20. Bx. 3. A pump, A, delivers 1 ton in 5"'; another, B, i ton in 8"; and a third, C, I is 15'" : how mucli water will they dtUver in 1'' iC" .' Ans. A, '»=i4tou6; B, 'j° = 87; C, ^ = 47. Total, 27-4 tons. Es 4. A boat. A, lauds 52 men in 28"' (going and returning) ; another, B. lands 68 mej in 41'" ; aud a third, C, lands 20 men in 23"'; how long will all take to land 220 At these rates, in 1'', A lands ^g x 52 men = 111-4; B, 5? x 68, = 99-5 ; and C, <§ x 20, = 52-2. Total m i'', 263-1 men. Now, as the number landed is proportionato to the time, we have 263-1 : 1" :: 220 ; 220 x i -r- 263-1, or o''-84 nearly. Ei 5. A boat, A, fills 8 tons of water in 34'' -, another, B, fills 5 tons in 4" ; and ■ third, C, fills i.J ton in if" ; in what time will they fill 107 tons ? (1.) In i", A fills ^ tons; B, J tons; and C, f tons; or altogether, ij=/ tons. This it I too in fj»3 of i", 107 tons in 28 x 107-=- 123 = 24l'-4. (3.) Having found the fraction expressing the joint effect for i"", or <;/ tons ; i^ is to he changed in tliat ratio, whicli will convert this into i, (ff^ by" E,v.), which gives the time for i ton ; this is then to be increased in the ratio of 107 : i. Note. — Such questions as in Ex. 4 and 5 do not usually admit of exact solution ; thus, in sny whole number of trips that can be proposed, the boats carry too much or too little. Each boat performs a certain quantity in one particular interval of time, and not continuouely, like a pump, or so much per hour : the reduction, therefore, to hourly rate, is not correct, but it is near enough for forming a tolerable estimate, which, in practice, is all that is wanted* To obtain as complete a solution as the question allows, we must take each boat's performance separately, and add them all up. Ex.6. The change of the sun's declination in i day is 1 8' 2 1" ; find the change for i" 34". 24" (1440"') : j8' 2i" ("oi") :: i*" 34"' (gi"') : x or, less exactly, 24'' '. i8'-3 :: i''-6 ; x. Ex. 8. Against ii" in a Table standg 6726, and against ii° 30' stands 6354 ; find the term corresponding to 11° 37'. 30 : 372 :: 37: X to be subtracted from 6726, which givi term required. Ex. 7. In a Table, against 36° stands the term 27943, and against 37° stands 28504; find the term corresponding to 36° 23'. 36° ^7943 37 ^8504 Diff 561 Hence 60 ; 561 :: 23 . jr which added to 27943 (because the terms increase while the argument* increases), gives the term required. 50. The process of finding a term which falls between two given terms, or, hs it is callsd, Interpolation, is sufficiently exemplified above ; but it is important to remark that it w not always necessary to work proportions at length. It is enough, for most practical • The argument is tne quantity at the side or head of the Table, for which the terms 01 :(uuititie£ in the bod; of the table are given. PROPORTION. 16 jiuri)yses, lo take a quantity, somewhere between the given terms, as half waj, or a third of the way, between them, according to tlie case. Tlie power of guessing tlie proportional part is acquired by practice, and saves time whicii otherwise would often be wasted in working to a superfluous degree of accuracy. On tlie otiier hand, when extreme precision is required, this pro- portioning alone is not enongii, but a correction is necessary, for which see the e.xplanation of the Tal)le for finding the Equation ol Second Ditferences. [2.] Double Rule of Threi, Direct. 01. Questions in the Rule of Three occur also in a more complex form ; thus, if 2 men do 7 yards of work in 3 hours, liow many yards will 13 men do in 11 hours? in which the answer is required to correspond not merely to a certain number of men, but also to a certain number of hours. This (juestion resolves itself into two: 1st, if 2 men do 7 yds. how many will 13 men do in the same time, or 3 hours? The answer to which is 45-6 yds. ; and, 2nd, if 13 men do Abh yds. in 3 hours, how many yds. will tiiey do in 1 1 hours? Hence the solution of such questions is called the Double, or Com])ound Rule of Three. Ex 1 . The example above (1.) I man does i of 7 yds., or 3-5 yds. in j"", and 13 men do 45-5 yds. 13 men do 45-5 yds. in 3'', or \s^i^ yds. in 1'', and tlierefore 166-87 in 11 houi-s. (2.) Tlie two statements as given above. (3.) 7 is to be increasi,d in the ratio of 13 ; 2, and tlien of 11 ; 3, Ei 2. If 9 men make 47 yds. in 4 days, how many yards will 17 men make in 31 days.* Ans. bti yds. El. 3. If 5 men do 64 yds. in 1 1 days, in how many days will 14 men do 37 yds. ? (1.) I man does 64 yds. in 55 days, or i yd. in c-86 days, and 14 men do i yd. in -86.4-14, a"J 37 yds. in 2-27 days. (2.) 5 m. : 64 yds. :: 14 m. : 179-2 yds. 179-2 : 11 :: 37 : 2-27 nearly. (3.) 11 is to be diminished in the ratio of 37 : 64, and then of 5 ; 14. »!». 4. A certjiin quantity of provisions lasts 170 men for 3 months; how much Is re- quired for 210 men for 2 months ? (2) 170 : I (whole) :: 210 : x = 210^-170. And .v : 2IO-S-I70 :: 3 : 1. (3.) The quantity is to be increased in the ratio of 210 '. 170, and diminished in the r«tio of 2 : 3. Kx. 5. A steam. vessel has fuel for steaming 13 days at 11 hours a-day ; how much m-a«t she take to steam 15 days at 18 hours a-day.' (3.) The fuel must be increased in the ratio of 15 : 13, and then of 18 : 1 1. {J « H "" {\% which is i|U, or i\\ nearly, or nearly doubled. Ex. G. Three boats fill 16 tons of water in 7 hours; how many boats, at the mau average performance, will fill 78 tons in 10 hours ? (1.) 3 b.,Hts fill i6tonsin7\ or ^of 16 = 1-3 tons in i\ and 23 tons in 10 hours. Thea. since 23 tons employs 3 boats, i ton employs ^ of 1 boat, and 78 tons will employ or lo-i boats. '2.) 7' : 16 1. :: 10° : x tons (--22-9' 22-<) t. :3 b.:: 78 1. : 102 h. (;j.) ] IS to be Increased in the ratio of 16; 78, and then liminishcd in the ritio of 10 ; ». 16 INTROUUCTIOH. 2. Inverse Proportion. 62. In direct proportion, as we have seen, more is always ftiJ- lowed by more, and less by less. But when the nature of the qiies*- tion is evidently such that more will be followed by less, or less by more, the proportion is no longer direct. For example, if 5 men do certain work in 4 days, in how many days will 7 men do the same work? Here it is evident that the greater number of men will require less than 4 days. Again, if a ship going 8 knots, sails a certain distance in 5 hours, it is evident that, if she goes at a. greater rate, she will perform the same distance in less than 5 hours. 53. In a question of work performed, the result is represented by the number of agents mnltii)lied by the time each works; tims, 6x5 or 30, represents the labour of 6 agents working for 5 hours, the unii of work being that performed by 1 man. If now, the work remain- ing the same, we double the number of agents, we shall obviously halve the time, since 12 men will do the work of 6 in half the time, and 12x2^=30. Or, again, trebling the number of agents, gives 18 X ^ of 5, or 18 x i=30. That is, while one factor of a given pro- duct is increased in the ratio of 3 : 1, the other must be diminished ia tlie ratio of 1 : 3, which last ratio contains the same terms as the other, but in a reverse or inverted onler. The four numbers consti- tuting two equal prodixcts are hence said to be in inveise proportion to each other In the example. No. 52, the number of men is increased in the ratio of 7 : 5, and the time is accordingly to be diminished in the ratio of 5:7; hence 4 days becomes 4 x 4, or 2^ days. [1]. Rule of Three Inverse. 54. In regard to the solution of these questions ; (1.) In the method of unity, the consideration of inversion does not present itself. (2.) As a question of proportion, the solution may be effected thus. Suppose the proportion were direct, then (example above, keeping the antecedents and consequents in their given order) 5 men : 4 days : : 7 men : x days. Now, we require a direct comparison between the number of men in the two cases, and the times in the 'wo cases ; hence we alter this to 5 men : 7 men : : 4 days : x days. But this would give x greater than 4, as 7 is greater than 5, whereas we know it must be less ; hence, inverting the last two terms, gives 6 : 1:: X -.A, or 7 : 5 : : 4 : x =—-—=—, or 2^ days. Hence the pro* i*ess (which is, perhaps, as little liable to mistake as may be expected m a question of some perplexity), is, 1, to write, in the form of a direct proportion, the given antecedents and their consequents ; 2, to close terms of like denomination ; 3, to invert the last two terms, and then to find the unknown term. E«. I. If 7 men do ccilmn work in 4 days, in liow many days will 10 men do it ? ( 1.) 7 men in 4 days ii i man in iS days, and 10 men in z-% days. PROPORTION. i I [%) Diroct form, 7 men : 1. d. :: 10 men ; days required. Like terms, 7 : 10 :: 4 '. days required. Inverting, 7 : 10 : : d. req. ; 4. Ans. ;. 8 days (.3 ) It is evident that 4 is to be diminished in the ratio of 7 to 10. ti 2. If 17 men do certain work in 14 days, how many men will do the same work in 4 days? (1.) 27 men in 14 days, is i man in 378 days ; and 378 -!- 4 gives 94J men. (2.) Direct form, 27 m. ". 14 d. :: men req. : 4 d. Closing like terms and inverting, men req. = 17 x I44-4»94{ men. (3.) 27 is to be increased in the ratio of 14 I 4. t' . 3. If 12 men do certain work, working 4 hours a-day ; how many men will it take to do the same work, working 7 hours a-day ? (I.) 12 men in 4 h. is 48 men in i h., and V in 7 hours, or 7 men nearly. ^2.) Direct form. 12 m. I 4 h. t: men required ', 7 h. Closing like terms and inverting, 12 x 4-5-7 = 7 men nearly. (3.) 12 is to be diminished in the ratio of 4 ; 7. Bt. 4. Certain tons of fuel last a steam-vessel 1 1 days, steaming 4 hours a-day ; how lonj will they last steaming 61 hours a-day .' (1.) 4 h. for 1 1 d is at the rate of i h. a-day for 44 d., and therefore 6} h. for 44 ->-6J, or 88-=- 13, which is 6-77 d., or 6 d. 185 h. (2.) Direct form, 11 d. '. 4 h. r. x dayi : 6.{ h. Closing like terms and inverting, a' = 44-!-6S = 6-7; d. (3.) Here 11 days is to be diminished in the ratio of 4 to 6J. Ej. 5. A certain quantity of fuel lasts a steam-vesael 12 days, steaming day and night ; how long will it last steaming 14 hours a-daj .' Ans. 20) days. Kt. 6. A pump, A, empties a cistern in 3 hours; another, B, in 2{ hours ; in what time will they empty it both working together ? (1.) In i'', A empties J of it, and B empties i-!-2j, or i^J, which is J. Hence in i" both together empty J + j, or {. Suppose, for greater convenience, the cistern to hold 10 tons ; then in i*" both empty '," tons, or i ton in i''-f-'|J', or i"" x ft, =ft ol i"", which is 10 tons in ^ of i'', or i;;*'. (8.) Stating the question directly, we should say, J-f J ( = J) ; the whole, or i : : time required : i\ But, the greater the fraction representing the hourly work done, the smaller must be the time required for any given quantity of work. Hence I ', J :: 1^ '. time required =^ of i''. (S.) Here i*", in which the fraction { is done, is obviously to be increased in that ratio which will turn { into i, or the whole ; and this ratio is f, for | x {= i. Ki. 7. A can do certain work in S*', and B the same work in 6* ( in what time will they both complete it together ? (1.) In i'' A does j, and B J, hence both together J-hJ, or ^. Let the work be repre. sented by 10, then in 1'' both do JJ, and tlierefore they do the unit of work in l"" + JJ, or ^ of 1". Hence they do the whole in 10 x ^ = y of i*', or 3^ . (2.) Direct form, ! + J I 1 (whole) :: time required : i' = V- {3. ) i"" is to be increased in the ratio of 24 : 7. Si. 8. Five pnmps empty a cistern in 1 3 hours ; how many must be put on to empty it is 3 J hours ? (1.) I pump in 65 hours gives i8-6 in 3I hours. (2.) 5p. : ij"" :: j:: 34". Ultimately, *-sx 3-^3-5, (3.) 5 is to be increased iu the ratio of 13 ; 3 J. Ki 9 Four pumps empty a cistern in 10 hoon ; how long will 7 such pumps t«koT Ans. 40 + 7=^ St>7. INTRODUCTION. 10. A certain .juantity of bread lasts i lo men zi days ; how long will it laai 74 men? (1.) 21 d. for no men is i d. for 2310 men, and 23io-i-74 gives 31-2 dajs. (2.) Direct form, no m. : 21 d. :: 74 m. : :r d. Closing lilie terms and inverting, a-=2i x iio+74=3i-2 days. (3.) It is evident tliat 21 is to be increased in tlie ratio of 1 10 ; 74. days at four-fifths allowance ; how long (1.) J lasts 21 d., J will last 4 X 21 or 84 days, and f, or whole allowance, ',♦ or i6-8 days. Hence J allowance will last 3 x i6-8 d., or 504 d., ana J, one half of this, or 25-2 days. (2.) J : 21 :: 5 :: required days. Closing and inverting, days required <=2i "1-^1 = 2$ 2 days. (3.) 21 days are to be increased in the ratio of J ; |, that is 21 x }-e|. Ex. 12. If it takes 54 yds. at J of a yard wide, to cover a surface ; how many yards will it take at J of a yard in width ? (1.) H yds. at I wide is 3 x 54, or 162 yds. at ^ wide, or 40-5 yds. at i yd. wida. This is 5 X 40- 5 or 202-5 y^s- at J wide, and J of this, or 5062 yds. at j vride. (2.) Direct form, 54 yds. ', f width i; yds. req. I |. Closing like terms and inverting, yds. req. = 54 x |^|=s 50*62 yds. (3. J Here 54 is to be diminished in the ratio of f : J, or of 15 ; 16. [2.] Double Rule of Three, Inverts. 55. As tlie inversion arises from a product remaining constant while both factors vary, questions of this kind may be solved directly by taking, in each of the two proportions necessary, those terms only which are directly ]iroportional to each other. For example, in a question of agents, work, and time, the first proportion would include work and time, and the second, agents and work. 111. Logarithms. 56. These are numbers calculated for the purpose of converting multiplication into addition, and division into subtraction. 1 . Use of Logarithms. 67. Every logarithm consists of two parts, the index and the decimal part;* thus, in the logarithm 2-80618, the index is 2, and tiie decimal part -80618. 68. To find the Logarithm of a given number. Find in the Table of Logarithms of Numbers the decimal part (for which see also the Ex])lanation of that table); and then api)ly the index by one of the two following rules: — (1 .) When the number consists of a whole number, with or with- out decimals, the index is 1 less than the number of fi^vm'es in the whole number. This part is also :8llcd the mantissa. LOGAIUTHMS. ] 9 Ex. 1. Find the log. of 52a. Against 512, iu the Table, stands •717671; then, sime there aie three figures in $". th» indei is 2; hence the log. is 2-717671, Ex. 2. Find the log. of 5-22. The log. of 5-22 ia o-7i767i, because there is one figure in the whole number, and ou< less than i is o. (2.) When the number consists of decimals only, count the number of ciphers between the decimal point and the first significant* figure after it, and subtract this number from 9 ; the remainder is the index. Ex. 1. Find the log. of '0058 14. The decimal part of 5814 is -764475 ; there are two ciphers before the 5, which 2 taken from 9 leaves the index 7 : hence the log. is 7-764475. Ex. 2. The log. of -5814 is 9-764475, for the number of ciphers before the -5 is notMufi which leaves 9 for the index. 59. To find the natural number of a given Logarithm. Look for the decimal part of tlie given log. in the body of the table, and take out the number from the side column and top. To place the decimal point. Add 1 to the given index of the log., and mark ofi' to the left this number of figures ; these will be whole numbers; the rest, if any, will be decimals. If tlie index is 9, put the dot before the first figure; if it is 8, prefix one cipher to the first figure, and place the dot laefore the cipher ; if it is 7, prefix two ciphers, and so on.f Kx. 1. Find the number to the log. 1-717671. The number (to 4 places') to -717671 is 5220 : adding i to the index i, gives 2, which, marked otf to tlie left, gives 52-2, the number required. 2i. 2. Find the number to the log. 8-581381. The number to 581381 is 3814; prefixing one cipher gives -03814, the number required. \Vhen the number exceeds four figures, see the explanation of llie table. 60. In using logarithms, it is proper to observe that the number (whether it contain decimals or not), and the decimal part of the logarithm, are in general true to the same number of figures, re- jecting prefixed ciphers ; thus, for instance, the log. 3-7575 corre- sponds to the number 57-21, and the log. ;3-7576 to 5722, nearly. So also, 8-7575 to -05721, and 8-7576 to -05722. This remark should be kept in view, because it is mere waste of time to employ more figures than are required to insure a certain degree of precision in the result. • That is, the first figure not a cipher. t As the index of the log. is 1 less th.in the number of figures in the natural number Itaelf, it would follow that the index of -3814 (for example) in which there are no significant figures, would be 1 less than nothing, the meaning of which is, that such a log. is reckoned on the opposite direction from a certain point, which need not here be further discussed. The index of such a log. is called negative .- ana as this is cmbarriLssing to beginners, 10 is added to the index 0, whi-reliy 1 less gives 9. But 9 is the index, properly, of a number consisting of 10 figures; however, as we have no such numbers to deal with, the ambiguity of thii Jnabli ununing is not exuerienced. 20 INTIIODUCTION. 61. The remark (No. 3.5) applies also to logaritlims -, thus, for example, if we propose to use only four figures of the log. -88 1385, we write "8814, which is evidently nearer to 'SSlSSo than •8Slo would be. Again, if we take four figures of •88134.3, we write '881 3. 62. To find the arithmetical complemeyit of any number or logarithm. Take every figure from 9, except the last, which take from 10. It is necessary to begin at the left. Kx. I. Find the arith. comp. of i'87045 | Ex.2. Find the arith. comp. of o'gijso arith. comp. log. required 8-12957 | arith. comp. log. 9-08650 63. A subtractive quantity is, by this means, made additive The process is equivalent to subtracting the number from 10, and the reason of it is evident on considering that to add 3, for example, and subtract 10, is the same as to subtract 7. In like manner, in- stead of subtracting 47"" 32% for example, we may add Vl"' 28' (the complement to 60), provided we subtract 1 hour (or 60); and thus any number of quantities, of which some are additive and some sub- tiactive, may be rendered all additive, provided that the larger numbers which are employed in taking the complements be tliem- (elves subtracted. 2. Certain Arithmetical Operations by Logarithms. [1.] MuUiplieation. 64. To multiply numbers together, add their logarithms together; the sum is the logarithm of the product required. Ei. 1. Multiply 530-9 by 27-22. 530-9 log. 2-725013 27-22 log. 1-434888 /Im. 14451. log. 4-159901 Ex. 2. Multiply -079 by 3-142. -079 log. 8-897627 3-142 log. 0-497206 .\ns. 0-2482 log. 9-394833 [2.] Dirhion. 65. From the log. of the dividend subtract thelog. of thedivioor; the remainder is the log. of the quotient required. If the logarithm of tlie dividend is the lesser of the two, increase its index by 10. •ii. 1. Divide 4280 by 365. Ex. 2. Divide 69-3 by 71-7. 4280 log. 3-631444 69-3 log. (+ 10) 1-840733 365 log. 2-562293 71-7 log. 1-855519 Am. 11-73 log. 1-069151 I Ans. 0-9665. log. 9-985214 [3.] Involution. 66. Involution is the process of multiplying a quantity by itself: the quantity thus multiplied is said to be raised to a power. 67. The first power is the number itself. The second power is the number multiplied by itself; this is also called the square. TSe third power is the number again multiplied by itself; this is also p«licd the cube. PRACTICAL GEOMETllY. 21 The number or quantity to be raised to a power is called the root; the number which indicates the power to wliich the quantity is raised is called the index. 68. To s/fuare a number. Multiply the log. of the number by 2; the product is the log. of the number required. When the number is a decimal fraction, subtract the index (after being doubled) from 10 multiplied by 2 (or 20), diminish the re- mainder by 1, and prefi.x the number of ciphers indicated by this remainder to the number corresponding to tiie logarithm. Ex. 1. Square 12-39. 12-39 log. i*09307i Ans. I53"5. log. 2M86142 Ex 2. Square "0592. •0592 log. 8-7723» Ans. -003505 log. 17-54464 17 from 20 leaves 3 ; deducting i gives » | 2 ciphers are, therefore, prefixed to 3505. 69. To cube a number. Proceed by tlie above rule, only reading 3 for 2, and 30 for 20. In like manner, to raise a number to the fcmrtA power, read 4 for 2, and 40 for 20, and so on. [4.] Svolulion. 70. Evolution is tiie reverse of involution, and is the process of finding that number which, multiplied by itself a certain number of times, will produce the given number. This number is called the root of the given number. 71. To extract tiie square root of a number. Divide the log. of the given number by 2, the quotient is the log. of the square root required. When the given number is a decimal fraction (that is, when the index of its logarithm is 9, 8, 7, &c.), increase the index by 10. I. 1. Find the square root of 1-53 '■S35 log. o-i86ic8 2 )0-186108 ij9 Sq. root req. 0-093054 Ex. 2. Find the square root of -003505. -003505 log. 7-54469 1 )17-54469 Sq. root req. 8-77234 72. To extract the aibe root. Proceed by the above rule, only reading 3 for 2, and 20 for 10. To extract the fourth root, read 4 for 2, and 30 for 10, and so on for other roots. IV. Practical Geomethy. 1. Definitions, 73. Geometry is the name of that science which relates to the measures of space. A PHOBLKM is something required to be done. 'VI INTRODUCTION. Parallel lines are lines so placed that the shortest distance between them is every where the same, as A B, C L>. Such lines evidently never meet. 74. A CIRCLE is a figure bounded by a curve line called the di- cuviference* of which every point is at tlie same distance from a point vvithin, called the centre. Thus, A B D is a circle, and C the centre. 76. The circumference is divided into 360 equal parts, called degrees, written thus, 360° ; each degree, into sixty equal parts, called minutes (60') ; each minute into sixty seconds (60") ; and also each second, into sixty thirds (60"'). Example, 11° 19' 46", eleven de- grees, nineteen minutes, forty-six seconds. 76. The circumference is also divided into 32 equal portions of 11° 15' each, called points of the compass. These are again subdi- vided into half points and quarter-points. The term point is used indifferently for the arc of 11° 15', and for a mere point of division of the circumference. 77. A straight line, A B, drawn through the centre, divides the figure into two equal parts, called semicircles, as A D B, A E B. The half circumference measures 180°. 78. Ihe line A B is called the diameter: it is evidently equal to twice tlie distance from the centre, C A, which is called the radius. language, circl« and circumferencp i oiicle is properly thp tur/ace or nrea oi ! often used indifferently tlie one fiv c f.^ure iuL'tuded within tlie ciicum PRACTICAL QEOMETRT. 23 79. If anotlier diameter, D E, cross this, and divide each semi- circle into two equal parts, the four equal parts, A U, B D, B E, E A, are called quadrants, and each of such portions of the circum- ference measures 90°. 80. Any portion of the circumference is called an arc, and the line joining its extremes is called a chord: thus the line B F is the chord of tiie arc B F. 81. An ANGLE is the inclination of two straight lines to each other; that is, the difference of the directions in which they lie: thus A B C, or B, is the angle contained by the two lines B A, B which are called the legs. An angle is not changed by increasing or diminishing the length of the legs, because the length of these lines has nothing to do with the directions in which they lie. 82. Since in describing a circle the radius moves round the centre C, exactly as the point of the compasses advances on the circumfe- rence, the angle A C B is measured by the number of degrees in the arc A B. 83. The arc A B is said to subtend the angle A C B. 84. An angle of 90°, as A C D (fig. in No. 77), which is anb- tended by a quadrant, as A D, is called a right angle. A circle con- tains four right angles, a semicircle two. 8.5. The angles A C D, BCD, being each 90', are equal ; and C D, which makes these adjacent angles equal, is said to be perpen- dicular to A B. 86. The difference between an angle and 90° is called its comple- ment ; the difference to 180° is called its v/ppkment. 24 INTRODDCTION- A.I1 angle less than 90° is called acute, as A. An angle greater than 90° is called obtuse, as 87. A PLANE TRIANGLE IS 3 figure Contained by three straight lines. When the three sides are equal, the triangle is called equilateral; when two of them are equal, it is called isosceles. 88. When one of the angles is 90°, the tr'.angle is said to he ric/ht - anyled; when each angle is less than 90°, it is said to be acute-angled; when one is greater than 90°, it is said to be obtuse-angled. Triangles that are not right-angled are called in general oblique- angled. 89. In a right-angled triangle, as A BC, the side AC, opposite the right angle is called the hypothenuse ; one of the other sides, as B C. is called the base ; and the third side, A B, the perpendicular. 90. A SPHERE, or GLOUE, is a solid figure bounded by a curve lurface, of which every point is at an equal distance from the centre. 2. Geometrical Problems. 91. The instruments necessary in constructing tlie figures in these problems are, a pair of compasses and a straight edge of any kind, as of a ruler, or, when such cannot be had, the back of the fold made by doubling a piece of thick paper. Also the parallel rulers are convenient. These may be of the common form, which needs no description here, or those called Marquoi's Rulers.* 92. The accuracy of a straight edge is tested thus. Draw a line with a fine pointed pencil, or steel pen, along the edge, between twc points near the extremities. Then turn the ruler over and draw another between the same two points : if the edge is perfect, the two jnes will appear as one; if not, there will be a space between them. • These last consist of a right-angled triangle, having one of its angles about 20°, and a flat ruler somewhat longer than the hypothenuse of the triangle, both of the same thickness. By sUding the triangle along the edge of the ruler, which is kept fixed, two sides of it move parallel to tliemselves. This parallel motion is perfect, which is not always tiie rase with tha ooromon parallel rulers, especially after long use ; and besides this, the triangle being light- angled, dispenses rith the trouble of drawinj; perpendiculars bj points. PRACTICAL GEOMETKY. 25 93. Problem. To draw a line tlirougli a given point parallel to anotlier line. C is the given point, A B is the line. Take the shortest distance from C to A B in the compasses ; set one foot on A B as at B, and describe a small arc ; then tlic line drHwn through C, so as to touch this arc, is the line required 94. Problem. To draw a line [)arallei to another line at a given distance from it. A B is the line, C D the given distance. Take C D in the compasses, place one foot near each end of A B, and describe two ares; the line drawn touching tiiese ares is the line rcfpiired. 7==^ !J5. Phublkm At a given point in a line to make an angle equal to a given angle. P is the point in the line PQ; A is the given angle. From the centre A, with any convenient radius (the longer the more accurate), describe an arc, C B ; from the centre P, with the saran radius, A B, describe an arc, D E ; take the distance from C to B in the com- pas:»es, and put one foot on D and the otiier on the arc at F, and join P F : tlien the angle F P D is equal to B A C, tlieir measures, V D and B C, being the same. 96. Problem. From a jmint M, in a straight line A M,to draw a perpendicular to it (fig. p. •2(i). (1 .) Draw a straiglit line any where, and set off by the compasses 5 equal parts upon it. With 3 of these parts in the compasses, as radius, describe from M, as a ceiitre, an arc at I ; then lay off 4 parts from M to A ; with 5 paits, as radius, describe from the centre .\ an »rc cutting the former arc at I ; join I M : this is the perpendicular required. INTRODUCTam. 1 he following methods are also used : (2.) When the point M is at or near the end of the line. Take a point P, such that a line supposed to join P and M may make the angle P M A about 45° ; and from P as a centre, with the radius P M, describe a small arc I, and another opposite, as K, draw the line I P K, and join the point where it crosses the arc K with M. K M is the perpendicular required. (3 ) A^'hen the point M is not near the end of the line. Take two points P, B, at equal distances, from M, and at P and l as centres with a radius exceeding- P M, describe two arcs, cutting each other at I ; join I M. This line is the perpendicular required. A. 97. Problem. From a given point without the line, as C, to draw a perpendicular to it. (1.) When the point is nearly opposite the middle of tlie line. Take in the compasses a distance exceeding the distance from C to the line ; and from C, as a centre, describe an arc, D E ; then, fron. 1) and E as centres, with a convenient radius, describe two arci cutting each other at I. CI is the perpendicular required. PRACnCAIi UEOMKTRV. 27 (2.) Wlien tlie given point, is towards tJie entl of tlie line. Take a point P"as centre, and with P C as radius describe an arc C D. Take anotlier point Q as centre, and witli Q C as radius describe anotlier arc cutting C D in 1. CI is tlie perpenaicular required. 98. Proislem To bistct a line A B, or to divide it into two equal parts. Take in the compasses a distance e.xccedinjj half the line, and from A and B, as centres, describe two arcs. Tlie line I K, joining the i)oints of their intersection, divides the lino A B into two equal parts, A M, M B. / M ■ \ / 99. Prodlem. To divide a line, A B, into any proposed number of enuiil parts, as fiv'o, for example. Draw a line A C, making about half a riirlit angle with A B. Draw- another line, B D parallel )o A C. On A C and B D lay otf INTROUUCTIOX. riv»; C(jual parts; join the points 1 ami 4, 2 and 3, &c. ; these iinct «iil divide A B into 5 equal 'arts. / A. \ In like manner, the line might be divided into any other rannbcr of equal parts. • 00. Problem. To bisect an arc A B, or an angle A fj B. From the points A and B, as centres, with a radius exceeding half the distance A B, describe two arcs cutting each other in I, and draw the line C I ; C I bisects the arc A B, and the angle A C B. If the angle alone is given, and not the arc subtending it, describe this arc from C as a centre, with any convenient radius. 101. Problem. To divide a circle into 2, 4, 8, &c. equal parts. Draw the diameter A B ; this divides the circle into two equal parts. From A and B, as centres, with a radius exceeding half A B, describe the arcs I and K, cutting each other above and below A B ; join I K : the line E D is a diameter crossing A B at right angles, and dividing t'.ie circle into the four quadrants, A E, E B, B D, and D A. Bisect the arc A D (No. 100); draw the diameter through C: this will bisect B E also. Bisect, in like manner, B D and A E. The circle is now divided into 8 equal parts, of 4 points each ; bisecting these last arcs divides the circle into 16 f qual parts, of 22°J each • PRACTICAL UKOMKTRV. dnd ugahi bisecting these dividts it into ttie 32 points of tlie comiiass o/Jl"' <;ach. All arc is divided into a number of parts not divisible by 2, as into .3, 5, 7, &c. parts, by trial. 102. PuoBLEM. To find the centre of a circle, or circular arc. Take two points, as A B, on tlie cirjiimference, and join them; bisect the line A B (No. 98), and at the middle point draw a per- rendicular (No. 96, 3d). Take a third point, D, join it with B; bisect the line B D, and draw a perpendicular at the middle Ihc two perpendiculars will cross at the centre. point. 10-'!. Pk(;ulem. To draw a circle throuuli three i^^iven jioints. iSiipposi; the tiiree points to lie in a circle, and proceed to tind tbr centre as above. It is easy to see that hovvever three points may be placed, some ciie circle will always pass through them; for an infinite number of circles may be drawn passing through two i)oints, and therefore some one of these must likewise pass through a third ])oint wherever situated. 3. ("strand ( 'oiinlriirtMU of the Scales. 104. These are flat, thin pieces of brass, ivory, or wood divided in'.o certain portions by lines, and serve for measiiniij^ or laying oil lir eu or disin id ait/jles 30 TNTROnUCTIOTf. Tho coiiiinoi. scale of equal parts lias genera'ly on ono side fnur or fi\rf tlirterent scales for cliH'erent measures, on each side of wliic!; one division is subdivided into 10 equal parts. 105. In the diagonal scale, the shorter lines dividing the length into equal portions (units) are crossed perpendicularly by 10 others extending the length of the scale. The end division, or unit, has its upper and lower edge subdivided into 10 equal parts, and diagonal lilies are drawn from the beginning of one division to the end of the opposite one. This ettects a further subdivision by 10, as an example will shew. To take the No. 5-28 from this scale by the compasses. Set one foot at .5, and the other at the second line on the lower vi['j;e of the subdivided unit, — this gives 6-2. "Now follow np the diagonal line at the -2 to the eighth of the long parallel lines, and, fixing the ]toint there, extend the other point to meet the line which rise-! at 5, crossing the breadth ; and the number Is taken. The same process serves for tens and units, as for units and tenths, and so on ; thus the No. 52-8, or 528, is taken as above. By placing the points of the compasses between, instead of oh, the 10 louir parallel lines, we may obtain a still further subdivision. >; ■.T-^-.^^^N^^>jv^,^-^.^^^v^^^^^^^ Diagonal -ScaL.. ■'/•"/"-■■'"/.^■■^■■■■^■■j>^-''-j:.^ -1 8 -« 1 1 H -: # B = = = = = = ^ = 2 i i = ^ ^ r ^ ^ = 5 B ' lOG. Angles are measured, or laid oH', either by means of the lines marking the divisions of degrees, or half degrees, at the edge of the scale, and which are numbered at each 10° or 5°, or by means of the Scale of Chords. (1.) To measure an angle by the marked divisions. Place the middle point of the scale (which is strongly marked) upon tlio angular point, and lay the edge along one of the legs; the other leg, produced, if necessary, shews, on the graduated edge, the degrees which the angle contains. (2.) To measure an angle by the scale of chords. Take in the comj)asses the chord of 60° otf the scale, and describe an arc: taki« tlu! distamte from A to B in the compasses, and, placing one foot at PRACTrCAL GKOMETKr. ?,l tli« boj^inning of the scale of chords, look liow nianj Jegroos the other foot extends to. Thus, for example, if A B extends to 27°, the arc A B, or angle, C, contains 27°. 107. To lay off an angle from a given line, as, for example, 27°, Describe an arc AB (fig. lOG), with the chord of 60°, from C, as centre, and set off the chord of 27° from A on A B ; join C B, and A C B is the angle required. When the angle to be measured or laid off exceeds 90°, measure or lay off 90°, and then the excess above 90°, 108. Tiie semicircle with a graduated edge is useful for this p'.ir|)ose ; hut the most convenient instrument, especially for using witli tlie chart, is a transparent horn semicircle, with a long silk thread attached to its centre.* 10!). To construct a scale of chords to any proposed radius. The radius is equal to the chord of ()()°; describe, therefore, a quadrant, divide it into portions of 30°, 20°, 10°, and so on; draw tlie several chords, and transfer them to the proposed scale. 4. Tlie Sector. 110. The Sector is a ruler, or scale, which folds into half iti length by moving round a large circular joint on which it is accu- rately centered. Several lines, or scales, are laid off from the centre to the extremity on both legs of the sector, as tangents, sines, &c., and others parallel to the edges. We shall refer here only to thai one which is called the line of lines (marked C L in the figure), on account of the great convenience of the sector in reducing a plan, or a figure, to another on a ditferent scale, dividing lines propor- tionally,t and in solving some simple questions which dej)end on |iroj)ortion alone. The line of lines is divided into 10 equal jiarts, and these again Hre siuiilarly subdivided. The distance from the centre to any point in tlie line of lines is called the lateral distance; and that between any point in the line of lines on one leg, and the correspoiuling point on the other, the trnnsverxe distance. • Sucti einiieirc'les, made of horn or other transparent material, and h.iviiiga long silk tliread attached to the centre to extend a straight line to any point beyond the circnmlVr- ence, are must useful, especially for chart work. They are commonly called protractors. t Another instrument, equally conveuient and portable, but more expensive, is tho fiTopurtional cvmiiasses. These C(jmpa6Sis open on a movable centre, so that the opening of one pair of points may, by moving the centre; l>« made to bear any proportion to th« opi.uug of the other pair of point«. o2 INTRODUCTION. The following examjales will illustrate the use of the Sector.* Ex. 1. To divide a lin« into a number of equal paits, as for ex. 7. Take the given line in the compasses; place one point on the division 7 on one leg of the sector, and open it till the other falls on the other 7. Then the transverse distance i to I is i-7th, 2 to 2 is 2-7ths, and so on j or the line 7, 7 is equally divided into the pans I, I ; 2, 2 ; &c. Ex. 2. To reduce a plan on the scale of 3 inches to a mile, to another scale of 2 inches Take the lateral distances on tlie scale of the 3-inch plan. Take 2 in the comp;isses j place one point at the division 3, and open the sector lill the other poini falls on the other 3. Then the transverse distances will be the distances on the pronostd plan. Ex. 3. A line of a given figure measures 85 ; find the measure of another line in the same figure. Take the given line 85 in the compasses and open the sector till their points measure me irnnsverse distance 85, 8-5. Then any other line of the figure taken in the compasses is mea-ured by finding the Cirre-ponding points in the two legs ■which exactly contain it, and multiplying the number shewn by la • See J. F. Heather on Mathematical Instruments, Lockwood & Co., Ludgata Hill. V. Raising the TfiiGONOMETaicAL Canon 111. Thi-i term implies forming the proportions or analogies pro- per for the solution of problems concerning right-angled triangles. Before, h&wcvcr, the student proceeds to the actual composition of these analogies, lie should be acquainted with the few propositions of geometry whicli are given in the following section. 112. Definition. An Axiom is a proposition assumed to be so obvious as to require no demonstration. The principul axioms whidi have been employed as the founda- tion of geouietrical reasoning are the following : — (1.) Geometrical magnitudes are said to be equal when one being placed on another coincides with, or exactly covers, it. (2.) Two magnitudes which are each equal to a third, are equal to each other. (^3.) If equals be added to equals, the wholes will be equal. That is, if two magnitudes be equal, and a third be added to e-jch, the two sums will b< (4.) If equals be taken from equals, the remainders will be equal. (5.) If the same or equal quantities be added to unequals, tiie Bums will be unequal. (ti.) If equals be taken from unequal^, the remainders will be unequal. (7.) The halves of equal things are equal. (8.) The doubles of equal thing.s are equal. 1 13. Def. a Geometrical Theorem is a ]ir(>uositi(>n in wliich some property of a figure is demonstrated. The term Proposition includes both Piv,i)lems and Theorems. 114. Df.f. a Corot.i.auv is an obvious Cviucliisioii oi' neee>»sttr;y inference, from a proposition. I. Theorems of (hwnclry. 1 15. A straight line, as A C, standing on anotiier, as 1) E, mokfis the adjacent angles, ACE and A C D, together eqnal to two ligUi angles. n For, draw C N at right angles to i ^ D E ; then D C N and N C E are two right angles ; that is, D C N, with N C A and ACE, are two right angles ; and since D C N and N C A nuike up D C A, therefore, UCA and ACE are two right angles. „ ^ k >ht lines, as A B, C D, inteisect or cross eaoli 116. If two straigiit lines, other, the o])i)osite and vertical angle; Since C E stands on A 13, the angles CEA and C E B are e(iiial c- to two right angles (No. ll;j). Again, since BE stands on CD, the angles C E B and BED are equal to two* right angles. Hence C E A and C E B are equal to BED and C E B. Take away the angle C E B, common to both these sums, and the remaining angles CEA, B E D are equal C E A, BED, are e<|Ual. (No. 11-2, 4). 117. If two triangles, as ABC, DEF, have two sides of the one, as A B, A C, equal to two sides of the other, as D E, D F, and have likewise the angles A, D, contained by those sides, equal, the two triangles are equal in all respects. For if the point A be laid on ^ D, and the line A B on D E, the point B will coiiiciver it. Hence the two remaining angles must be equal, or B is equal E, and C to F ; or, tiie triangles are equal in all respects. The above proves the mpthod No. 100. For .suppose A and I, B and I to be joined by linr.. then the two triangles C A I, GUI, h.ive the sides C A, A I equal to C B B 1, and the third Hiile rommoa Hence they arc eoint G, and bisecting A B, it would be proved that the angle A B G, or its equal CBD, i.s greater than A. 122. Any two angles of a triangle are together less than iwo right angles. Produce the side B C of the triangle ABC,toD. Then the exterior angle AC U of the triangle is greater than the interior and opposite angle ABC (No. 121). Add to each angle AC B, then A C D and ACB, are greater than ACB and ABC (No. 112, 5) ; and since A C D, ACB are equal to two right angles, A C B, and ABC are less than two right angles. The same may be i)roved of the othei angles by producing the other sides. 12:$. If a straight line ABmeeting two other lines CD, EF, makes the alternate angles CG H, G H F ecpial, the two lines are parallel. 717- For if they are not, they will meet on one side of A B; let them meet at I, then G II 1 is a triangle, and the exterior angle (' C« H is greater than the interior and oi)i>osite angle (J II F (No. 121 ). But these angles are ecjual by the supposition, therefore the lines do not meet towards I. In like manner it may be shewn that they do not meet on the 36 INTKODUCTIOX. other side of A B, and heiicfi that they do not meet at all ; that is, they are parallel. It appears by fig. 2, that the lines meet on that side on which the two interior angles are less than two right angles. For I G H, I H G are together less than two right angles (No. I'i2). 124. If a straight line AB (fig. 1, No. 123) falling on two lines C D, EF, make the exterior angle A G D equal to the interior and o])posite angle G H F (on the same side of A B), the two lines are parallel. Also, if the two interior angles D G H, G H F, are equal to two right angles, the lines are parallel. The angle A G D is by supposition equal to G H F, and A G D IS equal to CGH (by No. 116); hence CGH and GHF are equal, and they are alternate angles, and C D, E F are parallel. Again, since D G H, G H F are equal to two rigiit angles by the supposition, and since CGH, D G H are equal to two right angles by No. 115, CGH, DGH, are equal to D G H, GHF; take away the common angle DGH, and the remaining angle C G H is equal to G H F, and they are alternate angles, therefore CD, f i F are parallel. 125. If a straight line A B (fig. 1, No. 123) fall on two parallel lines C D, E F, it makes (1.) The alternate angles C G H, G H F, equal ; (2.) The exterior angle A G D equal to the inteiior and opposite angle GHF; (3.) The two iulerior angles DG H, GH F, equal to two right angles. (1.) If CG H be not equal to GHF, let it be greater; add to each the angle DGH; then the angles C G H, DGH are greater than the angles D G H, G H F, and C G H, D G H are equal to two right angles (No. 115) ; therefore DGH, GHF are less than two right angles. But, by fig. 2, No. 123, this is the case in which the two lines meet at I, whereas they are here parallel by the supposi- tion ; therefore C G H is not greater than G H F. In like manner it might be shewn that it is not less ; it is therefore equal to G H F. (2.) Since AGD is equal to C G H (No. 116), and CGH to G H F, therefore A G D is equal to G H F. (3.) Hence, adding D G H to A G D, G H F, tlie two A G D, DGH are equal to the two D G H, G H F. But A G D, D G F are equal to two right angles ; therefore DGH, GHF are equal to two right angles. 126. Prop. The exterior angle, as A C D, of a triangle (formed by producing one of the sides of the triangle), is equal to the sum of the two interior and opposite a angles, A B C and B A C. Produce the side BC to D, and draw CE parallel to BA. Then the angle E C D is equal „ ^^ to A B C since B D meets the p;iriillei8 B A ami CE(No. 125). Again, tlie alternate angles BAC, A C K, formed l>y A C, wliicli crosses tlie same jiarallels, are i(iiia>' (Mo. 125). Hence ACE antl ECD are togetlier equal to BAC and ABC; tiiat is, A C D, which is made uirof ACE and E C D, is e jual to B A C and ABC. 127. Prop. The tliree interior angles of a triafigle are together pq(uil to two riglit angles (fig. No. 126). By the above projiosition, ACD is equal to the sum of ABC and B A C. Add to each A C B ; then ACD and A C B are equal to the three angles ABC, BAC, and A C B, (No. 112). But ACD and A C B are equal to two right angles, therefore the angles ABC, BAC, and A C B, are equal to two right angles. Cor. 1. In a triangle which has one right angle, the other two angles make up a right angle; each of tiieni, therefore, must be less than a right angle, and each is the complement of the other to 90°. Cor. 2. If two triangles have two angles in the one equal, re- H|)ectively, to two angles in the other, they will also have the third jr remainina; angles equal. 128. Prop. The greater side of any triangle, as A C, is opposite lo the greater angle A BC. C A being greater than A B, make A D * e(jual to A B, and join D B ; then since AD is equal to A B, the triangle ABD is isosceles, and the angles ADB and "/ '^ \ ABD are equal (No. 1 19). But A B D /<-.. \ which is contained within A BC is less than ^^ \ A B C. Hence A D B is less than A B C. '■ — J„ Now ADB is ecjual to the sum of A (J B and C B D (No. 125); hence ADB is greater than A C B, that is A B D is greater than ACB, therefore ABC is greater than ACB. In like manner, by taking C D equal to C B, it would be ])roved that the angle B is greater than the angle A ; and, by taking D on BC, and BD ecjual to B A, tiiat the angle A is greater than the angle C. 129. Prop. The line drawn [jerpendiciilarlv from a given point C, to a right line A B, as C D, is the shortest that can be drawn from C on A B. Take any point E in A B, and join C E. c Then since 'in the triangle C E D, C D E is ] n right angle, the angle C E D is less than a right angle (No. 127, Cor. 1), and there- fore (No. 128) C E is greater than C D. The same proof applies to any point whatever taken in A B. * '■ " ^ CoR As the angle C E D is acute, wherever E may be taken, thei'c is but one line which can be drawn periiendiculai- lo \ R from C. 'AH INTRODUCTION. 130. Def. a PaiiillLlograui is a four-sided figure of which the opposite sides are parallel. 131. The opposite sides ofa parallelogram, as A B, CD, are equal; also the opposite angles are eipial ; and the diameter, or diagonal. G B divides it into two equal parts. Since AB and CD are parallel, and CB meets them, tlie alternate angles ABC and BCD are equal (No. 125). Also, since A C, JJ D, are parallel, and B C meets them, the alternate angles A C B, C B D are equal. Hence the two triangles ABC, BCD having ^ two angles equal in each, and the side BC adjacent to tiiem com- iiioii, are equal (No. 1 18). Hence A B is equal to C D, and A C to B D ; also the third angle A to the third angle ofiposite, D. Since the two triangles are equal, and make up the whole figure, each is half the parallelogram, or C B bisects A D. 132. The straight lines C A, B D (fig. No. 131) which join the extremities of two equal and parallel lines A B, C D are theuiselves both equal and parallel. The triangles ACB, CB D, having the two sides AB, CD equal, and the side BC common, and also the included angles ABC, BCD ecituil, are equal ; hence AC and B D are equal. Again, since the other angles are equal, ACB and C B D are e(|ual, and hence A C, B D are parallel. Tliis (iroves the method No. 93 ; for the equal distances laid off from C and B |ipr[iendiiular to A B, form two sides of a parallelogram, of which the other sides al.so are parallel. And the like reasoning applies to No. 94. 133. Parallelograms, as ABCD, A BEF, on the same base A R and between the same parallels A B, C F, are equal to each otiu^r. Since CD and E Fare each equal r n e r to A B, they are equal to each other. V V .^^ y' Add to each D E, then C D, D E, \ Y / are equal to E F, D E (No. 112, 3), \ / \ / or C E is equal to D F. Also A C \ / \ / IS equal to B D, and A E to B F, \ / \ / nence A C, C E are equal to B D, \ /' \ / DF, and the angles ACE, BDF, ^ if are equal, because AC is parallel to B D (No 12.5). Hence the tri angle A C E is equal to the triangle BDF (No. 1 17). Take away the triangle ACE from the whole figure A B C F, and the remainder is A E F B ; again, take away the triangle B D F from the same figure, and the remainder is ABCD; therefore since t'.ese triangles are equal the remainders are equal (No. 1 12, 4), or the |)arallelograms ABCD, ABEF are equal. CoR. Parallelograms on equal bases, and between the sanii* parallels, are equal. For since the bases are equal, either of ti)em pliiced on the other will coincide with it, and the above proof npplies. GKO.METRY. ,W 134. A PaniUelograin A BC D is double of a trianendicular to the tangent. 139. The angle at the centre of a circle, as A C B, is double the angle at the circumference, as A D B, both angles standing on the same arc A B. .Toin D on the circumference and C the centre, and ])roduce the line DC to E; then the e.xterior angle ACE of the triangle ACD is equal to the sum of the two interior and opposite antjles CAD, and C D A (No. 126). But C A D is equal to C D A, because C A and CD being equal, A C D is an isosceles triangle (No. 119). Hence A C E at the centre is equal to twice A D E at the circum- ference. Again, the exterior angle B C E of the triangle B C D is equal to the sum of C B D and C D B. But these angles also are equal, because C B and C D being equal, C B D is an isosceles triangle ; hence B C E at the centre is equal to twice B D E at the circum- ference. r.F.OMETRr. 41 ^l0^v, ill fig. 1 (where the iliainetci- of tlie eirelo jjasscs clear o( die arc A B), ACB is tlie ditterence of B C E aiui A C E, and is duuble of A D B, the ditterence of B D E and A ]) E. When E falls on AB, as in fig. 2, ACB is the sum of ACE and B C E, and is double the sum of the angles A D E and B D E. or the an-le A U B. 140. The aniile at tlie circumference is measured by luilf the arc Siibtendinii' it (fig. No. 1:39). As A C B at the centre is measured by the arc A B, it is evident that ADB at the circumference (which, bv the prop, is half ACB) is measured by half A B. Thus, if A B is 58°, the angle ADB will be 29°, for any point of the circumference at which D may fall, except between A and B. Tliis proves th? method No. 100, for, since C A, AI (supposing A, I, and B, I, joined) t-eequal to CB, BI, and C I common, tlie triangles CAl, C B I are ec|ual, — hence ACI •Dd I C B are eijual ; eacli therefore is lialf of A C B, and is measured by half the arc A B. 141. The angle in a semicircle is a right angle. If the arc A B increases to a semicircle, A moving to E and B to D, A C and C B (fig. 1, prop. 139) falling into the same line, form H diameter, the angle A C B becomes two rigiit angles or 180°, and then A D B, or half ACB, is 90". Hence tiie angle in a semicircle is a right angle. This theorem proves the method No. 96 (2), for since 1 K is a diameter, the angle at M, t point on the circumference, is the angle in a semicircle. 142. The angle in a segment greater than a semicircle is less than a right angle. The segment B A C of the circle being greater than a semicircle, the other segment BDCmnst be less than a semicircle ; and the Hngle B A C in the greater segment being measured by half the arc B D (', that is, bv a quantity less than half 180° {No. 140), is less than a right angle. 143. The angle in a segment less than a semicircle is greater than a right angle. The segment BAG being less than a semi- circle, the segment B D C must be greater than a semicircle, and therefore the angle B A C, which is measured by half BUC (No. 140) is greatei- than Im.'f two right angles or than one right angle. 144. A line, CD, drawn from xuj chord A B, is jierpeiidicular to a circle bisecting 42 INTRODUCTION. Join C A, C B, tlien C A and C B are equal by the ilef. of a circle (No. 74). Also A D and D B are e((ual, each being half of A B, and C U is common to the two triangles CAD, C B D. These triangles, therefore, having their three sides equal, are equal ; hence the equal angles C D A, C D B, opposite the equal sides C A, C B, being adjacent angles, are right angles. » Con. The line from the centre bisecting the chord bisects the arc A B. For since the two triangles, as above, are equal, the angles A CD and BCD, opposite the equal sides AD, DB, are equal, and biiiig at the centre are measured by the arcs on which they stand. The above proposition is the principle of the method of finding the centre of a ciiile. 145. Triangles bavins the same altitude are proportional to their bases. The altitude is the peipendicular distance of the vertex, or summit, from the base. Let the base B C of the triangle A B C be divided into any niim- her of equal parts, as three, B^, g h, AC, and EF the base of the triangle D E F, into four like parts, E?, ih, kl, l¥, then B C is to £ F as 3 to 4. Join the points A//, A //, and Di, D ft, D /. Then the triangles A B^, Agh, AhC, and D E i, Bik, JMil, THY are all equal, being on equal bases, and having the same altitude (No. 134, Cor.) Hence the triangle ABC contains three parts, of which D E F contains four, and, therefore A B C : D E F : : 3 : 4, which is the ratio of the bases.* 146. A line DE parallel to a side B C of a triangle ABC divides the sides A B, AC, intiie same proportion, that is, AD ; A B : : A E : A C. • If it be impossible to find a quantity, or measure, B^, wliicli ahall divide B C and E F into an exact number of equal parts, as 3 and 4 above (that is, when B C ami E F are said to be incommensurable) we must take a smaller ([uantity, and a greater number of triangles j and by taking this measure sufficiently small we may make the error of using it ins^■ad of the true proportion as small as -re please. Join B E, C D Tlien tho ti inn-l.^s B D E. CI) Eon the same base 1) E, anil between tlie same parallels 1) E, B C, are equal (No. KU, Cor.) Add to each tiie triangle A I) E, then the whole triangle A B E is equal to the trianole A P C (No.'l 14, 3). Hence the triangle A B E : A B C : : A D C : A B C. Now triangle ABE: triangle ABC:: base A E : base AC, since they have the same altitude, viz the jierjien. lieular drawn from B on A C or A C ju-oduced (No. 145). Also, triangle ADC: Diangle ABC:: base A D : base A B, And tiie triangle A B E is equal to the triangle ADC, hence the two |>ro])ortions are the same, and A E : A C : : A D : A B. In like manner, as the triangles A D E, E D B, have the same altitude, viz. the perpendicular drawn from E on A B, we have triangle A D E : triangle E D B : : A D : D B. Also since the triangles A D E, EDC have the same altitude, viz. the perpendicular from D on A C, triangle A D E : triangle E D C : : A E : E C. But the triani?^les EDC and E D B are equal, hence A D : D B.: : A E : E C. This pi,)of applies to the sector. The line of lines on each leg is the side of an isoscele* lriaii){le, and the transverse distances 1,1, 2,2, &c., are the bases of so many isosceles tri- «nj;)rs ; the angles at these bases being equal, the bases are parallel, and the sides of the leveral triangles so formed are proportional. 147. Def. Similar triangles are such as have the sides about the equal angles proportional. 148. Equiangular triangles, as ABC, DEF, have the cor- responding sides about the equal angles jiroportional, that ia. A B : A C : : D E : D F. Jjet tlie angles A and D be equal, as also B ^^ and E, C and F. * n. Place the triangle DEF on ABC, D |\ \ being placed on A, and D E on A B, and let I \ I \ CJ be the i)oint where E falls. '■/ \" e — ' » Then since the angles A and D are equal, I \ and D E is on A B, D F will fall on A C ; let, \ therefore, H be the point where F falls. Then ^ \ since A (} H is equal to E, and B to E, A (i H is eipial to B, and the lines G H and B C, which make equal angles with A B, an' therefore parallel. Hence, by No. 146, A B : A C ; : D E : D F. Cor. Hence equiangular triangles arc similar (No. 147.) 149. In a right-angled triangle ABC, a line B D drawn from the riglit angle perpendicular to the l)y])otheiiuse, divides the triangle into two similar triangles A B D, B D C. t* INTRODUCTION. The triangles ABC, A D B, Iiaving " each a riglit angle, and the angle A common, /''^l' have the third angle also equal (No. 127), / ] \ they are, tiieretbre, equiangular. ^^^ \ For the like reasons ABC and B D C y^ 1 \ are equiangular ; therefore the two tri- ° ^ angles ABi), BDC, are equiangular, and tiia sides about the equal ingles are proportional (No. 148). Hence (1) AC: AB :: AB : AD. (2) A C • C B : : C B : C U. (3) AB: AD ::BC : BD.* 2. Terms of Trigonometry, 150. These terms occur in all calculations in \vh ftiig'les are concerned. 151. PN(y is a riglit-angled triangle; a quadrant is describetii(r radius produced, is failed the tangeyit of the angle P C A, or arc PA. N\'hen the arc is small, A T but little excoedn P N ; when the arc is the tangent is j wheu the arc is small, the tangent and sine may be taken for each other, and for the arc. When the arc is 90°, the tangent is intinitely great. Tlie tangent is less than the radius, »tcording as the angle is less or greater than 45°. The coUiiifjeiit is the tangent of P C n, which is the complement of PCN, and would be drawn from the extremity of the radius CB, meeting C P produced. l.OJ. The line CT meeting the tangent, is called tlie secnnt. Tiie cosecant is tlie secant of P C n, and meets the cotangent. When the aic is 0, the secant is equal to the radius. When the arc is 90", the secant in infinitely great. The secant is always greater than the radius, as is also the cosecant. 156. The line A I^ is called the versed sine. 157. These quantities are calculated for a radius of the same constant length, and to each minute or smaller division of the quad- rant, and are inserted in Tables. Then, since the sides of all right- angled triangles having the same angles are oronortional (No. 148), the tables afford the means of finding the relations among the parts of a right-angled triangle, of any kind or dimensions, by simple proportion. For example, the sine of ;S0** is ^ the rad. (see No. 159, Cor.), or 0-5, the log. of which, by No. 58 (2), is y-698970, as inserted :n Table 68. These are the ]irinciples on which the Traverse Tables and »1'» Trigonometrical Tables are consti-ucted. 3. Prop"siliom of Trifjomiwrtn I5S. The sine of an arc is half the chord of twi^ Take the area A P, A Q e(|ual to each other, and join P Q. Then the angks PC A, ACQ are equal (No. 82). And since CP=CQ, and C M is common to tlie two triangles C P M, CQM, these trianirles are equal (No. 1 17); hence PM = ]\rQ; therefore P M, the sine of A P, is half PQ, the chord of twice A P. 159. Tlie chord of 60"' is equal to the radius. Let A P and AQ (fig. No. 158) be each :iO<', then the is m"; and since tlie three angles of the triangle PCQ ar< 180° (No. 127). C P Q and C Q P are together equal to 120° ' Also, since CP = ('Q, these two angles are equal (No. 119), and each, therefore, is CO*. The triangle is, therefore, equiangular, and eon- wquentlv, e INTROUUCTIOV. I GO. TI)(! secant of 60° is equal to twice the radius. Since I' N and AT are both perpendicular to G A, tlioy are parallel (No. 124), and the triangles C P N, CT A, are similar (No. 148), hence CT:CP::CA:CN, that is, as rad. : cos. 60*>, or as 1 to ^ that is, as 2 : 1. 161. The tangent of 4.j** is equal to the radius. Let P C A (fig. No. 160) be 4.5°, then C T A is also 45** (No. 127), hence the triangle is isosceles and tlie sides C A, AT are equal. ' ;" Con. Hence also, by similar triangles, C N = N P, or the sine and ens. of 45° are equal; as are also the tangent and cotangent. zh 4. Construct/ ti<) the Ciinoiis, and working them by Logarithms. 162. Take a right-angled triangle, as A B C, and supjiose auothtr similar to it, as PNC, drawn in a quadrant, as in No 151 ; then CA: AB ::CP: PN; that is, C A -. A B : : rad. : sin C (by 152). Tiie second triangle, PNC, is, in fact, here referred to for illustration only ; for it is evident, without it, that C A and A B themselves stand in tlie same relation to each other as that of radius and sine; hence By No. 1.52. CA : AB By No. 153. CA : CB By No. 154. CB : BA By No. 155. C B : C A 16.3. It is easy to recollect these analogies, each of which begins with two sides, by observing these condition-s. 1. One of the three sides must be made radius, and the analogy always begins with that side. 2. The other sides will then become sine, cosine, tangent, cotan- gent, secant, or cosecant, of one or the other of the two acute angles. The figures below sufhcieiitly illustrate the application of tho terms. c N rad. : sin. C. (1.) rad. : cos. C. (2.) rad. : tan. C. (3.) rad. : sec. C. (4.)* * The learner will much more speedily apprehend the purposes which the expressions of trigonometry answer in the sciences of calculation by considering these proportions as reprc- •enling the change of quantities in a certain ratio, as in No. 48 (.S). Thus AB in C \ dimiuKhed in the ratio of the sine of C to 1 ; C B in that of cosine to 1. A B is alKi (' B diminished or incrmsnl in thr ratio of tan. to 1, according as C is less or greater than 44° tnd C A is C B iticreuscd m the ratio of secant to 1. TRIOONOMETRT. 4/ To employ riglitly the tcnus .sine, cosine, kc, observe — 3. Tliat wlifin the hypothenune, or longest side (whicli is ojjposile llift riji'lit angle), is made the radius, The side opposite either of the aciife ati<>Ips is the sine of that angle; and the side adjacent to eitiicr angle is the cosine of that angle. 4. Wlien either of the sides eontaining the right angle (or leijs* as they are called), is made radius, the other side becomes tlie Utntjent of the angle opposite to it; and tiie hypothenuse becomes tlie tecnnt of that angle wiiicli is coutnined or included between tVieZ/'and tiie radius. The learner should be able to construct the above analogies (which he ^viIl find very easy; before he proceeds to the solution of any question, without regard to what is given or what is not given. 164. We now proceed to the calculation of a problem. 'J'lie above analogies or proportions consist of four terms each. Hence, if three are given, the fourth may be found (No. 46). But the radius is assumed in the trigonometrical fables as 1 (which is the simplest of numbers), and iieiice, of the three remaining terms, if two are given, the third may be found. Hence, in any right-angled triangle, consisting of three sides and two angles besides tlie right angle, if two parts which enter into any one of the above analogies are given, the third term of that analogy may be found. 16f>. The proportions may be solved by multiplication and divi- sion ; thus, suppose, CA (hg. No. 162) measures 37 feet, and the angle C is 29° .52', and we want to find A B. We have by No. 1G2 (1), C A : A B : : 1 : sin. C, whence (No. 46) A B = C A x sin. C (the 1 not being written). Now the sine of 29° .02', given in tables of natural sines (of whicii the loqs. are given in Table 68) is 0-498 nearly, hence A B=37 x 0-49,S = 18'426. But in order to save such tedious processes, logarithms are em- ployed in the manner described, No'^. 64 and 65. Thus, A B=37 X sin. C, becomes log. of A B = log. of 37 + log. sin. C. Again, if CA were re(|uired, aiul A B given, we should have CA = ABx l-=-sin. C; or, (supprcssiim- the 1). log. C A = log. AB-log. sin. C. 'l"hc following rules are deduced from these principles. The learner will do «ell to verify all his work by the Traverse Tables. Tliis proceeding is described in the explanation to the Traverse Tables. 166. The rule for working any analogy by logarithms is very simple, and there are but two cases: 1. In which it is re<|uiied to find one of the mean terms; and, 2. In which it is requireil to fin■< (he natural prn,;ress of ideas, immeilMelf/ folirm Ihc term riirliu... The mrthivt l'ol!o.rcd •! ilio shorter aud more elegant. Moreover, the nietliod just <;uoted, not being employed in TRIGONOMKTIIT. Case fl. Given the angles and one leg, to find the hypoilicnuM d the ullier Ic^. C is 171. Find A B and A 0. To find A C. Ti.lfe two sides, AC, C B, m«it« AC dius ; Ihcn, by No. 103 (3). Ex. C is 90°- Angle A is 30° 14', hence B is y)° 46', To find A B. T:ike the two sides, A B, B C make A •he hvpothenuse) radius ; then, No. 163. -^ 1 C : : rad. : sin. A ; A C : C B in nhich .\ B, an extreme term, is required. in which AC, an extreme term, is required. Hence, by No. 166 (2), we have to add Hence, by No. 166 (2). •Jie logs, of B C and rad., and subtract the C B 171 log. log. of sin. A.* A 30° 14' log. tan. — 9 7655 IC171 log. + 10, 12-2530 AC = 293-4 loss- 1-4675 A 30° 14' log. sine —9^020 AB=.339'6 log. 2-5310 I This might, like Case I., be worked differently. Thus, to find A B, we may make B C radius ; then A B : B C : : rad. : cos. B. Again, to find A C ; making B C radius, we have A C : C B : : ra'l. : Un. B. We might also, having found one of the unknown quantities, employ this quantity as a means of finding tiie rest; but in general it is better, when practicable, to depend only on the original quanti- ties given. Case III. Given the hyjiotlienuse and one leg, to find the angles iind the other leg. Ki. Angle C is to°, B A = 220-3, AC-- 101-9 "• ''"'' ""^ '"'K'* B- »"'' "'^» B C. To find B. To find B C. T«> ing the two given sides, ne have Takini; Ihe two sides, B C, C A, wo h»T« B A : A C : : rail. : sin. B ; 1 w'.iir^h sin. B, in extreme term, is required. AC 101-5 log. + 10, 12-0082 tiXziOi log. — 1-34 -,0 B = 27^ 33' sin. 96652 li C : C A : : rad. : tan B ; in which B C, an extreme term, is required. CA 101-9 log. + 10, I20tS2 B 27' 33' log. tan. — 9-71-4 B C= 195-4 log. 2-291 ' (Here, in computing by the canons, we arc obliged to employ B, as found.) »ny other srieiitifln process, every seaman who may require to e.xfend his scientific knowledtrs of these subjects will have to unlearn it and to adopt the other. The rules laid down abo>« icill be found, after very little practice, simpler and more intelligible, and therefore easier to recollect, than those of the old method. • Instead of subtracting the log. sine, cosine, and tangent, it is the same thing to aild ihe lof cosiT-nnt, snrarit, and cntanffent, because those la^it .ire the arithmetical comjdcmentt n the fir^i. We have oniitt«d tnis Ui the eiupiiplcg, to avoid confui-ing tlie learner. 50 INTttODUCTION. Case IV. Given the two legs, to find the hypothenuse and the UMules. Ex. The angle C (fig. in Case III., only marking B C as given instead of B X) is 90'- B C= 195-4, C A=ioi-s: fiiiJ B A and the angle A. To find angle A. AC : BC :: rad. : tan. A. Hence, by No. 166 (2), BC J95'4 log. + 10, I2"2909 AC 101-9 log.— 2-0082 A = 62°27' log. tan. 10-2827 Mnd B=.27 33 To find B A. Making B C radius, B A will become f>ta secant of B ; hence, BC : BA :: rad. : sec. B. Hence, by No. 166 (1), BC195-+ log. 2-290? B 27° 33' log. sec. io-c;23 BA = 220-3 log. 2-3431 As 10 is to be subtracted it is omitted in the index 11. A 39° 22', wlience C is 50° 38', required A 8 Ans. AB is 1II-3, andBCgi }. Ei. 4. Given the base AB 208, and angle A 35° 16'; find the hypoth. A C and the perpend. BC. Ans. AC = 254-S, BC=i4--i. El. b. Given the hypoth. A C 272, and base A B 232. to find the angles A and C, and B G Ana. A = 3i°28', C = 58'^ 32', BC = i4i. Ex. 6. Given the hypoth. C A 980, and base B C 720, required the angles and remaining leg. Ans. A 47° 17', C 42° 43', A B 664 «. VI. Mefhods of Solution.* 167. The solution of a qnestion in wlncli tlie result is re(iiiircd in nnmbers is obtained in three ways, namely, 1. Inspection; 2. Cal- cidation or Computation ; 3. Construction. (1.) Inspection usually implies taking out, ready calculated, from R table, the result corresponding to the elements of the particular question proposed. Tiie term has, however, a more general accepta- tion, being applied to the taking out, not merely of tlie result itself, but of quantities which compose it. This method being easy and expeditions, is the best for general practice when precision is not required; but as the tables adapted to tiiis kind of solution are necessarily limited, it is, on many occasions, iiot sufficient. ("2.) The general term Computation may be applied to every mode of solution by the composition of numbers only. Since, how- ever. Inspection includes the simplest cases of this kind, namely, iliuse in which either the required quantity itself, or the parts coni- * The matter in this section is, from its nature, adiijitrd .)iily tn the reader whi has made louie [irugiess in the subject. IMKODUCTION. 5UA The Solutiok of Obltque-ajtoled Plank TRiANOLEa. Case I. lu any oblique-angled plane triangle, given two sides and an angle opposite to one of them, or two angles and a side opposite to one of them, the remaining angles and sides are found by the following simple proportions : — As one of the given !>ide3 : sin. of its opposite angla :; the other given bide : sin. of its opposite angle. To find an angle, brgin with a side opposite to a kc angle Again, as sin. of one of the given angles : its opposite aids :: sin. of the other given angle : its opposite side. To find n side, begin with an angle opposite to a known side Ex. I. In the triangle A B G. given A C B 41" 13', iC 2S2 yards, and A B 2loyards, to find the rest. Now AB 210 being less tlian AC 282, the case ia mbigiious, and there :ire two solutions. At point C in the line BC make angle BCA = 4I°I3', 1 C l.iy off C A = 2S2, Hnd from A lay off A B = 210, C culling B'C in B and D, join AD. To find A B C and ADC. Ab AB 210 log. 7677781* ;ACB4i°i3' log. sin. 9 818825 ::AC 282 log. 2450249 : ABC 62° 14' log. sin. 9-946855 A BO = A DB.-. AI)B = 62° i4'-iSo = ADC 117' 46' ADC = ii7°46' + ACB = 4i=' 13' = 158° 59' - iSo" = DACai" i' ACli = 41° 13' + ABO = 62° 14' = 103° 27' - iSo° = BAG 76=33' To fin. I I! C. As AC B 4I°I3' log. cosec. o t8ii75» : A 1! 210 log. 2-322219 :: BAC76°33' log, sin. 9 987922 log. 2491316 !C 310' To find D C. As A C B 41° 13' log. cosec. 0-181 175*' : A B 210 log. 2 322219 :; DAC 21° i' log. sin. 9-554658 : DC 114' log. 2058053 ♦ Sf« note to p. 49 on the " Arithmetical Comiltment." 5lA PLANE TlilGOXOMETUr. Case [I. In any oblique-angled plane triangle, given two siiiea and the included angle, to find the rest. As the sum of the given sides : their difference :: taa. i sum of the unknown angles : tan. i their difference. The f difference being added to J sum will give the gre:iter angle, and bein' subtracted from it will give the less. The greater angles will be opposite the greater side. Es. 2. In the triangle AB C, given = 512 yards, (,- = 907 yards, and B 49' 10', to <-907+« 5i2 = c + (! 1419, c 907-11 5i2 = f-(t 395, }'. 49° lo'-iSo = A + C 130' 50' -=- 2 = '^ 65^ 25'. To find A and C. ia + c 1419 log. 6S4SolS» «-c 395 log. 2-596597 — ^ 65°2S' log. tan. 10-339642 ■3I°I9' log. tan. 9 784257 AsA 34° 6' log. cosee. 0251345* : a 512 log. 2-709270, :: B 49°io' log. sin. 9-878875 . A 691 log. 2-839490 31° 19' = C 96° 44', and 65" 25' -31° 19'^ A 34' 6'. Case III. In any oblique-angled plane triangle, given the three sides, to find the angles. From the half sum of the three given sides (S) subtract the two sides containing a required angle. To the logs, of these numbers add the arithmetical complement of the logs, of the sides; the sum of these 4 logs., rejecting 10 from the index, will be the log. sin. square, Table 69, of the required angle. Ex. 3. Inthe triangle ABC, given rt = 6, ft = 5. «nd 5 Ar. Co. log. 9-301030 c 4 Ar. Co. log. 9-397940 A 82°49' log. sin. square 9-640978 note to p. 19 on the " i tical Complenient," METHODS UK SOLUTION. 51 pDsi'iig it, arc tiikeii from tables, tlit- term Computation will lie i-iu- ployed in other cases, and always wlu-n precision is required and logaritluns are cnncerned.* (3.) Construction implies (in our present subject) drawing a figure of the actual case on a convenient scale, and in the proper proportions, the number of parts contained in tbe quantity required to be measured being taken from a scale adajited to the purpose. This process is tedious, and not, in general, capable of much pre- cjision, but it is the most readily intelligible of the three methods, and is, therefore, the least open to mistake. The seaman should, accord- ingly, be able to produce a figure of every case that admits one, and nhould acquire the habit of referring to the figure, in the mind as the only real security against mistakes in his work. The figure or natural representation of the case is, moreover, the foundation of the mathematical treatment of the question. 1 . Limits of Methods or Obacrvatioiis. 168. In every process of calculation, the elements which enter into it, and which are either observed at the time by instruments, or taken from tablas, are liable to eri-or. Every result, therefore, is, to Some extent, uncertain ; but the amount of error of the final result of this kind are usually divided into " rigorous" and " approximate," oi Indirect, as the latter are also called. In all solutions, however, we either deal directly with the quantities themselves, as arcs, angles, &c., in tlieir entire or integral state, or we corn- putt a difference from a certain value assumed or given, and thence find the required quan- tity. This last i)rocess is indirect, but tlie former may be effected indirectly also. Tha terms Integral and Differential would then, it is presumed, be more satisfactory, for the degree of appro.ximation obtained is altogether beside the question of the charai-ter of the solution. We do not, however, on the present occasion, depart from the usual terms. Wo •hall merely add, as some indistinctness prevails as to the properties of these different noiutions, that both are equally affected by errors of observation (as must of course follow, if they be both true), and thus the essential distinction between them, in practice, lies lu the different numbers of figures which they respectively require. There is another point on which we shall take the opportunity to make some remarks tnf the satisfaction of the scientific reader. In the present subjeci we are obliged, in most cases, to consider the required quantity, though really unknown, as if it were given, as it is an indispensable argument in reducing the elements ; — thus, in finding the longitude by clironii- meter, by the sun, we must assume a longitude in order to deduce the declination and eqna- t'on of time. Such solutions are, therefore, solutions by assumption, and the question naturally arises, What is the criterion by which to know whether the result is nearer tlie truth or further from it than the temporary value employed .' In general we have to solve, not the equation K=/(.r, y, z), but K, — ^ (x, y, z, u'), in whit'h «' is an assumed value of u , and w, a first approximation. The second approximation U iij=y (jr, y, 2, K|), and so on. Now, it is evident, without examining the successive difTerences u' — !/,, ", — Hj .... that the process is convergent, if u varies more slowly than u', that is, when -j-, < i. This is the case with all our problems within the limits i When 3-,>'. tl'e process is divergent, or the results are worse and worse ; and when ■= i, the assumption is reproduced. Again, when — / is positive, the results are all greater or all less than the tnith ; when negative, they are alternately Ino great, and too small, llenre. in (rneral. it depends on the data, and not on the greatness or smallness of the error o( niisnmption, whether the process ronverge oi not. The above, however, ajiplies, in strirt- 'ncii, only to tmull errors of assumption ) for largo cirora liighcr terms must be ciinsidrrcd. 52 INTUOOrCTION. oansed by an error in anyone ot'tlie data (or quantities given forilie solution oi' tho question) is very dift'erent under different circum- stances, being in some cases scarcely perceptible, while in others it may far exceed the very error to whicli it is due. If we agree beforehand that a probable error of observation shall not cauFC an error beyond a certain amount in the nisult, we must exclude all those cases in which it would produce a greater effect. and we thus assign li-aits to the method or observation. 169. Generally speaking, every element that enters into the computation is liable to error, and, therefore, each element will iuive its own indeiiendent influence in limiting the observation ; that is, in strictness, there will be different limits for each sejiarate element , but, for practical purposes, it is enough to assign the limits according to that element of which the error is most important. For instance, in finding the time by a single altitude of a celestial body, we employ its altitude and declination, and the latitude of the place. Now tiie latitude will often, and tlie declination sometimes, be correctly known, but the altitude can never, from various causes, be exem|)t from suspicion of inaccuracy ; besie early impressed with the importance of improving his judgment by continual exercise, instead of trusting on all occa- sions to a mechanical routine of computation. 174. It is worth wliile to notice, that in working to a certain de- gree of accuracy, as, for example, to minutes, it is generally enougli to employ the neares* whole minute; but when one of the quantities varies very rapidly, it may be proper to work closer ; for it is easy to see that the inaccuracy of half a minute in a quantity which is multiplied by a number greater than 1, is increased, and apjiears 33 a whole minute. [l.j Personal Error. 17.">. The several errors to which each observation is exposed, and which accordingly enter into the estimation of the degree oi dependance, are described in their proper places; but there is one ^liich, though sensible only in cases where a considera])le step has been made towards precision, is of universal application, and i.s, Jierefore, ))ro])erly noticed here. It is found that ditferetit persons lio not agree in the precise instant of observing the same phenomenon. Again, some persona nre in the habit of observing more or less closely than others. The kind of error which is obviously present in such cases, is called the jerhonal ciror, or etjuiiticn. St INTRODUCTION. 'I'wo observers have been found to differ 0' 4 in tlie sun's transit over tlie wire of a telescope. 176. Wlien two images, in contact, lie stationary before two observers, it is difficult to understand why one of tliein should see them overlap, or the other open, or wliy they should not agree in the measure. But when the images are in motion, the observer's anxiety is roused lest he may miss the observation, and the excite- nient may lead him to think that he sees tlie contact before it really takes place. Hence there is reason to believe that the personal equation is, in some degree, a mattei' of tempei'ament. It also seems well ascertained that the personal equation is not the same for the same individual at all times, and that it is greatly influenced by fatigue, by the effort of observing, and, in fact, by every cause that affects the nervous system. It may, therefore, be advantageous to bear these circumstances in mind preparatory to undertaking observations in which much accuracy is required. 177. The existence of this error shews that when much precision is required, observations taken by different persons should not be mixed together until cleared of ])ersonal errors, since they may at the outset be ])resumed to be affected by unaiual errors ; and it is probable that many discrepancies are due to this cause, in cliHerva- lions whotUer by tlifl same or different observers. 56a Spherics, Definitions and Principles. Sphrrics is that part of mathematics which treats of the positiong and magnitudes of arcs of circles described on the surface of a sphere. A Sphere is a solid formed by the revolution of a semicircle about its diameter; this diameter is immovable during the motion of the semicircle. The Centre and Axis of a sphere are the same as the centre and diameter of the generating semicircle, and as a circle has an indefinite number of diameters, so a sphere may be considered to have an indefinite number of axes, round any one of which it may be conceived to be generated. Every Section ok a Sphere made by a plane passing through its circumference is a circle. A Great Circle is formed by a plane passing through the centre of the sphere. A Small Circle is formed by a plane that does not pass through the centre of the sphere. A sphere is therefore divided into two equal parts by the plane of every great circle, and into two unequal parts by the plane of every small circle. The I'ole.s of a Circle of a sphere are those points on the sur- face of the sphere which are equally distant from the circumference of that circle. Thus the poles of a circle are the extremities of that diameter or axis of the sphere which is perpendicular to the plane of that circle. All points in the circumference of a great circle are equally distant from both its poles. Small Circles of the sphere are those circles which are unequally distant from both their poles. The Poles of every great circle are each 90° distant from that great circle on the surface of the sphere, and no two great circles can have the same poles. The Diameter of every great circle passes through the centre of the sphere, but the diameters of small circles do not pass through the centre. Thus the centre of the sphere is the common centre of all its great circles. Parallel Circles of a sphere are those small circles the planes of which are parallel to the plane of some great circle. All parallel circles have the same poles, and may be conceived to be conc.entric to the gnat circle thf-y are parallel to. 56a introduction. A Spherical Angle is the inclination of two great circles of the sphere meeting one another. It is measured bv an arc of a great circle intercepted between the legs of that angle, 90° distant from the angular point. A Spherical Triangle is a figure formed on the surface of tlie sphere by the intersection of three great circles. The SHORTEyr Distance between two points on the surface of a sphere is an arc of the great circle passing through those points. The Stereographig Projection * of the sphere is such a repre- sentation of its circles upon the plane of some great circle, and thence called the plane of projection, as would appear to an eye placed in one of the poles of that circle, and thence viewing the circles of the sphere. The place of the eye is called the projecting point or lower pole, and the pole opposite is called the opposite or exterior pole ; also the projection of any point on the sphere is that point in the plane of projection through which the visual ray passes to the eye. The Primitive Circle is that great circle on the plane of wliieh the representation of all other circles is supposed to be drawn. A Right Circle is one which is perpendicular to the plane of the primitive circle, and, if it be a great circle, its plane passes! tnrough the eye and it is seen edgewise, consequently it is represented by a straight line drawn through the centre of the primitive circle. An Oblique Circle is that which has its plane oblique to the eye, and is represented by a curved line. Spherical Trigonometry is the art of computing the measures of the sides and angles of such triangles as are formed on the surface of a sphere, by the mutual intersection of three great circles described thereon. A Spherical Triangle has three sides and three angles. A Right-angled Spherical Triangle has one right angle. The sides about the right angle are called legs ; the side opposite the right angle is called the hypothenuse. A Quadrantal Spherical Triangle has one side equal to 90°. An Oblique Spherical Triangle has all its angles oblique. The Circular Parts of a triangle are those arcs which measure its sides and angles. Two spherical triangles are said to be supplemental to one another when the sides and angles of the one are supplemental of the sides and angles of the other, and one in regard to the other is called the supplemental triangle. Two arcs or angles when compared together are said to be alike when both are less or greater than 90°. But when one is greater and the other less than 90°, they are said to be tinlike. In every spherical triangle equal angles are opposite equal sides, und equal sides are opposite equal angles. Stereograpliie means representing a S'.lid on a plane eurlace. sniKKicAL trigonomethy. B7a Anj two sides of a spherical triangle are together greater than tit- third side. Each side of a spherical triangle is less than a semicircle or 180°. In every spherical triangle the greater side is opposite the greater angle. The sum of the three sides of a spherical triangle is less than 360°. The sum of the three angles of a spherical triangle is greater than two right angles and less than six, or always will fall between 180° and 540°. In right-angled spherical triangles, the oblique angles and their opposite sides are of like affection ; that is, if a leg is less or greater than 90°, its opposite angle is also less or greater than 90°. In right-angled spherical triangles the hypothenuse is less than 90° when the legs are of a like kind; but greater than 90° when the legs are of a different kind. In any si^herical triangle /\s sine of either angle : Bine of its opposite side :: sine of another angle : eine of its opposite sid*, Eight Spherics. The celebrated Lord Napier, inventor of logarithms, contrived a general rule, easy to be remembered, by which the solution of every case of right-angled spherical triangles is readily obtained. In any right-angled spherical triangle there are five parts beside the right angle — viz., two legs, two angles, and the hypothenuse. The two legs, the complements of the two angles, and the comple- ment of the hypothenuse are called circular parts. In any case relating to right-angled spherical triangles three of these circular parts arc concerned — viz., two given and one sought. If the three concerned are all joined together, ignoring the right angle, the central one is called the middle, and the other two adjacent parts. But if only two are joined together these are called the opposite, and the other the middle part. These being known, all the cases of right-angled spherical tri.'ingles may be solved by Napier's rules. 1. The product of radius and sine of the middle part = the pro- duct of the tangents of the adjacent parts. 2. The {iroduct of radius and sine of the middle part = the pro- duct of the cosines of the opposite parts. N.B. — As an aid to memory the letter a occurs in tangent and adjacent; and the letter o in cosine and opposite. In the following examples, insteatl of subtractinf/ the log. sine, cosine, and tangent, it is the same thing to add the log. cosec, sec, and cot.; becauso thc'^e last are the arithmetical complements of the first (see note, p. 49). 58 A INTRODUCTION. Ex. 1. Ill the riglit-ftrgled sphe 40" 30', B 90°, to find the otiier parts. triangle ABC, given C 61° 50', R C {a) To find A. Had. COS. A = Bin. C . cos. a CCS. A = sin. C . cos. a C = 61° 50' log. sin, 9-945261 = 40 30 log, COS. 9 88 1 046 A = 47 54 log. COS. 91126307 To find A C {/>). Rad. COS. C . = cot, b . tan. a cot. b — COS. C . cot. a « = 4O°30' C==6i 50 4 = 61 4 log. cot, 0068501 log, COS, 9:673971 log. cot. 9742478 E.>!. 2. In the right-angled spherical t; 13° 26', B 90°, to find the other parts. To find G. Ead. sin, c = sin. i. sin. C sip. C = sin. c . cosec. J A = 1 1 3° 26' log. cosec. 0037383 c= 50 40 log. .sin. 9888444 C= 57 28 log. sin. 9925827 To find B C («). log. spc. 0198027 log. cos, 9-,S99536 log. COS. 9 797563 Ead. COS. J = To find A B (e). -COS. fl.COS. c « = 40° « = 6i c=So 30' 4 29 log. log. log. sec COS COS oii8q55 9-684658 9S03613 ngle ABC, giver A B (c) 50 '40 ', A C (A) A ^ To find A. 8 Had COS A = t an. c . cot. b COS A=t in. c . cot. h c =■■ 50" 40 A = ii3 26 I So 00 A=i2i 56 log. tan. 0-08-47 1 log. cot. 9 636918 log. COS. 9-7233&9 Note. — In the triangle A B C, J the hypothenuse being greater than 90°. and c Ir"^^ than 90°, A is of unlike affection to C, or greater than 90". Also A being greater lli;iu 90° its opposite side a must also be greater than 90°. Quadrantal spherical triangles are also solved by Napier's rules re- versed : using the quadrantal side as the right angle, the angles Bdjacent to it, the complements of the other two sides, and of ti.u angle opposite to the quadrantal side, as circular parts. OiiLiQUE Spherics. Case I. Given two sides and an angle opposite to one of them, to find the angle opposite to the known side. As sin. of a given side : sin. of its opposite angle :; sin. of the other given side ; sin. of it.s opposite angle. To find the 3rd side. As sin. 1 diff. of the two known angles : sin. g their sum ;: tan. ^ diff. of the two kiio-wn sides : tttu. ^ the third side. Or, as cos. | diff. of the two known aiigl.- : COS. ^ their sum :: tjin. ^ snm of the two known si:Wi ; tiXD. i the third tide. SriTKKICAL TRI 59j Case II Given two angles and a side opposite to one of them, to tiud tbe side opposite to the known angle. As sin. of a given iingle : sin. of its oppiwitr side :: Bin. of the other given iingle : sin. of its opposite side. Ai «iu. i diff. of the two knov 4- dift'. of the two known angle t,. ^ tlie third angle. 5 1 ditr. of the two kn their sum sum nf the two knov Cases I. and II. may also he solved by drawing a great circle from the unknown angle perpendicular to the opposite side. This divides the triangle into two right-angled triangles. The segments of the divided side may then be found by right-angled spherics. In t 55° 3S'. phene triangle A B C, given A 84° 52', V,C or (a) 67° 5', and A (■•) To find the other parts. As sin. a : sin. A :: sin. c : sin. C. 'a^6j°~s' logrco.sec.^035706 A = 84 52 log. sin. 9-9yS255 c = S5 38 bg. sin. 9 9|t6S7 C =63 12 log. sin. 9-95a''48 From B draw a great circle B D perpendii aftWliou, both less than 90°, BD falls witliii liar to A C. Angles A and C being of like Ihe triangle. Then by Napier's rules : To find A C (h). liud. cos. C = cot. a . tan. D C tan. DC = c..s. C . tan. a a = 67°^' log. tan. 0373907 C = 63 12 log. COS. 9 654059 DC = 46S' log. tan. 10027966 A D = 7 27 *-U lit Kad. COS. A = cot. c . tan. A D ^tan. A D=cos. A tan. e ^ = 55° 3S'' A ^ 84 52 AD= 7 27 To find B. As sin. a : sin . A :: sin, b : s in. B. = 67° 5' log. cosec. 0035706 A = 84 52 log. sin. 9'998255 i = 54 iS log. sin. 9-909601 B = 6i 25 log. Bin. 994356» log. tan.o-.65o3^ log. cos. 8 951096 log. tan. 9 1 16729 If A and C are of unlike affection — i.e. one greater and one less than 90° — the perpendicular will fall without the triangle, and tiie difference between A D and D C must be taken to find h. This also will solve Case II., given two angles and a bide opposite to one of them, t« find the otheu- pnrtu C Cn.V IXTROnUCTION Caoe III. Given two sides C the included angle. C Let ABAC and the included angle A be given. From one of the unknown angles at C draw a great circle P^rpendicular to the opposite side. Then in the right-angled triangle A D C find AU it the perpendicular falls within the triangle subtract AD irom AB to find D B, and if the perpendicular falls without the triangle add A D lo A B, and the sum is B D. ' To find B C. As cos.of A D : COS. of B D :: cosof A C : cos of BO. To find the unknown angles. As sin. of side just found : sin. of the given angle : : sin. of either of the given sides : sin. of its opposite angU, Second Mtthod. To find \ sum of the unknown angles. As cos. 1 sum of the two given sides : cos. \ their diff. :: cot. i the included angle : Un. \ sum of unknown angles. fCoTB.-This '\ sum of the unknown angles is of the same name as the i sum of the sides. To find 1 diff. of the unknown angles. As sin. i sum of the two given sides : sin. 4 their diff. •: cot. i the included angle : tan. i diff. of the unknown angles. The i diff. being added to the \ sum will be the greater angle, and being subtracted from it will be the less. .-r -n /-. / n o.o ,-' .t.H A R li-\ In the spherical triangle ABC, given B 125° 36', B C (a) 81 17. and, A B (e) W° 13'. to find the other parts: c= 59°I3' « = 8i°i7' E= 125 36 oi4i log. sin. 9 95S:;-j SrilKUlCAL TKIGONOMKTRY. Glj Case IV. Given two angles and the included side. In the triangle ABC given angles B, C, and side B C, a: to find the other parts. Where two angles and an included side are given, a great circle may be drawn from one of the given angles per- jiendicular to the opposite side, and the angle BCD instead of the segment B D found. The difference between BCD and the given angle C will give A C D. Then To find the 3rd angle. As sin. BCD: sin. A C D : : cos. B : cos. A. If the perpendii'ular falls within the triangle the angles B and A are of the s:ime name ; if it falls without the triangle they are of different names. The Second Method is the same as in Case III., only for cota. of half included angle use tana, of half included side. Case V. Given the three sides of a spherical triangle, to find the three angles. Find the half-sum of the three sides. Take the difference between this half-sum and the side opposite to a required angle, then add together the log. cosecs. of the two sides containing the angle, the log. sines of the half-sum, and of the difference between the half-sum and the side opposite the required angle : Half the sum of these four logs will be the log. cos. of half the required angle. In the i-f.herical triangle A B C, given A B (<■) 79° 56', B C (a) 1 19° 36', and A C (i) t4° 5', 10 tiud angle B. lop. sin. square of .•7" 41' 20", suiple- ment B. 2 B = 52 18 40 Case VI. The three angles being known, to find a side. Add together the log. cosecs. of the two angles adjacent to the required side and the log. cosines of the balf-sum of the three angles and the difference between the half-sum and the angle opposite the required side. Half-sum of these four logs, will be the log. sine of Lalf the required side. iiaii the longitude is rrchon»l from. Sec y. 30.). 58 NAVIGATION. Il>2. We may use citlier the longitude of one name or tlie sup. piriuent to 36U°, with the contrary name; thus, instcatl of l()ti° W. ■we n'ay say 194" E. 19;i. IiOnS, 61 Tlio (lip (lepoiuls on the distance in naiiticiil miles of tlie visible huil/.on. Tims, to the eye 30 feet above the sea tlie true tlij) is 6', or Jlie distance of the iiorizoii itself is about (i miles. This is easily proved tluis, Let C be the centre of the earth, the place of the observer ; then the line OB drawn touchin<5 the surface at. B determines B the farthest point visible to him. Draw OH perpendicular to O C, then ginee O B touches the circle af B, the angle CBO is a riu-ht anijle (No. 138, Cor.) Hence UCA is thewmplenient of C O B, and HOB is also the complement of COB (C0H=9()°), therefore A C B and HOB are equal. The depression is given in Table 8. 20G. The Altitude of a terrestrial or celes- tial object above the sea horizon is the angle included between the line drawn from the eye to the object, and the line from the eye to the horizon. Thus, the angle M A B is the altitude of the summit M. The altitude here, in consequence of the great elevation of the spectator at A, about ^ of the radius, or 330 miles, is less than tho dip, or the summit M is really below the true horizontal line A H. This mav take place when, from the small height of the object with respect to that of the observer, or its great distance, it is seen very little elevated ; but in most eases A M will fall above A H. 207. The rays of light which pass from any distant object on the earth suffer a change in their direction, which is called the terrestrhd refraction, by which the object appears in general higher than its true place. This effect is, on the average, about i'4 of the intercepted arc, or distance in miles, which are minutes of a degree very nearly. Thus, an object twenty-eight miles distant is raised about 2' above its true place. The sea horizon is thus raised by refraction, or the apparent dip (Table 30) is less than the true. This proportion, however, is subject to great irregularity, and varies between \ and ^ of the intercepted arc. The apparent eleva- tions of the summits of high land are thus subject to great variations, depending on particular states of the air. 208. The apparent place of the sea horizon differs also in differ- ent temjieratures of the sea and air. When the sea is warmer than the air, the horizon appears below its mean place, or that at which it appears when the air and water are of the same temperature, or the apparent dip is too small; when the sea is colder than the air, the horizon ap]>ears above its mean place,* or the apparent dip is too great. * Admiral W. F. W. Owen informs me that he found on one ocnasion, in observing ii star's •Ititudc, a change of 4' in the plare of the sea horizon, in the tropics, soon after sunset. Mr, Kisher observed a variation in the place of the horizon of 18' in the arctic regions. In summer the ice horizon was elevated, not dcjiressed ; in the winter it was depressed several minuti s. — {AppemlU 111 Cajitaia Parry's Voi/aye in 1821-3, p. 1 87.) Tlicse observations, how«v< r, ilo «ot nil folbnv the rule above. A table for correcting the r.ppaniit place of the sea horiZHii for the difli iince of ti nipciaturc ol 'he sea and the air, acoordini; tu the hcii^ht of the eve, wuiihl 62 NAVIGATION. Colonel Sahine '''fes a table of depressions observed from the gangway of H.M.S. Phcat-ant, at ISfr. liii. above the sea, in the Gulf Stream, ami after kaviiig it.* On Dec. 5, 182.', lat. 36°i N., long. 72°A W., at 10'' a.m., the temperature of the sea being "0°, that of the air 60°, the dip observed by WoUaston's dip sector was 4' 57", or 1' 6'" more than the lalde. At noon ihe temperature of the water had clianged to 62° 4, the air at 60° as beibre, the ship having passed from the warmer water of the .stream to the colder water of tlie rest of the "Cean, ani the dip observed was 3' 37". Fioin the result of iiis ol»ei vat oiis, Cjlonel Saliine considers that the navigator will be right nine times in ten in assuming that, wlien tlie sea is warmer than the air, the tabular dip is too small. In only one case, however, did this error ever amount to so much as 1' :>6", the sea being then at 49°, and the air at 38°, or the difference 1 1° ; and it is important to remark that tlie error of the table is by no means pr.'portional to the diftlreuce of these temperatures, which in one case was no less than 2!)°. Numerous instances are on record, in the accounts of modern navigation, of errors of observation arising from variation in the pUce of tlie sea horizon. 209. Besides the -vertical effect of refraction above described, gome instances have been recorded of a sensible change in the hori- zontal direction of objects. Mr. K. B. Martin observed a change in the true direction of a point of land in the Azores, towards sunset. He also mentions an extraordinary change in the direction of C. Grisuez light as seen from Eamsgate at the close of a very hot day ; on which occasion, also, distant objects were elongated horizon- tally till they seemed to separate into parts. ("Naut. Mag." 1847.) Lieutenant Wilke< ohserved from the summit of Mowna Ron, the sun's horizontal diiimcter 1 ngilnned ont lo twice and a half the vertical one. ('-Narrative of the United .Stare'. lA|il.irin^' I Expedition," 1838-42 ) In the Survey ot the Isthmus of Tehuante|iec, unl. r St h.;r Ci. Miro, in 1842-3, the refractions at San Mateo on tlie Pacific, " especially the lateral (Mies," pioduced the strangest illusions.f 210. The Tkopics of Cancer and Cafeicorn are the parallels of latitude 23° 28' N. and S. These are the dotted lines nearest the equator (6g. in p. 55). The sun is vertical at noon twice in the year to every place between the tropics, and never to any place outside of them. The space between the tropics is called the Torrid Zone, on account of its heat. 211. The Arctic Circle, or Nortli Polar Circle, and the Ant- arctic Circle, or South Polar Circle, are parallels distant 23° 28' from each pole, and are therefore in latitude 66° 32'. These are the dotted lines nearest the pole. Within these circles the sun does not set during part of the summer, nor rise during part of the winter. The spaces within these circles are called the Frigid Zones, on account of the cold. The spaces between the tropics and the polar circles are called the Temperate Zones. be useful ; but there arc scarcely any data fur the constrmtion of such a table, and the theory itself appears not to be complete. The above variation of the place of the apparent horizon, with mirage, reflected images, and other optical illusions, were tirst discussed, generally as ip'estions of unequal tempera- ture alone, by M. Biot, Mem. de I'lnstitut, 181)9. • Account ofExperiments to determine the Figureofthe Earth. London, 1825,p.4.54. t It is easy to conceive, that if a mass ol air of ditferent density from the rest he inter- posed between the spectator and the object, and i( also the sides or faces which he looks Ibrougb be not exactly parallel, it will have the effeet of a prism, and will seem to throw the o'lject to the right or left of its true direction. If the -nrlaccs are curved, the cHVcl ut uiu^inliing or diuiiuishiiii^ will occur at the tame tinie. CHAPTER II. Instruments of Navigation. I. The Compass. II. The Loo and Glasses. The necessary instruments of navigation are the Compass, hj the aid of which the course of the ship can be directed ; and the Log, which, with the help of sand-glasses for measuring small intervals of time, or a watch showing seconds, gives the velocity or rate of the ship, and thence the distance run in any interval of time. I. The Compass. 212. Before the invention of the Compass, the course; of the ship was directed by reference to the land, or to the position of the heavenly bodies ; but when those objects were obscured, the Beanian must sometimes have been much perplexed. The pointing or directive property of the magnet, on which the efficiency of the compass mainly depends, appears to have been known to the Chinese, and made use of by them in travel- ling by land and sea, in times of remote antiquity. The an- cient Greeks and Romans, though familiar with the magnet, were not apparently aware of its directive property, nor were their descendants till the beginning of the thirteenth century. About that time the seamen of the Mediterranean gradually became acquainted with the fact, that a piece of magnetised steel, shaped like and commonly called a needle, would, if allowed to turn freely about its centre, always come to rest in the same direction, and that, by reference to its pointing, they could roughly check or direct the course of the vessel. Thus, before the seamen of those days were two problems. First, the best means of giving to the needle freedom, to take up any horizontal direction, and of indicating the direction of the ship's head relative thereto. Second, In find the exact direction of the pointing of the needle, in relation to some known standard of direction. In other words, first the per- fecting of the mariner's compass ; second, a knowledge of what 13 now called its variation. Appai-ently, the earliest means used to allow the needle to take up any position in azimuth, was by thrusting it through ft piece of light wood or pith, forming with it a rectangular ciusiii 64 NAVIGATION. the wood or pitli being just sufficiently large to float the neeille, when the cross was placed in a vessel of water. Otherwise, the needle was poised at its centre on a sharp pivot, and inclosed in some form of box. Subsequently, the necessity for keeping the box horizontal, in the varying motion of the ship, was met by gimballing the compass-lox, and, for convenience, a circular disc of paper, called the fly, having a graduated circumference, was placed on the needle. The fly and the needle together was calK'd the card. The box was generally made of brass, shaped like a basin, and had a glass cover. A mark, called the lubber-line, was placed on the fore part of the compass-box, or bowl as it was commonly called, on the inside, indicating the direction of the ship's fore-and-aft line, from the centre of the card. The circumference of the card was divided into thirty- two divisions, called points ; these were subdivided into half- points and quarter-points. The four principal points, or, as they ai-e called, the cardinal points, are the North, South, East, and West ; the East being towards the right when facing the North. All the points of the compass are called by names composed of these four terms. The points half-way between two cardinal points are called after both of these points : they are the north-east (written N.E.) ; north-west (N.W.) ; south-east (S.E.) ; and south-west (S.W.). These points are sometimes called quadrantal points. A point half-way between one of these last and a cardinal point is called, in like manner, by a name composed of the nearest cardinal point and the adjacent point, N.E., N.W., S.E., or S.W. Thus the point between N. and N.E. is called north-north-east (written N.N.E.) ; the point between E. and N.E. is called eaatr noith-east (written E.N.E.); and ao of others. rXSTRUMEXTS OY NAVIGATION. fio ITie points *iext the eight principal points (namely, N., S., E., W., and N.E., N.W., S.E., and S.W.) take the word bif between the name of sucli point and the next cardinal point. Thus the. point ncA.-t to north, on the east side, is called North hij East; that on the West side is called North bij West. Thus, on in- specting the compass, it is easy to see the reason of the names E. by N., S.W. by W., &c. A half-point, which is the middle division between two points, is called after that one of its adjacent points which is either a cardinal point, or is the nearest to a cardinal point. Thus the middle division between N. and N. by E. is called uortli-/ia//-east (written N. ^ E.). Half-points near N.E., N.W., S.E., and S.W., take their name from these points. Thus we say N.E. ^ N., and N.E. i E., and N.E. by E. ^ E. The same holds for a quarter and for thi-ee-quarters as for a half-point. In speaking of these divisions of the card, brevity seems to have been the chief end, rather than the habitual reading of the card from left to right, or the reverse. Thus, we may say N.E. by E. ^ E. ; but continuing to the right, instead of E.N.E. ^ E. and E. by N. i E., it is usual to say E. by N. ^ N. and E. ^ N. The name of the opposite point to any proposed point is known at once, without referring to the compass, by sim.ply reversing the names or the letters which compose it. Thus the opposite of N. being S., and that of E. being W., the opposite point to S.W. by S. is at once known to be N.E. by N. The opposite of W. | S. is E. I N., and so on. Dividing the circumference of the card, by successive halving, into points, half-points, and quarter-points, was well adapted to the time, not very distant, when many helmsmen were unable to read. The quarter-point was also considered tlie smallest division a man, sometimes under the blinding influences of wind, rain, and spray, could well distinguish. Now, however, the cards of steering compasses are frequently divided to degrees, in addition and external to the point divisions. In cards of nine or ten inches in diameter, the degrees are suificiently large to be distinguished by men of ordinary sight. The degrees are always marked from North or South, towards the East or West ; tlie courses, therefore, are read from left to right, and vice versa, in alternate quadrants. This is apt to cause mistakes in steering. For this reason, and for precision and brevity in speaking, writing, and signalling, there is much to be said in favour ni marking the card from zero to 360 degrees, round by the right. Small compasses for shore work are thus marked generally. Repeating the points in any order is called boxing tlie com- p(tKs; to do this is, of course, one of the first things a seaman learns. In becoming familiar with tin' points of the comp!i«s tha m NAVIGATION. learner should bear in mind that their utility is far from being confined exclusively to navigation, and that in finding hii way across a new countiy, or through the streets of a strange city, no impressions will be so distinct or so permanent as those grounded on the points of the compass. 213. As the ship's course, which is sometimes expressed in points and sometimes in degrees, is always reckoned from the north or south point, the seaman has to refer at once, in using the Tables, to the number of points, or degrees, in any course given by name. The following table, whii-h exhibits the degrees, minutes, and seconds, in each quarter-point uf the cunipass, will be con- venient for reference : — N— £ N-W S- 10 S— W Vi-. Nurth. Nurth. Hdiith. South. NJE N^W SiE SiW i N^E NiW SiE SiW \ N|E Nf W SaE sjw NbK Nb W SbE SbW I N b !•: 1 E N b W 1 W SbEiE S b W } w 1} N b I-: i E NbWi W S b E i E S b W i w l\ N b E i E NbWa W . SbEJE S b W f w •f NNE NNW SSE SSW 2 NNEiE NNW J W SSE \ E SSWiW 2\ NNE 1 E NNW i W SSE 1 E SSW i w 2l NNEJE NNW a W SSEJE SSWJW 23 NEbN NWbN SEbS SWbS 3 NEiN NW f N SE-JS SWJS 3} N K 4 N NW^N SEAS SWIS 3.^ N£iN NWJN SE JS SWiS 31 NE NW SE SW 4 NEiE NW JW SEJE sw \ w 4f NEiE NWiW SEJE SWlW 4l NEfE NWJ W SE3E SAVaw 4| SEbE NW b W SEbE SWbW 5 NEbEiE NWbWiW SE b E i i: SW b W 1 w Sk NEbEJE NW b AV i W SEbEiE sw b w i w si NEbEJE NWbWaw SEbE^E sw b W 3 w Si ENE WNW ESE wsw 6 E b N } N WbNf N E b S 1 S W b s f s 6} E b N i N W b N i N EbSiS W b S 1 s 6', EbNiN W b N i N EbSiS W b .S i s 63 Eb N WbN EbS AVbS 7 EiN WJN EJS Wi.S 7i EiN WIN EiS AV i S 7.V EiN W i N EJS W i s 74 Ea.vt. WeM. E.ist. West. S 2 4S 45 5 37 30 S 26 '5 M 15 14 3 45 l6 52 30 19 41 'S 22 30 25 IS 45 28 7 30 56 '5 33 45 36 33 45 39 22 30 42 II 15 45 47 48 45 50 37 30 53 26 15 56 .5 59 3 45 61 52 30 64 41 15 67 30 70 iS 45 73 7 30 75 56 IS 7845 Si 33 4S 84 22 30 87 n '5 90 2H. The Azimuth Compass is a compass of superior tonstri tion, especially adapted for observing bearings. It is titled \vi TNSTRUMENTS OF NAVIGATION. 07 two vortical viiiies. The one near the eye in obsei-vinrr, hiis ;i ntiiTOw vertical slit, with coloured shades (or observing the sui;. The other Viuie has a wider slit or opening, having a vertical thread in the middle of it. In front of this vane is a reflector, for observing objects elevated above the horizon. The line join- ing the slit in one vane, and the vertical thread in the other, should pass over the centre of the card. The cards of azimuth compasses are always marked to degrees, and frequently to anialler divisions. In the Prismatic Azimuth Compass, a magnified image of the divisions of the card is read by reflection, in a prism attached to the fore side of the near sight vane. Azimuth compasses being required for taking bearings, are placed on a tripod for shore work, and on an elevated stand on board ship. 215. In the early part of the present century, when ships and instruments for navigation were rapidly improving, the compass was still a rude instrument, and not abreast of the requirements of the seaman. In 1820 Mr. Barlow reported to the Admiralty, that half the compasses he had at their request examined, be- longing to the Royal Navy, were useless. It is probable that the compasses of the Mercantile Navy were no better. In 1837 their Lordships appointed a committee to inquire into the matter, and, if possible, to find a remedy for an evil so pregnant, as they said, with mischief. This step was taken for the benefit of the Royal Navy, and the improvement which took place, both in the design and in the workmanship of the compass, in consequence of the recommendations of the Admiralty compass committee, was of immediate and lasting benefit to the public service. The Mercan- tile Navy was not so immediately benefited, as the proceedings of that committee were not made public. But doubtless the fact of there having been such a committee stimulated compass makers to seek information, and to apply it to the improvement of the mariner's compass. A great difficulty to be overcome, in a compass intended to be used on board ship, is the disturbance of the card caused by the motion of the ship. The Admiralty compass committee, while insisting on extx-eme lightness in the fly and fittings of the card, made considerable addition to its weight, by applying more needle power than would otherwise have been desirable, in order to secure steadiness. This was a fairly successful way of meeting the motion of ships at that date. But the violent and continuous motion, subsequently caused by the general adoption of the screw propeller, has been generally met, by suspending the compass bowl by springs or india-rubber. The difficulty of getting a compass that would be steady in small vessels and boats, led to the introduction of the Liquid Compass; that is, a compass having the bowl filled with liijuid instead of air. Tin; fir.st practiital liquid compass was patented 68 NAVIOATTOW. by Mr. Crowe in 1813. It was eubseqiiont-ly improved by other makers, and is now, when well made, a very efficient compass for all purposes. It is especially adapted to stand severe vibration, and the shock of gun-firing. For these purposes, and for use in boats, it has not yet been excelled. 216. In 1876 Sir Wm. Thomson patented a compass, which la regarded with much favour by navigators. At the circumference of the card is an aluminium ring ; the cap is held in the centre by radial silk tlu-eads, extending from it to the ring. Attached to the ring and threads is a disc of very light paper, its circumference having the usual compass graduations. All the central part of this disc is removed, still further to lessen the weight. Recognis- ing the fact, that the power of a magnet increases relative to its weight, as the size decreases, the needles are very small. They are suspended under the card from its circumference. The entire card is not more than one-fifth to one-tenth of the weight of compass cards generally, of the same size. The friction on the pivot is, therefore, proportionally diminished. By giving to the card no more needle power than would certainly overcome this much-diminished friction, it has a very slow period of vibration. The desirability of giving to a compass card a period of vibration that would not be isochronous with the roll of the ship, in order to maintain steadiness in a seaway, had already been pointed out by Mr. A. Smith, and by Mr. Towson. The bowl is protected from disturbance, also, by being suspended on a twisted wire gromet. This compass card, from the little friction on the pivot, is very sensitive at all times. From its slow period of vibration, it is steady when the ship is rolling ; and, by reason of the suspension of the bowl, it has considerable immunity from the disturbances caused by vibration, shakes, and sudden shocks. 217. Though a compass, when supjilied to a ship, should bo accurate and efficient, it is desirable that the seaman should be able to satisfy himself on these points. The following essentials should be looked to, in steering and azimuth compasses, as far as they apply to each kind respectively. The point of the pivot should always be in the same plane as the centre of the gimbals. The pivot should be sharp, or, when intended to be a little rounded, quite smooth ; it should be free from rust. The cap should be sound — that is, not cracked nor perforated — and free from dust or dirt, which sometimes gets into it. Placing the card gently on the pivot, it should be deflected two or three times, through a small angle from its position of rest, to see if it always comes back to rest at the same point. This would show if the needle power is sufficient to overcome the friction on the pivot. 'Select a position on shore, free from disturbances, from whence the bearing of some object is known. Measure horizontal angles INSTUUMENTS OF NAVIGATION. 69 fi-oiii it with a sextant, or other means, to three other objects, so selected that the correct bearing of four objects, about 90'^ apart, may thus be known. Now turn the compass round horizontally, so that the line from the centre of the card to the lubber-line coincides, in horizontal direction, with the line from the centre of the card to each object in succession. At each position of the compass, observe the bearing of the first object, by the siglit vanes. Assuming that the card is regularly divided, these observa- tions would show whether or not a course shaped, or a horizontal bearing taken, by the compass is correct. Placing the conipiiss on board ship in its binnacle, see that the bowl takes up its proper horizontal position in the gimbals ; that the lubber-line is vertical, and that a line from the centre of the card to the lubber-line is exactly in tlie same horizontal dii-ection as the fore-and-aft line of the ship. See that the thread in the sight vane is vertical, by testing it with a lilumb line ; and raise and lower the reflector, and see that the reflected image of the thi-ead coincides with the thread itself. This will show that the bearing of an object at any elevation, whether taken by direct bearing or by reflection, is correct. Metal pivots become blunted by wear, and steel pivots are also very liable to rust; jewelled caps naturally get worn and perforated by use, especially from the long-continued working of the screw propeller. They are also liable to be cracked by sudden concussion. Heavy cards are sometimes fitted with speculum metal caps, and work on jewelled pivots. Defective caps and pivots are a fruitful source of inefficiency in compasses, and require the esjjecial attention of the navigator. 218. At a time when ships had no compass in an elevated position, all bearings had to be taken from the steering compasses. These were low down to the deck, and therefore inconvenient tor that purpose. And subsequently, when most ships had an elevated compass, its position was frequently such, that an all- round view could not be obtained therefrom. The difficulty was met by the introduction of an instrument called a dumb card, or bearing-plate. It consists of a circular plate of metal, graduated like a compass card, and so gimballed that it may be revolved round a central pivot, in a horizontal plane. Adjacent to the circumference is a mark, similar to the lubber-line of the compass. It is fitted with sight vanes, shades, and reflector, for taking bearings. Tlie instrument may be placed in any position from whence the object, or objects, to be observed may be seen. The greatest care must be taken to see that the line from the centre; of the bearing-plate to its lubber-mark is in the exact fore-and- aft line of the ship. This may be 4one by referring it to some mark in the ship, exjictly in the fnre-and-aft line; or to snme mark, such as a IjoUard, which, from the position chosen for the 70 NAVIGATION. bearing-plate, is a known, small, and constant angle from tlie foie-and-aft line. If the direction of the ship's head by the hearing-plate, be made to correspond with the direction of the ship's head by any compass, then the bearings taken by the bearing-plate will be the same as if they were taken by that compass. And, con- versely, if the bearing-plate be turned round, so that the bearing of an object by it corresponds with its known correct bearing, the direction of the ship's head, as shown by the bearing-plate, is correct. This instrument, sometimes called a Pelorus, is exten- sively used. Another instrument, called a Palinurus, is sometimes used for getting true bearings. It is, simply, the mechanical con- struction of the celestial sphere, with its great circles. By means of time, latitude, and declination of some heavenly body, a line in the instrument may be set to the true direction of that body. All tlie parts of the instrument, when that line is pointed to the body, will be in the true astronomical direction, and the bearings on the horizontal circle of the instrument will be true bearings round the horizon. A mark placed as the lubber-line will, of course, show the true direction of the ship's head. It will be seen that, with this instrument, no calculations or azimuth tables are required to get a true direction. With respect to the use of such adjuncts to the compass, as have been briefly described, liability to secondary errors, both personal and instrumental, must be taken into account. To work directly, from a well-placed standard compass, appears by far the safest practice in navigation. Variation of the Compass. 219. The second problem before the early navigators was, to find the direction in which the needle pointed (No. 214). When the directive property of the magnet was first brought into use by seamen, it is probable that they continued for some time to steer by the sun and stars, as before. It was only when those objects were obscured, that they had recourse to a rude form of compass, to enable them to maintain their course, till their accustomed and more reliable guides appeared again. What the compass needle was to the seamen of those days, it is to the navigator of to-day. By it he can preserve a course, without reference to the heavenly bodies, for a longer or shorter time, and with more or less accu- racy, according to the perfection of his compass, and to tlie degree in which he is acquainted with the laws which govern its pointing. The natural standard of direction is the meridian. The hori- zontal angle contained between the direction of the meridiiui rSSTHUMKNTS OF NAVIGATION. ( I and the direction of tlie needle, is called the Variation of tlie L'ompass. It is termed easterly or westerly, according to whicli 6i(le of the meridian the north end of the needle points. The approximate direction of the meridian was easily seen in the northern hemisphere, by the position of the pole star. It must, therefore, have been well known, to all who noted tlio pointing of the compass needle, with any degree of care, that its direction did not coincide with the direction of the meridian ; or, in other words, that it did not, in all places, point to the nortli. This fact seems to have been brought most prominently into notice by Columbus. He found, on his first voyaue, in 14'J2, when well over towards the West Indies, that tbe needle pointed to the westward of north. In the seas which Columbus had hitherto navigated, as far as can be now judged, it pointed to the eastward of north. At the port in Europe from which he sailed the variation was, apparently, not less than two points easterly. Pro- bably, therefore, it was the change, and especially its going from easterly to westerly, rather than the existence of variation, whicli arrested the attention of Columbus. The first good determination of the variation, in England, was made in 1580, when the direction of the north end of the needle was about one point to the eastward of the meridian. Since that time, the variation has been observed with increasing frequency and accuracy. The following is an outline of the change in the variation in England. Commencing in 1580 at 11° 15' easterly, the north point of the needle moved towards the meridian, and crossed it in 1(>57, moving westward at the i-ate of 10' annually. The north end of the needle continued to move westward, with a diminishing ratf, till 1818, when it attained the limit of its western range, 24° ^58' westerly. Since that date the north point of the needle has moved to the ea.st with an increasing rate. The variation in London is now 17° :10' westerly, diminishing at the rate of 8' annually. The first attempt to give a comprehensive view of the direc- tion of the compass needle, in all parts of the world, was made by Halley, in a chart published in 1 700. This chart embraced the results of a voyage made by Halley himself, and such other information as was at that time available. Joining, by a line, the points on the earth's surface where the variation was the same, he traced, on a Mercator's chart, a series of lines of equal variation, extending over the Atlantic and Indian Oceans, and as far east as the meridian of 150°. Sevei-al similar charts, more complete and accurate, as the materials for compiling them increased in quantity and value, have since been published. The latest variation chart published by the Admiralty is all that the seaman can desire. On it the annual change of variation is bIso shown, enabling the navigator to obtain the variation very ckbt.'ly, at auy date subsequent to that of the publication of the 72 NAVIGATION. clmrt. CompariTig Halley's chart with those which have since been made, it appears that changes iu the variation, analogous to those observed in England, but of greater or lesser extent, have been going on nearly all over the world. The variation of the compass is thus shown to be a variable quantity, changing at a variable rate. Such being the case, the only way in which it is possible to make and maintain an accurate variation chart, is by the co-operation of navigators, in making and recording, for that purpose, observations of the variation of the compass, in all those parts of the woi-ld over Avhich they may sail. 220. Besides the change in the variation, which reaches its limits in long intervals of time, and is called the secular change, there are smaller changes, called periodical. Such is the diurnal change, wherein the needle moves through a small angle to the westward during the day, and retm-ns to the eastward during the night, in the northern hemisphere. In the southeru hemisphere, a similar change takes place, but in an oj)posite direction. The needle is also disturbed by the aurora, and by phenomena called magnetic storms. These changes are, iu the navigable parts of the globe, too small to be of any importance to the navigator. Neither is the pointing of the compass needle affected by atmospheric phenomena, such as fogs, rain, wind, or thundei'storms. Bui in caseu where a ship has been struck by lightning, the directive property of the compass needle has sometimes been impaired or destroyed. There is, however, one cause of disturbance of the needle which should interest the navigator. Humboldt, in the beginning of this century, observed that the needle, in certain places on land, was deflected from what may be called its normal direction, by some property in the ground. In previous editions of this work, several places are noted, where the variation was affected l)y the land, or by the ground in shallow water.* It is probable, from the practice of steering by the land when it is in sight, rather than by compass courses, that this distui-bance of the compass needle has escaped notice in some places whei-e it exists. It is, therefore, desirable that this unquestionable source of danger should be pointed out, that the seaman may be on his f^uard, when navigating near the land, or in shallow water, espe- cially in volcanic regions. Methods of determining the variation of the compass are given in Chapter VIII. 221. To correct compass coiirses and bearings for variation. The manner of doing this appears thus. Suppose one compass card to be placed directly over another, and the lower one to be irue. Now suppose the north point of the upper compass to be drawn two points to the right of the true by easterly variation, then the North point of the upper or muynetic compass corresponds • Comtnunder W. U. Moore of H.M.S. Perguin ^c. llic iicecilr. (55°) in 9 fuliunis, 2 miles Iruiu the shoix',, 11 euabt of AuhtiHlia. int Notice to MarinsrH, No. lo of 1 INSTRUMENTS l>F NAVIGATION. 73 to N.N.F. of the true compass, which point is to the riu^ht of N., and the South point corresponds to S.S.W. of the true compass, to the rif^ht of S., and so on. The contrary wo aid take phice v.ith westerly variation; hence to correct a magnetic course or bearing we have this rule. Rule. When the variation is easterly, apply it to the rvjlit of the compass course or bearing ; when wederhj, ap[>ly it lo thi; left, looking from the centre of the card over the point to be corrected. Ex. 1. Course by compass, S. J W.; fariation, 2j points easterly. Tkub Couhse, 2|^ points to tlie rifrlit of 6. i W., or S. 3 points W., or S.W. by S. Ex. 2. Course by compass, N. by E. ; T;iri.itiiin, 2 point westerly. 'I'lirK Course, 2 point.s to the left of N. by E., that is, N. by W. | To reduce a true course or bearing to the compass course or bearing, apply the variation the contrary way to that directed iibove. Ex. 3. Course or l)pariii^ by comj'; N. 84° E. ; variation, 19° W. TuuB CouusE, N. 65° E. Ex. 4. Ci'urse by compass, S. 4° ,'ariation, 17° E. Teue Couese, S. 13° \V. Ex 1. True course, N.E. by E.; varia in, I point easterly. Course by Compass, N.E. Ex. 2. True course, E. ^ N. ; variation ConiisK i)V Compass, E. by S. Ex. 3. True course, North; variation, iS" CMstrrly. CouusE DY Compass. N. iS° \V. Ex. 4. True course, West ; variatiou, 2.° westerly. Course by Compass, N. 6y° Vf, Deviation nf the Compass, 222. From the earliest times it was known that Jf a magnet, or a piece of ordinary iron, were brought near to a compass, it would deflect the needle in its pointing, and so make the compass iiidiratiims en'oneous. Compasses on board ship, therefore, wcu-e IK it jilaccd near to each other, and iron was rigorously kept away from their vicinity. With these precautions, though accidents Bometimes happened from iron in the vicinity of the couipass being overlooked, ships were navigated with a fair amount of security. But as iron became increasingly used in the construc- tion of ships, and by the introduction therein of steam engines, with their boilers and funnels, it was no longer possible to navi- gate, without systematically allowing for the deflection of tli« compass needle caused thereby. The horizontal angle, which the needle is deflected by the iron in or of the ship, is called the Deviation of the Compass. It is named easterly or positive (E. or +), when the north end of needle is deflected to the eastward ; and westerly or negative (W. or -), when deflected to the westward. The mode of ascertaining ami applying the deviation of +he compass, is the next problem to engage the alte ilion of the student of navi-atn^n. 74 NAVIGATION. WitLin half a century of the present time, many navigators dDubted the existence of the deviation of the compass; or, while admitting its existence, denied that it was of any practical importance. And the belief was not uncommon, that it was a constant error- -that is, that it was the same in amount with the ship's head in any direction. Those, however, who had studied tlie subject, or whom circumstances had made familiar therewith, atknowledged its importance, and recognised the necessity of iiscertainiiig the deviation of the compass, with the ship's head in all directions. 223. There are three standards from which to reckon an angle of direction. First, from the meridian, the direction of which can always be ascertained astronomically. A course or bearing tlius reckoned, is called a true course, or true bearing. Second, irom the direction of the magnetic north ; that is, from the direction of a magnetic needle, when uninfluenced by any con- tiguous iron, or by any such local disturbances as are mentioned in No. 220. A course or bearing thus reckoned, is called a nisignetic course or bearing. Third, from the direction of the compass needle, as shown by a compass which is instruinen- tiilly correct, placed in any position. A course or bearing thus rocK'oned, is called a compass course or bearing. The prefix correct may be placed to either of these quan- tities. The terms correct true, correct magnetic, correct com- piss, are used to distinguish the exact angles from those more or less approximate. The student must not confuse correct compass with magnetic. A correct compass course or bearing means a course or bearing accurately observed, with an accurate compass, regardless of any disturbance by which the compass may be influenced. 224. From the fact that compasses, in different parts of a ship, gave different indications, came the necessity for navigating by one especial compass, placed in a selected position. Such a compass is called the Standard Compass. It should be an azimuth compass, that is, one fitted for observing bearings ; and one essen- tial of its position is, that from it bearings can be taken all round the horizon, and at any altitude. Turning a ship round, so as to place her head on all points of the compass in succession, for the purpose of ascer- taining the deviation, is called swinging the ship. A ship may he warped or towed round, when lying at anchor or at moor- ings ; or advantage may be taken of her turning with the tide. Wherever there is room, it may be convenient to steer a ship n)und under steam. It is in all cases desirable that the slii[) should be checked in her swinging, and steadied on the point ou which it is desired to obtain the deviation. As the variation of the compass is determined by coni- [laruig the true bearing of an object with its uiiignetic bearing, IKSTKUMEXTS OF NAVIGATION. I 'J SO Ibe dori.dion of tlie compass is ascertained by compnrinnf the niaLTiiPtic bearing witb the compass bearinj^ — the compass, at Ibe time, beini^ deflected by the iron in and of the ship only. Any other disturbance, such as from the proximity of other ships or masses of iron, or the irregular influence of the land, is not devialion according to the definition already given. The first problem is, therefore, to determine the magnetic bearing of some object external to the ship. The sun is very commonly used; the true bearing is easily found, and the va,ria- tion being applied thereto, gives its magnetic bearing. A dis- tant mark on the land may also be used ; its true bearing may be found by the chart, or by measuring and applying the liori- zontal angle or difference of bearing between it and the sun, and the magnetic bearing by further applying the variation. A third method is to have a correct compass in a convenient posi- tion on shore, v^here it is free from magnetic disturbances. Then the bearing of that compass being taken from the standard compass, and the bearing of the standard compass being simul- taneously taken from the shore compass, the deviation of the standard compass is found by comparison. These methods are spoken of as, swinging by the sun, swinging by distant mark, and swinging by shore compass. When using a distant mark, it should be so far away that the radius of the circle, along the circumference of which the standard compass moves as the ship goes round, subtends a smaller angle than is of practical consequence in navigating. Otherwise the bearings must be corrected for parallax. There are many places where the true direction of lines, on which two known and conspicuous marks appear in one, are known. These lines, called transit lines, offer especial facilities for ascertaining the deviation. Looking from the centre of the card, if the bearing shown by the compass is to the left of the magnetic bearing, the needle is obviously deflected to the right, and the deviation con- Bequently called easterly. If the bearing shown by the compass IS to the right of the magnetic bearing, the needle must be deflected to the left, and the deviation westerly. 225. Though the deviation of other compasses is not of so much importance as that of the standard, it is usual to note the direction of the ship's head, as shown by them, when it is on each point by the standard. The deviation is usually tabulated for reference, in some form similar to the following, which ia com- monly called a Deviation Table. nraa hy St;.,„l.>r.i Cuul|..lM DcTiat Cum pZl Dirccllo . of Head by other Compasses 1 r..rt Steering L larboard Steering Bridge Ciiii. 1 1 76 UAVir.ATTON. The bearing-plate is frequently used in swinging. The vanea on the bearing-jihite, beinc- set to the known magnetic bear- ing of the sun, distant marJi, or shore compass, the magnetic direction of head is sliown by the lubber mark, when the plate ifl turned round so that the vanes point to the object. Tlius, Ihe deviation of the compasses on the magnetic points is sliown, and may be tabulated as follows : — Head Magnetic Direotiou of Head by Coinpisaes St,u dard Port Steering Starboard Steering Bridge Comp.n^ 1 226. It is customary to form a deviation table from observa- tions made on each point. But it may be convenient, or neces- sary, to form such a table with fewer observations, such as on every second or third point. Further, it may not be possible to get the observations exactly on the points. The problem, there- ft ire, is to form a deviation table with few observations, irregularly- distributed round the compass. This is done by drawing a curve of deviations in the following manner. Draw a vertical line on paper, and divide it as a com- pass card is divided. The vertical line will thus represent the circumference of the card unrolled, and formed into a straiglit iiue. Through each compass point draw a line at right angles to the vertical line. On these lines, with any convenient scale, lay off the deviation found on each point. On parallel lines, passing thi-ough any intermediate degree or division of the point, lay otf the deviation found thereon. Easterly deviation to be measured from the vertical line to the right, and westerly deviation to the left, marking, by a cross or otherwise, the positions thus deter- mined. Now draw a line which, without being irregular in direction, passes most nearly through the several marks. This line, in practice, will always be a curve. The distance of the point of intersection of this curve with any point line, from the vertical line, will give the deviation on that point, using the same scale as before. Example. — The following deviations having been observed, tiud the deviation on eacli compass point. North S O E N ■■{ E 6 o E NNE 10 o K NE 1 N •4 o E ENK 12 E E^N lO o E EbS 9 so E SEbE 6 E SE I o W «SE 2 oo W ■South o W SW 1, 3 o w SW ■,. \v AVSW o w We.t lO o w W bN- N II o \v NW 10 o \v NNW i W 6 3t> w ~ " " " ^°^^'"'. ■;;7";;\r ""^ ^\ X. — - X 1 T 1 '/ .__ ^^^^ fg^f / / / / y^ 1 : South icule i}/J)ena&/^ri, - 1 J / J ■ / '■ 1 ■. f : — r J V '■ X- — : ^^^ : -North A ::rr-. NAVIOATION. 227. Plotting these observations in the mannei" directed, and as shown in the foregoing diagram, the following table of devialioiis is obtained. North 5 o E NbE 7 45 E NNE lO o E NEb N 12 15 E NE 13 30 E NE h E >3 30 E ENE 12 45 E EbN II 45 E East 10 30 E EbS 845 E Eb E 7 15 E SEb E 4 30 E SE 45 E SEb 3 2 W SSE 3 30 W S b E 4 30 W South 5 S b w S ssw 5 S\V b 8 5 SW 5 30 S\V b w 6 30 W8VV 7 45 W bS S45 West 9 45 W bN 10 30 wxvv 10 45 NW b W 10 30 NW 9 45 NW b N 8 NNW 5 '5 N b VV 1 In the diao-ram shown, the vertical scale is made small as com- pared with the horizontal scale, in order to get it within the limits of the page. A sheet of ordinary ruled foolscap will be found very convenient for plotting deviations to form the curve. 228. The methods of ascertaining the deviation having been explained, the following are directions for applying the same to a compass course or bearing, so a? to obtain the magnetic course or bearing. The ship's head being on any compass point, and the devia- tion on that point being easterly, that deviation must be allowed to the right, to find tie magnetic direction of the ship's head ; and also to the right of any bearing taken by compass, to find the magnetic bearing. If tlie deviation on the compass course is westerly, it must be allowed to the left, to find the magnetic course or bearing. Example. — Shiji's head E.N.E. by compass, a point of land bore N. 10° W. What is the magnetic direction of the ship's head, and the magnetic bearing of the point, the deviation being as given in table 227 ? The deviation on E.N.E. is 12.45 E., which allowed to the right of N. 67.30 E., gives N. 80.15 E. as the magnetic direction of the ship's head; and allowed to the right of N, 10.0 W., gives N. 2.45 E. as the magnetic bearing of the point. In the same way, head being N.W. and bearing S. 40 E., the deviation on N.W. is 9.45 W., which allowed to the left, gives N. 54.45 VV. as magnetic direction of ship's head, and S. 49.45 E. as magnetic Lieanng of point. To turn mugm-tic course's or bearings into compass couisca or rN'STlUlMENTS OF NAVIGATION. E3 courses or bearinsrs into b*-arings, it is obvious that the deviation shoulil be allowed tbo opposite way. That is, easterly deviation to the left, and westerly deviation to the right. 229. To facilitate turning conij magnetic courses or bearings, and the reverse, certain graphic methods are sometimes used. The most com- mon is one called, from its inventor, Na|)ier's diagram. The example given, wherein are plotted, through a quadrant, the observations given in No. 22t), shows the use of this diagram for the purjiose named, as well as for forming a curve of devia- tions from few observations. The dotted compass point lines intersect the vertical line, at an angle of 60°, and the vertical scale and deviation scale areequal. There- fore, if the deviation found on any compass point be laid off on one of the dotted lines, or on a line paral- lel thereto, and, from the point reached, a line be drawn making an angle of 60° with the compass jioint line, it will intersect the ver- tical line at the magnetic point. ^- And, vice versa, if the deviation on -^ a magnetic point be laid oS" on one of the plain lines, or on a line parallel thereto, the return line, drawn as '" before, will reach the vertical line '' Rt the compass point. The three lines form an equil.ateral triangle, ..^ of which the ditference between compass and magnetic forms the base, the other sides being equal thereto, and to the deviation due -^ to the direction of head, whether ^' given by compass or magnetic. 2:30. Another method, called the straight line method, is due to Mr. Archibald Smith. Tt is only useful for showing, at a glance, the mag- netic course equivalent to any given compass course, and vice versa, when the deviation is known. Tt consists merely of two parallel vertical lines, each divided as ti.o circumference of a compass card is divided. Strai-ht lines ute 80 KAVIGATION, STRAIGHT LINE DIAGRAM. COMPASS AfAGN£T/C XOURS£S , */Cb N drawn, from the compass points on one Hue to the ma^-netic points on the other. In the annexed example, the deviation table through one quad- rant, given in No. 227, is thus treated. If a ship be steering any- compass course, shown on the lett-liand column, the corre- sponding magnetic course is shown on the right-hand column. NOfiT/j ^"'l if i*' is desired to steer any- magnetic course, shown on the right-hand column, the required conniass course is shown on the left-hand column. 2ol. A third method is to have two prints of compass cai-ds, one laid on the other. The upper card somewhat smaller than the lower, and capable of being rotated about the commdu centre. The lower card, being fixed, may be considered as re- presenting either true, or mag- netic, courses or bearings. Consider the lower card to represent true courses and bear- ings, and the north points of the two cards togethei-. Conceive ■/v£i£ the north point of the upper card, moved thiough an arc equal to the variation, away from the north point on the lower card, to the right when the variation is easterly, and to the left when the variation is westerly. Magne- tic courses and bearings on the upper card, and true courses and bearings on the lower card, will now be coincident. Similarly, if the lower card be considered as showing mag- netic courses or bearings, and the north points of the cards be separated by an arc equal to the deviation, then the compass courses and bearings on the upper card, will coincide with magnetic courses or bearings on the lower card. V£{>£ /V£6N f/£ £6M £AST rNSTnUMKN'TS OF NAVIOATIO^T. 81 DiMi^TMms on wliicli cnrvcs of deviation can be flr:iwn, so ris to show iiiilitf'tTOnt obsorviitions, and tiiiis elitiiiiuite their elU'cts, or to form the curve from few observations, are of un- doubted value to the seaman. But it is a question, whether any means such as have been described, for turning ma^° /^ ■i r fa i 4 ^^ ^ T LJ w- fe^ 'Tj] — -S| %J'\^ — i^ PT y ^ ^ ^rt- tf^ , r \\ 20 l-Jr^4f^ ^xK vV -m \ \/> ^ \v' K^ \\jy(^TTX ffO^^ ^ ^ ^ u ^ \M^ Maps showing the Magnetic Equator, lines ot Equal Dip, and Horizon- tal Direction of the Compass Needle. The parallels of latitude and the meridians are drawn at every fifteen degrees of latitude and longitude; the figures at the circumference denote the dip in degrees along the respective magnetic parallels ; and the direction of the magnetic meridians, compared with the direction of the gepgraphical meridians, shows the variation. Hemisphere from 120° E. to 60° W. Longitude. The points (©) to which the magnetic meridians converge are the magnetic poles, sometimes called, from the dip thereat being 90°, the poles of Verticity. The points ( » ) show the approximate position of the foci of maximum force. It is remarkable that these ^x points are within 160° of longitude. These maps, and the following table of horizontal force, are based on the good work on this sobject done by the late Sir K. Kvans, R.N. INSTKUMKNTS OF NAVIGATION. S3 be. The dip and total force, therefore, increase together in such a manner that the horizontal force continually diminishes. Tlie horizontal force is the only part of the earth's force by which the compass card maintains its due position. The sea- man is generally satisfied if this condition is fairly answered; but he must be sometimes painfully aware, from what is called the sluggishness of his compass, that this force is, at best, very feeble. The following table gives the comparative value of the hori- zontal force, in different positions ; the maximum value being considered as unity. COMi'AKATIVE VALUE OF HUKIZONTAL FORCE Ma ximum Value equal Unity East Lonu TUDE 1 Latitude 0° 040 041 3U° 0-43 •15° 60° 044 75° 043 90° 042 105° 043 120° 044 135° 0-4S 150° 047 165° 049 180° 048 N 60° 044 50 049 052 055 0-57 058 058 058 057 057 059 060 0'6q 0-59 40 060 064 0-6S 070 073 075 075 075 074 073 071 070 06S 30 071 075 079 083 087 089 090 0S9 087 084 82 oSo 076 20 07S oSi 0S6 90 094 097 097 096 094 092 0-89 086 0-84 10 0S2 085 o-SS 090 093 097 I 00 I 00 099 097 094 092 090 079 079 080 083 0-87 090 096 roo I 00 I 00 0-98 0-97 0-95 S 10 070 070 070 072 076 082 088 092 096 0-98 0-98 097 096 20 06 1 0-59 0-59 60 0-64 071 077 082 087 090 091 091 090 30 056 054 052 0-53 054 058 0-52 06S 071 075 078 oSi 0S2 40 0-5S 051 0-49 04S 049 0-50 051 054 055 057 062 065 008 SO 054 050 047 0-44 043 042 041 039 038 039 0-43 047 052 60 OS3 0-49 046 042 0-39 036 032 0-27 0-20 024 030 037 West Long ITUDE Latitude 1 0° 15° 0-37 30° 033 45° 0-29 60° _75^ 012 90° 010 105° 020 120° 029 135° 0-38 150° 165° ISO" 0-48 N 60° 040 0-43 046 50 049 0-45 041 037 034 032 036 043 049 0-54 055 057 059 40 060 055 050 0-48 047 050 056 060 064 065 065 obO 0(8 30 071 066 062 061 065 071 077 080 080 077 074 074 076 20 07S 074 072 072 077 085 090 090 08S 085 082 0S2 084 10 S2 079 077 079 084 089 094 0-95 092 0S9 0S9 090 90 79 07S 077 o-8o 083 089 0-92 093 092 090 092 093 09i S 10 70 071 073 076 080 084 0S7 088 089 88 091 093 096 20 61 065 0-68 070 074 079 082 0-84 08s 087 088 ogo 090 30 $(' 060 063 067 070 076 077 07S 07S 080 081 0S2 082 40 55 059 063 067 071 074 075 073 071 070 070 070 068 50 54 059 0-63 o6g 072 073 0&8 0O3 061 0-59 056 0'52 60 053 0-5S 063 0-6S 07. °-' 067 060 055 050 040 042 o'37 234. In dealing with the subject of compass adjustment, it will sometimes be useful for the seaman to know the value of the force with which the needle points on board ship, compared with the force with which it points on shore; or the force vvith which 84 NAVIGATION. it points when the ship's head is in one direction, compared wilh the force wit)i wliich it points when the head is in other direc- tions. It is necessary, therefore, to show how comparative mag- netic force is measured. If a magnetised needle, balanced on ila centre, be disturbed from its position of rest, it will, like a pendulum, vibrate through diminishing arcs, till it again comes to rest. The speed of the needle is increased when the magnetic ibrce is increased ; the force being proportional to the squax-e of the speed of the needle. That is, if the needle in one position makes 10 vibrations in any given time, and in another position makes ] 2 vibrations in the same time, the magnetic force in the first position is to the magnetic force in the second position as 10^ is to 12». It is convenient to measure the horizontal force and the vertical force separately. The horizontal force is measured by means of a flat and pointed needle, about three inches long. It ban a jewelled cap at its centre, which works on a sharp pivot. It must be used in a covered box, or compass bowl, to protect it from the motion of the air. It is brought horizontal by a small weight, counterbalancing the dip, and so vibrated in the horizontal plane. Horizontal force may also be measured by deflection. If a magnet be placed at right angles to the direction of the needle, the magnet will deflect the needle through a certain angle, depending upon the strength of the magnet, compared with the horizontal force. The smaller the force, the larger the angle of deflection of the needle, the force being as the cosine of the angle of deflection. Or the deflecting magnet may be moved round, and kept at right angles to the compass needle, and the horizontnl force measured by the maximum deflection the magnet is capable of producing, when thus applied. Vertical force is measured by means of a Dip Circle. This is an instrument having a flat pointed needle, with an axle passing through its centre of gravity, about which it can rotate in a vertical plane ; the axle being supported at the centre of a graduated circle. If the circle is placed in the vertical plane of the magnetic force, the needle will stand in the direction of that force, showing the dip, if it be acted on by the earth's force only. A small weight placed on the upper arm of the needle, bringing it horizontal, will be a measure of the vertical force. If the circle is placed at right angles to the plane of the magnetic force, the needle will hang vertically, where there is any vertical foice, and in this position may be vibrated, so as to measui-e that force. Measuring either horizontal or vertical force by vibration, the initial arc should be the same, in any positions wherein it is desired to compare those forces. The effects of friction, and the resistance of the air, are to cause the needle to take a little more INSTHUMENTS OF NAVIGATION. 85 time, in going throtigh tho larger arcs than the smaller, and altiniately to bring it to rest. The smallest arcs which can be conveniently used give the best results. 235. Studying the phenomena of the pointing of the magne- tised needle on the earth's surface, and comparing them with the effects of one magnetised needle, or steel bar, on another magne- tised needle, or steel bar, the conviction gradually giiined ground, that the earth is, or has the properties of, a large magnet. Those properties are two. First, Attraction and Repulsion : the property by which one magnet will attract and repel another, according to definite laws. Second, Induction : the property by which a magnet can impart magnetism, and so convert into a magnet liny piece of iron or steel, either by contact or mere proximity. The property of attraction and repulsion may be shown, by bringing two compass cards near to each other. The north part of one card will push away or repel the north part, and attract or draw towards it the south part, of the other. The ends of magnets are called poles, and we express the law of attraction and repulsion by saying, like poles repel, and unlike poles attract, each other. This attraction and repulsion may be due to two different kinds of magnetism in the poles, or to an excess of magnetism in one pole as compared with the other, or it may be a magnetic state, depending upon neither one cause nor the othex-. It will be convenient to spjak of the magnetic state of the north pole of the compass needle as positive, indicating it by the ti'gn +, and of that of the south pole as negative, indicating it by the sign — . The pointing of the magnetised needle appears to be, the direction it takes up in obedience to the law of attraction and repulsion existing between it and the larger magnet, the earth. Also, the increasing strength, with which the needle is found to point as the latitude increases, appears due to the approach to the magnetic poles of the earth. By the law of induction, a magnet when brought near to any piece of unmagnetised iron, induces magnetism therein; the neosite kinds. The similar magnetism to that of the near pole of the magnet is found in a remote part of the iron. Applying this law to the earth as a large magnet, the magnetism of iron and iron structures is apparently due to in- duction from the earth, and the end or part of ii'on which is towards the north will have positive magnetism. In dealing with the magnetism of iron ships, this property of induction, hitherto little thought about by seamen, becomes of great importance. The earth's magnetic force, by inducing inagiietism in the iron uf a ship, is the source of all magnetic disturbances of the compass. 86 KAVIGATION. 236. The question as to how the earth became magnetisecl will perhaps come into the mind — possibly it is, or was, magnetised bj induction, from some far distant cause. But magnetism may be induced by electricity. If an insulated wire is passed round a piece of iron, and the wire be considered as conveying an electric current flowing from positive to negative, the iron will become magnetised, and have positive and negative powei'S, as shown in the figure. If tlie trade winds flowing round the earth from the eastward, be considered as acting as a positive electric current, the earth would be magnetised with a negative pole to the north, and a positive pole to the south. Whether it is thus magnetised or not, the idea will aid the memory as to the magnetic state of the earth, show how magnetic forces may be generated by electricity, and suggest the possibility of compass disturbance, by the in- creasing use of electricity on board ship. 237. All iron is capable of receiving magnetism by induction from the earth. If the iron remain a long time in the same posi- tion, or if it be hammered or subjected to mechanical violence, part of the induced magnetism will remain. That is, the iron will show polarity in the same parts, after it has been moved into another position, relatively to the line of the earth's force. All magnetism, therefore, may be called induced magnetism. That which instantly passes awaj^, when the inducing cause no longer acts, is called transient magnetism. That which remains for a longer or shorter time, is generally called permanent mag- netism. The tevm permanent, in this extended sense, means all mugnetism that is not transient. The terms trans-permanent, sub-permanent, and permanent, may be used to indicate increas- ing degrees of permanency, if desired. It is, however, a question whether anything is gained by thus multiplying terms, as no definite line of separation can exist. Speaking generally, iron will receive or part with magnetism more or less readily, according as it is soft or hard. Hard iron or steel, when magnetised, will retain its polarity for a very long time. 238. The disturbing effects of iron on a compass, being caus(id by magnetism induced in the iron by the earth's magnetism, the possibility of so placing iron about a compass on board ship as to counteract the effect of the iron of the ship, is the problem of compass adjustment. Professor Barlow was the first to deal practically with compass adjustment, and the problem was subsequently completely solved by Professor Airy in 1839. That gentleman gave the results of Ilia researches and experiments in the following words : ' Bj INSTUUMKNTS OF NAVIGATION. 87 placing a magnet so that its action will take place in a direction opposite to that which the investigations show to be tlie direction ot the ship's independent magnetic action, and at snch a distance that its etiect is equal to that of the ship's independent magne- tism, and bj counteracting the efl'ect of the induced magnetism by means of the induced magnetism of another mass [according to rules which are given], the compass may be made to point exactly as if it were free from disturbance.' Briefly, this state- ment is to the eflect, that the permanent magnetism of the ship may be counteracted by the permanent magnetism of steel mag- nets, and the transient magnetism of the ship by the transient magnetism of iron ; the magnets and ii-on being placed near the compass, according to definite rules. In order to be able to consider together, the disturbing effects of the iron of the ship on the compass, and the action of magnets and iron in counteracting the same, a brief explanation of the latter is necessary, 239. Magnets, when used to adjust a compass, are applied, generally, either end on, or, as it has been termed, broadside on. If a magnet be placed near a compass, so that the centre of the needle is in the line of the magnet, the etfect of the magnet is to cause a force pushing away the north point of the needle, if the positive end of the magnet is presented, and drawing the north point of the needle towards the magnet, if the negative end is presented. In the figure, | if c represent the centre ^-^ — i-" ^ ^ of the compass needle, the arrows represent the di- C rection of the force on its ^ north end. This is called the end-on position of the magnet. If a magnet be placed near a compass, so that the centre of the needle is in the same plane as the magnet, and on a line drawn from the middle of the magnet, perpendicular to its direc- tion, the efl'ect of the magnet is to cause a force parallel to itself, pushing ■< ^ • the north end of the needle away from i the positive end of the magnet. In the i figure, if c be the centre of the coin- : piiss needle, the arrow shows the di- ; rection of the force on its north end. i This is sometimes called the broadside [ - ' +"1 position of the magnet. Magnets us.'d for compass adjustment are made of hard steel, and well ningnetised. Their magnetism may be considered as per- manent. Thus, by means of a magnet, a permanent magnetic force can be produced, pushing the north end of the compass needle in any desired direction. 240. The iron used in adjusting compasses should be soft malle- 88 NAVIGATION. E. mag. laU -f" . msg. Ui. 4- able iron, so that magnetism is readily induced therein by the carth^s force, and readily parted with ; that is, it does not become permanent. It is used for two jjurposes. For one purpose, it is in the form of an upright bar, placed, generally, before or abaft the compass. For another purpose, masses of chain or scrap iron in boxes, cylinders, or spheres, are used. These are placed besidt the compass, on the same level as the needle. 241. The action of the upright bar depends upon the earth's rei-tical force. In north magnetic latitude, the lower end has positive magnetism, and the upjier end negative magnetism. On the magnetic equator the bar may be considered as unmagnetised. In south magnetic latitude, the lower end has negative magnetism, and the upper end positive magnet- ism. Therefoi-e a magnetic force in any direction cau be produced, acting on the north end of the compass needle, varying in strength with the earth's vertical force, by placing the upper end of the bar in a suitable position. It is generally desired to make this force horizontal, as shown in the figure, where c is the centre of the compass needle. After Captain Flinders, R.N., who was the first to propose this, or, indeed, any mode of counteracting the effect of the ship's iron on the compass, iron thus used is called a Flinders bar. 2-12. The action of iron placed beside a compass, is not quite so simple as that of the Flinders bar. In the fig. let c be the centre of the compass needle, and the circle the outer circumference of the binnacle. Let a i-epresent a horizontal iron rod, placed radially north of the centre of the compass. In this position it will be magnetised by in- duction from the earth — the north end of the rod with I^ositive magnetism, and the south end with negative mag- netism. It will cause no deflection of the needle, be- cause the force is in the line of the needle. It will, how- ever, increase the force with which the needle points. :n: INSTHUMKNTS OF NAVIGATION. Conceiving the rod to be moved round the needle to the rij;bt, as the spokes of a wheel move round its centre, it will be seen that the amount of n)a<^netism in the rod will dimhiish as it goes round, till in the east position it may be considered as without magnetism. But as the rod leaves the north position, so the magnetic force of the rod, by being inclined to the needle at a greater angle, has a greater proportional efl'ect in deflecting it. From the combined action of these two causes, the maximum deflection of the needle occurs when the rod is in the N.E. position. Following the rod round, and noting the magnetism induced thereui by the earth's magnetism, and the etfect of the magnetic force, thus generated in the rod, in detlectiiig the needle, the fidlowing results will appear: — Rod North or South of the centre of the needle. Increase of force, no deflection of the needle. Rod N.E. or S.W. Increase of force, maximum easterly deflection of the needle. Rod East or West. No etfect on the needle. Rod S.E. or N.W. Increase of force, maximum westerly deflection of the needle. Thus it will be seen, that the effect of the rod is to cause a deflection of the needle, easterly and westerly in alternate quad- rants, and to increase the mean magnetic force. It will also be Been, that the etfect of two rods opposite to each other, is to double the effect of one. 243. Another instructive example of the effects of iron moving rod ph, .•ed tangentially. N round a compass is that of a similar Following the rod round, and noting the magnetism induced therein, and the effect thereof on the compass needle, as in the figure, the following results will be seen : — Near end of the rod North or South of the centre of the needle. No effect. Near end of the rod N.E. or S.W. of the centre of the needle. Westerly deflection of the needle. Near end of the rod East or West of the centre of the needle. Maximum westerly deflection of the needle. c. Near end of the rod S.E. or N. W. '^ of the centre of the needle. Westerly deflection of the needle. In this example, as in 2 12, the effect of two rods in opposite positions is to double the effect of one. When two rods thus placed tangentially, having their near 90 NAVIGATION. ends at North and East, or in any positions 90° apart, revolvG about the compass together, one rod will cause a maximum deflection of the needle, when the other rod has no effect thereon. As the effect of one rod increases, the effect of the other decreases ; and the combined effect of the two rods, thus revolving together, is a constant westerly deflection of the needle. If the rods are placed in the opposite direction from their point of contact with the circle, similar easterly deflections will be produced. The ii-on rod h.is been here used as an example, be- cause the e9"ects can be most simply shown thereby ; but other forms of iron (240) are generally used in adjusting compasses, to produce the same effects. Hollow iron spheres are used with Sir William Thomson's compass. Their action is that of a rod of the length of the diameter of the sphere, always standing in the line of the earth's magnetic force, and magnetised thereby. In the figure, where c is the centre of the compass needle, it will be seen that the hori- zontal force of the spheres deflects it, and aflTects its pointing force, in the same manner as the iron rod in 242. When east and west of the centre, however, sjiheres diminish the directive force on the needle, more than the forms of iron commonly used. Having briefly examined the means employed to counteract the ship's magnetic forces, the origin and effect of those forces, and the mode of applying the counteracting means, may now be considered. 244. An iron ship, in the course of construction, stands in the influence, or field as it is termed, of the earth's magnetism, and is consequently magnetised by induction. In north magnetic latitude, all upright iron structures, such as stern-post and frames, have positive magnetism in their loiver ends, and negative mag- netism in their upper ends. In south magnetic latitude, these conditions are reversed. In all latitudes, horizontal iron structures, such as beams and keel, have positive magnetism in theirnorthern ends, and negative magnetism in thinr southern ends. The ship throughout is, in course of building, permeated with magnetism in the direction of the inducing force. Part of the magnetism thus acquired in building remains after the ship has been launched, causing a permanent magnetic force, in some direction in the ship. INSTRUMENTS OF NAVIGATION. 91 lliis force tends to draw the north point of the compass towards that part of the ship which was south in building. Besides this permanent magnetism, the ship, as she sub- sequently turns about with her head in different directions, takes up magnetism according to her varying positions. The amount of magnetism iron will thus receive by induction, within the limits of the change in the earth's force, varies as that force ; the ends of beams, and other parts of the ship's structure, which are towards the north having positive magnetism, which changes and becomes negative when the direction of the shiji's head is reversed. It ia evident, however, that vertical iron will have magnetism which does not dejjend on the direction of the ship's head, bi t which will vary, in character and value, with the earth's vertical foi-ce only. 245. From these premises it will be seen, that there must be always a Constant force, and a Variable force, acting on the compass needle as the ship goes round. Therefore, if the direction and value of these forces are known, together with the law \rhich governs the change in the variable force, the deviation of the compass could be found without swinging the ship. Generally, it is easier to deal with the deviation than with the forces which cause it ; but a knowledge of the manner in which these forces act, facilitates very much the construction of a deviation table. Considering the commercial value of time, in all matters relating 10 shipping, this is a subject of no small importance. 24(5. It has been stated, that j^art of the magnetism acquired in building causes a constant force, in some direction, in the ship. The amount of deviation any force is capable of producing must decrease, as the force with which the needle points increases. Therefore, the deviation caused by the ship's permanent magnetism varies inversely as the earth's horizontal foi-ce. It is also clear, that, if the direction of the ship's permanent magnetic force is known, a permanent force by means of magnets (239) might be produced to counteract it; and if this magnetism of the ship, and of the magnets, were equally permanent, the adjustment would be perfect for all time and places. The transient magnetism of vertical iron also causes a force which is constant in direction and value, as the ship goes round. This force, however, changes with change of place, as it depends on the earth's vertical force for its value. The liability of the needle to be deQected thereby varies inversely as the horizontal force. Therefore, the deviation caused by the tran- sient magnetism of vertical iron will vary as, ver. force x :; =tan. dip hor. torce 247. The following diagram will show how the compass is ^^('.■^('d Ijy the transient magnetism of vertical iron, and the niiiiinii- ill which Flinders' bar (2 11) ctuiutcracts that cll'cot. 32 NAVIGATION'. Afteb Part of Ship's Upper Deck. Head East. North magnetic latitude. e--k- South magnetic latitude -(±>- s In north magnetic latitude, the upper partcf the ship's frames having negative magnet isui, a compass in the position (a) would liave its north point drawn to the westvrard. In south magnetic- latitude, it would be drawn to the eastward. It is certain that no fixed magnet would meet this change. A Flinders bar, how- ever, might be placed before the compass, so that its magnetism would exactly counteract that of the stern frames. The mag- jietisin of the bar would change, exactly as that of the stern frames, when the ship went into south magnetic magnitude. At a position (6), generally rather more than one-third of the distance between the stern and the funnel (/), the magnetism of the upper part of the boilers and funnel counteracts that of the stern frames, so that no bar is required. At the position (c), tlie bar would be lequired abaft the compass; at the position (''^»'«"1»' »° e»»t 1™"''- From(i)P= -116T, Wibstituting in (2)- 3 39 T = 11° semicircuUir on east point. Therefore T= -'' = -3-25° on east iioint. lu the Thames . — 3-25°x 2-42 (the t.in. of dip)= -7J°. Lat 30° S., Lon. 16° E. — 325° x - l 24 (the tan. of dip) = 4°. Therefore, a Flinders bar should be placed before the compass, capable of deflecting the needle 7|° in the Thames, and 4° at the southern position. These deflections, from the magnetism of the bar, will be in opposite directions, and will exactly correct the deviation caused by the transient magnetism of vertical iron. Clearly, the magnetism of the funnel, in this case, draws the north point of the needle aft, in north magnetic latitude ; and forward, in south magnetic latitude. A convenient form of Flinders' bar is fitted to the binnacle of Sir Wm. Thomson's compass. 25.'). The value of the semicircular deviation, on the east or west point, is a key to the value of the deviation caused by the H J)8 NAVIGATION. force in the fore-and-aft line, on every point of the compiiss. Similarly, the value of the semicircular deviation, on tlie north or south point, is a key to the value of the deviation caused by the force in the thwartship line, on every point of the compass. Aa the deviation on any point is made up of that caused by the forces in these two directions, added to that caused by the variable force, it is evident, that if the latter be known (No. 252), and the semicircular deviation be ascertained on two adjacent cardinal points, the deviation table can be completed. When the semicircular deviation is small, the following tab'« will be useful for that purpose : — Semicircular deviation cruised by the san 8 force, on each point, Semiclrcnlar recliouea n gilt ajid left from that car Ural poi nt, through drTiatiun on tlie aJjacen t quadra " point 1ft 2nd 3rd 4th 6th 6tb 7th 8tb 1 „ o . „ , / , , . ( I o 59 55 SO 42 33 23 12 2 I 58 I 40 I 25 I 7 46 23 3 2 57 2 46 2 30 2 7 I 40 I 9 35 3 55 3 42 3 20 2 50 2 13 I 32 47 5 4 54 4 37 4 9 3 32 2 47 ' 55 59 6 5 53 5 33 4 59 4 15 3 20 2 18 I 10 7 652 6 28 5 49 4 57 3 53 2 41 I 22 8 7 5' 7 24 6 39 5 39 4 27 3 4 I 34 9 8 50 8 .9 7 29 6 22 5 00 3 27 I 45 »o 948 9 '4 8 .9 7 4 5 33 3 50 I 57 Example. — The deviation (table 251) having been observed to be 8° 0' E. on the south point, and 7° 10' W. on the west point, what is the deviation on the N.W. b W. point? The semicircular deviation on the south point, allowing for the value in column I., must be 4° E. It is therefore 4° W. on the north point, and, from the above table, 2° 13' W. on N.W. b W., five points from north. The semicircular deviation on the west point must be 7° 5' W., it is therefore 5° 53' W. on N.W. b W., three points fi-om west. Therefore the whole deviation on N.W. b W. must be 2° 13'W. + 5° 53'W. + 4° 25' W. (the value in col. !.) = 12° 31' W. The semicircular deviation being the same in amount, with contrary signs, on opposite points, the deviation on S.E. b E. is 8° 6' E. + 4° 25' W. = 3° 41' E. In the same manner, the devia- tion on every point of the compass can be estimn.ted. There may be circumstances where it would be convenient to ascertain the position of the correctors necessary to apply to a compass, by measuring hor. force (234). The most simple way of looking at the problem is, to consider a ship lying with her head in any known magnetic direction. By placing a horizontal magnet at right angles to the compass needle, and so keeping it, the needle may be made to stand in the direction of the magnetic ixsti;umi;nts of navigation. 99 mcridiai). By placing another horizontal niagni't in the line of the magnetic meridian, the force with which the needle points iriaj- be made equal to the force on shore. Thus, all the forces due to the ship's magnetism, may be counteracted with the ship's head in the one direction. But when the ship's head is moved round, the needle will move away from the magnetic meridian, by reason of the change in the variable force. When the head is in the opposite direction, the deviation will be nearly equal to twice that caused by the variable force, and the needle will point with a force which will differ from the horizontal force on shore, by twice the value of the component of the variable force in the direction of the needle, nearly. Therefore, to counteract the force which causes the semi- circular deviation, the distance of the magnets from the card must be so adjusted, that the needle points with the mean value of the force found with the ship's head in the two directions, and with half the deviation found in the second position. Another way of dealing with the problem is suggested by considering the following facts. If the force with which the needle points is the same when the ship's head is east and west, there can be no constant force in the athwartship line. If it is the same when the ship's head is north and south, there can be no constant force in the fore-and-aft line. Therefore, when these conditions are fulfilled, there can be no semicircular deviation. Further, if the foi-ce is the same on the four cardinal points, there can be no quadrantal deviation. Working by force is a more delicate operation than working by bearings, and, under the circumstances in which the seaman lias generally to work, is scarcely capable of the same degree of accuracy. If advantage be taken of the known direction of docks, wharves, transit and other lines, there will be few occasions where it will be necessary to have recourse to measuring force. But with the two methods available, there should be no detention of ships in port for the purpose of compass adjustment. 256. Hitherto the effects of the vertical component of the ship's forces have not been considered, because a vertical force cannot deflect the compass-needle, right or left. But when a ship heels, a force previously vertical may be no longer so, and the position of the iron about a compass n)ay be so changed, as to introduce a new magnetic force. The deviation, caused by this change in a ship's magnetic forces, is called the Heeling Error. To estimate or correct the heeling error with theoretical accuracy is not an easy problem ; especially in certain positions in a ship, and with the semiuirc'ular deviation uncon-ected. The following remarks must be considered as applying to a compass, in such a position iia is usually selected for a standard compass, and having the semicircular deviation corrected. At a compass so situated, there will be a force upwanlB or dcjwnvviU-ds in the ship, caused by pei'- 1 00 NAVIGATION. maiient magnetism. The value of this force will depeiid, maiiilr, upon the direction in which the ship was built, and the position of the compass in the fore-and-aft line. It may be counteracted by a magnet placed end on (239), and vertically below the centre of the compass. If it is not counteracted, it will, by coming partly on one side when the ship heels, draw the north point of the compass to one side or the other. There will also be a force upwai-ds or downwards in the ship, fioiu the transient magnetism of vertical iron, depending for its value on the earth's vertical force, of which it is a constant fraction. This force, in north magnetic latitude, is that of a nega- tive pole under the compass, changing to positive in south magnetic latitude, drawing the north point of the needle to the high side of the ship in the former case, and to the low side in the latter. This force evidently should not be counteracted by a fixed magnet, but by a bar of soft iron, having, in noi'th magnetic latitude, negative magnetism in the end nearest to, and above, the compass. "05 of tlie earth's vertical force is about a mean value of the vertical force caused by induction therefrom ; therefore, in correcting the heeling error by a vertical magnet, the vertical force of the earth and ship should be brought to about 1'05 of the earth's vertical force, wherever the ship may be. Sometimes the position of the funnel, or an iron mast, may be such, that its vertical transient magnetism counteracts that of the ship ; this will probably be the case in a compass in such a position as d (247). Or it may be counteracted by putting the upper end of the Flinders bar, where one is used, above the level of the compass. Looking at the magnetic condition of athwartship iron, such as beams, passing under the compass, when, from the ship heeling, it departs from the horizontal position, it is evident that the higher ends will liave negative magnetism, drawing the north point of the compass-needle to the high side of the ship in north magnetic latitude. The reverse of this takes place in south magnetic latitude, therefore this force should not be counteracted by a fixed magnet. If a soft iron bar were placed horizontally athwartship, on each side of the compass, the magnetism induced therein would, if they were of suitable size and distance from the compass needle, exactly counteract the magnetism induced in the athwart- ship iron of the ship. This condition is nearly fulfilled by soft iron so placed as to correct the quadrantal deviation, so that no separate corrector is required for this part of the heeling error. Because the transient magnetism of horizontal fore-and-aft iron, below the compass, causes a vertical force which is zei'O when the ship's head is east or west, it is desirable to correct the heeling error when, the ship's head is nearly on those points. Then, if the quadrantal deviation is corrected, and the vertical INSTRUMENTS OF NAVIGATION. 101 force brought by a maijnet to the same value as, or a little niora than, the vertical force ou shore, the heeling error will be practi- cally corrected. The forces which cause the heeling error, by drawing the north end of the needle to one side or the other, must have their maximum effect when the ship's head is north or south. When the ship is rolling, the north end of the needle being drawn to each side alternately, causes the card to be unsteady. This dis- turbance of the eouipass-card has probably been more trouble to the navigator, than the error produced by heel. Thus, in dealing with compass deviation, there are two distinct problems : one, to ascertain its amount ; the other, to get rid of it altogether. At first sight, one or the other of these processes appears unnecessary, and in the early days of iron ships some thought that, with a table of deviation, there was no need for correctors ; others that, if the compass were corrected, there was no need for a table of deviation. Experience has long since shown that neither of these views was correct. Many iron ships could not be navigated unless the compass was, at least, partly corrected. On the other hand, though compasses are frequently BO well adjusted as to be without deviation, there are small changes subsequently which cannot be safely disregarded, render- ing a deviation table necessary. Changes which are gradual can be met by the ordinary daily observations, which should never be omitted ; but there are some changes which are sudden, against which the seaman must be on his guard. If a ship has been steering for some time on one course, she will acquire negative magnetism in the part of the ship towards the south. On first altering course, the north point of the compass is likely to be drawn, for a short time, towards that part of the ship which was previously south. This is espe- cially the case in changing from courses near east or west to those near north or south. Of course, the same effects follow when a ship has been some time in dock. Thin iron structures, such as funnels, funnel casing, or venti- lating cowls, are liable to change their magnetic state from strains or concussion, and so affect the deviation ot a compass placed near. Any shod: or strain which causes iron to vibrate or bend, and so cause movement in its particles, facilitates magnetic change. With the introduction of electric lighting on board ship, came a new form of compass disturbance. The magnetism of the large electro-magnets, in the dynamos at present used, may disturb a compass at the distance of sixty feet. Also, circling round the wires conducting electricity, and at right angles to their direction, is a magnetic force, going in one direction round the wire conducting the direct current, and in the opposite direction round the wire conducting the return current. Thus these forces counteract each other when the conducting wires 102 navigatio:t. uie together, but when they are separated cause a propo-i'tionnl Jisturbauce to the compass. The maximum value of this disturbance, for any speed of the dynamo, is apparent directly the dynamo ia started at that speed. So, by starting and stopping the dynamo, with the ship's head on two adjacent cardinal points, and noting the eifects, the value of the disturbance on every point of the compass can be ascertained. Table 255 will be useful for this purpose. 257. A method of measuring the effects of a ship's magnetic forces, in causing deviation, was introduced by the late Mr. Archibald Smith. He found that the deviation could be expressed, as in the following equation : — Deviation with ship's head on , j^ j ^. ^ . cos f + D . sin 2 (' + E . cos 2 C any point . . . . ) ' ' * ' The factors A, B, C, D, E, are called coefficients, and f is the direction of the ship's head by compass, reckoned round the cii'cle to the right. Therefore, in dealing with the equation, the sea- man, who generally has to deal only with angles not greater than a right angle, must consider the sign of the direction of the head, as well as that of the coefficient, in each term. A, the first term in the expression, is the value of the con- stant deviation (250). It may be found by taking the sum of the deviation on the four cardinal points, and dividing it by four. B is the maximum value of the deviation caused by the force in the fore-and-aft line (253). It is + when the force is towards the ship's head, and — when towai-ds the stern. It maj' be found by adding to the deviation on the east point, the deviation on the v.-est point with its sign changed, and taking half that sura. Any constant force in the fore-and-aft line, which causes this devia- tion, must cause a deviation = B . sin f, the second term of the expression, on every point of the compass. C is the maximum value of the deviation caused by the force in the athwariship line (253). It is 4- when the force is towards the ship's starboard side, and — when towards the port side. It may be found by adding to the deviation on the noi-th point, the deviation on the south point with its sign changed, and taking half that sum. Any constant force in the athwartship line, which causes this deviation, must cause a deviatiou = C . cos 5", the third term in the expression, on every point of the compass. D is the mean value of the deviation on the inter-cardinal points, caused by the vaiiable force (249). It may be found by adding to the deviation on the N.E. and S.W. points, the devia^ tion on the S.E. and N.W. points with the sign changed, and taking the fourth part of that sum. A force varying regularly, and causing this deviation, must cause a deviation = D . sin 2 f, the fourth term of the expression, on every point of the compass. £ is the mean value of the deviation on the cardinal points, 1^TSTKUMI■:NTS OF NAVIGATION. 103 can?etl bj the variabK' force (21-9). It may be found by adding' to the deviation on the north and south points, the deviation on the east and wast points with the sign changed, and taking the fourth part of that sum. A force varying regularly, and causing this deviation, must cause a deviation = E . cos 2f', the fifth term of the expression, on every point of the compass. The existence of the E shows that the axes are oblique (249). It is obvious that the foregoing statement of the effect of the forces in causing deviation is true only when each force is the only disturbing force on the needle ; it is true enough when those forces are small : in that case the resulting deviation is also small, and the sum of the five terms is equal thereto ; when the deviation is large, the coefficients must be determined with more exactness. With such deviations as are usually found, since the general adoption of compass adjustment, the method here given is sufficiently exact. The student must not consider the coefiicients as forces, or as in any way causing the deviation ; they merely measure it, with more or less exactness. And by their means the parts of the deviation can be particularised, in speaking and in writing, and a record of its value kept in five terms, of which two are generally zero. Excepting for this purpose, the treatment of the subject by coefficients, especially laborious methods of determining their exact values, and of deriving the ship's magnetic forces there- from, has never been greatly esteemed by navigators. 258. Professor Airy made use of the terms Eed and Blue, to indicate the two kinds or states of magnetism, of the nortli and south ends of the compass needle respectively. These terms have been of great use, especially in making clear, by coloured diagrams, the distribution of magnetism in iron ships. The terms positive and negative have been used in this chapter, being in accord with the terms used in the kindred science of electricity, which is daily becoming of more importance to seamen.* The subject of compass deviation and adjustment was tho- roughly investigated by a body of scientific men, shipowners, and others, interested in the subject, called the Liverpool Compass Committee. The results of their labours were published, in language intelligible to seamen, in three most valuable reports to the Board of Trade, 1856, 1857, 18GI. • I'rofessor (now Sir) George Biddell Airy, K.C.B., lias lived t.) see bis accurate and tlioroughly practical method of iidjiisting compasses, diviscd half a century ago, over- come all o|ipo>itiun, and he now, and for many years pas-t, uuiversally adopted. He has in other ways furthered ihc science of navigation, but in I'aciliiaiiDg the navigation o( iron ships he is pre-eminent. KxVVKiATION. ITie following Notes are the result of recent theory and experience. The numbers refer to Articles in the jfyresent edition. Alt. 215. The method of suspension by india-rubber has been discontinued, owing to its rajiid deterioration when exposed to heat and wet. 216. In Lord Kelvin's (Thomson) compasses the outer graduation of the numerals is inverted in the Navigational or Standard Compass to enable the card to be read direct with the azimuth mirror. The average period of a Thomson's card varies from thirty seconds for a ten-inch card to thirteen and a half seconds for a four-inch one. 219. The Variation at Greenwich was (1899) 16° 34' westerly, de- creasing 7' annually. 220. The simultaneous appearance of auroras and disturbances of the magnetic needle (magnetic storms) are manifestations of the same cause. The late Father Secchi held that thunderstorms exer- cised a perceptible influence on the magnetic needle. The disturbing element of land on the compass needle is recognised to be submarine. Theory confirmed by experience show that if the rocks are the upper extremities of a ridge in north magnetic latitudes they would attract and in southern repel, the red (paragraph 239) end of a compass needle. 223. The prefix correct to true, magnetic and compass courses is being discontinued, a true course is a compass one corrected for varia- tion and deviation ; a magnetic course, the same corrected for devia- tion, and a compass course, one uncorrected for variation and deviation. 232. The Dip of the needle at Greenwich was (1899) 67° 10', de- creasing \'l annually. 237. The expression, " magnetism by induction from the earth " is seldom used ; the magnetism of both earth and soft iron are produced by the same lines of magnetic force. 239. To avoid ambiguity, the pole of a magnet that attracts the north-seeking end of the needle is called blue and the repelling one red, bearing in mind the pole in the north end of a compass needle is a true south pole, and that in the south end of a compass needle is a true north pole. 244. Read paragraph at 237. Gaussin error is often developed by magnetic induction in a ship's iron beams, more especially when ])rOf>eeding east and west ; in fast Atlantic liners a Gaussin error of 8° to 10° is not unusual daring a voyage across the Atlantic. 249. A compass is usually corrected in the following order : the quaflrantal error, the heeling error, and lastly the semi-circular error. 256. In merchant vessels arrangements are usually made to place mSTRtlMENTS OF NAVIGATION. IOIJB the navigational compass beyond the magnetic field of the dynamo, but the necessaiy arrangements in a man-of-war may prevent this being carried out. A compass if within the magnetic field of a dynamo will be disturbed, the error altering with change of azimuth.' In the general tj-pe of dynamo suppUed to H.M. ships, designed for 80 volts at the terminals, the minimum distance of a compass should be 60 feet from a 300-ampere machine, increased to 70 feet from a 400-ampere one. A 600-amp6re machine being armour-clad and multipolar produces no disturbance on a compass 15 feet away. In the " Destroyers " the con-ection is made by an electro-magnet at the foot of the compass pedestal, with its poles reversed to those of the dynamo ; in second class cruisers (Apollo class) by exciting the shunt coils of both dpiamos, when only one is in use, the resulting disturbances are neutralised, provided the poles of the dynamos are gymmetrical to the middle line. In the electric lighting of a compai^s, the current is usually con- veyed to a 16 c.p. lamp by a twin cable, protected by phosphor- bronze braiding. The best po.sition is to place the lamp vertically above the axis of the compass needle ; occasionally a disturbance arises from the inductive effect due to the current in the filament of the lamp itself. A small electric light (half-candle power) is found useful for star azimuths at night or if fitted to a sextant for stellar observations. * For detailed information see The Hfrtriner'i Covipaas in an Iron S/iip, by (Captain J. ^Vhitly Dixon, B.N., sold by J. V. Potter, 146 Miooriei, Lun.iuu, K 104 KA VI G AXIOM. 11. The Log and Glasses. 1. The Log. "J59. The log consists of the log-ship and line. The log-flliip is a thin wooden quadi-ant, of about five inches radius ; the cir- ciihir edge is loaded with lead, to make it float upright, and at each end is a hole. The inner end of the log-line is fastened to a reel, the other is rove through the log-ship and knotted ; and a piece of about eight inches of the same line is spliced into it at this distance from the log-ship, having at the other end a peg of wood, or bone, which, when the log is hove, is pressed firmly into the unoccupied hole. At ten or twelve fathoms from the log-ship a bit of buntin rag is placed, to mark off a sufficient quantity of line, called stray- line, to let the log go clear of the ship before the time is counted. 260. The log-line is divided into equal portions, called knots, at each of which a bit of string, with the number of knots upon it, is put through the strands. The length of a knot depends on the number of seconds which the glasses measure, and is thus determined : The No. of feet in I knot : No. of feet in i mile : : No. of seconds of tlie glass : 3600 (ihc No. of seconds in an liour). The nautical mile being about 6080 feet,* we have, for the glass of 30 seconds, the knot = -3^° = 50-7 feet, or 50 feet 8 inches, for the glass of 28 seconds, the knot = ^^^ = 47-3 inches, or 47 feet 4 inches ; and so for any other glass. 261. The knot is supposed to be divided into eight equal parts, or fathoms (which they are very nearly). In the Royal Navy the kjiot is divided into tenths and the even fathoms only are reckoned, for the convenience of adding up the distance on the log-boa rd.f 262. The log-line should be repeatedly examined, by comparing each knot with the distance between the nails, which are (or should be) i^hieed oti the deck tor this piirpose, at the proper distance. The line should be wet whenever it is required thus to remeasure it, or to verify the marks. * The Gengiaphical Mile is generally defined to be tlic lentrih of a niinnte of ir? 1:2 iVc eartli's eqnjtor ; but the Nautical Mile as defined by hydiographers is the length of a minute of the meridian, and is slightly difterent for every ilitferent latitude. (6« Table 64a.) It is equal to a minute of arc in a eirile, whose radius is the radius of the curvature of the met idian, at the latitude of the place. t It is, of course, more systematic to divide the knot or mile into tenttis, ns in th« Traverse Ta'ile, instend of eighths ; btit Muyle tenths and fathoms may be used for each olhfs without sensible error. INSTRUMENTS OF NAVIGATION. 105 '26'^. As t[\e manner of heaving the log must be learned at sea. it is onl^ necessary to remark, for reference, tliat the line is to be faked in the hand, not coiled ; that the log-ship is to he thrown out well to leeward to clear the eddies near the wake, and in such a manner that iv may enter the water perpendicularly, and not fall flat upon it ; and that before a heavy sea the line should be paid out rapidly when the stern is rising, but when the stern is falling, as this motion slacks the line, the reel should be retarded. 264. (2) Massei/s fjog shews the distance actually gone by the ship through the water, liy means of the revolutions of a Hy towed astern, wliith are registered on a dial-plate. This log is highly approved in practice.* •235. When the water is shoal, and the set of the tides or current much atTected by the irregularity of the channel, or other causes ; and when, at the same time, either the ship is altogether out of sight of land, or the shore presents no distinct objects by which to fix her position, recourse may be had to the ground log. This is a small lead, with a line divided like the log-line ; the lead remaining fixed at the bottom, the line exhibits the etfect of the combined motion of the ship through the water, and that of the water itself, or the cur- rent ; and therefore the course (by compass) and di.stance made good are obtained at once.f Caution. — Logs, whether patent or common, are unsatisfactory instruments in these days of high speed. No patent log yet in- vented will stand the wear and tear of a fast ship for any length of time. To avoid this wear and tear they should be used only when coasting or in with the land. They will tell a different story in a head sea to what they do in a following sea. In slow steamers and sailing ships they are naturally more reliable. Still, logs must be used ; but it must be remembered they are beset with ivipedimerds, and their indications must not be implicitly trusted in critical times. Ry practice, seamen learn to estimate the rate of progress of the sliij) closely by the number of revolutions in a given time made by tlie engines; but this is only speed through the water ; the sailor has to consider carefully what that unstable element has also been doing. J Further, though ships may now better preserve a given course, and the di.stance run may be estimated more accurately than formerly, there are in modem iron ships elements of uncertainty about D.R. which still makes it perilous to close the land unless there are means of knowing with some certainty the ship's proximity thereto, especially where land has a bad reputation, as Ushant, C. Kinisterre, C. (iuardafui. Mocha I. in South America, &c. * Other logs on tins principle hftve since been invented and are in common use: DoMl.ly, Walker's laffrail log. They should be well oiled, and stowed away dean. t in numerous passages up and down the rivor Plate, whore the above circumstances ccnriir. Captain 0,,rd.,ii T. Falcon, in 1818-I9-20, made constant use of this log. J Stt Admiralty Current CliarLs, Tide Tables, and Sailing I/ip ctioiie, Nos. 951, 1)52. lUG NAVIGATION^. 2G6. (3^ The Glauses. — The long glass runs out in 30' or in 28"; the short glass runs out in half the time of the long one. When the ship goes more than five knots, the short glass is used, and the number of knots shewn is doubled. 267. The sand-glasses should frequently be examined by a seconds watch, as in damp weather they are often retarded, and sometimes hang altogether. One end is stopped with a cork, which is taken out to dry the sand, or to change its quantity. 268. When either the line or the glass is faulty, or when a line and glass not duly proportioned to each other are employed, the distance run is found as follows: — The number of feet in l*" is to the number of feet run out in an observed number of seconds, as 3600 (seconds in an hour) are to the observed number of seconds. Ex. Suppose 190 feet of line are run out in 22* : required the rate. The number of feet run out in l"" : 190 :: 3600" : 22'; hence the number of feet = L22Ji3529 = 31090 feet; which, divided by 6000 (as near enough), gives S'Z miles. CHAPTER III. The SailIxNGS. I. Plane Sailing, with Tkaverse, Current, and Windward Sailings. II. Parallel Sailing, with Middle Latitude, AND MERCATOR'S SAILINGS. III. GrEAT CiRCLE SAILING. 269. In considering the place of a ship at sea, with reference to any other place which she has left, or to which she is bound, these five things are involved : the Course, Distance, Difference of Lati- tude, Departure, and Difference of Longitude. 270. In practice these two general questions occur. 1st. The course and distance from one place in given latitude and longitude to another are given, and it is required to find the latitude and longitude of the otlier place. 2d. The latitudes and longitudes of two places are given, and it is required to find the course and distance from one to the other. The methods of solution, that is, the rules of calculation, by which the answers to such questions are obtained, are commonly termed Sailings. I. Plane Sailing. 271. In Plane Sailing, as the term implies, the path of the ship is supposed to be described on a plane surface. If the ship sails 1 mile on a given comse, she makes a certain D. lilt, and Dep. ; in sailing a second mile, on the same course, she THE S.\tLIN(.8. 107 imkf'rt good tlic' isaiiif 1). lar. aiifl Dep. as before. Thus the D. lat. Kiiil I)e|j. for 2 miles of Di>t. are twice those for 1 mile; for ;J miles of Di-^t. tliey are three times those for 1 mile, and so on ; that is, the total D. lat. and Dep. made good are proportional to the Dist. on the s|)hcre as they would be on a plane. Plane Sailing, accordingly, treats of the relations of the Course. Dist., D. lat., and Dep., and applies to right-angled triangles generally. But each mile of Dep. which the ship makes good corresponds to a Diff. of Long, which is different according to the latitude in vhich the ship moves (Note, p. 68), that is, there is no comstunf. pro- portion between the Dep. and Diff. Long, in two different lati- tudes, and therefore a question in which Diff. Long, is concerned is not within the province of Plane Sailing, except the case in which the ship is on or near the equator, where Dep. and D. Long, are the same thing. 272. (1.) The proportions, No. 162, p. 46, as adapted to the figures, No. 200, p. 59 (or to the third figure of No. 163, where the course is the angle ABC), give the proportions or canons, as they are called, of Plane .Sailing, ^^'e employ the following: Disf. : Dej.. : :: rad. ( = .) : 8in. Co., whence, Dep. = Dist. x sin . Co. (»•) Uist. : D. Lat. : I : COS. Co., D. Lat. = Dist. X cos .Co. (20 . I-at. : Dep. : 1 : tan. Co., Dep. = D. Lat. x tan . Co. (3.) . U: . DUt. : 1 : sec. Co., Dist. =D. Ut. xsec Co. (5.) (6) (a.) These equations put into logaritlims by the rules Nos. 64 and 55, p. 20, become Log. Dep. = log. Dist. + log. sin. Co. — lo (1.) Log. D. Lat. = log. Dist. +log. cos. Co.-io (2.) Log. Dep. = log. D. Lat. +log. tin. Co. — lo (3.) I-og. tan. Co. = log. Dep. + lo — log. D. Lat. (4.) Log. Dist. = log. D. Lat +log. sec. Co.— lo (5.) Log. sec. Co. = log. Dist. + lo — log. D. Lat. (C.) Which logarithmic equations contain the rules employed. On ordinary occasions four places arc enough. Case I. Given the course and distance, to tiiid the difference of iBtitude and departure. F.i. 1. .\ ship sails N.W. by N. 03 miles from lat. 49'' 30' N. ; find the D. Lat. and Dep. and also tlie Lat. in. 278. By Tn.fpecfion. Open Table 2 at 3 Points,* and against Hie Dist. 1*03 stand D. Lat. 85-6 and Dep. b7-2. Then 85-6 or 1° 26'-0 added to 49" 30' gives Lat. in 50' 55'-6 N. Whenever Ihc rniir»c i« given in points or divisions of a poinl, it nuist he turned d.gries (213; heluic entering 'I'rnvei-.e 'J'.!!.).; 1. If)X NAVrOATTON 27i. Bi/ Compulation. (1.) For (he D. Lat. To tlie log. cos. ot Dhe Oouvse (Table G8) add the log. of the Dist. (Tabk- 6 t) ; the Biiui {rejecting 10 from the index) is the log. of the D. Lat. (2.) For the Dep. To the log. sine of\hc Course add the log. of the Dist..; the sum (rejecting 10) is the leg. of tlie De\t. above. Course 3 points, Dist. 103. cos 9-9198 log. 20li8 log. 1*9326 (Tliis is tlie Canon (i.) in No. 272.) 3 points, or 33 45 Dist. 103 D. Lat. 8 s Course 33^45 Dist. 103 Dep. 57-2 (Tliis is the Canon ( 1 9'744/ 275. By Construction. Draw a line C N towards the nortli for the meridian. From the Lieutre C, witli the chord of 00° as radius, de- scribe a:i arc on the west side of C N, and lay otl" the chord of three ])oiiits, or 33"! to a (No. 107). Through a draw C a, this gives tlie angle N Ca equal to the Course, or three points ; lay off from a scale of equal parts C A equal to the Dist. 103; draw .\ B perpendicular to C N, then C B will shew on the same scale the D. Lat. 85-6, and A B the Dep. 57-2. Ex. 2 .V ship sails Dep., and also the Lat. S. 72° W. 216 miles from lat. 14° 1 1' N. : required the D. LhI. and il Dist. 216 05-4. Bi/ Inspection. The Course 71° and Dist. 216 give D. Lat. 66-7 and Dki Then 66'7, or 1' d'--;, subtruoted from 14° 1 1' N. leaves Lat. in 13° 4'-3 N. By Computation. Course 11° log. cos. 9-4900 I Course 72° log. sin. 9-9782 Dist. 216 loK V3345 Uist. 216 lug- 2-3345 D. Lat. 66-7 log. 1-8245 I t»^-f- ^°5'4 '"g- ^'i'-l 'r^\ By Construction. Draw & line C S to the soutliward for the meridian. By tlie chord of 60° lay off the arc 7 2 ^ to the westward, and draw CA equal to 216; draw AB perpendiciUar to C S, then C B is the D. Lat. 66-7, and A B the Dep. 205-4. These two e.xanijjles of construction are sufficient for all varieties of Case L When the course is to the eastward, C .\ is drawn on tiie riiiht side of the niej'idian C N or C S instead of the left side. Case IL Given the course and difference of latitude, to find tlie distance and the departure. Ex. 1. A ship sailing W.S.W. makes 47 miles D. Lat. : find the Dist. run and the Dep. 276. Bi/ Inxpection. Enter Table 1 with the Course fi points look in the D. Lat. colunm for 47; the nearest to -47 is 47- 1, a Ih« Ijit. of tlie ship is, from the nature of the case, already ^iveii. 277. By Cnmpiitntion. (1.) For the Dist. To the log. sec. of the Course add tiie log. of tlie 13. Lat. ; the sum (rejecting 10) i§ thb lo^. of tlie Uist. ('2.) For tlie Dcp. To the log. tan. of the Course add tiie log. o( (he D. Lat. ; the sum (rejecting 10) is the log. of the Dep. 6 points, or 67" 30' log. sec. 0-4172 D. Lat. 47 log. 1-6721 Dist. 122-8 log. TxSgj (This is tlie Canon (5.) in No. 272.) Course 67° 30' log. tan. 0-382S D. Lat. 47 log. 1-6721 DeI". 113-5 log. 2-0549 (This in the Canon (3.) in No. 272.) 278. J3j/ Construction. Draw the meridian line CS; lay off the course, or angle 8 C A, 6 points (No. 107); from C lay off C B the D. Lat. 47 ; draw B .-V peruendicular to C S, then C A is the Dist. and A B the Dep. This example will suffice for all varieties of Case IL When the course is to the northward, C N is drawn up- wards insteatl of C S downwards; and when the course is to the eastward, ' C A is to he drawn on the right siile of the meridian instead of the left side. Ex. 2. A sliip sails N. 54° E. and makes 119 miles D. Lat. : required the Distance lun «nd the Departure. By Iiurpection. Course 54° in Table 1, and D. Lat. 119-3, S"'. Lat 52 log. 1-7160 CoDESE 59^ I log. sec. 0-2883 (This is the Canon (6.) No. 272.) Course 59° i' log. sin. 9'933i Dist. 10 1 log. 2-0043 Dep. S6-6 log. 1-9374 (Thii! i. the Canon (i ) No. 272.) 284. Jiy Construction. Draw the meridian C S. Take C B, tlie D. Lat. 52, and through B draw BA per|)en- dicular to C S. Froui C as centre, with tiie Dist. 101 as radius, describe an arc cutting B A in A ; then the Course, S C A, measures 59°, and B A, the Dep., measures 86 6. This one example of construction will be sufficient. Eji. 1. Ei. 2. El. 3. di. 4. A ship sails from Flanibnrmigh He,u quired her Lat. in, and Dep. Ans. D. La Ejamples far Ejcercue. 54" 7' N., E. by N. i N. 264 •6N., Lat. in, 55''24'N.; D A ship from Lat. 49° 57' N. sails S.W. by W. 244 ni Dep. Ans. La s : required her Lat. in, an IN 47" 41' N. i Dep. 202-' A slii]i sail> S E. by E. from Lat. 1° 45' N., until =he arrives in Lat. o" 31' S. : quired her Dist. and Dep. .\ns. Dist. 244-8 ; Dep. 2c A ship from St. Helena in Lat 1 5° 55' S. sails N.W. \ W. till she is in Lat. 1 3° i find the distance she has run, and the Dep. Ans. Dist. 274-3 I Dep. K». 5. A sbii PS 135 miles northing, and 87-7 miles of Dep. westing: required hei id Dist. made good. An«. Coukse N. 33" \\. ; DiST. 161 n.ilc*. TIIK SAII,IN(iS. ]] 1 B> 6. A ship sMil.i 1 10 miles between N. anJ E., and makes i6o'-9 D. Lat : find the Coui>t mid Oep. Ans. Course N. 40° E. ; Uep. 135 milcg. El. 7. \ ship sails 244 miles between S. and W., and makes 136' D. Lat.; find llie Course and Dep. Ans. Course S. 56° 8' W. : Dei. io>-6. 1 . Resolution of one Course upon another. *28o. It is sometimes required to resolve the distance run upon a given course into the distance upon a proposed course £x. A ship is making good S. 70° W. 5} miles an hour: at what rate ia she neariog • port bearing S.W. } Draw the meiidian, A S, of the ship : of the port, S.W., and the Course S. 70' present the rate per liour (or for a smaller interval), as 54 knots. B then is the place of the ship at the end of this interval. The distancte, A P of the port, being very great, as compared with A B, a circle B D, described from P as a centre, is nearly a right line, and perp. to A P, and cuts off A D, the dist. by which the ship has neared P in an hour. Now A D is the D. Lat. to the Dist. AB, and the angle BAD as Course. BAD equal to "o"' — 45°, or 25°, and Dist. 5^, give AD equal to 5 knots, the rate required, and A D is A B resolved in the direction AP. p " When the number of degrees between the given and proposed courses e.xcecds 90, the ship is increasing lier distance from the port instead of closing it. It is proper to observe, that the ciiange in the distance of the port, made by the ship wiien not .steering- directly for it, is true only i'or its present bearing, and tiierefore iiulds only for a short time. 2. Traverse SaiUiiy. 286. This is a variety of plane sailing in which the ship makes two or more courses in succession. The process of reducing several courses, with the distances run on each, to the single course and distance which the ship would have mac'e good if she had sailed at once from the place she first left, to the place at which she last arrived, is called working a traverse. 287. To work a Traverse. (1.) Draw six vertical lines. Head the space to the left Courses, the first column Distances, the next two columns D. Lat. ; marking the first N. and tiie second S. ; head the last two columns Dep., marking one E. and the other W. This forms a skeleton Traverse Table. (2.) Set down the Courses, and the Distances against them, in order; look out in Table 1, the D. Lat. and Dep. to each Course and Distance. When the ship makes northing (that is, when the Course has an N. in it), set the D. Lat. in the N. column, other- wise in the S. column. When the ship makes easting (that is, when the Course has an E. in it), set the Dep. in the E. column, otherwise in the W. column. \3.) Add the D. Lats. in each column ; write the lesser of the two sums under the greater, atid take their ditt'erence. Do 'lie same with the Departures. 11 '2 MAVIftATlOfK. ('I.; Thesfi differences are the D. Lat. and Dep. made good on the whole, and each takes the name of the column it stands in. The course and distance are then found by No. 279. It may be advisable for a bcoinner, before he proceeds to take out the quantities fioni the Traverse Table, to write a dash in all places not to be occupied by a D. Lat. or a Dep., in order to avoid writing a quantity in the wrong column. The first example only is thus marked, because such helps are useless to an expert computer. Es. A ship sails S.W. by S. 24 miles; N.N.W. 57 miles ; S.E by E. J E. 84 uules i »nd South 3 5 miles : find the Course and Distance made good. Co>,.e, Disl, D. Lat. Dep. N. 1 S. E. 1 W. S.W. by S. N.N.W. S.E.byE.4E. South. ;; 55 5^-7 20-0 39-6 35-0 74-' 13-3 21-8 5^-7 94-6 52-7 74'' 35' 35'' 41-9 39-0 The D. Lat. 41 9 and Dep. 39-0, are found at 43° against the Dist. 57. Hence, since the ship has by the Traverse Table made southing and easting upon the whole, the Course is S. 43" E., and Dist. 57 miles. By Computation. Each portion of the process having already been separately considered in plane sailing, nothing remains to bp added here. 288. By Coiistriiclion. With the chord of 60 describe a circle; draw the meridian N S, and mark the centre C. By means of the scale of chords lay off S 1, ecpial to 3 points, or S.W. by S., for the first course. Lay off N 2, equal to 2 points, or N.N.W., for the second course. Lay off S 3, equal to 5i points, or S.E. by E. i E., for the third course. The fourth course, or south, is already laid off", being on the meridian. Now lay the edge of the ruler on C and on the point 1, and lay off by the compasses, or a scale of equal parts, the first distance, C a, 24. Place the edge of the ruler on «, laying it parallel to the line joining C and the point 2, and lay off the second distance, a b, 57. Place the ruler on the point b, laying it parallel to the line jjining C and the point 3, and lay off the third distance, be, 84. Lay the ruler on c, parallel to the meridian, and lay off cd, the fourth distance, 35. The point d is therefore the place at which the ship has arrived. Join Cd, then SCrf is the course, 43°, and Cd Uiti distance, 57. Also, ilrawiiig Dd perpendicular to OS, give* Tin- SAll.lNCiS. 13 DC the 1). Lat., and I)r/ tlir J^eji. wliieli will be found to measure i; y aiKJ 390. \ \ -y Tliu circle is here drawn outside the traverses altogether, without regard to the dimensions of the scale of chords, merely to shew the process more clearly. This example, after the practice which the learner will have al- ready had in drawing the figures in the preceding articles, will be siitficient for any ease that may occur. Kx. 2. A .hip sails N.N.E. ii miles; N.l miles J N N.W. 4 miles : required the Cours as; E. ^ N. 14 iiiilet ; : made good. WVst, Co„r., r.isi. N. s. E. 1 N.N.E. ,, .0-2 4-i N E. 3 E. 39 23-2 3'-3 E.IN. '4 '■4 ■3-9 West. ■■) '9 N.N.W. 4 3-7 ■•5 38-5 494 20-5 2C-5 28-9 The D. Lat. 38-5 in the N. col., and Dep. 289 in the E. col give Ik.irKSE N. 37" E., Dist. 4H miles. 114 NAVrCATlON. 289. The D. Lat. made good on the whole, as tluis found, boin-j applied to the Lat. left, gives the Lat. in. Thus, suppose in the above example the ship left Lat. 38'' 40' S. ; then :38'-5 northinj; places her in Lat. 38° I' 5 S* Examples for Exercise. Ex. I. A ship from Cape St. Vincent, in lat. 37° 3' N.. 43 mUes, S.E. hy S. 64 miles, and N.N.E. 2 made good, and also lier Latitude in. Ans. Course S. 34° E.-, Dist. 89 miles; Lat. in 35'' 49' N. Ex. 2. A ship from Cape Amber (N.E. extremity of Madagascar), in lat. 1 1"' 5;' S.» sailed as follows : — S S.E 4 E. 33 miles, S.W. by W. 40 miles, S.E. by S 44 miles ; N. 36 miles, S,W. by S. 44 miles, S.E. by E. 40 miles, S.S.W. i W. 33 miles • required the Course and Distance made good, and also what Latitude she is in. Ans. Course due South j Dist 140 miles ; the Lat. in is 14° 17' S. Ex. 3. Yesterday, at noon, we were in lat. zS' 34' N , and since then we liuve sailed N E. I E. 62 mUes, N. by E. 16 miles, E. J N. 40 miles, N.E. 3 E. 29 miles N. by W. 30 miles, and N. | W. 14 miles • what Course and Distance have w, made good, and what is our present Lat. ? Ans. Course N. 43°E. orNE. |N. ; Dist. 15!! miles; Lat. in 30° 29' N. Ejc. 4 . Yesterday, at noon, we were in lat. 44° 10' N., and since then we sailed the following courses (all true): S. 69^ W. 4 miles, S. 58° E. 15 miles, S. 66= E. 8 miles, S 66^ W. 12 miles, S. 1° E. 6 miles, S. 55° W. 2 miles, N. 21° E. 2 mUes, S 55°W. 28 miles. S. 32°E. 14 miles, S. 5 5"W. 4 miles : find what Course and Distance the ship ha» made good, and what is her present Lat. Ans. Con»gK S. I5°\V.; Disr. 55-0 miles; Lat. in 43° 17'N. 3. Current Sailing. 290. A current is named after the point towards which it runs or sets: thus, a current setting towards S.E. is called a south-east cur- rent. The mode adopted in speaking- of the wind, which is named according to tiie point from which it blows, is thus reversed in speaking of a current. f The term set, which is used to describe the direction of the cur- rent, is employed in the same way as in taking a bearing (No. 201) ; but it is necessary for tlie complete description of the current to state also its drift, that is, the distance through which the ship is carried or driven by its action. J 291. When the rate of a current per hour is known, the drift for iny number of hours is found by multiplying the rate by the number Df hours. Li like manner, when the drift in a number of hours has been * The beginner will proceed now to parallel saiUng, because, though current sailing Vl strictly a branch of plane sailing, yet some of the examples, for the convenience of arrangB- ment, involve the consideration of longitude. t It is easy to conceive that people would name a wind according to the quarter it blo»-| from, as bringing heat or cold, rain, &c., and a current according to the quaiter to which it carries them. X These terms have not in general been emjiloyed with sutticicnt precision. The term "drift" has been defined as the distance run per liour, or rate of the current. But as a seciind term for rate is superfluous, and as it is convenient to have a term expressive of the distance through which the ship has been carried by the current in any interval of time, we have used the word drift in the latter sense only. Thus the terms sel and drift are ii»;-J in speaking of the current as course and distatice are in speaking of the ship.. l.lNfJS, n.-i i.lint,^ tl.( ■ niiiiilioi- ( .riMii..s.,f.h<. Ex. by the c its rate. u;re, A ship a found to have drifted iit42 miles in 21 hours : required a.ceilaiiied, tlip ralo is fomiil by ili drift l)v tiie miinljer of Iiouin. Ex. i. A current nins z': quired its drift m 1 3 hours. '2!}2. Since tlie current sets tlie ship in a certain direction and nt a certain rate, while tlie shi]) herself is going tluough the water in another direction and at another rate, the course of a ship affected by a current becomes in general a case of traverse sailing, in which there are two courses and distances. Thus current sailing is analogous to traverse sailing, the two courses, instead of following in succession, being here considered as taking place at the same time. Tlie subjects for consideration in this section are, finding the place of a ship afl'ected by a current ; detennining the course under a par- ticular condition ; and, lastly, finding the motion of the current itself. Case I. Given the course steeret lo the weather beam of the chaser, the latter, however great her superioritj' of sailing, ceiscj to neiir the chase. See Naut. .Mag. 1838, .\ri. " Chasing," p. -146. TIIK SAILINCS ii;) ci.led tint no g-ouiitl or time is lost in stays: the fipplication of tlic Btiove rule, therefore, depends entirely on the probability of a chaiij;e of wind. In this subdivision \vc consider merely the general princijile o( wilino; with a foul wind. Other points involved in Shaping thf^ Course, as the combination of a currt'nt with a foul wind, the selec- tion of such a course as may, in certain cases, convert a foul wind into a fair one, the ttteets of local deviation which have been observed while sailing on diti'erent tacks, will be treated in the Chapter or Navigating the Ship, under the heads " Shaping the Course," " Erro' of the Course." 11. 1'arallel Sailing. 301. When two places lie on the same parallel of latitude, or due east and vvest of eacli other, the distance between them, esti- mated along a parallel, or E. and W. (which is all departure), i* converted into diH'erence of longitude; or, on the other hand, theii difference of longitude is converted into distance, — by the rules of Parallel Sailing. The principles of Parallel Sailing are contained in the t\\o fol- lowing propositions. 3U'2. Prop. A parallel of latitude is a circle of w Iiich the radius is proportional to the cosine of the latitude. Let EPQ be part of a meridian, p P the pole, E Q a diameter of the e<|uator, A a place whose latitude is the arc A H Take B Q equal to A E ; then B is the opposite point to A on the same parallel. Join A B crossing C P in n. ^ Suppose now a ship to move from A round the polar a.xis C P, preserving the same lat., or the angle PC A constant; then at the end of half a ^evolution she will be at B, and PCB will be equal to PCA. Then CA and (J B being equal, each being a radius, and the angles PC A, P C B, equal, and C n common to the two triangles AC?;, BC?), these are equal (No. 117). Hence A n is equal to B « ; and this holds for every point of the parallel. Hence A and B are on the circumference of a circle whose centre is n, in the line or diameter joining any two opposite |><)ints. Now A n (see tig. p. 44) is equal to the cosine of the arc A E, C E being radius; hence CE : An :: rafl. (= 1) : cos lat., which was to be j)roved. ■\m Prop. The lentrth of a ciicMlar arc is ]iro|)()rtional to its radius. Or, the Icnglh of A B : the length of ub W C .\ ; C.(. 120 NAVIGATION. C is tlie couuiioii ceiitie of tlie arcs A B, ub. Divide the angle C into any number of equal parts, as for ex. four, by tlie lines (J D, C E, OF; join the points A and D, &e. by the chords AD, D E, &o. Then tlie sides tl A, CD, &e. being equal, and the angles A C D, D C E, &c. being equal, the bases A D, D E, &c. are all equal (No. 117.) In like manner the chords ad, de, kc. "' ure all equal. Now the triangles CAD, Cad, being isosceles, and having one angle A CD common, have the remaining angles equal; they are thus equiangular, and therefore similar (148 cor.), and their sides are proportional (146) ; hence A D : « rf :*. C A : C a. We may multiply both terms of the ratio A D : a rf by anj number without altering its value (Nos. 37 and 7), whence 4 A D ; 4 « f/ :: C A : C «. Now 4 A D is the sum of the four equal chords A D, D E, &c., and 4 ad is that of the chords a d, de, &c. Hence, The sum of the equal chords of A B ; sum of the same number of equal chords of a i : : C A : C «. This proportion is evidently true, whatever be the number o( equal parts into which the angle C is divided. It would therefore hold equally for an immensely increased number of diminished chords, as for ex. of 1', or 1", or a miliiontli of 1", or infinitely less; it therefore holds of the aic itself, which we may conceive to he composed of an indetinitely great number of indefinitely small por- tions, each of which is aic or chord indifferently,* or arc A B ; arc a b w C A ; C a. (1). If A B be tlie equator, and a h a parallel, then C A : C « :; 1 : cos lat. Whence A B : « 6 : : I : cos lat. And since Diff. Long, is an arc of the equator, and an arc mea- sured parallel to it in any other latitude is called Dep., we have, D. Long. : Dep. :: i '. COS. lat., whence Dep. =D. Long, x cos. lat. ... (I) Dep. : D. Long. : : i : sec. lat., (162 (2) (4)) D. Long. = Dep. x see. lat (2) These are the equations for Parallel Sailing. (2), These equations, in logarithms, become Log Dep.^Iog. D. Long. + log. cos. lat (1) Log. D. Long.=log. Dep. +log. sec. lat. — lo ... (2) Case I. Given the distance run on a given parallel of latitude, to find the difference of longitude. 304. By Inspection. (1.) Enter the Traverse Table with the lati- tude as a course, and look in the D. Lat. column for the given distance; the Dist. against this is the Diff. Long, required. Ab, from the nature of the case, the sum of all the chords ;h it maj- approach indefinitelv near it, the arc is said to be 1? inereaied indefinitely. THE 8A1L1NOH. 121 Ex. A ihip rune 143 miles due W. in Lat. 38' 11': required the dlff. long, she maknj The lat. 38° as course, and 143 in the D. I.at. column, give the Dist. 181, or 3° i' : the UiFF. Long, required. (2.) Or employ Table 3, as directed in the Explanation of tlic Tables. 306. By Computation. To the log. sec. of the Lat. add the lojj. of the Dist. ; the sum (rejecting 10) is the log. of the Dirt'. Long. Ex. above. Liit. 38° 11' log. sec. 01046 Dist. 143 log 2;2_,53_ DiFF. Long. 181-9 log- 2-2599 ;i(Mj. Bif Construction. Draw a line AB cast and west, and lay off 143 on if; lay off the angle BAG equal to the Lat. or 38° in this case ; draw B C per- pendicular to A B, and meeting A C in C. Then AC is the Diff. Long, re- .luired. ^ Case IL Given the Diff. Long, of two places on the same parallel, to find their distance as measured along the parallel. .307. By Inspection. (1.) Enter the Traverse Table with the Lat. as course and the Diff. Long, as distance; the D. Lat. is the distance required. Ex. The diff. long, of two places in the patalie'i of 53° 10' is 12° 14': required their dU- rsncc as measured along their parallel. The lat. ^y as Course, and Dist. 734, gire in the D. Lat. column 442 nearly : the dis- tance required. (2). Or employ Tab. 4, as directed in tlie Explanation of the Table?. 308. By Computation. To the log. cos. of the Lat. add the log. of the Diff. Long. ; the sum (rejecting 10) is the log. of the distance required. Ex. above. Lat. 53° 20' log. i-ns. 9'776i D. Long. 12 14 or 734 log. 2-8657 Dist. 438-3 log. 2-6418 309. By Construction. Draw a line A B (fig. No. .306) of any length; lay off at A the angle B A (J equal to the latitude 63**; take AC equal to the Diff. Long. 734; fi'om G draw G B ))er])en- dicnlar to A B ; then A B is the Dist. required, and measures 442. 310. In parallel sailing the Distance and Departure are iden- tical. When the course is nearly, tliough not exactly, on a parallel, the distance run and the dejiarture are very nearly ecpial ; hence it is evident that parallel sailing will apply, nearly enough for common jiurposes, to cases in which the course is not exactly east or west. 311. In lats. below .'i", when the distance does not exceed 300 miles, the Dep. may at onro lie taken as the Diff. Long., as tlt« gienlpst error "ill Reiireflv exceed 1'. 122 NAVlGATIOiN 1. Middle. Latitude Sailing. 312. Tins IS a method (founded on tlie principle of ]>ariillel sailing) of converting the Departure into Difference of Longitude, nad tlie Difference of Longitude into Departure, wlien the sliip's ffOiirse lies obliquely across the meridian ; that is when, besides Departure, she makes Difference of Latitude. Suppose a ship make 100 miles dejiarture in going, on the same sourse, from lat. 38° to lat. 41°; this departure, if made good alto- gether in lat. 38°, would give 127 Ditf. Long, by No. 304 ; and again, if made good in Jat. 41°, it would give 132-5 J)ifi". Long. Now, since the ship has sailed between these two parallels, and not on either of them exclusively, her real Diff. Long, umst be between 127 and 132'5; and therefore we may conclude it to be not far from that which would result from a departure made good altogether in the middle parallel ; hence the name of the sailing. 313. Middle latitude sailing has thus the same two cases as parallel sai'ing; and, accordingly, the rules for inspection, compu- tation, and construction, already given, Nos. 304, &c., apply equally to this sailing, observing merely to read middle latitude for latitude. 314. When the latitudes of the two places are of the same name, the middle lat. is half their sum.* In using the Traverse Tables, it is enough to take the latitudes to the nearest degree. Ej. 1. A ship sails from lat. 51° 33' N. to 49° 9' N. : find the Mid. Lat. Lat. left 52° Lat. in 49 Ex. 2. A ship sails from lat. 2° N. to lat. 1° S. The ship moving near the equator, the consideration of middle latitude is omitted, and the Dep. taken as the Ditf. Long. Min. Lat. When the latitudes are oi contrary names, no sensible error can arise from taking the Dep. itself, made good from day to day, as the Ditf. Long. But in greater distances between places in opposite •atitiides it is proper to convert the Dep. made good in N. hit. into Diff. Long, by means of the north mid. lat., that is, half the N. lati- tude, and that made good in 8. lat. by half the S. lat. When, on the other hand, the Diff. Long, is to be converted into Dep., this rule does not apply. It will be near enough for common purposes, when the latitudes are either very nearly equal or very unequal, to employ, as the mid. lat., half the greater latitude. In * The rule which directs half the difference of the latitudes of two places on opposite Bides of the equator to be employed as their middle latitude, is erroneous. The error will be readily perceived in considering a case. .Suppose a ship sails S.E. from lat. 10* N. tor 10° S ; it is evident that her ditf. long, will be exactly the same as if, on reacliing the equa- tor, she returned to the same N. lat., steering N.E., since her course is the same, and she moves in the same lats. in both cases. Thus the mid. lat., which is the average of all tlie latitudes passed through, or the half sum of the first and last, and is here 5°, is independent of the distinctions of N. and S. Tlie common rule gives o for the mid. lat. ; wlience it would follow that the diff. long, made good by a ship in ranging tlirough all the latitude* between 10° N. and 10° S., or any other equal latitudes, however great, would be the same »K if she made good her departure altogether on the equator — a conclusion manifestly erro- inK, SAILINGS. 123 an intermediate case we may combine the two mid. lat.s., <;i\ing the e;reater weight lo tliat whicli corresponds to tlie greater latitude. Ex. I. Find the mid. lat. between 30° N. and 29° S. The lats. being nearly equal, half of 30°, or i ^^, may be taken as the .Mio. Lat Ex. 2. Find the mid. lat. between 30° N. and 2' S. Half of 30^, or is", may be taken as the Mm. Lat. Ex. 3. Find the mid. lat. between 30° N. and I5°S. The N. mid. lat. is 15, tlie S. mid. lat. is 7' nearly; now the mid. lat. 15 ciirrespondh to 30° of lat., and the other, or 7", to only half as much. Instead, therefore, of dividing th« §uui of the two by 2, we give to the first double the weight of the other, and divide by 3 j llius, 15+ 15 + 7, or 37 divided by 3, gives 12°, the Mid. Lat. required, nearly. I. Given the de])arture, to Hud the dift'erence of longitude. A ship from lat. 51° 9' N. sails S.W. by W. 216 miles : required her Lat. in ami Then Course 50^ and Dep. ijg'S in D. Lat. column give Dist. 279 or 4° 39', DiFF. Long, required. Casfi Ex. 1. Diff. Long, 315. £1/ Inspection. Find the D. Lat. and Dep., and the Lat. in, ]'iiid the Mid. Lat.; then, with the Mid. Lat. as Course, look for I lie Dep. in the D. Lat. column, the corresponding Dist. is the D, Long, retjuired. By Case I. of Plane Sailing, S. 5 pointg, Uist. 216, give D. Lat. 120 and Dep. I79'6 ; bence the Lat. in is 49° 9' N. Lat. left 51 9 N. I 100 ig Mid. iMt. 50° I 316. By Computation. Having found the Dep. and the Miti. Lat., add together tlie log. sec. of the Mid. Lat. and the log. of tlie Dep. ; the sum (rejecting 10) is the log. of the Diff. Long. Ex. above. Dep. i79'6 Mid. Lat. 50° 9' Mid. Lat. 50° 9' log. sec. 0-1933 Uep. 179 6 log. 2-2543 Diff. Long. 280-3 (4' 4o''3) log- ^■4476 yi7. By Construction. (Ex. 1.) Lav oft" S C .4 the Course 5 points, and take CA the Dist. 216;' draw AB perpendicular to CS. The figure is thus far complete for plane sailing, Case L Lay off" the angle BAL equal to the ]\rid. Lat. 50°, ani- responds to the greater lat., we may adopt it as the Mid. Lat. (Assigning the relative wcightJ Kith some further precision gives 3^40' as the Mid. Lat.) Course 4° (Mid. Lat.) and Dist. i ;a give I3i'7 in the D. Lat. col. ; this as Dep., and D. Lot. 83-8, give Course 57°4. Dist. 1570 miles. 319. By Compiitntion. Find the Diff. Long, and the Mid. Lat., to the log. cos. of the Mid. Lat. add the log. of the Diff. Long. : the gum is the log. of the Dep. Ex. above. D. Lat. 838, D. Long. 1319, Mid, Lat. 3'4o'. Mid. Lat. 3'' 40' log. cos. 9-9991 Diff. Long. C. Sierra Leon.-, lat. 8° 30' N. Lon C. St. Roque 5 28 S. D. I.nt. 13 58 Diff. Long. Or 838 mile. Or 19 Dep. 13.6 log. log. 3- 1202 31. 93 id the D. Lat. giver 1, the Course and Dist. The Dep. being now found (No. 279.) Construction. Construct the triangle for turning the Diff. Long, into Dep., as in No. 306 (reading Mid. Lat. for Lat.). Then liaving tli(.' D. Lat. and Dep. the process is compietehip from Tvnemoutli Castle, in Lat. 55° i' N. and Long. 1° 25' W., lails S.R. by S. 196 miles : what is her present latitude and longitude ' Ans. I.,at. in 50° 55' N. ; Diff. Long. 273m. ; Long in, 3° S' E. ti. i. A ship from Cape Clear, in Lat. 51° jO' N. and Long. 9 29' W., sails S.W. 263 miles : required her Lat. and Long. Ans. Lat 48° 20' ; Diff. Long. 288-7 . whence th3 Long, in is i+° 18' W. Ex. 3. Find the Course and Distance between Tynemoulh and the Naze of Norway. Ans. Course N. 57° 4»' E. ; Distance, 33i'3 mile* Ki. ■». Required the Course and Distance from a place A, in Lat. 51° 25' N. and Long 9" »9' W., to a place B, in Lat 36° 57' N. and Long 25° 6' V. Ans. Course S. 37° 45' W. j Distance, 1098 miles, Ex. 5. Re<|Uired the Course and Distance from a place A, in Lat. 56° 12' N. and Long. 2° 36' W. to a place B, in Lat. 57° 58' N. and Long. 7° 3' E. Ans. Course N. 71° 23' E. j Distance, 332 miles. El. 6. Required the Course and Distance from A to B ; Lat. of A 53° 18' N. ; Long, of A 0° 5s' E. i Lat. of B, 57° 58' N. ; Long. B 7° 3' E. Ans. Course N. 36° 34' E. ; Distance, 349 miles. 2. Mercators Sailino. 321. This sailing is employed for exact!}- the same pnrjooses as middle latitude sailing; but it is a perfect method, which the other is not. The calculations are performed by the help of a table of Meri- dional Parts, Table 6. 322. To find the Meridional Difference of Latitude. When the latitudes are of the same name, take the difference of the meridional parts for the two latitudes; when of contrary names, take the sum. Case I. Given the course between two places, and their latitudes, to find their difference of longitude. Ex. 1. (Lats. same name.) A ship from lat. 51° 9' N. sails S.W. by W. 216 miles: required the Lat. in and DifT. Long. 323. By Inspection. Having found the Lat. in, take out tli(? meridional parts (Table G) for it, and for tlie L:it. left ; find tiie Meridional Diff. Lat. (No. .322). With the Course, and Mer. D. Lat. in the D. Lat. column, find the Dep. ; this is the Diff. Long. By Ca,se I. No. 273, the Course 5 points and Dist. 216 give D. La^. 120 and Dep. i-'^-ei tliis D. Lat. subtracted from 51 9' gives Lat. in, 49' 9' N. I>at. in 49° 9' N. Mer. parts 3396 Lat. left 51 9 31583 Mer. D Lat. "TS7 Titc Course ; points and D. Lat. 187 give Di-p. 2S0, or 4° 40' the Diff. Long 324. By Computation. Find the Lat. in, and the Mer. D. Lai. To the log. tan. of the Course add the log. of the Mer. I). Lat.; the Hum (rejecting 10) is the log. of the T>. Long. Ex. above. Lats. 49' 9' and ^i'' 9', Course 5 points. 5 points log tan. 10-I7 5I >fer. D. Lat. 187 log. 2-27 iS DoK. LoNO. :-o-8, or 4° u/-8 loif. 2-4460 126 NAVIGATION. (This is the canon (3) No. 272. It will lie suffideiitly understood by observing that, la •ie 6g. below, C M is the Mer. D. Lat., and M L the DitT. Long., and C M : M L :; rad. • tan. M C L the course. This example is sufficient for any variety of the Case I. c 325. Bij Construction. Lay otf the course M C A, S b points W. ; take CA 216 the Dist. ; draw AB perp. toCS: the fig. CAB is, tiius far, the case for plane sailinir. Now lay ort'CM the Mer. 1). Lat. 187, and draw ML parallel to A B meeting C A Siroduced : M L is the Diff. .lono;. and measures 280. This exam])le of construc- tion is sufficient for Case L Ex 2. A ship from lat. 29° 40' N. sails E.N.E. till sne makes 72 miles D. Lat. : tind her Diff. Long. fly Inspection. Course 6 points and D. Jo" 51'- Lat. left 19° 40' Lat. in 30 52 _ 1^49 Mer. D. Lat. 84 Coarse 6 points and D. Lat. 84, give Dep. 203, or 3" 23', the Diff. Long. Case n. Given the latitudes and longitudes of two places to find the course and distance between them. E.N.E. till sne makes 7 . miles D. Lat. Lat. 72 give Dist. 188 r niles: the Lat Mer. parts 1865 Ushant, lat 48° N. long. Rx. Find the Course and Distance betwe r.nd St. Michael's, lat. 37° 44' N. long. 25° 40' W. 326. By Inspection. Take oat the mer. parts for the two lats. : find the Mer. D. Lat. and the Diff. Lono^. Enter the Traverse Table with the Mer. D. Lat. as D. Lat. and the D. Long, as Dep.: this gives the Course. Then with this Course and the true D. Lat. find the Dist., which is the distance required. Ushant, lat. 48° 28' N. Mer. parts 3334 Long. 5° 3'W. St. Mich. 37 44 2448 25 40 ^\'. 10 44 Mer. D. Lat. 886 2'o~3~7 True D. Lat. 644 Diff. Long. 1237 Then 886 as D. Lat. and Dep. 123-7 give Course 54°; and D. Lat. 644 givea 1095 miles, the Dist. required. 327. By Computation (1.) For the Course. Find the Mer. Diff. Lat. and the Diff. Long. From the log. of the Diff. Long. (adiliiig 10 to the index if necessary) subtract the log. of the Mer. D. Lat. : the remainder is the log. tan. of the Course. (2.) For the Distance. Find the course; then to its log. sec. add rlie log. of the true D. Lat. : the sum is the log. of the Distance. Ex. above. M. D. Lat. 886 ; D. Long. 1237 ; true D. Lat. 644. Dili'. Long. 1237 log. 3'0924 | Course ';4° 24' log. sec. 0-23^0 Mer. D. Dat. 886 log. 2-9474 Tr. D. Lat. 644 log. 2-S089 C.ciURHE 54= 24' Uii. 01450 I Dist. iii.6 loj 5-0419 TUK SAIUN08. ]27 6'2S. By Co'isliiicliuii. Draw tlie nieridiaii C S* tliroiigli one of thfi places, say Usliaiit, and on it lay off' the Mer. D. Lat., 886 from C to M. Diaw M L perijciidicidar to C S and equal to the Diff Long. 1237 ; join C L, and S C L is tiie Course. Lay otf CJ3 the trne D. Lat. on C S, draw BA parallel to LM and C A is tlie Dist. 1100". 32[). When the lat. is below 5" and the dist. less than 300 m., see No. 33-2. E.iam]iles for Ejcetche. K«. 1. .\ sliip, in Lat. 36" 40' S. and Long. 16" lo' E., sails W. N.W. until she arrives in Lut. 33" 10' S. : find the Dirt', of Long, and also the Long, come to. Ans. Diff. Long. 620'4\V. ; whence tlie Long, come to is 6° o' 10. fci. 2. A ship from Lat. 41° 25' N. 8nd Long. 15° 6' W. sails N.E. by E. for several days, and then finds by observation she is in Lat. 46° 40' N. : find what Diff. of Long, she has made ; also find lier Long. in. Ans. Diff. Long. 536; whence her Long, in is 6° 10' W. Ki. ;5. A ship, in Lat. 42° 30' N. and Long. 58° 51' W., sails S.E. by S. 300 miles: fi'nl the Diff. Long., and also the Long. in. Aus. Diff. Long. 219 miles; Long, in 55° 12' W Ei. 4. Find the Course and Distance between Tynemouth and the Naze of Norway. Ans. Course N. 57°4o'E. ; Distance, 331-4 miles. Ei. i. Reqviired the Course and Distance between Tynemouth and Helgoland. Ans. Course S. 81° 8' E. ; Distance, 324 miles. Kx. 6. Required tlie Course and Di.«tance from Diego Ramirez, in Lat. 56" 29' S., Long. 68 43' W., and C. Lopatka. in Lat. 51° 2' N., Long. 156*46' E. Ans. Course N. 46^ 21' E. ; Distance, 9346 milei 3. Selection of Mid. Lut. or Mircntor's Sailing. [1.] Finding the Ihjf. Lovy. 330. The difference of longitnde foniul by Mid. Lat. is true lete solution by Mercator's Sailing is effected with rer>- little more labour. (See No. 331 ) Tin: SAii.iN'os. I'JD n.ff. I-uiig. luaile good on any Course Jcpemls entii-fly up )m the liitituile in wliich the sliip actually moves. Kx 1. A ship sails from Lat. 70° N. ; 1st, N.E. 400 miles tn Lat. 74" 43', then S.E. 400 miles, when she returns to the parallel of 70°, having made Dep. 556 miles, and D. Long. 31° 18'. Kx. 2. She sails 556 miles on the parallel of 70°, making D. Long. 27° 34'. Ex. 3. Starting from 70°, as above, she sails S.E. 400 miles to Lat. 65° 17', then N.E. 400 miles to 70", having made 556 miles of Dep. and D. Long. 24*^ 54'. The 1st and 3d case, reducing the two courses to one by the Traverse Table, give tlie same Course and Uist. made good as in Case 2, viz. East 5.56 miles, or Dep. 5.56 m., and D. Long. 27° 34', which is erroneous. In Case 1, this Dep. is made good in the average lat. of 72°^ ; in Case 2, in 70°; and in Case 3, in 68°. It may appear perplexing to the student that the ship should return to the same parallel, after having made y^, given Dep., and yet that her long., that is, her position in the parallel, should be different in different cases; but lie must bear in mind that the Dep. has not been made good on the parallel, exce|)t in Case 2. If he lays off a case of the kind on the globe, he will perceive clearly the nature of the question. To olitain accurately the Diff. Long, each course should there- fore be separately considered. But, in general, except in very high lats., the distances are not large enough to introduce much ei'ror oit this account. III. Great Circle Sailing. 336. When the ship sails on a rhumb line (No. 198), her track cuts all the meridians as she passes them in succession, at the same angle; and thus, while steering a course, her head is kept on the same point of the compass until she reaches her intended port. This condition, namely, keeping tlie course constant, is the most con- venient in practice, and, besides, produces in all the calculations in which the place of the shij) is coTicerued the utmost simplicity of which they are capable. But the track on the rhumb line is not the shortest distance measured directly over the snrfiice of the sphere from one place to another, or the distance " as the crow flies," except when the course is due north or south, or east or west on the equator. The shortest distance between two points on the surface of a sphere is the portion or arc which they include of the circle passing through l>oth the points and the centre of the sphere. Such a circle is called a great circle* as distinguished from other circles whose centres do • The great cirule paj^sing through two plares may he found on a globe by stretching 1 thread evenly lietween them ; or, by turning the globe about till the twn pbucs fall on the apper edge of the wooden rim, or horizon of the globe, which thus marks the lirrlr. The distance between the points may be me.isured at once by laying the thread along the cquatoi uf the globe. The ojurses are found by measuring the angles between the thread and the oieridians ; the most convenient instrument for which is the horn semicircle, or protractor, u it is also called (No. 108) In order to compare the great circle vith the rhumb line the U:ter most be projected on the gl' ^^.. K i^O NWKiA'CION. not coinci J.e with tlie centre of the 8|>here ; as, for instance, the parallels of latitude, of wliich the centres are in the axis between the centre and the pole, and which aro called smidl circles. Hence sailing on a circle of the former kind is called Great Circle Sail- ing.* On this course, and on this course alone, the ship steers for her port as if it were in sight. The three arcs joining- two points on the surface of a sphere with each other, and with a third point, and having for their eonnnon centre the centre of tlie sphere, constitute a Spherical Triangle. In the problem under consideration the two places are the two points, and the third point is the pole, and the triangle is formed by the distance between the places and their colatitudes. Some of the rules in this section may be employed accordingly in other problems of spherical trigonometry. 337. Great Circle Sailing is adapted principally to the second only of the two cases, No. 270, or Shaping the Course; because tlie ship, even when moving on a great circle, must necessarily be kept on the same course (that is, on a rhumb line) for a short distance at n time, and her place may then be deduced by the rules already given in the preceding section with incomparably greater con- venience than it could by any rule in which the distance made good was rigorously considered as described on a circle. Although this sailing is thus restricted to one case, we shall, for the sake of clear- ness, divide the problem of finding the course by Inspection into two cases, namely. Case I. in which the places are on the same side of the equator, and Case II. in which they are on opposite sides. Case I. Bi/ Inspection. (The ulaces on the same side of tlie equator.) (1.) For the Dist. With the two lats. enter the Spherica. Traverse Table (Table o), and take out M and N. With the complement of the Diff. Long, as a Course and Dist. 1(10 (Table 2), find the Dep., and write it under N. Wl>^n the Diff. Long, is less than 90°, add this Dep. to N. ; when the Diff. Long, is greater than 90°, take the diff. of the Dep and N. . „ , .i With this sum (or diff.) as D Lat. and M as Dist. find the arc in Table 2: this is the Distance required in degrees of 60 miles each. (2.) For the Course. Having found the Distance. With the lat in, and the compl. of the Dist. in degrees, find M. and N ^W^ith the lat. to as Course and M as Dist. (Table 2), find the Dep., and write it under N. When the Diff. Long, is less than 90°, take the diff. between this Dep. and N. When the Diff. Long, exceeds 90°j take the sum of the Dep. and N. With this diff. (or sum) as D. Lat. and Dist. 100 (Table 2), find the Course. ling, lor 3 like na^ THE HAll.lNOS. ini The (JoiiJNe IS to be reckoned aceordiiip; to the following rule: Dirt. Im 11.811 90" (or 5400 miles). Dist. greater than 90° (or 5400 miles. | Dep. few than N. Course to be reckoned in N. lat. from S. in S. lat. from N. Dep. greater than N. Course to be reckoned in N. lat. from N. in S. lat. from S. , Course to be reckoned in N. lat. from N. in S. lat. from S. Ex.1. Find the Distance between St. Helena, in lat. i5°55'S., long. 5 44' W.. and pe Horn, in lat. 55' 59' S. and long. 67° 16' W., and the Course from each place to the The D. Long, between 5° 44' W. and 67° |6' W. is 61° 32' ; eompl. 28°. For the Distance. 16° and 56° (the lats.) give M i86-o N 42-5 28" (co-diff. long.; and Dist. 100 give Dep. 46-9 (D. Long, less than 90*.) Sum 89-4 The Dist. 1S60 and D. Lat. 89-4 give 61'^ nearly, or Dist. 3660 miles. The comp'.e- For the Course from St. Helena. For the Course from C. Horn. 16° (Lilt, m) and co-Dist. 29° | 56° (Lat. in) and co-Dist. 29° M 118-9 N 15-9 I M 204-5 N 82'i 56 (Lat. to) and Dist. 118-9 Dep. 98-6 16 (Lat. to) and Dist. 204-5 Dfp - 56-? (D. Long. /ew than 90°.) Diff. S2-7 Diff. 25-9 Dist. 100 and D. Lat. 82-7 give 34°, [ Dist. 100 and D. Lat. 25-9 give 75°, wliich is S. 34°W'., the Course required, which is N. 75° E., the Coursk required, because the Dist. is less than 90°, the Dep. because the Dist. is less than 90°, the Dep. t/reater than N, and the Lat. is south. ; less than N, and the Lat. is south. By Mercator's Sailing the Course is 50" from either place to the other, and the Distance J74.0 miles. Ex. 2. Find the Distance between Madeira, in lat. 32° 38' N., long. 16° 55' \V., and Bermuda, in lat. 32° 20' N.. long. 64° 51' W., and the Course from Madeira. Tlie D. Long, is 47° 56' ; the compl. 41°. For the Distance. 32° and 33° M 140-6 N 40-6 42 (co-D. Long.) and 100 Dep. 66-9 Sum 107-5 Dist. 141 and D. Lat. 107-5 give 40'', or 1400 miles, the Dist. required. For the Course. 33"^ (Mad.) and to- Dist. 50° M .S5-5 N 7,-4 32° (Berm.) and 185-5 "ep. 98-3 Diir. 20^ Dist. 100 and D. Lat. 20-9 give 78^, which is N. 78°W., the Course reiiuired, because the Dist. is lesi, than 90, the Dfp. greater than N, and the Lat. north. Kx. 3. Find the DiHrancp between a point in long. iSo° on the equator, and another in Ul. . 0° N., long. 140^ W., und the Courses between these points. For the DisUnce. Lats o* and 40° give M 130-5 and N o. Then 50° (the co-D. Long.) tnd Dist. 100 give Dep. 76-6 ; the sum of N and this is 76-6, and Dist. 130-5 with D. Lat. 76-6 givej 54°, or Dist. 3240 miles. For the Course from Lat. 0°. 0° and the co-Dist. 36' give M 113 "6, N oj 40° and 124 Ci»e Dep. 79-71 Dist. ico and D. Lat. 79*7 give 37°, which is N. 37° E., the Coursk required. For the Coarse from Lat. 40°. 40° and 36° give M i6r4, N 6i-o; o and Dist. i«i give Dep. ; Dist. 100 and D. Lat. 6i-o give 51°. which ig S. ^i°W., the Course required M the Dep. c II Ipm tli.in N. 132 NAVKJATION. 338. Case II. By Inspection. (Tlic places on opposite sides of the equator.) (1.) For the Distance. With the two lats. take out M and N. :Table 5.) With the complement of tlie D. Long, as Course (Table 2), and Disl. 100, find the Dep. When the D. Long, is less than 90°, take the difference between this Dep. and N ; when the D. Long, is greater t\mn 90°, take the With this diff. or sum as D. Lat. and M as Dist. find the Course or arc in Table 2. When the D. Long, is less than 90°. If the Dep. is greater than N, this arc is the Dist. required ; if the Dep. is less than N, take the supplement. When tlie D. Long, is greater than 90°, take the supplement of Hie arc. (2.) For the Course. Having found the Distance, with the Lat. in and the complement of tlie Dist. to 90° find M and N. With the Lat. to as course and M as Dist. (Table 2), find the Uep. When the D. Long, is less than 90°, take the sum^ of this Dep. and N ; when the D. Long, is greater than 90°, take the difference. With this sum or diff. as D. Lat. and Dist. 100 (Table 2), find the Course, which is to be reckoned as follows: — Dist. less than 90° (or 5400 miles.) Dist. greater than 90° (or 5400 miles ) Course lo be reclconed in N. lat. from S. in S. lat. from K. Dep. leas than N. | Dep. greater than N. Course to be reckoned Course to be reckoned in N. lat. from N. in N. lat. from S. in S. lat. from S. in S. lat. from N. Ex.1. Find the Distance between C. Palmas, in lat. 4° 22' N. long. 7°44'W., and Frio, in lat. 23°o'S. long. 41° 57' W., and the Course from each place to the other. The D. Long, is 34° 13' ; the complement is 65°, For the Distance. 4" and 23° (lats.) Rive M 108-9 J^' 3 >• 56° (co-Diff. Long.) and 100 Dep. 82-9 (0. Long tos than 90".) Diff. 799 Dist. 1C9 and D. Lat. 79-9 give 43°, or Dist. 2580 miles; the corapl. is 47". For the Course from C. Frio. 23° (C. Frio) and 47" M i i;9-3, N 45-5 4i (C. Pal.) and 159 Dep. 12 5 Sum 58-0 For the Course from C. Palmas. 4' {C. Pal.) and 47" M i47'o, N 7-; zy (C. Frio) and 147 Dep. 57-4 {D. Long, less than 90°.) Sum 64-9 Dist. 100 and D. Lat. 649 give 49^, which is S. 49'^W., the Course required, because the Dist. is leis than 90^ and the , bee Ex.2. Find the roursee and Diiitance between Diego Ramirez, in lat. 56^ 29' S. lona 68"43'W., and C. Lojiatkn. in lat sTi'N, long. ts6''46'E. Thr D. I^ng. is i34''-ii. thB cn-D. Long. 4;". Dist. 100 and D. L.it. 580 give cf, which is N. 55° E., tlie Coursf required, tlie Lat. is south. IJIK SAIMNOS, 1":] For tlir Distance. {<" .mil 56 j' give M iSg'o, N 1866. Then 44.^° and nisi, ico ir\f Di'p. 701 ; tin: Sinn of N. and Dep., or 2567 aa D. l.at., and Dist. 288, give 27 \ oi- Lli>r 153", or 9180 miles: the co-dist. is b-^'. For the Course from Diego Ramirez. 565" and 65° give M 399'i, N 296 6; 51 ' aiij J99 give Dep. 3100; the rfi/f. i3'4 and Dist. 100 give 82°: Coursh, N. 82° W. For the Course from C. Lopatka. 51' and 63^ give M 3500, N 242-4; 564' and 350 give Dep. 291-8; the dif. 494 and Dist. ico give 60^: Course, S. 60" E. 339. To find the Courses and tlie Distance between the places hy CompiitatioH. Find the co-latitudes of the places. If the places are on different sides of the equator, add 90° to tlie latitude of one of tiiem for its eo-hititiule. Find the D. Long., and take half of it. (1.) For the Cour.ses. Take half the sum of tlie colats. and half their diff. Add together the log. cot. of half the D. Long., tho log. sec. of the half sum, and the log. cos. of the half diffei'ence : the sum (rejecting tens) is the log. tang, of half the sum of the two courses. When the half sum of the colats. exceeds 90°, take the snpplt- nient of the resulting arc for the half sum required. To the same log. cot. add the log. cosec. of half the sum of the colats., and the log. sine of half their diff.; the sum (rejecting tens) is the log. tan. of half the difference of the two courses. The sum of the half sum ami half diff. of tlie two courses is the course from the place in the /smaller of the two co-latitudes to the other; the difference of the said half sum and half diff. is the other course. The course is to he reckoned from the N. point in north latitude, Bnrl from the S. ])oint in south latitude. Ex. I. Find the Courses on the grem circle, between St. Helfnii.iii hit. 15° 55' S., long. 5° 44' W., and C. Horn, in lat. 55° 59' S., long. 67° 16' W. The D Long, is 61° 32' ; half D. 30° 46'. Colat. 34° 1' (C. HonO 30° 46' 001.02252 02252 C.h.t. 74^,5 O^t- Heh-n.a) Slim 108 6 half sum 54 3 sec o 2313 coKec. O0918 cos. 97687 Uiir. 40 4 hull' ililf. 20 2 (•08.99729 sin. 9 5347 sin. 9 70S9 69° 35' tan. 04294 35" 24' t,an. 9-85T7" 69° 35' sec. 10^574 35 24 30 34 COS. 9 9350 CoCKSR, S. 104 59 E. from C. Horn, or N. 75° 1' E. 2 CotiKSE, S. 34 1 1 W. from St. Helena. bl 8 = 3668 ni.* Kx 2. Finil the Courses on the great circle between Diego Ramirez, iu lat. 56° 29' S., !■ n^'. 68° 43' W., and C. LopitkH, in lat. 51° 2' N., long. 156° 46' E. TheD. Long, is 134° 31'; theco-lats. 33° 31' and 141° 2'. The half sum of the required courses is 79° S', and the half diff. 18° 42'. The sum of these is the Couksr from eolat. 3^° 31'. or Diego Ramirez, S 97° 50' \V., or N. 82° 10' W.; the diff. is the CouRSK from C. I.'-i.alka, or S. 60° 20' E. (2.) P'or the Distance. Fyib )ve method,* or take the supplement of the Diff. Long, to 12'' or 180". Add together the two co-lats. Add together the log. sine square of the said supplement, and the log sines of the co-latitudes : the sum (rejecting tens) is the log. sine square of an auxiliary arc aif Write X under the sum of the colats., and take the sum and difference, and the half sum and half difference. Add together the log. sines of the last two terms : the sum (rejecting tens) is the log. sine square of the Distance required. f Log bine tcjuaro is identical with the log. Imver.sine of Inmaii's tables. 134 NAVIGATION. Ex. Find the Distaaee between St. Helena, in lat. 15° 55' S., long. 5° 4/ \V„ and C. Horn, in lat. 55° 59' S. and long. 67° 16' W. Diff. Long. 61° 32 ' Suppl. 118 28 log. sin. sq. 9-868247 Colat. 34 1 log. sin. 9747749 Colat. 74 5 log. sin. 9-983022 Sum 108 6 Arc X 78 8 log. sin. sq. 9-599018 Sum 186 14 Ditr. 29 58 5 '^'™ 9i 7 'Pg- sin. 9'999357 ^ Ditf. 1459 log. sin. 9-412524 DiST. 61° 4', or 3664 miles, log sin. sq. 94118S1 The Distance by Mercator's Sailing (No. 3'27) is 3736 miles, or 72 more. 340. The course on the rhumb line,* from one of two places to the other, is exactly the opposite of the course to that place from the other; while, on the great circle, as appears from the preceding examples, these courses are very ditfereiit. The ship, wliiie on tiie rhumb line, is always changing tlie direction of lier head with respect to her port, for which she never steers exactly until it is in sight, because this track cuts all the meridians at the same angle, and the meridians themselves are not parallel to each other ; but on a great circle she steers directly for her port, while, as the angle made by her track with the meridians is perpetually varying, the direction of her head appears by the compass to be continually changing. This track, accordmgly, is the only one on which the ship nears her port by tlie whole amount of distance which she makes good fiom intitant to instant. Great circle sailing includes the case of sailing on a meridian or due N. and S., and on the equator, because the meridians and equator are great circles. 341. While sailing at the same rate on the same rhumb, the ship always changes her latitude by the same quantity ; but while sailing at the same rate on the great circle she may change her latitude, not only by unequal quantities, but in opposite directions. For exam])le, suppose the polar seas navigable, then the shortest way for the ship to go from a point in the arctic circle (or any other parallel of north latitude) to another jioint ISO** of longitude from it, and ill the same latitude, would be to cross the ]>ole ; in which case she would first steer north and then south, whereas on the rhumb line she would constantly steer east or west. 342. The track on the great circle and that on the rhumb line difter most widely from each other in high latitudes, and between places on nearly the si-.me parallels. On the other hand, when the places are on opposite sides of the equator, the great circle and rhumb line intersect each other, and the difference between them is not so coiis))icuou9. In low latitudes, and in all latitudes when the course is nearly on a meridian, the two curves nearly coincide. 343. If the arc of the great circle passing through the two jilaces [noi bring both on the same meridim or on the equatorl be )>ro- • AUo call.d the luxodromic curve. rnr. saimnhs. 135 •liutfil bcyoiid tliem, and carried round the g)oI)o, il will pass fliroiigb two points diametrically op)iosite in latitude and longitude, which we have called vertexes, each of them heiiig the highest point in latitude S. and S., passed tlirough by the circle. The vertex is 90° from the point where the great circle between the places (or produced beyond tlieni) cuts the equator. When the course shaped on the great, circle from each place is less than 90° (reckoning both courses from the nearest pole), the vertex falls between the places. At this j)oint the ship, neither in- cieasing nor diniiuisliing her latitude for a time, steers E. or W. But when the course from one of the jjjaces exceeds 90'*, the vertex of the circle falls outside the arc joining them. 344. To find the Latitude and Longitude of the Verte.i. (I.) For the Latitude. To the log. cos. of the lat. of one of tlie places add the log. sine of the course, on the great circle, from this place to the other: the sum is the log. cos. of the lat. required. (2.) For the Longitude. Add together the log. cosec. of the latitude already employed, and the log. cot. of the course already employed: tiie sum is the log. tan. of the D. Long, between the vertex and the place worked from. Kx. 1. Find the vertet of the great cinle jjassini; througli Rio de Janeiro, in lat. 12° <;5' S. long. 43^ 9' W., and the Cape of Good Hope, in lat. 34° 22' S. long. iS' 30' E. The Course from Rio is S. 63^ 12' E., tliat from the Cape S. 84° 54' W. ; each of these courses, reckoned from S., being less than 90", the vertex falls between the places Latitude. Rio, lat. 22° 55' COS.* 9-9643 (.'ourse 63 12 sin. 9-9506 Lat. 34'- 42' cos. 9-9149 Ej. 2. Find the vertex on the great circle passing through St. Helena and C. Horn. By Ex. No. .S.S9, the Course from St. Helena is S. 34" 12'W., that from C. Horn is B. 104^ 58' E. J since one of these courses exceeds 90^, the vertex falls without. Ans. Lat. 57° 17' S.; Long. 85° 10' \V. 34.5. Wlien the sliip sails on a great circle between two places on the same side of the equator, she is always in a higher latitude than if she had sailed on the rbumb line;; hence, since both tracks coincide at their extremities, there must be a point in the great circle at which its distance from the rhumb line, measured on a meridian, is greater than anywhere else ; this point we shall call the point of Maximum Separation in Latitude. When the ship crosses the equator, there are two such points, the one being to the northward of the rhumb line in north lati- tude, and the other to the southward of the rhumb line in south latitude. 346. The track of the great circle between any two points • .*s none but the logarithmic sines, cosines, &c nre employed in this work, except in ^'l>. 'J.'i4, we shall hcni.'eforih,for brevity, dispense with the abbreviation tog. in the examples. Longitude. 22" 55 cosec 0-4096 cot. 9-7034 n Long. 52" 23' tan 0-1130 Ri 43 9W. Long. 9 14 E. 13fi NAVIGATION. may be conveniently shewn, by determining the latitude of its point of intersection with each of a certain number of intervening meri- dians, the degree of exactness being increased according to the number of meridians taken. To find the latitude of the point where the great circle passinpf through two places intersects any given meridian, Find the position of the vertex (No. 344). To the log. tan. of the lat. of the vertex add the log. cos. of the difference of long, between it and the given meridian, and the sum is the log. tan. of the required latitude. Ex. Find the latitude of the point where the great circle passiDg through St. Helena and Cajie Horn intersects the meridian of 30'' W. Vertex (Kx. 2. 344) lat. 57° 17' S., lung. S5" 10' W. Laiitiide 57" 17' tan 0'922 Diff. Longitude 55 10 eus 9 756S Required Latitude 41 39 tan 9 949<3 The log. tan. of the lat. oi tlie vertex heini; corstanf, the lais. of tlie points of iui.n. section of the great circle with au^ desired uuiubir of nieridiauo may tlms be rapidly ooniputed. .347. To facihtate the practice of Great Circle Sailing, Mr. J. T. Towson in 1847 devised a method by which, using a diagram and a table, the successive courses on the great circle can be found without the labour of calculation.* The manner of projecting the track, and of measuring the distance on Mereator's chart, are described in Chajj. V. Other matters demanding consideration when it is proposed to make a voyage on a great circle, are treated in the division of tlie work appropriated to Navigating the Ship.t • Towsoii's Tables for facilitnting Great Circle Sailiug. Sold by J. D. Potter, )4o Wiiiories. London, E. t Tlie Azimuth and Star-azimuth Tables of Burjwood and Davis also facilitate Great Circle Sailing. The lat. in being taken as the Lat., the lat. of the port biund to as the Pec, and the diff. long, as the Hour-angle, gives the Azimuth, which will be the True Course. From these the Great Circle Course may be prajeeted on the Chart. Hee Burd- Wood and Davis' Azimuth Tables, published liy Potter, 145 Minories. Kx., a ship bound from Cape Ki ;ig, entrance of Yedo Bay, to San Franci.sco. Cape King, li'- 34° 54' N., long 139° 53' E. San Francitco, lat. 37"' 4S' N., long. 122=29' W. Ditf long. 97° 38', or 6'' 30°' 32". L.it. in. Lat. bound to. ^^ Hon'r.'™cio TnTe™'oiIre'e Cnttius; Mcr. of 35'" 38° &''jO™ N. 54° E. 150° K in lai 41' 4' 38 5 50 >i- 61 K. ito !•;. „ 45 45 38 S 10 N. 6S E. 170 K. ,. 4S 48 38 4 30 N 75 !■;. i^o ., 49 49 38 3 5° N. S3 E. 170 W. „ 5u 50 38 3 10 N. 91 V:. iLo W. „ 50 N'. 100 V, 150 49 38 I 50 N. 109 K. 140 \V. „ 47 47 38 I 10 N. 119 p;. i-,o W. ,. 43 43 jS >!• «i' 1'- ^"'^a" l'r..ueiscu. CHAPTKR IV. Taking Dki'artuues, I Rt a Single Beauinc; and Distance. If. Determination ov Distance. III. Methods by the Chart. 348. Determining the place of the ship with reference to a point of land, or other position of known latitude and longitude, is called Taking a Departure. TKv' position of the ship with respect to a point of land or Cither fixed and conspicuous object is defined by the direction iu which siie lies, and her distance from it. The direction or bearing of tli3 ship from the land, being the opposite i)f the hearing of the land from the ship, is fui'nislied at once by the compass, or it may he found by observation of an Astrono- mirrd Jiraring ; but the distance from the point, when it cannot he estimated or guessed with sufficient precision, must be dcihieed by means of some further observation, taken at the same time as tiie bearing, or after an interval. When a former position of the shij) herself is adopted as a point of departure, the direction (or course) and the distance are deduced from tlie rcckunini;'. I. By a Sinole Bearing and Distance. .'Un, 'I'iie object being set by the comi)ass, its distance is esti mated by tlie eye. This, which is the common method of taking departures, is iieai enough when the distance is small ; but the error or uncertainty in the estimatiDn of the distance, which, perhaps, may be stated gene- rally at one-fifth of the whole, becomes considerable when the dis- tance is great. Distances thus estimated are generally overrated. II. 1)i:ti;i{:\iinati().\ of Distance. I . /iy two lieariiiys of the same Ohject. :ir){). W'licn tlic siiip's path lies acrn~s tiu; line of direclion of the .■>b)ect the; di-tiiiicc Clin he obtained liy two hciiriiigs and ihe distance nji. by tlie sliiji in I he inliTval oniiJic lictwccn llicin 138 I^AVIGATION. Take tlie bearing of the object, and note the number of points contained between it and the ship's head. After the bearing liaa altered not less than two or three points, note the number of points in the same angle again. Note. The course and distance netweeii the positions must be those actually made yr(W. (1.) To find the distance when the lasl bearing was taken. Enter Table 7 with the first number of points at the top and the second number of points at the side ; take out the number corresponding, and multiply it by the number of miles made good by the ship : the result is the dist. in miles at the time the last bearing was taken.* Ex. The Eildj stone bore N.W. byW.; after running W. by S. 8 miles, it bore N.N.E.: rei|iiirecl its Dist. at this l;isi bearing. The number of points between N.W.by W.andW. by S. is 4; that, between N.N.E. !\nil W. by S. is II ; uiidiT 4 at the top and against II at the side staiids 072, which multiplied" by 8 (miles), gives 5-8 miies, the Dist. required. The student can easily supply a figure. (2.) To find the distance when the first bearing was taken. Enter the Table with the supplement (or difference from 16 points) of the second number of points at the top, and the supple- ment of the first number of points at the side; takeout the multi- plier, and proceed as above directed. Ex. Find the Distance of the Eddystone at the time the first bearing (or N.W. by W. above) was taken. The second number of points is 1 1, the supplement of which is 5 ; the first number is 4 p ints, the supplement of which is 12 ; then 5 at the top and 12 at the side give tlie number 0-85, wliich nuiltiplied by 8 gives 6-8 miles, the Dist. required. When the number of points between the object and the ship'.s head at either observation is 8, that is, when the bearing is at right angles to the course, the distance may be found by the Traverse Table, by entering the table with the number of points at the other observation as a course, and the distance run as D. Lat. ; the corresponding Dep. is the distance of the object when observed at 90° from the course. 351. If the time be noted when an object is 4 points on the bow, and again when it is right abeam, the distance run in the interval on the same course is evidently equal to the distance off the object when abeam. This case is called the Four-point bearint appe.irtd b. the Naultcul Muyazine, vol. i. ^ ~ TAKING DEPAKTUKKS. ] ;;:) The error of the required distance produced hj an error in the dist. run, is a matter of simple proportion. For example, if the flist. run be -^ of itself in error, the distance required will also bo -iV of itself in error. Hence the dist. run should not be much less than the distance required. 2. % Sound. .552. An excellent mode of determining the distance is obtained by noting- the number of seconds elapsed between seeing- the Hash of u gun and hearing the report. Sound ti-jivels, in a calm, about 1 bJO feet in one second at a temperature of 66° Fahr.; hence it is easy to deduce the following approximate rule. Divide the seconds elapsed by 5, and subtract from the quotient iV of itself; the result is the Dist. in miles very nearly. V.\. The nuan of the intervals givco by 4 guns fired from C. Shilling was 14" I leciuirtd the Dist. of the ship. 5) '4-1 i-twelfthof i-S ■■! Dist. j-6 This method is capable of much precision when the gun and the ear are at the same temperature and at the same heigbt.* A mode- rate breeze in the direction of the sound causes a variation of about. 20 feet a second in the velocity ; a strong breeze more. 3. Bj/ the Altitude of lliyh Land. [1.] When the Object in sem on the Sea-Hnri:on. 353. The distance of the visible iiorizon from the spectator is e*oui the nature of the obiA-rwaum, it U enough to work to minutes only. TAKTXr, DEPATiTT'nrS. Ill nr.n, 19 .,. ; height of tlie eye l>l!.Ulllce. Alt. 20' Depr. -4 18 feet >ei|fht of tlie Peak, 1217: feet: nlima/»l band next day by the chronometer distance s to have and repeating the work, gives IC9 miles, been 1 1 5 miles. 359. When the altitude is great, or above 3", the following rule for tiie computation is preferable to No. 357 : — (1.) Correct tlie altitude for index error, subtract from it ^ of the estimated distance in miles, subtract further the true Depr. ol the eye (Table 8), and note tiie reinaiurler. When the height of the eye exceeds 30 feet, increase the le- mainder by -^V of the depression. (2.) Add the log. cos. of this lemainder to the log. cos. of the Depr. corresponding to the iieigiit of tiie mountain ; the sum (re- jectiuir 10) is the log. cos. of an are. From tliis arc take the said remainder, this leaves the Dist. of tiie summit in miles. Ex. Mr. Fisher observed the altitude of Mount Etna. 5° 15'; height of the eye, 30 feeti estimated distance, 8 leagues, or 24 miles : required its Distance. Alt. 5° 15' Etna, ht. 10900 ft. Dep. 1° 51' cos. 9-999^74 ^°*,''^ Z\\ Remainders « eo.. 9-998^55 5° 27' COS. 9-998029 Remainder 5 S D18T. 19 iiiiles. 360. Degree of Depeiulaiice. To judge of tliis, repeat tiie com- putation, using a new altitude, varied from the former by a number of minutes equal to the extent of the probable uncertainty. For example. Suppose in Ex. 1, No. 357, the altitude doubtful, or in error, 5'; repeating the work, with the altitude 46', gives the distance 23 miles, instead of 21 : hence we in'er that, supposing 5' to be in this case the utmost prohable uncertainty in the altitude, the Jistance may be depended upon to 2 miles. The greater the altitude the more accurate is the icsnlf. 361. Case II. When the height of the land is not known, tiie distance may be found while standing directly towards it, or from it, by means of two altitudes, and the distance nin in tlic interval between them. If the course is not more than two points out of the directioii of the object, the distance run may be reduced to the change of distance of the object by means of the Traverse Table. 362. The Observation. Observe the altitude. After a consider- able change in the altitude, observe a second altitude at the samp, height of the eye. Note tiie rate of sailing. Estimate the diataiicu at each observation. 363. The Computation. Find the true altitudes. No. 357. (1.1 Find from the rate of sailing the dist. run, and reduce it when ne- wwsary to the change of distance made good in the direction of the object, th:;s, — enter Tabit; 1 with the difference between the ship's 142 KAV1GATI0N-. coarse and tlit bearing of the object as a Course, and tlie Dist. run as Dist.; the corresponding D. Lat. is the change of distance required. To the lesser altitude add half the change of distance, and sub- tract the Depr. corresponding to the height of the eye ; call this the first remainder. From the greater altitude subtract the lesser alti- tude, and the change of distance; call this remainder the second remainder. Multiply the first remainder by tlie change of distance, and divide, the product by the second remainder ; the quotient is the distance in iiiik'S when t\\e greater altitude was taken. Ex.1. Observed altitude of Mount Etna. 1° 28'; estimated distance, 20 leagues. When J 8 miles nearer, observed the altitude 5° 15'; height of the eye, 30 feet: required tho bistdnce. - 28', deducting ^, Df6omUesor5',is.-23' 5° 15', deducting f^ of 22 miles or 2', ii Lesser Alt. 1° 23' 4 Dist. run +19 Depr. --_6 ist rem. i 36 or 96 Greater Alt. Lesser do. i''2 3'\ Dist. + 38 } 2d rem. or 5° 13' 1^ tl:e„''''^» ,9 miles. the Dist. required. Kx. 2. Observed the altitude of Dunnose 41', estimated distance 4 leagues or 12 milos After running -J miles directly from it observed the alt. 20'. Height of the eye, 10 feet. The 1st alt. reduced is 18'; the 2d, 40'. The Ut rem. is 18-7 ; the 2d, 14-5 : the Dist. required 9*7 miles. 364. Degree of Deperidance. This may be estimated by repealing the work with a new lesser alt., and also with a new change of dis- tance, differing from those used before by 1', and comparing these two results with the first. If they do not differ much, the case is evidently but little affected by small errors; if, on the contrary, they differ more than 1', it is shewn that errors of observation are increased in the result. Thus an error of i' in the lesser alt. produces in Ex. 1, above, only 0-3 of a mUe error In the distance required, while in Ex. 2, the latter error is t'z. Again, an error of i niilj in the change of distance produces in Ex. 1 only 0-7 of a miie in the r«sult, while in Ex. 2, it produces 24 miles. In ordinary cases an error of 1' or 2' is more likely to occur in an alt. than an error of 1 or 2 miles in the change of distance; and as precision is of less consequence in the greater than in the lesser alt. the value of the result will depend principally on the lesser altitude. The less the ist rem. is with respect to tlie 2d, tiie less is the effect produced by the above errors on the result. Thus, in Ex. 1, the 1st rem. is to the 2d, or 96 is to 192, as i to 2 nearly, and the case is good. In Ex. 2, on the contrary, the 1st rem. i8'7, is greater than the 2d, 14-5, and tlie result could not be depended upon within 2 or 3 miles. 365. Since these rules suppose the object to be referred to the eea-horizon, they apply to all cases in wliich the observer, though near the land, can descend so near the surface of the water as to tjbtjiin a perfect sea-horizon. On the other hand, whfn the lattr 44^ ; then the intersection of the lines AM, B M, is the centre of the circle ABO. In like manner lay oft' BCN, C B N, each eijual to the complement of 30^, or 60^; then N is the centre of the circle C B O, and O is th2 place of the observer. The drawing of the figure is materially simplified, in practice, by the bearing of the middle object, as this shews where the lines must fall. Ex. 2. Tlie angle between two objects A, B, is 47°, that between B and C is 107^ Lay off ABM, BAM, each equal to 43'; M is the centre of ABO. Lay off C B N, B C N, each equal to the complement of 107^, or 17' , then N is the centre of C B O. ^^■•M 370. Demonstration. Having laid ofi' two equal angles A B M BAM, and described a circle from M the point of intersection of AM,BM,bisect AB (fig. Ex. 1) in m, and join »vcen which it is requ'red to project the great circle, by a stRiight line. Bisect this line, and from the point of section erect a perpendicular to the line on the side next the Equator, continuing it, if necessary, beyond the Equator. 2._Wiih tlie middle hititude (hetwecn the two places) enter the following table, and take out the " corresponding pa-aliel.'* 3.- The centre ot the arc of the great circle, required to be drawn, will be the inter- Bection of this parallel with the perpendicular. 78 16 74 S9 71 26 67 S« 6.1 37 S9 25 SS ■; ■io ^b 46 41 18 M> :?i V ss 26 42 21 42 16 39 s 9 15 !^ 14 32 "S 19 50 25 9 J3J3o 30 S 35 52 a 41 '4 1 46 37 ^, 52 . S 57 25 <2 62 51 80 N.B — If greater accuracy is required the curve of the Great Circle should he drawn by the methods of Godlray, Tow- son, or by computation. 28 30 32 34 36 38 40 42 44 46 48 50 52 " 35 S4 6 24 56 I 13 389. Godfray's Great Circle Chnrt and Course and Distance Diagram answer all the coiiditions ot" great circle sailing as complet ly and as simply as Mercrtor's Chart does for sailing on a Rhumb. The track is a straight line which may be drawn "nd examined; then the various courses and the distances to be run upon each course are obtained, as also the distance fiom the ship to her destination, by a mere inspection of the diagram.* 3. Figures of Dif event TracJcs. 390. The track of a ship by Mercator's or by Middle Latitude Sailing, appears, as before stated (No. 378), a straight line on Mer- cator's Chart, on which the meridians and parallels of latitude are represented as straight lines. But on the globe such a course, unless it be N. or S., is really a sj^rroi, winding towards one of the poles, which it can never reach. A ship's keel cannot pass over a point which is kept at any angle on the bow. ♦ See Chart Diagram for the . fcold by J. D. I'ot eilitate the practice of Gr mmation of Courses and D' 145 Minories, London, E. e Sailing, with accompanying by Hugh Godfray, Esq., M..V. CHARTS. M9 The track by Parallel Sailing, on a circle on wliicli the ship always maintains the same distance from the pule, also appears a straicrht Ime upon the chart. Tlie track by Great Circle Sailing, excej)! wlicn on a meridian, appears on Mercator's Cliurt as a curve line. It may at ttrst seem inconsistent that a curve line can, in any case, represent a siiorter distance than a straight line ; but every point of this curve lire is nearer the pole than a point in the same longitude on the track by Merciitor: and accordingly, if we divide the curve into small por- tions, and measure each portion as in No. 382 ('2), or (3), in its o«ii latitude, we shall iind that the whole distance measures absolutely less titan the length of the rhumb line joining the places.* ll. CONSTUUCTION OF MeRCATOr's ChART. 391. The following itistructioiis are merely general : practice will supply details. In N. Lat draw a line along the foot of the paper for the parallel of lowest latitude. In S. Lat. draw the line along the top. Divide this line into degrees and parts, as 30', 15', 10', or 5'. Draw at the sides two perpendiculars to this line, for tiie graduated meridians. Find, by Table 6, the Mer. D. Lat. between the lowest parallel and 1®, or 30', &c. above it. Take with the compasses this Mer. D. Lat. from the equally divided parallel, and set it off from this line on tlie meridian to be graduHted. Find, in like manner, the Mer. D. Lat. between the said parallel and 2", or 1°, ke. above it. In this way the meridians are graduated. Parallels and meridians being drawn at convenient intervals, and the points of the coasts laid down, the coast-line is filled in by hand. III. PltOPKRTIliS OF ClORTAIN PROJECTIONS. 392. Since a small portion of a globular surface may be con- sidered, in a practical sense, as a plane, charts of coasts, and maps of * In order to verify, on a globe, the results of calculations relating to the great circle and the rhumb line, the latter must be projected on the globe. To do this, note on the chart the Intitude and longitude through which the rhumb line passes, at each 4" or 5°, or less, accord- ing to the degree of precision required ; then lay off these points on the globe, in tlieir several i4ts. and longs, by means of the moveable meridian. A curve traced by hand through the p.: lumcnt has Kcii iutiuducid wherein the dcjMh is indUatc'l *>] hjdiu:>ial c jirear(lof Admiralty, 187!>. H.M.S. dayc f , 18 1 . 1 t..ilial3 of Officer V^atch 1 I s 1 standard Comiiass Courses .... 1 Veather III Height Remarks Dircc- Force Bar. =. 1 2 3 4 5 6 8 9 10 11 12 course B stance Latitude Longitude Variation allowed Water Remiiinf True Bearing and No. on Sick-l->t Curren mad goo mile the wale DR. Obs. DR. Chro. Daily Expend" ^ Distilled 8 miles tcnliiy 1 ,.«. 2 3 4 6 6 7 8 9 10 11 12 1 Coal expended Signnlsj diirnii; ( 24 hoiiri For enpnM For..l,ip r„r.l..^tillin» 15J n. The Day's Work. 417. This is the process of finding the place of the ship, with reference either to her place at yesterday's noon, or to a departure taijen since, and comprises, 1 st, The Course and Distance made good ; 2d, The Lat. and Long, in ; 3d, The Bearing and Distance of some port, which is either to be steered for directly, or is an intermediate point of land, with refer- ence to which the course is to be shaped, so as to make it or to avoid it. 418. To work a day's work. (1.) Take the courses, with the distance run on each, from the log-board. When a departure has been taken, consider it is a course anl distance in the opposite direction. Correct each course for deviation of the compass, 229, or p. 159. If the variation has changed since the departure was taken, cor- rect each course separately. No. 221; if not, defer this correction. Every course affected by leeway must be corrected accordingly. The quantity, if not marked on the board, must be estimated from the circumstances. When the ship is on the starboard tack, allow the leeway to the left ; when on the p07-t tack, allow it to the right, the observer being supposed in the centre of the compass. When the ship is hove-to, take the middle point between that to which she comes up and that to which she falls off, for the compass course, and correct this for leeway. (2.) Having corrected the Courses thus far, take out to each the D. Lat. and Dep. from the Traverse Table, and find the Course and Distance made good by Traverse Sailing, No. 287, or by Traverse Tables (Table I.) If the variation has not been allowed for, apply it to the result- ing course, No. 221. (3.) Apply the D. Lat. to Lat. left : the result is Lat. in, No. 190. With the Lat. left and Lat. in, and the Course, find the D. Long. by Case I. of Mid. Lat. or Mercator's Sailing (No. 315 or 323), or by Traverse Table. If the Course is due E. or W., then proceed by Case I. of Parallel Sailing (No. 304) or by Traverse Table. Having the Long, left and Diff. Long., find the Long, in. No. 1 9!). (4.) Having now the Lat. and Long, of the ship, and those of the port to be worked for, find its Bearing and Distance ; if in the Lat. of the ship, by Case II. of Parallel Sailing, No. 307 ; otherwise by Case IT. of Mid. Lat., or Mercator's Sailing, No. 318 or 326; or by Traverse Table. To this Bearing apply the Variation and Devia- tion of the Comx:)ass, and so obtain from the True Course, the Course to he steered. To find the Course on a Great circle, eee No. 337 or 338. It is mere waste of time to work the Course nearer than to tlie whole degree ; for even if the compass could be depended upon to 1^, the ship cannot generally be steered within that quantity. THE SHIPS JOURNAL. 159 Courses. U.U N. s. E. W. S.E. by S. 3 25 17 S.S.E. i E. 23 203 loS S.S.E. 49 45 3 18S S. by E. i E. 24 230 70 S. by E. 6 59 12 S.W. by S. S 67 44 S.W. 7 49 4-9 S.W. by W. 7 39 5-8 W. by N. S 10 49 S.iE. 6 60 06 uS-5 40-, 200 200 ■■75 20-. Kx. 1. The sliip while hove-to for the first two hours, with light nirth-eastorlj winds, came up to E., and fell off S.S.E. ; taking S.E. by E. as the niidillo cour.se, ;Ubiw- :ng 2 Jits, leeway, and 3 miles distance, gives S.E. by S. 3 miles, .iftor which the courses and dists. follow as below. Lat left 29° 26' N., long, left 127° 42' E. : Tar. 3° E.: find the Lat. and Long, in ; also set of current in the 24 hours. Position by observation being Lat. 27'^ 55' N., Lung. 128° 43' E. D. Lat, 118 i^sS'S. Lat. left D.R. 29 26 N. Lat. in, D.R. 27 28 N. Lat. left 29° and Lat. in 27° j^ive Mid Lat. 28°. Then 28° and D. Lit. 14-5 give Dist. 16' E. Long, left 127 42 E. Long in, D.R. 127 58 E. To determine approxiniale current soo Nos. 290 to 297, aud 1015. Position by Obs.Lat.27''S5'N.,Long. I2S''43' E. Position by D.R. Lat. 27 28 N., Long. 127 ;S K. 27 45 In Lat. 28° DifT. Long. 45 = L), p. 397- n-i r> T 1 _ . IT. ■ r. Then D. lat. 27 and Dep. -so 7 The D. Lat. 1 17-5 and Dep. 20-1 give Course „• „<-„,„„„ m -ao n n ^ d , rj c o i"; T. -1 e ves CounsE N. Co J^., Di:>t. 48 in.. by Compass S. 10^ E. L>ist. 1 19 mdes. , <•,. ■ u ■',',• .0/ \ . .1 ■ I. • ^ set of LuuHENT in 24 hours. Applying 3°(var.) to the right gives Course -n i 1 i ,v, I- v. ■ • .1 S. 7° E. true. Then 7° and Dist, 119 give ^ Prol.able; the ship being in the l). Lat. I i8-i, and Dep. 145. K;'"'° ^iwo, or Japan Stream. In the foregoing example, the deviation of the compass has not been mentioned. From what has been said in Chapter II. it must be evident that the bearing taken for departure and the courses steered must be corrected for deviation, where there is any. As the deviaiion changes when the direction of head is changed, it is obvious that ciih Course must be corrected separately. To correct the Compass for Variation or Devial ion. Course by Compas given. I True Counts yiven. If Var. or Dev. East, allow to riglit. If Var. or Der. E,ist, allow to left. If Var. or Dev. West, allow to left. If Var or Dev. West, allow to right. Will give true course. I Will give magnetic course. To Correct the Compass Courses. En-sterly Variation or Deviation is + to all points between N. and E S. and W. Westerly Variation or Deviation is — from all points botwi'oii N. and E....S. and W Easterly Variation or Deviation is — from all points between N. and W....S. and E. Westerly Variation or Deviation is + to all points between N. and W S. and E. To Convert a True Course or a Correct Magnetic Course into a Compass Course. En-sterly Variation or Deviation is — from all points between N. and E....S. .md W. Westerly Variation or Deviation is + to all points between N. and E S. and W. Easterly Variation or Deviation is + to all points hetween N.and W S. aud E. Westerly Variatiou or Deviation is — from all points butwoen N.and VV....S. and E. In the following examples the Deviations from table of No. 227 have been applied to the Coinjiass Courses, to obtain the Correct Magnetic Courses. ICO THE SHIPS JOURNAL. Ex, 2, The Departure is taken from the Edcljstone, bearing N.N.E. 12 miles. Ship'i head S. by E. Toe ship ran S. by E. 14 (miles), S. by W. to, and S.W. by W. 8. Allow 25° westerly variation. Find the Bearing and Distance of U-^hant, and Course to be steerud.* The Departure gives a Course S.S.W. (No. 418 (I)). Correetin:; this and the other Courses from the Deviation Table, No. 227, S.S.W. becomes S. 18^ \V. (No. 228), S by E. become.s S. 16° W., S. by W. becomes S. 6° W.; and S.W. by W. becomes S. 50° W. Eddystone Lat. 50° 11' N. l>- Lit. 40_^-__ Lat. i.v, D.R. 49 31 N. Lat. left 50° and Lat. in ^gl" give Mid Lat. 50°. Then 50° and 10 6 as D. Lit. give Disf. 16', the D. Long. Eddj'stone Long. 4° 16' W. I). Long. 16 E. Long, i.v, D.R. I o^W. Lat. in 49° 31' Long. 4° o' llshant 48 29 54 I 2 = 62' I 4 = 64' Mid. Lat. 49°. Course 49° and Dist. 64 give D. Lat. 42 ; this, as Dep. and I). Lar. 62, give Bearimg S. 34° W., DisT. 75 m. Compass Courses. Dists Correct K. S. E. w. S.S.W. 12 S. 18° w 114 ,37 S. by E. 14 S. 16 E '35 39 S. by W. 10 S. 6 W. 9-9 10 .S.W. by W. s S. 50 W. SI 39-9 39 61 108 3-9 6-9 D. Lat. 39' 9 and Dep 6 9 give Co. S. 10° W., DisT. 41. Applying 25° to the left gives CooHSF S. 15° E. true. Then Ccnrse 15° and Dist. 4t give D. Lat. 39 6 and Dep. 106. Then Course S. 34" W. + Var. 25° W. gives S. 59° W. + Deviation 7° W. give S. 66° W., Course to be steered for Ushant. Ex. A ship from lat. 0° 5' N., and h ng. 0° 17' W., sails S.W. by S 7 miles, S. by E. 22, S.S.W. i W. 8, and N.E. by E. 20. V.ir. 19° W. Position by Obs. Lau 0° 15' S., Long. o°2oW._ Find Compass Course to be steered,* and tlie Dist. to"C. Palmas ; sperieneed in the 24 hours. Compass Courses. Dists. Correct Magnetic Courses. N. s. K w. S.W. by S. 7 S.29°W. 61 34 S. by E. 22 S. 16 E. 211 61 S.S.W. AAV. 8 S. 23 w. 7 4 3« N.E. by E. 20 N.70 E. 68 188 68 34-6 24-9 6-5 1 68 65 278 184 D. Lat. 278 and Dep. 184 give Co. S. 33° E., Di.sT. 33 miles. Applying 19° var. AV. to the lelt, gives Course S. 52° E. true. Then Course 52° and Dist. 33 give D. Lat. 20-3 and Dep. 26. To determine approximate Current, see Nob. »90 to 297, and 101.5. Lat. Obsd. 0° 1 5' S. Long. 0° 20' W. Lat. D.B. o 15 S. Long, o 9 E. Approximate Cureent West 29 ra. Lat. from 0° 5' N. h. Lat. o 20 S. LiT. IN, D.R. o IS Si Near the equator Dep. is D, Long., No. 311 ; hence, Long, from 0° 17' W. D. Long. 26 E. Long, in, D.R. o g E. By Obs. Lat. 0° 15' S. Long. 0° 20' W. C. Pal. 4 22 N. 7 44 W 4 37 = 277' 7 24 = 444- D. Lat. 277 and Dep. 444 give Course N. 58° W., and Dist. 523 miles; Course, N. 58° W. Thou -Var. 19° W. = N. 39° W. -Dev. 8 W. = N. 31 W., Compass Course to be steered. N.B. — On this course allow for cros.sing the Equatorial and Guinea Currents. * In shaping the Course, consider the direction and force of the tide may be found, tetnten the position of the ship and the port steered for. NAUTICAL ASTRONOMY. CHAPTER 1. Definitions. 419. This branch of the subject, as already tlcfinetl utkIcf the lioad Navijration, No. 179, relates to finding the place of the spec- tator on the surface of the earth by observation of the heavenly bodies. 4'20. To the spectator at the surface of the earth the heavens dppear to form a vault, or the upper half of a hollow sphere, of which he is the centre; the earth itself, or the ground or sea on which he stands, occupying the lower half. Any two points on the apparent concave or celestial surface, as two stars, for example, may be sup])osed to be connected by an arc of a circle drawn on that surface : and tiius the apparent celestial sphere may be conceived tn be marked with circles like the terrestrial globe. 421. The spectator stands with his feet towards the centre of the globe; that is, a plumb-line, which is vertical, passes through the spectator and this centre;* and thus the spectator always conceives himself on tlie summit of the globe.i' Suppose him now to descend the above line to the centre, and then suppose the upper half of the earth or globe to be cut off horizontally, that is, parallel to the horizon, or perpendicular to the plumb-line. The surface of the; lower half-globe, or hemisphere, so e.xposed, being produced on all sides to meet the concave celestial surface, is called the Rational • The earth is here supposed to he a globe ; the plumb-line does not exactly pass throujh the centre of the spheroid, but the difference is not worth notice here. t This is the principle of rectifying the globe, or placing the globe to shew the relatife poflition of the spectator and the heavens. To rectify the globe, as, for ex., for Greenwich, in 51° N. Lat. Place the globe on a level surface, so that the broad rim, or horizon, shall be horizontal. Take hold of the brass meridian, and turn the globe round in its stand (upwards or downwards) until the N. pole is 51'^ above the rim. Direct the N. point of the rim (now under the pole) to the true north. Turn the globe round its axis till Greenwich passes under the meridian j Greenwich will now be the upper- most point. The axis of the globe now makes the same angle with the wooden horizon thai the axis of the beaveus (or line joining the centre and the poles) makes iviili the horizon of the i\tee- tntur. M [G2 NAUTICAL ASTRONOMY. HonizoN. Every point of the eartli's surface lias thus a difierei.t rational horizon, but all these horizons have the same centre. 422. It becomes, in general, necessary, for considerations whicl'. will appear hereafter, to reduce celestial observations taken at the surface of the earth to what tney would have been if taken at tiie centre; in the following figures, therefore, the observer is supposed to be at the centre of the earth. The dimensions of tKe earth are so small in comparison with the vast distances of the stars, that the above change of place of the spectator from the surface to the centre, or to any other point, would produce no change whatever in the apparent places or directions of the stars ; and, accordingly, the magnitude of the earth, in drawing figures for general purposes, is neglected, the earth itself being considered as a mere point in the centre of the great sphere which circumscribes the stars. In the case of nearer bodies, as the sun and some others, and especially the moon, which, when viewed with delicate instruments, appear in ditlerent directions when seen from different points of the surface oi the earth, this apparent change of place is allowed lor by a special calculation. (See Parallax, No. 435) 423. The Zenith is the point vertically over the spectator, and distant 90° from the rational horizon at every point. The point opposite the zenith, or under the spectator's feet, on the other side of the centre, is called the Nadik. In fig. 1, NWS E represents the Rational Horizon; N S, the Meridian of the observer; N, S, E, \V, the North, South, East, and West points ; Z, the Zenith, which is seen directly over, or in one with the centre. This figure is drawn on the plane of the rational horizon, and shews the several circles as they would appear to an eye looking down vertically from a point at a great distance above the zenith. Fig. 2 is drawn on the plane of the meridian, and shews the several circles of the upper or visible half of the sphere, as they would appear to the eye situated at a great distanc3 due east of the sphere. In this figure the circle N WS E, or the horizon, appears as a straight lin» N S being seen edgeways ; while the meridian. DFTINfTIOXE. ] (J3 whicli ill ri;,'. 1 is tlie straiglit line N S, appears Iiere as tlie seiuici-cle N P Z S. Tlie E and W points are seen in one with the centre. Of these two figiirrs, that one woiiicl naturally be preferred which would hest illustrate a proposed case. Fig. I may generally be employed to exhibit the hour-angle and azimuth; and fig. 2 the altitude, when the celtstial body is near the horizon.* 424. P, the Pole of the heavens, is the point which remains fixed, whilst the rest of the celestial surface seen above the horizon appears to revolve. The pole P is here represented as the North pole ; the other extremity of the axis round which tiie sphere appears to revolve is the South pole, and takes the place of P when tiie figure is drawn for S. Lat. This pole is called the elevated pole. 425. The circle E M W, 90° from the pole, is the C'elestiai. Equator. The plane of the earth's e([uator, EMW, fig. p. .'j.5. No. 180, being extended to the heavens, marks on the sphere the celestial equator. 426. A Celestial Meridia.v is a semicircle passing through the pole of the heavens; PZS is the celestial meridian of the spectator. The ))lane of the terrestrial meridian extended to the heavens marks on the sphere the celestial meridian. 427. Circles of Altitude are circles passing through the lenith, and vertical at the place of the spectator. Thus Z A H is the circle of altitude jiassing through a star A. Such, also, are ZMS, ZPN. 428. The Prime Vertical is the vertical circle E Z W passing through the E. and W. points. In fig. 2, EZW does not appear, being in one with C Z, a radius joining the centre and zenith. When the observer is on the equator, the celestial equator and prime vertical coincide. 429. Altitude is measured on a circle of altitude from the horizon ; thus A H is the altitude of A. The arc A H is the measure of the angle A C H, which would be formed at the centre by two straight lines, C H and C A. The alt. of a body M on the meridian is M S, which is the measure of the angle M CS. 430. Parallels of Altitude are circles parallel to the horizon. 431. Zenith Distance is the arc included between the zenith and the celestial body, or the angular distance of a body from the zenith of which that arc is the measure. The zenith distance is, therefore, the complement of the altitude to 90°, as Z A. 432. The altitude of a celestial body, as seen from the surface of the earth, is called the apparent altitude ; as seen from the centic, die true altitude. A ray of light, proceeding from the body, when not in the zenith, to the eye, in traversing the earth's atmosphere, which is heavier, or denser, as it is nearer the surface, is bent more and more as i< • In like manner thf. figure may be drawn in the plane nf t!v mritor (n» in No». Ot, nt), in that of the prune verlicd, or any other circle. IGl KAUTICAT, ASTRONOJlTf, approaelies the earth, towards the perpendicular direction ; and as the spectator sees any object, not always in its true direction, but in that direction in which the light from it finally enters his eye, a celestial body appears higher than its true place. Thus, the ray S A, wiiich proceeds from a star, is more and more bent towards the vertical line A Z as it approaches the surface, whereby the spectator sees the star in the direc- tion A S', and therefore higher than its true position. The ray A Z, which traverses th( atmosphere perpendicularly, undergoes „^'. uo refraction. Thus to the eye supposed -^^^..J^ ^^^^^"^^"^a^ at the centre all rays would proceed — -^-^ without any deviation ; because lines drawn towards the centre of the sphere are perj>endicular to its circumference, parallel to whicM the atmosphere is disposed. 433. This alteration in the apparent place of a celestial body, caused by the atmosphere, is called the Astronomical Refraction. The astronomical refraction is at the zenith, and about 34' at the horizon ; hence a celestial body, when really on the horizon, appears elevated 34' above it, and is seen on the horizon when really 34 below it. From the same cause all the celestial bodies rise earlier and set later than they would were there no atmosphere. The refi'action varies with the density or weight of the air, being greater when the barometer is high, or the air cold, and less when the barometer is low, or the air warm. The m^an refraction, or that in the average state of the atmosphere, is given in Table 31, and corrections for different states of the air in Tables 32 and 33. Since refraction causes the object to appear too high, it is to be sub- tracted from the apparent altitude in reducing it to the true altitude. 434. Twilight is the effect of the illumination of the upper regions of the atmosphere by the sun, before he has risen or after he has set, at the place of the spectator. Twilight continues, gene- rally, while.the sun is less than 18° below the horizon. 435. Parallax in Altitude is the angular depression of a celestial body, in consequence of its being seen from the surfaco instead of the centre of the earth, thus: DEFINITIONS. IC^ llie body S, wliicli is vertical to the spectator (wlio always stands .vitli his feet towards tlie centre) at B, in the line C S, appears at T, being seen in the direction CST; while to a spectator at A the same body appears below T at U, or in the direction A S U ; the angle A S C, or T S U, which is equal to A S 0. No. 1 16, is tUeparulltui in altitude. (Tables 34 and 45.) The spectator at B sees S in the same line as if he were al ilie centre; that is, a body in the /.enith has no parallax. To a s])ectator at D, to whom S appears in the horizon, the depression, or parallax, is greater than at any other point. The parallax at the horizon is called the Horizontal Parallax. Since parallax makes the object apj)ear too low, it is to be added to tlie apparent altitude, in reducing it to the true altitude. 436. It is evident, by the fig. No. 435, that the farther off a celestial body is, the less parallax it will have ; and the nearer, the more. The sun has about 9" lior. par. : the moon has about 1*. I'arallax is matter of actual observation, and determines definitively the distances of the sun, moon, and planets. 437. The parallax will obviously be less if the eartli's radius is less. Now, the earth being shaped like an orange, the radius, or line from the centre to the surface, in any latitude, is less than at the equator ; hence the moon's hor. par. in the Nautical Almanac, which is the eqimtoreal hor. par., is too great for any latitude. The reduction is given in Table 41. 438. Since the apparent altitude is too great on account of refraction, and too small on account of parallax, the diff. between these quantities is the diff. between the true and apparent altitudes. This difference, or the combined effect of parallax and refraction, is called the Correction of Altitude. The moon's Corr. of Alt. is given in Table 39; that of a star is merely its refraction. 439. The Semi-diameter of a celestial body is half the angle subtended by the diameter of the visible disc. Tims to a spectator at S the semi-diameter of the body is half the angle subtended by the diameter D F, or contained between the lines S D, S F, supposed to be drawn from S to D and F; the half of this angle is D S C or C S F. and is called the seuu-diameter. It is evident that the semi-diameter will be greater as the body is nearer, and smaller as it is farther off. Thus the variations in the semi-diameter of the sun ])rove that the distance between the Bun and the earth varies at different times of the year. (Table 34.) 440. When the body S is in the zenith, it is nearer to the 8i)ec- tator by half the earth's diameter, C B, than when it is on the horizon ; hence it ai)pears larger when in the zenith. This increase of a})parent dimensions due to increase of altitude is sensible in the case of the moon only, and is called her Augmentation.* This Is given in Table 42. • The »pparent increase of the magnitiidcs of the sun and mot b B m".re optica; illusion, whatever explanation may be given of it ; IGR NAimCAI. ASTRONOMT. 441. The Declination of a celestial body is tiie portion of the nieridiaii between the equator and the body ; it is reckoned from the equator, and is either north or south. Thus, A B, tiff. 2, p. 162, i* the Declin. of A, and is north. Since the declination is measured on the celestial meridians, these Are called also declination circles. 442. Parallels of Declination are circles parallel to the equator, as the dotted line through A, in both figures, p. 162. Thus declination is reckoned from the celestial equator as latitude en the surface of the earth is reckoned from the terrestrial equator; and as both these circles are in one and the same plane, declination and terrestrial latitude corres])ond : that is, a star in 28'*N.Decl. jtasses every day vertically over all places in 28° N. Lat. 443. Polar Distance is the arc of the celestial meridian between a celestial body and the pole, or the angular distance of a body from the pole. When the Lat. and Ded. are of the same name, the pol. dist. is the compl. of the Decl. to 9U'', because the distance I'rom the pole to the equator is 90°; when the lat. and decl. are of different names, the pol. dist. is the sum of the decl. and 90°. Thus the pol. dist. of A is PA; tliat of A' in S. decl., fig. 2, is P A', which is the sum of 90° and A'B. 444. The Azimuth of a celestial body is the angle at the zenith contained between the meridian of the place of the spectator and the eii'cle of altitude passing through the body. It is reckoned to begin from that part of the meridian which is on the polar side of the zenith, that is, from the N. in north latitude; thus, the angle PZA is the azimuth of A. The angle MZA is the supplement of the azimuth to 180*. This is often used for convenience; thus, instead of N. 132" E., we say S. 48» E. 44,5. The angle N Z A or P Z A is the same thing as an angle N C II on the horizontal plane, contained between tiie north and south line C N, and a line from the eye at C to the foot of the circle of altitude H,* which is the "point of the compass" on which A is seen. Now the angle N C H is measured by the are N H ; the azimuth, accordingly, is measured by the arc of the horizon between the meridian of the place and the circle of altitude of the body. 'Jhe ship's course is the azimuth of the ship's head ; so, also, the hearing of an object is its aziinutii ; and difference of bearing is difference of azimuth. When a body is on the prime vertical, its azimuth is 90". Since refraction and parallax take place vertically, they do not affect tiie azimuth of a body. 446. The Amplitudi;; is the arc of the horizon between a celestial body at rising or setting and the E. or W. point, and is the coin- irhich the angles subtended by the discs are measured discover no change of magnitude. The constellations, as the Great Bear, Orion, &c., appear in like manner, when near the horizon, to occupy a vast space in the heavens, but when near the zenith much less. * This cannot be distinctly represented to the eye by figs 1 and 2, because in fig. 1 lb* poiuts Z and C coincide, and in fig. 2 the horizon N W S E appears as a straight line UEFINITIONS, 1G7 pleiiUMit ot tlie aziinntli ; thus E H is tlie !iiii|>litiKle of ii body risiiij; Rt II. Aiuplitiide is reckoned from the E. or \\ . ; thus, if E H is •27* the auiidiuide of H is E. 27° S. (I.) The great refraction at tlie liurizon affects sensibly the appa- rent aniplitiide. Thus, suppose the spectator in north hit. facing the I'ast, EQ part of tlie equator, EZ part of tlie prime vertical, A' a star having north deel. then E A' is the apparent amplitude at the instant of rising; but the star is known to be raised, that is, brought into view, in this case, by refraction, and therefore has not yet, in its revolution, arrived at the horizon ; A' is consequently to the left of the place A, where it would rise were there no atmosphere. Hence the arc A'A is applied to the right ' of the compass-bearing on which A' is observed, in order to correct the apparent place of tlie star for the eti'ect of refraction. This quan- tity is given in Table 59 A. In facing the west the line EQ (which would become W Q) would lie on the other side of the prime vertical, and the star would be seen to set to the riylit of its true j)lace. In south lat. the figure drawn above answers to setting, putting ^y. for E. (2.) As the elevation of the observer depresses the sea-horizon wliile it does not affect the place of the star, it produces a further effect of the same kind as that of refraction. In the case of the moon, as her parallax exceeds the refrac» tion, the opposite effect is produced ; that is, when she appears to rise, she has already, to an eye at the centre, passed the rational horizon : thus A would be the apparent place of the moon at rising, to the ritjhf. of the true place A'. 417. The latitude, or distance of the observer from the equator, is measured, on the celestial sphere, by the distance of his zenith from the celestial equator ; or Z M is the measure of the latitude, figs. p. 162. Suppose now U, a star of N. dccl., on the meridian at D., then M D is its decl. and Z D its zenith distance ; here Z M, the Lat., is the sum of the decl. and zen. dist. If D' be a star of S. decl., Z M is the diff. of Z D' and M D'. If a star d be between Z and P, the lat. Z M is the difference of M (/ and Z d. 448. Wl-.en the object is to tlie south of the observer, that is, when his zenith is to the north of the body, the zen. dist. is com- monly called N.; when his zenith i^j to the south of the body, the zen. dist. is called S. In fig. 2, ZD and Z D' are therefore called North, Zd is called South. It appears, hence, that when the Decl. and Zen. Dist. are of (he inme name, their smm is the latitude; when o( different names, their difference is the latitude. But when the star is below tlie pole, as at d', the Lat.ZM is 1C8 JAUTICAL ASTRONOMY. the Dlff. jf Md' and Zd', and M d' is the sum of M P and Pa* or of flu", and the couipl. of the dfcl. 449. M Z bein Aries (the Ram). I £= Libra (the Balance). 8 Taurus (the Bull). m Scorpio (the Scorpion). u Gemini (the Twins). ] f Sagittarius (the Archer). ffi Cancer (the Crab). I yf Capricornus (the Goat). SI Leo (the Lion). ^r Aquarius (Water Bearer), njl Virgo (the Virgin). | x Pisces (the Fishes). 4HI. Besides this perpetual motion from west to east, the sun is always changing his declination, which varies between 23° 28' N. und 23° 28' S. He crosses the equator twice in the year, namely, about the 20th of March, in coming up to us in N. lat. from the southward, and again about the 23d of Sept. in going to the souta- ward. 462. When the sun crosses the equator, he rises and sets at six o'clock in all parts of the world;* at these times, therefore, the days and nights are every where equal. 463. The two points in which the ecliptic, or sun's path, thus cuts the equator, are called the Vernal, or spring. Equinox, and the Autumnal. Equinox. 464. The sun attains his greatest N. decl. about June 21st, and the greatest S. decl. about Dec. 22d. The points at which the sun seems at these times to be stationary in declination before he dimi- nishes it, and at which the ecliptic and equator are most widely separated, are called the Summer and Winter Solstices. 465. As the light and heat received from the sun at any place vary with his altitude, and the time during which he remains above the horizon, and as both of these depend on the declination, the succession of seasons depends on the changes oftlie declination of the sun. The common or civil year, as most convenient for the affairs of life, includes the succession of the seasons. It is, therefore, the interval in which the sun leaves any parallel of declination and returns to it again, and is called a tropical year. Its length, that is, the average length of a number of such years, is 365'' 5''48"61'-6, of common or mean tiuie.f planets. Mare '', and the body is seen raised on the prime vertical by tlio effect of refraction ; unless it is the moon, which, from her parallax being greater than her refraction, is not seen at the precise time of her rising and setting. The object is above the horizon for 12 hours, and 12 hours below it. In this case the amplitude is 0, except from the effect of refraction. (5.) When the pol. dist. exceeds 90°, the celestial body rises and sets on that side of the E. and W. points which is farthest from the elevated pole ; the hour-angle at rising and setting is less than 6" : the time during which the body is above the horizon is less than 12 hours, while it is more than 12 hours below the horizon. The body does not pass the prime vertical above the horizon ; and the amplitude is i-eckoned towards the S. in N. lat., and towards the N. in S. lat. (6.) When the pol. dist. is less than 90°, the celestial body rises and sets on the same side of the E. and W. points as the elevated pole ; the hour-angle at rising and setting is greater than 6''. Tiie body is more than 12 hours above the horizon, and less than 12 hours below it. The amplitude is reckoned towards the N. in N. Lat., and towards the S. in S. Lat. ; the body passes the prime vertical twice The hour-angle at the passage of the prime vertical is less than 6^. (See Table 29.) (7.) A star having a certain declination always rises and sets in the same points, and passes the meridian and prime vertical, or any other circle of altitude at the same altitude, without regard to its R.A. rircles of altitude (excepting the meridian) do not pass through the centre, and that the length of the radius, or line drawn from the centre to the place of the observer, is different in different latitudes. The first of these conditions produces no sensible effect in practice, because the Time is not affected by it, and the same Latitude (though differing from the latitude on a sphere by the quantity in Table 52) results alike from all observations, of whatever kind, of B body not affected by parallax, — and thus the oblateness, however great, would always be neglected in determining a place by observation of the stars or the sun. By the second condition the parallax of the moon is affected, and a further correction of her apparent place becomes necessary. We have also described the first point of T as fixed, whereas it has a very slow motiosi. The stars, also, though called fixed, have slow proper motions. These and other points twt Me«'c»sary to our present suliject will be treated more at large in the Theory. DEFINITIONS. 177 (8.) As tlie piece of a star or ;iny celostial body is dotcrnilnod by its 11. A. and Decl., and as, at the jdace of the spectator, the peti- tion of the celestial equator, to which both these are referred, id fixed, it is easy to know whereabout any star is to be looked for at any time. When, as is couinionly the ciise, the time (mean or appa- rent) is given, the sun's hour-angle is known ; and therefore, when he is invisible, his place on the equator may be estimated. By means of the sun's nlace, and his 11. A., the place of the first point of Aries may be estimated; then the star's R. A. gives the place of its meri- dian on the equator, and its declination the place of tbe star with respect to the equator. When the sidereal time is given, the place of the first point of pose<2, without burdening bis memory with technical rules. In the absence of a globe, distinct ideas may be obtained of the actual positions of the celestial bodies by a circular card, as a compass-card, having the liours marked on the edge, and an axis, as a pencil, put through the centre perpendicular to the card. If this a.\is be laid N. and S., and the north end (in north lat.) raised up till it is inclined to the horizon at an angle equal to the latitude, it will represent the pol.-ir axis round which the celestial bodies revolve, the card representing the equator. The C' being brought up to the meridian, the hour of the day at the edge will shew the place of the sun's meridian at tho time. If the C' be made the first point of T, the hours become hours of R.A. ; if, then, the © be marked on the edge, on its proper R.A., and then turned round to the position proper to the hour of the day, the place of tbe first point of T is seen. Suppose, now, a small telescope were placed on the axis making an angle with tho plane of the equator, or the card, equal to the declination of some star, then, while this elar revolves parallel to the equator, the telescope, kept at the sime angle, could at any time be directed to wirds the star by merely turning the axis round, \ large instrument i6 y closing the wires. 1^0 NAUTICAL ASTRONOMY. the proper angle at which to set the index for a rough contact, and tiius saves time. It also effects some saving of time to liave the tubes of the telescope marked at the observer's focus. 493. When the angular distance between two objects is to be measured, the plane of the instrument is held in the line joining them, and the sight is directed to the fainter of the two. When, therefore, the brighter object is to the right, the instrument is held face upwards, and the image of the right-hand object brought to touch the left-hand object seen directly ; but when the brighter object is to the left (as in observing the distance between the sun and moon in high north latitudes in the forenoon), the instrument must be held face downwards, the sight being directed to the right- hand object. The contact must be made in the centre of the field, as directed above. [2.] Reading off the Angle. 494. The angle having been observed, its measure is to be read off. The arc being divided into degrees, and these subdivided into halves, thirds, &c., the smallest division contains several minutes, and the angle can thus be read, but roughly, from the arc itself. In order to read to 1', or a fraction of 1', a scale called a vernier is applied to the arc ; this is a portion of an arc having the same centre, and divided into one part more than an equal portion of the arc itself. The manner in which a more minute reading is obtained may easily be understood from the following example : — Suppose a division on the arc to be ^ of 1°, or 20', and the vernier to be equal in length to 19 divisions, or 6° 20', but divided into 20 equal parts ; then each of the divisions on the vernier is Jj of 6*^20' or 380^, that is 19', and therefore the difference between one division on the arc and one on the vernier is 1'. Suppose the beginning of the vernier and that of the arc to coincide, as in Fig. 1 ; then the first of the dividing lines of the vernier falls short of the first dividing line of the arc by i'; therefore, if we make these lines coincide, we advance the vernier i . Again, to make l^e second dividing lines of each coincide, we must move the vernier through 2', and so on. In Fig. 2 the o of the vernier stands between 20' and 40' after the division at 5", and the iil-st coincidence is at 9 ; hence the arc measured is 3° 29'. ng. 3. INSTRUMENTS OV NAUTICAL ASTRONOMY. 181 When the iiiJex is moved the contrary way, the o of the vernier goes off the arc, af seen in Ktg. 3. As the 20 of the vernier stands at 6° xo' when the two zeros coincide, if we move it i' to the riglit, the coinddjnce will occur at 19, and at 18 if we move it 2', and so cii. Hence, to measure an angle off the arc, we must read from the end of the vernier. The an shewn is 32' off the arc [3.] Adjustments. 49r). ({.') Tlie Index-Glass, or central mirror, must be perpeB- (licular to the platie of the instrument. Set the index about 60°; then, if the image of the arc in the mirror appear in perfect continuation with the arc itself, the adjust- ment is perfect; if the reflection seem to droop from the arc itsoif, tlie mirror leans back ; if it rise upward, the mirror leans forward. The position is rectified (in quadrants only) by the screws on tlie iiack. This adjustment generally rests with tlie maker, but it should be occasionally verified by the observer. (2.) The Horizon-Glass, or fixed mirror, must be perpendicular to the plane of the instrument. Set the index to 0, hold the instrument horizontally, look through the glass at the sea-horizon, or other distant object, and give the instrument a small nodding motion : then if the reflected image appear neither above nor below tho real object, the adjustment is perfect ; if the image be the lower, the glass stoops forward ; if it be the hit/her, the glass leans backward. The position is rectified by the screws. (3.) The line of sight of the telescope must be parallel to the |)lane of the instrument in which the index moves. Place the two wires of the telescope parallel to the plane of the instrument. Select two distant objects from 100° to 120° apart, as two stars, or the sun and moon, and make an exact contact at the lower wire, or that nearest the instrument. Now move the instru- ment so as to throw the images in contact upon the upper wire; if the contact is still perfect (the images having overlapped in the middle of the field), tlie adjustment is perfect ; if they have separated, the object-end of tlie telescope droops ; if they overlap, it rises. The position is rectified by the screws in the collar. When this adjust- ment is defective, the observed angle is always too (jreat. (See Table 54.) [4.] Index.P.nor. 496. The graduation of tne arc should commence at a certain point ; when this is not the ease, the Index-Error, as it is called, must be measured. The point at which the graduation of the arc is sujiposed to begin, is that at which the index stands when the mirrors are parallel, as is tiie case when the image of a distant object is seen to coincide with the object itself. The index-error, therefore, is merely the error of the place of the beginning of the divisions, and afiects all angles alike. To find the Index-]'2rror. (1.) By the Horizon Hold the instru- ment vertically, and make the image of the horizon coincide with the boriion itself as accurately as possible. If the 0, or zero of the Ex. 2. On fue arc 30' 10" Otf 33 40 Ind. Corr. add 3 30 • 45 IS2 NAUTICAL ASTRONOMY index, now stand at 0, there is no index-enor ; if it stand on the arc, tlie index-correction is so much subtracdve ; when o^tlie arc, additive.* Ex. The horizon and its image being maiie to coincide, the reading i.'? %' Oil the arc Then 3' U the Index Correction to be subtracted from every angle observed. Any distant object, or a brijjht star, answers the purpose. (2.) By the Sun. Measure the sun's horizontal diameter, f moving the index forward on the divisions; read off the measure which will 1)6 on the arc ; then cause the images to change sides by moving the index back; take the measure again, and read off; this reading will be off the arc: lialf the dilFerence of the two readings IS the index-correction. When the diameter on the arc is the greater, the correction is subtrnctive ; when the ksser, additivc.X Ex.1. On the arc 32' 10" j Off 29 5 !no. Corr. subtract i 10 1 In consequence of the spring or elasticity of the index-bar, the L-rror will be different for the onward and for the backward motion of tlie index. It has been recommended, tlierefore, to turn the tangent-screw right and left alternately, in making successive con- tacts, by which a partial compensation is obtained. This source of discrepancy is, however, effectually removed by taking all observa- tions, including tliat for index-error, with the same motion of the index-bar. The ontvard motion being adopted as the most natural, tlie tangent-screw is always employed to close the object and the reflected image, and is thus always turned in tlie same direction.^ One-fourth of the sum of the two readings should be equal to the sun's semi-diameter in the Nautical Almanac. Tiiis affords a test ot tlie accuracy with which the observation has been made. 497. Tiie adjusting screws are uefer to be touched except from * When the mirrors are parallel, a very distant object is exactly covered by its image ; but at a near object the distance between the mirrors subtends a sensible angle, or has sensible parallax, and this coincidence does not take place. The parallax of a 12-inch sextant St h.-Jf a mile distance is about 21", and is smaller for smaller dimensions and greater dis- tances, in simple proportion. Hence, for the purposes of adjustment, distances exceeding this should be employed. Captain Beechey suggests a method of adjustment by parallel rays. Naut. Mag. 1844. p. 505. f As the refraction increases towards the horizon, the lower limb is more raised than the upper limb, and the vertical diameter is shortened. This, at very low altitudes, produces d flattened or oval form in the sun and moon. X If both readings are on the arc, which can only occur when the index-error is nearly half a degree, the ind. corr. is the mean, and subtractive ; if off, additive. § Sir F. Beaufort, to whom I am indebted for the suggestion, acquaints me, that from the sensible influence of the spring of the index-bar in nice observation he ■uniformly adhered to this plan, and caused it to be followed by his officers. The late Captain Basil Hall informed me that he made it his practice to obtain the index-error both for the onward and the backward motion of the index employing the former error in all observations by the onward mntiou, such as the lunar disfarce wh«"n Increasing, and the latter in observations by tlie reverse motion, as for the Innar distsooe nberi decreasing. lylSTRUMENTS OF NAUTICAL ASTRONOMY. 183 necessiii/, and then with the greatest possible caution.* When two screws work against eacli otlier, care must be taken, in tightening one, to loosen tlie other if necessary. 498 Besides errors from these causes, there are others which are neither detected nor remedied so easily : the divisions on the art; are liable (though in these days in a very sliglit degree) to inaccu- racy, and the centering of the arc is not always perfect. f In order to test the accuracy of the arc in either of these respects, in different places, it has been proposed to measure the distance of two stars, comparing the distance with that shewn by a circle, or by an approved sextant, or deduced from calculation. J Tiie absolute error being thus found for certain places on the arc, the correction for any angle may be inferred by proportion. 499. As the two sides of the coloured glasses are not always exactly parallel, the shades may vitiate the angle. (No. 491.) Some observers find, by actual trial, the error due to any shade or com- bination of shades. Tlie shade in the eye-piece, as before stated, has not this defect ;§ but an image-shade is generally indis])ensable in taking a lunar observation. [5 J Methods of Increasing the Efficiency of the Stxtant. 500. Tlie necessity, under certain circumstances, of observing large angles, and the difficulty of measuring them, arising from the obliquity with which the rays of light, in such cases, fall on the central mirror, have led to the suggestion of various plans for extending tiie powers of the sextant. Capt. Fitzroy has employed an additional fixed horizon-glass, placed at a constant angle with the ordinary one, by Jiieans of which the image of an oiiject above, or to the right-hand of another in the * Particular attention is called to t'ciis point, because it is a common failing of " over- handy gentlemen" (to use Troughton's language) to "torment" their instruments. It is better that error should exist, provided that it is allowed for nearly, than that mischief should ensue to the instrument from ignorant attempts at a perfect adjustment ; and the skilful obser^'e^, instead of implicitly depending upon the supposed perfection of his instrument, wil! endeavour to avail himself of those cases in which errors, if they e.xist, will destroy each other. t It is also necessary that the two surfaces of the central mirror should be exactly parallel. This paralleli.sm can be tested only by observing an angle between two objects i2o'^ or 130° apart, and then repeating the observation with the mirror in a reversed position. Half the difference, if there is any, between the two results is the angle between the sur- faces. As in the best instruments the mirror is fixed, this cannot be put in practice, and the consideration is therefore omitted from the adjustments in the text. This error, how. ever, when it exists, is obviated by the method described in the next sentence of the text. t The stars for this purpose must be taken from the Nautical Almanac, as the places are required with precision. The true distance may then be computed by the rule No. 339 (2), using the Diff. of the stars' right ascensions for D. Long., and their polar distances for the colatiludes. The true distance may then be reduced to the apparent (which is that mea- sured by the instrument), by No. 842, substituting one of the stars for the moon, omitting the second corr., and applying the other star's correction the opposite way to that laid down in the tabulated directions for the star. § Working with the artificial horizon, the eye-piece of the Inverting tube should, if po.'Bible, be used insieay the same stroke. Both index-glasses are adapted to the same liorizon-glass.* Any angle is measured by putting one index forward upon the arc to any convenient number of degrees, and moving the other until both reflected images are seen in the horizon-glass. Each arc has its proper index-error. 502. Mr. C. George, R.N., has constructed a double pocket- eextant, by joining two small sextants by the face. This instru- ment, which scarcely exceeds the box-sextant in size, possesses for various approximate purposes, and for surveying, the advantages of the double sextant. t o03. The double sextant has some important advantages; it affords two alts, of the same or different celestial bodies in quick succession: this is a point of much consequence when the body appears for short intervals only, as between flying clouds, and also in observing at night, as it saves the disturbance to the eye caused by reading off; it measures the angular distance between opposite points of the horizon, J and thus serves as a dip sector ; it measures two terrestrial angles at the same instant, and thus serves as a director. The index-error of a compound angle measured by a double sextant is composed of the errors proper to each are. The error of parallelism (No. 495) in a compound angle is mate- rially reduced, since in practice each portion is less than 90°. 504. In observing altitudes at sea by the double sextant, set any angle on the upper sextant ; then, facing that part of the horizon nhich is opposite tlie sun, find his image, and bring up the horizon to the lower limb; by moving the lower index : the sum of the two readings is the suppl. of the alt. of the upper limb, affected by the dip and the index-error. Now unclamp the indexes, set the upper one to an angle less than the alt., find the image under the sun, and bring up the horizon to the lower limb: the sum of the readings is the alt. of the lower limb, affected by the dip and the index-error. Half the difference of the two sums is the app. zen. dist. cleared of the dip, semi-diameter, and index-error. * Admiral Beechey acquainted me that he constructed this sextant for the purpose of obtaining the miasures of the unfiles between two tenestiial objects at the same instant anil by one observer : a point of considerable importance in surveying, or in l'iyinf;do«n soundings, while the observer himself is in motion. A luriher advantage afforded by the ^instruction is, that when the right-hand obj-ct is too faint to be rifleeted, the sexttnl does not require to be inverted. The instrument is eonsiiucted by Gary. t Made by Gary. I The ditfcrenee between this angle and iSo" is twice the apparent dip. Thus, if this nngle, measured downwards, is 179° 48' 30", the apparent or actual dip is 5' 45". The dip sector, being mconvcuient and little used, is not described in the text. INSTRUMENTS UK NAUTICAI, ASTIJONOMV. 185 2. The litpeutini/ Rcfeclni\v JJiti- tudes, therefore, it is often impossible to observe with the qiiiclisilver except by a sextant witii additional powers.* On tiie otiier hand, when the altitude is low, the observer is obliged to inc-rease iiia distance from the quicksilver, by wliich it becomes difficult to keep sight of the image reflected in the fluid; and for altitudes less tlian 12° or 15° the observation is generally impracticable. 519. The roof should generally be placed upon asheetofsorao thin material, impervious to vapour, wliicli, condensing on the glass, obscures tiie image. A leaden stand about the size of an octavo volume, on three legs, and covered with cloth, into which the roo/ Bmks and excludes the external air, is convenient. 520. The film, or scum, which forms on the quicksilver, is pre- vented from running into the trough by holding the bottle inverted while it is poured out. A wooden scraper, fitting close to the inner breadth of the trough, has been found to remove the scum, which adheres to the wood. 521. The fluid proper for the purposes must possess the qualities of giving a bright image, and of quickly subsiding to a perfect level efter being disturbed, such as quicksilver, wafer, spirit, and otliers. An ingenious, handy, and portable mercurial horizon by the late Captain George, R.N., made by Gary, 181 Strand, is recom- mended. It consists of a disc of glass floating on mercury, in a vessel which it nearly fits, and it has an arrangement by which the mercury is introduced, ready filtered from an attached reservoir, and afterwards withdrawn, in a manner which saves a great deal of trouble. The glass floats without touching the sides of the trough, and the whole of the mercury below is ser- viceable. Anot^her advantage is, that the edges of the trough cut ofif proportionally less of the field of view, hence very low altitudes may be observed with this instrument- The glass must necessarily be of the best workmanship. When the air is calm, a piece of water, or a puddle large enough merely to exhibit the image, is often a complete substitute for the quicksilver. t 522. As the celestial bodies are sometimes distinctly visible when the sea-horizon is enveloped in mist,;]; attem])ts have been made to * To remedy this defect, it has oeen proposed to use a reflecting surface, inclined at a coiut&nt angle to the horizon, movable on a level surface or floating in quicksilver. Also, a •extant has been tixed, with its plane vertical, to a pill.ir turning on an upright axis, and the telesi-ope laid nearly horizontal by a spirit-level, the image of the body being brought down to a horizontal wire in the telescope. + A small piece of plate-glass levelled by a bubble is sometimes used, but the performance of thi« instrument is not always satisfactory. t Capt. Scoresby (" Journal of a Voyage to the Northern Whale Fisliery," p. I.'i9), re- marks, that fogs often cover the sea in the polar regions to the depth only of 150 or 200 feet, while the sky is perfectly clear. Her Majesty's sloop Zebra was a week without interruption in a dense fog, to the south- ward of the Snares, during the whole of wliich tiir? no observation could be taken, though *.he sun often shone brightly (Naut. Mag. 1844 ). The like circumstances occur in "the Smokes," on the onast of Africa. 190 NAUTICAL ASTRONOMY. obtain an artificial horizon adapted to be used on board ship, by means of the siu-face of a viscid fluid, and a mirror attached to a pendulum, which, by its weight, hangs vertically.* The objections to the first of these have already been stated. With regard to the motion of a pendulum, it is important to observe that when the ship comes to the end of her roll or lurch, it does not »t once rest in the vertical position, but continues to move onwards, or to swing, witli the velocity which it had before the shiji's motion was destroyed ; hence the ]3enduluui moves through greater angles than the ship. By combining, however, the viscid fluid and the pendulum. Commander Becher has obtained a method of measuring altitudes at sea, independently of the horizon, whicu appears, from the reports made upon it, to afford sufficient accuracy for common purposes, when the motion of the ship is not very great. f Outside the horizon-glass of the sextant is a small pendulum, an inch and a half long, suspended in oil ; to this is attaciied a horizontal arm, carrying at the inner end a slip of metal, the upper edge of which, when seen in a certain position, is the true horizon. The error is determined by observation of a known altitude, or by the help of another sextant, and is the same for all altitudes. It should be frequently examined. A lamp is attaciied for observing at night. 523. Admiral Beechey fitted, within the telescope of the sex- tant, a balance carrying a glass vane, one half of which is coloured blue, to represent the sea-horizon, and to which the celestial object is brought down. The amount of oscillation above and below the level is indicated by divisions on the glass, tlie values of which are determined by the maker. The instructions for using this instrument are as follows:— Bring down the object, as the sun's limb, to the edge of the blue and leave it there. As the ship rolls, catch with the eye the upper and lower divisions reached by the oliject, and call them out to an assistant. who writes them down with the time against each. When two or more such readings have been taken, read off the alt. and write it down. Take the mean of the readings of the vane and turn it into src according to the scale furnished. When the mean is above, tlie e-ige, add it, when heloiu, subtract it. Apply the maker's index-error; tlio result is the apparent alt. being clear of dip. Ex. Took an alt., and readings as follows; the divisions u' each: — h ro s Divis. " ' lo 50 o (+1) above \ Observ. Alt. 20 25 20 50 30 I - , |) below ^ Mean of Div. -b 50 50 (+1.S) above \ ^ 10 19 20 51 20 (-2) below ; Maker's IiiJ. Corr . - 40 Mean 10 50 40 (-J), 2.5 above, ^J below; diff. i App. Alt. 20 iS 40 below I the half is ^ of 12' or 6' to be mb. • It has also been attempted, but without success, to employ the principle upon which a icp while spinning tends to preserve a vertical position, by balancing a horizontal mirror on 11 pivot, and causing it to revolve with great velocity. t See Naut. Mag. 1844, p. 291. Several reports, with observations made bv this iiisf.M- 'iisiit, will be found in the Naut. Mag. of 1839, 1842, 1844, &c. IN8TRUMF.NT8 OF NAUTICAI, ASTRONOMT. 101 Care is to be taken to observe as near tlie centre of tlie field a* possible, and exactly under the sun ; the elbow should rest on some tirm support. With practice tlie instrument affords considerable accuracy ; and in smooth water the mean of some alts, will be within 2'. A lamp illuminates the telescope at night.* 6"24. An instrument for this purpose, indispensable when the horizon cannot be seen, will also be of great service as a check, when haze or fog, by its partial distribution, produces the ajipear- ance of tlie horizon where it is not.f The same applies to tlie uncertainty in the place of the sea-horizon which is often expe- rienced in moonlight nights. These instruments are very convenient on shore. 111. The Chrono.meter. d25. Tiie chronometer is a superior kind of watch, furnished with an apparatus by which the changes in the rate arising from the expansion or contraction of the materials by heat and cold are nearly obviated. Chronometers should be kept near the centre of gravity of the ship, which is a little below tlie water-line, and not far from the middle of the lengtii, not so mucli because the motion liere is less than elsewhere, as because the temperature below is not liable to sudden changes. In ships in which great attention is paid to the chronometers, they are usually kept in a small apartment abaft the mainmast, on a table, in cases lined with cushions of soft wool, which defend them from the jerks and vibrations of the ship. The table is secured to a beam of the deck below, and in small vessels sometimes rests on a stanchion rising from the kelson. Large chronometeis are placed in jinibals, in order to preserve a horizontal position, as inclining a watch from this position affects its rate. They have also been hung, perhaps with the view of obtaining both these objects together, in swing trays ; but as this method is found to be very unfavourable, it has been discontinued. | The chronometer-table has been itself placed in jimbals. It has also been supported by springs to diminish still further the effect of shocks. o'26. When a chronometer is placed on board it should always remain in the same position, that is, with the XII towards the same * Made by Cary. t Adm. Bayfield acquaints me that he has been complutcly deceived in the place of the borijon at the coming on of a fog. i Mi. Fisher acquaints me that he has found vn acceleration of seven seconds a-day produced by suspending a chronometer in a cot with five inches' swing. 192 NAUTICAL ASTRONOMY. part of tlie sliip, since it lias been found that distiirl)ing the positions Las altered their rates.* When a chronometer is transported from one place to another, it should be compared, before and after moving, with another chrono- meter or a good watch, in order to ascertain whether its regularity has been disturbed. 627. A chronometer sliould be wound up at regular intervals, in order that the same parts of the machine may undergo the same constant action ; it sliould, therefore, be wound up at the same hour e\ery day. In winding, the key should be turned steadily, and about half a turn taken each time, and the watch should be wound close up. After winding, tlie chronometer should be examined, to ascertain that it has not stopped. In winding up a watch, the key alone should be moved, as to turn the watch itself is to increase the velocity of winding. AVhen a chronometer is wound up after running down, it is set a-going by giving it a small horizontal circular motion. When a chronometer stops, it generally alters its rate. 528. It seems generally admitted that the jirincipal cause of the variation of the rates of chronometers is change of temperature,f and accordingly, in some ships, the temperature of the chronometer- room has been regulated by lamps. When the ship changes her climate, the rates do not ciiange at the same time with the temperature, but some time afterwards. J 529. It has been found that magnetism affects the rates of chro- nometers (see a pacer by Mr. Fisher. Nautical Magazine, 18;37). Hence it follows, that the magnetism of an iron vessel may pi'oduoe similar effects. Their rates will certainly be affected by the proximity of apparatus generating or conveying electric cun-ents. 630. Chronometers are generally found to perform best at the * This depei\ds, however, chiefly on the position of the arm of the balance. t Captain R. Owen, while employed in surveying in the West Indies, found a fall of 14° in Fahrenheit's thermometer (from 82^ to 68^) accelerated the rates 1"5 a-day, and a fall of 20' (from 82° to 62^) accelerated them two seconds a-day. X Admiral Fitzroy, who employed in his surveys of South America the unusual number of twenty-two chronometers, observes, that the ordinary motions to which chronometers arc subjected, both from the incessant action of tlie sea and in transferring them from one vessel to another, scarcely affect the rates of good watches ; and that, in general, temperature is the only cause of the alteration of rate. (Journal of the Royal Geographical Society, vol. vi.) Sir E. Belcher, however, when engaged in the survey of the west coasts of North Ame- rica, found the chronometers of H.M.S. Sulphur very materially deranged by the jerking produced by a looseness about the rudder-head and from towing the Starling, her tender ; and observes, that when these causes were removed the watches performed admirably. In the Instruction R^glementaire pour les Batiments de la Marine Royale, &c. (An- rales Maritimes, 18-10), it is recommended that the chronometers should be held in the hand during the firing of guns, and that in transporting a watch from one place to another it should be carried in both hands, in order to avoid giving it suddenly a circular motion, which may be communicated by taking it up by a handle, or becket, at the top of the case. M. Givry considers that the rates of the chronometers of La Coquille frigate, commanded by M. Duperrey on a scientific expedition, were altered by the severe thunder-storms expe- rienced on the coast of Timor, in August 1823. — Memoire sur I'Emploi des Chronometres a la Mer, par A. P. Givry, extracted from the Annales Maritimes, Paris, 1840. It has been surmised that the hot and moist climate of the coast of Africa has sj^oedily disturbed the rates of chronometers; but Adm. Vidal and Sir E iJelclier, in several years' ej:psriencu, have recoguioed no such efTecl. TAKINO OBftllfVATIONB, 193 beginning of a vo) age ;* many subsequently become useless froni iiregulciriiy, and some fail altogether. They are liable, also, to change tlieir rates suddenly, and then to reassume the former rates in a i'ew dajs.f 531. Since there seems no reason why any cause which alters the rate of one chronometer should not alter tiie rate of another i:i tiie same manner, the agi'eeuient of any number of chronometers, however great, cannot be unreservedly admitted as evidence for the truth of the time which they shew. Their irregularities, however, in this res])cct contribute to the security of navigation ; for since one chronometer often gains while another, under exactly the same cir- cumstances, loses, the discrepancies prevent the danger of trustmg too confidently to any single result. CHAPTER III. Taking Obseuvatioxs. I. Observing Altitudes. II. OnsEUVATiONS with and withodt Assistants. III. Employment of the Hack Watch. I ^^ Finding the Stars. 532. In treating of observations with reflecting instruments we shall refer chiefly to altitudes, as most convenient for the purposes of illustration. If, however, for the horizon, we substitute a celestial body or any other point, what is said of altitudes will ap])ly, with certain obvious exceptions, to angular distance generally. The; details pro]K>r to the particula" obeervations will be found under their respenive beads. I. Obseuvixg Altitudes. .0.33. The observer will do well to accustom himself to obtani a single sight with accuracy, and not to depend upon the accidental compensation of errors due to want of care. It sometimes happens that a single sight oidy can be obtained, and no good estimate of its * Advantage was taken of this circumstance in tlie late survey of part of the west coast of Afric-i by Admiral V'iil.il. who, by direction of the Uydrographei, proceeded at once to run down the coast from Sierra Leone to Corisco Bay, and returned to Sierra Leone as c|uickly *.« piissilile. The whole Diff. Long, between tliese points, as nie««ured in both runs, agreed Kitliin 1>. t Captain R. Owen remarks, that most of his chronometers took tlius a jump of one oi tvro seconds in the daily rate, more than once during his surveys in the West Indies. Otuei sificers have made aimilar reiuuka. 19'i NAUTICAL ASTRONOMT. value can obviously be tbniied if the observer knows his observHliom by thoir j^eiieral result only. 1. At Sea. [1.] Above the Sea Horizon. 534. The instrument must be vibrated or swung, so that th« linage may skim the horizon, for the altitude must be measured to the jioint vertically under the body,* No. 487. 635. When the altitude is al)Ove 60", it may be observed both from the opposite point of the horizon and from that under it, l)y the common sextant. Half the difterence of the two readings is tiie apparent zen. dist., No. 432. By this means the dip, with the un- certainty to which it is liable, and the index error, are removed. As the a])parent dip is always uncertain, and as the rules given in No. 2U8, though generally true, do not always hold good for small differences of temperature, it will be advisable, whenever precision is required, to attend to this consideration. 536. It is, in general, taken for granted that the dip is in the same state all round the horizon. This supposition M. Arago, in discussing the observations made l)y Sir E. Parry in his first polar voyage, by Capt. B. Hall in the ('liiiui Sea. and by M. Ganttier in the Mediterranean and Black Seas, thinks there is no reason to doubt. ("Coim. des Terns," 1827.) Capt. Pitzroy found however a difference of 16' on one occasion ; and Capt. Bayfield informs me that he has often observed the dip not to be the same all round the hoi-izon, more jiarticnlarjy on the coast of Labrador and in the Straits of Belleisle, where currents of unequal temperature prevail. See also note *, p. ]9(i. AVhen circumstances allow, alts, should accoi-dingly be observed at opposite points of the horizon. The mean of two alts, in such cases may not, indeed, be exactly true, but it is probably nearer the truth than one of them alone might be. For the same reason it is advisable to select stars on opposite bearings. When both the alt. and its supplement are tlius measured, and the alt. is in a state of change (as will always be the ease exce])t when the object is on the meridian), the time must be noted at each of the two contacts; and the half difference of the alt. and its suppi is the apparent zenith distance of the centre corresponding to the mean of the times. When the altitude is below 60° a sextant of additional powers, or a circle, is in general necessary for this observation. (See No. 504.) 537. When the altitude of a body is near 90°, it is pro])er, before attempting to bring down the reflected image, to ascertain, by re- * WTien the 4th Adjustment. No. 495 (3), is not perfect, we look at a point of the honzon not directly under the sun. Hence a tuhe should he used to insure the eye and the oontact of the images being at equal distances from the plane of the instrument. On tha lame ground. Dr. Maskelyne recommends the ohsen'er, when without a tube, to turn oa *iu kwei while causing the image to skim the horizon. (Nautical Almanac, 1774.) TAKING OBSF.IlVATlONd. 19j forence to tlic zonitli, or the compass, tiie precise pmiit over \vl;L~h the body is vertical. 538. When fog- obscures tlie sea-horizon from tlie deck, a new horizon may often l)e obtained by descending the ship s side, or from a boat. See No. 550, note. 539. When the limbs of the sun or moon are indistinct, altitudes of the centre are obtained by bisecting the hazy or cloudy disc upon the horizon.* 5-l0. In observing tlie moon's altitude there is a choice of the upper or lower limb when she is at the full, and also when the line of cusps, or horns, is vertical. At other times her illuminated limb, whether it be the upper or lower one, must be brought dovvr. to the horizon. Mistakes may arise in observing the moon's altitude at sea by Tiight. When the sky under the moon is unclouded, the upper edge of the illuminated part of the sea is the horizon ; but at other times long dark shadows are projected on the water, which render it dit- tieult, and sometimes impossible, to diseein the liorizon. When the moon's alt. and its supplement are both measured, if she is full, or if the line of cus])s is vertical, her alt. may be observed as directed in No. 535. But in other cases the same limb must be referred to the point of the horizon under her and to that opposite; half the difference is then the app. zen. dist. of the limb observed, and the semidiameter must be applied accordingly. When the horizon under the moon is unfavourable for observa- tion, and the supplement of the alt. alone is employed, correct the angle observed for index-error and dip, take the suppl. of the result to 180", and apply the semidiameter as to the alt. taken directly. 541. The obscurity of the sea-horizon in a dark night renders it difficult to observe the altitudes of stars or planets; but in the twi- light, when the sky is clear, the boundary of the sea exhibits a strong dark edge, most favourable for observation. The difficulty of reading oflF at night is easily overcome by having a well-trimmed dark lauthorn, and a handy assistant.t Wlieii the alt. ot a slar or a planet is measured bolli from the horizon under it and opjiosite to it, half the diff. of the two angles is the app. zen. dist. If the supplementary arc alone is employed, correct it for index-error and dip ; the supplement of the result is the apparent altitude. 54'2. When a telescope is used the unemployed eye must be closed, but when the |)lain tube is used it should, when convenient, be kept open, because the image being seen by both eyes under the tame magnitude, one assists the other. This should be practised in observing stars at niglit. La Caillc recommends keeping the eye some minutes in complete * Mr. Fisher tclla mo tliat he hiv3 rejieateiJIy emplojej, with i-oiiip'oto success, ftltitudea of the sun faintly seen through watery cUiuds, wlien those who had been used to depend solely upon the [jerfectly defined disc hail despaired o( an ohscrvation altogether. In such cases the altitudes have not greatly dilTerefl from each other, and the mean of several has been quite eoual tj an ordniary observation of the limb. t Aimall electric light (halt candle power) io found useful. 196 NAUTICAL ASTRONOMY. darkness before observing stars at nigbt. (Guejirattc, " Probleiiies d'Astron. Naut." &c., torn. i. j). 20, 18:^9.) 643. Different ))owers suit different eyes. Too low a ])o\M'r does not magnify enongb ; too bi^b a one makes it difficnit to k<'t|i tlie object in tbe field on tbe least motion of tlie instrument. 'J'lie observer, tberefore, will employ tbose powers only in wbicb tbe advantage gained by a larger image exceeds tbe disadvantage of •ncreased unsteadiness. A plain tube, bowever, sbould be used in all otber cases, botli for directing tbe siglit to tbe prjper point of observation, and for detience against disturbing ligbts. 544. All observed angles are vitiated by tbe errors of tbe instru- ment enumerated in tbe last Cbtipter, Nos. 495, 4S)8, and 499. Again, eacb observer lias in general some peculiarity in tlic manner of observing, or in tbe quality of the eye itself, wliicli gives rise to a personal error, the correction for wliicb is called tbe ■personal eijuation. No. 175. 545. Besides tbese errors, altitudes taken at sea are subject also to otbers wbicb change with circumstances. 1st. Tbe running of tbe waves causes tbe horizon to be in con- tinual motion; 2d. The rise and fall of t!ie observer, both fnun tbe tilting of the vessel by the waves, and by her rolling, cause the dip to be in continual cliange. The effects of these alternating motions will, in taking two or three altitudes, in part disappear. .3d. The place of the visible horizon changes with the tempera- ture of the sea and the air. See No. 208.* Also, since the .sea- horizon is formed by the eminences of tbe waves, it sbould be higher in bad weather. -j- Besides tbese distinct causes of error, the motion of the ship disturbs the attention and efforts of the observer. 546. Tbe height of tbe eye should be ascertained with some precision, that is, within two or three feet, because an error in the dip causes an error of the same amount in tbe altitude. This is of most importance when the observer is very near tbe water, as tbe dip then changes most rapidly; thus, it appears in Table 30, that a change of three feet in the height produces, near the beginning tit the table, a change of more than 1' in the dip, but near the end only * M. Givry observes (" Memoire sur I'EmpIoi des Chronometres," p. 23), tljat wlu-u the sea is shoal near the horizon, the relation of the temperatures of the sea and the air hiiiig different from that at places where the water is deeper, may produce extraordinary rcfracticin: uil he attributes to this cause errors amounting to 8' in the time deducx-d from some altiluiles taken near the mouth of tlie Jeba, in 1818, although circumstances appeared at the time in every respect favourable for obaervation. M. Givry remarks, further, that extraordinary refraction sometimes takes place in the neighbourhood of sandy plains, the heated air of which, passing over tlie sea, produces partial inequalities of temperature ; and he adds, that small undulations in the horizon are always indicative of irregular refraction. t It is stated, "Voyage autour du Monde," 1840, by M. Du Petit Tliouars, in tha Venus French frigate, that the observations sliewed tliis. It is probable, however, that tha errors of observation due to the motica woiiW, in general, far cxjced tliat due to the above ■lAKINM OBSERVATIONS. 107 4". All altitude oliscrveil at the toj) of a heavy sea will ('iffer coiisi- Hnrably from anollier taken at or helow tlie mean level.* If the altitude be observed above the deck, as in the top for instance, tiie horizon will apjjear better defined, and the variations of tlic dip by the shij)'s motion will be less sensible ; also the dif- ference of temperature of the sea and tlie air ajipears to alfect tiie plaee of the visible horizon less as the observer is more (devated. Hence it would appear that altitudes should be taken fron\ aloft when convenient. 547. Some observations on tlie lieights, distances, arid velocities of waves have been put on record of late years. Sir G. (Jrey,i- in his voyage home from Australia in 1837-8, obtaitied niinierous measures of the distance and velocity of waves, amongst «Iiicli are ihe following : — Vel. .45 Na iS-7 HI ft. Vcl. 195 r-6 Lieut. AVilkes (" U.S. Exploring Expedition") found the liighest waves in a heavy sea off Madeira from 14 to "25 feet high, and theii velocity 23 miles an lioiir; and at another time and place, wiih a remarkably higii and regular sea, 32 feet, with a velocity of 26 miles. The highest waves observed by Sir Jas. C. Ross, in the Nortk Atlantic, were 36 feet liigii. The highest sea seen by M. Lazarev, in the Russian Expedition of Admiral Bellingsliausen, 1819, was in 56° S. and 103° E.. but he does not state the height. In the Naiit. Mag. 1848, p. 228, are the following observations taken near the Cape of Good Hope: — Heiglit 17 f. Dist. 35 fatli. Vel. 21 miles. 20 43 t" 5° 24 21 55 to 57 26 to 27 .W8. NN'lien the spectator nears or recedes from tlic celestial btxiy, by the progress of the ship, the eti'ect ])roduccd on the allitude IS the same as tliat of a motion in the body itself, since exactly the same appearances result from the motion of either while the other remains fixed. Accordingly, in all observations, in which, from the sensible change of altitude, the time requires to be noted at each sight, the progress of the ship is included in the observed change of altitude; and the place to which the observation corresponds is that at which the ship was at the mean of the times. * The liii(;l)t of waves is asccTtained by placing one's self at »uih a height on the vessel, or her rigping, that the tops of the highest waves which pass near the ship may be seen on with the liisiant wclldetimd horizon, at the instant when the ship is at the bottom of the hollow between two heavy seas. The height of a wave thus observed, that is, the differenro of level lietnifn the summit and the bottom of the hollow (which difference is twice the height of the summit above the mean leeel), is very nearly the height of the eye alwve tJie bottom of the same hollow, the ship at the instant of observation being upright. Tlie die* tance is measured, when before the wind, by a line with marks on it. t Goiernor of New Zealand. 1 am indebted to the author for these observatioiu, of which 1 hnd a few only reduced for the course aud rate of sailing ol the ship. 198 NAUTICAL ASTRONOMY. [2.J Altitudes above the Shore Horizon. 549. It often happens that the horizon is concealed hy the inter- fention of land, while the level surface of the water marks on the Bhore a distinct horizontal line, which is a substitute for the sea- liorizon, and is called a shore- horizon. When the distance of the shore-horizon is known, enter Table 36 with this distance and the height of the eye, and use the correction therein instead of the dip in Table 30. Ex. From the height 20 feet, observed 1 Alt. 2818' ) merid. alt. 28° iS', above a shore-horizon, Corr. — 7 » miles and a quarter distant. | Alt. corrected for dip 7s~T7 550. When the distance of the shore-horizon, or water-line, is not correctly known, it may be found by means of two altitudes, the one being observed from tiie deck, and the other as high as possible, at the same time. Divide the difference of the heights in feet by the number of minutes in the diff. of alts. ; the quotient is the number of feet sub- tending an angle of 1' at that distance. Look in Table 9 for tliid number of feet, and the cori-esponding distance is the distance required. Ex. An observer, at the height of 91 feet above the sea, observed the sun's alt. 41° 3/ »bove the water-line of the sea ; another observer, at the height of 22 feet, observed it 41' 25': find the distance of the water-line, and correct the alt. for dip. The diff. of the heiglits, 69 feet, divided by 12 (the minutes in the diff. of alts.), gives 5'7 feet, which answers, in Table 9, to 3 miles, the DiST. required. Then the cor. in Table 35 to 3 miles, and height 22 feet, is 5', which subtracted from the alt. taken at 22 feet, gives 41° 20', the Alt. corrected for Dip. But as this result, like the preceding, becomes uncertain when the distance is very small, it is always advisable in such cases to en- deavour to find, by descending, a natural horizon.* 2. Observing Altitudes on Shore. 551. Altitudes are well observed above the sea-horizon from a hill or cliff of known height. Nos. 544, &c. ap])ly, with certain obvious exceptions, to altitudes of this kind taken on shore. 552. In taking the altitude of the lower limb in the quiek.=ilver, the loxoer limb of the object is made to touch the upper limb of the image in the quicksilver, as reflection inverts the object. In taking the altitude of the upper limb, the image of the body is in like manner brought below the quicksilver image altogether. Hence, when the sun is rising, and the loioer limb is observed, the images tre continually separating; but when the upper limb is observed, they are continually overlapping ; and the contrary when the sun is falling. It is useful to attend to this, as it is sometnnes doubtful, cs))ccially with the inverting telescope, which limb was observed. * This is the practice rccommcnilnl, nii his own rvpciiciici bj Dr. Scorcsby, '■ Vojng* to the Northern Whale Fishery, \^12, l-ondiMi," p. 141. TAKING OBSERVATIONS. 109 56;3 It is ailvisiilile, when circumstances permit, to move tli* iiitlex a little too niucii, whether forwards or bacirolonged, third differences will appear, and so on. When the 2d diff. is insensible, \ the sum of 2 alts., or ^ the ?um of 3 alts., or \ the sum of 5 alts., corresponds exactly to the middle of the time occupied in the observation ; but when the 2d ditf. is considerable, the arithmetical mean is in error by a quantity which is as follows: — The half sum of two alts, at the beginning and end of the interval differ from the alt. proper to the middle instant of the intei'val by l of the 2d diff. proj)er to the whole interval. The third of tiie sunt of tlie three alts, at the beginning, middle, and end of the interval, differs from the same alt. by Jj of the whole 2d diff. ; and the fifth jf the sum of 5 alts, at four equal intervals, by j'^ of the 2d diff. Ex. Lat. 5 1° 30' N. Decl. 22° 20' N. Hour-Angles. Alts. Diff. 2d Diff. 1st. qI' i6"'g« 60° 40' 8' 2d. o 20 o 60 34 35 5 33 ,. .Q. 3d. o 24 o 60 27 52 **■■* III •lih. o 28 o 60 19 58 7 54 , ,j 5tli. o 32 o 60 10 52 9 " The mean 2.1 Diff. is i' 1 1" for 4^" ; hence, as the 2d Diff varies as the square of the Interval (that is, is 4 times greater when the interval is douhled, 9 times greater when it is ♦.rehled, and so on), the whole 2d Diff. for 16'" is 4 times 4, or 16 times i' n", which ia 18' ^6". Then the mean of the 1st and 5th Alts, is 60° 25' 30", which differs from the 3d Alt. by 2' 22", or i-Slh of iS' 56". The mean of tlie 1st, 3d, and 5th Alts, is 60° 26' 18", which differs from the 3d by 1' 35", or i-i2th of 18' 56". The mean of the 5 Alts, is 5o'= zb' /li", which differs from the 3d by i' 11", or i-i6th of 18' 56". The error cannot be materially diminished by further increasing the number of alts. The correction for this error cannot be given in a concise and convenient form.* But in practice tlie intervals are not exactly eipial ; and even if they should be, the errors of observation wifl uCten conceal the 2d diff. When, therefore, from circumstances, altitudes can be obtained only at considerable intervals, it is projier to deduce a separate result from each. The 2d diff. of alt. disappears in two cases : 1st, when the object IS E. or W. ; 2d, wlien its motion is vertical. 569. The effect of the elevation of the s]iectator ujion the altitude observed in the quicksilver, is insensible in practice, since, even in the case of the moon, an elevation of a mile does not i)ruiluco a change of I" in her horizontal parallax. * The change 0' altitude in a very small portion of time depends on the latitude, and OB the azimuth of the object (see No. 669) ; but the 2d Diff.. or variatiun of the change of idt., which becomes conspicuous in a longer interval, di'|)cMils, furllu-r, upim the altitude itself, Xo exhibit this correction, therefore, a table ni treble enliy would l)e reijuired. TAKING 0USF.KVAT10N8. 201 II. Obskuvations with and without Assistants. 6()0. \\heii the arc observed is in a state of continual change, the ([uantity uieasiired corresponils to a particular instant of time. Wlien, therefore, the complete ohservation consists of varioua elements whose measures are required at tiie same instant, either the observer must have assistance, or he must himself obtain the "cveral measures in succession, and these must be reduceil afterwards to the same instant by calculation. When two or more altitudes at sea are required at the same instant, assistants have been employed to observe them. The inipro- ))riety of this custom w ill, however, appear on considering the nature of the errors of altitude (No. 545); for it is obviously impossible for an observer to keep the motion of the index so exactly adjusted to the irregular and often violent motion of the ship, as to be able to seize the altitude at command. 561. The assistant is useful chiefly in noting the time. An ob- servation of a set of altitudes, with tiieir times, for example, is con- ducted as follows: — (1.) The observer sets the index to the estimated alt. (No. 492); about i of a minute before he expects to complete the contact, he cries, " Look out!" at the instant of contact, he cries, '• Stop !" on which the assistant writes down the second, the minute, and the hour. The observer then reads off the degi-ee, nnnute, and division of the seconds, as 10", 20", 30", &c., which the assistant writes down. Three, Hve, or more altitudes make, generally, a set of W lien the assistants have watches shewing seconds, each takes his altitudes at leisure, and the whole is reduced to the same instant by calculation. (2.) The times are then added together, and the sum divided by the number of alts. 'J'he alts, are then in like manner added toge- ther, and the sum divided by their number is, when the second difference is not consideralde (3\o. 558), the alt. corresponding to the luean of the times. When the number of alts, is odd, and the intervals are nearly equal, the means will not ditier much from the middle time and its corresponding altitude. 562. When two sets of observations are taken by different jxr- sons, nearly at the same tnne, they are reduced to the same instant thus: — The difference or change of altitude (or other angular measure) in the time occupied by the observation is given ; then the interval between the given mean of the times, and that !o wiiich it is j)ro- jioseil to roiluce the observation, being tbiirid, the quantity to be applied to the altitude is determined by j)roi)ortion. For accuracy, the chanu:e of alt. must be properly computed by No. 6()!) or 671. .06;). Tiio ..b^(•rv(•r shuuhl, liowcvr, take tlie whole observation himself, a'ld he will liicn learn to otimaie hi^ results ai their leal 202 NAUTICAL ASTRONOMY. value, of wliich lie can bo no judge when they are taken l)y other jiersons. Wiien tlie observer takes his own time, he holds his watch in his hand, or places it either where he can obtain sight of it readily, or where he can hear it ticlv plainly. In the latter case, the first beat alter the instant of contact he counts 1, tiie next 2, &c. ; then, looking at the watch, he counts on till the second hand arrives at a marked number of seconds, as 10, 15, (fee; he then writes down these seconds, and after them the number of beats counted, to be sub- tructed. If the observer can count 10 or 20 seconds without an error of more than 1* or 2% he may put the watch wherever it is most conve- nient to inspect the face, and thus avoid the principal difficulty in taking the entire observation himself, especially at night. He then reads otl" the alt., and sets it down. The sum of the beats is to be deducted before the mean of the times is taken. Most watches beat 5 times in 2% or each beat counts 0'-4. Ex. After the instant of contact, i.). beats a.-e counted ; the seconrt-liand is then ■t 50', the min. 41, and the hour 10, and so on, as follows ; — 0" 42" 1°' subtrae t 14 hnu. 44 32 46 111. E.MPLOY.MENT OF THE IIaCK WaTCH. 564. This is a portable chronometer, or good watch, used for observation, to save moving the standard chronometer. Since the watch and chronometer will not in general go exactly together, they must be compared both before and after observation, in order to find wjiat time the chronometer shewed when the observation was taken. Thus, Within 5 or 10 seconds of a whole minute by the watch the observer tells the assistant to " look out" on the chronometer. At the minute he cries "Stop!" wlien the assistant writes the times, and takes their differences. This should be repeated two or three times, and the mean result employed. The observer can compare alone, by counting the beats of the chronometer till the expiration of the minute. If the difference between the watch and the chronometer be the snme before and after observation, the time of observation by the chronometer is at once deducd from that by the watch ; if not, a correction must be apjilied, aa in the following exaiu|>). AflerObs. IntCTV.iIn. Waloh ^i" : r" o» Chron. lo 31 184 Diff. 7 20 18-4 7 20 2 17 r3 1 line of observation by watch, 3'' 32"' 37*: required the time of do. by chron. The watch here has lost 3"3 on the chron. in 52". The observation taking place 21"' 37« by watch, alter the tirst comparison, we have 52'": 3" 3 :: 21'" 37*: i''"4, the loss of the watch on the chron. at the time of observ. ; this, added to 21'" 37", gives 21'" 3S'''4, which, add d to ici'31™ i!i«-4, gives 10" 52"' 56-S, the Time by Cubon. required. /jfio. M'lieii the times by watdi are separated by coiisiilerablo interval?, and the rate of the watcli is larjre, each time may requi.re to be thus cori'ected for its jirojicr gain or loss. IV. Finding the Stars. 566. Tiie most conspicuous stars have been designated, from remote antiquity, by names; besides which, tlie stars in each con- stellation or group aie distinguished, for reference, by letters and numbers. The letters chiefly used for tiiis purpose are the small letters of the Greek alphabet, which, with their names, are written as follows: — a alpha ^ zeta X lambda » pi f phi f> lieta n eta /i. mu {To x ^\ y gamma ( tbcta » nu n in 130° \V it is 8" 40" lateral Greenwich- ht when it is 61' 42'" UJore n.ion at this place, it i , 6" 42"' belc re 81' 40"', or i'' slC'" Greenwich, on the same day. Ex. 4. When it is noon in long. 40° E., it is 2'' 40"' before noon at Greenwich ; hence, when it is e"" 57'" a.m., or 5" 3'" before noon at this place, it wants 2'' 40'" and 5I' 3'", or 7'' 43" of noon at Greer.-»ich on tliis day ; or it is 16" 17"' on the day before. II. Rediction of the Ei.ement.s in the Nautical Almanac. 578. This Reduction is effected by Inspection, or by Logarithm*. No. 507. When extreme precision is required, a furtiier corrtjctioii is u(»c«;<»ary, on account of 2d Differences, No. 598. 208 NAUTICAL ASTRONOMY. 1. Reduction hy Inspection. [1.] The Suns Declmatim. 579. At Se:i,.—{\.) At noon. Take out of the Nautical Almanac, p. I., or Table (iO, the sun's decl. at noon of the day, and note whether it is increasing or decreasing ; take out of Table 19 the correction for long., and apply it, as there directed, to the decl. at noon. If the correction, when subtractive, exceed the decl. at noon in the table, the difiference is the decl. of the contrary name. Ex. 1. Nov. 13th, 1902, long 64° W. : fiiul the decl at noon. .Sun's decl. 13111, noon, I7°4S' S. (incr.) 64° VV. Table 19 +3 Rtn. DEcr.. 17 51 S. Ex. 2. March 20th. 1902, long. 178° W.- find ihe Sun's deil. at noon. Deel. 20ih, noon o 25' .S. { 4 .s. (2.) At a given hour. Ex. 1. Jtarch 21st. 187S, long. 123° \V., at 3'' P.M. : find tbe decl. Long. 123° W. = 8'' 12"" + 3''= Ii''i2"= ii'^. Hourly Var. 59"-i x 11-2 = 663" or +11'. Decl. 2lst, noon, 0° iS' N.fiiicr.) I23nv. +8'1 3" +3' J _ Red. Dkcl. o 29 For 3' A.M. the corr. will bo for 9'', or 9', suhtractive, and the Decl. is o' 17' N. Ex. 4. Sep . 22d, I S-S, long. 67° W.. u the Sun- decl. a' noon. .ong. 167° W. = ii" 8" =11'- 1 lourlvVar. ss-'-sx 11-1=6.19" or - 11'. Decl. 22d o'^ 16' N .{de cr.) 167° W. Table 19 -II Ked. Decl. IN 580. (3.) Ex. 1. May gth, 1S78, at 11'' 30'" mean time at Greenwich : find the Sun's declin. Hourly Var. 39"-s x ii'^Cor ii"-s = 454"-3 = +7' 34"'3 Decl. 9th, at noon, 17 2 3 58 -9 N. Ked. Decl. 17 3! 33 2 N. Ex. 2. Feb. 12th, 187S, long. 78° E., at Long. 78°E. = 5''I2'"- 7'-5o" = 2''38'" = 2'-6. Hourly Var. 50"-! x 26^ 130" or - 2'. Decl. I2th, noon. 13° 38' (S. (dar.) 78° E. +4' I 7" SO" -6'/ .^ Hed. Deci.. 13 36 S. l-'or 7'" 50"' A.M. the corr. is that for 4'' lo". or 3', additive, and the Decl. is I3°45'S. 1S7S, IS* 27™ mean 582. E.^. 2. March 21 time at Greenwich : iS"27'"-24i' = 8"33"'or8'-55. Hourly Var. 22d, 59"-2 x 8''-55 = 506 '-2 = - 8'26"-2 Decl. 22d, at noon, 041 42 6 N. Red. Decl. o 33 16 -4 N. [2.] TJte Suns Right Ascension, Ex. 1. June 6th. 1878. at 8" II" a.m mean time, long 1 7° W. : required the ?un K.A. Astron. Time, June, t,'' 20'' li" Long. 17° W. + I 8 Green. Time, June, 5 21 19 21"' i9"'_24'' = 2'' 41"" or 2'-7. Hourly Var. 6th, 10-31 x 2''-7 = - 27-8 R.A, 6tli, 4 57 26 4 Reo. R.A. 4"56~58 6 583. [3.] The Equal. Ex. 2. Nov. 29th, 1878, long. 103° E. tt apparent noon : find the Equation of Time. Astron. Time, Nov. 29'' o' o» 103° E. -6 5 2 Green. App. T.. Nov. 28 17 8 1 7'- 8'- - 24" = 6" 52»or6''-9. Hourly Var. 29th, o" 89 x 6'"9 = + 6'l Equation 29th, at noon, — 1 1" 30 o Kp.d. E = 5''48'"or ■i'-S Hourly Var. 25th, i* 25 x 5''-8= -7'-3 Equation 25th, at noon, +0" 20 -o Red. Ei, of T. +0 12 7 [Tefaceiy. 203. SUBORDIXATE COMPUTATIOXS. 209 (.".) \Vl>on the first deel. is increasing, ndd this prop, part to the (led. at noon ; when decreasinc) , subtract it. If the prop, part, when subtradive, exceed the dech itself, the difference is the decl. of the contrary name. ch 21'8"'. var. 21' 2Sih, noon. Uld. E«. Of T. 29'' 0° C" -6 52 28 >7 8 II -50 •0 11 29 ■0 21 •0 - 15 •I — II .so •0 -II 34 ■9 As the Equation of Time is generally required for a particular hour, the above method by Table 21 is more convenient that that by Table 20, in which the correction is given corresponding to the longi- tude, and the time at ship, without reference to the time at Green- wich. The first example worked by Table 20 will stand thus (uo STTH0I!1>INATK 211 further explanation being necessary, as (lie table is entered precisely like Table 19):— hx. 1. June 25th, 187S, long. 41° W. »t 3" 28" P.M. Ex. 2. March 26lh, 1S78, Ion?. lo.j" V), at 7" 42" A.M. (app. time). Eq. T. 25th,p.I,N.A. +2'"lS-5 ^ 26tl., +2_3I_^ Daily Vur. 127 41° W. +l-4\ ,~ 3" 28... +.-8) +3« Eq.25.h. +2 18-5 Kki.. Eq. OF T. +2 217 Astron. Time, March 25'' 19'' 42'" Eq, 25th, +6" 4-2 26th. +5 45 7 Daily Var. 185 12" 0" -9" 2) 7 4^ -5 yf- -9-5 109'^ K. + 5 b) 25th, noon. +6 4-2 i?K„. E«.ofT. +5547 .584. Accurately.— Vroceed as directed in No. 583, with more attention to precision in the several quantities. Ex. 1. Gr<-en. Date, June 25111, 1S7S, 5" 1 1- (app. time) ; find the Equation of lime. Ex. 2. Green. Date, Deo. 24th 1878. 15" 49" (app. time); find the Equation of Eq. 25th, page I., N.A. 2"' 1S-5 26tli, 2 31 -2 Eq. 24ih. N.A. -o'" io"o 25111. +0 20 -o Daily Var. 12 7 Daily Var. _30'3 6"o-,var. 12-7 3-2 1 1'", do. -l + 33 Eq. 25111. +2 18-5 15" 30™, var, 30- 19-4 19-, do. -4 -19 8 24th, Eq. -0 10 -o Ked. Eq ofT. +2 21 8 Kkd. Eq. ..fT. -o 98 [■>.] The Sultreal Time.* .58.1. Take from Table 2." the Acceleration corresponding to the hours, minutes, and seconds of the Greenwich Date; add them to the Sidereal Time at the preceding mean noon, from N A or Table 61. When the sum exceeds 24*', reject 24''. Ex I. Green. Date, Ni.v. IM. 190I, ^ Ex. '2. Green. Date, \[ari(i 23rd, 1901, jh 41"- 39>. find the .Sid. Time. By I 2o" 36" 57": find the Sid. lime. K/ 'J able* 61 and 23. I N.A. Sid. T. mean noon, Nov. 1st, 14** 40'"*3 I Sid. T mean noon, March 23d, o** I™ 7' o Accil. 3'' -5 j 20" 3 17 1 41- •. 36- 5 -9 3h' -o 57' -2 Ri;d. Sin. Time 14 40 -9 ' Rm Siu. Ti.mb 04 30 2 [5.] The Mnna's Horizontal Paallai. 586. At Sea. — As the Moon's Horizontal Parallax does not change more than 27" in 12 hours, it may be, in most cases, taken out of the Jsatitical Almanac at sight. .587. Accurateh/ ~{l.) Find the Greenwich Date. When the (freenwich time is less than 12", take out the hor. par. for the noon and miflnight of the given day; when it exceeds 12 ', take out the quantities for the midnight of the same day and the noon of the next. Take the difference between them, which is the variation in 12 hours. • The Sun's RiL'ht Asccn.sinn mav bo found mnghlv thus: -To the Sidereal Time in Table 111 apply the Kq of Time from Table BJ, a..i there rtirccted : tor ex., the Sidireil Time ou Ni>v. 1st, iQor. is 14*' 40""3. tKe l'!q. of Time is 16'" 3 .^iih. ; hen'-e, suhtractin^ i6'"*3 tVum 14I1 4o'"-3. yiies 14'' 24"', the Sun's R A. lequireJ. 212 NAUTICAL ASTRONOMY. (2.) Enter Table 21 with the Greenwich Time and the 12-hourly var., and take out the proportional part. When the horizontal paral- lax is increasing, add this prop, part ; when decreasing, subtract it from the horizontal parallax at the preceding noon or midnight. Ex 1. Green. Date, Jan. isth, 1S7S, Ex. 2. Green. Date, Aug. I2th, 1878, ,'.ll-: required the Hor. Pnr. 15" 28'" : required the H or. Par. H.P. I5ih, noon, 57' 45"-2 H.P. 1 2th, midn. 54' 56"-9 15th, midn. 58 12 7 I3fh, noon. 54 45 9 V.r. in ,2^ 27 -S Var. in 12\ It 5'"'". var. 27"-S +11 -9 3^2S", vnr i."-o -32 IS'li. noon, 57 45 -2 I2lh, midn. ?4 56 9 Kko. ]Iou. Pak. 57 57 , Rkd. Hon. Par. 54 53 7 When necessary to correct for latitude (No. 437), see Table 41, 892. [9] Ex. :!. Green Dale, Sept. nth I" 47"' : find Venus' K..\. K..'\. Sept. nth, nooci ii''37' Hourly Var.* nth, 5'-ixii'"-8 I Red. R.A. Venus II 36 Kiiiht As h, 1903, .'/ VeH'j^. Dat( 22" 47-°: find Venus' K,.\. R,.A. May 5th, noon Hourly Var.'* 5tli, I2*-9 X 22-8 Red. R.A. Venus 5" 17" 1903. 49-3 54-1 43-4 593. [10.] Declinati.m of Vti Ex. I. Green. Date, Sept. iitli, 1903, [l' 47'» : find Venus' Declination. Hourly Var.'* Sept. i iih 23"-9x III- 47'"= -4'42"-o Decl. Venus, Sept. nth, 6° 51 30 -o Red. DtrL. Venus 6 46 48 -o Ex. 2. Green. Date, Sept 11'' 47'°: find Venus' Declina Decl. Sept. Ilih, „ Sept. 1 2th, Daily Var. 11" 30'", var. 930 6-3 17-, 9 36-3 6° 51' 6 41 ?_ s, Sept. 1 93. Find the proportional part, and apply it to the Table 21 A;* thus: — • In common practice at sea the prop, part may be taken out at sight from Table 21 : when extreme precision is required the logarithms to four places only are not .sufticient. For ex., at sea, for the Time 7'' lO'", and Daily Variation '22' 27"-5, we enter the table with 22' 30", and take out at once (No. 50) the quantity about i between 6' 33 '-? at 7'' 0"', and 7' V-g at 7'' 30'", that is, 6' 40", or 6'-7. Now this mental interpolation is performed in very considerably less time than it takes to write down the quantities, while the small inac- curacy to which it is liable, amounting here to 6' 42 "-4 — 6' 40 ', or 2"-4 only, would he wholly inapjireciable in practice at sea. The logarithms in Table 21 A give in this case the result true to 0"-l; but if the prop, pari were above 8' the logs, could no longer be Upended Ex-. 3. (The K<|UntioM Date, June 25th, 6i' of Time) Green Gr. Time 6" 1 1- Daily Var. 12- loR. i;890 log. 3010 Prop. Part 3' log. 8900 Kx. 4. (Right Ascension of Venuk.) Green. M.T. 19K i-i". Daily Var. 4"' 54*. Gr.Time 19' 'V" Daily Var. 4"' 54- Zl Prop. Part 3- 55* 7X6, 8UBORl)IN.\TF. C0.MPUT.\T10NS. 215 Tako out from tliis Table the lo>r. of the Greenwich Time, and lidd to it tlie log. of tiie Daily Variation ; tlie sum is the log-, of ll)oi prop, jiart required. Ex. 1. (The Sun's Declination.) Gr< Date, M.-iy 13th, 11" 30'". Gr.Time iiii 30" log. 3195 Daily Var. 14' 41" log. 2129 Prop. Part 7' i"-6 log. 5324 Ex. 2. (The Sun's Riglit Ascensii Grter- Date, June 6th, 9'' 19'". Gr. Time 9*" 19^" log. 4^<^9 Daily Var. 4" 7'-5 lug. 7648 Proi. Part 1'" 36* log. 1-1757 3. Correction for Second Differences. 598. The quantities in the Nautical Almanac do not in geneial change uniformly, that is, by equal portions in equal times, but the differences of any scries of quantities taken in order exhibit differ- ences among themselves, or second differences, as in the case of alts., }i. 200. Ht-nce the proportional part found by the preceding rules is not always the actual change in the interval, but may require a correction, which is called the equation of second differences. The greatest error which can arise in any case from neglecting this correction, that is, the greatest value of the equation itself, is J of the whole 2d diff. ; this takes place when the interval for which the proportional part is required is half the interval for which the quantities are set down in the table. For example, suppose ttie second diff. of the sun's decl. to be 26" in 24'' ; the greatest error of neglecting the equation will be i-8th of 26", and will take place when the Green. Date is I2i', or midnight. 599. To find the Equation of Second Differences. Take the two quantities in the table ne.xt on each side of the given one, and set them down in order. Add together the 1st and 4tli, and the 2d aiul 3d ; write against the sum of the 2d and 3d, whether it be the greater or the lesser of the two sums. Half the diff. of these two sums is the 2d diff. Under the Tabular Interval, and with the Green. Date as inter- mediate time, enter Table 25 and take out the multiplier, by which multiply the 2d diff. ; this is the Equation of 2d differences. If tlie 2d sum is marked the greater, add the equation to the prop, part deduced by one of the preceding rules; if the lesser, subtract the equation. opnn u iheaing the true tenth, not only because the last figure ceases to change by lat. 7'' .tH'«, but because the last figure of any logarithm is itself but an approximation. Altliough logarithms afford material bervice in multiplication or division of many figures, yet in short and easy reductions they are attended, as is well known to experienced arith- meticiani^, with considerable loss of time, and should accordingly be resorted to only when they nwequivocally effect a saving of time and labour. It ia also important to observe that the facility of mental interpolntion constancy impro»<6 bf czeiciie, and that the habit bharpens the ucrcej^liun of arithmetical proportiviu. 21G NAUTICAL ASTKONOMY. ]3y Logarithms. To the prop. log. of thn 2(1 difF. add the ar. co. log. of the multiplier ; the sum is the prop. log. of the equation required. Ex. Greenw'oh Date, June lytli, 1878, if ii"' M.T.: find the Sun's Declination. Hie two declinations preceding are those of the i6th and 17th ; the two following are tboseof the iSthand 19th. June .6th, 23° 22 3'- 5 In Table 25, Tabular Interval 24" and 17th, 23 23 57 "3 13" J I'" give -124. igth, 23 25 26 3 This multiplied by 2475 gives f'oj, 19th, 23 26 30 -6 the EauATioN of 2d Dikfs.; which being 46 48 added to prop, part as found by No. 580, 46 40 23 6(y ■ealer) gives Declin. required. By Logs. id Diff. ^4 75 24'-75 p. log. 2-6400 Log. 9-0925 ar. CO. 0-9075 P- log- 3-5+75 600. This correction is of the most importance when the quantity attains its mtixlmum, that is, arrives at its greatest amount between two times given in the Nautical Almanac. This circumstance is known thus : — When the sum of the vars. in 1 hour opposite the Green, day and the following one is equal to the diff. of the vars. in 1 horn' oppo- site the Greenwich day and the preceding one ; for ex. on Dec. 20th, 21st, and 22d, the vars. in 1 horn- of the sun are l"-70, 0"-52, and 0''-66 respectively, lience the declin. is maximum at some time lietween the noons of the 21st and 22d. III. Conversion of Times. 1 . Intervals. [1.] To convert an Interral of Mean Time into an Interval of Sidereal Time. 601. Appro.vimately. — Increase the Intei-val by l'" fur every 6 hours, or by 10' for each liour, or by P for every 6'". 602. Accurately. — Add to the Interval the Acceleration (Table 2.S), corresponding to the liours, minutes, and seconds. Ex. 2. (Accurately.) The same ex. 'ntebv. in Si3. r. .-97 6' -or \ Interv. in Sid. T. [2.] To convert an Interral of Siderer,. Time into an Intrrnal of Mean Time. 603. Approximately. — Diminish the Interval by 1"" for every 6 hours, or by 10' for each hour, or by 1' for every 6"*. CO-i. AcciLrately. — Subtract from the Interval the Retardation* (Table 24), corresponding to the hours, minutes, and seconds. * Or from corr. spouding tubles iu N.viit. Abniinac. SUBORDINATE COMPUTATIOXS. 217 (Approximnt ■ly.) Conv urt E (Accurate!; .? The sanie S. r. i„to .M. r. 7" 13- '7- 7" >^'S-8i] /'i3-'7" o- au.l 2- - I 12 13'" -I 10-99 s M.T. 7 12" s U 17* . IN M.T. 7^12 6 -01 The above precepts relate to Intervals of time; the following are employed in the conversion of absolute time of one kind into that of another. [1- 2. Absolute Times. mvert Apparent Time into Mean Time. 005. Reduce the Equation of Time, taken from page I. of the Nautical Almanac, or from Table 62 by No. .583, or 584, and apply it to the given App. Time as directed in the said p;ige I. or in Table 62. If the Eq. of T. when subtractive exceeds the A.T., add 24'' to the A.T. and date the time on the day before. F.x. 1. March 2H, 1902, at 11'' 56™ 43" M.. A.T., long. 148° W. : tind .M.T. The (^reen. Rite is 2' 9" 49'". E(). T. 2J, i2"27«-8 3 1, '2 1 5 -6 Daily \'ar. 12 2 g* 49'". var. i2"-2 -5 -i 2il, 12 27 -8 lie I. Fq. T. +12 22 7 App. T. 23 56 43_ iAlEAN Time, 2(1 09 57 Ex. 2. Xov. 10, 1902, o'' 13"' 40' r.»i., A.T., long. 36° E : re,iuire.i .M.T. Green. Date, 35' W., at Iji' s"'!?-! Sid. T. : find M.T. The Rkd Sid. T. is o'' o"'37"'9 ; whence the appiox. M.T. is 1 1''4'"49'-3, and the Ret. to '■9 sub. leaves Mean Tii ,h 3„, [4.] To convert Mean Time into Sidereal Time. That is, having given tlie Mean Time, to find the R.A. of the Meridian. 608. In W. long, add the Acceleration for the long, to the Sid. T. at the preceding mean noon; in E. long, subtract it. To this reduced Sid. T. at mean noon add the given M. T. and the Acceleration for the said M.T. ; the result (rejecting 24'' if it e.xceed 24'') is the Sid. T. required. Ex. 1. June i9th, iS-g, long, lo' jg" 6* I-., at -j" ■i7'" 46'-6 M.T. : find Sid. T. Sid. T. at M. Noon, igfh. 6'' 29'"44'-3 Accel, for long, lo'' 39"' 6" + i 4S "o Red. S.T. M. Noon, 6 31 29-3 M.T. 3 37 46 -6 Accel. 3'' 29'-6 ) 37"' 6-, +35-8 47' •■' Sid. Time, 10 9 51 7 Ex. 2. Nov. 26tli, 1878, long. 8'> 51" ic" E., at 141" 55'" 7-8 M.T. ; find S.T. Sid. T. M. Noon. 26th, 16" 21" 7'-6 Accel for 8'' 52'" 15' — i 27 -4 Red. S.T. at M. Noon, 16 19 40 z M.T. ,4 55 7-8 Accel. 14'' 2>" iS'-o \ 55"' 9'^ +2 27-0 7-8 -o) Sid Time, IV. Houk-Angles. 1. To find the Hour-angle, Mean Time being givm. [1.] Hour-angle of the Sun. 609. Find the Green. Date; Reduce to it the Eq. of T., and apply it to the M.T. as directed p;ige II. of the Nautical Almanac, or the contrary way to that directed in Table 62 ; the result is A-T. If A.T. is less than 12'', it is the Sun's Hour-angle, reckoning from the meridian westwards ; if A.T. exceed 12'', subtract it from 24" : the remainder is t!ie Hour-angle, reckoning from the meridian pR.st wards Sl'BORUlNATIC COMPUTATIONS. 2ir> B». 1. M«y 19*1'- 1878. long- 57° 4' '^^'•. tt 3" 7" 46* M.T.: find the Sun's Hour. The Green. Onte is 19" 6" 56" 2'. Eq. T. 19th, rage II. + 3'"45"3 loili, +3 4^5 I 8 6' 56", var. 1-8 -8 Rud. Eq. T. M.T HODR-AMOLK, 3 4S-3 + 3 44 5 3 7 46 o 3 II 30-5 Ki. a. July 2d, 1878, Icng. 6 at 20" 26" 53* M.T.: find the Sun ant'le. Tlie Green. Date is i' iS'' i8" Eq. T. 2ii, Page II. 3" 3-', _3_ Daily Var. 16'' 19"", var. ii«-2 Suh. fioin M.T. M.T. 43 9 5. -6 53 o 20 23 3 30 610. \V hen tlie Sun'.s Hour-aii_>fIe is required from iiiidiiiglit, if A.T. is less than 12'', subtract it from 12'*; the remainder is tlie Hour-angle, reckoned westwards. If A.T. exceed 12'', subtract 12' from it; tiie remainder is the Hour-angle, reckoned eastwards. [2.] Hour-angle of a Star. 611. (1.) Find the Green. Date, to which reduce the Sid. T. at mean noon. (2.) To the M.T. add this reduced Sid. T., and from the sum (increased if necessary by 24'') subtract the star's R.A. ; the result is tlie Hour-angle \V. If the Hour-angle exceed 12*", subtract it from 24''; the remainder is the Hour-angle K Ej. I. July 2ist. 1878, long 32° 10' W., Ex. 2. Sept. 1st, 1878, long. 169^ 57' E. »t 9' 45" 2i» Rl.r.: required tlie Hour- at 8" 57" 39' M.T. : find the Hour anfle »ngle of Arcturus. ofAltair. Green. Date, ii'' 11'' 54" iV Green. Date, Aug. 31'' 11'' 37" 51". Sid. T. Mean Noon, ziNt, 7" 56'" 28-5 Sid. T. at M. Noon, 31st, 10" 38" 7-3 Aceel. II", 54-. lied. Sid. T. 7 58 25 -8 9 45 ?> 17 43 46 8 Accel. 21', 3 27 37-, 6-> 51', I M.f. Red. Sid. T. 10 41 40 5 M.r. 8 57 390 * R.A. HoOX-iHOLI, 3 33 18-4 19 39 19 5 * R.A. -19 44 53 s 23 54 ^6oW. HOUK-..C..P, 5 34 oE. El. 3. Oct. iBt, 1 nf Markxh. Ei. 4. Dec. 25th 878,1 187S .ng. 92" 48' K.. a , l,M,g. 86- 4S- M t 5'' 58" 19' M.T. : required tlie Hour-angl* Hora-ANGLE, 4" 20" 7-8 E. ■., a, 5^ r 35- MT.: find Higels Hour- .ngle. F.x. 5. Alarcli %n of Antares. , i«78, long. 110° 39' V lIoUK-A.NcLi.:, 5" 43'" 55* E. v., ai 11" 3'" 37- M.T.: find the H..nr.a„gl« H0UH-*II0I.E, s<- 15- 53 9- 1.. [3.] Honr-anrjle of a Planet or the Moon. 612. (1.) Find the Green. Date, and reduce thento the Sid. T. at moan noon, and the Il.A. of the body. (2.) Add this reduced SiA T. to the M.T., and proceefj ss for a star. 220 NAUTICAL ASTKOXOMT. lOx. I. Oct. I5tli, igygjong. 41° 44' W. It 6" $6" 54« r..M. BI.T. : find the Sloon' Hour-angle. Green. Date, Oct, 15" 9*" 43" 50', Sid. T. Mean Nuon, 15th, 13'' 35" jz'z Accel, g'' 43° so- li ert Sid. T. H.A. q" t s R.A. 9" lied. R.A. lied. Sid. T. w. r. f. li.A. Iio0K-* 287 13 37 81 4 40" 20-5 4 4^ 37-5 952^9 2 17 1-8967 43 50 0-6.35 I 39 9 20331 4 4° 2° '5 4 42 0-4 ,31, 37„, g.., 6 56 54 20 34 2-1 -4 42 0-4 15 52 i-7\V. Ex. 2. Fell, nth, 1S78, loi.s 87° 6' W., at 4'' 46" 48' A.M. iM.r. : tiiid the Hi.ur- angle of Mars. Green. Date, Feh. 10'' 22'' 35" i2». Sid. T. Mean Noon, 101 h 21" 21" 43-0 Aciel. 22" 3 36 -8 35° Si Hed. Sid. T. 21 15 is -6 Mars' R..\. 10th i"" i5'"57'-o Daily Var. 35" R.A. loth Red. R.A Red. Sid. T ;m.t. Mars' R.A. » 25-2 ^5• gives 21" 25" 25-5 4 46 48 26 1213 6 - 2 18 14-1 13__53__59 5 "'• o 6 o -5 E. 8 7 58'3E. 2. To fnd the Honr-avgle, the AUitvde being given. 613. By Inspection. See Explan. of Table 5. 614. By Computation. Atld togetlier the alt., lat., ami pol. dist., take half the sum, and from it subtract the alt. Add together the log. sec. of the lat., the log. cosec. of the ]iol. dist., the log. cos. of the half sum, and the log. sine of the remainder; the sum (rejecting tens) is the log. sine square of the Hour-angle.* of the logarithms give it to the Ex. 1. Alt. 37° 51', lat. ;i° 10' N., pel. dist. 70° 33', or decl. ig° 27' N. : find the Hour-angle. See Ex. 1, of No. 615. Alt. 37° 5"' Lat. 51 10 . . sec. 0-20269 Pol. dist. 70 33 ... cose( Sum 159 34 Half 79 47 ... COS. Rem. 41 56 ... sin. Hora- ANiiLE 3'' 31"' 47' sin. sq. =2552 9-24888 9"8249S 9"30204 E.\-. 2. Alt. 21° 19' 5", lat. 51° 9' 26" N. docl. 11° 14' 44" S. : find the Hour-angle. Alt. 21° 19' 5" Pts. for' Lat. 51 9 26 ...sec. 0-202536, -(■ 78 P.dist. loi 14 44 .. cosec. 0008414, -H 6 «77 173 43 >5 S6 5. 37.. 65 32 32 •■ cos. 8-738810, sin. 9-9 59 '67, 8-908937 — 201 ,. in. sq. 8-908736 2'" 19' 707 -3 29 i HOUR-AN-GI-E 2 12 I9-3 Ex. 3. Lat. 30^ ir24"N. Dcd. 14° 2' 46" N. Alt. 61=9' 17". Hour-angle il- 43™ 52'. When both the lat. and decl. are 0, the zenith distance in time is the measure of the Hour-angle. At sea it is near enough to take the alt., lat., and pol. dist., to the nearest minute; but if the sum is odd and greater that 170°, take the cos. and sin. to 30", because the neglect of this may make a sensible error in the Hour-angle. Log. I square. Table 69, is the same as the log. havrrs; 8UBORDINATK COMPrTATlONS, 221 [1.] Errors of I Zip Hour- Angle. 615. The following- rules give, very nearly, the effect of 1' error ill tie alt., hit., and pol. dist., and therefore for any small number of niin. or sec. in the like proportion : — (I.) Error of hour-anirle, or time, due to 1' error of alt.* Add together the parts for :iO" of the cos. and sine : the sum, divided by the parts for 1» (Tab. 69), gives the error required. When the alt. is too small, the hour-angle is too great; when the alt. is too great, the hour-angle is too small. (2.) Error of hour-angle, or lime, due to 1' error of lat.f Miil- tiplv the parts for 30" of the sec. by 2, and add the parts for the sine'; under the sum ]3ut the parts for 30" of the cos., and take the dirt".; divide this ditf. by the parts for 1'. When the lat. and true bearing are of the same names, the errors of the hour-angle and lat. are of the AY(/He kind ; when of contrary ;ianies, oi' contrary kinds. Ex In N. Lat., if tlie sun is to the N. of E. or W., and the Lat. employed is too great, the computed hour-angle wiU be too great; if the sun is to the S., in the same case too gmalt. (3.) Error of time, or hour-angle, due to 1' error of pol. dist. Multiply the parts for 30" of the cosec. by 2, and add the i)arts for 30" of the cos. ; under the sum put the parts for 30" of the sine; take the ditf., and divide it by the parts for 1'. \M)en the parts for 30" of the sine are less than the sum over them, the error of the hour-angle is of the contrary kind to that of the pol. dist. ; when greater, of the same kind. Ex. See Ex. 1, of No. 614. 51- 10 sec. 70 33 cose( 79 47 cos. 41 ;6 sin. • UM. 69 1 6 p. 83U J ^ Error 1 of AIL Cos. 354 Sin. 7 1 (Sum) 4"^ Error of Time 64 ■■T Sin. (Sum) .56 227 Cos. 3^ (i)itr.) .27 Error of Time of Pol. Dist. Cos. 354 (Sum) 398 Sin. 71 (Diff.) JI^ Error op Timj 3^7 The error of the hour-angle may, possibly, be made up of the sum of these three errors, but in most cases they will partially compensate. * To find, appro.Timately, the small interval of time corresponding to a small change of ■It. by means of the Azimuth: — .\dd together the log. sine of the change of alt., tlie log. cosec. of the azim., and the log. sec. of the lat. : the sum (rejecting tens) is the log. sine of the interval re€|uired. To find the same, by means of the Hour-angle : — Add together the log. sine of the change of alt., the log. sec. of the lat. and declin., the log. cos. of the alt., and tlie log. cosec. of tlie hour-angle : the sum is the log. sine, as above. One of these processes may, on some occasions, be convenient. + To find this error by means of the Azimuth : — Add together the log. cot. of the azim.. tlie log. sec. of the alt., and the log. sine of the error of lat. : the sum is the log. sine ot tlie 222 NAUTICAL ASTRONOMY. 3. To find the Hour-angle, the Azimuth hciny given. fil6. Add together the log. sine of the aziiniith, the log. cos. of the lat., and the log. sec. of the decl. ; the sum (rejecting teasy is the log. sine of the angle A.* Under A put the azimuth, reckoned from the elevated pole, and take half the sum. Take half the sum of the pol. dist. and colat., and half the ditf. Add together the log. tan. of the half sum of A and the azim., the log. cos. of the half sum of the p. dist. and colat., arid the log. sec. of the halfdiff. ; the sum (rejecting tens) is the log. cot. of an arc. When each half sum is less, or greater, than 90*', twice this arc ifi the Hour-angle required; but if one only of the half sums exceed 90°, twice liie suppl. of the are is the Hour-angle. Ex. Lat. 51° 30' N., decl. 20° i' N., azira. N. 110° ii' W. • find the Hour-angle. Az. IIO°2.' sin. 9-97201 P. Dist. 69° 58' Lat. 51 30 COS. 9-794'5 Colat. 38 30 74° 23' tan. ,i359 t)ecl. 20 2 A 38 25 Az. no zi Sum 148 46. sin. 9-793^7 half 74° 23' •Sum Diff. '3. 28 half 54 ,4 do. 15 44 COS. 9-7'i677 cot. 03 3694 4. To find the Hour-angle, the Altitude and Azimuth being given. 617. Add together the log. sine of the azim., the log. cos. of the alt., and the log. sec. of the decl. ; the sum (rejecting tens) is the log. sine of the Hour-angle. Ex. Alt. 40""' 25', azim. 69° 39', decl. 20^ 2': required tlie Hour-aiigU« Az. 69° 39' sin. 9'9720i Alt. 40 25 COS. 9-S«.5g Decl. 20 2 sec. 0-02711 GLE, 3" 17"' 48' sin. 9 88070 5. To find the Hour-angle on the Prime Vertical. 618. Bg Inspection. See Table 29. 619. Sg Computation. Add together the log. cot. of the )at. and the log. tan. of the decl. ; the sum (rejecting tens) is the log. COS. of the Hour-angle. find the Hour-angle of a cel««tiAl Ex. Lat. 31° 28', Decl. 14° 11' of the same name: find yo the prime vertical. Lat. 31° 28' cot. 0-21325 Decl. 14 II tan. 9-4026? HODR-.^NGLE, 41' 22'" 26' COS. '^I'^l 6. To find the Hour-angle at Rising or Setting. 620. Bg Inspection. When the decl. is less than 24°, take out ol • This inRlc A is the angle at the body contained between its pol. dist. and len. diit.. cf ujle PAZ, (ig. p 162. SCBORDIXATK COMl'UTATIONS. 22;? Tiifcle 26 the time of settin// ; this is the Hour-angle required. If is called also the Semidiurnal arc. When the dec!, exceeds 24", see No. 621, or Explan. of Table T) 621. Bi/ Computation. Add together the log. tangents of the lat. and dccl. ; the sum (rejecthig tens) is the log. cos. of the Hour- angle at rising or setting, or its supplement. \\'hen the lat. and deelin. are of the same name, take the supple, nicitl ; when oi contrary names the Hour-angle is that taken out. Ex.1. Lat. 48° 42' R deol. 20° 1 1' N. find tLe Hour-angle at rising or setting. Lat. 48° 4J' tan. 0-0562 Decl. 20 11 tan. 9' 56 54 1-6216 MuCR- 58 56 E.X. 2. find the H Lat. 3i°io'N. d ur-angle at rising eel. ..°I4'S ir setting. Lat. Decl. Hour-angle, 31° 10' II 14 5" 32". 24- tan tan 9-29«o 9-0796 7. To find the Hour-angle near the Meridian, hy the observed Change of Altitude. 622. The alts, must be on the same side of the meridian. Correct the diff. of alts, and the interval by adding the correction the following table : — Ti «E. i c 43"' '5' V 0' 0' 0" 6°15' o' 44" 10' 45' 3' 5'" 13 44 .6 30 , 30 50 11 4 7 ■20 45 2 2 45 056 4 ^5 23 46 30 3 7 I 3 4 43 25 47 45 4 15 26 48 3 5 30 I 17 12 5 ^' 28 49 15 6 45 I 25 5 4^ 30 50 30 8 8 ' 3+ 32 51 45 10 15 I 44 6 27 33 52 4 12 30 > 53 13 6 51 34 53 15 '4 45 2 3 35 54 30 >7 9 2 14 7 4> 36 55 45 15 2 26 37 58 5 ^3 30 2 39 14 8 36 38 .■)7 15 ^7 45 2 52 40 58 30 Q 10 3 >6 9 34 41 59 45 55 15 3 20 42 H 60 C ° 39 30 3 34 15 10 37 Add together the log. sin. of the diff. alts, (thus corrected), the log. cosec. of the interval (corrected), the log. sec. of the deelin., the log. cos. of the mean of the two alts., and the log. sec. of the lat.: the sum (rejecting tens) is the log. sine of the hour-angle at the middle of the interval, nearly. To find the hour-angle for the alt. nearest the meridian, subtract half the interval from this hour-angle. To find the hour-angle for (lie nh. furthest from the meridian, ofW half the interval to the hour- Hnong. take the diff'. between that for the proposed day and the day before. The diff. is the daily variation. Take from Table 28 the correction corresponding to the daily variation and longitude. In \V. Long, add this corr. to the time of 226 NAUTICAI, ASTRONOMY. mer. pass, on tlio given day; in E. Long, subtract it; the result is tlie time required. When one mer. pass, has 23^, and the next O*', 24" must be added to the hitter in finding the Daily Variation. F.I. I. Fin,! Mur. Pass 1878, lone. 46" W. Mer. Pass. i6tl., I7tli, of €. Jan. I .0" 9-1 n II 6 I 2 5 + 7-6 10 9 I 10 16 7 7 P.M. 6tli, E«. 2. July 24.11., 18; Hnd !lie Wlt. Pa«. of tilt Mer. Pass. Daily Var. 130° E. var. 47"-7 MEa. Pass. July 24tli, at 6"45» 8, long. 130° L Aloon. 23-19' 1-8 22 18 14 i Daily Var. 47 -7 46<'W. var. 61-5 Mkr. Pass, Jan. ibtli.at lo" 16- -16 -8 23 19 I -8 23 18 45 -o 628. As the lunar day, or the interval between the moon's mer. pass, and her return to the same meridian again, exceeds 24 hours or a mean solar day, an entire day passes at certaia intervals without a lunar transit. For ex. : — The moon passes the meridian on the 3d, at 23'' 50"", or 10™ before the noon concluding the 3d. The lunar day being, at least, 40"' longer than the mean solar day, the moon will not have reached the merid. by about 30'" at next lioon, or that concluding the 4th ; she accordingly passes the mend, about 0'' 30"' on the 5th, having skipped the 4th altogether There may thus be no mer. pass, on the day proposed.* Ex. 1. March 3rd, 187?, Snd the Moon's Mer. Pass. Mer. Pass. 2 D.iily V.ir. ,ong. 21° W. var. 39"-4 ng. 31° W. i3"44"-i ° »3 -5 39 4 Mer. Pa. March 3rJ at ' 46»- 1 13 46 Ex. 2. October 26th, 1878, long. 38" E.: find the Moon's Mer. Pass. Mer. Pass. 26'' o"" 7"7 25 * * 24 23 10 -2 Daily Var. 57 5 Long. 38° E., var. ST"5 5 7 »6 g 7 7 IMer. Pass. 26 o 2-0 October 26th, at o"" a," p.m. In W. Long., when the sum of the corr. and mer. j^ass. exceeds 24'', subtract 24'', and reckon tlie time on tlie next day. In E. long., when the corr. exceeds the time of mer. jjass., add 24'' to the latter, and reckon the time on the day before. Ex. 2. Suppose Ex. 2 above, the long to he 90° E. Long. 90° E., var. sT°-S - ' 3'°7 i6' o" 7 7 X. 1. Supp 3se Ex. 1 above, the 1 . .70° w. g. 170° w. va r. 39-4 +.8-0 2" 23 44 -I Mer. Pa «. 302 -I March yd. a O* 2"-I P.M. Mer. Pa: October 26tb, i''54"'/ 13 S4 * This occurs abont the time of conjunction with the sun, and the day skipped is marked <5 in the Nautical Almanac. In like manner a day is skipped at the loiver transit (under the. pole) at opposition. STTBORPINATE COMPUTATIONS. 227 [4.] Meridian Postage of a Planet. (J29. The nioridiiin passages of the planets, like those of the moon, are given in the Nautical Almanac to 0'"-l of mean time. A planet, of which the R.A. increases faster than that of the sun, ski] s a day at conjunction, as observed in No. 628 of the moon. On the other hand, when the R.A. diminishes, or the motion of the jilanet among the stars is reversed, two transits occur within the limits of the mean solar day. As the greatest daily variation of meridian passage of Venn* amounts to 6"" only, the mer. passages of the planets may be taken at once from the Nautical Almanac for all practical pui'posea. 2. Time of Passage of the Pnme VerticaL [1.] Of the Sun. 630. Approximatehj. Find the Ilonr-angle by Table 29 : this is the App. 'i'inie, approximately, of the afternoon passage; the supple- ment to 12'' is the Aj)prox. Appar. Time of the forenoon passage. Prin Ex. 1. Jan. 20th, 1S78, lat. 39° S. : tho times of the Sun's Paasage of the Ex. 2 find the ; Vertical. Lat. 55° (led. 23° 27' N., or 23I ', Hour, angle 4'' 52'", which is p.m. traii-sit : tti4 other passage is at ^*' 8" A.ii. Jan. 20th, Sun's Decl.20° 5' S., Table 29, lat. 39° and docl. 20°, give Hour-angle 4" 1 3"'. The AT. of the W. transit is 4" 1 3°' P.M., that of the E. is 12'' —4'' 13'", or V"" 47"' A-M- 631. Accurately. Having found the Approx. App. Time as abovo (No. 630), apply to it the long, in time; this gives the Green. Dato in Apj). Time. To this reduce the sun's declination, and compute the hour-angle by No. 619. Eic. I. Aug. »9th, 1878. required tlic App. Time of Pas'^agc P.M. at Tunby, in lat 51° 40 20" N., long. 4° 41' W. Part, for Ut. 5..r' 37 AT. OF Skttino • 7 i» Or at 5" I8'"A.M onzd. fi^8. To find tlie cliaiifre in the time of ajiparent rising or setting due to flio iiorizonfal refraction and tlie lieiglit of the spectator, No. 44(5 (I) and (-2). Jii/ Comjnitation. Add topjether the log. .secants of the latitude and d(X'liiiatioii, tlie log. cosec. of tlie lioiir-aiigle at rising or setting, Biid the log. sine of 34' + (le])r. for the height of the eye, Table 8 ; the sum is the log. sine of tlie portion of time required, nearly. Ex. 1. Find the difference of times ( Sunset to an eye at the level of the sea, an on the summit of the Peak of Teneriffe, o May 4th. Hour-angle at setting (No. 621), 61" 35"' 52 La*:. i8° i6' sec. o'055i Decl. 16 10 sec. 00175 Il.-Ang. 6'' 36"' cosec. 0-005+ 34'+ 1 17=2° 31' sin. 8-6.)26 Time reu. 12"' 3" sin. 87206 Ex. 2. Lat. 28° i6'N., dedin. 16° 10' N. : re(|uired the difference in I he times ol Sunset to the eye at the level of the sea, and elevated 16 feet above it. 1 1 our-angle at level of the sea, 6'' 35" 52'. Lat. sec. 0-0551 Decl. sec. 0-0175 Hour-angle cosec. 00054 34 -h 4', sin. 8-0435 Time reu. 3"" 2' sin. J-I2I5 This process is very nearly correct in low latitudes, but in high latitudes, where the body, instead of ra])idiy jiassing the horizon, partly skims along it, the result, when the dip is large, is too fimali. Thus, for the above depression, 117', in hit. .50° (and declination above), tlie time comes out 17'" 2;^', it should be 17" 38'; and in lat. 6()0 the re.sult, 24."- 17% should be 25™ 4'. 639. More accurately, find the Hour-angle of the given celestial body when below the horizon 34' 4- de])ression due to the observei's lieigiit, by No. 642; this is effected by using 34'-fdepr., instead ol 18°. The Uiff. between this Hour-angle and that found by No. 621 is the portion of time required.* 640. Since the moon's parallax exceeds the refraction, Nos. 433 and 436, she always ap])ears below her true place, and therefore ri.«es later, and sets earlier, than a more distant body of the same declination. Accordingly, in the preceding rule we must use, in- stead of 34', the diff. between the hor. j)ar. and 34', and the differ- ence instead of the sum of the latter and the depression. If the depression is the greater, the rising is accelerated, otherwise re- tarded. For the hor. ])ar. 61', these effects neutralise each oilier at the height of 6.50 feet; for .53', at 320 feet; that is, to the eye ,)laced at these heiglits the moon in these cases rises and sets nearly at her true time. strictness, however III oiriutiiran, iiuwrvci, suiiic Liirrci:iniii ibcn (he bod} is «een at a cunaiderablc drpressi (nubti active) is doe to the refmctioa it«I/ 230 NAUTICAL ASTRONOMY. 4. Tiniea of the Beginning and End of Twilight 641. By Inspection. See Explanation of Table 5. 642. By Computation. Add together 18°, tlie lat., and the pol. ^dist., take half the sum, and from it subtract 18°, or the upi)er term. Add together the log. sec. of the lat, the log. cosec. of the poL dist., the log. sine of the half sum, and the log. cos. of the re- mainder; the sum (rejecting tens) is the log. sine square of the nun's hour-angle when 18° below tlie horizon. This Hour-angle is the App. time of the end of twilight, p.m. ; and the supplement to 12'' is the App. time of the beginning, a.m. Note. — ^Tlie declination at noon, and 4, or even 3, places in the logs, are enough for this purpose. Ex.2. Dec. 2ist, 187S, lat. 55° i' N. : find the Beginning and End of Twilight. Const. 18° o' Ej. 1. April 22d, 1878, lat. 5i°46'N the Beginning and End of Twiliglit. Const I go Lat. 51 46 sec. 0-2084 F.D. 77 »47 15 31 cosec. 001 00 73 45 sine 9-9823 55 45 cosine 9-7504 End gi" 28°' sine sq. 9-9511 Lat. 55 I P.D. 113 27 1S6 28 see. 0-2416 cosec. o-o;74 93 '+ 75 >4 sine 9-9993 cosine 9-4063 sines - 3" 27'", or 2" 26'". The shortest duration is at the equator, when the sun moves through 18° in P 12"; at the poles it continues several months. When the lat. (of the same name with the deck) exceeds the conipl. of 18° + deck, the sim is less than 18° below the horizon at midnight, or twilight lasts all night, as for ex. with lat. 58° N., deck 21° N. VI. Altitudes. 1. Correction of the Observed Altitudes. 644. The corrections necessary to reduce an altitude observed from the sea-horizon with a sextant or circle to the true altitude, consists of the Index Correction, the Dip, the Correction of Altitude (or the joint effect of refraction and parallax. No. 438,) and, in certain cases, the Semidiameter. SURORDINATF, COMPUSA TIONS. 231 Wlien one of the instruments, No. 522 or 623 is used, the ]3ip is Oiuitterl ; the constant correction sliould be applied tlie fii-st thing. G4.5. The apparent alt. is deduced from tlie observed alt. by ap- plying all the above corrections except rerhiction and parallax. (i4(>. AMr'ii the altitude is less than 1U°, the mean refraclion in Table 31 may be in error more than 1', and should be corrected by Tables ;J2 and 33 if a barometer and thermometer are at hand. For precision, this is necessary in all cases. [ I . ] To Correct the Sun 's Altilmle. 647. At Sea. Ai)ply the Ind. Corr. ; subtract the dip corre- sponding to the heiglit of the eye, I'able 30; subtract the reliaction for tiiis alt., Table 31, to the nearest minute. When the iaicer limb is observed, add 16' to this reduced alt.; when the uppc7- limb is observed, subtract IG'; the result is the true or correcteil alt. of the sun's centre. Ex. 1. Obs. alt. of Q 2S° 54', inJ. Ex. 2. Obs. alt. of 42° 11'. ind. corr. +f, height of the eye i6 feet: re- corr. -17', lu■i^llt of the eye 30 feet: re- quired True Alt. of the centre. quired True Ah. of the centre. Obs. Alt. 28° 54' Obs. Alt. 42° 11' IdU. Corr. + 3 Ind. Corr. — 17 28 57 4' 5+ Dip -4 Dip -5 28 53 41 49 Refr. (for 29°) — 2 Rcfr. (for 42') 28 5. 4. 48 Semid. (lotv. I.) +16 Semid. (upper !.) -16 True Alt. 29 7 TrukAlt. 4. 32 Kx. 3. Obs. alt. Q 10° 4', iud. corr. t 2 , height of eye 18 feet : required the True Alt. of .Sun's centre. Tr.hAlt. .o",3 Ex. 4. Obs. alt. 42° 11', ind. corr. - -17', height of eye 30 feet : required the Tree Alt. of the centre. Tkuf. Alt. 41° 32'. 648. In the open sea, where an error of 2' or 3' of lat., and a corresponding error of long., are of no great consequence, the corr. of ait. for the sun (when liie loirrr liml) is observed), may be taken from Table 38, in which it is •,iveii to tlie nearest minute. X. 1. (Ex. 1 above.) Ex. 2. (Ex. 3 above.) Obs. Alt. Q 28 54 Obs. Alt. Q .0° 4 I:iJ. Corr. + % Ind. Corr. 28 57 7^ 6 Ht. 16 {., Alt. zy" Corr. lit. 18 f., .\1(. 10 \ Con • + 7 Trub Alt. 29 8 True Alt. 10 13 If the upper limb has been observed, proceed as above, ana deduct 32'. Ei. Obs. Alt. 88° 40', Ht. of Eye 30 f., Ind. Corr. - 5 , True Alt. 88° 14'. 649. Accnrateh/. Apply the iud. corr. and (at sea) the dip; rorrect the refr. bj' Tables 32, 33 ; take tlie scmid. and parallax from tile Nautical Almanac; and subtract the piuallax in alt., Table 34.. Miinite acci:racy in ait. at sea euii rarely be worth ti)c tri.(ubl«» 232 NAUTICATi ASTkoNOMt. oestowed upon it, from the uncertain state of the sea-horizon. The examples, No. 651, will serve, supplying the dip. 650. SVhen the altitude of eitlier limb of tlie sun is observed, and the altitude of tlie other limb (which will appear the same in the instrument) is observed from the opposite point of the horizon (No. 635), take half the dirt", of these angles and add to it the correction of alt. ; the sum is the true zen. dist. Ex. 1. Obs. Alt. Q S. 63''49'io", N. 115° 46' zo": required the true Zenith Distance. QN. 1 1 5° 46' 63 49 True Z. Dist. 25 58 59 N. Ex. 2. Obs. Alt. Q N. 81° 59' o", ll S. 97° 40' 30": required the trae Zenith distance. Q S. 97° 40' 30" N. 8. 59 o 2) 154130 Lpp. Zen. Uist. 7 50 4j RelV. + 8 Tkue Z. Dist. 7 50 53 S. 651. On Shore. When the alt. is observed from the quicksilver, apply the ind. corr. at once; halve the result, and proceed as in ^Jo. 649, omitting the dip. Ex.1. Jan. I Ft 1878, alt. (^ir the i the True Alt. 46° 12 Sub. 3', 4', and i' 8 Teuk All 46 4 having corrected for iiidei. error, subtract the corr. in Table 38. BlIBORDINATE COMPUTATIONS. 2.",3 Ej. S. Obs. alt. of the planet Venus 30^ 14', ind. eorr. + 3', height cf eye 12 feet : reqaire.1 the True Alt. Jbs. Alt. 30° 1+' Ind. Cjrr. + 3' 1 Table 38, -5 ) ^ Tbce Alt. 30 12 Ei. 4. Obs. alt. of the planet Mtn 78° 57', ind. corr. + 7, height of eye jo feeti required the True Alt. Obs. Alt. 78° 57 Ind. Corr. + 7' 1 , Table 38, -5 ) "*• ^ True Alt. 78 59 (i.').3. Accitrately. Proceed as for the sun, No. 640, omitting seinidianietcr. A star's corr. of alt. is the refraction alone, No. 438, p. 147. For a ])hinet, find the hor. par. in the Nautical Almanac; find the j)ar. in alt. corresponding, in Table 45, and deduct it from the refraction. Ei. 1 . Obs. Alt. of Sinus in the quick- liJver 37' 9' 35", ind. corr. —7' 30", bar. 30-2, therm. 42'' : required the True Alt. :^( Obs. Alt. 37' 9' 35" Ind. Corr. —7 30 2) 17^~~5 iS 31 2 M. Refr. 2' 53") Therm. + 3 Corr. —2 57 True Alt -^ 57 Ex. 2. Obs alt. of 5 37 ^5 38 11 Dip - 4 Semid -.5) «,°c', H.P. 55' True Alt. 60 s8 + 26 6. Z4 Ex. 3. Jan. 3d, 1878, long Ind. corr. + 3' 159° E., at 9" 10"- P.M !) 85° 42', height of eye 20 feet, True Alt. 86^ 1'. Ex. 4. July 5th, iS78,long 18 feet. 172° W., at 3' A.y..: J 14" 28', ind. corr. 0', bright of eye True Alt. 15" i'. 655. Acr.urateh/. (1.) Reduce the hor. par. to the Gr. Date, and find the semid. Table 40. Reduce the par. by Table 41, and augment the semid. Table 42. (2.) Take out the refraction for the limb observed, correct it for baroni. and therm. ; subtract this corrected refraction from the alt. and apply the augmented aemidiameter. (3.) To the log. sec. of the alt. thus reduced add the prop. log. of the reduced hor. parallax; the sum is the prop. log. of the parallax in alt. This par. added to the reduced alt. gives the true alt. of the centre. As, however, the degree of precision obtained by these prece])tj will rarely be required, we shall, in the following examjile, employ Table 39. Ex. 1. July 30th, 1S78. lat. 42° S., long. 42° 13' W., at 5'' 36 ' 39' 50", iud. corr. +2' 17", height of eye 22 feetj therm. 72 True Alt. e Gr. Date, 30th, S^ I r 30- H.P. 30th, Noon 59 55"6 30th. Midn. 60 6 2 I2-I.uurly Var. + 10 -6 8" 14", var. io"-6 + 7 •» 59 55 6 Eq.iat. H.r. 60 .8 Red. for Lat. "5 '2 Ued. U P. 59 5' f I corresp. to 59' 58 ' I 5' 21 Augment. 10 Aug. Semiil. 16 31' Obs. Alt. Ind. Corr. + 2' 17 Dip. -4 30 Aug. Semid. 36° 50' and 59' 4 58" iprin. 72°, sub. 3" M.T. obs. alt. T) :gi : required tha 36 37 37 + ■63 ' 36 54 8 45 56" — 2 _+4L 46 41 46 46 4 46 46 37 40 54 656. When the moon i.-; referred to the opposite point of the horizon. No. 535, half the ditf. of the alt. and its supplement is the zenith distance of the illumin..ted limb, to which ti:e augmented * The examf les being given merely iu illuatration of the nilfcs, no regard huH been p~id to the vuibility cf the 0100a at the time and place specified. SrnORDINATE COMI'UTATIONS. 2 "5 seinid. fa to be apjilieil the contrary way to that direoicil for tlie alt. In certain cases botli limbs can thus be observed, No. 540, and the semidiametcr avoided. "2. To Reduce the True to the Apparent Altitude. (1.1 For the Sun, a Star, or a Planet. 657. Take out the refraction to tlie true alt. as if for the aoj). alt., correcting; it, when necessary, for the baroin. and therm. ; sub- tract the parallax in alt., add the remainder to the true alt., and subtract the correction in Table 43. [2.] For the Moon. 6.58. Find her corr. of alt. for the true alt., as if for the app. alt., and apply the corr., Table 44. Ex. J 's Hor. Par. 59', True Alt. 48° 41' 12" 48° 41', and so', — -iS' 6") „ Corr! Tabic 44, i 28 ) " ^^ 34 App. Alt. 48 2 38 fi.')?). To reduce the app. alt. to the observed alt. for a particular instrument and given height of the eye, apply the ind. corr. the vjiposile way, and add the dip. 3. Reduction of Two Altitudes to an Intermediate Point of Time. ()60. Two altitudes observed at periods of time not distant, at^brd, by simple p.-oportion, the altitude at an intermediate time. (1.) Find the interval between the time of the 1st alt. and the time proposed, and call it the partial interval. (2.) To the prop. log. of the partial interval add the ar. co. pro]), log. of the whole interval, and the prop. log. of the ditf. of alts.; the sum is the prop. log. of the change of alt. in the jjartial interval. (3.) When the 1st alt. is the lesser, add this change; when it is the greater, subtract the change. Ex. 1. At lo*" iS™ 4" by watcb, obs. an alt. 54° 56'; at 10*1 29"' 1 1» obs. a seconJ ilt. 55" 12'; reijuircd the Alt. at 10'' 23"' 6». Alt. 54^56' "-.0^.8^ 4- j 3,,,, ,,.,„,. ,„3 55 '^ 10 29 II ) II 7 ar. CO. i>. log. 8-791 Diff. 16 I"-, log. 105' Change of Alt. 7' (T. log. 1-395 Alt. req. 55 3 Ex. 2. At 12'" s?"" 24* by watch, obs. an nit. 39° 2'; and at i'' 8"" 18' obs. a second alt 36' 42 : required the .Ml. at i'' i"' 29*. Change of Alt. —0° 53', and Alt. req. 38° 9'. Ex. 3. At c'' ;8'" 36' by watch, obs. an alt. 47° 33', and at i*' 5" 47*, obs. a second alt. 4.7' 52' I required the Alt. at i'' i'° 29*. Change of .\lt. + 8', and .\lt. req. 47° 41'. The altituf io'2 knots: required the Reduction for Run. The Rkduction is o'o. Ex. 4. Obs. a star's alt. 37° iS 40", bearing S.E. by E. 4 E., course N.W. by W. 4 W., rak 58 knots, internal 2'' z^"' : reduce the Alt. for Run. The Reduction is I'i'g to tub. ; the Am. 37°4''8. When the course at the 1st observation is directly towards tlie sun, the (list, run in the interval is tiie correction, and is to be added to the 1st alt. ; when directli/ from the sun, to be subtracted. Kx. Obs. sun's alt. 29° 7' 30", bearing E.S.E., course E.S.E., rate 5'4 knots, interval 3'' 6'" : reduce the Alt. for Run. The Reduction is i6''7 to add; the Alt. 29° 24'"z. fi62. To reduce the 2d alt. to the first place of observation. Take the bearing at the last observation ; find the reduction of th(! alt. as above, and ap])ly it to tlie 2d alt. the contrary way to that tlirectcd in (2) above. Ex. 1. Observed the sun's alt., sailed S.S.W. for 48'" at the rate of 34 knots, when the 2d alt. was taken, the sun bearing W.S.W. : required the Correction of the Alt. for Run. From S.S.W. to W.S.W. is 4 pts. The course 4 pts., and Dist. 2-8, give the D. Lat. 2*o to be subtracted from the 2d Alt. Ex. 2. Course N.W. by N., obser^-ed the sun's alt. After sailing for i'' 36" at 82 knots, observed the 2d alt. 39^44', the sun bearing E.S.E. From N.W. by N. to E.S.E. is 13 pts.; then the course 3 pts., and Dist. 13-1, giv» D. Lat. 10-9, which added to 39° 44' gives 39° 54''9, the Alt. reduced. When tlie course at the 2d observation is directly towanls the sun, tlie dist. run is tiie correction, and is to be subtracted from tho second alt. ; when directly from the sun, it is to be added. 5. To find the Altitude. [1.] Oh t/te Meridian. 6G.'3. For the sun, the moon, or a planet, find the time of Mer. Pa.ss., No. 623, &c., and reduce the declin.. No. 579, &c. Find the rohit. \\'hen the lat. and decl. are of the same name take the sum of the colat. and decl. ; when of different nam(!S, their ditf. ; the residt is tiie mer. alt. If the sum exceeds 90° take its complement. IJclow the Pole. Find the pi)l. dist., and subtract it from the latitude. [2.] On the Prime Vertical. 6f)4. By Inspection. See Table 29, and Explan. of Table 5. 66.'). Jiy Computation. (1 ) Find the approx. time of Passage, No. 6:j(J; to this reduce the declin., in the case of the sun, moon, or a jilanet (2.) Add together the log. sine ot the declin., and the log. cosec. 'A'iht lat ; the sum is tin; log. sine of the true alt. required. 238 NAUTTCAL ASTRONOMY Es. 1. Ju'y 12U1, 1S7S!, l,it. 5i''4S'N., king. 4° 56' W.: find tlie Suns Alt. on the Table 29, Lat. 51°, Decl. 21°, ,. ,... Hour-angle, or App. Time/ ^^ *" ■ Long. 4'- 56' W- + 20 Green. Date nth, 5 6 © Decl. 1 2th, zi-'ss'N .3th, 21 50 N Daily Var. S Daily Var. S' and 5'- gi^ es 2', whence Red. D.-cI. is2i° 56' Deol. 21° 56' sine 9-57I52 Lat. 51 48 cosec. o-rov66 Alt. 28 23 sine 9-676^8 Decl. 38° 40' sine 979573 Lat. 50 48 cosec CI1073 Alt. 53 44 sine 9-90646 Ex 3. Lni. 46° 14' N. : find the Alt ol Capella on the Prime Vertical. Decl. 45° 52' sine 9'85596 Lat. 46 14 cosec. 0-14136 Alt. 83 38 sine 9'997 3i [3.] To find the Allitude, the Hour-angle being fhen. 666. By Inspection. See Explan. of Table 5. 667. JBy Computation, Having (in tlie case of the sun, moon, or planet) foiiiitl the Or. Date and the declination. Take tiie sn]ipl. of the hour-angle to 12''; add together the pol. dist. and colat. Add together the log. sine square of the suppl. of the hour-angle, and the log. sines of the pol. dist. and colat. ; the sum (rejecting tens) is the log. sine square of an auxiliary arc x Write X under the sum of tlie pol. dist. and colat. and take the sum and diff, and half tlie sum and half the ditf. Add together the log. sines of the last two terms; the sum ^rejecting tens) is tlie log. sine square of the zen. dist. Ex. 1. Lat. 2 2° .5'N.. decl. 2° 49' S., hour-angle 2" 14"' 3 (working to the ne arest minute). Hour. angle ,1, .^n, 36. Suppl 9 45 z+ sin. sq. 9-96200 P. Dist. 92 49' sine 9'99947 Colat. 67 45 sine 9-96639 Sun, 160 34 Arcx •33 57 sin. sq. 9-92786 Sum -94 3' Ditf. 26 37 4S. 147 15 sine 9'733'* iD. 13 .8 sine 9-36'S2 Zen Dist. 41 ' '9' sin. sq. 9 09500 Ei. 2. Lat. 35° 15' N., decl. 20° o' N., hour-angle 4'' 53'" 19*. Alt. 24° 41'. Ex. 3. Lat. 19° 20' S., decl. 19° 20' S., hour-angle i^ 18'" lo'. Alt. 71° 35'. When the lat. is 0, we may use either N. or S. pol. dist. When the declin. is 0, the pol. dist. is 90°. When both lat. and declin. are 0. the z. d. is the hour-angle converted into arc. Ex. 1. Lat. o, decl. 23° 27' N., hour-angle 4"^ 30"' 14'. Alt Ei 3 Lat. 30' o N., decl. o, hour-angle 3'' 38'" 3c' A;.T. 30"*-. SUBORDINATE COM PTITATIONS. 239 [4.] nfnii the Altitude, thcAiimnth being gteen. 668. Add togctliei- tlic log. sine of tlie aziiii., tho log. cosine of Uic lat., and tliu log. sec. of the decl. ; the sum (rejecting tens) is the log. sine of an angle A (see note to No. 616), p. 222. Under A luit tiie azini. reckoned from the elevated pole; tako half the sum and half the ditf. Take half the sum of the pol. dist. and culat. Add togetlier the log. tan. of this half sum, the log. cos. of the lialfsum of th, azim. and A, and the log. sec. of tiieir half diti". ; tiie sum (rejecting tens) is the log. tan. of iialf the zen. dist. Ex. Lat. 51° 30' N., decl. 20° z' N., azimuth S. 69° 39' W., that is N. iio^ 21' W.i rrquireil the Alt. Az. 69° 39' sin. 9-97201 Colat. 38° 30 Lat. 51 30 COS. 9-794'5 P. Dist. 69 58 Decl Su a lug 28, i S. 54° 14 tan. 0-14246 .\ °, .r ^^' sin. 9-793^7 74 J3 COS. 9-43007 Az. 35 58 sec. 0C9186 Sum i+s'tI, JS. 74^ ^3' ^"47' tan 966439 Ditr. 71 56. J D. 35 58 For other Exa Zen. Dist. 49 34 Alt. 40 26 mples reverse those in No. 674. 6 To find the Change of Altitude in a Small Interval of Time. [ 1 . ] The Hour-angle and Altitude being given. 669. (1.) When the body is to the E. of tiie meridian, swJ^rarr half the interval from the hour-angle; when to the W. of the meridian, add half the interval: call the result the reduced hour-angle. (2.) Add together the log. cosines of the lat. and declin., the log. sine of the red. hour-angle, the log. sec. of the alt. and the log. sine of the interval ; the sum (rejecting tens) is the log. sine of the change of alt.* (3.) When the body is to the E. of the meridian, add this change to the alt.; when to the W., subtract it: the result is the alt. required. Ex. 1. Lat. 51° 30', decl. 22° 20', trae Ex. 2. Lat. 5 1° 30', decl. 22° 20', tnw alt 44° 47' 36", hour-angle 3'' 0'" o» to the E of the meridian: required the Alt. 10" alt W 44^ 47' 36", hour-angle 31' 0"' o* to the : find the Alt. 2o"' afterwards. »l"b,rwards. Hour-angle 3'' Co' E. lat. cos. 9-7942 3" o'"o'W. lat. COS. 9-7941 Half-int. - 5 decl. cos. 9-9661 A -I- 10 decl. cos. 9-9661 Red.ll.ang. 2 55 sine 9-8398 3 10 sine 9-8676 44" 47' 36" sec. 0-1490 int. sin. 8 6397 Chan-gk 1 24 I sin. 8-3888 44" 47' %(> 2 59 20 sec. 0-1490 int. sine 89403 sin. 8-7172 Alt. 46 11 37 LT. 41 48 16 The true alt. U 46° 12' 48", or the The true alt. i 41° 52 24", or the error procsii is here 1' 1 1" in defect. is 4' 8 ' in consequence of the length of the interval. • The prop. logs, may be used for the sines of the small arc and the interval, provided that the arithmetical complements of all the other quantities be employed, and the const, s -8239 added. The proper logarithm for the jiurpose is the log. of tiie small arc or the interval in seconds of arc ("). The inaccuracy attending the use of the sine, instead of iti ■re, in these computations is insensible, as the sine of 1 falls short of its arc by oidy p"*a^ the roe uf 2 by 1 "'5, aud that of 3 by 2"-9, or o*iy of tune. *240 NAUTICAIi ASTRONOMY. The method is more accurate as the object is more nearly E. or W. Thf proper alt. to employ in this computation is the middle alt. between those at the beginnins: and end of the interval; for greater accuracy, therefore, the work should be repeated with a new alt. tlius deduced. [2.] The Azimuth being given. 670. By Inspection. Multiply the change of alt. in 1"" of time, Table 46, by the interval, botii being in min. and decimals. Ex. Lat. Si", azim. 72°: find the change in Alt. in 3™ 12*. The change of alt. in i" is about 8'"7, which multiplied by 3-2 gives 28', the CaANoa required. 671. By Computation. Add together the log. sineof the azimutli (reckoned either from N. or S.), the log. cos. of the lat., and the log. sine of the interval of time; the sum (rejecting tens) is the log. sine of the change of altitude. It is more correct to use the azinmth corresponding to the middle of the interval of time.* Ei. Lat. 5 1° 49', azimuth of Arcturus 7 in 2-" 51'. 1° : find the change of Alt. in s"- 12', and also Az. iz" sine 99782 Lat. 51 49" COS. 9-7911 Int. 3"' IX' sine 8-1450 Change req. 28' 13" sine 7-9143 9-9782 9-791 1 Int. 2™ 5.« 80946 Change req. 25' 8" sine 7'5639 672. All bodies on the same or ojjposite azimuths change their altitudes at the same rate, whatever be their declinations. VII. Azimuths. I. To find the Azimuth, the Altitude being given. 673. By Inspection. See Explanation of Table 5. 674. By Computation. Add together the pol. dist., the lat., and the alt., take half th3 sum.f and take the ditf. between this half sum and the pol. dist. Add togetlier the log. sec. of the lat., the log. sec. of the alt., the log. cosines of the half sum and remainder; the sum (rejecting tens) is the log. sine square of the azimuth, J to be reckoned from the S. m N. hit., and from the N. in S. lat. * The above rules, Nos. 669, &c., relate to the change of the true altitude. To compare the change of alt. as shewn by an instrument with the true difference, in a given interval of time, a small correction woulil, in general, be necessary, on account of the change of refracti jii, and in the case of the moon, for tlie change also in her parallax in altitude. t The learner will observe that in this formula the pol. dist., lat., and alt., occur in tlie reverse order of that in No. 614, in which last their initials form the word alp. The 2d and 3d terras take secants ; the last two, cosines. X The angle obtained is the siipjjlement of the sagle P Z A in fig, 1, p. 102 SU BOH DrN ATK. COM P uTATIOMS. V.\. 1. Ijit. 5i°3o'N., alt. 4o°2?'to\iie W , *!t*-rj. 20*2' N. : required the Aziiiiutli. I'ol. Oisl. 69" 5S' l^t. 51 30 sec. 0-10585 V'L .^o 25 800.0-11842 >(" 53 80 56 J COS. 9-19711 10 58 j COS. 9-99198 AZIMUTH, S. 69° 39' W. sin. sq. 9-51336 Wlien tlie lat. is 0, if ti.e (Jecliii. is N. rt'fkoiieil from llie soiitli ; it' it is S. froin the iiurlli. W'licM the decliii. is 0, tlie aziiiiutii is •'eckoiiL'it. 0°, decl. 23° 27' Ex. -2. Lat. ii°i2'N„ decl. When botii tlie lat vertical. ;., alt. 4i°2' W. AziM. N. 12 1° 50' W., or S. 58" 10' VV. 3=, alt. 54° 30', to the East. Azim. S. 73° 53' E. nd dtnd. are 0, tlie ohjcct moves on tlie |)riine 2. To find the Azimuth, the Hour-angle being given. 67.5. (1.) Take half the sum of the pel. dist. and colat., and half 'he difference. (2.) Add together the log. cot. of half the honr-angle, the log. sec. of the half snni, and log. cos. of the halfdiff.: the sinn (rejecting tens) is the log. tan. of half the sum of the azimuth and another angle A. \VlR'n the half sum of the pol. dist. and colat. exceeds 90**, take the su]j])l. of the resulting arc for the half sum rerinired. To the log. cot. already employed add the log. cosec. of the half num. and the log. sine of the half diff. ; the sum (rejecting tens) ig the log. tan. of half the diff. of the same two angles. (3.) The sum of the resulting half sum and halfdiff. is i\\e greatei of the said two angles ; the difference is the lesser. When the ]>ol. dist. exceeds the colat. the greater of the two angles is the azimuth rerpiirod ; when the pol. dist. is less tiiaii llie colat., the lesser of the angles is the azimuth rerpiired Ex. I. Lat. lo'io'N., decl. 22° 14' .S., hour-angle i'' 44'" I7"\V. : rei,uiieJ the Azi'niuth. H. Angle i ''44"'i:" cot. 3-63548 cosec. 0-00235 n tan. o-o8i59 91 26 (suppl.) 5° 37 Sum N. 142 3 W. Azimuth (\t. dist. exceeds col.) Diir. 40 49 the other Angle, or A. ' S., decl. 1 1" 18' S., hour-angle 5I' 11'" 20" : the Azimuth 91" b', »!»« Half 52 8 cot. 0-63548 I' Dist. 112" 14' Colat. 79 40 Sura 191 54 Diir. 3» 34 J.S. 95 57 sec. 0-98439 4D. ■ 6 ,7 cos. 0-9S222 ii^ ii' tan. i-6u2Q9 El. 3. Lat. 13" 52' N., decl. 46° S' N., hour angle 1 1- E. of Me ifit'k B. 242 NAUTICAL ASTRONOMT. 3. To find the Azimuth, the Hour-angle and Altitude heimj giiJen. 676. Atld together the log. sine of the pol. dist. (or log. cos. of the decliii.), the log. sine of the hour-angle, and the log. sec. of the alt. ; the sum rejecting tens is the log. sine of the azimuth. Ex. 1. Hour-angle i 58° 40', pol. dist. 104." 24 Aamath. .9- .9-, alt. : required the Ex. 2. Hour-angle o'' 46'" 39% alt. 6fo', decl. 14° 24' (N. or S.) : required tlie Azimuth. Pol. Dist. sin. Hour-angle sine Alt. sec. AziM. 39°ii- si 9-9S6. 9-5305 0-2840 1. 98006 Decl. COS. 9-9861 Hour-angle sin. 9-3057 Alt. sec. 0-3430 AziM. 25^ 33' sin. 9-6348 Tills nictliod can lot sliew wlie tlier the body is to the N. or S. of 4. To find the Azimuth, not far from the Meridian, hj the ohseived change of Attitude in a small Intei-vnl of Time. Qll. liij Inspection. Divide tlie given chanoe of alt. by tlie interval, in niiii. and decimals; the quolient is the cliaiige of alt. in I™. With tliis change and the lat. enter Table 46, and take out tlie aziniiilli, which corresponds ajiproximatcly to the middle of the interval. Es. Lat. 35° ; the change of alt. in 20°" 12' is 59' : find the Azimuth. 59 divided by 20-2 gives 2-9, the change of alt. in i"', which gives tlie Azim. about 14°. 678. By Computation. Add together tlie log. sine of the change of alt., the log. cosec. of the interval, and the log. sec. of the lat. ; tl'.e sum Is the log. sine of the azimuth about the middle of the interval. Ex. \. Lat. 51° 26'; in s" 20* observed Z2' change of alt. : required the Azimuth. D. Alt. 22' sine 7-8061 Int. 5"' 2o' cosec. 1-6332 i/at. 5i°26' sec. c-20<;2 Azim. 26° 10' sine 96445 At about 3"' after the 1st observation. Ex. 2. Lat. 34 40'; in 20"' 12' observed 59' 6" cliange of alt. : Teejuired the Azimuth. D. Alt 59' 6" sine 8-2353 Int. 20"' 12" cpsec. 1-0554 Lat. 34° 40' sec. 0-0849 Azim. 13° 44' sine 9-3756 At about 10"' after the 1st observation. 679. This method will sometimes be useful, as for determining the variation, but it must be employed with caution; the interval should not be very small, the body- should not be far from the meri- dian, and both alts, must of course be observed on the same side. The degree of dci>endaiice is easily estimated by changir:g the diff. of alts, by the amount of probable error, as about \' or 2': Thus, 1' error of diflf. alts, produces in Ex. 1 an error of \°\, while in Ex. 2 it produces an irror of only 14'. * * The work of finding the Azimuth is much lessened by the use of suitable tablo.-s. Burdwood and Davis's Azimuth tables and Star Azimuth tables extend from the equator to 60" latitude, aud are published in a convenient form by J. D. Potter, H5 Minones, London, E. Such tables are itdispcnsable for the navigalian of iroushiis. i'tt also Lecky's " Wrickleis," for stars. CHAPTER V. Finding the Latitude. 1 Hf TUB MuKiuiAN ALTiTUDt;. II. By the IIeduction to thb Meridian. III. By Douule Altitude op the same Body. IV. By Double Altitude of different Bodies. V. By thh Altitude of the Pole Star.* 080. The pole lemains always in the same absolute fixed position from whatever point of the earth's surface it is viewed ; its altitude at any particular place is, therefore, always the sauie. The position of the equator, which is 90° from the pole, is also always the same at the same place, and is determined by reference to the celestial bodies, whose declinations are measured from it. The latitude of the place niay.tiierefore, be determined directly by observation, and indejiend- fiilly of the latitude of any other place. When the body observed is on the meridian (at which time its dititude ceases to change) the time is not noted; but if it is not on the meridian, either the absolute time must be given, or a second BJtitude must be obtained after a measured interval. I. By the Meridian Altitude. mplest, and in general the most satis! the latitude, is by observation of tli celestial body when on the meridian of the place. 'I- fi8I. Tlie simplest, and in general the most satisfactory, method of deterwiining the latitude, is by observation of the altitude of ii ridii * The several methods of latitude which are given in this work under the heads enuriic- ratod above, and which may be considered as distinct methods, of which the solul'cm deiieiuli an ciriunistances as elsewhere described, amount to eiRht. The seaman, who will reinenili|.rii:h l.i il, nnn i.iiimrims passages or channels taken, by reference In !, Ir ;il..iic, ;in.| ihii tlh iimc, and •Iririfnrc the longitude itself, depends on the Intitml' . In tin r il,i\^, ,.1", nl.c u -u, Ij -nut and continued velocity is Htta-npfl, in «»r- nn.v.^-'fN', ii :■ i^ol LiciliUrs aic Uiiii.mtK.l lor ilr- tiTiiiining the place oi • . i .|, Tr.- ' : i:,. i-iiin iiccoi'dingly should be furoislievi. nith a method of liiiii : j ..nii lit and satisfactory) adapted ti tverjr occasion that ih .. . ■ i-l : >!i, mi i n i t The manner of dc^i'.i.ni; i,k I.im ,iIl- h..in lui uui. ,di and declin. is fully described Ifl No. 152. 244 NAUTICAL ASTRONOMY. 1 Meridian Altitude of the Sun. 682. The Ohsrrvation. When tlie sun is near the nierion 17° 48' S, Obs. .Mi. . In'2S' •riu r. + Bar - > Semid. [•ar. True Alt. Z^n, Dist. Decl Lat. 23 4" I 5 3« 26 6 ■7S. 5 ■I « 69° 8- + I 10 2)69 9 10 Ex. 2. June 20, 1S78, long. 26° at midnight, obs. mer. alt. Q in the silver 26° 26' 20", index o', bar. 29*8 therm. 34°. Green. Date, AT. .Tune 20'' 10'' 15 Reduced Decl. 23=27' Obs. Alt. True Alt. Supp. Zen. Dist. 103 25 7 Decl. 23 27 16 N. Lat. 79 57 51 N. Ex. 3. July 27th. 1878, long, obs. mer. alt.0 in tliequicksilver 1 16" zenith N. ind. corr. +2' 15". bar. 30-1 therm. 60" ; required the Latitude. Green. Date (A.T.). 27'' o" 8'" Decl. 19° 12' 17' N. ; True Alt. 57' Lat. 51° 26' 13' N. 26° 26' 20" '3 '3 .0 -3 57 '3 n 46 + 13 25 7 ; Red. 46' 4' : 686. When the altitude of either limb of the sun is observed, and the alt. of the other limb (which will appear tlie same in tlie instrument) is observed fi-om the oj)posite point of the horizon (No. 5.35), take half the diif. of these angles and add to it the correction of alt. ; tlie siun is the true zen. dist. Ex. 1. Aug. 5th, Obs. Alt. Q N. iS7S,long.2 5°W. ii5"46'-3 63 49-3 Ex. 2. Oct. 2Cth, Obs. alt. Q N. Diff. Corr. of Alt. Z™. Di.st. Red. Decl. Lat. 1878, long. l°W. 105° 5' 74 32-2 Diff. i' 57 30 3- •* Corr. of Alt. 25 58 -5 N. + '4 .5 .f._-+N. Zen. Dist. Red. Decl. Lat. 25 58-9 N. 16 56-3 N. 42 55-1 N. 15 .6-6 N. 10 23-9 s. 4 51-7 N. Thus it appears that this observation, which is the most ciliciont in practice, is also the shortest in computation. Kx. 3. July 15th, 1878, alt. Q N. 93° 58', S. 85° 38', long. 71° W Ez. 4. Julj4tb, i8;S,alt. N. ST 59', S. 97" 4' ', long. 83° E. Lat. 2 5^3 9'-7N. Lai. 15 y 7 N. FINDING TIIK I.AHIUDE. 2 17 9. Meridian Altitude of a Star or a Planet.* 687. 'ITie Observation is the same as for tlie sun, but it is still more necossary to take separate altitudes of a star in order to avoid straining the eye to jierceive its small rise or fall when near tiie uieriilian. See No. 542. 688. The Computation. At Sea. (1.) Take tlic det-l. fitJu-r from the Nautical Almanac, or, in the case of a star, from 'V\\\<\v / 20 rs., ■■nli < ^ofcet. ' ; corr. + 3', eye i6feL-(. Obs. Alt. 33^ 17' S. ' " N A. VY ^44; tl e M.T. ol' .ncr. ,.as.. ( ,. j DaK- is Aug. 9"' la'' 0°, ami the Red. Di-cl. Ref. -I ! Trm-Alt. 33 11 S. Ziii. nist. 56 48 N. Suir's Uecl. 10 52 S. L.\T. 46 16 N. is 23° 39' N. Obs. Alt. 49°2o'N. In.lesCorr. +3') Dip -4 '. Ref. - I Red. Decl. 23 39 N- L.\T. 17 3 S. Ex. i. Dec. 2ist, 1878. obs. mer. alt. Aldebaran 50° 27' N. ; heiglit of eye 20 feet 1 required the Latitude. L\T. 23" 22' S. lix. 4. Jan. 1st. 187S. obs. mer alt. Sirius 81^ 13' S., iud. corr. —4', height of eye j8 feet: rccjuired the Latitude. Lat. 7° 38' S. F.x. 5. Feb. iSth. 187S. obs. mer. alt. Canopus 37"" 25' .S., ind. corr. +2', height of eye 16 feet: required the Latitude. L.at. o" o' Ex. 6. Feb. 1st, 187S. obs. mer. alt. Arcturus 80° 12' N., ind. corr. + 4', height nf eye iS feet: required the Latitude. Lat. 10° i' b. Ex. 7. Feb. i8th, 1S78, obs. mer. alt. x Lyrie. below tlie pole, 12° 30', ind. eorr. + 2', height of eye 18 feet : required the Latitude. Lat. 63° 44' N. Ex. 8. Oct. 6th, 1878, long. 87° W., obs. mer. alt. Mars 57° 45' S., index corr. -2', height of eye 18 feet. Ex. 9. July 6th, !878,long. 178° E., obs. m height of eye 20 feet. Ex. 10. J.in. 6th, :878, long. 169° W., obs. height of eye 15 feet. 689. Accurately. Take the decl. from the Nautical Almanac. For a planet find the (Jr. Date, and reduce its hor. par. aiul decl. Correct the refraction for the thermometer and barometer. 690. Stars which never set at the phu^e may be observed botii above and below the pole. In this case the latitude is half the sum of the altitudes corrected for refraction. 691. If two stars are observed on the meridian, on dilferent side3 of the zenith, and at equal altitudes, the result is independent of the rc'fraction, unless it changes in the inteival of tiie obserxations. If the altitudes arc not equal, the le.suit involves only tiie ditlerence of the refractions j)roper to each. Lat. 30° 15' N. dt. Jui.iter 57°5o'S., indexcor Lat. . 5 ■ +5'. r. alt. Venus 69° 54' S., ind.- X cor Lat. 9" 15' n' * Veiiua may oili^i be observed bf di\yiight, even in high 248 NAUTICAL ASTRONOM* 3. Meridian Altitude of the Moon. C92. The Observation. Tlie same as for tlie sun. See No. 540. 693. The Computatum. At Sea. (1.) Find the Green. Date by means of the time at ship; or, if tliis time is uncertain several minutes, find the M.T. of tlie moon'st mer. pass., No. 627, &c. Reduce thereto f,he moon's decl., No. 589, her hor. par., and take the corresponding Bemid. from Table 40, all to the nearest minute. (2.) Correct the observed alt.. No. 654, and proceed as for the sun. No. 683 (3). Ej. 1. Nov. 3d, 1878, lonR 150° 15' E., It 7'' 7" P.M. mean time at ship, cibs. alt. y^ 45° 13' S., height of eye 16 teet. M.T.S. Nov. r' 7' 7° liOng. in time — IQ ' E. M.T.G. Nov. "i 21 6 >'s Decl. at ii' 6", var. 1 1 9" Heil. Decl. Hor. Par. Semid. Obs. Ah. 1 J)ip -4"l, Si mid. +15/ ■4" 47' 45" S. — I II '4 46 34 S. 43 58 N. 14. 47 S. 2J 11 N. Ex. 2. May icth, 1878, a.m. 1<.m^'. W., ol)s. mer. alt. "j" 48° 48' S., IilI. e>e 18 feet. Moon's Jler. Pass. 19'' 15' M.T. Mer. Pass, at Long, in time M.T.G. May rs Decl. at as" 4", var. 69" Red. Decl 19 15 7_ 19 23 56' 33' 15 26 Ohs. alt. Dip Semid. .i6j 30' and H.l True Alt. Zen. Dist. Lat. «.^'. 1 34 a'». loth, 1S78. r.M , alt. j 59" 44' N., iiKlex corr. of eye 18 fett. Lat. 53° 4»' S. t:%. a. Dec. 2ist, 1S78, A.M. lon^'. 149^ I Lx. 4. A W'., obs. mer. alt. J) 84° 9' N. index eorr. E., ohs. me + a', height of eye 14 feet. - i', height Lat. 31° 14' S. I It will in general be loss of time to work nearer than to mi-nitei, because the moon's declination cannot be found to seconds unless the GrL-enwich time is known with precision.* 694. When both the upper and lower limbs are well defined, the BU]ip]. of the alt. can be observed, and the precept No. 683 applied. When only one limb can be observed, the semi-diameter must be ap])lied. 695. Degree of Dependance. The error of the resulting lat. is obviously the sum or dittei-iiicc of tlio errors of alt. and decl. The hit. by the sun at sea may be i1c|h"iu1i.m1 ii|hiii within 2' or less, thai by the moon not so nearly, ami the lat by a single star in a dark night perhaps not within 3' or 4'. • .Also as the moon at certain time.s changes her < h»r mer. alt. may differ considerably from the max aiiuutes may occur between these two altitudes Sc< FINDING TUK LATITUDE. 219 Errors of ob-iorvation or of tlie instrument nuiy be reniov(f TO THE MeKIOIAN. 696. When the sky is cloudy, or tlie weather variable, the sun or any other celestial body, though obscured wiien exactly on the meri- dian, frequently appears, for short intervals of time, both before and after the meridian passage. t \\ hen the body is near the meridian, tlie change of alt. in a small |)ortioii of time is very small ; and thougli the altitude near tlie uK^ridian changes at a different rate in different latitudes, yet the change of altitude in a given small interval is not sensibly affected by a change of several miles in the latitude, and therefore it may bo computed with tolerable accuracy, even when the lat. by account (which is used in the computation) is considerably in error. If, ac- cordingly, at the time of observing an alt. near the meridian, we know the hour-angle, we may find very nearly, by computation, the difference of alt. by which to reduce the observed alt. to the nier. alt., and which is thence called the Reduction to the Meridian. This method is, in ))oint of simplicity, but little inferior to the meridian altitude, to which it is next in importance ; and it particu- larly demands the attention of seamen, because, when the latitude by observation is left, as it too generally is, to the casualty of obtain- ing the merid. alt., it is frequently lost for the day. 697. The term "near the meridian" implies a meridian distance limited according to the lat., tiie decl., and also the degree of precision with which the time is known. The Limits are given in Table 47 See also Explan. of the Table. 698. Since the lat. by ace. is employed in com])nling tlie Rciinc- tion, it may be necessary, when this lat. has been tbiuid to be much in error, to repeat the work. * Though the lat. by a single star may not be very correct, yet the error will in genrnil Be much less than that of the D.R. The altitude of a star also atlorils a certain click against the mistake of ajiplying the sun's declination the wrong way ; and it may be remarked, that a single observation of the kind would have prevented all the delay, wear and Icar, and danger incurred in the cases mentioned in the note p. 244, from the ships being so far out of their proper latitudes. t Capt. Sir Richard Grant remarks that in H.M.S, Cornwallis, alts, of the sun ind Hars were rarely to be obuined while within the limits of the Gulf Stream, but they bad a nmmentary glimpse of the sun near noon once in two or three da^B. — Ncutical Magaiiue, 1H3H, p. 4a:. ^OO NAUTICAT- ASTllONOMT. 1. Reduction to the Meridian at Sea. [1.] Bulhe Sun. b99. T/te Obskvvation. When the sun is witliin the liniits in Table 47, observe two or three altitucies,* quickly, noting- the times. When the alts, are not observed very close together, eitliei- a separate result slionld be obtained from each alt. with its corre- sponding time, or the case should be solved by No. 717. 700. The Computation. (1.) Take the mean of the alts, and the mean of the times. (2.) Find the sun's hour-angle, or the time from noon, thus: 1 . When the App. Time has been lately determined ly observa- tion. If the ship has since made westing, subtract the diff. long, made {rood from the A.T. found ; if she has made easting, add the diff. long, to the A.T. : the result is the A.T. required. 2. When the A. T. has not been lately determined by observa- tion. Find A.T. by the chron. and the long, by ace, thus: To the G. M.T. (found by applying to the chron. the gain or loss up to the time) reduce the JEq. of T. and apply it to the G.M.T., as directed page II. of the Nautical Almanac, or the contrary way to that directed in Table 62 : the result is A.T at Greenwich. In W.low^. subtract the long m time from this Gr. T. (increased, if necessary, by 24''); in E. long., add it : the result (rej'scting 24'' if it exceed 24'') is A. T. at ship. When the A.T. of observation is p.m., it is the hour-angle re- quired; when it is a.m., subtract it from 24'': the rem. is the hour- angle. If A.T. is near 12'', subtract it from 12''; if it exceed 12^ reject 12'": the rem. is the hour-angle from midnight. Find tlie sun's decl.. No. .079. (3.) Correct the alt., No. (J47. (4.) Add togetlier tiio logarithm from Table 70 and the lo--. sme square of the hour-angle: the .sum is the log. sine of the Reduction. {ft.) Add the leiliiction to the true alt., unless the observation is near midnigiit, mIicm suhtruct it: the result is the mer. alt. at tho place where the alt. was observed ; and the resulting lat. is the lat, of the ship at the time of observation (not at nooii). Having the mer. alt., proceed by No. 683 (3). Ex.1. Aug. 5tli, 1S26. H.M.S. Leven. lat. by ace. 47" N. ; long, by ace. 25" \V. at 1 1'" 48" before noon; obtained true alt. 63° 54' to tlie soutbwaid ; reijuireil the Int. The reduced decl. was 17^4' N. Mer. alt. 64" o' Lat. 47-, decl. 17 ' [same name) II'" 48" sine sq. Red. 0° 6' sin. 63 54 Mer. alt. 64 o Zen. dist. 26 o N. Red. decl. 17 4 N, Lat. 43 4 N. Heiieatiug the work gives 43'^ 3' i more than one altitude would, for greater security, always be 1 shall, to avoid repetition, consider the term "altitude" in the : i, ua iui{>Jyiivg the mcau of two or more altitudes corresponding Fx 2. Ut. ^,'6'N.,Os.lc-cl liiiiiJ tlie Lutitude. The Red. FINDIXO THK I^TirUDE. i dccl. jo° 4' S., at oi' 54"' 12' I'.i 54', raer. ah 14° 55', : 2.51 sun's true alt. 14 tlie Latitude 55 Ex 3. Feb. 13(1, 1878, lat. by ace. 40° 5' S., long. 132° E., at II' 45" 20" t.K., oIm. alt Q 59° 40' N., iiidix corr. —2', eye lo IVet : find the Latitnde. lied. decl. 9° 54' S., true alt. 59° 49', Red. 1 1', Lat. 39° 54' S. K.I. 4. Dec. I2th, 1S7S, hit. by ace. 0° o', lon.i^. i6i° W., at o" II" 52' t.m., olis. alt. Q 66° 34' S., index eorr. —5', eve 16 feet: required the Latitude. Red. decl. 23° 7' S , true alt. 66° 41', Red. 11', Lat. 0° i' N. Ki. 5. June 21st, 187S, hit. by ace. 42° 18' S., long 53° E., obs. alt. ^23° 4'' N. Inde\ eorr. - l', eye 14 I'lel ; lime hy natch o* 50" 53* p.m., f.ist on A.T. 14" l8', ilill'. long made suiee 20' K. : hnd the Latitude. Red. duel. 23° 27' N., true alt. 23° 50', Red. 35', Lat. 42° 8' S. 701. When the number of minutes of arc, in the Refhiction, exceeds tlie number of minutes of time from the meridian, it is proper to refer to Table 48, to ascertain if it be necessary to eini)loy tlie Second Reduction. Ex. 1. (The preceding.) The number of min. in the Reduction, or 6, being less than the number of min. of time, or 1 1, it is not necessary to refer to the Table. To Compute the 2d Red. Double the loij. sine of the Red. ; add to it the log. tan. of tiie nier. alt. found, and tlie constant 9*6990: the sum (rejecting tens) is the log. sine of the 2d Red. This is to be subtracted from the 1st Red. (above the Pole), that ia applied to the alt. the contrary way to that of the 1st Red. Ex. 2. May 5th, 187,', lat. ace. 5" 3 N., long. 71° 10' E ; time hy natch 5'' 3" 7' p.m., t on app. time at ship 4'' 47'" 27': obs. alt. Q 77' 59' N ; height of eye 16 feet. Time by Watch 5'' S"" 3"' 7* Lat. 5°, nee 1 i6i°(»ame> a,,,,-) 0-992 Fa-vation. When the sun is within the limits in Table 47, observe altitudes as fast as convenient, noting accurately the times by watch, of which the error on Apparent Time must be known or found as soon as possible afterwards. When precision is required, note the barometer and thermometer. 707. The Comi>utation. (1.) Find the Green. Date for noon at the place, in apji. time, and reduce the decl. If the error of the \^atcll is given on M.T., reduce also the Eq. of Time. ';2.) By means of tiie error of the watch obtain A.T. at each altitude. To these App. Times take out the Reduction in seconds IVom Table 49. Take the mean of the Reductions. v3.) Find the mean of the alts., and correct it. No. 649 or 650. If the meiidian alt. is not observed nearly, deduce it. No. 663, &c. (4.) Add together the log. of the mean Reduction, the log. cos. rjf the lat. bv ace, the log. cos. of the decl., and log. sec. of the uier. alt.: the sum In the log. of the Rohirlion. (.*>.) .Al niioii, ii/ld llic Reduction suhtrurl it: llic rcsull is tiie iii'.T. iilt HF. LATITl'liR. \h- hi 2,-,3 Julv 9''. »i mean noon, and also the II. A. and decl. ; and for a planet, the lior. j>ar. ('2.) Find tlic lionr-ansjle at each alt. and inocecd as for the sun. When the watch shews Sid. Time, the hour-angles are obtained at onee. 715. The stars near the poles, and espe<'ially the pole-star, are the i)est adapted to this observation ; hccanse, fimn the slowness ol UK! motion m altitude, an error oi' time piotiuces but little error in the Reduction. 716. Errors of altitude, of whatever kind, are removed by em- ployinij two bodies on opposite sides of the zenith, ant' at equal ■iltitu-. cosee. of half tlie interval : the siini is the log. sine of half the ditf. of the times from noon corresponding to the two altitndes. (3.) Subtract this half iliH, .'Voni tlie half interval : the remainder is the time from lux^n (or mcritl. dist.) of the alt. nearest the meridian. (4.) Compute the Reduction to this time, and ajiply it to the alt. nearest the meridian, and jjroeeed as directed. No. 700. Tlie result is the latitude at the time and place where the alt. nearest the meridian was observed. Ex 1. April 5d, 188, hit. by to the soutlinard, reduced to laist Times by Wi '54' 35 Fnterral Lat. 46°, decl. 5°, ar. 6^ a' X., inns;. 17' \V., tlie true alts, of the of obseivatio.i as below. Red. decl. 5^23 true alt. 49" 10' 30" a.m., or rising. 49 23 53 P.M., or falling. diff. alt. .3 23 Lat. 46°, de,-l. 5", log. 0-324 11-56' sin.sq. 6-X,. Red. 0" 5' si... 7-'5S Gr. alt. 49 24 Mer. alt. 49 ^9 „ . which pTBR the I.at. 45 54 N. 34 58 log. 9676 Ditf. alts. 13' 23" sin. 7-590 Half. int. 17'"29' cosec. i-ii8 Half diff. —5 33 sin. 8-384 T. fr. noon li 56 (of greater alt. ) Ex. 2. H.M.S. Leven, Aug. loth, 1826, lat.by »cc. 46 N., long. 15° W., obtained tnie alt. 59^57'-2; after 28'" 42* true alt. 59° 2o'-5, the ship having little or noway. Reduced deil. at 1st alt. 15° 40 N. 46° and 1 5°, ar. CO. log. 9-573 | over the \ interval (which should be the Ditf. alts. 36- 42" Half int. I4'"2i' Half ditf. 14 39 This small . the. greater) is due to the error of the method itself, which becomes ajiparent in a long interval, and it shews that the alt. 59" 5;'- 2 is very nearly the nier. alt. This gives tha _ uted \ diff. Lat. 45" 43' N. Ex. 3. Dec. 23d, 1825, lat. by ace. 8° S., observed true alts. © 74° 26' a.m. and 74° 16' n., with the interval 36'" 37". Reduced decl. 23° 27' S. 0-S32 17"' 4' 7''4^ Red. 0° 32' sin. 7-974 - 1 (Table 48.) 74 ^6 75 W The Lat. is S° 24' S. This Ex. is fa» rithont the limits, Table 47. Ex. 4. Aug. 9th, 1826, lat. by ace. 45°N., long. 15" W., a.m., obtained true alt. to" 2(/-5. After 52'" 27- obtained true alt. 60° 30'. The 1st alt. reduced for i' nortbitj made gi'od in the interval is 60° 28-5. The diff. alts, i'-^ and a half interval 26™ i6' give half diff. I9'; the Red. is 31', and mer. ail 61" i', which, with i.-duced decl. i^" 57' N., give Lat, 44' =,V N. Ar. CO. log. 9-168 10' sin. 7-464 1 3°' iS' co^ec. I -098 - ' '4 SIB. 7730 >7 4 2G0 NAUTICAL ASTRONOMY. 732. When the alts, are equal, the half interval is the time from noon. 733. Degree of Dependuncc. It would not be easy to give a concise rule for this in long intervals. The rule No. 730 applies very nearly in short and moderate intervals, using, instead of the "middle time," the time from noon of the alt. nearest the meridian. [2.] Short Dovble AUitude of a Star. 734. Increase the interval by 1* for every 6'". Take the doel. from the Nautical Almanac, or Table 63. In other respects proceed as for the sun. [3.] Short Double Altitude of a Planet. 735. Find the Greenwich Date for the middle of the interval, and reduce the decl. Find the daily variation of R.A., and deduce by Table 21 the change of R.A. for the interval. When the R.A. is increasing, subtract this change from the interval ; when decreasing, add it. Increase the interval by the acceleration upon it. lu other respects proceed as for the sun. As the R.A. and decl. of a planet sometimes change very slowly, much of the above labour is not always necessary: particular rules for all such cases would, however, be superfluous. [4.] By the Moon. 736. Find the Greenwich Date as nearly as possible at each observation, and compute the R.A. Subtract from the interval the change of R.A., and add to it the acceleration. Reduce the decl. to the middle of the interval, as also the hor. par. and semid. In other respects proceed as for the sun. As a proper allowance for a considerable change of declination would complicate the rule, the moon can be employed satisfactorily in this observation only in cases of very short intervals, and when her declination changes slowly. 2. Double Altitude, one Altitude being near the Meridian. 737. When one of two altitude.s is taken near the meridian, and the other when the body has a large azimuth, the outer hour-angle (or that corresponding to the altitude furthest from the meridian) may be computed nearly (No. 614), since it will not be much affected by an error in the latitude by account.* The difference of the hour- angles being afforded by the measured interval of time, the other, or inner hour-angle, is found ; and the Reduction being computed thereto, the nier. alt. is deduced. See Nos. 722 and 723. 738. Limits. The inner alt. must be within the limits in Table 47, and the outer angle should be as nearly E. or W. as possible. AVhen the outer beaiing is not near E. orW.the outer hour- • The UitUudo by atrount, refers of course, to the place t( FINDING TIIL I..\riTUOE. Sfil •ngle may be sensibly affected by the error of the lat, by ace. ; and if the inner hour-angle be not very small, the work may require to b« repeated. [1.] By M* Sim. 739. The Observation. Observe the sun's alt, noting the time and tlio bearing. After a sufficient interval (No. 738) observe the second altitude. See note to No. 726. 740. The Computation. (1.) Reduce the decl. at both observa- tions, either by Table 19, No. 579, or by the Green. Date, No. 580, and find the outer pol. dist (2.) Correct the interval for tiic rate of tiic watch when large. Correct the altitudes. Wlien both observations are A. Jr., reduce tlie 1st alt. to the 2d place of observation. No. 661. Wlien both observations are p.m., reduce tiie 2d alt. to the |)lacc of the 1st, No 662. VVlien one observaticn is a.m., and the otiier p.m., reduce tiie alts, to the place of the alt. nearest the meridian. (3.) Witli the outer alt., tlie lat. by ace, and the outer pol. dist., compute the hour-angle. No. 614. (4.) Take tiie diff. between tliis hour-angle and the interval: tiiis is the iinier hour-angle. (5.) With this hour-angle compute the Reduction to the meridian and ajtply it (No. 700 (4) and (5)), to tlie alt. nearest the merid. The decl. which is to be applied to tlie mer. zen. dist. is that reduced to the time of the alt. nearest tlie meridian. Ex. 1. .July 13d, 1878, Int. by arc. 5+° 57' N., long. 1° 25' W., at about 7'' o"' a.m. , obs. alt. Q 24° -^o , bearing E. by S. by compass ; 4'' 50'" 12' afterwards obs. alt. 54° 26 , course S.S.E., rate 45 knots ; ind. corr. + 2', eye 18 feet : required the Lat. at 2d obs. From S.S.E. to E. by S., or 5 pts., and dist. in interval 20'- 3 give corr. of lit. +11. Decl. 251 at nrnn 20" 4'N. .\lt. 14° 5? Long. .» -0-1 Lat. 54 57 sec. 0-24CS6 5^ 0- + 3 ( "^ ' P. Dist 69 53 cn.ec. 0027:4 1st Red. Decl. 10 7 74 51 cos. 9-4i-;2 Int. 4" 3o'" — 2 49 58 sine 9-8X404 ■ 2d Red Cecl. 20 5 Houran. 5'' o'"i4' sin sq. 9-5^546 Obs. Alt. 24' 30' Obs. Alt. 54° 26' Interval 4 3-5 12 d.cor. + 2'l ^, b. 38 +10 1 + M1 ^'5 Inn.H..an. 30 2 sin.sn. 7 (,-2 Lat. 55° Decl. 20 (iflwc 'laiiie) o'27l H 42 2d Alt. 54 39 Red. + 28 sin. 7-906 rr. forinn +■ 1 1 .54 39 Alt. 24 '53" M...r. Alt. _5^^ The Alt. nearest M er. is here the 2d.) Zen. Dist. 34 i;3 Decl. 20 i Lat. "c4 58 N N N Ex. *■ April 3d, 1878. lat. by ace 46' 7' N., long. 14° \V. at about 8" lo" ah. nh». »h. Q 26' 10', sun S.E. ; 3I' 26" 35" afterwards (corrected for rate) obs. alt. Q 49' 8' t« Ihc nonlhwnrd ; course W. ; rale 6 8 knots ; indei —3' : eye 16 feet : find Lut. at 2d obi. From W. to S K ia 12 ji's. ; 4 (it«. and aist. ij I give corr. of lat tit. - 16'. The \A 262 NAUTICAL ASTRONOMY. red decl. 5° 20' N. ; the 2d, 5° 23 N. ; the 1st alt. (corr. for run), 16° i'; 2d alt ♦9° J6'- Alt. 26° i', lat. 46° 7', and P. dist. 84° 40', give hour-angle 3'' 49"' 41'. hence ina hour-angle 23"! 6' and Red. +18', Lat. 45° 49' N. Ex. 3. Dec. 3cth, 1825, lat. by ace. 8' S., long. 6° W., at about 4" S" 16" by watch, the mean of 3 alts. Q 49° 9'-4, bearing S. 44° E. magnetic, course W.N.W. 6 knots ; at 6'' iS" 52' mean of 2 alts. Q 73° 39', the watch losing 4"5 an hour on the chron., and the chron. gaining 6*'6 a-day ; height of eye, 16 feet ; ind. corr. + 1' ; reducefl decl. 23° 1 1' S. In the interval, 2W, the chron. gained about i-ioth of 6'-6 or c'-j, and the watch lost io'*i on the chron. ; the measured interval must therefore be increased by 9'**4, and becomes z>> iox'45'. From W.N.W. to S. 44° E. is 156^ ; course 24° and dist. 13 miles give D. Lat. 1 r-9, to be subtracted from the Itt alt. Alt. 49° 10', lat. 8° r, and pol. dist. 66° 49', give outer hour-angle 2'' 38"' i6"; the diff. of this and 2'' 10"' 45", or 27" 31', is the inner hour-angle, which, with alt. 73° 52', reduction 1° 27', and 2d reduction 4', give Lat. 8° 26' S. [2.] Double Altitude of a Star, one All. near the Meridian. 741. Increase the interval by 10' for each hour. Take the ilccl. from the Nautical Almanac, or from Table 63. In other respects proceed as for the sun. [3.] Double Altitude of a Planet, one Alt. near the Meridian. 742. Find the Green. Date at each observation, and reduce to it the R.A. and decl. Apply tiie change of R.A. to tlie interval, as directed No. 73.J, and add to the interval the acceleration upon it Proceed as for the suu. [4.] Double Altitude of the Moon, one All. near the Meridian. 743. Proceed by No. 736 as far as adding the acceleration. Reduce the decl. to each Or. Date, and the hor. par. and semid. to that nearest the meridian. Proceed as for the sun. 744. The moon may be advantageously employed for this pur- pose when the Greenwich Time can be nearly ascertained, and in all cases when near her maximum declination, because her polar distance may then be very nearly computed. 745. Degree of Dependimce. The error of the inner hour-angle 13 the same as that of the outer one, which, when the body is near E. \)r W., will be very small, even when the lat. by ace. is considerably in error. 3. Double Altitude, neither Altitude being near the Meridian. 746. When neither altitude is near the meridian, the computation is dill'erent from those hitherto given, of which the object is to Hnd the meridian altitude. We shall give, 1st, an ajipro.vimnte method, the object of which is to lind the correction of the lat. hi/ ncr. ; ;iik1, 2d, the rigorous metiiod, the object of which is to find ilie latitnde itself directly, both in Ivory's form (suited to the case in \\ liicli the decl. is the same at both obs<>rvati()ns) and in a general form. 747. The orinciple of tlie apiiruxiniiilt method will easily be FINDING TlIK LATITUDF,. 2G3 nmlerstood. Siijipose the time* to be computed at each ob:=crvalioii, then, if the interval between these cominited times agrees with that iR'fually shewn by a ijood watch, the latitude by ace. (which is ati clement of the calculation of the time) is obviously correct, but if oil the other hand, the computed interval does not agree with the interval by the watch, the disagreement indicates an error in the latitude by acc.,+ the amount of which is to be computed. 748. When the correction of the lat. by ace. exceeds 10' or 15', it may, generally, be advisable to repeat the computation ; but when it is less than 4' or 5' it may be considered rather as confirming the lat. by ace. within this limit, than as correcting it by so small a quantity. See, also, Nos. 722 and 72.3, which apply to this observation. 749. Limits. An observation that is usually a substitute for a better, which the state of the weather has prevented, or seems likely to prevent, from being obtained, must be taken when it offers itself; but when there is a choice of observations, the limits are as follows: — (1.) When tiie observations are on the same side of the meridian, the difference of bearing at the two observations should e.xceed the lesser true bearing. (2.') When on different sides of the meridian, the supplement of the diff. of bearing should exceed the lesser true bearing. The dift'. of bearing should, when possible, be 90". 750. The simplest case in com])utation. This will of course be selected when the weather allows a choice of observations. In N. lat. both altitudes are to be taken to the southward of E. or W. (or the ]irime vertical) ; in S. lat. both are to be taken to the northward of E. or W. When the lat. and ded. are of contrary names, the simple case is the oidy one that offers itself", and therefors applies to the sun during the six months which include the winter. When the lat. and decl. are of the same name, the hour-angle at each observation is to be less than the hour-angle in Table 29, or the altitude is to be ijreater than the alt. in that Table. [1.] Double AlliluilenflfieSm. 7;')1, T/ie Observation. Take the alt. (see note to No. 726), noting the time, and the true bearing. After the proper change of bearing take the other altitude, noting the time. As waiting for the proper change of bearing may risk the loss of the 2d alt. it will be prudent to j)rovide an altitude earlier to serve in case of accident. * As the hour-angles only are here mni-erncd, the ennsideration of Time, as found by ■ierv'ation, will present no diffirultv to a learner. + Admiral Sir Edward Owen informed me, that when in the North .Sea he made ronstant ■ of the method of finding the lat. by the discrepaney of the computed times, as he found (iiuch more convenient in practice, in rases where it was necefsary to profit by every oppor- lity of observation, than any solution of the Dovible Altitude us a question of latitude only. Lynn's Tables the same problem is worked by trial and error. In Capt. Owen's jnurnaia : ob»trvalion, sol'cd upon the same jirinciple as that hire adopted, constantly otciim. 261 NAUTICAL ASTROXOMT. Not(! at. each observation whether the sun is to tne nortliwaid or to the soutlnvard of E. and W. An example will shew how to select the simple case. Ex. 1. Oct. 3d, lat. 25° N. The lat. is N. and declin. south, and it is the simple case. Ex. 2. Sept. ist, lat 40° N. The decl. is S° N. ; hence (Table 29) the 1st alt. must Ixi taken after 6'' 39™ a.m. (which is the suppl. to 12'' of the hour-angle 5'' 2i"'J, and the 2d before i,*' 21™ p.m. (A. T.) ; or each ait. of the centre must exceed i2°-5. 752. The Computation. The approximnte method.* If the difference of azimuth is not considerable this method should not be employed. In low lats. it will accordingly be less serviceable than in high latitudes The proper limits for ihe solu- tion will be seen on inspecting Table 71; cases outside the limits should be rejected, and those bordering on them employed with caution, especially if the error of the latitude by account is large. (I.) Find the Green. Date at the first observation. Reduce the declin. to each time of observation. For the sun, it is immaterial whether app. time or mean time be used. In general at sea app. time will be preferable, because when the observation confirms the lat. by ace. the apparent lime at ship is determined. Find the polar distances (iNo. 443). (2.) If the rate of the watch is large, correct the interval for it. Correct the alts, and reduce the 1st alt. to the 2d place of observation.t No 661. (3.) With the alt., lat. by ace, and pol. dist., compute the hour- angle at each observation. No. 614. (4.) When the oliservations are on the mine side of the meridian, take the difference of the liour-anoles ; when on opposite sides, their sum. If this diff. or sum agrees with the interval by watch witiiin 10', or even 20', provideil the difference of azimuth is considerable, the lat. is confirmed, and the time is also obtaiuevl, nearly enough in the open sea. If they do not agree, jiroceed thus: — (5.) In N lat. if the body at both observations is to the south- ward of E. or W., it is the simple case (No. 750); if the body is to the norfhwiu-d of E. or W., mark such hour-angle V. In S. lat., if the body at both observations is to the northward of * Tliis method, besides affording the time when the lat. by ace. is not very erroneous, employs the azimiiths, which in practice is a considerable advantage, since the azimuth is the means of determining the degree of dependance of tlie lat. by double altitude. f As some misunderstanding has prevailed upon the necessity of correcting the interrat of time for the change of toiigiliiilp of llu- ship, the following illustration, which was given in »n8wer to the question, in tlir Nauticid Ahi^-azine, 1840, is here inserted : — Suppose at a place A, at 10 .\.m., iIic snii'.< alt. is observed 13" 18', and 3''40'" afterwards a 2d alt. is observed. These twn alls, willi the interval 'i^ 40" afford the latitude of A. Again, suppose at a place H an olis i\n- liail nl. mined the alt. at 10 a.m., or exactly at tlie same instant the observer at A tiM.lv li]> Ui ilt., ;iiul 3'' 40"' afterwards he obtains his 2d alt. 14' 15. Tliese two alts. will, thr ini.n.,1 :,'' HI'" afford the lat. of B. Now suppo.se a ship had left A at 10 a.m., having o!.t:nii,,l il„' 1 >| alt 13° 18', and at the end of al" 40'" she arrives at B, where she obtains lier 2d alt U 15'; then she has the given interval 3'' 40"' with the 2d alt. 14 15'; and it is clear that by reducing tiie 1st alt. observed at A, or 13 18', to what it would have been if observed at B (that is, in other words, correcting the l.st alt. for the mere c/iangf ff place), she has precisely the elements for dete."mining the lat. of B, which is required. Thus, when the interval is measured by a 'vatoli, no correction for longitude appears. ttndim; the latitudk. 2C5 E. or W., it is the simple case; if tlie body is to the southwurd of F« i>r W., inarlv micIi iiour-aiiijle V. If the bearing has not been observed, or if it is doubtful, look in Table '29; then, if the computed liour-anijle exceeds the liour-aiigle in the Table, mark it V ; if the comp. hour-angle is the lesser, w'.e iio mark. If both hour-angles are less than in Table '29, it is the simple case. (fi.) For the Correction of the Lat. Compute the azimuths at each observation, No. 676. (7.) When the observations are on the smiie side, both of the meridian and prime vertical, entt^r Table 71, Part I. witii the azimuths. When the observations are on different sides, either of the meridian or prime vertical, enter Part II. To the log. from Table 71 add tiie log. sec. of the lat. by ace, and the prop. log. of the error of the interval; the sum (rejecting tens) is the prop. log. of the correction of the lat. by ace. (8.) In the simple case (No. 750), apply the correction to the lat. liy ace. according to the following directions : — Observations on tlie same side of the Meridian Observations on diferent sides of the Meridian The Computed Interval being llie greater ' the lesser The Computed Interval being the greater 1 the lesser tu6. add mid 1 «<4. In the case in whicli one or both hour-angles are marked V (No. (5) above), apply the correction according to the directions in the next Table. Observations on the same side of Observations on different sides of the Meridian the Meridian The Computed Interval being Thf Computed Interval being the greater tlie tester the greater the leaser The greater The greater Both observa- Hour /_ bei.,g Hour /. being with the with the side of the Prime Vertical. greater i texser greater lesser and both marked V. A/.im. Azim. Azim. Azim. sub. add add «/A. sub. add The Hour / V The Hour /. Y The Hour / V The Hour / V being with the being with the being with the being wi/h the difffrent sides o( the greater /mer greater] lesser greater lesser greater Ussir 1 Prime Verlical, 3t one marked V. Azim. Azim. Azim. 1 Azim. Azim. Azim. Azim. Azim. «■•«. add add s„b. add tub. .«,i. add 2G6 NAUTICAL ASTnONO^fT. Note. This second Talile, wliiih contains the remaining four'fen out of eightten rases. Diay appear complicated in its general aspect. It is, however, easy of reference when Uw case is proposed. For ex. : — 1. Suppose the observations to be on different sides of the meridian ; of this poi.it, with B long interval, there can never be a doubt. Again, 2. Lei them be on different sides of the [irime vertical, of which there cati rarely be ant doubt. 3. Let the computed interva oe the greater. Then the precept add or sub. depends on the condition that the hour -angle marked V ii *ith the greater or with the leaser azimuth. Rx. 1. (Observ. same side both of Mer. and Pr. Vert.) May loth. iS7g, lat. by ace ° ii' N., long. 6i° W., at about 8'' o'" o' a m., obs. alt. Q 35 32 , bearing E. by S. ; I ill 8'" 31" A.M , obs. alt. Q 66° 58'; index —3', eye 16 feet; course during interval S. |E.; rate 4 knots : required the Lat. at zd observation. FromS.E.iE.toE. by S. or 2I pts. and dist. i2'4, corr of 1st Alt. +11'. Decl noon, joth, 10° J' N. Alt. Q 35 31' Alt. Q 66'^ 58' Ul Red. Decl. 2c i Ind. TiibleSS +1 35 4*^ 2d True Alt. + 9 3" 9"' + 2 2d Red. Decl. 20 3 Corr. ru 1st True Alt. 35 5- 1st Honr-angle. 2d Hour.angle. Alt. 3S°5'' Alt. 67° 7' Lat. 40 12 sec V. Dist. 69 59 CO ■ 46 2 ec. 0-02706 9-46552 Lat. P. Dist. 40 12 sec. 69 57 cn.scL 77 >6 88 38 0-11701 . 0-027.5 8'3775<- 37 10 sin . 9-7.'M3 2 1 31 sill. 9-^6440 Ut 11. -angle 3° 57'" 49" sii . .s<|. 939073 2d H. -angle oi- 50"'43« sill. sservations are on the same side of the merid., when the pol. dist. exceeds the colat., take the diff. When the pol. dist. is i'()ii(il to or less than the colat., take out the log. sine of the lat. by ace; then add together the log. sines of the decl. and mean of the the end of tlie operation, that the computer may content himself tlie sum or dilT. gives the result in lat. nearest to the lat. by ace, as ic two results will differ greatly. A and B are the places sf the body at the two observations; PA, PB the polar distances; Z A, Z B the zen. dists. ; A P B the polar angle or inter- val. P D is drawn perp. to A B, and dividing A P B into two equal parts ; Z F is perp. to P D. Then, Arc 1 is A D ; Arc 2 is Z F ; Arc 3 is P D. As P D is usually gre-iter than A D, from which it is determined, if h small error occurs in A D, P D will be in error still more. Arc 4 is D F ; Arc is P F. P F here is PD - 1) F; but when the pol. dist. is mu.h less than PZ, F may fall beyond D on P I) prodiictd, and then P F The colat. P Z Id then iVmnd from P F and Z F. FINDINCi THE lATITUDK. 200 alts, (already eniploved). It'tliH lust sum is less than the sia. of tlie lat.,' take the dijf. ;' \{ yreatfT, I lie sum. One place in the bgs. is enough, since, if the distinction is not strongly marked, the ca-e should be rejected. (7.) For the Latitude. To the log. sec. of arc 5 add the log sec of arc 2 ; the sum is the log. cosec. of the latitude. Note.— To save reopening Table 68 at the same place, logs, ttiken out at the same op.'Q Bif(, or repeated, are marked with the same letters. Ei. 1. (Obs. «anie side.) Lat. by ace. io° S, long. 7° E. ; true alts, of the bu;i, 58 '4°'. *nd 63° o reduced to the same place ; interval, 31"' 5+': required the Latitude. R -d. of Ded. in the Form, Ex. 1. D. 2GI. Correction of Alts, in the Foim, Ex. 1, Red. Decl Pol. Dist. In,. r-- 54- Half 16 27 Decl. 14" 14' Arc 1 3 59 Half.'lum 60° 50' HalfDitr. 2 10 Arc '2 15 2Z 14° 14' N. 104 24 sin. 8-85605 9-<)S6h(«) sin. 8«4-'9 W Ar. CO. I-.578. 9-68784 (c) sin. 8-5-757 W sin. 9-423--Z W p. 2(;6, then, Ist Alt. 58° 40 2u 63 Sum .21 40 Dirt-. 4 ^o Half Sum 60" 50 HalfD.ir. 2 10 9-39566 (a) 9-3967. Arc 1 (rep.) 0-00.05 (ft) 9-94112 (c) 9-99969 (a) Arc 2 0-0.58. (e) 9-95767 (Suppl.)7 5= Arc 3 104 34' cos 26 sec ... sin 53 Ai c4 24 79 33 Arc 2, sec. (rep.) 00. 58. (<• cosec. o'757-3 Criterion for Sum or Diff. of Arcs 3 and 4 . Pol. Dist. exceeds co]at.-iliff. Lat. 10° 4' Kx. 2. {same side mer.) Lat by ace. 43° 10' N. ; alts, of Capella, reduced to the same place. 22° 58' and 56° 14'; interval'by chronometer, 3'' 34'" 17": required the Lat. Interval red. 3'' 34"' 53'; decl. 45° 50' N. ; arc 3, 40" sj'. Criterion, sin. lat. 9-8 ; sura of sines of decl. and mean alt. 9-6 ; take the diff. of arcs 3 and 4. L.\t. 43" 29' N. Ex. 3. (obs. different sides.) Lat. by ace. 10° N. ; alts, of Castor, 63° 16' and 46'-* 12' ; tnterval by a watch, 3" 55"' 25'; decl. 32° 14' N. : required the Lat. Arc 1, 24° 33i'j Arc 2, 11° 54'; Arc 3, 54° sk' i Afc 5, 78' 58'. Lat. 10° 47^' N. 7.58. (1.) When the alts, are equal, this method is peculiarly convenient. Compute arcs 1 and 3, as above. Arc 2 is 0. Vor Arc 4. Add together the log. sine of the alt. and the log. nee. of arc 1 : the sum is the log. cos. of arc 4. When the })ol. dist. exceeds the colat., the diff. of arcs 3 and 4 ia the colat. ; otherwise their sum. Ex. Equal alts. 46° 51' ; pol. dist. 66" 33 ; interval, 4'' 37" 50*. Lat. by ace. 60°. Arc 1,31° 3o|' ; Arc 3, 6i° 10}'; Arc 4, 31° 9!'. Lat. 58" 59'. (2.) When the declin. is 0, the half int. is arc 1, and arc 3 is 90°. Ex. I^t. by ace. 60" N., decl. o, int. 2*' o"' o» j true alts. 18' 53' «nd 20° 42'. Arc 1 ;°o'; Arc 2, i^^ig^'; Arc 5, 26° 34'. Lat. 59"59|'N. Note. — If the time also is required from the observation, with the outer alt., lat. found, list. (red. to time of outer alt), find the hour-angle. No The sum of log. sec. lat. and log. sld. arc 2 is log. >nij p 5J70 WACTJCAL A8TRONO:iIV. IV iU Dovm.E Altitude of Dutehent Bodies. 759. The forms of solution described in Nos. 737 and 747 for the cases of two altitudes of the same celestial body apply to the altitudes of diti'ereiit bodies, the difference of their right ascensions supplying iu ])art, or entirely, the ])lace of the measured interval. Since the value of this observation, like the former, depends upon the ditlereiice of azimuth, the two bodies may often be so selected as to aH'ord the best possible result under the circumstances, while in the case of a single body the necessary conditions are not, generally, matter of choice. Hence this method may be practised with equal convenience in all latitudes. This observation is particularly convenient in the case of two stars, because, as the right ascensions of the stars change very slowly no reference to tlie absolute time is necessary. 760. \\ hen the two observations can be obtained at nearly the same time, this method has the advantage of being independent of the rate of the watch, and also of the errors of the ship's run ; but when an interval ehii)ses between tlie observations, allowance niu«t be made both for the rate and tiie run. 1. One of the Altitudes {of Two Bodies) bebiy near the Meridian. 761. Limits. These are the same as those given in No. 745. It must be remarked, that the rules for the limits apply to the bear- ings at the time the bodies are actually observed, whether there be an interval or not. For ex., if the sun be observed S.S.E., and tlie moon E. by S., the case is a good one; but if the observation of the moon were dalayed till she bore S.E., the case would not be good. 762. 'lite Observation. Take tlie alt. of the outer body, which should be observed as nearly E. or W. as possible. Then observe the alt. of the inner one; lastly, that of the outer one again, noting the times of each alt. 763. The Computation. (1.) For the sun, moon, or a planet. Find the Green. Date, and reduce thereto the R.A. and declination; and for the moon, her hor. par. and semid. For a star. Take the R.A. and decl. from the Nautical Almanac, or from Table 63. Call the ditf. of R.A., or its supjil., the polar an(j4e. (2.) Reduce the alts, to the same instant, and correct them. (3.) With the outer alt. and pol. dist. find the outer hour-anglr, and proceed as in No. 740 (4), to the end. I about s^ 55" P.M. M.T.; Ut. ace. 40° 15' S.. long. 38'=' 52' lUo (leiluced to the a»me instant) obs. alt. .-^Idebaiaii neM i', lieiglit of eye 18 Ccet : requirfd lla- Latitude. FIXDIXG THE LATITUDE. ■Hie Gt. Datf !s 6" S'' 30". Ald.lmran's obs. all. 33° 17', true alt fcturn-s Kid. U.A. xV 34" »4' Lat 40", UecL 16' (co„tr,Ty \ Aldeluran's K.A. + 14" 2S zS 56 n„me,) J I'olHf :in);V- 4 54 32 lO" 47' sin. B,|. I'he true Alt. of Sat. 11' 41', 0" I 3 sin lat. 40" 15', |>»l. (list. 33 II 85=' 6' give Saturn's hour- Mcr. Alt. 33 »5 a„sle _i_ii_L9 Zen. Uist. 56 35 S. Aldebaran's hour-angle to 47 Uecl. 16 16 N Saturn's Uecl. 4° 54' S. pol. .list. X5'> 6' Lat. 40 J9S. Alitebaran's ilecl. 16° 16' N. Ex. 2. Feb. zd, 187S, lat. by a7'. R'^J- die'- 19^ 22 S., (rae alt. 41° 48'. The hour-angle of a Anrirmneil.T com. puted from alt. 41° 48', lat. 40 , and p I. dist. 61° 35', is 3'' 50'" 33". 1 he diHerenee between the polar angle and the hour-angle of o Andromed* le.ivi-s .lupiter's hour-angle 19"' 27', which gwvi Ued. + id, mer. alt. 30'' 33', and Lat. I 40° 5' N. 54° 50' N., obs. alt. Regulus 17° 21, and 3" 40' nid. corr. -5', height of eye 16 feet: required the 12° 34' N. , H A. lligel 5" 8" 42', decl. 8" 21' S. ; alt. Kegulus, 17° 9', liourangle Regulus 5'' 11" 57'; hnur- ■ 5'- Lat. 54° 59' N. 76.5. When the body nearest the meridian is observed below the pole, add the hour-angle of the other to the polar angle; the suppl. to 12" of this sum is the inner hour-angle, to which con^jnik' tiio Reduction. Ei. March imt, 1831, off Cape Horn, lat. by ace. ^(i° ^o' S., long. 65° \V., ,«t nijlit, obi tnie alt. a Pavonii 24° 38', not loni; pant the mer. below the pole; and after J" if obs. alt. y Crucis 64° 47' ; both sUrs rising, and both to tile S. of E. Red. U.A. of J ipiter 20" 33" '■ R A. ofa An< romei ;le K 0" 2" •lupiter's U..\ Polar \n V 4 33 3' Kx. 2. Jan. 3d, afterwards obs. alt. LLti.ude. .878. Kigel !a.. by 26=46 S. R.A. Regulus, p..lar angle V 56-" angle Rigel .5- 5. 10'' I 2-, t Red ° 54-. d ue alt. to this eel Re -t- 272 NAUTinAF, ASTHONOMT. y C.Tix R A. Pi.lar Angle The liour-aDsrle of y Crux, computed from alt. 64° 47', lat. 56^ ^o', and pol.ilist. 33^50', is3"6'"i8'. This hour-angle, added to the pola/ Angle, gives hour-angle ofa Pavo 1 1'' o'" S*, or 59"' 52* below the pole. The Red. 'o iiiis is 38', and the nier. alt. 24"' o' give* I Lat. 56"44' S. (Decl. of, Pavo, 57^16' S.I t. Neither of the Altitudes [of Two Bodies) being neur the Meridian. 760. Limits. These are tlie same as for No. 749. 767. Tlie Observation. Take an alt. of the outer body, then of tlie inner one, and, lastly, of tlie outer one, noting- the times. At each observation note whether the body is to the iioithward or ■southward of E. or AV. (true). 708. The Computation. The approximate method. (1.) Take out tlie right aseens. of tiie bodies from the Nautical Almanac, reducing them, if necessary, to the Green. Date. Take the ditf. of R..4., or its supjjl. to 12", for the polar angle. If the 2d ait. of the first body be lost, proceed by No. 763. The result is the polar angle. (2.) Correct the altitudes. (3.) Compute the hour-angle of each body. When the bodies are on the satue side of the meridian, take tlie diff. of the hour-angles; when on oppo.'iite sides, their sum, for the computed polar angle. If this sum, or difF., agree tolerably well with the polar angle, tlie lat. by ace. is near enough; if not, proceed as in No. 752(5) to find the corr. of lat. £.1. 1. Feb. 25th, 1830. H.M.S. Eden, lat. by ace. ii°45'S., long. 19° W., took alts, of Canopus and Sirius as following, butli stars to the E. of the iner., and both to the BOUtbward of the £. point. Canopus. 5" 43"'"' 46°58''4 5 45 ^5 47 T1. 5 4+ "8 47 2-8 Sirius R.A. 6*' 37'"4o* Canopus 6 zo 11 Polar Angle 17 jg S" 4S-0 5 5° ° 5 49 Decl. i6''29'-7 S. 52 36-58. Canopus. 5" S'"' 4' +7°^7'-4 5 54 ° 47 33-4 5 5^ 3^ 47 30 '4 Pol. Dist. 73'3o'-3 Heaucing the alt. of Canopus to the time s"" 49" gives alt. required, 47" iS -4. The . of Canopus, 47° ii'b, and of Siriu.s, 71' 56'-7. Hour-angle of Canopus Hour-angle \^ 1™ 57' Pol. Disl. 37-23' UX. 47 14 Hour-angle of Sirius Ditto Canopus Dili'. 01 comput. Pol. Angle' Pol. Anfcle FINniNG THE LATITUDR. 'J 73 T»ble 71, I'art I., 14° and 75' 9'39« L:it. sec. 0-009 «■" 34* I'l-- l"g- r^zi (,'orr. ol lilt. 34' pr. log. o'7z3 The ob«. are tn the same side of the merid. and of the pr. vert. ; both hour-ai.fslei are n oe marked V; the oomput. int. the lesser: the greater hour-angle is with tlic grfator uimuth ; 34' is to be siiblracted from 1 1° 45', which gives the l^at. 11° 11' S. Ki. 2. (The Ex. No. 765.) Tlie oomputed hour-angle of > Pavo is 11'' 5"' &•; the (lift ^< which, and 3'' 6°' 18", is 7'' 58"' 42", tlie computed polar angle, which is greater Ihao )• 53'" 50". The error is 4'" 5;'. The azim. of « Pavo is 8", that of y Crux 71^°; the coir, of lat. by Table 71, >'art I., i» e', which, since in this case the (greater hour-angle 1 1'' 5"' o' is with the lesier azin.uth, is t( ho subtracted from 56' 50', and gives Lat. 56° 44' S., as by the other solution. Ex. 3. Dec. ist, 1878, lat. by ace. 41° i8' N. ; obs. alt. of Markab, S9" 2'. and that of Allair, reduced to the same instant, 23° 38' ; both bodies to the S. and E. ; ind. corr. —2'; height of eye 16 feet: required the Latitude. R.A.. Markab, 21'' 58" 45', decl. 14° 33' N ; R.A. Altair, 19" 44'" 52*, decl. 8° 33' N. ; true alt. of Markab, 58^ 55'i that of Altair, 23° 30' ; polar angle, 3'' 13"' 52"; Mar';ub's hour-angle, i'' 11'" 44'; Altair's hour-angle, 4" 24"' 26'. Then 4'' 24'" .6'— 1'' 11'" 44" — 3'' 12'" 42". Azimuth of Markab, 35°; azimuth of Altair, 80°. Corr. of lat. 11' to be added to 41° 28'. LATiTunii, 41° 39' N. Ex. 4. May ist, 1878, lat. by ace. 29° 48' S ; obs. alt. of Altair, 26° 24', and the obs. all. of Arcturus, reduced to the same instant, 32° 23'; the bodies on dilferent sides of tlia meridian, and to the north ; ind. corr. + 2' ; height of eye 14 feet : required the Latitude. K.k. of Altair, 19'' 44'" 52*, decl. S°33' N.; R.A.of Arcturus, 14'' 10" 9" ; decl. i9°4y'N.( polar angle, 5''34"'4i*; true alt. of Altair, 26° 20' ; do. of Arcturus, 32° 20' ; hour angle of Altair, j"" 31'" 43*; Arcturus' hour-angle, 2'' 2" 3"; error, o" 56*; azimuths, 62 and 34") oirr. of lat. 6' to tub. from 29" 't'. Latitude, 29^ 42' S- 769. The error of ttie correction of lat. is directly proportional to tlie error of the interval : hence, when tlie moon is eniployeii, licr U.A. should be computed for the actual time at Greeinvich, as given liy ti.e chronometer, or found from observation of a lunar distance rather than by means of the erroneous long, by account. Ex. April 7th, 1831, lat. by ace. 34° 40',?., long. 42° W. ; true alt. J 38° 27' to the N.W. At the same time, true alt. © 47" 44' to the NE-d ; Gr. M.T. by lunar obsei-vation, jh i^cii ,j. . required the Latitude. © R.A. I*" 2'" 41', pol. dist. 96° 42'; J R.A. 20'' 52"" 28", pol. dist. 74° 10'; ®'s hour- angle o'' 36"' 45» E. ; J ditto, 3'' 3 5"' 27* W. ; © 's az. 14° ; J ditto, 81°; suppl. of dilf. of R..\. 4'' 10™ 13'. The error of the computed polar angle is 1'" 59', corr. of lat. -h6', and Lat. 34^ 46' S. This Ex. may be worked by No. 763 (3), thus : the J 's hour-angle, 3'' 35"' 27', sub- tracted from 4'' 10'" 13', gives tbe ©'s hour-angle 34°" 46'. The Reduction to this is 49', and Lat. 34'' 45' S. 3. 77/c General Solution, for the same, or different. Bodies* 770. (1.) Find tiio polar angle. This, for the sun, is properly an interval of A.T ; but mean time is near enough. I'or a star, see No. 7o;i. For the moon or a planet, see Nos. 754, 755. • Though this method is general, yet it is not well adapted to ca.ses of short interval* (No. 727) ; because, in such cases, a small arithmetical inaccuracy ni the process may produce a considerable error in the resulting latitude, as the reader may easily convince biiiiself by working examples. This is the chief ground on which an approximate and bdirect method is of^en superior, in practice, to the rigorous method. In the figure in the note, p. 2«i», omitting the lines 1' I), Z fJ, and Z K, arc A i^ A H , I tod B <>re the placet of the same body at difTcrenl timeu, or uf dilftrcnt bidii> ; aiigit B tu NAUTICAL ASTRONOMY. For different bodies, it is the diff. of their R.A. Find the polar distances at each oijservation ; in assigning these, one pole must necessarily be assumed as the elevated pole, whether the lat. be approximately known or not. Correct the altitudes, and reduce them to the second place of observation, and find the zenith distances. (2.) P'or the Arc A. Take the suppl. of the polar angle ; and add the pol. dists. together. Add together the log. sine square of the biippl. and the log. sines of the pol. dists. ; the sum (rejcctiug tens) is the log. sine square of an arc x. Put j; unuer tlie sum of the pol. dists.; take the sura and diff. and half the sum and half the ditf. Add together the log. sines of the last two terms: the sum (I'ejecting tens) is tiie log. sine square of an arij A. (3.) For the angle B. Add together the arc A and the two polar dists.; take half the sum, and from it subtract the arc A and the outer pol. dist., notmg the two remainders. If the half sum is the lesser, subtract it from the other quantity. Add together tiie log. cosec. of A, the log. cosec. of the outer pol. dist., and the log. sines of the remainders: the sum (rejecting tens) is the log. sine square of the angle B. (4.) For the angle C. Add together the arc A and the two senith dists., and from half the sum subtract A and the outer zen. dist. ; note the two remainders. If the lialf sum is the lesser, sub- tract it from the other quantity. Add together the log. cosec. of A, the log cosec. of the outer zen. dist., and the log. sines of tiie two remainders : the sum (rejecting tens) is the log. sine square of the angle C. (5.) For the angle D. This is the sum, or diff., of B and C, according to the following directions : — In the case of the same body. I Pol Dist. greater thar Colat. Dist. less than Colat. greater Alt. greater Alt. ith tenner with greater Pol. Dist. greater than Colat. Pol. Dist. less tlian Colat. Interval diff. Note. — The difference of bearing in the interval must be less than i8o°. Is P B A ; angle C is Z B A ; angle D is P B Z larger and P A smaller, P B Z may be P B A + Z the included angle PBZ, give PZ. In the case of two stars, A and B ayi very ' computed for certain pairs of stars, and inserte Diatetlally shortened. — Tal/les for facilitating i LmnT. Shadwi.i,l, R.N. 1836. which is PBA-ZBA. When PZ is I A. Then the two sides PB, BZ, witD early constant, and have accordingly b<^en . in tables, by which the L-oni|Mitiition is ic Cowjiittatioit of Double Alttltidet, by FlNniN'n THR I,ATITTinF.. 27: 'd.) For the Latitutle. Take the siinplemeiit of D to 180" Take tLe sum of the outer polar and zenith distances. Add togetlier the loj^. sine square of the suppl. of D and the log. sines of the outer pol. and /.en. dists. : tlie sum (rejecting tens) is the log. sine square of an auxiliary arc y. Put tliis arc under tiie sum of the zen. and pol. dists. ; take the sum and diff., and half sum and half dilf. Add together the log. sines of the last two terms: the sum (re- jVoting tens) is tlie log. sine square of the colatitude, reckoned from tlie same pole as the pol. dists. Ex. I. Interval. 31"' 54'; the 1st and outer alt., corrected and reduced to the 2il place, ll ^8' 39'42"; the 2d alt. 62^ 59' 36" ; outer pol. dist. 104° 24' 30" ; the other, 104 '>4' i»". For the Ar A. Interval 0'' 3^"' H* Suppl. „ 27 6 sin. sq. 9-997761 Pol. Dist. 104" 24' 30" sin. 9-986.2, Pol. Dist. 104 24 12 ain. 9-986130 Sum 20X 48 42 Auily. arc x MO 3 4^ sin. sq. 9-970012 Sum 358 5^ =4 Diff. 5« 45 Half Sum 179 26 12 sin. 7992640 Half Uiff. 29 22 30 sin. 9-690660 Arc A r 57' 5^" sin. sq. 7-683300 For the Angle B. For the Angle C. Arc A 7° 57' 52" cosec. 0-858367 A re A 7° 57' 5^" "'««• 0-858,67 Ower p. d. 104 14 30 cosec. 0-013879 0p. time, ohs. alt. of the \> lestar, si°2o'; iii.l. corr. + 2' ; height of eye 16 feet: re- quired the Latitude. App. Time ii*' J"' R.A. © 6 58 R.A. Mer. li * Obs. Alt. 51° 20' li,d. Corr. +2'1 Table 38 - 5 ) "" ' 51 J7 Igi- o">. Alt. 50' Lat. IT'S N. I XcyO, at j' ired the Latitude. App. Time R.A. © It IT 38 56 R.A. Mer. * Obs. Alt. 53" 5-' liiH. Corr. -3 1 Tabic 38 -4 ) — 7 .5^on..a„. 5^° Lat. 53 44 54 53 774. Accuratehf. (1.) Find the Greenwich Date; reduce to it -111' Sid. 'I', at mean noon ; take oiit the star's R.A. and decl. from die Nautical Almanac, and find the pol. dist. Find the star's hour-angle. (2.) Correct the altitude, accurately, (3.") For the 1st Correction. To the log. sec. of the hour-angla add the jrop. log. of the pol. dist.: the sum (rejecting tens) is the prop. log. of the 1st Correction. For the 2d Correction. To the log. cosec. of the fiour-angle add tiic prop. log. of the pol. dist ; double the sum; add to this the iMnst. 1-5821 and the log. cot. of the altitude: the sum (rejecting t»;ns) is the |)rop. log. of the 2d Correction. (4.) When the hour-angle is greater than G*" and less than IS*", oaM tlie 1st Corr. to the altitude; when the hour-angle is less than 8'' or prealer than 18'', subtract it. Add the 2c' Correction in all cases 278 NAUTICAL ASTRONOMY. Kx. July 24tli, 1S90, long, o'' e™ W. ; at lo '24 " 12" 8 ohs. a t. of I'olarli. in quicksilver, 109° 36' 40"; ind. curr. -i' 30", ihe rm. 62^, bar. 30 melics: reijuircd Gr. Date, 24tli, 10" 30-" 13" Sid. T. mean noon, 2411. S" S'" 1S-2 10'' i'"3S'6) 30- 4 9f- +1 43-5 13' oj *n.A. ,h^^„2-l^ lied. Sid. Time S 10 17 Dccl. M.T. 10 24 12 8 Alt. 109 '36' 40 K.A. Mer. iS 34 14 5 Ind. Curr - 1 30 »R.A. -I 14 21 2)109 35 'o llour-an^zle 17 20 12-4 54 47 35 Or ' 5 20 f2 4 1st Coir. 2il Corn 1; T :. ":■} -40 S" 20'" 12' Soc. 07625 cosec. 00066 ■J'rue Alt. 54 46 55 1M> l°l6'56"P.L. 03092 r.L. 03692 1st Coir. 13 '7 IsiCorr. 13' I7"P.L. 1 1317 03758 2d Corr. Lat. I 1 1 2 S3 • 23 075 r6 Const. 1-5821 54" 47' cut. 9S4S7 2d Corr. l' ii"P.L. 2 1824 775. Degree of Dependance. The error is very nearly the same as that of the alt., as a small error of time produces but little efifect. N.B. — The Nautical Almanac method for obtaining Latitude from Pole Star is strongly recommended. Every year tables are calculated expressly for this purpose. Where accuracy is re- quired, as in observations for latitude made on shore, these yearly tables should always be used. CHAPTER VI. FlXDING THE TiMI: I. By a Single Altitude. II. By Difference of Altitude NEAR THE Meridian. III. By Equal Altitudes, IV. Eating THE Chronometer. 776. In consequence of the perpetual revolution of the celestial bodies, the hour-angle of any one of them affords the measure 0/ tiuie, No. 471, &c. By whatever method, therefore, the hour-angle may be determined, the time may be deduced. At sea, where the only fixed object to which the ever-ch;inging positions of the celestial bodies can be referred is the horizon, altitude is the only means of determining the time. I. Bv A Single Altitude. 777. The sun's hour-angle being app;irent time, when his iilt. is observed, the time is at once determined. In the case uf iiny viIum UNDINO TlIK TI.HR. 2 ,-<) celestial body wliicli does not pass tlie meridian witii the sun, it is necessary to allow for the difference of tiieir iiour-aiigles, or of their right ascensions (No. 471), at the instant of observation, by referring both bodies to the first point of Aries (from wliicli R.A.is reckoned), us will be described. 1 . A Ititmk ahuve the Horizon. 778. Limits. The body should be nearly E. or W., because, when on the prime vertical, errors, botii of the latitude of the observer, and of the altitude observed, [)roduce liie least effect on the iiour-angle. In genei-al, however, the body niay l)e observed at any time, wliile moving at tlie rate of not less than (i' of alt. in I'" of time; because in this case an error of 1' in the alt. will cause not more than 10' error of time, and the same error of hit. will in the same case cause a still smaller error of time. Tiie smallest azimuth, reckoned either from N. or S., which tlie body can have under this last condition, is seen in Table 46, in the column off)'. On the other hand, the alt. should not be observed when small, a>, for ex., under 10® or 15", on account of the uncertainty of refrac- tion, especially in very hot or very cold weather. 779. In lat. 60° 24' and upwards, 1' error of alt. niust always cause more than W error of time; the body should therefore be observed as nearly E. and W. as possible. In the tropics, on the other hand, tlie time may often be more correctly deterndned, when the body is less than an hour from tlie meridian, than at several hours from it in high latitudes. At sea, the uncertainty of the sea-horizon may sometimes be removed by observing to opposite points. Errors of alt. proper to the instrument, or to the eye, are obviated by observing the alt., of the same measure, on opposite sides of the meridian. [1.] Tnfnd Apparent Tme, and thence Mean Time, by the Altitttde of the Sun. 780. TheOktervfition. Observe a set of altitudes, (Number 557) at the projjcr limits, noting the times. See also No. 535. For accuracy, note the thermometer and barometer. 781. The. Computation. {] .) Having found the time corrc- upondiug to the altitude, find the Cireen. Date by the chronometer No. 575, which will be mean time; or by the time roughly estimated and the long, by ace. No. 576, which will generally be App. Time Hediice to this the sun's declination. No. 580, or, i'or common ]>uv- poses at sea, this may be done by No. 579. Find tlie sun's polar distance. No. 443. VA'hen mean time is rerpured, reduce the Equation of Time No. .583 or 584. (2.) Correct the alt. at sea by No. 647, or, ifgreatei- accuracy '\* re.s. alt. of .sun as hel"iw : rei|uiredjpp. and mean time, and the error of the watch on eaeli time, at the instant of ohserva|Ki. Note The differenres of the alts, and tlic timis are tak( means of their agreement with eacli oilier, No. 556 Dirt'. o" 35' 3i 34 l\ 32 7 ^^ _3^_J4 ■5 7 46 Time 9 31 33 Times by W. 9" 30"' 28- 27 Long. 14° W G.A.T. Jan. 22 56 26 D 33 Slow f, r M.T. 9 25 Clirnn, ol ( ) ™ior;'°"39-49- Chr. f, ton G :M.T. -2 31 G.M.I ofObs. 10 37 18 Ship M .T.ofObs. 9 40 5« 56 20 Long. See No. 8'27 14° 5' o" W. Ex. 2. JLirch 12th, at about 4'' \$"' p.m. mean time, lat. 50° 48' N., liing. 65° 5S' E. ; obs. alt. ij_ 14° 50' 10" ; curvesponding time by W. 4I' 13'" 54-; ind -2' 20" ; height of eye, iS teet : re.iuired A.T. and .ALT. and ' of the watch G.iM.T. :Maieli II'' 23- 51'", pol, dist. 93° 15', tme ait 14° 55', Eq. T. + 9"' 55" ; ho ancle i- m or A.T. 4'' 5'" 54'; walcli t'mt un A.T. 8'" ; IM.T. 4'' 15'" 49', walcli stow m'.T. i- 55-. • In thi.s exanip'e some of the quantities arc noted but at sea the nearest minute (to which the hour-angle i unless the observuliou itself is remarkably (jood. lUcdj is generally enough, FINOIXG THE TIMK. 281 T.x. 3. Oct. zotli, 1S7S, at sea, at 4'' 40" p.m. app. tii h.'i'iht i)f eye 16 IVet ; iiul. corr. - 2' ; at 4'' 28"' 56" b) w: A. r. and M.T. and llie Error of the Watch on each. pol. dis'. 79° 31', 1 A.T. S" 4O ; .M.I true alt. 23° 15', Kq. 4>- 17- 3f; Waich/a [2.] To find Mean T,mt. the Altilmhofa 782. T)it'. Ohservation is the same as for the sun, Nos. 541, 542. 783. The Computation. (1 ) Having found the means of the times and the altitudes, take from the Nautical Almanac, or Table 6:'., the star's R.A. and declin., and also from the Nautical Almanac, or Table 61, the sidereal time at mean noon for the given day. (2 ) Correct the altitude, No. 652 or 653. (3 ) Compute the star's hour-angle, No. 614. (4 ) When the star is to the W. of the meridian, add the hour- angle to the star's R A. ; when to the E,, subtract the star's hour- angle from its R.A. (increased if necessary by 24'') ; the result is the R.A. of the meridian. From the latter (increased if necessary by 24'') subtract the sidereal time at mean noon ; the rem. is the approximate M.T. P>om this last subtract the Retardation upon it, Table 24. Take out the Acceleration for the long. ; in W. long subtract the Accel, from the result, in E. long, add it ; the result, if less than 12'', is Mean Time; if greater than 12'', reckon the time on the preceding day. (5.) For App. Time. By the M.T. obtained, and the long, by ace, or by the chronometer, find the Gr. Date ; reduce the equation of time and apply it as directed in p. II. of the Nautical Almanac, or the contrary way to that directed in Table 62. Ex. 1. .Imii. 1st, 1902, P.M., lat. 50' 46' N., lonf;. 6l° 37' W., at 7'' 56'" iS' I)y watch olts. alt of Procyoti 15^ 40' to the S. ami E., eye 20 t'ect, ind. err. o' ; reiiuired the Muui and .ipp. Times, and tlie Error of tlie Watch. Procyon's R..-V. 7' 34" lO" j Decl. 5° 28' N. ; Sid. T. mean noon, 18'' 40" 48". Ind Corr. o' Tahlc-JS -8 15° 40'. Alt. 15° 32' _o I I-at. 50 46 True Alt. 15 32 Cl.r.last.mGr. ^215 (Jr. MT. 12 9 1 1 Ship M.T. _8_3 li Long, in Time 464 Long. 6l°3l'0"W. I lie Ued. Kq T. is 3" 34' 111* wulch sluw on X.'V. 3' U)\ P.D. 84 32 150 50 75 25 59 53 I Hour-angle -4I' 48- 12* c. 0-19895 * U.A. 7 34 lo isec.o 00198 R.A. Mer.( + 24'') 245 58 I Sid. T. M. Noon - iS 40 48 s. 9-401031 Approx. M.T. 8 5 10 ic 9-93702 1 Hit. - I 1 9 '•*i1-9'5j*>98 ~8 3~5f Accel. 61' 37' W. ^ ^40 j M.T. 8 3 TV I Time hy Watch 7 56 18 I Watch >hw on ALT. 6 53 ch tublraclcit from M.T. gives A.T. 7'' 59'" 37-, and 2.S2 NAUTICAL ASTKONOMY. Kx. 2. April 27tli, 1902, A.M.. lal. 20° 47' 45" S , loiij;. 31° f E. at 2'' 19'" 41" liy tell, <.biaiia-d true alt. ul Altair 25° 14' 20' to the E. ai.d N. : iKiinnd tlie M.l. o( U.A. 19'' 46'" 2', Decl. S" 36' 35" N., Sid, T. M. Noon 2'' lis'" 9". Alt. 25° 14' 20" Hour-angle -3'' 37" S* J HI. 29 47 45 s ec. 0-061561 • U..\. 19 46 2 I'.D. 98 3ft 35 ' osec. 0-004920 I! .V .Mer. 16 S 54 iJ3___38 40 ,Sid. \. M Noon -2 18 9 76 49 20 c 's. 9-357794 Approx. :\1.T. I3"50 45 51 35 s II 9-.S94046 K.t. 16 3^ 37- S« 11 scj. 9 31S321 "U 48 29 Accel. long. 31=7 E. t-o 20 Mea.n Ti.< E '"i3^S^ 49 784. The Observation is tlie same as for the sun. Sec, also, Nos. 540, 541, 542. 785. T/ie Coinputation. (1.) Ilavino; foiiiid the means of tlie times and of the altitudes, Kiid the Gr. Date as nearly as possible l)y the chron., No. 575, or 1)V the estimated M.T. and long, hy ace, No. 576. Redtice the moon's R.A., No 591, and dccl.,' No. 589, and thence her pol. dist. ; also her horiz. parall.. No. 586 or 587, and semid., Table 39. (2.) Deduce the ajip. alt., No. 654. Take ont the correction of alt.. Table 39. Correct the altitude. (3.) Comjtute the honr-anglc, and proceed as for a star, 783 (4). F.x. 1. .luly list. iS 8. A.M.h.t. 39' 57' v., loMfT. 8° 53 E.; ALT. at Green, by cli >' ll" 4S'", ohs. alt. 2) 74° to'E. ofnter.; eye 16 feet. >\ U.A. ("orr. o'' 33-19' 1 26 Ohs. Alt. Uip. -4'1 24° lO Red. It. A. 34 45 Semid. +.5/ + II J's Red. H.I 54' 13" 24 21 j-s Aug. Sem d. '4 53 Corr. Par. + 47 3's Decl. 8 '26' 35" N. True AU, 25 8 Red. Decl. 8 27 37 N. 90 ys R.A.(f 24'') o''34-4s' liour-angle -4 "6 45 I'ol. Dist. Si 32 23 Ii..\. or mer. 20 18 Alt. 25^ 8' .Sid. T..M. Noon 7 52 32 l.at. 39 57 sec. 0- II 543 Approx. IM.T. at sliii 12 25 -.8 IVI Dist. Si 32 coscc. 0-00476 Ret ' 146 37 12 "2YT6 73 i?i COS. 9-45822 A,-eel. for 8° 53' E. -6 48 .oi sin. 987226 M.T. at Slnp 12 23 31 4" le^+s- sio. sq. 945067 id, 187S, at about <)^ 30'" p.m., 1; ofn.er., tiineby watch g'' 24"' 27- 42" 40 Mars 23" 43' of Watch. O. r. Feb. 12" 18" JO", Mar's Red. li.A. !*■ 47" 13-, Red. Oeel. i <> 10 N., T.iie Alt •r 37'. 2S3 Ilm.rangle 4' 53" 39- W. Mais' R.A. J 47 33 It. A. of Mlt. 7 4' ■» Sia. T.M.Noon 22 9 I Approx. M.T. 9 32 '° Itet. -I 34 9-543> + r'<565' 9-55i97 7Sf). When the true G.M.T. is given hy a clironoineter, tlio melon's R.A. and decHnation may be correctly found. Wiien the moon is at her greatest declination, N. or S., a small error in tiie (n; Date will but slightly affect her pol. dist. An error of 1™ in the Gr. Date causes about 2^ error in the moon's reduced R.A. 787. If the errors of the watch, as found by observation of two bodies on different sides of the meridian, but on the same side of the prime vertical, by the same observer with the same instrument, bu not identical, that error is nearest to the true error of the watch which accomi)anies the greater or outer azimuth. If the azimuths are equal, the mean of the errors is tiie true error. 788. Deciree of JJepeiulance. The alt. and the hit. being in general, at sea, more or less uncertain, and the pol. dist. of the sini and moon being reducible with precision in certain cases only, the time is in general liable to three causes of error. See No. 615. When k is jiroposed to test the observation, the parts to 30'' for the sec, &c., will be taken out with those c[u:uitities. 2. /j// tlii; Altitude 0, or fJie ImhIi/ on the Ilviizon. 789. In low latitudes the entire orb of the sun is, during certarn seasons, frequently seen at rising and setting; and in the variaiile climates of higii latitudes it is occasionally visible, though more usually clouded at tlio.se times. When the instant at which either limi) touches the horizon can be distinctly noted, the time may be determined approximately; and though the degree of approximation be rude as compared with some other methods, yet the result may often be valuable, especially after one or more days without obser- vation. It is also a recommendation to this method, as a resourci; when others fail, that it is indejiendent of Q\QYy instrument except a watcrli or other means of measuring time.* (1.) Find the time of sunrise or sunset in Table 26. Apply to this the long, in time, as directed, No. 576 : the result is the Given. Date. Reduce ilie declination, and find the pol. dist. (2.) To the horizontal refraction, 33', add the depression. Table 8, and from the sum mhlract the semid. when the lower limb is olw ibf resulls with thoie 284 NAUTICAL ASTRONOMY. served, or (uld it when the upper limb is observed : the result ia the angular depression of the sun's centre below the horizon at tl'e instant of observation. (3.) Compute the iiour-angle of tiie sun below the horizon by No. 642, using, instead of 18°, the sun's depression.* (4.) At sunset tiiis hour-angle is app. time; at sunrise taili, 1S78. l.it. 51° 20' N., lonjr. 26' W., obscrvc.l the sun's lower limb at SctliiiK iKuili the lioriziin at 7'' 40™ 56" hy watrh ; eve 16 feet; required App. Time. p Deel. 18°, Table26^n«es App. Time Sun.vet 7" 35", L..ng. 26° W. i^ 44 (i.A.T. I2th ^ 19 Dec), nth iS°io'N Corr. +_6 «ed. Decl. 18 16 N. Hor. Refr. 33' Depr. o'2i' Depr. 4 Lnt. 51 20 sec. 0-2042-/ 37 P.D. 71 44 eosec. 0-02246 Semid. -16 123 25 Depr. Centre 21 . 6. 42 sin. 904472 61 21 COS. 96S075 A.T. 7'' 40" 7- sin.sq. 9S5210 Watch _7 4° 56 49 Watch /i.^ Kx. •_'. ,ear,-,i 01 r.r. Da I4i!i, 1S78, lat. 18° 39' N, lonij. 62° 3c' E., the snn's upper limb at rising lorizon at 5'' 46"" II" b_v watch; eye 20 feet: required App. Time. ,jrt ,^^1, om_ red. decl. 8° 3' S. ; depr. of sun's centre 54'; Hour-angk 5'' 52'" 54'; App. Time 6'' 7'" 6' a.m.; watch 2o'» 55' slow on A.T. 790. Degree of Dependance. This we have at present no certain (latxi for determining, more especially when the observation is taken from a considerable elevation, as from a hill. The terrestrial refraction does not, it should seem, affect the instant of the apparent passage of a celestial body over the visible horizon, since the rays of light from the horizon and those from the body are similarly affected ; and hence the uncertainty of the result is probably due entirely to that of the astronomical refraction at the time and place. It may be proper, accordingly, to admit an error of 2', at least, in the refraction ; and the effect on tlie result is then fbinid by merely adding together the parts for 30" of the cosine and sine, dividing the sum by the parts for P of the sine square, and doubline the result. Ex. wliich, ( In Ex. I, above, the parts an mhled, is 15", ilie eHect due \ nd 116: tl nor in the • In the tropics the method No. 638 may be substituted, using log. sine depr. ® cent. As an aid to the working of a snn cbronometer, Davis's " Chronometer" Tables will be found very useful: they contain hour angles calculated exactly for degrees of Laiitudh, Altitude, and Declination, with means of making allowance for the minutes w''ich must Ixi taken into account. J. D. Potter, 145 Minories, London, E., price 10s. 6d. flKDING TIIK TIMB. 285 IL Bv Difference of Altitude near the Meridian. 791. When tlie sun is too near tbe meridian for a satisfactory observation of a single altitude, the time may be determined approx- imately, and sometimes nearly, by means of the observed difference of alt. in a measured interval. The method has been already introduced in the Short Double Altitude, p. 256, and it was on the ground that the same observation might be usefully employed for 'I'ime also, tiiat the small corrections from p. 223, which are scarcely appreciable in the resulting latitude, were applied. It is also worth while, in finding the time by this metliod, to correct for change of declination. The method (as already shewn in Case II., p. 2.59) is available with alts, taken on both sides of the meridian ; but, as this case would be comparatively rare, the rules have been arranged for observations on the same side of the meridian only.* 792. Limits. The observations should botli be within an hour from noon. The interval should constitute a large portion of the mid. time from noon ; but it should not, generally, amount to the whole time from noon. The Observation is that in No. 726. 793. The Computation. (1.) Reduce tlie declin., by the long., to noon at the place, wliich will be near "uough. (2.) Find the interval, and correct the second of the times by watch for the rate iu the interval, when considerable. Correct the alts., and reduce the Ist to the place of the 2d ; find their mean and their difference. Correct the ditf. of alts., and also the interval by tiie quantity in the Table, p. 223. f (3.) Compute the hour-angle at the middle of the interval. No. 729 (2), and add half the interval. When the observation is p.m. this is App. T., and being compared with the second time by watch, shews tiie error of the watch. >\'hen the observation is a.m., take tlie suppl. of this time to 12''. Note. If the rising ur falling of the sun lia« not hfen distinctly noticed, or it is uncertain whether the alts, are on the same or iliffereiit sides of the meridian, ascertaiu the fact by the precept, No. 72S. • For the like reason, namely, not to increase unnecessarily the number of precepta, the observation below the pole is not treated ; this presents no difficulty. t T'lis is the (|mntity which, added to the sine, ni.ikes it equal to the aic, and by me-iiiD of it re einplo) the table of «ine» equally well f(,r arcs. 28 G NAUTICAL ASTRONOMY. Ex. 1. Muy i4tli, 1878. about 1 1" a.m., lat. 48° 4' N., long. 21° 11' W., at 1 i" 28" kT by watch, ob». alt. Q 58° 9'; at ii'' 51"' 50' by watch, oLs. alt. Q 59° 39' ; ind. coiT. — 1' 20" ; height of eye, 16 feet ; rate, 5^ knots ; a-head at Ut obs. : required the Ermj of the Watch. I'imes by 1 1 1"= 28°' 10' Watch ] 11 52 ;o Interv. Corr. 24 30 ^4 3 3 ® Decl. 14th iS°io'N. 2.''W. _4_I Uej. Decl. 18 41 N. Diff. Alts. i°i7' 51' Interv. -4'" 3 3' Decl. iS 41 Mean Alt. 59 5 Hour-angle o'' 44'" 4.(.' Alt. 58° Ind. Corr. Dip Alt. Q 59° 39' o' Corr. A Semid. 59 33 40 ZJI 59 33 10 + 15 51 58 .8 59 2d Alt. 55 49 Alts. 58° 21' II ■ 59 49 ' Mean Dift-. Carr. 1st Alt. 58 21 II sine 8-4C74 , Hour-angle cosec. 0-9710 Comp. Mid. T. sec. o-iyco Half Int. *^''' '^'°-,^,ll i T. of 2d Obs. < CO,. 221^^ Do. sine 92877 I computed by Watch Watct fast 15 -6 27 31 Ex. 2. Lut. 10° 41' .S., red. de.'l. 20° 56' N , alts. © mputed App. Time of 2d Observation, o'' 39'" o». 25 19 interval 12'^ 14* 794. Correction for Change of Declination. Wlieii tlie sun is on tlie iiR'iiJiaii, his motion in declination (which then takes place on the meridian) is \ieiy. to the horizon, and consequently affects the alt, by exactly the same quantity. When, on the other hand, that part of the sun's celestial meridian or declin. circle, on which he is, is parallel to the horizon, his change of declin. does not affect the alt. at all. Hence the correspondinij change of alt. is always between and the whole amount of change of declination. The 2d alt. differs therefore by the whole, or a part, of the change of declin. in the interval, from what it would have been had the decl. remained constant. When the motion in declin. tends to increase the alt. the 2d alt. is too great; otherwise too small. There is, however, no necessity, in this method, for a very nice process of correction, for when the mer. alt. is small, and the sun not far from the meridian, the motion, in declin. corresponds very nearlv to that of alt., and the entire change may be apjilied; and when, on the other hand, the nier. alt. is great, the motion in alt. is so rapitl, that a few seconds, in the estimation, are of no consequence in practice, or the whole quantity may even be neglected. Ex.1. May 3rd, 1878. lat. 26° 14' N., long. 161° W., at lo"! 31"' 1 8" bv watch, obtained true alt. © 71° 49', and at 11'' 7'" 2i» true alt. 77^ 46': find the Error of the Watch. The Hour-angle is 46™ i8*, Mid. T. 1 1"" 13"' 42., and Watch s/ow 24"' 22'. Ex. 2. Nov. 4th, 1878, P.M., lat. 63° 46' N., long. 54° \V. alt. Q 10° iS' i", and at 2'' 36™ 27' obs. alt. Q 10" 2' 29'. 16 feet, the ship having no way. The diff. alts, i 5' 40', and Int. 21™ 32' (corr. by I'l, give of decl. 17', added to 2d alt. gives diti". alts. 15' 2 56* by watch, + 2', height of Degree of DepenJance. As the interval may be meusiuwl FINDING TIIV T(MR 287 with precision, and as tlie lat., declin., and alt , are required approx- imately only, tlie value of tlie result depeiuls aluiost entirely on tbe dirt", alts. (1.) The error of the mid. time due to a j;iveii error in the diti". alt. is founu by taking away the sine employed, juid adding tiial of the dirt', alts, vitiated by a proposed error. The residt is more ti'ustvvorthy as the diff. alts, is greater. Ill Ex 1, No. 793, lat. 48° 4'N., an error of 30" in the ililV of alts, causes ic' error o< time ; tlie obs. alts, would be better nearer noon. In Ex. 1, No. 79 1, 30" error of diff. alts, eauses 4' erioi of time. In Ex. 2, No. (S.'J, 30" error of diff. alts, causes 21" error of tiii.e. In E.\. 2, No. 794, lat. 63" 46', 30" error of difi'. alts, causes 48". The rase is unfavour- able from the smallness of the motion in alt. (•2.) The chief meiit of the method is its insensibility to an (Mi'or in the latitude, which, under the same circumstances, renders the observation of a Single Alt. useless. The effect of a proposed error is found by changing the sec. lat. before employed for the sen. of the lat. proposed. In the following examples the effect of an error of lat. in the result by Single Alt. also is uoted for conijiaiison of the two methods. lu Ex. 1, No. 794, lat. 26° 14', 10' error of lat. (that is, using 26° 24') causes only 4* error of time. The effect of this error on the time by the single alt. 71^ 49' would be 28". In Ei. 2, No. 793, 10' error of lat. causes i" error of time. The error of time bv the single alt. 57' 17' would be 2'" 9'. Since a single alt. very near the meridian cannot be employed for finding the tiuie, and since the latitude at sea is usually uncer- tain some miles, uidess it has been determined very recently, the above method is adajited to finding the time at ship during ihat portion of the day when the single altitude is not ju'aclicable. III. By Equal Altitudes. 790. Since the altitude of a body which does not cliaiige its declination varies exactly at the same rate while rising on the IC. side of the meridian as while falling on the W. side, the same altitude occurs iit the same hour-angle on each side of the meridian, and the middle jioint of time between the instants of two equal altitudes is the instant at which the body passes the meridian. Hence the time and, consequently, the error oi the watch, may be found by observa- tion of equal altitudes. In the case of the sun, the middle ))oint of time, or the mean of the observed times of equal altitudes a.m. and p.m., is apparent noon. In the case of a star, or other C( lestial body, the mean of the observed limes corresjionds to the K.A. of the star when on the meridian, that is, to the sidereal time, which may be converted into A.r. or .MX 288 NAIITTCAT, ASTRONO-tT. 797. Since tlie sun cliangcs liis declination sensibly in iartje intervals of time, two equal alts. a.m. and p.m. do not in gcncrnl correspond to equal liotir-angles, ana it becomes necessary to apply to tlie mean of the observed times a correction, which is called the Equation of Equal Altitudes. The object of the computation is to find what time tlie watch Biievved when the body was on the meridian ; the rate, therefore, does not affect the result, unless it is irregular, in which case the mean of the a.m. and p.m. times is not the time shewn by the watch when the interval is half expired. In like manner, tlie variation of the sun's motion in R.A. (which is the variation of the equation of time) produces no effect, provided it be uniform. The irregularity of this variation is inconsiderable 1. Equal Altitudes at Sea. 798. When the course made good durins: the interval of tbe observation of two equal altitudes is true E. or W., the ship changes her longitude only by the portion of time which she gains or loses on the sun in the interval ; this change introduces no correction, and the only niiestion is tiie time by watch when the interval is half expired. But when the ship changes her latitude, the same altitude no longer corresponds to the same time from noon, and a correction becomes necessary.* 799. Thismethod, though but approximate, has some advantages: it is independent of the terrestrial refraction, provided this remains unchanged in the interval employed ; and the correction for change of lat., when necessary, requires the lat. and alt. to be but roughly known. In the tropics the interval may in general be very small, on account of the rapid change of altitude, and the correction for change of latitude in such cases may sometimes be omitted. In high lati- tudes, on the contrary, the ship's change of latitude considerably alters the time from noon at which the 2d alt. (which should be equal to the 1st) is taken : hence, in such cases, the method is less useful. Note. — As the equation of equal alts, is gener.a'ly a small quantity as compared with the correction due to change of phice, we shall not here consider it. If, however, it is required to introduce it, proceed afterwards to No. 806. 800. The Observation. Observe the sun's alt. before noon, noting the time. Note the instant of the same alt. of the same limb P.M. For greater accuracy, several equal alts, should be obtained. When the motion in alt. is quick, both limbs may be observed. 801. The Computation. (1.) Take the mean of the a.m. and r M. times by watch ; this, when the ship does not change her lat., is the mean time by watch of apparent noon. Then the Equation of Time applied as to Mean Time, will give the time of mean noon at ship as .shown by the watch. Applying to this the error of the watch on Greenwich will give Greenwich time at the mean noon of the ship, which is the longitude in time. ♦ N'.B. — The altitude should not be less than 70°, or the time from noon more than lo". FIXDINCi TIIK TIME. 2S'J (2 ) Correction for change of latitude. With half the interval aa an hour-angle compute the azimuth, No. 676. To the log. sine of half the D. Lat. made good, add the log. .sec. of the lat., and the log. cotan. of the azim. : the sum, rejecting tens, i.s the log. sine of the correction, in time. When the ship has approached the sun in the interval, subtract this time from the above mean ; when she has receded from the sun add it : the result is the time by watch at apparent noon. R.t. 1. June 8th, 1S26, lat. by ace. 6° N., at 2'' 43™ '* hy watch (a.m.) and at 3' °"' 3" (p.m.) libs. alt. Q 84° 30' to the northward ; course, N.N.VV. true, rate, 3J knots. TJie interval, 17"', gives DUt. run I'l mile and D. Lat. i. Alt. (true) 84° 46' sec. i"040 D. Let. 30" sin. 6-163 Decl. 22 50 COS. 9-965 Lat. 6° sec. o'ooi Ualf-Int. 8'"3i' sin. 8-570 Az. 22° cot. 0-394 Azim. 22° sin. 9-575 Corr. — o'' o"' 5" sin. 6-559 a ;i 3^ T. by Watch of App. Noon 2 51 27 or Watch /os<. Here the sun is to the nortliward, and the course is to the northward, or the ship hss tpproavlied the sun. Ex. 2. June 22d, 1828, at sea, lat. 4*^8., course S.W. true, rate 7^ knots, obs. alts of the sun to the northward ; ship receding from the sun. Alt. Q 59° 44 5° 55 is 12 Times 12" 29"' 57' am. 3° 53 3' 4-5 7 6 39* P.M. 37 45 Means 12 30 52 » 7 30 40 int. i" 37'" 5'- The Dist. ran in i" 37" Alt. 60° Dccl. 23i Half Int. 48"- 30- Azim. 221" Approx. T. h m.; D.Lat. 0-301 9-962 9-322 9-585 y Watch of no made good, 8' D. Lat. Lat. Azim. Corr. +0 on I 19 5- 4' 15" 4° 0-4I' 19 16 16 or Watch fast. sin. 7-092 cot'. 0-383 sm. 7-476 T. by Watch of App. Noow j 19 57 or error of tlie watch, fust. 802. Degree of Dependance. (1.) The error of time due to an error of 1' in one of the alts, is half that due to 1' cliange of alt.. No. 788 (I.) (2.) To find the error due to an error of 1' in the D. Lat. made good, divide the correction obtained by the D. Lat. For ex., 1' error •a Ex. 2 causes 5' error in the correction. 2. Equal Altitudes on Shore. 803. The method of equal altitudes is susceptible of consider.ible accuracy, but it can be completely put in practice on shore only, as the sea-horizon is always subject to uncertainty. [1.] The Sun, Morning and Kvenwg. 80.5. The Observation. In the a.m., when the sun is within the limits (No. 778), set the index of the sextant at the altitude, nearly ; chimp the index, and observe the instant of the alts, of both limbs, noting the times. Do the same in the afternoon, when the limbs will follow in reverse order. U 290 NAUTICAL ASTRONOMY. Tlie value of tlie method consists in tlie same altitude being repeated, without regard to the precise measure of it. But as the second or corresponding altitude is often lost by a cloud hiding the object, tilt usual practice is to set the index to certain whole divi- sions, as 10', 20', &e., and to observe the altitudes. The moving of the index destroys, indeed, tiie integrity of the method, since the second altitude is no longer identical with the first, but is merely inferred to be equal to it from the reading. The errors, however are greatly diminished by taking numerous altitudes : or a number of instruments may be employed, set to different altitudes. 806. The Computation. (1.) Reckon the time p.m. as I2\ 13\ &c., instead of O*", 1'', &c. Add together the A.m. and p.m. times of oTiservation ; take the mean of these sums, and divide it by 2. Take the difference between tlie 1st and 3d times (as set down in the txample below) to the nearest minute, and call it the interval. (2.) Find the Greenwich Date for apparent noon at the place; reduce the sun's decl. (p. I. of the Nant. Aim.) to the nearest minute only, marking it as of the same or contrary name to the latitude, and as increasiriff or decreasing. Reduce the equation of time, p. 1. Naut. Aim. (3.) Take the sum of the changes of the suu's declination for the 24'' before and the 24'' after the Gr. Date ; call this the double change.* (4.) Compute the equation of equal altitudes thus: — Part I. From Table 72 take out the logarithms A and B. To log. A add the log. cot. of the latitude and the prop. log. of tiie double change : the sum, rejecting tens, is the prop. log. of Part 1. Part II. To log. B add the log. cot. of the decl. and the prop, log. of the double change: the sum, rejecting tens, is the prop. log. of Part II. (5.) Apply these parts, which form the equation, to the ap])roxI- mate noon by watch, by the following directions. Declination increasing 1 Part I. Part II. Lat. an of the same 1 Declin. of contrary names. luf less than 12 hours. rval greater than 12 hours. sub. add add sub. Declination decreasing add sub. sub. add The result is the time shewn by the watch at the instant the Bim was on the meridian, or apparent noon by the watch, and there- fore shews the error of the watch on A.T. To obtain the error on M.T. To apparent noon, 0'' 0'" 0\ or * As the decl, in Table 60 u given only to the nearest from tins table, may be a minute in error. This will not bf tquiil alts. ; but, for precision, the Nautical Almanac i: minute, the daily change, as taken ause an error of 1* in the ctiuation nectssar;. FINDING THE TIMR. 29-1 12" 0"- «)', apply the reduced Equation of T. as directed p. I. of the Naut. Ahn., or Table 62: the result is the mean time of the sun's iiieridiau passage (as in No. 624). By comparing with this the time of apjiarent noon by the watch, its error on mean time is found. Three places in the logarithms give the equation to O'-l.* iJx. 1. Feb. 15th, 1830, at Ascension, lat. 7" 57' S., long. 14!° W., the following obser va(ioii3 of the sun's limbs were taken in the quicksilver, the sextant being clamped at Xi". A.M. P.M. Sums, deducting 24. id'' +5'°40" 17'' 19"' 19* 4'' 14"' 59" Reil. Decl. 11° 44' S. 10 47 54 17 27 85 4 '5 \'A Eq. ofT. 13'" 50-5 arf App. Noon by Watch 2 7 3^^ '^ Eq. of T. additive, or 1 , , ,„ - c Jlean Noon, No. 62-1 } '^ 5° 5 Watch fast on M.T. i 53 39 -7 Kx. 2. July a4th, 1S7S, lat. 55" i' N., long. 0" 6'" W., obtained following observal 6' 5i" I 27-5 I 7" i2'"39'-5... 7 8 57 - Sum g" ' 9- 30-5 19 24-5 ° 55 -o 19 27-5 9 43-7 sextant being clamped 1 ©'s Red. Decl. 19° 51' N. deer. Two daily change 25' it' Eq. ofT. 6"' 14'- 1 addit. Int. io*'2'"; Part I., i5'-6, lat. and decl. same name; decl. decrensiny, add. Part II., I'o int. less than 12'' ; decl. decreasing, subtract ; app. noon by watch, o'' 9'" 58*-3; Eq. of V. additive, or M.T. of Mer. Pass, o'' 6" i4'-i. Watch fast on M.T. qI' 3'" 44- 2. [2.] The Sun, Evening and Morning. 807. Instead of observing a.m. and p.m. on the same day, it i.s oucu convenient to observe on the afternoon of one day and the ruDrniug of the next. yVte Computation. (1.) Take the mean of the times as directed; No. HOG ; this is the approximate time by watch of apparent midnight. Find the interval as in No. 806. (3.) Find the Green. Date in app. time for midnight at the place ' It is often convenient, when all possible accuracy is required, to employ tlie logarithnu imbers. In this case, take the arilh. complements of the logs. A and B, employ tha ciiLs of the lat. and decl., and the log. of the two-daily change in seconds. Fx. (the above.) Leg. A 2-2iS3 ar. CO. 7-7817 IM. tan. 9-1450 39 iS' = i35S' log. 3-372; Part I. !• 99 log. 0-2992 7-5879 9' 3 54' 292 NAUTICAL ASTRONOMY. Jleduee tlie siiii's deel. ami the Eq. of Tiinp, (.3.) Find the double cliange, as before directed. (4.) Compute the equation of equal altitudes, apply the 1st part the contrary way to (5) : the result is the time by watch of a})parent miduight. Ex. Feb. ?2d, 1830, p.m., and Feb. 23d, a.m., lat. 7" 5/' S., long. 14J" W., ob- tained obst-rvatious of equal altitudes. P.M. A.M. Sums(— 12h). 5. ,8.3 . ,,„ , 5 .9 36 10 58 5 10 40-5 10 57 47- 41 36 Watch j-235 0-855 o-fii4 3-704 4'' I 4 > 4 ■ 8 "' 1 9' Deel . 1 2° 44' S. , decreasing. 8 17 Eq. of T. I 3'" 46-4, a8 5 39 log- A- Lat. cot. 43' 8" 4 ' 2 51-5 Double change, 43' 8" 8 .7-5 9 8-7 Part 11. Log B 2-367 Deel. cot. 0-646 0-6.4 2-5 3-627 Tlie int. is greater than ii", that used for log. A being its suppl. The Eq. of eq. alts, is -fo-3 ; the watch fast on M.T. 13.] Equal AlMttdes of a Star. 808. This observation determines the absolute time with much precision and convenience, as there is no equation of equal altitudes. 809. The Computation. (1.) The mean of the times shewn by the watcli is the time by watch corresponding to the sidereal time, or R.A. of the merid., which, in this case, is the same as the R.A. of the star. (2.) Find M.T. by No. 607, and thence the error of the watch. 810. Correction for Change of Refmction. As the method of equal altitudes is capable of much precision, and as the rate deduced may be much affected by small errors in the absolute time, it is worth while to make the proper correction for every cause of inac- curacy. A shift of wind or a fiiU of rain, in the interval, may be accompanied by a change of refraction, which, especially when the altitude is low, may produce a sensible effect. To allow for this, (1.) Find the correction of the refraction at both observations for the barom. and therm., Tables 32,33 ; then, when the corrections differ, (2.) To the prop. log. of their diff. add the prop. log. of the time the sun takes to move through his diameter (which, if not shewn by the observation, may be found by note *, p. 221), and the ar. comp. of the prop. log. of the semi-diameter; the sum is the prop. log. of a portion of time, /ta/f of which is to be applied to the time of noon, or midnight, thus: — 1st obs. A.M., or to the eastward, when the east. refr. is the greater, add; when the lesser, subtract. 1st obs. P.M., or to the westward, when the east. refi. it; the greater, subtract; when the lesser, add. riNDINC. TUK TIMK. 203 El. Mayziat, 1850, Fort VillagnKiioii, R jttained equal alts. 57° in the quicksilver, a.m. :i" If S3 tlian at the west. Reduced deel. zo° 50' N. (of cottt' vy name I El. of T. 3"'44'-7, milr. from A. T ,1c Janeiro, lat. zi" d P.M. ; the rcfr. at 7l.2."'5+' mil ,3^ 25- 6- 13 13 36 2 13 2Z 4 I Correction t ir unequal refraction. 3"' i' '5' 49" Corr.-^:-.] prop. log. 2-95 do. 1-77 Ar. CO. do. 2^ prop. log. 3-65 'Iff), double change 24' 56' The nt. eh from 7'' ii"' tu ■ 3'' »!'" gives the two parts 140 59 I 46 S9'7 I 23 29-8 Appro\. Noon Eq. Equal Alti the equation of eq. ahs. +5«-9. ■Watch 10" i3™i9"-6 ■5 -9 35-7 10 23 34-6 44-7 Corr. for Refract. App. Noon by Watch Eq. ofT. +12" Watch slow on A. T. 1 36 25 4 I Watch slotc on M.T. i 32 40 v 811. Dtgrce of Depcndance. The error of the equation of equal uhitiides caused by an error in tlic double change of decl. is a matter of simple proportion. The etleets of small errors in the lat. and dec!, are insensible, therefore neither the lat. of the place nor the declin. is required to great precision. But variations in the refrac- tion, not to be removed by corrections, will always leave the result iei some degree doubtful. On this account, the method, even under the most favourable circumstances, can rarely be considered as aSbrding extreme precision. IV. Rating the Chronometer. 812. The Rate of a chronometer is the difference of its error from day to day. It is called gaming wlieu the watch goes loo fast, end losing when it goes too slow. 813. When the chronometer is fast, either on G. M.T. or on the time at place, if the error is increasing, the rate is gaining ; if de- creasing, the rate is losing. When the chron. is slow, if the error i.'i increasing, it is losing ; li decreasing, it \s gaming. The amount of the daily rate (supposed uniform) is found by dividing tlie cliange of the error by the number of days in the interval between the observations. Ex. May 27th, at 9'' a.m. chron. slow 2'' 7'" i8« June 3d, at 5*' p.m. slow 2 651 Diff. of Error in 7'' 8i> o o 27 Then 27', divided by 7-33 days, gives 3'7 daily rate, gaining. 814. When the error is found to have changed fiom fast to slow, or from slow to fast, tlie rate is the sum of the errors divided by the n-imlier of days ela])sed. Ex. 1. June 2Sth, at 3 p.m., the chron. was C" 7"o fast ; on July 5th it wa« o» 16" I •low : required the Daily Rate. The sum 23* 1, divided by 7 (days), gives 3*-3, !oti>ig . 20 I NAUTICAL ASTRONOMT;. Ex. 2. On the I4lh, the chron. was o" 17* slow; on the 31SI, it was o" 12' fi&t : required the Rale. The sum o"' 29-, divided by 17, gives I'y, yaimtiy. 815. As the chronometer rarely goes for any lengtli of time ffiihout some irregularity, the rate slioultl lie deduceJ afresh al ,.veiv opportunity. This is done, 1st, by finding tlie absolute error on the time at place, by observaiion, after intervals of a few days ; 2dlj . by direct comparison of the interval of time shewn by the chronometer with tliat measured by a clock of known rate, or with the motion of a star. Also, as longitude is measured by time. No. 479, the absolute longitudes of places, when correctly laid down, and their differences of long, may be employed in a corre- sponding manner. All observations for the purpose of rating a chronometer should be made, if possible, on shore, on account of the uncertainty of the sea-horizon, because a small error in tlie absolute time may produce a great error in the daily rate deduced. Also, the observations should be made by the same person with the same instrument, and under the same circumstances, as nearly as possible. 1. By Comparison with the Absolute Time, or Longitude [1.] Bylhe Time. 816. The best observation (out of the observatory) for the pur- pose, is equal altitudes carried on for several days. The next in value is the same alt. repeated several days successively, in the same part of the day ; for the times determined by a.m. and p.m. sights on the same day do not, it appears, agree exactly either at sea or on sliore.* As the rate rannot be depended upon for a considerable length of time, it is necessary to take frequent opportunities of obtaining alts, on shore by the artificial horizon. It is pi-oper. therefore, to remark, that by a little care, and by not mixing a.m. and p.m. sights, the rate may be determined nearly as well as by oqual altitudes. 817. At sea, the lunar observation, No. 836, or, under very fa- voui'able circumstances, the moon's altitude. No. 864, affords the absolute error of the chronometer on G. M. T., and may discover, accordingly, if any considerable change in the rate has taken place ; but it would be highly injudicious to attempt to establish a rate from obsei nations so discordant as these usually are. 818. An excellent method lias been afforded of late years, of de- termining the error and rate of the chronometer by the establish- ment of time-balls at some observatories. These, with tiie (1. M.T. at the instant the ball is dropped, are given in Table 13. The time- ball obviates the necessity of observations for rate. 819. When the ship leaves any place, and after an interval not much exceeding a fortnight returns to it again, the error of the * The late Captain Hewett mrormetl me, that being obliged to keep account of the daily ra'i'R of liis chronometers, by means of altitudes observed from the sca-horizoii, while sni . reying the North Sea, in 11. M.S. Fairy, the constant discrepancies betwceu the ( u. and r M sighls rendered it necessary to employ the A..M. sights aluiie, TIN 1)1 NT. TIIK TI.MF. 295 chninonicter acciiiiiulated in licr absence is found directly by com- .liirniy: the time shewn liy the clirononieter with tiic times olilaincd by ohservation both at lier ilci)artiire and at her return. The error thus found affords the actual sea-rute, and tlie method, when it <-iiM be practised, is far more etticieiit than tiiat of deducing iiarhour rati's. Ex. By an observation taken immediately liefore the sliip'.s departure from a port tlie cJiron. was found slow 3'' 27'" 14". By an obser^-ation taken at her return, or 11*3 <1hvs afterwards, tlie error was -^^ 27"' 44*-5, or ^o'-j more. Hence the Rate during her absence lua been, on the average, 2"7 losiiiy. [2.] By the Lonijllnite. 820. Wlien, on making a well-determined point of land, the long. by ('hron. does not agree with the actual position of the ship, and when, accordingly, the chronometer must have been going at a ditt'erent rate from what was supposeil, it w ill be convenient to refer to the following Table. The land made unexpecteiily. Sailing W. The Chronometer has gained less, lost more. gained more, gained less, or or lost less, lost more, than allowed for. gained more, or lost less, Kx. A ship from India to the Cape of Good Hope makes the land unexpectedly. The ship is sailing \V., the land made too soon ; the chron. has therefore gained less or losi more than allowed for. But it must be borne in mind that chronometers do not preserve the same rates, generally speaking, for a long time together; and, therefore, after a considerable interval, as upwards of a fortnight, this method shews only the gain or loss uii the whole, not whether the. chronometers are gaining or losing now. 2. By Comparison of Intervals, of Time, or Lomjitude. [1.] By a Clock. R'21. The clirononieter being compared at different times with a clock of which the rate is known (as in No. 504), the difference of the errors for the intervals is obtained, and tlience the rate is deduced. The mode of comparison is already described, p. 203. [2.] By a Star. 822. Since every star returns to tiie same point of the heavens 3" o.VOl of mean time earlier every mean solar day, the ret'irn of the same star to the same altitude, or to the wire of a fixed telescope, (lay after day, determines the rate very cjrrectly. The alt. should 29G NAUTICAL ASTRONOMY. he considerable, in order to avoid errors of refraction, and the Icleseope, for the same reason, should be nearly in the meridian. To find the rate, multiply 3"" 55'-91 by the number of days elapsed, and subtract the product from the first time noted ; the re- mainder is the time the chronometer would shew if it went uui- forndy, and the difference between this and the time it shews is tiie difference of the error for the interval, which gives the daily rate. Ex. At an observation of a star on May ist, tlie chron. shewed 7'' 51™ i !• ; after foul days it shewed y"" 35"' 44"'6 : required the Daily Rate. First time noted 7'' 5 1"' 1 1' 7 35 =7-4 Gaining in four days 17-2 hence the daily rate is 4«- 3, jainiBy. The disappearance of a star behind any elevated object answers the same purpose. [3.] By Difference of Lnng-tude. 823. When the error of the chronometer upon the time at an^ known place A is compared with the error on the time at another known place B, the difference between these two errors is the ditt". long., in time, between the places. Hence if the difference of the errors does not agree with the Diff. Long, found from Table 10, or in Table of Secondary Meridians, p. 392, the discrepancy arises front a wrong rate having been employed in the interval between the observations for time, and the true rate may be found by trial, aa in the following example: — Ex. At Falmouth, Feb. 3d, at 3'' 20"" i8» M.T. by observation, the chron. shewed 4- 3 1'" 47', or was I '' 1 1"' 29" fast. At Funchal, on the 12th, at si" 30"' 27' M.T., or 9' i days afterwards, the chron. shewed 7'' 29'" 34*. The supposed rate, 2'-3 gaining. Tlie D. Long, in Table 10 A is 47" 28*. Required the true rate. Obs. at Falm., T. by chron. 4i'3i"'47' | Obs. at Funchal, T. by chron. 7'>29"'34« M.T. by obs. 3 20 18 2' 3x9- id. yam -21 r, fast I 1 1 29 I 7 M.T. by obs. 5 fast I 58 46 , ditto I II IQ Difference, or chron. I). Long. 47 17 This diff. should be 47" 28", or is too small by 1 1». By inspecting the process, it is ■fijent that the quantity 2i« (which, from the nature of the case, is supposed to be in error) is too large by 1 1". The rate, therefore, is lo' divided by 9-1, or I'-i gaining. When one error is fast and the other slow, make tlicm both fiist or both slow, by adding or subtracting any number of hours. 3. Keqnii(/ Account of the Chronometer. 824. In keeping account of the chronometer, the error on G.M.T. is entered in a book as fast or slow, with the date, and tiie rate is applied to this according as it is gaining or losing, day by dav. If, after a timr, the long, or (i.M.T. lie obtained independently, liii error ou G.M.T. is foiuui ; if this doe.s not agree will' tlic rate FlXinXO THE I^OXGITI'DK. 207 allowed, a new rate must be assigned from consideration of tlie «!ircumstances. 825. As it is impossible, without an independent reference, to determine whether a ehi-onometer, A, is gaining upon another, B, or B is losing while A goes as before, no direct rules of certain application can be given for reducing the rates of chronometers by mere comparison. Since, however, it may be presumed, in general, that in a number of watches the true time will be that shewn by the majority, regard being had to the quality of each, it is proper to keep au account, in which an approved watch being taken as the standard, the rest are severally compared with it evi>i-y day. It is convenient to distinguish the chronometers by letters, as A, B, C, &c., and to write the difference between A and B thus, A — B; that between A and C thus, A — C, over each column. Advantage should be taken of favourable opportunities of land- ing at well-determined places (sec Table of Longitudes accepted for Secondary Meridians, p. 392) for good observations of time, bi'cause the diff. long, between the places will at once discover any considerable change in the rate, afford means of correcting it, and be a means of obtaining the sca-ratcs of the chronometers. CHAPTER VII. Finding the Longitude. I. Bv THE Chronometer. II. By the Lunar Orservation. III. By THE Altitude of the Moon. IV. By an Occultatjon. V. By Eclipses of Jupiter's Satellites. 82G. The apparent motions of the celestial bodies parallel to the equator, produced by the revolution of the earth round its axis, being perpetual, no fixed point or circle can be obtained from which the longitude of the observer, which is measured, like right ascen- sion, on the equator, may be determined. Longitude, accordingly, can be ascertained only with reference to the meridian of some other place ; and, as it is measured by time (No. 103), it is determined by comparison of the time at place with the time at some other place. I. By the Chronometer. 1. Determination of the Absolute Loncjitxide. 827. The most convenient method of finding the longitude is by comparison of the time at place with the time at Greenwich, as shown by a chronometer. The mean time at place being found (Chapter VI.), take the difference between this time and tin- time by chronometer, brought up to the time of observation by applying the error with the rate. i;l)8 NArTfCAIi ASTRONOMY. WIjcti tiie time at Greenwich is the least, the lonp^. is 13.; \\\\fn the greatest, it is W. Rt. 1. TheM.T. at place is 5>'4S"'2"; the G.M.T. i§ 4" 15™ ii': hence the Long. o» the place is o'' 27'" 9", or 6° 47' 15" W. Ex. 2. The M.T. at place is 7'' I4"'22«; the G.M.T. is 2'' 6"' 57': hence the Long, is 5" 7"'2i;», or 76"' 51' 15" E. 8'28. Degree of Dependnnee. Tlie time at place, as deduced from ohservation, and tlie time shewn ))y chi-on., being both liable to error, tiie error of tiie resulting- longitude is made up of the sum or ditfei-ence of tiiese two errors. 829. When the r;ite of the chronometer has changed, and the long, is reqniied at a time past, the error of the chronometer at the lime proposed must be deduced from the two rates by consideration of the circumstances, as no rule can apply to all cases. 2. Determination of Difference of Longitude. 830. The ordinary nietiiod is to find the absolute longitudes ot both places by coiiinarisoii of the Greenwich mean time, as al)ove desflribed, and then to take tiie diti'erence between them. Ex. M.T., at a place A, is 3" 11"' 45', when the G.MT. is 7'' 7"' 18": hence the Innj i.f A is 3'' <;V" 3S' W. Again, some days afterwards the M.T., at a place B, is 2'' 19'" 45". wlien the G.M.T. is 6'' 26'" 34": hence the long, of B is 4i'6'"49«W. Tlie UiFK. Long, between the places is, therefore, 11'" 14", and B is west of A. 831. But it is more concise, in a question relating to a difference. only, to proceed without regard to the absolute longitude of either jilace, by considering merely the error of the chron. on the time at each of the two places, as in the following example : — Ex. 1. At 3'' I !■" 43' M.T., by obs. at a place A, the chronometer shewed s"" 1 1"' 19', or was 1'' 59"' 36' fast on the time at A. Again, some days afterwards, at 2'' I9"'45' M.T., iX a place B, the chron. (after applying the rate) shewed 4'' 30'" 35', or was 7.^ lo'" 50" fast on the Now it is evident that if A and B were in the same long., the chron., supposing the rate truly determined, would have the same error at each place ; and hence the dilference of the errors, i'' 59"' !6» and 2'' 10'" 50', or 11"' 14', is the Diff. Long. Since the chron. is faster at B than at A, the time at B is be/iind that at A, or B is west of A. Tlie ]iroceeding, reduced to a rule, is as follows : — Find, by observation, tlie error of the chron. on the time at jdace. Having moved to anotiier place, take an observation for tini'-heu the error is less tliaii tin: di"'. long.), add 5 or ti Fi\niN(i THE i.oNCiiTrnR. SDD •s t(i onch of fill' times l)y cliron. in order to render bolli tli« rs of the same kind. Ex. 2. At A, M.T. s*' 36" 'o't chroii. 6>> 36" 20«, error i"" o"> lo" fast At B, M.T. 3 28 30, chron. 4 9 20, error o 40 50 A west of B, DiFF. Long, o 19 20 Ki'l. Siiipo tlie wliolc value of a elironometric deteniiiiiation d('|i('iids ii])oii the rate of the chroiiouu'ter, and since the rale is lia'jle to change, the result is better as the time occupied in the run IS less. This, however, does not, in strictness, apjily to inteivak less than 24 hours; for the works go through an entire revolution in 24 hours, and the rate, which is determined for an entire day, may be unequally distributed over different parts of the 24 hours. Tor extreme precision, tiie rate should be known for given intervals on the dial-])Iate. H'-i'-i. Wlien the ship returns vvitliout loss of time from a place to that from which she set out, the opportunity will in general be veiy favourable for determining the ditference of longitude. 834. While a chronometer continues to gain or to lose, the ditfer- ence of longitude shewn by it between two places will be dirt'cicntly affected, according as it is measured eastwards or westwards: hence, if the differences do not agree, the true diff. long, will be between them. When the chron. gains on its rate, flic computed long, is to the west of the true long. ; when the chron. loses on its rate, the coni- jiiited long, is to the cast. If the rate is steady, the true ditf. long, will be coriccfly found by dividing the error according to the number of the days in tli»~ two j)assages. 3. Cuinmunication of Chronomclric Differences. 8-3.5. Individuals possessing one or more good chronometers fre- quently have op])ortunities of furnishing, verifying, or correcting meridian distances. It is proper, therefore, here to enumerate the considerations wiiich ir.Huence the value of the results, more espe- cially as many such determinations arc communicated to authority from time to time, which, liowever, not lieing accompanied with the details necessary ibr an estimation of their value, leniain uueui- ]d()ye(i. (1.) It is absolutely necessary to specify or to (.'escribe tlie cxacl spot of observation at each place. (2) The number of dai/s employed in the run, or in the interval between tlie observaiions for time, or both, if these differ much, togetiier with the number of chronometers, should lie expressed ; also, I'le imies and manner of rating, and the character of the rate, as steady or unsteady, should be bricHy noticed. (3.) Tile maker's name and the number of the chronometer should be specified, because tiic character of a watch alliuct8 the value «f * •lctcruiiij;ition in which il is eiiijiloyed. 800 NAUTICAL ASTRONOMY. (4.) When tlieic are several chronometers, the result given hj each should be exhibited. The general arithmetical mean should be given, and, besides this, an estimated mean, obtained by giving more or less weight to the several results, according to the performance r,( each chronometer, and of which the observer alone can be a judge. The two final results should be expressed in ti.me, and also in arc, for the more ready comparison of positions on the chart. (5.) The e.rlrriur dijfrrence of the greatest and least results by the different cliiDiioiiiiters employed should be stated, as this shews wliether the ciuononieters went well together or not; for, though their going together does not prove that all or any of them are right, their not going together proves that some of them are wrong. (6.) All observations for the longitudes of places are supposed to be made by nieiins of tlie quicksilver, unless the contrary is ex- pressed. Wlien the altitudes are taken from the sea-horizon, tlie result should, tlierefore, be distinguished by the word (sea). (7.) It will be useful to state the temperature of the chronometer- room, and to remark whether it has remained constant or been subject to variation. Also, the general direction of the ship's head should be noted. (8.) Lastly, every result should be given without any regard as to whether it agrees or not ivith received determinations. Many received positions are very erroneous, and the only means by which they can be decisively rectified are the comparisons of independent and impartial evidence. In the following example, D. L. is the abbreviation of DiflT. Long.; ch. is that of chronometers; d. that of days; and the ex- treme difference is denoted by the number of seconds enclosed in brackets, implying limit or boundary.* Ex. May, 1838, Capt. A., of H.M.S. , sailed from Barbadoes to Port Royal, Jamaica, the points of observation being Engineers' Wharf and Fort Charles. He carritd live chronometers, viz., No. 152, Molyneux ; No. 191, Breguet ; No. 702, Arnold and Dent; No. 650, Parkinson and Frodsham ; and No. 490, M'Cabe. The passage occupied seven days. The extreme difference of the results was 7 seconds of time. The arithmetical mean was i''8'»49»; the estimated mean, i''8"'52'. The temperature of the chronometer, room ranged from 78"^ to So" ; tiie ship's head chiefly west. These particulars, abbreviated, stand thus : — Oapt. A., May 1838, D. L. Barbadoi, (Eng. Wharf) to Port Royal (Fort Charles), 5 ch. 7 J- [7'] Aritli. Mean, ii' S"'49"= 17° 12' '5 Estim. Mean, 1 8 51 =17 13 o p. 402, to which the reodei u M. B. A. and D. P. and F. M'C. No No No. No No. 152 i^S 702 I 8 650 I S 490 I 8 •46' S3 Temp. 45 Head« 49 ni" to est. * This plan referred for otb was proposed in the Naut. ;r details of the subject. Mag. KINDINO THE LONOITUDR. 301 II. Tm: Lunar Obskkvation. Cl««nni; the DisLince, Nos. B42, 344,845 — Lunar Obs. by the Sun. No. 847 — Lunar Obg by a Star or a Planet, No. 849— Special Corrections, No. 851— Degree of D-jpemUnce, No. 858 — CiJeulation of Altitudes, No. 803. 836. The aiioiilar distance of tlie moon from any celestial body liciiiL^ in per])etual change, each of the several degrees of magnitude throiigli which it passes corresponds to a certain instant of time. .Accordingly, the distance of the moon from the sun and certain other bodies, at the end of every three hours, being given in the Nautical Almanac, the observation of this distance atlords the means of determining the time at Greenwich, and thence the longitude of the observer. This observation, on account of its great importance at sea, has been distinguished by Ihe name of the Lunar Observation. 837. If the distance between the moon and the other body were the same to the spectator, whether he were at the surface or the centre of the earth, tliere would evidently be nothing more to do tlian to measure the distance by an instrument, to find from the Nautical Almanac the Greenwich time corresponding, and to com- pare this time with the time at place. But the refraction of the sun, a star, or a planet, being greater than its parallax in altitude, causes one of these bodies to appear above its true place ; while, on the contrary, the moon's parallax in alt. being greater than her refraction, causes her to appear beloio her true place. Z is the zenith, S and B the true places of the sun (or star) and moon, S' and D ' their apparent i)laces. Then S D is the tnie distance, and S'l>' the aiiparent distance SS' is the sun's corr. of alt., dd' the moon's corr. of alt. In fig. I, where the j's alt. is the lesser, the app. (list, exceeds the true, for d' is fartiier from S than 5 is, and S' is also f;xrthcr from D than S is. In fig. 2, the app. dist. is the lesser. In fig. 3, both angles at S and D are acute, as is tlie case when the alts, are nearly erpial, and aiuays wlien tiie distance exceeds 8o°. 302 NAUTICAL ASTRONOMY. As 5 5' is always less than 5G', the arc » m, fig. 3, of a circle, having its centre at S, is nearly a right line, and j'w (which, from tiie apparent place of the moon, is here the excess of the app. dist. aho^e the true) is equal to ]>]>' cos. of tiie angle at ])'. The like rerm (or 1st correction of the app. dist.) for the sun is SS' cos. S, or SS' COS. S' nearly. This is the principle of the approximate nietiiods.* Hence the apparent distance between the moon and the other body differs from the trxte distance, e.Kcept in the particular case in wliich the two opposite effects happen exactly to compensate. Tiiis last circumstance may sometimes occur during the time that two bodies within distance are above tlie liorizon, but not being discover- able from the observation it is productive of no simplification. Tlie process of reducing the apparent to the true distance, or removing the effects of parallax and refraction, is called Clearing the Distance. 838. It is evident from the above that the difference between the true and apparent distances depends almost entirely on the cor- rections of altitude (No. 438) ; and, consequently, is affected by every variation, however minute, of those corrections. Also, since the most rapid change of distance is about 1* 48' in three hours, tlio effect of 1' error of dist. is 25' of long., or the effect of 15" error of distance is 6' of long., in the most favourable case. Hence it may become of great importance to the accuracy of the result, in many cases, that the heights of the barometer and thermometer should be noted at the time of observation. 839. Tlie lunar observation, wliich is tlie only independent me- thod of finding tlie longitude generally available at sea, is also, from not being confined like some others to a particular instant, of service on shore. A single observation, however, is not capable of affording a decisive result ; great practice is necessary for measuring the distance successfully ; and the application of so many small cor- rections as are necessary wlieii accuracy is required is, even with extraordinary care and some skill, scarcely compatible with extreme precision. 840. Limits. The distance must fall between the greatest and * The approximate process will *>•■ easily intelligible by attending to the following considerations. The moon must always be raised, and the sun or star lowered, to attain their true places. Now, when the moon is the lower of the two bodies, it is evident that raising her will diminish the apparent distance ; that is, her correction of distance must be sublractive. Again, when she is the higher body it is generally additive. When the sun or star is the lower body, lowering it will increase the app. dist. ; its corr. of oist. is therefore additive, but subtractive in general when the uppermost body. The angle at the lower body, Z j'S', orZS' j', is always acute, the corresponding angle at the other body will generally be obtuse when the altitudes are very unequal, and the dist. not great. The correction of di»t. in Method 1. is the D. Lat. corresponding to this angle as a roiirse, and the corr. of alt. as Dist. The sum or dift'. of the Dep. and N is the cosine o( the angle in question to the radius 100. When the dist. is less than 90' and the Dep. greater than N, the angle is acute, but obtuse when the Uep. is the lesser. Thus, in Ex. 1 the angle at the moon is 55°J ; that at the star, 76°. When the moon's alt. amounts to nearly 80", or when the distance is so small as 20 , M uid N vary irrcgu irly, and Method I. does not serve wcU. PINniNG TIIR I.ONCilTtTDF.. 303 If-ast (listaili'cs in tlic A"aii(icai Almanac. The alls, slionld not Lo less tlian 5° or iP : ami, when tire liaromctcr and tliernioniet<^r arc iioi at liaml, nut less than 12° or 15°, t'spucially hi very hot or very eul(i woathcr. As the chief jiart of tlie eompntation consists of clearing the distance, it will bo more convenient for reference to consider thin portion of the work separately. 1 . Clearincj the Distance. [ 1 .] Approximate Metliods. 841. In these methods the object is to find the correction of tlie apparent distance due to the corrections of altitude of each body. The first, or that by inspection, is performed by means of the Spherical Traverse Table ; and the second, by logarithms* is a useful and convenient process, without the embarrassment of various cii-ses, and renuiring oidy four ])laces of figures. The a|)pro.\imate methods are, in general, not susceptible of much ))recision when the distance is less than 2(>°. 842. Method I. By Inspection. (1.) For the Moon's Correction of Distance. With the moon's app. alt. and tlie conipl. of the app. dist. to 9()<», take out M and N. With the sun's or star's-f- alt. as Course, and M as Dist. find the Dep., which place under N. When tlie distance is les" E.x. 2. (Dist. greater than 90°.) App. alt. 13° 10'; app. alt. J 36" 6'; app. dist. 120" 29' 53". Hor. par. 59' 42" ; J corr. of alt. 46' 5S" ; © corr. of alt. 3' 56". (Co-dist. © 13° and 30°, M 118-5 N 13-3 J 36" and 118, Dep. 69J. («*m) S2-7 100 and D. Lat. 82-7, Course 34". 3' gives 2'- 5, 0° 2' 30" 56" 46 ®'s Correction. © 47° and 41°, M 194-3, N 93-2 J 37° and 194, Dep. 1168 (gr.) (.diff.) 23-6 Dist. 100 and D.Lat. iy6 give the Course 76° ; at which, Dist. 47" gives D. Lat. 1 1" (which add, since ii6-8 exceeds 93-2.) © corr. +0° o' 1 1" J 2 corrs. —25 39 -o 25 28 A. dist. 4^ 20 29 True Dist. 47 55 ' J's Con J 36'' and 30.^'', M 143-4, N 42-8 © 13!° and J43-4, Dep. _32^ (sum) 75-7 100 and D. Lat. 75-7 give Course 41'^. 46' gives 34' -7 34' 42" 58" 44 -35 26 J 2d corr. 120° and 47', 1 1" I „ 35, 6 ) -5 + 3 16 —0 3'; 31 —0 32 15 120 29 53 True Dist. '9 57 3S (of the Dep. and N) by the correction of alt., pointing off two more decimals than the product contains. The seconds may either be taken separately, or as decimals of a minute. This process, worked however rouglily, affords a check against a mistake in using the Traverse Table. Ex.1 of No. 842. Di«". 56-5 J corr. of alt. 45' 35 " 45-6 Prod. 2 576-4.J Pointing off two dec. 25-76 Diff. 23-6 © corr. of alt. 47" 47 __ Prod. 1109-2 Poiiitiug olf two dec. 11-09 •>' "' FINDING THE LONCITUDR. 305 Ex. S. App. a.t. 3 72°o ; npp. alt. J 17° ;'; app. Uist. 71° 18' 32", .-orr. of alt. )i": J corr. of alt. 46' 30". (Co-dist. I7i°.) J 17° and 174", M 117-4 N 15-6 ®72''»ndii7, Pep. 111-3 9S-7 100 uBd 95-7, Course 17". 46' 44 o" 30" rg -44 29 I 2d eorr. 72° and 46', 7" 1 „ 072" and 17°, M 3;,8-4, N 94-1 J 17" and 33X, Pep. 153-0 5ii-9 100 and jX-g, Course 54°. 16 ', © corr. + o" o' 9' -o 44 2il — c 44 19 72 18 jr TbCE DlST. 71 34 13 Ex. 4. (Correcting for the barom. and therm.) Suppose, in Ex. 2 above, the barora. i» 3C-7 in. and the therm. 38°; the J corr. of alt. will be 46' 54", by No. C55, and the a'* KcfT. of alt. 4' 9", No. 051. 46' 34 4^' 4' 3' •»" 54" 4J 9" 7_ -3; ^3 +3 ^5 True Pist. 119" 57' 50'' 843. Tlie following examples cxliibit those steps only wlilcli, in proceeding by No. 842, a practised coni]mter will find it necessary to write ilown. The errors are marked against each result as given in Dr. Inman's " Navigation." Ei. 1. © A. alt. 25° 20'; J A. alt. 25'' 35'. ' 21" i app. dist. 104" 37' 49". (Co-dist. H-i^.) of alt. i' 52" ; J corr. of alt. (5»°) 29' 36' [} -29 49 -o 28 36 '04 37 4 9 True Pist. 104 9 13 (3'toosinkUX Ex. 2. A. alt. Spic. Virg. 48° o'; A. alt. J 69° 48'. ^ corr. alt. si''; J ditto, 18' 39", H«r. par. 55'; A. dist. 55" 46' 34"- (Co-dist. 34".) 35^-7 .85-3 262-3 ,80.3 ii:--? >3' 54" 77-0 94- » 30 +0° 0' 48" — 14 24 f\ +2" —0 14 22 -0 13 34 55 46 34 True Dist. 55 33 ( 19" too small) El. 3. A. lilt. © 60' 39 ; A. alt. J 34"4''- ® O". alt. 28"; J corr. 43-40". Hor Vai. 54' 47"; A. dist 43 44 50". ^ Co-dist. 46-.) 175-1 711 296-9 186-8 .70-4 35' i» 82-0 16-4 11 -0° 0' 4" - 35 45 rv-" -0 35 33 -0 35 37 43 44 5° True Pist. 43 9 13 17" too smaUt It iK evident from these examples, whi'-h.wiih those before given, 306 NAtJTICAT, ASTRONOMY. exhibit a surticient variety of cases, that the method is accurate enough for navigation in the open sea. 844. Method II. By Logarithms. — Set down in order tliC sun's or star's ap|j. ah., the moon's app. alt., and the app. dist. ; take half the sum, and subtract from it the first term in order (sun's or star's alt.); call the rem. the 1st rem.; subtract the second term in order (the moon's alt.), and call this rem. the 2d rem. For the 1st Corr. To the log. cos. of the moon's app. alt. add the log. sine of the app. dist., the const. 9-6990, the log. sec. of the half sum, the log. cosec. of tlie 1st rem., and the prop. loj;. of the moon's corr. of alt. ; the sum (rejecting tens) is the prop. log. ol tlie 1st correction. For the 2d Corr. Take the difference between the moon's corr of alt. and the 1st corr. Enter Table 56 with the app. dist. and the moon's corr. of alt., and take out the seconds. Enter again with the above difference, take out the corresponding seconds, .-rnd subtract them from those taken out before : the rem. is the 2d corr. Apply this corr. as directed in the table. For the .3d Corr. To the log. cos. of the sun's (or star's) app. alt. add the log. sine of the app. dist., the const. 96990, the log. sec. of the half sum, the log. cosec. of the 2d rem., and the prop. log. of tiie sun's (or star's) corr. of alt.: the sum (rejecting tens) is the prop, log. of the 3d correction. (As the 2d, 3d, and 4th logs, are common to the two corrections, it will be convenient to take the sum of these three logs.) Subtract from the app. dist. the moon's corr. of alt. and the 3d corr.; add the 1st corr., the sun's (or star's) corr. of alt., and apply the moon's 2d corr. as directed in Table 56: the result is the true distance. Ex. 1. App. alt. 4-7° 31 ; app. alt. J 36° 52 ; app. dist. 48° 20' 29". Sun's corr. of alt. 47"; moon's corr. of alt. 45' 35". ©Alt. 47° 31' COS. 98296 J Alt. 36 52 COS. 9'903i Dist. 48 20 sin. 9'8733\ A. Dist. 48° 20' 20" 5 Corr. Alt. — 45 35 3d Corr. - 37 47 34 ■7 1st Co. + 19 4'! & Cor . Alt 47 J ■M Corr. + True Dist. 47 54 59 '3^ 43 9'699o; 9-9690 HalfS. 66 21 sec. 0-5967' 1st Rem. 18 50 cosec. 0-4910 2d Rem. 29 29 cosec. 0-3079 45' 35"P'--Iog-fJ9^5 47" pr- log- 2-3613 1st Corr. 19 45 pr. log. 0-9596 3d Corr. 37", 2-4678 Diff.* 26 A. Dist. 48°, and 3 Corr. Alt. 46', Tab. 56, 16" 26 6 2d Corr. + 10 i Ea. 2. App. alt. O 32" 36', app. alt. ? 65° 22', app. dist. 81° 15' 51"; Q's eorr. of rU. i' 22", I) 'e corr. of alt. 22' 27" ; n-quirod 'I'nie Distance. 1st Corr. 37", 2nd Corr. o, 3d Corr. o. True Dist. So° 55' 23". Ex. .3. App. alt. » 50° 44', app. alt. J 27° 50', app. dist. 93° 9' 6", ]) 's corr. of alt. 50' 25", * corr. of alt. 47". 1st. Corr. 4' 45", 2d Corr. o, 3d Corr. 9", True Dist. 92° 24' 4". * Tliis difF. is the moon's corr. of dist. by tlic method No. 842. The sun's or s'ar's corr. ul dist. is I'oimd in like manner, tlius ; 47"-37"= 10" (agreeing within l"). riNDlNfi THE r.ONOITUUK. .-^n: [2.] T/ie Htgoroiis Method. 84.1. In this iiietliod wo fiiul, bv <'Hlciilation, tlic true distaiu;e dirt-ctly from tlie apparent distance and apparent altitudes. (1.) Take both the app. aits, to the nearest even or odd minute, take tlieir sum, and call tlie supplement of it the Ist sujiplemmt . Subtract from this suppl. the moon's corr. of alt., and add to it the sun's or star's corr. of alt. ; call the result the 2 3« ' 52 ; app. dist. 48° 20 29 . Sun's corr. of alt. 47"; moon'g H. P. 58' 3 5"; mcm-scorr.ofalt 45' J5 © Alt 47° 52' > io. 36 52 84 2+ 1st Sup. 95° 36' 0" ■ 45' 35"+ 47". -44 48 X 7 5° 48' 48" 2d Sup. 94 5' '^ Sum 170 40 Diff. 19 2 24 2d Sup. 94 51 12 HalfS. 85 20 HalfD. 9 3' >^ sine g-998';5g > 36" :;o', H. P. 58', 9-99579=' 2. ~ S\ siue 9-218363 pt^. for" 149 35". -45 ©47°. -!4) -64 Log. Diff 8'9957i8 47 54 3^ add 29 TB.Dm. 47 55 1 sm. sGI. SOS NAUTICAL ASTRONOAIV. Wlion the observer is alone, lie will first observe the alt. of Ihe body farthest fro-n the lueritlian, then that of the other body, and then the distance ; concluding with the alts, in the reverse order • As precision is not necessary in the alts., one observation of the alt. will generally be enough at each time. Tlie time by watch is, of course, to be noted at each contact. (2.) To observe the distance. Set the index nearly to the dis- tance in the Nautical Almanac, at the nearest estimated Greenwich time; put down one or more shades to screen the central mirror, direct the sight to the moon, and, holding the plane of the instru- ment in the line joining the two bodies, vibrate it slowly round the line of sight as an axis till the sun's image is seen. Make a contact roughly, clamp the index, put in the telescope (previously adjusted to distinct vision by the moon), and complete the contact. See :)ote <;,, p. 182. The relative brightness of the object and image is most conve- niently adjusted by altering the distance of the telescope from the plane of the sextant by means of the screw for the purpose, as this motion causes a greater or lesser cpiantity of light to proceed to the eye from the silvered or brightest part of tiie mirror. Observe at least 3 or 5 distances, or, with the circle, 3 or 5 pairs. When, at sea, the ship has much motion, the observer fixes him- self firmly in a corner, or lies on his back on the deck, in order to remove, as much as possible, the sense of bodily effort and inconve- nience which disturbs the eye and the attention. (3.) For precision observe the moon's true bearing; if she is near the zenith, observe that of the star instead. 848. The Computation — (1.) Having reduced the alts, to the time of the mean of the distances. No. 6(50, find the Gr. Date. At sea, the Gr. Date is required only to the nearest hour ; but if the moon's alt. is not observed, it must be found with precision. Reduce the hor. par., and thence the semid., from Table 40. Augment the semid.. Table 42. For precision, correct the hor. par. by Table 41. (2.) Find the App. Alts, of the centres by applying the ind. corr., dip, and semid. Correct the observed distance for ind. error, and add the semi- diameters of the bodies: the result is the apparent distance. (3.) Find the Sun's Corr. of Alt. by subtracting the par. in alt. from the refraction. Find the Moon's Cor. of Alt. by Table 3S). Correct for the therm, and barom. whenever these instruments ai-p accessible. Tables 32, 33. (4.) Find the true distance by No. 842, 844; or, for precision, No. 84.5, and apply the corrections, Nos. 852 and 853. (5.) For the G'M.T. Find, in the Nautical Almanac, the two distances between which the true distance falls. Take out the first nf these, and set it down under the true dist., and write against it * The reason of this order, as a general rule in such rases, is, that the outer body prc- fenes uniformity in its change of alt. for a longer time than the other, and consequently its alt. may lie reduced, by simple proportion, to au ii.tcrmediate time, with less error than the ill, of the other body. See No. bM. FINntNi; THE LONGITUDE. 503 Its prop. ]o'^ f^ivcii ill the Nautical Almanac ; note also tlie tiiii« (that is, the tiiree hours) corresponding. Take the difference between the two distances thus set down, and from its pro|). log. subtract the prop. log. taken from tiie Nautical Almanac; tiie remainder is the proj). log. of a jjoition of time to l)e added to the time from the Nautical Almanac. Tlie result is the G.M.T. of the true distance. For jirecision, see No. 856. The G.M.T. being found, the long, is determined. Ei. 1. 11 M S. Eden, April ytli, 1831, Int. by ace. 34° 30' S., long. 42" W., walcli slon on tlie cliron. 8'' 16"' 31"; chron. slow of G.M.T. 4'' 54'" 33'; lieight of eye, 16 feet ; iDd forr. -7' 36" ; had the following observations : required tlie error of the chronometer. Thneu by Waich. Alt. "J AIlQ Dintance. ■i'' 57"'24' 39"*' •i 5« 36 47° 33' I I 29 66 o' 8" (the mean of tlirce sights., > 1 47 47 5i I 8 18 36 42 Reduction of tlie Altitudes to the time i'' 1" 29». J 39' 2', 12I' ST" 24*. 4" 3*' 41 . 2 20 18, 54 1-644 ® 47° 33'. o''5 8'"36', 1 19 8-7S2 47 5^. > 5 47. -5^ VJ ? Moon's Alt. 38 10 Redjced Obs.-Time, il" i"' Time by Watch Watch slow of Cliron. "■79b 8601 o'976 i-37» Sun's Alt. 47 41 Alt. J 38° lo'j Alt. Q47°4i'; Obs. Dist. 66°o'S". J H. P. on the 7th, nonn, 56' 34'' midnt. 56 59 Var. in i2i> T; Prop. Part for 2'', 4", H. P. 5638 Corresp. Sem. 15' 26", aug. do. 15 35". Gr. Date,* 7th Obs. 1 38° 10' Ind. Corr. — S' \ Dip - 4 Sem. — 16_|_— 28 jApp. Alt. 37 42 J App.Alt. 37° 40', H 2 pts. - 2- 1 38 +30 I +28 J Corr. of Alt. 43 33 Clearing the Distance (No. 8(2), to the End. Obs. Q Ind. Corr. Dip Ai>p. Alt. 47 56'. 43' 5" 7" 4'' Obs. Dist. 66" 0' 8 Ind. Corr. - 7' ^6" ) ]. Sem. +.5 35 + 4 © Sem +15 S9 ) +^3 ■;» 7 4S App. Dist. 66 24 6 © A pp. Alt. 48", Refr. 53" Par. n Alt. -6 Corr. of Alt. 47 J Alt. 37*/. »n. 58 .5 p. "44"'33"1'. IM.T.G. M.T.S. Loi Kx. 4. Sept. 3otli, 1S78, at 4'' -■4'" 46" I'.m , IM.P. at : ' 40' W.; obs. ali.Q 16° 12'; oils. alt. J^73^ 14'; "I's. Hi ip. l.it. 17° 9' S, lonj;. a . 60^" 22' 59'' ; lieiglit ol" I G.M.T. Sept. 30'' 1 1» 35"' 26". corr. H.P. 58' 59", aiij; .semid. 16' 21". Q's app. alt. 16" 24'. J's app alt. 73' 26', app. ilist. 60° 55' 2i"; 0's corr. of alt. 3' 8", J's eurr. of alt. 16' 32", true dist. 61° 10' 36'. Long. 102'' 47' 30" W. 3. Lunar Observation hy a Star or a Planet. 849. 77ie Observation.— Take the alts, ns directed, No. 847. In taking tlie distance, direct the view to the star, make the contact nearly hetween the star and the illuminated edge of the moon, wliether it lie the nearest or fartiiest limb; clamp the index, put in the telescope previously adjusted to distinct vision by the star, and com- plete the contact by bisecting or splitting the star upon the moon's When the moon is bright, it is necessary to use a shade. The setting of the inde.x, No. 847 (2), is ,i more important step in observing with the star than with the sun, for the amount of distance i.s often the only security for employing the right star. For jn-ecision, note the azimuth as directed No. 847 (.3). 850. T/ie Computation. (1.) Proceed by No. 848 (1). Fur a phiiiet, take out the hor. par. from the Nautical Almanac, and reduce it. (2.) Find the ajip. alts, as in No. 848 (2). l"'(ir the ap|i. (list., correct the observed dist. for ind. error. When the iiKircKt limi) is observed, add the moon's seiuid.; when the furthest, tuUtract it. * It lias been recommended to observe the star open of the moon's edge, leavini; a dark •pace of about 40'. But this dark space will appear differently in different telescopes ; and, iiiorenvcr, it is better to be in the practice of observing accurately than loosely. The inaccuracy which arises in bisecting a |ilanet when it is not, as we should say of the iniion, at the full, is but small ; since, even in the case of Venus, the only plani-t which ever appears a» a crescent whin observed with the ninoii, it i-.iii scarcely e.^cced 6' or 8'. It hu been propoaed to correct for this hy a special coiiipulatiou. 312 NAUTICAL ASTRONOMY. (^3.) Find the star's corr. of alt., which is the refraction. For a planet, apply the par. in alt. from Table 45. For the moon, take her corr. out of Table 39. For precision, correct for the height ot the barom. and therm. (4.) Find the true distance, and proceed as in No. 848 (4), to the end. Ex. July i6th, 1826, near midnight, lat. by ace. 27° 5' N., at 2>' 34"' 15" by She cnron., obs. alt. jl 35° 12'j obs. alt. Fomnlhaut, 12° 51'; obs. dist. farthest limb, 70° 1' 10". Ind. corr. -20" ; height of eye, 16 feet : required the error of the chron. supposed fast oa o.M.T. I"" 6<" 7.5». Time by chron. z^ 34"' I H.P- i6th. midnight 59' 41' Chron. fast. I 6 | 17th, noon 59 35 Var. in 12" 7 Red. H.P. 59 4' Corresp Sem. 16' 16"; Aug. do. 16' 27'. G. D. 6th, past midnt. 1 2« (.bs. Alt. » 35° >^' Hip -A Obs. Alt. * 12° 51' Obs. Dist. 70° i' 10' D.p —4 Ind. Corr. — 20 Sem. +.6f * A. Alt. 12 47 J Sem. -.6 27 J A. Alt. 35 24 A. Dist. 69 44 2J 35' 20', and H.P. 59'. 46' 47- * Alt 12° 47' 4. - ^'\ 4< , +33 I + 31 J Corr. of Alt. 47 .8 * Co r. of Alt. 4 >»' Clearing the Distance (by No. 812) to the End. 1 351° and 20°, M 130-7 N. 26-0 + 13" and 131 Dep. 29-5 (gr.) 3-5 5 1st Corr. —I 36" J 2d Corr. {'^'([^^ ] +6 ' and :o°, M 109 J 35° * Corr. J 2 Corrs. and 109 r -0 1 30 )ep. 62-5 54- > p. log. p. log. p. log. (gi; A. Dist. True Dist. Dist. at Mid. G.M.T. T. by Chron. + 42 69 44 ^3 69 45 5 70 3. .5 46 10 ,•- 26-55' 2 34 >3 •1747 •5909 •3162 Error, /a»7 I 7 i» Ex. 2. Sept. 7tli, 1838, P.M., lat. 3° 2' N., long. 4'' o"' W., at 12'' 57°' 8" by watch, obs. five distances of themoon's nearest limb from ,\ldebaran, 27°47' 12". App. alt. !(: 26° 32'; app. alt. 3> S3°34'; watch slow 9'" 17" of M.T. j ind. corr. —1' 10" : required the longitude. D red. H. P. 59' 48' ; true dist., by No. 815, 28° 37' 17" ; dist. at XV'', 29° 47' 47'. Long. 59" 56' W. Ex. 3. Sept. 2cl, 1840, P.M., lat. 3° 2' N., long. 60° o' W., at 8'' 48"' 39" by watch, obtamed the mean of 5 distances between Saturn and the moon's nearest limb, 89" 41' 55° j ind. corr. —1' 25"; watch slow of M.T. 7'" 33"; app. alt. J 53° 3'; app. alt. Sat. 23° 34'. Ex. 4. July I4tli, 1878, at 2' 10"' o" a.m., M.T. at sliii), lat. ti" o S., U«p. ;irc. 14.9' 30' E., obs. alt. Aiitaits 19" 33', olis. alt. _}) 51^ 48', obs. di»t. nuar limb 7^ xz' 49', lifight of eye 314 feet nxDixr THE LO^'on•UI»K 315 ", err. 11 .list. 79° r. 56' 4 38' .s". l". a.icc. sumul. * err. 2 44", J's c ", + ap orr. 34' >. alt. :9°28', 9", truf ilist. • 149° 33' !•:• at V s. alt. •JO"' A.M ; M .l5^-°54:.' T. atsliii), lat. ao^ 10' )s. .li^t. near li.ub 86° N.. loiiR 45' 44" aec.75°W. l.uiglUofc>-. r, M.r. .i.iiy 13' 4' 12- «'.s ai.p. Ul. 51^ 5./ app. 79' 29' 4''- Kx. .'i. June I9tli, 1S78, iil)s. alt. Vciuis 23'" 14', ob 16 tlvl. vJ.M.T. June 18' 21'' 30"", corr. H V. 55' 7", aii^'. seiiiid. i 5' 14", Venus' app. alt. 23° 10', J's app all. 53° 5' J app. dist. 87^ o' 58", Venn-.' corr. »' 9", J's corr. 32' 23". true '"■ ■» ' Suno to tlie riyhl rStar to the left Suno to the right rStar to the loft less than 90° greater than 90" sub. add add sub. sub. add J to the Westward add sub. sub. add Angle greater than 90° add sub. Lat. 48° N. ; moon's alt. 30*^; star's alt. 61°; dist. 54°; moon's azim. S. 72^ E. j Co-az. 18°, Co-ang. 56°, — -;— = 6", mbtractxve. Az. ■^^°, Ang. 34°, = 3", stiblractwe. 390 Hence the Correction is 85.5. When the moon is near the zenith, or when her alt. exceeds 80*?, with the lat. and the eompl. of the star's azimutii as an altitude, take out the seconds from Table 57, and divide then^ by 100; the quotient is the correction required in seconds. AVhen the star's azim. (reckoned as above) is less than !)!)°. subtract the corr., otherwise add it. * Since the angle at one or both bodies, which is given by the method No. Xf>, neressary in making the corrections, No. 852, 853, and since that method affords butli ; apiiroximation hf which the long, by ace, if greatly in error may be corrected, ami at t uanie time a check against any important error in the rigorous process itself, it will advisable to employ it on all occasions. The angle at the body may be found from No. 844, when 'hat method is employe thus: — Take the sum of the logs., rejecting the const. 9'C990 ana the prop, log.; the ar. c log. of this sum is the log. sine squaie of the angle required. En. No. 844. Sum of four logs. A HOLE at J) 55' 30 0-6641 *y careful exaniination of observations: of the moon, made near the same time in a fixed observatory. In general, the result will have more value as the jnoon's horizontal j)arallax is greater, because her motion is then more rapid ; on the contrary, the result is of less value as the horiz. par. is less. Since the changes of the moon's It.A., at their maximum and niinimuni, are nearly in the ratio of 5 to :{ and since the change of R.A. is in a considerable degree, though not in exact proportion, greater as her distance from the eaith is less, it is evident that the place of the moon at the time of i>bser\ation materially affects the value of the result.* 5. Computation of the Altitudes. 86:?. When the altitudes are not observed they must be calcu- lated. iM. T. is supposed to be given. (1.) Reduce to the Gr. Date tlie sid. time at mean noon, also the U.A. and decl. of each body, unless one of them is the sun, in which case reduce the e([uat. of time instead of his R.A. (2.) Find the hour-angles, Nos. 609 to 612, and compute the alt. of each body. No. 667. See No. 86"'5, 7 ♦ 17 2. 50 2 w. 2 28 Ked. S.T. II 20 31 © H.-ang. 2 9 58 M.T. 21 4.6 38 © Decl. 33 7 9 t \ 45 N. 46 38 .>-5866 Kq.ol-T. i.th, 3-23. 22 53 oh i«'55' 19727 12th, 3 44 5 41 '4 21 4 3? 'iS Red. R. A 5 43 9 Rb.l. Eq T. 3 24 Red. De,l. 4 36 58 N. 33 7 9 P. Dist. 85 23 J H.-A. 3 24 1' De<:l. 28° 36' 48' N. U ■3" J Decl. 28 38 P. Dist. 61 22 Computation of the Altitudes. © H.-A. 2" 9'%8' 5 H.-A. 3I' 24™ o« .Suppl. 9 50 2 tin. sq. 9-96461 9-99859 Suppl. 8 36 sin. sq. 9-91098 P.O. 85° 2 3' P. D. 61° 22' sine 9-94335 Col. 86 58 172 21 sine 9-99939 Col. 86 5S 14S 20 sine 9'999^9 Arc X- 146 36 sin. sq. 9-96259 Arc X 1,5 21 sm. sq. 9-85371 3'8 57 263 4. ^5 45 32 59 159 28 Bine 9-54500 131 50 sine 9-87221 12 53 sine 9-34824 .6 29 sine 9-4';29i 32° 29' sin. sq. 8-89324 54° 45' sin.sq. 9-3^';>i © Tr. Alt 57 3' jTr. Alt. 35 15 Corr. Alt. + I Corr. Alt. - 46 82° 16' 5. e A. Alt. 57 32 J A. Alt. 34 29 -55 82 ,5 56 + 15 55 -H 15 50 + 9 A. Dist. 82 47 5a 57° 3^', 37" J 34° ^0, H. P. 5 6', 44' 50" zJ. 9 — 4" 85°, -2" 3» 53 " -^43 + 39 2, 45 29 © Corr. of Alt. 30 85°, — 5 \ — I ] -^ 6 J Corr. of Mt. 45 35 Proceeding to clear the distance by No. 845, the log. diff. is 9-996092, and the true dist. 82°4'5i". The next dist. preceding is 82" 58' 33", at noon ; and the G. M.T. i''47"'o', or Long. 60° 5' 30" W.f * To adapt this form for computing the altitudes to the case of a planet, put the plmet'i hor. par. in the place of the equat. of time ; and in the next column the planet's K. A. t Tliis observation, and those in Examples 2 and 3 of No. 800, wfxe taken, with 9e»ei»] other*, by Sir Robert Schomburgh, to whuiii I am indebted for them. F«NDI\(; THE I.ONGITUDK. ."19 Til. Bv THE Moon's Ai.tmude. 8()4. Since Mean Time is deterniinefl i)y the lionr-aiigle and }\.\. o/ a celestial body, the U.A. may be deteriniiied from tjie M.T. rinii the hour-aiiglo, the latter being eom|nited from the observed aUittide. Now the moon's R.A. being- given in the Nautical Alma- nac for certain points of time, the time at Greenwicii corresponding to any given R.A. of the moon may be at once found. 'Jiie moon's altitude has accordingly been often tiius employed in determining the longitude ; but the method requires much caution, because an error of altitude produces, in the hour-angle coniputetl fiom it, a quantity greater than itself, except in the single case in >vliicii the oliserver is on the equator and the body on the prime vertical, when these errors are equal. Accordingly, since an error in the moon's hour-angle appears in its full amount in her deduced K.A., and since the R.A. changes at the rate of about 2"" only in ai. hour, the longitude required is vitiated to the extent of not much less than thirty times the error of altitude in the most favourable cases. It is evident, therefore, since the place of the sea-horizon is often doubtful from 1' to 3', that the result of a sim])le lunar altitude must be in general greatly inferior to that of a lunar distance, in wiiich a good observer rarely makes an error exceeding half a minute. But as many persons, who are not sufficiently expert in ihe lunar observation to obtain on all occasions a satisfactory lon- gitu]Ay it to tbe star's alt. found by computation ; for the time may sometimes be more nearly known than the lat., and the alt. of a star computed more nearly than it can be observed. For Ex. Suppose, in lat. 40°, the J bearing E.S.E. (true), that the place ot the sea horizon is i' 30" in error, and the tune in error 5'. Then the error of the H 's computeil hour-angle (and therefore of !ier R.A.) will be 9** (No. 671), and the resulting error of long, about 4'" 30', or i" 4' (Nos. 858, 864). Now the error of the computed alt. of a star E. or W. due to an error of 5' will here be 56" (No. 671) ; hence the error of the long., as deter- mined by the moon's alt. referred to this star, will be diminished in the proportion of 1' 30" to 56", that is, from 64' to 40'. 867. 2V/e Computation. (1.) Find the Gr. Date, and reduce to it the Sid. T. at mean noon, the moon's decl., and thence her \\6\. dist., her hor. par., and semidiameter ; correct the hor. par. by Table 41. (2.) Add the M.T. to the red. Sid. T. ; the sum (rejecting 21'' if it e.xeeed 24'') is the R.A. of the meridian. (:3 ) Correct the alt.* (4.) Compute the moon's hour-angle, No. 614. (5.) When the moon is to the E. of the meridian, adil her hour- angle to the R.A. of the mer. If the sum exceed 24'', reject 24''. VViien to the W., subtract tbe hour-angle from the R.A. of the nier., increased, if necessary, by 24'' : the result is the moon's II. A. (6.) For the G. M. Time. Set down in order this R A., that preee,o°i6'39"S. Dift'. for icw, 142" o°,6 39" 140", 9™, 2' 6" ) 2 %^ l-l] 2 ,6 Red. Decl. 18 55 S. Pol. Dist. 89 41 5 H.P. 5th, Mid. 6th, Noon Var. in I2i> 7"-2.ind iiJS Equat H.P. Corr. Table 41 C R.A. 35 '^-7 )o. at 61' 3 4 20 -1 3 6 41 -8 fi.M.T LO.NG . 6" 22" 1 5- . 2 so 5 or 42" 3.' w or of Ion or of 1' '. ; an error of f lat. causes c» 'of alt. pro. 9 of R. A., ur 868. Wlien two or three observations are taken on tlie same side of the meridian and prime vertical, the true long, is not the mean of the results, but is nearer to that which is furthest from the meridian. When two observations are taken on opposite sides of tlio nieri. dian and on the same side of the prime vertical, tiie right ascensions rorjlting will be affected in different ways by the same errors of altitude and latitude, and the true long, will be between the two results. 869. Degree of Dependance. This is determined by the effects produced on the hour-angle by given errors in the alt., lat., and pol. dist.. No. 615. It is evident, from the remarks above, that unless considerable care, and some skill, are devoted to diminishing, accord- ing to the circumstances of the case, the effects of errors of latitude and altitude, if cannot be prudent, notwithstanding the occasional »uceess of observations of tiiis kind, to depend upon the result r3 nearer than '\ of a Af^irfi'. 322 NAUTICAL ASTRONOMT. Od shore, when the lat. and time are accurately known lbs reeult may, with proper attention, he more satisfactory. No. 862 applies to this observation. IV. By AN OCCULTATION. 870. Tjie moon in lier perpetual revolution round the earth necessarily passes over every star or other body in her path at certain periods. Tiie disappearance of a star or planet, called the immersion, and the reappearance from behind the body of the moon, called the emersio7>, being instantaneous, the phenomenon affords tlie means of determining the longitude at all places where it is visible. At the instant of occultation the apparent R. A. of the moon's limb is the same as the R.A. of the star ; the effect of the paralla.x of the moon being removed by computation, the true R.A. is de- duced, and the G.M.T. thence found. 871. This observation affords, in favourable cases, the most decisive results, because it is both instantaneous and altogether independent of instrumental adjustments. On board ship the motion prevents the telescope, v/hich is almost always necessary, tiom being kept steadily directed to the moon, and in consequence the method has been very rarely jtractised at sea. The precise in- stant of the phenomenon is, however, not necessary in all cases ; it is enough that the observer is certain that at one instant he sees the star, and that at another he does not see it; because the whole resulting error in the time of observation in this case, and therefore .u the longitude itself, cannot exceed the time elapsed between two sights of the moon. 872. The M.T. at Greenwich, at which the moon and the star to be occulted are in conjunction in R. A., is set down in the Nautical Almanac, as also the parallels between which the pheno- menon is visible. As it would require a distinct calculation to learn beforehand approximately the time at which the phenomenon will take place, the observer may content himself with finding, from the long, by ace, the time at place of the conjunction ; he must tlien, at an early opportunity, single out the star, and watch the progress of the moon towards it. In general, when the star is to the eastward of the observer at the time of conjunction, the phenomenon occurs beforfi that time ; when to the westward, it occurs afterwards. 1. Occultation of a Star. 873. TTif! Observation. Note the instant of immersion or emer- bion as nearly as possible. 874. The Computation. (1.) Find the Green. Date, and reduce to it the Sid. Time at mean noon, the moon's declination, hor. par-, iumI semid. ; reduce the hor. par. by Table 41. FINDING TllK LONGlTtDE. 32S [2.) Find the geocentric latitude by subtracting from the lai. the reduction of lat., Table f)2. From the time at place find the star's hour-angle, No. Gil. (3.) For arc A. To the prop. log. of the reduced hor. par. add the log. cosec. of the geocentric lat. and the log. sec of the star's dccl.: the sum is the prop. log. of arc A. For arc B. To the prop. log. of the red. hor. par. add the log. sec. of the gcoc. lat., the log. cosec. of the star's decl., and the log. sec. of the liour-angle ; the sum is the prop. log. of arc B. For arc C. Add together the prop. log. of the red. hor. par., the log. sec. of the geoe. hit., and the log. cosec. of the hour-angle; (louhle the sum, add to it the const. 1-582, and the log. cot. of the btar's decl. : the sum is the prop. log. of arc C. (4.) When the lat. and decl. are of the same name, add A to the fctar's decl. ; when oi contrary names, subtract it. When the star's hour-angle is less than 6\ subtract B from tiie star's decl. ; when greater than G*", add it Subtract C from A. Call the result the prepared declination. (5.) For Part I. of the ]> 's Parallax in R. A. Take the diff. lietncen the tnoon's decl. and the prepared decl.; under this ditf jiut the semid. : take the diff. and sum. Add together the log. cos. of the prepared decl., the const. 11761, half the prop. logs, of the diff. and sum : the sum is the prop. log. of Part I. For Part II. Add together the log. cos. of the prepared decl., tlie const. 1'1761, and the sum of the 3 logs, used in arc C: the Sum is the prop. log. of Part II. When the moon is on or near the meridian, this Part disappears. (6.) Apply Parts I. and II. to the star's R. A., thus : — Part I. In an immersion, subt^'act ; in an emersion, add. Part II. When the > is to the E. of the Mer., subtract ; when U'., add. The result is the moon's R. A. (7.) Find the G.M.T., as directed. No. 867 (6.) + 4 56 •© (Decl. S. lat. S. a.ld.) De.1. 5 16 11 -6 Ek. Dec 9th, 1825, lat. 9" 40 fi.. long, by ace. j itrved the immersion of x Aquarii,* W. of the aneridian ; Ur. Date, 9th 9'' 19"' 2-,' K.-.I.S.T.atm.n. 17 11 13-7 Ml". 7 19 57 Sur'i R.A. 22 2« 39 Hour-angle i 2 31 ' Arc A. H.P.;4'38"p- log. 0-5178 Geoc. Lat. cosec. 0-7777 + Decl. sec. coo 17 P. log. 1-2972 A, +9' 4"-S fl& C- 4 » -8 r 51' -W., at 7» 19" 57- required the longitude. 5 S. Re 11701 2 p. log. 1-9910 DiflF. Sum. 22 30 45 19 30- 9 3 • 477> ', o'35"-6 2482Q 1 I 49 -4 8 -0060 3 p. log. ""^ Kx.2. 9 19 30 7 .9 57 ' 59 33 g.acc.-W. 3 3 or 29^53''9"W'. at loK 45... 53-2 M.T. obBeived the immersion of: Leonis, E. of the meridian : required the Longitude. Gr. Date io''47"', Red. S.T. 19I' 6'" 8-5, star's R.A. 10" 23'" 26-4, decl. 14° 58' 38''-8 N., J> icd.decl. i5°49'4o"N., H P. 55' 54"-9, Semid. 15' i6'-i, geocen. lat. 51° 57' 19". Arc A. 42' 33", D. 3'2i"-5, C. 2"-3. Prep. decl. i5"37'4S"o. Part I. 39'-9, Pt. 11. 2'" i2''-6. J R.A. loi' 20"' 33"-9. At lo'', lo'' 18"' ss'^S; at ii*', 10" 20'" 58*-5. ti .M.T. 10'' 48'" o'. By corr. of Part I. lo'' 47'" 45'. 2. Occultation of a Planet, 875. The Observation. The planet having sensible seniidiaineter, the plienonienon does not take place instantaneously. Note the instant of final disappearance, or the instant of reappearance. 876. The Computation. Subtract the planet's horiz. parallax from the reduced horiz. parallax of the moon. Also subtract its »emidianieter from the moon's semidiameter. In other respects proceed as for a star. 877. Degree of Dependance. A small error of Gr. Date will not sensibly affect the moon's parallax or semidiameter, and the de- clination is the only element liable to sensible error; Part I., there fore, is alone affected. To find the error in the long, in time, caused by 1™ error of Gr. Date. Find the change of decl. in l", add it to the diff. of declin., and recompute Part I. : the diff. between the result and Part I., as computed before, is the diff. or error of R.A. The error of long, in time will be, on the average, 30 times greater.* If the star pass very near the moon's upper or lower limb, the observation is not good. The inequality of the moon's surface, and an imperfect estimation ftf the figure of the earth, may cause small inaccuracies. The cases least liable to error on the several accounts enumerated are those which occur when the moon is near the meridian, and in which the central zone of the moon passes over the star. The emer- «ion from the dark limb is the case most distinctly marked. No. 862 applies to this observation. • Hence, to obtain the long, in time tiiie to !• or 15", the parallax In R.A. diu»I ba IfiK to 0*-003. This remark shews the ditticulty of ubtainiog eilreme precision troin anj •iuflc obiterTation. FTISDINO TFIE lONOITtDJt. Sf?5 V. By Eclipses of Jipitkr's Satellites. 8/8. Tiie eclipse or disappearance of a satellite in the shadow of the planet, called the Immersion, or the reappearance after eclipse, called Emasion, being a plienomenon which takes place at the same nhsolute point of time wherever the spectator may be pl.iced, affords ii ready method of finding the longitude. The diagrams of the positions of the planet and its satellites, as seen in N. lat., and other necessary information, are given in t!ic Nautical Almanac. The figures must be reversed in S. lat. It will be convenient for the observer to bear in mind, that when Jupiter comes to the meridian before niidniglit, the whole eclipse (both immersion and emersion) takes place on the E. side of the planet ; when after midnight, on the W. side. In an inverting telescope this will appear to be reversed. 879. Tke Observation. The telescope should have a magnifying power of not less than 40, and the observer should be ready some minutes before the time of observation, estimated by applying the long, by ace. to the time iti the Nautical Almanac. The sun should not be less than 8° below the horizon, nor Ju- piter less than 8* above it, for the phenomenon to be distinctly visible. 880. Tlie Computation. The difl^erence between the M. T. at place, found by observation, and that at Greenwich, is the long. Ex. Oct. 6th, 1822. near Igloolik, Int. 69° 21' N., immersion of the 1st satellite, lo'' 29'" 53 , M.T. The M.T. at Gr., in the Nautical Almanac, is \i,*' 56" o- ; the diff., jh jgm 27", long. W. 881. Degrf£ of Dependance. This method, tliougii easy and convenient, is not very accurate ; the eclipse is not instantaneous ; and the clearness of the air, and the power employed, affect consi- derably the time of the phenomenon. Observers have been found to (liti'er 40' or 50' in the same eclipse. The observation may be considered complete only when the im- mersion and emersion of the same satellite are observed on the same evening, and as nearly as possible under the same circumstances. Thus, if the satellite disappear a little sooner th;in if the air hail been clearer, it will emerge a little later from the same cause, and the mean of the two results iray l)c near the truth. The first satellite is preferable to tho others on account of the (frreter rapidity of its motion. 326 WACTIfAl, ASTRONOMY. CHAPTER VIII. Finding the Variation of the Compass. I. By the Amplitude. II. 13y the Azimuth. III. By Astro- nomical Bearings. IV. By Terrestrial Bearings. 882. The Variation is found by comparing the bearing of the sun or other celestial body, as shewn by the compass, with the true bearing as found by calculation. See No. 907. 883. When the time is known, the body may be observed, in the iiuiplest cases, at its passage of the meridian, at which time it bears due N. or S., or at its passage of the prime vertical, when it bears due E. or W. In other cases, the true azimuth may be found by calculation. When the time is not given the azimuth may be determined by observation of tlie altitude. When the altitude is nothing, or the body is on the horizon, as at rising or setting, it is usual to refer the bearing to the piime vertical, the angular distance from which (or the complement of the azimuth) is called the amplitude. The azi- muth may also sometimes be determined from the observed difference of altitude in a measured interval of time. The following rules are arranged more particularly for observa- tions of the sun ; but, after the explanations and precepts already given, no difficulty will occur in adapting them, when nece.ssary. to observations of other celestial bodies. I. By the Amplitude. 884. This method, which i* ))articularly convenient, is available twice a-day in fine weatiier, and at all seasons of the year. 885. The Observation* At sunrise, when the upper limb ap- is on the Iiorizon, observe its bearing, and continue to take rings of the centre, bisecting the sun's disc by keeping the up- k; * The usual instructions for taking an amplitude direct the snn to be ohsen-ed when his lower limb is half way between the centre and the horizon, at which time he is really on the hiiilzon, Nc. 433. But as it is not easy to seize the bearing at the required instant, and still less so to obseive several bearings e(|ually distributed on both sides of the proper position, whijb is essential to a correct result, the sun is commonly observed a whole diameter too low. The observation as recommended above is more convenient ir. practice, and the enxir »ri«ing from not observing the sun at the instant to wh>ch the true amplitude cor (No. 446 (1)), is removed by the correction. FINDING THE VARIATION OF THE rOMVASS 32? riKhl Ttirc on the upper liuib, until the lower limb ai>pear9. Read off each bearing?. At sunset, when the lower limb touches the horiz.on, proceed in like manner, until the apper limb disappears. See No. 2-2 1 . _ „, . . The mean of the readings, reckoning from the E. or M . poin'. i") the observed amplitude. 88b\ The Computation, by Inspection (1.) Enter Table 69 with t!ie Lat. and Declin., take out the amplitude, anrl mark it of the fiamc name as the Declin. (2.) Take from Table 59 A tlie correction. If this does not Hmount to nearly 1", it may in general be omitted. At liising. In N. lat. ajiply the corr. to the rii/lit of the ob- served amplitude. In S. lat. apply it to the left. At Setting. In N. lat. ajiply the corr. to the left of the ob- served amplitude. In S. lat. ai)ply it to the right. (3.) When the observed and true amplitudes are both N. or both S., their difference is the Variation. If one is N. and the other S., llieir sum is the Variation. Then, the observer being in the centre of the compass, when the observed am|>iitnde is to the left of the true, tlie Variation is East; when to the right, it is West. Ex. I. Jnue loth, lat. 17° N., long. IV W., olwerved sun's amplitude at setting, \V. ^° N. : required the Variation. Lat. 17", Decl. 23", Amp. W. 24° N. Obs. W.j£ N. Var. 16 W. Ex. 2. June loth, lat. 36° 40' S., long. 17'' W., obtained sun's amplitude at setting, W. ii''-3 N. : required the Variation. Lat. 36='7, Decl. 2 3°o, Amp.W. 29°-2 N. 37° and 13°, Corr. c" Obs. Amp. W. u El. 3. May 2gth, Ut. 47" N., long. 1 8- W., observed tlie sun's amplitude a» rising, E. 10° N. Lat. 47°, Decl. 21 J', Amp. E. ii"-; N. «o°and 22", Corr. o°o | p _ .. m Ob«.Amp.E. .o-oN.j E.^ N. Vab. 13 4W. Ex. 4. Sept. 25th, lat. f N., long. 151° E., observed the sun's amplitude at rising, E. 4° N. : required the Variation. Lat. 7", Decl i', Amp. E. :° S. Ob». Amp. K. 4^ N- Vab. s E. The Corr. hare ii o. The correction in Table .59 .\ i*> the same for a star or a |)larict as for the .sun, and is applied in the same way. When the moon is employed, the correction, which, in the case of the sun or a star, involves the sum of the dip and horizontal refraction, is the excess of her horizontal parallax over this sum. As the moon's hor. par. is 1°. anrl tlie refraction i°, in round numbers, this excess is about \°. which is nearly the quantify employed in Table ■')9A. 'i'his cor- rection, therefore, serves for the moon, but it must be ap|ili(Ml the contrary way to that directed for the sun. 887. The Computation, Accurately. (1.) Find the Greenwich Date and reduce the declination to it. (2.) To the log. sec. of the lat. add the log. sine of the declin.: the Huni is the log. sine of the amplituile. Apply the correction as Rborc. 328 NAUTICAL ASTRONOMY. 888. Bcgne of Dependance. In low latitudes the amplitucle ig (useeptible "of much precision ; in high latitudes refraction renders the result less certain. The relative temperature of the sea and ihe air produces no effect on the observed amplitude. IT, Cv THE Azimuth. 1. By Azimuth on the Meridian, 800. The Observation. When the sun approaches the meridian observe the azimuth, and continue observing till the same time after noon. The mean of the readings is the observed azimuth. When the sun is observed to the southward, if the observed bearing is to the E. of S., the variation is E. ; if to the W., it is W. When he is observed to the North, the contrary in each case. 2. By Azimuth from the Short Double Altitude, 891. The true azimuth is obtained from the observation of the dhort double altitude, p. 256, without regard to the apparent time. Case T. Observations on the game side of the meridian, No. 729. 892. The Observation. Observe the sun's azimuth during the interval between observing the alts., so as to obtain it at the middle of the interval. See No. 221. 893. The Computation. Having corrected the alts, and taken their difference, No. 729 (1), add together the log. sine of the diff. of a,lts., the log. cosec. of the interval,* and the log. sec. of the hit.: the Slim is the log. sine of the azimuth at the middle time from noon, nearly. El. (Ex. I, p. 358.) Lat. 34°40' S, diff. ofalts. 59' I, interval20'" IS', D. All. o" 59'-| 6in. 8 2^i;3 Int. 20'" 12" eosec. I 0554 Lat. 34° 40' see. 00S49 AziMiiiH 13°:^ sin. 9 3756 This azimuth cotnparcil with that observid woulJ afford the v.iriatioo. ♦ When it it intended to fina tne \'ariation by thii mi'thod at the same lime as tha l.atiiude, it will be convenient to take the sum of these three logs, first. The tiye logt. tniplo^ej in Ko. ''29 will tluis uft'ord two distinct results. FINDING THE VARIATION OF THE COMPASS. 829 894. Degree of Dependance. By adding to the result tlie difi". fur 30" ill the sine oF the D. alt., the effect on the azimuth of ^ in the diflF. alts, is seen, and the effect of an error, or small variation nf the D. alts, estimated. See also No. 679. Case TI. Observations on different sides of the meridian, No. 7:51. 895. The Obgervnfion. Observe the sun's azimuth when at the alt. nearest noon. See No. 221. 89fi. The Compufniion. Having found the time from noon of tlie greater alt., to the log. sine of this time add the log. cos. of the declin., and the log. sec. of the greater alt.; the sum is the log. sine of the azimuth at the time of observing the greater alt. Ex. (Ex. , p. 259.) Time from noon, I "•59- decl. 5.^°, greater alt. 49° 41 Great alt. 49" 41' Bin. 8-718 eos. 9-998 sec. 0-1 S9 Azimuth 4i° Bin. 8905 8. By Azimuth from Equal Altitudes. 897. The true azimuth may be obtained directly from the obser- vation of equal altitudes at sea, for time. No. 798. The azimuth, being computed as directed in No. 801, and compared with that observed at one or both of the times of equal altitudes, determines the variation. The altitude is required with more precision than for finding the time by the method, No. 798. This method is, however, not always eligible, because in low latitudes, where the observation of equal altitudes is favourable for the determination of time, the altitudes near noon are great, and therefore unfavourable for the observation of the azimuth. See No. 889. 4. By Azimuth on the Prime Verticnl. 898. The Ol)serv(ifion. Having found by Table 29 cither tho app. time or the altitude at the instant of the passage of ihe prime vertical, begin to observe a little before that time, and continue observing till the same time afterwards. The mean of the readings, when it is not accurately E. or W., is the variation. A.M. If the sun bear to the northward of E., the variation is E. ; if to the southward, it is W. P.M. If the sun bear to the northward of W., the variation is W. ; if to the southward, it is E. 899. As a celestial body, when on the prime vertical, changes its azimuth more slowly than at any other time, an error in the appa- rent time will be of little consequence, and the method will be found one of the most convenient in practice in high latitudes during the BIX months that include the summer. 330 NAOTICAL ASTRONOJrr. 5. Bi/ Azimuth deduced from an AKttvde, 900. TJie Observation. Take bearings of the sun's centre, notiiig the time of each reading. Take an alt. as soon as convenient before and after the bearings, noting the times. 901. The Computation. (1.) Having found the mean of the azimuths and of the corresponding times, reduce the alts, to the mean of the times, No. GCO, reduce the decl., correct the alt., and find the azimuth, No. 678 or 674. Ex. Feb. 19th, i828,r.ji.,Paia Bay, Nnples, lat. 40"'5o' N., long. I4'3' E., Mr.Fislipr observed the mean ot seven azimutlis of ihe snn by Kaier's compass. N. 223° 24' E. (ur 8. 43° 24' W.) Sun's true alt. 33" 34' j sun's reduced decl. n" 14' S. By Expl. Tab. 5, lat.4i°,alt.33\''M 15S9 N 57 5 Oecl. Ilj°,dist. 159 Dep. 310 (lesser) Sum 885 Dist. 100 and D. Lat. 88 5 give cnuife or Az. S. 28" W. Ditto observed 43^ Tab. I5i \V. 6. By Azimuth deduced from the Time, 902. The observation is already' described in No. 900. (1.) Find the Green. Date, to which reduce the declination and the elements employed in finding the hour-angle. (2.) Compute the azimuth, No. 675.* Ex. I. June 23rd, 1829. P.H .at Constii.tinople, lat. 41" l' N., long. 28° 59' E. ; tbe mean of seven times by cliroii. 4'' 43'° 15". and nf seven a/.imiitlis of the sun, observed by Mr Fisber with Kater's i.ompa>s, botrteen 286" 30' and 2SS', was N. 287° 16' E., or N. 73' 44' W- Reduced pol. dist. 66° 33'. Time 4" Cliron fast on A.T. 8un*« Hour-angle 4 Pol Dist. 66" 33' ColU. 48 59 43" > 5* 32 43 half 2" 19- 51* 17 34 »ec. o 27297 cos. 999488 tan. 0^2316 co«e«. 007269 sin. 9 183 83 14° 28' tan. 9 41183 half 57" 46' 8 47 69' 19' 14 28 ArJmnth N 83 47 W. Do. observed N 72 44 \V. Vab. ni~3 \V. Ei. 2. Dec. 27tb, !83I, Lisbon, lal. 38" 42' N., Ion?;. 9" S' \V., Mr. Fisber nh.crv.d »be mean of ten azimuths of the sun by Kater'.s compass (lietwein 165" and 166° 50') to be N 166" 7' E. The mean of the limes by chron. (between lO*" 7"' 30" and 10'' 15'" 45") nss 10'' II'" 47'. Chron. fust on A.T. 42"" l8"; red. pol. dist. 113" 22'. Computed Ai. N. 143° 44' E. ; Vah. 22' 23' W. • The work of finding the Azimuth is much lessoned by the use of suitjil'le tables. Burdwood and Davis's .\zimuth tables and Star Azimuth tables extend from the equator to 60" latitude, and are published in a convenient form riy .T. D. Potter, Hii Minories. London, E. Such tables are indispenEable for the navigation of iron shipa. See also Ltcky'e ' Wrinkles," for et»r». riNIUNG TIIK VAUIATION OF THE COMPASS. Slil III. By Astkonomical T5karings. 903. The true bearing of a point of land, or other terrestrial object, may be determined by means of the difference of hearing between it and the sun, or other celestial body ; the true bearing of the latter being deduced by observation, or computed from the time. The difference of bearing may be obtained directly by observing with the compass the bearings of both the sun and the object ; or by the sextant, when the sun is on the horizon. But as the obser- vation of two bearings at the same iustant cannot always be con- veniently made, the angular distance between the sun and the object is measured by a sextant or circle, and the bearing of the object alone observed. The difference of bearing is then deduced, by calculation, from the observed angular distance and the alti- tudes of the sun and the object. The true azimuth of the object being thus obtained, the varia- tion is deduced. 904. The Observation. Observe the sun's alt., then the angles between the objectand thenearestand farthest limbs; lastly, observe the sun's alt., noting the times of each contact. Take the alt. of the object, at the point from which the sun's distance is measured. When the variation is required at the same time, the bearing of the object must be obtained as nearly as possible at the time of the observation of the angular distance. 905. The Compntation. (1.) Find the means of the times and angular distances, and reduce the sun's alt. to the mean of the times. Find the Green. Date, and reduce the sun's decl.; find his pol. dist., correct the obs. ang. dist., and the alt. of the object for index-error, when necessary. .\ole For common purposes, when the observer is not much elevated and the alt. r^ the object docs not exceed a few minutes, the sun's decl. may be corrected at sight, tha dip. refiaction, paral'.a*, and ihe alt. of the object neglected, and the precepts (2) and (4) «iniitied. (2.) FiiTd the app. alt. of the sun's centre (by applying the ind.- Torr. dip, and semid.), and thence the true alt. by subtracting the refr. or corr. of alt. (3.) Find the sun's true azimuth. When the sun is not near the meridian, this is found by No. 674. When he is near the meridian it is better found from the time, No. 675. The lat. will be required more correctly as the sun is nearer tiie meridian, nnd less so as he is farther from it. (4.) For the corr. of ang. dist. arising from the point observed not being exactly on the true horizon. Take the diff. between th? ob.a. alt, of the object and the apparent dip, Table 30. 5b2 NAUTICAL ASTRONOJIT. To the log. sine of the reiiiiiiiuler add the log. sine of the sun'g Bpp. alt. and the log. cosec. of the ang. dist.: the sum is the log. sine ot the correction of the ang. dist. When the dip is lexs than the alt. of the object, add the corr. to the ang. dist. ; when the dip is the greater of the two, subtract it. (5.) For the diff. of azimuth. To the log. cos. of the corrected ang. dist. add the log. sec. of the sun's app. alt. ; the sum is the log. COS. of the diff. of azim. between the sun and the object. When the ang. dist. exceeds 90°, take the supplement of the arc found as the diff. of azim. (6.) For the Variation. Apply the diff. of azim. to the sun's azim., according to the case, which will be best understood by draw- ing a figure : the result is the true azim. or bearing of the object. The true bearing compared with that observed shews the variation. Kt. Dec. 4th, 1819. at 7'' 30" A.M., in Pernamhuco Koa/i, lat. S" 4' S., loiiR. 3^° S^' ^^'■> M. Givrv took the following alts, and angular dist., height of the eye 16 feet, ind.-corr. o — {Man.surl'Emploi,^c.) 7 26 10 23 23 1 190° 30' 30' Alt. 10 Mean 23 '9 5 95 '5 '5 Corr. 0. ( Green. Date, .3d, 21-47" Ued.Dpcl. 22' 10' 47" S. I'd. D.St. 67 49 (2) Olis. Alt. Arp. Alt. 23' '9'8 + 12-2 True Alt. 23 30 COS. 9-97788 ,. >q. 9 83071 (4.) Corr. of Ang. Disi sine Mlf) 10'- (dip) 4' --6 0) Alt. 23' 30' l)if.t. 95 >5 4 2 Corr. Ang. Dist. 95 I J 7242 ine 9601 osec. 0002 (.S & 6.) Computation of Diff. of Azim. Ang. Dist. 95° 17' COS. 89642 O Alt. 23 30 6CC. 00376 Suppl. O Az. Ohj. Az. Observed Vak. 84" '4 95 46 S 69 15 E. .S 26 3J \V, S 31 40 w. ~5 "W. FINDING THE VARIATION OF THE COMPASS. S'i'^ IV. By Terrestrial Bearings. 906. The true bearing or aziimith of a mountain, at a consider- able distance, is determined from its geographical position and that of the observer. As the true azimuth and the course on tiie great circle are the same thing, the problem is that in No. 339 ( 1 ), p. 133. But as mountains are rarely seen much beyond a hundrnd miles, it is near enough to proceed thus : — Find the D. Lat. and D. Long, between the places in minutes of ai-c. Turn the D. Long, into Dep., No. 318 or 319. Find the Course. No. 28U (1). This is the appro.'cimate azimuth. With the mid. lat. as a course, and the D. Long, as dist., find the Dep. ; this is a number of minutes, one-half of which is to be subtracted from the approx. azim. ; the remainder is the true azimuth, very nearly. ¥.x. Lat. 5o°6'N., long. 142" 50' W., find the true azim. of Mt. St. Elias in lit. 60° 18'. long. 140° 52'. D. Lat 12 and D. Long. iiS give Dip. 586, and Course 78° 26'. Then 60° and 118 %ivc Dep. loa 2 ; and 51' subtracted from 78° 26' gives the A/.iM. N. 77° 35' E. In low I»litiides, and in all cases when the object is near N. or S., the correction may be neglected. (For more predsion, see No. 39.5, p. 151.) 907. The term Variation, as defined in No. 882, and used in this chapter, is the difference between the true bearing of any object and its bearing by a compass. From what has been said in Chapter IL, this quantity must differ from the coiTect varia- tion by the instrumental error of the compass, by the local effects of the land, and, further, on board ship, by the deviation. There may be instrumental errors in a compass, which cannot be detected unless the correct magnetic bearing of some object ia known. For this reason it is desirable, when there is any reason to suspect the accuracy of the standai-d compass, that advantage should be taken of being in a port where the exact variation is known, to examine the compass according to the process described in No. 224. Errors in observed bearing, arising from the sight- vane not being vertical, or from the reflector being out of place, may be avoided by using low azimuth's amplitudes, or nearly horizontal bearings of terrestrial objects. Errors arising from tlie centre of the card not being in the same vertical plane as the line of sight, may be avoided by taking bearings of several objects distributed round the horizon. The true bearing of one object may be determined by process III. or IV., the others by horizontal angles therefrom. The effects of such local disturbances as are mentioned in No. 222 may generally be eliminated, either on land or at sea, by oLseiving iu several positions, with the view of getting ou oppo- 3.34 NAUTICAL ASTRON'OirV. Bite sides of the disturbing cause, and taking the mean of tlio results as the correct variation. When an observation is made at sea with a compass which ia instrumentally correct, and is free from local disturbance of the land or ground, the difference between a true bearing and a com- pass bearing, commonly called the Total Error, enahies the navigator to shape a correct true course. This is in general all that is actu- ally required for navigation. But such an observation would not dotermine the variation, unless the deviation is exactly known. A good value of the deviation may be obtained by interpolation, if the ship has been swung a short time previously, and again a short time after. Allowing the same ou the total eiTor will give the variation. When the compass is well placed, the mean of the total errors on two opposite cardinal points is a good value of the variation. A still better value may be obtained by taking the mean of the total errors on the four cardinal points. To obtain an accurate compass bearing, it is necessary that the ship's head should be steadied as directed in No. 248. When a ship's head is moving to port or starboard, the compass card is obviously liable to be dragged round in the same direction as the head is moving, by the friction on the pivot. On the other hand, in iron ships it has been found, that when the head is moving to the right, the compass-needle stands a little to the left of its due position, and vice versa. The last mentioned effect of the ship's mo- tion in azimuth is especially noticeable when the ship's head is near the north or south points. It is due, possibly, to the transient magnetism not instantly adapting itself to the position of tiie ship, as she moves round in azimuth. An exact bearing can be obtained by taking the mean of two, taken with the ship's head moving in opposite directions ; also an accurate deviation-table may be quickly obtained by turning a ship round to port and to star- board under steam, making use of the sun's azimuth, and taking the mean on the four cardinal points a« the variation, where it is aot otherwise known. Reduction of the True Course to the Course by Compass. 908. When the true course to be steered is determined, it must be reduced to the course by compass. The variation of the compass is to be applied (No. 221) ; the result is the correct magnetic caurtie. See p. 1.59. When the total error (No. 907) of the compass is known, it is to be applied to the true course, otherwise the deviation (No. 227) must be applied to the correct magnetic course; the result is the course by compass. CHAPTER IX. TiiK Tides. I. PUKNOMENA OF THE TlDfcU IF, RULES FOR FIND'NG THE TlMK OF Hkjh Watek. III. Tide-Observations. this chapter we shall attempt merely a general enumeration of the principal phenomena of the tides, with such other matters as aia In this the pri; of direct practical importance I. Phenomena of the Tides. 909. Tiie connexion observed in all ages, and, with particular exceptions, in all places, between the succession of high waters and the moon's meridian passage, has established the belief that thu moon is the cause of the tides. The principle of gravitation,ton which the motions of the eartli and the celestial bodies are calcu- lated, and their figures explained, has confirmed, and at the same time corrected, tliis belief, by shewing that sensible ett'ects must be f)roduced not only by the moon, but also by the sun, tiiough, from ler greater neaiiiess, the moon has by far the greater influence; and the general result would, naturally, until the observations were analysed, be attributed exclusively to her. 910. The attraction of the moon acting most strongly on those parts of the ocean which are nearest to her, that is, over which she is vertical, tends to draw these parts towards her, while their place is supplied by the water at the sides of the globe. And since the central parts are likewise more affected in the same action than the surface at the opposite or farthest side, the figure of the earth becomes elongated in the direction of a line drawn towards the luoon ; that is. the water is accumulated at the point exactly under • The readier may refer, tor ftddilional information, to various papers, by Sir John Lul>- l,ook and the Rev. Dr. Wliewell, in the Philosophical Tranaactiona, Jkc, 1833, particularly t.i " An EsBay towards a Map of Cotidal Lines," followed by other dissertations by l)r Wliewell ; and to " The Tides," by Professor George Howard Darwin {John Murray, Albemnrrle Street). t Thii^ princijjle is that there eub^iists ainnngst all particles o{ matter a mutual attrai tiua «hoM indei.fiity la inveraely as the square of the distance. ?,r,6 NAUTirAL ASTRONOMY. the moon, and at nnotlier point distant from tlie former 180° in latitude and longitude. The moon, in her progress to the westward, causes thus, at each meridian in succession, a high water, not bv •Irawing after her tiie water first raised, but by raising continually that under her at the time. The opposite high water, or, as it is called, the inferior tide, would, if tlie moon's action was uninterrupted, follow the other, or superior tide, after the interval of half a lunar day, or 12*' 24"' on the average. Again, the sun, acting in the same manner, though with less force than the moon (in consequence of his distance more than counterbalancing his greater magnitude), produces two tides, which would follow each other, if uninterrupted, after an interval of half a solar day, or 12 hours. 911. But, instead of four separate tides produced by the inde- pendent actions of both bodies on the mass of waters in their orig'u d ibrm, the effect produced is the same as if, after one of the bodies, as the moon for example, has given a form to the waters, the sun alters that form, the two separate actions thus producing a joint result. Hence the place at which it is high water is that at which the sum of the heights of the tides produced by the two bodies is greater than any where else. 912. When the sun and moon are on the meridian togetlier, their actions concur, and the tide is higher than at any other time. Tlie same holds when they are in opposition. These highest tides are called spring-tides, and occur after new and full moon. Again, when the sun and moon are 90° apart, their actions tend to neu- tralise each other; and the 7ieap-tides, which occur after the first and third cpiarters of the moon, are the smallest of all. (See No. 919.) 913. Since the sun and moon act with greater force as they are nearer, the effect of each body in raising the tide is gieater as its parallax is greater (No. 436). The highest spring- tides would occur, therefore, in January, about the time of the month when the moon's hor. par. is greatest. But the effect of both bodies is greater, generally speaking, as their alts, are greater, since when vertical the effect is greatest. This yieriod, therefore, depends on circumstances. 914. If the actions of the sun and moon were, as we have hitherto supposed, uninterrupted by obstacles or forces of any other kinds, the tides would be regular, and their calculation certain. But from the unequal depth of the ocean, and the barriers presented by continents which stand across the natural progress of the tides, their motion is interrupted, and the tide-ioave (as the accumulation of waters is called), abandoned by the forces which originated it, becomes subjected to the mechanical action proper to waves in general. 913. It is necessary to distinguish between the motion of a wave and that of a current. A wave is not an absolute transfer of the body of moving water in the direction of the motion of the waves, Lut is a motion i>i;rppndicular to the surface, or up and down. The TnKTIDKS. .''>o7 u.otidii of waves is roprcjiMiteil Iti tlio tlutlcriiig of a Hat; and llie -liakinLf of a sail. It is easy to see that liiis i;iii(l of motion is roiiipatiblc with iinmeiise velocity, v.itlioiit any ai>|)refiable current in tlie water itself; tlir.s the tide-wave appears to pass from tiie Cape of Good Hope to Cape Bianco in twelve hours. 916. The motion of waves is quicker as the water is deeper. Also, the largest waves are the swiftest; a fact illustrated by tlus superior velocity of a heavy sea over that of the rippling of a pool. W hen tiie water slioals, the wave is retaided and becomes steeper on the advancing- side, as is seen in the approach of waves to a shelving shore, and in the bores of rivers. The v^ilocity of waves is also considered to be greater as tiieir length (or distance from hollow to hollow) is greater ; thus the tide-wave, though inferior in height f waves may, in their combination, produce aiiiiurent irst. See H/iil. Trant. 1-5?., p. '54. Or this principle are explaineJ, also, tides whicli occur at irregular intrrvuU ^ A Report oi Ob»trvations made on the Tides in the Irish Sea, (dc, by Opt. P. W. Htwiney, R.K., PAU. Tratu. 1S48 ; sec also Xaul May. 1S49, p. 70. RoS NAOTICAL ASTRONOMY. yi8. The heiffht of the tide is the difference be! ween the lesel ol liigh water a?iil that of" low water.* The heiglit of the tide in the open ocean is supposed to be very small ; and the great heights observed on some shores are evidently d'le to the shoaling of the water and the narrowing of tlie channel. The tides are insensible or very small in inland seas ; as also in high latitudes, except from local causes. -t" 919. It is found, in general, that the tide is not due to the moon's transit immediately preceding, but to a transit which has occurred gome time before. The time thus elapsed between the transit at which the tide originated and the appearance of the tide itself is called the retard, or aye of the tide. Thus the tide on the western coasts of Spain and France is a day and a half old ; that at London is two days and a iialf oM. It appears certain that the age of the tide on the W. coast of Ireland is 2 days (p. 38), and on the S. W. coast l"" 20*" (p. 1 10).t It would appear further that changes in the parallax and decli- nations of the sun and moon ]iroduce their several effects on the tinie and heiglit of the tide after particular intervals. It is thus constantly necessary to discnnnnate between a tido which may happen after any particular transit and the tide which reailv corrc-poiids to that transit; thus, for example, if the moon pHsses the meridian at 4 p.m. to-day, and the high water occurs at 7 P.M., this tide will not in general be that which corresponds to the transit 3 hours before, but may have had its origin several transits liack. The transit to, which tiie tide really corresponds is found by examining the observations of the several preceding tides, the highest of which, lieiiig due to tlie united actions of the sun and moon, is known to coirespond to the moon's transit at 12 o'clock, noon or 920. The wean level of the sea is th'! middle between the levels of iiigh water and low writer. Though the heights of high water and those of low water may vary considei'ably, yet the mean level seems confined to very narrow hmits. Thus, at Singapore, where the heights of two consecutive low waters differ sometimes six feet, the mean level varies only a few inches.— P/«7. Trans. 1837. Hence it follows that heights measured above the sea should be referred to the mean level as the standard or zero, instead of that of either low or high water. It is not, however, to be supposed that the middle point between any two consecutive tides is the mean level. This will be the case * The ter?n range would be preferable to heic/ht, as it implies a distance between houn- diiries, as, for ex., the range of the barometer, tlie " height of the tide" is continually, in ciiinmon discourse, used for the height of the water. t Sir John Ross found a rise and fall of 8 feet in lat. 74° N. I On the Law of the Tides of the Coasts of Ireland, by G. B. Airy, Esq., Astronomer Kwl. Phil. Trans. 1845. This paper refers to a most extensive and complete series if nhwrvations made in 184'J under Gen. Colby, director of the Trigonometrical Survij chicllv for the puiiKiie of referring the elevations observed to the level of the s-a. Tnn TiDi-a. 339 only wlie'n two tides in succession attain tlie same liiyli-water level and the same low-water level, as at springs. 921. By the Establishment of the Port or Tide-hour has been commonly understood the apparent time of the first high water that takes place in the afternoon of the day of full or change. This Dr. Whewell has called the Vulgar Establishment. 922. The interval between the moon's transit and the high water next following is called a lunitidal interval. Tlielunitidal interval varies from day today during the fortnight between full and change. 923. The correct establishment is the lunitidal interval corre- sponding to the day on which the moon passes the meridian exactly at noon (with tlie sun) or at midnight. This is found by taking tho mean of all the times of H. W. for a fortnight. The Vulgar Estab. may thus be an hour, or considerably more, in error when used aa representing the H. W, on any day of the fortnight. The tide caused by the united actions of the sun and moon, when each of these bodies is in one of the positions most favourable for raising the water, is identified by its superior height. And it ia thus found (as observed in No. 919) that the interval by which the tide follows the moon on the day when the full or change occurs at 12 o'clock, or the lunitidal interval corres-ponding to that particular transit, is not the interval actually observed on that day. The estabhshment of the port, and also the height of the tide, appear to be subject to change. 924. Thediflerence between the lunitidal interval at each transit of the moon and the correct establisliment is called (by Sir J. Lubbock), from the period of its recurrence, the semi-menstrual inequality. This inequality is found to be different for different places; lence the time of high water at any place cannot, generally, be accurately deduced from that at any other place by merely applying the difference of time between the two establishments. 925. The tide is subject, in like manner, to a semi-menstrual inequality in the height. This inequality being, like that in the time, different for different places, the height of a tide at any one place cannot always be correctly inferred from the given height at any other. 926. It has been found that the morning and afternoon tides do not rise to the same height; the difference is called the Diurnal Inequality. This irregularity is the consequence of the sun and moon not being always on the equator. Thus, suppose the moon in 20° N. declin.: then the summit of the superior tide is in 20° N. lat., and of the inferior tide in 20° S. lat., each alternate tide having thus its greatest elevation in the other hemisphere. The diurnal in- equality is subject to steady rules, and may be predicted. 927. The maximum of the diurnal inequality c(m(Z.ut this interval, generally speaking, is different for each day of the fortnight. See No. 923. * Such tahles are given in the Tides published annually by the Kyorographic Office. Tiic errors of the predicted times do not apjjcar to exceed five or ten minutes, except io fiales of wind, when the time of high water may be altered upwards of half an hour. t This is often called «oii//iiny; but as in south latitude the moon passes the mrridiiio to Ihe northward, this term is not adapted to general use. £ The moon's age thus found may he more than a day in error, but b.'r merid. pass. will generally be less than an hour in error. 312 NAUTICAL \STUONOMT. r... ;. Fm.l the tlnu. of high walcr at Ki. ■>. I{e.|.,!r.d th e time of higli wate/ Falmouth, Oct. 3H, 1891. at Shields, March St'.t 1S91. EpHCi 1 89 1 20" 9" K|)acl iSgi 20' 9- n... Oct. 7 5 Do. March 29 II L»nys 3 Uays 31 3° '4 80 20 -29 >3 -59 2 21 iS S J'. Mer. Pass. "^8 = 0" 48- i6^S=i6"4S- Ti,lo-lw,„r +4 57 r.de-hour + 3 21 Time or ll.W. 5 45 ■••»• 20 09 12 24 V. 7 45'«. T:ilEO^^.^ E.. 3. Find the time ofl.igh water at .iverpool, March loth, S91. Tnlehour ii''23'° Tl-ME H.W. ii''23-p.i.. Ex. 4. March 30th, 1S91, find the time of high water at Portsni 0.1th. ■lide-hour II" 41" Time or ILW. 2" 53" r.«. Ex. 5. June 2.1, 1S91, find the time of high water at Liverpool Tide-hour 11' 23'" T1.ME or H.W. 7' 15" P.M. 933. Rule II. (1.) Take from the Nautical Almanac the M.T. of tlie moon's meridian passage, and correct it for the longitude by Table 28. (2.) Take from Table 15 the semi-menstrual inequality corre- sponding to this time, and apply it to the reduced time of mer. pass, as directed in the table. To this result add the tide-houi-, and the sum is the time of high water. (3.) When this time exceeds 12 hours, it is the time of high water past midnight, — that is, a.m. the next day. When, therefore, the p.m. tide preceding is required, it is necessary to employ the inferior transit of the moon. I'.x. 1. Aug. 6 h, 1891, find the time of high water at Shields. Long. 1° 2$' W. j tide-hour j"" 21"'. J'str. 6th Corr. for long. Sem. ineq. I 12 Inf. tr. 6th Sem. ineq. Tide-hour l" 5-A.X 51 3 21 Tide-hour Tu.toF H.W. 6th 4 33 r.M. Time or H.W. 4 12 A.M. El. 2. Aug. 29(h, 1S91, find Tide-hour II" 4I". High Wj imp of H.W at Porlsmouth. 29th, 7* 10" A.M. and 7'' S4"' rM. on 29th. Ex. 3. Marcli lllh, 1891, find the lime of high Tide-hour 8" O". High Watek I Ilh, S'' 32" a.m. er at Cheih. 53'" >■■"• (4.) When the time of tht; mcv.Mi's transit on the given day exceeds 12 hours, the transit occurs a.m. on the hcj;1 day (civil THK TIDK. 313 time). It is evident, therefore, that to obtain the tiinea of high water on the same day, we must, in such cases, employ the transit «!' the preceding dav. Subtract 12'' from the time of transit, to enter the table of the eemi-nienstrual inequality. To Kiid the other tide, we must employ the inferior transit as already directed. Ex. 4. April Sih. iSyr, fiii.l itir times of hi-li wntcr at ShieMs. J'str. April 7.I1 23" 4» „ I, n nil 'it springs ., 5th „ „ „ „ „ ;, ,, t>th „ „ „ „ „ y Trinity High-Water Mark, as established by Act of PailiamcMt in 1800, is cut upon a large stone on the lower enter wing wall of the Hermitage entrance of the London Docks. Trinity high- water mark is 12'63 feet above the Datnm used by the Ordnance Survey, i.e. Mean Jjovel of the sea at Liverpool; fherefoie by obtaining from the Ordnance map the level of any Bench mark and applying 1253 feet to it, the level of the Trinity high-water mark is found. The Trinity high-water mark will be found cut upon the Tower Whaii; and also upon the front of the Fi.shmoug'.rs' Hall Wharf, next above London liridgo. MAUTICAL ASTRONOMT, 111. TiDE-OlJSLKV ATKINS. fl3o. It ia cvKlciit, from what lias been said (Nos. 919, 9*^2 1, lliat tlio c'stal)lisliiiiciit cannot be trnly deduced from the notice of" a solitary high water; and tliat observations, continued, at least throjgh a semi-lunation, are necessary for even a tolerable approxi- mation. But the true establishment cannot be successfully deter- mined from a series of observations involving the seuii-inenstrual inequality, the various effects of changing declinations and paral- laxes, with temporary and local circumstances, exce|)t by persons not only thoroughly versed in arithmetical operations on an exten- sive scale, but well exercised in the particular intricacies of these laborious calculations. We have, therefore, confined ourselves hei'c to merely indicating the details which should accompany tide-obser- vations. (1.) The exact spot of observation must be specified. (2.) The instant of both high water and low water should be stated, with the heiy/it, or difference of the two levels, in feet and inches. As the water hangs for some time towards the turn of tiie tide, and as tiie tide-current may be independent, it is necessary to note the instant at which the water ])asses a fixed mark, both in rising and falling; the means of these times are the instants of high and low water respectively. The marks should be fixed in some j)lace to which the water passes slowly, because the waves, however small, contiinially washing over the marks, render it difficult to detect a small ri'se or fall of the water. The observations of both low and high waters of the 24'' are necessary for determining the Diurnal Inequality; hut as the time of this inequality is of less importance than the height, it will often be enough, in res|)ect to this particular point, to note the height alone. About mean wafer (or half tide) the surface rises or falls with greater velocity than at any other time, and accordingly the instant at which tiie water jiasses a fixed mark or a given horizontal line may be observed with greater precision than at any other time. Hence it has been recommended to notice the instant of passing one or two such marks, instead of the times of high and low water. — " On the Law of the Rise and Fall of the Sea's Surface during earn Tulvr—P/nl. Trans.. Part II. for 1840. It has been proposerl to |)lace tiie marks at half-tide, but ihif; dues not answer, espijcially wlierc thu diiiiiial incipiality is consider- ,S4(l THE TTDEvS. itl>l(^• The intervals slioiikl be short on eitlierside, of liijih and low Mater because the tides do not rise and tall with equal velocity. (3.) The times of slack loater should be noted. (4.) Tlie direction, and, in general terms, the force of the ivind^ fihould be stated, as, also, the heio;ht of the barometer. As the effects of winds and atmospherical changes are not con- fined to the particular hours during wliicii such causes are in action, it «ill be proper, when only a short series of observations can be ol)tained, to add further a brief notije of the state of the weather tor some time previous. Observations continued for a fortnight afford a first approxima- tion to the Tide-hour ; and wlien carried on for some months, this, with some other principal elements, may be obtained with consider- !ible accuracy. 937. The custom has prevailed of noting the establishment as the hour of the dny ; but it obviously should, as recommended by Dr. Whewell {Phil. Trans.] 833, p. •229), be considered merely as an interval. Since the correct establishment is measured from twelve o'clock, it may, indeed, appear to be indifferent whether we call it an absolute time or an interval ; but the absolute time of tiie tide is in all cases referred to the instant of the moon's transit, and it is absurd to talk of adding two absolute times together; as, for ex- iimple, adding three o'clock of the day to five o'clock of the day. Also, by considering the establishment as an interval only, we avoid confounding mean and apparent times. 938. The soundings on the charts are the depths at " low water ;" but this term may imply indifferently the mean low water of the whole year, or of the equinoctial spring-tides, of which the average is not always identical, or of those low waters only whicli were observed during the operations of survey. Since these may differ considerably from each other, the computed depth may be in eiror l)y the same difference. It might appear less equivocal if the lowest of all the low waters were understood ; but this, though a natural ]ihenomenon, and, so far, preferable to an imaginary standard, as an average, is still defective, since it is affected by winds. It would appear, therefore, as Capt. Beechey proposes,t that the standard low water should be identified as so many feet and inches bcJow the mean level, which appears to be the only element nearly constant. The mean level njay, it apjiears, be found approxinuitcly by observations of four conseculivu tides, which include the diurnal iiK'tpuility. * Adrn. Bayfield (to whom I am indebted for some important remarks and corrections lieie and elsewhere in the former editions) infoims me that in the St. Lawrence the alternate ebbs do not fall to the half-tide mark at ail when the diurnal inequality is ciMisiderable. Also Adm. Beechev acquainted me. as the result of numerous observations, that at Plymouth the half-interval of time between the passages over the half-tide marks requires j^j of the int. to be added to it for the loireit liitt of high water, in coDsequence of tU* id fall. Ittjio-t of Ubsirvatioiis," &c poual rii t "A NAVIGATING THE SHIP 1. Shaping the Course. II. Place of the Ship. III. Deikr- MINING THE Current. IV. Storms. V. Making the Land. 9:59. In the prpt-eding part of this volume each point of the Biii)jcct lias been treated separately. The present section, which will conclude the Practice, and to which the former chapters mny he considered subservient, contains matters of geneial reference in coiiductin"; the navigation of tiie shii). 1. Shaping the Course. ;tK). As soon as the ship is clear of the land, and circumstances permit, her head is put upon the course to be steered, the log hove, and the departure taken. When the course is to be shaped for a distant port, recourse is liad. in defect of )iersonal experience, to the Sailing Directions,* in order to learn what point to steer for, so as to profit by particular uiuds or currents, or to avoid dangers. Tiie bearing of such point is then worked for by |)arallel, middle latitude, or Mercator's .sail- ing, according to the case; or, a ruler being laid on the chart over the place of departure, and the point in (piestion shews the course, No. 381. 941. When the wind is foul, reference will be made to No. 299; luit, in the case of a prevailing foul wind, the proper line of proceeding will be indicated in the Sailing Directions. A steam-vessel will generally preserve her course without regard to the wind, except in long )>assages. * The Sailing Directions contain descriptions of ports and anchorages, with accounts of the winds, currents, and tides, for various coasts and seas. I!, sides Ousp .ind oilier piirti- rnl.irs, necessary for navigation alone, worlds of this kind lo.ii m .1! . Ii;,! p i .-, ^ from voyages and travels, hy which the reader may obtain clear il ! i ' ' [ i ol ilip •hiircg, climat«, and natural pheniimcna of most parts ol 1 1 I I i i h i ihic iiiformation respecting the inannera and customs of tlii' iiili. .huii , iln jmuIu d i », and •rlidcs ot incrchunduc. S4.8 NAVIGATING TITE SHIP. I. Sihitping the Course in a Current. 942. WHien tlie whole or any part of the voyage lies lliiougli a em-rent, having everywhere tlie same direction and velocity, it i^ |)roper to shape that coarse which shall keep the port on the same bearing (No. 294), because the ship will thus cross tlie current in the shortest possible time. But if the current be different in different jiarts of the voyage, this rule does not hold good. This ])oiiit cannot be pursued fiii-thnr in this volume. When the current, setting the ship away froni her port, is so btrong, or the wind so light, that the ship cannot ])reserve the *'earing of the port unaltered, she will be ke))t so that the course made good shall not be more than eight points from the bearing of the port; because, though she cannot thus near the port till circum- stances change, yet she will not increase her distance from it, as would result from shaping any other course. The application of all such rules must, accordingly, dejjend upon the circumstances of the case. 943. When tlie ship, having a fonl wind, is in a current of which the direction and rate are known, she should be kept as much as possible on that tack on which the current tends most to drift her to windward, or is least unfavourable in drifting her to leeward. For example. Suppose the course to be steered is S.W., tlie wind S.S.W., the current S.S.E., 2 knots. Tiien, on the larboard tack, lying west, and going, suppose, 6 knots, she will make good S. 70'^ W. 5-5 miles. No, 2!t2. On the starb. tack, lying S.E. and going 6 knots, she will make good S. 59° E., 8 knots. The distance made good in the direction o, the port when her head is S E. is o-8 miles per hour, No. 285; when lying west, this quantity is 5 miles. ndward on both tacks; but the larboard 2. Shaping the Course on a Great Circle. 944. When the ship sails on the arc of a great circle, the distance travei'sed in passing between any two points in her track is (as observed in Nos. 336, &c.) less than if she had sailed on a rhumb-line. A distinction of greater importance between these two tracks is, however, that every point of the great circle lies in a higher latitude than any point, having the same longitude, on the rhumb-line. Thus, if two ships sail from St. Helena to C Horn, the one upon the great circle, and the other on the rhumb- line, altering their longitude by the same quantity, the ship on the circle will be 440 miles to the southward of the other, when the two vessels are most widely separated ; that is, when the vessel on the circle is at the point of maximum separation latitude (No. 345). Now the difference of distance is only 76 miles in 3740 (No. 337, Ex. 1); whereas the difPerence of 440 miles in latitude may place the vessels in different winds. 945. A course taken anywhere between the great circle and the rhumb-liuc will always be attended with at least some saving t>f di»**.ance. SMAi'lNCi IlIK I'OUKSK. 31<) rh""' Tlmi, any course between A B and AT (the tangent of the circle il A, and shewing its direction at that point) gives a distance less tlian A B. Again, since tlie circle is the niininjimi distance hetwecii A and B, on the snrface of the globe, we may take a series of trac-ks between A and B on the other or po/ar side of tlie circle, increasing in length as they lie further from it, till we come to the dotted line %vhich represents a curve equal in length to the rhumb. Hence a ship sailing anywhere between A B and A U (the tang, which shews the direction of the dotted curve at A), — that is, through a space nearly twice as great as that between the rhumb and the circle, — - will still have less distance to describe than that on the rhumb-line. On this principle a partially foul wind may often be turned into a fair one. Tims, in the voyage alluded to above, the vessel on the circle, instead of passing 440 miles to the southward of the track on the rhumb-line, may pass at nearly tliis distance to the southward of the great circle, or between 800 and 900 miles to the southward of the rliumb-line; and yet, after all, she may make good a distance less than that on the rliunib-line, while the great difference of latitude may enable her to avail herself, for part of the voyage at least, of winds proper to regions far removed from those cros.sed by the rhumb-line. 946. When it is proposed to sail on a great circle the course is shaped with reference to the present place of the ship; and, there- fore, when she is found to have got off the original line laid down, the cour.se should, strictly speaking, be shaped anew. But, in prac- tice, this will rarely be necessary, since moderate deviations from the f;oi;rse will not sensibly alter the bearing of a distant j)ort, that is, the same course will serve as before. 947. In great circle sailing with a foul wind the ship will be put upon that tack in which she lays nearest the circle. The rule for windward sailing, which directs that she should be put on that facie in which she looks best u]) for her port (No. 299), is, therefore, strictly applicable. Indeed, it is oily on laying down the great circle, which alone shews the real direction of the port, that it can be de- cidi-d whether the wind is foul or not for a distant port. If the rhumb-line differs more than two points from the circle, it is evident that, by shaping the course on the rhumb-line and then laying the ship on the wrong tack, she will head more than eight IK)iu*» away from the tru'.- direction of the port, while on the othe? 350 NAVIGATING THE SHIP. tack she would lie within less than 4 points of the course. Thus a seaman not acquainted with the principles of great-circle sailing mav cause his ship to recede from her port instead of nearing it. 948. If the wind, when contrary, is in the direction of the great circle, one tack is as good as the other, and the selection must depend on the current, probable change of wind, or other cifcuiii- Btances. The ship should not, however, deviate from the circle so far as to have to shape a new course, for if she lias much deviated from that line wliich was the shortest possible, she must have altered her position for the worse. 950. In navigating the ship on a great circle, in high lats., the course should be sha.ped anew at each 60 or 80 miles of distance. The place of the ship is necessarily brought up by middle latitude or Mercator's sailing. A modification of great-circle sailing has received the name of Composite Sailing. It presents itself whenever the great-circle track, by passing too close to the Pole, becomes dangerous or impracticable on account of the ice which pervades those high latitudes. When this occurs, some one parallel of latitude is fixed upon for the maximum ; then the shortest route, under these circumstances, will consist of a portion of that parallel and of parts of the two great circles which touch it and which pass — one through the ship and the other through the destination. This combination of great-circle sailing and parallel sailing offers, there- fore, no difficulty. >See JJavis's Star Azimutli I'ables, p. I'M. Log, Course, and Bead Reckoning. See Nos. 95G to 969. 95 1 . Dead reckoning has not always met with the attention it de- serves. Dead reckoning is a fine art, dependent first upon a well deter- mined position to start with ; secondly a knowledge of the correct Vari- ation and Deviation, or total error of the compass steered by ; and thirdly on good steering and logging, to carry it on. Remember the remark of John Davis, the navigator, written in 1607, " the stredge * may be so disorderly handled as that thereby the Pylote may be abused." Dead reckoning is also dependent on a correct knowledge of probable cur- rents and tidal streams, on the winds that have been and are blowing. 952. Good Dead Reckoning can be attained by practice. See note (Rennel's) on p. 353, 359. Let the position by dead reckoning be considered a serious matter, to be carefully compared with the po- sition obtained by observation. If there is a difference between the positions, let that difference be accounted for, and if it exceeds that probably caused by weather, or by known tides or currents, let it be considered that the distance has been wrongly estimated, or the errors applied to the compass courses incorrect, or the ship badly steei-ed. (The stredge disorderly handled.) Let more care be taken the next day, and so on until a confidence is engendered in the dead reckon- ing that may be useful in closing the land in thick weather. • " Stredge " mav stand for stretch, a ttrm tot a ship's course. PLACR OF THE SHIP. 351 II. Place of thk Ship, I. By Dead Reckoning. See Nos. 051, 952. [1.] Keeping the Dead Reckoning. 954. Latitude D. R. The latitude by D. R. is deduced by n}^ j'lyiiit? tln! difference of lat. made good by the shiji to the lat. by observation of the preceding noon. ^Vllen the latitude was not observed at noon, but at some other time it is proper to note tiie lat. D. R. as " brought up;" becau.-e the lat. by D. R., when employed for comparison with the observa- tion, is of course considered as referred to the beginning of the day, unless the contrary is expressed. When, iiowever, tliere is no observation, the lat. by D. R. must be referred to the lat. D. R. at the preceding noon. 955. Lonyhvde D. R. The longitude by D. R. is deduced by apjilying the difference of longitude made good to tlie long. D. R. of the preceding noon. The long, by D. R. is usually carried on till a new departure is obtained, because the observations for longitude are not so decisive as those for latitude; for the chronometer may alter its rate, and the moon's distance from a star, or her R.A., may be much affected by a suihII error of observation. Hence, when the longitude by a single observation differs much from the account, it is not always consi- liered safe to adopt it until it has been confirmed by another ob- servation.* When, however, such confirmation is obtained, or two distances, observed at ilie same time on opposite sides of the moon, give results not differing much from each other,t the resulting * In vol. i. of the East Indi:i Directory, Ilorsburgh gives an exnmple of the danger of trusting to a sinjile chronometer for a length of iimc, or lo a single lunar, in the ca-e of the Taunton Castle, wliich got aground in ihc Straits of MozainUique in 1791. A lunar 5 days licfore had agreed with the cliron., but a lunar 12 hnurs liefore differe-d from it 1°. It was naturally considered thai the furmer lunar confirmed the cliron., and that ibe later observation was erroneous ; the contrary, however, turned out to be lliu t Horsburgh states that he has fnund the mean of two lunnrs, observed on oprmsio sides of the moon, nearly a degree in error. So strange a re.-iiU would seem, however, lo throw doubt on one o'the obser\ations. The Rev. G. Fi^l1e^, in the Appendix to Captain Parry's second voyage, p. 282, slates that the mean of •i.'jOO lunars observed in December differed U' from ilie mean of 2"iOi) observed in Manh following; iind that the mean of the observations mude in the siime summer differed 10' from these last, or '.'4' ff'-m the first. Capt. Kin;,', in hi? survey of Austr;ilia, uotiecs a discreiiaucy ol B siniilar kiud, lo tlie auiuunt of 12', al the (ioulburii Uluudi. 3.'52 NAVTGATIKO THE SHIP. longitude should be taken as a departure from wliicli to carry on the D. R. Although it is recommended not to alter the long, by D. R. on slight grounds, yet it can answer no useful purpose to persevere iu carrying it on after observations have proved it to be wrong. [2.] Errors of the Dead Rechmung. 956. These are the errors of the course :ind distance, with their effects upon the lat. and long, by account. An error of half a point in the course is equivalent to an error of -pj- in the dist. run, verj' nearly. 957. Error of the Course. The ship, besides moving in a path more or less serpentine from the action of the waves, and from imperfect steerage, is driven bodily by the wind, and often by currents and tides; hence the general direction of the ship's head is a very impei-fect index of her course by compass. Again, tlie course by compass is affected by the variation and by the devia- tion ; the latter, as already remarked, varies in different ships, and in different positions of the same ship. 960. Error of the Distance. The rate of sailing varies, from time to time, with the strength and direction of the wind, the quantity of sail set, the trim of the sails, the i-unning of the sea, and, in a slight degree, on the skill of the helmsman. Hence, since the log can be hove at intervals only, while the compass is constantly inspected, the distance run, unlike the course steered, is left in a great degree to estimation. While a vessel is steaming, her rate is, of course, less liable to change.* 961. The allowance to be made for the heave of the sea is doubtful. As regards the motion of the waves alone, it would appear that no such action takes place, and any effect of the kind must be referreil to the progressive motion which the water at the surface acquires from the action of the wind, and which affects both the vessel and the log. The existence of a surface-current accompanying a strong wind is established by the falling over or breaking of the tops of the waves, which subsides accordingly with the wind, and disappears long before the swell goes down. 962. In steam- vessels the log is found to give too much distance. This is accounted for thus: — The water at th^ surface being con- tinually urged astern by the paddle-wheels, preserves its motion for some time after the vessel is past; the log, therefore, unless thrown perfectly clear of this current, is carried in the direction opposite to that of the vessel. On this account it is proper to heave the log from the paddle-boxes. • By practice seamen learn to estimate tlie lale of sailing «itliin lialfa knot. miicI ilic numbi-r of revolutions in a given time of llie ciigiDes of a iliiji under .stiam furuisli u on-iins of determining l]i.r speed very closclj'. 5^ACK OF TIIK SHIP. 353 9fii. In consequence of the fore and after bodies of vessels in ^eiicnil being dissimilar, the resistance of the water to the rollin) <\w tes Klinders'8 opinion that the reckcining may be kept within S mili'S of di.stancc, aud Lair a p'i:nt in the course. 354 NAVIGATING THK SIIIK ence, s!nce experience establishes tliat, when several observations are taken together, their errors tend to compensate each other. 969. Under the head "D. R." is included the determination of the ship's place by bearing and distance of the land. When a point of land bears N. or S., the diff. lat. of the point and the ship is the distance; and consequently the error of the lat. is exactly equal to that of the distance, while a point or two of error in the bearing produces but small error in the lat. On the other hand, if the place bears E. or W., the ship's lat. is that of the point itself, and an error in the bearing produces in the lat. an error proportional to her distance. This applies to longitude by reading, in the above, long, for lat., »nd interchanging N. and S. with E. and W. [3.] VanntioH of the Time at Sea. 970. When the ship sails to the eastward, she meets the sun, and therefore anticipates the hour of the day by a portion of time equal to the diff. long, she makes good. In sailing to the westward, the contrary takes place. Hence in sailing eastward the apparent day is always less than 24 hours, and in sailing westward greater than 2i hours, by tlie diff. long, made good, in time. Thus a ship, in sailing round the world to the eastward, gains a day in her reckoning of time: for each day in which her head is to the eastward is less than the common day of 24 hours by the diff. long, made good ; and this goes on till the diff. long, has accu- mulated to 360°, or 24 hours. Hence, on completing the voyage (but without any relation to the time of performing it), the ship, by constantly gaining on the next day, is found to have completely anticipated it; so that, instead of finding it Wednesday, for instance, among tlie natives, it appears by her journal to be Thursday. In sailing roiind the world westwards, the ship in like manner loses a day. In these cases the voyage is performed in days of a different length from the average of 24 hours, and the whole period is made up of a different number of days.* 971. This alteration of the date in the journals of ships crossing the Pacific is often attended with considerable embarrassment to the reader, especially if he does not bear in mind the direction of the ship's route. In order to provide against this ambiguity, the navi- gator should insert the Greenwich I)ate at full length, in every case in which a reference to the absolute time may be required. 972. The variation of time, or the irregularity in the length of the day, falls on the hour or half- hour preceding noon, the last glass • Sir James Ross remarks that in crossing the meridian of 180° eastwards they made two Thursdays, and two Nov. 25ths, by which means their reckoning would correspond to that of Australia and England on their arrival. A short rule to estimate day and hour of arrival for steamships crossing the Pacific is: Going West: Add one day to assumed time of leugth of passage, and siil>- tr.te'. the Diff. Long, in time between the two Dorts. Going East : Subtract one day from assumed time of passage, and add the Difl'. Long, in timi. PLACE OF THE SIIH'. 355 or two not being turned. Wliou there is no observation for some daj's, the time is thus liable to be considerably in error. Tliis uncertainty in the absolute time causes no difficulty in bringing up observations to noon, or to any other time, nor in con- Mfcting observations made A.M. with others made p.m., because the courses and distances marked on the log-board are those corre- sponding to the actual intervals elapsed. t)r;5. It is evident, since the time at ship always has reference to the diff. long, made good subsequent to the observation for time, 1 iiat the account of the time is more correctly kept iu low than ia high hititudes. (See No. 967.) [2.] Place of the Ship by Observatinn. 974. Besides the latitude and longitude of the ship by observa- tion, we shall consider, under the above head, those obsei-vation.i from which the elements necessary in the calculation of her place at any time are obtained : as observations for Time, and tor the Varia- tion of the Compass. [I.] Latitude by Ohsenution. 975. In variable climates it is often advisable to take, early in the forenoon, an altitude of the sun, to be followed by another after the proper change of azimuth. No. 749, for a double altitude, iu (;ase the meridian alt. is not obtained. If the second alt. is observed within the limits of Table 47, the operation is simpler, and the result more satisfactory. If it is near the meridian, and the time is not very much in error, the second alt. alone determines the latitude by the reduction to the meridian, p. 249. In either of these cases the first alt. affords the apparent time, when the lat. has been ascertained. 976. (1.) The lat. will of course be obtained, when possible, by the meridian altitude of the sun. The short double altitude a.m. has the advantage of providing against the loss of this observa- tion,* and it enables the navigator to determine the place of the ship before 12 o'clock. The altitude of the moon on or near the meridian (Nos. 702, 703) may often be obtained during bright sunshine. Also, the moon's alt., combined with that of the sun, affords the lat. by double alt., No. 759, &c. The planet Venus may often be observed during the day.f • The only observation disturbed by the ship's change nf place (No. .548) is the mir. all. Suppose, lor ex., the ship is approaching the sun 12 knots, she raises him at the ram of 12" in I". Hence he coniinues to rise till he is so far pas: the nuriJ. as to have bcjjuii, by his motion in altiiudc, to fall at this rate. In hiyh lats. where the motion in alt. is slow, tin; interval will be considerable ; in lat. 60 he would appear to dip abont 5 rain. F ii., ami in the «ame case, with the ship receding from him, ho would dip about 5 inin. a.m. 1\, I nniputi; this time, see No. C22. t ll..i,bwrt;li «t.iies that he has observed the meridian alt. of Venus, ut the Cape of 856 NAVIGATING THE SHIP. When tbe planet is not bright enough to be distinctly visible to the naked eye, it may generally be found, when near the meridian, thus : — Compute the nierid. alt., No. 663 ; add to it the dip and refraction; set this angle on the sextant, put in the inverting tele- scope, screwing it close down to the plane of the instrument: then, directing the sight to the N. or S. point of the horizon, the planet should be seen in the silvered part of the glass.* 977. The lat. is found at night by observations of stars on or near the meridian, No. 687. The lat. by a star at night not only is useful in pi-eventing the accumulation of error in the D. R., but also serves as a check on the lat. by the sun (note *, p. 249). The observation of stars at night is, however, a very different observation from other altitudes by day, and, to ensure success, the observer should make it a matter of special pi-actice. It is, however, during the twilight that stars and planets may be m.ost advantageously observed at sea, as the horizon at that time is strongly marked, and, when not sufficiently so, may be rendered distinctly visible by the inverting telescope. In favourable cases Buchlat. may be depended upon with as much confidence as that of the sun. In north latitudes above 20° or 30°, the pole-star may always be observed when the sky is clear. [2.] Time by Observation. 978. The Time is generally found by a single altitude (p. 278), early in the forenoon, when the error of the ship's lat. produces no sensible error of time. It shoiild also be found late in the afternoon. In certain cases it may be found by equal alts., No. 798, the result of which is apparent noon ; and also approximately by the short double altitude (p. 285), and at sunrise and sunset (p. 283j. The time may likewise be deduced from one of the altitudes of a common double altitude (p. 276) ; but the latitude resulting from this observation not being very correct in general, and more espe- cially when the reduction of the alts, to the same place of observa- tion is large, the time deduced would not always be satisfactory. 979. When the sun and moon are both visible, and one of them is near the meridian, the lat. may be found, and also the time, which (Nos. 696, 757) thus has the advantage of being free from the errors of the reckoning, in like manner the alt. of a planet might be taken with that of the sun at the sam< instant, or some time after- wards (No. 764). 980. When the time is found at night by alts, of stars or of the moon (Nos. 782, 784), since the sea-horizon is often unfavourable for observation at that time, the result should be considered as of Good Hope, during hri^'lit sunshine. Capt. Ba.sil Hall, to whom I am indebted for several Taliiahle snggestioiiB, acqiiaiiiied me thai, on a voyage to Malta in H.M.S. Indus, in Aii;;MSt 1841, he observed the mer. alt. of Venus every day for a fortni^'ht. Capt. Wickham also Iclls me tliat he has found the lat. by Venus, in ihe tropics, at S' in the af ernoou. * ('apt. Hall in''ormcd mo that he had often found the lat. in this -way, both bj Vcuus uiu Jupiter, when tbe jilanets were altugetbci' invisible to the naked e^e. PLACE OF THK SHIP. SSV inferior value ; or stars sliould be observed on both sides of tJxs iiiL'i'idiai), ill order to diminish the effects of errors from this cause. The remarks on the observations of planets or stars by twilight for lat. (in No. 977) apply to observations for time. Stars may often be obtained nearly on the prime veitical, and on opposite sides of the meridian (No. 787) ; and the alt. for time should always, if pos- sible, be accompanied Avith another for lat., in order to avoid all reference to the reckoning. ysi. An approximation to the apparent time may be conve- niently obtained, during part of the six months that include the simin)er, by setting the index of the sextant to the apparent alt. of the sun's lower limb deduced from the true alt. of the centre, at the time of passing the prime vertical. Table 29; the hour angle at which the limb attains this alt. is then taken out from the adjacent Column. 982. Since the change of alt. of any celestial body is greatest at the equator and nothing at the pole, the time deduced by means of altitudes is more correctly determined in low than in high latitudes. (See Nos. 778, 779.) 983. Advantage should be taken of favourable opportunities of landing at well-determined places for good observations of time, because the difF. long, between the places will at once discover any considerable change in the rate of the chi-onometer, and afford the means of correcting it. Comparatively few places indeed are as yet laid down with sufficient accuracy for the general practice of this simple and decisive metlaod ; but, in proportion as the longitudes approach to precision, the differences of longitude will be employed by seamen as the means of obtaining, directly, the gea-rates of their chronometers, instead of waiting to obtain harbour-rates.* 984. Error of the Time at Sea. The time at sea, as found by a single altitude, can rarely be depended upon to less than 10' (Nos. 778, 779). If, therefbi-e, the ship's reckoning were correctly kept, her diff. long, applied to the time, as lonnd by observation on a former oecasiim, would give the time at ship within about 10' of the truth. But as the D. R. is always more or less in error, and as the error may be considered generally to increase with the time elapsed, the error of the time at ship may be considered as 10' j)lu8 the error of the difl". long, accumulated since the observation. [S.] LomjUmle b,j Oh.errat.on. 985. The longitude by chronometer may be ascertained when- ever the time is obtained. The long, by chron. is thus the most cfKcient check on the long, by account from time to time ; but after a lapse of time it may be greatly in error, as the rate is liable to change. See No. .531. • 'I'his iijin-jrunt remark is due lo Col. Sabiie. " .\ccouiil of K.NieiinKnts," p. 401. 858 NAVIGATING THE SHIP. When there is no chronometer on boai-d,the longitude byD. R. can be corrected only on making the land, or by a lunar observation, or sometimes by speaking another vessel. 986. When a satisfactoi'y longitude is obtained by independent means, as by observation of the moon, it should be adopted as a new departure taken at the instant of observation, instead of carry- ing it back to the preceding noon or any other time; because this last process, which is atteiivi-jd with no advantage, impairs the value of the observation by mixing with it the errors of the run. 987. Since the object of the lunar observation is to find the mean time at Greenwich at the instant of observation, the simplest and most direct application of the method is to find at once the error of the chronometer on G. M. T.; because this process is not embar- rassed by consideration either of the time at place, or of the change of long, in the interval between the lunar observation and the ob- servation for time. This is the practice of the most experienced navigators. 988. When there is no chronometer on board, the longitude itself must be found for the instant of the mean of the observed dis- tances. For this purpose the time at place is necessary. If, there- fore, either of the altitudes observed for the lunar is favourable for determining the hour-angle con-esponding, the time may be ob- tained from it, and being compared with the G. M. T. found by the lunar, the long, is determined. No. 827. If neither of the altitudes is fit for the purpose, the time must be found as soon as possible afterwards. In this case, add the interval elapsed to the G. M. T. deduced by the lunar : the sum is the G. M. T. of the observation for time. This time, compared with M. T. at place, gives the longitude. Ex. At 3" 1 1"" 26" by watch, obtained a lunar, \\hich gave O. M. T. 2" 14" 32-. Al 3'' 56™ i8' by watcli, obtainecJ an observaiion for time. Find G. il. T. at this sluouJ observation. T. by watch, of lunar 3''ir"26" I G. iM. T. of lunar 2" M^ja- JJiito of obs. for time 3 56 18 44 52 Interval 44 52 I G. M. T. at 21! obs. 2 59 24 989. In the Arctic regions, in summer, the presence of the sun at night prevents the stars from being seen ; also frequent fogs obscure the moon. Hence the lunar observation is much less avail- able there than in other climates, and the chronometer in conse- quence more valuable.* 990. The number of observations, either for latitude or longitude, which it may be proper to take for determining the ship's place, obviously depends on the distance of the land and on the state of the weather. For example, in making a passtige with a trade-wind, a much less degree of attention will be necessary than in unsettled weather, when the D. E. cannot be kept with equal correctness, * "An Account of the Arctic Ucyiims," S.C., by W. Scorcsby, JUQ. 2 vols. Edin- PI.AOK or THE SHIP. 359 or tluiri when the ship is in the neighbourhood of the land or s daiijjer.* It is always advisable, wlien any observation is talcen, to obtain, oither at the same time or as soon as possible afterwards, another of such a kind that the same error may produce different effects on the result ; whereby the two results being in error opposite ways, their mean will be preferable to either separately. The kind of observation proper fortius purpose, in any case, has been genemlly noticed in the Degree of Depmdnnce. See No. 9i)9. When the observation consists of one or more alts., the errors of observation may often be removed at sea by observing also the supplement of the alt. It is, however, proper to remark, that when che supplement is observed by an ordinary sextant or circle, it is, in consequence of its greater magnitude, much more affected by the error of parallelism (Table 54), when this is considerable, than ihe alt. itself. [4.] Ohsavalionsf.T the Variation. POl. The total error of the standard compass should be con- stantly observed and recorded, not only for the purpose of secure navigation, but with the view of determining the variation, and so helping to maintain, for the benefit of all seamen, a correct chart of its value. 903. The amplitudes of bright stars and planets may often be well observed, especially about twilight, when the horizon is stronglj defined. The observation is most convenient at setting, because a star may be followed to the place of its final disappearance below the horizon ; but it is not always easy to identify a star at rising. With care the eiTor of the course due to the compass alone should not exceed a degree : less accuracy is hardly compatible with good navigation in fast steam-ships. [5.] Ciimhinalion of liesiiUi. 907. As all observations are Ihible to errors, and as given errors of observation produce different effects according to the case, the results of different observations do not generally agree. In some cases the same errors of observation will cause all the results obtained under the same circumstances to be in error the Bame way, instances of which occur in Nos. 702, 868. In other cases, the effects of errors will tend to compensate. 998. In general, when the particular errors with which the observation is iift'ected are not known, the mean of the several results is employed, or the sum of the results divided by the number of observations. • Hennell remarks thnt the facilities afforded in these till t(. din, inJKh the n-.-Awiry (7/1- ■ ■ ■■ >'ii ybservationa will aet all rigl icilities afforded in these days for finding lonailudp mny leiihnn In the Ttckoiunq, on the ground ihdt the nexl lit. P. 79. 360 NAVIGATING THE SHIP. Since one of two lesiilts may be nearly oi' exactly true, and since it will rarely liaiipcn llial one i-^ precisely as iniieli too gi-eat as liie (itJier is too small, the mean of two results will generally be merely less ill error tlian the worst. 999. In taking the result of observations affected by the same constant error, care must be taken not to nii.x those of opposite kinds, Hs N. and S., or E. and W., but to take the mean of the two ditfer- /•iit rcsidts. For Ex. : Suppose the lat. is \^2%' by each of two stars N. of the zenith, and the instrument has a constant error of ]', thrn the lat. by one star S. will be 1° 26', and the true lat., 1°27', is the mean of'l" 28' and 1° 26'. But the mean of the three results, lakt'H pi-omiscuously, or one-thii-d of l°2^^', 1°28', and 1°2G', is l°27'2(y', which is not right. The same would be true, however great the number of observa- tions on one side, oi- however snuill on the other; and lienoe it is always proper to make this separation, which is also a means of detecting a constant ei'ror. For instance, if the moon's semidiameter in the Naut. Aim. is erroneous, the result of lunar observations of one limb will differ from that of observations of the other limb and, the mean of the two results, not of the whole indiscriminately, will ntford the true longitude. 1000. When tlie error of observation is given, the amount of the error of the residt may be computed. E.\ani]iles of this have already been given in most of the rules for \\\e Degree of Depemlanne Again, the efrect of a constant though unknown eri-or of observa- tion may sometimes be removed, as in No. 801, where the same error in each distance produces more or less error in long., exactly in ])roportion as the moon's motion in respect to each star is less or greater. 1001. \A'lien some of the several i-csiilts of different observations are' known from cii'cumstances to be bi'ttcr than others, it is jtroper to give to the su))ei-ioi- lesiihs a L;ie:itei- weight or iiitluence in the gerieral determinati, and dividiuirbv the sum of 3 and 2, or 5, gives 20', or the estimated result, I" 1 1"' ii)'. The preference of any one result to another under the same or different circunistances, or the degree in which one may be sup|)ose(i superior to another, must be left to that jiidgnienl or' tact which in the result of experience and (imstaiit atlelilion to a )Mrticular sub- ject, as it is obviously impossible to lay down rules of ecrtain appli- ralioii for such f|iiestioiis. 10(r2. Though it nsimllv happens that the mean of several obscr- valions is iieai' the truth, yet, as this is not cert.dn, we uiiinl not PLACE OF THE SHIP. 3G3 hastily rts.iimic Uiat tlie mean of even a very considerable niunber is R -letiiiite determination.* It is proper to bear in mind tlnit tlic elironometcrs, when they §i;ii'e, are ciliier all right or all wrong; hr.t that when tl ey disagree. some of them mnst be wrong.f See No. 5:}1. 1003. We shall here remark, also, that every determination wliatever is liable to the snspicion of having been influenced by the premature ado|)tioii of an apjiroximate mean. For ex.: e.n observer i-oll?ct3 6 or 8 observations; 2 or 3 of tiiese dilfcr widely from the rfii, and lliev are rejected fortliwiih. Succeeding observations are compared witt.. thf mean, and admitted or rejected accordingly. Now these outlying observations may happen to be as good as the others, if not better; but by this partial suppression of evidence the cpiesfion is pi-ejudged, and the increasing number of observations only tends to fix the erroneous determination more firmly. 3. Lnying off the Ship's Place on the Chart. 11.] Position in Latitude and Longitude. 1004. As the account of the ship's ])laee is closed at noon, the ship is pricked off at that time; also at 8 p..m., when tiie course is shaped for the night. The siiip's place is laid down by observations, wluni these can be obtained ; in other cases it depends upon the D. 11., or frequently upon both. lOO.'j. It is the practice of some seamen, besides taking the sliijj'g place by ohs., to mark also her place, as brought up by D. R., from her former |)ositioii by observation ; a line joining these two points stands thus as a leg apart from the ship's track. When the ship stands nearly on the same course, and carries the same witui for some time, this method has the advantage of exhibiting any constant eifect produced by a current, or by local deviation, or arising from not making a proper allowance for lee-way. 1006. Sine(! the determitiation of latitude is absolute and inde- ])endent (No. 680), the lat. of the ship should be marked whenever a satisfactory observation is obtained. 1007. The longitude, when determined by cliron., should be marked on the chart for the time at wliich the observation is taken, because thus it is unmixed with the errors of the run. It may be prudent, when there is but one chronometer on boai'd, and when observations of the moon are not practised, to assign a * Capt.Fitzroy's clironometric inea.siircs, the results of 20 or 2.5 chronometers, amounted, when added together, to 21'' 0"' 36 , or 36' more than the entire circumference. This seempd to lie considered, at the time, as a somewhat curious circumstance ; but it is evident that •ome excess or defect was to be looked for, since nothing but accidental compensation of errors could produce, out of a number of discordant elements, the preciae quaatitr 21'0'°0'. + .Adm Hcchejacrinaiiitcfl me that on OTIC occasion all bis chroiionieters agreed within I', bi-in-,' nearly 'M' in error, iind that llie single cbrononicter of the Stalling, the tender, w«» ri';iii. A'- ihi- large iiiajuiil,^ was c>iU6idert.l couclusivc, the error was near kuding M leriuui i'uaaLi(U«nv«3. 3G2 NAVIGATING THE SHIP. second track to the long, by D. K. alone, in intervals of making the land. 1008. As a tolerably good watch alters its rate but little from day to day, the ship's track, as laid down by chronometer, repre- sents truly the relative positions of the ship at different times, and therefore exhibits nearly the true figure of her track for a few days together ; while its absolute position in long, may, at the same time, be erroneous, if the error on Gr. M. T. is not well known. On the other hand, since the longitude by lunar, though of undoubted value, is not susceptible of much numerical precision ; the difference of two longitudes by lunar, separated by an interval of time, will not, in general, agree with the diff. long, as measured by a chronometer. Hence the track of a ship, as laid down by lunars, would exhibit violent irregularities of figure, while its abso- lute position in longitude would not be very far from the mean of all the lunar determinations. Accordingly, when the long, by chronometer is proved by lunar observations to be much in error, and it is required to correct the position of the ship's track, it will be proper to take a mean position among the several positions by lunar, and the lat. at the last lunar. This point being assumed as a departure, the track for the time previous may be adjusted. Sumner's MetJiod.* [2.] Pofitiott oil a Line of Bearing. 1009. When the lat. by ace. is uncertain, the resulting long, by chron. is uncertain in a corresponding degree ; but this long., far from being valueless, is capable of an important application, espe- cially when the ship is near the land. Suppose a second lat. by ace. near the first, as, for ex., 10' greater, a second long, by chron. will be found corresponding; in like manner we may suppose a third lat., with its corresponding long., and so on. Now these positions are those points in different latitudes at which the savie alt. is observed, and constitute the curve or circle of equal altitude, since the observer, moving over the globe so as to keep the sun always at the same alt., would move on a circle, the pole of which is that point where the sun is vertical. The small portion of this curve parsing through two positions near together would appear, on the chart, a straight line ; cind thus, if this line (being produced) passes through a point of land or other object, the hearing of such object is known, though the ship's jdace on the line of its direction is not known. 1010. The process of finding the line of equal alt. consists thus in * "A New and Accurate Method of finding a Ship's Position at Sea," by Capt. Tlioa. H. Sumvcr. Boston, 1843. In 1843, Commander Sullivan, K.N , not having heard of this work, foynd the line of equal alt. on entering the River Plate, and identifying the ship's place on it, in 12 fatliomi, hy means of tlie chart, shaped his course up the river. Thd idea may tlms h.iv,' .-u;,'L:ivsiod it. srlf to others ; but the credit of having reduced it to a method, aid lu.uK it puMio, belongs to Capt. .Sumner. ■ ■ Ai V fe 1 * ■« / '' SS' 31. , \i _ s ^ s ^ASi ** Jb JJ)' / ft . \ "1 ^" / . Eh PLACE OF THE SHIP. 36:-i BTOUininor two lats.by ace, findiiip; the long, by chron. corresponding to each, laying ofi' these two positions on the chart, and joining them by a straight line. But since the sun's bearing is 8 points or 90° from the direction of the line of equal alt., this line may be expedi- tiously obtained from one obs. only, by drawing a line through the assumed position of the ship at right angles to the sun's azimutli at time of obs., as found by Chap. Vil. p. 240; or from the Azm. Tables of Bui-dwood or Davis.* From a second obs. of the same or different bodies taken h.t a Buitable difference of bearing, another line of equal alt. is similarly obtained. The intersection of these two lines gives the position of the ship supposing the ship not to have changed her position in the interval. 1011. When the ship changes her place the true course and distance made good must be laid o& from the first assumed posi- tion. Through the point thus found a line must be drawn parallel to the first line of equal alt. Where this line cuts the second line of equal alt. will be the ship's position at the second obs. The diHerence of bearings of the sun or bodies used at the two observations should not be less than 25°, or the lines of equal alt. will cut too acutely. Example, sre Diagram. In the Iiish Channel, August i8th, 1890, at 9'' 36'" a.m., in lat. by aoc. 51° 35' N. thn lol■g.byob^. was 5° 51' VV., and the suns true bearins bf ing N. 130° K, the direction Ot the line of equal alt. A 15, drawn ihrouch position A, was N. 40° K. At ll'' 8'" A.M., in lat. by ace. 51° 31' N., the long, by obs. was 5° 30' W., and the tun's trne bearing being N. 160° E., the direction of the line of equal alt. G C D, drawn tliiough position C, was N. 70° E. The run of the ship in the interval (A E) was S. 79° E. iriie. distance 10 m. Through K the line K I'' is drawn parallel to A B ; this line cuts the line C D in G. 6 is the position of the ship at the second obs. in lat. 51° 29' N., long. 5° 39' 30" W. 1012. As the ship must be somewhere on the line of equal alt. drawn upon the chart, if this line falls upon a well-souaded chart, her i>osition maybe approximately known from the depth of water ol)tained at the time of obs. Thus on the line A B a depth of over ")() fms. would shew the ship to be at a sate distance from the Hnialls. Similarly on the line C D a depth of 40 fms. shews her to be about 23 m. from Liuney Head. The line of equal alt. at the first obs. should therefore be drawn as soon as the observations are taken and worked. When the coast trends parallel to the line of equal alt., the distance of the ship from the shore is ascertained, though her absolute position is uncertain. 1013. The lat. assumed should be as nearly correct as can be obtained by D. K. ; this is important when the alt. i.s high. In low 1 "iitudes, when one obs. falls within the limits of the problem for finding the lat. by Reduction to the Meridian (see Table 47), this method should be used in preference to " Sumner's." • 'I'he line of equal all. may be foujid by the change in hour angle and consequent chaiqjo in lung, duo tu a change of one inlli' iu lal. found liy .No. 615. RG I T7AVIGATIN0 THE SHIP. 1014. As the sun rises and sets to half the globe, the circle of equal altitude at rising and setting is the entire circumference. On the other hand, when he is in the zenith, this circle is reduced to a mere point, or, for opposite points of the sun's disc, covers 32 sea-miles. When the alt. is 89° 50', the radius of this circle is 10', or its extent is 20 miles ; when the alt. is 50°, the radius is 40'', or the extent 80°. Thus when the sun is low this circle is large, the small portion of it comprised between two assiimed lats. very nearly a straight line, and the sun's azim. the same from both ends ; but when he is high the circle is small, a small portion of it may be much curved, and the direction of the two extremities very different ; tha.t is, the bearing of the land, and the sun's azimuth, may be sensibly different from different parts of the same portion. An error in the assumed lat. has therefore most effect when the alt. is high, and least when it is low, which last is con- Bequently always the pieferabie case. As the change from or towards the object of 1 mile in the observer's jAace changes its alt. ]', the effect of an error of alt. is shewn by moving the line parallel to itself through the same amount. An error in the chronometer places the line of equal nit. too far E. or too far W., bodily, but does not alter its dircctlun. III. Determining the Current. 1015. Tlie direction and rate of the current are found from the change of jslace of the ship, or from experiment. In No. 297 examples are given of finding the current by the comparison of the place of the ship by D. R. with that by observa- tion, and also by reference to the land. In consequence, however, of the unavoidable errors of the reckoning, such determinations must be far from conclusive; and thei-e is no doubt that currents are often assumed to account for discrepancies between the D. K. Bnd observation.* The only decisive method is, evidently, to deter- mine astronomically the place of a floating body, or substance, not exposed to the action of the wind, at intervals of time. 1016. As currents are considered to prevail for a very small j)ortion of the depth of the ocean, it has been recommended to sink a weight to a considerable depth to serve as an anchor for a boat, from which the current at the surface is determined by the compass and the log. This method, however, can obviously dis- cover only the difference between the current at the surface, and that at the depth to which the weight is lowered. » From gold or carefully ki-pt D.R. a rcliiible Current in 24 hours may, however, be ullen obUiueJ. MAKING THK I.ANU. 365 IV. Making the Land. 1020. Wlicn confidence cannot be placed in the correctness of the longitude, it is proper, if circumstances permit, to make the latitude of the port, and then to run on the parallel for it. 1030. On approaching the land it will be prudent to charge the ship's place with some inaccuracy ; and the best reckoning can never supersede the necessity of a vigilant look-out. 1031. When the land is made, the ship's place should at once be laid off by the reckoning ; for the reckoning may be good, and if so, the ship's position, as laid down, will be correct, or nearly so. And, again, it is not uncommon, on making the land, especially in defective light, or on a new bearing, and consequently under an unaccustomed aspect, to mistake one point for another, or to make a considerable error in estimating the distance. Now the position laid down is that by whi^'h the ship's course is shaped on the chart, and if it depends on an erroneous bearing or distance, it may lead her too near the shore or a danger. The eflf'ect of moonlight is generally to make land appear more distant than it really is. 1032. Xavigation among coral reefs is facilitated by the clear- ness of the sea-water. On the reefs on the east coast of Australia, a depth of 5 fathoms was seen from the mast-head, at the dis- tance of half a mile ; in 7 fathoms a patchy bottom was well made out from the boat's gunwale; but in 10 fathoms the bottom was scarcely distinguishable from the dark blue of the open sea. 1033. In navigating among coral reefs it is recommended, as essential to safety, that the day should be cit-ar, the sun behind the ship, the water low, and, when the shoals are not clearly distin- guished, that the ship should anchor if possible. When the sun draws ahead, coral patches become less distinct; and hence caution is necessary, when making for coral reefs with the sun ahead of the i-hip. It is also remarked that the look-out, when placed half-way up the rigging on these occasions, sees better than from the mast-head, where the eye is dazzled by the glare.* When approaching to round a point of land or shoal, and for that purpose bringing it on what appears a safe angle on the bow, care must be (aken that the danger is brought aft — that is, that its angle on the bow is increased as the ship goes on. This is * When locking out forii light at night, the fact is often forRotten lhi\t from aloft the range of vision is much increased. By noting a star iminoiliately over the light a very correct bearing may be afterwards obtained! Ironi the standai-d compass. The infrinsio power of a light should always he considered when expecting lo make it in thick weal hoi-. A weak light ii easily obscured by Laze, and no dependence can be placed on iti being sees. 36(> NAVIGATING THE Sni?. especially necessarj' with a tide or current on the off-bow. Froin want of due caution in this respect, a sliip having onlj' Jow speed may get into a position with reference to a danger from which it may be difficult to extricate her. The custom of handling ships from forward makes this caution the more necessary. From No. 309 it will be seen that the seaman can certainly know when a vessel is outside any projecting or outlying shoal by an angle between two fixed marks on the adjacent land. Thus if A. and B (fig. ex. 1) are two marks on the land, and the circle OBA passes through those marks and outside any off-lying danger, then, when the angle subtended by the two marks is less than the angle AOB (in this case 46°) the ship cannot be within the circle OBA. The angle AOB has been called the danger-angle. Such angles may be most accurately measured with a sextant ; but the angle between any two bearings taken with a compass, if the ship's head is kept in the same direction while they are taken, is also correct, the bearings being equally affected by variation and deviation. But if such bearings are plotted as cross- bearings, and either the estimated variation or deviation is erroneous, the position of the ship so obtained would also be erroneous. When ships were navigated chiefly under sail, seamen were much less disposed to approach the land than now. The certain command of course and speed given by steam has led to closing the land, in order to save distance or for other purposes, in a way which would formerly have been considered unsafe. This prac- tice has not been unattended with loss, from the fact that general charts are made from surveys which were not intended for such close navigation. Harbours and their immediate approaches ai-e generally very closely sounded, but to survey every sea-coast in such detail would occupy very much more time than is generally avail- able. The mere fact that vessels have frequently passed close to the land in certain positions without accident, is far from being Buch reliable evidence of the non-existence of danger as the close sounding of an accurate survey.* 1034. The supply ot water is a matter of so great consequence as to justify a slight deviation from formal strictness of design in allusion to it. Most of the places at which water is procured are denoted in Table 10 by the letter w, but there are some general suggestions on the subject which may be highly important on occasions, and which it is, therefore, worth while to collect here for reference, more especially as the various works through which they are scattered cannot be generally accessible to seamen. (1.) The water carried by rivers into the seals often found at a considerable distance beyond the mouth. For, a cubic foot of fresh ♦ Further, though ships now heiter preserve any given course, and the distanee run is estimated more accurately than formerly, there are in modern iron ships elements of nneenainty about dead reckoning which still make it perilous to close the land, unless there .ire means of knowing with reilainli/ when the ship is in dangerous proximity llierctu. MAKINCi THE I,AND. P.CiJ wnter weiglis 1000 oz. avoirdiijiois, wliilc a foot of sa!* water wci^lis 1028 oz.; tlie fresli water is thus liglilei than salt in the ratio of 100 to 103, or by 1 part in 34 parts; and iience, when running into salt water, diffuses itself over the surface, where it remains till mixed by tiie agitating effect of the wind or other causes. Numerous in- stances are recortled of fresh water being thus found at considerable distances from the shore. Dampier, whose interesting voyages con- tain sagacious remarks on almost every circumstance that deserves the attention of seamen, relates that, being about 2 miles outside a small river, near Aclien, in Sumatra, they "found the water of s muddy grey colour, and on tasting it found it fresh ;'' and he adds, that in such cases " we must dip but a little way down, for sometimes if the bucket goes but a foot deep it takes u]) salt water with the fresli." A similar circumstance happened to the crew of the Alceste's barge, when conveying Lord Amiierst to Batavia, after the wreck of the ship, on his return from his embassy to China in 1817. Shipa have watered two miles outside one of the mouths of the Mississippi, {lie end of the suction-hose being carefully kept just below the surface. On the like occasions it has been observed that the water has been fresh on one side of the ship and salt on the other, tha dirt'erence (which of course is only superficial) being due, no doubt, to tiie protection afforded by the ship on one side against the effect of the wind to mix the waters. (2.) When rain falls on sand contiguous to the sea, the sand protects it from agitation, and it may remain a considerable time unmixed with the salt water. Accordingly, water is often found, esjjecially after a shower, by digging in sand, taking care to remove it slowly ; and advantage may no doubt be occasionally taken of the vicinity of a sandy shore or island to recruit water. Trie troops being greatly distressed for want of water in Egypt, Sir Sidney Smith pointed out, that wlierever date-trees grow, water was to be found ; and a hole hi-vrng been dug by his directions near some tix-es of this kind, and a cask sunk iu it, a sujjply waa obtained. Adm. W. II. Smyth (in his Memoir dei!crij>tive of the Kcsources kc. of Sicily and its Islands, London, 1824, p. 112) states that on both sides of the Channel (the Faro of Messina), ])ure, though rather harfl, fresh water, is procured, by digging a hole in the sand, within two or three feet of the margin of the sea; this supply is obtained by the filtering of the fiumare (torrents), the beds of wlucii, though apparently dry, are never utterly so. The shores here aJuded to are wide and flat, and consist of sand and gravel. In the sailing directions for the Nortli Atlantic, it is stated that water is always ])rocurabIe near the Is. de Los, by digging near the root of a cocoa-nut tree. Adni. Becchey describes water as found by digging in the coral rock and recommends selecling the higher spots, distant from the sea. Lieut. Huxton (Naiit. Mag. 1846, p. 12) states that water is procura'ble, notwithstanding dis- couraging appearances, at a trifling dc])tli in the sand, on the S.VV. coast of .Africa, to the northward of ^\'alvisch Bay. Kxteusive 368 NAVIGATING THE SHIP. irai.'ts (if coast, in different parts of the world, iire, however, described as absolutely without water. (3.) Water is often found by following the track of animals, which, whether wild or domesticated, form paths to watering places. It was by following a path made by goats at Ascension, that Dam- pier discovered the spring which bears his name. Capt. Fitz Roy Biates that water was found on Charles and James Islands in the (Jalapagos by following the track of the terrapin. (4.) Boats' crews or survivors of a shipwreck may find it useful to know that rain-water and dew collect round the stems of plants which shoot leaves upwards. Dampier (Voyages to the Bay of Cam- peachy, p. 56) remarks that it is often obtained from wild pines. ' These take root and grow upright from trees. The leaves hold a pint and a half or a quart. We stick oui- knives into the leaves, just above the root, and that lets out the water, which we catch in our hats, as I have done many times to my great relief." The cocoanut-tree, the fruit of which is found plentifully, but not everywhere, in the tropics, and chiefly near the sea,* and whose singular and beautiful form, reaching to the height of between 40 and 110 feet, renders it a conspicuous object as a mark, is denoted in Table 10, on account of its value to seamen, by a special symbol. The natives near Cape Grenville, Australia, carry with them, wlien travelling inland where they are not likely to find water, the juicy roots of a shrub (Naut. Mag. 1847, p. 178). Captain Stokes remarks that a pint of water has been collected by a sponge from leaves in the morning, even on the S. coast of Australia, where the dews are not so heavy as on the N.W. coast (Discoveries in Australia, &c., in H.M.S. Beagle, 1837-43," vol. ii. p. 12). (5.) Ice islands are frequently composed of pure fresh-water ice, which is found in jiools on the surface,i- or running down the sides; and watering in this manner is a general practice of ships in icy seas. It is often, however, difficult to land on ice; and in such circumstances Admiral Bellingshausen cannonaded an ice island, and sent the boats for the fragments splintered otf. A peculiar danger is incurred by landing, for the purpose of cutting away a portion, upon ice vvhich, fiom the advanced period of the summer, or the warmth of the air or sea, tends towards dis- solution. A blow of an a.\e may split the whole mass, and the two portions, in turning orer to acquire a new position for floating, may engulph the boat and the persons employed. (Scoresliy, Journal of a Voyage to the Northern Whale Fishery in the Battin, in \S>-2, ]j. 300.) A mass of ice is likewise often liable to turn over, to float in a new position, in consequence of having imdergone a change of form by thawing irregularly. The pools of water on the ice are often brackish in the autumn, • This has long been remarked. Dampier records that the finest he had ever seen grew 1 Trieste, a small island off Sumatra , overflowed at spring-tides. t In about 62° S. the U. S. Expl Exped. found on an iceberg a pond of p^ct■llt•lll water, I acre in extent, and 3 feet deep, covered witli a scum of ice lU iuclics tliiik. MAKINCi THE LAND. SGO when the ice becomes porous, and the salt water is drawn up by capillary attraction (Narrative of an Attempt to Reach tlie North J>ole in Boats, by Capt. W. E. Parry, 1827). Though excellent water is often obtained from ice, it appears by no means certain that this is always the case. Mr. Rae, who lefi Fort Churchill in July 1846, to explore the coast from " Dease and Simpson's furthest," to Fury and Hecla Straits, states " that they had much difficulty in finding water tliat was drinkable" (Naut. Mag. 1847, p. 620). Baron Vrangel (Le Nord de la Siberie, Voyage, &c., 1822, &c.), mentions that the salt left by evaporation on the surface of the ice, is mixed with the snow that falls upon it, and eaten as salt with food, though bitter and aperieni. lie found the green transparent ice brackish, the blue, fresh.* 1. Indications of Land. 1U.3.J. The neighbourhood of land is often indicated by the pre- sence of birds, and its jjosition inferred from the direction in which tliey take their tlight at sunset. Birds, however, are often found attending floating masses of seaweed, which they follow for the sake of fish, and which is found at all distances from land. The sudden appearance of birds flying round the ships at night aroused the attention of the officer of the watch, and was thus the means of saving D'Entrecasteaux's squadron from great danger near New Caledonia (M. D'Urville's Voyage in the Astrolabe, 1826; Paris, 183:5, vol. iv.) Adni. Beechey remarks that birds fly near reefs and islands in the Low Archipelago, and calls the attention of seamen to this circumstance. 1036. It has generally been supposed that the appearance o' particular birds denotes Ine laud to be near. Cook remarks (Isl Voy. vol. i. p. 53), that " they hid been so often deceived that tliey ceased to look upon aquatic birds as sure signs of the vicinity of land." He observes (1st Vcy. vol. ii. p. 37), that shags and some other birds seldom fly out of sight of land, and adds that he believes gannets, boobies, men-of-war birds, seldom go far out to sea. Sir I*^. Belciier, however, met constantly with the gannet, frigate-bird, tropic bird, and booby, at considerable distances from the land, in the N. Pacific (Narrative of a Voyage round the World in H.M.S Sulphur, 1840). Cook considered divers a sign of land (1st Voy. vol. i. p. 47). Admiral Bellingshausen makes a similar remarki' (Voyage of the Mirny and Vostok, vol. i. p. 215). • It is a mistake to suppose that merely filtering tlie water removes all noxious matters, ss the process merely arrests, mechanically, solid partiilcs. The Chinese purify water which lias become offensive, by mixing half an ounce of alum to one ton, and leaving it for soma lime. Sir E. Home tried this with complete success in H.M.S. North Star (Naut. Mag. Ibl6, p. 025). This use of alum has long been known ; powdered charcoal, and stirring clay in the water, have also been used. t The stormy petrel (Mother Carey's chicken of sailors) if fupposcd to foretell wind; Bellingshausen remarks, on the c«ntrary, that this bird made its appe;irauce (at least nc«j 4^ N. and 20' \V) before continued calms. Vol. i. p. OT. I< I! aiO NAVTfiATING THE SHIP. Adm. Beecliey remarks that black and white tern fly 40 miles troui uninhabited islands, but desert altogether those that are in- habited. 1037. Dr. Scoresby observes that in the Arctic regions birds desert closing spaces in the ice, and repair to others wliich are opening. 1038 As a current of water, interrupted by the rising of a shoal or coast from the bottom of the sea, is carried upwards by the |)iessure from behind, and as the water below is, in warm and tem- perate climates, considerably colder than that on the surface, a fall in the temperature of the surface-water has often been found on approaching a shoal or the land, and the thermometer has accord- ingly been confidently recommended as a guide in coming into :fOundings. But it is evident that this effect must depend upon the relative coldness of the water above and below, and also upon the fiepth and other circumstances of the current, and it has been found that the indication is neither so constant, nor so marked, as to be depended upon. Capt. Foster, and more recently Capt. Fitz Roy found no such change on the Abrolhos. Sir E. Belcher (Voy. in H.M.S. Sulphur, 1840-1, vol.ii. p. 292) found no perceptible change on entering soundings off the Cape of Good Hope, or in the N. Pacific. M. Du Petit Thouars (Voyage autour du Monde sur la Fregate La Venus, 1836-9, vol. iii. p. 419) paid particular attention to this indication, and remarks that the observations generally shew a lowering of the thermometer on approaching laud, but they disprove that the water on a bank is always colder.* 1039. The temperature of the sea has been observed 1o change several degrees, in intervals of time varying from a few hours to a day and a half previous to a change of wind, the water becoming gradually warmer when the wind was about to blow from a warm quarter, and colder in the contrary case. In squally weather the temperature has fluctuated. f 1040. The temperature of both the sea and the air is, however, so much influenced by the vicinity of ice in considerable mass, that the indications of the thermometer in such circumstances are highly important, more especially as fog, arising from the condensation of aqueous vapour by the cold, frequently occurs at the same time. When the vessel is to leeward of the ice the air is greatly cooled ; and, on the other hand, when the ice is to leeward and not far dis- tant, the water through which it has drifted will be found colder than elsewhere 1041. Auiv;rig»:t the signs of a near approach to land, on some occasions, are breakers. The depth of water at which they ap]>ear seems, however, very uncertain ; and it is sometimes difficult to • In the Galf-stream, and on the banks of Newfoundland, the thermometer is said to be r«:gu!ar in its changes. (Puidy's Sailing Directions for the N. Atlantic.) + Adm. Beechey records having made observations of this kind in tlie North Pc'HHc, oB C. Horn, and near Spitzbergen. (Beeehejr'» Vjyage to the Pacific, 8vo. vol. i. p. 32} i ^IjpeadU, p. 390.) MAKING THK LAND. 371 distinguish between breakers and topping sens. The late Coni- nmnder Mudge observed that a heavy swell often breaks in 9 or 10 fathoms, and always in 4 or 6 ; he adds that the swell is often heavier in a calm than in blowing weather. The sea is reported to break on the bar of the River Senegal in 8 fathoms.* Mr. Thomas, master of fl.M.S. Investigator, says that in the gale of August 1833, at the Shetlands, the sea broke overall rocks having less than 8 fathoms on them (Naut. Mag. 1835, p. 309). 1U42. The only certain indication, in the absence of external signs, is the depth of water, when soundings can be obtained. Plence sounding is an indisjyensable precaution; and neglecting to goiaid has, in courts of inquiry and courts-martial, always bijen deemed inexcusable. See pp. 343, 344. 2. Illusoyrj Appearances. 1043. While it is necessary to be on the alert for the discovery of danger, it is scarcely less so to be prepared against folsc alarms. For ex. : in a moonlight night, when blowing fresh, it is easy to fanc}' breakers and shoals, especially when on the look-out for them. Ert'ects of light and shade have so much resembled breakers as to raise alarm; and sunbeams in the horizon, seen through rain, have been taken for rollers. — (Voyage of H.M.S. Sulphur.) 1044. Clouds and fog-banks often resemble land so much as to deceive an experienced eye. Sir Jas. C. Ross observes, that the vapour-line near the margin of ice in the polar regions is always taken for land by novices. 1045. Many reported islands or shoals, of which the accounts given have been apparently circumstantial, have, doubtless, been trees, fish, alive or dead, or ice islands. Phipps (Voyage to the North Pole in the Racehorse and Carcase, 1773, p. 57) took a small piece of ice covered with gravel for an island. Weddell (A Voyage towards the South Pole, 1822) records that it was only on passing 300 yards from an ice island that they ascertained it was not solid land, but ice covered with black earth. He also mentions having taken the swollen carcase of a dead whale for a rock, — a mistake of frequent occurrence. Sir Jas. Ross met with an iceberg which had turned over unperceived, and presented a new surface covered with earth and stones, so like an island, that nothing but landing on it convinced them to the contrary (vol. i. p. 195). Lieut. Wilkes records that a supposed rock turned oiit on examination to be a large tree covered with weeds and surrounded by fish (U.S. Exjil. Exped.). 1040. Whales have probably, as Horsburgh remarks, been taken fur rocks. These fish float at the surface for a long time together, and, being covered with barnacles, grass, or seaweed, exhibit an » The sea is .stated to liavi- broken in 40 faihonis on the coast of Syria, in the gale ol Tic. 1840 (^Nuut. .'Mas. 1841. p. r.i^i) 872 NAVIGATINfi THE SHIP. appearance so like that of a rock that it is often difficult to believe tiie contrary.* 1047. Tlie sound of breakers or surf has often been found to be caused by a shoal of fish. Kerguelen (Relation d'lin Voyage dans la Mer du Nord, 1767-8, Paris, 1770, p. 121) saw a large shoal of small red fish that had the appearance of a sandbank, of the extent of two leagues, on which the sea was breaking, and the illusion was rendered the more complete by the great numbers of birds that accompanied it. Capt. Fitz Roy observes, that a shoal of fish seen under the water may have given rise to a report of a bank, which it much resembles. Weddell records having been alarmed in a fog by a cry of breakers, for which a noise produced by fish was taken. Vlost seamen's experience will supply similar instances.-)- It has been remarked that it is very difficult at a distance to dis- tinguish straggling ice and breakers from each other. 1048. A sound like that of guns is produced by the splitting of large masses of ice. Cook records an instance (1st Voyage, p. 47), and it is familiar to those who have been in the polar regions. 1049. The surface of the sea, in some parts of the world, is occasionally found streaked, for leagues together, by a matter which produces the "discoloured" aspect of shoal water, and which sailors suppose to be the spawn of fish. Water having this appearance is not approached without anxiety by those who are unaccustomed to it; and in those seas especially where coral reefs rise perpendicularly from very great depths, an increase of vigilance is demanded on such occasions. J 10.50. In these days, when the ocean is traversed by innumerable- ships, appearances which were strange or alarming to the first navigators have become familiar; and the dangers which the enter- prising men who first ventured upon an unknown sea were naturally disposed to multiply have disappeared from our charts. But in earlier times, when the solitary vessel had either no chart at all, or one put together from imperfect or incongruou," materials, the feeble state of navigation justified the excess of caution in reporting as a danger every suspicious appearance. Accounts, therefore, of new land or danger^, which are published from time to time, are not to be received without extreme caution, unless they state some circumstance which is decisive. * Sir F. Beaufort tells me, that in approacliing the River I'late, in command of H.M.S. Woolwich, a whale was reported as a rock, and believed to be so by every one on board. But knowing that no rock existed in the situation, he steered direct for it, and when about 30 yards distant it dived. In H.M.S. Tyne, in the South Pacific, we bore up for what seemed to be the wreck of a ship floating, with her quarter raised out of the sea, but which, on approaching it, turned out to be a whale. t Til these or other circumstances, which have given rise to reports of shoals, may perhaps be added the shocks which have been experienced by ships striking against whales or other large fish. t In the Alceste, while among imperfectly known parts of the Eastern Seas, we freijucntiv pa-sed tlirough water thus tinged with some colouring matter. Mr. Darwin (Voyages o( the Adventure and Beagle, vol. Ui.) considers the effect to be produced by auinialcnls:. MAKING rillC LAND. '^73 3. Dangers. 1051. WTien the ship, goint^ free, is found to be running into danger, the proper tack to haul to the wind upon is, generally speaking, that on which she will most rapidly increase her distance from it, because thus time will be gained, 1052. In high latitudes ice islands are often met with towards the close of the summer, or earlier. The presence of ice at night is often indicated by a peculiar effect of light, and in fog by a kind of blackness in the atmosphere (Scoresby's Arctic Regions, p. 255). On falling in with ice the ship is recommended to pass to wind- ward of it. It is observed that the smaller portions drift more quickly than larger ones, and that pieces of a round figure drift nearly before the wind, while angular pieces move irregularly. Ice islands have been met with to the southward of the parallel of 50° N., in the Atlantic, and in the Southern Ocean in 36° S. The Captain of the s.s. Forfarshire reports that, in Jan. 1891 icebergs were met with in the following localities : — From lat. 51° 30' S. to 49° 50' S.,and long. 46° 0' W., sixty-three icebergs, half a mile to 3 miles long, and 200 to 300 feet high, were seen. Also an ice island, estimated to be over 30 miles in length and 300 to 400 feet high, was passed at the distance of about 5 miles. From reports received there is reason to believe that icebergs may often be found in the positions given, and mariners are warned to give the localities a wide berth. See Admiralty Ice Chart, No. 1241 ; also Wind and Current Charts. A remarkable diminution in the strength of the wind is ex- perienced when to leeward of ice, even of very small extent. This is noticed by Sir E. Parry and by other navigators. 1053. There is also another source of danger, which appears to have increased of late years, and one less easily guarded against, in vessels which have been abandoned by their crews, in some cases unnecessarily, and which, having become more or less waterlogged, remain drifting about, 1054. To these may be added rollers, which term is applied to a very heavy swell rising on particular coasts, without any known cause, generally very quickly, and subsiding very soon, and which con- stitutes a formidable danger. H.M.S. Julia was wrecked in a calm at Tristan d'Acunha in a few minutes. More recently very severe loss was experienced at St. Helena. Rollers are noticed as a great danger on the coast of Guiana, where they break in 5 or 6 fathoms (Commander Darley in Naut. Mag. 1844, p. 619). The U. S. Expl. l^xpd. anchored off St. Francisco Nov. 1, 1841, the Vincennes Iteing in 7 fathoms, and 3 miles oft" shore. About 10 p.m. the rollers got up and broke with the continued roar of a surf. At midnight a sea broke heavily on board the Vincennes, a ship of 780 tons, dis- placed the booms and boats, and killed a man. The other ships, in deeper water, felt no inconvenience.* * ThoiiRh great (iangcris incurred from breakers in shiwl water, yet there arpiuaslson KliioU the graduiil glielving of the bottom dibbipatcs the bWell hy clegrcos without causing n •^74 NAVIGATING THE SIMP. 4. Dcteviniiiat'wn of Position 07 Danger. 1055. Out of Sight of Land. — When a rock, a slioal, or an island, is unexpectedly met with at sea, its bearing and estiuiatod distance are to be noted, with the time by chronometer. As tbe trne position can be determined by astronomical observation alone, the following directions are inserted for reference, the calculations being deferred to a convenient time. (1.) When the sun is visible. Observe his altitude, noting the time by chronometer (see the note, No. 726). This gives the lat., Nos. 681, 696, or 718, or the time, No. 776, or 791, and thence the long, by chronometer. (2.) When the sun and moon are visible. Observe both alts, •vith all possible care, and the lunar distance ; the lat. is hence found, Nos. 681 or 692, 696 or 703, or 759, &c., and thence thfi time, and the long, by chron. or by lunar. (3.) When the moon is visible. See Nos. 692, 703. In favour- able cases the alt. gives tlie long., No. 864. (4.) When the moon arid stars are visible. Obtain the lunar distance, and both alts, with care. See, also, Nos. 864 and 866. (5.) When the stars alone are visible. Observe altitudes near the meridian, and on opposite sides of the zenith, for lat. ; and near the prime vertical for time and long, by chron. Of the dangers to which navigation is exposed none is more formidable than a reefer a shoal in the open sea; not only from the almost, certain i'ate of the shi]) and her crew that have the misfortune m strike upon it, but also from the anxiety with which the naviga- tion of all vessels, within even a long distance, must be conducted, on account of the uncertainty to which their own reckonings are ever o])en. No commander of a vessel, therefore who might meet unexpectedly with any such danger, could be excused, except by urgent circumstances, from taking the necessary steps both foi- ascertaining its true position, and for giving a description as com- plete as a prudent regard to his own safety allowed. 1056. In Sight of Land. The position of a rock or a shoal may be determined by cross-bearings (No. 36C) when the variation and deviation are known. It may be determined more accurately by taking the bearings of three objects, and using the angle between the bearings (No. 368). The sextant may be used, in preference to the compass, for convenience and accuracy; the face should be held horizontal, and the angles measui-ed between points vertically under the objects, or determined by plumb-lines con- ceived to pass through the objects. No. 368. [1.] Report of New Discovery, or Correction of Position. 1067. In transmitting an account of a new discovery, or the correction of a position, the first consideration is the lat. or long., or dangerous break. On the coast of Barbary, in H.M.S. Adventure, under the command of Capt. W. H. Smyth, wc frequently, when" the wind was (lead on shore, ran to Ice.ward PUl of the oca, till we found a convenient dcptli of water for anchoring. MAKIXQ THE LANF*. 375 the si(ta;ition with respect to some other place. Attention should therefore be directed to the instructions at No. 835. It will, indeod, be evident on a moment's reflection, that the long, described merely, as is too often the case, as " long, by chron." without i-eference to some fixed point, is utterly valueless. Again, when such fixed point is mentioned, it is no less necessary to note the long, adopted: for ex.: "Long, by chron. from Callao," is little better than no allusion to place at all, as Callao appears in the tables in different -ongs. from 77° 10-5' to 77° 15-7'. When the determination depends on a lunar, notice should be taken, 1. of the skill of the observer; 2. of the instrument; and especially whether distances on opposite sides of the moon are observed ; also, 3. of the probab'e error of the time. 1058. After the position the {Joint next in importance is the extent, and general direction, if this can be assigned. Then follows height or depth, with notice of the appearance ; and then anchorage, landing, supplies, and natives. The seaman will find these matters of detail passed in review, in the same constant order, in the sj'm- bolised descriptions in Table 10 ; and he may render much service by taking the opportunity of recording these particulars on passing any of the numerous places of which we have no very exact accounts.* It will often be important to notice both the extent and appear- ance of islands, which have not been visited for a long time. Kru- seustern, in alluding to the growth of many islands by submarine formations, which are continually extending themselves, as esta- blished by Fleurieu, Flinders, and Beechey, remarks that Capt. Carteret discovered a small flat island so nearly at the level of the sea, as scarcely to deserve the name of an island, which he called Osnahurcjh. It was on this island that the Matilda was wrecked in 1792, as is proved by the agreement of her observations with those of Adm. Beechey, who found here the wreck of a ship. Thus the " small island " had, in 1827, an extent of 14 miles (Mem. Hydr. 18:J5, p. 94). Again, in warm climates, reefs at the level of the sea are covered by degrees with a low vegetation, which, in due time, is succeeded by trees. Many places, therefore, now known merely as reefs, or not noticed at all, will probably become hereafter conspicuous islands. 1059. Whenever a position is noted, the bearings of headlands and islands should be observed as accurately as possible. The neglect of this is seriously felt in the arrangement of positions. f Seamen may also supply very impoi-tant elements for correcting * If, in sending home such accounts, llie writer uses symbols, he must be very carorm to draw ihem in their perfect form, lest one may be takin for another. The great saving of time and sp»ce which they eti'ect claiuis the necessary attention in writing them legibly. ■f In the third and later editions of this work a discrepancy was admitted in the positions of Tunna, Annatom, and Erronan. from the want of bearings, though the places are in sight of each other. Capt. Dcuham, of II. M.S. Torch, rt'moved the ditficiilij. 376 NAVIGATING THE SHIP. tlie charts by observing- witli care the bearing of two points of land when seen in a line, or on with each other, or of a summit seen over a point. Such bearings are called transit bearings. 1060. Views should accompany all hydrograpliic notices, when there is any one on board who can draw. On these should be marked one or more bearings (selecting, first, that of the nearest point), and the angles measured hy a se.\tant between remarkable points or other objects; also the angular elevations of summits, as these last serve for the determination of heights. It is also important, where the range is considerable, to note the time of tide, beciuse the rise or fall of several feet in the water may cause a material change in the appearance of the sliore, and has also the effect of altering the apparent dimensions of an island witii shelving shores. Again, when the spectator is on shore, the place of the visible horizon varies with tlie height of the tide, being nearer to him and higher, when tiie water is higher (or when lie is less ele- vated above it), and further off and lower, as the waterfalls (or as he increases his relative height). Tlie consequence of this is, that an island beyond the visible horizon appears to the spectator on shore to be of different lengths at different times of the tide. A small pamphlet entitled "Notes bearing on the Navigation of H.M. Ships," lately issued by the Admiralty, will be found to contain much practical ejid useful ijiformation. EXPLANATION OF THE TABLES. In this division of the work the use and application, and, in some degree, the construction, of the Tables, are described. Rules are given for computing the terms in the Tables. These rules will be found useful for the purpose of verification ; for the computation of an intermediate term instead of the ordinary inter- polation ; and also when the computer may require, for a particular object, to employ a table on a more extensive scale than would be convenient for the general purposes of the collection. NAVIGATION* THE SAILINGS. These tables are nsed chiefly in the methods, Chapter III. Table 1. This is called the Traverse Tarle from its use in Traverse Sailing. 1. Direct Application. Table 1 contains the Diff. Lat. and Dep. for the Course at every degree, and for each mile of distance to 600 miles, with the time corre- spending to each degree. When the Course is given in points, it should be turned into degrees (No. 216). If it is less than 4 points or 45°, the table is to be entered at the top ; but from the bottom when it exceeds 4 points or 4.5". Ex. 2. Course 68°, Dist. 241 miles ; find Ex. I. Course 5:^ pts., Dist 74 miles; find the D. Lat. and Dep. In Tahle I, at 28° = 2^ points and against 74 in the Dist. column, are D. Lat. 65 3, and Dep. 347. the D. Lat. and Dep. In Table 1, over 68° at the bottom, and aguinst 241, are D. Lat. 903, and Dep. 2235. • The general division of the subject into Navigation and Nautical Astronomy naturally suggests the like division aniony the Tables. But, besides this, the computer cnnnot, in general, make proper use of the Astronomical Tables unless acquainted beforehand with his position on the globe. The Tables, therefore, relating to this last point, that is, those which are concerned in finding the position of the ship with reference to the place left, neces- sarily precede tlic others. The Table of Positions, which is usually found at the end of a collection of tables, is, according to this disposition, placed among those relating to Departures, since in actual navigation it is referred to only with reference to the place of the ship. The author is indebted to many individuals whose opinions are entitled to every comiideration for suggestions relative to the arrangement or order. It will, however, be obvious that no arrangement can be devised which shall be equally convenient for all persons at all times; and, perhaps, no plan is opin to fewer olycctions of weight than one in which regard is paid both to the classification of subjects and to the successive stages of the computations. [BB] 378 EXVLANATION OF THE TABLES. In like manner, in taking out the Course corresponding to a given D. Lat. and Dep., when the D. Lat. is greater than the Dep., take the Course from the top ; when less, from the bottom. (1.) To take out the D. Lat. or Dep. to a fraction of a degree. Ex. To find the Dep. to ii°i and Dist. loo. The Dep. to ii° is ig-i, that to 12° is 208 ; \ of the difference 17, or -4, added to 19' I gives 19-5, the Dep. required. In finding the D. Lat. this prop, part is subtractive. (2.) To find the D. Lat. or Dep. for a fractional Dist., as, for example, for 59-3 ; find it for 59, and then for 3 (dividing the last by 10). (3.) When the given Dist. exceeds 600 miles, divide it by 10, and mul- tiply the D. Lat. and Dep. found by 10. So, likewise, when tlie given D. Lat. or Dep. exceeds the limits of the Table, divide it by 10, and multiply the resulting Dist. by 10. Ex. 1. Course 31°, Dist. 1872 miles. The Course 31°, and Dist. 187, give D. Lat. 160-3, iiDd Dep. 963 ; hence the re- quired D. Lat. and Dep. are 1603 and 963 nearly. Ex. 2. D. Lat. 660, and Dep. 165, to find the Course and Dist. D. Lat. 66, and Dep. 16-5, give Course 14°, and Dist. 68 ; tlie required Dist. is, therefore, 680 nearly. This is near enough in general. For greater accuracy, in Example 1, take out the D. Lat. or Dep. for 600, and for the excess above 600. 2. Trigonometrical Quantities. If the angle A C B, fig.. No. 162, be considered the Course, and A C the Distance, then A B becomes the Dep. and C B the D. Lat. Hence, by No. 162, the Dep. corresponding to the Dist. 100 is the sine for the radius 100. The D. Lat. to the Dist. 100 is the cosine for the radius 100. In like manner, the Dep. to the D. Lat. 100 is the tangent for the radius 100. Tlie Dist. to the D. Lat. 100 is the secant to the radius 100. Thus also the D. Lat. to the Dep. 100 is the cotangent; and the Dist. to the Dep. 100 is the cosecant to the same radius 100. The trigonometrical quantities (which are calculated for radius 1) are deduced from the numbers thus found in the Traverse Table by marking off two decimals. Ex. 1. Find the Sine of 27°. At the arc 17°, the Dist. 100 gives the Dep. 45-4. The Sink is, therefo/e, -454, the log. of which is 9-657 (Nos. 58 (2) and 59, p. 19). This is the log. given in Taole 68. Ex.2. Find the Cosine of 56°. At 56°, the D. Lat. to the Dist. 100 is 55-9, the Cosinb is *559, tlie log. of which is 9'747. Ex. 3. Find the Tangent of 58°. At 38^ the D. Lat. 100 corresponds to Dep. 78':, the Tangent is -782, the log. of which is 9893. Ex. 4. Find the Secant of 42°. At 42°, th& D. Lat. too corresponds to the Dist. 134-6, the Secant is 1-346, the log. of which is 0-129, <"" in Table 68, 10-129 (No. 160, Note). Ex. 5. Find the Cotangent of 54°. At 54°, the Dep. 100 corresponds to D. Lat. 72-7 the CoTANG. is -727, the log. of which is 9-861. Ex. 6. Find the Cosec. of 18°. At 18°, the Dep. 100 corresponds to Dist. 323-4, th» CoSEC. is 3-134, the log. of which is 0-510. [1.] Solution of Right-Angted Trianglet. These tables are useful in solving approximately cases of right-angled triangles, as also in roughly verifying the results of questions of the kino wlien obtuined by logarithms. EXPLANATION OF THE TABLES. 379 Ex. p. 48. Angle A 50", CA 28 feet, find AB and EC. At 50°, the Dist 28 gives the D. Lat. 18, which is AB, and the Uep. 21-4, or C B. Ex. p. 49, Case IL Angle A 30<>, BC 171 ; find A B and AC. Course 30° and Dep. 855 give Dist. 171, <'r BC 342, and D.Lat. MSi.or AC296-2. Ex. p. 49, Case III. AB 2203, AC lorg ; find the Angle B and BC. Pist. 220 and Dep. 103-3 "e the nearest, and give 28° for the Angle B, and the D Iju •rBCi94. 8. Proportional Quantities. Mr. A. C Johnson, R.N., in his valuable pamphlet on " Finding Latitude and Longitude in Cloudy Weather," * has shown how Table I. may be used to correct the Longitude for error in Latitude. With the complement of the object's bearing at sights as a course, and error in Latitude as a Diff. Lat., take out Dep. This converted into Diff. Long, will be the correction required. East: When the true latitude is South West: When the true latitude is South of the approximnle, and azimuth of object ' of the approximate, and azimuth of object between N. and E., or between S. and W. | between S. and E., or between N. and W. Gt when the true latitude is North of ; Or when the true latitude is North of the approximate, and azimuth of oliject ] the approximate, and azimuth of object between S. and E., or between N. and W. 1 between N. and E., or between S. and W. Ex. In Lat. 45° S., sun be^irin? S. 55' W., ship by observation was in long. 3^-45 W., but the error in bit. was found to be 18 m. South. 'complement of Azimuth 35". Then Course 35" and Diff. I^t. 18' give Dep. I2''6, Dep. l2'-6 and Lat. 45° give Diff. Ix)ng. 18'. True lat. South of approximate, and azimuth between S. and correction is E. Long, from Observation 3° 45^- Correction ir- '8 E . True Long 3 27 ^'''■ Published by J. D. Potter, Agent for Admiralty Charts, 145 Minories. [Tofice p. 378. (1.) To tnm statute miles into nautical or geograpTiical miles. t ..' ^'^'"^«™''e = 08684 geogr. I Ceogr. mile = 11515 statute miles. At 61 , the Dist. and Dep. correspond to statute and yeogr. miles. (2.) To ixxTu feet per second into nautical miles per hour. At 36°, the Dist and Dep. corregpond to feet and miles; thus the rate of 10 feet pcj •ccond IS II miles an hour, nearly. *^ The measures and souBdings on foreign charts are reduced, in like manner, to our own scales. 380 EXPLANATION OF THE TABLES. (1.) To turn Danish Favne into English Fathoms. I fav.= i-ozq2 fath. i fath. = o-97i6 tav. At 76°, the Dist. and Dep. correspond to fathoms and /aune; thus, loc fame arc lot fath. nnarly. (2.) To turn Danish Feet into English FeH. I Dan. foot (/orf) = 1 -0270 Eng. feet, i Eng. foot— 0-9737 Dan ft At 77'. the Dist. and Dep. correspond to Bnr/liah and Danish feel : thus, 200 Danish feet »re 205 English feet nearly. (3.) To turn Dutch (Amsterdam) Feet into English Feel. 1 Amst. foot = 0-9287 Eng. ft. i Eng. foot = 1-077 Amst. ft. At 68°, the Dist. and Dep. correspond to Dutch and English feet. Thus, 300 Dutch feet are 278-2 English feet nearly. (4.) To turn Dutch Palms into English Feet. I palm = o-3283 ft. 1 foot=3'046 palms. At 19°, Dist. and Dep. correspond to palms axii feet. Thus, loo palms are 31-6, or more nearly, 32-8 feet. (5.) To turn French Brasses into English Fathoms. I hrasse=o-888 fath. i fath. = 1-126 brasse. At 62°, the Dist. and Dep. correspond to brasses and fathoms. Add 1 in 180. Tins 100 brasses are 176-6, or more nearly 177-6 fathoms. (6.) To turn French Metres into English Yards.* I metre= 1-0936 yard, i yard = o-9i44 metre. At 66°, the Dist. and Dep. correspond to yards and metres. Thus, 300 yards are 274" 1 xeties nearly. (7.) To turn French Feet (Pieds) into English Feet. I pied= 1-0658 ft. I foot = o-9383 pied. At 70°, the Dist. and Dep. correspond to pieds and feel. Thus, 200 pieds are 211 feet (8.) To turn French Toises into English Fathoms. I toise = 1-0658 fath. i fath. =0-9383 toise. At 70°, the Dist. and Dep. correspond to toises and fathoms. Thus, 200 toisee arc zi; fatlioms nearly. (9.) For tlie Prussian Foot (Fuss), see Danish. (10.) To turn Russian Arsheens into English Feet. I arsh. = 2-3343 ft. 1 foot = 0-4284 arsh. At 25°, tlie Dist. and Dep. correspond to feet and arsheens. Deduct i in 60. Tims 86 arsheens are 203 feet, or more nearly 200 feet. (11.) To turn Russian Sashes (Sazhens) into English Fathoms. 1 sazh.= 1-1671 fath. i fath. = 0-8568 sazh. At 59^, the Dist. and Dep. correspond to fathoms and sashes. Thus, 300 fatlioms nr« 2571 sazhens. Thus, the arsh. = 28 in. ; the sazheti = 7 f., and the wrst ^12) = 500 sa:hens. • The following French mea.sures occur frequently : — Metre =39-37079 Eng. In Decimetre = I- loth met. = 3-937079 Centimetre= i-iooth met. = 0-393708 Millimetre = I- loooth met. = o-O'qt?! EXPLANATION OP THE TABLES, 381 To turn Russian Verstx into Nmitical Miles. 1 verst=o'5759 mile, i mile= i'7364. verst. At 35°, the Dist. and Deo. correspond to veratt and mites. Add r in i6o. TLiis, juo rersta are 172-1, or more nearly (adding -6) I7i'7 miles. (13.) To turn Spanish Brazas into English Fathoms, I braza = o-9i5 fath. 1 fatl).= 1-092 braz. At 66°, the Dist. and Dep. correspond to brazas and fathoms. Thus, 200 hraiRf an: 183 fathoms nearly. (14.) To turn Spanish Varas into Yards I vara = 0*9 142 yard, i yar(l= 1*0964 var. At 66°, the Dist. and Dep. correspond to varas and yards. Thud, 300 varas are 174-3 Tarda. (15.) To turn Swedish Fiet into English Feet. I Swed. foot (/orf) = o-9739 Eng. foot, i Eng. foot = 1-0268 Swed. foot. At 77', the Dist. and Dep. correspond to Swedish and English feel. Thus, 300 Swedish tect are 292-3 English feet. To compute a Term. For the D. Lat. To Jie log. of the Dist. add the log cos. of the Course ; the sum is the log. of tlie D. Lat For the Dep. To the log. of the Dist. add tlie log. sine of the Course; the sum is the log. of the Dep. Table 3. Dep.^rture and Corresponding Difference ofLoncitudr This Table shews the number of minutes of Longitude in any number o( nautical miles from 1 to 10, mea.sured E. and W., in lats. under 70°. Ex. 2. Lat 31° 30', Dep. 8- 7m. ; Sndth^i D. Long. 31I. 8 9-3« Ex. 1 Ixing. 49' Lat. 49°, Dep. 27m 20 (2 X 10) ; find the D. io-a8 7 ... 10-67 •7 D. Long o-8» degree may be effected 2, above. 9-33 ^o^,f„r D. LoN 933 30',+ -05 9-38 + -81 D. toi 0-7 U. L.ONO. 4>'iS In general, interpolation for any fraction of ; nearly enough at sight, as in Ex. 2; but when accuracy is required, find the D. Long, for ^' the two whole degrees, including the fractional 3' • lat., take the diff. of the two results, and with ^^' it enter the col. headed D to 1°, take out the j)arts and add them. , The Table may often he useful in parallel and mid. lat. sailing; though, to be properly adapted to this purpose, it should be greatly extended. Its chief utility lies in the reduction or comparison of longitudes in plans not graduated. To rompule a term. To the log. of the Dep. add the log sec of the Lat.; the sum (rejecting 10) is the log. of the 1). Long. Table 4 Difference of Longitude and Cohresi'onding DKt'AiiTi'R.? 'I'liis Table shews the number of nautical miles in any number of minute.s Df longiluilc from I to 10, in lata under 71° i82 EXPLANATION OF THE TABLES. Ex. 1. I dt. 64°, D. Long. 272'; find Dep. 64", 200 88-0 T'' 3°"7 Dep. ii9'6 Ex. 2. the Dep {, D. Long. 4''6 ; find 3-68 o*0 3, for 30'. Ine remarks on Table 3 apply to Table 4, e.xcept that the parts for the Iraction of a degree are to be subtracted. To compute a term. To the log. of the D. Long, add the log cos of the Lat. ; the sum (rejecting 10) is the log. of the Dep Table 5. Spherical Traverse Table This Table is named from its being used with the common or plane Traverse Table, in cases which involve Spherical Trigonometry. The Table is entered with the lesser of two given arcs or angles at th<- top, and tiie other at the side ; thus, to take out M and N for 64° and 15^, enter with 15° at the top and 64° at the side, then M is found 236 2, and N 54 9* Interpolation for a fraction of a degree is easy, because M and N always increase. In general, it is enough to take M or N at sight, as directed No. 19 ; thus, for ex., to find M fur 59° 47' and 66° 18', that is, for 59| and 66^, we may take 496. For greater precision, take the differences between each two terms con- cerned, and proceed to proportion separately for each. The Table solves by inspection, approximately only, but very expediti- ously, several problems. This method, besides being near enough for many practical purposes, will often be useful as a check against mistakes in longer methods. (1.) To find the Hour-angle from the alt. No. 613. With the lat. and decl. find M and N. With the alt. as Course, and M as Dist. find the Dep. When the lat. and decl. are o^ contrary names, take the sum of the Dep. and N. The course answering to this sum as D. Lat. and Dist. 100 is the Hour-angle required. When the lat. and decl. are of the same name, take tlie diff. of the Dtp. and N. When the Dep. exceeds N, the course answering to this Diff'. as D. Lat. and Dist. 100 is the Hour-angle; but when the Dep. is less than N, the supplement of the said course is the Hour-angle. angle. X. 2. Lat. 51° 10 S., i° 51': required the H I9°l and 51°, xM i68-6, N 44 ii^j and 169, Dep. 3.;. {sum) 79' Hour-angle, i*" 31"'. 7'N. Ex. 1. Lat. 15" 32' N., decl. 8^ 35' 1 s!V 15° 26': required the Hour-angle. I5°4 and %°i, M 104-9, ^^ 4'i I5"4 (alt.) and 105, Dep. 28-0 {aum) 32-1 Hour-angle, 4'' 44"". * It will be perceived, on inspecting the examples, that after M and N are taken out to the given arcs, the arithmetical process is very similar in all the ])roblems ; very little prac- tice will, therefore, render the several uses of the Table familiar. As the process of conipu- lEition consists in the addition or subtraction of two numbers only, thus taken out by Inspection, it will be difficult, if not impossible, to find general solutions more concise. As M is always greater than N, they can never be confounded together. It is because the Dep. always increases with the course, that it is used in pnfc renrc to ttie D lat. in the tolutions by this Table, the rules being adapted accordingly EXPLANATION OF Tnii TABLIS, :583 Ht. i. Lat. 56" 50' S., decl. 56° 10' all. 64.^ 47'; required the Hour-angle. 57° and 56°, M 328-3. N 228-3 65° and 328, Dep. 297-3 (diff.) 690 HoCB ANCLE, 3'' 5" fsinre the Dcp. wrf»N). Ei 4. Lat. 47' 3' N., decl. 11° 3/' N. alt. 8° 2o': required the Hour-angle. 47°and22°J, M 158-7, N 44-4 8°j and 159.. Uep 23-0 (dijT.) Tn Course, s"" 11"'; or HotTR-ANGLK, 6'4y" (since the Dep. is less than N). When the lat. or the decl is 0, N is 0, anil the Dep. is to be taken aa tlie D. Lat. to 100; the C'ours« corresponding is the Hour-angle required. Ex. 5. Lat. 0°, decl. 14° N. or S., alt. ': required the Hoar-angle. o and 14°, M 103- 1 27° and 103, Dep. 468 Hour-angle, 4'' 8"". Ex. 6. Lat. 38" N. or S., decl. 0°, alt. 27^^: required the Hour-angle. 0° and 38°, M 126-9 27° and 127, Dep. 577 Hour-angle, 3'' 40°'. (2.) To find the Hour-angle on the Prime Vertical, No. 618. With the decl. and colat. find N; with 100 as Dist. and N .is D Lat find the Course. F.x. Lat. give HovR-AN 59° S"e N. 41-5; Dist. 4.-5 D. La C.3.) To find the Hour-angle at rising and setting, No. 620. Witli the lat. and decl. take out N. With the Dist. 100 and N as D. La*, find the Course. When the lat. and decl. are of contrary names, this is the Hour-angle required ; when of the same name, take the snppl. to 12 hours. 2. Lat. 31° N., decl. 40' S. : find ir-angle at rising or setting. 31° and 40° give N 50-4 id 50-4 give 4'', the Hour-anoi.« Ei. 1. Lat. 51° N., decl. 27° N. : find the Hour-angle at rising or setting. 27^' and 51° give N 62*9 Dist. 100 and D. Lat. 62-9 give Course 3''24'",and the Hour-angle required 8''35"'. required. (4.) To find the effect of Refraction, &c. on the abovr. No. 6.'38. With the lat. and decl. take out .M. With M as Dep. and the Hour-angl-3 at ri.^ing or setting as Course, take out the Dist. Multiply this Dist. by tne sum of 34' and the depression to the height, Table 8 ; the product divided by 1500 is the portion of time required in min. and decimals. Ex. 1, No. 638. Lat. 28° and Decl. .6°giveM 117-8. Then Lat. 28° N. and Decl. 16- N. give Hour-angle at setting, b^ 35"'. The suppl. of this, as it exceeds 6'', or 5I' 25"' aa Course, and Dep. 117-8, give Dist. 119. Dist. 119 mult by 34 + 117, or 151, is 17969 ; which, -f- by 1500, gives 1 i^-g. (5.) To find the Time of Twilight, No. 641. With the lat. and the sun's decl. find M and N. With the Course IS"-" and the Dist. M find the departure. When the lat. and decl. are of same name, add this dep. to N ; the Course corresponding to the sum as D. Lat. and Dist. 100 is the A. T. of the beginniug of twilight, a.m. When the lat. and decl. are of conlrary names, take the diff. between tho above Dep. and N ; the Course corresponding to this diff. as D. Lat. and Dist. 100 is the time twilight begins, a.m., xvhen the Dcp. is greater tliaii ti; and the time it ends, p..m., when the Dep. is less than N. r.acb of these times is the supplement of the other to 12'. i4 EXPLANATION OF THE TABLES. El. Lut. 30° N., iun'« decl. lo' N. ; required Beginning and End of Twilight. 20" and 30° give M 122-9 *™1 ^ 21. Course 18° and Dist. 123 give Dep. 38 (grrater), me name) »um 59. Dial. 100 and D. Lat. 59 give Course 3'' 56™, the time it BtaiNS 11.: hence it End? at S^ 24'" p.m. (6.) To find the altitude on the Prime Vertical, No. 664. With and the coiat. find M. With the decl. as Course and M as Dist. find the Dt-p. With Dist. 100 and this Dep. find the Course. Ex. I.at. 52°, DecL 22°. o and 38° give M 126-9, *^° Dist. I X and 47'6 give Course or Alt. 28"}. Ex. 3, No. 665 (worked to the nearest degree), gives Dep. means that the Alt. is 90°, or it is an extreme case. ind Dist. 127 give Dep. 47-6. 100, equal to the Dist. which (7.) To find the Altitude, the Hour-angle being given. No. 666. With the lat. and decl. take out M and N. With the corapl. of tlitj hour-angle to G*" as a Course, and Dist. 100, find the Dep. When the lat. and decl. are of contrary names, take the diff. of this Dep. and N. When the lat. and decl. are of the same name ; if the hour- angle is less than G"", take tlie sum of the Dep. and N; \i greater than G*", take the diff. With this sum, or diff"., as Dep. and M as Dist. find the Course, which is the alt. required. Ex. 3. Lat. 56° 50' N., decl. 56° 10' Hour-angle, 3'' 5"". 56° and 57°, M 328-3, N i2S-3 2*' 55°' and 100. Dep. 69-0 (TOM) 297-3 164- 1 and 148-6 give Alt. 65°. Ex.4. Lat. 22° .S , decl. 3° N., H angle, 2i' 15 ". 3° and J 2°, M 08-0, N 2-1 3" 45°' 82-9 {Aiff.) 80-8 kLT. 49 , Ex. 1. Lat. 15° 32' N., decL 8° 35' S., Hour-angle, 4'' 45"': required the Alt. 8°4 and i5°5, M io4"9, N 4-1 i* IS"" and Dist. 100 Dep. 32-2 {cont. name), diff. 28-1 Dist. 105 and Dep. 28-1 give Co. I5°J the Alt. Ex. 2. Lat. 47° 3' N., decl. 22° 37' N., Hour-angle, 6'' 50'". 22°J and 47°, M 158-7, N 44-4 o"" 50"" and 100 Dep. 21-6 {diff:) 22-8 159 and Dep. 22-8 give Alt. 8°. When the lat. or decl. is 0, N is 0, and the Dep. taken as Dep., with M as Dist. gives the course. When both lat. and decl. are 0, the alt. is the compl. of the hour-angle in arc. (8.) To find the Azimuth, the Altitude being given. No. 673. With the lat. and alt. take out M and N. With the decl. as course, and M as Dist., find the Dep. When the lat. and decl. are of contrary names, take the sum of this Dep. and N ; when of the same name, their difference. With the dist. 100, and this sum or diff. as D. Lat., find the course, which is tlie azimuth required. When the lat. and decl. are of contrary names, this azimuth is to be reckoned from the S. in N. lat. and from the N. in S. lat. When they are of the same name, — when the Dep. is less than N, reckon the azimulii from tiie S. in N. lat., and from the N. in S. lat.; when the dep. is greater than N, reckon the azimuth from the elevated pole, or from the N. in N. lat. The azimuth is reckoned E. or W. as the celestial body is to the E. or W (»f the merid. lit the time proposed. EXPLANATION OV THK TABLES. 385 HU. 1. I.at. 10° S., alt. sS^+o' to E-d., 4ed. 14° 14' N. (contrary names). lo^tDd sS"! M 1958 N 29-0 14"} and 196 Pep. 49-0 {.um) 78-0 100 and D. Lat. yS-o give 39°^, the if.ii. req., which (in S. lat.) is N. 39°^ E. Ex. 2. Lat. 51° 30' N., alt. of Arctuiui 40^25' to W-d., decl. 20^ 2' N. (>ame name). 5i°land4oJ M 211-2 N 107-3 20° and 211 Dep. 72-2 100 and D. Lat. 35-1 give 69'J, or Az.m, req., S. 69"} W,, as the Dep. is the Itiier When the Lat. is 0, N is 0, and the Drp. itself beronus the D. Lat, hich, with Dist. 100, gives the Course. When tlic Declin. is 0, the Dep. is 0, and N becomes the D. Lat., which, ith Dist. 100, gives the Course. Ex. 3. Lat. o, declin. 21° N., alt. 61°. | Lat. o and 61 M 206-3 ' 21 and 206-3 Dep. 73-8 42°. E.\. 4. Lat. 48° S., decl. o, alt. 34'. 48° and 34° M 180-3 N 74-9 o and 180-3 D^P- ° 100 and 74-9 give Course 4i°J, the Azimuth. To compute M and N.* For M, add together the log. secants of the given arcs, add '2 to the index, and reject the tens ; the sum is the log. of .VI. For N, add together the log. tangents, and proceed as for M. M and N for 15° 40' and 69° 11'. .5=40' log. sec. 0-01644 69 M log. sec. o-4493> M 192-2 log. 2-46575 log. tan. 9-447«7 log. tan. 0-41999 N73-8 log. .-86786 Table 6. Mekidional Parts. These are the number of minutes corresponding to each degiee and minute of lat. on Mercator'« chart. For ex., the mer. parts to lat. 39° I'J" are 2560. \ The mer. parts are given to each minute of latitude as far as 78°. To compute a Term. Add 45° to half the latitude, and take out the log. tan. of this sum (rejecting 10), take away the decimal mark. The process may now be completed ariffimetiraHij, thus: — Complete this number to 7 figures by annexing ciphers, or, if the index is 11, to 8 figures, and multiply by 000079157. But it is more convenient to use logs. Consider the log. tan. thus pre- pared, as a natural number, and take out its logarithm. \\'hen the lat. is less than 1.3° 6' prefix the index 5, when between 13° 6' and 78° 34' 44" prefix 6, and when above this last, 7. Add the const, log. 6-898489 ; the sum is the log. of the mer. parts. • By the plane Traverse Table. With the greater arc as a course, and D. Lat. 100, take out the Dist. and Dep. With the other arc a» course, and the said Dist. as D. Lat., take out the Dist.; this is M. With the said Dep. as D. Lat. take out the Dep.; this is N. When the D. Lat. 100 is not found exactly, take out tlie Dist. and Dep. for the next lesa, •n/an)uZa, Tojifoua), Ac, as also Otaheite {Tahiti), in which the o is not, however, absolutely, erroneous. We have sometimes marked the pronunciation by an accent, aa Battanta, Galapagos, Tongafabou, &c. It must, however, always be borne in mind that each different people rails the same place by difl'erent names ; this accounts for the discrepancies in names given to numerous islands. Notation and Details. Everything in parentheses is additional informa- tion (to be explained under the Symbols), but which does not relate to the position. Ex. Col. (30) C. X>li (pk. 1040 f., N I'-S) . . . denotes that there is a pk., &c., but the position is of C. Xyli. Col. (5.i) Ras Gurdiin 1 (rk S.E. 3m.) denotes there is a rock, &e., but the poaition in of Ras Guiilim. Col. (SI) Ft. Sipang, a ik (rks. 511).) . . . denotes a rk. (.awash) otf Pt. S— , and tke. also 5m. out, htit ihe /wsit/on is that of the rock close otF. The seaman must draw no conclusions from the absence of details ; he is not, for example, to infer that a place is safe merely because it is not marked dangerous. Uses of the Table. This Table has, in navigation, two applications : Ist. It furnishes points of departure in leaving and in making the land, under which head arc included, also, islands made in passages, and dangers to b<# 390 EXPLANATION OF THE TABLES. avoided in shaping the course ; 2nd. It gives the positions of ports and anchorages for the more complete regulation of the chronometer. Places, therefore, not belonging to one or the other of these two classes are un- necessary, because, in such circumstances, generally, the ship is either in pilot- water, or is navigated by the chart alone. Lights, however, are inserted in greater number, because a ship in a fog may pass an outer light unseen, and learn her position from an inner 1. Arrangement of the Positiom. It is proper here to describe the principles on which this Table has rOeeu constructed, and to which allusion was made in the preface to the first edition. It will be admitted, as remarked (pref. p. viii), that the relative positions of places are of much greater consequence in navigation than their absolute positions. For no astronomical observations taken at sea can be implicitly depended upon within at least one minute, and the chronometer, in consequence of not preserving exactly the same rate, ceases, after some days, to afford the true longitude of the ship. Since, therefore, the absolute longitude of the ship herself cannot be determined with certainty, the knowledge of the precise longitude of any position, as a rock, or a shoal, which she may be near, is but of little service. But, on the other hand, a tolerably good account of the ship's change of place, in short intervals of time, is afforded by a chronometer even of inferior quality, and hence it becomes of paramount importance that the places which the navigator employs as points of departure should be rightly placed with respect to each other, whether they are in their true positions or not. Previously to Cook's voyages, which may be considered as the com- mencement of modern hydrography, the only method (besides the rude and imperfect determination of the ship's run) of obtaining the longitude of every new land made, was the lunar observation. But as that method, from its inaccuracy, fails altogether in exhibiting truly relative positions (No. 1008), chronometers were employed in combining together the results of observa- tions taken at different places, of which numerous instances are recorded by Horsburgh in his East India Directory. Since, however, the observations made at two places are not in general equally good, this method of com- bining observations with chronometrie differences has the disadvantage of impairing the better determination of the two, and in consequence throws a diflBculty over the connexion of either of them with a third place better known. Succeeding navigators, proceeding in the same way, have ob- tained other results of observation, and other chi-onometric diffeiences ; and, in consequence, the hydrogi-apher who has not the means afforded him of instituting a critical examination of the several positions, or of their connexion with each other, is driven to the necessity of taking a mean between each new result and those adopted from former ncvigators, and thus the whole mass of positions is kept in a state of perpetual fluctuation, from which it is impossible that universal precision can ever be obtained. In marine surveys, again, different meridians have been assumed, and different longitudes of the same meridian. In some cases the long, of the meridian assumed has not been given ; in others, the meridian itaelf has not been specified at all. EXPLANATION OF THE TABLES. 39] If, however, instead of thus throwing open the discussion of every place at each new voyage of discovery or surveying expedition, and un- settling all that had previously been done, without any assurance that the new series of positions would not in its turn be unsettled again, navigators and bydvographers would agree to con.-'idtr, for the time heing only, certain important stations, as already established in longitude, whether really so or not, with the view of referring all the subordinate positions to them, the- imlistinctness which now hangs over absolute and relative position would be forthwith cleared up. The question would be narrowed into the determination of chronometric diffi rcnces alone, until favourable opportunity occurred for the definitive determination of a fundamental position. Accurate chronometric measures would be no longer lost to the world by being merged in the uncertain results of a few astronomical observations ; and the labours of each navigator would always maintain their proper value, in.stead of being set aside, as they must inevitably be, on the appearance of a new survey, in which the data are exhibited in a distinct form. The works of different navigators, and of the navigators of different countries, could be brought into immediate comparison, a task which is at present often difficult and uivsatisfactory, if not impossible. The labours of the hydrographer would be materially .simplified ; and as the points to which inquiry should next be directed would, by this system, be distinctly brought into view, the whole subject would advance steadily to its ultimate perfection. The following instances may be cited in illusti-ation : — The long, of Rio de Janeiro (Fort Villagagnon) had been by some stated to be 43° 15', by others i'S" 9', while both parties adopted 56° 13' as the long, of Monte video (Rat Lsland). Now the true D. Long, of these places is 52™ 18', probably within P or 2% certainly within 4^ ; but the diff. of 43° 15' and 56° 13' is 51" 52'', or an error is admitted on one side of 26' in a rnn of about 10 days. Had attention been earlier directed to differences of longitude as measured from fundamental points, such inconsistencies would speedily have disappeared. Accordingly, it was proposed (Naut. Mag. 1839, On the longitudes of the principal maritime points of the globe) to adopt certain points under the name of >SecunJarij Meridians, this general term being used to distinguish them from the prime meridians, as Greenwich, Paris, &c., from which the longitudes in the tables or on the charts must be reckoned. The longitudes (from Greenwich) accepted for the Secoivliry Meridians, on ivhich Table 10, and the Admiralty Charts now (189S) depend, have been amended from Telegraphic determinations to 1887.* The points selected are so far distant from each other that the errors of their relative positions could not be easily discoverable by the ship's chronometers ; and they must themselves depend on astronomical observations, of which it is important to remark, the number necessary for an unimpugnable determination appears to be very great. The Secondary ^[eridians, with the districts for which they are intended generally to serve, and their adopted longitudes, frmn Oreenwich, are as follows : — the last edition wns 25 : consi Jeriible cor- S93 EXPLANATION OF THE TABLiS Tablk op Longitudes accepted for Secondakj- Meridians. shores of atlantic ocean, and neighbourl^ng seas. Cofenhigeu^Observatori/)- - 12 34 48 E. = 050 192 Kattegat, Coasts of Nor- way ; Sweden. St. Petersburg {Pulkowa Obsei- 30 19 40 E. = 2 01 187 Baltio, White, and Black vatory) Seas. Paris {Observatory) - - - 2 20 15 E. = o 09 210 Coasts of France, West coast of Italy ; Algeria. Lisbon {Dome of Royal Obser- 9 II 10 W. = o 36 44 7 ) „ , ,. „ ,„ valory-)* J tt / I Coasts of Spain and Por- Cfiaiz(SanFernamhObseri-atory) 6 12 24 W.= o 24 496] '"§*'• Pola Observatory - - - 13 50 45 E. = o 55 230 Adriatic. I West coasts of Italy, Malta (Spencer's Monumeul) \ - 14 30 40 E. = o 58 027 j Greece, Sicily ; North ^ coast of Africa. GihrahaT {Dockyard Flugslaff) ® S 21 27W. = o 21 258 Alexandria (Lightbouse) • - 29 51 40 E. = i 59 267 Egyft and Syria. Smyrna {Milton Dariigciz point) 27 09 42 E. = I 48 388 Grecian Archipelago. Constantinople (Si. Sop/»«) - 28 58 59 E. = i 55 559 Black Sea. Madeira, Fnnchal {British Con- sul's House)* 16 54 30W. = I 07 38-0 > MaAeiTSi {Fori St. Jago)* - - i65353W.= i 07 35 6 Azores, Madeira, Canary Madeira (Po7«(iWia)t- - - 16 55 01 W.= I 07 401' and Cape de Verde Porto Grande, Cape Verde Is- - islands ; West coast lands {Flagstaff in front of I of Africa to Fernando Brazilian Submarine Telegraph Po. Co.'s Office)* . - . 24 S9 22W.= I 39 57S/ Newfoundland, St. John's (C^aiH 52 40 47 W.= 3 30 43-1 Newfoundland and La- Rock Battery) brador. Halifax, Nova Scotia {Naval 63 35 21 W.= 4 14 21-4 British North Americii Yard Observatory)^ and Canada. Boston, United States (CumAr«fye Observatory) 71 7 39 W. = 4 44 3061 Key (Cay) West, U.S. Nav.il ' United States ; North Storehouse {Observing Spot)\\ 81 48 24 W. = 5 27 136, America. Key (Cay) West {Liyhlhouse)\\ 81 48 04 W. = 5 27 12-31 » U.S. TelcKraphic determination in 187S-9 from Greenwich. Published by U.a Government, 1880. t Telegraphic determination, 1875, from Berlin, by Professor Auwers and Dr. Gill © Telegraphic determination from Malta by H.M.S. Sylvia, 1886. J Depending on being i' 8" west of Fort St. Jago by chart. § Telegraphic determination in 1851 and 1872 from Washington, and from Greenwich. II U.S. Telegraphic deterjninatlons in 1875-6 from Washington. Published by V.S. GovernmeDt, 1877, No. 65. EXPLANATION OF TUE TABLES. 3W Vera Cruz (San Juan ile Ulha Litihtlivuse)' 96 07 57 W. > 6 24 31 8' Havana (.J/ono /,i;;/(//i(iii.sc)f - S2 21 3oW,= 5 29 260 Santiago de Cuba ( C/uhcu tfu^ ten/. South a!iglf-)j 75 50 30 W. = 5 03 220 Port Roj-al, Jamaicn (Fort CA(.r/e.s)t 76 SO 38W.= 5 07 225 Aspinwall {Aspinwatl Light- home)] 79 54 45 W. = 5 19 39 o San Juan de Puerto Rico (3/orro Liyhi/wiise')\ 66 07 2S W.= 424 29-9 Virgin Islands, St. Croix ( /,«». Telegraphic determinations in 1875-6 from Washingto Government, 187 7, No. 65. X U.S. Telegraphic determinations in 1878-9 from Greenwich. Published by U.S. Government, 1880. § Telegraphic determinations in 1881, by Dr. Gill from Aden. II Telegraphic determination, 1881, by Dr. Gill from the Cape of Good Hope. *" Telegraphic determination, India Trigonometrical Survey, 1878. •* Transit of Venus expedition, 1874. tt Transit i>f Venus expedition. 1874 (meridian distance from Rodriguez^ 394 EXPLANATION OF THE TABT.ES. „ , „ h. m. 3. Madras (OJsem(/o(;0* - - So I4 51 E. = 5 20 594 Bay of Bengal. Andaman Islanils Port Blair (Ob»ervatory, Cliathnm hd.^ 92 43 00 E. = 6 10 520 Andaman Islands. JAVA, CHINA, AND JAPAN SEAS. Batavia (Oiierra/o;;;/)! - - 106 4S 37 E. = 7 07 14-5 W. Coast Sumatra, Jaf* Eastern Archipelago. ISanjuwangi (fori i/<;cc/iOt - 114 22 55 E. = 7 37 317 Adjacent islands. Singapore! ( Grtra's transit pier 103 51 15 E. = 6 55 250 Malacca Strait, South in rear of Muster Attendant's part of China Sea, Pala- Office-)\\ wan. Cape St. James {Lighthouse)\\ - 107 04 55 E. = 7 08 19-5 Coast of Cochin China. Manila iCatlieclral)\\ - - - 120 58 06 E. = 8 03 52 4 Philippine Islands. Hung Kong ( Oirficrfra/)!! - - 114 09 31 E. = 7 36 3Sl', Hong Kong (_Obser»ulury Kau- lung) 114 10 25 E. = 7 36 417 I Coasts of China. Hong Kong (Pulos Pier) - - 114 09 43 E. = 7 36 388 \moy {Kulunqseii Signal StafTfW 118 04 03 E. = 7 52 l6-2 Shanghai {British Consulate FUig- staff)\\ 121 28 55 E. = 8 05 557 Yellow Sea and Korea. Vladivostok! (Scharnhorst's Sta- tion) 131 52 44 E. = 8 47 310 Russian Tartary. Nagasaki (iWina^e Po.nO II - 129 51 13 E. = 8 39 249 ^ Yokohama {Flagstaff' English. [ Japan. VictuaU'iiig Depoty^ 139 39 13 E. = 9 iS 36-9' AUSTRALIA, TASMANI.\, AND NEW ZEALAND. e-ya-aey {Obserralortj)*!, - - 151 12 23 E. = 10 04 49 5 1 Australia and adjaceni Hydney {Fort Macquarie)** - 151 13 00 E. =10 04 520) islands. Sloreton Bay {Cape Morelon Lighthouse)]^ 153 28 CO E. =10 13 52-0) ■ro^vt,sme{Flagsl„JfPiUHill)B 146 49 54E. = 9 47 19-6 r)„,_„,.„. Cooktown {Boatshed at inner end [ U"i^'^°siand. of Jetty, Pilot Station)® 145 15 12 E. = 9 41 OO'SJ Cape York {Sextant Hock) - 142 32 48 E. = 9 30 092 ) Samarai {Dinner I.) China Strait {Observation spot)(p 150 39 47 E. =10 OJ 39'I j Port Essington {Site of old Go- \ rcniment House) 132 09 iSE. = 8 48 372 ' North-west Coast of Port Darwin {Transit pier, east '' Australia. extreme of cable House)'^ 130 50 37 E. = 8 43 22-5 I Swan River (5'TOtt'i,/e//.y)ft - 115 44 30 E. = 7 42 580 West Australia. Adelaide (Snapper ;«)/«n J j - 138 30 50 E. = 9 14 034 South Australia. PortPhillip(Me/4ou™e06ie)V.)jJ 144 58 32 E. = 9 39 54-1 Victoria. • Telegraphic determination, India Trigonometrical Survey, 1878. f Telegraphic deterniiiiation from Singapore by Professor Oudeni.ins in 1871, adojit- ing U.S. determination of Singapore, 1881-2. J Telegraph determination through Singapore and Port Darwin (in connection with Greenwich), in 1 S83. Communicated by Mr. Ellery, Government Astronomer at Mel- bourne, in letter dated J.tnuary 8, 18«5. § From Green's transit pier the old Observation spot in FuUerton battery, Singapore, bears S. 5° 37' W. (true) distant 169 foet. li U.S. Telegraphic determination, 1881-2.. Published by U.S. Gov., 1883, No. 65b. f Telegraph determination through Singapore and Piirt Darwin (in connection with Greenwich), in 1883. ** Depending on Fort Macquarie being 47" E. of Sydney Observatory on chart. tt Depending on Fort Macquarie, Sydney, being in 151° 13' 00" E. ffi Telegraphic determination from Sydney by HM. ships Dart and Lark, 1886. * Meridian distance from Townsville, H.M.S. Dart, ISiC. il Telegiaph determination through Singapore and Port Darwin (in lireenwich), in 1883. EXrr.ANATlO!^ OF THE TAlU.Kb. 396 TaiiinaBiB. Hobart ( Site of Fori MulgiaveY 147 20 35 K. = 9 49 225 TasmaniH. New Zealand. Wellington (Pi- piteapoiul) 174 47 02 E. =11 39 081) New Zealand. Ml. Cook (0/<- l New Zi-alana. wrv,iL,ri,)f 174 46 38 E. =11 39 06-5) TACIFIC OCEAN. f^vnks, Oralau (Site of r.U 178 51 00 E. =11 55 240 Fiji Islands, South- vresl School-house) Pacific Ocean. Tahiti (Point Venus extreme) - 149 29 00 W. = 9 57 560 South-east Pacitic Ocean. Honolulu (A'i«3"s C««.'(/e)t - 157 5' 53^V. = io 31 275 North Pacific Ocean. F.squimalt harbour ( Dun/:e flem/, 123 26 45 \V. = 8 13470 Vancouver Island and site of Obse> vittonj) British Columbia. San Irancisco (port Poi«( Liyhl- hoHse, south side of entritnce)l 122 28 38 \V. = 8 09 545 California. San Salvador, La Libertad (Fier hend)% 89 19 22W.= 5 57 175, Mexico -md Ftu-idor Panama {Cathedral, Southtower)\\ 79 32 12 W. = 5 .8 088 f *^""-'' ''"'* l-'^fS'l'"-- Vaaama (JVortJi-ecist bastion)\\ ■ 79 32 03 \V. = 5 18 082, I'Mta iCalhcdriil touier)^ - - 81 07 I7\V.= 5 24291 Lima (1S0U//1 fo««- 0/ Calheilral)S, 77 00 02 \V.= 5 08 106 1 Callao(San Lorenio Lighlhoitse^ 77 15 44 W. = 5 09 029 V Arica {Church spire, lijletiu Malrijr)% 70 20 00 \V. = 4 41 200 Valparaiso (C«/)o/a ofExchange)% 71 38 36 \V.= 4 46 344' Magellan Strait, Sandy point {Bmtt-housc)^ 70 54 03 W. = 4 43 3621 Magellan Strait, Port Famine \ Magellan Strait. {Fitz linn's Ob$. spot)" 70 56 37 \V.= 4 43 .^65) West Coast of Soi;th America. MtTidi((ns adopted in the construction of Foretyn C'karU. Russia, Sweden. Denmark, Norway, Holland, Austria, and the United States o< America adopt the Meridian of Greenwich. France adopts the -Meridian of Paris, assumed to be in Long. 2° 20' 15" = 0'' 09" 2I'0' E. of Greenwich. Spain adopts the Meridian of San Fernando, Cadiz, assumed to be in Long. 6° 12' 24" = o"' 24" 49-6* W. of Greenwich, or 05' 22" E. of Old Observatory. Portugal adopu the Meridian of the Observatory, assumed to be in Long. 9° 11' 10" ■=0^ 36'" 447- W. of Green wich.ff Thi; Pulkowa Observatory of St. Petersburg (sometimes referred to in Russian Charts) is assumed to be in Long. 30° 19' 40" = 2'' I" 187' E. of Greenwich. The Royal Observatory of Naples (sometimes referred to in Italian Charts) ii assumed to be in Long. 14^ 15' 7"'3 = o'' 57" 00-5' E. of Greenwich. • Transit of Venus expedition of 1874. f Telegraphic determination from Sydney, 1S83. J U.S. Telegraphic determination in 1870 from Washington. I U.S. Telegraphic detcrmiuations, 1883-4, from Washington. Published by U.S. Government in 1885, No. 76. II U.S. Telegraphic determinations in 1875-6 from Washington. Pub.ished by U.S. Government, 1877, No. 65. ^ From Professor Auwers (German Transitof Venus expedition), 1882. Bymeridian distances measured in H.M.S. Nassau, 1866-69, from Kio de Janeiro (Fort Villegagnon being considered in 43° 09' 29" W.), the longitude of Sandy Point is 70" 54' 06" W. By meridian distance measured in H.M.S. Si/lvia, 1882, from Monte Video (Kat Island being considered in 56° 14' 00" W.), the longitude of Sandy Point is 70° 54' uS'- W. •• Depending upon Sandy Point, being i;i 70° 54' 03" W. ft The longitude of Lisbon castle deduced Iroin the U.S. telegraphic longitude of th< fjdhon Royal Obscrvatorv (in 9° 11' 10" W.) is 9° 07' 55" W 896 EXPLANAHON OF THE TABLES. [I.] Sijmhoh denoting the Values of the Determinations. The symbols 6®© attached to certain places, indicate the degre* of precision with which their positions are supposed to be known. The circle represents the horizon of the place ; the line thus — a parallel of latitude; and the line thus | a meridian. Accordingly, the meaning of the symbols, generally, is as follows : — 1. O implies undetermined either in lat. or long. 2. 9 implies determined in latitude only, or the longitude wanting 3. CD implies determined in longitude, or the latitude wantinc;. 4. ffi implies determined both in latitude and longitude. A dot under the O \mf\\es aggravated uncertainly. As very few places are determined in the strict sense of the wed, while, on the other hand, no known place can be said to be absolutely undetermined, the sense attached to these two words must be defined by the purposes which the symbols are intended to serve in hydrography or in the navigation of a ship. The different degrees of determination are indicated by the position ot the symbol. 1. The symbol O denotes a donbt of not less than 2' of lat., or some- what more of long. It is used when the authorities differ from each other, or themselves : thus Capt. W. F. W. Owen places Cape Nun in 28° 41' N., and Lieut. Arlett in 28" 46', the long, not being well known. This symbol placed after the name in the side column denotes that the district generally is imperfectly known, as parts of the Eastern Archipelago. 2. The symbol 6 indicates the latitude well enough determined for ordinary purposes, but the longitude defective. It occurs frequently, 3. The symbol ® occurs rarely. 4. The symbol ® after the name ot a, point, implies a tolerably precise determination. It would have been prefixed to Pulo Aor, col. 67, but this island is 2 m. from E. to W., and the precise point of observation is not specified. When placed after the name in the side column, it implies trigono- metrical survey, subject to future, though probably small, correction ; as, for ex., parts of our own coasts, the coast of Holland, Iceland, Greece, Italy, India, Corsica, R. St. Liwreuce, Massachusetts, Rhode I., &c. When placed before the name in the side column, it denotes final determination. The coasts so distinguished are part of our own, and it should have been attached to France. This final characteristic cannot obviously be applied until the secondary meridian is fixed.* When no symbol is attached either to the district or to the points of * The attention of seamen is particuhivly called to the considerations in the 'ext. By having distinctions established, in the Table, between correct and uncertain positions, the navigator will have his circumspection awakened on approaching land of doubtful situation ; and on leaving it again he will be enabled to avoid erroi-s or perplexity in hii reckoning consequent on adopting an erroneous point of departure. It is also hoped that a further important end will be answered by the use of the pymbols, and t.sat intelligent individuals, thus made aware of the deficiencies or error* «f the charts and tables, will, for the benefit of navigation and hydrography, aviiiltliem- lelves of opportunities to determine or verify doubtful positions. EXPLANATION OF THE TABLES. J597 the coast, it is implied that we are not in possession of such additional evidence as might serve to form a definite opinion on the accuracy of the several points. The Secondary Meridians take no symbol, since, though not all finally determined, they are assumed as the leading points of the arrangement. 2. DescriptioH-Sijmhols. The importance of abbreviations and symbols in saving time in writing is so generally felt that most persons who write much, habitually employ certain signs, intelligible to themselves, to save the tedious repetition of the same letters and syllables. Suitable and expressive symbols are, however, not merely a conve- nience to the writer, but afford, in general, the advantages of distinctness, e.xplicitness, and economy of time to the reader, together with another oi etill greater consequence, namely, certainty. This last assertion will not, perhaps, be so generally assented to as the former, but the truth of it is easily established. For example, a seaman in any particular part of the world opens a book to learn where he may find a good anchorage. His eye naturally looks for the word "anchorage " or "anchor," as it would for a sign or symbol. Having found the word, he is then obliged to read tlie entire sentence which contains it, in order thoroughly to comprehend the meaning ; since, without a clear understanding of all that is said about anchorage, it is not safe to act. Now this sentence, though it relates, as we suppose, in some way to anchorage, may not contain at all the information that he requires; it may, for example, allude to some ship having partially or unsuccessfully searched for an anchorage, or it may merely intimate that no good anchorage has been found between some place in the neighbourhood and another more distant. Moreover, it is often difficult, from the arrangement of the matter, to know the precise point the account refers to, without reading back. If, on the con- trary, the reader's eye catches the symbol *, or this symbol so modified as to express with clearness " no anchorage," or " good anchorage," or " bad anciiorage," or " anchorage at times only," or " confined to a small space," his work is done at once ; he seizes in an instant the information that is given, and his mind is altogether unembarrassed by circumstances of narration, or the consideration of suppositions, inferences, and condi- tions, which often tend to obscure language in full development. There are numerous other matters which, on like grounds, demand conspicuous indication : such as the dimensions of islands and shoals the leading particulars of dangers ; the chai-acter and appearance of land, for the purpose of distinguishing one point from another; the class of vessels to which a harbour is adapted ; channels ; landing-places ; as also notice of water, refreshments, and fuel, &c. But, besides the mere notice or indication, it is often no less necessary to denote qualiti/, or character, as good or bad ; thus the seaman should know whether the inhabitants of a place be may visit are likely to assist 1 is wants or to massacre bis crew ; that is, whether the character of the people is friendly or hostile. The consideration of quantitij has a powerful influence on the indica- tions of language. One place has some trees upon it ; another is well wooded ; another densely wooded. It is entirely by increase of quantity that we pa.s8 Liom trea to wood, uud from v:i)ud to fi/rest. In like manner, 398 EXPLANATION OF THE TABI>ES. it is no less the abundance than the superior quality of the water, refresh- ments, &c., that determine the selection of the place at which to obtain supplies. The following cases exemplily the great conciseness of expression and clearness of symbols which iicay be considered as appropriate. ffi'j' A harbour for smaller sized vessels (t.e. of which the depth is not always so much as 3 fathoms) having 18 feet water at high water, and 6 feet at low water, spring tides. The symbols represent twenty words, in the space of two or three letters, besides indicating the rise of the tide, which is found by sub- tracting the lower depth from the upper. S" A harbour (as above), having 18 feet at high water, and dry at low watei. These symbols represent eighteen words. w' Water, in abundance, and of good quality. jP4m. Lying North-north-east and South-south-wtst, and extendiitg 4 mile«. The last symbols represent twelve words ; and the compass symbol exhibits to the eye, without reference to the names of the points, the two opposite quarters of the compass in which the line of direction is con- tained. The reader must be distinctly iuformed that the symbols do not, in any way, interfere with the usual purposes of this Table, and therefore he may, if he please, disregard them altogether. He will, however, never do wrong in taking any known sign in its usual sense, as those symbols and abbreviations which have come into general use are here adopted as the groundwork of the system. The seaman who may find some little difficulty in learning to read these signs at first, may wish that the information they contain was printed at greater length. But there is no room for this, as the Tables are already too bulky ; and it is only through the remarkable condensation aflPorded by the symbols that such informa- tion can be given at all. But when he has once taken the trouble to learn the system, which he will find veiy easy, he will, on the contrary, be induced to prefer the short and concise, positive, and unmistakable symbol to the tedious, indiscriminative, and not seldom obscure process of language written at length. There is no doubt that proper symbols would be of great advantage to seamen in consulting books and tables relating to Maritime Geography, and also Charts ; and we shall now enter on the system of which the first steps occurred to me while preparing the second edition of this work m 1841. [1.] General Rales for the Emploijmeut of the Symbols. 1. An abbreviation, or an appropriate symbol, is assigned to each point of information ; as It. light ; * anchorage ; w water.* 2. A zero, or cipher, below, and to the right, denotes 7io, or none ; aa Wo no water, St o no anchorage. Note. — This zero is of as much consequence as I lie symbol itself, and is the only Becondary or subordinate sign that is so. It may, at first sight, seem awkward to write the symbol, and then to destroy it, as it were, by the zero ; but it is the neee^sary jjro- cess of thought : when we wish to say " no water," we necessarily direct the mind to water as the subject, and then add that there is none of it To leave out the symbol altogether would not e.\press the privation of the tlnni/, but merely that we had nothing to say upon it. * In employmg these signs it is essential that capitals and small letters should not be confounded. EXPLANATION OF THE TABLES. 395/ 3. A. symbol inverted bas it« meaning reversed : thus the boatliook, k landing, inverted, as 1, would denote embarJcing. 4. A hollow letter implies temporary or occasional, in opposition to the solid letter implying pennauent ; thus F (after It.) denotes a permanenl fixed It. ; Fan occasional fixed It. 5. The symbol repeated denotes the same thing at il ifferent places, or not everywhere ; as **, anchorages, in certain places. 6. A symbol followed by the same with the zero sign denotes at times; as wwc, water at times (literally, water and no water). iVofc.— This is, in general, equivaleni to the hollow letter above j bat all symbol" cannot conveniently be printed in tlic hollow form. [2.] Cvmpnnent Siyne. These are used only in combination with others. 1. The line — denotes the surface of the sea ; everything above this is, accordingly, conceived as above the level of the sea, and below it, below that level : as li. a rk. always aluve the surface ; rk. a rk. always below the surface, i.e. sunken. A symbol between two such lines, that is, between two levels, denotea .iwash, as eS. Such is, for example, the Vrach, off Alderney, which shows only at low spring-tides. 2. A line thus | denotes vertical. 3. The cross +, with a number denoting the point in the proper (juarter, constitutes the Compass Symbol ; thus -f denotes ENE. The cross with the N. pt. turned a little to the right would denote magnetic, as aflFected by Easterly Variation ; turned to the left, as affected by Westerly Variation. 4. A square, or oblong, implies enclosure, whether partial or total; as ffl, an anchorage enclosed, represents harbour. 5. Brackets [i] imply within Uvvits ; as [$] anchorage confined to a natrow or limited space; [2] a shoal patch, with 2fms. on it, that is, 2fms. confined to a small space; [t] trees confined to a small space, a clump. When a letter denoting dimension (as c, f, m), with or without a number, and inserted in brackets, follows the word Id., or a term de- scribing a danger, it indicates extent; thus [Im], "within the limits of 1 mile," that is, extending 1 mile, [c] A cable's length, or so, in extent. [3c] Three cables in extent. [.3.] Sulisidiury Sign: These are the dots under, the apostrophes over, and the accents or letters to the right of, the .symbol. JVofe.— The subordinate signs follow, and never precede, the symbol They denote, 1st, Quantity ; and 2nd, Variety. I. The quantity-signs are the dots and apostrophes. (1.) The dot (below) denotes plenty, abundance ; as w plenty of wafer. The dot has this acceptation in the weather symbols, p. 156. Two dots denote a greater abundance, and three dots express the highest degree for which language has a term : thus f a tree or trees ; one dot would denote many trees; t wood (well wooded), and three dots would denote forest, or densely covered. (2.) The apostrophe (above) implies scarcity; as w water not plentiful. This sign is adopted from its use in contractions, as in su^h words as 400 EXPLANATION OF THE TABLES. can't ; whence it becomes associated with the idea of diminution. It is placed above in order still further to contrast with the plenty-sign or dot, and to prevent the possibility of confounding one with the other, even in the case of almost total obliteration. Two apostrophes would denote great scarcity, and three, the almost entire absence of the thing indi- cated. II. The variety-signs are the letters, accents, or any other symbols as convenient, to the right of the symbol, and above or below it. (1.) The most general of these is the accent, which denotes some variety of the thing symbolised : thus N, S, E, W, denoting the true points of the compass, N', S', E', W, denote the magnetic points of the compass.* (2.) In things having quality, that is, which may be good or bad, the accent is placed ahove to denote superior, or good quality, as opposed to inferior, or had quality, denoted by the accent helow ; as w' good water, w, bad ditto ; *' good anchorage, *, bad ditto. Two accents would denote the next, and three the highest, degree for which language has a term : as w" water very good, w"' ditto excellent; Xii anchorage very bad, *,,, the worst possible, or where a ship should anchor only in great distress. (3.) The letters used for these secondary distinctions must obviously take their signification from the thing symbolised, and likewise their position above or below : as w" river water, good ; or w^ ditto, bad. P, people run (from ships), who are, generally, the worst characters. As the subsidiary signs are independent of each other, any number of them may be employed at convenience : as ^' water scarce, but good ; w, water scarce and bad ; ^ n water by digging, in plenty, but very bad. The notation is thus comprised in a primary or class symbol, a quantity- sign, and a variety-sign. The vacant spaces following the names of places being, by this plan, turned to account, much important information is inserted without in- creasing the size of the volume. f It is also proper to observe that, as the signs represent ideas or things, and not words (with a few excep- tions), the system is independent of any particular language. The abbreviations and symbols used in the Table are, for reference, alphabetically arranged in the following " A special notation for this purpose is much requireci. In Purdy's "Sailing Direc- tories," both the magnetic and the true bearing are given in order, as "the bearing and distance of the Capes Teulada and Malfatan are E. | S. [E. J iV.] 8 miles." Here E. J iV. refers to the true compass ; but tliis can only be known by referring to the notice at the beginning of the book, unless the reader is aware that the variation at the place is westerly. The italic letters are already required for those passages in which, from the importance of the remark, the whole sentence is italicised ; but the notation E' I S' presents every advantage which a notation should possess : it is perspicuous, un- equivocal, concise in the extreme, and elegant. We must be careful to accent all the letters : thus N' E', not N E' ; for this last com- bining true N. and magnetic E., presents no idea whicli occurs in practice. A second accent denotes, furtlier, local deviation, as N"E", which shews, at once, that there are two corrections necessary to reduce it to true NE. This notation wouhl remove much of the difficnliy which often arises in endeavouring to combine bearings taken under different circumstances. This notation need not, from the nature of the case, appear in ships' logs. t It is no part of our design to enter all information which can be conveyed in symbols. A few leading points have been inserted where it seemed advisable) th« reader must refer forother details to the Sailing Directions, or to voyages. The symbols, however, will answer the further purpose of affording the means of making extracts, or of taking notes, of certain particulars, in a very small space, and in a very short time. EXPLANATION OF THE TABLES. 401 General View. 9 (Anchor) Aiifhoragefor large vessels. $ ' good do. $ , bad do. $o no do. a do. for smaller vessels. i' good do. T, bad do. g Harbour for large vessels, or having always 3 fathoms water. [B Harbour for smaller vessels, or having at times less than 3 fathoms. The depth at H.W. and L.W. springs is denoted by the figures annexed above and bilow. Ex. l.[Itg.20ft.atH.W.aDdl2ft.atlow. Ex. 2. ffi'o". left, at H.W. and dry at low water. When the depth at high water, of a harbour which dries iit low water, is not known, it is ex- pressed (for the present) by the letter n, implying some number not given ; ex. Stonehaven, [2° Note. — In cases in which these details are not well known vacancies are left, which will be filled up on a future occasion. t Ball. ♦ l'. Time ball dropi ed at 1 p.Ji. bk. Bank B. Bav. bll. Bell. A/, blue. 6/A. black. ->- Birds. As birds frequent some places in preference to others, they may afford a means of identification. [, (Boathook).— See Landing. T Bold to.— See Component Signs, 1, 2. [ ] BnicketB — See Component Signs, 5. 3 Break, or breakers. $$^ do. at timet. »■ Brushwood (a tree without a trunk), h Burn {or/uel). (E (fuel enclosed), a coal depot ; coaling station for steam-vessels. On some of the shores of the Polar Sea, and elsewhere, b denotes drift-wood. In some places peat, as at New I. Falklnnds. Where trees oi brushwood occur, the symbol b is omitted, as, though many woods do not burn when green, fuel may be picked up io sach place*. -i^e Table II C. Cape. Cath. Cathedral, c. Cable's length. ! (Note of admiration surprise), danot?» Caution, or rails attention, aa Current ! II Channel, or passage, passages. II II Several channels ; ||35, chan. with 35fms.; H^ no channel. At a river the symbol relates to the entrance. Chap. Chapel. Ch. Church. El Coal depot. I Cocoa-nut tree, or trees ; f f 1 a clump of cocoa-nut trees ; :^ [t] two clumps do., and so on. Compass symbol.— See Compoii. Signs, 3. crl. coral. 5 Danger, dangerous ; 55 dangerous in different places. 5(, (no danger) safe, d Days. Depth of water, denoted by the no. under the mark — , as ( four fms. ; 3 f , 3 feet. The depth is that at low water. The depth relates to the bar, where there is one. Distance is expressed in leagues, or miles ; as C. Lookout, rks. 1 I., implies rks. 1 league from the Cape ; 5 2m., dan- gerous 2 miles out ; 5^, |m., no dan- ger, may be approached within i a mile ,5^ic.,safe at iacable distance; S -|4 2 1. a danger NE. 2 leagues. Dk. yd. Dockyard. Dry, or above water. — See Comp. Signs, I. E East. E' magnetic E. Entrance. — See Channel, extr. Extreme, extremity. F after a light, denotes that the flame has a fixed, not a changing appearance. —See It. F denotes a It. (flame) of a fixed cha- racter, but only shewn orcasionallr —See General Rules, No. 4, p. 399, Fl. after a It. denotes flashes. — See It. fl. Flag. fl. St. King-staff. Hd. Head. D n 402 EXPLANATION OF THE TABLES. A High. ho. house. hum. hummock. I. Island. The compass-syrnhol after an island shews the direction, or lay. of the longest diameter, and is followed by the length of this diameterin leagues, miles, or cables. Ex. 1. % 3m. denotes NNW. and SSE. (true), and extending 3 miles. Ex. 2. EVV 6im. denotes lying E. and VV. (true), extent 6^^ miles. Note.— These bearings are'all TRUE. The bearing, though given to 2 points only, is near enough for the pur- poses required, as it can be in error only 1 pt. The distance is noted with more or less precision, accord- ing to the case, and is not always to be taken as an exact measure. When the extent is very small, the bearing or direction is omitted ; as Rcckal, [2c.], or 2 cables in extent. I after a liyht, denotes intermitting.— See It Is. Islands. The compass-symbol and dis- tance following shew the extent and general direction of the group, as described above in Id. The number after Is. denotes the number in the group, as Wallis Is. 9. I, Landing (a boathook, the hook to the ground) ; [^ no landing ; H^ land- ing at times ; [,' good do. ; l, bad. L Leagues. When a number of leagues follows next to the name, il denotes the number of leagues tho place is visible— as Tiger I. 17 1., denotes Tisible 17 leagues. When the 1. stands next after a compass indica- tion, it implies of course a distance measured in the given direction ; as U. ^ 5 1., islands NW 5 leagues. I low. It. light. The capital letter next after the light denotes the character of the flame, as F fixed, I intermittent, E revolving, Fl. flashing or varied by occasional flashes, or rapid change in the intensity. The number of feet (which stands the last among the particulars of the light) denotes the height of the lantern or flame above high water. Where this is not known, the range in miles is inserted. When a It. stands on a summit, the ab- breviation sum. is inserted ; when, therefore, sum. does not appear, the It, however high, is usually not on the summit. Hi. The compass indication and no. of feet next after 2 Its., denute their bearing and dist. asunder — the spec- tator looking at ihem from the sea ; thus, the Lizard Its., lying N72°E and S 72° W, are seen in one, fronj a ship to the westward, or loward* the ocean, in the direction N 72° E Note.— These bearings are all TRUE, and they are intended to adord a means of determining the state of the compass when the ship is in « line with the 2 Its. in one. m. miles. After a shoal or danger, denotes tho distance ; as rf. 3m., a reef 3 milef distant. mid. middle. Mk. or mk. mark. mo. mouth. Mt. mount. N North. N' magnetic N. f Palm-tree. ( ) Parentheses, contains extra or adJi- Passage.— See Channel. Patch. — See Compon. Signs, 5. Penins. Peninsula. P People — or peopled. Po Uninhabited. P' People of favouTable character. Py — of unfavourable do. pk. Peak. Pt. Point, being part of a name, a-; Hart- land Pt. pt. point li River. After a It. denotes recolviTitif. r red. rf. Reef. _ rf, rf. always dry ; rf, rf. always co- vered ; r¥, rf. awash, r Refreshments, that is, ve^'etables, fruit, and moat. As fish is often procurable where there are neither vegetation nor inhabit- ants, it is expressed by the separate symbol f, denoting r under the _^ Rising gradually. _>:i- Rising in the middle, as I. Fuerle. rk. Rock. __ rk, dry ; r2, sunken ; rk, awash. The number under a Hue, a 2. denotes the depth in fras. over a sunken rk. rks. Rocks; a compass indication, with a number of miles or cables, denotes the extent as described under Island, rky. rocky. S South. S' magnetic S. i^_^ Saddle-shaped, as Huafo I., a valley.— See Sloping, Rising, sd. Sand, or sandy. This quality is noticed occasionally, as sand often atforiis water, it is used in cleaning, and turtles lay their eggs in sand. EXPLANATION OF TABLES. 403 •hi. Shoal. A compae* indication with m. i.r c, denotes the extent. — See Is- land. The number under a line, standing next after shl. denotes the depth of water over the shoal, as Ridjje 5. Bboal patch. — See Compon. Signs, No. 5. ^ Sloping downwards, as Gdoso Cape. i^ i Sloping down to a bluff. T Sloping bottom, or change of soundings gradual, may be approached with safety by attention to the lead. Big. St. Signal staff, or station. X Steep, or precipitous (not absolutely vertical).— See Component Signs, 1,2. Note. — This is quite independent of high. A headland may be low yet precipitous. T Steep to. St. Saint. Sta. Santa. Tel. Telegraph. * Tree, trees ; [ t ] a clump of trees i 2 [f-] two clumps; 3 [^] three clum|js. ^ well wooded. ♦ (A tree without a trunk), brushwood. Vert. Vertical. W West. W magnetic West. w Water (for drinking), w' good do., Wj bad do, w^ no water, ww^ water al limes. w do. (under the surface) to be got bj digging. The bearing and dist. following the w point out the place with reference to the jiosition given, as Koron w' N. 2m. denotes good water North 2m. of Koron. ic, wh. white. The following examples exhibit the method : — E,\. 1. Island, ^j* 7m., A, * „, U^E, % ' SW s, w'r,,, P,. An island li/ing NE and SW, extending 7 miles ; high; no trees; no passage to the eastward; a good anchorage on the SW side in S fathoms; where wurer, scarce, but good, is to be found, but tio other refresh- ments ; the people of bad character. Ex. 2. Paddeway Bay. g [5m.] w, r, 5^. A liarbourfor large vessels, extending 5 miles, having lo fathoms water ; refreshments to be had ; no dangers. Ex. 3. Shoal, \ 4m,, rk. at'NW end, ^^^. J, [,„. A shoal, lying WNW and ESE 4 mites j a loci always above water at the NW end, the occasional resort of birds, bold to, and no landing on it. Ex. 4. N. Watcher, small, *, (Omega Shis. E'bS' >., 5, T) It. B. 159f. N. Watcher, small, well wooded. Light Revolving 159 feet high. Omega shIs. lie EbS magnetic, ^ni., are dangerous, and steep to. Ex. 5. Guaso or Kenn I.. ^ 8ni. /, f , 7" . r, w, ?,. Low, covered with trees, or wooded, soundings gradual, refreshments, water to he obtained by digging, people ot bad character. 3. Lights, Characteristics, &e. The lights shewn in lighthouses are divided into several classes, Fixed, Flashing, Revolving, Occulting, and Alternating (seep. 925). Thefixed light maintains the same appearance ; the other classes change, some alternating by slow degrees between bright and dim, some flashing more or less suddenly, and others varied by eclipses. Colour is also employed partially as a means of distinction. Lights axe distinguished from each other also by the flirterent intervals of time in which the changes succeed each other.* It is to be borne in mind that every light which varies its lustre is liable, when seen from a distance, to become altogether invisible during the period of lesser brilliancy ; that is, a revolving light may seem to be eclipsed. Also, elevated lights are often entirely obscured by clouds. As objects painted white frequently disappear in fog, while objects of a red colour remain visible, buildings serving for marks are often painted with red and white stripes, or bands. • Seamen are generally content with the mere fact of revolution or intermission, and do not trouble themselves to measure the interval. This, therefore, is an occasion on which it is very useful to be able to count seconds, for all persons do not carry seconds wafj-hes, and it is not always possible for the same person to hold the watch to a lamji «nd to see the light at the same instant. 404 EXPLANATION OF THE TABLES. The lighthouse, or building, being useful as a guide by day, many lighthouses are accordingly painted in order to answer this second purpose. All the distances given in the Admiralty Light Lists and on the charts for the visibility of lights are calculated for a height of an observer's eye of 1.5 feet. The table of distances visible due to height, at end of each Light List, aftbrds a means of ascertaining how much more or less the light is visible should the height of the bridge be more or less. The glare of a powerful light is often seen far beyond the limit of visibility of the actual rays of the light, but this must not be coii- founded vt'ith the true range. Again, refraction may often cause a light to be seen farther than under ordinary circumstances.* The power of a light can be e.stimated by remarking its order, as given in the Light Lists, and in some cases liy noting how much its visibility in clear weather falls short of the range due to the height at which it is placed. Thus, a light standing 200 feet above the sea, and only recorded as visible at 10 miles in clear weather, is manifestly of little brilliancy, as its height would permit it to be seen over HO m. if of any power. The Admiralty Light Lists, corrected yearly, should always be con- sulted as to the details of a light, as the description in the Sailing Direc- tions may be obsolete, in consequence of changes made since publication. 4. Compass-names of Points of Land. Navigators and hydrographers have not hitherto adopted any constant rule in the application of compass-names to the projecting angles of land. Thus, Krusenstern says (Mem. Hydr. ii. p. 283), " The north point of Owhyhee, which Vancouver calls the west point," &c. This extreme diversity of expression establishes the necessity of a systematic employ- ment of such terms. The north point of an island may be considered, 1. as that point which is to the northward of the middle or body of the island ; or, 2. as the northernmost or extreme north point. In a circular island both terms agree, but in irregular forms they are ambiguous ; thus Krusenstern calls the S. extreme of Atooi, " the S.E. pt.," probably from its position S.B.-d of the body of the island. It will, perhaps, be admitted, that, in a purely practical subject, such n • It is not unlikely that a liglit ni.iy be found sufficiently powerful, by the addition of a proper reflector, to illuminate the clouds, and, in a fainter degree, the atmosphere itself, over a lighthouse. The pale light in which a distant town appears enveloped at night i the distinctness of the forms of tlie clouds over a large city, illuminated by it* ordinary lamps ; and the vivid glare diffused over the heavens by a fire, show that the atmosphere renders the reflected light visible at a considerable distance. It is merely ;i question of intensity. If a sunbeam were admitted through a hole in the earth in a dark night, it would appear in tlie atmosphere as a column of astonishing splendour. As the light suggested would have a conical or shaft-like appearance, and would exhibit no flame, its proper designation would be a shaft-light. The shaft might, by the disposition of the reflector, be vertical, or inclined seawards or landwards, or be kept in motion, and the eff'ect would be a great relief to the already exhausted resources for varying the appearance of lighU. This idea of Raper's is now carried out, and the illumination of the clouds by the new Klectric Flashing Light at Ushant has been seen from a distance of 70 miles. EXPLANATION OF THE TABLES. 4()0 ruodt! of expression should be selected as is best adapted to application. provided no error be thereby involved. But, in this question, both efficacj in practice and precision of language concur in directing the use of terms according to their absolute significatioiis. Thus, if we call a southerly point of Atooi the "S.E. pt.," we leave it doubtful whether there is land to the (southward or not ; and, therefore, a ship could not, without reference to the chart, venture to run ; but if we call the soutli point by the proper term, this doubt is not suggested, since the word "south" declares tliat no other part of 'he coast projects so far to the southward. Accordingly, in this work, the conipass-naines N., S., E., or \V., denote the extreme projecting point in that direction, without regard to the figure of the rest of the coast. A point which is an extreme both in latitude and longitude, as, for ex., the S.E. projecting Cape of Saniar (Philippines) we call what it is, namely, the South and East extreme, and so of the .S. and W., N. and E.. N. and \V. points. [1.] A:::liiguous Tenns. Another case in which serious ambiguity may arise from the want of critical rules in such matters, and which may witii propriety be noticed here, occurs in such phrases as "the Lizard lights in one clear the Manacles to the eastward." This is intended to imply that the ship passes to the eastward of the rocks ; but, by omitting all mention of the ship, the bearing might be supposed to relate to the rocks, as would be the case if another verb were put for "cleared," as "saw the M. to the eastward," in which cases the ship is clearly to the westward. If the sentence ran " clear the ship to the eastward," no obscurity could exist, yet " clear the M. to the eastward," also puts the ship to the eastward. There must be something very defective in an expression which keeps the same meaning when reversed. It would be well to adopt the rule that the bearing specified should relate to the thing mentioned, and not to anything else absent or under- Btood ; thus, in the above phra.se, the term " eastward " should be held to relate to the rocks, and not to the ship, just as in " clear the ship to the eastward," it relates to the ship, and not to the rocks. It might be dangerous to force a reform too suddenly in technical ex- pressions, however vicious ; but, on the other hand, no expression can maintain its ground when proved to be wrong. In the meantime it will be proper to use a fuller form of phrase, such as " clear the M., leaving them to tlie westward." In the course of time, " leaving them" would be dropped, and "e should have the expression in its correct form, the bearing relating to the thing mentioned. Some ambiguity necessarily attaches to the word " pass," because it is both active and neuter ; thus, " passing an island to the westward," does not altogether declare whether the ship passes to the westward or leaves the island to the westward. It is often, in like manner, a matter of doubt whether bearings given in the description of a light relate to the light itself or to the spectator : thus, " a light obscured from N. to E." may mean either " invisible from the N.E. quarter" (that is, when hearing S.\V.-d), or "invisible to a spectator in tilt S.VV. quarter" (or bearing N.E.) This ambiguity is removed by the same rule, which supposes the spec- tator always in the centre of the compass, and, therefore, that the bearing •[lecitiiil relates to the point mentionetl. The above phrase should, there- fore, be held to mean the lii;ht invisible when biaring between N and E. 106 EXPLANATION Of TUE TABLES, Table 11. Places at which Docks, Wet or Dry, or Slips, mat BE FOUND, Repairs made, Coals obtained, &c. This Table bas been corrected from the most recent information. For fdller details see the Admiralty Dock Book for 1890. Table 12. Navigable Distances. This Table, in former editions, aflPorded the means of estimating ap- proximately the length in days of passages from port to port, but steam having made the table obsolete, it has been replaced by one showing the Navigable Mercatorial Distances in Nautical Miles between the Principal Ports of the World, arranged geographically. The sailor, knowing the speed at which his vessel can be driven in fair weather and fonl, also the probable force and direction of the winds and currents he is liable to meet during the voyage, will be able by Table 12 to quickly make a fair estimate of the time of arrival at the port or ports to which he may be bonnd.* There is some difficulty in giving at sight the distances between ports lying in different oceans. An attempt has been made to connect the first-class ports by inserting auxiliary tables where the distances between London, Liverpool, &c., and the Chinese and Australian ports are directly given. In other cases a little addition will be necessary. Care has been taken to give prominence to the great corners or turning, points of the world, as Gibraltar, Aden, Galle, Cape Leeuwin, Pernambuco, Cape Verde, &c. The Mediterranean tables are connected with the principal ports in both hemispheres by tables from Gibraltar and Port Said. Required the distance between Vera Cruz and Brisbane by Cape of Good Hope; by Cape Horn; and by Suez Canal; also between Genoa and vSan Francisco ; and Famagousta and Zanzibar. Vera Crtiz to Pernambuco . . 4,205 Pernambuco to Cape of Good Hope 3,346 Cape of Good Hope to Brisbane . 6,680 Vera Cruz to Gibraltar . Gibraltar to Port Said . Fort Said to Brisbane . Genoa to Port Said Port Said to Hong Kong Hong Kong to San Francisco 15-662 1,428 6.465 6.444 Vera Cruz to Pernambuco . Cape Horn to Brisbane to Cape Horn • 4.20s = 3.2S9 • 5.995 « 3.489 Genoa to Gibraltar Gibraltar to San Francisco . . 852 . 12.569 13.421 Famagousta to Port Said Port Said and Zanzibar . 250 . 3-108 3.358 • It must be remembered that ships in .sailing or steaming round the world, gain a day in their reckoning, going East ; and lose a day going West. This alteration of date may be attended with some embarrassment if care is not taken to insure accuracy, by referring the days and hours of departure and arrival to Greemvieh time by means of the Greenwich Date : iSec No. 481 and " Variation of Time at Sea," p. 354. A short rule to estimate day and hour of arrival for steamships crossing th» Pacific Ocean is : Going West : Add one day to assumed time of length of passage, and tubtract the DifF. Long, in time between the t-wo ports. Going East : Subtract one day from assumed time of passage, and add the Diff. Long, in time. EXPLANATION OF THE TABLES. 407 Tarle 13. Time Signals. This Tabic she-ns, for all parts of the world, where the Time Signals are made from which the error of the chronometers on Greenwich Mean Tioo can be obtained, and by which, if the length of stay jiermits, they can also be rated. For more detailtd information see List of Timo Signals, published yearly by the Admiralty. Table 14. Epacts of Years and Months. The Table contains the Epacts for certain years, and for the first aay of each month. The Epact for the year is the moon's age on January 1st. The Epact for the month is her age on the first day of the month, supposing her to change on January 1st at noon. .As a mean lunation is 29"* IS*" 44™, the moon describes, in 365 days, twelve complete lunations, and lO** IS*" of the thirteenth; hence, on each 1st of Januan,' her age is IC IS*", on the average, more than on the preceding Ut of January, and II'' IS*" if the preceding year was leap year. Table 1.5. Semi-Menstrual Inequality. The Table contains the Semi-menstrual Inequality for the places enu- merated. Its use is shewn in the examples, p. 2^42. The Table was con- structed by combining together the several semi-menstrual mequalities of the places specified, together with a few observations at St. Helena, to which place, also, the Table therefore may be applied.* Table 16. Rise and Fall of the Tide. The Table shews approximately the space through which the surface oi irater rises or falls at given intervals from high or low water. It is entered yith the said interval at the top, and the range for the day at the side. Ex. 1. It ia high water at a dock-sill at 1 1'' iC" a.m.. and the water is 3 1 ft. deep, the range is 14 ft. : find the depth at izt" 15'". From 11'' lo"' to iz"" 15"' is 55'" (or i'') ; then ander 1''. against :+ft., is i r., which is the fall of tide in i"", and being subtracted from 31 ft., leaves 2,-1, the depth required. Ex. 2. It is low water at 4i> 50" p.m., and the depth is i ft. At a place where the range ia 17ft. find the depth at 8'" 30". 3'' 40™ and 17 give 1 1 4, which, added to 2, gives i3'4,the depth required. If the range for the day is not known, a rough estimate may be formed from the spring and neap ranges. The Table may serve for reducing, approximately, the soundings taken at any particular time of the tide to the low-water depth. Thus, the depth 10 feet is obtained at P .'jO'" after low water : the range between this low irater and the succeeding high water is II feet; then l*" 50™ and II give * 1 am m.lebtcd for this useful table to the late Mr. Dessiou, of the llydrog. Office, master in Her Majesty's navy, who was employed at the Admiralty in reducing tlie greater part of the tide observations made at our ports for many years ; a task which Dr. Whewell considers, in the amount of labour and in the judgment displayed in the mode of proceeding, as not inferior to any discussion of large masses of astronomical or other obsenations by modem calculators, and of which some idea may be formed from the dr. ttmstance tint Lo'>don alone furnished 13.00(1 obsprvatioun. 408 EXPLANATION OF THE TABLES. 08, which, deducted from 10 feet, leaves 92 feet, the reduced low-water depth. The results are onlj' approximate. It has beeu remarked, at least at some places, that the rise and fall do not correspond, and that the water falls more rapidly at first.* Care must be taken iu using this Table where there is a large Diurnal Inequality (see Nos. 926-928), To compute a Term. With the time from high or low water as a course, and the Eauge as dist., find the diif. lat., and subtract it from the range ; the remainder is the rise or fall. NAUTICAL ASTRONOMY. REDUCTION OF THE ELEMENTS IN THE "NAUTICAL ALMANAC." These Tables are used in the rules from p. 205 to p. 228. Tables 17 and 18. Aec and Time. These Tables contain the corresponding divisions of Time and Arc. Their use has been exemplified in Nos. 570 and 572. Table 19. Coerection of thb Sdn's Declination at Noon at Sea, FOB Longitude and Time. This Table contains the correction for the sun's declination at noon, as taken out of the Naut. Aim. or Table 60, for reducing it to any other long. Ihan that of Greenwich, or to any other houi- of the day than noon. The correction is the variation of the declination, and, as it depends chiefly on the deolin. itself, the declLn. is employed as the argument instead of the day of the month. The Table is entered with the declin. at the top, and the Long., or the time, at the side. See examples, No. 579. Table 20. Correction of the Equation of Time at Noon, at Sea, FOR Longitude and foe Time. The Table is entered with the daily variation at the top, and the longi- tude, or the time, at the side; the correction, in the body of the Table, is in seconds of time. See the examples. No. 583. Table 21. Foe eeducinq Daily and 12-HonELY VARUTiONS.t This Table shews the proportional part for each half-hour of the 14}^, or each 15™ of the 12'', corresponding to any daily or 12-hourly variation from 1' to 30', or 1" to 30 ". * With such irregularity will also be taken that caHei. tide and half tide, \a some places where the fall of the water is checked about lialf ebb, and a temporary rise takes place, as in the superior height of the night tides in the river Columbia, observed by Sir K. Belcher. t Fur the defiign of this very convenient table I am indebted to Capt. W. Kamsay, R.N. CXrLA.VATION OF THE TAhLEB. 409 When tho variation exceeds 00, lake the parts for 30 aud for the excess »bove 30. Consider minutes ot time above 0'" or 30™ as hours, and write the mill, of the proport. part as seconds, and the seconds as thirds. Examples are given in No. 580, and many others. For extreme precision, the even columns (2', 4', ttc.) only must be used, because the odd columns are often 0"'05 in defect, as are all those for ;iO". 'J'he Table serves for reducing the R..4. and Decl. of the sun and planets, the Equation of Time, the Moon's Horizontal Parallax, and Semi-diameter ; and also for various other purposes, as proportioning for tiie rate of a watch, tlie drift of a current, &r. TABot Hi A. LOGAUITH.MS FOK REDUCING DaILY VARIATIONS. This Table contains logarithms for reducing i!4-hourly variations. lt« use is described in Xo. 597 (2). To compute a Term. From tne const. 315836( the log. of 1440, the uumber of min. in 24'', or of seconds in 24") subtract the log. of the given time or arc ; read hours or degrees as min., and min. as seconds. Ex. I. Find the Log. for 1 1' zS". Const. 3* 1 584 II- 28- =.688' log. 2-8376 Log. req, 0-3208 Ex. 2. Find the Log. for 21' 2; Const. 3-1584 21' n" = 1287" log. 3-1096 Log. req. o 0488 Table 22. For REDUctNG the Moon's Declination. The Table is entered with the difference for 10™ (from the Naut. Aim.) tt the top, and tlie minutes of tlie Greenwich Date at tiie side. Ex. Green. Date, ii'"27"', Diff. for 10"', 136". 27"' and 130" 5' 51' 6 i6-2 Proportional Part 6 7-2 Tlie parts may be taken out to the seconds of the Greenwich Date by reading minutes as seconds, and seconds as thirds. Table 23. .Acceleration. This is the change of the sun's mean Right Ascension in a mean solar day. It is employed in reducing the Sidereal Time at mean noon to the Green. Date, and in converting Mean Time into Sidereal Time. The .Acceleration is itself a portion of Sidereal Time. Tari.e 24. Retaiidation. This is the change of the sun's mean Right Ascension in a sidereal day. It is employed in converting Sidereal Time into Mean Time. The Retardation is itself a portion of Mean Time. For examples of the use of these two Tables, see Nos. 585, 602, &c. Table 25. For finding the Eouation of Second Differences. The use of this Table is described in No. 599. The colnmn headed l"" (which may be read 1° or 1') is adapted to all tables in which the ilit*)rvals are sex;ige«imallj divided. EXPLANATION OF THE TABLBK To compnte a term. Multiply halt' the difference between the Tabulai Intt-rval anil the proposed Interval by the latter, and divide the product, by the square of the Tabular Interval. Tabular Interval ii'", Pioposeil Interval s*" 40™, ar 5'- Tab. Int. iz'- Proposed 5-7 15. HaliDiff. 3-1 ■y-! = o'iz27, the muitlplSpr. flMES OF CERTAIN PHENOMENA. These Tables are employed in the methods, p. 205, &c. Table 26. Apparent Time of the Sun's Rising and Setting.* The Table is entered with the Latitude at the side, and the Sun's De- clination, at the top, when these are of the same name ; but at the bottom when of contrary names. Thus, in lat. 31° N., the sun, when in 4° S. decl., rises at G*" 10™ a.m., and sets at b'^ SO"" p.m. This is the Civil Time nf the rising or setting of the sun's centre, to the eye at the level of the sea, and without the atmosphere. For greater exactness see No. 638. To compute a Term. See Nos. 620, 6-21. TABLb; -27. Approximate Apparent Times of the Meridian Passagb* OF THE Principal Fixed Stars. Table 27 A. Correction of the Times in Table 27. The times are given in Table 27 for the 1st of each month, and the .neridian of Greenwich. To find the time of passage for any other day, sub- tract the portion of time corresponding to the day of the month in Table 27 A from the time in Table 27. For an ex. see No. 62.5. The Table is adapted to 1902, but will be within 2"" for many years. Table 28. Correction of the Moon's Meridian Fassaoe. The Table is entered with the Daily Variation at the top, and the Longitude at the side. The Daily Variation in W. long, is the difference between the time of the moon's transit on the given day and the next ; in E. long, it is the difference between the moon's transit on the given day and the day before. In W. long. a^iT. for 5 1° W. 7 I Corr. for 132° E -is > Time req. 9 11 a.vu Table 29. Hour-Angle and Altitude op a Body dpon the Primb Vertical. The Table is entered with the Declination at the top, and tlic Latitude (of the satne name) at the side. Ex. Lat. 50' and 0's Declin. 10°, give his Hour-Anele i;" 26"", and .\lt. i3''-2, or 13" 12'. The alt. which, partly for space and partly for distinction, is noted to the nearest 0°-l, or 6', will not be in error on this account more than 8'. Thus the alt. 13^-1, which is properly 13° 6', may be between 13° 3' and 13° 9' ; but 13° 2' is 13°-0, and 13° 10' is 13°-2. Hence, taking I3°-l as 13° 6' cannot entail an error exceeding 3'. The error will generally be less. This alt. being the /rue alt., the sun or a star will pass the prime vertical at an alt. grealer than the alt. given, by the diff. between the true and obs. »lts. ; the moon, on the contrary, at a U.sser alt., by this amount. As no star of which the declin. is greater than the lat. passes the prime vertical, such cases do not appear in the table. The Table shews at once, roughly, the effect of an error of 1° of lat. in determining the time by a single altitude in the most favourable case. Ex. Lat. 45' N., Decl. 3' N., the times are the same for 3° or 4° of latitude ; that is, a gross error of lat. is of no consequence in computing the time of passage. But if tha body have 23^ of declin. an error of 1° of lat. will cause an error of 3'" or 4"' in that time. By reversing the lat. and declin., the hour-angle and altitude become those of a body at its greatest elongation, or azimuth, from the pole. To C'jmpttfe the Hour-angle, see No. 619. To compute the Alt., see No. 6G.5. ALTITUDES. These Tables are used in the rules, p. 280, &c. Table 30. Apparent Dip of the Sea-Horizon. This is the angular depression of the sea-horizon below the trne level, in ordinary states of the atmosphere, and when the aea and air fre of eqnal teraperatnre. 412 EXPLANATION OF THE TABLES. The apparent dip is the true depression (Table 8), diminished bj^ about -j3y of itself. As this correction varies with the state of the air near the horizon, altitudes taken at sea, especially low altitudes, are not to be depended on where great accuracy is required. See No. 208. Table 31. Mean Astronomical Refraction The Refraction is given for the barometer at 30 inches, and Fahrenheit b thermometer at 50°, according to Ivory.* The diff. to 10' of alt. is inserted. Ex. 1. The i-efraction at 20° is 2' 39' . Ex. 2. The refr. to the alt. 38° 35' is i' I3"3, deducting -z, or i' i3"'i. The tenths of seconds are omitted at altitudes below 35°, on account of the uncertainty at low alfitudes. To find the Refraction approximulehj. With the alt. as course and dep, 68, find the D. Lat. ; this is the refraction in seconds. For the refr. is pro port, nearly to the tang, of the zen. dist., and is a8"-2 at zen. dist. 45° Ex. Alt. 10', ds courie, and Dep. 58, give 329", or 5' 29", the refr. required. Table 32. Correction of the Mean Refraction for the Height OF the Thermometer. t The Table is entered with the Alt. at the top, and the degree of Fahren- heit's therm, at the side. When the therm, is helow 50°, the correction ia added to the mean refr. ; when above 50°, it is subtracted. Ex. Alt. 17° 10', therin. 72°; the corr. is 8", which, subtracted from the mean refr., j' 7", gives the true refraction 2' 59". To find the Correction, nearly. Multiply the mean refraction in seconds by 2, and by the difference between the height of the therm, and 50°, and divide the product by 1000. Ex. Alt. 5', therm. 3S'. The mean refr. 9' 54", or 594", mult, by 2 and by I», is 14256, and this divided by 1000 gives 14". Table 33. Correction of the Mean Refraction for the Height OF THE Barometer. rhe Correction is given to each tenth of an inch. The Table is entered like Table 32. When the barom. is above 30 inches, the correction is to bs added ; when below, subtracted. Ex. Alt. 17° 10', barom. 29-2 in. ; the corr. is 5", and true refr. 3' 2' . To find the Correction. Multiply the mean refr. in seconds by the dif- ference between the height of the barom. and 30 inches, and divide the product by 30. Ex. (Above.) 3' 7", or 187", mult, by -8, and divid. by 30, gives 5". * The refractions now used by astronomers axe those according to Bessel. Iiory's exceeds these by 09" at alt. 45°, by 2" at alt. 20°, and 5" at alt. 10°. The difference of the tables IS scarcely worth a more extended notice. t This correction involves the term -7— (t— 50). Tlie ' asiD»tns\hW.—Phil. Tram. 1823, p. 476. EXPLANATION OF THE TABLES. 413 Tablk 34. Trk Son's Parallax in Altituije and Semidiameteb. These are given for convenience on some occasions, but not for extreme precision. To cmnpiife the Sun's Parallax in AUihide. Take the hor. par. in the Naut. Aim. as dist., and find the D. Lat. to the app. alt. as cour.se. Table 35. Dip of a Shoee-Hoeizon. Tl-.p Table shews the Apparent Dip to be used instead of the dip in Table 30, when the distant sea-horizon cannot be seen, and the altitude is observed from the water-line on the beach. The distance of this line may either be estimated nearly, as it is always less than the true dip due to the height of the eye (Table 8), or it may be found by the method No. 550. To compute a Term. Take the diff. between the depr. to the eye (Table 8) and the dist. of the beach-line, and divide by twice this last ; atid the quotient to the app. dip in Table 30. Table 36.* This Table contains the scales of the Centigrade and Ueauniur ther- mometers, corresponding (approximately) with that of Fahrenheit. The zero of the two former, or the freezing point of water, being 32° ot of Fahr., and their boiling points 100° and bO'- respectively, while that o( Fahr. is 212"=; the following rules are derived for the conversion of the scales. To convert the Centigrade into Fahrenheit. Multiply the degrees of the Centigrade by 9, and divide the product by 5. When the Centigrade degrees are above 0, add 32° to the quotient; when below C (or marked — ), sub- tract it from 32°. To convert Reaumur into Fahrenheit. Multiply the degrees by 9, and divide the product by 4. Apply the quotient as directed above. Ex. Centig. — ify, find Fahr. ii-y x 9 = los^j, this + 5 =2i-i, which mbtracted from 32' gives lo^-g. To extend the Table. For the Centigrade add 0555, &c., and for Reaumur 0-444, &c., for each 1° of Fahr. Table 37. This Table contains the Engli.'ih measures corresponding to the Jlelre, Kilometre, Decimetre, and Millime/rcA See p. 3«0. Thus 30 centini. are 1 1'81 inches ; 3 kiloni. are 1-618 nautical miles. The barometer scale, in English inches, and millimetres (approximately), is annexed. To reduce the French to the English barometer scale. Divide the rail' limetres bj 25-4, the quotient is the number of English inches required. * Ad nnmerons valunlile works relating to Navigation are pulilished by the French, and as other Continental nationa frequently employ the langnage of that country in liydrngraphic document!!, Tables 36 and 37 art added, for the ready reduction of such French measure* as most frequently occur. + The quantititts are taken from the Annuaire, for 1846. The metre is the lO-nrilliooCb part of the quadrant of a meridian. 414 EXPLANATION OF THE TABLES. When the French scale is given in inches and lines (or 12ths of an inch), multiply the inches by 1'065, the product is English inches. To extend the barometer scale, add 2-54 millimetres for each O'l of an incli. Table 38. Corrections of Altitude of the Sun aud Stars. The Table contains the gross corr. of alt., or the corrections enume- rated in No. 644, exclusive of index error, to the nearest tenth of a minute, using Bessel's Mean RefractiouB. For examples, see No. 648. Table 39 The Moon's Correction of Altitudb. The Table contains the Correction to each minute of iiorizoutal parallax and every 10' of alt. ; for the barom. 30 inches, and Fahrenheit's therm. 50"^. Ex. The corr. to app. ait. 15° 30' and hor. par. 56', is 50' 31". For seconds of parallax. Look among the columns on the right side ol the page, and against the alt., and take out the seconds, which add to the correction. For minutes of altitude. Take the seconds from the extreme right of the page, and apply them as there directed. Ex. Moon's App. Alt. 35° 37', Hor. Par. 57' 32" ; fiud the Correction of Altitude. 35° 3°' a"d 57' 45' 3" 32", parts 26 I 7' parts, —4/ 22 Correct, req. 4i 25 To correct for the Barom. and Therm. Take the corrections from Tables 32 and 33, but apply them to the correction of alt. the conlrury wap to that directed. Ex., No. 655. To compute a Term. Correct the app. alt. (of the centre) for refraction To the log. sec. of this alt. add the prop. log. of the horizontal parallax ; the sum is the prop. log. of the parallax in alt. From this subtract the refrac- tion ; the rem. is the correction of alt. The Table does not give the correction with precision at low alts.* Table 40. Corresponding Horizontal Parallax and Semidiameter of the Moon. As these two elements are generally required together, the Table renders it necessary to reduce the parallax alone to the Greenwich Date. Taule41. Diminution of the Moon's Horizontal Parallax for thk Spheroidal Figure of the Earth. » The Table is entered with the Horizontal Parallax at the top and the Latitude at the side ; the seconds corresponding are to be subtracted from the equatorial hor. par. The compression employed is jjj^. * In all these tables of refraction the eye is supposed at the level of the sea ; when the observer is at very great elevations, lo v altitudes cannot Ije corrected with precision by the tables in common use. The refraction is in such cases too great. EXPLANATION OF THE TABLT.S, 415 Table 42. AoGMENTArioN of the Moon's Sicmidiametkh. The Table is ciiiored with the Moon's Semidiamcter at the top at.J hei Altiliile at the side; thi seconds corresponding are the excess by which hei apparent seniidiarneter at her actual altitude exceeds that at whieli it woult* appear it' seer, from the centre of the earth. See Nos. -439 and 440. Tables 43 and 44. Fok converting True into Apparent .Altitudes. These contain the further correction necessary in reducing a true to an apparent altitude, after adding the refraction and subtracting the parallax See Nos. 657 and 658. Table 45. Parallax of the Planets in Altitude. The Table is entered witli the Planet's Horizontal Parallax at tlie top, anc its Altitude at the side ; and the corresponding seconds taken out. To compute a Term. Enter the Traverse Table with the alt. as course and the hor. par. as dist., and take out the D. Lat. Table 46 .\zimuth corresponding to the C hange ok Altitude IN l™ OF Time. The Table shews the Change of Altitude in i" of Time at any ,\ziinuth in Latitudes below 66°. The azimuth is reckoned either from N. or S. The Table shews also, roughly, the true bearing when the change of alt In 1"° is given. See also No. 677. T'he column of 6' limits the azimuth for finding the time. No. 778. LATITUDE. fflESE laoies are employed in the rules in Cbap. V., p. 243. Table 47. Limits of the Reduction to the Meridian at Sea. This Table shews how long before or after noon the sun's altitude may be observed, so that the Reduction shall not be in error more than 2' when the time is 1"" in error. The Table, therefore, shews the Litnits of this method for common practice at sea. If the time be in error, or doubtful, 2"', 3"", &c., the Reduction will, at the limits, be in error, or doubtful, 4', 6', &c. In lik( manner, if the error of time be less than 1"", that of the Reduction will be less than 2', in the lame proportion. If the time is doubtful 2™, 3", &c., and we require that the error of the Reduction shall not exceed 2', we must take for the limit J, ^, &c., that set down ; thus, if in lat. 48° N., decl. 10° N., the time be doubtful 3"", »•; must take the alt. M'thin * of 28"', and that is, t('' from ivoon. 416 EXPLANATION OF THE TAKJ.ES. Wlien the time from noon, of observation, exceeds the limito set down, the error of the Reduction (caused by l"" error in the time) will exceed 2" in the same proportion ; thus, in the above case, if the alt. be observed 56" from noon, the error of 1"" in tlie time will cause 4' error in the Reduction. The time in the Table is that hour-angle, nearly, at whicli the n ambei of minutes (of time) is equal to the number of minutes (of arc) in the Reduction. To find this Hour-Anyle. To the constant 0-4771, add the log. from Table 70 ; the sum is the prop. log. of the hour-angle required, in time.* Table 48. Value of the Reduction at which the Second Reduction amounts to 1'. The Table contains, against each Mer. Alt. under 85°, that value of the Reduction at which the 2d Reduction amounts to 1' ; and therefore shews whether it is necessary or not to compute the latter. I the mer. alt. 68^ and the (fiist) Red. computed to be 47', then the errof o) omitting the 2d Red. cannot amount to i' ; but if the 1st Red. were 54', the omission of th^ id Red. woidd cause an error of more than 1'. One eighth of the quantity in this Table is that (1st) Reduction at which the 2d Red. amounts to 1". Thus, in Ex. No. 707, p. 252, the mer. alt. is 60°, the value of the 1st Red. in the Table is i^ 3', i-8th of which is 8'; hence, if the Red. exceed 8', the 2d Red. trill exceed i". To compute a Term. To the constant 6-7648 (the sin. of 2'), add the log. cot. of the mer. alt.; half the sum (preserving 10 in the index) is the log. sine of the reduction required. Ex. Const. 67648 Mer. alt. 60° 50' cot. 9-7467 Red required 1° 2' log. sin. 8-2557 To find the time from noon, or the hour-angle, to which this (1st) Reduction corresponds: from the log. sine of the Red. subtract the log. ir> Table 70, the remainder is the log. sine square of the time or hour-angle required. Ex, 1. Lat. 60° N., dec!. 14=' N. (mer. alt. 44='), Red. 1° 24'; 8-3SS-0-I30 = 8-25S. the sin. sq. of I^ I"" 53% the hour-angle required. Ex. 2. Lat. 29° N., decl. 17" S. (mer. alt. 44="), Red. 1° 24', gives o"" 47" 3'. These precepts concerning the Reductions are, of course, merely ftpproximations near enough in practice. Tables 49 and 50. 1'or computing the Reduction to the Meridian in Seconds. See No. 707. The seconds forming part of the 1st Reduction (Table 49) are taken out to the min. and sec. of the hour-angle. When the sun is observed in the forenoon, the Table is entered with the time from midnight, for convenience. * Mr. Towson has constructed convenient tables for reducing an alt. observed neat the merid. to the mer. alt., which are published by the Hydrographic Office (J. D. Potter, agent). EXPLANATION OF THE TABLES. 417 The spx'nib for tlic 2(1 Reduction (Table 50) are taken out for the iour-aiiu'lp t'l (tin nearest 10'. To compute n Term in Table 49. To the consi. 50!.")45o, add the log. iine square of the hour-angle : the .-Jum is the log. of the number of seconds. To compute n Term in Table 50. To the const. 5-6155 add twice the log. sine sq. of the hour-angle ; the sum is the log. of the 2d Red. Ex. Find the Reduction, and also tlie 2d Red., in seconds, for the hour-angle iS" 4' Const. 5'6i5+5 I Const. 5615 H. Ang. iS"' 4* sin. sq. 7-5734' sin. sq. x 2 5-147 Reddct. I544"S log. 3-18886 I 2d Red. 5"-S log. 0-761 Table 51. Correction of the Altitude of the Pole-Star at Sea. The Table is entered with the Altitude of the star al the top, and the Right Ascension of the Meridian at the side. The quantity taken out is to be applied to the star's true alt. as directed, ex. No. 773. The last column contains the variation in ten years, which is always sub tractive from the correction in the Table. As the observation at sea is imperfect, the correction has been computed (o whole minutes only. The quantity is the D. Lat. answering to the star's hour-angle as course »nd 77'as dist. (the star's pol. dist. in 1S90), together with a second correction computed in No. 774.* Table 52. Reduction of the Latitude. This is the diflference between the latitude as actually found by any astronomical observation and what it would be if the earth were a sphere, which last is called the geocentric latitude. To reduce the lat. by observation to the geocentric latitude, subtract the reduction of latitude. This quantity, which is also called the atiffle of the vertical, is at the iiquafor arul at the pole, and is greatest in tat. 45°. The compression assumed is jjg ; that is, the polar radius is supposed to He shorter than the equatorial radius by yj^ of the latter. LONGITUDE. These Tables are employed in the methods, Chapter VIL p. 297 I'able 53. Couhection of the Lunar Distance for the Contraction OF THE Vertical Semidiameter. The Table is entered with the Alt. at the top and the Angle contained between a plumb-line through the body, and the line joining the other hody.t See No. 852. • The Niiutical Almanac method strongly rccommonded. f The argument in this table, in the usual form, is the angle which the semidiameter in the direction of the other body makes with the horizon ; but it is diUficult to imagine the horizon where it is not, whereas the plumb-line is an absolute standard everywhere. E E EXPLANATION OF THE TABLES. Table 54 Error of Observation arising from an Error in thr Parallelism of thk Linf. of Sight. The Table shews the Error on any observed angle less than 120°, arising from the line of sight not being parallel to the plane of the sextant or circle. See No. 495 (3). As the observer will not, knowingly, allow this adjustment to remain defective, or observe elsewhere than in the centre of the field wlien the ad- justment is perfect, the Table serves rather to shew the consequence of such errors than for the purpose of applying a specific correction. To compute a Term. To twice the log. sine of the error in the paral- lelism of the telescope, add the log. tan. of half the angle measured; the sum is the log. sine of the required error in tho observed angle. Ex. Error of parallelism 12', angle measured 97°: required the Error of the Angle. 12' log. sin. 7-5429 X2 5'o8s8 97°, half, 48° 30' tan. 0-0532 Error req. 2"-8 sine 5'1390 Table 55. t-OR correcting the Lunar Distance for the Spheroidal Figure of the Earth. The Table is entered with the Latitude and the Moon's Altitude. The mtmbers are noted to the nearest 10. See No. 853. To compute a Term. To the log sine of the red. of lat. add the log. sine of the mean horizontal parallax (in Table 40=57'), and the log. sine of tlie alt. ; the sum is the log. sine of a small arc, which multiply by 100. T\BLE 56. For compijiing the Moon's Seco.\d Correction of Distance. Enter the Table with the App. Dist. at the top or bottom, and tlie Moon's Corr. of Alt. at the side, and take out the seconds. In the same column taka out the seconds standing against the corr. of ilist. (No. 842 or 844) at the side. The difference between the two numbers thus taken out is the 2d corr. required.* When the Dist. is less tlian 90^, add; when greater, subtract. Ex. App. dist. 48°; J 's corr. of alt. 46 ; con- of dist. 26'; find the Second Corr. 48° and 46' 17" 26 _6 Second Corr. j 1 to be added. To tumjiHte a Term, approxwmtely (1.) To square an arc in nunutes. Find the square of the number of min. ; divide it by 60 : the quotient is the number of seconds in the square required, roughly. For greater accursriy, increase the quotient by Jjp of itself. (2.) With the app. dist. as Course, and the said square as Dep. find tlie D. Lat ; half i\ni is the term required. * ^s1.J3 2d corr. may be dispensed with altogether by repeating the work, No. 844, p. 30(1 asing the mean of each true and app. alt. and tlie mean of the app. and first found di^i The tesult, with care, will agree very nearly with the rigorous proceos. KXPLANATION OF THE TABLEC 419 !■>. Corr. (of alt. or of dist.) 55', app. dist. 31°. 55 squared (by Table H) 3025, divided by 60 5o''4 add i.2oth 1 "5 Required saiTARE of 55' 53 Dep. 53 and Course 31° give D. Lat. 88 ; the term is 44.". P/ibLE 57. Correction of the Greenwich Mean Time for thr Second Difference of the Lunar Distance. This Table is entered at the top witli the Approximate Interval, and at the side, with the Diff. of the Prop. Logs, standing against the two distancen in the Nautical Almanac, which include the given true distance. For an example, see No. 8.57. To compute a Term, approximately. Multiply together the approx. inten'al in hours and tenths, its compl. to a*", the diff. of the prop. logs, above ('attending to the decimal point), and 1400. Ex. Approi. interval, i"" 10"', diff. prop. logs. 64; then ra x i-S x 0*0064 ^ 1400 = 19". the required term. Table 68. The Error of the Ship's Place and ok the Longitudb IN Time, corresponding to an error of Tin theLunar Distance. The Table is entered with the Latitude at the top, and the Prop. Log. against the lunar dist. in the Nautical Almanac at the side. Ex. Lat. 50'', prop. log. ; Soo ; an error of i' in the lunar dist. will cause an error 0/ 19 miles in the ship s place, in Departure, and i™ o' error of long, in time. Since it is the actual distance of the ship from the shore that we are 30ncerned with at sea, rather than the nominal diff. of long., this Table will ifford a useful check on the supposed place of the ship in making the land by a lunar observation. The error of long, in time is also the error of the G. M. Time, as deter- mined by a lunar observation. To compute a Term. Divide 2700 by the 3-hourly change in minutes; the quotient is the error in inin. of long, in arc at the equator. For any particular latitude see No. 307 I'ABLES FOR DETER.MINING THE VARIATION OF THE COMPASS. 'these 'J'ables are eiiiidoyed iu Cliapter VIIL p. .326. IaHLE .iy. .V.MI'LITUIOES. The Table shews the True Amplitude of the sun (or of any other celes- tif.. body, having the same declination), at rising or setting. It is entered w th the Decl. at the top and the Lat. at the side. To find the .Amplitude by the Traverse Tables. With and the Ut. 420 EXPLANATION OF THE TABLES, find M With M as Dist., and the Decl. as Course, find the Dap. With 100 as Diat. and this Dep. find the Course. ■ ,^ , f fh« B« Oomp«iaiio«. To the log. sec. of the lat. add the log. sine of the Declin. ; the sum is the log. sine of the amplitude. Ex. Lat. 17", Uecl. 23°; find the .Vmplitude. Lat. 17° o' sec. 0-0194 Decl. 23 O sine 9-5919 Amplitude, 24° 7' s^"- 9-6ll3 Table 59 A. Correction of the Observed Ampluude. Dip, multiply the sum by the correcbon in the Table, and divide by 3. . red. the quotient is the coirection reqi Ex L't • 164 4 (parts 66) 66 8 (parts 131 .^ 10) 13 Log. req. 424471 II. Inverse Process; to fiiid the namber corresponding to a given log. 1. When the iiataral number is not required to consist of moi-e than four figures, it is taken out at once. Ex. Given the log. 645820, required the natural number. The nearest log. in the Table is 645815 ; the figures at the side arc 442, annexing to which that at the top, or 4, gives 4424, the ncjibku required. The placing of the decimal point is directed in No. 50. 2. Whiii the Number is to consist of Jive fignres. Take out the next less log. to the one given, and note down the four figures of the corre- sponding number. Note the diff. U. Subtract this next less log. from the given one, and look for the re- mainder among the parts standing against D, in the lower part of the Table ; note the figure at the top under which the remainder is found, and add it to the four taken out. 3. When the Number is to consist of six figures, the more direct and accurate method is to take the diB'. between the given log. and the next less in the Table, annex 2 ciphers, and divide by the diff. between the next less and the next greater : the quotient is the number of figures to be annexed to the natural number, answering to the next less log. The placing of the decimal point is directed in No. 59. Ex. I. (Fin fig..) Fiu.l the No. to Ex. 2. (Six figs.) Find the No. t loix. 42447 •• the log. 424471- Given 424471 Given log. 424471 Next less (2657) 424392 D. 164 Next less (2657) 424392 79 Rem. 79 Next greater 424555 163 5th fig. 4, mxt less 66 Then 7900 ^ by 163, gives 48, and tl KUMB. rcq. 26574 numb. req. is 26574S. Taule 64a. Spheroidal Tables; showing the length in feet of a degree, minute, and second of lat. and long. ; the corresponding number of statute miles in every even degree of lat. ; and 'number of nautical miles contained ia 1 degree of long, under each even degree of lat. TAnr.E 65. Natural Sines, Cosines, &c. These quantities are convenient for working problems such as that criven in No. 25-i. Taui.e 66. Log. Si.ves of Small Arcs to each Second. The Table contains the log. sines from to 1° 30' (or log. cosines from 88° 30' to 90°), to each second. Five places are given as far as 1° and six beyond. The Table is applicable to log. tangents, thus : to find the log. tan. add the log. sec. to the log. sine; to find the arc to a given log. tan., find it as for a sine, subtract from the given log. the log. sec, and consider the rem. as a sine For lOths of seconds proceed by proportion, or, in very small arcs, as directed for proportional logarithi;i9. The last method is true in the 5th place for arcs under 5'. 424 EXPLANATION OF THE TABLES. Table 67 Log. S/nes of Small Arcs to Ten Seconds. The Table contains the log. sines from 1° 30' to 4° 30' (or the log iosines from 85° 30' to 88° 30'), to each 10", with parts for single seconds. The parts are true for each 2' and 7' in the units' place of the arc, and very nearly for others, as the parts under 32' serve from 1° 30' to 1° 3.^', and those under 37', from 1° 35' to 1° 39'. The error of using one column for the next will rarely amount to half a second. The parts for the log. cos. are to be taken as for the .sine of the compl. of Ihe arc; thus, the parts for cos. of 87° 42', being those for sine of 2° 17' are found under 17'. Direct Process. Find the sine or cos. for the next less 10", add the part« for the sine, subtract those for the cosine. Ex. 1. The log. sine of 1° 23 37" is 8-617417 for 1^ 22' 30", adding the parts under 12' for 7", or 356, which gives 8-617773. The log. cos. of 87° 46' 14." is 8-590181 for 87° 46' 10", deducting 218 (the parts for 4" under 12'), or 8-589963. Inverse Process. For the sine look for the next less ; for tlie cosine look for the next greater ; note the deg., min., and 10". Take the difF. between the sine or cos. taken out and the given one; look for it in the col. of parts ; take out tlie corresponding seconds and add them. Ex. 1. Find the arc to the log. sine 8-508462. Given 8-508462 Arc 1° 50' 50" Next less 8-508321 2 Pts.at32' Til Ex. 2. Find the arc to the log. cosine 8-75856'- Given 8-758561 Arc 86° 42' 40" Next gr. 8-758688 3 Pts. ati7' 127 Arc req. i 50 52 1 Arc req. 86° 42 43 For extreme precision proceed by proportion. The Table is used for tangents by the rules in expl. Table 66. Table 68. Logarithmic Sines, Cosines, Tangents, Cotangents, Secants, and Cosecant:*. The Table contains the terms to half-minutes, and to six places. The second column and the last but one contain a time scale, cor- responding to the upper and lower degree ; thus 73° 33' 30" corresponds to 4'' 54"" 14'. This scale is very convenient for converting arc and time, but it is introduced to suit those rules in which the time itself is an argu- ment. The parts for each second are given, beyond 9° ; from 4° to 9°, to each 10" ; but under 4° the variation is too rapid for their insertion, and recourse will be had for precision to Tables 66 and 67.* The parts are true for the middle term of the argument ; thus, the parts from 20° 30' to 20° 45', are true for 20° 37'|, and approximate for the rest, but the inaccuracy in the extreme case corresponds only to ^ of 1". It is, of course, the more correct way to take the parts with reference to the rurtrest term, and to apply them accordingly ; thus, to find the sine of 9° 40' 28", find it for 9° 40' 30", and subtract the parts for 2". • The (Uff. D., in the early portion (inserted merely for uniformity), is not that of two consecutive terms, but corresponds to halft\\e tabular interval on both sides of a term. This is done to avoid breaking the continuity of the horizontal Unes, which most occuj »ben actual diffs. are exhibited, and is teasing to the eye. EXPI-ANATION OF THE TABLES. 425 tor greater accuracy proceed by proportion. Diuct Process. When the given angle is less than 45", its log. sine, Stc. »re taken from the top ; when greater than 45°, from the bottom ; thus, the log. sine of 28° 17' is 9-675624; the loi;. sine of 84° 3' is 9-997654. In like manner, the log. sine 9-45^060 corresponds to the arc 16° 27', the cotangent 9-47714 to the arc 73° 18'. The log. sine of an angle is the log. cosine of the complement of the angle to 90°, whether in excess or defect; so, likewise, the log. cosine is the log. sine of the complement ; and the like holds of the tangent and cotan- gent, secant and cosecant. When the given angle exceeds 90°, find the log. sine, tangent, or secant, for the supplement to 180°. But it is generally easier to find the log. co- sine, ro-tangent, and co-secant, for the excess above 90°. Ei. 1. The log. sine of 127° 50' is the log. sine of 52° 10', or the log. cos. of 37" 50', which is 9'8975i6. Ex. 2. The log. cos. of 163° 49' is the log. cos. of 16° 11', or the log. sine of 73° 49', which is 9'9S244i. Ex. 3. The log. cosec. of 97° 4' is the log. coeec. of 82° 56', or the log. sec. of 7° 4', which is 0-003312. In like maimer to find the log. co-sine, co-tangent, or co-secant, of an arc above 90°, take out the log. sine, tangent, or secant, of the excess above 90°. To find the log. sine, &c. of an arc given to seconds. Find the log. sine (or cosine, &c.) for the next less minute or half-minute; take out the part> for the Beconds, or for the excess above 30". For the sine, tangent, and secant, add the parts. For the co-sine, co-tangent, and co-secant, subtract them. Ex.1. Find the log. sine of 53° 25' 13". 1 Ex. 4. Find the log. cosine of 72° 10' 45'. 53° 25' o"8ine 9"9047ii I 72° 10' 30" 9H85879 13 parts + 20 15 parts —98 Log. cos. req. 9-485781 Ex.5. Find thelog. cotang. of 84° 3' 3 84=3' o"cot. 9'0'7959 20 parts 408 ; 2 41; -449 Loo. SINE req. 9-904731 Ex. 2. Find thelog. tan. of 11° 19' 54". 11° 19' 30" tan. 9*301624 24 parts 4- 262 Log. TAN-, req. 0-301886 I Log. cotang. req. 9-0175 10 Ex.3. Find the log. sec. of 38° 42' 46". E,\. 6. Find thelog. cosec. of 68" 14' 11". 38" 42' 30" 0-1077 1 6 68° 14' o" cosec. 0-032124 16 parts ■♦-27 11 parts —9 Log. SEC. req. 0107743 I Log. cosec. req. 0-032115 In working to five places, the last figure of the parts must be dropped, the remainder being increased by I when the figure dropped exceeds 5. In working to I' of time, the parts for 15'' are to be employed. In the earlier part of the Table, half the D. for 30'' may be conveniently employed. It is convenient in dealing with parts of contrary application, to mark those additive with -(-, and subtractive with — ; to sum cacli kind sepa- rately ; and to take the diflf. of the two sums, marking it with the sign ol the greater. .\n example will be found, p. 264, top, the parts are, -h 18, -r 5, — 97, and -f 35 ; the sum of the -f ones is -|- 58, then the difference between 58 and 97 is 39, to be marked — 39, or subtractive. Inverse Process. To find the .-Vrc, to seconds, corresponding to ■■{ tuivvv log sine &c. : 426 EXPLANATrON OF THE TABLES ror the sine, tangent, or secant, take out the next less i for the fivsine, co-tangent, or co-secant, take out the next greater ; and note the degree and (uraiite, or half-minute, of the quantity thus taken out. Take the diff. between this quantity and the given one ; find the reuiaindei in the column of Parts ; take out the seconds corresponding and add then', to the arc noted. El. 1. Find the arc to the log. sine 9i'-.2+70. Given 9-202470 9^ 10' 0" Neit less 202234 18 Rem. 236 Ex. 2. Find the 9-897796. 57- 47' 0" 8 arc to the log. cosin« Given 9«9779« Nextgr. 897810 Rem. 14 Arc req. 9 10 i8 Arc. req. 37 4.7 8 When the parts are not given for seconds beyond 10 (as for the log. Sine and tang, from 4° to 8°), if the remainder exceeds the j)art3 given, take away the parts for 10" or 20" ; add 10" or 20" accordingly, and also the seconds corresponding to this last remainder. Ex. 1. 9-127945- Find the /" 38' 30" arc to the log. tangent Given 9''^79+5 Next less 127651 10 Ex. 2. 881005. Find the 7° 33' 0" arc to the Given Nextgr, log cosec. 88100C 881431 10 Parts X 20 Parts 428 31S 8 Rem. '3 + 7 Rem. iia Arc req. 7 38 48 Arc req. 7 33 27 ed, the When greater |)recision than that afforded by the parts is requ log. sine, &c., or the arc, may be found by means of the proportional part ol the diff. between two terms, or for 30". The log. cosec. is the arith. compl. of the log. sine. The log. cotan. is the ar. co. of the log. tan. The log. sec. is the ar. co. of the log. cosine. The log. tan. is the sum of the log. sine and log. secant ; thus all may b« obtained from the log. sine. T.\BLE 69. Log. Sine Square.* The title is an abbreviation oi' t/ie logarithm of the square of the sine of half the arc. The log. sine square is given to each 15" of arc or 1' of time. In order to lessen the bulk of the table, the index, and one or two figures, ar« taken up at the head of the column, unless these figures change, when tlm whole is given in full. Five places only are inserted as far as O*" 44™, and six afterwards. Each column contains 15', or 1"" ; the minutes and quarters (of arc ), above the next less 15', are given on the left-hand side, and the seconds of time on the right. Thus the log. sine square of 143° 37' 15 ', or 9-95547a, is found under 143° 30' and against 7' 15", and corresponds to P"" 34" 129' The parts for seconds, when not the same for the whole page, are given for the first and last columns ; parts for intermediate columns are therefore between the given parts. 1. Direct Process. To find the log. sine square of an arc to the nearest ttcond. Take the log sin. sq. for the next less 15", and add the parts for the seconds. To find the log. sine square for the tenth if a second of time. CousidM* This table is identical witlx the Los. Ha ; of luman's Tables. KXPLANATION OF THE TABLKS. 427 ihc tenths as seconds of arc, take out the parU, increase tlieni by half, and add tlie sum to the log. sine square of the whole second. Ei. t. Fin J the log. sine squire of j E.x. 2. Find the log. sine square of 38° 11' iz 3" 42'" 57-3- 38° 11' 15" 9-029400 3''42'"57« 9'339466 7 parts 43 parts to 3", 12, 12 + 6= 18 Log. sin. so req. 9029443 I Log. 91N. sa. req. 9-339484 The log. sine square to seconds in the early part of the Table, where, on account of the groat anil irregular variation, no parts are given, is found by proportion. . Find the log. 9 ne square of i ° 36' 4"- ."36' 0" 6-2899. Then 1 5 : 226 : : 4 : 60, the parts, and the . 36.5 29217 LOO. SINE aaUARE required is 6-29051. diff. 226 12. Inverse Procesi. To find the arc, to 1', corresponding to a given log. aine s(|uare. From the given log. sine square subtract the next less in the Table, to which take out the arc, noting it down. Find the seconds at the bottom corresponding to the difference, and add them to the arc. Ex. Find the arc, to i", coi-responding to 9-029443. Next less 9-029400, arc 38° 11' 15" I 43 at D. 90 gives 7", which added to given -029443 I 38° 11' I5"givethe ARC required,38° 11' 22". diff. 43 I To find the time, to the tenth of a second, corresponding to a given log. •ine square. Find the time corresponding to the next less log. sine square in the table Take the diff. between the given and the next less logs. Find this diff. among the parts ; take out the seconds of arc corresponding, and subtract from it 1 -3d of itself. The rem. is the number of tenths, to be added to the time of the next less. The above is correct enough for common practice, but for greater pre- cision the difference between two terms must be employed, and the result deduced by proportion. To compute a Term. Take the log. sine of half the arc and double it. Table '0. Logarithms for computing the Reduction to the Meridian at Sea. The Table is entered with the Declination at the top and the Latitude at the side. The cases omitted are not eligible. See No. 700. The cases which appear above the vacant spaces in Part L are those in which the body passes the meridian between the pole and the zenith ; those below the spaces are the more common cases, or those which occur between the tropicn and the arctic circles. To rom/tute a Term. Add together 0-30 1 03, the log. cosines of the lat. and decl., and the log. sec. of the meridian altitude. The process of computing the meridian alt. may be avoided thus: when the lat. and decl. are of the same name, employ the Jog. cosec. of their difference (unless tie body is below the pole, when employ the cosec. ol their sum), whin of contrari/ names, the cosec. of their sum. EXPLANATION OF THE TABLES. lat. 9 c( Decl. 17 C( Diff. 8 C( Log. required :) Lat. 9° N., 0-3010 9-9946 9-9806 BC. 0-8564 1-1326 r Ex.2. {Contrary I I Decl. 17° S. ^) Lat. 9= N, 0-3010 Lat. 9° COS. 9*9946 Decl. 17 ' COS. 9-9806 Sum 26 cosec. 0-3582 Log. required o'6344 When the lat. exceeds 62° or the decl. exceeds 23°, the logarithm must be v.omputed. Table 71. LocARiTH.MS for computing the Correction of thl Latitude by Account. The Table is entered with the two Azimuths, either of the same body ai different times, or of two different bodies. See No. 752 (7). Tlie cases omitted are not eligible. Part I. is used when both altitudes are taken on the same side both o( the meridian and prime vertical, and Part 11. when on different sides of either of these circles. To compute the Log. fur Part I. To 8*8239 add the log. cosecants of the azimuths, and the log. sine of their difference. For Part II. To 8-8239 add the log. cosecants of the azimuths, and the log. sine of their sum. Azimuths mme side). 70° W. 70 cosec. 1 1 cosec. 59 sin. Log. required 8-8235, 0-0270 0-7194. 9"933' 9"S°34 Ex. 2. Azimuths S. -/o' 1 1° E., or N. 70° W. and S dijferent sides). ii°W. (0 Az. Az. Sum Loo. required 88239 0-0270 0-7.94 99946 9-5649 Table 72. Logarith\ for computing the EguATioN of Equal Altitudes. These are given to each 10°>. See No. 806 (4). To compute Log. A To 3-28534 add the log. of the interval (in seconds of time), and the log. cosec. of half the interval ; take the arith. compl. ol the sum. To compute Log. B. To 3-28534 add the log. of the interval (in seconds), and the log. cot. of half the interval; take the arith. compl. of the sum. E.\. Interval 4'' 30"'. Commute the logs. A. and B. 3-S3534 I 3'»8534 4> 50'" = 16200* log. 4-20951 4-20951 2 15 cosec. 0-25526 I 2'' 15°' cot. 0-17511 7-750" I 7"6'^996 Log. a. 2-24990 I Log. B. 2-3300 Table 73. The Logarithmic Difference This quantity is given for Fahrenheit's thermometer at 50^ and the Bs.fometer at 30 inches. The Table is entered like Table 39. The parts for " of parallax and tor of alt. are apj lied as diiected in the Table. EXPLANATION OF THK TABLL3. 429 The parts for the sun's or star's alt. an' given at the bottom. To correct the log. dift". for any other height of the tlierraonieter am) barometer than those given in the Table. Find the correction of the mean refraction for each body by Tables 32 and 33. With the moon's alt. and her atmospherical correction, thus found, as jeconds of parallax, take out tlie parts. With the sun's (or star's) alt. as tho moon's ait., and his atinospher. corr. as seconds of parallax, take out the parts. When tlic atmospherical correction is +, add the parts to the mean 07 ordinary loi;. diff. ; when — , subtract them. Ex. (Me lor. par. 6o' Ex. Tlie 88 and therm. 8+°. me corrected for bar. 29-8, Mean log. diff. ^ ^_ 9-99672. B Th. 84." -8*^''' '1 Bar. 29-2 _-, < J Atmos. corr. -11 -11 ^ Th. 84.° Bar. 29-2 Atmos. corr. - 9 -29 -I.J -89 Log. dikf. 9-996632 42 J 8 alt. 10 8' parts —17 j 42" -42 ! © 10° — 8) Required Los. oirF. When a planet is employed, consider it as a star, and its horizontal parallax as seconds of moon's parallax. With its alt. take out the parts and tubtraci tliem. To compute the Log. Diff. Add together the log. secants of the app. alls., and the log. cosines of the true alts. ; the sum is the log. diff. Ej. j a. Alt 'or the mean state of the al Mean State. I 27' 18' o" sec. + 51 5 2g 10 5 COB. 18', Hor. Par. 60' 42". A. Alt. 10' 20': required the Log. Diff. iCre, as also for the therm. 84°, and barom. 29-2 in. Corrected for Therm, and Barom. 0-051285 58 COS. Log. Dirp. -4 33 15 27 COS. Log. diff. The results by the two methods agree as nearly as can be expected from processes in which each of the several parts employed has its own particular inaccuracv. Table 74. Pboportional Logarithms. These logarithms are given to every second of time, or arc, for 3'' or S'^ The Table is entered with the hour or degree and the minute at the lop, and the second at the side; thus the prop. log. of 1° 2' 27" or of l"" 2" 27' is ■4697, that of I" 2' is 2-2410. The index proper to quantities above 19'" (or 19') is suppressed for convenience. To find tho prop. log. of ail arc under 18', to the tenth of a second. Put the proper index, and find the decimal part due to ten times the arc. Ei. Find the prop. log. of 7' i3"-7 ; the index of 7' 13" is i ; the dec. part of the log. fln« to 70' 137'', or 72' 17", is 3962, the prop. log. required 18 1-3962. So tlie prop. log. of an arc, under I' 48" may be found to the hundredth of a second by multiplying by lUO. 430 KXPLANATION OF THE TABLES. To find llie arc or time to the tenth of a second to a given prop. log. exceeding ) -0000. Look in the Table till the decimal part again occurs, and iivide the arc by 10. Ei. Find the time to the prop. log. 2'5io6. Look for 1-5106; the nearest found \» 1*3 1 10, against 5'" 3 3', or 333'; hence the time required is 33''3. Four places are enough for common purposes; but since the fourth placf ceases to change by I after P ]3", a greater time than this cannot be found truly to 1". So also, a time exceeding 2'' 26'" cannot be found tridy to 2'. This defect may be avoided in some cases by employing the complement of the interval to 3^ To convert a given log. sine of an arc less than 1° 30' into a prop. log. add 8'7190 to its arithmetical complement. To convert a prop. log. of an a.c into a log. sine, less than 1'^, add 8-7190 to its arith. compl. Ex. 1. Convert the log. ime 8-3507 Ex.2 Convert the prop. log. of into « prop. log. or 8573, into a log. sine. log. sine 8-3507 pr. log. 0-8573 ar. CO. 1-6493 ar. CO. 9-1427 const. 8-7 190 8-7J90 Arc 1° 17' 5" Prop. log. 0-3683 Log. sine 7-8617 When the terms of an analogy are all sexigesimals, the rules given in p. 20, Nos. C4, &c., apply to the proportional logarithms; but if two of the terms are not sexigesimals, the arith. complements of the logs, of these last must be used.* To compute a Prop. Log. From 4-03342 (the log. of 10800, the number of second's in S"" or 3°) subtract the log. of the given time or arc in seconds; the result is the prop. log. required. Ex. Find the prop. log. of jh , ,n, ^g.. const. 4-03342 x" ll">2g« = 7888', log. 3-89697 Peop. log. 0-13645 The Tables close with the Abbreviations adopted in the Admiraltj Charts, with explanatory notes. These should be committed to memory by sailors. * The proportional logarithms are often convenient, but they might l-e leplaced witL advantage by common logarithms. The prop, logs., unlike the common logarithms, conti- nually decrease instead of increasing with the argument. This progression is always repug- nant to the mind, and should be avoided when the change involves no sacrifice Again, these logarithms require every factor with which they are combined to be inverted , that is, for ex., instead of multiplying by 2, they oblige us to divide by 2. This, even to an expert •-oraputer, is the cause of perpetual mistakes in the changing of constants ; but to a beginner It has the mischievous effect of entirely destroying, in processes which may nevertheless be identical, every vestige of analogy. If common logarithms, with the same scale and the index prefixed, were enipli>yed, the logarithm attached, in the Nautical Almanac, to the lunar distance, would involve the con- etant for 3*". Such logarithms would answer all the present purposes without being open to any of the above objections ; the log. in the Nautical Almanac would then be additive instead of suhtractive. The proportional logarithms, originally computed for the purpose of sim- plifying a single step in a single computation, are an example of the ill effects of gaeriticing %iv,tm\ utility to a partia". end ; and the substitution of others, at a favourable opportunity, h rfcorantended as a reform deservi-ig atteition. TABLES. TRAVERSE TABLE TO DEGREES — 1 1° OM-^^j DistJD.L .ulDep. Dist. D.L ^[Dep. Disr.lD.I.at. Dep. Dist.|D.Lat Dep. Distb. Lat. Dep. ~T~ 0' o-o 61 61 I , 121 I2I-0 181 1 i8i-o 3-2 241 241-0 4'- 2 1 I 1 o-o 62 6i ' I I 122 122-0 r I 182 1 182-0 242 4-2 3 1 3 o-i 63 63 °\ ' I 1-23 123-0 I 1831 183-0 243 243 4'- 4 ' 4 o-i 04 64 : 124 124-0 2 184 184-0 244 -44 4' 3 S i 5 o-i C5l 65 I I 120 125-0 2 2 185 185-0 245 245 4' 3 6 , 6 O-I CO 66 I 2 126 126-0 2 180 186-0 246 246 4'3 7 7 Q OM 671 67 I 2 127 127-0 2 187 187-0 247 247 4" 3 8 8 O-I 68 68 1 2 128 I28-0 188 188-0 248 248 4 3 r 0-5 91 9' I 6" 151 I5I-0 211 2II-0 271 271 4'7 32 32 0-6 92 92 I 6 152 152-0 212 212-0 272 272 4-7 33 33 0-6 93 95 I 6 153 153-0 2 213 213-0 273 273 4-8 34 34 0-6 94 94 I 6 154 154-0 214 214-0 274 2 74 d 4-8 35 35 0-6 95 95 I 7 155 155-0 215 215-0 278 275 4-8 36 36 0-6 96 96 I 7 156 156-0 216 216-0 376 276 4-8 37 37 0-6 •97 97 1 7 157 157-0 217 217-0 277 277 4-8 38 38 0-7 98 98 I 7 158 158-0 218 218-0 278 27S 4-9 39 39 0-7 99 99 I 7 159 159-0 219 219-0 279 279 4-9 40 40 0-7 100 I 7 160 .60-0 220 220-0 280 280 4-9 41 41 ^ 0-7 -m ,01 'o^nr g 101 .61-0 221 22I-0 •281 281 4'9 42 4=' 0-7 102 102 I 8 162 162-0 222 222-0 3'9 282 2S2 4"9 43 43 0-8 103 103 I 8 163 163-0 223 223-0 3"9 283 283 4-9 44 44 0-8 104 ' 104 I 8 164 164-0 9 224 224-0 284 284 5-0 45 45 0-8 105 105 I 8 165 165-0 9 225 225-0 285 285 5-0 46 46 0-8 106 106 I 8 106 166-0 9 226 226-0 286 286 5-0 47 47 0-8 107 107 : I 9 167 167-0 9 227 227-0 287 287 5° 48 o-S 108 108 ol 1 9 168 I6S-0 9 228 228-0 288 288 5-0 4!) ^9 0-9 109 109 1 I 9 169 9 -:29 229-0 289 289 5-0 50 5° 0-9 110 1 I _9_ 170 l-?-o 230 230-0 290 .-9° .,5-' 51 5' ^ 0-9 ur TIT "o"" 9 TfT ^TTT ~ ~ 231 29r 177 5-> 52 52 0-9 112 112 ! 2 172 I--2-0 232 232-0 292 292 5-1 53 53 0-9 1131 113 2 173 3 233 233-0 293 293 5-1 54 54 0-9 114' 114 2 174 i-4'O 3 234 234-0 294 294 51 55 55 115 115 ^ 173 3 235 235-0 295 ^-95 5' 56 56 I-o 116 116 1 -1 170 176-0 3 230 236-0 296 296 5-2 57 57 I-o 117 "7 1 2 177 177-0 3 237 237-0 297 297 5-» 58 ,58 1-0 118 118 I 178 I7S-0 3 238 238-0 298 298 5-' S9 59 ' I-o 119 119 I 179 179-0 239 239-0 299 299 c 5-1 fin ' 6o-o 1 i-o 1201 I20-0' 2 1 180 i8o-o 3-1 240 240-0 300 300-0 5-^ Uisl.jDep. JD.Lat UistJ D.-i). Id. Lat Dist Dep. D.La>. Dist. Dep. D. Lat Dist. D..,.. D. 1,.'. 8 9" £" j6^" TRAVERSE TABLE TO DEGREES 1° Oh 4m DisL D.Lat Dep. Dist D.Lat Dcp. Dist. D.Lat Dep. Dist.;D. Lat. Dep. Dist. D.Lat. Dep. 301 301-0 5-3 361 360-9 63 421 420-9 7-3 481 480-9 8-4 541 5409 95 302 3020 53 362 361-9 6-3 422 421-9 7-4 482 j 4S1-9 8-4 542 541-9 95 30.-5 3030 S3 363 3629 6-3 423 4229 7-4 483 482-9 P 543 5429 9-5 304 3040 S3 364 3(yy9 6-4 424 423-9 7-4 484 1 4S3-9 ^•5 544 543-9 9-5 305 3050 53 36.) 364-9 6-4 425 4249 7-4 4S5 ' 4849 8-5 54.-. 544-9 95 306 3060 5-3 366 365-9 6-4 426 425-9 7-4 486 1 485-9 8-5 546 545-9 95 307 307-0 54 367 366-9 64 427 4209 7-4 487 486-9 8-5 54 7 546-9 9-6 308 3080 54 368 367-9 6-4 428 427-9 7-5 488 487-9 8-6 54S 547-9 96 309 3090 5-4 369 368-9 6-4 429 428-9 7-5 489 48S-9 86 549 548-9 9-6 310 sir 3100 3110 5-4 5-4 370 57T 369-9 370-9 6-5 430 429-9 7-5 490 49r 4S9-9 8-6 8-6 550 551 ^549-9 5509 9-6 65 431 430-9 7-5 490-9 9-6 312 3120 5-4 372 3719 6-5 4.32 431-9 7-5 492 491-9 8-6 5.52 5519 9-6 313 3'3o 5-5 373 372-9 6-5 433 432-9 7-5 493 492-9 P 553 552-9 9-7 314 3140 5-5 374 373-9 65 434 433-9 76 494 493-9 !'7 554 553-9 97 315 3' 50 5-5 375 374-9 6-5 435 434-9 7-6 495 494-9 8-7 555 554 9 9-7 316 3160 5-5 376 37S-9 6-6 436 435-9 7-6 496' 495 9 8-7 556 555-9 9-7 317 317-0 55 377 3769 6-6 437 i 436-9 7-6 497 1 4969 8-7 557 556-9 9-7 318 31S0 5-5 37S 377 9 66 438 ' 437-9 76 498 1 497-9 8-7 558 5579 9 7 319 319-0 5-6 379 378-9 6-6 439 ' 438-9 77 499 49S 9 88 559 558-9 320 3200 _5-6 380 379-9 6-6 440 4399 ^7-7 500 499-9 8-8 560 559-9 98 321 32 1 "S 5-6 ssT 380-9 67 441 1 4409 7-7 soil 5009 8-8 seT 560-9 9-8 322 322-0 5-6 382 3819 67 442 441-9 7-7 50i 501 q 8-8 562 561-9 9-8 323 323-0 5-6 383 3S2-9 67 443 4429 7-7 503 502-9 88 563 562-9 9-8 324 324-0 56 384 383-9 6-7 444 443-9 504 5039 88 564 563-9 9-8 325 3250 5-7 385 3849 67 445 444-9 7-8 5o:> 50 1 9 88 565 564-9 9-9 326 ; 3260 5-7 386 385-9 6-7 446 445-9 7-8 506 S059 89 566 5659 9-9 327 3270 57 3'i7 386-9 6-8 447 4469 7-8 507 5069 89 567 566-9 9-9 328 32S-0 5-7 388 3S7-9 6-8 448 1 447-9 7-8 SOS 507-9 89 568 5679 9-9 329 329-0 S-7 339 388-9 6-8 449 1 44S-9 7-8 509 508-9 8-9 569 568-9 99 330 330-0 5-8 390 3S9-9 6-8 450 1 449-9 78 510 509-9 8-9 570 569-9 99 33? 33 'o 5S 391 390-9 6-8 451 1 450-9 79 511 510-9 90 571 570-9 100 332 332-0 5-S 392 391-9 6-S 4.52 451-9 7-9 512 511-9 90 572 57'-9 100 333 3330 ^1 393 392-9 6-9 453 4529 7-9 513 5129 9-0 573 572-9 1 0-0 334 333-9 5-8 394 3939 6-9 454 453-9 7-9 514 1 513-9 9-0 574 573-9 100 335 1 334-9 5-8 395 3949 6-9 455 454-9 7-9 515 514-9 9-0 575 574-9 100 33'"' 335-9 S-9 396 3959 6-9 456 455-9 8-0 516 515-9 90 576 575-9 10-0 337 1 336-9 5-9 397 396-9 1^ 457 4569 So 517 516-9 91 577 5769 IO"I 338 337-9 S9 398 397-9 69 45S 1 457-9 So 518 517-9 9-1 578 577-9 10 I 339 33S-9 5-9 399 398-9 7-0 4 59 458-9 80 519 518-9 91 579 578-9 lo-i 340 341 339 9 340-9 59 400 401 3999 460 , 4599 461 1 4609 8-0 520 5199 91 580 579 9 5809 lo-i 155? 70 ~8^ m 520-9 lo-i 342 341-9 60 402 401-9 7-0 462 1 461-9 8-1 522 521-9 91 582 581-9 10- 1 343 342-9 6-0 403 402-9 7-0 463 1 462-9 8-1 523 522-9 9-2 583 582-9 10-2 344 343-9 60 404 403-9 7-1 464 . 4639 S-i 524 523-9 9-2 .584 583-9 10-2 345 344 9 6-0 405 404-9 7-1 465 464-9 8-1 525' 524-9 92 585 584-9 10-2 346 345-9 60 406 1 4059 7-» 466 1 465-9 81 526 1 525-9 9-2 586 585-9 102 347 346-9 6-1 407 4069 71 467 , 466-9 8-1 527 1 5269 9-2 587 5869 102 348 3479 6-1 408 ' 407-9 71 468 467-9 8-2 528 ! 527-9 9-2 588 5879 102 349 SA^V 6-1 409 • 40S 9 7-1 469 468-9 8-2 529 528-9 9-3 589 5889 'O3 350 35T 349-9 350-9 6-1 4 1 1 400 9 7-2 470 1 469-9 8-2 530 531" 529-9 5309 9-3 590: 5899 591 r 590-9 ■03 6T~ 411 410-9 7-2 471 ' 470-9 2" 9-3 10-3 352 35 '-9 6-1 412 411-9 7-2 472 471-9 8-2 532 53«-9 9-3 592 591-9 IO-3 353 3529 6-2 413 412-9 7-2 473 1 472-9 8-2 533 532-9 9-3 593 1 592-9 103 354 353-9 6-2 414 4>39 7-2 474 [ 473-9 8-3 534 533-9 9-3 594 j 5939 '03 355 354-9 6-2 415 414-9 7-2 475 1 474-9 8-3 .535 534-9 94 595 ' 594-9 10-4 356 3559 6-2 416 4«5-9 73 476 , 475-9 8-3 536 5359 9-4 596 1 595-9 104 357 356-9 62 417 1 416-9 7-3 477 476-9 8-3 537 536-9 94 597 1 596-9 10-4 358 3579 6-2 41S 417-9 73 478 1 477 9 8-3 538 537-9 9-4 598 ] 597-9 10-4 359 35S9 63 419 4rS9 73 479 1 478 9 8-4 5.-i9 5389 9-4 .599 598-9 10-4 360 359 9 6-3 420 419-9 7-3 480 ; 479 9 84 540 , 539-9 94 600' 599 9 10-5 Dial Dc-p. I).L-,t. Dist. Dcp. D. Lat Dist. n.-p. D. Lat. DUt.l Dep, D. Lat Dist.l Dep. D. Lat. 81P 5h 56"- 1 TABLE 1 TRAVERSE TABLE TO DEG REE8 ~\ 2^ 0" 8™ J D.st.D.Lal Dep. DistJo.L.it. Dep. Uist. D.Lat. Dep. Dist-lD.Lat. Dep. Dist.| D.Lat. D.p. 1 i-o o-o 61 6i-o ' 2'I 121 120-9 4-- 181 i8o-9 6-3 241 1 240-9 8-4 2 \ .-0 o-i 62 62-0 2-2 122 121-9 4-3 182 181-9 6-4 242 241-9 ;i 30 o-i 63 63-0 1 2-2 123 122-9 4'3 183 182-9 6-4 243 242-9 8 4 4-0 O-I 64 64-0 124 123-9 4-3 184 183-9 6-4 244 243-9 5 5-0 0-2 65 65-0 125 124-9 4'4 185 184-9 6-5 245 244-9 « , 6-0 0-2 66 6b-o 126 125-9 4-4 186 185-9 6-5 246 245-9 7 ■ 7-0 67 67-0 127 .26-9 4-4 187 186-9 6-5 247 246-8 8 8 ; 8-0 °'3 68 68-0 128 127-9 4-5 188 187-9 6-6 248 247-S 9 9-0 0-3 69 h-c j i;4 129 128-9 4-5 189 188-9 6-6 249 248-8 10 o'3 70 130 125-9 4-5 190 189-9 6-6 250 249-8 TV c-4 71 7I-0 2-5 131 130-9 4-6 191 190-9 6-7 251 250-8 8 8 12 Il'O 0-4 72 72-0 2-5 132 131-9 4-6 192 191-9 6-7 252 251-8 8 8 IS i 13-0 °'5 73 73-0 2-5 133 132-9 4-6 193 192-9 6-7 253 252-8 8 8 14 I I4-0 74 74-0 2-6 134 133-9 4-7 194 193-9 6-8 254 253-8 8 9 15 ' M-o 0-5 75 75-0 2-6 135 134-9 4-7 190 194-9 6-8 255 254-8 8 9 U; 1 i6-o 0-6 76 76-0 2-7 136 "35-9 196 195-9 6-8 256 255-8 8 9 17 1 17-0 0-6 77 77-0 2-7 137 .36-, 4-8 197 196-9 6-9 257 256-8 9 18 1 i8-0 0-6 78 138 >37-9 4-8 198 197-9 6-9 258 257-8 9 19 ! 19-0 0-7 79 79-0 2-8 139 138-9 49 199 6-9 259 258-8 9 20 1 .o-o o'y 80 2-8 140 139-9 4-9 200 199-9 260 259-8 _^ 21 : aio 0-7 81 8 I-o 2-8 141 140-9 4-9 201 200-9 7-0 26r 260-8 9 22 22-0 0-8 82 82-0 2-9 142 141-9 5-0 202 201-9 7-0 262 261-8 9 23 23-0 0-8 83 82-9 2-9 143 142-9 5-0 203 202 -9 7-1 263 262-8 9 24 24-0 0-8 84 83-9 2-9 144 1439 5-0 204 203-9 7-1 264 263-8 9 25 25-0 0-9 85 84-9 145 144-9 5-1 205 204-9 7-2 265 264-8 9 26 26-0 0-9 86 85-9 146 145-9 5-1 206 205-9 7-2 266 265-8 9 27 27-0 0-9 87 86-9 147 146-9 5-1 207 206-9 7-2 267 266-8 9 28 28-0 88 87-9 148 147-9 5-2 208 207-9 7-3 268 267-8 9 29 29-0 i-o 89 88-9 149 HS-9 5-2 209 208-9 7-3 269 268-8 9 30 i-o 90 150 149-9 5'2 210 209-9 7-3 270 269-8 9 "sT 31-0 11 91 90-9 3-2 TsT 150-9 5-3 211 210-9 7 "4 27r 270-8 9 32 32-0 i-i 92 91-9 152 151-9 5-3 212 211-9 7-4 272 271-8 9 33 33-0 1-2 93 92-g 3-2 153 152-9 5-3 213 212-9 7*4 273 272-8 9 34 ri 94 93-9 3-3 154 j 153-9 5-4 214 213-9 7-5 274 273-S 9 35 35-0 1-2 95 94-9 3-3 155 154-9 5-4 215 214-9 7-5 275 274-8 9 36 36-0 '•3 96 95-9 3-4 156 155-9 5-4 216 215-9 7-5 276 275-8 9 37 37-0 i'3 97 96-9 3-4 157 156-9 5-5 217 216-9 7-6 277 276-8 9 38 38-0 '•3 98 97-9 3-4 158 1 15-9 5-5 218 217-9 7-6 278 277-8 9 39 39-0 1-4 99 98-9 3-5 1591 158-9 5-5 219 218-9 7-6 279 278-8 9 40 40-0 '■4 100 99-9 1 3-5 160 1 159-9 5-6 220 ^'9-9 7-7 280 279-8 9 41 ! 41-0 1-4 101 100-9 1 3-5 161 i 1609 5-6 221 220-9 7-7 281 280-S 9 42 ' 4:^0 ■•5 102 .01-9! 3-6 I62! 161-9 5-7 222 221-9 7-7 282 281-8 9 43 : 43-0 103 102-9 3-6 163 162-9 5-7 223 222-9 7-8 283 282-8 9 44 44-0 '■5 104 103-9 3-6 164 163-9 5-7 224 223-9 7-8 284 283-8 9 45 450 1-6 105 104-9 3-7 165 164-9 5-8 225 224-9 7-9 285 284-8 9 9 46 460 1-6 106 105-9 3- 7 166 ,65-9 5-8 226 225-9 7-9 286 285-S 10 47 ! 47-0 1-6 107 106-9 3-7 167 166-9 5-8 227 226-9 7-9 287 2S6-S 10 48 1 480 108 107-9 3-8 168 167-9 5-9 228 227-9 8-0 288 287-8 10 19 ; 49*° 109 108-9 3-8 169 168-9 5-9 229 228-9 8-0 289 2SS-S ^0 ! 50-0 1'7 110 109-9 3-8 170' l6q-9 5-9 230 229-9 S-o 290 289-8 10 51 1 51-0 ^T- 111 1IO-9 3'9 171 i 170-9 6-0 231 230-9 8-1 loT 2'l-8 To 52 52-0 1-8 112 111-9 3-9 172 171-9 6-0 232 231-9 8-1 292 10 53 53-0 1-8 113 112-9 3'9 173 172-9 6-0 233 232-9 S-i 293 292-8 10 54 54-0 1-9 114 113-9 4-0 \7i 173-9 61 234 233-9 8-2 294 293-8 10 55 5 5-0 ly 115 114-9 4-0 175 174-9 6-1 235 »34-9 8-2 295 294-8 10 56 1 56-0 116 1159 4-0 176 "75-9 61 236 235-9 8-2 296 295-S 10 57 1 57-0 117 1.6-; 4'' 177 .76-9 6-2 237 236-9 8-3 297 296-8 10 58 580 118 J17-9 4'i 178 177-9 6-2 238 137-9 8-3 298 ;97;S 10 5S 1 59-0 119 .iS-9 4-2 179 178-9 6-2 239 238-9 S-3 299 10 60 1 6o-o ''' 120 119-9 4'i 180 179-9 6-3 240 239-9 8-4 300 -99-8 10-5 ^l"^ U.Lat Dist Uep. D.Liit Dist Dep. U. Lat. Dist Dep. D. Uu Dist Dep. D. Lat. 8 ^° Sk 52'" TAELK 1 4155 TK AVEliSE TAliLE TO DEUKEES 1 2° Ohe- 1 Ui6t.:D.L.t 301 30O-S Dep. 10-5 Dist.'o.Lat. 361 1 3608 Dep. Dist. D. I.a. Dep. Dist.'n. Lat. Dtp. Dist. D. Lat Dep. .2-6 421 420-S .4-7 481 , 4S07 16S 541 5407 .89 302 301 -S 10-5 362 361-8 12-6 422 42.-8 .4-7 482 481-7 168 542 54'-7 .8-9 303 302 S 106 363 1 362 8 12-7 423 4228 .4-7 483 4S2-7 168 543 542-7 189 304 ! 303S 10 6 364 1 363-S 12-7 424 423-8 14-8 484 483-7 16-9 544 543-7 .90 305 304 8 10-6 365 : 364 8 127 425 424-S 14-8 4S5 4S4-7 .6-9 545 544 7 190 306 [ 305-8 107 366 ; 365-8 12-8 426 425-7 14-9 486 4857 16-9 546 545-7 190 307 306S .07 367 3668 .2-8 427 4267 149 487 [ 486-7 170 547 546-7 19-1 308 307-8 10-7 368 367-8 12-8 428' 427-7 14-9 488 ■ 4S7-7 170 548 547-7 191 309 30S-S loS 369 36S-8 12-9 429 , 42S-7 15-0 489 ' 4S8-7 17-0 549 548-71 '9-1 jm 309 s 10-S 370 3698 129 430 \ 4297 15-0 490 ' 4S9-7 17-1 550 549 7 1 '9-2 311 , 3I0-S " lo-S 371 370-8 12-9 431 430-7 .50 491 490-7 .7-1 551 55071 19-2 31-j' 311 S 10-9 372 1 37 1 -8 130 432 431-7 15 I 492! 4917 .71 552 551-7 .9-2 313 312S 10-9 373 1 372-8 .30 433 4327 151 493 492-7 17-2 553 552-7 '9-3 314 313-8 10-9 374 1 373-8 .3-0 ■m 1 433-7 '5' 494 493-7 17-2 554 553-7 193 315] 3I4-S no 373 3748 I3-I 435 1 434-7 15-2 495 494-7 17-2 555 5547 19-3 316 ! 315-8 II 376 3758 131 -136 { 435 7 15-2 496 4957 '7-3 556 555-7 19-4 317 ■ 3168 no 377 376-8 «3-i 437 4367 152 497 496-7 '7 3 557 556-7 '9-4 318 1 317S III 378 377-8 13-2 •*'38 437-7 '5-3 498 4977 '73 558 5577 319| 3188 379 378-8 13-2 439 438-7 '5-3 499 498-7 '7-4 559 558-7 .9-5 320 1 3198 1 1-2 380 379-8 13-2 440 1 439-7 ^53 500 499 7 17-4 560 559 7 19-5 321 "320-8 112 sir 380-8 13-3 441 1 440-7 '54 501 500 7 '7-5 loT 560-7 '9-5 322 i 321 8 II-2 382 38.-8 J 33 442 441-7 15-4 502 501-7 17-5 562 56' -7 196 323 ' 322 8 II-3 383 382-8 13-3 443 442-7 '5-4 503 502-7 175 563 5627 19-6 324 32 v8 II-3 384 3838 .34 444 443-7 15-5 504 5037 176 504 563-7 .9-6 325 1 32i-8 113 385 3848 13-4 445 444-7 '5-5 505 504-7 176 565 564-7 .97 326 325-8 II-4 386 385-8 135 446 ! 445-7 .56 506 505-7 17-6 566 565-7 .9-7 327 i 326-8 1 1-4 387 386-S .3-5 447 i 446-7 15-6 507 506-7 17-7 567 566-7 '9-7 328 327 8 n-4 388 387-8 448 ' 447-7 15-6 508 507-7 17-7 568 567-7 19-8 329 1 328 8 115 389 3SS-8 '36 449 j 448-7 '5-7 509 508-7 17-7 569 568-7 198 330 ! 329-8 331 1 3308 II-5 390 391 389-8 390-8 136 .36 450 1 449-7 451 t 4507 '5-7 '5-7 51(1 511 509-7 510-7 17-S 570 In 569-7 570-7 '99 19-9 115 '7-8 332 ! 331-8 1 1-6 392 391-8 13-7 452, 45'-7 '5-8 512 5.17 '7-8 572 571-7 '99 333 1 332 8 11-6 393 3928 13-7 453 1 452-7 15-8 513 512-7 '79 573 5727 200 334 333 8 11-6 394 393-8 13-7 4541 4537 '58 514 513-7 17-9 574 573-6 200 335 334-8 11-7 395 394-8 138 455 454-7 '59 515 5'47 .7-9 375 574-6 200 336 335-S 11-7 396 395-8 13-8 456 455-7 159 516 5'5-7 18-0 376 575-6 20-1 337 336-S 11-7 397 396-8 .38 457 ' 456-7 15-9 517 5.67 18 5766 20 . 333 337 8 11-8 398 397-8 13-9 458: 457-7 .6-0 518 517-7 181 578 577-6 201 339 338S irS 399 398-8 .39 459. 458-7 16-0 519 518-7 .81 579 57S6 202 340 339-8 341 i 3408 11-9 400 J99:8 401 ! 4008 JS9_ 140 4C0 , 459 7 461 1 460-7 16-0 520 521 J'^7 520-7 .81 .8-2 580 "ssT 579-6 5S06 20-2 20-2 342 34 1 -S 11-9 402 401-8 14-0 462 i 461-7 16-1 522 52.7 182 582 58.-6 20-3 3J3 1 342-S 120 403 1 402-S 14-0 463 ! 462 7 161 523 5227 18-2 583 582-6 20-3 344 3438 120 404 1 4038 141 464 j 463-7 16-2 524 523-7 '8-3 584 583-6 20-3 345 344 8 120 405 404-8 14-. 465 4647 162 525 524-7 '8-3 585 584-6 204 346 34S8 121 4()f, 1 405-8 14-2 466 465-7 16-2 526 525-7 1 8-4 386 585-6 20-4 347 34O8 121 407 406-8 14-2 467 , 466-7 .6-3 527 5267 i8-4 587 5S6-6 20-4 348 3478 121 40S 1 407-8 14-2 468 467-7 '6-3 528 527-7 18-4 588 5876 20-5 349 : 348-8 122 409 40S-8 14-3 469 468-7 .6-4 529 528-7 .8-5 589 588-6 20-5 350 351 3498 350-8 12-2 12 2 410 1 409-8 411 ; 4108 .4-3 '4 3 470 409-7 471 4707 16-4 530 J29-7 _.8:5 r.90 5S96 20-5 .6-4 531 5307 "8-5 5906 20-6 352 35'-'' 123 412 1 4n-8 144 472 47.7 16-5 532 53'-7 18-6 592 59.6 206 353 3528 123 413 1 412-8 14-4 473 4727 16S 533 5327 .8-6 593 5926 20-6 351 353-8 12-3 414 j 413-8 14-4 474 473 7 16-5 534 533-7 .8-6 593-6 207 355 3548 124 415; 414-8 •4-5 475 474-7 16-6 535 534 7 '8-7 595 594-6 20 7 356 355-8 124 416 4.5-8 '45 476 475-7 .6-6 536 5357 1 87 596 5956 207 357 356S 12-4 417 416-8 '45 477 476-7 166 537 536-7 iS-7 597 596-6 20-8 358. 357-8 12-5 418 4.7-8 '46 478' 477-7 .6-7 538 5377 iSS 598 597-6 208 359 358S 419 418-8 146 479 4787 .6-7 539 5387 18-8 599 598-6 20-8 360 3598 12-5 420 4.9-8 146 480 1 479-7 .67 540 539-7 188 6u0 5996 209 ^ d:,.. D. Lat ^ "■'•^ D. Lat. Dist.| Dfp. D. Lai DUt. Dep. D. Lat Dist. Dep. JD.Latj 88° 5h 52"> 1 486 TRAVERSE TABLE TO DE 3REES 3° 01. 12." Dist D.Lat| Dei.. Dist.|D. Lat Dep. Dist.lo. Lat Dep. Dist D.Lat Dep. Dist.D.L;.t. Dep. 1 :-o| o-i 61 1 60-9 3'- 121 1 120-8 6-3 181 18G-8 9-5 241 1 240-7 1 12-6 2 2-0 o-i 62 61-9 3-2 122 1 .21-8 6-4 182 i8i-8 9-5 242 1 241-7' 12-7 3 3'° ' 0'2 63 62-9 3-3 123 .22-8 6-4 183 182-7 9-6 243 242-7 I 12-7 4 4'° 0-2 64 63-9 3-3 124 .23-8 6-5 184 183-7 9-6 244 243-7 ' 12-8 5 5-0 0-3 65 64.9 3'4 125 124-8 6-5 185 184-7 9-7 245 1 244-7! 12-8 6 6-0 0-3 66 «5-9 3-5 126 125-8 6-6 186 185-7 9-7 246 245-7, 12-9 7 yo 0-4 67 66-9 3-5 127 126-8 6-6 187 1S6-7 9-8 247 246-7 1 12-9 8 8-0 0-4 68 67-9 3-6 128 127-8 6-7 188 187-7 9-8 248 247-71 13-0 9 9-0 0-5 69 68-9 3-6 129 12S-S 6-8 189 188-7 9-9 249 248-71 13-0 10 lO'O 0-5 70 69-9 3-7 130 129-S 6-8 190 .89-7 9-9 250 249-7 1 13-1 11 ii-o 0-6 71 70-9 3-7 nr 130-8 6-9 191 .90-7 251 250-7 1 13-1 12 I2-0 0-6 72 71-9 3-8 132 131-8 6-9 192 191-7 lo-o 252 251-7! .3-2 13 I3-0 °'7 73 72-9 3-8 133 132-8 7-0 193 192-7 lo-i 253 252-7 1 13-2 14 I4-0 0-7 74 73-9 3-9 134 133-8 7-0 194 193-7 10-2 254 253-7 •3-3 1,5 15-0 0-8 75 74-9 3*9 135 134-8 195 194-7 IO-2 255 254-7 '3-3 16 i6-o 0-8 76 75-9 4-0 136 135-8 7-1 196 '95-7 10-3 256 255-6 ■3-4 17 lyo 0-9 77 76-9 4-0 137 136-8 7-2 197 196-7 IO-3 257 256-6 13-5 18 iS-o 0-9 78 77-9 4' I 1.38 137-8 7-2 198 197-7 10-4 258 257-6 '3-5 19 I9-0 79 78-9 4-1 139 138-8 7-3 199 .98-7 10-4 259 258-6 13-6 20 i-o 80 79-9 4-^ 140 139-8 7-3 200 199-7 10-5 260 259-6 jr6 21 21-0 IM 81 80-9 4-2 141 140-8 7-4 201 261 260-6 ^yi 22 2I-0 I-I 82 81-9 4-3 142 14.-8 7-4 202 20I-7 10-6 262 26.-6 13-7 1 23 23-0 1-2 83 82-9 4-3 143 142-8 7-5 203 202-7 10-6 263 262-6 13-8 24 24-0 1-2 84 83-9 4-4 144 143-8 7-5 204 203-7 10-7 264 263-6 .3-8 25 avo ■•3 85 84-9 4-4 145 144-8 7-6 205 204-7 10-7 265 264-6 '3-9 26 26-0 1-4 86 859 4-5 146 145-8 7-6 206 205-7 10-8 266 265-6 '3-9 27 2"0 1-4 87 86-9 4-6 147 146-8 7-7 207 206-7 IO-8 267 266-6 14-0 28 2So 1-5 f8 87-9 4-6 148 147-8 7-7 208 207-7 10-9 268 267-6 14-0 211 -9"° 1-5 89 4-7 149 148-8 7-8 209 208-7 10-9 269 26S-6 14-1 30 3°-° 1-6 90 89-9 4-7 150 149-8 7-9 210 209-7 270 269-6 14-1 31 310 1-6 91 90-9 4-8 137 7-9 211 210-7 ii-o 271 270-6 14-2 32 32-0 1-7 92 91-9 4-8 152 ITvl 212 211-7 ii-i 272 271-6 14-2 33 33-0 1-7 1 93 9-'9 4-9 153 152-8 S-o 213 212-7 ii-i 273 272-6 34 34-0 1-8 94 93-9 4-9 154 153-8 S-i 214 213-7 11-2 274 273-6 ■4-3 35 35-0 1-8 95 94' 9 5-0 155 154-8 8-1 215 214-7 II-3 275 274-6 14-4 3S 36-0 i'9 96 95'9 5-0 156 155-S 8-2 216 215-7 11.3 276 2-5-6 14-4 3/ 36-9 '■9 97 96-9 157 156-8 8-2 217 2,6-7 11-4 277 276-6 14-5 38 37-9 98 97'9 j-i 158 157-8 8-3 218 217-7 11-4 278 277-6 14-5 39 38-9 2-0 99 98-9 5-2 159 158-8 8-3 219 218-7 11-5 279 278-6 40 39-9 2-1 100 99-9 5-2 160 159-8 8-4 220 219-7 11-5 280 279-6 14-7 IT 40-9 2-1 Tor 100-9 5-3 ToT 160-S 8-4 221 220-7 11-6 281 280-6 .4-7 42 41-9 2-2 102 101-9 5-3 162 161-8 8-5 222 221-7 II-6 282 281-6 ,4-8 43 1 42-9 2-3 103 102-9 5"4 163 162-8 8-5 223 222-7 11-7 283 282-6 14-8 44 J43-9 -■3 104 103-9 5-4 164 163-8 8-6 224 223-7 11-7 284 283-6 ■4-9 4.i 1 44-9 105 104-9 5-5 105 164-8 8-6 225 224-7 285 2S4-6 14-9 4i; ! 4 5-9 -■4 lOB 105-9 5-5 166 i6f-S 8-7 226 225-7 ii-S 286 285-6 15-0 47 146-9 2-5 107 io6-; 5-6 167 166-8 8-7 227 226-7 11-9 -287 286-6 15-0 48 47-9 = ■5 108 107-9 5-7 168 167-8 8-8 228 227-7 11-9 288 2S7-6 49 48-9 109 ioS-9 5-7 169 8-8 229 228-7 12-0 289 2S8-6 15-1 50 499 2.6 110 109-9 5-8 170 169-8 S-q 230 229-7 12-0 290 2S9-6 15-2 51 509 2-7 111 -iT^rj^ 171 170-8 8-9 231 230-7 12- 1 291 290-6 152 5? 51-9 2-7 112 .11-8 1 5-9 172 171-8 9-0 232 231-7 12-1 292 291-6 '5-3 53 52-9 2-8 113 112-8 j 5-9 173 172-8 9-1 233 232-7 12-2 293 292-6 15-3 54 S3-q i'8 114 1,3-8' 6-0 174 173-8 9-1 234 233'7 12-2 294 293-6 '5-4 55 54-9 ! z-9 1 115 .14-8 6-0 175 .74-8 9-2 235 »34-7 12-3 2.95 294-6 ■5-4 56 5S-9 2-9 116 1.5-8 6-1 176 175-8 9-2 236 ^35-7 12-4 296 295-6 15-5 57 56-9 j-o 117 .,6-8 6-, 177 176-S 9-3 237 236-7 12-4 297 296-6 '5*5 58 57'9 3-0 118 .17-? ' 6-2 178 1 177-8 9' 3 238 237-7 12-5 298 297-6 .5-6 59 58-9 119 iiS-S ; 6-2 179 1 .78-8 9-4 239 23S-7 12-5 299 29S-6 60 599 3-' 120 1I9-S 6-3 180 179-8 9-4 240 239-7 1 12-6 300 299-6 ir- Uist. Dep. D.Lat Dist Dep. p.Lat Dist. Dep. D. Lat. Dist Dep. D. Lat. EiTu Dep. D. Lat 87 ° 5M8- j TKAVERSE TABLE TO DEGKKES | S° Oh 12"' 1 DiBt !d. I.at D>p. Di>t D. Lat Dep. Dist D.Lat Dep. Dist D.Lat Dep. Dist. D. Lat Dop. 301 3006 !".77" 361 360-5 iS-9 421 420-4 22-0 481 480-3 25-2 541 S40-2 28-3 302 301-6 15-S 362 36.-5 19-0 422 421 4 22-1 482 481-3 252 542 541-2 28-4 303 : 302 6 15-9 363 362-5 19-0 423 422-4 22-2 483 4S2-3 25-3 543 542-2 28-4 304 303-5 159 364 363-5 19 1 424 4234 22-2 484 483-3 253 544 543-2 28-5 305 304-5 160 365 364-5 19-1 425 424-4 22-3 485 484-3 254 545 544-2 28-5 3U0 30V5 160 366 365-5 19-2 426 ' 425-4 223 486 485-3 25-4 546 545-2 28-6 307 3065 161 367 366-5 192 427 , 426-4 22-4 487 4S63 25-5 547 546-2 286 308 307-5 i6-i 368 367-5 19-3 428 427-4 22-4 488 487-3 255 548 547-2 28-7 309 308-5 16-2 369 368-5 '93 429 4284 22-5 489 488-3 25-6 549 548-2 28-7 310 3095 16-2 370 3695 194 430! 429-4 225 490 489-3 25-6 550 5492 28-8 3lT 3105 16-3 371 370-5 19-4 431 1 430-4 22-6 491 490-3 25-7 551 550-2 28-8 312 311-5 16-3 372 371-5 19-5 432 43'-4 22-6 492 49 '-3 25-7 552 S5'-2 28-9 313 312-5 16-4 373 372-5 '9-5 433 432-4 22-7 493 492-3 25-S 553 552-2 289 314 3>3S .6-4 374 373-5 19-6 434 433-4 22-7 494 4933 259 554 553-2 29-0 315 3>4-5 16-5 375 374-5 19-6 435 434-4 228 495 494-3 259 555 554-2 29-1 316 315-5 166 376 375-5 197 436 435-4 22-8 496 4953 260 556 555-2 29-1 317 3«6-5 16-6 377 376-5 19-S 437 436-4 22-9 497 496-3 260 557 556-2 292 318 3>75 i6-7 378 377-4 19-8 438 437-4 22-9 498 497-3 26 I 558 557-2 29-2 3ia 31S-5 16-7 379 3784 '99 439 438-4 23-0 499 498-3 26-1 559 558-2 293 320 319-5 16S 380 379-4 19-9 440 _±39-± 23-0 500 499-3 26-2 560 5592 29-3 li^r 320-5 i6-S 381 380-4 200 441 4404 ^3-1 501 5003 26-2' 561 560-2 29-4 322 3215 169 382 381-4 20-0 442 441 4 23-' 502 50'3 26-3 562 56.-2 29-4 323 3225 16-9 383 20-1 443 442-4 23-2 503 502-3 26-3 563 562-2 29-S 324 3235 17-0 384 383-4 20-1 444 443-4 233 504 503-3 26-4 564 563-2 29-5 325 324-5 17-0 385 384-4 20-2 445 444-4 233 505 504-3 26-4 565 564-2 296 326 325-5 17-1 386 385-4 20-2 446 445-4 23-4 506 505-3 26-5 566 565-2 29-6 327 326-5 171 387 3864 20-3 447 446-4 23-4 507 506-3 26-5 567 566-2 29-7 328 327-5 17-2 388 3874 20-3 448 4474 235 508 507-3 266 568 567-2 29-7 329 328-5 17-2 389 388-4 20-4 449 44S-4 23-5 509 508-3 26-6 569 568-2 29-8 330 3295 ■7-3 390 389-4 20-4 450 4493 23-6 510 5093 267 570 569-2 29-8 337 330-5 17-3 391 3904 20-5 451' 450-3 23-6 511 5'0-3 26-7 571" 570-2 299 332 331-5 17-4 392 391-4 20-5 452 45 '-3 23-7 512 5"-3 26-8 572 5712 29-9 333 332-5 '7-5 393 392-4 20-6 453 452-3 23-7 513 512-3 268 573 572-2 30-0 334 3335 •7-5 394 393-4 206 454 453-3 23;S 514 5'3-3 26-9 574 573-2 300 335 3345 17-6 395 394-4 20-7 455 454-3 515 514-3 27-0 575 574-2 30-1 336 335-5 17-6 396 395-4 20-7 ■»5fi i 455-3 23-9 516 515-3 27-0 576 575-2 30-1 33- 336-5 177 397 396-4 20-8 457 456-3 239 •")17 5 '6-3 27-1 577 5762 302 338 337-5 17-7 398 397-4 208 458 457-3 24-0 518 5'7-3 27 I 578 577-2 30-2 339 33«-5 ■7-8 399 39S-4 20-9 459 1 4583 240 519 518-3 27-2 579 578-2 30-3 340 339-5 178 400 399-4 20-9 460 1 459-3 24-1 520 J'9 3 27-2 580 5792 3°-3 sTT 340-5 17-9 401 400-4 210 461 4603 24-1 521 5203 27-3" 581 , 5S0-2 30-4 342 341-5 17-9 402 401-4 2I-I 462 461-3 242 522 521-3 27-3 582 581-2 30-4 343 342-5 180 403 4024 21-1 463 462-3 24-2 523 522-3 27-4 583 5S22 30-5 344 3435 180 404 4034 21-2 ^'64; 463-3 24-3 524 523-3 27-4 584 583-2 30-S 345 344-5 iS-i 405 404-4 212 465 1 464-3 24-4 525 524-3 27-5 585 584-2 30-6 34 <; 345 5 i8-i 400 405-4 21-3 466 1 465-3 24-4 526 525-3 275 586 585-2 30-6 347 346-5 18-2 407 406-4 213 467 4663 24-5 527 526-3 27-6 587 586-2 30-7 348 347-5 182 408 407-4 21-4 408 467-3 24-5 528 527-3 276 588 587-2 30-7 849 34S5 '8-3 4 09 40S-4 214 469 468-3 246 529 5283 27-7 589 588-2 30-8 350 349-5 18-3 410 4094 21-5 470 469-3 246 530 529-3 277 590 5S9-2 309 ssT 350-5 i8-4 4ir 4T04I 21-5^ 471 470-3 " 247 53 f 530-3 27-8 591 590-2 30-9 352 35 1 S .84 412 411-4' 21-6 472 47'-3 24-7 532 53'-3 27-8 592 591-2 31-0 353 352-5 18-5 413 412-4, 21-6 473 472-3 24-s 533 532-3 279 593 592-2 310 354 353 5 '8-5 414 413-4 217 474 473-3 24-8 534 533-3 279 594 593-2 3«-' 355 354-5 1 8-6 415 414-4 21-7 475 474-3 24-9 535 534-3 280 595 5942 311 356 355S 186 416 415-4, 21-8 476! 475-3 24-9 536 535-3 28- 1 596 595-2 31-2 357 356-S 187 417 416-4; 21-8 477 476-3 250 537 536-3 28 1 597 596-2 3'-2 358 357-5 18S 418 417-41 21-9 ■»"8| 477-3 250 538 5373 282 598 5972 3'-3 359 358-5 1 8-8 419 418-41 21-9 479 47S-3 25-1 539 538-3 28-2 599 598-2 3'3 360 3595 189 420 419-4 22-0 480 479-3 25-1 540 539-3 28-3 600 599-2 3'-4 Uist. Dep. J). Lat. ]Jist. D.p. JD. Lat IJist. Dep. D. Lat. iJist. Dep. D. Lat m,. Dep. D. Lat. 87° 6" 48"^ TRAVERSK TABLE TO DEGREES 16"- 4° 0^ Dist. l).Ut Dep. Dist. D.Lat. Dep. Dist D. Lat. Dep. Dist.lD.Lat. Dep. Dist.'D. Lat. Dep- 1 '~ 0;. 61 6o-9 4-3 121 120-7 S-4 181 i I80-6 12-6 241 ' 240-4 i6-8 2 ! 2-0 I 62 8 4-3 122 121-7 8 5 182 j 181 6 12-7 242 1241-4 ■ 6-9 ■A 3-0 2 63 8 4"4 123 8 6 183 1 182 6 12-8 243 . 242-4 4 4-0 3 64 8 4-5 124 123-7 8 6 184 183 6 12-8 244 243-4 1--0 5 5-° 3 65 8 4-5 125 124-7 8 7 185 184 5 245 ; 244-4 17-1 « 6-0 4 66 8 4-6 126 125-7 8 186 185 246 ! 245-4 17-2 7 ! 7-0 5 C7 8 4-7 127 126-7 8 9 1871 186 5 247 1 246-4 17-2 8 1 8-0 6 68 8 4"7 128! 1,7.7 8 9 188 1 187 13-1 248 247-4 17-3 !) ' 9-0 o 6 69 8 4-8 129 1 128-7 9 189 1 188 5 13-2 249 248-4 '7-4 10 1 lo-o 1 o 7 70 Ji 8 4'9 _m I29^7_ 9 1 190 1 189 i. ■3-3 250 249-4 11 i.-o 8~ 71 Y 5-0 131 130-7 9 I 191 j 190 S 13-3 25r 250-4 ■7-5 12 ii-o 8 72 8 S-o 132 131-7 9 2 192 191 5 13-4 252 251-4 17-6 i.-i : .3-0 9 73 8 5-' 133 132-7 9 3 193 1 192 5 ■3-5 253 252-4 17-6 14 .4-0 74 8 5-2 134 133-7 9 3 194! 193 5 '3-5 254 253-4 ■7-7 l.i I5-0 75 8 5-2 135 '34-7 9 4 195 1 194 5 13-6 255 254-4 17-8 u; : i6-o I 76 8 5-3 136 135-7 9 5 196' 195 5 ■3-7 256 *55-4 ■7-9 17 1 lyo 77 8 5-4 137 136-7 9 6 197 196 5 13-7 257 256-4 17-9 11! i iS-o 3 78 8 5-4 138 137-7 9 6 198 197 5 ■3-8 258 257-4 18-0 19 1 19-0 3 79 8 5-5 139 138-7 9 7 199 19S 5 13-9 259 258-4 18-1 20 1 jo-o 4_ 80 8 5-6 140 139-7 _^ 8 200 199 i. 14-0 260 259-4 iS-i 21 1 zo-9 I 5 81 T 5-7 141 140-7 9 8 201 200 5 14-0 2C1 260-4 18-2 22 I 21-9 5 82 8 5-7 142 141-7 9 9 202 201 5 14-1 262 261-4 18.3 2-A 1 22-9 6 83 8 5-8 143 142-7 10 203 202 5 14-2 263 262-4 18-3 2-1 1 23-9 7 84 8 59 144 '43-6 10 204 203 5 14-2 264 263-4 18-4 25 ! 24-9 7 85 8 5-9 145 ,44-6 10 I 205 204 5 14-3 265 264-4 i8-5 26 , 25-9 86 8 6-0 146 145-6 10 2 206 205 5 14-4 266 265-4 18-6 27 1 26-9 9 87 8 6-1 147 ,46-6 10 3 207 206 5 •4-4 267 266-3 iS-6 28 i 27-9 88 8 6-1 148 .47-6 10 3 208 207 5 14-5 268 267-3 ■8-7 29 1 2S-9 89 8 6-2 149 148-6 10 4 209 208 5 14-6 269 268-3 18-8 30 1 29-9 I 90 8 6-3 150 149-6 10 i_ 210 209 J_ .4-6 270 269-3 18-8 ■M ! 30-9 ~ 91 T 6-3 151 150-6 ^0 5 211 210 5 14-7 271 270-3 18-9 ;(2 1 31-9 2 92 8 6-4 152 151-6 10 6 212 211 5 14-8 272 271-3 19-0 ;« 3^-9 3 93 8 6-5 153 ,52-6 10 7 213 212 ■49 273 272-3 19-0 ■■f4 ! 33-9 94 g 66 1.54 153-6 10 214 213 5 14-9 274 273-3 19-1 ;i.j 34-9 4 95 94 8 6-6 155 154-6 10 g 215 214 5 15-0 275 274-3 19-2 :<(■< 359 5 96 95 s 6-7 156 155-6 10 9 216 215 5 15-1 ■276 275-3 19-3 37 36-9 6 97 96 8 68 157 ,56-6 11 217 216 5 15-1 277 276-3 19-3 38 37-9 7 98 97 8 6-8 158 ,57-6 11 218 217 5 15-2 278 277-3 '9-4 39 38-9 7 99 98 8 6-9 159 158-6 11 I 219 218 5 ■5-3 279 278-3 ■9-5 40 39-9 8 100 _99 8 y-o 160 159-6 II 2 220 111 J. ■5-3 280 279-3 '9-5 ^n~i 40-9 T 101 T 7-0 161 160-6 II ~r' 221 5 '5-4 "2(0" 2S0-3 19-6 42 1 41-9 9 102 lOI 8 7'i 162 161-6 11 3 222 221 5 '5-5 282 281-3 19-7 43 42-9 103 102 7-2 163 162-6 II 4 223 222 5 15-6 283 2S2-3 19-7 44 1 43-9 I 104 103 7 7-3 164 .63-6 11 4 224 223 5 •5-6 284 283-3 19-8 45 44-9 I 105 104 7 7-3 165 .64-6 11 5 225 224 5 15-7 285 284-3 19-9 46 459 2 106 105 7 7^4 166 165-6 11 6 226 225 4 ■5-8 286 285-3 47 46-9 3 107 106 7 7-5 167 166-6 11 6 227 226 4 ,5-8 287 286-3 20-0 48 47-9 3 108 107 7-5 168 167-6 11 7 228 227 15-9 288 287-3 20-1 49 489 4 109 loS 7 7-6 169 168-6 11 229 22S 4 16-0 289 288-3 20-2 50 1 49*9 51 ^0-9 5 110 loq J_ 7-7 170 169-6 II 9 230 ^^9 ± i6-o 290 289-3 20-2 6 111 I 10 7 7-7 TtT 170-6 11 9 •231 230 4 16-1 291 290-3 20-3 52 : si-9 6 112 7 7-8 172 171'6 12 232 231 4 16-2 292 29.-3 20-4 53 : 52-9 7 113 I 12 7 7-9 173 172-6 12 I 233 232 4 i6-3 293 292-3 20-4 5-1 1 53-9 8 114 113 7 8-0 174 173-6 12 I 234 233 4 16-3 294 293-3 20-5 55 1 54-9 8 115 114 7 8-0 175 174-6 12 2 235 234 4 16-4 295 294-3 20-6 56 ;5-9 3 9 116 i'5 7 8-1 176 175-6 12 3 236 ^35 4 16-5 296 295-3 20-6 57 ; 56'9 4 117 .16 7 8-2 177 176-6 12 3 237 236 4 .6-5 297 296-3 20-7 58 1 57-9 4 118 ■17 7 8-2 178 177-6 12 4 238 237 4 ■ 6-6 298 297-3 20-s 69 58-9 4 I 119 iiS 7 8-3 179 178-6 12 5 239 238 4 .6-7 299 298-3 20-9 60 59-9 4-2 120 II9-7 8-4 180 179-6 12-6 240 239-4 16-7 300 299-3 »o-9 Diit. Dep.JD.Lat Dist Dep. iD.Lat Dist Dep. D. Lat. Dist Dep. D.Lat. Dist Dep. D.Lat. S( ^ " '5^ 44'^_.. TABLE 1 TRAVERSE TARLE TO DEGREES — 4° Oh le^n Dist. D. Lat. Dcp. Dist. D. Lat. Dep. Dist. D. Lat.l Dep. Dist. D. Lat.l Dep. Dis^j D. Lat. Dep. 301 y^-i 2I-0 361 360-1 25-2 421 420-0, 294 481 479-8 33-5 541 539-7 377 :.o.> 30.3 2I-I 362 36I-. 25-2 422 421-0 29-4 4S2 480-8 336 542 540-7 37s 3.1:!! 30J2 21-1 363 362-1 253 423 422-0 295 483 481-8 337 543 54'7 37 9 3114 303-2 21 2 364 3'53-> 25-4 424 423-0 29-6 434 4828 33-7 544 5427 37-9 3115 i 3042 21-3 365 364-1 25-5 425 424-0 29-6 485 483-8 33-8 545 543-7 380 308 : 305 2 213 366 3651 25-5 426 424-9 29-7 486 484-8 339 546 544-7 38-. 307 306 2 21-4 367 3661 25-6 427 4259 29-8 487 485-8 33-9 547 5457 38-1 3ns 307-2 2I-S 368 367-. 257 428 426-9 29-9 488 486-8 34-0 548 546-7 382 309 308-2 21-6 369 368-. 25-7 429 427-9 29-9 489 487-8 34-1 549 547-7 38-3 310 3092 21-6 370 3691 25-8 430 428-9 300 490 4888 34-2 550 54S7 _38:3_ 311 3102 21-7 371 370- 1 25-9 iM 429-9 30-1 491 T8W 34-2 551 5497 3S-4 312 3II-2 21-8 372 371-1 25-9 432 430-9 30-1 492 490-8 34-3 552 5507 38-5 313 3122 218 373 1 372-1 26-0 433 431-9 302 493 491-8 34-4 553 5517 3S-5 314 3132 21-9 374 373-1 261 434 432-9 3° 3 494 492-8 34 4 554 5527 38-0 31-> 314-2 22 375 374-1 26-2 435 4339 30-3 495 493-8 34-5 555 5536 38-7 310 315-3 22 I 376 375-1 26-2 436 434-9 30-4 496 494-8 346 556 554-6 387 317 3162 22-1 377 376-1 26-3 437 435-9 30-5 497 495-8 34-6 557 555-6 38-8 318 317-2 22-2 378 377-1 26-4 438 4369 30-6 498 496-8 34-7 558 5566 38-9 319 31S-2 22-3 3-9 378-1 26-4 439 437-9 306 499 497-8 34-8 559 557-6 389 320 3192 22-3 380 379-' ^6,5. 440 438-9 30-7 500 498 8 34-S 560 jiS;6 390 I2I 320-2 22-4 381 Iso-T 266 44r 439-9 308 501 499-8 34-9 561 559-6 39- « 322 321-2 22-5 382 381-1 266 442 4409 30-S 502 5008 35-0 562 560-6 .39-2 323 322-2 22 5 383 382- • 26-7 443 441-9 30-9 503 501-8 35-0 563 561-6 39-2 324 3232 22-6 384 383-1 268 444 4429 31-0 504 5028 35-1 564 5626 39-3 323 324-2 227 385 384-0 26-9 445 443-9 31-0 505 503-8 35-2 565 563-6 39-4 326 3252 22-7 386 385-0! 26-9 446 444-9 31-1 506 50481 35-2 566 564-6 394 32- 3262 22-8 .387 386-0; 27-0 447 445-9 312 507 505SI 35-3 567 565-6 395 328 3272 22-9 388 387-0 27-1 448 4469 31-2 508 506-81 35-4 568 566-6 39-6 329 328-2 230 339 3880 27-1 449 447-9 313 509 507 8 j 35-5 569 567-6 39-7 330 3292 23-0 390 389-0 27-2 4.50 4489 314 510 508-8 .351. 35-6 570 571 56S-6 '569^ _39-8_ 398 331 3302 23-1 391 390-0 273 451 449-9 3«-5 511 509-8 332 33'-2 392 391-0 27-3 452 450-9 31-5 512 510-81 35-7 572 570-6 399 333 332-2 23-2 393 392-0 27-4 453 451-9 31-6 513 5II-8! 35-S 573 571-6 400 334 33.V2 23-3 .394 3930 27-S 454 452-9 31-7 514 5>2-7i 35-S 574 572-6 400 33-. 334-2 234 395 3940 276 455 453-9 3'-7 515 5'3-7 1 35-9 575 573-6 40-1 33e , 335-2 23-4 396 395-0 27-6 456 454-9 3'-S 516 514-7 36-0 576 574-6 40-2 3362 23-5 397 3960 27-7 457 455-9 3'-9 517 5 '5-7 360 577 5756 402 338 337-2 236 398 3970 27-8 458 4569 3'-9 518 516-7 1 36-1 578 576-6 40-3 339 33S-2 23-6 399 , 39S-O 278 459 457-9 32-0 519 517-7 36-2 379 577-6 40-4 340 339-2 237 400 3990! 27-9 460 458-91 32-1 520 51S-7 36-2 580 578-6 40-5 341 II40T 238" Th" 4000 280 461 459-9 32-2 521 519-7 36-3 531 579-6 40-5 .342 341-2 23-9 402 40.-0 2S-0 462 4609 32-2 522 5207 36-4 582 580-6 40-6 .'i43 342-2 239 403 4020 28-1 463 461-9 323 523 521-7: 36-4 583 5816 40-7 3-t4; 343" 24-0 4-7 3.58 357-1 250 4IS 4170: 292 478 476-8 333 533 5367 37-5 598 596-6 417 3.VJ i 358 I 25-0 419 4180 292 479 477-8 334 539 537-7 376 .599 597-6] 41-8 360 3591 25-1 42o 4190 293 1 480 478-8 33-5 .540 538-7 37-7 600 5986 41-9 Dist.l Dep. D. Lat Di-t Dcp. T). Lat.|l>ist Dcp. D.Latlnist Dcp. D.Lat Dist Dep. b. Lat. 80' 5" iV^ no TRAVERSE TABLE TO DEGREES 5° O" '20-" Dist. D.Lat! Dep. Dist D.Lat Dep Dist. D.Lat. Dep. Dis .D.Lat Dep. Dis-JD. La;.| Dep. "f ,.o| o-i' til 6o-8 5-3 121 120-5 10-5 181 180-3 15-8 241 240-1 1 21-0 2 1 z-o o-z (i2 6i-8 5-4 122 121-5 182 181-3 15-9 242 241-1 21-1 3 3-oio-3 03 62-8 5-5 123 122-5 10-7 183 182-3 15-9 243 242-1 4 4-0 0-3 ()4 63-8 5-6 124 123-5 10-8 184 183-3 16-0 244 243-1 21-3 5 5-0 65 64-8 5-7 125 124-5 10-9 185 184-3 16-1 245 244-1 21-4 (i 6o 0-5 06 65-7 5-8 126 125-5 186 185-3 16-2 246 245-j 21-4 7 7"o 0-6 07 66-7 5-8 127 .26-5 ii-i 187 186-3 16-3 247 246-1 1 21-5 1 8 1 8-0 0-7 68 67-7 59 128 127-5 11-2 188 187-3 16-4 248 247-1 21-6 9 1 9-0 0-8 69 68-7 60 129 128-5 11-2 1H9 188-3 16-5 249 24S-. 21-7 10 1 lo-o 0-9 70 69-7 6-1 130 129-5 11-3 190! 189-3 16-6 250 249-0 21-8 11 ii-o i-o 71 70-7 6-2 131 130-5 II-4 191 190-3 16-6 251 250-0 21-9 12 I2-0 i-o 72 71-7 6-3 132 131-5 11-5 192 191-3 16-7 252 251-0 22-0 13 lyo i-i 73 72-7 6-4 133 132-5 11-6 193 192-3 16-S 253 14 lyg 1-2 74 73-7 6-4 134 133-5 11-7 194 193-3 16-9 254 253-0 ; 22-1 15 14-9 1-3 75 74-7 6-5 135 '34-5 11-8 195 194-3 17-0 255 l(i 15-9 '•4 7fi 75-7 6-6 136 135-5 11-9 196 '95-3 17-1 256 255-0 i 22-3 17 .6-9 1-5 77 76-7 6-7 137 136-5 11-9 197 196-3 17-2 257 256-0 22-4 18 17-9 1-6 78 77-7 6.8 138 "37-5 12-0 198 197-2 17-3 258 257-0 22-5 19 i8-9 1-7 79 78-7 6-9 139 13S-5 12-1 199 198-2 '7-3 259 258-0 22-6 20 ■99 »■? 80 79-7 7-0 140 ■39-5 12-2 200 199-2 ■7-4 260 259-0 22-7 21 20-9 1-8 81 8o-7 7-1 141 1 140-5 12-3 201 200-2 17-5 26r 260-0 22-7 22 21-9 '•9 82 8i-7 7-7 142 141-5 12-4 202 201-2 17-6 262 261-0 22-8 23 22-9 2-0 83 82-7 7-2 143 142-5 12-5 203 202-2 17-7 263 262-0 22-9 24 23-9 2-1 84 83-7 7-3 144 •43-5 12-6 204 203-2 17-8 264 263-0 23-0 25 24-9 2-2 85 84-7 7 '4 145 144-4 12-6 205 204-2 17-9 265 264-0 23-1 2« 25-9 2-3 86 85-7 7'5 146 '45-4 12-7 206 205-a 18-0 266 265-0 23-2 27 26-9 -■4 87 86-7 7-6 147 .46-4 12-8 207 206-2 18-0 267 266-0 23-3 28 27-9 -■4 88 87-7 7'7 148 147-4 12-9 208 207-2 18-1 268 26.-0 23-4 29 28-9 89 S8'7 7-8 149 j 148-4 13-0 209 208-2' 18-2 209 26S-0 23-4 :«) 2-6 90 89-7 7-S 150 149-4 13-1 210 209-2 1 i8-3 270 269-0 23-, liT 3-'-9 2-7 91 90-7 7-9 151 150-4 13-2 ITT 210-2 18-4 271 270-0 23-6 32 31-9 2-8 92 91-6 8-0 152 151-4 13-2 212 2II-2 18-5 272 271-0 23-7 33 32-9 2-9 93 92-6 8-1 153 152-4 13-3 213 212-2 18-6 273 272-0 23-8 34 33-9 3-0 94 93-6 8-2 154 153-4 13-4 214 213-2 18-7 274 273-0 23-9 35 34-9 3-1 95 94-6 8-3 155 154-4 •3-5 215 214-2 18-7 275 274-0 24-0 36 35-9 96 95-6 8-4 156 '55-4 .3-6 216 215-2 18-8 276 274-9 24-1 37 36-9 3-2 97 96-6 8-5 157 156-4 13-7 217 216-2 i8-9 277 275-9 24-1 38 379 3-3 98 97-6 8-5 158 157-4 13-8 218 217-2 ig-o 278 276-9 24-2 39 38-9 3-4 99 98-6 8-6 159 158-4 13-9 219 218-2 19-1 279 27.-9 24-3 40 39-8 3-5 100 99-6 8-7 160 '59-4 13-9 220 2.9-2 19-2 280 2-S-9 24-4 IT 40-8 3-6 101 IOO-6 8-8 161 160-4 14-0 22r 19-3 281 279-9 i =4-5 42 4.-8 3-7 102 IOI-6 8-9 162 161-4 14-1 222 221-2 19-3 282 280-9 1 -4-6 43 42-8 3-7 103 I02-6 9-0 163 162-4 14-2 223 222-2 19-4 283 2S1-9 j 24-7 44 43-8 3-8 104 103-6 9-1 164 163-4 14-3 224 223-1 19-5 284 24-S 45 44-8 3-9 105 I04-6 9-2 165 164-4 14-4 225 224-1 19-6 285 283-9 24- 8 4(i 45-8 4-0 106 105-6 9-2 166 165-4 14-5 226 225-1 19-7 280 284-9 24-9 47 46-8 107 106-6 9-3 167 166-4 14-6 227 226-1 19-8 287 285-9 25-0 48 4-2 108 107-6 9'4 168 167-4 14-6 228 227-1 19-9 288 2S6-9 25-1 49 48-8 4-3 109 io8-6 9-5 169 ■4-7 229 22S-I 20-0 289 287-9 =5- = 50 51 49-8 4'4 110 109-6 9-6 170 169-4 .4-8 230 229-1 20-0 290 50-8 4*4 TiT 1 10-6 9'7 171 .70-3 14-9 2-n 23O-, 20-1 291 2S9-9 1 25-4 52 51-S 4-5 1 112 III-6 9-8 15-0 232 231-1 20-2 292 290-9 25-4 53 52S 4-6 113 II2-6 9-8 173 15-1 233 232-1 20-3 293 291-9 25-5 54 53-8 4-7 114 1. 36 9-9 174 15-2 •234 233-1 20-4 294 252-9 1 25-6 55 54-8 4-8 115 II4-6 lO-o 175 15-3 235 234-1 20-5 295 293-9 25-7 56 55-8 4-9 110 115-6 lo-i 176 15-3 236 235-1 20-6 296 294-9 25-8 57 56-8 5-0 117 116-6 10-2 177 176-3 >5-4 237 236-1 20-7 297 295-9 2';-9 58 57-8 5-, 118l .17-6 10-3 178 177-3 15-5 238 237-1 20-7 298 296-9 26-0 .-.9 58-8 s-i 119 118-5 ;o-4 179 178-3 15-6 239 238-1 20-8 299 297-9 26-1 fiO 59-8 5-2 120 119-5 10-5 180 179-3 '5-7 240 239-1 20-9 300 298-9 26-1 Dm. Dep. D.Lai ^ Dep. D.Lat Dist. Dep. D. Lat. Dist. Dep. D.Lat.! Dist. Dep. D. Lnt. 85° .5'' 4 (jiiT" TKAVEUiSE TABLE TO DEGREES 5" Oh^O'" 1 Dist. D.Lat Dep. Dist. P. Lat. Dep. Dist. D. Lat. Dep. Dist. D. Lat. Dep. Dist 541 D.Lat 538-9 Dep. 47-=. 301 2999 262 367 359-6 31-5 421 4194 36-7 481 4792 41-9 302 3008 263 362 360-6 31-6 4-J2 , 420-4 36-8 482 4S0-2 42-0 542 539-9 47-3 303 30. s 264 363 3616 3.-6 423 j 421-4 36-9 483 4812 42-1 543 5409 47-4 304 302S 265 364 3626 3' 7 424 1 422-4 37-0 484 482-2 42-2 544 541-9 47-S 305 3C3S 266 365 363-6 3'S 425 1 423-4 371 485 4832 42-3 545 542-9 476 306 304 s 267 366 364-6 3'9 426 1 424-4 37-1 486 484-1 42-4 546 543-9 47-7 3(17 305-8 26S 367 3656 320 427 1 425-4 , 37-2 487 485-1 42-4 547 5449 47-7 308 3068 26-9 368 3666 428 426-4 37-3 488 4S6-1 42-5 548 545-9 478 309 307-8 269 369 3676 32-2 429 1 427-4 37-4 489 487-1 42-6 549 5469 47-9 310 3088 27-0 370 368-6 3^3 430 ' 428-4 1 37-5 490 ^± 42-7 550 5479 48-0 311 309-S 27-1 371 369-6 32-3 43! , 429-4 37-6" 49T 489-1 42-8 551 54S9 48- . 312 3108 27-2 372 370-6 32-4 432 1 430-4 37-7 492 4901 42-9 552 549-9 48-2 313 311-8 27-3 373 3716 32-S 433 431-3 37-7 493 491 I 430 553 5509 4S-3 314 312-S 27-4 374 3726 32-6 4.34 432-3 37-8 494 492-1 431 554 551-9 48-4 315 313S 27-5 375 373-6 32-7 435 433-3 379 495 493-1 43-1 555 552-9 484 316 3M8 275 376 374-6 32-S 436 434-3 38-0 496 494-1 43-2 556 553-9 48-5 317 3'5-8 27-6 377 375-6 329 437 4353 38-1 497 495-1 43-3 557 5549 4S-6 318 3168 27-7 378 3766 330 438 436-3 38-2 498 4961 43 4 558 555-9 48-7 319 317-S 27S 579 377-6 33-0 439 437-3 38-3 499 497-1 435 559 5569 4S-8 320 3188 27-9 380 3786 33 I 440 1 438-3 38-4 500 498-1 43-6 560 557 9 488 321 319S 280 381 3795 33-2 441 439-3 38-4 501 499-1 437 561 Iss-s 48^ 322 320-S 2SI 382 380-5 33 3 442 440-3 38-S 502 500-1 43-8 562 559-8 49-0 323 32 1 -S 282 383 381-5 33-4 443 441-3 38-6 503 Soi-i 43 8 563 S60S 49-1 324 322S 282 384 382-5 33-5 444 442-3 38-7 504 502-1 439 564 561-8 49-2 325 323 8 28-3 385 383-5 336 445 443-3 388 505 503-1 44-0 565 562-S 49 3 326 324-8 28-4 386 3845 337 446 444-3 3S-9 506 504-1 44-1 566 5638 49-4 327 325-8 28-5 387 385-5 33-7 447 445-3 39-0 507 505-1 44-2 567 564-8 49-S 328 3267 286 388 386-5 33-8 448 446-3 39-1 508 506-. 443 568 565S 49-6 329 327-7 287 389 3S7-5 33-9 449 447-3 39-1 509 507-1 44-4 569 5668 497 330 328-7 28S 390 388-5 340 450 44S-3i 39-2 510 50S-1 44-5 570 567-8 49-7 331 329-7 289 391 389-5 34-1 451 ! 449-3 ' 39-3 511 5090 44-5 571 568-S "4^8" 332 330-7 28-9 392 390-5 34-2 452 450-3 1 39-4 512 510-0 44-6 572 569-8 49 9 333 33'-7 290 393 391-S 34-3 453 451-3! 39-5 513 511-0 447 573 5708 50-0 334 332-7 29-1 394 3925 34-3 454 452 3 1 39-6 514 512-0 44-8 574 57. -8 50-1 335 3337 292 395 393-5 34-4 455 4533 39-7 515 5130 44-9 575 5728 50-2 336 334-7 293 396 394-5 34-5 456 454-3 39S 516 514-0 450 576 5738 503 337 335 7 29-4 .397 395-5 346 457 455-3! 39-8 517 515-0 45-1 577 574-8 50-4 338 3367 29-5 398 396-5 34-7 458 456-31 399 518 5.6-0 45-2 578 575-8 50-4 339 337-7 29-6 399 3975 34-8 459 457-3 1 40-0 519 517-0 45-2 579 5768 50-5 340 3387 296 400 J?8;5_ 34-9 4 60 ; 458-2 40-1 520 j,8-o 45-3 580 J77:8 506 341 339 7 297 4(n 399-5 35-0 461, 459-2 402 ¥21" 519-0 45-4 581 578-8 507 342 3407 29 8 402 400-5 350 462 , 460 2 40-3 522 5200 455 582 579S 50-8 343 341-7 299 4o:i 401-5 3S-I 4 63 i 461-21 404 523 521-0 45-6 583 5808 50-9 344 342-7 SOO 404 4025 35-2 464 1 462-2 1 40-4 524 522-0 45 7 584 58.-8 50-9 ■345 343-7 301 405 4035 353 465 , 463-2 40-5 525 5230 45-8 585 5S2-8 51-0 340 344-7 302 40G 4045 35-4 466 i 464-2 40-6 .526 524-0 45-9 586 583S 5n 347 345-7 303 407 405-4 355 4 67 4652 40-7 527 525-0 45-9 587 584-8 51-2 34S 346-7 303 408 406-4 356 468 1 466-2 40-8 526-0 46-0 588 5S5-8 51-3 349 3477 304 409 4074 35-7 469' 4672 40-9 5-29 5270 46-1 589 586-8 51-4 350 34S7 30-5 410 408-4 35-7 470 1 468-2! 41-0 530 52S0 46-2 590 5S7S 51-5 351 3497 306 411' 409-4 35-8 471 , 469-2, 41-1 531 529-0 T6-3" 591 588-7 -1F6 352 3507 307 412 4104 35-9 472 1 470-2 [ 4I-I 532 530-0 46-4 592 589-7 5 1-6 353 35'-7 30S 413 411-4 36-0 473 471-2! 41-2 533 531-0 46-5 593 590-7 5.7 354 352-6 309 414 412-4 36-1 474 . 472-2 41-3 534 532-0 46-6 594 591-7 51-8 355 3536 30-9 415 4134 36-2 475' 473-2 41-4 535 5330 466 595 592-7 51-9 356 3546 310 416 414-4 36-3 476: 474-2 41-5 536 533-9 46-7 596 593-7 520 357 355-6 417 415-4 36-4 477 1 475-2 41-6 537 534 9 468 597 594-7 52-1 358 3566 3 '-2 418 4.6-4 36-4 478, 476-2 417 538 555-9 469 598 595-7 S2-2 359 357-6 i'i 419 417-4 36-5 479 477-2 41-8 539 5369 47-0 599 5967 52-3 360 3S86 3'-4 420 418-4 366 480 478-2 418 540 537 9 47-1 600 597 7 52-3 Di.t Dep. D Lat IJist Dep. D. L^.t Uist Dep. D.La, Disl Dep. D. Lat. Dist Dep. D.Lat Hr>" 5'' 40"" j 442 TRAVERSE TABLE TO DEGREES 1 6° Ot.04-.. 1 D.tL D.La Dep, Dist D. J.at Dep. Dist D. Lat Dep. DistJD. Lat Dep. DistlD.Lat. Dep. 1 ~T7 o-i 61 6o-7 4 121 120-3 12-6 181 i 180-0 18-9 241 239-7 25-2 2 i-o o-z 62 61-7 5 122 izi-3 iz-8 182! i8i-o 19-0 242 240-7 25-3 3 °"i 03 62-7 6 123 122-3 12-9 183 182-0 19-1 243 241-7 4 4-0 0-4 64 63-6 7 124 123-3 13-0 184 183-0 19-2 244 242-7 25-5 5 0-5 65 64-6 8 125 124-3 13-1 185 184-0 19-3 245 243-7 25-6 C 0-6 66 656 9 126 IZ5-3 13-2 186 185-0 19-4 246 -44-7 25-7 7 67 66-6 127 126-3 13-3 187 I86-0 19-5 247 245-6 25-8 8 8-0 j 0-8 C8 67-6 I i^7'3 i I3'4 188 187-0 19-7 248 2^6-6 25-9 !» 9-0 1 0-9 69 68-6 2 129 12S-3 13-5 189 1S8-0 19-8 249 247-6 26-0 9-9 i-o 70 71 69-6 X 130 .29-3 13-6 190 189-0 19-9 250 248-6 26-1 10-9 I-I 70-6 4 IsT 130-3 13-7 litV 190-0 20-0 laT 249-6 26-2 12 11-9 1-3 72 71-6 5 132 13-8 192 190-9 20-1 252 250-6 26-3 13 12-9 1'4 73 72-6 6 133 132-3 13-9 193 191-9 20-2 253 251-6 26-4 14 : 13-9 '•5 74 73-6 7 134 133-3 H-o 194 192-9 20-3 254 252-6 26-6 1.5 , 14-9 1-6 75 74-6 8 135 134-3 14-1 195 193-9 20-4 255 253-6 26-7 K; , 15-9 i"7 76 75-6 9 136 135-3 14-2 196 194-9 20-5 256 254-6 26-8 17 I i6-9 1-8 77 76-6 137 136-2 14-3 197 195-9 20-6 257 255-6 26-9 18 ' 17-9 i;9 78 77-6 z 138 137-2 14-4 198 196-9 20-7 258 256-6 27-0 19 1 iS-9 79 78-6 3 139 138-2 14-5 199 197-9 20-8 259 257-6 27-1 2(1 19-9 80 79-6 140 139-2 14-6 200 198-9 20-9 260 258-6 ■.M , 209 -2 - 81 So-6 ~S 7 141 140- z 14-7 201 199-9 261 259-6 ■J2 2. -9 2-3 82 8i-6 6 142 141-Z 14-8 202 200-9 21-1 262 260-6 27-4 23 22-9 2-4 83 82-5 7 143 14Z-2 14-9 203 201-9 21-2 263 261-6 2-5 24 ! 23-9 ^•5 84 83-5 8 144 143-2 15-0 204 202-9 21-3 264 262-6 27-6 23 i 2+-9 2-6 85 84-5 9 145 144-2 15-1 205 203-9 21-4 265 263-5 27-7 2G ; 25-9 2-7 86 85-5 146 145-2 15-3 206 204-9 21-5 266 264-5 27-8 27 1 26-9 2-8 87 86-5 I 147 146-z 15-4 207 205-9 21-6 267 265-5 27-9 28 ! 27-8 2-9 88 87-5 z 148 147-2 15-5 208 206-9 21-7 268 266-5 2!* ; 2S-S 89 88-5 3 14!) 148-2 15-6 209 207-9 21-8 269 267-5 ^8-1 1 30 ; 29-8 3-1 90 89-5 ±_ 150 149-2 15-7 210 208-S 22-0 270 268-^; 28-2 1 31 1 30-8 3'2 91 90-5 5 151 150-2 T^s~ 211 209-S 271 269-5 28-3 32 31-S 3'3 92 91-5 6 152 151-2 ■5-9 212 210-S 272 270-5 28-4 33 3i-S 3'4 93 92-5 9 7 153 152-2 16-0 213 211-S 22-3 273 271-5 2S-5 34 I 33-8 3-6 94 93-5 9 154 153-2 16-1 214 212-8 "•4 274 272-5 2S-6 35 , 3+-8 3-7 95 94-5 9 9 1.15 154-2 16-2 215 213-8 ir.i 275 273-5 28-7 31! 1 35-S 3-S 96 95'5 1 56 155-1 16-3 216 Z14-8 27c 274-? 28-8 37 1 36-8, 3-9 97 96-5 I l.->7 156-1 16-4 217 215-8 22-7 277 >75-5 29-0 38 ; 37-S 4-0 98 97-5 z 1.58 157-1 16-5 218 216-8 22-8 278 276-5 29-1 39 i 3S-8 4' I 99 98-5 3 1.59 15S-1 16-6 219 ZI7-8 22-9 279 277-5 29-2 40 i •9-8 41 1 40-8 4'2 100 99-5 i_ 160 159-1 i6-7 220 218-8 23-0 280 27s- ; 29-3 4-3 Tor 100-4 6 161 160-1 16-8 221 219-8 23-1 281 279-5 29-4 42 Ui-S 4'4 102 101-4 10 7 162 i6i-i 16-9 222 220-8 282 280-5 29-5 43 U2-S 4-5 103 102-4 10 163 162-1 17-0 221-8 23-3 283 281-1 29-6 44 43-S 4-5 104 103-4 10 9 164 163-1 I7-I 224 222-8 23-4 284 2S2-4 29-7 4o 44-8 4'7 105 104-4 II 165 164-1 17-2 225 223-S 23-5 285 2S3-4 29-S 46 i4S-7 4-8 106 105-4 II I 166 165-1 17-4 226 224-8 ^3;6 286 284-4 29-9 47 146-7 4; 9 107 106-4 11 z 167 166-1 17-5 227 225-S 287 285-4 30-0 48 j 47-7 108 107-4 II 3 168 167-1 17-6 228 226-S 23-.S 288 286-4 30-1 49 |48'7 5-1 109 108-4 II 1(;9 168-1 17-7 229 227-7 23-9 289 287-4 30-2 50 49-7 5-2 110 109-4 11 5 170 169-1 I7-S -230 228-7 24-0 290 288-4 50-3 il' 50-7 5-3 TTT 1 10-4 II 6 171 j i-c-i 17-9 231 1 229-7 24- r •291 289-4 30-4 52 1 51-7 112 111-4 II 7 iS-o 232 230-7 24-3 292 290-4 30-5 53 i 52-7 5-5 1!3 112-4 1 1 8 173 1 1-2- 1 iS-i -233 231-7 293 291-4 30-6 51 , 53-7 5-6 114 113-4 1 1 9 171 : i-;-o iS-2 234 2-,;-7 ^4-5 294 292-4 30-7 55 54-7 5'7 115 114-4 12 17.->l .-4-oi iS-3 235, ;;3-- 24-6 295 293-4 30-S oi; 55-7 5-9 116 115-4 12 I 176 i .-5-0, .S- + 23li ! I31-- 2,|'7 296 294-4 30-9 57 ; 56-7 6-0 117 116-4 12 2 177 176-0 iS-5 237 235-7 24-8 297 295-4 31-0 ■^8 57-7 6-1 118 117-4 12 3 178 177-0 iS-6 238 236-7 24-9 298 296-4 31-1 59 1 58-7 6-2 119 118-3 12 4 179 17S-0 18-7 239 237-7 25-0 299 297-4 3'-3 eo 1 59-7 6-3 120 1.9-3 12-5 180 179-0 18-S 240 ^-38-7 25-1 300 29S-4 3'-4 Dist! Dep. D.Lat Dist. Dep. D.Lat Dist. Dep. D. Lat. Dist. Dep. D. Lat. Dist. Dep. D.LsL 84° " Ifi' ^" 1 443 TRAVERSE TA13LE TO DEGREES | c oxai" 1 Dist. 301 I). Lat. Hep. Dist.jD. Lat Dep. Dist 421 D.Lat 4187 Dep. Dist 481 D. Lat 478-4 Dep. 50-3 Dist 541 la., 53S-O Dep. 299-3 315 361 359-0 37-7 44-0 56-S 302 300-3 31-6 362 360-0 : 37-8 422 4197 44-1 482 479-4 50-4 542 5390 56-6 303 301-3 31-7 363 3610 37 9 423 420-7 44-2 483 4S04 505 543 540-0 56-7 304 3023 31-8 364 3620 38-0 424 421-7 44-3 484 481-3 506 544 541-0 568 305 3033 31-9 365 363 qI 381 425 422-7 44 4 485 482-3 50-7 54 5 542-0 56-9 306 304-3 320 366 3O40I 383 426 423 7 44-5 4S6 483-3 50-S 546 5430 57-0 307 3053 32-1 367 3650 38-4 427 424-7 44-6 487 484-3 50-9 547 544-0 57-1 308 306-3 322 368 I 366-0 1 38-5 428 425-7 44-7 488 485-3 51-0 548 545-0 57-2 309 307-3 32-3 369 367-0' 3S-6 429 426-6 44-8 489 4S6-3 51-1 549 546-0 57-3 310 _3oS3 -J2:4_ 370 36S-0 3S-7 430 427-6 44-9 490 .487:3 512 550 547-0 57-4 3TT 309-3 32-5 371 369-01 38-8 431 428-6 450 491 4883 51-3 551 548-0 57-5 312 3'o-3 32-6 372 370-0' 389 432 4296 45-2 492 489-3 51-4 552 549-0 57-6 313 311 3 327 373 371-0: 39-0 433 4306 453 493 490-3 51-5 553 550-0 57-7 314 312-3 1 32-8 374 371-91 39-1 434 431-6 45-4 494 491-3 Si-6 554 55.0 57-9 315 3'3-3 329 375 372-9 1 39-2 4 35 432-6 45-5 495 492-3 517 555 552-0 580 316 3'4-3 33-0 376 3739! 39-3 436 433-6 45-6 496 493-3 51-8 556 553-0 58-1 317 315-3 33-' 377 3749! 39-4 437 4346 45-7 497 494-3 51-9 557 554-0 5S-2 318 316-3 33-2 378 3759! 39-5 438 435-6 45-8 498 495-3 52-0 558 5550 5S-3 319 317-3: 33-3 379 376-9 39 6 439 436-6 45-9 499 4963 52-1 559 556-0 58-4 320 3'S-2 33-4 3M0 377-9! 39-7 440 437-6 46-0 500 497-3 _5i:3_ 560 5569 58 5 321 319-2 33-6 381 37S-9 39-S 441 4386 46-r .501 498-3 52-4 561 557-9 586 322 320-2 33-7 382 379-91 39-9 442 4396 46-2 502 499-3 52-5 562 558-9 5S-7 ,•323 321-2 33 s 383 380-91 400 443 4406 46-3 503 500-2 52-6 563 5599 588 324 322-2; 33-9 384 381-9 40-I 444 441-6 46-4 504 501-2 527 564 560-9 59-0 325 323-2 34-0 385 3S2-9 40-2 445 442-6 46-5 505 5022 52-8 565 561-9 591 326 324-2! 34-1 386 383-9: 40-3 446 443-6 46-6 506 503-2 52-9 566 562-9 59-2 327 325-2 i 342 387 3S4-9. 40-5 447 444 5 46-7 507 504-2 53-0 567 563-9 59-3 328 3262; 34-3 388 ; 385-9 406 448 445-S 46-8 508 505-2 53-1 568 5649 594 329 327-2 34-4 389 386-9, 407 449 446-S 46-9 509 S06-2 53-2 569 5659 59-5 ssT 3282 "329-2 34-5 390 3S7 9 40 8 450 451 447-5 T4sy 470 510 507-2 50S-2 _53:l 53-4 570 571 5e6-9 596 597 34-6 391 388-9 : 409 567-9 332 330-2 34-7 392 3S9-9 4I-0 452 449-5 47-2 512 509-2 53-5 572 568-9 59-8 333 331-2 34-s 393 390-8 4I-I 453 450-5 47-3 513 510-2 53-6 573 5699 599 334 332-2 34-9 394 391-81 412 454 451-5 47-5 514 511-2 53-7 574 5709 6o-o 335 333-2 350 395 392S 41-3 455 452-5 476 515 512-2 53-8 575 571-9 60- 1 336 334-2 351 396 393-8! 41-4 456 453-5 47-7 516 5132 53-9 576 572-9 602 337 335-2 35-2 397 394-8: 41-5 457 454-5 47-8 517 5142 54-0 577 5739 603 338 336-1 35-3 398 395-8 41-6 458 455-5 47-9 518 515-2 54-1 578 574-9 60-4 339 3371 35-4 399 396-8 41-7 459 456-5 48-0 519 516-2 54-2 579 575-8 60-5 340 341 33S-I 339-1 _35J_ 35-6 400 397-8 41-8 460 461 457-5 45S-S 48-1 ^8^ 520 521 517-2 -SYS-T 54-3 :so 581 576-8 6o-6 401 1 398-8! 41-9 54-5 577-8 6o-7 342 340-I 35-7 402 1 399-8 I 42 462 459-5 4S-3 522 519-1 54-6 5.S2 578-8 60-8 343 341-1 358 403 1 40O-8| 42-1 463 460-5 48-4 523 520-1 54-7 583 579-8 609 314 342-1 360 404 401-8 42-2 464 461-5 48-S 524 521-1 54-8 584 5S0-8 6I-I 345 343-1 361 405 ! 402-8 42-3 465 4625 48-6 525 522-1 54-9 585 S8.-8 6i-2 346 344-1 36-2 406|4O3-S 42-4 466 463-4 48-7 526 523-1 55-0 586 5828 61-3 347 345-1 363 407 404SI 425 467 464-4 48-8 527 524-1 55-1 587 583-S 6.-4 348 3461 36-4 408 405-81 42-6 46S 465-4 4S-9 528 525-1 55-2 588 5S4-8 61-5 343 3471 36-5 409 4068, 42-7 469 466-4 490 529 526-1 55-3 589 58S8 61-6 3iO 351 348-1 366 410! 4078 42-9 411 1 4087,430 470 471 467-4 468-4 49-1 530 531 527-1 528-1 554 55-5 590 591 586S 5878 617 ~6.^ 349-1 1 367 49-2 352 350-1 368 412 409-7 43" 472 469-4 49-3 532 529-1 55 6 592 58SS 61-9 353 351-1 36-9 413 4107 43-2 473 470-4 49-4 533 530-1 55 7 593 5898 620 354 352-J 370 414 411-7 43-3 474 471-4 495 534 531-1 55-8 594 590-8 62-1 355 353-1 371 415 4127 43-4 475 472-4 49-6 535 5321 559 595 591-8 62-3 356 354-0 37-2 416 1 4137 43-5 476 473-4 49-8 .536 533" 1 560 596 5928 62-3 357 355-0 37-3 417 1 4147 43-6 477 474-4 49-9 .537 534-1 56-1 597 593-8 62-4 358 3560 37 4 418, 4157 43-7 478 475-4 50-0 538 555-1 56-2 598 594-7 625 •'59 357-0 37-5 41914167 438 479 476-4 50-1 539 5361 56-3 599 595 7 62-0 3l-,0 Dist. 358 Oj 37-6 Dcp. |D.Lat 420; 417-71 439 Dist.i Dep. D.Lat 480 477-4 Dep. 50-2 540 Dist. 537-1 Dep. 56-4 D. Lat 600 Dist. 596-7 Dcp. 62-7 D. Lat. D. Lat. 81" S" 3G'" 1 444 TRAVERSE TABLE TO DEGREES 7° O"- 28™ Diit.|D.Lal| Dep. Dist D. Lat. Dep. Dist D.Lai Dep. DisLD.Lat.| Dep. Dist D.Lat. Dep. T|—:— - 61 6o-5 TA TTT 120-1 14-7 181 .79-7 122-1 241 239-2 29-4 2 1 2-0 ! 0-2 62 6i-5 7-6 122 121-1 14-9 182 180-6 22-2 242 240-2 29-5 3 3'0 °"4 63 62-5 7"7 123 122-1 15-0 183 1816 1 22-3 243 241-2 29-6 4 1 4-0 0-5 64 63-5 7-8 124 123-1 15-1 184 182-6 22-4 244 242-2 29-7 5 [ 5'° 0-6 65 64-5 7-9 125 15-2 185 1S3-6 22-5 245 2432 29-9 6-0 0-7 66 65-5 8-0 1-26 125-1 15-4 186 1S4-6 22-7 •246 244-2 30-0 6-9 0-9 67 66-5 8-2 1-27 126-1 '5-5 187 185-6 22-8 247 245-2 1 30-1 7-9 68 67-5 8-3 128 127-0 15-6 188 1S6-6 22-9 248 246-2 1 30-2 8-9 i-i 69 68-5 8-4 129 128-0 15-7 189 187-6 23-0 249 247-1 30-3 10 1 9-9 1-2 70 69-5 8-5 130 129-0 15-S 190 iS8-6 ■ 23-2 250 248-1 , 30-5 11 IO-9 1 1-3 71' 70-5 8-7 131 130-0 16-0 Tin 189-6 23-3 •251 249-1 30-6 12 ii'9 1-5 72 71-5 8-8 132 131-0 i6-i 192 190-6 23-4 252 250-1 30-7 13 12-9! 1-6 73 72-5 8-9 133 132-0 i6-i 193 191-6 23-5 253 251-1 14 j 13-91 '-7 74 73-4 9-0 134 i6-3 194 192-6 23-6 254 252-1 31-0 15 t H-9 1 .-8 75 74-4 9-1 135 134-0 i6-5 195 '93-5 23-8 255 253-1 31-1 '5-9 1-9 76 75-4 9'3 136 135-0 i6-6 196 194-5 23-9 •256 254-1 31-2 17 i6-9 2-1 77 76-4 9'4 137 136-0 i6-7 197 '95-5 24-0 257 255-1 31-3 18 17-9 2-2 78 77-4 9"5 138 137-0 i6-8 198 196-5 24-1 258 256-1 , 31-4 19 18-9 2-3 79 78-4 9-6 139 138-0 16-9 199 «97-5 24-3 259 257-1 1 31-6 iL 19-9; ^-4 80 79-4 9'7 140 139-0 17-1 200 198-s 24-4 260 258-1, 31-7 .0-8 .-6 "aT 8o-4 99 141 •39-9 17-2 201 1 99' 5 24-5 •261 259-1 . 3'-S 22 21-8! 2-7 82 8i-4 142 140-9 '7-3 202 200-5 24-6 •>62 260-0 i 31-9 23 22-8 2-8 83 82-4 10- 1 143 141-9 17-4 203 201-5 24-7 263 261-0; 32-1 24 23-8 2-9 84 83-4 10-2 144 142-9 '7-5 204 202-5 24-9 264 262-0 [ 32-2 25 24-8 85 84-4 10-4 145 >43-9 17-7 205 203-5 25-0 265 263-0, 32-3 26 25-8 3-2 86 85-4 10-5 146 144-9 ■7-8 200 204-5 25-1 266 264-0 32-4 27 26-8 3-3 87 86-4 10-6 147 I45'9 17-9 207 205-5 267 265-0! 32-5 28 27-8 3 '4 88 87-3 10-7 148 146-9 18-0 206-4 25-3 26B 266-0 ■ 32-7 29 28-8 3-5 89 10-8 149 '47-9 18-2 •209 207-4 25-5 269 30 29-8 3'7 90 89-3 ii-o 150 148-9 iS-3 210 25-6 270 26S-0 ll-l 31 30-8 3-8 91 •JO- 3 151 149-9 i8-4 211 209-4 25-7 271 269-0 33-0 32 31-8 3-9 92 91-3 \]'l 152 150-9 iS-5 212 210-4 25-8 272 270-0 33-1 33 32-8 93 92-3 11-3 153 151-9 18-6 213 211-4 26-0 273 271-0 33-3 34 33-7 94 93-3 11-5 154 152-9 iS-S 214 212-4 26-1 274 272-0 33-4 35 34-7 4-3 95 94-3 11-6 155 153-8 i8-9 215 213-4 26-2 275 36 35-7 4-4 96 95-3 11-7 156 154-8 190 216 214-4 26-3 •276 273-9 33-6 37 36-7 4-5 97 96-3 11-8 L57 155-8 19-1 217 215-4 26-4 '277 274-9 33'8 38 37-7 4-6 98 97-3 11-9 158 156-8 19-3 218 216-4 266 278 275-9 33-9 3U 38-7 4-8 99 98-3 12-1 159 157-8 19-4 219 217-4 26-7 279 276-9 34-0 40 39-7 4-9 100 99'3 12-2 160 158-8 19-5 220 2,8-4 26-8 280 277-9 34-1 41 40-7 5'° loT IOO-2 12-3 161 159-8 19-6 221 219-4 26-9 28r 278-9 34-2 42 41-7 5-: 102 IOI-2 12-4 162 .62-8 19-7 222 220-3 27-1 282 279-9 34-4 43 42-7 103 I02-2 12-6 163 i6i-8 19-9 223 221-3 27-2 283 280-9 34-5 44 43-7 5'4 104 103-2 12-7 164 162-8 224 222-3 27-3 284 281-9 34-6 45 44'7 5-5 105 104-2 165 163-8 20-I 225 223-3 27-4 285 282-9 34-7 46 45-7 5-6 106 .05-2 12-9 166 164-8 20-2 226 224-3 27-5 286 283-9 34-9 47 466 1 t-7 107 io6-2 13-0 167 165-8 20-4 227 225-3 27-7 287 284-9 35-0 48 47-6 , 5-« 108 1C7-2 13-2 168 166-7 20-5 228 226-3 288 49 48-6 6-0 109 io8-2 13-3 169 167-7 2C-6 229 227-3 27-9 289 286-S 35-2 50 49-6 6-. 110 109-2 I3'4 170 i68-7 20-7 230 228-3 290 28.-8' 35-3 51 506 6-2 TTT II0-2 13-5 171 ,69-7 20-8 231 229-3 "8-2 291 52 5.-6 6-3 112 III-2 13-6 172 170-7 2I-0 232 230-3 28-3 •292 289-8 ' 35-6 53 526 6-5 113 II2-2 13-8 173 171-7 21-1 233 231-3 2X-4 293 290-8 35-7 54 53-6 6-6 114 113-2 13-9 174 J 72-7 21-2 234 232-3 28-5 •294 291-8 35-8 55 54-6 6-7 115 114-1 14-0 175 173-7 21-3 235 233-2 28-6 295 292-8 , 36-0 56 55-6 6-8 116 II5-I 14-1 176 174-7 21-4 236 234-2 28-8 296 293-8 36-1 57 56-6 6-9 117 I16-I I4'3 177 .75-7 21-6 237 235-2 28-9 297 294-8 36-2 58 57-6 118 II7-I 14-4 178 176-7 21-7 238 236-2 29-0 298 295-8 36-3 59 58-6 7-2 119 I18-I 14- 1 179 1 .77'7 21-8 239 237-2 29-1 299 296-s ; 36-4 60 59-", 7-3 120 1 19- 1 14-6 180 1 178-7 21-9 240 238-2 29-2 300 297-S 1 3«-6 Dist. Dep.JD.Lat Dist. Dep. D.Lai Disti Dep. D. Lai. Dist. Dep. D. Lat. ^ Dep. D. LaU 83 ° 5''3S2'" 1 TABLE 1 TRAVEKSK TABLl TO DEGKKES 7° 0'>28'° Hist D.Lat Dep. Dist. D. Lat Dep. Disr. D. Lilt Dep. Dist. D. Lnt 477-4 Dep. Dist. D.Lat. Dep. .^nl 2qS-7 367 361 358-3 44-0 421 1 417-9 S.-3 481 58-6 541 537-0 65-9 .■((12 2997 36-8 362 3593 44- ■ 422 418-8 5'-4 482 478-4 58-7 S42 537-9 1 66-0 303 3007 369 363 360-3 442 423 419-8 51-5 483 479-4 58-8 543 53S9 66-2 304 301-7 370 364 ! 361 3 44-4 424 420-8 5.-7 484 480-4 59-0 544 5399! 66-3 305 302-7 37-2 36.-, 362-3 44-5 425 421-8 51S 485 48.-4 59-. 545 1 540-9 1 66-4 306 3037 37-3 366 363-3 44-6 426 4228 51-9 486 482-4 59-2 .546! 54J-9: ^6-6 307 3047 37-4 367 3643 447 427 423 8 52-0 487 4S34 59-4 547 542-91 66-7 308 305-7 375 368 365-2 44-S 428 1 424 8 52-2 488 484-3 59-5 548 543-9 1 66-8 309 3067 377 369 3662 45-0 429 1 425-8 52-3 489 485-3 59-6 549 544-91 66-9 310 3077 37-8 370 367-2 45-1 430 426-8 52-4 490 486-3 59-7 550 545-9 67-0 311 30S7 37-9 371 36S2 45-2 IsT'l 427-8 52-5 491 487-3 59-8" 55r 5469 1 67-1 312 3097 38-0 372 369-2 45-3 432 428-8 52-6 492 488 3 59-9 552 547-9 1 67-2 313 3>07 38-1 373 370-2 45-5 433 429 8 528 493 4S9-3 6o-i 553 548-9: 67-4 314 3"-7 383 374 371-2 456 434 1 430 8 52-9 494 490-3 602 554 549-9 67-S 315 312-6 38-4 37.i 372-2 45 7 4.3.5 43,7 S3-0 495 49.-3 60-3 555 550-81 67-6 316 3 1 3-6 385 •376 1 373-2 45-8 436 432-7 S3-I 496 4923 6o-5 556 551-8 678 317 3146 3S-6 377 1 374-2 45-9 437 433-7 533 497 493-3 60-6 557 552-8, 679 318 315-6 387 378 375-2 46-1 4.38 434-7 53-4 498 494-3 Oo-7 558 553-8 68-0 319 316-6 389 376-2 46-2 439 4357 53-5 499 495-3 6o-8 559 554-8 68 I 320 Jiz:6 39-0 .■i80 377-2 46-3 440 4367 _531&^ 500 496-3 __6i-o 560 555-8 _683 321 3.8-6 391 381 378-1' 46-4 441 1 437-7 53-7 5or 497-2 61-r 56r 556-8 68-r 322 319-6 39-2 382 379-1 46-5 442 1 43S7 53-9 502 4982 6l-2 562 557-8 68-5 323 3206 39-4 383 380-1 46-7 443 I 439-7 54-0 503 499-2 613 563 5588 686 324 321 6 395 384 381-1 46-8 444 ' 440-7 54-1 504 500-2 61-4 564 559-8 68-7 325 3226 39-6 385 382-1 46-9 445 4417 54-2 505 501-2 6.-5 565 5608 ' 6S-9 326 323-6 39-7 386 383-1 470 446: 442-7 54-3 506 502-2 6.-6 566 561-8: 690 327 324-6 39-8 387 384-1 47-2 447 443-7 545 507 503-2 6r8 567 5628. 69-1 328 3-5S 400 388 3S5-I 473 448 444-7 54-6 508 504-2 61-9 568 563-S 692 329 3265 401 389 I 386-1 47-4 449 I 445 6 54-7 509 505-2 62-0 569 564-8 693 330 _32ZJ 40-2 .390! 3S7-I 47-5 4 50 j 446-6 548 510 506-2 62-1 570 565-8 694 33r 32S5 403 391 388-1 47-6 451 447-6 55-0 sir 507-2 ! 623 571 566-7 1 696 332 329-5 40-5 392 389-1 47-8 452 4486 55-1 512 50S-2 624 572 567-7 i 697 333 330-5 40-6 393 390-1 479 453 449-6 55-2 513 5092 625 573 5687 698 334 33'5 40-7 394 39I-I 480 454 450-6 55-3 514 5.0-2 626 574 569-71 69-9 335 33=5 40 S 395 3920 4S-1 455 45 '-6 55-4 515 511-1 627 575 570-7 1 70-. 336 3335 409 396 393-0 48-3 456 452-6 55-6 516 5t2-i 62-9 576 5717 70-2 337 , 334 5 411 397 1 3940 , 48-4 457 453-6 557 517 5I3-. 63-0 577 5727 70-3 338 335-5 41-2 .■i98 i 395-0 4S-5 458; 4546 55-8 518 5.4-1 63-1 578 573-71 70-4 339 1 3365 4I-3 399 396-0 4S-6 459 455-6 55-9 519 5.5-. 63-2 579 57471 70-5 340 ; 337-5 41-4 400 3970 48-7 460 4566 56-. 520 5.61 63-4 580 575-7 70-7 841 1-33^-4 41-6" 401 3980 48-9" 461 457-6 -56^2- 521 5I7-I 63-5 581 576-7" 708 342 1 339-4 4"'7 402 399 490 462 458-5 56-3 522 518-1 63-6 582 577-6 i 70-9 343 1 3404 41S 403 4000 49-1 463 459-5 56-4 523 519-1 637 583 578-61 710 344 [ 341 4 41-9 404 ^ 401-0 49-2 464 460-5 56-5 524 520-1 638 584 579-6 1 71-2 345 342 -4 420 4O.0 4020 494 465 46.-5 56-7 525 52I-I 640 585 580-6! 71-3 346 1 3434 42-2 405 1 403-0 49-5 460 462-5 56-8 526 522-1 64-1 586 581-6 1 7.-4 347 , 344-4 42-5 407 404-0 1 496 467 1 463-5 56-9 527 523-. 642 587 5826 7.-5 348 , 345-4 42-4 408 405-0 497 468 1 464-5 57-0 528 524-1 64-3 588 583-6 7.-6 349 ! 3464 425 409 405-9 498 469 1 465-5 57-2 529 525-0 64-5 5S9 584-6 7.-8 350 1 347 4 426 410 i 4069 50-0 470 1 466-5 57-3 530 5260 64-6 590 585-6 _2iy_^ 351 34S4 428 411 1 4079 50-1 471 467 -s 57-4 531 527-0 647 59 1 586 6 72-0 352 349-4 42-9 412 1 4089 50-2 472 468-S 575 532 5280 64-S 59a 587-6 72-1 353 350-4 43-0 413 409-9 50-3 473 469-5 57-6 533 529-0 64-9 593 588-6 72-2 354 35.-4 4ri 414 1 410-9 50-4 474 470-5 57-8 534 530-0 65-1 594 5S96 72-4 355 1 3523 43-3 415: 41,9 506 475 471-5 57-9 535 53 '-0 65-2 595 5906 72-5 356 ! 353 3 43-4 410 4129! 507 476 472-4 580 536 532-0 65-3 596 59 '-S 72-6 357 t 3543 43-5 417 1 413-9 50S 477 473-4 58-. 537 533-0 65-4 597 592-5 727 •358 355-3 436 41S 414-9: 509 478: 474-4 582 538 534-0 65-6 598 593-S 729 359 3563 43-7 419 4159 5'-i 479 1 475-4 58-4 539 535 65-7 599 594-5 730 360 3573 43-9 420 416-9 j 5'-2 480 i 476-4 58-5 540 5360 65-8 600 595-5 73. Dist. Dep. D. Lat, Dist. Dep. |l).Lat. Dist. Dep. D. Lat. Dist. Dep. D. Lat. Dist DepT D. Lat. 8:r 5" 32'" 1 TRAVERSE TABLE TO DEGREES 1 B Oh 32" 1 i 1 DisuJD.LatjDep. Dist D.Lat. Dep. DistJ D. I.at. Dep. I)ist.|D.Ut. Dep. Dist|D. Lat.l D.p. | 1 j roi c-i 61 6o-4 S'5 121 119-8 16-S 181 179-2 25-2 241 ; 238-7 33:5 ._, n-o <^"3 02 6i-4 8 6 122! 120-8 17-0 182 i8o-2 25-3 242 239-6 ;i 3-0 0-4 03 62-4 S 8 123 121-8 183 18.-2 = 5-5 243 240-6 33-S 4 4'0 0-6 04 63-4 8 9 124 122-8 17-3 184 182-2 25-6 244 241-6 34-0 5 5-0 0-7 05 64-4 9 125 123-8 17-4 183 1S3-2 25-7 245 242-6 34-1 (i 5'9 0-8 00 65-4 9 2 1-28 124-8 17-5 180 1S4-2 25-9 246 243-6 34-2 7 6-9 i-o 07 66-3 9 3 127 125-8 17-7 187 185-2 26-0 247 244-6 34-4 « 7-9 11 08 67-3 9 5 128 126-8 17-8 188 186-2 26-2 248 245-6 34-5 9 S-9 '"3 09 9 129 1 127-7 i8-o 189 1S7-2 26-3 249 i 246-6 34'- 10 1 9-9 i'4 70 ll'l _A 7 130 1 128-7 ■ S-i 190 188-2 26-4 230 ; 247-6 ' 34-8 11 j IO-9 1-5 71 70-3 9 9 1311 129-7 18-2 191 1 189-1 26-6 251 24S-6 34-9 12 ! I.-9 i"7 72 71-3 132! 130-7 18-4 192 190-1 26-7 232 249-5 35-i l^f 12-9 i-S 73 72-3 10 2 133 131-7 .8-5 193 191-1 26;9 '253 250-5 35-2 14 1 13-9 ly 74 73-3 10 3 134 132-7 i8-6 194 192-1 234 251-5 35-3 Ifl 14-9 75 74-3 10 135 133-7 i8-8 195 193-1 255 252-5 35-5 l.i 1 I5-S 2-2 70 75-3 10 6 130 >34-7 1S-9 190 194-1 27-3 250 253-5 35-6 17 , i6-8 24 77 76-3 10 7 137 135-7 19-1 197 195-1 257 254-5 35-8 \H I7-S 2-5 78 77-2 10 9 138 136-7 19-2 198 196-1 27-6 258 255-5 35-9 19 i8-8 2-6 70 78-2 139 137.7 19-3 199 197-1 259 256-5 36-0 20 21 29± 2-8 80 79-2 1 140 138-6 19-5 200 198-1 27-8 200 257-5 36-2 20-S 2-9 "sT So- 2 3 141 139-6 19-6 201 1 199-0 28-0 201 258-5 36-3 22 21-8 3"! 82 8i-2 142 140-6 19-8 2C2 1 200-0 2S-1 262 259-5 36-; 23 22-8 3'2 83 82-2 6 143 141-6 19-9 203 201-0 28-3 203 260-4! 36-6 1 24 23-8 3'3 84 83-2 7 144 142-6 'iO^ 202-0 28-4 204 261-4 36-7 23 24-8 3-5 83 84-2 8 145 143-6 20-2 205 1 203-0 2S-5 205 262-4 36-9 2« 3-6 80 85-2 140 144-6 20-3 2061 204-0 2S-7 206 263-4 27 26-7 3-8 87 86-2 I 147 145-6 20-5 2071 205-0 28-8 207 204-4 37-2 2H 27-7 3-9 88 87-1 2 148 146-6 208 2o6-o 28-9 208 265-4 37-3 29 28-7 4-0 89 88-1 4 149 •47-5 20-- 209 207-0 29-1 209 266-4 37-4 30 29-7 4'- 90 89-1 150 148-5 20-9 '21o|2o8:o_ 29-2 270 267-4 37-6 31 30-7 4-3 91 90- J 7 131 '49-5 21-0 211 1 208-9 29-4 27r 268-4 37-7 32 31-7 4-5 92 91-1 8 152 "50-5 21-2 212 209-9 29-5 272 269-4 37-9 33 32'7 4-6 93 92-1 9 153 151-5 21-3 213 210-9 29-6 273 270-3 38-0 34 33-7 1 4-7 94 93-1 154 152-5 21-4 214 211-9 29-8 274 271-3 38-1 3.5 34'7 4'9 95 94-1 2 155 •53-5 21-6 215 212-9 29-9 275 272-3 3S-3 31; 35-6 5-0 90 95-1 4 150 154-5 21-7 210 213-9 30-1 276 273-3 38-4 37 36'6 5-2 U7 96-. 5 137 155-5 21-9 217 214-9 30-2 277 274-3 3S-6 31i 37-6 5-3 98 97-0 6 158 156-5 218 215-9 30-3 278 275-3 38- 3!) 38-6 5-4 99 98-0 S 159 157-5 22-1 219 216-9 30-5 279 276-3 3S-S 40 39-6 i 5-6 100 99-0 9. 100 158-4 22-3 220 30-6 280 '277-3 39-0 '41 40-6 5-7 101 loo-o 2 101 159-4 22-4 ■J21 21S-8 30-8 281 27S-3 39-1 42 41-5 5-8 102 loi-o 2 102 160-4 22-5 222 219-8 30-9 282 279-3 39-2 43 42-6 60 103 I02-0 3 103 161-4 22-7 223 220-8 31-0 283 280-2 39-4 44 43-6 6-1 104 103-0 5 104 162-4 224 221-8 31-2 284 1 281-2 39-5 45 44-6 ' 6-3 105 104-0 105 163-4 23-0 225 222-8 31-3 285 282-2 39-7 40 45-6 ; 6-4 100 105-0 8 100 164-4 23-1 226 223-8 31-5 '286 283-2 39-S 47 4('-5 1 b-5 107 106-0 9 107 165-4 227 224-8 31-6 287 284-2 39-9 4(; 47-5 i 6'7 108 107-0 108 166-4 23-4 228 225-8 31-7 288 285-2 40-1 49 4^*5 6-S 109 107-9 2 109 167-4 23-5 229 226-S 31-9 289 286-2 40-2 50 49-5 1 7-0 110 108-9 3 170 16S-3 230 227-8 32-0 290 287-2 61 50-5 1 ^ ITT 109-9 4 TjV 169-3 23-8 •231 22S-8 32-1 291 288-2 40-5 52 51-5 7-2 112 iio'9 6 172 170-3 23-9 ■232 229-7 32-3 292 289-2 40-0 53 5^-5 7-4 113 II1-9 173 .7.-3 24-1 233 230-7 32-4 293 290-1 40-S 54 53-5! 7-5 114 112-9 9 174 172-3 24-2 234 231-7 32-6 294 291-1 40-9 55 54'5 7"? 115 113-9 175 173-3 24-4 235 232-7 32-7 295 292-1 41-1 56 55-5 7-8 110 114-9 I 170 174-3 24-5 236 233-7 32-s 290 293-1 41-2 57 56.4 7-9 117 115-9 3 177 175-3 24-6 237 234-7 33-0 297 294-1 4'-3 58 57-4 ii'i 118 116-9 4 178 176-3 24-8 238 235-7 1 33-1 298 295-1 59 58-4 8-2 119 1I7-S 6 179 177-3 24-9 239 236-7 33-3 299 296-1 41-6 1 60 59-4 1 8-4 120 118-8 16-7 180 178-2 25-1 240 1 237-7 1 33-4 300 297-1 i 4>-i' Disl. De,.. U.Lat Uist. Dep. D.Lat Dist. Dep. D. Ut. Di... Dep. ...... Dist.l Dep. |D. Lai. 1 82 ° -^^ 1 TRAVEl{i>E TABLE TO UEGIiEKS j 8° 0''b2» DistJo. Lat Dcp. Dist D.Lat Dep. Dist D.Lat. Dep. Dist D. L;it Dep. Dist D.Lat Dep. 301 29S0 41-9 361 357-5 50-2 421 416-9 1 5S-6 481 4763 66-9 541 535-7 75-2 302 2990 42-0 362 3585 50-4 422 417-91 5S-7 482 477 3 67-1 542 536-7 75-4 303 3000 42-2 363 359-4 50-5 423 418-9 589 483 4783 67-2 543 537-7 755 304 1 30 10 423 364 3604 50-7 424 4198 590 484 1 479-3 67-4 544 5387 757 305 : 3020 425 365 361-4 508 425 420-8 59-2 485 480-3 67-5 545 539-7 75-8 306 1 3030 42-0 366 362-4 509 426 421-8 593 4S6 481-2 67-6 546 540-6 759 307 1 304-0 42-7 367 563-4 51 1 427 422-8 59-4 487 482-2 67-8 547 541-6 76-: 308 j 3050 42-9 368 364-4 51-2 428 4238 59-6 488 483-2 67-9 548 542-6 76 2 309 306 43-0 369 365-4 51-4 429 424-8 59-7 489 4S42 68-1 519 543-6 76-4 310 307-0 ^3-1 3 70 366-4 5' 5 430 425-8 59-8 49U 485-2 68-2 5.50 5446 765 3riT307-9 43-3 371 T67-4 51-6 431 426-8 ' 60-0 491 1 486-2 "68-3 551 545-6 -76^6 312 30S-9 43-4 372 368-4 51-8 432 4278 601 492 487-2 6S-S 552 546-6 76-8 313 309-9 43-6 373 369-3 5'-9 433 42S-S 60-3 493 4S8 2 68-6 553 5476 769 314 310-9 43-7 374 370-3 52-1 434 429-S: 60-4 494 4S9-2 68-8 554 5486 77-1 3I5j 3II-9 43-8 375 371-3 52-2 435 430-7; 60-5 495 4902 6S-9 555 54'^ 6 77-2 3it;j 312-9 44-0 376 372-3 52-3 436 43171 60-7 496 491-2 690 556 550-6 77-4 317,1 3>3-9 44-1 377 373-3 52-5 437 432-7 j 60-8 497 ; 492- 1 69-2 557 551-5 775 318 1 314-9 44-3 378 374-3 52-6 438 433-7 1 61-0 498 1 493 I 69-3 558 5525 77-6 319 1 315-9 444 379 375-3 527 439 434-7 1 6i-i 499 1 494-1 695 559 553-5 77-8 320, 316-9 44-5 380 376-3 440 435-7 1 61-2 500 495-1 696 560 5545 77-9 321 317-9" 44-7 381 377-3 ~53^ 4T1 436-71 614 501 496-. 69-7 561 555-5 -78^ 322 318-S 44-8 382 378-3 53-2 442 j 437-7 I 61-5 .502 497-1 699 562 5565 78-2 323 3198 45-0 383 379-2 53-3 443 438-7 j 61-7 503 498-1 700 563 1 5575 78-3 324 1 320-S 45-' 384 3802 534 444 4397, 61-8 504 499-1 70-2 564 5585 78s 325 321-8 45-2 385 381-2 53-6 445' 4406! 61-9 505 5001 70-3 565 559-5 786 326 322S 454 386 3S2-2 53-7 446' 441-6 i 62-1 506 5010 70-4 566 560-5 78-8 327 323-8 45-5 387 3S3-2 539 447 ' 442-6' 622 507 1 502-0 70-6 567 561-5 78-9 328 324S 457 388 3S4-2 54-0 448 1 443-tJ 1 62-4 508 i 503 568 562-5 79-0 329 325'8 45-8 389 385-2 54-1 449 444-6! 62-5 509 j 504-0 70-8 569 563-5 79-1 330 331 3268 327-8 45-9 46- f 390 391 386-2 54-3 450 451 445-6! 626 510 511 5050 5060 709 71-1 570 571^ 56451 79-3 565-4'| 79-4 387-2 54-4 4466 62-8" 332 3287 46-2 392 3S8-2 54-6 452 4476 629 512 507-0 71-2 572 5664' 796 333 3297 46-3 393 389-1 54-7 453 448-6 630 513 50S0 71-4 573 567-4: 797 334 i 330-7 46-5 394 390-1 54-8 454 449-6 63-2 514 5090 71-5 574 5684 79-8 3-35 33' 7 46-6 395 391-1 55-0 4 55 450-5 63-3 515 5100 716 575 569-4 80-0 336 3327 46-8 396 392-1 5S-I 456 451-5 63-S 516 510-9 71-8 576 5704 80-1 337 3337 469 397 393-1 55-3 457 452-5 63-6 517 5119 71-9 577 5714 So-2 338 3347 47-0 398 394-1 55-4 458 453-5 63-7 518 5129 72-0 578 5724 80-4 1 339 335-7 47-2 399 3951 555 4.i9 4545 63-9 519. 513-9 72-2 579 573-4 805 340 336-7 473 400 396-1 557 460 455 5' 640 520 1 514-9 72-3 580 574-4 806 341 3377 47-5 40 1 397-1 55-8 46 r 456-5 64-2 521 515-9 72-4 581 575-4 80-8" 342 iiH 47-6 402 398-1 56-0 462 457-5 64-3 522 510-9 726 582 576-4 S0-9 343 j 339-6 47-7 403 399-1 56-1 463 45S-5 64-4 523 5179 72-8 583 577-4 8I-I 344 ! 340 6 479 404 4000 56-2 464 459-5 646 524 518-9 730 584 578-4 81-3 345, 3416 4S-0 405 401 50-4 465 460-4 647 525 519-9 73-1 585 579-4 81-4 346 342-6 4S-2 406 402-0 56-5 466 4614 64-9 526 520-9 73-2 .586 580-3 8i-6 347 3436 4S3 407 403-0 56-6 467 4624 65-0 527 521-S 73-4 587 581-3 817 348 344-6 48-4 408 404-0 56-8 468 4634 65. 528 5228 73-5 588 582-3 81-S 349 345-6 48-6 4(i9 405-0 569 469 4644 65 3 529 523-8 73-7 589 583-3 820 350 3466 4^-7 410 4060 57-1 470 465-4 65-4 530 524-8 _73l 590 591 584-3 5S5-3 S21 82 2 351 347-6 489' TiT 4070 57-2 471 466-4 -65^6 '53T "5^5^ 73-9 352 348-5 49-0 412 4080 57-3 472 467-4 657 532 5268 74-1 592 5863 82-4 353 349-5 49-1 413 4090 57-5 4 73 468-4 65-8 533 527-8 74-2 593 S87-3 82-5 354 350-5 49-3 414 409-9 576 474 4694 660 534 528-8 743 594 588-3 82-6 355 351-5 494 415 4109 57-8 475 470-4 66-1 535 529-8 74-5 595 5S9-3 S2-8 356 352-S 49-5 416 4.1-9 57-9 476 471-3 66-2 536 530-8 74-6 596 590-3 83-0 357 353-5 497 417 4129 580 477 472-3 66-4 537 5317 74-7 597 591-2 83-. 358 354-5 498 418 4 "3 9 582 478 473-3 66-5 538 532-7 74-9 598 5922 83-2 359 355 5 500 419 4149 58-3 479 474-3 66-7 539 533-7 750 599 593-2 83-3 360 356-5 SOI 420 4'59 58S 480 475-3 66-8 540 534 7 75-1 600 5942 S3-S D.SU Dep. D. I,at. Dist. Dcp. D. Lat Dist. Dep. D. Lat. Dist. ..,. D. Lat. Dist. Dcp. D. Lai. 82° ,.^. 1 448 TABLE 1 TRAVERSE TABLE TO DEGREES i 9° 0'36. 1 Dist.|D.Latj Dep. 0i3t. D.Lat. Dep.| QistJ] a.Lat. Dep. 3ist. D.Lat. Dep. Dist.D.Lat.! Dep. 1 3 4 5 6 7 8 .^ 13 ' 14 1 I^i 17 Ui 19 4-0 4-9 5-9 6-9 7-9 8-9 9'9 0-5 0-6 0-8 0-9 I-: 1-3 1-4 1-6 61 62 63 64 65 66 67 68 69 70 60-2! 6i-2 1 62-2 1 63-2 64-2 65-2 66-2 67-2 9-5 9-7 9'9 lo-o 10-2 10-3 IO-5 10-6 10-8 1 1-0 121 122 123 124 125 126 127 128 129 130 119-5 120-5 121-5 122-5 123-5 124-4 'All 127-4 128-4 18-9 19-1 192 19-4 19-6 19-7 19-9 20-3 181 18.3 184 [ 185 186 187 188 189 190 178-S 179-8 180-7 181-7 182-7 183-7 184-7 185-7 .86-7 .87-7 1 28-6 28-9 29-1 29-3 29-4 29-6 29-7 241 1 238-0 ! 242 1 239-0 ■ 243 1 240-0 ! 244 241-0 1 245 242-0 246 1 243-0 247 244-0 ■248 244-9 249 245-9 25£^6_9_ 37-7 li 39-0 39-1 IO-9 II-9 .5-8 i8-8 iq-8 i'7 1-9 ^;3 ^•7 2-8 3-0 71 72 73 74 75 76 77 78 79 80 7I-I 11-3 77-0 12-2 78-0 12-4 79-0 12-5 131 Vi-2 133 134 135 136 137 138 139 140 129-4 130-4 131-4 132-4 134-3 135-3 136-3 •■IP, 20-5 20-6 20-8 21-3 21-4 21-6 21-7 21-9 191 192 193 194 195 196 197 198 109 ■200 188-6 189-6 190-6 19.-6 192-6 1936 .94-6 ;^9i-^5 .97*5 29-9 30-0 30-3 30-5 30-7 30-8 3I-0 3I-I 31-3 252 253 254 255 256 257 258 259 260 =47-9 248-9 249-9 250-9 251-9 252-8 253-8 254-8 255-8 256-8 393 39-4 39-6 39-7 399 40-0 40-2 40-4 40-5 40-7 40- 8 41-0 4. -I 41-3 4'-5 41-6 41-8 41-9 41-1 42-2 -IT 22 23 24 25 26 27 28 29 ;o-7 21 -7 23-7 24-7 S57 26-7 27-7 28-6 3-3 3*9 4' I 4-2 4-4 4-5 81 82 83 84 85 86 87 88 89 90 8o-o 8i-o 82-0 83-0 m 87-9 88-q I2'7 12-8 13-0 13-1 ■ 3-3 :p 13-9 14-1 141 142 143 144 145 146 147 148 149 150 139-3 140-3 142-2 143 -2 144-2 III: 147-2 149-1 1 50- 1 151-1 152-1 153-1 1 54- 1 155-1 156-1 157-0 158-0 22-4 22-5 22-7 23-0 23-2 23-3 23-5 '201 202 203 204 •205 206 207 •208 209 210 211 212 213 214 215 216 217 218 219 2-20 198-5 199-5 200-5 201-5 202-5 203-5 204-5 205.4 206-4 207-4 B 31-9 32-1 32-4 32-5 32-7 32-9 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 289 •;>90 257-8 258-8 259-8 260-7 ill Zl 265-7 266-7 31 32 33 34 35 36 37 38 39 50-6 3,-6 32-6 33-6 36-5 37-5 4-8 5-0 5-2 5-3 Pe 5-8 59 61 6-t 92 93 94 95 96 97 98 99 100 89-9 90-9 91-9 92-8 93-8 94-8 95-8 96-8 97-8 98-8 14-2 I4'4 14-5 14-7 14-9 15-0 15-2 151 152 153 154 155 156 1&7 158 159 160 2^-8 23-9 24-1 24-2 24-4 24-6 24-7 24-9 2 5-0 208-4 209-4 2IO-4 211-4 213-3 214-3 l\ll 2.7-3 33-0 33-2 33-3 33-5 33-6 33-8 33-9 34-1 34-3 34-4 267-7 168-7 269-6 271-6 273-6 274-6 2?i:^ 42-6 42-7 42-9 43-0 43-2 43-3 Te 43-8 44° 44-1 44-3 n-t 44-7 44-9 45-4 41 42 43 44 4,-. 4(i 47 411 49 50 51 52 53 54 55 56 07 58 59 (iO 40-5 41-5 42-5 43-5 44-4 Itt 47 '4 48-4 49-4 ' 50-4 5«-4 r--i 53-3 54-3 55*3 56-3 6-4 6-6 6-7 6-9 7-2 7-4 7-5 7-7 7-8 101 102 103 104 105 106 107 108 109 IK 99-8 IOO-7 103-7 104-7 \m 107-7 I08-6 16-1 16-3 i6-4 16-6 167 16-9 I7-I 17-2 161 162 163 164 165 166 167 168 169 170 159-0 i5o-o 161-0 162-0 163-0 164-0 164-9 16,-9 166-9 1 167-9 25-2 25-3 25-5 ia 26-1 26-3 26-4 26-6 '221 222 223 224 225 226 227 228 229 230 218-3 219-3 220-3 224-2 226-2 227-2 34-6 34-7 34-9 35-0 35-1 35-4 35-5 35-7 III 277-5 278-5 ■|"8^ 8-1 8-4 8-6 8-8 8-9 9' 9-2 1 9-4 112 113 114 115 ue 11 11 12 109-6 110-6 III-6 112-6 'Ml 17-4 17-5 17-7 17-8 i8-o 18-1 1S-3 i8-5 18-6 iS-S 171 172 173 174 175 176 177 17E I7t 18 1 168-9 169-9 170-9 171-9 172-8 173-8 174-8 175-8 176-S 177- 26-8 26-9 27-1 27-4 27-5 27-7 27 s 28-0 28-7 231 232 233 234 23f 23C 23- 23 23 24 229-1 ^-33-' ,1: ?^ 36-4 36-6 36-S 36-9 37-1 37-2 37-4 37-5 ■292 293 294 295 29( 297 291 299 30C 290-4 129.-4 292-4 293-3 294-3 295"3 296- 1 f6--'5 46-6 46-8 46-9 Eil^j"^ .JD.Lat Dist.j Dep. JD.LatJDis t. Dep |d. I.a t.Di.t.| l),-p D.L-.u,jl)i» . Dep ID. La \ pio ;, TABLE 1 TRAVKKSE TAULE TO DEGREES | 9° OhSG" 1 Dist D.Lat JDep Dist D.Lat.' Dep. Disl D.Lat Dep. Dist D.Lat Dep. Dist 541 D.Lat D.p. 301 2973 1 47-1 361 3566 565 421 415-8 65-9 481 475-1 75-2 534-4 S46 302 29S3 472 362 3575 56-7 422 4168 66-0 482 75-3 542 5354 84-7 303, 299-3 1 47-4 363 358-S S6S 423 417-8 66-2 483 477-1 75-5 543 536-3 84-9 304 1 30O-3 47-6 364 3595 56-9 424 418-8 66-3 484 4780 75-6 544 537-3 85-1 30j 301 2 47-7 .•!G5 360-5 57-1 425 4198 66-5 485 479-0 758 545 538-3 S5-3 306; 332-2 47-9 366 36>5 573 426 420-8 66-6 486 4800 75-9 540 539-3 85-4 3or i 303 2 4S0 367 3625 57-4 427 421-7 66 8 487 4810 701 547 5403 85 6 30S : 304-2 48-2 368 3635 57-6 428 422-7 67-0 488 4820 76-2 548 541-3 857 309 ' 305 2 4S-3 369 3645 57-7 429 423-7 67-1 489 483-0 764 549 542-3 85-9 310 3062 48-S 370 3654 57-9 4 30 _4247 425-7 67-3 "67^4" 490 i 4S4-0 491 485^ 76-5 767 550 531 543-3 5443 860 -86^2' 311 1 3072 4S-7 371 r366-4 -58^1- 431 312 30S-2 4S-S 372 1 367-4 SS-2 432 4267 676 492 485-9 76-8 532 545-2 86-3 313 309-1 490 373 , 36S-4 58-4 433 427-7 677 493 4S6-9 77-0 353 546-2 86 5 314 3101 49-1 374 369-4 58-5 434 428-7! 679 494 4S79' 771 554 547-2 86 6 315 3"i 49-3 375 3704 5S-7 435 429-61 68 I 495 1 488-9 77-3 555 548-2 86 8 316 3121 49-4 376 371-4 58-8 436 430 6 1 6S-2 496 4S9-9 775 556 549-2 87-0 317 3'3' 496 377 372-4 59-0 437 431-6 68 4 497 490-9 77-7 557 550-2 S7-1 318 3 14- 1 49-8 378 373-3 59-1 438 432-6 68-5 498 4919 77-9 5.58 5512 87-3 319 3151 49-9 379 374-3 59-3 439 4336 68-7 499 4929 78-0 359 552-2 87-4 320 3161 50-1 380 3753 59-5 440 434-6 68 8 500 493-8 78-2 560 5531 87-6 321 317-0 50-2 381 3763 "59^6- 441 435-6 1 69-0 501 4948 7S4 501 5S4-I 87-7 322 31S0 50-4 382 377-3 59-8 442 436-6 69-1 .502 495-8 78-5 562 S55-I 87-9 323 3190 50-5 383 378-3 599 443 437-5! 69-3 503 496-8 78-7 563 5561 88-0 324 320-0 50-7 384 379-3 60-1 444 438-5, 69-5 504 497-8 7S-S 564 557-1 SS-2 325 321-0 508 385 3S0-3 60.' 445 439-5' 69-6 505 49S-8 79-0 565 558-1 S8-3 32G 3220 51-0 .386 381-2 604 446 440-5 69-8 506 499-8 79-1 366 5591 88-5 327 3230 51-2 387 382-2 60-5 447 441-5! 69-9 507 500-8 79-2 567 560-1 88-6 32S 3240 5'3 388 383-2 607 448 4425 70-1 308 501-7 79-4 568 561-0 88-8 329 3249 5"-5 ,3S9 384-2 60-9 449 4435 70-2 509 502-7 79-5 569 562-0 88-9 330 3250 5'-7 390 3S5-2 610 450 J441 70-4 310 J^37 79-7 570 563-0 89-. 331 326-9 Si-S^ 391 3862 61-2 451 445-4 706 5111 504-7 798 571 5640 -8-9-r 332 3279 51-9 392 387-2 61-3 452 446-4 70-7 512 505-7 801 572 565-0 S9-4 333 32S9 52-1 .393 388-2 61-S 453 447-4 70-9 513 506-7 80-2 573 566-0 895 334 3299 52-3 394 389-! 6i-6 454 448-4 71-0 514 5077 So-3 574 567-0 89-7 335 3309 52-4 395 390-1 6i-S 435 4494 71-2 515 508-7 80-5 575 5680 89-9 336 3319 52-6 396 39" 62-0 456 450-4 71-3 516 509-6 806 576 5689 90-1 337 332-S 52-7 397 392-1 62-1 437 451-4 71-5 517 5.06 808 577 569-9 90-2 335 333S 529 398 393-1 62-3 458 452-4 717 518 SII-6 S0-9 378 5709 90-3 339 334S 53-0 399 394-1 62-4 459 453-3 71-8 519 1 5126 8ri 579 571-9 90-5 340 335S 532 400 395-1 626 460 ,454-3 72-0 .520! 513-6 JllA^ 5S0 _5729 90-7 3^ 336-S 533 401 396-1 1 62-7 461 455-3 72-1 521 1 514-6 81-4 581 573-9 90-9 342 337-8 53-5 402 397-0 629 462 456-3 72-3 522 5156 8i-6 582 574 9 91-0 34V3 33SS 537 403 39S-0 63-0 463 457-3 724 523 516-6 Si 8 383 575-9 91-2 344 339s 53-8 404 399-0 63-2 464 458-3 72-6 524 5176 81-9 584 576-9 91-3 .•(43 340-S 54-0 405 400 oj 63-4 465 459-3 72-7 523 5«S-6 82-1 585 577-9 91-5 341; 3417 54- • 400 401-0' 63-5 460 460-3 729 526 5195 82-3 586 578-8 91-7 317 3427 54-3 407 402-0, 63-7 467 461-2 73-1 527 520-5 824 587 579-8 91-8 34S 3437 544 408 403-0 63 8 468 462-2 73-2 528 521-5 S26 588 580-8 92-0 349 3447 54-6 40J 4040 64-0 469 463-2 73-4 529 522-5 82-7 589 58 1 -8 92-1 350 3457 54-8 410 1 4OJ-O1 64-1 1 470 4642 73-5 330 523-5 82-9 .'igo 5828 92-2 35T 3467 549 411 405-91 64-3 1 471 4652 73-7 531 524-S "83-f .591 isy^ 924 352 3477 551 412 406 91 64-5 472 466-2 73-8 532 525-5 832 592 584-8 925 353 34S7 55-2 413 407-91 64-6 473 467-2 74-0 533 S26-5 83-4 593 585-7 92-7 354 349-6 554 414 408-9 64-S 474 4682 74-2 534 5275 835 594 586-7 929 355 3506 55-5 415 409-9 64-9 475 469-2 74-3 533 528-4 in 595 5^7 7 93-1 356 35-6 55-7 416 4109 65-1 476 470-1 74-5 536 5294 83-8 596 588-7 V3-2 357 3526 5i-9 417 411-9 65-2 477 471-1 74-6 537 530-4 84-0 597 589-7 93-4 358 353 34-9 23-8 197 194-0 34-2 257 253-1 44-6 18 »7-7 3-1 78 76-8 13-5 138 135-9 24-0 198 195-0 34-4 •258 254-1 44- S 19 i8-7 3'3 79 77-8 139 136-9 24-1 199 196-0 34-6 •259 255-1 45-0 20 I9"7 3-5 80 78-8 13-9 140 137-9 24-3 200 197-0 34-7 260 256-1 4S-1 TT 20-7 ~W "sT 79-8 1 I4-I 141 138-9 24-5 201 197-9 34-9 261 257-0 45-3 22 21-7 3-8 82 8o-8 14-2 142 139-8 24-7 202 198-9 35-1 262 258-0 45-5 23 22-7 4-0 83 8i-7 14-4 143 140-8 24-8 203 199-9 35-3 263 259-0 45-7 24 23-6 4-2 84 82-7 14-6 144 141-8 25-0 204 200-9 35-4 264 2600 45-8 25 24-6 4-3 85 83-7 .4-8 145 142-8 2 5-2 ■205 201-9 35-6 265 261-0 46-0 2(1 25-6 4-5 86 84-7 14-9 146 143-8 25-4 206 202-9 35-8 266 2620 46-2 27 26'6 4-7 87 85-7 15-1 147 144-8 25-5 207 203-9 35-9 267 262-y 46-4 28 27-6 4-9 88 86-7 ■5-3 148 145-8 25-7 208 204-8 36-, 268 263-9 46-5 29 286 5-0 89 87-6 15-5 149 146-7 25-9 209 205-8 36-3 269 264-9 46-7 30 29-5 ^'^ 90 88-6 15-6 150 I47-7 26-0 210 206-8 36-5 270 265-9 46-9 31 30-5 5-4 91 89-6 15-8 151 148-7 262 211 1 207-8 36-6 271 266-9 47-1 32 31-5 5-6 92 90-6 160 1521 149-7 26-4 212 208-8 36-8 272 267-9 47-2 33 3»-5 5-7 93 91-6 16-1 153 150-7 26-6 213 209-8 37-0 273 268-9 47-4 34 33-5 5-9 94 92-6 16-3 154 151-7 26-7 214 210-7 37-2 274 269-8 47-6 35 34-5 6-1 95 93-6 .6-5 155 152-6 26-9 215 211-7 37-3 275 270-S 47-8 36 35-5 6-3 96 94-5 i6-7 156 ■53-6 27-1 216 212-7 37-5 276 271-8 47-9 37 36-4 6-4 97 95-5 i6-8 157 154-6 27-3 217 213-7 37-7 277 272-8 48-. 38 37-4 6-6 98 96-5 17-0 158 155-6 27-4 218 214-7 37-9 278 273-8 48-3 39 38-4 6-8 99 97-5 17-2 159 156-6 27-6 219 215-7 38-0 279 2 74-8 48-4 40 39-4 6-9 100 98-5 17-4 160 157-6 27-8 220 216-7 38-2 280 175-7 48-6 TT 40-4 7-1 101 99'5 17-5 161 158-6 28-0 22r 217-6 38-4 isT 276-7 48-8 42 41-4 7-3 102 100-5 17-7 162 ■59-5 28-1 222 282 49-0 43 42-3 7-5 103 IOI-4 17-9 163 160-5 28-3 223 219-6 lU 283 27S-7 49-1 44 43'3 7-6 104 102-4 18-. 164 161-5 28-5 224 389 284 279-7 49-3 45 44-3 7-8 105 103-4 18-2 165 162-5 28-7 225 221-6 39-1 283 280-7 49-5 46 45-3 8-0 106 104-4 18-4 166 163-5 28-8 226 222-6 39-2 286 281-7 49-7 47 46-3 8-2 107 105-4 i8-6 167 164-5 29-0 227 223-6 39'4 287 282-6 49-8 48 47-3 8-3 108 I06-4 18-8 168 165-4 29-2 228 224-5 39-6 288 283-6 50-0 49 48-3 S-5 109 107-3 1S-9 169 166-4 29-3 22!) 225-5 39-8 289 284-6 50-2 50 49"- 8-7 110 '9"' 170 167-4 29-5 230 Il^ll. 39-9 290 2Se6 50-4 TT 50-2 3-9 TTT 109-3 19-3 171' 168-4 29-7 231 "7-5 40-1 291 286-6 505 52 51-2 9-0 112 1 10- 3 19-4 172 169-4 299 232 228-5 40-3 292 287-6 50-7 53 52-2 9-2 113 111-3 19-6 173 170-4 30-0 233 229-5 40-5 293 288-5 50-9 54 53-2 9-4 114 112-3 19-8 174 171-4 30-2 234 230-4 40-6 294 289-5 51-1 55 54-2 9-6 115 175 172-3 30-4 235 231-4 40-8 295 290-5 51-2 5C 55-1 9'7 116 114-2 20-1 176 173-3 30-6 236 232-4 41-0 296 291-5 51-4 57 56-. 9-9 117 I I 5*2 20-3 177 174-3 30-7 237 »33-4 41-2 297 292-5 51-6 58 57-1 lo-i 118 116-2 20-5 178 175-3 30-9 238 234-4 41-3 298 293-5 5'-7 59 58-1 10-2 119 II7-2 20-7 179 176-3 31-1 239 235-4 41-5 299 294-5 51-9 (iO 59" IO-4 120 118-2 180 '77'3 31-3 £40 236-4 41-7 300 1 295-4 52-1 Dist. Dep. D.Ut Diet. Dep D.Lai Distj Dep. D. Lai. Dist Dep. D. Lai. nist| Dep. D. Lat. 8( 1° b^ 20"" TABLE 1 TKAVERSE TABLE TO DEGREES | 10° O" 40"' 1 Di?t. D.La.. Dep. DisL D.La.. Dep. Dist'o.LatJ Dep. Dist. D. Lat. Dep. Dist. D. Lat. Dep. 301 .90-4 52-3 361 355-5 627 421 414-6 73-1 481 473-7 835 541 5328 93-9 303 297 4 525 36-J 3565 629 422 415-6 73-3 482 474-7 83-7 542 5338 94-1 303 298-4 526 363 357-5 63-0 423 416-6 73-5 483 475-7 83-9 543 534-8 943 304 2994 52-8 364 35S5 632 4-i4 417-6 73-<> 484 476-6 84-1 544 535-7 945 305 3004 530 365 359-5 634 425 418-5 73-8 485 477-6 84-2 545 5367 94-6 306 30 1 -4 53-' 366 360-4 636 426 419-5 740 486 4786 84-4 546 5377 948 307 3023 533 367 361-4 63-7 427 4205 74-2 487 479-6 84-6 547 5387 950 308 303-3 535 368 3624 639 428 421-5 743 488 480-6 84-7 54S 539-7 95 I 309 304-3 53 7 369 363-4 64-1 429 422-5 74-5 489 481-6 849 549 540-7 95-3 310 305-3 53 s 370 3644 64-3 430 J2ys 747 490 4826 J51L 550 5416 95-5 sTT 3063 540 371 365 4 644 431 424-5 74-9 491 483-5 85-2 551 542-6 95-6 312 3073 54-2 372 366-4 646 432 425-4 75-0 492 484-S 85-4 552 543-6 95-8 313 30S-2 54-3 373 367-3 64-S 433 4264 75-2 493 485-5 85-6 553 544-6 96-0 314 309-2 54-5 374 368-3 650 434 i 4274 75-4 494 486-5 85-8 554 5456 96-2 315 3102 54 7 375 369-3 65-. 435 j 4284 75 5 495 4S7-5 85-9 555 546-6 96-3 316 311-2 54-9 376 370-3 65-3 436 ; 4294 75-7 496 4S8-5 86-1 556 547-5 96-5 317 312-2 55-1 377 371-3 65-5 437 4304 75-9 497 489-4 86-3 557 548-5 967 318 3"32 55-2 378 372-3 65-6 438 431-3 76-1 498 490-4 l^A 558 549-5 969 319 3'4-2 55-4 379 373-2 65-8 4.-) 9 432-3 76-2 499 491-4 86-6 559 5505 97-0 320 315-' 55-6 3S0 374-2 660 440 433-3 764 500 492-4 86-8 560 J5'-5 97-2 321 3161 55-8 381 375-2 "66^ 441 434-3 766 501 493-4 87-0 561 552-5 974 322 317-1 559 382 3762 663 442 435-3 768 502 494-4 87-2 562 553-5 97-6 323 3'Si 56-1 383 377-2 66-5 443 436-3 769 503 4953 87-3 563 554-4 97-7 324 319-1 563 384 378-2 66-7 444 437-3 77-1 504 496-3 87-5 564 555-4 97-? 325 320-1 56-4 3S5 379-2 669 445 43S-2 77-3 50,5 497-3 S7-7 .565 5504 98- 1 326 321-0 56-6 386 3S0-1 67-0 446 4392 77-5 506 4983 87-9 566 557 4 98-3 327 3220 56-8 387 381-1 67-2 447 4402 77-6 507 499 3 567 558-4 9S-4 328 323-0 57-0 388 382-1 67-4 448 4412 77-8 508 5003 88-2 568 559-4 986 329 324-0 57-1 389 383-1 676 449 4422 780 509 501-3 88-4 569 560-3 98-8 330 3250 573 390 384. 677 450 443-2 78-2 510 502-2 88-6 570 561-3 990 331 326-0 57-5 39T 385-1 67-9 451 444-2 78-3^ 511 5032 88-7 571 562-3 991 332 3270 57-7 392 3860 681 452 445-1 785 512 504-2 889 572 563-3 99-3 333 3279 578 393 387-0 68-2 4.53 446-1 78-7 513 505-2 891 573 564-3 995 334 3289 580 394 3SS-0 68-4 454 447-1 788 514 5062 89-2 574 ; 565-3 996 335 3299 582 395 389-0 68 -6 455 448-1 79-0 315 507-2 89-4 575 5663 998 336 330-9 58-4 396 3900 688 456 I 449 I 79-2 516 50S-2 896 576 1 567 2 1000 337 33 > -9 58-5 397 391-0 6S-9 457 1 450-1 794 517 509-1 89-8 577 1 568-2 1002 338 3329 58-7 398 392-0 69-1 458 451-0 79-5 518 510-1 89-9 578 5692 100-3 339 333 9 58-9 399 3929 69-3 4 5-J 1 4520 797 519 511-1 90-1 579 570-2 1005 340 J_34:8 59-1 400 J93J9 _69_:5_ 460 453-0 799 520 Jj-:i 90-3 .580 ! 571-2 1007 341 335-8 59-2 401 394-9 696 461 4540 8o-i 521 5«3-' 90-5 581 1 57"2 2 1009 342 336-8 59-4 402 395-9 69-S 462 455-0 80-2 522 514-1 906 582 5732 loro 343 337-8 59-6 403 396-9 700 463 4560 804 523 5'5-i 90-8 .583 574-1 101-2 344 338-8 59-8 404 397-9 70-2 464 4570 So 6 524 516-0 91 584 1 575 I 101-4 345 339-8 59-9 405 398-9 70-3 465 4579 808 525 5170 91-2 585' 5761 lorC 346 3407 60-1 406 399-8 70-5 466 458-9 809 526 518-0 91-3 586 i 577-1 101-7 347 3417 6o-3 407 400-8 707 467 4599 81-1 527 5190 91-5 387 578-1 101-9 348 342-7 60-4 408 4018 709 468 460-9 Si-3 528 520-0 917 588 579-1 I02-I 349 343-7 60-6 409 402S 710 469 461-9 ^■■s 529 5210 91 9 589 5800 102-3 350 3447 608 410 403-S 71-2 470 : 462-9 81-6 Si '8 530 .531 521-9 92-2 590 591 581-0 5820 102-4 ~I02 6 nr 3457 6i-o ITT 404S 7r4 471 ! 4638 5229 332 3467 6.-1 412 405-7 1 71-6 472 1 464-8 82-0 532 523-9 92-4 592 583-0 102-8 353 347-6 61-3 413 406-7 71-7 473 1 465-8 82-1 5.13 524-9 92-5 593 5840 102-9 354 3486 61-5 414 407-7 719 474 ! 466 8 82-3 534 5259 927 594 585-0 I03-I 355 349-6 6i-7 415 408-7 72-1 475 I 467-8 82-5 .535 5269 92-9 595 5S6-0 '03-3 356 350-6 61-8 416 409-7 72-2 476 4688 827 5.-! 6 527-9 93-' 596 586-9 ■03-5 357 35'-6 620 417 4107 72-4 477 469S 828 537 528-8 93-^: 597 5S7-9 1036 358 3526 622 418 411-7 72-6 478 4707 830 5:i8 529-8 93 4 598 588-9 I03S 359 353-5 624 419 4126 728 479 471-7 832 539 530-8 93-6 599 589-9 1040 360 354-S 62-5 420 4'3-6 72-9 480 4727 83-4 540 53I-8 93& 600 590-9 1042 Diet. 0*7 V. Lat t7u.. W D.Lat Diet. Dep. D.Lat. Dist. Dep. D. Lat. Dist. Dep. D. Lmi. 80° ^..o„„. 1 TABLE 1 TRAVERSK TABLE TO DEGREES ir Oh 4?-" Dist D.Latj Dep. Dist D Lat Dep. Dist D.Lat Dep. Dist ^ Dep. Dist.[D. Lat Dep. vo 0-2 61 59-9 II-6 121 1. 8-8 23-1 181 177-7 34-5 •241 1 236-6 46-0 2-0 0-4 iJ-2 6o-9 II-8 122 II9-8 23-3 182 178-7 34-7 242 j 237-6 46-2 »"9 0-6 63 6i-8 I2-0 123 120-7 23-5 183 179-6 34-9 2431238-5 46-4 3'9 0-8 64 62-8 12-2 124 I2I-7 23-7 184 180-6 35-1 244 [239-5 46-6 4"9 i-o 65 63-8 12-4 1-25 122-7 23-9 185 181-6 35-3 245 1 240-5 46-7 5-9 I-I 66 64-8 12-6 1-26 123-7 24-0 186 182-6 35-5 246 24,-5 46-9 6-9 1-3 67 65-8 I2-S 127 124-7 24-2 187 183-6 •247 242-5 47-1 7-9 IS B8 66-8 13-0 128 125-6 24-4 188 184-5 35-9 248 243-4 47-3 8-8 6!) 67-7 129 126-6 24-b 189 185-5 36-, 249 244-4 47-5 TT 9-8 1-9 70 68-7 13-4 130 127-6 24-8 190] 186-5 36-3 250 245-4 47-7 IQ.g 21 IT 69-7 13-5 1311 1286 25-0 191 187-5 36-4 25r 246-4 47-9 ii-S 2-3 72 70-7 13-7 132 .29-6 192 188-5 36-6 252 247-4 48- 1 ii'8 2'5 73 71-7 13-9 133 130-6 25-4 193 189-5 36-8 253 248-4 48-3 13-7 2'7 74 72-6 14-1 134 131-5 2 5-6 194 190-4 37-0 254 249-3 48-5 14-7 2-9 75 73-6 14-3 135 132-5 195 191-4 37-2 255 250-3 15-7 3-j 76 74-6 14-5 136 '33-5 26-0 196 192-4 37-4 256 25,-3 l8-8 16-7 3-2 77 75-6 I4"7 137 134-5 26-1 197 193-4 37-6 •257 252-3 49-0 ly? 3'4 78 76-6 14-9 138 135-5 26-3 198 194-4 258 -53-3 49-2 i8-7 3-6 79 77-5 1 15-1 189 136-4 26-5 199 195-3 38-0 259 254-2 49-4 20 JlL 3-8 80 78-5 1.5-3 140 '37-4 26-7 200 196-3 38-2 260 255-2 49-6 "fT 20-6 4-0 TT 79*5 15-5 141 138-4 26-9 201 '97-3 384 261 256-2 49-8 22 21-6 4-2 82 8o-5 iS-6 142 139-4 27-1 202 198-3 3«-5 202 257-2 50-0 23 22-6 4'4 83 8i-5 143 140-4 27-3 203 199-3 38-7 263 25S-2 50-2 24 23-6 4-6 84 82-5 i6-o 144 141-4 27-5 204 200-3 38-9 264 259-1 50-4 25 24-5 4-8 85 83-4 16-2 145 142-3 27-7 205 201-2 39-1 265 260-1 50-6 26 25-5 5-0 86 84-4 16-4 146 143-3 27-9 200 202-2 39-3 266 26,-1 50-8 27 26-5 5-2 87 85-4 i6-6 147 •44-3 28-0 207 203-2 39'5 267 262-1 50-9 28 ^T<: 5'3 88 86-4 i6-8 148 145-3 I ='8-2 208 204-2 39'7 268 263-1 51-1 29 , z8-5 5'5 89 87-4 17-0 149 146-3 1 28-4 209 205-2 39-9 269 264- 1 51-3 JJOj.9-4 90 17-2 150 147-^1 ^8-6 210 206-1 4°-' 270 265-0 51-5 31 30-4 S'9 91 89-3 17-4 151 ,48-21 28-8 211 207-1 40-3" 271 266-0 51-7 32 31-4 6-1 92 90-3 17-6 152 149-2 29-0 212 20S-1 40-5 272 267-0 51-9 33 32-4 6-3 93 91-3 17-7 153 150-2 29-2 213 209-1 40-6 273 26S-0 52-1 34 33"4 6-5 94 92-3 17-9 154 29-4 214 210-1 40-8 274 269-0 52-3 35 34*4 6-7 95 93"3 i8-i 155 152-2 29-6 215 211-0 4I-0 •275 269-9 52-5 36 35"3 6-9 96 94-2 18-3 156 153-1 29-8 216 212-0 41-2 276 52-7 37 36-3 7-> 97 95-2 i8-5 157 154-1 30-0 217 213-0 41-4 277 271-9 52-9 38 37-3 7'3 98 96-2 ,8-7 158 155-1 30-1 218 214-0 41-6 278 272-9 53-0 39 38-3 7-4 99 97'2 189 159 156-1 30-3 219 215-0 41 -s 279 273-9 53-2 40 39-3 7-6 100 98-2 160|i57-i 30-5 220 2160 42-0 280 274-9 53-4 41 40-2 7-8 101 99-1 19-3 161 158-0 30-7 221 2,6-9 42-2 281 VV 53-6 42 41-2 8-0 102 lOO-I 19-5 102 159-0 30-9 2-22 217-9 42-4 282 53-8 43 42-2 8-2 103 lOI'I 19-7 163 160-0 223 218-9 42-6 283 277-s 54-0 44 43-2 8-4 104 I02-I 164 161-0 3i'3 224 219-9 42-7 284 2-8-8 54'= 45 44-2 8-6 105 103-1 20-0 165 162-0 31-5 225 220-0 42-9 285 279-8 54'4 48 45*2 88 100 104-1 20-2 1S6 ,63-0 31-7 220 221-8 43-1 286 54-6 47 46-1 9-0 107 105-0 20-4 167 163-9 31-9 227 222-8 43-3 287 281-7 54-8 48 47-. 9-2 108 106-0 20-6 108 164-9 32-1 228 223-8 43-5 288 282-7 49 48-1 9-3 109 101-0 20-8 169 165-9 32-2 229 224-8 43-7 •289 2S3-7 55-' 50 49-1 9-5 110 I08-0 2I-0 170 ,66-9 3--4 230 1 225-8 43-9 290 284-7 55"3 51 50-1 9-7 111 109-0 2 1-2 171 167-9 32-6 231 226-S 44-1 291 28 5-7 55-5 52 51-0 99 112 109-9 21-4 172 168-S 32-8 232 227-7 44"3 292 286-6 55-7 53 52-0 lo-i 113 110-9 21-6 173 169-8 33-0 233 228-7 44-5 293 287-6 55-9 54 53'o 10-3 114 1II-9 21-8 174 170-8 33-2 234 229-7 44-6 294 288-6 56-1 55 54-0 io'5 115 I 12-9 21-9 175 171-8 33-4 235 1230-7 44-8 295 2896 56-3 56 Sl-o IO-7 116 113-9 170 172-8 33-6 236 231-7 45-0 ■296 290-6 56-5 57 56-0 10-9 117 114-9 22-3 177 173-7 33-8 237 232-6 45-^ 297 291-5 56- 58 1 56-9 ii-i 118 ..5-8 22-5 178 174-7 34-0 238 233-6 45-4 298 292-5 56-9 59 5.-9 II-3 119 II6-8 22-7 179 175-7 34-^ 239 234-6 45-6 299 293-5 57-1 60 ,8-9 ..■4 1-20 117-8 22-9 IHO ,76-7 34-3 240 235-6 45-8 300 294-5 57-:: D:8t. Dep. D.Laijoist. Dep. D.Lat Dist. Dep. JD. Lat. -■ Dep. D.Lat. Dist. Dep. D. Lat, 79° 5" 16"' j 453 TRAVERSE TABLE TO DEGREES 11" Oh 44" Dist. 301 D. L«t. 2954 Dep. 57-4 Dist. 361 D. Lat. Dep. Dist. 421 0. Lat. Dep 80-3 Dist. 481 D.Lat. Dep. Dist. 541 D.Lat. Dep. 354-3 689 4132 472-1 91-8 531-0 103 2 302 296-4 57-6 302 355 3 69-1 422 414-2 80-5 482 473-1 92-0 542 5320 103-4 3U3 2974 57-8 363 356-3 693 423 415-2 807 483 474-1 92-2 543 5330 1036 30-» 2.KS-4 5S0 364 357-3 69-5 424 416-2 So-9 484 475-1 92-4 544 5340 .03-8 305 2994 5S-2 365 358-3 69-6 425 417-2 8i-i 485 4761 92-6 545 5350 1040 306 3003 5S-4 366 359-2 69-8 426 418-1 813 486 4770 92-8 516 535-9 104-2 307 301-3 58-6 307 3602 70-0 427 419-1 81-5 487 478-0 930 547 536-9 104-4 3o8 302-3 58-8 308 361-2 702 428 420-1 817 488 4790 932 548 537-9 104-6 309 3033 59-0 309 362-2 704 429 421-1 81-9 489 480-0 93-3 549 538-9 1048 310 3043 592 370 363-2 _7o-6 430 422-1 82-1 490 481-0 93-5 550 539-9 1050 311 305-3 59-3 37l 3f'4l 70-S 43! 423-0 'S22 491 48 1-9 936 55I 540-8 105-1 312 306-2 595 372 365-> 710 432 424-0 82-4 4 92 4829 938 552 541-8 1053 31 o 30-2 597 373 366-1 71-2 433 425-0 82-6 493 483-9 94-0 553 5428 105-5 314 30S2 599 374 367-' 714 434 426-0 S28 494 484-9 942 554 543-8 1057 315 3092 60-1 375 36S-1 7.6 435 4270 830 495 485-9 944 555 544-8 105-9 316 3102 60-3 376 369-1 71-7 436 42S0 S3-2 496 486-9 94-6 556 545-8 106-1 317 311 ' 605 3:7 3700 71-9 437 42S9 83-4 497 487-8 94-8 557 546-7 1063 318 312 1 6o-7 378 3710 72-1 438 4299 836 498 48SS 950 538 5477 106-5 319 313" 60-9 379 372-0 723 439 430-9 838 499 489-8 95-2 559 548-7 106-7 320 3141 61-1 380 3730 72-5 440 4319 84-0 500 4908 95-4 560 5497 1069 321 3J5> 6i-3 381 374-0 727 441 4329 84- 1 501 79.-8 95-6 5oT 5507 107-f 322 61-4 382 3749 72-9 442 433-8 843 502 4927 958 562 5516 107-2 323 3'70 616 383 375-9 73-' 443 434-8 S45 503 493-7 96-0 563 5526 107-4 32i 3180 6i-8 384 3-/6-9 73-3 444 435-8 84 7 504 494-7 96-2 564 553-6 107-6 325 3190 62-0 385 377-9 735 445 4368 84-9 505 4957 96-4 565 554-6 1078 326 3200 62-2 386 378-9 73'7 446 437-8 85. 506 496-7 96-6 560 5556 108-C 327 3210 624 387 3799 73-S 447 438-8 8S-3 507 497-7 96-S 567 5566 108-2 328 321-9 626 388 3S0S 74-0 448 439-7 855 508 49S6 970 508 557-6 1084 329 322-9 62-S 389 3818 74-2 449 440-7 85-7 509 4996 97-2 569 5586 1086 330 331 3239 324-9 63-0 390 391 382-8 "383^8 74-4 74-6 450 451 441-7 4427 85-9 86-1 510 511 5006 973 97-5 570 571 _559:5 560-5 108 8 1090" 501-6 332 325-9 63-4 392 384-8 74-S 452 443-7 86-2 512 502-6 97-6 572 561-5 109- 1 333 3268 635 393 385-7 75-0 453 444-6 86-4 513 503-S 97-8 573 562-5 1093 334 327-8 63-7 394 386-7 75-2 454 445-6 86-6 514 504-5 9S0 574 563-5 109-5 335 32S-S 639 395 3S7-7 75-4 455 4466 868 515 505-5 98-2 573 564-5 109-7 336 3298 64-1 396 38S-7 75-6 456 4476 S7-0 516 506-5 98 4 576 5654 1099 337 330S 643 397 3897 75S 457 4486 87-2 517 507-S 98-6 577 566-4 IIOI 338 33 > 8 64-5 398 390-7 759 458 4496 S7-4 518 508-5 98-8 578 567-4 110-3 339 332-7 64-7 399 39i'^ 76-1 459 4505 87-6 519 509-4 990 579 5683 1105 340 3337 64-9 400 392-6 76-3 460 _45i:s 87-8 520 510-4 99-2 580 5693 1107 341 334-7 65-1 4111 393-6 76-5 401' 452-5 88-0 521 5114 99-4 581 5703 1109 342 3357 65-3 402 394-6 76-7 402 453-5 SS-2 522 512-4 99-6 582 5713 iii'i 343 3367 65s 403 395-6 769 403 454-5 88-3 523 513-4 99-8 583 5723 111-3 344 337-6 656 404 396-5 77-1 404 455-4 88-5 524 514-3 loo-o 584 5732 1115 345 33S6 65-S 405 3975 773 405 456-4 SS-7 525 S«5-3 100-2 385 574-2 III 7 346 3396 660 406 398-5 77-5 466 457-4 88-9 526 516-3 1004 580 575-2 III 8 347 340-6 662 407 399-5 77 7 467 458-4 89- 1 527 517-3 100-6 587 576-2 II2-I 348 341-6 664 408 400-5 779 468 459-4 893 528 518-3 1008 588 5772 1 12-3 349 3426 66 6 409 401-5 7S1 469 460-4 89-5 52rf 519-3 loro 589 578-2 II24 350 351 _3431 344 5 66-8 670 410 4i: 4024 4034 78-2 78-4 470 471 _46.-3 462-3 89-7 530 531 5202 521-2 101-2 To I -4 590 59r 5791 580-1 II26 II2'8 89-9 352 34SS 67-2 412 4044 786 472 463-3 90-1 532 522-2 1016 592 581-1 II30 353 346-5 67-4 413 405-4 788 473 4643 903 533 5232 101-7 593 5S2-1 1132 354 3475 67-S 414 406-4 790 474 4653 90-4 534 524-2 ior8 594 583-1 113-3 3G5 34S-4 677 415 407-3 792 475 466-2 906 535 525-1 102-0 595 584-0 ■ 13-5 350 349-4 679 416 408-3 79-4 470 467-2 908 536 526-1 102-2 596 5S5-0 "37 357 3504 68-1 417 409-3 79-6 477 468-2 91-0 537 527-1 1024 597 5S6-0 113-9 358 35 '-4 68-3 418 410-3 79-8 47n 469-2 91-2 538 528-1 102-6 598 587-0 114 I 359 352-4 685 419 411-3 800 4 79 470-2 91-4 539 5291 102-8 599 5SS-0 1 143 360 353-4 687 420 4123 80- 1 480 471-1 91-6 540 530-1 ^ 600 5S90 "45 Diu Don. l>. I.al. Dist. Dep. D. Lat. Dist Dep. D. LMt Dist. Dep. D.Lai. Dist. Dep. D..,. 1 79' 6" 16" 1 TABLE 1 TRAVERSE TABLE TO DEGREES | 12° 0^48- 1 Uist. D.Lat Den. Uist. D. Lat. Dep. Dist.JD.Lat Dep. Dist.JD.Lat Dep. DisL D.Lat Dep. "T" i-o 0-2 61 59-7 12-7 121 1.8-4 25-2 181 177-0 37-6 241 235-7 50-1 2 2'0 0-4 62 6o-6 12-9 122 1.9-3 25-4 182 17S-0 37-8 242 236-7 50-3 3 2-9 06 63 6r6 I3'i 1-23 .20-3 25-6 183 179-0 38-0 243 237-7 50-5 4 3'9 0-8 64 62-6 13-3 124 121-3 25-8 184 180-0 38-3 244 238-7 50-7 3 4" 9 ro 65 63-6 '3'5 125 j 122-3 185 18. -0 38-5 245 239-6 50-9 6 5'9 1-2 66 64-6 13-7 126 1 123-2 26-2 186 1S.-9 38-7 246 240-6 7 6-8 '•5 67 65-5 13-9 1271 124-2 26-4 187 .82-9 38-9 247 24.-6 51-4 8 7'8 1-7 68 66-5 14-: 1-28 125-2 26-6 188 .83-9 39-. •248 1 242-6 51-6 9 8-8 19 69 67-5 1 14-3 1-29 1 126-2 26-8 189 184-9 39-3 249 243-6 5.-8 10 9-8 2-1 70 68-5 1 14-6 130 i 127-2 27-0 190 185-8 39-5 250 244-5 245-5 52-0 11 2-3 71 69-4 14-8 131 I28-I 27-2 loT .86-8 39-7 251 52-2 12 11-7 i-5 72 70-4 15-0 132 .19-1 27-4 192 187-8 39-9 252 246-5 13 12-7 2-7 73 71-4 15-2 133 .30-1 27-7 193 188-8 40-1 253 247-5 52-6 14 I3'7 2-9 74 72-4 15-4 I.'!4 .3.-1 27-9 194 .89-8 40-3 254 248-4 52-8 15 14-7 3-1 75 73 4 iS-6 135 132-0 28-1 195 .90-7 40-5 255 249-4 53-0 16 "5'7 3-3 76 74-3 iS-8 136 133-0 28-3 196 .9.-7 40-8 ■256 250-4 53-2 17 ,6-6 3-5 77 75-3 16-0 137 134-0 28-5 197 .92-7 4.-0 257 25.-4 53-4 18 17-6 3-7 78 76-3 16-2 138 135-0 28-7 198 >93-7 41-2 •258 252-4 53-6 19 4'0 79 77-3 16-4 139 136-0 28-9 199 '9+-7 41-4 •259 253-3 53-8 20 ' 19-6 21 1 zo-5 4' 2 80 78-3 16-6 140 136-9 29-1 200 195-6 4,-6 2(;o 254-3 ! 54-I 1 4"4 81 79-2 16-8 141 137-9 29-3 201 196-6 41-8 26r 255-3 : 54-3 22 U. -5 4-6 82 8o-2 17-0 142 138-9 29-5 202 197-6 42-0 262 256-3 54-5 23 1 2.-5 4-8 83 8i-2 17-3 143 ■39-9 29-7 203 198-6 42-2 203 257-3 54-7 24 1 23-5 5'° 84 82-2 17-5 144 140-9 29-9 204 199-5 42-4 264 258-2 54-9 25 ,24-5 5'^ 85 83-1 17-7 145 .41-8 30-. 205 200-5 42-6 265 259-2 55-> SB *5'4 5'5 86 84-1 17-9 146 142-8 30-4 206 20.-5 42-8 266 260-2 55-3 27 26-4 5-6 87 85-1 .8-, 117 143-8 30-6 2071 202-5 43-0 267 26. -2 55-5 28 27-4 5-8 88 86-1 .8-3 148 1 144-8 30-8 208 203-5 43-2 268 262-1 55-7 29 28-4 6-0 89 87-1 .8-5 1491 145-7 31-0 209 204-4 43-5 269 263-, 55-9 30 ^^3 6-2 90 88-o|.8-7 150 146-7 3.-2 210 205-4 43-7 270 264-1 56-. 31 303 6-4 91 89-0 .8-9 JET 147-7 31-4 In 206-4 43-9 271 265-1 56-3 32 3i'3 6-7 92 90-0 19-1 152 148-7 3.-6 212 207-4 44-1 272 266-1 56-6 33 32-3 6-9 93 91-0 153 149-7 3.-8 213 20S-3 44-3 •273 267-0 56-8 3J 33-3 7'i 94 91-9 19-5 154 150-6 32-0 214 209-3 44-5 274 268-0 57-0 35 34-2 7-3 95 92-9 19-8 155 151-6 32-2 215 2.0-3 44-7 275 269;° 57-2 36 35-2 7-5 96 93-9 20-0 156 152-6 32-4 216 2.1-3 44-9 276 57-4 37 36-2 7'7 97 94-9 20-2 1-57 153-6 32-0 217 2.2-3 45-1 277 270-9 57-6 38 37-2 7-9 98 95-9 20-4 158 154-5 32-9 218 2.3-2 45-3 278 27.-9 57-8 39 38-. 99 96-8 20-6 159 I55-5 33-. 219 2.4-2 45-5 279 272-9 58-0 40 41" 39-1 8-3 100 97-8 20-8 160 156-5 33-3 220 215-2 45-7 280 .273-9 58-2 40-1 8-5 Tm 98-8 21-0 161 157-5 33-5 •221 2.6-2 45-9 isT 274-9 58-4 42 41-1 8'7 102 99-8 21-2 162 .58-5 33-7 222 2.7-1 46-2 282 275-8 58-6 43 42-1 8-9 103 ioo'7 21-4 163 159-4 33-9 223 218-1 46-4 283 276-8 58-8 44 43-0 9-1 104 101-7 21-6 164 .60-4 34-1 224 219-1 46-6 284 277-8 59-0 45 44-0 9-4 105 102-7 21-8 165 16. -4 34-3 225 220- . 46-8 285 278-8 59-3 46 45-0 9;6 106 103-7 22-0 ICB .62-4 34-5 2-26 22.-1 47-0 286 279-8 59-5 47 46-0 107 104-7 22-2 167 163-4 34-7 227 222-0 47-2 287 280-7 59-7 48 47-0 lO'O 108 105-6 22-5 168 .64-3 34-9 228 223-0 47-4 288 28.-7 59-9 49 47'9 10-2 109 106-6 22-7 169 .65-3 35-1 229 224-0 47-6 289 2S2-7 60-1 50 48-9 10-4 110 107-6 22-9 170 166-3 35-3 230 225-0 47-8 290 283-7 60-3 "5r 499 ,o-6 111 108-6 23-1 171 167-3 35-6 •23! 226-0 48-0 •291 284-6 60-5 52 lo-S 112 109-6 ^3-3 172 163-2 35-8 232 226-9 48-2 292 2856 6o-7 53 i,i'8 no 113 110-5 23-5 173 1 169-2 36-0 •233 227-9 48-4 293 286-6 60-9 54 5Z-8 II-2 114 111-5 23-7 36-2 234 228-9 48-7 294 2>S7-6 6.-1 • 55 53-8 11-4 115 112-5 23-9 175 17.-2 36-4 235 229-9 48-9 295 288-6! 61-3 , 56 54-8 II-6 116 113-5 24-1 176 36-6 •236 230-8 49- ■ 296 289-5 6.-S 57 55-8 II-9 117 114-4 24-3 177 173-1 36-8 237 23.-8 49-3 297 290-5 6.-7 58 56-7 118 115-4 ^4-5 178 174- 1 37-0 '238 232-8 49-5 298 291-5 62-0 59 57-7 12-3 119 1.6-4 24' 7 179 175-1 37-2 239 233-8 49-7 299 292-5 62-1 60 58-7 12-5 120 117-4 24-9 180 .76-1 37'4 240 234-8 49-9 300 293-4 62-4 Uist Dep. D.Lat Dist. Dep. D.Ui D^. D,.p. D. L-.it. Dist. D.p. D. Lat. i^Tt Dep. D. Lat, 7i )° 5" ia"^ TKAVEllSK TAliLE TO DEG KEES 1-1=' Oh 48" Dist. 301 D.Lat. Dep. 294 4 626 Dist. D. Lat. Dcp. Di.-t.b. Lat. Dep. Dist Id. Lat. 1 Dep. Dist D.Lat Dep. 1125 361 353-1 75-0 421I4..-8 87-5 4705 lOO-O 541 529-2 ■M-2 2954 62S 362 3541 75-2 422 ; 4128 87-7 482 471-5 100-2 542 5302 1127 :m3 290-4 630 363 355-1 754 423 j 413-8 87-9 483 4725 100-4 543 531-1 1 12-9 3(U 2974 63-2 364 356 75-7 424] 414-7 8S1 484 473-4 100-6 544 532-1 113 I 303 29S3 (-iA 365 357-0 759 425 415-7 88 3 485 474-4 100-8 545 533-1 113-3 306 2993 636 366 35S-0 76-1 426 416-7 88-6 486 4754 loi-o 546 534-1 1135 307 3003 638 367 359-0: 763 427 417-7 88-8 487 476-4 lOI 2 547 5351 i'37 308 301-3 64-0 368 3600' 765 428 418-6; S9-0 488 477 3 101-4 548 5360 1139 30'.l 302-2 642 369 3609! 767 429 419-61 89-2 489 478-3 IOI-6 549 537-0 1 14-1 310 3032 644 370 371 361-9 76-9 362-9 77-1 430 431 4206 89-4 42.-6 89-6 490 49 r 479-3 4S0-3 101-9 I02I 550 551 5380 538-9 1 14-4 114-6 311 3042 646 312 305-2 648 372 3639 77-3 4.32 ! 422 6 89-8 492 481-2 1023 552 539-9 1148 313 306-2 651 373 364-8, 77-S 433 423-5 90-0 493 4822 102-5 553 540-9 II 5-0 1 314 3071 65-3 374 365-81 77-7 434 424-5 90-2 494 483-2 102-7 554 541-9 1152! 31.-, 30K-I 655 375 366-8 77-9 435 425-5 90-4 495 484-2 102-9 555 542-9 115-4 310 300-1 657 376 367 8 78-2 436 426-5 90-6 196 485-2 103-1 556 543-8 j;5;6 317 310 I 659 377 368-8 78 4 437 427-5 90-8 497 : 486-1 103-3 557 544-8 Si-i 3"i 66-1 378 3697 78-6 4.38 428-4 91-0 498 1 487-1 103-5 558 5458 1 16-0 319 3120 66-3 379 3707 78-8 439 1 429-4 9'-3 499 48S-1 103-8 559 546-8 1162 320 3130 66-5 380 371-7 79-0 440} 430-4 91-5 500 489-1 104-0 560 547-8 1 16-4 321 314-0 -66Y 381 372-7" 79-2 441 I 431-4 9'-7 501 490-0 104-2' 561 54S-7 n66 322 3150 669 382 373-7 79-4 442 : 432-3 91-9 502 491-0 104-4 562 549-7 1168 323 315-9 67-1 383 374-6 79-6 -4-13 1 433-3 1 92-1 .503 492-0 1046 563 550-7 1170 324 3169 67-3 384 375-6: 79-8 444 1 434-3 i 92-3 504 4930 1048 564 551-7 117-2 325 3'7-9 67-0 385 3766' 80-0 445 435-3 92-5 505 494-0 IC5-0 565 552-7 1174 326 3>S9 67-8 386 377-6 80-2 ■'*>6 1 436-3 92 7 506 495-0 105-2 566 553-7 1176 327 3>9-9 68 387 378-S 80-4 44 7 437-2 92-9 507 495-9 105-4 567 554-6 II7-8 328 320-8 68-2 388 379-5 80-7 448 438-2 93-1 1 508 496-9 105 6 568 555-6 1 18-0 329 321-8 684 389 380-5 S0-9 449 439-2 93-3 509 497-9 1058 569 556-6 118-2 330 322-8 686 390 381-5 81-1 450 440-2 93-5 510 498-9 106-0 570 _557:S,_iiS-5 331 323-8 ~68^ 39 r 382-5 "8".T '451 44I-I 93-7 511 499-8 106-2 571 558-5 118-7 332 321-7 69-0 392 3834 Sis 452 442-1 93-9 512 5008 1064 572 559-5 iiS-9 333 325-7 69-2 393 3S4-4 81-7 453 443-' 94-1 513 501-8 106-6 573 560-5 1191 334 3267 69-4 394 3854 819 454 444-1 94-4 514 502-8 106-8 574 561-5 119-3 335 327-71 69-6 395 3S6-4 821 455 445-1 94-6 515 503-7 107-0 575 562-4 119-5 336 32S7 69-8 396 3S7-3 823 456 446-0 94-8 516 504-7 107-2 576 563-4 1197 337 329-6 1 70-0 397 388-3 82-5 457 447-0 95-0 517 505-7 107-4 577 564-4 1199 338 3306: 703 398 3S9-3 82-7 458 448-0 95-2 518 506-7 107-6 578 565-4 1 20- 1 339 33' 6 1 70-5 3!) 9 390-3 82-9 459 449-0 95 4 519 507-7 107-8 579 566-4 120-3 3411 332-6 1 707 400 3913 83-1 460 450-0 95-6 .52) 50S-7 loS-i 580 567-4 120-6 341 333-5' 709 401 342-2' "S3-4 46T 450-9 95-8 521 5096 108-3 581 568-3 1 20 8 342 334-51 71-1 402 3?3-2 83-6 462 45 « 9 960 522 5106 108-5 582 569-3 121-0 343 3355 71-3 403 394-2 838 463 452-9 962 523 S.16 io8'7 583 570-3 1212 344 3365 715 404 395-2 84-0 464 453-9 96-5 524 5«2-5 1089 584 S71-2 121-4 345 3375 717 405 396-2 84-2 465 454-8 96-7 525 5'35 109-2 585 572-2 121-6 346 33**-4 719 406 397-1 84-4 4 66 455-8 96-9 526 514-5 1094 .586 573-2 1218 347 339-4 72-1 407 398-1 84-6 4G7 456-8 97-1 527 515-5 109 6 587 574-2 1220 "48 3404 72-3 408 399-1 84-8 468 457-8 97-3 528 5'65 1098 .588 5752 122 2 34'J 34 ■•4 725 409 400-1 85-0 469 458-8 97-5 .529 5«7-5 IIOO 589 576-2 122-4 35£ 342-4 343 3 727 410 401-0 402-0 85-2 470 459-7 1 97-7 530 5.-U" 518-4 5'94 1 10-2 590 591 _577J. S78-. 1226 122-8 73-0 85-4 460-7 979 IIO-4 352 3443' 732 412 403-0 85-6 472 461-7 y8l 532 520-4 1 10 6 592 5791 123-0 353 345-31 73-4 413 404-0 85-S 473 4627 98-3 5.33 521-3 1 10-8 593 5S00 123-2 354 346-3 736 414 405-0 86-1 474 463-6 534 5"3 mo 594 5S1-0 123-4 355 3472 738 415 405-9 86 3 475 4646 9S-7 535 523-3 III-2 595 582-0 123-6 356 34S2 74-0 416 406-9 865 476 465-6 9S-9 536 524-3 IU-4 596 5830 123-9 357 349-2 74-2 417 407-9 867 477 4666 99-1 537 525-3 111-6 597 5840 124- 1 358 350-2 74-4 418 408-9 869 478 i 4676 99-4 538 5262 II18 598 584-9 1243 359 351-2 746 419 409-8 87-. 4 79 468-5 99-6 539 527-2 1 120 599 5S5-9 124-5 360 3S2-^ 74-8 420 4108 87-3 480 1 4695 99-8 540 528-2 II2-3 600 586-9 124-7 Dist Dcp, D. Lat Dist Dep. D.Lat Dist Dep. D.Lat Dist Dep. D.Lat Dist Dep. D. Lat. 78" 5I' 12" TABLE 1 TRAVERSE TABLE TO DEGREES 1 13° C'sa* 1 Dist O.Lat -D-;;- Dist Id. Lat Dep. Dist D. Lat, Dep. Dist D.Lat.j Dep. Dist D.L-.t.|Dep. 1 ro 0-2 61 59-4 13-7 121 117-9 27-2 181 176-4 40-7 241 234-8 54-2 2 rg 0-4 62 60-4 13-9 122 ^7-4 182 177-3 40-9 242 ^35-8 54-4 3 2-9 0-7 63 6i-4 14-2 123 ii9'8 27-7 183 178-3 41-2 213 236-8 54-7 4 39 0-9 64 62-4 14-4 124 I20-8 27-9 184 179-3 41-4 244 ^37-7 1 54-9 fi 49 65 63-3 14-6 125 I2I-S 185 i8o-3 41-6 245; 238-7 ; 55-1 6 ^8 '■3 66 64-3 14-8 126 122-8 28-3 186 18. -2 41-S 2J'J 1 ■9-4 4-8 80 77-6 ii UO^ .35-8 33-9 200 ■94' 48-4 260 252-3 61-9 21 10-4 5-1 81 78-6 19 141 .36-8 34-1 loT 195-0 48-6 261 253-2 63-1 iK 21'3 5'3 82 79-6 ■9 142 137-8 34'4 202 196-0 48-9 2f;2 254-2 63-4 1 23 5-6 83 143 138-8 34-6 •203 197-0 49-1 263 255-2 63-6 24 23-3 5-8 84 8i-^ 20 144 139-7 34-8 •204 197-9 49-4 -264 256-1 63-9 25 M-3 6-0 85 82-5 20 145 140-7 35-1 205 198-9 49-6 265 257-1 64-, 26 25-2 6-3 86 83-4 20 146 141-7 35-3 206 199-9 49-8 266 258-1 6i-4 27 6-5 87 84-4 21 147 142-6 35-6 207 200-9 50-. 267 259-1 64-6 28 27-2 6-8 88 85-4 21 148 143-6 208 201-8 50-3 268 260-0 64-8 29 7-0 89 86-4 21 149 144-6 36-0 209 202-8 50-6 269 2610 65-, 30 29- 1 7-3 90 S7-3 21 150 ■45-5 36-3 210 203-8 50-8 270 2620 65-3 31 30-I TS 91 88-3 22 151 H6-S 36-5 211 204-7 51-0 271 2630 65-6 32 3I-0 92 89-3 22 152 ■47-5 36-8 205-7 51-3 272 2639 65-8 33 32-0 8-0 93 90-2 22 153 14S-5 370 213 206-7 5>-5 273 264-9 66-0 34 33'o 8-2 94 91-2 22 154 149-4 37-3 214 207-6 5. -8 274 265-9 66-3 36 J4-0 8-5 95 92-2 = 3 l.'io 150-4 37-5 215 2o8-6 52-0 •275 2668 66-5 36 34-9 8-7 96 93-1 23 156 37-7 216 209-6 52-3 •276 267-8 66-8 37 35-9 9-0 97 94-1 23 137 152-3 38-0 217 210-6 5^-5 277 268-s 67-0 38 36-9 9-2 98 95-1 23 158 •533 38-2 218 211-S 52-7 278 ^il.i 67-3 39 37-8 9-4 99 96-1 24 159 "54-3 38-5 219 212-5 53-0 279 67-5 40 jS± 9-7 100 97-0 24 160 .55-2 38-7 2--'0 zvyj, 53-2 280 271-7 67-7 "JT jr8 9-9 loT 98-0 24 lef .56-2 389 2-21 214-4 53-5 281 272-7 68-0 42 40-8 102 99-0 24 162 157-2 39-2 222 215-4 53-7 282 273-6 68-2 43 4.-7 10-4 103 99-9 24 163 158-2 39-4 223 2.6-4 53-9 283 274-6 68-5 44 42-7 10-6 104 100-9 ^5 164 159-1 39-7 2-24 2.7-3 54-2 284 275-6 68-7 45 43'7 109 105 IOI-9 165 .60- 1 39-9 •225 218-3 54'4 285 276-5 68-9 46 44-6 106 ioa-9 25 166 161-1 40-2 226 219-3 54-7 286 277-5 692 47 45-6 II-4 107 I03-S 25 167 162-0 40-4 •227 220-3 54-9 287 278-5 69-4 48 46-6 .,•6 108 104-8 26 168 163-0 40-6 228 55-2 288 279-4 69-7 49 47*5 11-9 109 .05-8 26 169 164-0 40-9 229 222-2 55-4 289 2 So -4 69-9 50 48-5 110 106-7 26 170 .65-0; 4I-. 230 223-2 55-6 290 281-4 70-2 31 49-5 12-3 TTT 107-7 26 171 165-9 41-4 "2 ST 224-1 55-9 ■JoT 2S2-4 70-4 52 50-5 12-6 112 I08-7 27 172 166-9 4''^ 232 225-. 56-. 292 283-3 70-6 53 ] 51-4 12-8 113 I09-6 27 173 167-9 4>'9 233 226-1 56-4 293 284-3 70-9 51 52-4 13-1 114 IIO-6 17 174 168-8 42-1 •234 227-0 56-6 294 285-3 7.-I 65 53-4 "3;3 115 III-6 27 175 !^o-S 42-3 235 228-0 56-9 295 286-2 7>-4 58 54-3 116 II2-6 28 176 42-6 236 229-0 57-1 •296 287-2 71-6 57 55-3 13-8 117 113-5 28 177 171-7 42-8 237 230-0 57-3 297 288-2 7.-9 58 56.3 ,4-0 118 114-5 2 8 178 172-7 43-J 238 230-9 57-6 •208 289-1 72-1 S» 57-2 ,4-3 119 115-5 28 8 179 ■73-7 43-3 239 231-9 57-8 299 290-1 72-3 60 58-2J14-5 120 115-4 29-0 180 >74-7 43-5 •240 232-9 58-. 300 291-1 72-6 DiBtj Dep. D.Lai Dist Dep. D.Lat Dist Dep. D.Ut. Dist Dep. D. Lat Dist Dep.|D.L-,U.| 76° .M- 1 TRAVERSE TABLE TO DEGREES 56»" 14" O" Uist. D. Lat. Dep. Dist. n. Lat. Dep. Dist. D. Lat. Dep. 101-8 D^. 481 D. Lat. Dep. 116-3 Dist. 541 D.Lat. 5250 Dep. 301 2920 72-S 361 350-2 87-3 421 408-5 466-7 130-9 302 2930 73-0 362 35 '•2 S7-6 422 409-4 I02-I 482 4677 116-6 .■■4 2 5259 .31-2 303 2q40 73-3 363 352-2 87-S 423 410-4 102-3 483 46S6 116S 513 5269 131-4 304 2949 73-5 364 3532 88-0 424 411-4 102-6 484 I 469-6 1171 544 527-9 131-6 305 295-9 73-8 365 354-1 88-3 425 4123 1028 485 ' 470-6 1173 545 528-8 131-9 306 2969 74-0 366 3551 88 5 426 413-3 103-0 486 471-5 117-6 546 529-8 132-. 307 297-8 742 367 356-1 88-8 4-i7 414-3 103-3 487 472-5 117-8 547 5308 132-3 308 298-8 74-5 368 357-0 890 428 415-3 103-5 488 473-5 1180 548 531-7 132-6 309 299-8 74-7 369 35S-0 S9-2 429 416-2 103 8 489 474-5 1183 549 532-7 132-8 310 300S 750 370 359-0 S9-5 430 417-2 1040 490 475-4 1.8-5 550 _5137 _L31-o ■3TT 3017 75-2 371 359-9 S9-7 431 418-2 104-2 491 476-4 1188 551 5346 13.3-3 312 3027 75-5 372 3609 900 432 419-J 104-5 492 477-4 1190 552 535-6 133-6 .•!13 303-7 75-7 373 36.9 90-2 433 4201 104-7 493 478-3 1 19-2 553 536-6 1338 314 304-6 75-9 374 362-9 905 434 421-1 105-0 494 479 3 119-5 554 537-5 134-0 315 305-6 762 375 363-8 907 435 422-0 105-2 495 4803 119-7 555 538-S 134-3 316 3066 76-4 376 364-S 909 436 423-0 105-5 496 48. -3 1200 556 539-5 134-5 317 307-6 767 377 3658 91-2 437 424-0 105-7 497 4S22 120-2 557 540-5 134-8 318 308-5 769 37S 3667 91-4 438 425-0 1059 498 483-2 120-4 658 541-4 1350 319 3095 77-2 379 367-7 9.7 439 4259 106-2 499 4S4-2 120-7 559 5424 135-2 320 310-5 77-4 380 36S-7 919 440 4269 106-4 500 ^S5:i 121-0 560 543-4 J35i 321 31 1-4 It^' '381 369-6 922 447 427-9 106-7 .501 4S6-, 12. -2 561 544-3 1357 322 312-4 77-9 382 370-6 924 442 42S-8 1069 502 4S7-1 .21-4 562 5453 135-9 323 3134 78-1 383 371-6 926 443 429-8 107-1 503 4S8-0 .21-7 563 5463 136-2 324 314-3 78-4 384 3726 92-9 444 4308 107-4 504 4S9-0 1220 564 547-2 1365 325 3153 78-6 385 373-5 93-1 445 4317 107-6 505 4900 I22-I 565 5482 .366 326 3'6-3 78-S 386 374-5 93-4 446 432-7 107-9 506 491-0 1224 566 549-2 .36-9 327 3>7-3 79-' 387 3755 93-6 447 433-7 108-1 507 491-9 122-6 567 550-1 .37-1 328 318-2 79 3 388 376-4 93-8 448 4347 loS-4 508 492-9 122-9 568 551-1 .37-4 329 3192 79-6 389 377-4 941 449 435-6 ioS-6 509 493 9 I23-I 569 552-1 .376 330 3202 79S 390 378-4 94-3 450 436-6 ioS-8 510 494-9 .23-4 570 553-1 137-9 331 3211 ~8"oT" 391 379 4 94-6 451 437-6 109-1 sir 495-S 123-6 571 554-0 .38. 332 3221 80-3 392 3S03 94-8 452 438-5 109-3 512 496-8 123-8 572 555-0 138-3 333 3231 80s 393 381-3 95-1 453 439-5 109-6 513 497-8 I 241 573 556-0 138-6 334 324-0 80-8 394 3S23 95-3 454 440-5 109-8 514 49S-7 .24-3 574 557-0 .38S 335 3250 Si-o 395 383-2 955 455 441-5 1 10- 1 515 499-7 124-6 575 557-9 139-1 336 3260 81-3 396 3S4-2 95-8 456 442-4 110-3 516 500-7 .24-S 576 55S-9 .39-3 337 327-0 Si-5 397 385-2 96-0 457 443-4 1105 517 501-7 125-0 577 559-9 139-5 139-8 338 327-9 817 398 386-. 96-3 458 444-4 IIO-8 518 5026 125-3 578 5609 339 328-9 82-0 399 3S7-1 96-5 459 445-3 mo 519 503-6 125-6 579 561-8 1400 340 341 3299 3308 82-2 "825- 4U0 401 38S-1 3S9-1 967 97-0 460 4cr J46-3 447-3 111-3 1115 520 .52T 504-6 5055 125-8 1260 5S0 ssT 562-8 563^8 140-3. .405 342 33 > -8 827 402 3900 97-2 462 448-2 111 7 522 506-5 126-2 582 564-7 140-8 343 332-8 83-0 403 391-0 975 463 449-2 1 120 523 507-5 .26-5 583 565-7 .4.-0 344 333-7 83-2 404 3920 97-7 464 450-2 1122 524 5084 126-8 584 5667 14.3 345 3347 83-4 405 3929 98-0 465 451-2 112-5 525 509-4 127-0 585 5676 14. S 346 335-7 83-7 406 393-9 982 466 452-1 112-7 526 510-4 127-2 586 5686 141-8 347 336-7 83-9 407 394 9 98-4 467 453-1 113-0 527 511-4 127-5 587 569-6 142-0 348 337-6 84-2 408 395-8 9S7 468 454-1 1132 528 512-3 127-8 588 570-6 142-3 349 338-6 S4-4 409 396-8 989 4 69 455-0 113-4 529 513-3 128-0 589 571-5 142-5 350 3391 S4-7 410 397-8 99-2 470 456-0 113-7 530 5143 128-2 590 572-5 1428 351 340-S 849 TTT 1^8^ 99-4 471 4570 1139 531 5153 128-5 591 573-5 .430 352 34 1 -S 85-. 412 399-7 997 472 457-9 1 14 2 532 516-2 128-8 592 574-4 143-3 353 342-5 85-4 413 4007 999 473 4589 1 14-4 5.33 517-2 1290 593 575 4 143-5 354 343-5 85-6 414 401-7 474 459 9 .14-6 534 51S2 129-2 59 4 576-4 143-S 3S5 344-4 85-9 415 402-6 100-4 475 460-9 "49 535 519-1 1294 595 577-3 1440 356 3454 416 403-6 IO0-6 476 461-S I151 536 520-1 129-7 596 578-3 .442 357 346-4 86-3 417 404O 100-9 477 462S 115-4 537 521-1 1299 .597 579-3 144-5 358 347-3 86-6 418 4055 lOIl 478 4638 1 15 6 538 5221 1302 598 580-3 144-7 359 348-3 86-8 419 4065 101-3 479 464-7 II59 539 523-0 130-4 599 58.-2 144-9 360 349 3 87-1 420 4075 101-6 480 4657 54(1 5240 130-6 600 582-2 145-1 Di»t. Dep. D. Lat Dist Dep. D. Lnt I)^. Dep. D. Lat Dist. Dep. D. Lat. Dist Dep. D. Lat. 70° 5^ 4m 402 TRAVERSE TABLE TO DEGREES | 16° !» 4™] Dist. D.Lai Dep. Dist.JD. Lat Dep. Dist. D. Lat. Dep. Dist.D. Lat Dep. Dist.|D. Lar.j Dep. ro 0-3 61 58-6 16-8 121 ,16-3 33-4 181 174-0 49-9 241 1 231-7 1 66-4 1-9 0-6 62 59-6 17-1 122 117-3 33-6 182 174-9 50-2 242 232-6 66-7 0-8 63 6o-6 '7'4 123 118-2 33-9 183 '75;9 50-4 •243 233-6 67-0 3-8 !•! C4 6i-5 17-6 124 119-2 34-2 184 50-7 241 *34'5 67-3 4-8 i'4 Co 62-5 17-9 125 34-5 185 177-8 51-0 245 -35-5. 67-5 5-8 66 63-4 lS-2 126 121-1 34-7 186 178-8 51-3 246 -36-5 67-8 6-7 1-9 C7 64-4 18 5 127 I22-I 35-0 187 179-8 5i'5 247 237-4 68-1 7"7 68 65-4 18-7 128 I23'0 35-3 188 51-8 248 238-4 6S-4 8'7 2-5 69 66-3 19-0 129 124-0 35-6 189 1S1-7 52-1 249 239-4 68-6 10 9-6 2-S 70 67-3 jn. 130 125-0 35-8 190 182-6 Jl^- 250 240-3 68-9 11 " IO-6 "yo 71 68-2 ,9-6 IsT 125-9 36-1 Tor 183-6 52-6 251 241-3 69-2 II-5 3-3 72 69-2 19-8 132 126-9 36-4 192 184-6 52-9 •252 242-2 69-5 12-5 3-6 73 70-2 133 127-8 36-7 193 185-5 53-- 253 243-2 69-7 13-5 3-9 7-4 20-4 134 12S-8 36-9 194 186-5 53-5 254 244-2 70-0 14-4 4' I 75 72-1 20-7 135 129-8 37-2 195 187-4 53-7 255 245-1 70-3 I5' + 4' 4 76 73-1 20-9 136 130-7 37-5 196 188-4 54-0 •266 246-1 70-6 i6-3 4-7 77 74-0 137 131-7 37-« 197 189-4 54-3 257 247-0 70-8 17-3 5-0 78 75-0 21-5 138 132-7 38-0 198 190-3 54-6 258 248-0 71-1 iii-3 5-2 79 75-9 21-8 139 1336 38-3 199 191-3 54-9 259 249-0 71-4 20 19-2 5" 5 80 76-9 22-1 140 134-6 3S-6 200 192-3 55-' 260 249-9 71-7 21 20-2 jti 77'9 22^ 141 1 .35-5 38-9 •ioT 193-2 55-4 261 250-9 71-9 22 211 82 78-8 22-6 142 1365 39-1 202 194-2 55-7 262 251-9 72-2 23 22-1 6-3 83 79-8 22-9 143 •37-5 39-4 203 195-1 56-0 263 72-5 24 23-1 6-6 84 8o-7 23-2 144 13S-4 39-7 204 196-1 56-2 264 253-8 72-8 25 24-0 6-9 85 8. -7 23-4 145 '394 40-O 205 197-1 56-5 265 -54-7 73-0 26 25-0 7-2 86 82-7 23-7 146 140-3 40-2 206 198-0 56-8 266 ^55"7 73'3 27 26-0 7"4 87 83-6 24-0 147 141-3 40-5 207 199-0 57-1 267 256-7 73-6 28 269 7"7 88 84-6 24-3 148, 142-3 40-8 208 199-9 57-3 268 257-6 73-9 2y S-o 89 85-6 24-5 149 143-2 41-1 209 200-9 57-6 269 258-6 74-1 30 2S-S 90 86-<; 24- 8 150 144-2 41-3 210 201-9 57-9 270 259-5 74-4 liT 8-5 ^r 87-5 25-1 151 145-2 41-6 211 202-S 58-2 271 260-5 74-7 32 30-ii S-8 92 88-4 ^5'4 152 146- 1 41-9 212 203-8 58-4 272 261-5 75-0 33 13.-7 9-1 93 89-4 25-6 153 147-1 42-2 213 204-7 58-7 273 262-4 75-2 34 1 3Z-7 9'4 94 90-4 25-9 154 148-0 42-4 214 205-7 59-0 274 263-4 75-5 35 33-6 9-6 95 91-3 26-2 155 149-0 4»-7 215 206-7 59-3 275 264-3 75-8 3fi 34-6 9'9 Oti 92-3 26-5 156 150-0 43-0 216 207-6 59-5 276 265-3 76-1 37 35-6 97 93-2 26-7 157 150-9 43-3 217 208-6 59- 8 •277 266-3 76-4 38 36-5 10-5 98 94-2 27-0 158 151-9 43-6 218 209-6 60-1 278 267-2 76-6 39 37'5 10-7 99 95-2 27-3 159 152-8 43-8 219 210-5 60-+ 279 268-2 76-9 40 38-5 100 27-6 160 153-8 44-1 220 211-5 60-6 280 269-2 41 39-4 II-3 ToT 97-1 27-8 wV 154-8 44-4 •221 60-9 281 270-1 77-5 42 4.0-4 I. -6 102 98-0 28-1 102 '55-7 44-7 222 213-4 61-2 282 271-1 77-7 43 4>-3 II-9 103 99-0 2S-4 163 156-7 44-9 223 214-4 61-5 283 272-0 78-0 44 4a-3 104 28-7 164 157-6 45'=' •224 215-3 61-7 284 273-0 45 ,43-3 12-4 105 100-9 28-9 165 158-6 45'5 2-25 216-3 62-0 285 274-0 7S-6 46 44"- 12-7 106 :o,-; 29-2 166 159-6 45-8 226 217-3 e'-l 286 78-8 47 45'- 13-0 107 102-9 -9"5 167 i6o-5 46-0 227 218-2 287 275-9 79-1 48 46-1 13-2 108 103-8 29-8 168 161-5 46-3 228 219-2 288 276-8 79-4 49 47-1 13-5 109 .04-8 30-0 169 ,62-5 46-6 229 63-1 289 277-8 79-7 50 48-1 110 105-7 30-3 170 163-4 46-9 230 221-1 63-4 290 278-8 79-9 51 49-0 "iVT nr 106-7 30-6 i7r 164-4 47-1 231 2221 63-7 •291 279-7 8o-2 52 50-0 I4'3 112 107-7 30-9 172 .65-3 47-4 232 223-0 63-9 292 80-5 53 50-9 14-6 113 173 166-3 47-7 233 224-0 64-2 293 2S1-6 8o-8 54 ^i'9 14-9 114 I09-6 3 1 '4 174 167-3 48-0 234 224-9 64-5 294 i 282-6 8ro 55 52-9 15-2 115 iio's 31-7 175 168-2 48-2 2;t5 225-9 64-8 295 283-6 81-3 56 53-8 >5'4 116 111-5 32-0 176 169-2 48- 5 2;i(; 226-9 65-1 296 284-5 81-6 57 54-8 15"7 112-5 32-2 177 48-8 237 227-8 65-3 297 285-5 S1-9 58 5^8 i6-o 118 113-4 3-'5 178 171-1 49-1 238 228-8 65-6 298 286-5 82-1 59 56-7 .6-3 119 114-4 32-8 179 172-1 49-3 239 229-7 65-9 299 2S7-4 82-4 60 57-7 16-5 120 115-4 ;3'i 180 173-0 1 49-6 240 230-7 66-2 300 28S-4 82-7 Dist.lDei.. D.Lnt Dist. Dq,. IDXal Dist.| Dep. p. Lat. Dist. Dep. JD. Lat. Dist. Dep.|D.Lat,| __ 740 4hr,,v.> 1 463 TRAVERSE TABLE TO DEGREES 16° 1" 41D Dist.'D. Lat! Dep. DistJn. Lat Dep. Dist. b. Lat. Dep. Dist.lo. Lat. Dep. Dist D. Latl Dep. 301 2S9-3I S2-9 361 3470 99-5 421 1 404-7 1 160 481 462-4 ■32-5 541 S20-1 1491 302 2903 83-2 362 34S-0 997 422 1 405-6 116-3 482 463-3 1328 542 521 0, 149-4 .103 291-2 S3-5 363 3489 423 i 406 6 1 16-6 483 464-3 ■33' 543 522-0 .49-7 .■i(H 1 2922 83-8 364 3499 1003 424 4076 116S 484 465-2 '33-4 544 523-0 1500 305 2932 1 840 365 350-S 100-6 425 408-5 M7-I 485 466-2 '33-6 545 5239! 150-2 306 1 2941 ! 84-3 366' 351-S 100-8 426 409-5 117-4 486 467-2 133-9 546 524-9 150-4 307 2951! 84-6 367 1 352-S lOI-I 427 410-4 ■'7-7 487 46S-1 '34-2 547 5259 1507 308 2960, 849 368 1 353-7 101-4 428 4114 "7-9 488 469-1 '34-5 548 526 8 1510 309 297-0; 85-1 369 1 354-7 101-7 429 4.2-4 1182 489 470-1 134-S 549 527-8 '513 310 2980, 85-4 370 1 355-6 1019 4-30 ; 4^3 3 1.8-5 490 471-0 135-0 550 528-7 151-6 311 29S-9' S5-7 371 1 3566 102 -2 431 j 4^4-3 lYS-S 491 4720 ■353 '551 5297 1519 312 299 9 1 86-0 372 357-6 102-5 432 415-2 ..90 492 4729 >35-6 552 5306 .522 313 3009! 86-2 373 358-5 102-8 433 416-2 119-3 493 473-9 ■359 553 53' 6, ■ 52;5 314 301 -Si 86-5 -■'74 359 5 103-1 434 4172 1.96 494 474-9 136-2 554 5326 315 3028 868 375 360-4 103-3 435 4181 1.99 495 475-S ■364 555 533-5 1530 316 303-7 S7-1 376 1 361-4 103-6 436 419-1 I20-I 496 4768 ■367 556 534-5 153-2 317 304-7 87-3 377 j 362-4 103-9 437 420-0 1204 497 477-7 137-0 557 535-4 '53-5 31S 305-7 S76 378 1 363-3 1042 438 421-0 120-7 498 47S-7 137-3 558 536-4 ■538 319 306-6 S7-9 379 , 364-3 104-4 439 422-0 121 499 479-7 ■37-5 559 537-4 ■54-1 320 307-6 88-2 380 , 365-3 1047 440 422-9 .2.-2 500 4806 137-8 560 5383 154-4 321 3^'8-5 88-4 381166^ 105-0 441 4239 12f5 501 481-6 .381 561 539-3 •54-7 3ii2 309s 88-7 382 367-2 105-3 442 424-9 502 4826 .38-3 562 5403 154-9 323 3105 890 383 368-1 105-5 443 425-8 I22-I 5U3 4835 138-6 563 54 '-2 155-2 324 311-4 89-3 384 1 369-1 105-8 444 4268 122-3 504 484-5 1389 564 542-2 ■55-4 325 3' 2-4 89s 385! 370-1 I06-I 445 427-7 1226 .■.05 485-4 1392 565 543' ■557 326 3'3-3 898 386 37IO 106-4 446 428-7 122-9 506 486-4 1394 566 544-"' .560 327 314-3- 90-1 387 372-0 106-6 447 429-7 1232 507 487-3 ■397 567 545-^ ■56-3 328 3>5-3 90-4 388 372-9 106-9 448 4306 123-4 508 488-3 140-0 568 5460 ■ 56-6 329 316-2 906 389 373-9 107-2 449' 431-6 123-7 509 489-3 ■40-3 509 547-0 156-9 330 331 ji7_:2 31 8-2 ^90-9^ 91-2 390 374-9 391 1 375-8 107-5 107-7 450 432-6 •»51i"433 5 124-0 510 511 490-2 140-6 570 571 ^11 _L57:i '573 124-3 49.-2 .40-8 332 319-1 9I-S 392 j 376-S loSo 452 434-5 124-6 512 492-1 141-1 572 549-8 157-6 333 320-1 91-8 393 1 377-8 108-3 453 1 435-4 1248 513 493-' 141-4 573 550S '57-9 334 321-0 92^^ 394, 37S-7 108-6 454: 4364 .25-1 514 494-1 141-7 574 551-81 158-2 335 322-0 92-3 395, 379-7 loS-S ■455 1 437-4 1254 515 4950 14.-9 575 552-7 15S-4 33C 323-0 926 396 1 3S0 6 109-1 456 1 438-3 125-7 516 496-0 1422 576 553-7 158-7 337 3239 929 397, 3816 109-4 ''57 . 4393 125-9 517 4969 142-5 577 554-6 .590 338 3249 93-1 398 1 382-6 1097 458 ! 440-2 126-2 518 497-9 .428 578 5556 ■59-3 339 3258 93-4 399 383-5 1099 4,59; 441-2 126-5 519 1 498-9 1430 579 556-5 '59-5 340 341 326-8 '327-8 93-7 -100 384-5 401 3S54 li57 460 442-2 461 i 443T .268 127-0 520 1 499 8 .521 , 5008 '43 3 1436 580 581 Ji 7-5. 55S-4 '59-8 1 601 940 342 328-7 94-2 402 3S64 1 10-8 462 444-1 127-3 522 50.-7 .43-9 582 559-4 160-4 343 329-7 94 5 41)3 3S7-4 mo 463 1 445-0 127-6 523 5027 144-1 583 560-4 1606 344 3307 94S 404 388-3 111-3 464 ■ 446-0 1279 524 5037 144-4 584 561-3 161-0 345 33>6 95' 405 389-3 1116 465 I 447-0 I2S-I 525 5046 ■44-7 585 562-3 161-3 346 3326 953 ■106 390-2 1119 466 447 9 I2S-4 526 505-6 145-0 586 563-2 1616 347 3335 956 407 391-2 112 I 467 448-9 128-7 527 506-6 ■45-3 587 564-2 161-8 ^■•8 1 334-5 959 40S 392-2 1 1 2-4 468 1 449-8 129-0 528 507-5 145-6 588 565-2 162-1 3'" 464 TRAVERSE TABLE TO DEGREES 1 17° Ihgm 1 DistJD,LatJDep.| Rist. D. Lat.j Dep. Dist. D. Lat. Dep. Oi. D.Lat. Dep. DisJo. Lat.j Dep. 1 i i-o 0-3 61 5«-3 17-8 121 115-7 35-4 181 .73-1 52-9 241 230-5 70-5 2 1 1-9 0-6 62 59'3 i8-i 122 116-7 35-7 182 174-0 53-^ 242 231-4 1 70-8 o'9 63 6o-j 18-4 123 117-6 36-0 183 175-0 53-5 243 232-4 7I-0 4 3-2 64 61-2 1-24 118-6 36-3 184 176-0 53-8 244 233-3 71-3 5 4-8 1-5 65 62-2 19-0 125 119-5 36-5 185 176-9 54-1 245 234-3, 71-6 ti 5-7 1-8 66 63-1 19-3 126 120-5 36-8 186 177-9 54-4 246 235-3 71-9 7 1 6-7 2*0 67 64-1 19-6 127 121-5 37-1 187 178-S 54*7 247 236-2 H ] 7-7 ^•3 68 65-0 19-9 128 122-4 37-4 188 .79-8 55-0 248 237-2 72-5 9 8-6 2-6 69 66-0 129 !23'4 37-7 189 180-7 55-3 249 238-1 72-s 10 : 9-6 ^•9 70 66-9 20-5 130 124-3 38-0 190 1S1-7 55-6 250 [239-. 73-' 11 1 lO', J.J 71 67-9 TsT 125-3 38-3 m- 182-7 55-8 251 1 240-0 1 73-4 1 12 11-5 3-5 72 68-9 2I'I 132 .26-2 38-6 192 183-6 56-1 2.52 241-0 ! 73-7 13 12-4 3-8 73 69-8 21-3 133 127-2 38-9 193 184-6 56-4 253 241-9 1 74-0 1 14 I3'4 4-1 74 70-S 21-6 134 128-1 39-2 194 185-5 56-7 254 242-9 74-3 1 15 I4'3 4'4 75 71-7 21-9 135 129-1 39-5 195 186-5 57-0 255 243-9 74-6 IG 4-7 76 72-7 136 130-1 39-8 196 187-4 57-3 256 244-8 74-8 17 i6-3 5-0 77 73-6 22-5 137 131-0 40-1 197 188-4 57-6 257 245-8 75-1 ii; 5'3 78 74-6 22-8 138 132-0 40-3 198 189-3 57-9 258 246-7 75-4 1!» i8-2' 5-6 1 79 75-5 23-1 139 132-9 40-6 199 190-3 58-2 259 247-7 75-7 20 19-1 5-8 80 76-5, 23-4 140 133-9 40-9 200 19,-3 58-5 260 248-6 76-0 21 20- 1 6-1 81 77-5 23-7 141 134-8 41-2 201 192-2 58-8 261 249-6 76-3 22 2I-0 6-4 82 78-4 24-0 142 135-8 41-5 202 193-2 59-1 262 250-6 76-6 23 22-0 6-7 83 79-4 24-3 143 136-8 41-8 203 194-1 59-4 263 251-5 76-9 24 23-0 84 80-3 24-6 144 137-7 42-1 204 195-1 59-6 264 252-5 77-2 25 23-9 7'3 85 8i-3 24-9 145 13S-7 42-4 205 196-0 59-9 265 253-4 77-5 26 24-9 7-6 86 8:-2 25-1 140 139-6 42-7 206 197-0 60-2 266 254-4 77-8 27 25-8 7'9 87 83-2 25-4 147 .40-6 43-0 207 198-0 6o-5 267 255-3 78-1 28 26-S 8-2 84-2 25-7 148 141-5 43-3 20s 198-9 60-8 268 256-3 78-4 21) 27-7 g-r 89 26-0 149 142-5 43-6 209 199-9 61-1 269 78-6 SO 28-7 8-8 90 86-1 26-3 150 151 >43"4 43-9 210 200-8 6i-4 270 258-2 78-9 _ TT 29-6 9'' "aV 87-0 26-6 144-4 44-1 211 201-8 6. -7 271 259-2 79-2 3i! 30-6 9"4 92 8S-0 26-9 152 145-4 44-4 212 202-7 6j-o 272 260-1 79-5 33 h-6 9-6 93 88-q 27-2 153 .46-3 44-7 213,203-7 62-3 273 261-, 79-8 34 32-5 9-9 94 89-9 27-5 154 '47-3 45-0 214 204-6 62-6 274 262-0 80-. 35 33'5 IO-2 95 90-8 27-8 155 148-2 45-3 215 205-6 62-9 275 263-0 80-4 36 34'4 10-5 96 91-8 28-, 156 149-2 45-6 216 206-6 63-2 276 263-9 80-7 37 35"4 lO-S 97 92-8 28-4 157 150:1 45-9 217 207-5 63-4 ■277 264-9 810 38 36-3 II-I 98 93'7 28-7 158 151-1 46-2 218 208-5 1 63-7 278 265-9 8. -3 39 37'3 11-4 99 94-7 28-9 159 152-1 46-5 219 209-4 1 64-0 279 2668 Si-6 40 38-3 100 95-6 _2£2_ 160 153-0 46-8 220 210-4 1 64-3 280 267-S 81-0 41 39-2 12-0 101 96-6 29-5 161 154-0 47-1 221 211-3 64-6 281 268-7 S2-2 42 40-2 12-3 102 97-5 29-8 162 154-9 47-4 222 212-3 64-9 282 269-7 82-4 43 4I-I 103 98-5 30-1 163 '55-9 47"7 223 2.3-3 65-2 283 S2-7 44 42-1 12-9 104 99-5 3°'4 164 156-S 47-9 224 214-2 65-5 284 271-6 S3-0 45 ,43-o ,yz 105 IOO-4 30-7 165 157-8 225 215-2 65-8 285 272-5 83-3 46 !44-°l >V4 106 101-4 31-0 166 158-7 4S-5 226 216-1 ; 66-1 286 273-5 S3-6 47 ' 44-9 13-7 107 102-3 31-3 167 159-7 48-8 227 217-1 66-4 287 274-5 839 48 45'9 14-0 108 103-3 31-6 168 160-7 49-1 228 218-0 66-7 288:275-4 84-2 49 46-9 14" ) 109 104-2 31-9 169 i6i-6 49-4 229 219-0 67-0 289 276-4 84- 5 50 47-8 4-6 110 105-2 32-2 170 162-6 49-7 230 67-2 290 277-3 84-8 IT 48-8 H'9 111 io6-i 32-5 171 163-5 50-0 231 220-9 67-5 •291 278-3 85-. 62 49" 7 15-2 112 loyi 32-7 172 164-5 50-3 232 221-9 67-8 2!t2 279^2 85-4 63 50-7 i5"5 113 108-1 33-0 173 165-4 50.6 233 222-8 68-1 293 85-7 54 5,-6 15-8 114 109-0 33'3 174 166-4 50-9 234 223-S 68-4 294 281-2 86-0 55 «-6 161 115 33-6 175 167-4 51-2 235 224-7 68-7 295 282-1 1 86-2 1 5C 53-6 : i6-4 116 110-9 33'9 176 168-3 51-5 236 2257 69.0 296 283-1 1 86-5 1 57 54-5 16-7 117 111-9 34-2 177 169-3 51-7 237 226-6 69.3 297 284-0 86-8 58 55-5 17-0 118 112-8 34- S 178 170-2 52-0 238 227-6 1 69-6 298 285-0 87-1 59 ! 56-4 17-2 119 .13-8 34-8 179 171-2 52-3 239 228-6 69-9 299 285-9 S7-4 CO 1 57-4 •7-5 120 1.4-S 35-1 180 52-6 240 229-5 70-2 3001 2869 8--7 Dis-..|Dep. D.Lat l)ist Dep. U.La Dist Dep. |D.Lat.|Dist Dep. D.Lat Dist 1?- D. Lat. 73° 4" sa-"" TABLE 1 465 TKAVKRSE TABLE TO DEOREES | 17" Ihsm 1 Dist. D.Lat. Dep. Dist. D. Lnt. Dep. DiBt. D.Lat Dep. Dist D.Lat Dep. Dist 541 D.Lat 517-3 Dtp. 1582 301 2S7S 8S0 361 345-2 105-5 421 4026 .23-. 481 460-0 140-6 302 2SS-S 1-6 362 346-1 105-8 422 403s '23-4 482 460-9 140-9 542 518-3 1585 3(« 2S97 363 347-1 106-1 423 4045 1237 483 461-9 1412 543 519-2 158-8 301 2907 SS9 3«4 3481 106-4 424 405-4 124-0 484 462-8 141-5 544 520-2 159-1 305 2C)!-6 89-2 ;!G.") 3490 106 7 425 4064 124-3 485 463-8 141-8 545 521-2 1593 306 2926 89-5 366 350-0 107-0 426 407-3 124-6 486 4647 142-1 546 522-1 '59-6 3or 2935 S98 3G7 350-9 I07-3 427 40S-3 124-8 487 4657 142-3 547 523-1 159-9 3^^l 294-S go- 1 36S 35'-9 107-6 428 409-3 I25-I 483 4607 142-6 548 524-0 160-2 295-5 903 369 352-S 107-9 429 4102 125-4 489 467-6 142-9 549 5250 1605 310 2964 906 370 353-S IoS-2 430 411-2 125-7 490 468-6 5.50 526-0 1608 311 2974 909 371 354-8 IOS-5 431 412-1 1260 491 469-S 143-S 551 526-9 l6t-l 312 298-3 912 372 3557 ioS-8 432 413-1 126-3 492 470-5 143-8 552 5279 161-4 313 299-3 915 373 3567 109 I 433 4140 1256 493 471-4 144-1 553 528-8 ,6.7 314 3002 91-8 374 357-6 109-4 434 4150 126-9 494; 472-4 144-4 554 5298 162-0 315 30I-2 921 375 3586 1096 435 4160 1272 495 473 4 1447 555 530-8 162-3 316 302-2 924 376 359 5 1099 436 416-9 127-5 496 474-3 145-0 556 5317 1626 317 303-1 927 377 300-5 U02 437 4179 127-8 497 475-3 145-3 557 5327 162-9 318 3041 930 378 361-4 1 10-5 438 418-8 128 I 498 4762 1456 558 5336 163-2 319 3050 93-3 379 362-4 1 10-8 439 419-8 128-4 499 477-2 145-9 559 534-6 1635 320 J06^ 93-6 380 363-4 iii-i 440 420-7 128-6 500 478-1 1462 560 535-5 1638 164-1 321 3069 939 381 3643 m-4 441 421-7 1289 501 479-1 146-5 561 5365 32-.' 307-9 94-1 382 3653 ni-7 442 422-7 129-2 502 480-1 146-S 562 537-5 164-4 323 308-8 944 383 366-2 112-0 443 423-6 129-5 503 481-0 147-1 .563 538-4 164-6 324 309-S 94-7 384 367-2 1 1 2-3 444 424-6 129-8 504 482-0 147-4 564 5394 164-8 325 310S 95-0 3S5 36S-1 1126 445 425-5 1 30- 1 505 482-9 1477 565 540-3 .65-: 326 3117 95-3 386 369-1 1 12-9 446 426-5 130-4 506 483-9 1480 566 541-3 165-4 327 3127 95-6 387 370-1 113-2 447 427-4 130-7 507 4S4-8 148-3 567 542-2 165-7 32S 3136 95-9 388 371-0 113-4 448 428-4 131-0 508 4S5S 148-6 568 543-2 1660 3 29 314-6 96-2 389 372-0 "37 449 429-3 131-3 509 486-7 148-9 569 544- 1 166-4 330 315-5 _9^5_ 390 j72_:9_ 1140 450 4303 I3.-6 510 487-7 149-1 570 545-1 166-7 331 3165 96-8 391 373-9 "4-3 451 431-3 131-9 511 488-7 149-4 571 T46T 1670 .•532 3>7-5 97-1 392 374-8 1 14-6 452 432-2 132-2 512 489-6 149-7 572 547-0 167-2 333 31S-4 97-4 393 3758 U4-9 453 433-2 132-4 513 490-6 150-0 573 548-0 1675 334 3'9-4 97-7 394 3767 115-2 454 434 I •327 514 491-5 150-2 574 548-9 .678 335 3203 97-9 395 377-7 1155 455 435-1 133-0 515 492-5 1505 575 549-9 168-1 336 32 '-3 98-2 396 378-7 J J 5-8 456 436-0 133-3 516 493-4 150-S 576 550-8 168-4 337 3222 985 397 379-6 457 437-0 133-6 517 494-4 151-1 577 551-8 16S7 33S 323-2 98-S 398 380-6 1.6-4 458 438-0 133-9 518 495-3 151-4 578 552-7 169-0 339 3242 99-1 399 38.-S 1 167 459 4389 134-2 519 496-3 1517 579 553 7 1693 340 J.is± 994 400 J825 1 1 7-0 460 439-9 134-5 520 J9j_:± 1520 580 5546 1696 341 326-1 997 401 3834 117-2 461 440-8 134-8 521 498-2 152-3 581 5556 1699 342 327-0 1000 402 3844 117-5 4B2 4418 135-1 522 499-2 1520 582 5565 1702 343 32S0 IOO-3 403 385-4 1 1 7-8 463 4427 135-4 523 500-1 152-9 583 557-5 1705 344 328-9 ICOO 404 386-3 iiSi 464 4437 135-7 524 501-1 «53-2 584 55S-4 1 70 8 345 3299 1009 405 3873 iiS-4 465 4446 136-0 525 502-0 153-5 585 5594 171-1 346 3308 101-2 406 3SS-2 11S7 466 4456 136-2 526 503-0 153-S 586 560-4 171-3 347 33 '-8 I0I-5 407 389-2 1 19-0 467 446-6 136-S 527 503-9 154-1 587 5613 1716 34S 332-S 1018 408 390-1 119-3 468 447-5 1368 528 504-9 154-4 588 562-3 1719 349 333-7 102-0 40:) 391 I 1196 469 44S-5 137 1 5-29 5059 154-7 589 563-2 172-2 350 3347 102-3 410 J?2^ 1199 470 4494 1374 530 506-8 1550 590 564-2 172-5 351 '3356 I02-6 411 3930 1202 471 450-4 137-7 .531 1 507 8 1553 sgT 565-1 172-8 352 3366 102-9 412 3940 1205 472 451-3 138-0 532 508-7 1550 592 566-1 173-1 853 3375 103-2 413 394*9 120 8 473 452-3 1383 533 509-7 155-9 593 567-1 1734 354 338-S 1035 414 3959 121 474 453-3 138-6 534 510-6 156-2 594 56S0 1737 353 3395 103-8 415 396-8 121-3 475 454-2 138-9 535 511-6 '5^i 5 '..5 569-0 1740 856 3404 104-1 416 397-8 1216 476 455-2 139-2 536 5126 156-8 596 5699 1743 357 34 1-4 104-4 417 3987 121-9 477 456-1 139-5 537 513-5 157-1 597 5709 174-6 358 3423 104-7 418 3997 122-2 478 457-1 139-8 538 514-5 157-3 598 5718 1749 359 3433 1050 4 19 4007 122-5 479 458-0 i4&'o 539 5'5-4 157-6 599 5728 1752 360 3442 "OS 3 420 40 1 -6 I? 2-8 480 4590 140-3 540 5164 157-9 600 573-8 1754 Dlst Dep. U. I/... Dist Dep. D.Lat. Di8t Dep. D. Lai. Dist Dep. D. Lat. Dist Dep D. Lat. 73" 4" 5'2'" J 4«6 TABLE 1 TRAVERSE TABLE TO DEGREES - 1 18° 1^12-^ 1 Dist. D.Lat] Dep.| Dist. D. Lat. Dep. Dist. D.Lat. Dep. Dist. D.Lat. Dep. Dist D.Ut.l Dep. 1 i-o 0-3 61 58-0 i8-9 121 115-1 37-4 181 172-1 55-9 241 229-2 74-5 2 i-g 0-6 62 59-0 19-2 122 116-0 37-7 182 173-1 56-2 242 230-2 74-8 3 2-9 o'9 63 59'9 19-5 123 117-0 38-0 183 174-0 56-6 243 231-1 75-1 4 3-8 C4 60-9 19-S 124 117-9 38-3 184 175-0 56-9 244 232-1 75-4 8 ;-8 '■5 65 6i-8 20-I 125 118-9 38-6 185 175-9 57-2 245 233-0 75-7 6 S"7 1-9 6C 62-8 20-4 126 ..9-8 38-9 186 176-9 57-5 -246 234-0 76-0 7 6-7 67 63-7 20-7 127 120-8 39-2 187 177-8 57-8 247 234-9 76-3 8 7-6 2'5 68 64-7 21-0 128 121-7 39-6 188 178-8 58-1 248 235-9 76-6 9 8-6 2-8 69 65-6 21-3 129 122-7 39.9 189 179-7 58-4 249 236-8 76-9 10 9'5 3'i 70 66-6 21-6 130 ,23-6 40-2 190 1S0-7 58-7 250 237-8 i 77-3 lo-s 3'4 ~1\ 67-5 21-9 131 124-6 40-5 191 iSl 7 59-0 T^T 238-7 1 77-6 12 II-4 3'7 72 68-5 132 125-5 40-3 192 182-6 59-3 252 239-7 1 77-9 13 12-4 4-0 73 69-4 22-6 133 126-5 41-1 1!« 183-6 59-6 253 240-6 I 78-2 14 '3'3 4' 3 74 70-4 22-9 134 127-4 41-4 194 1 84- 5 59-9 254 2+1-6 1 78-5 15 '4"3 4-6 75 7i'3 23-2 135 128-4 41*7 195 185-5 6o-3 •255 242-5 78-8 16 15-2 4" 9 76 72-3 23-5 136 129-3 42-0 196 186-4 60-6 256 243-5 , 79-1 17 i6-2 5'3 77 73-2 23-8 137 130-3 42-3 197 ^Y^ 60-9 257 244-4 79-4 18 17-1 5-6 78 74-2 24-1 138 131-11 42-6 198 61-2 258 245-4 79;7 19 iS-i 5'9 79 75-1 24-4 139 132-2 43-° 199 189-3 61-5 259 246-3 20 19-° 6-2 80 76-1 24-7 140 133-1 43*3 200 190-2 61-8 260 247-3 Sc-3 21 200 6-5 81 77-0 25-0 141 134-1 43-6 •201 62-1 261 2+8-2 8o-7 22 20-9 6-8 82 78-0 25-3 142 135-1 43-9 202 192-1 62-4 262 249;2 81-0 23 219 7'i 83 78-9 25-6 143 136-0 44-2 203 193-1 62-7 263 81-3 24 22-8 TA 84 79-9 26-0 144 137-0 44-5 204 194-0 63-0 264 251-1 81-6 25 23-8 Tl 85 8o-8 26-3 145 i37'9 44-8 205 195-0 63-3 265 252-0 81-9 26 247 8-0 86 8i-8 26-6 146 138-9 45'i 206 195-9 63-7 266 253-0 82-2 27 i5'7 8-3 87 82-7 26-9 147 •39-8 45-4 207 196-9 64-0 267 253-9 82-5 28 26-6 S-7 88 83-7 27-2 148 140-8 45-7 208 197-8 64-3 268 254-9 82-8 29 27-6 9-0 89 84-6 27-5 149 141-7 46-0 209 198-8 64-6 269 255-8 83-1 30 28-5 9-3 90 85-6 27-8 150 142-7 46-4 210 199-7 64-9 270 256-S S3-4 31 29-5 9-6 •Jl S6-5 28-1 143-6 46-7 211 200-7 65-2 271 257-7 83-7 1 32 30-4 99 92 87-5 28-4 152 144-6 47-0 212 201-6 ^5-5 272 258-7 84-1 33 31-4 IO-2 93 88-4 28-7 153 '45-5 47-3 213 202-6 65-8 273 259-6 84-4 34 3^'3 10-5 94 89-4 29-0 154 1465 47-6 214 203-5 66-1 274 260-6 84-7 35 33-3 IO-8 95 90-4 29-4 155 147-4 47-9 215 204-5 ^^•* 275 261-5 85-0 36 34-2 ii-i 96 91-3 29-7 156 148-4 48-2 216 205-4 66-7 276 262-5 85-3 37 35-2 II-4 97 92-3 30-0 157 149-3 48-5 217 206-4 67-1 277 263-4 85-6 38 36-1 11-7 98 93-2 30-3 158 150-3 4S-8 218 207-3 67-4 278 264-4 85-9 39 37-1 I2-I 99 94-2 30-6 159 151-2 49-1 219 208-3 67-7 279 265-3 86-2 40 38-0 12-4 100 95-1 30-9 100 152-2 49-4 220 209-2 68-0 280 266-3 86-5 41 39'° 12-7 101 96-1 31-2 ToT 153-1 49-8 221 210-2 6S-3 281 26-2 f;6-8 42 39'9 13-0 102 97-0 31-5 162 154-1 50-1 2111 282 26S-2 87-1 43 40-9 i3'3 103 98-0 31-8 1C3 155-0 50-4 223 212-1 68-9 283 tV 87-5 44 4I-S 13-6 104 98-9 32-1 164 156-0 50-7 224 213-0 692 284 87-8 46 42-8 13-9 105 99-9 32-4 165 156-9 51-0 225 214-0 69-5 285 271-1 8S-1 4G 43-7 14-2 106 IOO-8 32-8 166 157-9 51-3 226 214-9 69-S 286 272-0 88-4 47 44-7 14-5 107 lOi-S 33-1 167 .58-8 51-6 227 215-9 70-1 287 273-0 88-7 48 45-7 14-8 108 I02-7 33-4 168 159-8 51-9 228 216-8 70-5 288 273-9 89-0 49 46-6 15-1 109 103-7 33'7 169 i6o-7 52-2 229 217-8 70-S 289 274-9 S9-3 50 47-6 15-5 110 ,04-6 170 161-7 5^-5 230 liS-7 71-1 290 2-5-S S9-6 51 48-5 .5-8 lllj 105-6 j 34-3 171 162-6 52-8 231 219-7 71-4 291 276-8 S9-9 52 49-5 i6-i 112 1 106-5 1 34-6 172 163-6 53-2 232 220-6 71-7 •2;i2 90-2 58 50-4 ,6-4 113 107-5 34-9 173 164-5 53'5 233 221-6 72-0 293 27S-7 9°' 5 54 51-4 i6-7 114 .08-4 35-2 174 165-5 53-8 234 222-5 72-3 294 279-6 90-9 55 52-3 115 109-4 35-5 175 ,66-4 54-1 235 223-5 72-6 295 280-6 91-2 5fJ 53-3 17-3 116 110-3 35-8 176 167-4 54-4 236 224-4 72-9 296 28.-5 91-5 57 54'2 17-6 117 111-3 36-2 177 16S-3 54-7 237 225-4 73-2 297 2S2-5 91-8 58 55-i 17-9 UK 112-2 36-5 178 169-3 55-0 238 226-4 73-5 298 283-4 92-1 59 56-1 i8-2 1191 "3-- 36-8 179 170-2 55'3 239 73-9 299 284-4 92-4 (iO 57-1 i8-5 120 ..4-i|37-i 180 171-2 55-f 240 ^28-3 74-2 300 2S5-J 92-7 O.stlpep. D.La Dist. Dtp. Id.U DistJ Dep. Id. Lilt Dist Dep. D. l.ul Dist Dep. D. L«l. 72° 4" 48- 1 TABLE 1 467 TUAVEKSE TABLE TO DEGKEES T2^~ 18" 1" Oist. D. Lat. Dep. Dist. D.Lat. Dep. Dist. b. Lat. D..p. Dist D. Lat. D.p. Dist. D. Lat. Dep. 301 2863 930 .361 343-3 1116 421 400-4 1301 481 457-5 i486 541 514-5 167-2 302 287-2 93-3 362 344 3 1119 422 401-4 •30-4 482 458-S 148-9 542 515-5 167-5 303 937 363 345-2 112-2 423 402-3 1307 483 459-4 149-3 543 516-4 167-9 304 289-1 940 364 346-2 112-5 424 403-3 131 484 460-4 149-6 544 S«7-4 16S-2 305 2901 94-3 365 347-1 112-8 425 404-2 131-3 485 461-3 149-9 545 518-3 168-5 306 291-0 94-6 366 1 34S-I 1131 426 4052 1317 486 4623 150-2 546 5193 16S-8 307 292-0 949 367 j 3490 113-4 427 4061 1320 487 463-2 1505 547 520-2 1 69- 1 308 292-9 95-2 .-368 350 113-7 428 4071 132-3 488 4642 150-8 548 52 1 -2 169-4 309 2939 955 369 350 9 1140 429 40S0 1326 489 4651 151-1 549 522-1 1697 310 294S 95S 370! 351-9 114-3 430 409-0 132-9 490 4661 151-4 550 523-1 170-0 311 295-S 96-r 371 3529, 1 147 431 409-9 133-2 «T 467-0 151-7 551 5240 170-3 312 296-7 96-4 372 353-Sj 1 150 432 4109 133-S 492 468-0 152-0 552 525-0 1706 313 2977 96-7 373 354-S! 115-3 433 411-8 133-8 493 4689 152-3 553 5259 1709 314 29S6 970 374 35571 "5-6 434 412-8 1 34- 1 494 469S 152-6 554 5269 171-2 315 1 2996 97-4 375 356-7 1 15-9 435 413-7 134-4 495 470 8 153-0 555 527-8 171-5 316, 3005 97-7 376 357-6 116-2 436 4147 1347 496 4717 153-3 556 5288 171-8 317 3015 980 377 358-61 1 16-5 437 415-6 «35-' 497 4727 1536 557 5297 172-1 318; 302-4 98-3 378 359-5 1 1 16 8 4:3s 416-6 1 35 -4 498 473-6 1539 558 530-7 172-4 319 1 303-4 986 379 360-51 117-1 439; 4175 1357 499 474-6 154-2 559 531-6 172-7 320 3043 98-9 380 361-4 117-4 44U 41S5 1360 500 _475-5 154-5 560 532-6 1730 321 305-3 99-2 381 362-4 1 177 441 "4T94 1363 50T 476-5 "154^ 561 5335 173-3 322 306-2 99-5 382 3633 Ii8-i 442 420-4 1366 502 477-4 155-1 562 534-5 173-6 323 3072 99-8 383 364-3 .18-4 443 421-3 136-9 503 478-4 155-4 563 535-4 173-9 324 30S-2 100 I 384 365-2 118-7 444 4223 137-2 504 479-3 1557 564 536-4 174-2 325 309-1 100-4 385 366-2 1190 445] 423-2 •37-5 505 480-3 150-1 565 537-3 174-6 326 3101 100-7 386 367-1 119-3 446 424-2 137-S 506 4S12 1564 566 53S-3 1749 327 311-0 ion 387 368-1 1196 447 425-1 138-1 507 4822 156-7 567 539-2 175-2 328! 312-0 101-4 388 3690 1 19-9 448 426-1 .384 508 4S3-2 157-0 508 540-2 175-5 329 312-9 '101-7 389 3700 120-2 449 427-0 .38 8 509 4S41 157-5 569 541-1 175-8 330 313-9 1 I02-0 390 3709 1205 450 4280 .391 510 485- 1 1576 570 542-1 33r 314-8! 102-3 391 3719 120-8 451 428-9 139-4 511 T86-0 1579 571 543-0 "176-4 332 3>5-S 102-6 392 372S 121 I 452 429-9 139-7 512 4S7-0 15S-2 572 5440 176-7 333 3167 1029 393 373-8 121 5 453 430-8 1400 513 487-9 158-5 573 544-9 177-0 334 3'77 103-2 394 374-7 121-8 454 43 1 -8 140-3 514 488-9 158 S 574 545-9 177-i 335 3IS-6 ■03-5 395 375-7 122-1 455 432-7 140 6 515 489-8 159-1 575 546-8 177-6 336 319-6 103-S 396 3766 1224 456 433-7 1409 516 490 8 159-4 576 547-8 17S0 337 320-5 1041 397 3776 122 7 457 434-6 141-2 517 491-7 159-7 577 548-7 178-3 338 321-5 104-5 398 378-S 1230 458 435-6 141-5 518 492-7 1600 578 549 7 17S6 339 322-4 104-8 399 379-5 1233 459 436-5 141-8 519 493-6 160- ? 579 550-6 17S9 340 323-4 105-1 400 380-4 J1^6 460 437-5 142-2 520 494-6 1607 580 _55i-6 1792 341 324-3 ' '05-4 401 381-4 1239 461 438-4 1425 521 495-5 161-0 581 552-5 179-5 342 325-3 1057 402 382-3 124-2 462 439-4 142-S 522 4965 161-3 582 553-5 1798 343 326 2 106 403 383-3 ■ 124-5 463 440-3 143-1 523 4974 i6i-6 583 554-4 180-1 344 327-2 106-3 404 384-2, 124-9 464 441-3 143-4 524 498-4 161-9 584 555-4 1804 345 1 32S-I ! 106-6 405 385-21 1252 465 442-2 1437 525 499-3 1622 585 556-3 180-7 346 329-1 1069 4U6 386-1 1 125-5 466 4432 144-0 526 500-3 162-S 586 557-3 181-1 347 330-0 , 107-2 4117 387-1 1258 467 4442 144-3 527 501 2 1629 587 5582 1814 348 331-0 107-5 408 388-0 :26-i 468 i 445-1 1446 528 502-2 ]6V2 588 5592 .817 349 331 9 107-9 409 389-0 126-4 469 4461 144-9 529 5031 '635 589 5601 1S20 350 332-9! 108-2 410 3899 126-7 470 4470 145-2 530 504-1 163-8 590 56.1 182-^ 351 333 S 108-5 411 3909 127-0 T71 44S0 1456 531 5050 164-1 591 562-0 1827 352 334 8 ■ ioS-8 412 391-8 1273 472 4489 1459 532 506-0 164-4 592 563-0 1830 353 335-7 ; «09-i 413 392-8 127-6 473 4499 146-2 533 506-9 164-7 593 563-9 ■83-3 354 3367 1 109-4 414 393-7 127-9 474 450-8 146-5 534 507-9 1650 594 5649 1S36 355 3376 >09 7 415 394-7 '28-3 475 4518 146-8 535 50S-8 165-3 595 565-8 1839 356 3386 1 100 416 395-61 128-6 476 452-7 147 I 536 5098 165-6 596 5^6 8 184-2 357 339 5 "o 3 417 3966 1 28- 9 477 453-7 1474 537 510-7 165-9 597 5677 184-5 358 340-5 1 1 ic-6 418 397-5 1292 478 454-6 1477 538 5117 .66-2 598 5687 .848 359 341-4, 1 10 9 419 398-5 129-5 479 455-6 148-0 539 5126 106 i .599 5696 185-. 360 3424 1 I ' I 3 420 399-S 129-8 480 456S 148-3 540 5136 166 y 600 5706 185-4 Dist Dcp. U.Lai. Dist. Dcp. D. Lnl Dist d;^ D.La, Dist. Dep. D.Lat Dist Dep. D. Lat "< 'J' •P' •Th'^ 468 TABLE 1 TRAVERSE TABLE TO DEGREES 19° ]h 16^ 1 DistJD.La Dep. Dist D.Lat Dep. Dist D.Lat.j Dep. Dist D.Lat Dep. Dis-Jo. Lat.l Dep. tit; 0-3 61 57-7 19-9 121 1 14-4 39-4 181 171-1 58-9 241 227-9 78-5 2 1-9 0-7 62 58-6 122 115-4 39-7 182 172-1 59-3 242 22S-8 78-8 3 2-S i-o 63 59-6 20-5 123 .16-3 40-0 183 173-0 59-6 243 229-8 79-1 4 3-8 1-3 64 60-5 20-8 124 40-4 184 174-0 59-9 244 230-7 79'4 5 47 1-6 65 61-5 21-2 125 118-2 40-7 185 174-9 60-2 245 231-7 79-8 6 Pe 2-0 66 62-4 21*5 126 119-1 41-0 186 175-9 60-6 246 232-6 80-1 7 2-3 67 63-3 21-8 127 4>-3 187 176-8 60-9 247 ^33-5 80-4 8 7-6 2-6 r>8 64-3 22-1 128 121-0 41-7 188 177-8 6.-2 248 234-5 80-7 9 «-5 2-9 m 65-2 22-5 129 122-0 42-0 189 178-7 6.-5 249 -35-4 81-1 10 _2:i 3-3 70 66-2 22-8 130 122-9 42-3 190 179-6 61-9 250 236-4 S.-4 11 10-4 3-6 71 67-1 23-1 131 123-9 42-6 191 180-6 62-2 251 237-3 8.-7 12 1 II-3 3-9 72 68-1 23-4 132 .24-8 43-0 192 181-5 62-5 252 238-3 82-0 13 I 12-3 4-2 73 69-0 23-8 133 125-8 43-3 193 182-5 62-S 253 239-2 82-4 14 13-2 4-6 74 70-0 24-1 134 126-7 43-6 194 183-4 63-2 254 240-2 82-7 15 14-2 4-9 75 70-9 24-4 135 127-6 44-0 195 184-4 63-5 255 241-1 83-e 16 15-1 s-» 76 71-9 24-7 136 128-6 44" 196 185-3 63-X 256 242-1 83-3 17 i6-i 5-5 77 72-8 25-1 137 129-5 44-6 197 ,86-3 64-1 257 243-0 83-7 18 17-0 5-9 78 73-8 25-4 138 130-5 44-9 198 187-2 64-5 258 243-9 84-0 19 i8-o 6-2 79 74-- 25-7 139 131-4 45-3 199 188-2 64-8 259 244-9 84-3 20 i8-9 6-5 80 75-6 26-0 140 132-4 45-6 200 189-1 65-1 260 245-8 84-6 21 19-9 6-8 8i 76-6 26-4 141 ■333 45-9 201 190-0 65-4 261 246-8 1 85-0 1 22 20-8 7-2 82 77-5 26-7 142 I34'3 46-2 202 191-0 65-8 262 247-7 85-3 23 21-7 ys 83 78-5 27-0 143 135-2 46-6 •203 191-9 66-1 263 248-7 85-6 24 84 79-4 27-3 144 136-2 46-9 204 192-9 66-4 264 249-6 86-0 25 23-6 1 8-? 85 So-4 27-7 145 137-1 47'2 205 193-8 66-7 265 250-6 86-3 26 24-61 8-5 86 8. -3 2S-0 146 13S-0 47-5 206 194-8 67-1 266 251-5 86-6 27 25-5 8-8 87 82-3 28-3 147 139-0 47-9 207 195-7 67-4 267 252-5 86-9 28 26-5 9-1 88 83-2 28-6 148 139.9 48-2 208 196-7 67-7 253-4 87-3 29 27-4 9'4 80 84-2 29-0 149 140-9 48-5 209 197-6 68-0 ■269 254-3 87-6 30 28-4 9-8 90 8;-i 29-3 150 141-S 48-8 210 198-6 68-4 270 255-3 87-9 31 29-3 ^ 86-0 -1^ 151 142-8 49-2 211 199-5 68-7 271 256-2 88-2 32 30-3 IO-4 92 87-0 30-0 152 143-7 49-5 212 200-4 69-0 272 257-2 88-6 33 31-2 10-7 93 87-9 30-3 153 144-7 49-8 213 201-4 69-3 273 258-. 88-9 34 32-1 ii-i 94 88-9 30-6 154 145-6 50-1 214 202-3 69-7 274 259-1 89-2 35 33-1 11-4 95 89-8 30-9 155 146-6 50-5 215 203-3 70-0 275 260-0 89-5 3C 34-0 11-7 96 90-8 31-3 156 147-5 50-8 216 204-2 70-3 276 261-0 S9-9 37 35-0 I2-0 97 91-7 31-6 157 148-4 51-1 217 205-2 70-6 277 261-9 90-2 38 359 12-4 98 92-7 31-9 158 149-4 51-4 218 206-1 71-0 278 262-9 90-5 39 36-9 12-7 99 93-6 32-2 159 150-3 51-8 219 207-1 71-3 279 263-8 90-8 40 I 37-8 13-° 100 94-6 32-6 160 151-3 52-1 220 208-0 71-6 280 264-7 41 i 38-8 13-3 loT 95-5 32-9 WiT 152-2 52-4 221 209-0 72-0 28r 265-7 91-5 42 39-7 13-7 102 96.4 33-2 162 153-2 52-7 222 209-9 72-3 282 266-6 91-S 43 40-7 14-0 103 97-4 33'5 163 154-1 53-1 223 210-9 72-6 283 267-6 92-1 44 4i'6 14-3 104 98-3 33'9 164 155-1 53-4 224 2.1-8 72-9 284 268-5 92-5 45 42-5 14-7 105 99-3 34-2 165 156-0 53-7 225 12,2-7 73-3 285 269-5 92-S 46 43-5 15-0 106 IOO-2 34-5 166 157-0 i 54-0 226 213-7 73-6 286 270-4 93-1 47 44"4 ■5-3 107 IOI-2 34-8 167 157-9 54-4 227 214-6 73-9 287 271-4 93-4 48 45'4 15-6 108 I02-I 35-2 168 158-8 54-7 228 215-6 74-2 2H8 93-8 49 46-3 1 6-0 109 103-1 35-5 169 159-8 55.0 229 2.6-5 74-6 289 273-3 94-1 50 47-3 i6-3 no 104-0 170 160-7 55-3 230 217-5 74-9 290 274-2 94-4 51 48-2 i6-6 111 105-0 36-1 171 161-7 55-7 231 218-4 75-2 291 275-1 ; 94-7 276-1 1 95-1 52 49'- i6-9 112 105-9 36-5 172 162-6 56-0 232 219-4 75-5 292 53 50-1 I7"3 113 106-8 36-8 173 .63-6 56-3 233 220-3 75-9 293 277-0 1 95-4 54 51M 17-6 114 107-8 37-1 174 164-5 56-6 234 221-3 76-2 294 278-0 95-7 55 51-0 '79 115 108-7 37'4 17s .65-5 57-0 235 222-2 76-5 295 278-9 96-0 56 5-'9 l8-2 116 109-7 37-8 176 166-4 57-3 236 223-1 76-8 •296 279-9 96-4 57 53-9 >S-6| 117 1 10-6 38-. 177 167-4 57-6 237 224-1 77-2 297 280-S 96-7 58 54-8 189 118 I1I-6 3S-4 178 238 225-0 77"5 298 281-8 97-0 59 55-8 19-2 119 II2-5 179 169-2 58-3 239 77-8 299 282-7 97-3 60 56-7 19-5 120 113-5 39-1 180 170-2 58-6 240 ^26-9 300 2S3-7 97-7 Di,t.JDep. D.Lai Dist. Dep. D.Lat Dist. Dep. D. Lat. Di.st. Dep. D. Lat. Dist. Dep. |d. Lat. 71° ' - 4-44- 1 469 Tli AVERSE TABLE TO DEGREES ~i 19° 1" 16n. 1 Di>t 301 D.Lat Dep. Dist.iD. Lat. Dep. Dist. 421 D. Lat. ^P. 137-0 Dist. 481 D. Lat. 454-8 Dep. 156-6 Dist.JD. Lat. 541 51,-5 D.p. I76-I 2S46 980 361 341-3 1.7-5 398-1 302 2S5-5 983 362 342-3 1.7-8 422 399-0 137-4 482 4557 156-9 542 512-4 .76-4 303 286-5 98-6 363 343-2 1.8-2 423 400-0 137-7 483 4567 IS7-2 543 S.3-4 .76-8 304 2S74 990 3B4 344-2 ..85 424 400-9 1380 484 457-6 ■ 57-6 •'544 5.4-3 '77' 305 2SS-4 99-3 3G5 345-1 1. 8-8 425 401-8 13S-4 485 458-6 157-9 545 1 5.5-3 .77-4 306 2S9-3 99-6 366 346-1 119-. 426 4028 1387 486 459-5 158-2 546 5.6-2 177-7 307 2903 99 9 367 , 347-0 1.9-5 427 4037 .39-0 487 460-5 158-5 5*7! 517-2 178-. 30S 291-2 100-3 368 3480 1.9-8 428 404-7 139-3 48S 461-4 15S9 548 1 5.S-I '78-4 309 292-2 1 IOO-6 369 348-9 .20-. 429 4056 139-7 489 462-4 .592 .549 519-1 1787 310 293-1 1 100-9 370 1 349-S .20-4 430 406-6 .400 49(1 4633 159-5 550; 5200 .79-0 311 294-1 IOI-2 371 3508 .20-8 4.il 407-5 140-3 T9I 464-3 .598 551 52.0 179-4 312 2950 ior6 372 351-7 .2.-. 4.32 408-5 .406 492 465-2 .60-2 552 52.-9 '797 313 2959 IOI-9 373 352-7 12. -4 433 409-4 .41-0 493 466-1 160-5 553 522S .80-0 314 296-9 102-2 374 3536 I2I-7 434 410-4 141-3 494 467-1 .608 554 523-8 .80-3 315 297-S 102-5 375 354-6 122 . 433 411-3 .4. 6 495 46S0 .611 555 524-7 .80-7 316 29S-S 1029 376 1 355-5 122-4 436 412-2 141-9 496 4690 161-5 556 525-7 iSi-o 317 2997 103-2 377 3565 .22-7 437 413-2 142-3 497 469-9 161-S 557 526-6 181-3 318 300-7 103-5 378 357-4 123-0 438 4.4-1 .42-6 498 4709 162-1 558 527-6 .8.-6 319 301-6 103-S 379 1 35s 4 123-4 4:i9 415;. 142-9 499 471-8 1624 559 528-5 1820 320 302-6 104-2 3R0 1 359-3 1237 440 •432 500 4728 .62-8 560 5295 .S2-3 321 3035: 104-5 381 360-2 .240 441 4iro ■43-6 .501 4737 I63-1 561 530-4 182-6 322 304-5 104-8 382' 361-2 124-4 442 417-9 M39 502 4747 ■63-4 562 531-4 1829 323 3054 105-1 383 362 I 124-7 443 4.8-9 144-2 503 4756 163-7 563 532-3 nil 324 300-3 105-5 384 363-1 125-0 444 4.98 144-5 504 476-5 .64-1 564 533-2 325 307-3 ' 105-S 385 364-0 125-3 445 420-s 144-9 505 477-5 164-4 565 534-2 '83-9 326 3oS-2j 1 06- 1 386 365-0 125-7 446 421-7 145-2 506 478-4 .647 566 535' 184-2 327 309-2 1 106-4 387 365-9 126-0 447 422-5 1455 507 479-4 .650 567 536-1 184-6 328 310-1 ! 106-8 388 366-9 1263 448 4236 145-8 508 480-3 165-4 568 5370 '84-9 329 3II-I I07-I 389 367-8 126-6 449 424-5 146-2 509 4S.-2 1657 569 5380 185-2 330 331 312-0 1074 3'30|'077 390 391' 3697 .270 450 4:,1 425-5 4264 146-5 .468 510 511 482-2 "4S3-1 166-1 570 571 5389 5399 185-6 .85-9" 127-3 .664 332 3139 108-1 392 370-6 .27-6 4.52 4274 147-1 512 4S4-1 .66-7 572 5408 333 314-9 1084 393 371-6 .27-9 453 42S-3 147-5 513 4850 167-0 573 54' 7 1 86-5 334 315-811087 394 3725 .283 454 429-3 147-8 514 486-0 167-4 574 5427 .86-9 335 316-71 109-1 395 373-5 .286 455 4302 14S-1 515 4869 .677 575 543-6 187-2 336 317-7! 1094 396 374-4 I2S-9 456 431-2 148-4 516 487-9 .68-0 576 5446 .87-5 337 31S6, 109-7 397 375-4 129-2 457 432-. 1488 517 4S8-S .68-3 577 545-5 187-S 338 319-6 1 100 398 3763 1296 458 433-0 149-1 518 489-7 168-7 578 546-5 188-2 339 320-5 1 10-4 399 377-3 129-9 459 434-0 149-4 519 490-7 .690 579 547-4 188-5 188-8 189-1 340 321-51 U0-7 322-4 uro 400 3782 401 i 379-2 130-2 460 461 434-9 435-9 ^497 150-1 520 521 ^v6 492-6 _i69-3 169-6 580 .581 54S-4 5493 130-5 342 323-4iiii-3 402 380-1 130-9 402 436-s 150-4 522 493-5 1700 582 5503 '89-S 343 324-3 11 1-7 403 381-0 13'-^ 463 437-8 150-7 523 494-5 170-3 583 55. -2 .89-8 344 325-3 1 1 120 404 382-0 13' 5 404 43S7 .51-0 524 495-4 .70-6 584 552-2 .90-1 345 326-21 1 1 2-3 405 3S29 131S 405 439-7 151-4 525 496-4 .709 585 5531 .90-4 346 3271 112-6 406 383-9 .32-2 406 4406 1517 526 497-3 1712 586 554' 190-8 347 328-1 1 130 407 384-8 132-5 467 441-6 152-0 527 498-3 171-6 587 555-0 .91-1 348 329-0 1 13-3 408 385-8 132-8 468 442-S 152-4 528 499-2 171-9 .588 55.V9 .91-4 349 3300 113-6 409 1 3S6-7 "33-1 469 443-4 152-7 529 500- . 1722 589 5569 191-7 350 330-9! 1 13-9 410 i 3S77 133-5 47U 444-4 153-0 530 _5°iL' 172-5 590 557 S 192-1 351 3319114-3 41 r 3S8-6 133-8 471 445-3 153-3 53r 502-0 1729 591 558-8 .92-4 352 3328,1.4-6 4 12| 3S9-6 I34-" 472 446-3 1537 532 5030 173-2 592 559-7 1927 353 333*|"4-9 413 1 390-5 134-4 473 447-2 154-0 533 503-9 1735 593 560-7 193-0 354 3347 '■ 5-2 414, 3914 134-8 474 448-2 154-3 534 504-9 173-8 594 561-6 193-4 355 3357, "56 415' 392-4 135-1 475 449" ■54-6 535 505-8 174-2 595 5626 193-7 356 336-6 115 9 416 1 393-3 ■35-4 470 450-1 155-0 536 506-8 '74-5 596 563-5 194-0 357 3375 '"6-2 417! 394-3 1357 477 451-0 155-3 537 5077 174-8 597 564-S 194-3 358 33«-5'"6 5 418, 395-2 136-1 478 452-0 '55-6 538 5087 175' 598 565-4 194-7 359 3394 "69 419' 396-2 1364 479 452-9 •55-9 539 509-6 '75-5 599 566-4 195-0 360 340 4 1 "'7-2 420 397-1 136-7 480 453-8 156-3 540 5.06 175-8 600 5673 I9S-3 Disc I»i-p. j D.Lat. I^. Dep. D. Lai. Dist. -u.r D. Lat. Dist. Dep. D. Lat Dist. Dq.. D. Lat. 71° 4h iV" 470 TABLE I TRAVERSE TABLE TO DEGREES 20° l*- 20™ Dist-ID.Lat Dep. Dist. D. Lat. Dep. Dist D. Lat. Dep. Dist. D. Lat. Dep. DistJD. Lat. Dep. 1 0-9 o'3 61 57'3 50-9 121 113-7 41-4 181 1 70- 1 61-9 241 j 226-5 82-4 2 1-9 62 58-3 122 1.4-6 41-7 182 171-0 62-2 242 227-4 82 8 3 2-8 I'd 63 59-2 21-5 123 II5-6 42-1 183 172-0 62-6 243 228-3 83 1 4 3-8 i'4 64 6o-i 21-9 124 116-5 42-4 184 172-9 62-9 244 229-3 83 5 5 4" 7 i"7 65 6ri 125 117-5 42-8 185 173-8 63-3 245 230-2 83 8 6 5-6 66 62-0 22-6 126 118-4 43-1 186 63-6 246 231-2 84 I 7 6-6 »"4 07 63-0 22-9 127 "9"3 43-4 187 175-7 64-0 247 232- 1 84 5 8 7'5 »"7 68 63-9 -3"3 128 43-8 188 176-7 64-3 248 233-0 84 8 9 «-5 3" I 69 64-8 23-6 129 I2I-2 44-1 189 177-6 64-6 249 234-0 85 2 10 9-4 3-4 70 65-8 23-9 130 122-2 44-5 190 .78-5 65-0 250 234-9 _!l X 11 10-3 3-8 71 66-7 24-3 131 123-1 44-8 191 179-5 65-3 2511235-9 85 8 12 "•3 4' I 72 67-7 24-6 132 124-0 45'i 192 180-4 65.7 252 236-8 86 2 13 12 2 4-4 73 68-6 25-0 133 125-0 45-S 193 181-4 66-0 253 237-7 86 5 14 I3'2 4-8 74 69-5 25-3 134 125-9 45-8 194 182-3 66-4 -254 238-7 86 9 15 14-1 5-> 75 70-5 25-7 135 126-9 46-2 195 183-2 66-7 255 239-6 87 16 15-0 5-5 76 7'-4 26-0 136 127-8 46-5 196 184-2 67-0 256 240-6 87 6 17 i6-o 5-8 77 7^-4 26-3 137 128-7 46-9 197 185-. 67-4 257 241-5 87 9 18 i6-9 6-2 78 73-3 26-7 138 129-7 47-2 198 186-1 67-7 258 242-4 88 19 17-9 6-5 79 74-2 27-0 139 130-6 47-5 199 187-0 68-1 259 243-4 88 6 20 i8-S 6-8 80 75-^ 27-4 140 .31-6 47-9 200 187-9 68-4 260 261 244-3 88 ± 21 1 19-7 7'2 81 76-1 141 132-5 48-2 •201 ,88-9 68-7 245-3 89 3 22 20-7 7-5 82 77' I 28-0 142 133-4 48-6 202 189-8 69-1 262 246-2 89 6 23 '21-6 7'9 83 78-0 28-4 143 I34'4 48-9 203 190-8 69-4 263 247-1 90 24 22-6 84 78-9 28-7 144 135-3 49-3 204 191-7 69-8 264 248-1 90 3 25 23-5 8-6 85 79-9 29-1 145 136-3 49-6 205 19Z-6 70-1 265 249-0 90 6 26 24-4 8-9 86 So- 8 29-4 146 137-2 49-9 206 193-6 70-5 266 2iO-0 91 27 »5"4 9-2 87 8i-8 29-8 147 138-. 50-3 207 194-5 70-8 267 2,-0-9 91 3 28 26-3 9-6 88 82-7 30-1 148 139-1 50-6 208 '95-5 71-1 268 25I-S 9- 7 29 27-3 9-9 89 83-6 30-4 149 140-0 51-0 209 196-4 71-5 269 252-8 92 30 28-2 10-3 90 84-6 iSli 150 141-0 S1-3 210 197-3 71-8 270 253-7 92 ± "IT 29-1 10-6 91 85-5 31-1 151 141-9 51-6 2Tr .98-3 72-2 ^ 254-7 92 7 32 10-9 92 86-5 152 142-8 52-0 212 199-2 72-5 272 255-6 93 33 3ro II-3 93 87-4 31-8 153 143-8 52-3 213 72-9 273 256-5 93 4 34 31-9 II-6 94 88-3 32-1 154 144-7 52-7 214 201-1 73-2 274 257-5 93 35 32-9 I2-0 95 89-3 3^-5 155 145-7 S3-0 215 202-0 73-5 275 258-4 94 I 36 33-8 12-3 96 90-2 32-S 156 146-6 53-4 216 203-0 73-9 276 259-4 94 4 37 34-8 12-7 97 91-2 33-2 157 J-1-7-5 53-7 217 203-9 74*2 277 260-3 94 7 38 1 35-7 13-0 98 92-1 33-5 158 148-5 54-0 218 204-9 74-6 278 261-2 95 I 3!» 1 36-6 '3-3 99 93'o 33-9 159 149-4 54-4 219 205-8 74-9 279 262-2 95 4 40 1 37-6 i3"7 100 94-0 34-2 160 150-4 54-7 220 206-7 75-^ 280 263-, 95 S 41 1 38-5 14-0 101 94' 9 34-5 161 151-3 55-1 221 207-7 75-6 28r 264-, 96 I 42 39-5 14-4 102 95-8 34'9 162 152-2 55-4 •222 208-6 75-9 282 265-0 96 4 43 40-4 I4"7 103 96-8 35'i 163 153-2 55-7 223 209-6 76-3 283 265;9 96 8 44 l4'-3 15-0 104 97"7 35-6 164 154-1 56-1 224 210-5 76-6 284 97 1 45 42-3 I5'4 105 98-7 35-9 165 155-0 56-4 225 77-0 285 267-8 97 5 46 43-- I5'7 106 99-6 36-3 166 156-0 56-8 226 212-4 77-3 286 268-8 97 S 47 44-2 i6-i 107 IOO-5 36-6 167 .56-9 57-1 227 213-3 77-6 287 269-7 98 2 48 45-1 i6-4 108 101-5 36-9 168 157-9 57-5 228 214-2 7S-0 288 270-6 98 49 1 46-0 i6-8 109 .02-4 37-3 169 158-8 57-8 229 215-2 78-3 289 271-6 98 8 50 1 47-0 lyi 110 .03-4 37-6 170 159-7 58-1 230 216-, 78-7 290 272-5 99 1 61 '47-9 '7'4 111 104-3 38-0 171 160-7 58-5 231 217-1 79-0 291 273-5 99 5 52 ! 48-9 17-8 112 105-2 38-3 172 161-6 58-8 232 79-3 292 274-4 99 9 53 49-8 i8-i 113 106-2 38-6 173 162-6 59-2 233 ViS-l 79-7 293 275-3 2 54 50-7 18-5 114 107- 1 39-0 174 163-5 59-5 234 219-9 80-0 294 276-3 100 6 5i'7 i8-8 115 io8-i 39'3 175 164-4 59-9 235 8o-4 295 277-2 100 9 50 52-6 19-2 116 109-0 39'7 176 16^4 6o-2 236 221-S 80-7 296 278-1 101 57 53-6 I9'5 117 109-9 40-0 177 166-3 60- 5 237 222-7 8i-i 297 ^^'!i 101 6 58 Wl 19-8 118 iio'9 40-4 178 167-3 6o-9 2.?« 223-6 8i-4 298 101 9 59 1 55-4 20-2 119 •"■^ 40-7 179 61-2 230 224-6 81-7 299 2Sro 102 3 CO 56-4 20-5 120 41-0 180 169-1 6i-6 240 225-5 82-1 300 281-9 I02'b Dist Dep^ D.Lat Dist Uep. 'oXat Dist Dep. D. Lat. Dist Dep. D.Lat oil Dep. D. Lat. Ti )° 4" 40™ TABLE 1 TKAVEUSE TAUI.I- TO DEUKEES 20° Ih 20" Dist. D. Lat. Dcp. Dist. D.Lat Dep. Dist. D. Lat. Dep. Dist D. Lat. Dep. Dist. D. Lat. Dep. 301 2S29 103-0 361 339-2 1235 421 3956 144-0 481 452-0 164-5 541 508-4 ".^50 302 2S3S 103-3 362 340-2 123-8 422 396-6 1443 482 4530 1648 542 509-3 185-4 303 284- 7 103-6 363 341-1 124-2 423 397-5 144-7 483 453-9 165-2 543 5103 185-7 304 2857 104-0 364 342-1 124-5 424 398-4 145-0 484 454-8 165-S 544 5112 1800 305 2866 "04-3 365 3430 124-8 425 399-4 145-4 485 455-8 165-9 545 512-1 1S6-4 306 2S7-6 104-7 3i;6 3439 125-2 426 400-3 145-7 486 456-7 166-3 546 513-1 1868 307 28S-S IC50 .■i67 344-9 125-5 427 401-3 146-1 487 457-7 1666 547 514-0 187-1 308 105-4 3GS 345-8 1259 428 402-2 1464 488 458-6 1669 548 515-0 1S7-4 309 290-4 1057 369 346-8 126-2 429 4031 146-7 489 459-5 167-3 549 515-9 1S78 310 ■■ill 291-3 1060 1064 370 'sTT 347-7 348-6 1266 430 431 404-1 147-1 490 491 460-5 167-7 550 5.6-8 517-8 18S-2 1885 292-3 126-9 405-0 147-4 461-4 168-0 551 312 2932 1067 372 349-6 127-2 432 406-0 147-8 492 462-4 168-3 552 5187 iSS-8 313 294-1 107-1 373 350-5 1276 4.33 406-9 148-1 493 463-3 168-6 553 5197 189-. 314 295-1 107-4 374 351-5 127-9 434 407-8 148-4 494 464-2 168-9 554 520-6 1S9-4 315 296-0 107-7 375 352-4 128-3 435 408-S 14S8 495 465-2 169-3 555 521-S 189-8 316 297-0 108-1 376 353-3 128-6 436 409-7 149-1 496 466-, 169-6 556 522-5 190-2 317 2979 108-4 377 354-3 1290 437 410-7 149-5 497 467-0 1700 557 523-4 190-5 31S 29S-S 108-8 378 355-2 129-3 438 411-6 149-8 498 468-0 170-3 5.58 524-4 190-8 319 2998 109-1 379 3562 1296 439 412-5 150-2 499 46S-9 170-7 559 525-3 19.-2 320 3007 1095 380 357-1 130-0 440 4135 150-5 500 469-9 1710 560 526-2 19.-6 3^ 30.-6 1098 381 358-0 130-3 441 414-4 1508 501 470-S 171-3 561 527-2 19.9 322 3026 IIOI 382 359-0 130-7 442 415-4 151-2 502 471-7 1717 562 528-1 192-2 323 3035 no-s 383 359-9 131-0 443 416-3 151-5 503 472-7 172-0 563 529-0 1925 324 3045 no 8 384 360-8 131-3 444 417-2 151-9 504 4736 172-4 564 5300 192-9 325 305-4 II1-2 385 361-8 131 7 445 418-2 152-2 505 474-5 1727 565 5309 I9J2 326 306-3 1115 386 362-7 1320 446 4191 152-5 506 475-4 173-0 566 531-8 1936 327 3073 1118 .387 3637 132-4 447 420-0 152-9 507 476-4 173-4 567 532-8 1939 328 30S-2 1122 388 364-6 132-7 448 421-0 153-2 508 477-3 1737 568 533-7 194-2 329 3092 II2-S .389 365-5 133-1 449 421-9 153-6 509 478-3 174-1 569 5347 194-6 330 331 310 I 3110 II2-9 I 13-2 390 391 366-5 133-4 1337 450 451 422-9 423-8 153-9 510 511 480-2 174-4 570 535-6 "536-6 195-0 195-3 3074 154-3 174-8 TtT 332 3120 113-6 392 36S-4 134-1 452 424-7 154-6 512 481-1 175-1 572 537-5 1956 333 312-9 H3 9 .393 369-3 134-4 453 4257 154-9 513 4S21 175-4 573 538-5 1959 334 3'39 :i4-2 394 370-2 134-8 454 426-6 155-3 514 483-0 175-8 574 539-4 1963 335 3'4S 114-6 395 3712 135-1 455 427-6 155-6 515 484-0 176-1 575 540-3 1966 336 3"57 1149 396 372-1 135-4 456 428-5 156-0 516 484-9 176-5 176-8 576 541-3 197-0 337 3.67 "5-3 397 373-1 135-8 457 429-4 156-3 517 485-8 577 542-2 197-3 338 3>7-6 115-6 .398 374-0 136-1 4.58 430-4 1567 518 486-8 177-2 578 543-2 197-7 339 3iS6 1 16-0 399 374-9 1365 459 431-3 157-0 519 487-7 177-5 579 544-1 19S0 340 3'9-5 1163 400 375-9 136-8 460 432-3 157-4 520 488-7 177-9 580 5450 198-4 34r 320-4 ii6-6 401 3768 137-2 461 433-2 1577 521 4896 .78-2 587 y46-o 19S7 342 321-4 1170 402 ' 377-8 1375 462 434-1 15S0 522 4905 17S-5 582 546-9 1990 343 3223 "7-3 403 , 3787 137-8 4G3 435-1 158-4 523 491-5 178-9 583 547-9 199-4 344 3233 117-7 404 379-6 138-2 464 4360 15S7 524 492-4 179-2 584 548-8 199-8 345 3242 l!s-° 405 3806 ■3S-5 465 437-0 1590 525 493-4 179-6 585 549-8 200-1 346 325-1 406 381-5 138-9 466 437-9 1594 526 494-3 1799 586 550-7 200-4 347 3261 U8-7 407 3'<2-5 139-2 467 438-8 1597 527 495-3 180-2 587 5517 200 8 343 327-0 1 190 408 383-4 139-6 468 439-8 1 60- 1 .528 4962 180-6 588 552-6 201-2 349 328-0 1 19-4 409 384-3 139-9 469 4407 i6o-4 529 4971 l8i-o 589 553-5 20. 5 350 .32_S9 1 19 7 410 ; 3S5-3 470 4417 160-8 530 498-1 18.-3 590 554-4 2018 351 329-8 1201 411 3S62 "1406 471 442^" l6l-l 53r 499-0 iSr6 59r 555-4 202-1 352 330S 120-4 412 387-2 140-9 472 443-S ■ 6i-4 5.32 499-9 181-9 592 5563 2024 353 33'7 1207 412 388- 1 141-3 473 444-5 i6i-8 533 500-9 182-3 593 557-3 202-8 354 3327 1211 4K 389-0 141-6 474 445-4 1621 534 501-8 182-6 594 558-2 2032 355 3336 121 4 415 390-0 1419 475 4464 162-5 535 502-7 183-0 595 559-1 203-5 356 3345 121 8 416 390-9 142-3 476 447-3 1628 53P 5037 1833 596 560-0 2038 357 335-5 122-1 417 39 '-9 142-6 477 448-2 163-2 537 5046 183-7 597 56.-0 204-2 358 3364 122-5 418 392-8 1430 478 449-2 1635 538 505-5 184-0 598 56.-9 204 6 359 3374 122-S 419 393 7 143-3 479 450-1 163-S 53!) 506-5 184-3 599 5629 204-9 360 33^3 I231 420 394-7 143-7 480 451 1 ■ 64-2 540 507-4 i»47 600 5638 205-2 l>i^t Jk-p. U.Lai DUt Dep. D.Lat Dist Dep. D. Lat Dist u,. D. Lat. Dist Dep. D. Lat. 70" 4»»40"' ' 472 TABLE 1 TRAVERSE TABLE TO DEGREES 21° 1" 24"- J)ist.|u.Lal Dep. Dist. D.Lat.JDep. Dist.;D. Lat. Dep. Dist. D.Lat. Dep. Dist. D. Lat. Dep. I 0-9 0-4 61 56-9 21-9 121 113-0 43-4 181 169 64-9 241 225-0 I'.'* 2 i-o 0-7 02 57'9 1-22 113-9 43-7 182 169 65-2 242 225-9 86-7 3 2-S 63 58-8 22-6 123 II4-8 44-1 183 170 65-6 ■243 226-9 87-1 4 3'7 '■4 64 59'7 22-9 1-24 115-8 44" 4 184 171 65-9 •244 87-4 5 4'7 65 60-7 *3'3 125 116-7 44-8 185 172 66-3 245 22S-7 87-8 6 5-6 2-2 60 6i-6 126 II7-6 45-2 186 173 66-7 246 229-7 88-2 7 6-5 2-5 07 62-5 24-0 127 118-6 45-5 187 174 67-0 247 230-6 11'^ 8 7-S 2-9 68 63-5 24-4 128 119-5 45-9 188 175 67-4 248 23. -5 88-9 9 8-4 3-2 69 64-4 24-7 129 120-4 46-2 189 176 67-7 249 232-5 89-2 10 9-3 3-6 70 65-4 25-1 130 121-4 46-6 190 177 68-1 250 233-4 89-6 J J 10-3 3'9 71 66-3 25-4 TisT 122-3 46-9 191 178 68-4 251 234-3 90-0 12 4'3 72 67-2 25-8 132 123-2 47-3 192 179 68-8 252 235-3 90-3 13 I2M 4'7 73 68-2 262 133 124-2 47-7 193 69-2 253 236-2 90-7 14 13-1 5-0 74 69-, 26-5 134 125-1 48-0 194 181 69-5 254 237-1 91-0 15 I4-0 5*4 75 70-0 26-9 135 1260 48-4 195 182 69-9 255 91-4 U; 14-9 5'7 76 71-0 27-2 136 127-0 48-7 196 183 256 239-0 91-7 17 15-9 6m 77 71-9 27-6 137 127-9 49- 1 197 183 9 70-6 257 239-9 92-1 18 i6-8 6-5 78 72-8 28-0 138 128-8 49-5 198 .84 8 71-0 •258 240-9 92-5 19 I7'7 6-8 79 73-8 28-3 139 129-8 49-8 190] 185 8 259 241-8 92-8 20 i8-7 7-2 80 74-7 28-7 iii 130-7 50-2 200 |. 86 7 71-7 260 242-7 _93:L 21 j 19-6 7"5 81 75-6 290 141 131-6 50-5 201 187 6 72-0 261 243-7 93-5 22 1 20-5 7-9 82 76-6 29-4 142 132-6 50-9 202 188 6 72-4 262 244-6 93-9 23 21-5 8-2 83 77'5 09-7 143 •33'5 51-2 203 189 5 72-7 2(i3 245-5 94-3 24 22-4 8-6 84 78-4 30-1 144 134-4 51-6 204 190 5 73-1 264 246-5 94-6 25 23-3 9-0 85 79-4 145 135-4 52-0 206 191 4 73-5 265 24-4 95-0 2t; 24-3 9-3 86 8o-3 30-8 146 136-3 52-3 206 192 3 73-8 266 248-3 95-3 27 25-2 9-7 87 81-2 31-2 147 '.37-2 52-7 207 •93 3 74-2 267 249-3 95-7 28 26-, lo-o 88 82-2 31-5 148 j 138-2 53-0 208 194 74-5 268 250-2 96-0 29 27-1 10-4 89 83-1 31-9 149; .391 53-4 209 '95 I 74-9 269 251-1 96-4 30 28-0 IO-8 90 84-0 32-3 150 ! 140-0 53-S 210 '96 1 75-3 270 252-1 96-8 -w- 28-5 I J. I 91 85-0 32-6 TsT 141-0 54-1 211 197 "0^ 75-6 277 253-0 97-1 32 29-9 11-5 92 85-9 33-0 152 141-9 54-5 212 197 9 76-0 272 253-9 97-5 33 30-8 ii-S 93 86-8 33'3 153 142-8 54-8 213 ,98 9 76-3 273 254-9 97-8 34 31-7 12-2 94 87-8 33'7 154 143-8 55-2 214 199 8 76-7 274 255-8 9S-2 35 32-7 12-5 95 88-7 34-0 155 144-7 55-5 215 7 77-0 275 256-7 9S-6 3fi 33-6 96 89-6 34'4 156 145-6 55-9 216 201 7 77-4 276 257-7 98-9 37 34' 5 I3'3 97 90-6 34-S 157 146-6 56-3 217 202 6 77-8 277 258-6 99-3 38 35'5 .3-6 98 91-5 35"! 158 147-5 56-6 218 203 5 78-1 278 259-5 ,Z^ 39 36-4 14-0 99 92-4 35'5 159 .48-4 57-0 219 204 5 78-5 279 260-5 40 37-3 '4-3 100 93*4 3 5-8 160 149-4 57-3 220 205 ± 78-8 280 26,-4 100-3 ^1^ I4'7 101 94" 3 161 150-3 57-7 221 206 3 79-2 281 262-3 100-7 42 i 39-2 15-1 102 9';-2 36-6 162 151-2 58-. 222 207 79-6 282 263-3 loi-i 43 40-1 15*4 103 96-2 36-9 163 152-2 58-4 223 208 2 79-9 283 264-2 101-4 44 I4I-1 158 104 97-1 37'3 104 153-1 58-8 224 209 I So-3 284 265-1 45 1 4^-0 i6-i 105 37-6 165 154-0 59-1 225 210 I 285 266-, 102-1 40 42-9 i6-5 106 99-0 38-0 166 155-0 59-5 226 211 8i'o 286 26--0 102-5 ■il 439 i6-8 107 99'9 3S-3 167 59-8 227 211 9 81-3 287 267-9 102-9 48 44-8 17-2 108 38-7 108 156-8 6o-2 228 9 81-7 208 26S-9 103-2 49 '4S-7 17-6 109 I0I-8 39-1 169 1S7-8 60-6 229 213 8 82-1 289 269-8 103-6 50 |46-7 17-9 110 I02'7 39-4 170 .58-7 60-9 230 214 82-4 290 270-7 ,03-9 ^17?^ i8-3 TTT I03-6 1^ 171 159-6 61-3 231 215 82-S •291 271-7 104-3 I04-6 52 48-5 i8-6 112 104-6 40-1 172 160-6 61-6 232 216 83-1 292 272-6 53 ] 49-5 19-0 113 105-5 40-5 173 161-5 62-0 233 217 83-5 293 273-5 105-0 51 50-4 19-4 114 .06-4 40-9 174 .62-4 62-4 234 218 83-9 294 274-5 105-4 55 51-3 19-7 115 107-4 41-2 175 1 163-4 62-7 235 219 84-2 295 275-4 105-7 56 1 52-3 116 108-3 4.-6 170 164-3 63-1 236 84-6 296 276-3 io6-i S7 1 53-2 20-4 117 109-2 41-9 177 .65-2 63-4 237 221 84-9 297 106-4 58 54-1 20-8 118 42-3 1711 166-2 63-8 238 222 85-3 298 2^8-2 106-8 ^h-o 211 119 IIIM 42-6 179 167-1 64-1 239 223 85-6 299 279-1 107 2 21-5 120 112-0 43-0 180 168-0 64-5 240 224-1 86-0 300 280-, 10-5 Dis^ep. .Lat Dist. Dep. D.Lai Dist. Dep. D. L-dt. Dist. Dep. D.Lat. Dist. Dep. D. Lat 69-^ 4^ 36^" TABLE 1 TKAVEU!5E TABLE TO DKGRKES 1 21° Ih 21'" Dist D. Lat D.p. Dist D.Lat Dep. Dist D. Lat. Dep. Dist D. Lat. Dep. Dist. D. Lat. Dep. 301 zSro 1079 361 337-0 129-4 421 3930 1509 781 449-0 172-4 541 505-1 193-9 302 2SI-9 108-2 362 337-9 1297 422 394-0 151-2 482 450-0 1727 542 5060 194-2 3U3 2S29 ioS-6 363 3389 1 30- 1 423 394-9 151-6 483 450-9 1 73- 1 543 507-0 ■946 3U4 2S38 108-9 364 339-8 130-4 1308 424 395-S 152-0 484 "^'i-s 1735 544 507-9 195-0 305 2847 109-3 365 340-7 425 396-8 152-3 485 173S 545 50S-S 195-3 306 2S57 109-7 366 341-7 131-2 426 397-7 1527 486 453-7 174-2 546 509-8 1957 307 2S66 iio-o 36- 342-6 131-S 427 398-6 1530 487 4.S4-6 174-5 547 510-7 .960 308 2S7-S 110-4 368 343-5 131-9 428 399-6 153-4 488 455-6 174-9 548 511-6 196-4 3U'J 2SS-5 II0-7 369 344-5 132-2 429 400-5 1537 489 4565 1752 549 512-6 iy6-8 310 311 289-4 lil'i 370 371 345 4 346-3 132-6 1330 430 431 401-4 154 I i54'5 490 49 r 4574 458-4 175^ 1760 550 55 f 513-5 514-4 197-1 197-5 2903 111-5 4024 312 291-3 lU-S 372 347-3 133-3 432 4033 154-8 492 459-3 176-3 552 515-4 197-8 313 292-2 112-2 373 348-2 133-7 433 404-2 155-2 493 4602 1767 553 5163 198-2 314 2931 112-5 374 349-1 134-0 434 ■105-2 155-5 494 461-2 177-0 554 5.7-2 .9S6 315 294-1 112-9 375 350-1 134-4 435 406-I 155-9 495 462-1 177-4 555 5.82 198-9 316 295-0 II3-2 376 351-0 1347 436 407-0 156-3 496 463-0 177-8 556 519-1 199-3 317 2959 II3-6 377 351-9 135-1 437 4080 1566 497 4640 178-1 557 5200 199-6 318 296-9 114-0 378 3529 135-5 438 40S-9 1570 498 464-9 178-5 558 2000 319 297-S "4-3 379 353 S 135-8 439 409 8 157-3 499 465-8 178-8 559 52.-9 200-3 320 29S-7 114-7 380 354-7 136-2 440 410-8 1577 500 466 S 179-2 560 522-S 2007 321 299-7 115-0 381 355-7 136-5 441 4117 -FJb^o 501 4677 1795 561 523-S 20. 322 3006 115-4 382 356-6 136-9 442 412-6 15S4 502 468-6 179-9 562 524-7 201-4 323 301-5 115-8 383 357-5 137-3 443 4136 158-8 503 469-6 1S0-3 563 525-6 201-8 324 3025 116-1 384 35S-5 137-6 444 414-5 159-1 504 470-5 lSo-6 564 5266 202-1 325 303-4 1.6-5 385 359-4 138-0 445 415-4 1595 505 471-5 iSi 565 527-5 202-s 326 3043 116-S 386 360-3 138-3 446 4164 159-8 506 472-4 1S.3 566 52S-4 202-8 327 3053 117-2 387 361-3 138-7 447 417-3 160-2 507 473-3 1S.7 567 5294 2032 328 306-2 117-5 388 3622 1391 448 418-2 160-5 508 474-3 1S2-0 568 5303 203-5 329 307-1 117-9 389 363-" 139-4 449 419-2 1609 .509 4752 182-4 569 531-2 203-9 330 30S1 118-3 iiS-6 390 ^642 365-0 139-8 140-1 450 45r 420;!^ 421-0 161-3 "161-6 510 511 476-1 477-1 182-8 183-." 570 571 5322 533-1 2042 2046 309-0 332 3099 1190 392 365-9 140-5 452 422-0 162 512 4780 183-5 572 534-0 205-0 333 310-9 "9-3 393 3669 1408 4.53 422-9 162-3 513 478-9 183-8 573 5350 205-4 334 3n-8 119-7 394 367-8 141-2 454 423S 162-7 514 4799 1S4-2 574 535-9 205-7 335 312-7 120-1 395 36S-7 141-6 455 424-8 163-1 515 4808 184-6 575 536S 206-1 336 3'3-7 120-4 396 3697 141-9 456 425-7 163-4 516 48 17 184-9 576 537-8 2064 337 3146 120-S 397 3706 142-3 457 4266 163-8 517 4827 1S5-3 577 53S7 206-8 338 3'5-5 1211 398 371-5 142-6 458 427-6 164-1 518 483-6 1856 578 5396 207-1 339 316-5 •2i;5 399 372-5 143-0 459 428-5 164-5 519 484-S 186-0 579 5406 207-5 340 3'7-4 400 J73-4 143-4 460 429-4 1649 520 4S5-5 1S6-4 580 ^541-5 207-9 341 31 83 122^ ■m 374-3 143-7 461 430-4 165-2 521 4S6-4 1867 581 542-4 -15^ 342 319-3 1226 402 375-3 144-1 462 431-3 165-6 522 487-3 187-1 582 543-4 20S6 343 3202 122-9 403 3762 1444 463 432-2 165-9 523 488-3 187-4 583 544-3 208-9 344 321 I 1232 404 377-1 1448 464 433-2 166-3 524 489-2 187S 584 545-2 209-3 345 3221 ■ 23-6 405 3781 145-1 465 434-1 1666 525 490-1 188-1 585 546-2 209-6 346 124-0 40c 3790 145-5 466 435-0 167-0 526 491-1 188-5 586 547-1 2.00 347 3239 124-4 407 379-9 1459 467 436-0 167-4 527 492-0 188-9 587 54S0 2.04 348 3249 1247 408 3S09 1462 468 4369 167-7 528 492-9 189-2 588 5490 2107 34!» 3258 I25-I 409 381-8 1466 469 437-8 1681 529 493-9 189-6 589 549-9 2. 11 .•)50 351 3267 327-7 125-4 125-8 410 382-7 3837 146-9 147-3 470 471 43S-S 4397 16S-4 1688 530 531 494-8 1899 590 591 5508 55. S 2.1 4 495-7 190-3 352 32S6 126-1 412 3V6 147-7 472 4406 169-2 532 496-7 1907 502 5527 2!2-2 353 3295 1265 413 385-5 148-0 473 44 > -6 .69-5 533 497-6 1910 593 5536 212-5 354 330-5 126-y 414 386-5 148-4 474 442-5 169-9 534 498-5 191-4 594 554-6 212-9 355 33>-4 127-2 415 3^T4 148-7 475 443-4 170-2 535 499-5 191-7 595 5555 2132 356 332-3 1276 416 388-4 149-1 476 444-4 170-6 536 500-4 192-. 596 556-4 2136 357 333-3 127-9 417 389-3 149-4 477 4453 170-9 537 501-3 192-4 597 557-4 213-9 358 334-2 128-3 41S 390-2 1498 478 446-2 171-3 538 502-3 192-8 598 558-2 214-3 359 335-1 128-7 419 391-2 150-2 479 447-2 171-7 539 503-2 1932 599 5592 2.4-7 SCO 336-1 129-0 420 392-1 150-5 480 448-1 1720 540 504-1 193-5 600 560-1 2.5-0 Dist. Dc-p. D.Lat Dist. Dep. D.Lat Dist. Dep. D. Lat. Dist Dep. D.Lat Dist. Dep. D. Lat. 69° 41, SG™ TB AVE RSE TABLE TO DEGREES 28"" 22 ° 1" Disl. D.Lat Pep- Distlo. Lat.| Dep. DistJD. Lat. Dep. Dist. D.Lat. Dep. Dis. D. Lat. _Dep. "7" 0-9 0-4 61 56-6 22-9 121 ' 1 12-2 45-3 181 167-8 67-S 241 223-5 90-3 2 '■9 o'7 62 57-5 ^3-2 122' 1 1 3 - 1 45-7 182 163-7 6S-2 242 224-4 907 3 I'l 63 58-4 23-6 123 1140 46-1 183 169-7 68-6 243 225-3 9.-0 4 3"7 '■5 64 59-3 24-0 124 i 115-0 46-5 184 170-6 68-9 244 226-2 91-4 4-6 i"9 65 60-3 1 24-3 1-25 1 115-9 46-8 185 171-5 69-3 245 227-2 91-8 6 5-6 66 61-2 1 24-7 1-26 116-8 47-2 186 172-5 69-7 246 228-1 92-2 6-5 2-6 67 127 II7-8 47-6 187 173-4 247 229-0 92-5 8 7"4 3-0 68 63-0; 25-5 128 118-7 47-9 188 174-3 70-4 248 229-9 92-9 9 8-3 3'4 69 64-0 ! 25-8 129 II9-6 4S-3 189 175-2 70-8 •249 1 230-9 93-3 10 0-3 3-7 70 64-9 ■ 26-2 130] 120-5 48-7 190 176-2 71-2 250,23.-8 93-7 11 4" I 7' 65-8 26-6 131 121-5 49-1 Tor I77-I 71-5 251 232-7 94 -o 12 ii-i 4-5 72 66-8 1 27-0 132 122-4 49-4 192|i7S-o 71-9 252 233-7 94-4 13 I2-I 4" 9 73 67-7 27-3 133 123-3 49-8 193 178-9 r? 253 234-6 94-8 14 13-0 S"2 74 68-6 27-7 134 124-2 50-2 194 179-9 254 235-5 95-2 15 13-9 5-6 75 69-5 28-1 1.35 125-2 50-6 195 180-8 73-0 255 236-4 95-5 16 14; 8 6-0 76 70-5 28-5 136 50-9 19C 181-7 73-4 •256 237-4 95-9 17 6-4 77 71-4 28-8 137 127-0 51-3 197 182-7 73-8 257 238-3 963 l6-7 6-7 78 72-3 29-2 138 128-0 51-7 198 183-6 74-2 •258 239-2 96-6 19 17-6 7-1 79 73-2 29-6 139 128-9 52-1 199 184-5 74-5 259 240-1 97-0 20 i8-5 7-5 80 74-2 3°-° 140 ,29-8 52-4 200 185-4 74-9 •260! 241- . 97-4 21 , 19-5 7'9 til 75-' 30-3 141 130-7 5-8 •201 186-4 75-3 •261 1 242-0 97-8 22 , 20-+ 8-2 82 76-0 30-7 142 131-7 53-2 202 187-3 75-7 262 1 242-9 98-1 8-6 83 77-0 31-1 143 132-6 53-6 203 188-2 76-0 263 243-8 98-5 24 22-3 9-0 84 77-9 3'-5 144 133-5 53-9 204 .89-1 76-4 264 244-8 989 25 23-2 9-4 85 78-8 31-8 145 134-4 54-3 205 190-1 76-8 265 245-7 99-3 2G 1 24-1 9'7 86 79-7 32-2 146 135-4 54-7 206 191-0 77-2 266 246-6 99-6 27 250 87 32-6 147 136-3 55-1 207 191-9 77-5 267 247-6 loo-o 28 260 10-5 38 8r6 33-0 148 137-2 55-4 208 192-9 77-9 268 248-5 100-4 26-9 10-9 89 82-5 33'3 149 138-2 55-8 209 193-8 78-3 269 ! 249-4 100-8 30 27-8 90 83-4 33'7 150 139-1 56-2 210 ■94-7 78-7 270 250-3 lOI I 31 28-7 11-6 91 84-4 34-1 151 140-0 56-6 211 195-6 79-0 271 j 25.-3 .0.-5 32 29-7 12-0 92 85-3 34-5 152 140-9 56-9 212 196-6 79-4 272 252-2 10. -9 33 30-6 12-4 93 86-2 34-8 153 141-9 57-3 213 197-5 79-s 273 253-1 102-3 34 31-5 12-7 94 87-2 35-2 154 142-8 57-7 214 19S-4 80-2 274 ! 2 54-0 35 32-5 13-1 95 88*1 35-6 155 143-7 58-1 215 199-3 80-5 275 1 2 55-0 103-0 3fi 33-4 '3-5 06 89'o 36-0 156 ■44-6 58-4 216 200-3 80-9 276 2559 .03-4 37 34-3 i3'9 97 89-9 36-3 157 145-6 58-8 217 81-3 277 256-8 38 35-2 14-2 98 90-9 36-7 158 146-5 59-2 218 202-1 81-7 278 257-8 104-1 39 36-2 14-6 99 91-8 37-1 159 147-4 59-6 219 203-1 82-0 279 258-7 104-5 40 3yi 15-0 100 92-7 37-5 160 148-3 59-9 220 204-0 82-4 280 259-6 104-9 41 38-0 '5'4 101 93-6 137-8 161 149-3 60-3 22r 204-9 82-8 -281 260-5 105-3 42 i 38-9 ir7 102 94-6 ! 38-2 162 150-2 60-7 222 205-S 83-2 282 261-5 .05-6 43 39-9 i6-i 103 95-5 38'6 163 151-1 61-1 •223 206-S 83-5 283 262-4 106-0 44 40-8 i6-s 104 96-4 hg-o 164 152-1 61-4 2i24 207-7 83-9 284 263-3 1064 45 :6-9 105 97-4 39-3 165 153-0 6i-8 225 208-6 84-3 285 264-2 106-8 46 42-7 17-2 106 98-3 39-7 166 '53-9 62-2 226 209-5 84-7 28G 265-2 107-1 47 43-6 17-6 107 99-2 40-1 167 154-8 62-6 227 210-c 85-0 •287 266-1 107-5 48 44-5 ig-o 108 40-5 168 155-8 62-9 228 211 ^ 85-4 288 267-0 107-9 49 45'4 i8-4 109 loi-i 40-8 169 156-7 63-3 229 212-3 85-8 289 268-0 108-3 50 46-4 18-7 110 I02-0 170 157-6 63-7 230 213-3 86-2 290 268-9 108-6 19-1 111 I02-9 7F Dist.JD.La:. Dep. Ui8t.:D.L:it 1 Dep. Dist. D. Lat. Dep. Dist. D.Lat. Dep. Dist. D.Lat. Dep. 301 279-1 I12-7 361 3347 '35-2 421 390-3 '577 481 4460 lSo-2 .541 501 6 202-7 302 2S00 H3-I 362 335-6 135-6 422 391-3 ,58-1 482 446-9 iSo-6 542 502-5 20 VI 303 280-9 "3-5 363 3366 136-0 423 3922 0-8-4 483 447-8 1809 543 503-4 203-5 304 28 1 9 113-9 364 3375 136-3 424 393-' 158-8 484 448-8 IS, -3 544 504-4 203-8 305 2S2S 114-2 365 338-4 1367 425 3941 '592 485 449-7 J817 545 505-3 204-2 306 2837 1 14-6 366 339 3 137-1 426 3950 159-6 486 450-6 .546 506-2 204-6 307 284-6 115-0 367 340-3 137 S 427 395-9 159-9 487 451-6 182-4 547 507-2 205-0 308 2856 115-4 368 341-2 137-8 428 396-S 160-3 488 452-5 182-8 548 50S-1 2053 309 280-S 115-7 369 342-1 138-2 429 397-8 .607 489 453-4 183-2 549 509-0 205-7 310 311 287-4 288-4 116-1 116-5 370 371 343-1 13S6 430 39S-7 161-1 i6r4 490 454-3 183-6 550 510-0 206-1 206-5 344-0 139-0 431 1 399-b 491 455-3 .84-0 551 510-9 312 2893 1 16-8 372 344 9 139-3 432 ' 400-5 161-S 492 456-2 184-3 5.52 511-8 2068 313 2902 117-2 373 3458 139-7 433 401-5 162-2 493 457-' 184-7 553 5127 207-2 314 2911 117-6 374 346-8 1 40- 1 434} 402-4 162-6 494 458-0 185-1 554 513-6 207-6 315 292-1 iiSo 375 347-7 140-5 435 1 403-3 162-9 495 459-0 185-4 555 5'4-6 208-0 316 2930 11S3 376 348-6 140-8 43fi 404-3 163-3 496 459-9 185-8 556 515-5 208-3 31T 2939 1187 377 349-S 141-2 437 405-2 163-7 497 4608 186-2 557 516-4 20S7 318 294-8 1191 378 350-5 1416 438 406-1 1641 498 461-8 186-6 558 517-4 209-1 319 295S 1195 1 19-8 379 351-4 141-9 439 407-0 164-4 499 462-7 1860 559 518-3 209-4 320 2967 3S0 3523 142-3 440 1 408-0 164-8 500 463-6 187-3 560 5192 2098 321 297-6 120-2 381 353-3 142-7 441 40S-9 165-2 .501 464-S ".87T 561 520-1 210-2 322 2986 1206 382 354-2 I43-I 442 409-8 165-5 502 465-4 188-0 562 521-0 210-5 323 299-5 121-0 3S3 355-1 143-4 443 4107 165-9 503 466-4 18S-4 563 522-0 2109 324 3004 121-3 3S4 3560 143-8 444 4117 166-3 504 467-3 iSSS 564 522-9 2113 325 30'-3 121-7 3S5 3570 144-2 445 412-6 166-7 505 4682 189-2 565 523-8 2117 326 302-3 122 I 3S6 3579 144-6 446 1 413-5 167-0 506 469-2 189-S 566 524;S 212-0 327 3032 122-5 3S7 35SS 144-9 447 414-5 167-4 507 470-1 189-9 567 212-4 328 3041 122-8 388 359-7 145-3 448 4 '5-4 167-8 508 4710 190-3 568 526-6 212-8 329 3050 123-2 389 360-7 145-7 449 416-3 168-2 509 471-9 1907 569 5275 213-2 330 337 306-0 306-9 123-6 390 361-6 16?! 146-1 146-4 450 417-2 168-5 510 472-9 191-1 570 528-5 213-S 1240 451 418-2 16S-9 511 ^75^8 191-4 571 529-4 2139 332 307-8 124-3 392 363-5 146-8 452 419-' 169-3 512 474-7 191-8 572 5303 214-3 333 308-8 124-7 393 364-4 147-2 453 420-0 1697 513 475-6 1922 573 5312 2147 334 3097 1251 394 365-3 147-6 454 420-9 1700 514 476-6 192-5 574 532-2 215-0 335 3106 125-5 395 366-2 147-9 455 421-9 170-4 515 477-5 1929 575 5331 215-4 336 3I1-5 125-S 396 367-2 148-3 456 422-8 170-S 516 478-4 1933 576 534-0 215S 337 312-5 1262 397 368-1 1487 457 4237 171-2 517 4793 193-7 577 534-9 216-2 338 313-4 1266 398 369-0 '49 I 45s 424-6 17.5 518 480-3 1940 578 535-9 216-5 339 3>4-3 127-0 399 3699 149-4 •159 ■ 425-6 171-9 519 481-2 194-4 579 536-8 2i6g 340 JiS-2 127-3 400 370-9 149-8 460 , 426-5 172-3 520 482-1 194-8 580 537-7 217-3 341 316-2 127-7 401 37" -8 150-2 461 1 427-4' 172-7 521 18^ 195-2 581 T3ST 217-7 342 3'7 I 1281 402 3727 1506 462 428-4 ■73-0 522 484-0 195-5 582 5396 218-0 343, jlSo 128-5 403 3737 1509 463 1 429-3 '73-4 523 484-9 '959 583 5405 218-4 344 3190 1288 404 1 374-6 •5'3 464 430-2 173-8 .524 485-8 196-3 584 541-4 218-8 345 3199 129-2 405 375-5 151-7 465 1 431-1 174-2 525 486-7 196-7 585 5424 219-2 346 320S 129-6 406 3764 152-1 466 432-1 174-5 526 487-7 197-0 586 5433 219-5 34- 3217 130-0 407 377-4 152-4 467 i 433-0 '74-9 527 488-6 197-4 587 5442 219-9 348 3227 '303 408 378-3 152-8 468 433-9 175-3 528 489-S 197-8 .588 545-' 220-3 3J9 3236 130-7 409 379"2 «53-2 469 434-8 ■757 529 4904 198-2 589 546-1 220-7 350 3245 131 I 410 380-1 153-6 470! 435-8 176-0 530 491-4 198-5 590 J47-0 221-0 35! 325-4 i3>5 «3i-8 411 IsTT >53-9 471 436-7 176-4 JsV 492-3 198-9 59r 547-9 221-4 332 326-4 412 3820 1543 472 437-6 176-8 532 493-2 199-3 592 548-9 221-8 353 3273 132-2 413 382-9 154-7 473 438-6 177-2 533 494-2 199-7 593 549-8 222-2 354 328-2 132-6 414 ^'Pl 1551 474 439-5 177-5 534 495 1 200-0 594 5507 222-5 355 329-2 '33-0 415 3848 •55-4 475 440-4 177-9 535 496-0 2004 595 551-7 222-9 356 3301 '33-3 416 3857 155-8 476 44'-3 178-3 536 496-9 200-8 596 552-6 223-3 357 331-0 1337 417 3866 1562 4771 442-3 '78-7 537 497-9 201-2 597 553-5 2237 358 3320 134 • 418 3876 156-6 478 ; 443-2 1790 .538 498-8 201-5 598 554-4 224-0 359 3329 134-5 419 38S-S 156-9 479 444-1 1794 539 4997 201-9 599 555-4 224-4 360 333-8 1348 420 389-4 '57-3 480 445-0 179-8 540 500-7 202-3 600 556-3 224-8 nkli Dip. I). Lit Dist.l Dep. D. Lat. Dist. Dep. D. Lat. Dist. Pep. D.Lat. Di.t Dep. 'D.Lat. 08" 4hg2n. 476 TABLE 1 Di8t,D.Lat|Dep. Dist.U. LatJDep. DistJD. Lai. Dep TRAVERSE TABLE TO DEGREES 23° D.Lat.j Dep. Dep. 181 j i66-6 1«2| 167-5 183 i6S-5 184 ! 169-4 185 j 170-3 72-1 73-1 74-0 74" 9 I75-S 34-8 132-9 Z33-S ^34-7 135-6 136-6 258 237-5' 250 238-4 ■2m 239-3 2C1 240-3 ■202 241-2 'MS 242-1 2G4 243-0 205 243-9 21)6 244-9 2ti7 245-8 2(J8 246-7 ■>m 247-6 270 248-, 271 249-5 272 250-4 273 251-3 274 252-2 275 253-1 27« 254-: 2V7 255-0 2V8 255-9 27U 256-8 280 257-7 197-0 197-9 198-8 199-7 2CO-7 201-6 258-7 259-6 260-5 261-4 262-3 263-3 264-2 ■■ 288: 265-1 289 j 266-0 290 I 266-n 287 51 46-9 52 47"9 53 48-8 64 49-7 55 50-6 6« 5"'5 57 52-5 68 sr4 59 H-1 60 55-2 ■Jill 267-9 292 268-S 293 269-7 294 270-6 295 271-5 296 272-5 297 273-4 298 274-3 299 275-2 SOO 276-2 Dist. Dep. D.Lat Dist Dep. D.Lai Dist. Dep. D. Lat. D Dist.j Dep. [D. Lat. 477 TRAVERSE TABLE TO DEGREES 23° Ih 32° Dist. D Lat. Dep. Dist.'o. Lat Dep. Dist D. Lat Dep. Dist D. I^t.' Dep. Dist. D.Lat. Dep. 301 277-1 1 1 7-6 361 332-3 141-1 421 387-S 164-5 481 442-7 iSSo 541 4980 211-4 302 1 77S0 1 1 So 362 333-2 i4>-5 422 388-S 164-9 482 443-7 188-4 542 498-9' 211-8 303 27S9 118-4 363 334-1 141-8 423 3894 •65-3 483 444-6 i88-8 543 499-8 212-2 304 279-8 IISS 364 335-1 142-2 424 390-3 165-7 484 445-5 1892 544 500-7 {212-6 305 2So-S 119-2 365 3360 142-6 425 391-2 166-1 485 4464 189-5 545 501-7; 2130 306 281-7 "9'6 366 336-9 '43-0 426 392-1 166-5 486 447-3 189-9 546 502-61213-4 307 282-6 120-0 367 337-S ■43-4 427 .393-1 166-8 487 4483 190-2 547 503-5; 213-8 3118 •S3-5 1204 3(;8 338-7 143-8 428 394-0 167-2 48S 449-2 190-6 548 504-4:2142 309 2S4-4 120-S :m 339-7 144-2 429 394 9 167-6 489 4501 1910 .549 505-31214-6 310 .uT 2S5-4 286-3 121-2 370 37T 340-6 341-5 144-6 430 431 395-8 396-7 16S0 490 4510 191-4 550 506-3 2150 12 1 -6 145-0 1 68 -4 491 451-9 191-8 .551 5072 215-3 312 287-2 I2I-9 372 342-4 145-4 432 397-7 1688 492 452-9 192-2 552 508-1 215-6 313 2SS-1 122-3 373 343-4 145-7 433 398-6 169-2 493 453-8 192-6 553 509-0 1 2160 314 2S9-0 1227 374 344-3 1461 434 399-5 169-6 494 454-7 193-0 554 5099 216-4 315 1 2000 123-1 375 345-2 146-5 435 4004 1700 495 455-6 193-4 555 510-9 '216 8 316! 2C10 9 '235 376 3461 146-9 436 401-3 170-4 4'JC 4566 556 511-81217-2 317 1 2QI-S 1239 377 347-0 147-3 437 402-3 1708 497 457-5 194-2 557 512-7 217-6 31S; 2>)27' 124-3 378 34S0 147-7 438 403-2 171-1 498 458-4 194-6 558 513-6 218-0 319 293-6,1246 379 348-9 1481 439 404-1 171-5 499 459-3 195-0 559 514-S 2.8-4 320 2046 1250 .-iSO 349-8 ; 148-5 440 405-0 171-9 500 460-2 195-4 560 515-5 2188 32I 2q;'S ' 125-4 381 350 7 ! 148-9 441 405-9 172-3 501 461-2 195-8 561 5164 2192 322 2964 125-S 382 351-6 149-3 442 406-9 172-7 502 462-1 1962 562 517-3 219-6 323 297-3 126-2 383 352-6 1497 443 407-8 173-1 503 463-0 196-6 563 518-2 2200 324 298-2 1266 384 353-5 1500 444 40S-7 173-5 504 463-9 197-0 564 519-2 220-4 325 299-2 127-0 383 354-4 150-4 445 409-6 173-9 505 464-9 197-4 565 520-1 220-8 326 300-1 127-4 386 355-3 1508 446 410-5 174-3 506 4658 197-8 566 521-0 221-2 327 3010 127-8 387 356-2 151-2 447 411-5 174-7 507 466-7 19S-1 567 5219 2216 328 301-9 128-2 388 357-2 1516 448 412-4 1 175-1 508 467-6 198-5 568 522-8 2220 329 302-8 128-6 389 358-1 152-0 449 413-31175-4 509 46S-5 198-8 569 523-8 222-3 330 303-8 128-9 390 3590 152-4 450 414-2 175-8 510 469-5 199-3 570 524-7 2227 33r 304-7 129-3 397 359-9J 152-8 isT 415-2 176-2 511 4704 199-7 571 525-6 223-1 332 30S-6 129-7 392 360-8 153-2 452 4161 176-6 512 471-3 2000 572 5265 223-4 1 333 306-5 130- 1 393 361-8 153-6 453 4170 177-0 513 472-2 200-4 573 527-4 223-8 334 307-5 130-5 394 362-7 154-0 454 417-9 177-4 514 473-1 200-S .574 528-4 2242 335 308-4 130-9 395 3636 ■54-3 455 4.S8 515 474-0 201-2 575 529-3 2246 336 309-3 131-3 396 364-5 154-7 456 4198 178-2 516 475-0 201-6 576 5302 2250 337 310-2 131-7 397 365-4 I5S-I 457 420-7 ,78-6 517 475-9 1 202-0 577 531-1 225-4 338 311-1 1321 398 3664 155-5 458 421-6 179-0 518 476-S 2024 578 532-0 2258 339 312-1 132-5 399 367-3 155-9 459 422-5 179-4 519 477-7 I202-S 579 533-0 226-2 340 3130 i_329 400 368-2 ■56-3 156-7 460 461 423-4 1 179-7 520 521 478-6 479-6 2032 580 533-9 2266 313-9 ■33-2 401 369. 4244 180-1 2036 581 534-8 227-0 342 3M-S 133-6 402 370-0 157-1 462 425-3 180.5 522 480-5 1 204-0 582 535-7 227-4 343 3'5-7 1340 403 371-0 "57-5 463 4262 1809 523 481-4,204-4 583 536-6 2278 344 3.b-7 1344 404 37" -9 157-9 464 427-1 i8i-3 524 482-3 ! 204-8 584 537-6 228-2 345 3>76 134-8 405 372-S 158-3 465 42S-0 181-7 .525 483-2 205-2 585 538-5 228-6 346 3'S-5 ■352 406 373-7 158-6 466 429-0 182-1 526 4842 1 205-5 586 539-4 2290 347 3 '9-4 135-6 407 374-6 159-0 467 429-9 182-5 527 485-11205-9 587 540-3 2294 348 320-3 1360 408 375-6 «59-4 408 430-8 182-9 528 486-0 206-3 588 541-2 2298 349 321-3 136-4 409 3765 159-8 469 431-7 1S3-3 529 486-9 1 206-7 589 542-2 2302 350 322-2 .36-8 410 377-4 i6o-2 470 i 432-6 1837 5.30 4878 1 207-1 590 J431L 2306 351 323-1 "37-2 411 378-3 160 6 471 433-6 [ 1S40 531 4888 '207-4 JdT 544-0 231-0 352 324-0 '37-5 412 379-3 161-0 472 434-5 184-4 532 489-7 2078 592 5449 231-3 353 324-9 ■37 9 413 380-2 161-4 473 435-4 184-8 533 490-6 20S-2 593 545-8 231-7 354 325-9 138-3 414 381-1 161-8 474 436-3 .85-2 534 491-5 20S-6 594 546-8 2320 355 3268 138-7 415 382-0 162-2 475 437-2 185-6 535 492-5 2090 595 547-7 2324 356 3277 '39-' 416 3S2-9 162-5 476 438-2 186-0 536 493-4 209-4 596 54S6 232-8 357 3286 '39-5 417 383-9 162-9 477 439-1 1S6-4 537 494-3 209-8 .597 5495 233-2 358 3295 139-9 418 3848 163-3 478 4400 186-8 5.-38 4952 210-2 598 550-4 233-6 3.-,9 330-5 >40-3 419 3|51 1637 479 440-9 187-2 539 496-1 210-6 599 551-3 2340 360 33.-4 1407 421) 386-6 164-1 480 Dist. 441-8 1S7-6 I). Lat 540 Dist. 497-1 211-0 600 552-3 234-4 nisi. Dep. n. Lat. Dep. D. Lat. Dc-p. Dep. D. Lat. Dist. Dep. D. Lat (>r 4>' 28'" 1 478 TABLE 1 TRAVERSE TABLE TO DEGREES 24° 1" 36"^" Disu D.Lat Dep. Dist, D.Lat.lDep. Dist.JD.Lat. Dep. Disu D. Lat. Dep. Dist.|D.Lat. "Dep. 0-9 0-4 61 55-7 24-8 121 IIO-5 49-2 181 165-4 73-6 •241 220-2 98-0 A 0-8 62 56-6 25-2 122 111-5 49-6 182 166-3 74-0 242 22. -I 98-4 2-7 1-2 63 57-6 123 II2-4 50-0 183 .67-2 74-4 243 222-0 98-8 4 3'7 1-6 64 58-5 "e-o 124 II3-3 50-4 184 168-. 74-8 244 222-9 99-2 5 4-6 2-0 65 lit 26-4 125 114-2 50-8 185 169-0 75;^ 245 223-8 99;7 5'5 2-4 66 26-8 126 115-1 51-2 186 ;^o-8 246 224-7 6-4 2-8 67 6l-2 27-3 127 116-0 51-7 187 76-1 247 225-6 .C0-5 T3 3'3 62-1 27-7 128 1169 52-1 188 171-7 76-5 248 226-6 IC0-9 8-2 37 09 63-0 2X-1 129 117-8 52-5 189 172-7 76-9 249 227-5 101-3 10 9-1 4'1 70 63-9 28-5 2S-9 130 118-8 529 190 173-6 77-3 250 22g-4 101-7 U 1 lo-o 4'5 -jv 64-9 131 119-7 53-3 191 '74-5 77-7 251 229-3 ilC2-, 12 no 4'9 72 65S 29-3 132 120-6 53-7 192 175-4 78-. 252 230-2 1 102-5 II-9 5'3 73 66-7 29-7 133 121-5 54' I 193 176-3 78-5 253 231-1 i .02-9 .2-8 5'7 74 67-6 30-1 134 122-4 54-5 194 177-2 7S-9 254 232-01 1C3-3 13-7 6-1 75 68-5 30-5 135 123-3 54-9 195 17S-1 79-3 255 233-0 ] 103-7 14-6 6-5 76 69-4 136 124-2 55-3 196 .79-1 79-7 ■256 233-9 .04-1 .5-5 6-9 77 70-3 3i"3 137 125-2 55-7 197 257 234-8 104-5 i6-4 7'3 7« 71-3 3i"7 138 126-1 56-1 198 180-9 80-5 258 235-7 104-9 '7'4 7'7 79 72-2 32-1 139 127-0 56-5 199 i8i-8 80-9 259 236-6 105-3 i8-3 8-1 80 73-1 3^"5 140 127-9 56-9 200 2or 182-7 8.-3 260 ■261 237-5 'IC5-S TT 19-2 8-5 "ifr 74-0 32-9 141 ■HFr 57-3 183-6 8.-S 8-9 82 74-9 33-4 142 129-7 57-8 202 184-5 82-2 262 239-3 i '^6-6 2I-0 9-4 83 "•^ 33-8 143 130-6 58-2 203 185-4 82-6 263 240-3 107-0 21-9 9-8 84 34-2 144 131-6 58-6 204 1S6-4 83-0 264 241-2 107-4 21-8 10-2 !!5 77'7 34-6 145 132-5 590 205 .87-3 83-4 265 242-1 .07-8 23-8 10-6 86 78-6 35-0 !46 59-4 206 188-2 83-8 266 243-0 loS-2 24-7 ii-o 87 79-5 35-4 147 134-3 59-8 207 189-1 8+-2 267 243-9 1C8-6 28 25-6 1 1-4 88 8o-4 35-8 148 135-2 60-2 208 190-0 84-6 208 244-S 1C9-0 29 26-5 II-8 89 8i-3 36-2 149 136-1 60-6 209 190-9 S5-0 269 245-7 109-4 30 27-4 12-2 90 82-2 36-6 150 137-0 61-0 210 191-8 85-4 270 246-7 109-8 31 28-3 12-6 91 83-1 37-0 161 137-9 61-4 211 192-S S5-8 271 247-6 110-2 29-2 13-0 92 84-0 37-4 152 138-9 6.-8 212 193-7 86-2 272 2485 llCb 33 30-1 13-4 93 85-0 37-8 153 139-8 62-2 213 194-6 86-6 273 249-4 34 311 13-8 94 85-9 38-2 154 140-7 626 214 '95-5 S7-0 274 250-3 ' III-4 35 32-0 14-2 95 86-8 38-6 155 141-6 63-0 215 196-4 87-4 ■275 251-2 I III-9 36 32-9 .4-6 96 87-7 39-0 156 142-5 63-5 216 197-3 S7;9 276 37 33-8 15-0 97 88-6 39-5 157 143-4 63-9 217 .9S-2 277 253-1 i II2-7 38 34-7 15-5 98 89-5 39-9 158 144-3 64-3 218 199-2 S8-7 ■278 39 35-6 15-9 99 90-4 40-3 159 ■45-3 64-7 219 200- 1 S9-. •279 1 254-9 ! "3-5 1 40 36-5 .6-3 100 91-4 40-7 160 .46-2 65-1 220 201-0 89-5 280 255-8 1 113-9 1 41 37-5 16T 101 92-3 4I-I ICl 147-1 65-5 221 loT^g" 899 281 256-7 114-3 42 38'4 17-1 102 93-2 41-5 162 148-0 65-9 222 202-8 90-3 282 257-6 114-7 43 39'3 17-5 103 94-1 41-9 163 148-9 66-3 223 203-7 90-7 283 258-5 115-1 44 40-2 17-9 104 95-0 42-3 164 149-8 66-7 224 204-6 9. -I 284 259-4 115-5 45 41M i8-3 105 95-9 42-7 165 150-7 67-1 225 205-5 91-5 285 260-4 115-9 40 , 42-0 iS-7 106 96-8 43-1 166 15.-6 67-5 2-26 206-5 91-9 286 26,-3 ii6-3 47 4-'9 19-1 107 97-7 43-5 167 .52-6 67-9 227 207-4 92-3 287 262-2 116-7 48 43'9 19-5 108 98-7 43-9 168 >S3-S 68-3 228 92-7 288 263-1 117-. 4it 44-8 19-9 109 99-6 44-3 169 154-4 ej-i 229 209-2 93-. 289 264-0 11--5 50 45"7 '"•3 110 100-5 4iX 170 '55-3 230 9^-5 290 264-9 iiS-o TT 46-6 20-7 111 45-1 TtT '/'\ 69-6 isr 21 J -o 9+-0 -^ 265-8 i.S-4 52 47'5 21-2 112 I02-3 45-6 172 70-0 232 211-9 94-4 292 266-8 iiS-S 53 48-4 21-6 113 46-0 173 I5S-0 70-4 233 212-9 94-8 2!I3 267-7 119-2 64 49"3 22-0 114 104-1 46-4 174 159-0 70-8 234 213-8 95-2 294 268-6 I'o-o 65 50-2 22-4 115 105-1 46-8 175 159-9 71-2 235 214-7 95-6 295 269-5 86 51-2 116 106-0 47-2 176 i6o-8 71-6 236 215-6 96-0 296 270-4 .20-4 67 52-1 23-2 117 .06-9 47-6 177 i6i-7 72-0 237 216-5 96-4 297 27.-3 .20-8 58 ; 53-0 23-6 U8 107-8 4S-0 178 162-6 72-4 238 2.7-4 96-8 298 272-2 121-2 59 , 53-9 24-0 119 108-7 4S-4 179 163-5 72-8 239 21S-3 97-2 299 173-2 12.-6 fi" ; 54-8 -4'4 120 109-6 48-S 180 164-4 1 73-^ 240 2.9-3 97-6 300 274-1 122-0 Dist. Dep. U.Lii Dist Dep. D.Lai Dist Dep. D.Ut Dist Dep. D.Lat Dist Dep. D. Lai. 66^ 4''- ^4"" 1 TRAVERSE TABLE TO DEGREES 24" Ih 3(3m Dist'D.Lat D.p. Dist D. Lat. Dep. IJist D.Lat ^ Dist. D.Lat Dep. Dist D.Lat Dep. 301 2750 122-4 361 320S 146-8 421 384-6 1712 481 439-4 195-6 541 494-2 2200 302 2759 122-8 362 3307 147-2 422 3855 171-6 482 440-3 196-0 542 495-1 220-4 303 2768 1232 363 331-6 1476 423 3864 172-1 483 441-2 1965 543 496-0 220-9 304 1 277 7 123-7 364 3325 148-1 424 387-3 1725 484 442-1 1969 544 4969 221-3 305 27S6 124-1 365 3334 .485 425 38S-2 1729 485 443-0 197-3 545 497-8, 2217! 306 2795 124-5 366 334-3 1489 426 389-2 173-3 486 444-0 197-7 546 498-S 222-1 307 2804 124-9 367 335-3 149-3 427 390-1 173-7 487 4449 198-1 547 499 7 2225 308 281-4 125-3 368 336-2 1497 428 391-0 174-1 488 445-S 1985 548 5006 2229 309 2823 125-7 369 337-1 1501 429 391-9 174-5 489 446-7 19S9 549 501-5 2233 310 2832 126-1 370 338-0 150-5 430 3928 174-9 490 447-6 1993 550 502-4 2237 311 284-1 126-5 371 '338-9 150-9 431 393-7 175-3 491 4486 1997 551 503-4 224-1 312 285-0 1269 272 339-8 151-3 432 394-6 175-7 492 4495 200-1 552 5043 224-5 313 2859 127-3 373 340-7 151-7 433 395-6 176-1 493 450-4 200-5 553 505-2 224-9 314; 286-8] 127-7 374 341-7 1521 434 396-5 176-5 494 451-3 2009 554 506-1 2^5-3 315 287-8 128-I 375 342-6 1525 435 3974 176-9 495 452-2 201-3 555 507-0 225-7 316 2S8-7 12S-5 376 3435 1529 436 177-3 496 4531 201-7 556 5079 226-1 317 2S96 1289 377 3+4-4 '53-3 437 399-2 177-7 497 454-0 202-2 557 508-S 2266 318 290-5 1293 378 345-3 153-7 438 400-1 17S-2 498 4549 2026 558 509-7 227-0 319 291-4 129-8 379 346-2 154-2 439 401-0 178-6 499 455-8 2030 559 510-6 227-4 320 292-3 J 302 380 347-1 154-6 440 402-0 179-0 500 456-S 203-4 560 5116 227-8 Im" 293-2 130-6 sir 34S-1 155-0 441 402-9 179-4 501 457-7 203-8 561 512-5 j 228-2 322 294-2 131-0 382 3490 155-4 442 403-8 179-S 502 45S-6 204-2 562 513-4' 22S-6 323 295-1 1314 383 349-9 155-8 443 404-7 1S02 503 4^9-5 204-0 5C3 5143 229-0 324 2960 i3>-S 384 350-8 1562 444 4056 180-6 504 1 460-4 205-0 564 515-2 2294 325 2969 132-2 385 351-7 1566 445 400-5 iSi-o 505 i 461-3 205-4 565 5161 229-8 326 297-S 1326 386 3526 157-0 446 407-4 181-4 506 j 462-2 205-8 566 517-0 2302 327 I 2987 1330 387 353-5 157-4 447 408-3 iSi-8 507 1 463-2 567 5180 2306 328 299 6 133-4 388 3544 157-8 448 409-3 1S2-2 508 j 464-1 2066 568 5189 231-0 329 1 300-5 "33S 389 3554 158-2 449 410-2 1S2-6 509 465-0 207-0 569 5'9-S 231-4 330 1 301-5 >34-2 390 356-3 15S6 450 4II-1 183-0 510 465-9 207-4 570 520-7 231-8 331 1 302-4 134-6 39T 357-2 1590 451 ^412-0 183^ 511 466-S 207-8' 571 521-6 2322 332 j 303-3 135-0 392 358-' 159-4 452 4129 183-8 512 4677 208-2 572 522-5 232-7 333 304-2 135-4 393 3590 1598 453 413-8 184-3 513 4686 208-7 573 5234 23 VI 334 305-1 135-9 394 359-9 160-3 454 414-7 1S47 514 469-5 2091 574 524-3 233-5 335 306-0 1363 395 1 360 8 1607 455 415-7 .85-1 515 4705 209-5 575 525-3 233-9 336 1 306-9 1367 396 1 361 8 161-1 456 4.66 185-5 516 47' 4 209-9 576 526-2 : 234-3 337 1 307-9 137 I 397 3627 161-5 457 417-5 185-9 517 472-3 2103 577 527-1 j 234-7 333 1 308-S '37-5 398 363-6 161 9 458 41S4 186-3 518 473-2 210-7 578 528-0 2:; 5- 1 339 3097 137-9 399 364 S 162-3 459 419-3 186-7 519 4741 2II-I 579 528-9 235-5 340 341 3106 J 383 400 401 365-4 366-3 1627 460 461 421-1 1871 187-5 520 4750 2II-5 2II-9 580 581 529-8 530-8 2359 236-3 3"5 163-1 521 475-9 342 312-4 '39' 402 367-2 1635 462 4220 1S79 522 4-6 8 2123 582 531-7 236-7 343 313-3 139-5 403 368-2 1639 463 423-0 1S83 523 477-8 2127 583 532-6 237-1 344 3U3 •39-9 404 369-1 1643 464 423-9 1SS-7 524 4787 2131 584 533-5 2375 345, 3152 •403 405 370-0 164-7 465 424-8 1S9-1 525 4796 2135 585 534 4 2379 346 3'0-I 140-7 406 370-9 165-1 466 425-7 189-5 526 4S0-5 2139 586 535-3 347! 3170 1411 407 371-8 ■65-5 467 4266 1899 527 481-4 214-4 587 536-2! 2]8 8 348; 3' 7-9 141-5 408 1 3727 1659 468 427-5 190-4 528 482-3 214-8 588 537-1 2392 349) 318 S 1420 409 1 373-6 1664 469 42S-4 190-S 529 483-2 215-2 589 538-0 j 239-6 350! 3'97 1424 410! 3745 166-8 470 429-4 191-2 530 484-2 215-6 590 539-0 2400 351 1 3206 142-8 411 375-5 167-2 471 430-3 191-6 531 485-1 2160 591 539-9 240-4 352 3216 1432 •112 376-4 167-6 472 431-2 192-0 532 486-0 216-4 592 540-8 240 8 353 322-5 143C' 413 3773 1680 473 432-1 192-4 .533 4S69 216-8 593 541-7 1 241-2 354 323-4 1440 414 37S-2 168-4 474 4330 192-8 534 487-8 2172 594 542-6 1 241-6 355 3243 1 144-4 415 3791 16S8 475 4339 193-2 535 488-7 217-6 595 543-5' 2420 356 325-21 l.,4 8 416 3S0-0 169-2 476 434-8 1936 536 4896 2180 596 544 4' 2424 357 326-1 : .45-2 417 380-9 169-6 477 4358 194-0 537 490-6 218-4 597 545-4' 2428 353 3270] 145 <"' 418 381-9 170-0 478 436-7 194-4 538 491-5 218-S 598 546-3 2432 359 3280 Mi'O 419 382-8 1704 479 437-6 1948 539 492-4 219-2 599 547-2 243 6 360 328-9 1464 420 3837 1708 480 438-S 195-2 540 493 3 2196 600 548-1 244-0 Distj Uep. IJ. Lut Disi Dep. D. Lat Dist. Dep. D.I. at l)i-.t. T)~ D. L;il. i^. Dep. JD.Lal. CG°" 4h2[.n ] 480 TRAVERSE TABLE TO DEGREES 25° 1" 40^~ Dist Tn.La Dep. Dist D.Lat Dep. Dist.JD. Lat. Dep. Dist D.Lat |Dep. Dist D.Lat i D-^l^- I 0-9 o'4 61 55-3 25-8 ~m 109-71 5I-I 181 164-0 765 241 2.8-41' >oi-9 2 1 1-8 0-8 C2 56-2 26-2 122 1.0-6 51-6 182 164-9 76-9 242 219-3 102-3 3 1 2-7 ••3 63 57-1 26-6 1-23 111-5 52-0 183 165-9 77-3 243 220-2 ,02-7 4! 3-6 '■■7 64 58-0 27-0 124 ,12-4 52-4 184 166-8 77-8 244 221-,!, 03-1 5 45 65 58-9; 27-5 125 .13-3 52-8 185 167-7 245 1 .03-5 6 5-4 2-5 66 59-8 1 27-9 126 114-2 53-2 186 16S-6 78-6 246 223-0 1040 7 6-3 3-0 67 6o-7 28-3 127 J15-1 53-7 187! 169-5 79-0 247 223-9 104-4 8 7-3 j 3-4 68 6i-6 28-7 1-28 54-1 188 170-4 79-5 248 224-8 .04-8 9 S-i 3'8 69 6i-5 29-2 129 I. ("9 54-5 189 171-3 79-9 249 225-7 105-2 10 9-1 4-2 70 63-4 29-6 130 117-8 54-9 190 172-2 80-3 250 226-6 105-7 TT lo-o 4-6 71 64-3 30-0 131 iiS-7 55-4 191 173-1 80-7 isr 227-5 106-1 12 10-9 5-1 72 65-3 30-4 i:i2 119-6 55-S 192 174-0 81-1 252 .06-5 13 II-8 5-5 73 66-2 30-9 133 120-5 56-2 193 174-9 81-6 253 229-3 106-^ 14 I--7 5-9 74 67-1 31-3 134 56-6 194 175-8 82-0 254 230-2 107-3 15 136 6-3 75 68-0 31-7 135 122-4 57-1 195 176-7 82-4 255 231-1 107-8 16 >4-5 6-8 76 68-9 32-1 136 123-3 57-5 196 177-6 82-8 256 232-0 108-2 17 >5-4 7-2 77 69-8 32-5 1,37 124-2 57-9 197 .78-5 83-3 257 232-9 108-6 18 i6-3 7-6 78 70'7 33-0 138 125-1 5«-3 198 179-4 83-7 258 233-8 109-0 19 17-2 8-0 79 7. -6 33-4 139 126-0 58-7 199 180-4 84-1 259 234-7 109-5 20 i8-i «-5 80 72-5 33-8 140 126-9 59-2 200 1S1-3 84-5 260 235-6 109-9 21 19-0 8-9- 81 73-4 34-2 141 1 127-8 59-6 2or 182-2 84-9 261 236-5 110-3 22 19-9 9-3 82 74-3 34-7 142 128-7 202 183-1 85-4 262 237-5 .10-7 23 20-8 9;7 83 75-2 35-1 143 129-6 60-4 203 184-0 86-? 263 238-4 24 21-8 84 76-1 35-5 144 130-5 6o-9 204 184-9 264 239-3 WVb 25 22-7 IO-6 85 77-0 35'9 145 131-4 6i-3 205 185-8 86-6 265 240-2 1 1 12-0 26 23-6 ii-o 86 77-9 36-3 146 132-3 6i-; 206 186-7 87-1 2661 24.-1 1 1.2-4 27 24-5 II-4 87 78-8 368 147 62- 1 207 187-6 87-5 •2671 242-0 1 I.2-S 28 -5-4 II-8 88 79-8 37-2 148 134-1 62-5 208 iSS-5 S7-9 ■_'li." 24;'iy 113-3 29 26-3 M'.l 89 8o-7 37-6 149 135-0 63-0 209 189-4 88-3 -2(;9'24rs .13-- 30 27-2 90 8i-6 38-0 1.-.0 135-9 63-4 210 190-3 88-7 •270 ^++;:_,j^:^ 31 131 ~9r 82-5 38-5 151 136-9 63-8 211 191-2 89-2 271 245-6 114-5 32 29-0 '3-5 92 83-4 38-9 152 137-8 64-2 212 192- 1 89-6 272 246-5 1.5-0 33 • 29-9 13-9 93 84-3 39-3 153 .38-7 64-7 213 193-0 90-0 273 247-4 1 1 5-4 34 30-8 14-4 94 85-2 39-7 154 139-6 65-1 214 '93-9 90-4 274 248-3 .15-8 35 317 .4-8 95 86-1 40- 1 155 140-5 65-5 215 194-9 90-9 275 249-2 Il6-2 36 3S-6 15-2 96 87-0 40-6 156 141-4 65-9 216 195-8 91-3 276 250-1 1.6-6 37 33-5 ,5-6 97 87-9 41-0 157 142-3 66-4 217 196-7 91-7 277 251-0 117-1 38 1 34-4 i6-i 98 88-8 41-4 158 143-2 66-8 218 197-6 92-1 278 252-0- 117-5 39 35-3 i6-5 99 89-7 41-8 159 144-1 67-2 219 198-5 92-6 279 252-9 117-9 40 1 36-3 .6-9 100 90-6 42-3 160 145-0 67-6 2-20 199-4 2m_ 41 37-2 17-3 101 91-5 42-7 161 145-9 68-0 22r 2eo-3 93-4 254-7 iiS-8 42 38-1 177 102 92-4 43-1 162 146-8 68-5 222 201-2 93-8 282 255-6 43 39-0 l8-2 103 93-3 43-5 163 147-7 68-9 223 202-1 94-2 283 256-5 ji9;6 44 39-9 iS-6 104 94-3 44-0 164 148-6 69-3 224 203-0 94-7 284 257-4 45 40-S 19-0 105 95-2 44-4 165 149-5 69-7 225 203-9 95-1 285 258-3 120-4 46 41-7 19-4 106 96-1 44-8 166 150-4 70-2 226 204-8 95-5 286 259-2 120-9 47 42-6 19-9 107 97-0 45-2 167 151-4 70-6 227 205-7 95-9 287 260-1 I2I-3 48 43-5 20-3 108 97-9 45-6 168 152-3 71-0 228 206-6 96-4 288 261-0 I2I-7 49 44-4 20-7 109 98-8 46-1 169 153-2 71-4 229 207-5 96-8 289 26.-9 122-1 50 45'3 211 110 99-7 46.5 170 154-1, 71-8 230 208-5 97-2 290 262-8 122-6 "sT 46-2 21-6 1 1 1 100-6 ■ 46-9 171 155-0 72-3 231 209-4 97-6 29ri 263-7" "123-0 52 47-1 22-0 112 I0I-5 47-3 172 155-9 72-7 232 210-3 98-0 292 1 264-6 123-4 53 48-0 22-4 113 102-4 47-8 173 156-8 73-1 233 98-5 ■293 265-5 .23-8 54 48-9 22-8 114 103-3 48-2 174 157-7 73-5 234 212-1 98-9 •294 266-5 124-2 55 49'S 23-2 115 104-2 48-6 175 158-6 74-0 235 213-0 99-3 295 267-4 124-7 56 50-8 23-7 116 105-1 49-0 176 159-S 74-4 236 213-9 99-7 296 268-3 I25-I 57 51-7 24' I 117 106-0 49-4 177 .60-4 74*8 237 2,4-« 297 269-2 125-5 58 52-6 24-5 118 106-9 49-9 178 16, -3 75-2 238 215-7 ioo'6 298' 270-1 125-9 59 53'5 24-9 119 107-9 50-3 179 162-2 75-6 239 216-6 loi-o 299 1271-0 .26-+ 60 54-4 25-4 120 io8-8 50-7 180 ,63-1 76-, 240 217-5 soi-4 300 271-9 126-8 Dirt. Dep. D.Lat Dist. Dep. ID.Lat' Dist. Dep. D. Lat. Dist. Dep. D.Lat. Dist.j Dep. D. La. 65° 4" ao^ J TABLE 1 481 TRAVERSE TAULE TO DEGREES 1 25° l" 40'" DistD.Lat. Dep. Dist D.Lat Dep. Dist.b. Lat.! Dep. Dist.b. Lat Dep. Dist D.Lat iDep. 301 872-8 1272 361 327-1 152-5 421 381-5 177-9 481 435-9 203-3 541 490-3' 2286 30i 1 273-7 1 127-6 362 3280 '53-0 422 382-4! 178-3 482! 4368! 203-7 542 491-2 229-0 303 274-6 12S-0 363 329-0 153-4 423 3S3-3I 1787 483 437-7 204-1 543 492-1 2294 30-1 275-SJ 128-4 364 329-9 153-8 424 3X4-2 179-2 484 4386 204-5 544 493-0 229-9 305 276-4 ' 128-9 365 330-S 154-2 425 385 1 179-6 -485 ; 439-5 204-9 545 4939 2303 306 277-31 129-3 366 3317 154-6 426 3860 iSo-o 486 i 440-4 2054 546 494-8 230-7 307 278-2 1 129-7 367 332-6 155-1 427 387-0; 180-4 487! 441-3 205-8 547 495-7 2311 308 279-1 130 I 368 3335 '55-5 428 1 387-91 180-9 488 1 442-2 206-2 548 496-6 231-6 309 2S0-0! 1306 369 334-4 155-9 429 388-8 181-3 459 4431 206-6 549 497-5 2320 310 2S09 131-0 370 335-3 156-3 4,30 389-7 1 181-7 490 ' 444-0 491, 444-9 207-1 550 55^1 _498-4 499-3 232-4 2328 311 2S18 131-4 371 336-2 156-8 431 1 3906 182-1 207-5 312 1 2S2-7 j i3rS 372 337-> 157-2 432 j 391-5 1S2-5 -492 i 445-9 2079 552 500-2 233-2 313 2S3-6 132-2 373 338-0 157-6 433' 392-4 183-0 493 j 446-8 208-3 553 501-1 233-7 314 1 284-5! '327 374 3389 1580 4.34 1 393-3 1 183-4 494 1 447-7 554 5020 234-1 31.1 285-4: 133-1 375 339-8 158-5 435 394-2 1S3-8 495 448-6 209-1 555 5030 2345 316 286-4] 133-S 376 340-7 158-9 436 395-1 184-2 496 449-5 2096 556 503-9 235-0 317 287-3, 133-9 377 341-6 1593 437 1 396-0 1 1S47 497 450-4 2100 557 5048 i 235-4 318 288-2' 134-4 378 342-5 '59-7 438 396-9, 185-1 498 451-3 210-4 558 505-71 2358 319 289-1 ' 134-S 379 343-5 160-1 439, 397-S 185-5 499 4522 ' 2109 559 506-6 236-2 320 29001 135-2 380 344-4 1606 440- 39S-7, 185-9 500 453-1 ' 211-3 560 5075 2366 321 [ 2909 135-6 381 345-3 161-0 441 1 399-6 1S6-3 501 ' 454-0 21 17 561 508-4 j 237 1 322! 291-8 136-1 382 346-2 l6i-4 442 400-6 1868 502 454-9 212-1 562 509-3 237-S 323 292-7 136-5 383 347-1 161-8 443 1 401-5 1S7-2 503 . 455-8 1 212-5 563 5102! 237-9 324 2936 136-9 384 1 348-0 1623 444 402-4 187-6 504' 456-7. 2130 564 Su-i 238-3 325 294-S 1373 385 3489 162-7 445 , 403-3 ISS 505 ! 4577 213-4 565 5120 238-7 320 2954 '377 3S6 349-8 163- 1 446 404-2 188-5 506 4586 213-8 566 512-9 239-2 327 296-3 1382 387 350-7 163-5 447 405-11 -88-9 507 459-5 2142 567 5138 239-6 328 297-2 13S-6 388 35 '-6 163-9 448 406-0 189-3 508 460-4 214-7 568 5 '4-8 240-1 32'J 298 I 139-0 389 352-S 164-4 449 ' 406-9 1897 509 461-3' 215-1 569 515-7 ' 2405 330 2990 139-4 390 353-4 164-8 450 407-8 190-1 510, 4622 215-5 570 516-6, 240-9 33r 3000 139-9 '391 354-3 165-2 45 f| 408-7 ' 190-6" 5Tr; 463-1 215-9 "stT 517-51 2413 332 3009 140-3 392 355-2 1656 452 4096 191-0 512 , 4640 2164 572 518-4: 241-7 333 301-8 140-7 393 3561 1661 453 410-5 191-4 513 1 464-9 216-8 573 519-3: 242" 334 3027 141-1 394 1 357-0 1665 454 411-4 191-8 514, 465-8 217-2 574 5202 2426 335 3036, 141-5 .395 358-0 166-9 455] 412-3 192-3 515 466-7 217-7 575 521 1 ; 2430 336 304-5 1420 •■=96 35S9 167-3 456, 413-2. 192-7 516 467-6 2l8l 576 522-0 243-4 337 305-4 142-4 397 359-8 167-7 457 414-1 193-1 517 4685 2185 577 522-9 1 243-8 338 306-3 1428 398 360-7 168-2 458 415-1 193-5 518 469-4' 218-9 578 523-8 ! 244-.1 339 307-2 143-2 .399 361-6 1686 4 59 4160 194-0 519! 4703 219-3 579 524-7; 244-7 34U 30S1 "43 7 400 1 362-5 169-0 460 4169 194-4 .';20 471-2 219-8 580 525 6 1 245 1 341 309 o> 144-1 401 363-4 1694 461 417-8 1 194-8 521 472-2 220-2 siT" 5265 |'245-5 342 3099 144-5 402 364-3 169-9 462 418-7: 1952 522 473-1 220-6 582 527-4 2460 343, 3'OS 144-9 403 365-2 170-3 463 419-6 1956 523 474-0 221-0 583 5283 2464 344 311-7 145-4 404 366-1 170-7 464 4205 1961 524 474 9 221-4 584 5293 246-8 345 312-6 I45-S 405 367-0 171-1 465; 421-4; 196-5 525 475-8 2219 585 5302 247-2 346 3'3-5 146-2 406 367-9 171-6 466 422-3 1969 526 476-7 222-3 586 531 I 2477 347 1 314-5 146-6 407 368-8 1720 467 4232' 197-3 527 1 477-6 222-7 587 532-0 24S. 348! 315-4 147-0 408 369-7 172-4 468, 424-1 197-8 528 , 478-5 223-2 588 532-9 248-5 349 3'6-3 147-5 409 I 370-6 172-8 469 4250 198-2 529 4794; 223-6 589 533-8 248 9 1 350 317-2 147-9 410|J7r5 JJIl 470 4259! 198-6 530 531 480-3, 2240 590 .591 5347 535 6 2494 2498 351 318-1 148-3 411 t 372-5 173-7 471 426-S """1990" T8T-2 224-4 352 ; 3190 148-7 ■»I2 373-4 174-1 472 42771 199-4 532 482-1 224-8 592 536-5 2502 353 319-9 149-2 413 3743 "74-5 473 4286' 1999 533 1 483-0 225-3 593 537-4 2506 354 3208 149-6 414: 375-2 174-9 474' 429-6' 200-3 534 ' 483-9 225-7 594 5383 251 I 355 321-7 150-0 415 1 376-1 175-4 475 430-5: 200-7 .535 ; 4S4-8 2261 595 539-2 251-5 356 322-6 150-4 416! 377-0 175-8 476 43 '-4' 201-1 536 4S57 226-5 596 540-1 251-9 3"'' 1 323"5 '50-S 417 1 377-9 1762 477 432-31 201-6 537 486-7 1 226-91 597 541-0 2523 358 1 324-4 151 3 418 378-8 1766 47H 433-2 1 2020 538 4S7-6 2274 598 5419 2527 359 325-3 15 1-7 419 3797 177-0 479 434-1 i 202-4 539 4S8-5 227-8 599 5428 253 I 360 326-2 152-J Dist Dep. ;D. I.at. 420 3806 Dist. Dep. 177-5 D. Lat. 480 435-0 202-8 540 489-4 228-2 600 543-8 253-6 Disl.^ Dep. ! D.Lat. ,^ Dep. D. Lit, Di.^f. Dep. D.Lai. db" ~~ 4"~20"'" 482 TRAVERSE TABLE TO DEGREES | 26" 1M4^ 1 Di8t. D.UtJDep. Dist D.la, Dep. UisJD.I.at.l Dep. Dist. D. Lat Dep. Dist D. Lat.j Dep. 1 0-9 0-4 61 54-8 26-7 121 108-8 53-0 181 162-7 79-3 241 2.6-6 1 105-6 2 1-8 0-9 62 55-7 27-2 122 109-7 53-5 182 163-6 79-8 242 217-5 .06-1 3 2' 7 ■■3 63 56-6 27-6 123 iio-6| 53-9 183 164-5 80-2 243 218-4 >o6-5 4 3-6 rS 64 57-5 28-1 124 111-5 54-4 184 .65-4 80-7 244 219-3 '07-0 5 4-5 2'2 65 s8-4 28-5 12s 54-8 185 166-3 81-1 245 220-2 107-4 6 5'4 2-6 66 59'3 28-9 126 113-2 55-- 186 167-2 81-5 246 221-1 I07-8 7 6-3 5-1 67 6o-2 29-4 1-27 1 14- 1 55-7 187 I68-I 82-0 247 222-0! 108-3 K 7'2 3'5 68 6i-i 29-8 128 115-0 56-1 188 169-0 82-4 248 222-9 IC8-7 81 3-9 69 62-0 129 115-9 56-5 189 169-9 82-9 249 223-8 109-2 10 9-0 4-4 70 62-9 30-7 130 116-8 57-° 190 170-8 83-3 •250 224-7 IC9-6 11 90 4-8 71 63-8 31M TsT 117-7 57-4 191 171-7 83-7 25? 225-6 iio-o 12 1 10-8 5-3 72 64-7 3.-6 132 118-6 57-9 192 172-6 84-2 •252 :f'.^ 110-5 13 1 1 1-7 5-7 73 65-6 32-0 133 119-5 58-3 193 '73-5 84-6 253 110-9 14 12-6 6-1 74 66-5 32-4 \M 120-4 58-7 194 174-4 85-0 254 22S-1 111-3 15 13-5 6-6 75 67-4 32-9 135 121-3 59-2 195 '75-3 85-5 255 229-2 111-8 16 14-4 7-0 68-3 33"3 136 122-2 59-6 196 176-2 85-9 256 230-: 112-2 17 15-3 7-5 77 69-2 33-8 137 123-1 6o-i 197 177-1 86-4 257 231-0 112-7 18 l6-2 "•9 34-2 138 124-0 60-5 198 178-0 86-8 -238 231-9 113-1 19 lyi S-3 79 71-0 34-6 139 124-9 60-9 199 178-9 87-2 259 2r-;8 113-5 20 i8-o 8-8 80 35'i 140 125-8 6,-4 200 179-8 S7-7 260 1.4-c ^r 189 9-2 -^ 72-8 35"5 141 .26-7 6i-8 201 i8o-7 88-1 wT 234-6 114-4 22 .9-8 9-6 82 35'9 142 127-6 62-2 202 iSi-6 88-6 262 =35-5 114-9 23 20-7 85 III 36-4 143 12S-5 62-7 203 182-5 S9-0 263 236-4 24 21-6 IO-5 84 75'5 36-8 144 129-4 63-1 204 183-4 89-4 264 25 22-5 ii-o 85 76;4 37-3 145 130-3 63-6 •205 184-3 89-9 265 238-2 116-^ 26 23-4 "•4 86 37'7 146 131-2 64-0 206 185-2 90-3 266 239-1 116-6 27 24-3 iiS 87 78-1 38-. 147 132-1 64-4 207 186-1 90-7 267 240-0 117-0 28 25-2 ^:? 88 79-1 38-6 148 133-0 64-9 208 186-9 91-2 268 240-9 117-5 29 26-1 89 8o-o 39-0 149 133-9 65-3 209 187-8 91-6 269 241-8 117-9 30 27-0 13-2 90 8o-9 39' 5 150 134-8 65-8 210 188-7 92-1 270 242-7 118-4 TT- 27-9 .3-6 91 8,.8 39-9 ViT 135-7 66-2 217 ,89-6 92-5 •271 =^43-6 iiS-S 32 28'8 140 92 S2-7 40-3 152 136-6 66-6 212 190-5 92-9 272 244-5 119-2 33 29-7 14-5 93 40-8 153 137-5 67-1 213 ,91-4 93-4 273 245-4 119-7 34 306 «4-9 94 4-5 41-2 1.54 138-4 67-s 214 191-3 93-8 274 246-3 35 31-5 ■5-3 95 85-4 41-6 155 139-3 67-9 215 193-2 94-2 275 12C-fl 36 32-4 ,5-8 96 86-3 42-1 156 140-2 68-4 216 194-1 94-7 276 248-I 121-C 37 33-3 i6-2 97 87-» 42-5 157 141-1 68-8 217 195-0 95-1 277 249-0 121-4 38 34- i i6-7 98 88-1 43-0 158 142-0 69-3 218 '95-9 95-6 278 249-9 121-9 39 35-1 17-1 99 89-0 43'4 159 142-9 69-7 219 .96-8 96-0 250-8 122-3 JL ■7-5 100 89-9 43-8 160 143-8 -0-1 220 I97'7 96-4 280 25.-7 122-- 41 leT i8-o 101 908 44-3 161 •44*7 70-6 221 1 .98-6 96-9 281 2526 123-2 42 3y7 .8-4 102 91-7 44-7 162 145-6 71-0 222 199-5 97-3 282 253-S 123-6 43 38-6 i8-8 103 92-6 45-2 163 146-5 71-5 223 200-4 97-8 283 254-4 124-1 44 39-5 19-3 104 93"5 45-6 164 147-4 71-9 224 201-3 284 255-3 124-5 45 40-4 19-7 105 94"4 46-0 165 148-3 72-3 225 98-6 285 256-2 124-9 46 4i"3 20-2 106 95'3 46-5 166 149-2 72-8 226 203-1 99-1 286 257-1 125-4 47 42-2 20-6 107 96-2 46-9 167 150-1 73-2 227 204-0 99-5 287 2580 125-8 48 43-1 2I-0 108 97-1 47-3 168 151-0 73-6 228 204-9 99-9 288 258-9 126-3 49 44-0 21-5 109 9S-0 47-8 169 .51-9 74-1 229 205-S 100-4 289 259-8 126-7 50 44-9 ^'•9 110 98-9 4S-2 170 152-8 74-5 230 206-7 100-8 290 260-7 I27-I 45-8 22-4 HI 99-8 48-7 171 j. 53-7 75-0 231 207-6 101-3 •291 1 261-5 12-6 52 46-7 22-8 112 100-7 49-1 172 154-6 75"4 232 101-7 -292 1 262-4 I2S-0 53 47-6 23-2 113 I0I-6 49' 5 173 '55-5 75-8 233 209-4 203 263-3 I2S-4 54 48-5 23-7 114 102-5 50-0 174 156-4 76-3 234 210-3 102-6 294 264-2 55 49-4 24-1 115 103-4 50-4 175 157-3 76-7 235 211-2 103-0 295 265-1 129-3 56 50-3 ^4-5 116 104-3 50-9 176 158-2 1 77-2 236 212-1 103-5 296 266-0 129-8 57 51-2 25-0 117 5''3 177 159-1 77-6 237 213-0 103-9 297 2669 130-2 58 52-1 23-4 118 I06-1 51-7 178 i6o-o 78-0 238 213-9 104-3 298 267-8 130-6 59 530 25-9 119 107-0 52-2 179 160-9 78-5 239 2.4-8 104-8 299 268-7 CI' 539 26-3 120 52-6 180 161-8 7S-9 240 215-7 105-2 300 269-6 '3''5 D. Lai. Dist.|l>jp.' O.Lat Dist. Dep. D.L„t EiT. Dep. D. Lat. Dist. Dep. D.Lat. Dist. Dep. 64 4M«" j TABLE 1 483 TKAVERSE TAI3LE TO DEGREES | 26° If 44" 1 Dist. D. Lat. Dcp. Dist. n. Lat. Dcp. Uist D. Lat. Dep. Dist. D. Lat. Dep. Dist D.Lat. Dep. 801 2705 132-0 361 324-S "^5^ 421 378-4 ,S4-6 487 432-3 2109 541 4S62 237-2 302 2714 1324 362 325-4 158-7 422 379-3 185-0 482 4332 21. -3 542 487-. 237-6 303 2723 132-8 363 3263 159-1 423 380-2 185-4 483 434. 2117 543 4880 2380 304 2732 133-3 364 327-2 159-6 424 3Sri 185-9 484 435-0 544 488-9 238-5 305 274-1 '337 365 328-1 1600 425 382-0 .863 485 1 435-9 212-6 545 489-8 238-9 306 2750 1 34-' 366 3290 160-4 426 382-9 186-7 486 : 436-8 213-0 546 490-7 239-3 307 2759 134-6 367 3299 160-9 427 383-8 187-2 487 437-7 213-5 547 491-6 239-8 308 276S '35-0 358 330S 161-3 428 384-7 187-6 488 438-6 213-9 548 492-5 240-2 309 2777 "35-5 369 331-7 161-8 429 385-6 18S1 489 439-5 2.44 549 4934 240-7 310 311 2786 279-5 135-9 ■36-3 370 37T J321 333-S 162-2 1626 430 431 386-s 387-4 18S-5 188-9 490 491 440-4 44.-3 214-8 550 551 494-3 2411 241-5 215-2 495-2 312 ;to4 136-8 372 3344 1631 432 388-3 1S9-4 492 442-2 215-7 552 496-1 242-0 313 2.M-3 1372 373 335 3 163-5 433 3S92 189-8 493 443-1 2161 553 497-0 242-4 314 282-2 1377 374 336-2 164-0 434 390-1 190-3 494 4440 216-6 554 497-9 242-9 315 2S31 1 38- 1 375 337-1 164-4 435 391-0 190-7 495 444-9 217-0 555 498-8 243-3 316 284-0 1385 376 3380 164-8 436 391-9 1911 496 445-8 217-4 556 499-7 243-7 317 2849 1390 377 338-9 "65-3 437 3928 191-6 497 446-7 217-9 557 500-6 244-2 318 285-8 139-4 37S 339S 165-7 438 393-7 192-0 498 447-6 218-3 558 50.-5 244-6 319 2867 139-8 379 340-7 i6o-2 439 394-6 192-4 499 448-S 2187 559 502-4 245-0 320 321 287-6 288-5 •40-3 140-7 380 381 341-5 342-4 1666 '167-0 440 441 395-S 396-4 1929 500 501 449-4 450-3 219-2 560 503-3 504-2 245-5 2459 193*3 2196 561 322 289-4 141-2 382 343-3 167-5 442 397-3 .93-8 502 451-2 220-1 562 505-. 246-4 323 290-3 141-6 383 344-2 167-9 443 30S-2 194-2 503 452-. 220-5 563 506-0 246-8 324 2912 142-0 384 3451 .68-3 444 399-1 .94-7 504 453-0 221-0 564 506-9 247-3 325 292-1 142-5 385 346-0 I6S-8 445 400-0 195-1 505 453-9 221-4 565 507-8 247-7 326 1429 386 346-9 169-2 446 400-9 .955 506 454-S 221-8 566 508-7 248-1 327 2939 143-4 387 347-8 169-7 447 401-8 .960 ,507 455-7 222-3 567 5096 24S6 32 S 2948 388 348-7 170-1 448 402-7 196-4 508 456-6 222-7 568 5.0-5 2490 329 295-7 144-2 389 349-6 170-5 449 403-6 196-8 509 457-5 223-1 569 5114 249-4 330 2966 144-7 390 _3_5o-5 171-0 4.50 404-5 197-3 510 458-4 ^231 570 5.2-3 249-9 33T 297-S 145-1 391 35' 4 171-4 451 405-4 197-7 511 459-3 224-0 571 5.3-2 2503 332 298-4 145-6 392 3523 .718 452 406-3 19S-. 512 460-2 224-4 572 5'4-. 250-S 333 299-.> 146-0 393 353-2 172-3 453 407-2 19S-6 513 461-1 224-9 573 5.5-0 251-2 334 300-2 1464 394 3541 1727 454 408- 1 1990 514 462-0 225-3 574 5.5-9 251-6 335 301-1 146-9 395 355-0 173-2 455 409-0 199-5 515 462-9 225-8 575 5.6-8 252-1 336 3020 '47-3 396 3559 173-6 456 4099 199-9 516 463-8 226-2 576 5.7-7 252-5 337 302-9 147-7 397 356-8 174-0 457 410-8 200-3 517 464-7 226-6 577 5. 86 252-9 338 3°3^ 148-2 398 357-7 1745 458 411-7 200-8 518 465-6 227-1 57S 5.9-5 253-4 339 304-7 148-6 399 358-6 174-9 459 412-6 201-2 519 466-5 227-5 579 520-4 253-8 340 305-6 149-0 400 359-5 175-4 460 A13LS_ 201-7 520 467-4 2280 580 521-3 254-3 .•41 306-5 I49-5 401 360-4 175-8 461 414-4 202 1 521 468-3 22S-4 5S1 5222 254-7 342 3074 149-9 402 361-3 1762 462 415-2 202-5 522 4692 2288 582 523-. 255-1 343 308-3 150-4 403 3622 1767 46.-1 416-1 2030 523 470-1 2293 583 524-0 25S6 344 309-2 1508 404 3631 177-1 464 417-0 203-4 524 47.-0 2297 584 524-9 256-0 345 3101 151-2 405 364-0 1775 465 417-9 2038 525 47. -9 230-1 585 525-S 256-4 :!46 311-0 1517 406 364-9 17S-0 466 4.8-8 204-3 526 472-8 230-6 586 5267 256-9 347 311-9 1521 407 365-8 178-4 467 419-7 204-7 527 473-7 231-0 587 527-6 257,3 348 312-8 1526 408 366-7 178-9 468 420-6 205-2 528 474-6 23.-5 588 528-S 257-8 349 3'37 '530 409 367-6 179-3 469 421-5 205-6 529 475-5 231-9 589 529-4 258-2 350 35 r 3 '4-6 3>5-5 JJ34 153-9 410 411 J6S:£ 369-4 1797 180-2 470 47 r 422-4 423-3 206-0 206-5 530 531 476-4 477-3 2323 2328 590 591 530-3 531-2 2586 259. 352 3»64 '543 412 370-3 180-6 472 424-2 206-9 532 478-2 233-2 592 532-1 2595 353 3>7-3 154-7 413 371-2 181-1 473 425-. 207-3 533 479-1 233-6 593 5.33-0 2599 354 3182 155-2 414 372-1 181-5 474 426-0 2078 .534 480-0 234-. 594 533 9 260-4 355 3'9-" .556 415 373-0 iSrq 475 426-9 208-2 535 480-9 2345 .595 534-8 2608 356 3200 156-1 416 373-9 182-4 476 427-8 208-7 536 481-8 2350 596 535-7 261 3 357 320-9 1565 417 374-8 1S2-8 477 428-7 2091 537 4827 235-4 597 5366 2617 358 321-8 156-9 418 375-7 183-2 478 429-6 2095 538 4836 235-s 598 537-5 262-1 35'i 322-7 157-4 419 376-6 .83-7 479 430-5 2100 539 484-5 2363 599 538-4 2620 ■■■•'" 3236 .578 I). I.at. 420 377-5 184-1 480 O^st. 43.4 210-4 1). Lat 540 Dist. 485-3 236-7 D. Lat, 600 Dist. 539-3 263-0 I). I.Mt. Di.t; ').., Dcp. D. L.it. Dep. Dep. Dep. 04" 41, ic- 1 484 TABLE 1 TKAVERSE TABLE TO DEGREES 27° Ih 48"> "j Dist D.Lat Dep. Dist D.Lat Dep. Dist D.Lat Dep. Dist.JD.Lat. Dep. Di»t.JD.Lat.| Dep. | 1 0-9 0-5 61 54-4 27-7 TTT 107-8 54*9 181 1 161-3 82-2 241 214-7 109-4 2 1-8 0-9 62 55'2 28-1 122 I08-7 55-4 182, 162-2 82-6 242 215-6 109-9 3 2-7 '■4 63 56-1 28-6 123 109-6 55-8 183 163-1 83-1 243 216-51,10-3 4 3-6 1-8 64 S7-0 29-1 124 IIO-5 56-3 184 163-9 83-5 244 217-4, 110-8 6 4-5 2-3 65 57-9 29-5 1-25 56-7 185 164- 8 S4-0 245 218-3 111-2 6 5-3 2'7 66 58-S 30-0 126 112-3 57-2 180 165-7 84-4 246 219-2 111-7 7 6-z 3-1 67 59-7 30-4 127 57-7 187 i66-6 84-9 247 112-1 8 7'1 3-6 68 6o-6 30-9 128 1 14-0 58-1 188 167-5 85-4 248 22I-0 112-6 9 8-0 4*1 69 61-5 3i'3 129 114-9 58-6 189 168-4 85-8 249 221-9 113-0 10 _S^ 4-5 70 62-4 ±':L 130 115-8 59-0 190 1 ,69-3 86-3 250 222-8 ,13-5 11 9-8 5-0 71 63-3 32-2 TsT II6-7 59-5 191 170-2 86-7 251 223-6 114-0 12 IO-7 5-4 72 64-2 32-7 132 117-6 59-9 192 171-1 87-2 252 224-5 114-4 13 I. -6 5-9 73 65-0 33-I 133 118-5 6o-4 193 172-C 87-6 253 225-4 114-9 14 I2-S 6-4 74 65-9 33-6 134 119-4 60-8 194 172-9 88-1 254 226-3 115-3 15 '34 6-8 75 66-8 34-0 135 120-3 61-3 195 173-7 88-5 255 II5-8 16 •4-3 7-3 76 67-7 34-5 136 121-2 61-7 196 174-6 89-0 256 228-1 116-2 17 I5-I 7-7 77 68-6 35-0 137 I22-I 62-2 197 175-S 89-4 257 229-0 'ii6-7| Hi i6-o 8-2 78 69-5 35-4 138 123-0 62-7 198 176-4 89-9 258 229-9 117-1 19 ,6-9 8-6 79 70-4 35-9 139 .23-8 63-1 199 177-3 90-3 259 230-8 117-6 20 I7-8 9-1 80 71-3 36.3 140 124-7 63-6 200 178-2 90-8 260 231-7 118-0 IT i8'7 9-5 81 72-2 36-8 141 125-6 64-0 201 179-1 91-3 261 232-6 118-5 22 19-6 lo-o 82 73-1 37'2 142 126-5 64-5 202 i8o-o 91-7 262 233-4 118-9 23 20-5 10-4 83 74'o 37-7 143 127-4 64-9 203 180-9 92-2 263 234-3 1 19-4 24 21-4 IO-9 84 74-8 38-1 144 128-3 65-4 204 181-8 92-6 264 235-2 119-9 25 22-3 II-3 85 75-7 38-6 145 129-2 65-8 205 182-7 93-1 265 236-1 120-3 26 23-2 11-8 86 76-6 39-0 140 130-1 66-3 200 183-5 93-5 266 237-0 120-8 27 24-1 12-3 87 77"5 39-5 147 131-0 66-7 207 184-4 94-0 267 237-9 121-2 28 24-9 12-7 88 78-4 40-0 148 131-9 67-2 208 '85-3 94-4 268 238-8 121-7 2!> 258 13-2 89 79-3 40-4 149 132-8 67-6 209 186-2 94-9 209 239-7 30 26-7 13-6 90 8o-2 40-9 ISO 133-7 68-1 210 187-1 95-3 270 2406 122-6 -JT TTF 14-1 91 8i-i 41-3 -m 134-5 68-6 2U I88-0 95-8 27r 241-5 I23-0 32 28-5 I4'5 92 82-0 41-8 152 '35-4 690 212 188-9 96-2 272 242-4 123-5 33 29-4 15-0 93 82-9 42-2 .36-3 69-5 213 189-S 96-7 273 243-2 123-9 34 30-3 I5'4 94 83-8 41'7 154 137-2 *r 214 190-7 97-2 274 244-1 124-4 35 31-2 15-9 95 84-6 43' I 155 138-, 215 .91-6 97-6 275 245-0 124-8 36 32-1 ,6-3 96 S5-3 43-6 156 139-0 70-8 216 192-5 98-1 276 125-3 37 33-0 i6-8 97 86-4 44-0 157 139-9 71-3 217 '93-3 98-5 277 246-8 125-8 38 33-9 17-3 98 87-3 44-5 158 140-8 71-7 218 194-2 99-0 278 147*7 126-2 39 34-7 17-7 99 44-9 159 I4i'7 72-2 219 195-1 99-4 279 24S-6 126-7 40 35-6 i8-2 100 89-1 45-4 160 142-6 72-6 220 196-0 99-9 280 249-5 127-1 TT 36-5 i8-6 loT 90-0 45"9 161 '43-5 73-1 221 196-9 100-3 281 250-4 12T-6 42 37-4 19-1 102 90-9 46-3 162 144-3 73-5 222 197-8 282 251-3 I2S-0 43 3S-3 ■9-5 103 91-8 46-8 163 145-2 74-0 223 198-7 101-2 283 252-2 128-5 44 39-=' 20-0 104 92-7 47-2 164 146-1 74-5 224 199-6 101-7 284 253-0 128-9 43 40-I 20-4 105 93-6 47-7 165 147-0 74-9 225 200-5 102-1 285 253-9 129-4 4(i 41-0 20-9 106 94-4 48-1 166 •47-9 75-4 225 20I-4 102-6 286 254-8 129-8 47 4'-9 21-3 107 95*3 48-6 167 .48-8 75-8 227 103-1 287 255-7 130-3 48 1 42-S 21-8 108 96-2 1 49-0 108 149-7 76-3 228 203-1 103-5 288 256-6 130-7 49 143-7 22-2 109 97-1 i49-5 169 150-6 76-7 229 204-0 104-0 289 257-5 131-2 50 i 44-6 22-7 no 98-0 I 49-9 170 151-5 77-2 230 204-9 jo+-4_ 290 25S-4 61 45-4 = 3-2 III 1 98-9 50-4 171 152-4 77-6 231 205-8 , 104-9 291 259-3 1321 52 46-3 23-6 112 99-8 50-8 172 153-3 78-1 232 206-7 i 'OS'S 292 260-2 .32-6 53 47-2 24-1 113 100-7 51-3 173 154-1 78-5 233 207-6 105-8 293 261- 1 133-0 64 48-1 24-5 114 101-6 5. -8 174 155-0 79-0 234 208-5 1 '°6-2 294 262-0 133-5 6fi 49-0 25-0 115 102-5 52-2 175 '55-9 79-4 235 209-4 ■<>6-7 295 262-8 133-9 P« 49-9 -5-4 116 103 4 170 156S 79-9 236 210-3 I 'O7-1 296 263-7 '34-4 67 25-9 117 104-2 I 53M 177 157-7 80-4 237 211-2 107-6 297 264-6 134-8 58 51-7 26-3 118 ,05-1 53-6 178 158-6 8o-8 238 2I2-I 108-0 298 265-5 135-3 59 52-6 26-8 119 106-0 54-0 179 159-5 81-3 239 213-0 .oS-5 299 266-4 •35-7 60 53-5 27'2 120 106-9 ,' 54-5 180 160-4 8i'7 240 213-8 i09'o 300 267-3 .36-2 Dist Dep. D.Lai Di.t| Dep. JD.Lat DisU Dep. D. Lat. Dist. Dep. JD. L«t. Dist. Dep. D. Lat. 63" 41' li.'"' 1 485 TRAVEUSE TAIiLE TO DEGKEES | 27° Ih 48» 1 Dist Id. Lat 1 Dep. Dist. D. LatJ Dop. Dist D.Lat j Dep. Dist D.Lat.l Dep. Dist. D.Lat Dep. 301 ' 268-2 j '36-7 361 ] 321-7; 163-9 421 375-1 ,191-1 481 428-6 1 218-3 541 482-0 245-6 302 269-1 ' 137 1 362 3225 1644 422 376-0 191-6 482 429-4:2188 542 482-9 2461 303 2700 1376 363 323-4 164 8 423 376-9 : 192-0 483 -130-3 ' 219-2 543 4838 246-5 304 2709 ■ 380 364 1 324 3 165 3 424 3778 192-5 484 431 2 219-7 544 484-7 2470 305 27 IS ■38-5 363 325-2 1657 425 3787 1930 483 432-1 220-1 345 4856 2474 306' 2727 ■38 9 366 ' 326-1 166-2 426 379-6 193-4 486 433 220-6 546 486-4 2479 307 2735 1394 367 327-0 166-6 4:;7 380-5 193-9 487 4339 221-1 547 487-3 248-4 308] 2744 139-8 368 3279.167-1 428 381-4 194-3 488 434-8 2215 548 488-2 2488 309 2753 140-3 369 3288:167-5 429 3S2-2 194-8 489 435-7 2220 549 4S9-1 2492 310 276-2 140-7 370 1 329-7 1680 430 3831 i95-2 490 4366 2224 550 4900 2497 311 277-1 141-2 3711 330-6"! 168-4 431 384-0 195-7 491 437-5 222-9 53 r 490-9 250-1 312 27S0 1417 372 331-5 '168-9 432 3849 1 96- 1 492 438-3 223-3 552 491-8 2506 313 3789 142- 1 373; 332-3 169-3 433 385-8 1966 493 439-2 223-8 353 4927 251-0 314 279-S 1426 374 1 333-2 1698 434 3S6-7 1970 494 440-1 224-2 554 4936 251-5 315 2S0-7 143-0 373 334 1 , 1703 435 387-6 1975 495 4410 2247 555 4945 2520 316 2816 143-5 376; 335-0 ■ 170-7 436 388-5 197-9 496 441-9 225-2 556 495 4 252-4 317 2S2-5 143-9 377 1 335-9 171-2 437 3894 198-4 497 442-8 2256 557 4963 2529 318 2^y3 144-4 378 33U-8 171-6 438 3903 1989 498 443-7 226-1 558 4972 253-3 319 284-2 144-8 379 3377 172-I 439 391-2 1993 499 444-6 2265 659 498-1 2538 320 2S5-1 J45-3 380 3386 1725 440 3920 199^8 500 4455 2270 560 4990 254-2 321 2860 145-7 381 339-5 1730 441 3929 2002 501 446-4 2^75 561 499-8 2547 322 286-9 140-2 382 340-4 173-4 442 393-8 200-7 502 447-3 2279 562 5007 255-1 323 287-8 146-6 383 341-3 173-9 443 394-7 201-1 503 448-2 22S-4 563 501-6 2556 324 288-7 1471 384 3421 174-3 444 3956 2016 304 449-0 228-8 564 502-5 2560 325 1 289-6 147-6 3SS 343-0 174-S 445 396-5 2020 505 449 9 2293 565 503-4 256-5 326 1 290-5 1480 386 343 9 175-2 446 397-4 202-5 506 450S 229-8 566 504-3 2570 327 291-4 148-5 387 344-8 175-7 447 398-3 2029 507 4517 2302 567 5052 2574 328 292-3 148-9 388 345-7; 176-2 448 399-2 2034 508 4526 2306 568 506-1 2579 329 293-2 149-4 389 346-6 176-6 449 400-1 203-8 509 453-5; 231-0 569 5070 258-3 330 294-0 _149-8 390 347-5 i 177-1 450 401-0 204-3 510 -454-4, 23i:5_ 570 5079 25S8 33r 294-9 150-3 391 34S-4 177-5 451 401-8 204-7 511 455-3 1 231-9 571 508-7 259-2 332 295-8 1507 392 349-3 17S0 452 402-7 205-2 512 456-2 232-4 372 5096 2597 333 296-7 151-2 393 3502 178-4 453 403-6 2057 513 457-1 2329 573 510-5 200-1 334 297-6 151-6 394 351-1 178-9 454 404-5 206-1 514 458-0 1 233-3 574 51 1-4 2606 335 2985 1 52- 1 393 3520 179-3 435 4054 206-6 515 458-8 233-8 575 5«2-3 261-1 336 299-4 152-5 396; 3528 179-8 436 406-3 207-0 516 459-7 1 2342 576 513-2 261-5 337 300-3 153-0 397 1 353-7 l8o-2 4>7 407-2 207-5 517 460 6 1 2347 577 514-1 262-0 338 301-2 153-S 398 1 3546 180-7 438 40S1 207-9 518 461-5 2352 578 515-0 262-4 339; 3021 153-9 399 355-5 181-2 459 4090 208-4 519 462-4 '2357 379 5159 262-9 340 3029 1544 1548 4U0 401 356-4 181-6 357-3 182-1 460 461 409-9 410-8 2088 209-3 520 521 463-3 464-2 236-1 580 516-8 517-7 263-4 ^6^8" 341 3038 2366 381 342 304-7 1553 402 358-2 1S2-5 462 41. -6 2098 465-1 237-0 382 518-5 264-3 343 3056 155-7 403 1 359-1 183-0 463 4125 2102 523 466-0 237-5 583 5194 264-7 344 306-5 156-2 404 3600 183-4 464 413-4 2107 324 466-9 237-9 584 520-3 265-2 343 307-4 156-6 405 360 9 183-9 465 4'4-3 2H-I 325 467-8 • 23S-4 .385 S2I-2 265-6 346 30S-3 157-1 406 361-8 184-3 466 415-2 2116 526 468-7 ' 2388 586 5221 2660 347 3092 157-5 407 362-6 I S4-S 467 4161 2120 327 4695 2393 587 5230 266-5 348 3101 158-0 408 363 5 iSs-2 468 417-0 212-5 328 4704 239 7 588 523-9 267-0 349 3U-0 158-5 409 I 364-4 1857 469 4179 2129 3:; 9 471-3 2402 589 524-8 267-4 350 351 3"9 15s 9 1594 410 [365-3 41 1 ; 360-2 186-1 i86-6 4W 418-8 4197 2134 2I3S 330 .031 472-2 2406 473-1 2411 590 591 525-7 526-6 2679 268"3 312-7 352 3'3-6 159-8 412 1 367 1 1871 472 4206 214-3 332 474-0 241-5 592 527-5 2688 353 3M-5 160-3 413 368-0 187-5 473 421-4 2147 333 474>) 2420 593 528-4 269-2 354 315-4 160-7 414 1 36S-9 188-0 474 422-3 215-2 334 4758 2424 594 5293 2697 355 S^O-i 161-2 415 3698 188-4 473 423-2 2157 335 476-7 : 2429 595 530-1 270-1 35(i 3 ■7-2 161-6 416, 370-7 188-9 476 424-1 2161 536 477 6 243 4 596 531-0 270-6 357 3>8-i l(-.2-I 417 371-6 189-3 477 425-0 216-6 537 478-4 243-8 597 531-9 2711 358 3' 9-0 162-5 418 372-4 1S9S 478 425-9 217-0 538 479-3 244-3 593 5328 271-5 359 3>99 163-0 419 1 373-3 190-2 479 426-8 2175 539 4802 2447 399 5337 2720 360 320S 103-4 420 j 374 2 190-7 480 4277 217-9 510 481-1 245-2 !!' 5346 272-4 D.Lat Dist. D.p. [). Lai Dist.J Dep. D. Eat. ^ Dep. D.Lat. Dijt. ^>-I-' Dist. Dep. m" . 4'> r^'" 486 TABLE 1 TRAVERSE TABLE TO DEGREES 28° l* 52"' Di3t[D.Lat Dep. D.t. D.Lat. Dep^ Dist. D.Lat. Dep. Dist. D. Lat. Dep. Dist D. Lat. Dep. I 1 0-9 0-5 -^7 53-9 28-6 121 106-8 56-8 181 .59-8 85-0 241 212-8 .13-1 2 iS 0-9 C2 54-7 29-1 122 107-7 57-3 182 160-7 85-4 242 213-7 113-6 S 2-6 1'4 C3 55-6 29-6 1-23 108-6 577 183 i6i-6 85-9 243 214-6 114- 1 4 3-5 1-9 04 56-5 30-0 1-24 109-5 58-2 184 162-5 86-4 244 215-4 .14-6 5 4'4 2'3 65 57-4 30-5 125 110-4 58-7 186 163-3 86-9 245 2,6-3 115-0 B S'3 2-8 66 58-3 31-0 120 111-3 59-2 180 ,64-2 87-3 240 217-2 115-5 7 6-2 3-3 67 59-2 31-5 127 59-6 187 165-1 87-8 247 218-1 116-0 a yi 3-8 68 6o-o 31-9 128 113-0 6o-i 188 166-0 8S-3 248 1 16-4 9 79 4"^ 69 6o-9 32-4 129 6o-6 189 166-9 88-7 249 219-9 116-9 10 8-8 4-7 70 6i-8 32-9 33-3 130 114-8 610 190 167-S 89-2 250 220-7 117-4 11 97 -■■, 71 62-7 131 115-7 6,-5 191 16S-6 89-7 Y5T 221-6 117-8 12 10-6 5-6 72 63-6 33-8 132 116-5 62-0 192 169-5 90-1 252 222-5 118-3 13 "'5 6-1 73 64-5 34-3 133 117-4 62-4 193 170-4 90-6 253 223-4 118-S 14 '-'4 6-6 74 65-3 347 134 62-9 194 171-3 91-1 254 224-3 119-2 15 13-2 7-0 75 66-2 35-2 135 1192 63-4 195 172-2 91-5 255 225-2 119-7 16 14-1 7-5 76 67-1 357 136 63-8 196 173-1 92-0 256 226-0 120-2 17 15-0 77 68-0 36-1 137 I2I-0 64-3 197 ■73-9 92-5 257 226-9 120-7 18 '59 ^•5 78 68-9 36-6 138 121-8 64-8 198 ■74-8 93-° 258 227-8 I2I-1 19 i6-8 8-9 79 69-8 37'J 139 122-7 65-3 199 175-7 93-4 259 121-6 20 17-7 9 4 80 70-6 37-6 140 ,23-6 65-7 200 176-6 93-9 200 229-6 122-1 21 i8-5 " 99 ~Hl 71-5 38-0 141 124-5 66-2 201 177-5 94-4 261 230-4 122-5 22 19-4 IO-3 82 38-5 142 125-4 66-7 202 17S-4 94-8 202 231-3 123-0 23 20-3 83 73-3 39-0 143 126-3 67-1 203 179-2 95-3 203 232-2 123-5 24 2f2 II-3 84 74-2 39-4 144 127-1 67-6 204 iSo-i 95-8 264 ^33;i '23-9 2.-. 221 85 75-1 39-9 145 128-0 68-1 205 1810 96-2 265 124-4 2fi 23-0 12-2 86 75-9 40-4 146 .2S-9 68-5 200 iSi-9 96-7 266 234-9 124-9 27 12-7 87 76-8 40-8 147 129-8 69-0 207 182-8 97-2 267 235-7 J25;3 2li 24-7 88 77-7 41-3 148 130-7 69-5 208 183-7 97-7 208 236-6 29 25-6 13-6 89 78-6 41-8 149 ,31-6 70-0 200 1S4-5 98-, 269 237-5 J26-3 30 14-1 90 79-5 150 132-4 70-4 210 185-4 9S-6 270 238-4 126-8 "sr 27-4 14-6 91 8o-3 42-7 151 133-3 709 211 186-3 99-1 27r 239-3 127-2 32 92 8i-2 43-2 152 134-2 71-4 212 187-2 99-5 272 240-2 127-7 33 29-1 i5'5 93 82-1 437 153 135-1 71-8 213 188-1 loo-o 273 241-0 128-2 34 30-0 160 94 83-0 44-1 154 136-0 72-3 214 189-0 100-5 '274 241-9 128-6 35 30-9 i6-4 98 83-9 44-6 155 136-9 72-8 215 189-8 100-9 275 242-S 129-1 30 31-S :6-9 90 84-8 45-1 156 »37-7 73-1 216 190-7 101-4 270 243-7 129-6 37 31-7 ■7'4 97 85-6 45-5 157 .38-6 737 217 .91-6 101-9 277 244-6 130-0 38 33-6 17-8 98 46-0 158 139-5 218 192-5 102-3 278 245-5 130-5 39 34-4 iS-3 99 87*4 +6-5 159 140-4 74-6 219 193-4 102-8 279 246-3 131-0 40 35-3 iS-8 100 88-3 46-9 160 141-3 75-1 220 _I9£_2_ 103-3 280 247-2 131-5 41 36-2 19-2 loT 89-2 47-4 TeT 142-2 75-6 22r I95-I 103-8 281 248-1 131-9 42 37-1 19-7 102 90-1 47-9 162 143-0 76-1 222 196-0 104-2 282 249-0 132-4 43 38-0 103 90-9 48-4 163 143-9 76-5 223 196-9 104-7 283 249-9 132-9 44 38-8 20-7 104 91-8 48-8 164 144-8 77-0 224 197-8 105-2 284 250-8 133-3 45 39-7 105 92-7 49-3 105 1457 77-5 225 198-7 105-6 285 251-6 133-8 4C 40-6 21-6 106 93-6 49-8 160 146-6 77-9 220 '99-5 106-1 286 252-5 134-3 47 41-5 22-1 107 94-5 50-2 167 '47-5 78-4 227 200-4 106-6 287 253-4 '34-7 48 42-4 22-5 108 95-4 50-7 168 148-3 78-9 228 201-3 107-0 288 254-3 135-2 49 43-3 109 96-2 51-2 169 149-2 79-3 229 201-2 107-5 289 255-2 J35;7 50 44-1 23-5 110 97-1 qi-6 170 150-1 79-8 230 203-1 loS-o 290 256-. TT 45-0 23-9 111 98-0 52-1 171 1510 80-3 231 204-0 108-4 29r 256-9 136-6 52 45"9 1^44 112 98-9 52-6 172 151-9 80-7 232 204-8 108-9 292 257-8 137-1 53 468 1 24-9 113 99-8 53-1 173 152-7 Sl-2 233 205-7 109-4 293 258-7 137-6 54 47-7 U5-4 114 1007 53-5 174 .53-6 81-7 234 206-6 109-9 294 259-6 138-0 55 48-6 25-8 115 IOI-5 54-0 175 154-5 82-2 235 207-5 110-3 295 260-5 138-5 5(; 49'4 26-3 116 102-4 54-5 170 ■55-4 82-6 230 208-4 iio-S 296 261-3 139-0 57 50-3 26-8 117 103-3 54-9 177 156-3 83-1 237 209-3 111-3 297 262-2 139-4 5H 51-2 27-2 118 104-2 55-4 173 157-2 83-6 238 1II-7 298 263-1 139-9 59 52-1 27-7 119 105-1 559 179 .58-0 S4-O 239 2M-0 112-2 299 264-0 140-4 60 53-0 2S-2 120 106-0 56-3 180 158-9 84-5 240 211-9 112-7 300 264-9 140-8 Dist Dep. D.Lat Uist Dep. D.Lat Dist Dep. D.U.t. Dist Dep. D. Lat. Dist Dep. V. I-at. 62° 4 ^■^ TABLE 1 487 TUAVERSE TABLE TO DEGREES 28° l'>52'" 1 Dist.b. I,at.( Dep. Dist D.Lat iDep. DistJo. Lat.' Dep. JDist.lD. Lat Dep. Dist D.Lat Dep. 301 2657 •4 '3 361 318-7 169-5 421 371-7! 197-7 481 4247 225-S 541 477-7 2540 302 266-6 141-8 362 319-6 1700 422 372-6 198-1 482 I 425 6 226-3 542 4786 254-5 3U3 207-5 1423 363 320-5 170-4 423 373-5 1 198-6 483 1 426-5 226-8 543 479-4 2550 •■•ah 26S-4 1427 364 321-4 1 170-9 424 374-3! 199-1 484 427-4 227-3 544 4803 255-5 305 269-3 1432 365 3222 171-4 425 375-2 199-5 485 4283 2277 545 4S1 I 255-9 306 2702 1437 366 323-1 171-8 426 376-1 200-0 486 429-2 228-2 540 4S2-0 256-4 307 2710 144-1 367 3240 172-3 427 377-0 2005 487 430-1 22S-6 547 482-9 2569 308 271-9 144-6 368 324-9 1728 428 377-9 200-9 488 430-9 229-1 548 483-8 257-3 309 272-8 145 I 369 325-8 173-2 429 37S-8 201-4 489 431-8 2296 549 484-7 2578 aio 2737 274-6 145-5 1460 370 371 326-7 1737 430 379-6; 201-9 490 432-6 2300 230-5 550 551 4S5-6 486-5 m 327-5 174-2 431 380-5 1 202-3 491 4335 312 27SS 1465 372 32S4 174-6 432 3S1-4' 2028 492 434-4 231-0 552 487-4 259-1 313 276-3 146-9 373 329-3 175-1 433 382-3 203-3 493 435-3 231-4 553 259-6 314 277-2 147-4 374 330-2 175-6 434 383-2 2038 494 436-2 231-9 5.54 489-2 2601 311 278-1 1479 375 331-1 176-1 435 384-1 204-2 495 437-1 232-4 555 490-1 2606 310 j 279-0 14S4 376 332-0 176-5 430 384-9 204-7 496 4379 2329 556 490-9 261-0 317 1 2799 148-8 377 1770 ■137 3858 205-2 497 438-8 233-4 557 I 491-8 26,-s 31S 2So7i 149-3 378 3337 177-5 438 386-7 205-6 498 439-7 2338 558 492-7 262-0 319 2Sr6; 1498 379 334-6 177-9 439 387-6 206-1 499 440-6 234-3 559 493-5 2625 320 282-5- 150-2 380 381 335-5 178-4 178-9 440 441 388-5 : 206-6 3S9-4 1 207-0 500 501 i4lj_ 442-3 2352 560 361 494-4 2629 ■ ijl 283-4: 150-7 3364 495-3 263-4 32-i 284-3, 15I-2 382 3373 179-3 442 390-21 207-5 502 4432 2356 502 496-2 263-8 323 285-2 I5.-6 383 338-1 .79-8 443 391 1 1 2080 503 444-1 2361 563 497- 1 264-3 324 286-0 152-1 384 3390 jSo-3 444 392-0. 20S-4 504 445-0 236-6 564 49S-0 264-7 325 286-9 1526 385 3399 445 392-9 1 208 9 505 •145-9 237-1 565 498-9 265-2 326 287-8 •531 386 3408 1812 446 393-8 209-4 506 446-8 237-S 306 499-8 265-7 327 2887 tsys 3»7 341-7 iSi-7 447 394-6 1 209-9 507 447-6 238-0 367 500-7 2662 328 2S9-6 154-0 388 3426 182-2 448 395-5 ^ 2IO-3 508 448-5 238-5 568 5016 266-6 329 2905 154-5 389 343-4 182-6 449 396-4 1 210-8 509 449-4 2390 569 502-4 267-1 330 331 291-3 292-2 154-9 390 397 344-3 183-1 430 397-3 1 211-3 39S-2I 21 17 510 511 450-3 451-2 239-4 570 .->71 503-3 267-6 268-0 155-4 345-2 183-6 451 239-9 504-2 332 2931 "55 9 392 346-1 1840 432 399 I , 212-2 312 452-1 240-4 572 505-1 26S-5 333 2940 156-3 393 3470 184-5 453 399-9 212-7 513 4529 2408 573 50S-9 2690 334 294-9 156-8 394 347-9 185-0 454 4008 2 1 3- 1 514 453-8 241-3 574 506-8 2694 335 295-8 157-3 395 3487 185-4 455 4017; 213-6 515 454-7 241-8 575 507-7 269-9 336 2966 157-7 396 349-6 185-9 456 402-6 2 1 4- 1 510 455-6 242-2 576 5086 270-4 337 297-S 158-2 397 350s 186-4 457 403-5 214-6 517 456-4 2427 577 509-4 2709 338 298-4 .5S7 39S 351-4 186-9 458 404-4 215-0 518 457-3 243-2 578 510-3 271-3 339 2993 159-2 399 352-3 1873 459 405-2, 215-5 519 458-2 243-7 579 Sll-2 2718 340 joo;2 159-6 400 353-1 354-0 187-8 460 401 _4o6-l 216-0 4070" 216-4 520 521 4591 244-1 .580 512-1 _272-3 272-7 341 30101 1 60- 1 401 188-3 460-0 244-6 581 513-0 342 301-9 160-6 ■102 354 9 188-7 462 4079 216-9 522 460-9! 245-01 582 513-9 273-2 343 3028 i6io 403 3:558 189-2 403 4088' 217-4 523 461-8 245-5 1 583 514-8 2737 344 3037 161 5 404 356-7 189-7 404 4097 217-8 524 4627 2460 584 5157 274-2 345 304-6 1620 405 357-6 1 90- 1 405 410-5, 21S-3 525 463-5 246-5 585 516-5 2747 346 305s 162-4 406 358-4 1906 406 411-4 218-8 526 464-4 246-9 586 517-4 275 1 347 306-4 1 162-9 407 3593 191 I 407 412-3 219-2 527 i 465-3 247-4 587 518-3 275-5 348 307-2 163-4 4I'8 360-2 191-5 468 413-2 219-7 523 466-2 247-9 588 519-2 276-0 349 308-1 163-S 409 361-1 1920 469 414-I 220-2 529 467-1 248-3 589 520-1 276-5 350 351 309-0 3099 164-3 164-8 410 3620 192-5 470' 415-0 2207 530 468-0 248-8 590 521-0 277-0 411 3629 193-0 ln\ 4.5^8 i"22.-r 531 468-9 249-3 591 '521"^ 277-4 352 310-8 165-3 412 363-7 193-4 472' 416-71 221 6 532 469-8 249-8 .592 522-6 277-9 353 31 '7 165-7 413 364-6 1939 473 417-6 2221 533 470-7 250-2 593 5235 278-4 354 312-5 166-2 414 365-5 194-4 474, 4185 2225 534 471-5 2507 594 5244 2788 355 3'3-4 166-7 413 366-4 194-8 473 419-4 223-0 535 472-4 251-1 395 525-3 2793 356' 314-3 1671 416 367-3 195-3 476 420-3! 223-5 536 473-3 ^.516 590 526-2 279-8 •157 1 315-2 1676 417 3682 195-8 477 421-1 223 9 537 474-2 252-11 ,597 527 1 2803 358 316-I 168 I 418 3690 196-2 478 4220 224-4 338 475-1 2526 598 528-0 2S0-8 359! 3169 168-5 419 369-9 196-7 479 4229 224-9 539 ' 476-0 253-1 599 528-9 2Sr-3 -ifiuj 317-8 1690 420 3708 197-2 480 423 8 1 225-3 540 476-8 2536 600 5298 2817 ^.;rD.p: I). I.ai. ZQ Dep. D. Lat. Dist Dep. D. Lilt, Di.-t.| Dep. D. Lat Dist. Dep. D. Lat. 02° 4'' a-" 1 TRAVKRSE TABLE TO DEOREES 29° J- SG"- Dist. D.Lat Dep. Dist. D.Lat.|Dep. DisLD.Lut. Dep. Disi.D.Dit. Dep. Dist.'o. L-dt. Dep. '~ o'9 o'5 61 53-4 29-6 121] 105-8 58-7 181 1.58-3 S7-8 241 1 210-8 II6-S 2 1-7 62 54-2 30-1 122 1 106-7 59-1 182 159-2 88-2 242 1 211-7 117-3 3 2-6 '■5 63 55'' 30-5 123] 107-6 59-6 183 160-1 88-7 243: 212-5 117-S 4 3"5 1-9 64 56-0 31-0 124 108-5 6o-i 184 160-9 •244 1213-4 118-3 5 4-4 2-4 65 56-9 31-5 1-25 109-3 60-6 185 16, -8 89-7 ■245 214-3 118-8 e, 5-2 2-9 66 577 32-0 126 1 10-2 6i-i 186 162-7 90-2 •246 215-2 119-3 7 6-1 3-4 fi7 58-6 32-5 I27i lu-i 6i-6 187 163-6 90-7 •247 2,60 119-7 8 ' TO 3-9 68 59-5 33-0 128 [..2-0 62-1 1118 164-4 91-1 248 : 216-9 •J 7-9 4'4 69 60-3 33-5 129 I 112-8 62-5 189 165-3 91-6 249 217-8 1207 10 S-7 4-S 70 6i-2 1 33-9 130 1 .13-7 63-0 190 166-2 92-, 2.-)0: 218-7 11 9-6 71 62-1 34-4 131 1 114-6 63-5 191 167-1 92-6 ■251 i 219-5 1217 IJ IO-5 72 63-0 34-9 132iii5'4 64-0 192 167-9 93-1 252 i 220-4 122-2 i:i 11-4 73 63-8 35-4 133 116-3 64-5 193 168-8 93-6 253 1 221-3 1227 14 74 647 35-9 134 1 17-2 65-0 194 .69-7 94-1 254 1 222-2 15 I3-I 75 65-6 36-4 135 1 118-1 65-4 195 170-6 94-5 2.55 223-0 123-6 k; 14-0 7fi 66-5 36-8 136, 118-9 65-9 196 171-4 95-0 256 223-9 124- I 17 14-9 77 67-3 37-3 137 119-8 66-4 197 172-3 95-5 ■257I22+-8 124-6 18 15-7 78 68-2 37-8 138 120-7 66-9 198 173-2 96-0 ■258 225-. 125-. 19 i6-6 9-2 79 69-1 38-3 139 12,-6 67-4 199 174-0 96-5 269 226-5 125-6 20 1 ITS 9-7 80 70-0 38-8 140 1 122-4 1 67-9 200 174-9 _ 97-0 260 227-4 1 126-, TT iS-4 IO-2 81 70-8 39-3 141 123-3 6S-4 201 175-S 97-4 26r 22S-3 126-5 22 19-2 107 82 717 39-8 142 1 124-2 6S-8 202 176-7 97-9 262 229-2 127-0 23 20-I I I -2 83 72-6 40-2 143 125-I 6Q-3 203 1 177-5 98-4 263 230-0 127-5 24 21-0 II-6 84 73-5 407 144 1 125-9 69-S 204 178-4, 98-9 264 230-Q 128-0 25 21-9 I2-I 85 74-3 41-2 145 126-8 70-3 205 179-3 99-4 265 231 -8 12S-5 26 227 12-6 86 75-2 417 14(i 127-7 70-S 206 1 80 -2 99-9 266 1 232-6 129-0 27 23-6 I3-I 87 76-1 42-2 147 12S-6 71-3 148 129-4 71-8 207 iSi-o 100-4 267^233-5 ,129-4 28 24-5 13-6 88 77-0 427 208 181 -9 :oo-8 268 234-4 129-9 29 25-4 I4-I 89 77-8, 43-1 149 130-3 72-2 209 1 182-8, 101-3 269 235-3 130-4 30 26-2 14-5 90 787! 43-6 150 131-21 72-7 210 183-7 |ioi -8 270 236-1 130-9 31 27-1 I5-0 91 79-6 , 44-1 151 132T 73-2 211 ! 184-5 102-3 271 237-0 131 -4 32 28-0 15-5 92 80-5 44-6 162 1132-9 73-7 212 185-4 102-8 272 237-9 131 -9 33 93 8i-3 45-1 153 i 1 33 -S 74-2 213 1S6-3 103-3 273 238-8 132-4 34 297 i6-s 94 82-2 45-6 154 134-7 74-7 214 187-2 103-7 274 239-6 132-S 35 30-6 17-0 95 83-1 46-1 165 135-6 75-1 215 iSS-q! 104-2 275 240-5 133-3 36 31-5 17-5 96 84-0 46-5 1061136-4 75-6 216 188-9 104-7 276 241-4 133-8 37 32-4 17-9 97 84-8 47-0 lo7 137-3 7'5-' 217 1S9-8 105-2 277 242-3 ■ 134-3 278 '243-1 ' 134-8 38 33-2 i8-4 98 857 47-5 15SI13S-2 76-6 218 190-7,105-7 39 34-1 1 i8'9 99 86-6 48-0 159 139-1 77-1 219 191 -5 106-2 •279,244-0 135-3 40 35-0 1 194 100 87-5 , 48-5 160 1139-91 77-6 220 192-4 106-7 280 1244-9 1357 41 35-9 19-9 101 88-3 49-0 101 140-8 78-1 221 193-3 107-1 281 245-8 ,36-2 42 367 20-4 102 89-2 49-5 162 141-7 78-5 222 194-2 ,07-6 282 246-6 136-7 43 37-6 20-8 103 90-1 499 163 ,42-6 79-0 223 195-0 108-1 283 ^47- 5 137-2 44 38-5 21-3 104 91-0 50-4 164 I43-4 79-5 224 195-9 108-6 284 248-4 137-7 45 39'4 21-8 105 91-8 50-9 165 144-3 225 196-8 109-1 285 249-3 138-2 46 40-2 2»-3 106 927 5i'4 166 145-2 80-5 220 197-7 I09-6 286 250-1 138-7 47 4I-. 22-8 107 93-6 51-9 167 .46-1 8i-o 227 198-5 287 251-0 139-1 48 42-0 *3'3 lOK 94' 5 52-4 168 146-9 81-4 228 199-4 IIO-5 288 251-9 .39-6 49 ' 41-9 23-8 109 95'3 52-8 169 147-8 81-9 229 200-3 III-O 289 252-8 140- 1 50 1 437 24-2 110 96-2 53'3 170 148-7 82 -4 -230 201-2 III-5 290 253-6 140-6 51 44-6 2A-1 ill 97-1 53-S 171 149-6 82-9 231 202-0 112-0 291 »54-5 141-1 52 45'5 25-2 112 54'3 172 150-4 83-4 232 202-9 II2-5 292 255-4 .4.-6 63 46-4 257 113 98-8 54-S 173 1 151-3 83-9 233 203-8 JI3-0 293 256-3 142-0 54 47*2 26-2 114 99-7 55-3 174 152-2 84-4 234 204-7 113-4 294 257-1 .42-5 55 48-1,267 115 I0O-6 55-8 176 153-1 84-s 235 205-5 113-9 298 258-0 143-0 56 ■ 49-0 27-1 116 ioi'5 56-2 176 153-9 85-3 23(; 206-4 1 14-4 296 258-9 H3-5 57 1 49'9 27-6 117 102-3 56-7 177 154-8 237 207-3 114-9 297 259-8 144-0 58 50-7 28-1 118 103-2 57'2 178 '55-7 S6-3 ■J.-i8 208-2 II5-4 298 260-6 '44-5 59 51-6 28-6 119 104- 1 577 179 ,56-6 S6-S 239 209-0 II5-9 299 26,-5 145-0 80 5^-5 29-1 120 105-0 58-2 180 157-4 87-3 240 209-9 ii6-4 300 262-4 '45-4 DiatJ Dep. D.La Dist Dep. iD.Lai Dist Dep. D.Lat Dist Dep. D. Lat. Dist. Dep. D.Lat 61^ 4" 4" j TUAVEHSE TABLE TO DEGREES 29" Ih 5G™ Uist. 301 D. Lat. 2632 Dep. DIst. D. Lat. Dep. 'Dist. D. Lat. Dep. Dist. D. Lat. Dep. Dist. D.L.t. Dep. 145-9 361" 3157 1750 421 368-2 204-1 481 420 7 1 233-2 541 473-2 262-3 302 264-1 146-4 362 316-6 175-5 422 3691 204-6 482 421-5 233-7 .542 474-0 262-S 303 2650 1469 363 3175 1760 423 369-9 205-1 483 422-4 234-2 543 474-9 263-2 304 265-9 147-4 364 318-3 1765 424 3708 205-6 484 423-3 2346 544 475-8 263-7 305 2667 1479 3r,5 319-2 177-0 425 371-7 206-0 485 424-2 235-1 545 476-6 2642 306 2676 148-4 366 320-1 1774 426 372-6 206-5 486 425-0 2356 .546 477-5 264-7 307 26S5 148-8 367 321-0 177-9 427 373-4 207-0 487 425-9 236-1 547 478-4 265-2 308 26q-4 149-3 368 3218 17S-4 428 374-3 207-5 488 426-S 2366 548 479-3 265-7 309 2702 149 S 369 322-7 178-9 429 375-2 489 427-7:237-1 549 4S0-1 266-2 310 271-1 150-3 370 _313_1 1794 430 376-1 3769 209-0" 490 491 _428 5_1 237-6 429-4 ' 238-0 550 551 481-0 48T9 2666 267-1 ITiT J72-O 150-S 371 324-5 179-9 431 312 272-9 i5'-3 372 325-3 180-4 432 377-8 209-4 492 4303:238-5 552 482-8 267-6 313 2737 151-7 373 326-2 1808 433 37S-7 209-9 493 4312 239-0 553 483-6 268-1 314 2746 152-2 374 327-1 1813 434 379-6 210-4 494 4320 239-5 554 484-5 268-6 315 275-5 152-7 375 52S-0 iSi-8 435 3S0-4 210-9 495 432 9 240 555 485-4 269-1 316 276-3 153-2 376 328-8 436 381-3 211-4 496 433 8 240 5 556 4S6-3 2695 317 277-2 153-7 377 3297 Is-s 437 382-2 2II-9 497 4347 2409 557 487-1 2700 318 27S1 154-2 378 330-6 183-3 438 383-1 498 4355 1 241-4 558 488-0 2705 319 279-0 1547 379 33 '-4 .83-7 439 3S3-9 212-8 499 436-4; 241-9 559 4889 2710 320 321 279-8 ~28o-7 1551 1556 38U 38! -SJ 1S4-2 TS47 440 441 3S48 385-7 213-3 213"8 500 501 437-3 242-4 438-2 242-9 560 561 489-S 271-5 2720 4906 3-22 281-6 1561 382 334-1 185-2 442 386-6 214-3 502 439-0 2434 562 491-5 2725 323 2S2-5 1566 383 334 9 185-7 443 3'*7-4 214-8 503 439-9 243-9 563 492-4 272-9 324 2833 157-1 384 335-8 1S6-2 444 388-3 215-3 504 4408 244-3 564 493-2 273-4 325 284-2 157-6 385 3367 186-7 445 389-2 215-7 505 441-6 2448 565 494-1 273-9 326 285-1 158-1 386 337-6 187-1 446 3900 506 442-5 , 245-3 566 495-0 274-4 327 286-0 1585 387 3384 1876 447 390-9 2I67 507 443 4 245-8 567 4959 4968 274-9 328 2S6-8 1590 388 339-3 1S8-1 448 3918 217-2 508 444-3 246-3 568 2754 329 287-7 159-S 389 340-2 1S86 449 392-7 217-7 509 445-2 , 246-8 569 497-7 275-9 330 331 288-6 1600 1605 390 391" 341. 3419 189-1 189-6 450 451 393-5 2182 2IS-7 510 446-1 1247-3 570 498-5 499-4 2763 276-S 289-5 394-4 447 247 8 -yiT 332 2903 161-0 392 3428 1900 452 395-3 2I9-I 512 447-8 1 248-2 572 5003 277-3 .•)33 2912 161-4 393 343-7 190-5 4.53 396-2 219-6 513 448-6|24S-7 573 501-1 277-8 334 292 I 1619 394 344-6 1910 454 397-0 220-1 514 449-5 249-2 574 502-0 278-3 335 293-0 1624 395 345-4 191-5 455 397-9 220-6 515 4504 249-7 575 502-9 27SS 336 293S 162-9 396 346-3 192-0 456 398-8 22 11 .')16 451 3 '2502 576 503-7 2792 337 294-7 1634 397 347-2 192-5 457 399-7 221-6 517 452-2 1 250-6 577 504-6 279-7 338 295-6 163-9 398 348-1 1930 458 400-5 222-0 518 4531:2511 578 505-5 280-2 339 296-5 1644 399 3489 193-4 459 401-4 222-5 519 453-9 251-6 579 506-4 2S0-7 340 34 r ^97-3. 298-2 1648 165-3 400 401 3498 350-7 1939 194-4 460 461 402-3 520 521 454-8 2521 252-6" 580 581 507-2 5081 403-2 223-5 455-6 281-7 342 299-1 1658 402 351-6 1949 462 404-0 224-0 522 456-5 ' 253-1 582 509-0 282-2 343 3000 166-3 403 352-4 ■95-4 463 4049 224-5 523 457-4 , 253-6 583 5°9-9 282-7 344 300-8 166S 404 353-3 "95 9 464 405-8 225-0 524 4583 254-0 584 510-7 283-2 345 301-7 167-3 405 354-2 196-3 465 406-7 225-4 525 459-11 254-5 585 511-6 2836 34G 302-6 .67-7 406 355-1 1968 466 407-S 225-9 526 460-0 ' 255-0 586 5125 284-1 347 303-5 1682 407 197-3 467 408-4 2264 527 460-9 ' 255-5 587 513-4 284-6 34S 304-3 1687 408 356-S 197-S 468 409-3 226-9 528 461 -8 256-0 588 5>4-3 285-0 349 3052 1692 409 3577 198-3 469 410-2 227-4 529 462-6 256-5 589 515-1 285-5 350 .isT JO0-, 307-0 1702 410 411 358-6 359-4 19S-S 199-3" 470 471 411-0 227-9 '228-3 530 531 463-5 256-9 464-4 : 257-4 590 591 5i6_o 516-9 2860 -286T 411-9 352 3o7-S> 1 707 412 3603 199 7 472 4128 22S-8 532 465-3 2579 592 517-7 287-0 353 308-7 171 I 413 361-2 473 413-7 229-3 533 466 1 ] 258-4 593 51S-6 2875 354 3096 171 6 414 362-1 2007 474 414-5 229-8 534 467-0 25S-9 594 519-5 28S-0 355 310-5 172 I 415 362-9 201-2 475 415-4 230-3 535 467-9 i 259-4 595 520-4 288-5 356 3"3 1726 416 363S 201-7 476 4>6-3 230 8 536 46S 8 1 259-9 596 521-2 288-9 357 5.22 17?. 417 364-7 202-2 477 417-2 231-3 537 469-6 260 3 597 522-1 2S9-4 358 , 3"3-i 1736 418 365-6 2027 478 4.8-0 231-7 538 470-5 i 2608 598 5230 2899 359 i 3'40 1740 419 366-4 203 I 479 418-9 232-2 539 471-4:261-3 599 523-9 2904 360 , 3'4-8 174-5 ■'^u 3673 2036 489 419-8 2327 540 4723 261-8 600 524-8 2909 Dist 'J'^l^ D.Lat. I)is.t JKp. D.L.,. Dist Dep. ,D.La, Disl Dep. U. Lat Dist "DepT l"-^ 61° 4" 4™ 1 TRAVERSE TABLE TO DEGREES 1 30° ai-O" 1 DisuJD.Lal| De].. Dist. D. Lilt. Dep Dis D.Lat Dep. Dis D.Lat Dep. Dis..!D.Ln..JDep.| 1 j 0-9 1 °-5 01 52-8 30-5 121 104-8 60-5 181 156-8 90-5 241 U0S-7 ,20 5 2 1 1-7 i I'O 02 53'7 31-0 122 105-7 61-0 182 157-6 91-0 •242 209-6 3 2-6 ■;s G3 54-6 3'-5 123 106-51 61-5 183, 158-5 91-5 243 210-4 ,21-5 4 . 3-S 64 55-4 32-0 1-24 107-4 62-0 184 ■59-3 92-0 244 211-3 5 ; 4-3 2-5 65 56-3 3--S 125 108-3 62-5 185 160-2 92-5 245 212-2 122-5 G S'i 3-0 66 57'- 33-0 12c 63-0 180 161-, 240 2130 123-0 7 6-1 3-5 f;7 58-0 33-5 127 63-5 187 i6i-9 93-5 247 213-9 123-5 8 6-9 4-0 68- 58-9 34-0 128 1 10-9 64-0 188 162-8 94-0 •248 2,4-8 124-0 9 7-S 4" 5 09 1 59-8 34-5 129 64-5 189 163-7 94-5 •249 2,5-6 124-5 10 8-7 5-0 70 1 6o-6 130 112-6 65-0 190 164-5 95-0 250 216-, 125-0 11 9-5' 5-5 71 6i-5 35-5 131 113-4 65-5 isjr i6;-4 95'5 251 217-4 125-5 12 ic/'4 6-0 72 62-4 36-0 132 114-3 66-0 192 166-3 96-0 252 218-2 ,26-0 13 II-3 6;5 73 63-2 36-5 133 115-2 66-5 193 167-1 96-5 253 2I9-I 126-5 14 III 74 64-1 134 ii6-o 6-0 194 168-0 97-0 254 220-0 15 13-0 7-5 75 65-0 37"S 135 116-9 67-5 195 168-9 97-5 255 220-8 127-5 Ki 13-9 g-o 70 6-8 38-0 136 190 169-7 250 221-7 17 14-7 8-5 77 66-7 38-5 137 iiS-6 68-5 IS7 170-6 98-5 257 222-6 ,28-5 18 156 g-o 78 67-5 39-0 138 119-5 69-0 198 171-5 99-0 258 223-4 129-0 19 i6-5 9-5 79 68-4 39-5 139 120-4 69-5 199 172-3 99"5 259 224-3 129-5 20 17-3 lo-o 80 69-3 4°-° 140|.2r2 200 173-2 200 225-2 ,500 21 i8-2 lo's 81 70-1 40-5 141 122-1 70-5 •201 174-1 100-5 261 226-0 130-5 22 19-1 82 7i'o 41-0 142 123-0 71-0 202 '74-9 262 226-9 131 23 19-9 ll°s 83 71-9 41-5 143 123-8 71-5 203 175-8 101-5 263 227-8 131-5 24 20-8 84 72-7 144 124-7 72-0 204 176-7 102-0 264 228-6,1,2-0! 25 21-7 12-5 85 73-6 4-"5 145 125-6 72-5 205 177-5 102-5 '205 229-5 132-5 26 22-5 13-0 80 74-5 140 ,26-4 73-0 206 178-4 103-0 266 230-4 133-0 27 23-4 '3-5 87 75-3 43-5 147 127-3 73-5 207 179-3 103-s 267 231-2 133-5 28 24-2 14-0 88 76-2 44-0 148 12S-2 74-0 208 180-1 104-0 208 232-1 134-0 2!) 25-1 >4-5 89 77-1 44-5 149 129-0 74-5 209 181-c 104-5 269 233-0 134-5 30 31 15-0 90 91' 77-9i45-o 150 129-9 75-0 210 i8i-9 J05-0 270 233-8 135-0 26-8 "5-5 78-8 45-5 151 .30-8 75-5 211 182-7 105-5 271 234-7 135-5 32 27-7 i6-o 92 79-7 46-0 152 131-6 76-0 212 183-6 .06-0 272 235-6 136-0 33 ; 2S-6 i6-s 93 So-s 46-5 153 132-5 76-5 213 184-5 106-5 273 236-4 136-5 34 1 29-4 17-0 94 8i-4 47-0 154 I33'4 77-0 214 185-3 107-0 274 237-3 137-0 35 30-3 'T5 93 82-3 47-5 155 134-2 77-1 215 186-2 107-5 275 2382 137-5 ■6G]ii-z iS-o 90 83-1 48-0 150 135-1 78-0 216 1S7-1 loS-o 270 239-0 .3S-0 37 32-0 i8-5 97 84-0 48-5 157 136-0 78-5 217 187-9 ,08-5 277 239-9 138-5 38 32-9 19-0 98 84-9 49-0 158 136-8 79-0 218 188-8 109-0 278 240- 8 39 33-8 '9'5 99 85-7 49' 5 159 137-7 79-5 219 1S9-7 1C9-5 279 241-6 139-5 40 41 34-6 35-5 100 Tof 86-6 ,o-o 100 ,38-6 220 190-5 280 242-5 140-0 ^°;5 87;5 50-5 101 139-4 80-5 221 191-4 110-5 28r 243-4 140-5 42 36-4 102 51-0 102 140-3 8i-o 222 192-3 282 244-2 141-0 43 37-2 21-5 103 89-2 5>-5 163 141-2 81-5 223 193-1 III-5 283 245-1 141-5 44 38-1 104 90-1 52-0 104 142-0 S2-0 224 194-0 284 246-0 142-0 45 39-0 2^;5 105 909 5^-5 105 142-9 82-5 225 194-9 112-5 285 246-8 1 142-5 40 39-8 KlO 9r8 53-0 106 1438 83-0 226 195-7 113-0 280 247-7 143-0 47 40-7 ^3-5 107 92-7 53-5 167 ,44-6 83-5 227 .96-6 113-5 287 248-5 143-5 48 4. -6 24-0 108 93'5 54'o| 168 I45'5 84-0 228 197-5 114-0 288 249-4 144-0 49 42-4 24' 5 109 94'4 54'5 109 146-4 84-5 229 198-3 114-5 '289 250-3 144-5 50 43-3 25-0 110 95-3 170 147-2 230 199-2 115-0 290 25,-, 1 145-0 51 44-2 -i'5 TiT 96-1 S5"5 171 148-1 85-5 '231 200-1 115-5 '291 252-0 145-5 52 45-0 26-0 112 56-0 172 149-0 S6-0 232 2CO-Q 292 252-9 146-0 53 45'9 26-5 113 97-9 56-5 173 149 -8 86-5 •233 20,-8 u6°s 293 253-7 146-5 54 46' 8 27-0 114 98-7 57-0 174 150-7 234 202-6 117-0 294 254-6 147-0 55 47-6 -7'i 1 15 99-6 57'S 175 151-6 87-5 233 203-5 117-5 295 255-5 147-5 5(! 48-5 2S-0 116 100-5 58-0 176 152-4 880 ■230 204-4 290 256-3 14S-0 57 49'4 28-5 117 101-3 58-5 177 I53'3 88-5 237 11S-5 297 257-2 148-5 58 50-2 29-0 118 59-0 178 154-2 89-0 238 206-1 1:9-0 298 258-1 149-0 59 51-1 29-5 119 103-1 59'5 179 155-0 89-5 239 207-0 119-5 299 258-9 149-5 «i0 52-c 30-0 120 103-9 6o-o 180 155-9 90-0 240 2078 120-0 300 259-8 150-0 Dist Dep. D.Lai DistJ Dej,. D.Lat )ist. D,.p. 3.L:.t. Jisi. D,.p. D. Lot. )ist. Dep. D. La..| 4'Mr 1 491 TRAVERSE TABLE TO DEGREES QQO 2" 0"» Uist. D.Lat. r»cp. DistJ D.Lat. Dep. Dist. D. Lat.l Dep. 1 )ist. ). L.t. Dep. Dist. D.Lat Dep. 301 2607 150-5 361 312-6 iSo-5 421 364-6 210-5 481 4166 240-5 541 4685 270-5 302 261-5 1510 362 1 3'3-5 '««-o 422 365-5 2110 482 417-4 2410 542 469-4 271-0 30." 2624 '5' 5 30 -i 314-4 181-5 423 3663 21 15 483 418-3 241-5 543 470-3 271-5 304 2633 1520 364: 315-2! 182-0 424 367-2 2120 484 419-2 242-0 544 471-1 2720 305 2641 1525 365 316-1 182-5 425 36S-I 212-5 485 420-0 242-5 545 472-0 272-5 306 2650 153-0 366: 317-0 1830 426 368-9! 2130 486 4209 2430 546 472-9 273-0 307 2659 153-5 367 3'7-S 183-5 427 369-8 j 213-5 487 421-8 243-5 547 473-7 273-5 30S 2667 154-0 363 3'87 1840 428 370-7 1 214-0 488 4226 244-0 548 474-6 274-0 309 2676 154-5 369: 319-6 184-5 429 371-5 214-5 489 423-5 244-5 549 475-5 274-5 310 311 26SS 2693 .550 '55 5 370 ' 37T: 320-4 185-0 321-3 '85-5 430 431 372-4 373-3 215-0 490 49T 424-4. 245-0 2455 550 5.il ^76;! 477-2 27S-0 275-5 215-5 425-2 312 2702 1560 372 322-2 1S60 432 374-1 492 426-1 ' 2460 552 478-1 2760 313 156-5 373 323-0 [ 186-5 433, 3750 216-5 493 426-9 2465 553 478-9 276-5 314 2719 1570 374' 323-9 187-0 434! 375-9 217-0 494 427-8. 2470 554 479-8 2770 315 2728 '575 375 324SI 1S7-5 435 376-7 217-5 495 4287, 247-5 555 480-7 277-5 316 2737 1580 376 325-6; 1880 436 377-6 2180 496 429-6 248-0 556 481-5 278-0 317 2745 .58-5 377 326-5 1 iSS-5 437 378-5 2185 497 430-4 248-5 557 482-4 278-5 318 275-4 1590 378 327-4 189-0 438 579-3 2190 498 431-3 1 249-0 558 4S3-3 2790 319 2763 '595 379 32S-2 1S95 439 380-2 219-5 499 4322 1 249-5 559 484-1 279 5 320 321 277-1 2780 1600 1605 380 381 329-1 i 1900 330-0 1 190-5 440 441 38'-. 2200 500 "soT 433-0 1 250-0 560 561 4S5-0 2800 381-9 220-5 433-9 250-5 T8T? ^5 322 278-9 1610 282 330-8 1 191 442 382-8 221-0 502 434-8 251-0 562 486-7 281-0 323 279-7 161 5 383 3317 i9'-5 443 3S3-7 221-5 503 435-6 251-5 563 487-6 28.-S 324 280-6 1620 384 3326 1920 444 384-5 222-0 504 436-5 252-0 564 488-5 282-0 325 2S15 162 s 385 333-41 '92-5 445 385-4 222-5 505 437-4 252-5 565 4S9-3 282-5 326 2823 1630 386 334-3 193-0 446 386-3 2230 506 438-2 253-0 566 4902 2830 327 283-2 163-5 387 335-2 •93-5 447 3S7-1 2235 507 439-1 253-5 567 491-1 283-5 328 284-1 1640 3360 194-0 448 388-0 2240 508 440-0 254-0 568 491-9 2840 329 2849 .645 389 336-9 194-5 449 388-9 224-5 509 440-8 254-S 569 492-S 2845 330 331 2858 ^6T 1650 390 391 337-8. 33S-6 195-0 195-5 450 451 389-7 2250 510 5lT 441-7 ^55^ 255-5 570 571 493-6 2850 285-5 .65-5 390-6 225-5 442-6 4945 332 287-5 1660 392 339-5 i960 452 391-5 226-0 512 443-4 256-0 572 495-4 2860 333 288-4 1665 393 340-4 196-5 453 392-3 226-5 513 444-3 256-5 573 496-3 286-5 334 289-3 1670 394 341-2 1970 454 393-2 227-0 514 445-2 257-0 574 497-1 2870 335 2901 167-5 395 3421 197-5 4 55 394-0 227-5 515 446-0; 2575 575 497-9 'IP 336 291-0 1C80 396 343-0 198-0 456 394-9 22S0 516 446-9 258-0 576 498-8 2880 337 291-9 1685 397 3438 198-5 457 395-8: 228-s 517 447-8 258-5 577 499-7 288-5 33S 292-7 1690 398 344-7 199-0 458 3966' 229-0 518 448-6 2590 578 5005 289-0 339 293-6 169-5 399 345-6 199-5 459 397-5 2295 519 449-4 2595 579 501-3 289-5 340 294-5 170-0 400 3464 2000 460 398-4 230-0 520 450-3! 260-0 5do 502-2 2900 34r 2953 ■705 4 of 147^3- "200-5 "46T 399-2 230-5 521 451-2 2605 581 I031 290-5 342 2962 1710 402 348-1 201-0 462 400-1 231-0 522 4521 261-0 582 5040 291-0 343 297-1 171-5 403 3490 201-5 463 ' 4010 231-5 523 452-9 2615 583 504-9 2915 344 2979 1720 404 3499 2020 404 1 401-8 232-0 524 4538 2620 584 5058 292-0 345 298-8 172 5 405 350-7 2025 405 ; 402 7 232-5 525 454-7 ; 262-5 585 5066 2925 340 2997 1730 406 351-6 2030 465 4036 233-0 526 455-5 ; 263-0 586 5075 293-0 347 300-5 '735 407 352-5 2035 467 404-4 233-5 527 4564 263-5 587 50S-4 293-5 348 301-4 1740 408 353-3 2040 408 405-3 234-0 528 457-3 264-0 588 509-2 2940 349 302-3 "745 409 3542 2045 409 4062 234-5 529 458-1 ; 264-5 589 5101 294-5 350 3031 1750 410 3551 2050 470 407-0 2350^ 530 4590 1 265-0 590 5110 2950 35 r 3040 '75-5 Tn 355-9 205-5 471 1 407-9 2355 531 459-9 265-5 591 ^511-8 295-5 352 304-8 1760 412 3568 2060 472 4088 2360 532 460-7 2660 592 512-7 2960 353 3057 1765 413 357 7 2065 47.-! 4096 236-5 533 461-6 266-5 593 5.3-6 2965 354 3066 1770 414 358-5 2070 474 4105 2370 534 462-5 267-0 594 5'4-4 297-0 355 3074 ■77-5 415 359-4 207-5 475 411-4 2375 535 463-3 267-5 .yj5 5 '5-3 297-5 356 3083 1-80 416 3603 208 476 412-2 238-0 536 464-2 2680 .■)96 5162 2980 357 309-2 17S-5 417 361 1 20S-5 477 4131 238-S 537 465-1 2685 597 5170 298-5 35» 310-0 1790 418 362-0 209-0 478 4140 2390 538 4659 2690 .598 5179 2990 359 3109 '79-5 419 362-9 209-5 479 4.48 239-S 539 4668 269-5 599 5.8-8 2995 360 3U-8 iSoo 420 363-7 2 1 00 480 4'5-7 240-0 540 467-7 2700 600 519-6 300-0 Dist !"^p. D. I.at Dist ■»,: D. Lat Dist Uep. D. Lnt Dist D.,,. D. Lai Dist ; Dep. |D. Lai. 00° 4»>0"' 1 492 TABLE 1 TRAVKRSE TABLE TO DEGREES 31° Ob 4m Dist-D.Lat Dep. Dist. D. I.at. Dep. Dist.]D. L;u. Dep. Dist. D.Lat. Dep. 1 Dist. D.Lat.| Dep. . c, o'5 61 52-3 3i'4 121 103-7 62-3 181 155-1 93-2 241 206-6 124-1 2 i-l i-o 53'i 3i'9 122 .04-6 62-8 182 156-0 93-7 •242 207-4 124-6 3 2-6 1-5 63 54-0 3^-4 123 105-4 63-3 183 156-9 94-3 243 208-3 125-2 4 3-4 2-1 64 54-9 33° 124 I06-3 63-9 184 157-7 94-8 244 209-1 125-7 5 4-3 2-6 65 55-7 33-5 125 107- 1 64-4 185 158-6 95-3 245 210-0 126-2 6 5' 3'i 66 56-6 34-0 126 loS-o 64-9 180 159-4 95-8 1 246 210-9 126-7 7 6-0 3-6 67 57-4 34-5 127 .08-9 65-4 187 160-3 96-3 247 127-1 8 6-9 4' I 68 58-3 35-0 128 109-7 65-9 188 161-1 96-8 •248 212-6 127-7 9 T7 4-6 69 59-1 35'5 129 IIO-6 66-4 189 162-0 97-3 249 213-4 128-2 10 8-6 5-2 70 6c-o ;6-i 130 111-4 67-0 190 162-9 97-9 250 214-3 128-8 TT 9'4 5-7 71 6o-9 36-6 131 II2-3 67-5 191 163-7 98-4 "23r 215-1 129-3 12 IO-3 6-2 72 6. -7 37-1 132 II3-I 6S-0 192 164-6 98-9 252 216-0 129-8 13 ii'i 6-7 73 62-6 37-6 133 114-0 68-5 193 165-4 994 253 ;;6-9 130-3 14 I2-0 7-2 74 63-4 38-1 134 114-9 69-0 194 166-3 99-9 254 130-8 15 12-9 7-7 75 64-3 38-6 135 115-7 69-5 195 167-1 100-4 •255 2i8-6 131-3 Ifi 13-7 8-2 76 65-1 39'i 130 ii6-6 70-0 196 168-0 100-9 256 219-4 131-8 17 .4-6 8-8 77 66-0 39-7 137 117-4 70-6 197 168-9 IOI-5 257 220-3 132-4 18 15-4 9'3 78 66-9 40-2 138 71-1 198 169-7 258 22I-. 132-9 1 19 .6-3 9-8 79 67-7 40-7 139 119-1 71-6 199 J70-6 102-5 •259 133-4 20 IO-3 80 68-6 _4i-2_ 140 72-1 200 171-4 260 222-9 133-9, 134-4 T ig-o 81 69-4 4i'7 141 120-9 72-6 201 172-3 103-5 267 223-7 i8-9 11-3 82 70-3 42-2 142 121-7 73-1 202 173-1 104-0 262 224-6 134-9 23 197 II-8 83 71-1 42-7 143 122-6 73-7 •203 I74-0 104-6 263 225-4 135-5 24 20-6 .2-4 84 72-0 43'3 144 123-4 74-2 204 174-9 264 :f'} 136-0 25 1 21-4 112-9 85 72-9 43-8 145 124-3 74-7 205 175-7 I05-6 265 136-5 2(; 2.-3|i3-4 86 73'7 44" 3 146 I25-I 75-2 206 176-6 106-1 260 22S-0 ,37-0 27 23-1 13-9 87 74-6 44" 8 147 126-0 75*7 207 177-4 106-6 207 22S-9 137-5 28 14-4 88 75'4 45'3 148 126-9 76-2 206 178-3 107-1 268 229-7 138-0 20 24-9 14-9 89 76-3 45-8 149 127-7 76-7 209 179-1 107-6 269 230-6 13S-5 30 25-7 15-5 90 77-1 46-4 150 128-6 77-3 210 180-0 108-2 270 231-4 139-1 31 76^ 76^^ 91 78-0 46-9 Tm 129-4 77-8 211 j8o-9 108-7 271 232-3 139-6 32 27-4 i6-5 92 78-9 47-4 152 130-3 78-3 212 109-2 272 233-1 140-1 33 -8-3 lyo 93 79-7 47-9 153 78-8 213 182-5 109-7 273 234-0: 140-6 34 29-1 17-5 94 8o-6 48-4 154 132-0 79-3 214 183-4 274 234-9, H'-i 35 i8-o 95 8i-4 48-9 155 132-9 79-8 215 184-3 110-7 275 235-7 141-6 36 30-9 .8-5 96 82-3 49-4 156 133-7 ?o-3 216 '^V 111-2 276 2366 1 142-2 37 31-7 19-1 97 83-1 50-0 157 134-6 80-9 217 111-8 277 23-4 >4i-7 38 32-6 i9;6 98 8+-0 50-5 158 135-4 Si-4 218 186-9 112-3 278 238-3 143-:^ 39 33-4 99 84-9 51-0 159 136-3 81-9 219 187-7 112-8 279 239-1 >43-7 40 34-3 20-6 100 85-7 51-5 160 137-1 82-4 220 i88-6 113-3 280 240-0 144-2 41 35-1 211 101 S6-6 52-0 161 138-0 l"y 221 189-4 113-S 281 [ 24C-9 1 144-7 1 42 36-0 21-6 102 87-4 5^-5 162 138-9 222 190-3 114-3 282 241-7 .45-2 43 36-9 22-1 103 88-3 53-0 163 139-7 84-0 223 191-1 114-9 283 242-6 145-8 44 37-7 22-7 104 89-1 53-6 164 140-6 84-5 224 192-0 115-4 284 243-4 146-3 45 38-6 23-2 105 90-0 54-1 165 141-4 85-0 225 192-9 1.5-9 285 244-3 146-8 46 39'4 23-7 106 90-9 54-6 166 142-3 85-5 226 193-7 1 16-4 286 245-1 ■47-3 47 40-3 24-2 107 91-7 55-1 167 143-1 86-0 227 194-6 116-9 287 246-0 147-8 48 4I-I 24-7 108 92-6 55-6 168 144-0 86-5 228 195-4 117-4 288 246-9 148-3 49 42-0 25-2 109 93'4 56-1 169 144-9 8j-o 229 196-3 117-9 289 247-7 14S-S 50 429 25-8 110 94-3 56-7 170 145-7 87-6 230 222J- 290 248-6 149-4 51 43-7 26-3 111 95-1 57-2 171 146-6 88-1 ■231 198-0 119-0 291 249-4 149-9 52 44-6 26-8 112 96-0 57'7 172 147-4 88-6 232 198-9 119-5 •292 250-3 150-4 53 45"4 27'3 113 96-9 58-2 173 148-3 89-1 233 199-7 293 251-2 150-9 54 46-3 27-8 114 97-7 58-7 174 149-1 89-6 234 200-6 120-5 294 252-0 151-4 55 47-1 115 98-6 59-2 175 150-0 90-1 235 201-4 295 252-9 151-9 5fi 48-0 28-8 116 99'4 59'7 170 150-9 90-6 236 202-3 121-5 •296 253-7 152-5 57 48-9 29-4 117 177 151-7 91-2 237 203-1 122-I 297 254-6 153-0 58 49 '7 -99 118 loi-i 1 6o-S 178 152-6 91-7 •238 204-0 122-6 298 255-4 153-5 .01) 50-6 30-4 119 io2-o| 6i-3 179 153-4 92-2 239 204-9 123-1 299 256-3 I54-0 60 5'-4 3°-9 120 IC2-9 i 61-8 180 154-3 92-7 240 205-7 123-6 300 257-1 1 154-5 Dep. D.La Dist, iJcp. D.U Dist Dep. D.L-al Dist. Dep |D.l,a. Dist Dep. 'd. Lat. 1 59° 3^ 50'" TABLE 1 TRAVEliSE TAI3LK TO DEGREES | 31° 2h4m 1 Dist.D.Lat, IXp. Dist.D.Lat. Dep. Uist.'D. Lat. 1 Dep. Dist. D.Lat. Dep. Dist.JD. Lat. Dep ^ 25S0 1550 361 1 309-4 185-q 421 3609 216-S 481 412-3 247-7 541 463-7 278-6 302 258-9 '555 3G2 310-3 186-4 422 361-7 217-3 482 413-2 2482 542 4646 279-1 iWi 2597 .56-1 363 1 3.. 2 1S70 423 362-6 2179 483 414-0! 248-8 543 4654 279-7 304 1 2606 156-6 364 1 3120 187-5 424 1 363-4: 218-4 484 414-9 2493 544 466-3 2802 305 1 261-4 157-1 365 ( 312-9 1 88-0 425 364-3 21S-9 485 415-71 249-8 545 467-2 2807 306 1 262-3 157-6 366 313-7 188-5 426 365-2 219-4 4SR 416 6 j 250-3 546 4680 281-2 307 263-2 .58-. 367, 314-6 1S9-0 427 , 366-0 2199 487 417-41 2508 547 468-9 281-7 SOS 264-0 158-6 368! 315-4 189-5 428 366-9 220-4 488 418-3! 251-3 548 4697 2823 309 1 264-9 1592 369 3:6-3 1 90- 1 429, 3677' 221-0 489 419-2 i 251-9 549 4706 282-S 310 265-7 J597 370' 317-2 1906 430 1 3686 221-5 490 4200 i 2524 550 471-4 283-3 311 2666 i6o-2 371 1 318-0 191 I 431 369-4 1 222-0 49 1 j 420-9 252-9 551 472-3 Tsys 312 267-4 160-7 372 318-9 191-6 432 370-3 222-5 492 421-7 253-4 552 473-2 284-3 313 268-3 161-2 373 319-7 1921 433 371-2 223-0 493 422-6 253-9 553 4740 284-8 314 269-2 .6.-7 374 320-6 192-6 434 372-0! 223-S 494 1 423 4 2544 554 474 9 285-3 315 270-0 162-2 375 321-4 1931 435 3729 2240 495 , 424-3 2549 555 4757 2858 316 270-9 162S 376 3^2-3 193-7 436 373-7 224 6 496 425-2 2555 556 476-6 286-4 317 271-7 163-3 377 3232 194-2 437 374 6 1 225-1 497 4260 2500 557 477-4 286-9 318 272-6 163-S 378 324-0 194-7 438 375-4 225-6 498 4269 256-5 558 478-3 287-4 319 273-4 164-3 379 3249 195-2 439 376-3! 226 I 499 427-7 257-0 559 479-2 287-9 320 _274:3 164-S 380 325-7 1957 440 377-2 i 226-6 500 4286 _257^ 560 4S00 288-4 321 275-2 165-3 381 326-6 196-2 441 3780] 227-1 501 : 429-4 1 258-0 561 4809 288-9 322 2760 1658 382 1 327-4 196-7 442 3789 1 227-7 502 : 430-3 25S6 562 48.-7 289-5 323 276-9 166-4 383 3283 197-3 443 379-7 228-2 503! 431-2 259-1 563 482-6 290-0 324 277-7 166-9 384 329-2 197-S 444 3806 228-7 504 432-0 2596 564 483-4 2905 325 2786 167-4 385, 3300 ■98-3 445 381-4 229-2 505 432-9 2UO-I 565 484-3 2910 326 279-4 1679 386 3309 198S 446 3S2-3 229-7 506 433-7 260-6 566 4S5-2 29.-5 327 280-3 168-4 387 331-7 199-3 447 383-2 2302 507 4346 261-I 567 486-0 2920 3-2S 28 1 -2 16S9 388 332-6 199-8 448 384-0 230-7 508 435-4 261-6 568 486-9 292-5 329 282-0 ,69-5 389 333-4 200-4 449 384-9 2313 509 436-3 2622 569 487-7 293-1 330 282-9 170-0 390 334-3 200-9 450 385-7 231-8 510 437-2 262-7 570 48S 6 293-6 331 ~2§3-7 170-S "59ri75T 201-4 451 386-6 232-3 511 1 438-0 263-2 571 489-4 294-1 332 2846 1710 392 3360 201-9 452 3874 232-8 512 438-9 263-7 572 490-3 294-6 333 2S5-4 171-5 393 3369 202-4 453 388-3 2333 513 439-7 264-2 573 491-2 295 1 334 286-3 1720 3^4 337 7 2029 454 389-2 233-8 514 4406 264-7 574 -192-0 2956 335 287-2 172-5 395 3386 2034 455 3900 2343 515 441-4 2652 575 492-9 296-. 336 2880 1731 396 3394 204-0 450 390-9 2349 516 4423 2658 576 493-7 296-7 337 2S8-9 1736 397 340-3 204-5 457 391-7 t 235-4 517 443-2 266-3 577 494-6 297-2 338 2S97 174-1 398 341-2 205-0 458 392-6 235-9 518 1 4440 2668 578 495-4 297-7 339 2906 1746 399 1 342 205-5 459 393-4 236-4 519 444 9 2673 579 496-3 298-2 340 291-4 J15;i 400 i 342 9 J060 460 394-3 2369 520 445-7 267-S .■-■80 497-2 2987 341 202-3 J 75 -6 •401, 3-13 7 206-5 461 395-2 237-4 521 446-6 268-3 581 498-0 2992 342 ; 293-2 402 1 344-6 207-0 462 396-0 23S0 522 447-4 2689 582 498-9 2998 343 294 1767 403 345-4 207-6 463 396-9 238s 523 448-3 269-4 583 4997 3003 3U 2949 1772 404 3463 208-1 464 397-7 I 239-0 524 449'2 269-9 584 500-6 3008 345 295-7 177-7 405 1 3472 20S-6 465 398-6 1 239-5 5-25 450-0 270-4 585 501-4 301-3 346 296 6 08-2 406 1 34S 209-1 ■166 399-4 240 526 4509 2709 586 502-3 301-8 347 297-4 17S-7 407 , 348 9 2096 467 400-3 240-5 527 451-7! 271-4 587 503-2 302-3 348 2083 1592 408 1 3497 210 I 46S 401-2^ 2410 528 452-6! 271-9 588 504-0 302-8 349 ! 299-2 179-8 409 1 3506 210-7 469 402-0 2415 529 453-4 272-4 589 504-9 303-3 350_, 3000 180-3 410| 351-4 211-2 470 ' 402-9 ' 242 1 530 454-3 273-0 590 505-7 3039 351 300-9 TES^a 411 3523 211-7 471 403-7, 242-6 531 4552 2735 591 5066 304-4 352 301-7 181-3 412 353-2 212-2 472 404-6! 243-1 532 4560 2740 592 507-4 3049 353 3026 I8I-8 413 354 212-7 473 405-4' 2436 533 456-9 2745 593 508-3 305-4 354 3034 1823 414 354-9 213-2 474 4063 244-1 534 457-7 2750 594 5092 3059 355 3043 1828 •115 1 355-7 213-7 475 407 2 1 244-6 535 4586] 275-5 595 5100 3064 356 305-2 ■834 416 3566 2143 4080 245-2 536 459-4; 2761 .596 5109', 307-01 357 3060 ■S39 4>- 357-4 214-8 477 4089, 245-7 537 460-3 276-6 597 511-71 307-5 358 306-9 184-4 418; 3583 2153 478 409-7 246-2 538 46.-2 277-1 598 5126 308-0 359 307-7 .84-9 419' 3;9-2 2158 479 410-6; 2467 539 ' 462-0 1 277-6 599 5134 3085 360 3086 185-4 420 . 360 216-3 480 j 4>l-4, 247-2 540, 4629 278-1 600 5143 3090 |)i«t -0,7 D.Lat. l)ist.| Dep. D. Lat Dist Dep. Id. Lat. Dist.l Dep. D. Lat Dist. D.p. D. Lat. 50° 3" SG- 1 494 TRAVERSE TABLE TO DEGREES S2" oil yn, Dist D.Lat^ Dep. Dist. D. Lnt. Dep. Dist Id. LaJ Dep. Dist. D.Lat. Dep. Dist. U. Lat. Dep. 1 0-8 0-5 61 51-7 32-3 121 102-6 64-, 181 153-5 95-9 241 204-4 127-7 2 1-7 i-i 62 52-6 32-9 122 103-5 64-7 182 154-3 96-4 242 205-2 128-2 3 2-5 1-6 63 53-4 33-4 123 104-3 65-2 183 155-2 97-0 243 206-1 ,28-8 4 3-4 2-1 64 54-3 33-9 124 105-2 65-7 184 156-0 97-5 244 1 206-9 ,29-3 6 4-2 2-6 05 55-1 34-4 125 106-0 66-2 185 156-9 98-0 245 207-8 129-8 « 1 5-1 1 3-^ 00 56-0 35-0 120 io6'9 66-8 186 157-7 98-6 246 2c8-6 130-4 7 5-9 3-7 07 56-8 35-5 127 107-7 67-3 187 158-6 99-1 247 209-5 130-9 8 6-8 4-2 08 57-7 36-0 128 108-6 67-8 188 159-4 99-6 248 210-3 131-4 •J 7-6 4-8 09 58-5 36-6 129 109-4 68-4 189 160-3 100-2 249 131-9 10 8-5 5'3 70 59*4 37-1 130 IIO-2 68-9 190 161-1 100-7 250 212-0 132-5 Il~ 9V3 5-8 71 6o-2 37-6 IsT Ill-I 69-4 191 162-0 101-2 251 212-9 135-0 12 .0-. 6-4 72 6i-i 38-2 132 III-9 69-9 192 162-8 IOI-7 252 213-7 I33-; 13 ii-o 6-9 73 6i-9 38-7 133 70-5 193 163-7 102-3 253 2.4-6 154-1 14 ,.•9 7"4 74 62-8 39-2 134 113-6 71-0 194 .64-5 102-8 264 215-4 ,34-6 16 12-7 7-9 75 63-6 39-7 135 114-5 71-5 195 165-4 103-3 255 216-3 135-1 10 13-6 8-5 70 64-5 40-3 136 115-3 190 1662 103-9 250 217-1 ,3;-- 17 14-4 9-0 77 65-3 40-8 137 116-2 72-6 197 167-1 104-4 257 217-9 ,36-2 IS I5'3 9'5 78 66-1 4i"3 117-0 73-1 198 .67-9 104-9 258 2,8-8 ,36--! l!» i6-i 79 67-0 41-9 139 117-g 73-7 199 i68-8 105-5 259 2,9-6 ,37-2 1 20 17-0 io'6 80 67-8 4-'4 140 74'S 200 169-6 106-0 200 220-5 13-8 21 17-8 11 I 81 68-7 1 4^-9 141 .19-6 74-7 2or 170-5 106-5 201 221-3 138-3 22 iS-7 11-7 82 (>rS 43'5 142 120-4 75-2 202 171-3 107-0 262 138-8 23 19-5 83 70-4 44-0 143 121-3 203 172-2 107-6 203 223-0 '39-4 24 20-4 12-7 84 71-2 44-5 144 76-3 -204 173-0 I08-I 204 223-9 139-9 25 13-2 85 72-1 45'° 145 123-0 76-8 205 173-8 108-6 205 224-7 140-4 26 22-0 .3-8 86 72-9 45-6 146 77"4 206 ■74-7 109-2 200 225-6 141-0 27 22-9 14-3 87 73-8 46-, 147 124-7 77-9 207 '75-5 109-7 267 226-4 ,4,-5 28 23-7 14-8 88 74-6 46-6 148 125-5 78-4 208 176-4 110-2 268 227-3 ,42-C 2!) 24-6 15-4 89 75-5 47-2 149 126-4 79-0 209 177-2 1IO-8 269 218-1 142-5 30 = 5-4 15-9 90 76-3 47'7 150 127-2 79-5 210 178-1 111-3 270 229-0 I43-. -w 26-3 i6-4 91 77-2 "^ 161 128-1 2iT 178-9 iii-X 271 229-s 143-6 32 27-1 17-0 92 78-0 48-8 152 128-9 80-5 212 179-8 112-3 272 230-7 144-1 33 28-0 17-5 93 78-9 49-3 163 129-8 81-1 213 iSo-6 112-9 273 231-5 144-7 34 28-8 iS-o 94 79-7 49-8 154 1306 81-6 214 iSi-5 113-4 274 232-4 145-2 35 29-7 i8-5 95 8o-6 50-3 155 131-4 82-1 215 ,82-3 113-9 275 233-2 145-7 3fi 30-5 19-1 90 8.-4 50-9 150 132-3 82-7 210 ,83-2 114-5 270 23+-, 146-3 37 31-4 19-6 97 82-3 5'-4 157 83-2 217 184-0 115-0 -277 ^34-9 146-8 3H 98 51-9 158 83-7 218 184-9 115-5 278 235-8 147-3 39 33-1 1 20-7, 99 84-0 52-5 159 134*8 84-3 219 116-1 279 236-6 147-8 40 33-9 j 21-2 100 84-8 55-0 100 135-7 84-8 220 186-6 ii6-6 280 ^37-5 148-4 41 34-8 2r7 101 85-7 53"5 101 .36-5 85-3 221 187-4 II7-I 28r 238-3 148-9 42 35-6 1 22-3 102 86-5 54' > 102 "37-4 85-8 222 ,88-3 1.7-6 282 239-1 149-4 43 36-5 22-8 103 87-3 54-6 163 138-2 86-4 223 189-, 118-2 283 240-0 150-0 44 37-3 U3-3 104 88-2 55'i 164 139-1 86-9 2-24 190-0 118-7 284 240-8 I 5c- 5 45 ,38-=U3-8 105 89-0 55-6 105 139-9 87-4 2-25 .90-8 119-2 ■285 241-7 4(; j 39-0 1 14-4 100 89-9 56-2 160 140-8 S8-0 220 191-7 II9-8 •286 242-5 Ijl-e 47 39-9 1 =4-9 107 90-7 56-7 107 14. -6 88-5 2-27 192-5 120-3 287 143'4 152-1 4(i 40-7 1 25-4 108 91-6 57-2 108 142-5 89-0 228 ■93-4 120-8 288 244-2 ,52-6 49 4i-6h-6-o 109 92-4 57-8 109 "43-3 89-6 229 194-2 I2I-4 289 245-. 1 .?3-' 50 42-4 U6-S 110 93-3 58-3 170 144-1 90-1 230 195-1 -21-9 -290 =45-9 1 '53- 51 43-3 27-0 TTT 94-1 1^ TtT 145-0 90-6 231 195-9 122-4 29r 246-8!, 54-= 52 44-1 27-6 112 95-0 59-4 172 145*9 91-1 232 196-7 122-9 292 247-6 154-- 53 44' 9 28-1 113 95-8 59'9 173 146-7 91-7 233 197-6 123-5 293 24S-5 155-3 54 4S-8 28-6 114 96-7 60-4 174 147-6 92-2 234 .98-4 124-0 294 =49-3 I55-S 55 46-6 29-1 115 97-5 6o-9 175 148-4 92-7 235 199-3 124-5 295 250-2 156-3 5(i 47-5 l»9-7 116 98-4 6i-5 176 ■49-3 93-3 230 125-1 296 251-0 156-9 07 48- 3 30-2 117 99-2 62-0 !77 150-1 93-8 237 201-0 125-6 297 251-9 15-4 58 49-2 30-7 118 62-5 1711 i5i'o 94' 3 238 201-S 126-1 2!t8 252-7 15-9 59 50-0 31-3 119 ico'9 63-1 179 151-8 94" 9 239 202-7 126-7 299 2 53-6 158-4 (iO 50-9 3. -8 120 101-8 63-6 180 152-6 95-4 240 203-5 127-2 .■100 = 54-4 159-0 Uist 13^ D.La Dist Dep. U.Lat Dist Dep. D. Ut Dist Dep. D. Lat. Dist Dep.;D..,J L 58° 3^52"' 1 TABLE 1 495 TRAVEKSE TABLE TO DEGKEES 32° 2" 8» Dist D. Lat. Dep. Dist D. Lat Dep. Dist. D. Lilt. Dep. Dist. D.Lat. Dep. Dist 541 D.Lat 458-8 Dep. 286-7 301 255-3 159-S 361 306-2 i9>-3 421 357-0 223-1 481 ; 407-9 254-9 302 256-. 1600 362 3070 191-8 422 357-9 223-6 482 408-8 255-4 542 459-6 287-2 303 2570 1605 363 307-9 1923 423 358-7 224-1 483 4096 2559 543 460-s 2877 304 257-S 1611 364 3087 192-9 424 359-6 224-7 484 410-5 ' 256-5 5-14 461-3 305 258-7 1616 365 3095 193-4 425 360-4 225-2 4,85' 41 1-3 2570 545 4622 288-8 306 2595 162-1 366 3104 193-9 426 361-31 225-7 486 : 4122 257-5 546 463-0 289-3 30" 260-4 162-7 367 3if2 1945 427 362-1 1 226-3 487 415-0 2581 547 4639 289-9 308 261-2 163-2 368 312-1 195-0 428 363-0 226-8 488 1 4139 258-6 548 4647 290-4 309 262-1 163-7 369 3129 195-5 429 363-8 227-3 489 4147 259-1 549 4656 2909 310 262-9 _L64-3 370 3r3-8 196-0 430 364-7 227-8 490 415-6 1 259-6 5.50 466-4 291-5 wr ~26jS 164-8 37T 314-6 196-6 431 365-5 178^: 491 416-4 1 260-2 551 467-3 2920 312 264-6 165-3 372 315-5 197-1 4.-i2 366-4 22S-9 492 417-3, 260-7 552 46S1 292-5 313 265-4 165-8 373 3'6-3 197-6 433 367-2 229-4 493 418-I 261-2 553 469-0 2930 314 266-3 166-4 374 317-2 198-2 434 3681 230-0 494 1 4190 261-8 554 469 8 1 293-6 315 267-1 166-9 375 318-0 1987 435 368-9 230-5 495 1 4198 262-3 555 4707' 2941 316 268-0 167-4 376 318-9 199-2 436 369-8 231-0 496 420-6 2628 556 471-5 1 2946 317 26SS 1680 377! 3197 199-S 437 3706 231-6 497 4215 2634 557 4724 2952 318 269-7 168-5 378 320-6 200-3 438 371-5; 2321 498 1 422-3 263-9 558 473-2 295-7 319 270-5 1690 379 1 321-41 2008 439 372-3 232-6 499 423-2 264-4 559 474-1 296-2 320 271-4 1696 -•ISO' 3223! 201-3 440 373-2 1 233-1 500 1 424-0 1 265 560 474-9, 296-7 "32r 272-2 1 70- 1 381 : 323-1 1 201-9 441 1 374-0 2337 501 1 424-9 265-5 561 475-81 '297-3 322 273'i 1706 382 1 324-0 1 202-4 442 1 374-8 234-2 502 ; 425-7 2660 562 476-6 ! 297-8 323 273-9 1711 383 , 324-8 ■ 202-9 443 375-7 234-7 503 4266 266-5 563 477-5 2983 324 274S 171-7 384 1 325-7 1 203-5 444 376-5 235-3 2.15-8 504 427-4 267-1 564 478-3 298-9 325 j 275 6 172-2 385 I 326-5 1 204-0 445 377-4 505 428-3 267-6 565 479-2 2994 326 ! 276 5 172-7 386 1 327-4! 204-5 446 3782 236-3 506 429-1 2681 566 4S00 299-9 327 1 277-3 '73-3 387 1 328-2' 205-1 447 3791 1 2369 507 430 2687 567 480-9 300-5 328 278-2 I73-S 388 1 329-1 , 205-6 448 379-9 237-4 508 ' 430-8 2692 568 48.7 301-0 329 2790 ■74-3 389 329-9 206-1 449 3S0-8 237-9 509 4317 2697 569 482-6 301-5 330 331 2799 1749 390 39r 330-8 206-6 207-2 4 50 451 3S1 6 23S-4 382-5 239-0 510! 432-5 270-3 2708 570 _4834 484-3 302-1 302-6 280-7 1754 331-6 511 433-4 332 28 1 -6 175-9 392 3325 207-7 452 3S3-3 239-5 512 434-2 2714 572 4S5-1 303-2 333 2S2-4 1764 393 3333 20S-2 453 384-2 1 2400 513 435-1 271-9 573 4860 3037 334 2S3'3 177-0 394 334-* 20S-8 454 1 385-01 240-6 514 4359 272-4 574 486-8 304-2 335 284-1 177-S 395 335-0 2093 455 385-9 2411 515 4368 2729 575 487-7 304-7 336 285-0 1780 396 335-8 209-8 456 386-7; 241-6 516 437-6 273-5 576 4S8-51 305-3 1 337 2S5-8 178-6 397 336-7 2IO-4 457 387-6 1 242-2 517 438-5 2740 577 489-4 305-s 338 : 286-7 179-1 398 337-5 210-9 458 388-4! 242-7 518 439-3 2745 578 4902 3063 339 2S7-S 179-6 399 338-4 211-4 459 389-3 i 243-2 519 440-2 2750 579 491-1 306-8 340 2S8-3 180-2 400 339-2 1 211-9 460 390-1 1 243-8 391-01 244-3 520 521 441-0 441-9 275-6 ^276-T 580 581 ^919 4928 J074 307-9 341 289-2 |«07 401 340-1 212-5 461 342 290-0 402 340-9! 213-0 462! 391-8 2448 522 4427 1 2766 582 493-6 308-4 343 290-9 181 7 4U3 34,-8 213-5 463 392-7 2454 523 443-6 277-2 583 4945 309-0 344 291-7 1823 404 3426; 214-I 464 393-5 245-9 524 444-4 2777 584 495-3 30/5 345 292-6 182-S 405 343-5 2146 465 394-4 246-4 525 ; 445-3 278-2 585 496-2 310-0 346 2934 .83-3 406 344-3 215-1 466 395-2 246-9 526 4461 2787 586 497-0 310-5 347 2943 183-9 4U7 345-2 2157 467 396-0 247-5 527 446-9 279-3 587 497-8 311-1 348 205-1 184-4 408 3460 216-2 468 396 9 1 2480 528 447-8 2798 588 498-7 311-6 349 2960 184-9 409 1 346-9, 2167 469 3977 248-5 529 44S6 280-3 589 499-5 3I2I 350, 296-S .85-4 41(1 347-7 [ 217-2 470 3986 249-0 5-30 1 449-5 2809 590 500-3 3126 351 ' 2077 1S6-0 411, 34S6! 2178 471 399-4 249-6 531 ! 450-3! 281-4 591 501-2 313-2 352 2'iS-S 1S65 412 1 349-4 2183 472 400-3 250-1 532' 451-r 281-9 592 5020 313-7 353 2994 1870 413 350-3 218 S 473 401-1 250-6 533 1 452-0 ' 282-4 593 5029 314-2 354 : 3002 1S76 414 1 351-1 2194 474 402-0 251-2 534 452-8 , 2S3-0 594 503-7 314-8 355, 30I-I 188-1 415 3520 2199 475 4028 2517 535 , 453-7 1 283-5 .595 5046 315-3 356 301-9 1886 416 352-8 220-4 476 403-7 : 252 2 536 454-5 1 284-0 596 5054 3158 357 302 8 1892 417 353-6 221-0 477 404-5 1 252-8 537 455-4 2846 597 5062 316-4 358 ; 3036 1897 418 3545, 221-5 478 4054 253-3 538 456-2 285-1 598 5071 316-9 359 3045 1902 ■»'!' 1 355-3 222 479 406-2 253-S 539 j 457-1 285-6 599 5080 3174 360 305-3 1908 420 356-2, 222-5 480 407-1 2543 .540 I 457 9 2S6-2 600 508-8 318-0 Distj Dcp. ]). I.at. Dist. Dep. D.Lat. Dist. Dep. D.Lat, Distj Dep. [d. Lat. Dist. Dep. D. Lat. f,8° 3" 52-° 498 TRAVEKSE TABLE TO DEGREES 34° 2" 16" Dist.JD.L8t| Dep. Dist. D.Lat. Dep. Dist. D.Lat. Dep. Dist. D.Lat. Dep. Dist|D. L.t. "^ 1 0-8 'o-6 61 50-6 34" » 121 100-3 67-7 181 150-1 101-2 241 199-8 134-8 2 1-7 ij 62 51-4 34-7 122 loi-i 68-2 182 150-9 101-8 242 200-6 135-3 3 »'5 '■7 63 52-2 35-2 123 I02'0 688 183 151-7 102-3 ■243 201 5 135-9 3'3 64 53-1 35-8 124 102-8 69-3 184 15^-5 102-9 -244 202-3 136-4 41 2-8 65 53-9 36-3 125 103-6 69-9 185 153-4 103-5 245 203-1 137-0 5-0 3-4 66 54-7 36-9 126 104-5 70-5 186 154-2 104-0 246 203-9 137-6 5-8 39 67 55-5 37-5 127 105-3 71-0 187 155-0 104-6 247 20+-8 138-1 6-6 4" 5 68 56-4 38-0 128 106-1 716 188 155-9 105-1 248 205-6 138-7 7'5 5-0 69 57-2 38-6 129 106-9 72-1 189 156-7 105-7 249 206-4 139-2 5-6 70 58-0 39-1 130 107-8 72-7 190 157-5 106-2 250 207-3 139-8 ir 9-1 6-2 71 58-9 39-7 131 108-6 73-3 191 158-3 io6-8 "2?T 20S-1 140-4 12 9'9 6-7 72 59-7 40-3 132 109-4 73-8 192 159-2 107-4 252 208-9 140-9 IO-8 7'3 73 6o-5 40-8 133 110-3 74-4 193 i6o-o 107-9 ■253 209-7 141-5 11-6 7-8 74 6.-3 41-4 134 1111 74-9 194 160-8 108-5 •254 210-6 142-0 12-4 8-4 75 62-2 41-9 135 111-9 75-5 195 161-7 109-0 255 211-4 142-6 13-3 8-9 76 63-0 4^-5 13C II2-7 76-1 196 .62-5 1096 250 143-2 14-1 9-5 77 63-8 43-1 137 113-6 76-6 197 163-3 110-2 257 213-1 143-7 18 14-9 lo-i 78 64-7 43-6 138 114-4 77-2 198 164-1 110-7 258 213-9 144-3 19 10-6 79 65-5 44-2 139 115-2 77-7 199' 165-0 111-3 259 214-7 144-8 20 lie ir2 80 66-3 44'7 140 78-3 200 165-8 111-8 260 215-5 145-4 21 '7'4 II-7 81 67-2 45-3 141 1.6-9 78-8 201 166-6 112-4 261 216-4 145-9 22 l8-2 12-3 82 68-0 45'9 142 117-7 79-4 202 167-5 113-0 262 217-2 146-5 23 19-1 12-9 83 68-8 46-4 143 1186 8o-o 203 168-3 113-5 263 218-0 147-1 24 19-9 13-4 84 69-6 47-0 144 119-4 80-5 204 169-1 114-1 264 21S-9 147-6 25 20-7 14-0 85 70-5 47-5 145 205 II4-6 265 219-7 148-2 26 21-6 14-5 86 71-3 48-1 146 121-0 81-6 206 170-8 115-2 266 220-5 148-7 27 22-4 151 87 72-1 48-6 147 121-9 82-2 207 1716 iiS-8 267 221-4 149-3 28 23-2 15-7 88 73-0 49-2 148 122-7 82-8 208 172-4 116-3 268 222-2 149-9 2U 24-0 l6-2 89 73-8 49-8 149 123-5 83-3 209 173-3 116-9 269 223-0 150-4 30 '4-9 i6-8 90 74-6 50-3 150 124-4 83-9 210 174-1 117-4 270 223-8 151-0 31 »5'7 17-3 91 75'4 50-9 151 125-2 84-4 211 174'9 uS-o 271 224-7 151-5 26-5 17-9 92 76-3 5'-4 152 126-0 85-0 212 175-8 118-S 272 225-5 152-1 33 27-4 93 77-1 52-0 153 126-8 856 213 1766 119-1 273 226-3 152-7 34 I9-0 94 77-9 52-6 154 127-7 86-1 214 177-4 119-7 274 227-2 153-2 35 29'o 19-6 96 78-8 53-1 155 86-7 215 178-2 275 228-0 153-8 29-8 96 79-6 53-7 156 129-3 87-2 216 179-1 120-8 276 228-8 154-3 37 30-7 97 8o-4 54-2 157 130-2 87-8 217 179-9 121-3 277 229-6 154-9 38 3''5 98 8i-2 54-8 158 88-4 218 .80-7 121-9 278 230-5 155-5 39 3^'3 21-8 99 82-1 55-4 159 !lr8 219 i8i-6 122-5 279 231-3 156-0 40 33-2 22-4 100 82-9 55-9 160 132-6 i9-5 220 182-4 123-0 280 232-1 156-6 41 34-0 22-9 W 83-7 56-5 161 133-5 900 •221 ISyz 123-6 281 233-0 157-1 42 34-8 ^3-5 102 84-6 57-0 162 134-3 90-6 222 184-0 124- 1 282 2338 157-7 43 35-6 24-0 103 85-4 57-6 163 135-1 91-1 223 184-9 124-7 283 234-6 158-3 44 36-5 24-6 104 86-2 58-2 164 136-0 91-7 224 185-7 125-3 284 ^35-4 158-8 45 37|3 25-2 105 87-0 58-7 165 136-8 92-3 225 .86.5 125-8 285 236-3 159-4 46 25-7 106 59-3 166 137-6 92-8 226 187-4 126-4 286 237-1 159-9 47 39-0 26-3 107 88-' 59-8 167 138-4 93-4 227 188-2 126-9 287 237-9 160-i 48 39-8 26-8 108 89-5 6o-4 168 139-3 93-9 228 189-0 117-5 ■288 238-8 161-0 49 40-6 27-4 109 90-4 6i-o 169 140-1 94-5 229 189-8 12S-1 289 239-6 161-6 50 4i'5 110 91-2 6:-5 170 140-9 95-1 230 190-7 12S-6 290 240-4 162-2 TT 4-"3 28-5 111 92-0 62-1 171 141-8 95-6 231 1 191-5 129-2 ~29\ 241-2 162-7 52 43-1 29-1 112 92-9 62-6 172 142-6 96-2 232! 192-3 129-7 292 242-1 163-3 53 439 29-6 113 93-7 63-2 173 '43-4 96-7 2.33 193-2 130-3 293 242-9 .63-8 54 44-8 30-2 114 94-5 63-7 174 •44-3 97-3 234 194-0 130-9 294 243-7 164-4 55 45-6 115 95-3 64-3 175 145-1 97-9 235 194-8 131-4 296 244-6 .65-0 56 46-4 31-3 116 96-2 64-9 176 "45-9 98-4 236 ■95-7 132-0 296 245*4 .65-5 57 47-3 31-9 117 97-0 65-4 177 146-7 99-0 237 196-5 i3i'5 297 246-2 166-1 58 48-1 32-4 118 97-8 66-0 178 147-6 99-5 238 197-3 133-1 29« 247-1 166-6 59 48-9 33-0 119 98-7 ,66-5 179 148-4 239 19S-1 133-6 299 247-9 ,67-2 60 49-7 33-6 120 99-5 67-1 180 149-2 100-7 240 1990 134-2 300 248-7 167-8 Dist.| Uej,. D.Lat Dist Dt-p. D.Lat Dist. Dep. D. Lat. Dist Dep. D. Lat. Dist. Dep. D.Lat.! 56 ° 3h44m 1 TABLE TRAVERSE TABLE TO DEGREES ( 34° 2" IB" 1 Dist. D. Lat. Dep. Dist, D. Lat. Dep. Dist. D. Lat Dep. Dist. D. Lat. Dep. Dist. D. Lat. Dep. 301 2495 168-3 361 299-3 201-9 421 349-0 235-4 481 39S-8 269-0 541 448-5 302-5 302 2504 i6S-9 362 300-1 202-4 422 3499 236-0 482 399-6 269-5 542 449-4 303-1 303 251-2 169-4 363 300-9 203-0 423 350-7 236-5 483 4004 270-1 543 450-2 3036 304 2520 1700 364 3018 203-5 424 35'-5 237-1 484 401-3 270-6 544 451-0 304-2 305 252-9 170-6 365 302-6 204-1 425 352-3 237-7 485 402-1 271-2 545 451-8 3048 306 2537 171-1 366 303-4 204-7 426 353-2 238-2 486 402-9 271-8 546 452-6 305-3 307 254-5 1717 367 304-3 205-2 427 354-0 23SS 487 4038 2723 547 453-5 305-9 308 2553 172-2 368 305- « 205-8 428 354S 239-3 488 404-6 2728 548 454-3 3064 309 256-2 172-8 369 305-9 206-3 429 355-7 239-9 489 405-4 273-4 549 4552 3070 310 257-0 '73-3 370 3^(>1 2069 430 356-5. 240-4 490 406-2 1 274-0 550 _45^o _307J_| "311 2578 1739 371 3076 ~207-i 431 357 3 2410 491 407-1 j 274-6 551 456-8 308-1 312 25S7 174-5 372 308-4 20S0 432 358-> 241-6 492 407-9 275-1 552 4576 3087 313 2595 175-0 373 309-2 208-6 433 359-0 242-1 493 408-7 2757 553 458-4 309-2 314 2603 175-6 374 310-1 209-1 434 359-8 2427 494 409-5 2762 554 459-3 3098 315' 2612 176-1 375 310-9 209-7 435 S60-6 243-2 495 410-4 276-8 555 4601 310-3 316 2620 176-7 376 3"-7 436 361-5 2438 496 411-2 277-4 556 4609 3.0-9 317 2628 177-3 377 3126 210-8 437 362-3 2444 497 4120 277-9 557 461-7 ! 311-5 318 2637 177-8 378 313-4 211-4 438 363-1 244-9 498 412-8 278-4 558 462-6 312-0 319 2645 17S4 379 314-2 211-9 439 364-0 245-5 499 413-7 2790 559 463-4 3126 320 1 265-3 178-9 380 315-0 212-5 440 364-8 246-0 500 414-5 2796 560 464-2 3.31 321 2661 179-5 ssT 3«5-9 213-0 441 3656 246-6 501 415-3 280-1 561 465-1 1 3137 322 267-0 iSoi 382 316-7 213-6 442 366-4 247-2 502 416-2 280-7 562 465-91 314-3 323 2678 lSo-6 383 317-5 214-2 443 367-3 2477 503 417-0 28. -3 563 4668 314-S 324 268-6 181-2 384 31S-4 214-7 444 368-1 248-3 504 417-8 28 1-8 564 467-6, 3.5-4 325 2695 i8i-7 385 3192 215-3 445 36S-9 2488 505 418-6 282-4 565 468-4! 315-9 326 270-3 182-3 3S6 320-0 215S 446 369S 249-4 506 419-4 2S29 560 469-2 1 316 5 327 271-1 182-9 3S7 320-S 2.6-4 447 370-6 250-0 507 420-3 2S3-5 567 470-1 1 317-1 328 271-9 1S34 388 3217 2170 448 371-4 250-5 508 421-1 284-1 568 47091 3«7-6 329 2728 1840 389 3225 217-5 449 372-2 251-1 509 421-9 284-6 569 471-7! 318-2 330 273-6 184-5 390 323-3 218 1 450 3739 251-6 2522 510 422-8 285-2 -2'85^8 570 472-6 ■ 318-7 473-4 1 3193 331 274-4 ,85-. 391 3242 21S-6 451 511 423-6 571 332 275-2 185-6 392 3250 2192 452 374-7 2528 512 424-4 286-:! 572 474-2 1 319-9 333 276-1 1S62 393 325 8 219-8 453 375-6 253-3 513 425-3 2S6-9 573 475-0 ; 320-4 334 2769 1S6-8 394 3266 220-3 454 376-4 2539 514 426-1 2S7-4 574 475-9 3210 335 277-7 «87-3 395 3275 220-9 455 377-2 2544 515 426-9 I 2S8-0 575 476-7 321-S 336 2786 187-9 396 32S-3 221-4 456 378-0 2550 516 427-8 2S8-5 576 477-5 322-1 337 279-4 188-4 397 329-1 222-0 457 3789 255-5 517 428-6 289-1 577 478-3 : 3227 338 2S0-2 1S9-0 398 330-0 222-6 458 3797 256-1 518 429-4 289-6 578 4792 323-2 339 2810 1S9-6 399 3308 223-1 459 380-5 256-7 519 430-3 290-2 579 480-0 323-8 340 281-9 190-1 400 33'-6 2237 460 381-3 257-2 520 43I-1 290-8 580 4808 3243 347 282-7 190-7" 401 332-4 224-2 461 ISiT 257-8 521 431-9' 291-3 .5811 481-6, 324-9 1 342 2835 191-2 402 333-3 224-8 462 383-0 258-3 522 4328 291-9 582 482-5 325-4 343 284-4 I9I-S 403 334- » 225-4 463 3S3-8 258-9 523 433-6 292-5 583 483-3 3260 344 285-2 192-4 404 334-9 225-9 464 3S4-7 259-5 524 434-4 2930 584 484-1 3266 345 286-0 192-9 4U5 3358 226-5 405 385-S 260-0 525 435-3 2936 585 485-0 j 3272 346 2869 '93-5 406 336-6 1 2270 466 3S6-3 260-6 526 436-1 294-1 586 485-Si 3277 347 287-7 1940 407 337-4! 227-6 467 387-2 261-1 527 436-9 294-7 587 4S6 6 32S 2 348 28S-5 194-6 408 338-3 228-1 468 3S8-0 2617 528 437-8 295-3 588 487-5 328-8 349 ; 2893 1952 409 3391 228-7 469 38S-8! 262-3 529 438-6 2958 589 488-3 1 329-4 350 ! 2902 _i95-7 410 339-9 229-3 470 3897! 262-S 530 439-4 296-4 590 489-2 i 329-9 351 1 2910 196-3 411 340-7 1 229 8 471 390-51 263-4 -bEi 4403 296-9 .591 490-0 j 330 5 352 2918 196 8 412 341-6 230-4 472 391-3 263 -9 532 4411 2974 592 490-81 331-0 353 2927 197-4 413 342-4 i 230-9 473 392-1 1 264 5 533 441-9 29S-0 593 491-6 1 331-6 354 2935 1980 414 3432 231-5 474 393-0 1 265-0 534 4427 298-6 594 492 5 1 332-2 355 1 2943 19S-5 415 344- 1 232-1 475 3938 ; 265-6 535 4436 2991 595 493-3 1 332 7 356' 2951 199-1 416 3449 232 6 476 394-6 266-2 536 444-4 2997 590 494-1 333-3 357 2960 199-6 417 345-7 233-2 477 395-5 266-7 537 445-3 3002 597 494-9 333 8 358 1 2968 2002 418 346-5 233-7 478 396-3 267-3 538 446-1 300-8 598 495-8 334 4 359 1 2976 2007 419 347-4 234-3 479 397 ■« 267-9 539 4469 301-4 599 496 6 1 334 9 3C0 298-5 2013 420 348-2 234 9 480 397-9 26S-4 540 447-7 3020 600 497 4 335 5 Di6t.| Del.. dTu, Dist Di-p. D. Lat. Dist Dep. D. Lat i^ Dep. D. Lat. Dist Dep. jD. Lat. 6G° .SMJ™ 1 500 TABLE 1 TRAVERSE TABLE TO DE GREES 35° 2" 20" J)ist.D.La Der- Dist D.Lat. Dep. Dist.'o. Lat Dep. Dist.b. Latl Dep. Dist.!D. Lat.l Dep. 1 1 0-8 0-6 61 1 50-0 35-0 121 1 99-1 69-4 181 148-3 103-8 241; 197-4; 138-2 2 1 1-6 i-i 02, 50-8 : 35-6 122 99-9 182 149-1 104-4 242 .98-2 13S-8 3 2-5 1-7 03 51-6 ; 36-1 123 I0O-8 70-5 1H3 149-9 105-0 243 199-1 '39-4 4 3-3 2-3 64' 5^-4 36-7 124 io,-6 184 150-7 105-5 244 199-9 140-0 5 4i 2-9 65 53-2 37-3 125 .02-4 71-7 185 151-5 106-1 245 140-5 6 4-9 3;4 60 1 54-1 37-9 120!. 03-2 72-3 180 152-4 106-7 246 201-5 141-1 7 5-7 07 54-9 38-4 127 104-0 72-S 187 153-2 107-3 247 202-3 141-7 8 6-6 4-6 68 55-7 39'° 128 104-9 73-4 188 154-0 107-8 248 203-1 142-2 9 7-4 5'2 69 56-5 39-6 129 1057 74-0 189 .54-8 108-4 249 204-0 142-S 10 I 8-2 5"7 70 57-3 l_i°-^ 130 .06-5 74-6 190 155-6 109-0 250 204-8 143-4, 11 9-0 1 6-3 71 58-2 407 131 107-3 75-1 191 156-5 109-6 251 205-6 144-0 12 9-8 6-9 72 59-0 41-3 1.32 108-1 75-7 192 157-3 110-1 262 206-4 144-5 13 10-6 7-5 73 59-8 41-9 133 108-9 76-3 193 158-1 110-7 253 207-2 145-1 14 11-5 8-0 74 606 42-4 134 109-8 76-9 194 158-9 111-3 254 208-1 '45-7 15 12-3 8-6 75 61-4 43 -o 135 110-6 77-4 195 159-7 111-8 255 208-9 146-3 It; 13-1 92 76 62-3 43-6 130 111-4 78-0 190 160-6 112-4 250 209-7 1468 17 13-9 9-8 77 63-. 44-2 137 78-6 197 161-4 113-0 257 210-5 147-4 18 14-7 IO-3 78 63-9 44-7 138 113-0 79-2 198 162-2 113-6 •258 211-3 148-0 19 ,5-6 10-9 79 64-7 45-3 139 113-9 79-7 199 163-0 114-1 259 148-6 20 '6-4 ii'S 80 65-5 45-9 140 1 14-7 80-3 200 163-8 114-7 200 213-0 149-1 21 17-2 I2-0 "sT 66-4 46-5 14i: 115-5 80-9 201 1646 115-3 2cr 213-8 149-7 22 i8-o 12-6 82 67-2 47-0 142 116-3 8i-4 202 .65-5 115-9 262 214-6 150-3 23 i8-S 13-2 83 68-0 47-6 143 117-1 82-0 203 .66-3 .16-4 203 215-4 150-9 24 19-7 138 84 68-8 48-2 144 ii8-o 82-6 204 167-1 117-0 264 216-3 151-4 25 20-5 14-3 85 1 69-6 48-8 145 118-8 83-2 205 167-9 117-6 205 217-1 152-0 20 14-9 86 70-4 49-3 146 119-6 83-7 200 168-7 118-2 200 217-9 152-6 27 22-1 15-5 87 71-3 49-9 147 84-3 207 169-6 118-7 267 218-7 153-1 28 22-9 161 88 72-1 50-5 148 121-2 84-9 •208 170-4 119-3 208 219-5 153-7 29 23-8 i6-6 89 72-9 51-0 149 122-1 85-5 209 171-2 119-9 209 220-4 ■54-3 30 24-6 17-2 90 73-7 51-6 150 122-9 86-0 210 172-0 120-5 270 154-9 31 25-4 17-8 91 74-5 52-2 151 123-7 86-6 2111 172-8 121-0 271 222-0 155-4 32 26-2 i8-4 92 75-4 52-8 152 124-5 87-2 212 ■73-7 iIi-6 272 222-8 156-0 33 27-0 iS-9 93 76-2 53-3 153; 125-3 87-8 213 174-5 122-2 273 223-6 .56-6 34 27-9 i9'5 94 77-0 53-9 154 I26-I 88-3 214 175-3 122-7 274 224-4 157-2 35 28-7 20-I 95 77-8 54-5 155 127-0 88-9 215 176-1 123-3 275 225-3 157-7 36 29-5 20-6 96 78-6 55-1 156 127-8 89-5 210 176-9 123-9 276 158-3 37 30-3 21-2 97 795 55-6 157 128-6 90-1 217 177-S 124-5 277 ;;6-9 158-9 38 3>i 21-8 98 8o-3 56-2 158 129-4 90-6 218 178-6 125-0 278 227-7 159-5 39 31-9 22-4 99 8i-i 56-8 159 130-2 91-2 219 179-4 125-6 279 228-5 160-0 40 32-8 100 8. -9 57-4 100! .3.-. 9.-8 220 iSo-. 126-2 280 229-4 160-6 41 33-6 23-5 Tor 82-7 57-9 101 1 .31-9 92-3 221 181-0 "716^8- 281 230-2 161-2 42 34'4 24-1 102 83-6 58-5 162! 'i--7 92-9 222 18.-9 127-3 282 231-0 i6i-- 43 35-2 24-7 103 84-4 59-1 103 .33-5 93-5 223 182-7 127-9 283 231-8 162-3 44 360 25-2 104 85-2 59'7 104 134-3 94-1 224 183-5 128-5 284 232-6 162-9 45 36-9 25-8 105 86-0 6o-2 165 135-2 94-6 225 18+3 1291 285 233-5 ; '63-5 40 377 264 106 86-8 6o-8 100 136-0 95-2 226 185-1 i2;-6 286 234-3 I 164-0 47 385 107 87-6 6i-4 107 136-8 95-S -227 185-9 287 235-1 164-6 48 39-3 27-5 108 88-5 61-9 108 137-6 96-4 228 186-8 130-8 288 235-9 165-2 49 40-1 28-1 109 89-3 62-5 1091 13S-4 96-9 229 1S7-6 131-3 289 236-7 165-8 50 41-0 28-7 110 90-1 63-. 170 1.39-3 97-5 230 188-4 131-9 290 237-6 166-3 51 41-8 29-3 111 90-9 63-7 171 1 140- 1 98-1 ^3r 189-2 132-5 291 238-4 166-9 52 42-6 29-8 112 91-7 1 64-2 172 140-9 9S-7 232 190-0 133-1 292 239-a 167-5 53 43-4 30-4 113 92-6 1 64-8 173 141-7 99-2 233 190-9 >33-6 293 240-0 i68-i 54 44'2 31-0 114 93'4 65"4 174 142-5 99-8 234 191-7 134-2 294 240-8 16S-6 55 4^1 3i'5 115 94-2 66-0 175 143-4 100-4 235 192-5 i34-« 295 241-6 169-2 50 45-9 32-1 110 95-0 66-5 170 144-2 100-9 236 193-3 ■35-4 296 242-5 169-8 57 46-7 32-7 117 95-8 67-1 177 145-0 101-5 237 194-1 135-9 297 243-3 170-4 58 47-5 33'3 118 96-7 1 67'7 178 145-8 I02-1 ■238 195-0 136-5 298 244-1 170-9 59 48-3 33-8 119 179 146-6 102-7 239 195-8 137-1 299 244-9 171-5 60 49-1 34-4 120 98-3 6S-S 180 "47-4 103-2 240 ,96-6 137-7 300 245-' 172-1 Dist. Dep. D.Lat Dist. Dep. D.Lat Dist. Dep. D.Lat. Dist. Dep. D. Lat. Disl. Dep. D. Lat. 55° 3M0™ { TABLE 1 501 TRAVERSE TABLE TU DEGREES 85° 2" 20>° Dist.JD. Lat. Dep. DistJo. Lat. D.p. Dist. D. Lat. Dep. Dist. D.Lat. Dep. Dist. D.Lat.l Dep. 301 2466 172-6 361 2957 207-0 421 344-9 241-5 481 394-0 275-9 541 443-2 3103 302 2474 173-2 362 296-5 2076 422 345-7 242-0 482 394-8 276-4 542 444-0 3109 303 248-2 173S 363 297-4 20S-2 423 346-5 242-6 483 395-7 277-0 .543 444-8 311-4 304 2490 "743 364 29S-2 ' 20S-8 424 347-3 243-2 484 396-5 277-6 544 445-6 3.2-0 305 2499 174-9 365 2990 209-3 425 348-. 243-8 485 397-3 278-2 545 446-4 3126 306 1 2507 175-5 366 299-S 2099 426 349-0 244-3 486 398-1 278-7 546 447-3 313-2 307 i 251-5 1 76-. 367 3006: 210-5 427 349-8 244-9 487 398-9 279-3 547 4481 313-7 308 252-3 176-6 368 301-5 2II-I 428 350-6 245-5 488 399-8 279-9 548 448-9 314-3 SOS j 253-1 177-2 369 302-3 2 1 1-6 429 351-4 246-0 489 400-6 280-s 549 449-7 314-9 310^ 253-9 311 j 254-8 _L77l 1784 370 37T 303-1 I 212-2 303-9, 212-8 430 431 352-2 2466 247-2 490 491 401-4 402-2 281-0 T8T6 550 551 450-5 315-4 3160 3531 4514 312 255-6 .78-9 372 304-7 213-4 432 3539 247-8 492 4030 282-2 552 452-2 316-6 313 256-4 179-5 373 305-6] 213-9 433 354-7 248-3 493 403-9 282-8 553 453-0 317-2 314 257-2 I So- 1 374 306-4 214-5 434 355-5 248-9 494 404-7 283-3 554 453-8 317-7 315 1 25S-0 1S07 375 307 2 215-1 435 356-3 , 249-5 495 405-S 283-9 555 454-6 318-3 816 I 25S9 1812 376 308-0 2.5-6 436 357-2 250-. 496 406-3 284-5 556 455"5 318-9 317 1 2597 181& 377 308-8 2.6-2 437 3580 250-6 497 407-1 285-. 557 456-3 319-5 318: 2605 182-4 378 309-6 2.6-8 438 358-8 25.-2 498 408-0 2S5-6 558 457-1 320-0 319! 261-3 183-0 379 310-5 217-4 439 359-6 251-S 499 4088 2S6-2 559 457-9 320-6 320 1 262-1 321 j 263-0 1S3-5 1841 380 381 311-3 312-1 -Sf 440 360-4 252-4 500 501 4096 286-8 560 56"l 458-7 32.-2 36.-3 252-9 4.0-4 287-4 459-6 321-8 322 263-8 184-7 382 312-9 2.9-. 442 362-1 2535 502 4II-2 287-9 562 460-4 322-3 323 2646 185-2 383 3.37 2.9-7 443 362-9 2541 503 4I2-I 288-5 563 46. -2 3729 324 265-4 185-8 384 314-6 220-2 444 363-7 254-7 504 412-9 289-1 564 462-0 323-5 325 266-2 .86-4 385 315-4 220-8 445 364-5 255-2 505 413-7 2S97 565 462-8 324-1 326 2671 .87-0 386 316-2 221-4 446 365-4 255-8 506 414-5 2902 566 463-7 324-6 327 267-9 187-S 387 317-0 222-0 447 3662 256-4 507 415-3 290-8 567 464-5 325-2 328 268-7 1 88- 1 388 317-S 222-5 448 367-0 256-9 508 4I6-I 291-4 568 465-3 325-8 329 269-5 188-7 389 31S7 223-1 449 367-8 257-5 509 4.7-0 29.-9 569 466-1 326-4 330 331 270-3 189-3 ~ 1 89-8 390 391 319-5 223-7 450 45T 368-6 258-. 258-7 510 417-8 292-5 570 571 466-9 326-9 327-5 271-1 320-3 224-3 369-4 IlT 4IS-6 293-1 467-8 332 272-0 190-4 392 224-S 452 370-3 2592 512 419-4 293-7 572 468-6 32S. 333 272-S 191-0 393 321-9 225-4 453 371-1 2598 513 4202 2942 573 469-4 328-7 334 2736 191-6 394 322-8 226-0 454 371-9 260-4 514 42.-. 294-8 574 470-2 3292 335 274-4 192-1 395 [ 323-6; 226-5 455 372-7 26.-0 515 421-9 2954 575 4710 329-8 336 275-2 192-7 396 324-41 227-1 456 373-5 26.5 516 422-7 296-0 576 471-9 330-4 337 276-1 193-3 397 325-2 227-7 457 374-4 262-. 517 423-5 296-5 577 472-7 331-0 338 276-9 193-9 398 326-0 2283 458 375-2 262-7 518 424-3 297-1 578 473-5 331-5 339 2777 194-4 399 326-9 22S-8 459 376-0 263-3 519 425-2 297-7 579 474-3 332-1 340 341 J7S1 2793 .95:0 1956 400 327-7 229-4 230-0 400 4gT 37i| 377-6 263-8 264-4 520 521 426-0 156^8 298-3 T98^8 580 581 475-1 476-0 332-7 401 : 32S-5 333-3 342 ' 280-2 196-1 402 , 329-3 2306 462 378-5 2650 522 427-6 299-4 582 476-8 333-8 343 ' 281-0 1967 403 1 330-1 23. -I 463 379-3 265-5 523 4284 3000 583 4776 334-4 344 ' 281-8 '97-3 404 3309 231-7 464 380-. 266-1 524 429-3 300-5 584 478-4 335-0 345 282-6 197-9 405 1 33,-8 2323 465 380-9 266-7 525 430- . 301-. 585 479-2 335-6 346 i 283-4 198-4 406 1 332-6, 2329 466 381-7 267-3 526 430-9 301-7 586 480-. 336-1 347 284-3 1990 -*o" ' 333-4 233-4 467 382-6 2678 527 431-7 302-3 587 480-9 3367 348 2S5-1 iyy-6 408 3342 234-0 468 383-4 268-4 528 432-5 302-8 588 481-7 337-3 349 2S5-9 2002 ''OSi 3350 234-6 469 384-2 2690 529 433-4 303-4 589 4S2-5 337-9 350 286-7 2007 2013 -•lol 3359 235-1 470 471 385-0 3S58 2696 270-r 530 531 434-2 304-0 304-5 590 591 483-3 "484-2 338-4 3390 35TI 287-5 411 1 33671 2357 435-0 352 288-3 201-9 412; 337-5 236-3 472 386-6 270-7 532 435-8 305-1 592 485-0 3396 353 , 2S9 2 202-5 413; 338-3, 2369 473 387-5 271-3 533 436-6 305-7 593 485-8 340-2 354, 2900 203-0 414 339-1 237-4 474 3S8-3 2719 534 437-5 306-3 594 486-6 340-7 355 2908 2036 415 1 340-0 2380 475 389-1 272-4 535 43S-3 306S 595 487-4 341-3 356! 291-6 204- 2 416 1 340-8 2386 476 389-9 2730 536 4391 307-4 596 488-3 3419 357 i 292-4 2047 417 341-6 239-2 477 390 7 1 273 6 537 439-9 308-0 597 4S91 342-5 358 293-3 2053 41 s 3424 239-7 478 391-6 1 274-2 538 4407 3086 598 489-9 343-0 359 ; 294-1 2059 419 343-2 240-3 479 392-4 2747 539 441-5 309-1 599 490-7 343-6 360 1 2949 206-5 420 1 344-1 2409 480 393-2 1 275-3 540 442-3 309-7 600 491-5 3441 iDist^^ Dep. D.Lat iJist.' Dop. iD. Lat Dist Dep. la Lat Divt Dep. D. Lat Dist i;e7 D.Lat r 55° 8" 40"^ TRAVERSE TABLE TO DEGREES 36° 2h24n> Dist.jD.Lat Dep. Dist.JD.Lat Dep. Dist.lo. Lat. Dep. Dist D.Lat Dep. Dist. D. Lat.j Dep. j I 0-8 61 49-4 35-9 121 97-9 71-1 181 146-4 106-4 241 195-0 141-7 2 1-6 C2 50 36-4 122 98-7 7i'7 182 147-2 107-0 242 195-8 142-2 3 »-4 63 51 37-0 123 99-5 72-3 183 148-1 107-6 243 196-6 142-8 4 3-2 64 51 37-6 124 IOO-3 72-9 184 148-9 108-2 244 '97-4 143*4 5 4'o 65 5^ 38-2 125 73-5 185 149-7 108-7 245 198-2 144-0 6 49 66 53 38-8 126 I0I-9 74' I 18G 150-5 109-3 246 199-0 144-6 7 5-7 67 54 39'4 127 102-7 74-6 187 151-3 109-9 247 199-8 145-2 8 6-S 68 55 40-0 128 I03-6 75-i 188 152-1 110-5 248 200-6 145-8 9 7-3 69 55 40-6 120 104-4 75-8 189 152-9 iii-i 249 201-4 ,46-4 10 8-1 70 _ii 41-1 130 105-2 76-4 190 153-7 111-7 250 202-3 146-9 TT 8-9 71 57 41-7 131 106-0 77-0 ToT 154-5 112-3 251 203-1 147-5 12 9-7 72 58 42-3 132 106-8 77-6 192 155-3 112-9 252 203-9 148-1 13 lo-s 73 59 42-9 133 .07-6 78-2 193 156-1 113-4 253 204-7 148-7 14 II-3 74 59 43-5 134 I08-4 78-8 194 156-9 114-0 254 205-5 '49-3 15 ii-i 75 60 44-1 135 109-2 79-4 195 157-8 114-6 255 206-3 149-9 16 12-9 76 61 44-7 136 79-9 196 158-6 115-2 256 207-1 150-5 17 .3-8 77 62 45-3 137 110-8 80-5 197 159-4 115-S 257 207-9 151-1 18 14-6 78 63 45-8 138 1.1-6 81-1 198 160-2 116-4 258 208-7 151-6 19 ■5-4 79 6 139 112-5 8i-7 199 161-0 117-0 259 209-5 152-2 20 i6-. 80 64 ^ t 140 113-3 82-3 200 161-8 117-6 260 210-3 .52-8 21 lyoi 12-3 81 65 r 47-6 141 1 14- 1 82-9 201 .62-6 118-1 261 153-4 22 17-8 12-9 82 66 3 48-2 142 114-9 83-5 202 163-4 118-7 262 212-0 154-0 23 i8-6| 13-5 83 67 48-8 143 115-7 84-1 203 164-2 119-3 263 212-8 154-6 24 19-4 141 84 49-4 144 116-5 84-6 204 165-0 119-9 264 213-6 155-2 25 20-2 14-7 85 68 50-0 145 117-3 852 205 165-8 120-5 265 214-4 155-8 26 21'0 ■5-3 86 69 50-5 146 118-1 85-8 206 166-7 266 215-2 .56-4 27 2I-S 15-9 87 70 51-1 147 .iS-9 86-4 207 167-5 121-7 267 216-0 156-9 28 22-7 i5-s 88 71 SJ-7 148 119-7 87-0 208 168-3 122-3 268 216-8 '57-5 29 23-5 89 72 5^*3 149 120-5 87-6 209 169-1 122-8 269 217-6 158-1 30 24-3 17-6 90 _Z1 8 52-9 150 151 121-4 88-2 210 ,69-9 123-4 270 218-4 158-7 31 25-1 lS-2 91 73 — 53-5 122-2 88-8 211 170-7 124-0 271 219-2 159-3 32 25-9 i8-8 92 74 54' I 152 123-0 89-3 212 171-5 124-6 272 159-9 33 26-7 19-4 93 75 54' 7 153 89-9 213 172-3 125-2 273 220-9 .60-5 34 27-5 94 76 55-3 154 124-6 90-5 214 173-1 125-8 274 221-7 .6i-i 35 20-6 95 76 55-8 155 125-4 91-1 215 '739 .26-4 275 222-5 i6i-6 36 29-1 21-2 96 77 56-4 156 .26-2 91-7 216 '74-7 127-0 276 223-3 162-2 37 299 21-7 97 7« 57-0 157 92-3 217 '75-6 127-5 277 224-1 162-8 38 30-7 22-3 98 79 57-6 158 92-9 218 .76-4 118-1 278 224-9 163-4 39 31-6 22-9 99 80 58-2 159 12S-6 93'5 219 177-2 I2S-7 279 225-7 164-0 40 32-4 23-5 100 80 9_ 58-8 160 129-4 94-0 220 178-0 129-3 280 226-5 .64-6 41 33-2 24-1 101 81 59*4 161 130-3 94-6 22r 178-8 129-9 281 227-3 165-2 42 34-0 24-7 102 82 6o-o 162 95-2 222 179-6 130-5 282 228-1 165-8 43 34-8 25-3 103 83 60-5 163 131-9 95-8 223 ,So-4 131-1 283 229-0 ''A'^ 44 35-6 25-9 104 84 6i-i 104 132-7 96-4 224 iSi-» 131-7 284 229-8 166-9 45 36-4 26-5 105 84 6i-7 105 '335 97-0 225 182-0 I3J-3 285 230-6 .67-5 46 37-2 27-0 106 85 62-3 160 •34"3 97-6 226 182-8 132-8 286 231-4 168-1 47 38-0 27-6 107 86 62-9 107 135-1 98-2 227 183-6 133-4 287 232-2 168-7 48 38-8 28-2 108 87 63-5 168 '35-9 98-7 228 184-5 134-0 •288 233-0 169-3 49 39-6 28-8 109 88 64-1 109 136-7 99-3 229 185-3 '34-6 289 2338 ,69-9 00 40-5 29-4 110 89 64-7 170 137-5 99"9 230 186-1 135-2 290 234-6 ■ 170-5 51 4i"3 30-0 111 89 ~ 65-2 171 .38-3 IOO-5 231 1S6-9 135-8 291 235-4! i7'-o 52 42-1 30-6 112 90 65-8 172 139-2 232 .87-7 ,36-4 292 236-2 i 171-6 53 42-9 31-2 113 9' 66-4 173 140-0 101-7 233 188-5 137-0 293 237-0,172-2 54 43-7 3'-7 114 9^ 67-0 174 i40'8 102-3 234 .89-3 ■37-5 294 237-9 172-8 55 44-5 32-3 115 93 67-6 175 I4I-6 102-9 235 190- 1 .38-1 295 238-7 173-4 56 45-3 32-9 116 93 68-2 176 142-4 103-5 236 190-9 138-7 296 ^39-5 174-0 57 46-. 33'5 117 94 «8-8 177 143-2 104-0 237 191-7 ■39-3 297 240-3 174-6 58 46-9 3+'' 118 95 5 69-4 178 144-0 104-6 238 192-5 139-9 298 241-1 175-2 59 47-7 34-7 119 96 3 699 179 144-8 105-2 239 '93-4 140-5 299 241-9 '75-7 60 48-5 I 35-3 120 97-1 70-5 180 145-6 .05-8 240 .94-2 141-1 300 242-7 176-3 Dist Dep.D.Ut Dist D !'• D.Lat Dist. De,.. D. Lat. Dist. Dep. D. Lat. Dist. Dep. D. Lat. 54» 3" 36™ 1 508 TRAVERSE TABLE TO DEGREES 36° 2" 24-" Dls. D.I..t Dep. Dist. D. Lat. Dep. Dist. D. Lat. Dep. D,„. D. Lat. Dep. Dist. D. Lat. Dep. 301 243-5 1769 361 292-1 212-2 421 340-6 247-5 ^17 3S91 282-7 541 437-7 3180 302 244-3 1775 362 292-9 212-8 422 341-4 248-. 482 390-0 283-3 542 438-5 318-6 303 245-1 1 78- 1 363 2937 2134 423 342-2 248-6 483 390-8 283-9 543 439-3 3191 304 2460 178-7 364 294-5 214-0 424 ; 343 249-2 484, 39.-6 2S4-5 544 440-2 319-7 305 246-Sl 179-3 365 295-3 2146 425, 3438 249-8 485 1 392-4 285-, 545 44,0 320-3 306 2476 179-9 366 296-1 215-1 426] 34^7 2504 486 393-2 285-6 546 4418 320-9 307 24S4' 1S0-5 367 296-9 215-7 427 345-5 251-0 487 39+0 286-2 547 442-6 3215 308 249-2 iSi-i 368 297-7 2.6-3 428 3463 251-6 488 394-8 286-8 548 443-4 322-1 309 2500' iSi-6 369 298-5 216-9 429 347-1 252-2 489 395-6 287-4 549 444-2 322-7 310 2508 182-2 370 ^9_9:3. 217-5 430 347-9 j5^8 490 396-4 288-0 550 445-0 J23:3 311 '25Tb 1828 371 300-2 218-1 431 348-7 ! 253-3 491 397-3 "^88^6 551 445-8 3238 31-> 2524 ■83-4 372 3010 218-7 432 3495 1 253-9 492 398-1 2S92 552 4466 324-4 313 2532 1840 373 301-8 219-3 433 ; 350-3 254-S 493 39S-9 289-8 553 447-4 325-0 314 254-0 184-6 374 3026 2.9-8 43i 351. 255-1 494 3997 290-3 554 44S-2 325-6 315 254-9 1852 375 303-4 220-4 435 35.9 255-7 493 400-5 290-9 555 449-0 326-2 316 255-7' 1S5-S 376 304-2 221-0 436 352 7 256-3 496 40.-3 29,-5 556 449-8 3268 317 250-5: 1S6-4 377 305-0 221-6 437 3536 2569 4'.I7 402-1 292-, 557 4507 3274 318 257-3; 186-9 378 30S-8 222-2 438 i 354-4 257-5 498 402-9 292-7 558 451 5 328-0 319 25S-1 ; 187-5 379 306-61 222-8 439, 355-2 2580 499 403-7 293-3 559 452-3 328-5 3'-'0 258-9 1 1S81 3S0| 307-4! 223-4 440, 3560 2586 500 404-5 293-9 560 453-1 329-' 321 259-7',' "1S8-7 3S1 308-2, 224-0 44ir356 8| 259-2 501 4053 294-5 561 453-9 329-7 322 260-5 IS9-3 332 309-1 224-5 442 1 357-6 259-8 502 406-1 295-0 562 454-7 330-3 323 261-3 'S99 3.-<3 309-9 225-1 443 3584 200-4 503 407-0 295-6 563 4555 330-9 324 262-1 1 190-5 384 310-7 225-7 444 ' 359-2 261-0 504 407-8 296-2 564 456-3 331-5 325 26J-9 1910 385 311-5 2263 445 ! 3600 261-6 505 408-6 296-S 565 457-1 332-1 326 263-7, 19 ■ -6 386 312-3 226-9 446 360-8 262-2 .506 409-4 297-4 566 457-9 332-7 327 264-6 192-2 387 313-1 227-5 447 361 6 2628 507 4,0-2 2980 567 45-8-7 333-3 328 265-4, 1928 388 3'3-9 228-1 448 362-4 263-3 508 411-0 298-6 568 459-5 333-8 329 266-2: 193-4 389 314-7 228-7 449 3633 2639 509 411-8 299-2 569 460-3 334-4 330 33T 267-0 1040 267 8 , 19+6 390 3155 229-2 229-8 450 451 364-1 364-9 264-5 265-. 510 4.26 2998 570 46,-, 4620 335-0 3356 3911 316-3 511 4.3-4 300-3 571 332 2686 1 195 2 392 317-1 230-4 452 365-7 265-7 513 4.4-2 300-9 572 4628 336-2 333 269-4' 1957 393 3180 231-0 453 366-5 2663 513 4.5-1 30.-5 573 463-6 3368 334 270-2 , 196-3 394 1 318-8 231-6 454 367-3 206-9 514 1 4,5-9 302-1 574 464-4 337-4 335 27JO 1969 395 319-6 232-2 455 368-1 267-5 515 4,6-7 302-7 575 465-2 338-0 336 271-8 197-5 396, 320-4 2328 456 I 368-9 26S-0 516 4,7-5 303-3 576 466-0 338-5 272-6 198 I 397 1 321-2 233-4 457 369-7 268-6 517] 4,8-3 303-9 577 466-8 339-1 333 273-5 1 198-7 398 1 322-0 233-9 458 1 370-S 2692 518 419-1 304-4 578 4676 339-7 339 274-31 199-3 399 , 322-8 : 234-5 -159; 371-3 269-8 519 4199 305-0 579 468-4 3403 340 275-1 1 199 9 400 1 323-6 1 235-1 460 372-2 270-4 520 420-7 J05:6 580 469-3 340-9 341 1 275-9 200 4 401 324-4! 235-7 461 373 o| 27. -0 521 42.-5 306-2 581 470-1 341-S 342 1 276-7; 2010 402 325-2, 2363 462, 373-8 1 2716 522 422-3 306-8 582 470-9 342-1 343 1 2775; 201-6 403 3260 2369 463 1 374 6 272-2 523 423-' 307-4 583 471-7 342-7 344 278-3 ' 202 2 404 326-9 2375 464, 375-4 1 2727 524 4239 308-0 584 472-s 343-2 345 279-1 202 -8 405 I 3277 238-. 465 376-21 273-3 525 424-7 308-6 585 473-3 3438 346 279-9 203-4 406 1 328 5 238-7 466 377-0 t 2739 526 425-5 3092 586 474-1 344-4 34- 280-7 2040 407 329-3 239-2 467 377-81 274-5 527 426-4 309-7 587 474-9 3450 348 281-5 204-6 408 330-1 468 378-6, 275-. 528 427-2 3103 588 475-7 345-6 349 2S24 205 I 409 1 3309 2404 469 379-4 275-7 529 428-0 3,0-9 589 476-5 346-2 350 283-2 205-7 410, 33'7 24.0 470 380-2 2763 5.30 428-8 jij:5_ 590 ^7J. 3468 "351 284-0 2063 411 332-5 241-6 471 3S1-1 276-9 531 429-6 3I2-I 591 478-2 347-4 352 2848 206 -9 412 3333 242-2 472 38 '-9 277-4 532 430-4 3.2-7 592 4790 3479 353 285-6 2075 413 3341 2428 473 382-7 278-0 533 431-2 313-3 593 479-8 348-S 354 2S6-4 20S I 414 334-9 243-4 474 383-5 278-6 5.34 432-0 313-9 594 480-6 3491 .■155 2S7-2 20S7 415] 335» 243-9 475 ' 3843 279-2 535 432-9 314-4 595 48,-4 349-7 356! 2S8-0I 209- J 416! 336-6 2445 476 385-1 2798 536 4337 3,50 596 4822 3503 35'7| 2S8-8| 209 S -417! 3374 245-1 477 385-9 1 280-4 537 434-5 315-6 597 483-0 350-9 358, 289-61 210-4 418, 338-2 245-7 478 3867 2810 538 435-3 3,6-2 598 4838 3S1-5 359 2904 211 419! 339-0 246-3 479 387-5 28.-6 539 436- ■ 3168 599 4846 3521 360 DisL 29«-3 21 1-6 4-20 1 339-8 Dist. Uep. 246-9 480 388-3 282-1 540 1 436-9 Dist.| Dep. 3174 D.Lat 600 Dist 485-4 3527 I>ep a,... O.Lat Dist |d.p. D.I^t Dep. D. Lat. 5 1° Sh SG™ 1 504 TRAVERSE TABLE TO DEGREES | 37° 2h 28"> \ Dist. D.Lat| Dep. Dist.D.Lat. Dep. Dist-D. Lat. Dep. Dist. D. Lat. Dep. Dist. D. Lat.j Dep. | 1 0-8 0-6 CI 48-7 367 121 96-6 72-8 181 144-6 .08-9 241 192-5 145-c 2 1-6 1-2 62 49-5 37-3 122 97;4 73-4 182 145-4 109-5 242 193-3 145-6 3 2-4 1-8 63 50-3 37-9 123 74-0 183 146-2 243 194-1 146-2 4 3-2 2-4 64 51-1 38-5 124 99-0 74-6 184 146-9 110-7 244 194-9 .46-8 5 4.-0 3-0 65 51-9 39-1 125 75-2 185 147-7 11.-3 245 195-7 147-4 6 4-8 3-6 66 52-7 39-7 126 ,00-6 75-8 180 148-5 111-9 240 196-5 .48-0 7 5-6 4'2 67 53-5 40-3 127 101-4 76-4 187 149-3 112-5 247 197-3 .48-6 8 6-4 4-8 68 54-3 40-9 128 77-0 188 150-1 248 198-. 149-3 9 7-2 5-4 69 55'i 4'-S 129 103-0 77-6 189 150-9 113-7 249 198-9 149-9 10 8-0 6-0 70 55-9 42-1 130 103-8 78-2 190 15.-7 114-3 250 199-7 150-5 151 1 11 8-8 6-6 71 567 427 131 104-6 78-8 -m 152-5 114-9 251 200-5 12 9-6 7-2 72 57-5 43'3 132 105-4 79'4 192 153 3 115-5 252 201-3 151-/ 13 IO-4 7"8 73 58-3 43'9 133 106-2 So-o 193 154-1 1.6-2 253 202-1 152-3 14 11-2 8-4 74 59-1 44'5 134 107-0 8o-6 194 154-9 116-8 254 102-9 152-9 15 12-0 9-0 75 59'9 45'i 135 I07-8 81-2 195 155-7 117-4 255 203-7 153-5 16 1 2- 8 9-6 76 607 45'7 130 108-6 81-8 196 156-5 118-0 256 204-5 154-1 17 13-6 77 6. -5 46-3 137 109-4 82-4 197 157-3 118-6 257 205-2 154-7 18 1 H-4 IO-8 78 62-3 46-9 138 83-1 198 158-, 119-2 258 206-0 155-3 19 1 .5-2 II-4 70 63-1 47'5 139 III-O 83-7 199 158-9 119-8 259 206-8 155-9 20 i6-o I2-0 80 63-9 48-1 140 111-8 84-3 200 159-7 120-4 260 207-6 156-5 -w i6-8 12-6 -sr 647 487 141 112-6 84-9 201 160-5 121-0 261 2C8-4 157-1 22 17-6 132 82 65-5 49' 3 142 113-4 85-5 202 ■ 6,-3 121-6 202 209-2 ■57-7 23 i8-4 83 66-3 50-0 143 114-2 86-1 203 162-1 122-2 203 .58-3 24 19-2 14-4 84 67-. 50-6 144 115-0 86-7 204 162-9 122-8 264 210-8 158-9 25 15-0 85 67-9 51-2 145 iiS-8 87-3 205 163-7 123-4 265 2.1-6 159-5 26 20-8 15-6 86 51-8 140 ii6-6 87-9 206 164-5 124-0 266 212-4 i6o-. 27 21-6 l6-2 87 69-5 52-4 147 117-4 207 165-3 .24-6 267 2.3-2 160-7 28 22-4 i6-9 88 70-3 53-0 148 89-1 208 166-1 125-2 268 2.4-0 .6.-3 29 23-2 I7'5 89 7I-I 53-6 149 119-0 89-7 209 166-9 125-X 269 214-8 .6.-9 30 24-0 .8-1 90 71-9 54-2 150 ..9-8 90-3 210 167-7 126-4 270 2.5-6 TT 24-8 .8-7 91 727 54-8 151 .20-6 90-9 211 .68-5 127-0 27r 2.6-4 163-. 32 25-6 19-3 92 73-5 55-4 152 121-4 91-5 212 J 69; 3 127-6 272 217-2 163-7 33 26-4 19-9 93 56-0 \r,s 122-2 92-1 213 128-2 273 164-3 34 27-2 20-S 94 75-1 566 154 123-0 92-7 214 170-9 128-8 274 2.8-8 164-9 35 28-0 95 75-9 57-2 155 123-8 93-3 215 171-7 129-4 275 2.9-6 165-5 3C 28-8 21-7 96 767 57-8 150 124-6 93-9 216 172-5 130-0 276 220-4 166-1 37 29-5 22-3 97 77-5 58-4 157 125-4 94-5 217 173-3 1306 277 22.-2 166-7 38 30-3 22-9 98 59-0 158 1262 95-1 218 .31-2 278 222-0 167-3 39 311 23-5 99 79-1 596 159 127-0 95-7 219 174-9 279 222-8 167-9 40 31-9 100 79-9 6o-2 160 127-8 96-3 220 175-7 132-4 280 223-6 ,68-5 ir 327 24-7 lOI 807 6o-8 ToT 128-6 96-9 221 176-5 133-0 281 224-4 169-1 42 33-5 25-3 102 8.-5 tl't 162 129-4 97-5 222 177-3 133-6 282 225-2 169-7 43 25-9 103 82-3 163 130-2 98-, 223 178-1 134-2 283 226-0 170-3 ■44 35-1 ^6;5 104 83-1 62-6 164 131-0 98-7 224 178-9 ■34-8 284 226-8 170-9 45 35-9 105 83-9 63-2 165 .31-8 99-3 225 179-7 135-4 285 227-6 171-5 40 36-7 27-7 106 847 63-8 160 132-6 99-9 226 180-5 136-0 286 22S-4 47 37-5 28-3 107 85-5 64-4 167 '33-4 IOO-5 227 136-6 287 229-2 172-7 48 38-3 28-9 108 8^-1 650 168 134-2 228 182-? .37-2 288 230-0 173*3 49 39-1 29-5 109 65-6 169 135-0 101-7 229 182-9 137-8 289 230-8 173-9 50 39-9 30-I 110 87-8 66-2 170 135-8 102-3 230 183-7 138-4 290 23.-6 174-5 "5r)4^ 30-7 1 11 88-6 66-8 171 136-6 102-9 231 184-5 .39-c 291 232-4 175-1 52 4I-5 3'-3 112 89-4 67-4 172 137-4 103-5 232 1S5-3 139-6 292 175-7 53 42-3 31-9 113 90-2 68-0 173 13S-2 104- 1 233 186-1 .40-2 293 234-0 176-3 54 43-I 32-5 114 91-0 6S-6 174 139-0 104-7 234 186-9 140-8 294 234-8 1-6-9 55 43-9 33-1 115 91-8 69-2 175 139-8 105-3 235 187-7 141-4 295 235-6 177-5 56 44'7 33-7 116 92-6 698 176 ,40-6 105-9 230 .88-5 142-0 296 236-4 178M 57 45-5 j 34-3 117 93-4 70-4 177 141-4 106-5 237 189-3 142-6 •297 237-2 178-7 68 46-3 1 34-9 118 94-2 7I-0 178 142-2 107-1 •238 190-1 143-2 298 238-0 179-3 59 47-1 35-5 119 95-0 7. -6 179 143-0 107-7 239 190-9 143-8 299 238-8 .79-9 1 60 47-9 136-1 120 95-8 72-2 IKO .43-8 108-3 240 191-7 144-4 300 239-6 1 .80-5 DiTu Dep. iD.Lal Dist, Dep. D.Lat ^- Dep. 1). l.at. Dist. Dep. 1). Lat Dist.' Dep. D. Lat.| 53° ~~ 3i^32^^^| TABLE 1 TKAV£Ki>E TABLE TO DEGREES 316 319 iSil 1817 182-4 183-6 184-2 184-S 1S78 18S-4 1S90 189-6 190 2 190-S 191-4 192-0 192-6 1932 193S •94-4 195-0 1^56 196-2 196-S 1 97 4 201-6 202-2 202 S 208-2 20S-8 2112 211-8 212-4 2130 2136 Dist.'D. Lat. Dep. DistJo. Lat. Dep. Di 217-3 *^ 2435 244-3 245 I 2459 246-7 247-5 248-3 249-1 2499 250-7 251-5 2523 253-> 2539 254-7 ^55J_ 256-3 257-1 257-9 258-7 259s 2603 261 1 261-9 262-7 263-5 2643 265-1 265-9 266-7 2675 268-3 269 I 269-9 270-7 271-5 272-3 2731 2739 2747 2755 276-3 277-1 277-9 278-7 2795 , a8o-3 352 281 I S.W 281 9 .•i.04 i 282-7 - 2835 3.16 2843 3A7 2S5 I 358 I 285 9 2867 360 1 287-5 DistJ Dep. D. Lat. Distl Dep. ID. LatJDiet. Dep D. Lat. D; 3£S- 253-4 2540 254-6 2552 255-8 2564 257-0 257-6 25S-2 2588 259-4 260-0 260-6 261-2 261-8 262-4 263-0 263-6 264-2 264-8 265-4 2660 266-6 267-2 267-8 26S-4 269-0 2696 270-2 2708 271-4 2720 272-6 273-2 273-S 274-4 275-0 275-6 276-2 276-S 277-4 2780 278-6 2792 279-8 2804 2810 2S1-6 282-3 282-9 283-5 284-1 2847 2S5-3 2859 2865 287-1 287-7 288-3 2S8-9 384-1 384-9 3S5-7 3S6-5 3S7-3 38S-1 3S8-9 3S9-7 390-5 391 3 392-1 3929 3937 394-5 395-3 396-1 396-9 3977 39S-5 _3_9?:3_ 400-1 400-9 401-7 4025 4033 404-1 404-9 405-7 4065 407:3_ 40S-I 408- 9 4097 4105 4113 412-1 412-9 413-7 414-5 415-3 416-1 416-9 417-7 418-5 4193 420-1 420-9 421-7 422-5 423:1 424-1 424-9 425-7 426-5 4273 428-1 4289 429-7 430-5 4313 289-5 290-0 2906 291-2 291-8 292-4 293-0 293-6 294-2 294-8 2954 2960 296-6 297-2 297-S 298-s 299-1 299-7 300-3 300-9 301-5 302-1 3027 303-3 303-9 304-5 305-1 305-7 306-3 3069 307 -s 308-2 30S-8 309-4 310 o 3106 31 1-2 311-8 3124 3_i3:o 3136 314-2 314-8 3154 3160 316-6 317-2 3'7S 31S4 319-0 D.Li 319-61501 3202 1 59-2 3208 i 593 3214 ,yj4 322-0 5tf5 3226 596 3232 597 323-8 698 324-4 3250 600 D.Lat. Dist. 432-0 4328 4336 4344 435-2 4360 436-8 437-6 438-4 4 39-2 440-0 4408 441-6 442-4 443-2 444-0 444-S 445-6 446-4 _447:^ 44S-0 448 -s 449-6 450-4 451-2 452-0 4528 453-6 454-4 _455:^ 456-0 456-8 457-6 458-4 4592 4600 460-8 461-6 462-4 463-2 464-0 464-8 465-6 46614 467-2 46S o 46S8 469-6 4704 4 71-2 4720 4728 4736 474-4 475-2 4760 476-8 477-6 478-4 479-2 Dep. 3256 326-: 326-8 327-3 327-9 328-5 329-1 3297 3303 330-9 331-5 3321 332-7 333-: 333-9 334-6 335-2 335-8 336-4 337-0 337-6 33S-2 338-8 339-^ 340c 3406 341 341-8 342-4 3430 3436 344-3 344-9 345-5 346-1 346-7 347-3 347-9 348-S 349-1 349-7 350-3 350-9 351-5 352 352-7 353-3 3539 354-5 355'. 3557 356-3 356-9 3575 358-1 3587 359-3 3599 360-5 361 Dep. D.Lai, 506 TRAVERSE TABLE TO DEGREES 38° 2'' 32™ Dist.lD.Lat Dep. Dist D. Lat. Dep. Dis> D. Lat. Dep. D.St. D.Lnt.j Dep. Dist. D. Lat. Dep. -fr 22 23 24 25 2C 27 28 20 30 0-8 1-6 »-4 3-2 3-9 4-7 I'-l 7-1 7-9 0-6 rS 2-5 3-1 3-7 4-3 4-9 11 6. 62 63 64 65 66 67 68 69 70 48-1 48-9 49-6 50-4 51-2 52-0 Irl 54-4 55-z 39-4 40-0 40-6 41-2 41-9 42'5 43'i 121 122 123 124 125 126 127 128 129 130 IP. 96-9 99-3 loo-i 100-9 10I-7 102-4 74-5 ,'5- 1 75-7 76-3 77-6 78-8 79-4 181 182 183 184 185 186 187 188 189 190 .42-6 143-4 144-2 145-0 145-8 .46-6 147-4 J48-1 148-9 149-7 ,,,■4 112-7 113-3 113-9 114-5 115-1 115-7 116-4 241 242 243 244 245 246 247 248 -249 250 190-7 191-5 192-3 193-1 lilt 197-0 148-4 149-0 149-6 ,50-2 ,50-8 151-5 ,52-1 151-7 153-3 153-9 8-7 9-S 10-2 II-O II-8 12-6 13-4 14-2 15-0 i,-8 6-S 7"4 8-0 8-6 92 9-9 IO-5 "■7 ,2-3 12-9 •3-5 14-2 148 15-4 i6-o .6-6 17-2 17-9 i8-, 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 55-9 56-7 57-5 58-3 59-1 59-9 6o-7 ll'l 63-0 6;-S 64-6 65-4 66-2 67-0 67-8 68-6 69-3 70-9 43-7 44-3 47'4 49-1 131 132 133 134 135 136 137 138 139 140 104-0 104-8 105-6 106-4 108-0 109-5 110-3 8o-7 81-3 85-6 191 192 193 194 195 196 197 198 199 200 150-5 151-3 152-1 152-9 153-7 '54-5 nil 156-8 .57-6 117-6 118-2 ,iS-8 ■i9;4 120-7 ,21-3 121-9 122-5 123-1 ■251 252 253 254 255 256 257 258 ■259 260 199-4 200-9 20,-7 202-5 203-3 204-1 204-9 154-5 156-4 i .6-5 »7-3 i8-i .8-9 19-7 20-5 21-3 22-1 22-9 23-6 49-9 5°-5 51-1 51-7 5^-3 52-9 53-6 54-1 54-8 ';s-4 141 142 143 144 145 146 147 148 149 150 111-9 112-7 113-5 1 14- 3 116-6 86-8 87-4 89-9 90-5 91-1 91-7 92-3 201 202 203 204 205 206 207 208 209 210 158-4 160-8 16,-5 162-3 163-1 163-9 164-7 .65-5 ,23-7 124-4 ii 126-8 127-4 128-7 ,29-3 261 262 263 264 265 266 267 268 269 270 206-5 207-2 208-8 209-6 210-4 212-8 16,-3 i6,-9 162-5 163-2 163-8 164-4 165-0 ,65-6 166-2 31 32 33 34 35 36 37 38 39 40 24-4 25-2 26-0 26-8 27-6 28-4 29-2 29-9 30-7 3>-'i 19- 1 19-7 20-3 20-9 -';5 22-8 23-4 24-0 24-6 91 92 93 94 95 96 97 98 99 100 7'-7 71-5 73-3 74-1 74-9 75-6 76-4 77-2 78-0 78-8 56-0 56-6 57-3 57-9 SS-5 59-1 59-7 tl 6i-6 151 152 153 154 155 156 157 158 159 160 ill 121-4 122-9 123-7 124-5 125-3 126-1 93-0 93-6 94-2 94-8 95-4 96-0 96-7 97-3 97-9 98-5 211 212 213 214 215 216 217 218 219 220 166-3 .67-. 167-8 ,63-6 169-4 170-2 171-0 171-8 172-6 173-4 129-9 130-5 131-1 13,-8 ,32-4 133-0 133-6 135-4 271 272 273 274 275 276 277 278 279 280 213-6 214-3 215-, 166-8 167-5 168-1 ,68-7 ,69-3 ,69-9 170-5 171-2 ,7, -8 172-4 41 42 43 44 45 46 47 48 49 50 31-3 33-1 33-9 34"7 III 37-0 Wl 39'4 25-2 25-9 26-5 27-1 28-3 101 102 103 104 105 106 107 108 109 110 79-6 80-4 8i-2 82-0 82-7 P'' 84-3 li 622 62-8 64-6 65-3 65-9 67-7 161 162 163 164 165 167 168 169 170 126-9 127-7 129-2 130-0 134-0 99-1 99-7 100-4 10I-6 I02'2 102-8 103-4 104-0 104-7 221 222 223 224 225 226 227 228 229 230 ,74-2 174-9 ;;« 177-3 178-1 178-9 179-7 ,80-5 ,81-2 ,36-1 136-7 137-3 137-9 138-5 139-, 139-8 140-4 ,41-0 ,41-6 281 282 283 284 285 286 ■287 288 289 290 221-4 223-0 lilt 226-9 227-7 228-5 :;i-6 ,74-2 174-8 i]i\ 176-7 177-3 177*9 178-5 51 52 53 54 55 56 67 58 5» 60 40-2 410 41-8 41-6 43-J 44-1 44-9 45'7 46-5 47-3 3i;4 32-6 33-2 339 34-5 35-1 35-7 36-3 36-9 111 112 113 114 115 116 117 118 119 120 87-5 88-3 89-0 89-8 90-6 91-4 92-2 93-0 93-8 94-6 6S-3 69-0 696 70-8 7'-4 72-0 72-6 73-3 73-9 171 172 173 174 175 177 178 179 180 >34-7 •35-5 .36-3 137-1 137-9 138-7 ■39-5 140-3 141-1 .4.-8 105-3 105-9 106-5 I07-I 107-7 108-4 109-0 .09-6 110-2 110-8 231 232 •233 234 235 236 237 238 239 240 182-0 182-S 183-6 184-4 187-5 ,88-3 ,89-, ,42-2 142-8 143-4 144-1 144-7 145-3 ■45-9 ,46- 5 147- , 147-8 291 292 293 294 '295 29C 297 298 299 300 229-3 230-1 230-9 231-7 23X-5 »33-3 'X :^^:8 180-+ ,8,-0 ,8,-6 ,Si-2 ,82-9 ;;;: 184-7 Dist Dep. D.Lai Disi Dep. iD.Lai Disl Dep. D. Lat. Dist Dnp. |D. Ldt DisL Dep. Id Latl 52° ShaS"' 1 TRAVEKSE TABLE TO DEGREP:S 38» Oh 32m 1 Dist 301 D.Lat Dep. Dist. D. Lat.j Uep. Dist.lD. Lat Dep. Dist.D. Lat D.p. Oist.JD. Lat.j Dep. 1 2372 185-3 3G1 2S4-S 222-3 421 331-8 259-2 481 379-0 2Q6-2 541 426-3 333-1 302 23S0 185-9 362 285-3 222-9 422 332-5 259-S 482 379-8 296 8 542 427-1 3337 303 23SS 180-6 363 2S60 223-5 423 3333 260-4 483 3S0-6 297-4 543 427-9 3343 304 2396 1S7-2 364 286-S 224-1 424 334-1 261-0 484 38.-4 29S-0 544 i 428-7 3350 305 2403 187-8 365 2S7 6 224-7 425 334-9 261-7 485 3S2-2 29S-6 545 1 429-5 335-6 306 241 I 1S8-4 366 288-4 225-3 426 335-7 2623 486 383-0 299-2 546 430-3 336-2 307 241-9 1S9-0 367 289-2 226-0 427 3365 2629 487 3838 299-8 547 431-0 3368 308 2427 1S9-6 36S 290-0 2266 428 337-3 263-S 488 384-5 300-4 548 431-8 337-4 309 2435 190-2 369 290-8 227-2 429 338-1 264-1 489 385-3 301-1 549 432-6 3380 310 2443 190-9 370' 2916 227-8 4.30 3388 264-7 490 3S6-1 301-7 550 _433-4 338-6 311 2451 191-5 371 292-4 22S-4 431 3396 265-4 497 3S69 302-3 551' 434-2 339-3 312 245-9 192-1 372 293-1 229-0 432 340-4 2660 492 3S7-7 3029 552 4350 339-9 313 246-6 192-7 373 293-9 2296 433 341-2 266-6 493 388-5 303-5 553 435-8 340-S 314 247-4 "933 374 294-7 230-3 434 342-0 267-2 494 389-3 304-2 554 436-6 341-1 315 248-2 1939 375 295-5 230-9 435 342 s 267-8 495 3901 304-8 555 4374 341-7 316 249-0 1946 376 296-3 2315 436 343-6 26S-4 496 3909 305-4 556 4381 342-3 317 249-8 195-2 377 297-1 232-1 437 344-4 269-1 497 391-6 306-0 557 4389 3430 318 250-6 195-8 378 297-9 232-7 438 345-2 269-7 498 392-4 306-6 558 439 7 3436 319 251-4 196-4 379 29S-7 2333 439 345-9 2703 499 393-2 307-2 559 440-5 344-2 320 321 2522 197-0 197-6 380 381 _299-4 300-2 234-0 2346 440 441 J46:7 347-5 2709 271-5 500 501 3940 394-8 307-8 "308-4 560 561 441-3 442-1 344-8 345-4 2530 322 253-7 19S-2 382 3010 235-2 442 348-3 272-1 502 3956 3091 .562 442-9 3460 323 254-5 198-9 383 30.-S 235-8 443 3491 272-7 503 3964 309-7 563 443-7 346-6 324 255-3 199-5 384 302-6 236-4 444 3499 2734 504 397-2 3103 564 444-4 3472 325 256-1 200-1 385 303-4 237-0 445 350-7 274-0 505 397-9 310-9 565 4452 347-8 326 2569 200-7 386 304-2 237-7 446 351-5 274-6 506 398-7 311-6 566 446-0 348-5 327 2577 201-3 387 305-0 2383 447 352-2 275-2 507 3995 312-2 567 446-8 349-1 328 258-5 201-9 388 305-7 238-9 448 353-0 275-8 508 400-3 3128 568 447-6 349-7 329 259-3 202-6 389 306-5 239-5 449 353-8 276-4 509 401-1 313-4 569 ! 448-4 350-3 330 331 2600 T6o^ 203-2 203-8 390 _3073 308-1 240-1 '2407 450 451 354-6 277-1 277-7 510 511 401-9 402-7 3140 5-0 449-2 3509 T^r6 355-4 314-6 571 450-0 332 261-6 204-4 392 308-9 241-3 452 356-2 278-3 512 403-5 315-2 572 450-7 352-2 333 262-4 205-0 393 3097 453 3570 278-9 513 4042 315-8 573 451-5 352-8 334 263-2 205-6 394 3'OS 242-6 454 357-8 279-5 514 405-0 316-4 574 4523 353-4 335 264-0 206-3 395 3" 3 243-2 455 358-5 2S01 515 405-S 3171 575 453-1 3540 336 264-8 206-9 396 312 1 2438 456 359-3 2S0-7 516 406-6 317-7 576 453-9 3546 337 265-6 207-5 397 312S 244-4 457 3601 281-4 517 407-4 3183 577 454-7 355-2 338 266-3 208-1 398 3>3-6 245-0 458 3609 2820 518 40S2 318-9 578 455-5 355-8 339 267-1 208-7 399 314-4, 245-7 4 59 3617 2S2 6 519 409-0' 319-5 579 456-3 356-4 340 2679 209-3 400 3152 246-3 460 362-5 283-2 .-^20 409-8; 320-2 580 457-1 ^57-1 341 268-7 1 209-9 401 316-0 246-9 461 363-3 283S 521 410-6 320-8 581 457-8 357-7 342 269-51 210-6 402 3'6-s! 247-5 462 364-1 284-4 522 411-31 3214 582 458-6 358-3 343 2703 211-2 403 3176 248-1 463 3649 285-. 523 412-1 1 322-0 583 459-4 358-9 344 271-1I 2II-8 404 318-4 248-7 464 365-6 285-7 524 4129 322-6 584 4602 3595 345 2719 212-4 405 319-1 249-3 465 366-4 2S63 525 413-7, 323-2 585 461-0 360-2 346 272-7 213-0 40G 3199 2500 466 367-2 286-9 526 414-5 323S 586 461-S 360-8 347 273-4 2136 407 3207 250-6 467 3680 287-5 527 415-3 3245 587 4626 361-4 348 274-2 214-3 408 321-5 251-2 468 368-8 28S-1 528 4>6-lj 325-1 588 4633 362-0 349 275-0; 2149 409 322-3 251-8 469 3696 288-7 529 416-9! 325-7 589 464-1 362-6 350 275-8 ^15-5 410 323-11 252-4 470 370-4 289-3 530 417-61 326-3 590 464-9 363-2 351 ^6^ 2161 4111 323-9 2530 471 371-2 290-0 531 -418-4 326-9 591 T6T7 "363^8 352 277-4 2167 412 [ 324-7 1 253-7 472 371-9 290-6 532 419-2 3275 592 466-5 3644 353 27S-2 217-3 413 325-5 2543 473 372-7 291-2 533 420-0 328-2 593 467-3 3651 354 2790 21 So 414 3262 2549 474 373-5 291-8 534 4208 3288 594 468-1 365-7 355 279-7 21S6 415 3270 1 255-5 475 374-3 292-4 .535 421-6 3294 595 468-9 3663 356 280-5 219-2 416 327-8 256-1 476 375-' 293-1 536 422-4 3300 596 469-7 366-9 357 281-31 219-8 417 3286 2567 477 375-9 2937 537 4232 330-6 597 470-5 367-5 358 282-1 1 220-4 418 i 329-4 257-4 478 37''-7 294-3 538 424-0 331-2 598 471-2 368-1 3S9 2829 221-0 419 1 330-2 2580 479 377-5 2949 539 424-7 331-8 599 472-0 368-7 360 2837 221-6 420 1 331-0 258-6 480 378-2 295-5 540 425-5 3325 600 472-8 3694 DUt. Dep. D. Lat. Dist.! Dep. O. Lai. Dist. Dep. D. Lat. Dist. Uep. D.Lat Dist. Dep. D.Lat 52= Sh 28^^ TRAVERSE TABLE TO DEGREES | ;w° 2" 86"^ 1 l_)ist.|D.Lat Dep. Dist. D. Lat. Dep. Dist.JD. Lai. Dep. DisL D.Lat. Dep. Dist.JD. Lat.| Dep. 1 1 0-8 0-6 61 47'4 38-4 121 94-0 76-1 181 140-7 113-9 241 187-3 151-7 2 1-6 13 62 48-2 39-0 122 94-8 76-8 182 141-4 114-5 •242 188-1 152-3 3 2-3 1-9 63 49-0 39-6 123 95-6 77-4 183 142-2 115-2 243 188-8 152-9 4 3-1 2-5 64 49'7 40-3 124 96-4 78-0 184 143-0 115-8 244 1896 153-6 5 3'9 3-1 65 50-5 40-9 125 97-1 78-7 185 143-8 116-4 245 190-4 154-2 4-7 3-8 66 51-3 41-5 120 97-9 79-3 180 144-5 117-1 ■246 191-2 154-8 7 5'4 4'4 67 52-1 42-2 127 98-7 79-9 187 145-3 117-7 247 192-0 155-4 « 6-2 5-0 68 42-8 128 99-5 80-6 188 146-1 118-3 248 192-7 156-. 9 7-0 5"7 69 53-6 43'4 129 100-3 81-2 189 146-9 118-9 249 193-5 • 56-7 10 7-8 6-3 70 54-4 44-1 130 81-8 190 147-7 1,9-6 250 194-3 157-3 II ^'5 6-9 71 55'2 44-7 131 101-8 82-4 191 .48-4 251 1951 15S-0 12 9'3 7-6 72 56-0 45'3 132 102-6 192 149-2 120- 8 252 195-8 158-6 13 8-2 73 56-7 45'9 133 103-4 83-7 193 150-0 121-5 253 196-6 159-2 14 10-9 8-8 74 57'5 466 134 104- 1 8^-0 194 150-8 254 197-4 159-8 15 1 1-7 9'4 75 58-3 47-2 135 104-9 195 151-5 122-7 255 19S-2 .60-5 16 12-4. 76 591 47-8 136 105-7 sd 190 152-3 123-3 256 198-9 .61-1 17 13-2 10-7 77 59-8 48-5 137 I06-5 197 153-. 124-0 257 199-7 i6i-7 18 14-0 II-3 78 6o-6 49-1 138 107-2 86-8 198 153-9 124-6 258 200-5 .62-4 19 14-8 79 6i-4 49' 7 139 108-0 87-5 199 154-7 125-2 259 163-0 20 15-5 12-6 80 62-2 jo-3_ H£ ioS-8 88-1 200 '55-4 125-9 260 202-^ ,63-6 21 16-3 I3'2 81 62-9 51-0 141 109-6 8S-7 2or 156-2 126-5 201 202-8 ! 164-3 22 I7-I 82 63-7 5. -6 142 1 10-4 89-4 202 157-0 127-1 262 203-6 1 .64-9 23 17-9 14-5 83 64-5 52-2 143 iii-i 90-0 203 157-8 127-8 263 204-41 165-5 24 iS-7 15-1 84 65-3 52-9 144 III-9 90-6 204 158-5 128-4 264 205-2! 166-1 23 19-4 15-7 85 66-1 53-5 145 91-3 205 159-3 129-0 265 205-9:166-8 2fi 20-2 i6-4 80 66-8 54-1 146 113-5 91-9 200 i6o-i ,29-6 266 206-7 1 167-4 27 2I-0 lyo 87 67-6 54-8 147 1 14-2 92-5 207 160-9 130-3 267 207-5 ' 168-0 28 21-8 17-6 88 68-4 55-4 148 115-0 93-1 208 161-6 130-9 268 208-3 1 168-7 29 22-5 18-3 89 69-2 56-0 149 115-8 93-8 •209 ,62-4 131-5 269 209-1 169-3 30 23-3 i8-9 90 69-9 56-6 150 116-6 94-4 210 163-2 132-2 270 209-8 169-9 ir 24- 1 19-5 91 70-7 57'3 151 117-3 950 211 1328 271 210-6 170-5 32 24-9 20-1 92 71-5 57-9 152 118-1 95-7 212 Ut-s 133-4 272 2II-4 171-2 33 25-6 20-8 93 72-3 5S-5 153 118-9 963 213 165-5 134-0 273 212-2 I7I-8 34 26-4 21-4 94 73;: 59-2 154 119-7 96-9 214 166-3 134-7 274 212-9 172-4 35 Z7-2 22'0 95 59-8 155 120-5 97-5 216 135-3 275 213-7 173-1 36 2S-0 22-7 96 74-6 6o-4 156 121-2 98-2 216 167-9 135-9 270 214-5 173-7 37 28-8 23-3 97 75-4 6i-o 157 122*0 98-8 217 1686 136-6 277 215-3 174-3 38 29-5 23-9 98 76-2 6. -7 158 122-8 99-4 218 169-4 137-2 278 216-0 175-0 39 so- 3 24-5 99 76-9 62-3 159 123-6 219 170-2 137-8 279 216-8 175-6 40 3'-' 25-2 100 7T7 62-9 160 124-3 100-7 2-20 171-0 138-5 280 2.7-6 176-2 -w 31-9 258 Tor 78-5 63-6 TeT 125-1 101-3 221 171-7 139-1 281 218-4 176-8 42 32-6 26-4 102 79-3 64-2 162 125-9 222 172-5 139-7 282 219-2 177-5 43 33-4 27-1 103 8o-o 64 '8 103 126-7 102-6 223 173-3 140-3 283 219-9 .78-1 44 34-2 127-7 104 8o-8 65-4 164 127-5 103-2 224 174-: 141-0 284 220»7 178-7 45 35-0 j 28-3 105 8i-6 66-1 165 128-2 1038 225 ■74-9 141-6 285 221-5 179-4 46 35-7 28-9 106 82-4 66-7 100 129-0 104-5 220 175-6 142-2 286 222-3 47 36-5 29-6 107 83-2 107 129-8 105-1 227 176-4 142-9 287 223-0 iSo-6 48 37-3 30-2 108 83-9 68-0 168 1 130-6 105-7 228 177-2 143-5 288, 123-8 l8l-2 49 38-1 30-8 109 84-7 68-6 109 131-3 229 178-0 144-1 289 224-6 18.-9 50 3^9 31-5 110 S5-5 69-2 170 132-1 lo--* 230 178-7 144-7 290 225-4 182-5 51 39-6 32-1 TTT 86-3 -6^ 171" 107-6 ■231 '79-5 145-4 •291 226-1 183-1 52 40-4 32-7 112 87-0 70-5 172 >'3r7 108-2 232 i8o-3 .46-0 292 226-9 1S3-S 53 41-2 33-4 113 87-8 7I-I 173 134-4 108-9 233 iSi-i 146-6 293 227-7 184-4 54 42-0 34-0 114 88-6 7I-7 174 135-2 109-5 234 i8i-9 147-3 294 228-5 .S5-0 55 42-7 34-6 115 89-4 72-4 175 136-0 1 10- 1 235 1S2-6 147-9 295 2*9-3 185-6 56 ;43-5 35-i 116 90-1 73-0 170 136-8 110-8 230 183-4 148-5 296 2300 186-3 57 44-3 35-9 117 90-9 73-6 177 137-6 111-4 237 184-2 149-1 297 230-8 186-9 58 45-1 36-5 1I« 91-7 74-3 178 138-3 112-0 238 185-0 149-8 298 231-6 .87-5 59 45-9 37-1 119 9-'5 74-9 179 139-1 1.2-6 239 185-7 150-4 299 232-4 CO Dist 466 Dep. 37-8 120 93-3 75-5 180 139-9 113-3 240 .86.5 151-0 300 233-1 18S-8 D.Lat Dist. iJep. D.Lat Dist. Dep. D. Lai. Dist. Dep. D. Lat. Dist. Dep. Id. LatJ 3 1° ='- 1 50G TRAVEUSE TABLE TO DEGUEES 89° 2" 86-° Dist D. Lat Dep. Dist D.Lat Dep. Dist D.Lat.l Dep. Dist.Jo. Lat.[ Dep. Dist.JD. Lat. Dep. 301 233-9 189-4 361 2806 227-1 421 3272 1 264-9 -tsi ! 373-s ' 302-6 541 I 4204 3404 302 2347 1900 362 281-3 227-8 422 328-0 ■ 265-5 .82 374-6 3033 542 421-2 3410 303 235S 190-6 363 282-1 22S-4 423 32S-7 266-2 -183; 375-4 3039 543 422-0 341-7 30-t 236-3 «9'-3 364 282-9: 229-0 424 3295 2668 484 376-1 304-5 544 422-7 342-3 305 2370 191-9 365 2S3-7 229-7 425 3303 267-4 185 376-9 305-2 545 4235 342-9 306 237-S 192-5 366 284-4 230-3 426 33«-i 2680 486 377-7 305-8 546 4243 343-6 307 238-6 193-2 367 2S5-2 230-9 427 331-9 268-7 487 37S-5 306-4 547 425-1 344-2 308 239-4 I93-S 368 286-0' 231-5 428 332-6 269-3 ->88 379-3 307-1 548 425-9 344-8 309 240-1 '944 369 286-8 232-2 429 333-4 269-9 489 380-0 307-7 549 426-6 3455 310 240-9 1950 370 287-6; 232-8 430 334-2 270-6 490' 3S0-8 308-3 5.50 427-4 346-1 311 2417 1957 37T "288-31 233-4 431 335-0 271-2 491, 381-6 30S-9 551 42S2 3467 31:2 2425 1963 372 289-1 1 234-1 432 335-7 271-8 492 j 382-4 309-6 552 429-Q 347-4 313 2433 19J9 373 289-9 2347 433 336-5 272-5 493 i 383-1 310-2 553 429-7 348-0 3U 244-0 197-6 374 2907 235-3 434 337-3 273-1 494 3S3-9 310-8 554 430-5 3486 315 244S 198-2 375 2914 236-0 435 338-1 2737 495 3S47 3115 555 431-3 349-2 3Ifi 2456 198S 376 292-2 ' 236-6 436 33SS 2743 496 385-5 3121 556 432-1 349-9 317 246-4 199-5 377 293-0 237-2 437 339-6 275-0 497 386-2 3127 557 432-8 3505 318 247-1 200-1 378 293-8: 2378 438 3404 275-6 498 'l^'°. 3133 558 4336 35i-« 319 247-9 200-7 379 294-5 1 238-5 439 341-2 276-2 499 3878 314-0 559 4344 351 7 320 24S7 201-3 380 295-3 l_?39-i 440; 3420 276-9 500 3886 3147 560 435-2 3524 3ir 249-5 2020 381 296-1 1 239-7 441 I 3427 2775 501 389-4 315-3 561" 435-9 353-0 322 250-3 2026 382 296-9! 2404 442 3435 27S1 502 3901 315-9 562 436-7 353-6 323 2510 203-2 383 297-7 241-0 443 344-3 278-7 503 390-9 3165 563 437-5 3543 324 251-8 2039 384 298-4! 241-6 444 345-1 279-4 504 391-7 317-1 564 438-3 3549 325 252-6 204-5 385 299 2 ' 242-2 445 345-8 280-0 505 392-5 317-8 565 4391 355-5 326 253-4 386 3000 242-9 446 346-6 280-6 506 3932 318-4 566 439-8 356-2 327 254-1 205-7 387 300-8 2435 447 347-4 281-3 507 3940 319-0 567 440-6 356S 323 254-9 206-4 33S 301-5 244-1 448 3+8 2 281-9 508 394 S 319-6 568 4414 357-4 329 255-7 207-0 389 302-3 244-S 449 3490 2S2-5 509 3956 320-3 569 442-2 358-1 330 337 256-5 207-6 390 391 303-1 245-4 2460 450 451 349-7 283-2 283-S 510 511 J96-3 397-1 3209 321-6 570 571 443-0 35S-7 359-3 257-2 20S-3 3039 3505 443-7 332 2580 208-9 392 304-7 2467 452 351-3 2844 512 397-9 322-2 572 444-5 359-9 333 258-8 209-5 393 305-4 247-3 453 352-1 285-0 513 39S-7 322-S 573 445-3 3606 334 259-6 2102 394 306-2 247-9 454 352-8 285-7 514 399-4 323-4 574 4461 3612 335 2604 210S 395 307-0 ■ 248-5 455 353-6 286-3 515 400-2 324-1 575 446-9 36.-8 336 26.-1 211-4 396 307-8: 249-2 456 354-4 286-9 515 401-0 3247 576 447-6 .362-4 337 261-9 212-0 397 30S-5 249-S 457 355-2 287-6 517 401-8 325-3 577 448-4 363-1 333 262-7 212-7 398 309-3 250-4 458 355-9 288-2 518 402-5 325-9 578 449-2 363-7 339 2635 213-3 399 3.0-. 251-1 459 356-7 2888 519 403-3 3266 579 450-0 364-3 340 341 264-2 2650 213-9 214-6 400 401 3109 311-6 _yi2 460 357-5 2S93_ 290-1 520 52r 404-1 4049 327-2 327-8 580_j 45^ 581 451-S 3650 461 35S-3 365-6 342 265-8 215-2 402 312-4' 2529 462 359-1 290-7 522 4057 32S-5 582 452-3 366-2 343 2666 215-S 403 3132, 2536 463 359-S 291-3 523 406-4 3291 583 453-1 3669 344 267-3 2164 404 314-0 254-2 464 360-6 292-0 .J24 407-2 3297 584 4539 3675 345 26S1 2I7-I 405 314-81 254-8 465 36 ■•4 292-6 525 40S0 330-4 585 454-6 368-? 346 268-9 217-7 406 3'S-5 255-S 466 362-2 2932 526 408-8 3310 586 4554 3688 347 2697 218-3 407 316-3 256-1 467 3629 293-s 527 409-5 331-6 587 4562 3694 348 270-5 2190 408 3-7 I 1 2567 468 363-7 294-s 528 4103 332-3 588 4570 3700 349 271-2 219-6 409 3179 2573 469 364-S 295-1 529 411 1 332-9 589 4578 370-6 350 351 2720 '2728 220-2 220-8 410 411 318-6 2580 319-41 2586 470 471 J65-3 3660 295-7 296-4 530 531 411-9 4126 333-5 334-1 590 _458-5 4593 371-3 3719 352 2736 221-5 412 320-21 259-2 472 366S 2970 532 413-4 334-8 592 460-1 372-5 353 2743 222-1 413 321-0 1 2599 473 3676 297-6 533 414-2 335-4 593 ' 460-9 373-2 354 2751 222-7 414 321-8 2605 474 3684 298-3 534 415-0 3361 594 461-6 3738 355 2759 223-4 415 322-S 261-1 475 369-2 298-9 535 415-S 3367 595 462-4 374-4 356 276-7 2240 416 323-3 261-8 476 3699 299-5 536 416-5 337-3 596 463-2 375-1 357 277-S 224-6 417 324-1 2624 477 370-7 300-1 537 4173 3379 597 4640 3757 358 278-2 225-3 418 324-9 263-0 478 371-S 3008 538 418-1 3.18-5 598 464-8 376-3 359 2790 225-9 419 32561 2636 479 372-3 301-4 539 418-9 3391 599 4655 3769 360 2798 2265 420 3264 264-3 480 3730 302-0 540 4196 339-8 600 4663 377-6 ^t Dep. D. Lat. Dist. Dep. D. Lat. Dist. Dep. D. Lat. Dist. Dep. D. Lat. Dist. Dep. D. Lat 51" S^ 24" 1 TRAVERSE TABLE TO DEGREES " 40 21>40n> Dist D.Lat Dep. Dist. D. Lat. Dep. Dist. D. Lat. Dep. Dist D.Lat. Dep. Dist D.Lat.| Dep. T o-g 0-6 61 46-7 39-2 TiT 92-7 77-8 181 138-7 116-3 241 1846 , 154-9 2 '•5 13 62 47-5 39-9 122 93-5 78-4 182 139-4 117-0 242 185 4 155 6 3 2-3 '•9 63 48-3 40-5 123 94-2 79-1 183 140-2 I17-6 243 186 156 2 4 3'i 2-6 64 49-0 41-1 124 95-0 79-7 184 141-0 I18-3 244 186 9 156 8 5 3-8 3-2 65 49-8 41-8 125 95-8 8o-3 185 141-7 llS-Q 245 187 157 5 6 4-6 3'9 66 50-6 42-4 126 96-5 81-0 186 142-5 ;i9;6 246 188 4 158 7 5*4 4-5 67 5i"3 43-> 127 97-3 81-6 187 143-3 247 189 158 8 8 6-1 5-' 68 52-1 43'7 128 98-1 82-3 188 144-0 12C-S 248 190 159 4 9 6-9 5-8 69 52-9 44'4 129 98-8 82-9 189 144-8 121-5 249 190 7 160 10 7-7 6-4 70 53-6 45-0 130 99-6 83-6 190 145-5 250 221 5 16c 7 TT 8-4 1 7-. 71 54'4 45-6 IsT 84-2 Im 146-3 122-8 •251 192 "^ 161 "T 12 lo-o ^'' 72 55-2 46-3 132 loi-i 84-8 192 147-1 123-4 252 193 162 13 8-4 73 55*9 46-9 133 I0I-9 85-5 193 147-8 124-1 253 193 8 162 6 14 10-7 9-0 74 56-7 47-6 134 102-6 86-1 194 ,48-6 124-7 254 194 6 163 3 15 II-5 9-6 75 57-5 48-2 1,35 103-4 86-8 195 149-4 125-3 255 ■95 3 163 9 16 12-3 10-3 76 58-2 48'9 136 104-2 S7-4 196 150-1 126-0 256 ,96 1 164 6 17 13-0 10-9 77 59-0 49-5 137 104-9 197 150-9 126-6 257 196 9 165 2 18 1 1-6 78 59-8 50-1 138 105-7 88-7 198 151-7 127-3 258 197 6 165 8 19 11-6 12-2 79 6o-5 139 j°6:5 89-3 199 152-4 259 198 4 166 5 20 15-3 1^-9 80 6r3 51-4 140 90-0 200 153-2 128-6 260 ■99 2 167 21 i6-i 13-5 81 62-0 52-1 ur 108-0 90-6 201 154-0 129-2 261 199 9 167 T 22 .6-9 I4M 82 62-8 52-7 142 108-8 91-3 202 «54-7 129-S 262 7 168 4 23 17-6 14' 8 83 63-6 53-4 143 109-5 91-9 203 '55-5 130-5 263 201 5 169 1 24 184 15-4 84 64-3 54-0 144 110-3 92-6 204 156-3 131-1 264 202 169 7 25 192 i6-i 85 65-1 54-6 145 iii-i 93-2 205 157-0 131-8 265 203 170 3 26 19-9 i6-7 86 65-9 55-3 146 III-8 93-8 2061 157-8 132-4 •260 203 8 171 27 20-7 17-4 87 66-6 55-9 147 .12-6 9+-5 207 158-6 133-1 267 204 5 6 28 i8-o 88 67-4 56-6 148 113-4 95-1 208 159-3 133-7 268 172 3 2'J 22-2 i8-6 89 68-2 57-2 149 114- 1 95-8 209 .60-1 134-3 269 206 1 9 30 23-0 29J_ 90 '91 68-9 57-9 150 114-9 96-4 210 160-9 '35-0 270 206 8 >73 6 31 23-7 19-9 69-7 58-5 161 115-7 97-1 211 i6i-6 135-6 ^ 7^ T-^ ■^ 32 1 24-5 20-6 92 70-5 59-1 152 1.6-4 97-7 212 162-4 136-3 272 208 8 33 i5-3 21-2 93 71-2 59-8 153 213 163-2 136-9 273 209 I 175 5 34 26-0 21-9 94 72-0 6o-4 154 118-0 99-0 214 .63-9 137-6 274 209 9 176 1 35 i6-8 22-5 95 72-8 611 155 II8-7 99-6 215 .64-7 13.S-2 275 1210 7 176 8 36 27-6 96 73"5 6.-7 150 119-5 100-3 216 165-5 I38-8 276 4 177 4 37 28-3 23-8 97 74-3 62-4 157 1 20- 3 217 166-2 139-5 277 1-8 29-1 24-4 98 75-" 63-0 158 I2I-0 101-6 218 167-0 140-1 278 178 7 39 29-9 25-1 99 75'8 63-6 159 121-8 102-2 219 167-8 140-8 279 179 40 25-7 100 76-6 64-3 ICO 122-6 102-8 220 141-4 280 i. 180 IT 3i'4 26-4 101 77'4 64-9 161 123-3 103-5 221 169-3 142-1 M" 215 180 T 42 32-2 102 78-1 65-6 162 I 24- 1 104-1 222 142-7 282 181 3 43 32-9 27-6 103 78-9 66-2 163 124-9 104-8 2-23 170-8 '43-3 283 8 181 9 44 33'7 28-3 104 79"7 66-8 164 105-4 224 171-6 144-0 284 6 182 6 45 34'? 28-9 105 80-4 6rs 165 lli'l .o6-T 225 172-4 144-6 285 3 183 2 46 5 5-2 29-6 106 166 127-2 106-7 220 173-1 145-3 286 1 183 8 47 36-0 30-2 107 82-0 68-8 167 127-9 107-3 227 173-9 145-9 287 9 1S4 5 48 36-8 30-9 108 82-7 69-4 168 I2S-7 228 174-7 146-6 288 6 185 1 49 37-5 3i'5 109 83-5 169 129-5 108-6 229 175-4 147-2 289 4 185 8 SO 38-3 1 32-1 110 84-3 70-7 170 130-2 109-3 230 ■47-8 290 1S6 4 51 39-1 32-8 HI 85-0 71-3 W 131-0 109-9 231 177-0 148-5 •291 "9" ^F T 52 39-8 33'4 112 85-8 72-0 172 131-8 110-6 232 177-7 149-1 292 18- 53 40-6 34"' 113 86-6 72-6 173 132-5 111-2 233 178-5 149-8 293 5 18S ■ 54 |4i-4 34-7 114 87-3 73-3 174 '33-3 1II-8 234 179-3 150-4 294 189 c 55 42-1 35'4 115 88-1 73-9 175 134-1 112-5 235 180-0 151-1 295 189 6 5C 1 42-9 36-0 116 88-9 74-6 176 134-8 236 180-8 151-7 296 190 3 57 43-7 36-6 117 89-6 75-2 !77 .35-6 113-8 '237 181-6 15--3 297 5 19c 9 58 44-4 1 37-3 90-4 75-8 178 ,36-4 114-4 238 182-3 153-0 298 228 3 191-6 59 45-- 37-9 119 91-2 ,6-5 179 ,3,., 115-1 239 183-1 153-6 299 22Q 192-2 6(1 46-0 38-6 120 91-9 180 137-9 240 .83-9 154-3 300} 229-S 192-s Uist Dep.JD.Ul Dist Dep. aut Dist Dep. D.bit Du~t Do,,. D.Lat. Dist.! Dep. D.l nt 5( >'-■ 3" 20" 511 TRAVERSE TABLE TO DEGREES 40° 2h 40'" Diet. 301 D. Lat Dcp. Dist. 361 D. Lai. Dep. Uist. 421 D. Lat. Dep. Dist. 481 D. Lat. Dep. Dist. 541 D. Lat. Dep. 230-6 •93-5 276-5 232-1 322-s 270-6 36S-5 309-2 414-4 347-7 302 231-3 1 94- 1 36-2 277-3 2327 422 3233 271-3 482 3692 3098 .-,42 4152 348-4 303 232-1 194-8 363 278-1 2333 423 324-0 271-9 483 3700 310-5 543 4160 3490 304 232-9 "95-4 364 2788 234-0 424 324-8 2726 484 370-8 311-1 544 416-7 349-7 305 2336 196-1 365 279-6 234-6 425 325-6 2732 485 37>-5 311-7 545 417-5 3503 306 2344 iq6-7 366 2804 235-3 426 326-3 273s 486 372-3 312-4 546 4183 3510 307 235-2 ■ 97-3 367 2S1-1 2359 427 327 I 274-5 487 3731 3130 547 4190 351-6 308 2359 19S-0 368 2819 236-6 428 327-9 275-> 488 3:38 3136 548 4198 352-2 309 236-7 1986 369 2S2-7 237-2 429 32S-6 275-8 489 3746 314-3 549 4206 352-9 310 317 237-5 •99-3 199-9 370 283-4 237-8 430 329-4 276-4 490 491 375-4 376-1 3'4-9 3>S-6 550 551 421-3 422- 1 353-5 3542 23S-2 2S4-2 '23S-5 431 3302 277-1 312 239-0 200-6 372 285-0 239-1 432 3309 277-7 492 376-9 316-2 552 422-9 354-8 313 239-S 201-2 373 285-7 239-7 433 33'-7 278-3 493 377-7 3169 553 4236 355-5 314 240-S 201-8 374 2S6-5 240-4 434 332s 279-0 494 378-4 317-5 554 424-4 356-1 315 2413 202-5 375 2S7-3 241-0 435 3332 279-6 495 379-2 31S2 555 4252 3568 316 242-1 203-1 376 288 241-7 436 3340 280-3 496 3800 3>S8 556 425-9 3574 317 242-8 203-8 377 28S-8 2423 437 334-8 280-9 497 3S0-7 3'9-5 557 426-7 358-0 318 243-6 204-4 37S i 289-6 2430 438 335-5 281-6 498 381-5 320-1 558 4275 35S7 319 2444 205-1 379 290-3 243-6 439 336-3 282-2 499 382-3 3208 559 4282 359-3 320 245-1 _2057_ 380; 291 -I 244-3 440 337J_ 282-8 500 j83:o 32 '-4 560 429-0 3600 321 245-9 206-3 381 291-9 244-9 441 337-8 283-S .5or 383-8 322-0 561 4298 360-6 322 246-7 2070 382 2926 245-6 442 338-6 284-1 502 3846 322-7 562 430-5 361-2 323 247-4 2076 383 293-4 2462 443 339-4 284-8 503 385-3 323-3 563 431-3 361-9 324 2482 208-3 384 294-2 2468 444 340- 1 285-4 504 386-: 3240 564 4321 362-5 325 249-0 20S9 385 294-9 2475 445 3409 2S6-0 505 386-s 3246 565 4328 363-2 326 249-7 2096 386 295-7 248-1 446 341-7 2S6-7 506 387-6 325-2 566 4336 363-8 327 2505 210-2 387 296-5 1 248-8 447 342-4 287-3 507 388-4 325-9 567 434-3 364-5 328 251-3 2108 388 2972 , 2494 448 343-2 2S8-0 508 389-2 3265 568 435-1 365-1 329 252-0 211-5 389 298-0 250-1 449 344-0 288-6 509 3899 327-1 569 435-9 365-8 330 2528 212 I 390 29S-8 250-7 450 344-7 289-3 510 390-7 327-8 570 436-6 366-4 331 253-6 ^2-8 3-Jl 299-5" 251-3 451' 345-S 2899 511 391-5 T28^ 57T 437-4 367-0 332 2543 213-4 392 300-3 2520 452 3463 290-5 512 392-2 329-1 572 438-2 367-7 333 255-1 214-1 393 30I-I 252-6 453 347-0 291-2 513 393;o 329-7 573 438-9 368-3 334 255-9 214-7 394 253-3 454 347-8 291-8 514 3304 574 439-7 369-0 335 256-6 215-3 395 302-6 253-9 455 348-6 292-5 515 394-S 331-0 575 440-5 3696 336 257-4 216-0 396 303-4 254-6 456 349-3 293-1 516 395-3 33"6 576 441-2 370-2 337 258-2 2166 397 304-1 255-2 457 350-1 293S 517 396-1 3323 577 4420 370-9 338 2589 217-3 398 304-9 255-8 458 3508 2944 518 3968 332-9 578 442-8 371-5 339 2597 2179 399 305-7 256-5 459 35'-6 295-0 519 397-6 333-6 579 443-5 372-2 340 260-S 2i8;6^ 400 3064 257-1 460 352-4 295-7 .520 398-3 334-2 580 _444-3 372S 341 261-2 219-2 401 307-2 257-8 461 353-1 296-3 521 399-1 3349 581 445-1 3735 342 262-0 219-8 402 308-0 2584 462 353-9 297-0 522 399-9 3355 582 +45-8 374-1 343 262-8 220-5 403 308-7 2591 463 354-7 2976 523 4006 3361 583 446-6 374-8 344 263-5 22rr 404 309-5 259-7 464 355-4 298-3 524 4014 336-8 584 447-4 375-4 345 264-3 221-8 405 3102 2603 465 3562 2989 525 402-2 337-4 585 44S-1 376-0 346 265-1 222-4 406 3"o 2610 466 357-0 299-5 526 4029 3381 586 448-9 376-7 347 265-8 223-1 407 311-8 261-6 467 357-7 300-2 527 403-7 33S-7 587 449-7 377-3 348 266-6 223-7 408 312-5 2623 468 35S-5 3008 528 404-5 339-4 588 450-4 3780 349 267-4 224-3 409 313-3 262-9 469 359-3 301-5 529 4052 3400 589 451-2 3786 350 35r 26S-1 268-9 225-0 225-6" 410 3>4-i 314-8 263-6 264-2 470 3600 302-_I_ 530 531 4060! 340-6 >6 8, 341-3 590 591 4520 4527 379-2 3608 i 3028 3799 352 2696 226-3 412 3'5-6 2648 472 361-6 303-4 532 407 5 341-9 592 453-5 3805 353 270-4 226-9 413 316-4 2655 473 3623 304-0 533 408-3 342-6 593 454-3 381-2 354 271-2 227-6 414 3i7-> 266-1 474 363-1 304-7 534 409-1 343-2 59 4 4550 381-8 355 2719 228-2 415 1 317-9 266-8 475 3639 305-3 535 409-8 343-9 595 455-8 382-4 356 272-7 22SS 416 1 3I«7 2674 476 364-6 3060 .536 410-6 344-5 596 4566 383-1 357 2735 229-S 417 1 3194 268-1 4-7 365-4 306-6 537 41 1-4 3452 597 457-3 383-7 358 2742 230-1 418 320-2 26S-7 478 3662 307-3 538 412-1 3458 .598 458-1 384-4 359 2750 2308 419 321-0 269-3 479 366-9 307-9 539 412-9 1 346-4 599 4589 385-0 360 275-8 23.-4 420 321-7 2700 480 367-7 308-5 540 413-7 347-1 600 459-6 3857 DisL Df-p. 'd. Lat IJist Dep. D. I,at. Dist.| Dep. D. Lat Dist Dep. D. Lat. Dist. Dep. D. l^t. r.O" 3'' 20"' 1 512 TABLE TRAVERSE TABLE TO DEGREES 41° 2i> 44"' D»t D.Lat Dep. Dist D.Lat.! Dep. Dist.jD.Lat.| Dep. Dist D.Lat.j Dep. Dist.JD. Lat Dep. ~r 0-8 61 46-0 40-0 121 91-3 79-4 181 . 36-6 |., 8-7 241 181-9 15S-1 2 1-5 '•3 62 46-8 40-7 122 92-1 So-o 182 137-4: 119-4 242 182-6 158-S 2-3 2-0 63 47-S 41-3 123 92-8 80-7 183 .38-1 .20-1 24.1 183-4 .59-4 3-0 2-6 64 48-3 42-0 124 93-6 S.-4 184 .38-9|i2o-7 244 184-1 160-T 3-8 3-3 65 49-1 426 125 94-3 82-0 185 139-6 ;i2i-4 245 184-9 160-7 4-5 3-9 66 49-8 43-3 126 95-1 82-7 186 .40-4 .22-0 246 185-7 .61-4 5-3 4-6 67 50-6 44'° 127 95-8 83-3 187 I4I-I 122-7 247 186-4 162-0 6-0 5-2 68 5»-3 44-6 128 g6-6 84-0 188 I4I-9 I 123-3 248 187-2 .62-7 6-8 5-9 69 52-1 45-3 129 97-4 84-6 189 142-6 .24-0 249 187-9 .63-4 IT rs' 6-6 70 52-8 130 9S-. 85-3 190 143-4 124-7 230 18S-7 .64-0 8-3 7-2 71 53-6 1P6" 131 98-9 85-9 191 144-1 125-3 25r 189-4 164-7 9-1 7-9 72 54-3 47-* 132 99-6 86-6 192 144-9 126-0 252 .90-2 .65-3 9-8 8-5 73 55'' 47-9 133 100-41 87-3 193 145-7 126-6 253 1 .90-9 .66-0 10-6 9-2 74 55-8 48-5 134 .ofi 87-9 194 146-4 127-3 234 191-7 166-6 II-3 9-8 75 56-6 49' 2 135 I0I-9 88-6 195 127-9 255; 192-5 167-3 121 IO-5 76 57-4 499 136 89-2 196 147-9 128-6 256 j 193-2 .68-0 17 1 12-8 II-2 77 58-1 50-5 137 I03-4 89-9 197 I4S-7 129-2 2.57 1 1 94-0 16S-6 18 , 13-6 II-8 78 58-9 51-2 138 104-1 90-5 198 1 149-4 129-9 258 1 .94-7 169-3 14-3 12-5 79 59-6 5>-8 139 104-9 91-2 199 1 150-2 130-6 259! .95-5 1699 20 .5-1 13-1 80 6o-4 52-5 140 105-7 9.-8 200! 150-9 131-2 2B0 .96-2 170-6 -2r i;-8 13-8 HI 6i-i 53-1 1411 106-4 92-5 201 151-7 131-9 261 i .97-0 22 i6-6 .4-4 82 6i-9 53-8 142 1 107-2 93-2 202 152-5 132-5 262 197-7 171-9 23 j-4 ,5-. 83 62-6 54-5 143 1 107-9 93-8 203 153-2 133-2 263 198-5 172-5 24 ]8-i .5-7 84 63-4 55-1 144 108-7! 94-5 204 154-0 133-8 264 199-=' 173-2 25 ,8-9 i6-4 85 64-2 55-8 145 109-4 95-1 205 154-7 134-5 265 200-O 173-9 26 .9-6 I7-I 86 64-9 1 56-4 146 110-2 95-8 206 '55-5 135-1 266 200-8 174-5 27 20-4 1 "7-7 87 65-7 |57-i 147 IIO-9 96-4 207 156-2 .35-8 207,201-5 175-2 28 21-1 i8-4 88 66-4 57-7 148 111-7 97-1 208 157-0 136-5 268 202-3 175-8 2!) 21-9 ig-o 89 67-2 58-4 149 112-5 97-8 209 157-7 137-1 269' 203-0 176-5 30 Tr 22-6 I .9-7 90 67-9 59-0 150 113-2 98-4 210 ,58-5 137-8 270 203-8 177-1 23-4 1 20-3 -oT 68-7 59'7 151 114-0 99-1 In 159-2 138-4 271 204-5 177-S 32 24-2 1 21-0 92 69-4 6o-4 152 114-7 99-7 212 160-0 139-1 272:205-3 178-4 33 24-9 21-6 93 6i-o 153 115-5 100-4 213 i6o-8 139-7 273 206-0 179-1 34 25-7 ;22-3 94 70-9 6i-7 154 Il6-2 loi-o 214 .6. -5 140-4 274 206-8 .79-8 35 26-4 23-0 95 71-7 62-3 155 117-0 101-7 215 ■ 62-3 141-1 275 207-5 .804 36 27-2 23-6 96 72-5 63-0 156 117-7 102-3 216 163-0 141-7 276 208-3 181-1 37 27-9 24-3 97 73-2 63-6 157 118-5 103-0 217 163-8 142-4 277 209-1 181-7 38 2S-7 249 98 74-0 64-3 158 119-2 103-7 218 164-5 143-0 278 209-8 .82-4 39 29-4 25-6 99 74-7 64- 9 159 120-0 104-3 219 ,65-3 143-7 279 210-6 1S3-0 40 30-2 26-2 100 75-5 65-6 160 120-8 105-0 220 166-0 .44-3 280 2II-3 .83-7 IT 30-9 26-9 101 76-2 66-3 161 1 121-5 105-6 221 166-8 145-0 28r 2I2-I 184-4 42 31-7 27-6 102 77'o 66-9 162 1 122-3 .06-3 222 .67-5 .45-6 282 212-8 185-0 43 32-"; 28-2 103 7T7 67-6 163 123-0 106-9 223 .68-3 146-3 283 213-6 185-7 44 33-2 28-9 104 78-5 68-2 164 .23-8 107-6 224 169-, 147-0 284 214-3 186-3 4S 34-0 1 29-5 105 79-2 68-9 163 124-5 108-2 225 .69-8 147-6 285 215-1 46 34"7 1 30'2 106 s2-o 69-5 166 125-3 226 170-6 148-3 28C 215-8 187-6 47 35"5 1 30'8 107 8o-8 70-2 167 126-0 109-6 227 171-3 148-9 287 216-6 J8S-3 48 36-2 1 31-5 108 81-5 70'9 168 126-8 228 172-1 149-6 288 2.7-4 188-9 49 37-0 32-1 109 82-3 71-5 169 127-5 II0-9 229 ,72-8 150-2 189-6 50 1 377 32-8 no 83-0 72-2 1701 128-3 III-5 230 .73-6! 150-9 290 1 218-9 190-3 ^r 38-5 33'5 TTT 83-8 7^-8 171 129-1 112-2 231 174-3 j i5"-5 291 2196 190-9 52 39-2 34" I 112 84-5 73-5 172 ,29-8 112-8 232 175-1 \ 152-2 292 220-4 .91-6 53 40-0 34-8 113 85'3 74"' 173 130-6 113-5 233 293 192-2 54 40-8 35'4 114 86-0 74-8 174 131-3 114-2 234 I76-6 ;53-5 294 221-9 192-9 55 4>"5 36-1 115 86-8 |75-4 175 132-1 114-8 235 177-4 154-2 295 222-6 193-5 56 42-3 36-7 116 87-5 lyfi-i 1761 132-8 115-5 236 .78-1 154-8 296 223-4 194-2 57 43-0, 37-4 117 88-3 176-8 177' -33-6 ii6-i 237 178-9 155-5 297 22+- 1 194-8 58 43-8 h8-. 118 89-1 77'4 178 134-3 116-8 238 179-6 156-1 298 224-9 .95-5 59 44-5 1 38-7 119 89-8 78-. 179 i35-> 117-4 23!l 180-4 156-S 29Sl 225-7 196-2 60 , 45-3 ! 39-4 120 90-6 78-7 180 135-8 iiS-i 240 181-. 1.57-5 30»| 226-4 ,96-8 Dist.l Dtp., D.Lai Uist. Dep. D.Lat Dist.[ Dep. D.Lat. OistJ Dep. Id. l.at. D,st.| Dep. D.Lat. 49° 3'- If."- 1 TRAVEllSE TABLE TO DEGREES 41" 2'-44» 1 Dist. D. Lat. Dep. Disi.'o. Lat. Dep. Di-t. D. Lnt Dep. Dist. D. Lat. Dep. Dist D. Lat Dep. .mi 227J 197-5 36: 272-5 2369 421 3'77 276-2 481 363-0 315-6 541 4083 354-9 302 227 9 19S1 362 273-2 2375 422 3'8S 2769 482 3638 3-62 542 4090 3556 30.1 22S7 I9S» 3B3i 2740 238-2 4 23 3'92 2775 483 3645 3'6-9 543 4098 3562 304 22g-4 199-4 364 2747 238-8 424 3200 27S-2 484 365-3 3'7-5 544 410-6 356-9 303 2302 1 200 I ■■i63- 2755 239-5 425 320-8 2788 485 3660 318-2 545 4113 357-5 306 2309 2c«8 366 276 2 240-1 426 321-5 279-5 486 366 8 3-8 8 346 412 I 3582 .•i07 2317 201 4 .-ifi7 1 277-0 2408 427 322-3 2S0- r 487 367-5 3>9 5 54 7 4.28 3588 n08 2325 202 r .36^ 1 277-7 2414 428 323-0 2S08 488 368-3 3201 548 4136 359 5 309 2J3* 2027 .369 27S5 242 I 429 323-8 281 5 489 369-0 3208 549 4143 3602 310 2340 203 4 .370^: 2792 2427 4.30 324-5 i 282. 490 369-8 3215 550 415 I 3008 311 2347 2046 371 2800 243-4 431 325 3 1 282 8 491 3706 322 I aTT 4.5-8 "36 15 312 235-5 204-7 372! 2808 244 I 4.32 326-0 283-4 492 371-3 3228 532 416-6 3621 313 2362 205-4 373: 281-5 244-7 433 326 8 284-1 493 372-' 3234 553 417-3 3628 3U 2370 2060 374! 2S23 245-4 434 327-5 2S4-7 494 372-8 324-1 554 4181 3634 313 2377 206-7 37 3 1 283 o| 2460 435 3283 2S54 495 3736 324-7 553 4189 364-1 3I« 23S5 2073 376 1 2S3S' 2467 436 329-1 1 2S60 196 374-3 325-4 556 4196 3648 317 2392 20S0 377 j 2S4-5 : 247-3 437 329-S 1 286 7 497 375-1 326-0 557 4204 3654 31H 240 oj 2oS-6 378 ] 285-3 1 248 438 330-6 1 2S7-4 498 375-8 3267 558 421 I ;6t,-i 319 240S 2093 379 1 286 o| 24S7 439 33I-3 288-0 499 3706 3274 559 4219 366-7 320 24.5 2099 380 ! 286 8 249 3 440 332-1 28S7 500 3773 3280 560 4226 367-4 321 -423 2in-fi 381 1 2S75 2500 441 332-S" 2S93 .501 378-1 1T87 561 4 2 3' 4 368-0 322 2430 211 3 382 2S83 2506 442 3336 2900 .502 3789 3^9-3 562 424 I 36-S-7 323 2438 2II9 383 2891, 2513 443 334-3 2906 .503 3796 3300 563 4249 369-4 321 2445 2126 384 2S9S j 251-9 444 335' 291-3 504 3804 330 6 564 4257 370-0 325 2453 2132 383: 2906 252-6 445 335-8 2920 505 381-1 331 3 565 4264 3707 326 2460; 2139 386 1 291 3! 2532 446 3?6-6 2926 506 38.-9 3320 566 4272 371-3 327 2468 214-5 387 292-1 2539 447 337-4 2933 .507 3826 3326 567 427-9 3720 328 247-5 2152 388 2928 2546 448 338-1 293-9 503 3333 568 42S7 3726 329 24S-3 2159 389 1 293 6 2552 449 3389 2946 509 384-' 333 9 569 4294 373-3 330 2491 2165 390 294 3 255-9 450 339-6 295-2 510 384-9 334-6 570 4302 3740 331 24T8 217 2 391 , 295 I 2565 431 3-to-4 295-9 511 ^^ll^ 3352 571' 4309" 374-6 33.' 2506 2178 392 I 295 8 257-2 452 341-1 29:>-5 512 3864 3359 572 431-7 375-3 333 2513; 21S5 393 2966 2378 433 341-9 297-2 513 3872 3365 573 4324 375 9 334 2521 2191 .-i94 297-4 1 2585 434 3426 2979 514 3879 337-2 574 4332 3766 335 252S 219 8 .-193 298-1 2592 455 3434 29S-5 515 38S-7 337-9 3 75 4340 377-2 336 2536 2204 396 29S 9 1 259 8 4 56 344 I 1 299 2 316 389-4 3385 576 4347 377-9 337 2543 2211 397 i 29961 260-5 437 344 9 299-8 517 390-2 339-2 577 435-5 3785 338 255 ■ 2218 39-*: 3004 261-1 458 3457 300-5 518 3909 339-8 578 4362 379-2 339 255-8 222-4 3119 301 1 j 2flS 459 3464- 301-1 519 39'-7 3405 579 4370 3798 340 2566 223 I 400 30.9 2624 460 3472] 301-8 320 392-4 34i-> 580 437-7 3805 3(1 257-4 223-7 JuT 3026 263-T 461 i 347 91 302-5 .3-21 393-2 34T^ 581 '43-8^5^ TSV2 342 258 I 1 2244 402 .3034 2637 462 1 3487 303-> 522 3940 3425 .382 4392 3818 343 258-91 225-0 403 304-.' 264-4 463 3*9 4 303-8 523 394-7 343-1 583 4)0-o 3825 344 259-^' 225 7 4'14 3049 2651 464 3502 304-4 524 395 5 343-8 584 4407 383-2 310 260 4 1 2263 403 3057 2657 465 3509 305- ■ 525 3962 344-4 585 441 5 3838 3 46 2611 2270 406 3064; 266-4 466 351-7 i 305-7 526 3970 345-' .586 4423 3845 347 2619 2277 407 307-2 1 2670 467 3525 3064 527 397-7 345-7 587 4t3-o 385-' 348 262 6 228 3 408 3079 2^7 7 468 353-2 307-0 528 39S5 346-4 588 4438 385 8 3 4 J 2634^ 229-0 109 .3087 26S-3 469 3540 307-7 329 3992 3470 589 444 5 3864 330 2642 229-6 410 3094 269-0 470 3547 308-4 530 4000 347 7 590 445-3 3871 33T 26?^ 2303 4Tr 310-2 T6^ 471 355-5 3090 531 4007 ■348^' 597 4460 I877 332 2657 2309 412 310-9 270-3 472 3562 3097 532 401-5 3490 592 4468 3884 353 2664 2316 413 3"-7 2710 473 3570 310-3 5.33 402-2 349-7 593 447 5 3S9' 354 267-2 232-3 4U 3'2S 271 6 474 357-7 3n-o 534 403-0 350-3 594 4483 3897 3S5 2679 2329 41.5 3>32 272-3 475 3585 311 6 535 4038 35' 595 449-1 3004 336 2687 233-6 416 3'4-o 2729 476 359-2 3'2 3 536 404-5 .351-6 396 4498 3910 357 269-4 2342 417 3'4 7 2736 477 3600 3129 537 405-3 352 3 597 4506 391 7 338 2702 2349 418 3 '5-5 274-2 478 3608 3<36 538 406-0 3520 .598 451-3 3923 •139 2709! 2355 41/) 3-62 274-9 479 3615 3'4-3 539 4068 353-6 599 452-1 393-0 360 271-7 236-2 420 3 '7-0 2756 480 3623 3'4 9 540 407 s 354-3 600 4528 3936 l)i*t Dep. D. Lat. Dist. Dep. D. Lat. Di.st D^ D. Lat. Di.-I.i Dep. D.Lat. Dist Dep. D. Lat. 40- -.^ "■.» 614 TRAVERSE TABLE TO DEGREES 1 42° 2" 48™ 1 DistJO-Lal'Dep. Dist D. Lat _^ Dis.jD. Lat ! Uep. Dist jP.Lat |Dep. DisJD. Lat Dep. ~r 0-7 1 0-7 01 45'3 40-8 121 89-9 8ro 181 1 .34-5 1,21-1 241 179-1 16.-3 2 '■5 >'3 02 46-1 4i'5 122 90-7 81-6 1(12 •35-3 121-8 242 179-8 ,61-9 3 I-2 03 46-8 42-2 123 91-4 82-3 183 136-0 122-5 243 180-6 162-6 4 3-0 2'7 04 47-6 42-8 124 92-1 83-0 184 136-7 123-1 244 ,8,-3 163-3 5 3'7 3'3 65 48-3 43*5 125 92-9 83-6 185 137-C 123-8 •245 182-1 163-9 6 4' 5 4-0 66 49'° 44' 2 12c 93-6 84-3 180 138-7 124-5 246 182-8 164- 6 7 5'i 4-7 67 49-8 44-8 127 94-4 1 85-0 187 139-c 125-1 247 183-6 165-3 8 5'9 5-4 08 50-5 45-5 128 95-' 1 85-6 188 •39-/ 125-g 248 184-3 165-9 !) 6-7 6-0 09 5"'3 46-2 129 95-9 86-3 181 140-5 126-5 •249 185-0 1666 10 7 '4 6-7 70 52-0 46-8 130 96-6 87-0 190 141-2 127-1 250 .85-8! 167-31 1 1 sT 7'4 -7T 52-8 47-5 W\ 97'4 87-7 191 1 141-9 1 I27-S 251 ,865! 168-0 12 89 8-0 T2 S3'5 48-2 132 98-1 88-3 192 142-7 128-5 252 168-6 13 9;7 8'7 73 54-2 48-8 133 98-8 89-0 193 ■43-4 129-1 253 169-3 14 9;4 74 55-0 49-5 134 99-6 S9-7 194 144-2 129-8 254 i88-S 170-0 Id III 75 557 50-2 135 100-3 90-3 195 '44-9 130-5 255 189-5 170-6 16 119 10-7 7fi 56-5 5°"9 136 91-0 190 '45-7 131-1 256 190-2 171-3 17 12-6 "•4 77 57'2 5i'5 137 10I-8 91-7 197 1464 131-8 257 1910 172-0 lil I3-4 78 58-0 52-2 138 102-6 92-3 198 147- 1 132-5 •258 191-7 172-6 1!» ' .4-1 12-7 7!» 58-7 5i'9 I3!t 103-3 93-0 199 147-9 133-2 259 192-5 173-3 2(» 1 14-9 80 59-5 53-5 140 104-0 93-7 200 148-6 ■33-8 200 .93-2 ■ 174-c 1 in-!"TiT 14- 1 81 6o-2 54' 2 Ml 104-8 94-3 •201 149-4 '34-5 2?n- 194-0 174-6 22 i6-3 14'7 02 609 54' 9 142 105-5 950 202 1 50- 1 135-2 262 '94-7 175-3 2.; >5'4 03 Ci-7 55'5 143 106-3 95-7 •203 150-9 135-8 203 195-4 176-0 n lyS 84 62-4 56-2 144 107-0 ^6-4 204 .5.-6 ■36-5 264 196-2 176-7 25 i8-6 ,6-7 85 63-2 56-9 145 107-8 97-0 •205 152-3 137-2 205 196-9 177-3 2b- 19-3 ■7'4 8(> 63-9 57-5 140 108-5 97-7 206 153-1 137-8 266 197-7 ?; 18-1 «7 64-7 58-2 147 .09-2 98-4 207' 153-8 138-5 267 178-7 28 20-8 i8-7 88 65-4 58-9 148 iio-o 99-0 208 154-6 139-2 268 199-2 179-3 2'( 21-6 19-4 8»' 66-1 59-6 149 iic-7 99-7 ■209 155-3 |>39-8 269 199-9 .?'1J2?J_ do' 66-9 6o-2 150, I J 1-5 210 156-1 |, 40^5 270 200-6 180-7 HI 1 23 o 20-7 ill 67-6 60-9 151 1122 loi-o 211 156-8,141-2 271 201-4 JS1-3 3J 1 23-8 1 ^'-4 92 68-4 6i-6 152 1130 I01-7 212 157-5 141-9 272 .82-0 33 1 24-5 122-1 !)3 69-1 62-2 153 M3-7 I02'4 213 158-3 142-5 273 202-9 182-7 34 25-3 22-8 94 69-9 62-9 154 1 114-4 103-0 214 1590 143-2 274 203-6 183-3 35 ! 26-0 ^3-4 95 70-6 63-6 155 115-2 103-7 215 1 159-8 •43-9 275 204-4 184-0 3fi 26-8 24-1 •to! 71-3 64-2 150 115-9 104-4 210 i6o-5 '44-5 270 205-1 184-7 1 37 27-5 24-8 97 72-1 64-9 157 116-7 lOCl 217 161-3 .45-2 277 205-9 185-3 38 2S-2 25-4 98 72-8 6r-6 I5R 117-4 105-7 218 162-0 '45-9 278 206-6 1860 ■S'J 29-0 26- 1 99 73-6 66-2 159 118-2 .06-4 219 162-7 146-5 279 207-3 186-7 40 29-7 26-8 100 ioT 74-3 66^ 100 .18-9 107-1 220 ,63-5 147-2 280 208-, 187-4 TT i^-s 28^1 75-1 67-6 TeT ;'9:6 107-7 22r 164-2 147-9 281 208 -8 188-0 42 31-2 102 75-8 68-3 102 108-4 222 165-0 148-5 282 209- 6 .88-7 43 32-0 28-8 103 76-5 68-9 163 121-1 109- 1 223 165-7 149-2 283 210-3.189-41 44 29-4 104 77-3 69-6 104 121-9 109-7 224 166-5 149-9 284 211-j 190-0 1 45 33-4 30-1 105 78-0 70-3 105 122-6 1 10-4 225- 167-2 150-6 285 211-S 190-7 46 34-2 30-8 UlO 78-8 70-9 166 123-4 iii-i 220 i i68-o 151-2 286 212-5 191-4 47 34*9 3i'4 107 79-5 71-6 167 124-1 111-7 227 168-7 1519 •287 213-3 192-0 48 35'7 32-1 108 72-3 168 124-8 112-4 228 ,69-4 ;5^-6 28a 214-0 49 36-4 32-8 109 8i-o 72-9 169 125-6 113-1 '229 •289 214-8 195-4 50 37'2 33-5 110 Si-7 73-6 170 126-3 113-8 230 1^0-9 153-9 290 215-5 194-0 51 37-9 111 82-; 74-3 171 I27-J 114-4 23r 171-7 .54-6 291 2.6-3 194-7 52 38-6 34- S 112 83-2 74' 9 172 127-8 115-1 232 172-4 155-2 292 217-0 195-4 53 394 35-5 113 84-0 75-6 173 128-6 .15-8 233 173-2 155-9 293 217-7 196-1 54 40-1 361 114 84-7 76-3 174 \'V 116-4 234 173-9 156-6 294 218-5 196-7 55 1 40-9 36-8 115 85-5 77-0 175 117-1 2:« 174-6 157-2 295 219-2 197-4 56 4'-6 37-5 116 86-2 77-6 170 Ifo-l 117-8 230 175-4 157-9 290 220-0 .98-] 57 I 42-4 38-. 117 86-9 78-3 177 131-5 1.8-4 237 176-, 158-6 297 220-7 .9S-7 58 |43-> 38-8 118 87-7 1 79-0 I7» 132-3 ii9'i 238 176-9 • 59-3 298 221-5 199-4 59 43-S 39-5 119 88-4 79-6 179 .33-0 1 l,y-8 239 177-6 1599 299 _60_|_44-^ DUt ' l>ep. 40-1 120 89-2 8o-3 180 1 133-8 1 120-4 240 178-4 160-6 tool "■'' '"'JA D.L-dt )isl. De,,. 3. Lai )i8t.| Dip. 1 n. I.al >istj l)pp. 1 n. ut )isl.! Dep. ,D. I,„t 1 4 H° " n-i^"' 1 TABLE 1 TKAVIvllSK TAW.K TO DlCGKEliS | 42° 2>> 48» 1 ni»u D. Lit Dep. Dist. D. Lat-j nep. Dist. D. Lat. Dep. Dist. D. Lat. D.p. Dist. D.Lat Dep. ;«M 2237 20 1 -4 361 268-3' 241-6 421 312-9 28.-7 481 357-5 3219 541 4021 162-0 302 224-4 362 269 oj 242-2 422 3'36 2S24 482 358-2 3225 542 4028 3627 3(13 225-2 202-8 363 ;69 8 242-9 423 3'44 2830 483 3589 3232 543 403-S 363-.! 304 2259 2034 364 270 5 j 243-6 424 3'5 ' 2S3-7 484 359 7 3239 544 404-3 3640 305 2266 204-1 365 271-2, 244-2 425 3-58 2844 485 3604 324-6 545 4050 3647 306 227-4 204-8 366 27201 2449 426 3.66 2851 486 36.2 325-2 546 <-o5-8 3654 307 2281 2054 367 272 7 245-6 427 3'7-3 285-7 487 36.-9 3259 547 4005 366 ,108 228-9 368 273 5 246 2 428 3>S-I 488 3627 3266 .Hi 407-2 3667 309 2296 2068 369 2742 , 246-9 429 3.8-8 2S7I 489 363-4 327-2 549 40.S-0 3674 310 2J0 4 207-4 .-(70 2750 2476 430 3>96 287-7 490 364-1 3279 550 40S-7 3680 311 2311 20S-1 371 275-7 1 248-3 4 11 320-3 2'SS-4 4¥r 364-9 328-6" 55 r 409-5 368-7 3IJ 23'9 20S 8 372 276 5 1 248-9 432 321 2S9-. 492 3656 3292 552 4. 02 3694 313 232-6 2094 373 2772 2496 433 3218 289-7 493 3604 329-9 5.53 4.10 3700 3H 233-3 210 1 374 2779 250-3 434 3225 290-4 494 367-> 330-6 554 411-7 3707 31S 234- 1 210 8 375 2787 2509 435 3^y3 29. -I 495 307-9 3313 555 4.24 3714 3lfi 234S 211-5 376 2794 25.6 436 3240 29.7 496 368-6 33' 9 556 4'3-2 3720 317 2356 2121 377 2S0-2 2523 437 324S 2924 369-3 332-5 557 4'39 3727 318 236-3 212-8 378 280 9 ' 252 9 438 3255 293. 49S 370-1 333-3 5.58 4147 3734 319 237 1 2135 37D 28171 2536 439 326-2 293-8 499 3.08 333 9 559 4'54 374-1 320 =37i> 2I4-I 380 2S2-4I 2543 440 3270 2944 500 37r6 334-6 560 416-2 374-7 3:^1 238-6 2I4S -iSf 283-1 , 2549 4 if 3277 295-1 hiW 372-3 3353 561 4.69 37'5-4 3l'2 2393 215s 382 2S3-9 , 255 6 442 328-5 295-8 502 3731 3359 562 4176 376-1 323 240-0 2I6-I 383 284-6 1 256-3 443 3292 290-4 503 373-8 336-6 563 4.X-4 3767 324 2408 2168 384 285-4! 257-0 444 330-0 297-1 504 374-S 337-2 564 4.9-1 377 4 32. i 2415 217-5 385 286-1 i 257-6 445 330-7 297-8 50.5 375-3 3579 565 419-9 378-1 32r, 2423 2IS-I 386 2869 2583 446 33 > -4 298-4 506 3760 3386 566 420-0 3787 327 2430 218-8 387 287-6 2590 447 332-2 299-. 507 3768 339-3 .567 421-4 3794 328 2438 2195 388 28S-3 2596 448 3329 29^8 508 377-5 339-9 568 422-. 380- . 329 2445 220 I 389 2891 2603 449 333 7 300-4 509 3783 3406 569 4228 3807 330 J45-2_ 220-8 390 2898 2610 4.io 3344 30' I 510 3790 341-3 570 4236 381 4 331 2460 221 5 .391 2906 2616 45T 3352 301-8 5TT 3797 341-9 bfY 4243 382-1 332 246-7 222-2 392 291-3! 2623 452 335 9 3025 512 3805 3426 572 425> 382-8 333 2475 2228 .393 292-1 2630 4.i3 3366 3031 513 38.-2 343-3 573 425S 3834 334 2482 2235 394 292-8 2636 454 3374 3038 514 3820 343 9 574 420-6 384-1 335 2490 2242 .-195 2935 264-3 4. -.5 338-. 3045 515 382-7 3446 575 4273 3848 33R 2497 224-8 396 294-3 265-0 456 338-9 305-' 516 383 s 3453 576 42S0 3854 337 2504 2^55 .397 295-0 265-7 457 339-6 3058 517 384-2 3460 577 4288 3S6. 338 251-2 226-2 398 295-8! 2663 458 3404 3065 518 3849 346-6 578 4295 386-8 339 2519 226-8 399 296-5 1 267 459 341 I 307-1 519 385-7 347 3 579 4303 3874 340 252-7 2275 400 297-3 : 267 7 460 341-8 3078 520 3804 348-0 580 4310 388 . 341 253-4 228-2 4Tri 298-0 ' 268-3 46 f 342-6 30S-5 5 J 1 3872 348-6 sirr *3i-» 38S8 342 254-2 2288 402 29S 7 1 2690 462 3433 3'J9 ' 522 3S79 349-3 582 4325 3894 343 2549 2295 403 299-5 269 7 463 344 ' 309 8 523 388-7 3500 583 4332 390 1 344 2556 230-2 404 300 2 1 270-3 464 344 S 310-5 524 389-4 3506 584 434-0 390 8 34 S 256-4 2309 405 3010 2710 465 345-6 311-2 525 390. 35'-3 585 4347 3914 340 257-1 231 5 406 30.-7 27.-7 466 340-3 3i'S 526 390-9 3520 586 4355 3921 34? 2579 232 2 407 301s 1 272-3 467 3470 3 "2-5 527 391 6 3526 587 436-2 392 8 34-5 315-2 530 531 393 9 3946 354-6 3553 590 59r 438-4 439-2 3948 395 4 2750 471 352 261-6 2355 4 12 306 2 275-7 472 350-8 3'58 532 395-3 3500 592 4400 3961 353 2623 2362 413 3069 2764 473 35'-5 3'65 5.-(3 396-1 3566 593 4407 3968 G54 2631 2369 414 3077 2770 474 3523 3'72 534 396-8 357-3 594 4414 397-5 3 55 263-8 2375 415 308-4 2777 475 3530 3.7-8 535 3976 3580 595 4422 3981 35fi 2646 2382 416 3091 278-4 476 3537 5.85 536 39S-3 358-6 596 4429 398-8 357 2^53 238-9 417 309-9 2790 477 3545 3 '9 2 5->7 399-' 3.593 597 4437 3995 35H 2660 2396 418 3"o6! 2797 478 355-2 3'99 538 399S 3600 598 444-4 400. 359 2668 240-2 419 311 4; 2804 479 3560 3205 539 4006 3606 599 445-2 4008 3fi0 2675 2409 420 3I2I 2810 480 356-7 32^2 540 4013 36 > -3 600 Disl. 445'9 401 5 n. L..t. Km. IJ.P. I>. Ut. l,i... Dep!' D. Lat. Di... Dcp. \). Lai. uZ. De^ . 48' a" 12'-- 516 TABLE 1 TRAVERSE TABLE TO DEGREES 43° a- 52=" DistJn.t,atiDep. Distju. Lat, Dep. Dist. 1). Ut. D.p. IJisf D.Lut. Dep. Oisi. D.l.iit. Dep. > 4 6 « 7 H c-7 '? 2-9 3-7 4'4 5-> 5-9 6-6 7-1 '•4 2-7 3-4 4"' 4-8 5'5 6-1 6-8 62 03 01 03 fiO 07 on 0!) 70 ... IP. 46-8 47-5 4?-3 490 49'7 50-5 51-2 41-6 4^'3 43-0 43-6 44-3 45-0 45-7 46-4 47-1 47'7 121 122 123 124 123 120 I2f! 129 1311 88-5 89-2 90-0 90-7 91-4 92-2 92-9 93-6 94-3 9,-. 1 86-6 S8-0 88-7 lf!l 182 183 184 185 180 187 188 189 I9:l 132-4 133-1 133-8 ■35-3 136-8 '37-5 138-2 139-0 123-4 124-1 .24-8 125-5 126-2 126-9 127-5 B 241 242 243 244 245 -.'46 247 •248 249 230 176-3 '77*7 178-5 179-2 179-9 1806 ■8i;4 182-8 164-4 .67-1 167-g 168-5 .69-1 12 13 14 13 If .7 18 19 20 21 23 24 25 2fi 27 2H 2!l 30 So 8 8 9-5 10-2 11-7 12-4 13-2 7-5 8-9 9'5 IO-2 IO-9 II-6 12-3 13-0 72 73 74 7ft 70 77 7« 79 lio 51-9 5i'7 53-4 54'' 54-9 55-6 56-3 57-0 S7-8 58-1 48-4 49-1 49-8 50-5 511 5. -8 52-5 53-2 53-9 ,4-6 131 132 133 131 133 1311 137 138 139 140 95-8 90-0 90 7 91-4 92-1 92-S 93-4 94-1 94-8 9'i-5 191 192 193 194 I9S 190 197 198 199 200 ■39-7 14C-4 141-2 1419 142-6 >43-3 144-1 144-8 ■4S-5 146-3 130-3 130-9 .31-6 132-3 133-0 >33-7 '34-4 •251 252 253 254 •255 256 257 258 239 21,0 ill 188-0 lqO-2 17.-2 171-9 '^rl 175-3 176-6 177-3 15"4 l6i i6-S 17-6 .8-3 190 19-7 21-9 ■4-3 15-0 15-7 .6-4 17-0 III 81 112 »3 84 85 80 87 88 89 90 6o-7 tt 62-9 65-6 64-4 Zi 5 5-2 III 57-3 58-0 58-7 59-3 6o-o 6o-7 61-4 141 142 143 111 145 140 147 11)1 149 130 103-1 .03-9 .04-6 \:ii 106-8 107-5 108-2 109-0 •09-7 96-2 968 97-5 98-2 98-9 99-6 100-3 100-9 101-6 102-3 •201 202 203 201 203 200 •207 208 209 210 147-0 147-7 .48-5 1492 149-9 .50-7 151-4 .52-1 137-1 z: 140-5 141-2 141 9 142-5 145-2 201 202 263 2(|-4 263 2BC 207 208 269 270 190-9 191-6 192-3 193-1 1938 194-5 if; »97-5 178-0 178-7 i8o-7 .82-8 Zi 31 32 33 34 35 3fi 37 38 32 70-9 71-7 72-4 73-. 62-1 62-7 63-4 64-, 64-8 III 668 67-5 68-2 151 152 133 154 155 150 157 168 159 160 IIO-4 111-9 112-5 113-4 1 14- 1 114-8 'X 117-0 103-0 103-7 104- 3 105-0 105-7 106-4 107-8 108-4 109-1 212 213 214 215 210 217 218 219 2-20 «54-3 if: 158-7 ■ 59-4 i6o-2 160-9 ■45-3 nil '47-3 148-0 148-7 149-4 150-0 271 272 273 274 273 276 277 278 279 280 199-7 2C0-4 203-3 204-0 204-s .85-5 186-9 188-2 iii 190-3 191-0 41 42 43 44 45 4G 47 48 49 30 31 52 53 54 35 5(; 57 5!) r,ii «(l 30-7 3 '•4 32-2 32-9 33.fi 34-4 35-' III 37-3 38-0 38-8 39-5 40-2 41-0 4'-7 42-4 45'' 43-9 28-0 286 29-3 30-0 30-7 31-4 32-1 32'7 33-4 34' > 34-8 III 36-8 37-5 38-2 38-9 39-6 40-2 40-9 101 102 103 104 105 106 107 108 109 110 111 112 113 114 113 110 117 lUI 119 120 IP 76-8 77-5 78-3 79-0 79-7 8o-4 68-9 696 i°i 72-3 73-0 73'7 74-3 75-0 161 162 163 104 lAft 160 167 108 169 170 117-7 119-1 119-9 120-7 121'4 122-9 123-6 i»4-3 109-8 110-5 112-5 113-2 1.3-9 114-6 115-3 115-9 ■221 222 223 224 223 226 227 228 229 230 16, -6 162-4 .63-1 .63-8 164-6 \tll .66-7 150-7 151-4 152-1 '53-4 154-1 154-8 '55-5 156-2 156-9 •281 282 283 284 •283 286 287 288 289 290 Toll 207-0 207*7 208-4 209-2 ITe 211-4 TiT-8 2.3-6 214-3 215-0 215-7 2.6-5 2.7-2 2.9-4 191-6 192-3 193-0 >93-7 194-4 .95-1 ■95'7 196-4 197*1 197-8 .98-f 1991 199-8 2C0-5 2C1-9 202-6 203-3 203-9 204-6 n.Lat 8i-2 8. -9 82-6 ll'. 84-8 85-6 tl 87-8 75'7 76-4 77'' 77-7 78-4 79-1 79-8 tl 81 8 171 172 173 174 175 170 177 178 179 125-8 126-5 128-7 129-4 130-2 130-9 I3r6 II6-6 ;:8^:^ 118-7 119-3 120-7 I21'4 122-8 231 232 233 234 235 236 237 238 239 210 :?? 170-4 171-1 171-9 1726 ■73-3 174-1 174-X '75-5 :^8- 'frl \tl 161-6 162-3 163-0 163-7 291 •292 293 •294 295 29fi 297 298 299 300 D.L.ii Dist. Dep. D.lu, IJi.t. Dep. D. l.iK. IJist Dep. 1). lai. I,i6t. Dep. 47- 3^».. TABLE 1 517 TKAVKUSE TABI.K TO UEUKKKS 43" 2" 5'2» Dist D.Lat Dc-p. l>ist I). Lat D>p. Dist D. Lat »ep. Dist I). LMt nep. Dist D.Lat D>.p .'101 2 20- 1 2053 361 264-0 2462 421 307-9 287-1 481 351S 328. 541 395-7 369-0 302 2209 206-0 362 264 8 i 246-9 422 3086 287-8 482 3525 3287 542 3964 369-7 303 2216 2067 363 265-5 1 247-6 423 309-4 2885 483 3532 329-4 543 397 I 3703 371 301 222-3 2073 3G4 266 2 24S 3 424 310-I 289-2 484 354-0 3301 544 397-9 305 223-1 20S0 .•!65 267-0,2489 425 310S 289-9 485 354-7 330-8 545 398-6 37'-7 306 223-8 20S7 366 267-7 2496 426 3.1-6 290-5 486 355-4 3}i 4 546 399-3 3724 307 2245 2094 3B7 26S-4 250-3 427 3! 2-3 291-2 487 356-2 332 I 547 400-1 373-1 308 2253 210 I 368 269-. 251-0 428 3'3o 29.-9 488 356-9 3328 548 400-8 373-7 309 210-7 369 269-9 251-7 429 3.3-8 292-6 489 3577 333 5 549 40.-5 374 4 310 226-7 211-4 370 2706 2523 430 431 3152 2933 2939 490 491 358-4 3342 550 4022 403-0 375-1 3758^ 311 227-5 212 I '^tT 271-312530 359-1 [334 9 312 2282 212 8 372 272 I 2537 432 3160 2946 492 35981335-5 552 403-7 3765 313 228-9 2>35 373 272 8 254-4 433 3167 295-3 493 360 6 1 3i'> 2 553 404-4 377 1 314 2297 2142 374 273-5 |25S-' 4:!4 3 '7-4 296-0 494 36.-313369 554 405-2 3778 315 2304 214S 375 274-3,255-8 435 296-7 495 362-0 337-6 555 4059 378 5 31G 23 1 -I 2155 376 2750 , 256-4 436 3189 297-4 496 3628 338-3 556 406-6 3792 317 2318 216-2 377 275-71257-1 437 3 '9-6 2980 497 363-S 338-9 557 407-4 379 9 31S 2326 2169 378 2765 1257-8 438 3203 298 7 498 364-2 3396 558 408. 3806 3ia 2333 2176 379 2772; 258-5 439 1 32,-1 299-4 499 364-9 3403 559 408-8 38.-2 320 J340^ 218-2 380 277 9 1 259 2 440 321 8 300-1 500 3657 3410 560 4096 381-9 321 2348 2189 381 278 7 ' 259-8 44 r 322-5 300-8 soT 366-4 34 1 7 561 4J03 3826 32J 2355 219-6 382 2794 1 260-5 442 3233 301-4 502 367-> 34-4 562 4. 10 383-3 323 236-2 220-3 333 2S0-1 261-2 443 3240 302-1 503 367-8 343-0 563 4.1-8 3840 324 237-0 221-0 384 2808 1 261-9 444 3247 302-8 504 3686 343-7 564 4125 3846 325 2377 2217 E85 281 6 12626 445 325-S 303-S 505 369-3 3M4 565 413-2 385-3 326 2384 222-3 386 2823^263-3 446 320-2 304-2 506 370-0 345-1 566 4.4-0 380-0 327 239-2 2230 387 2830! 263 9 447 3269 304-9 507 370-8 3458 567 4'4-7 386-7 32S 2399 2237 388 2837 1 264-6 448 327-7 305-5 508 371-5 3465 568 4'54 3874 329 240-6 2244 389 284-5 1 265-3 449 3284 3062 509 3723 347 1 -69 4162 38S-1 330 311 241-4 242-1 2251 390 2852 2660 286-0 266-7^ 450 451 3291 T29-9 3069 307-6' 510 373-0 347 8 348 5 5-0 571 4.69 3887 389-4" 225-7 391 373-8 4.7-6 332 242-8 2264 392 286-7 267-3 452 330-6 308-3 512 3745 3492 572 4'8-3 390- 1 333 2435 227-1 393 287-4 2680 453 33 > 3 309-0 513 375-2 349 9 .i73 4.9 I 390-8 334 244-3 227-8 394 288-2 268-7 454 332-1 309-6 514 376-0 3505 574 4.98 391-5 335 245 ' 228 5 395 288-9 1 269-4 455 332-8 310-3 515 3766 35' 2 575 4205 392-2 336 245-7 2292 396 2896' 270-1 4 56 333-5 311-0 516 377-4 35 '-9 576 421-3 392-8 337 246-5 2298 397 2904 ! 270-8 457 334-3 311-7 517 378-2 352-6 577 4220 393-5 33S 247-2 2305 398 291-1 271-4 458 3350 3>2-4 518 378-9 353-3 578 422-7 394-2 339 2479 231-2 399 291 8 272-1 459 335-7 3 '3-0 519 3796 354-0 579 423-5 394-9 340 248-7 2319 400 2926 2728 460 336-5 3'37 520 380-3 3546 580 424-2 3956 34T 24/4 2326 401 293-3 273"5 461 337-2 3 '4-4 5iT 381-. 355-3 581 424-9 396-2 342 250-1 2332 402 2940 2742 4t;2 337-9 3'5 1 522 38.8 3560 582 425-7 3969 34 i 250-9 2339 403 294 7 274-9 463 338-7 3158 523 3S26 356-7 583 426-4 397-6 344 2516 2346 404 295-5 '2755 464 339 4 3165 524 383-3 357-4 584 427 I 39S-3 345 252-3 2353 405 296 2 276 2 465 3401 3'7-i 525 3840 358-' 58 5 427-9 399-0 3<6 253-> 2360 406 296 9 , 276-9 466 340-8 3>7S 526 384-7 35S-7 586 4286 3996 £47 2538 2367 407 297-7 1 277-6 467 34>6 3>8S 527 385-5 3594 587 429-3 4003 34!. 254-5 237 3 1 408 298-4 ' 2783 4b8 3423 319-2 528 386-2 360- . 588 430 . 401 ■■U9 255-3 I 2380 40J 299-1 , 278-9 469 3,30 3199 529 3869 3608 589 4.508 401 7 350! 256012387 410 2999 279-6 470 343 7 3205 530 3S7-6 36. 5 590 431-5 4024 3511 256 7 1 2394 411 3006 28J-3 471 344 5 32'-2 537 3884 362-1 591 4323 403-1 352, 257-4.2401 412 3013 2810 472 345-2 3219 532 389 . 362-8 592 4330 4037 353 1 2582,2408 413 302-1 281-7 4 73 345-9 322-6 533 3899 \ 3153-5 593 433-7 404-4 354 1 25891241-4 414 3028 282-4 474 3467 323-3 534 390 6 1 364-2 504 4345 405-1 355 259 6 '242. 415 303-5 283 475 347-4 324-0 535 39'-3;364 9 595 435-2 405-8 356 260-4 242 8 416 304-3 2837 476 3481 3246 536 392-01365-5 596 4359 400 5 337 261-1 2435 417 3050 2,S4-4 477 3489 325-} 537 392 8 1 366-2 597 436-7 407-2 358 261-8 2442 418 3057 2851 478 349-6 326-0 538 393-5*3669 598 437-4 4078 359 2626 2448 419 3064 2S58 479 3503 3^67 539 394 2 367-0 599 438. 408 -, 360 263-3,24_5.5 420 3072 2864 480 35r. 3274 540 394 9 I 368 3 6P0 43S8 4092 DUt. D.'p. h) Jm. DLst, n.p. 1). Lat iJitt. Dep. n. Lat. Dist. Dcp. D.Lai. l)i,t. 'd^p.' I). Lai 47' fth R™ J TRAVERSK 'l'4BLE TO DF.OREE8 j 44° 2-36- 1 I)ist.!D.U.|Dep. Dis.. D.Ut. Dep. DistJD.Lat. Dep. Dist D.Ut Dep. Dist.D.U.t. J^L I 1 c-7 0-7 Ul 43-9 42-4 121 87-0 84-1 181 130-2 125-7 241 ■73-4 'f-7-4 2 1 1-4 "•4 (i2 44-6 43' 122 87-8 84-7 182 130-9 126-4 242 174-1 16S-1 3 2-2 (!3 45-3 43-8 123 88-5 85-4 183 131-6 127-1 243 174-8 i(.8-S 4 »-9 2-8 (.•4 46-0 44-5 1 24 89-2 86-1 184 132-4 127-8 244 175-5 .69-5 5' 3-6 3-5 05 46-8 45-1 125 899 86-8 185 133-1 128-5 245 176-2 ^-3 (if; 47'5 45-8 126 90-6 87-5 186 133-8 129-2 246 177-0 170-9 7 SO 49 (i7 48-2 46-5 127 91-4 88-2 187 ■34-5 129-9 247 '77 7 171-6 8 5-8 S-6 Ii8 48-9 47'2 128 92-1 88-9 188 135-2 1306 248 .78-4 172-3 9 6-5 63 li!) 496 47-9 129 92-8 S9-6 189 136-0 131-3 249 '79' '73-0 10 7"^ 69 70 50-4 ±«16 130 1 93-5 90-3 190 136-7 132-0 250 179-8 173-7 ]] 7-9 7-6 71 511 49-3 131 94-2 910 191 '37-4 132-7 25T lJ^-6 '74-4 12 S-6 8-3 72 51-8 50-0 132 950 91-7 192 138-. '33-4 252 .8.-3 175-1 13 9-4 1 9-<' 73 5^-5 507 133 95 7 924 193 .38-8 134-1 •2.-I3 .82-0 '75-7 U 10-. 9-7 74 53-2 5'-4 134 964 93-1 194 139-6 '34-8 ■254 182-7 .76-4 15 .0-8 .0-4 76 540 52-1 135 971 938 195 140-3 '35-5 ■2.i5 183-4 177-1 le , i.-5hii 7ii 54-7 52-8 136 97-8 945 196 141-0 ,36-2 256 184-2 177-8 17,. ^-|. --8 77 55-4 53-5 137 985 95-2 197 141-7 .36-8 257 184-9 178-5 18 .2-9 1 12-5 78 56-, 54'^ 138 99-3 9V9 198 142-4 '37-5 258 1S5-6 179-2 1!) ■3-7 132 79 56-8 54-9 139 1000 96-6 199 143-1 138-2 239 1863 '799 20 '44 139 80 57-5 55-6 140 1007 97-3 200 ■43-9 138-9 260 2C1 1S7-0 187-7 180-6 "aT 151 146 81 58-3 56-3 141 101-4 979 201 144-6 139-6 181-3 22 15-8 15-3 82 59-0 57-0 142 9S6 202 '45-3 140-3 262 188-5 182-0 23 >6;5 i6-o 83 59-7 57-7 143 102-9 99'3 203 146-0 141-0 263 .89-2 182-7 24 i6-7 84 6o-4 58-4 144 103-6 204 146-7 141-7 264 189-9 .83-4 25 17-4 85 611 590 145 104-3 100-7 205 '47-5 142-4 265 190-6 184-1 26 i8-7 181 86 61-9 59-7 146 105-0 101-4 206 148-2 143-1 266 .9. 3 184-8 27 19-4 i8-8 87 62-6 6o-4 147 105-7 207 148-9 143-8 267 .92-. 185-5 28 20-I 19-5 88 63-3 6,-i 148 106-5 102-8 208 149-6 '44-5 268 192-8 186-2 29 20-9 20-I 89 64-0 6i-8 149 107-2 103-5 209 1503 1452 269 '93-5 1869 30 31 21-6 22-3 20-8 215 90 64-7 625 150 107-9 104-2 210 151-1 •45-9 270 .94-2 .87-6 91 65-5 63-2 151 108-6 104-9 211 146-6 271 194-9 1S8-3 32 230 92 66-2 639 152 1 109-3 105-6 212 151-5 '47-3 272 '95-7 188-9 33 237 22-9 93 66-9 646 153 1101 .06-3 213 153-1 148-0 273 196-4 1896 34 24'5 23-6 94 67-6 65-3 154 iio'8 107-0 214 1539 148-7 •274 197-1 190-3 35 25-2 24-3 95 68-3 660 155 111-5 107-7 215 '54'7 149-4 ■275 '97-8 .9.-0 3C 259 25-0 96 69-, 667 IS6 108-4 216 '55"4 150-0 276 198-5 .9.-7 37 266 257 97 69-8 C7-4 157 112-9 109-1 217 156-1 150-7 277 199-3 192-4 38 27-3 26-4 98 70-5 68-1 158 113-7 109-8 218 156-8 151-4 278 193-1 3!) 28-1 27-1 99 71-2 68-8 159 1144 110-5 219 '57-5 152-1 279 200-7 193-S 41* 28-8 27-8 100 71-9 69-5 160 115-1 220 .58-3 _£52-8_ 280 20 1-4 '94-5 IT 29-5 28-5 101 72-7 70-2 161 ..58 11,-8 •221 159-0 ■53-5 281 202-1 195-2 42 30-2 29-2 102 73-4 70-9 162 116-5 112-5 222 159-7 154-1 282 202-9 195-9 43 309 29-9 103 74'' 71-5 163 117-3 113-2 223 ,60-4 >54-9 283 X03-6 .96-6 44 3"-7 30-6 104 74-8 72-2 IC4 118-0 "3 9 224 i6i'3 105 75"5 729 165 1.8-7 114-6 225 i6i-9 156-3 '285 205-0 1980 46 33-> 32-0 l(l(i 7^:3 73-6 166 119-4 115-3 226 162-6 157-0 286 205-7 198-7 47 33-8 32-6 107 74-3 167 1160 227 i63;3 • 57-7 287 206-5 '99-4! 48 34-5 33-3 108 7T7 75-0 168 120-8 ..6-7 228 158-4 288 207-2 joo-i 49 35-2 34-0 109 784 757 169 121-6 117-4 229 164-/ 159M 289 207-9 200-8 50 36-0 34'7 110 79-1 76-4 170 122-3 118-1 230 165-4 '59-8 290 20S-6 20.-5 51 36-7 35-4 TTT 79-8 77-1 171 123-0 1188 23r 166-2 .60-5 291 209-3 202-1 52 J7-4 36-. 112 8o-6 77-8 172 123-7 119-5 232 166-9 161-2 292 210-0 202-8 &a 38-1 368 113 8. -3 78-5 173 1244 233 167-6 16.-9 293 210-8 203-5 S4 3«-8 37-5 114 82-0 79-2 174 125-2 120-9 234 ,68-3 162-6 294 211-5 204-2 55 39-6 38-2 115 82-7 79-9 175 125-9 121-6 235 169-0 163-2 295 204-9 56 40-3 38-9 116 83-4 8o-6 176 126'6 122-3 236 .69-8 163-9 296 212-9 2056 67 41-0 39-6 117 84-2 8'-3 177 127-3 1230 237 170-5 164-6 297 2.3-6 206-3 58 41-7 40-3 118 84-9 82-0 178 123-6 238 171-2 i6v3 298 2.4-4 207-0 6M 42-4 41-0 119 856 S27 179 128-8 12,-3 239] .7. -9 i66-o 299 2.5-. 207-7 60 120 86-3 83-4 180 .29-5 1250 240 1 172-6 166-7 300 2.5-8 208-4 Uistj Dep. j U.Lai Disi 1).,.. D.l.al Uist U.p. U. Lat. Dist.| Dep. D. I.at. ni.st Dep.|.M..J 4( ^ - 7,M. 1 TKAVKHSK T.VBI.E TO D KU 1< K KS _ 44° 'ihSG" I)i8t. .SOI D. W. 2.6-5 Dep 209-1 Disi 361 2597 Dep. 2508 Dist. 4-.>l I). L«i. 302-8 D.p. 292-5 Dii-f. 481 n.u, Dep. 334-1 Dist.'D.Lat Dep. 3758 3460 541 389-2 .(OJ 2172 2og-8 36'> 2604 251-5 (2-2 3036 293-2 482 346-7 334-8 542 3899 3765 • iort 21S0 2105 363 261-1 2522 4-.'3 304-3 2938 483 347-4 335 5 543 3906 3772 :i04 21S7 2112 364 2618 252-9 l-.'4 3050 294-5 484 3482 33b-2 544 391-3 377-9 ;■"'•■' 2194 ill 9 365 2626 253-6 425 305-7 2952 485 3489 336-9 545 392-0 3786 220 I 2126 366 2633 2.=4 3 426 3064 2959 486 3406 3376 546 392-8 379 3 a i7 2208 2133 367 2640 2519 427 307-2 2,66 487 350-3 338-3 547 3935 3800 .iUS 221 6 2140 368 2647 25^-6 4-28 3079 297-3 488 351-0 3390 548 3942 380-7 ■1(19 2223 2147 31.9 265-4 256-3 4-i9 3086 2980 489 35>-7 339-7 549 3949 3814 .110 22JO 2237 215-4 2160 370 37T 26b-2 266-9 2570 2577 430 431 309-3 3100 298-7 299-4 490 "49! 3525 340-4 341-1 5.50 551 J95-6 3964 3821 353-2 382-7 .112 2244 2167 372 2676 2584 43-J 3>o8 3001 492 3539 34>8 652 397-1 3834 .11 ;) 225-2 2174 373 26S-3 2591 433 311-5 3008 493 354-6 3425 553 397-8 384- 1 .■iU 2^5-9 2181 374 2690 434 3015 494 355-3 343-2 554 398-5 384-8 .1 1 .) 220-6 2i8S 375 2698 2605 435 3129 3022 495 350-1 343-9 555 3992 385-5 :;16 2273 219-5 376 270-5 261-2 436 3136 302-9 496 3568 3446 556 400-0 386-2 .11" 22S0 2202 377 2712 261-9 437 3144 3036 497 357S 345-2 557 400-7 386-9 .■118 228-8 220-9 378 2719 262-6 4.-18 3'5 ' 304-3 49"^ 3582 345-9 5.58 4014 387-6 .119 2;.9S 221 6 373 2726 263-3 4 19 3158 305-0 499 358-9 346-6 559 402-1 388-3 3-.'0 2302 222-3 380 27iA 2640 440 3'65 J057 500 359-7 3473 560 4028 3890 .121 2309 223-0 387 274 1 264-7 447 317-2 306-4 .50T 360-4 -348-0 561 403-6 3897 322 2316 223-7 382 274-8 265-4 442 3180 3070 502 361-1 3487 562 4043 390-4 .ij;i 232-3 2244 383 275-5 2661 443 3187 3077 503 361-8 3494 563 4050 391-1 .■)24 233- 225 I 384 2762 266-8 444 3>94 3084 504 362-5 350-1 564 4057 391-8 325 =338 2258 3S5 2769 267-5 445 3201 309-1 505 3633 350-8 565 406-4 392-5 .■t2rt 234-5 2:65 .386 277-7 2681 446 3208 3098 506 364-0 35'-5 566 4072 393-2 327 2352 227-2 387 2784 2688 44 7 3215 3'o-5 .507 364-7 352-2 567 4079 393 9 .•12S 2359 227-9 388 2791 269-5 448 322-3 3I1-2 50.'< 3654 352-9 568 40S-6 394-6 .•|-.'9 2367 2286 389 279-8 2702 449 323-0 3119 509 3661 3536 569 409-3 395-3 .130 2374 2292 390 2S05 2709 450 3237 312-6 510 3669 3543 570 4100 3960 .131 23S-1 229-9 39T "28F3 2716 451 324-4 3>3-3 HT 3676 3550 571 410-7 3967 332 23S8 230-6 392 2S20 272-3 452 325-2 314-0 512 368-3 355-7 572 411-5 397-3 333 239-5 2313 393 2827 2730 453 3^5-9 3>4-7 51.-? 3690 356-4 573 4122 3980 314 240-3 2320 394 2S3-4 273-7 454 326-6 3'54 514 3697 357-1 574 412-9 398-7 33.-. 241-0 2327 395 284-1 274-4 455 327-3 3l6l 515 3705 357-8 575 413-6 399-4 316 241-7 233-4 396 2x49 2751 456 328-0 3'68 516 3712 358-4 576 4143 400-1 337 242-4 234-1 .397 285-6 275-8 457 328-7 317-5 517 3719 359' 577 4151 4008 .138 243" 2348 398 286-3 2765 458 329-5 3>8-2 518 3726 359 8 578 415-8 401-5 ,339 2439 2355 .399 2870 277-2 459 3302 3>8-9 519 373-3 360-5 579 4165 4022 340 341 244-6 245-3 236-2 2369 400 4or 287-7 -288-T 277-9 460 461 3309 33'-6 3196 320-2 520 .521 3741 3748 36.-2 361-9 .580 5S1 4172 417-9 4029 4036 27S6 342 2460 2376 402 289-2 2793 462 332-3 3209 522 3755 362-6 582 41S7 4043 343 2467 2383 403 289-9 2800 463 333-1 321 6 523 3;62 .363-3 583 419-4 405-0 344 247-5 2390 404 290-6 280-7 464 333-8 322-3 524 376-9 3640 584 420-1 405-7 34 5 2482 2397 405 291-3 281-3 465 3345 3230 525 377 7 364-7 585 4.08 4064 34 r, 248-9 240-4 406 292-1 282-0 466 3352 3237 526 378-4 365-4 586 421-5 407 1 347 2496 2411 407 292-8 282-7 467 335 9 3244 527 379 ' 3 61 587 4223 407-8 348 250-3 241-7 4 OS 293-S 283-4 468 3367 325-1 528 3798 3668 .-.88 423-p 408-s 349 251 I 242-4 409 294-2 2841 469 337-4 3258 52 J 3805 367-5 .589 4237 409-1 350 251 8 2431 410 2949 284-8 470 338-1 3265 5:10 381-2 3682 590 424-4 409-9 351 252-5 243-8 411 29 V7 285-5 471 338-8 3272 53T "382-0 368-9 59r 425-1 410-5 3.52 2532 24 4 5 412 296-4 2862 472 339-5 3279 532 .382-7 369-6 592 4259 4112 353 2539 245-2 413 297-1 286-9 473 340-3 328-6 533 383-4 3703 593 4266 411-9 354 254-6 245-9 414 297-8 2876 474 34" 3293 534 384-1 3710 .594 4273 4126 355 2554 2,66 415 29S-S 288-3 475 341-7 3300 535 384-8 3717 595 4280 413-3 356 2561 247-3 416 299-2 289-0 476 3424 330-7 536 3856 3724 596 4287 4140 357 2568 2480 417 3000 289-7 477 343" 331-4 537 386-3 373 I 597 4295 4'4 7 358 257-5 2487 418 300-7 290-4 478 343 S 3321 538 387-0 3737 598 4302 4154 359 2582 2494 419 3014 2911 479 3446 3327 5:19 3877 374 4 599 430-0 "'?' 360 2590 2501 420 302- 1 29 18 480 345 3 3334 540 388-4 375. 600 431-6 416-8 I)i»t.' Uep. D. I.a.. Dist. DepT D. L»i. Hist Dep.' I). IM. \)hl. »;;: D. L:lt. Dist. Dep. D. Ut. 40" 3" 4™ 1 520 TABLE 1 TRAVERSE TABLfi TO DEGREES 45 ° 3hou. DistJll.Lat I 1 0-7 Dep. Dist.D.Lat. Dep. Dist. D. Lat. De,.. Dist. D.Lat _I>p^ Dist D. Lat.l Dep. 0.7 61 1 43-> 43-1 121 85-6 85-6 181 12S-0 12S-0 241 170-4 f 170-4 2 .-4 '■4 62 43-S 43-8 122 86-3 86-3 !82 .28-7 128-7 242 171-1 171-1 3 2-1 63 1 44-5 44-5 123 87-0 87-0 183 129-4 1294 243 171-8 4 2-8 2-8 64 45-3 45-3 124 87-7 87-7 184 130-1 .30-1 244 172-5 172-5 5 3'5 3'5 Co 46-0 46-0 125 88-4 88-4 185 1308 .30-8 245 173-2 173-2 6 4" 2 4- 66' 46-7 46-7 126 89-. 89-. 186 131-5 131-5 246 173-9 173-9 7 49 4-9 67 47'4 47-4 127 898 89-8 187 132-2 1322 247 174-7 174-7 a 5'7 5"7 68 48-1 48-1 128 9°' 5 90-5 188 132-9 132-9 248 175-4 175-4 9 6-4 6-4 69 48-8 48-8 129 9. -2 91-2 189 133-6 .33-6 2491 176-. 176-i 10 7-> 7'i 70 49 5 49-5 130 91-9 91-9 190 134-4 '34-4 250 1 176-8 176-8 U 1 7-8 7-8 71 50-2 50-2 131 926 926 191 135-1 135-1 251 177-5 177-5 12 8-5 ^■5 72 50-9 50-9 1.32 93'3 93*3 192 ,35-8 135-8 252 .7S-2 13 1 9-2 9-2 73 5.6 51-6 133 94-0 94-0 193 136-5 136-5 253 !78-9 .78-9 14 9-9 9-9 74 52-3 5^'3 134 94-8 94-8 194 137-2 i37-» 264 .79-6 .79-6 16 10-6 10-6 75 53-0 53'0 135 95'5 95"5 195 >37'9 137-9 255 180-3 180-3 16 M-3 II-3 76 53'7 53-7 136 962 96-2 196 .38-6 1386 256 1810 181-0 17 .20 J2-0 77 54-4 54-4 137 96-9 969 197 ■39-3 139-3 257 181-7 181-7 18 ■2-7 12-7 78 55-^ 55-2 138 97-6 97-6 198 140-0 140-0 258 182-4 182-4 19 13-4 >3-4 79 55"9 55-9 139 98-3 98-3 199 .40-7 140-7 259 183-1 183-. 20 14-1 14-1 80 56-6 566 140 99-0 99-0 200 141-4 .4.-4 260 1838 183-8 ^r 1^ 14-8 81 57-3 1 57-3 141 99-7 99-7 2or 142-. 142-1 '26r 184-6 ■ 84-6 22 iS-6 iS-6 8.> 58-0 58-0 142 100-4 202 142-8 .42-8 262 185-3 185-3 23 .6-3 if'; 3 83 58-7 58-7 H3 .OI-] 203 ■43-5 143-5 263 1S6-0 1S60 24 lyo 84 594 ' 59'4 144 .0.-8 .01-8 204 144-2 144-2 264 1S6-7 186-7 25 17-7 17-7 85 6o-i 6o-i 145 02-5 .02-5 206 145-0 145-0 265 '87-4 .87-4 26 .8-4 18-4 86 6o-8 6o-£ 146 .03 1 206 145"7 145-7 266 1S8-1 .88-1 27 .9-. 191 87 6,-5 6i-s 147 103-9 .03-9 207 146-4 146-4 267 .88-8 .88-8 28 .9-8..9-S 88 62-2 62-2 148 .04-7 .04-7 208 147-1 147-1 268 .S9-5 .89-5 29 20-5 20-5 89 62-q 62-9 149 .05-4 105-4 209 .47-8 147-8 269 .90-2 30 1 Z.J 2.-Z 90 6,-6 636 150 I06-I 106-1 210 148-5 148-5 270 190-9 190-9 31 |2.-9 21-9 In 64-3 ~6rJ i5r .c6-8 1068 2iT .49-2 149-2 27r .9.-6 191-6 32 1 22-6 22-6 92 65-1 6s-. 152 107-5 107-5 212 149-9 149-9 272 .92-3 192-3 33 23-3 23-3 93 65-8 65-8 153 108-2 108-2 213 .506 150-6 273 193-0 193-0 34 24-0 24-0 94 665 66-5 154 .089 1089 214 .5.-3 151-3 274 '93-7 193-7 35 24-7 24-7 95 67-2 67-2 155 109-6 109-6 215 1520 152-0 275 ■94-5 194-5 36 2 5-5 ^5-5 96 67-9 67-9 156 110-3 110-3 216 152-7 .52-7 276 195-2 1952 37 26-2 26-2 97 68-6 68-6 157 217 153-4 153-4 277 195-9 195-9 38 26-9 26-9 98 69-3 69-3 158 111-7 111-7 218 .54-1 154-1 278 1966 196-6 39 27-6 27-6 99 70-0 159 .12-4 112-4 219 154-9 154-9 279 197-3 197-3 40 28-3 28-3 100 70-7 70-7 160 1.3-1 ..3-1 220 .55-6 155-6 280 198-0 198-0 TT ^9-° 29-0 101 71-4 71-4 161 ,.3-8 113-8 221 .56-3 156-3 28r 198-7 198-7 42 29-7 29-7 102 72-1 162 ..4-6 1.4-6 222 157-0 157-0 282 199-4 199-4 43 304 103 72-8 72-8 163 115-3 115-3 223 ■57-7 157-7 283 2C0-1 44 311 31-1 104 73-5 73-5 164 ii6-o 224 158-4 158-4 284 200-8 1 2CO-8 45 31-8 3. -8 105 74-2 74-2 165 ..6-7 ..6-7 225 159-1 159-1 285 201-5 i ioi-5 46 1 32-5 3^-5 106 75-0 75-0 166 ..7-4 ..7-4 226 .59-8 159-8 286 202-2 202-2 47 33-2 33-2 107 75'7 7S-7 167 i.Sm 227 160-5 160-5 287 202-9 202-9 48 33'9 33"9 108 76-4 76-4 168 .18-8 118-8 228 .6.-2 161-2 288 203-6 203-6 49 34-6 34-6 109 77M 77-1 169 119-5 1.9-5 229 161-9 161-9 289 204-4 204-4 SO 61" J5-4 36-1 2£± no 77-8 77-8 170 230 1626 .62-6 290 205-, 205-. 36- , 11 1 78-5 78-5 171 .20-9 120 9 S31 163-3 .63-3 "29r 205-8 205-8 62 36-S 36-8 1 12 79-2 79-2 172 12. -6 .21-6 ■232 164-0 .64-0 292 206-5 2C6-5 »3 37-5 37-5 113 79-9 79-9 173 122-3 122-3 233 .64-8 164-8 293 207-2 64 38-2 38-2 114 So-6 8o-6 174 .230 123-0 234 .65-5 165-5 294 207-9 207-9 66 38-9 389 115 8i-3 81-3 175 123-7 .23-7 235 .66-2 1662 2!I5 208-6 20S-6 56 39-6 39-6 116 82-0 S2-0 176 .24-5 .24-5 236 ,66-9 166-9 296 209-3 ■ 209-3 ■''7 40-3 40-3 117 82-7 S»-7 177 125-2 125-2 237 167-6 16--6 297 210-0 210-0 1 68 118 83-4 83-4 178 .25-9 125-9 238 .68-3 168-3 298 210-7 2.0-7 59 4i'7 4i'7 119 84-. 84- . 179 iz6-6 126-6 239 .69-0 169-0 299 211-4 2. .-4 60 4-4 4^-4 120 84-9 84-9 180 .27-3 127-3 240 .697 165-7 300 212-1 Dist. De,,. IJ.I... 'iZt Dep. D.I.;, Disi j Dep. D. L;il D.sl Do,,. D. I.-Ji Dist Dep. D.T.»t 4 )° ~3 7)m TKAVEKSK TABLK TO UEUKLES 45° yxo- 1 Dist. D.Lat. Dep Dist. D. Lai 1 Dep. Dist D.Lat D..p. Dist.JD. Lit Dep. Dist D. Lat Dep. 301 2128 212-8 361 2553 255-3 4-21 2977 297-7 481 340-1 340-1 541 3S2-5 382-S 302 213-5 2135 36-2 256O 256-0 422 298-4 298-4 482 340-8 340-8 542 .3832 3832 3l>3 2143 2143 363 2567 256-7 423 2991 299-1 483 3415 341-5 543 3839 3839 304 2150 2150 364 257-4 2574 424 299-S 299-8 484 342-2 342-2 544 384-7 3847 305 215-7 2157 .■i65 258-1 258-. 425 3005 300-5 485 342-9 342-9 543 385-4 385-4 306 216-4 2164 366 2588 258-S 426 301-2 301-2 486 343-6 3436 546 386-1 3861 3ij7 217 I 2171 367 259-5 259-5 427 3019 301-9 487 344-3 344-3 547 386-8 3868 308 217-8 2,7-8 368 2602 260-2 428 302-6 302-6 488 345-1 3451 548 387-5 3875 309 2185 21S-5 369 260-9 260-9 429 303-4 303-4 489 345-8 345-8 549 3882 388-2 310 2192 219-2 370 261-6 261-6 430 304-1 304-1 490 346-5 ^3465 550 388-9 388-9 311 2199 2199 37 1 262-3 2623 431 304-8 304-8 491 347-2 347-2 551 3896 3896 31V> 2206 220-6 372 2630 2630 432 .305-5 3055 492 347 9 3479 552 3903 390-3 3)3 2213 221-3 373 263-8 263-8 433 305-2 306-2 493 3486 348-6 553 391-0 39 1 -o 314 2220 374 2645 264-5 •134 3069 3069 494 3493 349 3 .554 3917 3917 315 2227 222-7 375 2652 2652 4 35 3076 307 6 495 350-0 3500 555 392-4 392-4 316 2234 2234 376 2659 265-9 436 308-3 3083 496 3507 350-7 556 3931 393-1 317 2242 2242 377 2666 2666 437 3090 3090 497 3514 3514 557 3939 3939 318 2249 2249 378 267-3 267-3 438 309-7 3097 498 3521 35^-1 5.58 3946 394-6 319 225 6 2256 379 26S-0 2680 4.39 310-4 3104 499 3528 3528 559 395 3 395-3 sao 2263 2ZSi 3M0 26S-7 2687 440 311 I 3" ' 500 353-5 353-5 560 3960 3960 321 2270 227-0 381 2694 269-4 411 3"8 luS 501 3543 354-3 561 396-7 3967 322 2277 2277 .382 270 I 270-1 442 3'25 3125 502 3550 355-0 562 397 4 397 4 E23 2284 228-4 383 2708 270-8 44i 3'33 3'33 503 355-7 355-7 563 398-1 398-1 32j 2291 229-1 384 271-5 27.-5 444 314-0 3140 504 356-4 356-4 564 39S-8 3988 325 2.9 s 229-8 385 2722 2722 445 3M-7 314-7 505 3571 357-1 565 399-5 3995 .126 2305 2305 386 272-9 272-9 446 3'54 3'5 4 506 357-8 357-8 566 4002 4002 327 2JI2 231-2 387 273-7 2737 447 3161 316-1 507 3585 358-5 567 4009 4009 328 2319 231 -9 388 2744 2744 448 316S 316-8 508 359-2 359-2 568 401-6 401 6 329 2326 2326 389 275-1 2751 449 3' 7 5 317-5 509 3S^)-9 3599 569 402-3 402-3 330 331 233;3_ 23n 233-3 234-1 390 ~276l 2758 "2767 4 50 3-8-2 318-9 3189 510 "511 360-6 361-3 3606 361! 570 403-0 403-0 4038 451 571! 403-8 332 234S 234-8 392 2772 277-2 452 3196 319-6 512 362-0 362-0 572 404-5 4045 333 235s 235-5 393 2779 277-9 453 3203 320-3 513 3627 362-7 573 405-2 405-2 334 236^ 2362 3M4 2786 278-6 454 321 3210 514 3635 3635 574 405-9 4059 335 2369 236-9 395 2793 2793 455 3217 321-7 515 3642 3642 575 4066 4066 336 237-6 237-6 .396 280 280 456 3224 3224 516 3649 3649 576 407-3 407-3 337 2383 2383 .397 280-7 i 2S0-7 4 57 323-2 3232 517 365-6 3656 57 7 4080 408-0 338 2390 2390 398 281-4 28 I -4 458 323-9 3239 518 366-3 3663 578 408-7 408-7 339 2397 239-7 399 2S21 282 1 459 3246 3246 519 3670 367-0 579 409-4 4094 340 240-4 1 2404 40'i 2S28 2S28 460 3253 3253 520 3677 3677 ^-^80 1 410- 1 4,0-1 34 1 241 1 : 241 1 4or 2836 283-6 461 3260 3260 521 368-i 3684 581 ["4108 4,08 342 2418. 24. -8 402 284-3 284-3 462 326-7 3267 522 369-1 369-1 5S2 41 1-5 4115 343 242-5! 242-5 403 2850 2850 463 327-4 327-4 523 ,69 8 369-8 583! 412-2 4122 344 243 2 j 2432 404 2857 2857 464 3281 328-1 524 3705 370-5 584 4,2-9 4129 345 24401 24(0 405 2864 2864 465 328-8 3288 .525 37 1-2 3712 585 4,37 4137 346 2447 1 2447 406 2871 2S7-I 466 3295 329-5 526 3719 371-9 586 4,4-4 4,44 347 245 4 1 245-4 407 287-8 287-8 467 3302 3302 327 3726 3726 587 4151 4151 348 246 I 1 246 1 408 2885 288-5 46s 3309 3309 528 3734 3734 588 4,58 4158 M49 1 2468 1 246 8 409 2892 2892 469 33 > -6 3316 529 3741 3741 589' 46-5 4165 350 [ 247-5 ' 247-5 410 2899 2899 470 332-3 ! 3323 530 _3_74l 374-8 .590! 4,7-2 4,72 351 1 24^*2 2482 411 2906 290-6 47T 3.331 3331 531 375-5 375 5 .5911 4179 4179 352 ! 248 9 1 248 9 41/ 291-3 291-3 472 333 8 333-S 532 3762 370-2 .592 41S6 4186 353 1 249 6 1 2496 413 2920 292-0 473 3i4-5 334 5 533 3769 3769 593 4,9-3 419-3 354 25031 2503 414 292-7 2927 474 335-2 335-2 534 3776 377-6 594 1 420-0 4200 335 2510 2510 4 15 293-5 2935 •»75| 3359: 3.^59 535 378-3 378-3 .595! 4-0 7 420-7 356 251-7 2517 416 2912 294-2 ■•76 3366; 3j6 6 536 3790 3790 596! 4214 421-4 357 2524 2524 417 294-9 294-9 477 337-3 1 337-3 537 3797 379-7 .597 i 422 I 4221 356 253' 253> 418 295-6 295-6 478 33S0 338 o| 538 3804 380-4 :m 422-8 422-8 359 253 9 253-9 419 290-3 296-3 479 3387 338-7 539 ^l'\ ^I'l 599 4236 4236 360 2546 2546 420 2970 2970 480 3394 339 4 540 381-8 3818 600 424-3 4243 Ui.t. Drp. Id. Lat. Oist. Dep. ju.Lat. Di.-t. nc|.. D. r,at. t)i,t. Do p. D.Lai Dist. Dep. D. Lat. 4->' S^O" 1 \jit. DIJPARTURE AND CORRESPONDING DIFFERENCE OF LONGITUDE ^ Departure Part* j 1 1_J 2 3 * 1 b 6 _7_ 8 9 10 Dtol° 15' 1 30' 45' -0^ l-oo 2-00 3-00 5-00 h-cQ 7-00 8-00 9-00 lo-co HW oi 0-02 0-03 i roo 200 3-OI 4-01 1 5-OI 6-OI 7-02 8-0.. 9-02 10-02 0-08 02 1 0-04 I CI l-OI 3-02 4-02 5-°3 603 7-04 S-04 9-05 10-06 0-12 03 o-o6 0-09 8 lOI 2'02 303 4-041 5-05 6-o6 7-07 8-08 9-09 10-10 0-14 °3 0-07 o-io 10 1-02 2-03 3-05 4-06 1 S-o8 6-09 7- 1 1 8-1, 9-14 10-15 0-16 04 0-08 0-I2 12 ■ ■oz Z-04 3-07 4-09 5-'l 6-13 7-i6 8-i8; 9-20 10-22 0-18 04 0-08 o-ij 14 .03 2-o6 3-09 4-12 5-15 618 7-2 I S-24' 9-^8 10-31 0-20 °5 o-io 0-15 15 1-04 1-07 4-14 5-i8 6-21 7-25 8-28, 9-32 10-35 0-22 °5 0-11 0-16 16 1-C4 2-o8 3-12 4- 16 S-20 6-24 7-28 8-32 9-36 10-40 0-24 06 0-12 0-18 17 1-05 2-09 3->4 5-23 6-27 7-32 8-37 9-41 .0-46 0-26 06 0-I3 C-19 18 2- 10 3-M 4-21 526 6-3. 7-36 8-41 9-46 10-51 0-28 07 0-14 .9 I 06 2-12 3-17 4-M 5-29 6-35 7-40 8-461 9-52 .0-58 30 07 0-15 0-22 M I 06 2-13 5-19 4-26 5-3^ 6-39 7-45 8-5. J_ 9-58 10-64 0-32 08 21 1-07 2-14 3-21 4-18 5-36] 6-43 7-50 8-57 9-64 10 71 0-34 "o" oS" O-iy 0-25 22 i-oS 2-l6 3-24 4'3' 5-39. 6-47 7-55 S-63 9-71 IO-79 0-36 09 0-18 23 1-09 2-17 3-26 4-35 5-43 6-52 7-60 8-69 9-78 10-86 038 09 019 0-28 24 1-09 2-19 3-28 4-58 5-47 6-57 7-66 8-76 9-85 10-95 0-40 0-30 25 3-3' 4-41 5-52 6-62 7-72 8-83 9-93 11-03 0-42 10 0-2, 0-31 26 III 2-23 3-34 4-45 5-56' 6-68 7-79 8-90 ;°;°.j;.;.3 0-44 II 0-22 0-33 27 112 2-24 3-37 5-6.! 6-73 7S6 8-98 0-46 11 0-23 0-34 28 '■'3 2'27 3-40 4-53 5-66 j 6-8o 7;93 9-06I 10-19 11-33 0-48 12 0-24 0-36 29 ,•14 2-29 3-43 4-57 5-72 6-86 9-15 10-29 11-43 0-50 12 0-25 0-37 30 KIL 3-46 4-62 5-77 6-93 8-08 9-24 10-39 11-55 0-52 13 1 0-26 0-39 31 117 ^'33 3-50 4-67 5-83 7-00 8-17 9-33 10-50 1.-67 0-54 ~o 13:0-27 10-40 32 2-36 3-54 4-7i 5-90 7-08 8-2"; 9-43 10-61 11-79 0-56 13. 028 I 0-41 1 33 1-19 2-38 3-58 4-77 5-96 7-15 8-35 9-54 IO-73 11-92 058 '4 0-29 0-43 34 2-41 3-62 482 6-03 7-24 8-44 9-65 10-86 12-06 0-60 15 0-30 1 0-45 35 1-22 2-44 3-66 4-88 6-,o 7-32 8-54 9-76 10-99 12-21 0-62 ■5 0-31 ,0-46 30 1-24 ^•47 3-71 4-94 6- 18 7-4^ 865 11-12 12-36 0-64 16 0-32 U-48 37 1-25 2-50 3-76 501 6-26 7-5' 8-76 I0-02 11-27 12-52 0-66 16 0-3310-49 38 1-27 ^•54 3-8. 5-08 6-35 7-6i 8-8? 10-15 11-41 ,2-69 0-68 17 0-34 0-51 39 129 2-57 3-86 5'5 6-43 7-7Z 9-01 10-29 iijS 12-87 070 •7 0-35 0-52 40 1-31 2-6i 3-91 5-" -±y- 7-83 9-14 10-44 11-75 13-05 072 18; 0-36 1 0-54 TT '■33 2-65 3-98 5-30 -6T3 7-95 928 io-6o 11-93 13-25 0-74 ~ ,8|o-37 0-55 42 '■35 269 4-04 538 6-73 8-07 9-42 10-77 13-46 0-76 19 1 0-38 0-57 43 '•37 ^•73 4-10 5-47 6-84 8-20 9'57 10-94 12-31 13-67 0-78 1910-39 0-58 44 '•39 2-78 4''7 5-56 6-95 8-34 9-73 11-12 12-51 13-90 0-80 0-60 45 2-83 4-24 5-66 7-07 8-49 9-90 11-31 12-73 14- 14 0-82 20 0-41 0-61 46 1-44 2-88 4-3» 5-76 7-20 8-64 IO-08 11-52 .2-96 14-40 0-84 21 0-42 0-63 47 "■47 ^■93 4-40 5-87 7-33 8-8o 10-26 11-73 13-20 14-66 0-86 21 0-43 0-64 48 '■49 2-99 4-4« 5-98 7-47 8-97 .0-46 1196 13-45 14-94 0-88 22 0-44 0-66 49 1-52 3-05 4-57 6'io 7-62 1 9-15 10-67 12-19 13-72 15-24 090 22 0-45 0-67 50 1-56 311 4-67 6-22 7-7SI 9-33 1089 12-45 14-00 .5-56 .5-89 0-92 0-94 -- 21 13 0-46 0-70 IT 1-59 3-.8 4-77 6-36 7-95 9-53 12-71 14-30 0-47 52 1-62 3-^5 4-87 6-50 8-12 9-75 11-37 1299 14-62 16-24 0-96 1+ 0-48 072 53 1-66 3-3^ 4-98 6-65 8-31 9;97 .1-63 13-29 »4'9S 16-62 0-98 14 0-49 0-73 54 i-yo 3-40 5-IO 6-8i 8-51 1 1 -9 1 13-61 15-31 17-01 1-00 0-50 0-75 55 '■74 3-49 5-^3 6-97 10-46 12-20 '3'95 ■ 5-69 '7-43 1 02 15 c-51 0-76 56 "•79 3-58 5-36 7""S 8-94 10-73 12-52 14-31 16-09 17-88 1 04 26 0-52 0-78 57 1-84 3-67 5-5' 7-34 9-i8 12-85 14-67 16-52 18-36 106 26 0-53 0-79 58 ■ ■89 3-77 5-66 7-55 9"44 11-32 13-21 15-10 16-98 1887 108 17 0-54,0-81 1 59 1-94 3-88 5-82 7'77 9-71 ,1-65 ■3-59 '5-53 17-47 19-42 1-10 17 °-55 0-82 60 6-00 8-0O lO-OO 1 I2-CO H'oo 16-00 18-00 20-63 1-12 28 0-56 0-84 2-c6 4-'3 6,o 8-^5 10-31 ,2-38 14-44 16-50 • 8-56 Tu 'Z IF 0-57 0-85 62 213 4-26 1 6-39 8-52 .0-65 12-78 14-91 17-04 .9-17:21-30 1-16 29 0-58 o-8v 63 4-4, l6-6i 8-8i 13-22 15-42 17-62 .9-82 22-03 1-18 29 c-59 0-88 64 2-28 4-56 6-84 9-12 11-41 13-69 ■5-97 .«-25 20-53 22-81 1-20 30 o-6o 0-90 65 2-37 4-73 7-ic 9-46 ..-83 14-20 .6-56 18-93 21-30 2 3-66 1-22 30 0-61 iC-91 1 66 2-46 4-92 7-38 9-83 12-29 '4-75 17-21 1967 22-13 14-59 1 24 31 j 0-62! 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3-, 5 3-94 4-73 5-5^ 6-30 7-09 7-88 39 0-78 ■■55 2-33 3-II 3-89 4-66 5-44 6-22 6-99 7-77 4U °"'7| --S^ 2-30 3 -06 3-83 4-6o 5-36 6-'3 6-89 7-66 41 0-75 1-5. 2-26 3-02 ' 3-77 14-53 5-28 6-04 6-79 7-55 42 0-74 1-49 2-23 2-97 3-72,4-46 5-20 5-95 669 7-43 43 u-73 1-46 2-19 2-93 3-66 4-39 5-12 5-85 6-58 7-31 44 0-72 I "44 2-i5 2-88 3-60 4-3» 5-04 5-75 6-47 7-19 45 0-71 1-41 2-12 2-83 3-54 4-24 4-95 5-66 6-36 7-07 4C 0-69 '■39 2-o8 2-78 3-47 4->7 4-86 5-56 6-25 6-95 47 068 ,•36 2-04 »-73 3-4' 4-09 4-77 5-46 6-,4 6-S2 48 0-67 '■34 2-01 2-68 3-35 4-01 4-68 5-35 6-02 6-69 49 0-66 1-31 "■57 2-62 3;^8 3-94 4-59 5-M 5-90 6-56 50 0-64 "■-9 i-;6" S91 ^•57 3-86 4-50 5''4 5-79 6-43 0-63 2-52 3''5 T^ 4-4' 503 5-66 6-29 52 0-62 1-23 1-85 2-46 3-*9 4-3' 4-93 5" 54 6-i6 53 o-6o I-8I 2-41 3-01 3-6, 4-21 4-8. 5-41 6-02 54 0-59 1 ri8 1-76 2-35 2-94 3-53 4- 1 1 4 '° 5"J9 5-88 55 =••57 I .-16 172 2-29 2-87 3-44 4-02 4 59 5- .6 5-74 56 0-56 I-I2 1-68 2-24 2-8o 3-35 3-91 4"47 5-03 5-59 57 0-54 1 1-09 1-63 2-i8 2-72 V^7 3-8, 4-36 4-90 5-45 58 0-551 ■•o6 '•59 2-12 2-55 3-7' 4-24 4-77 5-30 59 o-'olrco 1 '-55 2-c6 2-58 3-09 3-6. 4-12 4-64 5-16 (iO 1 '-SO 2-00 -211° 3-0° 3-50 U-CO 4-S0 5-00 lil " "^-48 ; 0-97 r^s 1-94 2-42 2-91 1 3-39 r?88 4-36 4-85 62 0-47 c-94 ,■4. 1-88 »'35 2-82 3-29 3-76 4-'3 4-69 63 0-45 0-91 ,•36 1-82 2-27 2-72 3-.8 3-6j 4-09 4-54 64 0-44: 0-88 .•32 1-75 2-19 2-63 3-07 3-5. 3-95 4-38 1 65 0-42 0-85 .•^7 ,•69 »-54 2-96 3-38 3-80 4-^3 ! 66 o-4.'c-8. ; 1-22 1-63 2-03 2-44 2-85 3-25 3-66 1 4-C7 67 c-39 0-78 |.-I7 1-56 '•95 »-34 »-74 3-'3 3-51 1 3-9' 1 68 0-37 0-75 1 '-'i '-SO 1-87 2-25 2-62 3-00 3-37 1 3'75 69 0-36. c-71 1 ■•08! 1-43 '■79 »-i5 2-51 2-87 323 i 3-5S i ! - 524 TART.E 5 SPHERICAL TRAVliKSt; T.KUl.K 0° 1 'n' 2° 3° 4° 5° G= o M 1 N INI M N 1\I N M 1 N w 1 N M 1 N 1 2 3 4 5 C 7 a 9 10 11 12 i;f u lA Ifi 17 III 19 20 IOO-4 IOO-5 IOO-7 loro 10I-2 IOI-5 I I0O-3 izt .00-8 0-3 100-3 IOO-6 100-8 o;3 0-5 1C0-3 100-4 100-5 100-9 101-4 101-7 0-3 0-4 °-5 0-5 0-6 0-9 El Eli 0-5 0-6 0-7 0-9 i-o i-i ico-8 100-9 101-1 101-4 101-6 101-9 0-8 0-9 1-2 1-4 ■•5 1013 101-5 ■ 01-8 i'7 iS IOI-9 I02-6 I03-, 103-5 I04-0 .04-6 I05-I io5-« 106-4 I01-9 102-6 103-1 103-5 104-0 104-6 105-2 105-8 106-4 0-3 0-4 0-4 0-4 0-5 0-5 n 0-6 0-6 101-9 102-3 102-7 104-6 Eli 0-7 0-7 0-8 0-9 0-9 ■•3 102-4 102-8 103-7 104-2 104-7 105-3 1-3 '-4 '-5 1-6 1-7 1-8 1-9 102-5 102-9 105-4 106-0 ,o6-7 '-4 '-5 1-6 '■7 1-9 ?:; i-4 ^-5 102-3 102-6 .03-3 103-5 103-9 104-4 104-7 105-5 106-2 106-8 ■-7 1-9 2-3 2-5 2-8 3-0 3-i 102-4 102-8 Wrl 104-1 104-6 105-1 ■ 05-7 IC6-3 107-0 2-4 2-6 2-8 3-0 3-2 3-4 ^^8 21 22 23 24 2.-, 26 27 28 2!) ao 107- 1 io7-« ioS-6 109-5 IIO-3 III-3 II2-2 113-3 114-3 II5-5 107-9 108-6 109-5 110-4 113-3 1 14-4 115-5 0-7 c-7 0-7 0-8 0-9 0-9 107-2 107-9 108-7 109-5 in-3 112-3 113-3 114-4 115-4 '•3 '•4 ■•5 rl '•7 1-8 1-9 1-9 107-3 108-0 108-8 109-6 110-5 111-4 112-4 113-4 .14-5 .15-6 2-1 I'l »-4 2-6 2-7 2-8 2-9 3-° 3-' 3-3 3'4 3-5 3-7 3-8 3-9 4-1 4-i 4-4 4-6 4-7 4-9 5-' 5-i 5-4 ?. 6-0 6-2 107-4 ;o8-9 109-7 110-6 111-5 II2-5 115-7 2-7 2-8 3-0 3-1 3-4 3-5 3-7 3-9 107-5 108-3 109-0 109-9 iio-S 111-7 113-7 114-8 115-9 3-4 3-5 3-7 3-9 4-> 4-3 4-5 4-7 4-8 5-0 107-7 108-4 109-2 1 10- 1 1109 111-9 112-8 4-5 4-7 4-9 5-' 5-3 5-6 11 31 32 33 34 J.-) 3(i 37 3« 39 40 41 42 43 44 45 4(i 47 4K 4!) AO :,i 53 54 5G 57 5» 59 UO II6-7 117-9 119-1 120-6 112-1 .23-6 125-2 .26-9 I2S-7 130-5 : I ,16-7 117-9 ;S 1236 ^; 128-7 130-6 '■3 ■■3 '•4 '•4 t 1-6 i'7 ''9 ■■9 1.6-7 118-0 119-3 120-7 123-7 125-3 !3o-6 ^;3 i'4 I'l z'7 2-8 T^ 3> 3-3 3-4 3-5 3-6 3'7 3-9 4-0 4'i 116-8 II8-1 IS .23-8 125-4 127-1 128-9 130-7 .16-9 118-2 119-5 120-9 122-J 123-9 125-5 129-0 130-9 4-4 4-5 4" 7 4-9 5-" S-3 5-5 5-7 5-9 117-1 118-4 119-7 122-5 124-1 125-7 127-4 129-2 131-0 5-3 5-5 5-7 5-9 6-2 6-4 6-6 6-8 7-1 119-9 121-3 122-7 124-3 .25-9 127-6 129-4 .31-3 6-8 7-1 7-4 7-f 11 8-5 8-8 132-5 ,34-6 136-7 139-0 141-4 149-4 ■.III 139-0 141-4 .44-0 ■46-6 ■49-5 :i::6 136-8 139-1 141-5 144-0 ,46-7 '49' 5 152-5 '55-7 132-7 >34-7 136-9 139-2 141-6 144-2 146-8 149-7 152-6 155-8 132-8 >34-9 137-1 "39-4 141-8 144-3 .47-0 149-8 152-1 '55-7 6-1 8-0 8-3 133-0 135-1 137-3 139-5 142-0 147-2 153-0 156-2 7-6 11 8-4 8-7 V. 9-7 10- 1 133-2 135-3 137-5 139-8 142-2 '44-7 147-4 150-3 ■53-3 156-4 9-' 9-5 9-8 10-1 10-5 10-9 158-9 162-4 i66-i 170-1 ■:,u T, 194- J 1 ■5-9 162-; 166-2 170-2 I74'4 178-9 1S3-6 iS«-7 194-2 2'3 -■4 2-6 ■ 1'7 3'o 166-3 170-2 ■74'4 17S-9 ■94-3 4-3 4-5 4-6 4-8 5-0 6-0 159-1 162-6 166-4 I74-6 179-5 >94-4 200-3 6-9 7-- rl 8-1 8-4 8-7 9-' i66-6 2CO-5 S-6 8-9 11 10-4 10-8 11-6 166-8 170-8 1-5-0 1:9-5 1R4-3 .8/4 194-9 10-8 11-2 11-6 12-1; 13-0 '3-5 14-0 14-6 15-1 159-8 163-3 167-1 171-1 '75'^ ;;;:: 1S9-7 195-2 n-9 16-S TARLE 525 SPIlEUlCAIi TRAVKHSE TABLK 0- 1° ,0 :<" ^l._ b" ^ (f ^~^ _M N M 1 N IM N mTn" il_ N M ; N _M X fit 2o6-3 ^ 106-3 1 3-. 206-4 6-3 206-5 9-4 206-8 12-6 207-1 1 15-8 207-4 19-0 (i2 213-0 213-0 3-3 2.3-2 6-6 2.3-3 9-9 113-5 13-1 113-8 16-4 214-2 .9-8 g:< zio-j 220-5 3-4 220-4 68 220-6 10-3 220-8 '3-7 iii-i '7-1 22.-5 10-6 64 :iS-i 7-1 228-4 10-7 128-7 14-3 129-0 '7-9 129-4 2. -5 65 236-6 136-7 3-7 236-8 7-5 236-9 1 1-2 i37'i 15-0 137-5 18-8 237-9 22-5 «« 145-8 H5-9 3-9 246-0 7-8 246-2 II-8 146-5 15-7 146-8 19-6 247-2 23-6 'i7 -5S'9 256-0 4 ' 156-1 8-2 256-2 12-3 256-6 .6-5 256-9 20-6 257-3 1 »4-8 «H 166-9 267-0 267-1 S-6 267-3 13-0 267-6 "7-3 268-0 11-7 168-4116-0 m 279-0 279-1 279-1 9-' 1-9-4 13-6 279-7 18-2 280- . 11-8 280-6 Z7-4 70 71 292-4 292-4 307-2 292-6 9-6 292-8 '4-4 293-1 19-2 193-5 24-0 ^94-0 28-9 307-2 307-3 .0-1 307-6 .5-2 307-9 20-3 308-3 1 15-4 308-9 1^ 7i 323-6 323-7 313-8 10-7 324-1 16-1 324-4 21-5 324-8 26-9 315-4 31-3 1 7:t 342-0 342-1 342-2 II-4 341-4 17-1 341-9 22-9 343-3 i8-6 343-9 34-4! 74 362-8 362-9 363-0 12-2 363-3 18-3 363-7 24-4 364-2 30-5 364-8 36-6 386-4 386-4 386-6 130 386-9 ■ 9-6 387-3 26-1 387-8 32-6 388-5 39-2 7ii 4n-3 404-0 4.3-6 14-0 413-9 21-0 414-4 28-0 4.4-9 35-1 4.5-6 42-2 77 444' 5 444-6 444-8 15-. 445-1 11-7 445-6 30-3 446-. 37'? 447-0 43-5 7« 4S.-0 48.-0 8-2 481-3 .6-4 481-6 24-6 481-1 32-9 482-8 4.-2 483-6 49 4 79 524-1 524-2 9-0 514-4 18-0 524-8 27-0 515-4 36-0 526-. 45-0 527-0 54-1 TO 575-9 ° 576-0 9-9 576-2 19-8 576-7 29-7 577-3 39-7 578-2 49-6 579-' 59-6 7^ 8° 9" 10° " .2^ ■ '■»" « M N .M 1 X iM N M ! N M N ^> N M N 7 It 'Zl I'l 102-0 1-0 ~ !» IC2-0 >-9 102-2 2-2 I02-5 1-5 II) ic;-3 2-2 I02-; 2-5 .01-8 103-I 3 ■ iF 102-6 2-4 102-9 .03-. 3-' 103-4 3-4 103-8 ~y^ 1 1 ij 103-0 2-6 103-2 y'o .03-5 3-4 103-8 3-7 ,04-1 4'1 .04-5 4-5 I 1 i:t 103-4 2-8 .03-6 3-i 103-9 3-7 ,04-2 4-' 104-5 4-5 104-9 4-9 .05-3 5-3 1 * icyi 3-' .04-1 3-5 104-3 3-9 104-6 4-4 105-0 4-8 105-4 5-3 ,05-8 5-8 i.'i IC4-3 3-3 104-5 3-8 .04-8 4-1 105-1 4-7 105-5 5-1 105-8 5-7 .06-2 6-2 ii; .04-3 3-5 105-0 4-0 105-3 4-5 .05-6 106-0 5-6 106-4 6-. 106-8 6-6 i; 105-3 3-7 105-6 4-3 105-9 4-8 106-2 5-4 106-5 5-9 IC6-9 6-5 107-3 7-' II! 4-0 106-2 4-6 106-5 5-' 1C6-8 5-7 107-. 6-3 107-5 6-9 107-9 7-5 HI 1^6-6 4-1 ic6-8 4-8 107-1 5-5 107-4 6-1 107-7 6-7 108-1 7-3 .08-5 7-9 ■-'11 107-2 4;5 ■ 07- 5_ y± 107-7 5-8 108-1 6-4 108-4 7-1 108-8 7-7 109-2 8-4 2T 107-9 4-7 108-2" 5-4 108-4" 6-1 108-8 6-8 1C9-1 7-5 109-5 8-2 109-9! 89! 22 108-7 5-0 108-9 y 109-2 6-4 109-5 r> 109-9 7-8 110-3 8-6 1.0-7 1 9-3 2:» 1C9-4 5-1 109-7 6-0 iio-o 6-7 110-3 7-5 1 10-7 8-3 I ii-i 90 "1-5 1 9-8| 24 I10-3 5-5 no- 5 ti 110-8 7-0 III-O 7-9 1..-5 8-7 111-9 9-5 112-3 10-3 2.) II 1-2 5-7 1 1 1-4 6-6 111-7 7-4 11.-9 8-2 ..2-4 9-1 112-8 9-9 1.3-2 10-8 26 112-1 6-0 112-4 6-8 111-6 7-7 II2-9 8-6 113-4 9-5 113-7 114-2 1 1-3 ■-'7 113-1 f5 113-3 7-i 1,3-6 8-1 ..4-0 9-0 114-3 9'9 114-7 lo-S .15-2 irS ■ill 114-1 6-5 114-4 7-5 114-7 8-4 115-1 9 "4 1 15-4 10-3 115-8 "■3 ll6-2 12-3 2.) 1 1 5-2 6-8 115-5 7-8 115-8 8-8 1.6-1 0-8 116-5 ,0-8 116-9 ..-8 1 17-3 12-8 •Mt .■6-, 7-' 1.6-6 8-1 1.6-9 9-' .17-2 10-2 ,17-6 11-2 1.8-0 12-3 "8-5|'3-3| : IP 9° .00 II " - 12° W 1 N 13=~ M N M 1 N M 1 N M N "aTI __N M 1 N 41 ■ 40-. 11-9 140-4 .3-6 140-7 '5't 141-2 .7-0 141*6 ■ 8-8 142-1 20-5 142-7 1 22-3 45 '4^-5 12-3 142-8 14-0 143-2 15-8 ,43-6 17-6 144-1 19-4 .44-6 21-3 145 ' ->' ' 4« 145-0 12-7 '45-4 •4-5 ■45-7 16-4 146-2 ■8-3 .46-6 20-1 147-2 22-0 ■47-7 23-9 •17 '•}7'7 13-2 148-. 15-1 148-5 17-0 148-9 i8-9 .49-4 20-S 149-9 22-8 150-8 24- s 4H ,50-6 13-6 150-9 ,5-6 151-3 17-6 151-7 .9-6 152-2 2. '6 .52-8 »3-6 ■53-4 256 43 ,;5-6 14- r ■53-9 16-2 •54-3 18-2 154-8 20-3 «55-3 22-4 '5 5-9 24-4 156-4 26-6 50 .56-7 14-6 157-1 .6-7 157-5 18-9 158-0 2I-0 158-5 23-2 1590 25-3 '59-7 ^7-5 51 1601 15-2 160-5 1 17-4 160-9 19-6 16. -4 21-8 16,-9 24-0 162-5 26-2 163-1 -^ 52 ,63-6 '5-7 ,64-0 18-0 16+-+ 20-3 165-0 22-6 .65-5 24-9 166-1 27-2 .66-7 29 5 5:i ,6-4 ■ 6-3 ■ 67-8 18-6 1682 .68-7 23-4 169-3 25-S ,69-9 170-5 30-6 54 .71-4 ,6-9 171-S 19-3 172-2 21-8 172-8 24-3 ■73-3 26-8 ■73-9 29-3 174-6 3.-8 rt.i •75-7 '7-5 176-1 176-5 22-6 177-0 1776 27-8 17S-2 304 .78-9 33c 5(i i8o-2 180-6 20-8 181M ^3-5 181-6 26-^ i8:-2 28-8 .82X 3'"5 183-5 342 S7 .85-0 18-9 185-4 21-6 185-9 24-4 .86-4 27-1 .87-0 29-9 187-7 32-7 35-5 5« ■90- 1 19-6 190-6 22-5 191-1 ^5*3 i9,-6 28-2 189-2 31-1 192-9 34-0 193-6 36-9I SO ■95-6 20-4 ■ 96-. 23-4 1966 26-4 197-2 29-3 '97-8 32-3 1985 35-4 199-3 38-4 (iO joi's 21-3 '4' 3 202-5 ^7-4 203-1 ??12. 33"7 204-5 J^ 205-3 40X (iT 207-8 22-1 208-3 25-3 208-8 2S-6 2099 T^8 35-1 210-9 38-3 211-7 41-6 «2 2.46 23-1 215-1 26-4 215-7 29- S 216-3 33-^ 117-0 36-6 217-g 40-0 218-6 45-4 B;t 221-9 222-4 27-6 223-0 31-1 223-7 34-6 224-4 38-1 225-2 4'-7 226-1 45-3 (i4 229-8 25-2 230-4 231-0 3^-5 23.-6 36-1 232-4 39-3 233-2 43-6 234-1 47-3 65 238-4 26-3 238-9 30-1 239-6 34-0 240-3 37-8 241-0 4' 7 241-9 45-6 142-8 49-5 6(; 247-7 17-6 248-4 31-6 H«-9 35-6 249-7 39-6 250-5 43-7 251-4 47-7 252-3 5.-8 «7 ^579 28-9 258-4 33-1 1 259-1 37*3 259-9 4<-5 260-7 45-8 261-6 50- 1 262-7 54-4 «8 269-0 30-4 269-6 34-8 270-3 39-2 271-1 43-6 271-9 48-1 272-9 52-6 274-0 57-. 69 281-1 32-0 36-6 »g2-5 4>-3 283-4 459 284-3 50-6 285-3 55-4 286-4 6o-. 70 294-6 33-7 2-. 5- 3 38-6 296-0 43-5 296-9 48-4 »979 53-4 298-9 58-4 300- ._ 63-4 TT 309-5 55-7 40-8 311-0 46-0 311-9 51-2 312-9 56-4 314-0 61-7 315-2 1 67-0I 72 3260 37-8 326-8 43'^ 327-6 48-7 328-6 54-3 329-6 59-8 330-8 65-4 332-, 71-c 73 344-6 40-2 345-4 46-0 346-3 5. -8 347-3 57-7 6i-7 348-4 63-6 349-7 69-5 351-0 75-5 74 365-5 42-8 366-4 49-0 367-3 55-- 36S-4 369-6 67-8 3^0-9 74-1 372-3 8o-5 75 389-0 45-8 390-2 5»-5 391-2 59-1 39»-3 65-8 393-6 7^-5 395-' 79-3 396-5 86-2 76 416-5 49-^ 4'7-4 56-4 418-5 63 5 4>9-7 70'7 411-. 78-0 422-6 85-2 4^4-3 926 77 447-9 53-: 448-9 60-9 450-1 68-6 54»-4 .76-4 45»-9 84-2 454-5 92-. 456-2 .co-c 7« 484-6 57-8 485-7 66-1 487-0 74-5 488-4 83-0 490-0 91-4 49.-7 .00-0 493-6 !o?-6 7'J 528-0 63-1 529-2 72-3 530-6 81-5 531-2 90-7 533-9 5358 .09-3 537-9 |"8 8 80 580-2 69-6 58,-5 79-7 583-. 89-8 584-8 586-7 IIO-2 588-7 .209 59>-0|'3^-9 1 I 18" Ifi- 1 ^^^ 1 3° 1 _N_ 20' '~ M N iM N M N M N M 1^ IM AI N 14 106-2 6-2 If' .c6-7 6-7 107-2 T^- 16 7-1 107-7 7-7 108-2 8-1 17 107-8 7-6 108-3 108-8 8-8 109-3 9-3 _ 18 108-4 8-1 io?-9 8-7 109-3 9-3 109-9 9-9 1.0-6 10 19 109-0 8-6 1C9-5 9'- 9-9 1 .0-6 Iri 1 1 1-2 ;; ...■9 .1-9 20 109-7 9-> 1 10-2 9-8 1 10-7 10-4 ..1-3 111-9 1.2-5 JilL . .32 Jl' IT 11^-4 9-6 110-9 10-3 111-4 '°'° 112-0 1.-7 .12-6 12 .,3-3 13-2 114-0 14-0 22 111-7 10-8 112-3 1 11-6 .12-8 1 13-4 .3 1.4-. 13-9 1148 '4" 23 112-0 10-6 112-5 1 1-4 1 13-0 12-2 113-6 .3-0 114-2 13 114-9 14« i.S-6 I5'4 24 112-8 1 1-1 113-3 11-9 113-9 12-8 ■14-5 .3-6 115-1 '4 115-8 ■5-3 .16-5 lS-2 25 II3-7 .1-6 114-2 '-'5 .14-8 13-4 115-4 14-3 ii6-o '5 1.6-7 161 117-4 170 2fi 114 6 12-2 ■3 ■ 115-7 14-0 116-3 14-9 117-0 '5 117-7 17-0 1184 17-7 27 115-7 12-7 1.6-2 ■3-6 116-8 14-6 117-4 ,;-6 118-0 16 118-8 ■7-5 ,19-4 ■ 8-5 2« 116-7 '3-3 117-3 14-2 117-8 15-2 11S-4 .6-3 119-. 17 1,9-8 iS-3 ,20-5'.9 3| 29 117-8 .3-8 118-4 14-8 iig-9 15-9 11,-6 .6-9 ig 120-9 19-1 ,2.-7,.0-3| 30 iig-o '44 119-5 1 '5-5 120-1 16-6 ■ 20-7 ■ 7-6 121-4 .8 122- 1 .9-9 .32-9 2_ro 31 120-2 1 ' 5'o 120-8 1 i6- 1 121-4 122-0 1 18-4 122-7 '9 5 "iTTT|^o-7|.24-. 12,-9 32 ,:,-5 lS-6 ,Z2-l| 16-7 .7-9 135-3 I.9-. ,24-0 20-3 .24-7!3.-5|'35-5i..-7| TABLE 527 .SPHKUICAL TRAVKKSK TAIMJ: n u* lA" M 1 N 17° 18° 19° 20° M r N M i\ M N M 1 N M 1 N M 1 N Xi M ;(.■> 40 " 4:< 44 4,-. Hi 47 41) 4;i .iO '--■9 124-3 izj-S 127-4 129-0 130-8 132-6 '34'5 16-2 16-8 ;8:^ I8-S '9;5 22-4 23-2 24-1 is 27-7 '8-7 29-7 123-4 124-9 .26-4 128-0 129-6 131-4 133-2 137-2 ■39-3 141-6 '43-9 146-4 149-0 151-8 154-7 157-8 161-1 '7-4 18-1 i8-S '9-5 10-2 20-9 21-7 22-s »3'3 24-1 25-0 25-9 26-8 17-7 ..S-7 29-8 30-S 31-9 125-5 128-6 130-3 131-0 '33-9 135-8 nfs 140-0 Zl .47-1 '49-8 152-5 •55-5 15S-6 161-8 ,8-6 ■9;3 20-8 2.-6 22-4 23-2 24-. 124-7 .26 < .29-2 .30-9 132-7 134-6 136-, 19-9 21-4 23-0 23-9 24-8 25-6 16-6 2S-5 29-5 ;::; ;::! 35-J 36-4 125-4 126-8 128-4 130-0 131-7 133-4 135-3 137-3 2.-9 23-6 24-5 25-4 26-3 27-3 28-2 19-3 30-3 31-4 3r6 34-s 36-, 37-4 38-7 126-1 127-6 129-1 130-7 132-4 134-2 136-1 13-2 24-1 25-0 25-9 16-9 17-9 28-9 .26-9 .28-4 129-9 131-5 133-2 135-0 .36-9 138-9 23-6 24-6 III 27-4 28-4 29-5 30-5 "3. -6 32-8 33-9 35-1 36-4 37-7 39-0 40-4 4. -9 43-4 .;6-5 138-7 140-9 Hrs '45-7 148-4 151-1 154-0 ■ 57-1 .60-3 24-9 III 27-7 28-7 29-7 30-7 31-8 33-0 34-2 138-6 143-0 145-4 147-9 1 50- 5 ■53-3 156-3 ' 59'4 162-7 '39-3 141-5 '43-8 146-2 148-7 151-4 154-2 157-1 i6o-3 163-6 140-1 142-3 144-6 147-0 149-6 152-2 155-1 158 I l6]-2 164-5 19-9 31-0 32-1 33-i 34-4 35-7 36-9 3S-2 39-6 4.-1 141-0 143-1 145-5 147-9 150-5 153-2 ,560 159-0 .62-2 .65-6 h-2 5(t .i!t r.i) 163-8 167-4 ■75-5 '7^7 Is'*'-' ^94; 5 2C6-I 30-s 331 34-3 3 5-6 ll'l 399 4'-5 43-1 ;64;5 i;6-i I's--! 190-1 '95-3 33"' 34-3 35-6 30-9 31-3 39-7 4<-3 42-9 44-6 46-4 165-3 .69-0 172-9 177-0 18.-4 1S6-0 'iii 2c8-i 35-4 36-7 3S-0 39-5 40-9 42-5 44-2 45-9 :9-^ .66-2 :•■:■ 192-0 '97;3 209-1 37-8 39-' 40-6 42-1 43-7 45-3 47-' 48-9 50-9 53-0 167-1 170-8 174-7 178-9 204-2 210-3 40- 1 41-6 43" ' 44-7 46-4 48-2 50-0 5.-0 ^6-3 168-1 171-8 175-7 189-1 194>2 199-6 205-3 211-5 4^-5 44-1 45-7 47-4 49-2 51-0 53-0 55' 57-3 59-6 169- 1 172-8 176-8 185-5 190-3 195-4 200-8 206-6 2.2-8 44-" 46-6 48-3 SO-. 52-0 54-0 56-0 M (;2 li.i «4 (i.-; «7 «ii «!l 7" 212-6 219-5 235-1 ^3-9 ^53-4 263-8 28^6 45-0 46-9 48-9 51-1 53'5 56-0 58-7 61-7 64-9 68-5 220-3 228-0 236-2 245-0 = 54-5 265-0 276-4 302-7 48-3 50-4 52-6 54-9 57-5 60-2 63-2 66-3 69-S 73-6 2 14-6 221-6 129-1 237-3 246-2 255-8 266-2 277-7 190-3 304-2 5.-- 55-9 $■1 6. -5 64-4 67-5 78-8 247-4 1 65-6 257-. , 68-7 267-6 1 71-0 279- ■ 75-7 291-8 79-* 305-7 i 84-0 23.-6 63-s 239-9 66-6 248-8 69-7 280-7 80-4 293-4 84-6 307-4 89-3 '-18-2 225-3 241-3 250-3 260-0 270-7 282-3 295-1 309-2 62-, 64- 8 67-6 -:0-6 73-8 77-3 81-1 85-2 S9-7 _94JS ic6-o 112-6 128-5 .38-. 149- . 162-c .77-1 195-3 2.9-5 226-7 234-4 242-8 251-S 261-6 272-4 284-1 2969 3111 65-7 68-4 71-4 74-6 78-1 8.-7 85-7 90-1 94-8 100-r 71 7:f 74 7-' 74i-9 ! 33-4 142-9 1 35"' ■43-9 36-9 ,45-0 3S-7 ,46-2 40-5 '47-4 148-7 44-3 42 '44' 34-6 145-1 36-4 ,46-2 3S-2 '47-3 40-. ,485 42-0 149-7 43*9 151-0 45-9 43 .46-5 35-8 '47-5 37*7 '4«-5 39-6 ■49-7 41-5 ,50-9 43-5 152-1 45-5 '53-5 47-5 44 .48-9 37'J 149-9 39-0 15.-0 4,-0 152-2 43-0 '53-4 45-0 '54-7 47-' ,56-0 49-2 45 151-5 38-4 •52'5 40-4 153-6 42-4 '54-8 44-5 ,56-0 46-6 '57-3 48-8 158-7 50-4 4f! .54-2 39-7 '55-3 156-4 44-0 157-6 46-, .58-8 4S-3 160-2 50-5 16. -6 52-8 47 ■ 57M 41-2 ■ 58-1 43'3 •59-3 45"5 160-5 47-8 ,6, -8 50-c 163-1 52-3 164-6 54-6 4(1 i6o-i 42-6 16,-2 44'9 162-3 47-1 163-6 49-4 ,64-9 51-8 166-3 54-2 167-7 56-6 49 163-3 44-2 164-4 46-5 1656 48-8 ,66-8 ; 5,-2 53-6 169-6 56-1 58-6 50 1666 45-7 167-8 ,69-0 5°-6 '70-3I 53-> ,71-6 55-6 173-, ^ ,74-6 60-7 62-9 51 170-2 47-4 171-4 49-9 ,72-7 52-4 '73-9 55"o '75-3 57-6 ,76-8 ,78-3 52 174-0 49-1 175-2 5''7 176-4 54" 3 '77-8 57-0 '79-2 59-7 ,80-7 62-4 182-3 65-2 53 17X-0 50-9 179-2 53-6 180-5 56-3 ,8,-9 59"' ,83-3 61-9 ,84-9 64-7 186-5 67-6 54 182-2 528 \IU 5 5-6 184-g 58-4 186-2 6.-3 64-2 ,89-3 67-1 190-9 70-1 55 186-7 54-8 57-7 ,89-4 60-6 ,90-8 63-6 ,92-4 66-6 ,94-0 69-7 195-7 72-8 56 ,9,-6 56-9 ,92-9 59'9 '94-3 62-9 '95;7 66-0 '97-3 69-, 199-0 72-3 200-7 75-5 57 .96.7 59-1 ,98-0 62-2 '995 65-4 68-6 202-6 7,-8 204-3 75-' 206-1 7S-5 58 6.-4 203-5 64-7 205-0 67-9 206-6 7,-2 208-2 74-6 78-0 211-8 81-5 59 2o8"o 63-9 209-4 67-2 210-9 70-6 2,2-5 74-' 2,4-2 77-6 216-0 81-2 217-9 84- 8 60 214-2 66-5 215-7 2':'-3 73-5 2,8-9 77-' 220-7 80-8 222-5 84-5 88-2 Gl 220.9 69-2 2225 72-9 224-1 76-6 225-8 ^^ 227-6 84-, 229-5 88-0- 231-5 9.-9 r>2 22S-2 1 72-2 229-7 76-0 231-4 79-8 233-2 83-7 235-0 87-7 237-0 9'-7 239-1 (i3 i35-9 75-3 237-6 79-3 139-3 83-3 241-, 87-4 243-0 9'-5 245-1 95'7 247-2 loo-o 64 244-3 78-7 246-0 82-8 247-« 87-0 249-7 91-3 25,-7 95-6 253-8 ico-o 256-0-104-5 65 253-5 82-3 255-2 86-6 257-1 9,-0 259-0 95'5 26,-, 263-3 104-6 265-6:109-3 66 263-4 86-2 265-2 90-7 267-. 95-3 269-, 27, -3 104-7 273-5 109-5 275-9 '"4-4 67 274-1 90-4 276-0 95-2 278-0 280-, ,04-9 109-9 2S4-7 1,4-9 287-2 I120-0 68 285-9 95-0 287-9 290-0 105- 1 292-2 294-5 ,,5-4 797-0 120-7 299-6 126-1 69 298-9 301-0 ,05-3 303-1 1,0-6 305-4 |,, 6-0 307-9 12,-5 310-5 127-1 313-2 132-7 70 313-2 105-5 3>5-3 I,,-o 3.7-6 1,6-6 320-1 :l"Ji 322-6 128-1 325-3 '34-0 328-, 140-0 71 329-0 111-5 33'-3 "7-3 333-7 ,23-3 336-2 ,29-3 33S-9 '35-4 34'-7 ,4'-6 344-7 T^ 72 346-6 iig-i 349-0 ,24-3 351-6 130-6 354-2 ,37-0 357-' '43-5 360-0 ,50-, 363-2 156-8 73 366-4 125-6 132-, 371-6 138-8 374-4 ,45-6 377-4 ,52-5 380-5 '59-5 383-9 166-7 74 388-6 '33-9 39'-3 140-9 394-' 148-0 397-' '55-3 400-3 162-6 403-6 ,70-, 407-2 177-7 7-i 4'3'9 '43-3 4,6-7 150-8 419-7 158-4 422-9 ,66-5 426-3 174-0 429-9 ,82-0 432-6 1 90- 2 76 442-8 I 54-0 445-8 162-0 449-0 ,70-3 452-5 ,78-6 456-' ,87-0 459-9 '95-6 463-9 204-4 77 476-2 166-3 479-4 175-0 482-9 1S3-9 486-6 ,92-S 490-5 202-0 494-6 21,-3 498-9 220'7 78 515-2 igo-6 5,8-7 190-9 522-5 ,99-7 526-5 209-5 530-7 2,9-4 535-' 229-5 539-8 239-7 79 56,-4 ■97-5 565-3 207-8 569-3 218-4 573-7 229-, 578-3 239-9 583-, 250-9 588-2 262-1 80 6.6-9 621-1 229-1 625-6 240-7 630-4,252-5 635-41264-5 6,0-7 I276-6 646-3 289-0 ^~ 28° 29° 30° 31° 32° 33° „ =«f _ J ~^ M N M N iM ^ N Al'l N M 1 N IM 1 N ivi \^ : 28 .28-3 28-3 1 1 29 " 119- 5 29-5 130-7 30-7 ! 1 30 :3o-g 30-7 132-0 31-0 '33-3 1 33-3 1 ! in- 132-1 3,-9 '33*4 1 33-3 134-7 34-7 ,;6-,|36-, 1 32 ■33-5 33*2 134-8 34-6 ,36-2 It' '37-6 37-5 ,39-0 39-0 33 135-0 34-5 ,36-31 ;6-o ,37-7 .39-1 ' 39-0 ,40-6 1 40-6 147-2 47-3 blMlEIUCAI, VUAVERSE TABLK 28" 2a' _ 30° 3 ■Ai° Xf 84' n ■M M 1 N M 1 N M 1 N M -JL. M 1 ,\' M 1 N I\l ^ ■ 36-6 3 5;9 ■37-9 i 37-4 139-3 38-9 ,40-7 40-5 .42-x!4-. .43-8 43-S '45-5 45-5 X, .38-3 ,39-6 38-8 14. -0 40-4 .42-4 42-. 143-9 43-8 '45-6 45-5 '47-3 47-2 ■M 140-0 38-6 141-3 40-3 142-7 41-9 144-2 43-7 .45-8 45-4 '47-4 47-2 '49-' 490 :*7 141-8 40-1 .43-z 41-8 .44-6 43-5 .46-. 45-3 .47-6 47-' '49-3 48-9 .5.-0 50-8 ■Ml >4>-7 41-5 145-1 43'3 .46-5 45-' 14S-0 46-, 149-6 48-8 .5. -3 50-7 .53-1 52-7 :i9 '4i-7 43-1 147-1 44-9 .486 46-7 1 50- 1 48-7 .5.-7 506 .53-41 52-6 .55-2 54-6 40 .4-8 ' 44-6 149-3 46-5 150-7 48-4 152-3 5°-4 •53-9 5--4 '55-7 54-5 '57-5 56-6 41 ■5C-.J+6-. 151-5 48-2 153-0 50-2 .54-6 52-2 .56-2 1?3 .5S-0 56-4 ,59-8 ft 4i ■5^--4 4-9 '53 9 499 ■55-4 52-0 .57-0 54-1 j58;7 56-3 .60-4 58-5 162-3 60-8 4;t 154-9 496 .56-3 51-7 ■57-9 53-S 159-5 56-0 58-3 .63-0 60-6 164-9 62-9 44 >57-5 5'-3 :5S-9 53-5 .60-s 55-8 .62-2 5S-0 ■63-9 603 .65-S 62-7 167-7 65-1 4.-> 160-z! 53Z .61-7 S5-4 .63-3 57-7 165-0 60-. .66-8 b2-5 .68-6 64-9 170-6 67-4 4i; 163-0 55-' .64-6 57-4 i66-i 59-8 167-9 62-2 .69-7 64-7 ,71-6 67-2 ,73-6 69-8 47 ■ 66-1 S7-0 167-6 59-4 .69-3 6.-9 .71-1 64-4 670 .74-8 69-6 176-9 72-3 41! 169-3 590 170-9 6. -6 172-6 64- ■ 174-3 66-7 Vjll 69-4 .78-2 72-1 180-3 74-9 4!( ■ 72-6 6l-2 ■74-3 63-8 .76-0 66-4 177-8 69-. 179-7 7.-9 .8. -7 74-7 183-9 77-6 .■>r 176-2' 63-4 ■77-9 65-1 179-. 68-8 .8.-5 71-6 .87-4 74-5 ,85-5 77-4 187-7 80-4 i«o-o 65-7 1S1-7 68-4 183-5 70-3 .85-4 74'^ 77-2 .89-5 80-2 191-7 83;3 .'I'i 184-0 68- r 185-7 70-9 1S7-6 73-9 189-5 76-9 191-5 80-0 193-7 83-. 195-9 .'i:t 188-2! 7C-6 190-0 73-6 19.-9 •/6-6 .93-8 79;7 .95-9 ^^9 .98-1 86-2 200-4 89-5 .■>« 192-7 73-j ■94-5 76-3 .96-4 79-5 198-5 200 -6 86-0 202-9 89-4 205-2 92-S .■>.■> >97-5 75'9 199-3 79-2 201-3 82-4 203-4 85-8 205-6 89-2 207-9 92-7 210-3 96-3 ■ii; zoz-s 78-8 204-s 82-2 206-5 85-6 208-6 S9-, 2.0-9 92-6 213-2 2.5-7 •■>7 2079 8o-o 209-9 85-4 88-9 214-2 92-5 2.6-6 96-2 2.8-9 .oo-o 221-5 103-9 r.!i 2.3-7 85-' 2.S-S 88-7 2.7-9 92-4 220-2 96-2 222-5 100-0 225-0 .03-9 227-6 107-9 :.!) 219-9 ^S-5 222-0 92-2 224-2 96- r 226-5 228-9 104-0 231-5 .08-1 234-2 1.2-3 lid fiT 2.6-5 233-6 228-7 96-0 230-9 233-3 .04-. .08-4 J^IIL 108-2 238-5 .12-5 241-2 1.6-81 95-9 ^-35-8 loo-o 238-2 104-2 240-6 243-2 I 12-7 245-9 117-2 248-8 .2,-7| 71 331-1 146-1 334-3 .52-3 337-6 .586 34.-. 344-8 iM:i 178-4 .S8-6 35V7 '85-3 '95-9 347-9 H4-4 351-2 .61-0 354-7 167-7 358-3 ■74-5 362-2 ■81-5 366-2 370-S 7- 366-5 ,63-6 .70-6 373-7 .77-7 377-5 184-9 38.-6 .92-3 385-9 '999 390-3 207-6 7:1 5S-4 '73-9 391-1 .81-3 394-9 i88-8 399-0 ,96-5 403-3 204-4 407-s 212-4 4.2-6 220-6 74 410-9 .85-4 4.4-8 .93-9 4'3-9 201-3 423-2 209-5 427-8 2.7-9 432-6 226-5 437-6 235-2 75 4!76 .98-4 44.-8 2^6-8 446-. 450-7 224-2 455-6 234-3 460-7 242-4 466-0 25,-7 7" 46S2 113-3 472-6 222-3 477-3 23r6 482-2 24.-0 487-4 250-6 492 9 260-5 498-6 270-5 77 s°ys 230-3 508-3 240- . 5'3-3 250-1 5.8-6 260-3 524-2 270-7 530-1 28.-3 536-2 292-. 7« 544-7 549-9 260-8 555-4 27. -6 .6,-. 282-9 567-2 294-0 573-5 305-5 580-2 3'7-3 7:' S93-0 273-5 599'^ 285-2 605-2 297-0 6,1-4 309-1 6i8-o 321-5 624-9 334-' 632-2 347-c III) 652-2 301-5 658-4 3'4-4 665-0 3^7-4 671-8 340-8 679-0 3 54-4 686-7 368-3 694-6 382-5 ^J*-- ~1 3«» _Jt7° J 3K" 37S'7 75-5 .78-4' 78-31 i:t 166-9 65-3 169-0 67-7 .7.-2 70 3 173-5 7^-9 .75-9 75-5 .78-5 78;2 «t ,69-7 67-6 171-8 70-2 .74-1 _^ .76-4 75-4 .78-9 78-2 .'84-2 1 83-9J 630 SPHERICAL TRAVERSE TABLE n 35° _.3- ° 38° 39° _i<'"_ .Zl'^l M N Jl^ J^ N M 1 N M 1 N [M N M N 45 172-6 70-0 174-8 72-7 177-1 75-4 '79-5' 78-. ,82-0 1 8.-0 184*6 83-9 187*4 86-9 46 176-7 72-5 177-9 75-2 180-2 78-0 182-7 80-9 .S5-2|83-9 187-9 86-9 ,90-7 90-0 47 179-0 1 75-1 ,8. -2 77-9 183-6 80-8 i86-i 838 1SS-7 1 868 191-4 90-c 194*3 93-2 48 ,82-, 77-8 '84-7 80-7 .87-1 83-7 189-6 86-8 .92-3 89-9 195-1 93-2 198-0 96-5 49 186-1 ; 8o-5 .88-4 83-6 190-9 86-7 192-4 899 .96-, 93-2 199-0 j 96-5 50 .89-9 1 83-4 192-3 86-6 194-8 89-8 '97-4 93-1 200-2 96-5 203-1 j.oo-o 206-1 '°3-6 51" 194-0 86-5 ■96-4 89-7 199-0 93-1 201-6 965 204-5 |ioo-o 207-4 ,03-6 2.0-5 107-3 52 198-3 89-6 200-0 93-0 203-4 964 206-1 100-0 209-01103-6 212-0 107-4 215-2 111-3 53 10I-8 929 205-4 96-4 208-1 loo-o 210-9 103-7 213*8 .07-5 2,6*9 111-3 220-2 115-4 54 207-7 96-4 210-3 100-0 213-0 103-7 215-9 107-5 21S-9 111-5 222-1 115-5 225-4 II9-6 55 212-8 loo-o 215-5 103-8 218-3 107-6 221-2 I1I-6 224-3 115-6 227-6 .19-8 231*0 124-1 56 218-3 103-8 221-0 107-7 223-9 111-7 226-9 .15-8 230-1 233-4 124-4 237-0 57 224-1 107-S 226-9 111-9 229-9 ii6-o 233-0 120-3 236-3 124-7 239*7 129-2 243-3 133-9 58 230-4 I12-1 233-3 ,i6-3 236-3 120-6 239-5 125-0 242-8 129-6 246-3 134-3 250-0 ,39*1 59 237-0 .16-5 240-0 121-0 243-1 125-4 246-4 130-0 249-8 134-8 253-5 139-7 257-3 144-7 60 244-2,121-3 247-2 125-8 250-4 130-5 253-8 ■35-3 257-4 .40-3 261-I 145-3 26,-0 150-6 TT 251-8 I126-3 255-0 131-1 258-3 135-9 261-8 140-9 f^-t 146-1 269-3 1514 273*3 156-8 62 260-0 131-7 263-2 136-6 266-7 141-7 270-3 ,46-9 ,52*3 278-. 282-2 163-5 63 26S-9 137-4 272-3 142-6 275-8 147-9 279-5 ■53-3 283-4 15S-9 287-5 164-7 291-9 170-6 64 278-5 143-6 282-0 149-0 285-6 154-5 289-5 .60-2 293-5 166-0 297-S 172-0 302*3 178-2 65 288-9 150-2 292-4 155-8 296-3 i6i-6 300-3 .67-5 304-5 173-7 308-9 179-9 313-5 186-4 66 300-1 157-3 303-9 163-2 307-9 169-2 312-0 ■75-5 316-4 18.-9 321-0 188-5 325-8 195-2 67 312-4 165-0 3,6-3 171-2 320-5 177-5 324-8 .84-. 329-3 190-8 334-' 197-7 33-ri 204-8 68 325-9 173-3 330-0 179-8 334-2 186-5 338-8 '93-4 343-5 200-4 348-5 207-7 353-7 215-1 69 34°- 7 182-4 344-9 189-3 349-4 196-3 354-1 203-5 359-1 211-0 364*3 218-6 369-7 I26-S 70 356-9 192-4 36.-4 190-6 366-1 207-0 371-0 214-6 376-2 222-5 381-7 230-5 387-4 238-8 71 375-0 I203-4 379-7 21 i-o 384-6 2i8-8 389-8 2269 395-2 235-2 401-0 243-7 407-0 252-, 72 )95-i 215-5 400-0 223-6 405-2 231-9 410-7 240-5 416-4 249-2 422*4 258-2 428-8 267 5 73 417-5 229-0 422-8 237-6 428-3 246-5 434-0 255-5 440-1 264-9 446-5 274-5 453-2 284-3 74 442-9 244-2 448-4 253-4 454-3 262-S 460-4 272-5 466-8 282-4 473-6 292-6 480-7 303-2 75 471-7 261-3 477-6 271-1 483-8 281-2 490-3 291-6 497-2 302-2 504-4 313-3 511-9 324-5 76 504-6 280-8 510-9 291-4 517-6 302-2 524-6 3>3-4 531-9 324-8 539-6 336-5 547-7 348- 77 542-7 303-3 549-5 3>4-7 556-6 326-4 564-. 338-4 572-0 350 8 580-3 363-5 589-0 376-^ 70 587-2 329-4 594-5 341-8 602-2 354-5 610-i 367-6 6.8-9 I3810 627-9 394-8 637-3 4C9-C 7!» 6398 360-2 647-8 373-8 tf,:] 387-7 665-i 401 9 674-4 4.6-6 684-1 431-7 694-4 44-; 80 703-0 1397-1 711-8 412-1 427-4 730-8 443-1 -41-0 459-2 751-8 475-9 763-0 493-': 42° 43° 44° 45° 46° 47° _ 4 3° '^ M N M N M N i\I 1 N M 1 N IM N M X 42 181-1 81-1 1 43 184-0 84-0 187-0 87 ' 44 187-. 86-9 190-1 90 193-3 93-3 45 .90-3 90-0 '93-4 93 196-6 96-6 200'0 ico-o 46 193-7 93-2 .96-8 96 200-1 loo-o 203-6 103-5 207-2 107-2 47 •97-3 96-6 200-5 100 203-8 103-6 207-4 107-2 211-1 111-0 2.5-0 115-0 48 20 1- 1 100-0 204-3 103 207-8 107-3 211-3 iii-i 215-1 115-0 219-1 119-1 223-3 123*3 49 205-1 103-6 20S-4 107 211-9 11 l-I 215-6 115-0 219-4 119-1 223-5 123*4 227-8 127*8 (10 209-3 107-3 212-7 1 1 1 216-3 1.5-1 224*0 iili 228-2 127-8 232-5 132-4 51 213-8 111-2 217-3 i'5 220-9 224-7 ■23-5 22S-7 127-9 233-0 132-4 52 218-6 II5-2 222-1 119 225-8 I23-6 229-7 128-0 233-8 132-5 238-2 •37-3 242-7 142-2 ft3 2236 II9-5 227-2 231-0 12S-2 235-0 132-7 259-2 137-4 243-6 142-3 248-3 Ii47*4 54 228-9 232-6 128 236-5 132-9 240*6 .37-6 244*9 142-5 249*5 .47-6 254 3 152-9 55 234-6 .28-6 238-4 133 242-4 137-9 246-6 .42-8 25,-0 147-9 255-6 153-1 260-6 158*6 56 240-6 133-5 244-5 248-6 143-2 252-9 148-3 257-4 153-5 262-2 159-0 267-3 ,64*7 57 247-7 138-6 251-0 "43 255-2 .48-7 259-7 154-0 264-3 159-5 269*2 165-1 274-4 "71-0 58 253-9 I44-' 258-0 •49 262-3 ■54-5 266-9 160-0 271-7 165-7 276-7 .,71-6 282-0 177-7 59 261-3 149-9 265-5 155 269-9 160-7 274-6 166-4 279-5 172-3 284-7 .78-5 290-2 184-8 60 269-, ,56-0 273-5 161 278-0 .67-3 282-8 173-2 287-9 293-3 1X52 29S-9 192*4 1. 277-6 |i62-4 282-0 168-2 286-7 174-2 291-7 180-4 296-9 .86-8J 302-4 193-5 308-3 ^ 632 TABLE 5 SPHERICAL TRAVERSE TABLE 1 " '56" 57" 58° 59° «0° M 1 N M 1 N 62° •= M 1 N M 1 N M 1 N i^i i n" 56 3.9-8 p.9-8 1 1 1 j 1 1 57 32S-3 1228-3 337-. 1237-2 1 1 ! 58 337-5 1237*3 346-5 |»46-4 356-. 256-. ' j 59 347-2 1246-7 356-5,^56-3 366-4 266-3 377-0 277-0 60 357-71*56-8 367-2 I266-, 377-4 277-2 383-3 288-3 400-0 300-0 61 36S-9 J267-5 378-71277-8 3S9-5 1288-7 400-5 300-2 4.2-5 ,312-5 425-5 325-5 62 380-9 Z7S-8 39.-. 1289-6 402-0 I30.-0 4.3-6 3.3-0 426-0 325-8 439-4 339-3 453-7 353-7 63 393-9 ,291-0 404-4 1302'; 415-7 314-1 427-7 326-6 440-5 339-9 454-3 354-1 469-2 369-. 64 407-9 303-9 4.8-8 I315-7 430-5 328-. 446-5 343-2 442-9 34. -2 456-2 355-1 '^i?'5 36,-9 485-9 385-6 65 423-1 3'7-9 434-0 1330-2 459-4 356-9 473-2 57.-4 488-. 386-9 504-0 403-3 66 439*7 45'-4 345-9 464-0 359-4 477-4 373-8 49.-7 389-0 507-. 405-2 523-7 422-4 67 457-7 349*3 469-9 3628 483-0,377-0 496-9 392-1 511-9 ,398-S 527-9 425-0 545-1 443-1 68 477-4 366-9 490-. 38.-. 503-7 1396-1 5.8-3 411-9 533-9 I428-7 550-6 446-5 568-6 465-5 S'J 499 ° 386-2 512-3 401-. 526-6 ,4.6-9 541-8 433-6 558-1 45.-2 575-6 470-0, 594-4 4899 70 522-9 407-3 536-8 14^3-- 55.-7 :4:i9-7 567-7 457-3 584-8 475-9 603-1 495-7 622-8 71 549-3 430-6 564-0 J447-2 579-6 J464-8 596-4 483-3 614-3 1503-0 633-61523-9 654-3 1546-2 72 578-7 456-3 594'- :473'9 6.0-7 492-5 628-3 512-2 647-2 J533-1 667-5 I555-2 689-3 !57S 8 73 611-6 484-9 628-0 503-7 645-4 523-4 664-. 544-4 684-1 I566-7 705-5 590-1 728-5 ,6.5-2 74 648-8 517-0 666-1 537-0 684-6 558-. 704-4 580-5 725-6 604-0 748-3 629-. 772-8 655-9 75 690-9 553'3 709-4 574-7 729-1 I597-3 756-2 62.-] 772-7 646-4 796-9 673-3 823-0 70. -9 76 739-2 594-6 758-9 6.7-6 780-0 64.-9 802-6 667-5 S26-7 694-7 852-6 723-6 880-5 754-3 77 795-0 642-2 8.6-2 I667-0 883-1 724-5 838-9 :693-2 863-. 720-9 889-1 750-2 9.6-9 78.-4 9469 1814-6 7H S60-. 697-5 907-6 752-9 933-9 783-0 961-9 ,8.4-9 992-1 848-8 .024 ;884-8 ly 937'2 762-7 962-3 792-2 989-0 823-3 .018 856-2 ,048 89.-. 108. 92S-1 11.6 967-6 HO 1030 840-8 .057 873-3 .087 907-6 ...8 943-9 .152 I9S2-3 .188 1023 .227 1067 63" 64° 65° 66° 67^ _ 63° 60° "^ M N M 1 N M 1 N M N M ! N M 1 N 1\I 1 N 63 4«5-^ 385-2 64 502-5 402-4 520-4 420-4 65 521-2 420-9 539-8 439-7 559-9 459-9 66 54.-6 440-8 560-9 460-5 581-8 48.-7 604-5 504-5 B7 563-7 462-4 583-8 I483-0 605-6 505-2 629-2 529-1 655-0 555-0 6H 5SS-0 485-8 608-9 1507-5 63]-6 530-8 656-3 555-9 683-2 583-1 7.2-6 612-6 I 6!) 6.46 ,51.-3 636-5 J534-. 660-3 558-7 686-1 595-1 714-2 1613-7 744-9 644-8 778-6:678-6 70 644-0 1539-^- 667-01563-3 69. -8 589-2 7.8-9 16,7-1 748-3 J647-3 780-5 6S0-0 ii£9Jli£I 71 676-6 570-0 700-7 1595-4 726-8 622-8 755-2 652-3 786-1 1684-2 819-9 7. 8-8 857-15756-6 903-0 80. -8 72 7.2-8 604-0 738-2 63. -o 765-7 660-0 795-6 69. -3 828-2 J725-. 863-9 76.-7 73 753-4 64.-9 780-2 670-6 809-3 70.-4 840-9 734-6 875-3 770-6 9.3-0 809-6 954-4 852-. 74 799-1 684-4 8Z7-6 715-0 858-4 747-9 892-0 783-3 928-5 821-6 988-8 879-2 968-^5 863-2 .002 9C8-5 75 85. -o 732-5 8S.-4 765-i 9.4-2 1800-4 949-9 838-2 923-7 .078 972-2 76 9.0-5 787-2 942-9 IS22-3 978-1 i860-. .016 900-8 1058 944-9 1.03 992-7 1153 11045 77 979-i 850-1 .014 I8XS-. .052 928-9 .093 972-9 ..38 .020 .187 .072 1241 1112S 7» .059 I923-3 1097 ]964-6 1087 11009 ..83 1.057 1231 ..08 1284 ..64 1342 I1226 79 ..54 I.OIO ..96 |]055 1240 1.03 .2S8 |..55 134. .2.2 '399 .273 .462 11340 80 .268 |.,.3 .3.4 I..63 .363 }l2.6 14.6 .274 .474 |1336 1537 |i4C4 .607 1.477 70° 71° 7-2° 73° 74° 75° 76° "7" M 1 N M 1 N M N i\l 1 N M N M 1 N M i\ 70 854-9 1754-9 i 71 898-. 1797-9 943-5 ,843-5 72 946-2 845-6 994-0 J893-8 1047 1947-2 73 .000 898-6 105. 949-9 .008 1 1 70 1070 74 .061 958-> ...4 .0.3 1.74 .073 .241 114. 13.6 .2.6 75 1130 1025 ..87 .084 125c 1149 1321 .221 .402 .30. 1493 1394 1 76 .209 J1102 1270 .165 1234 1414 1312 1500 1399 1597 1497 .709 1609 77 .300 ..90 .366 ;i258 1439 1333 .520 14.7 16.3 .511 17. 8 .617 .838 1737 7« .406 1.293 1477 |>366 1556 .448 1645 1539 1745 .64. .858 1756 1988 1 .S87 70 .532 I14.3 .6.0 ii494 .696 1583 1793 .683 .90. 1794 2025 1920 2116 [2063 80 .684 j.558 .769 1.647 .864 I1745 1 .970 ^ 1978 23S0 I2275 TABLE G MEKIDIONaL pahts I.ATITUDI .^3= 60 120 bi 121 62 122 6^ 64 124 65 ,.5 66; 126 671 12^ 6S| 128 69! 129 ^1 542 603 543 604 544 605 545 I 606 546 607 '|16° 48 108 49 '09 167 227 168 228 169 5S4 586 588 589 590 59' 592 653 5a 1,0 .70 S' III 171 Si 11: 172 S3 .13 173 54 114 174 55 ■■5 175 5^ ,.6l,76 5' ..7 177 5^ ..8 I7« Z38 298 <;r, j,,,, 17,12391 299 I 360 TABLE n MFRIDICNAL PARTS LATITUDE a 4 5 f) 7 8 9 19° 1 20° 21° 1290 1291 1292 1293 1295 1296 1297 1298 1299 22° 23° 24° 25° 26° 9.0 28° 29° 30° 31° 32° 1 33° ii6i 1163 1,64 ,.65 ij66 1167 !l69 1 1 70 1171 1227 1228 1229 1230 1232 1233 1234 1235 ■3 54 nil nil ,361 1419 1420 1421 1422 1423 1424 1425 1426 1427 1428 .484 ;ii 1490 149! 1492 '493 '494 1550 ■55^ ■552 ■553 ■554 1556 ■557 1558 '559 .,60 1616 1618 \lll 1621 1622 ,623 1624 1625 1626 .684 1685 1686 1687 1688 1690 169. ,693 ■694 ■75^ ■75^ ■753 ■755 1756 '757 175S \]ll ,76. 1819 1821 1822 .823 1S24 1825 1826 1827 XI 1888 .S90 189, .892 1893 ,894 '895 ,896 .89S ■899 .958 '959 ;?£ ,963 1964 1965 1966 1967 1969 2028 2030 2031 2032 2033 2034 2035 2037 2038 2039 2101 2102 2103 2104 2,0s 2107 2108 2109 10 12 13 14 15 16 17 18 (9 1178 1179 1182 .236 1240 1241 1242 1243 IS44 1245 1301 1302 1303 1304 1305 1306 1307 1308 1310 .367 1368 .369 1370 1371 ■37^ ■373 ■374 1430 ■43 ■ 1432 ■433 ■434 ■435 1436 ■437 .438 ■439 1497 I49S '499 1500 1502 1503 1504 .505 ,56. 1562 'III '57° '57'- 1628 i 1632 .633 ,634 1635 '637 1; ,698 1699 1700 1703 1704 1705 1764 1765 1766 1767 ■ 768 ,769 1770 1772 '773 1831 .S32 IS33 1834 ■835 1837 1838 '839 1840 1841 1900 1901 1902 1903 ■905 ,906 1907 .908 1909 1970 '97' 1972 Z\ .976 1978 '979 19S0 2040 2041 2043 2045 2046 2047 2048 2050 2051 2111 2113 2114 2115 2116 2117 2119 20 21 22 23 24 25 26 27 28 29 1187 J 190 1191 1 192 1246 .248 1249 1250 1251 1252 J253 1254 -^ 1311 13.2 1313 >3H 1315 13.6 1317 1318 1319 1320 ■375 .376 ■377 i 1384 ■385 1440 144 1 ■443 ■444 •ill ■447 ,448 '449 1450 .506 1507 IS08 1509 1510 1511 ■5'3 1514 ]l\l 1572 '573 1574 "575 if 1639 1640 1 642 1644 1645 1647 '.649 .706 1707 1708 1709 1714 \]]l "774 "775 1776 "777 1778 17S0 .781 1782 '7S3 1842 1843 •ill .847 1848 1S49 I852 '853 1911 19.3 1914 1915 19.6 1917 .918 .920 1921 1922 .98. 1983 1984 •$i 1987 1988 '^9° 1992 2052 2053 2054 2056 2057 2058 2059 2060 2061 206, 2123 2125 2126 IWl 2129 2132 2133 2134 30 31 3-2 33 34 35 3(i 37 3« 39 40 41 42 43 44 45 46 47 48 49 1193 1 194 ■>9| 1196 119S 1199 J^57 '^ 1261 .262 1264 nil 1267 1322 1324 1325 1326 1327 1329 1330 .331 1332 1333 1334 ■335 1336 133S 1339 1340 1341 1 341 .386 .388 1389 1390 1392 ■393 ■394 ■395 1396 145 1 ■45^- '453 '455 1456 ::^^ .46. ■5^7 1518 1519 1520 1521 1522 1524 \l:l ■527 :i .586 ,588 '5«9 '59° 1591 .592 ■593 .65, r n\l ii 1724 1727 1785 1787 17S9 '79° "79' 1792 "793 '794 "795 ,854 1855 Z •it 1861 1862 .863 ,864 1923 1924 1925 1927 .928 1929 ■93° 1931 1932 ■934 ■993 ■994 "995 ■99- 199S '999 2C04 2064 2065 2066 2067 2069 2070 2073 2075 2135 2139 214c 2141 1208 1209 .268 1271 1272 1273 B 1277 ■397 ■398 '399 1400 140 1 1402 1403 1405 1406 1407 ■462 ,463 1464 .465 .467 1468 .469 1470 ;:72 1528 1529 1530 •53' 1532 "533 1535 1536 \^ '594 '598 '599 1600 .601 1602 1603 .604 1661 1662 .663 1664 1666 1667 1668 ,669 1670 .67. 1729 1730 '73' '732 '733 '734 ■735 1736 1738 "799 1801 1802 1806 .807 1865 1866 1868 .869 1870 i87^ ■ 872 1873 1875 ,876 ■935 2°°5 1936 2C06 '937 2007 1938 2008 '939 2°'° 1941 I2011 1942 2012 '943 2°'3 '944 ^°'4 194512015 2076 2078 2079 2082 2083 2084 2085 2086 2147 2,49 2.50 2151 2152 2153 \?^ 50 5! 52 .13 54 55 56 57 5« 59 1224 1278 1281 .283 1284 1285 1286 1287 .288 >343 1344 ■345 1346 ■347 1348 1349 1350 1352 ■353 1408 1409 1410 .41, 14,2 .413 .414 141 5 .4.6 .4.8 '47 5 ,476 ■477 '479 1480 1481 .482 ,483 1539 1540 1541 1542 ■543 ■544 1546 ■547 ■548 '549 1605 1608 .609 1610 1611 1612 16,3 .6,4 16,5 1672 'III 1676 .677 167S 1679 1680 16S1 "74° 1741 1742 '743 ■744 1746 ■747 1748 ■749 1S08 ;8°9 1S17 1818 .S77 187S 1879 18S0 18S1 1883 ,885 1886 1887 1946 1948 '949 '95° '95' 1952 '953 ■955 .956 '957 2017 2018 2019 2020 2024 2027 20SS 20S9 2090 20QI 2092 2094 \7^ 2097 2098 III', 2162 vs 2165 2167 1168 2.69 2>70 19" 20- •jr 1 22^ 23° 21" 25° 26' 2K° 1 29° j 30' 1 31" ! 32° 33^ 535 .AlERiniONAL PARTS LATITUDE 34° 1 36° J- 37° Jj!!!lLf!: 40= ] 41° 42° 43° 44° 1 45° 1 4C° 3203 4«" 1 3292 t:;:!":;;^ 23 iS -393 2+68 1 254 262 2702 2782 '~Mj 2946 3030 1 311 2173 2^4^ 2319 = 394 2470,2546 2624 1 2703 278 2864 2947 303 3117I 3204 1 3293 2 2174; 2247 2320 239s 2471 1254a 2625 2704 27S4I2866 2949 303 31. 32c6 3295 3 2175 2248 2396 2472 2545 7627 2706 2786 2867 2950 3034 312c 3207 3296 i 2176 2249 2323 2398 2473 2550 2628 2707 2787 2869 295 3036 312 3209 3298 2178 2250 2324 2399 2475 255' 2629 2708 27S8 2870 2953 3037 3123 3299 (. 2179 2252 2325 2400 2476 2553 263- 2710 2790 2871 2954 303S 3124 3212 3301 7 2IS0 2253 2327 2401 2477 2554 2711 2791 2S73 2956 304c 3126 3213 3302 H 2I8I "54 2403 2478 2555 2633 2712 2792 2874 2957 304, 3127 3214 33°3 'J 10 2IS2 21S4 ^255 2257 _2329 2330 ^404 24S0 2481 2557 2634 ,2714 2794 28^ 2958 3°43 1111 3305 2405 2558 2715 2795 2960 304; 3130 5217 3306 1 1 2! 86 2258 3^332 2406 2482 2559 2637 2716 2797 2878 296, 3046 3131 3219 3308 12 2259 2333 2408 2484 2560 2638 2718 2798 2S80 2963 3°47 3'33 3220 3309 13 2187 2260 2334 2409 24S5 2562 2640 2719 2799 2881 2964 3048 3 "34 3222 33" U 2188 2261 2335 24:0 24S6 2563 264, 2720 2801 2882 2965 3050 3.36 3223 3312 13 2190 "e^ ^337 241 1 2487 2564 2642 2722 2S02 2884 2967 3051 3'37 3225 33'4 Ifi 2191 2338 2413 2489 2566 2644 2723 2803 2885 2968 3°53 3139 3226 33'6 17 2192 2I4 ^339 2414 2490 2567 2645 2724 2805 28S6 2970 3054 3140 3228 3317 18 2193 2266 2340 2415 2491 2568 2646 2726 2S06 2888 2971 3055 3142 1 3229 33'9 19 20 2194 2196 2268 2341 24.6 ilii 2569 2648 2727 2807 2889 2972 3H3I323I 3320 1I6F »343 2418 »494 2571 2649 2728 2809 289. 2974 30581 3144 13232 3322 21 2197 2270 ^344 2419 1 2495 2572 2650 2729 2892 2975 3060 3146,3234 3321 22 2198 2271 ^345 2420 2496 2573 2631 2731 2811 2S93 2976 306, 3'47i323?l3325l 23 2199 2272 2346 2422 2498 2575 2653 2732 2S.3 2895 2978 3063 3 '49 3237,3326 24 2200 2274 2348 2423 2499 2576 2654 2733 28.4 2896 2979 3064 3150 3238 3328I 25 2202 2275 ^349 2424 2500 2577 2655 2735 2815 289' 2981 3065 3152 3240 3329 2fl 2203 2276 2350 2425 2501 2578 2657 2736 2817 2899 29S2 3067 3'53 3241 333' 27 2204 2277 2351 2427 2503 2580 2658 2737 2818 2900 2983 3068 3'55 3242 3332 28 2205 2279 »353 2428 2504 258. 2659 2739 2820 2902 2985 3070 3156 3244 3334 2!) 30 2207 2280 ilii a4l9_ 2505 25?1 2661 2 "4° 2S21 2903 2986 307, 3245 Mil 3337 2281 2355 2430 »5o6 2584 2662 2742 2822 2904 29S8 3073 Ti?9"^ 3247 31 22C9 2282 2356 2432 1 2508 1^1 2663 2743 2824 2906 298.; 3°74 3,60 3248 3338 32 2283 2358 243? 2509 2665 2744 2825 2907 2991 3075 3162 3250 3340 33 22 I I 2285 ^3 59 2434 2510 258S 2666 2746 2826 290S 2992 3077 3.63 325' 334' 34 2213 2286 2360 2435 2512 2589 2667 2747 2828 2910 2993 3078 3165 3253 3343 35 2214 22S7 236. 2437 2513 2590 2669 2748 2829 2911 2995 3080 3166 3254 3344 36 2215 2288 2363 2438 2514 2591 2670 2750 2830 2913 2996 3081 3256 3346 37 2216 2290 2364 2439 2515 2593 2671 275' 2832 2914 2998 3083 3169 3257133471 38 2217 2291 2365 2440 2517 2594 2673 2752 2833 2915 2999 3084 3171 3259 3349 3'J 40 2219 2292 2366 -442 25.8 2595 2674 2754 2834 2917 3000 3172 3260 3350 2220 2293 1168- 2443 2519 2597 2675 2755 2836 29.8 3002 3087 3173 3262 3352 41 2221 2295 2369 2444 2521 2598 2676 2756 2837 2919 3003 3o88|3'75 3263:33531 42 2222 2296 2370 2445 2522 2599 267S 2-58 1 2839 2921 3005 3090 3176,32651 335? 43 2224 229- 237" 2447 2523 2601 2679 2759 2840 2922 3006 3091 3'78 3266 1 3356 44 2225 2298 2373 244!i 2524 2602 2680 2760 284. 2924 3007 3093 3179 3268 3358 4ft 2226 2299 2374 2449 2526 2603 2682 2762 2843 2925 3009 3094 3269 3359 4H 2227 230, 2375 2451 2527 2604 2683 2763 2844 2926 3010 3095 3182 3271 3361 47 222S 2302 2376 2452 2528 2606 2684 2764 2845 2928 3012 3C97 3.84 3272 3362 48 2230 2303 2378 2453 2530 2607 26S6 2766 2847 2929 3°'3 3098 3185 3274 3364 49 ifll,ll£i 1379. '454.2531 1 2608 2687 2767 2848 293. 3014 3'°o l!l7,i27lL Oil 50 2232 23061 2380 2456 2532 2610 2688 I76T 2849 2932 ^^ 3101 3188 3277 3367 51 2233 2307 238. 2457 2533 2690 2770 285, 2933 3017 3103 3190 3278 336S 52 2235 2308 2383 2458 2535 2612 2691 277> 2852 2935 3019 3104 3191 3280 3370 33 2236 2309 238412459 2536 26i4 2692 2772 2854 2936 3020 3105 3192 328: 3371 54 2237 2311 2385 j 246. 2537 26.5 2694 2774 2855 2937 3021 3107 3 '94 3283 3373 35 2238 2312 2 3 86 1 2462 2538 2616 2695 2775 285612939 3023 3.08 3'95 3284,3374 5« 2239 isn 238812463; 2540 26.7 2696 2—6 2858 2940 1 3024 3110 3 '97 3286 3376 57 2241 2514 2389 2464 2541 26,9 2698 2778 2859 2942 3026 3111 3198 3287 3378 58 2242 23.6 2390 2466 2542 1 2620 2699 277y 2860 2943 3027 3i'3 3200 3289 3379 V.I 2243 2317 2391 12467! 2 544 1 262. 2700 2-80 2862 2944 3029 3 1 14 3201 3290 1 3381 ■^ 35" 3H' 1 37' ' 3B° j 30- 1 10" 41" 42" i.r 44- 45" 46" -|— TABLE 6 .- MERIDIONAL PARTS LATITUDE 41)' 1 50^ 1 51° 52° 1 53° 1 54° 55° 5G° 57° 58° 1 59° 60° fil° 1 62° C3° 33?^ 3474 3569 3665 3764 3865 3968 4°74 4.83 4294 1 4409 4517 4649 14775 4905 1 ilH 3476 3570 3667 3765 3S66 3970 4076 41S4 4296 4411 4519 4651 4777 49° 7 2 33**5 3478 357^ 366S 3767 3S68 3971 4077 41S6 4298 44'3 453' 4653 4779 4909 3 3387 3479 3574 3670 3769 3870 3973 4079 4188 43C0 44'5 4533 4655 4781 4912 4 3388 348. 3575 3672 3770 387. 3975 4081 4190 4302 44'7 4535 4657 4784 49 '4 5 3390 3482 3577 3673 377^ 3873 3977 4083 4192 43C4 4419 4537 4660 4786 4916 6 339" 34S4 3578 3675 3774 3875 3978 4085 4194 4306 4421 4539 4662 47S8 49 '8 7 3 393 3485 3580 3677 3775 3877 3980 4086 4'95 4308 44^3 454' 4664 4790 4920 H 339+ 3487 3582 3678 3777 3878 39S2 40S8 4'97 4309 44^5 4543 4666 4791 4913 !) 3396 3488 3583 3680 3779 3880 39S4 4090 4'99 43" 4427 4545 4668 4794 491 > lo 3397 3490 3585 3681 3780 3882 1 3985 4092 4201 43'3 4429 4547 ' +67° 4796 4917 11 3399 349^ 3586 3683 3782 3883 3987 4094 4203 4315 443' 4549 4672 479S 49:9 12 3400 3493 3588 36S5 37S4 3885 3989 4095 4205 4317 4433 455' 4674 4801 493' 13 3402 3495 3590 3686 3785 3887 399' 4097 4207 4319 4434 4553 4676 4803 4934 14 3403 3496 359' 3688 37S7 3889 3992 4099 4208 4321 4436 4555 46-8 4805 4936 15 3405 3498 3593 3690 3789 3890 3994 4210 4323 4438 4557 46S0 1 4S07 4938 16 3407 3499 3594 3691 3790 3892 3996 4103 4212 43^5 4440 4559 4682 4S09 494° 17 340S 3501 3596 3693 3792 3S94 3998 4104 4214 43^7 4442 4562 4684 4S1. 4943 \H 3410 3503 3598 3695 3794 3895 3999 4106 4216 4328 4444 4564 4687 48.4 4945 19 34.1 3504 3 599 3696 3795 3897 4001 4108 4218 4330 4446 4566 46S9 4S.6 l?il 4949 •-'U 3413 3506 3601 3698 3797 3899 4003 4110 4220 4332 4448 4568 4691 4S18 21 34>4 3507 3602 3699 3799 3901 4005 4112 4221 4334 445° 4570 4693 4820 495' 22 34.6 3509 3604 3701 3800 3902 4006 4223 4336 445^ 4571 4695 4822 4954 23 3417 3510 3606 3703 3S02 3904 400S 4115 4225 4338 4454 4574 4697 4824 4956 24 3419 3S'2 3607 3704 3804 3906 4010 4117 4227 4340 4456 4576 4699 4S26 495S 25 3410 35'4 3609 3706 3806 3907 4012 4119 4229 4342 4458 4578 479' 4829 4960 26 34Z2 35'5 36,0 3708 3807 3909 4014 4231 4344 4460 4580 4703 4S31 4963 27 34^3 35'7 36.2 3709 3S09 39" 4015 4122 4232 4346 4462 4582 47°5 4S33 4965 28 34^5 351S 36,4 37" 38,1 39'3 4017 4124 4^34 4347 4464 4584 4707 4835 4967 29 30 3427 3520 36,5 37'3 3812 39-4 40'9 4126 423^ 4349 14466 4586 47'" 1131 4969 34zS 13511 3617 3714 3814 3916 4021 423S 435' 4468 45S8 4712 4839 4971 31 3430! 35^3 36. S 37.6 38,6 39.8 4022 4130 4240 4353 4470 459° 4714 4842 4974 32 343' 35^5 3620 37'7 381713919 4024 '4132 4242 4355 4471 4592 47i6 4844 4976 33 3433 3526 3622 37'9 3S19 3921 4026 4133 4244 4357 44 '4 4594 4718 4846 4978 34 3434 3528 3623 3721 3S2. 3923 4028 4135 4246 4359 4476 4596 4720 484S 498. 35 3436 35^9 3625 3722 3822 3915 4029 4137 4^47 436: 4478 4598 4722 4850 4983 36 3437 353' 3626 3724 3824 3926 4031 4139 4249 4363 4480 4600 4724 4S51 4985 37 3439 353^ 3628 3726 3826 3928 4°33 4141 4251 4365 4482 ' 46°2 4726 4855 49S7 38 3440 3534 3630 3727 3S27 3930 4035 4142 4253 43^7 4484 4604 4728 4857 499° 39 3443 3536 3631 3729 3829 393^ 4037 4 '44 4^55 4369. 4486 4606 4859 4991 3537 3633 373' 383. 3933 1 4038 4,46 4257 4370 4488 4608 4733 486. 4994 41 3445 3539 3634 373^ 3832 3935 4040 4.48 4^59 4371 449° 46,0 4735 4863149961 42 3447 3540 3636 3734 3834 3937 4042 4150 4260 4374 4492 4612 4737 4865 1 49991 43 3448 3542 3638 3736 3836 3938 4044 4152 4262 4376 4494 46.4 4739 4S68 5001 44 345° 3543 3639 1 3737 3838 3940 4045 4'53 4264 4378 4495 4616 4741 4870 5003 45 345' 3545 364. 3739 3S39 3942 4047 4'55 4266 4380 4497 46.8 4743 4872 5005 46 3453 3547 3643 374' 384. 3944 4049 4'57 4268 4382 4499 4620 4745 4874 5C08 47 3454 3644 374^ 3S43 3945 4051 4'59 4270 4384 4501 4623 4747 4876 5010 48 3456 3550 3646 3744 3844 3947 4052 4161 4272 4386 4503 4625 475° 48:9 50 r 2 4!) 3457 355' 3647 374'' 3747 3846 3949 395' 4054 4162 4--74I 4388 4505 1 4627 14751 4SS1 50.4 3459 3553 3649 3848 1^ 4164 4175 439° 45°7 4629 4754 4883150,7 51 3460 3555 365. 37^<- 3849 3952 4058 4.66 4^-77 4391 4509 463, 4756 48S5 50:9 52 3462 3556 3652 •■ 50 385' 3954 4c6o 4168 4^79 4394 45" 4633 4758 4SS7 5°!' 53 3464 3558 3654 i-75= 3853 3956 406, 4170 42X1 4396 45'3 4635 476c 4890 5023 54 346s 3559 3655 3754 3854 3958 4063 14172 4283 4398 4515 4637 4762 4892 502S 55 3467 3561 3657 3755 3856 3959 4065 4173 42S5 4399 45'7 4639 4764 4894 15028 5(; 3468 35621 3659 3757 3858 3961 4C67 4.75 42S7 4401 45'9 4641 4766 4896 503c £7 3470 3564 1 3660 3759 3860 3963 4069 4177 42S9 44° 3 4521 4643 4769 4S98 5°33 5li 5471 3566 3662 3760 3S6, 3964 4070 4' 79 4-9' 4405 4513 4645 477' 4901 5035 1.9 347 3 3567 3664 3762 3863 3966 40-2 4'8. 4292 4407 4515 4647 4773 4903 50;- liT 50= 51° V 53° 54° j 55° 1 5(i° il 58° 59° 60° 6.°|62°| 63' T/M'.I.E G 537 AIKRIDIOXAL PARTS LATITUDE '|-«.o Ki' Cfio 1 67° 1 68= 69° 1 70° 1 71° 72° 73° 74° 1 75° yiT' 77" 1 78' 5°39 5'79 53»4 5474 563, 5795 5966 6,46 6335 6534 6746 6970 7210 746717745 5042 5.81 5326 5477 563J 5797 5969 6 '49 6338 6538 6749 6974 721417472 7749 2 5044 5.84 5328 5479 5636 5S00 5972 6.52 634. 654. 6753 6978 72.8 I 7476 17754 3 5046 5.86 533' 5482 5639 5803 5975 6.55 6345 6545 6757 6982 7222 7481 7759 4 5049 5.8S 5333 5484 5642 5SC6 5978 6158 6348 6548 6760 69S6 7227 7485 7764 o 5051 5191 5336 5487 5644 58=9 5981 6161 635. 6552 6764 6990 723. 749° 7769 6 5=53 5'93 5338 5489 564/ 58,. 59% 6i64|fi354 6555 6768 6994 7*35 7494l7i.'-i 7 5°55 5195 5341 549^ 5650 58.4 5986 5,67 6358 655X 67-1 6997 7239 7498 7778 fli ?ot8 «jo8 5343 5495 5652 58,7 5989 6.70 636. 6562 6775 700. 7*43 750i 7783 9 5060 52CO 5346 5497 Jhl 5820 5992 ^■7316364 6565 6779 7C05 7247 75=7 7788 7793 IT 5062 5203 5348 5500 5658 5823 5995 6.7716367 6569 6782 70c 9 7*5* 75'* 11 ,065 5205 SJ5' 5502 j66o 5825 5998 61X0 637. 6572 6786 70.3 7256 75.6 7798 12U06- 5207 5353 55=5 5663 5828 6coi 6.83163:4 65-6 6790 7017 7260 75*' 7803 13 1 5o6oi?2io 535« 55=7 5666 5831 60G4 6.S6;6377 6579 6793 7C2. 7*64 75*5 78cS U W7' 5212 5358 5510 5668 5834 6C07 6. 89 63S0 6583 6797 7025 7268 753° 7813 IS 5074 5214 536. 55'3 567. 5837 6010 6,92 63?4 65S6 68c. 7029 7273 7535 78.7 IC 5076 5217 5363 55'5 5674 5839 60.3 6195 6387 6590 6804 7=33 7277 7539 7822 17 5°7S 5219 5366 55.8 5676 5S42 6016 6,98 6390 6593 6808 7037 728. 7544 7827 IK hcg. 5222 536S 5520 5679 5845 6019 620. 6394 6597 68.2 7=4' 72s 5 7548 7832 19 5C83 5224 537> 55^3 5682 5848 6022 6205 6397 6600 6815 1 7=45 7289 7553 7837 2..|so85 5226 5373 5526 5685 585. 6025 6zc8 64CO 6603 68.9 7=48 7294 7557 784* 21 5088 5229 5376 5528 5687 5854 6c2S 621 1 6403 66c7 6823 7052 7298 7562 7847 22 5090 5231 5378 553' 5690 5856 603. 62.4 6407 6610 6826 7056 7302 7566 7852 23 5=9- 5^34 53S0 5533 5693 5859 6034 6217 64.0 66,4 6850 7060 73=6 757' 7857 24 5°95 5236 5383 5536 5695 5862 6037 6220 64,3 66.7 6834 7064 73" 7576 7862 25 5=97 5238 5385 5539 5698 5865 6c40|6223 64.7 662. 6X38 7c68 73'5 758c 7867 26 5=99 5241 5388 554' 5701 5868 6=43 6226 6420 6624 684, -072 73'9 7585 7872 27 5102 5243 5390 5544 57=4 5871 6046 6230 6423 6628 6845 7076 73*3 7589 7877 2H'S>"4 5246 5393 5546 57=6 1 5874 6049 6233 6427 663. 6S49 7c8o 73*8 7594 7SS2 29 5.C6 5248 5395 5549 57=9:5876 6052 6236 6430 6635 6853 7=84 733* 7599 7887 W ^T^ 5250 5398 555» 5712 5879 6055 6239 6433 6639 6856 70S8 7336 76=3 789* 31 5111 5^53 5401 5554 57'5 6058 6242 6437 6642 6860 7C92 734' 7608 7897 32 5»'3 5-55 5403 5557 57'7 58851606. 6245 6440 6646 6864 7=96 7345 76.2 79=* 33 5"5 5258 5406 5559 5720 5888 6064 6249 6443 6649 6868 7 ICO 7349 7617 79=7 34 5. .8 526c 5408 5562 5723 5891 6067 6252 j 6447 6653 687. 7.C4 7353 7622 79.2 33 5120 5263! 541 1 5565 5725 5894 607c 6255! 6450 6656 6875|7'=8 7358 7626 79.7 1 3(! 5122 5265 5413 5567 5728 5896 6073 6258 6453 6660 6879 |7"2 7362 763, 79** 37 5125 5267 S4'6 5570 573' 5899 6076 626, 6457 6663 6883 7..6I7366 7636 79*7 38 5127 5270 5418 5573 5734 59C2 6079 6264 6460 6667 6886 712c 7371 17640 793* 3!) 5'^9 5272 54i> 15575 J736 59=5 60S2 6268 6463 6670 6890 7.24 7375 1-645 7937 40 S'3» 527? 54*3 5578 5739 5908 1 6085 627, -6^7 6674 6894 7.28 7379 7650 7942 41 5'34 15^77 5426 5580 5742 £,..|6c88 6274 647c 6677 6898 7132 7384 7654 7948 42 5.36 5280 5420 55'>3 15745 59'4|b=9> 6277 1 6473 I 668. 690117136 7388 -659 7953 43 5'39 528Z 543. 5586 1 5747 59i7|6c94 628D 64-716685 6905 7.40 7392 7664 7958 44 5141 5284 5433 5588 57 5'' 59iy 6097 62S3 6480 1 6688 69=9 7-45 7397 7668 7963 45 5'43 5^S7 5436 559' 5753 5922 6.00 62X7 64S3 i 6692 69,3 7149 740. 7673 '79t8 4C 5146 52S9 5438 f594 5756 5925 1 6103 6290 6487 1 6695 69,7 7>53 74=6 7678,7973 47 5148 5292 544' 5596 5758 59281610616293 6490 6699 6920 7'57 7410 76X3 7978 4B 5'5> S»94 5443 5=99 576. 593' 61C9 6296 6494, 6702 6924 716. 74 '4 768- '7983 40,5-^3 .5121 5^99 5446 560. 5764 5934 h2i 6299 ,649716706 6928 21^ 74.9 ^^9*17989 5448 5604 5767 5937 6,,; 63=3 65== 67.0 [6932 7.69 74*3 7697(7994 51 5.58 5301 545' 5607 5770 5940 6ii8 6306 6504 67.3 6936 7'73 74*7 77=2 1 7999 521 5160 '53=4 5454 <6io 577' 5943 6121 6309 6507 67.7 6940 7177 743* 7706. 8cc4 53 5.62 5306 545fi ■56,2 5775 5946 6124 63.2 65,, 6720 6943 7.81 7436 77"i8cc9 54 5.65 5309 5459 56,5 5778 5948 6.27 63.5 65.4 6724 6947 7185 744' 7716 80.4 65 5.67 53" 5461 56.7 578' 595' 6,30 63.9 65.7 6728 695. 7.89 7445 772. 8.2c 5B 5.69 53'4 5464 5620 5783 5954 6.33 6322 1652. 67;. 6955 7>94 7449 7725 8025 57 5'72 53.6 5466 5623 5786 5957 6,36 63=5;6524'6735 6959 7-98 7454 773° 8050 :h 5>74 53'9 5469 5625 5789 j 5960 6140 6328 652816738 6963 7458 7735 8=35 51) 5.76 53»> 5471 5628 579» 15963 6,43 6332] 653.1 6742 6966 7206 7463 7740 8040 ' «..' BS" HBO 1 ,r 68" 1 69° liT 71° 1 72° 1 73° 74° 1 75° 76° 77" Tr" TABLE 6 1 MERIDIONAL PARTS LATITUDE ' i'.f 1 50° 1 5P 52° 1 53° 1 54° 55° 5G° 57° 58° 1 59° 60° «1° 1 62^ 03° 3381 3474 3569 3665 3764I3S65 3968 4074 4183 4294 1 4409 45 = 7 4649 14775 4 9°5 1 iiH 3476 3570 3667 3765 3866 3970 4076 4. 84 4296 44 1 1 45=9 465. 4777 49° 7 2 33^5 3478 357^ 3668 3767 3868 3971 4°77 4.S6 4298 44'3 453' 4653 47:'9 4909 3 3387 3479 3574 3670 3769 3870 3973 4079 4188 43C0 44'5 4533 4655 478. 49' = 4 3388 3481 3575 3672 3770 387. 3975 4081 4190 4302 44'7 4535 4657 4784 49 '4 5 339° 3482 3577 3673 377^ 3873 3977 4083 4192 4304 4419 4537 4660 49'6 6 339" 3484 3578 3675 3774 3875 397S 4085 4'94 4306 4421 4539 4662 4788 49'8 7 3393 3485 3580 3677 3775 3877 39S0 4086 4'95 4308 44=3 454' 4664 4790 4920 8 3 39+ 34S7 3582 3678 3777 3878 3982 40S8 4'97 4309 44=5 4543 4666 479= 49=3 <) 3396 3488 3583 3680 3779 3S80 3984 4°9C 4199 43" 44=7 4545 4668 4794 49=5 To 3397 3490 3585 368. 3780 38S2I3985 4092 4201 4313 44=9 4547 ' 4670 4796 49=7 II 3399 349^ 3586 3683 3782 3883 3987 4094 4203 43'5 443' 4549 467 = 479S 49=9 12 3400 3493 3588 36S5 3784 3885 39S9 4095 4205 43'7 4433 455' 4674 4801 493' 13 3402 3495 3590 3686 3785 38S7 399' 4097 4207 43'9 4434 4553 4676 4803 4934 U 3403 3496 359' 3688 37S7 3889 3992 4099 4208 4321 4436 4555 4678 4805 4936 15 3405 3498 3593 3690 3789 3S90 3994 4101 4210 43^3 443S 4557 46S0 4S07 4938 16 3+07 3499 3594 3691 3790 3S92 3996 4103 4212 43 = 5 444° 4559 46S2 4809 494° 17 340S 3501 3596 3693 3792 3S94 4104 4214 43 = 7 444= 4562 4684 48.1 4943 IX 3410 3503 3598 3695 3794 3895 3999 4.06 4216 4328 4444 4564 4687 48 14 4945 19 3411 35°4 3599 3696 3795 3897 4001 4.08 4^18 4330 4446 4566 46S9 48,6 4949 ^ 34'3 3506 3601 3698 3797 3899 4003 4110 4220 433 = 4448 4568 469: 48,8 21 341 + 3507 3602 3699 3799 3901 4005 4112 4221 4334 445° 4570 4693 4820 495' 22 34.6 3509 3604 3701 3800 3902 4006 4"3 4223 4336 445= 457= 4695 4822 4954 23 34'7 3510 3606 3703 3S02 3904 4008 4115 4225 4338 4454 4574 4697 48=4 4956 24 3419 3512 3607 3704 3804 3906 4010 4"7 4227 4340 4456 4576 4699 4S26 495S 25 3420 35'4 3609 3706 3806 3907 4012 4"9 4229 434= 445S 4578 479' 4829 4960 26 34Z1 35'5 36.0 3708 3807 3909 4014 4231 4344 4460 4580 4703 4S31 4963 27 34^3 3517 36,2 3709 3809 39" 4015 4122 4232 4346 4462 458= 47°5 4833 4965 20 34^5 35.S 36,4 37" 381. 3913 4017 4124 4234 4347 4464 4584 4707 4S35 4967 2!J 30 34^7 35ZO 36,5 37'3 38. 2 39'4 4019 4126 4236 4349 4466 4586 471° 4837 4969 34ZSJ35I1 3617 3714 3814 39.6 4021 4'i8 4238 435' 4468 4588 47' = 4839 497= 31 3430! 35^3 361S 37.6 38.6 4022 4130 4240 4353 4470 459° 47 '4 4842 4974 32 343' 35^5 3620 37'7 381713919 4024I413Z 4242 4355 447 = 459= 4716 4844 4976 33 3433 3526 3622 37'9 3819 39^' 4026 4133 4244 4357 44 '4 4594 4718 4846 4978 34 3434 3523 3623 3721 3821 39^3 4028 4135 4246 4359 44V6 4596 4720 4848 498. 35 3436 3529 3625 3722 3822 39^5 4029 4'37 4247 436, 447S 4598 47= = 4850 4983 36 3437 353' 3626 3724 3824 3926 4031 4'39 4249 4363 4480 4600 47=4 485= 4985 37 3439 353^ 3628 3726 3826 3918 4033 4141 4251 4365 4482 '4602 47=6 4855 49S7 38 3440 3534 3630 3727 3827 3930 4035 4142 4^53 4367 4484 1 4604 47=8 4857 4990 3!t •111 344^ 3443 3536 363. 3729 3829 393^ 4037 4144 4255 4369 44S6 4606 473' 4859 499= 3537 3633 373' 383. 393314038 ^^ 4^57 4370 4488 4608 4733 486. 4994 41 3445 3539 3634 373J 3832 3935 4040 4.48 4259 437= 449° 46.0 473 5 4863,49961 42 3447 3540 3636 3734 3834 3937 4042 4150 4260 4374 449= 46,2 4737 4865 1 4999 1 43 3448 3542 3638 3736 3836 393S 4044 4152 4262 4376 4494 4614 4739 4S68 5001 44 3450 3 543 3639 1 3737 3838 3940 4045 4'53 4264 4378 4495 46.6 474' 4870 5003 45 345' 3545 364. 3739 3839 3942 4°47 4'55 4266 4380 4497 46.8 4743 4872 5005 46 3453 3547 3643 374" 384. 3944 4049 4'57 4268 4382 4499 4620 4745 4S74 5C08 4/ 3454 3548 3644 374^ 3843 3945 405, 4>59 4270 4384 45°' 4623 4747 4876 5010 4« 3456 3550 3646 3744 3844 3947 4052 4.61 4272 4386 4503 4625 475° 4879 5012 4!) 3457 355' 3647 iZ4l 3846 3949 4054 4162 4274.1 4388 4505146271475= 4S8. 50.4 50 3459 3553 3649 3747 3848 395' -^ 4.64 4275 439° 45°7 462914754 4883150.7 51 3460 3555 3651 37-1 <- 3849 3952 4058 4166 4=77 439= 4509 4631I4756 4S85 5019 52 3462 3556 3652 - JO 3851 3954 4c6o 4168 4 = 79 4394 45" 4633 1 4758 4SS7 5°=' 53 3464 3558 3654 i-75- 3853 3956 406, 4170 4281 4396 45'3 4635 1 4760 489° 5°=3 54 3465 3559 3655 3754 3854 3958 4063 4172 42S3 4398 45'5 4637 4762 4892,5026 55 3467 3561 1 3657 3755 3856 3959 4065 4'73 42S5 4399 45'7 4639 4764 4894150=8 5ti 3468 35621 3659 3757 3858 3961 4067 4'75 4287 440' 45'9 464, 4766 4896 503c tT 3470 356413660 3759 3860 3963 4069 4'77 4289 4403 45=' 4643 4769 4898 5°33 5(i 5471 3566 3662 3-60 386,13964 4070 4'79 4291 4405 45=3 4645 477' 4901 5035 .)« 3473 3567 3664 3762 3S6; 3966 407. 4181 4292 4407 45 = 5 4647 4773 49° 3 5°;- 4!»- 50'' or 52° 53° 54° j 55° 5(i° 57' 58° 59° 60° 61° 1 62° 63' TAI'.I.K G 537 AIKKIDIONAL PARTS 1 LATITUDE ' ~\ ' I M" fia» ; CC° 1 67° 08° 00° 70° 1 71° 72° 73° 74° 7r,° 70° ]ir' V 5039 5'79 5324 5474 563, 5795 5966 6.46 6335 6534 6746 6970 7210 7467 7745 1 5042 51S. 5326 5477 5633 5797 5969 6.49 6338 6538 6749 6974 72.41 7472 7749 2 5044 5.84 532S 5479 5636 5800 597= 6.52 63+. 654. 6753 697S 7218 I 7476 7754 3 5046 5186 533' 5482 5639 5803 5975 6.55 6345 6545 6757 6982 7222 7481 7759 4 5049 5. 88 5333 5484 5642 5SC6 5978 6.58 6348 6548 6760 6yS6 7227 74S5 7764 5 5051 5191 5336 5487 5644 58C9 598' 6.6. 635. 6552 6764 6990 72jl 7490 7769 6 5°53 5'93 533S 5489 5647 58.. 5<;^4 6.64 6354 6555 6768 6994 7235 7494 7.',M 7 5<'55 5195 5341 549- 5650 58.4 5986 5.67 6358 6558 677. 6997 7239 7498 7778 «i' wd uq8 5343 5495 5652 5817 5989 6,70 636. 6562 6775 7243 750s 7783 9 '5060 5200 5346 5497 56^5 5820 5992 6.73 6364 Mi 6779 7005 7247 2i°7 77S8 10 1 5062 5203 5348 5500 5658 5823 5995 6.77 6367 6569 67S2 70c 9 7252 7512 7793 11,5065 5205 5J5' 5502 3660 5825 5998 6.8c 637. 6572 6786 70.3 7256 75.6 7798 li ';o67 5207 5353 5 5° 5 5663 5828 6coi 6,83 63:4 6576 6790 7017 7260 7521 7803 13 1 5060; ?2IO 5356 55°7 5666 583. 6004 61S6 6377 6579 6793 702. 7264 7525 78cS U S071 5212 5358 5510 5668 5834 6007 6. 89 6 3 So 65S3 6797 7025 7268 7530 7813 lA 5°74 52.4 5561 55'3 567. 5837 60.0 6.92 63?4 65S6 680. 7029 7273 7S35 7817 IC 5076 5217 5363 55>5 5674 5839 60.3 6.95 63S7 6590 6804 7033 7277 7539 7822 17 507S 52,9 5366 5518 5676 5842 60.6 6.98 6390 6593 6808 7037 7281 7544 7827 IH 508, 5222 536S 55=0 5679 5845 60.9 620. 6394 6597 68.2 7041 7285 7548 7832 I!) 5CS3 5224 5371 55=3 5682 5848 6022 6205 6397 6600 6S15 7045 72S9 7553 7837 2^ 5085 5226 5373 5526 5685 585. "6025 6208 6^ 6603 68.9 7048 7294 7557 784* 21 5088 5229 5376 5528 5687 5854 6c28 621. 6403 6607 7052 7298 7562 7847 22 5090 5231 5378 553' 5690 5856 603. 62.4 6407 66.0 6S26 7056 7302 7566 7S52 23 5=9- SM4 53S0 5533 5693 5859 6034 6217 6+.0 66.4 6S30 7060 7306 7571 7857 24 5''95 5236 5383 5536 5695 5862 6037 6220 64.3 66.7 6S34 7064 73" 7576 7S62 2S 5^97 5238 5385 5539 5698 5S65 6040 1 6223 64.7 6621 6S38 7c68 73'5 7580 7867 26 5099 5241 5388 554' 5701 5868 6043 6226 6420 6624 6S4. 7072 73'9 7585 7872 27 5102 5^43 539° 5544 5704 5871 6046 6230 6423 6628 6845 7076 7323 7589 7877 2H'S'-4 5246 5393 5546 5706 5874 60+9 6=33 6427 663. 6849 7c8o 732S 7594 7SS2 29 5.06 5245 5395 5549 5709 5876 6052 6236 6430 6635 6853 7084 7332 7599 7887 789 = 3i7 77^ 5250 5398 555= 5712 5879 6055 6239 6433 6639 6856 70S8 7336 7603 31 5111 5^53 5401 5554 57'5 58S2 60CS 6242 6437 6642 6S60 7092 7341 7608 7897 32 S"3 5-55 5403 5557 57'7 5885 !6c6. 6245 6440 6646 6864 7096 7345 76.2 7902 33 5"5 5258 5406 5559 5720 58SS 6064 6249 6443 6649 6868 7 ICO 7349 76.7 7907 34 5118 526c 5408 5562 57=3 5S9. 6067 6252 j 6447 6653 687. 7.04 7622 7912 3.") 5120 5^6.3 541 1 5565 57=5 5S94 6070 6255 6450 6Cs6 6875 7.C8 7358 -6:6 79.71 3f. 5122 5265 54'3 5567 57=8 5S96 6073 625S 6453 6660 7. .2 7362 763. 7922 37 5'*5 5267 54.6 557° 573' 5899 6076 626. 6457 6663 6883 7..6J7366 7636 79=7 38 5127 5270 S4l8 5573 5734 5902 6079 6264 6460 6667 6886 7.20 737. 7640 7932 3!) 5129 527215421(5575 5736 5905 60R2 626S M3 6670 6S90 7.24 7375 7.28 7379 7645 2937. 40 513^15275 5423 5578 5739 5908 1 60S 5 6271 6467 6674 6894 7650 794= 41 5134 5^77 5426 5580 574= 59.i|6c88 6=74 6470 6677 6898 7.32 7384 7654 7948 42 5.36 s^So 5426 55"3| 5745 59.416091 6277 6473] 668. 690. 7.36 7388 7659 7953 43 5.3915282 543 > 5586 5747 59'-' 1 6094 6280 6477 6685 6905(7.40 7392 7664 7958 44 5141I5284 5433 5588 5750 59 ly 6097 6283 6480 66S8 6909 7'45 7397 7668 7963 4.5 5.43 5^S7 5436 559' 5753 5922 6.00 62S7 64S3 6692 69,3 7 '49 7401 7673 79t8 40 5146 5289 5438 5594 5756 5925 1 6103 6290 6487 6695 69,7 7153 7406 7678,7973 47 5148 5292 5441 5596 5758 59=8 6.06 1 6293 6490 6699 6920 7157 74 '0 7683 7978 4K 5151 5294 5443 5=99 576. 5931 6.09 . 6296 6494 6702 6924 7.6, 74 '4 768-I79S3 4»| 5^3:5^97 _5446 j6oz 5764 J2I± II2I 6299 6497 6706 6928 22h 74 '9 7692,7989 7697 1 7994 .-.0| 5155 5^99 544« 5604 5767 5937 bus -6^ 65C0" "6777 -6^ 7.69 7423 ftl SIS? 5301 545' 5607 5770 5940 6. .8 6306 6504 67.3 6936 7"73 7427 77C2 1 7999 52 1 5160 ■53<:4 5454 56.0 577' 5943 6.2. 6309 6507 67.7 6940 7177 7432 77c6 , 8cc4 ■.3 5,62 5306 5456 56,2 5775 5946 6312 65.. 6720 6943 7.8, 7436 77"i8cc9 .-.4 51651 5J09 54 59 56,5 5778 5948 6127 63,5 65,4 67=4 6947 7185 744' 77'6 80,4 fi.-i 5.67!53'> 546. 56.7 57«. 595' 6,30 63,9 65.7 6728 695, 7. 89 7445 7721 8.:c 5fi 5.69 5514 5464 5620 5783 5954 6.33 6322 652. 6731 6955 7'94 7449 7725 8025 A7 5171 5316 5466 5623 5786 5957 6.36 63=5 65=4 6735 6959 7.98 74 54 7730 80 30 m 5174 53'9 5469 5625 57S9 15960 6328 6528 1 6738 6963 7458 7735 S"3 5 .V.I 5.76I532. 547. 5628 579=15963 6I43 633 = 6531 [6742 _696^5_ 7206 7463 7740 8040 ' .H" 1 050 «BO r,r ! Bn° 1 fifl" 1^ 71° -^r^ 74° 75° -li^ 77" 78" TABLl- FOK FINDING THE DISTANCE OF AN OBJECT. BY TWO IlBAIilNOS AND Tllli DISTANCE llUN BETHKEN Til KM |1^ III Difference between the Course and the 1st Beariii-. 5|^ Points. Points. 2 2i 3 •a 4 4i a|.^ e\H 7 1 Vi H 84 « H U) 34 •00 4 ■IJ 1 5 r69|,-oo ..60 0-8S 1-4S 1 H .-.7 rfab li ^■5+ °'74 i-^"; rSs -S7 24.1 Ui """ 0-58 0-65 0-71 o-:7 0-83JO-90 0-97 11-03 i-ii .•.9|.-4. ■•55 '' ''^"1 tabu: 8 TRL'K DEI'KKSSION OI{ DISTANCE OK THE ! SEA HOKIZON 1 Heislit'DppJsquart Hei;^lit'].)e|i.'.Si|Uar Heisb<|Dep.|square(Dep.Sq.w.-e| II 1 ' :i2!i:i" 6i'l 372 12900 ' 121', 1464 .8,', 32761 Mo 1 4 :)4o:»' 62 1 384^ 131(13 .22 I 14884 182 33'24 )i(l 1 9 35 1:*' 63 3969 13397 .5129 183 33489 14 J 16 •MH\ 64 4C96 13615 12. '5376 .84 33S56 ■1>\ 2C 3740 65 4225 13036 125 .5625 '85 I 342»5 .•)!!( 36 3lf.w! 66 4356 14001 .26 .58-6 .86 1 34596 43 :t 49 3!)74| 67 4489 14202 .27 16,29 187 34969 i)ti (j 1 fc4 4(103; 68 4624 14502 .6384 .88 35344 71-7 8: 4213 j 69 476. 14737 .29 ,6641 .89 3572. HII a 1U7" -TT 100 4337 1 70 1 4900 14070 .30 169CO '9° 36100 III 44(il 7'i 504' 15197 ^ .7.6, .9. 3648, 127 '44 4.-«7 72 5184 15429 132 17424 192 36864 14U 169 47l« 73 5329 15004 133 17689 '93 37249 17:< .96 4(140 74 5476 15901 ■34 17956 '94 37636 l»» 22? 4970 75 5625 10139 135 18225 ■95 38025 226 [e 256 5112 76 5776 16300 136 18496 196 384.6 25 17 729 0700 87 7^69 19140 147! 2.609 207 1 42849 (;»4 784 C!I55 88 7744 19401 .48 2.904 208 43264 7-14 2, ; 84, 7012 89 7921 19664 149 2220, 209 436S1 797 1 3° 1 9c° 7172 '^ 8100 19930 150 22500 44.C0 H50 1 31 961 7332 .riT S281 20197 '5' 2280, 777 44521 906 32 1024 7402 92 8464 20405 '52 23,04 2.2 44944 «(;4 1 33 IC89 7650 93 8649 20736 153 23409 2.3 45369 1023 1 34 II56 7H24 94 8836 21008 '54 237.6 2.4 45796 I0«4 1 35 ,22, 7007 95 9025 21202 '55 24025 2'5 4622, 1147 36 '^96 (it 50 96 92.6 21558 156 24336 2,6 46656 1211 37 ,369 0330 97 9409 21830 157 24649 217 47089 127« 38 "444 0504 98 9604 22115 .58 24964 218 47524 134« 1 39 0070 99 9801 22397 '59 252S1 219 4796. 1410 1 40 i6co 0052 lOCCO 22080 ,60 256C0 48400 UH7 4' ibCi ImSJ loi I020I 22904 161 2592, "22T 4884. I5U1 45 .764 9210 IC2 IO4C4 23251 162 26244 222 49284 lafi 43 18+9 9303 103 .c6c9 23540! 163 26569 223 49729 I7I.< 44 1936 9577 IC4 10S16 23030 .64 26896 224 50,76 I7!)2 45 9700 105 11025 24121 165 27225 225 50625 1872 46 2U6 9951 ic6 1.236 24415 ,66 27556 226 5.076 1954 47 2209 10135 107 "449 24711 167 278S9 227 5'529 2(t31» 48 2304 10325 108 1 1664 25008 168 28224 228 5.98+ 2121 49 2401 10518 109 1188. 25307 .69 28,6. 229 52441 2212 50 2500 1 107121 iio| 121CO 25600 .7012S900 230_ 52900 2:joi I 5. 1 260. 1 1090H III ,2321 25911 ,T, 1 2024. 7TT67 23!>3 52 2704 II 105 112 12544 20215 172 29584 232 53824 24B.-. 53 2809 11304 ■'3 12769 20521 29929 233 54289 2581 54 1 2916 11500 114 12996 20829 30276 234 54756 2«77 55 ■ 3^15 11709 "5 13225 27139 30625 235 55225 277-> 56 , 3'3« 11M13 .16 13+56 27451 30976 236 55696 21170 57 3-49 12120 "7 13689 27704 31329 237 56,69 2977 58 3364 1232(1 iiS 13924 28079 3,684 238 56644 301)1 S9 348' 12530 119 14161 28390 '79 32041 239 57121 »ni(; 1 60 1 3600 12749 I20J I44CO 287 1 5 iSo 324CO 240 57600 1 '■77 354 5-3' 7-o8 5 8-84 io-6i 17 69 .9-46 21-23 23-00 2477 26-53 28-30 3<- 07 31-84 33-6. 35-38 37-15 38-92 42-46 44-23 46-00 47-76 4953 540 TABLE m INDEX TO MAMTIME POSITIONS. Adelaide Adtn.Gulf Admirrtlty Ids Adriatic Africa, North coabt I, iNorth-west coast „ West coast „ South coast Alacranes Alaska iitian Ids Almirante Ids Amazon River Americi, North { „ „ North coast „ Easr coast „ Wes. coast „ Gulf of Mexico America, South „ „ E st coast West coast Central Amsterdam Id Amur Hirer Antarctic Ocean Antigua Arabia Archipelago, Arctic „ Grecian „ Great Eastern •! Arctic Sea s Argentina Arru Ids Ascension Asia, North-east coast „ North co«t Asia Minor Auckland liles Austral Isles ,, North-Wfst coast .......... ,, \Vest coast „ South coast ,, East coast „ ^orth-east const l.-landsand Shoals East- \ ward of J Azores B Kaffin's fay Bahama 1 Is Balearic IsIth Bampton ihoal Banda Sea „ IJ» COLUMN 105 Bank's Land 142 15S 141 «3 106, 107 So I Si Bashee Ids 41-43 Tj 1 • a,j.„[. 46,47 160 3S, 39 56.57 do 62 Bermudas 41 Bcriiado Ids Bl.K-kSi-a 33. 34 "35 144 81.87 5S 94 164-166 109 I 10 143-153 Boothia Gulf Bourbon 149 153 175 1S2 Brazd 15S. 159 British Isles 164-10S 170-174 .74..75 C 176 ■75. 1/6 39.40 35.36 46.47 40.41 >6j ■"66^^ 169 157 53 Canaries Camlia Cape Colony 139-143 Cape Verdes 63-66 Si-99 141 144 f; iroliue Arciii[i> la"n 137, 13S 1S2 Caroline Id South 1' icilic 167 93 Celebes '. SS. Sg 174. 175 94 (' vl m So ■ ■■■. 57.58 117 170-172 71-75 67-71 34,35 121 99 China. South and Ka-i coists China Sea 100 102 Islands in 69 ■ 68 102 105 Cochin 75 loS, 109 109-11 1 112 Christmas Id., Indai, (lean Cockburn Id 58 143 ., I ' ■ Conneclicnt 151 Cook Ids 122 140 :53. 154 J2. 23 Corea 78 2^^, 93 94 Cozumel Cru/.cl Isles .60 58 TABLE 10 B^l ' IM)KX TO MAIUTIME l>O.SlTK)N'S | r COLUMN 154. 155 '63 '43 37 121 140 >5' 117 "7 174 37 117 1^3 2-4 7 6 158 44 125-127 120 91,92 9> .52. .5S 75 143 16,17 .8, 19 139 124 149 VJ 152 123, 124 95.96 141 3°. 3' '75 163, 164 43.44 .47. 148 n Hainan Id 71 ',i4 5« 5 sg 60 6f,6i to 11^, 161 169 '45 121 121 l!S2 59-63 55^58 49 I'J S, 9 9 9, 10 24. 25 .7%8 '55 '44 '39 76. 78 120 89,90 9' «'7 79.80 36 $ 124 79 145. '46 55 '35 '43 10 76 97 '59 117-119 127 82,84 CuniW-rland Ms Hawaiian Ms Heard Ids. D Hanger M ])avis Strait . . Hindustan, West coast Horn, Cape Hudson's Bay Hull Id Demerura IKninark I Ducie Id E Easter Id lev. CaDc \2u^^ Ecuador Indian Ocean Ids „ Islands oil- Madagascar Ionian Ids Eiivpt Eiiiabeth Id Ellicelds England, South co.,.t North coast „ West coast East coast n East coast F Fn-ro Ids „ South coast „ Eastcoa.st J Ealkland Iils Fiji Ids .lames K..ss Strait Flint Ids Flores „ Sea Florida Japan Jarvis Id . . Formosa Set Fox Id Juan Fernandez France. North coast K Kamehntka „ West coast „ South coast... Friendly Isles FunOj- Bay of G O.ilapagos Islands Keeling Isles Kerguelen I,and Kerniadee Ids L Gilh.trt Isles Grant land .. I.accadives I.adroncs Lancaster Sound Lapland Greenland Gtiadeloure Guatemala Guiana . Loyalt)- Ids 542 TABLE 10 INDEX TO MARITIME POSITIONS Macas'sr Strait McClintock Chanuel Madagascar „ Islands North of.. Madeira Magnetic Pole Malabar coast Malacca Strait Maiden Id Maldives Maine Marquesas Marshall Ids Martin Vas Martinique Massachusetts Mauritius Meiaco Sima Ids Melbourne Melville Puninsnla Mexico, Gulf of „ Eastern coast „ Western coast Mindanao Mississippi Morocco Mosquito coust Muzaiubi(|ue K Nassau Id N^ivigator Ids Newfoundland , New Britain „ Brunswick „ Caledonia „ Grenada „ Guinea „ Hampshire „ Hebrides „ Ireland and Islands N.E. „ Jersey „ Orkneys „ Shetlands „ Soutli Wales „ York „ Zealand, Middle Id. .. . North Id „ Stewart Id Nicaragua Noowook North Carolina „ Devon „ Sumeiset Norway ;.. Nova Scotia Novaya ^Biul^a O Okhotsk Sea Oregon Orknevs 4S, 49 49 45 158 150. 151 5S 75 106 144 1 58, 159 159, 160 175. 176 85 ■59 39 146. 14 >3i, '3 149 15' 169 169 108, 109 >5' i'3. "4 1 15. 116 Pacific Ocean, N.irth Islands off West coast of America I-lands N.W. of Sandwich Ids. ... Isliiids in Central Pacific Paeifie Ocean, South Islands off West coast of Au.er ca Islands North-west of Low \^ Archipelago J Islands N.E. of Solomon I" Palawan Palmerston Id Panama .. „ Isthmus Paracel Ids Parry Ids Pechili Gulf Pelewlds Penrhvn Id P. rsia"u Gall' Perth, West Australia Peru Pescadores Ids Philippine Ids Phoenix Ids Pitcaiin Id I'ockUngton reef Porto Rico Prince Albert Land „ Edward's Id „ Regent Inl. t of Wales Land Prussia Q Qiieensland R Red Sea, Wes'ern shore „ „ Eastern shore Reirson I.I Rhode Id Rocas Rodiigue Rus.sia S St. Ambrose Id .. ., Domingo „ Helena „ Lawrence Gidf I Paul's, Indian Vieean"""!!!!!!!!" „ „ Rocks, .\tlantic „ Thomas „ Vincent Saghalin Id Sala V Cunnz S.imou Ids San Salvador Santa Cruz, West Indies „ „ I.slands, Pacific TABLE 10 INIM'.X TO MARITIME POSITIONS Sardinia ;■ collanii, P ase coast , ^^ e>l CO i-t ScN S\ria Tartary Tiismania Tema Reef .... Texas Tierra del Fue- Timor Toliago Tonquiii Gulf . Torres Str.iiia . COLUMN 4 57 5-6 68 Trinidad, South Allanlic West Indies CO^. Tripoli, Africa Sjria 37.38 36 TiistandAcunha Tubuai Id 45 bo Tunis 38 63.67 140, 141 119, 120 5> 129. 130 44. 45. 16S, 169 Turkey { U Union Ids 32. 33- 34 36.37 121 104. 105 176, 177 i5S E'lstern 179-KS2 ■49-153 '58, '59 176 143 19. 20 20 139 120 86. 87 64 67 93 65 120 Gulf of Mexico „ Alaska V Vancouver Id Venezuela .79-182 176. 177 162, 163 28 Victoria, Ausinili;i 142 13. 14 Virginia 152 3". 37 78.79 107. 108 121 ■59 169. 170 70 113. 113 W Indies '53 163 Windward Ids 158 V Vu.Mia-1 160 TABLE 10 WAiuriME rosmoNs LATITUDES AND LONGITUDES OF THF OliSERVATOUlES AND SECONDARY MERIDIANS, THE FKINCIPAL nEADI.ANDS, PORTS, ANCHORAGES. ISLANDS, AND MOUNTAINS IN THli; WORLD. (J) Places BRITISH ISLES. ictNwicii Onsi f 1" Paul's Ciitheili VATORY, "1 Greenliitlie, ferry Sht-eniess. fl. st Chatliam l)k. vd . K'inu's slairs Mai-Mi.-. ' '.'l: :■ -.-,1, NCh. De.il, Telct;iai)li Tun 5i°2S'6 51 30SJ 51 27-2{ 51 26 8| 51 23-8| 51 234 51 197 51 143 51 23-3 S. Foielaud, 2 Its. S78°AV] l;U-f..FI. (uleciiic) 3r4f., ' -•fl"f- J I'"vrr. e;:, CaMlf lv.U-loii.,S'„',,lt.V'«l-fi.l ■"It. fl' J l)iia;;eness, It. E lU7f. Vur.ie shl., It. V. Wd u,\ R 'JO', 30f. / RiilgL- sill., Si-t. V Kve, m'J, Cluirdi lI,iMiiif,'s, 2 liyhts, 4U0f.,1 F C(Jf J'\ Rc.ichy Hd..It. El. JSif. Neuhavtn,IIl\f,\ViiierIt.F41f. Brighton, pier It. Fs 35f. Slioreham, E'b'', 2 Its. N1°E1 7501'., F 421., F 23f., nf. / Selsra Hill, high ho Chichesler, ffl '.,", Cli , R. N. Cul snuMirli, m, K. N. Cull.,1 nSKKV.lTOllY, ♦ 1" / lian.pt"n, St. Mii'h. spire St, 2 Us. N3S"E 73uf., 1 Cowos Castle St. Caiherine's Ft., It. Fl."l (ek'Ciric) 178f. / Needles It. Occ. 80f. Christchnrch, ESS. N enlr. ... Poole, ID^f, Branksea Castle... St. Alban's Hd Weymouth, EV, It- F' 23f.... Poilland, 2 Its. NjjnV ) 1509f, F 2IOf., 1361'. / SI ti4 SI 7S SI 4-8 SO 5S-o' 50 56-2 50 49 50 49! 50 48 ol 50 54-o| 50 424, SO 46 o 50 34-5; 50 3971 50 43 9! 50 4i7| 50 35 SO 36 61 o 57 lOa-t ■ o 167 o 447 35 b 1 23 2 I 267 I 255 I 24-2 I 242 58-2 1 162 o 43 5 o 360 o 48-5 467 1 6 I 24? I 327 I 17-7 I 177 » 35-5 50 31 2 2 27 s (2) PI a lOOf. .. Bridport, E ei ExHiouth, [E-^ Torquay, It. i"' 15f. Berry Hd., fl. st Dar.mouth, S, 3 Its. F Start Ft , It. El. 1" 2041'. I'rawie Pt Silcmbe, ffiV, Fi.rt Chailes Bolt Hd.,43Uf, fl. st Eddyst.melt. Fl.72f. Plymouth, m. Uu Wise, fl. st, brkw.,Wend,It.Occ., bell Rame Hd Looe Id., sum Fowev, m, Castle Gribbln's Hd., beac. 324f. Dodraan, 37yf. Gerran, spire Falinouih. H , PeiidennisCastlt St. Anihuny, It.R 20- BSf, Black Hd,fl. st Manacles, sum Lizard, 2 lis., F N72°E, 2:!of. .^t. Michael's .Mt Penzance, ffi.U jiier, iT' ai lof. St. I.HvenV Ft., fl. st Uiindle-tone beacou Wolf rk.. It. R Longship's It. Int. 8Mf. St. Agnes, It. R I'" I3Sf. St. Martin's. Day Mk. ... St. Marv'-!, (l.st Bishop i-k., It. Fl Uu;.... Lat. N Lon. W IVest Coast. C. Cornwall St Ives, Hi, Steeple Godrcvy Id., T.'^um St. Agnes, beac. 62 If. Trevose Hd., It. Occ. 2()4r. ... Padstow, [3, Ch PentirePl Tinlagel. Ch Ilarilaiul I't.. i,:i,i.)f.. It. Fl. Luutly I, l,L",in, 2lis. R2-\ 5401-., F 47(ir. J Bder.ird,(B.oi liraunlun.lts. \ S70°E 9331'., Occ. 931'., 44f. ( MoitPt Ufraconibc, Si""' 't- V' 127f. Bridgewater ffl.or Burnham. 1 2 Its. S70°\V 1500f., Occ. )• r23f. j Flatholm I., S pt.. It. Occ.\ 156f. J 50 427 50 37 SO 28 SO 24 SO 21 SO 13-4 50 50 193 SO 13 2 50 10-9 50 220 50 2C-3 50 19 so 26 SO 197 50 19-1 50 13 SO 107 50 88 50 »-3 50 0-4 50 2-f 49 577 50 50 7 I 50 50 49 567 50 4" I 49 53-6 49 5»'o 49 55-0 146 i8-5 33 32-5 354 39S '■4 lOI For ludex 10 Maritime Posilions, ste p. 540, TABLE 10 MAUITIMK I'OSrnoN.- Placcs 150f... Oreat Hangman Hill, Bristol, ffi.Oiiluiiial Newpoit, [E.LMi It F39f. .. ('jrliff. S, Oiistoin lio Nasi. I'l., •-' lis. NSa^W, F 182i: 2lilf. I S.. G..V SwM. sen. E, |.icr It. T'^bf.yrf. \V„iinsH.l., J.,I64f Pembrev, E. It. I' S.if. ir.f ... ICa'dvI.',\ IJiii., Spt., It. Fl J H.I.. 142f. St. .•Vnn's Its. N41°\V 610f., \ •iV 192f.. 1.09f. / Millnrd, m,cu IVnibn.kf Dk.yd., NW corner Smalls r£s..NS 'JC, It. Int. U'.if.l (".rasholin I.. % 3c., sum. 146f. Ilamsev!.,NSllm..snm.444r. S.Mitli Bishop ik., It. R 1441... Si. Davi.l'sCath Sttumble Hd PivclljTois l-.54f. Caidiyan I., ^ 4c., sum. 193f. AbcrjsTwith, E V. 't- F. Castle' Cader Idiis. 3.i49f. Snowdnn, 35S0f. Banlsey I. ^f l^m., It. Occ.\ 129f. J Cacrnaivon, ffiV, It. F' .^Of. ... S. Sack It. R U"' I97f. Ilolyheail, ffi. ItfF 2lif., hell Skerries, jfi Urn, lis. Int. llTf. Tt. I.jniis, It.Occ. 128f. Beaumaris, QQ Great 0;me's Hd., It. F 325f. Iloylake, 1-. F3lf. Hidsion.lt. F 228f. l-easowe, It. F 94f. Black rk., II. R' 77f. Liverpool, g, St. Paul's Ch.... ()bsirvator>-,< 1' CfMsby, It. K 9.if. Konnby SKmark Rossell sea mark Wyre, It. K 30f., bell Fleetwood, ffij. It. F 90f. ") NWcxtr / I.ai]caster, Casilc Walney I.,% 7m.. S pt., lt.1 R70f. J Black Comb, I9l9f. S. pt.. Call of Man C.is'kton, It. F 22f. I).,u;;las, It. F lU4f. N.pI..AviePt.,ll. RlUCf. Peel. lt.F27f. Ki. Bees lid., It. Occ. 333f. ... Wbiieliaven, 03=?. It. R 52f.... Ilariinglon, ffl, pier It. F ^ 44f..Tf- ; VVorkingtoD, 03, It. F 42f. 1 "t-jf. f Marvport. X. S pier, F .'J2f... Cai lisle. Cathclr.a Aonan. Church 4S0 8-5 i8-3 200 253 250 159 200 237 241 249 267 246 248 3' 4 323 55-2 57-3 55-6 30 2-9 32 4'4| 90 25-0 136; 308 33-2 367 38y 430 53-S 59 2 3" 59 2 3> 5 2 597 3 106 3 330 3 58? 3 560 4 20 4 150 4 4'o 4 555 5 '05 5 '5 4 57 ? 5 400 5 2S 7 5 207 5 245 5 1 00 5 35 4 46? 4 415 4 39 5 4 5? 3 54 5 4 45 4 480 4 247 4 420 4 37 o 4 365 4 "7? 4 52 3 5> 2 3 II o 3 47 3 77 3 2-7 2 595 3 00 3 3-5 3 40 3 30 3 >7 3 10 2 48? 3 105 3 19-5 4 500 4 39 C) 4 2S0 4 220 4 420 3 38 o 3 35 7 3 3"- 5 2 560 3 '5 <; . 325f. Port Palrick. EC. It. F 38f. ... Coisewall Pt., It. R 112f. L-ugl, Ryan. ES, It. F 46f. ... Stranraer, \^f^, Church Ayr, OQ y, 3 It- SS4°E S.iOf., 1 1^? Silt-, F sn J SCOTX.AIiri>, 'West Coast. Ailsa Cr i-, 10!.sf„ 1, FI. eof Pladda, 1;r. 2F I. ■)(»., 77f Ardiossi.n, dj'S, It. Fl. 251'. ., Irvin.', II, Ch Creenock, ffl. spire I'ort GUis^row, S, basin GLisgow, new bri^lge UliSKKVATORY Camphelton, g. It. F' 18f. ... Mull of Caniire, It. F 297f. ... Ben Tuirek. 1516". Ma..INaHo. Dun Aid Rhinnsof Isla. It.onOer^al I. Fl. 150f. / Colonsav I., ^ 6ni., N pt. ... Ohan, S, Church Lismoiv I.. ^ 9m., It. F 103f Fort William Ben Nevi.s, 4368f. Dubh Ariach rk lona I., ^3m,Wpt I. of Mull, Caliack Pt Ben More, SlSSf. Skerryvore rks.. It. R 1.50 t.... Tirey I., ^ llm.,Se.\tr. Dubh Sgeir rk Coll. I., ^lOm., N&E pt.,1 rks j Make Id., Innerah I't Rum 1., NS 7111., S pt , VVpt Canna I., jf 4in., W |)t Skye r., NeistPt Diinve;;Kan 11(1 Fladdaehuan Islet, N end Skeir Grariich Ru Hunish Ru Re.i Ru CovKMch HuSloer H.ind;. I., fUni]. 4(mf. sum.... liulgie I , [\m.-\. 14(if. C. Wraih ll. R"' 400f. Far-oiii Hd Roan I., «j I]m., mid Siralhy Hd Thni>o Holbnrn Hd Dunnet lid . It. F 34Gr. Dnncinshv I'd p. niland Skerries, ii, l,',n,.,-) lis. N pt, 2F 14()f., ir'uf. J 54 41 54 38 I 54 50-3 55 05 54 58 5 54 5-J5 55 28 55 I5-2 55 25 6 55 3f'7 5S 368 55 43 55 569 55 562 55 5' 9 55 52-7 55 250 c: 18 55 34 55 35 55 40 S6 8 56 24-5 56 27-5 S64S 56 48 56 8 56 187 56 3'i-4 56 25-5 56 194 56 26 56 3 '5 56 4'-5 56 50 56 562 j7 05 57 3 57 252 57 30-8 57 44-8 57 47 > 57 4^5 S7 5'(> 58 65 58 16 58 230 58 37-5 58302 58 3V3 58 360 5833 58 35 S8404 58 39 R46 TABLE 10 MAKITIMK PI Tiumpan Hd ittolLcwis, It. F170f. ._,..lIon Hd Scarpa I., W pt Rona I., SK sum. 360f. Sulisker I., 8 sum Flaniien Is., Kodorlic im 8l. Kilda, pk. 122(>f. Roc-kal [2i'.]. (ark N73<-E,l J-"'"0 ' Hebrides. R:irra lid.. It, In'. f.H.lf. liana I., N pt. of Fi.iniy Kiis liay I., NS .-?«)., S end .. S. Uist I., NS 17ui.. E pt.,1 UshinisI), It. Occ. I76f. ...J Hunid Vula, Wpt Mnna.h Is , K\V 4m.lt. Kl ISnl II.i!,kier Is, N Loch, !2iir. .. N. llistl., EW 1.5m., W pt. .. Bcnu-raj 1.. # Sm., N pt. ... I'ahbavl.. E\V2ni., S pt Sc-alpav. ("ilas I. EW aim.,! ; I<., Im., N'\Voui-,Weii way, U. K SGI. Lat. N Eon. W 56°47'i 57 4 57 3 57 »8 57 14-5 57 3>-6 57 42-3 57 362 57 44 57 453 57 S>4 57 545 5^^ "-5 5S 108 58 157 58 308 58 14-6 58 17 59 70 59 5-4 58 17 57 490 57 36-, liurra Nc-s Hoscnr^s Mull II. 1 Kirkwall, pier It. F 31 f. B.ou;;h ot Bii-a. ini StroUiuess, (H'", Church Ccpinsha I., -^ Im., mid Auskery I Sirun-a I., \ 7m., Lamb Hd. Sandav 1, ^ 11m., Tresness Siartft. F't.Of. N.Ronaldsha I., -g- 3m., It. \ F 140f. ( - — ^ Sironinc-s, or S pt. liunpbrake bhl Hd. Noup Hd Sacquov IM. . Stuur Roiay . S. pt., or Briiu Shetlands. Fair I., ■§■ im.,h, T, pk. 71 If. Sumhurgh IM., li. F 3'.i0f. ... Mousar.,4klim,s,an Hard IM Eerwirk. ffl, Inrl 5 K^-s, IM.. ^.-,rf OntSk Burra \'iic Ness . li 60 83 60 254 60 29s 7 175 7 "■5 7 27-5 7 417 7 407 7 li 7 II-5 7 14-5 6 38'2 6 15 6 8 6 157 7 IS 7 10 5 4S-5 6 87 7 39' S 347 '3 41-5 2 55-5 2 54 5 2 52 2 2 510 2 495 2 420 2 575 3 200 3 17-5 2 40 2 34 2 320 2 2S5 2 225 2 237 2 37 2 53 3 4 ° 3 4? 3 255 3 '3 5 Fetlar I., % 6m., E pt. .. Balta I., NS 1 Jni., S pt. N. cxir. outer Slack rk. GlonpH..lin, 3c.,sum. ... Hva.orNKpt Roeiness Hill, 147fif Wt ()-sa Skerry, rks. J* 4c... E^h.l Ness'Skerry Fufrlo.' Skerry Ve Skerries. ^ Im., mid, Skelda Ness , Fitfull Hd.. 929f. FoulaI,4fe3m.,^,sum. 1 Faero Islands. Monk rk., 3nf. , Suderoe I., % 5 I., S pt. Grt. Di My-geno.sl.,EW4m„\V) ^ FujTloe I., NS 2jm.. E pt....Ci Nalsoe I.. % 5m'., S pt Thoisluivn. It. F3.5f. llaldervig Church Noss Hd., 577f., It. R ot Caithness, nee, Tain, [EtS, spire 'arbetness. It. liil. 17: Chanonry Pt., It. F 40f. Bur;;!. Hd Coveisea Skeriies, It. U IGlIf Cnlkn, Castle hill Banff, di", N pier. It. F' 28f. Troup IM., pt Kinnainl's IM., It. F" f-'Of... Fraserhnr;,'h,2 Its. F' 201., 33f Rattray Pt I'eterlieud, S ffiV, Keiih luel Buchauness, It. Fl. 1311' Aberdeen, \^-}, OiiSKKv.^TORi Girdleness, 2 its. F \\-^ Stonehaveu. [E",2 Its. E'i ;;!f... M.ii.trose, di;;, Seurdy Ness It. Ii.t 124f. Red lid, 2.'..M- Bell rk., It. R"' '.i.lf. St. .\ndrews, [Jl. Cli Fifene.^s, fl. st M.iy I., % Im., h. Fl. 2^n|■. Leith, ffi), pier Its. F Edinburgh, Ou.s. Blackford 60 3S'2 60 44-4 60 51-5 60 44 2 60 37 (o 32 60 3-!-o 60 28-5 60 204 60 22-5 60 SS 59 54 61 23 61 265 62 70 or 58 5 62 25 62 18 5 58 28-6 58 IO'2 57 487 57 51 9 57 407 57 41-0 57 351 57 34 5 S7 286 57 421 57 43 4 57 414 57 403 57 4>7 57 4f9 57 41-5 57 37 57 3°' 57 2 '^•2 57 89 57 85 56 58-0 ^i: 37 56 33 7 56 281 56 27 56 276 S(- 260 204 =,11 167 SI' HI 55 589 55 55-5 TAPJ.E 10 MAlilTI.MK POSITIONS I. on. ENCX.A»ri>. East Coaist. St. Al.l.'s ll.l., II. l-'l. 2- KviiiK.iith, Chunh ... liiTaick, (X'-;'. spire ... Fiini Is..-.' Us. N.-IG'^WSGIM., I U .ill". S7f.. I'M. -I.^f. / cIr-vkii liiii. -jur-sf. N. SiinUfi'lanJ I't., iijill CVqiiei 1., It. FS.if. Hlytli. DQI), 2 Its. F Tjnomouili. It. U 154f., G.stlt N. ShicMs, ffi, Cli Niwcasile, lirnljje, N cud Siinil.rlaiid. ffi. Churcli llarll' |)0|il, 3j'o, Cliurcli Se.iton. iS, 2 lis., high It. F89f. Tees Hiver, entiaucc S oikton. Chureh Redoar, Church Whitliy, m. 2 Us. F 240f. Srarboniugli, ffij, It. F' .5bf.... Flaiiihoiough Head, It K-'-'l 2Mf. / Bridlington Quay, Mill, Eo ■•• Hull, ffi, citadel Killiugholuie, 3 Its. F68t'., outei Spurn Its., N66°W, Occ.& F"! 9.3f,.54K j Innur Dowsing, hciicon Sniili.'s Knoll. % "in., 4, S pt lliinstantim Ft., It. Occ. lU'Jl. Cn.iiier, It. K274f. IlaslM,nMn;h, It. F I:i6f. Wiiiurion, It. F llOf. Varinoiith, [E, spire Lowcstofl. 2 Its. N28W 2490f. \ liev. iindF I2:JC., 4UI. .../ South wold, Churcli A I borough, steeple Orlorduess, !t. Int. 91f. I )rl'ord, steeple I.andguaril Fort Harwich, ffi??,. Its.F NG2«\V 1 t;80!:, 4.')f., 271'. / Walton, lower .Maplin, SK pt., Occ. 3Gf., bell F.islret rk.. '.IJf.. It. K 14^1". ... Cioiikliav.u,a;;Nentr.ll.FG7f. Mpz.u lid 56° 2'o 56 34 56 47i 55 59 9, SS 55 55 52-3' 55 45-«i 55 402 55 370 55 29 55 347 5) 201 55 7-5 55 1-3 55 07 54 58 7 54 54 5 54 41 8 54 40'3 54 37-« 54 34-0 54 36 9 54 287 54 170 54 70 54 S-2 53 44-6 53 3S 7 53 347 53 >84 52 4S 52 57 52 55'5 52 492 52 430 52 36-8 52 29 2 52 52 52 52 57 5' S('-i 5> 55 51 5'-8 5' 35 5» 253 5' 233 51 286 5 5" 325 H.ar Haven, ffl. Hear l..!.um.l 8871-. / 5' 37 5| West 3° 8'o 2 43 2 2 3S'2 2 5'5 I 590 I 470 1 39? 2 y 1 38-? I 320 I 300 I 250 1 267 I 35'5 I 21 5 I 107 1 122 I 87 I 187 I 3 5 o 342 o 235 o 50 0117 o 200 O 12 East o 33? 2 14 297 1 190 I 3^? I 41 5 I 437 « 455 I 407 I 360 ' 34 5 I 32-2 I 192 I 167 AV.st 9 3' 9 36 2 9 427 9 49 5 9 5' 2 9 52 ? Pla Hnn-ry Hill, I81f. Uantry, Ch Koancarrig I., It. F 55f. Call rk null ik.. It. I'l. 27lf. I'od's Head Srarrirt I., suuiiiiit Hulus lid Skclligs, It. F l-5f. liray Hd Viilentid, S, Crouin ell's \ Fort, It. F a4f. / Great Foze ik Tearaght rk., It. Fl. -j;"!!. (irt. 14l.i.-kelt, ^f- .iin , N pt.... IJrandon Hill, ai2Gt. Tralee Lit. I^auipliire 1., It. [ F56f. J K. Shannon. E, Kerry lid. ... I'arberi, It, F .">8t. Umrick, ffl.Catludial '41 40-8' 392 34 355' 397| 436 47 40-2 53 56 277f. Loop lid.. It. U. liallaid Ft., tower , Hags lid Arraii Is., Eeragh 1., It. K| llof. J Inisheer I., h. F 1 lof. .. mack Hd Galway, ffl. Mutton I., It. 1 '••3-"-- ; Skiid rks , lin. .Skirdniure .. SIvuelld ,2lis. SlS^t:415f., | ■K^'»'ll.i)-., F lU4f. / Inisliark Hd Clare 1., N pt., It. F 3401. .. Inisligort, It. F .'iGl Westport Newport, [XI Uillsrk Achil Hd.,2:i.'i;(., pt Hl.ick rk., It. K --'S.'.r. Kajilc I., 2 Us. N4y^i;3'.i5f., [ 1^^20t; J Knis Hd Sia-rks., Nst Downpatrick Hd Killala, m l{.i!lina, a!,'.|''f" Sligo Uiack rk.. It. F Tyf. Innis Murray I., \V end Halljshaiiiion, i',-, Ch Donegal, ffi't' St. .John's ]',., KiUibejiS, It.) F H8f. J Uathlin O Hirne Is., It. F llCt Oawros Hd., pt Aian I., Kinrawros It. K 233t'. Slag rks Bloody Foreluud Hill, lOi-iOf. ITortti Coast. Tory r., «- 2 .0111.. It. on N | 5. '53 53 24-0 53 ^,6 1 53 49-5' 53 4^s: 53 48 1 S3 S3 53 S3 53 58-5! 54 4-2 54 'H 54 .8-5 54 SS 19-6 S4 II •4 bb S4 ■ 8 51 2S7 54 3t>-2| 54 39 5 54 34" 54 337 54 496I 55 09 SS 4b 55 82 55 .65 55 "25 55 152 TABLE 10 MARITIME PUSniONS Limebarner slil Fana.l I't., It. Oec. 127f. liimcrana, H, Cli Diinaif II.] Malm Hil., tover Irinistialiul, It. K ISIf. Slii-ve Sueai-ht. 2009f. :innislm>v,nHii.,2lis.S62°El i 460f., F 67f. & 92f. / . I/Ondonc. 121f... xford College, tower Lat. N Lon. Vf Soutli Coast. TusUar rk.. It. R'-'" 108f. Cariisore Pt Hook It. F 152f. Waterl'ord, ffiij bridge Duncannon fort, 2 Its. F vert. "(^ Dof. and 431'. ) Dunmnre, m, pier It. F^- 4-lf'. Biownst-.n Ud., 1021'., 2 tow.. Hehviek Hd Unngarvan, Balliuacuurty ( Pt, It. F.52f.,w J Minehead, It. Int. 28.5f. Ballv.ottmI,lt. Fl 19of. .. Yuughal, Ol.lf. F 7Sf. Ruelie Pt., 2 Us. Occ. and F 1 , ,, , , 98f.,60f. J 5' 47S [aulbon line I., tower 51 505 Cork. Custom hou.sc 151 53.~ 54 55 S 54 46 I 54 43'5 54 36 54 367 54 387 54 '5 54 190 54 "3 54 lo-S 54 20 54 106 53 58 7 53 476 53 42 S 53 36" 53 35 S 53 29'6 53 2i'7 53 23"2 53 20'5 53 18'' 53 9'2 52 57 9 52 20 52 12 I 52 IO-3 52 7'4 52 16 52 13 52 9 52 7 52 3 S2 4'5 51 59 5 51 49 5 51 566 7°48' 7 377 7 27? 7 32 7 22 2 7 >3'7 7 20 • 6 55-5 7 i9'5 6 392 6 307 6 102 6 87 6 3'5 6 152 5 4i'2 5 485 5 56'? 6 10 5 32 5 36 o 5 430 5 40 5 55'? 6 77 6 19 7 6 177 6 13- 6 15 6 10 7 6 02 6 30 6 205 6 9 6 77 6 90 6 00 6 28? 6 12-5 6 21 7 6 55''7 6 59'5 7 7 7 32 7 33 7 35'? 7 59 7 50-5 8 152 8 182 8 277 Barry Hd ! 5i°42' Sevrn H.ls., 'I'l-legr, Galev Hd.. S pt. . Stags, off Toe Hd.,1 Baltimore, m EVROPE. Bi:i.GIVAC. Dunkirk, E, It. F, Fl. 1931'.. . Nieuport, ml, 't. F' 98f.. 1 (NW of town) J Osiend, (Sl,4lis., EoneF189r Blinkenberg. It. F 831 Heijst, It. F 26f. Flushing, ffi. It. F49t. Middclljurg Sehouwen. W end of I., It. 1 Fl. 171f. J Bergen op Zoom, Ch Goedereede, Ii. on Cli. F 1481 .Antwerp, m. Cath : Hclvoetshiys, It. F 49f. Brielle, E, Church Rotterdait., (11, Caih The Hague, St. Jauies' Ch. .. HOI.I.AirD. Scheveningen, It. Rev. 157f... Katayk, Coast It. F 82f. Noidwyk, It. F 6St'. Alkmaar Zandvort, It. F 75f. Eguiont Its, 2F I25f., 120f. .. Kykduin, lis. ri87f. and 45f Hel.ler, S Texell.,^ llin., Wpt Medemblik, Ch Maiken I., It F 52f Amsterdam, ffi, W .'^lee le .. Haarlem, Grt. Cli. tower Leaden, Observatniy Vliel.nd, It. F iDlt'. Ter Schelling, It. R 1» 177f.. Aim land, beacon Sehiennonikong. 2 Its. F ) 139f. and 14;f. J Roitum I., beac Borcum, It. F, Fl. 207f. PRTXSSZA.. Emden, Hotel de Villi Waiigeroog 1., /, It. Fl 108f... Bremer or Weser It. v., fl. 1 r28l., bell, guns / Brenun, Observatory Wilhehnshaven, OiisBiiVATOKV HelJgol,nd I., It. F22.^f. Neuwerkl.,lt. F,F'l. 126f. Cuxhaveri, It. F, Fl. 701. Gluek.stadi, pier It. F' 30f. ... 51 418 51 36-2 51 342 5' 318 51 281 51 29 We-t 52 63 52 12 o 52 146 52 37 9 52 22-3 52 37'2 52 571 32 57 7 53 3 52 46'4 52 276 52 22-5 52 22-9 52 9'5 53 178 53 2> 6 53 27'0 53 29', 53 22- 1 53 476 5348 53 4-6 53 3> 9 54 loS 53 55'2 53 525 53 47 ' TABLE 10 MAKITIMK POSITIONS N Lou. E (12) Altmin, Oljservaiory 53°32'7 Hamburg, Obsehvatoky | 53 33 SSJVMAKK. ir..rM I't., t(.. ouui- sl.l. i lliinisholuMuri., lU U ai8f... Hiiishails Nist The Skaw, pt., /, It. V 1-I4f. .. Hircsh.iliiifn, ll. F, Fl. S(5f. ... Kladsirand, Cluirih N'l.iiit'en, lis, 2 F o6f., bell ... I.jes'j I., jji lOiii.. B\riiiii Ch... Anholt I., Ept., It.FI. I3at.... Hsselo, It. K Uff. Aalborg Fi.rnas, It. Fl. 69f. Aarhiis, Cath Thuno I., It. F lOOf. liaa^o. li., S pt.,F a9f. Apeiiradft As-ens. Chuirh FlcD-burj; Sioellai.ds rf., N jmd W pt. ... Keef ness. It. F 79f! S|>ro-o, It U I34f. Nychurg, Ch Fakkel.irrg, It. S pt. L;inge- 1 laud, F 129f. J Spoisbicrg, It. Fl. U'3f. Nakkch>ad.:ilts. N89°\V,F1 I47f., 98f. j Elsineur, Kronborg, It. F, Fl. { I'Of / CoPKNiiAGKN.g, University, 1 t)l!SKRVATl)l4f. SHin.ii.iinde, It. F 2()7f. 9°56'5 9 SS-S 55 35 7 40 57 OS S362 57 35 9 56 57 43-8 10 3s 5 57 292 ■0 37 5 57 27 'o 337 57 IS ■I 54 57 1 5-1 II 02 56 44 3 <■ 392 56 11 7 II 43 57 27 9 55 56 267 ■0 575 56 95 10 130 55 5t'9 10 27-0 55 177 9 480 55 26 9 25 2 55 "6 " 9 53 7 54 469 9262 56 S II 15 55 560 10 407 55 44 7 10 525 55 20 10 58 55 187 10 477 54 44 4 10 42 55 586 II 520 56 7-2 12 21 56 2-2 ■2 37S SS 4'-2 12 347 55 >7 12 27 54 57 '2 3i 54 338 II 580 54 30-5 12 4 55 '9 IS 12 55 '77 14 4'') 54 59 '5 5 55 14 42 54 20-5 10 87 54 297 II I4\2 54 24 II 19 53 52' 10 41-5 53 535 II 277 54 '07 12 57 54 5-5 12 90 54 286 12 30 s 54 •8-3 '3 55 54 409 13 262 54 25 5 13 280 54 21 ■348 54 15 ' '3 557 53 550 14 iSo fort Sti'ttin O.lbcr .lei-shoft, ll. U I6Jf. IK'l.i, It. 1< l20r Kixl.i.li, It. F 2.31f. .Nculalir«as>cr, It F 7Sf. DuMizig. Obsi'rvat. ry ... PiUaii. ID, It F96f. Konigsbrrg, Observatory Hrii-,tur On, It K 1641.... .Meuiel, m,It. F 98f. ,;::} RTTSSIA. Libau, E, Pilot's Toiver, F, Fl. Iu.Jf. Windau, Cliurch Lyser Ort, It. F 118f. Uomesness, It. F, Fl. 64f. Runo I., It. F 2101 Kiga, HI, Cathedral Pernau, Giiin. Church .irensburg S« alter Ort, It Osel I.. S pt, ( Rev. lUf. / Filsand, VV pt. of grt Id., 1 K Dfif. / Duger Ort, It 5m. Ed. of pt,\ F. Fl. 334f. / Winkuva O.lensliolm, ll. Fl. Il:,f. Parker Ort, It. F U7t'. Sourop.lt. F l.ir.f Naryen I., It. N pt.. U l:i«f. ... Revel. St Olaiis Church Wolf beacon Kokskar, It F 106f. Ekhol.ii, U. F, Fl. lO.Sf. Stoneskar beacon Roclskar I., U. Fl ti .f. Little Tioiiter.s W pi Great Tiouters, E sum Hogland. \ 6m., N. pt. 2 Its.") S'byW'u6ra.,F384f.,33f. I lower J Laven-kar I , N pt I'eni I., E pt Seskar 1., NVV pt, It Fl. 97f. C. Kol-anpia, Church Dolirci N„ss Pt Tulboukii., It. Rev. 9.5f. KiniiMa^lt, a, St Andrew Ch. Sr. I'l.ri.usBUKO. Acad, of 1 Science, OnSKiiVAToHY... J P0UI.KOVA, OUSKKVATOBY ... Stirs Pi., It F I17f. Hiork.) I., S pt., tower Civkovu rk., beacon Wiborg Aspo beacon ...•• Nerva tower Souiniars I., It ReT. 89f. Lippu I., beacon Frederickshaiuin I.ovisa, m Orrengriind, bcac. 103f (ill I'ellirif;., or Glosholin ... 56 309 57 239 57 34 57 48 57 48 56 57-0 58 23-2 58 '5 ' 57 54-6 58 23 58 SS 59 12 59 '8-3 59 235 59 279 59 36-4 59 266 59 35 59 42 o 59 4' 59 495 59 58-2 59 50-0 59 S' 60 6-3 60 2-0 59 59 7 59 5(i-5 59 463 bo no 60 157 60 I r6 60 427 60 177 60 148 60 12-4 60 143 60 34 60 27 6 60 16-6 Co "34'u 35 49? 205 402 41-2 54" 21 340 2' 43 22 39 23 '5 24 6-5 24 30 22 30 21 50 22 13 22 18 23 23 o 24 3 24 24 24 320 24 47 24 48 25 3 25 49 20 21 26 420 26 53-. 27 '4 5 26 58 5 27 51 28 50 28 23 5 28 34 7 29 o 29 33 29 40 30 18 J 30 197 29 3 28 43 i 28 42 : 28 46" 27 13 27 5.S : 27 39 5 27 3f 27 12 26 16 26 27-. 25 5,, 550 TABLE 10 MARITIME POSITIONS Placi-3 Socleiskar tow. pilots. It. V, ^ Fl. l-24{. / Helsingfors, Obskhvatohv .. Sveabur^; Uenskar, It. F 164f Se^it'lskar, hcac Ilango, li. F. FI. liaf. .\l.o, OI.serv,itciry llto. It. F 13Ut' liogskar I,:if;skar, It. F 1001'. Nyliainn, heacoii Hiigsteii, lieacun Nystad, Knskar, It. F l.'iif. .. Liiko, beacon Sabliskar, beacon P>jornehorj; Sioikallc sill., S I't. «t. ... .Moikcpaa, beacon Fallskar, Lcacoii WasH. Chiircli KmsiJi-en, beacon Nonskar, It. R I05f. Walsoiaine Is., N pt H. Isin^kall, rk, Bf. Ny Carleby. Cliurch Kejsarsklubb, beacon Ganila Carleby, Xpili, It. F, \ Fl. 21f. / Isallark.,!t. F .■JSf. N.ilikiaincnsliL.sf. liiahcsia.U'lMiirb Carl;, I., W h. F. Fl lOlf. ... lllcab.rg, Cl.nr. h Ulkogniiini. h.ac.in Malnrcn, It. F 78t Rodkallen rks., grt, nibl. It. 1 R 84 J Stiir lieblicn. beacon Bjnn.k I iibh. beacon (irt.Fjhdra-I.,niid.lt. U 101 f (iadd. It. on S pt. of Is. F 70f llmca li.iihlen, beacon SkaJi^nd(!e, beacon inio 1., N pt., beacon .idiksvall niMhlde, pt , It. E pt. Fser F«i(-!!!!!!!!!'! Ni:;nin,l, ,■'( S Qi.aiken.Cn.lemo Sv.ii-ikluijbeii, It. R I 6o= 7 I 6o 97 6o 84 59 56 I 59 49 7| 59 46 i 59 46-0 60 27 o 59 465 (..o 43 60 56 61 277 61 290 62 ivo 62 162 62 45 62 54-' 6 J 40 63 4 3 63 II : 63 J4 63 27 63 35 63 32 o 63 43 63 57 3 63 5' 64 200 64 36 64 4''5 65 2 65 I 65 24 65 32 65 508 65 19 65 19- 24 57-2 24 597 24 25' 23 34 23 22 22 57 22 175 21 22 20 55 ■9 55? >9 57 19 25 21 I 21 9 21 22 21 48 21 20 21 23 20 50 22 34 22 52 23 27 25 54 24 3' 24 34 25 30 24 51 23 34 24 10 64 28 65 4S -. . 63 36 o 20 46 63 49'5 20 iS 63 26 j 20 4 63 1 2 O 19 O 62 360 1 8 o 62 379 "7 57 62 14 I 17 44 61 43 7i >7 7; 61 37 I 16 30 61 17 7j 17 5 61 10 17 21 60 403 17 9 60 44 17 33 60 31-5' iS 23 60 2951 18 41 60 l6-2j iS 54 60 9 8, 18 50 (U) Places Arholina, beacon Soilerarm, It. U 99f. Svenska Hogaine Stockholm, S. OnsKRVATORV Gronskiir, It. F II If. ^and^o^t It. F, Fl. 146f. Knskar, beacon Hafriiige, beacon Haradskar, beacon Sparo, beacon Westcrwyk Kalmar, Church Gottska Sanilo, W pt Faro I., Holm lid , It. R \ lOOf. J Gothland, S pt. Hobor;^-, It. \ Kev. 190f. J Ostergarnsholin Wisby South Carlso (.dan.l, N. Hd., It. F 10.3f. — Slid., U.F 132f. Cliri^tianopcl Ulklippor rk.-;.,lt. F,F1. lOOf.... Ca,-Ucr.)n;i, m. It- F, Fl. 58f. Carlshamn, 2 Its. F 58f., 17f.... Ilino I., It. F, Fk 218f .\luis CiiorislKinin, It. Alt. 301'. Ysi.id, Church Falsicrlio, It. F 78f. .\Ialiiiii. It. F, Fl. tiHf., Ch LaiuNkrona, 2 Its. F ,-('jf., 48f KulK-n, It. Krv. 2S^f. En-elholni. It. Air. I.il HallandsWadero, It. F, Fl.i;7f Halinstadt, foit Falkenher.L', Ch Morup-tan.'e. It. F 9jf Warberg. Cas.le Niddmgen, 2 Its.. 2 F Btif , hell. IWIu-a F, Fl. & F. isler Is., It. Kev. l!7f.. .ustcr, 21ts.'F,"Fi.'214t NORWAY. n.knr.'it'FrFi. sVf'!! , It. K l.--4f It. Kev. U4r. .. ,mgcn I., It. 2F \ liausand, 2 H, Ch. l.on. E 59°5i'o 19° 7' 59 45'2 '9 24 59 27 19 31 59 206 18 35 59 '7 «9 2 58 44-5 17 52 58 42 17 25 58 35 17 19 58 8-9 16 59 57 429 16 44 57 456 16 3S 50 395 16 22 58 24 j 19 II 57 57 56 55 2| 57 26-51 57 38-6 57 19 57 22 56 i.S 56 155 19 22 17 59 17 6 16 24 16 3( 55 56 s '5 42 50 8 56 103 56 I o 55 55-5 55 33 5 55 25 8 55 23 I 55 37 55 52-4 56 27 56 iSo 56 16 56 27- 1 56 404 56 540 56 55 2 57 6-4 57 '82 57 32 57 3S0 57 3S6 57 42-3 57 53 5 58 202 58 54 58 42 59 o 59 17 59 I'-S 59 7-5 59 13 59 547 5S 58 58 56 58 10 I 58 52 58 4- 58 9 15 14 520 14 5> 14 18 14 22 ■3 49 5 12 49 : 13 oc 12 500 12 41 12 275 12 50 ■2 33 12 517 12 30b 12 21 7 12 145 II 54 3 II 39 II 36: II 407 'I 5«5 II II TABLE 10 £51 MAIUTIME ro^irioNS (IS) riaccs Flokkero I., ffl, vks. to S .. Hvviiitfen r.. It. F. KI. 129f. Na7.o, It. r, Fl 16.3f. Mstersteeii, It. Kl. 12Sf. JfddiT.ns, rf. \V pt ■riiiigeiiics, It. K '-"Jf. IIvi,lin..'S,., It. (Vr. U!lf. .. SkM.K-sn:t;s, It. K 7.^f. ll,);,v.inie. It. F6if. ll.^iiv. ■.' lis. N »°\V. -ir.St. F S..r lIu.i-ork.,U. F. Fl. 7-.if. I! .llltlKloi-, S pt I,,-,vi^'. It. F47r. , Oil.le, Cliiircli Kors tiord. 1. entr. . n-rgepi. S Hlnnioe I Uilvoer Is . W pt. . Aspo I., NVV pt. , V. ragrnnd Scnuing skar rk. . Siadtland. N\V pt., R.indo, It. F laSr Aalcsiind, Church Lrpsoiev, li. F2.1f. Muldu, Church Kviihuiiii, It. F, Fl. 1281 Christian^uiiil. It. F 65f. Nightingali; rks., outer .. Grip.lt Hav tluc, rk Munk Ilului. It. F ns(. .... Troudliiem, Cathedral T.itcr lid Vigtcn Is, Wextr rks NW cxlr. rks. . I'.tesiik-, It. V 3af. Svinghhoc, rk Skal svcc, rk TriEn Is , Siihohn, It. Fl. 1 1 SI Ilestiuando Pk Kunna, sum Lofolcii lds.,Skonivu;r,lt. Fl. "l '■;if / I.nl.,l.„ I'l Skr:iavcn. sum. COOf. ■Iran.. I., N pt W. V«go 1 ,N pt l.augo I., W pt., rks. olf. And...-. N pt rronisiic. ()b»cr>atiiry Ilv.di,-. NWpt Iliiinim rlVst. Meridian pillar.. Vand... N pt Arnij. NF, pt Sorocn 1.. W pt N pt , or Tarhalsm .. U..lf>o Is, N pt.lt. F Ulf... K.inski.ioM.-ii Ft 57 5"^° 57 5S S 5S 6 58 4b 59 2 59 3 59 8 59 19 59 i« 3 59 252 ■19 35 60 I 59 47 60 4 60 8 60 24 60 32 62 2 61 13 61 17 61 39 62 i( 62 20 62 246 62 2S-2 62 35-5 62 443 63 I 63 7 63 23 f>i 14 62 51 63 27 63 25 S 63 40 6+ 46 65 2 64 47-4 65 5 t'5 5 65 24 6 5 24 65 40 65 3S 65 59 66 26 66 32 66 57 67 24 67 49 5 68 9 6,S II 6S 20- '•S 37 69 20 69 39- 70 14 70 40- 70 17- 70 13 70 39 70 53 71 6 71 11 7" "03 I.on. E 7° 57' 7 29- 5 7 32 6 34 5 24 5 35 5 24 5 '8 5 '9 4 535 5 '5? S '1 4 59 5 ii 6 332 4 57 5 >S 4 46 4 28 4 44 4 27 4 35 5 « 5 '7 5 35 5 6 9 6 165 7 10 7 '4 7 39 7 S 7 37 6 I! 10 24 10 23 7 8 19- 10 24 10 37 45 17 21 50 32 " 54 12 50 14 44 '5 39 13 59 14 14 16 8 18 57 o 19 16 25 40 5 19 36 20 49 21 55 23 '9 23 59 25 400 25 4rd Kyii Vardo I Hybatschi I., C. Noiiieiski ... Knla, town U. Kildin I., E pt RUSSIA. Sviatoi Noss., It. F 238f. • ;. Orluv, It. V->-2-2f. Sosnovels, It. F 13yf. Tetriiia, vill., Cha|i Kouzomcii, vill, iLiid T.uiria lulalaks. Monastery em, fhin-ch ....e^ni, St. Michael Chinch ... Jijgliiiisk I., N pt.. It. F 140f A'rkhangel, g, Tiinity Ch. ... .M.mdiu;:aI,It.I>un.iH.Fl30f. C. K.rets C. Voionov .Mezen, K|.ipli:niy Ch C. Kanushin, near bio.ik C. Kanin Noss luvev I., NS .lOm., N pt.... C linssian C. Mr.llll-k, NOVA-TA ZEMI.YA. C. Menchikotr North Goi.se Cape Suchoi Noss C. Speedwell (• Nissan ()l:i..-e Is ('. liiMi.aivk Mal..tclikinSlr.it. F.entr.... Graveli..esU K . I'. I'l ,. AlpRvl I'lpl^'S, CE'^ I. de T.Miquet, 2 Us. F 174f. 1. de Heiek It Occ. I15f 'ibcville, Ch. of Notre Dame . Valery sur Somme, ffl ;niux, It. F, Fl. 92f. ivyun. ffi. It. F44f., Sf. iepi'e,[Jj;;,\Vjeliy,lt.F43f.,I!.f , Aiiivji. R.ii).'ir. o 23 69 5S ■" 525 69 19 70 45 72 13 73 4« 74 57 76 20 77 2 76 19 73 8 72 10 26-4, ■ 27 41 31 7 32 o 33 I i3 30 39 490 41 22'2 40 43 35 1 7': 36 5 1 5 34 28 32 32 3t 3S7 38 85 36 5' 3 40 33 5 40 l6-2 39 45 42 197 44 170 43 4^7 43 32 5 49 20 54 40 59 10 58 58 66 16 71 35 57 42 51 50 53 30 55 35 61 39 67 43 6S s6 5630 55 34 50 57 6 50 52-2 50 445 50 4'9| 50 329 50 3'7 50 24 o 50 7-1 50 11-4! 2 67 I 5'-? I 35-2 ■ 372 ' 340 I 387 « 35 '7 « 33'7 I 50 b I 3S0 50 ir7| I 310 50 39 I 22 2 49 560 • 49 55 ' o TABLE 10 MARITIME POSITIONS Pla Lat. N Lon. W ' St.ValerjonCanx. (Il,F,F1.43f. I Fei'amp. |i;,Mt. . II Roches DunvresKW: E\V ; .ls..[ti I, It. -I J-'ll^'l J luiers rks., ^,f .5 1., N\V | ; M breaker! Maitresse Id. jSt. Germain \C. Carteret, i , It R 262f Coiitances, Cath.. 30-2f. Granville, ffl-y.C. Lihou, lt.1 I l''l-54f. / IMt. Si. Michel (■anaUe, Church i llcrpin rk St. Malo, EE'i,\ Church La CoiichOe rk C. Frehel, T , sum., It. K 2.WI Grand Lejon ik St. Brieuc, Cathedral Horame rk., beacon Hcauxde Riehat.lt. F 148t,.. TrcRuier, Cathedral Seven Is., ^4 4m.. It F, Fl I81f Tria(!..z,sliI.,E\V4m.. Wc.xir 49 i6'6 49 203 49 11-2 49 205 49 184 49 29-9 49 34-3 49 364 49 41-8 49 403 49 38 6 49 43 4 49 42'9 49 41-6 49 434 49 25'3 49 253 49 27 o 49 2K0 49 25-5 49 236 49 125 49 1 1-3 49 152 49 >y9 49 94 49 65 49 I 48 522 48 59 48 5S-3 48 390 48 41 48 4>-l 48 45-0 48 309 48 53-6 48 54-5 48 47-3, 48 52 8 48 53 F,; o°42'7 O 22? 2 20 2 O 3> 7 Wl O 15 2 o 27? 0210 31 1 I4'5 I 87 I 16? I 137 I 157 I 34-7 I 37? 1 570 2 12 2 2170 2 22s 2 330 2 41 o 2 320 2 277 2 227 2 230 2 117 2 70 2 49 2 48 I 367 • 30-5 I 507 1 50 2 1-5 2 3 2 igo 2 39 7 2 457 2 550 3 5-0 3 '37 3 30 3 44 I Morlaix, ffl.It. F 28i)f. St. Pol de Leon, (B, Cath. 1. de Bas, E\V 3ui , h., V side, R"'223f. I. Vierge, Ii. F. Fl. 108f. .. Abervrach, W It. F' 59f. .. 'West Coast. Ushmt, J- 4in., It. Fl. (elc-\ fic)272f. J Kermorvaii, It. F 72f. Pt. .St. Matthew, It. R 177f. ... Brest, ( )bservatory 1. de Sein. It. F, Fl. 148f. Outer, or Wst. rk Andierne, Church Penmarch rks.. It. R I34f. ... GIe.ianI.,PcnrietI.,It.F,Fl.\ I18C. J Quimper Riv., Benodet, Ch.... L'Orient. tower Port Louis, Church I. de Groix, % 4m., It. F 1931. Port Ilali-ueu, It. E jetty, 1 F39f. .".. f Teign.uis,.. It. V, Fl. ,,( Port Navalo, pr.. It. 1' 7L'f Penlan Pt . It. F liSf Belle Isle, ^■; l()m , li. Coul- 1 far liav. H 27 Of j — Port deValai-, It. F :»)f. .. Hoedic 1., ^ l-Jra , -e Fl ■ rk , It R 79f. Gu6r;nile, Ch., )77{ '.'.'.'.'.'.'.'.'..'. Croisic, Church Aiguillon low., (on 'vith the ^ tourileCommerce,N32^K) / Port St. Nazaire, ISIolc, lt.1 Occ. 26f. J PaiuibcEul, Church Nantes, Catli.-dral I e Pilier I., It F. Fl. lo.^f. ... Noirmonslicr 1., S pt I.d'Yeu, ii, .i'.m., St. Sau- 1 veur Church" J Lt.X\Vp,.n, F 177f. St. (iillcssur \ic, Clinrch ... cs d't Pi. .1.- C.oinn du Con, It. 1 yj-Jf / Pt. de rAiguillon, It. F 43f. .. 1. lihe. %^4m., Baleines.It.l on N pt. Fl. 166f. / — Port St. M in in. It. F' .'J6f. — S pt., de Chauveaii.lt. F 59r Rocliellc,2 I1.S. F 79f., 461' Oleron I., ^ I6n,.. N pt., 1 Chassiron, It. V lii4r. J Aix I.. It. Fl. Gtif. Rochelbrt, Hnsi.ital 4S°40' 48 410 48 44 48 38 48 369 48 28 5 48 21 7 48 19- 48 23 6 48 27 48 3 48 I 47 47 9 47 44 47 526 47 447 47 42 5 47 38-9 47 292 47 27-5| 47 329' 47 1S7 ■9 47 205 7 179 7 39 5 47 '97 47 '77 47 '4-6 47 163 47 '7-3 47 I3-' 47 2-6 46 5381 46 42-4| 46 43'' 46 417I 46 29 8| 46 2971 46 13 46 20S' 46 161 46 1471 46 12-4 46 So| 46 941 46 28 46 06 45 566] TABLE 10 MAIUriME POSITIONS Places Ut. N 1 I-oii. W (20) Lat. N Lon. W Pt. de 1.1 Coubre, It F 121•.... Cold.>lliln. It. (Uiv. Gironde) 1 Kcv. i94f. ; Pie. deGr.ivc, It. Occ. 85t. .. Bordiaiix, St. Andre — ()llSERV\TOI(Y Ba-.sind'Aniichon.C t>rret,"l II. 1^ IG7f J B.iyonne, Gith Pt, St. Martin de Biamtz.l It. Fl. '2)t)f. J St. .lemi de l.ii/, Cliurcli Socu;i, It. K lli)f. Furnterabia, Vh C. HiRui.-ra. I'. R 197f. Port P;isndi;;o Mt.. liOiif. San Ciprian, li. F 121f. .Mt- Faro, I79t)f. Port Baniiiero, g. I^ Kstaca, 1 It. R3.i6f. J iPort Vivero, ffl. town IC. Ortegal, A, i, tow. (SI I l'4orpt.) / ('. Prior. i,It. F4ir,f. M Miie Vinioso, 785f. IVrrol, g. mole (•..nifia, aa, lt.F, Fl. .T12f..... S^arpis Is., KW Uin., It. | F. Fl. a.llf. ' J (,'. \ilhino, i, NE pt., It. F l 24.3f. i (' Torinana, X , pt (• Fini-t.rre, It. K iCdf. f^ii.ijal Pt.. It. F88f. . ( . Corrobedo, It. F 1061. Ons I.. ^ .-tm., Ir. F. Fl. 42lf. CcsU., NS4m..l'. F,FI. 6iP4f. c. ,><,ll,.|,o. h. It. F 7Jr. I Vign, Ji. K lo'Jt. 45 4' 5j 45 SS-z] 45 34 I 44 so-3; 44 50-3 44 387; 1 3'; o 345 3'? 1 150 I 2S5 I 330 I 39 7 43 237 43 '97 43 27°; 43 27 I 43 '^8j 43 202 43 21 [ 43 2S0 43 3 43 279 43 30 43 25 43 287 43 30 7 43 34-2 43 35 5 43 420 43 36 ! 43 35-5| 43 347 43 32 43 43 43 43 43 47-2 43 40-5 43 46 43 34' 43 29 43 28-5 43 225 43 215 43 'O 43 4 42 Si 42 44 42 34 42 225 42 '2-5 42 6 42 '5 2 54 3 3 3 5 3 27 3 36 4 5>-5 5 7? 5 '8? 5 5 495 6 275 6 50 7 2 7 8 7 25 7 35 7 4'-5 7 7 547 8 8 8 14? 8 245 8 SO? 9 "3? 9 18 9 -SS 9 *. 9 S 8 55-5 ? 54-5 8 53 8 4! >It. Nossa Sufiora del alba, 1 r-7tif. /' Mt. Peneda, 4542f. POSTUCAI.. r>cf. K. Mino. Pt. Pico: Vlana, II1,2 Its. F Ki7f. Mt. Destrello de Malhada,! 3602f. J 0|>orto, ffi=;]. Fort Si. .Jjas ) da Foz / Aveiro, New B.ir, E;^ Ml. Caraiimllo, .■i274f. Mount Bnsaco. I793f. , Coinibr.i, University C. .Mondipo, It. F .■)02f. Fi;;ui-ira, E}?, It. F .'iBf. N'azaretli IJmiings, It. R .365f. C. Carvoeiro, pt.. ll. F ISOf... Monte Junto, 2135f. Mafra C. Roea, It. R- .59«f. Mt. Cintra, sum. IGOOf. DaGnia, It. F 167f. St. .lulian, fort, It. F 12M. .. LisnoN, g.MAKiNK Obs., [B HOVAI. OBtiEKV.ATOKV C. E-.pichcl, 1, A, It. Fl. 53.if Setub.il, S C. Sines, /, i,lt. F ISOC. Monchique Mtns.,siiiu Foia,1 29.091- / C. St. -^ i, It. R| Sajrns I't.. Semaphore La^os, Piedade Pt. C. Carvoeiro, lowe V,. Sta. Maiia, /, It. F 109f. ... Mt. Figu, 1365f.... 42" 10' 41 5S 40 53 41 88 40 39 40 325 40 23 I 40 I2-S| 40 II I 40 9 39 36 39 25 -ol 39 21-8 39 " 38 56 38 47 3846 38 418 38 JO-4 38 42-2 38 42-5 38 24-9 38 32 37 57-5 37 18 37 I 36 597' 37 47' 37 5-2 36585 37 6 R. Guadima, ffi,V,.CanelaI.,l 2 Its. F IU9I., 431. /, Palos 37 1{. Giiadalquiver, San Lucar I L'lOkout J Rota, p'lT Cadiz, S. Observatory S Fki St. Sebastian, It. F, Fl. C. Tralal-ar, It. F. Fl. Tar.fa, It. F 130f. , Paloinos I Algccira.s, mole 1 68f.. 36 36 DO 36 36 36 36 GinniLTAn, Dockyard Flag- 1 M«ff J Eiiiopa Pt., It. F 1501". 36 73 36 O2 554 TABLE 10 MAIUTIME POSITIONS .,ln;.n, m. <• l'.'-)! .le. It F, I- 1 1 i-l. 7, Mii'ag.., $n, ' •) Sm-ratif, A, 1, It. 1', l-' . \ yi'nf Mf . v. Fl. 72 l-oit A-iiilis, C.silc r. Tin.is.., A, i. It. r 480f. ,. C.iiiiiL'iiia, Escoiniirera I., 1 It. F. •-'■-'.W. J C. (i.- r..l s, It. R 263f. ('. CclViT:! 1. rii..;i. Ki'.N r. of rU Sj | i. F,KI. IMif. J AlicMiite, Castle, (It. F' -Jtif.).. Mt Hoidaii, j,'Mp C. Nao, Fpt C M, AT.t.inio. It. U 57 .M(M.K..,Mi.,J497f ValoTHia. It. V 39f., mule (J. Canct, tower ........... \ Oiopesa. It. F, FI 74f. , I til iil.roti'8 : .>fi-Jf. I'ort Alla()Mi-s, I'l. de l.i Bafia l''.l.n. Ii„ S passage 0. Hoik, tower C. Tortosa, Biida, It, Hev.\ 174f. ; C. f>il(.ii, pt.. It. i\ Fl. 1391'... Tair:.g...ia, ll. F 54f. H^ircrliiiui, ffijy mole It. 1', "I l-1.4."if. ! J Ml. .lui, fort Maaio F, Fl. 1 3*. .87 36 25 36 29 i(J 33 36 38 36 43 3643 36 42 36 44 38 ':8 3'' 41 36 5*^3 36 43 36 45 30 5& 37 23-4 37 253 37 32 ..7 33-5 38 10 38 20-3 ,8 36 3S 43 38 48- 38 48 39 II 39 26 S 39 430 40 4 40 23 39 54 40 335 40 41-0 40 490 40 42-4 41 21 4" 324 4« 43- 41 496 42 17 42 19-2 Vre.st S°ig'7 5 -6 5 9 5 »3 4 37 3 28 3 I 3 3 2 42 2 28 6 2 11-2 2 6? » 54-5 ' 34-5 I 28 I 7 o 9 Ka~t o 9 o 25 o 42 o 39 o 53 o 45 o 54 « >5 2 II 258 3 S J 12 3 14 3 « 3 »7 3 '7 3 «9 FRAHCE. St. Pedro de Buda, fon,„ C. S-rnclla C. Hearn, It F 7h\(. r.irt V.iidres, !t. Fl. 98f. IVrpignaii La Nouvelle, It. V .iuf. ... Naibc I dral i,,F .Wf, F lost'. FortBre.scun.hSEl. Aide, Mt..lt. K4l.ir Cetie. S, Ft. Louis, I .Montpelier Aigue» iM..rtes, It. F 3n(. W. Mo. orKlione,Cani..rgiie, ) 2 lis. F I2.if.,38l' J P.de Bone, ffi, 2 lis. em. F\ 49f., 9.'>l' J C, Courunno Marsedle, St, Jeau Fl., F 30f. Obskkvatc»hy Pl.ner 1., It Fl. 2(171. Mt.St.Miel)ael,t>emaph.,1341l. 1. Hioii, KW In,., lower Cassis, ID, Port, 2 1.8. F 92f., ) 311 ^ J Cassidtiigne rli Cioiat I'oit, li.F4Ul' Baiidol, Chiireli C. S.cie, f^eniaphure TouIoM, m. tll.servatory (ird. Hilieaii, It. ¥ 1121. Pon,uer,lesl.,#4.n.,Spt.,\ It. F, Fl. 2621. j Port Cross l.,^ 2,',iu., Fort 1 Vigie .'. J Tiian I., ^ 4iin., NE pan, 1 It. F24(ii'. J C. Caiiiarat. It. U 42Gf St. 'I'ropez Frejus, t C. Koiix. X. *,suni. iGOUr..., Cannes, S lower Lenin Ix., KW 2111.. Sextr.iks C. Garnupe, It. V cWSf. Aiitilii-s, [a'Mwrli.li. F,F1,49I St. L^ientdii Var Mee. St. Fianeis Cluireli - Uii-r.itVATonv,,\Ionl-gios,. Villa Franea, ffl C IVrrat, ll I!ev. 229f. Monaco BAIiSARIC XSI.es. nriiif ntera I., ^b 3in.,SK pt., 1 K-P ■'■'•'">•■ J S pt.jor I'l. Angaila, i ■iza, Port St. Antonio, ffl,"l .■jcia I., It. Ucv. 2S9f. J Co: Pt., ll. Int. I80f. Cabierai...|(i3'm.','5«lV.',Pt.'l Aiisiola, ll. Uev. 404f. ... j 42 31-3 42 43 43 O'S 43 »' • 4i 15-5 43 '7 9 43 23^ 43 37 43 32 o 43 207 43 236 43 >9 43 "9 43 13 43 «o 43 128 43 87 43 103 43 82 43 32 43 7 5 43 » 42 59 42 59-9 43 z' 43 '20 43 14 43 25 43 28 43 32-9 43 30 43 338 43 33" 43 407 43 420 43 433 43 42 43 400 43 43 k^ 38 39 38 3S 38 59 4 39 5 3S 54-3 3° 10' "3 75 70 53 4-0 02 3 30-0 30-2 3 42'2 S3 80 41 4 59? 3 21 7 7? 7 TABLE 10 MAKITl.ME I'OSITIONS (S3) I'lacen , CI ! I I'ttl M^ijorca, C. Siiliunj, /, * , K50f. C. HIaiao. i, li. Vi'Mf. m..le, It. F 3r,t: ... V. Cilia Kigm-ra. T . It. K Dnifjiiiiora !., jf 2m., It. n. Il80f. Mt. Oal.>t7.o, :m3(. <;. K.irnieiiton, JL , It. K 51 C. I'era, i, It. K, Fl. '^41 39 SS Minorcn, C. Dartuch, /, T,"l It. F, Fl. 71f. / C. najoli, i.low. a.iCf ('. Ciivalk-ria, //, i. It. K 3(19', 40 58 .MalHM,, Ifi.li. F;:ir. 39 5.; .\jn;I., L\V ^in..lt. Ucv. 17 If 39 4S I.at. N I Ixjn. E 39° '6' 39 22 3) 34- 39 28 39 39 39 5S 39 43 BARniNIA. Kazzoli T., It. F2S-.'f. (• .Itlla IVsta. T,ll. K. Fl.22()f. Ton Tonus, [B. It. F 47f. A-inara I., # lOm., I239f. ... C. Falcone, low. filof. C Argcntcrj, sum C.Caccia, T,P.C..nle,a,snin. AlphcTo. Catliciiral C. Marargiii, rk ('. Maiimi, tow. on N pt M;il .liv.nircM-ks. iP3rn.. mid. (■o..,., ,li Donna, rk.[*e.] .,. C. St. .M.rco, toner 0. Fiasca Orisiano, grt. towt-r Mt. Areiiciito (or finger ofl Or.slano), 271:;f. / C. I'ecora, pt., low Sl IMetro ]., NS 5Am., 702f.... St Antioco 1., NS 9in., S\ snni. -81f. J T.inirk., T. SOuf- C. Teul..d.i, i, T.mini. 72.^f Port Mallaiaiio. ffi. tow C. Sparlivento, It. F 264f. C'agliari, w. St. I'ancras Cli.... Cavoli l.(offC.(:arbonara),tow. C Ferralo, i , 8iif. pt Ml. Seven Brothers, 318Gf. ... € Hellavista, It. F.'i41f Ml. (icnnargeutu, 6l02f. C. ('..niino,pt I.iinbarra, pk. 43.)lf. Tav..laral..#3im., Fpt. ... ('. Figari, sum Kock f aprcra I.. NS .'iin., swin Madaleoa 1, old lort C. Cr-o, Sl. F^i.rcn Pt. Perall. COBSICA. S Uiraplia I., It. R\ 41 1»3 41 ' 40 50-2 41 5 40 573 40 437 40 33- 5 40 335 40 197 40 2-5 39 59 39 528 39 51 2 39 46 39 54-3 39 357 39 27- 1 39 97 38 583 38 516 38 5' 9 38 S3-' 38 52-5 39 132 39 61 39 «7-5 39 185 39 558 40 1 40 3' 4 40 510 40 548 40 59-9 41 169 41 129 4« >34 2 47 2 38 5 2 32 2 19 2 3' 3 '3 3 28-5 3 495 3 48 4 55 4 180 4 «7 9 207 9 9? 8 247 8 182 8 122 8 90 S 102 8 19? 8 235 8 24-0 8 .7-2 8 265 8 27 8 3<7 8335 8 25? 8 177 8 20-O 8 25 2 8 39? 8487 8 5^-5 9 77 9 3' 5 9 400 9 265 9 435 9 19 9 50 5 9 110 9 450 9 39 7 9 290 9 29 9 240 (24) Places ':::!} Calvi, Ft. Hivcllata, It. F 2891'. C. Kosso, W pt Sangiiinares Is., J* F, Fl. .3-.Mf. Ajaccio. Cathedral . C. Mi.ro, 8\V pi C. CaiiipoMoro, m, tower Pt. Seiieieso. A, e.\ir C. Feno, It. F 6.>f. Uoiiifario, g. It. F 9Sf. Pertusalo, It. K VJUf. Port. Sta. Manza, g, Pt. Ca pieciolo, tower PoitoVecchio, ffi.ChiapcPt. It. F, Fl K. ixir. Fioienliiia, tower Bastia, [E, Uiagon ha.-ton, ] It. F 82f. j M.ulle St^llo. 4.i.32f. Fiiioecliiarola, toner C.St. Martin Veiitiiiiiglia I't Mt. Grande, aioor C. del Armi Port Maurizio, mole h.l C. de la Mele, /, Gallinara I., tower Finale, Church Noli, Coiiv. St. Francisco Vado, Fort St. Lorenzo Snv..na, [a'■^ Citadel Pollark Genoa, a, 3 ll.s., Int. 340f., 1 F 921', F 691'. / Pt. Chiipa, sum C. Porio Fiiio, tort Si'strl di I>evante, lort Fort V'cnere, g, N enir Tino I., I-. Fl. (i K-ctric) 3S4I'. Spe/.zia, g. Castle MonicAliissinio, .^213f. Viaieggio, Saiii'S Arno ){., month, fort Pisa, leaning tow Florence, nuomo Halora, shoal. It. F 60f. Leghorn, g. It. li"" I.54f. Gorgoim 1., NS Ijm.. A, mid. Val di Vetrorf.,V3ni., W pt. Casiaguetto, fort C. IJ.iia, lower Casli;:li. ;i, to tort !{. Omiirone, mouth Foiiniehe, 5(, 2m., N one 32f. Talamone St Stcfano, centre of town ... .Mt. Ar;;entario. telegraph Capraia I., 5P 4m., fort I'.ilmaiola I., NS im., It. 1 P. I'-l •■'•■'•'I- ■ / Klha, N extr , " "' C. Vi 42°35'2| 42 14-.? 41 52'S 41 5S-0 41 44-5| 41 385' 41 340 4" 238 41 23S 41 22'2 41 251 4' 36 42 170 42 41 8 42 475 42 593 43 43 43 45 43 50 43 49 43 53 43 58 44 2- 44 99 44 ' 44 15-5 24 44 20-0 44 lS-2 44 16-4 32 44 I 6-3 .. 3 43 5'-8 43 40 8 43 43 5 43 40 8-2 107 . 597 42 55 7 48- 1 42 460 39 42 34-6 42 323 42 264 42 23 2 43 32 42 5 '9 42 526 7 33 7 43 7 37 7 54 7 59( 8 II 8 13 8 19< 8 227 8 245 8 277 8 46 ; 8 540 9 105 9 14 2 9 25 5 9 527 9 5' 9 52 ? 10 14 10 157 10 \C 10 2.) " '5 5 10 12-7 10 177 9 53 5 10 21 10 32 10 297 10 31 7 10 44 s 10 53t 11 o ■ >o 53 ' II 8 lO 2h 10 247 TABLE 10 MARITIME POSITIONS Places Lot. N Lon. E Elh.i, I'lirto Feriajn. | SMIa fort, 20uV. — W.rxtr.orPt. MoitiMliiuio — Port Lonofone.Ciiad. rh.... — Mt. Calamita Pianc,5aI,NS3ni.,/,lt.lic-v.'\ HDf. /■ Af'iioa rk.,or W. Foniiielie. ef. .Moiiieonsio I., % Sm., iO-Gf. GIglii. I., %5iii., S pt Giaiiuti I., ^ 2m., S |it. ■ l'"oriiiica di Burano CivitaVecchia, a,lt.F,Fl. I21f. C,I.ina,o,rf. [>,.] TilMT, H. Fuin.icin.., 2 Irs. F. Riiiiie, St. IVtet's, dome Tort Anzi... ffi, It. F. Fl. 92C, MnnK-Ciicell.., It. F I25f. ... iVrraciiia, It. F 26 Gieta, It. F, Fl, St. Ca-\ theiinelow., 2:i7f. J Mola, watering pi Ca.stel Voltnrno Paniiarola I., NS I^'m., N pt. Pdiiza I., i» 4m., (It. F 2ilOf.) Zannnne I., EW Im., It. F,\ l'l-3ff. j IJ.Ue, rks Vaiidolecrt I., ^ liin., J ,\ Fort St. Niccla / Iscl.in I., % ."Jim.. Castle, E pt. Pnici'la I.. NS 2m., N pr.,1 It. r76f. ; Baia, Castle C. Miseno, pt., It. F, Fl. 292f. Pozzu.ili, Chnreh Naples, Olis. Capodi Monte... , mole It. F. Fl. I6lf.... Torre del Greco, VV extr Mt. Vesuvius, 390nf. Ca.stelamare, It. F. Fl. I05f.... Pt. Canipa. ella, It. Int. s7f'.'.'.'. Ca|iii I., EW 3.1,., S or") Carena Pt , It. F, Fl. 238f. ( Mt. St. Angelo, 4680f. Galli rks., tower Salerno, 2 Its. F 28r., 13f. ^''}|42°4S'3 42 458 42 438 42 35 42 21-5 42 20 3 42 19 42 142 42 230 42 57 42 2 41 46 41 542 41 539 41 269 41 J34 41 17 Palo It. F67.if.. Mt. Cocuzza St. Eutemia (J. Vaticano, It. F, Fl. 3.)4f .. Sejlla lieggio Church, It. ¥ Stronih'jli, 30D0f. .... I'anaria I., N pt Secc^adi Capo .ip..ri 41 150 41 25 40 567 40 540 40 582 40 504 40 47 5 40 439 40 462 40 487 40 46-5 40 49-2 40 51 8 40 503 40 47-2j 40 49 40 41-5 40 37 -^i 40 34-0 40 32 oj 40 39 I 40 340 40 39 40 14 40 o 40 1 39 4S0 39 37 39 '& 39 3 JS 37-2 38 24 3S 14 5 38 7 38 48 2 38 38-; .?8 37 : 38 M-. 38 29 IO"20'5 10 62 10 6 10 37 10 18-5 10 55 1 11 65 >i '35 II 47 11 50 12 13-5 12 272 12 2S7 «2 37-5 •3 45 J3 «57 «3 34 7 13 36-0 13 570 12 51 5 12 58 2 13 3 7 "3 62 13 260 >3 577 14 10 14 147 14 157 14 2r'7 14 26 ■ 14 28-2 14 225 14 195 14 II 7 14 31 14 25-5 »4 45 14 53 15 18 15 33 15 487 15 50" 16 16 16 15 '5 50 15 56 IS 45-0 '5 39 15 "37 '5 45 14 545 14 507 14 sb Vulcano I., 160If., It. F, Fl... Felieudi I., 25981'., Church .. Alieudil., su.i.mit, 21-2f. Ustiea I., # 3m., Uonio- 1 Mono pt.. It. ¥, Fl. 3281'. / SICII.V. Faro I., It. F, Fl. 147f. Messina, g, it. P, PI. 134f. ... Scaletta, (ort Trizzi T.wer Mt. Etna, lo,874f. Catania. Sciara Biscari, Ii.F', 1 PI.9Sf. J C. Sta. Croce, It. F 91f Augusta Port, a, It- P, Fl. 881. C. I'auagia, pt Syraeuse, S, w. r, It. F 82f.... C. Aloirodi Purco.lt. Fl. 108t, 3S°22'i i4°59'o 38 34 ■ 14 342 38 32 7 3S 42 s 13 117 Pas.saro I., NS Im., It. P, PI. t '•■^7f. j — S. extr., or Coirenti I C. Sealamhri, It F 12 If. Terra Nuova, Col I.icata. Casile, It. F aif Rossello, It. P, Fl. .•!24t Girgenti, ffi, Jlole It., 3 Its. 1 CBiancc, 9uf., (.shI. ^m. S), \ tower J C. St. Marco, fort, tow C Graniiola, It. F I23f. Mazzara, Cathedral Marsa'a, It. F, Fl. 6sf. Trapani, [H, Cul.iu.bara, It. \ F, Fl. 134f. / St. Julian, Castle Mariiimo I., MS 3m , 23:Gr., 1 N pt., Castle / r.<>vansoI ,^3m.,Npt.,T.tow Favignana I., EW ."iui., St. 1 Cath. Gistle, I249f. J Poivelli rks., ^ fm., T liclie. It. F85f. C. St. Vito, It. F, V\. \-i-2f. ... ;tel a Mare, Peirolo Pt li Gallo {10921.), li.Fl48r i.KK.MO, S, Observatory ... Zatf.ir.ma, It. F 11 If. •mini, forr.lt. F 3l)f. C. Orlando, X , Cast C. Calava Milazzo, It. F 288f. Skerki Bank, 1 Keiths rf., I Pautellaiia I., S. Leonardo,',^ windmill J sum. 2730f. Grahams shl., lof. 3$ 15-8 38 11-2 38 17 37 34-4 37 45 37 29 37 145 37 128 37 65 37 30 37 00 36 55 2 36 41 2 36 385 36 47 37 2-9 37 60 37 175 37 17 37 23 2 37 29-5 .^7 337 37 292 37 474 38 07 38 227 37 5'<7 38 1-6 37 557 38 4-5 37 59 38 I II 38 25 38 135 38 67 38 65 37 59-5 38 2-2 .^7 59 38 98 38 I2S 38 161 JS 397 15 35 2 15 277 15 11; IS 0-: IS 6 15 14 15 170 ■5 >S-5 IS 21 IS 80 »S 97 IS 5-2 14 297 14 ISO >3 570 ■3 277 «3 325 »3 »7 12 402 •2 35 7 12 27 12 30? 12 36 12 37 12 210 12 192 12 270 12 26 12 44-: 12 54 13 ly: 13 21-5 13 3'S >3 4--: 14 I-; 14 27 14 45 ( >4 54 15 140 37 455 'o ■ 37 48 6 10 56 6 36 50 36 46! 37 9 Linosa I., *|j i;;m, landg. cove 35 S' S| 12 520 Eampion I., J' Jm I, impedusa I., EW Km., T ,\ 35 32-8 35 29 2 12 3S 2 TABLE 10 T>rn MAKlTIiMK I'DSITIONS Valetta, m. Palace Shkncebs Monument St. Elmo, It. F 1671'. SE exir., Pt. Uellamara.\ (rf Urn.), It, R 1.^11. J G»/.oI.,'\ 9m., N\V pt„or i C. Ueniitri, It. Hev. 4001. J XTAX.V. C. delle .\niii. tnw., It. F.Tiaf C". S.aitivfiilo, !•'. Fl. 2l(if. ... liriizzano C .Marina de MoU' stcraci C. HiEiuto. pt C. Colonne, luF 133f. Cotrone, It. F 30f. Ft Alice, tower Pt. dol Triomo, tower Kosito Tarento. ^, Citadel v.. Si. Vito, It. F, Fl. LSOf. ... Port Ctsareo, tower , mid. (N pt., U9f.) Lat. N Lon. E (28) 35°53'8 i4°3i'2 35 5.io, 14 307. 35 54 • 14 3'-5 35 49-2 «4 34 I 36 42 14 '32 37 57- 37 55' 38 2 3-* 26 38 53 39 f 39 5 39 24 39 37 39 59 40 28- 40 24- 40 15 5 5: '6 i 'fi 16 5 '7 ADRIATIC. Kl. .■? i C O ranto, Telegr. (E pt. of \ Iia'y) J Fort Otraiito, a,li. F 19-f.... Bniidisi, S,, Ttlrgr., It. F\ lOGf. J T.Tre della Testa .Monopoli, Telegr, It. F .'idf... U.iri, St. Cataldo, It. F, Fl. 1 49f. / Molfetta,tow.,U. F. Fl. (isf. ... Harlctla. ffi', (li. F). 691'. Manltwionia, It. F, Fl 65f. ... Mt. Nero. 3336f Vies e, Sui Crocc, It. F Teimoli. tower Treiiiiti Is., jj* 3m.. Semaplioie Piaiiosa I., /, EW Ic, K pi Pelaso.-a l8.,2,% hn.,lt. F.Fl Pt. Pcniia. tower , Oriomi, C:li., It. F .391'. , Mt. liian.astello, 7B97f. Montepayano, ll'4ef. (riiilianova ColoDclla, Slim. I096f. Uroiiaiiiare, Chunh I'eda'O, C^hiirch Feriiio, Call)., 11971'. I.orclio. ('li.,.')ti.5f. Mount Conc-io, Telegr Ancona, It. N mole, .'Hf. SiniRapli.'i, If. F 45f. luno. It. F 581'. 47-7 5' I 86 6 ' 393 41-4 57-1, 8-3 '3 18 297 18 31 ■65 16 360 16 187 IS 55 5 15 41 16 II 2 '5 •5 305 15 45'? 16 16 '4 430 14 24-5 '3 39 13 595 >3 59 '3 54 13 52-2 '3 53-0 13 435 13 37 '3 3<'-5 "3 30 5 13 '3 '3 07 Pesaro, It. F 3()f. Himini, It. F «7t'. Havinna, tower Ooio, III, W 1110. of the Fo. .. C'hiogiia. ffi, I'atheilral Port Malaiiiocco, E. N mole . S. Nieolo, Port Lido, ffi, 1 fort. It. 9f. j" Venice, Sr. Mark Venice, lubtituto di .Mar Mer Piavu Veccliia, It. K UGf. li. Taglianiento, fort month...' Port Buso, It. Kev. I U. | (Inido, Cli. (It. F) Mo.falcom-, ('linuli ! Tricfte. E, li. Kl St.i 'IVrc-al niolehil. IMf ; Capo d'lstria, Cluinli P.nmo, Si. G. (;iin.cl. Sahore Pt., Pi. IJassania, It 1 F U2f J Citta nuova, CO, Church Parenzo, Cliurcli Rovigiio, HI, Pelago I., It. 42 f. POI.A, ffi, OllSKHVATORY C. Promon <)re, Porer rk , It. \ F nif., (rk. SSE iim.) / Alh,mu,(;hmeh Fianona, Church Fiunie, clock tower Porto Ke, Di Usiro Pt., It. F, 1 Fl. .'•.4f. / Segna, mule, It. F 27f. Carli*paj20, mole Nona, Caihedial Zara, It. F 17 Zara 'Vecchia Galiolark UnieBay, Lslet, [2c.] Sunsego I., ^W 2iii , 3oOf. si.ni Giiviz/.a 1., [Am.] Sette Bocclie' Clian., N or 1 Bonastni Pt J Mt. VelaStrazza, 1070f Zuri I., \ 7m., E pt., Mas-] Sehenico, Castfl Vc.rliia. It. | F I8f. J Zirona piccohi, 1.. snin Tran, St. John's Church Sjialiito, Boticella pt., It. F, 1 Fl. 3.5f. / Makaiska, It. F Solia 1., % 11)111., SK pt Brazza I., EW 7 1. St. Vito, \ 8ig. St mid / U-s»inaI.,E\V 12l.,Pokon-\ jidol I., U. F 761'. i Li.-sa I , EW 9111., Port St. 1 Georgio, .SI. Francis Cli.. 2 lt!<. K72f.. 141 J }"''SiR-st Pclago„|<'liMi.,-( lllOOf., t / Pomo rk., [ii'.], i ProiMlo I.. K\V Im., (off W ) I.a ' ^\ 55'3 4 3 25 48 129 20 26 26 262 28-t, Bnsi 45 38-2 45 43 4) 40'6 45 483 45 388 45 32-7! 45 3i'6j 45 29 5I 45 i8-8 45 '3-6 45 2-2 44 518 44 452 45 5'' 45 8-2 44 59 6, 44 3" 7! 4t 146; 44 6-8 43 56-31 44 43'5| 44 38 I 44 30-9, 44 24 44 i2-3j 43 59 j 43 375 43 i7'5, 43 >9 j 43 167^ 43 9 j 43 34 42 S8 I 43 I7( 43 5'5 42 59 I 12 125 12 23 12 170 12 207 12 23 s 12 205 12 205 '2 33 13 6. '3 '5 13 23 . 13 32 ■ 13 46 2 13 29-5 13 337 13 35 7 13 36-7 13 507 13 53'5 14 7'7 14 no 14 26 7 14 342 14 54< 15 4-; 15 II 2 15 120 15 207 14 33 14 490 15 2 15 44 15 537 16 4 .6 I5-. 16 267 17 ri 16 23 '6 375 16 27 16 10 J 16 >5 15 27 7 16 37 553 TABIiE TO MAIUTIME POSlTIUiNS I Lat. N Bi.i t'a/,/.a I., -^f im., sig. st Ca/.iiula 1.. 5p Im l.a-.K.ta I., EVV 7m., SL I Ucoi-ge Chap.. It. F 342f. J l,iigosliuirks.,EW3|m.,Esuin. M.leda l.,%7 1., W pt - I'ort I'alazzo, g. luin l!aj,'Msa, ffi,f..rt, VV b ..st .\Iarka„al,s.,Krp.,%:i....,M,m Moloma I., sum Vt Osiro, It. F, Fl. 2C3f. Kallaro, Saiiita Vetcrt;narli, :»60r. liudiia, Urcck Cliurch .'Viitivaii, Volovica I't., ll. F... .Men Jits I'r., It. F 3.-3t Dalcigi.o, lll.UiCala lu'a-li ... C. K.idoni, 4U0f., It. Kl C. Pall, sii.n Diirazzo, iiiole, It. F 5L'f. C. l.aghi, tower Avioua, or Valuria, g, \v,"( Custom house / Sasseiio I., % 2m., sum. lOudt, V. I.iuguetla, i , 229uf Ml. Cica, ti.-KiUf. ^.lepi Tignoso, It. F Port Gomc-iiitza, m. D^- Parga, w, Madonna I. Mt. Zarotlu'ma, 3000f. Prevesa, Fort Giorgio Voni/.za zoviAir isi.Es. FauoI.,^|a 3jm.,l3:i9i.,lt. FM v\. 34i,f .■; / Mvilera, NS 2m , sun 42"574 42 46 42 460 42 45 42 430 42 45 42 47 42 46-8 42 38-9 42 34 42 29 9 42 23' 42 2.S' 42 19 42 16-5 42 5-3 41 57 41 55 41 35 41 247 41 lS-2 41 10-2 40 27-2 40 29- 40 267 40 IS 40 29 39 54-3 39 472 39 297 39 39 3« 567 38 55 tSanu.thiaki 1., 4|i 2ini,, N pt Corlii, Ciiadcd, It. F24IIK ...a> — C. Drasti — Mt. St. Giorgio, 1288f — C. Bianco, pt — Vido ]., Fort, Al.xauder... Paxo I., i|j 4',Mi.. iNW pt., 1 Laka, It. F41(5f. / — I'ort Gajo, E Antipa.xo 1., % 2in., E pt Sta. Maura. It. F moU-, .'J4f. .. — Se-ola rk., 1141'. — Mt. Stavrota, 3700f. — S extr., C. Uucato, X, 20Ut: Ithaca, N pt — Vathy, Port, S. Lazaretto — SE pt., or Iganiii Pt Ceplialonia, N cstr. heo-) / 17° S'o 17 9 i5 310 '6 43 16 53-0 17 90 17 18 17 217 iS 70 18 120 18 23-5 18 3. 7 18 46-5 18 52 18 505 19 45 19 95 19 12-5 19 272 19 24-2 19 27? 19 255 19 267 19 14 2 19 177 19 35' 19 48-2 ■9 55-5 19 58-5 20 17-1 20 25 20 38 20 462 20 537 19 27 19 36 19 3I-5 19 567 19 415 19 480 20 77 19 565 20 85 20 43 20 335 20 385 20 33-7 20 406 20 43 5 20 46-7 20 340 20 25 20 265 20 29 Ccphalonia, St. George, Cas- Sum., or -Mt. Elato, 52lti • S pt., or C. Monda Z tnte, N pt., or — Mt. VachroM — S pt., C. Wat — leraki I't. ... , It. Fysr. , Dragomcsti E Oaia I , pk., Messaloiiglii ({(mnudia, Casil..- I.epanto. Castle Corinth, Acropiili.s Mnrea Castle, centre Patras, v.'. It. F, Fl. 65f. C. Papas, ruined fort Montague rks., 2, \ im., Kf. Konoupoli Pt C. Glaivnza, ruin K;istro Toniese, 7y5f. C,Kaiakelo,/i Slaruphaiies Is., ^ 2im., J ,\ /.It. F 1271- ." / C. Kunello Pioti I., NS 2m., suiti. CO.)!'.... Sphaghia I., % 2iiu., S pt. ... Navaritio, Pvlos I., It. F" 11 Of. Mt. St.Nieoio, 1542C. Modon S.ipieiiza I., NS 5m., sum. -4Uf. Cabrera I., % 5m., S e.xtr. ... dlo . Venelicol., NS lJim,(Ants. 1 SSE 2m ).siim"57Uf. J Korou, w' N 2m., r, Livi- \ diaPt .■ J Kalamata, highest ruin C. Kiiries Mt. Makrino, 7900f. C. Grosso, i , h, sum. C. Matapan, X, A, It. i.iaf. C. Stavri Maraihonisi C. XjIi.Cpk. l(H(i(. N l'-.'ii,pt Servi 1., NS .'i.iui., S and E pt C St. Aiigelo,"/!, X.l't Ccrlgo I., N. pt.,C. Sp.tthi,\ It. F, Fl. 362f. / — Foit St. Nikolo fo 1., NS 8c., ;,5lit., T "'t.lus rk,, [;.m,] jn I., J- :|'m,, 4 lot'. ■ngotto !.,# (in..,sum. 1 38° S'5 20°34o 38 8-5' 20 41 o 38 36 20 48 37 56-2 37 48 S 37 39 37 42-5 37 45 37 482 20 422 20 427 20 50 20 59-2 20 562 20 545 3S 32 21 s 38 187 21 7 3S 21-9 21 257 3i 17 21 31- 38 19-5! 2: 462 38 23'S| 21 490 37 53 5 22 52 38 185 38 151 38 127 37 55 38 6 37 56 8 37 53 7 37 38 37 15 3 37 'o 37 3-4 36 54 5 36 54 36 530 36 4S-4 36 466 36 4 36 429 36 4' 7 36 475 37 36 547 36 5t'-5 36 40 36 28-6 36 22-5 36 36' 36 44- 36 48-2 36 39-0 36 27-0 36 26 j6 23 o 21 470 21 435 21 235 21 o 21 23 21 85 21 87 21 190 21 02 21 .34 21 33 5 21 405 21 41 21 420 21 425 21 42 2 21 47 ' 21 527 21 537 22 22- 22 13 22 22 : 22 495 22 59 5 2^ 120 22 57-2 36 13- 36 77 56 55 23 u< 35 5<^ 23 13 35 58-5 23 IS 135 so-ij 23 IS I TAPLE 10 MAIilTlMK I'osrnoNS (31) Places Mt. Kritliiiia, 260(if. Kar.ivi I., ik., T Fiilcomra I.. % l}ni., A, siini Hi-lnPoiiloI.,ay IJm., T.suni Speziia I., % 4, tin., sum. 8121; Tiikeri I.. NS lin., N sum. ... Napoli ili Romunia Hydra, jp Ilin.,suni. I0.3uf... Stavioiiisi r., K\V fjxn St. Cicurpe d' Arbora I., % \ 3m., mm. SIC pan, IllS.if. J I'oros I., KW Dill., a', W ( pt., It. F 96f. ( Meihana, .Mi. Klivlona. 9429f. Kpina [., # 8ii.., Mt. St.\ Bias, on S part, 17o2f. ... J Kalamaki, K. eiit. canal I.i-um. ^111 , sum , .ulo I.. NS 2111 , NS 8m., Mt. Si. { SEpait / I., (Askauia), 4» ) Anaphi \., -^ 7m., sum Ileriiionisi 1 Staiiipal.a !.. nr Astropilaia, 1 ,}*4l.. SWsum / Levita I., EW 4m.. E pt I Z.nari I.. ^ 2m., W pt j Aniorgo I., jP 18m., sum. 1 near mid., 21751'. / Karol., EW 4m., mid Skmosa I., ->i, '.'im.. SEpt. ... Il.r.idBl., ,f*4m.«um 37 56 2 37 58' 37 58-3 37 38S 37 44-3 37 38-5 37 530 38 71 37 59-5 37 37"3 37 37 >S 37 10 37 27 36 48 36 33 36 405 36 45-3 36 493 36 46 36 38 36 37 36 40 36 427 36 369 36 220 36 IS ;6 23 36 32 36 32 37 o 36 58 7 .36 5° 7 36 53 36 510 3(' 497 23 3S0 23 43 7 23 44 24 I 7 24 37 24 67 24 21 24 19 24 26-2 24 32 24 36 24 30 24 38 5 24 IS 24 9 24 23 2 24 227 24 33'5 24 39 24 35 24 55? 25 6 25 210 25 427 25 28 7 25 13 26 320 26 177 25 40 25 33-0 25 27 5 Plarcs r.. # 121,,. 2.W(lf..\ Coraka, It. F, Fl. 19.if./ Nax.>s I., ^ 18m.. i[i. Zia, 1 SE-dofmid.. .WJdf. J — N pt., or C. Staura Paros C. K lldirii, or IJuev ik Anilparo.s, KS 7m. S pt Strniigjlo I., # l!m., S pt. . Siiipodia, jp Ij^m Myeoni 1., ^'sm., E sum.) 115()f. / Rhema, NS4lTn., Spt I-aNaia, rk., (rk.W Jin.) Svra I., KS 9iii.. I ll.'.f. — Gaidar.., It. K 2j4f. Jcira I., jp 5in., W pt 'I'inus I., «j ISiii., 2.i40f. Aiiilros I.. *!, 22in., Ml. Ko-\ vari, W >ide, mid., 32(IUf. / — C. Fas-a, It. F, Fl. 708f. .. Kaloyeri i-ks., NS 2m Nf(>ropont, Euri].:o. It. F 39f. — C. Don), islet off, 93f — C. Kumi — Mt. Delphi, ,')7Uif. G.of Volo,C.Kavcjulia,lt. F 85f Volo, fort L;.f. N Skyro I., % 5 1,, rf. N end, 1 Mt. Kokhilas, 2oG5f. ... / Skyro Poulo, [Im.], 61 7f. ... Skantzura I., NS 1 1., mont.... Adelphi Is., 2P Urn., .i21f. ... Khelidromi, # i'l., N sum. 1 lo90f. j SkopelosI,4J5llm.,>um.2149f. Skiathosl., ^ 6m., » , Mt. 1 Stavros, 1448f. .....' / Pclago, NS 2 1., sum. lO.'iOf. Psathoura I., It. H. 12yf. ... M(. Pelion, 5310f. Ossa, Mt., 64U7f. 37° I '8 37 «2S 37 9 37 145 36 560 36 562 37 25 37 27-5 37 22-0 37 217 37 28-9 37 25-5 37 362 37 350 37 501 37 57-6 38 10 38 28 7, 38 9-4' 3839 i 38 37-4' 39 6 i 39 240 38 49 7 50 39 5„ 39 58 39 10 39 88 39 "-4 39 204 39 30 39 2(> 5 39 48 o TVRKEY. Mt. Olympus, 9;oJf... Salonika, g C. Kassandra, /, It. Fl 25°3''? 2S 33 <- 25 «4 25 567 25 50 24 57 5 25 35 25 27 2 25 140 25 24 557 24 59-, 24 39 5 25 '45 24 50-5 24 41 7 25 17 23 3f"; 24 36-5 24 9 7 23 507 23 4 22 56 5 24 36 5 24 22 24 6 23 59 23 53 23 40? 23 28 2 24 3 24 10 7 23 3 22 42 o 40 47 22 40 37 8 22 39 57-2' 23 C- Pxilluri, / 13955 I 23 C. Drapuno, 880f. ' m cA fl -,-, Mt. Athos, sum. 6349£ Pilaf Tepc, 6U;if. KavalaB., It. F USf , Tliaso I., NS 14m., sum. 34281'. 40 41 7 0. Feuar, It. F 72f. 40 56 7 Marona, hill, 21?4r. 40 527 (; Makii, w', -f Im 40 49-5 l)e.lea;;atoh, It. liev. Il.',l'. ... 40 50 Knos 40 420 Xeros I., NS im 40 365 26 Samothraki, \ I2m., 5248f... W pt., C. Akrotiri, t Znrafa ik ■aii I., ^ 5jm.. 973f mnos, f>^ 7 I., W pt , or C. \ Moiirtzephlos, Mior. / Moudio.s. ffl 39 56 5 23 40 9S| 24 40 535. 24 40 55 40 27-0 25 35-5 40 282 25 27 c 40 275 25 505 39 3''0 25 17 39 58-7 25 20 39 520' 25 16 ? TABLE 10 MAiaXIME POSITIONS Plates I Lat. N Lon. E (34) I, at. N Lon. K Lemnos, S pt., or C. Irene ... — Nand Ept., C. Plaka Imbros, ^ 51. sum. lH59f. ... — W pt, orPt. Anflaka Dardanelles, Asia Casile, It. \ F50f. / Gallipoli, It. Rev. 120f. Koutalai I., Roun rk , It. F 1 49f. ..; Marmara I., Fanar Adasi,\ It. F. Fl. 1.34f. / Tasha harb., S, Liiran liodo.-tQ ekii, It. F 184f. Constantinople, St. Sophia Bo'^porus Stiraglio pt.. It. F, \ Fl. 117f. j Roumili, It F I9nf. Fanar Bonmnu, li F S.^f. .. Proti I., [Im.] Vill. E fide .. Dil Biirnu, It. F 40f. I>niid C. Bos Burnu, lOoOf. GemlikorKios Kalolimiio I., NS 4m. N sum. BX.ACK SEA. Kill. Fl. 1 C. Karabourm't, N pt, .3r,2f. j C. Kouri Cizopol Boiirgas, Minaret Akhi6lo. Mosque C. Emeneh, E pt.. It. Fl. 207f- Varna, Mosque, mid C. Kaliami, rnin C. Shablerlt..FI20f. Kiistenjeh, C, It. F 6Sf. Portitski M.mth Danube R., Sulina mo. \t.\ F70f. / Serpent's I., w. It. R I94f. ... Ts.iregradskoe mo. 2 Its. "1 F.'iaf. / Akt-rman, Church C. Fi.ntaue, It. F 2001'. Odessa, S.Reidovi mole, It. 1 F, Fl. 63f. : J OltSERVATOnY Berezan I., % ^m., fort Kinboum It. v. 2 vert OteliaUov., Church Nicolayev, a, Ol-scrvatory ... Khersot), Cathedral Tendra I., /,■% 8ui.N eud,b.rac, - It. Rev. 961'. hell Armiansk, Church C. .latkaii, It. K 117f Eu|iatoria pt. It. F, Fl. .')2f. ... C. Khcrsoiicse, /, U. Rev.l 1161' ; Suvasiopul, S, Church , C. Sariich, pt C. Aitodor, It. F .3l.'if. 39°46'6 40 1-7 40 106 40 72 40 90 40 240 40 31- 40 38 40 295 40 59 40 58-5 41 03 40 57' 7 40 54 40 44 5 40 45 7 40 32 40 26 40 34 25'2r5 25 270 25 49'0 25 400 26 245 26 41 27 28 s 27 45 27 36? 27 31-0 27 5S0 28 59-0 Mt. Tchatirdag, SW sum.. C. M>g.. I'heodosia 0. Chaouda, S pt.. It. 120f. C. Takli,lt Kertch, E, Church.... 7? 29 29 2? 29 35 29 3° 7 29 55' 28 47 29 9'5 28 32 41 217 4' 527 42 263 42 30'3 42 340 42 42 43 >2'o 43 22 43 327 44 105; 44 40-5 45 9-3| 46 48 46 II 9 46 22-8 46 30 46 28-5 46 35'6 46 35"4 46 36-4 46 58-2 46 37-7 46 217 46 18-9 46 7 45 20' 7 45 9-7 44 35 44 37'9 44 23 42 253 29 37 28 41-2 28 30 27 437 27 307 27 405 27 55'7 27 565 28 297 28 37 7 28 4 10 29 17 29 40-5 30 14-2 30 29-7 30 202 30 45'S 30 46 30 45'5 31 23 31 29? 3' 31 580 32 380 31 320 3' 30-2 33 43 32 297 33 '5 33 22-2 33 295 33 44 34 7 7 -atla 44 'o 34" 17? 467 35 7 57-Oj 35 22 35 26 Yenikaleh, !t. Fl 409 C. Kazaniip, sum. ... Arabat, E bast Glienitche.-k, It. F 81 Bprdiansk, It. F IhSt C. Bielnsarai, It. F 7; Mariuprd, Church ... Taganrog, It. F 1611'. Azov, Cathedral ... Longnos, 2 Gheisk, It. F 34f Tanian , Anapa, It. F98f Ghclcnjik, m, furt .Soukoum, I'ort, It. Rev. 121f., C. I3atoum, Mosque, It. F 65 Re/, Tr.hizondc, ffl. It. Fl. 105f. ... C. leros, T,Npl„lt. Fl. 98f... Triboli lieresoun C. Yazon, /, rks Euuich, S. Mosque Samsoun, N It. F 56f. C. Kiz'l Ermak, W. mo. riv... Sinopc, Castle, It. F 344f. C. Imljeh, IL F, Fl. 92f C Kereuipch, ll. Fl. 262t'. Amiisira, E exir.ll. Fl. 312f.. C. Babi, It. F6.i7f. Kcphktrn Ada-si I., It. F 961. . ASIA MINOR. 45 o 44 59'5 45 5'9 45 21-2 45 23-1 45 280 45 I7'9 46 II o 46 46 4t> 52-5 47 53 47 122 47 70 46 48 46 43 45 i3'0 44 54 44 33 4 43 >7 42 59'3 41 394 41 3'0 41 41 35 5° 3627 36 29 5 •m.. W extr rf.NW-d., \ J Rabbit Is., /, ^ Tenedoil.jSjG sum C. Baha, fort . Mt. Ida, 57.50f. Aiiramjti Mitylcni, % 13 1., K pt.,-| C. AtriaMavia J — Mt. Olympus, 30791'. — W.pt. C. Sigri.lt. Rev. 1801 Smyrna, mill on Dauagaz ^ I'T i Vourla Scahi, fountain C. Karaliouruou. pt Scio, NS 27m., N sum. 41571 Veiiclico I.. ottS pt.of Scio, T Psaia I., % .im., S pt Antipsara, W pt. ,.. C. Blanco , C. Koraka, T Sighaj.k, ES 39 5S'5 39 5° 39 282 39 42 39 355 39 o'7 39 4'2 39 4 7 39 13 38265 36 39'2 35 54'o 35 29 5 34 52 36 48-2 37 207 37 355 38 57 39 2b 5 .38 3S 38 '7 36 44 37 '8-S 38 3-2 40 16 40 59 7 41 37'0 40 315 39 460 39 260 38 49 38 24 37 4I-5 37 '77 36 21 2 35 '25 34 5< 33 '7? 32 245 31 30 175 26 3-7 26 5 26 4-5 26 505 27 25 26 377 26 2 26 55 25 5' 27 97 38 217 38 399 38 33 7 26 38 80 26 26 47'5 26 227 38 32 38 32 38 1 6 38 6-5 58 t2 25 35 25 3> 2fi 147 26 36 7 26 48? TABLE 10 r.6l MARITIME POSITIONS I'ljces Scala Nur.va, It. F 98f. , Sacnsiim Daf;li. 4l3Uf. , C. Moiiodecidri, ruia Wrick rk. alf. Builro.m, g, Castle , Port (iiova C. Kri.., W pt. lujah I't Symi t.. gip. NS 9ni. S islet,! Trompeito / C. Aloupo ARCHIPEZ.ACO. Samos, Mt. Kerki, 472jf. — Vaihi ffl, port. It. F 260f... — S pt., or C. Coloniia Furni Is., NS Um.,S extr. 1 rk. Nikaiia. ^ 22m. W pt., or\ C. Kipas It. F. Fl / Mt. Melissa. 33P0f. Gaiilaro, E\V 4m. sum. 720f. Arki, % 4m. N pt I'atmos, NS "m. Prasso Islet... — Scala. g, pier Lipso, % 4*m. SW pt I^ro. ^, Sni., Mt. Kli.li, lOtOt. KHl'tnno, ^ 10m. Mt. I'ara- \ Mva, 22.i0f. / Sajihunidi, ^ |'SI 37 39«| 37 21-3 37 90, 37 20 37 35' 36 410 36 394 3G 307 36 330 37 43 S 37 47 i 37 383 37 as 4' 37 31-2 37 32-2 37 28 i] 37 249 37 >6o 37 19 5 37 '82^ 37 107 36 58-8j 36 53-0 36 431 3^ 305 36 355 36 356; 36 261, 36 122 36 269 36 87 35 52-4 35 5'-2 Stakid 1, 2 Is., [2ui.l N one , Tniii Nisia Kinrlii Ni,i ... Siriia I.. 10871'. Adelpiix Is.. None... Ovol., ITOf. Candla. C. Krio Pondikoiiisi, 7.ii)f. \iiT a Gr.il)U«a, N point X exlr, C. Si.«da. A, i, Klanifl, SB, It. F 8.if. (:.T.ipiti It. F 82f.. 35 134' 35 34 7 35 3S6 turn. 35 41 : 35 308 I 35 361 35 28 I I Rliitjinno, it. F •Of. '.J 35 27°l6'S 27 90 27 130 27 177 27 27 5 28 22 27 54? 28 10 26 385 26 58 26 527 26 31 2 25 59-5 26 47 26 5S 7 26 44 5 26 347 26 34 o 26 44-2 26 515 27 00 26 56-7 26 56-5 26 57-5 27 no 27 35 27 210 27 33? 28 16? 27 43? 27 470 27 56-0 27 10 27 14 26 50 26 51 26 29 26 14 26 25 26 45 26 41-; 26 38-5 25 35 5 23 317 23 2.S 23 34 23 43 7 24 I 24 7 7 24 9^ 24 20 2 (•%) Plac C. Stavros Me|,'alo Kaslron, CE,(It.F .531.) Stnndia I., summit, 870f. C.St.John,m ,SW2^n Yanisadcs Is., N pt., Paxi-"l mada j C. Sidero, It. Rev. l.SSf. C. Salimion, or Plaka C. Zakro Kupho Nisi, S pt .Gaidaro Nibi, W pt !c. I.ittinijs JMt. Ida. 8O60f. Q 1 Paxi.nadia Is., Wend, llBOf. ' Sph,ikia Gavdo I., % 5m., It. Rev, llSlf Gavdo Pulo.lfe Uni., 440f. ::} XARAMANIA. 35°25'6 35 206 35 27 i 35 20 5 35 23 I 35 «9 35 9-2 35 5-2 34 547, 34 523 ^^ 547, 35 13-3 35 o 35 12 34 5° 3+ 552, M, — Cape, It F 13lf. Kanighatch, g , watering placi- I-inosa 1 , 3271'., sum C. Siivelah Makry, S, theatre Highest sum., 59'<0f. C. Seven Capes, W pt. T Volosl., T Port Vathy, g, sarcophagus... I'urt Sevedo, S, lank C. Roxo, Hipsili I., T Kakava I , ^f- 4m. S. W pi... I'hincka Pr„m. !t. T, S pt. ... Khelidonia Is. NS 2m., S islet 36 Granibousa I., *|j Ini., w' ) NE (iart / Yan«r. vole .Mt. Takhtalu, 7800f. , C. A ova, i.wW-d Adali.i. CB, It. F 131 1'. , Esky Adalia, theatre, w^,, b(,...r36 C. Karabournu 36 Ahiya, fflo, SEpt 36 C. Anaraour, i Chelindreh, S, w C. Cavaliere, i , S pt. (w N-d.) Provencal I., jp 2m., Wq Castle, bum Pt. I.issan ai Kahbeh, /, slil. i off, It F 49f. Lamas Hiv,, T , W C. Karadiish, It. F 131f. ... Ayas, tower on I 36 si-i 36 43'9 36 5'-5 36 46-^ 36 3V2 36 38-1 ,3b 3 1 8 36 21 3613 36 11 S 36 103 36 6 3b 9-b SYRIA. Ak-xn.ulr R.is.l Kh V 49f..., Antidch Rasel 15a/.it , Ras Ilin Hani, It. FI. 4.'if. .., I.atakivah, ffi, w, li. F 49f. 36 355 36 192 36 12 35 52 35 354 24 S'^y 25 ') 25 142 25 47 26 ii'5 26 197 26 195 26 : 26 87 25 4' . 24 45 24 470 24 35 24 S7 24 4 28 190 28 207 28 3o;' 28 29 b 28 540 29 9 7 29 I4-2 29 l:: 29 25 29 39 29 4' 29 40 29 52 30 9 30 26 2 30 30 30 28 30 38 30 47 31 26 3' 43 32 ' 32 49 33 22 33 437 33 48 33 59 34 177 35 21 35 48 Ruadl.,lt. ri. 92f. 36 97 33 46 36 8 35 47' = 35 42 : 35 3071 35 45 S '34 S'7 35 SI iTripoli, HMmkine I., It. F 67f. I 34 3^ 35 4? |fci6 Beirut, It. FI. V2o(. 135 54-2 35 28 562 TABLE 10 MARITIME POSITIONS Places Damascus, Madinet-elArus... Mt. Hermon, sum. 90.53f la, Jezirch, 2 Its. F' 62f.... Sur, 2 Us. F oGf. Acre, It. F' 46f. C. Carmel Cont. It. F, Fl. 400f. Jaffa, It. Rev 69f. Jehusaleji. Kubbet es Sok- \_ ill, or Dome of the rock j Ascalon, ruins El Arish, fort ; CVPRTTS. C. Arnaut C. Crmachiti Kyrcnia, It. F 6Sf. N and E extr., C. St. Andr Famagoiista, It. F 491'. C.Grego Lamaca, It. F 42f. C. Chiti, /, tow Limasol, It. F 25f. C. Gatto. / C. Bianco, A C. Papho E&YPT. Port SMid. It. Fl. 175f. Nile, Rosetta mouth - Damietta mouth, Kawa ( Burun J Damietta, Engl. Cons It. Rev. ISOf. Cairo, tow. of Janissaries Great Pyramid, sum.(487f.) 1 now 460f. J Aboukir, B., Nelson I :XANDUIA, S, It. R 180f... Arab's tower Ras al Kanais. pt •saMatroo, g, w, Pt.La- 1 e, ,58f. TRIPOI.I. RasalMilhr Tebruk, S, Saracen gale ...., Uomba, or Bhurdali I Kas al Tvn, sum , Dern.ih. it ReV. 92f. Pi. Zauaiii (Ras al Ililil").... iMarsa Sousa, a, Arserjal Has Sim Toliiicitah, pt. of ihe Kotlion. licngliazi. It. Rev. -2f. arah I Marsa Boureig.ih, ruin Bouskeifa I Ben Gahouali, ruin Mar.Ka Zafran, Port Chebek ...i 31 C. Misiatah, Ras Torug, It.l I Fl. l.-iSf. / 3^ Marsa Oiigrab, Ras al Tabiah 32 Lat. N Lon. E 33°3o'6 36°iS'5 33 25-5 35 5' 33 345 55 2i-r 33 '&7 55 "I ? 32 55-5 35 4 32 49 S 34 58 32 2 7| 34 44 3' 465, 35 H7 31 3901 34 327 31 6s 33 480 35 68 32 i6-2 35 247, 32 557 35 20 33 I 87 35 42-2 34 36 5 35 77| 33 57-2 34 56-5! 34 65 34 55 2; .33 37 7 34 49-9 33 36 ? 34 40-2 33 17 34 33 7, 33 2- 34 3S>2 32 42-2 34 44-8 32 23 7 3' '57 31 30s 32 19? 30 19 5 3J 33 3> 52 31 24 3' 3" 30 2-1 31 48 3" 51 31 155 29 586 31 11-71 29 5'7 30 59 7| 29 347 3' 154 27 52 31 22-9J 27 155 31 313 26 387 3« 37-5 '' "■ 16 36 15 13? '4 26? Places Lat. N Lon. E Lebida, Citadel I 32''387 I4°i6'5 Ras al Tajourah, E pt | 32 53 5 13 232 Tripoli, S, It. R llof. '32 544 13 112 Piirt Zouaga I 32 48-51 12 277 Zoarah 1 :;2 55 TVltZS. Al Biban bank, Zcra spit Jerba I., Houmt-souk, It. F ... Kabes Dzara pier , Surkenis li. Nathor Tr. Jcbel Thelj, NE sum Spbax, It. F 38f Kerkeuah Is., ^, 91., /, RasT Sinub J — NE extr., Gzira Kcbir — Banks Eastern buoy It Kadijah, tov\er, 50f. Mfhudiab, Casile Kuriat Is., It. F 98f. Monastir, fcrt Gliadir Soussa, It.F Jebel Zaghwan, 4078f. Hammainet Castle Has Malimur Kalibia, It. F 269f. Rasal Asuad (hIL H.I.) C.Bon. 1200f.lt. Int. 412f ... Zeml.ra, H^, 2.\m. sum. 1324f. Jelicllrsas, 2.536f Tunis, Goleta. ffi, It. F 30f. ... C. Carthage, It. R 482f. Pianal., EW Im., It. F 651.... Cani, rks. ^ 2m. It. F 12Uf ... Ben/ert, fort, It. F" 46f. C. 11 Guerra Frat.Ui, rks. ^, West Rock... Galita I., ^ 3in. pk. Monte \^ Giianlia, 1240f j Sorello, rks., Avenger reef ... AI.GXERS. 33 26-5 33 53-5 33 54 34 '4'2 34 25 34 44 34 36-7 34 49 34 515 35 35 304 35 4S 5 35 454 35 49 36 21-5 36 23-3 36 27 5 36 497 36 58 37 5 37 7-4 3636 36 485 36 524 37 108 37 21-2 37 17 37 199 37 37 31-3 37 237 Tabarca, N tow I.a Cal.i, E.lt. F55f. I lioni, North jetty Pt., It. F 63f.' C. de (iarde, It. F, Fl. 46yf. ...I Ferro 1 ' R,is Iladid, or C. deFer, lt.\i IMiilippi-ville, 2 Its. F...... ' Sr-i^'ina I., It. F ISOf. Codo, It., F33f I C. Bu-aroni, (Peak 35791. ),1 | It. F 564f. on cape / ! Mansa Z.:iloun ' Jiiljelli, 2 Us. F I Mt. liabor, 6->00f. j Bong'c, pier end. It. F 23f. ; ('. Carbon, It. R 722f. Pisiin, rks , % Im., w., W pt.. Mt. Azafoun, 43G0f. , C. Benqut.lt. F 208f. C.Tedics Delivs, pier. It. F33f. C. Matifou, It. Fl. 2421 TABL'E 10 MARITIME POSITIONS (39) Algier5,MarineT.,It R 115f... — Obskhvxtouy C. Caxiiie, It. Rnv. 2lnf. Sherschel. ffl, fort It., F 12lf. C. Tene«, It. R 292r. Paloinos I., rk. ^. 8.'>f. Mostayhanem.It. F llaf. Ar/.cii I.. It. F fifif. C. Ker.at, i,A, 1 ■s>er sum. .. I't. Aliuju, 2li5l)f.. pt Oran M:irsa el Kebir, It. F 1 I2lf. ; C. Fa:con, I. S, It. Rev. 3-lOf... Hahibas Is., J^ 3iii. w, sum. "1 It. F340f. J MOROCCO. Zafnrinels,, EW li m. W^ fxt stini. 44lf.. It. K J MelilU. 03 C. Trc< Korea.*, N pt. mid All.oian I., jP Im., It. F ll.^f. C.Qnillates Mostaza Tetuan, Ctistomho Cciita, lu R .i90f. Tan;;iir, IJatterv, It. F J8f. ATZiANTIC OCEAN. Madeiras. Porto S.into. Ji 7m., 1660f. Stvx. rkf. NWofP. Santo, ,i Di'scrtas. % 1 2m. sum. IGIOI. - S. or Apnlha pt Madfira, KW. 30m., E pt.,"( It. F, Fl. 343f. j FUNCIIAI, Bitii.CoNS. (33 — l'0NTINHA,lt. F 112t. riraiKuivo, eioof. West, or I'iirgo pt Salvages, 2 grps., j|4 l.'im.l NK breaker / Great Salvage, % I |m., \V Slim. Great Illoa, ^ 3m., sum Cauariea. Alegrnnza, ^ 2.'.m., 9.19f.,l I I't. Dehiido, lt:R57f. ...j ICIara, ^ Im.. N pt Graeiosa, -f .'im. w^ SW pt... Fast rock, [.tc.] I.,an»arolc. 4* .•)2m., NW [)t... - S pt — Arecifi', (Port N; ■■• J I fort Gabriel, 2 Its. F 47 C &35f. I .obos I., ^ 2m., N pt.. It. 1 FKSf. / 'uerteventura, ^ 53m., NW pi - Port Cabras i-- S pLor Pt. .landia, /, It.^ ' Hev. I08f. / Lat. N Lon, 36 47-8 j6 49 36 36 8 36 3« 36 263 35 56-3 35 52-5 35 54 35 53 35 443 ° 417 35 464 o 472 3" 3' 3 2? 2 56-5 o 55 7 o 45 West (40) I'laces 33 50 33 " 32 31-3 32 23 32 434 32 383 32 377! 32 4501 32 48 30 8-6 30 7-5 35 "o 2 257 35 iSj 2 570 35 27 2 59 35 58 3 2 35 '65 3 45-5 35 97 4 265 35 37 5 >S 35 53-6 5 '7 35 47-2 5 48 2 16 195 16 24 10 307 16 27 16 39 5 16 545 16 55 16 570 '7 '7 15 497 29 180 29 127 29 164 29 27 28 500 13 322 '3 .32 7 13 200 13 480 13 470 28 570 '3 32s 28 45S '3 48 5 28 42 2829 14 I •3 S>7 28 30 •4 i2 Grand Canary, NS 25m.,\ ^^Vpt / — Palmas, mi)Ic head. It. F 25i: — Maspaliimas pt.. It. F I90f. — Isleta,ii4 2m.,KF,F1.81"f Tcnerife I., N pt., Anaga rk..., — Sta. Crur.. Brit. Consul, w'" — S pt. or Pt. Rasca — Pe;ik, I2,172f. — Wc.xtr., ; — Orotava, port Gomcra, EW Urn., W pt — Sum. H40f. LieiTO, or Firro, ^ 15m. N"| — W extr., Orchiiia pt. (orl Meridian of Ferio) / Palma, Cumiilida Pt., It. R 2()7f. — S pt. orFuenciilicnte — Sta. Cruz, loit Saa Miguel Azores. Corvo, ^ 4m., w, N pt Flores, NS 9iii., N extr — Sta. Cru?., fort Fayal, % lira., W pt — Horta, Sta. Cruz, castli,! It. F28f. / Pico. ^ 25m., Pk. 8400f. ? .. — E St. George, ^ 29ni., S audi KP' J — N and W pt. outer rk Graclosa, ^ 7in., W. pt I'niya. castle Tercera, EW 1 6m. Praya Angra, Custom ho Sum. 3495f. St. Miguel, r, K or ArncH pt., F, Fl, 219f. J — D.lgada, It. F 20t., Cus-\ loiii-Iio. quav / — West pt. or Pt Ferraria,! It. bad _;■ St. Mary 1., % 9m., town — mid., sum. HiHOf. Forniigas, NS 'I'm., GOf. Dollabaiats shl. [Ic], i.f.5 ... Cape Verdes. St. Antonio, j^ 22m. N pt.,\ It. F23f. / — West pt — Sum. 74()Of. — Tarafal ». wat. place — South pi — NE, Bullpt.lt. F,FI. 543f. St. Vincent, EW ICm., S pt.... — Poitro Gka.mik, ffl. Bird 1 I., It. F306r. J — Flagstaff of Tkle- 1 GRAI-H Offick j I St. I.ucil^^7m., N pt I— Village, ruins, SW side, w.: [Branca, 'i, 3m., N pt L.it. N Lou. W 28° 9'6| I5°43'2 28 70! 15 25 27 438; IS 34 •5 255 16 85 ,6 ,47 16 4 16 390 '6 55 16 320 17 205 '7 13-5 «7 55 18 10 17 47 17 49 7 «7 44 5 28 366 28 282 28 28 16-5 28 20 28 25 28 65 28 67 27 505 28 50 28 26 7 28 39 43 5 39 3' 6 39 270 38 35-6 383 38 28-0 38 247 38 325 38 45-2 39 4-2 39 32 37 38 38 9 38 435 37 49 37 44-2 37 517 36 56-6 36 585 37 i6-2 37 137 31 7? 3« 130 31 80 28 505 28 38 5 28 250 28 30 27 467 28 202 28 47 27 585 27 4? 27 137 27 20 5 25 8? 25 52 2 25 95 25 6 . 24 47 5 24 44 5 7 40 25 22 s 7 4 25 «7 6 572 25 190 6 547 25 'SS 7 7 24 590 6 47 24 590 6 547 25 07 16 533 24 505 16 490 24 47 o 16 450 24 45 5 16 410 24 41 > 5C4 TABLE 10 MARITIME POSITIONS Places Razn. ;, T, EW2m.,niicl St. Nicolas, \ 25ni., N pt — East pt — South pt — W.St pt Sal, NS 17m., N pt — NWhill — MaitiiiezPk, 1340f. — Wreck, or SE pt — South pt Bonavista, EW 18m., N rf.\ and pt / — Hai-iwell rf., 5, NIC pt — East extr. or S.ndliead, \ outer rk / — South pt. (rks.) — English roail, Small I., 1 It. F91f. / — New town, ch Lctonrks.. [Im.], rf, 5, f Mavo, NS 12m., N rf., Nl a"'»lKpt J — Norili i)t — Sr.uih pt — English town. Fort San ) Jose, It. F 62f. J St. Jago, % 31m., E pt — PurtPraya, Ttmerosapt.,1 It. F85f. / — Mt. St. Antonio, 7400f. ?... — Wistpt, extr — North, c r Bighude pt Fogo, EW 1.5m., Npt — Fort Carlotta, It. F 116f. ... — Peak, 9760f Brava, NS Om., W pt — Souih pt -Two Islets, EW 5m., Wextr. Lat. N Lon. W BERMUDAS. Mount hill. It. F 208f. . Nonh rk West extr. of reefs South extr. of reefs ..., Dockyard, cluck tg Wreck hill , 32 21-7 32 284 32 16 32 12 ,32 19-4 32 167 Gibbs Hill, It. Rev. 362f. 32 15 Penedo de San Pedro, Paul's rks, [Jm.] mill, rk., ouf. .?} il2f.. C. Spartel, Mt. Habile, 3000f. Araish. \y' Jebel Sarsar, or pk. of 1' Mehedia, 456f. Sallce, CD C. Darel B.ida Azamor, j-7 ON 1.1 oS o 55-5 35 47-2 35 I2-8 34 54 34 27 3i 38 24 37 24 20-5 24 o 24 185 24 262 22 55 o 22 5<-5 22 56 22 5.3-5 22 57 22 57 22 41 22 40 22 49-5 22 57 22 555 23 10 23 II 23 120 23 IO-5 23 13? 23 26 23 30-7 23 39 23 48 23 460 24 21-5 24 305 24 20 24 45'? 24 427 24 43' 64 387 f'4 47 7 65 3 64 52 64 51-5 64 547 64 51-5 16 o 5 557 5 43 6 9 5 47 6 36 6 4<'> 7 36 8 «S Places Mazagan, ^y', r' North C. Blanco, 170f. C. Cantin, i, 21 If. (rks. off) Sati, Mosque, 209f., 'J' Jebel Hadid, S \V sum. 2 1 OOf , \ tomb J Mogador, or Souirah, JS, w r C. Telelneh, 700f. pt .'... C. Ghir, i, I235f.pt ■Mt. sum. E of C. Ghir, 4400f Sta. Cruz, or Agadir, f H. Sous, bar Macas, or Messa U., Castle ... Cleaveland Shi. ? Fogo Pk., 297nf. C. Noun, i, T, 170f. O R. Noun, or Soleiman ? Port Cansado, 0, enir C.Juby,/, [*] False C. Bojador C. Bojador. /, W pt Penha Grande, 300f. C. Seven Capes, Central C. ... Durnford Pt., cnir R. Ouro,[E Down of Ciiitra, or peaked ( i sand hi.l,w / C. Barbas, i C. Blanco, i , 15uf., (w N-d.) 1 (5SW-d. .5m.) /■ Arguin bk. (lim. of 8, g), Nl extr / — West extr — South extr C. Mirik, /, 5 2 or 3 1. oif Portendik, w^, R, 2 t near ... Mosquito Lagoon 9 Barliarie Pt Senegal, E, St. Louis, (bar,"! 8), fort fl. St., and It. F .../ C. Verde, C. Almadie, It. F 8.5f — Paps, lt.R371f. C. Manuel, It. F171f. Goree I., \ 4c, [H, A. St., fort... Auiboroo bk., W )it., I .... Bird I., ^ 2m., Pilots, fl. sL... R. Gambia, ^, IH, Bath. fl. st, C. St. Mary, / Bald Cape (Is. 4m. W-d.) Casamanza U., It. F 52f. G. Roxo, /, Sand bill, f Falulo breakers, \ 3m., T , 1 Wpt J Fort Cacheo, Portug. Settleni. Cayo Is., /, T, f,Spt Bijoug'aIs.'p„'w'ext'r.b'rcak-'-i' er 30in , out / — South breaker Pullaml. [Im],?. *,(rfs.,-| SW8m.) / Alcatraz reefs, # 7m., NF, \ Id.- / Conflict rfs., S and E prong... Rocky Head, y Rio Nunez, w, P„ Sandy I. ... C. Verga, rt. / Mt. Kakulimah, 2900f. 7 41 I 360 s I 19-5, 465' 33 6 17 24 19 55 1 386 399 16 I 177 50 52 9 45 8, TAIILE 10 565 MARITIME POSITIONS (•••■!) Pla.es Is.de Los EW 6m, w', r,1 Crawford Id..En^I. Esl.ib / — Woiic, Tain.ira I., 8 1. \ I T , 5 ' E, W pt / Sallahtook Pt YellaboiI.,EW2m.. t.Wclill V. Sierra Lione.lt. I'.FI. 75f. [Q. Freitown, N battery iMilse C. Sierr. I C. Shilling,/, t.snni over... IJananas Is., jf* 5m., w, 1 Gov. lio J Maintain Is., E\V.im.,oiit.rrk. .SI. Is of St. Ann.N\VpatrIrs,.'i Turtle Is.,/, N Id., [Am.] Slierbom I., W pt.,<.r C. St. ( Ann, t / R. Sliebar, E entr., or Man:i Pt. U. UaliiniK, Kaniasiyun l.\ [lm.],W elbow / C. Mount liiv.. town C. Mount, w, pk.. I(i60f. ... . C M.surado, 8 1. X, w, It.1 F 240f. / Monrovia. Govt, ho Marslmll. Agent's ho Grand Bassa.Ainer. Agent's lio. Tahocannec rk Trade Town Mt. Tobacco, 830f. Ctstos, factory R Smguin, r, b, Pt. Sa'iyuin lil'iobarra pt Seltra Krno King William Town, Europ. \ (act'vrys J Colovrk I Gulf of Guinea. r. Palmas, It. F Taf.'U pt Kad.tlihoo bliiflf ival Mountain, 1.3l5f .... ; ng George Town C. I.ahou Ill ad of the Bottomless Pit, lOo isini R, cirtr. bar, nf. pollonia (abandoned) Axini, Dutch fort I' Three Pis., 5„ -Jm , li. F 75f. I Dix Cove, t, fort I KIniina, Dnlih fort C. Coast Casile. It. Foil Fort \ William, 192f. / 2 Accra, Fort James, Ll.. h. \ FliOf. / 3 Camel's Hump, 12(iUf. K Volla, Wpt., /, CMtr ('. St. Paul, / (no distinct \ rape), f / .I.dia Coffee Quitia Danish, r, SE hast Little Popo, >«', (,. NWshcd... Grt. Pope (bar. 8) Whydnh.a. St West I3°4S'S 9 274 o 28 9 4 '3 20 8 570 13 iSi 8 300^ r3 18 5 8 299 13 14-5 13 117 13 3 13 34 13 4 12 58 12 31 II 387 II 23 II 21 10 50 10 49-0 10 227 10 46 10 I 9 54 9 14 9 347 9 202 9 20 8 50 8 43 7 54 7 54 7 58 7 40 7 34 7 23 7 01 6 45 6 43 6 19 6 191 6 81 5 541 5 48 5 44 5 47 5 264 5 127 4 59'^ 4 54 4 49 4 22-1 4 24-8 4 39 4 57 4 58 vL 4 59 4 523 4 447 4 47-8 5 4-8 S 6 7 44 ? 7 21-5 6 54 6 48 6 3 4 3' 3 57 3 23 2 35 2 147 I '3/ 5 3' 8] o 11-5 5 37 I o 31 5 460 o 41-2 5 50 5 52 5 55-: 6 136 58 o 597 . , I 36? 6 16 I I 54 6 189 2 50 Porto Novo (no ] lort) Badagry, shore hut Lagos, entr. [iml bar 9 f., \ It. F70f. ( Oddv Sand beach K. Benin, bar I5f. NW pt K. Forcados, entr. S pt R. Quorra, or Niger, E pt C. Formosa, /, f (no distinct 1 cape) f" NewCaleb:,ri;,.i)tr ; I . W |it lionny R.. rnir. , I', i; jil , ) T, r, ron^Hi (inn. r ; Old Calebar, Tom Shot's I't.... Mt. Camcroons, 1.376uf. Cape Camcroons Rumby Mimntftins, sum Qua Mount., 2.5 1 An<.b.isB,MondolehI.[!m.] 1 h. t, w, Spt .' J Sncllnhapt. (rf. 3m. off) The Mitre, 394()f., S sum C St. .lohn, t C(iri>coI,/, t C. Es ciras Gaboon R.,f w, Libreville, It. F King George Town Fernand.) Po, ^ 40ni. S^.lm.l C. Bullen. or N pt ; — Peak, 10710f — S. pt, or C. Barrow — Clarence Cove, \y',h, Ade- \ laide islet (H, 1'. F J Princes I.. NS 9m. N rk. off... — St. Antonio B., fort Sta. "| Anna / Brothers, 2 Is., NS 2»m.. S on. St. Thomas I., J^ 25m. sum.~) 7020f. / — St 1. Anna de Chaves, fort | St. Sebast., It. F 35r. ... / — IlhadasRoIlas[lm.Joff\ S.pt / Aniobona, \ 4m., S^ ... . \ Turtle L, [Im.], 1 , w, r / — Sextr., rk. off I3X.ANDS IN SOUTH ATX. ANTIC. Ascension, EW 7im., Fortl Thornton, It. F, IH / - Green Mm., 282l)f - Cross Hill, 850f. on with \ Gr. Mt., S71°E J St. Helena, Ji 9m., Diana's "\^ Pk.27<)"l. J — Obseiivatory, ♦ l' G.M.T. Fernando Noronha, !»., J* 1 6m., Sand W. exir. pt. ..J — peak, on SE side Riias [4m.], rf NW end 5C6 TABLE 10 MARITIME POSITIONS Places Lai. S Lnn. 10 Trinidad I.,% 4ni.,2020f.S.pt. Martin Vas. 3 Is., NS l^m. ... Trisan d'Acunlia, [6ni.] "I Waterfall, N side / Inaccessilde Is., 16 I., /^, (,, '\ w, W one / Nightingale I. [2in.] Gmi(;h's I. [5ni.], 4385f.,1 ^ Npt J® Nazareth R., Fetish town, W 1 entr f C. Lope/., /, T,f C. St. Catherine, [t] Settee R., a high t Majunjha I?., r, Matooii Pt.... Loang.. R., entr. Black Pt.,B , [ f ],w"'.Sandv | Pt.,/ ej Lendana Pt., It. F lUf. Kabcnda Pt., It. F 50f. Congo R., P,, Pt. Padron — S. entr., or Shark's Pt, T , \ Foreh blnif. It. F 78f. Ainbriz, t „, It. F Dande Pt. and riv C. Lajiostas, rks. , It. F, Fl. 2 1 Of. St. Paul de Loando, @3, [H. \ H.St, m J Palmairinhas Pt., It. F, Fl. 57f. C. Ledo, /(, t,pt 0. St. Bras, E, f Nova Redoridij, r, -w^ I, Quicoinbo B., ;8 Im. out, 1 ^..Spt /® St. Philip de BengULla, f, w,, 1 St. Philip's Bonnet, It. F J 394f. J Logito R, w'" r Salinas Pt'., /^ t a°t |it., It. F, e Eleiihant B., Sl.Pof "W^.l Monks, 01- Friars, rks. e 12or Uf. J C. St. Marv, T , w„ Little Fish B., Ponta do \ Giraul, It. F 64f. / C. Negro, 200f., I pt., Diaz's "j Pillar / Port. Alexander, ^. r w Great Fi.-h B., w, P', Tiger \^ Pt., T,5„ 2c / Nourse II. (temporary) O C. Fri., r. Cross (or Sierra) | Mt, Col<|ilhoun, 17 or 18 1... 9 Wahi-ch B., ffi, f w^, 1 j faclor.v. It. F24f. J 1 Port Sandwich, or d'llheo, 1 E.f t /! Il.llan.'s Bird I. [2c.], Tf.\\ SW :,m., -, I / 37 17 37 27 40 19 29° 1 9' 28 51 12 i8-; 1236 12 29 9 44 East 9 I 843 9 6 9 26 10 38 11 45 12 13 12 17 12 53 >3 S 13 19 •3 17-5 13 '3 ■3 54 >3 48 13 '8 13 46 13 32 12 59 12 33 12 12 11 58 12 o II 46 11 54 12 2 »3 57 14 30 14 25 14 32 Mercury I. ['jm.J O An^Ta Pcquecia,f,wN lOni., 1 SW or Pedestal Pt / Seal L [Im.], w„ Possession 1.. % 3ra., rfs. off, w^, S pt Arched rk., luof. . Orange R., ^, bar '28 38 C. Voltas.w 28 44 Ivoussie R O 29 40 :}° 25" 46' 26 34 26 58 IS" o- IS 8 IS 14 "5 13 15 19 16 28 16 32 17 10 CAPE COI.0NY. • Elcpl.at ,R.| 01ifant'sR.,< C. Dohkin . C. Dcseada, i, A I Berg R., en^tr. (w' 5m. up) ...I Britannia rk | St. Helena B., Pt. St. Martin,/ Pt. PateriH ster, or W pt Sunken rock ? Saldanha B., f, r, w,Ship rk., 1 at N pt / — Houtjes B., m, Hout. pt.... — Schapen L, iy', W pt Das.seii I., % 2m., /, ^, ■«■„, 1 2ni., cent J BockPt Robbcn I., % lini. It. F 154|-. Table B., Green Pt., It. F\ 65 ft. [H J Devil's Peak, 3270f. CaPK OcSKRV.iTORY, ♦ I' \ G.M.T. ii''46" 5- / Cape of Good Hope, It. Rev. ( Bellow's rk Simon's B., Dk. jd C. Hangklip Danger Pt., /, rks. 2m. blutf .. Quoin Pt C. Agulhas,Sextr. of Africa, 1 It. F 128f. J Pt. Struys, 5 3m C. Infanti, S pt., Sebastian B. C. Bariacouta C. Vacca Flesh Pt C. St. Blaize, It. 1'' 240f. Knjsna R., [J], entr. L Plettenburg B., w, r, r, S pt. \ or Seal C J C.St.Fiancis,rf.,;3,T,lt.F1.118f. C. Kecif,/, It. Rev. 93f. (rf. 4m.) Algoa B., Port Elizabeth, It. l F225f. I Bird Is, £-3iu.. Ept.lt. F80f. Pt. Padron Kowie R., entr. Port Alfred, \ It. F40f j Grt.Fish Pt . R., entr Keiskania, R., entr. W pt Cove rks., centre Buffalo R., East London, F 4.^'. C Morgan Hole in the Wall 18 12 18 19 18 23 18 13 17 41 17 59 42-2 17 542 SI 17 46 17I 17 54 17 580 33 33 33 26-2| 18 67 33 33s' 18 19 33 49 2 18 22 33 542, 18 245 33 57 2 18 267 33 56-0 18 28 7 21-2 18 295 23 18 29 7 11-3 18 260 23-2] 18 49-5 19 177 19 38 5 20 0-7 20 142 20 51 21 184 21 55 21 570 22 9 5 23 37 23 25 i3 505 26 17a (3 46-sj 26 28 53 36 26 54-2 3I-4' 27 7 296 27 85 167 27 29 s S-i 27 49-! I 7, 27 550 42 i; 28 24 7 32 29 lb TABLE 10 MAIflTlME IH) (<7) ru I Lat. Rame II. ad St. Jolin's K.. eiitr C. Natal I'ort Natal, [E, bar S, S p^\ of hay, It. Uev. 282I'. J Fislicr's H Dunif.ird I'l C. St. Lucia St. I.uciii K., enT. C. Vidal Goldowii's Blind river Delagoa I!.. C. Collato, 260f... — C Injack, N pi. of St. 1 Marv I.. 265f. / Port Melville. Elephant l.,\ w SW side. Gil.boii U" ft. ( ICn-.'lisli K, KeubeQ pt., lt.l F 134f. J Innampura U., eiitr. Pt. Zavora K C. Con ient s, U 1., siimll rk., ^ 15f. / Barrow Hill, Hurra, It. F 1 80f. / Innaiiihan B., ^, town C. Lady Grey, 'J5f. C. St. Sebastian, 10 1., pt. 1 ^2.V. / 25 "6 3i 3'-5 24 285 35 '2-5 24 S'S 35 305 23 45-51 35 32 2 Buzarouta Is.. N pt., or C. 1 Bazarouta, .'JDOf. / Inverarity shl., Miailjuano ... Chiuwan I. [.^.m.j. I, f,\ Singunc, It. F36f. j Sofala R.. bar. tjf. fort PuMRue R.. Beira, It. red Zambesi R., Kdngoni R. \ mouth. It. 8.if / Kiliman R., bar »f., /, f ,1 Pt. Tagalane, li. F.i2f. .../ Acorn rk Primi-ira Is., Casuaripii, or1 Razal., t W, Wc, b / Mt. Coikhurn Aiipochc U.. \Vst.,[onia"| bk.[ln..] J — Matiimede I.,/, f , rf.*., cent. — K., Custom ho St. Antonio, H, S pt , rf. 1 1 [2m.] J Huddorfsshl Moginkwali R , Funco pt. , Purt Mocamba, N pt., entr., T, ffl, pk.,al>. 2000f. Mnzambiqup, g, Sebastian Fort fl.vtair, It. K. green 42f. Mt. Pao Mount Mezfl. I0f'5f. Tilangonya I, # 2m., S pt C. Afelamo Penda shl , K eilr Loguno Peak Sorisa Pt MaiKih«n<. P. 3l°4S'4 29°I4'5 3' 345 29 53 o 29 53 29 163 29 02 28 325 25 260 28 96 26 55 26 40 25 580 25 58 29 287 3' 3« 33 21 515 32 275 32 26s 32 3S-0 32 53 32 58 33 o 32 542 32 36 22 55 35 36-5 22 6 35 29 21 310 35 280 20 42 35 10 ao 38-2 34 535 20 107 34 43 >9 50-2 34 505 '8 53 36 117 iS 1-4 36 57 »7 37 I 38 13s 17 65 .39 4 16 29 16 47 16 205 16 13 '5 57 "5 47 ■5 32 IS 8 14 50 «4 43 38 56 39 32 40 2 39 56s 40 44 7 40 25 _ 40 38 14 51 o 40 500 14 250 40 50 ■ 4 150, 40 500 14 21 o 40 31; "3 328 40 3V» 12 58 40 36 (4H) Places Pomba Bav, g, Npt.,entr., T ArimbaH.-ad ;i)0 I., #■ 5m., Ibo Blurt, It. \ F51f. J Maliato L, ^ 2 m.. N and E iit. I. dos Mattos, [im ], rfs. ) 2m. out '. / Fungu Nanie^'Ud, E. pt. of reef Tambuzi I,, E\V lini,, rfs. 1 2m , w' J Maziniba, fort Nu.nba I., ,f .-im., E pt '!""-'"* '. ''-P' ('. l).l;;a(io, pr., It. F 59f. C. Ildvounia Matui.da Pt C. Paman, Hi.ll ik Mikindanillr Kmzi Vill M n^'ulho K,, b, w, M^idjovi | Kks J MADAGASCAR. Sextr.. C. St. Mary Star bk.. SWp„rt, 2f Star reefs, NS 3 1., T W, S one Lcvrn I, [|u..],cenlr.- Harrac outa'l., [im ] Sr. Augiistine B., Tent rk. ... Noss Veil, or Sandy I M.ir.lerer's Bav, N pt Murder L, rf. 2m,, SW ('. St. Vincent Mouron r, r Barron Is., /, *, S danger ... — Smyth's islet, on rf. ^ , 2.im J Coffin I.,/, (5 2 I.) NW extr., G. St. Andrew Chtsterfiel.l bk. []m.]. r Bojanna B., W er lalde C... Beniba ooka B., E, r, E or ) Majunga Pt / Makumba I Majanibo B., g,entr. W pt.... Nareenda B., g, cuir. Wpt.... Luzall., bar-j, ffi,entr Saucassee I, NS 4sm., N pt... M"Cluer Pt '. Kraridza I., NS 2m., N pt. ... I'a-sandava B., Ninepin I.,\ It. F 184f. / Passage I. [Jm.] Daliyniple B., m, <", w, b.enlr. Miirialioulali Pk Noss Bell I., NS 13m., N pt... Minow I,N. pt C. St. Sebastian (Is. 5m. \ off).Pt / Woody I., [J m.] Port Liverpool, g, entr. N pt. N extr., C. Amber AiiiIht .Mountain Britiiib Sound, ffl,cntr.,Cla- 1 reu««Id J C I,.)wrv Porte Lookc, ffi. B«tlinr-t Pt 12" 55'! 12 38 2 12 200 II 582 II 49 II 28 5 n 213 II 185 II 9-5 10 51 10 413 10 2S7 25 389 25 39 25 25 25 125 25 30 23 35' 23 38' 22 12-5 22 5-3 21 525 20 1 8-3 18 41 18 18 I 17 290 16 n 16 17 «5 59 44 "o 44 160 44 55 43 437 43 3U 43 160 43 '3-5 43 1S5 44 >7-5 44 ■ 43 44 7 43 45? 44 29 43 53 45 '6 15 42-91 46 18 s 13 420 45 55 7 ■5 >i7l 46 57 5 '4 40-3! 47 24-5 ■4 369 14 3'^7 14 150 ■3 535 13 282 13 28-2 >3 30 14 6 13 '22 "2 495 12 277 12 167 '2 33 " 57 5 '2 345 12 138 47 4 10 47 33^ 47 47? 47 45 48 130 48 277 4S o- 48 IS 48 167 48 370 48 437 48 39 ? 49 9 S 49 '7" 56S TABLE 10 MARITIME POSITIONS (49) Pla Port Lcven, g. Lingo rk Nushe Bavracoiita. [Im.] Aiulniva B., l?trry Hd Manambatoo ViU , t, Voliemai- Pt Mananliar, Table Hill C. East, outer I Dumford Noss, pt Port Clioiseiil, town C. Ballones, pt Tangtang, S,fl- st St. Mary's I.. # U 1., N. pt... — ]. Madame, or Quail 1.,om 1 Wside.Estalil., It. F31f./ Fenciive, town F.mle Pt. ViU., r, L Prune I., vi.. 51., t Tamatave Ft., | Foiig Is., small, S one Vat Oman dri Mahanuru, town Fanantara, town Rangazava, town Footuk, town Maiiambatoo (South), town .. Loodatoo. town St. Luce, N islet Pt. Yiapere, extr Fort Dauph-«i, fl. st I2°46's 12 48 12 56 !> 13 14' 13 235 14 39 7 15 I5-S 16 15 273 .6 14-0 16 425 16 40 17 230 17 404 Lon Islands off MCadagrascar, L, [1 I], *, 6if. , T.Spr [2>].l, J Hassan da India, [2 St. Juan da Nova /,5, ^ Mayntta, KS 7 1., Pamanzi I., - It F Johanna, NS 8 1 , pk., E pai -To«n, w,r,P' Numachao Mohillah Comoro, NS 12 1., T, t 1 ^ N\V, SEpt /^ — Norih-east pt O 19 17!- 19 54 c 20 SI 2 20 582 24 4<^ 24 I7V 2+ 367 24 447 24 59-; 25 1-3 Geyser sh., SW elbow Borneo .slil Glorioso I. and rls, [. t *, T, Isle du W pi ,151 hunimnrk.in SK pt , lidt.J Aldabrals., i:W8l.,S?t,I f, w pt.. 7or. ( Cosmoledo Is., [.3 1.], Ia«r., no 1 entr., f, [d:] S;-S\V, or African Coast continued Lindy K., w, r, fort MchingaP. Vill Kiswcre H', ffi,Rushin?i Vdl 12 46 12 15 12 lie 12 25 II 54 19-5 9 46 9 22-, 9 4' 10 65 9 59-5 9 44 9 25O 9 8 57c 49^53 2 49 55 49 54 5 49 56 5 50 I? 50 >37 50 295 50 95 49 50? 49 520 49 44? 50 27 49 520 49 26 2 49 33' 49 30 49 27 49 237 49 2 4S 50 48 3" 48 307 47 30 47 23 47 '5' 47 122 47 57 39 41 42 47 45 IS 44 27-1 44 22 43 42 43 ii 43 39 .'Uth 7 565 97 5 43 Quiloa, Ukyera reef, E cxtr ... Sungal., 4|5 Urn.. SEpt Mafi.i I., d* y 1-. W. or K.si- \ niani pt J Pauna Pt e,\tr [ 7 Latham's I., [ic], I. sd.. mid.' 6 54-2 Zanzibar I., % 1 6 1., * , S pt. 1 1 (- 0. , or Kizimkaz, w, It J ^ — English Consulage 6 — N pt., or NuMgwe Pt., lt."l Rev. 105f. J Mazeewy I., and rfs., [Um.].. Tungaty, Mt., 15 1., S pk Pemba I., NS 13 1., /, t, S) or Said pt / — North- East pt 1 4 54' — Port Chak chak. m. Mo- 1 sal I., [Im.]. SW. pt f Waseen Peiks, 15 1., mid oni Mombaza, /, t , w, r, P,, fort Melinda (Leopard rf. 3m. "| oH), Pillar J Ras Goniany. N pt Ozy Pi., i,Kiv. 2|- 5m.;rf. 4in Lamo B., S, Wpt, or K s , Kattow ) rk.. 47 22 46 30-5 46 12-2 47 3' 47 45 7 39 43 39 44 39 37-5 39 iy? 39 31? Patta B., m Palta, town Kwyhoo I , Sst. of Julia Diindas Is., pk. 1551'. Simmambaya, Settlem. . r.it. Gibbons Port Durnford, S, Foot N. entr Tola I., huts Port Kiama, Doubt rk., 1 entr Ki^mayo L, ^ 3m., N 1 Juba R., bar, P,, entr. . Rrava, town Marka. town Magadoxa. to Murot hill .. Ras Asuad, /, i, pt. . Lis Awath !asal Khyle !as M..bl.eiv, i'N, s : extr. of Africa, Ra fuun, 500f , t S, w, 1 lor Iladeoa, (boats) . a^ L!.i C. Giiardafui(Nl' 5 293 4 54-2 5 157 4 30 4 40 3 12S 3 2 375 2 1S7 2 157 2 140 2 9 o 40- o 36 S 14-5 N( 1 68 I 44-1 i) 31 39 357 39 34? 39 56 39 300 39 1 1-2 39 «8 39 60 3S 520 39 39 39 5>S 39 37-5 39 20 39 41- 40 18 2 40 177 40 40 567 40 56? 41 r? 41 75 41 182 41 54'? 42 35 42 200 42 39-2 44 3 44 51 45 247 2 4i-3| 46 17 ? 4 342 48 60 5 32-8| 48 40-0 7 43-5 49 45 7 9 290 50 502 Gulf of Aden, Abd'l Koory, % 71., h. ^<', W pt Stilt's white rks. or Kal Fa- ^ roou [Im.], 282f., mid..../ Brothers, 2, ^\g 4il. E,or Durjy Socotra, E\V 70ra., W extr. pt. — NW extr., Ras Bedoo,300f. — Gollonsier, vilL.w, r, b — Tamtireed. r. w. Mosque... — E pt., Kii- K'dresscr, I. 10 .34 11 9 II 500 12 '35 12 26 12 7 12 33 12 39 12 41- 12 390 ■ •' >s 34 51 10 51 10 51 16 52 3 52 8 53 '<5 53 '57 53 2' 7 53 267 53 59 5* 27 TABLE 10 AIARITIME POSITIONS il) Places Socotra, Wadde Frllingk, w,\ reservoir / — SW pt., IJas Kattamiic,\ sum. over, 146 jf. j R«is Ahileh, /. Ka^Feluk, i.SOOf. T Mcyet, or Rurnt I., h, -^, w, 1 Sside, T,430 f. ( Berberuli Sandy pt., It. F 4!if. Ziyla,r, P, Cape Obokh.lt. F 64 f. P.as Bir(«' \V 4ni.), It. F. ... High BrothtTS, 5, % 4m.,1 rks, large one / .Icbel Searjan. vole., sum Dumt iiah I , [Jm ], A, pk. ... Asab, It V Ras H iliil, sum Mohablakah Is., 3, # 2m., \ SW. Flar,40f. J Rakhmat 1 , 282f. Jebel Ahayil I., 150f. Bam rock, lOf. Eid town Kurdumivat I., 180f.,[2m.],"l A, vole / Hanfi lah B., Daranisas 1 , 1 25f. W. reef / Shumna I., It. F 59f. Howakel I.. 5)* 7 ni.,sum.,72or. Massowah I., [.^m.], w, r, b, \ t', It. F47t". / Dahalak bank, SE cxtr., Mo- \ jeidi, [l^m.],A / — N extr,, llarmil 1., ^ \ 5m.,/, ?,Ept / Dabaluk Kebir, % 10 1. Dilncin I.,30f. Tow, rs, hill Khor Nowaret, ffl.ry Sha- 1 tirchi J Ras Asis Low Sandy Is., % 12 \.,E\ extr., Eddom Sheikh I..../ Trinkifjt Harbour Kchirl..[3m.],«... •awakii 1 2° 28' S4"'l3'7 12 22-5 53 297 2 ■ 57 50 50 'i I 14 47 16 25 44 Sim.]. T E, sum... Ashrafi Is.. 'if. F H.-Jf. lias Glaiil). It. F ir>.5f. Ras Zafarana, It. F «3f. Mt. Agrib. cGharib). 5740f. ... Suez, Port InRAHiM, S \^ MOLE IID J Toor, barb., ffi, w'" Mount Sinai, 7450f Ras Mohammed, 1, 90f.,| peninsula J Akabah, fort, w Tirahn Is., \ 3ni., pk., 700f.... 23° 56' I 24 12 24 39 24 56 26 6 25 18! 27 12 27 27 27 387 27 47-3t 28 20-9] 29 65! 28 67 29 56-2 28 137 28 32 27 452 29 28 27 552 Eastern Shore. Sillah Is., \ 6m., /, crl., S pt Moilah, w, f, $„ — High pk., 9()00f. Jcbel Antar, 2500 or 3000f. ... Riackah 1., % 2m.. / Mushabeah 1., \ 5m., /, T \ w, Wextr / Shab Shaybah, or Palinurus \ rfs.,[4m.], T. t^, Sjmid./ C. Bareedy, mid. pt , T Sherm Yembo, ffi Ycmbo, the port of Medina, ■vi' r. entr JebelSoubah. 4500f. Shab Subbah, or 7 shls., % \ \ 3 1., S, Wlim / Thetis, rf.. [im.]. T,5 Sherm Rhabuc, S,r, w, P, ... Abu Madafi .Tiddah. a. 5 \VS\V7m.,high '(^ mosque. Ed. of town.. KaddHomeis.Sf. [2im.] W pt '. ":} ith :•:} Ivun&iad Shab Mubarak, rk, [Im.] Khor Nohud Shab el Juroah, [Im.] Sell Makawar, [Im.], (5,1 N\V3I.) / Gizan Fort Jcbcl Tccr, vole, [ljni.],"( 800f.,l:o / Kotumah I., % 3m I.oheyyah Fort ivamaran I.,NS3 l.,w,l>,SsHm. Zel.ayir Is., »!, 5 1., N extr., 1 Quoin rk., innf. / 27 37 27 40 27 37 26 34 26 10 25 38 24 6 24 16 24 9 24 45 23 18 23 40 23 38 22 43 22 2 21 283 18 15 i >7 36 16 58 ■6 53 '5 32 5 '5 4 35 47 35 o 35 S 35 52 34 J6; 34 5°7 33 587 34 2-; Z:-. 48 ji 4^5 33 6-; 32 397 32 54' 32 33-5 33 37 33 5S-; 35 2S 35 45 36 28 36 21 36 27 37 7 37 33 37 54 38 . 39 3 37 58 39 "3 39 26 40 12 4' 3^ 40 9 41 275 40 50 5 41 20 42 29 41 50 42 16 42 39 42 34 42 3 570 TABLE 10 MARITIME POSITIONS Ph.. (54) Places Lat. N Lon. E 15° 2' 14 47 14 7 14 22 14 S-2 42°I0'2 42 56 42 45-: •3 534 42 42-2 13 47-2 42 47 3 382 42 35 5 ;;;? 43 140 43 27 12 39 43 26 ■2 35 12 43 12 472 12 46 «2 45 13 215 43 56 44 10 44 58-5 45 07 45 3 45 40 46 45 47 32 48 40 49 7 49 26 Zeliayir I., large one, [3m.1,1 S. sum. ;34f. :.J Hodeidah Hus Zebccd, w'" Im. N Avoeetrock, 8 Jebcl Zukiir I., 2o47f., %1 IOm.,/i, High islet, 216f. / — Tongue 1., 166f. Haruish Is., 133af., NS 6 I., "( Haveoekl j — SW rocks, 22f. iSIocha, Pier end lii.hel Mandeb, pk IVriin I., [4im.], S, It. U I a49f'. on summit J ARABIA. IJas Arab. S pt. of Arabia, /, 5 Mt. Ht. Aiiiony, 27721. Aden, Has Marhut C. Aden, sunimii, 1776f. Kas Marsl.igb, It. F 244f. Sugra, w', r, Castle Howtlia, w', r, f A Larn-like pk., 5284f. Ras Kbelb, /, sandy, no point Makalleli Jubul Dhebab, a table land ... Sliabah, Sultan's resid., r, w,... C Bogashu Palinurus shl. 2Mm. % 2111., ) irspt .'. / C. Fartak, 26 1., 1 I hurbat All Kas el Ahmar C. Merbat, /, rkv., f, w, Jebel Kiukeri, ISUUf. Ras Nils, 20 1., S pt., / KuriaMuria Is, KW 45m., 1 Wone,Haski,#l,^m,,pk./ — Sodn, % .-jni., pk., i:510f., w — Hulinea, E\V 7m., NE | blutt; 1645f., w, J — Kibliyah, E\V 2m., pk., 1 53Uf., w„, rk. W 3m.... j' Ras Slierbedat, i,w4m.,W... C. Colette, vis. 16 1., pt Mazeira I , ^f^ 13 1., 6001'., \ Spt / — N pt., or Riis Jei Ras.Iibsli Ras el Kbubbeh Kas al Hcd, S.indy Pt., / , PERSIAir GUI.F. Ras Abu Daud 83 192 58 555 Maskat, r, w, f, Eisbet's rk. e 23 377 5^ 3t>'o -- Saddlebill, VAMt 123 351 5S 3:; •K-ziret .lun, 107f. 22 50-5 57 58-5 Olive Sboal, of. 2251 I 57 57-2 JebelKostagabluirof.hel ,^ .Ieb(.-1 Akhtbar J J *» J Hi'keb 23 427 57 54-; Suwik, fun and town | 23 51-5 57 26 foliar, town and fori I 24 2r5[ 56 46 16 55 16 58 17 3 17 14 50 39 52 16 53 3 53 52 54 42 55 2 55 18 >7 27-2 55 357 >7 ^96, 55 51-2 17 327' 56 2-2 17 292 56 19 '7 53 56 20 '8 58'S 57 460 20 43-5 56 52 21 27-5 59 21 5 22 14-4 59 49 22 a 59 48 Sihenas, town |24°45'[ 56" 29' Dibbab, town 25 38 1 56 17 Sliam IVak, 6750f. 25 587! 56 14-5 C. Mussendoni Peak, 875f. ...! 26 219 56 3^ Great Quoin, 540f. 26 30 | 56 31 Nl Ras Sheikh Masnd... , Sb:im, fort, r, w', P' .. Ras el KbeyLiieh, r Sbargah, w, t , Vbuiiiabi fort Sir I5eni Y:is, X pt. .. Rug Z..kkum sbl. [:i] Ras Luttan Sir Abu Neyr, NS 2', pt. 24Uf. '. J I Zirkuh I., 540f., S pt Girneyn I., IQof. Das I., [lim], S pt., 143f. ... Arzeni'li, 20Uf. Dalmeh, 244f. Deyni, 9f. Sbiriio I., 40f. Halul,18tlf. I KasRekken Shah Allum shl. [ii] I I5ahrainI.,.Mauau.ab,town,r,w| Mah»rag I., N pt. Kennieshl. [2^'].. Al Kran, 5f. Herguz, 3f. Araby, 31'., sandy Farse, lOf , sandy Ras al Gbar Ras .Musbab, /, ... Garu I Kibbr I Rasal Arth Kuweit, N end tow Feylecheh I., \ 7i B.israli Custom He Ras Tanub, / Ras at Tamb Khargd I., NS 4m , /, w. N pt. Kharg I.,% 5u!.,w', fort.NE© Abu-Sha!.r, ffi, w, r. Resi- \ dency ffi/ Asses' Fars, 5ni. inlaiid, 250l)f. Ilunmiocks of Dreng, S one. | Kas Jlu'taf.Spt.""!'.'.!!!!".".!!... Barn Hili, 4r,(iUf. KasNabend,/ Shevkh Shavh, ll'dl., I., %1 14m., w, i',, E i,t ; Iliiuleiabi I., EW 4ui , /, 1001. Sumberrun Shl., [6j Gays, 12nf, % 8m., /,f-, T ,1 r.w, P„Ept / Erur I., 4(;")f.. NS 4ni., N pt. Has Uo-laudi,/, pt l'H"'«l'l- [*'"■].= Nabvu Evur I, [Im.], 120f.... Seri I,, .'iof. [3m.]. S pt Buniusa I. [3m. j, SfiOf, peak 26 154 26 1-4 25 48 25 22 24 29 24 21-5] 24 48-: 25 54" 25 15 24 52 24 56 25 9 24 46 24 33 24 57 25 2 25 40 2b u 26 255 26 14 26 18 27 35 27 43 27 56 27 47 27 59 27 ii 28 II 28 49 29 4 29 20 29 23 29 23 30 32 30 8 29 58 29 20 29 15-4 20 591 28 29 28 4 27 41 27 49- 5 27 48 26 31 26 19 26 30 26 26 26 7 25 53 25 53 TABLE 10 f>71 MARITIME I'OSrnONS (55) Places Lat. N Lon. E Jczt. Nabu Tumb [ Im.] ' 2& Je»t. Tuinli [3in.], 1651., w... 26 l!a^illuh Chapel 26 Hinjar I., # 5m., S pt 26 Kesin, fort I 26 Lnri-k I., # 5.\m., «„ Jm.,\Lg Npt. ' /I Iloriiiuz I., EW 4m.. fort. X pt. 27 Handir Ablias, Slicikli's 1 | „ hm,s.ffi. f }|"7 Kuhi Mubaruk, rk 25 C. Jashak, /, sandy pt., Tomb 25 RisTagin,/ 25 Has Maidiini /,(shl_3m.) 25 Has Gurdim. i, (rk., SE3m.) 25 Uas Miitakiiddim 25 Chahbar, $ ', r, w', Telegraph 25 Uas Fasta 25 Gwatar, vill 25 Has Jiyiini 25 Guadar Telegraph 25 i Ha< Shahid ' 25 I I'a.fMi Telegraph ' 25 iAstal.ih I., EW 3m., (rk.,1 j,, I 2a.. S) J I ^5 Ormarah, Telegraph 25 Has Malan ' 25 Sunniijani, r, it, .Tain's ho. ...' 25 R..8 Miiwari, or C. Mome.l I,. shl., 3m J Lacoa.livas, /, f , t„ Bassas de IVIio bk., % 22l.,"l T. Npt.,57 j' — rf., NS 6m., T , S dry 1 sand (Cherbaniani) ... / nyramjiore.rT., NS 13m., S p.irt Belra-par, rf., NS 7m., Id.,^ I [Im.J.Nextr.,/ J I'ereiniil-par, rf., ^ 7m., T , 1 I Id. NE ; J lAncutta, [3lm.],P, f.mid.... jTingaro ; Pittie, [ie.], sand, -«■ lAmeni, [l|m.] Cardamtim, and rfs., NS Gm... Chittae, [2m.] Kiltan, [3m.], S pt E cxlr., Klicalpeni bk., NS ) .5m., 8, mid / Underoo, EW 3tm., rks.,1 N-d. /, f , w, E"end / Kalpcni, 2 Is., ^ 7m., t , S pt. Cuhrutee, [2,>.], rf. W-d, 1 T, t.w j Seuheli Par, Id., N, [2c.] — Sextr. ol rf., T i4'7 55° 9' 157; 55 '«7 392 55 16? 55 52 56 17 56 217 56 27-5 56 17 57 28 I 4S 1 35 « 9 o SI o 55 45 1 6 ■ >3 I 40 1 29 ' '3 o 47 o 3 o 3' o 5 9 56 Mi T. P',1 J 57 45 7 58 55 59 6-5 60 7-2 60 27-7 60 37? 61 25-2 61 30? 61 422 62 19-2 62 587 63 28- 63 49 64 36-5 65 12-2 6635' C6 39- 5 72 32 71 52 71 50 72 II 7a o 72 10 72 18 72 32 72 41 72 44 72 42 72 5« 73 56 73 42 73 35 72 36 Malliva Is., 19 /)/,w, b,f j Nillandoo Atolls, 2, ||, NS 1 131., Id. at S entr., f , w', J. on W side onir. [E J Collomandoo Atell, EW 10 1., 1 Karn-duo-doo I., w', g... / Adou Matte Atoll, ^* 9 ].,\ Nand Ept. Id / — S extr.. Id., (entr. g, -f -| 3m., SJ / Suadiva Atoll, NS 15 1., W1 side, entr. to g, 10 J Phoowa Moloku I., w', N pt. Sextr.,AddooAtoll, EW.'il. w, b, f, Gung I., ffl,E Almli ;pt.y &. Seychelles. Wextr.,I.l!oudcnse,small.t Marie Loui^c I., small, f_, 1 (rf. oft, J) '../ S extr., I. Oe Ncuf, small, » I. Etoilc, [l.im.], /, * Poivre Is., two, [lm.],rf8., NEpt Isle de Kochcs, (bk.s. 4 1.), North beach St. Joseph 'Is., E jit O D'Arros I., NE pt TABLE 10 MARITIME POSITIONS (57) Places ■■i Eagle, or Rcmire I., [im ], \ ^ I /, *,rfs. 2m., w„, n£ pt. J = African Is., small,/, $' W,\ C w„. North I J 5 1 1. Platte, [im.], rfs. 3m " La Peile rf., Centre Mahe I., % 13 1., f , Port | Victoria, Hodoul jetty ... ', — It. F 37f. OQ Sreef Silhouette I., [3m.], /(, *,1 Npt / Recifl., [l^.i.],150f.,--,mid^ E cxtr.. Frigate I., [i;im.],1 550f., P, rf. S\V, mid / Pra-linl., 12 1., t N, Wpt.... CurieuseI..EW2in.,w, $,mid. Uenis I., NS 3m., /, f,lt. F"! 60f. / Ne.\tr., Bird I., [2m.], /, *,1 ^, w, mid / French Shoal, [5 or 6m.], 'I ■•^J Roqucpiz, /. sandy, rfs j Aiphonse, /, f, SE pt Coelivy I../,sandy, %8m..\ t.t NW,Nv', f, Npt....J Ag.ilcsi'S, I. and retfa, \ 1 ] ,-, 1.. t, NWpt I S:ivad.iMilhalik..5fms. pn:c'i John de Nova, or Farquliar | Is., # 8 1., w, t, Grande \ Porte J McLeO(l,orMarq. ofHuntlyl bk., [2 1.], 10 I St. Pierre, [ I \m.\ I. * , NWpt. Providence 1., [2m.], w, r. I, 1 Village / Umzintoblk. coral 11 fms. ... Tromelin, [\m.\ I, or Sable 1 1., S, Npt J C'«rgados Carajos reefs, -j^T 9 1., /, T E, f, S extr.. 4 52-5 53 237 v\ 55 22 55 'Z-S 4 37-2 55 275 4 37 55 31 4 270 55 167 4 34-8, 55 50 4 352; 56 r? 4 174 55 44-? 4 16 55 47 7 3 4^ 2 55 40 3 427 55 125 3 58 6 24 7 OS 7 6 54 42 60 4 52 45-? 56 17 10 215 56 32 9 12 I 60 21 10 7 I 51 10 2 9 55 I 50 15 919 I 50 43 5 9 14 5' 2-5 9 395 5' 'S '5 51 61 54 277 — Baleinc shl., rf , [| -- Esiablislimcnt .... Albatross I.. [In,.], , Chagos Arcblpelago. Speakers' bk., ^ 8 1., T,e,l NE pt..^ / Blenheim rf., # 6m., T , N pt Salomon Is., ^ 5im., (B,N\ Id.,Eofentr..orI. de Passe _/ — SW, or Boddam I Peros Banhos, 27 Is , # 6 \.,^ I, a, I. de Passe, E sid entr., mid I — Dianinnd I., [Ijm.], cstabl. — S extr., Foquet 1., 7, * ... Benares .shl, % Ijm., T.niid.c Victory bk., ^ 4m,, E pt , a ... Great Chagos bk., # C2 l.,-1 T,Eextr.,B / - NrJwm-sI, [_lm ],/, * ... 16 48-9 16 407 16 265 16 15 o 59 31-5 59 32? 59 37 5 59 36 5 4 45 5 9 5 215 72 34 72 25 72 127 72 97 5 140 71 460 5 15 5 27 5 '5 5 33 6 5 71 427 7' 46 71 37 7a 33 72 43 72 16 (58) Pl.iceo I 'Ut. S Great Chagos bk., N extr.. 5. . — NW c xtr., Eigle Is., # \ 5m.,/, t, N pt /■ — W entr , Danger I., [lim.] Egniont, or Six Is., % 6111., [ T, SE Id., f J Pitfs bk., ife 10 I., T.\ Npt., 10 ; — West extr., TO A Reef, NS2 I Ganges' bk., ^b 4ni.,Wextr.5 Diego Garci.i NSl3in.,/. ^,| t , f. w, Mid I., E entr.../ — South pt Mauritius, Pout Louis, "(^ jSIaitello Twr., Ft. George ) — Round L, [Im.]. 1049f. ... — Peter Botte, 26U0r. — Grand Port, Fouquet Id , \ It. F 108f. / Bourbon L, ^t 1 4 1. St. Denis, "( 2 lt.s., F, vert., 8Df. j --Pt. of Bel Air, It., F 148f. — South extreme Rodrigao,EW1.5m.,v's rfs., 5 1. to S\V-d., Venus Keeling Is., f ,/, N Id, [flm.] — S grp.. Borneo Coral Is , I a, NS8m., S pt J — Direction I., [Jm.]. SW pt 5°39 6 IO-; 623 6 40 6 49 7 13-5, 7 26 ' 12 I., J, L NW, Flyii Christmas I., EW 3 1., vis. I ;W, Flying. . Enderby's land, pt. uncertain... Bouvet's I O Thompson's I Q Prince Edwards L, 2 [5 1.], \ and [3 1]. h, *„, West I./ Marion I., East cape Crozct's Is., Hog I., A, i,] $„, (arf. SE9m.) / Kerguclen's land, i|,- 32 1..") Christmas Harb., g, b S I side, N pt-, or C. Frantjois J — Bligh'.s Cap, A, f „. 230f.... — C. St. I>ouis O — C. Challenger — E extr., C. Sandwich Heard or McDonald Is., % 1 50m. Meyer rk.,NWexir./ St. Paul's, ^f 3m., S60f., $ ^ E, r, Ninepin rk. on E J- side, (w'im.) J Anis'crdani [4m.], \i^, suni.1 27601'. I 12 5-. 10 25-3 67 30 54 20 53 56 46 34 46 52 46 10 48 40 48 27 49 f5-5 49 43' 49 II 57 290 57 47 ; 57 33' 5 S7 467 55 3& 5 55 39 96 51 96 54 96 33' 3 105 43 37 56 37 53 5 50 2S 68 38 70 s 7° 33' 5 5i 72 3' 38 427 77 .^ 7 37 50-7 77 3' 5 TABLE 10 573 MAUITl.MK I'OSITIONS vaysl mo. j cliangiug, Kiike Man iTie, lown ... Itate.fort Pt. Jigat, or Divarka, temple... Cnical Hill Diu IM.. pt , It. Fl 106f. -M.ind, Watch Towur .tar:ib;\(l, ffi.lt. V 7-if Shall.i-tl., [Jm.J.rfs. In... mid Goapiiauth I't., it. F 68f. I'erm I., rfs. NS 5m, ll.\ F129f. / Gogo, town, w, i. It. F 5jf. ... Cariihay, fl. St Sfirat Castle Vaux's tomb, Ta;.!!, It. F ( I30f. / Damaon, r, It. F St. John's Highland Vcrsavah fort ISassean R Tfiraporc Pt. BouniT. ffl, E, Observe, ^ — Lighthouse, It. Fl. laef. ... — Kund.ri, It. F 1481". Coulaba I Chaoiil. E,5 Uijpuri Harb. Pt., It. F 17af. liuncuot U.. lof. bar Sevtrndroog r., / Angcn.icel Harb., g, fort.l S eiitr J ZyghiirPt., t, m Ratnagiri ("en, ll. F ."JOSf. (Jeriah Pt., A, fl. St., g Angrial.k.,NS7 1., T , n S |.t. Vm-oila rks., [.im.], 20f., 1 T.beac, It. F lOOf. j .Afc'oadaPl., w"',(Goa),3], r,\ It. Hev. 280f. / M rcnagua, r, fl. st 1st, George Is., ['.'m.], A, ouli-i iC. Kamas, //, 1. W e.xir iOyster rks, [Am. J, It. V 2IOt. jCarvvar Hd....". Unjudiva 1., [Jm.] Merjcc U., w'", b, bar 2, K | hlufl- J iFortifiedl., w, [Im.] l'';reon I., vis. 8 1., T l{ar.alorePk,44.-)2f. St. Mary's rks., Sin. out, | larjie one J Prcmiera, or Mulkv rks Mangali.re hill. It.F 240f. ... ISarn l.ill .Mt. l)illy,8or9l Canaiiorc, pL, T . W, It. F C4f. •I'lllclirrv, r,w',lt. F 88f. ... Si.rr.n .■ rk.. 20f., T '...lint. h. F I03f. 23 57 67 25 69 iS? 22 50 22 28-5 69 9 22 14 I 6S 57 20 57 j 71 iS 20 40 7, 70 51 20 42 7 70 59 20 516 71 22- 20 54 71 31 21 12-3 72 65 21 35 3 72 20 21 400 72 16 5 22 170 72 355 21 I2-0 72 47 21 57 72 37-5 72 49 72 43 72 46 72 49 72 40 72 490 72 4S0 72 48 72 51 72 54 7256 73 1 73 5 73 14 73 'o 73 >6 73 22 20 2 19 7 19 18 19 52 '8 53 '8 53 7 18 42 1837 18 34 18 17 '7 57 17 47 17 33-4 17 16 "6 59 16 31 16 18 15 53 15 295 15 24i 15 21 15 4-2 14 49 '4 47 14 45 14 3° 14 185 14 1 13 SO 13 20 13 11 12 52 12 40 73 46 73 467 73 45' 73 547 74 2 74 10 74 5 74 21 74 23-v' 74 18 74 51 74 40 74 38 74 SO 75 1 75 "' 75 2.7 75 2S 30 I 75 .30 15-2, 7S 45 7 Pla< Cranjranore It., fort, bar sf. Cuchin,w,r,bar uf.,(lt. F lOOf.) Quiloan, fl. st Anjenga, L,. w„ A- st Tievandriim Pagoda C Comorin, pt — Peak Minikoi I., It. Rev. I CM'. . Maii^iKir Pt., 7- T 'I ncliindoie pagn.la Punnecoil, \v, r, b I'aumbeu Pt., Ibrt Calpentyn, fort Nc-(iinbo Colombo, r, w. It. Fl 13.")f. ... Kalituia Pt.de Galle, [B, S, r, ^y, fl."! St., It. F lOOf. / .\dam's peak, TdOOf. Matura, b. w, fort Dundra Hd., It. 150f, /, f ... Great Bassas, rkf., [liii.] 1 T,S, It. Hev. 1101: / Klephant rook, inland Litilc Bassas, rks., li. Fl. 1 101. Koniario IJaitiialoa, (bar ef), b, w,"l It. F 47f. J Vendeloos IS., N or Klu-I Chilitivo I.,.-)o'f' F.ml Pt.,lt. F, Fl 104f. riincoinalw, S, It. F lO.if., | Fori Fiedeiick J IV-nI.[im-].'k..*.99f. ... Miiktivn Ilouse, (shI. 4in.) ... Mirk House IVdroPt., J,(shl.5ni.).... BAY OF BEMCAI.. Pt. Calimere. /, 1 Me^'opatam, w, r.bar, It. F Siil Five while pagodas I'lanqueb.ir CnK-ro nShl Port.. Novo, w fnil'lalore. town nnd riv., w, 1 I'niidiclurry, It. F m(. Fl net. !.! '....../ .;..vilang Madras, [H, Obsehv.itokv, t -Ft. St. Gorge, It. Fl. 128f... Pnlicat, It. F G8f. eghon. It. Rev. 107f. Mootapilly shl., [Im.], s, T,1 ' «"' J I't. i)ivi,it F4sr. Miisulipatiim. It. F fiOf Nar-apoiir, pt., /, * Pt. (Jordewar, It. F 83f. n^^a. town r,at. N Lcn. K I0"I2' 9 58 8 53-5 8 399 8 290 8 40 8 232 8 .5 S 22 8 30 8 40 9 17 8 15 7 12 6 5O 6 35 6 52 5 57 5 55 6 II 6 21 6 245 S 7 83^ 8 35 5 8 437 9 9 32 5 9 5 79 45 79 48 79 505 79 57-5 So 12-5 So 29 80 33 80 35-5 81 29 8. 52 Si 4] 81 19 81 15 81 12 5 80 49 80 30 So 37 80 II 48 So 15 4' 80 14 7 4 7 80 17 25-2 80 IQO 53 80 25 So 18 59 3i ^ 574 TABLE 10 MARITIME POSITIONS Places Lat. N Lon. I (62) Pla Lat. N Lon. K Vizagapatani,n. st Saiilaiiilly, It. F 173f. Cliicacole Gi.palpur, It. F 85f. Ganjara, ti. st JuL'iiinaut pagodas, lai-i;e Hlack Pagoda Palse Ft.,/, t,lt.occ. 129f. ... Mjpiirra L. [-4m.], S pt Pt. Palmiras, /, f , (sh. 2 or\ 3 1. off) J Balasor R., t o, Clmndipiii-, ) It. F I06f. / Kedgeree, It. F 62r. Saugoi- L, Middleton Pt.a It. F, FI. 74f. j Calcutta, !S]. Furt William ... Diamond Uarb., Scmapliore ... Liicki puor Chitiag.Mig, town, jetty ■^ Kiver, Ijjr 2, fl. ft. at mouth Kutabdia L, -^ 4 1 , /, If , It. 1 FonWsi.le 126f. / Shoal Patch, [Im.] I Elejihant Pt, vis. 5 1., rks. ott Tabic Land, 8.300f. ? St. Martin reef, [Vm.] — L, NS 5m , S pt. rk^ Ovsti-r Id., 5, rfa.. It. F 7.if. .. Mosque Pt., or Fakcer's Pt. .. Akiab liarb., ffl, fl. St. , Great Savage, It. F, Fl. '..Sf... 15uronj;o L, \ 6 1., hum. S pi Kcniaii kown toung nk., 12 1, Terrihles NS Um., \V lim. ., Kyook Plioo, m, fl. St. Beacon L, [im.] Clicduba l.,\ 6 1 , W pt voli — Town, r, w — South pk., ITOiif. Free L, [Ini.], 250f. *, mid. Sandoway, town Foul L, 5!^ 2m., sum. Vestal Shi., I, [im.] Kocky Pt Gwa, Mosque St. John's, or Ch. rks., [im.] Calventnra rks., ^^ 2 1.1 NWgrp / Milestone rk Coronge L, ^ 2m., S pt Shoal, awash, [im.] R..undCape ..". 0. Negiais Diamond L,[lm.],/. t,mo.\ of I'egu K., (rks. off) .../ PoiiamPt., i, t Agnadarr. ^ 2m., It.R KUphant Pt., f , pagoda Rangoon R., bar s, City.l Dagon Pagoda / — Eastern Gro\e, It F 93f... Riv. Settang, E pt enlr., /, f . Martaban , Maulmain, pagoda Qiiickme, pagoda,(rf. I Jm.).. Ainhcist, paj^oda I7°4i'6 iS 5 18 lyo 19 13 19 225 19 50 19 52 20 194 20 41-3 20 41 21 26- 21 50- 21 39 22 335 83° 17' 83 3S 83 53? 84 52 85 3 85 56 86 8 86 44 87 7-0 87 9 87 55 7 22 14 21 52 21 9 20 38 20 34 20 8 20 52 19 49 19 48 19 22 19 264 18 54-5 iS 52 18 51 18 41 .8 26-5 18 26 18 3 18 2 17 36-5 17 33 5 17 270 16 55 16 40 16 31 16 29 16 16 16 1-5 91 50 9> 50 91 43 92 3 92 23 92 12 92 207 92 3i 92 53 92 54-0 92 537 93 2 93 28 93 16 93 32- 93 26 93 28 95 425 93 41 93 55 94 18 94 6 94 14 94 34 94 35-5 94 20 94 14 94 18 94 H'S 94 12 94 125 94 '05 5 5i-5| 94 15-5 IS 49-5 94 23-5 15 42 94 II 16 28 7j 96 19? 16 47 ■ 16 w 16 28 16 32 16 30 16 3 16 47 Double L, [l,m.],lt Fl64f. ... CallagonkL", f;S6m.,w NE, \ N fum J PadogaPt, Bluff Pt Mosc.is Is., Ngrp.,N Id — South grp., S extr The Cone, vis. 16 I Reef I., Tavoy N., It F 3091. Capl.. [>.] Tavoy Pi., pagoda, 1 , 1? , w, b Tavoy town .' Tavoy l.,\ 6 1., pk. (w, S] part), Port Owen, EB,E-d, ■w, b, Clyde Pt J Mcrgiii,SE corner of Court Ho Kabosa, I., I;i00f, ^t 3i"'->1 sum J W. Canister, [2c.], h, i Tenasserim I.. NS 3;yni., sum SirCh. Metcalfe L, ^ 3m., \ snm J GrcMtWestern Torre.s[5m.], ( Wsum., U13f. / Hlack rk., -pis. 8m Forrest Str.iits, High I., I392f. Twins, NS 10m., S one, [Im.] Horsburgh I., [fm.], vis. 7 ' St Matthew's I., sum. vis. 1 — Hastings Harb., ffi,wWo,"\ harb. pk J . Victoria, W pt of Paki ChanR ( Western rocky I., & rks. [im.} Chance I., ^ ."im., peak, \ vis. 12 1 J Middle I., [llm.], vis. 8 or 9 I Saycrls., NS"4l., T, 11k., 334f Jimkseilon, or Salang I., NS -j 8 1., (ahighmt. vis. 12 1.), Spt, Lem. V.ialan — Puket, town, S, r, w .. Pulo Rajah, or Tiiya, 10641.... Brothers, 2, NS 3m., S pt Sangald, or Guilder rks., rf,"l A T / Telibon I., ffi,r, SW part B-iton- Is., 2, E or Dome, 1 28I5f J Pnlo Ladda, [5.n.], Bassl Harb., a. peak, lOOOf.... / Queda, town, ffi S'-SZ'S 97°34'5 5 34 5 97 38 15 12 14 27 >3 47 13 36 13 32 13 3'-3 '4 3 '3 5 12 26 12 47-6 96 8s 96 23 97 20 97 35 97 37 97 32 97 33 PreparisL.# 8m., T E, t ,"\ rcefoffE side Spt J Gie;it Coco I., NS fim.. t , 1 i,h, w? It. on Table L, ]■ F 19.5 r. J Little Coco I , NS 2',n.., t,l f S|.t J Great Andnman, Port Corn- \ wallis, H.nsl, Id., ffi j - Saldlellil!, 24001'. N pk. ... Sir lln;;h 1. S estr — PoiiTlii.MR, (^'haiham L... - Ross I, It. F 159f Sisier.-i, 2, [Im.], Eone Brothers, 2, ^ 3m., None .. II 23 II 15 10 28 10 12 9 58-0 10 5 9 585 9 51-5 9 24 9 4 8 4« 7 464 7 5> 7 36 7 28 7 'o 7 '3 6 32 6 12 6 6 14 505 14 125 13 58 13 '7 5 97 47 97 45 97 53 98 24 yS -.3 98 36 97 51-5 97 43 97 507 97 47 97 275 97 39 98 1S5 97 41 97 525 98 12 98 II 5 97 33 97 52 97 5' 97 48 97 40 5 qS 20? 98 22 98 49-5 99 24 99 '9 99 44 100 18 93 39 93 222 13 12 95 II 47 93 4 7 II 4 1 -2 92 430 II 41 92 45 II 11-2 92 45 II 4 92 392 TABLE 10 67? I.ittle Andainnn, NS 7 l.,\ t,Sh:,y.(IVwNpt.).../ S. S.i,t,nt.I, [Im.]. «1., f .. l''l:itUM'k,[;iO vils.], sr. (<)n\ Invisible Hk.) ;■ Volcanc. i.r Bmrcn I„ UJSf.... Naicondam, T. 2330f. Kar Nil obar I., Sawi B Haiti Malv, or Quoin, 1 [llni.], ♦, wi. 150r J Chaura. [lim.]. (. 343f. IVressa, ^' 4 1.,^, 8yrf,l spt ; Til.ingchonir. K\V 4 1., f,\ Md.uiani Pk., 1058f. / Kamorta I., 238f., Nankauri 1 Ilr.. Naval Pt / Kaclial I., 835f. pk Meroi-, small, / Little Nicohar, #41., t,\ Mt. Deol)an. I42t(f. / Grt. Niciibar, 21051'., Kun- 1 dull., 400f. I — Pygtiialioa Pt STRAIT OF MAIiACCA. Pulo Pera, vis. 7 1., »o, T ... Penang I.,NS 4 l.,sum. 2713f. — George Town, S, IH,"| fort Cornwallis, It. Rev. 107f. J Saddle I.. [lm.l Pulo Dindiiig, *(( i^m., h. f,,'\ w F„Port Pancore,lt.F.../ Salangor fort, It F Sunibelan, or n Is., jt^ 7tn., 1 vis. 7 I., ^, white rk J .Taral., [im.], T, f Parcelar hill UouDil, or S. Arroa, h, f,\ (rks. oH") I C. Kaehado, 1, t. It. F 44Cf. Malacca, St. Fai.l hill. It. ( F 180f. f Water Is., A, f , large or S, w JIi. Moar, A, «f Mt. Formosa, (bk. WSW 2 1.) Po. Pisaiig, t,lt Kl. 325f ... SiNdAPORK, QjJ, FULLKIITO.N \ HATTKItY J Pt. U'liiania, (Is., 3m. out) ... H.irbukit hill, 64.5f. PiMlra Hranca, T, N\V, 5 1 S. IIor>biirgli, It. Fl. lOlf.J ll,nt-,i,g hill, 12(.0f. - BUck ik Pn. Ri.ndo. ( 7>/)uro«y),426f. 1 rk» tjd / M.MUTIMK Lat, N I.on. K °33'S 9»°28's 2S| 92 I2-S 8 93 30-2 9 14-2 92 45-7 8 497 92 5' 93 2 93 1' 93 42 93 49-5 9S 567 100 14 827 8 13 8 297 8 2 7 57 7 307 7 20 7 13 «4S 5 42 S 25 5 24-5 100 20-? 5 13 '100 10 4 133100 342 3 20 lOI 12 4 2 100 30 4 o !ioo 9 2 52 loi 25 2 49 100 35 a 12 102 15 2 4 ^102 19 I 59 102 40 I 49 I102 54 I 27 103 "15 I 17 2 103 51-2 I 22 I104 16 I 24 104 II I 20 104 246 I 5 '104 26 I 145 104 34 « 35 95 77 I (64) Lat, lx)ri. K. Pulo Wai *^ 3 1., vis. 12 l.,\ TS, Spt f IJiini I., or Malora It. F G2f. Po.Nancv.(bay S, w,b, t ,\ I Np'- ■ / PulnBiass.,/.. N.h. Kcv..i2.if. Golden or Queen's Mmall), Spt. ...Q lianjak Is., Middle Is., Po 1 Sorimg Alu / Pule. Lakoita,/, t Pulo Hal.i O PuloNias,%22l., Wpt.,1 Tauj.mg Letang / ^ — South pt., E, r, w, J _ Telok Dalam J ^ Nako Is., Asu TapanuU B., I., S, Siboga ... PuL.Dua Taiiujong Road Natal B., So, Natal 9 Aycr Bangies, Po. Parka... e Po. Pinie, Batu Bclobang, \ ^ B 3 I j" U Mt. Ophir, 9472f. .!! C Tanali Ma^sa I., N pt O Po. Bojo, It. Fl.seif. O Siberoet, N pt. Sigeb — West I O Sipora I., Hurloek Bay — S pt., C. Marlboroiigh ...O N. Pagi 1., N pt — SW pt , or Ft. Baiu O S. Pagi I., Spt. Sibaru I Trieste I., Po. Meg'i,") LI in,-].', t 1 En;;ano I , ij^ 7 1., P„ W \ pt., Koniang J — South pt., Kcnemei Priaman, fl. st Padang I, It. Rev. 180f. ...6 Pnlo Baringin IndrapuraPt.,/, f. Moko .Muko BvncuUn, It. F — Po. Tikus, It. F 44f ManaPt O Kawur or Sanibat Pulo PisaDg, [ 1 Jm.], It. 67C TABLE 10 MARITIME POSniONS Ivioe Rond, w, r O Bnukiinat I!, rkv. S )it Liitle Fortune I.,'[lm.]. I,\ STRAIT OF SITWrA FlatPt.. It. Fl. 213f. O r-abiian I, % 7m., \V cttd ... Keyset's Pk., 7412f. KaUimhayang Haili., ffi,w,r."l Klai.al J Piilo Lagtindi, g, mid. N \ side ; Teliik Belling, It. F 4.-,m.,7, (rks. 2n,. KWi, ,.k. .Misr I Ai..vv, f ,w,r.,(,lt.SW-d),fi.st North M., small, vis. 7 1. ...... Thousand Is., Northern- 1 most Diia I J — Peblakan, or W. Id Ariunuiid..nrk., [Am.], lOf.,^ North Waiclier, small, *,") (,()nngashl,E'b S' ini., - 5 T ),lt. K.159f '....J Two Brothers, *, J^, N one... Ly,.nshK,[lc.]. d, T Bnmwers shls , 2 rfs , [^in.].., Shahbunder shl., E lini Trcel.Npt Lucipara I., [Im.], t, w', 1 (rf. SSE, 2ni.) ....'.' J First Point, /, level, f Banea, S extr., Dapur 1. 120f. — Parmesang hill, IGOSf. — Nangka Is., 3, great one, \ U-, b, Npt. 28.')f. ; — Monopin Hill, H56f. — Kalian Pt., It. F 170f. — Frederic Hendric rks — NorthorMengkuduPt.. islet — Goonung, or Mt. Marass, "(^ E sum., 2300f. J — Eextr.,BerikatPt., 660f.... — Entrance Pt., (SE extr. of | Lepa), Murong J Fairlie rk., [ic.], jf., T .^and I., [I I.], B all round ... 5 55 5 47 5 5 26 5 46- 2 5 50 5 28 5 475 5 55 6 47 6 45 6 31 6 9 5 59 S 5'-5 5 58 6 3 5 52 5 42 5 24-5 528- 5 13 S 12 5 9 5 12 5 4- 5 7 3 46 3 13 3 o 3 8 2 35 2 5 1 58 1 29-3 ' 52 2 34 3 2 3 27 107 3 30 "^7 io3°56' 104 14 104 24 '04 33-5 104 47 104 40 105 157 105 39 105 43 105 II 105 15 105 15 105 27 105 2J ■05 32 (05 49 7 105 55 ic6 2 105 50 106 2S io5 23 106 44 2 105 54 106 13 106 3 106 31 105 56 105 8 104 58 '05 53 : 105 52 to6 51 106 54 Shoal-water T., It F 200f. Vansittart shls., NS 3 1., 1 Spt J- Saddle I., Klatnhau, 2661'. Table I., Goesik, llGf. Piilo I.eat, sy 6m., Alce.^ie 1 (wrecked there), It. F 39f. J Long I., EW lOm., W pt Billiton, Po Selio, to SW | [4m.], S pt. 242f. 1 — S pomt, Kalumpang, (sbl.l l'"out) / — Shoals on E side E. ^ I'r'Jtet ; — Burnng Mandi Pt It. I200f. .'.'..'...?....„'/ C'arnbee shl.. rks Canning's ik . [ic], 3, T, 5..- Caspar I., [ 1 i.ti:], 8l2f. Tree I, [IniJ, -Idf., '.'or 3 f Warren Hastings rf. B. hideierk, lof. Sttardif.,3, J Magdalen slil., [Ic], 5, T,crl. Newland shl., 2, 8, T A I'almer shl O Se\ern shl, [3m.], lof. O Vega shl., [ic.J, 9f, T 5 ...Q Shoe I., Kebatu, 346r Discovcry,WeMbk., [lin.]. !d — East bk., [im.]. Id., '2f ... Osterley slils..*[6 I.], N one... Cireneester bk.. [^in.] Montaran Is, EW 12 1., N K 1 exir. or Catlurina rf / W. grp., Nan;;kaT.,pk. 54UI... Ontario rl'., [^,n.], T , 5 (a 1 coral rf. \\ ;iin., :i) J Senitu. EW 2 1., H75f., w,^ Wond / Carimata, [.Si 1.], w, b, i k. , 337sf J Pei.ebangan, -f 2 1., A, w', 1 I'k- n22f J Gteig Shoals. N. Creig Greigshls., Gwalia Pulo Toty Pnlo Doean Po. Tndjn, or Seven Is., % 1 i-m., t, NW one / Pulo Vartlla, (Is. [3m.] ),4.5(ll Pulo Taya, [3m.], 63uf. Po. Sinkip, S pt. C. Bulu Alang Kalem, [2m ], 1 Linga I., % sum. 3y21f. East Domino, [Im.] , Pollux rk., 5 Terobi. 112f. Fndeiii k rk., [3c.]. 2, 03 ,, ... I'ulo Panjang, EW 4m., 1 390f, E pt J Eat. Eoi "s;;;Ttir 3°I9'2I07^ 3 10 1 107 3 2 I107 2 59 S 107 2 49 107 2 52 |io7 3 i5-5i>o7 3 164 107 3 3 '08 2 45-31108 2 323107 I 37 6 106 I 10 2 106 I 75 106 109 3 47- 3 39 3 35 3 '7-7 '08 3 16 2 loS 2 307 loS 2 30 !io8 I 595 108 108 o 54 5 '05 58 ^105 1 S iios o 48 104 o 43'6 104 o 38 104 o 24 104 o II 104 o 6 104 North I 0125 104 o 424 104 38 5 105 1 I 104 325 345 46 39 14 TABLE 10 577 MAUITIME I'DSITIONS Batacarang Pu •rabong PL C. Baroe Rhio Str., Garras I., W side 1 entr., h. F 12lf. / — PuloSau, h. Fl08f. Gf. Carimon, S pk., I4-4f. ... Little Caramon, ^ 3.ii., »,1 T NE, N pk., 10G2I'. / Bucalisse I., L NK pt Pulo Koupat, N pt., T Rccc-an R., Lalaug liesar I. ... N. ani S. Brothers, # 5iii.,l t. None / Bittoo Batra R Pulo Varelltth, 8 1.. *, b,P,... Delhi R Prauhilali I't . (rf. .3m.) Diamond Pt.. /. t ® Pedir Pt.,or B;itoo Pedir ...ffi CHINA SSA. Piilu'liu^'V, f ,wH-„.sum.2046f. Pulo Aor.'ay ajm.. 1805f. ... Pulo Peman^'il. ISO/f. PuloTiornan XS10m.,.3444f.,1 N pt., r„, b. w, P, I Si. B;irhe. [3m.], A, w, 75af.... Direction I., sum. 639f. Pulo Datioo, //, SE pt Gre n Id., centre St. Esprit Is., ^ 4 1., 817f. ... Wellstead rk., 5 Ellen shl., rks., [,',c.]. if. S>. Julian, summit 537f. Tumbelan Is., n^ 6 I., t,[ Great summit 1300f / — Gaprk ..„ Europe slil., rf., [Ini.]. 5 Camel I., summit 574f. Saddle I., summit 307f. Barren I., summit 80f. VictoryJ.,summit 28.if., 8 1. t Acasta rk., ^r., T Whit* rk., A IlOf. Repon, 69.'>f. Pull) Domar, 27of ,♦(>, T Djimaja. % .W., S pt Tokong Bel.-.uer, Pilhir rk. ... Pulo .Selei, 48Uf. St. Pierre Is., 2 S. Hajcck I Sirh:l^-an Id., Ko.i Hd., 765f. Krpalo.1 West I , 86.^f., N end Soiibi I., N end. 200f. JaekitoD rfs., E extr l,ow I., [1 l.],Neiid N. n..)Cock I.,A. rf., S-d Elphiiistone rk., [Im.J, 70f. ... Kc*tr.,Se3 3 47 3 46 4 53 5 16 5 29 5 5 39 2 18 2 28 2 36 2 55 io4'>5i' 104 23 103 48s 103 22 102 23 loi 39 100 34 98 46 99 34 99 30 9841 97 52 97 30 95 55-2 95 272 104 85 104 31 104 19 104 10 o Si>o7 13-5 o 14-3 108 2 o 8-2Jio8 362 O 44 7 "07 19 o 37-5 '07 I o 324107 53 o 412 107 31-2 557 'c6 43 5 1 10 107 32? I 12-5 107 345 I 11-3107 235 I 117 '06 53 I 19 3 107 22 I 317 106 255 I 34 7 106 185 1 39 106 19 a 18 \ios 35 2 21 6J105 53 2 44 5 '05 23 2 48 105 43 3 27 jio6 16 3 12 iio6 30 1 51 7108 39 2 17 |io8 54 2 33 |'o8 59 5 2 3951C9 "O 2 4.3-5 '08 35 3 3 !'o8 51 2 56 [107 56 107 48 >07 34 107 51 loS 3 3 I 3 -6 3 23 3 a (fis) Places Great Natuna, NS 40m., N pt — Mt Rauay, on E side, I890f. .Micullerr. Selouan I., [1 I.], S sum Low pyramidal rks., Z.'if. Success breakers, [2ni.] 1 Semione, or Saddle I In. Natunas, f , N islet. Blair Harliour, ffi Pulo Varcla, rk., * , rf. 2ra.... Howard shl., I I'ulo Brala, 10 1., rks., N 5 1. PuloCapas Trin^ano R., w, r, bar Great Redang I., pk Pulo Lantinjia Prinliau Is., outer one Pulo Lozin, smill, "f. Kalantan R., bar, w' E. P.,lauiPt Koh Krah, grp., large one ... CariiomPt S n.ni I , [2 1.?], iOOOf. sum. How l.uing, Mt., 7m. iu-"\ laud, 4326f. / Koh Tarkut (Po. Cin ?) 1 (peaks, 1815f., ^ 5ui.) ... j Bangkok R., ltF44f. Bangkok, Brit Factory Siacu, now Ayutbia, mid Koh-si-cliang I., NS 4iii.,') «'.Npt / Koh Leum I., [Jui.], 44jf. ... C. Li..nt Chalan I., [ic], 40r., T, Caw.sbaffMt .lunkRoekPt Kusrovie rk ; Pt.. Huniba town Teeksia R., mouth Cambodia Pt Po. Way, 2 Is., fif Im., a.'JOf... Puo Panjang Is., EW 3m., \ 5.iOf., w, h, r., great one... / Pulo Oby', # 2Jm., w, 104Gf.... Saigon, City C. St. Jamks, S.3m., It F482 Briito shl., [!>.], J. T Pt. K.ga, S„, (Mt. Taicou, 1 Z't-) J Ceicer de Terra, /, ♦ o, « 3m. C. Padaran, A. i, T,lt PI. .. False C. Varela, (Camranb 1 Harb., ffi;. A j 4 4 4 8 4 3 4 23 4 3' 4 5' 2 38 3 '9 108 25 107 49 103 47 103 38 '03 38 4 49 '03 39 5 '3 103 14 5 21 103 6 54b 103 I 5 50 5 55 102 44 7 21 107 6 12 102 19 t s8 loi 17 8 25 100 44 856 99 49 9 33 100 I II 38 99 33 12 12 99 59 13 29 .00 35 >3 446 100 2S- 14 22 .CO 3b 13 II 100 47 12 57-5'ioo 38 12 35 100 57 12 28 'ico 57 103 4 102 47 102 45 '03 7 104 10 104 54 104 42 102 52 103 27 104 48 12 31 12 8 " 7 10 52 'o 35 10 6 835 9 55 9 18 82s 46 7 106 42 ly 8 107 5 29 107 49 ; 108 48 109 I Nhutrang B., ffl, w, b, riv., bar, 7f., Trie I , pk. I640f. Three Kings, rks., T, Hone- Cohebiirb., ffl, w, 15f. ... C. Varela, or Pagoda G., A, T.pt Pert.iruled rk., rks Conical Mountn., 18rof. ... Pliuyen llarb., ffi. .Vest I. 10 1; n 13 12 12 12 55 109 20 109 16 109 27 109 26 58 |IC9 25 5 II 109 10 23 iicj 15 5??5 TABLE 10 MARITIME POSITIONS (09) riace Lat. N Lou. E (70) 13 45 CoumonL'Harb..ffi,Gainl'aHd.i I3°3i PiiloCaml.ir, ^;im.,6l 13 37 Quinhone Harb., E.G. San-\ ho, A, i J Charlotte Bk.. [3m.]. s, T ... Brothers, # 3m., E one. A, t .. I'ulo Coi.dorc Is., [;)!.], S,\ w, To. 1954f., U. F696f.... / Itojiil liisliop, % 32m., To I.it. Caiwiek, sumiiiit bSf. Great Catwick, ♦ „, .^,196r .. Yiisiiii shl., J Piil.i Sapalu, ♦„. -»-, 34r,f. .. HdllnnJ bk.,2', T. centre Piilo Ci icer de Mer. jl* .•iim.,1 r., highest peak 360(..'..... J 1 09° 1 6' 109 19 109 16 5<37 106 9 840 106 41 9 40 9 59-5 10 29 108 14 lOT 4 108 55 Vanguard shl , E and W 7 1 . s Grainger slil., J Prince of Wales bk., j, S part Prince Consort bk., 15, 1.^'°^" fSWend INK „ Amboyna Cay, centre Owen sbl„ [2m.], erl., I Spratly or Storm I., 8f. Rifleman bk., nf., , rf. London rfs., W reef — eay...ffi — central rf., d ffi — East rf., Eextr e — Cuarteron rf , d ffi Fiery Cross rf., 5^ 1 15m., I. "j or NVV Investigator, | e SW bank, beacon J Luconia breakers. South — shls., Seahorse breakers ... — Friendship shl., [3 l.],\ '. Npt ^, f Louisa shl., [3m.]rks., Jmid. Roval ChHrlotte slil., 1 ^ ['>.], rks (O Swallow shl., [4m.], rks. at 1 Ept ( South Viper shl.? O North Viper shl. ? O Ardasier shl., J^ — Gloucester shl O SWSh.a .^ O Investigator, rf., E\V 51.,"1 ^ Wpt /O Cay Marino ? O S. Oornwallis shl. ? Q] Pearson shl., rks., NS 2m. ol Gnnges O' Sin Conn I Ol Discovery, Great rf., NS1 ' 7ni., d.,Nend |' ®| 10 16 I109 2-: 9 58-4109 6 10 39 1 108 43 10 32 1I08 56 — Small rf., d. Western or Flora Temple Tizard Bank, Itu Aba I. — Nam Yit I ad rf rf. >09 43 no 295 no 30 109 55 » 3 7 46 7 58 7 3'-5"' 32 7 57 5>" 45 7 5'Sii2 555 8 38 jiii 55? 8 403 n I 39 8 51 9 112 155 8 55 112 21 8 495 112 382 8 51 jii2 so 9 35 i'i2 54 5 S 3 "2 42 5 31 112 33 5 5S "2 31 6 20 113 18 6 57 !ii3 35 7 23 113 50 7 30 |"5 o o _ I. .J ,5 7 37 7 50 14 50 '4 35 114 12 ■'3 44 114 10 8 5 S 30 8 52 856 9 25 I 9 42 10 7-5'i3 53 > ..4 2 10 IS 113 37-5 to 225 114 21-5 I 114 22 10 23 114 42 «3 i'4 I J Places Pennsylvania O — Anoth.rdo O Hdlf Moon shl., a, 3m., 1 Spt -^ / Hoyal Captain shl., rks NE Investijiator O Pen n sy 1 vania ^ O Boml)ay shl., rf., W pt., T ... Sabina shl Q Pennsylvania, shls., i^4 1.], "\ ^ mid J ^ Pennsylvania O Ganges O Loai-ta L and rfs., S. L, t ffi — Ci.y. Wetid ® Sonbie rf., d., centre gj jTliitu I. and rfs., W end ...® Trichnt shl., N end, d North Danger, a ^ , 2 islamls, I 10 to lof. / I Brown, 5 o |Bro«n,shl o [3 1.], 9 32 9 26 9 42 9 49 «7 ■5-5 39 30 28 56 "5 10 IS iii5 10 40-5lii4 10 44 1114 10 55 114 11 2 114 II 31 114 10 30 'o 35 J..... rO 1043 Norili Pennsylvania O Carna ie shl.,'3 O Ancklaud, S, T O Fairy Queen, 5 Q Sealmrse or Itouth bk., -^ \ 9ni., J} / Templar bk., NS 4m , H ...Q Coc/iiii Chill ued/,onnm). 10 20 •o 34 10 so u 7 Buffalo I., or rk., T,98f. 14 9 Turtle I., small, I 14 22 Taniquain R., bar 14 35- C. Batangan [15 16 I'ulo Canton, vis. 9 l.,rt'. SE, w, 15 23 Qui-Quik, S, w, C. Bantam...! 15 25 Col'ao C:ham, False, Honoiig,/(: 15 49 C'ollao Chatn I., % 5m., h,\\ ,. t' W, summit 1230f. / [ ^ " C. Turon j 16 7 >6 5 16 20 Turoti Bay, g, w. r, Turon I C. Choumay, West C R. Hue Fo, bar 5, fort, W \ entr J Tiger L, [Im.], 230f S. Watcher, 272f. Hon Tseu, Goat L, 475f. iS 6 106 26 Hon Mat, Eastern I., 144f. ... 18 49 105 58 Vinh, fort at entr. Ngan 1 o _ - KaR .:...) 'S47 J.05 43 Laeht Ktien Harbour 19 45 105 Hon W^ 1 19 205105 575 Thunh-hoa town 19 48 lios 45 Song Ka River, Ninh Laclit 1 ,„ c J,^ , Custom Ho /:^° ^Y 14 — Fort Ba Laeht ; 20 19 I106 27 Niglilingale I.,BatchIongvi. ...' 20 7 107 Hon Dan, It. F 148f. 20 40 106 47 Norway Is., S rk 20 37 107 ' '" 43-5 '6 33 >7 9 '7 55 I^iiiao I., S pt. ... Ktia Doi or Bamoi 20 585 TABLE 10 679 MAKiriME POSITKtNS Places Gmitaii Is., E cape I-oshiishan I., 804f. C I'aklmig I.ons Moiin R., Ouloi Pi.... Pakhoi K»ahtau Pt., .376 3 16 14 i6 36 108 41 108 575 109 12 '09 33 109 36 110 3 no 8 no 282 no 34 no 23 in I no 55 no 41 no 195 16 40 16 58 11 14 12 32 n 54 II 44 'ni 36 112 54 ,112 44 ■S 41 "3 43 15 5 117 49 >9 33 113 2 19 12 |n3 54 20 42 116 425 20 14-5 no 16 5 20 295110 32 5 20 54 1 10 36 21 34 in 47 21 28 112 22 21 35 112 34 21 47 113 I 21 52 113 IS 21 57 'n3 43 PI. ices Haipong I., ^ 3m., S part,l Asses' Ears / Great Lema, jf- 6m., w, E pt. Laiitao pk., 305nf. Macao, Guia fort. It. Bev.:a9f C.inion, English factory Hong Ko.ng, ^^ 9m , Vic- | tnria, N side, Cath. (5] .... j C. Cllinson. It. F 2il0t. Mirs Bay, ffi, rk. mid. enir. ... A high summit, 28IOf. .Single I., [3c.]. T .Mcndo/.a I., [Im.]. T , 480f. ... Pokai Pt., sum. N lm.,1 6-0 f. J Pedro Blanco. A, T Whale rk., small, T Che lang piali Pt.,T Si-ki.k., 80f.,T Cup chi Pt., 2 1 Of., rks. S 2m.... Breaker Pt, /, rky.. It. Occ. "l 152f. J Tonglae fort C. of Good Hope, It. Int. 171f Swatau li. K, Fl. 200f. Namoa L, EW I2ni , 1934f. ... Lamock Is., J^ 8 m., Boat rk. ■|'at.le Hill, 1767f. Chelsieu rks., [Im.], 20f. Brothers, 2, *jj 2m., S one ... Tonsang Harb., g, entr., "1 pagoda J South-east I., [Im. | S Merope shl, ^f 5m., s,l SP'-. T / Chapel I., i,lt. F, Fl. 227f.... Cliauehat rks., /, E extr. .\J10N, E, Kulangseu Semph. Quemoy I., ^ lOm., S pt Dodd 1., [le.]. It. Occ. 147K... West Peak, a Mk., 17 Uf. Hoo-e-tow Pt., 8uf. Chimmo, (South), Pag..da I. .\lt. Keu-sau, pagoda, 7B0f. ... Chung.ehi Pt., 4U0f.,(rks. oil') Cliin chii, g, Passage I Pyramid Pt., (rks. off) xMeichow I., # 5m., Spt — Sorrel rk., ['.m.], 60f. Ockseu Is.,5f' 2m.,lt.Rev.28GI. Ping-hai l-omzeerk., [Im.], (rks off) Lam-yit I., % 8ui., peak Yit Is., 5(i, Eextr., Kcefl. ... Chimney I., EW 2m., N pt. ... South reef, fini.] Turnabout I.^ [Jm.], It. F 2i7f. Hae tan I., iSS 17m, pk, 1 on NE side, 1420f. / Kwing 1., [2m.], (off NE1 piirt of Hae-tan), E pt. ... / While Dogs. prp.. il^ 4m., \ Middle D..g,lt.F,F1.257f./ Sea Dog rk., small, T E ' Kivcr Min., Temple Pt 22 39 22 42 22 48 22 56 Lat. N Lon. E 21° 54' 114° c/ 22 5 114 19 22 16 I113 58 22 II-4M3 3S 23 69H3 150 22 169II4 95 22 i5-7!>'4 '5 22 27-51114 255 22 31 ,114 32 22 24 n4 40 22 31 I1I4 50 22 34 I "4 54 22 18-5115 7 22 30-5 115 o "5 34 115 46 116 45 116 28 116 59 5 "6 3' 5 23 14 5 n6 48-5 23 199116 4; 5 23 26 "7 4'5 23 11-4 23 39 23 29 23 325 23 44 23 47 24 6 24 10-3 24 21 I 24 26 8 24 24 24 26- 1 24 40 24 3' 24 38 24 43 24 46 24 50 24 52 25 I 25 2 24 58-8 25 II 25 7 25 12 25 18 23 1 25 23 25 20 25 36 536 25 58 120 I 26 5 119 50 26 8-4 1 19 377 20 iS 1 19 48 117 14 117 9 117 15 117 42 ■'7 33 "7 43 iiS 6 118 135 118 9 nS 40 118 19 nS 29-2 118 20 ■ "8 33 1 18 40 n8 38 118 46 nS 49 nS 57? 119 1. 1 10 22 I '9 31 "9 45 "9 43 [119 50 "9 57 119 49 H9 55 580 TABLE 10 maritime; rosiTioNS (74) Places rk. Alligator rk., small, 40f. Tung-jice Is., ife 3m., T S,"l sum. 8.)31 J Double P.ak I., -f- S.^m.,! w, pk. IlSOf. !..../ Pih-stang Is . [5m.l, N Id. ... A dangerous rk.. )3;3„ Fiil-vanu 1,^5- 4m.,w'NE,l m ^-d. sum. 17(iOf. / Tmc Is., [2 l.J, E one, sum. 1 Seven Siars, iks , [2m.] CUft rk Nam-quan. g. Bate I Pih-quan Pk., 5m. iulaud Castellated rk Nam-ki I., grp., ^ 7m., w,^ 740f., t J Pih-ki-shan Is., EW 4m. .Coin 1. liuoin Wan chu-fu, city I'e-shan I.S., [2m.], K one S. Foreland, I., [.Vm.] Cliik-liok I ,[im':j. i,760f... N. Foreland I , [im.] Taiehow Is., % S'"- S pt,1 or Fingers / — Shang-ta, grt. one, ww, 1 Npt / — North Id., [and rfs., Jm.]... Square I Tung-ehuh, or Bella Vista, "\ ^ 2m., sum. 700f. 1 Hai-mun, S of entr. ot R. 1 Taichow, citadel J Falll., [Im.] Hirshan Is., ^f 5m., f, S or"! Saddle I^320f., w J Eight feet rk., (N of do.) Triple I.. [2c.?] C. Conivay Montague I., ^ 4m., 740r., 1 Ept J Sheipoo Kweeshan Is., [6m.], grt "I one, sum 400f. J — Patahecock I., [3c.'j, h — E exlrtme Chusan Is.. S extr., Tinker rk. — Taouhwa I., % 7m., sum. T 1680f. J — Chookea I., NSeim.jpk.t uenf. ] — Outermost, Tongting.^ [2c.]. 161f. J Cone I., small Chusan I., % 7 I., Tmg-hae, 1 citadel / Chin Hae Ning Po, pagoda Friendly Bluff, Talnn:: I., 980f. Fisherman's [s , EW, E\ extr, Brother, T / 26 i6 26 9 26 23 26 36 26 42 26 52-2 26 56 25 59 27 37-4 27 50 2S I 28 5-5 28 16 28 22-4 28 33 28 23 28 30 28 32 28 35 28 422 28 40 28 50 2851 28 56 28 59 -9 3 29 10 29 13 29 26 29 22 29 27 29 36 29 48 29 54 29 51-5 30 4 29 57 29 5> 7 30 6 1 9° 56' 20 o 20 12 20 245 20 29-7 20 97 20 42 20 49 20 47 20 242 20 27 20 57 21 25 21 II? 21 13 20 36 21 30 21 42 21 42 21 37 21 S3 21 54 21 26 21 50 22 13 22 17 21 53 21 55 22 35 22 27 22 6 21 43-5 21 33 5 21 34 22 56 Fisherman's Is.,MonleVideo, ] \ 2m., T, 9961., »„ Steep I., it. Fl. 243f. Lukon Is., 3l3f., [im.], T ... Beehive rk., T, 46f. Ts i-«m I., EW 8m., Pen- 1 nellPt / Childersrk., T Barren Is., [Im.], rky., T ,1 l.iOf. J Saddle Grp., ^^ 13in., E 1 Sad., Spt, T, 692f. J — N. Saddle, EW 2m., T , 1 N pt., It. Rev. 273f. ... | Rugged Is., EW lOm. SW ( Horn, 50f. / Gutzlaff I.. [Jm.], It. F 270i: Yang-tse Kiang, beac. 35f. ... Arialne rks., [Ic ] Amherst rks., [Ic.]. 26f. Wusung, forr. It. F SOf. Shangii.4.1, Brit. Consulate Nankin, city, porcelain tov.... Hankow, Bouncer I.. It. F Sha-»ei-shan, rk.. It. F 229f.... Tsung Ming I., ^ 10 \ ,\ Kpt / Ashl.pt., NNE 61 30 12 30 26 30 22 30 25 30 37 3° 45 30 42 30 36 30 48 5 30 5> 31 9 31 II 3" 23 31 147 32 2 30 33 3' 25 Is. in G. of Whang-ho. 1 _ ow /" \Vl,ang-ho, or Yellow R. ...Q Hae-chow, ciry O Tower Pt Kyauchau Harb., Nli hill ... Ka tih-neaou I Surveyors I Urh Taou, or Staunt0f. Greiit Wall, Ee.-ctr. Ninghai... Haluian Pri'm Neuchwang Hulu shan B., N pr Iron I.. 7.iOf. Liau-ti shan Promontory C'ap rk., 400C. Talicn Whan Bav, entr. S.in- ■> shantow Is., S extr / Kn.onnter Rk.. llf. 38 4 38 21 38 23 37 4« 37 o 38 58 38 53 39 58 40 44 40 43 39 30 3S 57 38 43 38 48 3853 38 34 TABLE 10 oSl MAIilTl.MK POSITIONS noiinrt r.. small, 'JOOf. Itdck, like a jiiiik, Slii-sinu .. Ilai juu-lau I., S pk. I370f... 38 56 39 3 122" 12' 122 45 123 XO 23 12 6 119 257 23 15 q 119 40 23 19-2 1 19 195 23 2+2119 '95 23 23-4 23 287 23 32 Pesc3dor>s Is., Junk I., 260f.. — Kast I, Nend — \\Is.,# 51., t „} ,,^'.P! / 1 orj-sima, 413f. 26° 10' 26 13 26 4 26 47 26 51 26 42 26 43 27 S 27 2 Formova, S cape. It. K 180f. Lanibay I., [2jiii.], summit Ape Hill. I HOC, Ta-kau... FiTt Zealandia, It. F 6of. ... h.rt Kok-si-k..n WaiicUau Bank,,? Table Hill, 36uf. Tam-sui liarb., ffl. Wliite Fori Sura Eastward, 2800f. ... -ki Pt. Pmnacle I., [Jm.], || S t-TasI- [1™.]" .\gmcourt I., [Im.] Kelungharb., g, Kuin rk. .. Kelung I., [^in.J, .'iSOf. East extreme ol Formosa San-o B.iy, Obs., W M.le Mt. Morrison, 12,8.50f. Blackrofk B., outer rk Saniasaiia I., [Im ], rky Kumi I.. I-n!ih-K«oli, ^ 6in. Hummock I., [im.], mid Sandy I., EW .Im., W pt Koo-kiensan I., Ji 15m, 1 (w'SW), Wlim J — N cxtr , Patchusan I., J^ 6 L, N pt. .., ■I'ort Hadd.ngtun, ffl, W\ pt. entr j Typinsan I., 5|j 16m., t.Kpt — I. off N extr., Eeki-mali... — I.oflSW parr, Koo-re-nial ■ >apin-6u I., IlSlf., NE"l side / T;-a-usaI.,EW4m., J.mid... lUlcigli rk., 2;of. 26 22 126 44 Koomisang I., llOSf.. EW") 8m., (rk. S2m.), N\V pt. / Tusinia I., 60f. 26 355126 Tuna»lice I., Kuin. 60.'Jf. 26 2i 127 10 Agiinyrh pk., 30lif. 26347127 14 2f 55 22 205 120 22 38 ,120 23 o 1120 23 6 [120 23 3> 119 24 540120 25 10-4 121 25 12 121 25 18-4 121 25 26 121 25 29 [122 25 38 |'22 25 8-6I2I 25 12 JI2I 25 2 |l22 24 355 '21 23 29 [120 23 6 5 121 22 394 121 24 25 24 '3 24 4 24 18 24 26 24 37 24 250 24 43 24 55 24 42 25 57 25 SS 122 59 123 36 '23 49 '23 43 '23 47 125 29 125 14 '25 «3 23 29 23 40 '24 34 Yerahu-slma, pk. 687f. Kiikirouma I., 22U7I., C.1 Ohoiabu / Suliihur I., Iwo-simas. 54If... — C. Saiialana Ii.ro >ima, C. Kataki Amami 00 Sima, Yiomi — lono Misaki Kikai git sima, pk. 864f. Sandon rks., 30f. Yoko sima, 1700f. -sima, NS 7 1., The Sound South I., Ko-S,ikiPt .. C'olnett I., or Kotsu Sima, 800t Iki I., NS 3 1., islet ott'N end Outo Is., Uku sima, pk. 842t. — Hira simii, pk. 6631'. — # 21 1.. S\V ext. Ose 1 Saki, It. R ; Tama-no-Ura, SB, S pt. enir. i'ori Sima, I'allas rks., \ Srk., 60f. j Me Sima grp., Uri Sima,"! (Asses' Ears), 607f. / Hirado or Spex St., Taskc ll. NaNGASAKI, MlNAGE Pt Siigatsu no Ura, Kame-ura ) B., S, entr j Taka-sima or Symplegades, \ 2I0f. j Tsukarase or Ectribniion \ ks., 96f. / Kami no Knshiki, pk. 1.1021'. ! Sliinio no Ko-hiki, S pt jKusakiiki Sima High I., 53Uf. HasimaSaki Ni)nia no liana Okaimon Daki Pk., .3020f. ... Kogosima, It. F 45f. C. Tschitsehiigoir, Satano ) Misaki, It. K200f. / (;. Hisaki O shima. It Fl. 287f. T.iSaki,290f. Akatmidsu Hd Eexlr, Kiusiu, Sura Saki ... I27"i5' 127 41 127 41 i 21 '■ '7 128 2 '27 49 5 28 25 28 26 5 27 21-5 128 35 27 38 '^8 555 27 52 |l2S 14 27 525128 53 28 00 28 17 28 31 28 17-5 28 445 28 48 129 9 129 19 129 42 129 59 129 47 129 2 34 «9 '29 «3 34 55 '29 34 '5 |'3o 6 33 52 |l29 40 ii i6-5,:29 65 29 145 28 36 Si I 32 37 32 41 32 14-5 32 '5 128 375 128 65 128 23 5 33 23CJ129 33 5 32 444129 5' ? 31 27 129 43 5 5 129 44 129 54 129 4' 129 26 130 II 5 '30 7 130 32 31 355 '3° 33 7 3' 5° 3' 37 30 5' 3' 45 3' 25 3' " 30 59 31 i6s 3' 3« 3' 47 32 29 130 395 '3> 75 '3' 25 131 295 131 40 132 6 582 TABLE 10 MARITIME POSITIONS. Kiiro-sima, or Sta. Clara, 1 2n2Sf. earn ( Iwoga-sima, Volcano I., 233If Takesima, Apdlos I., 742f. Nagarobeor Jul!?, [I l.],22'J7f Yakiinu-sima,^ 5;.,C. Vaiake Tanega siina. MS 6 1., t , N pt Pinnacle I., tiala Sima,3400f KutsDO-sima, 2230f. Snwa-sima, act. volcano, 2706f. Tokara Sinia, Pennell, 860f.... Sikok I., W. pt., or C. Misaki — S extr., or Isa-saki, 1500f. — C. Muriito-saki — Ka!no(la-saki, Sima Isnini Tomangai, It. F Hiogo, (Ki.bc-), Kawa-saki .. Akaslii Palace Naruto pass.ige, Nagasc Seto-l'chi, Sakaide — Imahari Palace — Malsuyama Nipon, S pt., Siwo MIsaki I.,^ It. F 163f. J 17.3f. iOf. Iro-o-Saki. li. F l8.-|f. VrU'S I., [■JS.'iOf. vol.],II,,(ii.. Isiirngi Saki, It.FI Yedo G., Yokohama, Naval | Store J C. King, No-Sima It. F \33( Innb.iyL-saki, It. Kev. 168f. ... [■ovonia Kinkuwasan I., 14701'., lu Fl I'^f J Toilo .Siki .Sirica Saki, It. F loOf. Kosu-sima, volcano 20nof...... Redfield rks., 20f., Southern... Mikura I., [1 1.], mid Broughtun rks., 60f. (Kan- ) n^iniba) / Fatsizio, 2840t'., S end Aoga-sima, lOOOf. Bayimnaise Id., 26f. Sujith 1., 421f. Nipon, N pt., Oinasaka-sima... Tatsnpi-saki, 362f. Biiterii rks., 18f. Hatamura Tabu sima, E extr., 150f. Awa-sima, NE extr., 680f. ... Sado 1 , % 13 1., N pt. Wasak — South pt YutMsma, [2m.], «f , 40f. Astrolabe rk.. Nana siinn, 200f. Rokko saki, C. Noto, It. F 152f. Oliama Harb., It. V Oki Is., #20i.5f.. N pt Mino Sima 1., [I 1.], 492f. ... 30" SO' j 1 29- 56- 30 475 '3° 18 30 49 1 1 30 26 30 27 30 27 30 50 29 41 29 5if 30 o 29 38 "3° 13 130 30 131 4 "29 33 129 52 o JI29 56 iS 129 44 29 75129 14 33 205 132 I 32442133 '7 33 14 134 II 5 33 50-5 134 49-5 34 17 :i35 I 34 405135 112 34 395^134 595 34 «4 ''34 39 5 34 19 ,133 51 34 4 133 o 33 51 132 45 5 33 26 35 264 139 39? 34 54 35 39 36 5« 139 53 140 56 141 15 38 17 141 36 < 39 33 41 26 '42 5 141 29 34 12 33 56-8 33 52 139 9 138 49? 139 34 33 39 3i 2 32 29 31 55 31 26 139 177 1.39 50 ■39 43 139 54 140 I 41 34 41 16 40 3' 40 2 39 II- 38 29- 38 19- 37 50 37 49 37 35 37 31 35 30 362. 34 47 140 3140 1I39 139 9139 6139 9138 ■38 ;1J6 136 '■37 '35 Places Tsu no Sima, li. FI. 142f. Simonoscki Strait, Shirasu, ) ll. F'44f. / — Isaki, It. F 122f. Yezo I., # 95 1., S extr,\ or C. Sirakami. It.K 120f. ( Ko-sima I., lOOOf. O. Sima I., [2in ], 23:)9f. Hakodate, Kamida Creek ... © C. Y'esiin. 2063f. Volcano B, P. Endenno H'. . C. Yer mo, (rks. oH'), 3.oOUf., It. AkishiB E. exir., C. No\shap, It. F Skotan I., pk. i400f. Kun.ishir I., # 21 1., C.} Moimoto / C'. Sirotoko N extr., C. S..ya, Sonai, It. I FI. I.i2f. J- Refunsiri I., C. Karanunai Tariiri Is, Choresiri, 577f. ... Oterrani, It. F 162f. C. Ni.vosilzoo, It. Fl. 248f. ... C. Siitsnki Okus.ri I., Gomiga saki KOREA AWD TAR- TARV. Low Barren Is., [1 1.]. S one Pillar rk., 13.5f Sir Jas. Hall'.- grp.,Cliong do. I. Sconl R., cnt. Kuroila 1 Clifford Is., W. !., 412f. Korean Archipelago, Gue- "(^ „ rin I., 3S2t. / '-' — Nan San Do, 579f. — fllodeste I., 119U: — Ross 1., 190il. Port Hamilton. Obs. spot ffi Quelpart, -^ 111., Beau ) tort I. oft NE part J Sentin. 1 1., 3401'. Sir ll.ParkesSd. Obs. I Fusan Hr., Its. F C. Clonard Dagelet I., ilatsu Sima, pk. 1 4000r. / C. Duroch PortLazaref Broughton B., isl. Hodo C. Bruat, 1542 Tuman LUa R., entrance Expedition Bay,Tchurkhoda... C. Gamova Vladivostock, Scharn- \ horst's Suiion J A^kold I.,li. Fl. 590f. C. Kruilov Sian wuhu Bay, S pt. Siai- 1 ehu R J St. Vladimer Bay.OrekhovaPt SnltVon C, i;iOiif. H.Hr.i.ouia IP, Tullo 1 34°2i' '30°S' 33 59 130 47 33 57-6 131 I 41 24 140 13 41 21 139 48 41 30 139 22 41 47 1140 43 7 41 47-5 '4' Hi 42 19 9 140 595 41 55 ;i43 16 43 2-4144 517 43 25 ,145 46 43 455146 36 44 25 146 32 44 18 145 23 45 31 141 54 45 17 44 24 43 14 43 19 4^ 37 42 15 140 59 141 16 141 07 140 22' '39 51 139 33 ^3r7 3746 37 30 36 37 124 34 124 39 ■ 24 44 126 3 ■25 33 36 7 126 35 21 34 42 34 4 126 2 ■'■5 14 125 7 34 1-4 127 18s 33 297 126 565 35 7 36 4 128 42 ■28 395 129 2 129 3S 37 31 130 52 3846 39 19 39 41 128 16 127 25 127 45 40 s« 42 176 42 379 42 33-4 129 40 130 42 130 4S 7 131 147 43 6-8 131 52 7 42 438 42 40 132 217 i33 4 42 54-2 133 50 43 5.V7 47 '9^, 49 iS 135 27 139 4 140 19 TABLE 10 MAIilTIME POSITIONS (,79) Place C. Sicnrkuiii Casiries H., It. V 262f. ... Amur R.,Nikolaevsk Cathedral .'^ajhalin I , C. Jonquicre, 1 li. F360f. / Tiharaikove ossa Pt Kosotinai R.,ad Miinneron I., Totumusiri I.,") UOOf. / C. Notoro, iL F 135t'. Kamcn Opasnosti, 2nf. Kiirsakovsk Uuad, It. F C.Sireu.ko C. T..nin Uobben F., 48f. Ticliminev C. Patence C. Dclisle de la Croyeie C. Lnevenstcm C. Elizabeth (". Mnria C. Golovatchcff , 50" 6' 140^43 51 25-5140 55 S3 8-1 140 43 5° S3 '42 7 48 46 '141 50 47 587,M2 137 C. Khnb,iroff U inecke 1 .Shai.tar Is., E\V 20 1., E one,"| I Procofietf, [4ni.], E pt. J M. Ouda, mouth tit. Jonas I., [Im.], *„ 1200f. I'lirt Aian Okhotsk C.Bligan C. I'iagliin Gh.jin>k. lt.F Penjinsk Yetorup T., # 43 1, Spt.,1 C. Rickard J — Npt, C. Vrics Urupl., j)4 I- I., SW pt rvramid rk.,ofFy and E pt... li'roiighton I., [1 1.], /i, »o •• .Siinii-ir I., jf 10 1., S pt., or \ C. Rollin (Sianuiii) / Broirghton K Hashua I., [,.k.], (rks. S\V-d.) .Matua I., t^aijclie I'k Raikoke I.. [I 1.1, sum .Musirl8.,S C. Oneta, Shiasbkotan I.,^ 4 1. Kharim-kotan I., [I 1.], pk. ... Orieko an I.. J^ 2 1., S pL ... Makanrushi I., [2 1.], mid. ... raraimisliir I., ^ 20 1., S pt Sliirinki I., [2 l.J .sliumshu I., NS 3 1., mid Alaid I., [2 l.J, n.id XAMCBATXA. V. Ongon Hi-lsheruthk, cnt. R (;. Ix>patka Mt. VilutchiD, 7060f. Avatcha B., ffl, Ecntr., lt.\ F526f. ( - - St. PptfT »nd St. Taul, Ch. 45 54 45 4'< 46 40 46 I 46 50 4832 49 13 48 42 S> > 54 3 54 24 54 17 53 25 53 30 54 18 55 2 54 44 56 25 56 25-. 59 22 58 40 59 13 61 53 6a JO 44 25 45 40 45 37 46 19 46 44 46 49 47 >3 47 5> 4S 6 48 16 48 35 48 56 49 >■ 49 '9 49 5' 50 I 50 IS SO 46 50 54 58 o 52 45 50 53 52 42 52 52-5 142 2 142 10 142 44 143 26 '43 27 "44 45 •43 9 "44 55-5 143 47 '43 '5 142 47 142 iS '4' 53 141 3 139 52 138 27 '35 24 '43 '8 138 21 '43 '4 '5' 37 156 15 160 37 162 56 146 56 148 45 '49 32 'SO 27 150 28 '5' 37 151 56 '52 47 '53 '2 '53 '5 '53 44 '54 8 '54 35 154 47 '54 32 '55 23 '54 58 1^6 26 '55 32 '57 SO 156 14 156 46 158 22 158 470 53 "O'SS 435 (80) Place* n. Sl.ipunski Kronotsky, pk., ln,6I0f. C. Kronotsky Kluolievski, vole, I6.13If. ., C. Kamchatka Behring I., ij, 16 1., NW pt... — South pt Copper. or Midni I., S pt. C. St.ilbovoi, A, i C. Ozernoi Kar.i^hiubky I., ^ 20 1., N pt - South pt C. Oliitorsky C. Navarin, h ly of Archangel Gabriel,") NE pt., or C. King J C. St. Thaddeus It Anadyr. C. Alexandra Krest.i Gulf, C. JNIeechken .. C. Hehiing C. Tuhukotski Plover Hd Arakam I., E pt Metihignie B., entr., pt. /. .. C. Krlcougoune ' ".awrence B., E pt. entr .. East Cape, SE extr., 2521f. .. C. Serdze Kamen (Behring, 1 2«) J Jinretlen (Nordenskiold, \ 879-80) / Barney, or Koliulchin I., S pt Herald I., 900f. Kellett land, or Wrangell l.,~[ C. Hawaii J Mount Long. 2500f. C. North of Cook, 105f. C. Jakan C. Shelagskoi Bear Is , E or Column I — Westone l)e L'ing Is., Jennnettel - Bennett I., C. Emma E Mouth of Indigirka R.,pt... C. Sviatoi Lynkhow 1., S pt ■ ^.kl.ov I.S., EW 70 1.. New \ Siberia, C. Kamenuoi ...J North I., Eiguriu C. Mufasch, mo. of the lana... lA'na R., mo., N, or It 1 Olenik a iV '.' Us'chani'la'iV"!. . . iieluiskin, N extr. of Asia C. Vega Einsamkeit I Yenisei Gulf, E pt, Dixon 1 Harbour / Gulf of Obi, Drovianoi Pt. ... White I.. C. Schubert Ohdorsk 53° 6' 160° 4' 54 47 54 54 S6 8 56 o 55 17 54 43 54 33 56 40 57 37 59 13 58 28 59 57 62 16 62 42 64 42 65 29 65 o 64 17 64 21 64 46 6531 65 29 65 37 66 3 67 o 67 7 67 27 7' '9 70 58 71 7 69 4 t>9 40 70 2 70 38 70 50 76 45 76 40 7' 72 52 73 10 75 10 76 16 7' 3S 73 27 73 22 77 40 77 36 77 40 73 •S 72 43 73 7 66 32 TABLE 10 MARITIME POSITIONS ronlianak R., I'a djiing I. ... Ran«kai Pt Sftin ijang I , Biiro' g Is., Lamukutan, N pk Sanihas K,, Foit Sorg Tanjong Api, /, f , S 2in., w' Taiijoni; ])ato, A..' .'.., Marnndum I., small. 120f. T.injiing Sipniig.ark.(rks..5m.) Tnion- P.v. It. I' 49or. S.irawak li., New fort ., , Sink Pt., /, It. F Mt.Silungun, I5U0f. Tanjong Barram, /, rf. off ? .. Mt. Mulii, «oool'. Bruni, or Borneo, city palac( Mcaro I., E pt I.abiian I , Ram-ay Pt Pulo Tega, 8, A' d 3 1. N i-nd Castle Pk., ISOOf. Pulo Gaya, % 4m., It F Samarang Bk., 31 Veraon Bk., fj Fury rks Saracen Bk., b\V extr Mangalonn I., small, 55 Amboiig B., w Kini Baiu, Mm., I3,700f. Mafanani l.«.. [.5111.], W pt. .. N. Furious .^hl.. 7 N exir., Samiianmango Vt.,\ Kalamjiunian 1., t.fif / Bala SE, gan I., iP UUf., Kaliit I., ,1* 7 1, 1., 2-1 .I....J K\V, \ pk. .l87Uf- -/ — E side, Baiicowan I., S pk. Mang-i Is., \ 3 l, (rfs. 1 ■\VS\V3l.). S' I / — N one, Salingsingan I Balabac I., NS 7 I., 1900f ,1 S pt , or C. Melville / Calandorang B., It F I19f. ... Palawan, j)* 80 1., S extr.,1 or Pt. Buliliiyan / Bulanhau hill, N end ofl range, 3,500f. J Albion head York breakers, [5m.], 1 foot Table Pt UluganB.,N\Vhead — Watering B High I , off Port. Barton, 1 lOSOf. J Malampaya Sd., Pancoh Tapiutan 1., (Riigg. Is.), N pt. Cabuli I., [Im.]. 560f. Dumaran I., J^ 5 I., E pt., \ P.raieUd / Carlandagan I., KS 2m., E pt. Barbacan, Stockade Port Royalist, It. F 43f. Detached I., East I.. [Im.], / Kanaron I., [>i.]. '-'O^'t- Lat. N Lon. E (82) ' 57-5 2 5 2 3-5 I 48 I 44 1 33 2 46 3 48 4 36 4 7 4 522 5 04 5 "65 5 44 5 47 6 o 5 36 5 44 6 6 6 II 6 18 6 7 642 7 13 7 175 7 125 7 32 7 34 7 49 S o 8 40 lo 31 10 52 «c 35 ■o 39 9 44 8 S3 [I 14 09"io oS 56 oS 45 08 42 oS 58 09 19 09 40 5 09 65 10 21 10 325 10 21 1 1 21 13 47 >3 58 15 14 >4 54? '5 4 >5 >5 '5 38-5 16 5 ■6 3 14 53 15 25 15 18 ■5 35 16 19 '6 33 16 16 16 17 16 43 16 49 ■7 57 17 iS'S 17 16 17 16 16 59 17 27 17 10 17 24 17 58 iS 8 18 38 18 45 18 48 19 4 '9 23 19 15 19 29 Places Nangaloo Is . [1 1.], NE pt... Yloe I., [3 I.J. S pt., rock otf Liiiicapan, N\V pt Tres Reyes, rk«., [im.] Dclianl., [Im.] Tara I., % 3m., TSIIf., N pt... Bu^uanga I, ^ 12 1., N j.t. .. Colocoto rks., [Im.] Culiou l.,\ 7 I., Culion Vblllpplne Islands. Hunter Rock Merope .shI.. [2m.] Apo sill., ^ 2 1. ? Is. t , 1 Apo I J Falmouth Bank. KS 2 l, N pt Panagatan slil.. EW 3m ,5f... Scmirara Is.. N pt.. [.5m.], 1 — S pt., or Pirate I., $'„. | w,(alake),SEpt / Kiniluban, [1 I.], rcmkblc^ spire on W extr J Manignin I Poi.tud bank Manamoc I. and rfs., [2 1.], pk. Cuyos I. — Grt. or Cuyo I , Town... e — E extr. or Tagauayan ... O — S extr.. Iinalaguau,303f.O — fSWextr., islei, Paya,90f. O Sombrero rk., [10 yds.] ... e White rk., 24f. e Ambolim I., S end, (slils. \ SEd) / Port Mangar.ni Town Pt. Lumiulau 9 Sablayan Pt Mamhurao R 9 C. Calavite 9 Paluau B.. vill, w Mt Calavite, 2C00f. Pt. Escarseo Silonay I Pt. Dumali, (sum. ^- 3m.) ... Pt. Davagan Pt. Pandan I.ibagao I., [Sm.], 4IOf Bin I., Pt. Bin A, N pt. Golo I., SEend... Lubang I., ^4 1. — Looc Bay Cabras, or Goat I., It. Fl C. Santiago, (Minerva rk.~| ESESm.) j Fortune I., [Im.]. 450f. Fri^ir, 120f. oil' Pt. Limbones Cavitp, It. F 30f. Manila CATiiiiDiiAL Oraui . Corregidor I., It. Fl. 639f. Pt. Lu/,on, or Hornos .... Port Subee, Grande I. ... Pt. Caponcs, large I. off. A Yha, town Lat. N Lon. E I20°I0 I1I9 42 119 43 120 6 [20 19 !2I 21 '9 53 120 58 lii 16 121 20 121 22 120 46 I 36 5 121 40 I 21 121 40 I 18 ' o SI o s8 o 4S o 48 o 43 o 26 21 13 21 45 20 36-5 21 33 2 21 121 s 2 31 120 54 2 50 120 45 3 '5 !>2o 3VS 3 26 |i2o 175 3 23s 120 29 2 3 287J120 24 3 31-6120 592 3 27 |i2i 13 3 6 2 38 2 17-5 2 12 2 9 3 385 3 52 3 43-8 3 54 3 46 4 4 121 34 121 32 121 23 120 40 120 29 120 37 5 .20 54 5 120 58 ■20 3i 4 29'5 I 4 35-5 ' 4 48 4 2331 4 2S-5 ' 4 47 4 sss:i2o 05 5 20 1119 s>^ TABLE 10 685 MAUniME I'OSITIONS (H.I) Places MMMngloc, town Heniiana mayor I., I'r. Caiman, if. S\V Tambobo Pt Bolinao. Tol. Station Port Sual, It. F 79f. Dagupan K., It. F 29f. Pt. San Fernando, It. F\ asf. J Pt. Darigayos Port Santiago P(. Dilc .Mr. Hulagao, 36S!9f. Pincet I., Spt Culili Pt C. Bnjeador, /, $ 2m Pt. Ma>raira Caraballo Hill Cabicun(;aii Pt .\parrl, town, $' is J. Engano, Hermanos Is. L:,t. N Lon. F, 15°33 15 48 'S 55 16 05 16 24 16 6 16 s >6 375 16 51 17 18 '7 34 17 38-5120 31 "9°57' 119 47? 119 46 '19 43 5 "9 56 120 75 120 195 Dedicas rks., h, pkd Uuinapac rks., h, J , \\ W Camignin I., # 4 I., (Portl S Pio Quinto, t ' W, w), [ vole, vis. 20 1., Fcinl I.... J Fuga, or New H:ibiijan,i K\V 5 1 , I'urt Mii.-a, t ' at \V Knd '.) Daliipiii, VIS. 11 I., l:^, rks. \ S-d., N pt / Calavan, [3 1.], h, J, rf., \ NWpt. ) Wyllie rks., 2, -^ 2in., N \ pa" / Claro Babuyan, [.5 I], A,1 vole. E end J lialintang, or Richmond Is.,"l 3, [II.?], A. i, T,So. N Sahtan I., NS .5m , S pt Ihugos, NS im., S pt Di-qucz, (Goat U.\ [Jm.], \ W. pt / Catan, or Monmouth, # \ 9m., r, w', N sum. 38ii6f./ — San Domingo. Cathedral .. IJiogo, (Grafton I.), [fm.],"l 848f. / Ibayat, (Onmge I.), ^ 8m., T r, t W. N sum., or Sta. Rosa, 680f. J .Mabudis. ^ Urn Y'Ami. [Jm.]' (North Islet 1 is SSW 2m.) / Gadd's 3.1 or Cumbrian "\ break / Little Hotel Toba^'O. [.\m,] .. Boicl Tobago, % 8m.'? f , 1 NEpk. 1850f. ; V.la Rete rk»., [■2m.].~[ "'• J 17 40 18 5 18 30 18 40 18 31- 18 38 2 18 213 18 35-5 '9 3 18 58 ■855 ii> 52 19 9 19 22 «9 30 19 31 120 22 120 28-7 120 345 120 52 120 54 121 6 121 37 122 65 (84) I'laces 21 16 121 13 121 22 121 39 21 590 z« 57 121 57 121 58 121 37-2 121 365 12' 335 120 82 Yligan Pt .Mt. Dos Cuernos, 4()08f. .. Tumango Port, N pt. entr. O 0. St. Ildefonso O Port Lanipon Polillo I., % 7 I., Banlal Pt.,(Is. SK-d.) / — South point O Jomalie I, [.J 1], E pt ...O Maulamat I O Cahileie I., [4m ]. S pt. ...O Alabat I, [3 1.],/, N pt. ...O Jesus Pt O Samur I o Mntandumatcn, /, Is Q San Miguel B., Canton ) _ I., VVof entr. [lm.].../0 1. Batavanan, % .■)m., N pt.... Sisiran Port, ^. l!asi nibanes I., E\V 3m., W pt. Calandnanes I., -^ 12 l.,l ^ 1.1. Nof, [I 1.], lotpt. /" S or Tagnntun Pt O Volcano of Isaro Volcano of Alhay, «274f. Uapurapu I., [3 1.], Unguy Pt. Pt. Montupan, rfs. 3m Volcano of Buliisan . St. Bernardino I., [2c.],*„,l II Eand W, 1501 J S pxtr. of Luzon, Calintan I Los Naranjos Is., [2 1.],^ Raza I / Capul, % 7m., N pt Port Sorsogon, g, town Ticao I., % 5 1 , N pt., S") Miguel I / — Port San Jacinto, on E 1 side, m. w, r ; Masbate I., Bugui Pt — Jintotolol — Port Barreras, on N side, 1 a,Npt. entr / Burias I., Busin It F Cabcza de Bondo, 12.i0f. Mnrinduque I., % 81., Mar- \ langa Pt j — St. Andre, pt. 751f, Kj ... Pagvilaol., ji I 1., SPt Pt. Locoloeo Mt. Labo, sum. 3363f. L Verde, % 5m., NE pt " angas, town, r Pt. Natoco Maricaban I., EW 2 I., rfs. \ ind W pts., Wpt J Maestro de Campo I., [1 I.]1 Port Concepcion ; Dos Hirmanas, Isabel I., I.'M) . Banton I., [1 1.], NK pt ra I., [2m. J, N end I'ablas I., NS ab. 12 L,"l Cabezo, 24n5f. / P. I>oog Town, ffl Homblon I. Port, It. K Lat. N Lon. E 1 8° 2o'5 '7 30 ■6 43 16 5 '4 43 '5 5 •4 43 14 35 14 30 14 15 14 14 14 22 14 3' 14 17 14 4 14 9 '3 55 ■4 5 14 8 '3 3' ■3 39 ■ 3 16 •3 II 13 85 12 47 12 46 122" IS' 122 6 122 14 121 46 121 34 122 6 122 4 122 17 122 19 121 50 55 26 124 4 '24 13 24 9 23 21 '23 41 24 10 24 13 7 124 124 12 31 124 5 12 22 124 8 '23 59 ■23 36 12 43 12 323 12 36 II 51 '2 33 13 12 13 33 '3 53 13 39 13 40 13 33 5 3 45 '3 38 3 41 3 o » 57 12 50 123 15 123 7-5 123 24 122 5.S ■22 35 121 52 21 25 121 18 5 3 121 2 21 44 = ' 5^>-5 22 6 12 7 22 10 TABLE 10 MARITIME POSITIONS Silmjan I., %5l., pk 6424f.,"\ Pt. Cavit / Cresta del Gallo I., [Im ],S Samnr I., % 42 I., Batagl.,1 NS5m., Npt J — Pon Pdlapa, Ciilapan I. ... ^ Byrongon, town — S and K extr. I — Manitani I , [I 1.], S pt.... Candiiuy I., It. F 33t Par..t;an Pt Sibugay I ,Non.l, [1 I.] I. dc la Mi-sa, [I l.J, Bjgsi \ P"1I J Bliian, % 71., Tincaiisaii I.... C'ariii.sa I., small, S pt I. del fl:.to, rk T.i^'apiila, 5p 6in., E pt Leyte I., % .S? 1., 1 Gi^'aniangan islet J Poit Pnlonipon, town CaniMtes Is., NW one, Tulan:; Lat. N Lon. E (86) I2°i6' i22°38'7 12 II'5 122 42-5 Pauaon I.. 2.3l3f., S pt Bohiil, EW 15 1., Naniaimoo Pt — West point, or Pt. Duljo ... Zehii, / 35 I., Tanon Pt — Zebu town.S, Ion, It. K 42f. — NE, or Bulalaqiie Pt. Doon Is., SW I O Calangaman I., at E extr. "| of arf. / Siquijor, # 7 1., Pc Minaliitar Nepros I., ^ 38 I, Siatou Pt.. — Pt. Sojoton, T — North Pt., Ylacaon I Panay ,14 32 1., S pt, h, i,l Juraqiarao islet J S. Jose de Buenavista Naliipapt rf. Manignir. Pt Pmio, e.'Of. Borocay I., 4361'., N pt Pontud, [Ijm.j Port Batan, S Olutaya Islet Zapato Miiyor "■ totolo I, [1 I.], 120f. Bulacaue Gi^antes Is., [2 1.], Vaidajon Culebra Islet Baligiiian IsUt Ilo IloFort It F21f. 12 43 >2 37 II 42 10 54 10 58 11 26 II 44 Suluan, [1 1.] Malhon I., [4 I.], K pt lo 43 Uiii.igat I., Pt. Desolation.. Gibuson I., N pt Siarga.i I., Sapao Pt, 620f. .. P. Sibunga, eritr., S 9 54 9 55 9 47 9 ~S 9 25 17-5 1 17 I2S 5 125 o 125 25 125 52 125 38 '24 S3 124 46 124 27 124 17-5 124 20 124 6 124 I 124 15 124 16 24 24 24 18 24 44 25 2 25 4 25 165 24 36 23 42 123 19 23 54 124 4 23 36 24 15 Places 1 Pt, N pt. Mindanao . iripao, gg, town 9 10 .23 42 9 2 122 59 9 59 122 27 II 2 123 II 10 24 '2' 57 5 10 44-5 121 55 II 13 121 59 !■ 37 121 40 II 46 121 50 II 59 121 54 II 50 122 15 11 16 122 30 II 38 122 50 " 45-5 123 2 II 50 123 8-5 " 37 ■23 95 II 38 123 22 II 22 123 '4 II 12 123 20 10 42 122 36 10 46 125 58 10 43 125 49 10 28 ■25 38 10 28 125 28 10 4 126 3-5 9 4' 126 I 9 49 125 26 9 47 •»5 3'7 PtCauit Catel,town O Pt Pusan C. St Allgll^ti^, or Pan- 1 _ dagitan /O PalniasI O Davao R., It. F 27f. V. Sirangani I., NS 4 1., w', \ b, bill, S end / PtTiiiaka, vis 12 1., T ..... Glan Masila R.,lt F 33f. .. Volcano, 36U0f LenoBay O Mindanao, R. enir o Pollock Cove, S. w, P,, fori Bongo I., ^ 5m., SW pt Tigiima Pt Flecha Oluntanga I.,S pt ("ocos I, small, 690f. Sta Cruz Is., 2, E one Sanibo:ing.i, w, r. Gov. Ho. "1 It. F35f. J Caldera Port Sibuco B Pt. Balangonan, i^ Murcielagos I Pt. Sindangan Pt Blanca Aliqnay I., /, t, TS Silino I., /, *, TS Pt. Tabud, It F43f. isamis town Pt Siilauang Cagayan, anchorage Pt Bagaeay Camiguin I., [4 1], 533Sf... Sulu Sea. Sultana Bank, 55 Cagayanrs Is., 5, /, % • (if- I Nend) / Calusa, [,3c.], 4: „, J Anuling I Cavelli I., 124f., [*], NE\ extr J — Reefs, .SW extr. Jessie Bcazley rf. Toob Ba-alia, shI., ^ 1 \.,\ rk. Sexir / — Shi., S\V-d, S rk St. ilichacl's 1., Manuki Manukan, 32f. J — Banoawang, I23f. — Bancoran, 140f. Cugayan Sulu Is., 3, large | oue, A, f , rk. at emr. \ © of circ. basin J — Keenapoussan I — S cxir., Mulegee Is., T.'o M^irabahcnauaD Talaiitam bk., 5 Pearl Bank, ent Tawi Tawi, Bongola, X Manuc -Mauca, S pt Lat X 1,0 I. E 9°i7'5 7 48 7 14 6 14 5 35 5 45 545 6 45 7 16 7 21 6 44 I 6 525I1 655 6 57-5 7 20 7 47 8 75 8 II 832. 8 45 8 42 8 9 8 38 8 30 8 59 9 " 1 26° 1 4' 126 22 126 25 126 6 126 28 125 36 125 25 125 16 125 15 125 25 1 1 24 00 124 124 115 7 18 123 39 7 4&-5"23 25 7 22 |i23 22 7 16 7J122 485 122 14 22 3; 122 4'5 '21 575 122 '22 5 5 122 26 122 39 123 45 '23 '3 123 24 123 22 123 475 124 295 12} 40 24 49 124 44 9 59 9 47 9 36 9 44 121 25 9 14-2 120 52 2 9 105,120 457 9 2511948' 8 49 119 55'5 119 51 iiS 28 » 435 7 426 7 44'8'iiS li 7 56 6 6 59- 7 "'3 6 53 6 34 S 42 S 48 5 3 4 47 118 41 118 29 118 26 19 27 19 39 '9 475 19 505 TABLE 10 r,s7 MARITIME POSITIONS Sibiitii I., N pt , Doi-Can, W pt Cap, N end I'aiigootaran Is., Ubian !.,'[ 72»„ Spt / Kulas^ien, rfs., E pt Salleol()okit Is Griffin rk< N extr., Teyn^a I., sniall, /, ? Sanpboys Is., small, S end ... B.isilan I., EW 11 1., .3970f.,1 R. I't. Malan.il / — Pasanhan, g, \V, Isabcla fort Cocos I , B90f'. Sibago, A, E islet, 935f. Bubiian, E pt., 794f. Taiieantana, small, pk..9.38f.... Bulan, EW 4 1., /, w, E pt. ... Simisa, N pt Suhi, EW 12 I., w, r, b, \ Port, It. F 3.5f.. ...■.....■ / Sula.l.lc I.. E pt I'aia I'k., 14.34f. Kabinsaii Is., 2, /, t.ISoacoa Slassi Pk., 1714f. Simaluc Pk., 127f. Sigboye jia^sage, Dangerous Pi. Borneo. Banguey, NW pk., I876f.. Bancawsn 1., S pk Q Mallaw.illre 1.. NW pk., 582f. Pt. Sugm Lankayan I., t, loof. O Libarran I, 140f. Bat'nan I., 228f. Sanaena I., [5 1.], pk. 4000f. gkoka B., Tahoa pa B. C. Djenee North I°2 0'4 120° 44' 5 I 19 121 3 I 20 121 25 I s 122 57 I 7 ,124 45 I 30 124 46-5 I 2S 125 2 1 39 124 42 1 47 124 47 I 54 125 6 I 48 125 II I 41 125 10 I 33 125 17 I 22 125 5 o 56 124 47 o 26 124 27 O 30 122 58 o 47 [120 9 o 58 :i2o 34 o 9 121 35 O 47 121 36 O 13 122 12 46 123 27 1 58 J2I a I 17 I2J 3' 1 57 123 5 2 53 Hoorn Is., EW 4m., rk. Payung Dekat. B.iT.iviA, Orskrvatory ♦ 1 0", G.M.T. 7''7'» Ur.' .../ Karawau^ I*c. Tanj. Sedari. .Sedari if,, [.'J, 11 Panian.ikan I' f,E 122 33 3 27 122 28 3 35 3 54 5 13 5 42 5 28 , city, "im. inland SaleagkeU Pt ni rk C. L;i.'isa, or Biera Sarontant; Salayerl., % 13 1., Npt Whale rf.. 5 Biilekmnbo, ww^,, fl. st Mansfield shL, ?, Bolloh Mt. Larapo Batang C. Bulu Bulu Java. Button, Toppers I Pulo Babi, EW 3m., W pt. .. Bantam, fl. st Ml Karang, 5833f. 123 4 ■23 15 122 48 122 37 5 43 122 30 S 19 ,121 ss 4 3 121 40 2 40 1 120 42 2 55 120 13 3 18 '120 29 4 3S ,120 27 4 32 120 iS 5 4 50 120 22 5 IS !'2o 32 5 35 ii2o 28 5 39 ,120 30 5 45 ji20 29 6 7 |120 19 5 315 120 12 5 45 ,120 12 5 21 J119 56 5 42 1I19 4S 5 54-2 105 558 5 48 7 106 15 6 1 7 106 8 6 14-5 106 o 7 5 56-3 106 16 IBoumjijes'ls., It. k ICIienboM, li. F 46f. I— Pk., 10,07.'>f. iTe-al, It F45f. Pekalon-an, It. F SOf. ... Mt. Selamat, (vol.), 11,22 Bapang shl.. [2m.], 3 Mt. Snmhing, 10,9 4. if. ... S imarang. It Fl. 107f. ... ; .lapar.i, I'o. Panjaa.; 5 jiMand.ilika I., It F. 280f. . jLiut, Juana, It. F 49f. ... *; L.-r.m Pt E |Aur AurPt .= |P.inka Pt, /, fl. st Sourabaya, citadel, It. F • Madira, EW 29 I., NW pt.,\ C Modung / — East pt., Lapv Pt — Sumenep B,, fort Paian^an I.. [Im ] Ho,' I., or Sapiidi, it, 9in , 1 W pt.,lt. F 19Jf. / Po. Kam.ili Pasuruan, It F b2{. liesuki. It. F 391. Pt China 0. Sedano Karang Maas, Meinders rk., 1 U. F56f. / Mt. Merapi B.vnjuwangie.Ft.Utrkcht 1 •■•F / Tanj. Soloka, E pt of Java ... South pt. of Java, Ba iicaan ... 5 56 6 43 6 54 6 51 Nusa Barun..; I., EW 9ni., 1 i, f ,Kamal Pt / Semiru, Mr., 12,U0f. ;Arjund. Mt., 10,320f :Sempo I.. EW 5m., S pt § jScgoro Wedi B, Klappa I. ... ^ Skeirk Pa hit>in B., E pt., c-ntr liembaagan I, % 14m., in- 1 let o( I'yl.itiap, It. R655f. / C. Sanchang C. Genteiig Zand Bay, t Vi, Paiichur Pt. Po. Tinjil, or Trouwers I., I 5|6^4.n., Wpt f Kelapii, or Breakers I., EW (^ ;!m., rks. W pt ; C. Sanglan Sira, (rks. SE), \ T , 1575f. sum (' Java HJ., Fiistpt.,h. Fl. 260f. 5°47'7 io6"28' I 6 7 6 106 48 s 5 575 106 50 5 5 56-3107 o? 5 58 5 107 21 5 56 107 25 6 12 107 46 6 11 108 18 108 225 loS 34 2 108 24 2 109 8 6 51-5109 41-? 7 145109 13 6 34 5 '09 50 7 23 no 4 6 57 no 24 S 6 346110 37 6 23 no 547 6 41 5111 9" 6 38 III 27 s 6 46 III 567 6 53 112 34- 7 I35"2 44 I 6 54 3 "2 49 6 585114 7 7 2 113 54 6 58 114 20 7 5-3 "4 i<5 7 6 114 477 7 37 5 "2 55 7 435"3 41? 7 3-^ "4 2? 7 49 "4 28 7 05 114 26 8 3 7 "4 15 s 8 12 8 114 23 8 42-5114 30 8 46 7 "4 31 5 I 8 27-5 113 25? 8 6 5 112 55-2 7 45 7"- 35 5 8 27 ,112 425 8 22 III 435 8 24 i"i 425 8 IS |"i 5 7 46 6 109 » 7 44 '«07 5° 7 23 |«o6 24 7 II 106 24 6 58 3 105 4I' i 7 o los 33 6 49 ,'°S '6 6 45 3 '°S «»T TABLE 10 589 MAKITIMK POSITION'S Lat. S Lon. E (;i2) Places Jara Sea to Flores Sea. Woerdeu Castle, rk., or Pa- iiiatMikan, (slil. i -f 3in.) Pulii Kackit, BooiiipjeS, [Ijm.], It. U91f Kariiiiun, Java Is., KW i 13 I., ir, b, W e.xir., or \ Katang rk ) — Karimun I., % .Om., S\V Pt.fl.st 1 Hastings fk., 5 Baveau I., ^ 12m., 2000f., | w, r, N pt , Mantegi ... J — Sankapura Bay Arrogant rk., [i^m.], T Grt. Solonibi), % 6in., 1^,1 flat hill, 620f. !'.. f I-ittle Solombo, [3m.],/, f \ llSf. .■./ Arends, ( 3m ], N e.id Kaning Takat grp., a, 4 ]., 1 rks.. \V pt / Kangeang, &g 9 l.,KetHpang B. Pandjang. E\V 3 1., E pt., 1 (rks. oir). P. Maurit's Belliqueux rf. 4) Turkey, Polo or Am.k 1 Kangeang Is , and slils., N I, Ara han J Sakalaor H.istings I., / Paeinoster Is., I'ulo Tei- 1 gah, N\V, Paposa, (rks. 21) J NE Paternoster Bankaivan;; Postilion Is., itj 12 1., /, t, T , N island, Jailarau... J — E. I., Puman Tawan — Lamarua I., small Brill shl., Taka Reaatayu, ] [4m.], T,3, lt.F,FI.68f.J Mamalaki I., small, rfs., | E... liusah I., # 2 1., S pt Vesuvius rk Jam pea I., ^^ .5 1. (Kam- j banigi B., SE sidf, f, I »'). Spt j KalaoI.,E\V6 l.vks., W-d. 1 2 I.. P„, SWpt. I f Bonerato I., jj* 4m , (|| \\\\ a^), Bonerato / M.irianne shoal (1820), | [2I.J, SWI J o Kalao Toa I., Cornelia IM. ... Madu I., ^ 2 1., W pi. rks., T Kabia. or Perch I Post-horse Id. (Kauna) Angelica rf., [4rn.], centre ... Rusa Ilajah, t . II S, 4.i93f , pk. Kuw l.inguete, 1902f., (rf. I 2n..),pk ] HegadisPk Token BlsI Is., S lim., Si- \ ngka, Spt / 6° IS' 107^525 5 56 ,108 225 5 48-3 no 8 I 5 sys "o 26? 6 S-S '"2 30 S 43 "2 41 5 515 "2 39 Token Bcsi Is., Kaka Rf., 1 South rk ; — N limit, Wanyy Wangy, I vis. 7 l.sum J — St. Matthew's Is., «ti 51., i lloSK pt ] Vel(ltho.-n I., [.5m,], I, f,\ Moro ilaho, centre J Ball to Flores. Bali, % 3.3 1., h. Sit. Acting, 1 lU,.'JUOf. J ;5 B.dong B., Bukit pt ^ I).. 1:1:.... I, V cu< 12 57 114 26 "4 335 "4 55 115 17 '15 555 5 12 5 33 5 27 5 2 7 o 6 so 7 10 7 46 "5 "-5 6 19 [IIS 29 6 31 116 o 631 657 7 30 6 38 633 "5 44 116 IS 117 lO'S 1x8 21 118 47 6 50 119 II 7 i8s "S 6 6 7 ^118 57 6 43 120 19 6 44 1120 26 7 6 120 24 7 7 ,«2o 39 Lombok, ^ 23 I., ilt. )!in- 1 jmi, ll.SIOf. ; — Labuan-Tering B — Pandam.in pt. {C. Banko) Sumliawa. E\V 51 1., SWI pt., Tafell)erg j — Sumhawa, town Flat I., Maiang [I 1.], E end Gulfof Saleh, Kakit 1, pk. ... Setonda I., W pk .\lt. Taiuboni, 9070f., volcano Joro Batu Pt Bira.i Bay, S. tort Simgean:; I., 6I80I'., pk Sap*,li Pt GiliBantal.. [2 I.], T, pk. ... L euwenkop pt Komoilo, or Mangarei, NS \ 7 I., It, i, Sclioor-teen ... J 6" 7' S -8 5 27 6 7 8 21 8 49 S (J 8 6-s 82s 8 44 S 44 9 OS 8 28 8 8 8 38 8 6 8 14 8 14 8 27 8 II 8 45 8 25 851 84s 7 29 7 25 7 31 6 54 7 27 7 4? 5 17 8 S 6 7 6 3 121 to 121 48 121 43 122 12 122 I 122 16 ,121 44 I122 6 ,122 40 ;'24 5 Flores, E\V 67 1., Alligator B. 8 48 Terang and B iri Ba^s Bari... 8 20 Potta Bd., Potta ■ 8 18 Giliting 8 35 Tower I., EW 1 I., 120iif. j 8 53 lEndc B., ^, Aloso Pt 8 52 Lobetobie, volcano, 7120f 8 35 Flores Head, or Iron Cape ... 8 3 ^ Larantuka lload ! 8 18 ^ Ivambing, S entr. Flores Sti t.^ 8 39 Adonara. ^,f 12 I., town ; 8 14 ISolor, j{4 U 1., S pt , islets ort'...| 8 36 Komba I, vol., ISDOf. ' 7 47 Ix)mblcn, ^f* 12 I , E pt I 8 14 I— -Mt. Lauiarar.ip, .i880l. 8 31 Pantar, if- Hal.i I., oil' S\V pt 8 25 — North Eustpt 8 10 O.nbay, EW 17 1., Dalolo 8 12 — Ea t pt., Leisumbu 8 18 Timor, ^ 85 1., SW or Oy- 1 \^ j, sina Pt J , •* I. Koepang.ft. Concordia, ll.F47f 10 99 S w„.i„. 1). g jj 9 20 ! 9 14 i 9 10 I 8 59 WeHg. I't. I24'l0' '23 35 124 21 ■24 37 "5 5 "5 5 H4 25 s 116 27 116 3 115 49 116 44 117 24 117 25 117 58 117 44 117 58 118 29 iig 8 119 10 11851 19 so 120 n 120 42 122 16 120 14 121 39 122 48 122 47 123 I 122 SI 123 9 122 52 123 3" ,'23 54 123 25 123 52 124 14 124 23 125 10 '23 35 123 40 124 5 nail. 690 TABLE 10 MAIUTIME POSITIONS Places Lat. S Lon. E Dilhi, town, r, Custom ho , It. F E pt., t' R. Po. Jackce, or^ ^ Nusa Bessie, sum. 350f. ... J Kalaeko, town Noy Mini K, t Semao, # ol, S pt Rotti, ^ U l.vis. 12 1., Cy-\ rus B.on SE side, w, rj" — Pull. Dina, off S |t Pulo Van, i\s 4m., /, t , N end SaTu,EW7 1.,WC. Mesara... — East pt., /, (rks. off) Ba.ijoan, EW 7m., S\V pt., /. Dana, or New I., [1 1.],) S part, 120f. / Sumba or Saiiilahvood I., ^ ■\ 24 1., C. Lambuya, (rks.) / Palmedo Road Paddewav B., S, [5in ] i.i, 1 r, So, Ari( tonn aiich-e. / E point, (;. Mandyuli C. Blackwood Banda Sea. Camhing, or Passage I., ^ 1 4 1., A. Spk, 3273f. / Babi I., sum O Wetta, ^ 19 1., Sau to«n, 1 on SEside, $ / Gunong Api, vole. 13781'. (Lucipara, 5 Is., N Id Kis.sa 1., 803r.. Piiia laniling Roma. [3 1.], h. Uwakekeu .. Letti I., Serwaiu, Church .. Moa, ^61.,* E, Buffalo 1 Pk., 4100f. f Lakor, |3 1.], /, E end Luang. [1 I.], h, I" O Seni.at.in. [.5 l.J, W pt.. Elo O Damma Is., NS Al. 8Il7f. 1 Kulewatte H:irhour J 'I'au, [3 1.]. 2U'.'0f., Ilo LajaniO Nila. [■! 1.]. r.S9S(. snm Scrua, 2 Is., [3 1.], W. I Uird I., or I'o. Mano, 880f. ... Wetan, 3; E, li6llf Baha, w, P,, S pt. 3000f. Masella, S pt. S-39f. 9 6 lo 5 10 22 lO 58 10 48 10 34 10 27 10 37 10 49 9 42 9 25 9 37 10 12 10 23 2S°36'2 27 20 26 12 24 18 ^23 25 •23 5 22 55 122 41 21 41 22 o 21 31 119 45 120 12 120 51 120 297 8 18 125 35 8 2 125 45 7 S3 j"26 24 6 39 I126 36 5 28 |'27 29 8 67127 8 7 42 |i27 20 8 IO-2 127 405 Teiiimberls.,]|„; Timor Eaut, | tjP 34 1 , S end, .Jermata J Selaru, Woody I., small Oliliet, village, 413f. I.arat, % 6 I., Lamilesar Vordate. ^ 2 1., t, Sobiani... Sera I., Aha Mulii I , Nuskalbur Arru Is., NS 35 1., /, f,T.\ P„ S extr., Ennu I., ioof. J — SW limit, Bayn — Po. Babi, small — N\V extr.,Wassir — C. Watale Juhong — Dobho Harb., ^, pt Tjando Is.. N lim O 8 12 7 2 6 52 6 17 5 33 7 50 7 55 7 17 6 58 7 44 6 3S 7 6 128 2 128 13 1 28 39 1 28 48 128 40 129 7 129 28 130 o 130 18 "29 33 129 45 129 515 131 14 130 48 131 27 >3> 58 131 55 130 56 ■3' 37 134 31 134 7 134 9 '34 13 134 32 134 14 132 33 Places Grt. Ki I., # 1.5 1., t, t 3000C, C. Borang .'...../ — Niija — Madua Pt Little Ki I., Rumadan I — Ki Doulan, vill., T , w, r, \ b, ($' 3ni. N), pi r ... / Nusa Telle Is., Fadd I O — Koorl., Spt O UranI Kclmui I., S pt Matabella Is., 2 gruups, grt., Kasiwooi, S pt ; | Manov(dko I.. Sera S« ruaki- Wiseleat O Coram L, [3 1.]. NE pt Banda Is, 5, W, or Po.\ Rhun / — NW one, or Swanji — Banda, -^ 6m., Fort Nassau — East one, Ru/.engain O Bouro L, % 27 1., P.dpatu 1 I't, T I — Mt. Tumahu, 85301'. Cajeli B., r> w', b, Fort 1 Defence j East point, or Pt. Tela South pt , or Balou P kka ... Amblaw I., [2 1.]. NE pt. ... Manipa (., /i, (rk. Urn. \V),1 Ept., Lubu ". / Kelang, A, || \V, W pt Boano, h, 1 , SW pt 5 42 6 3 5 28 5 40 5 25 4 46 3 59 4 33 Ccram, % 59 1.. Pt. Seeal — Sawaai Harb Wahaay Ilarb., viU., w'",) r, 1). fort ; Pasahafi Pt Leuwarden slil., [2m.]. T , rks- Waru B., f, w, r, IJ.mi Po. Parang, or Leuwarden I, \ Spt J Po. Maduranj;, small Oreat Kelliiig 1., K [t O Ceram Laut, Gesser I O — K(.n O Amboina I.. ^ II 1., SW,"! or Alang Pt.. T J Amboina (_'itv. Koi't Victoria... Noessaniva Pt., T Ilaruku I , ^f* 8ni., SW pt. 1 Islet / Saparua I.. ^ 11m., fi.rt Nusa Laut, % 7m., Nalahia B. Bowakan Hammond's L, [3 1.], S pt. .. Taliabu, EW 18 1., Lekiiobi.. Mangola, 16 1., EW ||o, Lisa- 1 niatula I., 1164f. J Vesuvius B., t Sula Besi, NS 10 I., S and \ Ept., Ipa / •32 57 132 53 132 42 131 58 132 o >3> 52 >3' 44 i3> 3S 131 23 13" '4 131 26 129 38 129 40 129 53 130 2 126 3 6 3 IS 3 22-8 3 21 3 54 3 52 3 20-5I27 40 3 12 127 38 3 ' '27 51 127 6s 127 16 126 37 127 17 3 33 2 57 2 48 2 52 3 o 2 55 3 22 3 21 3 37 3 5' 3 3 3 57 27 55 29 29 129 42 130 24 130 33 ■30 35 130 48 •30 59 130 47 130 52 131 12 •27 £7 128 105 3 41-2 3 46 338 3 4 5 '28 3 38 128 46 • 54 I 52 • 57 I so • ss a 2i •23 45 124 1 124 27 TABLE 10 '.01 MAlilTIME POS^^ON^ , 2400f. Oby I,atta. [2 1] S pt Goin-mo, 85of., \V pt Po. Giise, [5m.]. T , rks. bE, 1 Spt. / Tap.ll., NVVpt Brsa, E pt. Obv Major, ^19 I., SE i.t. , Wai lxx>kisi>n- 1., ^ 3 1., 5f , N pt. K.kik I.. A ■. I,a«i.. I.. A Po. Pisang, vis. 11 1 Griisvenor shl , [-Im ]. 3f Bii Is., i, P. Esplee O Graml Canary, w, E pL, \ NVVpt J Mysole, EW 14 1., Lungu HasU I., Spt Cllolo. Gilolo, 2^ 67 1., SE, orCo-1 ciiamit Pi I Weda Is., [3 1.]. E liiii. ...O lyoi, [.ill!.]. S pt Gel.v. iL ; I.. Port Fou, ou \ SWside, m, w, r J — Norih-West pt Sh.impee Is.. 3 or 4, NS 3 L ... Canton Packet shl., if. Caihtrine Is., 3, I iXrda>!.ur Islet Aurora bk , !!'. Weda, t Ddeprisa Pt Po. M.ar. t,/, llo Wossa, -village, w, r, b PL Monat Pt. Wiiigamele, (rks 1 1.) ... Pt. Salaway, (rks. 1 1.) Waiering-place, N of Galela ") Tiabu / Bisoa Pt O Kau, [2 1.]. mid Morty, # 21 1., Npr., (rf.),l T J — South West pt.. Lints I. ... T.iaknra, N pt. Talabu Pt Dyilolo, town 'I'crnate.jf^ 6m., sum..5l8Uf , ) Fort Ocaipgc, on E side... J Tidore, [2 I. J, mm. .5900f. .. » I'ntibakkerl., [2m.]. 1160f... .= .Metir, [3 I.], sum. 2800f. " W.lf 111 Makyan, [5 m.], sum. 41661 r.a'ta-I,atl« Is , Japi Urt. T.iw„lly, ,{4 7 I., SW 1 I't.M J Batian, % 17 I.. A, Se!,.ng 1 I., (mid. (if S roast) .../ — Padanp, Coal Station I.at. I Lon. E South 1'29' I 52 I 39 I 12 I i6 I 44 I 32 I 30 I 29 I 24 I 19 1 10 « 45 I 53 o 56 o 40 o 3 o 6 o 30 o 35 o 4 o 45 129 o 43 1 27° 1 6' '27 33 128 22 127 17 '27 37 128 o 128 g ■28 37 128 42 >28 53 129 26 129 25 129 37 128 27 128 39 ■29 34 129 21 129 15 128 43 128 55 129 5 129 23 o 18 127 52 o IS 128 31 o 7 128 55 35-5128 34 1 I 128 28 I 9 |i28 38 ' 33 !'28 43 1 51 '127 52 2 13 ,127 55 2 23 128 II 2 44 128 20 I 57 128 13 I 7 127 27 o 48-0 127 21 o 40 127 25 o 33 |i27 22 o 27 127 24 O 12 |l26 53 o 20 127 23 Si-nth O 17 :I26 59 o 29 |i27 3 o 54. If 27 34 o 44 127 25 I Lai. Tifiiri, sum. 587f. Mayo, N pt. 1280f. Biarro, sum Riiang, vol., 2.3.30f. .Siao, pk., 5924f. Mukaltho I., 394f. Nennung Is.. South I C Kalama, || North I., N extr. .. Saiigir, «j 8 1., Taruna B., 1 *. r J — North pt., Salima Louisa .shl HaMock Is.. Kabalusu — Mtares, South pt Anda I , Ariaga I , Charruca shl Iphigenia rks.. South rk Nanusa Is., Merampi Pk., ■( 666f. j Talauer Is., NS 15 1., N pt., ^^ Mamaga J — Nusa I — Salibabu L, % 5 1., S\ P' J — Kaburuan, ^ 3 I., S I pt. Northumberland shl., [2m.] ... Eye I., [im.] Syang, [3m.], /, w, SW^ P'.I j Wyang, r.r Vayag Is., iL\ 6 I., NW e.\tr., Laborde Islet J — SE extr, Laliishe l.,\ [lm.],(rks. SE) / El n, or Irie Is., EW 4m., I Kpt / Orni.sby shl., T N, N pt Budd I.,/, t O Aiu Is., about 20 small, /, | S, rls. T, Wirisoi / Aiu Baha, [3m.] Asia Is., 3, /, SW and small- ) est ; Po Manuaran, [2m.], || S, (^ ' J Buccleuch shl., [3m.], I ?, ?... Waigiu. EW 22 1,, SE pt.,-1 orPuPigot / — BoniL,[3ni.],ffiSWd.,l Npt r — OfTak Harbour, S, w, 1 — NW pt.,'c"Eorrest".'.'.'.'.'.... Buttons, [Im.] Ki.ib, NS6m., pk Balabalak, [2ni.], W pt Gag I., [7m.], N pt Pi(;(«n L. t. --■, W pt B.atanta, EW 15 1., W pti C. Maho / — Mnrchesa Bay, Toe Pt. ... Salawatti, 10 1.. Uadv Pt. 592 TABLE 10 MARITIME POSITIONS C") XfEW GVINEd.. Brehes Pt., or C. Wilson ...O Threshold Pt O C. Spencer, or Foul Pt.,1 (rl's. 2m.) / Sele Pt W. Brother, or Pinion I Sabra Pt isangs Is., Po. Sabuila,") SWpt / Mae Ciller's Inlet, Head, or ) E lim. of the bay / Tatingar Pt C. Sapey, (sum. 3020f.), W 1 pt. (Balk) / C. KHffura Po. Adi, or 'Wessels, % 8 l.,"l Wpt. t J Bird I., [im.] (VoH) Lamansiere Hill, NW sum.~( 2460f. / Triton B., Fort Dubus Lakahia Mt., 4.';64f. Charles Louis Mts., gsiof. ... C. Buru, vis. 10 1 VlakkePt Wamuka R., mouth O C. Steenboom Snowy Mountains, sum. ^1 I4,000f. / Dourga Strait, E pt C. Valsche, (W pt. of Fr> de- 1 rickHenryl., 5p36 1.).../ St, Barlbolomew I Deliverance I., small, rfs. ...C Mt. Cornwallis,vis. 9 1 Bristow I., [5m.], /, t.SEl pt ■. / Fly River, Tree I Aird Hill, 12G0f. Blackwood, Pt., /, t Mt. Yule, 10,046f. C. Possession Port Moresby, Jane I C. Hood 0. Kodney, SE pt Dufaurel., [1 I.], sum South Cape, Suau 2 48 3 41 4 7 4 9 4 21 3 44 3 47 4 27 4 40 4 SO 4 13 7 22 i3i°57' '3' 27 '3' «S 130 57 131 6 >.^i 57 ■31 38 33 46 32 I 32 42 132 55 '33 205 133 36 134 7 134 7 '34 45 '36 '5 34 45 '35 'o ■5 136 29 37 7 138 34 137 40 Adeic I., [2e.l, /, [t]. 1I<,W... llossel I., EW 7 1.,/, t, l\„y W. C. Deliverance..;'. / Sndist I., Mt. Kiu 2G45f. ... Fox, orRenard Is. f [i \.1A Wpt / St. Aignan I., EW 10 L, El pt., C. Henry J Deboyne Is., [2 1. ?], N pt. ... Bunvouloir Is., E extr La-eine Is., [2 1.], Dawson \ 8 17 9 35 9 25 9 9 8 41 7 28 7 52 8 I4-5 8 36 9 255 10 7 (9S) Places Ouessant I., small Teste I., (Wari), East I More.-by I., Fairfax Pk.. 1740!. China Sr., Samaiu I. Mission Lydia I., (Nuakata), pk., 10101. Possession B East Cape, Anchor I., E pt.... DEntrecasteaux Is., S pt.,") C. Ventenat, (Is. S-d.) ... / Welle I., r2 1.]. E part, (rls.) Goodenouiih 1., pk., TOOUf. ... 0. Vogel, Glen I C. Nelson 1. lliche. Mitre rk Lat. S Lou. E 39 28 141 47 142 31 143 «4 143 36 [44 20 [44 28 146 46 146 22 147 7 147 42 14S 22 149 48 150 14- II 29 154 »6S II 233154 177 II 30'6 153 26 10 54 10 41 10 405 10 25 10 23 152 S8 '52 55 152 23 152 6 'SI 25s Poeklingfon shI., EW 10 l.,l rks., 5Erk J Laughlaii Is.. 9, EW 5ui., 1 /, t, low Erk J Caiinac rk., *,high Woodlark Is'., % 13 1., P',\ North point / — West Rock Yanaba, Sharp I O Jouvenoy I., [2m.] Jurien I., [1 I.], mid Lagrandierc I., [2 I.], E pt — Trohriand Is., C. Denis Lusaiicay Is., & rfs., EW, & \ others W-d, unexplored, ]■ NE e.xt., North I J C. Cretin. Cretin Is C. King Wil.iam Mount Disraeli, ll,OUOf.. 0- Rigny RichL, [1 1.], A Dampier I., ^1* 5 1., ab .^0001 Vulcjn I.. [2 1.], conical, 4000f. C. della Torre Lesson I., [2m.], /(, conical .. Blosseville I., [Im.], llOOf. .. Garnot I., [3m.], conical Jacquinot L, [3m.], J Deblois I., [A 1.] lioissy I., [1 1.], T ?• N pt... Victoria Bay, D'Urvillel D'llrville I., [3 1.], pk. near] W end I Gilbert I, [4m], /, E pt., \ (rf.) J Bertraiid L, /, 1| W, t Torricelli Mountns , \V sum. "| 4 1. inland / Eyries Mt., very A, W sum. \ 3 1. inland j Mt. Bougainville Humboldt B., Ol.sn 1 Cyelops i\It., vis 20 I., !■', su Pt. Brama. bil. Aral.. Ll.iui.], 2 Is. W-d. Jiiinna I., |lm.] Jomi or Moa Is , »!, 2 1., N "° S'6i5i''i5'5 10 58 151 52 10 36 8 151 05 10 35-8150 397 10 16 I151 05 10 34-6150 42 2 10 13-2 100 53 7 o 107 151 9 37 li5' 3 9 21 5 150 14 9 45 j'5o 4 8 59 i'49 20 7 59 '48 9 5 10 45-4 '55 517 9 19 '53 40 9 .8 ,53 28 9 3-5 152 47 9 16 '52 13 9 29 152 40 8 45 '5' 45 8 39 151 22 852 ■ SI 8 8 24 151 4 50 48 6 43 '47 53 37 5 58 146 29 5 29 '45 58 4 49 4 40 4 5 3 5' 3 33 336 3 30 3 24 3 21 3 12 3 '6. 146 13 '45 58 '45 2 '44 3' '44 48 '44 34 '44 35 ■ 44 24 ■44 9 '44 3 '43 29 3 '7 '43 io 3 >3 3 'o ,.43 '7 '43 'o 2 50 141 15 2 40 '140 51 2 56 J140 42 J 30 TABLE 10 MAIUTIME POSITIONS (99) Places I IM.S Lot). E (100) C. n'Urville./,f,(riv-W-d.?) Kuiudu I., E pt Jappen I., Ansus Harbour ... Nau I 'PerschelliiiR Is.. E pt Ilaerlem Is., [4 I.j, W one ... Pu Pinxter, Wpt Hoog, Sniilh pt Angertniis I., E pt Meosaui I Jubl C. Oran S"ari Mefiirl., I64f. Mysory Is., % 2n 1., A, Ept.... — Mt.Schoutuii.Kaiori, I640f. — W pt., C. Saavedra Mioskaroar I I 48 1137 2 1 44 '35 49 2 19 136 19 2 55 '35 54 3 5 >35 52 3 24 !"35 46 2 5'S'3S 5 2 38 l'35 3 1 57 ii34 48 2 33 '34 24 I 22 134 17 I I 5>34 53 I 10 136 45 o 47 1135 37 o 38 1I35 19 o 18 1135 3 Arfak Mountaius, 9l6rf. 1 li 133 59 Port Dorei, Mauat-u-ari 1 054 I134 7 C. Miiinori ' o 48 1134 8 C. Maiami | o 29 [133 12 C. Good Hope I o 19 Ml. Dicera-s 8in. inhind I o 32 Mispalu Is , .\uisti.rdam I. ...| o 19 ;I)nvtl>en I'l llVr'a H.I.,/, i C. K,erwe.r Van UU'iiien's Inlet, w. untr. Norman U., Kimlierly Tel. Stn. AlhiTt R.. Kangaroo Pt Wrlle^ly Is..N i-xtr., rockyislei — Pisonia I., small — E extr., Bountiful Is., 2,1 # am., Ept J — Sweers I., # 5m., f, \v,~\ f, b, S pt.. Inspection I Hill, lO.lf. J SirEd. PillewMs., %I2l.a Ncxtr.,ark / — Vanderlin I., ^ 6 I., N 1 pt, or C. Vanderlin .../ ^ W.stl., NEpt Maria L, jf* 7ni., N pt Groote Evlan.lt, NS li l.,\ SEpt, O.n I. S.-im.)...; — Central Hill, vis. lo 1 North-East I.s., [7m.], E cxir. liickertoD I., [4 1.], sum Woodah I., i, 4 1., S pt Nicols I., [."Jm] C. Shield C. Grey Ml. faledon Mt. Alexander C. Arnhcm Hruml.y Is., NE pt. C. Wilt.erfcroe O Tnant I., small | WcsmI's Is., C. Wi swl, 1801. I Arnli^Im B.. «ntr., Malli- 1 son's I., W pt /| Browns Strait, Pi. Dale I 41 41 12 59 141 40 '3 5« I'4' 34 16 58 I141 I 17 266 140 56 '7 35 ' 139 495 16 18 139 26 16 29 |i39 56 '<> 39 j'39 59 17 8-213941 I IS 29 '37 4 '37 8 136 46 j«3S 54 ;'36 58 136 41 ;«37 ' '■36 15 136 13 ,'36 19 136 23 136 42 '36 33 136 44 '37 'S 32 14 so 14 16 «3 57 '3 39 '3 45 >3 34 13 27 13 20 '3 o '2 53 '2 39 12 i6- II 46 5 136 42 " 53 '36 35 11 39 136 48 10 59 ,136 45 12 II .136 6 11 36 136 5 Places Crooodile Is., North I C. Siewart, rky Liverpool R., Haul-round I I'U Cuthbert, (slils. 3 I. out ||) Goiilbura Is., N-irth I., # 1 7m., N pt / Pi. Brogden, rky l)e Courcv Hd MiicCluer I., »k 2in., N pt. .. New Year I, small, \y M.im-y shl., [5in. |, j' , Ch-.ikcr I., NS 7 1., N pt.,1 C. Croker, (rksNW-d.) J Orontes rf.. [Im.], t I't. Smilh, [rks. Im.] PortEssington. Gov. Ho. .. Vashon Hd., (.shl. 2m.), N^ pt J C. Uon, 130f. Burford I., [Im.] Greeiihill I . NS 5m., Webb ) Pt.,(rf.off) I Field 1., [4m.] /, (off mo.1 of S. Alligator B ), \V pt.J C. Hotham, sbl. NE d Vernon Is., [3 1.], S side of "1 Clarence Strt., W pt / Melville I,, % 2.i 1., E pt — Pt. Jahleel — N and W pt,. C. Van D e ) men,/, s.ndy, (slil. 5ra.) / Bathurst I., Brace Pt — C. Helvetius — S extr., C. Foureroy ICortb-West Coast. Pout Dakwin, PALMEns "1 TON, E extr. of Cable Hi. J Port Paterson, ffl. Rait Pt., 1 on E side j Patcrson's B., Quail I., w'" ... Pt. Hlaze... Peron Is., % 5 1., N pk C. Eord, (rks. 2m.) Port Keats, ffi. Tree I't C. Hay, (.shls. -f 5 I.) Pt P.aree, 8.if., (a rf. ott) ... Cambridge G., Lacrosse l.,"| % 4m., W pt., 6(i()f. ...J — Wyndham C. Dussejour, (rk. oti'), sum \ over J Mt Casuarina. 800f. Lesueur I., [and rks. 1 I ] Is., 2Uf., and ly, (Stewarll rks. aui) .../ C. Talbot .Tones I., lOf., small,/, sandy... C. Bougainville Troughton I., 20f., sandy, \ \.rfs.im] ] Shls., bks., [Holuthurlaandl olhrrsJ,untxplored,W lim. / C'uvsiiii I., 20f., [rim.], rfs. N TABLE 10 MAUITIME POSITIONS (101) Places (102) Placet Lat. S Admiralty Gulf, Port Wai-1 render. Crystal Hd J C. Voltaire, flat hill, (1^1X1. \ inland) j Condillac I., smt)ll Montalivet Is., W extr. shl. .. Maret Is., (rfs. W 2 1.), N pt. Lamarck I C. PomI, islet off Pt. Hardy Port Nelson, S, Careening"! B. beach ]' Prince Resent's R., Mt. Tra- 1 lalgar, sum / Port George IV., t ', w', b, 1 I4°28' I25°58 '4 14 >4 . M 23 14 45 ■4 45 14 58 ■3 6 4 124 '25 45 '25 125 6 125 41-5 Augustus I. Pt Colbert I Adieu Ij 16 15 '3-5 14 51 Freycinet grp.. W island White rock islet Red I Champagiiy Is., ^ 7in.,) Uegerai do. sum / Adele I., [rfs 4m.], 8f., *„ ... Beagle bk., [3 5m.], 15f. Pt. Hall, sum Doubtful B., Raft PL, w Cockill's Is, [2 1.]. W pt Mac Leay Is., N extr. reef. .., Caffarelli I., ^ 2im.. mid. .., Brue rk .' Hidden I., W pt High I., [2m.].290f. Port Ushorne, [|m.], 7, ^y ... King's Sound, Pt. Torment .. — Derby — yitzKoy R. mo.. Escape] Pt / — Pt. Cunningham, N\V | art Skeleton Pt.,w' S«an Pt C. Leveque, 83f., (an islet oft) Rowley shls., Impirieuse | shl. NS 3 1., N. Sandy I., 8f. J — Gierke's rf., or Minstrel 1 shl., N Sandy I., 8f. ... f — Mermaid shl., [3 1.], pas- | sage on E side | Scott rf., a lagoon, NS 6 1 , T W, I. sand and crl., Sandy I., 8f. Seringapatam rf., EW 5m.. | j sf., T, N pt J I Browse I., [Im.], /, 2or. | D'Artagan thoal, 10 ' Corona shoal, 5 i Dry sand, lOt'., (Ship Cartier, 1 i 1800) j Hiberniarf, 1810 Ashmore shl., Middle I Troubadour (1843), 9 Coral bank, 7 | I Lynedoch, shl. [^m.], 7 j >5 >3 15 19 15 32 15 19 15 40 16 35 15 46 '5 54 >6 3 15 57 16 14 20 20 16 39 17 24' 16 41-5 I '4 3 125 4 124 34 124 42 124 32 124 19 124 13 2 ■23 14 '23 30 124 21 124 26 124 4 '23 39 123 18 >2J 4 123 27 123 20 123 30 123 35 123 39 '23 34 "23 7 123 o iS 51 19 21 '9 3S 21 49 22 3 23 33-5 18 40 23 38 C. Borda Beagle B.,N Hd Laccpede Is., W one, [and] rks. 3L].15f., sand / C. Baskerville Pt. Coulomb, rf. Ini C. Boileau, sandy Pt. Gantbcaume C. ViUaret, 150f. C. Latouehe Treville, 250f. ... C. Bossut, Casurinarf. C. Jaubert, 45f. Mt. Blaze, 60f. Amphinome shls., outer B Bed.ut I., 20f., rf. S\V, ] [>•] J Turile I., 35f., [im.J. if., f ... Port Headland, Hunt Pt C. Thonin, rf. N Gengraphe shls., 2, N\V one, ) ['"<•] J Depuch I., wwo, 514f. Port VValeott, (Tien T.rt Robinson, Dixon I Lcgendre I., 55f., % 8m.,] NWpt, / Dampier's Archipelago, ^'\ 10 1., Rosemary I., [.3m.], W sum. 250f. J Hampton Ilr., Channel I r. Preston Montebello Is., NS 4 I., ||„,] Ritchie rf. J — Tremouille Is., *, Wo, b, \ fl.gis'et, 21f. f — Try;,l rks.. NS 4m., N] extr / Barrow I., # 4 I., f, (rf 1 ICm. from S end), C. Dupuy J Forlcsoue 1!.. mouth lii.sily I.. 21f. Ashburiou R., (Onslow),) m.)urh i N Miiiron I., pk. 70f. NWCape \jre8t Coast. Exmouth Gulf, B. of Rest.] Npt / Pt. Cloates C. Farquhar, sand, I C. Cuvier, 40Uf., i. rock] oft- / Bernier I., if 4 1., Koksl Id. oft- Npt J '-' Dorrc I., tP 6 1., i , T .(Dam- ■] pier's rf. S 4m.), S pt., or C. St. Crirq J Gascoyne Rd.,Gascoyne R., \ beacon I 1 6° 40' 16 50 16 50 17 9 17 21 17 38 17 58 18 19 18 28 '8 43 IS 58 9 595 19 43 19 35 •9 54 20 18 2 1 1 20 205 20 16 20 tS,s 20 IS 20 28 20 35 20 40 21 37 21 465 24 «3 24 44 22 16-5 22 lO 22 10 22 II 22 45 21 51 s 21 37 21 365 19 3~i 19 19 19 6 18 55 •8 35-7 18 13 ■7 555 17 445 17 i3i 17 3? 16 51 16 42 .6 .25 '5 23 '5 35 15 27 16 6 '4 595 14 56? "3 ^3 113 10 "3 4 "3 39 5 TABLE 10 MAHITIMK l>t)SIT10XS Shark 15., Dirk Hartogs I..-> % 13 I, i,N pt..orC. I Inscription, W extr. of [ Australia J — Cape Peron, 66f. -. BnbaB St epPt Gantlnttume B . Ued Ft Houtnian rks., Sjj 16 1., t'y'i Mw„, b, r. North I., ' [Um.] J — Wallabi grp .Evfningrf.,~| (Miildle Chaoiiel S of [ do.), Spt J — NorthEast rf., [im.] -Eastergrp., [3l.'|, (Zee--| wvk Chan. S of do.), Rati.. N pt. J — Snapper bk., [2m.]. i — I'elsart grp . EW 4 U\ SW part, Wreck Pt. .../ Mt. Fairfax, 60.3f. Wizard Pk., 640f. Champion B, (Geraldlon),") Moore Pt.. It. RllOf. / P..n Don^ari. or Ueiiison,! It. K. Li-aiidL-r Pt. beacon/ Mt. IVron, (.1 1. inland) Ml. Lesiieiir. (do.) C. I.e.'chenhault Kottencst 1., # 5jm., lt.~l K211f. : J Fhkkmantle, Scott's Jetty Swan R., Perth, Gov. House... Garden I.,% 5iin., NW pt... Coventry rk Peel O. Boavard Koombanah B.. w, It. F 117.. Bussclton, It^F 63f. Naturali.stc, rf.. [im.], sf. C Naturaliste.....". Geographe rk Soutta Coaat. C. T>eeuwin, (rks. 2 I. out) ... lx)w Black Pt Pt. irEntrccasteaux, i, vis. ) 10 l„(Id.,/, rk., %3m. S) ( White topped rks C. Chatham, vis 10 1., (Islets ) S) / I't. Nuyts. vis. 8 I W Cape Howe, i Eclipse Is.. [I 1.] .Maude rf., ^^o l):ild Hd., vis. 12 I.. Spt I!r. aksea I., It. F .184^ King George's Sound, w, b,! Princes* Harh., S, New J. Govt buildings J Mt. (iardner, sum Bald I, i^i 3m., (rk. S Im.)... .Sealer's ledge Haul off rk ('. Knob, sum L;it. S I ton. E 25<'2r/4 1 12° 58' 25 30-5 26 40s 26 85 27 42 "3 30 113 40 113 85 114 105 28 18 "3 35 2833 113 41 28 25 "3 50 28 42-5 "3 475 28 42 114 I 28 59 "358 28 45-4 28 297 114 4'7 114 47'o 28 471 114 35 29 17 I "4 55? 30 7 30 "3 3. .8 ■15 9 115 10 115 30 32 0-3 115 30? 32 3-3 31 574 32 89 32 22 32 27 32 34 33 19 33 38 33 15 33 32 115 44-5 ..5 5.7 "15 395 IIS 30 115 44 115 40 "5 39 115 21 "4 55 ■14 58 34 20 114 54 34 21 115 6 34 25 115 29 34 52 116 I 35 4 >'6 '3 35 2 116 28 35 5 '"6 38 35 9 !"7 40 35 '2 i'>7 53 35 '3 |"7 56 35 7 "8 I 35 4 118 3 35 2-2 1 17 54 35 o '118 8 34 55 «i8 27 35 10 ;ii8 27 34 43 iiiS 40 54 ji 119 14 (104) Places PL Hood, (Doubtful Is.,\ 3m. Ed.) / East Mt. Barren, vis. 14 I. ... Seahs' Is., (rks. N), I Kocky islets Esperanee B., W pt., Ob-"|^ serv. I., small j C. Le Grand, (islets off) Lucky B West grp.. SWst I.. [2m.] ... SW, or outer danger Mondrain I., NS 3.^m., vis. "| 10 I., 3, S sum / S extr. of Archip., Termina- \ tionl., [Im.]. vis. 9 I. ... / Twin rks., [rfs. 2m., T] Draper's I., [im.] Twin pks., vis. 9 L, (pks. "| #2m.) / A break nt times, SW one ... Douglas Is., [Ini.J Middle I., sj* 4iu.. b, w^.\ SWsum / C. Arid., rky.. SE pt C. Pa-ley. sum. Um. inland... Pt. Malcolm, /, sandy (rk. 1 j|-3m.), rk / SE IsKs. [1 1]., mid Pollock rf.,[lm.], 3, T liound I., small I'.astern grp., NS 3 1., S extr. Pt. Culver, X Pt. Dover Low sandy pt Ild. of Grt. Australian bight... Nuyts rfs., outer ditachid ... Fowler B., Port Eyre Tele- 1 graph Office J Pt. Bell,/ Purdies Is., ^ 5m, w^. f„, "l S I, 83f. / Smoky B., I.aura B Is. of St. F-rancis, NS 2 1., \ Wg. f^. Hart I., 65f. J Y.italarf. Pt. Brown Streaky B., Port Blanche Olive i., [lim],82f, ris. N...| C. Bauer, i, W pt I Pt. Westall, I C. Radstoek, i Pt. Weylaml, i, Venus Hr.... Waldegrave I , 120f, W extr. Waterloo B., SE pt Flinders I., jf* 7m., N pt. 20.'if Ward's Is., 16'.?f Pearson's Is, NS 2 U, 2 pks., \ S L460f. J Pt. Drummnnd. i Coflin's B.. Pi. Sir Isaac — Port Douglas, Coffin lid. 1 Station / Grcenlv Is., [1 1.]. pk. 755f.... Whidbiy Is.. [2 I.]. Wgrp.,-\ 3t)2f , 4 hummocks, S extr. / Lat S Lon. E 34° 24' 33 57 34 6 34 5 33 56 34 24 34 >3 34 1 34 18 34 10 34 8 34 I 33 56 33 48 34 20 34 34 34 5 33 52 32 55 32 3«-5 32 22 3' 29 32 9 32 39 32 33 3248 32 44 32 44 32 55 33 12 5 33 '5 33 36 33 39 3 33 41 33 45 34 00 34 9 34 2b 34 37 34 39 34 47 596 TABLE 10 MARITIME POSITIONS Roekv Isl., small, /.. C. Wiles, 1 Liguanea I., # 2m . rf. S-d , C. Catastrophe, S pt. i ..., William's I., [1m.] Neptune Is.,/, S I., 12i)f. Gambler's Is.. S pt., peaked rks Dan{terous rf. C. Donnington Port Uncolii, IS. w, Cliuroh... Pt. Bolmgbi Sir Jos. Hanks gip., S extr.,1 Slickncy I., lOOf. / — Winceby 1., 33f., N pt South B., Shipping place Franklin Harbour Pt. Lowly, It. Fl .57f. Port Auj;usta, fl. ft Mt. Brown, ab. 3174f. Germiin, It. on pier F , Port Pirie. jetty Port Broughton, jetty Pt. Riley, i , Walhiroo, pier. It. F 23f Tipara B., (Moonts), It , Pt. Pearcc, Waidaiig I Port Victoria, Waurallee, It. F Port Minlaeowie Port Tiirton, jetty Corny Pt., P. It. F 98f. C. Spencer, Sst. of 3 pts., 258f. Altliurpe Is., It. Fl. 350f. Port Mooro«ie Troubridge, It. R 8If. Edithburgh, It. F ... Port Vincent, Surveyor Pt. ... Port Alfred. Kooley Wurta ... Androssan, It. F Port Wakefield, It. F Pout Adelaide, Snappeb 1 Pt / Adelaide, town hall Mt. Lofty, 23301'. Glentlg, It. F 29f. Port Noarlunga, jetty Port Willunga, Sjetty C. Jervis, A, It. F Kangaroo L, EW 28 1., N) pt, Pt. Mar.sden / C. Borda, It R 510f. — SW extr., C. Couedie, 9af. — Pelorus rk., 40f. — C.Willoughby.lt R247f ... Port Victor, Harb. Master's ") house J Murray R , Goolw.i jetty C Bernouilli,(C.Jafra),U. E1 lOOf., A tandy / Hobc,C. Dombey, obelisk, 7fif Rivoli B., Penguin 1., S pt. ... W. Cape Banks, sandy. It. R 1 92f. Lat. S Lon. E 34°49' 34 49 5 .34 57 35 o 35 59 35 1-7 35 20-5 35 >2 34 49 34 43-5 34 43 3 34 33 34 41 34 2g-2 34 23 33 44 33 o 32 297 32 307 33 33 33 33 33 34 34 33 34 34 34 1 34° 43 •35 22 '35 41 135 37 136 o 135 585 '36 7 '36 30 136 12-5 '35 595 '35 5'-5 136 4 136 16-5 136 17-5 ■35 55 ■; 136 57? 137 472 '37 457 .38 .■ '37 592 138 I '37 55-2 '37 56 137 37? 137 34 '37 '9 5 '37 29 137 277 '37 21 '37 05 '36 53 '36 515 •37 3'-5 35 7-5 '37 49-7 35 55 '.>7 45 ■ 34 47 |'37 5'7 34 37 4' '37 53?. 34 26 1137 555 34 12 ;I38 87 34 46S138 307 34 56-2138 357 34 59-2 '38 425 34 59 '38 305 35 96 138 28 35 16-4138 275 35 37 138 6 35 345 137 38 35 457136 35? 36 4'5|'36 42? 36 7-3137 3'-5 35 5' j'3S 8 35 34 i|i38 375 35 31-2 138 47-? 36 57 ,'39 40 37 10 2 '39 447 37 31 1140 li 37 545 '40 23 Northumberland, It. R 150£'38 4-2 1140 40 (106) Places Glenelg R., entrance C. Bridgewiiter, i,441f. C.Nelson, i,lt. F250f. Portland B., Laurence rk Percy I.. [Im.], i, 153f. P. Fairy, (Bellast), Griffith "\ I., It F, Fl. 4If. J Lady B., (Warrnanibool), | Middle L, (Its. FlOOf. and 87f.) J C. Otwav, h, i. It. R 3U0f. ... Apollo Bay. /,, It F Louttit Bay, Mt Saint "l George, 657f. ' PortPiiii.lip, Melbourne, 1 New OBSERVATonY / — Pt Lonsdale, It F 54f. C. Schank, It F, Fl. 328f. Phillip I., \ 10m., vl^„ W I pt, Pt. Grant / C. Lipirap, i, pt Gl niiie Is., NS 3m., 4.i6f.,l Spt / Cl.ftI S pt. of Australia. Wilson's) Promontory, i , It. F 342f / Mt. Wilson, 235uf. Bass Strait. King I., NS 35m.. N pt. 1 C. Wickham It F 280f. J — S Pt, /, C. Stokes — H.irbiugcr rks.. 2, ^ 2ni.,"l II -27. outer, or SW rk..../ — New Year Is., w, NW rk... — CurrieHr., It Fl. 150f. Ri ill rks., [3m.]. NW, 2.')f. .., Bell rf., Im., S end Black Pyramid, 240f. Redondo, rk., 1, 1130f. Moncoeur Is., small, E extr. ... Crocodile rk Curtis I., [2m.], 1060f., 1 (Sugar loaf, S 3m.) J Devil Tower, -^, 350f. Hogan I., [lim.], 430f. Judgment rlT. Pyramid, 300f. Kent Is..3.# 6.1m., Deal I.,\ w„b, It U95'7f. J Wright rk., sn.all, 20or....^..... Endeavour rf., Beagle tf.,-) and Craggy I., *jj Sm., S [ pt., or Craggy I J Sisters, 2. ^ 7m., NE one.) sum. 636f. I Flinders I., ^^ 36m., W 1 pt, or C. Frankland, ... / — Stnleski pks., 2, at S part, ) 2550f. / — Babel Is., off E tide, 1 ™" / Hummock I., ^ 6m., Low ^ Fumcaux Is. oH' S pt ...J Lat S ! Lon. E 38= 3'7 I40°59'5 38 22 1141 24 38 26 I141 3i 38 24 6 141 40 5 38 252 142 0-5 38 238 142 IS 38 243 142 28-< 38 5«7|i43 3' 38 457 143 4« 38 33-9143 57 37 49-9.144 58-5 38 177:144 37 38 297 144 53'2 38 3'-6:i45 7 38 55 '45 56 39 7 I '46 15-5 39 10 |I46 20 39 8 I146 25-: 39 3 5 '46 2^5 39 356 40 10 39 34 '43 57 '43 56 '43 52 39 40 39 56 40 15 40 24 40 28 39 14 146 23 5 39 '4 |'46 34 39 215 140 .io5 39 28 5146 39 39 23 39 13 39 30 39 49 39 30 39 35 146 47 '47 ' 147 10 '47 '6 '47 '9 147 32 39 39 '47 59-? 39 52 '47 46 40 12 !l}8 6 39 58 ,148 21-5 40 7 '47 445 TAELE 10 MAKITI-MK POSITIONS (107) Places Goose I., [I'm ], w, S pt,"( It. F lOOf. J Barren I.. K\V aim., Mt. 1 Miinri), on N\V part, \ 2300f. J Presorvaiion I., |ik Cl..rke I.. i|4 8m, S pt l^.ok-out rk., (SWofdo) ... Moriarty bk., SE pf. 40°I9' |I47°4S' 40 224 148 75 TASMANZA. C. Grim, i,l,lk West Pt, s:in(ly [Mt. Nurfilk .Mt. Heemskerk, vis. 10 1 I Macijuarrie Harh., 23, bar) Ef., f , w, f, entr. I / C. Sorell, /, rkv. pt. I I't. Hibhs, e -'m Hockv I't.. a rf. Mt. (le Witt, vis. 12 1 I'ort Davey, ^. w, b, pyra- ) I midal rk., entr. / Siijarloaf rks Sou-.h-wcst C, lOOOf., i S"Uth C .\Ia:.Lsuyker Is.. # 7m., 1 SW, or Needle rk / MeHstone, h, rugged, || N Peiira Blanca, (Ed.lystone\ Im. E).J, / Sidmouth^rk., [ic] Rurick rk Recherche B., 2 ffi, w, b,1 S port / HuonR.^Swan Port, ffl, ■*,... Actseon rf. Bruny, Id., ^ 9 1., S pi., or^ Tasman's H-l., i / — SW pt., or C. Bruny, It. 1 R335f. / — Fluted CHjt HoBAH-rON, IB, FOHT MlTI.-l Storm B„ C. ICaoul Port Arthur, ffl, w, f, Se \ maphore J C. Pillar, i, Tasman's I., off J d3.,Tii. 12 L / Hippolile rk., 70f. Maria I., NS 4 1., Oyster! B, ww„, Wside, T .../ — Pyramid, olTS pt — Sura, at N end, 3j00f. C. Bougainville S'.houten's I., % 6m., S islet off C Degerando St, Patrick's Head Kddystone Pl, It. F, Fl. 132f Ml Cameron, (8 1. inland ilo.), 17:inf. lllackrf..[IJra.].. Swan Is., [3m.]. 90f.j w,. It. ) at Bpt, R lOOf. / lofj 40 29 40 35 40 33 40 36 41 .S4 42 ii-i 42 II 42 3S 43 o 43 25 43 35 43 39 43 41 1^8 4 148 10 148 75 14S 17 144 407 144 3** ' 144 57 145 10 145 '35 145 10 145 IS '45 30 43 'o i'45 50 145 55 145 56 146 I •46 S3 146 II 43 44-5|i46 23 43 5' 5 146 S9'5 43 47-5 '47 7 43 59 "47 42 43 34 I '46 54 43 '4 147 5 43 34 '4b 59 43 3« '47 '92 43 287147 8 43 22 J147 24 42 534 147 205 43 '3 43 9' 43 6 42 40 42 45 42 37 42 30 42 21 42 16 4' 34 40 59 40 59 40 50 40 44 47 47 '47 507 48 2 48 2 148 3 14S 75 148 o 148 18 148 17 148 18 148 20 147 56 148 16 148 8 (108) Phi C Portland Waierhouse I., ^ 2.^m., t , t 1 SE s, N pt / Ninth I., small Mt. Arthur, a 1 inland, 4300f. Tenth I., small Port l)alrymple.S,I^.wHd.,"> It. K U2f. / Flinders Pt Kinu Bay. NW, or Black-\ man Pt J Valenlitie Pk., 7 1. inland, I 400()f. / TaMe Cape, It. F 3'jOf. Rocky Cape, sum 2m. in- \ land, lOdOf., (ark. 2rn.)../ Circular Hd., L. 48.51. N pt... Walker I., NS 3m., N pt Three Hummock I., ^ 7m.,) w, SWside / Hunt, r I., NS 13m., 300f . \ t„, ». t E, Ni>t / North hlnek rk Albatross I., [Im.J, I25f. sum. C. W^llinpton.. Corn r Inlet, ffl - Alhcrlon, tov Is. to SE.d., ^ Clitfy I.. It. Kl 180f. Gabol., [lim]. It. F , entr. S pt. vn 5m., E. 01 791'.. Lat. S Lnn. E 40-44' JI47'57 7 40 46 147 38 40 so 147 177 4' 16 147 17 40 56 2 147 o 41 3'4I46 4*'? 4 ^146 44 3 '45 57 41 4 ^146 44 41 22 H4S 45 40 567145 457 '45 3' '45 '7 '44 55 40 26-5|!44 51 o 40 24 144 48 40 29 1144 39 40 22 144 397 ' Uucui III, th« t lul t\t-t* ci cbu.i\ C.Howe, J, Ti islet close) ■>ff / C. tireen, pt., It. Fl. I-t4f. Twofold B., Edcn,^, b, w„) RedPt., It. Fl25f. / Mt. Dromedary, 27061 Montague I., i2ni.]. T,AV, \ rky.,lt F, Fl. 25Uf ( Pt. Upright, i Ulladulla Warden Head, It. ¥ 35 C. St. George, It. alt. 224f. ... 35 .Tervis B , Corranbean 35 Kiama, It. F 34 Wollongong, It. F 56f. ' 34 Botany Bay, \S3 '2-S 24 25 153 25 >S |i52 5S-5 24 45 152 24s 24 1-5 151 46 24 65152 455 23 32 ,15' 45 23 16 23 lo-i 151 44 151 56 22-7 23 53 '5 23 29-5151 14 23 95 '5' S 23 24 1150 32 23 7-5 150 42 22 44 {151 o 22 41 I150 52 22 31 7 '50 47 22 12 150 30 22 327150 185 22 65 150 3 21 59 149 49 22 17 149 37 21 57 150 42 21 39 1150 14 21 27-5 149 53 21 19 149 42 21 49-4 149 30-7 21 3' 5 '49 3' 21 9-5 149 16 21 3 '49 '5 20 54 '49 3 20 40 149 12 20 357 148 54 20 31 14S 545 21 5-7149 567 Cumberland Is., Bailey I., \ »20f. / — Shaw's Pk.,N part of r.1 [4m.]. 1.324f. j — Kenedy Sd., Brush I., 621, Dent I., It. Rev. I20f. Whitsunday l.,pk. 1426f. Havnian I., N pt., 844f. PortMoUeS' Hd., 22of. Mt. Dryander, 2690f. Gloucester Head. 1 555f. PortDenlson, Obsy.Ft., W1 side of Stone I J Naresrk., 2Gf. Holborae I., [Im.], 360f. Mt. Abbott, i:410f. C. Upstart, (sum. l.'JlOf),! NWpt.,(w-|j Im.).../® C. Howling Green, li, R 70f.... C. Cleveland, It. R 206f: TowNsviLLE Pilot Flag-"! STAFF J Mt. Eliot, 3980f. Magnetic I., [.5m.]. 1628f. ... — Bay rk., It. F 96f Palm Is., b, w, large one, % ] 8m., 1890f., SEpt J Hinchinbrook I., Pt. Hd-] lock, 270f. J — Mt. Bowen, 36.50f. — C. Sandwich, rks. 2m Cardwell Rockingham B.. Goold I.,] [2m.], w"'W,sum. 13-5f.J Dunk I., % 3m Double Pt., rks. SE 5m. .„... Flyingfish Pt., Its F Frankland Is., % 4m., S and 1 EL, 220f. / Fit7. Roy L, [2m.], w, b, ( NEpk., 860f., t'W J C. Grafton, I273f. Cairns Landing-place, Its. F... Green I., [and rfs. 3m.], 90f.... Port Douglas, It. Rev. 82f. Low Is., It. R6.5f. Snapper I., [l^m.], w„, SE] pt., 350f. / Archer Pt., It. F 220f. C. Tribulation Endeavour U., Cooki-own ] Pilot Station, It. Fi70f....J 21- 3' 20 28 20 29 20 22 20 16 20 19 20 15 '9 58 '49^34 149 6 '49 4 14S 57 14S sS 5 148 54 148 52 '48 345 148 27 Turtle rf., [3m.], f, N pt C. Bedford, 818f., i, (shl.\ Im.) j C. Flattery. 2pks., 863f., pt.... Lizard I., [3m.],I167f. Eagle I., [Im.], /, t, (shl-l S-7 55 17 20 IS 42 'S 7 «3 26s 144 '52 36 '52 4' 152 52 148 3' 14S 28 145 48 5 '45 45 '2 39 '43 49 12 40-5143 50-5 12 25 ]I43 48 12 12 5 143 55 11 58 ji43 5S 12 6 143 47 " 55 |'43 49 II 445 144 6 II 51 |i44 5 II 36 144 I ? II 265144 o :i I45'44 5 «o 23 '43 555 Fly entrance. -5, [im.] Cumberland entrance Murray Is., [4in.], grt. one,"| f.pk.-OOf. / Flinders' entr., ^^ 4in., S pt.,"! T J Hall's Pyramid, ISlOf. I.,i.rd Howe I., 28341'.. w' Seriniraji^atam and Eliza-") letli rf, mid J Middleton rf A rock Oipcl bk., 55 F. rricrs' bk., n, 3y8o Catol.k.. j8 Wreck rf., (Pori.oise Ciito, 1803) Eastern extremi Island Sir (Tames Snumarez bks., 1 [.'i leasues], SW Cay / Frederick, shoal, (sliip.l '812) / Kcnn rf., ^t 9 miles, low,"! T.S / Boobv shoal, NW extreme .. Mid.'Bcllona Hcllona shl., NW Uellona shl., S Ball's rks , )r|ioise audi EW 7 1,1 mity. Bird f Bainpton shl., [17 leagues], "I Sonth-West part. Avon J Islands, 2, [2 miles], /, ^ J Bampton I., 17f. IJeward I, 20f. Mellish Cays, [4 I.], mid Lihou shoal. [15 I.], K lim. ? Tergrosse Islets, 2, rfs., W pt. Coringa shl.. Id. lOf., rfs.,") Chilcott I / Bougainville shls., 2, S, NS\ 6 1., N pt.? J 0.-prcy shl., % 10m., S pt. ... Torres Straits. Possession I., ^ ."im., rky., 1 »„, wWj,, centre / Double I.,[4m,],218f..N.sum Prince of WaUs' I., 5 I.,) Heath Pt J - Spt,orC. Cornwall Wallis Is., shl., N one, 60f. ... Thursday I., V:-vi;n Pt.,fl. st. Ooode 1., It. F.-!45ft Booby I., [Jm.]. SOf., *,\a, .^,r,ww„,"P.,st Office ''J ® Proudfoot »hl., a. It. vc». occ Eastern Fields, [7 1. ], E cnil, * Boot rf., NS 4 1., (shls, SE-d and SWd) "' I'c.rtlock rf., N 1., (shls.\ ).Npt..../ Lat. S I Lon E 10° I' 1 144° 3' 9 52 5 "44 8 9 55 '44 1 3' 45 3' 31 5 29 56 29 28 24 o 25 '5 23 23 23 14 159 4 '59 4 160 15 '59 "8 '55 32 «55 33 15s 28 158 31 58 52 20 477|'58 27-2 21 473 '59 34 160 36 19 33 19 8 19 13-5 17 25 17 10 17 43 16 50 «S 31 «3 SO 158 16 158 30 '58 557 '55 53 152 12 150 42 '49 57 147 7 '46 34 ■0 5 142 19 10 27 142 26 10 35 7 142 II 10 46 10 51 'o 35 «o 337 142 10 142 1 142 12 142 8? 10 36 141 540 10 32 141 22 10 s '45 45 958 '44 40 928 144 Si 600 TABLE 10 MARITIME POSITIONS (113) Places Lat. S Lon. E East Cay Anchor Cay, (S liui. of\ Bliph'scnrr.) / Bramble Cay, saiidbk., 12t'., ) ^, (Blk. rks. if-3in.) .../ Darnley I., or Eroob. (at W \ edge of rfs., # Uui), ww„, P„ hill 6luf. J Nepeiin I , Stephen's I.,/, t Pearce Cay D:ilrymple I Kennt-l I., village Yorkels,, 2, W Id, viUiige ... ArdenI A.irerd I., villjKe Half-way I. and rfs., ^ 4ni., T NVVpt [ Cocoa-Nut I., 2, [4m.]. E\ I't / Dove I Diiiigcness rf., S pt Dungeness I.. E\V 4in., \S\ pt J Warrior I., [I^m.], at S pt.1 of Warrior rf. J Tcirtle-backed I., 268f., f .. Long I., ^ 4m., *, rfs.'\ E-(l, W pt J Oablia I., Brothers, liilLs, h .. Poll rk Uarvey rks. Mt. Ernest, 807f. North Posse-sion I Brinks I., Mt. Augustus, ) 1.310f. J Mulgrave I., peak, 68Gf. Duncan Ik., Whale I., N pk. .. Jervisl., [2l.],525f. Cook hcct Alert Reef, [Jm.] ar&w ZEAXiAirn. Farewell Spit, bush end pt.,"t It. Rev. 120f. J C. Farewell Mount Olympus, 5400f. Rocks Pt C. Foulwind, It. R I90f. Grey R., Its. F HokitikaR., lt.Fl22f. Abut Hd., extr Mt.Cook. 1.3„')49f. Cascade Pt.,N extr ilford So., Freshwater ) basin / Pembroke Pk., 6710f • George Sound, Anchorage 'J Cove, Nside / I'hoinpsoa Sound, Dcas \ Cove, hd J Breaksea Id., NEpl Five Fingers Pt., Dusky B. ... 9 2J 144 9 8 143 9 353 '43 I 9 34 9 31 9 30 9 37 9 46 9 45 9 53 9 58 10 6 10 4 '43 65 '43 ' 142 565 '42 53 142 57 ■42 45'5 142 4S7 142 37 o 155 142 28 : o 52 142 19 o 10 142 19 o 8 I142 8 o 15-5142 3; 9 58 142 10 'o 23 141 11 9 52 '40 38 40333173 3 40 30 '7242 40 52 |I72 35 40 58 ;I72 4-5 41 455 '71 287 42 26 \^\ 13 42 42 170 59 43 7 170 17 43 33 5 170 12? 44 168 24 % 44 403 '67 SS7 h 44 35 167 54 ^ 44 553 '67 267 -<' 45 .I7'66 58-2 :§ 45 347, '66 3S7 -< 45 44-2 ■ 00 ^^ Places West Cape Chalky I.,(S,ntr. of IWkl Cloud iriUt). Npt / Puysegur Pt., It. Fl. ISUI. Sandhill Pt Sulander Id., [Im.], I lOOf. .. Black rk.Pt Mt Anglem 32{)l)f. Codfish I., \ 3in., NW rocks Ernest I., W head of M.isou B Wedge I.. # Im., cent SWCape Port Pegasus, cove abreast 1 Anchorage island J Wreck rf.. [^m.] Port Adventure, Enir.ince"! I-. Kpt J Paterson Inlet, Glory Cove, hd North Trap, \ 2,\m., .5f., E |.t South Trap, ij. NS 2ii)., S pt. Snares, [i ;.], 470f., rr, W I,i Centre I., It. F 26.jf. Awarua, Blutf Hr., Starling \ Pt., It. F 30f. J Ruapuke I. (group 5!^ 10m.), ^ Npt J ilope 46 41-5 '67 537 46 45 I'' 7 57 46 46 167 377 46 57 !l67 42 47 13-5167 21 5 47 17 |'67 30 47 II 7 '67 417 47 6 |i68 18 47 47j>68 '4? 46 58 5 168 10 7 47 22-2 166 55'? 47 33 l'67 53 48 7 1 166 29 46 28 46 37 N.igL'eit Pt., It. F250f. Saddle Hill C. Saunders, It. Rev. 2I0f. .. Taeri I., [^Jm ], mo. of T riv Otago Haib., TaiioaHd.. It. F Whalers' Home Pt.,Merangi. ; It. Firof. J C. Wanhrow, Oamaru, U.F.. Waiiangi R., luo Timaru, It F 85f. Banks' Pininsula, Akaroa") Harb., S,Whead,lt.Fl. 270f. J — East point Port Cooper, gg, Lytt. Cust. T ho '. / Christchurch ' Table Id Huranui R ' Kaikora Penins., E pt Kaikcira Range, sum. 97uOf.' Ben More. 4360f. ' C. Campbell, It. Rl.Mf. Wairau R., It. F38f. Port Underwood, E head Brothers, It. Fl. 258f. V. .Jackson , Sleihen'8 I., [Im.] D'Urville I., Port Hardy, ^ Earm, Wooding Pt. .../ — Greville Harb., S head ... Current Basin, Cross Pt Nelson, It. F60f. Astrolabe rd., Adele I., NE pt. Separation Pt Clifton, anchorage 45' 54' 1 1 66' 26 45 59 46 10 46 16 46 36 66 357 66 38 167 22 '66 55 167 S3 168 23 168 33 169 3 46 45 46 41 46 272 ibg 51 45 55 |'7o 22 45 53 170 46 46 4 [170 15 45 47 ,170 45 45 24 45 7 55 44 23 43 54 43 46 43 36 7 43 32 41 30 41 21 170 53 172 44? 172 37 '73 5 173 'S '73 44 '73 4> 174 2 174 '8? '74 5 174 s '74 27 174 20 '74 « 40 40 40 466173 55 40 50 '73 48 40 56-3 '73 52 41 15-6173 17 40 589 '73 5 40 47 i'73 2 40 50 172 52 TABLE 10 MARITIME POSITIONS Places Lon. E (116) Places Kapiti I.. ^ 5m.. sum. I780f. Mana I., (off Porirua Harb.), 1 ^ ]\m., sum. NW pt. .../ C. Tcrawiii, extr Port Nicholson, S, East or^ Pencarrow Hd., It. F riof. / Wkllinoton, I'ipitea 1't. ... — Mount Cook.Obskbvatory Taourakira Hd ., extr C. Palliser, extr Flat Rock, extr Castle Pi., extr C. Tiimagain, E extr. C. Kidnappers, extr Ahuriri Koad (Na|.ier) Bluff \ It. F160f. / Mahia Peninsula, Table Cape Ponland I., S extr.. It. R 30uf Poverty B., Gisborne It. F Ariel rks., centre. S Gable end Forelnnd. white gab. Tolago B.. Moiu Ilcka islet...* Open B., N pt Mt. Hikurangi, 533.if. • East Cape islet, 420f. Matakawa Pt. C. Runaway, ej Waikaua P't.... Mt. Edgecumbe, E sum. 257.')f. Wbite I., 863f. Tauranga Harb., g. Mt. \ Monganui, entr. E side ... j Motiti I., iP 3ra., N pt Mayor I., [2m.], UlOf. Tairna R Mercury B., Oyster R. mo. ... Alderman Is., [4m.]. E orouteri 36 Red Mercury L, [lira.]. E pt. 36 Great Mercury I., % 4m., N pt.l 36 Richard's rk 36 Cuvier I., [lim.], sum 36 Channel I. {Talwupu), 270f.... 36 C. Col Wile I 36 Corotnanilel Harbour, g. | 1 ^^ Jnhula I J Riv. Thames.Gruhamstuwn, 1 It. F / Pauhenehe spit. It. F oOf. Bean rocks, It. F 50f. Auckland, g, Depot Pt. ...ffi TiriTiri I., It. F300f. on SE pt. Kawau B., Fish Pt., E entr. Great Burrier I., 2330,% 71., 1 S pt. C Barrier / — Port FitzRoy, W pt. of E i °S2 «74'SS 5-8174 48 17-2.174 38? 22-0174 52-0 16 5 '74 47 18 174 457 26 174 56 375 '75 '7 '5 '75 585 54-5176 142 176 385 '77 8 '76 57 178 I 177 53 178 3 175 185 178 18 178 21 2 178 23 '78 3 178 36 178 21 178 I '77 46 176 45 40 295 39 38 39 28-7 39 6 39 18 38 4' ss 44 38 32 38 io-8 37 58 37 S3 3740 37 32 37 3' 37 38 38 6 36-4176 " 176 25 176 15 '75 54 175 48 176 7 '75 59 '75 49 '75 58 '75 48 '75 21 175 22 — Wellington Hd — Id. off N end, N or guillesPt. „ j\ Horn rk 36 Simpson rk 1 36 Mokou Hinou Is., ^ l^m.,) . It.F385f. ; ^i Rodney P« I 36 Bream Tail I 36 Moro Tiri Is., EVV .'5m., i; pt. 35 '75 25s '75 33 '75 '2 '74 52 '74 49? I '74 56 27-0 174 485 22 175 33 12-0175 225 175 '8 175 27 '75 9 174 5' «74 37 '74 49 C. Tewara. or Bream Hd. ... Wangari Harb., gg. Passage I. Tulukaka Harb, N head Poor Knights' Is., N one, 6?0f. Wangararu Harb.. Grove Pt Waimangaroa pt., It. F. on \ liarf.. C. Brett, (Whd. of B. of Is) Port Ru'^sel, wharf. It. F 2l)f. C. Wiwiki * Cavalli Is., great, NE extr ... Stephenson 1., N\V pt Wangaroa Harb., Peach I. ... Flat Hd., (E. hd. of Doubt- 1 lessB.) * / Mongonui Harb., White's Pt. C. Karakara, extr Parenga-renga Harb., coal pt. North Cape, islet C. Reinga * C. Maria Van Diemen, islet "( It. Rev. 330f / Three Kings, 995f., NE one, 1 NE pt / Reef Pt.,W.enJ. of Ahaipara B. Herekino, S pt H..kirtnga R., entr. fl. st Monganui Bluff, 20tOf., bluff Kaipara Harb., ^, shls. 1 1. ~| out, N. entr. It. Fl 278f....i Manukau Harb., S. South ) Hd., It. F 38.)f. / Waikato R.,Maralai Vill Whaingaroa Harb., ,S entr. pt. Karehoa Jit., 2370f. * Gannet Id., summit, TOf AoteaHarb., entr., N hd Ka Whia Harb.. HI. S hd. ... Albatross Pt., N extr TeruaPt Mokau R., enir IJaleigh, It. F New Plymouth, It. F lOOf. ... C. Egraont, extr.. It. F 103f.... .Mt. Egraont, 8270f. Patca K., Carlyle, It. F 130f WaitotaraPt » U. Wanganui, N or (Jastle 1 cliff. It. F 6.5f. / U. Manawalu, M It. F 44£ ... I.at. 35°52' 35 5' I 35 38 j 35 29 I 35 23 3, 35 19 I 35 'o I 35 '6 35 9 35 o 3458 35 '71 34 55 ' 35 0-3 34 47-3, 34 307, 34 25 34 26 34 285' 35 " i 35 "82 35 32- 1 1 35 46-3! 36 243' I 37 3 I 37 24-3( 37 46-5, 37 SO 37 57 37 59 38 49i 38 62j 3823 38 42 5 39 o 39 3'' 39 "7 59 18 39 47 39 52 39 57 40 27 2 74 21 74 8 74 107 73 58- 73 475 75 46-7 73 35 73 335 73 25? 73 73 45 72 41 72 38-7 73 5 73 " 73 23 73 347 74 33i 74 47? 74 53-3 74 51 74 35 74 49 74 49 74 43 5 74 40 74 387 74 '5' 74 2 73 46 74 5 74 3' 74 44 75 • 75 '47 TABLE 10 MAUITIME POSITIONS Aucklana Islands. Bishop and Clerk Macquarrie I., NS \2 1., N pt. Judge and Clerk , Cani|.hell 1. [3 1.], 1867f.,\ South harb.. Shoal pt. .../ Auckland Is., NS 8 l.,S.C. 200Uf. West e.xtrenie Disapp' intment I., [1 I.] .. C. Bonnet Sarah's Bosom, Terror Govt Bri.-tow fS., 5 Antiiodes I.. Depot, I320f.. Bounty Is., E\V 3|ni., 290f. Ctaattaam Islands. Chatham Is , 'NVhan-Kauri, n, 20 1., S. isl., Tarakoi- koia Pyramid. .i66f. — Rangiauria,PittI.,3iP7m , t , Moutapu pt. (rks. 2m.), 791f. — Great I., ^ 13 l, S pt. Pt. Evcque — Port Waitangi, w, Pt. Hanson — E exir., Wakuru I. (rf. 2m.), Ept — Beriier rk., 150f., [2m.], W pt — North-west reef, extr. pt Juan Fernandez I., 3000f.,1 # 4 1., Cumlierland B. F( irt J — S.pt.,Sta.Cl.iraI.,EW2u. Masafuera I., 6023f. St Ambrose I., I512f., W> rock (St. Felix, 472C.) ... j Sala y Gomez, rks. [ini.],l vis. I5m .'. J Easter I.. -^ 4 1., 1767f.,\ Perouse Pt., Cook's Bay... / Ducic I., j|* 2m., 14f., NE pt Elizabeth I., ^ 5m., NE pt... Pitcairn I., % 2m., luoof.,1 Adamstown / Oeuo I. [2jm.], N pt Xow Arctaipela^o. Disappointment Is., 2, "1 Wytoohe I., SE pt / ^ — Tetopofo^ Otoohoo I ^ Clcrmunt'1'onncrrc l.(/feno), ) or Minerva, % IOm..SEpt. J 55" IS- 54 40 54 19 Ea'^t .58' 56' .58 56 159 10 52 334169 87 50 56 1166 4 50 50 165 57 50 37 166 o 50 51 I166 15 50 325 166 125 ' 166 18 1 78 50 26 49 39 47 4J 43 57 43 44 43 58 43 3« 179 o West 176 17 176 II 5 '76 35 176 31 176 10 '75 48 •76 S3 33 37 6 78 S3 33 45 3i 455 26 277 27 10 10s 28 109 26 24 40 3 '^4 4S 24 21-3 128 19 25 36130 8 24 1313041 141 12 141 24 13620 "8 34 (118) Places Stile I. (PuAorKAa), ^ 7m., \ SE pt J Narcissus, or Gierke I. \ ,-, ( 7o5 5' 23 205 23 4' 23 75 21 31 22 o 21 25 20 45 20 45 23 8 22 12 21 50 21 38 18 42 18 30 18 16 140 41 17 40 140 39 13830 139 10 '37 8 13842 '38 47 140 40 '38 50 '39 '4 140 59 ? •7 23 165' 16 13 '5 44 19 24 19 17 19 18 '9 37 19 8 19 12 18 46 4' 30 '4' 55 '42 3' 142 9 '38 43 '38 49 '39 iS 140 25 140 40 TABLE 10 MAIUTIMK POSITIONS 1 (119) rhices 1 Lnt.S Lon. W (120) Places Lat. S Lon. W '7°3''6i49''34' D. of Gloucester Is. 2. E,-) or Miirgaret I. (A«A«- e 20^42' «'/">") J Anu Anurunga. W Id e 20 38 Oaheitc I., Papeete narh,-| '43" 5' m. w Molu-uta Is., Its. E J Mur.a, or Eimeo, Mt. Tolii- \ 1 '43 '9 vea. perforated pk.,.397.5f. ) '7 32-5" ' "~ 149 4a 7 St. Paul's I. ^Kert/;lia (Mopiha)... 16 52 '54 Romanzofi I. (T/Xvi). [.3iii.] ... 14 56 M4 33 Seillyls.. [2l.J./,rfs.. f.PoG .631 '54 43 ''rfmTr..'.i!'"'!!:.!.C.}''4^^ .45 Baiingshausen L 1548 "54 25 — Ura I.. # 4 I.. S pt ' 14 44 145 «4 Waterlandt. or Wilson's I 1 - - - '... - Marqueaaa. (A/«mA.). #41., Ept. .../ .4 ^3 j.4. 5" Marquesas. »•, r, b, E extr.,1 10 21 '38 25 PcacockI.(^/m),jii4I.,\Vpt 14 33 '46 24 Ari.inerk.. 13f. i Mag.lalena I. {Falahiva),\ NS 8m.,3150f.. Hanavave ' i. Bird I. («dW«), N pt 17 48 '143 7 17 29 143 31 10 271 '38 39 -1 Croker 1. (//oru(A<). Npt. ... 5- Adventure I. (Afotutunya).^ t ■ N\VP«s, „.../ H' J '7 3 j«44 25 St. Pedro I. {Motane),\^ 1640f..SEpt.rk ../O 10 I 13S48 •K iRaelTxky I., or Seagull ^p.,1 16 42 ^141 9 Sta. Christina (Tmt-ata),^ ah. 3280f , Resolution B.. . Eside J Dominica I.. 3.'i20f. (Hivti- \ 1 S&Won«. Glutei. (//-<<)/ 9 563 '39 7 ■^ Tchitchagoff I. (^Tahanea),} NWpt / 16 46 1^4 58 „ Miloradovitch I. {FaaUi),\ ,642 L. „ S i Ou).PerigotIJ.(Pfl«mu«)( 9 44S 'ja 527 NWpt / 10 42 "», f i Hood I. (Fatuhuhu), [4m.], 1 .a ab. II80C., i, »„Pc. J 9 26s 1 38 55 Wittgenstein I. {Fak,ir(f>ii),'\ *!, 101.. t f.J SW 14o-' toava Pyramid J 16 2 '45 36 ^ Washington I. (f/«-/,«/(a), ) [31 ]. ab. 2805f., Hannav ). S 56 '39 32 Greisr 1. f A7««1. r.lm.l. N. nt 16 7 146 Jj '45 30 15. (Mnlullaane) J 1 Chain l. (Anaaj.TunUurj. pa'-s. 17 20 Adam 1. (Ua-pa), 4042f..\ Hakahe-tau B / - Karaka, E\V 5 I., entrance ... 16 4 ■44 59 9 21 140 4? Kauehi I., % Uni.,Spt. •5 56 145 II Nukahiva. [6 1.],ab. 3800f.,1 TIaro King's I.. N pt • C Af, '44 37 14; 34 headof AunaMariaB....J Ilergests rks. iMotu.iU).\ 130f. /^ 8 553 '40 47 Oarlshoff I. {AratHa), W pt.b' IS 33 8 4'7^'40 36 Kurick Is. (Arulua), # S pt. 15 26 14644 ; Ha;;enHistcr X. (Amtlati).'\ IS 18 146 15 Ma.se(E.ao). ab. 2000f, pk.Q 8 I 140 40-5 i NEp. / Coral rt., [& shl. 2 1.] O 7 53 140 22 Klizabc.h I. (7oa«), E pt. \ Otuni / I.Aural. (A'.i«/»/ra), W pt. ... Dean, or Vlieg -n I. (A^oir-I 155s 145 50 15 40 .46 51 Islands Nortb-west of low Archipelago. 1 w^p^.l.l.'::.^..^::'.':.^.":} 14 46 ,147 50 = Starlmckl., [11.?]. 1 , 0,\ S\ i5;.,w. pt / |. MaMenI.,r.-tl.],w,L', ft 1.1 5 37 '55 56 Krusenslern I. (TiMtatt)A •4 58 148 14 Tuheiava pass / i 30f.,W |.t Settlement ... / 4 3 '55 ■ Auroral. {Ma/uitea), 2aOf.l Npt / IS 48 148 13 Jarvis I.,40f. [2m.]. /, *..\ l„. J ; Caroline Is..numerous,small. I 18f. /, r, 5f. T. South \ island Settlement J 23 159 54 Lazaruff 1. {Malaiwa, A/a- 1 /.m,[5ra.].Xf,Ii.Wpt./ 14 S4 148 40 •^ ■^ 10 150 14 5 Socletr Island*. is" Vostok I., [•m.].ab. 80f.,l rfs., f , lag.". L.,, Boat pas<. J 10 6 '52 23 .Maitea I. flj 7 m., P,, lS97f... '7 S3 148 5 "* Flint I..50f /, f Settlement... II 26 151 48 OTAnKiTE I. {Tahiti), ij,\ 12I.,IT. VB.vt,8. lt.F82f./ 17 292149 29 1 Suwarrow Is, 4, small. I'o. 15f. Penrhyn I.. % 4 1., /, lag. 1 ■3 '3 |'63 13 9 J158 55 _ — Bummit.Orohena. 732 If.... 17 37 |i49 28 r. *f.P,50f..Wpass./ 604 TABLE 10 MARITIME POSITIONS (121) Places Reirsonl., 60f.( Ifokaliiwqn'i, \ Church [2m.], /, f , P ... (' Humphrey I., 65r., Churcli 1 (Monahihi) / Bernardo, or Danger Is.. 3, "I small, S I25f., PukaPukaJ Tenia Reef, S Nassau, or Ranger I.?, small, \ /, w, h, P„, 70f. J Vnlon Islands. GinfeHermo8a,20f.[l, >.].-) or Swain's I., ^ I ,t. L,. [ Duke of Clarence I., ( AV/(«- ^l nono), NS 7m., lag. ||„, t *■ o. SEI J Duke of York I. {Onlnfu). 1 -%4m., lag.llo, t t,L,. !"■ \ Bowdiich I.. 8iir. (/■■.■/m'« %7m.,h,g.||o, t f , L, Spt Pboenlx Islands. Mary or C.inton I., 15f.,1 West Entrance / IIuIlIs.,5,E\V5m.,/, 8, lag., 1 t !f, \V, Wpt J Sidney I., l.lf., W pt., /, w„... PhcEnix [2m.], 20f., /. sand,l T, Noith point / Birnie I., 6f., & rfs. [2m.], ) J, I, •„. centre ; Enderbnry I., 2.')f., % 3m.,'] t. Pier on W side / Gardner, or Kemin I., 40f.,] /, lag. II,, *„,,-<-, centre.../ M'Keanl., [im.],25f., *„i[^ Sapa Island, tuc. Four Crowns or IJ.iss Is.,] 4, small, 346f. {Morotiri') j Rapa, orOparoI.,2172f.,P'. \ w, S, Abnrei Bay, entr J Osborne, or Nielsen rf., \i!. ] Ertstpt ] Maria Theresa reef? iL'Orne bank I Haymet rocks? Lat. S Lon. W 10" 2' i6i° 5 5 lo 23 5 i6o 59 10 528 165 51-5 " 7 ;'65 35 11 33 3 '65 27 9 >3 170 52 "7" 447 8 397 172 28 1 9 28 171 9? 2 S9171 425 4 30 i7« «3? 4 274171 16 3 35 3 SS 4 377 3 35 2 171 33 171 10 •74 39? 174 16 27 55-5143 285 1 27 35'7ii44 >7-2 27 1-6 146 17 37 o 151 13 27 42 157 44 37 II 160 13 Vavitao I. (flooafooi), NK pt. 23 50 Tulmai I. [2 1.], vis. 10 1.. 1 CD, t 'I, Z ^, w, h, [' .;23 22 Anchorage J Run tu I. (Oheleroa), NS\ „ _ 4ni., ab. I300f. South pt./ ■> Riniilara I., [3m.],3l5f. 22 45 Hull I.,[l l.],ab.66f.,(/34j)0 21 49 •47 40 •49 36 Cook Islands. Mangaia I., [2 1.], ab, 650f. ] rfs. t„ C Rarotonga I., [3 I.], 2920f.] t„,t', r, 1", NWpt / Parry, or Mauki I., 1201.,] [2m.]./. f,Spt / Miticro 1 , 92f., NS 4m., /, | [f ]. Tomb on W coast.../ Vatiu 1. (.•//(.. ■).394f., [5m.], 1 to. l,SW Peak J Fenua iti {Tuhutea), .501.. ) [lm.],/,t f.UW,w„,li, Hervey Is., 2, (Manual. S,] Aaotu, N), 60f., ^ 2 I.. ||o. rfs. 3ni., * t, 5: O.N I... J Whytootack'ie I. {Aim- 1 laki). [& rf. \ 3 1.], . e 360 f., Npt J Palmerston Is., NS 4m., ||o.] * T, $0' ■"<>■ f- •^s""'"---/ Beveridge, Middlcton, or 1 Nicholson shl., jj., NS 3 1., !, (entr. ^), SW pt J Savage I. (Niue). NS 11m.,] * *. T, P„NWpt. / Antiope reef sravlffator Islands. Rose I., 33f., and rf. l^m., Manua I., ^ 6m., 2500f., i , \ t f,LLo.Tau village .../ Ofu I., EW 3m.. f , West I. Tutuila, ^4 9 1., Huhner B. ... — I. oflF N, or Coxcomb Pt., ] Vatia / — West cape I., It. F — Pango-Pango barb., g , w, ] b, r, tower rk.W of enir.... / ITpolu, % 16 1., 3200f.,Nuu-\ lua islet off SE pt., 120f./ — Fangaloa B., Elds pt. — Apiaharb.,g,w"',f, 2lts.] F., 13 & 197f. / — Tofua Mount, Crater, ) [Im.], 3200f. (' — Wextr. Manonol., 400f,\ [Im.], t,||„ E, w, - ( — Safaiu barb., S Villag. pt Aimlima 1., [.>m.], 472f., T,] t t J Savaii, I., %14l.,5400f.,t,\ w, r, E pt. rf. J — N pt., (Mataatu harb.,] Wd., t s, w,f.b) .../ — South pt.Tanga — West pt., Feliulupo ■n Cur ii;oa reef r Kcppcl I., 350f., ] ^ 2i°55' 21 14 20 7 19 49 •9 59 19 49 •57°56' •59 45 •57 22 •57 43 •57 43 158 49 '8 57-5 ^59 49 I 18 3 163 10 20 2 167 49 19 o 169 50 18 14 168 20 14 32 168 II 14 14-2 169 32 14 11-5169 395 14 21 170 51S 14 158170 4^-5 14 21 170 52 14 177 170 40 I 14 2 171 22 2 13 542171 297 •3 49 7|^7^ 44-$ •3 5' \ili 55? •3 50 ,'7» 4 •3 565 •7« 477 13 492 172 6 ■3 42-3^7» 8s 13 28 172 21-2 13 486 •5 3' '5 S8 •73 44 •73 52 TABLE 10 MARITIME POSiriONS Verr»de«, or Boscawcn,"! (Xiua-tabuu.laU.u). [& J rks., ab. 6m.], ab. 2000f.,r J GcKxi Hope I. (A'm.o/«),1 550f.,F, [aim.], N Wind, vill J Ze|.h)r reef \V.sllis Is., 197f. (Ceo). 9-) t ■ ffi S, *„ b, r, Jlua Mission J Home R, 2, Alofa, ^i, I'k.l I200f. J — Fotiina, Mt. Schouten, 1 2500f., Sigave B J Bayoiin.iise bk., is Field Bank Robbie Bank IsabelU Bank TuscMrora Bauk ■ lice Islands. I. (Nuraklla), vis. I ik , grp , NaJtuluilii South I5"52' I,on. (124) West '73°5o •75 4> •5 34 I i6 03177 6 I 13 20 7 176 10 I 14 21-4177 562 14 16 1178 10 12 8 :i79 43 li 17 174 44 " 3 176 53 12 27 177 17 II 49 "rS '4 liee, 2 Is., (Fa«.,/w/), ) NS 14m., t ;f , la^'. ' e t', h, *, Npass J De I'eysterls.. (.ViM«/Wmu),"] ^9m., f.lag.cntV.NW, , T5 inside, Spt J Tracy I., (Oai77 lo 6 6 1I77 20 6 iS 176 20 5 39 176 6 2 39 176 52 2 33 '75 55 ' 52 i'75 30 " 27 [175 59 I 24 I176 31 I 12 1174 43 o 4S5 174 28 X..rth '73 5' 2 '73 375 173 22 o 8 o 19 3 20 3 45 South o 52 Kermadec Islands, Ac. Raoul, or Sunday is. , 1 627f. mid 29 Havre rk |3i EspcraTice rk., small, 077t". 9 31 .Macaulay 1 9 30 Curtis Is., 2, ab. SOOf. 30 fibow....... N Jlinervajf, K elbow 23 S ^'linejva rf., mid. 23 Wolverine shoal Q 25 Pylsiaart L, [Im.], 700^,"" T, t i, P /:" Pelorus reef 11 5 22 '72 58 '72 44 7 '69 3S 166 Si West '77 55 78 59 '78 55 1 78 32 78 36 178 50 79 5 30 I' 79 4 20 '176 12-5 5' i>76 25 Friendly Islands. Cattow I., small F,oa I., NS 4 1., ab. 600f.,1 II N, mid / Tougatahou I., % 7 1., /, w., ) r, t>. P,. Van Dieman pt. / — N side, Niukalofa. It. F ... Reef, (H.M.S. North Star) ... Iloiiga Ilapai, (S & Wst. of 1 I 2ls.),[lm.],201lf.,t,.^,|,o/ ' Annamuka I., (Aa«ii(/«i), I I [1 1.], lag.. /, f,fl ...|e I Hapai Is., E\V 16 1., S, or \ I Fonua-ika | Falcon I. volcano (now m ^houn I Leibiika I., j^ 5m., Mission 1 I Stat. NW side, f / I Ilaano I., % 4ui., E pt., 1 Moui-tea / N Id., or Ofo-hmga, [Im.] ... K .0 I., [1 1], pyr., 303Uf., i Tofoa I., [Oni.], ab. 18901'., i Coral rf., (SirE. Hume) L, [1 1. ?]. ab. 1790f 305 '74 53 24 |'74 5' 4 '75 22 80175 "7 50 174 30- 36 175 21 15 |l74 46 8 J174 42 187I17S 25 482174 20 Vavu \.AllnJlutu\ Tambu, N pt / Thithia, 540f, NE rass.,i NS 4m., t f , S\V pt, [ (rf W 3ni.) J Tavutha I., \ 4m., S pt.,~( (rfs. ^), SOiif. / Katafanga I., 180f, small,) rfs.. pk )■ Mango I., 670f., [4m.], SW It. Vatu Vara I., 10301., NS 1 4ni., pk / Ythata I., 840f , [& rf EW 1 5m.], Boat pass | Expli.ring Is, &rrs. -^^ Si,") 20^40' 1 78^42' 21 2 I7S 48 20 44 178 51 19 49-4178 13 19 12-5178 25 19 7517S 32 iS SI 178 35 18 39 178 30 iS 9-5:178 56-s 43-5I179 s 79 16 Tliikorabia h ri'cf. N Cairn, 6f J — Muiiia,9.50f. pk — Vanua Mbalavu, 93nf,1 Black Sivan pt / Naiiamba I., sfc S™-. sum.) 610f J I, 17 28 17 2SS«79 3' 5 "79 30-7 ■78 39 «7 '4-3 17 12 7 I'laces Nanuku reef, Nuiiuku Levu'\ S extreme, 70f. / Nuku-Mbasanga I., 70f. small Ngele Levu rf., EW lOm.,) Ngele I., 60f. / Va-tauua I., small, 90f , mid. Buddrcef, Thombia I., 590f , \ pk J Thikombia I., (Farew.U),! Nst. of the Is , *t 3m., ^ rfs.,||o,Aa««/« Ka(«,480f.J Tiviimi I., 4040f, ^ 8 1., \ South Cape J Rarnbe I., 1550f, C. Georgia "iiiua Levu I., ^ 33 l.T 2428f., E, or Undu Pi., "- NuPutn J Savu Savu Pt Sextr., VuyaPf — Yendua I., pk., 641f. W \ extreme / — Dana's Peak, 2428f. — N extr. of rf. lining N ) coast, 3m. off Kial., TSOf / Moala I., [& rfs., # 4 I.],) ab. I.'>3.'-)f., t t,(rf 3m.), N pt. of reef J Matuku I., 1256f., [& rf. I NS 4m.], Matuku harb. J Goro I., (S'oro). NS 9m.,) I710f., t N\V, N pt. .../ Horse-shoe rf, [Tliar/Mu-\ //.omo), [lm.],5, Npt. ... ( Nairai I., NS 4m., (rfs.) 4ra.), Needle Pk., 10:8|-. ( Ngau I., pk., 2345f. EW ) 8m., (rfs. S,W) / Mumbolithe rf., small, S pt. .. Mbatiki I., {Danela Naka} »'"■■). [in, rf. / Wakaia I.,NS 4m., 595f, Ept M koiigai I., NS 3m., rfs., \ Spt / (Jlokungai Pa.';sage.) Vatu e thakc, or Passage I., "1 small, 304f / OvvLvuI., if 8m, 2089f,1 IjKVUka, Site of Sciiooi.- ' HOUSE, (Its. F 240 & t9'Jf ) J Viti Levou, EW 29 I,) Lat. S Ixjn. \Viir l6°43' I79°26'5 16 18 179 14* 16 53179 87 15 5-7 179 24 16 275179 397 >S 45 >7 I 16 325 16 6 16 48 7 17 I 16 49 16 42 16 10 '79 53-5 East ■79 56 79 59-? 80 6-5 i7» 19 ■78 55-5 '79 5 '79 58-5 '79 45 179 26 179 17 19 10 17 14 17 38 '7 47 5 '79 25 18 o 18 I4'2 17 46 I 7 223178 52-5 7 9-5 '79 o? '79 16 178 465 '79 7 «7 ' 16 58 16 46 4000f., f , Rewa roads, . Nukulau I J — Nasalai reef. It. Fl. 4.if .. — Suvahurb.. S", w, h, S^.-) Suvapier,(lts.F3.0& 12.-.f.) J — W.St extr., Naxula Pt. ... — Muani Vatu Pk , 4000f. ... Manaiiutlia grp., Hudson's )^ Is , Mana I / — Waial., Ji 5in., sum., 18741 Yasawa group, west extr. of 1 the Is., WiwB I., [2m.], (»hl. S) J — Naviti, 740f., pk — Timboor I '7 36 17 28 17 22 5 17 407 18 IO-2 18 8 18 8 17 405 17 17 '79 '7 ? 79 »9 '79 9 '79 « 178 58-5 178 47 17S 51 '78 3'-5 178 42 1 78 26 176 54 T7 5 5 '77 ifi '6 43 )'77 3'-5 TABLE 10 CO? MAUITI.MK ruSITIONS PUucs Koimrt I., (/,<•»« Ah/o«).1 iOuf.. small, (II VV-d) .../ Vatu I^ilc I., llUf., ^ 8m., \ /, i, iN. Wpt / Thakiiu U-klfka or Fljiiig\ Kisli shl J Mbi-nga I., [Sm.], L W, \ pk. 1130f. / — S pt. of rf. round I:igoon ... Ono I., [oin.], Ilo. pk. IllOf.... Kaiidavii, Mt. Chullenger, ] 2180f., sP- 9 I., ft,]. (So i™) ) N. Asirolahe reef, Sulo I-,") It FI. 96f. J Great Astrolabe reef, N pt.... — N'galoa harb., N'galoa — Denham I., W extreme ... Hammond reef Rotumah I., goOf, Sj. .3l.,1 t f , r', I", Oiiiafa / Ea(;leston reef Charlotlcbk., is Pundora rf. Mitre I., {Fiituka), [lm.],l vis. 4 1., *.Po / Chcny I., (Anmii-). [.3ni.] ... Tucupia, [3in.], 30uuf., T.I t f.l* / Conway rf., [-ic], 6f.. T .Mathcw rk., [^m.l, Vi.lcanic, \ ■«e-^f.Lo. - •■"■ / Hunter I., [>.],974f.,|.e ... Hiilliante slmal Walpolc I., [l.jm.], 229f., 1 tcLcPo.Spt / Durand rf , [jni.], &$^, T, «... Norfolk I.. 1039f., Svdm^y 1 lJ.,tlai; a'atr '. / ImOjaltj ZsIanilB. Mare or Hiitiinuia Is., ,S pt... — K pt, C. Coster — Tan.lineB., X Boucher I., 90f. [4m.], f.l mi. I / CImbroI I., K pt, C. Pine — Wreck Bay — SKpt.O. deFlotie U>eaor Halgan I., [6 1.] — Oidiy I., Bishop Sd Ilk-aupr^Is., [2 1], /, f.NEl M i Aurolaberfs , 2,flj 10l,\ _ ||„, East reef / O Pelric re.f. 2nf., x I of Pines [31.]. lag.. «W.l f f. P„ Alciiieiie I / SE elbow of if „ i6''4o' i8 31 i8 36 77°46' 77 37 77 4S 23 178 8-2 «8 3>i>77 59 18 S3 178 297 18 585178 22 18 41-3 •9 5 19 8 12 21 11 47 12 II " 55 II 36 21 45 22 20 78 32? 78 3>-5 78 II? 77 57 ■77 50 173 '3 "72 5 170 10 i6g 40 168 43 '74 377 171 20 72 5 70 5 22 24 23 «4 22 38 'lOS 567 22 2 I16S 39 29 37 i(i7 5** 21 40 16S 12 21 24 1.08 7 5 21 32 '167 50 21 55 '67 49 21 I !i67 24 20 45 167 8 21 9'5'67 "85 20 43 166 36 20 28 '166 30 20 22 166 14 19 SO 16s 56 18 35 J164 22 22 42-5 167 28 5 23 I 1167 2 Kew Caledonia. New Cal.donia, ^ G,5 L,\ .5360f, Ept,Naii I J C. Coronation (Unia) Baladeharb.,j6,(rfs 21.), Id NWextr.,TiaI, (shI ) Yande I., peak lOOOf. C. Ueverd, (shl. 3 1 ) Port St Vincent, a, J^,, *,-) | -f 3.\m., i f, Entr., (ris. ; sj- 4m.), Tenia I J Port Nuumea. It. F red , Aniedee, It. F 164f. Del.pls.,/, t.rfs.Tguel. ... D'Entrecastiaux rfs., SW \ pt. Boat pass / Huon Is., Bond reef, f^m I, 1 /, t , (rfs. 3 I ), N Three rocks 20f. Fairway rf. New Hebrides. Ancityum r.,E\V 31. 2788f..1 t t , w'", b, P„, P. Inyeii / Erninan I., (Futuna), \ [I 1.?], 193ir.,NW pt...J' Tanna I., si, 8 1., t f , r, 1',, 1 Port Resolution, S / — Volcano, 4m. inland, 980f. Imnier I., small, /, P. HOf. ... Knoinan™, Dillon Bay, on "1 Wside, w J Sandwich! (B/u(0, ^ 10 1., | t f , Havannah liar- I bour J Threehilll.,(i)/«(),2l71f. j (rl- Kpt.. /3) I e Monument rock, 39rf., [1 1.], 1 (Is W-d.) ) Ap 1 , 28C)0f., [C I.], Dia- 1 inonj B., (Oiuimat.it) J Lopevi I., 4755f., pk e Ambrym I., 4380f., EW 6 1., I Dip Pt j l'e:ilecost I., (Arngh). NS 1 11 l.,2(XX)f.,SiecpCliff I?. J Aurora I., (A/ui«o),NS 111,1 200()f., f , w, I), LMka rere ] Lepers I., (^o4a), 40001'., 1 Duin Dui J Mallicollo I., 4|, 181., Port 1 . f-andwich, a ; ^ — Espi(--le B St Barilio oinew I., (jVu/o), 1 EW 3 I., islet SE pt ] Espirilu Santo I., sfe 22 1., 1 t-'W pt, or C. Lislmrne ... J — North pt, or C. Cum- 1 berl;ind J Poit Olry Pie de I'Etoilc, (Star I.). 1 (.U.r«/a/,u),290()f.,[l m ]. I Ik- X.ro J '5'5i67° 3'5 2 166 525 17-2164 290 18-5163 57 22 5 163 49 45 164 22 I ■65 57 i6-2 29 3> 166 272 166 29 ■ '63 35 4C 162 46 54 162 56 161 46 20 153 169 447 '9 3" 170 I. 19 31-3 '69 275 19 324169 245 19 16 ii69 37 18 47 s 168 58 "7 3- 17 16 16 475 16S 24-5 _ 168 10 16 30-C16S 21 16 14 167 54 7 5 40 168 8 14 58 15 19 '67 43 16 25 5167 47 5 15 58 5''67 107 '5 43 '67 15 IS 38 166 46 5 14 38 166 39 'S '•3167 5 5 14 29 167 59 TABLE 10 MARITIME POSITIONS Places Claire I., (Merigi), smnll, 200f. Vamia Lava, 3 1 20f., P. Pat- \ teson. NusaPt ) Santa Maria, ( Gaita), 2300f , \ LakovaB / Bligli I., (Ureparapara),\ 2440f., peak / Torres Is , (^iaia). Tegua 1 I., 600f., Hayter B / Santa Cruz Islands. Vanikoro I., La Pcroiise. % "1 Um.. sum. 3031f. J — Ocili harb.,on E side. ffi... Toiipoiial ,(orEdgecumbeJ,\ Basilisk lir / Sta. Cruz I. , ( Ndeni). 1 800f , \ ^8 l.,E pt., C. Byron.../ — S pt., C. Mendaiia Volcano I., {Timilmla) Swallow gninp(A/aalu),] ^g as 1., f , E pt., or C. ]- S.irviUe J — Makira h.irbour — NK pt., C. Kecherche Throe Sisters, % 3 1 , 2501'., "1 N one, (Alila) / Contrarietc I., (f//««a), NS \ 7in., I200f., j.k J Ufii I., 676f., Selwyn B Makita I., (.Vai«), i\, 34l.,1 S pt., orC. Zule / — Mt. Kolovrat. 4-.>7.';f. .Mir B.,y — NW pi., C. Astrolabe, 1 MaLIu harbour ;' Lat. S I.OU. E (130) Places H '7' 14 17 '3 32 '3 IS 1 67^48' 167 305 167 25 167 20 16633 II 37 166 51-5 II 404 166 550 II 20 ji66 30 10 41 ,166 S 10 53 1165 52-5 10 243 165 46 7 10 17-5 166 18-5 10 6-2'i6s 41-7 10 14-5 i65 54-5 9 48 1 166 53 9 57 167 o 10 I 167 s 5162 42-5 S 4 35 ■59 9 •59 30 4 4S 157 4 4S 15s 20 >o 54 1O2 265 :o 50-8 162 25-5 10 49 162 21 10 25 5 161 27 10 10 1161 19 10 8 161 54 9 46 |i6i 57 10 15-2 i6i 42 9 45 ;i6i 3" q 5-5'i6o 57 8 59 leo 43 8 22 160 30 Gower I., [4 1], /, t, S I -I pt :..../°, Uamos Is O GiiadaUanar I., \ 26 1., ( I Marau souml, Ferguson 1./ — South pt., C. Henslow — Mt. Lainmas, A, SOOOf. ...I — Wanderer B., Boyd Creek — South-west pt., C Hunter — North extr., C. Espi ranee Florida L, 1500f.,Mboli hr.,~| , Tree I j"i Buena Vista I., 1050f., pk. ... Russell Is., I600f., Pavuv Pk '-:.} Murray I. {Burahoi) [Im.J.I ; lOOOf. J[ St. George I., 1(5 4 1 , || N, 1 | Astrolabe Creek, B, w, Vi r„, f, P„, S cuve J Isabel I , ^ 40 1., S pt.,"! 2050f., C. Prieto (Vi- J. tora I.) J — Mt. Marescot, 3900f. — Port Praslin Q — C. Comfort, (rfs. 21 ) ] New Georgia I., (Marovo),'] EW 14 1., Is. (W d.-), S . pt., or C. Pitt, GamUi J Benduva I., 2.i00f , C. Pleas- 1 7° 56' 8 19 9 50 9 59 9 45 9 41 8 9 49 9 14 9 3-5 8 53 5 9 5 9 I 8 36 8 14 7 25-5 7 19 8 45 160 160 487 160 35 160 o '59 395 '59 47 •59 4' 60 17 160 I 59 26 58 185 158 6 58 IS Rendova harbour.. Xolieara Inlet '57 24S 8 ?3-5'57 •? '57 •75 Eddystone rk., {Xaroi:a),-\ llDOf., P„ (shIs 5, ^ 3m.), barb, on W coast.. .J Guizol., J e Vella Lavella, C. Middlcton, 1 3000f. / Choiseul I., I800f., ^ 33 l..") E pt.. C. Lahce / — Bambatani ; — Kangopassa — Clioiseul B., Kcdmau I.,V (sM. 2 1.) /■, Shorlland Is., 676f.. [6 \.y\\ SE pt , C. Stephens J 1 Tr.asury Is., (Mono), [3 1.], 1 ] /, t , Blanche harb., Wat- \ son I J Bougainville I., ^tj 441., C. \ Friendship, E end j' — C. Le Cras. (Id., [2 1.?]) — Gazelle harbour — Mt. Ball.i. 10,171f., 5 1,,) inland J — CTAverdi — Bukal., t f .N Cape — Summit of Buka I., 130fif. — Queen Carula harbour Indispensable rf., S pt — NW pi Hennell I., 400f., «(, 12 l.,1 8 16 8 57 6 433 7 6 35 5 5<^ 5 30 5 o 5 "6 5 'o '3 2 12 15 II 52 156 295 156 50 156 30 •57 49 156 40 •56 34 156 24-5 '55 52? •55 5 154 54 •55 « '54 35 '54 33 • 54 29 100 31 •59 59 7 160 . jBcllona I,, 400f., [3 l.J, SE 1 pt ) TABT.E 10 MAUITIMK POSITIONS Jtow Ireland and Jtew Britain. Snblereef Fead Is., or Abparris, ^91,1 '• llo- f • S, or Goodman I. J Lyra shI., «!i 4 I , J or !, 1 centre j ^ Sir Charles H.irdv.or Verus 1 Is.. 330r.. [6 1.], E pt. ... r St. John I., •loOf., [.Tl.],l ^ t f .to. Kpt J Kann I.i., [I I.], (rky. Isl. 1 2 I.), centre ( ^ Gerret Denys I.. [5 1.]. 1 600f.. "l (highest of these islands). f 1, P. mid J San Francisco I., 6.')0t'. Gardner I., and Fishpr's 1,1 (.3 Is. E-d.,a>hl. W-d?) 1 NSlO 1., ab. 1600f., N pt. Fisher I J Sqiiallv I.. [3 1.], /, t.l p (small Id. S-d..||„) / *^ Mathias'I. [8 1.]. A, vis.) 4.101., {Tumiara), sum. / ^ Cape Santa Maria O — Holy Haven, S side New Ireland.W pt..C. Tesihki — Piirt Carteret, ffi, Cocoa-"] nut I.. 800f., NE pt., w„, wN, f , f J — Port Praslin, g.SE com., » — C. St. r,eor;;e Saudwich I., [4 1.]. pk. 60f>f.... Mausoleum I., Byron Sirait, ) fi56f. ) New Hanover, 164(if., ^ i H I., N pt., or C. Salomon ' Sw.ert I — W pt., C. Quien Clharlolt Portland U , KW 7m., /, | large I / Duke of York I., [3 1.], «',-| f. Port Hunter, N side, Mitchell Pt J Father sod Son reefs. Father | reef J New Britain, J& S.'i 1., 1 Blanche B., Matupi I. ... I — Father Pk., vol., 4000r. ... — C. Palliser — SIC pt. C. Orford. i . SE extr. — C. Qnoy (pk. »f- 3m.) — Pt. lieecUey — Port Montapue. J . w, \ _ r. Pi. Roebuck / ^ — South Cape, rky. islet ...Q — C. Ann — C. Glouresier Pnportail Is., sum O W.llaumei I.. NS 5 1.. S pt ... Whirlwind reef, centra C I.at. S Eon. E 3°3.'>' 3 24 ' 53 4 3° 4 3 3 32 3 8 2 50 2 36 I 40 1 40 '54°.i6' '54 43 153 28 ■54 13 'Si 45 '53 30 '52 39 '52 43 150 30 149 40 * 153 14 47-5 '5° 57 5 42 150 39 I 41-4152 42? 498152 48-; 51 152 485 55 '5° 49 20 150 14 I 28 149 55 37 '49 39 55 '52 28 55 '5' o 5 ' 4 37 5 20 5 37 6 9 IS 632 5 46 5 28 4 54 5 10 4 5' 15' 3' 152 205 152 10 15" 47 151 2 150 36 149 48 14821 I4S 23 151 21 150 O I4.S M Ronke I., % 7 1,*, t.-l Dam pier Strait, Euilier j Anchorage, C. Kinj; ) — Tupinicr I., [I L], A, ^^ I.ottin I., [4m.].upw. of .'jOOOf. Long I., NS 5 1., Keaumur | Pk. at N end, 2ii00f. j MciiieL, 2150f.,EW4m.,niiM North L. small, hot spring, 1 sh.al, 5m. N\V ..J Gipps I., hot springs Victoria reef Albirt reef Sherbunie rf.. KVf 4 I., rks. I ■iOf, SEpart J Circular ri., [1 1.], T, (al lag- II >fW) I Sydney shl., rks Elizabeth L, [2m.]. /, f.| [l]NE,P W.J Punly Is.,t,3Is..P„,(Mole, 1 Mouse, & Bat), Bat I. ...J Admiralty Islands. Jesu Maria I., 7l)0f., [& rls."l 3 1.], 5, P^. S\V pt., t ... I Vandula I., 600t., [Im.]. f , P' I^s Reyes, 3, ,f 3 1., NE one San Gabriel L, 12f., [2 1.1, 1 Wend ......../• Admiralty L, SOOOf., EWi 161., NEpt.Nesros Is. ../ — Nares H', D'Enirecas-^ tcau rf.. E ext. r J We tern Islet, [im.], (bk.") *f- I 1.) .". i Sugar loaf, 800f. icliorites Is., 3, sm.'(!l,\ [3 1.],/, L. t f.P i immerson I Hermit Is., 5001., Alacrity ) „ H-. Peme I ( ^ Boudeiise I L'Echicjuier Is.. .30 or niore.) /, rfs.. 8, NEextr / -SW extreme Durour L, small, flat Matty L, small, Bit Ti-er I., NS 7m., P Two I", (ruporlid 1877) TABLE 10 MARITIME POSITIONS Lat. Lon. W (134) NORTH PACIFIC OCEAN. Galapairos, and Islands oil AVest Coast of Hartb America. Hoo.l I.. i\ 9m., 640f., T,") Gard i-r B. on NE side, • ^.I'.^'o ^-J M;ic^'o»en rf, [Im.], a rk. ... Chatham 1.,^ 4m , T . 2490f. \ E pt.. Mt. PiU, b, 800f.... ( Freshwater B., S side,"l wateiinfT place J Charles I., ^ 9m., ITSdf., i w W. Post Office B., $ ', w„, r, Davliglit I't I Gardner I..' [im.], 760f.,l (rk. if S^m.)' / VIbemarle I., NS 7.^m,"( 4700f.,\vw„, Iguan.i Cove/ N;irborough I., EW 17m., 1 C. Douglas, 3720f. ( Ind'fatigMble I., EW 23m., 1 Conwiiy B., Eden I J Jame- 1., % 20m., .Tames 1!., 1 on W side, $ , w, E Cove J Redondork., 85f., T Towers' I., ^ 4m., 211f.,\ Ept / Abingdon I.. ^ 7m., *, t'\ Spt.. w^. Po, raid. 19501'. ) Wenman I.. •%■ 2m., * o>\ 830f., t ^- / Cul|)epperI.,[lm.],5oOI., 4-, T Malpelo I., Slim. 1200f. Oh-os I., [4m.],f, Chatham 1 B., Nside, Nv -j^ / Clipperton rk., 40f., lag. I.,1 NS3m., /, S / Soeorro I., ab. 3707f., *o»\ w„. BmithwateB ( Clarion, or Cloud, EW 8m.,) I', w„.f,P„, Monument rk.j Btiiedicito I., ^ 3m., 97Sf.,\ i, mid / RoeaPartida, llOf. O South l''23'4 89" 40' I 9 o 44 o 564 »9 555 89 Ib'S 29? I 15-4 90 27-2 o 590 91 2S 5 91 405 90 33 90 51 91 365 4 Alijos, or Lobos, rks., 4, 112f. Guadalupe I., NS 4 1., 4523f., 1 S islet J Islands In Central Pacific. Baker I. (Guano'), 20f. Howland I. (Guano), 20f. Christmas I., NS 6 1., Iag.,1 * 1,Vo. t W, Cook Id. / Eanningl.,[2m.],lig., t,l „ w', f, P, English H' ... ]■ ° Washington, or New York ] I., [|m.], f, f.rf. 3m.,^ *„,[<„vill.,pr,WextremeJ PaJmvra I., EW 5 1., lag.,i w„^P„, Palm Point / Norih o 14 O 21 34 1 23 I 40 4 O 5 33 10 17 iS 43 18 22 19 18 18 59 24 57 29 2 o 13-5176 29-5 400 176 40 1 57-3157 28 1 3 5''3i59 22 4 43 160 24-5 5 5=-3;i62 5 89 555 81 32 87 1 109 10 no 57 114 46 no 50 112 8 Kingman shoal, S.E. Jolinston Is., [7m.], (rf. 1 ^7m., |lJ,mid J Owhyhee I. (Hawaii), NS 1 4 1., S pt., Ka Lae I Mauna Loa, nit., IS.GfiOf'. Mauna Kea, 13,80nf East pt., C. Kmnukahi Byron B , Hdo. li. F 155f. — N pt., Upohi PL Kawaihae B., It. F !>0( Karakakoa B. {Keula-} ke/iua), Cook's MonumeutJ Mowee I. (.Vu«0, % 14 1.1 E pt. Kauiki Hd , 3921.../ — Kid.ikole Pk., lO.O.IOf. ... — Laliaina town. It. F Tahourowa I. (,KaIulaiii).~\ #5 1., ♦^.W pt.,(if. ' O 2m.) J Raiiail.,% 7 1., J„, P:.la«ai-\ Pk., 3000f. J Morotoi I. (Mi./olia,). EW\ 11 I., *„, Ept., (Laui- kaula) J — West pt. (Lae-o-ka"| Laau), It. F 50f. J Woahool. (O,(/ii0. ^ 13 1-.1 Ept. (Makapuu) / — S, or Diamond Pt., 761f... — Honolulu, King's cottage — Konahuanui Pk., (Pali), \ 3175f. )■ — Pearl Locks (Honouliuli) — Laeloa Pi., IL F43f. — WestpL (Kaena) — North pt. (Kahuku) Atooi I. (Kmiai-), # 11 l.,"l, Nawiliwili Hr., Sugar ho. ( — Hanalac B., Charlton farn — Waialeale Pk., 50001'. — -Wairaea Oneihow I. {i\itluiu). -,\'' 7 1., \ Oku PL J — South pt.,C. Kawaihoa — Kaeo Pk.. ISOOf. Taho.a-aI.,(A«»^,),[lm] ... BirdI.(,1/o.], 170f. Marorf.,W pt., 8j3, vis. 5m.... I.aysan I., S, 25f. Lisiansky I., [Im.], rt" 2m., 1 /, sandy, w„, (rf. J- 2 I.) / 6°23 16 45 19 29 19 50 19 30 l62°l8-2 169 28 •55 42 '55 38 155 32 '54 5> "9 439155 7 20 16 1155 53 3 155 5« 156 27 9 29 156 0-5 20 427 156 17 20 52-5156 42 20 28 20 49 21 9 21 6 21 18 156 45 156 54 '56 43 157 19 157 39 '57 49 157 52 «57 47 1-5158 I 21 17 15S 7 21 34 1 1 58 17 21 43 '57 59 21 58 22 13 22 3 21 57 21 58 21 46 21 53 2' 39 23 35 23 46 159 2-2 159 30 159 3' 159 40 160 55 160 18 160 10 160 32-5 164 39 166 16 25 0-7,167 59 25 2b 1170 30 25 48 171 55 26 o 174 o TABLE 10 on MARITIME POSITION'S Places r-at. N Lon. K Penrl& Hermes rf., SK I Midway I., SW pt. of Sami \ I..."f- -J Cure I., (Ocean, Stavers), I, \ Sand Island, 20f. J West 27°47'8,i75°5'' 28 12 177 22 28 257,17s 297 Bontn and Volcano Islands. Bunin Is., No 14 1., N, or 1 Parrv's grp., % 3 I., N rk. J | *' Kater I., [Arks, l^m ], N rk. 27 Peel I., NS5m., SW islet 27 — Port I.loyd, a, w', f, Kvnse BaileyK, Ane Tinia | 28 Rock, I O 29 Uosario(or DUappointmeni) j j I., H8r., [Im.J, rky.i, J-;27 *o-fl I I Volcano K, 3, Sulpliur I., \ I jit 5m., 644f. I ^ — N Id., .San Alessandr<..25r)4f., 25 —Sid., San. Aupustii o.3039f. 24 Forfana (late ArzoliUpo) 1 . . 25 I Kock,7f. O 24 Kica de Ore rk., or Lot's "1 I I Wile, 466f. j\^ Hasa I, % 5ra., *, 220f. ...Q 24 Burodino Is., 2, NS 4 1., U ,<: Sandy, Pc, None, 40f. ...J Pai ece Vela(Bishop.Douglai!, "j Nantilus), a rk 12f., in a ug., [ii.],e J I Enst 45 142 7 27 56142 142 9 141 58 18 1141 28 43 140 4J-5 2 ,137 59 Xadrones. SintaHosasho.lI O] Giinm.or Gualian I., # 9 \.,\ Cocoa I / — San Luis de Apra, S.'y- r, 1 fort / — North pt., Pt. Ritidian R.)tal., it* 4 1., about 800f. ... Aguijan I.. [1 1.], centrw TinianL, NS4 1., LN.An--! son's B. at SW part, t „ \ w, r, Anson Hay ) Sflyp:.n I., ^4l..ab. 1200f.,l t.w.r, (rf. W-.I.), Npt./ Bird I., or Furallon de .\Ie- 1 dinill.V5f*2m.,ab. SOf.rks. /■ Analaxan I., A, $„, f , K pt Zcalancia bank (Piedra»\ _ de Torres) S / *- Giipuan I., NS2in., Ept Alaniapan I., 231 Of., E part... Pagan I., W ind. lOOOf. Aprigan I., P., W end Assumption L, [3m.], 2»48f. 1 1 \v,«-,t / L'rraras, 3 rks Farallon de Pajaros, 1089f. ... 140 22 131 22 131 20 136 13 144 15 144 38 12 30 13 13 13 258 14 S' |'4S 3 14 59-4 145 36-2 15 '7-5 '45 465 Grampus Is. (Sebastian Lo- ] bos?). E.D J Marcus I.. 6Uf. Wake, or Haloyon I., [3m.], 1 I, lag., *, f 0, Wo. f, 8f... J Caspar Rico, or Cornwallis, 1 (Toangi), vis. 5ni., Scylla rks., NS21 I nxarsball Islands. Bikar, or Dnws.m Is., [4l.],1 9t.SI / Button, or Kutusov Is. \ ^ (W,V//0, N I f^ S grp., Taka Is., S pt 25° 10' 1146° 40' 21 14 !i54 o ig II 166 31 14 50 169 5 16 146 16 20 16 405 .454. "45 46 1652 '45 49 17 I8S "7 35 iri 3-5 1850 ■ 45 5'-5 '45 52 '45 53 ■45 37 '9 45 145 290 20 20 32 145 21 :44 i4 II, Ailiih). Is., % 5 ... — peniur I J Count Ileiden.or Lekiehls., \ SI, 8 I., S pass. 14f. j Jcmo I., or Steep to O New Year I.. {Miudi), NS (^ •■im., /, f J Chatham Is., N grp., Ro- 1 manzoir, (Oldia), Port } Noel, E islet I S-grp., Erikub, i|j 8 I., S 1 rxtr., (/ImA) ( Calvert Is., % 10 I., NW 1 one, (Kaven) J • South extreme Inoetson I.<., (Aurli), '^ 4 L,"l NEpt j Arrowsmith Is., (Majiiru),\ iL 6 1., Caroline I., W. pt. J Arlino Atoll, Ine I JMulgravc Is., [6 1, ?], sm:ill, \ ris., ||„, Port Hhin ) iKc.its sllioal, ! iBosto I, or Ebon Is., Jurij ) I \ Bonham Is., (./u/«0, ^ 8 1., 1 SE pass J Hunter L,[2m.l,(AV0 Baring Is., Naraorik O Elmore, or Odia Is., ^ 7 South Pass MusquiUo Is,, Hi 12 1., r , W pt. Nania I ,ib r., 14f. MentschikofT Is., % 20 Ebadon I Lac I., W pass Uia, I r Catharina Is., NW I .Sclianz Is., i\f 5 1., Wultho I., Uf. Hnngelab, or Pescadores Is., 14f., 1*0, Souih I Rongcrik Is., ^ 18 1., B."k I Ailingince Is., Knox I 'Biiikini or Eschholtz le., % I 7 I, NW extr 12 14 II 18 '« 3 10 27 9 28 85s 851 8 30 8 2t 7 10 6 53 6 14 5 55 4 365 5 42 5 35 7 'S 8 14 8 19 9 22 8 58 9 21 10 10 If IS 11 24 70 15 69 54 169 46 170 o 169 22 169 42 '70 55 70 17 170 8 70 49 171 10 171 2 '7' 13 '7' 43 71 46 '73 38 68 4t ! 169 43 169 9 168 5 165 4S 168 3 167 28 166 53 166 27 165 36 166 6 167 o '67 35 166 36 165 25 612 TABLE 10 MAIilTlME POSITIONS Places La-, N I,on. E ,gro,,p.,l Eniwetok, orBr [8 1.1, ?fc West Point ..J — SE islet, or Parry Arecifos, or Providence Is , 1 rls,[|o?, Uyelang I., I4f.j Greenwich Is., {Kapinga- maranyi) Indiana reef Two Is. (reported 18/7) ... Caroline Islands. Ualan I., (Strong I.). ^ 8in.,"| Coquille Harli. on N\V '. side, a, w, r. NR islet ...J — Mt Crozer, ah. 2I55I. Pingelap, or MacAskill Is.,! 3, [2m.], Tugulu I J Duperrey Is. & rf., -^ 3m., or 1 MokilL.Spt r SeniavinaIs.,3Brps.,%I31.,'] Punapil,, EW 5 1„> }, . P,. Tolocolme Pk., 28filf.J Aiidema Is., # 3 1., rfs., S pi. Pakin, or Paguenema Is.,\ Kapenuar I / Ngatik Is., EW 3 1., /, t f , I ii„ p„Ept ;■...../ Bordelaise 1., S. Augtistin I., l 107f., [im.], J (5 NW. . rf. SE3 1.) I Monteverde Is., Nukuor, E ) pt., 5^ 2 1., lap; / Mortlock Is.,%6 1., *,Lu-> kunor I., EW 7m., lag. | Port Chamisso, ffl, ^ f , ( ww„, Entr J — Etal Is., NS 4m., N pt — Ta, or Sotoang grp-. S pt. Namoluk Is., lOOf., (Tui-l, Bonie), 3, ^f 3m,J j Losap I D'Urvillel., 3 islets on a rf.,! I, t.(3 J Triik Is. (Hogolu), % 15 1., ) P„ S islet e / -Tsis !.,[>.], rfs., t i.\ wN, t NW, Npt. ...e J Mourileu grp., ^ 7 1., E isle Namolipifan grp., j|^ 5 l.,\ lag. II S, Namune islet... ( Lutke I.,orEastFi.iu,[i'm.],1 rfs., t I, WW,, / Nanionuito grp., EW 15 l.,1 E islet, Pisaras j — N e.\tr.,or Ma<;ur islet — W extr., or Ulul islet Martyrs' Is., NS 7m., t,"( - P', Nisid., OUap ...;.. /O — S Id. Tamatam,( W Id. l ^ Fanadik) /O Enderby Is. 2, f ,f, (abk. T.-J ^- 2 I.),(NW one, Alet; • SE one, Pozoat) J II 21 162 25 9 42 '161 I ■54 45 160 18 146 o 5 >9 |i63 25 6 145 160 52 639 653 6 44 7 6 5 48 7 37 3 52 5 55 6 53 6 59 7 i«5 8 42 82s 833 8 34 8 597 8 36 7 37 7 32 '59 S3 158 12 '57 54 157 43 "57 3'-5 '55 9 55 o 53 58 '53 '6 '5= 43 152 34 '5' 58 '5' 48-5 52 26 5' 49 51 26 50 32 ■49 3' ■49 30 7 20 149 T7 Lat. N I^n. E Suk I., or Pulusukl., NS.l ' 2m.,/, f J O, lanihe anil Nile Shoals,! ^ [.Im.]. 8f., P.D /C; P.keIotCoqume,|Am.],ona1 I rf. *f.Po /| Faiu I., We.,-t, rf. ^ 5m., | ! islet in middle, f / i Satawal (Tucker) I., | Im.]. P Srt-ede Is., (Lanioirek), 6,\ j 2 1., S& E islet /, — Elato Is..NS2l, N pt I Olimarao Is., ^ 2in.. N islet... Faraul.p Is., 3, [2m.], | ^1 iag-.Spt ; ®! Ifalik Is. (Wilson), [2ni.], 1 I lag., SW extr ) Ulie Is, (Thirteen Is.), EW \ j 6m., E, or Raur I. (ffi 15 E, II .SE), N pt J luripik (Kama), 2 is., ^ I 2i'"-.Ept / Sorol, Philip Is., S.E I. ... Fejs, or Tromelin I., [I.-n.]. /, t, nolau'., *o. L,. 30f. Uluthi Is. (M.nckenziu). ^ 7 )., lasr. /, t, N exir., Mogmog I -Sixtr,PMpelugI Yapl., llSOf., NS31., J,(rf. S-d.), Tomil B., It. F, 2h(. Hunter's reef. Matelotas Is. (Nt'oli), ^ 9 I-.', t f.llo. SI — North I., l.^Of. 6° 40' 149=21' 15 53 '45 39 '5 32 '45 42 8 9 /47 42 8 3 146 50 7 22 [147 6 7 27 ,146 31 7 30 '46 19 7 43 ;'45 56 8 35 "44 36 7 '4 144 30 Pelew Zslands, &.c. Palao or Pelew Is.. ^ 29 1 1., 1 , P, (rfs. NW-d ), \ e Korror IP / — Kajangle I., [2m.], (rf. ) 4 1.) Baobeltaob, Angaur I., 4 Pulo Maricrc, Warren I Hastings I., NS 2iii., ' 'is. 4 1., t I Pulo Anna, or Current I., [^m.],/, ii (rf. W, Im.), VIS. lOni Sunserol Is., or St. Andrew, small,/, ^,11^. vis. 1 2m. Nevil I., or Lord North, % ■>).,/, t,(rf E) Helen, or Carteret shl., 5 ^|4 5 1., rks. 4r, N pt. islet, 2 * David'*, or Freewill Is, 4.^ 5 1.,/, t f.P'mid., vis. 18m 640 ■43 11 S 6 9 46 140 24 j'40 35 10 6 ■39 46 9 46 9 25 9 58 8 15 835 ■39 41 138 6 ■3823 '37 35 '37 40 7 19 ■34 32 8 3 7 47 6 50 '34 38 ■34 33 ■34 10 4 «9 .3228 438 132 2 S 20 132 16 3 2 '3' 5 3 '3' 52 57 ■31 21 TABLE 10 fin (189) ARCTIC Fran* Joskph Land, Wile- ] zck I., C. Hnnsa f C. Flora,. Jackson wintereii 1 (189.'i-6) / C. JIary Harmswortli Frrtlerick Jackson I. Niinsen | wintered (18Ho-fi) | 'C. Germanid, TiOOf IlvidlUnd Nanspn's farthest (I89.i) /■>.»«■.< farthest { 1 895^ Capt. Cagni's farthest (19011) C. Gr.nt Gillis Land (1707) O I K ns Charles Is.. East extr O East ■23' 5y° 3- disli Foreland, N extr. Spltzbergen. Sn eerenberg, t', fisd Hacklujts Headland Cloven Cliff ® Moffen I., r^m], /, Npt Vertegeir Unok, 7" ® TreurenbcrgB , HeclaCove, t ' Hinlopen St. Hyiierite I. ...ffi North Cape Walden I., *), Um., b., NW pt. Liitle Tahle I.,"[im.], 7oOf.... Charles XII. I Parry's farthest (July 1827). C. Leigh Smith C. Molen Kyk Yse Is., E. pt O Thousand Is., High rk Sf.r Fiord, Fox NesH ® Hope I., si^ 9m.. W pt S. Cape, or Look-out Hornsunds Pk., 4560f Bel Sd , Separation Pt (B ' 77 lie Smnd, pt. S side, entr...Ol 78 Charles 1., S., or Saddle Pt. O 78 Fair Forelan-? Q 78 Cape Mitra 79 Bear, or Cherie I., 1200f.,"| ^ SonihH' ; O Jan Mayen I.,C. Northeast,"! or Young's Korilaiid / — Mt. Ket-renberg, 6836f. ... — C. South , Iceland. 71 S 7" 4 70 49 Poriland 1 6j 23 llvalshak rk I 64 40 K. extreme, or Pt.Gepirhuk...' 65 S C. Langanae* '66 23 C. lU-vsnig 66 ^j GrimBey L, «, 4in., N pt I 66 34 .Mcvenklini ' 67 9 N^.Tlh C '66 28 42 o 55 15 57 45 63 o 96 30 36 o 32 40 26 40 II 15 '■ 5 II 45 16 57 19 o 20 14 19 2 25 30 16 50 16 18 14 50 "4 7 29 18 West 7 5" '4 30 16 18 18 34 22 2h Place* W. pt.. or Staalliur::huk Siieeleldsyokel, 4696f. Kiikiavig, Hohnenshaven V. Kcikianes. It. F 180f. -Mt. H.rkhi. .■;364f. Osier 'i'iJkel, .'J964r Westnianoerne Is., S pt Greenland. ('. Hsniarck Sl,annon 1.. ^ 8 I., S pt.,1 or C. Philip Broke / 1'. nduluni Is., 2, -J^ 5 1., 3000f C. Borlase Warren C. Hold wirh Hoiie of Hud- \ .son. 3(K)0f. / IloMtekoe, EW 3 1., SEpt. ... ('. Parry O Traill I., C. Young O Canning L, C. Waidlaw ...Q Liv rpool I.. NS 23 1, S pt. ... — Church Mt., 2967f. Rathlione I., E pt C. Brewster, 1 C. Tupinier O King Christian IX. Land,\ Leifs I., 2300f. J Hoidsadlen I C. Moltke C. Adelaer C Farewell, vis. 30 1 C. Desolation Fredcrickshaab Church Lichtenfels Godihaab Holstiinburg Whalehsh Is., Kronprind-'l sens I., $, fl. St / Disco L.^Issungoak Pt — Nirth pt.. Iglorpait — Godhavn Wavgrtf, or Hare I., [5m.] ... black Head Sanderson's Hope Upernivik C. Sliacklelon, UOOf. Devil's Thumb, 1300f. Red Head Sabine's Is., SW one O (;. York, Immagen C. Dudley Digges, i,8nof. ... North Star B.. (Saunders 1 wintered 1849) J Cary's Is , Southern (;. Parry Hackluyt I. (^Agi)aijsuak},Vf ^il. C Alexander Port Fonlke HenssclaerB.(Kane wintered ~1 1853-4-5) / MGary I C. Calhoun C, Constiiulion Joulsl.ind I.nf. N Lon. W 65 30' 24°30' 64 48 23 43 64 8-6 21 53 63 49 22 40 6^ 58 <9 38 63 36 •9 33 63 24 20 15 76 47 .830 74 55 17 33 7438 18 30 74 «4 «9 ^3 73 26 20 29 73 29 20 40 72 22 22 2 72 16 21 52 7" 47 70 26 21 55 71 4 21 37 70 40 21 15 70 II 22 68 42 25 5 65 55 35 30 6S 3 39 5 b3 30 40 22 61 49 42 59 49 43 54 60 44 48 6 61 59 49 44 63 3 5° 47 64 10 51 4'5 66 56 53 42 68 589 S3 «40 69 39 SI S5 70 19 54 3«' 60 13 9 53 42 70 27 54 45 71 .38 55 5" 72 42 56 15 72 469 56 27 73 44 56 40 74 20 56 47 74 S8 57 >5 75 25 58 50 75 55 t'<^ 33 76 8 68 43 7632 68 45 76 40 72 41 77 26 71 8 77 19 72 30 78 II 73 2< 78 18 73 7837 70 53 79 16 6s 80 6 67 23 80 33 66 30 81 22 63 3« fll4 TABLE 10 MARITIME POSITIONS Flacca Rest, Lat. N Lon. W Thank-God Ilr., Hall C. Bryant Mt. Hooker C. Britannia, 2050f. C. Beaumont Markhani 1., C. Neuniajer Lockwooil I., Lociiwood' farthest (1882) C. Robert Lincoln O Grant and Grlnnell Iiand, 37' 23 82 30 82 44 82 48 83 I 83 25 83 32 C. Alfred Ernest ••• 82 14 C. C.dnmhia 83 7 C.Joseph Henry 82 49 Ma^l^ilam•sfarthe^•t (1876) ... S3 20' C. Sheridan (Sir G. Naresl „ ^ wintered 187.'5-6) J C. Union 82 IS 43 81 32 79 58 79 38 78 43 6i°37' 54 46 50 41 49 00 50 30 48 o 40 45 39 35 85 55 70 23 63 36 63 7 Discovery Harbour C. Baird C. M'Clintock C. Louis Napoleon C. Sabine C. Isaliella Clarence Head Ootiourg Is., East L„ Prin- ) cess Charlotte Jlouument J ITortb Devon. C. Horsburgh C. Osborn C. Warrender C. UuUen C. Hurd, i Riley Beechev I. (Franklin win- \ tered" 1845-fi) / Baring U. (Belcher wintered ■) 1x53-4) / N. Cornwall, Mt. Greenwich Parry Islands. 76 41 75 39 74 55 74 24 74 28 74 22 74 32 74 40 74 43 75 40 77 36 6446 H 32 70 50 72 19 74 '5 75 33 77 48 Cornwallis I., C. Hotham — .AssistMme B. .. Giittith L, % 8 1., Spt Lowther I., ,,P 9 I., S pt Bathnrst 1., C. Cockburn.A .. — l.yall I'l — Sherard ()^bl.rn I.,N pt... Byam Martin I., C.GiUman.. MelviUcI., #441, Win.-l ter Harb. (Sir E Parry } ffi wintered 1819-20) J — W extreme, C. Russell.. — N extreme, Markham L Eelington I., C. Nares Prince Patrick I., Land's End I'ldyuia Is., Ireland's Eye 74 38 74 37 74 28 74 26 75 3 76 39 76 47 75 o 79 3 81 42 81 51 85 o 90 3 91 48 91 45 91 52 94 41 Banks Iiand. 74°33' 74 14 G. M'Clure Buy of Mercy (Investi-\ gator abandoned 18.>'i)...J ii.ce Alfred, C C Kellett . Nelson Head Princess Roval Is.l (M-Clurewinieredl8J0-l)J Prince Albert Xand. ri)ice of Wales Str., Peel Pt C. Wollaston 17' 3 Baring 17° o C. B.ek (Rae's farthest IS 482 75 14 117 40 77 00 109 43 75 34 119 30 76 16 124 6 77 49 115 30 125 28 24 13 54 19 5 18 9 117 o V^ollaston and Victor. a C. Lady Franklin Cambridge B. (Collinson\ •., tered 185-2-3) J Point Back Lind 1, South pt Gateshead I King -William I.and. ctoria Strait (Erebus and , . Tenor abandoned 18-18) J I ■' ^^ C. Felix '69 55 Pt. Franklin 69 28 C Crozier 69 4 C. Hersehel 68 42 Mount Matheson 68 45 68 33 113 10 69 5 105 «o 68 55 103 16 6837 102 5 7025 100 38 Prince of -Wales I.and. Cape Swinburne .... Pt. Allen Young MintoHead Parker I Palmerston Pt., 6()()f. Cape McClure Nortta Somerset, C. Rennel Leopold Is., N one, 1, E pt.. Port Leopold (James Ross wintered 1848-9) Batty Bay Fury Pt. (H.M.S. Fury-j abandoned Aug. 1825; Sir \ J. Boss wintered 1832-3) | C. t:; Bellot Strait, Pt. 1 (M'Clintock wintd, nnedy-l 158-9)/ Cockbnrn Island. C. Kilter 71 12 72 10 73 4 74 "4 74 7 72 50 74 7 74 3 73 5° 73 13 7* 23 72 a 71 54 73 2 99 00 101 55 102 40 100 35 97 44 96 36 03 '4 89 53 90 12 91 8 9' 53 93 '7 94 '4 89 59 TABLE 10 MAlUriME POSITIONS (Parry win-l 5;, St:>ny I./ Cha u-session Mt , 22()0f. . Walter Baihm-st . Graliam Moore O . Bonen O .Adair O plies' Monument, 1, 40f. O npe Kaper . Kater O Cumberland Island. Lat. N Lon. W (144) 73°«3'6 73 5° 73 S3 73 5° 73 52 73 22 73 28 72 56 72 21 71 32 70 33 69 44 69 12 C. SearU- Oj67 13 Cape Dier of Davis 0,66 48 Mt. Kaleigh,/i O 66 34 C. WaWnghani O 66 4 C. Mercy of Uavis Cumberland bd., Nijad- 1 I luk Harbour J j — Kingaile Fiord, Union Hr. Kin^-avva Fiord O I — Harrison Pt 61 21 R. solution I, 4), 13 1., E\ ^ I pt., or C. Warwick / " — Spt., or HMtton's Had-l land, or C. Best / [Lower Savaj.'e I Saddleback I Q ■ Upper S.ivage I., ^ 3 1., E pt. O ' 62 33 North Blurt' 62 32 64 51 65 7 66 23 67 16 64 57 62 33 63 45 61 40 I Fox Xiand. King Charles Cape O 64 22 Queen's C o' 64 45 ('. Wcst«n O 65 35 C. Oorchcster Q 66 21 I't. Pi'regiinr(Fox'.'> farthest, "| 631) / Sontbampton Island. fhampton I.s., sij 83 ].,-) 18:)9, Rae 1854) J Stanley Isl.md Hull Bay Boothia Isthmus, Jo.sepliine B MA(iNKricPoLE(18Sl) C. Nikolas C. Hobson .Murehison Promontory, "^ Northern pt. of America./ Elizabeth Harbour Victoria Harb. (Ross ahan-\ iloncd the Victori.i I831--2) J Felix Harb., M'Uiarmid I. \ (Uoss wintered 1829-30) / Pelly Bay, Parker Peak C. Chapman Rae Isthmus, C. Simpson C/'apc llichardson 70 8 70 7 69 34 68 45 68 49 69 32 69 45 69 47 70 16 70 36 70 6 60 49 69 33 69 o 68 28 67 48-: 68 14' 66 28 68 39 68 55 68 29 168 9 6S 12 68 31 68 17 67 '3 68 32 68 44 69 20 69 39 70 5 70 25 71 26 C. Engleficld, Fury and"l Hcela Sirait / C. Ha.loAcll, (N head of do.) Igloolik I., EW 9m.,T (Parry wintered 1822- ® 3). Ept. J .Ulagiiuk Ooglit Is Ooglit L, [2m.]./. C Jerniain C. Penrhyn Winter 1., ^I, 10m.. /, S] pt., or C. Fisher (Pari-y \ ffi wintered I8>l-2) J 70 38 ' 91 46 70 93 91 25 69 597 9t 5" 68 25 69 15 67 20 68 50 69 S« 69 57 5 69 21 69 12 68 58 68 24 67 47 67 25 66 1 1-4 »9 i'} 89 " 87 2 85 IS 85 30 85 26 81 31 81 30 81 4 81 38 82 o 8. 25 83 100 616 TABLE 10 MAKITIME POSITIONS Baffin I., ^ 7m., SK pt. . U. pulse B., huaJ Fori Hoi Wiiger U., S cape ol eiitr. HUDSON'S BAY. Lat. N Lon.W (14(i) 65° 40' 66 33 65 -3 ,Wa!ZgI...O,63 21 Cliesterficl — H. ad ol Marble I., E part O Whale Cove O C Esquiniaus- O Chuichill. Battery Beacon... O C. Churchill O Vork, factory, r^, f C. Tatnara O Severn Fort O C. Lookout O C. Henrietta Maria .Mbany Fort O Moose Fort Rupert's House O East Main Fort O North Bear I O Agoomska I., % 17 1., S pt. O South Cub O Eong I., J2 6 1., S pt O Richmond B,, cntr O South Belchers, ccni re O King George's I^., centre ...Q Sleepers, N jiart O Brothers, East Bro O Ottawa Is., NEI O C. Dufterin O Smith I O 62 41 62 10 61 8 58 46 58 52 57 2 57 22 55 58 55 23 55 9 52 12 51 '3 5' 23 52 10 54 27 52 49 53 57 55 o 56 14 55 55 57 30 58 18 58 37 59 55 58 46 60 50 I., # Mnnsfield Soutli r — N)rth pt C. Woslrnholmc Dignes 1-., W e Notliughau, I., S pt., (5 shl. ; Salisbury 1., ^g 9 I., SE pt.... Mills I., N pt O Charles I.. V. Mu.ses Gates O C. AV egg-. Island O Stnpart Bay C. Hope's Advance Creen I O Akpatokl., Eii.d Koksoak R., Tlie Wort, 165f... FortChimo :|o^6. 33 ....0I62 37 ....0'fi2 37 ...■OJ62 34 '} O 63 6 X.ABBASOR. C. Chidleigh, ISOOf. Button Is., NS 3 1., vis. : NE pt Eclipse Harb„Mt. Bache, ; Niiehvak B., H. B. Co. Pc Hebron Mission Station.. Mt.Thorcshy,2773f.,roi Manvers, w, b Nain Kupedalc Harh. Obs 64 4 62 47 62 31 61 33 61 17 60 ,8 60 10 5820 60 33 60 51 56 53 83°29' 86 56 87 28 91 14 95 50 90 30 92 50 94 o 9t 10 93 14 92 26 91 lo 89 12 85 13 82 45 81 50 80 40 78 29 78 32 81 6 81 o 79 42 78 48 77 '5 89 48 80 to 80 40 80 o 79 38 79 " 79 7 79 52 77 26 77 50 76 30 77 50 74 o 74 o 71 33 70 2 67 52 66 36 6S 7 68 18 64 15 64 39 64 2 63 52 62 40 56 32-9 61 407 55 371 60 12 s Places Aillik Harb., C. Mokkovik .. Webeck Harb., Harbour rock; White Bear Is., Middle I., 1901: Hamilton Inlet, Rigoulette .., — Goose B., Babbit 1 Cape Porcupine, 343f. Outer Gannet I., I04f. Cartwrigh' Hb„ Caribou Castli Gready Harb Indian Tickle, Indian Id., 360f Roundhill I., 1741. Occasional Harb. Obs C. St, Frai cis. list. C. St. Lewis. Si. Le>vis rk. .. Battle Is., Double I., 130f. Table Head Belle Isle, ^ 9ni., It. F 470f. Cliateau B., Castle I., S pt. ... Amour Pt., It. ¥ir,hf. Greenly I, It. Rev. lOOf. Bradore hills, sum. 1264f. Old Fort I., [I.Vm.] , Shagrks " Eagle Harb., E side. entr. Grt. Meeatina I., ^ 3,lm.,l _rf^, SEpt J Murr Is. and rks., [1 I.],l Kextr J Little Mecatina I., -^ 6m., 1 Spt / St Mary rks., ['.'m.], S pu .. South Maker's ledge C. Whittle, (rks. jf- 3ni.) Quirpon I., N pt., or C.\ Bauld, T.lt. Alt. 141f. ...J Bell L, (Send) C. St. John, Gull I., It. Occ. I .5'2.5f. J Toulinguet Is, It. Rev. 33.5f.... Seldom-come-by Harbour, "( Cann I., It. F 85f. / Offer Wadham, It. F lOOf. Funk L, 46f. C. Freels, Stinking I., !t. Occ. Greenspond I., 85f. C. Bonavista, It. Kev. 150f. ... Catalina Harb., Green l.,\ It. F92f. / Bon.tvenrure Head New P^rlican, Bloody Pt Baccalieu I.. It. Fl. ;i80f. Harbour Grace, (It. F 40f. on ) beach) J C. St. Francis, It. F 123f. Sr. John's (Cuainbock"! Battkry) / 0. Race, It. Kev. 180f. C. Pine, It. F 314f. Trepassy Harb., (Shingle neck) C. St. Mary, It. Rev. 300f. I'lacentia Harb., It. F 180t" Burin Harb., It. Rev. 430f. Laun, GL Uun K. C. Chu I.at. N Ix>n. W 55°'3'5 54 545 54 28 54 10 53 23 53 56 54 o- 53 42- 53 48 53 34'2 53 26 52 40 52 33 5 52 2'- 52 15 52 6 51 53 59'i8'? 58 n 56 55' 58 ^s ? 60 57 56 31-5 56 59 7 56 2V7 55 59-5 55 36 55 44-: 55 41-; 55 37: 55 33 55 41 55 22-: I 55 50 5' 275 56 5' 51 22 7 57 IO-: 51 34 SI 22 51 10 5' o 50 44 50 13 5° 9 50 II 49 4^ 48 420 48 302 48 .69 47 S5i 9 47 41-4 47 48-5 47 340 46 S9'4 4b 37-1 46 43-3 46 49-5 47 ■4 47 04 4» .■.0-5 .SS 41 58 53 58 50 59 21 59 45 59 57 55 25 55 355 55 21 54 475 54 '07 53 45' 53 'o 53 "45 53 2-2 53 : 53 21 5 52 475 53 12-5 52 470 52 407 53 4 3 53 31 7 53 22 2 54 >iS 54 55 55 . TABLE 10 MARITIME ruSlTION3 (M7) PlMce* St. Pii-rre I., Galanlry It.") Fl. -ildf / Great Miquelon I., C.Blanc, \ It. Occ. lO.Sf. J Pass I., Its. F 281f. and agTI. Biirgeo I., Boar I., It. F"l 207f j 1,11 Poile Bay, Ireland I..\ It. Fl. 6'f. J C. Kav, It. Rev. 130f. Cod Koy 1., S side of Boatl Hill) / ('. St. George, (Red I., SE pt) ('. St. Gregory C;..n- Head, (NWextr.) Port Saunders, (NF, pt. of"l entry) / Rich Pi., It. Fl. 1.30f. FerroIIePt., (Co%e PL NET '•xTO J Flower Cove, (Capstan Pt.) ... Green 1., (I.'JO fms. from NE 1 -d) / C. Norman, It. Rev. 1381'. Natoslninan Pt., S edge, (R. "| nio. ^(- 4m ) / MinganIs.,EW15l,,Bowun1 r"£s.,Eextr / Collins' ^hl., ^ 2m., 7. S pt.... Clearwater Pt., SW extr Perroqiiets, It. ReT. 87f. Riv. St. John, enir. E pt Seven Is.. Ir. F 200f. Grt. Cawee I., [jm.], 250f. ... Kgg I., It. Rev. 70f. I't. .Monts. It. F lOOf. Quebec .S, NE bastion QUEBKC OIISERVATORY 46 Wiilfe&Monicalra'sMonument 46 Green I., It. F 60f. 48 C. Chatte, It. Rev. 120f. I 49 St. Anne's Mounts, NE one, | I o 3973f. I r* ('. Magdalen. It. Alt. 147f. ... 49 <;. Gaspe, It. F 3.Wf. 48 Douglas town, gg, w 48 AnticostiI.,«ij41 l.,Ept.,or-( | ,„ 46''46'o 47 6 47 29 47 if>S 47 38 47 370 47 52-5 48 33-8! 49 23 49 55 3 50 38 5 50 41 6 51 2-2 51 1S2 SI 242 5 1 380 50 6 50 10 50 12- 50 14 50 '7 50 6 49 507 49 38 49 197 46 49 1 485 486 60 52 ■ 5-6 45 46 ••■/i Heath I't, It. Fl Bagot liluff. It. Fl. 75f. Shallop Creek, D=]. entr I 49 .South-west pt.. /, It. R lOOf. ...! 49 Ellis Bay, H, W entr., or C."l Henry / M' West point, It. F 112f. 49 Bonaventure I., [lim.], i,"( Lo ,„ 250f., II E / h^ ^9 I.eandcr shl., [Jm.], » 48 25 Macqiiereau Pt 48 12 ihaleur B, Carlisle 48 I - Dalhousie I. It. K 3nf. ' 48 4 56°io'o 56 24 56 12 57 35 58 22 59 18? 59 23-7 59 1. 5? 58 14-5 57 50 57 >8 57 242 57 27 S'^ 44 5 56 33-7 55 54 2 63 I 63 5 63 27 64 II 64 20 66 23 67 I 67 10 67 22 71 >37 7" 13? 7' '3'5 69 25 66 46 66 49 65 19 61 42 62 IS 64 23 5 64 32 64 10 64 18 64 48 65 lA 66 22- Places Miscow I., Ji 8m., NE pt.,") Pt. Birch, It. F -9f. / Miramichi B., Portage 1., ■^\ 4m., S pt,lt. F45f. / Pt. Es( umeuac, It. F 70f. Richihucto Harb., [2, mo Fort Moncklon Prince Edward's I., % 33l.,1 N Cipe, It. R80f. / — HichmondB.,a, Royaltv Pi East pt.. It. R lOlif. Charlotte town, St. 1 Peter I., It. F 70f. / Magdalen Is., # 19 I. — Bird Is., 2, [7c.], E one UOf. Bi yon, or Cross I.,% 4m., \ w.Ept / East I,, E extr Doyle rf., [.ic.]. 5, 5 Entry I., [l^m.], 580f., f... AmhiTst 1., r,-Mf. w, 6,~1 Spt.,lt. All. lU7f. / — Deadinanl.,[3c.], T W. I rf. E I St. Paul I., J2 3m.. 4aUf., w ) SW, It. at N pt. F 14iif...j C. Breton I., # 33 I., C.\ North.lt R 74f. / St. Ann's Harb., m, w. Beach ) Pt,lt. F24f. J Sydney Harb., S, It. at E \ sid-, entv., F "Of / Scatari I., EW 2 1., S K, | NEpt.,lt.R 90f.,52m. ... ;" r.nuisburi;, S,w, I), It. F 1201 C. Porllan,! .Madame I., EVV 9.n., S pt. ... PiirtHi.od.ffl,w,l),J«f,te-au-1 Corps I., at entr j C. St. Lawrence NOVA SCOTIA. Sable I., i:W 7 m., 1 It. F 12-f. NW bar, NW extr., «.. PictouHarb.. ffiis.lls. 2F...e C. St. George, It. R 3.50f Gut of Canso, NW entr , It. 1 F llOf. / 0. Canso, Cranberry I., 2 Its. ^ F vert. 89f. and 54f. / White Head I., S pi., It. Fl. 55f Country Harb., ^, Green I., "1 ItF-Mf. J Wedge I, It. F8If. LiscombHaib., ^.I.ll. Alt.) 6'lf / Ship Harb., g. Briers' I., \ w, b, Bearrk. 8f. / Brig rk.,_5f., T Pollock rk., [jc], nf. Halifax, ^.[13, Dkyd. tablei Sambro I.. It. F 115f., » 2m.. IVnniinl Pt 47 5 46 42 46 3 46 34 46 27 46 7 47 5' 47 48 47 37 : 47 35 47 17 47 13 47 16 47 14 < 47 2 46 17 46 16 46 2 45 53 45 50 45 2S 46 o 47 2 43 58 45 4'- 45 53 45 4'- 45 20 45 12 45 6 45 « 44 59 44 44 44 39 44 26 44 27 64^29' 65 3 6, 48 64 5, 64 4 63 59 63 43 6i 5S 63 ic 61 97 61 25-: 61 24 5 61 S7 62 14 60 S 60 23 60 32 60 7 59 40 59 57 fio 6 61 3 61 36 60 38 59 46 60 3S 62 40-: f" 55 61 295 60 55 61 8 61 33 61 53 61 58 62 45 62 >,7 63 5 7 63 35 2 63 i} 63 37 TABLE 10 MARiriMF, POSITIONS 49) Places Mnr^arei's B , S, Shut-in I. Tamo..k I Mal:,g.Ki.li Hari... a. Cross 1 I., [liiu.]. It., 2 lis. Vert. ). disi. :kf I C.L"Have,i, 107f., (Black ) rk. Im.) j Coffin I.. It. R e.^f. Little Hope I., [2c.],2If. Gull rk.. It. B'o6f. Sliclhmne Harl)our, m. T IM-NuU's I., SK pt., i,r, I w, 2 1ts.F vert. 120f. an J 6.ir. ) Brazil rk., [3 vds.], 9f. C. Salilf, (_SE pt. of small 1 I., /, f , W en.l ailvanc- [ ing Ini. in i years), i , ( 6 .im., It. R 5.3f. J Blon le rk., small, 5 Seal I., [2m.],Spt., S I',m.,1 t, It. ]•' 9HI'. I TusketIs.PubnicoIIarl..,S \ r, w, b, tntr f C. FoiircVui, /i, *„, It. R 117f. lyineher rk., 8, small, faf. C St. Mary Bi jer's I., # 4m., It. V 9>t.... Annapolis Ilarb., g, Pt. ) Prim, It F-6i: / Black rk., pt., It. ¥ 451". Haute r.,w, $. It Int. 365f.... C. Cb gn.ctn, A. T C. Knr..gL\lt. FI20f. Quaco, It. R. Ilof. Ciuaco 1 dgr, [1 1.] C. Spi ncur Si. Jobii's, Ea, Partridge I., "t It. F ll9f / ^ C. L preau. It. F 80f. Wolf Is., jP 33m., i T,lllOf..\ Northst j Etang, barb., g, lower S pt ... St. Andrew's, S, N pt.. It. "1 F.42f / Caiiipob..llo I., N pt,, It. F \ 64f. / VNITEO STATES. Qiioddy Hd., It. F 13:if. .^... Old Proprietor shI., [lr.],rf... Grand Manau, # l-l'm., w,! r, ||W,5„NI0pt J Gannet rk., It. Fl. int CC.f. ... Libbv I., oft' Macliias B Machias Seal Is, 2 Its. \ F 66f. and .54r. J Nash's I., entr. Pleasant R. It. F47r. , Petit Manan, S pt.. It. F, Fl 125f. (5 2 to 5ni.) liakct's I., It. Fl. I05f. Castine, lu F 13Uf. I.at. N Lon. W 63^54' 64 6 64 18 44 2 43 49 43 39 64 38 64 45 65 43 37-5 65 16 43 24 43 37 43 47 43 52 44 7 44 >6 44 42 45 lo 45 151 45 "9 45 36 45 '9-5 45 14 45 12 45 «4' 45 37 44 59 5 45 4 45 4-3 44 44 49 44 30 44 46 6537 65 52 66 9 66 25 65 47 64 46 65 I 64 57 64 47 65 32 65 20 65 55 66 3-5 66 28 66 41 66 49 67 3 66 54 66 57 66 37 66 47 67 22 67 6 67 « 67 S2 6S 12 (l.-,0) PI a Owl's Head. It. F in.5f. Mt. Hcsert rk. It. F 75f. ... Cnsln's Ledge, 7" T, J [im I Haute, Ji .itn., Saddleback hdge, 10 E-d., It. F.^lf.. Matinicus I ai>d rks , [4m ], .n rk.. F 90f White Head, l,lt. F79f. .Monhi R 17Vi Petnaqii Burnt If L, [im.], T.lr. Pt., It. F T.'jf. ... nd.. It. F61f. .„ . L, It. F 180f. Casbe'sled-e, 5^, |Jm] 'ortl.ind, S, City Hall — It, W entr., F 101 f. C. Eli/.abetli,2lis,[3()0yd>.], F, Fl. and F 143f. :■:•:} Wood L, entr. Saco Harb., 1 It. F, Fl. 63f. / Agatnenticus Hills C. I'ori oisc. Goat L, SW part, It. F38f. Bald Head Boon I., [im.J, /, It. F 133f.... York Hari)., [J!=; Whale's Back, It? F. Fl. 6.5f.... Portsmouth, Fort Constitu- 1 tiou, It. F "Of. J Is. of Shoals, [3 m.], S or 1 White L, It. R87f. / Newbury Port, [B, bar sf., 1 2 leading Its. F on N pf. '. of Plumb I., movable J Ipswich Bay. It. F, Fl. 50f. ... Annisquam Harb., ij, It. "j iOf. 0. Ann.lts. NS. on Thatcher 1 I., alts. F 16.5f. (.Salvage^^ N-d., 2m.) J C..\nnHarb., ffi.lt. onTen- I Pound I., F49f. / 43 58 42 56 J44 I 43 47 U3 59 I 43 46 43 50 '43 49 I 43 416 42 50 43 39-2 43 37 43 33 6 43 27 43 '3 43 21 43 13 43 7 43 9 43 4 43 3'5 42 5S 42 41 42 39 8 42 38"4 42 36 Salem, a. City Hall Baker's 1., [^m.], 2 1 s. FS7, 1 ^'J»- J M irhlehe.id, h. F 4:!f. St. (Jeorgc's shIs., EW 7 \.,\ >^\y.o,-.h\.v:ut.: / Little George'., I-,] liosrciN, ffl, Cambridge Obs... — N side, main outer entr., \ It. R lUf. / I'h mouth, a. Gurnet Us., \ ^l'33f. ( Barn-table.H'I, bar.. It. F;i3f. I?illiug.sgatc I., It. F :,■>{ Race Pt.. It. K, Fl. ilf. C. Cod, high, or T.uro, lt.\ Fl9.5f. / Nausset, 3 lis. F 93f. Chatham Harb., 2 Its. F HOf.,1 4' 43'2 41 516 42 3 7 42 24 41 si-6 4' 403 41 33 70 19 70 41 70 26 70 34-5 70 29 70 39 70 42 70 490 70 46 70 41 70 34-7 70 40 42 31-5 70 540 42 32-2 70 47-5 42 30 2 70 so 41 43 67 47 :;2i8 68 71 77 42 197 70 537 42 02 70 36 2 70 10-5 70 45 70 15 70 4 69 57 ? 69 57? 70 oc TABLE 10 MAHITlMl!; POSITIONS (151) Place* Lat. N Lon. W (152) Place* Lat. N Lon. W Nantucket I., EW 5 l..(shls.-) "l{ii.s." E-d. 4 1.;, N,o.} Sindy Pt., It. F -Of. J Asscatcagne I., # 6 1., /, S^ 37' 55' . 4J°23' 70° 3' en.l.lt. FI53f.,shls.oft-. .. i Smith's L, # 10m., C. I 37 7 75 54 - Brant Pt., town, It. F43f.... 41 "TS 70 s? aiailes(shKot0.1lF1.160f. / N.ntuckrt, S shls., old do., 1 #2.}m..Npt / 41 S 69 so Baltimore, Batlle Monument 39 17-4 76 37-5 J — New do., KW 2\m., 8 1 pt. »f. .'. J Martha's Vineyard, EW 6 l.,\ NEpt.,orC. Puge.lt. 55f. / 40 57 69 50 Annapolis. Stiite House 3* 587 38 2 76 297 76 19 Pt. Look-out, entrance to | Potomac I{., It. F 431. ...J H .3 Washington, Capitol 18 5r4 77 2-0 1 — Holmes Harb.. ffl .WChop. 1 it.Feof. / 41 288 70 36? WashmgtonNaval Observatory New Pt. Comfort, li. F60f...". 3S 53-0 37 iS 77 27 76 17 > — ■W|.t.,Gaynd., It.PI. 10'\ i:2f. J Nomin's Land, [Im.], stat. \ Back River Pt., It. F, Fl. 35f. 76 16 70 505 36 56 Roanoke Marslies, It. F 33f... 35 49 75 42 Cutteliunk, IL V 42f., atS1 :J C. Ilatteras./,sand,(shls. 3 1.1 SE).lt.Fl. 19lf / andWpt. of Id / NewBedloid. ffl,I)umplin-,l or Hound Hill, It. V 43f./ 41 25 S 75 3> 70 557 = Oeracoke Inlet.lt. N.Mde,F7.5r. 35 65 75 59 ^ C. Loolv-out, shl. -t 3 1., U \ It. F 15Gf. J 34 37 7531 Sakonnet Pt, It. F. Fl. "Of. ... 41 265 71 12 < C. Fear, slil. -fe 5 1., Bald ] 33 52 78 llri-tol Episcopal Ch 41 400 41 496 41 295 71 17? 71 247 71 19? Head, It. F 30f. J "^ Georgetown 33 22 79 18 "s IJcaver-mil Pt., ur Khode 1. 1 North L, S pt, 32, bar if.,"! 5 It., it.Fesf. i entr.. It F 8.if. / Pt. .India., Ii. K 6:f. 41 22 71 29 C. Rom.iin, /, ♦.,ltU154f., 1 bl,.ck I., NS Sm., N pt.,\ li. F61f. J 71 35 (shl. SEd. 6ra.) J Charleston, S, Fort Ripley, ~l ltF4yf. / 32 464 79 54 1 Sionington, town, S pt., lt.1 F 5uf / 41 196 71 545 — Sullivan's I., It. F 57f. ... N Edisto Inlet 3246 32 33 79 51 80 12 New London, it. Vvcntr.FOOf. i Kalkner I., It. F, Fl. 98f. 32 26 8041 i New Have... a,ll. Fsrf. 41 145 72 54-5 Port Royal, ffi, Paris I.,\ 32 18 8040 4. 18-5 41 28 72 56-5 73 255 Back It F 1301. J Savannah Kiv..m,Jybee I., 1 It Fl50f. / Norwalk L, It^F, FK 52f.7.;'... j2 ' 8051 Long I., # 34 1., E or Mon-\ tank Pt.,lt. F, Fl. 169f.... /• 32 49 81 7 41 4-2 71 si-o Sapello L, north entr. to"l 3> 23 8. .7 i; New York, f8, Cily Hall 40 427 74 •^ DoboySound,ltF,F1.79f.J "^ Kire Nliiid It Fl lG8f Darien, town 3< 25 3' 8 "33 8. 23 ■_ Fort Tomkins It. 1' ?yf. 40 360 74 31; .-^ St. Simon's I., It. on S pt, ) .^ Princess Hay, It. F, Kl. lOTf... 40 -,04 74 132 F, Fl. 108f. ; • Sandy Hook. :» Us. V 901.1 1 Liitle Cumberland I, ^\ and 2 beacon Its. F ] ' ^o 270 74 07 5 1., N pt, (entr. St. An- J. 30 59 81 25 Nevisiiik, 2 lis., F 2481. 40 237 73 59-5 drew'sSound), It F78t..J ?■ Barnegat Inlet, S side,It.Fl.l (Shi. 2in.) ; 74 60 Amelia L,^l.'?m.,Npt,(S , ptofStMary Inlet), It. U. 30 40 Si 26 Little E^'gHaib..@a,Tuckirl beach, 1.. F, Fl. 5Jf. / 39 30 74 175 8. 25 St John's Riv., CHo.Sentr., \ Grt. Kgg ILirh.QG. bar, entr.. 39 19 74 35 .Jacksonville, It F 84f. .../ "^ C.May, (shls. bW), It. U167f S8 SS-8 74 5S-5 St .\ugustin»(bar),[Il';!, N 1 ■^ pt of Anastasia I., It F, , Fl. 165f. J 29 53 81 17 Egg L. It. K 50f. 39 " 75 8 Cohanscy Creek, It. F 46f. .. 39 21 75 22 s Musquito Inlet, coitb sidel 29 5 80 55 „ Philadelphiii. State House...® 39 570 75 95 ofent, U. F 157f. / lU-cdy I., b. Fl. .lef. 39 30 75 34 C. Canaveral, w, north-east 1 28 28 8032 ^ Bombay llnok, It. F 46f. 39 217 75 3' pitch. It R 139f. ; -s 39 345 39 >i 75 36 75 24 27 33 2657 26 9 8023 80 5 80 3 Mabon's Kiver. It. F STf. Jupiter Inlet entr., It F&1 C. Henlopen, (J 2 1. 8\V), 1 ^ ll.K IL'BC. /® 38 466 75 5 Fl. U6f. / .New Iliv. Inlet, fort Delaware Breakwaier, westl end, It. K, Fl. 47f. j 38478 C. Florida, Fowey rocks. It \ FUlf. J 2535 80 6 620 TABLE 10 MARITIME POSITIONS (153) Places Lat. N Lon. W ( 54) Places Lat. N Lon. W 25 24 49 8o°i2'7 80 30 80 445 Samana, or Attwood's Cay,"l *,T,Wpt J Plana Cays, EW 10m.,/, t, I T, hill, Wpt., t. 1., w'... J Taramer Cay, S 1 I 23 55 73° 49' Lo«erM.>tacumba I„ # 3m.,-| wpt. (w"'N) y 22 35 73 38 1 Sombrero Cav, It. F U4f 24 375 81 67 Marignana I., rf. EW lOl.,) Sand Cay, It. r,ri. llOf. 24 27 81 527 ',t,T,S, Centre hill, HOC; " tt CajWesi.NWpass.,lt.F50f.... 24 .57 81 U Hoistv rf., EW 5m., T , 5. 1 -sS.'.i;;ss ".■!■".'::':}!- 334.. ,ss -« NWCay r ^ 1 Grt.lnagua.^Lil.,/, t,ll.RI20f 20 56 73 41 TortugasE\V9m.,shIs.W) | — Man of War B , W s.de. well 71 4 73 39 •ll.,,;Wpt.,ForiJeffer- e 24 38 S2 S3 Little Inagiia, EW 3 1.. N pt... 21 3^ 73 son, It. F 65f., (5 6m._)J Caicosbk., ^ 22 1., Srk 21 3 7' 45 ■^ - \Ve< Caicos, # 7m.. S pt. 21 37 72 30 BAHAMA ZSX.ANOS. ^ - Ea-t Harbour, wat. pi Turk's Is., # 6 1., N extr.,1 21 31 7" 32 7! 8 Matanilla, shl. [5], T 79 4 79 7 It. Fl. I08f. / ^' Memory rk., [ic.l, Uf.? T ... 26,7 - Hawk's Ne^t, ■»w„.$;J;, e'21 263 71 los B«hama I., EW 22 ).. W, or 1 Seulement Pt., ? / 26 41 79 7 71 "8 Sq lare Handkerchief, EW \ -"Soalli-east"Pt.(socall-l 6d), [t] K, w / 26 28 78 40 30m., NE breaker / Silver rk.. % 15 1., Cay, (^ 6958 Grt. A bacon I., % 23 1., It. \ SWrE ...J nearS pt., R 160f. / East Pt North rks 53 35 69 55 69 22 68 53 =q 26 20 76 59 76 58 20 ElbnwCays,*,U. Fl23f. 26 31 Bajo Navidad, / 7 l.,N pt.n, T Greai Bahama Bk.,i|j 110 1..-) , . Grt Isaac rk.. [|,n.], 4nf. f Bernini Is., [7m.],/, ?,SW\^ pt.. w J CUBA. 25 41 Cuba, flj 217 1., E pt., C.~l Gun Cav, It. R 80f. 25 34-5 24 56 79 '9 79 9-0 Ma\si, It. F 128f., /,rf. Im./ Barracoa. fort ..0 Orange Cays, Id., [|m.],13f.,-l Cay Guinchos 20 21 41 \ 74 28-5 74 5.i 75 36'5 75 50 C. .Moa, Cay, »' . 22 45^ 22 22-8 78 8 77 35 5 Pt. Lncrecia, It. R H2f. ?I I-obosCay, T,lt. F 146f. Port Naranio, K, Wpt., /I, i 21 Diamond Pt., 5T T " 10 -ort del Padre, g ->! 7625 77 8-7 St. Domingo Cay, 15t., 1 f ... 21 42 75 45 Pt. Maternillos, It. R 176f.. ... 21 40 C.y Verde, -2f. 75 II-5 I. Guajaba, \ 10m., W pt. ... 21 5S 77 36- Grt.Ragiied I., beac. h,ll 1 15f. AVaterCav. [l.\m.] Cay Confites 77 39 78 19 23 75 44 ® Cayo Romano, 2 is., ife 16l.,\ Long I., 4,19 1.,/, f, T.Npt 23 41 75 '9 NWpt J '■- -5 22 51 23 56-5 74 51 80 28 19 7748 80 250 CaySalbank,N.Elbow,lt.F96f Cay Sal, bk., %2U1.,4, Cayl ca Exun,al.,%8 l.,entr.harh.E 23 33 75 4S .. Sal, [im.], w. =f.Npt....J EleutheraI,%22l.,t.T,Si)t 24 -^i 25 9 25 3S 76 9 76 9 76 44 23 24 56-5 -Dogrks., i|j 5m., Ept -Anguillals., ^7m., w„,-| spt / 79 5' ^: -Npt.,hill,(shIs.EaridW3l.) „ E'.'g and Royal Is., West I. ... 25 30 76 55 = New Providence I., EW 5 1., 1 25 56 Nicolrto rf., Medano I , S-d. ... ^1 12 80 21 -?, Xass.iu, mv,. It. F68f.... 1 Bahia de Cadiz, It. R IT.'if. ... 23 12 So 30 =q - E pt., Goulding Cay, w SW; 25 7 | 77 36 Green Cay, [2m.], ^Z 124 3 1 77 > i Piedras Cay, It. F. Fl Matanzas,Bay, T .S.Severmu \ Castle...... / 23 .4-2 81 87 81 37 Andros I., % 32 1., Masiic Pt... . 25 4 77 57 Berry Is., NS 9 1., T,w, r,l Pan de Matanzas, 1277f. 23 iq 81 45 E lim., or Frozen Cav ... } HAVANA,aM0RK0ll.R144f. 23 p-4 82 2.-5 Great Stirrup Cavs.r.lt. F" flf. 25 49 7 77 54 Managua Paps, 2, EW 2m., I 57 82 22 Little Salvador, % 5m.. W pt 24 36 732f., Wone / ■"■ St. Salvador, % 14 1., NW pi — East pL( Columbus's lanilfidl 24 41 24 8 7546 75 >7 Port Mariel, ffi entr. 23 23 8244 83 i>7 Bahia Honda, S CerroMorillo Concepeionrandrks. 2l.],5, 1 /, f . T, I'd. Wpt / 23 50 75 8 Pan de Guaijaibon, 2532f. 22 48 83 24- 8448 Cdlorados rfs, rks., 5, T , W pt Wailing's I., -^ 5 1., Dixon ~l 24 6 7426 W extr., C. St. Antonio, /. 1 t,T,rky.,(shl.2t-"m.,iii), ) 21 li. R128f. J Hill. It. Fl. 165f. / S) 84 572 R.imCay, EW3l.,ww„.Spt 23 37 74 5° Mira por vos, % 3 1., S, NE rk.j 22 6 74 28 C. Con-ientes, /, sand, f 21 4S-1 84 3> Crooked I.,,J* 14 l.,$^,ww,.l fi , ., ,„., Spt,, Castle I.. It. V iLW./l" ^ /4 20 5 - Bir.l Ruck, It. R IWf. 22 50 5I 74 2J 83 50 5 8332 CaysofSanFelipe,SWpart.1 _, „ T. l\m /Oj^'' 55 TABI;E 10 MAUniMK POSITIONS 058) Places I. of I'incs, K\V 16 1., S pt. .. Kosario Channel, 3, S vnt Jardint'S, w'", E extr Cay de Fiedras. It. F 27f. Pl;icer de Xagua, [3m.], 1 .. Xagiia a, ffi,lt.F, Fl. 82f. ... Trinidad, mole Cavo Blanco, 20f. Manzanillo O C. de Cruz, rf. 2m., T,lt. F,l '■•'•114t. / Tarquino Pk., 8.400r Sastiaoo de Cuba, g, r,"l w, It. F,F1. 228f.,Murro I Castle J — Rlanca Battery Guantanamo.orCuniberland \ Harb., g, E head j" Cayman Brack, sji 31., t,Ept l.itt. Cavnian, ^ 7m., /, 3 f . \ Eend / Grt. Cayman, EVV 6 !.,/,■] f .t,* *o, w„r,town, © Fnrt Guur-e J -Kastpt., t,/3 1n. 2I°24'4 82-56' 21 37 81 55 21 39 81 2 31 SS 81 3 21 37 8035 22 43 82 18 22 I 80 30 21 42 79 59 21 36-6 79 53-5 20 20 77 10 >9 499 77 455 19 56 I 76 45 •9 574 75 52? I 20 0O-3 75 505 19 452 79 44 19 42 ! 79 58 19 177 Si IQ 19 JAMAICA. Jamaica, % 43 l.,E pt.,or Pt.~| .Morant, It. R ll.if. J Port Antonio, 2 g, w, fort, | It. F54f. / St. Ann's B., S, I.rf>ng wharf, w Falmouth Ilarb., Q3 ", bar, fort Monteijo B.,fort Lucia Harb.,, Ept., ^,l,^j' ST. DOMINGO. St. Dominjjo.EW 1 20 1., E pt., \ C. Engano.(5hl. N 3m.)... / C.Kafael, .Mt. Rcdonda, 2m. \ inland / 17 551 76 117 18 11-3! 76 18 264' 77 18 306 77 18 294. 77 18 28 1 7i 18 28 i 78 18 21-4 78 18 23 i 78 18 168 78 18 123! 78 17 51 j 77 17 48-5 77 '7 43 I 77 17 5i-5 77 17 560 76 76 >7 52 ■7 53 17 25 16 48 ■7 36 17 6 IS S3 17 25 18 33 8 „.] 68 187 685s (,1.16) Placet Eat. N lx>n. W Town of Savana la Mar, fort C. Samana, rugged. A, i 2^ Port Plata, It. R 137f. Old C. Franvais, ^ Pt. Lsabelle Monte Christi B.,*, f, w C. Haytieii Harb., ffi, w, t,\ turret d'Estaing J Aeul, S : 'Tortuga I., % 7 I., E pt.. / ... Nicolas' Mole, S, « , Fort \ St. George / Cape Fou aives, ffl. Pi. Vcrrier St. Marcos Pt, h, i Gonaive I., ^ 10 1., f , \V pt. Port-au-Prince, r, w'. Fort \ Alexander. It. F 461'.^..... ( Roclulois shl., [1 I.], rks.,3f. Cavmites,*, 5 || S, Sliuf. NE pt. C.'D.ime Maiie, W pt., (w 1 SE2m.) ; C. Tiberun, A, ^, T, ^y, hi in bay) / La Hotte niouniain-i, 740Uf. ... NavasaI.,r2m.].300f.,T, ^.l /<-, f, mid. N side / Formigas shl., ^ 2 1., 5, N pt Pt. Gravois I. Vache, [3 I.], T S, NW pt. Aux Cayes C. Jaquemel, ffi. Wharf Mountain, 8900f. C. False Beata L, NS 4m., I, f, t\ NW, NW pt, 80f. / Fraylc rk., 50f. Alta Vela, A, T,-'>00f C. Mongon .„ Pt. Avarena I't Caldera, or Salinas Pt Nisao St Domingo, City, K'%\ Consulate. It R IIU. J L Saoiia, EW 4 l.,X,Cana Pt Mona L, EW 6m , C-', w,"! W end, B, rfs. 2m.), I75f., C. San Juan J DesechoI.,[lui.],T,t,vis.l2l. POKTO RICO. Aguila Pt., Ir. R 128f. Siioal>i 2 I. off W coat, Bajo Galhmio. [:,] B of Mayaguez, U. F AguaililU B, It. Fl., r. w'" Porto Rico, g. Morko, It R I74f. NE extr.. orC. Juan, (rks.). It F, Fl. 266f. Anvil, 3700f. SE pt.. C. Mala Pusq Caxo de Muertus I., [Im.], ( * W 8), S rk.. It F, Fl. 297r. ,90 3' [9 18 19 47 19 40 19 57 '9 53 19 467 19 45 20 I •9 495 19 44 19 257 19 2 18 554 18 33-2 18 39 "8 .39 18 -^6 18 22 18 23 18 25 '8 35 18 I 18 6 18 12 18 13-5 18 21 17 45 17 367 ■7 57 17 28 17 50 18 7 i8 12 18 13 ■8 3 18 227 17 58 69 8 70 38 (,9 52 71 I 71 40 72 117 72 22 72 34 73 22-, 73 29 72 427 72 50 73 18 » 72 20 73 13 73 40 74 27 74 28 74 3 75 2 75 45 73 56 73 43 73 46 72 33 72 o 71 40 7' 32 71 41 69 52 68 32 67 51 67 292 67 IS 67 21 285 67 289' 66 75 18 23 18 19 17 59 65 36 65 47 65 49 6634 TABLE 10 MAKITLMli POSITIONS 1 (157) Places 1 Lat. N Lon. W (158) Places 1 Lat. N Lon.W Port Ponce It Fl 39f. 17° 58' 66° 40' 06 57 Guadeloupe, Vieux Fort, pt....| I5°S7' — Basse Tei re. Fort Irois ® 16 05 6 1 "42' Pt, Guanica ,_ 61 45? — Souffricre, vole. .'j.iOUf 16 5 61 39 CARZBBEE ISIiANDS. 1 De'irade, # "m , N pt 16 21 4 16 10 s ?.v Petite TeiTe, It F IU8f. C.ilel>ra,orPassagL.I.,%7m,] (ffi SE. w,f,b),Culebrita ^ Mane Galante,% 10m., w W, 1 IS 54 61 19 18 19 65 14 " GrandBjurg,lt.F. 46f.....J St. Thomas I., % 4 1., ffi, ] Dominica, % 9 1., A, 5„ lm.,\ IS 38 El. r, 1.. F 95f., E eutr., FortChristian J IS 20-4 64 55-7 4747f., N pt J — Kosean, t.wn. It. F 15 174 61 23 IS 14 18 181 64 51 64 42 '5 13 1 St. John'sI.,KW;jI., liamHd >)„r ,an I., 4Wf., Man of^ War H., on W side. S.N pi. J 18 20 64 37 Avesl.. [lie], 10f.,w?*W... 15 42 63 37 7 Toriola, # lrn,..ali. 1780f. ( Town, S.w.r.Fort Hurt Pt./ .8 25 I 64 365 Martinique, % 11 1., Mt.\ Pelee, 4428f. J 1448 61 10 ,■!: G.ngerl.. [Im.] 5J0f., i ... 18 24 64 28 S- — St.Pikbkk.St.Marthe, \ 14 43-9 61 II? •^ Virgin Gorda, ^ 3 1., pk 1 1370f.. Fast pt / 64 18 5 .? Battery. Its. 2 F J ; — Fortli03al.a3.lt. F laif... 14.3b 61 4? Anegarta,% 3 !.,/,*. 8,(1 f. SKI, 3 1.).Wpt.,w,30f. J 14 48 5 60 52 60 53 18 45 64 247 — Caravel rk., 96f., *o. " - Sta. Cruz, ^ 7 1., 1184f. \V,1 •7 45 6434 St.Lucia,NS10l.,4000f.,Npt. 14 5 6057 6 E pt . / -Port Castries, S.Vigie,! It. FSOOf. (■ 61 I 1 — Christianstced, g, Lang's T OBsfiRVATOBV, Transit pier, It. F J >7 447 64 4'? - Wpt.,2Sugarloaves,4M,\ *. vis. 16 1 J 13 47 61 5 « Sombrero, [>.],/./■, w^,-| St. Vincent L,NS 5 1., 3000f... 13 23 61 II ^,37f., *„lt. li l.iuf; ^ ■-;; — Kingston, Fort Charlotte, 1 13 9 13 5 61 13? 61 12 "'^^:.^^:!l.'-":^:}® It F 640f 1 18 .67 63 15-5 Bequia I,5|i2l,*'W, w',1 Anguilla,a^l4m.,213f.,w„,-| ^ Cust. ho J ® 18 132 63 4? a Admiralty Bay, f,b,Npt. J St.MartinI.,EW8m.,w„,r,\ b, sum. 136ir. J 18 s 63 3? Grenada, -^ 51., 2749f., (a^l 2m.),Spt / II 59 61 42 — Fort Mavigot, It. F 66f. ® IS 41 63 5-5 — St. George, S.El, tort,lt.F 12 3 61 45 S. Bartholomew, % 5m., N \ 62 48s Pk-992f. J Barbados, % 6 1., 1104f.,) Ept.,lt.,|B J 13 99 59 255 Saba [3in.]. A, T,2820r. St.Eiistaiiiis,4|,4m.,A,I950f.,-) 17 3« 17 292 63 14 62 S9 13 57 13 5-2 59 37? 59 367 1 — BriJ-ctown, Engr.'s Wharf ■s St. Christopher, ^ 6 1., vv, r, ) Mt. Misery. 4313f. j — St. George's Ch.. It. F 37f Nevis, [21.], w, r. 3.595f sum 17 22 62 48 GTJI.P OP MEXICO. 25 7 25 51 81 S 8. 42 .7 IS 17 12 6243 62 33 C. Romano,/, »,(bk. SW 1 9m.,;.f.) r — Charleston, SW pt., w 17 88 62 36 Saniahel I., (2i''-, r, w, b, U.-\ F, Fl., P8I-. / 2627 82 1 Harbuda, ^ Urn., vis. 6 l.,"! »„. r, * BWpt.;S&Ept.. Tampa B., Fgmoiit Cay at \ entr It F SCf. / ® 27 36- 1 82 46 17 33 61 43 5 1 1 2nof J '7 3S-8 61 495 .\ni'lole Cavs. It. Fl. lUOf. ... Cedar Cays; Depot Cay, (sill. \ ,1- 7m.). It. F. Fl. 7.^f. ... / 28 10 29 6 8252 83 4 — River fort, SW side © A.NTiGt;A,%12m.(5N),l.S30f.l 17 6-2 61 505 -a St. Miirk's, It. H entr. F 83f... 30 4-4 84 10-5 Sr.JonN'sCATHE..UAi.r'| ~= Dog L, [6m.]. II 3 E, ||„ W.... 29 46-3 84 38? -English Ilarb., a,^^ E), I Dockyd., flagstaff / 17 00 61 45-7 St. George I, (Harb.Sl '">,■( C. St. George, lt.F73f.J* 29 35 3 85 3 — Boggy "s Pk., 1.339f. Ucdondo, * ., 600t'., * n 1 ^ W T ( 17 a 1 61 51 16 555 62 iS 7 C. St. Bias./, (shl. -|r4m.),-l lt.Fl. 198f. J 29 40 85 ii Montserrat, sjj 3 ]., 3OIIOI'., \ w, T,Npt ; 16 49-31 62 117 P.nacolaB.. ffi. Fort Bar- "1, rancMS, It. Fl 210'. ( 30 20 S 87 19 — Plymouth, w', l,„ll. Follf 16 422 62 13 Mobile, m. It. E entr., R 33f 30 136 88 07 GuaJe!oupe,[12I.],487iif.Npt 16 11 1 61 26 s — Choctaw Pt.,lt. F47f. 30 40 S8 TABLE 10 623 MAUITIME POSITIONS 59) Places Ship I., tf ""i-i f ; w N, 1 mid. i \V pt.. It V 54t'... ; * Car 1., EVV 5m., f , W pt.,\ It. F / Clianiteltur Is., ^.1, w.h, |o \ SW, It. N pt, F58f. / Mississippi Uiv., NU puss., \ Frank's I ; — South Pass, It. Kl. 108f. ... — SW Pass, It F I28f. New Orleans, Citv Hall T.mbalier I., fV 7m, It. F.l Kl. Illf. / Ship I., sho»l, It. K U5f. South wist reef. It. F 56f. .. .«ahinc Puss, Texas Pt., bar"! «f., nionnd. It. l"l. 85f. ... / Bolivar Pt., It. F 117f. Galvest. n I., # 7 1., A 3 t \ mid., NEpt / San Luis Hatb., bar T5f., town .\l!.tigorda Ua)-, bar sf.. It. F ( •Jif. / Ariinsa« Pass, 8f., It F 59f. ... S.intiago, iiarra de, Tf., It F 1 60f. ( Kio Grande, or Bravo del\ Noi te, U.S. Observatory J MEXICO. I!i.. Fernando, or Tigre .. O B.irrade Santaiider. ..f. O B ,rra del Cie'ia o' (.'erro delMecute. 10m. in hind J I Tampico. b.ir isf., 5,fl. St. "> ' It Fl. Hlf. C. Roxo I.ai. N Lon. W 30°I2'6 88°58' 30 137 89 10 88 53 89 o 89 10 89 235 90 67 90 21 91 5 9' 3° 93 5' 94 457 94 457 95 6 96 25 27 51-5' 97 3 26 6 I 97 10 25 574 97 7-2 30 3 29 tis 29 28 s8-5 29 577 29 3 28 55 29 23 29 43 29 22 29 21 29 4 28 2C-2 Lobos I., [am.], 35f., f,} ^ w, f, (rf. N2m.) / ^ Tuspam shI., islets, t ' Mexico, city, St. Augustine ... Vkba Cbuz, w, rr,,, San"l Juan de Ulloa, It. R "9f. / Sacr ficios 1., [and rf. Am.] ... Oriziba, mount, 17,895f. Core del Pcroic, Pk., 13,995f. Alvarado, bar of. 8, It F 2461'. Tii.\tla. volcano li.xa P.irtida, w, f I't. Znpotitlan, 1 ?,»•'" ...Q Goaza' i>aln, w, h I<;rnia, Ch. in square, t ■ »'... I'nmpcclic, X', *, r. Fort) San Jo»c, It F'J.-.r. / 25 23 23 48 22 38 22 47 22 16 21 35 21 2S 21 I 19 257 19 125 !9 10-2! 19 5 19 29 18 51 18 30 18 44 ■8 35 18 10 18 38 98 43 97 52 98 3 97 49 97 22 97 «3 97 10 99 S 96 8 96 5 5 97 «5 97 7 95 48 95 9 95 3 94 48 94 26 92 44 18 38-4' 91 53 19 2t ; 19 484, 90 44 90 3*': 19 so I 90 33 (160) Places Cclestun, It. F95f. Pt Palmas, f Sisal, $,. w, b, fort, Itl I F60f. J - Sisalrk..[fin.], 6f.,(Siiake I 2 I and Madagascar slils. } I I NW-d7 1.) i J, Progresso, It. F 57f. Lagartos, R. San Felipe .. I C. Catochc, /, t,(Nptof Jolbos I., ^ 6 1.) Contoy I., % 4m., /, ?, N pt. Mugeresl.,^5m..80f.,l: t^,\ w, b, S pt, Stone turret... J Cozumell., ^ 8 1., 70f., t,l Npt '..J Ascension B., Noja spit 20° 53' le Areas, [2ra.],rks., *,VVCay Obispo, shls., 2, ji 5m., s, ||, N one, beac. buoy Triangles, 3 Is., # 7m., /, \ rk., *„, '<-, b, E one ... J Engli,hhank, [s] Baxo Nucvo, [2e.], xf.,\ /, 5, beac.35f. ; Cay Arenas, Sandy I., [•'Jm,], /, -^, beac. 20f.,N pt Alacranes, % 5 I., rks., 5, Whale rock -Port,lIl,PerezI.,[4c.],1 huts / BONSVRAS. Chinchorrobk., or Northern Triangles, 8 1., Great Cay, Npt Ambergris I., or Cay, E or Rietl't, J 2m — S pt Ltho reef, # 10 1., SE pt. Half Moon Cay, J.h.FfSf. Turiieffe, rfs.,# 10 1., Man- ger Ciiy, 3 Its. F53f., 49f. Glover rt, ^ 5 1., 8 pt Belize, ffl. Fort St George, *,,lt. F4:;f. Dolphin Hd., 5ra. inland .... Cockscomb Mt. 4000f. Pt. Icaeos. (V N Sm.) li. Dulce, ciitr., W pt C. Three Pts., /, -f , (shls. 4 or 5 I.), NW pt, w, Omou, St Fernando, fort ... Saddle hill, 1760f. Sal roiks, pt fangn-jo Pk., 8040f. TruxiUo, fort C. Honduras, or Caslilla, / . lUillal., ji^ 7m., !, NEpk. Salu.adina shl.. [Im.J llogls.fl I.], highest hiin on W. I / Rattan I., if 9 1., } , Coxen bay. It F >8 37 18 6 iS 23 17 12 17 36 16 41 17 293 >7 17 I 16 48 I 16 143 «S 49 15 58 >5 47'2 15 450 '5 55 15 38 '5 55 7 16 2 16 75 '5 54 <5 58 16 18 90<>24' 90 IS 93 2-; 87 6 86 49 S6 40 ■ 86 44 7 87 27 91 59-2 92 13 92 13 91 56 92 5 91 23 89 49 89 43 2 S7 20 87 50 87 23 87 i3 87 46 87 53 88 13 85 24 88 38 88 36 88 47 88 39 5 88 3 7 87 58' 87 38 86 53 85 59-: 86 4 !-6 52 7 87 4' 86 32 7 8635 624 TABLE 10 MARITIME POSITIONS (161) Places Rattan Is.. Port Koyal narb.,\ ffi,w',f,C.c'orgeC;iy,N Wpt. ) Baihuret I.. 5 1 I. E Bonacca I., jft 3 1., gg NW 1 andSE,/', t ,f,sum. 1200f. ( Misteriiisa bk., gp-8 I. n.S pt. rs Swan Is., 2, E\V 4m., W 1 one, T.w^r, Ept J ® Poyas Pk., 3700f., 12m. inland C. Camarun, projecting, I Black R.,bar8, w', b P.itook R Caratasca lag., entr. Bf., E pt .. False Cape. A, S shl C. Gracias a Dies, /, f, w^, b.. Bank off C. Gracias, N part... — East exir., n Caxones,or Hobbies,^ 41.. E pt. CayGorda,[2m.],»o,c3E-d. \ 2 1) J Margate rf., % lOin , E pt. ... MosquiloCays, f 601'., (wW \ 5m., t S I), SE part j Rosalind bk., SE shl. part, I «. [s™-] I Serranilla bk., Cays. EW \ 25m. S, beacon Cay, «f. I Serrana bk., ^ 6 1., 8, SW | Cay, 32f. / QuiiaSnenobk.,rf.,NS81.,S pi. Kcmcador Cay, ^ 6m., 7f., * , \ w.Spt. T I Old ProvidiDceand CatnlinaT Is., [rfs. 5 1.], w'W, b, r, ^ *oW, sum. U90f. J St. Andrew's I., ^ 8m., 50f. , ( w'", r', SW cove ( Courtown bk., ^ 7ra., SW) Cay, f„.w ( Albuquerque Cays, [4m.], $ VV Brangman's Bluff, tl S, w, |.. Rio Grande, bar ef. P. ail Laioon. entr., N pt. (slil.' Slewfi,lds. ml=, (shifting V bar), r.Wpt. of Uuff. / Little Corn I.,/, f ,[Um.],l Wpk ) GreatCornI,5}«2.im.,A, f,\ w„b,r,* *„SVVpt.,snm. J Pajaro I., small, 155f. San Juan de Nicaragua,"! (called Grey-town, 1848), ' [$], w'" upriv., b. r ... I Pt. Arenas <£ Mt. Cartago. ll,100f. 6 Pt. Blanco, Grape Cay, E\ ofdo.,(w\Vlm.),lt.F60f./ ® Curreta Pt., w W 2m Boca del Toro, g, fort, w' \ -ilm.. r„,b / Blanco Pk.. ll,740f. Shepherd's Harb., a, Cay, 1 \ 2^in., White hut ... / Zapadilli Ca>;, % 3m., E p Eat. N Lon. W 6°24'3 86°I9'2 6 26 6 28 8 44 7 25 5 44 6 o 5 57 S 49 5 237, S3 43 5 13 ' «3 22 4 59 I S3 n 85 55 S3 53 84 56 85 3 84 56 84 18 ' 59-3 2 170 2 9: ' 3« o 55 o 567 »2 10 80 56 83 6 80 17 79 5« 80 24 81 9 80 2 Si 29 81 54 83 22 83 32 83 38 83 41 82 36 82 597 8343 83 43 83 43? 83 48 83 25 82 40 9 20-5' 82 IS-? 9 >7 j S3 4 9 144, 82 207 9 '5 82 2 Places Chiriqui, lag., S, Chical Molariv J * Valiente Pk., 72-2f. © Escudo I., % 2^m., /, f ,1 ^ wWpt. J ® High pk., 5251f., (^ 6m. \ of Buppan bluff) ( '^ Castle Choco, 6342f., 5 I.l inland J XSTHMVS OFFAM AKA. Chagre. w riv., rr^,, San | Lorenzo, fort f AspiNWAi.L, or Coi.o.v, It. F 60f. Porto Bcllo, rr„, @, Fort | St. Jeronvmo / Farallon Su'cio, rk Pt. Manzanilla, A, i e Pt. San Bias, /, (rf 2m.) ...e Mandinga, if .Muletas Archipelago, E pt. ... Pt. Musqnitos Finns L, [lm.],A, t,NEpt... C.Tiburon, i,A,rky.,( J;ii \V) Pt. Caribana, (shl. ^ 5m.) ... I. Fuerte, [I^m ], -^^^, ?• f ,5 CispataHarb.,S,Eastpi.Zapote Santiago de Tuln, E entr. San Bernardo Is., [3 1.], /. t ,\ Nst. one / Tortuja shls.. 2, outer, [:] ... Rosirio Is., [2 1.], Wtt. one... Cartagena, ffi, Dome ffi — Entrance, fort, It. F 60f ... Pt. Canoas, /, A, over, (rks. 1 S W-d. 3m. 5f.) / Pt. Galra, / PurtSahaniUa.a, It. F,F1.98f. MagdalenaRiv.,bar, ||;j,b,w„"(^ C. Augusta / Sta.Marta,S,Morro,lt.F328f© C. Ajjuja, i , A, T , (rks. 3c.) C. San Juan de Guia Haclia, 5, It. F 9nf. Vela, (islet 2c. off. 5„), E pt. Bahia Honda, * ', 8 shl. in I mid. entr., E pt J Pt. Gallinas, (shl. 2m.) Druid shl., [2], T E Pt. Espada Zapara Castle Maracaybo, G],,_., bar, entr., "| (shifts) /■ — Town, 2(Jm. up the lake, \ti(. Pt. Arenas Caro Pi. Cardon, I C. San Roman Pt. ManzaniUa 8°59'o 8i°55'7 9 >o-5; 81 55 9 64 81 345 8 427 837 9 197 9 22-; 9 325 9 39 9 39 9 35 8 38 9 24 9 24 9 31 0256 o 19 o 34 47 1 o I 6 I 15 VENEZVEIiA. Monjes, S„. N rks , Oruba I., ^ 5 1., Purt Ca-\ hallos, It. Curasao 1., ^ 12 1., Mo Christof S. Christoffel, 1200f. 2 29 2 29 ^ABLE 10 625 MARITIME POSITIONS (16.1) L,t. N Lon. W Curasao, Rif fort, St. Ann, S LilllcCura9ao,(2m.],/.lt.K7r)f biien Avr« I., ^t, 6 1., l-acrel pt.. It. F85f. / Avcs Is.. 2 grp-, E\V 5 l.,"l Wonc, [2 1.]..-, Sid..../ I.OS Roqnes, K\V 8 I., Poril i:i Koquo, N side. * ', w, ^^ h, N pt..lt. R2(i8f. J Orchila, [Ttn.], W pt., rk. IOC St. Juan H.. Cay St. Juan...e Tucacas. S, Oiv house Porto Caliello, m< It- Fl.82f.... La Guiiyra. * „ «•, r'.Trio- \ ^ chera Bastion, It. K300f. / ^ Caraccas, .lOOOf., 7m. inland- Peak, or Silla de Caracuas, 1 5m. itiland, 8:.00r. J Pt Maspa, (rks. off) Oniinella, 70f. C. Codcra. /, T , ( * ' W 7, 1 Corsair B.), W pt / Morro.ol Barcelona,(City -|j 1 21m) / Cumaiia, Fort Antonio, w'.lt. "1 F44f. J Pt. Escai^eo Tonuga I.,K\V4 1., Oriental I't. Blanquilla I.. NS 2 1., (;,*„,) 5„, w W, 5:N\V), Npt..../ Herinanos. % I Om., T , S„. S rk. Margarita I.. E\V 12 1., (N I Coast 5„), N pL, C. I.-ila / — Pampatar, Cas.le — West extr iSolal., rk. 5 Tpsii-os U., ifc 2im., 5„, $ ") S\V 8, w„ vis. i I., Grt. I./ Carupano B., It. F 13()f. Iiree P.iints, 5„ iin (Wpt. of Dragon's 1 Mouth) Pt. Fdleto, moui nuco R of Ori- \ / TrlDldad and Tobag:o. Trinidad, .|^ 20 1., V. pt., PU 1 Galera, /. rky J — Guajgiiarare Bay — Cliacachacare I., [2m.]. "| 8.3(if., E fide of Dra [ gon's Moutli). snm. ... ) — PoKT Spain, ffi, fort It. F "( .SOf. / — West pt., Pt. Icacos, T , It. \ F39f. ( — SIC pt., Pt. Galcota, vis. 61. Tobapo, j> 8 L. N pt., Mar- ( Mel / — .S\V , It., shoal, fini. S\V ... — U...kly li.iy. It. FonEpt... CVZANA. Orinoco. F, mo, (shls.),rrah 1-. [•I i J. N pt 66 38-5 10 36C1 66 56 5 36 66 7 5 10 63 54 10 38 8 42 1 to sj P'. Barima, It. v. F, !i,5nf.. Mocomoco Pt R. Giiayama. entr.. (bk. N 6 1., "( hills to SW-d. inland) ...j Ceo Pt.,/,. f o:- C. Nas-au, E pt. of Pauroma K.,(sl.l.) R. Esseqniho, beacon E of Lejtuwan I / — Fort Zealand R.Di'merara. HI'?, b.ir, I ea< (5or6f 9Tn Ed.inl8J4) ) Georgetown, li. R Id.tl. Berhice R , shl.. [B, bar if.. Crab I., [Im.], /, t J — F.-rtYork Coreiityn R., (shls. 3 I.),) Nickerie Fort Coppcname R.. E pt , entr. G R. Surinam.Fiirt Am-tcrdam.. — Paramaribo, Church Post Orange R Maroni, W Dt.,lt. F 76f. .. Maua K, Establ. on W bk. Saint, or Devil's Is.. .S,[am.],~| * -fe, Sone. w, it. F 197f./ Cayenne, ffi, fort, li. F l:!Of.. ^Mother rk., [^m.], jiilot sign.. Gunner's Is., jp^ 2m., E, or) g't.one i Pt. BL-hague, /, f , at E entr. "( of Aproiiak Riv / Argent Monnt C. Orange, /, t C. Cachipimr, /, t,NEpart.. Mt. Maye Mar,ica I., [3 I.], /, Old Cape) Noith Cabo do Norte O B..iliqne I., [7m.], N pt. , .Macapa, fort MeNiaiiaI.,j|i II I., 8 W, 1 Kpt / BRAZIIi. Krescas 1., [2i^.']" ......... C. Ma;:oari, NE pt I*AR,v, Custom House ... liraganza shl. and bks., % \ 7 1, It. F,30f. J Salinas, vill ,S Cajetuba I., N pt Aialaia Pt., It. Rev Caiie Is., NE part C. Giirujii, N pt Pi. Tamaiidua I. St. .loao, j|4 4 1,1, w. It. ) F 78f. J ItaclumiPt., t,li.R 147f. . Maranli.tm, lE;i.*'.''tCtt-"l thednil... ^ / Coroa Grande shl., rks.. eeni F.,rt St. Marcos, It. F 119f 656 TABLE 10 MAKITIXIE POSITIONS Places Lat. S Lon. W Places Manoel I.uiz slil., jT., [1 l],l , Wo, ^" rl< / Silvashl I. St. Anna, [:m.], (rls. -f 1 1.), t.lt. R 190 f. .../ T.aiK/oes Uiandis, W pt " anaVelha, B. Paranuliyba,! It. F i Jeiicoicoara w, r, E sand | ill / Almufedas, vill., S:oeple in t Mt. Milancias, isolaicd sand 1 11 J Ceara, Clinrch tower Pt. Macoripe, It. F 8.if. , Ja;:uardie I}., bar, $0^, w,"\ N pt., It. F / Morro Tib:io, red sand hill .. Pt. do Mel, t ? Cslils.), N"! pt J Pi. T.ibaiao, N sand hill Ureas, sills., 3, T N, N edge.. C. St. Roque, /, i Rio Grande do None, g, | Circular Fort on Icdgu, > (w im.), It. F 43f. J Piirahvbado Norte Riv.,[Jl'f, 1 Pedra Secca, It. R 52f. ... / Fort Cabcdello, f C. Braneo. sand, 1 ,(2 J at pt ? ) Pt. de Giiia. E extr. of S. Amer Olinda Pt.,It. Oec PernambUiO, [H 'f„ bar, w', 1 ti, Fort Picao,"lt. R I C. St.Agostinho 5s^, t ,Cli. sum Mt. Sellada, S yk St.AleixoI., [2c.], w Tatnandare, S, fort Mae.io J , w, fort, ( * ^, It. R 1 208f.) / K.St. Francisco. S, or Samoco ( Ft.,/, t, $ lira.,lt. F59f./ Itabajana Mts., sum 'IVes Irniaos. .3 mts., 3 1. in- "^ and, SEhill / Mt. Masiirandupio, lOm. inland I5AHIA. ^, El, C. St. An-1 TONIO, It, R I40f. / * Mono St. Paulo, It. R27ff. .. Qu.imannu B., Ft. de Muta .. Os Ilheos, rks., large one St. George, town, fort Porto Seguro, E, r, Cathedral Abrolhos I.s., [l.^ni.], tWl m., St. Barbara, It. Rev. ?9f J Cruz, Ch Rio Doce, W pt., enlr. Kspiritu Santo B., w', r, b, 1 Sta. Luzia, It. F 66f. .' / Guarapari, Ch Culvada Islet, 4m. out, ||, W.. C. St. Thome, /, (bks. 1 5m. \ off). It. Fl. 157f. j t. Ann Is., 3, if 4n)., v,h,\ Slim, grt j 0°5I' O 32 2 |6 2 50 2 47 256 3 12 3 43 3 42 4 25 4 3> 4 49 4 55 5 = 4 50 5 30 5 45 44° 17' 44 "9 43 3S 43 22 41 44 40 28 39 48 39 '8 38 32s 38 27 37 45 37 48 37 18 36 53 36 28 36 16 35 16 35 " 6 56 6 57 ! 7 8 7 26 8 I 8 3-' 8 20 8 25 8 j6 8 43 9 39 10 29 10 47 11 16 12 24 34 49 34 50 34 48 34 47 34 50 34 52 34 56 35 " 35 o 4 35 5 35 39 36 24 37 23 37 >7 38 4 13 07 38 32 3852 38 56 39 o 13 23 13 52 >4 47 14 494 16 26-8 17 58 16 17 3 19 37 20 439 20 44 39 o 38 41 39 0-: 39 46 40 16 40 27 40 21 41 o 4' 4' Anchoras Is., [I 1.]. E one ... C.Frio, ([. # 2im.,*^).-l S pt.. It Fl. 3U0t J C. Negro, /, 5o 3m., pt Marieas Is., ^ 1 1.. ?„. Sst. ... Haza I., [fm.]. It. R31.5f. ... Ilio Janeiro, g, fort Villa- 1 _gas.'non, [H. It. I- .59f. ) Rio Janeiro, Obsekvatoby ... GabiaMt Pt. Guaratiba, hill Marambaya I.,EW 8 l.,T S,") \V lit., (E enir. of Ilha . Grande B., w,b), hill 2066f. J Lage rk., 18f I. Grande, EW 6 1.. ffi N,\ E. pt., or Pt. CasteliianosJ UhaiubaCh Pt. Cairo(,-u, E sum. of mt. ... Porcos Is., [rks. 4ni.], * ', S bill Busios Is., [2m.], SE one St. Sebastian, (ffi, w, r, b), \ J %ol St. Sebastian I 15 1., S pt. . Mont deTiigo, A, t .Moela, It. F334f. ." Santos Harb., g, r, w' 7in. ) up river, t. Arsenal /' Pt. Tdjpu -■ilcatrasses Is., rjis., S 5in., "( sum ..J Eage de Santos, rk. 7f. Qucimada, Is., 2, ^ 10m., \ large or outer one / Isuape R BomAbrigo,I.,[lim.],/j, t, 1 It Fl. 504f.(* E, Cananea, J ffl,bar5) J Mt. Cardoz FiguciraI.,[im.?],160f.,*o.T Paranagua B., g, town I. do Mel, % 3m., It. F ! 262f ( Coral I., [Im.?], 64f., 5„ 2m... R. Guaratuba, pt., hill St. Francisco I., ^ 6 1., A, ( f ,C. JoaoDiaz,lt.F309f. / Tamboretes Is., [I 1.], f_ ,Sonc Itapacoroya Pt., N part Pt. Bombas .4rvoredo I., % 2m., t, h.^ F, Fl. 292f. ; Anhatomirim, w N 2m . r, "( b, fort, fl. St., It. F la.'j'f. / * St. Calherincl.,^ 10 I., O,] NW-d.), Npt ) — Nostra Senhora de Dcsterro Pt. dos Naufragados, It. Rev. 1 I49f. / Pt. Pinheira BatubaPt.,lt. F 69f. Eagoa, (City Im. W-d.) bar... C. Sta. Marta RioGrnnde do Sul, entr.2, vi', 1 1', E pt. lov.er, It. F, Fl. \- I0)f. I 22°40'5 23 i-s 22 57 23 « 23 37 22 54 8 22 544 22 59 23 36 43 4-4 23 6-6 23 97 23 25-9 23 182 23 329 23 445 23 47 23 57 23 558 46 19 24 I 46 24 24 6 45 40 24 .8 46 II 2428 46 40 24 37 47 22 24 59 25 22 25 31 26 21 26 47 27 8 27 iS 27 2SS 27 225 27 35 27 49 27 54 2S 28 5 28 39 41 = 45' 4' 57 42 39 42 54 43 87 43 lo': 43 I? 43 32 43 49 7 44 52 45 37 44 35 45 32 44 59 45 2« 47 52 48 6 48 3 48 28 48 18 48 22 48 36 48 33 48 32 48 47 48 29 48 22 48 345 48 25-7 48 32 48 32 48 35 4S 40 48 48 48 50 52 7 TABLE 10 MAHITIME POSITIONS VRVOVAT. c. rdonio, It. !■' \n:(. ...... Hjn-er .k., s.nall. /3/3o C. >t., or Pi. Kas: Pi. Mi-daiui, .shi.fini.), S sum Mar Ciiiqnito, (entr. impract.) C.C(irriinics,/<, i,12(if.,K-uiii Pt. M..g..le8, A. i_, I04f., 5 2in Gurj;uen R., ||„ Sierra Ven ana, 3.i00f. Ilaliia Blanca, Mt. Uerinosi>,1 It. K ICSf. J — Fort Ar-ciitino K. Coloraoos, bar 7f. Unii.n B., I7f., Indian Ud,\ 4.5C., i. ♦.*',!; / S.in lUasHiirb, BB.w',l/",r, \ r. Main Pt 3.M., \V etitr. ( R. Negro, liar 9f. ? Suuth i Barrama, r. li. It. F 14. "if. J Port St. Aiitoni... g. w, b. E i hd., or Villaririo Pt., (l,k. 4m. S), hum 4Uf. ) Siena dp Sn. Antonio, 170(lf... Port San .lo-ef, w^, li.W licad.pt. Viildez lVnins..Pi. None! Ini. Pt. Delg^ida, 2(101., SE cliff ... Nui-vo G., E, or Nuivo lid., 1 i.SODf.. T,(w'. 10 / — \V hd., Niiilas Pt. 240f., 1 rks. 2m., Kcl.ff J Ralaberria r?., # 3m., N and\ Ept / Port St. Elena, w„,b,, S Heud C. Two Bays Arce I., [Im.], SEsum The Oven, or Prince Regent \^ haven, ^, entr j Mi'drano rks Tova I., % 4m., (Cove -f.l 1'. '.'".«) / C. Aristar.alial, (rks. oH) Salamanca Pk., 700f. C. Three Pw., ab. 2000f., »„ 1 lin., NE pitch / C. Hinn^ at pt,\ Pen^in I J («iriu-> rk Monic Video, ab. .Iiiof 34°25' 34 30 34 40 35 « 34 535 34 57 34 5V5 34 2S 34 365 34 4S 36 19 36 59 37 47 3« 5 35 57 38 36 38 117 38 59 41 3 40 49 4> 42 42 42 41 14 4^ 42 53] 42 58 44 »S 4432 44 55 45 « 45 45 lO 45 6 45 45 >3 34 47 6 47 ■a 47 45 1 47 55 1 48 7 1 48 14 1 53°47' 53 5' 54 9 54 52 54 577 55 55' 56 14 57 5' 7 58 22-2 57 53-5 56 45 56 41 57 22 57 29 57 3'-^ 58 40 61 565 61 39 62 IS 62 4 62 7? 62 8 62 48 64 54 65 12 64 25 63 48 63 37 64 » 64 3U 65 S 65 22 65 31 (1C8) Watchman C , /, (shl. 2 I., 5)... Bellaeo rk., or E(ld>>toiie, 6f... C. Ciirioso, /, sirijied Wood's Mt., vis. II I Pcit St. Julian, 0), Slioll Pt... C. Francisco de Paulo. X Port Sta. Cru7., bar uf., Mt. \ Entrance, oaSside. i ,:i'M'. / Coy Inlet C. Fairweather, ah. 300f. Port Gallegos, ffl, Ob.-n. \ mound j' Cape Virgins 65 29 65 40 65 53 65 56 66 30 67 20 65 5' 65 44 65 555 -i 65 42 '^. 65 V 66 26 FAIiICZ.A>rD ZSXAJVOS. Jason Is.,%9 U,» ||,W Cay.. Grind Jason, ife 4in., 12101... White rk New I., NS 5m., m -fe. NW pt. Bird I., EW is^m., 41.0f. West Falkland, ^ 25 1 , Port \ Stephens, g, entr. E pt. / C. Meredith, S extr. 2yOf. Albemarle rk. I snf. Port Edgar, g, S head. sum... C. Tamar, 15or., N cliti'. sum.. Port Egmom. Cove, ruins Wreck 1., EW 3m., W extr.... Port San Cailos, S. w. b, 1 F'anning Hd., SW sum.... J Eddvstone rk.. 200f. Ea-t" Falkland, # 27 I., Port \ .Salvador, g. Shag I., entr. ( C. Caryslon, NE chtt' Port Louis B.Stttlem., fl.st. e E extr.. C. Pembroke, It. F 1 1 Ot Port William, Stanley S,»', 1 r, f, b. Gov. Store ho / Lively !., NS7m.,SEpt.,(iks.) Sea Lion Is. and if., EW \ 11m., Wextr. I Geor};e I., ^ 7m., rks. W\ 2ni.. SW pt / Beamhene I., [1 Jm.], 2001., I (rk. ^ 5m.?),''s pt / South Georgia, sfe .30 1., C. 1 North, pt.. or C. Bi.llcr... / Wallis I., EW 4m., W pt Aniienkov I., [2m.], pk Green I Moltkc Harbour, Obsn. spot.. Clerks' rks., ^f 2 1., ^, S extr Siiagtks Q IMarquis de Traveri-e Is., A, | N one, Zavodovi-ki, [3in.] | — W one, or I.Teskov, [2ni.] Candlemas !•., KW 6m., Ii, \ vole, K one / Sauuilers' I., ^ 6ni., sum.. Mimtague I., [3 1.], Cupe.. Bristol I., [3 I.], Ept Southero Tliule Is., [3 1.]. E pt E extreme of group, rk.. Lat. S r^.n. W 4S°2i' 66° 20' 48 29 66 12 49 '« I 67 37 49 '37 67 45 5 3 67 49 42 50 9 67 37 68 22 69 8 68 55-5 5' 33-3| 68 59-2 52 202 68 217 50 58-5! 51 3-2 5' "7 51 42 52 II 52 II 52 15-2 52 13 52 07 5' ■/ 5t 21 51 10 SI 272 51 10 5> 237 5t 252 5' 32 ! 5' 407j 51 41 2 5« 47 52 25 52 223 52 557 60 52 61 17 60 54 60 412 59 29 60 3 to 14 59 7? 59 25 58 19 57 SOS 58 7 57 42 57 5' 58 25 59 85 59 477 53 59 37 28 54 4 54 37 55 2 54 309 55 4 5348 38 .4 37 3 36 2 36 5 34 38 42 45 56 18 27 29 564- 28 10 57 '0 2645 57 52 5827 59 59 26 60 49 26 24 26 44 26 18 27 «3 4t 20 TABLE 10 MARITIME POSITIONS Places Laurie I., EW 7 1., E pt., C.\ Diiiidas, 559f. / ^Imiy Is. HlOf. S one Siiddlu- I., [4inl Wpk., 164.3f Coronatiun !.,% 1^ '•. Esuin. 1 5397f. / — NWpt.,or Pt. Ptnguin .., Despair rk Inaccessible Is., [4m.], 337t... Cornwallis I.. [2m.] Elephant I., ^ 9 1., E sum. ... — Rocks, NW-d., outer O'Brien I., [Im.] Hocks O Brid^'einan I.,[-2m.],600f.\ volcano / ^ Ki,.gGe..rgeI..#13l.,l Ept., or C. M,lvi!ie...J V Ri.lley I., [2m.] Livingston I., ^ 10 I., NW 1 pt., C. Shirreif / DioepiionI..NS10m.,Port1 Poster, m. Mt. Pond.../® Smith I., E\v 7 1., Mt. Fos-1 ler, 6600f. / William rk C. Possession Astrolabe I., EW 4m., mid. ... Joinville I., EW 15 1., S pt.,~| or C. Purvis /| C. Seymour | Mt. Haildinuton Bisooe Is., Pitt I., r — Adelaide I., h, i Alexander I., N pt, St. Peter I ANTARCTIC OCEAN. Sir Jas. C. Ross' furthest Mt. Erebus, 12,400t: Mt. Sahine Balleny Is Adelie Land, Geology Pt TIERRA BEX. FVECO. Pt. Catherine, / r.St.Sebasiian, i ,190f., Nsum. I'euas, SEclirt' San Diego,/, i,E pt ten I., C. .St. John Vancouver, C. Kendall ... C. St. Bartholomew Good Success B.,t ',w,b, S hd. C. Good Success A, 1 , rks. close Ushuwia, Bea-lc Channel, [ New I., ji Hm.,'5„."pt."Wallcr airneveldt Is., [Sjm.], ecut... lorn, ab. I3^1f. tnit I., EW 14m., West C. — St. Martin Cove, g, b, w... i;,'e IJ., g, Pyramid I PaLsc C.Horn Ildef'on^o Is., sjj 5m., 100f.,mi(l. 6i 2 6o 43 6o 46 '60 33 60 36 60 40 61 4 61 6 61 o 61 32 61 43 62 10 62 2 61 48 62 2S 62 55 6 63 2 63 17 63 45 63 16 63 39 64 13 64 12 65 20 67 15 6S 51 68 57 78 4 77 ii 71 42 66 44 6635 52 33 53 "y 53 5'-5 54 4' 54 423' 54 49 8 54 54 j 54 49 54 55 I 54 49 4 55 II 55 49 55 59 55 50 55 51 55 3' 4 55 43 I 55 50 45 53 46 40 47 12 47 3!* 54 28 54 45 55 4-^ 55 52 56 50 56 40 57 30 58 o 60 28 60 30 62 47 63 o 61 50 58 20 55 48 56 32 5S 2 65 3S 68 15 73 10 90 46 East 161 o 166 58 i6g 55 163 II 140 10 AVcst 68 46 68 10 67 33 65 7 63 435 64 6 66 46 65 13 65 22 68 185 66 33 66 48-5 67 16 67 55 67 34 68 5-5 68 3 69 iS (170) Places Diego Ramirez Is., NS 5m., 1 .587f. / York Minster C. Castlereagh, (Stewart Hr. ~l NE-d) ( Lat. S LoD. W 56"'3«' 55 25 b»"43'? 70 3 54 565 7« 29 Townshend Harb.,i: '".islet, N' 54 423 71 557 Tower rks., 2, [1 im.]. S & Est. 54 37 C. Noir, (8 2m.), 600f , S pt....| 54 30 C. Gloucester, W pt 54 5 C. Inman, (rk. ^ 2m.) 53 19 Dislocation Harb., S, (w^)...! 52 54 C. Deseado. Ii. (rky. I 2m. oli') 52 44 C. Pillar, N cliff. 52 43 SOUTH AMERICA. ■West Coast. C Vir" >4f.. C. Possess on, Refi Direction Hill Beac S.i.NllTP0INT,B0AT-H0. It.F 261 Port Famine, tent N side \ Bay / C. Froward,( S extr.of America ) Port GMllant, Cross Id Mt. Sarniiento, 73301'., 2 pks Mt. Buekland, ab. 40ill)r. ... Port Angosto, Hoy Pt Tuesday B., Cascade Pt. .. Port Churruca. Diaz 1., GOf. Port Taraar, Mouatt Id 73 3 73 6 73 .30 74 19 5 74 37 74 45 ShoU B., Obs. spot Otter B., Obs. Pt Fortune B., Low I Isthmus B., Obs. Pt Columbine Cove, islet Mayne Harb., head of Str. ., Puerto Bueno, Obs. Rock Foil Grappler, Obs. Pt Eden Harb., cove, (staff) Halt B., Obs. I Island Harb., Obs. I Gualaneco Is., S. Pedro I., 1 4101'. J 52 20-2i 68 52 24 I 68 52 18-3' 68 52 22 I 69 53 9-9 70 53 38-2! 70 53 54-6 71 1S5 53 42 71 597 54 28 70 525 5426 70 237 53 I3'5 73 =25 52 50-2^ 74 29 5 53 i'4 73 56 52 56-5 73 46 5 52 44 5 73 53 52 22-5 73 40 52 I5S 73 41 52 9-6, 73 365 51 53'3: 73 41-5 51 iS-S, 74 4 50 594 74 117 49 25-3 74 17 5 49 7 5^ 74 252 48 sri 74 21 48 si 74362 47 44 74 525 ■e.stminstcrHull.[lm.],I12nf. 52 38 rangelists, Sug. loaf. 360f. ...' 52 24 ry, or Narborough ]it. 52 16 na I'k. Isabel,/,, i,(pk. abridge 1., C. St utrks., lof. .... Ire dc Dies Ar W 52 8 51 50 51 30 50 49 50 36 Three Pis., Rugged Hd.,1 2U00f., (rks. 2m.) /[5° M rt Henry, ffi', w, b, W h»ad| 50 o ;. Corso I.,SW sum., (shls. \ ^„ ,._ 5m.), 1420r. M49 464 74 22 75 4 74 55 74 48-5 75 II 75 22 75 40 75 32 75 23 75 205 75 3^3 ky spit 49 11-5 75 50 I TABLE 10 c;l'9 MARITIME POSITIONS (171) Parallel rk., 2m. inland, 2S0Of. Diindei' rk., 4->f. P..rt Sia. liarliara. g, W head Guaiai.eco Is., Hyroii I., W pt. C. Marhudo, *,, (rks. 2m.)0 riircelll.,[:im.|, t,S\Vrk.O Port Oiwav, S, S eiitr.. sum. C. Trcs Monies, i, I300f., pt. C. Kapcr. rk. close C. G.illegos, T San Eslevaii, port, w, S^, mtr.. Hellverrk-^., [Im.] C. Ta) Uo, 2850r., 1 , S Im , 1 Wpt / Hnamblin I., 700f., NS3I.,1 t.Whd i Yptiri, or Narborongh I., %"] 9m., (Siotcliwell Karb., ' SE. b, w), S, or Jobn Pt.J !'ortLow,a,w"-,b,f. HuaO eaiiec I., % 2m., S pt. .../ Hiinfo I., fij I3m . :> £, rona Hd., It. F, Fl. 224r. — C. Malalqui Iliiecliucticiiv Hd Crcoliado Vole, 7.5()()f. l"havapir,n Vole., 8000f., sum. C. Q.ielal, T Pt. Galcra, W pt.. It. F, Fl. \ 180f. / Gouzales Hd., N pitch Fort C'orrnl Valdivia, S, Niebla bluff,! It. F 121t. / Miicha I., % 7m., (rks. Gm.,"! *,-i«and^f.L„r„,b,w"'). sum.. ]2.")0f. J T.icapel Hd..(i:. I,iubu, Kd.) I>ota I'oint, It. R I8l)f. Sta. Maria I., NS 6in., /. S,-\ (rks.ij-il., w',b,r),lt.Fl. 2.i8f. J Araucii, fort Paps of Bio Bio, SOOf., SW \ sum ( Coneopcion, ffi, Ciiy, raid, at \ river / Talcahuano, w, r. b,, Quiri- \ quina I., IL K213f. / Pt. Carranza. rks Uiv. Maulc, Church rk., (barl -|*li"'.).5 / Bncakmo Hd., (Uapel shl.,1 1-2m.) J Alt;arroba Pt Carauiurlla Pt., rk Uell of CJiiillota, 620nr., 7 1. 1 inland i Aconcagua, 28, 080f., 25 I. in- ) 1-d / Vai.i'Araiso, ffl, Q KxriiANCK Curoi.j Fort Sr. Antonio, i Lai. S Lon. W 48" 46' 4S 5 5 45 2 47 46 47 26 46 55 46 49 5 46 59 46 49 46 35 46 18 46 4 45 53 43 48-5 43 36 43 «7 4> 47 42 II 41 46 43 " 3 42 48 41 3 40 2 39 51 z<) 529 39 52 38 23 37 36 37 5 36 59 37 IS 36 48 36 49 5 3636 35 37 35 «97 33 52 33 26 a 6 32 57* 32 385 33 21 33 19 75°3'' 75 375 75 25 75 20 74 29 74 39 75 >6 75 26 75 37 5 75 35 75 9 75 "5 75 55 75 <2 74 457 73 595 74 46 74 23 73 52 74 >I 74 o 72 457 72 31 5 73 577 73 437 73 267 73 26 73 24 73 557 73 38 7 73 n 73 "9 73 «'7 73 2-2 73 3 71 427 71 44 7 71 62 69 577 71 38s 7' 38 5 Ilorcon B., ( t ',w'. r,b), Hd., 1 (rks. l.^m.) / Papado B'.. G"bernador .Mt. ... Picliidanque B.,$s, Locos I.... Mt. Talinay, 2.300f. Pi.Lcnguade Vae3,(B. E-d. * ) llerradurade Coipiimlio, ffi, \ w„. b„, SW corner / Coquiml)0,a3,iv,.l).r,(LSis-T nal-hill), Turluga Pt., It. ' F, Fl. 'J8f. J Pajiros Islets, 2, % 3ui., N 1^ St. Wonc J Chaneral I., [2ni.] Ilnasco Port. $,, w'", pier It. Ilerradura Pi., i, \,\ \\^ . ... Co|iiapo, $ ,,!,„ w ,r .li ,la-.d \>\ Morro Pt Port CaldL-ra, W hd., It. F, I Fl. I21f. J FlamenC'S port, S head BullenaPt., rks . Grande Pt., h, ^ E, W sum. ) l.'>72f. / I'aposo vill.,w,h. White Hd... Jara IM., i,wN AntofaL'asta, Custom ho.. It. 1 Faof. ; Mt. Moreno, (Jor^e, old), | — Coiistitiiln.nR !..[*'], LeailinL' bluir, i-l.'i oil' .. Mt. Mexillones, •>:M)i . {: inland) CobijaB., \^'. r, 11. bt. [ — Pk., 3330f. C. St. Franei^i'o, or P.i.ii Arena Pt, /, $ lo R. Loa, llo, w„. and Galley Cliipana B., *', tail of pt, \x„ Lobo, or Blanco Pt, A, i , , Carrasco Mt., 562jt'. GruesoPt., /, i , L Iqniqne,i*,Id.,lt.F,FI.96f. I'ichalo Pt., projeiting Pisiigua.Gulleyand R., ||(,w,... C. Lobos Arica. w"', r, Iron Chuki (Inglesia Matii.t) PERV. Mount Sahama, 22,3.')0f. Morro of Sania, 3890f. . Coles Pt., /, sandy, (shIs. >i.) Ylo, vv, t), rivul. mo I't. Mexico, /, t Islay, portof Arequipa, Cus- | torn ho ] A rcq ui pa Mount Misli, 20,320f. Cornejo Pt 10 52 Qui lea, l„ I... Cove, W hd. ... 16 42 3 Mt. Cainana.(iMt. likjB^a fori): 16 37 Pescadores Tl., *<,, (rkS lm.)j 16 24 I't. liomas, t'<'\'. w., tNE,L'E, 1 Npt / CamtasHd.,S pt „ Sangailan I., % 2^m., Ii, i.l N sum : ; Pisco, ([,', w', S 2m. of Pa-\ racca vill.). r.ft, pier It. Fj Chincha Is., J' 3in., N pt. ... Jcrro Aziil W, , //, 1 A-iark., [1 j, rks.,pk., L' E Chilca Pt., i, .-um. 300f. — Port, t', El, rock I'achacaniac I,s , i|5 1 l.,400f..~l 5„ W-d., None / Morro Solar (Bay, $5), 860f.. C.iiXAO, San Lnreiiz i I.. ^ -| 4.;n)., I284f., C. Sr. LouKX/.o, It. F 980f. ( - a, [B- r,w,S, Arsenal, fl. St. Lima IUthkdbal, South'! Tower _^. ( [ormigas rks., [Urn.], 25f.,'i T.Sone .". / Pescador Is , T, 8„, larffe. Salinasnill,(UauraIs.SW-d.) Pelade rk., small Huaelio B., $ ' 5, [,', r, w,b, pt * ', r, w, viil.,W pt. Darwin Pk., 5800f. Giiaimey B., * ', tpw^, r, b' ... Legarto Hd., 1 , eliras Pt., * N Mt. Moiigon, A, W sum. 39001 C'asma B., L,, w, r, b Samanco B., I.', w', r, li, huts.. Mt. Division, 3 pks., 1880f. ... Perrol B., w„, N pt I.,[l.Jra.],*'NE,L'w,r Santa IJ., ^ s, wat. pi Chao Is., h,r-e, [>.], I20f... Guauape llill,ab. 700r., (Is.) ^8m.) / Hiianchaco Road, l.,,, r, w, Ch. "'rnxillo,( I im. inland), w„,r, | CI. ( acasmayo Pt., $ , L„ w, r, b, ^ mole It. F 6.if. / Mt.Snlivan,.5oOQf.,I7m.inIand !i Hill, 640f., mole It. F65f. i.bayeque Rd., S *,to."l ^ o. r, bg j' ^ Loliosde Afuerals., N.S3m.,~) ah. lOOf., *„, Wo, b„, 8„ J Chichal de At'nera J Lolios de Tierra, NS 2 1., $ -)*, \ spt J 1,1 50f. K., t', Scdiuta CI IcKe of i6°38' '5 5° 15 20- '5 9 14 57 14 41 14 40 14 20 14 IS 14 II 13 50 >3 45 13 3S '3 3 12 4S 12 31 12 293 12 iS 12 II II 9 10 497 10 30 10 6 10 7 9 5S 9 38 9 2S 9 156 9 II 9 7 9 2 9 o 827 8 S 8 7-5 7 24 7 17 6 565 6 46 6 54 6 28 3 5 55 i 5 35 5 12 67°49' 68 30 75 23 75 23 75 32 75 51 75 547 76 77 75 137 76 167 76 287 76 10 76 247 76 307 76 387 76 50 76 495 76 557 77 37 77 157 77 los 77 o 77 46 77 16 77 36 77 49 77 37 77 44 77 46 78 9 78 10 78 12 78 18 78 22 78 29 78 34 78 36 78 39 78 38 78 45 78 53 79 S 79 o 79 33 79 '77 79 52 79 567 80 so-2 81 6 80 467 8r 5-? Places Patta, Cathedral Tower . Pariiia Pt., i, 8U1. , 0. Blanco, A. 1 , 5^ MalpeloPt., I, t , ECUADOB. Sta. Claral.,[lim.].shls.,lt. F, Fl. 2.56t PunaJ.,#9l., Pr. Ks|mtiola, Consulate, It. F I31f. Gu^ynquil, w, r, b, Arsennl .' Mount Chimborapo, 20,49Sf.. St. Elena Pt., It. F, FI. 470f.. Salangol., [lni.],w.||oE PlHtH I., i)j 3m., 7'JOf., It. F. C. .St. Lorenzo Manta, It. F 88f. Mount Cotopaxi, 19,613f..... Quito, 9,343f. C. PassaJo GaleraPt. Atiicames, tovn, w, (shIs.) ... K>meralda R.,Coquito Pt., It. F Pi. Mangles Tuniaco Rd., Morro Chico .. COX.OIIIBXA.. Pt. Guaseama T. Gorgona,5P5m., 1296f, N pt. Pt. Cliiranibira C. Corrientes C. Francisco de Solano Pt. Caracoles ., Pt. Guarachina,(S side, e G. St. Michael) L Key, % i 1 , Pt. Coco; I. St. Jose, [2 1.], S pt.. Panama, E@,NEbast. .. Tabopa I., [2 Oioque Is, " Pt. Chanie Pt. Mala Point Pneicos. [2m.], vill. -^, ^ %2»m.,pk CENTRAXi AKERICA. Hicaron I., (Qnicara). (and^ islet S). NS om., S islet / Quiho I., % 7 I., Adelarda Pt .Moniuosa 1., [.'.ni.] Bahia Honda, "s, w, Seiiti-I nela I., at entr.,Cw-p2in )/ Magietic Is., (otl' I'oril Nncvo, m. [4e.] J® Pt. Burica. Id. off Vindarock Ladrones Is U. of Duke, C. Matapalo.l (•■k.«. off) J Cai-io I., [lm.],404f,(w"' -j* 1 ■'"•) '• J Nicoya G., Puntas Arenas 1 Haib., ffl, w, f, Pan de '• Azuear J C. BI.1DC0, ^, f, (islet S,l I'm.. ||), lyaf. J Gnin.mos P(.i..t, (reef oil) ... SGTiTlT 5° 5' I 3 o 56-8 o 43 o 14 o 21-5 North o 50 53 1 o I 35 I 4y6 2 37 3 o> 4 17 5 29 6 17 7 40 8 6 8 13 8 12 8 57-2 8 47-3 8 35-0 8 39 55S 81° 7'2 80 24-5 78 47 80 59 80 52 8. 3 80 55 So 427 78 iS 78 22 80 297 80 s 79 53 79 415 79 5 78 44 5 78 24 78 10 77 29 77 32 77 27 78 16 78 217 78 54 79 32: 79 35 79 41 79 58 7 31 7 28 8i 53 82 .5 7 435 81 32 8 5 81 49 8 23 8 6 tliP 7 52 82 26 8»3 8317 843 S3 53-2 SS 7 I 9 54 I 85 41! TABLE 10 63 1 MAHITIMK I'OSITION'S ri;i.'. S, Vira- \ ; C. Velas Culebra, d res h St. Elet.a SnliimsB., Salinas Is., [3c.] . PurtSt.Juan.Sblutl'.lt. F4a0f. C. Dcsolado l«aleji).g.r,b,Cardoii I., 1, 1 i'm.,Npt.,(wIm.),lt.K64l./ Vulcan Viejo, 5670f. Pt. ConseKUina, (Volcano,! 28.)Of.,-|i3l.) / G. of Coiuhagua.orFon-cca, i Port de la Union, ffl. w', r, J Chiciiivne Pt '. J S. Miguel, vol., 71.l4f. LiBKUTAD. I ,. f, PiekJId. It. F Pt. Kiinedios, /, t .(rf.^.'Jin.) Acajutla, vill., *' n, L„lt. K.. San Jose de Guatemala,"! Custom I.O.. It. F / AcMti'iiangii Volc.mo, 12,S90f. Mount Tacaua, 14.0uOf Lat N Lon. \V (176) Places io°2r5 10 35 SS°S3' 8S 43- 85 58 'o 535 u 2S 85 43-5 II 152 85 535 11 59 86 42 12 279 87 127 12 41 87 1-5 " 585 87 35 13 25-51 88 18 13 2S-8 89 192 "3 30 •3 34 4 14 29 15 85 liar. 'rauc. de Tcluiantepce, bar Salina Cruz, Morro, 2441'. Port Gujtulco, rky. islets Galera Point Acapulco,a.w',r,ForiStl Diego. H / ® Pt. Tequepa .Morro Petatlan, 640f Pott Sihuatenejo, NW bigbt... Istapa, or Isla Grande U Mangrove bluff, .151'. Tejiipan Papa, 5660f. Colima Volcano, I2,00()t". ManzaniUa B., *', w„ village- Port Navidad, S bead, 7l)5t.... Pt. Farallones, (rk.s. oil) C. Corrientes, flat, f_, .'iUf.f. ... Corventa rk., 2.5r. ..'. TresMaria.s U.,ii Juaiiito.l.TOf. Mt,Si.Juan, 75.'>Of.. .5 1. iiiiaml San Bias, w^ r, r, Arsenal Isabel I., w^. b„. pk. 280f. Cliamatlali., W eiil. pi Mazatlau, w„ Cast, ho Ciiliacnn R., Altita Railway 1 Station / I. .St. Ign:.cio. [Im], i.4G5f. F.-tcrro do Ajiabampo, bar ... Pi. Uosa I.obos I., [.^1.], -.U.SWpt... (ort |C. Haro, It. K, Fl. .lief.., iTclas lie Cahra, Ifia.'Jf.. 1. St. Pedro Nalasco, In71f... T.buK.n I., [9 l.J, WiUard I't ,:ii.-if. , U: t,p c* irdl '5 59 93 SS 3 94 45 95 125 15 44'4] 96 8-2 "5 57* 97 4'-5 16 50-8 99 55-7 17 16 ;IOI 4-5 17 3' 5 «oi 27 17 380 loi 3-3 17 403IOI 40 17 55-5102 12 18 24 1 103 II >9 25 103 ^Tl 19 32104 19-7 19 " 104 43 19 23 5 105 3 20 24 1105 42 5 20 45 "05 5' 21 43 1106 41 21 26 '104 585 21 32-5 "05 19 21 52 |io5 53-5 22 47-5 106 2 23 11-7106 272 24 377 107 56 25 26 109 24-? 26 16-3 109 17-2 26 40 1 1 09 407 27 21 iiio 38" 27 55-4110 55 27 505 110 547 5 24 27 58 28 SI 30 16 112 36 112 52 Uoi-ky lihiff, 408f. Colorado l{.,I'ort Isabel beacon San Felipe Pt., 940f. Guardia I.. 5ji 13 1., Pt. 1 Refugio j Sta. Tei-esa B., N pt I. Toriuga, [2in.], li)16f. Sta. Inez. Pt Mulege, t lldefonso I., [tin.], 3S7f. La Giganta Pk , 5794f. Loreto Carmen I., 1572f., J^ 4 l.,\ Salinas B / Catalina I., [7ni.]. l.')48f., pt... Sta. Cruz I., [.Iin.], pk., l.'iuOf San Jo.-i^ I.. ^ li 1., 2077f., \ Amoitajada B., N |it, ...J ICspiritu Santo I., % I 1., 1 I.upona Pt / r.a Paz Cerralbo I., ^ 5 1., 2477f., \ Montana rock J Pi. Arenas San Jose, Mission, r, w"" C. St. Lucas, rks., A, ^ ., (w, 1 vill.-p),25lf. / Magilalena B., g , Custom ho. It. C St. Lazaio, Mt. l.'iOOf. San Juanico Pt I'l. Abreojos 1. Asuncion, lOOf. Port St. Bartholomew, N hd. I. Cerros, 3955f., NS 8 l.,\ Mono Redondo / Is. San Benito, W one, 6J0f... I'laya Maria B I.SanGcroninio.[I 1.], 172f.e St. Qiiintin, ffi, Sextant Pt. ... C. Colnett, S\V pt., 4(i0f. Todos Santos Bay. Enseii-\ cda Pt., 370f. / C"ronadosrks..% 5ni.,Sisl., 1 Gr4f. J Lat. N Lon. W Houndary Obelisk . Diego, S, w, Pt Loma,-( It. Fl. 462f. f . Juan B., $ , s, I ,. outer rk.. Si. Pedro B ,[Ii;,w,r,lt.Fl. 156f. CoHez Bank, -ii . Clemente I., 5|, [6l.;\, SE* Sta. Catal.na I., % [i. l.].\ Rapcr B., Barracks J St. Nicolas I., ^, tint.. Joh.1 ) Bepg rk., [2c.]. NW-d.... r SU. Barbara I.. [2m.] i. i. Cruz I., [7 1.]. Anacapal I?., Obsi-rv. Pt / a. Rosa I., [3 l.].Becherl B. Observ. Pt / San Miguel I., Cuyler Hr., 1 3I°20' 3' 46 3' 2 29 33-' 28 25 27 26 27 3 26 535 26 37 26 6 26 0-5 25 595 25 42 25 16 24 54 5 24 24-2 74 10 24 8 ii3'40' 114 42 114 49-5 "I 53 III 56 III 575 II 7 10 47 10 43 10 387 1 10 20 109 47 24 38-3112 87 Prince I. 24 47 112 17s 26 2 112 17-5 26 42 "3 33 27 6 114 17-7 27 39-8 11452 28 1-3 ■ IS.. 28 18 1.536 28 SS 1.4 32 29 48 ns 477 30 22 115 59 30 57 1 16 195 32 32 .17 7-5 32 40-2JI17 «4-7 33 269 33 43 2 32 26 32 49 117 46 118 17 M9 6 118 2S-2 33 26 1 18 297 3i 21-7119 41-7 33 28-5119 2? 34 1-6119 32 34 1 130 a? 34 3-3 120 30 TABLE 10 MA UI TIME rosi 1 IONS (177) Places St. linrliara. It. F ISUt. Ft. Cone, prion, It. II. i;i.5f. ... Ft. ArguilUi San I,uis OI'i^iM, Whali-r I ... Ft. Finos T. It. V 9 If. .MoHter. V. w,w, r, b, fort F.. AnoNmvo ....' Furallnnes rks., [Im.], ]:k.,\ It Fl. 360f. / St. Francisco, Fokt Ft., It. \^ F 1241., S side, entr / Mt. Bolhones,37C.if., 10 I. inl. Ft. de los Riye.s, It. Fl. 2'J6f... C. Uode^a, (IImss. Sior. w) ... Ft. Arena. It. F 156f. C. Mendocino, It. Fl. 423f. ... Humboldt B , It. F 53f. Crescent Cii v, Pt. Si. George, "1 It. Fl. 80f; ) C. Urford, It. F 25t)f. C. Grc<:oi-y, Empire Citv, | It F, Fl. 751. '..J C.Perpetua Yaquina Hd., It. F 61f. C. Look-out Columbia R., Fort Astoria .. — C Disappointment, It. F \ 232f. / SIioalw.atcr I?., Toke Pt., It 1 F. Fl. 8.5f J Grav's Ilarb., ffi, bar, Pt. 1 B'own / Ft. Grcnville UestruetionI.,rf. Waini Flicttery rks ". C. Flairery, Tatoucli I., It. 1 F lt,2f. J Neeah B., Wyadda I., SW pt, New Uungeness Pt., It. F lOOf. Port Discovery Whidbeyl., Admiralty Hd.,") It. F il9f. / Admir.ilty Inlet, Foul- 1 weather Bluff J — Seattle Town — Hood Ciiual, Union City... Pug.-t Sound, Ni.-quaIIy — Olympia Town Smiili, or Blunt I., It. Fl. 9UI. Mount Baker, 10,694f. Semiahmoo Bay BRITISH COIiVntBIA. Roberts Ft., W side Fraser River, It. F 52f. — Garry Pt — New Weslm.,Milit. Burravd Inlet, Atkinson It. Rev. 119f ... — City of Vancouver, Cana- dian and Pacific Railway ' Wliarf J Bowen I., Roger Curtis C Howe Sound, Plumper Cove. TVxada I , Pi. Upwood •:::} Lat. N 34"237 34 26 S 34 35 35 95 3' 37-9 36 3fi 37 6 57 4' 37 485 I .on. I20"43'2 120 28 120 39 120 45 121 56 '21 53 122 20 123 o 122 287 37 529 >2i 54 5 37 S9-&|i23 '■■2 3-S 1771123 45 38 57-5II23 44-2 40 26-3124 24 5 40 46 1 1 24 13-2 42 50-1,124 33-7 43 20-6^124 23-2 44 18 iI24 6-7 44 406124 47 46 16-5 124 0-7 123 50 124 3-2 46 43 124 4-5 46 56-2 .24 8 47 >X3 47 40-5 48 10-3 48 232 48 225 48 II 48 5 5 48 94 47 563 47 36 47 21 47 7 48 19 48 49 49 o 49 o 49 37 49 7 I 49 13 49 20 124 i6'5 124 28-5 124 46 124 44-7 124 362 123 6 122 545 122 39-5 122 37-2 122 21 123 7 122 40 122 55 122 51-5 121 46 122 45-5 '23 55 123 170 123 120 "22 54-5 123 16 .23 6 49 20-3 123 26-2 49 24'6|I23 29-2 49 29-7 1:4 S 7 (178) Places Texada, Marshall Pt Jervis Inlei, Hardy I.,S\Ve Mystery Rock Hernando I.. S pt Mittleiiatch I., 2onf. Valaez I., C. Muil-e Thurlow I., Kno.s B Fort Neville, Robber's Nob. Foi-t Harvey, tide pole idet Wells pass, Tr.icey Hb ,Siar Bluiiden Harb., Byrne.s I.... Slingsby Chan., Dalkeith Pt C. Caution ..„ Fort S.-in Juan, pinnacle rk., \ N side of Bay / Sooke Inlet, Secretary I Race I., It. Fl. IHf. EsQULMALT H., m, w, r, IH.l DUNTZK HkaI) / Victoria Harb., Laurel Ft. . Nanaimo Hb., Ur. Benson's ho Nanoosc Harb., entrance rk... Baynes Sd., Henry B., Beak Ft, Seymour Narrows, Plumper \ B.,W pt ( When B., Cormorant I., blutf Beaver Harb., shell islet P. Alexander, GoUtas Chn.. ^ islet in centre of the port / Bull Hb., Hope L,Npt. Lid. Is. C. Scott, 500f., sum. of cape... T, iangle L. 680f., Scott Is.,Wpt. C. Russell, 5 1 C. Paluievslon, 5 | QuatsinoSd.,ent., mt. I2-of., 5 — Observatory rk., N harb. ... — Observ. I.. Koprino Harb... — Kitten I., Hecate Cove ... — Reef Pt Gierke reefs, W extreme C. Cook, or Woody Pt.,\ Solaiiderl '. / Nasparti Inlet, Head beach... Sulivan reefs Lookout I.,S, W extreme Ninety-eiglit- feet Island Kvuquot Sound, Shingle Ft.,\ ent. of Narrowgut Creek. J Thirlv-feet Island Totchu Pt., 5 Esperanza Inlet, Obscr. rk., "1 Queen's Cove / Nuchatlitz In., Port Lang- 1 ford, Cohvood I J Ferrer Pt Bajo Pt., rf. 3m Nootka Sound, Friendly Cove Estevan Pt., S extr., rf. 2m. ... Hesquiat Harb., Boat Cove, 1 leading Mt. 2726f. / Refuge Cove, vil. on W side... Flores L, summit 3000f. Sea Otter rk.. 6f. Clayoquot Sound, Obs. L,1 Hecate B J Lat. N Lon. W 49''48'o 49 437 49 54'8 49 58 49 57 50 0-7 50 24-2 50 311 50 34 50 51 50 544 5' 47 51 9-6 48 33'5 48 19-6 48 177 127 48 123 42-7 ,123 322 48 2581123 267 48 25-4 123 23 49 10-2 123 566 57 49 365 50 100 50 350 50 42 • 50 50-8 50 54'S 50 46-7 50 51-9 50 41 50 36-5 50 27-5 50 29-4 50 30 50 324 50 21-3 50 12-3 5" 6-5 SO 11-3 50 4 5 '27 41 50 00 127 26-5 49 477127 21 7 49 599 '27 95 49 552127 16 49 512127 9-s 49 52-7 127 o 49 47'3 126 57 49 447126 597 49 375126 507 49 355 "26 37'S 40 22-1I126 32-5 49 27-5 126 25-5 49 208126 167 49 i8-2|i26 9 49 11-5126 8-5 49 154 125 502 24 51-2 25 22-S 127 40 127 56 128 267 129 6'5 128 23 s 128 19 128 3-7 ■ 28 3-7 127 52-2 127 36a 128 o '27 55 127 57-2 127 38 TABLE 10 ():^3 i-MARITIME POSITIONS Lrtt. N I-ou. \V Goivlliind rks , 10 to ISf. 49" 3'6|l2S°5r7 Barclay Souml. Obs. I., Al- 1 I ,„ „ o'.,. -„« herui C:vM.. S.am,. H.rl>. / "9 'S^^^ 500 — Oh>erT. I., Island Harb.... 48 547125 i? — Dnngi-rrk ...48 492125 18-5 — Cape Beale, It. Fl. 16»f. ... 48 47 V'^S 13 VirKiii rks., 50f. '51 17 Iz8 13 Pi-arl rks., 15f. 51 22 |i28 2 Dalkctih rt q> 51 4712740 Sa'ety Cove ® 51 317127 565 3 jGoldstrcnni Harb © 51 433 '-8 05 .i jNaiiiM Ilarb 51 517 127 525 ^ LotiKJilin Harb '52 86,128 102 ~ Kvuuiiipt Harb 51 12-3128 115 " C'Swaine O 52 18 |i2S 32 Carter Bay 52 497128 245 Holmes Bay 53 164 129 52 Stewart Anehomge 53 52 5 130 52 Al|ihii Bay 53 52 ,130 17-5 C. Ibbctson O 54 I il.^o 36 DumanBay.OlisiTvatorvPt.... 54 202130 275 P. Simpson Fort 54 335130 262 Queen Charlotte's Is.. ^T I 55 l.,S pt C. St. Jame-s [ O 5' 55 >3 (rks. -t lOOOf.) J 1 — C.Henry O 52 555132 21 — Skidegatc I., Anchor Cov.® 53 12-5132 142 — Hippa I., [II.], village... O 53 33 "o^ S8 -Frclciiukl O 53 59 '33 9 — Pt. Norih O 54 '5 '32 $(> VHZTEO STaXES. Alaska. ! Port Stewart, S.Sst islet C. Chacon C. Muzon Forrester's I.,NS 4m., S pt(rks.) ('. Addington Port Protection, g, Pt. Baker Coronation Is., [3 1 ], S pt. ... Hazy Is C. Ommanney Sitka, ffl. Arsenal, lu F C. Edgecumbe, JSJOf. C. Cross, rks C. Spencer, rks C Fairweather Mt. Fairweather, 15..')ll0f. Port Mulgrave, ffi, I't. 'ruriur Pt. Manby 55 383 '31 47 54 4' '32 ' 54 40 [132 41 54 48 133 35 55 27 1133 52 56 20-5 133 39 55 50 >34 '2 55 54 '34 32 56 10 |I34 37 57 29,135 197 57 56 58 >3 58 5. 58 58 59 33' 13s 49 '36 3' '36 35 '37 50 '37 27 '39 43'0 59 45 '40 «7 Mt. St. Elias, I9,50Uf. 60 20 140 58 ('. Suckling 60 I I144 15 "Tlii;,!^':..!.!^;:} 59 52 1.4450 Port Ktches, BB, Phipps Pt.... 60 21-2 146 50-? Montaguel.jSpt. cellar 59 46 148 o C. Puget '59 56 148 30 PL Gore 59 II 150 5a C. Elizabeth, E pt, 59 9 151 42 .Anclior Pt., S hrt 59 49 151 47 lliamna Pk., I2,066f., vol 60 3 153 o Pt. Campbell 61 4 150 9 "'.ii:;.:^T!:;"!:!':!:[!!;^!:}isc'« -5330 (ISO) C. Dougla.s E pt Barren Is , [5 l.],A, Ept Pt Banks Kadiak I., Ji 27 1., Ept.,C. 1 Greville, or Tolstoy, rks. I — St. Paul Harb — Trinity Is., SW pt Chirikoff I., [.■! I.], N pt Shumagln Is., Nagai I., San- 1 born Harb J .^annakh I., sum. 18501'. Iliiimak Pass.Ugamok I., S. pt Unalashka, jft .,,;, ]., ]^l^^. i link Port, a, church J ® Rogosloffl.,['2m.],||„.i.k,,344f. llninak I., Vsevidoff, vol 80nof Yimaska I., ^ 51., sum. 2864f Amiikhta I., [2 I ], 3738f. ... Sgiiam I., 5(1 5m., 20981'. 1 SWpt I Amiial., EW 12 1, ?„ (ik! -f 5m.) Suchikoti' B / Alka I, j|4 20 I., vol.,1 4988f.. N..zaii B J ® Sitcliin I , [2 1.]. A, vol., .5083f. Kanaga I , tiP 9 I., N pt Tanaga I., EVV U 1.. (w in 1 Bay, tV d.), aw pk. TKiSf. J Gareloi, or Burning I., or] "Volcano, [2 1.], 5;334f. ... / Amatignak I., li)21f., Westpt. I. of Seven Monninins. Se- 1 niisopochiioi, 3l22f. [31.] J Amchitka I, % 1 1 1., Con- \ stantine Harbour J ® Kyska I., NS 8 1., Kyskal Harbour / BouMyr I., [1 1.]. (rks. El 6 1.), mid. 1145f. J Agattu, [4 1], sum Q bemiclii, :il^., # 2 1., Alaid 1 i. «I8|- / Attn, E\V 15 1., 30S4f., W \ pt., C. Wrangel / — Chichoguff Harb Pribc-lotris., St. Paul I., EW\ 8l.,NEpt.,(rf. E2I.).../ — St. George I., % 4 1., E pt. I. Amak, [1 I.], rk. NW-d.... Port Moller, ^, tongue, S pt. C Strogonuv, (1. oil) Bristol B., C. Conslantine, "1 (bks. S-d.4 1.) / — Nagnck R.,SuworoH'vilI.... HagcunK-ister I., J^ 6 1., S pt, C. Newcnham C. Avinoff, Anogogmutc Nunivak I., E\V231., N pt.,\ C. Etolin J I.St. Matliew.iljIOl., 1500f.,1 KK pr., C. Upriglit J — llitll 1., liiml', li 1.], N pr 58° 54' 58 58 5838 \V,.,«t '5.5° '7' 151 50 152 12 57 37 152 57 47'5 56 23 55 56 152 197 '54 40 '55 34 55 8' '59 582 54 25 3 162 44 54 '2 164 57 S3 50 2 '66 307 53 575 53 '5 52 36 52 28 167 58 168 20 170 47 171 17 52 17-5 172 36 52 22,73 22 5 52 106 '74 '5 52 5 5.56 176 8 '77 5 5' 53 ■78 9 5' 47 5 '78 52 5 51 18 179 12 5' 56 •79 37 5 5' 23'6 179 I0-? 5' 59' '77 29-2 52 34 '75 45 52 25 '73 '0 52 45 '73 52 52 58 172 27 52 55'7 173 "5 57 '5-2 West 170 7 56 36-7 169 27-5 55 56 56 52 '63 3 160 35 15842 58 25 158 44 58 40 5834 5841 59 39 •57 3 i()0 50 162 5 '63 45 6027 166 5 60 18 172 4 60 32 172 40 834 TABLE 10 MAUITIME POSITIONS St. Lawrence, % 30 I.,\ NKpt i - West i;t., C. Sanachno C. Romantznf, 7nf. Mouth ol Yukon 11 1. Smart. [3 1.] St. .Mich , el, fort C. Darl.y Sledge I., [2111.], Aziak I't. Uoiliiey King I , [1 I.]. N pt., 7(iOf. . I'ort Clarence, g, w, Pt.l Spenc>r / 63=15' 63 26 61 52 62 20 63 23 63 26 64 17 64 30 64 39 65 o 65 167 i68''3S' 171 50 166 10 164 20 162 37 C. Prince of Wales (extreme 1 W pt of America) J Fairway rock Diomeile Is , 2, N one, or\ Haimanciff I., [5in.], S pt J Koizeliue Sound, C. Espin- ) bera Liveruoul Dinidfe I.L'ith Berwii'k Tynomouth SmiilerUiud Hull Great Clriuisby Kings I.juu Ipswich Cork I.imcrick Slipo I.rai.loiMl.rry Belfast ).iirni- Droclicla Cliristiftusiiml Troudheim Cherbourg St. Picrr.' St. Helii-r's Dix Cove I'ort BKiir I-'-iiang Kobe Mobile O.-aka New Orleani Uakodadl Nassau Havaim Santiago dcCub» Cienfuegos Batiivia Port au Prince Sainaraue Porto Uico Aiiiboiu* Sta. Cruz Ternate Antigua Barbados A.lflai.le Porto Bello Hrisbaue Maryborough Port Spain Demerara Campecha Maranhara ? Napier Wangaroa Bahia Tahiti liuenosAyres St. John's Port Stanley, Montreal Falkland la. f Coronet PiC'tOU Sydney Hnlifaic Valparaiso Coquimbo lianulcn St. John's, AntotagasU New Brk. Iqninue r.utland Pnrtsinouth K.istou Sr New York Mazathm Philadelphia tiu.ay,ua,s Portlan.l Cliarlcstou K^quluMult TABLE 12 63f) I I t£-^^'^ o I 5 2 1 " - - ' i| IS??;; im§M m\ mi Siilill filial . Plr" tll»il"- 1^ ils IIA l58Sl '^ 5 a 8 -' §3 a g58 5^=? ,tm !2^3-gS; rS.RS ^' iS E S- ? g. S 8> j^ S § S 2 '?'2 n £ 1 1 ^l 5?, &■!:£• n 2 1 p p S ;; ll ^i II lllll Ills II S|,| llli III iiniiiifiiiiiPH ;iSl \m Mmim Ur^^r^? fe imp ■ I IP' Jill Ainmu R?,f ;5<3- iss ;a?s,^?iKs lilllll ^ MS --idtr^s^^^^m^ o cn?^Io<» ^m'S^Sot^ """■"" "~~ is i^-^ ^Isslsa I O' " " " - " "-" lIllJj S6^.2 &pi>oco 0\« rno CO O. O lo r^ O ■B M 'OO O >o f. 0> O. O'i? ro Ch'O W Ov t^ O « rrno yD i § ,= "^;il M « w'^S- m^^ S- 5 i? ^ S> Si ;:^ E^ S-a vS IS S R Qj m^mmM-^^ 0 O to r- O 5i o" ^ m-^ -■^■° n : 5- " |1 f£iMM.IIllMilMii_^ 3'i^ I H i litis sill Ills iHlliallllj 21 |*|f p5.--j;g,j; s|«|l?3 i III"! sH-ssR^sl??: ;|isSj J|||l>siiii Si Pa s° ■ g£.x J 1.1 II 2 jg = . I c e 3 '-' 5> S. K CO ?. cj < liii $m *^ s §»TO ^^ Si's ^ ■§! 5 ^ r jJS-'J >.2 a'-'3 :IIM5|i JS'SS'S'g''! Hi TABLE 12 £2 I" ni!%? ij flf's 1 1 llsi stss: ^taS III £.■3 S i^ r i-i ill £ o ^.-o ^ a JT ? »co lii iJl go|.3 „ i-^ 5 5 SI ftsl^ " i " iiS iWl'l!!! °^[ti<-'-°'8r^ !l:^HHH iltlilgHlll lUsBmi^.H inmumm 1 IsllilllllH Eiiliiif.lil llllslillil lit iMIls silHssllSH'SsssH'ssH ^£C >^■-^MC^^^^Jfr^f^c^c^c^c^ to r^ tr^ r^ p-#0 S 4f^ m"^^ n M O. W^ m(D O- rocS o" fO S 5 n" M «■ R^'Si'^ r^? 1 1 HS I |H S; S I fffl ?| III III llllf II i'?i§iii,?m f II It iiiiif II mill i-i'isflllli 5_.5... II.L.. iii.i:iii-.ijiili.iin.iii. I Sl'S.Po'g; lllllll .si' |1I| cocca ° ] 1 1 is'gsgg || s |Sg n'^^^ .^cS-S,? S-^S S-S^ ; ^"B :€-; ilsllif-g.iUij^isI J H t. ~ c e 6 o < ci e S S (£ c« S«tc " TABLE 12 C39 , g R S"8-°J H SOO>j-g ■ ;;s: si »-'? = I I I Iff KgS:^ gS<^ s §5-5 s= i5 ;: ::s3 Iss-sj SI 1^ ^ !^Li.8Ssr ^M,FiH? ^ ^ * '^ S ^^ ^ f*0_^ SKsrJ?! J^IIIpII^ «c'aa-<(xii.>;;- IlitlllillllJI Jiillillilllfll o itlH|||||Hn| Ililfllliflflfl lllilfllllHfH! I^Ef imnuBimi :: S:::| :::::::: 640 TA13LE 12 ;•! ??,^-§ = K5 S- i^lll = 5,2 Hill -lias IS I" III M Hill o 1 iE-5m 2 pSi"||||?l5||||| iummu If^sM^^lft HiElHfl! rlillllk Z «= o - O f- RS o t -c -Q O • c O * f- 5 S |- |?,^?!JS^ TABLE 12 611 5 ^ L:2s".=g l|lp|||f; £jr: RCRRo'S xiiiiip^ K s|S|"|^3-| S I miiii II Ss 15^^ 1§3-H2§ gss.sssjg: IC^*S ^0\o>o Oin f^r^ t^~- I t-oo O O « <*) 5t^ o^ t^o o .^^•SSStRSSS :lH3:5f^ lllldllllll £?r?5=lSS8§§iKgSi ||HfH|S|^|S^S 5 \ kS S" - ^ S- Ijig ^ 3:^ !4- 5 " S *" V^- 2 3 ; 5— ^,.„.„„o Vil\ lllli ^l|!?5S ^iH ^^|S^? p|HI it\m •si s-ft^ a||SS5 lllsis . S-l K~§> 8 ^i!??? g tffl • 2 jl* IP II iR§ll V »;S fea ggj "'Si" " a^ R%JSS?? [H«] 642 TABLE 12 Ij^^iss: ^R-g.-5c??^ Us^^^svzz asHL^I'llJpi l^-rSo^oil^J] O « « «'-)fo06'° ?,'8 ^ Km < ^ S .-„ 2 c rilr 4^2 si i^ ^p" ""-- i;-??^ r^Hi 'S.K.R?'Sg,^'E.SS,B-g'5 ' "rt (oS t^M O N « o" r>0 oo" O W ■ IS: SSl^ll :: :| :j|i ::::::::: :S :: : ^$£S-A§. Ill .9Si^ g ^ ^ |S^ J a ^IlllitjllWilfllilil-l %s.§~. IBi £ III 11 11"-' Imi^ sS£§Sg|, llssSI:; vow -L!!— f I si It |H||^ ill-? 'llll sop ■i raioii g J3AO(I nnH J ^oSsBltj^ I 'U'lOK ^ DO-ON r.«« ( E S-"^ O* J^ O- O ? HrJ ;?! n' -V f^ g. lO^ s = £ S-" "S. 5"f-S§ .?.« .» 'i 1 S.'s :cs = s'e??m?'^.s>8i J|IS'2??R^I'I^HsS'sl'i| |HJI.H|g e3 ^g3 f:S.3; ■g J " r_. > c s "" 2:12 - c^rr"^*^ s^S «*2 w- °s « N w - - -" ^^ U.^ N -C S^ « *? W « -O ^ ^^O" - I^ 8 g "^"g^ ^ I" ? J'to'"^ p!ot*^ CO ">0 "^ ^»|J'0<« « O j; - j; O <; O jg J>-cj. J - t-.apM -MJJ -iiutjqg - •Shoe S .^i?,^ oajimg R [sipiiua'o I « lasso's "5 si §2'£S,.?«'? ?« ^ 5 S R R. S 3; §: - - ~ £ Jj^N^J ''° '-~ =■ 2 S 2 °"^ ?'?£'! -a«qv i!Hr^ mjai r^nr? HUH -a«H --Hrls PL, BSS§»-°Sa sS' mS' i; 8" - - S o' 111- -Ills iMmmm osmojx I (52Ka!4xS6i "IIS- J_ Ills -apni= ansso |"S ra §..8 J • .2 >-.S 5 ■« C m lilESifll = § 8 • -2. g -^ Hlilililf lilllllillll R^SRW C4-4 TABLE 13 TIME SIGNAls, ISOV ( It will be noticed thit many countries have now adopted a uoiform time svstem Great Britain, Belgium, Netherlands, Sp ,in, and Portugal li.ve adopted Gr« .tnnda.d. In Ireland the mean time of the Ciservatory at Dublin is the stand ird, 25-" 22 enwich mean time u a slow of G.M.T. Austrin-Hiingarv, Denmarlt, Germanv, Italy, Norwav and Sweilm.and the Brii h Colony of Malta h»ve .flopt.-d the Meridian of 15° E. from Greenwich as a standard, or i hour fast of G.M T. This is known as Mid 1 European time. France and A'geria use the Meri lian of Paris, g"- 2i« fast of G.M .T I Cape Colony has adopted the Meridian of 221° E. as a standard, or ij h mrs fas' of G.M.T. This is known as Cape Co'ony mean time. E.'vpt and Natal have adopted Meridian ot 30° E., or 2" fast of G.M. T. | J pan has ad. pted as a standard the Meridian of 135" East from Green *ich, or 9 ,ours fast of G.M.T. Th'a is known as .Japan mean time. Siraits Settlements, Mer. of Ft. Fullert.m, >in-«p .re 6'' 55- 25' fast of G.M r. In the Cclonv ot W.st Austral a and Phillipinc la'ands, the standard lime of the Meridian of 120'' E. of I Greenwich, or 8 hours fast of (i.M.T., ha* been established. In the Colony of South Australia the 8t.-indard time of the Meridian of 142° 30' E. of Greenwich, cr 9 hours 30 min. fast of G.M.T., has been established. In the Colonies of Q eensland, New South Wales, Victoria, and Tasmania ths standard time of the I Meridian of 150° E , or 10 hours tast of G.M.T. has been established. I New Zealand has adopted as a standard the Meridian of 1724° E. from Greenwich, or iij hours fa,t of | G.M.T. This is known as New Zealand mean time. In the United Stales of Ameri.a, at the Atla-tic ports and Cuha, the standard time of th» Meridian of 75° \V. of Greenwich, or 5 hours slow of G.M. P. has been established. At PaciHc ports and Biilish Columbia 1 the standard time is that of the Meridian of 120' VV., or 8 hou s slow of G.M.T.' j ' Time of Signal being Greenwich u. Long. Plac« Signal 1 Si'uation of Time ad pted Signal Time of "Tg-r Greenwich Mean Time Lrcd Mean 1 im- • ' » 1 h m 8 h m 8 h m B SI 28 39N. 000 Greenwich . Ball RoA-al Observ itorv . I 00 00 1 00 00 (12 SS 00 and 1 12 57 30 51 26 45 N. 44 45 F,. Sheerneas . Bill Garrison Flagstiff . I 00 00 > 2 59 SI 13 17 N- .2422E. Deid . . Ball Tekgraph Tower . I 00 00 I OS 37 J " SS ooai'd 51 7 15 N- I ig 40 v.. Pover . Gun Drop B ttery . Dock Yd. Semaphore 00 00 OS 19 12 S7jx> SO 48 oN. 1 6 i8«'. Portsmouth . Ball 55 35 12 SS 00 50 8 45 N. S 2 45 W. Kaloxuth . H.1II HendenniH Citt e . I 00 CO 39 49 SO S3 39 !*• I 24 5W. Southampton Ball South Ca«tle . 1 0000 54 24 12 55 00 SO 22 oN. 4 10 20 \V. Uevonport . B^ill Mount Wise . 43 ly 12 55 00 Gun 43 19 51 36 SS N. 3 55 35 W. 3 036VV. Swansea Gun On old Eastern Pier 1 0000 044 '8 53^24 4S- Liverpool Gun Birken>-ead, Mor- peth Do.k I 0000 04758 — ^6 27 56 N. 2 58 45 W. Dundee. Gun I 00 00 048 05 047 16 _ 55 57 '3 N- 3 10 ,54 W. Eiliuburgh . Ball Nelson's Monument. j 12 55 ooand _ _ Gun Edinburgh Cstle . I 00 00 47 16 1 12 57 00 5S 032N. I 27 28 W. North Shields Gun Near Albert Edward Dock 54 10 - SI S3 53^'- 8 27 17W. Cork . Gun Victoria Quay . I 00 00 26 II 51 SI 9N- 8 16 37 W. Qiieenstown . Gun Ne« Mtlitarv Hosp. 1 00 00 26 53 53'o45N. 6 IS30VV. Dublin . Ball Ducks Board Bui ding I 00 00 03458 — j 1 2449 I'N. 66 58 00 E. Karachi Ball Me'ewether Pier . !2o 32 8 I 00 00 20 27 8 .8 55 SI N. 72 50 33 E. Bombay! Ball Bombay Castle . '20 08 44 Clock Tower, Dorks 115 00 00 I 00 00 eo 03 44 .8 57 13 N. 72 50 46 l<,. „ Ball 7 SI 16 14 55 00 6 56 34 N. 79 50 34 E. Colombo Sema. Master Attendant's . I22 54 i 4iSoot 22 49 I 16 46 oN. 96 10 E. Rangoon . Ball Sailors' Home . . 1.7 35 20 00 00 17 30 20 .3 547N. 80 17 37 E. Madras . Sema- |h re Jl.isier Attendant's 19 39 00 22 33 2SN. 88 20 la E. Calcutta B.ll Fort William . . 19 06 39 I 00 00 19 01 39 — „ IPall Port Commissioner's 19 06 39 I 00 00 19 01 39 22 .744 N. 1.4 10 8F.. Hongkong . Ball Kauung Tower . J17 23 18 I 00 00 17 18 ,8 I .7 33 N. 103 5° 53 '-• Singapore . Ball Ft.C.nningFlagstairi8 4 35 I CO 00 18 00 00 I 'S45N 103 50 00 E. Ball I'uloBr.ni . .1,8 4 35 I 00 CO 18 0000 6 548S. 106 53 07 E. Batavia. . iDisc, TanjiigPriok Basin,, 6 52 28 00 00 .6 47 28 ,. 1 Discs 1,8 00 00 I C7 32 17 55 00 7 12 10 S. 112 43 40 E. Sourabaya . Discs Kalimas Kivcr 16 29 OS 16 24 OS .5 55 S. S 42 30 W. St. Helena . B 11 Ladder Hill Flan Stan 1 0000 37 TO 1= 55 00 Pall 1 iine Office . 37 10 12 55 00 5 3~48 N. II 30 \V. Accra . Flag Telegraph Odice . .1"^ II 00 00 8 48 4S S. 13 13 20E. 'PauldeLoandaj Ball Observatory . 7 7 I 00 00 037 • For more detailed and later informalioM on Time Sinnals see Admiralty List ot Time sign Is, sold by J. D. Potter, AgeiJII ;oi A.lmiralty f hartg, U6 Minories, E. ■1 K.f. BBitioD i u time. ,M.r..ea.t mc, albo at e ' 15" a.iB. TABLE 13 TlilE SIGNALS, IHOa Time of Signal being m Greenwich Lat. Long. Place Signal aJopted Situation of Time 1 Signal Time of Preparatory Greenwich! Local Mean Time Mean Time Signal . ,. 1 o . ,. ~b m 8~ b m 8 h m 9 33 54 24 S. .8 25 15 E. Table Bay* . Ball At Alfred Docks . 00 00 .3000 Gun On Imhoa Battery . ' 00 00 I 3000 _ 34 II 35 S- .8 25 58 E. Simons Bit . Disc Telegraph Office . 1 00 00 I 30 00 23 55 00 33 57 43 S. 25 i7 19 E. Port El.zab'etU Ball At the Lighthouse . 1 00 00 I 30 00 33 36 10 S. 26 54 5 E. Port Al'red . Ball — 00 00 I 30 00 33 I 50 S. 27 34 15 E. East London Ball Signal HiU . . 1 00 co r 30 cx) 2T 52 30S. 1 3, 3 oE. Natal . Ball North Entrance Point 22 55 59 20.0 58.15729 oE. Mauritius . Ball Signal Mt. Pt. Louis 21 oy 47 I 00 00 21 04 47 32 3 <3S- «I5 44 15 E. Fremantle . BaU Arthur Head . . 17 42 57 16 57 00 34 5' 6 S- 138 28 50 E. Adela.det . Ball At the Seniapliore . 15 30 00 43 55 «5 ^5 00 37 52 7 S. :I44 54 47 E. Port Phillip . BaU Gellibrand Point . .5 00 00 39 39 14 55 00 33 9<»S,!,44^, ooE. — Ball Telegraph, Geeloiig. 15 00 00 37 24 14 55 00 33 16 27 S. 144 39 45 E. — Fla;; QueeiisclitT Signals . 15 00 00 38 .39 33 51 41 S. 151 12 23 E. Sydney Ball Obseryatoiy . . ,5 cx) 00 I 04 49 14 5^ 03 32 55 43 S. 151 47 28 E. Newcastle . Ball Custom House . .5 co 00 I 07 10 14 55 00 27 28 3S. 153 I 31 E. Brisbane . Ball Signal Tower . .5 00 00 I 12 06 14 55 00 42 53 22S ,,47 20 23 E. Hobart . jBall Fort Mulgrave . 15 00 00 49 20 14 5000 (Gun Queen's Battery . i — 43 3'< 42 S. 172 44 50 E. Lyttttlton . BaU Observatory . . 13 30 00 I 00 59 13 25 00 41 16 50 S. 174 46 55 E. Wellington . BaU Railway Whai-fJ . 12 30 00 09 08 4> 49 oS. .70 39 oE. Otago . . BaU Sigiml Staff, Port 12 30 00 II 52 36 OnceTweek 36 so 44 S.! 174 45 52 E. Auckland . B.V11 Post Office FlagstatI 12 30 00 009 03 12 25 00 47 J4 10 Ni 52 40 27 W. St. John's . Gun Signal Hill . 3 3° 43 ? 00 00 4. Vs 42 N 66 3 45 W St. John, N.B. Ball New Custom House 4 45 00 46 48 23 N 7. «t7W. Quebec. . Ball At Citadel . . . 60000 I IS II 5 55 00 45 31 oN. 73 33 15^- Montreal . Ball Harbour OfCce S 00 00 5 47 4 55 00 32 19 22 N. 64 49 33 W. Bermuda! . Ball Dockyard Flagstaff 4 19 18 4 14 18 23 08 30 N. 82 20 SOW. Hayana Ball Naval Office . 5 00 00 II 30 36 4 50 00 .400 53N'- 6. 00 Sow. St. Lucia . BaU Harbour Master'i Office, Castries 4 04 00 00 00 3 59 00 6 48 48 N. 58 9 52 W. Demerara . Ball General Post Office. 3 52 39 03 00 3 47 46 10 39 oN.I 61 30 38 W. Trinidad . Ball Observatory Tower 4S602? 5 49 30 N. 55 8 48 W. Paramaribo . Disc Guardship 3 40 35 00 00 3 35 35 12 645N. 68 56 44 W. Cura<,-ao Flag Guardship . 4 35 47 00 00 4 30 47 22 54 24 S. 43 10 2. W. Bio de Janairo Drum Mount CasleUo . 3 52 41 GO 00 2 47 41 34 52 33 3-, 57 54 43 W. Rio del. Plata BaU Dock Engine Ho. . a SI 39? 23 00 00 2 47 39 34 35 5" S. 58 22 ,5 W. Buenos Aires BM Hyd. Office . S 1648 I 23 19 5 14 48 51 13 15N. i 4 24 15 E. Antwerp Discs Hauseali, House . I 00 00 I 17 37 12 55 00 51 26 33 N. 3 35 48 E. Flusliing D.SC8 Stone Tower of sluice 23 45 37 00 00 2J 40 37 51 49 iqN.j 4 740E. Hellevoe\8tui9 Discs Marine Establishment 23 43 29 00 00 23 38 29 52 22 40 N. , 4 54 45 E Amsterdam . Disc Commercial Quay . 23 40 21 00 00 23 35 21 515439N.I 4 29 47 E. ' Rotlerdam . Dmca Gale Building . 23 42 01 00 00 13 37 01 52 57 50N-I 4 46 36 E. W.UemBOord Discs Marine Office . . 23 40 54 GO 00 23 35 54 533. 54N.1 8 B48E., W.lhelms- ; Ball Observatoiy . . 23 00 00 II 32 35 20 50 CO - 1 hftvent •BaU „ 1 00 00 32 35 23 57 00 53 32 5' N. 8 34 7 E. Bremerhavm ) Ball S.W. of Lighthouse 33 00 00 II 34 16 22 so CO 'BaU „ 1 00 00 34 16 23 57 00 S3 52 24 N. 8 42 30 E. Caxliaven J BaU E. of Lighthouse . 23 00 00 II 34 50 22 5000 1 'BaU 00 00 34 SO =3 57 °o S3 3^30 N. 9 58 57 E. Hamburg . BaU On the Kaiser Quay ] oc 00 39 56 23 50 00 =4 .9 18 N. .o%4oE. Kiel . . iBaU II 40 39 22 so 00 (Gun Guardship . . 23 00 00 II 40 39 — 53 54 36 N. 14 15 58E. 1 Swiuemund*. J BaU S.W. o( Lighthouse 22 00 00 10 57 4 ai so 00 — 1 M (Ball „ 1 3 00 00 3 57 4 2 5000 54 24 18 N. 18 40 10 E. Neufahrwaaaer BaU I 14 41 22 5" 00 5h 2 4 N. 12 37 24 K. Elsinore Ball Quarantine House . 00 00 50 30 23 55 00 57 42 34 N.: II 58 oE.| Gothenburg . Ball Navigation School . 00 00 47 52 23 55 00 55 40 42 N. ' 12 3S 7 E. ' Coijenliagen . Ball Nikolai Tower . . 00 00 so 19 23 55 00 53 37 oN. .30, .5E ' Malm,. . . BaU SchtK)l of Navigation 00 00 52 02 23 55 00 56 09 28 \.' 15 35 36 E. Carlskrona . Ball Dockyard Tower . 00 00 . .23 23 54 00 59 19 >oN 18 4 44E.| Stockholm . Ball Scliool of Navigation 00 00 I la 19 23 55 "-o t B-tllB 'Iroppeil at I* od" oo*. staodftrd times, : UDC« ft »e*k. { On S.ttunlayi only. ^ BftlJ dropped at i^ oo^ oo*, Mld-Europcao t the Auntrallan CoIODle* and N'ew ZeaUimi. I At I>m*rHr«, on WwJncBday nrd Saturday only. ,«, throughout GcriDnny and r TIMK SHiNAl.S, iyO'2 | Time of Signil being niide Gre.n.ich Lak L..Dg. Place Si-nal adopted Si'uationofTime Signil liin.- of Prepiraror^ bgnal Gr.-enw'ch MeanTinv Local M an 1 im. o . /. h m ■ h ni 1 h m s 56 56 52 X. 24 05 30 E Riga . . Bll Sailors' H-me. . 23 23 32 59 54 23 .8 32 59 59 24 X. 29 45 54 '•' KronstHdt . B.U Marine lelesjraph . 22 00 56 21 52 56 59 56 31 X. 30 .8 22 E. St. IVlersb r;,' (iun Fo,t Petri-Paul . 21 58 41 00 00 — 60 9 ^9 N- 24 57 7 K Helsin-ur;, . B»l. Observatory . 22 20 II 00 00 22 16 11 60 26 57 N'- 22 17 43 K. Abi. Ital Navigating School . 22 30 51 00 00 22 24 51 65 . .9N-. 25 3^ 30 F" Uleabirg . Bail Xa\igati"n Sjhool . 22 ,7 58 00 00 22 .2 58 63 25 40 X. 10 22 4 E. Tromlhiem* . B 11 Ohst^rvatory . 23 0000 23 41 28 22 45 00 65 23 S3 N- 5 '8 35 E. Borsjeii*. . B.ll Ob ervatory . 23 00 00 23 21 13 22 45 00 59 45 44 N- 10 43 33 E- Hhrutiauia* . Drum Ob eiv.toty . 23 0000 23 42 54 22 55 00 49 38 42 X. 1 37 34 VV. Cherbourg . Die Marine Observatory 21 50 39 10 CO ooT 21 45 39 48I246N. 4;9 48VV. Brest . . Flag Observatory . 21 50 39 00 oot 21 45 39 47 44 45 S. 3 21 isW. LOri. nt Ball H«rb,mr Tower . ooooot 21 45 39 45 59 13 X. I 5 50 W. K u as . Ball, on Tower . . . 21 50 39 10 00 oot 21 45 39 4556 loN'. 05735W K.K?hefott B 11. on St. Louis Tower . 21 so 39 00 oot 21 45 39 38 42 1 8 X. 9 8 24 W. l.sb n . B,ll Naval S.hool . . ii6 4S « 3' 45 36 27 4. N. 6 12 24 W. Cadu . . B»ll Observatury . I 2+ 50 I 0000 I .4 SO 43 7 "X. 5 55 27 E- Toulon . . Ball Naval Observatorj- . 31 50 39 ooooot 21 40 39 36 47 oX. 3 3 '5E. Alh'ier . C.ck Town Hall . C ock shows Pa is Mean n e. i, 25.0 V. 8SS"E. Geu««:. . Gun Fort Ca^tellaccia . 23 00 00 I23 35 41 22 5500 44 6 5SN. 9 49 33 E. Spczia . . Gun Lagi.ra Moe . 23 CO 00 23 39 18 40»8 2oX. .7 14 ,oR. Taranto Ball S'. Angel.. Canile . 23 00 00 8 57 22 55 00 44 52 8X.! 13 so 4SK. Pola . Ball Harbiur Castle .230000 '235523 22 55 00 45 38 56 X. 13 45 30 E. Trieste . Ball Lighthouse . . 23 00 00 23 55 02 22 55 00 45 19 36><'- 14 25 44 E. FiuTie . Ball Si air, Mole end . 23 00 00 23 57 43 22 55 00 44 31 49^- 14 28 6 E. Lussin Piccolo Discs S.vV. Qiav . . 23 00 00 23 57 52 35 53 SON. M 30 55 E. Malta . . (Ball Palace Val tta . 23 00 00 23 58 4 22 55 00 1 Ball fust 111 House . 23 00 00 23 58 4 22 55 00 4050 SN. 14 IS 30 E. Naples . Hall Vincenz . Mole . 23 00 00 '23 57 2 22 55 oo 3. II 39 ». 29 S3 IS E. Alexandria! . Ball Fort Napoleon . . 22 00 00 23 59 33 21 55 00 31 IS 45 V- 32 18 45 E. Po.tSaidll . Ball High Light Ho . 22 OD 00 00 00 21 55 oo 46 58 2. X. 3, s8 28 E. Nicolaev (Black Sea) Olessa . Ball Observatory . . 21 52 06 00 00 2. 47 6 46 29 oX. 30 4S oE. Ball Russian S.X.C. Office 21 57 00000 21 52 00 41 31 30X. 1 70 40 20 V. W.indsHoUlI Bull Water Tow. r . 5 00 00 17 19 41 29 36 S. 71 19 39 W. Xovport Ball Torwdo Station 5 00 00 14 4> — 40 43 oN. 74 25 W. New York . Ball Union Telegraph Office SOOc» 003 58 4 55 00 39 56 4S>J- 75 9 'oW. Phiadelpliia. Ball Mariiine Exchange S 00 00 23 59 23 4 5000 39 17 5^S.[ 76 36 57 W. Baltimore . Bai B iltimore Railway . S 00 00 23 53 32 38 53 39 ^-j 77 3 8W. Watliincton . Bal Nav.l Oh-crvatory . S 00 00 23 51 47 4 5000 37 oX. 76 i8 25\V Ha> pton Koads B.ll Hvgei. Hotel . 5 00 OD 23 54 46 32 4 5o>>- 1 81 5 'oW Savannah . Ball Custom House. 23 35 .39 — 29 57 8X.| 90 3 50 W New Orleans. Bdl S .gar Hou-e . 5 00 00 22 59 43 4 55 00 29 .8 oN.I 9447 3o\V Galveston . Ball Lew Building 5 00 00 23 4 55 00 37 47 40 >• 122 23 35 \V 38 S53N.,.22i6.6W Sun Francisco Ball Tower of Ferry Ho.** 8 00 00 23 50 23 7 55 00 Mare Wand . B.ll The Observatory" . 8 00 00 23 5° 55 7 55 00 49 17 30^-1123 7 o\V Vancouver . Gun Brock'on Point 17 00 00 33 . soX.l 7. 3830VV Valparaiso . Ball Naval School . 4 46 34 00 00 4 4' 34 21 .8 ,3 X. 157 5, 47 A' Honolulu Whi.fe Steam Mills . 12 00 00 I 28 33 14 36 S. 120 58 E. Manila . Ball Metcondogical Office '16 00 OD 3 52 >5 55 00 2051 56 N. .06 39 54 E. HaifoDg . Bill Observatorv . '13 53 20 «3 43 » 232, 43N. .164030E. Swat u . . Ball H..rbour Office .'16.305 OD 00 24 27 25 M. 118 3 33 K A inoy . Gun Kulangseu . .16 07 44 CO 00 1602 +4 31 14 7N. 121 29 loE. Shangai . B 11 Semaphore . '15 54 03 00 00 •5 49 3 37 33 10 N. ,21 25 20 E. Cbiu . . Ball Mastnear Tower Hill 15 54 20 I 00 oo* 34 I oX. ,3; I. oE. Kobe . . Ball On the Bund . .15 00 00 00 00 _ 41 46 35\V. 140 43 50 E Hakodate Fl.g Obsy.Fl.s-ntr. .1.50000 22 55 14 55 00 43 7 oX. 131 52 44 E Vladivostock Ball l&Gun Harbour Office .15 12 29 00 00 IS 07 20 J Qu t Parin mean time. 00'" 00" Mlrt-Eoropoan timt. throughout Norn-ay, Amtrla, and Italy, kept 18 standar.l time ot the meridian or 30"* E. . Port Said dropped also at S'' a m. and ^l' p.m , ttand^rd t AU time tialls on the A'l. nlio and Quit of Mexico coasts ot the United S'ates are .Iropi 1 meridian West from Greenwich— equivalent to 5' 00" oo" pm. Greenwich mean time. •• Bulls dropped at noon, me,»n time ol ijotb uierilian Weist from Oreen«ich N3.— Wbcn the report of the gun is used allow for time ot jwaage of tound. Set p. 13>. 546 TABLE 14. EPACJS 1 Years Mnnlhs d h d h Tear Epact Y.ar ~Tt Tear E,.act Epnot Mouth d b d b d b 1801 20 9 1197 27 6 1903 2 II 1909 9 4 Jan. O O July 3 20 1S92L I 10 1898 8 8 1904L «3 2 1910 19 19 Feb. 1 II Aug. 5 7 189S '3 5 1899 19 o igo."! 24 17 1911 O 22 Mar.h 29 II .Sep.. 6 i8 1894 24 5 1910 O 2 1906 5 «9 1912L «i 13 April I lO Oct. 7 5 1895 S o 1901 lo 17 1907 |6 II 1913 23 4 May I 21 Nov. 8 17 1896L '5 '5 1902 21 8 19081. 27 a 1914 4 7 June 3 8 Uec. 9 4 TABLE 15. SEMIMENSTRUAL INEQUALITY or the Time of High Water, 1 For London, Liverpool, Pembroke, K :imsgate, Sheerncss, Portsmouth, Plymouth, and Brest. 1 Moons' som Mo.n's t^em Sem. Moon's Sera. Transit Incq. Trnn-it I.ieq. Tran24 131 13 6; 13 9 14c Hi 01 OS rq 2q 40 56 66 80' 94 107 120 131 14- 1 14-9, '55 «5-9 18 01 of 12 21 3 ' 45! 59 7-4 90; 106 121 >3S 148 ■5 9 16817-5 170 20 02 06 '•3 23 3-6 50! -6-6 8^ 100 117 13-4 iVo 16-4 177 187 194' 198 200 -.;o 22 02 07 15 2-613 9 55! 7-2 qi no' 129 148 ib-s 181 iq-4 205 21-3 21 S 22 24 02 16 2-8 4-S 60 79 qq 120' 14- 1 Ibl 180 197 21 2 224123-3 23 S 24c 24 26 0-2 08 17 30 4 b b'Si 86 107 13-0,153 ■7-4 19S 21-4 230 24-3I 25-2 258 2bO 26 2S 02 o-!^ 19 33 5-0 7-° 9-2 Ufa ,4-o.b-4 i8-8 230 247 26-11 27-2' 27S 28-C 30 02 oq 20 3S S-4 75 99 124 15-0 176 201 22-q 24-6 26- S 28-029-1 298 300 30 32 02 I 2 1 37 S7 80 10-5 13-2 160' 18 8 21S 240 263 283 299 31-0 31 8 320 34 OS 10 23 40, 6 I 85 II-2 140 170; 200 22-8 2SS 27-9, 30 29631-8 3>7 330 337 340 36 o-s 2-4; 42 6-4 90 118 14-9 i8-o 21-1 242 270 33-6 .34c 357 3bo 38 03 2-5J4-4 6S 9-5! 12-5 157 19-0' 22-3 25-5 28-5 31-2 336 35-5 3b-9 377 380 38 40 o-S 27 47 71 100^ 132 l6s 200, 235 26-8 300 329 353 37-3 38-8 39 7 400 40 42 o-t 2-8 4-9 75 10-5 I3S 17-4 210 246 3'S 34-5' 37' 39-2 40-7 417 42-0 44 2 9 5'l7-9 no; 145 182 220| 258 29s 33 36 I 3S'9 411 427 437 44-d 44 46 0-3 I 4 n 5-41 8-2 115 151 iqo 230. 270 30f 34S 37-8: 406 42-9; 44-6', 457 460 46 04 I '4 3-2 5 618-6 12 158 198 24-ol 28-2 320 360 39-4| 42-4 45-8 44-61 47 6 480 »0 z± "5 JJ sU "-•5 '^-l 207 25 29-3 JX6 jn 41-1144 I 46-7 48-51 49b i2.2 .SO TAIUJ- 17. TABLT' 18 647 AKC. j " HM. M. S S. o o 0-00 o 4 1 4 1 0-07 o 8 2 8 2 013 O 12 3 12 3 o i6 4 16 4 0-27 5 20 5 0-33 o 14 6 24 6 0-40 o a8 7 28 7 0-47 12 8 52 8 0-53 o 36 9 36 9 o-6o 40 10 10 0-67 ~J1 44 11 44 U 0-73 48 12 4ii 12 080 cx 13 52 13 0-87 °k 14 j6 14 0-93 15 1 15 rco « 4 16 > 4 16 1-07 I 8 17 I 8 17 113 18 I 12 18 !9 1 16 19 1 16 19 1-27 20 20 1 20 20 '•33 30 2 21 1 24 21 140 40 I 40 22 1 28 22 ■ •47 50 3 *° 23 ' 3» 23 ■ 53 60 4 24 , 36 24 160 70 4 40 25 I 40 25 1-67 80 5 »o 26 I 44 26 '•73 90 6 27 1 48 27 r8o 100 6 40 28 > 5^ 28 1-87 110 7 10 29 ■ 56 29 '•93 120 8 30 2 30 2-00 130" 8 40 31 i 4 31 2-07 140 9 20 32 2 8 32 ^'I' 150 33 2 12 33 160 10 40 34 2 16 34 2-»7 170 II 20 35 2 20 35 »-33 180 12 36 2 24 36 2-40 37 2 28 37 2-47 38 2 32 38 1-53 39 2 36 39 2-6o 40 2 40 40 2-67 41 2 44 ~w 1-73 42 2 48 42 2-8o 43 I 5^ 43 2-87 44 2 56 44 i-93 45 3 ° 15 3-00 46 3 4 46 3-07 47 3 8 47 3"'3 48 3 " 48 3-20 49 3 -6 49 3-»7 50 3 20 50 HI TT 3 14 51 3-40 52 328 52 3-47 53 3 3* 53 3-53 54 3 36 54 3-60 bi 3 40 55 3-67 M 3 44 56 3'73 H 348 57 3-8o M 3 51 58 3-87 M 3 56 59 3-93 TIME. 1 "• " M. , ..,■"1 r 1 15 15 i« o-o o-i ° 5 30 -2 30 30 o-i 3 45 3 45 45 0-3 4 5 60 4 I I 0-4 6 75 6 ' '5 ' '5 0-5 7 5 90 6 1 30 1 30 0-6 9 105 7 ' 45 ' 45 07 10 5 8 2 1 0-8 12 '35 9 ^ '5 1 '5 0-9 '3 5 ■ 50 10 2 30 10 2 30 165 II » 45 11 » 45 180 12 3 12 3 '95 13 3 '5 13 3 '5 14 3 30 U 3 30 225 15 3 45 15 3 45 240 l(i 4 16 4 ° »5S 17 4 '5 17 4 >5 270 18 4 30 18 4 3° 285 li) 4 45 19 4 45 300 20 5 20 5 3'5 21 5 '5 21 5 '5 H 330 22 5 3° 22 5 30 23 345 23 5 45 23 5 45 34 360 24 6 24 6 L 25 26 6 .5 6 30 26 26 6 ,5 6 30 27 6 45 27 64$ 28 7 28 7 29 7 '5 29 7 '5 30 7 30 30 31 7 30 7 45 7 45 32 8 32 8 33 8 '5 33 8 15 34 8 30 34 8 30 35 8 45 35 8 45 36 9 ° 36 9 37 9 '5 37 9 '5 38 9 30 38 9 3° 39 9 45 39 9 45 40 10 40 10 41 10 15 41 10 15 42 lo 30 42 10 30 43 43 10 45 44 II 44 II 45 II 15 45 11 15 46 II 30 46 II 30 47 II 45 47 II 45 48 48 12 49 12 15 49 12 15 60 12 30 50 12 30 M- 12 45 51 12 45 52 13 52 13 63 '3 '5 53 '3 «5 54 13 30 64 13 30 55 '3 45 65 '3 45 56 14 66 14 57 14 15 57 14 IS 58 14 30 58 14 30 5» '4 45 69 '4 4i 648 TABLE 19 c OKI lliCTION OF THE SUN'S DECI-INATION AT NOON, AT SEA, rOK LONGITUDE AND FOK TIME Decliiialion Time from NOMJ VP 2° 4° [6° 8° i 10°| 12° 14° IC° 17° I«°[l9°j20° 21° 214° 22° 22i°|23"|23i- 0' 10 20 30 40 ao 60 70 80 yo 0-7 ••3 2-0 2-6 3-3 39 4-6 5-1 0-7 ' 3 JO 2-6 3-3 3-9 4-6 5'^ 5-9 o' 0-7 ■•3 '9 2-6 3'3 3-9 4"5 5> 5-8 o' 3-2 o' \ o 0-6 o 12 I 1-8 I 2-5, 2 y 3 3-7: 3 4-31 4 5-0; 4 5-6 i 5 6 8 4 6 2 8 4 0' o'|o- 0-6 0-5' 0-5 • •, 10 10 >:7 >;6';5 3-4' 3-2! 2-9 4-0 3-7[3-4 4-S 4-2 3-9 5-1 4-S:4-4 0-5 0-9 '•4 i:i 3-2 3-7 4-J 0-4 09 1-3 21 ',i 3-4 3-9 o-g 0-7 1-2 I-O .•6 .-4 2-0 1-7 2-4 2-1 2-8 2-4 3-2 2-8 3-6 3-2 0' 0-3 06 0-9 J-2 '•5 1-8 2-1 2-4 2-7 0' u 0-8 i-o ■•3 1-6 1-8 2-4 °-5 0-7 0-9 II '■4 1-6 '•9 21 0' 0-4 0-6 0-8 10 1-2 •■4 1-6 1-8 0-3 0-4 °'5 0-6 0-8 o'9 0-, 04 0-4 0-5 0-6 0-7 c-8 0'' 0" 40 1 20 2 2 40 3 20 4 4 40 b 20 (1 100 110 120 130 140 150 KiO 170 180 6-5 7-1 7-8 8-5 ?■' 9-8 IO-5 6-5 7-2 7-8 9-8 IO-4 6-4 7-' 7-7 8-4 9° 97 10-3 1 1-6 11-4 6-2 6 6-8 1 6 9'3l 9 9-9' 9 IO-5 lo ii-i 10 6 8 3 6 S'7 u 7 "4 8-0 8-5 91 9-7 10-3 5-3! 4-8 5-9|5-3 6-4| 5-8 rl 6-7 8-0 7-2 8-5 7-7 9-. 8-2 9-6; 8-8 4-6 5-0 5-5 59 ^:t 7-3 7-8 8-3 43 4-8 5-2 5-6 6-0 6-5 69 7-4 7-9 3-9 3-6 4-3 3-9 4-7 4-3 5-1 4-6 5-5, 5-0 5-9! 5-3 tWo 7-2|6-4 3-0 39 4'4 y 5-5 2-7 3-0 3-2 3-5 3'8 41 Pe 4-9 2-3 ^•5 2-8 3-0 3-3 4-0 43 2-0 2-2 2-4 2-6 2-8 3-0 3-2 "•3 '•9 ^■3 0-9 c-9 'i '"4 40 7 20 8 H 40 !) 20 10 10 40 :i 20 12 In W. Long For Time, when the Declin. is increasing. In E. Long. When the Declin. is ji;-;^^;;;^;-;;; add , wh.;n the Declin. is decieating. sub. TABLE 20 CORRECTION OF THE EQUATION OF TI.ME, AT NOON, AT SEA , FOR LONGITUDE AND FOll TIME froni ^oon 1 Daily Variation V 2* 1 4' 6- 8* 10' 12* 14» W 18* 20« 22. 24* 26- 28* 1 30- 1 0° 1 1 (»" 0"' 10 I 0-. ; °'3 0-3 0-4 0-4 o-b 0-7 0-7 20 l|o-2 0-3 4 0-6 0-7 o-S 0-9 11 '■3 '■4 ■■s! ■■7 30 o"1 O'S 7 0-8 1-2 •"3 1-7 2-0 2'2 2-3 1 »-5 2 40 2 0-4 0-7 9 i-i '■3 1-6 1-8 2-7 2-o; 3-i| 3-3 M 3 0-6 0-8 1-4 i'7 '•9 2-2 2-, 2-8 3-3 36 3-9 4-J m 3 0-7 i-o 3 ''7 2-3 2-7 3-3 4-0 4'3l 4'7, 5'c 4 70 4 0-8 1-2 6 1-9 2-3 2-7 3-> 3-9 4" 7 S' 5-4 5-8 80 4 0-9 i'3 8 2-2 2-7 3-1 Vb 4-4 4-9 r3 5-8 6-2 1 6-7 no 100 ~~ ± i '■5 2 2-8 3'° 3"3 XL TT 1^ 5-0 VS b-S 70 7-4 T7T .•6 6-1 6-7 7"2 7-8 8-3 t> 4(1 110 6 1-2 1 1-8 1 2 4 1 3'' 3'7 4-3 49 6-7 7-3 7-9 9-2 120 7 ■•3 2'0 2 7 3"3 4-0 4-7 Vl b-7 7-3 8-0 8-7 9-3 lo-c 8 130 7 "•4 2-2 2 9 V6 4' 3 s-> s-s 7'2 7-9 8-7 9-4 lo-i 140 8 .•6 2-3 3 4' 7 S-4 b-2 7-8 8-6 9-3 io'9 11-7 I.-.0 8 V8 b-7 8-3 9-2 lo-o "•7 12s ISO 9 1-8 2-7 3 6 V3 6-2 7-1 S-o 8-9 9-8 .0-7 II-6 12-4 '3-3 170 9 1-9 2-8 3 8 S-7 b 6 94 ,o-4 ..-3 '2-3i>3-2 ■4-2 180 1 I 3-0 4'o 7-0 90 lO'U .3-o|.4-o M^ In W. Long. In E. Long. uhe..,heE^n.t.i.|~;;;|;::lt in the Eauai is \ ""'"""S- " m tne tquai. is j j„„„.i„g^ , Id. 1 i.r limi', nlmii th»^ r,,|iK(l. 1- r...-. r.iMr.- . .i.l.I , "1 ■n tl..> I'q..;.!. is Hrnrnshr-. sub — — PAiu.r 21 (U?> FOB REDL'CINO DAII.V AND TWELVK-IIOUKI.Y VARIATIONS rct.T. I„ter. \ arialion in H* or in 18* r •J IV 4' •^ 1 0" 30" 0" 1 30" 0" ;«)" U- : 3«'" •" 30" (C 0" 30 » 30 8 30 3 30 4 30 1 0- 0" 1ft :to 1 45 1 15 30 4o 2 15 O 2-5 o 3-7 5 6-2 7-5 8-7 10 11-2 1-9 3-7 5-6 7-5 9-3 11-2 131 IS i6-8 2-5 5 7-5 12-5 22-5 9-4 12-5 156 219 0' 0" 3-7 7-5 0° ;i.7 30 33-7 0' 0" 4-4 8-7 13-1 17-5 = P 59-4 ° 5 ^15 25 30 35 45 0' 0" ,1-2 16-9 :28;j " 33-7 39-4 0' 0" 6-2 12-5 25 31-2 ° 37-5 43-7 0' 0" 6-9 27-5 34-4 41-2 0+8-. 55 1 1-9 5 30 U 30 7 ■« 8 30 9 SO 30 45 3 15 30 45 4 16 30 45 ,2-5 13-7 22-5 23-7 .8-7 206 22-5 24-4 26-2 28-1 30 31-9 33"7 3S-6 25 275 30 32-5 35 ° 37'5 40 42-5 45 47-5 31-2 34-4 37-5 40-6 43-7 46-9 50 53-1 56-2 ° 59-3 ° 37-5 4. -2 45 48-7 > 37 • 7-5 43"7 48-. 52-5 56-9 1 1-2 1 5-6 I 10 I 14-4 I i8-7 so ° 55 1 ' 5 I 10 ' '5 I 30 ' 35 5b-2 1 1-9 ' 7-5 I i8-7 I 244 I 30 I 35-6 I 41-2 I 46-9 I 2-5 1 87 ' '5 • 27-5 ' 33-7 I 40 I 46-2 I 52-5 I 587 I 8-7 . .56 1 22-S I 294 I 35-2 I 43-' 1 50 1 56-9 ^ 3'7 2 10-6 10 30 11 30 12 30 13 u1 30 lo 30 It; lU :io 30 5 (1 311 15 30 45 7 15 :m) 45 B 15 30 45 !» 30 45 25 30 31-2 32-5 337 ° 37-5 39-4 431 Ih 50-6 52-? i4-4 50 52-5 ° 55 57-5 1 25 ' S I 7-5 I 2-4 1 21-4 , 30-6 > 15 I 18-7 I 22-5 I 26-2 I 30 > 33-7 ■ 37-5 I 41-2 ' 45 ■ 48-7 I 275 I 31-9 I 36-2 1 40-6 ' 45 1 49-4 i?i 2 6-9 I 40 I 45 1 50 ' " ^ >5 2 25 . s^-5 ■ 58;. 2 94 2:^6 2 26-2 2 3. -9 1 37-5 2 43' I 1 5 2 30 2 362 2 42-5 2 48-7 * 55 3 '-I 2 17-5 2 24-4 2 38- 1 i 45 2 519 ^ 587 3 5-6 3 12-5 3 i9"4 ° 37-5 38-7 40 41-2 42-5 43-7 :% 47-5 48-7 I 19 ■ V" I 5-6 ' 7-5 I 9-3 I !|-2 I I3-I ' '5 I 17-5 I 22-5 I 30 1 32-5 ' 35 I 3-5 : ^18 1 40 I 43-1 1 46-2 ■ 49-3 :g ! 3-7 22^:^ 2 15-6 ih 2 33-1 1 37-5 2 III 2 50'6 2 30 5 35 J 45 2 50 ^ 55 3 3 5 3 'o 3 15 2 48-7 = S4"4 I U 3 33-7 3 39-4 3 7'5 3 '3-7 if; 3 38-7 3 45 3 5>-J 3 57'5 4 3-7 3 262 3 35'' 3 40 3 46-9 3 53-7 4 0-6 4 7-5 4 144 4 21-2 4 28-, at 30 ■Jl 30 ^■^ M ■>3 30 .'i 30 J.i .«) 26 :*o 27 30 JR :to 19 :«) 10 :u) 45 11 15 .10 45 12 15 :io 4* 13 15 30 45 II 15 ,•«! 45 1.^ II 50 51-2 52-5 ° 53-7 55 56-2 57-5 58-7 ■ '5 I 168 I 187 1 206 I 22-1; I 24-4 I 26-2 I 28- I 1 30 I 31-9 I 40 . 4'--5 < 45 > 47-5 I 52-5 ' 55 I S7-5 1 2-5 2 14-3 2 17-4 2 20-6 2 III 2 30 2 33-1 2 30 i 33'7 - 37-5 2 41-2 i 45 1 48-7 2 52-5 2 56-2 3 3 3-7 - 55 ^ 59-4 3 3-7 3 8-I 3 12-5 3 '6-9 3 21-2 3 J5-6 3 3° 3 34*4 3 -° 3 =5 3 5° 3 35 3 40 3 45 3 50 3 55 4 4 5 3 45 3 50-6 3 S6-z 4 ''9 4 7-5 : T, 4 24-4 4 lO 4 .6-2 4 ^^■5 4 28-7 4 35 4 *''- 4 47" 5 4 53-7 I 6-2 4 35 4 4""9 4487 4 55-6 5 --5 I Zt 5 23" I 2-5 > 3'7 ■ 5 1 6-2 ' 7-5 ; _»-7 I ii-5 1 13-7 ' 337 . 35-6 > 37-5 ' 39-+ I 41-2 1 431 ■ 45 I 46-, • 48-7 1 so-6 2 5 j 2 36-2 1 7-5 ^ 39-4 2 ,0 1 2 42-5 1 12-s ! 2 45-6 2 17-5 » 5'-9 2 20 2 5s 2 22-5 2 58-1 2 25 3 1-2 1 ^7-5 3 4-3 -- .-," 13 7-5 3 7-5 3 II-2 3 '5 3 '»-7 3 i»-5 3 26-2 3 30 3 33-7 3 37;5 - 45 3 38-7 3 43> 3 47-5 3 5'-9 I tl 4 5 4 9'4 4 '3-7 4 iS-i 4 ::'i 4 10 4 >5 4 to 4 »5 4 3° 4 35 4 40 4 45 4 50 4 55 5 5 3-7 5 9-4 Ih 5 3'-9 ; 37-5 ^^^ 5 37-5 5 43-7 5 5° 5 5-5 6 4-4 6 112 6 i8m 6 ^2 ; 610 TABLF. 21 — FOR RKDUCING DAILV AND TWELVE-HOUllLY VAKIATIONS VariaUon in 24" or in 12" Inter- 24'- Inter- " ~ 6^ 7' 8' 9' ,0' 1 0" 30" 0" 30" 0" 30" 0" 30" r 30" 0'' (»■■ 0" 0'" o' o" 0' 0" 0' 0" 0' 0" 0' 0' 0' 0" 0' 0" 0' 0" 0' 0" 0' c" 30 15 o Ts 8-1 8-7 9-4 10 IO-6 II-2 II-9 12-5 131 1 30 o 15 162 17-5 i8-7 20 21-2 22-5 23-7 2S 262 30 45 2V5 24-4 26-2 281 30 319 33-7I 35-6 ° 37-5 39-4 2 I 30 32-5 35 37-5 40 42-5 45 47-5 50 52-5 30 15 37-5 40-6 43-7 046-9 30 53-1 56-2 59 4 I 2-5 , s-6 3 30 45 48-7 52-5 056-2 I I 3-7 ' 7-5 ' '5 I i8-7 SO 45 51-5 56-9 . 5-6 I 10 I 14-4 I i8-7 I 231 I 27-5 I 31-9 4 2 > 5 I 10 ' '5 I 20 I 25 I 30 ' 35 I 40 > 45 30 15 _' 7-5 I 18-7 1 24-4 I 30 .35-6 I 41-2 146-9 I 52-5 I s8-i 5 30 ' -5 I 212 I 27-5 > 33-7 I 40 .462 1 52-5 I s8-7 2 5 2 II-2 30 45 I 22-5 1 294 . 36-2 I 43-1 I 50 . 56-9 2 3-7 2 IO-6 2 .7-5 2 24-4 G 3 I 30 ' 37-5 > 45 I 52-5 2 2 7-5 2 15 2 22-5 2 30 2 37-5 30 15 ' 37-5 .45-6 • 53-7 2 1-9 2 10 2 181 2 262 2 34-4 2 42-5 2 50-5 7 30 > 45 • 53"7 2 2-5 2 20 2 28-7 2 37-5 2 46-2 2 55 3 3-7 30 45 I 52-5 2 19 2 20-6 2 30 2 39'4 2 48-7 2 58-1 3 7-5 3 ■6-9 8 4 2 2 10 2 20 2 30 2 40 2 so 3 3 '0 3 20 3 30 30 15 i 7-5 2 i8m 2 28-7 2 394 2 50 3 0-6 3 11-2 3 21-9 3 3»-5 3 43-' 9 30 i -5 2 37-5 2 48-7 3 3 11-2 3 22-5 3 33-7 3 44 3 56-2 30 45 i 34-4 246-2 2 58-. 3 10 3 21-9 3 33-7 3 45-6 3 57-5 4 9-4 10 T~ir 2 30 2 42-5 2 55 3 7-5 3 20 3 32-5 3 45 3 57-5 4 10 4 22-5 30 U I 37-S 2 50-6 3 3-7 3 '6-9 3 30 3 43-1 3 56-2 4 9-4 4 22-5 4 35-6 II 30 2 45 2 587 3 12-5 3 26-2 3 40 3 53-7 4 7-5 4 21-2 4 35 ' 4 48-7! 30 45 2 52-5 3 6-9 3 21-2 3 35-6 i s° 4 4-4 4 i8-7 4 33-1 4 47-5 5 '-9 12 C 3 ° 3 "5 3 30 3 45 4 4 >5 4 3" 4 45 5 ° 5 '5 30 15 3 7-5 3 23-1 3 38-7 3 54-4 4 10 4 25-6 4 41-2 4 569 5 '2-5 5 28-1 13 30 3 >S 3 3"-i 3 47-5 4 3-7 4 20 4 36-2 4 52-5 5 8-7 5 25 5 41-2 30 45 3 "-5 3 39-4 3 56-2 4 ■3-' 4 30 4 46-9 5 3-7 5 20-6 5 37 5 5 54-4 14 7 3 3° 3 47-5 4 5 4 22-5 4 40 4 57-5 5 15 5 32-5 5 5° 1 6 7-51 30 15 3 37-5 3 55-6 4 '3-7 4 31-9 4 50 5 8-, 5 26-2 5 44-4 6 2-5 6 20-6 15 30 3 45 4 3-7 4 22-5 4 41-2 5 ° 5 37-5 5 56-2 6 15 6 33-7 30 45 3 5^-5 4 >>-9 4 3'-» 4 5°-6 5 'o 5 29-4 5 48-7 6 8-I 627-s' 646-y 16 8 4 4 20 4 40 5 5 20 5 40 6 c 6 20 6 40 70 30 15 4 7-5 4 28-. 44S-7 5 9'4 5 30 5 5°-6 6 II-2 6 31-9 6 52-5 7 '3-' 17 30 4 15 4 36-2 4 57-5 5 >s;7 540 6 ,2 6 22-5 643-7 7 5 7 26-2 30 45 4 22-5 4 44'4 5 6-2 5 5° 6 ,.-9 6 33-7 6 55-6 7 17-5 7 39-4 18 9 4 30 4 5^-5 5 15 5 37-5 6 6 22-5 6 45 7 7-5 7 30 7 52-'; 30 15 4 37-5 5 0-6 5 13-7 5 46-9 6 10 6 33-1 6 56-2 7 ■9"4 7 42-5 8 5-6 19 30 4 45 5 8-7 5 3^-5 5 56-2 6 20 6 43-7 7 7-5 7 31-2 7 55 8 iS-7 30 45 4 5-'5 5 >6-9 5 4>-2 6 5-6 6 30 6 54-4 7 18-7 7 43-' 8 7-5 8 31-9 20 10 5 ° 5 25 5 5° 6 .5 6 40 7 5 7 30 7 55 820 8 45 30 15 5 7"5 5 33-> 5 58-7 6 24-4 6 50 7 -s-e 7 4"-2 8 7-9 8 32-5 8 58- 1 21 30 5 >5 S 4'-» 6 7-5 6 33-7 7 7 26-2 7 52-5 8 18-7 844 9 .1-2 30 45 5 "-S 5 49-4 6 i6-2 6 43-> 7 10 7 36-9 8 3-7 8 30-6 X 57-5 9 24-4 22 11 5 3° 5 57-5 6 25 6 52-5 7 20 7 47-5 8 IS 8 42-S 9 10 9 37-5 30 15 5 37-5 6 5-6 6 33-7 7 1-9 7 3° 8 's-' 8 26-2 8 S4-4 9 22-5 9 50-6 23 30 5 45 6 .3-7 6 42-5 7 II-2 7 40 8 37-5 9 6-2 9 35 10 3-7 30 45 5 5^-5 6 2.-9 6 51-2 7 20-6 7 5° S 194 8 48-7 9 181 9 47-5 10 16-9 24 12 6 6 30-5 7 7 30 8 8 30 9 9 30 10 10 30 30 15 6 7-516 38-1 7 «-7 7 39-4 8 10 8 40-6 9 11-2 9 4'*9 10 I2-C 10 43-1 85 30 6 15 6 46-2 7 'y-sl? 48-7 8 20 8 5.2 9 21s 9 5J*7 10 IS .0 56-2"' 30 45 6 22-5 6 54-4 7 26-2 7 58-' 8 30 9 ,-9 9 33-7 10 5-6 10 J7-5 II 94 16 13 6 30 7 1-5 7 35 8 7-5 8 40 9 '2-5 9 45 10 17-5 10 50 II 225 30 15 6 37-5 7 IO-6 7 43*7 8 16-9 8 50 9 23'i 9 56-2 10 29-4 .1 2-5 .1 35-6 27 30 6 45 7 i8-7 7 52-5 8 26-2 9 9 33-7 .0 7-5 10 41-2 II 15 II 487 30 45 6 52-5 7 ^6-9 8 -2 8 35-6 9 .0 9 44-4 10 18 7 10 531 11 27'S 12 1-9 28 14 7 7 35 8 10 S 45 9 20 9 55^ 10 30 '■ 5 II 40 12 IS 30 15 7 7-5 7 43-1 8 18-7, < 54-4 9 30 10 5-6 10 41-2 II 169 II 525 12 28-1 » 30 7 >5 7 5'- = 8 27-519 3-7 9 40 10 162 10 S2-5 II 287 12 5 |12 41-2 30 45 7 22-5 7 59*4 8 36219 .3-1 9 50 .c :6-9 II 37 II 40-6 12 i7-s;i2 54-4 15 7 JO 8 7-5 845 |9 22-<; 11 15 II 52-5 12 30 |I3 7-5 TAB LI' 21 651 FOR REDUCING D.VILV AND T\VELVE.HOURI,Y VAKUTIONS 1 lot.r. viil 24'" Inter- vhI 12^ Variation ii. 24'- or in 12'' | ir 12' 13' 14 15' 0' 1 :«." 0" 1 30" 0" 1 30" 0" 1 30'- 0" j -JO" 0^ 0" 0'' 0" o' o" 1 o' o" 0' o"l 0' 0' 0' 0" 0' 0" 0' 0" 0' 0" 0' o'- ' 0' 0" 90 15 13-71 14-4 15 1 15-6 .6-2 ,6-9 175 i8-i 18-7 194 1 30 o.T-sl 28-7 30 1 31-2 32-5 ° 33-7 ° 35 36-2 ° 37-5 3«-7 30 45 4i-2| 431 45 0469 48-7 50-5 52-s 544 56-2 58-1 2 1 ° 55 57-5 1 25 ' 5 ' 7-5 1 10 I 12-5 ' '5 I i'-5 30 15 I S7 . II-9 > '5 I 21-2 1 24-4 I 27-5 I 30-6 ' 33-7 , 36-9 3 :jo I ii-5 I 26-2 1 30 > 337 > 37-5 I 412 ' 45 I 48-7 I 525 . s6-2 30 ; 45 1 36-2 I 40-6 • 45 1 494 I 53-7 I 58-i 2 2-5 1 36-9 2 11-2 2 .5-6 4 2 I 50 ' 55 2 2 5 2 10 2 IS 2 20 2 25 2 30 2 35 :«» 1 'i ^ r? 2 .5 1 ^ -6 2 26-2 z 5. -9 2 37-5 2 48-1 2 48-7 2 54-4 » (1 30 z 17-5 2 23-7 2 36-2 2 42-5 2 48-7 i 55 3 1-2 3 7-5 3 13-7 30 45 z 31-2 2 38-. 2 45 2 51-9 258-7 3 5-6 3 12-5 3 19-4 3 26-2' 3 331 fi 3 ^ 45 2 52-5 3 3 7-5 3 '5 3 225 3 3° 3 37-5 5 45 ' 3 52-5 30 15 2 58-7 3 6-9 3 "5 3 23-1 3 3'-J 3 39-4 3 47-5 3 55-6 4 3-71 4 "-9 7 30 3 12-5 3 21-2 3 >o 3 3«-7 3 47-5 3 56-2 4 5 4 '3-7 4 22-5 4 3, -2 30 45 3 26-2 3 35-6 3 45 3 54-4 4 3-7 4 '3-' 4 J3-5 4 3>-9 4 4'-2 4 S°(> 8 4 3 40 3 50 4 4 10 4 20 4 30 4 40 4 5° 5 1 5 'o :«» 15 3 5;-7 4 4'4 4 '5 4 ^i-b 4 36-z 4 46-9 4 57-5 5 8-I 5 i8-7 5 294 » u ■M + 7-5 4 i8-7 4 30 4 41-2 4 52-5 5 3-7 5 15 5 26-2 5 37-5| 5 487 30 45 4 zi 2 4 33-' 4 45 4 56-9 5 8-7 5 20-6 5 32-5 5 44-4 5 56-21 6 8-1 jiTT 5 4 55 4 47-5 5 o| 5 .2-5 5 ^5 5 37-5 5 50 6 2-5 6 ,5 6 27-5 30 15 4 48-7 5 '-9 5 .5 1 5 '-S-. 5 4'-2 5 54-4 6 7-5 6 20-6 6 33-7 646-9 1 1 30 5 J-5 5 26-2 5 30 , 5 43-7 5 57-5 6 II-2 6 25 6 38-7 6 5^-5 7 6-2 30 45 5 162 5 40-6 5 45 5 59-4 6 13-7 6 28-1 642-5 6 56-9 7 25-6 12 6 5 3° 5 45 6 6 15 6 30 6 45 7 7 '5 7 30 7 45 30 15 5 +3-7 5 594 6 ,5 6 30-6 6 46-2 7 1-9 7 '7-5 7 33-" 7 48-7 8 4-4 13 30 5 57-5 6 .3-7 6 30 6 46-2 7 i-5 7 i8-7 7 35 7 5>-2 8 23-7 m 45 6 .1-2 6 28-. 6 45 7 1-9 7 -8-7 7 35-6 7 52-5 8 94 8 26-2 843-. 14 7 625 6 42-5 7 7 17-5 7 35 7 52-5 8 10 8 27-5 845 9 2-5 30 IJ o' 15 6 38-7 6 56,, 7 >5 7 33-' 7 5'-2 8 9-4 8 27-5! » 45-6 9 3-7 9 219 30 65-5 7 30 7 48-7 8 7-5 8 262 8 45 1 9 3-7 9 22-5 9 4>-2 30 45 7 6-^ 725-6 7 45 8 4-4 8 23-7 8 43-' 9 ^-5 9 21-9 9 4>-2 10 06 i<; 8 7 10 7 40 8 8 20 8 40 9 9 20 9 40 10 20 30 15 7 33-7 7 54-4 8 .5 8 35-6 8 56-2 9 '6-9 9 37-5 9 58-1 10 i8'7 10 39-4 17 30 7 47-5 8 8-- 8 30 8 5. -2 9 >^-5 9 337 9 55 'o i6-2 10 37-5 10 58-7 30 45 8 23-. 8 45 9 6-9 9 28-7 9 50-6 .0 .2-5 10 34-4 10 56-2 IK » 8 15 8 37-5 9 ° 9 "-5 9 45 .0 7-5 10 3^ 10 52-5 II 15 • 37-5 30 15 8 28-7 8 51-9 9 '5 9 38-1 10 24-+ .0 47-5 n 33-7 I 56 9 II) ■M 8 4V5 9 6-2 9 3° 9 53-7 17-5 ■■ 5 I. 28-7 'J 525 2 i6-2 :w , 45 8 56-2 9 20-6 9 4S ■ _9^ ° 33-7 '°o ]l: ii 23-5 II 46-9 12 JI-2 2 35-6 ■20 ro~o" 9 10 9 35 10 25 50 II 15 II 40 12 5 12 30 » 55 :' 57-5 12 23-1 12 48-7 3 H-4 21 30 9 37-5 10 3-7 10 30 10 56-2 I 22-5 1. 487 12 15 12 412 13 7-5 3 33-7 30 45 9 5"-^ 10 181 10 45 II 11-9 I 38-7 12 5-6 12 32-5 12 59-4 .3 26-2 3 53-> 22 11 n '° 1 32-5 11 II 27-5 ■ 55 12 22-5 12 50 '3 >7-5 '3 45 ♦ 125 :«) 15 10 18-7 46-9 II 15 II 431 2 11-2 2 39-4 ■3 7-5 13 35-6 '4 3-7 4 3>-9 23 30 10 32-5 II 30 ■I 58-7 2 27-5 2 56-2 '3 25 "3 53-7 4 22-5 4 5'-2 30 46 ,0 462 . .5-6 II 45 12 14-4 2 43-7 3 13-1 3 42-5 14 11-9 4 4'-2 5 10-6 21 12 I I 30 12 12 30 3 3 30 4 14 30 5 5 30 :«i 15 I. .3-7 I 44-4 12 15 .2 45-6 ±±1. 3 46-9 4 17-5 .4 48-. 5 ■8-7 5 49-4 2.-. :to . 27-5;ii 58-7 12 30 I13 1-2 3 32-5 4 3-7 4 35 15 6-2 5 37-5 6 8-7 30 44 I 4>-J >J 'V 12 45 1:3 16-9 3 48-7 4 20-6 4 52-5 15 24-4 5 562 6 28-1 2fi 13 I 55 12 27-5 ij 13 32-5 4 5 4 37-5 5 'o 'S 425 6 IS 6 47-5 ., *' 15 2 8-7 12 4>-9 13 15 113 48-1 4 21-2 4 54-4 5 27-5 16 0-6 6 33-7 7 6-9 27 30 2 22'5 ,2 56-2 >3 3° '4 3-7 4 37-5 5 II-2 5 45 '(> >8-7 652-5 726-2 30 45 2 36-2 13 ,c-6 '3 45 '4 ■9'4 4 53-7 5 28-1 6 2-5 16 36-9 7 II-2 7 45-6 2ft 14 2 50 13 25 14 14 35 5 'o 5 45 6 20 16 55 7 30 8 5 ■Ml 15 3 37 13 39-4 14 15 H 50-6 5 26-2 6 1-9 6 37-5 17 13-' 7 48-7 8 24-4 -. 30 3 '7-5|'3 53-7 14 3° >5 6-i 5 42-5 6 i8-7 6 55 17 3.-2 8 7-5 8 43-7 30 4.i 3 3'-2 '4 8-1 14 45 >5 ^'-9 5 58-7 -6 35-6 7 '2-5 >7 49-4 8 26-2 9 3-' M> n 1ft 3 45 '"4 "-5 15 !,; 37-5 6 ,5 |,ft 52-5| 7 3" j'8 7-5 8 4S 9 »^S 652 TABLE 21 FOR REDUCING DAILY AND TWELVK-HOURI.Y VARIATIONS i liiler- val 241. 12*' Variation in 24'' or in 12'^ j 16' 17' 18' 19' 20' 0" 1 30" 0" 1 30" 0" 30' 0" 1 30" 0" ; 30" 0<. 0" 01. 0"> 0' o"| 0' 0" 0' 0" o' 0" 0' 0" 0' 0" 0' 0" Co" 0" 0' 0" 30 15 o,o|o.o-6 21-2 21-9 22-5 23- 1 23-7 24-4 25 25-6 1 30 04c 04. -2 425 43-7 45 46-2 47; 5 48-7 50 51-2 M 45 . , ,-9 ■ 3-7 ■ 5-6 1 7-5 I 94 I 13-1 . 15 1 .6-9 2 1 , 20 1 2-5 1 -5 I 27-5 1 30 . 3^-5 . 35 . 37-5 I 40 I 42-5 30 15 1 40 ' 43» I 46-2 I 49-4 I 52-s . 55-6 I 58-7; 2 .-9 2 5 2 8-1 3 30 2023-7 2 7-5 2 11-2 2 15 2 18-7 2 22-5 1 ^6-2 2 30 2 33-7I 30 45 2 20 2 24-4 2 28-7 2 33-1 2 37-5! 2 41-9 2 46-2! 2 50-6 - 55 2 59'4 4 2 2 40 1 2 45 ^ 2 50 ^ 55 3 i 3 5 3 10 3 .5 3 20 3 -5 30 15 3 o!3 5-6 3 ll-2i 3 16-9 3 22-5- 3 28-1 3 33-7! 3 39-4 3 45 3 50-6 5 30 3 20 3 26-2 3 3=-5| 3 38-7 3 45 [3 5'-J- 3 57-5 4 3-7 4 .0 TT6^ 30 46 3 4° 3 46-9 3 53-7, 4 IO-6 4 7-5 4 '4-4 4 21-2 4 28-1 4 35 4 4'"9 6 3 4 4 7-5 4 "5 4 =2'5 4 30 4 37-5 4 45 4 S^-S 5 s 7-5 30 15 4 20 4 28-1 4 36-^ 4 44'4 4 5^--5l 5 0-6 5 8-7 5 .6-9 5 25 7 30 4 40 448-7 4 57-5 5 6-2 5 '5 1 5 ^3-7 5 3^-5 5 4'-2 5 5° 5 ^8-7 30 45 5 5 94 5 iS-7 5 28-1 5 37-5 5 46-9 5 s(>■^ 6 5-6 6^5 624-4 8 4 5 :o 5 30 5 40 5 5° 6 6 10 6 20 6 30 6 40 ; 6 50 30 15 5 40 5 50-6 6 1-2 6 ,.•9 6 22-5' 6 33-, 6 43-7 6 54-4 7 5 1 7 15-6 9 30 6 6 II-2 6 22-5 6 33-7 6 45 1 6 56-2 7 7-5 7 .8-7 7 3° 7 41-2 30 45 6 20 6 3.-9 6 43-7 6 55-6 7 7-SI 7 I9'4 7 3.-1 7 43-. 7 55 8 6-9 10 5 640 6 52-5 7 5 7 '7-5 7 30 1 7 41-5 7 55 8 7-5 8 20 tttJ 30 15 7 7 13'' 7 26-2 7 39-4 7 5^-51 8 5-6 8 18-7 8 31-9 8 45 1 8 58-1 II 30 7 20 7 33-7 7 47-5 « II-2 8 15 1 8 28-7 842-5 8 56-2 9 10 9 23-7 30 46 7 40 7 54-4 8 8-7 8 23-. 8 37-51 8 51-9 9 6-2 9 20-6 9 35 1 9 49-4 12 6 8 8 15 8 30 8 45 9 ° i 9 '5 9 30 9 45 30 15 8 20 8 35-« 8 51-2 9 6-9 9 "-5! 9 38-> 9 53-7 10 94 lo 25 '10 40-b 13 30 X 40- 8 56-2 9 '=5 9 '8-7 9 45 'O '-^ 10 17-5 10 33-7 10 50 II 6-2 30 45 9 0.9 16-9 9 33'7 9 5^-6 10 7-5'io 24-4 10 58-1 II 15 II 31-9 14 7 9 20^ 9 37-s 9 55 10 12-5 10 30 10 47-5 '. 5 II 22-5 II 40 III 575 30 15 9 40 9 58-1 10 162 .0 54-4 10 52-s II IO-6 .. 28-7 .' 469 12 5 !i2 23-1 16 30 10 10 i8-7 .0 37-5lio S(>■^ II 15 .. 33-7 II 52-5 12 11-2 .2 30 i.2 48-7 30 45 10 20 10 39-4 10 58-7111 iS-i I2 "'^ II 569 12 16-2 .2 35-6 12 55 13 14-4 lt> 8 10 40 In 1 1 20 II 40 12 40 .3 13 20 I13 40 30 15 11 41-2 12 1-9 \l 22-5II2 43-1 .3 3-7 .3 24-4 13 45 14 yh 17 30 11 20 II 41-2 12 2-5 12 23-7 .145 l'3 6-J .3 27-51.3 48-7 14 10 14 312 30 45 II 40 .2 1-9 .2 45-6 '3 7-5i'3 19-4 13 5. -21.4 .3-. .4 35 .4 569 1*1 •J 12 12 22-S 12 45 13 75 13 30 |J3 5^-5 14 15 1.4 37-5 15 ,15 22-5 30 15 12 20 12 43-1 .3 6-2 13 29-4 13 52-5!i4 .5-6 14 38-71.5 .'9 .5 25 '.5 48-1 l» •fo 12 40 >3 3-7 ■3 =7-5 13 5'-i 14 15 114 38-7 .5 2-5.5 26-2 15 50 |ib 13-7 30 4i ■3 13 20 =3 ^4-4 '3 48-7l'4 M-i '4 37-5 '5 .-9 .5 26-2!i5 50-6 ,6 ,5 .6 39-41 20 10 '3 45 14 .0 114 35 15 :.5 25 15 50 |i6 15 1640 .7 5 1 30 15 13 40 14 5-6 14 31-2 14 56-9 15 22-5i'5 48-1 16 13-; 16 39-4 17 5 17 3o-(> 21 30 14 14 26-2 ■4 5^-5 15 18-7 15 45 1-6 ..-2 16 37-5 .7 3-7 17 30 ;'7 56-2 30 45 14 20 14 46-9 ■5 'Vl 15 40-6 16 7-5 16 34-4 17 1-2 17 28-J 17 55 18 21-9 22 II 14 40 '5 7-5 >S 35 ■ 6 2-5 16 30 ji6 57-5 17 25 17 52-5 18 20 !i8 47-5 30 15 15 15 28-1 ■5 56-2 i6 24-4 16 52-5'i7 20-6 17 48-7 18 16-9 18 45 |i9 13-1 23 30 15 20 15 48-7 ,6 17-5 16 46-2 .7 .5 [.7 43-7 18 12-51841-2 19 10 19 38-7 30 45 15 40 16 94 .6 38-7 17 8-1 17 37-5 .8 6-9 18 362 19 5-6 19 35 2C 4-4 24 12 16 16 30 17 17 30 18 18 30 19 19 30 30 16 16 10 16 506 17 21-2117 5'-9 18 22-5 18 53-1 .9 23-7 1.9 54-4 20 25 ,20 55-6 2o 30 1640 17 11-2 .7 4'--S ■» '3-7 .8 45 1-9 .6-2 19 47'5^° "8-7 20 50 |2I 21-2 30 46 17 17 3»-9 .8 3-7 18 35-6 19 7-5119 39-4 20 ,1-2 20 43-1 2. 15 !,, 46-9 ■M 13 17 20 '7 5^-5 .825 '8 57-5 19 30 ]20 2-5 20 35 21 7-5 21 40 ^22 11-5 :io 15 17 40 18 I3-. 18 46-2 19 194 19 52-5 20 15-6 20 58-7 21 31-9 22 S |22 J8-I 27 SO 18 18 337 >9 7-5 19 41-2 20 15 20 48-7 21 22-5 21 56-2 22 30 j23 3-7 30 46 18 20 18 544 ■9 j8-7 20 3-1 20 37-5|2i 11-9 21 46-2 22 20-6 22 55 23 29-4 28 U 18 40 19 15 19 50 |20 25 21 2. 35 22 10 22 45 23 20 i»3 55 30 15 19 19 35-6 20 I, -2^046-9 21 22-5 2. 58-1 22 33-7 23 9-4 23 45 iJ4 JO-6 29 30 19 20 19 56-2 20 32-U21 8-7 21 45 I22 21-2 " 57-. 23 33-7 =4 "t- 1-4 4^ 2I 30 46 19 40 20 169 20 sr-j'-i 30-6 22 7-5!=-- 44-4 23 zrz^ -k 5X-1 24 35 25 II 9I SO (1 16 ^•- 30 1=3 7-S -.3 45 \~i -'--S J.S 25 37-5) TAr.i.r. 21 KOR REDUCINO DAIKV AND TWELVIMIOURI,^ VARIAIION.S Infr. llitfr- \'ariation in 24'' or in H" 'v.,. 24' val or 22' 23' 24' 2.S 12'' 0" 30" 0" 30" 0" :io" 0" 30" ^•" 1 J«- 0» II'" 1,1. (in. o' o- 0' 0" 0' 0" 0' 0" 0' 0" o' 0" c' 0" 0' 0" 0' 0' 0' 0' 3«» 15 o 26-z 26-9 27-5 28-1 28-7 29-4 30 30-6 31-1 31 9 1 30 o 52-s 53-7 55 056-2 ° 57-5 58-7 1 I 1-2 1 2-5 ■ 3 7 30 45 I i8-7 I 20-6 I 225 I 24-4 I 28-1 I 30 I 31-9 ■ 33-7 I 356 •2 1 ' 45 1 47-5 I 50 I 52-5 ' 55 ■ 57-5 2 2 2-5 1 5 2 7-5 M 15 2 14-4 2 17-5 2 20-6 2 23-7 2 26-9 2 30 2 331 2 36-2 2 39-4 a 30 1 37-S 2 41-2 1 45 2 48-7 2 52-5 2 56-1 3 3 3-7 3 7-5 3 II 2 no 45 3 3-7 3 8-1 3 '=5 3 169 3 21-2 3 =5-6 3 30 3 344 3 387 3 43' 4 2 3 3° 3 35 3 40 3 45 3 50 3 55 4 4 5 4 10 4 >5 30 15 3 $6-1 4 1-9 4_I'l 4 131 4 .8-7 4 =4-4 ^ 3^ 4 35-6 4 41-2 4 46'9 J 30 4- "-5 4 28-7 4 35 4 41-2 4 47-5 4 53-7 5 5 6-2 5 .x-5 5 '*■? r,o 45 4 +8-7 4 55-6 5 =-5 5 9-4 5 16-2 5 I3-' 5 5 36-9 5 43-7 5 5°-6 t; 3 5 '5 5 22- S 5 30 5 37'5 5 45 5 5i'5 6 6 7-5 6 15 1 6 22-5 ■M 15 ; +'"i 5 49-4 5 57-5 6 5-6 6 13-7 6^1-9 6 30 638M 6 462 6 54 4 7 30 6 7-5 6 162 6 25 6 33-7 6 42-5 6 51-2 7 7 8-7 7 >7-5 30 45 6 33-7 6 431 6 5^-5 7 1-9 7 11-2 7 20-6 7 30 7 39-4 7 487 7 58M 8 4 7 o 7 10 7 20 7 30 7 40 7 5° 8 8 10 8 20 8 30 30 15 7 26-j 7 36-9 7 47-5 7 58-1 8 19-4 8 3° 8 406 8 51-2 9 '9 y 30 7 51-5 8 3-7 8 15 8 26-2 8 37-5 848-7 9 9 II-2 9 11-5 9 33-7 30 45 8 i8-7 8 30-6 8 42-5 ±ss± ^Jll. 9 iS-i _9j^ 9 53-7 .0 5-6 10 5 8 45 8 57-5 9 10 9 i = -5 9 35 9 47-5 TTTI^ 10 25 10 37-5 30 1ft 9 ii-z 9 =44 9 37-5 9 50-6 10 3-7 .0 i6-9 10 3° 10 431 10 562 II 94 11 30 9 37'5 9 5''i 10 5 10 18-7 .0 32-5 10 46-2 II II 13-7 11 27- s II 412 30 45 lo 37 .0 .8-. 10 32-5 .0 46-9 .1 15-6 II 3° II 44-4 I. 58-7 12 13-1 12 C iO 30 10 45 II I? II 30 ■ I 45 12 11 15 12 30 12 4; 30 15 .0 56-2 11 11-9 •■ =7-5 II 43- 1 .. 58-7 12 14-4 12 3" 12 45-6 13 1-2 13 169 13 30 II 11-5 .1 38-7 '■ 55 12 27-5 '= 43-7 ■3 13 .6-2 •3 315 13 487 30 45 u 48-7 .2 5'6 12 22-5 12 39-4 .2 56-2 13 131 '3 30 13 46-9 '4 3"7 14 20-6 U 7 11 15 12 32-5 ■ 2 50 ■3 7-5 13 25 '3 4^-5 ■4 14 I7'5 ■4 35 •4 51-5 30 15 •^ 4''- .3 262 n_'7-5 ■3 45 .3 35-6 '3 53-7 14 II-9 '4 30 14 48-1 ■ 5 6-2 15 24-4 15 30 '3 7'5 '4 3-7 14 225 14 41-2 15 15 18-7 '5 37-5 .5 56-2 30 45 '3 33'7 13 53-I .4 12-5 14 319 14 5. -2 15 10-6 '5 30 16 49-4 16 8-7|.6 27-. 1 le 8 1+ 14 20 14 40 15 20 15 40 16 16 20 16 40 I17 1 :io 5 ,4 26-z 14 46-9 '5 7-5 .5 28-1 .5 48-7 .6 9-4 16 30 16 506 17 II-2 17 31-9 17 n .Ml '4 5-'5 '5 '3'7 '5 35 ■5 56-1 .6 7-5 16 38-7 ■7 17 21-2 17 4=-5 18 3-7 30 45 .5 40-6 ,6 2-5 .6 244 16 46-2 17 8-1 17 30 17 5'-9 18 137 18 35-6 18 !) 15 43 16 7-5 .6 30 .S 5Z-5 '7 15 '7 37-5 18 .8 22-5 1845 >9 75 30 15 16 in ,6 34-4 ,6 57-5 -7 20-6 '7 43-7 .8 6-9 18 30 18 53-1 ir l6-2 ■9 394 19 30 .6 37-5 .7 -5 |>7 48-7 ,8 ,2-5 .8 36-2 19 19 23-7 19 47-5;»o ii-2| 30 45 17 }'7 17 28-1 ■7 5^-5 1!^^ .8 4. -2 19 56 '9 30 ■9 54-4 20 187 2^3-1 20 10 17 30 '7 55 18 20 ■8 45 19 10 '9 35 20 20 25 20 50 ^' .5 30 15 17 56-2 18 47-5 19 13-1 ■9 38-7 20 44 20 30 20 55-6 11 21-2 21 46-5 21 30 ,? 22-5 \l Is? 19 15 19 41-2 20 7-5 20 33-7 21 21 26-2 21 52-5 22 .8-7 30 45 ,8 48-7 19 15-6 19 42-5 20 9-4 20 36-2|2i y, 21 30 21 56-9 22 23-7 22 50fr 22 11 19 15 19 425 20 10 20 37-5 =■' 5 21 32-5 22 22 17-5 22 55 23 22-5 30 15 19 4''^ 20 9-4 10 37-5 2. 5-6 i' 33-7 22 1-9 22 30 22 58-. 2J 26-2 23 544 23 30 ;o 7-5 20 36-2 1' 5 21 33-7 22 2-5 22 31-2 ^3 23 28-7 13 57"5|H lO'i 30 45 20 33-7 21 31 21 32-5 22 1-9 22 312 23 06 -3 30 =3 59-4 24 28-7 24 58-1 24 12 21 21 30 22 i22 30 23 23 30 =4 24 30 25 I25 30 30 15 21 26-2 21 56-9 !liZJ. 22 58-. 23 26-2 23 28-7 =3 59'4 id. 30 25 0-6 25^-2 26 19 25 :«i 21 525 =1 55 =i 57' 5 24 28-7 25 15 31-2 26 2-5 »6 33 7 M 4i 22 J8-7 ^l 50-6 = 3 ii'S -i 544 24 26-2 24 58- > 30 26 .-9 »6 33'7l»7 5"6 ■K 13 22 45 M •7-5 23 50 24 22-5 H 55 25 I7-5 26 26 J2-5 »7 5 1»7 37-5 30 15 13 11-2 13 44"4 24 17-5 24 50-6 25 23-7 25 569 16 30 27 3-1 27 362 118 9-4 27 30 ^3 37-5 24 II-2 24 45 25 i8-7 = 5 5i'5 »6 262 »7 17 33-7 28 7-5 U8 41-2 30 45 24 3-7 24 38-. 25 i;'5|25 46-9 26 »I-2 26 55-6 30 28 4-4 18 38-7;29 i3-' 28 14 »4 30 »5 5 25 40 26 15 26 JO 27 15 28 28 35 29 10 29 45 30 15 =4 Sf>^^ = 5 3'"9 26 7-5 »6 43I 17 18-7 17 54'4 28 3° 29 5-6 29 4''i|30 '6'9 29 30 15 22-5 .5 58- 26 35 *7 ..• = 17 47-5 28 23-7 =9 2, ,6 . 3° '»-5i30 48-7 30 45 M +8-7 26 256 =7 I'S.^? 59'4 28 i6-2 28 53- ■ •9 30 ,0 6-9 JO 43-7|3' »<^-6 30 U .6 ,5 26 5^-5 '7 3^ |'-8 7-5 28 45 29 22-5 30 3^ 37-5 !' '5 l3" 5» 5 «'>4 TABLE 21 FOR REDUCING DAILV AND TWELVE-HOURLY VARIATIONS V ariatioii in 24' or ir 12" | loter- Inter- val 26 ^ _J7- .8' 29' 30' 1 .r 12i> 0" 30' 0" 30" 0" 30" 0" 30' 0" 30" 01. 0'" 0'' 0"' o' o" ~^o~ 0' 0" 0' 0" 0' 0" 0' 0" 0' 0" 0' 0" 0' 0" 0' c" •M 15 o 32-5 33'i 33-7 34-4 ° 35 ° u-t 36-2 36-9 37-5 38-. 1 30 I 6-2 ' 7-5 I 8-7 I 10 I 12-5 I 137 1 15 I i6-2 :w 45 • 37-5 > 394 I 41'2 I 43-1 ' 45 ; 46-9 . 487 I 50-6 I 52-5 • 544 2 (( 1 2 12-5 2 15 2 17-5 2 22-5 2 25 2 27-5 2 30 2 32-5 .•{(1 15 Ills 2 45-6 2 48-7 2 $1-9 ^ 55 2 58-. 3 1-2 3 4'4 3 7-5 3 IO-6 :i 30 3 -5 3 .8-7 3 2J'5 3 26-2 3 3° 3 337 3 37-5 3 41-2 3 45 3 48-7 30 45 3 47-5 3 5'-9 3 56-2 4 0-6 4 5 4 94 4 '37 4 .81 4 J2-5 4 ^6-9 4 U 2 ♦ 25 4 30 4 35 4 40 4 45 4 5° 4 55 5 ° 5 5 30 15 4 5°-5 AJlll -L_1Z 5 9-4 5 15 Ai£l 5 26-2 5 3>-9 5 37-5 5 43-' 6 30 5 zs 5 3'"2 5 37'5 5 437 5 50 5 56-2 6 2-5 6 8-7 6 15 6 21-2 :w 45 ? 57 5 6 4-4 6 ,1-2 6 181 6 25 C3.-9 6 38-7 645-6 6 52-5 ft 59-4 (> 3 6 30 6 37-5 645 6 52-5 7 7 7-5 7 15 7 "-5 7 30 7 37-5 3U 15 7 ^-5 7 IO-6 7 iS-7 7 26-9 7 35 7 43-' 7 5'-2 7 59"4 8 7-5 8 15-6 7 30 7 35 7 43-7 7 52-5 8 .-2 8 10 8 i8-7 827-5 8 36-2 8 45 8 537 •M 45 8 7-5 8 .6-9 8 262 » 35-6 845 8 54-4 9 3-7 9 '31 9 "■$ 9 3'-9 u u 4 S 50 9 9 '° 9 20 9 30 9 40 9 50 10 10 10 :w 15 9 «^ 5 9 23-1 9 33-7 9 44-4 9 55 .0 5-6 10 16-2 10 26-9 10 37-5 10 48-1 1» 30 9 45 9 562 10 7-5 10 i8-7 10 30 10 412 10 52-5 'I 3 7 II 15 II 26-2 :»o 45 'o_ir± 10_29M. 10 41-2 10 53-1 >> 5 II .6-9 II 40-6 II 52-5 12 4-4 10 5 II 2-5 II 15 11 27-5 II 40 II 525 '2 5 12 17-5 12 30 12 42-5 30 15 \° 2°-5 II 35-6 .1 48-7 12 1-9 12 15 12 28-1 12 54-4 13 7-5 13 20-6 II 30 >> 55 12 8-7 12 22-5 12 362 12 50 13 37 13 17-5 13 31-2 '3 45 13 587 30 45 12 27-5 12 41-9 .2 56-2 13 IO-6 13 25 •3 39-4 '3 537 14 8m 14 22-5 14 36-9 12 C 13 •3 '5 13 30 '3 45 .4 14 15 14 30 '4 45 15 >5 >S 30 15 '3 3^-5 13 48-' 14 3-7 14 19-4 14 35 14 506 15 6-2 IS 21-9 '5 37-5 •5 53-1 i3 30 ■4 5 14 21-2 '4 37-5 '4 53-7 15 10 15 26-2 '5 42-5 .5 587 16 .5 16 31-2 30 45 ■4 37-5 ■4 54-4 15 II-2 .5 28-1 >5 45 .6 1-9 16 18-7 16 35-6 16 52-; '7 9 4 14 7 15 10 IS 17-5 '5 45 .6 2-5 16 20 16 37-5 16 55 17 12-5 17 30^ >7 47-5 3U 15 ■5 4^-5 16 06 16 ,8-7 16 ;6-9 16 55 17 13-1 ^im 17 49-4 'ULl lA 30 .6 ,5 16 33-7 16 52-5 17 II-2 17 30 17 48-7 .8 7-5 18 26-2 18 45 ■9 37 3() 45 ,6 47-5 17 6-9 17 26-2 17 45'6 18 5 iS 24-4 18 43-7 19 31 19 22 5 19 4I-9 16 8 17 20 17 40 18 18 20 18 40 19 19 20 19 40 30 15 >7 52-5 18 I3-I 18 33-7 18 54-4 19 15 .9 35-6 .9 56-2 20 i6-9 20 37-5 20 58-1 '.7 30 .8 25 18 46-2 19 7-5 19 287 19 50 20 32-5 20 53-7 21 15 21 36-2 30 45 ■8 57-5 19 194 19 41-2 20 3-1 20 25 20 III 21 8-7 2, 30-6 21 52-5 22 14-4 lit 9 19 30 19 52-5 20 15 20 37-5 21 21 22-5 21 45 22 7-5 22 30 22 52-5 30 15 20 2-5 20 2 5-6 20 48-7 21 II-9 21 35 21 58- 1 22 44-4 23 7-5 23 30-6 lU 30 20 35 20 58-7 21 225 2, 46-2 22 33-7 " 57-5 ^3 45 24 X-7 30 45 21 7*5 2. 31-9 21 562 12 20-6 22 45 23 9-4 23 337 23 58-1 24^22^ 24 46'9 20 10 21 40 21 5 22 30 "~55^ 23 20 23 45 24 10 24 35 25 25 25 30 h5 22 12-5 22 38-1 23 3-7 23 29-4 ^3 55 24 20-6 25 46-2 25 II-9 ^5 37-5 26 31 21 30 22 45 23 II-2 ^3 37-5 ^4 3-7 24 30 24 562 25 22-5 25 48-7 26 .5 26 4,-2 30 45 23 17-5 23 44*4 24 II-2 24 38-' ^5 5 25 31-9 15 58-7 26 25-6 26 52-5 |27 I9-4| 22 II 23 50 24 17-5 24 45 25 125 25 40 26 7-5 26 35 27 2-5 27 30 27 57'5 30 15 24 22-5 24 50-6 25 iS-7 2; 46-9 26 15 26 43-- 27 11-2 27 39-4 28 7-5 28 35-6 23 (» 30 ^4 55 25 23-7 15 5^-5 26 21-2 26 50 27 i8-7 27 47-5 28 16-2 »S45 29 13-7 30 45 25 27-5 25 56-9 26 26-2 26 55-6 27 25 17 54-4 ^8 23-7 28 53-> 29 22-5 29 51-9 24 12 26 26 30 27 27 30 28 28 30 29 29 30 30 30 30 :w 15 .6 32-5 27 3-1 27 33-7 |i8 4-4 28 35 29 5-6 29 36-2 30 12-5 30_£9 3° 437 30 37-5 5i__Li 25 30 ^7 5 27 36'2 28 7-5128 38-7 29 10 29 4.-^ 31 15 31 46-2 30 45 27 37-5 28 9-4 28 41-2 29 131 ^9 45 30 ,6-g 30 487 3. 20-6 3> 5^-5 32 24-4 26 13 28 42-5 29 15 29 47-5 30 20 I30 52*5 31 25 31 57*5 J2 30 33 »-5 30 15 28 4°-5 29 5-6 29 48-7 30 21-9 3° 55 31 28M 52 1-2 32 34*4 33 7'5 33 40-6 27 30 29 15 29 48-7 30 22-5 30 56.2 31 30 32 3-7 31 37*5 33 >>■» 33 45 30 45 29 47-5 30 21-9 30 56-2 31 30-6 32 5 3^ 39-4 33 "37 33 48-. 34 "5 34 56-9 2» U 30 20 3° 55 31 30 3» 5 32 40 33 >5 53 5° 34 ^5 35 35 35 30 15 30 52-5 3. 28-1 32 3-7 31 39-4 33 >S 33 50-6 34 26-2 35 '-9 35 37-5 36 I3-I 2;( 30 3" »5 32 1-2 31 37-5 33 137 33 50 34 26-2 35 2-5 35 38-7 36 15 36 51-2 30 45 3> 57-5 32 34-4 33 "'^ 33 48-1 34 15 ]35 '-9 35 38-7 36 15-6 36 5^-5 37 29'4 30 (» 15 32 30 33 r$ 33 45 34 22-5 35 135 37-5 36 ,5 36 52-5 37 30 38 7-5 TABLE 21 A LOOAKITHMS FOR KEDUCINO DAII.V VARIATIONS MIn. Hours, Degrees, or Minutes MIn. !fcc. I 1 2 1 3 1 4 5 1 6 1 7 ; 8 1 9 10 11 U .-3801 .-0792 903. 77S1 b8.2J6oii 535' 477' 4260 3802 338S ~ 1 3-584 1-3730 1-0756 9007 7763 6798 6C09 534' 4762 4252 3795 33X1 2 ^■8573 .-j66o 1-0710 S983 7745 6784 5997 5330 4753 4244 3788 3 375 3 i-6!i,i I-J590 .0685 8959 7718 6769 5985 5320 4744 4236 37X0 3368 4 .•5563 1-3511 .-0649 8935 7710 6755 5973 55.0 4735 422X 3773 3362 6 1+594 '•3454 1-0614 89.1 7691 6741 596. 5300 4716 4210 3766 3355 6 .•38or 1-3388 1-0580 8888 7674 6716 5949 5289 47'7 4212 3759 3349 7 i"3'33 '■?3S3 .0546 8865 7657 6712 5937 5279 4708 4204 375» 3342 tl ^•*553 1-3159 1-05.1 XX42 7639 6698 5925 5269 4699 4196 3745 3336 !l i-xu+i 1-3.95 1-0478 88.9 7621 66X4 59'3 5259 ^690; 4 'ii 3319 10 1-.584 '•3'33 1-0444 8796 7604 6670 5902 5249 46X1 4.80 3730 1 3323 II 1-1170 .•3071 1-0411 8773 7587 6656 5S90 5239 4673 4.72 3723 1 33.6 12 1-0792 1-3010 .-0378 X75. 7570 6642 5878 5219 4664 4164 3716 133.0 13 10444 1-1950 I-034S 8728 7552 6628 5S66 51.9 4655 4156 3709 3303 14 l-CIll 1-1S9. 103.3 8706 7535 66.4 5855 5209 4646 4148 3702 3297 13 1-9X23 .-1833 .-0180 S683 75'8 6600 5843 5'99 463X 4141 3695 319. IG 1-9541 ••2775 .•0148 8661 7501 6587 5832 5.89 4619 4'33 3688 3184 17 1-9179 .-27.9 .01.6 8639 7484 6573 5820 5'79 4610 4125 368. 5178 18 1-9031 .•1663 .0.85 8617 7467 6559 5809 5.69 +6., 4117 3674 327, 19 .■X796 .-1607 .-0.53 8595 745' i79I 5'59 4603 j^o9 J66^ 3165 15" •JO ■•8573 '■^553 87?r 7434 T^ 5786 5 '49 4594 4102 3660 1^ 21 1-836. .-1499 1-009. X552 74'7 65,8 5774 5'39 4585 4094 3653 3^5» 22 1-8159 1-1445 1-0061 8530 7401 6505 5763 5.19 4577 4086 3646 3146 •23 1-7966 .1393 1-0030 8509 7384 6491 5752 5.20 4568 4079 3639 3139 23 24 1-7781 ,-134. roooo 8487 7368 6478 5740 5..0 4559 4071 3632 3133 24 2.i .-7604 1-1289 0-9970 8466 735' 6465 5729 5718 510c 455' 4063 3615 3227 25 2« '•7434 1-2239 0-9940 «445 7335 645: 5090 4542 4055 36.x 3220 2»; 27 1-7170 1-2.88 0-9910 84H 73'« 643S 5706 508. 4534 404X 36.. 31.4 27 2« 1-7111 .1139 0-9881 8403 7302 6425 5695 5071 4525 4040 3604 3208 28 •29 ,-6960 .-1090 0-98,2 8382 7186 64.2 5684 506. 45'6 4032 3597 |3'0' 29 3U .-68,1 1 • 104 . 0-9823 8361 7170 6398 5673 505. 4508 4025 3590 3'95 IcT 31 1-6670 '■'993 0-9794 834. 7254 6385 5662 5041 4499 4017 3583 3.89 31 32 1-6531 .-.946 09765 8310 7238 6372 565, 5032 449' 4010 3576 3.83 32 33 1-6398 .1899 0-9737 8300 7222 ^359 5640 5013 4482 4002 3570 3.76 33 34 1-6169 .-1852 0-9708 8179 7206 6346 5629 5013 4474 3994 3563 3170 34 3.". .-6143 .-.806 0-96X0 8259 7190 6333 56,8 5003 4466 3987 3556 3.64 :«; 1-60ZI 1-.76. 0-9652 8139 7'74 6320 5607 4994 4457 3979 3549 3'57 36 37 1-5901 .-.7.6 0-9625 S119 7'59 6307 5596 4984 4449 3972 3542 3'5' 37 :m .•5786 .-.67. 0-9597 8199 7'43 6294 5585 4975 4440 3964 3535 3'45 38 39 ■•5673 .-1627 0-9570 8179 7'i8 6281 5574 4965 4432 3957 3529 I'Jl 39 40 ■•5563 .-.584 0-9542 8159 7112 6169 5563 4956 4424 3949 3522 3'33 40 41 1-5456 .-.540 095.5 8.40 7097 6156 5552 4947 44'5 3942 35'5 3126 41 42 '•535' .1498 0-9488 8110 708. 6143 554' 4937 4407 3934 3508 3.20 42 43 1-5149 '■'455 0-9461 8.01 7066 I'K 553' 4918 4399 1 3927 3501 31.4 43 44 1-5149 .-.4.3 0-9435 8081 7050 6118 5520 49.8 4390 39'9 3495 3.08 44 45 1-5051 '■'37- 0-9408 8061 7035 6205 5509 4909 43X1 39'2 3488 3102 45 4r. 1-4956 1-133. 0-93X1 8043 7020 6.93 5498 49CO 4374 39"5 348. 3096 46 47 1-4X63 1-129C 093^6 8013 7005 6180 5488 4890 43 ,•4180 1-0977 0-9.53 7873 6885 608. 5403 48.7 4300; 3838 341. 304. 55 5(i 1-4102 1-0940 0-9.28 7854 687. 6069 5393 4808 4191 3X3. 34'5 3034 5fi 67 1-4025 1-0901 0-9.04 7836 6856 6057 5382 4798 4184 3824 3408 3028 57 5R ■'3949 .•0865 0-9079 78.8 6841 6045 5372 4789 4276 38.7 3401 3022 58 59 1-3875 ,■0818 0-9055 7800 6827 6033 536. 4780 42*8 3809 3395 30.6 5B 60 ,-,801 .-o79» 0-9031 77X. 6812 602. 535' 477' 4160 3801 3388 3010 60 1 1 * 3 ~ri 5 1 « 7 1 8 1 9 1 10 In 056 TABLE 21 A LOGARITHMS FOR REDUCING DAII.V VARIATIONS ] Ml> Hours, Degrees, or Minute! Mia. 12 13 14 15 16 17 18 19 1 20 j 21 1 22 1 23 3010 2663 2341 2041 1761 '498 .249 101510792 [0580 0378 J0185 300+ 2657 2336 2036 .756 •493 .245 10.. 0788 0576 0375,0182 1 Z998 2652 2330 1 2031 1752 .489 1241 1007 1 0785 °573 0371 0179 2 2991 2646 2325 2027 '747 14S5 .237 1003 I0781 0570 0368 0175 3 2986 2640 2320 2022 '743 .48. 1233 0999 1 0777 0566 0365 0172 4 2980 2635 2315 2017 .738 1476 .22910996:0774 0563 036, 0169 5 ^974 2629 2310 20I2 '734 1472 1225 [0992, 0770 0559 0358 0166 6 2968 2624 2305 2008 1729 [ 1468 .22. 0988 0767 0556 0355 0.63 7 2962 2618 2300 2003 .725 .464 1217109841 0763 0552I0352 0.60 2956 26.3 2295 I 1998 2289 j 1993 '720 t '459 .7161 1455 .213 I 0980 1 0759 0549 0348 0157 0153 9 2950 2607 .209 '0977 0756 1 0546 °3+5 2944 2602 228+!i9S8 '7" '45' .205^0973 1 0753 1 0542 034J 0150 II 2938 2596 2279 .984 1707 1 1447 .20. ,0969 ^0749; 0539 0339 0147 12 ^933 2591 2274 '979 1702 1443 .197^0965 0745 0535 °335 0144 13 2927 2585 2269 '974 .698 .438 ..93 I 0962 074. 0532 0332 0141 14 2921 25S0 2264 .969 1694 1434 1189 0958I0738 0528 0329 0138 15 2915 2574 2259 .965 .689 1 .430 1,85 0954:0734 0525 0326 0135 16 1909 2569 2254 .960 .685 1 .426 1.8. 0950 '073. 0522 0322 17 2903 2564 2249 '955 1680 .422 . 178 0947 0727 05.8 03.9 oizS 18 2897 .2558 _2244 '95° 1676 1417 "74 0943 0724 05.5 0316 0125 10 20 289. 2553 2239 .946 .67, ,4.3 1.70 0939 ,0720 0511 °{n 0122 20 21 2885 2547 2234 1941 1667 '409 1.66 0935 J07.6 0508 0309 01,9 21 22 2880 2542 2229 1936 1662 1405 ..62 0932 1 07 1 3 0505 0306 o,,6 22 23 2874 2536 2223 1932 i6c8 140 1 ..58 0928 1 0709 0501 0303 0,13 23 24 2868 2531 2218 '927 .654 '397 "54 0924 1 0706 0498 0300 0110 24 25 2862 2526 2213 1922 1649 1392 1150 0920 ! 0702 0495 0296 0107 25 2G 2856 2520 2208 1917 .645 .388 ..46 0917 I0699 0491 0293 0104 2« 27 2850 25.5 2203 1913 .640 .384 1 142 0913 0695 0488 0290 27 2B 2845 2510 2198 1908 .636 .380 .,38 0909 1 C692 0484 0287 0098 2« 29 _2839. "93 1903 .632 .376 0905IC6S8 048' 0283 ^94 2!l 30 2833 2499 2.88 I 1899 1627 1372 ..30 09^ 068s 0478 0280 1 0C91 30 31 2S27 2493 2l8l 1894 1623 .368 1126 0898 06S1I0474 0277 0088 31 32 282. 2488 2178 .889 1618 1363 "23 0895 0677 0471 0274 0085 3.' 33 2816 12483 2173 ,885 .6.4 1359 I1119 0891 0674 0468 0271 0082 33 34 281012477 2168 1880 1610 '355 ; 1 "5 0887 0670 0464 0267 0079 31 X, 2804 1 2472 2163 1875 1605 ■ 35. .."Ic883 0667 0461 0264 0076 35 3fi 2798 2467 U>59 187. 160. '347 "07 jc88o 0663 0458 0261 0073 30 37 2793 2461,2154 1866 '597 '343; "03 0876 c66o ■=454 0258 37 3H 2787 2456:2149 1862 .592 '339 '°99 0872 0656 045.1 0255 0067 38 39 2781 245112144 ■^57 .588 ,3351.095 0X68 0653 ^04+7 0444 211L 0064 3a 40 *775U445|2'39 ,852 .584 .33. 1 .09. 10865 0649 0248 006 1 40 41 2770 244012134 1848 '579 1326 .088 0S61 0646 0441 0245 0058 41 42 2764 2435 2129 .843 '575 132Z ' 1084 1 0858 0642 c+38 0242 0055 42 43 2758 143" 2124 .838 '57' 13.8:. 080 '0854 0639 C+3+ 0239 0052 43 44 2753 242+1 21 19 1834 .566 .314: .076 0850 0635 0+3' 0235 0048 44 45 2747 2419:2114 .829 .562 ,3.o'>o72icS46 0632 0+271 0045 45 4(1 2741 241412109 1S25 1558 [1306 106810843 0628 1 04^4 C229 0042 4»i 47 2736,240912104 1820 1553 1 1302 ;o64|o839 0625 042,! 0226 C039 47 48 2730 2403:2099! 1816 1549I 1298, ic6o:oS35 062. 04.8:0223 0036 48 4!) 2724_! 2398 : 2C95 i_il> ■ I ■54'il "94 jo^j 0832^ c6i8 104.4 |0220 0033 4» ao 2719 2393 1 2090 [ 1806 j 1540! 1290 1053 0828 06.4 1 04..! 02. 6 50 rii 2713 2388 I 2085 1S02 [.536 11286;. 049 1 0824 c6ii 0408 1 02 13 0027 51 52 2707 238212080 '797 1 =532 1282 1 .045 '0S21 0608 0404.02.0 0024 52 53 2702 2377! 2075 '793 '527 1278 ; .041 10817 [06041 040. 0207 CC2 1 53 54 2696 237212070 1788 .523 .2741 '037 08,4 060. 0398 0204 0018 54 55 2690 2367 2065 1784I1519J 1270 1034 0810 0597 0394 0201 CO15 55 54i 2685 2362 2061 1779 'SIS .265 .030 0S06 0594 039. 0.97 50 57 2679 2356 2056 1774 1510 ,26, 1026 0803 0590 C3S8 0194 0009 57 AS 2674 2351 2051 .770 ■ 506 1257 1 .022 0799 0587 03S4 019. 0006 58 6!» 2668 2:46 1 i040 ,765 1502 .253].o.S 0795 C583 038. 01S8 0003 50 60 266^ 2341 I 2041 ,76, .498 ,249^ 10.5 0792 0580 1 0378 0185 1 000c «<) )•• 13 1 14 1 15 1 W; 1 17 I 11! i 19 1 20 1 21 \ 22 | 23 [ T.VBLK 2> es? FOR RBDaCINO TIIK .MOONS DliCMNATlON Al Difference lor 10" 10" 1 20" 30 ■ 1 40" 50" ! fio" 1 70" no" 00" j 100" 1 110" 1 120" 1 130" 1 2 3 4 S a 9 in 0'."0'2' o 7I0 .4 8(0 16 10 20 °' 3' 6 9 12 15 iS 21 24 27 30 0' 4' 8 12 16 24 28 36 40 °' 5 10 II 20 25 30 35 40 45 50 0' 6- 12 .8 24 36 41 48 54 14 28 ° 35 49 56 • 3 0' 8' 16 24 32 III 56 > 4 1 12 0' 9' 18 l]l 45 54 ' 3 10' 30 40 50 1 30 . 40 jo'i,' 22 <= 33 44 VI ' '7 1 28 0' 12 24 I'i 1 1 12 1 24 \i 2 39 c 52 ' 3" 1 44 > 57 12 i.j 14 1.-) Ifi 17 III l:( 211 14 16 17 18 .9 28 32 34 It 40 ° 33 36 39 III SI 54 ° 57 1 44 48 til 1 ' 4 I 8 1 12 I 16 1 20 ° 55 I I 5 I 10 ' '5 I 20 • ^5 I 30 ' 3; I 40 I 6 I 18 I 24 1 30 Itl ' 54 2 1 17 1 24 • 3> I 38 ' 45 1 52 ' 59 2 6 2 >3 2 20 \'i 1 44 ' Si 2 2 8 2 16 2 24 2 32 2 40 • 39 1 48 ' 57 2 6 2 15 2 24 2 33 2 42 2 51 3 1 50 2 2 10 2 30 2 40 2 so 3 3 'o 3 JO 2 11 2 23 2 34 :t5 3 7 3 18 3 »9 3 40 2 12 2 24 us 3 ' 3 3 I 6 ' 9 • 'S 1 18 I 24 > -7 I 30 I 24 < 28 I 4'^ ' 44 . 4« I 56 I 45 1 50 > 55 2 » 5 2 10 i '5 i 25 2 6 2 12 2 18 2 24 n? 2 42 2 48 » 5+ 3 2 27 2 34 2 41 2 48 2 55 3 i ].? 3 23 3 3° 2 48 2 56 3 4 3 '2 3 20 3 =18 3 36 3 '(4 3 52 4 3M 3 »7 3 36 3 45 3 54 4 3 4 '2 4 21 4 30 3 30 3 40 3 5° 4 4 10 4 20 4 30 4 40 4 50 5 ° 3 51 4 I til :;i 4 57 5 8 5 '9 5 3° 4 >i 4 24 4 3« 4 48 5 5 ' = 5 »4 5 36 I 'I III 4 59 5 >2 l\l I 'I 6 17 6 30 HI 32 33 34 3.i 3B 37 38 3!) 40 31 32 ° 33 34 ° 35 36 :]i 39 I 4 I 6 • 8 ii: ! 16 . 18 III ' 39 I 42 ' 45 I 48 ■ 5" I 54 • 57 It 2 16 ■i • 11 2 40 ^ 35 2 40 2 4.5 2 50 1 55 3 ° 3 5 3 'o 3 '5 3 ^o 3 6 3 12 3 '8 3 24 3 30 3 36 3 4= 3 48 3 54 4 3 37 3 44 ^8 4 5 4 1- III 4 33 4 4° 4 8 4 16 4 24 4 3^ 4 40 4 48 4 56 5 4 5 '» 5 20 4 39 448 5 '5 5 H 5 33 5 4» 5 '° 5 2° 5 30 5 4° 5 50 6 6 10 6 20 6 30 6 40 5 41 6 47 6 58 7 9 7 20 6 12 6 24 6 36 648 7 7 Z4 7 36 7 48 6 43 6 56 7 9 7 JJ ^11 8 I 8 14 8 27 8 40 41 42 43 «4 45 4fi 47 48 4!) 50 41 42 43 44 :ti 4- 04S Will ,26 2 , 1 28 2 12 ' 5°|^ '5 , 32 1 2 .8 . 38 ^ X- I 40 1 2 30 III I : 3 8 l\l 3 J5 3 3° 3 35 3 40 3 45 3 5° 3 55 4 4 5 4 10 4 6 4 12 4 18 4 »4 4 3 = 4 36 4 4J 4 48 4 54 5 ° 4 47 4 54 l.i 5 22 5 ^9 5 36 5 43 5 50 5 2S 5 36 5 44 5 52 6 6 8 6 16 6 -., Ill n^ 6 4^ 6 54 7 3 7 '- 7 i' 7 30 6 50 7 7 20 7 30 7 40 7 50 8 8 10 ? 20 8 30 8 40 ? 50 9 c 9 10 9 20 9 3C 9 40 9 5° 10 7 3' 7 4» 8 59 9 10 8 12 8 24 8 36 8 48 9 9 12 9 24 9 3* 9 48 9 '9 9 31 9 45 9 58 10 II 10 24 10 37 10 50 51 52 53 54 55 :,r, "7 .-,(1 60 54 55 It c 58 c 59 I 48 U 4^ I 50 1 2 45 . 5'.1»4S . 56 2 54 > 53|i 57 1 0)3 ]lt\Vd 3 4" 4 35 3 44 i 4 40 3 48; 4 45 3 5J|4 5° 3 S'U 55 ;:8 5 H ^8 5 5: 6 4 6 :i 6 18 6 2^ ill 6 46 653 7 648 6 56 7 4 7 l» 7 jS 7 3^ 7 44 7 5 = 8 US :;; 8 51 9 ° iivcit 9 54 ■- 48 10 1; ill TO 16 II 12 10 27 II 24 10 38 III 36 10 49 II 48 .. o|.2 e 'I 3 II 16 II 29 11 4» 'I 55 12 8 12 21 II 34 u 47 13 658 TABLE 29 r — - •OR R EDUCING THE MOON'S DECLINATION M ICO" Difference for lO"- 140" 160" 170"" 1" 2" 3" 4" b" 1 6'" j 7" i r 1 9" |10""| 1 o- 14' O'.S' o".6' 0" .7"" o""-i o'"-2 o'"-3 o"-4 o""-5 o'"-6 o"'-7 o'"-8 o"-9; A 2 28 30 32 34 0-2 "4 •6 •8 10 1-2 '■4 • •6 1-8 2 3 42 4.; 48 51 0-3 ■6 ■9 1-2 1-5 1-8 21 2-4 2-7 3 4 ° 56 I ■ 4 I 8 0-4 •8 1-2 1-6 »o 2 "4 2-8 3-2 36 5 ' '5 1 20 I 25 0-5 10 '■5 2'0 »'5 3-0 3-5 4-0 45 5 « 1 24 I 30 1 36 1 42 06 I -2 1-8 2'4 3° 3-6 4"2 4-8 5-4 6 7 1 38 " 45 « 5- ' 59 o"7 '•4 2-1 2-8 3-5 4' 2 49 5-6 6-1 7 8 1 52 2 8 2 16 0-8 1-6 2-4 3"2 40 4"8 5-6 6-4 7-i S 9 2 6 2 1 ; 2 24 » 33 0-9 1-8 3-6 4-5 5-4 6-3 7-2 81 9 10 2 20 -111 » 4S 2 40 2 50 I'O 2-0 3-0 4-0 ,0 6-0 7-0 8-0 9-0 II ^ 34 2 56 3 7 II 2-i 33 4"4 5'5 6-6 7'7 ~¥% 99 ~7i~ 12 3 3 '2 3 24 1-2 2-4 3-6 4-8 6-0 7-2 8-4 9-6 jo-8 12 13 3 i 3 '5 3 28 3 4" '•3 2-6 3'9 5"2 6-5 78 9-1 IO-4 1 1-7 ■ 3 14 3 16 3 30 3 44 3 58 1-4 2-8 4"2 5-6 7-0 8-4 9-8 11-2 12-6 '4 15 3 30 3 45 4 4 15 •■5 3-0 4" 5 6-0 7-5 90 10-5 12-0 ■3-5 ■5 10 3 44 4 4 16 4 32 1-6 l'2 4-8 6-4 80 ,'i! II-2 12-8 144 i5 17 3 58 4 "5 4 32 4 49 •■7 3-4 5> 6-8 8-5 II-9 13-6 '5"3 17 1« 4 12 4 30 44S 5 6 1-8 3-6 5-4 7'2 90 IO-8 12-6 14-4 162 18 19 4 26 4 45 5 4 5 23 19 3-8 5-7 7-6 9-5 "•4 >3-3 15-2 17-1 '9 20 4 40 5 5 20 5 40 20 4-0 6-0 8-0 lo-o I2-0 .4-0 160 i8-o 21 4 54 5 "5 5 36 5 57 21 4'2 6-3 8-4 IO-5 .z-6 >4-7 16-8 18-9 "TT" 22 5 8 5 30 5 52 6 ,4 2-2 44 6-6 8-8 Ii-o 13-2 '5-4 17-6 .9-8 23 5 22 5 45 6 8 6 3. 2'3 4-6 6-9 9-2 II-5 i6-i i8-4 20-7 231 24 536 6 6 24 6 48 24 4-8 7-2 9-6 I2-0 14-4 i6-8 19-2 2.-6 1 24 25 5 5° 6 .5 6 40 7 5 2'5 5-0 7-5 lo-o 12-5 150 '7-5 20-0 1 22-51 25 1 26 6 4 6 30 6 56 7 22 2-6 5"2 7-8 10-4 13-0 156 23-4 1 26 27 6 18 6 45 7 '2 7 39 2-7 5 '4 81 lo-S ■3-5 162 IS-; 21-6 24"3 1 27 1 28 6 32 7 7 28 7 56 2-8 5-6 8-4 1 1*2 140 i6-S 19-6 224 25-2 28 21, 646 7 15 7 44 8 13 29 5-8 8-7 II-6 '4'5 i7'4 20-3 23-2 26-1 29 30 _7 2. 7 30 8 S 30 3-0 6-0 9"° 12-0 15-0 i8'o 240 27-0 JfL 31 7 '4 7 45 8 ,6 8 47 3-1 62 9'3 '-■4 '5"5 i8-b 217 24-8 1 27-9 32 7 28 8 32 9 4 3"2 6-4 9'6 12-8 160 19-2 22-4 256 2S-8 32 33 7 4» 8 ic 848 9 21 3'3 6-6 9-9 13-2 i6-c 19-8 23-1 26-4 29-7 33 34 7 56 8 30 9 4 9 38 3"4 6-8 136 17-0 20-4 23-8 27-2 30-6 34 36 S 10 S 45 9 20 9 55 3'5 7-0 10-5 14-0 '7'5 24*5 28-0 3>-5 35 3(1 8 24 9 ° 9 36 10 12 3-6 7"2 '4'4 iS-o 21 6 25-2 28-8 1 32-4 36 37 8 38 9 '5 9 5^ 10 29 3"7 7'4 1 11 14-8 i8-5 22-2 25-9 29-6 1 33-3 37 38 9 30 10 8 .0 46 3-8 7-5 II-4 152 i9'o 22-8 26-6 30-4 1 34-2 38 39 9 ^6 9 45 10 24 " 3 3-9 7-8 "•7 156 '9 5 23-4 27-3 3'-2|35-> 39 40 9 10 10 40 II 20 4-0 S-o I2-0 i6-o 20-0 24-0 28-0 32-0 1 36-0 40 41 9 34 10 15 .056 11 37 4'i 8-2 12-3 '6-4 20-5 24-6 28-7 32-8 36-9 ' 41 42 ^948 1030 11 12 11 54 4'2 8-4 12-6 i6-8 25-2 29-4 33-5 37-8 42 43 10 45 II 28 4-3 12-9 '7'2 21-5 258 30-1 34-4 38-7 43 44 10 16 II 44 12 28 4 4 8-8 13-2 176 22-0 26-4 35-2 39-6 44 40 10 30 II 15 12 II 45 4'5 9-0 '3"5 iS-o 22-5 2 7*0 3'5 36-0 40-5 45 46 10 44 II 30 12 .6 13 2 4-6 92 13-8 i8-4 23-0 27-6 36-8 41-4 46 47 11 45 12 32 13 19 4-7 9'4 14-1 i8-8 23-5 128-2 329 37-6 423 47 48 II 12 12 48 13 36 4-8 (>-6 14-4 192 24-0 28-8 33-6 38-4 43-2 48 3 4 •3 53 4'9 ys >4*7 .9-6 24-5 29*4 34-3 39-2 44- 1 49 60 II 40 12 30 .320 14 10 5'° lo-o 'S'o 200 250 30-0 35-0 40-0 45-° 5° TT 11 54 12 45 13 36 14 27 5'i ,0-I 15-3 20-4 25'5 30-6 35'7 40-S 45-9 1 5> 62 12 8 13 13 52 14 44 5"2 10-4 ■ 5-6 26-0 31-2 36-4 4.-6 468 52 6i 12 22 '3 >5 14 8 >5 > 5'3 ic-6 15-9 21-2 26-5 3'-8 37-1 42-4 47-7 \ 53 64 12 36 13 30 14 24 15 18 5*4 lo-S i6-a 21-6 32-4 37-8 43'' 48-6 5+ 65 12 50 »3 45 14 40 '5 35 5'5 ii-o i6'5 22-0 27-5 J3-0 38-5 44.0 49-5 55 66 •3 4 14 .4 56 .5 52 5.6 1I-2 168 22-4 aS-0 33-6 39-2 44-8 50-4 56 57 13 iS 14 15 15 12 i5 9 5-7 11-4 171 22-8 28-i 34" 39'9 45-6 5»-3 57 68 13 32 14 30 15 28 16 26 5-8 11-6 17-4 23-2 I9-0 34-8 40- 6 46-4 52.2 58 69 .3 46 '4 45 >5 44 • 6 43 5*9 II-8 17-7 23-6 29-5 35-4 41-3 47-2 53- . 59 fiO 14 15 i5 17 6'0 iS-o 21 30-0 21 42-0 48-0 , 54-0 j bo j TABL1-: 23 TABLE 2i 659 ACCELERATION 11 M 8 M I S s Dec. o 9-86 I o-,6 I • oo 19-71 2 0-33 2 -00 29-57 3 0-49 3 -01 ° 39-43 * 0-66 4 -CI 49-28 5 0-82 5 •ei 59-14 6 0-98 6 -C2 I 9-00 7 1-15 7 •02 I 18-S5 8 «-3' 8 02 I 28-71 9 1-48 9 -02 ' 38-56 10 1-64 10 -03 I 48-42 l7~ 1-81 II •03 . 58-28 12 1-97 •03 2 8-13 l.'t 2-13 13 -04 z 17-99 14 2-30 14 •04 2 27-85 15 2-46 li -04 2 37-70 16 2-63 16 •04 2 47-56 17 2-79 17 -05 2 57-42 IS 2-96 18 -05 3 7-27 1<) 3-12 1-J •05 3 >7-.5 20 Xll. 20 :£i 3 26-99 21 3-45 21 -06 3 36-84 22 3-6, 22 -06 23 3 46-70 2.t 3-78 23 •06 24 3 5656 24 3-94 24 •07 ^^ 25 2S 4-1 1 25 26 -07 ■°7 27 444 27 28 4-60 28 •08 29 4-76 29 •08 .-iO 493 30 -08 31 5-09 "IT ^ 32 S-26 32 -09 33 5-42 33 -09 34 5-59 34 •09 35 5-75 35 36 5-9' 36 37 6-08 37 38 6-24 38 6-40 39 40 6-S7 40 ~ TT 6-74 41 42 6-90 42 43 7-06 43 44 7-23 44 45 7-39 45 48 7-56 4li 47 47 48 7-89 48 4!) 8-05 49 sn 8-21 50 -'4 51 ,S-,8 51 52 18-5+ 52 53 IS-, 53 54 8-87 54 55 9-04 55 5« ,-20 5f; 57 9-36 57 58,9-53 58 5!) 9-69 5<> W 9-86 eo 1 -,6 1 HIOIARDATION j II i\I S s S Def. 1 983 ^^ ~ 2 19-66 2 0-33 2 -00 3 29-49 3 0-49 3 •ci 4 39-32 4 0-66 4 -01 5 49-15 5 0-82 i -01 ^ 58-9S c. 0-98 « •01 7 I 8-Si 7 1-15 7I -02 8 I iS-64 8 1-31 « 02 I 28-47 9 '-47 U •02 10 ■ 38-30 10 ■ -64 10 •03 IF 1 48-13 II 1-80 11 "^ 12 ■ 57-95 12 '-97 12 ■°3 13 2 7-78 13 2-13 13 •04 14 2 17-61 14 2-29 14 •04 15 2 27-44 15 2-46 15 -04 l(> 2 37-27 16 2-62 16 •04 17 2 47-10 17 278 17 -°5 18 2 56-93 18 2-95 18 •05 19 3 6-76 19 311 19 •05 20 3 '6-59 20 3-28 20 J05 21 3 26-42 21 3-44 "2r -06 22 3 36-25 22 3-60 22 •06 23 3 46-08 23 3-77 23 •06 24 3 55-9' 24 3-93 24 •07 25 4- 10 25 •07 26 4-26 26 •07 ■27 4-42 27 28 4-59 28 •08 29 4-75 29 •08 30 4-91 30 ■08 31 5-o8 31 "^ 32 5-24 32 •09 33 5-4' 33 •09 34 5-57 34 •09 35 5-73 35 36 5-90 36 37 6-06 37 38 6-23 38 39 6-39 39 40 16-55 40 41 6-72 41 42 6-88 42 4S 7-04 43 44 7-21 44 45 7-37 45 46 7-54 46 47 7-70 47 48 7-86 48 49 8-03 49 50 8-19 50 51 51 52 8-1 52 53 8-68 53 54 8-85 54 65 9-01 54 56 19-17 5« 57 i 9-34 i-l 58 19-50 58 f.a 1 9-67 59 «iO 1 9-83 60 J TABLE •2.3 ri)R FINDING TUE KQUATION OK SIXOM) UIFFEKENCBS Tabulak Intebval 1 pller. 1 Log-riu 24 Hours 12 1 ours ' 3 llc.lirs ! Hour 01' 12" 23MH" 01' 0" 111'54' 0''l"'5 2"58"-.- •0041 7-5i6i5 24 23 30 12 11 48 3 2 57 1" 59' 79>35» 3G 23 24 18 11 42 45 2 55-5 •012Z 808591 48 23 12 24 11 30 6 2 54 2 58 •0161 8-20713 I 23 30 11 30 7-5 2 52-5 8-30028 22 48 36 11 24 y 2 51 3 57 •0238 8-37566 1 24 22 30 42 U 18 10-5 2 49-5 •0275 8-43878 1 3U 22 24 48 11 12 12 2 48 4 50 •0311 849292 1 4a 22 12 54 U 6 13 5 2 46 5 •0347 8-54017 2 22 1 II 15 2 45 5 55 •0382 8-58200 2 12 21 4tl 1 10 54 10 5 2 43-5 •0416 8-61943 2 24 21 30 1 12 10 48 18 2 42 6 54 ■0450 8-6532, 2 .J(i 21 24 1 18 10 42 19-5 2 40 5 •04S3 8-68393 2 48 21 12 1 24 10 30 21 2 39 7 53 •0515 8-71204 a 21 1 30 10 30 22 5 2 37-5 ■0547 8-73789 :i 12 21 48 1 36 10 24 24 2 36 8 1 52 •0578 8-76,-6 a 24 20 30 1 42 10 18 25-5 2 34!:. ■0608 8-78389 3 30 20 24 1 48 10 12 27 2 :i3 il ' 51 •0637 8-80448 3 48 20 12 1 64 10 28-5 2 3I« 1 •0666 8-82368 4 20 2 10 30 2 80 10 SO •0694 S-84164 4 12 19 48 2 6 9 54 31 5 2 28-6 ■0722 8-85846 4 24 19 30 2 12 9 48 33 2 27 II 49 •0749 8-87426 4 36 19 24 2 18 y 42 34 5 2 25S •0775 ' l^SSgn 4 48 19 12 2 24 9 30 30 2 24 12 48 •0800 1 8-90309 5 19 2 30 9 30 37 5 2 22-5 •0825 1 8 91627 5 12 18 48 2 30 9 24 39 2 21 13 47 •0S49 8-92871 5 24 18 30 2 42 9 18 40 5 2 19-5 8-94045 5 3« 18 24 2 48 9 12 42 2 18 14 40 •0S9+ 8-95195 5 48 18 12 2 54 9 43 5 2 10-5 •0916 S-062C, 6 18 3 9 45 2 15 15 J2^ ■0937 ! 8-97'97 « 12 TTIiT 3 8 54 405 2 13-5 ■0958 8-98.36 C 24 17 30 3 12 8 48 48 2 12 16 44 •0978 S-99C24 C 36 17 24 3 18 K 42 49-5 2 105 •0997 S-99S64 C 48 17 12 3 24 H 30 51 2 9 17 43 ■J015 9-00658 7 17 3 30 8 30 52-5 2 7-5 •J033 9-01409 7 12 10 48 3 30 8 24 54 2 18 42 ■1050 9-02119 7 24 16 30 3 42 8 18 55-5 2 4-5 •1066 9-02789 7 3G 10 24 3 48 K 12 57 2 3 19 41 •1082 9-03421 7 48 10 12 3 64 8 6 58-5 2 1-5 •1097 9-04016 8 10 4 8 1 2 20 40 9-04576 8 12 15 48 4 7 54 1 1-5 1 58-5 •1125 8 24 15 30 4 12 7 48 1 3 1 57 21 39 •.138 9-05595 8 30 15 24 4 18 7 42 1 4-5 1 55-5 •1150 9 06057 8 48 15 12 4 24 7 36 1 1 54 22 38 •1.61 9-06487 y 15 4 30 7 30 1 75 1 52-5 9-06888 12 14 48 4 3r; 7 24 1 9 1 51 23 37 ■1182 9-07260 9 24 14 30 4 42 7 18 1 10-5 1 49>5 •1191 9-07603 9 30 14 24 4 48 7 12 1 12 1 48 24 36 •1200 9-07918 y 48 14 12 4 54 7 1 13-5 1 40-5 •1208 9082061 10 14 5 7 1 15 1 45 25 35 •.2.5 1 9-08468! 10 12 13 48 5 « 6 54 1 10 5 T43 5 •1221 9-08703 10 24 13 30 5 12 48 1 18 1 42 20 34 •1228 9-089.2 10 30 13 24 5 18 6 42 1 19 5 1 40 5 •1233 9-09096 10 48 13 12 5 24 30 1 21 1 39 27 33 •J237 9-09255 n 13 5 30 fi 30 1 22-5 1 37-5 •I24I 9-09388 11 12 12 48 5 36 6 24 1 24 1 30 28 32 ■1244 9-09498 11 24 12 36 5 42 « !«■ 1 25-5 1 34 5 •'247 9-09582 II 30 12 24 5 48 6 12 1 27 1 33 29 31 •124.5 9-09643 11 48 1 12 12 5 .-,1 6 6 1 2»-5 1 31 8 1 ■12,0 1 9-09679 "2 u 1 12 1 1 30 'iri 'H 9-0969. TARLE 26 661 APPARENT TIME OF THE SUN'S RISING AND SETTING Declinatiom, of the Kimo Niime an the Latitude LaL 0° Ki.. Sett. r 4° 6° 8° 9° 10° His. ! Sett. Ris. Seit. Ris. Sett. Ris. Sett. Ris. Sett. Ris. Sett. 6 R 10 1-2 U 1« III 2■^ 21 25 2fi 27 28 20 30 M 32 3J 34 35 36 37 38 39 6 o 6 o 6 o 6hom 6 6 o 6 o 5 59 6"o>" 5 57 5 55 5 S5 6 6 I 6 2 6 2 6 3 6 4 6 5 6 5 6 Hi 5'P 5 55 5 54 5 53 5 51 6 6 1 6 2 n 6 6 6 7 6 8 61. on, 5 59 5 58 V^ 5 54 5 53 5 52 5 51 5 so 6'. on ii 6 6 6 7 6 8 1.1 5 59 5 58 5 57 5 55 5 54 5 53 5 5' 6 I 6 2 i ' 6 5 6 6 6 7 6 8 6 10 6 12 e"" o"'[ 6'' 0'" 5 59 6 ' 5 57I6 3 5 47U .3 ll 5 57 5 57 5 57 5 57 n^ 5 56 5 56 5 5f 5 56 6 4 5 54 5 54 5 54 5 53 5 53 5 53 5 5^ 5 5^ 5 5> 5 51 6 6 6 6 6 6 6 7 6 7 6 7 6 S 6 8 6 9 6 9 5 5' 5 5' 5 50 5 5° 5 49 5 49 548 548 5 47 5 47 6 10 6 I. 6 II 6 ,3 5 48 5 48 5 46 5 45 5 44 5 44 5 43 6 ,2 6 12 i " 6 14 6 14 6 15 6 16 6 16 6 17 6 IS 5 47 5 4-6 5 45 5 45 5 44 5 43 5 42 5 4' 5 4' 5 40 6 14 Sil 6 17 6 I9 6 19 6 20 5 45 5 44 5 44 5 43 5 42 5 4> 5 40 "I 5 38 6 ,5 6 ,6 6 16 III III 6 21 6 22 6 22 6o 5 55 5 55 5 55 5 55 5 55 5 55 5 55 5 55 5 55 5 55 6 5 5 5' 5 5° 5 5° n^ ^8^ 548 5 47 5 47 6 9 6 '' 546 5 46 5 45 5 44 5 44 5 43 5 42 5 42 5 41 5 40 6 ,4 6 ,4 6 ., 6 16 6 16 6 17 6 iS 6 18 5 41 5 4' 5 40 5 39 5 38 5 37 5 37 5 36 5 35 5 34 6.9 vz 6 21 6 22 623 6 24 6 25 6 26 5 39 5 38 i 36 5 35 5 35 5 34 5 33 5 32 5 31 6 2. 6 22 6 23 6 24 625 6 25 6 26 6 27 6 29 6 29 5 37 5 36 5 35 5 34 5 33 5 32 5 3' Ki 5 27 III til 6 27 6 28 629 6 31 40 41 42 43 44 45 46 47 48 4!) 50 51 «2 53 54 65 66 67 68 59 6 c 6 6 o 6 o 6 o 6 5 54 5 54 5 54 5 53 5 53 5 5^ 5 51 5 5' 5 5' 5 51 5 47 546 5 4^ 5 45 5 45 5 44 5 43 5 43 5 4^ 5 42 6 .4 6 IS l\l 6 17 6 ,7 6 li! 6 iS 5 40 5 '! 5 38 5 37 5 36 5 35 5 34 5 33 5 V- 6 21 6 22 6 22 6 23 fi 24 6 2S 6 26 6 27 6 2S 5 33 5 32 5 3' 5 30 5 29 5 '8 5 27 5 25 5 24 5 23 627 6 28 6 29 630 6 3, 6 32 6 33 6 35 6 36 6 37 5 29 5 28 5 27 5 26 5 25 5 24 5 22 5 21 5 '9 5 >8 6 3, 6 32 III III 6 38 6 39 6 41 6 42 526 5 25 5 23 5 22 5 21 5 >6 5 '5 5 13 ill III is 6 42 6 44 6 o 6 6 o 6 5 5° 5 49 5 49 5 49 5 48 5 48 5 47 5 47 6 I2 5 4> 5 40 5 39 5 39 5 38 5 35 ^:2 6 21 6 21 6 22 V.l 6 25 6 26 6 27 5 3' 5 3° Hi 5 17 5 ^5 5 ^4 5 13 5 J' 5 20 6 40 5 21 S 20 5 '9 iii 6 39 6 40 6 41 l\\ 6 46 6 48 6 so 6 52 6 54 5 >6 5 '5 5 '3 5 '■ !1 5 4 5 ' 4 59 644 645 647 6 49 6 50 6 52 6 54 656 6 59 5 " ri 5 4 5 2 4 59 4 57 4 54 4 52 6 49 lit 658 7 I 1 1 7 8 60 61 (i2 63 «4 65 <;« «6i 6 o ll 5 46 5 46 5 45 5 44 5 44 5 43 5 4» 5 4^ fi 14 6 16 5 31 5 31 5 3° 5 ^8 5 17 5 J6 5 »3 6 2S 6 29 6 30 6 32 6 33 6 34 ft 35 6,6 5 ">* 5 >fi 5 '4 5 12 5 10 5 8 5 5 S 4 6 42 1% 6 48 6 so 6 S4 6 sfi 5 4 5 ' 4 59 4 56 4 53 :ift 4 44 6 56 6 59 7 10 7 13 7 16 4 56 4 54 \ii 4 44 4 41 4 37 4 34 7 4 7 fi 7 9 7 "2 7 16 7 >9 7 23 7 26 4 49 4 46 4 43 4 39 4 35 4 3' 427 4 24 7 II 7 14 7 17 7 21 7 25 7 29 7 33 7 36 Lat. Se„. 1 Ri,. SetuJRis. S.t.JR.. Se„. Ris. Se... Ris. S.'tt. Ris. -•:-| I.Mtitudo HBd Dprlinntion of r.mi.ary N.mM 1 602 TABLE 26 APPARKNT TI.MHS OF THK SUN'S RISING AND SKTTINU Oeclikation, of ihe nume Name as tlie Latitude Lat. 4 8 10 U Iti 18 11° 12° 13° 14° 15° 16° r Ris. 1 Sett. Ris. 1 Sett. Ris. Sett. Ris. Sett. Ris. Sett. Ris. 1 Sett. Ris. [ Sett. 6hom 5 59 5 56 5 5+ 5 5^ 5 5' 5 50 6»o" 6 I 6 6 6 g L? 6 13 6 14 6i>o" 5 58 5 57 5 55 5 53 5 5^ IS 5 46 S 44 6 > i ^ 6 5 6 8 6 9 6 16 6hom 5 58 5 56 5 55 5 53 5 5' 5 49 5 48 5 45 5 43 61.0". 6 2 ii 6 13 61. 0". 5 58 5 56 5 54 5 52 5 5° 5 48 5 46 5 44 5 4' 61' 0'" 6 2 6 4 6 6 6 8 6 ,0 6 12 6 ,4 6 ]6 6 19 5 58 5 56 5 54 5 5' 5 49 5 47 5 45 5 42 5 40 6ho„. 6 2 6 4 6 6 1,; 6 ,8 6 20 6hom 5 56 5 53 5 51 5 49 5 46 5 44 5 41 5 39 6ho„, 6 ,4 6 16 5 58 5 55 5 53 5 50 5 48 5 45 5 43 5 40 5 37 5. o»- 6 2 'i 5 6 7 6 10 6 „ 6 ,<; 6 17 6 20 6 23 20 21 22 23 24 25 26 27 28 29 5 44 5 43 5 4^ 5 4' 5 40 5 39 5 38 5 37 5 36 S 3S 6 16 6 17 6 18 6 ,9 6 20 6 21 6 22 6 23 5 4^- 5 4' 5 4-= 5 39 s 38 5 35 5 34 5 33 6 18 6 .9 6 2° 6 22 6 23 6 24 6 25 6 26 6 27 5 41 5 40 5 39 5 38 5 36 5 35 5 34 5 33 5 32 5 3> 5 29 5 28 Vd 5 24 5 23 5 21 5 20 5 >8 5 17 6 ,5 6 20 6 21 6 22 6 24 6 25 6 26 6 27 6 28 629 5 39 5 38 5 37 5 36 5 34 5 33 5 32 5 31 5 30 6 21 6 22 6 23 6 24 6 26 6 27 6 28 629 6 30 6 32 5 35 5 34 5 33 5 31 5 3° 5 29 5 27 526 6 22 6 24 ^2! 6 27 629 6 30 6 3. 6 33 6 34 5 36 5 35 5 33 5 32 5 31 lit 5 26 5 25 5 23 6 24 Hi 6 28 5 34 5 33 5 32 5 30 5 29 5 27 5 26 5 24 5 23 6 26 6 27 6 2S IE i 6 39 30 31 32 33 34 35 3« 37 38 39 5 34 n^ 5 3' 5 30 ni 5 26 5 ^5 ? »4 6 26 6 27 6 2g ii 6 34 6 35 636 5 32 5 31 5 29 5 28 5 ^7 5 26 5 24 5 23 5 22 5 20 6 28 6 29 6 31 6 32 6 33 6 34 6 36 6 37 638 6 40 6 34 6 36 6 37 6 39 6 40 6 42 643 5 27 5 26 5 24 5 23 5 21 5 20 5 iS 5 17 5 '5 5 13 6 33 6 34 6 36 637 p: 6 43 6 45 6 47 5 24 5 23 5 21 5 20 5 17 5 J5 5 '3 5 12 5 >° 6 36 6 37 6 39 6 40 642 643 645 6 47 648 6 50 5 22 5 20 5 19 5 17 5 15 5 >4 5 12 5 'o IS 638 6 40 6 41 643 6 45 6 46 6 48 6 50 Si: 5 '9 l'^ 5 '4 5 "2 5 >i ; ? 5 5 5 3 64. 6 42 6 44 6 46 6 48 6 49 6 51 6 53 MS 40 41 42 43 44 45 46 47 48 49 5 i^ 5 J> 5 io 5 '8 5 17 5 15 5 H 5 " 5 "0 S 8 6 38 6 39 St: 6 46 6 48 6 50 6 S2 5 '9 5 '7 5 '6 5 '4 5 '3 5 n 5 9 5 7 5 5 5 3 6 41 6 43 6 44 646 til til 5 >5 5 14 5 " 5 '° 5 8 5 7 5 5 5 3 5 ' 4 58 6 45 6 46 648 6 50 6 52 6 53 6 55 6 57 6 59 7 2 5 >2 5 ■■^ 11 5 4 5 2 5 4 58 4 56 4 53 n: 6 56 6 58 7 7 2 7 4 7 7 5 4 5 2 4 5*5 4 53 ^8 11 658 7 7 2 7 4 7 7 7 9 7 '2 5 4 5 2 I58 456 4 53 :^8 446 4 43 If, 7 7 4 7 7 7 9 7 12 7 H li 4 5' 4 46 4 43 4 4" 6 59 7 2 7 4 7 6 7 9 7 " 7 14 7 17 7 "9 50 51 52 53 54 55 56 57 58 59 5 6 5 4 5 i 5 ° 4 58 4 56 4 53 4 5° 4 47 4 44 6 54 6 56 6 58 7 7 2 7 4 7 7 7 10 ?:^ 5 • 4 59 4 57 4 54 4 52 4 49 4 47 4 44 4 40 4 37 6 59 7 > 7 3 7 6 7 8 7 >i IT. 4 56 4 54 4 5> 4 49 446 4 43 4 40 4 37 4 33 4 30 7 4 7 6 7 9 7 11 7 14 7 '7 7 20 7 23 7 27 7 30 4 5' 4 48 4 46 4 43 4 40 4 37 4 33 :i6 7 9 7 12 7 14 7 20 7 23 7 27 7 30 ' 3J 7 38 446 4 43 4 40 4 37 4 33 III I'l 4 14 7 H 7 17 7 20 7 23 7 27 7 34 7 37 7 42 7 46 4 40 4 37 4 34 4 3" 4 27 4 23 4 '9 4 '5 ♦ 11 4 6 7 23 7 26 7 29 7 33 7 37 7 41 7 45 7 49 7 54 4 35 4 3' 4 28 4 24 r;^ 4 12 4 8 4 3 3 58 3 52 3 46 3 40 3 33 3 25 3 .6 3 7 3 • 7 25 7 29 7 36 7 40 7 44 7 48 7 52 7 57 8 2 8 8 8 .4 8 20 8 27 8 35 8 44 8 59 m 61 62 63 64 65 66 66 i 4 4' 4 38 4 34 III 4 i' 4 i« 4 1+ 7 '9 III 7 30 7 34 7 39 7 4^ 7 46 4 34 III 4 '7 re 4 3 7 26 7 30 7 34 7 39 7 43 7 48 7 54 7 57 4 26 4 '7 4 >2 4 7 4 > 3 55 3 5» 7 34 7 38 7 48 7 53 7 59 4 18 4 3 3 57 3 5> 3 44 3 40 7 42 7 47 7 52 7 57 8 ^ 8 16 8 20 4 9I7 5> 4 4 7 56 3 59 8 1 3 53 8 7 3 47 8 13 3 40,8 20 3 32 18 28 3 28|8 32 4 « 3 55 3 49 3 43 3 36 3 20 3 '5 7 59 8 5 8 11 8 17 8 24 8 32 8 40 8 45 Lat. Sett. Pis. Sett. Ris. Sett. 1 Ris. Sett, i Ris. Sett. Ris. Sett. R.S Sett. Ris Latiti deam Decl nation of cm. larii J 1 TABLE 20 COS Lftt. APPARENT TI.ME OK THE SUN'S Ri.srr ie aa 8 5 41 6 19 5 4" 6 20 5 40 6 21 5 39 6 ji U 5 4> *■' '9 5 40 6 2C 5 39 6l> 5 38 5 37 6 23 5 36 624 5 35 fi 15 16 5 39 1* »' 5 37 6 23 5 36 6 24 5 35 6 25 5 33 6 27 5 3» 6 28 5 3' 6 29 IH 5 ^6 6 7+ 5 34 6 26 5 33'* 27 5 3' 6 29 5 30 6 30 5 18 6 32 5 28 6 32 'W 5 33 1^ -7 5 31,6 29 5 30 , 6 3° 5 18 6 32 526 634 5 14 6 36 5 24 6 30 21 5 3' |6 ^9 5 3° 6 30 5 iS 1 6 32 5 16 6 34 5 14 6 36 5 22 6 38 5 22! 6 381 ■2i 5 30 6 30 6 32 5 26 ! 6 34 5 14 6 36 5 " 6 38 5 21 6 39 5 2o| 6 40! •23 5 .8 6 3. 5 'ft 6 34 5 24 6 36 5 1- 6 38 5 -• 6 39 5 '9 6 41 5 '8 6 42 24 5 »H« 33 5 -5 6 3S 5 23 6 37 5 1' 6 39 5 '9 641 5 >6 6 44 5 '5 645 2.-. S ^51* 35 5 -3 6 37 5 1. 6 39 5 '9 6 43 5 '4 6 46 5 '3 647 ■2li 3 H 6 36 5 -' 6 39 5 19 6 41 5 '7 6 43 5 15 645 5 -2 6 48 5 •« 649 27 5 Z2 6 jS 5 »° 6 40 5 '7 6 43 5 '5 6 45 5 ' = 6 48 5 "o 6 50 5 9 6 5, 2H 5 10 6 40 5 '8 642 5 >5 6 45 5 >3 6 47 5 '° 6 50 5 8 6 52 5 7 6 53 29 5 .8 fi 41 5 -6 6 44 5 .3 647 5 " 6 49 5 8 6 52 5 6 5 3 6 ,4 5 4 6 56 30 S i-|'i43 5 '4 6 46 5 " 1 6 49 5 9 6 51 5 6 654 ^" 5 2 658 31 5 >5 645 5 '1 648 5 96 5> 5 7 6 53 5 4 6 56 5 > 6 59 5 ° 7 32 5 -36 47 6 50 5 7 6 53 5 4 6 c6 5 2 6 58 4 59 7 I 4 57 7 3 33 5 ■ ' 6 49 5 '8 6 52 5 5J6 55 5 1 6 58 4 59 4 56 7 4 4 55 7 5 34 5 9i6 5> 5 6 6 5+ 5 3;6 57 5 4 57 7 3 4 53 7 7 4 52 7 8 3.i 5 7 16 53 5 4 6 56 S >|6 59 4 58 7 2 4 54 7 6 4 5- 7 9 4 49 7 «' 3S 5 51^ 55 5 2 6 58 4 59 I 7 I 4 55 7 5 4 5: 7 8 448 7 >2 4 46 7 14 37 5 36 58 5 7 4 56 1 7 4 4 S3 7 7 4 49 7 I' 4 45 7 IS 4 44 7 i6 38 5 ■ 1 6 59 4 58 7 2 4 53I7 7 4 50 7 to 4 46 7 14 4 43 7 17 4 41 7 19 39 4 59(7 > 4 55 7 5 4 5':7 9 4 48 7 '2 4 44 7 16 4 4° 7 20 438 7 22 4il 4 57l7 3 4 53 7 7 4 49 i 7 • I 4 45| 7 15 4 41 7 '9 4 37 7 23 4 35 7 25" 41 4 54I7 6 4 50 7 10 4 46 1 7 .4 4 42 7 i8 4 38 4 33 7 27 4 3' 7 29 42 4 S^i7 8 4 48 7 '- 4 43:7 >7 4 39 7 21 4 35 7 25 4 30 7 30 7 32 43 4 49! 7 i> 4 45 7 '5 4 4' I 7 19 436; 7 14 7 29 4 27 7 33 4 24 7 36 44 + 47 7 13 4 4- 7 18 4 38 '7 22 4 33 7 27 4 28 4 23 7 37 d 2, , 7 39 4 I 4 44 '7 .6 4 39 7 21 4 35 7 25 4 30 7 30 4 15 7 35 4 20 7 4'3 4 .7 7 43 4ti 4 4>i7 19 4 36 • 7 24 4 3' 7 29 4 26 7 34 7 39 4 16 7 44 4 13 7 47 47 4 38 , 7 22 4 33 '7 27 4 18 7 31 4 13 7 37 4 '7 4 12 7 48 4 917 5' 4H 4 35 7 »5 4 30 7 3° 4 15 7 35 4 '9 7 4' 4 13 7 47 4 7 7 53 4 5 7 55 49 4 3^ '_ii 4 17,7 33 4 n 17 39 ±11 7 45 4 9 7 5' 4 3 7 57 4 ° 8 .ifT 4 29 7 3' 4 13 7 37 4 >7|7 43 4 ■• 7 49 4 5 7 55 3 58" 8 2 3 55 8 5 .il 4 ^5 7 35 4 19 7 4> 4 '3 7 47 4 7 7 53 8 3 54 8 6 3 5° 8 ic 52 7 38 4 '5 7 45 4 9 7 5' 4 » 7 58 3 55 8 5 348 8 12 3 45 8 «5 53 4 18 7 4- 4 '■ 7 49 4 4 7 56 3 58 8 2 3 50 8 itt 3 43 8 17 3 39 8 21 ,14 4 '4 7 46 4 7 7 53 4 3 51 8 8 3 45 8 ,5 3 37 8 23 3 33 8 27 ."I'l 4 9 7 5« 4 - 3 55 8 5 3 47 8 ,3 3 39 8 21 3 3" 8 29 3 27 8 33 .iH 4 5 7 55 3 57 8 3 3 49 3 4' 8 .9 3 33 8 27 3 24 8 36 3 20 8 4C j; 4 X 3 5* 8 8 3 44 8 16 3 35 8 25 3 26 8 34 3 '7 843 3 '- 8 48 iH 3 55 8 5 3 46 8 14 3 38 8 22 3 =8 832 3 >9 8l, 3 9 S 5. 3 4 8 ^6 59 lj49. 3 43 8 II 8 -7 3_40 8 20 3 ->' 8 29 8 39 849 3 9 ^ 55 9 5 9 '5 3 34 1 8 16 3 24 18 36 3 >3| 8 47 1 2" 8 58 2 51 9 9 2 45 (il 3 36 8 24 3 26 8 34 3 ,6 8 44 3 5I 8 55 1 53 9 7 2 40 9 20 2 34 9 26 fi2 3 19 8 31 3 .8:8 42 3 7 8 53 1 55 9 5 242 9 18 2 28 9 32 2 21 9 '.9 fi3 5 " 8 38 3 .0 8 50 2 58 9 2 2 44 9 '6 2 30 9 30 2 14 9 46 2 6 9 54 i;i 3 '3 8 47 > "19 ° 1 47 9 '3 2 16 9 44 1 ^X 10 2 I 48 10 1: «.•> 3 3 ' 57 2 50,9 10 - 35 9 =5 2 Ji I ^2 I 38 10 22 I 26 10 34 fiA ' 55 9 7 1 37 19 13 9 39 2 2 9 58 ' 39 10 21 I 10 10 50 2 5' 8«i 2 46 9 "4 - 3° 1 9 3° 2 12 948 I 51 10 9 I 26 10 34 48 12 c 1 L«t. 's....|',;„. S,;r 1 R.s. Sett. Ris. .Sell. 1 His. Sett. His .Sell. Ria. S.tt. His 1 I.Hli urf^n n-tl>. liimti in of n. T7<,T7 .Valines. 1 TABLE 27 ArrKOXIMATE APPARENT TIMES OF THE MERIDIAN PASSAGES OF THE PRINCIPAL FIXED STARS OS THE FIBST DAY O? EACH MONTH, 1902. a Andromedie Alpheraie y Pegosi Algenib a Phcenicis a Cassiopeee Schedar B Ceti Deneb Eaitoa : Ursffi Minoria , Eridani Andromedee Arietia Ceti Polaris Feb. Mar. April May June July Aug. Sept. Oct. Nov. , Dec. Mirjak A Idebaran Capella Bigel Nath 1723 2321 3219 2917 2515 2013 24I 5 24 2 III I 2223 2821 3719 3417 3015 2513 29 5 37| 3 24 1 3323 41 21 5019 4717 43 5 5', 3 38! I 4923 5522 420 117 57 5 55 3 42, I 53 23 59 6 40 4 27 2 37! o 4322 5220 4918 4616 41^14 46'i2 581 i 6 50' 4 37 2 48; o 5423 321 018 56 7 14I S 13 12' I 1823 2721 2419 ( 7 18 5 5 3 16 I 2223 31 21 2819 24 [ 8 13 6 04 II 2 17, o 2622 232. 8 33 6 2oj 4 31 2 37: O 4622 43 2( 9 46: 7 33' 5 44' 3 5° i 59 23 56,21 52 10 25I 8 12 6 23' 4 lo 26 8 13' 6 24 36 9 40; 7 37 9 45 7 42 9 53 7 55 .0 12: 8 9 ■I 2, 8 59 23! 6 34 4 40 2 49 o 46 = AlnUam Phact Betelauese Menkalinan 43j 8 30 6 4 47! 8 34| 6 45 I "J J If 51,14 5513 7i" II 9 8 17 13 15 19 13 31111 3s| 9 32 17 19,15 2313 35 II 39' 9 36 18 1416 18 i4_35 1^+ '° 31 18 3416 3814 50JI2 5410 5 19 4717 51 16 314 7,12 ■ 38, o 3522 3i|20 26 18 31 16 4314 47,12 4, 2 39 o 3622 32|2o 2718 31 16 4314 4712 43 4220 3718 41 16 53J14 57 12 54 8 4817 015 413 I 3 19 ; Argus Geminorum , CaniB Majoris ■ Cani8 Majoris a Canis Minoris (8 Geminorum i Argus S Argus a Hydr II 6, 8 53; 7 i'i__8 8_55_7_ |ii 38J 9 25' 7 36 5 42, 3 5 ;ii 48, 9 35' 7 46,' 5 52 4 11 57i 9 44 7 55 6 '4 i' 12 II 9 58, 8 96 15; 4 2. 12 44'io 3t; 8 42 6 48 '12 501037 848 6 54 ^12 55 10 42 8 53 6 59 3 56 o 5322 49 3 o o 57 22 53 3 5 I 222 58 53' 18 57 1 ^23 14!: 4823 44: 5823 54: 7, o 3; 8,13 5 13 13 10 719 II 17 23 '5 2713 23 9 I9_i3 '7 25 15 29,13 26 39,19 4317 5515 59>3 56 4919 53 '8 516 9 •;8 2 16 181 161 2816 2 14 28 a Leouis yi Leonis 7) Argfls . ■3 58 II 14 39i2_ 15 19 13 4 57 2 54 o 50,22 4520 4919 533 o o 56I22 5120 5519 7,17 iilis 8 5 83 5' I 122 5621 019 1217 16 IS 13 5 29 3 26; I 22|23 17I21 21^19 33 17 37,15 34 45 9 56 8 2 6 II 4 8^ 2 423 5922 320 15 18 1916 16 2610 37| 8 43 6 52 4 49, 2 45, o 4° 22 44 20 56^i9__o i6_56^ 611 17^23' 7 32 5 29 3 25J I 2023 2421 3619 4o|i7 37 17 II 28 9 34 7 43! 5 40' 3 36| I 31 23 3521 47 19 51 17 48 551 II 10 17 8 6 7] 4 31 58, 23 o 302 ■5 34 18 31 46 18 42 63 corvi !!!!!!]!.'!!!!!"!!!!! o Canum Venaticorum 7) Ursas Majo $ Centauri ... a Draconis a Bootis a' Centauri o Libroe Zuben el Genubi S Ursas Minoris Kochab )8 Librie Zuben el Chatnali a CoroniB Borealis Alphacca 17 37;i5 2413 35, 17 45ii5 3213 43 ■A_7iS 54i_4_5: 18 36 16 23 14 34; 19 0,16 47 14 58 : 19 13,17 4, 9 13, 7 loj 5 8, 9 17 7 14 5 10 3 S! 4ii 9 50 7 47 5 43 3 38: 49 9 58 7 55 5 51 3 46: 49, 8 46 6 42 13 41 13 17,1 Ophiuchi 7 Draconis a Lyrnj a Agnilee a Pavonii ., g Cygni a Cephei f Pegasi a Gruis $ Gruis Unukalhai Bas Alhague Bastaban Vega Aluiir 9 18,17 5,15 16 13 22 II 9 27:17 14 15 2513 31 II ! J I ! 9 49,17 3615 4713 5312 o I|I7 4815 59,14 512 o 717 5416 5J14 II 12 20 20 28,18 1516 2614 3212 41 7 18 34JI63514 51 13 o 523 1721 2119 17 923 2l!2I 2519 21 4223 5421 5819 54 50! O 2 22 6I20 3 4 8 2 12 O 2422 28 20 24 4 37I 2 41; o 5322 57 13' 9 1°: 7 6| 5 13 5: I 1723 21 20 9 23 7 19| 5 14 3 18; I 30,23 34 31 9 28 7 24| 5 19 3 23] I 3523 39 40, 9 37: 7 33, 5 28 3 32 - " I I 2 9 59 7 55 5 50; 3 54 1410 III 876 4423 48, 6 o lo's :l22 18 10 171 551 53, > 5913 1519 217 I3[i5 19 13 281 39,19 26,17 3715 4313 521 5419 41,17 521' 'O-- -■ .684 12 34I 6 29' 4 33' 53' 6 48 4 52 II 6 56 " 49, 9 2 I 16123 i: 5 20' 3 32; 1 36j23 3: 46 20 33 18 44 10,20 5aji9 8 37;i9 47 I 222 4920 5919 617 15 15 1 3423 21 21 3: 1 5423 4i;2i 5: 2 32, O I9'22 3< 2 55l o 42,22 5; 3 18, I 523 16 3 53 I 4023 5 4 8j I 55, o ' 4 16 3 301. 16 48 14 57 12 55 10 SO 16 5014 5912 57 17 15,15 2313 21 7 54 52 8 47 6 51 5 3; 3 ; 16, 9 ii| 7 15 5 27| 3 3: 561 9 51, 7 55 6 7, 4 i: 8,11 3 9 7 7 19 5 2; 3618 45'i6 4214 5919 817 515 35 9 39 7 51 oil 55 9 59| 8 II, 6 12 33 10 37, 8 49 I 12 56 II o; 9 12 17 28 IS 2413 1911 23! 9 35 7 39 '8 315 5913 54 II 58,10 10 18 18 lb 14 14 9 12 13,10 25 8 2n 18 2616 2214 17 12 21 10 33 8 37 TAin.K 27 A « OKRK( TIDN OK THK TIMKS IN TAIiLK 27 FOU THK DAY OK THE MONTH. To Ipe SubtracUd. 0.y> Jan. 1 Keh. M«r. 1 Apr. | M.y June July Aug. 1 Sept. Oct. Not. 1 Dec. 1 •-• 3 ft li 7 II 9 o> 0" o 4 o 9 o 13 Iti O 26 o 30 o 35 o 3 '3 > 17 38 42 46 50 53 57 036 40 43 47 50 :\\ \ \ 37 40 44 48 51 ° 55 59 : I 1 10 40 :p 1 • 4 > 9 > >3 1 17 52 57 1 6 I 10 ' '5 I 19 2.-J 2."> •I'll SO .tl 1 i6 ' 3' > 35 ' 39 ■ 43 • 47 ' 56 - 4 2 8 ' '9 \\l I 30 nt 1 42 ' 45 I 14 I >7 I 24 . 28 :^; 1 39 ' 43 ' '3 I «7 I 21 > »5 1 28 I 32 . 36 1 40 I 44 I 47 ■ 18 1 26 1 30 ' 34 1 38 \ 46 1 50 ' 55 1 59 1 23 1 27 1 3' » 35 J 39 • »5 I 29 • 33 • 37 I 41 • 45 I 49 > 53 • 57 1 16 1 19 1 23 ' 27 • 3' \\t I 42 » 45 1 49 > 51 1 16 1 19 '.21 1 30 ' 34 > 37 1 41 1 44 1 14 T 21 I 25 I 29 • 33 ' 37 I 41 I 44 I 48 I 52 I 21 I ^5 I 30 • 34 I 38 I 42 > 47 > 5' I 55 ■ S9 I 32 ' 37 1 5c • 55 ' 59 \ \ 2 12 CORRECTION OF THK TIME OF THE MOON'S MER. PASSAGE Long. Daily Vf ri«lion of the Moon's Meridian Passage Long. 42" 44™ 4g„ 48" oO" 62" 54"! SG" S8" 60"| 62" 61" 66" H. M. n" 1" I" I" I" I" ,,„ 1" I"! I" I" 20 10 I I 1 1 2 2 2 2 2 2 45 20 2 2 3 .1 3 3 3 4 4 I 20 ;i(i .-? 4 4 4 S s S .S 5 2 III s ■i S 6 6 7 7 7 7 2 40 .ill 6 6 7 7 « 8 P 9 9 3 2J fill 7 7 8 9 10 10 10 II II 7(1 8 9 9 10 I 10 II II 12 j 12 '3 '3 4 40 H'l 4 14 >S 5 20 !i(l 10 II 12 >.5 13 14 14 ■sl 15 16 16 6 inu 12 12 H ■4 15 1 16 lb "7 '7 18 18 6 40 nil ».3 1,? «s 16 16 17 18 18 ■9 20 20 7 20 Vii) 14 M 16 17 18 19 iq 20 21 21 22 8 c \.M 'S 16 •7 19 19 20 21 22 22 23 24 S 40 III) 16 •7 18 19 20 2< 22 2.3 23 24 2S 26 9 20 i.*.ii 17 I8 20 22 2» i 23 24 2S 26 27 27 10 ifiii 18 20 20 21 23 24 25 26 27 28 28 29 10 40 1711 20 21 22 2.3 a4 2S 25 26 27 28 29 30 3> II 20 i«'i 2.) 21 22 23 ^< JL "i'" 29 30 3- 32 3,3 12 666 TABLE 29 HOUR ANOLE AND ALTITUUE OF A BODV UPON THE PRIME VERTICAL 1 I^L Declikaiion .- 3° 4° 6° ^ 7° 8° H. A. Alt. II. A. .Mt H.A. Alt. If. A. A!'. H. A.lAlt. II.A.|Alt. 11. A.I AIL II. A.I Alt. 2 3 4 5 (J 7 8 n 10 4 o 4 4» 5 ^ 5 >4- 5 Ji 5 »7 5 3> 5 35 5 17 30-0 '9-5 '4 5 ;:: 6-4 5-8 3 13 4 4 26 4 42 4 54 5 ^ 5 9 5 '4 41-8 ;?! 19-5 i6-6 '4"5 11-6 2 46 3 33 4 ° 4 >9 4 31 4 43 4 5> 486 369 30-0 ^54 22-1 ■9-5 ■7-3 2 28 3 13 3 4= 4 I 4 '5 4 27 53-1 4.-S 34-9 30-1 26-5 13-7 lit 4 I 56-4 45-7 1 4 2 46 3 >4 3 34 41-9 37-0 3 3 !44-6 I 50 1 19 62-8 53-3 12 13 14 15 16 17 10 20 5 39 5 4> 5 43 5 44 5 45 5 46 5 47 5 48 5 48 5 49 5-3 4 8 4-5 3-9 3-6 3-4 3-- 3' 2-9 5 19 5 =5 5 =8 5 30 5 3^ 5 34 5 35 5 37 5 38 8-? 7T ^:| 5-8 4 57 5 3 5 8 5 " 5 "5 5 '8 5 => 5 23 5 ^5 5 »7 .5-9 14-6 134 125 l'-7 10-9 10-3 9'7 9'- 8-8 4 36 4 43 4 49 4 55 4 59 5 4 5 7 5 >° 5 >3 5 '5 21-6 i6-8 .5-6 '47 13-8 131 12 4 4 13 4 ^3 :]8 4 44 4 49 III 5 • 27-2 24-8 22-8 I9'7 ]8-4 3 49 4 1 4 '1 4 20 4 28 4 34 4 40 4 44 :;? ■?> 23-8 11-3 20-9 19-8 '8-7 ■7-8 3 13 3 39 3 5' 4 •■ 4 '9 4 15 III 39-7 35-9 32-8 25-2 24-6 i3;i 20-8 1 55 3 '4 3 5= 3 43 3 53 4 3 4 10 4 '7 4 24 4 29 46-8 42-0 s; 31-5 30-3 28-4 26-8 21 22 23 24 2.1 20 27 2H 29 30 w 32 33 34 35 3« 37 38 40 -JT 42 43 44 45 46 47 48 49 50 5 5° 5 5° 5 5' 5 5' 5 5' 5 52 5 5- 5 53 S 53 5 53 5 54 5 54 5 54 5 54 5 54 5 55 5 55 5 55 5 55 2-8 ^■7 2-6 -•5 ^;3 i-o '•9 '•7 1-6 1-6 '•5 >;5 '■4 i'4 '■4 '■4 i'3 ■•3 1-3 5 39 5 40 5 41 5 4^ 5 43 5 44 5 44 5 45 5 45 5 46 5-6 5-3 5-' 4"9 4-7 4-6 44 43 4' I 4-0 I'l ri 3-6 35 34 3-3 3"- 3-' 5 ^9 5 30 5 3i 5 33 5 34 5 35 , 36 5 37 5 38 5 39 8-4 80 7-7 74 7'i 6-8 66 tt 6-0 5 .8 5 io 5 ii 5 »4 5 ^5 5 17 5 18 5 3° 5 3' 5 3 = IO-7 IO-3 9-8 9-5 U B 5 7 5 '0 5 'J 5 '5 5 '7 5 '9 5 10 5 11 5 14 5 15 14-1 lit 11 4 "■9 11-5 10-7 10-3 5 1° 5 18 l6-2 '5 5 149 I'rl III '14 4 45 4 49 III 4 59 5 1 5 4 5 7 5 9 5 " 198 ill i6-i '5'5 ;[6 14- 1 4 35 4 39 4 43 446 4 5° 4 53 4 56 4 59 5 1 5 4 "1 17-8 >7-2 5 47 U^ 5 48 5 49 5 49 5 49 5 5° 5 5" 5 50 5 5' 5 5« 5 5' 5 5^ 5 5* 5 5^ 5 53 5 53 5 5' 5 5-3 5 40 5 41 5 4' 5 4^ 5 43 5 43 5 44 5 45 5 45 .45 5-8 5-7 5-5 54 5-i 5-I 5-0 4-8 4-7 5 33 5 34 5 35 5 36 5 37 5 38 5 39 5 39 5 40 5 4' 7-S 7-6 74 7'2 7-0 6-8 6-7 .•1 6-2 5 17 5 18 5 19 5 30 5 3> 5 31 5 33 5 34 III 97 9-5 91 8-7 8-5 7'8 5 1° 5 11 5 13 5 14 5 15 ^1^ 5 19 ill 5 31 5 33 5 34 5 35 5 36 5 37 5 37 5 38 5 39 5 40 U4 ;H _94 9'i tl 8-6 S-i 8-2 80 7-8 5 '3 5 '5 5 '6 5 18 5 1° 5 11 5 14 5 18 5 19 5 30 5 3' 5 31 5 33 5 34 5 35 III '3-7 '3-3 12-3 11-7 II-4 10-9 5 6 5 8 5 '0 5 '1 5 '4 5 '5 5 '7 5 '9 5 1° 5 11 '5-7 '5-1 14-8 '44 '3'7 134 '15 5 56 5 56 5 57 5 57 3-0 3-0 »-9 2-8 1-8 H 2-6 5 46 5 47 5 47 5 48 548 5 48 5 49 5 49 5 50 4-6 4-5 44 4' 3 :-^ 4' 4-0 4-0 3-9 5 4» 5 4^ 5 43 5 43 5 44 5 45 ''{ 5 4"^ 5 47 6m 6-0 5-3 5 37 5 38 5 38 5 39 5 40 5 4> 5 41 5 41 5 43 5 43 7-6 7-5 7-3 7'i 6-8 6-7 66 6-5 107 10-5 9-9 9-7 9-6 94 9*3 9' 5 13 5 14 5 15 5 17 5 18 5 19 5 30 5 3> 5 3- 5 33 "■3 Io-8 IO-6 10-5 51 52 53 54 55 56 57 5« 50 60 (>: 5 57 5 57 5 57 5 57 5 57 5 57 5 57 5 57 5 58 5 58 5 59 ■•3 '•3 ■•3 1-2 1-2 1-2 1-2 12 5 54 5 54 5 54 5 54 5 54 5 55 5 55 5 55 5 55 5 55 5 56 2'6 i-5 ^■5 i-5 ^4 2-4 »4 2-4 »-3 i-3 1-3 5 50 5 5' 5 51 5 5- 5 5» 5 5^ 5 5^ 5 5i 5 53 5 53 5 53 3-8 3-8 3-8 3-7 \i 35 3-5 3-5 3-4 5 47 si! 5 49 5 49 5 5° 5 5° 5 50 5 51 5 5' 5-' 5-0 5-0 t-l 4-8 4-7 4" 7 4-6 4-6 5 44 5 44 5 45 5 45 S 4*^ S 4'' 5 47 S 47 5 48 5 48 5 49 6-3 6-3 6-2 6-0 5-8 5-8 5-8 5'7 5 40 5 4> 5 41 5 41 5 43 5 44 III 5 46 5 47 7'7 7'6 75 74 7-3 7'1 7-1 7-1 7-0 6-9 6-8 III 5 39 5 4° 5 40 5 4' 5 41 5 43 5 44 5 44 9-0 8-6 ii 8-3 i:= 8-0 S 34 5 37 ^8 5 39 5 40 5 4' 5 4' ; 41 10-3 ij 9-6 9-5 94 93 9"i 9> TABl.K 20 CG7 HOUR AN7k-2 1 40 2 16 1 41 3 3 -6 3 28 3 39 3 49 3 57 4 4 65-5 566 50-5 IK 34-z 32-2 30-5 . 35 66-6 2 1.158-0 2 35 52-1 i 54 47-5 3 9 43-8 3 "|4''-7 3 33 38'. 3 43 35-8 3 5- 133-9 1 32 2 6 2 30 - 49 3 4 3 .7 3 ^8 3 37 67-5 59-2 53-4 49-0 453 4-3 39-7 37-4 . 29 2 26 2 24 ^ 59 3 '2 3 ^3 6S-5 60-3 54-7 50-3 467 43-7 4.-. . 26 692 :;:;■? 2 40 5"-5 2 54 [48-0 3 7 45-0 I 23 1 55 2 .8 2 36 2 50 69-9 62-3 56-8 52-6 49-2 > 5^ 2 14 70-5 57-8 53-7 •-'2 23 ■-'•1 2« 27 2B 29 30 4 J! 4 28 4 32 4 3" 4 41 ::5 4 5' 4 54 4 5'' 22-6 20-9 20-I '9-5 ■8-3 4 >" 4 '6 4 »» 4 17 4 3' 4 35 4 39 4 43 4 46 4 49 290 m 25-3 H-3 ^3-3 3 58 |3-^ 4 530-6 4 ..29-2 4 .6 28-0 4 2, ,26-8 4 26 25-8 4 3o'24-S 4 34 240 4 38 ^3-i 4 4" "-4 3 46 3 53 4 4 6 4 '^ 4 17 4 30 4 34 4 37 4 40 4 44 4 47 Vsl 4 54 4 57 4 59 5 ' 355 33-7 32-. 30-7 »9-5 '8-3 III 25-4 24-6 3 4' 3 48 3 55 4 7 4 >7 4 " 4 26 38-8 369 35'' 33-6 32-1 30-8 29-7 2S-6 27-6 26-7 lii 3 44 3 5' 3 57 : I III 4-5 40-2 3?-2 36-5 34-9 33-5 32-2 3.-0 29-9 28-9 3 3 3 H 3 ^3 3 32 3 40 3 47 3 54 3 59 4 4 4 9 46-2 43-7 k-o-3 39-5 37-8 36-2 34-8 33-4 3.-2 1 47 ^ 59 3 .0 3 20 3 28 3 36 3 43 3 49 3 55 4 ■ 50-3 47-4 42-7 40-7 39-0 37-4 35-9 34-6 33-4 M 33 :» 35 3« 37 :<8 3!» 1 40 4 59 5 ' 5 4 5 6 5 8 5 10 5 '• 5 '3 5 '5 5 16 '7'7 17-2 16-7 i6-2 158 '5-4 15 I .4;? ■4-4 14- 1 4 5^ 4 54 III 5 i 5 4 5 (• 5 8 5 '0 5 •■ ■9-7 Te 17-6 17-2 i6-8 i6-4 .6-0 ■5-7 444 4 47 4 50 4 53 4 56 4 58 5 5 3 It 21-7 2, . 20-5 199 .9-4 .8-9 .8-5 .86 ;':5 23-8 23-1 22-4 2.-8 20-7 '9'7 '9-3 .8 8 4 30 4 33 4 37 4 40 4 43 4 4f> 4 49 4 5' 4 54 4 56 25-9 25-1 24-4 23-7 23-1 22-5 21-9 21-4 209 20-5 4 22 4 26 4 30 4 33 4 37 4 40 III 4 48 4 51 280 27-2 26-4 25-5 24-9 24-3 23-7 23-1 22-6 22-. 4 14 4 .8 III 4 30 4 33 4 37 4 4° 4 43 4 46 30-2 29-2 2S-4 27-6 26-8 26-. *5-5 24-5 237 4 6 4 " 4 -5 4 '9 4 ^3 iii Ho 32-4 30-4 280 26-6 26-0 41 42 43 44 4.'. 46 47 411 4U )l 1)2 ihi M M 6« »7 .'» 5 .8, .3-8 5 '9j'3-5 5 271. 2-1 5 28,,2-o 5 29 ,.-8 5 '3 5 '5 5 >6 5 18 5 '9 5 »' 5 " 5 M 5 ^5 5 »6 •5-3 '5 i '4'7 '4-5 14-2 14-0 ■3-7 '3-5 ■3-3 .32 5 8 5 >o 5 iJ 5 "4 5 '5 5 '7 5 .8 5 io 5 '" 5 " l6-2 '59 '5-7 '5-4 .4-6 14-4 5 3 5 5 ii 5 '3 5 14 5 '6 5 '7 5 '9 .8-5 .8-1 17'7 ■7-4 .7-. .6-8 16-5 .62 .6-0 '5-7 4 58 5 1 5 3 5 5 5 7 5 8 5 >o 5 '^ 5 14 5 '5 .9-6 .8-5 '7-3 4 53 4 56 4 58 h 5 .° 5 .1 21-6 20-8 10-4 20-0 .96 ■9-3 19-0 .8-7 .8-4 4 48 4 5' 4 53 1$ I : 5 4 5 6 5 8 5 " i:t \'i 5 22 23-2 22-9 B 20-7 20-4 >9-7 4 43 1^4-8 4 46 24-3 It.kl 4 5 3-22-9 m 5 2 2. -4 5 42.-. 5 3'j'>-6 5 jx "^ 5 33'>'-3 5 34 "•' 5 35 no 5 35|'o-« 5 3"|>o-7 5 37 lo-ft 5 ^9 5 3' 5 3^ 5 33 5 34 5 35 12-9 12-7 iz-6 12-4 "•9 5 ^4 5 28 5 »9 5 30 5 3' 5 33 .4-2 .4-0 •■',1 '3-5 ■3-3 13-0 5 ^0).5-5 5 " ■5-3 5 ^3 '5-» 5 14 '4-8 5 i6 14-7 5 ^7 '4-5 5 ^? >4-3 5 29^I4-J 5 20 5 i> 5 ^3 5 ^4 5 --6 5 27 .6-8 .6-6 .6-4 .6-1 '5-9 ll-l 5 '3 5 15 III 5 JO 5 -' 5 23 5.4 .8-. ■7-6 '7-4 17-2 .7-0 .6-8 166 19-4 .9-2 .8-9 .8-7 .8-4 i8-2 .8-0 17-8 5 820-s 5 .0^20-2 5 '2 >9 9 5 ■4|'9-7 5 .6 .9-4 5 .7 '9-2 5 .9|.9-c TABLE 20 HOi;u ANOLK ANDAI/riTUDE OF A BODY UPON THK PRIM! . Vt RTIC AL Lnt. Declination jjo 10° 11° 12° 13° 14° 15" 16° H. A Alt. H. A. Alt. II. A Alt. II. A |AU. II. A.IAlt II. A Alt. H. A Alt. H. A.|Alt. 03 fiO r.l 62 «;{ ra tin fiO (■'7 (!» (i'J 70 5 38 5 39 5 4° 5 4' 5 4' 5 +i 5 +3 5 44 5 45 5 45 5 40 5 47 10.5 IO-4 IO-3 lo-z lO-I 100 p 5 3« 5 37 5 38 s 38 5 39 5 4° 5 4' 5 4» 5 43 5 44 5 44 5 45 11*7 11-4 "'■I 10-9 IO-8 lo-S 10-7 ic-6 5 33 5 34 m 5 39 5 4^^ 5 43 5 44 I2°8 12-7 12-6 12-5 12-4 5 3' 5 3 = 5 33 5 34 III Hi 5 39 5 40 5 4' 5 4J .4-0 .3-8 'I'l '3-5 '34 ■3-3 13-2 I2-S 5 28 5 29 5 3' 5 32 5 33 5 34 III 5 37 5 39 5 40 5 4' 15-2 15-0 ■5-9 14-S .4-6 >4-5 '4-4 '4-2 14- 1 140 \l-l 5 26 5 27 5 23 5 30 5 3' 5 32 5 33 III 5 39 .6-4 l6-2 .60 '5-9 '5-7 15-6 ■5-5 '5-3 15-2 15-1 I5-0 14-9 5 23 5 24 526 5 27 5 29 5 30 5 3' 5 33 5 34 5 '1 5 36 5 37 17-6 '7-4 17-2 17-0 i6-8 16-7 166 ■6-4 '6-3 16-2 16M .6-0 5 10 5 22 5 23 III 5 28 5 29 5 3' 5 32 5 33 5 35 5 3^ '.tt 18-0 I7-8 17 6 17-4 '7-3 '7-2 I7-0 ° J 7" Uf ^ lit" 20" 21° 22° 23° 24^ 1!) •JO 21 •-'3 21 25 2« 27 2(| 23 1 50 63-9 ; ..i58-7 2 29 54-8 1 43 S'-3 1 56 48-4 3 7 4n-° 3 ■6:43-8 3^5|4.-8 3 33 4o-t 3 40 38-5 3 47 37-> 3 5^ 35-8 ' '7 > 47 - 9 i x6 2 40 » S3 3 3 3 '3 3 22 III ±±L 3 49 3 55 4 4 5 4 9 4 >4 4 iS 4 12 4 -5 4 =9 7. -6 646 59-6 55-6 5»-3 49'4 47-0 44-8 429 41-1 39-6 38-2 > .6 7^-1 ' 45 65-3 2 6,6c-3 ^ ^3l56'4 ^ 37 153-1 2 50 50-4 3 048-0 3 .045-8 3 1943-9 3 ^6 yi 3 34 40-6 1 14 ' 43 - 4 2 21 1 35 72*6 57-2 54-0 5'-3 48-8 46-8 44-8 43-i > '3 1 41 2 2 2 iS 2 32 2 44 2 55 3 5 3 "3 73-' ti 58-0 54-8 i;:8 :a j;-8 38-7 lU 35-6 34-7 33*8 1 II ,' ^' 2 16 2 42 2 53 3 2 3 !■ 3 19 3 26 3 33 3 39 3 45 3 5° 3 55 4 4 5 IP- 62-4 58-7 55-6 52-9 50-6 48-5 2 14 2 40 2 5' 63-0 59-4 56-3 53-7 'A 63-fi 6o-o 57-0 54-4 52-1 50-1 46-7 45-2 43-8 42-5 4'-4 40-3 38-3 37-4 36-6 35-8 35-' 34*4 B 2-1 31 32 33 34 35 3(; 37 38 39 40 J1 4 X 4 'i 4 16 4 20 4 *4 4 28 4 3' 4 35 34-6 33-5 3^-5 3'-5 30-6 29-8 29-1 28-3 27-7 36-8 35-7 34-6 33-5 32-6 3'-7 30-9 30-1 3 40 3 46 3 51 3 57 4 * 4 7 4 >i 4 >5 4 "9 4 ^3 39-2 33-6 31-7 31-9 3'-i 30-4 3 31 3 37 3 44 3 49 3 55 4 4 4 4 9 4 '3 4 17 4.-6 40-2 38-8 III lit 33*7 32-9 32-1 iii 3 4' 3 47 3 52 3 57 4 2 4 7 4 II 46-7 45-0 43-4 42-1 4C-6 39-6 38-5 37-5 36-5 35-6 3 3 9 3 '7 3 24 3 3' 3 37 3 43 3 49 3 54 3 58 49'3 47-5 45-8 44-3 42-9 4'-7 40-5 39-4 38-4 37-4 3 7 3 '5 3 23 3 29 3 35 3 4" 3 47 3 52 41 42 43 44 45 46 47 48 49 50 fil S2 53 64 56 56 67 68 B9 6(1 438 4 41 III 4 49 4 5' 4 54 4 56 4 58 ±.L 5 3 5 5 5 7 5 9 5 >• 5 "^ ^:a 5 IS 5 «9 26-5 ^5-9 24-4 24-0 23-6 4 31 4 35 4 38 4 41 4 '14 4 47 4 49 4 58 4 54 4 57 28-, fe-l 26-2 ^59 ^5-4 2^ 24- 2 = 3-8 4 27 4 3° t36 4 39 4 42 4 45 448 4 50 4 S3 29-7 = 7-9 ¥ 26-4 25-9 -5-5 2S-I 4 -' 4 -5 4 '-8 4 3' III 4 4' III 4 49 31-4 30-7 30-1 29-5 28-9 27-9 27-4 26-9 26-, 4 15 133-2 4 19 32-4 4 3°j3°-4 4 33,29-8 4 36 29-3 4 39 28-8 4 45127-9 4 10 4 13 4 '7 Hi 4 3" 4 35 4 38 4 41 34-8 34-0 li-l 32-0 30-8 30-3 29-7 29-3 4 3 4 7 4 '2 4 16 4 20 4 23 4 27 4 30 4 33 4 37 36-5 35-7 34-9 34-2 33-5 32-9 32*3 3'-7 1-2 0-7 3 57 4 I 4 6 4 10 4 '4 4 18 4 22 4 25 4 29 22-1 21-8 215 II'2 10-9 10-6 20-4 ao-2 199 '9'7 4 59 5 ' 5 3 5 5 5 7 5 9 S '■ 5 '3 S '5 S >7 ^34 23-1 22-8 »r9 21-6 11-4 2I-I »o-9 4 55 4 58 5 ° 5 J 5 4 5 6 5 8 5 '° 5 '^ 5 "4 24-8 24-4 240 23-7 ^-3-4 23-1 22-8 22-6 22*3 12-1 4 5> 4 54 4 56 4 59 5 ' 5 3 76-. '5-7 ^5-4 25-0 24-7 24-4 24-1 238 13-5 J3-3 4 48[27;5 llllll'l 4 55I26-3 4 58(25-9 5 °2 5-6 5 2125-3 5 4 25-0 I l^^ 4 44 446 4 49 4 52 4 54 4 57 4 59 5 > 5 4 5 6 28-8 27-6 27-2 26-8 2^^ 2 5*9 2,-6 4 40 4 43 4 45 448 4 5' 4 53 4 56 4 58 5 I 5 3 a o-i 9*7 i 7-8 7*4 7-1 6-8 4 35 4 39 4 42 4 44 4 47 4 5' 4 53 '* 55 4 58 5 0; 1-6 II °-7 °'l 9-8 9-4 t° 61 «2 «3 64 l;i «9-5 5.8 5 i° 5 " 5 -4 20-7 20-5 zo'3 5 21 2.8 21-6 2 1-4 5 '3 13-0 n^^:-6 5 19 ;= = "4 5 '■ 242 5 >3 23-9 5 >5 2 3'7 5 '7 123-5 5 8 5 1° 5 '5 25-4 15-1 24-'; 5 6 5 8 6-5 6-3 60 5-8 5 3|-/-7 5 527-4 5 8,7-2 5 ioli6-9 TABLE 29 669 UULK ANO -K AND ALTITIIUK OF A BODY UPON THE PRIME VERTlCAl, l^t Declination --IT" M.A.I Alf. .'9!_^ 20'= 21* 22° 23° 84° H.A ^l< (i.A.iAir. H.A Alt 11. A Alt. H.A Alt. H.A lAlt. H.A. All — — h „ ~^ h „. „ ~J~ "h T ~~^ h ., ~^ h ,. J, TT-^ „ K6 5 ^7 iS-S 5 ^5 '9;9 5 13^1-0 5 1' 22-2 5 '9 13-3 5 17 24-4 5 >4 15-5 5 .2 26-7 <;« 5 ^S iS-- 5 24 20-8 5 13 i2-0 5 1' 23-1 5 '9 24-2 5 '6 »5-3 5 '4 »6-4 07 5 3C •8-5 5 's ;9-6 5 26|2c-7 5 14 2,-8 5 " 22-9 5 10 14-0 5 -8 25-1 5 .6 26-2 eu 5 3^ IS-+ 5 30 ■9-5 5 28|20-5 5 26 21-6 5 14 22-7 5 " 23-8 5 10 24-9 5 19 26-0 6» 5 33 182 5 5' '93 5 30 20-4 5 18 »';5 5 26 22-6 5 14 23-6 5 11 14-7 5 1. 25-8 70 5 34 iS' 5 33 '9'i 5 3. 1^0.3 5 30 5 18 22-4 5 26 13-5 5 14 24-6 5 »3 »5 6 H 25» 20'' ■2r 2B^ 29° 30° 31° 32° 2(; I S [7+-6 1 j 27 I 35 68-6 ' 7,74-9 2H I 55|64-2 1 3+j69-o 1 6 75-3 2!» 6o-6 . 53 64-7 ' 33 69-5 I 6 75-5 :w ^ ^5 57-7 ^ 9,6.-. 1 51 6V2 > 31 69:8 • 5 m ' 4 76 I TT 2 36 55' 2 22158-3 2 8 61-8 ' 5'i65-7 I 31 70-3 32 i 47 52-9 1 35 155-8 2 21 58-9 1 7 62-4 I 50 66-2 I 30 70-6 1 4|76-4 33 2 56 50-9 ^45153-0 1 33 56-5 2 20 59-5 2 6 62-9 1 49 66-6 . 29'7ro . 3 17 5-6 SJ 3 5 49-1 » :5:5> 6 2 44 54-3 1 31 57-1 2 19 60-1 1 5163-4 I 4S;67-i . 28I7.-4 35 3 '3:4-'-5 3 3i49-S 1 53 51-3 2 42 54-9 2 31 57-7 2 17 60-7 2 463-8 > 47i67-5 36 5 >■ kS-i 50-6 2 51 53-0 2 41 55-6 2 29 58-3 2 17 6i-2 1 3164-3 37 3 i7J44-6 3 .9I46-7 3 10 490 3 5'-3 2 51 537 2 40 56-2 2 28 58-8 2 .6 6,-7 38 3 33430 3 »5J45-4 3 '7 47-5 3 8 49-7 1 59 5'-9 2 49 54-3 2 39 56-8 1 18 159-3 39 3 39 ^'J 3 3^44-' 3 14 46-2 3 .6 [48-2 3 7 50-4 2 58 52-6 1 49154-9 1 38157-3 •10 J_45.4JM_ 3 38I43-; 3 -0 44-9 3 13 46-9 3 '5 49-0 3 6 51-1 1 58|5."2 1 47 55-5 41 3 50 {40-' 3 43|4>-9 3 36 43-8 3 19 45-7 3 " 47-6 3 '4 49-6 3 5|5>-7 2 56 ■53-8 42 3 55 39-i 3 49 4°-9 3 41 41-7 3 35 44-6 3 18 46-4 3 20 48-3 3 13 50-3 3 4 '51*4 43 4 038-3 3 54 400 3 48 4'-7 3 4' 43-5 3 34 45-3 3 17 47-1 3 20 49-0 3 'i|5'-o 3 >9l49'7 44 4 4|3--5 3 59 39-1 3 53 40-8 3 46 42-5 3 4044-3 3 33 46-0 3 16 47-8 45 4 9 ;6-7 4 3 383 3 57 39-9 3 51 41-6 3 45 43-3 3 39 45-0 3 31 46-7 3 15 48-5 46 4 >3 360 4 8|37-5 4 2 39-1 3 56 40-7 3 5' 42-4 3 44 44-0 3 38 45'7 3 31 47-4 47 4 17 35-3 4 "z 36-8 4 7 38-4 4 I 399 3 55 4"-5 3 49 43-> 3 44 44-8 3 37 46-4 40 4 »' 347 4 .6 36-1 4 1' 37-7 4 6 39-2 4 40-7 3 55 42-3 3 49 43-8 3 43 45-5 49 4 14 3+-0 4 20 35-5 4 >5 37-0 4 10 38-4 4 5 400 3 59 41-5 3 54 43-0 3 48 44-6 50 4 i8|33-5 4 13 34-9 4 '9 36-3 4 14 37-8 4 9 39-3 4 4 40-7 3 59 41-1 3 54 k3-7 Tf 4 3' 31-9 4 ^7 34-3 4 13 35-7 4 18 37-1 4 13 38-6 4 8 ,o*o 4 4 4'-5 T78'|43-o 62 4 35 3^-4 4 30 33-8 426 35-1 4 22 36-6 4 17 38-0 4 >3 39-4 4 8 40-8 : ii:ri 63 438 3-9 4 34 33-3 4 30 34-6 4 26 36-0 4 1" 37-4 4 '7 38-8 4 "1 40-1 J4 4 41 3"-5 4 37 32-8 4 34 34* • 4 30 35-5 4 15 36-8 4 11 38-2 4 16 39-5 4 12 |40-9 55 4 44 3'-' 4 4° 32-3 4 36 33-6 4 33 35-0 4 19 36-3 4 15 37-6 4 20 38-9 4 .640-3 58 4 47 30-6 4 43 3'-9 4 40 33"i 4 36 34'5 4 31 35-8 4 28 37-' 4 14 38-4 4 20 39-7 57 4 49 30-3 4 46 3'-5 4 43 32-8 4 39 34-0 4 36 35-3 4 31 36-6 418 37-8 4 14 39-1 58 4 52 P9'9 4 49 |3'-' 4 46 32-4 4 41 33'b 4 39 34-8 4 35 36-1 4 31 37-4 4 28 38-7 59 4 55 19-5 4 52 3'^-7 4 49 32-0 + 45,33-1 4 41 34"4 4 39 35-7 4 35 36-9 4 31 38-1 CO 61 4 58 19-i 4 55 !3°-4 4 51 Hi 4 48 [31-8 4_4i 340 4 41 3511 4 39 36^ 4 35 37-7 5 28-9 4 57|3°-> 4 54 31-3 4 5' 31-5 448 33-7 4 45 34-8 4 41 36-, 4 39 37*3 «2 5 3 ^8-6 5 0129-7 4 57 30-9 4 54 31-' 4 5' 33-3 4 48 34-5 4 45 35-7 44136-8 «3 5 5 »8-3 5 - m'9-5 5 30-5 4 57 3.-8 4 54 33-0 4 51 34-' 448 35-3 4 46 |36-5 «4 5 7 i8-o 5 5l»9'i 5 1 30-3 5 ° 3'-5 4 57 32-6 4 55 33-8 4 SO 35-0 4 49136-1 •ij 5 10 17-8 5 7 28-9 5 5 30-1 5 3 311 5 31-3 4 58 33-5 4 53 34-6 4 51 35-8 liA 5 " 27-6 5 '0 5 8 298 5 5 30-9 5 3 31-0 5 33-2 4 56 34-3 4 55135-4 «7 5 '4 17-5 5 '1 28-4 5 '0 19-5 5 8 30-7 5 5 3. -8 5 3 2-9 4 59 34-0 4 58 35-. «8 5 '7 »7-3 5 '5 i8-2 5 ■! »9-3 5 10 30-4 5 8 31-5 5 7 2-6 5 > 33-7 5 •34-8 fl9 ! "9 ,6-9 5 17 i8-o 5 '5 »9-' 5 '3 30-2 5 'I 3>-3 5 9 1-4 5 5 33-5i 5 4 134-6 70 $ »« .6-7 5 .,.7.1 5 >7 23-8 5 .5 30-0 5 '3 31-1 5 " 2-1 5 833-1 5 7 134-3 „l _ 670 TABLE 29 HOUR ANGLE AND ALTITUDE OF A BODV UPON THE PRIJIE VERTICAL J.at. Declinatiok 1 33° 1 34° 33° 36° 37° 88° 39» 40« H.A.fAlt. H. A. Alt. H A Alt. H. A.i Alt. H. AJ Alt. II. A.' Alt. H. A Alt. H. A All. — — b m Ii m — ~ -h — — ~ h 111. ~ — ~, — ~ ~i — ^~~ "h a — — t-a, — ~] 34 1 3J76-9 33 . ^8 7. -7 I 2 77-1 3r> I 47 67'9 I 27 72-0 2 77-4 1 1 37 z 2;64-8 > 46 68-3 ^7 72-4 I > 77-6 1 1 38 6;-3 45 68-7 I 26 j72-7 • •'77-8 39 2 27 59-9 2 14 62-7 65-7 .4569-. . 26J73-0 I ilyg-o 40 41 2 47 [56-- TIT 60-4 14 632 2 o!66-i . 44169-4 . 26:73-3 I ] 78-2 , , 78-5 58-5 25i6.-o 2 .3:63-6 2 0:66^ . 44;69-8 1 25 /3 6 42 » 55 154-5 2 46 56-7 36 59-0 2 25,6f4 2 13 64-. . 59;66-9 1 44 70-. ' 25 73-9 43 3 3J53-° ^ 55 5«M 45 57-2 2 35 159-5 2 24 6. -9 2 .2 164-5 ' 59 167-3 ' 43 70-5 44 3 II 5'-6 3 3I53-6 54 55-7 2 45i57-8 2 35 6o-o 2 24 62-4 2 .264-9 • 59:67-71 15 3 i8 5o-a 3 10 5^3 54-2 2 54 '562 2 44 58-3 2 34 160- 5 2 24 '62-8 I .2 65-4 46 3 25 49- 3 '7 51-0 10 52-8 3 254-8 2 53 56-8 2 44 58-8 2 34|6.-o 2 23 63-3 17 3 33M-' 3 24 49-8 17 51-6 3 9 53-5 3 I 55-4 2 53:57-3 2 44 59-3 2 34 6.-5 48 3 37 47-I 3 30 48-g 24 50-5 3 '7 52-3 3 9 54-. 3 > 155-9 2 53 157-8 2 44 599 49 3 43 46-2 3 36 47-8 3° 49-5 3 23 5.-. 3 .6 52-8 3 954-7 3 1 565 2 53 58-4 50 3 48 45J, 3 4^ 46-8 46-0 ji 48:1 3 30.'5o-. 3 23 3 >6l53-5 3 9 55J. J_i 5?8 '51 3 53;44-5 3 48 42 47-6 3 3649-' 3 30 ToT 3 23152-4 3 .6 54- 1 3 9 52 3 58143-7 4 243-0 4 742-3 3 53 45-2 47 46-8 3 42 48-2 3 36 49-8 3 30 51-4 3 23 53-0 3 '6 54-7 53 3 58 44-4 53 45-9 3 47 47-4 3 42 48-9 3 36 50-4 3 30 52-0 3 23 53-6 54 4 3 437 58 45-1 3 53 46-6 3 47 48-. 3 42 49-5 3 36 5'-' 3 30 52-6 55 4 12 41-7 4 7 43-0 3 44-4 3 58 145-8 3 53 473 3 47 487 3 42 50-2 3 36 5'-7 56 4 .641-1 4 .2 42 4 7 43-8 4 3 45-. 3 58 46-5 3 53 47-9 3 48 49-4 3 42 50-8 57 4 20 40-5 4 16 41-8 43-' 4 7 44-5 4 3 45-8 3 58 47-2 3 53 48-6 348 50-0 58 4 24 40-0 4 20 41-2 16 42-5 4 '» 43-9 4 8 45-2 4 3 46-5 3 58 I47-9 3 53 49-3 486 59 4 28 39-4 4 24 40-7 20 42-0 4 .6 43-3 4 "2 44-6 4 8;45-9 4 4|47-' 4 8I46-6 3 59 60 bl 4 32 '39-0 4 28 4°-2 1 ii 4'-S 4 21 42-7 4 17 44-° 4 '3j4£3_ 4 4 47-9 4 36,38-5 4 32 39-7 29 41-0 4 25 42-2 4 2. 43-5 4 .7144-7 4 '3 46-0 4 9 47-3 62 4 39 [38-2 436 39-3 4 33 40-5 429I4.-7 4 26 42-9 4 22 44-2 4 .8 45-5 4 .4 46-7 63 4 43 137-7 4 40 38-8 36 40-1 4 33 4>-3 4 30 42-5 4 26 43-7 4 23 449 4 '9 46-2 64 4 47 [37-3 4 43 38-5 4 40 39-6 4 37 40-8 4 34 42-0 4 3° 43-2 4 27 44-4 * ^l 45-7 63 4 49 36-9 4 47 38-. 4 44 39-3 4 4' 40-4 4 38 4. -6 4 35 42-8 4 3' 44-0 4 28 45-2 66 4 53 36-6 4 50 37-7 4 47 38-9 4 44 40-0 4 42 41-2 4 39 42-4 4 35 43-5 4 32 44-7 67 4 56 36-3 4 53 37-4 5' 38-5 448 39-7 4 45 40-8 4 43 42-0 4 40 43-1 4 37 44-3 6fi 4 59 36-0 4 57 37-1 54 38-2 4 52|39-3 4 49 40-5 4 46 41-6 4 44 42-7 4 4. 43-8 69 5 2 35-7 5 36-8 58 37-9 4 55 139-0 4 53 40-. 4 50 4. -2 4 48 42 4 4 45 43-5 70 5 5 [35-4 5 3 365 37-6 4 59I38-7 4 56 398 4 54 40-9 4 5'|42-o 4 49 43-2 "^ 41° 42° 43° '14° _L^.1_ 46° 47° 4H° 1 42 ■ 078-6 1 43 I 25 74-1 I 78-8 1 41 I 43 7o-g I 25 74-4 79 -c 1 43 . 5S 68-1 ' 43 71-1 »5 ■74-7 I 79-- 46 2 ,2 65-8 I 58 68-5 43 7"-5 . 25 74-9 I 79-4 1 47 22363-8 66-2 58 68-8 ' 43 . 25 75-2 I 79-6 1« 2 3+I62-0 2 --3 64-2 66-6 . 58 69-2 I 43 72-2 > 25 75-5 I 79-8 49 2 44:60-4 2 33|62-4 -3 646 2 .2 67-0 ' 58 69-5 I 43 72-4 I 25 75-7 I 79-9 50 i 53I58-9 2 44I60-9 34 62-9 2 23 65-, 2 12 6r4 Ul 69-9 1 43 72-7 1 25 111 51 3 '157-6 2 53 59-4 44 61-3 - 34i6r4 2 24 65-5 > 59 70-2 , 44 73-0 52 3 95^-4 58-. 53 59'9 2 44 6. -8 2 34 63-8 2 24 65-9 68-1 ' 59 70-6 53 3 "SlsS-^ 3 9 56-9 58-6 2 53 60-4 24462-3 2 3565-2 2 2^ 66-3 2 35 64-7 2 45 63-2 2 .3 68-5 54 3 23 S4-.' 3 '7 55-8 9 57-5 3 =■ 59-2 2 541*0-9 2 45 628 225 66-7 W J 3 .° 153-2 3 24 54-8 17 56-4 3 'O 58-0 3 259-7 2 546.-4 236 65-, 6« 3 36l52-'3 3 30 53-8 24 55-3 3 '7 56-9 3 >o 58-5 3 3'6o-2 2 55 6.-9 2 46 63 7 67 3 43|5'-5 3 37 52-9 3' 54-4 3 25 55-9 3 .8i57'5 3 ■'59' 3 3:60-7 2 5 5 62-4 «8 3 48 5°-7 3 43 52-. 37 53-S 3 32 55-'' 1 =5 '56-5 3 '9 158-^ 3 '- 59-6 3 4 16.-2 W 3 V|rt9'5 % 49 5'-3 44|S»-7 3 38 154-' 3 32 155 6 3 26 157-0 3 2C it 3 i3j6o-2 H. 3 59 \9--- 3 55 506 Ji ILi m 4.il 5 45 54-1 3 33l56;i 3 27 J_20 ^Jtll 4 5 48-6 49'9 i" J5 51-5 T^ 53-9 3 40J55-3 3 34 i6Tl3 28 58-2 02 4 10 48 c 4 6 49 3 ;o 6 15 56|5"8 3 52I53-2 3 4*! 54- 5 3 4' 55-9 3 35 57-3 M 4 M 147-4 4 1' 48-7 i 499 4 ^-\.-r 3 57|52-5 3 53 153-8 > 48 iflii^ 56-5 TABLE SO TABLK 3 1 671 DIP .MK.AN ASTKONO.MICAl, KliKK.VCllOX. (Barometer, 30 incl.es. Falireiiheit's Tliei momeler, M^) A|.p. Alt. !D.tc4 A|.,,. Kefruc. j |„'l .\|, Kefracj ,0 ^X liefrac.j'lfj I'lT- He,...i^d lit Dip. 0^ 3+''7"I,„' (." Ill r:ri;^' 12° 5(1 4' I' , , 35° ( ".'^.•7; 1 3^ '5 13 ( 4 8 :« I 21-7 4" ( 1 u 30 23 102 8 6 - I: 4 5 36- ■50 28 41 94 8 I 2( ■47 i I -.4 27 7 7 50 3( 3 59 37 ( ■47 a 25 41 -g 7 50 4( 3 56 3( I i6-o 4 5 6 7 8 1 Js 2 12 2 25 1 if; 1 34. i 3 itj ! 4 ^4 4 J7 4 4<1 5 I 5 '3 V^ 658 7 'S 10 '-•(1 ao 4I> 23 9 73 67 62 58 53 49 46 40 45 50 55 7 (» 7 45 7 40 7 35 7 30 7 25 5( 14 10 20 30 3 53 3 5° 3 47 3 45 2-7 :' 1-5 38 ( 30 39 30 40 . .4-6 I 13-3 I 10-7 ■47 •43 •43 •43 ■42 •40 ■38 •35 30 2 10 :i2^ '7 34 5 10 15 7 20 7 >6 7 II 40 50 15 3 40 3 37 41 42 I 71 I 4-8 1 •' •-0 21 Sii 1() 9", 40 4r> M 55 20 25 30 :« 40 46 50 5.> :< 5 10 i.i 20 25 '5 5» 42 40 39 38 37 36 35 34 33 3^ 3- 30 20 25 30 35 40 45 50 7 7 7 3 6 59 It g 10 20 30 40 50 Ifi 10 3 3^ lis 3 ^5 3 »3 3 II 3 >9 ? "7 3 "5 3 '3 3 11 3 9 Isl 2-3 2-2 li 2-0 2-0 '■9 "9 44 45 40 47 48 49 50 I 0-4 058-4 56-3 54-4 52-6 50-7 490 ■34 ■34 ■33 •3» ■3' -30 -»9 •28 ■»7 -26 •26 •»s •»5 '4 59 14 42 14 26 14 10 '3 55 13 41 >3 »7 13 13 55 H 5 10 15 20 25 30 i" >• 6 20 6 16 6 „ 20 30 40 50 17 30 18 30 51 52 53 54 55 56 57 ° 47-3 45-6 44-0 42-4 40-9 39-4 37-9 6(1 7 37 13 26 35 6 9 19 2 48 33-71 »3 C5 70 75 7 St^ S 14 8 3> 12 47 ^5 24 40 6 6 30 20 :«) - 44 1 39 2 35 >-4 00 01 T G2 40 45 1 2 jt 45 50 6 3 6 80 8 48 12 10 55 5 57 21 03 29-8 •»» 8i 9 4 .i5 11 58 5 54 30 2 27 ' ^ 04 •21 90 II 47 22 5 5 51 22 ' '■ -21 100 9 5' " 3" 2, 10 5 4li 30 2 2C ' ' RO 26-0 ■20 110 10 19 ji 5 45 23 i-o 07 20 1 '.;() I,') II 15 5 4^ •30 = 13 20 ISO II 14 ■■ 5 20 25 5 39 24 2 10 I 22-4 -20 HO ISO " 39 '2 3 10 5^ '9 5 36 30 ^ 0-9 70 20 ■ 46 35 5 33 25 71" 160 12 27 10 37 18 40 5 3' 30 72 ^ .9-0 •20 170 Ifln 12 50 13 12 45 .0 ,9 50 10 5^5' 20 30 ' 59 I 56 0-9 73 74 •'9 •19 190 ftoo fin ■3 34 '3 55 55 5 10 2 9 54 16 16 20 I'll 27 30 28 :^t o'8 0-8 0-8 0-7 0-7 75 70 77 I \ll ■/2() 260 2H0 >4 36 >5 >5 15 52 16 27 1." 9 3« 9 30 1 if ■5 50 1 5 I ' 4 56 j T48~] 30 2!» 30 ' 47 > 45 ' 43 78 79 80 ■> 12-4 "■3 10-3 •'7 ■>7 •17 9 ^3 ! 10 30 1 41 <^ 7 Rl -FT 8-1 6«i 5'' 4*> SOd 17 ;« ivi'\ 30 40 50 2 4^6 1 4 3^ 4 ^8 30 31 30 32 30 ' 39 • 37 ' 3; ' 33 0-6 0'6 0-6 c-6 6 12 B3 R4 c BO Oc IK c •«7 ••7 ■17 •<7 33 40 45 8^^ '4 ■3 8 42 10 4^5 a I -0 17 c •17 8 36 20 *^'' ! 1 30 I 28 l« Uc •17 8 30 4 18 1 •» U 1 26 '' ' fill c 17 8 24 __ ^0 4 .4 1 * 1 30 1 2s ; '' ■" 'HI c 1 >7 er^ TABLR 32 CORRECriON OF THE MEAN REFRACTION FOR THE HEIGHT OF THE THERMOMETKR 1 A LTITIIDES . 1 4" Z.i*l ~z. e^\r 74° "Z 9° 1 10° 12° i_^ |_20^ 30° 40° 50° T^l'M'] add arfrf «<« add »dd add add orfrf add arfrf add add add add add adrf add 69' 61' 57' 54" 5'' 48' 46' 43' 39' 36' 30' »5' 8"i 5*7 ^'s 66 58 55 5" 4S 46 43 41 37 34 19 23 77 5-4 2-4 63 56 5^ 49 46 44 41 39 36 32 28 22 7-4 5-2 »-3 60 53 50 47 44 42 39 37 34 31 26 21 7-0 4-9 21 57 5° 47 44 42 40 37 36 32 29 25 20 6-7 4' 7 2-0 55 48 45 42 40 37 35 34 3' 28 14 '9 6-3 4-4; '-9 5' 45 4^ 40 37 35 34 31 29 26 21 18 6-0 4'* 1-8 jL 4- 4° 37 35 33 32 3° »7 25 21 17 J* 4-0 i'7 -°- 44 "40 37 33 31 30 26 23 10 16 5-3 3'7 1-6 4^ 37 35 33 3" 29 28 16 24 '9 15 5-0 3'5 "■s 39 33 3> 29 28 26 25 22 20 •7 '4 4-6 3-3 ■4 c 36 30 29 27 25 H 23 21 '9 16 '3 4-3 3-0 '■3 33 27 26 25 24 22 21 »9 >5 12 4-0 2-8 1-2 2« 30 26 24 23 22 20 »9 16 "4 II 3-7 2-6 11 28 28 ^3 21 20 •9 18 16 15 12 10 3-3 2-4 1-0 30 26 20 •9 18 '7 16 ■5 13 II 9 30 0-9 :h2 ■ '9 18 17 16 ■5 '4 13 1 10 8 2-7 '•9 _o-8_ 34 21 17 TT '5 '4 13 >3 ,2 ",o T 7 7~ 2-4 •■7 0-7 "^ 36 18 '5 •4 13 10 9 6 '•5 0-6 38 ■5 " 10 10 9 9 g 5 1-8 '? c-S •to 13 10 10 9 9 8 8 7 6 4 >S \ 42 10 8 g 7 7 7 6 6 5 08 0-4 44 7 6 6 5 5 5 5 5 4 3 0-9 0'6 0-3 4C 5 4 4 4 3 3 3 3 1 0-6 0-4 0'2 48 2 1 2 • 0-3 0-2 50 L-2- sub. .»a: ««i 1^ 7^ "^T -iih TuaT tui. wb. lUb: iii«: 73r ^ Ts: ^ 1^ 52 Z 2 2 2 I I 1 I I I I 0-3 O'l 64 4 4 4 3 3 3 3 3 2 » 0-6 0-4 0-2 5« 7 6 6 5 5 1 1 4 4 3 0-9 0-6 0-3 58 9 8 7 7 7 5 5 3 0-8 0-3 60 II 10 10 9 9 8 X 8 7 6 4 '•4 i-o C2 14 12 10 9 9 8 7 5 i'7 1-2 11 64 17 '4 >3 12 12 II 9 9 6 2-0 ■•4 66 '9 16 '5 '4 ■3 12 12 10 7 3_ 2'2 1-6 0-7 68 II IT 16 16 >5 14 12 II 8 Ts o-S ~^ 70 ^3 '9 18 17 16 >5 '5 •3 •2 8 2-8 0-8 c 72 ^5 20 '9 18 '7 16 '5 •3 9 30 0-9 lA = 3 22 21 ■9 18 17 16 14 3'3 fti ^9 *5 13 22 20 '9 17 16 3-6 i-i 1 78 3> 27 »5 24 22 II 20 18 •7 II 3-8 1-2 80 33 28 27 25 24 13 22 20 11 4i 1-3 82 36 30 28 27 25 24 23 21 '9 '3 4-3 1-3 84 38 J±. 32 30 28 27 16 24 22 20 '4 46 1-4 'W "4°" 34 32 30 ~28~ 17 26 23 TT ~7F '5 TT" 4' 9 3;4 i-s 88 43 35 33 3' 18 27 14 22 '5 5' 1-6 90 45 37 ^1 33 3° 30 28 16 23 16 5-3 1-6 92 47 39 35 33 3' 19 27 14 '7 5-6 '■7 8^. 49 40 38 3S 34 3^ 28 16 iS 5'8 1-8 9fi 5' ♦1 42 40 37 37 34 32 29 27 *3 ■ 8 6- 1 4" 3 '■9 98 53 46 44 4' 39 37 3 5 33 3° 28 23 19 6-3 U 1-9 100 55 4S 45 43 40 38 36 3S 3> ^9 '4 >5 «-5 °| TA?,'..E 3.1 879 COKKK .TION I K Tin; MEAN R KKKACT lO.N ioR im; litiauT i,F THE BA to.'* ITO ETh R R»r. Ali DES 4=' 5' 54- ef er 7" 7J"| r 9^ 10" 12" 15" 20" 30°J40°J60°70°!>0° • «J. 1 1 ,Jd 27-4 6o' •lo" 46", 42" 40" 37" 35" 3 3" 29" 2 7" 22" 18" m" 8" s'« Vo i'8 27 ^7 48 44 ! 4' 3li 3«. 34 3* 28 2b 21 '7 '3 ss 3"8 ° •J7-7 S+ 46 42 39 37 34 3^ 30 27 »s 20 17 12 S-3 3-7 ° •-•7 » S' 44 ¥> ' 37 3? 33 3> 29 2b 24 20 16 12 5'; 3-5 ■J7-!i 4S 4- 38 , 36 33 3' 29 28 2S 2:; ■9 'S I 1 4-8 3-3 •^IIMI + b 40 37 34 31 3° 28 26 24 21 '4 II 4-b 3-1 :2i! 1 ■H ^8 35 i- 30 2S J7 2S 22 20 '4 10 4-4 TO ■-'(12 4' 36 33 ^ 3' 29 27 25 =4 2. ■9 17 '3 10 <> 2-9 •-'11 .-) 'i9 U 31 29 »7 »S ^4 22 20 18 ■ 6 12 9 6 39 2-7 Jil-4 ^7 "i» 29 1 27 »i 24 22 21 19 ■7 M 12 8 3-7 I'li ,') 10 27 ' i5 24 22 21 20 18 lb ■4 1 1 8 3-4 2'4 ■>nij 32 2S 26 : 24 22 21 20 18 '7 IS ■3 10 7 3-i 2-2 ai-4 '.'(J 7 1° 26 24 1 22 21 >9 18 17 »S '4 9 7 >-o 1-9 '0-9 31 3 ■JHS 22 ] 20 '9 18 17 lb "3 II 9 4 '2'8 ■.'i:-» i^ 20 .9 ■7 i5 H 'S " 10 8 6 i'7 8 ° ■Ml ■i:i-u t^ 20 .8 .7 16 'S >4 ■3 12 II 9 7 S 3 *'3 i-b 0-7 31-0 •-■id i!! 16 15 14 13 ■3 II iO 8 6 5 3 2-' 1-4 Ob — 309 30 8 ■.'!(■■.• ,J 16 IS 1 '4 n 12 .. M 9 9 6 4 '■3 l."J3 16 '4 f, 12 ti 10 10 9 8 7 4 2 1-6 o-i; 30 7 •jy 4 '4 li II 10 10 8 X - b 3 2 !i-4 10 0-4 30C L'!r,i II 10 9 S 8 6 S 3 2 1.-IO-8 °' 1 30-5 2!)fi 9 i 7 7 6 6 S S 4 , 0-9 0-6 0'3 30-4 •M7 b 6 S S ■i 4 1 4 4 3 2 . io-7|°-5 0-2 T.IH 4 4 4 3 3 3 3 I I I |0-5|0-3 O-I ■MU I 2 2 I I I I O-I 30-1 •»)0 oj ° ° ° " 1 ° ° 300 TABLE 3i THF SUNS PARALLAX IN ALTITUUK, AND SDMIDIAMETER DIP OF IHE .SHOKi; HORIZON \lottt Altitdde Montb. 3J J li 2 ■-•i 3 34 4 5 « Ut. »r the Eye in t. 0" j \0° 20= 30°| 40=1 50-^ CO"] 70°J80'j 90° £ 6 3 3 I0il5'2O 4ll;8 ^ 5 7 31 4, 6 3 4 5 3I 4 5 3, 4 S 1 *, * 1 i 25'30l3,5 40 Jan. 1 fi-b. 1 Mar. 1 A,.r. 1 Mnv 1 ■uiicl .6-17' •6 15 .6 9 t6 1 '5 53 >} 17 8'; 8-7 8-6 8-5 8-4 8-'; 8-6 8'i[7'6!6-7|5'6 4'4!;-o,i-5 8-6 8-2 7-6 6-6|5-6 4-3!3-o.-5 8-58-. 7-516 615-5 4-3 3-0. -5 8-4 8-0 7-4l6-5 5-5 4-3 2-9>-5 8-3,8-o|7-3 6-5 5-4 4-^2-9 '-S 8-j|8-o;7-3|6-4|54|4-^-9.-S 0" I .6' ..5" 16 9 16 , '5 53 ■5 +7 's 45 Dec. 1 Nov. 1 Oct. 1 S..p,. 1 A up:. 1 Inly 1 ^83;!40 45 »3 16 9 8 7 <574 TABLH 36 TABLE 37 CORRKSPONDINO ThERMOMETURS, Fahrenheit, Centlgiade, Reaumur. C. R. F. C. R. 20 -i7°8 -17-2 -i6-7 -l6-i -■5-6 -15-0 -1+-4 -'3'9 -'3-3 ^Ti-7 -10-6 - 9-4 :B - 7-i - 6-7 -14-2 -.3-8 -13-3 -12-9 -12-4 -10-7 - 9-8 60 61 62 63 64 65 60 67 68 70 71 72 73 74 75 76 77 78 79 80 .5-6 161 i6-7 17-2 .7-8 .8-3 .S-9 19-4 20-6 124 12-9 13-3 13-8 14-2 '4-7 15-1 \tl 16-4 ■ 6-9 - 9"3 - 8-9 - 8-c - 7-5 - 6-7 - 5-8 - 5'" 21-7 22-8 23-3 239 24-4 25-0 25-6 261 26-7 ^71 i8-2 i8-7 191 2C-0 20-5 20-9 TTs" 23-1 23-6 24-0 24-4 24-9 ^5-3 25-8 21 22 23 24 25 26 27 •/« 29 30 :il 32 33 34 35 36 37 38 39 40 - 6- 1 - 5-6 - 5-0 - 4'4 - 3-9 - li - >■? - 4-5 - 4''] - 4"c - r( - r - 1- 81 82 83 84 85 86 87 88 89 90 27-2 29-4 31-1 - 0-6 0-6 "•7 2-8 3-3 3"9 4'4 3- 91 92 93 94 95 96 97 98 99 3 100 32-8 33-3 33'9 34"4 35-0 35-6 36-, 36-7 37-2 37-8 26-2 26-7 27-1 27-6 28-0 28-4 28-9 30-2 42 43 44 45 46 47 48 49 50 5-0 5« 6- 1 6-7 7-2 7-8 tl 9 '4 4' 5- 5- 6- 6- 7' 7" 8- . 101 ^ 102 J 103 104 i 105 1 106 107 103 ^1?^ 38-3 38-9 39-4 40-0 40-6 41M 4'-7 42-2 42-8 43'3 30-7 311 31-6 32-0 3^-4 32-9 "■| 33-8 34-^ 34'7 A 52 53 54 55 5C 57 58 59 1 IO-6 "'7 12-2 12-8 '33 '39 14-4 I^6 8- 8- 9' 9- 10- lo- 11- i 111 9 112 3 113 8 114 2 115 7 116 . 117 6 118 119 4 120 439 44'4 Hi 46-7 47-2 47-8 48-3 489 35-' 35-5 36-0 36-4 36-9 P 38-7 39-1 CoRRKSPONDINO FbCNCU A ESfillRH MllA8t)R«8 | Km. KilomMrc, MMre. Decimetre, Cemini6lre, Milliinelrc. c Kno Nautical Miles, Kect, Inche». Fr. English 1 Fr. Eng Miles Feet Feet In. In. No. corr to curr.'to Mill. In. "kii. "utr" D£cim. Cent. Mill. 1 0-539 3-28 0-33 0-39 0-04 640 2--2 2 1-079 6-56 0-66 0-79 0-08 643 25-3 3 i-6i8 9-84 0-98 1.8 012 645 25-4 4 2-. 58 13-12 1-31 '-57 0-16 648 J5'5 5 2-697 16-40 .-64 1-97 0-20 650 25-6 6 3-237 19-68 1-97 2-36 0-24 653 25-7 7 3-776 12-97 2-30 2-76 0-28 655 25-S 8 4-3.6 26-25 2-62 3''5 0-3. 6.58 25-9 9 4-855 jm 2-95 3-54 °-35 660 26-0 ^kT 5-394 32-8, 3-28 3-94 0-39 663 26-. 20 10-79 65-62 6-56 7-87 0-79 665 26-2 30 16-18 98-43 9-84 I. -81 i-i8 668 26-3 40 2.-58 131-2 13-1 '5-75 '"57 670 264 50 26-97 164-0 .6 + 19-69 1-97 673 26-5 00 3^-37 ,96-9 19-7 23-61 2-36 676 26-6 70 37-76 229-7 23-0 17-56 2-76 678 26-7 80 43-'5 262-5 26-2 31-50 3'5 681 26-8 90 jl:ii 295-3 29-5 35-43 3-54 6S3 26-9 -Too 53-94 328-1 32-8 394 3-94 686 27-0 200 107-9 656-2 7-87 688 27-1 300 .61-8 984-3 .1-81 691 27-2 400 215-8 1 3 12-4 '5-75 693 27-3 500 .69-7 1640-4 .9-68 096 17-4 600 323-7 1968-5 13-62 698 ^7-5 700 377-6 2296-6 17-56 701 27-6 800 43'-5 2624-7 31-50 704 17-7 900 485-5 2952-8 35-43 706 27-8 1000 539-4 3280-9 39'37 709 27-9 711 714 28-0 28-1 716 28-2 719 2S-3 721 28-4 721 28-5 7-26 28-6 729 28-7 732 28-S 734 2ly. 737 290 739 29-1 742 29-2 19-3 747 29-4 749 29-5 752 296 754 29-7 757 29-8 759 29-9 762 30-0 765 30-1 767 30-2 770 30-3 772 30-4 775-30-5 777 30-6 780 ;o-7 782 30-8 7H5 30-9 7«7|3.-c L._J (.-"IclilXTluNS OK ALTirLUE UF TllK Kl-N AND .VlAKd tInTolving Dip, Kefraction, ©'s Semid. and Piiiallax), FOn APPBOXIVATB DSE AT SEA. The SUN. Add the Corr. to the Alt. of the Lovitr limb, exctpt uhere marked -. Height of the Eye in Feet. J Alt. 8 10 [ 12 1 U 1 16 1 18 1 20 1 22 1 24 1 26 1 28 1 80 82 34 37 40 45 50 60 JAlt. ^' -; . ' . |T-| ri~i~i n /i n n , 44 2-6 23 2-0 17 1-4 1-2 I-O 07 05 03 Ol_-i -•'3 ,1~, -i'-3 — 1-7 -.'J i,! fl 3-5 32 2-9 2-6 2-4 2-1 1-9 1-6 1-4 1-2 10 08 07' 502 o-o — 0-4'— Q-i -I -5 5 -07 5i 0-0 6 5i 4-2 3-9 36 3-3 3" 2-9 27 2-4 2-2 20 1-8 i-e 1-4 i 2 I-o' 0-7 o-3'-o-i i-o 0-6 6 4-9 40 4-3 40 37 35 33 3' 29 26 24 2-3 2-1 1-9 17; i-^ S-4 5' 48 45 43 40 3-8, 36 34 32 3° 28 2-6' 2-4 2-2! 2-0 ^ 1-6 1-2 0-6 6' 7 60 s-6 53 so 4-8 46 43 4-1 39 37 35 3.3' j-ij 29 27' 2-5 67 6-4 6-1 5-8 5-6 S'i S'l 4^9 47 45 4-3 4-1, SV 37 3-5 3-3 2-ll 1-7 fo 7 8 2-9' 2-6 1-9 8 2-6 9 9 7-4 71 68 6-5 63 60 58 56 5^4 5-2 50 4-8: 46: 44 4-2 4-0 ■^■6 1-1 lu 8-0 77 7-4 7-1 6-8 6-6 64 6-i 5-9 57 s-5 54' 5-21 5-0 48 ~T^S'~4^Pvq 8s 8-1 7-8 7-6 7-3 7t 68 66 64 6-2 60 5-8 57I c-cl 5-,: ^oi 4.7I 4., ~3-2"lu' 37 11 4-1 12 11 12 1 s-9 8-t. S-2 s-0 77 7-5 7-2, 7-0 &■» &-b 6-4 6-2 6-.I 5-9 57 5.5! y\\ 4.7 14 9-5 9-2 8-9 S-6 8-3 8'i 79 76 74 72 7i 6-9 67 65 6-3! 6-i 57 ti 16 ,00 97 9-4 9- 88^ 8-6 84 Sr 80 78 7-5 7-41 7-21 7-0, 6-8 66 l\\ [^ 47|l4 52 16 5-6 18 5-9 20 18 ,io-4lo-i 9-8 9-5 92: 90 88 85 83 8'i 7-9 ^f y-k 7-4' 7-2; 69 6^ 6-^ 20 I07IO-4IO-I' 9-8 9-5' 9-3 91 89 87 Ss 83 81! 7-9 77l 7'5 7-2 6-9' 6-6 22 II-OIO-6IO-3IOI 9-8 96 93 9i 89 87 85 8-3 8-2 8o{ 771 7-51 7-2 6-8 6-2 22 25 II-3IO-9 10-6 10-4 loi 9-9 96 94 92 90 88 87! 85 8-3' 81 7-9^ 7-5 7-, 6-1; 25 30 II7II-3IIOIOSIO-5IO-3IOO 98 96 94 92 91: 8-91 87! 8-4~8^2[~78-7^c|~6^ W 35 .20II-6I.-3U-..0-SIO-6IO-3.0-. 9-9 97 95 9-4 9-2 90 87: 8-5! 81 rsl 7-: 35 40 i2-2ii-8ii-5ii-3iioio-8io-6io-3io-i 9-9 97 9-6 9-4 9-2: 9-0 8-8: 8-4 80' 71! 40 4fi i2-4i20u7ii-5ii-2iioio8io-5io-3io-i 9997 9-5 9-4 91 8-9 8-5 8-2| 7-5 45 .'.0 12-5 I2-2II-9II-6II-3II-I 109 107 10-5 10-3 lo-l 9-9 97; 9-5 g-^' 9-1 8-71 83 7-7 50 60 I27I2-4I2-I il-8ii-6'ii-3ii-i io-9io7locio-3,o-i 99 9-8 gc gn 8'9 8-5 7-9 60 70 ' " i2-9i2bi2-3i2-oii-!sii-5ii-3iii 10-9107 IO-5IO-3 loi! 9-9 9-7 9-5 13-112-7 12-4 12-2 1 1-9111-7 1 1 -4 1 1 -2 1 1 -010-810-610-4 10-3 lo-ij 9-8, g-6 9-1 8-7 8-1 70 9-2 8-9 8-3 80 9-4I 9-0 8-4; 90 80 90 13-2 12-9 12-6 12-3 12-0 u -8 1 1 -6 1 1 -4 1 1 -2 1 1 -010-810-6 10-4 10-210-0 9-8 Month Jan. Feb. 1 Mar. April 1 May ! June July Aug. Sept. Oct. Nov. Dec. Correction 1 to Bun's alt. J , , , 1 - - , , -03 -02 -0. +0. + 0-2 + 03 A ST.A.R. Subtract the Corr. Height of the Eye in Feet. in 12 14 16 ' 18 20 22 24 26 28 30 32 34 37 40 1 45 1 50 60 T~\~'~7~\~\~l'~, — ; — 7\V 1, 1 4 14-8 >S"' 'S'4 is'-? i6'-o i6'-2 i6'-4 i6'-6 i6'-8 i7'-o 17-2 17-41 17-6 17-9 18-I 18-4' 18-8 19-6 J ■'i 13-8 I4-I 14-4 147 150 152 15-4 156 158 i6-o 16-2J 16-4; 16-6 16-9 17-1 17-4 i7-7ii8-5 54 56 58 60 6-2 6-3, 6-5 6-7 7-0 7-2 7-6 8-o| 8-5 46 60 3-9 4-2 45 47 5-0 52 54 56 5-8 6-0 6-2 6-4 6-5 6-8 7-0 7-4 78 8-3 «0 ♦SO 3-7 40 4-2 45 4-8 50 5-2, 54 S6 5-8 6-0 6-1 6-3 6 6' 6-8 7-1 7-s 8-T 6<. 70 3$ 38 40 4-3 45 47 50 52 54 56 S7i 59 6-1 6-3 6-6. 69 7-3 7-9 70 80 3-3 3 5 3-8 4 I 4-3 46 4- * 50 52 54 S-6 5-7i 9 6 2 64' 67 7-il 7 7 81J 676 COKRECTION OF THE MOON'S APPARENT ALTITUDE (Barometer, 30 it.clies. FHl.ienheil's Tliermometer, 50-) ir Horizontal Pardlax "of Par Corr. for " of Par. add. 11 S3' 1 54' 55' 1 6ff 57' 1 68' 1 59' 1 fiO' 61' "o^ 2" 4" C" ~r 19 li'io 14 21' li^22 14 23 14 24 14 25 14 26 H 27 14 0" ;' 4 i' 8" 10 2, 6J2. 6 23 624 6 25 6 26 6 27 6 28 6 29 6 10 10 14 16 18 20 22 5'h 5. 24 S125 51 26 51 27 51 28 51 29 SI 30 51 20 20 24 26 28 30 2428 25 2826 2827 28 28 28 29 28 3028 32 28 30 30 34 36 38 40 25 5S 26 5827 58128 58 29 58 30 58 31 58 32 58 33 58 40 40 44 46 48 £0 27 21 28 2.|29 2I|30 2. 31 21 32 21 33 21 34 21 35 21 SO 50 52 54 56 58 1 ^n'9 29 39|30 393' 3932 39 33 39 34 39 35 39 1^9 4 6 -T 10 29 49 30 49131 4932 49133 49 34 49 3 5 49 56 49 37 49 10 10 14 16 ig 20 30 56 3' 5632 56:33 56,34 56 35 56,36 56I37 56 38 56 20 20 24 26 28 30 3> 57 32 57 33 5734 57,3? 57 36 5737 57,38 57 39 57 30 3° 34 36 38 40 3^ 54- 33 5434 54'35 5435 54 37 5438 54 39 54 40 54 40 40 44 46 48 SO u 34 4635 4636 4f 37 46 38 46 39 4640 46 41 46 50 5° Jl. 54 4 56 58 2 35 3636 36 37 30 58 36 39 3640 3641 36 42 36 6 -«- 10 35 2236 22,37 22 38 22 59 22 40 2241 22|42 22 43 22 to 10 14 16 18 20 36 4 37 4]38 4 39 4 40 4 41 442 443 4 44 4 20 20 24 26 28 30 36 44 37 44,38 44 39 44 40 44 41 44 42 44|43 44 44 44 30 30 34 36 38 40 37 21 38 »'l39 21 40 21 41 21 42 21 43 2144 21 45 21 40 40 44 46 48 50 37 55 38 55139 55 40 55 4" 55 42_55 43 55144 55 45 55 50 Jl. 54 jL JL 3 38 28 39 28|40 2841 28 42 28 43 28 44 2S45 28 WTi ~o" ~T 4 6 8 10 38 59 39 584c 584" 58 42 58 43 58 44 5845 58 46 58 10 10 14 .6 Ig 20 39 27 40 2741 2742 27 43 26 4426 45 2646 26 47 26 20 20 24 26 ag 30 39 53 40 5341 5342 53 43 53 44 53 45 53'46 53 47 53 30 30 34 36 38 40 40 19 41 1841 1843 ,8,44 18 41 4242 4243 4244 42 45 18 46 I8i47 IS 48 18 40 40 44 46 48 50 4° 42 4542 46 42 47 4' 48 41 60 5° 54 56 58 4 41 5 4» 5 43 444 445 4i46 4|47 4 4!^ 49 4 T 4 —T ~T 10 41 26 42 26143 25 44 2545 2546 25147 25 48 2 5|49 25 10 10 •4 16 18 20 4. 46 42 45 43 45 44 45145 45 45 446 4 46 4547 45 48 44,49 44 20 20 24 26 28 30 42 4 43 4 44 4 47 348 3 47 2.48 2. 49 3 50 3 30 30 34 36 38 40 42 22 43 22 44 1* 45 2,146 2. 49 21 50 20 40 40 44 46 48 60 42 39 43 38 4438 45 33I46 38 47 3848 37 49 37 2l.ll 50 50 52 54 56 58 5 42 54 43 54 44 54 45 54 46 54 47 5348 53 49 53 5*^ 53 4 T 1" 10 43 9 44 9 45 9 46 9 47 9 48 849 8 50 8 51 8 10 10 14 16 ig 20 43 24 44 23 45 23 46 23 47 23 48 2249 22 53 22 51 22 20 20 24 :6 28 30 43 37 44 37 45 37 46 36 47 36 48 3649 36 5° 35 5' 35 30 30 34 36 38 40 43 50 44 5° 45 49 46 49 47 49 48 4949 49 50 48 51 48 40 40 46 48 SO 44 2 45 I 46 I 47 I 48 I 49 050 yi 52 50 50 54 56 JL (i 44 "4 45 '3 46 13 47 13 48 12 49 '2 50 12 51 11 52 II "T" 4 e 8 10 44 24 45 24 46 24 47 23 48 23 49 23 50 22 51 22 52 22 10 10 14 16 18 20 44 35 45 34 46 34 47 34 48 33 49 33 50 33 51 32 52 32 20 20 22 24 26 28 30 44 45 45 44 4644 47 44 48 43 49 43 50 43 51 42 52 42 30 3° 34 36 38 40 44 54 45 54 46 53 47 53 48 53 49 52 50 52 51 52 52 52 40 44 46 48 r,o 45 4 46 3 47 3 48 2,49 2 50 I 53 c 50 J2- 52 Jl. 56 JL 7 45 '2 46 12 47 II 48 Ii|49 II 50 10 51 10 52 9 53 9 ~b 6 8 10 45 21 46 20 48 19 49 19 50 .8 51 iS 52 17 53 17 10 10 ■4 16 18 20 45 29 46 28 47 28 48 27 49 27 50 26 51 26 52 25 53 25 20 20 24 26 2S 30 45 36 46 35 47 35 48 34 49 34 50 33 51 33 52 32 S3 32 30 30 34 36 38 40 45 43 46 42 47 42 484. 49 4' 50 40 51 40 52 39 53 39 40 40 44 46 48 add SO 45 49 46 49 47 48 48 48 49 47|5° 47 51 46 52 45 53 45 50 50 52 J±. 56 58 8 45 55 46 55 47 54 48 54 49 53 50 53 5' 52 52 52 53 51 0" 4 6 8 1 , 10 46 2 47 1 48 49 i^ 49 59 50 59 51 58 52 57 53 57 10 !0 '4 16 iS 2 20 46 7 47 7 48 6 49 5 50 5 51 4 52 4 53 3 54 2 20 20 22 24 26 28 30 46 .3 47 I* 48 .2 49 »■ 50 10 51 10 52 9 53 8 54 8 30 30 32 ! 34 36 38 40 46 18 47 17 48 17 49 '6 50 15 51 15 52 14 = 3 "3 54 '3 40 44 46 47 60 4623 47_23 48 22 412: 50 20 5. 20 52 19 53 18 54 18 SO 49 53 55 JL. 4628 47 »7 48 27 49 »6 50 25 51 24 52 24 53 23 54 22 4 6 8 10 46 33 47 32 48 31 49 31 50 30 51 29 52 28 53 28 54 27 10 10 14 i5 18 8 20 46 37 47 36 48 36 49 36 5° 35 51 34 52 34 53 33 i\ 32 20 20 24 26 28 9 5 30 46 4 47 4" 4840 49 39 50 38 51 37 52 37 53 36 5> 35 30 30 34 36 37 40 46 45147 45^45 44''i-9 43 50 42:51 41 52 40 53 39 54 39 40 39 43 45 47 60 46 49|47 4S48 4749 47 50 46J51 45 52 44 S3 43 $■> 42 50 49 53 55 57 TAnLi: no COKRKCriON OF THE .M( )()Ns APPAKt.vr Ai.nruDE 1 (Bdromewr, SO inche«. I- Hlire.iheit's Tliei mometer, 50°) i: Horizontal P»iallax "of Corr. for " of Par. aJ / / „ , „| , , ^^ «1 ^^ 10 d 46 53 47 5^+8 5'' 49 5° 50 49,51 48 52 47 53 46 5446 2 4" 6 s" aJ,l 10 46 56:47 5548 54 49 53 5° 53 5" 52 52 5" 53 50 54 49 10 10 12 14 16 ig 20 47 047 594S 5S49 57 50 5651 55 52 54 53 53 54 52 20 20 22 24! 26 18 llo 30 47 3 48 149 '5° ° 50 59 51 58 52 57 53 5654 55 53 5854 57 30 29 3' 33 35 37 2I0 40 '47 648 5'49 4] 50 2 5. 1:52 52 59 40 39 4> 43 45 .- 3{i 60|47 84S 7:49 6 SO 5lS_L_4:52 3 ii _2j54^_ii55_c 50 49 -LL 53 55 57 4 , 11 U 47 n 48 ici49 9 5° 7 5' 652 5 53 4(54 3i55 2 4 ~r 8 6 I 10 47 '3:4s "2149 ■' 50 10 5" 9,52 7 53 654 555 4 10 10 12 '4 16 18 6 ' 20 47 1548 '4I49 '3 50 12 51 11,52 9 53 8,54 7i55 6 20 20 22 »4 25 »7 7 ^ ao 47 1 7148 1649 '5 50 14151 13:52 II 53 £4 955 -^ 30 29 3' ; 33 35 37 8 2 40 47 >94S 1849 '7 50 16 5" >5:52 13 53 12 54 "55 .c 40 39 4' t « 45 47 a 2 OOI47 2.J+S 2o;49 •, 5° 18 5. .6,52 .5 53 If 54 1355 ■■ 50 _49_ 51 ! S3 Jl. ,57 12 47 234S 22^49 21 50 19 51 1852 17 53 '5 54 '4^55 '3 z 4 6 8 10 47 25I48 2449 »* 50 21 51 20I52 .8 53 54 '6i55 '4 10 10 12 •4 ■ 6 Ig 20 47 »7 48 2549 24 50 23 51 21 52 20 53 '9 54 '7 55 16 20 20 21 13 25 »7 30 47 28 48 2749 25 50 24 51 23 52 27 53 54 '8 55 17 30 29 3' 33 35 37 40 47 30 48 2849 27 50 25 51 24 52 12 53 21 54 20 55 '8 40 39 4' 43 45 47 .W 47 3' 48 29I49 28 50 26 5' 25 5? ^3 53 22 54 21 55 >9 50 49 51 S3 55 57 i:t 47 3' 48 3049 29I50 ».7 51 26 52 24 53 23 54 21 55 2c 2 1 4 6 » 10 47 33 48 3149 30 50 2S '5 27 52 25 53 23 54 22 55 20 10 10 12 14 16 Ig 20 47 34 48 3249 31 50 29 51 27 52 26 53 24 54 22 55 21 20 '9 25 27 30 47 35|4S 33149 3i 50 30 51 28 52 26 53 25 54 23 55 21 30 29 3' i 33 35 37 40 47 354S 3449 32 50 30 SI 29 52 27 53 25'54 23 55 22 40 39 4' j 43 45 47 1' 0" 60 47 36I48 34I49 33 50 31 5' 29 52 27 53 26154 24 55 22 50 JLJjil 54 56 2 3 .4 47 37 48 3549 33 50 3. 51 30 5228 53 26J54 24 55 22 ~^ 4 T 8 10 47 37 48 35 49 33 50 32 51 30 52 28 53 26 54 24 55 22 10 10 12 14 '5 '7 4 20 47 37 48 36(49 34 50 32 SI 30 52 28 53 2654 24 55 22 20 ■9 21 23 25 27 t.o 30 47 3848 36149 34 50 32 SI 30 52 28 53 26 54 24 55 22 30 29 3' 33 35 37 60 40 47 3848 3649 34 50 32 SI 30 5228 53 26 54 24 55 22 40 39 4' 43 45 46 70 SO 47 3848 36I49 34 47 3^^48 36[49 34 5° 32 52 28 5i_ 26i54 24 55 22 50 48 5° 52 54 5M 80 alo 16 50 32 51 30 52 28 53 26J54 2455 22 4 6 — 10 47 3848 36 49 34 50 32 51 30 52 28 53 2654 2455 22 10 10 12 '4 '5 '7 20 47 3848 36 49 34 50 32 51 30 52 28 .3 2554 2355 21 20 19 21 { 23 25 27 30 47 3848 36 49 34 50 31 51 29 52 27 53 25154 2355 21 30 29 3' 33 35 37 40 47 3848 36 49 33 50 3' 51 29 52 27 53 24I54 2255 20 40 39 40 42 44 46 50 47 V\t^ 3 5 49 3 3 50 31 SI 28 52 26 53_ 2454 22I55 19 50 JIjJ^JL^ 54 56 !6 47 3V« 35 49 32 50 30 51 28 5TI6 53 2354 2155 19 2(4 6 8 10 47 ?7 48 34 49 32 50 30 51 27 52 25 53 22;54 2055 .8 10 10 12 1 13 '5 17 20 47 3648 34 49 3' 50 29 51 26 52 24 53 22,54 '9 55 '7 20 19 21 J 23 25 27 30 +7 3548 3^ 49 3' 5028 5. 26 52 23 53 2i!54 18155 .6 30 29 1 3' 1 33 35 36 40 49 3° 50 27 5' 25 5222 53 2054 >7i55 >5 40 38 40 , 42 44 48 1 50 i .S2 1 54 46 .y 47 3448,32 49 29 50 26 5' 24 52_2, 53 1954 i6!55 '4 50 56 W'S 47 33148 31 4928 5026 5> 23 52 2o|53 '854 '5,55 '3 "^ 1 2 ' 4 6 8 wh. 10 47 3348 3°49 27 50 25 51 22 52 .9 53 17,54 '4^55 " 10 .0 .2 .3 '5 I- 20 47 3'-'48 2,'4, 26 50 24 5. 2, 52 18 53 '5 54 '3'55 -o 20 19 21 : 2; 25 •-7 I'o 30 47 3>'48 28-49 '-s'so " 5. 20 52 17 53 '4 54 "55 9 30 29 30 I 32 34 36 2 c 40 47 3-48 27 49 -4;5o -' 51 i8|52 ,6 53 '3 54 '°'55 7 40 3S 40 42 44 46 Jo 50 4^ 29'48 26|49 23 50 20 5. .7152 .4 53 "54 9'55 6 60 48 5° 1 52 53 Jl. 4,0 ,n 47 28:48 25]49 22[50 19 51 i6|s2 .3 53 '054 7i55 4 (1 1 1 ' 4 [ 6 8 '.io 10 4' 26,48 23I49 20 50 17 51 I5'52 ■2[53 9 54 655 3 10 9 " »3 1 '5 '7 fie 20 47 2548 22J49 1950 16 5' '452 1053 7 54 4 55 ' 20 19 21 1 23 I 25 27 7|o 30 47 --448 2149 18 50 15 5' •2;52 953 5 54 2 54 59 30 28 30 I 32 1 34 36 8|0 40 4- 23,48 2049 .6 50 13 5' >°'52 7153 4 54 154 58 40 3S 40 1 42 ■ 44 46 911 50 47 2i'48 1849 1; 5° '- 5' 852 5'53 255 59 >t 56 60 47 1 49 1 5' ( 53 55 lit 47 2C48 1749 '3 50 10 5' 7,52 4153 °53 5 ',54 54 1 11 4, 6 8 111 47 1848 1549 >2 50 8 5> 5,52 252 59 53 55 54 52 10 9 .. 1 .3 .5 17 20 47 1748 13 49 SO 58,1 54I5. 51 c;-, 47 S4 44 :.n 4: ' 49 1 5' 53 55 TABLE 39 CURRIiCTlON OK THE MOONS AVP A RENT AI/riTUDE (Bdro.neter, 30 inches. Fal.rei.l.eii'i. Thermometer, 50°) . 1 Apr Alt. llorizonlal Purallai "of Fill. Corr. for " of Par. c dd. 53' 1 64' 1 05' 1 5G' 57' t 58' 50' 1 BO' | CI' 0" jiljiiijulji: ■2U 6 47 i2'48 749 jV 5950' 5651' 5252 49 53 45 54 4' 2" 4" 6 7 iu/>. 10 47 9V 5'49 '49 5*|50 545' S°'S^ 47 53 43:54 39 10 9 II 13 >5 17 2lt 47 748 3:48 5949 5650 5*5' 48|5^ 44 53 41 54 37 20 '9 24 26 1' 30 47 5'4S ':48 57:49 545° 5051 46,52 4^53 38|54 35 30 28 30 1 32 34 , 36 40 47 347 594S 5549 5'iS" 4851 44(52 40I53 36I54 32 40 37 1 39 1 4' 43 45 50 •21 47 I 46 59 47 57,48 5349 4950 4551 4152 3853 3454 J£ 50 47 i 49 i 5' 52 54 47 55'48 5':49 47l5° 43 5' 39:52 35|53 3ii54 27 — j— 2--T 6 7 10 46 5747 53!48 49:49 45'50 4', 5' 37,52 33|53 29154 46 5547 51148 47|49 4315° i^.S' 3452 3053 2654 25 lu 9! " '3 •5 211 22 20 '9 20 22 24 26 m 46 5 347 49:48 44i49 4o|5° 36,5' 32I52 2853 24I54 '9 30 28 30 32 34 35 8 2 ■10 46 5147 4648 42149 3850 34:5' 2952 2553 21:54 17 40 37 39 4' 43 1 45 01 2 so 464s 46 ,b 47 44;48 40^49 35'5° 3' 5' 27:52 23I53 '8'54 '4 50 47 JL _5° 52 1 54 47 4248 37149 33:5° 29^51 24*52 20 53 '6154 ,, ~|— 10 46 4447 39:48 35'49 3°|5o 26;5. 22|52 17 46 4147 37I48 3249 28I50 23151 19I52 14 53 >3'54 8 10 9 11 ! 4 '5 .7 20 53 io;54 5 20 18 20 1 22 24 26 30 46 3947 34I48 3°49 2515° 21 46 3647 32I48 27I49 2315° '8 5. 16152 .2 53 7|54 3 30 28 30 1 31 33 35 •10 51 '3 52 9 53 4'54 40 37 39 41 43 j 44 50 46 3447 29-48 25 49 2o|50 j^ 51 I. 52 6 53 '153 _57 50 ^ 48 ' 5° 52 1 54 23 46 32I47 2748 22 46 29147 2448 19 49 '715° '2 51 8 52 58J53 53 2 ] 4 — — 10 49 '5l5° '° SI 5 52 52 5553 5° 10 9 '5 1 '7 20 46 26|47 2248 17 49 '25° 7 5' 57 52 52I53 47 20 18 20 22 24 1 26 30 46 2447 19I48 14I49 9 SO 4 5° 59 5' 54 52 49 53 44 30 28 29 i 3> 33 35 40 46 2147 i6|48 1 1 49 6 50 1 5° 56 5' 5> 52 46 53 4' 40 37 39 1 40 42 44 , 50 46 1847 13I48 8I49 3 49 58|5o 53 5.485243 53 Jl 50 46 1 48 5° 51 S3 ' 24 46 1647 11I48 s|49 ° 4V 55|5o 5° 5' 45'52 39 53 34 — l-T-j— ~ 7 10 46 .3,47 848 2I48 57 49 52 5° 47 5' 4'|52 36 53 31 10 9 •■ "3 '5 iC 20 46 iO|47 5|47 59'48 54I49 49^5° 44 5' 3S52 33 53 28 20 18 20 22 24 25 30 46 7!47 2|47 56'48 5'i49 4b|5° 4° 5' 35:52 3° 53 24 30 27 29 3> 33 35 40 46 446 5947 5448 4SI49 4315° 37 5' 3252 26J53 40 36 38 40 42 44 50 4b 246 56|47 5' 48 4549 39 5° 34 5. 28152 23I53 _17 50 46 1 47 1 49 ^ 53 9 3 25 45 5946 53147 47 48 4249 36|5° 3' 5' 25^52 19:53 '4 (1 "ITI 2 4 5 ■J 10 45 56 46 5047 44 48 39|49 3315° 27 51 21:52 ,6i53 10 9 1" '3 '4 16 20 45 53 46 47 47 4' 48 35149 2915° 24 51 '852 I2]53 6 20 .8 ! 20 22 23 25 30 45 49 46 4447 3848 32I49 26|5o 20 5' 1452 9:53 30 27 29 1 31 33 34 40 45 46 46 4047 35|48 29I49 23150 17 5' ",52 5152 59 40 36 38 14° 42 43 50 45 43 46 3747 3148 25I49 1950 13 51 7 52 152 _55 50 45 47 I 48 51 52 2fi 45 4° 46 3447 2848 22I49 '650 10 51 45' 58:52" 52 2 i 4 5 in 45 37i46 3'147 2548 I9]49 '2|50 6 5' °5i 54:52 48 10 9 I. 1 13 14 16 20 45 3446 2747 2i;48 i5]49 915° 3 50 5651 50:52 44 20 23 1 25 30 45 3'!46 24147 1848 "149 5!49 5915° 53 5' 46!52 40 30 27 29 30 32 1 34 40 45 27:46 2147 1448 849 2!49 55 5° 49 5' 42'52 36 40 36 38 39 4' 43 50 45 24:46 1747 "'48 4:48 58I49 5'|50 45 5' 38:52 32! 50 45 47 48 _l^-ii. w~ir 45 20I46 14(47 74S i|48 54I49 485° 4' 5' 3552 Is 2 1 4 5 7 10 45 '7,46 '°;47 447 5748 5°49 4415° 37 5' 3' 52 24 10 9 II 1 12 '4 16 20 45 '346 747 047 5348 4749 4° 5° 33 5' 2752 20 .8 20 21 23 25 I p 30 45 'o'46 3:46 5647 5°i48 4349 365° 2951 2352 j6 30 27 28 30 32 34 40 45 646 046 5347 46148 39'49 3250 2551 1952 12 40 35 37 39 1 4' 43 50 28~0 44 59 45 56:46 4947 4248 3 5 49 28:50 21 51 1452 _7 50 4-1- 46 1 48 50 52 45 52:46 4547 38:48 3' 49 »4;5° '7 5' 1° 52 3 2 1 4 5 7 10 44 5645 49+6 4247 34'48 2749 20,50 13 51 651 59 10 9 II 12 '4 • 6 20 44 5245 45:46 3847 3 ';4S 2349 1650 951 251 55 20 18 19 21 23 25 30 44 4845 4'j46 3447 2748 '949 '2 5° 5 5° 585' 44 4545 3746 3047 23'48 1549 850 150 5351 5° 30 26 2« 1 30 32 33 40 46 40 35 37 1 39 40 42 « .-.0 44 4'45 3446 2647 1948 ■■49 449 565° 49 5" 42 50 J^Jl_ _12__1' 29 44 3745 3046 2247 '5148 749 °|49 525° 45 5' 37 ^TT 2 3 5 7 10 44 3445 2646 '84, "48 348 S6'49 485° 4° 5 ' 33 10 9 .4 .6 20 44 3045 2246 1447 747 59 48 5 ' 49 44 5° 365' 28 20 19 21 23 24 30 44 2645 1846 1047 2|47 5548 4749 39 5° 3' 5' 24 30 26 28 1 3° 32 33 40 44 22'45 14146 646 58!47 5.48 43'49 3550 2751 '9 40 35 1 37 38 40 4: 60 44 184; l6'46 246 54I47 4648 3849 -(O^o t;,! ' , 1 1 1 I 1 <; TiO 44 ! 45 ' 47 49 pc TAni.i' no C79 ( OKRKCrrON OF Tin; IMOONS APPARKNT Al /niuuE 1 (B.rometer, 30 iiiclien. FnlTeHlieit'. Thermooi«t«r 50P 1 if: Horizontal Parallax "of Corr. fo r " of Par. arfJ. H _6y|_6 4' 56' 1 5«' sr 1 5fl' 1 sn' 1 fio' 1 cr Par. e" 2" *" 6" 8" oy t> / - ^ . , J . , 47 4148 34'4» 16.50' 1S51' 10 7 ^, „ ,, „ so ♦4 H45 045 5S46 5° 2 J 5 7 10 44 '045 »,45 5446 4'' 47 3848 3o;49 i'[5o >3 5' 5 10 9 10 i» '4 16 $iih. 20 44 644 58|45 50:46 42 47 3348 2549 '7l50 9 5' I 20 17 '9 21 14 30 44 24+ 5445 4*'I4* 3747 ^948 i'!49 '»'5° 4J5'' 5* 5045 4146 33 47 1548 '6'49 8]49 59150 5' 30 26 28 19 33 i 40 43 5S44 40 34 36 38 4' 1 ,'.0 4 3 5444 4545 3746 2947 20I48 12)49 3 49 5515^ 46 50 43 45 47 48 50 I 3T"~0 + 3 5044 4i'45 3346 24!47 '6:48 748 58[49 5015° 4' 2 3 7 1 Kl r, 4644 3745 18146 2o|47 1 1 48 2'48 5449 45 5° 37 10 9 10 II 16 I •JO 43 4144 33 45 24'46 1547 747 5848 4949 4050 3^ 20 "7 •9 20 14 .10 43 37 44 lS|4(; 2046 1147 247 5348 4449 35'50 27 30 26 17 29 31 40 43 33 44 244<; 1546 646 5-47 4848 3949 31:50 22 40 34 36 38 4 .'lO 32-U 43 »9+4 2045 1146 »46 5 3'47 4448 3 549 ^61 5° '7 50 JJ. J±_ 46 3 "T -4? 7 4 43 H44 '545 6,45 57,46 4*147 39J4S 30J49 2150 12 10 43 »044 .145 J 45 5346 4347 34.48 2 5'49 1650 7 10 8 10 12 '5 20 43 '6,44 6,44 5^145 4846 39 47 29^48 2049 ill 50 , 20 '7 '9 20 14 ■M 43 "44 244 5345 4346 3447 24I48 15I49 649 56 30 15 27 19 31 40 43 743 5744 4845 3946 1947 2048 '049 '149 5' 40 34 35 H 4' 50 43 3 43 5344 43 45 3446 24147 15I48 548 56:49 46 60 41 ~ 46 3 -— At 7 :»:) 4i 5^143 4844 3945 Z9!46 '9 47 10:48 0I48 5049 4' 10 4^ 5443 44 44 34 45 H46 '5 47 547 55:48 45I49 36 10 8 10 12 '5 20 4- 4943 3944 2945 2o;46 'o 47 047 5o'4S 40149 30 46 55147 4=48 3549 ^5 20 17 18 13 ao 4- 4543 3 5 44 14'45 >5;46 5 30 15 17 28 31 40 4.1 4043 3044 '945 'o;46 46 5o'47 40|4S 3049 20 40 33 35 37 40 50 ^Jiil 25I44 '4'45 5*1-5 55 46 4547 35148 24I49 '4 60 4» 44 _45_ 3 ■^ 48 7 :i4 4i 3 "43 TTs-ro,;r~o 45 50 46 40 4719 48 1949 9 —^ 10 42 z6i45 ■ 6 44 6;44 55 4; 45146 34 47 14 48 1449 3 10 8 IC '5 20 4- I ',43 11 44 '44 50 45 4046 19 47 .9 48 848 58 20 .6 .8 20 13 30 4^ '7143 6 43 5644 45 45 35 4624 47 .4 48 348 53 30 15 17 28 3" 40 42 1245 I 43 5 '44 4045 30 46 i9|47 8 47 5848 47 40 33 35 36 40 60 42 -42 11 43 46,44 3545 24 46_14'41_3 47 SikS 4' 50 4' 43 44 46 _48 7 35 4J 3 41 r- 43 4':44 3045 '9 46 846 57 47 47:48 36 3 5 10 4> 584* 47 43 36:44 1545 '446 3:46 5147 4148 30 43 3'|44 1045 9145 5846 47I46 3648 25 10 8 10 M '3 '5 20 4' 534- 4= 20 16 18 20 21 13 30 41 48 42 37 43 i6;44 1545 3|45 5:|46 41147 3048 19 43 i'44 944 58I45 47146 3647 2448 13 43 '644 4,44 53;45 4'|46 3=47 '948 7 30 14 26 28 *9 3' 40 41 434* 3^ 40 33 34 36 3! 39 60 4. 38^'- 60 4' 41 44 46 47 \ 3fi *' 3|42 "22 43 "043 59144 4845 3646 25:47 1348 2 43 543 54'44 4*45 3'46 I9;47 7,47 56 ~~o" 1 3" 5 6 2 10 4. »S42 17 10 8 10 M '3 '4 3 2.1 41 2341 12 43 043 4844 3745 1546 '3 47 2 47 50 41 55 43 43 44 3 '45 i°46 8^46 5647 44 20 16 18 •9 13 4 30 41 .«4i 7 30 14 26 27 19 3' 5 40 4' 1341 I 41 5043 38,44 16,45 '446 1,46 5047 38 40 31 34 35 37 39 6 SO 41 U' 56:42 4443 3244 2o;45 845 56:46 4447 33 50 40 41 44 45 47 7 .(7 4' 341 5''4i 3943 1744 '545 3 45 5'J46 39,47 ^7 2 S 5 6 8 10 40 5841 46,42 5443 2244 944 5745 4546 3347 21 10 8 10 11 ■5 "4 9 5 20 4= 534' 4142 2843 1644 444 5245 3946 2747 15 20 16 17 '9 21 22 :«) 40 4841 3542 2343 1143 5844 4645 3346 2147 9 :«t 14 26 28 19 3' 40 40 43 4' 3042 1843 543 53444045 2846 1547 3 40 31 34 35 38 60 ♦0 3'4' 2542 '243 043 4744 3445 2246 94b 57 60 40 4' 43 44 46 :ifl 40 314, 1942 742 5443 41J44 2945 1646 3^46 51 2 3 5 6 10 40 2741 1442 141 4843 36,44 13 45 '045 57,46 44 10 8 9 '4 20 40 2241 941 5641 4343 3044 '745 445 5'46 38 30 16 17 '9 20 30 40 .64, 341 ?042 3743 Hl44 "44 58I45 45I46 3* 30 13 li 27 28 '2 40 40 1 1 40 58 41 4542 3243 i8i44 544 52*45 3946 26 40 3' 33 35 36 38 60 40 640 524' 3942 1643 13:43 5944 4645 334ft :c .V) 39 4' 41 44 l45_ W~i\ 40 040 474' 3341 io;43 7143 53,44 4045 17,46 '3 ~ 3 5 1^ ^h 10 39 5540 41 41 2842 1443 i'43 4744 34:45 2146 7 Ift g 9 1 1 12 1 14 20 39 4941^ 364' 1141 9'4i S5l43 4''44 18J45 .4'46 ■ 20 15 '7 '9 20 1 22 8J5 30 39 44 4" 3"4' "741 3,41 49143 3544 ":45 84.; ^ 30 13 15 17 28 30 »l5 40 39 3^4-- 2(;4' "4' 57 »i 43'43 1944 •6'45 i4i 48 40 3' 31 34 36 1 37 60 b« ;t4' .94' 54' ^'4= 3-43 2344 9'44 ^64^ 4: .-,0 _1 40 45 1 4< TABLE 39 r CORRECTION OK THE MOONS APPARENT ALTITUDE (Barometer, 30 incl.es. Falirenlieit's Tlie. mometer, 50°) add. 1 Horizontal Paiallax "of Par. Corr. for " of Par. 63' 1 64' 1 55' 1 56' 57' 1 68' 59' 1 CO' 1 Bl' 0" 2" £^| C" 8" iS e 39 i7!4°' '34° 594'' 4542:' ii\43 '7 44 344 49,45 3. ,(' 0" 3 5" 6" 10 39 1^ 40 8140 5441 3942 25^43 IIJ43 57^44 43;45 25 10 8 9 11 14 20 39 '6 40 240 4841 334= 1943 5,43 5 1,44 3645 == 20 IS 17 iS 20 21 30 39 '■ 39 564c 4=41 =814= 134= 5943 +4,44 3045 '« 30 =3 24 26 = 7 29 40 39 5 39 5140 3641 ==,4i 7 4= 53 43 38,44 =445 9 40 30 11 33 1 35 36 50 38 59 39 4Sl4o 3041 164* '4= 4643 3=44 i7 45 3 60 38 40 41 1 43 44 il 3« 5+ 39 3940 =4|4: ■o|4> 55,4= 4043 =5,44 i ■ 44 56 1 3 4 6 10 38 48 39 33,40 1841 441 4942 3443 '944 4;44 49 10 7 9 12 14 20 38 4^- 39 2740 1240 5841 4342 2843 1343 58^44 43 20 15 16 iS 19 21 30 38 37 39 ==,40 6,40 5 1 41 3642 2143 643 5144 36 30 21 = 4 = 5 27 28 40 38 31 39 1640 0140 4541 3042 is'43 043 45,44 30 40 30 31 33 34 36 50 38 25 39 10 39 54I40 39'4i 244^ 9!4^ 5343 38144 23 50 37 39 40 3 4= 4 43 6 42 38 I9[39 4:39 48;40 33;4' i8[42 214= 47:43 3 = 44 16 10 38 .338 5839 4=40 =7|4' >>4> 564= 4043 =5 44 9 10 7 9 10 12 13 20 38 8138 52I39 36,40 2.|4i 541 4942 34[43 >8 38 238 4639 3040 1440 59;4i 43I42 2743 II 44 3 20 15 16 18 19 21 30 43 56 30 22 =4 = 5 =7 28 40 37 56138 4039 2440 840 52 41 3642 =>43 5 43 49 40 = 9 31 3= 34 36 r.!. 50 37 5038 34J39 "840 ='40 46 41 30I42 144= 58 43 4= 50 37 38 40 41 4 43 6 1 , 43 37 4438 28,39 '=39 56,4° '^° 41 2314= 7|4= 5' 43 35 I 3 10 37 3838 ==39 639 4940 33 41 >74= "4= 44 43 =8 10 7 9 10 12 '3 2 I 20 37 3=38 1638 59 39 4340 =7 41 1041 544^ 38 43 => 20 ■5 16 17 '9 21 3 2 30 37 2638 1038 5339 3740 =0 41 441 47,4= 31 43 14 30 22 =3 = 5 26 28 ^|3 40 37 20 38 3 38 47 39 30:40 14I40 57,4' 4o:4^ =4 43 7 40 =9 30 3= 33 35 53 50 37 1437 57138 4" 39 =440 740 50,41 34'4= "7 43 50 36 38 39 4' 4= 64 9 6 U 37 837 5' 38 34 39 '7140 .J40 44:41 2742 10 4= 53 I 3 4 6 10 37 =37 45 38 28 39 1139 5440 3741 20,42 3 4= 46 10 7 9 10 II '3 20 36 5637 39 38 2. 39 4I39 4740 3041 •3'4" 564= 39 20 >4 16 17 19 21 30 36 50|37 32 38 .5 38 58J39 4' 40 2^41 641 49'42 32 30 22 = 3 =4 26 =7 40 36 43,37 26 38 9 38 5'|39 34,40 1740 594" 4=4= =5 40 = 9 30 31 33 34 50 36 37[37 2038 2 38 45'39 =740 .o'40 53 41 35 4= '8 50 36 _1Z. _Z9_ 3 4° 4 ~< 4S 36 3' 37 "3I37 56 38 38I39 2,40 3-40 4641 =8!4= 'I !0 36 25I37 7 37 49|38 3=i39 '4139 56|4o 39,4- ='|4= 3 10 7 8 10 II 13 20 36 19 37 137 4338 =5 39 7 39 504° 3=;4> '44! 5^ 36 1236 5437 36I3S 1939 139 43^40 2541 7141 49 20 '4 '5 •7 18 20 30 30 21 22 =4 =5 27 40 36 6|36 4SJ37 30:38 1=38 54139 36'40 18,41 0;4i 42 40 28 =9! 3. 3= 34 oO 36 36 42 37 =3l38 538 47 39 =940 "40 5 = 39 22'40 4,40 45 lLi+ 50 35 JL jL 39 41 16 35 53'36 35 37 1737 59'38 40 4.1^ 4 6 10 35 4736 =9 37 1037 5=38 33:39 "539 56,40 384' =0 10 7 8 10 II 12 2;) 35 4-36 2= 37 437 4538 =6,39 8J39 4940 3' 4' 1 = 20 14 '5 17 18 '9 30 35 3436 16 36 57137 38,38 =o;39 i|39 4='40 =44' 5 30 =3 =5 26 40 35 =836 9|36 5037 3=38 ■3:38 54'39 3S40 16:40 57 40 28 29 30 3= 33 50 35 ==136 336 4437 2538 6i38 47 39 =8'40 940 50 50 Ji_ 36 1 37 39 4^ 47 35 "5 35 56I36 37 37 '8,37 59|38 40 39 =i,40 =]40 43 I 3 4 5 10 35 935 49I36 3037 II 37 5=138 3339 1339 54'4o 35 10 7 8 ? II 12 20 35 =,35 43!36 =3i37 437 45,38=5 39 63947:4028 20 14 IS 16 iS '9 30 34 56,35 i6\i6 17136 5737 38I38 1838 5939 39I40 20 30 20 22 =4 26 40 34 49 35 =9136 10I36 5037 31(38 1I138 5=,39 3=14° ■ = 40 = 7 28 3' 3 = 50 34 43 35 =3!36 3 3^ 43 37 =4'38 4 3* 44 39 =540 5 50 J±. -15_ ji_ 39 48 34 36:35 16135 56,36 3637 17137 5738 37 39 '7i39 57 3 4 5| 10 34 =9 35 9135 49,36 30 37 1037 50,38 3039 io'39 50 10 7 8 9 II 12 l' 1' 20 34=3 35 3:354336=33^ =137 4=|38 ==39 =,39 4= 20 13 '5 16 17 '9 2 I 30 34 i6|34 5635 36,36 1636 55 37 35 38 15 38 5539 34 30 20 =3 =4 = 5 3 2 40 34 10134 4935 29136 836 4837 2838 7,3s 4739 27 40 = 7 28 '? 3 = ■1 3 50 34 3'34 4=35 ==[36 .'36 4i!37 =0:38 038 39 39 '9 50 33 J±^ jL 37 4 J_8 5 U 9 7 10 33 56134 36I35 '5|35 54'36 34|37 i3:37 5=,38 3=;39 " ■ i 10 535034=935 83547,36=7137 6[37 4538 24I39 3 10 6 8 9 10 12 20 33 43 34 ==35 ■ 35 4036 1936 5837 37138 "7(38 56 20 13 14 16 17 19 30 33 3634 1534 54 35 3336 '=136 5' 37 30:38 9,38 48 30 20 21 22 =3 =5 40 33 =9 34 834 47 35 =636 5:36 44 37 ==38 I 38 40 40 26 27 29 30 31 50 33 73 14 I 34 40 35 1935 5^:36 3637 1517 5438 3 = 50 3= '4 35 36 38 ( TABI.K 39 6S\ tORHECTlON OK TUK MOON'S APPARK.NT Al TITUUK I ( IWDineter, 30 inclies. Faliieiiheit'a TlieritKimeter, 50°) J A|.p. Alt. Horizontal Pnnillai "of Par. Corr. for "of Par add 53' 1 64' i 65' 1 5C | 57' | 58' j 50' ! fiO' fil' 0" '^jFJZ. 7; ■^33 54I34. 33I35 " 3 5 5°i36 2937 7 37 46 38 2; 0" I 3' J „ ^ 1(1 33 933 4-|34 1635 4|35 43:36 2i]37 37 38 38 .6 10 6 7 9 10 j 1 1 20 33 = 33 40|3+ '9)34 57 35 35 36 '436 52 37 30 38 9 20 '3 '4 '5 17 1 18 3(1 3^ 55'33 33 34 "^34 5° 35 28,36 636 44 37 22 38 . 30 •9 23 1 24 >ub. 40 3 = 4SJ33 26,34 4 34 4235 J'i35 59J36 37 37 '5 37 53 40 25 27 28 i 29 31 60 3i_ 4^133 "9,33 5-^34 35135 '3'35 5'36 29I37 7 37 45 50 32 Ji_ 34 1 36 37 m' 31 55(33 'J 33 5°|34 ^^'i'^ 635 43 3* i' i^ 59l37 37 2 4 i 5 10 i«|33 5^33 43I34 ii|34 SSi35 3f' 3* '3 36 5'|37 29 10 6 7 9 .0 1 ,1 3 20 ")2 2i!32 5833 3634 1334 5135 2836 6 36 43 37 2- 20 12 '4 '5 .6 1 .7 :to 3: ■4,32 5' 33 2934 6,34 43 35 2" 35 5^ 36 3 5 37 '3 30 '9 "? 21 22 24 40 731 4433 2"i33 59:34 36135 >3j35 5": 3627 37 5 40 25 26 28 29 30 .■)0 ji CI32 3-33 '+33 5'l34 i8'35 5!35 4= 36 19 36 57 50 3' J^ -il_ -il ^36 7 5 82~0 ;i 53 3i 3° 33 733 44:34 2'i54 5** 35 35 36 .1 36 48 ° ■ 2 t 4 5 8 6 10 3' 4032 2332 5933 36^34 1334 5035 27 36 3 36 4C 10 6 9 10 II 7 20 jl 3932 1532 5233 29:34 5:34 42|35 19 35 55 36 32 20 12 13 '5 16 17 30 ^I 3232 8132 45:33 21I33 58 34 34 35 " 35 47 36 24 30 18 '9 21 23 40 ;i 2; 32 ''^^ 3-33 '4:33 5= 34 27 35 3 35 39 36 16 40 24 26 27 28 29 50 11 '-!3' 54l3i 3°i33 6|33 43 34 '9134 5'; 35 V 36 8 50 32 33 _li 35 53 3' .031 4-132 23:32 59133 35 34 "|34 47 35 23 35 59 ~0^ 1 2 4 5 10 33' 39:32 '5I32 5'133 «7 34 3:34 39 35 "5 35 5' 10 7 8 10 1 1 20 50 56I3' 32I32 8132 44J33 >9 33 5534 3' 35 7 35 43 20 ]s '3 14 '5 17 30 30 49 31 25 32 0^32 36,33 12 33 47|34 23 34 59 35 35 30 '9 20 21 23 3 4 40 3° 3' '7 3' 5332 2833 4 33 40,34 '5 34 5' 35 26 40 24 25 26 27 29 SO 3° 21 3' '° 31 45I32 2l!32 56 33 3234 7 34 42 35 '8 50 J^ 3' 3' 3L _15_ 5 B4 30 27 3< 3 31 38J32 13I32 4» 33 2433 59 34 34 35 " 2 3 10 3° 20 30 55 31 3032 6j32 41 33 '6,33 5' 34 26 35 ' 10 6 7 8 1 9 10 20 30 '5 30 48 31 23I31 58,32 33 33 8,33 43 34 '8 34 53 20 12 13 ■4 '5 16 8 30 3° 6 30 40 31 15131 50132 25 33 033 35 34 '0 34 44 30 17 19 20 21 12 9 7 40 -9 58 30 33,31 831 42J32 17 30 26I31 C31 3532 9 30 .8|3o 53 31 27J32 I 32 5233 27 34 ' 34 36 40 23 24 26 27 1 28 50 12. 32 44 33 '8 33 53 3428 50 29 _3o_ ^|_^ .34 5 56 -9 44 31 3633 10 33 45 34 '9 I ^ 10 -9 36 30 11130 45,3. 19,31 54 32 28 ,3 2 33 36 34 " 10 6 7 8 9 10 20 ^9 2913° 3:30 3713' "13' 46 32 20 32 54 33 28 34 2 20 II 14 15 '6 30 19 22I29 56I30 30 3. 43' 38 32 '2 32 46 33 20 33 54 30 17 18 19 20 22 ,1 40 -9 '4 29 48 30 12 30 5631 30 32 3,32 37 33 " 33 4 = 40 23 24 25 26 27 1 , 50 't, -9 28 7 59 29 41 30 14 29 33I30 7 30 48,3. 22 30 40J31 14 3' 55 3' 47 32 29 33 3 32 54 33 37 50 :8 J±. 3' 32 , 33 2 3 1 33 28 ^ 2I 3| 4 10 28 52 29 2S;29 59 30 32!3' 6 3' 39 32 '2 32 46 33 '9 10 6 7 8 : 9 ic 3 2!) 28 45 29 1829 51 30 2430 58 31 31 32 4 32 37 33 '■ 20 1 1 12 '3 14 1 5 4 30 28 29 '=29 43:3= '6;30 Sc 31 23 31 56 32 2933 2 30 '7 18 '9 20 21 7 I 40 28 30 29 3129 36:33 9:30 42 3> '5 31 48 32 2C132 53 40 22 23 24 25 26 50 28 22 28 55:29 2830 .130 33 3. 6 3' 39 32 12132 45 32 332 36 50 28 29 J' JL V. 57 IF ~ 28 4-29 2029 53:30 25 30 58 31 31 0' ~s~ I 4 10 28 7;28 4029 1229 4530 17 30 50 3' 55:32 27 3' 4632 19 10 5 7 8 10 20 28 0,28 32'29 429 3730 9 30 423' '4 20 '2 '3 '4 '5 30 27 52|28 2428 5629 2930 130 3331 5 3. 38I32 .c 30 16 17 18 '9 20 40 27 44,28 172S 49,29 2r29 53 30 25 3° 57 31 1932 J 40 21 '■? 23 24 26 50 27 ;7j28 9,28 41,29 1329 45^30 17 30 49 3' 20 1LJ3 50 27 jL 29 J5L 3' W~0 2928 1I28 33 29 529 36 30 8 30 4C 31 12 3' 44 0" I 3 4 i 10 27 27 5328 25 18 S7I29 28 30 30 32 3' 3 3' 35 10 5 6 7 8 9 2 20 '4 27 4528 17 28 48,29 10129 51 30 23 30 55 3. 26 20 II '3 '4 '5 3 30 27 6 27 3828 9 28 40,29 1229 43 30 14 30 46,31 17 30 16 '7 18 ") 10 4 3 40 :6 ';9 27 jo:28 I 28 3229 329 35,30 6,30 37i3i S 40 21 23 24 »5 6 50 26 ^.;27 22i27 53 28 24I28 55I29 26,29 57130 2830 59 50 26 27 28 29 3^ 7 ';•} 26 43127 14:27 4;'»8 '6[28 47,29 18I29 4930 2030 51 "(T i~ 3 4 10 26 3627 6;27 37J28 8|28 3929 929 ^c 30 1 1 30 42 10 5 6 7 B 20 26 282658272918 028302, .293230 23033 20 •' 13 •4 y 30 26 20,:6 5i'27 21I27 52,18 22I28 52I29 2329 5330 24 30 •5 16 '7 18 '9 4'i :6 12I26 4327 13'27 4328 .4:28 44::9 '4'29 4 5 3'^ '^ 40 21 12 23 24 •'' ■h 5;2^ 5527 5,27 35:^? 3,-" 33I--9 6|:9 -.f^--.'- >■ 50 26 2- 28 '"' COURECTION OK THE MOON S APPARKNT AI/riTUDE (Bar meter SO InchM Fahrenbeit'i Thermometer, 60°) HoriT^ontal Parallax | "of Corr. for :iirj!!_-^l H 64' 1 55' 66 57' 1 58' 1 50- ( 60' 61' Par. ■^ Jli Jl'j^l 8" 1> , A , „ / ,, , ,j , J , ,J , „ ; z „ „ ,, 60 d »5 57i6 J7|i6 57 X7 27 27 5728 27'^28' 57129 27 '9 57 2" 3' 4 1(1 25 49j6 1926 49 »7 19 27 4828 1828 48129 18 29 48 to 5 7 8 9 211 Z5 4" 16 "^6 4- 27 10 27 4028 10 28 3929 9 =9 39 20 1 1 12 '3 ■4 ;iu Zi 33 »6 i'z6 r- 27 2 27 32^8 . 28 3129 29 30 30 «5 16 17 18 '9 40 ^5 ^^^S 55,^0 »4 26 54 27 2327 53 28 2228 5. 29 21 40 20 21 22 »3 =4 b» .5 .8x5 47|x6 16 »6 45 »7 '5^7 44 28 .328 42 29 12 50 21. 26 27 28 = 9 «ro »5 io,»5 39:^6 ^ z6 37 ^7 6i7 35 28 4I28 34:29 3 1 2 3 ^ 10 IS 2»5 3'h6 ° 2629 26 5827 27 27 5628 2528 54 10 5 7 8 9 20 H 5415 2325 52 26 2026 49'27 18 27 4728 i6[2S 44 20 10 10 II 12 13 30 24 4625 15-5 43 26 1226 4127 9 27 38 -S izi 35 27 2927 5828 26 30 '4 '0 16 17 18 40 -4 3''^5 7-5 35 26 426 32 27 I 40 ■9 21 22 23 60 -4 3014 59 »5 ^7 25 5526 24 26 52 27 2027 491=8 17 50 =4 JI 26 = 7 28 62 24 22 24 5125 19 25 47M "5 26 43 27 1127 4o!28 8 2 4 10 24 14 24 42 25 10 25 3826 6 26 35 = 7 3=7 3.=7 59 10 5 6 6 8 20 24 6 M 34 25 2 25 30 25 58 26 26 26 5427 2227 49 20 9 10 II 12 ■3 30 23 58 2426 -4 54 25 22 = 5 49 26 1726 45I27 12:27 4c 30 ■4 '5 16 17 18 40 23 50 24 .8 2446 25 13 25 4i|26 8|26 36I27 3 =7 3' 40 18 '9 20 21 22 50 23 42 24_io 24 37 *5 5 24 56 11 V: 25 23 25 59 26 27 26 54 27 22 50 ^3_ 24 = 5 20 27 63 ^3 34 24 2124 29 25 5' 26 18 26 45 27 12 o| I 4 10 23 26 23 53I24 21 24 4? 15 '5 25 42 26 9 26 36 =7 3 10 ■ .0 6 8 20 23 18 »3 45 24 12 24 39 25 6 25 33 26 26 27 26 54 20 1 1 1 12 '3 tnh. 30 23 10 ^3 37 24 4 24 31 =4 57 25 24 = 5 5> 26 18 26 44 30 13 14 15 1 16 17 40 23 2 23 29 n 55 24 22 24 49 ^5 >5 25 42 26 9 26 35 40 iS 21 M '" 60 22 54 23 21 24 14 24^40 25 6 iUi i5_59 26 26 50 22 _£J_ =4 J±. 26 22 3 1 eTT 22 46 23 12 23 39 H 5 24 31 24 58 25 24 25 5o'26 16 "IT 2 3 10 22 38 23 4 ^^ 30 23 56 24 22 24 49 25 15 25 41 26 7 10 4 6 8 ^'4 20 22 30 22 56 23 22 23 48 24 14 -4 40 25 6 25 32 25 58 20 9 10 II S 4 30 22 47 23 '3 '-3 39 M 5 24 31 =4 57 25 23 25 48 30 '3 '5 15 16 65 40 22 13 22 39 ^3 5 M 3' 23 56 24 22 24 48 =5 '3 = 5 39 40 ■7 '9 20 21 71" AO 22 31 22 56 23 22 24 13 Mil 25_29 50 22 23 2^ 21- 8|7 66 = ' 57 12 22 22 48 ^3 '3 23 39 24 4 24 29 =4 55 25 20 ^ 2 3 9 8 10 -' 49 22 14 22 39 ^3 5 23 30 23 55 24 20 =4 45 25 II 10 4 6 w 21 41 22 6 22 31 22 56 23 21 23 46 24 II 24 36 25 I 20 8 10 ■ I 1; 30 21 33 2' 57 22 47 23 12 23 37 24 2 24 27 24 52 30 12 "4 15 16 40 21 24 21 49 22 14 22 39 ^3 3 23 28 =3 53 24 17 =4 4= 40 17 18 '9 2C 60 21 16 21 41 21 57 22JO 22 21 2j_54 ^3 '9 ^ 33 50 21 22 23 24 wTT 21 32 2246 23 10 =3 34=3 59 24 23 o~ 2 3 10 21 21 24 21 49 22 12 22 37 23 ' =3 =51=3 49|»4 '4 10 4 6 7 20 20 51 21 15 21 40 22 4 22 52 23 1623 4024 4 20 S 10 10 II 30 20 43 21 7 21 31 ^> 55 22 19 22 43 =3 7=3 3'=3 55 30 12 >4 14 15 40 20 35I20 59 21 46 22 34 22 57,23 21 23 45 40 16 iS 18 •9 60 20 50 21 14 21 37 22 I " 4; .2I23 35 oO 20 21 22 23 87-^ 20 18 20 42 in;7rii 2' 5» 22 15 22 3923 2J23 26 o~ 2 3 10 20 10 21 43 22 6 21 30j22 5323 16 10 4 5 7 20 20 2 20 25 20 48,21 11 21 34 21 57 22 20,22 43^23 7 20 8 9 10 II 30 '9 53 20 16 20 3921 2 21 25 21 48 22 I I 22 34:22 57 30 1 1 '3 '4 14 40 '9 45 20 8 20 3020 53 21 i6|2i 39 22 222 2422 47 40 '5 17 18 18 60 19 36 >9 59 20 22;:0 44 2j7k30 21 5222 15^22 3! 50 '9 21 21 22 C8 19 28 19 51 20 n'20 36;20 5S|2. 21 2. 4322 5;2"n8 (T 2 3 10 19 20 19 42 20 4;2o 2720 4921 II 21 3421 5622 ,8 10 4 5 7 20 '9 33 19 55,20 1S20 4021 2 21 2421 4622 9 20 7 9 10 10 30 '9 3 19 25 19 47:20 920 3120 53 2, .jli, 37 = > 59 30 1 1 12 13 •4 40 18 54 19 .6 ,9 38I20 020 2220 44 21 511 2721 49 40 15 16 17 >7 60 18 46:19 8 '° 56'=. .8I2. 39 50 18 20 zo 21 69 18 3818 59119 21:19 4220 4J2o 25 18 2918 5019 12 19 3319 5420 16 20 472. 8,= . 3C ~0~ o~ s" 10 20 3720 5921 2C 10 4 5 6 20 18 21 18 4219 5I19 2419 4520 7 20 2820 49=' ■= 20 7 8 IC 30 18 1218 33 18 54I19 15119 3619 57 20 .820 39=' c 30 II '^ 13 13 40 18 4118 :51s 45:19 6I19 2719 48i20 9,20 3c :o 5 40 '4 ■ 5 ; 1* 17 M 17 5518 16. S 3718 57ji9 >S'9 39:'9 59-^ -'-'^ 4 .-.0 18 '5 *" Jl — , CBS LOKREcriON OK TilK .MOON'S APPAHENT Al TITUDt: 1 (Il«r..mMer. 30 inche.. Falireiiluii's Tliermometer, 60°) ■it 53' lloriionul Parallax "of Par. Corr. for " of Pur. 8" ^ < 54' 55' ac 57' 1 Sff 1 .'iS' 1 fiO' 1 61' 0" r 1 4" ! (,"' 1 iy '} , J ; „i ; J - J , „ ^ „ ^, 70 r! 17 47 '8 7 18 2S 18 48 ■ 9 919 29,9 5020 10 20 31 I 3" ■: 3S:'7 59 18 19 ■ 8 39 19 019 2019 4020 120 21 10 3 4 6 -'0 17 3°|'7 5° .8 .0 18 30 18 51.9 1.;,, 3119 51 20 II 20 7 7 9 30 .- I.. 7+1 ■ 8 I 18 21 18 41 19 I'ly 21 .9 41 20 I 30 .0 ■ 1 II '3 40 ■7 I3''7 33 '7 5^ 18 121S 3218 5^.9 'A'9 3^ 19 52 40 15 >4 15 .6 50 17 4'"7 2+ .6 56.7 15 '7 44'^ 3 ■7 35 '7 54i 18 23.84319 '-'>9" 18 1418 33ii8 53;. 9 .2 ■9 4^ 50 ■7 .7 18 -V _i9_ 3 71 19 32 I 1 i" 10 .6 47^17 6 17 26 '7 45 ,8 418 2^18 43|'9 3 19 22 10 3 4 4 6 •JO 16 3S 16 58 .7 17 ■7 36 17 55,'8 15 .8 3.i"8 53 .9 .2 20 6 7 8 9 30 ■ 6 30:16 49 17 s 17 27 .7 46 '8 5 ,8 24!. 8 43 .9 2 30 .0 .0 II 12 •0 if 21 16 40 .6 59 17 18 .7 3-"7 56.8 .5;. 8 33 .8 52 40 13 '3 >4 "5 ^lO 16 i; .6 31 16 50 ■ 7 9''7 2S'i7 46|i8 5l'8 24 .8 42 60 .6 '7 18 72~0 16 416 23!i6 41 17 017 18 17 37ii7 55 18 14 18 32 ~ ] I .5 SS''6 .4 16 32 16 51^17 9117 27 17 46 18 4 .8 22 10 3 4 4 5 20 ■5 47 16 5 16 23 16 41,17 17 18 17 36 ■7 54 .8 13 20 6 7 7 8 ;»o 15 38 15 56 16 14 .6 32.6 50:17 8 17 26 '7 44 18 3 30 9 10 10 1 1 40 15 29 ■5 47 16 5 .6 23 ,6 4. .6 59 .7 '7 •7 35 '7 53 40 >3 '3 14 :>n iJ_19 15 56 .6 14^16 321.6 49 n 7 17 25 ■7 43 50 15 .6 16 17 73 1 5 12 15 30 ■5 47 16 5, 16 22'l6 40 16 57 '7 15 ■7 33 "0 I I T 10 1 5 3 15 38 15 5616 13,16 30 .648 >7 5 17 23 10 3 3 4 5 •JO ■4 55 15 12 15 29 15 46,-6 4;'6 ^' .6 38 16 55 '7 >3 20 6 6 7 8 30 14 46 ■5 3 15 20 ■5 37'5 54;>6 M .6 28 .6 45 ■7 3 :v> 9 9 11 40 ■4 37 '4 54 15 II 15 2815 45|'6 * .6 19 .6 36 16 52 40 H ftO ■4 45 >5 i 15 19 15 36 IS 52 16 9 16 26 1642 50 '4 15 >5 J^ mb. ITli 14 20 '4 37!h 53 15 io|i5 26115 43 .559 16 16 16 32 ~o" T 1 ~~r 10 14 1 1 14 28 14 44 ■5 V5 '7!'5 33 15 50 16 6 16 22 10 3 3 4 5 1 I 20 ■4 3 14 19 14 35 14 5' '5 7|"5 ^4 '5 49 15 56 16 12 20 5 6 6 7 2 2 :;o 13 54 14 10 14 26 14 4214 5815 14 .5 30 15 46 16 2 30 8 9 9 10 3 3 40 ■ 3 4S'i4 >ii4 >7 ■4 33|'4 49 >5 4- 15 2° 15 36 '5 5^ 40 II '3 4 4 so 13 36 13 52I.4 8 14 2414 39^14 55I15 11J15 26 15 42 50 13 '4 '4 15 '5 5 5 7.n) .3 28 ■3 43 '3 59 ■ 4 I4|i4 30J14 45 •5 > 15 16 '5 32 ~^ I 1 6 6 !(' 13 19 13 3413 50 .4 5 .4 H'4 36 14 5' 15 6 15 22 10 3 3 , 4 5 7 I 20 13 25 13 41 ■3 56114 "''4 26 .4 41 14 56 15 12 20 5 6 7 8 8 30 ■3 I 13 .6.3 31 13 46 14 1 14 16 14 32 '4 47 '5 2 30 8 8 .0 9 9 40 'i 53 13 7 '3 2= '3 37i'3 52'4 7 14 22 ■4 37 14 51 40 10 I. .2 .-.0 Jir 12 44 12 5013 4 13 2813 43'>3 57 14 12 14 27 14 41 50 13 -LL -7- -^ Jl '3 "9 '3 33j'3 48 14 2 .4 17 14 3. 5" 10 12 41 12 55 13 913 24ji3 38 '3 5^ H 7 14 2. 10 2 4 2!) 12 17 12 3212 46 13 013 14 13 28 '3 4^ >3 57 .4 11 20 5 7 30 12 9 12 2312 37 12 51 .3 513 19 '3 33 '3 47,'4 ' 30 7 8 9 40 .2 .41,2 27 12 41 12 5513 9[i3 23]i3 37 .3 50 40 9 10 ' 10 ."lO ■Ii^iii_j:ili! 12 32I12 46{i2 59:13 i3{i3 27 13 4c 50 _^|_^ '4 77 .. 42I.1 $(>['-- 9 .2 23;i2 36,12 50:13 3 .3 17 "^"30 ~ I ""T 10 11 331" 47'2 12 13I12 27112 401: 53 13 2C 10 2 3 4 20 .. M.. 371. 5- 12 4112 17 12 3012 43 12 56 13 .0 20 4 5 6 30 ,1 .51. 28.1 4> II 54I12 712 2012 33 12 46 '- 59 30 8 40 M 7"i >9H 3= 11 45|" 58'^ "''2 24 12 36 12 49 40 9 .0 ; 10 10 .-.0 .0 581,1 10! 1 1 25 ■ 1 36III 4812 l'l2 I4I12 26 12 39 ■,o I. II j .2 i .2 i; 7H 10 491. ,,, 14 II 26:11 39 II 51 12 412 16 12 29 -o-|-rn- ~T 10 10 4010 52 11 5 II 17 II 2911 4211 5412 6 12 19 10 2 3 1 3 4 20 10 31 10 43 10 55.1 S II 20,11 3i| 56 .2 S 20 4 5 i 5 6 30 10 22J,0 34;.0 4610 58,11 lol.l 22,1 34I1I 46 .. 58 30 6 7 7 8 40 10 13 10 25,10 3-10 49" '" 'V' "■*." 3^ .1 48 40 8 9 1 9 10 .•.0 10 5|to 16,10 2810 39!io 51:11 3'ii h'ii 26J11 38 50 10 ..III 12 711 9 561° 7,.o .9.0 3°:'0 4V° 53M 4," >(>\^^7 ~0 ""o" 1 10 9 471 9 5«|'o 9'0 2I1IO 3II0 43 "o 54 ' ■ 6ii 17 10 2 3 20 938949'° 010 iiio 2210 3310 4410 5611 7 20 4 5 3l>- 9 ;9| 9 4(. 9 51 ,0 ;|io nlio :4i,o 34;io 45I10 s^ 30 5 4'i, 9 :o 9 31 9 4r 9 5:,,o ^\,o 1410 1510 -i^.c 4^ 40 7 9 •■'T'i'" 9 3=1 9 43| 9 53|.c 41-0 ,5.0 =5.0 3^ ■"'" 9 10 : ir " 684 TABLE 39 CDRRKCTION OF Till; MOONS APl'ARENT ALTITUDE (Barometer, 30 indies. F,.lim.Iieit's TI.ei momete r,50°; i App. Alt. Horizontal Parallax "0 Par Corr. for " of Par orfj. 53' 1 6* 1 55' 1 56' 1 57' 1 58' ! 50' 1 60' [ CI' 0' JjiIj: \JL S» (1 9 '- 9 12 9 ^ 1 , |9 33 9 44 9 54 '„f-,i.- = 0' ^ 1 0" ,■ 1 ,' III 8 53 9 3 9 H 9 24 9 34 9 44 9 55''° 5''o 1 10 2 1 2 2 1 3 '20 8 44 8 54 9 4 9 '4 9 24 9 35 9 45| 9 55 10 20 3 44 3(1 « 35 8 4, 8 55 9 5 9 '^9 25 9 35 9 45 9 54 30 5 56 40 8 26 8 36 846 8 55 9 5 9 '5 9 2S 9 34I 9 44 40 7 7.7 50 8 17 8 27 8 36 846 8 56I9 5 9 >5l 9 24I 9 34 50 8 L1J-1- 9_ 81 S 8i8 IS 8 27 |8 37 8 46 1 8 55! 9 5J 9 14J 9 24 __ 10 7 59 8 9 8 18 8 27 8 36I845 8 55! 9 4 9'. 8 45 8 54I 9 3 10 1 2 2 20 7 >,-' 7 59 8 98 18 8 27 8 36 20 3 ! 4 30 7 41 7 50 7 59!» 8 8 .7 8 26 83 8 44! 8 52 30 4 r T 40 7 3^ 7 41 7 50 7 59 8 7 8 16 8 2 8 331 8 ^2 40 6 6 ( 7 50 7 U 7 32 7 4> 7 49 7 58 8 6 8 I 8 23! 8 32 50 7 8 ! 8 8? 7 '4 7 ^3 7 3> 7 40 748 7 56 '8~5 8,3|1-IT ~0 1 " ; ■ i ' 10 7 5 7 >4 7 " 7 30 i 7 38 7 46 7 55 8 3| 8 .. 10 1 \ ,. I , 1 2 20 6 57 I 5 7 >3 7 21 7 29 7 37 7 45 7 53 8 , 20 3 3 1 3 1 3 30 6 48 6 55 7 3 7 n 7 '9 7 27 7 34 7 42J 7 5< 30 ( 4 4 I 5 40 6 38 646 6 54 7 I 1 9 7 17 7 24 7 32; 7 4=^ 40 5 6 ^ s^i. 60 6 29 6 37 6 44 6 52 659 7 7 7 14 7 22 1 7 29 01.1 6 I 7 7 7 -J- (la 6 20 6 2g 6 35 ! 6 42 — (> 57 7 4 7 12 7 19 ~ir Q '~°~ 10 6 II 6 ,9 6 z6 « 33 6 40 6 47 6 54 7 7 9 10 I I 2 „ ' 20 6 2 6 9 6 16 6 23 '6 30 6 37 6 44 ^ 5 6 58 20 2 2 3 3 3 •1 7 7 30 5 53 6 6 7 6 141621 6 27 6 34 64 6 48 30 3 4 4 40 5 44 5 51 5 58 6 46 M 6 iSl 6 24 6 3 6 37 40 5 5 i 5 50 Hi 5 42 548|S5Sl6 . 6 S| 6 14I 6 2.; 6 27 50 6 6 1 6 84 5 J6 5 33 5 39I5 45!5 5> 5 58 6 4| 6 ic 6 17 T~ 10 5 17 5 23 5 30 5 36 5 42 5 48 5 54! 6 6 6 10 1 I 8 8 20 5 8 5 14 5 ^0 5 ^6 5 32 5 38 5 44 5 5° 5 56 20 2 » 9 30 4 59 5 5 5 '■ 5 I? 5 i2 5 28 5 34 5 40 30 3 J 40 4 5° 4 56 5 ' 5 7 5 '3 5 '8 5 24 5 29 40 4 5 60 4 41 4 47 4 5^ 4 57 5 3 5 8 5 '4 5 '9 5 24 50 -J_ _i- -i- X 85 4 3 = 4 37 4 43 1 4 48 4 53 4 58 5 4 5 9 5 14 "0 10 4 ^3 4 28 4 33 4 38 4 43 448 4 53 458 5 4 10 I I 20 4 '4 4 "9 4 24 4 29 4 34 4 38 4 43 448 4 53 20 2 2 30 4 5 4 10 4 14 4 "9 4 »4'4 28 4 33 4 38 4 43 30 2 " 40 3 56 4 4 5 4 10 4 14 4 >9 423 4»& 4 32 40 3 3 50 3 47| 3 5' 3 56 4 ° 4 4 4 9 4 >3 4 '7 50 4 4 3.i 3 38 342 346 3 5° 3 55 3 59 4 3 4 7 4 '1 c ~^ ~5~ 10 3 29 3 33 3 37 3 4' 3 45 3 49 3 53 3 57 4 > 10 I 21 3 -0 3 23 3 27 3 3' 3 35 3 43 3 47 3 5= 20 I 3(» 3 ' I 3 '4 3 '8 3 22 3 25 3 29 3 33 3 36 3 4c 30 2 2 40 3 = 3 5 3 9 3 '2 3 '5 3 19 3 22 3 26 3 29 40 2 3 50 «7 » 53 » 43 i-ii 2 59 3 2 3 6 3 '6 3 19 50 3 3 -1- 4- -f- 2 47 2 50 » 53 * 5^12 59 3 2| 3 5; 3 8 10 » 34 ' F 2 40 2 43 2 46 2 49 2 52, 2 55 2 58 10 I 20 ^ ^5 2 31 2 34 » 42 2 45 2 48 20 I I 30 2 16 2 19 1 14 2 ^-2 " 2 32 2 35 2 37 30 I 1 40 2 7 I 10 2 12 2 14 2 17:2 19 2 24 2 27 40 2 2 50 . 58 2 1 3 2 5|2 7i2 9I 2 12 2 ,4 2 16 50 2 2 88 1 49 > 5' ' 53 ' 55 I 57 ■ 59 1 "2 2 2 4 2 6 "IT "F~ "V ~1^ 10 ' 40 I 42 I 44 I 4b , 50J > 5' > 53 > 55 10 20 I 31 ' 33 ' 34 , 36 I 40 1 41 143 20 I 1 I 30 I 12 I 13 I 15 I 26 I 30 1 31 I 33 ' 34 30 I 1 I I 1 40 ' >3l I 14 I M I 17 I 21 1 22 1 24 40 1 f I 60 ' 4 > 5l I 6 ' 7| I 10 I 11,1 12 50 I I ' 1 i 2 80"0 54IC 56 57 581059 I o| ^ ~ I 2 1 3r 1 "o~ 10 45 46 47 048 049 50 51! 52 52 10 1 20 36 37 038 38 039 04.0 41 41 42 20 1 30 l;|o 28 28 29 29 ;ol 3C 31 31 30 40 iSjo 19 19 i9|o 20 21 40 - Q , Cj 50 ■Ml ' ' 1 ' ' i ' TABLE 40. COKUECTION OF TI E MOO n'8 EQUATOni I. PARU^UI FOR or THE EAKTH. CompresBio 1 J-, (Clarke) 293 Horizontal Parallax Lat. 54' 56' 58' 60' 62' 00 "•o "■0 "•0 "0 "•0 8 on 02 02 02 o'a 16 0-8 09 0-9 09 0-9 20 i'3 14 1-4 i'4 J-5 'M 20 20 21 28 25 2-6 27 2'8 82 3' 32 3'4 35 3b rs 40 4' 42 4 4 40 4b 47 4-9 5-1 52 44 53 S'S ■i7 59 61 M 6-3 70 62 b-Q 7i 74 76 79 56 7-6 79 82 8-4 87 60 a-3 8-6 8-9 92 9S 04 «-9 93 9-6 9-9 102 q-i 99 102 109 104 107 ii-i •■■5 76 104 108 1 1-6 120 80 107 III .1-5 1.9 12-3 TABLE 42 AUGMENTATION or th E .MOONS 1 SEMIDIAMKTER 1 A pp. Alt. Semidiameter 14' 13' 16' 17' 30" 0" 30" 0" 30" 0" 0° c'l O'l O'l o"i o'l o'l 2 6 0-6 0-7 0-8 0-8 4 1 I- 1 '•1 1-4 ■■5 U I 1-6 1-9 2-0 H 2 2-1 i'2 i-4 J-S 17 10 2 '•7 2-8 VO v» 33 12 3'- )■) 3-5 3-7 40 U ■! V8 4'' 4'4 4-6 lU 1 4> 4'4 4-7 5-0 5-2 III 4 4-6 4-9 s-s S-9 •21 4 S'l S7 6-0 6-4 6-7 21 S 60 64 6-8 7-2 77 27 6 6-7 7-2 7-6 81 8-6 .'to 6 7-4 7-9 8-4 8-9 94 XA 7 S'ol 8'6 91 9-b ro-3 :w s 8-6: 9-2 9-8 ■Ml 8 9 - ' 99 lo-s I I'l M-8 42 9 11-8 12-6 ■tr, ") 10 3 1 110 11-8 .2-.; in 4(1 IC-9J I. -6 12 '4 >V> 14-0 51 IC 12-9 >V7 .46 S4 1 1 M-8 12-6 ■VS »4-3 15-1 ■'-7 I 1 I2-, ' iri 14-0 148 '57 «;» ■1 ,yo IV9 ,4-8 'V7 >*7 7" 12 IV7 '4-7 'S'7 .6-6 ■ 7-« 7« 1 3 MM ";••! ■ 5-, I7'3 i»-4 :mi rr^ ,41. iv(> 161 i8-6 rAfji.i: 43 PABLF. 41 CORRECTION 1 rOR nEDUCING THE rnUE ALTITODE 1 or THE SUN OK A SI All T 1 THE APPA,.E.TA.T.T.„. | Alt. Corr. All. Corr. sii6. s,.h. 5° C o' 1 6" 7° 30' o' 6" 6 20 o 15 8 ° 5 i 40 !) o 3 6 11 10 o z fl 20 10 O I « 40 '-'5 o o 7 o 7 TABLE 45 PARALLAX IN ALTITUDE OF A PLANET Planet's Horizontal Parallax " I 2" 3" I 4" 6" «" I 7" I 8" I 9" lO" 20" 30" S"9 (>-9 79 5-8 6-8 [ 7-7 5-6 , 6-5 [ 7-5 3-4 49 5'7 6-6 4-6 5-4 4-9 5'7 COKKIXTION II BEDIJCI.VG THE T II U E .TITUHE of THE MO( TO THE API-AIIENT ALTITUDE HoiiaonMl Parilli.x 54' I 58' I 61- o 51 o 47 o 41 o 38 « TABLE 40 68r AZIMUTH, AND (JORRESPONUINO CUANOK Ot ALTir ,„. 1 IM 1™ or TIMB I.UI Change of Altitude in 1" 1 13' 0' 1 r 1 2' 9' I 4' 1 5' 6' 7' 8' 1 it' 10' II' 12' 14' \^ 0" (,o 4''l 8° .»», .sH .9° »4' 28" ii° 37 4» 47° 5-/ 60- 69° 87° 1 O 4 8 .2 IS i .9 »4 28 3» 37 4» 47 53 60 69 87 •1 O 4 8 12 15 1 20 »4 28 3i 37 4^ 47 53 60 69 u o 4 8 12 1 l6 ! 20 J4 28 31 37 4^ 48 54 61 H ° 1 4 1 « 12 1 |6 1 20 24 28 1 33 37 4^ 48 54 61 1(1 o 1 4 , 8 12 1 l6 1 20 24 28 !^3_ 38 43 48 54 62 TT o 1 4 \'~T "HTi .6 i 2o ^4 28 33 38 43 48 55 62 "72" 12 o 4 ^ 12 1 l6 1 20 »4 28 33 38 43 49 55 62 1.1 o 4 1 '^ 12 i l6 1 20 *4 »9 33 38 43 49 55 63 1 U o 1 4 8 12 1 l6 ( 20 »4 »9 33 38 43 49 56 63 1 15 o 1 4 8 12 , l6 20 »4 »9 34 38 44 49 56 64 1 IK o 1 4 8 .2 .6 20 ^5 29 34 39 44 5° 56 64 1 17 o * ! 12 , l6 ! 20 »5 »9 34 39 44 5° 57 65 IH o 4 » .2 , l6 j 2, 25 »9 34 39 44 5° 57 66 19 o i 4 1 » .2 ,6 2, »5 3° 34 39 45 5' 58 66 81 1 1 20 _4_l_ » 12 ; i6 i 21 ^5 30 45 5> 58 67 21 o 4 1 12 1 17 2. ^5 30 TT l^lTfi" 51 59 'W -w 22 o 1 4 1 12 ; 17 21 26 30 35 40 46 51 60 Cg 23 o 4 1 .3 ; 17 21 26 30 35 4' 46 53 60 70 24 o 4 1 13 '17 2. ! 26 3> 36 4' 47 53 61 7= a o 4 ' t 13 i 17 '■^ 26 3' 'i 4' 47 54 62 73 S6 o U 9 13 1 I- ; 22 26 3' 36 4» 48 55 63 75 27 ° 4 9 13 ' 17 1 22 27 3^ 37 4» 48 55 64 77 28 4 1 9 13 ' 18 ! 22 ^7 3» 37 43 49 56 65 79 S9 ° 4 i 9 13 ; 18 1 22 27 3* 37 43 50 57 66 8» ao o ' 4 1 9 13 1 ig 1 23 27 33 38|44 5° _5L 67 31 ° 1 4 9 13 ' >8 ; ^3 28 33 — 44 5' 59 69 32 9 •4 1 >8 *3 28 33 39 u 5^ 60 7' :<:< ° 1 5 o Hi 19 »3 28 34 39 53 61 73 34 o 9 •4I '9 »4 »9 34 40 46 54 62 75 36 o 9 H ; '9 24 29 35 4" 47 54 64 78 36 o 9 14 19 *4 30 35 4> 48 55 65 81 37 o lO 14 ! 19 25 3° 3* 4* 49 57 67 :«« o lO 15 1 20 i5 30 36 43 49 58 69 so o 5 lO 15 1 20 25 3> 37 43 5' 59 7> 40 _5 s_ lO 26 3, 38 44 52 60 73 41 5 i 'o 1 '5 1 II ^T 32 38 45 -^-ZT T6" 42 o ■ o 27 33 39 46 4 64 8. 43 o IC 16 21 27 33 40 47 55 66! 44 o II 16 ' 22 28 34 40 48 57 68 1 43 o II 16 1 22 28 34 4' 49 58 1 7. 1 46 o 5 II >7| »3 19 35 42 5° 60 ( 74 1 47 o 6 II •7 U3 29 36 43 5' 62 78 ' 4a o 6 11 17 1 23 30 37 44 53 64 85 4!l o 6 I* 18 24 3! 38 45 54 66 Ml o 1 6 1« Jlj.ll. 3' 38 47 56 69 oi o 6 11 19 1 25 32 39 48 58 7- .-.2 ■ 2 19 26 33 4' 49 60 77 6:) 13 19 26 34 4^ 5> 62 8S 64 o n 20 27 20 28 35 36 43 44 53 54 ^1 .'i6 o '4 21 1 28 37 46 57 73 ft? o >4 22 29 38 47 59 78 68 o "5 22 30 1 40 49 62 M 7 M 23 31 1 40 5' 65 i 60 o « .5 24 iz 1 4i S3 _69_ ■cT ym-*- M 33 43 1 56 1 74 1 «2 6 li 35 45 58 84 1 «3 $ »7 36 47 62 114 9 Ik ^7 37 49 6« 1 1 1 hb o 9 1 28 39 ! 52 70 1 1 ! i 1 1 ee O 9 j K, 29 , 41 1 55 1 «^; ! 1 1 ! ■ 1 1 TAB 1. 1' 48 LIMITS, AT SKA, OF THE REDUCTION TO THE MERIDIAN. 1 Declination of the >ame Name as ihe Lat. | Lat. 0° 5° 10° 15° 20° 23° 0° o" O" 0" 3™ o^S" 0" 8- o"ii- O..14- 5 o 3 3 0508 10 10 : 1 3 0306 7 15 I 3 0003 5 20 o n 6 0300 •25 o 14 II 9 0603 30 o 17 15 12 09,06 S 35 O 21 16 13 10 8 W o 25 02? 20 17 i 14 I* 44 29 26 024 21 18 16 4X 33 31 028 25 22 20 52 038 36 033 30 27 26 56 044 42 39 36 1 34 32 60 52 49 47 44 41 39 64 I 57 55 52 49 47 68 I 10 I 8 1 6 1 3 I I 058 Decl nation y[ contrary Name to th Lat. 3 ° 1 8 II 13 5 10 3 S 5 8 8 II J3 14 16 16 iS 15 8 II 13 16 19 21 20 II 14 16 19 22 24 25 14 17 19 22 25 27 30 17 20 23 25 28 30 35 24 26 29 32 34 40 'o'^Y 28 30 33 1 36 38 44 29 32 34 37 1 40 42 48 33 036 39 41 44 46 52 38 41 44 46 49 51 56 44 47 so 52 55 057 60 52 55 57 I 00 1 I 3 « 5 64 I I 3 I 6 »hilevisi le. 68 I 10 I 13 I 16 VALUE OF THE REUUC •ION. AT WHICH Til E 2»" RED" AMOUNTS TO !• Mer All, „.,. Mer Ait. Reduc 5° 4" 40' 45= .°23- 4 16 41; 1 21 7 3 i7 •17 I 20 » 3 41 48 1 19 9 5 zi 49 Id 3 'S fl(l I 16 1 1 3 8 r>i 12 52 1 I- i:{ 2 ^; .53 1 12 14 1 2 46 54 ■|o .40 .■i,-. ■ 9 16 I 35 .if! 1 8 17 2 30 57 Iff ,=>« I 6 19 2 21 SO 20 2 17 (i(» ■ 3 21 (11 22 (i^ 1 23 2 7 63 S9 24 ^ 4 (;4 58 25 2 2 (;.i 26 ' 59 nu ° 55 27 . S6 (i7 54 28 ' 54 68 ■^ 53 29 69 30 I 49 70 50 31 ' 47 71 32 I 45 72 47 3a ' 43 73 46 34 1 41 74 44 ■Ao ' 39 7J 43 36 76 3; I lb 77 40 38 ' 34 78 38 39 • 3: 79 ° 37 40 > 3' 80 ° 35 41 I 29 81 33 42 I 27 82 31 43 1 26 83 44 I 24 84 27 TABl.K in 689 TABLE 49 "roK COMPUTINuTh. reduction TOjrHE^MEBllHAN^8.rr|Nl^ II H IN SK(;»". Houns 1 9. 25'° 1 2fi"' 1 27'" 1 2;i"' 2!)'" 3(1"' 1215-9 n^S 9 1429-7 '53-5 1649-0 ,764-6 eo 1 1217-5 .3^-6 1431-4 '5393 .650-9 1766-6 f>» 2 12292 1329-3 '433-2 '54'-' .652-8 .'--0-- r.B :< 1230-8 .33.-0 14349 1542-9 .654-7 >''7 4 1232-5 ■33i'7 .436-7 .544-8 .656-6 .772-4 5B 5 1234-1 M34-+ .438-5 1546-6 .6585 '774-4 Aft (I •235-; .336-. .440-3 .548-4 1660-4 .776-3 54 7 1 = 37-3 ■337-8 .442-1 1550-2 .662-3 53 K 1239 '339-5 •443 9 .552-. .664-2 1780-3 52 9 124c 6 1341-2 Jiiil «?53-9 .666-1 Jll-IL 51 10 1242-3 '34'<>1 •447'4 '555-8 .668-0 .784-2 i«r II 1243-9 .3446 '449-2 .557-6 .669-9 .786-2 4!» IJ 1245-6 . 340-3 1451 '559-5 .67.-9 .788-2 4f! l.t 1247-2 .348-0 .452 8 ■56^-3 .673-8 ,790-, 47 U 1248-9 '349-7 ■454-5 .563-2 '675-7 ,792-, 4).' 10 1250-5 '35'-4 .456-3 1565-0 .6776 '794-' 45 lU 1252-2 '353-i 1+58-. .566-9 .679-5 .796-. 44 17 .253-8 '354'9 ■459-9 ■568-7 . 681-4 ,798-1 43 IK '=^5-5 .356-6 .46.-6 .570-5 .683-3 42 1!) 125-1 .358-3 .463-4 .572-4 .685-2 lS02-0 41 2(1 ,258-8 .360-. .465-2 ■574-3 .687-2 1804-0 411 21 1260-4 .36.-8 .466-9 .689-, .805-9 3!» ■J2 1262-1 .363-5 .468-7 .5-8-0 .69.-0 .807-9 38 ■r.i 1263-7 .365-2 .4-0-5 ■579-S .692-9 ,809-9 37 24 1265-4 .36-0 ■472-3 i;8i-7 .694-8 .8. ,-9 3(i 2.'> 1Z67-0 .368-7 1474-0 '583-5 .696-7 .8.3-9 35 2B 1268-7 1370-4 '475-9 ■585-3 .698-6 ,8,5-8 34 27 1270-3 .372-1 '477-7 .587-2 1700-5 ,8,7-8 33 211 1272-0 '373-9 '479-5 'S89-' .702-5 .8.9-8 32 29 "73-7 1 '375-6 .481-3 i59oj^ ■704-4 .82,-8 31 :«i ' = 75'4| '37y4 ■483-' 1592-7 1706-3 ,823-8 3(t :379-' .4849 1594-6 ,708-2 ,825-8 2,'» :»2 .278-8 .380-8 14S6-7 .596-5 ,827-8 28 3.» .280-4 .382-5 .488-5 .598-3 .7.2-1 ,829-8 27 :t4 '384-2 .490-3 .600-2 .7.4-0 .83,-8 2« 35 .283-8 1385-9 .492-1 .602-1 .715-9 '833-8 2S ;733-4 ,85,-8 k; 4.1 1300-5 .403-4 1510-2 .620-8 '735-3 ,853-8 15 4t; 1302-2 .405-2 1 5 1 2 ■ r, .622-7 '737-2 ,855-8 14 47 1303 9 .406-9 ,51,-8 1624-6 ,739-2 ■857-8 n 4« .,05-6 .408-7 ■ 5, 5-6 1626-5 .74. -2 ,859-8 12 VJ '307-3 .4.0-4 'S17-4 16283 '743-' II ^iiT .'309-0 1412-2 15.9-2 .650-2 '745-' 7867-8 10 .-.1 .3.0-7 .4.3-9 1521-0 .632-. .747-0 ,865-8 u 52 .3.2-4 '4'5-7 1522-9 .634-0 ■749-0 .867-8 8 J13 .3.4-1 .4.7-4 <524-7 .635-9 .750-9 .869-8 7 .^1 I3'V7 .4.9-2 1526-5 .6377 .752-9 .87. -8 « ft.-. '3'7-4 i4»o-9 .528-3 .6396 .754-8 ,873-8 5 ftfi .J19 . .422-7 1530-2 .64.-5 .756-8 ■875-9 4 •■'7 .310-8 1424-4 .532-0 1643-3 .758-7 .877-9 3 :>H '3'»-5 1426-2 .533-8 1645-2 .760-7 .879-9 2 .-.it 1374-2 .427-9 .535-6 .647-1 .762-6 .882-0 1 fiO 13:5-9 1429-7 .537-5 .649-0 ,764-6 ,884-0 - 31'" 33'" 32'.. 1 31"' I :to~ 1 o,Jn, »■ II ll,.r«. I Kon (;OMPUTIN(J HK a'l REDUCTION IN SECONDS 2nJ M„ur Angle. Hed. Angle 3 ,-|0 03 4 0-4 4 30 0-4 26 30 20 40 2(; 50 27 27 10 27 20 27 30 27 40 27 50 28 21! 10 28 20 28 .30 28 40 TABLE 51 CORRECTION OF THE ALTITUDE OF THE POLE-STAR FOR 1890. 1 R.A. Mer. Altitudes R.A. Mer. Altitudes > O' 80» 50° 70° 80° 0° 30° .50° 70° 80° L m sub. sub. sub. sub. sub. b m add add add add ~1M' 1^ I°I3' i°.3' i°i3' i°.3' i°i3' 1> 1-13' i°i3' I°I3' I°I4' l°I4' 3' 30 « »S » 15 « »5 • «5 J >5 12 30 1 15 • '5 I '5 1 15 I 16 3 1 1 17 I 17 I 17 • "7 I 17 13 1 17 I 17 I 17 I 17 I 17 3 1 30 I 17 1 17 I 17 « 17 I 17 13 30 I 17 I 17 I i; I 17 > '7 3 2 I i6 I 16 1 16 I 16 I 16 14 1 16 1 16 1 16 I 16 I 16 3 2 20 I 14 I 14 I 14 I 14 « 13 14 20 I 14 1 14 I 14 I 14 I 14 3 2 40 I 12 I 12 I 12 I II 14 40 I 12 I 12 I 12 1 12 I 13 3 3 1 9 I 9 » 9 • 9 1 8 15 I 9 « 9 I 9 I 10 1 10 a 3 10 • 7 > 7 « 7 « 7 I 6 15 10 « 7 1 8 I 8 I 8 I 9 2 3 20 1 6 « 5 ' 5 I 5 » 4 15 20 I 6 1 6 1 6 1 6 ' 7 2 3 30 I 5 1 4 « 4 I 4 > 3 15 30 I 5 I 5 > 5 ' 5 T~^6" 2 3 40 « 3 I 3 I 2 I 2 I I 15 40 « 3 « 3 ' 3 « 4 « 5 2 3 50 I I 05S 15 50 I I I I I I 3 2 4 058 058 058 57 56 16 058 59 59 59 2 4 10 56 056 55 55 S3 16 10 56 56 56 57 59 1 4 20 54 54 54 ° 53 52 16 20 54 55 55 56 57 I 4 30 52 51 51 50 49 16 30 52 52 52 53 55 I 4 40 49 49 048 48 46 16 40 49 49 50 51 52 I 4 50 46 046 45 45 43 16 50 046 47 47 48 50 I 5 44 44 44 43 41 17 44 045 45 46 48 I 5 10 41 41 41 038" 40 37 17 10 41 42 42 43 045 I 5 20 038 038 36 034 17 20 038 39 39 40 043 5 30 35 35 34 33 31 17 30 35 036 036 37 41 5 40 32 32 31 30 28 17 40 32 33 33 34 37 5 50 29 28 028 27 24 17 50 29 29 30 31 33 6 26 25 25 23 21 18 26 26 27 28 30 6 10 22 22 17 18 10 22 23 23 25 27 6 20 19 18 18 16 14 18 20 19 19 20 21 24 6 PO 16 16 15 14 II 18 30 16 17 17 19 21 6 40 13 12 12 10 8 18 40 13 13 14 15 iS 6 50 9 9 8 7 4 18 50 9 10 II 15 7 6 5 5 l>.f I a,ld 19 6 6 7 9 II ° 7 10 IJ °.i 2 I 3 19 10 3 47/6. 4 sub. 5 6 9 ° 7 20 I 2 2 4 6 19 20 I 1 sub. sab. 4 ' 7 30 4 4 s 6 9 19 30 4 3 2 I 2 sub. 2 ' 7 40 7 8 8 10 12 19 40 7 7 6 s , 7 50 11 11 12 13 16 19 50 II 10 9 8 5 2 8 14 15 15 17 19 'M (1 14 "o^i^ 13 12 9 2 8 10 17 18 18 20 20 10 17 17 16 15 12 2 8 20 21 21 22 23 26 20 20 21 20 20 18 16 2 8 30 24 25 25 26 29 20 30 24 24 23 22 20 2 8 40 27 28 28 30 32 20 40 27 27 27 25 23 2 8 50 30 30 3' 32 34 20 50 30 29 29 28 25 2 9 33 33 34 35 37 21 33 32 32 31 29 2 9 10 036 036 37 038 40 21 10 36 036 35 34 32 3 9 20 39 39 40 41 43 21 20 39 39 038 37 35 3 9 30 42 42 43 44 45 21 30 42 4J 40 38 3 9 40 45 045 46 47 ^48 21 40 45 C45 044 46 043 45 41 43 3 3" 9 50 47 47 47 48 50 21 50 47 46 10 50 51 5i 52 53 22 50 so 50 49 47 3 10 10 53 53 53 54 55 22 in S3 53 52 52 50 3 10 20 55 056 056 57 058 22 20 55 55 55 54 53 3 10 30 57 57 57 058 59 22 30 57 056 56 56 55 3 10 40 59 59 59 I I I 22 40 59 59 59 058 57 3 10 50 I I I I I 2 t 3 22 50 I 1 I I I I I 59 3 11 • 3 1 3 ' 3 ' 4 I 5 23 > 3 I 3 1 3 I 2 1 1 3 11 20 I 7 I 7 1 7 1 8 23 20 I 7 I 7 I 6 I 6 I 6 3 11 40 I 10 I 10 T 10 I 10 I 10 23 40 1 10 I 10 « 9 I 9 I 9 3 12 • 13 ' '3 * '3 I 14 I 1.) 24 ' >3 • '3 ' >3 ' '3 1 >3 3 TABLE ,J2 REDUCTION OF LATITUDE Compression ' 293 (CUrke's figure of the earth) L«t.| Red. L«t.| Bed. Lat.i Red I 9 45 10 4 40 • 1 4 21 41 4 45 42 S 8 4!l S TO 44 5 51 4.1 W 6 31 47 6 ^1 48 7 <2 49 ^0 7 H 50 21 7 SO bl .S2 23 ] 8 25 .■I.S 24 1 8 42 .S4 2.-. 8 58 .l.^ »« 9 .4 .'if, »7 9 28 57 »« 9 43 58 W 9 56 b9 S.'! 9 I 6« 8 44 67 (!8 S ,0 69 7 52 70 7 34 7 15 Vi 6 ^s 6 IS 74 6 T.| 75 S 53 S 12 5 «o 78 4 47 V".l 4 25 80 HI .338 3 >5 2 51 84 2 27 I 38 I 14 HI 49 TABI.r 53 fioa CORRECTION OF THK LUN.^R DISTANCK FOR THE CONTHACTIOH or THE TK.I.CAL SE3I1DIAMETEH Alt. Angle between the L»n.Di«. and the Pl„n,l, I,i,„| 0° |.0» 20" |30° Uo^lso^lwlTo" 80°|90°| ;r 5>' 49" 4S' sri 30-1 21- .3-1 6' ,. 3" 35 3^ 21 1 ,5 9 4 , •' ^4 12 6 7 II 20 16 '9 16 18 '4 I S ° " " 10 4 •' 10 y 9 Q 9 7 1 p i 4 * 1 ' 20 30 3 3 2 1 « I J Q ° 01 ° T.ABLE 54 ERROR OF OB.SERVATION ARISING 1 FROM KRKOR OF PARALI,ELISM | (tllSHT Angle Error „f Parallelism „f the Telescpe | 10- 20' 1 30' iO-\50'\l-'0-\\''Wy20'^ 10" 20 .'to 40 .iO bO 70 80 SO 100 110 120 I I I 2 ° 5 70 .6 80 ,9 330 52 4CI 2 48 . .el o'6' II 17 23 19 36 oil ' 3 ■ >5 1 30 I 49 0' 7'lo' 10' .5 20 23 30 0310 40 40 51 : 26 1 11 I 42 2 13 2 2 13, 2 28 3 14. TABLE 55 F m CORRECTINO THE LUNAR DI.srAN( E I,. luJe >fo.,n'« Altitude 0° lO" 20° 1 30° 1 40° .10° ' CH° |7«° 80° |90° 0-^ )r .W" • «7 . R,i . R2 . no ■ 77 ■ 74 ° 2: 40 60 go 90 100 120 120 .0" " too 130 150 170 190 " i" 200 240 270 300 110 310 ° 70 140 100 260 34° ,60 l8o " 250 310 380 430 470 " 200 300 39> 4ho 53° 570 fioo Mo . 64 ° 240 250 450 540 610 «6o 6,0 26 . .11 . .17 " ♦00 500 *IO *,o 740 780 79c " 310 450 580 6,0 780 8jo 890 s:i 180 S^o 7-,r, 870 95" 99<^ c ,,^ J-'" i^" 7rr< «40 9S" '-r ic8r ,,cc| ■„. .,0| 74'^ 9CO 1 990 1 -'■■ '1 694 TABLE 56 F OR COMPUTING THK M OOf JS 5 ECO \D CORRECTION OF D STANCE J s"*^~ sa Apparent Dist aiice U Z Z 15° 16° z 18° z 23° 26° 30° 34° 38° 44° 50- 60° ;^ zy add ~ ~ 1 5' i'' 1" 1" i" l" 1" l" i" 0" 0" 0" 0" 0" 0" 0' o"l 8 I 2 2 2 2 I 1 I I o| 10 4 3 3 3 3 3 2 2 1 2 2 I I I 11 5 4 3 3 3 2 2 2 2 1 ( . 12 5 5 4 4 4 3 3 3 2 I o| 13 6 6 6 5 5 5 4 3 3 3 2 2 I o| U 7 7 6 6 6 5 5 4 4 3 3 2 I 15 9 8 7 7 6 6 5 5 4 3 3 2 2 j c 16 9 8 8 7 7 6 5 5 4 3 2 - 17 II _!. 9 8 8 7 6 _L 4 _J_ _J_ 3 ° i 18 ,2 11 .. -iT 9 9 "8 7 6 5 4 3 ~r ~~v i 19 '4 ■3 II 9 7 6 5 5 3 3 20 15 '4 13 II II 10 8 7 6 5 4 3 1 21 17 '5 14 '3 '3 12 9 8 7 6 4 3 , 22 >7 16 15 14 ■3 12 10 9 7 6 4 23 20 ■9 17 16 »5 >4 13 II 9 8 7 5 4 c ■24 22 20 >9 18 16 15 '4 12 9 7 5 4 25 »4 22 20 19 18 17 ■5 13 II 9 8 6 5 26 16 24 22 ■9 18 16 ■4 12 9 6 5 27 i8 26 24 22 20 17 >5 13 1 1 9 7 _^_ c -w lo" 27 "IT 24 22 21 >9 16 H 12 10 7 6 29 3: 29 27 26 -f 23 20 17 •5 >3 II 8 6 30 34 3> 19 27 26 24 22 »9 16 H 12 8 7 3 31 36 34 3' 29 27 26 23 17 '5 12 9 7 3 32 39 36 33 3' 29 27 2; 21 18 •5 13 9 7 33 4' 38 35 33 3' 29 26 12 "9 16 '4 8 34 44 40 38 35 33 3' 28 24 21 >7 ;i i? 8 35 46 43 40 37 35 33 29 »5 2» »9 9 2 36 49 45 42 39 37 35 3' 27 23 20 17 12 9 4 37 Jl. 48 45 4- 39 37 33 28 24 21 _lL 12 10 -JL — -^ -w 55 5' 47 44 4" 39 35 30 26 22 »9 «3 11 39 57 53 5° 46 43 41 36 3' 27 23 20 14 II 2 1 C 1 40 60 56 52 49 46 43 38 33 29 24 21 '4 12 41 63 59 55 51 48 45 40 35 3° »5 22 >S 12 42 67 62 57 54 5° 47 42 36 32 27 23 16 >3 43 70 65 60 56 53 50 44 38 33 28 24 21 17 14 44 73 68 63 59 5; 52 46 40 35 29 25 17 •4 45 76 7> 66 62 S8 54 49 42 36 3" 26 18 •5 46 80 74 69 64 60 W 5' 43 38 27 '9 »5 47 83 77 71 67 63 59 53 45 40 33 29 16 7 3 -JL- ^iT 87 81 75 70 66 62 55 47 4> IV 30 TT 17 49 9' 84 78 73 08 64 58 49 43 36 3' 22 18 g 50 94 87 81 76 7' 67 60 5- 45 38 32 23 18 51 98 9' 85 79 74 70 62 53 47 39 34 24 '9 52 95 88 82 77 73 65 56 48 35 24 53 106 9S 9' 85 80 75 67 58 5° 42 36 2; 21 54 110 102 95 89 83 78 70 60 52 44 38 26 21 5.1 114 ,06 98 92 86 8i 72 62 54 46 39 27 22 56 118 95 89 84 75 64 s6 47 4. 28 23 57 123 III 106 99 93 87 78 67 58 49 Jl. ^i. a4 '° _5_ -w >»7 118 109 102 96 90 81 "!r ^60 1 s, 1^ 21; 5 i 59 ■3' 122 "3 106 99 93 83 62 53 ts 39 3' 25 5 ' «0 136 126 "7 .09 103 97 86 74 64 54 47 40 33 26 6 ; 1 ! sub. A sub. ^. ~r ~rrr 1 1 180° 120° 110° 100- 90° TABLE o', 695 CORRECTION OF THK GRKKNWICII MEAN TIME FOU THE 2d difference OF THE LUNAR DISTAKCE ill Interval Hi Interval 1 O" 1" 0'' 1 1. o" 10 20 30 40 o" lo"" '2n 30 o'"| 10 20 30 40 .,T 0"' 10 20" SO 6 12 18 24 30 36 42 48 64 o> C 3 3 » + 4 5 1 6 7 7 7 I' 3 3 4 1 7 9 '3 3 4 1 7 '4 '5 ■ g '9 1' I I 8 9 '4 '5 17 ig >9 »3 3 I 8 '3 -^ 18 '9 »3 i; .9 4 It 77" 2« 4 6 9 ■3 '5 >7 18 20 24 26 28 29 3' 33 2« 4 6 7 9 '4 '5 17 114 120 120 132 138 144 150 15G 1G2 o" 8 9 9 9 "3 13 14 '4 •4 .4- >5 16 17 "9 ^3 24 »4 11 26 27 20' ^3 -4 ^s. 17 28 29 3° 3> 3^ 33 34 11 37 .4- 26 27 28 30 3' 3» 33 37 39 40 4' 43 44 28- 30 3> 33 1^ 37 39 4^ 42 43 tl 48 49 5' 52 54 31' 3^ It 37 39 40 42 44 45 47 49 50 5^ 53 55 «7 58 It' 37 39 4' 43 44 46 li 50 5> 53 55 57 5i* 60 62 64 35- 37 39 40 42 44 47 48 5^ 53 55 57 59 61 ^' 64 66 3 5" 3' 39 4' 45 47 4« 52 6c 62 ^^ 67 «iO 66 72 78 84 90 •M 102 108 >9 22 24 26 28 30 3=^ 33 168 174 1«0 1»6 I!)2 I'm 204 210 211; I .-J m 40 30 20 10 o"" 50- 40 30 0^ 50 40 30" 20 10 o"" 50 40 30 sM 2h ; ih 3" 2- 1" Interval Interval TABLK 58 ERROR OF THE SHI "S PLACE IN NAUTICAL MILES, | AND OF THE LONG. IN TIME, Ci)rre9|Hinding to an Error of 1' in the Lunar ■"— 1 •^nCr- Change Latitude Error of NBut.Alm. 3 hours 0° 10° 20" 30° j 40° 50° j 60° 70° 80° Time. 2218 I "48' mil. 2S ^5 "23 ,nil 19 "'6 12 4 I 40 I 45 26 26 »4 22 17 •3 I 44 2407 I 42 27 27 13 17 '3 5 . 48 2596 > 39 28 »7 26 14 18 >4 5 I 52 2685 > 37 29 28 25 19 '4 5 ■ 56 ' 34 30 29 26 >9 '5 5 2962 » 3> T 30 27 20 >5 5 1 4 3103 1 28 3* 31 28 21 16 5 2 8 3259 1 25 33 3» 28 21 ■ 6 6 2 12 3415 1 12 34 33 19 17 6 2 16 8622 I 20 35 34 22 17 6 2 20 S«88 I 17 36 35 31 23 18 6 2 24 s«eo I 14 37 36 32 24' .8 6 2 28 I 11 38 37 33 »9 14 ] 19 »3 7 1 3» TABLE 59 ( AMPLITUDES Lit DecLiyATioK 0° 1° >]3.r-o 5° 6" 7° ■&" 9° 10° 11° ..° 13° 14° l^° ~ ~ „ „ ~7~ ^ ^ „ " „ „ o" 0° l-o 20 30 4-0 50 6-0 7-0 8-0 9-0 lo-o I ro I2-0 13-0 14-0 15-0 10 o i-o 20 3-0 4' 5-' 6-1 7-0 8-1 9' lo-i ir2 I2'2 132 14-2 15-2 15 i-o 2-1 3-' 4^ 5-i 6-2 T-i 8-3 9*3 10-4 "■4 12-5 '3-5 '4-5. 15-6 20 o I-I 2-1 3-2 4-3 5-3 6-4 TS 8-5 9-6 IO-6 11-7 12-8 ,38 '49 160 25 o VI 2-2 33 4-4 5-5 6-6 ri 8-8 9-9 ii-i 12-4 '3'3 144 '5-5 i6-5 :io o 12 2-3 3-4 4-6 5-8 69 81 9-3 10-3 11-6 12-7 139 150 i6-2 '7-4 32 o 1-2 ^'4 3-5 4-7 5-9 7-1 8-3 95 IO-6 ii'S 13-0 14-2 ■5-4 i6-6 .7-8 34 o 1-2 2-4 3-6 4-8 6-0 7-2 84 9-7 IO-8 I2-I 13-3 H'S iS-7 17-0 i8-2 35 o 11 1-4 3-7 49 61 7-3 8-5 9-8 no 12-2 '3-5 '4-7 •5-9 17-2 i8-4 3r; o 1-2 21L 3'7 4'9 6-2 7-4 8-7 -O. III 12-4 136 14-9 161 '7-4 i8-7 W ~^ 1-2 2-5 3-7 5-0 6-3 7-5 8-8 II-3 12-6 13-8 .5-. i6-4 17-6 .8-9 3il o ■■3 »-5 3-8 5-' 6-3 7-6 8-9 IO-2 "•4 12-7 14-0 >5-3 166 '79 .9-2 39 o 2-6 3-*! 5» 6-4 7'7 90 10-3 11-6 12-9 .4-2 '5-5 i6-8 .8-, 19-4 40 o ■•3 2-6 39 5'^ 6-5 7'8 91 10-5 II-8 131 14-4 '5-7 17-1 i8-4 19-7 41 o ■■3 2-6 4-0 5-3 6-6 8-0 9-3 IO-6 12-0 '3'3 14-6 i6-o >7-3 18-7 20-0 42 o "■3 2-7 4-0 5-4 6-7 8-1 9-4 IO-8 I2-I 13-5 14-8 l6-2 .7-6 190 20-4 43 o 2"7 4'' 5-5 6-8 8-2 9-6 no 12-3 13-7 15-1 'f5 17-9 '93 20-7 44 o ]-4 2-8 4-2 5-6 7-0 8-3 97 iri 12-6 14-0 ■5-4 i6-8 i8-2 ,96 2I-I 45 o ''4 2-8 4-2 5-7 7.. 8-5 9;9 II-3 12-8 14-2 15-6 17-1 185 20-0 21-5 46 o 1-4 29 4' 3 5-8 7'^ 8-6 II-5 130 '4-5 '5-9 17'4 JlJL 20-4 2. -9 47 "o~ ■■4 2-9 4'4 5-S 7-3 8-8 IO-3 '3-3 '4-7 162 'y7 ■9-3 20-8 48 o i'5 3-0 4' 5 60 7'5 9-0 10-5 I2-0 >3-5 15-0 166 181 '95 21-2 22-7 49 o '■5 3-0 4-6 61 7-6 g-2 10-7 12-2 13-8 '5-3 169 V 21-6 j 23-2 1 50 o J-5 3-' 4'7 6-2 7-8 9-3 10-9 12-5 14- 1 >5-7 ■7-3 189 20-5 22-11 23-7 1 51 o 3'^ 48 6-4 8-0 9-6 I2S 14-4 i6-o 17-6 19-3 209 22-6 24-3 52 o 1-6 3-3 49 6-5 81 9'7 11-4 131 14-7 i6-4 i8-o 19-7 214 23-1 24-9 53 o 1-6 3'3 5-0 6-7 8-3 11-7 '3'4 15-1 i6-8 .8-5 20-2 219 I3"7 = 5-5 54 o '•7 3 "4 5'' 6-8 8-5 10-2 '3'7 •5-4 17-2 .8-9 20-7 22-5 24-3 26-1 55 o 1-7 3'5 5-1 7-0 8-7 10-5 12-3 14-0 ■5-8 ,7-6 19-4 21-2 23- I 24-9 26-8 56 o 1-8 3-6 1 5-4 7'^ 9-° IO-7 12-6 14-4 l6-2 i8-i; 19-9 21-8 25:1 27-6 57 ~ 1-8 3-7 5-5 7"4 9-2 II-l 12-9 14-8 i6-7 .8-3 20-5 22-4 24-4 26-4 28-4 58 o 1-9 3"8 5-7 7-6 9-5 1 1-4 '3-3 15-2 17-2 19-1 2I-I ^'0 251 27-2 29-2 59 o '•9 3-8 5'8 7-8 9'7 117 '3"7 >5-7 17-7 19-7 23-8 259 28-0 30-2 60 o 4-0 60 80 14-1 162 i8-2 20-3 246 26-7 28-9 3 1-2 61 c 21 4'' 6-2 8-3 10-3 12-5 .4-6 i6-7 i8-S 25-4 27-6 29-9 32-2 62 c 21 4'3 6-4 8-5 IO-7 12-9 151 17-3 ■9-4 21-9 23-9 263 28-5 310 33-4 63 o 2-2 4-5 6-7 8-8 ii-i '34 15-6 17-9 24-8 27-3 29-6 32-2 34-7 64 o 1-3 4-6 69 9' ii-c 13-9 l6-2 iS-s 20-9 23-3 25-7 28-3 30-9 33-5 36-2 65 ° 2-4 4-8 T' 9 5|..-9 144 i6-8 .9-3 i -.-7 24-2 268 29-5 ill 349 37-8 TABLE 59 A CORRECTION OF THE AMPMTUDi: OBSERVED ON THE HORIZON, FOR THE EFFECT OF BErn„CTIO.V. (Heiglit of the Eve, 16 Ceet.) I.at. — 1 0° 10° 1 15° I 18° [20° 23°l24°| 10 211 30 40 60 55 60 6:. \ 3 5 7 9 1 I , 3 5 9 4 0° 0-. 0-2 0-3 0° 01 0-3 °7 0° 0° o-i 0-3 0-4 0-9 '•3 ■■7 \ 3 5 8 8 3 5 8 9 TABLE 59 AMPLITUDES 1 Lat. 19' Declination | '«- ifiil I7^'I74"J I8°|i«i° 195° 20° 1 201° 21° 1 211° 2r 22.° •.•3°(23J°| 1 1 1 „ „ g . ^ ^ l6-5l 17-0 I7'5 iSo 1X-5 .9-0 >9-3 »o-o 20-5 21-0 2. -5 22-0 22-, 23-0 23-5 10 lb-2 16-71 17-3 .7SI.8-3 .8-8 .9-3 .9-9 20-3 20-8 2.-3 1.-8 22-3 22-9 23-4 23-9 1.1 «7-'|i7-7 .8-1 .8-7 19-2 -9-7 202 20-8 2.-3 21-8 22-3 21-8 23-3 23-9 24-3 I7-I .7-6.8-. ■ 8-7 19-2 '9-7 20-3 20-8 2.-3 2. -9 22-4 22-9 23-3 24-0 24-b 2,-. -'4 I7-7;'8-3|'!i-8 ■9-4 .99 20-5 22-5 22-7 23-3 23-8 24-4 24-6 III 26-1 :ki .8-6 19-. 19-7 20-1 20-9 2. -5 22-. 22-7 23-3 23-8 244 25-0 2,-b 2b-2 27'4 32 .90 19-6, 202 20-i 21--J 22-0 22-6 23-2 23-8 24-4 25-0 2,-6 26-8 27> 23-0 ;u 19-+ lO-O 20'6 ai-3 2. -9 22-5 23-. 23-7 24-4 25-0 2,-6 26-2 26-8 27-, 28-1 28-7 .9-b 20- 3I 20-9 2.-S 22-2 22-8 23-4 24-0 24-7 23-3 25-9 27-2 27-8 28-, 29-1 I9-q| 10-51 21-2 2.-8 22-4 23-. 23-7 24-4 2 = -o 25-6 2b-3 26-9 27-6 28-9 29-5 37 20-I 20-« 2. -51 22'. 22-8 ^3-4 24-0 ^4-7 25-3|26-o 26-7 27-3 28-0 28-6 29-3 29-9 *t 20-5 2.-I 2.-8,22-4 23-. i3'7 24-4 25-1 25-7 1 26-4 27-0 277 28-4 29-0 297 303 3!l 20-8 21-4 2Z-, 122-8 13-4 24-. 24- X ^3-4 26-. 26-8 27-3 28-, 28-8 29-, 302 3C-8 21-1 21-8 22-423-, 23-8 «4-^ 25-. 25-8 26-5 27-2 27-9 29-3 30-0 3°7; 3'-3| 41 21-4 22-. 22-8 i3-S 2V2 24- b ^3-3 26-2 269 ! 27-6 28-3 29-0 29-8 30-, 3.-2:3.-8i 42 22-5 23-2 23-S 24-6 iS-3 26-0 2b-7 27-4(28-. 28-8 29-5 30-3 3>-° 3. -7 32-4 22-1 23-b 24-1 25-0 25-7 26-4 27-. 27-8 28-6 29-3 30-1 30-8 31-5 32-3 33-c 22-5 ^r^ 24-0 24-7 25-6 2b-2 2b-9 27-b 28-4 29-1 29-8 30-0 3 ■•4 32-1 329 33-b 2Z-9 13-7 24-4 25-2 25-9 2b-7 27-4 28-2 28-9 29-7 30-4 3.-2 32-0 32-8 33-3 34-3 23-^ 24-1 2,-b 27-2 ^7-9 z8-7 29-5 1 30-3 31-0 3. -8 32-6 ^3-4 34-2 35-0 47 23-8 14-6 ^S-4 26-2 26-9 ^7-7 28-5 29-3 30-. i 30-9 3>7 32-3 33-3 34- > 34-9 337 »4-- 25- 1 2V9 26-7 ^7-5 28-3 29-1 29-9 30-7 31-6 32-4 33-2 34-0 34-8 337 36-5 25-6 26-, 27-1 28-1 28-9 29-7 306 31-4 32-3 33-> 33-9 34-8 337 3b-, 37-4 ir-i 27-0 27-8 29-6 30-4 3'-3 32-. 33-0 33-9 34-8 33-6 36-3 37-4 38-3 Si 17-7 28-, 29-4 30-3 3I-I 32-0 32-9 1 33-8 34-7 33-6 3b-, 37-3 38-4 39-3 b2 26-b i7-S 28-1 29-2 3.-0 31-9 3Z-8 33-7 1 34-7 33-6 36-3 37-3 38-4 39-4 40-3 27-1 28-2 29-. 30-0 30-9 3.-8 32-7 33-7 34-6 1 35-6 36-3 37-3 38-3 39-5 40-5 '4.-41 »4 2X-9 29-8 30-8 31-7 32-7 3 3-6 34-b 35-6 36-b 37-6 38-fa 39-6 40-6 4'7 42-6 bo .8-7 29-7 ,o-6 3.6 32-6 33-6 34-6 33-6 36-b 37-b 38-7 39-7 1 40-8. 4>-8 42-9 44-0 1 29-5 30-5 3'-5 32-5 33-5 34-6 33-6 36-6 37-7 38-8 39-8 40-9 42-1 43-2 44'3 45-4 67 3°-4 3'-4 3^*5 33-S 34- ■; 35-6J36-7 37-8 38-9 40-0 41-. 42-3 43-4 44-6 4,-8 47-0 bti 3. -3 32-4 33-5 34-t' 35-7 368 37-9 39-0 40-2 4'-7 42-3 43-8 4,-o 46-2 47'5 487 3^-! 33'S 34-6 33-7 3b-S 38-0 39-2 40-4 4.-6 42-8 44-1 43-4 4b- 7 48-0 49-3 ,c-6 3V4 34-6 3V8 37-0 38-2 39-4 40-6 4. -9 43'2 445 45-8 47'. 48-3 49-9 ,2-8 34-6 3S-8 37-. 38V 39-6 +0-S 4»-2 43-5 44-8 46-2 47-7 49- . 50-6 ,2-. 337 55-2 3V9 37-1 38-; 39-8 41-2 4^-3 43-9 45-3 46-8 48-2 49-8 31-3 ,2-9 ,4-6 ,8-0 17-4 38-7 40-1 42-9 44-3 45-8 47-3 48-8 SO- 5 33-8 33-6 37'4 394 6.-, 64 „-o 40-4 4.8 43-3 44-8 46-4 48-0 496 3'-3 53-0 54-8 36-7 38-7 608 63-0 6,-3 4C-7 42-2 43-8 45-4 47-0 48-7 50-4 52-2 54-0 5b-o 58-0 60-. 62-4 64-9 70-4 TABLE 59 A CORKKCTION OF Illi; A M I'Mll'DK OBSKKVKl) (IN TIIK HdRlZciN, FOB THE ErrECT or hefhactiom. (Height of the Kyp, 16 feet.) Ut. .W.._ 1 0' 10"! 16° in° 20°|22° 23° 24° 0° o°| 0° 0° o" 0" qO 0° 10 .0-1 0-. o-i o-i 1 O'l 30 0-3 0-3 0-3 •» °'% 3fl 3 ! o'3 03 04 0'4 3 ti 40 3I0-7 °7 0-7 0-8 g hi 60 66 ] 0-9 1 0-9 .-2 j .-3 '■4l 'i I 4 9 1 > 4 fi98 DECLINATION OF THE SUN, for the Year 1901, At Apparent Noon at Greenwich. Day Jan. 1 2\ 28 -2 22 S7 1 3 22 52 4 2246 5 22 40 6 22 33 7 8 22 18 9 22 lO 10 22 I i 11 21 52 12 2. 43 13 2' 33 14 21 23 15 21 12 16 21 I 17 20 49 18 20 37 19 20 25 20 20 12 21 '9 59 22 19 46 j ys iq 32 24 19 18 'Jo '9 3 -2b 18 49 '27 \PA 28 29 18 2 30 17 46 31 17 29 Mar. 16 55 16 38 16 20 16 2 15 44 15 25 '5 I 14 48 >3 49 13 29 13 9 12 48 12 28 12 7 II 46 II 2S 10 42 10 20 9 58 9 36 9 14 8 52 8 29 8 7 ; 7 44^ 7 21 6 58 ;6 35 [6 12 S 49 5 26 5 2 4 39 |4 IS_ 3 52 3 29 3 5 2 41 2 18 ' 54 I 30 I 6 o 43 o 19S o~5N o 28 52 1 16 « 39 2 3 2 26 2 50 3 13 3 37 April 423N 4 46 5 9 S 32 5 55 6 18 6 40 7 3 7 25 7 48 8 10 832 8 54 9 15 9 37 9 58 10 20 10 41 11 43 12 3 12 23 12 43 13 3 13 23 13 42 14 I 14 20 14 39 Ai.g Sept. 8 9N 8 27N 7 54 8 5 7 38 7 43 ; 22 7 21 7 6 6 59 6 so 6 37 6 34 6 IS 6 17 5 52 6 o 5 29 5 42 5 7^ 5 25 4 44 S 7 4 21 4 49 4 31 4 12 3 53 3 34 3 15 3 58 3 35 3 12 2 49 9 53 9 32 8 49 I 16 o 53" o 29 o 6N o 17S 41 1 4 I 27 I 51 3 It 3 24 3 47 4 II 4 34 4 57 5 20 5 43 6 6 6 29 6 51 7 14 7 37 7 59 8 21 8 44 9 6 9 28 9 5c lo il_ 10 33 10 54 11 15 II 36 11 57 12 18 12 39 12 59 13 19 13 39 13 59 14 37 [21 5» 14 56 22 3 15 15 22 12 15 33 22 20 15 52 22 27 16 10 I 22 34 16 27 I 22 41 16 45 22 47 J 17 19 17 35 17 52 18 8 18 23 1838 18 53 19 8 19 23 19 36 20 28 20 41 20 52 21 4 21 IS 21 25 21 35 22 S3 22 59 23 8 23 12 23 15 23 18 23 21 23 23 23 25 23 26 23 27 23 26 23 25 23 23 23 21 23 19 23 16 23 12 23 8 15 II 15 29 15 46 16 54 17 II 17^7 17 42 17 58 13 18 57 19 II 19 24 19 37 ■ 9 50 20 15 20 27 20 39 20 50 21 I 21 II 21 21 21 31 22 35 22 41 22 47 22 53 2 2 58 23 3 23 7 _ ,23 II 28 23 14 23 17 23 20 23 22 23 24 23 25 23 26 23^r 23 27 23 27 23 26 23 25 23 23 23 22 23 19 23 17 23 13 2310N 23 6 23 2 22 57 22 52 22 46 22 40 22 34 22 27 22 20 22 I2~ 22 5 21 56 21 48 21 39 20 59 20 48 25"37 20 25 20 14 20 I 19 49 19 36 19 23 19 9 18 55 iS 41 18 27 .°8iiN'8°32N| 17 57 8 10 17 42 7 49 17 2b 7 27 17 10 7 4 16 54 6 42 16 38 6 20 16 21 5 57 16 4 5 35 15 47 5 12 15 29 i 4 49 15 II 4 27 14 53 4 4 14 35 3 ■»■ 14 17 3 18 13 58 2 55 13 39 ^ 31 13 20 2 8 13 I I 45 12 41 I 22 12 21 0,8 12 I 35 II 41 12N II 21 12S II ° 35 10 40 58 10 19 I 22 9 58 I 45 9 37 2 9 15 2 32 K 54 13S 21 43-; 33 21 52 52 1 22 I 10 22 10 18 35 18 50 19 5 19 19 1933 1 19 47 1 20 20 13 20 25 20 38 20 49 21 I 21 12 21 23 21 33 22 30 22 46 22 S- 22 57 23 - 23 7 23 II 23 IS 23 18 23 20 23 23 23 24 23 26 23 27 23 27 23 27 23 26 23 25 23 24 23 22 23 19 23 16 23 13 DECLINATION OV THE SUN. fo R THK \ (All 190 J» At Apparent Noon at Greenwich. n., w Feb. Mar. April May June July Aug. Sept Oct. Nov. Dec. 14 9S. 21 40S. 45s. 17 21S. 7 5SS. 4 12N. 4 48J*- 21 56N. 23 I'.N. 18 16N. I 37 N. 2 S^ •2 23 17 4 7 33 4 35 IS 6 22 4 23 7 7 10 4 58 IS 24 22 12 23 3 6 47 5 21 lis 42 22 20 122 s8 18 I 8 16 3 13 14 28 21 SO ;i 22 55 16 47 1746 7 54 336 14 47 '21 50 4 22 49 16 29 17 30 7 32 4 IS 6 22 S 5 23 43 16 II 6 24 s 44 16 22 27 22 S3 17 14 7 10 4 23 15 25 22 If. 6 22 36 '5 53 60 6 7 16 17 22 34 22 48 .658 6 48 446 15 43 22 24 7 22 29 ■5 35 5 37 1 6 29 16 34 22 40 22 42 16 42 6 25 5 9 16 I 22 31 H 22 22 .5 '6 5 14 ; 6 52 16 50 22 46 22 35 16 25 6 3 5 32 16 19 122 ',." 9 22 14 ■4 57 4 SI 7 14 17 7 22 52 22 29 16 8 5 40 5 55 16 37 122 44 Id 22 6 1438 4 27 7 37 17 ^3_ 22 S7_ 22 22 IS SI 5 18 6 18 16 SJ_|22 50 11 21 57 14 19 4 4 7 59 |i7 39 23 2 22 14 IS 33 4 55 6 4t 17 11 I22 56 li ;i 47 «3 59 3 40 8 21 17 54 23 6 22 6 IS .6 4 32 7 3 17 27 23 1 11 .1 38 '3 39 3 17 8 43 18 9 23 ID 21 58 1458 4 9 7 26 17 44 '23 6 14 2. 28 •3 >9 2 S3 ,95 18 24 23 13 21 50 14 40 346 748 18 23 10 15 2. .7 12 59 2 29 ! 9 26 18 39 23 16 21 41 14 21 3 23 8 II 18 16 '23 14 16 21 6 1238 2 6 9 48 18 S3 23 19 21 32 14 3 3 833 18 31 :23 17 IT 20 55 12 17 I 4* 10 9 19 7 23 21 21 22 13 44 2 37 8 55 18 46 123 20 IS 20 43 II 56 I i8 10 30 19 21 23 23 21 12 13 25 2 14 9 17 19 I 123 22 19 20 31 II 35 55 10 SI 19 34 23 25 21 2 13 5 I SI 9 39 19 16 23 24 20 20 19 u 14 31 II 12 19 47 23 26 20 51 12 46 J J7_ 10 I 19 30 23 26 sr 20 6 ■20 ,g 53 10 53 7S- II 33 20 2327 2040 12 26 I 4 10 23 19 43 23 26 10 31 17N. II 53 20 12 23 27 20 28 12 6 41 10 44 19 57 i23 27 •21 ,9 39 •24 19 2S 10 9 40 12 14 20 24 23 27 20 16 II 46 17N II 5 20 10 ;23 27 9 47 14 12 34 20 36 23 26 20 4 II 26 6S. II 26 20 23 23 20 •25 .9 .. 9 25 I 28 12 54 20 47 23 2S ,19 52 II 5 30 II 47 20 35 23 25 26 18 56 2 3 I 51 13 13 20 58 23 24 19 39 10 45 53 12 8 20 47 23 24 27 18 41 8 40 2 15 13 33 21 9 23 22 19 26 10 24 I i6 12 29 20 58 23 22 '28 18 26 8 18S. 2 38 13 52 21 19 23 20 19 13 10 3 I 40 12 49 21 9 23 20 •29 '18 10 3 2 14 II 21 29 23 17 18 59 9 42 2 3 13 9 21 20 23 17 30 '17 54 3 25 14 30 21 38 23 I4N. 18 45 9 20 2 26'j. 13 29 21 30S. 23 14 31 |l7 38S- 3 48 V. N. 21 47N-I ,18 30N 859N 13 49 S. 23 loS. DrcUNATION OK THE SuN, VO K 1904. 1 23 6S. 17 25S. 7 38S. I 29S.1l 2N.22 iN'23 8N. Ts 5"n^ 82.N 3 78. 14 23S. 21 4.SS. ■2 2J I 17 8 7 15 4 52 IS 20 22 10 23 4 17 49 7 59 3 31 14 42 21 57 .3 22 56 .651 652 S 15 15 38 22 18 22 59 17 34 7 37 3 54 15 I 22 5 4 22 50 i6 iS 6 29 5 38 15 55 22 25 22 54 17 18 7 15 4 17 15 20 22 14 S 22 44 16 16 6 6 61 16 13 22 32 22 49 17 2 6 53 4 40 15 39 22 22 6 22 38 ■558 5 43 6 24 16 30 22 38 22 43 16 46 631 5 3 15 57 22 29 7 22 31 15 39 5 20 6 46 16 46 22 44 22 37 16 29 6 8 S 26 16 15 22 36 8 22 24 15 21 4 56 79 17 3 22 50 22 30 16 12 546 S 49 16 32 '22 43 9 22 16 15 2 4 33 7 3' 17 19 22 55 22 23 15 55 S 23 6 12 16 so 22 40 HI 22 8 14 43 4 9 7 54 17 35 23 22 16 15 38 5 I 6 35 17 7 '22 55 11 21 59" 14 23 346 ' 8 16 17 so 23 s 22 8 IS 20 438^^ 658 .7^r"i3'o l-J 2. 50 14 4 3 22 8 38 18 6 23 9 22 15 2 4 IS 7 20 17 40 23 5 13 21 40 ■3 44 2 59 90 18 21 23 12 21 51 14 44 3 52 7 43 17 56 23 .) u 21 30 13 24 2 35 9 21 18 35 23 16 21 43 14 26 3 29 8 5 18 12 ,23 13 I.') 21 20 13 4 2 II 9 43 18 50 23 19 21 34 14 7 3 6 8 28 18 27 23 H. ir. 21 9 12 43 I 48 10 4 19 4 23 21 21 24 1348 2 43 8 so 18 43 23 K. 17 2058 12 22 I 24 10 25 19 18 23 23 21 14 ■3 29 2 20 9 12 iS 58 23 22 18 2046 12 I 10 10 46 19 31 23 25 21 4 13 10 I 56 9 34 19 12 23 24 19 20 34 II 40 37 117 19 44 23 26 20 S3 12 5' « 33 956 19 26 23 25 '20 20 22 II 19 13.S. II 28 19 57 23 27 20 42 '.2 3l_ I 10 10 17 19 40 ,23 2(. '•2T 20 9 10 58 1 1 .V. 1 1 48 ' 20 9 ^23 27 20 31 12 II 046 10 39 19 54 23 27 22 .956 10 36 35 12 9 20 21 23 27 20 19 11 SI 23N 20 7 23 27 'J I 19 42 10 14 58 12 29 20 33 23 26 20 7 II 31 II 21 20 19 23 27 ■2t 10 28 9 52 1 22 12 49 20 44 23 25 .9 55 II 10 24 S. II 42 20 32 [23 2^ 19 14 9 30 I 45 13 8 20 55 23 24 19 42 10 50 47 ■2 3 20 44 23 21; J'i 10 9 8 29 13 28 21 6 23 22 19 29 10 29 12 24 20 55 23 23 IS 45 8 46 2 33 13 47 21 16 2X 20 119 16 10 8 I 34 12 44 21 6 23 20 •2H IS 29 823 2 56 14 6 21 26 23 18 19 2 9 47 I 57 13 4 21 17 23 IS 29 rS 14 8 OS 3 19 14 25 21 36 23 15 18 48 926 2 21 13 24 21 28 23 IS 30 17 58 3 4i 14 44^'-2l 45 23 12.\. iS 34 ' 9 4 2 44 S. 13 44 21 38S. 2i II 3 1 17 1-' 4 '..V 21 vi^' "^ '0^' X ,,iN M 1"^ -■' '-^ TABLE 60 A CORRECTION OF THE SUN'S DECLINATION, .n Table 60, ' FOE THE YEARS FOLLOWING 1901, 1902, 1903, 1904. — vlr Following Years. Given Years. Following Years. 1901 1905 1909 1913 1917 1921 192.5 1901 190,5 1909 1913 1917 1921 192.5 1902 1906 1910 1914 1918 ; 1922 1926 1902 1906 1910 1914 1 '.< 1 8 1922 19-26 190S 1907 1911 191.T 1919 ' 1923 1927 1903 1907 1911 I9I5 1919 1923 1927 1904 1908 1B12 1916 ^ 1924 1928 1904 1908 1912 1916 1920 1924 19-.'8 s«b. sub. sub. suh. tvh. suh. suh. svjh. Sid). svh. suh. suh J»n. 1 o'l o'-3 o'-4 o'-6 o'7 o'-9 June 30 o'-l 0'-3 o'-4 o'-6 o'7 o'-8 10 0-2 o-S 08 10 \\ 1-6 July 10 0-2 O-S 0-8 i-o 1-3 1-6 ■20 04 07 II 1-4 2-2 20 04 0-7 II 1-4 1-8 2-2 30 05 10 «S 20 2-5 3-0 30 o-S i-o IS 2-0 2-S 30 Feb. 10 06 II 1-6 2-2 2-8 3-4 Aug. 10 o-S II 17 2-3 2-S 3-4 20 06 1-2 1-9 2-5 3-" 37 20 0-6 1-3 1-9 2-S 3-2 3-9 28 07 •■3 20 2-6 3-3 4-0 30 07 ••4 2-0 27 3-4 4-1 Mar. 10 07 I 4 2-1 2-8 3S 4-2 Sept. 10 07 1-4 2-1 2-8 3-S 4-2 201 07 I 4 2-1 2-8 3-6 4 3 20 0-7 1-4 2-1 2-9 3-6 4-3 \a,. add oM add add add add add add add add add 30 j 07 1 -4 21 2-8 3-5 4-2 30 0-7 1-4 2-1 2-8 3S ' 4-2 Apr. 10, 07 1-4 21 27 3-4 41 Oct. 10 0-7 1-4 2-0 27 3-4 4-1 20 0-5 >;3 1-9 2-5 3-2 3-9 20 0-6 '-3 1-9 2-5 ^'l 3 9 SO 0-6 17 23 2-8 3-4 30 o-S I-I 1-6 2-2 2-8 3J May 10 o-S 09 IS 2-S 3° Nov. 10 °-s 10 1-4 1-9 2-4 2-8 20 04 08 1-2 1-6 1-9 23 20 0-4 0-8 1-2 >S 2-0 2-S 30 0-3 0-5 08 10 '■4 17 30 0-2 o-S 0-7 I-o 1-3 1-6 June 10 0-2 0-3 04 O-S 0-7 09 Dec. 10 0-2 0-3 0-4 0-6 07 0-8 20 o-o o-o O'l 20 O-O 0-0 01 o-i 0-2 0-3 suh. ,v«/). snh. Vh. \ °",', ^nh. ..»A. !-uh. $„h. mh. suh. snh. 30 01 03 0-4 06 07 0-8 30 °' 0-3 0-4 06 07 0-9 TABLE 61 SIUKUKAL TIME, for ihk Y«ar 1901, At Mean Noon at Greenwich. Da> Jan. Fel). h m h ai Mar. April h m h m May June h m h m July Aug. Sept. Oct. Nov. Dec. h m h m h m h m h m h m 1 184. -8 2044 22 34-4 36-6 234-9 4 37-1 635-4 837-6 1039-8 1238-1 '4 40-3 16 38-6 2 18457 2047-9 22 38-3 040-5 238-8441 6 39-3 841-5 1043-8 1242 14 44-3' 16 42-S| :' 18 49-7! 20 51 -9 22 42-3 44-5 2 42-8 4 45 643-3 845-5 1047-71 1246 14 48-2; 16 46-S 4 iS 53-6! 20 55-8 22 46-2 48-4 246-7 448-9 647-2I 849-4 10 51-6 1249-9 14 52-1 16 50-4^ 5 1857-5 205^8 2250-2 052-4 2 50-6 452-9 651-1 853-4 1055-6 12 53-9 14 56-1 16 54-3 6 19 1-5 21 3-7 22 54-1 056-3 2 54-6 4 56-8 6 55-1 857-3 1059-5 12 57-8 IS 16 58 -3 7 19 5-4 21 7-6 22 58 I 0-3 2 58-S 5 0-8 6 59 9 1-3; II 35 13 1-7; «5 4 .7 2-2 8 19 94' 21 I I -6 23 2 1 I 4-2 3 2-5 5 4-7 7 3 9 5-2 II 7-4; 13 s-7, IS 7-9 17 6-2| 9 19 lyy 21 15-5 23 5-9 I 8-1 3 6-4 5 8-67 6-9 9 911111-413 9-6 15 11-9: 17 lo-il 10 19 17-3 21 19-5 23 9-9 I 12-1 3 10-4 5 12-6 7 10-9 9 i3-ii II 15-3; 13 136 15 15-8; 17 i4-i| 1 1 1921-2 21 23-4 23 13-8 I 16 3 14-3 5 i6-5'> 14-8 917 II 19-2 13 17-5 15 19-7 17 18 1 \'J 19 25-1, 21 274 23 17-7 I 20 3 i8-2 5 20-5 7 i8-7 921 II 23-2, 13 21-5 1523-7 1722 l:i 19 29-1 21 3'-3, 23 21-7 1 23-9 3 22-2 5 24-4; 7 22-7 9 24-9 II 27-1 13 254 15 276 17 25-9 H ■9 33 21 35-2 2325-6 I 27-9 3 26-1 5 28-3 7 26-6 9 28-8 II 3I-I 13 29-3 15 31-6 17 29-8 15 1937 21 39-2 23 29-6 I 31 -8 3 30-1 5 32-3, 7 30-6 932-8, II 35 1333-3 15 35-5 1733-8 16 1940-9 21 43-1 23 33-5 I 35-7 3 34 536-2734-51 936-71 II 39 1 1337-2 1539-4; 17 37-7 17 1944-S 21 471 23 37-5 I 39-7 338 1540-2738-5 940-7,1142-91341-21543-4,174,-7 18 1948-8 21 51 2341-4 I 43-6 341-9544-1 742-4 944-6, II 46-8 1345-1 1547-3 1745-6 19 1952-7 21 54 23 45-3 I 47-6 345-8 548-1, 746-3; 948-6, II 50-8 1349-1; 15 51-3! 1749-6 '-'0 19 56-7 21 58-9 20 0-6 22 2 -J 2349-3 I 51-5 2353-2 I 55-4 3 49-8 5 52 750-3 952-51 II 54-7 1353 1 1555-2 7 54-2 956-4' II 58-7 13 56-9 15 59-2 ■753-5 17 57-4 3 53-7 555-9 •-'2 20 4-6 22 6-8 23 57-2 I 59-4 3 57-7 5 59-9 7 58-2 10 0-4 12 2-6 14 0-9 16 3-1 .8 ,-4 i!:i 20 8-5' 22 10-7 i-i 2 3-3 4 1-6 6 3-8 8 2-1I 10 4-3 12 6-6 14 4-8 16 7 18 5-3 '.'4 20 12-4 22 14-7 s-i 2 7-3 4 5-6 6 7-8,8 6-ij 10 8-3 12 10-5 14 8-8 16 II 18 9-3 2.5 20 16-4 22 iS-6 9 211-2 4 9-5 6 11-7; 8 10 1 10 12-2 12 14-4 14 127 16 14-9 18 13-2 26 20 20-3 22 22-6 12-9 2 15-2 4 13-4 6 15-7! 8 13-9 10 i6-2 12 1S-4 14 16-7 16 18-9' 18 17-2 27 20 24-3 22 26-5 16-0 2 19-1 4 17-4 6 19-6 8 17-g' 10 20-11 12 22-3 14 20-6 16 22-8 18 2I-I 28 2028-2 2230-4 20-8 2 23 4 21-3 6 23-5' 8 21-8 10 24 12 26-3 14 24-5' 16 268 18 25 29 20 32-2 24-8 2 27 4 25-3 6 27-5 8 25-8^ 10 28 12 30-2; 14 28-5 16 30-7] 18 29 4 29-2 6 31-4 8 29-7 10 31-9 12 34-1 14 32-4 16 34-6 18 32-9 m 20 36-1 28-7 2 30-9 ■M 2040 32-7| 4 33-2 1 8 33-7 1035-9 14 36-4| 1836-9 SlDHKRAI. TlMK, FOR 1902. 1 18 40-8 20 43 1 22 33-4 35-6 2 33-9 4 36-1; 6 34-4] 8 36-6 10 38-9! 12 37-il 14 39-3' 16 37-6 2 18 448 2047 1 22 37-4 39-6 2 37-9 440-1 6 38-4 8 40-6 1042-8 12 41 -I. 14 43-3 16 41 -6 3 IS 48-7 2050-9 2241-3 0435 241-8 444 1642-3 844-51046-71245 11447-21645-5 4 1852-62054-92245-2047-5245-7448 1646-2^ 848-51050-71249 1 14 5' -2 1649-5 5 18 56-6 20 588 22 49-2 51-4 2 49-7 4 51-9 6 50-2 8 52-4 10 54-6 12 529 14 55-ij 16 53-4 6 19 0-5 21 2-7 22 53-1 55-4 2 53-6 4 55S 6 54-1 8 56-3 10 58-6 12 56-8 .4 59-> >6 57-3 7 19 452' 6-72257-1059-3257-6459-8658-1 9 0-3 11 2-5 13 0-8 15 3 17 1-3 8 19 8-4 21 10-6 23 I |i 3-23 1-55 3-77 2 9 4-2 II 6-513 4-7| 15 6-917 5-2 9 19 12-3 21 14-6 23 5 I 7-2' 3 5-5 5 77 7 6 9 8-2 II 10-4; 13 8-7I 15 10-9I 17 9-2 10 19 16-3 21 18-5 23 8-9 I ii-i| 3 94 5 11-6 7 99 9 "2-1 II 143, »3 >2-6 15 14-8, 17 I3« n 1920-2 21 22-5 23 12-8 I i5-i: 3 133 5 '5-6 7 13-8, 9 16-1 Ti 18-3' 13 16-6 15 18-8 17 17-1 12 19 24-2 21 26-4 23 16-8 I 19 1 3 17-3 5 '95 7 17 8 9 20 1 II 22-2^ 13 20-5 IS 22-7 17 21 l;! 19 28-1 21 30-3 23 20-7 I 23 i 3 21-2 5 23-4 7 2i-7| 9 239 II 26-2, 13 24-4J 15 26-7| 17 24-9 M 19 32-1 21 34-3 2324-7 I 26-9 3 25-2 5 27-4 7 25-7, 927-9 11 30-1, 13284 15 3o-6| 17 28-9 15 1936 1 21 38-2 23 28-6 I 30-8 329 I 531 3 7 29-6 9 31-8 II 34-r 1332-3 1534-5. 17 32-8 Ifi 19 39-9 21 42-2 23 32-6 I 34-8 3 33-ii 5 353, 7 336, 9 35-8 1 1 38 | 13 36-3' 15 38-5 .7 36-8 17 1943-9 21 46-1 23365 I 38-7 3 37 5 39-2, 7 37-51 9 397 n 4" 9 13402 15424 1740-7 18 1947-S21501 340-4 I 42-7 340-9' 543-2 7414 943-7 II 45-9 '3 44-2J 1546-4 1744-7 1» 1951-82154 ' 2344-4 I 46-6 344-9 5 47i[ 745-4I 9476 II 49-8! 1348 I 15 50-3 1748-6 20 1955-7:2157-92348-3150-5348-81551 749-3, 9 5' -5' II 53-8 1352 15 54-3 17 52-S 2 f 1959-722 1-9 2352-3 I 54-5' 3 52-8, 5-55 7 53-3 9 555' " 577 i3 56 15582 17 56-5 22 20 3-6 22 5-8 23 562 I 58-4 3 56-7; 5 58-9' 7 57-2 9 59-4; 12 i-6[ 13 59-9 16 2-1 18 0-4 2:i 20 7-522 9-8 0-22 2-4' 4 0-7,6 2-98 1-2 10 3-4 12 5-6 14 3-9 16 6-1 18 4-4 24 20 1 1 -5 22 13-7 4-1 2 6-34 4-66 6-8j 8 5-1 10 7-3 12 95 14 7-8 16 10 18 8-3 2.5 20 15-4 22 17-7 8 , 2 10-3' 4 8-5610-88 9 1011-31213-5 14 11-8 16 14 18 12-3 26 20 19-4 22 21-6 12 2 14-2 4 12-5 6 14-7 8 13 10 15-2 12 17-4 14 15-7 16 17-9' 18 i6-2| 27 20 23 3 22 25-5 15-9 2 18-1 4 16-4 6 18-6 8 16-9 10 19-1 12 21-4 14 19-61 16 21-9 18 20-l| 28 20 27-3 22 29-5 19-9 2 22-1 4 20-4 6 22-6' 8 209' 10 23-1 12 25-3 14 23-6, 16 25-8 I824-II 29 20312 02)8226 424-3626-5824-81027 11229-2 14 275 i6 29-7i 1828 no 2035-1, 0277230 428-3630-5828-81031 11233-2 •4 31-5 1633-71 1832 31 20 39-i| 031-7 4322 |8 32-7| 1034-9J 1435-4 |.8 35-^ TABLE Gl SIDKREAL TIME, fok the Yiak 1903, At Mean Noon at Greenwich. Dai .Ian. heb. Mar. April May June July Aug. Sept. Oct. Nov. D.-c. hm hmhmhmhmhm h m h m h m h m h in 1 i8 39-8 20 42-i' 22 32-5! 347I 2 33-o: 4 SS'^' 6 33-5 8357 1037-9 1236-2 1438-4 16 367 2 18 43-8^ 20 46-0 22 36-4^ 38-6 2 36-9 4 39-i! 6 37-4 8 39-6 10 41 -8 12 40-1 1442-3 16 40-6 3 18 477 20 50-0 22 40-3 042-6 2 40-8 4 43-1 6 41-3 843-6 1045-8 12 44-1 1446-3 16 44-6 4 18 517' 2053-9 2244-3 046-5! 2448 4 47-o>45-3 847-5 10497 1248-0 1450-2 16 48-5 5 IS 55-6 20 57-S 22 48-2 50-4: 2 48-7 4 50-9, 6 49-2 8 51-4 10537 12 51-9 14 54-2 16 52-4 6 IS 59-6 21 I -8 22 52-2, 54-4' 2 52-7 4 54-9' 6 53-2 8 55-4 1057-6 12 55-9 1458-1 16 56-4 7 19 3-5 21 57 2256-1 058-3 256-6 4 5S-8| 6 57-1 859-3 ■■ 1-5 1259-8 15 2-1 17 o-j 8 19 7-4 21 9-7 23 o-i I 2-3 3 0-6 5 2-87 I -I 9 3-3 " 55: 13 3-8 15 6-0 17 4-3 9 19 11-4 21 13-6 23 4-0 I 6-23 4-55 6-77 5-0 9 7-2 II 9-4 13 7-7 15 9-9 17 8-2 10 19 15-3 21 17-6 23 7-9 I 10-2 3 8-4 5 107 7 8-9 9 II-2 II 13-4 13 11-7, 15 13-9 17 12-2 11 19 19-3' 21 21-5 23 II -9 I 14-1' 3 12-4 5 14-6 7 12-9 9 15-1 II 17-3 13 15-6 15 17-8 17 16-1 I'.' 19 23-2 21 25-4 23 15-8 I 18-0 3 16-3 5 ■S-5l 7 ■6-8 9 19-0 II 21-3 13 19-5 15 21-8 17 20-0 13 19 27-2, 21 29-4 23 19-8 I 22-0 3 20-3 5 22-5: 7 20-8 923-0 II 252 1323-5 15257 17 24-0 M 1931-1 21 33-3 2323-7 I 25-9 324-2 S 26-4I 7 24-7 9 26-9 II 29-1 13 27-4 15 29-6 17 27-9 1,'; 19 35-0 21 37-3 23 27-7 1 29-9 3 2S-2 5 30-4, 7 28-7 930-9 11 33-1 i3 3>-4 15 33-6 17 31-9 IG 19 39-0, 21 4>-2 23 31-6 I 33-8 3 32-1 5 34-31 7 32-6 9 34-8 II 37-0 1335-3 15 37-5 1735-8 17 19 42-9 21 45-2 23 35-5 I 37-8 3 36-0 5 38-31 7 36-5 9 3S-S II 41-Oj 13 39-3 15 41-5 17 397 18 1946-9 2149-1 2339-5 I 41-7 3 40-0 5 42-2 7 40-5 942-7, II 44-9 13 43-2 15 45-4 17 437 19 19 50-8 21 53-0 23 43-4 I 45-6 3 43-9 5 46-11 7 44-4 946-6 II 48 -g 13 47-1 15 49-4 1747-6 20 19 548^ 21 57-0 23 47-4 I 49-6, 3 47-9 5 50-11 7 48-4 950-6 II 52-S| 13 51-1^ 15 53-3 17 51-6 21 195S-722 0-923513 I 53-5 3 5i-« 5 54-0; 7 52-3 954-5' " 56-7! 13 55-0 15 57-2 17 55^-5 22 20 26 22 4-9 23 55-3 I 57-5 3 55-8 5 58-0 7 56-2 9 58-5 12 0-7 13 59-0 16 1-2 17 59-5 2:! 20 6-6 22 8-S 2359-2 2 1-4 359-7 6 1-98 0-2 10 2-4 12 4-6 14 2-9 16 5-1 18 3-4 24 20 10-5 22 12-7 3-1 2 5-4 4 3-6 6 5-9 8 4-2 10 6-4 12 8-6 14 6-8 16 9-1 18 7-3 25 20 14-5 22 16-7 7-1 2 9-3 4 7-6 6 9-8 8 8-1 10 10-3 12 12-5 14 IO-8, 16 13-0 18 11-3 2f> 20 iS-4 22 20-6 011-02 13-2 4 11-5 6 13-7 8 12-0 10 14-2 12 165 14 14-7, 16 17-0 18 15-2 27 20 22-4 22 246 0150 2 17-2 415-5 6 17-7, 8 16-0 10 1S-2; 12 20-4 14 18-7 16 20-9 18 19-2 2K 20 26-3 22 28-5 1S-9 2 21-1 4 19-4 6 21-6; 8 19-9 10 22-1 12 24-3 14 22-6 16 24-8 18 23-1 29 20 30-2 22-9 2 25-1 4 23-3 6 25-6, 8 23-8 10 26-1 12 2S-3 14 26-6 16 28-8 1S27-1 30 20 34-2! 26-8 2 29-0 4 27-3 6 29-5 8 27-8 10 30-0, 12 32-2 14 30-5' 16 32-7 18 31-0 31 2038-1I 030-7, 4 3'-2| 1 8 31-7, 1034-0, ! 14 34-4 .8 34-9 Sidereal Time, for 1904. , 1838-9 2041-1I 22 35-4,037-7 2 35-9 4 38-2 6 36-4 8 38-7 10 40-9 12 39-2 14 41-4' 16 39-6 2 1842-8: 2045-1 22 39-41041-6 3 39-9 4 42-1 640-4 842-6 1044-8 12 43-ij 1445-3 1643-6 3 1846-8 20490 2243-3 045-5 243-8 446-0^644-3 8 46-5! 10 48-8, 12 47-0 14 49-3 16 47-5 4 1850-7 2052-9 2247-3 049-5 247-S 449-0 648-3 850-5I 10527 1251-0I 1453-2 1651-5 5 1854-7 2056-9 22 51-2 053-4 2 51-7 453-9 6522 8 54-4' 10 566 12 54-9 14 57-2 16 55-4 c 18 58-6, 21 0-8 22 55-2 57-4! 2 55-7 4 57-9 6 56-1 858-4^11 0-6 1258-9 15 i-i 1659-4 7 19 2-5 21 4-8 22591 I 1-3; 2 59-6 5 1-8 7 o-i 9 2-3' II 4-5 13 2-8 15 s-o 17 3-3 8 19 6-5 21 8-7 23 3-0, I 5-3i 3 3-5 5 5-8 7 4-0 9 6-3 II 8-5 13 6-8 IS 9-0 17 7-2 9 19 10-4 21 12-6 23 7-0 I 9-2:3 7-5 5 97 7 8-0 9 IO-2 II 124 13 10-7 15 12-9 17 11-2 10 iq 14-4 21 l6-6 23 10-9 I 13-1 3 I1-4 5 13-6 7 II -9 9 141 11 16-3 13 14-6 15 16-9 17 15-1 11 19 18-3 2r2o-5 23 14-9 I 17-1 3 15-4 5^17-6 7 15-9 9 iS-i II 20-3 13 iS-6^ 1520-8 17 19-1 12 19 22-3 21 24-5 23 18-8; I 21-0 3 19-3 5 21-5 7 19-8 9 22-0 II 24-2 13 22-5 15 24-7 17 23-0 13 19 26-2 21 28-4 23 22-8! I 24-0' 3 23-2 5 25-5; 7 23-7 926-0 II 28-2 1326-5 1528-7 1727-0 14 19 30-2 21 32-4 23 26-7 I 289^ 3 27-2 5 29-4 7 27-7 9 29-9I II 32-1 13 30-4 15 32-6 17 309 15 1934-I1 21 36-3 2330-6 1 32-9; 331-1 5 33-4 7 31-6 933-9 11 36-1 13 34-3 1536-6 1734-8 16 19 38-0 21 40-2 23 34-6 I 36-8 3 35-" 5 37-3 7 35-6 937-8,1140-0 1338-3 1540-5 17 3^-8 )7 1942-0, 21 44-2 23 38-5 I 407 339-0 5 41-2 7 39-5 9417 11 44-0 1342-2, 1544-5 1742-7 18 1945-9I 21 48-1 2342-5 I 44-7 343-0 5 45-2 7 43-5 9 45-7i II 47-9' 13 46-2 15 48-4 17 46-7 19 19 49-S 21 52-1 2346-4 I 48-6 3 46-9 5 49-1^ 7 47-4 9 49-6| II 51-8 n 50-1 15 52-3 17 50-6 20 •9 53-8 2156-0 23 50-4 I 52-6 350-8, 5 53-1 7 51-3 953-6, 11 55-8 12 51-1 1556-3 1754-6 21 ■9 57-7 22 O-O 23 54-3' I 56-5 3 54-8, 5 57-0 7 55-3 957-5! II 5»-7 13 5-'^-o 16 0-2 17 58-5 22 22 3-9 23 58-2 2 0-5 3 58-7 6 1-0 7 59-2 10 1-5! 12 37 14 i-o 16 4-2 18 2-4 23 20 5-6 22 7-8 2-2 2 4-4 4 2-76 4-9 8 3-2 10 5-4 12 7-6 14 5-9 16 S-i 18 6-4 24 20 9-6 22 11-8 6-1 2 8-3 4 6-6 6 8-8 8 7-1 10 9-3 12 11-6 14 9-8 16 12-1 18 10-3 25 20 13-5 22 15-7: 10 i! 2 12-3, 4 IO-6 6 12-8 8 ii-i 10 13-3 12 15-5 14 13-8 16 16-0 18 14-3 2(; 20 17-5 22 197 14-0; 2 16-2; 4 14-5 6 167 8 15-0 10 17-2 12 19-4' 14 17-7 16 19-9 18 18-2 27 20 21-4 22 23-6 17-9 2 20-2 4 18-4 6 20-7 8 18-9 10 21-2 12 23-4' 14 21-7 1623-9 1822-2 28 2025-32227-6, 021-9224-1 422-4,624-6822-9 10 25-1' 12 27-3 14 25-6 16 27-8 18 26-1 29 20 29-3! 22 31 5 25-8: 2 28-1 4 26-3! 6 2S-6; 8 26-8 10 29-0! 12 31-3' 14 29-5 16 31 -8 1830-0 3() 20 33-2] 1 29-8 2 32-0 4 30-3! 6 32-5 8 30-8 10 33-0 12 35-2' 14 335 16 35-7 18 34 :li 20 37-2 i °3i-7; 4 34 -21 [834-7 1036-9 [14 37-4, U8 37-9I TABJ.E ti2 EQUATION OK TnilO, rov. ti.f Vkar 11)01, For Apparent Noon at Greenw cl.. Day J.n. odT Feb. Mar. April May June July Aug ! Sept. Oct. Nov. Dec. lib Im'^m 1 "siiT suU. 1 3-34-I3-46 12-38 n3 53 ,12 26 3 49 '3 3 2 21 ,3 39 6 4 siib.o 15 10 30 16 21 10 40 :) 4 30 14 o 12 14 3 30 3 10 2 12 i 3 50 6 35 10 49 16 22 10 16 ■» 4 5« "4 6 12 I 3 13 3 17 2 2 1 4 r 5 55 54 II 7 16 21 9 53 5 5 25 14 12 II 48 2 55 3 22 1 52 4 12 5 SO 1 • '•» 11 25 16 20 9 28 6 5 52 14 >6 II 34 2 37 3 28 J 42 4 22 s 44 : « zi II 43 16 18 9 3 7 6 ]8 14 20 II 20 2 20 3 33 I 31 i 4 32 s 37 1 ' 54 12 I 16 16 8 3^ 8 6 44 14 23 II 5 2 3 3 37 I 20 4 42 s 30 2 14 12 181 16 12 8 11 9 7 9 14 25 10 50 I 46 3 41 1 9 4 SI 5 23 i 234 12 34 '16 8 7 45 10 7 34 14 2_6 10 34 1 29 3 44 57 45 5 oiS 14 5 915 6 _i.SL 12 50 16 2 15 56 7 18 6 50 ll 7 5« 14 27 10 19 I 13 jT46 3 15 13 6 12 8 22 14 27 ID 3 056 348 33 5 17 4 56 336 13 21 15 49 6 22 13 8 45 14 26 946 41 I 3 49 21 5 24 ' 4 46 3 57 1336 15 41 5 54 1-1 9 7 14 24 930 25 3 50 .«./.. 8 ; s 32 4 36 4 18 13 50:15 ii 5 20 1 j 9 29 14 22 9 13 addo 10 3 50 addo 4 |5 38 4 25 4 39 14 4 15 23 4 57 Ifi 9 50 14 J9 856 ,«t.o 5 3 49 17 ; 5 45 4 13 5 14 17 15 13 4 28 17 10 10 14 15 8 39 19 348 30 1 5 50 4 1 5 21 14 29 15 I 3 58 18 10 30 14 II 8 21 33 3 47 43 : 5 56 3 49 5 43 14 41 i 14 49 3 29 IP 10 49 14 6 8 4 046 3 45 56 [ 6 3 35 6 4 ■4 53 14 37 2 59 •-'0 u 8 14 ■■ 25 13 53 746 T28 I I 12 3 42 3 38 1965 I 22 6 8 3 22 625 15 3|i4 23 2 29 2 rs 6^ 15 Hi 14 8 II 42,13 46 7 10 I 25 3 35 I 35 6 II 2 S3 7 7 15 23 13 53 I 30 ■-':! 11 58 '3 38 6 52 I 37 3 30 I 48 6 14 2 38 7 28 IS 32I13 37 •J4 12 13 13 30 634 I 48 326 2 I 6 IS 2 22 7 49 15 40 13 21 030 ■-'.-. 12 28 13 21 6 .5 I 59 3 20 2 14 6 17 2 6 8 10 IS 48 13 3 ««/.. •-'i; 12 41 13 1' 5 57 2 10 3 '4 2 27 6 17 1 I so 830 15 54: 12 45 add 30 12 54 13 I 5 39 2 20 3 8 2 39 6 17 j I 33 851 :6 I 12 26 59 ■J8 13 12 SO S 20 2 30 3 I 2 52 6 17 1 I 16 9 II 16 6 12 6 I 29 •-'y ■3 17 1 S 2 2 39 2 54 3 4 6 IS 58 931 16 II II 45 I 58 :10 >3 2S| 4 43 2 47 2 47 3 16 ,6 14 40 9 51 16 14 II 24 2 27 :il ■3 37 1 42s 2 38 611 22 16 17 2 56 Equat ION or Tnir, for 1905 . ad,l «rf,/ add «./-. add add 1 »ub. >ub. 1 5'25- .3-42- I2-40' «./,/4"io' 2-54' Hii. 2"'32' 3'"25-]6"io' orfJo^io* lo" 4' i6"i8- «,&.„". 7- 'I 3 53 13 50 12 28 3 52 3 2 2 23 3 37 6 7 5«/,.o 9 10 23 16 19 10 45 4 22 '3 57 12 16 3 34 3 9 3 49 6 3 28 lo 42 16 20 10 22 ■i 4 49 14 4 12 3 3 16 3 15 » 4 4 5 58 47 II I 16 20 958 ■'■ 5 '7 14 9 II 50 2 59 3 21 I 54 4 11 5 53 I 7 n 19 16 19 9 34 *>" 5 44 14 14 II 36 2 41 3 26 I 43 4 21 548 I 26 n 37 16 18 9 9 7 6 JO 14 18 11 22 2 24 3 31 I 32 4 32 5 41 I 46 n 54] 16 IS 843 X 636 14 22 11 8 2 7 3 35 I 21 4 42 5 34 2 7 12 12 16 12 8 17 9 7 2 14 24 'O 53 I 50 3 39 I 10 4 51 5 27 2 27 12 28 '16 8 7 51 U) II 7 27 7 5' 14 26 14 27 10 38 10 22 1 33 I 17 3 42 058 5 0|5 19 S 9 5 10 2 48 3 8 12 4s|i6 3 13 i|iS 57 7 24 6 57 3 44 46 12 8 15 14 27 10 7 I I 3 4 y 44 14 19 9 tub. 3 49 IS S4S'4 18 4 54 14 13' 15 15 4 30 1" .0 5 14 16 843 IS 3 48 28 5 51 14 6 5 IS 14 26, 15 5 4 7 l« 10 25 14 II 8 26! 29 346 41 5 56 3 53 S 37 14 38I14 53 3 38 1 '' 10 44 14 6 8 8 43 3 44 54 6 3 40 5 58 14 50 14 40 3 8 .() 11-20- '4,° _7 50' _^.5A 3 42 • 7 6 5 3 26 6 19 IS I 14 27 238 \'l 1354 732I I 9 3 39 I 20 6 8|3 12 640 15 II 14 13 1358 2 8 •.;2 " 37 ■3 47 7 14. I 22 3 35 > 33 6 II 1 2 57 7 I IS 21 « 39 -:i 11 53 13 39 6 %,b. I 34 3 31 . 46 6 14 2 42 7 22 IS 30 13 42 ' 9 -'■I 12 8 13 30 637 I 46 3 27 I 58 6 16 2 27 7 43 1538 13 25 39 2.5 12 23 13 i«» € Canis Majoris Adara a- Geminorum Cattor a Canis Minoris Procyn,, Geininoruin Pollux C Argus 2 t. 2 2 i 2 2 2 6 21 44 6 31 56 6 40 44 6 54 42 728 13 7 34 4 8 41 57 9 22 40 + '33 3-47 264 236 384 3'4 368 2 II I 65 2-95 52 38 27 S. 16 29 5 N. 16 34 43 f^- 28 50 9 S. 32 6 29 N. 5 28 52 X. 28 16 4 N. 39 43 '6 S. 54 20 32 S. 8 13 30 S- a Hydrae Alpiard a Leonis Regulut y' Leonis Algeiba 1) Argfls 1. 2 2 var. 2 2. 3 2 2, 3 I 2. 3 3 ■033 10 14 28 10 41 II 10 57 34 11 8 47 " 43 58 11 48 34 12 21 2 12 29 8 12 51 21 + 320 3 3' 232 3-74 3-20 ]:X 330 3'4 281 12 27 22 N. 20 20 50 N. 59 9 30 S- 62 17 27 N 21 4 18 N. 15 7 52 N. 54 15 3 N. 62 32 41 S. 22 50 38 S. 38 Si 30 N. -'97 -200 + 200 + 200 -195 a Ursa Majoris Dubl.i: ! Leonis Zosma Leonis Denebola y Urs* Majoris Phecda Corvi .... a Canum Venaticorum « Virginis Spica V CrsjE Majoris Btnttmitch I 2 I 3. 4 I I 3 2 2 2 «3 '9 55 •3 43 36 13 56 46 14 1 41 14 .1 6 14 .12 49 14 45 21 14 5> '5 " 37 «S 30 27 2-37 419 1-62 273 40s + 33' -022 + 322 254 367 63' '35 278 1-39 203 293 478 10 38 22 S. 49 48 44 N. 59 S3 26 .S. 64 5' '3 N- 19 42 II N. 60 25 ID S. '5 37 35 S- 74 33 5' N- 9 51 S. 27 3 4N. 6 44 24 N. 19 31 55 S- 26 12 36 -S. 68 50 39 .S. 52 22 31 -N. 12 37 58 N. 5' 30 2 N. 38 4' 26 N. 8 36 14 N. 57 3 20 S. + .89 -181 + 176 + 150 + 151 -'47 + '3S -'23 -IIS + lOI + 8-3 :r8 - 28 - 05 + 3-2 + 93 -11-2 a Oraconis Thuban a Bootis Arcturui a' Cenlauri a Libix Znben el Genubi Ursa; Minoris Koclmb I.ibr* Zuben el Chamali a Scrpentis Unuhalhai 0' Scorpii 2, 3 3 3 2 2, 3 2 15 39 20 '5 59 37 16 23 16 .638 4 17 28 10 17 30 17 17 54 "7 '8 li 33 '9 45 54 20 17 44 a Scorpii A.,tare:i a Trian^uli Australis Draconis Alwaid a Ophiuclii Rat Alhague y Uraconis Ratlaban a Lyt^e Veya a AquilK JItair a Pavo.iis a Cjgni Deutb a Ccphci AUcrnmin 1. 2 2. 3 2. 3 2 2 2 21 39 "6 22 I s6 22 36 42 22 52 7 22 59 47 + 204 144 2-95 3?o 360 44 55 22 N. 62 9 42 N. 9 24 59 N. 47 26 4?.'^. 47 24 28 S. 30 9 8S. 14 40 2 N. + 127 -173 -187 - 190 + '9-3 1 oi^i"^ :::::::::::::::::::::" p Oruis a Piscis Aust. Fomnlha<,t a Prgaai Idarkab LOGARITHMS OF NUMliKRS No. No. Log 1 to lUO Lop. 0-000000 to 2-000000 1 No. Log. No. Log. No. Log. No. 1 Log. I 21 1-322219 41 .■6,2784 01 785330 8! .■908485 301030 ■22 1-342423 42 .-623249 lij 792392 K2 .■9,38,4 0477121 23 .-36,728 43 1-633468 03 79934' 83 .■9.9078 6c2c6q 24 ,-38021. 44 1-643453 (14 806,80 84 '•924279 J 6.^8970 2J 1-397940 45 1-653213 (;5 812913 85 .■929419 0-778. S> 2fi 1-414973 4G 1-662758 00 8. 9544 80 .■934498 0-845098 27 1-431364 47 1-672098 07 826075 87 '•9395.9 0-903090 28 1-447158 48 .■681241 118 832509 88 '■944483 0-954243 29 1-462398 4!) 1690196 K!) 838849 80 '■949390 Id TT :to 1-477121 50 1-698970 70 845098 00 '■954243 1-041393 31 1-49,362 51 1-707570 71 S51258 01 ,■95904, 12 1-079181 32 1-505150 52 1-716003 72 857332 92 .■963788 la 1-113943 33 1-518514 53 1-724276 73 863323 93 ,■968483 14 .•146.2S 34 j-53.479 54 1-732394 7-1 869232 94 ,■973.28 15 .■17609. Sd ,-544068 55 1-740363 75 875061 95 '■977724 ifi 1-204120 36 .-556303 5C ,-748188 76 880814 96 .98227, 17 .-230449 37 1-568202 57 '■755875 77 886491 97 .■986772 18 '•255273 38 .•579784 58 ,-763428 78 892095 98 .99,226 l!» .-278754 3U 1-59.065 50 ,-770852 79 897627 99 ,■995635 20 1-30.030 40 .-602060 «0 .-778.5. 80 .■903090 100 No. 1 000 to 1 1 49 Log. to 0603-20 No. 1 1 2 3 4 ' 1 « 7 8 1 9 D. 100 000000 000434 000868 00130. 00.734 002,66 002598 003029 00346, 00389, 432 101 004321 00475. 005181 005609 006038 006466 1 006894 C0732, 007748 008,74 428 102 008600 009026 00945. 009876 0)0300 010724 0,1147 01.570 011993 0,24,5 424 103 012837 0.3259 C13680 0.4.00 014521 0.4940 0,5360 015779 016,97 0,6616 42c 104 017033 0.745. 017868 0.8284 0.8700 0,9, ,6 0,9532 019947 02036, 020775 4,6 105 021189 02.603 022016 022428 02284. 023252 023664 024075 0244S6 024896 4,2 10(J 025306 0257.5 026125 026533 026942 027350 027757 028,64 02857. 028978 40S 107 029384 029789 030.95 030600 03.004 031408 03,812 0322,6 0326,9 03302, 404 108 033424 033816 034227 034628 035029 035430 035830 036230 036629 037028 400 109 037426 03782; 038223 038620 0390.7 039414 039811 040207 040602 04099S i97 110 041393 041787 042.82 042576 042969 043362 043755 044,48 044540 044932 393 1 1 1 045323 0457'4 046.05 046495 046885 047275 047664 048053 048442 048830 3!? 1 12 049218 049606 049993 050380 050766 051153 05,538 051924 052309 052694 386 113 053078 053463 053846 054230 054613 054996 055378 055760 056,42 056524 383 lU 056905 057286 057666 058046 058426 058S05 059.85 059563 059942 060320 379 N^ » 2 3 4 5 6 7 8 — T-l 1). 12S456789 1). 1 -2 3 4 5 6 7 8 9 3711 38 76 .13 .5. .89 227 265 302 340 408 4' 82 ,22 ,63 204 245 286 326 367 3»0 38 76 114 152 190 228 266 304 342 410 4. 82 .23 164 205 246 287 328 369 .■182 38 76 115 153 191 229 267 306 344 412 41 82 124 165 206 247 288 330 371 3H4 38 77 1.5 .54 192 230 269 307 346 414 41 83 124 166 207 248 290 331 373 386 39 77 .16 154 193 232 270 309 347 410 42 83 125 166 208 250 29, 333 374 388 39 78 116 155 194 233 272 310 349 418 42 84 125 167 209 251 293 334 376 .",:»() 39 78 117 156 195 234 273 312 351 420 42 84 126 .68 2.0 252 294 336 378 3.')2 39 78 118 157 196 235 274 314 353 4-22 42 84 127 169 211 253 295 338 380 .■iy4 39 79 .18 15S 197 236 276 315 355 424 41 85 '27 '70 2.2 254 297 339 382 3<)(; 40 79 119 158 .98 238 277 3'7 356 4-2(; 43 85 128 170 213 256 298 34. 383 398 40 So 119 159 199 239 279 318 358 4-28 43 86 .28 171 214 257 300 342 385 400 40 80 120 160 200 2.|0 280 320 360 430 43 86 .29 .72 215 25S 301 344 387 402 40 So 12 1 161 20. 241 281 322 362 432 43 86 130 173 216 259 502 346 389 40.t ,0 Si .2. .62 202 242 283 323 364 434 43 87 130 174 217 260 304 347 391 4Uti 41 81 122 .62 203 244 284 325 365 rABi.i: Gi ro7 LOG.VIUTIIMS OK NUMBERS N.I. IJiJO to 1499 Log. 0G0G98 to 175802 No. 1 2 S 4 .■i 6 7 8 9 I> 115 060698 061075 06,452 061829 062206 062587. 062958 063333 0C3709 0640X3 3-6 116 06445S 064831 065106 065580 065953 066326 066699 C6707. 0674+3 067815 373 117 o6Si«6 068557 068917 069298 069668 070038 070407 070776 07 "45 071514 370 IIU 0718S2 072250 0726,7 071985 073351 073718 074085 074451 0748.6 075.82 366 0715+7 07S9'» 076276 076640 077004 0^7368 07773' 078094 078+57 0788.9 363 Tm 079. Si °79543 079904 080266 0S0626 0SC987 0S1347 0S.707 082067 082426 360 121 08278, 083,44 083503 oS386^ 084219 084576 084934 085291 085647 086004 357 12J 086360 0867.6 08707 ■ 0S7426 087781 088,36 088490 089.9S 089551 355 12:1 089905 0902 58 09061. 090963 091315 09.667 092018 092370 09271. 351 124 093422 093772 094121 004471 094820 095,69 095518 095866 096215 096562 349 12."> 0969,0 097157 097604 097951 0982,8 098644 098990 °99335 099681 .OCC26 3+6 1 2(i 100371 ,00715 ■0^059 io^403 101747 102091 ■01434 .02777 ,03,19 .03462 3v3 127 103S0+ ,04,46 ,04487 104828 ■05169 1055,0 ■0585, .06.91 ,0653, 106871 3+. 1 2» '075+9 107888 .08227 .08565 108903 109241 109579 ,09916 1,0253 3;s 12 5278 1.5611 "5943 ..6276 .■6608 116940 333 i:u 117271 117603 '•7934 .18265 ■18595 118926 119256 1195S6 ■19915 .20245 330 132 ,20574 120903 ■2123. 121560 ■2.888 122216 .22544 .2287. 123^98 .23525 328 i:i:i ■23852 124,78 ■24504 124830 ■25,56 .2548 ■ ■25806 .26,3. 126456 12678. 315 134 127105 127429 '^7753 ■28076 ■2S399 .28722 .29045 .29368 129690 .300.2 313 i:ift '30334 ,30655 130977 .31298 .3.6.9 '3'939 .32260 .32580 ,32900 .33219 321 i:tf> '33539 133858 ■34'77 134496 ,348.4 '35.33 '3545' '35769 136086 .36403 3-8 i:t7 136721 ■37037 '37354 .3767' '37987 .38303 ,380.8 .38934 .39149 .39564 3.6 i:ti) ,39879 ,40,94 140508 140822 '+"36 141763 ■42076 142389 .42702 3'4 i:!ii ,+50,5 '433^7 1436,9 '4395' 144263 '47367 '44 574 '44885 ■45.96 '45507 .458.8 111 309 Ull 146128 .46438 ■46748 147058 ■47676 ■47985 ■48294 ,48603 .4S9.. Ul 1+9-19 1+95^7 .49835 ■ <,OI42 ,50449 .50756 151063 ■5.370 ,5,676 .5.982 307 142 ,52288 '5'-594 152900 .53205 ,535,0 .538.5 .54^20 . 54+14 ,54728 .55032 305 143 '55336 155640 '55943 ,56246 ,56549 .56852 '57'54 '57457 '577 59 15806, 303 144 15S362 ,58664 ■58965 ,59266 ■59567 .59868 .60168 ■ 60469 ,60769 161068 30. 145 ,61368 ,6,667 ■61967 ■62266 ,62564 ,62863 .63.6. ■63460 ,63758 ■64055 199 UU '6+3 53 164650 ■64947 165244 ,6554, .65838 .66.34 166430 ,66726 ■67022 297 147 .673.7 ,676,3 167908 168203 168497 .68791 .690S6 ■69380 169674 .6996S 195 148 170262 '70555 170848 17114. '7'434 17.716 172019 ■723.1 .71603 ,72895 193 14!t 173,86 '73+78 .73769 174060 '7435' '746+. '7+931 .751" »755'i ■75802 29. D. No. I 2 3 4 5 « 7 8 9 I). 1 2 3 4 5 6 7 « 9 D. 1 2 3 4 5 6 7 8!) 2!»0 29 5« 8-7 1 6 145 ,74 203 232 161 334 3 67 .00 .34 .67 200 234 267 30' 2!I2 Z9 58 88 I 7 146 ,75 204 234 263 331; 34 67 .0. .34 ^68 202 235 269 302 2!<4 2, 59 88 1 8 ,47 176 206 235 265 .33B 34 68 lo^ 135 .69 203 237 270 304 21K; 30 59 8, ■ 8 ,48 ,78 207 237 266 34( 34 68 .02 ^36 ,70 204 238 272 306 2!)« 30 60 89 1 9 ,49 ,79 209 238 268 342 34 68 103 137 ,71 205 239 274 308 .•)()0 30 60 9c .2 , 50 ,80 210 240 270 344 34 69 ,03 138 172 206 24. 275 3.0 302 30 60 9' ' ■ ■s^ ^8^ 211 242 272 34H 3 69 104 138 173 2c8 242 277 311 3(14 30 61 91 IJ 2 152 182 2^3 243 274 34!) 3 70 .04 ^39 ^74 209 244 278 313 306 3i 6, 92 12 2 153 184 214 245 ^75 350 3 70 ^05 ^40 .75 i.o 245 280 3.5 308 3' 62 92 12 3 154 185 216 246 277 352 3 70 .06 14^ 176 !■■ 246 282 317 310 31 6z 93 12 4 155 186 2^7 248 279 .3,'.4 3 71 106 142 .77 212 248 283 3.9 312 31 6z 94 .2 5 156 187 2^8 250 28, 35fi 3« 71 ^07 142 178 214 249 285 3»o 314 31 63 94 ,2 6 ^57 .88 220 25^ 283 .35R 36 72 10- ^43 179 2,5 25, 286 322 319 32 63 95 ' = 6 158 ^90 221 253 284 360 3f 72 ,c8 144 iSo 216 252 288 324 318 32 64 95 'J 7 ^59 '9' »J3 J54 J86 3«2 3f 71 .09 .45 .8. 217 153 19° 316 320 32 64 96 M 8 160 192 224 256 288 364 3f 73 .09 .46 181 2i8 255 291 328 322 32 64 97 '2 9 .61 .93 225 258 290 366 3 73 ' ,46 .83 220 256 293 329 324 32 65 97 ' 162 ^94 227 259 292 366 3 74 I .47 .84 22. 258 294 33. 326 33 65 98 1 ^63 196 228 261 293 370 3 74 ' II 148 185 222 259 296 333 32fl 33 66 1 164 197 230 262 295 372 3 74 ■ ■2 149 186 223 160 198 335 330 33 *« 99 ' 2 165 198 131 264 297 374 3 ■2 .50 .87 114 i6i 199 337 .132 33 f>6 3 166 199 232 266 290 :t76 3 -S ■■s '50 '88 216 163 JO. 338 708 TABLR 01 LOGARITHMS OF NUMBERS No. 1500 to 1899 Log. 176091 to 278525 No. 1 2 3 4 5 6 7 8 9 D. 150 176091 .7638. 176670 .76959 177248 177536 .77825 .78. ,3 ,78401 ,78689 289 151 178977 179264 179552 179839 180,26 1804,3 .80699 1809&6 ,81272 18,558 287 152 18.844 .82.29 .82415 182700 182985 ,83270 '83555 ,83839 ,84,23 ,84407 285 153 1846;, .84975 .85259 185542 ,85825 ,86,08 .8639, ,86674 ,86956 187239 283 151 18752. .87803 188084 188366 ,88647 ,88928 189209 1S9490 .8977. 190051 155 .90332 1906.2 190892 ,91,7, ,9,451 ,9,730 .920.0 .92289 ,92567 192846 279 156 .93125 193403 .9368. ,93959 ■94237 '945>4 194792 195069 ,95346 195623 278 157 .95900 .96.76 .96453 ,96729 ,97005 .9728. '97556 ,97832 ,98,07 ,98382 276 158 .98657 198932 199206 199481 ■99755 200029 200303 200577 200850 201,24 274 159 160 20.397 204120 201670 201943 202216 202488 202761 203033 203305 203577 203848 272 20439. 204663 204934 205204 205475 205746 206016 206286 206556 Itil 206826 207096 207365 207634 2079C4 208,73 208441 2087,0 208979 209247 269 162 209515 209783 210051 2,03,9 210586 2,0853 2, ,12, 2,1388 21.654 2, ,92, 267 163 212.88 2.2454 212720 2129S!. 2,3252 2,35,8 2,3783 2 ,4049 2,43,4 2,4579 266 16J 214844 2.5.09 ^'5373 2,5638 2,5902 2,6,66 2,6430 2,6694 216957 264 lo5 2.7484 ^'7747 218010 2,8273 2,8536 2,8798 2,9060 2,9323 2,9585 2,9846 2(2 166 22010S 22037c 22063, 220892 22, ,53 22,4,4 221675 22,936 222,96 222456 21 1 167 2227.6 222976 223236 223496 223755 2240,5 224274 224533 224792 22505, 259 168 225309 225568 225826 226084 226342 226600 226858 227,15 227372 227630 258 169 227887 228144 228400 228657 229,70 229426 229682 229938 230,93 256 ITO- 230449 230704 230960 231215 231470 231724 231979 232234 232488 232742 255 171 232996 233250 233504 233757 234011 234264 2345'7 234770 235023 235276 253 172 235528 23578. 236033 236285 236537 236789 237041 237292 237544 237795 252 173 238046 238297 23X548 23S799 239049 239299 239550 239800 240050 240300 250 174 240549 240799 241048 24,297 241546 24'795 242044 242293 24254, 242790 249 175 243038 243286 243534 243782 244030 244277 244525 244772 2450,9 245266 248 176 ^455n 245759 246006 246252 246499 24674s 24699, 247237 247482 247728 246 177 ^47973 248219 248464 248709 248954 249,98 249443 249687 249932 250,76 245 178 2 S0420 250664 250908 251,51 25,395 25,638 25,88, 252,25 25236S 252610 243 179 180 252853 253096 253338 2535S0 253822 254064 254306 254548 254790 25503. 242 24, ^55^73 2555'4 255755 255996 256237 256477 2567,8 256958 257198 257439 181 257679 257918 258,58 25S398 258637 258877 259„6 259355 259594 259833 239 182 26007. 260310 260548 260787 261025 26.263 26150, 261739 261976 262214 238 183 26245. 262688 262925 263162 263399 263636 263873 264.09 264346 264582 237 184 2648.8 265054 265290 265525 26576, 265996 266232 266467 266702 266937 235 185 267,72 267406 267641 267875 2681,0 268344 268578 2688.2 269C46 269279 234 186 269513 269746 269980 270213 270446 270679 2709,2 271:44 271377 27,609 233 187 27.S42 272074 272306 272538 272770 273C01 273233 273464 273696 273927 232 188 274>58 274389 274620 274850 275081 2753" 275542 275772 276002 276232 23c 189 No 276462 276692 27692. 277.5. 277380 277609 277838 278067 278296 278525 D. 1 2 3 4 r. 7 !) !) U. 12345li789 D. 12345678 !t 228 13 46 68 91 J14 137 160 182 105 260 26 52 78 104 130 ,56 182 208 234 230 23 46 69 92 115 138 161 184 107 202 26 52 79 105 131 157 183 210 236 232 23 46 70 93 .16 .39 162 186 209 204 26 53 79 106 132 158 185 211 238 234 23 47 70 94 117 140 164 1S7 211 206 27 53 80 >o6 >33 >6o >86 213 239 236 24 47 71 94 118 141 165 189 212 208 27 54 80 107 134 161 188 214 241 238 24 48 71 95 119 143 167 190 214 270 27 54 8i 108 135 ,62 189 216 243 240 24 48 72 96 120 144 168 192 216 272 27 54 82 109 136 163 190 218 245 242 24 48 73 97 121 145 '69 >94 i'S 274 27 55 82 110 137 ,64 ,92 219 247 244 24 49 73 98 122 146 171 195 220 276 28 55 8 3 110 138 ,66 ,93 221 24S 240 25 49 74 98 123 J48 172 197 221 278 28 56 8 3 III 139 ,67 ,95 222 250 248 25 so 74 99 124 149 174 198 223 280 28 56 S ,12 140 ,68 196 224 252 250 25 so 75 ICO 125 150 175 200 225 282 28 56 8 5 "3 14' '69 197 226 254 252 25 50 76 loi 126 MI 176 202 227 284 28 57 8 5 114 142 170 199 227 250 254 25 51 76 102 127 152 178 ^°^ "9 280 29 57 86 114 143 172 200 229 257 25b 26 51 77 102 128 154 179 2CC 230 288 29 58 86 115 .44 ,73 202 230 259 25S 16 52 77 ,C3 129 155 181 2C6 232 290 29 58 87 116 .45 174 203 23a lb. TABIR 04 r09 MKiARITHMS OK NtlMBF.RS No. 1900 to 2349 Log. :.'7K7.)4 to ^/O.'^H:} No. 1 2 3 4 5 6 7 8 1 [a 190 27S7U 278982 2791" 179439 179667 279895 280.23 28035. 280578 280806 228 I'Jl 281033 28,261 28,488 28,7.5 28,942 282.69 282396 2S2622 282849 283075 117 192 283301 283527 »S3:53 283979 284205 284431 284656 284S82 28,,C7 18533= 226 \m 2SS5S7 285-82 286007 286232 286456 286681 286905 287.3c 2S73S4 2S75-8 225 194 2S7S02 288026 28824, 288473 2S8696 2S8920 289,43 289366 28958, 28,8,2 113 19.-. 290035 290257 290480 290702 290925 29.. 47 29,369 29159. 29,8,3 2,2034 22: I9(i 292256 292478 292699 292920 293,4, 193363 293584 293804 294025 294246 22. 197 294466 294687 294907 295.27 195347 295567 195787 296C07 296226 296446 22c 198 29666.- 296884 297,04 197 3 '-3 197541 29776. 197979 298.98 298416 7986,5 2.9 199 mi 298853 29907. 299289 2995.7 199725 29094, 300,6, ,00378 3005,5 3C0813 n? 301030 30,247 301464 30,68, 30,898 3021.4 30233. 301547 302764 302980 201 303196 303412 303628 303844 304059 304275 30449. 304706 30492. 305136 2.6 202 S^SISi 305566 305781 305996 3062,, ,06425 506639 ,06854 307068 307282 2.C 203 307496 507710 307924 308,37 30835, 3C8564 508778 30899. 309204 3094.7 i'3 204 309630 309S45 3,0056 3,0268 3,04s. 3,0693 3,0906 3, ,1.8 3. .3,0 31.542 1.2 205 3"754 ,.,966 3"i'77 312389 3,26co 3-28.2 3.302; 3'3i34 3'3445 3.3656 2.. 206 313867 3,4078 3,4289 3,4499 3,47,0 3,4920 ,,5.30 3 '5340 3'555' 3.5760 2.0 207 3 '5970 3,6,80 316390 316599 3,6809 ,.70.8 ,.7227 317436 317646 3 '7854 209 208 3.806; 3,8272 3,8+8, 3,8689 318898 ,.9.06 3'93'4 3.9522 3.9730 3,9938 208 209 "2T0- 320146 320354,3^^562 320769 ,20977 32, .84 32,39. 3i'598 321805 3220,2 207 206 322219 322426 322633 322839 313046 313151 313458 313665 32387, 314077 211 324282 ,2448s ,24694 324899 325.05 3253,0 3255,6 32572, 325916 326.3. 205 212 326336 32654, 316745 326950 317.55 317359 317563 317767 317,71 328.76 204 213 328380 328583 318787 32899, 329.94 329398 32960, 329805 330008 33011. 203 211 33<^4>4 3306,7 3308.9 33,022 33.225 33'4i7 33,630 33.832 331034 331136 202 215 33M3S 332640 332842 333044 333146 333447 333649 333850 33405. 334153 102 216 3J4454 33465s 33«856 335°57 335157 335458 335658 335859 336059 336260 20. 217 3,6460 336660 336860 337060 337160 337459 337659 337858 33S058 338157 20c 21S 338456 338656 33S855 339054 339153 33945' 339650 339849 340047 340246 '99 219 340444 340642 ,4084. 34.039 341137 34'435 34.6,2 34.830 342028 342225 J98 '97 220 34:^413 342620 3428.7 3430>4 3432.2 343409 343606 343802 343999 344.96 221 34439^ 344589 344785 34498, 345'78 345374 345570 345766 345962 346.57 196 222 346353 346549 346744 346939 347.35 347330 347515 347720 3479'5 3481.0 '95 223 34830'i 348500 348694 348889 349083 349178 349471 349666 349860 350054 1,4 ■J24 350248 35044^ 350636 ,50829 35.023 35.2.6 35,4.0 35.603 35'796 35,989 '93 225 352.83 35^75 352568 35276, 351954 3S3'47 353339 353531 353714 3539,6 .13 22f. 354.08 3545°' 3 54493 354685 354876 355068 355260 355451 355643 355834 .92 227 356026 3562,7 356408 356599 356790 356981 357.71 357363 357554 3 57744 19. 22« 357935 358,25 3583,6 358506 358696 358886 359076 359166 359456 359646 190 229 •230 159831 ,6,728 36002 5_ 3602,5 360404 360593 360783 360971 36..6, 36.350 36'539 .8, 36,917 362,0; 362294 ,62482 ,6267. 361859 363048 363=36 363414 788 ■231 ,636,2 363800 363988 ,64,76 364363 36455' 364739 364926 365 "3 365,0, .88 232 365488 365675 365862 566049 366236 366423 3666.0 366796 36698, ,67.69 .87 ■>',^ 36-356 367542 367729 3679'5 368.0. ,68287 368473 368659 ,68845 36,0,0 .86 2.W ii-'iii 369401 369i8^ ,69772 369958 370.4, 3-0,28 ,■'05.3 370698 370883 .85 No. 2 3 4 5 6 7 8 9 D. D. > 2 3 4 a 6 7 8 9 D. 1 2 3 4 5 6 7 8 9 \Hi lg 57 55 74 9- "° '-9 »47 >66 208 2. 41 62 ?3 104 125 146 166 187 laii 19 37 56 74 93 Ml 130 149 167 210 2. 42 63 84 .05 .26 147 168 189 188 19 ;8 56 7s 94 113 131 ISO 169 212 2. 42 64 85 .06 127 148 170 191 l!l(l 19 3? 57 7* 9j "4 '33 '5^ '7' 214 2. 43 64 86 .07 .28 ,50 17. .93 19J 19 38 5« 77 96 115 134 154 173 216 22 4, 65 86 108 130 15. 173 .94 m 19 39 58 78 97 116 136 155 175 218 22 44 65 87 109 131 15, .74 196 196 20 39 59 78 98 "8 'V '57 >76 220 22 44 66 88 ,,0 .32 .54 .76 .98 198 20 40 59 79 99 "9 >39 M? '78 222 22 44 67 89 III 133 155 178 200 inn 2o 40 60 80 100 110 140 160 180 221 22 45 67 90 112 134 157 179 2C2 >m lo 40 fti Si ioi 121 141 ift: 182 226 23 45 68 90 113 .56 ,.8 ,8, 203 iOI 20 41 Ai 82 1-2 122 143 .6, .84 2'J8 23 46 6S 9, 1:4 ij; 16c .82 inc ;i.f. 21 41 62 82 103 ,24 ,44 165 ,8; 710 TABI.K n* LOGARITHMS OF NUMBERS No. 2350 to 2849 Log. 371068 to 454692 No. 1 2 3 4 5 6 7 8 9 D. 371068 371253 371437 371622 37.806 37.991 372175 372360 372544 372728 .84 236 37i9'i 373096 373280 373464 373647 373831 374015 374.98 374382 374565 1 84 237 374748 374932 375"5 375298 37548. 375664 375846 376029 3762,2 376394 .83 238 376577 376759 376942 377124 377306 377488 377670 377852 378034 378216 .82 239 24 U 375398 378580 37S76. 378943 379.24 379306 379487 379668 379849 380030 .8. "78T 38021 1 380392 380573 380754 380934 381,15 38.296 38.476 38.656 381837 241 382017 382197 382377 382557 382737 382917 383097 383277 383456 383636 <8o 242 3838.5 383995 384174 384353 384533 3847.2 384891 385070 385249 385428 .79 243 385606 3857851385964 386,4» 38632. 386499 386677 3868S6 387034 387212 .78 244 387390 387568 I 387746 387923 388. 01 388279 38S456 388634 388989 178 245 389.66 389343 389520 389698 389875 390051 390228 390405 390582 390759 177 246 390935 391.12 391^88 391464 391641 3918.7 39.993 392.69 392345 392521 176 247 392697 392873 393048 393224 393400 393575 39375. 393926 394101 394277 176 248 39445^ 394627 394S02 394977 395.52 395326 39550. 395676 395850 396025 '75 249 396199 396374 396548 396722 396896 39707. 397245 397419 397592 397766 '73 2a0 397940 3981.4 398287139846. 398634 398808 398981 399154 399328 399501 251 399674 399847 400020 400.92 400365 400538 4007 1 1 400883 401056 40122S '73 252 40 140 1 401573 401745 40.9.7 4020S9 402261 402433 402605 402777 402949 172 253 403121 403292 403464 403635 403807 403978 404.49 40432c 404492 404663 'T 254 404 8 34 405005 405.76 405346 4055.7 405688 405858 406029 406199 406370 .7. 255 406540 4067.0 40688. 40705. 40722. 40739. 407561 40773. 407901 40807c i-c 250 408240 408410 408579 40S749 4089.8 409087 409257 409426 409595 409764 169 257 405933 410.02 4.027. 410440 410609 410777 410946 411. ,4 411283 41,45, ,69 258 41.620 41.788 4.1956 412124 412293 4.246. 412629 4.2796 412964 4,3132 ,68 259 4.3300 4.3467 413635 4.3803 413970 414137 4.4305 4.4472 414639 4,4806 167 167 260 4'4973 415140 415307 4.5474 41564. 4.5S08 4.5974 416,4. 416308 1 416474 201 416641 4.6807 4.6973 4.7.39 417306 417472 4.7638 417804 4.7970 418135 166 202 418301 4.8467 4.8633 418798 4.8964 419129 4.9295 419460 4,9625 4,9791 .6s 263 419956 420.2. 420286 42045. 4206.6 420781 420945 42. ..0 421275 421439 .65 264 421604 42.768 42.933 422097 42226. 422426 422590 422754 422918 423082 164 265 423246 423410 423574 423737 42390. 424065 424228 424392 4^455 5 4247.8 164 266 424882 425045 425208 42537. 425534 425697 425860 426023 426186 426349 163 267 426511 426674 426836 426999 427.6. 427324 427486 427648 427811 427973 162 268 4^8135 428:97 428459 42862. 428783 428944 429.06 429268 429429 42959. 162 269 270 4^975^ 429914 430075 430236 430398 450559 430720 43088. 43.042 43.203 161 161 431364 431525 43.685 43.846 432007 432167 432328 432488 432649 432809 271 431969 433.30 433290 433450 433610 433770 433930 434090 434249 434409 ]6o 272 434569 434729 434888 435048 435207 435367 435526 435685 435844 436004 '59 273 43e.<3 416322 43648. 436640 436799 436957 437.16 437275 437433 437592 .59 274 43775" 437909 438067 438226 4383S4 438542 43870. 438859 4390.7 439.75 .58 275 43S333 439491 439648 439806 439964 440.22 440279 440437 440594 440752 ■58 276 440909 44.066 44.224 44.38. 441538 44.695 441S52 442009 442,66 442323 '57 277 442480 442637 442793 442950 443.06 443263 443419 443576 443732 4438S9 157 278 444045 444201 444357 4445.3 444669 444825 44498. 44SI37 445293 445449 .56 279 445604 445760 4459.5 44607. 446226 446382 446537 446692 446848 447003 155 ^80 447158 447313 447468 447623 447778 44793 3 [448088 44S242 448597 448552 '55 281 448706 448861 449015 449,70 449324 449478 1 449633 449787 449941 450095 '54 282 450249 450403 450557 4507.1 450865 45.0,8145. .72 451326 451479 45.633 '54 283 451786 451940 452093 452247 452400 452553 452706 452859 453012 453165 .53 284 4533>8 45347' 453624 453777 453930 454082 1 454235 454387 454540 454692 153 No. 1 2 3 4 5 1 6 7 8 . |D. D. 1 2 3 4 S 6 7 8 9 D. 123456789 152 I, 30 46 61 76 91 .o« 121 ny 170 .7 34 51 68 85 .02 ..9 ,36 .53 154 M 3' 4* 62 77 92 io« 123 139 172 .7 34 52 69 86 .03 .20 .38 155 156 16 31 47 62 7« 94 109 12^ 140 174 17 35 52 70 87 .04 122 .39 .5- 158 16 32 47 63 79 9, II. 126 142 176 18 35 53 70 88 ,06 .23 .4. ,5s 160 16 32 48 64 80 96 112 128 144 178 iS 36 53 7. 89 .07 .25 .42 .60 102 16 32 49 65 gi 97 113 130 146 180 .8 36 54 72 90 .08 .26 144 .62 104 .6 33 49 66 82 98 IIS 13' H* 182 ,8 36 55 73 9. .09 .27 .46 .64 If.r, 1- ■,-, ^0 66 ?3 ICO m6 133 i4f) 184 iX 3-. S5 -4 92 1.0 129 ,4- if'" W ,- ,., ,r. ft. S, ,., ,,S ,;, ,,, TAPIR 04 7!1 No. UKiARlTllMS OF NUMBKRS •2850 to 3349 Log. 46484.'i to .5249 1 h No. « 1 1 2 1 3 4 5 f. 7 8 9 1) ?85 454845 454997 455>5° 455501 455454 455606 455758 455910 456C62 4561.4 2o« 4563661456518 456670 45682. 456975 457.15 457176 457428 457579 45-751 287 45^881:45803; 458.84 458356 458487 458638 458789 458,40 459091 45,242 '5' 288 459591 459545 459694 459845 459995 460,46 460296 460447 46'5')7 460:4s '5' 239 2\>n 4608981401048 462398 462548 461.98 461348 461499 46,649 46,799 46,ojS 46209^ 46-2.18 .150 150 462697 462847 462997 463,46 463296 463445 465594 463744 291 463893 464042 464.9. 464340 464490 464639 464788 464936 465085 465134 149 292 465385 l46;i;5i 465680 465829 465977 466,26 466274 466413 4665-, 466719 149 293 46686S 467016 467.64 4673.1 467460 467608 467756 467904 468052 +68200 ,+S 294 46854-468495 468643 468790 468,38 469085 469233 469380 46951- +69675 .48 295 4698'-'- 469969 470..6 470163 470410 470557 470704 47085. 470,98 47.145 147 296 471291 47 .,58 47.585 47.751 471S7S 471015 471.7. 4713.8 472464 +726,0 <4f 29? 4-2903 473049 475.95 47 554' 473487 475633 475779 475915 474071 .46 298 474116 4-4562 474508 474655 474799 474944 475090 475135 47558. 475516 ,46 299 300- 4-56-1 47-121 4-5S.6 47-16-6 475961 _476.o7 476252 476597 476541 4766S7 4-'6S32 476976 '45 '45 4774". 477555 477700 477844 477989 478.33 W8278 +78+22 301 4-8566 47871. 4-S855 478999 479.45 479187 47943. 479575 479719 479865 '•4 302 480C07 4S015I 480294 480438 480582 480725 +80869 48 .01 2 48.156 48.299 144 303 48.445 4S1586 481729 481S72 4S2016 481.59 482302 482445 4825S8 4S273. '45 304 482874 483016 483.59 4S3302 483445 483587 483730 485871 4840,5 484.57 ■43 305 4845^^ 1 484442 484585 484717 4S4869 48501. 485.55 485195 485457 485179 .42 306 4X5-21 I485S63 486005 486,47 486289 486430 486572 4867.4 4S6S55 486997 142 307 48-138 48-280 48-41. 487563 487704 487845 4879X6 488,27 +8826, 4S84.0 .41 308 48855. 4886,2 48X833 488974 489.14 489255 4S9396 489537 489677 4898.8 .41 309 489958 49C099 490239 49oi«o 490520 49066, 4,0801 49094, 49.081 491222 14c 310 491362 49.502 491642 7,7787 491922 492062 49110. 49154. 4,248, 492621 ,4c 311 492-60 492900 493040 493«79 4933'9 493458 495597 493757 495876 4940,5 '59 312 494155 494194 494455 •]945;» 4947 ' I 494850 494989 495.18 495167 495406 '59 313 495 544 495683 495811 495960 496099 496238 496576 4965.5 496653 49679. '59 314 496930 49-068 497206 497344 497483 49761. 497759 497897 498055 498.75 .58 31,i 4985'. 498448 4985S6 498714 498862 498999 499'37 499175 4,94,2 499550 ,38 316 499687 499824 499961 500099 500236 500374 5005,1 500648 500785 500921 '37 317 501059 50.196 50.555 501470 50.607 50,744 50,880 5010,7 501,54 5022,1 318 502427 502564 502700 502837 50*973 503,09 503246 503382 5035,8 503655 n6 319 505-9" 503917 S04063 504.99 504335 50447, 504607 504743 504878 505014 .36 3W 505150 505286 50542. 505557 505695 505828 505,64 506099 506234 506370 321 506505 506640 506776 5069,, 507046 507,8, 5073.6 50745. 507586 507721 '35 322 507856 50799. 508126 508260 508395 508530 508664 50S799 50S954 509068 '55 323 509203 509357 509471 509606 509740 509874 510009 5,0,43 510277 5104., '34 324 510545 5.0679 510813 5.0947 5.1081 5111.5 5>'349 5,1+82 5,,fii6 5.1750 325 5.188, 5.10.7 5.1.5. 5.2284 512418 5.255, 5,2684 51281S 5.295. 5,3084 '55 326 5ni.8 5.555. 5.3484 5.36.7 5>3750 5.3883 5.40.6 5.4149 5,4181 5.44.5 '55 327 5.4548 5.46X. 5.48.3 5.4946 5 '5079 5152.1 5.5544 5.54-6 5.-^0, 51574. 155 328 5.5874 5.6006 516139 5.6271 5.6403 516555 5,6668 516800 516932 5,7064 '51 329 330 5.7.96 517328 5.7460 5.7591 5.7714 5.7855 519.7. 5.7987 5. 8, ,9 5,825. 5,8382 '51 151 5.8514 5.8646 518777 5.8909 5.9040 5.9503 5.9454 519566 5.9697 331 5.9S28 5'9959 520090 520221 510353 520484 5206,5 510745 520876 51,007 '5' 332 5=.. 58 51.26, 5ii44 28 43 57 7> 85 99 114 ,28 1.32 13 i6 40 53 66 79 9z ic6 119 lit 14 29 43 58 71 86 ,c, ,,5 130 1:14 13 27 40 ?♦ 67 80 94 107 121 Hr, ,5 19 44 58 73 88 ,02 1,7 131 1.36 14 27 4> 54 68 82 95 ir9 ,2 = 1(8 15 30 44 59 74 89 104 1,8 ,33 I3S 14 28 41 55 69 83 97 110 134 l.-)0 15 30 45 60 75 r-o ,05 .10 135 :i0 14 28 41 56 70 84 98 1.2 i;6 1.V2 .5 30 46 6, 76 91 ,06 ,■•:• ,37 "12 TABLE m LOGARITHMS OF NUMBERS No. 3350 to 3899 Log. 525045 to 590953 No- 1 2 3 4 5 6 7 8 9 D. 129 335 525045 525>74 525304 525434 525563 525693 525822 525951 5260S. 5262,0 336 526339 526469 526598 526727 526856 526985 527, ,4 527243 527372 52750, .29 337 5276J0 527759 527888 5280.6 528,45 528274 528402 528531 528660 5287S8 .29 33K 528917 529045 529174 529302 529430 529559 529687 5298,5 529943 530072 .28 339 530200 530328 530456 530584 5307,2 530840 530968 531096 53.223 53"35" ,28 340 55H79 53.607 53'734 53.862 53,990 532.17 532245 532372 532500 532627 TIs" 341 53^754 532882 533009 533"36 533264 53339' 5335'8 533645 533772 533899 "27 342 534026 5J4"53 534280 534407 534534 534661 534787 5349'4 53504" 535'67 "27 313 535294 535421 535547 535674 535800 535927 536053 5361S0 536306 536432 ,26 344 536558 556685 5368,, 536937 537063 537'89 5373'5 53744' 537567 537693 126 345 5378'9 537945 538071 538"97 538322 538448 538574 538699 538825 538951 126 346 539076 539202 539327 539452 539578 539703 539829 539954 540079 540204 •25 347 540J29 540455 540580 540705 540830 540955 54.080 541205 541330 541454 125 348 54' 579 541704 54"829 54"953 542078 542203 542327 542452 542576 542701 '25 349 542825 542950 543074 543 "99 543323 543447 543 57' 543696 543820 543944 124 124 350 544068 544192 5443 "6 544564 544688 544812 544936 545060 545183 351 545307 54543" 545555 545678 545802 545925 546049 546172 546296 5464,9 ,24 352 546543 546666 546789 5469.3 547036 547 "59 547282 547405 547529 547652 ,23 353 547775 547898 54X02, 548,44 548267 548389 548512 548635 548758 54888. '23 354 549003 549.26 549249 54937' 549494 5496,6 549739 549861 549984 550,06 '23 555 550228 55035' 550473 550595 5507"7 550840 550962 55,084 55.206 551328 122 356 55 '450 55"572 551694 55.8,6 55'938 552060 552,8, 552303 552425 552547 122 357 552668 552790 5529,, 553033 553"55 553276 553398 5535"9 553640 553762 121 358 553883 554004 554126 554247 554368 554489 554610 55473" 554852 5 54973 121 359 555094 555215 555336 55 5457 555578 555699 555820 555940 55606, 556,82 ,2, 360 556303 556423 556544 556664 556785 556905 557026 557"46 557267 557387 ,20 361 557507 557627 557748 557868 557988 558.08 55822X 558349 558469 558589 120 362 55S709 558S29 558948 559068 559,88 559308 559428 559548 559667 559787 ,2C 363 559907 560026 560146 560265 560385 560504 560624 560743 560863 560982 "9 364 56. .0, 56.22, 56.340 56,459 56,578 56.698 56. 8.7 561936 562055 562174 "9 365 562293 5624,2 56253. 562650 562769 562887 563006 563'»5 563244 563362 1,9 366 5C3481 563600 5637,8 563837 563955 564074 564192 564311 564429 564548 1,9 367 564666 564784 564903 56502, 565'39 565257 566555 565494 5656.2 565730 ,18 368 565848 565966 566084 566202 566320 566437 566673 56679. 566909 ,,8 369 567026 567.44 567262 567379 567497 5676,4 567732 567849 567967 568084 I'l. 370 568202 5683,9 56S436 568554 568671 568788 568905 569023 569.40 569257 371 569374 56949, 569608 569725 569842 569959 570076 570,93 570309 570426 >"7 372 570543 570660 570776 570893 57,0.0 571.26 571243 57'359 57"476 571592 '"7 373 57.709 57"825 57"942 572058 572174 57229. 572407 572523 572639 572755 116 374 57^87^ 572988 573 "04 573220 573336 573452 573568 573684 573800 5739'5 ,|6 375 57403" 574"47 574263 574379 574494 574610 574726 574841 574957 575072 1,6 376 575.88 575303 5754"9 575534 575650 575765 575880 575996 57611, 576226 I,c 377 57634" 576457 576572 576687 576802 5769.7 577032 577'47 577262 577377 "5 378 577492 577607 577722 577S36 57795" 578066 578.8. 578295 578410 578525 "5 379 57X639 578754 578868 5789S3 579097 5792,2 579326 57944' 579555 579669 '"4 380 579784 579898 5800,2 580,26 5S024. 580355 5S0469 580583 5S0697 5808,, ""4 381 580925 58.039 58, ,53 58,267 58.38. 58,495 581608 58.722 58.836 58.950 ""4 382 582063 582.77 58229, 58 2404 5825.8 58263, 582745 582858 582972 583085 ""4 383 583.99 5833.2 585426 583539 583652 583765 583879 583992 584,05 5842.8 ""3 384 58433" 584444 584557 584670 584783 584896 585009 585.22 585235 585348 ""3 385 58546, 585574 5S5686 5S5799 5859.2 586024 586,37 586250 586362 586475 "3 386 586587 5S6700 5868,2 5S6925 587037 5S7.49 587262 5S7374 587486 587599 387 587711 587X23 587935 5S8047 588160 588272 588384 588496 588608 588720 ,12 388 588832 588944 589056 589,67 589279 58939" 589503 5896.5 589726 589S3S , .2 389 5899^0 59CC6, 590.73 590284 590396 590507 590619 590730 590842 590953 6" No. I 2 3 4 5 6 7 8 9 D. 12 3456789 D. 1 2 3 4 5 6 7 8 9 112 II 22 34 45 56 67 78 90 101 122 12 24 37 49 6. 73 85 98 no HI II 2 34 45 57 6S So y. .03 124 ,2 25 37 50 62 74 87 99 '"2 lie 12 2 35 46 58 70 S. 93 IC4 126 .3 25 38 50 63 76 88 10, ,13 118 12 2^ 3 5 47 59 -' 83 .4 'c6 128 13 26 3S 5, 64 77 90 i'-2 1:, IJO 12 2.1 l:iO ,3 26 39 5- 65 -8 0. ..4 M^ TABLE Hi LOGARITHMS OF NUMBERS No. 3900 to 4449 Log. .591065 to 648262 Ko. :<90 1 2 3 4 5 6 7 8 9 D. 59'o65 59>>76 591187 59'399 59.5.0 59.61, 59.73'- 591843 59.955 592066 .191 59!>77 592288 59^399 591510 59262, 591731 592843 59^954 59306+ 593'75 , , , 3!)2 59r-S6 593397 593508 5936.8 593729 593840 59395° 594061 594.7. 594282 1 , , 39.1 594393 5945°3 5946.4 594724 594834 594945 595°55 595.65 595176 595386 1,0 .394 595496 595606 59S7'7 595827 595937 596047 596.57 596267 596377 596+87 no 39.i 596597 596707 596817 596927 597037 597146 597256 597366 597476 597586 1 10 396 597655 597805 597914 598024 598134 598243 598353 598462 598572 59868, no 397 598791 598900 599009 599.19 599128 599337 599+46 59955* 599665 599774 109 398 599883 599992 60010. 6002,0 600319 600428 600537 600646 600755 60086+ 109 399 600973 60,082 601191 60.299 601408 60,5,7 601625 601734 60,843 60,9,, 109 400 5oio6o 602,69 602277 602386 602494 602603 6027., 602819 601928 603036 TSg 401 603144 603253 603361 603469 603577 603686 603794 603902 6040,0 60+,. 8 ,08 402 604226 604334 604442 604550 604658 604766 60+87+ 604981 6050S9 605,97 108 403 605305 605413 605511 606596 605628 605736 605844 60595. 606059 606,66 60617+ ,08 404 60638; 606489 606704 6068,, 6069,9 607026 607133 60714, 6073+S ,07 405 6°745S 607562 607669 607777 607884 607991 608098 608205 6083,2 6o8+,9 107 406 608516 608633 608740 60S847 608954 609061 609,67 609174 60938, 609+88 .07 407 609594 609701 609808 6099.4 610021 610128 6.0234 6,0341 610++7 6.0554 .07 408 6,0660 6,0-67 610873 6,0979 611086 6,1192 61,298 611+05 6,15,, 6, ,6.7 ic6 409 6.1723 6,1829 6,1936 6,2042 612,48 6,1154 6,2360 6,1+66 6,1571 6,2678 ,06 4TF 6,2784 Til8^ 612996 6,3102 613207 6,33,3 6,34,9 6.3515 6,3630 6,3736 1^ 411 6,3842 613947 614053 6.4.59 6,4164 6,4370 6.4475 6,4581 6,+6S6 6,4791 Ic6 412 6.4897 615003 6.5,08 6.5113 6.53,9 6,5424 6.5529 6,5634 6.57+0 6,5845 105 413 615950 616055 616160 616265 6,6370 616476 616581 6,6686 6,6790 6,6895 105 414 617000 6.7.05 617210 6,73,5 617420 6.7525 617629 6.7734 617839 6,7943 105 415 6:8048 6.8.53 618257 618362 618466 618571 6,8676 6.8780 618S8+ 6,8989 105 416 6.9093 619.98 619302 619406 6,95,, 6,9615 6,97,9 6,9814 619928 620032 104 417 620.36 620240 620344 610+48 620552 610656 620160 610864 620968 62,072 104 418 621176 62.280 621384 611488 621591 62,695 611799 61,903 622C07 622,10 104 419 6222,4 6223.8 622421 622515 622628 622732 622835 622939 6230+1 623,46 _I04 420 623249 623353 623456 623559 623663 623766 623869 625973 61+076 624,79 103 421 624282 624385 624488 62459. 624695 62+798 624901 625C04 625,07 6252,0 103 122 6253,2 6254.5 6255,8 62562. 625724 625827 625929 626032 626,35 626238 103 123 626340 626443 626546 626648 626751 616853 626956 627058 62716, 627263 ,03 424 627366 627468 62757: 627673 627775 627878 627980 618185 628187 425 628389 62849. 628593 62869; 628797 62S900 619001 629,04 629206 629308 102 426 6294.0 629512 6296,3 629715 6298,7 6299,9 630021 630123 63021+ 630326 102 127 630428 630530 63C63, 630733 630835 630936 63,038 63.139 631241 63,3+2 102 428 63,444 63.545 63,647 63,743 63,849 63195, 631051 632,53 632255 632356 10, 429 430- 632457 63^559 633569 632660 63176, 632862 631963 633064 633.65 633266 633367 -7^ 633468 633670 63377. 633871 633973 634074 634.75 634276 63+376 431 634477 63457S 634679 634779 634880 63498, 63508, 635,81 635283 635383 ■ 01 432 635484 635584 6356S5 635785 635886 635986 636087 636187 6362S7 636388 100 433 656488 636588 636688 636789 636889 636989 637089 637.89 637290 637390 434 637490 637590 637690 637790 637890 637990 638090 638,90 63S290 638389 100 435 638489 638589 638689 638789 638888 6389S8 639088 639,88 63928; 639387 100 436 639486 639586 639686 639785 639885 639984 640084 640,83 640283 640382 99 437 64048, 640581 640680 640779 640879 640978 641077 641,77 64,176 64.375 99 4.38 64.474 64.573 641672 64,77, 64,871 641970 642069 642168 6+2:67 6+2366 99 439 440 642465 642563 642661 642761 642860 642959 6+3058 643.56 643255 6433^4 644340 99 99 643453 64355. 6+3650 643749 643847 6+39+6 644044 644.43 6++2+2 441 644439 644537 644636 6.H7 34 644832 64493. 645029 6+5,17 6+5226 6+532+ 98 142 645422 64552, 6456,9 6457.7 6458.5 6459.3 646011 6+6,10 6 + 6218 6463C6 98 4(3 6+6404 646502 646600 646698 646796 64689+ 6+6992 647089 647,87 647285 98 444 647383 647481 64757, 647676 647774 647872 64796.; 648067 648,65 648262 98 No. I 2 3 4 5 6 7 8 9 n. D. I 2 3 4 5 6 7 8 9 I). 1 2 3 4 5 fi 7 8 9 1 98 lo 20 19 39 49 59 69 78 8S 106 ,1 11 31 41 53 64 74 85 95 100 10 lo 30 40 50 60 70 80 90 108 ,1 22 32 43 54 65 76 86 9- 102 ,0 10 3' 4< ^> *-• ;■ »;- 9x nn ,, ^2 33 +4 55 66 77 88 99 Ui TABLE ni LOGARITHMS OF NUMBERS No. 4450 to 4999 Log. 648360 to 698883 No. 1 1 1 2 3 4 1 5 1 6 7 8 9 D u:< 648360 648458 648555 648653 6487501648848 648945 649043 649,40 649237 9" tu< 649335 64943 ^ 549530 649627 649724164982, 649919 65C016 6501,3 6502,0 97 11/ 650308 650405 650502 650599 650696 650793 650890 6509S7 651084 65.181 97 448 651178 651375 65,472 65,569 65,666 651762 651859 651956 652053 652,50 97 44",» 651246 65^343 652440 652536 652633 652730 652826 652923 653019 6531,6 ■'w 653213 653309 653405 653502 653598 1 653695 65379" 6538S8 653984 654080 4JI 654'77 654273 654369 654465 654562 654658 654754 654850 654946 655042 96 4:) 2 655138 655^5 655331 655427 655523 6556,9 655715 6558.0 655906 656002 96 4:1:5 656098 656194 656290 656386 656482 656577 656673 656769 656864 6,6960 96 4&4 657056 657152 657^47 657343 657438 657534 657629 657725 657820 6579.6 96 4:>5 658011 658107 658202 658298 658393 65848S 658584 658679 658774 658870 95 4.)fi 658965 659060 659155 659250 659346 65944, 659536 65963, 659726 65982, 95 457 659916 66001, 660106 66020, 660296 66039, 660486 66058, 660676 66077. 95 4 "18 660865 660960 661055 66, ,50 66,245 661339 66,434 66.529 66,623 661718 95 450 661813 661907 662002 662096 662,91 1 662286 662380 662475 662569 662663 _95_ ificT 662758 662852 662947 66304, 663135 I663230 663324 663418 663512 663607 94 4C1 66370, 663795 663S89 663983 664078 664172 664266 664360 664454 664548 94 462 664642 664736 664830 664924 665018 665,12 665206 665299 665393 665487 94 463 665581 665675 665769 665S62 665956 666050 666.43 666237 666331 666424 94 464 6665,8 666612 666705 666799 666892 666986 667079 667173 667266 667360 94 4G5 667453 667546 667640 667733 667826 667920 66S013 668,06 668,99 668293 93 466 668386 66S479 668572 668665 668759 66S852 668945 669038 669,3, 669224 93 467 6693,7 669410 669503 669596 669689 669782 669S75 669967 670C60 670,53 93 468 670246 670339 67043, 670524 6706,7 6707,0 670802 670895 67098S 67,080 93 469 470 67. .73 67,265 6713S8 67145, 671543 672467 67.636 67,728 671821 67.9.3 672005 ~9^ 672098 672190 672283 672375 672560 672652 672744 672836 672929 471 673021 673, ,3 67320 673297 673390 673482 673574 673666 673758 673850 92 472 673942 674034 674,2^ 6742,8 6743,0 674402 674494 674586 674677 674769 92 473 67486, 674953 675045 675'37 675228 675320 6754<2 675503 675595 675687 92 474 675778 675S70 67596^ 676053 676,45 676236 676328 6764,9 6765,, 676602 92 475 676694 676785 676876 676968 677059 67715- 677242 677333 677424 6775.6 9' »70 677607 677698 677789 677881 677972 678063 678,54 678245 678336 678427 9' 477 6785.8 678609 6787C0 67879, 678882 678973 679064 679155 679246 679337 9. 47g 679428 679519 679610 6797CO 67979' 679S82 679973 680063 680154 680245 9> 479 480 680336 680426 6805,7! 680607 680698 6S0789 "68 1693 680879 680970 68 1060 "68^7^ 681,5, JlL 68,24, 681332 681422 681513 68,603 681784 681874 682055 9° 481 682,45 682235 682326 6824,6 6S2506 682596 6S2686 682777 6S2867 682957 90 482 683047 683,37 683227 6833,7 683407 683497 683587 683677 683767 6S3857 90 483 683947 684037 684127 6842,7 684307 684396 684486 684576 684666 684756 90 484 684845 684935 685025 685114 685204 685294 685383 685473 685563 685652 90 485 685742 68583, 68592, 686010 686100 686,89 686279 686368 686458 686547 89 486 656636 6868,5 686904 686994 687083 6S7172 6S726, 687351 687440 89 487 687529 6876,8 687707 687796 687886 687975 688064 688,53 688242 688331 89 488 68S420 688509 688598 688687 6S8776 688865 688953 689042 689,3, 689220 89 489 490 6893C9 690,96 689398 689486 689575 689664 6S9753 68984, 689910 6900,9 690107 89 690285 690373 690462 690550 690639 690728 690S16 690905 69093 491 691CS, 691,70 69,258 69,347 69,435 69,524 6916,2 69,700 69,789 69.S77 88 192 69,965 692053 692,42 692230 6923,8 692406 692494 692583 692671 692759 88 19:5 692847 692935 6930Z3 693,,, 693,99 693287 693375 69,463 69355. 69.639 88 494 693727 6938,5 693903 69399, 694078 694.66 694254 694342 694430 694U7 SS 495 694605 694693 69478, 694868 694956 695044 695,3, 6952,9 695307 695394 88 496 695482 695569 695657 6" 5 744 695832 6959.9 696007 696094 696182 69626Q 87 497 696356 696444 69653, 6966,8 696706 696793 696880 696968 697055 697.42 87 498 697229 697317 697404 697491 697578 697665 697752 697839 697926 698C.4 87 199 698,0, 698,88 698275 698362 1 698449 69S535 69S709 69S796 698SS3 8- N^ 1 2 1 3 1 4 5 6 7 8 1 9 D. 1 2 3 4 5 6 7 8 9 D. I 2 3 4 5 6 7 8 9 SH 9 iS 26 35 44 53 62 70 79 93 9 ,9 28 37 46 56 65 74 84 89 9 .8 17 36 44 53 ("■ 71 80 94 9 ,9 28 38 47 56 66 75 8^ 911 9 iS 17 56 45 54 63 71 8> 95 9 .9 28 38 47 57 66 76 S6 91 iS 17 -,1 4=; 15 64 7-5 82 96 .0 .9 29 -,S 48 s8 6- - S6 ■12 ., ■« ^i -,- ,ft ^. t^4 -.V 8-, 1 97 ,' ,., re, -,,, 48 ^8 M -8 S- | T\ni.p. ni- LOCAHITIIMS OF NUMBKUS No. .0000 to 5549 Log. C98970 to 744-2 15 | No. 1 2 3 4 5 r, 7 1 « 9 D. 87 r.iirt 698970 699057 699144 69923. 6993.7 699404 69949. 699578 699664 69975. .'•(11 699S58 699924 700098 700.84 700271 700358 700444 70053. 7006.7 87 502 700/04 700790 700877 700963 70,050 701.36 70,222 70.309 70.395 70.482 86 .■■>03 701568 701654 70174. 70.827 70,9,3 70.999 702086 702.72 702258 702344 86 J04 702431 7025.7 702603 702689 702775 70286. 702947 703033 703. .9 703205 86 .io:> 703291 703377 703463 703549 703635 70372. 703807 703S93 703979 704065 86 JOO 704151 704136 704322 704408 704494 704579 704665 70475' 704837 704922 86 .'id 7 -05008 705094 705179 705265 705350 705436 705522 705607 70569; 705778 86 .iOf, 705864 705949 706035 706120 706206 70629. 706376 706462 706547 706632 85 5119 706718 706803 706888 706974 707059 707.44 707229 7073.5 707400 70748s 85 85 51? 707570 707655 707740 707SS26 7079,. 707996 70808. 708.66 70825. 708336 511 708421 708506 70859. 708676 70876. 708846 70893. 7090.5 709. CO 709.85 85 512 709270 709355 709440 709524 709609 709694 709779 709863 709948 7.0033 85 513 710117 7.0101 7.0187 7,0371 710456 7.0540 7,0625 7,0710 7.0794 7.0879 85 5U 710963 711048 7,1.32 71,217 7, .30. 7.1385 7, .470 71.554 71.639 7. .723 84 515 7.1807 7.1892 71,976 712060 7.2144 7.2229 7.23.3 7.2397 7.248. 7.2566 84 51G 712650 7>2734 7.2902 7.2986 7.3070 7.3154 7,323s 713323 7.3407 84 517 71349' 713575 713659 7.37+2 7.3826 7.39.0 7.3994 714078 7.4.62 7.4246 84 :.1H 7'4330 714414 714497 7.458. 7.4665 7.4-49 7.4833 7.49.6 7. ;ooo 7,';o84 84 519 7.^67 715251 '15335 7.5418 7.5502 7.5586 7.5669 7.5753 7.5836 7.5920 84 520 7,6003 7.6087 7,6,70 7.6254 7.6337 7.642. 7.6504 7.65SS 7.667. 7.6754 83 521 716838 71692, 717004 7.7088 7.7.7. 7.7254 7.7338 7.742. 7.7504 7.7587 83 522 7.767. 717754 717837 717920 7.8003 7.8086 7.8.69 7.8255 7.8336 7,84.9 83 523 7.8502 718585 7,8663 71S751 7.8834 7.89.7 7.9000 719083 7.9.65 7,924s 83 524 7'933' 719414 719497 719580 7.9663 7.9745 7.9828 7.991. 7.9994 720077 83 525 720159 720242 720325 720407 720490 720573 720655 720738 72082. 720903 83 52fi 720986 72.068 72. .51 721233 72.3.6 72,398 72.48. 72.563 72.646 72.728 82 527 72181. 72.893 721975 722058 722140 722305 722387 722469 722552 82 528 722634 7227.6 722798 72288, 722963 723045 723.27 723209 -2329. 723374 82 529 7^3456 723538 723620 723702 723784 723S66 723948 724030 724. .2 724.94 82 "87 530 724276 724358 724440 724522 724604 724685 724767 724849 72493. 7250.3 531 725095 725.76 725258 725340 725422 725503 725585 725667 725748 725830 81 532 725912 725993 726075 726,56 726238 726320 7:640, 726485 726564 726646 82 533 726727 726890 726972 727053 727.34 7272.6 727297 727379 717460 8. 534 72754" 727623 727704 727785 727S66 727948 728029 728. .0 728.9. 728273 8, 535 728354 728435 7285.6 728597 728678 728759 72884. 728922 729003 729084 8, 536 729165 729246 729327 729408 729489 729570 72965, 729732 7298.3 729893 8, 537 7299"4 730055 730.36 7302,7 730293 730378 730459 730540 730621 730702 8, 53» 73'~'782 730863 730944 731024 73, ,05 73. .86 73.266 731347 73.428 73.508 8, 539 73'5i'9 73.669 731750 73.830 73.9.. 73.99. 732072 732.52 732233 732313 8, 540 732394 732474 732555 732635 732715 732796 732876 732956 733037 733"7 80 541 733'97 733278 733358 733438 733518 733598 733679 733759 733839 7339.9 80 542 733999 734079 734.60 734240 734320 734400 734480 734560 734640 734720 80 543 734800 734880 734960 735040 735120 735200 735279 735359 735439 7355.9 80 544 735599 735679 735759 735838 735918 735998 736078 736.57 736237 7363.7 80 545 736397 736476 736556 736635 7367.5 736795 736874 736954 737034 737113 So 546 737193 737272 737352 737431 73751. 737590 737670 737749 737829 737908 79 517 737987 73S067 738.46 738225 738305 738384 738463 738543 738622 738701 79 54 « 738781 738860 738939 7390.8 739097 739.77 739256 739335 7394.4 739493 79 .'■49 5.')0 739572 739651 739731 7398.0 7398S9 739968 740047 7^0836 740.26 740284 79 79 740363 740442 740511 740600 740678 740757 7409 ' 5 740991 74,073 551 741152 741230 741309 74,388 74.467 74.546 74.624 74.703 74.782 74,860 79 .=.r,2 74'939 7420,8 742096 742.75 742254 742332 7424.. 742489 742568 742647 79 55.T 742725 742804 742882 74296. 743039 743. .8 743.96 743275 745353 74343. 78 .554 No. 7435'° 743667 743745 743823 743902 743980 744058 744.36 744215 78 1 2 3 4 5 6 7 H n. 12 3 4 5 6 7 8 9 I). 1 2 3 4 & 6 7 8 9 78 8 i6 25 31 39 47 55 62 70 83 8 17 25 33 41 50 58 66 75 79 S lA 24 3» 39 47 55 63 71 84 8 17 15 34 41 50 59 67 76 HO X 16 24 32 40 4g 56 64 72 85 8 .7 25 34 42 5, 59 68 76 -1 s 16 24 32 40 40 1" '''; -'■. »i\ n 1-^6 34 43 52 60 69 -- -.' 8 1^ ;■, ;-, 41 ■o s" "'' -1 »; 'J 1- r». -.s -r. ^- •" "" '* ri6 TABLE 6i LOGARU'HMS OF NUMBERS No. 5550 to 6099 Log. 744293 to 785259 No. 1 2_ 3 1 4 •O B 1 7 8 9 D. ftS.i 744^93 744571 744449 744528 744606 744684 744762 744840 7449'9 744997 78 .S56 745075 745'53 74523' 745309 745387 745465 745543 74562. 745699 7+5777 78 65/ 745855 745933 7460.. 746089 746.67 746245 746323 746401 746479 746556 78 558 74663+ 746712 746790 746868 746945 747023 747.0. 747.79 747256 7473)4 78 559 7474:11747489 747567 747645 747722 747800 747878 747955 748033 748.. _78 77 7481 88 748266 748343 74842. 74S498 748576 748653 74873. 748808 74S885 561 748963 749040 749.18 749.95 749272 749350 749427 749504 749582 749659 77 562 749736 7498.4 74989. 749968 750045 750.23 750200 750277 750354 75043' ■'7 563 750508 750586 750663 750740 750817 750S94 75097. 75,048 75'. 2£ 75.202 77 564 75'179 75'356 75'433 75.5.0 75.587 75,66+ 75.74. 75.8,8 75.895 75'972 77 565 75:048 752.25 752202 752279 752356 752433 752509 752586 752663 752740 77 56C 752816 751893 752970 753047 753.23 753200 753277 753353 753430 753506 77 56; 753583 753660 753736 7538.3 7538S9 753966 754042 754.. 9 754.95 754272 77 568 754348 7544*5 75450. 754578 754654 754730 754807 754883 7<;496o 755036 76 569 755'>i 755'89 755265 75534. 7554.7 755494 755570 755646 755-12 7 55799 76 570- 755875 75595' 756027 756.03 756.80 756256 756332 756408 756484 756560 'W 571 756636 7567.2 756788 756864 756940 75-0.6 757092 757.68 757244 757320 76 572 757396 757472 757548 757624 757700 757775 75785. 757927 758003 758079 76 573 758155 758230 758306 758382 75S458 758533 758609 75S6S5 75876. 758836 76 574 758912 758988 759063 759'39 759214 759290 759366 75944' 7595.7 759592 76 575 759668 759743 7598.9 759894 759970 760045 760,2. 760.96 760272 760347 75 576 76o4,,2 760498 760573 760649 760724 760799 760875 760950 ^6.025 76.10, 75 577 761176 76.25. 76.326 76.402 76.477 76.552 76.627 76,702 76.778 76.853 75 578 761928 762003 76207S 762.53 762228 762303 76237S 762453 762529 762604 75 579 762679 762754 762829 762904 762978 763053 763.28 763203 76327S 763353 ■ 7S 580 763428 763503 763578 763653 763727 763802 763877 763952 764027 764.01 75 581 764176 76425 > 764326 764400 764475 764550 764624 764699 764774 764848 75 582 7O4923 764998 765072 765.47 76522. 765296 765370 765445 765520 765594 75 583 765669 765743 7658.8 765892 765966 76604. 766.15 766,90 766264 766338 74 584 7664,3 766487 766562 766636 7667.0 766.85 I766S59 766933 767007 767082 74 585 767.56 767230 767304 767379 767453 767527 76760. 767675 767749 767823 74 586 767898 767972 768046 76S.94 76S268 76S342 7684.6 768490 768^64 74 587 76863S 7687.2 768786 768860 768934 769008 769082 769,56 769230 769303 -4 588 769377 76945. 769525 769599 769673 769746 769820 769894 769968 770042 -4 589 7701 >s 770189 770263 770336 7704.0 7704S4 770557 77063, 770705 7-0778 -4 590 770852 770926 770999 77.073 77.146 77.220 77.293 77.367 77.440 77.5.4 74 591 771587 771661 77.734 77.88. 77.955 772028 772102 772.75 772248 73 592 ■nz^iz 772395 772468 772542 7726,5 772688 772762 772835 772908 77298. 73 593 773055 773-28 77320. 773274 773348 77342. 773494 773567 775640 7737.3 73 594 7-3786 773860 773933 774006 774079 774.52 774225 774298 77437. 774444 73 595 7745'7 774590 774663 774736 774809 774882 774955 775028 775.00 7-5.73 73 596 775H6 7753'9 775392 775465 775538 7756.0 775683 775756 77S829 775902 75 597 775974 776047 776.20 776.93 776265 776338 77641. 776483 776556 776629 73 598 776701 776774 776846 7769.9 776992 777064 777.37 777209 7772S2 777354 73 599 7774^7 777499 777572 777644 7777.7 7777S9 777862 777934 778006 778079 _72 600- 778. 5> 778224 77*296 77836S 77844. 7785.3 778585 7786<;8 778730 778802 501 77S874 778947 7790.9 77909. 779.63 779236 77930S 779380 779452 779524 72 602 779596 779669 77974" 7798.3 779885 779957 780029 780,0, 7S0.73 780245 72 603 780317 780389 78046. 780533 780605 780677 780749 78082, 7S0893 780965 72 604 78.037 781. 09 78, .8. 78.253 781324 78.396 78.468 78.540 78. 6. 2 78.684 72 605 -8'755 78.827 78.899 782042 782.14 782,86 782258 ,82329 78240. 71 606 782473 782544 7826.6 78268S 782759 782S3, 782902 782974 783046 783. ,7 72 607 783.89 783260 783332 783403 783475 783546 7836,8 783689 7S376. 7S3832 71 608 783904 783975 784046 7S4..8 784,89 78426, 784332 784403 784475 7845^6 7. 509 784617 784689 784760 78483. 784902 784974 7S5045 785. .6 785. 87 -85259 7. No. 1 2 3 4 5 7 » 9 TT n. 1 2 3 4 5 6 7 8 9 D. 1 2 3 4 5 6 7 8 9 71 7 14 II iS IS 45 SO ^7 (•4 75 7 .5 22 30 3- 4S 52 60 6- 72 7 14 =1 -<) •>(• 4-! SO sS 6, 76 8 ,5 23 30 38 46 s; 6. 68 "^ 7 n 2i 19 -,6 +4 ^i sS ''^ 77 S 15 !•; 31 38 46 ^4 62 69 M 7 .$ 1. ■!" ;- ^.> ;t so ^~ 7R ? 16 :-, ;i \n 4- 55 <•• T TAR IF nt 717 LO(MKlTHMS OF NUMBKRS No. C 100 to 6649 Log. 785330 to 82->756 | 610 1 2 3 1 4 1 5 C 7 8 9 P. 785330 78540. 785472 785543 7856.5 785686 785757 785S28 785899 7X5970 71 611 786041 7861.2 786.83 786254 786325 786396 786467 786538 786609 786680 7< 612 786751 786822 786893 786964 787035 7S7.06 787.77 787248 7873.9 787390 7« 613 787460 78-53> 78760Z 787673 787744 7878,5 787885 787956 788027 788098 "1 614 788168 788239 7883.0 78838, 7S845, 788522 78S593 788663 788734 7S8804 7' 615 7S8S75 788946 7890.6 789087 789-57 789299 789369 789440 7895.0 7, 616 7S958, 78965. 789722 789792 789S63 7S9933 790004 790074 790-44 7902,5 70 617 790285 790356 790426 790496 790567 790637 790707 790778 790848 7909,8 70 618 790988 79.059 791.29 79.199 79,269 79.340 79.4.0 79,480 79,550 791620 70 6iy 620 79169. 79139^ 79.76. 79. S3. 79.90. 79,97, 792672 79204. 792... 792,8, 792252 792322 7° 792462 792532 792602 792742 7928.2 792882 792952 793022 70 621 793092 793.62 79323, 79330. 793371 79344' 7935.. 793581 79365. 79372, 70 622 793790 793860 793930 794000 794070 794.39 794209 794279 794349 7944>8 70 623 794488 794558 794627 794697 794767 794836 794906 794976 795045 795. '5 70 624 795-85 795^54 7953H 795393 795463 795532 795602 795672 79574. 795S.. 70 625 7958S0 795949 796019 7960S8 796158 796227 796297 796366 796436 796505 ^ 626 796574 796644 7967.3 796782 796852 796921 796990 797060 797.29 797,98 69 G27 797268 797337 797406 797475 797545 797614 797683 797752 79782, 797890 69 628 797960 798029 798098 798.67 798236 798305 798374 798443 7985.3 798582 69 629 630 79865. 7987- 798858 798927 798996 799065 799-34 799203 799272 69 79934> 799409 799478 799547 7996,6 7996S5 799754 799823 799892 79996, 631 800029 800098 800Z36 800305 800373 800442 8005,1 800580 800648 69 032 8007.7 800786 800854 800923 800992 80.06. 80. .29 801,98 80,266 80.335 69 633 80.404 80.472 80.54. 80.609 80,678 80,747 80.8.5 801884 801952 80202, 69 634 802089 802.58 802226 802295 802363 802432 80x500 802568 802637 802705 69 635 802774 802842 802910 S02979 803047 8031.6 803,84 803252 80332, 803389 68 636 803457 803525 803594 803662 803730 803798 803867 803935 804003 80407, 68 637 S04.39 804208 S04276 804344 8044.2 804480 804548 8046.6 804685 804753 68 638 80482. 804889 804957 803025 805093 80516. 805229 805297 805365 805433 68 639 80550. 805569 805637 805705 805773 80584. 805908 805976 806044 806, ,2 68 640 806.80 806248 8063.6 806384 80645, 8065,9 806587 806655 806723 806790 68 641 806858 806926 806994 80706. 807,29 807,97 807264 807332 807400 807467 68 642 807535 807603 807670 807738 807806 807873 80794 1 808008 808076 808,43 68 643 808279 808346 8084.4 80848. 808549 8086,6 808684 808751 8o88.8 67 644 808886 808953 80902, 8090S8 809.56 809290 809358 809425 809492 67 645 809560 8096x7 80969+ 809762 809829 809896 809964 8.0031 8.0098 8.0.65 67 Wf. «.0233 8.0300 8,0367 8.0434 8.050. 8,0569 8,0636 810703 8.0770 8. 0837 67 647 8.0904 S1097. 8. .039 8. ..73 8,1240 8,1307 811374 8. .44, 8. .508 67 648 8. .575 8.. 642 8. .709 8M776 8.. 843 81,910 81,977 812044 8.2.. I 8,2.78 67 C49 8.2245 8.23.2 8.2379 8.2445 8.25.2 8.2579 8,2646 812713 812780 8.2847 67 67' 050 8.29.3 8.2980 813047 8, 3, ,4 8,3,8, 8.3247 8,3314 813381 813448 8.35.4 051 8.358. 8.3648 8,37.4 8.378. 8,3848 8.39,4 8,3981 8,4048 814114 8.4.8. 67 052 8.4248 S143.4 3,43Si 8.4447 8,45.4 8,458, 814647 8,47,4 8147S0 8.4S47 67 653 8.4513 8.4980 8,5046 8.51,3 8.5.79 8,5246 8.53.2 8.5378 815445 8.55.. 66 654 815578 8.5644 8.57.. S.5777 8,5843 8.59.0 8.5976 8,6042 816109 8.6.75 66 055 8.624. 816308 8.6374 8.6440 8,6506 8.6573 816639 8,6705 8,677. 8.6838 66 056 8.6904 816970 8,7036 8.7.02 8,7.69 8.7235 81730. 8.7367 8.7433 8.7499 66 657 8.7565 S.763, 8,7698 8,7764 8.7830 8,7896 817962 8,8028 8,8054 8.8160 66 658 8.8226 8.8292 8,8358 8,8424 8.8490 8,8556 8,8622 8,8688 8,8754 8.8820 66 059 660 8.8885 8,895. 8,90,7 8,9083 8.9.49 8,92,5 819281 8,9,46 8,94,2 8,9478 66 ^6r 8.9544 8,96.0 8,9676 8,9741 8.9807 819873 819939 820004 820070 820,36 661 82CZO. 820267 820333 820399 820464 820530 820595 82066, 820727 820792 66 002 82C858 820924 820989 82,055 82, ,86 821251 82,3.7 82,382 82.448 66 003 82.5.4 82. 579 82,645 8217.0 82.775 82,84, 821906 82,972 S22037 822,03 65 604 812.68 82223, 8222,; 822364 822430 822495 822560 822626 822691 822756 65 No. > 2 3 4 5 6 7 8 9 D. U. 123456789 D. I 2 3 4 5 6 7 8 9 05 6 I] 19 i6 31 39 45 51 58 68 7 '4 20 27 34 4' 4» 54 «i 00 7 13 »o 16 33 40 46 53 59 69 7 14 21 j8 34 41 48 55 6j 0- 7 13 10 17 33 40 47 54 60 70 7 ,4 2 1 28 35 42 49 56 63 t» - .4 30 17 34 41 48 ,4 6i 71 7 -4 2. ^8 35 43 50 57 64 718 TABLE (U LOGARITHMS OF NUMBKIW No. GG50 to 7 199 L<.g. H-2-282-2 to So7-27-2 No. 1 2 3 4 5 C 7 g 9 D. G6i Xl2«2i 8228S; 822952 8230,8 823083 823,48 8232,3 823279 823344 823409 65 C6G ?=3474 823605 823670 823.35 823800 823S65 823930 823996 82406. 65 067 8.4.26 824256 82432. 824386 82445, 8245,6 82458. 824646 82471, 65 6(j8 «247 76 S24S4. 824906 82497. 825036 825,0. 825,66 82,2,, 825296 82536, 65 669 6;o 825+26 825491 825556 825621 S256S6 82575. 8258,5 8258S0 825945 8260,0 65 826075 826.40 826204 826169 826334 826399 826464 826.28 826593 826658 65 671 S26723 8267^7 S26S52 8269.7 8269S, 827046 827... 827,75 827240 827305 65 672 827369 827434 827499 827563 827628 '827692 827757 82782, 827S86 82795. 65 67;t 828015 828080 828.44 828209 828273 "28338 828402 82S467 82853, 828595 64 674 828660 82S724 828789 828853 8289,8 828982 829046 829.,, 829,75 829239 64 675 829304 829368 829432 829497 82956, 829625 829690 829754 8298,8 X29S82 64 o76 8^9947 8,00.. 830075 830204 830268 830332 830396 830460 S50525 64 677 8305S9 S 306 5 3 8307.7 8,078. 830845 830909 830973 83.037 83, .02 851166 64 678 83.2,0 83.294 83.358 83,422 83,486 83.550 83,6,4 85.678 83.742 851806 64 679 831870 83.934 832573 83.998 832062 832700 832,26 832.89 832253 8323.7 832,8. 832445 _64_ 64 S32509 832637 832764 S32828 832892 832956 835020 833083 681 833'47 8332.. 833275 83333S 833402 833466 833530 833593 833657 83372. 64 mi 833784 83,848 8,39.2 833975 834' 39 834,0, «34.66 S3423O 834294 834357 64 683 8,44^. 834484 S 34 548 8346,. 83467$ 834739 834802 834S66 834929 834993 64 681 83,056 S35.20 835.83 835247 II35310 «35J7J 835437 835500 835564 835627 63 685 835691 835754 8358.7 835S8, «359«- »,6oo7 83607, 836,34 836.97 S36261 6, 686 8,6,24 8363S7 836451 8365,4 836577 83664, S36704 836767 836S30 836894 6, 687 836957 837020 837083 837,46 837210 837273 837336 837399 837462 837525 6, 688 8,7588 837652 8377.5 8,7778 837841 837904 837967 838030 838093 838156 6, 689 690 8582.9 838282 838345 838408 838471 1 838534 838597 838660 838723 83S786 ^, 83SS49 8389.2 838975 8„o,8 83910. 839,64 839227 839289 839352 8394,5 691 839478 83954. 839604 839667 839729 839792 839855 8399,8 8399S. 840043 63 692 840.06 840.69 8402,2 840294 840357 840420 840482 840545 840608 84067, 63 693 840733 840796 840859 84092, 840984 84,046 841.09 34.. 72 84,234 84.297 6, 694 84.359 84.4^.2 84.485 84,547 84,6,0 84,672 84.735 84.797 84,860 84,922 63 695 S4.985 842047 84 •• . 10 842.72 842235 842297 842560 842422 842484 842547 62 690 842609 842672 842734 842796 S42859 84292, 842983 843046 843.08 843.70 62 697 843233 843295 843357 843420 S43482 8^3544 843606 843669 84373. 843793 62 698 843855 S43918 84,980 844042 844.04 844166 844229 84429. 844353 8444.5 62 6')9 844477 844539 84460. S44664 845284 844726 845346 844788 844850 8449.2 844974 845056 62 IT 700 S45098 S45.60 845222 845408 845470 845532 845594 845656 70i 34S7<8 845780 845841 845904 845966 84602 8 846090 846.51 846113 846275 62 1 702 846337 846399 84646, 846523 8465X5 846646 846708 846770 846831 846894 62 703 846955 847017 847079 847.4. 847202 847264 847326 84738S 847449 8475.1 62 704 S47573 847634 847696 847758 S478.9 84788, 847943 84S004 848066 848,28 705 84.S.89 S48251 8483.2 848374 848435 848497 848559 848620 848682 848743 62 706 848805 S48S66 848928 8489S9 S49051 849.. 2 849.74 849-35 849297 849358 6, 707 849419 84948. 849542 849604 849665 849726 849788 849849 8499,, 849972 6, 708 850033 850095 S50.56 8502.7 850279 850340 850401 850462 850524 8505S5 6, 709 710 850646 8 50707 850769 850830 S5089. 85C952 85.564 85.0,4 85.075 85. .36 85.-97 6. 61 85.258 85.320 85,38. 85.442 85.503 85,625 85. 686 851747 85.S09 711 85.870 85.93. 85.992 852053 8521.4 852.75 852236 852297 852358 8524,9 61 712 8524S0 85254. 852602 852663 852724 852785 852846 852907 8 52968 853029 f , yi3 853150 8532., S53272 853333 853394 853455 8535.6 853577 8536,7 714 853698 853759 853820 85388, 85394. 854002 8540O3 854.24 854.85 854245 6, 715 S 54306 854367 854428 8544S8 854549 8546,0 854670 85473. 854792 854852 6, 716 854974 S55095 855.56 8552,6 855277 855337 855398 855459 717 855519 855580 855640 85570, 85576, 855S22 855882 S55943 856003 856064 6, 718 856.24 S56.85 856245 856306 856366 856427 856487 856548 856608 85666S 60 719 No. S56729 S56-89 856850 S569.0 8569-0 85-03. 85-091 857.52 8572.2 857272 60 D. 2 1 :i ! 4 6 7 1 8 D. 1 2 3 4 5 6 7 R 9 n I 2 3 4 5 6 7 s 9 00 6 11 iS =4 30 36 41 4R i;4 63 6 ,, ,9 25 ,. ,S 44 50 5- 61 6 ,1 iS =4 30 3- 45 49 Si 61 6 1, 19 26 32 ,? 45 M 58 62 6 ,2 ,<) =5 31 37 43 i'> 5" 6.. 6 .3 ,9 26 32 39 45 5' 58 TAr.T.F. 04 719 LOUAKITIIMS OF NUMBERS y.n. 7--'(>0 to 7749 Log. 857032 to 889-240 J No. 720 1 2 3 4 5 6 7 8 9 D. *5733i 857393 857453 ^575'3 857574 857634 857694 857755 8578,5 857875 60 721 857935 857995 858056 858.16 S58.76 858236 858297 ^.58357 8584,-' 858477 60 722 !^5«537 858597 858657 8587,8 858.78 85S838 858898 858958 8590.8 859078 60 723 8(9.38 859198 859258 8593.8 859379 859439 859499 859559 8596,9 859679 60 724 S59739 859799 859859 859918 859978 860038 860098 860.58 8602,8 860278 60 725 S6033S 860398 860458 86051S 860578 860637 S6C697 860757 8608,7 860877 60 726 86C937 S60996 86.056 861116 86.176 86.236 86.295 86,355 86.4.5 861475 60 727 861534 86.594 86.654 86.714 861773 86.833 86,893 86,952 862012 862072 60 728 S62131 862191 86225. 862310 862489 862549 862608 86266S 60 729 730 S62728 862787 862847 S62906 862966 llTcl] 863085 863144 S63204 863263 60 863523 S63382 863442 86350, 863561 863620 863680 863739 863799 86385S 59 731 863917 863977 S64036 864096 864,55 8642.4 864274 864333 864392 S64452 59 732 >'645" 864570 864630 864689 864748 864808 864S67 S64926 864985 865045 59 733 865.^4 865.63 865222 865282 86534, 865400 865459 8655,9 865578 865637 5, 1 -34 865696 865755 8658.4 865874 S65933 865992 86605, 866.10 866169 866228 59 735 866287 866346 866405 866465 866524 866C83 866642 866701 S66760 8668,9 59 730 866878 S66,;37 866996 S67055 867,14 867,73 867232 86729, 867350 867409 59 737 867467 867526 867585 867644 867703 867762 86782, 867880 867939 867998 59 738 8680^6 868. .5 868292 868350 86S409 868468 86S527 8685S6 59 739 710 86S644 S6S703 868762 868821 868879 S68938 868997 S69056 869642 8691,4 S69.73 59 869232 869290 869349 869408 869466 869525 869584 869701 869760 59 741 869818 S69S77 869935 869994 870053 870,,, 870,70 S70228 870287 870345 59 742 870404 870462 87052, 870579 870638 870696 870755 870813 870872 870930 58 743 870989 87.047 87. ,06 871164 87,223 87,28, 871339 87.456 871515 58 744 87'573 87.63, 87.690 871748 87,806 S7.S65 87.923 87198' 872040 872098 58 745 872.56 8711.5 872273 87233. 872389 871448 872506 872564 872622 872681 58 746 871739 871797 871855 8729.3 871971 873030 873088 873.46 873204 873262 58 747 87331. 873379 873437 873495 873553 8736.. 873669 873717 873785 873844 58 748 873902 873960 8740.8 874076 874,34 874192 874250 874308 874366 874424 58 749 874482 874540 874598 874656 874714 874772 874830 874888 874945 87 5°°3 Jl T50 87506. 8751.9 875.77 875235 875293 875351 875409 875466 875514 875582 58 751 875640 875698 875756 8758,3 875871 875929 875987 876045 876,02 876,60 58 752 8762.8 S76276 876333 87639. 876449 876507 S76564 876622 876680 876737 58 753 876795 876853 8769.0 876968 877026 877083 877.41 877.99 877156 877314 58 754 877371 S77419 877487 877544 877602 877659 8777.7 877774 877831 877889 58 755 877947 878004 878062 8781,9 878177 87S234 878292 878349 878407 878464 57 756 878511 878579 878637 878694 878751 878809 878866 878924 87898, 879039 57 757 879096 879.53 8792.1 879268 879325 879383 879440 879497 879555 8796,2 57 758 879669 879726 879784 87984' 879898 879956 880013 880070 880,27 880,85 57 759 760 880242 880299 880871 880356 8S04.3 88047. 880528 880585 880642 8S0699 88127, 880756 57 8808.4 880928 880985 88 1042 881099 88,156 88,2,3 88,328 761 88.385 88.442 88.499 88.556 88.6.3 88.670 881717 88,784 88184, 88,898 57 702 88.955 882012 8S2069 882.26 882240 882297 881354 8824,, 8S246S 57 7C3 882525 88258. 882638 882695 882752 882809 882866 882923 8829S0 883037 57 764 883093 883.50 S83207 883264 88332. 883377 883434 88349, 883548 883605 57 7CJ 88366. 8837.8 883775 883832 1883888 883945 884002 884059 884, ,5 884,72 57 766 88+229 884285 884342 884399 854455 8845.1 884569 884625 884682 884739 57 767 884795 884852 884909 884965 885022 885078 885,35 885,91 885248 885305 57 768 88536. 8854.8 885474 88553. 885587 885644 8S57C0 885757 885870 57 769 770- 885926 885983 8S6039 886096 886152 8S6200 8S6265 88632. 886378 886434 5'' m?,T 886 547 886604 886660 8867,6 886773 886S29 886885 886942 886998 771 887054 8871. 1 887,67 887223 887280 887336 887391 887449 88756. 56 772 S876.7 887674 887730 887786 S87842 887898 887955 8880,; 888067 888.23 56 773 888179 888236 888292 88834S 888404 888460 8885,6 888573 888629 888685 56 774 No. S88797 888853 888909 888965 88902, 889077 889.34 889,90 889246 .5i 1 1 2 3 4 5 6 8 1 9 [). 0. -. 2 3 4 5 6 7 8 9 U. I 2 3 4 .', C 7 8 9 .'.6 6 11 17 22 2« H 39 4i 50 ,i9 f. .2 .8 24 29 35 41 47 53 .. 6 11 1- 23 28 34 40 4h (;i M S 12 .8 24 3.. ;6 41 48 54 720 TABLE Gt LOGARITHMS OF NUMBERS j No. 7730 to 8^99 Log 889302 to 9190^6 No. I 1 2 1 .. 4 1 .^ 6 1 r sis D. 56 r?5 SS9302 88935818894.4 8899-3 «89974 8S9470 889526 1 889582 S89638 8S9694 889750 1 889806 7?« 889862 89C030 S90C86 890.4. 1 890.97 1 890253 j S9C3C9 1 890565 56 777 89042. S90477 S90533 890589 S9C645 8907C0 890756 S908. 2 8908681890924 56 778 8 90980 891035 1 891091 89.. 47 89.203 8912591 891314 891370 1 89. 426 89.482 56 779 78? S9'537 S92095 891503 89. 649 89. 705 89.760 89.8,61891872 891928189.983 89,2^ 892595 56 56 892.50 892206 S92262 8923.7 892373 j 892429 892+84 1 892540 781 892651 S92707 892762 892818 892S73 S92929 8929S5 893040 1 893096 89J.5. 56 782 89 3 207 893262 8933.8 893373 893429 893484 893540 8935951893651 853706 56 783 S93762 S93817 S93873 S93928 893984 1 894039 ! 894C94 894.50 894205 89426. 55 784 8943.6 S9437. 894427 S94482 894538 1 894593 1 S94648 894704 894759 894814 55 785 89+870 894925 894980 S95036 89509. 895146189520. 895257 8953.2 895367 55 780 895423 895478 895533 895588 895644 895699 1 S95754 895809 895864 895920 55 787 S95975 896030 896085 896.40 896.95 89625. S963C6 89636. 8964.6 89647, 55 788 896526 89658. 896636 896692 896747 896S02 896857 8969.2 896967 897022 55 789 897077 S97.32 897>87 897242 897297 897352 1 897407 897462 8975.7 S97572 ^5_ 790 S97627 8976S2 «97737 897792 1 897847 1 897902 [ S97957 1 S980.2 898067 898.22 55 791 898.76 89823. 898286 898341 S98396 89845. 898506 I 89856, 898615 898670 55 792 898725 89S780 S98835 898890 898944 898999 1 899054 899 1C9 899164 8992.8 55 793 S99273 899328 8993X3 899437 899492 8995+7 j 899602 899656 899711 899766 55 794 899S2. 899875 899950 899985 900039 90009+1900149 9C0203 900258 9003.2 55 793 900367 900422 900476 90053. 9005S6 9C0640 9C0695 9C07+9 1 9C080+ 900859 55 79(i 9009.3 900968 90.022 90.077 90. .3. 90.. 86 90.240 90.295 90,3+9 901404 55 797 90.458 90.5.3 90.567 90.622 90.676 901731 901785 90.8+0 90.894 90.948 54 798 901003 902057 902.12 902.66 90222. 902275 902329 90238+ 90243S 902492 54 799 ioo 902547 902601 902655 9027.0 902764 9028.8 902873 902927 90298. 903036 54 903090 903.44 903.99 903253 903307 90336. 903+16 903+70 903524 903578 54- 801 903633 903687 90374. 903795 903849 903904 903958 90+0.2 904066 904.20 54 802 904.74 904229 904283 9743 9"797 9. .850 9.. 903 91.956 912009 9.2063 9.2.69 53 817 9.2222 9.2275 9.2328 9.238. 9'2435 9.2488 9.25+. 9.259+ 9116+7 9.27CO 53 818 912753 9.2806 912859 912913 912966 9.30.9 9.3072 913.25 9.3.78 9.323. 53 819 820 9.3284 9'3337 913390 9>344; 9'3496 914026 9>3549 9,3602 914.32 9>3655 9.3708 9.376. 53 913814 9.3867 9.3920 9>3973 9.4079 9. 4. 84 9.4237 9.4290 53 821 9'434, 914396 914449 9.4502 9>4555 914608 9.4660 9'47i3 914766 9.48.9 53 822 9.4X72 914925 9.4977 9.5030 9.5083 9.5.36 9.5.89 9.524. 915294 9.5347 53 S23 915400 9'S453 9'5505 9"5S58 915611 9.5664 9.57.6 9.5769 915822 9.5875 53 821 9.5927 9.5980 9.6033 9.6085 9.6. j8 9.6.9, 9.624J 9.6296 9.6349 9.640, 5 3 82i 916454 916507 9.6559 9.66,2 9.6664 9.67.7 9.6770 9.6822 916S75 9.6927 53 826 9.69S0 9'7033 9.7085 9.7.38 9.7.90 9'72+3 9 '7295 9.734S 9,7400 9'7453 53 827 917506 9'755« 9.76.. 9.7663 9.77.6 9.776S 9.7«2o 9>7X73 9.7925 917978 52 828 918030 9.8083 9.8135 918.88 9.8240 9.S293 9'S345 9.8397 9.8450 9.8502 52 829 No. 9'*55i 9.8607 918659 9.87.2 9.8764 9. 88. 6 9.8869 9.892. 9.8973 9.9026 52 I 2 3 1 4 5 6 7 8 9 n D. I 2 3 4 3 6 7 8 9 ». I ? 3 4 J 6 7 S 9 52 s .0 .6 z> .6 3, 36 4- 47 55 5 ,, .6 22 27 33 38 44 49 b^ c J I 16 11 26 32 37 42 4S 56 6 ., .7 22 28 34 39 45 50 54 5 II .6 22 27 3^ 3* +3 4'/ TABLE Gi LOGAIUTHMS OK NUMBERS 1 No. 8300 to 884:) Lor. 91 11078 to 946894 j No 1 1 i 2 1 ;i 1 4 1 5 1 fi 1 7 i « 1 !l D 830 9190-!! 919130 919,83 919235 9'9^87 919340 919392 919444 9.9496 9.95+9 831 919601 919655 919706 I 919758 9,9810 [ 9,9862 91991419,9967 9200.9 91007 ■ 832 92012; 920176 920228 1 920280 1 920332 1 920384 920436 j 9204S9 920541 910593 B33 920645 920697 920749 I 920801 i 920853 1 920906 920958 921010 921062 92,114 8.54 921166 92.218 92,27c 92.322 9»'374 921426 921478 921530 921582 921634 835 9216S6 9».738 92,-90 921842 921894 92.946 921998 922050 922.02 922154 83G 922206 922258 9223,0 922362 9224.4 922466 922518 922570 922622 922674 807 922725 9"777 922829 922SS1 922933 922985 923037 923089 923140 923192 52 1 838 9^3^+4 923296 923348 923399 91345. 913503 913555 923607 923658 9137.0 5» 1 839 925702 9238.4 923S65 923917 923969 92402, 924072 924,24 924,76 924228 5» 924279 924331 92.;.383 924434 924486 924558 924589 92464, 924693 924744 841 924796 924848 924^99 924951 925003 925054 925,06 915.57 925209 92526, 842 5,25312 925364 9^54'5 925467 9255.8 915570 925621 915673 915725 915776 843 925S28 925S79 9=593' 925982 926034 926085 926137 926188 926240 92629, 844 926 34X 926394 926445 926497 926548 926600 92665, 926702 926754 926805 84") 926857 926908 926959 92701, 927062 917.14 927165 927216 92726S 927319 81i; 91-370 9^7+" 927524 917576 927627 927678 927730 91778, 927832 847 927S85J 927935 927986 928037 928.40 928191 928242 928293 918345 818 92S396192S447 928498 928549 928601 928652 928703 928751. 928805 918857 819 928908 928959 929010 929061 929T12 929,65 929215 929266 9193.7 929368 929419 929470 929521 929572 929623 929674 929725 929776 929827 919879 8,-. I 929930 929981 930032 930083 930.34 930185 930236 930287 930338 930389 8a2 930440 930491 930542 930592 930643 930694 93'^745 930796 930847 930898 853 930949 93.000 93105. 931102 93. '53 931203 93.154 93.305 93.356 931407 851 93145S 931509 93.560 93.6.0 931661 93,712 931763 93,8,4 93.865 93,9.5 855 93.966 932017 932068 9321.8 932.69 932220 932271 932322 932372 932423 856 93H74 93^5^4 93»575 932626 932677 932727 931778 932829 932879 932930 857 932981 93303. 933.33I933.83 933134 933185 933335 933386 933437 858 933487 933538 933589 933639 933690 935740 93379. 933841 933892 933943 859 933993 9 34° 44 934094 934.45I934.95 934246 1 934296 934347 934397 934448 860 934498 934549 934599 934650 1 934700 9347 5" 934801 9348';2| 934901 934953 ~5o~ 861 935003 93S°54 935.04 935.54,935105 935155 935306 935356 935406 935457 862 935i°7 935558 935608 9356581935709 935759 935809 935860 9359.0 935960 863 93601, 93606, 936.11 936,62 [9362,2 936262 936313 936363 9364.3 936463 864 936514 9-6564 936614 936665,9367,5 936765 9368.5 936865 9369,6 936966 50 865 937016 937066 937. '7 937.67 937117 937267 9373'7 937367 9374.8 937468 50 866 93-518 937568 9376.8 957668 9377.8 937769 9378.9 937869 9379,9 937969 867 93S019 938069 938,19 938.69 9382,9 938269 9383.9 938370 938420 938470 50 868 9385"! 938570 938620 93S670 938710 93S770 938820 938870 938920 938970 50 869 9590201939070 939,20 939,70 939220 939170 939310 939569 9394.9 939469 50 870 959;'9'939569 939619 1 959669 9397.91939-69 9398.9 939869 959918 939968 "1°^ 871 940018 1 940068 9401 18! 940168 9402,8 940267 9403.7 940367 9404.7 940467 872 940516 9405O6 940616 1 940666 '. 940716 940765 9408,5 940865 9409.5 940964 50 873 941014 941064 9411,41 941,63 941213 941263 94.3.3 94,362 94.4.1 94,462 874 941511 941561 94,6, , 1 941660 94. -.0 94,760 94.809 941859 94,909 94,95s 50 875 942008 942058 942,07 1 942,57 942207 942256 942306 941355 941405 9+1455 50 876 9*2504 942554 942603 942653 9.; 1702 941751 94280, 94185. 942901 942950 50 87- 943000 943049 943099 [943148 945.98 9431+7 94319" 943346 943396 9+3+45 49 878 943495 943 544 943C93 1943643 943692 943741 94379. 94384. 943890 9+3939 49 879 943989 944038 I944C88; 94413- 944186 944236 944185 944335 944384 9+4+33 49 l"8ll 944483 |94453i|9445S' 194463' 944680 944729 944779 944828 944877 944927 +9 381 9449-6 1 945025 945074: 945 "H 945.73 945222 945171 945311 945370 9+5+'9 +9 882 945469 945518 945567:9456.6 945665 9457'5 945764 9458.3 945862 94^912 +9 883 94 596 • 9460,0 946059 946108 946.57 946207 946256 946305 946354 946+03 49 884 946452 946501 94655.1946600 946649 946698 946747 946796 946845 94689+ j49. No. I 2 1 S 4 5 6 7 8 9 D. IJ. 1 2 3 4 5 6 7 8 9 1). 1 2 3 4 5 6 7 8 9 19 5 10 15 20 24 29 34 39 44 51 5 10 15 20 25 31 36 41 4* 51) 5 10 15 20 25 30 35 40 4"; 52 5 10 16 21 26 31 36 42 4 1'2'2 TABLE 64 X.UUAlUrilMS Ol'- NUMBERS No. 8850 to 94 1 9 Log. 946943 to 974005 No. »»5 1 2 3 4 5 6 7 8 9 U. 946943 946992 94704. 947090 947,40 947.89 947238 947287 947336 947385 49 886 947434 947483 947552 94758, 947630 947679 947728 947777 947826 947875 49 887 947924 947973 948022 948070 948,, 9 948168 948217 948266 9483,5 948364 •♦9 948413 94S462 9485.. 948560 948609 94S657 948706 948755 948804 94S853 49 889 94890^ 948951 948999 949048 949097 949146 949195 949244 1 949292 949341 »9 syo 949390 949439 949488 949536 949585 949634 949683 949731 1 949780 949829 49 H91 949878 949926 949975 950024 950073 950,21 950170 950219 950267 950316 49 892 950365 950414 950462 9505., 950560 950608 950657 950706 950754 95C803 49 893 950851 950900 950949 950997 95.046 95.095 951143 95,192 95,240 95.289 49 991 95>338 95.386 95H35 95.483 951532 95.580 951629 95.677 95,726 95.775 49 B95 951823 95.872 95.920 95.969 9520.7 952066 952114 952,63 9522,, 952260 48 996 952308 952356 952405 952453 952502 952550 952599 952647 952696 952744 48 897 952-92 95284. 952889 952938 952986 953e34 953083 953,31 953180 953228 48 899 953^76 953325 953373 953421 953470 953518 953566 9536.5 953663 95371. 48 899 9537*0 953808 953S56 953905 953953 954001 954049 954098 954,46 954.94 48 48 900- 954243 954291 954339 954387 954435 954484 954532 954580 95462S 954677 901 954725 954773 95482. 954869 9549:8 954966 955014 955062 955,10 955.58 48 902 955207 955255 955303 955351 955399 955447 955495 955543 955592 955640 48 903 955688 955736 955784 955832 955880 955928 955976 956024 956072 956.20 48 904 956168 9562.6 956265 9563.3 95036. 956409 956457 956505 956553 956601 48 905 956649 956697 956745 956793 956840 956888 956936 956984 957032 95708c 48 906 957128 957176 957224 957272 957320 957368 957416 957+64 957512 957559 48 907 957607 957655 957703 957751 957799 957847 957894 957942 957990 95803S 48 908 958086 958.34 95S.8. 958229 958277 958315 958373 958421 958468 958516 48 909 910' 958564 9586,2 958659 958707 958755 958803 958850 958S98 958946 958994 48 959041 9590S9 959>37 959.85 9.19232 959280 959328 959375 959423 95947. 48 911 959518 959566 9596,4 95966. 959709 959757 959S04 959852 959900 959947 48 912 959995 960042 960090 960,38 960,85 960233 960280 960328 960376 960423 48 913 960471 9605.8 960566 9606.3 960661 960709 960756 960804 96085. 960899 48 9U 960946 960994 96.041 96,089 961,36 961184 96123, 961279 96.326 96.374 47 915 96,42, 96.469 96.5,6 961563 96161, 96,658 96,706 961753 96,80. 96.84S 47 916 96.89s 96.943 961990 962038 9620S5 962,32 962180 962227 962275 962322 47 917 962369 9624.7 961464 9625,, 962559 962606 962653 96270, 962748 962795 4-' 918 962843 962S90 962937 962985 963032 963079 963126 963174 96322. 96326S 47 919 9633.6 963363 9654,0 963457 963504 963552 963599 963646 963693 963741 47 920 963788 963835 963882 963929 963977 964024 964071 9641,8 964165 964212 47 921 964260 964307 904354 96440, 964448 964495 964542 964590 964637 964684 47 922 964731 964778 964S25 964872 96+919 964966 965013 96506, 965108 965.55 47 923 965202 965149 965296 965343 965390 965437 965484 96553' 965578 965625 47 924 965672 965719 965766 9658,3 965860 965907 965954 96600, 966048 966095 47 925 966.42 966.89 966236 966283 966329 966376 966423 966470 9665,7 966564 47 926 9666,, 966658 966705 966752 966799 966845 966892 966939 966986 967033 47 927 967080 967127 967,73 967.20 967267 967314 967361 96-408 967454 967501 47 928 967548 967595 967642 967688 967735 967782 967829 967S75 967922 967969 47 929 930 068062 96S109 968,56 968203 96S249 968296 968763 968343 968390 968436 IT 96S4S3 968530 96S576 968623 968670 968716 9688,0 968856 968903 931 968950 968996 969043 969090 9691361969.83 969229 969276 969323 969369 47 932 9694.6 969463 969509 969556 969602 969649 969695 969742 969789 969835 47 933 969882 96991S 969975 970021 970068 970114 970161 970207 970254 9703^0 47 934 9r''347 970393 970440 9704S6 970533 970579 970626 970672 970719 970765 46 935 9708.2 970858 970904 970951 970997 971044 971090 97,137 971183 97.229 46 936 97.276 97.322 97.369 971415 971461 97150S 971554 97.601 97.647 97.695 46 93; 971740 97.7S6 97.832 97,879 97.925 971971 972018 972064 972. JO 972.57 46 938 972203 972249 972295 972342 972388 972434 972481 972527 972573 972619 46 939 972666 9727.2 972758 971804 972851 972897 972943 972989 973035 973CS2 46 910 973>28 973-74 973220 973266 9733.3 973359 973405 973451 973497 97354 3 46 1)41 No." 973590 973636 973682:973728 973774 973820 973866 973913 973959 974005 46 1 ' 1 ' 4 5 6 7 9 1 9 D. D. 1 2 3 4 5 6 7 8 9 D. I 2 3 4 » 6 7 8 9 1 •6 5 9 14 i8 I, 28 32 57 41 48 5 JO 14 ,9 24 29 34 38 4; 1 47 5 9 14 19 23 28 33 jg 42 49 5 10 ,5 10 24 29 34 39 44 1 . .., f TABI.F. 64 723 LOOARITHMS OF NUMBERS No. 'J420 to 9'j99 Log. 974051 to 999U57 No. 942 1 2 3 1 4 5 1 7 ! 8 1 9 u. 46~ 974051 974097 974«43 974189 97413s 974181 9743»7 974374 9744,0 97446f 913 9745'» 974558 974604 974650 9-4696 974741 974788 974834 974880 974916 46 911 97497^ 9750.8 975064 975. .0 975-56 9752-^1 97514S 975194 975340 975386 46 94.') 97S431 975478 9-5514 975570 9756.6 975662 975707 975753 975799 975845 46 940 9:'589' 975937 975983 976029 976073 976.2. 976.67 976212 976258 976304 46 94 7 9763,0 976396 976442 976488 976533 976579 976625 97667. 9767.7 ^76763 46 918 9-68c>i 9T6854 976900 976946 976991 977037 9770S3 977129 977.75 977220 46 949 977266 9'73'i 977358 .977403 977449 977495 97754. 977586 977632 97767S j6 46 93F 977714 977769 9778.5 977S6. 977906 977951 977998 978043 978089 978.35 9J1 978. s. 978216 978272 9783.7 978363 978409 978454 978500 978546 97859. 46 9j;i 978637 978683 978718 978774 9788.9 978S65 9789.. 978956 979002 979047 46 9.'):! 979'=95 979'38 979.84 979230 979175 97931. ,979366 9794.1 9794S7 979503 46 9.'il 9795+« 979594 979639 979685 979730 979776 97981. 979867 9799.1 979958 46 9:10 98C003 980049 980094 980140 980.85 98023. 980276 9S0322 980367 9804,2 45 9.jG 980458 980503 980549 980594 980640 98C685 980730 980776 98082. 980867 45 9.>/ 9809.1 980957 98.003 98.048 98. 093 981.39 98.184 98,229 981275 981320 45 yjH 98.366 9814.. 98.456 98. 501 981547 98.592 981637 98.683 981718 98.773 45 959 98'8.9 98227. 98.864 98.909 98.954 982000 982045 9S2090 982.35 982,8, 9S2226 _45 9823.6 982362 982407 982452 9S2497 981543 982588 982633 982678 45 9lil 9JZ713 982769 9828.4 9S2859 982904 982949 9S2994 983040 983085 983.30 45 902 983175 983220 983165 9833.0 983356 983401 983446 98349. 983536 98 3 58, 45 9G:i <)^bi6 983671 9837.6 983761 983807 983852 983897 983941 983987 9S4032 45 904 9S4077 984.22 984.67 9841. z 984157 984302 984391 984437 984482 45 905 984527 984572 984617 984662 984707 9S4751 9S4797 984842 984887 984931 45 900 984977 985022 985067 98 5.. 2 985.57 985202 985247 985292 985337 985382 45 907 985426 985471 9855.6 98556. 985606 98565. 98,696 98574. 985786 985830 45 908 985875 985920 985965 9«6o.o 9860.5 986,00 9S6144 986,89 986234 986279 45 909 986324 986569 9864.3 986458 9S6503 98654S 986593 986637 9866S2 987.30 986727 45 970 9S6772 986817 98686. 986906 98695. 986996 9S7040 987085 9S7.75 45 971 9S7219 9S7264 987309 9f7353 987398 987443 987488 987531 987577 987622 45 972 987666 98771. 987756 9«-goo 987845 987S90 987934 9S7979 988024 988068 45 973 988. .3 988202 988247 988291 988336 98S3S. 98S425 988470 9885.4 45 974 988559 9S8604 98864S 98S693 988737 988782 988871 9889.6 988960 45 9;5 989005 989049 989094 989.38 989.83 989227 9891/2 9893.6 98936, 989405 45 970 98945c 989494 989539 989583 989628 989672 9897.7 98976. 989806 9898,0 44 977 989S95 989939 989983 990028 990072 990.. 7 990.6. 990206 990250 990294 44 978 990339 990383 990428 990472 9905.6 990561 990605 990650 990694 990738 4') 979 980 9907S3 990827 9908- , 9909.6 990960 991004 99.049 J9|093_ 99.536 99. .37 99'. 82 99,625 44 44' 991226 99.270 99.3.5 99.359 99.403 991448 99.492 99.580 981 99.669 99.7.3 99.758 99.802 99.846 991890 99.935 99.979 992023 992067 44 982 992.1. 992.56 992200 992244 9911S8 991333 991377 992421 992465 991509 44 983 991554 992598 992642 992686 992730 991774 992819 992863 992907 99295. 44 984 992995 993039 993083 993.17 993.71 993216 993260 993304 993348 993391 44 985 993436 993480 993514 993568 9936.3 993657 99370. 993745 993789 993S33 44 980 993877 993921 993965 994009 994053 994097 994.4. 994.85 994129 994173 44 987 9943 '7 99436. 994405 994449 994493 9H5 37 99458. 994625 994669 9947.3 44 988 994757 99480. 994845 994889 994933 99,977 99501. 995065 995.08 995.51 44 989 990 995,96 995240 995184 995318 995371 9954.6 995460 995504 99 5 547 99S59' 44 44 995635 995679 995713 995767 9958.. 995854 995898 995942 995986 996030 991 996074 996.17 996.6, 996205 996149 996293 996337 996380 996414 996468 4-1 992 9965.1 996555 996599 996643 996687 996731 996774 9968.8 996S62 996907 44 993 996949 996993 997037 ; 997080 997.14 997.68 9971.2 99715s 997299 ;97343 44 991 997386 997430 997474' 997517 1 99756. 997605 997648 997692 9977361 997779 44 995 997823 997867 9979.0 997954] 997998 99804. 998085 998119 99*'7» 9981.6 44 1 990 998259 918303 998347 99»390 998434 1 998477 99851. 998564 998608 998651 44 997 998695 998739 998782 998826 998869 1 9989.3 998956 9990C0 999043 9990X7 44 99H 999.31 999.74 999218 999261 1 9993051999348 999392 99943 S 999479 ;995ii 44 999 999565 999609 999651 999696 1999739 1999783 999826 _99987o 9999 . 3 1 9999 57 I). " 1 2 3 1 4 1 .^ r. 7 1 « 1 •t D^ii~r !» 4 5 6 7 8 -J D. 1 2 3 4 .'. C 7 8 "9 4.1 4 9 13 '7 31 26 30 34 39 45 4 9 '3 IS 22 27 31 36 40 44 4 9 '3 18 22 26 31 35 40 4fi 5 9 14 .8 23 zS 32 37 41 724 SPHEROIDAL TABLES. COMPRESSION ,h. Latitude Longitude. 1 i III Length in feet of 1 iJI Length in feet o( . 1 Hi 2 fill' ^ ^ Deg.«c. Minute. Second. ^ ll Degroe. Minute. Se<-on 1. 68704 362755-6 6045-93 10077 60410 365233-7 608723 101454 2 68 704 362760 I 604600 100-77 2 60-373 365012-7 6083 54 101392 4 6S707 362773-6 6046-23 IOO-77 4 60-261 3643500 607250 .0. 208 6 687.1 362795-9 6046-60 100-78 6 60074 363246-3 6054-.. .00-902 H 68717 362X271 6047 12 10079 8 59-814 36.703-0 602S-38 100-473 10 6S725 362866-9 6047 78 100-80 10 594S0 35972. -7 5995-36 99923 12 68734 362815-2 604859 looSi 12 59072 357304-8 5955-08 99251 14 6S745 3629718 6049 53 100-83 14 58-592 354455-1 5907-59 9S460 16 68757 3630363 605061 100-84 1<> 58040 35"75-7 585293 97-549 18 68771 6051 -Si 100-S6 18 574.6 3474705 579.-18 95520 20 687S6 3631879 6053 13 10089 20 56-722 343343 7 572240 95 373 22 6S8oi 363274-3 6:>54 57 10091 22 55-958 33.'33 3.0031-2 5.67 .9 86119 34 68923 3639'3-« 6065 22 10.-09 34 49-976 303.. 4 2 505.-90 8,198 36 68946 364034 9 6067-25 IOI-.2 36 48758 295827-2 493045 82.74 3b 68970 364159-5 606933 101 16 38 47-481 288178-9 4802-98 80050 40 68-994 364286-3 6071-44 101. 9 40 46-146 280178-2 4669-64 77Si7 42 69-018 3644149 6073-58 loi 23 4 -J 44-757 271834-7 4530-58 75509 44 69042 364544-4 6075 74 .0. 26 44 433.3 263.5S-3 4385-97 73-100 46 69-067 364674-4 607791 .01 30 46 4.8.7 254. 5P2 4235-99 70600 48 69-092 364804-1 60S007 10.33 48 24484S2 40S0-80 6S-013 oO 69-116 364932 9 608222 10.37 50 38-676 235236-5 392061 65-.;43 52 69-140 365of'0 2 6084-34 52 37035 225335s 375559 62 50; 54 69-164 365185-4 6086-42 10. -44 54 35-350 2.5157-2 3585-95 50 7nO 56 69187 365307 9 60S8 47 101-47 56 33-623 2047140 3411-90 56 86 5 58 69210 365427 609045 loi 51 58 3.856 19,0183 32)3-64 53 S9 1 60 69231 365542-2 6092-37 101-54 60 30-051 .830833 3051-39 SO 856 62 69252 365652-9 600422 101-57 62 28-2.1 17.922 I 2865-37 47 7S6 64 69-272 365758-5 6095-98 I0I-60 64 26-337 16054S-6 2675-8. 44 597 66 69291 3658586 6007-64 101-63 66 24-432 148976-3 248294 41382 68 69-309 565952-7 609921 10.-65 68 22498 1372.9-7 38.. 70 69326 366040-2 610067 10.6S 70 20-538 125293-2 2088-22 34-S04 72 69341 366120-7 610201 101 70 72 18-553 1132.. 4 18S686 31-44S 74 69355 3661939 610323 10172 74 16-547 1009S9-1 1683.5 28-053 76 69-367 3662596 6104-32 101-74 76 14-5.ii SS64.-6 .477-30 24623 78 69378 366316-7 6105-2S 101-75 78 12478 76.840 1269-73 2.-162 80 693S7 366365-8 6106-10 101 77 80 10-421 63631-8 106053 17676 8Si 69-395 366,06-3 6.06-77 .0.-7S 82 8-352 5.0006 850-01 14-167 84 69401 36643S0 6107-30 101-79 84 6272 3S306-. 63S44 10-641 86 69405 3664607 61076S 101-79 S6 4.86 25563-9 42607 7101 88 69408 366474-4 610791 101-80 8S 2 094 1.7899 213-17 3553 91) 69-409 366479 6107-98 101-80 90 00 00 vidfd by R, will give the 'enrth, .hies, of a minute of longitude in I's corre- eof lonBiuido. atitudc, and arc published by J. D. rottor. 725 TABLE 65. NATURAL SINES, COSINES. &c. . Sine. Co sec. Tangent. Cotang. Secant. Cosine. • oooo Infinite •0000 Infinite roooo 10000 90 1 •OI75 572987 •0175 572900 1 0002 -9998 89 2 ■0349 28 6537 -0349 28 6363 1-0006 -9994 88 ;! ■0523 10 1073 -0524 1 9 08 1 1 I 0014 -g986 87 i •069S 14-3356 -0699 14-3007 I 002 J -9976 86 5 •0S72 "4737 ■087s 114301 1 0038 •9962 85 8 •1045 0-5668 ■1051 9-5144 1-0055 -9945 84 7 •I2ig 82055 •1228 8-1443 10075 -9925 «3 8 •1392 7 '853 ■1405 7 1154 10098 -9903 8S 8 ■.564 63925 -15S4 6-3.38 I 0125 -9877 81 Id •I7J6 S7SS8 •1763 50713 10154 -9848 80 II •1908 52408 ■1944 5 '446 10187 -9816 79 12 ■2079 4S097 •2126 47046 10223 -9781 78 11 ■2250 4'4454 •2309 43315 10263 -9744 77 14 •2419 41336 •2493 4 0108 10306 •9703 76 IS ■25S8 3S037 •2679 37321 1-0353 ■9659 75 16 •2756 36280 ■2867 3-4874 10403 -9613 74 ir •2924 3-4203 •3057 32709 1-0457 •9563 73 18 •3090 3236. •3249 30777 10515 -95' 1 72 19 •3256 30716 •3443 29042 10576 •9455 71 ■^0 •3420 29238 -3640 27475 10642 -9397 70 VI •3584 *7904 •3839 26051 IC711 -9336 69 •2% ■3746 36695 ■4040 24751 10785 -9272 88 23 •3907 a- 5 593 -4245 2-3559 1-0S64 -9205 67 24 •4067 24586 •4452 22460 1 0946 9135 66 25 ■4226 23662 •4663 21445 1 1034 -9063 65 26 •4384 22812 ■4877 20503 1-1126 -8988 64 27 ■4540 22027 -5095 1-9620 1 1223 8410 63 28 •4695 2 1301 ■5317 1-8807 1-1326 -8829 62 29 •4848 2-0627 •5543 I -8040 1-1434 -8746 61 30 •5000 20000 •5774 17320 « '547 -8660 60 31 •5 ISO 1 0416 ■6009 16643 1. 666 -8572 59 Si •5299 18871 •6249 I 6003 1-1792 -8480 58 33 •5446 1S361 •64C4 1-5399 1-1924 -83S7 57 34 ■5592 17883 •6745 14826 1-2062 -8290 56 3i •5736 1-7434 -7002 14281 1-2208 -8192 55 36 •5878 17013 •7265 1 3764 1-2361 -8090 54 37 6018 16616 •7536 1,5270 1-2521 -7986 53 38 ■6157 16243 -7813 1 2799 1 2090 -7S80 52 39 •6293 15890 -8098 ■ 2349 1-2868 ■777' 51 40 •6428 15572 •8391 1 1918 1-3054 -7660 50 41 •6561 ••5243 -8693 1 1504 13250 -7547 49 42 ■6691 1 4945 •9004 11 106 1-3456 •7431 48 43 •6820 1-4663 •9325 1-0724 13673 -7314 47 44 ■6947 14396 •9657 •0355 13902 -7193 46 45 ■7071 1-4142 10000 I 0000 14142 -7071 45 "" O.^ino. Secant. CotaoK. Tanprnt. Cosec. Sine /2r> TABLE 66 LOG SINKS OF SMALL ARCS TO EACH SECOND _«_ Of or 0° 1' 0" 2' 1 0= 3' 0" 4' 0° 6' 0° 6' 0° 7' 0° 8' 0° 9' 1 // 1 6- 6- 7- 7- T r 7- 7" — 00 46373 76476 6-94085 06579 16270 24.88 30882 36682 41797 K(l J 4-68557 47090 76836 6-94325 06759 164,4 24308 30986 36772 4^87-/ 59 2 4-98660 47797 77193 6-94565 06939 16558 24428 3.089 36862 4^957 5« 3 5-16270 4849^ 77548 6-94803 07. .8 .6702 24548 3. .9. 36952 42037 57 4 5-28763 49'75 77900 6-95039 07296 .6845 24668 3.294 37042 42117 5« 5 5-3845+ 49849 78248 6-95275 07474 .6987 2^787 3.396 37.32 42.97 55 « 5-46373 50512 78595 6-95509 0765. .7130 14906 3,498 42277 54 7 5-53067 51165 78938 6-95742 07827 17271 25024 3,600 373.0 42356 53 8 5-5S866 5.808 79278 6-95973 08003 ■74' 3 25.42 3.702 37399 42435 52 9 5-63982 5244a 79616 6-96204 08177 '7553 25260 3.803 37488 425. 5 51 IF 5-6«557 53067 79952 6-96433 08351 .7694 25378 3.904 37577 42594 "50" II 5-72697 53683 80285 6-96661 08525 '7834 2549 s 32005 37666 42673 49 12 5-76476 54291 80615 6-96888 0869S 17973 256.2 32106 37754 4275' 48 13 5-7995^ 54890 80943 6-97113 08870 .8.12 25728 32206 37842 42830 47 14 5-83170 55481 81268 6-97338 09041 .8250 25845 32306 37930 42908 a; ir, 5-86167 56064 8159. 6-97561 092.. .8389 25961 32406 3?o,8 42987 4.1 l«i 5-88969 56639 8.911 6-97783 0938. .8526 26076 32506 38,06 43065 44 17 5-9.602 57207 82230 6-98004 09551 .8663 26192 32606 38.93 43 '43 43 18 5-94085 57767 82545 6-98224 09719 .8800 26307 32705 38280 4322, 42 \H 3 46589 50709 54471 57934 6. 140 64,26 66920 69545 72020 ,436* 57 • 4 46661 50774 545 3' 57989 6.192 64.74 66965 69587 72060 74400 6« b 46733 50840 54591 58044 6.243 64222 67010 69630 72.00 74438 55 f> +6805 50905 54651 58100 6.294 64270 67055 69672 72.40 74476 54 7 46876 50970 547" 58155 6.346 643,8 67.00 697.4 72.80 74514 53 8 46948 5'o35 54771 58210 6.397 64366 67,45 69757 72220; 7455. 62 9 IF 47019 5 1 100 54S30 54890 58265 6.44S 644.4 67,90 69799 72260 74589 51 50 47090 51165 58320 6.499 6446. 67234 6984. 72300 74627 II 4716Z 51230 54949 58375 6.550 64509 67279 69883 7*340 74665 49 12 47^33 5'^94 55008 58430 6160. 64557 67324 69925 72380 74703 48 i:< 47303 5"359 55068 58485 6,652 64604 67369 69967 72419 74740 47 11 47374 5'423 551*7 58539 6.703 64652 674, '3 70009 72459 74778 id 15 4744 S 5.488 55.86 58594 6.754 64699 67458 7005, 72499 74815 45 Ifi 47S>5 5'55^ 55*45 58649 6.805 64747 67502 70093 7*538 74853 44 17 47586 516.6 55304 58703 6,855 64794 67547 70135 72578 74891 43 lu 47656 5.680 55363 58758 6.906 64842 6759. 70177 726.8 749*8 42 lU 2(t 477^6 5-744 55422 588.2 58866 6.957 64889 67636 702.9 72657 74966 41 47797 5.808 55481 62007 64936 67680 7026. 72697 75003 40 21 47867 51872 55539 58921 6*058 64983 67724 70302 72736 75040 39 22 47936 5.936 55598 58975 65030 67768 70344 72775 75078 3H 2:< 48006 5 '999 55656 59029 62! 58 65078 678.3 70386 728.5 75'i5 37 24 48076 52063 55715 59083 62209 65125 67857 70427 72854 75153 3fi 2J 48.45 52126 55773 59>37 6*259 65.71 6790. 70469 72894 75190 35 2« +S..5 52.90 55831 59.91 62309 652,8 67945 705.0 72933 75*27 34 27 48284 5"53 55889 59*45 61359 65165 67989 7055* 72972 75264 33 2H 48353 523.6 55948 59*99 62409 653.2 68033 70593 73011 75302 32 29 30 48421 4849. 5^379 56006 5935* 6*459 65359 68077 70635 73050 75339 31 52442 56064 59406 62509 65406 68,2. 70676 73090 75376 30 31 48560 5^505 5612. 59459 62559 65452 68.65 707.8 73.29 75413 29 32 48629 52568 56179 ;95'3 62609 65499 68208 70759 73.68 75450 28 :<3 48698 5263. 56237 59566 62659 65545 6S252 70800 73207 75487 27 34 48766 52693 56295 59620 62708 65592 68296 7084. 73246 755*4 2« :t.) 48833 5^756 5635* 59673 62758 65638 68340 708S3 73285 75561 25 ■Mi 48903 52818 564.0 59726 62808 65685 68383 70924 733*4 75598 24 :»7 48971 52S8. 56467 59780 62857 6573. 68427 70965 73363 75635 23 :tii 49039 52943 56524 59833 62907 65778 68+70 7.006 73401 75672 22 :ti) 49107 53005 56582 59886 62956 65824 685.4 71047 71088' 73440 75709 21 40 49'7S 53067 56639 59939 63006 65870 68557 73479 75745 20^ 41 49-43 53'^9 56696 59992 63055 659.6 6860. 7.129 73518 75782 19 42 493" 53'9' 56753 60045 63.04 65962 68644 71170 73557 758.9 in 43 49379 53253 56810 60097 63'53 66oc8 68687 712. 1 73595 75856 17 44 49446 533'5 56867 60.50 63203 66055 6873. 71251 73634 75892 Hi 4.-. 49513 53376 56924 60203 63252 6610. 68774 71292 73673 75929 15 4ff 495«. 53438 56980 60255 6330. 66146 688.7 71333 737" 75966 11 47 49648 53499 57037 60308 63350 66.92 68860 71374 73750 76002 13 411 49715 5356. 57094 60360 63399 66238 68903 71414 73788 76039 12 49 i.O 49782 49849 53622 57150 604.3 63448 66284 68946 71455 73827 76075 11 53683 57206 60465 63496 66330 68989 71496 73865 76.. 2 "TT 61 49916 53744 57263 605.7 63545 66375 69032 71536 73904 76.48 9 .'/J 49982 53805 573'9 60570 63594 6642. 69075 71577 73942 76185 n Ki 50C49 53866 57375 60622 63642 66467 691.8 71617 73980 76221 7 64 50115 539*7 5743' 60674 6369. 66512 69.61 71658 740.9 76258 H Sft 50181 53988 57488 60726 63740 66558 69204 7.698 74057 76294 A .'ii; 50248 54049 57544 60778 63788 66603 69*47 71739 74095 76330 4 •••7 5=>3'4 54.09 57599 60830 63837 66649 69289 71779 74133 76367 3 .-.8 50380 54.70 57655 60882 63885 666,4 69332 718:9 74171 76403 2 .-.9 50446 54230 577" 60934 63933 66739 69375 71859 741.0 76439 1 liO 50512 54291 i 57767:60985163982 66784 694.7 71900 74248 76475 " IIU' 49JllH° 4(li»y^ 47'i»9' 461119" ii'm" 44'J89' 43' «9' 42i89'' 4I'89° 40 '" -1 728 T.\BLE (ir LOG. SlNES OF SMALL ARCS TO EACH SECOND // 0" 20' 0° 21' 0° 22' 0'= 23' 0° 24' 0^ 25'|o° W 0° 27' 0' 28' |o' 29- ii- ?• 7- T r T \r \r 7- r \r 76475 78594 82545 84J93! 86.66:87870 89509 91088 1926.2 A') I 76s.. 7S629 80647 82577 84424 86.95,87897 89535 9,, ,4^926:7 5:» 2 -6S4S 78663 806S0 82608 84454 86224 87925 89562 9,140] 92662 .')o a 7b-M 78698 S0713 82639184484 862,3 87953 89589 9"65|926S7 57 4 76610 78732 80746 8267, 845,4 86282 8798, 896.6 9119. 192712 .5li 5 766,6 78766 80779 82702 84544 863,, 8S0OS 89642 912.7 92737 ;,.-, 6 7660Z 78S01 80S12 82733 84574 86,40 88036 89669 91243 9276, .'.4 7 76728 78835 80R44 82765 84604 86368 88064 89696 9,269 927S6 .13 il 76764 78869 80877 82796 84634 86,97 8S092 89722 9,294 92S,, ^)2 "IF 76800 78903 809,0 8466+ 1 86426 88, ,9 89749 1 9.320 92836 51 50 ' 768,6 78938 80942 82859 84694 86455 88,47 89776 9.346 [9286, 11 76872 7S972 80975 82890 84-24 86484 88,75 89802 9,37, I92S86 49 u 76907 79006 8,008 82921 S4754 86„2 88202 89829 9,397 929,0 48 i:i 76943 79040 8,040 82952 84784 8054, S8230 898,6 9.423 92935 4- 14 76979 79074 8,073 82983 848,4 88258 89882 9,448 92960 40 1.') 77015 79108 8, ,05 830,5 S4843 86598 S8285 89909 9,474 92985 4.5 I« 7705> 79142 8,„S 83046 84873 86627 883.3 189935 9,500 93C09 44 17 77086 79.76 83077 84903 8^656 88340 89962 43 Hi 77122 79210 8,203 83,08 84933 86684 88368 89988 91551 193059 42 lit 2(1 77.58 79244 8. 235 83,39 84963 86-., 88395 900,, 9.576 93084 91602 93.08 41 "4" 77193 79278 8,268 83,70 84992 8674. 88423 9c 04, 21 77229 793.2 8,300 S320, 85022 1S6770 88450 90068 9.627 93.33 39 22 77264 79346 8.332183232 85052 1 86799 88478 90094 1 9.653 193.58 3H Mi 77300 79380 8.365 8,263 S50S2 86827 8850, 90,2, 9,678)93182 37 li 77335 794.4 8.397 83294 85,,, 88533 90,47 9.704 93207 3fi 2.1 77371 179448 8,429 83325 8514, 86S84 88560 90,74 91729 9323, 35 •iti 7-406 j 7948. 8.461 83356 85,7, S69., 88,87 90200 9,2,6 34 27 77442: 79515 8.494 8,387 85200 8694. 886,, 90226 9.780 9328, 33 28 77477 79549 8,526 834.7 85230 86960 88642 90253 9,806 93305 32 '■at ■Ml 77512 77548 79582 8,558 83448 83479 85259 86998188669 90279 9.83. 93330 31 30 796.6 8,59, £5289 87026 88697 90305 9,857 93354 :u 77583 79650 8,6.3 83510 853,8 8705, 88724 1 90332 9,882 933-9 2!» ;<-' 776.8 796S3 8.655 8354, 85348 8708, 8S75, 9035S 9,907 93403 2}' x.\ 77654 797.7 8,687 8357. 85377 87.., 88779 90384 9.933 93428 •» .u 77689 7975. S.7.9 83602 85407 87.40 88806 904,, 91958 93452 2« :(.-. 77724 79784 8,75, 83633 85436 S7168 S8833 90437 9,983 93477 25 :iii 77759 798.8 8,783 83663 85466 87.96 88S60 90463 92009 9350, 24 :t7 77794 7985. 8,8,5 8,694 85495 87224 88888 90489 92034 93526 23 ■Mi 77829 79885 8,847 8,725 S5525 872,3 889,51905,5 92059 93550 22 ■Ml 77864 799. 8 8,879 83755 85554 8728, 88942 j 90542 92085 93575 "20 -7899 79952 8.9,, 8,786 85583 87309 88969 90568 92, ,0 93599 77934 79985 8,943 8,8,7 856,3 87337 88996 90594 92.35 9362, 19 42 -7069 800,8 8,975 8,847 85642 87366 89023 90620 92,60 9,648 1« 4:1 8oo,z 82007 8,878 8567. S7394 89050 90646 92,86 93672 17 44 78039 8C085 82039 83908 85700 89077 90672 922,, 93696 16 4.'i 78074 80, ,8 820-0 83939 85-'3o S7450 89,05 90698 92236 9372. 15 4fi 80, ,2 82,02 8,969 85759 89.32 90725 9226, 93745 U 47 78.44 80,85 82134 84000 8,788 87506 89.59 90751 922S6 93769 13 411 78.79 802,8 82,66 840,0 858,7 87534 89,86 90777 923.1 93794 12 W 782,3 8025, 82,98 84060 8,847 87562 892,3190803 92336 93818 II -8248 80284 »2229 8409, 85S76 87590 89240 90829 92362 93842 10 SI 78283 8226, 84.2, 85905 876.8 89267 90855 92387 93866 9 52 783.8 8035' 82293 84.5. 85934 87646 89294 924.2 9389. K s.-t 78,52 80384 S2324 84,82 85963 87674 89320 90907 92437 93915 1 54 78387 804,7 82356 842,2 85992 87702 89347 90933 92462 93939 ,15 -8422 80450 82387 84242 8602, 877,0 89374 90958 92487 93963 5 ,'i(i 78456 804S3 824,9 84273 86050 87-5S 8940, 90984 925,2 93988 4 ■■i? 7849. 805,6 8245, 84303 86079 87786 89428 92537 94012 3 .•|l) ■8525 80549 82482 84333 86, oS S-814 89455 9,0,6 9256Z 940,0 2 -S560 80582 825,4 84363 8-842 89482 9,062 92587 94060 1 -S594I 8061,] 82,-4, 84393 86.66 8-8-0 89509 9,088 ,26,2 94084 " t!)" ■M'.H'J :ty'|H!)^ 371 19° ■^ Ol- SMALL ARCS TO I- At 11 SECOND ,,, |0':«)'|tf'3l' 0° 32' 0° 33 1 0" 34' V)°3d' 0° :'6' 1 0° 37' d" 3H 0' 31( „ ~ -■ 7" T r 3- 8- 8- 8- 8- 9+084. 95508 968S7 98223 7-99520 C0779 02002 03,92 04350 05+78 1 4 94.8. 9560, 96977 983.. 7-99605 OCS61 C20S2 0327c 04+26 05552 All 5 94105 95625 97000 98333 7-99626 008«2 02102 0329c 04445 0557. 5r. 6 94129 95648 97022 98355 7-996+7 00903 02123 03309 0+464 05589 64 7 94253 9567. 97045 98377 7-99669 00923 02. + 3 03329 0+483 05608 S3 11 94277 95695 97068 9S398 7-99690 009+4 02.63 03348 04502 05626 r)2 9 94501 95718 97090 98+2^ 7-99711 00964 02,83 0336S 0+521 056+5 61 5(1 ITT 94325 95741 971.3 984+2 7-99732 OC985 02203 03387 04540 05663 II 94349 95764 97.35 98+64 7-99753 01006 02223 03407 04559 05682 4!l I'j 9437 3 95787 97.58 98+86 7-99775 01026 02243 03426 04578 05700 4H i:i 94397 9581. 97.80 98308 7-99796 010+7 02263 03446 04597 057.9 47 1 1 94421 95834 98529 7-99817 01067 02283 03465 04616 05737 4e i.i 94445 95857 97225 98551 7-99S38 01088 02303 03484 0+635 05756 45 Hi 94469 95S80 97247 98573 7-99S59 oiicS 02323 03504 04654 05774 44 17 94492 959°3 97270 98595 7-99880 01129 02343 03523 0+673 05792 43 111 945.6 95926 97292 98616 7-99901 011+9 02362 03543 04692 0581, 42 id 9+540 9595° 973'5 98638 7-99922 02382 ^ 0+7.0 05829 05S+8 41 9456+ 95973 97337 98660 7-99943 01.90 0+729 •Jl 9+SS8 95996 97359 986S2 7-99965 02422 0360, 04748 05866 39 ■22 9+6.2 960,9 97382 98703 7-999S6 01231 02+42 03620 C4767 05S85 .-{» 23 94636 960+2 9-404 98725 8-00007 01252 02+62 036+0 047S6 05903 37 ■2i 94659 96065 97426 98747 8-00028 02482 03659 04805 05921 3f; -.'■■s 94683 96088 97449 98768 S-C0049 C1293 02502 036-8 04S24 05940 35 2B 94707 96.., 9747. 98790 8-CO070 01313 C2522 0369S 0+8+3 05958 34 27 947 3 > 96134 97493 988.2 8-00091 01333 025+2 03717 0+861 05976 33 28 94755 96157 97516 98833 8-OCI12 01354 02561 03736 0+880 05995 32 29 9+778 96.80 97538 98855 8-00,33 01374 0258. 03756 0+899 060., 31 9+801 96203 97560 98876 S-00154 0139s 02601 03775 0+918 0603. 'W :i\ 9+826 96226 97583 98S98 8-00175 01415 02621 03794 0+937 06050 29 :n 948+9 96249 97605 98920 8-00196 01435 02641 03813 04955 0606S 2(1 33 94S73 96272 97627 989+1 8-002 17 01+56 02661 03833 04974 06086 •J 7 :u 94897 96295 97649 98963 8-00238 0.476 02680 03852 0+993 06105 2(; So 94921 963.8 97672 98984 8-00259 01496 02700 03871 05012 06,23 25 ■Mi 94944 9634. 97694 99006 8-00279 0.5.7 02720 03891 05030 06,41 24 ;«; 94968 96364 977.6 99027 8-00300 0.537 02740 03910 050+9 06159 23 3« 9+991 963S6 9-738 99049 8-00321 01557 02759 03929 05068 06,78 22 To" ;50.5 96+09 97760 99070 8-003+2 0.578 02779 039+8 050S7 06,96 21 95'^39 96432 97782 99092 8-00363 0.59S 02799 03967 05105 062,4 2(1 41 95062 96455 97805 99.13 8-0038+ OJ618 02819 03987 05124 06232 19 42 95086 96478 97827 99>35 8-00+05 0.639 02838 04006 05143 0625, Id 4a 95.09 96501 978+9 99156 S-00426 0.659 02858 0+025 05.6. 06269 17 44 95'33 96524 9787. 99178 8-C0447 0.679 02878 04044 05.80 06287 IM 4.'> 95 '57 96546 97893 99199 8-00467 0.699 02898 04063 05.99 06305 15 4«> 95.80 96569 979'5 99221 8-00488 0.720 02917 04083 05218 0632+ 14 47 9520+ 96592 97937 99242 8-00509 0.740 02937 04,02 05236 063+2 13 48 95227 966.5 97959 99264 8-00530 01760 02957 04121 05255 06360 12 49 9525. 96637 979S1 99285 80055. 0,780 02976 ^4140 05274 06378 1 1 5« 95274 96660 98003 99306 8-0057. 0.801 02996 04159 05292 06396 IF M 95298 96683 9S025 99328 8-00592 01821 03016 04,78 05311 06+1+ « .■2 95>2. 96706 980+8 99349 8-00613 018+, 03035 0+.97 05329 o6+3-i H M 95344 96728 98070 99371 8-00634 01X61 03055 04217 05348 06+51 7 »4 95368 9675. 98092 99391 8-CC654 01881 03074 04236 05367 C6+69 ft ft.l 9539> 96774 9S114 994.3 8-00675 0.901 03094 04255 05385 06+87 A AH 95415 96796 98136 99435 8-C0696 01922 03114 04274 05404 06505 4 t>7 9>'438 968.9 98157 99456 8-00717 0.9+2 03133 04293 05422 0652; 3 :>!{ 95461 96841 98.79 99477 8-00737 0.96Z 03153 04312 05441 065+1 2 s« 954S5 96864 9«20, 5549S 0-C0758 0.982 03.72 04331 05+60 06560 1 i;(i 9^5^-8 96887 98223 99520 _£oo7^ 03,92 04350 05+781 06578 1 « """ »• JfriH!!" 28'l v.," 27' Ha° 2fi H!l° 2S' 89-^ 24' (19 -23' (1!)' 22' B!t 2r8fl°20' " " ' '— " ■' 1 TABLE 66 I,OU. SINES OF SMALL ARCS TO EACH SECOND 1 'L 0° 40' 0-41' 0° 42' 0='43' 0° 44' 1 0° 45' 0°46' 0" 47' 00 48' o°4a' ^^ s- 8- %■ 8- 8- Ig- 8- g- 8- J.-'- 06578 07650 0S696 097,8 10717 11693 12647 '358. 14495 '539' tiO 1 06596 07668 087,4 09735 '0733 "709 ,2663 13596 145,0 15406 59 2 06614 07685 08731 09752 10750 "725 ,2679 145^5 15420 08 3 0663Z 07703 08748 09769 10766 "74' -694 I3627 14541 '543 5 57 4 06650 07721 08765 09786 10782 "757 ,3643 14556 15450 5o 06668 07738 08783 09802 10799 "773 12726 ,3658 '457. 15465 55 t> 06686 07756 0S800 098,9 10815 "789 12741 '3673 .4586 '5479 54 7 06704 07773 088,7 09836 10S32 ,,805 •2757 ,3689 .460. 15494 53 H 06722 07791 08834 09853 10848 ,,821 12773 ,3704 .46.6 15509 5'i 06740 07809 0885. 0S868 09870 ,0864 '.837 ,278s '37'9 '3735 ,463. 15523 50" 06758 07826 09886 108S1 ,,853 ,2804 ,4646 15538 11 06776 07844 0S8S6 09903 ,0897 ,1869 ,2820 .3750 ,466, 15553 49 i-> 06794 0786, 08903 09920 10914 ,,885 ,2835 .3765 ,4676 15568 48 i.t 06812 07879 08920 09937 10930 ,.901 ,285, ,378, ,469, 15582 47 14 06830 07896 08937 09953 10946 "9'7 .2867 ,3796 ,4706 15597 46 i:. 06848 07914 08954 09970 ,0963 "933 ,2882 138.1 14721 156.2 45 Hi 06S66 07932 0897. 09987 10979 1,949 ,2898 13827 14736 15626 44 17 06884 07949 08988 10004 ,0995 ,,965 129,4 13842 14751 15641 43 10 06902 07967 09006 10020 ,,98. ,2929 13857 ,4766 15656 42 10 06920 07984 09023 10037 ,,028 1,997 12945 13873 147S. 15670 41 20" 06938 08002 09040 ,0054 ,,044 ,2013 ,296, .3888 14796 15685 40 21 06956 08019 09057 10070 ,,o6i ,2029 12976 13903 .48.1 15700 39 22 06974 08037 09074 10087 ,,077 12045 ,2992 13919 14826 157'4 38 2;{ 06992 08054 0909, ,0104 ,,093 12061 ,3007 13934 1484. 15729 37 ■n 0701C 08072 09,08 10120 11,10 12077 ,3023 13949 14856 15744 3o 25 07028 08089 09,25 10,37 ,,,26 12093 ,3039 13964 1487. 15758 35 26 07046 08,07 09,42 10,54 11,42 12109 ,3054 13980 14S86 15773 34 27 07063 08,24 09159 10170 11159 ,2125 ■3070 1599s ,4901 .5788 33 ■m 07081 08,41 09176 10187 "'75 12141 13085 14010 14915 15S02 32 2:1 07099 08159 09,93 10204 ,1191 12157 1310, 14025 14930 .58.7 31 ;to 07117 08,76 092,0 ,0220 1,207 12172 ,31.7 14041 14945 .5832 30 :u o7«35 08,94 09227 10237 ,,224 12,88 13132 14056 14960 15846 29 32 07153 09244 10254 ,1240 12204 13148 1407, •4975 1586, 28 3:1 07171 08229 0926, ,0270 ,1256 12220 ,3,63 ,4086 .4990 '5875 27 :m 07189 08246 09278 ,0287 .1272 12236 >3'79 14101 15005 .5890 26 3.-. 07206 08263 09295 10303 11289 12252 ,3,94 141,7 ,5020 15905 26 ■Mi 07224 093,2 103Z0 11305 12268 132,0 ,4,32 '5035 15919 24 37 07242 08298 09329 10337 11321 12284 13225 14147 ,5050 15934 23 38 07260 083.6 09346 10353 i>337 12300 1324, ,4,62 15065 15948 22 39 40 07278 08333 09361 09380 ,0370 "354 123.5 ,3256 14178 15079 15963 21 20 07295 08350 10386 "3^? '^33' ,3272 14193 15094 15978 41 073,3 08368 09397 10403 ,,386 '2347 ,3287 14208 15109 1599= 19 42 07331 08385 094,4 10420 ,,402 ,2363 '3303 14223 ,5,24 16007 18 43 07 H9 08403 0943, ,0436 ,,418 12379 '33'8 14238 15139 16021 17 44 07367 08420 09448 10453 "435 .2395 ■3334 14253 15154 .6036 It; 4 A 07384 08437 09465 ,0469 "45' 12410 '3349 14269 15169 .6050 15 46 07402 0S455 09482 ,0486 ,,467 .2426 '3365 ,4284 15183 16065 14 43 07420 08472 09499 ,0502 ,,483 12442 ■3380 14299 15.98 .6079 13 48 07438 0S4S9 095,6 ,05,9 "499 .245S ,3396 143,4 15213 .6094 12 49 60 °74S5 08506 09533 '0535 ,,5,5 12474 ,34" ,4329 .5228 16109 11 07473 08524 09550 10552 "53> .24S9 ■3427 14344 15243 16.23 10 ■il 07491 0854. 09567 ,0568 "548 ,2505 ,3442 14359 15258 16138 9 A2 07509 08558 095S3 ,0585 "564 ,252, ,3458 14375 15272 16152 8 53 07526 08576 09600 1060, ,,580 '-537 '3473 14390 15287 16.67 7 .54 07544 08593 096,7 ,06,8 ,,596 '^553 .3489 14405 15302 16181 6 55 07562 086,0 09634 ,0634 1,6,2 ,2568 13504 ,4420 '53'7 ,6196 ft A6 07579 08627 0965, ,065, ,1628 ,2584 '35'9 '443 5 '533^ .62.0 4 57 07597 08645 C966S ,0667 ,,644 ,2600 '3535 14450 15346 16225 3 5H 076,5 08662 09685 ,0684 ,,660 126,6 '3550 14465 15361 ,6239 2 A!) 07632 08679 0970, 10700 ,,677 1263, ,3566 ,4480 15376 .6254 1 6'0 07650 08696 09718 10717 ,1693 ,2647 .358. 14495 '539' .62 68 ivi" ly H9" 18 nr 17' 89° Hi' 89" 15' iV.f U' 89' 13' 89° I2'|89° 11' nr 10 '^' 1 T.ABI.K CM 731 LOG. SINES OF SMALL ARCS TO EACH SECOND // 0^ 50' JO^ 51' 0' 52' 0' 53' !o" 54 Io" 55' 0" 5R' 0^ 57 0' 511' 'o' 59' " 8- 8- S- 1 8- 8- s- 8- 8- 8- 8- n i6j6X .7128 .797' '8798 196.0 20407 2, ,89 2,958 22713 23456 «l> 1 162S3 17141 .7985 '38.2 ,9624 20420 2,202 2,97, 22726 2346S 59 •J 16297 17156 .7999! '8826 .9637 20433 212,5 2,983 22738 23480 58 3 .6;,, 17171 18013, '8839 19650 20446 21228 2,996 22751 23492 57 4 1A3.5 .7.85 18027 .8853 .9664 20460 2,24, 22009 22763 235°5 56 a 16340 17199 18041 18867 19677 20473 21254 22022 22776 235'7 55 n ■'555 17213 1S055 188S0 1969. 204S6 2.267 22034 2278S 23529 64 7 16369 17227 18069 18894 .9704 20499 2,280 22047 2280, 2354' f:i ■ 6384 17241 18082 18908 .9717 205,2 2,293 22060 228,3 23554 52 It .6,98 17256 18096 1S921 '973' 20525 2,306 22072 22826 2356^ 51 ■50 io 16413 17270 18110 18935 '9744 20538 21319 22085 22838 23578 1 1 16427 .7284 18,24 .S948 '9757 20552 2133. 22098 22850 23590 49 12 1644, 17298 18138 .8962 '9771 20565 2.344 22863 23603 48 i;t 164,6 17311 18,52 18976 19784 20578 2'357 22,23 22875 236,5 ■«7 II 16470 .7316 .8166 18989 '9797 2059. 21370 22,36 22888 23627 id 15 16485 17340 .81S0 190031 19811I20604 2,383 22,48 22900 23639 45 IS ■ 6499 '7355 .8193 1 190.6 j ,98241206,7 2.396 22161 229,3 23652 44 17 16513 17369 .82071 1903°' .9837120630 2.409 22173 22925 23664 43 IM 16528 ■7383 .822. 19044 19S5. 20643 2.422 22186 22937 23676 42 1!) 16542 '7 -,97 .8135] 19057 .9864 20656 2.434 22,99 22950 23688 41 ■M .6557 .74.. 18249 '9071 '9877 20669 21447 222,, 22962 23700 40 :il 1657, '74-5 18263! 19084 .989, 20682 21460 22224 22975 237'3 39 22 .6585 '7439 18276 19098 ,9904 20696 21473 22237 22987 23725 38 J-A 16600 '7453 ,8290 19111 '99'7 20709 21486 22249 22999 23737 37 ■-'4 16614 ■ 7467 .8304 19125 '993' 20722 21499 22262 230,2 23749 •M '.'J .6628 .748' 18318 19.39 '9944 20735 2,5,, 22274 23024, 2376: 35 •J(! 16643 '7495 .8332 .9152 .9957 2074S 2,524 22287 23037 23773 34 •.'7 16657 17510 18345 19>66 1.997, 2076, 21537 22300 23049 23786 33 28 16672 '75^4 ,8359 .9.79 :99«4 20774 21550 223,2 2306, 23798 32 •-■a 16686 16700 '7538, '8373 .9.93 '9997 20787 2,563 22325 23074 238,0 31 '755J ,8387 19206 20800 2,576 22337 23086 23822 30 »i 16715 .7566 ,840, 19220 20024 208,3 2,588 22350 23098 23S34 29 ;«.' 16729 '7580 ,84,4 ,9233 20037 20826 2,60, 22363 23,,, 23846 28 :i3 16743 '7594 18428 ,9247 20050 20839 216.4 22375 23123 23859 27 :<4 16757 17608 .8442 ,9260 20064 20852 2.627 223S8 23136 2387, 20 :<.! .6772 17622 18456 ,9274 20077 20865 21640 22400 23,48 23881 25 HO 16786 17636 ,8469 ■9287 20090 2087S 21652 22413 23,60 23895 24 :«7 i68co .7650 ,8483 '930' 20,03 20S9, 2.665 22425 23'73 23907 23 :»8 168,5 17664 18497 193.4 20, ,7 20904 2.678 22438 23185 239,9 22 :t!» 16829 17678 .8511 '9328 20,30 209,7 2.69, 22451 23197 23931 21 40 16S43 17692 .8524 19341 20,43 20930 2.703 22463 23210 23944 20 41 16858 17706 18538 '9355 20,56 20943 2.7.6 22476 23222 23956 19 42 16872 17720 .8552 1936S 20.70 20956 21729 22488 23234 23968 18 4:( 16886 '7734 18566 19382 20.83 20969 21742 22501 23247 23980 17 44 16900 17748 18579 '9395 20.96 20982 2'754 225,3 23259 23992 l«i 4.1 169.5 17762 18593 .9409 20209 20995 21767 22526 23271 24CC4 16 4r, .6929 .7776 ,8607 .9422 2,008 21780 22538 23284 240,6 14 47 .6943 17790 18621 .9436 20236 2,02, 2.793 2255. 23296 24028 13 411 .6957 17804 .8634 19449 20249 2.034 2.805 22563 23308 24041 12 4« 50 169-2 16986 19463 20262 21047 2.8,8 22576 23321 23333 24053 11 -fo" 17832 18662 19476 20275 2.060 2.83. 22588 24065 51 17000 .7846 .8675 .9489 20288 2I086 2.844 2260. 23345 24077 9 52 17014 17860 .8689 .9503 20302 21856 226,3 23357 24089 8 «3 17029 "7874 1S703 .95.6 203.5 2.099 21S69 22626 23370 24,0, 7 54 17043 17888 18716 .9530 20328 211 12 21882 22638 23382 241,3 • 54 17057 179OJ ■ 8730 '9543 2034, 2, ,25 21895 2265, 23394 24,25 5 6(> 17071 17916 18744 '9557 20354 21.38 2.907 22663 23407 24'37 4 •'•7 ■70S 5 17930 '8757 19570 20368 21.5, 21920 22676 23419 24,49 3 58 17100 '7943 18771 '9583 2038, 2, ,64 2'933 22688 2343' 24,6, 2 59 17114 '7957 18785 1 '9597 20394 21,77 21945 2270, 23443 1 24173 1 «0 17128 17971 .8798! 19610 20407 2. .89 21958 22713 23456124186 ^^ m 9- mi «'|B9 7', "'J 8'jll9' 5-189" 4'^ 1)9 :t (19 2' 89" 1' 89° 0' ~7r Co»,N, 1 r62 T.\BLK fi6 LOG. SINES OF SMALL ARCS TO EACH SECOND 1 " 1° 0' JO ,- 1 ,0 2' 1°.Y 1° 4' r 5' r 6' h-r 1° 8' 1 r=' H' " 8- 8- %■ 8- 8- 8- 8- |8- %■ 8- 241855 249033 256094 263042 269881 2766.4 283243 289773 296207 302 546 60 1 241976 249152 2,62.1 263157 269994 276725 =83353 2898S, 296313 30265, 59 2 242C97 249270 236328 263272 2701D7 276S36 283463 289989 296420 302756 58 3 242217 2493S9 256444 263387 270220 276948 28357= 290097 296526 30286, 57 4 242338 249507 25656. 163502 270333 277059 283682 290205 296632 302965 56 5 242458 249626 25667S 263616 270446 277170 28379. 2903,3 296739 303070 55 i; 242578 249744 256794 26373. 270559 277281 28390, 290421 296845 303175 54 7 242699 249863 256911 263846 270672 27739= 2840,0 290529 29695. 303280 53 « 242819 249981 257027 263960 =70785 277503 284,20 290637 297057 303384 5'2 J)_ 242940 250.00 257144 264075 27089R 277615 284229 290745 297.64 303489 51 10 243060 2502,8 257260 264.90 271010 277726 284339 290852 297270 303594 ^50" 1 1 243180 250336 257376 264304 271.23 277837 2S4448 290960 297376 303698 49 12 243300 i5°455 =57493 2644.9 27.236 277948 284557 291068 297482 303803 48 13 243421 250573 257609 =64533 271349 278059 284667 291175 297588 303907 47 14 M354I 25069, =57725 264648 27.46. 278,70 284776 291283 297694 3040,2 46 1.5 24366. 250809 257842 264762 =7'574 27S28, 284885 291391 297800 304.17 ia 16 243781 250927 =57958 264877 27.6S7 27839. 284994 29,498 297906 304221 44 17 243901 25.045 258074 26499. 27.799 =7850= 285,04 291606 29S0.2 3043=5 43 18 244021 25.164 258.90 265.05 271912 2852,3 291713 298. .8 304430 42 l'» 244141 ll}llL 258307 265220 272024 27S724 2S5322 29,821 298224 304534 41 40 20 244261 25.400 =584=3 =65334 272137 278835 ^8-5-^ 291928 298330 304639 21 244381 2515.8 =58539 265448 272249 278946 285540 292036 298436 304743 39 22 244501 25.636 =58655 265562 272362 279056 285649 292,43 298542 304S47 38 23 244621 ^51754 25877. 265677 27=474 279.67 285758 29225, 29864S 304952 37 24 ^4474" 25187. 258887 26579. 272587 279278 285867 292358 298754 305056 36 25 244S61. 251989 259C03 265905 272699 2793SS 285976 292466 298859 305,60 35 26 244980 252.07 259.19 2660.9 272811 279499 286085 292573 298965 305265 34 27 245100 252225 259235 266.33 =7=9=4 2796.0 286,94 292680 299071 305369 33 28 245220 ^5^343 =5935' 266247 273036 279720 2S6303 =9=787 299177 305473 32 29 H5339 252460 259466 266361 iZlIii 279831 2864,2 =9=895 293002 299282 305577 M oO ^45459 252578 259582 266475 273260 27994, 286521 299388 30568, 31 ^45579 252696 259698 266589 =73373 280052 286629 293109 299494 305785 29 32 245698 2528,3 259814 266703 =73485 280.62 286738 2932,6 299599 305890 28 33 245818 252931 259929 266817 =73597 280272 286847 =933=4 299705 305994 27 34 H5937 253049 260045 26693, 273709 280383 286956 =9343' 2998,0 306098 26 35 246057 253.66 260,61 267045 27382. 280493 287064 =93538 2999,6 306202 25 30 246176 253284 260276 267158 =73933 280604 287,73 293645 30002 , 306306 24 37 246296 25340. 260392 267272 174045 2807.4 287282 =9375= 300,27 3064. 23 38 2464,5 ^53519 260508 267386 »74'57 280824 287390 293859 300232 3065.4 22 39 246534 253636 260623 267500 174269 2S0934 287499 293966 300338 306618 21 lo 40 246654 ^53753 260739 2676,3 27438' 28.045 287608 1 294073 300443 306721 41 -46773 25387. 260J54 267727 =7+493 281155 287716 2941S0 300549 306S25 19 42 246892 253988 260970 26784, 274605 28. 265 287825 294287 300654 306929 18 43 247011 254105 26.085 267954 2747'7 28.3-5 287933 294394 300759 307033 17 44 247131 254223 26.200 268068 274828 28.4S5 288042 294500 300865 307.37 16 45 247250 254340 26,3,6 268,8, 274940 281595 288,50 294607 300970 30724. 15 46 247369 ^54457 26,43, 268295 275052 281705 288259 294714 301075 307344 14 47 247488 ^54574 26,546 268408 275164 281S.5 288367 294S2, 301,80 30744S 13 4)1 247607 254691 26,662 26S522 275275 28,925 288475 294928 30,286 307^5= 12 4!l 50 " 247726 247845 254808 26,777 268635 =75387 282035 28S584 295034 301391 30765; 11 254925 26,892 268749 =75499 282.45 2SS692 29514. 301496 307759 10 61 247964 255042 261007 268862 1756.0 2S2255 288800 295248 301601 307863 9 52 248083 i55'59 262122 268975 275722 282365 288908 =95354 30.706 307966 8 53 248202 255276 262237 269089 =75833 282475 2890,7 295461 30.8.. 30S070 7 54 24832, ^55393 =6=353 269202 =75945 282585 289125 295568 30.916 308.73 e 55 248440 255510 262468 2693,5 276057 282695 289233 295674 302021 30S277 5 50 248558 255627 262583 269428 276,68 282805 295781 302.26 30S3S0 4 57 248677 =55744 262698 269542 276279 2829,4 289449 295887 302231 30S484 3 58 248796 255861 262S.3 269655 27639' 2S3024 =89557 295994 302336 30S587 2 5!l 2489,4 25597S 262927 269768 276502 283134 289665 296100 302441 30S691 1 fiO 249033 256094 263042 26988, 2766.4 283243 289-73 296207 302546 30S794 " H8'' o9' 88" 58' 88 57' 88° 56' 88" 55' 88" 54 88= 53' 88" 52' 88' 51' 1 88^ 50' '" 1 rn? LOG. SINES OF SMALL ARCS TO KAtll SECOND ._ 1° w 1= ir r 12' l" 13' r 14' 1 1° 15' l" 1«' 1° 17' V 18' 1° 19' // g- 8- 8- 8- 8- 8- 8- 8- 8- JCS794 3 '4954 32.027 327016 332924 338753 344504 350.8. 355783 36.3.5 60 3oS«9g 3.5056 32. .27 327, ,5 333022 338849 344600 350175 355876 36.407 5'J 3OVO01 3«5'57 32.228 3171.5 333.10 338946 34469s 350368 355969 36.498 r.« 309104 315^59 32.328 3173.4 3332,8 339042 344790 350462 356062 36-590 57 309208 31536. 321429 3i74'3 3333.5 339.39 344885 350556 356154 36,681 :.« 3093U 3.5463 32.529 3275,2 3334-3 339135 344980 350650 356247 36-773 55 3094.14 3.5565 32,630 3276,, 3335.. 339331 345075 350744 356340 361S6+ 54 i^9S'7 3.5667 321730 3277.0 333608 339428 345-70 350S38 356431 36.956 53 309620 3.5768 32.830 327809 333-06 339514 345265 350932 356525 3620+7 52 309724 3.5870 32193, 327908 333804 33962. 34536. 35.026 3566.8 362.39 51 w 309827 3-5971 322031 328007 33390. 3397.7 345456 35. ..9 356710 362230 00 309930 3.6073 322,3. 328.06 333999 3398.3 34555. 35.1.3 356803 4'J 310033 3-6.75 32223, 328204 334096 339909 345646 35.307 356895 3624 n 48 310136 3.6277 322332 328303 334-94 340006 345740 35.40. 356988 362504 47 310239 3.6378 322432 328402 33419- 340.02 345835 35.494 357080 362596 46 310342 3.6480 322532 32850. 334389 340.98 345930 35.588 357.73 362687 45 310445 3.658, 322632 328600 334486 340294 346025 35.682 357165 3627-8 44 3.0548 3.6683 311731 328698 334584 340390 3+6,20 35.77s 357358 362S70 43 31065. 3.678s 322832 328797 33468. 340486 3462.5 35.869 35745° 36296, 42 3.0754 316886 322932 328896 334779 340582 3463.0 35.963 357543 363052 41 "io" "20" 3.0857 3.6987 313033 328995 334876 340679 346405 352056 357635 363143 21 317089 313.33 329093 334973 340775 346499 352150 357718 363234 39 3M063 3.7.90 313133 329192 33507. 34087. 3+6594 351143 357810 363316 38 3.1.66 3.7292 313333 32929. 335.68 340967 346689 351337 3579-1 3634-7 37 31.268 3.7393 313433 319389 335165 34.063 346784 351430 358005 363508 3(> 3"37i 3.7494 313533 319488 335361 34.. 59 346S7S 351514 35S097 363599 35 •21} 3 "474 3.7596 323632 329586 335460 341255 346973 3526.7 358.89 363690 34 27 3 "577 317697 313731 319685 335557 34.350 347068 3527.1 35818, 363-8. 33 2« 31.679 3.7798 323832 319783 335654 341446 347.62 352804 358374 363872 .'('2 29 3.1782 3.7900 323932 319882 33575. 34,5421347157 351898 358466 363963 31 3IJ 3.1885 3 . 800 . 314031 3299S0 335848 34.63S 347351 35199' 358558 364055 "3(7 31 3"987 3.8.02 324132 330079 335946 34-734 347446 353084 358650 3641+6 29 32 3.2090 3.8203 324232 330.77 336043 34,830 34754. 353.78 358741 364137 21) 33 3.2.93 3.8304 31433' 330276 336,40 34.926 347635 35317. 358835 364328 27 34 3.2295 3.8406 31443. 330374 336237 34202. 347730 353364 358917 36+419 2(1 35 312398 3.8507 31453. 330471 336334 342.. 7 347824 353458 3590.9 36+509 25 36 312500 3.860S 324630 330571 33643' 3422.3 3479'9 35355' 359'.' 3646C0 21 37 312603 3.8709 314730 330669 336518 341309 34S0.3 353644 359103 36+69. 23 38 312705 3.88.0 314830 330767 336625 342404 348.C8 353737 359195 364781 22 39 ^28oi 3.89.. 314919 330866 336-22 342500 34S202 35383. 359387 3648-3 21 40 3.29.0 3190.2 3250291330964 3368,9 342596 348197 353914 359479 364964 20 41 3.3013 3.9113 325,29 33,062 3369.6 34269. 34839. 354017 359571 365055 11' 42 3>3"5 3.92.4 315118 33,160 337013 341787 348485 354110 359663 365146 lli 43 3'3i'7 3.93.5 325318 33.159 337.09 3418S2 348580 354103 359755 365136 17 44 3.3320 3.94.6 315417 33'357 337106 341978 348674 354196 359847 365317 16 45 3 '34" 3.95.6 315517 33.455 337303 343074 348768 354389 359939 365418 15 46 3'35»4 3.96.7 315616 33'553 337400 343-69 348863 354483 36003, 365509 14 47 313626 3.97.8 315716 33,65. 337497 343165 348957 354576 360,22 365599 13 48 313729 3.98.9 315S15 33.749 337593 343360 34905- 354669 360214 365690 12 49 3.38,. 3.9920 32592+ 33.847 337690 343456 349-45 354761 360306 36578. II Ifl' 60 3'3933 32002. 326024 33.945 337787 34355- 349240 354855 560398 36587- 51 3'4035 320121 326,23 331043 337884 343646 349334 354948 360490 365962 9 .5J 3'4'37 320222 326223 332.41 337980 343741 34942S 35504. 360582 366053 8 .-.3 3"4»39 320323 326322 332239 338077 343837 349522 355.33 360673 366.43 7 o4 3H34» 320423 32642, 331337 338.74 343933 3496.6 355116 360765 366234 6 45 314444 320524 326520 331435 338170 344028 3497.0 3553.9 360857 366314 5 56 3.4546 320625 326620 331533 338367 344-13 349804 3554.1 360948 3664.5 4 57 314648 320725 3167.9 33263. 338463 3441.9 349898 355505 36.040 366505 3 .-)i; 3'475'' 320826 326818 331719 3 38 560 3443.4 349993 355598 36,132 366,96 •2 ■,a 3.485^ 320926 3269,7 332826 338656 344409 350087 35569- 36,223 3666S6 1 no 3'4954 321027 327016 3. '9^4 338753 344504 350181 355783 36.3.5 366-77 ■7I ~^ IIH' 4»' 8B^ 48- 88" 47' j SB" 48' 88" 45' 88" 44' 88' 43' 88 4-2'iH8'- 41'! H8' 40 1 " """""1 TABLE 66 LOG. SINES OF SMALL ARCS TO KACIl SECOND // l" 20' 1 1° 21' 1° 22' 1° 23' 1 r 24' 1° 25' 1^ 2(;' 1° 27' 1° 28' 1° 29' _L 8- 8- 8- X- |8- 8- 8- 8- 8- 8- •66777 372171 377499 382762 387962 393,0, 398,79 403199 408,6, 4.3068 b-o 1 366S67 372260 377587 382S49 38S048 393186 39S263 403282 408:44 4.3149 59 2 J66958 372350 377675 382936 38S.34 393271 39834S 403363 408326 4.3230 68 3 367048 372439 377763 383024 38S22, 393356 398432 403448 408408 413311 57 4 j6-,39 37252S 377852 383111 388307 393441 3985.6 403532 408490 413393 50 5 3671291371617 377940 383,9s 388393 393526 3986C0 4036,51408572 413474 55 ft 367319 372707 378028 383285 388479 3936,1 398684 403698 1 408654 413555 54 7 367410 372796 378116 383372 3S8565 393696 398768 40378, 408737 4,3636 53 8 367500 372885 378204 383459 393781 398852 403S64 4088,9 4.57.8 52 9 367590 372974 378292 383546 388737 393866 398936 403947 40890, 4,3799 51 lu 36768. 373063 378380 383633 393951 399020 404030 408983 4138S0 50 1 1 367771 373153 378469 383720 388909 394036 399,04 404113 409065 4,3961 49 12 367861 373242 378557 383807 388995 394121 399,88 404196 409,47 414042 48 13 367951 37333' 378645 383894 38908, 394206 399272 404279 409229 1 414123 47 U 368042 373420 378733 383981 389,67 394291 399356 404362 4093., 4.4204 4(1 13 368.32 373509 37882, 38406S 389253 394376 399440 404445 409393 4.42S6 45 lU 368222 373598 378909 384155 389338 394461 399524 404528 409475 4.4367 17 3683. z 373687 378997 384242 389424 394546 399607 4046,1 409557 4.4448 43 18 368402 373776 379084 384329 3895,0 39463, 399691 404694 409639 414529 42 20 368492 37J^ 379172 384415 389596 394715 399775 404777 409721 4,46,0 40 368582 373954 379260 384502 389682 394800 399859 404859 409S03 4,469, 21 368672 374043 379348 384589 389768 394885 399943 404942 409S85 4.4772 39 22 368763 374132 379436 384676 389853 394970 400027 405025 409967; 4. 48 5 3 23 368853 374221 379524 384763 389939 395055 400,, 405.08 410049 1 4.4934 37 34 368943 374310 379612 384850 390025 395139 400.94 405191 410.31 415015 3« 25 369033 374399 379700 384936 390,11 395224 400278 405274 4.02.2 4.5096 35 2G 369.23 374488 379787 385023 390196 395309 400362 405356 410294 415.77 34 27 3692,3 374577 379875 385, ,0 390282 395393 400445 405439 410376 4.5257 33 ill 369302 374665 379963 385197 390368 395478 400529 405522 410458 415338 32 2!l 369392 3747 54 38005. 385283 390453 395563 4006.3 405605 410540 4.54,9 31 ItiT 369482 374843 3S0.38 385370 390539 395647 4..0696 4056S7 4.062. 415500 30 31 369571 374932 380226 385457 390625 395732 400780 405770 410703 4.558. 29 32 369662 37502. 380314 385543 3907,0 395817 400864 405S53 410785 4.5662 28 S3 369752 375109 380401 385630 390796 395901 400947 405935 410867 4.5743 27 34 369842 375198 3804S9 3857.6 390882 395986 40,03, 406018 410948 415S23 2(; 35 369932 375287 380577 385803 390967 396070 40, .15 406101 41103c 4.5904 25 30 370021 375375 38o6f4 385890 391053 396155 401,98 406.83 411112 4.5985 24 37 3701H 375464 380752 385976 391138 396240 40,282 406266 411,93 4. 6c 66 23 38 370201 375553 380840 386063 391224 396324 40,365 406348 41,275 4.6,46 22 39 40 370291 375641 380927 386,49 391309 391395 396409 401449 40643 I 411357 4,6227 21 3703S0 375730 38.0.5 386236 396493 401532 406514 41.438 4,6308 41 370470 375819 38. .02 386322 3914S0 396578 401616 406596 1 41. 520 4.63S9 la 42 370560 375907 ,8,.9o 386409 39.566 396662 40.699 406679 411602 416469 IS 43 370649 375996 38.277 386495 391651 396746 40.7S3 406761 41.6S3 4.6550 17 44 370739 1 376084 38.365 3865S2 391736 39683. 40,866 406844 41.765 4,663. 16 45 370829 376.73 381452 386668 39.822 396915 40,950 406926 41.8+6 4.67.1 15 46 370918 376261 381540 386754 391907 3970C0 402033 407C09 4. ,92s 4.6792 14 47 371008 376350 38,627 386841 391993 397084 402, ,6 407091 412009 4.6S72 13 48 371097 376438 381714 386927 392078 397.68 402200 407173 4.209. 4.6953 12 49 50 371187 3r'i77 376527 38,802 3870,3 392163 397253 402283 407256 4.2.72 4.7034 "uT 3766.5 38,889 387100 392249 397337 402366 407338 4.22C..J4171.4 51 371366 376704 381977 387.86 392334 39742. 402450 407421 412335 417195 9 52 371456 376792 382064 387272 392419 397506 402533 407503 4124.7 417275 H 53 371545 3768S. 382.51 387359 392504 397590 4026,6 407585 4.2498 417356 7 54 371635 376969 382239 387445 392590 397674 402700 407668 412579 417436 H 55 371714 377057 382326 387531 392675 39775S 402783 407750 4.266, 417517 5 56 37.813 377146 3S24.3 3876.7 392760 397843 402866 407832 4.2742 417597 4 57 37'9o3 377234 382500 387704 392845 397927 402949 407915 4.2S24 4.7678 3 58 37.992 377322 3825S8 387790 392930 3980.. 403033 407997 4,2905 4.7758 2 69 372082 377411 382675 387876 3930,6 398095 403,16 40807c) 4.2986 4.7S39 1 60 37217. 377499 «ll° 38' 3S2762 387962 393101 398.79 413,99 40816, 88° 32- 4.3068 4179-9 // 88° 39' 88 ■ 37' 88° 30' 88' 35' 88° 34' 88 33' 88 31' ii8° 30' " - 1 TABLE G' 7155 LOG. SINES OF SMALL ARCS TO TEN SECONDS O 1 0" 1 10" 20" 30" 1 40" 50" 1 CO" 1 Purti d > )i 8- 8- s- 8- 8- 8- 1 31) 4I79I9 +.8721 419524 420325 42.123 41,91, 4227,7 32' 37' 88 29 I 31 41*717 423511 424304 425096 415886 426675 427462 r- 78 74 Hfl 2li 1 S2 417462 418248 429032 4298,5 430597 43'377 43i'56 2 ,56 ,48 HI! 27 1 s:i 431156 431934 4337.0 434484 435157 436029 436800 3 235 223 118 26 1 34 436SOO 437569 438337 439,03 439868 440632 44' 394 4 3,3 297 m 25 1 3,-. 441394 442,56 4429.5 443674 44443' 445,85 44594, 5 39, 371 811 24 1 36 44594' 446694 447446 448,96 448946 449694 450440 6 469 445 88 23 1 37 450440 45,, 86 45.930 452673 4534'4 454-54 454893 7 5+7 5'9 KB 22 1 311 454893 45563' 456368 457.03 457837 458570 45930, 8 626 594 88 21 1 3» 459301 460032 46076. 46,489 4622,, 46294, 463665 9 704 658 88 20 1 40 463665 464388 465. .0 465830 466550 467268 467985 42' +7' 88 19 1 41 467985 468701 4694.6 470129 47084, 47'553 472263 1' 7. 67 88 18 1 42 472263 471971 473679 474386 47509, 475795 476498 2 141 135 88 17 1 43 476498 477200 47790. 4^860, 479299 479997 480693 3 2,2 202 88 11; 1 44 4S0693 48,388 4S20S3 482776 483467 4S4.58 4S4848 4 282 269 88 15 1 4.'< 4848+8 485535 4S6224 4X6910 487596 4S8280 488963 5 353 336 88 14 1 4i; 488963 489645 490326 491C06 49.685 491363 493040 6 42+ 404 88 13 1 47 493040 4937>5 494390 495064 495736 496408 497078 7 49+ 47' 88 12 1 4« 497078 497748 49S4.6 499084 499750 5004,6 50,080 8 565 538 88 11 1 4ft 501080 5°'743 502405 503067 503717 504386 505045 9 635 6c6 88 10 1 5» 505045 505702 506358 5070,4 507668 50S32, 508974 52' 57' 88 9 1 :.i 508974 509625 5.0175 510925 5"573 5,221, 5,2867 1" 6+ 62 88 « I o2 5.2867 5'35'3 5.4'57 51480, 5 ' 5444 5,6086 5,6726 2 ,29 ,23 8« 7 I A3 516726 5'7366 5.8005 5.9280 5.99.6 52055, 3 ,93 ,85 8H 6 1 54 520551 S2„86 51.8.9 52245, 523083 5137.3 514343 4 257 246 88 5 1 bb 524343 514971 515599 526226 526852 517477 528.02 5 32, 308 m 4 1 56 528.02 528725 519347 529969 530590 531209 53.82S 6 386 370 88 3 I 57 53.82S 531446 533063 533679 534195 534909 535513 745043. 88 2 1 5H 5355^3 536.36 536747 537358 537969 538578 539,86 8 5,4 493 88 1 1 59 539186 539794 54040, 54,007 54.6,2 542216 542819 9 579 5 54 88 2 542819 543411 544023 544624 545"4 545813 546422 2- r 87 59 2 1 546422 5470.9 5476,6 5482,2 548807 54940. 549995 I" 59 57 87 58 2 2 549995 550587 55. .79 55'770 55236, 551950 553539 2 ,,8 ,,3 87 57 2 3 553539 554.16 5547.3 5553'° 555885 556470 557054 3 ,77 ,70 87 51; 2 4 557054 557637 5582.9 55938. 559961 560540 4 235 227 87 55 2 5 560540 561,19 561696 562273 562849 563415 563999 5 295 2S4 87 54 2 (i 563999 564573 565146 5657.9 566290 56686, 56743' 6 355 340 87 53 2 7 56743. 568000 568569 569.37 569704 570270 570836 7 4.+ 397 87 62 2 H 570836 57.40, 571965 571518 57309' 573653 5741 >4 8 473 454 87 51 2 9 5741.4 574774 575334 575893 57645' 577009 577566 9 531 5'o 87 50 ilM 577566 578.11 578678 579131 579786 580340 580892 12' 17' iT7":rr 2 II 580892 58.444 58.995 582546 583096 583645 584,93 '" 55 53 87 48 2 12 584193 58474, 585288 585834 586380 586915 587469 2 ,09 105 87 47 2 13 587469 5880,3 588556 589098 589640 590,8, 59072, 3 ,64 ,58 87 48 2 14 59072. 59,260 59'799 591338 591875 5934'i 593948 4 2.8 2.0 87 45 2 L". 593948 594484 5950,9 595553 596086 5966,9 597.51 5 273 263 87 44 2 IV, 597.51 597683 598214 598745 599174 599803 600332 6 31S 316 87 43 2 17 600332 600859 60,387 60,9,^ 602439 602964 603489 7 3S1 368 87 42 2 18 6034S9 6040 , 2 604536 605058 605580 606,02 606623 8 437 41. 87 41 2 1!) 606623 607.43 607662 608,8, 608699 609217 609734 9 49' +73 87 40 2 2 654377 654843 655308 655773 656238 656702 5 237 229 87 24 3 30 656702 657.65 657628 658090 65855= 6590.4 659475 6 284 .75 87 -'3 2 37 659475 659935 660395 660855 66.3.4 66.77= 662230 7 33= 3=' 87 22 2 311 662230 662688 663.45 663602 664058 6645.3 66496S 8 379 367 87 21 2 .-t!* 2 4(1 664968 665423 665877 66633. 666784 667=37 667689 9 4=7 4.3 87 20 87 l!l" 667689 66S141 668592 669043 669494 669944 670393 42' 47' 2 4 1 670393 670842 67.29. 67,739 672. 8 7 67=634 6730S0 1" 45 43 87 18 2 42 6730S0 6735=7 673972 6744.8 674S63 675307 67575' 2 89 86 87 17 2 43 675751 676.94 676638 677080 677522 677964 678405 3 133 .30 87 16 2 44 678405 678846 6792S6 679726 6S0.66 680605 68.043 4 .78 .73 87 15 2 45 68.043 68.48. 68.9,9 682356 682793 683230 683665 5 223 216 87 14 2 4(> 683665 6S4.0. 684536 684971 685405 685S38 686272 6 267 259 2 47 6S6272 6S6705 6S7.37 687569 68800. 68843= 688863 87 12 2 1» 688863 6S9293 6897=3 690.52 69058, 69.0.0 69.438 8 356 346 87 11 2 4!) 69.43S 69.866 692293 692720 693,46 693572 693998 9 400 3>*9 87 1(1 2 50 69399S 694423 694848 695=7= 695696 696.20 696543 52' 5;' 87 » 2 51 696543 696966 697388 6978.0 698232 698653 699073 I" 42 41 87 8 2 52 699073 699494 699913 700333 700752 701.71 70.5S9 2 84 82 87 7 2 53 701589 702007 702424 702S41 703258 703674 704090 3 .26 .22 87 (i 2 54 704090 70+505 704920 705335 705749 706163 706577 4 168 .63 87 5 2 55 7C6577 706990 707402 7078,5 708226 70863? 709049 5 209 204 87 4 2 50 709049 709460 709870 710280 7.0690 7,1099 7. .507 6 25. 244 87 » 2 57 711507 71.916 71=3=4 7,2731 7.3,39 713546 7.3952 7 =93 =85 87 2 2 5(C 713952 7 "43 58 7,4764 715169 715574 7'5979 7,6383 8 335 3=6 «7 I 2 5!) 716383 7.6787 7>7'90 7«7593 7.7996 718398 7,8800 9 377 366 87 88 59 3 (1 718800 7.9202 7.9603 720004 720404 720804 7=1204 2' r 3 I 721204 72.603 722002 72=401 722799 723197 7=3595 I" 40 39 8li 5« 3 2 7=3595 723992 7=4389 724785 7=5181 7=5577 725972 2 79 77 88 57 3 3 7=597= 726367 7=6762 727156 7=7550 727943 7=8337 3 ,.9 ..6 88 58 3 4 7=8337 728729 729.22 7=95>4 729906 730297 730688 4 15S 154 8(; 55 3 5 730688 73.079 731469 731859 73==49 73263S 733027 5 .98 .9; 88 54 3 « 733027 7334.6 733804 734>9= 734579 734967 735354 ' '" 2-0 m 53 3 7 735354 73574° 736126 7365.= 73689S 737=83 737667 88 52 3 8 737667 738052 738436 73SS20 739=03 739586 739969 8 3'.; 309 88 51 3 9 739969 74°35= 740734 74. .,5 74'497 74.878 742259 9 356 347 81; 50 3 10 742259 74=639 7430.9 743399 743778 744"57 744536 12' 17' 88 49 3 11 744536 744914 745=93 745670 746048 7464=5 7+6S02 '" 38 37 H«> 48 3 12 746802 747178 747554 7479 3'-- 748305 748680 749055 2 75 73 88 47 3 13 749°55 749430 749804 750178 75055' 750924 751297 3 ,.3 ..0 88 48 3 14 75'=97 75.670 75=04= 75=4'4 7527S6 753'57 7535=8 4 .50 .46 88 45 3 15 7535=8 753898 754=69 754639 755008 75537S 755747 5 .88 i«3 8(; 44 3 16 755747 756.16 756484 75685= 757220 -57587 757955 6 226 220 88 43 3 17 757955 7583=. 75S688 759054 759420 759786 760151 7 263 256 88 42 3 18 760.5, 7605.6 76088. 76.245 761609 76.973 76=337 8 30. =93 88 4 1 3 19 762337 762700 763063 7634=5 763787 764,49 764511 9 338 329 88 41) 88 39 3 20 76451. 764872 765=34 765594 765955 7663.5 766675 22' 27' 3 21 766675 767034 767394 767752 768469 768828 '" 36 3 5 88 38 3 22 768828 769.85 769543 769900 770257 7706.3 770970 2 7. 70 «(i 37 3 23 770970 7713=6 77.681 772037 77=39= 77=747 773'OI 3 ,07 .05 88 31; 3 24 773.01 773456 773810 774'63 7745-7 774870 775223 4 .43 139 86 35 3 25 775==3 775575 7759=7 776279 77663. 7769S2 777333 5 17S .74 88 34 3 2t; 777333 777684 778035 778385 778735 779085 779434 6 2.4 209 88 33 3 27 779434 779783 780.32 780480 780829 78. .77 78.524 88 32 3 28 78. 524 78.872 7822.9 782566 7829.2 783259 783605 8 286 2^8 86 31 3 29 783605 78395- 784296 784641 7849S6 78533' 78567s 9 3=' 3'3 88 30 3 30 785675 7860.9 786363 786707 787050 :^87393 787736 88 29 / CO" _50"_ 40" 30' 20" 10' 0' ParU / c OS.NIi """■ \ TABLE 07 LOG. SINKS OK SMALL ARCS TO TEN SECONDS | o / IV 10'- 20" 30" 40" 50" f.O" Parts / S- 8- 8- 8- s- 8- 8- ^~ H MO -Ss6-5 -86o>9 786363 7S6707 787050 787393 787736 32 37 Hfi 29 :i :ii 7S--;6 788078 78S421 788762 789.04 7S9446 7S97S7 '" 34 33 (IB 21! :> .■(■-• 790468 790808 79.149 79.488 79.S28 2 68 66 f!(; 27 :) :i;t 79ISZ8 ] "91167 792506 792S45 793.83 79352. 79 3 8 59 3 .02 100 f!fi 2(i :i 34 7'?5S59 -94'97 794534 794872 795-08 795545 795S8. 4 ,36 ,33 (!(i 25 :i :t,-. 79^XSi 7962.8 796553 796S89 797224 797559 797894 5 ,70 ,66 !»; 24 :f .'w; 79"'i9+ 798229 798563 798897 79923. 799564 799897 6 204 .99 III! 23 :' :'' .99897 8C0230 SC0563 800896 801228 80.560 1 80,892 7 23S 232 ■M 22 8U1S92 802223 802554 802S8; 8032,6 802546 803S76 8 272 266 W; 21 :t :(ii S03S76 804206 804536 S04S66 .805.95 807.65 805524 1 805852 9 306 299 nc, 2(1 nr, \'.» :t 40 S05S51 S06.81 806509 806837 807492 S078.9 42' 47' :i II S07S19 808.46 808473 808799 809.26 809451 809777 1" 32 32 nr, ifl 3 *2 809777 810.03 8,0428 8.0753 81.078 8, ,402 8. .726 2 65 64 lid 17 :t i:t 811726 8.2050 8,2374 812698 8.302, 8.3344 8.3667 3 97 95 no h; ;i 44 8.3667 8.3989 8.4312 8,4634 8,4956 8.5599 4 ,30 ,27 Wi 15 :i 4.i 815^99 8.5-y20 8.624. 8,656, 8,6882 8.7:02 8.7522 5 ,62 ,59 8fi 14 .1 40 Si7;2i 8,78,. 8,8161 8,8480 8.S799 8.91.8 8.9436 6 ,95 .9. 88 13 3 47 8,9436 8>9755 820073 820390 820708 82,025 82,343 7 228 223 «(i 12 :i 411 8ZI3+3 82.6,9 82,976 822292 S22609 822925 823240 8 26, 254 «(; 11 3 4!t S232+0 825556 S2387, 824186 824501 8248,6 825,30 9 293 286 ill; 10 825.30 825444 825758 826072 T.b^ 826698 8270,, 52' 67' 81! 7 74 842076 S4-37''. 8426S0 842982 S43283 843585 9 280 274 eu 4 II 843585 843886 844, 8X 844487 844787 1 8450S7 845387 2' 7' 85 :,'.) 4 I 8+53S7 S456S7 S45987 8462S6 8465S5 S46884 847.83 1" 30 29 85 58 4 2 847183 84748. 8477S0 848078 848376 848673 84897. 2 60 58 85 57 4 3 84X971 84926S 849565 S49862 850,59 850455 850751 3 89 88 85 :,r, 4 4 850751 851047 85>343 85,639 851934 852229 852525 4 119 ,,7 85 55 4 5 852525 8528,9 8531.4 853408 853703 853997 85429. 5 ,49 146 85 54 4 r; S5429. 854584 854878 855,7, 855464 855757 856049 6 179 .75 85 53 ■i 7 8 56049 S56342 856634 856926 8572.8 8575.0 857S0, 7 209 204 85 52 4 8 S5780, 858092 858383 858674 858965 859255 859546 8 238 234 85 51 4 !) 859546 855836 860,26 8604,5 860705 860994 86,283 9 26S 263 85 50 1 III "86Tl8r 86,572 86,86, 862,49 S62438 862726 8630,4 12- ir 85 4U 4 II 863014 863302 863589 863877 864.64 86445, 864738 1" 30 28 85 48 4 12 S64738 865024 8653,, S65597 S65883 866,69 866455 2 57 56 85 47 4 13 866455 866740 867025 8673,0 867595 867880 868,65 3 86 84 H5 4(! 4 U 868165 868449 868733 8690,7 86930, 8695S5 869868 4 ,,4 ,,2 85 45 1 15 869868 870.5, 870434 8707,7 87,000 87,282 87.565 5 ,43 ,40 85 44 ) k; 8-. 565 87,847 872,29 8724,0 872692 S72973 873255 6 ,72 ,69 85 43 ^ 17 8-3^55 873536 873817 874097 874378 874658 874938 85 42 4 111 874938 875218 87549S 875777 876057 876336 8766,5 8 229 225 85 4 1 4 1!) 8766.5 876894 877.72 87745. 877729 878007 8782S5 9 257 253 115 41) 4 2(» 8^8285 878563 87884, 879.,S 879395 879672 879949 22' 27' fl5 311 4 21 879949 880226 880503 880779 .38,055 88,33, 88.607 1" 28 27 85 38 4 22 S8.60? 881883 882^58 882433 882708 882983 883258 2 55 54 85 37 4 23 883258 883533 S83807 88408, 884355 884629 884903 3 82 8, 85 38 4 24 884903 885,77 885450 885723 885996 886269 4 ,,0 ,08 85 35 4 25 S86542 8868,4 S87087 887359 88-63, 887903 888,74 s ,37 .35 85 34 ) 2fi 888.74 888446 8887,7 888988 S89259 889530 88980: 6 ,65 ,62 85 33 1 27 88980. 89007, 890341 8906,2 S90882 89.15. 89,42, 7 192 ,89 85 32 1 2K 89,421 89,690 89,960 892229 892498 892767 893035 R 220 2,6 85 31 1 2;i 893035 893304 89357* 893840 894.08 894376 894643 9 247 243 85 30 1 .W 89464, 8940,. 895.78 895445 8957.2 895979 1 896246 85 2!) T~7~ fid" :.o" 40' 30'- 1 20" ; lO' J 0" P,„l,, / COSINR 1 7-.]^ TABLE G8 LOS. SINES , COSINES, tke. 1 __ 1 Oh O" 0=' 777 m. Sine D. Cosec. Tangent D. Cotang. Secant [d. Cos,ne 60 ~«0~ "o" ~o" — oo X — oc 00 10 ococco lO-ccccco 2 6-162696 477I2I '3-8373'?4 6-162696 477121 1.3-837304 10 00c oco 10-coccoo 58 3( 1 4 6-463726 22.849 .3-536274 6-463726 221849 .3-536274 10 ococoo lO-OCCOOO 36 09 :iu a 6-6398,7 .46. 28 .3-360.83 6-639S17 146.28 ■ 3-360,83 10 000000 lo-oococo 54 30 2 8 6-764756 .09.45 13-235244 6-764756 109145 13-235244 10 oocooo ■O-OGOOOO 5-2 58 30 6-861666 87.50 .3-138334 6-86i666 87150 13-138334 10 ooooco lo-cocooo 50 30 3 li 6-940847 72550 13-059.53 6-940847 72551 13-059153 10 000000 io-cooooo 48 57 30 u 7-007794 62,48 .2-992206 7-007794 62.48 ■2-992206 10 000000 lo-cooooo 4S 30 4 Id 7-o6s-86 5435S .2-9342.4 7-065786 543 57 ■2-934214 10 000000 10-coocco 44 56 30 18 7-11697, 48305 .2-S8306. 7-116939 48305 .2-88306, 10 000000 ■o-occooo 4-2 30 5 30 30 7-162696 43465 ■^•^37304 7-. 62696 43466 12-837304 ■ coooco ■ o-oocooo z 55 7-204089 39509 .2-7959.. 7-204089 39508 .2-7959., ■ OOCOOI "o^ 9-999999 S •i4 7-241877 362.2 .2-75S.23 7-241878 362.3 .2-758.22 ■ 00000, 9-999999 36 54 30 se 7-276639 334H .2-72336. 7-276640 33423 12-723360 ,0 00000, 9-999999 34 30 7 •w 7-308824 3.034 .2-69. .76 7-30S825 31035 .2-691175 ,0 00000 1 9-999999 32 53 30 30 7-338787 28963 .2-66.213 7-338788 28964 12-66.2.2 ,0 00000 1 9-999999 30 30 8 32 7-3668.6 27.53 .2-633.84 7-3668.7 27.52 .2-633.83 10 000001 9-999999 28 52 30 3J 7-393H5 ^5554 .2-606855 7-393.46 25554 .2-606854 ,0 00000 1 9-999999 •26 30 !( 18 7-417968 24.33 ,2-582032 7-4.7970 24134 .2-582030 00000 1 9999999 '24 51 30 :<« 7-441449 22863 12-55855. 7-44.451 22863 .2-558549 ,0 000002 9-999998 ■22 30 30 40 22463726 2,7.9 .2-536274 7-463727 2.7.9 .2-536273 10 000002 o_ 9-999998 9-999998 20 18 50 30 7-484915 20685 .2-5.5085 7-484917 20685 .2-5.5083 ,0 000002 1 1 4J 7-505118 '9744 .2-494882 7-505.20 19744 .2-494880 10 000002 9-999998 16 49 30 4rt 7-524423 .S885 12-475577 7-524426 .8886 12-475574 ,0 000002 9-999998 14 30 12 4« 7-54^906 .8098 .2-457094 7-542909 .8098 .2-45709. 10 000003 9-999997 12 4« 30 50 7-560635 •7374 .2-439365 7-560638 ■7374112-439362 ,0 000003 9-999997 10 30 13 J'i 7-577668 .6706 .2-422332 7-577672 .67061.2-422328 10 000003 9-999997 8 47 30 W 7-594059 16087 .2-40594. 7-594062 .6087 ■2-405938 10 000003 9-999997 8 30 U .',0 7-609853 155.2 .2-390147 7-609857 14512 ,2-390,43 10 000004 ° 9-999996 4 iG 3f> 5a 7-625093 ■4977 12-374907 7-625097 14978 ,2-374903 ,0 000004 9-999996 2 30 la 1 7-6398i6 _>447i .2-360.84 7-639820 14478 ,2-360,80 ,0 OC0004 59 4o 30 ..1 7-654056 .4010 .2-345944 7-65406, ,40,, 12-345939 000004 17 9-999996 58 30 16 4 7667845 ■3573 ,2-332,55 7-667849 13573 12-332151 ,0 000005 9999995 56 44 30 « 7-6?i2o!) .3.6, ,2-3,8792 7-6812,3 13,6, .2-3,S787 ,0 000005 9-999995 54 30 17 S 7-694173 '2774 ,2-305827 7-694.79 ■2775 ,2-30582, ,0 000005 9999995 32 43 30 Ml 7-706761 .24.0 ■2-293238 7-706768 ,2409 ■ 2-293232 OOOr.o6 9-999994 50 30 IS li 7-718997 .2064 7-719003 ,2065 ,2-280997 ■ 000006 9-999994 ^ 42 30 H 7-730896 .1738 ,2-269,04 7-730902 11739 ,2-269098 10 000006 9-999994 46 30 1!» ]6 7-742478 1.430 ,2-257522 7-742484 11429 ,2-2575.6 ,0 000007 9-999993 44 41 31) 18 7-753758 ...35 ,2-246242 7-753765 11137 ,2-246235 10 000007 9-999993 42 M 20 '^0 7-764754 .085S ,2-235246 776476. ■ 0858 ,2-235239 ■ C00007 9-999993 40 40 30 •2-i 7'775477 .0593 ,2-224523 7-775485 10593 ■2-2245,5 10 000008 9-999992 38 311 21 ■ti 7-785943 .0340 12-2,4057 7-785951 ,0342 ,2-2,4049 ■ c 0000 8 9-999992 3J 3» 30 •i6 7-796162 .2-203838 7-796170 ,o,oo ,2-203830 ■ 000009 c 9-99999' M 30 2-2 •iS 7-806146 '987° .2-. 93854 7-So6^55 987. ■2-193845 ■ 000009 9-99999, :n 38 30 30 7-815906 965. .2-. 84094 7-815915 9652 ■2-184085 10 000009 9-99999, 30 30 23 je 7-825451 9442 ■2-174549 7-825460 9442 12-174540 10 CCOOIO 9-999990 •28 37 30 34 7-834791 9240 .2-, 65209 7-83480, 924, .2-^65,99 ■ COOOIO 9-999990 -2fl 30 24 3« 7-843934 9048 ,2-, 1:6066 7-843944 9048 ,2-, 56056 ■ 0000 ■ 1 9-999989 24 36 30 ■M 7-852889 8864 ,2-,47,,, 7-852900 8S64 ,2-, 47, 00 ■ 0000 ■■ 9-999989 •22 30 25_ 40 7-861662 8686 ,2-, 38338 7-86,674 8686 ■2-, 38326 ■ OCOO, 1 9-999989 18 35 30 7-870262 85.5 ,2-, 29738 7-870274 85,6 ,2-, 29726 To" 0000 12 "3" 9-999988 26 44 7-878695 8352 ,2-, 2, 305 7-S78708 8353 ,2-12,292 ■0 0000,2 9-999988 16 34 .111 4a 7-88696-3 8.95 ,i-,,3032 7-88698^ 8,95 ,2-, ,30, 9 ,0 0000,3 9-991987 14 30 i7 48 7-895085 8042 ,2-, 049, 5 7-895099 8043112-10490, ,0 000013 9-999987 12 33 30 30 7-903054 7896 .2-096946 7-903068 78971,2-096932 ,0 0000,4 9-999986 10 30 28 54 7-910879 7756 12-089.2. 7-9,089., 7755 ,2-089,06 ,0 0000,4 I 9-999986 s 32 311 M 7-9.8566 76.9 .2-08.434 7-9,858^ 7620 ■2-o8,4^9 ,0 0000,5 1 9-9999S5 a Ml 29 311 7-926.19 74S8 1207388. 7-926134 7488 12-073866 ,0 0000,5 I 9-999985 4 31 ,10 JB 7-933543 736. .2-066457 7-933559 7362 .2-06644, ■0 0000.6 I 9-999984 2 30 rtii m. --940842 7238 .2-059.58 7-940858 7239 ,2-059,42 I D 9-999983 3(1 / // Cosine 0- SecaiiP Cotang. D. Tangent Cosec. Sine 89° A" S8' r~ TARLfi (58 739 f" I,OG. SINfc;S. COSINES, &.:. 1 2"' 0^ 1 ' " '■^ 1 Sin. 1 D. Cosec. 1 Tangent I D. 1 Counj. S-.cant D Cosine -•I'" :)(> 7-9+0842 7:3s 12-059, 581 7-940858 :7239 .2^059i4i 9-999983 ss: :)!' :in ■2 7-9+8020 7,19 11-05,980 7^948037 71:0 1205.963 10 ccoo,7 9-999983 3(( 31 1 7-9550S2 1 7005 11-0449,8 7-955'oo 70c 5 1 2^044900 10-00CO.8 9-999982 56 29 :iii r. 7-96203.1689+ 11-037969 7-967049 689+ 12^03795. 10-00C018 9999982 .'■)4 30 :t-j « ;-968S70 6785 I1031130 7-968889 67S7 '-■o3"" .0-00C019 9-9.^998. 52 '28 ,1(1 1 10 7-975603 6682 I1-014397 7-975622 6682 12-024378 10-000019 9-999981 50 31' 3:t I'i 7-982233 6580 .2-0.7767 7-982253 6580 12-0.7747 10-0C0020 9-999980 48 -27 30 II 7-98876+ 6482 .2-o.,236 7-988785 6483 12-01 12.5 .0-C0002. 9-999979 4a 31 ru lU 7-995198 6387 .2-004802 7-9952.9 6387 12-00478. .0-CC002. 9-999979 44 •2(.- 3D IH 8-co,53X 629+ .,-998+62 8-CO.560 6295 1.-998440 I0^CC0022 9-999978 42 31 To 20 S-007787 6204 ,,-9922,3 8-007809 0204 11-992.9. '°-ooco23 9*999977 40 38 25 31 8-0139+7 6. .6 .1-986053 8-0.3970 6.18 11-986030 '0-CCC023 9*999977 Ml •24 8-O20O2I 6032 .1-979979 8-020045 6032 I. -979956 .O-COO024 9999976 3ti 24 :m ■u; 8-026011 5949 11-973989 8-026035 5950 ..•973965 .0-00002^ 9-999976 34 31 :t7 ■M 8-031919 5869 11-968081 8-03.945 5869 11-968055 .O-CCOO25 9999975 32 23 jii 30 8-0377+9 579° 11-962251 8-037775 5r-ji 1,-962225 .0-000026 9^999974 30 3( ■Mi :h 8-0+3501 57,5 11-956+99 8-043527 57>4 1,-956473 IO-COOO27 9999973 28 22 .10 3J 8-0+9178 56+0 1.-950822, 8-o+9'.o5 564, 1,-950795 10-000027 9-999973 28 30 :t!) 3(1 8-05+78. 5567 ..-9+52.9 8^05.+8o9 5569 .,-94519, 10-000028 9^999972 24 21 30 3S S-0603.+ 5+98 11-939686 80603+2 5498 11-939658 10-000029 9 99997. 22 .10 40 40 8-065776 5+28 1.-934224 8^c658o6 5419 "■934194 IO-OCOO29 9-99997. •20 18 20 8-07.171 5362 .,-928829 8^07120. 5362 ..■928-99 10-000030 9-999970 41 41 8-076500 5296 ,,-923500 8^07653, 5197 .1-923469 IO-COCO3I 9-999969 18 Ifl 311 40 8-0S176+ 5232 ,,-9,8236 8^08.795 5133 11-9.8205 .0-000032 9-999968 14 30 42 4H 8-086965 5.70 ,,-9,3035 8^o86997 517, ..-9.3003 .0-000032 9-999968 12 \n .10 30 8-092.04 5. 09 ,,-907896 8^C92.37 5,,o .,-907863 .O-CCCO33 9-999967 10 .3(1 43 5-2 8097.83 5050 1,-9028,7 8^0972.7 5050 "■901783 .O-OCO034 9-999966 8 17 30 51 S-. 02204 +991 ,1-897796 8. 02239 4993 ..■89776, IO-OCO035 9-999965 30 44 M 8-.07.67 4935 ..-S92S33 8^.07203 493 5 ..■892797 10-000036 9-999964 4 \ti 30 5S 8-.. 207+ +880 ..•887926 8^..2..0 488, ..■887890 .O-OCCO36 9-999964 2 .10 45 30 3 8-1.6926 +825 ..-883074 S^ii6963 4826 "■883037 .0-000037 9-999963 87 Ij 8-.21725 4772 ..-878275 8^.2. 763 4773 ..■878237 .0-000038 9-999962 IK 1 8-126+7, +72, ,,•873529 8-. 265.0 472, "■873490 9-99996, 56 U 30 (, 8-131.66 4669 .•868834 8^.3.2o6 467, .0-000040 9-999960 54 3(1 47 » 8-. 358.0 +620 .•864.90 8-135S5' V620 11864149 IO-OCOO4. 9-999959 52 13 30 10 8-1+0406 4571 ■■859594 8-140++7 4571 "•859553 .0-00004. 9^999959 50 30 40 1-2 S-,44953 4513 .■C55047 8^ 1+4996 4515 ..■855004 .O-OCOO42 9^999958 48 12 30 II S-.+9+53 4477 ,.■850547 8- "49497 4478 ..■850503 .0-000043 ■ 9^999957 4« 30 49 IC S-. 53907 443 > .•846093 8-. 53951 4431 ..■846048 .0-000044 ' 9-999956 44 11 ,?n 18 8,583.6 4387 .•84.6?+ 8-. 5836, 43S8 ..■84.639 .O-OOCO45 1 9-999955 42 .3C 50 20 8-. 6268. 4343 ,-837319 S-.62727 4343 ,r832273 IO-OCOO46 9-999954 40 10 30 22 8-. 67002 +299 .-832998 S-, 67049 430. ..■83295. 10-000047 9-999953 38 30 51 14 8-. 7. 280 +258 ,■828720 4258 1. -828672 .0-000048 , g-999951 36 11 30 ■US 8"«755'7 +2,6 ,-824483 8^;75566 42.7 ..-824434 .0-000049 9-99995' .'<4 30 .VJ w 8 1797.3 + ,76 . -820287 «■. 79763 4177 ..-S20237 .0-000050 9-999950 32 f) TO 30 8-.33S69 + .36 .•8.6.3, 8, 839,9 4'37 M-8.608. .0-00005, 9-999949 30 3(1 .'>:i 12 8-.8798S 4096 1-8. 20.5 81S8036 4097 ..-81.964 .0-000052 9999948 28 7 30 31 8-. 92062 +059 ,•807938 8-192. .5 4060 ..-80-885 IO-COOO53 9-999947 ■2« 3(1 54 3« 8-196102 +02. .-803898 8-, 96. 56 4022 .1-803844 IO-COOO54 9999946 ■24 (.- 30 3>1 8-200,04 398+ ,-799896 8-200.5, 3985 ..-79984. ,0-000055 9-999945 22 30 .v. .11) JO 8-20+070 3ili ,-79593= 8-204.26 3949. 1. -795874 9999944 20 Id S-2080CO 39,2 .-792000 8-208057 39'3 .1-791943 10^000057 9-999943 5H 41 8-21,895 3877 ,-788,05 8-2.1953 3878 .1-788047 10^000058 9-999941 11^ 4 30 4fl «-^'5755 3843 .-784245 82.58.4 3844 11-784186 .o^oooo59 9 9999+1 IJ 30 •i7 4H 82,958, 38,0 1-7804.9 82,964, 38.. 11-780359 To^ecoo6o 9-999940 12 3 .10 .50 8-223374 3776 .-776626 8^223434 3777 .,-776566 .0-00006 1 9-999939 10 .w :.!! .V2 8-227.34 3743 ,■772866 8-227,95 3745 ..-772805 .0-000062 9-999938 8 2 10 .M 8-23086, 3712I ,•769,39 8^230924 .■769076 .0-000063 9-999937 It 30 Afl Ml 8'i34557 3680 1 1-765443 8^23462. 368, .■765379 0-000064 9-999936 4 1 .10 .W 36491 .-761779 8^238286 365, ,■76,7,4 0-000065 9-999935 1 30 fiO 4j 8-24. 85J 36., 1-758145 8^24.92. 3620 .•758079 0-000066 9-999934 777j=H fosinr 1 D. 1 Srrant rolnnp. 1 I). 1 T(ingr..t Cosec. 1 n. Sine T 8;r^ 5" ft'i"' 1 740 TABLE R8 LOG. SINES, COSINES, Sen. 1 (1- 4"' 1° J i„ "? Sine 1 D. Ca-wc. Tnn^enl D. Co,.n,. Secant Parts Cosine m. si fiO n 8-241855 1 3619 11-758145 8^24i92i 3-6;^ "-758079 ,0 000066 9^999934 30 ; ■; 8-2,1.5459 3589 11-754541 8^245526 3590 "-754474 ,0 000067 l"o 9^999933 58 30 1 ^ 8-249033 3559 11-750967 8-2+9.02 3560 1,-750898 ,0 000068 2 9-999932 50 59 :)0 li X-252578 353" 11-747412 8-252648 3532 "-747352 ,0 000069 .-J 9-999931 54 30 2 „ 8-256094 3502 11-743906 8-256,65 3503 "-743835 JO OC007. 4 9-999929 52 5» 31) 10 S-259582 3474 11-740418 8-259654 3475 ..-740346 .0 000072 5 9-99992S 50 30 3 1-2 8-263042 3446 11-736958 8^26j,i5 3448 1.-7368S5 .0 000073 6 9-999927 48 57 30 U S-266475 3419 11-733525 8-266549 3420 .,-73345' .0 000074 7 9-999926 46 30 4 111 8-260881 3393 11-730119 8-269956 3304 '.-730044 .0 000075 8 9-999925 44 5H 1)4 8-273260 3366 11-726740 8-273337 3367 ..•;26663 .0 OCC076 9 9-999924 42 30 5 •iO 8-276614 334' .1-723386 8-2766,, 3342 ..•723309 10 000078 10 U c 9-999922 40 5.5 30 22 8-279941 33'4 11-72C01 ) 8-280020 33.6 ..•7.9980 10 OC0079 9-999921 « •i4 8-283243 3290 ..-7.6757 8-283323 329. .1-7.6677 ,0 000080 12 9-999920 3C 54 30 20 8-28652, 3265 1. -7. 3479 8-286602 3266 ..-7,3398 10 00008 . 1.3 , 9-999919 34 30 7 2H S-2S9773 3241 8-289856 3242 ..-710.44 ,0 000082 14 , 9-9999,8 32 53 30 8-293002 3216 '■•706998 8-293086 32.8 ,,-7069,4 10 000084 15 , 9-9999.6 30 30 8 32 8-296207 3'93 1.-703793 8-296292 3 '94 ,.-703708 10 000085 16 , 9-9999.5 28 52 30 34 S-2993SS 3170 11-700612 8-299474 3.7. 11-700526 ,0 00C086 17 I '/9999'4 20 30 9 3(1 8-302546 3 '47 11-697454 8-30263+ 3.48 ..■697366 10 000087 18 , 9-999913 24 51 30 :i» 8-30568. 3124 ..-6943.9 8-305770 3.25 ..•694230 10 00C089 19 , 9-99991, 22 31) 10 '." 8-308794 I. -69,206 8-308884 ..•69,,, 6 10 OC0090 20 , 21 , 9-9999'o 9-999909 -20 r.o 1 S-3.,885 5080 .1-6881,5 8-3,1976 308. ,.•688024 z 00C09. IS 30 11 44 8-314954 3058 .,•685046 8-3,5046 3059 ..•684954 00C093 22 I 9-999907 Hi 49 30 40 8-318001 3036 .,•68,999 8-3.8095 3038 ,,•68,905 10 OCOC94 2,-) , 9-999906 11 30 12 4.S 8-321027 .,•678973 8-32, ,22 30.7 ,,•678878 10 000C95 24 , 9-999905 12 41! 30 50 8-324032 2995 .,-675968 8-324,29 2996 ..•67587. ,0 OC0097 25 , 9-999903 10 30 )3 52 8-327016 ^974 ..-672984 2975 ,.•672886 10 OC0098 26 I 9-999902 8 47 30 54 8-329980 ^954 ..-670020 8-330080 2956 ..■669920 10 C00099 27 1 9-99990. C 30 u 50 8-332924 ^934 ..-667076 8-333025 2935 ..•666975 10 OCO.OI 28 , 9-999899 4 46 30 58 8-335848 2914 ,.-664.52 8-335950 29.6 I .•664050 ,0 coo, 02 29 , 9-999S9S 2 30 15 \ 8-338753 2895 .1-66,247 S-338S56 2S96 ,,■66, ,44 ,0 000,03 30 , 9-999897 55 45 S-341638 2876 ..-658362 8-34,743 2877 ,,■658257 ,0 000,05 1 9 999895 58 30 1 le" ■) 8 -344504 2856 ..-655496 8-3446.0 2S58 ,,-655390 ,0 000.06 2 9-999894 5(1 44 30 8-3+735^ 2858 .,-652648 8-347459 2840 ..-65254. ,0 000.08 .S 9-999892 51 .■|i> •7 » 8-350181 2S20 ,.-6498.9 8-350289 1282, ..-6497,, ,0 000.09 4 9-99989. 52 43 10 8-352991 2801 ..-647C09 8-353,01 I2803 ..-646S99 10 5 9-999890 50 30 18 12 8-355783 2784 ,,-64^2,7 8-335895 I27S4 .,-644.0; 10 000,, 2 6 9-999888 48 42 30 U 8-358558 2766 ,,-64,442 8-35867. 2768 ,,-64,329 10 OCC..3 7 9-999887 40 30 19 10 8-361315 2748 ,.-638685 8^36 1430 2749 ..-63S570 ,0 0001,5 8 9-999885 44 41 3» 18 8-364055 2731 ,,•635945 8-364.7. 2733 ..-635829 ,0 000,, 6 9 9-9998S4 42 30 20 30 22 8-366777 2714 ,,•633223 8-366895 27'5 ..-633.05 ,0 coo,, 8 9-999882 3S 40 8-369482 2697 ,,-6305,8 8-36960. 2699 1,-630399 To" 000,, 9 9-999881 21 24 8-372171 2680 ..-627829 8-372292 268. ,,-627708 10 9-999879 30 39 30 20 8-374843 2664 .1-625.57 8-374965 2666 "■625035 10 000,22 9-999878 34 30 22 28 8-377499 2648 .1-622501 8-377622 2649 ,,-622378 10 000,24 9999876 32 3K 30 30 8-380138 2631 ..•619862 8-380263 2633 ,,-619737 10 OC0125 9-999875 30 30 23 32 8-382762 26.6 ..•617238 8-3S2889 26,7 1,-6,7,,, 10 000127 llfi ' 9-999873 -28 37 30 34 8-385370 2600 ,,■6.4630 8-385498 2602 ,,-6,4502 10 000,28 17 . 9-999872 ■20 30 24 30 8-387962 2585 .,•6.2038 8-388092 2586 11-6.1908 10 000,30 18 I 9-999870 •24 36 30 38 8-390539 2569 ,,•60946, 8-390670 257. 11-609330 10 000,3, 19 I 9-999S69 -22 30 25 30 42 8-393101 ^554 11-606899 S-393234 2556 11-606766 10 000,33 20 , 21 , 9999867 20 35^ ' 30 8-39564> »539 .1-604352 8-395782 2540 1,-6042.8 To coo 1 34 9-C09S66 20 ■H 8-398179 2525 n-60,821 8-3983.5 2526 1 .-60.685 10 000,36 22 , 9-999864 1(1 34 30 4(1 S-400696 2510 "•599304 8-400834 2512 11-599,66 10 000,37 23 , 9-999863 14 ;« 27 4S 8-403 '99 ^495 .,•59680, 8-403338 2497 ,-.-596662 10 000,39 24 , 9-999861 12 33 30 50 8-405687 2481 .1-5943.3 8-405S28 2483 11-594,72 10 000.41 25 , 9-999859 10 30 28 52 8-408161 2467 ,,•59,839 8-408304 1468 .,-59,696 10 000,42 26 1 9-999858 ^ 32 30 54 8-410621 ■■=453 "■589379 8-4. 0765 2455 .1-58913; 10 000144 27 I 9-999856 :«) 29 50 8-413068 2440 ,,•586932 8-4.3213 244' .,-586787 10 000,46 28 , 9-999854 4 31 30 58 8-415500 2425 ,,•584500 S-415647 2427 "■584353 10 000,47 29 , 9999853 2 311 :«) 6 8-417919 2412 8-418068 24.4 ,1-58,932 10-C00149 30 2 9-999851 30 TU 1! Cosine D. Secant Cotang. D. Tangent Cosec. Tarts Sine ^'^1 88° 5..54™- 1 1)1' LOU. SINES, COSINES, i*.:. — n f,™ J" ~ ' ' 1™ Sine D. Cosen. Tangent D. _Cotang^ Secant Parts Cosine 9-9,98;, m V'\ Tr: 8-4. 79-9 24.2 .,-5^208, 8-4.8068 24.4 ..-58.932 .0-CC0.49 TillfTl X>20325 2399 ..-579675 8-420471: 240. ■'■5795=5 .0-000.5. 1 "0 9-9,984, .'111 ;J1 1 4 8-422717 2386 ..-577283 8-422869 = 387 .1-577.3. .0-C00152 2 9-99,848 .'.!> 2'.l :m| r, 8-425096 = 373 .1-5749°+ 8-425150 237+ .1-57+750 .0-000.54 ■i ,■,998+6 .'j4 30 :v2 H 8-427462 = 3 59 ■■•57=538 8-4276.8 2362 .,-572382 .0-000.56 4 9-999844 5-2 21! 3, 10 8-4298.5 = 347 ..-570.85 8-429973 =3+8 .1-570027 10-CCO.57 5 9-9998+3 511 .10 33 11 8-432.56 =335 ..-5678+4 8-+323.5 2336 ..-5676S5 .0-000.59 6 9-99,84, ,., 27 30 li 8-434484 ..-5655.6 8-43+645 2324 ..-565355 .0-000.61 7 9-99983, Iii 3S in 8-436800 i 2309 ..•563200 8-436962 23.. .1-563038 10-C00.62 8 9-999838 2(; 30 j IK 8-430,03 I2297 11-560897 8-439267 ==99 "•560733 10-C00.64 9 9-999836 4-2 .30 3.-) j-ii 8-441594 1 "86 .,-558606 8-44^560 2287 ■■•5584+0 .0-C00.66 1(1 I U . 9-9,9834 411 25 30 ^n 8-443674 ==73 ..-556326 8-4+38+. 2275 ..•556.59 10-C00.68 9-999832 36 8-44594. 226. ..-554059 8-446.10 2263 "•553890 .0-000.69 1-2 . 9-99983, 3li 24 JO ■u; 8-448.96 2250 ..■55.804 8-448368 2252 ..•55,632 .0-OCO.7. i:( . 9-999829 14 311 37 ■i< 8-450440 2238 ..-549560 8-4506,3 2240 "■5+9387 .0-0C0.73 14 . 9-99,827 32 23 3(1 30 8-452673 2226 1.-5473=7 S-452847 2228 "■S+7'53 10-CC0.75 l5 I 9-999825 ,10 30 3« 3-2 8-454893 22.6 I. -545. 07 8-455070 22.7 ..•54493c .0-000,76 16 . 9-999824 ., 22 .'III M 8-457.03 22C3 ..-542897 8-45728. 2206 ..•5427., .0-C00.78 17 . 9-,„S22 ill 311 :«' Mi 8-45930. 2.93 11-540699 8-45948. 2.94 ..-5405.9 10-000.80 18 1 9-9,9820 ,| :>.i r.o :t* 8-46.489 2. 82 ..-5385.. 8-46.670 2.84 .1-538330 10-000.82 lU , 9-9998,8 ]., J0_|40 8-463665 2.7. 1.-536535 8-463849 2,73 1.-536.5. ,0-000.84 ,0-000,86 20 . 21 . 9-9998,6 ■" -.>() 11 8-465830 2.60 ..-534170 8-466016 T76T ..-533984 9-9998 J-i 11 Ji 8-467985 2.49 ..•5320.5 8-46S.72 2.5, 1.-531S28 .0-000.87 22 1 9-9998.3 l(i l!l 30 4r, 8-470.29 = ■39 ..-52987. 8-4703.8 2.40 ..-529682 IO-00O.8, 23 . 9-9998' ■ 30 42 4M 8-47:263 2,28 "•5=7737 8-+72+5+ 2.3. ■■■5=75+6 .0-C00.9. 2+ , 9-99,809 1-2 l(! 30 30 8-474386 21.8 ..-5256.4 8^+7+579 2, .9 ..-52542. 10-000.93 25 2 9-999807 in 30 43 3i 8-476498 2.08 I. -523502 8-476693 - ..-523307 .0-OC0.95 26 2 9-99,805 g 17 30 54 S-47860, 2097 ..-52.399 8-478798 209s I. -52. 202 .0-000.97 27 2 9-99,803 1^ 44 M 8-480693 2088 ..-5.9307 8-480892 2089 ..-5.,.oS 10-000.99 28 2 9-99980. 1 1« 30 r,n 8-482776 2077 I. -5. 7224 8-482976 2080 11-517024 10-CC020. 29 2 9-999799 .J 30 45 7 8-484848 2067 1-5.5.52 8-485050 2069 ..•5.4,50 .0-OC0203 30 2 9-999797 S3 15 30 8-4869.0 2Sir 1-5.3090 8-4871.5 2060 ..-5.2885 .0-0C0205 1 9-999795 4li 4 8-488963 2048 .-5. .037 8-489.70 20+9 ..-5.0830 IO-CC0206 2 9-999794 M 14 311 f' 8-49.006 2038 .-508994 8-4912.5 2041 ..-508785 IO-OC020S 3 9-999792 54 .1, 47 "* S-493040 2029 .•506960 8-493250 2030 .1-506750 .O-0C02.0 < 9-999790 5-2 i:> 30 111 S-495064 20.9 .•504936 8-495276 .1-504724 .0-0002.2 5 ,-,99788 511 30 4n 1-2 8-49:078 20.0 .-502922 8-497293 2012 .1-502707 .00002. 4 6 9-99,786 IN 12 30 l< 8499084 2CO. .-5005.6 8-4993CO 2C02 ..•500700 10-000216 7 9-999784 I'J 30 4» iO 8-50.080 .99. 1-498920 ■99+ ..•+,8702 .0-C002.8 8 , 9-999782 44 II 30 IX 8-503067 .983 .-496933 8-503287 .984 ..•4,67.3 IO-OC0220 9 . 9-999780 4-2 30 .->() ao 8-505045 8-50,0.4 .1973. '•+9+955 8-505267 .976 ■■■+9+7 53 .0-COC222 10 , 9-999778 9-999776 411 ~ .965 .-492986 8-507238 .,66 ..•+92762 .O-COO224 51 21 8-508974 ■955 .-+9.026 8-509200 .958 ..•4,c8oo .O-CCO226 12 I 9-99977+ 30 'J 30 ■M 8-510925 "947 ■•+89075 8-5. ..53 ■9+9 ..•48S847 .O-CCO22S 13 I 9-999772 31 30 52 •is 8-5.2867 .938 .-+87.33 8-5,30,8 .940 ..•486,02 10-00023, 14 . 9-99976, 3'2 II 30 30 8-5.4801 .930 .-4S5199 8-515034 .93. ..•484,66 IO-COO233 15 . 9-999767 30 311 53 3-i 8-5.6726 .92. ■■+832:+ 8-5.696, ■9=3 ■■■+S3039 IO-C0O235 16 , 9-999765 28 7 30 .« 8-5.8643 .9.2 ■•+8.357 85. 8880 19.5 ..-+8.120 ,0-000237 17 1 9-999763 •2(1 30 54 M 8-52055. .904 '•+79++9 8-520790 .906 11-+79210 0-000239 18 , 9-99976. •24 »; 30 ;« 8-52245. .896 ■■+77 5+9 8522692 .898 ..-+7730S 0-C0024, 19 , 9-999759 22 30 55 4i 8-5243+3 1888 ■■+75657 8-524586 .890 ..•+754.4 0-CC0243 .0-OC0245 20 1 9^9997 57 9-999755 5 8526226 .879 ■■47377+ 8-526472 1881 ..-+73528 ;« ■41 8-528.02 .87. .■47'898 8-5283+9 1874 ..-+71651 0-CC0247i'22 2 9-999753 Hi 4 30 411 -52,96, .S64 1-47003. 8-5302.8 1865 11-469782 .0-000249 23 2 9-99975. 14 30 ')' 4S 8-53.828 .855 .-468.72 8-532080 ■857 ..-467920 .0-C00252 24 2 9-99,748 12 3 30 30 8-533679 .847 .-46632. ^■535933 .850 1.-466067 0-C00254 25 2 9-99,746 10 30 3fi .•)-2 8-5355-3 .840 1-464477 8-535779 .842 11-464221 .0-0002 56 26 2 9-9997+'! ^ n T 31 8-537358 .83. .-462642 8-5376,7 .83+ 1.-462383 0-000258 27 2 9-999742 fl 30 50 311 8-539.86 .824 .-+608.4 8-539++7 ,826 ..-460553 0-C00260 28 2 ,-,,,740 4 1 30 3S 8-54,007 .8.7 .-+58993 8-54126, ,8,8 ..■45873. .0-C00262 2!) 2 9-999738 • 30 CO _8_ 8-5428.9 .809 .-+57.81 8-5+3084 .8. . ..-456916 C-CC0265 30 2 9-999735 II 'Z ■?• Csine I>. Srcaiit Cotang. 'v.' Ta.,K,-„t Ci.see. Parts Sine m. T„ Hrt ;,h ;,._,„ "" 742 TABLE 6S LOG. SINES, COSINES, &c. ()'' 8'" 2° 1 TTT m Sine D. Cusec. Tangent D. Cotang._ Secant Parts Cosine m ' ". 0" 8-542819 ,809 ..-457'8' 8-543084 1811 .1-456^.6 0-000265 „ 9^999755 52 w 30 8-544624 i8o[ 11-455376 8-544S9. 1804 ..-455.09 0-000267 1 9-999733 30 1 8-546422 I79■^ 11-453578 8-54669. .796 .1-453309 °;°^269 2 9-90973, 60 59 3a 8-548212 1786 ,.-45'78S S-548483 17S9 11-451517 3 9-999729 54 30 2 8-549995 '779 ,,-450005 8-550268 1781 11-449732 0-000274 4 9-999726 52 58 30 8-551770 1772 ,,-448230 8-552046 '774 "•447954 0-000276 5 9-999724 50 30 3 8-553539 ,765 ,.-44646, 8-5538.7 1767 11-4461S3 0-000278 6 9-999722 48 57 30 8-555300 1758 1. -444700 8-5555SO 1760 ..-444420 0-000280 7 I 9-999720 40 4 8-557054 1750 ..-442946 8-557336 '753 ..-442664 0-000283 8 , 9-999717 44 50 30 8-55880. ■743 ..•441,99 8-559085 '745 11-440915 0-000285 9 1 9^9997'5 42 30 5 8-560540 '737 .,-439460 8-560S28 1.-439.72 0-000287 10 . 9-999713 40 38 r.5 30 8-562273 1729 11-437727 S-562563 1732 "•437437 0-000289 9-999711 6 8-563999 1723 11-436001 8-56429. '725 ,1-435709 0-000292 12 . 9-999708 3C 54 30 •20 8-5657,9 ,7.6 "-43428 1 8-5660.3 17. 8 I. -433987 0-000294 13 . 9-999706 34 30 7 28 8-567431 ,709 ..-432569 8-567727 17,, .1-432273 0-000296 14 1 9-999704 53 30 30 8-569,37 1702 ..-430863 8-569435 ,705 11-430565 0-000299 15 1 9-99970. 30 30 g 32 8-570836 1696 11-429164 «-57"37 .69S 11-428863 0-00030, 16 1 9-999699 »S 82 30 3-1 8-572528 1689 11-427472 8-572832 .692 11-427168 0-000304 17 . 9-999696 20 I, 36 8-574214 1682 11-425786 8-574520 .684 1.-425480 0-000306 18 1 9-999694 24 51 lo' 38 8-575893 1676 11-424107 8-57620. ,679 11-423799 0-000308 19 . 9-999692 22 30 H 8-577566 .670 11-422434 8-577877 .672 11-422123 0-0003,. 20 2 21 2 9-999689 20 18 50 S-579232 ,663 .,-420768 ^•579545 .665 11-420455 0-0003,3 9-999687 u U 8580892 ,657 ..-4.9.08 8-58.208 .660 11-4.8792 I 0-0003.5 22 2 9 999685 10 49 .0 46 8-582546 ,650 .1-417454 8-582864 .652 11-417.36 ' 0-0003.8 23 2 9-999682 14 48 8-584193 ,645 I. -4. 5807 8-5845.4! .647 ..-415486 . 0-000320 24 2 9-999680 48 30 SO 8-585834 1638 11-4.4.66 8-586157 1 1641 ..-4.3843 0-000323 25 2 9-999677 10 30 13 it 8-587469 1632 11-412531 S-587795 .634 .1-412205 0-000325 26 2 9-999675 g 47 30 51 8-589098 ,625 I. -4. 0902 8-589426 .628 11-410574 . 0-000328 27 2 9-999672 30 14 S'J 8-59072, 1. -409279 8-59.05, 1622 I. -408949 . 0-000330 28 2 9-999670 4 4« 30 5« 8-592338 1614 ..-407662 S-592670 1616 .1-407330 . 0-000332 29 2 9-999668 2 30 i:. 9 8-593948 ,607 1. -4060 52 8-594283 i6n 11-4057.7 1 0-OC0335 30 2 9-999665 51 45 30 8-595S53 ,602 I. -404447 8-595S90 1604 .1-404110 1 0-C00337 1 9-999663 u; 4 8-597152 ,596 ..-402848 8-597492 1598 ..•402508 0-000340 2 9-999660 ,ili 44 30 8-598745 ,590 11-40125, 8-599087 '593 ..-4009.3 I 0-OC0342 3 9-999658 54 30 17 8-600332 >sH .1-39966S 8-600677 1586 11-399323 . 0-000345 4 9-999655 52 43 30 10 8-601913 ■579 .1-39S087 8-602260 ,58. 11-397740 1 0-OC0347 5 9-999653 50 30 18 12 8-6034S9 '572 .1-396511 8-603839 1,76 11-396.61 1 0-000350 6 1 9-999650 48 42 30 14 8-605058 ,567 1.-394942 8-605411 1569 ..-3945S9 1 0-000353 7 1 9-999647 40 30 19 16 8-606623 ,562 "■393577 8-606978 1564 ..-393022 1 0-000355 8 1 9-999645 44 41 30 18 8-608181 '555 11-3918,9 8-608539 .558 ..-39.46. I 0-000358 9 1 9-999642 42 30 20 20 8-609734 '55' ,.-390266 8-6.C094 ,.-3899061 0-000360 10 1 11 1 9-999640 38 40 30 8-6,1282 '5'H 11-38871S 8-6.1644 '547 .1-388356 . 0-000363 9-999637 21 24 8-6,2823 '539 11-387,77 8-6.3189 1542 ..-3868.. 1 0-000365 12 I 9-999635 30 39 30 20 8-6,4360 '534 ,,-385640 8-614728 1536 ..■3^5272 ' 0-000368 13 1 9-999632 34 30 •-'2 28 8-6,589, 1529 ,,-384109 8-616262 '53' ..-3S3738 1 0-00037. 14 1 9-999629 32 38 30 30 8-6,74,7 1522 ..-382583 8-6,7790 1526 ..-3822,0 , 0-000373 15 1 9999627 30 30 1 23 32 8-6,8937 ,5,8 ..-38.063 8-6,93.3 152c .1-380687 1 0-OC0376 16 I 9-999624 ^8 37 1 30 34 8-620452 ,5,2 "•379548 8-620830 ■5'5 "•379170 1 0-000378 17 2 9-999622 -20 30 24 3fi 8-62,962 ,508 ..-378038 8622343 1510 "•377657 1 0-00038. 18 2 9-9996.9 24 3(i 30 38 8-623466 1501 "•376534 8-623850 ,505 11-376150 1 0-0003S4 19 2 9-9996,6 22 30 25 40 8-624965 '497 ..-375035 8-625352 ■499 11-37464S ' 0-000386 20 2 21 2 9-9996.4 20 18 35 30 8626459 1492 "•373541 8-626849 '494 .1-37315. 1 0-000389 99996" 20 44 8-627948 i486 ..-372052 8-628340 1489 ..-37.660 1 0-OC0392 22 2 9-999608 10 34 30 46 8-629432 1481 ..-370568 S-629S27 .484 11-370173 . 0-OC0394 23 2 9-999606 14 30 27 4S 8-6309,. '477 ..-3690S9 8-63,308 '479 .■-368692 . 0-000397 24 2 9-999603 12 33 50 8-632385 1471 .,-367615 8-632785 '474 ..■3672.5 1 0-OCO400 25 2 9-999600 10 30 28 .52 8-633854 1466 ..-366146 8-634256 1469 "■365744 1 0-000403 26 2 9-999597 ■i 32 30 !,i 86353,7 1462 1.-364683 8-635723 1464 .1-364277 1 0-000405 a? 2 9-999595 ,■ 30 29 50 8-636776 ,456 ■1-363224 8-637184 '459 11-362816 1 0-C0040S 28 3 9-999592 1 31 30 .■is 8-63S230 '45- .1-361770 8-63864. 1455 1.-36.359 , 0-OC04.. 29 3 9-999589 2 30 :«) 10 8-639680 ,446 11-360320 8-640093 1449 ..-359907 1 0-0004.4 i!Li 9-999586 30 Co8i,>e D. Se(-ant Cotang. D. Tangent Cosec. Parts Si. S-648174 1419 11-351726 S-648704 ,421 ..-35.296 10 000430 6 I 9-999570 48 •-'7 30 14 8649690 1413 11-350310 8-650,23 ,4,7 "•349877 10 OC.0433 7 1 9-999567 40 30 34 '« 8651101 1410 11-348S98 8-651537 1412 "•348463 .0 000436 » 1 9-999564 44 2(i .w IS 8-65=508 1404 .1-34-492 8-652947 1407 1,-347053 10 000439 ft 1 9-99956, 42 .10 35 so ■n 8-6539.. .400 .1-346089 8-6,435* 1403 "•345648 10 CC0441 10 I 9-999558 z _2*_ 8-65530* '396 "•34469* ^•655753 '399 ..-344247 10^ 000444 9-999556 .<» ■n g-656701 1391 11-343298 8-657,49 '393 11-342851 10 000447 12 . 9^999553 .16 24 w te 8-658090 1386 11-341910 8-65854' . 1-34,459 10 000450 13 . 9-999550 30 37 •iS 8-659475 1382 11-340525 8-659928 1385 .,-340072 IC :oo453 14 1 9^999547 3-2 23 .w .i» 8-660855 1378 11-339145 8-66,3,, 138, .1-3386S9 10 000456 15 , 9-999544 30 30 ■.id 3-2 g-661230 '373 11-337770 8-662689 .376 11-337311 ,0 OCO459 16 2 9-99954, ■28 22 TO :U 8-663602 '370 11-336398 8-664063 1372 "•335937 10 000462 17 2 9-999538 -2li 30 »!l .18 8-664968 1364 11-335032 8-665433 1367 "•334567 10 00C465 J8 2 9-999535 24 21 30 .18 8-66633, m6i 11-333669 8-666799 .364 ,,■33320, 10 C00468 19 2 9-999532 ■n 30 i!L 40 S-667689 .356 "■33*3" 8-668.60 '359 1, •33.840 10 00047, 20 2 9-9995*9 '20 \i g-669043 '35* .1-330957 8-669517 '355 "•330483 Vo 000473 21 2 9-9995*7 18 30 41 u 8-670393 1348 .1-329607 8-670870 '35' ii^329i30 10 000476 22 2 9-999524 16 Hi .10 Vt 8-671739 '343 11-328261 8-6722.8 1346 11-327782 ,0 000479 23 2 9-99952, 14 30 42 A» 8-6730S0 1340 1,-326920 8-673563 '343 "•3*6437 ,0 000482 24 2 9-999518 1-2 18 .10 50 8-6744.8 '335 .1-325582 8-674903 ,338 ,,-325097 10 000485 25 2 9-999515 311 4H 3J »-67575' '33' 11-324249 8-676239 '334 11-32376. .0 000488 26 3 9^9995'* g 17 10 .M 8-677080 1327 1,-322920 8-677572 ,330 .,-322428 10 000491 27 3 i 9^999509 B .10 «4 .W 8-678405 '3*3 ,,•321595 8-678900 ,326 ,1-321,00 10 C00494 2S 3 9' 999 506 4 ft 30 ! J* 8-679716 1319 ,,-320274 8-680214 ,322 .1-319776 10 000497 29 3 1 9^999503 •i 30 liL" 8-681043 '3'5 "•3.8957 8-68,544 iili 11-318456 10 000500 30 3 ! 9-999500 •iff 58 16 30 8-68Z356 1311 11-317644 8-682860 ,3.4 11-317140 To" 000503 1 : 9^999497 46 1 ^ 8-683665 .308 11-3.6335 8-684,7* ,3,, 11-3.5828 10 000507 2 9999493 56 U .10 i B 868497' 1303 1, -315029 8-685480 ,306 1,-3,4520 10 0005.0 9-999490 51 30 47 1 « S-686272 1299 .1-3.3728 8686784 1302 11-3132.6 10 C005.3 4 9-999487 5-2 13 30 iO 8-687569 '-95 .1-3.243. 8-688085 ,299 .1-3119.5 10 0005.6 5 , 9-999484 50 3 40 1? 8-688863 1292 11-3. ,137 S-68938, ,294 11-3,06,9 JO 0005.9 6 1 9-9994S1 4H 12 .10 14 8-690151 1288 11-309848 8-690674 ,291 11-309326 10 000522 7 1 )^999478 4fi 10 4» Ifi 8-691438 1283 11-308562 g-69,963 1287 ..-308037 ,0 000525 « 1 , ^999475 44 11 .to IS 8-692720 1280 11-307280 8-693248 ,283 ..-306752 10 OC0528 9 1 9^99947* 4-2 30 .'lO m ■n 8-693998 1*77 11-306002 8-694529 ,180 ..-30547. ,0 00053. 9999469 40 10 8-695272 ,1-304728 8695807 '*75 ..-304193 To^ 000534 9-999466 AI ■It 8-696543 1 269 11-303457 g-69-08, .272 ..-3029.9 .0 000537 12 1 9999463 3f- 9" .in in 8-697810 1265 11-302190 8-698351 ,268 ..-301649 ,0 00054. 13 1 9^999459 .14 30 S2 ■» 8-699073 1262 11-300927 8-6996.7 126; 11-300383 10 OC0544 14 1 9^999456 3-2 « .10 .10 8-700333 1257 11-299667 8-700880 .26. 11-299120 10 000547 15 2 9^9994 53 30 3U 53 n 8-70.589 1*55 11-2984,1 8-702139 '*57 ..-29786. ,0 000550 IB 2 9999450 ■28 7 .10 .14 8-702841 1250 11-297159 8-703395 .254 ..-296605 10 00055; 17 2 9999447 •26 30 54 3« 8-704090 1247 11-295910 8-704646 .250 11-295354 .0 000557 18 2 9^999443 (i :io .« 8-705315 1243 11-194665 8-705895 .247 11-294.05 10 OC0560 19 2 9^99944° ■i-t 30 5(i 10 .10 ■ n 8-706577 1240 1, -293423 8-707140 J}*1 11-292860 10 000563 20 2 9^999437 -20 5 JO 8-7078.5 -^6- 11-292185 8-70838. ,,-29,6.9 To^ 000566 9^999434 .W 1 u 8-709049 '*33 11-290951 8-7096,8 1 2 36 11-290382 10 000569 2-2 2 9^99943 . 16 4 .10 4« 8-7 10280 1229 1 1-289720 8-7.0853 '*33 11-289147 10 000573 9-999427 u .10 S7 4« 8-711507 1226 1,-288493 8-712083 ,228 1.-287917 10 000576 24 2 9-999424 1-2 A 30 .^0 8-712731 1222 ,,■287268 8-7.33.. 1226 .1-286689 10 000579 25 3 9-999421 10 311 M .V2 8-713952 1219 ,1-286048 8-7.4534 ,222 11-285466 10 000582 2fi •! 9-999418 2 10 ^4 8-715169 1216 11-28483, 8'7'5755 1219 11-284245 10 000586 27 3 9999414 111 o9 M 8-7.6383 1212 11-283617 8-7.697* .1-2S3028 10 OC0589 -J« 3 9-99941, 1 .10 .1M 8-717593 1208 11-282406 8-7.8.86 .2.2 ..-^8,8,4 10 000592 -29 5 9-999408 10 liO la 8-718800 1205 8-7.9396 1209 .1-280604 10-000596 30 3 9-999404 ■"rJ Conine D. Secnt Cotang. 1 D. Tangent Co»ec. Farts Sine ^ 77/ ^7- - - ' :.. „;.-- 1 TABLE 68 S, CC LOG. SINE SINES. &c. Oh 12'" ~~^ / // m. Sine D. Cosec. Tangent D. Cotang. Secant i Parts Cosine ™ ' " IT '"^ 8-718800 1205 II-28'200 8-7.9396 ■ 209 ,,-280604 ■ 000596! 9-999404 ftS "60" 30 1 8-720004 .1-279996 8^72o6o3 1205 "-279397 ■ 000599 1 9-99940. 38 3" 1 4 8-721204 "99 ,1-278796 8^72, 806 1202 ii^278,94 ■ 000602 2 9-999398 36 5!t 30 5 8-722401 "95 11-277599 8^723007 1,98 ..•276993 ■ coo6c6 3 9-999394 54 3(1 2 3 ^■723595 .1-276405 8-724204 1196 "-275796 10 000609 4 9-99939. 32 58 30 1.1 8-724785 ;;^9 ..-27S"5 8-725397 1,92 ■ r2746o3 ■0 0006,2 5 , 9-999388 50 3 12 8-725972 1.8:; 11-274028 8-726588 ,,89 ir2734,2 0006,6 6 I 9-999384 4H ra 30 14 8-727156 ,,83 ■,•272844 8-727775 1,85 ■ r272225 ■0 000619 7 1 9-99938. 40 311 4 la 8-728337 1179 1, -271663 8-728959 ,,83 ■ ■•27^o4^ ■0 000622 8 ■ 9-999378 44 S 30 4C 8-745670 1 1 32 ,,•254330 8-746344 ,,36 ,,■253656 ■ 000674 23 3 9-999326 14 30 12 48 8-746802 ,,•253,98 8-747479 .134 ,,-25252, ■ OC0678 24 3 9-999322 12 48 30 30 8-747930 1127 ,,•252070 8^7486,i ,,30 ,,■25,389 0006S, 25 3 9-999319 Id -" 13 32 8-749055 1 124 .,•250945 8^749740 ,,27 ,,•250260 ■0 0006 85 2fi 3 9-9993.5 47 30 51 8-750178 .121 ,,-249822 8^750866 ,125 "•249134 00068S 27 3 99993.2 li 311 U 56 8-751297 III8 ,1-248703 8-75.989 II22 ,,-248o,^ ,0 000692 28 3 9 999308 1 4(1 30 5S 8-752414 .1,5 ,,•247586 8-753.09 III9 ■ 1-246891 ■ 000695 29 3 9-999305 2 13 13 8-7535^« III3 ,,•246472 8-754227 II16 "-245773 OC0699 30 3 9-999301 47 4.'. 8-754639 I 109 ,1-24536, 8-755341 1113 ,■■244659 To" 000703 1 9-999297 \6 4 8-755747 1107 ,,•244253 8-756453 11-243547 10 000706 2 9-999294 56 44 30 6 8-75685^ I 104 ,.•233,48 8-757562 1107 I. -242438 10 0007,0 3 9-999290 54 30 »7 8 8-757955 ,,•242045 8^758668 IIO5 ,■•24,332 ■ 0007 ■ 3 4 9-999287 52 48 30 10 8-759054 !o98 ,.-240946 8-75977. ■ ,■240229 ■ 0007,7 5 1 9-999283 50 30 18 12 8-760,5, 1096 1,-239849 8^760872 1099 ,,■239128 ■ 00072, 6 1 9-999279 48 42 30 14 8-707245 1092 I, -238755 8-76,970 ,097 ■■■23S030 ,0 000724 7 1 9-999276 46 30 i'J 18 8-762337 1090 ii-237663 8-763065 .093 ,■■236935 ■ 000728 8 1 9999272 44 41 30 18 8-763425 X088 ,,•236575 8-764.57 ..-235843 ■ C00732 9 I 9^99926S 42 30 — - 20 8-7645.. 8-765594 .084 S-765246 ■ 0S8 .1-234754 ■ 000735 10 1 9-99926; 40 III 30 1082 1 1 •234406 8-766333 ■ 086 ■.■233667 To 000739 9^97926, 21 24 8-766675 .079 ■ ,•233325 8-7674.7 1083 ..■232583 ■ 000743 12 1 9-999257 36 3!t 30 •20 8-76775^ 1076 ,,•232248 8-768499 ,080 ,■■23,501 10 000746 13 2 9-999254 34 3(1 22 28 8-768828 1074 ,1-23.172 8-769578 .077 ,■■230422 ■0 000750 14 2 9-999250 32 .■)8 30 30 8-769900 ,07, ,,•230100 8-770654 ,075 ir229346 ■ 000754 15 2 9-999246 30 30 23 32 8-770970 ,069 ,,•229030 8-77,727 ,072 ,■•228273 ■ 000758 16 2 9-999242 28 :«7 30 34 8-772037 1065 ,1-227963 8-772798 ,070 ir227202 ■ 00076. 17 2 9-999239 -26 3(1 24 36 8-773.0. 1064 11-226899 8-773866 ,067 ,■■226,34 10 000765 18 2 9-999235 24 :«; 30 38 8-774163 ,060 .,■225837 8-774932 ,064 ,,■225068 .0 000769 19 2 9-99923. 22 3(1 25 30 4« 42 8-775223 1058 11-224777 8-775995 1062 ,,■224005 .0 000773 20 2 21 3 9^999227 20 7" 8-776279 .056 .■•223721 8-777056 ,059 11^2229++ ■ 000776 9^999224 26 44 8-777333 1053 ■,•222667 8-7781,4 1057 ii'22i886 ■ 000780 22 3 9-999220 16 84 30 46 8-7783^5 ,050 ,,^22,6^5 8-779169 ,054 ir22o83i 10 000784 23 3 9-999216 14 3( 27 48 8-779434 104S ■ ,•220566 8-7S0222 105, ii^2,9778 ,0 000788 24 3 9-9992.2 12 88 30 50 8-780480 ,045 ,,•2,9520 8-78.272 .049 ■ ■•2^8728 ,0 000792 25 3 9-999208 10 30 28 32 8-78.524 ,043 ,,•2,8476 8-7S2320 ,047 .,■2,7680 ,0 000795 26 3 9-999205 8 82 30 54 8-782566 ,040 ■,•2,7434 8-78336; 1044 ■,•2,6635 ,0 000799 27 3 9-999201 6 30 29 56 8-7S3605 1037 ..•216395 8-784408 104, ■■■215592 10 000803 28 3 9-999197 -" 81 30 58 8-78464. .036 ,,■215359 8-785448 ■ 040 "-2.4552 ■ 000807 29 4 9-999,9; 30 :»n 1ft 8-785675 ,,•2,4325 8-786+86 .036 "■2.35'4 . 0^0008,, 30 4 9999,89 811 r;? "S Cosine IT Secant Cotang. D. Tangent Cosec. Paits Sine m. ~1^ .^4.- 1 TABLE G8 \A)G. SINES, COSINES, &c. 1 O*" 14'" 3° _ 1 L-^ Sine IJL 1 Cosec. Tangent 1 D. Cotang. Secant Parts] Cosine //"/ :)(» 8-7S^675 1032 11-2,432, 8-786486 ,036 ,■-2135,4 ic^cooS,, 9-999,89 46 T«» HI i 8-78670^ ,03, ,,•213293 8-78751, 10,4 .1-2,2479 1 0^0008,5 l"o 9-999.85 .',H .10 .11 4 8-787736 ,028 8-788554 10,2 ,1-21,446 10-0008.9 2 9-999.8, .51-. •-'!» :.. (> 8-788762 1025 ,■■21,23! 8-789585 ,029 "-2,0415 , 0^000822 3 9-999'7S 01 30 :)j S 8-789787 1023 8-7906.3 1027 11-209387 ,0^000826 4 1 9-999174 m '.'li :i(i 10 8-790808 ,020 ,1-209,92 8-791639 ,025 ,,-20836, io^ooo83o 5 1 9-999,70 .'lO 30 .13 u 8-791828 IOI9 11-208,72 8-791662 ,022 ,,-207338 .0-0008,4 6 1 9^999'66 It ■-'7 :)o 11 8-791845 10,5 11-207,55 8-793683 ,1-2063.7 .o-coo8,8 7 1 9-999,62 j() 30 34 Hi 8-7938,9 1014 ii-2o6i4. 8-79470, ,0.8 .1-205299 ,0-000842 H I 9-999,58 u •J(i .10 l.s 8-794871 ,0, 1 11-20512X 8-7957'8 .0,5 "•204282 .0-CCC846 9 I 9-999,54 4-i 30 .(.i JO 8-795881 ,009 11-204, ,9 8-79673. "•20,269 .0-C00850 10 1 9-999,50 40 ~ 8-796S89 1006 11-203,,, 8-797743 ,0. . ,.•20225- .0-CC0S54 9-999,46 3f' •ij 8-797894 ,004 ,1-202,06 8-798751 ,008 "•201248 .C-OC0858 12 2 9^999,42 3;) .10 30 8-800896 997 11-199,04 8-801765 .,-,98235 .0-000870 15 -2 9-999,30 30 .-)o .18 3-J 8-80.892 995 11-198,08 8-802765 998 "■'97135 10-OC0874 16 2 9-999,26 -28 22 30 3J 8 80288 5 992 11-197115 8-803763 997 .,■.96257 .0-CC0878 17 2 9-999,22 ■in .-III 39 M 8-803876 990 11-196,24 8-804758 994 ,,-195242 .0-CC0S82 18 2 9-999, ,8 ■n 21 30 38 S- 804866 988 ,,•195134 8-80575. 992 ,,-194249 .0-C00886 19 3 9-999114 ■it 30 40 Jll 8-805852 986 II-, 94148 8-806-42 990 ..-.9315S 10-C00890 20 3 21 3 9999"o ■" 2(! 8-806837 ,1-193163 8-80773' ~w .,-,92269 .0-OC0894 9-.^ 99106 41 41 8-807819 9S2 11-192181 8-8087,7 986 ,1 .9.283 .0-C00898 22 3 9-999.02 Hi Ill 30 Hi 8-808799 979 ,1-19120, 8-80970, 983 "-.90299 10-000902 23 3 9-999098 14 .30 42 4.S 8 809777 976 11-190223 8-8,0683 .1-.893.7 10-OC0906 24 3 9-999094 1-1 Ul 30 50 8-8,0753 975 11-189247 8-811663 978 "-.88,37 .0-OC09.0 25 3 9-999090 III 30 43 .51 S-81.726 971 ii-,S8274 8-812641 977 .1-.S7359 ,0-0009.4 26 3 9-9990S6 „ 17 30 SI S-8,2698 97' 11-187302 8-813616 974 "•,86384 10-C009.8 27 4 9-9990S2 li 41 .'Hi 8-813667 968 ,1-186333 8-8.4589 972 ..■,854.. .0-C00923 28 4 9-999077 4 li; 30 M 8-8,4634 965 ,1-185366 8-8.5560 970 "•.84440 .0-000927 29 4 9-999073 ■1 .111 4S 15 8-815599 _9fit ,,-184401 8-8,6529 968 ir^llL 30 4 9-999069 9-999065 ftS ir, 8-8,6561 962 11-183439 8-8.7496 966 ,.•.82504 ,0-000935 1 0" 4(; J 8-8,7522 959 ,,•,82478 8-8. 846. 963 ..•.8.539 10-CC0939 2 9-99906. .-ili li ,10 S-8,8480 958 11-1S1520 8-8,9413 962 .,•.80577 .0-0C0943 3 9-999057 .54 30 ^7 't 8-8,9436 955 ,,•,80564 8-820384 959 ,,■1796.6 ,0-000947 4 1 9-999053 .-1-2 13 .10 10 S-S20390 953 ir, 796,0 8-82.342 958 ,.-178658 ,0-000952 5 . 9-999048 00 311 J 11 li S-821343 95' 11-178657 8-822298 955 . ••177702 ,0-000956 6 1 9-999044 4H 12 30 11 8-822292 949 ,1-177708 8-823253 953 "•176747 ,0-000960 7 1 9-999040 Hi 30 4!t Ki 8-823240 9+7 ,,-,76760 8-824105 95' "■'75795 .0-C00964 8 I 9-999036 11 11 .10 IS 8-S24186 944 ,,-,758,4 8-825.55 949 "-'74845 ,0-000968 9 . 9 9990,2 12 311 All .10 •«) 8-825,30 943 .,-,74870 8-826,0, _947 ..-■73S97 ,0-000973 10 1 11 2 9-999027 40 -^ 8-826072 94' ,,•,73918 8-827049 94 5 ,,-172951 ,0-000977 9-999023 r.! •H 8-8270,, 93S ,,-,7298, 8-827991 943 1 ,-,72008 ,0-00098. 12 2 9-999019 M •1 30 ■m 8-827949 937 8-828934 941 "■,71066 .0-C00985 13 2 9-9990.5 30 S2 ■IX 8-8288X4 9'H ,,-,7, ,'6 8-829874 93S ,,-.70,26 .0-000990 14 2 9-9990,0 3-2 B 30 30 8-829818 933 , ,-,70,82 8-8308.2 937 "•.69,88 .0-000994 IS 2 9-999006 30 30 .'i3 .K 8-830749 93' ,■•16925, 8-83,748 935 .,•.68252 ,0-000998 16 2 9-999002 28 7 .10 31 8-83,679 928 ,,•,6832, 8-832682 933 ,,■,673,8 ,0-00,003 17 2 9-998997 -211 31 .'•4 :m 8-S32607 917 "•'67393 8-8336,3 93' ,,■.66,87 .0-00,007 18 3 9-998993 2 4 li .10 :in 8-833.31 924 ,,-,66468 8-834543 929 "-'65457 .000. on 19 3 9-998989 22 30 .>n AD 8-834456 913 "•16,544 8-83,47, _926 .,■.64,29 ,o^co.o.6 20 3 21 3 9-998984 20 4,1 8-835377 920 ,,• 164623 8-8,6397 915 ..■,63603 .©■001020 9-9989R0 .'ir; " 8836297 9,9 .,•■63703 8-83732, 913 .,•,6.679 .O^0O1024 22 3 9-99S976 hi 4 30 4li S-8372,5 9'7 ,,■,62785 8-8,8243 912 "•.6.757 10^C01029 23 3 9-99897, 1 1 30 •■-7 It 8-838,30 9'5 ■■•,6.87c 8-839,63 9.9 ,,■160837 .0-C0.033 24 3 9-998967 1-2 3 .w .'lO 8-839044 9,2 ■■•,60956 8 84008. 9'7 ,•1599,9 ,0-00,037 25 4 9-99X903 10 30 .'.H .W 8839,56 911 ■■•160044 8-840998 9'5 ,•159002 ,0^00.042 26 4 9-9989,8 K 2 :lli .-.1 8-840866 909 ■ ,•,59,34 8-84,9.2 9,4 ,•158088 0-00.046 27 4 9-998954 ii 311 .■>;» ,'rli 8841774 907 ■■•,58226 8-84282, 9.1 '-'57'75 0-C0.050 28 4 9-99895': 4 1 30 .•iM S-842680 9c6 1-15731" 8-843735 9,0 ,•,5626, 0-001055 29 4 9-99S94, ■I ;iM «rl 16 8-843,85 9°3 ■■-, 564,5 8-844644 _907_ _r, 5,3^6 ^co^59 30 4 ^9894 1 1. / //| m. (;..»in,. 1 I). Secant Cotang. .1 D, 1 TanRent Cosec. |l'nr,tl Sine -ri 86° o'- - r" J 746 TABLE 68 LOG. SINES, COSINES, &c. | Ob l(jm 4° / / ' "?• Sine 1 ParU Cosec. Tangent Parts Cotang. Secant Parts 1 Cosine m P ~o" 8-84358 5 ,,-,564, 8-844644 ,f, 55356 io-oo,o<;9 19-998941 iiiiioi 3(1 8-84448 7 1" 30 ,,■15551 8-845551 r- 30 ,,-,54449 ■ o-oo.of4 l"o ,9-998936 5« M 1 8-84538 7 S 60 ,,•,546,3 8-846455 2 60 "•'53545 ,o-ooic68 2 9-99S932 .I!! 30 8-846Z8 . 3 89 "■'53714 8-847358 3 90 ,,•,52642 ■ 000.073 3 c 9-998927 54 30 2 S-847tS 4 1,9 ,1-1528,7 8-848260 4 .20 ..•,5,740 10-001077 4 1 9-998923 5-2 as 30 8-84807 5 ,49 ,,-,51922 8-849159 5 .50 ,,-,5084, .0-00.08. 6 I 9-9989:9 50 30 3 8-84897 6,79 ,,•15,029 8-850057 6 ,80 ..-,49943 .0-00.086 6 1 9-9989:4 4« 57 3( 8-84986 ,,-,50,38 8-850952 72,0 ,,,49048 .0-001090 7 1 9-998910 4(i .10 4 8-85075 8238 ,,•,49249 8-851846 8239 ,,-,48,54 ■ o-oc,o95 8 1 9-998905 41 se 30 8-85.63 9268 ,,•,4836, 8-852738 9269 ,,-.47262 ,0-00,099 9 1 9-998901 42 3(1 S 3« 8-8,.,^ 10298 ,,-,47475 8-85362S 10299 ■,■,46372 10 2 9-998896 40 38 55 .30 8-85340* 1 29 ,■•146592 8S54517 1 »9 ■ ■-,45483 ,0-001,08 9-998S92 « 8-85429 1 58 ,,•,45709 8-855403 ■» 59 "•'44597 ,0-0011,3 12 2 9-998887 36 54 30 8-855,7 ,1-144829 8-856288 3 88 ,, ,437,2 ■ 0-00,,. 7 13 2 9-998883 34 30 7 23 8-856049 4 ,,7 ,,-,43951 8-857.7. 4 1,7 ..-,42829 14 2 9-998878 32 53 3(1 30 8-8569Z6 5 ,46 ,, -143074 8-85S053 5 .46 ,,-,41947 IO-00,.27 IS 2 9-998873 30 30 8 3-2 S-S5780, 6 ,75 ,1-142199 8-858932 6 ,76 ..-.4,068 16 2 9-998869 '2.8 52 30 .34 S-858674 7204 ii-,4.326 8-8598,0 l^°i ,,-,40.90 ■0-00. .36 '7 3 9998864 2S 30 !) 3(1 8-859546 8 233 ■1-140454 8-86c686 ,,-,393,4 ,0-001,40 IH 3 9-998860 24 51 30 .IS 8-860415 9263 11-139585 8-86,560 9264 ,,-,38440 ■0-001,45 l!» 3 9-998855 •2-2 30 10 40 8-861183 10292 11-, 387. 7 8-862433 10^93 "•.37567 ■0-00II49 20 3 9-99885' •20 50 30 VI 8-862,49 1 29 11-137851 8-863303 1 29 ,,•,36697 10-001,54 21 3 9-998846 18 30 II 44 8-8630,4 2 57 11-136986 8-864,73 a 58 ■,-,35827 ■ 0-001159 22 3 9-99884. l« 49 3(1 41! 8-853877 3 86 11-136123 8-865040 3 86 .1-134960 23 3 9-998837 14 12 48 S-864738 4, ,4 1,-135262 8-865906 4 ,,5 11 •.34094 .0-00.168 24 4 9-998832 12 48 30 50 5-865597 5 ,43 1 1-134403 S-866769 6,44 ..•.3323. .0-001173 25 4 9-998827 10 311 i:< 52 •866455 6 ,72 "■'33545 8-867632 a 173 ,,•,32368 .0-00,177 26 4 9-998823 8 30 54 7 200 .■-,32690 8-868492 7 2oi ,,•13.508 .0-00.182 27 4 9-9988.8 (i u M -868^65 8229 I1-, 31835 8-86935, 8230 I. •,30649 .o-oo.,87 28 4 9-998813 4 4li 30 M •8690,7 9257 ,1-130983 8-870208 9 259 ,.•129792 ,o-oo,,9. 9-998809 ■' MX ii. 17 -869868 10 286 ■,-,30132 8-87,064 10 288 ..-■28936 ,0-00,196 30 5 9-998804 «3 4.' 30 2 ■8707,7 1 28 ,1-129283 8-87.9.8 1 »8 ..-,28082 ,0-00,20, 1 9-998799 lU 4 -87,565 2 56 ■,-,28435 8-872770 1 56 ..-.27230 ■ 0-00,205 2 9-998795 44 311 n ■872410 3 84 ,,•,27590 8-873620 3 8s II-. 26380 ,0-00,2,0 3 9-998790 54 30 17 s ■873255 4 1,2 ,1-126745 8-874469 4 113 11-125531 10-001215 4 , 9-998785 .V2 43 .10 ID ■874097 S ,40 ,,-,25903 8-8753.7 4,4, I. -.24683 .0-00I2,9 5 1 9-9987S1 50 .10 IB 1-2 i -874938 6 ,68 ,,•,25062 8-876,62 fi.69 ■.•123838 10-001224 A 1 9-998776 48 42 30 U i •875777 7 ,96 ,,•,24223 8-877006 7 .97 1 1-122994 10-001229 7 1 9-998771 4rt 30 I!» Ki I -8766,5 8224 ,,-,23385 8-877849 8225 l,-,22,5. 10-00,234 8 I 9-998766 44 41 3(1 IS S ■*!7745> 9252 8-878689 9254 ..•.213,, 10-00.238 9 1 9-998762 42 3(1 30 ■20 g -878285 ,.•,2,7,5 8-879529 0282 iri2047i 10-001243 10 2 11 2 9-09S757 40 40 30 •22 "; ■879,.8 I 27 8-880366 1 28 ,,•1.9634 .0-001248 9-998752 21 ■24 8 '879949 2 55 ,•,20051 8-88,202 2 55 ..•,,8798 ,0-00.253 U 2 9-998747 3(i 3!» 30 •2(i 8 -880779 3 82 ,-i ,922, 8-882037 3 83 ,,•,.7963 0-001258 13 2 9-998742 30 22 ■It 8 -881607 4 1,0 ■■"8393 8-S82869 ..■,,7.31 0-00.262 14 2 /99873S 32 38 .30 30 8 -882435 5 ,37 ,•1,7567 8-S8370, 5 ,38 ,,•,,6299 0-00,267 15 2 9^998733 30 23 3-2 8 ■883258 6 ,6s ,•,,6742 8-884530 fi .66 ,,•,,5470 0-001272 16 3 9^998728 28 37 30 34 8 -88408, 7,92 ,-,,59,9 8-885358 7 .93 ,.-..4642 0-0O.277 •7 3 9-99S723 •2« 30 24 »r, 8 -8S4903 8 220 ,•,,5097 8-886,85 ..-,,38,5 0-00.282 18 3 9-998718 21 38 30 38 8 -885723 9247 ,-,,4277 8-8870,0 9249 ,1 1 12990 0-001287 19 3 5-998713 2-2 .10 2.-. 40 8 -886542 027, ,•,,3458 3-887833 276 "•..2.67 0-001292 20 3 21 3 51-998708 20 35 42 8 8873,9 ' ^7 ,-,,264, 8-8886i5 1 27 "•'"345 0001296 5-998704 2G 44 8 888,74 2 54 ,-,,,826 8-889416 2 54 ,•,,0524 0-00130, 22 4 9-998699 10 34 30 4« 8 -888988 3 81 .•,,,0,2 8-890295 3 8, ,•■09705 °;°o>3of 23 4 9-998694 14 30 >1 \* 8 88980, 4 108 ,-,,0,99 8-89. ..2 4 ,09 ,-,08888 24 4 9-998689 12 33 to 50 8 8906,2 5 135 ,•,09388 8-89.928 5 ,36 ,-.08072 0-00 1] 16 25 4 9-998684 10 30 m 52 8 •89,42, 6 162 ,•,08579 8-S92742 6 ,63 .-107258 0-001321 26 4 j-998679 n 32 <0 5( 8 892229 7 ,89 ,•,0777, 8-893555 7 ,90 ,-.06445 0-C01326 27 4 9-998674 n 30 2» 8 4° " 1? Sinr i PutJ Cosec. Tangent Parts 1 Cotan,. Secant | Parts Cosine »? r :ii» u 8 •89+64 3 I. •.0535- §•895984 [■■■■04Oi6 ,0-00.341 9-998659 *a|a(. 1 jn •i S-S954+ 5 1" 2« ...0+555 8^89670, 1 27 . ■■.03209 ,0-00.5+6 l"o 9-998654 :ii) ■M 4 S-S9624 5 » 53 11-.03754 8-8975961 2 53 ..-. 02404 2 9-998649 51 •-'9 m e S^897o+, 3 79 ..•.02956 8^898+oo 1 3 80 ■■-■0^600 lo-To'.lle 3 , 9998644 .54 *i ;t2 8 8^S9784 4 .c6 .■•■02.58 8^899203 4 ,07 ■I-. 00797 10-00.56, 4 1 9-998639 i-i 2H JO 10 8S9863 5 .32 ■ .•■0.362 S^9Cooo+ 5 ,33 ..-099996 ■o^oo,366 5 I 9-998634 SU JU :w 15 8-89945 6,59 .■•.00568 8-9C0S03 6 ,60 "-099'97 io^oo,37. 6 1 9^998629 IN •■i7 M, 14 8-9C01I 7 185 1. .-099775 8-90.60, 7 ,86 ■.098399 ,o^oo.376 7 I 9^99862+ 46 M 16 8'90ioi ..•098983 8^902398 S213 ■1-097602 .o^oo,38^ 8 ■ 9^99S6,9 44 L'i; .10 IS 8^90i8o- 9238 .■•098^93 8^903,93 9 2+0 ■ ■■096S07 ^•oo.586 2 9^9986,+ 4-2 ;75 ■.•076638 8-924893 7 .77 ..-075107 0-00.55. 7 ■ 9-998469 46 .'111 4» 16 8-924.. 2 8 201 ..•075888 8-925649 ..■07435. 0^00.536 8 I 7-998+6+ 44 II .n i.S 8-924''<6i 9226 ..•075.39 8-,26403 9227 ■ ■■073597 0^00.542 9 2 J-998458 42 •'" •22 8-02^609 1025. ..-07+39. S^927.56 "^53 ,,■072844 0^00.547 10 2 ^-998453 '" 10 S-926555 1 25 ..-0736+5 8^927908 1 25 ■■■072092 0^001552 J-998++8 ■■'" i ■21 8-927.00 i 49 ■■-0729C0 8^928658 2 50 ■■■07.3+2 o^oo^558 1-2 2 ^998442 :I6 !l .111 •26 X-927844 3 74 ..■072.56 §•929407 3 74 .■■070593 o^oo^563 13 2 r998437 :i4 311 i.' 1 •2.1 8-928587 4 99 ..-07. +13 8-930.55 4 99 ..■0698+5 o-oo^569 14 3 •998451 ii-i )l I'l .111 S-92932S 5,23 ..-070672 8-930902 5 ,2+ ..■0691,98 o-co^574 15 3 •998426 .'111 30 .Vl :i2 8-930068 fi 148 ..■069932 8-93.647 6 .+9 ..■068355 °-oo>379 16 3 •99842. •2S 7 I'l .14 8-930806 7 .73 ..■069 19+ 8-93239, 7 .74 ■ 067609 o^co^585 17 3 •998+,; ■2I> ."rl M 8 93.5+4 8 .97 ■ .■068+56 8-933,34 8 199 ■■■066866 0^00^590 18 3 •998.1.0 II 1; 111 :tx a-9U28c 9 222 .-067720 8-933876 9223 ■ ■o66^2+ 19 3 ■998404 30 — u 8-9330.5 247 1 06698.; 8-9346,6 2+8 1-06538+ o^ooi6oi 20 4 ■998599 IS :, "•933749 1 24 .06625. 8-935355 1 2+1 ,.•0646451 -^^Tm, 21 4 •99S59+ .'iC j " 89H48. a 48 .•0655.9 8-936093 2 49 ■ •063907 OC0^6,2 22 4 •9985SS 16 4 H, 1 46 8^9552.2 3 73 .■064788 8-936830 3 73 .•065,70 o^oo,6^7 23 4 ■998385 14 .10 A? 1 4" 8^93 5942| 4 97 1 ■ •064058 8-937565 4 98 1-062+35 o^oo,62 5 i* 4 ■998377 12 :t .III ■■" 8936671 5 12. .•063329 8-938299 5 .22 1-06,70, o-oo^628 25 4 ■998572 10 ■jn .-iH 1 -.2 8937598 6 .45 .•062602 8-939032 fi .47 1-060968 0-00.63+ 26 5 ■998566 f) •_> .in 1 ''I 8-93S.25 7 170 .-06.875 8-939764 7 .7. .•060236 0-C0.639 27 5 ■99836, H 311 ■••" ' •■"' 1 8-938850 8 194 .•061 150 8-940494 8 .95 ,-059506 o^oo,64 5 2S 5 -998355 4 1 IK 8-939573 9 2.8 .-060427 8-94,22+ 9220 ,-058776 o'co,65o 29 5 ■99835c ■2 .111 ir >o 8-940296110 242 .•059704 8-9+, 952 0244 .,-058c48 0-00,656 30 5 -998344 n " m. Cosinr | Parts Senant Cotanc. 1 Parts 1 THiip-nt | ^■7>s<^cr Parts 1 Sine | m'. «:.' .".•' JO'" 1 TA1U.I-: G8 LOG. SINES, COSINES, *.c. | 01. OQn, 5° 1 r ti (T m Sine Parts Cosec. Tangent Harts Cotang. Secant Part Cosine «n ' ' 8^94oi96 . ^^^\ S-94,952 ,,-058048 10 -00.656 9-998344 40 '6~r .10 8-941017 1" 24 1,-058983 8-942679 I" 14 ,,-0573^1 10 -001660 1" 9-998339 ;,i 10 I 4 S-9+.738 2 48 ,.-058262 8-943404 2 48 ,1-056596 .0 -001667 1 9-998333 5li h'i 30 8-9.V2457 3 71 '>"°57543 8-944129 3 72 ,10558-, .0 ■001672 3 I 9-998328 ,'i4 .1" 'J 8 8-945174 4 95 ,,-056826 8-944852 4 96 ,,055148 .0 -00.67S 4 I 9-99S322 52 f.8 30 10 8-94389 5 ,,9 ,1-056,09 8-945574 11-054426 .0 -00,684 5 , 9-998316 50 30 3 11 8-944606 6 ,43 11-055394 8-946295 6 .44 ,,-053705 10 -001689 6 1 9-9983" 48 57 .10 14 8-945321 7 ,67 1,-054679 8-9470.5 7 .68 ,,-052985 10 •ool^oo 7 , 9-998305 40 30 4 'rt 8-946034 8 ,9, ■ r-053966 8-947734 8 .92 ,.•052266 .0 8 2 9-998300 44 W, .1(1 IS S-946745 92,4 1,-053255 8-94845. 9 2.6 ..•05.549 .0 -00.706 9 2 9-99S294 1-2 30 5 30 *' 8-947456 10 238 ,,-052544 8-949168 10 240 rro5o832 10 -00.711 10 2 9-998289 38 55 30 8-948166 ' ^3 ,,-05,834 8-949883 1 1 24 ,,•0501,7 10 C01717 9-998283 6 i4 8-94SS74 2 47 „-05„26 8-950597 ! 2 47 I .•049403 10 00,723 12 2 9-998277 30 54 .10 •ill 8-949581 .-» 70 ,,-0504,9 8-95,309 3 71 ,,-048691 10 001728 13 2 9-998271 34 30 7 •28 8-950287 4 94 ,,-049713 8-952021 4 95 ,1-047979 10 C01754 14 3 9-998266 3-2 63 30 30 S-950992 5 :,7 1,-049008 8-952732 5 1,8 ,1-047268 10 001740 15 3 9-998260 30 30 )< .VI 8-951696 6 ,4, 11-048304 8-95344, 6 ,42 ,,•046? 59 .0 00,745 -.6 3 9-998255 -28 52 30 3) 8-952398 7 164 I, -047602 8-954.49 7.65 11-045S5. .0 00,75, 17 3 9-998249 -20 30 9 .Hi 8-953100 8 ,88 11-046900 8-954856 8.89 ..■045.44 .0 001757 18 3 9-998243 -24 51 30 38 8-953S00 92,, , ,-046200 8-955562 92.3 ,,•044438 10 00,762 19 4 9-998238 ■n 30 III 40 4; 8-954+99;i0^3S ,1-04550, 8-956267 10 236 ,,•043733 .0 00,768 20 4 21 4 9-998252 in 50 8-955197 J 23 ,,-044803 8-95697r 1 23 11-043029 To 00,774 9-99S226 1 1 4h S-955894 a 46 ,1-044,06 8-957674 2 47 1. -042326 10 00.780 22 4 9-998220 le 4!) jo; 40 8-956590 3 69 ,,•043410 8-958375 3 70 ..-041625 10 00,785 23 4 9-9982,5 14 30 12 14S 8-95-2S4 4 92 ,1-042716 8-959075 4 93 .1-040925 10 00,79, 24 5 9-998209 r2 48 30 .^0 8-957978 5 ,,5 ,,•042022 8-959775 5 ,,6 11-040225 10 00,797 25 5 9-998203 III 30 13 '32 S-958670 6 ,38 , 1-04,330 8-960473 6 ,40 .1-039527 10 00,805 26 5 9-998,97 g 47 30 54 8-959362 7 161 .,•040638 S-96,,70 7.63 ,,-038830 10 00, 80S 27 5 9-998192 6 30 14 .50 8-960U.2 8 ,85 ..■039948 8-96,866 8 186 ,.-038.34 10 00,8,4 9-998,86 4 40- 30 =S 8-96074, 920S .1-039259 8-96256, 9209 ..•037439 ,0 OOIS20 29 6 9-998180 -2 3) _15_|a» 8-96.429 1023, .1-03857, 8-965255 10233 11-036745 10 00,826 30 6 9-998174 3» 45 30 •2 8-962116 1 23 ..-037884 8-963947 1 23 11-036053 \o 001852 1 9-998168 in 4 8-962801 S 4S ..-037.99 8-964639 2 46 ,1-03536, 10 2 9-998163 511 44 3» li 8-963486 3 68 ..-036514 8-965329 3 69 ,1-03467, .0 00.843 3 , 9-998157 54 30 17 8 8-9641-0 4 9, I. -035830 8-966019 4 92 1.-03398, .0 00.849 4 , 9-998'5i 52 43 .10 10 8-964852 5, ,4 .1-035,48 8-966707 5 ,,5 ,1-033293 10 5 1 9-998145 511 31, l» 1-2 8-965534 6,36 .1-034466 8-967394 6 ,37 ,1-032606 10 00. 86, fi . 9-998139 48 42 ,10 14 8-9662,4 7,59 .1-033786 8-96808, 7 160 .1-03,9,9 10 00.S67 7 . 9-998133 4>l .10 lit 1« 8-966893 8,82 .1-033,07 8-968766 8 .83 M-31234 ,0 C0.8-'2 8 2 9-998128 44 41 30 18 8-967572 9205 ,1-032428 8-969450 9206 .1-030550 10 CO. 878 9 2 9-998:22 4-2 30 •2(1 30 ■20 8-968249 10 227 ,,-03, 75' 8-970153 10 229 ,1-029867 10 00,884 10 2 9-998.16 40 411 X-968925 1 2-' ,,-03,075 8-9708,5 1 23 ,.-029.85 ~^ 001890 9-998110 21 ■2) 8-96960G 2 45 ,,•030400 8-97.496 2 4, 11-028504 .0 00,8,6 12 2 9-998104 m 3!) 30 ■2(i 8-970274 3 67 ,,-029726 8-972,76 3 68 11-02782+ 10 00.902 13 3 999S098 34 :io 22 ■28 8-97C947 4 ?9 11-029053 8-972855 4 90 ..•027145 ,0 00,908 14 3 9-99S092 3-2 3(t 30 30 8-97.6,9 5 1,2 8-973532 5.15 ..•026468 10 OOI9I4 15 3 9-998086 30 31 23 32 8-972289 6 ,34 ,,-0277,, 8-974209 6 ,35 ..•02579. 10 00.920 16 3 9-9980S0 28 37 30 34 8-972959 7,56 ,,-027041 8-974885 7. 58 1^025115 10 001926 '7 3 9-998074 ■2« 30 24 3ii 8-973628 8 ,->9 ..■026572 8-975560 8,80 iro24440 10 001932 18 4 9-99806S ■24 3«> 30 3h 8-974296 9 201 ..•025704 8-976235 9205 1, -023767 10 CO, 938 19 4 9-998062 52 30 30 4- 8-974962 'l?'il 8-976906 10226 . .-013094 10 00,944 20 4 21 4 9-998056 ■20 3.-. ~~30 S-975628 1.-024372 8-977578 1 22 11-022422 10^ 00,950 9-998050 20 41 8-976293 2 4^ .1-023707 8-978248 2 44 I. -021752 10 00,956 22 5 9-998044 Hi 34 30 4(i 8-976956 3 66 1.-025044 8-9789,8 3 67 10 00,962 23 5 9-998038 14 3r 27 4M 8-9776,9 4 88 8-979586 4 89 11-020414 10 00,968 24 5 9-99«°3H Vl 33 50 8-978280 5 no 11-02,720 8-980254 5 .1. ..•0.9746 10 00.974 25 5 9-99S026 10 .10 28 5-2 8-97894, 6 ,32 ,,-021059 8-9S0921 fi >33 ..-0.9079 .0 00.980 2fi 5 9-99S020 s 32 30 VI 8-979600 7 ,54 ,,-020400 8-98,586 7.56 1.-0,84.4 10- 00,986 27 5 9-99S014 li 30 2!) ,'ili 8-980259 S .76 ,1-0,974, 8-98225, 8.78 .1-0.7749 .0- 00.992 28 6 9-998008 4 31 31- 5H S-9S09.6 9 ,98 ,,•0,9084 8-9829,4 9200 00.998 29 6 2 30 30 22 8-98'573 10 220 ,1-0,8427 8-983577 10 222 .1-0.6425 .0-002004 .-10 6 9-997996 30 -rn_^. (- osii.e Parts Secant CotanK. Parts Tangent | Cosec. | Parts Sine ^ 111 ,^l° ■""-■ 1 TABLE 08 719 LOG. SINES. COSINES, &c. Oh o.jm 50 lo'" m Sine Part* 1 Co»ec. T^igent Part. Cotang. Secant I'artjil Cojine tn / // ~o 8-981573 lll'-V.^V 8-983577 ■ 11-0,0423 0-C02CC4 ■ :9-99-996 ii "air V) 2 8-982228 8-984238 1"22 J j -0.5762 o-no20io I 9-99799' ;h so 31 ^ 8-982883 2 43 11-0,7117 8-9S4899 2 44 2 9-95-984 M -.il ICJ a 8-983536 3 65 ,.-0,6464 S-085559 3 66 11-0,444, 0-OC2C22 3 9-99797S r,\ 30 32 s 8-98+. S9 4 87 1,-0,58,1 89862,7 4 88 ;|;oj3783 0-002028 4 9-9Q7972 52 28 30 10 S-9S4S40 5 ,09 ,.-0,5,60 8-986875 5 1,0 0-002035 5 9-997965 .'jij 3U 33 I'i 8-985+91 6 ,30 ,1-0,4509 8-987531 6,3, ,1-0,2468 0-002041 6 9-997959 4H •-'7 30 n S-9«6.4. 7 ,52 1,-0,3859 8-988187 ' '53 1, -01,813 o-co-^047 7 9-997953 if, 3« 34 IB 8-986789 S,74 1,-0,3211 S-988842 8,75 1,-0,1,58 0-002053 8 9-997947 41 2t; 30 10 8-98:^437 9 '95 11-012563 8-989496 9197 1,-010504 0-C02059 9 9-99794. 42 3« 3j 30 TO 8-988083 102,7 ,1-0, ,9,7 8-990,49 '"-■9 ,1-009851 0-002065 OC02071 10 9-997935 3S ^: 8-988729 1 2, 8-99080, 1 22 .,-009,99 9-997929 38 « 8989374 2 43 ,,-010626 S-99,45, 2 43 11x08549 0-C02078 12 9-997922 :«i 2? 30 ■2li 8-9900.7 3 64 ,1-009983 S-99210, 3 65 ..-007899 0-002084 13 9-997916 34 30 37 ■m 8990660 4 85 ,1-009340 8-992750 4 86 11-007250 0x02090 14 9-997910 32 23 10 8-99.302 5 ,07 11008698 8-99339S 5 ,c8 11-006602 0-002096 IS 9-997904 30 30 38 ■K S-991943 6 128 11-008057 8-994045 6,29 .1-005955 0-002,03 16 9-997897 -28 22 30 34 S-992583 7 150 11-0074,7 8-994692 7.5. .1-005308 0-OC2,C9 17 9-997S91 20 30 39 3C 8-993222 11-006778 «-995337 8 ,73 11-004663 18 9-997885 ■24 21 30 39 8-993860 9192 ,,-006140 8-99598, 9.94 .1-0040,9 0-00212', 19 9-997879 -22 30 40 40 42 8-994497 10 214 ,,-005503 8-99O624 10 2,6 11-003376 0-C02I28 20 21 9-997872 20 If) 30 8-905,33 1 2, .1-C04867 8-997267 1 2,1,1-002733 ■ 0-002,34 9-997866 11 44 8-99„68 2 42 ,,-004232 8-9979c£ 2 43 ,,-002092 . 0-002140 22 ;-99786c Hi 1» 30 ■;ii 8-996402 3 63],, -003598 8-9985+9 3 64 ,.-00,45, ' 0-002146 23 9-997854 14 30 42 48 8997036 4 84111-002964 8-999,88 4 85 ,,-C008l2 , 0-002153 24 9-997847 12 111 30 5U S-997668 5 ,o5|ii-co2332 8-999827 0-002,59 25 9-99784, 10 311 43 J2 8-998299 « ,26 11-00,70, 9-00046^ 6 12s ,0-999535 ■ 0-002165 26 9-997835 H 17 30 W 8-99S930 7 >47 11-001070 9-001,02 7 149 ,0-998898 0-002,72 27 9-997828 30 44 M 8-999560 8 ,68 ,,-000440 9-00,738 8 ,70 ,0-998262 0-002178 28 9-997822 4 lU 30 W 9-0C0.88 e 189 ,0-999812 9-002373 9,9. ■0-997627 0-002,84 29 9-9978,6 ■2 30 48 23 9-0008,6 10 210 ,0-999,84 9-003007 102,3 ,0-996993 10-996360 0-C02I9, 30 9-997809 37 15 9001443 1 21 ,0-998557 9-0036+0 0-G02197 i ■7 9-997803 46 4 9-002069 2 41 10-997931 9-004272 a 42 10-995728 0-002203 9997797 ^li 14 30 6 9-002694 3 62 10-997306 9-004904 3 63 ,0995096 9-997790 34 30 47 S 9-0033,8 4 83 .0-996682 9-005534 4 8+ ,0-99+466 O-0022,6 9-997784 52 13 31) 10 9-00394. 5 ,04 10-996059 9006,64 5105 10-993836 0-002223 I 9-997777 50 30 48 12 9-004563 6,24 10-995437 9-006792 6 126 10-993208 1 0-C02229 9-99777. 48 L2 30 14 9-005,8; 7 .45 ,0-9948,5 9-007420 7 147 10-9925SO 1 0-002235 9-997765 46 30 1 4!) IC 9-005S05 8 ,66 .0-994195 9-008047 8 167 10-991953 1 0-CO2242 9-99-'758 44 i n 1 31) IH 9-006425 9 ,87 ,0-993575 9-008673 9 188 10-99,327 1 0-002248 9-997751 42 30 50 20 9-007044 10 207 .0-992956 9-009298 10 209 .0-990702 1 0-002255 9-997745 38 1(1 9-007661 T"2o" ,0-992339 9x09923 I 2, .0-990077 1 0-00226, 9-997739 51 21 9-008278 2 4, , 0-^99.7" 9-0,0546 2 4, .0-989454 ' 002268 , 9-99773= 3b 30 28 9-008894 3 6, ,0-991,06 90,, ,69 3 62 ,0-988831 1 0-002274 9-997726 34 30 .52 •Oi 9-0095,0 4 82 10-990490 9-01,790 4 83 .0-9882,0 . 0-C0228, 9-9977'9 32 30 30 9-0,0124 5 ,02 ,0-989876 9-0,24,1 5 .03 ,0-987589 ' 0-002287 9-9977.3 30 ,53 -.2 9-010737 6,23 10-989263 90,303, 6,24 ,0-986969 . 0-002294 9-997706 28 30 31 9-0, ,350 7 143 10-988650 9-0,3650 7 145 ,0-986350 1 0-002300 9-997700 20 ,54 .to 9-01,962 8 ,63 .0-98S038 9-01426X 8,65 ,0-985732 , 0-002307 9-997693 24 30 It 9-0.2571 9,841,0-987428 9-0,4886 9 ,86 ,0-985, ,4 1 0-C02313 9-997687 -22 5.5 40 9-013.82102041.0-9868.8 9-0,5502 10 207 ,0-984498 . 20 21 0-9976SC 20 -^ 9-0,3791 1 20 .0-986209 90,6,18 1 20 ,0-983882 , 0x02326 9-997674 .56 II 9-014400 2 40 ,0-985600 9-0,6732 2 4, 0-002333 22 9-997667 Hi 30 40 9-0,5007 3 6, ,o-9S4993 9-0,7346 3 6, ,0-982654 . 0-002339 23 9-99766. 14 57 l^ 9-0.56,3 4 8, ,0-984387 9-0,7959 4 81 ,0-98204, I 0-002346 24 9-997654 12 30 00 90,6219 5 ,01 10-983781 9-018572 5 102 10-981428 I 0-C0235J 25 9-997647 III 58 12 9-0.6824 6 ,2, 10-983176 9-0,9,83 6 ,22 ,0-9808,7 1 0-002359 26 9-99764, H M .'.1 9-0,7428 7 .41 ,0-982572 9-019794 7143 10-980206 1 0-002366 27 9-997634 y.) 30 9-01:031 8 161 ,0-981969 9-020403 8,63 ,0-979597 , 0-C02372 2« 9-997628 4 31) 5» 9-... 8633 9 ,82 10-98,367 9-02,0,2 9.83 ,0-978988 1 0-002379 2S 9-997621 2 cu 249019255 10 201 10-980765 9-02,620 10 204 10-978380 1 0-OC23S6 30 9-9976,4 II 777 ». Cosine Part. Secant Cotang. Part. Tangent C.ouc. '^ Sine [-' T/, 84° .')'■ m" I 750 TABLE 68 LOG. SINES, COSINES, &r. 0^ :>4'" 6^ 1 II in Sine Parts Cosec. Tangent Parts 1 Cotang. Secant Parts Cosine L^-|"' T ~ 9019235 10-980765 9-02,620 .0-978380 10-002386 9-9976,4 36l CO 30 2 9-019835 1" 20 10-980165 9-022227 1" 20 ,0-977773 ,0-002392 1" 9-9976C8 58 30 1 4 9-C20435 2 40 10-979565 9-022834 2 40 .0-977166 10-002399 2 ^-99760. jC h'J 3U U 9-021034 3 60 .o-97«966 9-023439 3 60 .0-97656, .0-002406 3 , 9-997 594 54 30 2 H 9-021632 4 79 10-978368 9-024044 4 80 ,0-975956 .0-C02412 4 , 9-997588 52 'M 30 10 9-022229 5 99 10-977771 9-024648 5 101 10-975352 ,0-0024,9 5 , 9-99758. 50 3(1 3 n 9-022825 6 1,9 10-977175 9-02525, 6 ,2, 10-974749 10002426 6 , 9-997574 48 57 30 u 9-023421 7 .39 10-976579 9-025853 7 ,41 ,0-974,47 ,0-002432 7 2 9-997568 4(1 50 4 i« 8159 .0-97598+ 9-026455 8 ,6, ■0-973545 io-oo24;9 8 2 9-997561 44 5S 30 18 9-0246.0 9 .79 10-9753QO 9-027055 1 9 ,8, ,0-972945 ,0-002446 9 2 9-997554 42 oO 5 22 9-025203 10 .99 1 20 .0-974797 9-027655 HO 20, ,0-972345 10-002453 10 2 11 2 9-997547 40 iL 9-025795 .0-974205 9-028254 1 20 10-97,746 ,0-002459 9-997541 « 24 9-026386 2 39 10-9736.4 -2 40 .0-97,. 48 10-002466 '2 319-997534 30 iA 30 26 9-026977 3 59 10-973023 9-029450 3 59 10-970550 10-002473 13 3 9-9975^7 34 30 7 23 9-027567 4 78 10-972433 9-030046 4 79 10-969954 10-002480 14 3 9-997520 32 5.-< 30 30 9-02X.56 5 98 10-971844 9-030642 5 99 10-96935S 10-002486 15 3 9-9975'4 30 30 8 32 9-018744 6 1.8 .0-971256 9-03,237 6 119 10-968763 10-002493 16 4 9-997507 -23 52 30 34 9-029332 7 137 10-970668 9-03.83, 7 139 10-968,69 10-002500 17 4 9-997500 -2fi 3(1 9 30 9-02991? 8 157 10-970082 9-032425 j 8 ,59 ,0-967575 10-002507 18 4 9-997493 24 .11 30 3S 9-030504 9 176 ,0-969496 9-033017 1 9 178 ,0-966983 ,0-0025,3 19 4 9-997487 -2-i 30 10 30 40 9-031089 10 .96 .0-9689.. 9-033609 "> '98 .0-966391 ,0-002520 20 5 21 5 9-997480 •20 50 30 9-031673 1 19 .0-968327 9-034200 1 ao .0-965800 10-C02527 9-997473 il 44 9-032257 2 39 .0-967743 9-03479. 3 39 .0-965209 ,0-002534 22 5 9-997466 l(i 49 .10 40 9-032839 3 58 .0-967.6, 9-0353801 S 59 .0-964620 10-00254, 23 5 9-997459 14 12 48 9-053421 4 77 10-966579 9-03596914 78 .0-96403. ,0-002548 24 5 9-997451 12 48 30 50 9-034002 5 97 ,0-965998 9-036557 5 98 .0-963443 10CO1555 25 6 9-997445 10 30 13 52 9-034582 6 116 ,0-9654,8 9-037144 6 ,,7 ,0-962856 ,0-00256, 26 6 9-997439 8 47 3) 54 9-035162 7 .35 ,0-964838 9-037730 7 137 ,0-962270 10-C02568 27 6 9-99743^ 30 u 5(1 9-035741 8 .55 10-964259 90383,6 8,57 0-96,684 .0-002575 28 6 9-9974^5 4 4f! 53 9-036319 9 .74 10-96368. 9-03890. 9 ,76 .0-96,099 10-002582 29 7 9-9974,8 2 30 }±_ as 2 9-036896 '0 193 1 19 10-963,04 9039485 IIO 196] 0-9605.5 10-0025S9 30 7 9-997411 35 45 9-037472 ,0-962528 9-040068 ! 1 .9 1 0-959932 10-002596 1 9-997404 16 4 9-03804S 2 38 ,0-96,952 9-04065, 2 39 0-959349 .0-002603 2 9-997397 50 44 30 (, 9-03S623 3 57 10-961377 9-04,232 3 58 0-958768 ,0-0026,0 3 , 9-997390 54 30 17 8 9-039197 4 76 .0-960S03 9-04,8,3 4 77 0-958,87 10-002617 4 , 9-997383 52 43 30 10 9-039770 5 95 0-960230 9-042394 5 97 0-957606 ,0-002624 5 , 9-997376 50 3( 18 12 9-040342 61.4 0-959658 9-042973 6 ,,6 10-957027 10-00263, 6 1 9-997369 48 42 30 u 9-040914 7 135 0-959086 9-043552 7 135 0-956448 .0-002638 7 2 9-997362 46 3( 19 l(i 9-041485 8 .53 0-9585,5 9-044,30 8 ,54 0-955870 .0-002645 S 2 9-997355 44 41 3» 18 9-042055 ,0-957945 9-044707 9 174 0-955293 ,0-002652 9 2 9-997348 42 3( 20 30 '" 9-042625 191 0-957375 9-045284 10 ,93 1 ,9 0-954716 0-954,4, ,0-002659 10 2 11 3 9-997341 38 40 30 9-043194 1 19 0-956806 9-045859 .0-002666 9-997334 21 24 9-043762 2 38 0-956238 9-046434 2 38 0-953566 .0-002673 12 3 9-997327 36 39 30 211 9-044329 3 56 0-955671 9-047C09 3 57 0-95299. ,0-002680 13 3 9-997320 34 30 22 2S 9-044895 4 75 0-955105 9-047582 4 76 0-9524,8 ,0-002687 14 3 9-997313 32 38 30 30 9-045461 5 94 °-954539 9-048155 5 95 0-95,845 .0-002694 15 4 9-997306 30 30 23 32 9-046026 6,13 °-953974 9-048727 6 1,4 0-951273 .0-00270. 16 4 9-997299 28 37 30 34 9-046590 7 .32 0-9534,0 9-049298 7 133 0-950702 ,0-002708 17 4 9-997292 •26 30 24 36 9-047 1 54 S.51I 0-952846 9-0,9869 8 ,53 0-95013, ,0-0027,5 18 4 9-997285 24 36 30 33 9-047717 9 169 0-952283 9-050439 9 172 0-949561 ,0-002721 19 4 9-997278 -22 30 2,5 40 42 9-048?79 .88 0-951721 9-051008 10 191 0-948992 ,0-002729 20 5 21 5 9-99727. 20 35 30 9-048840 '^ 0-951160 9-05,576 i ,9 0-948424 0-002736 9-997264 2(; 44 9-049400 0-950600 9-052144 2 38 0-947856 0-002743 22 5 9-997257 16 34 30 40 9-049960 3 56 0-950040 9-0527,1 3 56 0-947289 0-00275, 23 5 9-997249 14 30 27 48 9-050519 4 74 0-949481 9-053277 « 75 1 0-946723 0-002758 24 6 9-997242 12 33 30 50 9-051078 5 93 0-948922 9-053843 5 94 0-946.57 0-002765 25 5 9-997235 10 30 2fl 52 9-051635 6 .1. 0-948365 9-054407 6 ,,3 0-945593 0-002/72 26 6 9-997228 8 32 30 54 9-052.92 7.30 0-947808 9-054972 7 ,32 0-945028 0-002779 27 7 9-99722, 6 30 2y 5<) 9-052749 8 149 0-94725, 9-055535 8 ,50 0-944465 0-002786 28 7 9-9972,4 4 31 30 58 9-053304 n 167 0-946696 9-056098 9 ,69 0-943902 0-002794 29 7 9-997206 2 30 .•)0 2S6 9-053859 186 0-94614, 9-056659 Cotang. Parts 0-941341 0-00280, 30 7 9-997,99 30 TT> "? Cosine I'arts 1 Secant Tangent Coeec. Parts Sine m. TT, 83° 5" 34"' 1 TABLE C8 751 Lot;. SINES, COSINES, &c. | If -JG'" G'' '" m Sine 1 TarU { Co^er. Tangent ParU Cotang. Secant I'artal Cosine}-" / // 30 ~ir ./OC3859 ,0-9461., 9056659 10-94334. 10-C02S0. 9-997.99 34 "iiiT w •2 9054413 <■■ 18 ■0-945587 9-05722. 1" 19 10-942779 10-001808 l"o 9-997.92 .'.» 311 SI 4 9054966 2 37 ,0-94,034 9C577XI 2 37 ,0-942219 .0-0028,5 2 9-997,85 5li 2;) 30 l> V'^555'9 3 5; 1094448, 9-05834. 3 56 .0-94,659 10-002822 3 1 9-997178 M 311 32 8 9-05607114 73 ,0-943929 9-058900 ■» 74 .0-94.. CO .0-002830 4 1 9-997,70 M •-'b 30 10 9-056622, S 9z ,0-943378 9059459 5 93 10-9405 p .0-002837 5 , 9-997.63 30 31. 33 11 9057172' 6 ,.c .0-942828 9-060016 6 .11 10-939934 .0-002844 6 1 9-997,56 4H ■21 30 14 9-057722 7 128 .0-942278 9-060573 7 130 10-939427 .0-00285, 7 2 9-997,49 40 30 34 IS 9-058271 8 147 ,0-94.729 9-061,30 8 .49 ,0-938870 .0002S59 8 2 9-997,4, 44 ■Jl. 30 18 9058820 9 .65 ,094,, 80 9-06,685 9 167 ,0-9383,5 10-C02866 9 2 9-997'34 4-2 31, 36 9-059367 .0-940633 9-062240 10 186 10937760 10-C02873 10 2 H 3 9-997.27 40 3H ■J!> 30 9059914 T'Ts^ ,0-940086 9-062795 1 ,8 .0-937205 ,0-002880 9-997,20 3« •i4 9060460 2 36 .0-939540 9-063348 2 37 .0-936652 10-C02888 12 3 9-997, ,2 36 24 30 M 9-061006 3 54 ,0-938994 9-06390, 3 55 .0-936099 10-C02S95 13 3 9-997,05 34 30 37 S3 9-06,55, 4 73 10-938449 9-064453 4 73 10-935547 10-C02902 14 4 9-997098 St •23 30 30 9-062095 5 9, ,0-937905 9-065005 5 92 .0-934995 10-C02910 15 4 9997090 30 3(1 3« 31 9-062639 6 ,C9 .0-93736, 9-065556 6 ,,0 .0-934444 10-002917 16 4 9-997083 •28 22 30 31 9-063,8, 7 ,27 10-936819 9-066,06 7 ,29 .0-933894 10-C02924 17 4 9-997076 -20 311 39 30 9-063724 8,45 ,0-936276 9-066655 8 ,47 'o'933345 10-002932 18 4 9-997068 ■24 21 3» 9064265 9,63 ,0-935735 9-067204 9.65 .0-932796 10-002939 19 4 9-99706. •i-i 3(1 40 40 9-064806 10 ,81 .0-935194 9-067752 10,84 '°-93"48 10-002947 20 5 9-997053 •20 20 M 4-2 9065346 1 ,8 .0-934654 9-068300 1 ,8 .0-93.700 10-002954 21 5 9997046 18 3(J 4( 4-1 9-065885 2 36 ,0-934. .5 9-068846 a 36 .0-93, ,54 10-00296. 22 5 9-997039 10 lil 3(1 46 9-o664;4 3 54 ,0933576 9069393 3 54 ,0-530607 .0-002969 23 6 9-99703, 14 3(1 42 4S 9-066962 4 72 10-933038 9-069938 * 73 ,0-930062 ,0-002976 24 6 9-997024 I'i \H ■111 50 9-067499 S 90 ,0-932501 9-070483 S 9, ,0-929517 ,0-002984 25 6 9-997016 10 3(1 43 3-2 9-068036 6 ,07 ,0-93,964 9-07.027 6109 10-928973 10-C0299, 26 7 9-997009 H 17 :iii 34 9-068572 7 ,25 ,0-931428 9-071570 7 "7 10-928430 10-002998 27 7 9-997002 6 44 SC 9-069,07 8 ,43 ,0-930893 9-072,13 8,45 10-927^87 10-003006 28 7 9-996994 4 16 30 3» 9-069642 9 161 .0-930358 9-072655 »i6] 10-927345 10-003013 29 7 9-996987 •2 3(1 4» 27 9-07CI-6 10,79 ,0-929824 9-073197 10 .ti 10-016803 ,0-003021 30 7 9-996979 3il 15 9-070709 1 ,8 ,0-929291 9-07373* I 18 10-92*262 10-003028 1 9-996972 46 I 4 9-07,242 2 35 10-928758 9-074278 1 36 10-925722 10-C03036 2 , 9-996964 36 14 30 8 9-07,7741 3 53 ic-928226 9-074817 3 54 10-925183 10-003043 3 I 9-996957 34 30 47 8 9-072306 4 71 ,0-927694 9075356 4 72 10-924644 ,0-00305, 4 1 9-996949 5-2 1:1 lu 9-072836 5 88 ,0-927,64 9-075895 5 90 .0-924.05 ,0-003058 5 , 9996942 50 3(. 48 I'i 9-073366 6 ,06 10-926634 9-076432 6.07 .0-923568 ,0-003066 6 2 9-996934 48 .2 30 14 9-073896 7,24 10-926.04 9-076969 7 125 ,o-92303i .0-003073 7 2 9-996927 4G 3.1 49 10 9-074424 8 ,4, .0-9255-6 9-077505 8 .43 ,0-922495 ,0-00308, 8 2 9-9969,9 44 I 1 1 30 lit 9-074952 9 ,59 .0-925047 9-07S041 9 .6. ,0-92,959 ,0-003089 9 2 9-9969" 42 311 50_ n 9-075480 10 ,77 10-924520 9-078576 10 .79 10-92,424 ,0-003096 10 3 11 3 9-996904 40 10 9-076007 ' '7 .0-923993 9-079.10 1 ,8 ,0-920890 ,0-003,04 9996896 si 14 9-07653; 2 35 10-923467 9-079644 2 35 ,0-920356 .0-003,,, 12 3 9-996889 38 !l J« ■iC 9-077058 3 5^ ,0-922942 9-080.77 3 53 ,0-9,9823 .0-003., 9 13 3 9-99688. 34 30 62 w 9-077583 4 70 ,0-9224.7 9-0807.0 4 7, .0-9,9290 ,0-003.26 14 4 9-996874 3-2 )l 30 30 9-078,07 5 87 0-92,893 908. 241 5 89 ,o-9,875<, 10-003.34 Ifl 419-996866 30 30 53 j-i 9-07863, 6 ,05 0-92,369 9-08.773 6 ,c6 0-9,8227 10-003142 16 4 9-996858 ■ilt 7 30 34 9-079,54 7 ,22 0-920846 9-082303 7 .24 0-9,7697 10-003.49 17 4 9-99685. ■211 64 36 9-079676 8 ,40 0-920324 9-082833 8 ,42 0-917,67 10-003.57 18 5 9-996843 ■24 6 30 M 9-080,98 9 157 0-9,9802 9-083362 9 160 0-9.6638 19 5 9-996835 ■n 30 66 30 40 4? 9-0807,9 10 175 0-9,928, 9-08389. 10 177 0-916109 10-003172 20 5 21 5 9996828 •2. .i :m 9-08,239 ' >7 0-9,8761 9-084419 ■ .8 0-915581 .^3T8c 9-996820 6C 44 9-081759 2 34 0-9, 824, 9-084947 2 35 0-9,5053 10-003,88 22 6 9-9968.2 16 4 30 4« 9-082278 3 52 0-9,7722 9085473 3 53 0-9,4527 ,0-003,95 23 6 9-996805 14 30 07 48 9-082797 4 69 0-9,7203 9-086000 4 70 0-9,4000 ,0-003203 34 6 9-996797 1-2 3 50 9-0833.4 5 86 09,6685 9-^86525 S 88 0-9,3475 .0-C0321, as 6 9-996789 10 S8 32 9-083832 6,03 0-916,68 9-087050 6,05 0-912950 10-0032,8 26 7 9996782 H 2 30 34 9-084348 7 ,2, 0-9,5652 9-087574 7 ,23 09,2426 ,0-003226 27 79-996774 6 M sa 5fl 9-084864 8 ,38 0-9,5.36 9-08X098 8 140 0-9,, 902 ,0-003234 28 7!9-996766 4 1 30 5S 908C3S0 9 =55 0-9.4620 9-088621 9.58 09, ,379 ,0-003242 29 7l9-99675» 2 10 60 2a 9-0858941IO 172 1 0-9.4.06 9-089.44 '10 .75 1 °-9'o8 56 ,0003249 .■10 8|9-99«7 5' ol ',-T, Cosine j Part. | Sr.ant Cotanj;. | Paris | T.inpcnt Cowo. Part.s 1 Sine m. B;)*' S" -.i'j"' \ 752 TABLE G8 LOG. SINES, COSINES. Ike. ()i. 28'" 7^ '4- m. Sine Parts Co-seo. Tangent | Parts Cotang. Secant 1 Parts | Cosine •?• 60' 9085894. 10 914106 9-089,44] .0 9,0856 10 003249 !9-y967 5' 32 30 2 9-0864.09 I" 17 10 913591 9-089666 1 17 10 910334 003257 1 • 9-996743 58 3(1 1 4 9 0«69rz 2 34 10 9,3078 9-090187 2 35 10 9098,3 003265 2 1 9-996735 M 59 30 6 9-087435 3 51 10 912565 9-090708 3 52 10 909292 003273 3 I 9-996727 54 30 2 8 9-0S7947 « 68 10 912053 9-09,228 4 69 ,0 908772 10 0032S0 4 1 9-996720 5(1 30 10 9-08X459 5 85 10 911541 9-091747 5 87 ,0 908253 10 9-9967,2 50 3(1 3 12 9-o8.'*97o 6 102 10 911030 9-092266 6 104 10 9°7734 C03296 6 2 9-996704 48 .■i7 30 u 9-089+80 7 ..9 10 910520 9-092784 7 121 ,0 907216 003304 7 2 9-996696 4« 3(1 4 Ifi 9-089990 8 ,36 10 910010 9-093302 813S ,0 90669S 10 003312 8 2 9-996688 44 .'ill 30 IS 9-0905C0 9 .53 10 909500 9-093819 9156 10 906181 003320 9 2 9996681 4-2 30 5 ;" 9-091008 10 170 10 908992 9'°943 36 10 175 10 905664 10 003327 10 3 9-996673 40 4r 9-09 1 5 16 1 17 10 908484 9-094851 1 '7 10 905149 003335 9-9966C5 C u 9-091024 2 34 10 907976 9-095367 2 34 ,0 904633 003343 1-2 3 9-996657 M 54 3() ■ll\ 9-092530 •■' S'' 10 907470 9-09 588, 3 51 10 904119 10 003351 13 3 9-996649 34 30 7 •is 9-C93037 4 67 10 906963 9-096395 4 68 ,0 903605 003359 U 4 9996641 3-2 &:t JU 9-093541 5 84 10 ,06458 9-096909 5 86 ,0 903091 10 003367 15 4 9-996633 30 311 11 3-2 9-094047 6 ,01 10 905953 9-097422 6 103 ,0 90x578 10 003375 16 4 9-996625 -2S .'>2 30 34 9-094552 7 118 10 905448 9-097934 7 120 10 902066 10 003383 17 4 9-9966.8 20 30 !< .Ki 9-095056 8 133 10 904944 9-098446 8 137 10 901554 10 003390 18 5 9-9966,0 ■24 r>\ 3(1 3S 9'095559 9 151 10 904441 9-098957 9 .54 10 901043 10 003398 19 5 9-996602 ■2-2 30 1» 30 9-096062 10 168 10 903938 9-099468 10 171 ,0 900532 10 003406 20 5 21 6 9-996594 •20 18 no 9-096564 1 17 To" 903436 9-099978 1 '7 ,0" 900022 To" 003414 9-996586 II 44 9-097065 2 33 10 902935 9-100487 2 34 ,0 899513 003422 22 6 9-996578 10 1!) 30 \Si 9-097566 3 50 10 902434 9 -,00996 3 5, 10 899004 003430 23 6 9-996570 14 3(1 12 48 9-098066 4 67 10 901934 9-, 01 504 4 68 ,0 S98496 10 003438 24 6 9-996562 lo 4H 30 50 9-098566 5 83 10 901434 9-102012 5 85 ,0 897988 003446 25 7 9-996554 30 1.1 .■i-2 9-099065 6 100 10 900935 9-, 02519 6 ,0, ,0 S97481 003454 26 7 9-996546 8 47 30 54 9-099564 7 1.6 10 900436 9-, 03026 7 iiS lO 896974 10 003462 27 7 9-996538 C 3(1 u hi\ 9-100062 8 133 10 899938 9-103531 8 135 10 896468 003470 28 7 9-996530 4 46 30 .08 9-'co550 9 .50 10 899441 9-104037 9.52 10 895963 10 003478 29 8 9-996522 2 30 Ift 29 9-101056 9-101552 10 166 1 16 10 10 898944 9-104541 10 169 10 895458 003486 30 8 9-996514 31 58 4.'i 30 898448 9- 105046 1 17 10 894954 To 003494 1 9-996506 Ifi 4 9-102048 * 33 10 897951 9-105550 2 33 10 894450 10 003502 2 1 9-996498 5li 44 21. 6 9-102543 3 49 10 897457 9-106053 3 50 10 893947 10 003510 3 1 9-996490 54 30 17 8 9-103037 4 66 10 896963 9- ,06556 4 67 10 893444 10 0035.8 4 1 9-996482 5-2 4:i 10 9-.0353. 5 82 10 896469 9-, 07058 5 84 10 892942 10 003527 5 1 9-996474 50 30 l« 11 9-104025 6 99 10 895975 9-,c7559 6 ICO 10 89244. 10 003535 6 2 9-996465 48 42 14 9-104517 7ms 10 895483 9-10S060 7 1,7 10 891940 10 7 2 9-996457 4fl .3(1 lit 16 9-105010 8 132 10 894990 9-108560 8 ,34 10 89,440 10 003551 8 2 9-996449 44 41 18 9-105501 9.48 10 894499 9-109060 9 150 10 890940 10 003559 9 2 9-99644, 4-2 30 20 ■20 9-105992 10 .65 10 894008 9-109559 10 167 10 89044, 10 C03567 10 3 " 3 9-996433 40 40 3(1 9-106483 I 16 To 893S'7 9-11C05S 1 17 TiT 8S9942 To" 003575 9-996425 21 ■24 9-106973 « 33 10 893027 9-110556 2 33 10 889444 10 ro3583 .2 3 9-996417 3n533 8,32 10 S86467 10 003632 18 5I9-996368 •24 36 3(1 :i8 9-1 10387 9 .46 8896,3 9- 1 14028 9 149 10 885971 10 003641 19 5 19-996 3 59 •22 311 25 ;;; 9-110873 -.0 163 889127 9-114521 10 165 10 885479 10 C03649 20 5 9-996351 20 3.^ 30 9-111358 T— To^ 888642 9-115015 1 16 kT 884985 To 003657 21 6 9-996343 2C 44 9- 1 1 1842 2 ^^ 10 888,58 9-115507 2 33 10 884493 10 003665 2-2 6 9-996335 IG 34 30 4(j 9-112326 3 48 10 8S7674 9-115999 3 49 10 884001 10 003674 23 6 9-996327 14 30 27 4H 9-112S09 4 64 10 9-116491 4 65 10 883509 10 003682 24 7 9-996318 12 33 •M 9-113292 5 80 10 886708 9-116982 5 82 10 883018 10 003690 25 7 9-996310 10 311 28 it 9- '•3774 6 96 10 886226 9-,, 7472 6 98 10 S82528 10 00369S 26 7 9-996302 8 32 30 54 91 14256 7 112 10 SS5744 9-1,796^ 7 114 10 88203a 10 003707 27 7 9-996293 8 3(1 ■29 5(i 9-"4737 R129 10 8S5263 9-118451 8 131 10 88 1548 10 0037,5 28 8 9-996285 4 31 30 5S 9-115218 9 14^ 10 8S4781 9-1,8941 9 147 10 881059 10 003723 29 8 9-996277 2 3(1 ■M 30 9-115698 10 161 10-884302 9-119429 ■0 -63 10-880571 10-003731 30 S 9-996269 m. 30 , n m. Cosine Parts Secant Cotaiig. Varts Tangent Cosec. Parts Sine sl>' w^ m^ 1 TADI.K GS LOG. SINES, COSINES, ice. Qh 30m 70 /// m. Sine Part. Cobec. Tangent Parts Cotang. Se.-ant 1 Parts 1 Cosine m 1 ■■ ■M 91. 569 0-884302 9" "9429 0-88057. .0-003731 9996269 30 :«> 311 9-. .6,7 1" .6 0-883823 9-119917 I" .6 0-880083 10-003740 1 ' ( 9-996260 „ 31 9-..6656J 2 32I 0-883344 9 -.20404 2 32 0-879596 10-003748 a 1 9'996252 Si- •21) JO 911715 3 48 0-882865 9-120891 3 49 0-879.09 .0-003756 9-996244 .'14 :t2 9-11761- 4 64 0-8S2387 9-121377 4 65 0-87S623 10-003765 4 1 9-996235 5-i ■2B 311 9-118090 5 80 0-8819.0 9-12.863 5 8. 0-878137 10-003773 S 1 9-996227 .-;() 3, :« 9-11856- 6 95 0-881433 9-122348 6 97 0-877652 10-003781 6 2 9-996219 48 27 30 9-119045 7 III 0-880957 9-122S33 7 ..3 0-877.67 7 2 9-996210 40 34 9-119519 8 127 0-880481 9-. 23317 8 129 0-S76683 .0-C03798 8 2 9-996202 44 2C 30 9-1 19994 9 14; 0-880006 9-123801 9 .46 0-S76199 .0-003807 » 3 9-996193 3C 35 30 ■rt 9-110469 10 159 0-87953. 9-124284 10 ,62 o^8757i6 10-003815 " 3 9-996185 10 25 9-120943 I 16 0-879057 9-124766 1 .6 0-875234 ,0-003823 9-996177 ~^ 3C '^.< 9-121417 1 3. 0-878583 9-125249 2 32 0-874751 10-003832 12 3 9-996.68 30 24 30 w 9-121890 3 47 1 0-878110 9-. 25730 3 48 0-874270 10-003840 13 4 9-996160 34 30 H ■IS 9-122362 4 63 1 0-877638 9-. 262,1 4 64 0-873789 10-003849 14 4 9-99615. :n •.'3 3U 30 9-.22S35 5 79 ■ 0-877.65 9-126692 5 80 I 0-873308 .0-003857 15 4 9-996,43 30 31 :«j 32 9-123306 6 94 1 0-876694 9-127172 fi 96 1 0-872S28 10-003866 16 5 9-996.34 ■iH -.'-J 30 34 9-123777 7 110 1 0-876223 9-12765, 7 112 I 0-872349 10-003874 17 5 9-996126 ■u; 31! 39 3(1 9-124248 8 126 1 0-875752 9-128.30 8 128 1 0-871S70 10-003883 18 5 9-996.17 ■it 21 30 314 9'iH7>8 9 141 1 0-875282 9 144 I 0-87.39. ,0-003891 19 5 9-996109 ■i-2 M 40 H 40 9--5.8- ■0.57 I 0-874813 9-129087 10 160 I 0-870913 10-003900 20 6 21 6 9-996.00 '"' 20 9-125656 1 16 1 0-874344 9-129564 1 ,6 1 0-870+36 ,0-003908 9-996092 30 41 <» 9-.26,2S U 31 1 0-873875 9-130041 2 32 1 0-S69959 .0-0039.7 22 6 9-996083 lU 19 30 40 9-126593 » 47 J 0-873407 9-130518 3 47 , 0-869482 .0-003925 23 7 9-996075 14 42 4R 9-127060 0-872940 9-. 30994 4 63 1 0-869006 .0-003934 24 7 9-996066 l-i 18 30 SO 9-i275t7 5 78 1 0-872473 9-. 3. 469 5 79 . 0-868531 .0-003942 25 7 9-996058 10 30 43 5-i 9-127995 6 93 1 0-872007 9-. 31944 6 95 . 0-868056 .0-003951 96 7 9-996049 ^ 17 III SI 9-128459 7 109 1 0-87.54. 9-. 32419 7 .11 1 0-867581 ■0-003959 27 8 9-99604, (1 44 Sli 9-128925 8 ,24 1 0-871075 9-132893 8 127 . 0-867107 28 8 9996032 J h; 30 5H 9-129390 9 140 1 0-870610 9-133366 9.42 1 0-866634 .0-003977 29 8 9-996023 ■i 311 45 M 31 9-,29854 10 ,55 1 0-870146 9-. 33839 10158 . 0-866,6. .0-003985 30 8 9-9960,5 z» 15 9-130318 1 15 I 0-869682 9-1343.2 1 16 I 0-865688 ic-003994 1 9-996006 ~M id 4 9-. 30781 2 3' ■ 0-869219 9-134784 a 3. . 0-865216 10-004002 2 1 9-995998 ,'lli u 30 6 9-131244 3 46 1 0-868756 9135255 3 47 1 0-864745 .0-004011 3 I 9-995989 54 47 8 9-131706 4 62 I D-868294 9-. 35726 4 63 . 0864274 10-004020] 4 1 9-995980 S-i 13 30 1 10 9132168 5 77 1 0-867S32 9. 36197 5 78 . 0-S63803 10-004028 S 1 9-995972 so 30 48 ! ,. 9. 3263c 6 92 1 D-8673-0 9-.36f67 6 94 1 0-863333 10-004037 6 2 9-995963 4H \-i 30 j H 9-133091 7 108 I 3-866909 9-137136 7 uoji 0-862864 0-004046 7 2 9-995954 4« 30 4« ,« 9-'3355' 8 123 1 D-8664+9 9-, 37605 8.25 . 0-862395 0-CO4054 8 2 9-995946 44 II 30 ,H 9-1340" 9 139 I 3-865989 9-.3S074 9 .4. 1 3-861926 0-004063 9 3 9-995937 4-i 311 ^0_| .to 9-13447010 T54|i =-865530 9-. 38542 10_157 J_ 3-86,458 10-004072 10 3 " 3 9-99592S 40 10 30 ■i-l 9-134929 I 15 I D-865071 9-139C09 1 16 1 3-86099. 0-004080 9-995920 311 i\ '". 9-'35387 2 30 1 3-864613 9-. 39476 2 31 1 3-860524 0-004089 12 3 9-9959,, 30 !• 30 9-135845 3 46 1 3-864,55 9-'39943 .1 47 1 3-860057 0-004098 13 4 9-995902 34 311 .12 ■if, 9-136303 4 61 1 3-863697 9-. 40409 •I 62 1 3-859591 0-004.06 14 4 9-995894 :n M 30 9-136760 5 76 1 ^•863240 9-140875 } 5 78 . 3-859.25 0-0041,5 15 4 9-995885 311 30 53 n 9-137216 6 91 1 3-862784 9-141340 6 93 1 3-858660 0-004.24 16 s 9-995876 •w 7 lO M 9137672 7 106 1 3-862328 9-14.805 7 109 , 3-858195 0-004133 " 5 9-995867 ■11, 311 44 M 9-i3«i28 8 122 I 3-861872 9-142269 8 124 1 5-85773' 0-00414, 18 5 9-995859 -« li 30 38 9-138582 9 137 1 3-8614,8 9' "42733 9140 ' 3-857267 0-004150 19 6 9-995850 ■fi 311 .5.^ 311 40 9-139037 3-860963 9-. 43196 10 155 I 3-856804 0-004,59 20 6 21 6 9-995841 ''" 5 9- 13949' 1 15 1 3-860509 9-143659 1 15 1 3-856341 0-004168 9-995f3> 30 5(; 41 9- "39944 2 30 ■ -860056 9-144121 2 31 I V855879 0-004,7- 20 6 9-995823 10 i 30 Hi 9-140-.98 •1 45 > 3-859602 9-1445S3 3 46 I 3-8554.7 0-004,85 M 7 9-995815 14 M\ «7 4' 9- 1408 5° 4 60 I 3-859,50 9-145044 4 61 1 3-854956 0-004194 24 7 9-995806 \i .1 10 SO 9 14 < 302 » 75 > 3-858698 9-145505 5 77 I 3-854495 0-004203 25 7 9 995797 III 311 68 j«| rM'75J « 90 1 3-858246 9-. 45966 fi 92 1 3-854034 0-0041,1 26 8 9-995788 H •J 9-. 42205 7.05 1 >-85779> 9-1464:5 7 108 1 '•853575 0-00422 I 27 8 9-995779 1; 31! 59 Sli 9142655 8 121 I V857345 9- .46885 8 123 1 3-853.15 0-004229 W 8 9-99';77i 4 1 30 rm 9-143106 9 136 1 3-856894 9''4:344 9 .38 1 3-852656 0-004238 29 819-995762 ■i 30 «0 32 9-14355V"' '5'!' ,-856445 9-.4-S03 10 154 1 .•852.97 0-004247 30 9 9-995-53 Sine n (1 T7f^ Conine i Parts j Secant Cotang. 1 Parts | TanRent | Co.ec-. j Parts ■^■\"' 82^ 5h 28- 754 TABLE 08 LOG. SINES, COSINES, .\c. 1 Oh 3'jm go j / »|m. Sir.e Parts Cosec. Tangent Parts Cotang. Secant Parts! Cosine |™- / n 9-143555 856445 9-147803 10 852197 10-004241 9-995753 za w 30 2 9-144005 »" -5 10 855995 9-14826. '" .5 10 85'739 .0-004256 l"o 9-995744 30 1 4 9->44453 2 30 10 S55547 9". 48718 a 30 10 851282 .0004265 2 , 9-995735 5(1 o9 30 G 9-1+4902 3 45 10 85509S 0-149.75 3 46 .0 850825 IO-C04274 3 I 9-995726 54 30 2 B 9-H5349 4 59 10 85465. 9-149632 4 61 850368 10 C04283 4 1 9-9957.7 32 SI) 30 10 9-'45797 5 74 10 854203 9-150088 5 76 10 8499.2 10-004292 5 1 9995708 50 30 3 li 9-146243 6 39 10 853757 9-150544 6 9. 10 849456 10-004301 6 2 9995699 48 .■>7 30 14 9-146690 7 104 10 8533.0 9-151000 7 106 849000 .0-004310 7 2 9-995690 JO 4 lU 9-147136 8 119 10 852864 9- "5 '454 8 122 10 848546 10-004319 8 2 9-99568. 44 5G 30 la 9-147581 9 .34 10 852419 9-. 5. 909 9 .37 10 84809, 10-004328 9 3 9-995672 42 30 5 •20 ■12 9-.4So26ilO .49 10 85 1974 9-.52363J10 152 10 847637 10-004336 10 3 '1 3 9-995664 38 M 9- 14847 ■ ' >5 To" 851529 9-152816 1 .5 To 847184 10-004345 9-995655 6 9-148915 ■2 29 10 851085 9-153269 2 30 10 84673. .0-004354 12 4 9-995646 30 44 30 •M 9-149358 3 44 10 850642 9-153722 3 45 10 X46278 .0-004363 13 4 9-995637 34 30 7 ■iS 9-149802 4 59 10 850.98 9-. 54174 4 60 10 845826 . J-004372 14 4 9-995628 32 53 30 30 9-150244 5 74 10 849756 9-154626 5 75 10 845374 ,0-00438, 15 4 9-9956.9 30 30 8 32 9-150686 6 88 10 8493.4 9-155077 6 90 844923 10-004390 16 5 9-9956,0 ■28 52 30 34 9-151128 7 103 10 848872 9-15552S 7 105 10 S44472 ,0-004400 17 5 9-99560, 20 30 9 38 9-15.559 10 84843. 9-155978 10 844022 10-004409 18 5 9-99559' ■24 61 30 38 9-152010 9I33 10 847990 9-156428 9 135 10 843572 10-004418 19 6 9-995582 •22 30 10 42 9-152451 !0j47_ 10 847549 9-156877 10 150 10 843.23 10-C04427 20 6 21 6 9-995573 20 flO 30 9-152891 ' '5 10^ 847.09 9-157326 ' '5 10 842674 10-004436 9-995564 u 44 9-153330 2 29 10 846670 9-'57775 2 30 10 842225 .0-004445 22 7 9-995555 10 49 30 4() 9-153769 3 44 10 84623. 9-158223 3 45 10 84.777 .0-004454 23 7 9-995546 14 30 12 4S 9-154208 4 58 10 845792 9-15867. 4 60 10 841329 10-004463 24 7 9-995537 12 48 30 511 9-154646 5 73 10 845354 9-159118 5 75 10 840882 .0-CO4472 25 7 999552S JO 30 13 52 9-155083 6 87 10 8449.7 9-159565 6 89 10 840435 .0-00448. 26 8 9-995519 8 47 30 54 9-155521 7 102 10 844479 9-. 600.. 7 104 10 839989 10-C04490 27 8 9-995510 U 14 56 9->55957 8 117 10 844043 9-160457 8,19 IC ";-)543 10-004499 28 8 9-99550. 4 46 30 58 9-156394 9 131 10 843606 9-160901 9 .34 830098 .0-004509 29 9 9-99549. 2 30 15 33 9-156830 10 146 JO 843.70 9-. 6. 347 10 .49 10 838653 10-004518 30 9 9-995482 27 58 45 30 9-157265 I 14 10" 842735 9-161792 > »5 10" lisTcS 10-004527 1 9-995473 16 4 9-157700 2 29 10 842300 9-.62236 J 29 10 837764 10-004536 3 ' 9995464 .'0 44 30 13 9-158135 3 43 10 841S65 9-162680 3 44 .0 837320 10-CO4545 9-995455 5-1 30 17 8 9-158569 ♦ 58 10 841431 9-163123 « 59 10 836877 10-004554 4 I 9-995446 52 43 30 .0 9-159002 5 72 10 840998 9-163566 5 74 10 836434 10-004564 5 2 9-995436 5C1 30 IS .2 9- "59435 6 87 10 840565 9-164008 6 88 10 835992 .0-004573 6 2 9-995427 48 42 3C 14 9-159868 7 101 10 840,32 9-164450 7 .03 10 835550 10-004582 7 2 9-9954.8 40 30 13 10 9-160301 8115 10 S39699 9-164892 8 118 10 S351C8 10-004591 8 3 9-995409 44 41 3D 18 9-160732 9130 10 839^68 9-165333 9 133 10 10-C04601 9 3 9-995399 42 30 ■20 20 9-161164 10 144 10 838836 9-165774 10 147 10 834226 10-C04610 10 3 9-995390 40 40 ~30 9-. 61595 1 14 To^ S38405 9-166214 • >5 10 833786 .0-004619 9-99538. 21 24 9-162025 2 29 10 837975 9-166654 2 29 10 833346 10-004628 12 4 9-995372 30 39 30 20 9-162456 3 43 10 837544 9-167093 3 44 .0 832907 .0-004638 13 4 9-995362 34 30 22 2S 9-162885 * 57 10 S371.5 9167532 4 58 10 832468 10-004647 14 4 9*995353 3-2 38 30 30 9-163315 6 71 10 8366S5 9-167971 6 73 10 832029 ,0-004656 15 5 9-995344 30 30 23 32 9-163743 6 86 10 836257 9-168409 6 SS 10 831591 .0-004666 16 5 9995334 •28 37 30 34 9-164172 7 100 10 835828 9-168S47 7 102 10 831153 10-C04675 " 5 9-995325 20 30 24 36 9-164600 8 114 10 835400 9-169284 8 .17 10 830-16 .0-004684 18 6 9-995316 94 36 30 3S 9-i65',27 9 128 10 834973 9-169721 9 13. 10 830279 .0-004694 19 6 9-995307 ■a 30 3& 30 40 42 9-165454 9-165881 10 143 10 834546 9-170157 10 146 10 8298,3 10-004703 2U 6 2) 7 9-995297 20 85 1 14 "10 834119 9-170593 1 14 10 829407 .0-0047.2 9-995288 29 44 9-166307 2 28 833693 9-171029 2 29 10 82897. 10-004722 22 7 9-995278 JO 34 30 40 9-166733 3 42 10 S33267 9-171464 3 43 10 828536 10-CC4731 23 7 9-995269 14 30 27 48 9-167159 * 57 10 S3284. 9.71899 4 58 10 828.0, 10004740 24 7 9-995260 12 33 30 60 9-167584 6 71 10 8324.6 9-172333 6 72 10 827667 10-CO4750 2S 8 9-995250 10 90 28 62 9- 168008 6 85 10 83.99^ 9-172767 e 87 10 827233 10-004759 ■»« S 9-995241 8 32 30 64 9-168432 7 99 10 831568 9-173201 7 101 10 826799 10004769 27 8 9-995232 6 30 ■29 60 9-16^856 8 ,13 10 831144 9-173634 8 116 10 826366 10-004-178 28 9 9-995222 4 31 30 53 9-169279 9 127 10 830721 9-174067 9.3c 10 825933 .0-C04787 29 9 9-9952,3 2 90 30 "/ // 34 9-169702 10 141 10-830298 9-174499 10 145 10-825501 .0-C04797 30^^ Parts 9-995203 SO in. Cosine Parts Secant Cotang. I Parts Tangent Cosec. Sine in /// 81° 5" £6^ TABI.r 68 UHi !=INES. CObl.Viis. .\r. \ 0" a4"' 8= -^ '" *? Sine Pares Coscc Tnnsent Parts Cotang. Secant Parfs Cosinf 5-995203 at ■M\ w 9-.69-C 10-S3029S 9-174499 10-82550 .0-C0479- 3'' 2 9-I70I2 1" .4 ,0-829875 9-17493. '■ '4 ,0-825069 10-004806 I'c 1-995 194 5." .11 31 •) 9''7o;4 2 28 10-829453 9-175362 2 29 ,0-824638 ,0-004816 2 , r995'S4 ;o >'.) 3l( 8 9-17096 3 42 10-829032 9-175793 3 43 10-824207 .0-00482, 3 1 r995.75 .VI ;i' 32 8 9-i7i38r 4 56 10-8286,1 9-176224 4 57 10-823776 10-004835 4 I 9-995165 3 Hi 10 9-I7.8.C 5 70 10-828190 9-176654 6 72 10-823346 .OC04844 6 2 9-995.56 511 :iii S3 12 6 84 .0-827770 9-. 77084 6 86 ,0-822916 ■0-0C4854 6 2 9-995,46 AH ■21 30 14 9- 1 7265c 7 98 .0-827350 9-. 775. 3 7 .CO 10-S22487 .0-004863 7 2 r995.>7 4U .11, 34 16 9-I73C7C 8 112 .0-8-.6930 9-177941 8,,, 10-822058 ■0-C04873 8 3 9-995127 u '.:(; 30 le 9''734''9 H .26 10-R26;,, 9-17837. 9.29 loll'.lci 10004S82 B 3 ,■995.18 42 ;ii. 35 211 22 9-173908 10 ,40 10-826002 9-, 78799 "» '43 10-C04892 10 3 11 4 ■)-995ioS 40 •25 TT^ilB > .4 ■0-825674 9, 79227 I ,4 108207:3 10C0490) 9'995':99 3« 2^ 9''74"-h| 2 i8 ,0-825256 9-179655 ; 2 28 .0-820345 ■ 0-C0491 , 12 4 9-995089 JO •24 30 2a 9.75.6,1.-. 4, ,0-824839 9-, 80082 3 43 ,0-8,9918 ,0-004920 13 4 9-995080 M : .0-820687 9-184350 3 42 .0-8.56:0 ■ 0-0050^6 23 7 9-994984 u 30 43 48 9-. 79726 4 55 .0-8202-4 9-. 84752 * 56 .0-8.5248 ■ 0-005026 24 8 9-994974 12 Itl 30 50 9-1S0139 5 69 10-81986, 9-. 85175 5 70 .0-8.4825 ,0-005036 25 8 9-994964 10 311 43 32 9-1805^ 6 82 ,0-819449 9-185597 « »4 .0- 8, 440 3 10-005045 26 8 9'994955 g 17 30 54 9-180963 7 96 10-8,9037 9-.86o,8 j 7 98 ,0-8139.82 10-005055 27 9 9'994945 e 44 5S 9-. 8. 374; 8 MO ,0-8,8626 9-.S6439I 8 113 .0-S.356. ■0-C05065 28 9 9-994935 .1 IG 30 5S 9-.8.7S5: 9 .24 ,0-8,82,5 9-186860 1 9 127 ■0-8,3.40 ■ 0-C05075 29 9 9-994925 2 311 4S 3U 35 9-. 82. 96 in ,,7 10-S17S04 9-1S7280 10 141 ,0-812720 ,0-005084 30 10 9-9949,6 25 15 9-.826C6, 1 ,4 10-S17394 9-187700 1 14 ,0-812300 ,0005094 1 9-994906 4(1 4 9-.8;o,6 2 27 10-8.6984 9-i88,20 a 28 ■0-8, ,880 10-005104 2 I 9-9,4896 5li 14 30 e 9-183425 3 4. 10-8,6575 9-18S539 3 42 .0-8.146, 10-005113 3 I 9-9948S7 54 30 47 e 9-.83SU * 54 10-8,6166 9-188958 4 56 ,0-81,042 ■ o-oo5^23 4 , 9^994877 52 13 10 9-184243 5 68 10-8,5757 9-189376 6 70 ■0-8,0624 ■ 0-005133 5 2 9-994S67 50 30 48 12 9. 8465. « 82 .0-3.534, 9-189794 « 84 ,0-8,0206 10-C05143 6 2 9'994857 ■ 8 12 30 II 9-. 85059 7 95 1.0-8.494. 1 9-1902.2 7 98 .0-809788 10-005153 7 2 9-994847 40 30 4» 10 9-. 85466 8 .09 .0-8.4534I 9-190629 8 I,. .0-80937, .0-C05162 8 3 9-9,4838 J4 1 1 30 19 9-. 858^4 9 122 .0-8,4,26 9-191046 9 125 .0-808954 ,0-005,72 « 3 9-994828 n 30 50 30 20 9-186280IO 136 ,0-8,3720 9-191462 10 .39 .0-808538 ,0-005,82 10 3 9-994«.8 38 10 9-.866K6 1 ,3 108133.4 9-i9'S78 1 14 ■O-808,22 10-00519; ,-9948oS Al 24 9-187092, 2 27 .0-8,2908 9. 92294 2 28 .0-807706 10-005202 12 4 9-99479S 36 !» 30 m 9-. 8749*' 3 40 .0-8,2502 ,■.92709 3 41 .0-807291 ,0-00521, 13 4 ,-,94789 34 30 S2 28 9-.879=-!| « H ,0-8.2097 9. 93124 « 55 10-806876 10-00522, '4 5 9"99477'/ .12 8 30 30 9-.883r.8, S 67 10-81,692 9->93539 5 69 0-80646. 10-005231 15 5 9-994769 ,10 311 S3 32 9-.887.2 6 8, ,o-S,,28S 9''93953 6 83 0-806047 10-C05241 16 5 9'99475'.- 28 7 in 31 9-. 89. .6 7 94 .08.0884 9-194367 7 97 0-S05633 10-00525, 17 6 9"994749 20 311 54 3(1 9-. 89';. 9 8io8j .0-8,048, 9-194780 S 110 0-805220 10-C05261 18 6 9'994739 24 C 30 is 9-. 899231 9 .2. .0-8,0077 9 195193 9 124 0804807 ■0-005271 19 6 9-9,4729 22 .311 nr, 40 9-. 90325"' 115 ,0-809675 9-195606 10 ,38 0-804394 10-005280 20 7 9-99472C 20 6 30 il 9-190728 1 13 ,0-809272 91960, 8 I 14 0-803982 10-005290 21 7 9-9,47 ic 18 30 M 14 9-.9"3o| ■> 17 ,0-808870 9-. 96430 3 27 0-803570 10-005300 22 7 9-99470C 10 4 3(1 10 9-19. 5321 3 40 ,0-808468 9-. 96842 3 4, 0-803,58 ,0-0053,0 23 8 9-99469C 1.1 311 57 It 9-19.933 * 53 ,0-808067 9-197253 * 55 0-802747 0-005320 24 8 9-994680 12 3 30 50 9-I92334 S 67 0-807666 9-. 97664 8 68 0-802336 0-005330 ad 8 9-99467C III 311 8R 52 9-192734 « 80 10-807266 9-198074 6 82 0-801926 0-005340 2fl 9 9-99466C 4 2 M 54 9-. 93134 7 93 0-806865 9- 198484 7 96 0-80.5, 6 0-005350 27 9 9-99465^ 1; 3« 5<> 50 9"'93534 8 107 .0-806466 9-198894 8 109 o-So,,o6 c-005360 28 9 5-99464' 1 1 30 5S 9-'93933 9 120 0-806067 9, 99304 9123 0-8CP096 29 10 9'99463<; ■1 .11 fiO »6 9'. 94332 133 10-805668 9M997i3_ Cotang. 137 0-8C02S7 o-co5t8o •10.O19-99462' m. n ^l¥l Coirine Part* Secant Parts Tangz-nt Co^-or. ,, 1 ' ^1 81^-' ft" 24" 75(5 ABLK 08 LOCJ. SINES, COSINES, ii ■. O'' :JU"' y^ 1 '^ m Sine Parts Cosec. .0-80566!, Tangent 1 Pai-tsI Cotang. Secant Parti Cosine ^1- 24J till ~~n 9->9433 9-199715 I10-8CC287 ,0-00538 3 9-99462C :ii •2 9-19473 1" .3 .0-805265 9-2C012, 1" 13 .0-799879 ,0-00539 ^ 1" 9-9946, L 58 1 30 1 4 9-19512 2 26 .0-80487 9-2C0529 2 27 .0-79947 .0-C0540 n 2 , 9-994600 50 JS'J 30 U 9''9552 3 39 .0-804473 9-200937 3 4c .0-799063 .0-0054,01 3 1 9-994590 54 2 a 9-1959; 4 52 .0-804075 9-201345 4 54 ,0-798655 .0-CO542 . 4 1 9-994580 52 6H M 10 9-196322 5 65 .0-803678 9-20,752 5 67 .0-79S248 .0-005430I 5 2 9-994570 50 3(i 3 i-i 9-196715 6 79 .0-803281 9-202159 e 8, ■0-79784, .0-00544 . 6 2 9-994560 48 57 3li H 9-197115 7 92 10-802885 9-202565 7 94 ■0-797435 .0-C05450I 7 2 9-994550 11 :!(i 4 Id 9-19751 8 105 .0-802489 9-202971 8 ,08 ,0-797029 ,0-00546 8 3 9-994540 44 hi; 30 in 9-197907 9 ..8 10-802093 9-203377 9 121 ,0-796623 .0-C0547 9 3 9-994530 42 :o 30 22 9-198302 10 131 11 .44 .0-801698 9-203782 10 ,34 11 148 ,0-7962,8 ,0-00548 10 3 11 4 9-9945.9 10 S.-) 30 9-198697 ,0-801303 9-2041S8 ,0- 797811 ,o-co549 9-994509 e ■u 9-199091 12 .57 10-800909 9-204592 12 161 ,0-795408 ,0-00550 12 4 9-994499 30 44 30 26 9-. 99486 13 170 10-8005.4 9-204996 13 175 .0-795004 ,0-0055, 13 4 9-994489 34 311 7 28 9-199879 14 .83 .0-800.21 9-205400 14 ,88 .0-794600 .0-00552 14 5 9-994479 32 b'i 30 30 9-200273 15 .97 10-799727 <,-20!,8o4 15 20, ,0-794.96 10-00553 15 5 9-994469 30 30 fl 32 9-200666 16 2.0 10-799334 9-206207 162,5 ,0-793793 ,0-00554 16 5 9-994459 •28 52 30 M 9-201059 17 113 .0-798941 9-206610 17229 ,0-793390 ,0-005552 17 6 9-994448 2I> 311 30 9-201451 ,«236 10-798549 9-207013 18 242 ,0-792987 ,0-005562 18 6 9-994438 24 51 30 38 9-201843 19249 .0-798.57 9-207415 19255 ,0-792585 ,0-005572 19 6 9-99^428 22 30 -L*l_ JO 9-202234 20262 21 275 10-797766 9-207817 20269 21 282 ,0-792,83 ,0-005582 20 7 9-9944.8 20 50 9-202626 ■0-797374 9-2082,8 ,0-79,782 ,0-005592 9-994408 11 4J 9-203017 22288 .0-7969S3 9-2086.9 22295 ,0-79,38. ,0-005602 22 7 9-994398 10 4!* 30 40 9-203407 23 301 10-796593 9-209020 23 309 ,0-790980 ,0-0056,3 23 8 9-994387 14 30 12 48 9-203797 24 315 .0-796203 9-209420 24 323 ,0-790580 ,0-005623 24 8 9-994377 12 4(1 30 50 9-204187 25328 10-795813 9-209820 25336 ,0-790180 ,0-005633 25 8 9-994367 10 30 13 52 9-204577 2634, .0-795423 9-2,0220 26350 ,0-789780 ,0-005643126 9 ,0-005654127 9 9-994357 8 ■fl 3U 54 9-204.966 27 354 .0-795034 9-2,06,9 27363 ,o-78938i 9-994346 30 14 50 9-205354 28367 10-794646 9-2,1018 28376 ,0-788982 ,0-005664 28 9 9-994336 4 4(i 30 58 9-205743 29380 10-794257 9-2114,7 29390 10-78S583 ,0-005674 29,0 9-994326 2 30 15 30 37 9-206131 30393 10-793869 9-2118,5 30 403 10-788,85 ,0-005684 30 ,0 9-994316 23 45 30 9-206519 ' '3 10-793481 '•il'el' I '3 10-7S7787 ,0-005695 1 9-994305 16 4 9-206906 2 25 10-793094 2 26 ,0-787389 ,0-005705 2 , 9-994295 50 44 30 B 9-207293 3 38 10-792707 9-2,3008 3 39 ,0-786092 ,0-0057.5 3 1 9-994285 .51 30 "7 8 9207679 4 51 10-792321 9-2,3405 4 52 ,0-786595 ,0-005726 4 1 9-994274 52 43 3(1 10 9 208066 5 64 10-79,934 9-2,3802 5 65 ,0-786,98 ,0-005736 5 2 9 994264 50 30 18 12 9-208452 6 76 10-791548 9-2,4198 6 79 ,0-785802 10-005746 6 2 9-994254 48 42 30 14 9-208837 7 89 10-791,63 9-2,4594 7 92 .0-785406 10-005757 7 2 9-994243 40 30 19 10 9-209222 8 102 10-790778 9-2,4989 8,05 10-785011 10-005767 8 3 9-994233 44 41 30 18 9-209607 9115 10-790393 9-2.5385 9 ,,8 10-7846,5 10-005777 9 3 9-994223 42 30 20 20 9-209992 127 10-790008 9-2,5780 10,31 ,0-784220 10-005788 10 3 9-994212 40 40 30 22 9-210376 1 140 10-789624 9-2,6,74 11 144 .0-783826 10-005798 11 4 9-994202 38 M 31 24 9-210760 2 153 0-789240 9-2,65'8 2 157 .0-783432 ,0-005809 12 4 9-994,91 36 39 30 20 9-211143 3 .66 9-216962 ,0-783038 ,0-0058,9 13 4 9-994,8, 34 3(. 22 23 9-2.1526 4 .78 0-788474 9-2,7356 4 ,83 10-782644 ,0-005829 >■» 5 9' »94i7. 32 38 30 30 9-21.909 5 .9, 0-78809, 9-2,7749 5,96 ,0-005840 15 5 9 •'94,60 30 30 23 32 9-212291 6 204 0-787709 9-218142 fi 210 .0-78,858 ,0-0058,0 16 5 9-994.50 28 37 30 34 9-212674 7217 0-787326 9-2,8554 7 223 ,0-78,466 ,0-00586, 17 6 9-994,39 -20 24 30 9-213055 8229 0-786945 9-2,8926 8236 ,0-78,074 ,0-005871 18 6 j-994,29 24 36 30 38 9-213437 9242 0-786563 9-2, 9j, 8 9 249 ,0-780682 .0-005882 19 6 }-994"8 -22 30 25 40 9-213818 0255 1 26S 0-786182 9-2,97,0 O262 1 275 ,0-780290 10-005892 20 7 21 7 r 994^08 18 35 9-2.4.98 0-7^-802 9-220,0, 0-779899 10-005903 ^-994097 2(1 41 9-2.4579' •2280 0-785+21 9-220492 2288 0-779508 10-005913 22 7 ■994087 10 34 30 40 9-214959' 3293 0-78504. 9-220882 330, 0-779,18 10-005924 23 8 -994076 14 30 27 48 9-2.5338' 4 306 0-84662 9-22,272 4 3.4 0-778728 10-005934 24 8 -994066 12 33 30 .10 9-2.57.8' 53,9 0-784282 9-22,662 5327 0-778338 ,0-005945 25 8 ■994055 10 30 28 52 9-2.6097' 633, 0-783903 9-222052 6341 0-777948 ,0-005955 26 9 c •994045 8 32 30 51 9-216475' 7344 0-783525 9-222441 7354 0-777559 ,0-005966 27 9 t ■994034 30 2fl 50 9-2168545 « 357 0-783146 9-222830 8367 0-777170 ,0-005976 28 10 c ■994024 4 31 30 58 9-2.72322 9 370 0-782768 9-223218 9380 0-776782 10-005987 29 10 •9940,3 2 30 30 aa 9-2176093 0382 0-782391 9-223607 393 0-776393 10-005997 30,0 5 -994003 30 ' " " Cosine Parts Secant Cotsng^ Parts Tangent Cosec. Parts Sine ■^1 ~7r TABLK GH 767 LOG. SINES, COSINES, &c. ] 0" 38- r 1 /// ^ Sin. IPart. Cowc. TaiiKent Parts f-Qtang. Secant Parts ' Cosine '^ 3(1 ■ii~ 9-J>76=9 .0-78239. 9-223607 .0-776393 .0C05997 19-994003 Z2 M ■2 9-^.7987 •" .2 10-7820.3 9-2239,4 '" '3 . 0^776006 ,o-oo6co8 9-993992 58 31) 31 4 9-118363 2 ^5 .0-8.637 ,-224382 2 25 .0-7756.8 10-0060, 8 2 , 9-993982 .■iO •Ji) 30 n 9-^'874o!3 37 10-78.260 9-224769 3 38 1077523. ,0-006029 3 , ,•,,3,7. 54 .111 ;k « 9-2,9116 4 50 .0-780884 9-225,56 4 5. 10-774844 ,0-006040 4 , 9-993960 5'2 2» 30 10 9-219492 5 62 .0-780508 9-125543 5 64 10-774457 ,0-006050 5 2 9-993950 50 30 J3 i-i 9-2.9868 6 74 10-780132 9-225929 6 77 10-77407. .o-oc6c6i 6 2 9993939 48 27 3C II 9-220243 7 87 .0-779757 9-226315 7 ,0 .0-773685 ,0-006072 7 2 9-993928 46 30 34 ro 9-220618 R 99 .0-779382 9-226700 8 102 .0-773300 10-C06C82 R 3 9-9,3, .8 H 20 30 18 9-220993 9 ..2 .0-77,007 9-227086 9 ..5 .0-7729,4 10-006093 » 3 9-993907 42 30 M w 9-22,367|l« .24 .0-778633 9-22747' 10-772529 .o-oc6,o3 10 4 9-973897 40 1* 30 m 9-221741 11 136 .0-778259 9-227855 11 .40 ■0-772,45 ,"^c6,,4 11 4 9-993886 38 311 .'IP •21 9-2221 isll2 149 .0-777885 9-228239 12 ,53 ,0-77,76, 10-006,25 12 4 9993875 30 24 30 ■28 9-222488 13 .6. .0-7775.2 9-228623 13 ,66 ■0-77.377 10-006,36 13 5 9-993864 31 311 37 •28 9-212861 14 174 .0-777,3, 9-22,007 14 ,7, ,0-7709,3 .0-006,46 '-• 5 ■'-993854 3-2 23 30 30 9-223234 15 .86 .0-776756 9-229390 15 ,92 .0-770610 10-006157 15 5 9-993843 311 30 38 32 9-223606 16 .98 .0-776394 9-229773 16 204 10-770227 10006,68 16 6 9-993832 ■28 22 30 34 9-223978 172.1 .0-776022 9-230156 17 2,7 .0-769844 .0-006,78 17 6 9-99?«22 ■20 3(1 39 30 9-224349 18 223 .0-77565. 9-230539 18 230 .0-75946, 10-006,89 IR 6 9-993 <,. •il 21 30 38 9-224721 19236 .0-775279 9-23092, 19 243 10-76507, ,0-006200 19 7 9-993«oc t2 311 4» 12 9-225092 20248 21 26. .0-774908 9-231302 2025, 21 258 ,0-7686,8 10-0062, , 20 7 21 7 9-9-;3789 10 20 9-225462 .0-774538 9-23.684 ,0-7683,6 ,0-Oc622, 9 993779 41 41 9-225833 22273 10-774.67 9-232065 1-22 28, =0-767,35 ,0-006232 22 8 9-993768 IB I'J 31) 1« 9-226203 23 286 '0-773797 9-232446 23 2,4 ,0-767554 ,0-006243 23 8 9-993757 14 311 42 48 9226573 24 2,8 10-773427 9-232S26 24307 10-767-.74 IO-CC6254 24 9 9-993746 12 l» 30 50 9-226942 253,0 .0-773058 9-233206 V- 320 .0-766794 >o-co6265 25 9 9-993735 10 311 43 Si 9-227311 26323 .0-772689 9-233586 26 352 ,0-7664,4 .0-006275 2fi 9 9-993725 8 17 30 51 9-227680 27 335 .0-772320 9-233,66 « 345 ,0-766034 10-C06286 27.0 9-9937.4 6 3(1 44 50 9-228048 28348 .0-771,52 9-234345 28 358 .0-765655 .0-0062,7 2R,o 9-993703 4 IB 30 58 9-2284.6 29360 10-77.584 9-234724 29371 ,0-765275 10-006308 29,oj,-,9369,. 2 30 IL 39 9-228784 30372 9-235.03 30383 .0-764897 ,0-0063.9 30 ,1 9-99368. 21 58 15 9-229.5. 1 .2 .0-77084, ,-23548. 1 .2 .0-7645,, .0-006330 ~~0 9-993670 4i> 4 9-2295.8 a 24 10-7704S2 9-235859 2 25 ,0-764,4, .0-006340 2 1 9-993660 56 u 30 9-229885 3 j6 10-770. .5 9-236237 ■^ 37 ,0-763763 .0-00635, 3 I 9-993649 54 30 47 8 9-230252 4 48 .0-76,748 9-2366,4 ,0-763386 ,0-006362 4 1 9-993638 S-i 13 311 10 9-2306.8 5 60 .076,382 9-23699, 5 62 ,0-763009 ,0-006373 5 2 9-993627 50 3(1 w \-l 9-2309S4 6 73 . 0-7690, 6 9-23736S 6 75 ,0-762632 ,0-006384 6 2 9-993616 48 12 30 11 9-23.349 7 85 10-768651 9"237744 7 87 ,0-762256 .0-006395 7 3 ,■9,3605 40 3(1 4» ir, 9-23.7.5 8 97 ,0-768285 9-238.20 8 ,00 10-761880 .0-C06406 8 3 9 993 594 41 1 1 30 IS 9-232079 9 .09 10-76792. 9-238496 9 1,2 10-76,504 .o-oo64>7 9 3 9993583 12 30 ^ •20 9-232444 10 12. 11 .33 .0-767556 9-238872 10,25 U ,37 ,0-761,28 ,0-760753 ,0-006428 10 4 11 4 9-993572 38 10 9-232808 ■0-767.92 9-239247 ,0-006439 9-993561 r>i 2-1 9-233172 12 .45 .0-766828 9-239622 12 ,50 ,0-760378 10-006450 12 4 9-993550 36 .9 30 ■20 9'^33536 13 .57 .0-766464 9-239996 13 162 10-760C04 ,0-00646, 13 5 9-993539 34 3(1 5-1 !» 9-233899 .4.69 .0-766.0. 9-24037. 14 ,75 10-759629 0^006472 14 5 9-993528 32 n 30 9-234262 15 1?, .0-765738 9-240745 15 ,87 10-759255 0-006483 15 6 9-9935'7 30 30 .->.■: 3-2 9-234625 lfi,,3 ■0-765375 9-24.118 Ifi 2CO 10-758882 0-0064,4 16 6 9-993506 28 7 30 31 9-234987 17 206 , 0-7650.3 9-24.492 17 2,2 .0-758508 ,0-006505 '7 7 9-993495 20 30 .■14 Vi 9-235349 182:8 10-76465, 9-24.865 18 224 ,0-758.35 ,0-006516 18 7 9-993484 21 fl 30 38 9-2357.. 19 230 .0-764289 9-242238 19237 ,0-757762 0-006527 19 7 9-993473 ■22 3" ■zi- 40 9-236073 20242 21 254 .0-763,27 10-763566 9-2425,0 ,-242,82 20249 2) 26, 10-757390 10-006538 20 7 21 8 9-993462 20 30 9-236454 .0-7570,8 0-006549 9-99345' oh 41 9-2367SS 22 266 10-7632.-.5 9 •'433 54 22274 ,0-756645 0-006560 22 8 9-993440 10 4 311 IB 9-I37155 23 278 .0-762845 9-243726 23 2 85 .0-756274 0-C0657, 23 8 9-993429 11 :m .'•7 9-2375<5 24 290 .0-762485 9-24409- 24 299 10-755903 .0-006582 24 , 9-9934,8 12 3 ■'" 9-^7875 25 302 10-762.25 9-244458 253,, ,o^v5,552| ,0-006593 25 9 9-993407 10 3(1 o8 .V 9-2382352(5 314 .0-76.765 9-244839 25 323 10-755161I 0-006604 26 , 9-9,33,6 n 2 10 M 9-23859427 327 ,0-76.405 9-245209 27 336 10-75479, ,0-0066,5 27,0 9-993385 .30 .i!l jft 9-238953^8 3,8 .0-76.047 9-245579 28 348 10-75442, 0-006626 28,ol9„33-4 4 1 3.) 58 9-2393.229 35. .0-760688 9245949 29 35,110-754051 0-006637 29,, [,-,,3353 30 ,1 9-99335. 2 30 liO «o ,-23,67030 36, ,0-760330 9-2463.9 10 3-4:0-^3681 0-CC564, 1) "" ^ Cosine 1 Parts | Srrant CotanR. Parts 1 -ninKi.,,! | Co..,.. Parts S,.. "•?• TTT .. ^^^_ ^- , :,H .o-" j ?68 TABLK 68 LOG. SINES, CUSINKS, .V-. O'- 40"- 10^ T Im " "o Sine Parts Cosec. Tangent Part" Cotang. Secant Parts! Cosine ' SO till 9-23967 2 10-760330 9-2463,9 .0-7536S 10-CC6649I I9-99335. 3 31) 'i 9-24001 1" 12 10-759972 9-246688 I" 12 10-753312 .o-oo66bc l"o 19-9933401 1 J 9-24038 2 24 10-759614 9-247057 2 24 10-752943 10-00667 2 1 9-993329 56 59 3n o 9-24074^ 3 35 ,10-759256 9-247426 3 36 .0-752574 10-0066SJ 3 I 9-993318 54 30 2 8 924110 * 47 .0-758899 9-247794 4 49 .0-752206 .0-00669 4 2 9-993307 5-2 68 30 10 9-24145 5 59 .0-758542 9-24S162 5 6 10-75. 83S .0-C0670. 6 2 9-993296 M 30 3 l•^ 9-241814 6 71 10-758186 9-248530 6 73 10-751470 10-006716 6 2 9-993284 8 57 3(1 iJ 9-242170 7 83 10-757830 9-248897 7 85 .0-751,03 10-006727 7 3 9-993273 4 i8 9-257269 30365 .0-74273. ,0-006987 ^11 1 9-993013 1 9 43 30 9-250631 10-749369 9-257630 10-742370 .0^006998 9993002 h; ■1 9-250980 2 23 10-749020 9-257990 2 24 .0-742010 2 1 9 99299^ ^ 44 311 9-251329 3 34 10-748671 9-258350 3 36 .0-74.650 ,0-00702. 3 I 9-992979 ^ 30 17 8 9-251677 4 46 10-748323 9-2587.0 4 48 10-74,290 .0-007033 4 2 9992967 5 43 ■■' 10 9-252025 5 57 10-747975 9-259069 5 59 10-74093. ,0-007044 .S 2 9992956 i 30 IS li 9-252373 6 69 10-747627 9-259429 6 7. .0-740571 .0-007056 6 2 9-992944 4 42 an n 9-252720 7 80 10-747280 9-259787 7 83 .0-740213 .0-007067 ' 3 9992933 ■< 30 n i(i 9-253067 8 92 10-746933 9-260146 8 95 10739854 ,0-007079 8 3 9-992921 4 41 M IS 9-253414 9 103 10-7465S6 9-260504 9 107 ,0-739496 10-007090 9 3 9-992910 4 30 -1^ ■22 9-25376. ..5 1 126 .0-746239 9-260863 ,,9 11 13, ,0-739,37 10-007,02 10 4 11 4 9-99289S 4 -^ 9-254107 10-745893 9-261220 .0-738780 .0-C07.13 9-992887 38 •21 •2J 9-254453 2,38 i°-745547 9-26.578 2143 10-738422 .0-007125 12 5 9-992875 30 39 10 •ill 9-254799 3 149 0-745201 9-261935 3 155 10-738065 10-007156 13 5 9992864 34 30 •22 ■28 9-255144 4 161 0-744856 9-262292 4,67 10-73770S .0-007,48 14 5 9-992852 3-2 30 311 30 9-255490 5 ,72 0-744510 9-262649 5178 10-73735, 10-007159 15 6 9-992S41 30 30 23 32 9-255834 6 ,84 0-744166 9'263oo5 6 190 10-736995 0-007,71 16 6 J-992829 -28 37 30 34 9-256179 7195 0-743S21 9-263361 7 202 10-736639 0-007182 17 6 r9928.S -2(3 30 24 30 ;-256523 8207 0-743477 9-2637.7 82,4 0-7362S3 10-007194 18 7 ^992806 24 3(; 30 38 9-256867 9218 0-743.33 9-264073 9226 0-735927 0-007206 19 7 ^■992794 n 30 %6_ JO 4^2 9-257211 0230 1 241 0-742789 9-264428 O23S 1 250 0-735572 0-007217 20 8 21 8 r992783 20 3S 30 9-257554 0-742446 9-264783 0-735217 0-007229 ■992771 18 26 j 44 r257898' 2 253 0-742102 9-265.38 2262 0-734862 0-00724, 22 8 -992759 10 34 30 46 9-258241' 3264 0-741759 9-265493 3274 0-734507 0-007252 23 919-992748! H 30 ■21 48 9-258583' 4 276 0-7414.7 9-265847 4 28s 0-734.53 0-007265 24 9 9-992736 1 1-2 33 30 311 9-258926' .5287 0-741074 9-266201 5 297 0-733799 0-007276 25 10 ■99-724 10 30 •28 52 9-259268' 9-259609'- 6299 0-740732 9-266555 6309 0-733445 0-007287 26. -9927.3 » 32 30 54 7 310 0-740391 9-266908 732. 0-733092 0-007299 2710 •99270. 30 2U id 9-259951' 8322 0-740049 9-26726. 8333 0-732739 0-007310 28,1 -992690 4 31 311 58 9-260292' 9 33-. 0-739708 9-267614 B 345 0-732386 29II t -99267S -2 30 30 iZ 9-260633: 1345 0-739367 9-267967 3^7 10-732033 0-007334 30 12 9-992666 30 " \ m. Cosine Parts Secant CotHMS. Parts 1 Tan^'i-nt Cosec. Parts 1 Sine m TTT 7r 3iri „ " - 9 16065 .0-739367 9-267967 ,0-731033 IO-CC7334 9-991666 xa i«r 30 i 9j6c97q 1" 11 10-739026 9-2683.9 r' ,2 ,0-73,681 ,0-007346 l"o 9-991654 SH 91 ■\ 9-i6>3H 2 22 .0-738686 9-26867. 2 13 .0-73,319 ,0-007357 2 , 9-992643 J« 29 30 9-25.654 S 34 .0-738346 9-169023 3 35 ,0-730977 .0-007369 3 , 9-99263, M 32 a 9:61994 * 45 .0-738006 9-169375 4 46 ,0-730625 .0-00738, 4 1 9-9926,9 52 2H 30 10 9262334 5 56 .0-737666 9-169726 5 58 ,0-730174 ,0-007393 5 2 9-992607 50 30 33 u 9162673 67 10-737317 9-270077 6 70 ,0-719913 ,0-007404 6 2 9-992596 48 27 30 II 9-2630.2 7 78 10-736988 9-170428 7 8, ,0-729571 ,0-0074,6 7 3 9-992584 46 34 10 926335 8 90 .0-736649 9-170779 8 93 .0-71921. ,0-007418 8 3 9-991571 U 20 30 18 9-2636S, 9 Id .0-73631. 9-171.19 9 ,05 ,0-72887, ,0-007440 9 4 9-992560 42 30 3d "jo" M 9 264C27 10 112 11 .23 '0-735973 9-171479 11 128 ,0-72852, .0-C0745. 10 4 11 4 9-991549 40 25 9-264365 .0-735635 9-271829 .0-728,71 .0-007463 9-991537 36 J4 9-264703 IQ 135 10-735:97 9-272.78 12 ,39 10-717822 .0-007475 12 5 9-992525 36 24 30 •«> 9-265040 13 .46 .0-734960 9-272517 13 ,5, .0-727473 10-007487 13 5 9-992;, 3 34 3" 37 tu 9-265377 14 157 .0-734623 9-171876 14 ,62 .0-727.14 ,0-007499 14 6 9-991501 32 23 JO 30 9 2657.4 IS .68 .0-73+2S6 9-173115 15 .74 .0-726775 ,0-0075,, 15 6 9-992489 30 30 38 32 9-26605. 16 .79 .0-733949 9-173573 16 ,86 ,0-716417 ,0-007521 16 6 9-991478 28 22 30 34 9-2663S7I17 .91 ,0-7336.3 9-17391' 17 ,97 ,0-716079 ,0-007534 17 7 9-99^66 28 30 39 30 9266723 19 202 .0-733277 9-274269 18 109 ,0-72573, ,0007546 18 7 9-992454 2-1 21 30 38 9-267059 19213 10-732941 9-274617 19 21, 10-715383 ,0-007558 19 7 9-991441 •22 30 i!L 10 9-267395 20 224 21 Z36J .0-732605 9-274964 20 131 21 144 ,0-725036 ,0-007570 20 8 21 8 9-992430 20 18 20 9-267730 .o--i227o 9-275311 ,0-724688 ,0-007581 9-9924,8 ti n 9-268065 22 24 7 1 IO-73I935 9-175658 22156 .0-724342 ,0-007594 22 9 9-992406 16 I!) 3:1 U) 9-26S399 23258 10-731601 9-276005 23267 10-723995 ,0-007606 23 9 9991394 14 30 42 9-26g734;24 269| 10-73 i»66 9-17635. 04 279 .0-723649 ,0-0076,8 24 9 9-991381 12 18 31 iO 9-269068 25280 0-730931 9-176698 M190 .0-723302 ,0-007630 25,0 9-991370 10 30 43 ■ii 9-269402 26 292 0-730598 9-277043 26301 .0-722957 ,0-00764, 26,0 9-991359 8 17 30 .^J 9-269736 27303 0-730264 9-277389 27314 .0-7216,, ,0-007653 27,, 9-991347 6 30 44 36 9-270069 28315 0-729931 9-177734 28315 0-712166 .0-007665 28,1 9-991335 4 16 30 5S 9-270402 29326 0-729598 9-178079 29337 0-71192, .0-007677 29 , , 9-991323 2 30 ii- 43 9-^70735 30 3^ 0-729265 9-278424 30349 0-71.576 ,0-007689 30 ,2 9-991JI1 17 15 30 9-27.067 0-728933 9-178769 1 ,, 0-72,13, 0-00770, 1 0I9-991199 4fi 4 9-27.400 2 22 0-728600 9-179113 2 13 0-710887 ,0-007713 2 ,19-991187 36 14 30 « 9 99 0-726282 9-28,5.6 9 ,02 0-7,8484 ,0-007798 9 4 9-991102 42 30 .■)0 '^ 9-274049 10 no 11 121 o-:i595' 9-28,858 .0,.4 0-7,8.42 ,0-0078,0 10 4 11 4 9-992.90 38 10 3<1 9-174379 0-72561. 9-28220, 11 .15 0-7,7799 .0-007822 9-991178 51 U 9'i747oll 12 .32 0-725292 9-1S2542 12,36 0-717458 0-007834 12 5 9-991166 .36 ■i6 9-275038;i3 1421 0-724962 9-281884 13,48 0-7,7, ,6 0-007846 13 519-991154 34 30 : 0-007943 9 991057 ..<; II 9-27799'l*' 14> 1 0-722009 9-285947 22250 0-7,4053 o-oo''68 22 9 9-992044 10 4 30 >C 9-2783. S23 252! 0-72.682 9-2S6186 23 16, 0-7,37,4 23 9 9991031 14 30 ■■>7 48 9-278645 24263 °-7ii3;5 9-1S6614 24 173 0-7,3376 0-C07980 24 10 9-99:020 12 a 3'1 30 9278971 M174 0711019 9-186963 2S 284 0-713037 0-007992 25 ,0 9-99:008 10 30 5H li 9-279297 M285 o'7i0703 9-18730, 28295 0-7,1699 oco8cc4i26,o 9-991996 8 2 10 ^^ 9-179623 27296 0-710377 9-187639 27 307 0-7,136, 0-cc8c,7j27,. 9-99'983 „ 30 v.) i« 9-279948 Mjc; 0-710052 9-187977 28 3,8 0-7,1023 o-oc8o29|28., 9-99.97, 4 1 30 5>< 9 18.-.274W ;i8i c-7.9726 9-1883,5 [29 33^^ 0-7. ,685 0-008041; 29 ,2 9 99'95' 2 n<> 4« 9-28o599i-«> 319 ! 0-7.94CI 9- 2886, 2 JSO 34. 1 0-7,, 348 i->-oc8o5j 30 ,2 Cc-fc. ' Parr- 9991947 TTT m f:.,.,n. I'^n- Se^rt ( ,.-,.n«. y,n> ; T»nsrn» | Sme ml .._ . .__. 760 TABLE 68 LOU. SINES, COSINES, &c. Oh 44- 11° T -° Sine Parts Cosec. Tangent | Parts Cotang. Secant | Part Cosine as 1^ 9-iS059 10-71940 9-288652 10711348 .0-008053 , 9' 99 ■ 947 •i 9-Z80922 1" II 10-719076 9-288989 1" 1 1C-71101, 10-0080661 l"c 999 '934 .30 1 J 9-.8..4 S 21 10-718752 9-289326 2 22 10-710674 .0-008078 2 I 9-99.922 .50 o'J :w u 9-28157 3 32 10-718427 9-289663 3 33 ,0-7.0337 0-00809C 3 I 9-991910 51 30 2 8 '■'sLic * 43 .0-7.8.03 9-289999 4 44 o-ooS.o 4 2 9-99,897 52 58 3U III 5 53 .0-7177S0 9-290335 5 56 ,0-709665 0-008.15 5 2 9-90.885 50 30 :t 1-2 9-282544 6 64 10-717456 9-29067, 6 67 10-709329 0-008,27 6 2 9-99,873 48 '>! .id IJ 9-282867 7 75 .0-7.7133 9-291007 7 78 10-708993 0-008140 7 3 9-90,^60 46 30 4 Iti 9-28319C 8 86 9-791342 8 89 .0-708658 0-008,52 8 : 999 .848 44 56 31) IK 9-283513 9 96 10-7164S7 9-291678 9 100I.0-708322I 0-008,64 9 4 9-99.836 4-2 30 5 •10 9-2S3836 10 io7]io-7i6i64 9-292013 10 111 10-707987 10 4 9199 '82 3 41) S« ■M T2 9-2S4.58 11 iiS .0-715S47 9-292347 11 122 .0-707653 0-008189 11 5 9-99,8,, 38 3,< G il 9-284480 12 12S .0-7.5520 9-292682 12 ,33 .0-7073,8 0-008201 12 5 9-99i79q 30 54 :tn ie 9-284802 13 ,39 .0-7.5.98 9-293016 13 145 .0-706984 0-0082,4 13 5 999.780 34 .10 7 is 9-285124 14 ,50 .0-7.4S76 9-293350 14 ,56 .0-706650 0-00S226 14 6 9-99'774 32 53 30 30 9-285445 15 160 .0-714555 9-2936S4 15 ,67 .0-706316 0-00S239 15 6 9-99176, 30 30 8 32 9-285766 16 17, .0-7.4234 9-2940.7 16 17S .0-705983 . 0-00825, 16 7 9-991749 -28 52 :iii 3^ 9-2S6087 17 182 .0-7139,3 9-294351 17 189 .0-705649 . 0-008264 17 7 9 99.736 -20 30 » 30 9-286408 18 ,93 ■0-7.3592 9-294684 18 200 .0-705316 . 0-008276 18 7 9-99.724 24 51 :» 38 9-286728 19 203 .0-7,3272 9-295016 19 211 .0-704984 . 0-008288 19 8 9-99.7.2 -2'2 30 10 40 9-287048 202,4 21 225 .0-712952 9-295349 20 222 21 233 .0-70465, . 0-008301 20 8 21 9 9^91699 9-99,687 -20 50 9-287368 .0-7,2632 9-295681 .0-7043 ■- I 0-C08313 II 4-1 9-287688 2-2 235 .0-7.2312 9-296013 22245 .0-703987 . 0-008326 22 9 9-991674 U! 49 :)(! 40 9-288007 23 2+6 .0-71.993 9-296345 23256 .0-703655 . 0-008338 23 10 9-99.662 14 30 12 48 9-288326 24 257 .0-71,674 9-296677 24 267 10-703323 1 0-008351 24 ,0 9-991649 1-2 48 jii 50 9-288645 26267 .0-71.355 9-297008 25278 10-702992 1 0-008363 25 10 999,637 10 30 13 32 9-2S8964 26 278 10-711036 9-297339 26 289 10-702661 1 0-008376 26 11 9-99.624 8 47 ;iij 51 9-289282 27289 10-710718 9-297670 27 300 10-702330 1 0-008388 27 1, 9-99.6.2 311 U 5B 9-289600 28 300 10-710400 9-29S001 2831, 10-701999 I 0-00840, 28,2 9-991599 4 4« jii 58 9-289918 293.0 .0-7,0082 9-298332 29322 10-70,668 . 3-008414 29 12 9-99.586 2 30 la 45 9-290236 3032, 10-709764 9-298662 SG334 .0-701338 1 .-008426 30 12 9'99.574 15 58 45 30 9290553 I 10 10-709447 9-298992 10-701008 I rco8439 I 9-99156, IC 4 9-290870 2 21 ,0-709,30 9-299322 2 22 10-700678 1 .-008451 2 I 9-991549 50 44 au 6 9-2911S7 3 3. ,0-7088,3 9-299651 3 33 10-700349 1 .-008464 3 I 9-99,536 51 30 17 8 9-291504 4 42 10-708496 9-299980 4 44 .0-700020 . .•008476 4 2 9-991524 5-2 4.-} M III 9-29.820 5 52 ,0-708180 9-300309 5 54 .0-699691 1 .-008489 5 2 9991511 50 311 18 12 9-292137 6 63 ,0-707863 9-300638 fi 65 10-699362 . .-008502 6 3 9-99149S 48 42 30 It 9-192453 7 73 10-707547 9-300967 7 76 10-699033 1 3-008514 7 3 9-991486 40 30 19 10 9-292768 8 84 .c-707232 9-30,295 8 87 10-698705 I .•008527 8 3 9-991473 44 41 .III IS 9-2930S4 9 94 ,0-706916 9-30,624 9 98 .0-698376 . .-008540 9 4 9-991460 42 30 -':) •22 9-293399 .05 1 1.5 ,0-706601 9-30,95, 109 1 120 10-698049 . .-008552 19 4 11 5 9-991448 10 ii_ 9-293714 10-706286 9-302279 10-69772, . .-008565 9'99>435 21 ■24 9-294029 2 .26 ,0-70597. 9-302607 213, .0-697393 ! -008578 12 5 9-991422 30 M JO ■20 9-294344 3 i;6 0-705656 9-302934 3 142 10-697066 1 -008590 13 6 9-991410 34 311 .'2 ■28 9-294658 4 .47 0-705342 9-30326, 4 153 .0-696739 1 .-008603 14 6 9-991397 32 38 .11) 30 ;-294972 5 ,57 0-705028 9-303588 5,63 10-6964.2 1 -0086,6 15 6 9991384 30 30 •-•:» 32 9-295286 6 .68 0-7047,4 9-3039,4 6 174 10-696086 I -008628 16 7 9-991372 28 ■il .<« 31 9-295600 7 .78 0-704400 9-30424. 7 ,8; 10-695759 1 -008641 17 7 9-991359 20 30 24 30 9-295913 8 .88 0-704087 9-304567 8196 ,0-695433 , -00S654 18 8 9-991346 -24 30 .11 3H 9-296226 9.99 0-703774 9304893 9 207 ,0-695,07 ,c -00S667 19 8 9-99'333 -22 30 ■J.i 40 9-296539 20g 1 220 C-703461 9-305218 1 229 ,0-694782 ,c -008679 20 8 21 9 9-99.32I 20 -»5 30 9-296852 0-703,48 9-3°5544 ,0-694456 1 -008692 9-991308 ■J(i 41 9-297164 2230 0-702836 9-305869 2240 ,0-694.3. .c -008705 22.9 9-991295 16 34 .111 40 9-297476 3241 0-702524 9-306194 325, ,0-693806 IC -008718 23 10 9-991282 14 30 •-'7 4R 9-297788 4 251 0-7022,2 9-3065,9 4 262 .0-69348, IC -.008730 24 10 9-991270 1-2 33 11 ■io 9-298100 5 262 0-701900 9-306843 5 272 10-693,57 , -008743 2511 9-991257 10 30 '211 .1-2 9-29S412 fi 272 0-70,588 9-307168 6283 ,0-692832 ,c -008756 26 11 9-991244 n 32 .11 .11 9-298723 7283 0-701277 9-307492 7 294 ,0-692508 1 •008769 27 11 9-991231 30 2!) .50 9-299034 8293 0-700966 9-307816 8 305 10-692,84 . -C0S782 28 12 9-99121S 4 31 .Ill 5H 9-299545 9304 0-700655 9-308.39 93.6 ■0-69,86, , -008794 29,2 9-991206 2 30 :tii ^ 9-299655 1) 314 0-700345 9-308463 03271 ■0-691537 . -008807 a" .3 9-991193 30 '// m. Co.sine Piirt.-! Sn-ant Cntan-. | Parts Tangint Cosec. Parts Sine ^l"1 7s- :^ i.»- 1 TA11M-: 08 7f)l l,{)U. SINKS. COSINKS, Sec. 1 0" 41;"- 11" ' \ ''~' «? Sine 1 Parts | Cosec. Tanient Part* Coung. Secant Parts Cosine m I'" *r ;--9965 ■ 5 10-700345 9-308463 .0-69.537 ,0-008807 9-99,193 I¥| mT I .to 9 '-9996 6 1" 10 ■0-700034 9-308-86 1" I. .0-69,2.4 .0-008820 T'o 9-9911 So 3(1 31 9 l^-'Oi? 6 2 21 10-699724 9-309,09 2 21 .0-69089, 10-008833 2 . 9-99,167 sr ■-'!! 30 9 JC058 5 3 3. 10-699414 9-309432 3 32 ,0-690568 .0-008846 3 I 9-991.54 51 .Ill 32 9 30089 5 4 41 10-699105 9'3'--97 54 ♦ 43 ,0-690246 ,0-008859 4 2 9-99114, 5-2 28 30 10 9 30120 5 5. 10-698795 9-310076 5 53 ,0-689924 ,0-008872 5 2 9-991.28 50 30 33 1-2 9 ,0151 , 6 6, 10-698486 9-3. 0399 6 64 ,0-68960, ,0-008885 6 3 9-9911.5 4H ■27 30 U 9 3'- 8* 7 7. .0-698.77 9-310720 7 75 10-689280 ,0-008897 7 3 9-991.03 40 30 34 III 9^302i3 8 82 10-697868 9- 3.. 042 8 85 .0-688958 .0-0089.0 8 3 9-99.090 44 •-•(i 30 IS 9-30244 9 92 10-697560 9-31,364 9 96 .0-688636 .0-008923 9 4 9-99.077 42 30 as 20 9-30J-4 10 102 11 113 .0-697252 9-31.685 in icj II ,,7 .0-6883.5 .0-687994 .0-008936 10 4 " 5 9-99. C64 40 25 930305 10-696943 9-312C06 .0-C08949 9-99.05, 36 947 •22 30 40 40 9-305819 20205 21 215 .0-694,8, 9-3.4885 20213 21 224 .C-685..5 .0-009066 20 9 21 9 9-990934 •20 IR 20 30 -^\u 9-306125 .0693875 9-3.5204 .0-684796 .0-009079 9-990921 *\, • ■" 9-306430 22225 .0-693570 9-3'55^3 22235 ,0-684477 .0-009092 22 10 9990908 10 19 JO 9-306736 2373; ,0-693264 9-31584. 23 245 .0-684.59 .0-009105 23 .0 9-990895 U 30 42 4S 9-307041 24 245 ,0-692959 9-3,6,59 24 256 10-683841 .0-009.18 24 .0 9-990882 12 18 30 50 9-307346 25 256 ,0-692654 9-316477 25 267 1.0-683523 .0-009,32 25.1 9-990868 10 30 43 5i 9-307650 26266 ,0-692350 9-3,6795 26 277 '0-683205 .0-009,45 26 I, 9-990855 f, 17 30 54 9-30795^ 27276 10-692045 9-3. 7. .3 27 288I10-682887 ,0-009,58 27,2 9-990842 r, •■in 44 .W 9-308259 28 286 .0-69,74, 9-317430 28 299 10-6S2570 .0-009,71 28 ,2 9-990829 t III :ui ."iH 9-308563 29 207 10-69I437 9-3.7747129309 .0-6C2253 io^oc9i84 29,3 9-9908,6 2 .10 45 30 «7 9-308867 30 3C7 ,o-69,i33 ,0-690830 9-3,8064 9-3-«38. 30 320 .0-68,936 10^009,97 .30,3 9-990803 13 1.-. 9-309170 1 10 1 10 .0-68.6.9 ,0^0092,0 ! 9-990790 4R 4 9-309474 2 20 ,o-690526 9-3.8697 2 21 .0-68,303 10-009223 2 I 9-990777 .10 14 .» 6 9'309777 3 30 ,0-690223 9-3.9013 3 3, ,0-680987 .0-009237 3 1 9-990763 54 30 47 a 9-310080 4 40 .0-6S9020 9-3.9330 4 42 ,0-680670 .0-009250 4 2 9-990750 52 13 .10 10 9-310382 5 50 io-6S96,8 9-3,9645 5 52 .0-680355 .0-009263 5 2 9-990737 50 .10 48 1-2 9-31068; 6 60 ,0-6893,5 9-3-996. 6 63 .0-680039 ,0-009276 6 3 9-990724 48 12 30 II 9-31C987 7 70 ,0-6890,3 9-320277 7 73 ,0-679723 ,0-009289 7 3 9-9907.. 40 ..0 ^'lo 111 9-3"j89 8 80 ,0-6887,. 9-320592 8 84 ,0-679408 ,0-009303 8 4 9-990697 44 1 1 IH 93'iS9' 9 90 .0-688409 9-320907 9 94 ,0-679093 ,0-0093,6 9-990684 42 30 .30 •20 9-311893 II 110 ,0-688,07 9-32.222 10 ,04 II ,,5 ,0-678778 .0-009329 10 4 " 5 9-99067, ■w in ^TIT?I 10-687S06 9-32.536 ,0-678464 '0-009342 9-990658 .M 51 9-312495 12 120 ,0687505 9-3^i8;i 12 ,25 ,0-678.49 ,0-009355 12 5 9-990645 30 9 30 ■20 9-3'^796 13 13c .0-687204 9 322165 U .36 .0-677835 ,0-009369 13 6 9-99063, 34 .1.1 S2 ■2.S 9-313097 14 >40 ,0-686903 9-3-M79 14 146 .0-677521 ,0-009382 14 6 5-9906,8 32 8 .30 .30 9313397 15 150 0-686603 9-322793 5 .57 .0-677207 .0-009395 15 7 5990605 30 311 .53 .r2 9-313698 6 .60 0-686302 9-323. c6 i; .67 .0-676894 .0-009409 16 7 5-99059, 2-1 7 3n 31 9-313998 7 170 0-686C02 9-323420 7 .78 ,0-676580 .0-009422 17 8 5-990578 2(1 30 .-.4 .«1 9-314297 8 180 0-685703 9-323733 8 ,88 ,0-676267 .0-009435 18 8 5-990565 24 .1 .30 -.IK 9-314^9" 9 190 0-685403 9-324046 9 ,99 ,0-675954 .0-009449 19 8 5-990552 22 m M n 9 31489- 20 2C0 21 210 0-685,03 0684804 9-324358 20 209 21 219 ,0-675642 0-C09462 20 9 21 9 5-990518 20 ~ 9315196 9-324671 0-675329 0-009475 5-990525 r>r, 41 931549: 22 220 0-684505 9-324983 22 230 0-6750,7 0-009489 2210 5-9905,, 10 4 .30 III 9-31';793 23 230 0-684207 9-3-5295 23 240 0-674705 0-CO9502 23 ,0 5-990498 14 .•111 S7 lu 9-316092 24240 c-683908 9-325607 24 25, 0-674393 0-009515 24,1 9-990485 12 3 30 50 9- -1639c 25250 c-6836,0 9-3259.9 5 26. 0-67408, 0^009529 25,, 9-99°47' 10 30 .^n .52 ,•3.6689 26260 c-6833., 9-3262;. 86 272 0-673769 0-CC9542 26,2 9-990458 » 2 :in 1 51 /316986 2727c 0-6830.4 9-326542 |27 282 0-673458 0-009555 27,2 9-990445 .01 ■■••■> \ '« 9-317284 28 280 0-6827,6 9-3268531282^3 0-673.47 0-009569 28, 2 19-99043. 1 1 .3,. I .-,. 1 9-317582 2929c 06824.8 9-327.64 29 303 .0-6728361 C-OC9582 29.3|9-99C'4'8 2 311 >-^< i»alrii7879 OJCO 0-682,2, 9-127475 |30 313 .0-672525 0-009596 301519-990404 -^'-|n,:| („.„.] P«rt," S,-.-anl Cotoiig. 1 Parts Tancent | C.-.c.-. Part;.' y .5S 30 1 4 9-51847 2 20 .0-68, 527 9-3*8095 2 20 .0-671905 0-C09622 2 , 9-99037.^ 56 .'.9 30 C 9-3.876 3 29 .0-68,23. 9-328405 3 3, ,0-67,595 0-009636 4 1 9-990364 54 30 2 8 9-3.906 ♦ 39 .0-680934 9-328715 4 4, ,0-67.285 0-009649 4 2 9-990351 52 58 30 9-3.936 5 49 ,0-680638 9-329025 5 5, .0-670975 c-009663 8 2 9-99033: 50 30 3 [i 9"3'9*';S 6 59 ,0-680342 9-3*9334 6 6, .0-670666 0-009676 6 3 9-990324 48 57 30 N 9-3'995'l 7 69 .0-680046 9-329644 7 72 .0670356 0-009690 7 3 9-9903. c 48 30 4 16 9-310240 8 78 ,0-67975. 9-3*9953 8 82 .0-670047 0-009703 8 4 9-990297 44 5G 30 IS 9-32054; 9 88 ,0-679455 9-33026* 9 92 .0-669738 0-0097,7 9 4 9-990285 42 30 6 30 22 9-320840 10 98 11 ,08 ,0-679,60 9-330570 10 ,02 11 ,,3 .0-669430 0-009730 10 5 11 5 9-99027C 38 9-32. .35 .0-678865 9-330879 10-669,2. 0-009744 9-990256 6 24 9-32.430 12 ..8 ,o'67?57o 9-33"87 12 ,23 .0-6688,3 0-OC9757 12 5 9-990243 m r,i 30 20 9-32J724 13 117 .0-678276 9-33H95 13 ,33 10-668505 0-OC977. 13 6 9-990229 34 7 28 9-3220.9 14 ,37 .0-67798. 9-33.803 14 ,43 IO-66S197 0-009785 14 6 9-9902,5 32 53 30 30 9-3223.3 15 ,47 .0-677687 9-332... 15 ,54 10-667889 0-009798 15 7 9-990202 30 30 8 32 9-32*607 Ifi ,:y 10-677393 9-3324.8 16 .64 .0667582 0-CC9812 16 7 9-990188 28 82 30 34 9-3*29^0 17 ,67 ,0-677.00 9-35*7*6 17 .74 .c-667274 OCC9825 17 * 9-990,75 20 30 9 3C 9-323194 18 ,76 .0-676806 9-333033 18 184 10-666967 C-CC9839 18 8 9-990161 24 SI 30 39 9-353487 19 186 .0-6765.3 9-333340 il9 .95 10-66666C 0-009852 19 9 9-990.48 22 30 10 40 42 9-323780 M ,96 21 206 .0-676220 9-333646 20205 21 2.5 .0-666354 0-CC9866 20 9 21 9 18 50 30 9-324073 .0-675927 9-333953 10-666047 0-0C98S0 9-990.20 n 41 9-324366 22 2,6 ,0-675634 9-334*59 |22 225 .0-665741 0-009893 22 ,0 9-990107 16 49 30 40 9-324658 2S225 10-675342 9-334565 23236 10-66543; 0-CC9907 23 ,0 9-990093 14 •0 12 48 9-324950 24235 ,0-675050 9-33487. i24 246 .0-661:129 0-00992. 24 1, 9-990079 12 48 30 50 9-325*43 25 245 10-674757 9-335'77 25256 ,0-664823 0-C09934 25,, 9-990066 10 30 13 52 9'325534 2<5 255 ,0-674466 9-335482 26 266 .0-6645,8 . 0-009948 26.2 9-990052 8 47 30 54 9-325826 27 265 ,0-6741-4 9-335788 27 277 .0-6642.= 1 0-C09962 27,2 9-990038 6 30 14 50 9-3261,7 28 274 10-673883 9-336093 28287 .o-66,907 . 0-009975 28,3 9-990025 1 46 30 58 9-326409 29284 ,o-67359. 9-336398 29 297 .0-663602 1 0-CO9989 29,3 9-9900,1 2 30 15 16° «9 2 9-326700 SO 294 ,0-673300 9-336702 30 307 lc-66;29R 1 0-0.0003 30.4 9-989997 9-989984 11 45 9-32699. 1 10 10-673009 9-337007 1 ,0 .0-662993 I 0-0100.6 1 4 9-32728, 3 ,9 ,0-6727,9 9-33731. 2 20 .0-662689 I 0-010030 2 , 9-989970 ■SO 44 30 6 9-327572 3 29 ,0-672428 9-3376.5 3 30 .0-662385 I 0-0,0044 3 , 9-989956 54 30 17 9 9-3*7862 4 38 ,0-672,38 9-3379'9 4 40 .0-66208. . 0-0,0058 4 2 9-980942 52 43 30 10 9-328.52 5 48 .0-67I848 9-338223 5 50 .0-66.777 ■ 0-0,007, S 2 9-989929 50 30 18 12 9-328442 « 5S 0-67,5^8 9-3385*7 6 60 .0-66.473 ' 0-0,0085 6 3 9-9899,5 48 42 30 11 9-328731 7 67 0-67,269 9-338830 7 70 10-66. .70 . 0-0,0099 7 3 9-989901 4C 30 19 IG 9-32002. 8 77 0-670979 9-339'33 8 80 .0-660867 . 0-0,01,3 S 4 9-989887 44 41 30 18 9-3293IP 9 86 0-670690 9-339436 9 90 .0-66056., . 9 4 9-989873 42 30 30 20 9-320500 10 96 11 106 0-67040, 9-339739 10 ,0, 11 ... 10-66026. . 0-010,4.0 10 5 11 5 9-989860 40 40 9-32988S 0-670,,2 9-340042 .0-659958 1 0-0,0.54 9-9S9S46 21 21 0-330.76 12 1,5 0-669824 9-340344 12 .2. .0-659656 1 0O.O.68 12 5 9-98983* 30 39 30 2.1 9-330465 13 .25 0-669535 9-340646 13 .3, .0-659354 . 0-0.0.82 13 6 9-9S98.8 34 ,30 22 2S 9-330753 14 134 0-660247 9-340948 14 14, .0659052 . D-010.96 14 6 9-989804 .« an 30 3(1 9-33I04I 15 ,44 0-668959 9-34.250 15,5, .0-658750 . 3-0.02.0 15 7 9-989790 30 30 23 32 9-331^20 6 ,54 0-66867. 9-34.55* 16 ,6. 0-658448 , D-0.0223 16 7 9-989777 ■;9 37 30 34 0-33.6.6 7 .63 0-668384 9-34.853 17 .7. 0-658147 1 '■010237 17 8 9-989763 -2.1 30 24 30 9-3UOOt 18 .73 0-668097 9-34*. 55 IS .8. 0-657845 . D-0,025, 18 8 9-989749 24 3(i 30 38 9-332.9' 9.82 0-667809 9-342456 19 .9, 0-657544 I ro.0265 19 9 9-989735 ■22 30 2.-> 40 0-372478 20 ,92 21 202 0-667522 9'3427';7 20 20, 0-657243 . 3-010279 20 9 21 9 9-98972. 18 35 0-3-.2764 0-667236 9-343057 0-656943 . 5-0,0293 9-989707 2(i -1-1 9-33305. 22 2.1 0-666049 9-343358 29 22. 0-656642 , 3-0,0307 22,0 9-989693 16 34 30 4«| 23 22, 0-666663 9-343658 2323. 0-656342 . -0,032, 23 10 9-9S9679 14 30 27 4» 0-333624 24 230 0-666376 9-343958 24241 0-656042 . -0,0335 24,, 9-989665 12 33 in 9-3339'o 25240 0-666090 9-344258 25252 0-655742 I -0.0349 25,. 9-98965' It .30 2fl .V2 9-334")5| 2fi 250 0-665805 9-344558 26262 0-65544* ' ■0.0363 26.29-989637 8 32 30 54 0-33448. 27 259 0-665519 9-344858 27272 0-655142 . -010377 27.2 9-989623 '1 .10 2!) sr, 9-3347671 28 269 0-665233 9-345157 28282 0-654843 , -0,0390 28.3 9-9S96.0 ■•I 31 30 .5H 9-335052, 2927R 0-664948 9-345456 39292 654544 > 3-0.0404 29 "3 9-9*9596 H ,10 an SO T3U337; W288 0-664663 9-345755 TO 302 0-654245 . -0.04.8 30 .4 9-989582 JLi SO TTT m. Cnsirif Parts 1 Secant | Cotang. pI^ Tangent C.^ec. , Parts Sine «n.| '" 77^ .5M0" 1 TABLE (3S LOG. SINES. COSINES, &o. U" 50'" I '2" 30 m. Sine P..rta Cosec. Tangent Parts Cotang. Secant | Parts C-..ne ™ ■;i(i 933533" 10 664663 9-34W55 10 654245 10 1 04 1 3 9-989 5S2 T5 30 2 9-3356- ' 9 10 664378 9-346054 1" 10 .0 653946 .0 010432 l" 019989568 5K f .■51 4 9'3359'-'6 2 19 10 664C94 9-346353 2 20 .0 653647 10 010447 2 . 9-989553 56 2ft 30 9'33*'9 3 2X IC 663S09 9346651 3 30 10 653349 .0 0.0461 3 1 9-989539 51 3U 32 r, 9-;36-^"5 4 38 10 663525 9-346949 -» 39 .0 65305. 10 010475 4 2 9-989525 52 28 30 10 9'336759 5 47 IC 663.4. 9-347248 5 49 10 652752 10 0104S9 5 2 9-9895" 50 30 33 12 9^33-043 6 56I.O '62957 9-347545 6 59 10 65*455 .0 0.0503 6 3 9-989497 4H 27 30 9'3373-6 7 66 10 662674 9-347843 7 69 10 052.57 .0 0.05.7 ' 3 9-989483 40 30 34 16 9-337610 « 75 .0 662390 9-348141 8 80 10 65.859 10 0.0531 8 4 9-989469 44 26 18 9-337893 9 85 10 662 IC7 9-348438 9 89 .0 65.562 .0 010545 9 4 9-9*'9455 12 30 3.i •20 9-33S.-6 10 94 U .03 .0 661824 9-348735 10 99 11 .09 10 651265 10 0.0559 10 5 " 5 998944 ■ 40 2i_ 30 9-33^459 To^ 66.541 9-349032 To 650968 10 0.0573 9989427 36 u 9-338742 13 113 10 661258 93493-9 12 118 10 65067. .0 0.0587 12 6 9-9894.3 30 24 •26 9-339024 13 .22 .0 660976 9-349626 13 ,28 10 650374 10 01060. 13 6 9-989399 34 31; 37 9-3393'=7 14 132 .0 660603 9-3+9922 14 i;S 10 65C07S 10 0.06.5 14 7 9-589385 32 23 30 9-339589 15 14, 10 6604.. 9-350218 15 .-48 .0 649782 10 010630 15 7 9-989370 30 30 3B 32 9-33987' 16 150 10 660129 9-350514 16 .58 .0 649486 10 0.0644 16 8 9-989356 28 22 30 3A 9-340152 17 160 10 659848 9-350810 17 168 10 649190 10 0106,8 17 8 9-989342 20 30 39 30 9-340434 18 ,69 10 659566 9-35.106 18 .78 10 648S94 10 0.0672 18 g 9-989328 24 21 9-340715 19 179 10 659285 9-35.401 19 1S8 10 648599 .0 0106S6 19 9 9-9893.4 22 30 40 40 9-340996 20 188 21 197 10 659C04 9-35.697 20 197 21 207 .0 648303 10 010700 20 9 9-989300 18 20 30 9-341277 To" 65S723 9-351992 To^ 648008 10 0.07.5 9989285 41 4J 9-341555 22 207 10 658442 9-352287 22217 .0 6477 '3 iO 010729 22 .0 9-989271 10 19 30 46 9-341839 23 216 10 65S.61 9-352582 23 227 .0 6474.8 .0 0.0743 23 11 9989257 14 30 42 4.S 9-342119 24 226 10 657881 9-352876 24 237 647,24 10 010757 24 11 9989243 12 18 30 50 9-3+^399 25235 10 657601 9-353'7' 25247 .0 646829 10 010772 25 12 9-98922S 10 30 43 52 9-342679 26244 10 657321 9-355465 26257 10 646535 10 010786 2612 9-9892.4 8 17 30 54 9-34*959 27 2S4 10 657041 9-353759 27 266 10 64624. 10 0.0800 27.3 9-989200 6 30 44 5« 9-343239128 263 10 656761 9-354053 28 276 645947 .0 010814 2813 9-989.86 4 16 56 9-34351829273 10 656482 9-354347 29 2S6 645653 10 0.0829 2914 9-98917. 2 30 45 30 51 9-343797 30282 1 9 10 656203 9-354640 30 296 — 645360 ^ 0.0S43 30 14 9-989.57 9 58 15 30 9-344076 10 6559-4 9-354934 1 .0 10 645066 10 0.0857 1 9'9'^9'43 4H i 9-344355 2 18 10 655645 9-355"7 2 ,9 644773 10 0.0872 2 1 9-989. 2k 50 u 30 9-344634 3 28 .0 655366 9-355520 3 29 10 6444S0 .0 010886 3 I 9-9891.4 54 30 47 e 9-344912 4 37 10 655088 9-3558'3 4 39 10 644187 .0 010900 4 2 9-989.0C 52 13 3U 10 9-34519. 5 46 10 654809 9-356105 5 48 10 643895 10 0109.5 5 2 9 9890S5 50 30 40 12 9-345469 6 55 10 65453' 9-356398 6 58 10 643602 10 010929 6 3 9-98907. 48 30 14 9-345747 7 64 10 654253 9356690 7 68 .0 643310 .0 010943 7 3 9-989057 49 ill! 49 IG 9-346024 .0 653976 9-356982 8 77 64301S 10 0.095S 8 4 r98904.- 44 11 30 18 9-346302 9 83 10 653698 93572-4 9 87 .0 642726 .0 010972 9 4 9-98902^ 42 3.1 1 50 2-2 9-346579 10 92 11 101 .0 653421 9-357566 10 97 11 106 .0 642434 .0 010986 10 5 " 5 9-98901^ 40 38 11 3. 9-346857 10^ 653'43 9-357857 642.43 .0 1 1 00 1 9 988999 31 9- 347 '34 12 III .0 652S66 9-358.49 12 1.6 10 64.85' .0 011015 12 6 9-988985 30 u 30 •20 9-34741C 13 120 10 652590 9-358440 13 126 64.560 10 011030 13 6 9-9S897C w 31 62 •28 9-347687 14 129 10 652313 9-358731 14 135 10 64.269 10 0.1044 14 7 9-988950 ,1-2 8 30 30 9-347963 15 .38 .0 652037 9-359022 15 145 640978 10 011058 15 7 9-988942 111 30 63 32 9-34S24C 16 .47 10 65176c 9-3593'3 16 .55 640687 10 01.073 16 8 598892- 2» 7 .30 34 5-3485.6 17 iw 10 65.484 9-359603 17 164 10 640397 .0 0..0S7 17 8 9-9889':. ill 31^ A4 3C 9-348792 18 .66 10 6512C8 9-359893 18 ,74 10 640.07 10 01 . .02 18 9 ;-98889^ 1 'i 30 3S 9-349067 19 175 10 650933 9-360.84 19 .84 639816 10 011116 19 9 9-988S84 22 3C S.i 30 « 9-349343 9-349618 20 184 21 .93 10 6506,7 9-360474 20 .93 21203 10 639526 10 o"'3i 20 10 21 10 9-988869 IS 5 ~30 To" 650382 9-360763 To" 639^37 .0 0.1145 9-988855 56 44 9-349893 22203 .0 650.07 9-56.053 22213 10 638947 .0 oiiito 22 II 9'o^o-*'. IC 4 .30 9-350168 23 212 .0 649832 9-36.343 23 222 638657 10 011174 23 I. 9-9S8826 14 30 ■'1 4S 9-350443 24 221 10 649557 9-36.632 24232 63836S 10 0..189 24 .i 9-988811 12 3 SO 9-350718 25230 .0 649282 9-36.92. 25 242 10 638079 10 0.1203,25,2 9-988797 10 30 bn • 2 9-350992 26239 .0 649008 9-3622.0 26 2S1 10 637790 .0 011218 26.2 9-98S782 K 2 30 lA 9-351266 27 249 .0 648734 9-362499 27261 10 63750. 10 01.232 27.3 9-988768 fi .30 .19 :c 9-351540 28258 .0 64846c 9-362787 28271 .0 6,72.3 .0 01.247 28,3 9-988753 4 1 .10 •H 9-3518.4 29267 .0 648.86 9-363076 29 280 10 636924 .0 01.26. 29.4 9-988739 •2 30 (;(i 52 m. ,-352088 30 176 TO ^111 9-363364 30290 10 636636 .0-0.. 276] 30 .4 9-9S8724 ^ C-osine Parts Secant ro.»ng. Parts'! angent (-nsiT. ! Parts Sine 77. s^ H- \ 7rA TAUr.F. G8 l.OU. SINKS, COSINES, Jkc. 1 Oh 5._„n ,yO 1 ' ' It • Sine PRrt. Coaec. 1 Tangent 1 Parts 1 Cotang. S«-41.l' 1 Parts Cosine •?-|"1 T! , 9-3520« ,o-6479i2| 9-363364 1,0-636636 io-o,,276| !,-988724 8 '^ .1.1 -2 9-35236 '" 5 ,0-647638 9-363652 1" 10 10-636348 10-01,29 |-c 9-,X87cr 5M .10 1 4 9-35^63 2 ,S ,0-64736 9-363940 2 19 10-63606C 10-01,30 2 , 9-98869 .51 oH .in 1 9-35190 3 27 10-64709 9-364228 3 29 .0-635772 IO-0,,32C 3 I 9-,8868c .54 1 .10 2 s 9-353"8 4 36 ,0-646815 9-3645.5 4 38 10-6354S1, 10-01,334 4 2 ,-988666 5-2 .ill 10 9-35345 5 45 ,0-646546 9-364803 5 48 10-635197 10-0,1349 5 2 ,-,8X65 .51 3(1 3 li 9'35372 6 54 10-646274 9-365090 fi 57 10-6349,0 10-01,364 6 3 9-988636 IN 67 3< u 9-353995 7 63 10-64600 9-365377 7 67 .0-634623 10-011378 ' 3 9-988622 4li 30 i I'i 9-354^7 8 72 10-645729 9-365664 8 76 10-634336 10-0,1393 8 4 9-98*.-6o7 II iH m 18 9-354543 9 8, 10-645457 9-36595, 9 86 10-634049 10-01,408 9 4 9-98859' 1-2 3(1 o 'ill 9-3548.5 10 90 U 99 .0-645185 9-366237 10 95 11 105 ,0-633763 10-01,422 10 5 " 5 9-988578 III ,55 30 9-355087 ,0-6449,3 9-366524 .0-633476 ,0-01,437 9-988563 :l^ 6 ■i\ 9-35535" 12 ,oS ,0-644642 9-3668,0 12 1,4 10-633190 ,0-01,452 12 6 9-988548 30 64 .1(1 ■«i 9-355630 13 ,,7 10-644370 9-367096 13 ,24 .0-632904 .0-0,, 466 13 6 9-988534 34 30 7 7S 9-355901 U ,26 10-64409, 9-367382 14 ,33 .0-6326,8 14 7 9-988519 .12 ,■•.:( .1(1 30 9-35617^ 15 .35 10-643828 9-367668 15 ,43 ,0-632332 .0-0,, 4,6 15 7 9-988504 311 311 B 3-.' 9-356443 16 ,44 10-643557 9-367953 16 ,52 10-632047 io-o,,5,i 16 8 9-9S8489 ■28 r,> .M 34 9-356713 Is \ll 10-643287 9-368239 17 ,62 .0-63,761 10-01,525 17 8 9988475 ■2(i 30 !» 30 9-3569li4 .0-643016 9-36S524 18 ,71 10-631476 10-0,, 540 18 , 9-988460 -24 51 .11) .19 9-357154 19 171 10-642746 9-36S809 19 181 .0-63, ,9, 10-01,555 19 9 9-988445 ■ti 30 ML 40 9-3575H 30 181 »1 ,90 ,0-642476 10-642206 9-369094 20 1,0 21 200 10-630906 10-0,1570 20 ,0 21 ,0 9-,S843o 18 50 30 9-357794 9-369378 ,0-630622 100,, 5S4 99884.6 11 44 9-358064 M .99 ,0-64,936 9-369663 22209 10-630337 10-01,59, 22,, ,-988401 III 4!» .10 4« 9-358333 M 20« ,0-64,667 9-369947 23 219 ,0-630053 io-o,,6,4 23,, 9-988386 14 30 12 4M 9-35S603 34 217 ,0-641397 9-370232 24 22S ,0-629768 ,0-0,1629 24 12 9-988371 1-2 48 ill 50 9-358872 M 126 ,o-64..28 9-3705,6 25238 .0-629484 .001,644 3S,2 9988356 111 l.'l 5-2 9-3S9H' 36 23s ,0-640859 ,-370799 26248 10-629201 ,o-o,,658 36,3 9-988342 H 47 ;io 37 244 10-640590 9-371083 27257 10-6280,7 ,0-011673 27,3 9-988327 n 3(1 U 5(1 9-359678 38 253 ,0-640322 9-371367 28267 10-628633 ,0-01:688 38,4 ,■9883,2 .1 4« .111 5H 9-359947 39262 ,0-640053 9-371650 29276 .0-628350 .0-01,703 89,4 9-988297 •2 311 IS 53 9-3602,5 30 271 ,0-639785 9-371933 30 286 10-628067 .0-011718 30.5 9-988282 7 45 .)ll •2 9-360484 ' 9 ,0-6395,6 9-3722,6 1 10 .0627784 10-011733 1 9-9S8267 30 ic 4 9-360752 2 ,8 ,0-639248 9-372499 2 ,, .0-627501 00, ,748 3 I 9-988252 5« 44 .tn (1 9-36,01, 3 26 ,0-63898, 9-372782 3 28 10-6272,8 0-011763 3 I 9988237 54 30 i; 8 9-361287 * 35 10-6387,3 9-373064 * 37 10-626,36 10-011777 ♦ 2 9-988223 5-2 43 .III 10 9-36,554 S 4+ 10-638446 9373347 5 47 10-626653 10-0,1792 5 2 9-9X8208 30 IR T7 9-36,822 6 53 10-638,78 9-373629 6 56 10-626371 10-0,, 807 6 3 9988193 48 42 .1(1 14 9-362089 7 62 ,0-6379,, 9-3739.' 7 65 10-626089 ,0-0, ,822 7 3 9-988,78 4li 30 III III 9-362356 8 70 10-637644 9-374.93 8 75 10-625807 ,o-o,,837 8 4 9-988,63 41 41 .111 IS 9-362623 9 79 ,0-637377 9-374475 9 84 10-625525 10-01,852 9 4 9-988,48 4-2 30 ■Jll •2(1 9-3628S9 88 ' 97 .0-637,1, 9-374756 93 i '03 .0-625244 0-624962 .0-0,1867 10 5 " 5 9988133 39 4P 30 "air 9-363,56 10-636844 9-375038 ,0-0,1882 9-98S,,8 21 ■21 9-363422 2 106 .0-636578 9-3753.9 ,0624681 10-01,897 12 6 9-98S103 M 39 30 2(i 9-3636SS 3 ,,5 0-6363,2 9-375600 3 122 0624400 10-011912 13 6 9-988088 31 ■.•2 ■2S 9 363954 4 .24 ,0-636046 9-37588. 4 131 0-624,19 0-01,927 14 7 9-988073 3-2 3H M 30 9-364220 5 ,33 10-6357S0 9-376,62 5 ,40 0-623S38 00, ,942 15 7 9-988058 30 30 2:t .i-! 9-364485 6 ,42 ,0-6355,5 9-376442 6 150 0623558 16 8 ;-, 88043 ■28 37 311 34 9-36475, 7 .5, 0-635249 9-376723 7 158 0-623277 0-0,19— • 17 8 5-988028 •20 -M 3(1 9-3650,6 8,59 0-6349S4 9-377003 8,68 0-622997 0-01,987 18 9 J 9880,3 3f. .1(1 3H 9-36528, 9 ,68 0-6347,9 9-377283 9 ,78 0-6227,7 0-0,2002 19 9 9-9S7998 S-2 311 2.S 40 9-365546- ■0 '77 1 186 0-634454 9-377563 ,87 1 ,96 0-622437 0-0,20,7 •20,0 21 ,0 5-987983 18 35^ :)0 9-365810? 0-634,90 9-377843 0-622157 0-OI20'2 5-98-968 211 44 9- 36607 55 « 195 0633925 ;:o6 0-0,2047 22,, /987953 3( :i(i 111 9-3663395 13 203 0-63366, 9-378402 ' 3215 0-62,5,8 0-0,2063 33 1, r987937 14 27 48 9-3666045 A 111 0-633396 9-37868, ' 4 224 0-62,31, 0-0,2078 24 ,2 ■987922 1-2 33 3(1 ,5(1 9-3668685 S 22, 0-63-,. 32 9-378960 ' 5 234 0-62,040 0-012093 25 ,: -9S7907 30 Jll rrj 9-3671312 fi 230 0-632869 9-379239 2 6 243 0-62076, 0-012 108 36 ,3 -987892 < -<2 ,w il 9-36-3952 7 239 0-632605 9-3795.8 s 7 252 ,0-620482 0-0,2,23 3713 -987877 li 30 2il ,1. 9-3676392 «* 248 0-63234. 9-379797 ! 8 262 ,0-620203 0-012138 28,4 ■987862 4 11 3(1 9-367922|2 9257 0-632078 9-380075 1 9271 10619925 0-012153 39,4 ■9S7847 •2 30 to s« r368.«sl: 0265 0-63,8,5 9-3S0354 .1 0280 ,0-619646 O-O1216S 30,5 c Parts -987832 Sine ¥■ 111 ' " (•.i.->ne 1 Parts 1 S«-ii,.t Cotang. Parts Tangent TAlil.K (',8 70 LOG, SINES, tOSlNKS, *c. 0'' 54'" \:i° ' ' Sine 1 Parts | Cosec. Tangent | Parts 1 <:otang. Secant Parts 1 Cosine ^i'" 'id 9'56Sil 9-369499I 5 43 10-630501 9-38.743 5 46 10-6,8257 ,0-0,2244 5 3 9-587756 50 1 31, 3;i 9-369:6 6 52 10-630239 9-382020 6 55 10-6,7980 ,0-0,2260 6 3 9-98774C 4a 27 30 9-37002 7 61 10629977 9-3S2298 7 64 ,0-6.7702 .o-o.>,27 5 7 4 9-987725 4li 311 34 9-37028 8 70 .0-6297.5 9-382575 8 74 .0-6.7425 •* 4 9-9877 >f Jl 'if, 30 9-37054 9 78 ■0-629454 9-382852 1 9 831.0-617148 10-012305 » 5 9-987695 Vi 311 JO ■n 9-37080 10 87 ;" 95 .0-629.92 9 383.29 lU 92 .0-6.687, 10-01232, 10 5 11 6 9-987679 M 25 9-371061 10-628931 9-383405 .0-616595 .0-012336 9-987664 M 1A 9-3-133CJ12 .04 10-628670 9-3836S2 12 no .0-6,63,8 ,0-012351 12 6 9987649 Mi 24 JO •M 9-37i59>jl3 113 .0-628409 9383958 13 120 10-616042 .0-0,2366 13 7 9-987634 3J 30 37 ■a 9-371852I14 .22 .0-628.48 9-384234 14 129 ,0-6,5766 .0-0.2382 14 7 9-987618 3'i 2:1 M 30 9-372113 .5,30 .0-627887 9-3845,0 15 .38 10-6,5490 ,0-012397 15 8 9987603 30 311 38 3-i 9-371373 .6 .39 .0-627627 9-384786 If, ,47 .0-615214 ,0-0,24 '2 16 8 9-9S758S ■M 22 M ;n 9-372634 17 148 IO-627366 9-385062 17 156 10-6,4938 ,0-012428 17 9 9-987572 m 30 39 ,l« 9-372894 18. 56 10-6271C6 9-385337 18 166 ,0-6,4663 10-012443 18 9 9-987557 -24 21 30 38 9-373'54 19165 10-626846 9-3856.2 19 ,75 10-6,4388 ,0-012458 19,0 9-987542 ■il 3) 40 JO 9-3734>4 20.74 21 182 .0-626586 9-38588S •20 ,84 21 193 ,0-6,4,12 10-012474 20 ,o 31 II 9-987526 '"' 20 .111 9-373674 .0-626326 9-386.63 10-613837 ,0-0,2489 9-9875" 41 44 9-373933 22 .91 .0-626067 9-386438 22 202 10-6,3562 10-0,2504 22., 9-987496 III 19 .11) lli 9-374>?2 23 200 .0-625808 9-386712 23 212 10-6,3288 10-012520 23,2 9-987480 14 311 42 4S 9-374452 24 208 .0-625548 9-386987 24 221 10-6130,3 10-0,2535 94 12 9-987465 12 III ,111 50 9-374711 25 217 10-625289 9-38726, [25 230 ,0-6,2739 io-oi25;i M.3 9-987449 lU 30 4a 5-2 9-37+970 26226 .0-625030 9-387536 126 239 ,06,2464 10-012566 28 .J 9-987434 H 30 54 9-375228 27235 .0-624772 9-387810 27248 ,0-6,2,90 ,0-0,258, S7.4 9-9874,9 1, 30 44 9-375487 28 243 .0-6245.3 9-38808+ 28 258 ,0-6,1916 10-012597 28,4 9-987403 4 Ki 30 9-375745 29252 0-624255 9-388358 29267 ,0-6, ,642 10-0,2612 9915 9-987388 ■i 30 46_ 30 9-376003 30 261 0-623997 9-38863, 30 276 ,0-6,1369 10012628 30 15 9-987372 s .10 9-376261 1 8 0-623739 9-388905 ' 9 ,0-6,1095 ,0-0,2643 i 1 9-987357 4(; 9-376519 a .7 0-623481 9-389178 2 ,8 10-610822 ,0-0,2659 S I 9-987341 51, 14 :io 9-376777 3 25 0-623223 9-389451 3 27 10-610549 ,0-0,2674 S 2 9-987526 54 30 47 9-377035 * 34 0-622965 9-389724 4 36 10-610276 ,0-0,2690 4 2 9-987310 5-2 13 30 9-377292 5 42 0-622708 9-389997 5 45 10-6,0003 ,0-0,2705 » 3 9-987295 50 30 48 9-377549 6 5, 0-622451 9-390270 6 54,10-609730 ,0-0,272, « 3 9-987279 4)1 12 30 9-377806 7 59 0-622194 9-390543 7 63 .0-609457 10-012736 7 4 9-987264 40 30 4!) 9-3-'8o63 8 68 0-62.937 9-3908.5 8 72 .0-609185 10-012752 8 4 9-987248 44 11 3ft 9-378320 9 76 0-62168C 9-391087 9 81 10-6089,3 ,0-0,2767 9 5 J-987233 4-2 30 7 3tl 10 9-378833 0-62. .67 9-39,632 11 99 j 0-608368 10-012798 ^•987202 51 24 9-379089 12 102 0-6209,1 9-39.903 12 ic8 10-608097 10-0.28,4 12 6 5-987,86 3ll H 30 ■M 9-379346 13 .11 0620654 9-392.75 3, 18'. 0-607825 ,0-0,2830 13 7 ,•987170 34 30 52 ■a 9-57960, U 1,9 0-620399 9-392447 4 127110-607553 ,0-0.2845 14 7 -987.55 3-2 9-380614 8.53 0-6,9376 9-39353' |18 .63I10-606469 ,0-0.2908 18 9 -987092 ■24 30 -Vl 9-380879 9 162 1 0-619121 9-393802 |19 172110606,98 10012923 19 10 r -987077 ■a io 6.-. *! 9-38..34 » .70 J 11 .79 ■ o-6i8866 9-394073 !0 ,8,1 1 190! 0-605927 0-012939 -^-012955 20 10 5 21 11 c -98706, '"' 5 9-38.389 0-6.86,1 9-394343 0-605657 -987045 AC 44 9-38.643 «2 187 I 0-6,8357 9-3946,4 22 ,99], 0-605386 0-012970 22 , 1 5 -987030 10 1 3U 4« 9-38. 89S K ,96 ■ o-6i8io2 9-394884 -Xl 208 1,0-605,, 6 0-012986 -'3 ,2 5 •9870,4 14 311 .17 4» / 382.5244 204 . 0-6,7848 9-595.54 24 2.7 .0-604846 0-013002 24 ,2 5 -9S6998 12 i) ,10 50 9- 382406^*5 2.3 . 0-6,7594 9-59542412.5 226 ,0-604576 0-013017 20,3 5 -986983 10 30 M< it 9-382661 Sfi 222 I 0-617339 9395^74 :26 235 '10-664306 0-0.3033 26,4 5 •986967 n 2 JO 54 9-3829i4>7 230 . 0-617086 9-395963 27 244 0-604037 0-0.3049 27,4 5 •98695, II :tii 5;» 56 /383. 68,282391.0-6.68321 9-396233 28 253 0-603767 00,3064 28,5!r986936 4 1 ' *•! •M 9-3X3422,29 147 iio-6. 6578 9-396502 29262 0-603498 0-0,3080 29,5 [9-986920 •2 w (U) I S« 9-58567530 256 ;io-6i6525 9-39677, 3027, 0-603229 0-0,3096 30,619-986904 I 11 / //' ■n.| Coz-inr | ParU | Srcmit totang. j Parts Tangent CoHfc. Parts 1 Sine [ "•l-^l 7(:0 _r,,, ^rn ] 766 TADLE 68 LOG. SINES. CO-SINES, Xc. )" 56''> 14'=' *" ? Sine Parts Cosec. Tang :nt Parte Cotang. Secant 1 Parts 1 Cosine 1^- i 1) 9-383675 6,6325 9-39677, ,0-603229 ,0-0,3096 _ ;9-9i6904 "i" " 9 ,0-602960 9-986888 w 30 1 4 9-384.X= 2 17 -6,58,8 9-397309 2 ,8 ,0-60269, 10-013,27 9-9E6S73 5fl |o9 30 938+415 ■■' 25 -6,5565 9-397578 3 27 ,0-602422 .o-o.j-43 9-986857 54 1 30 2 u 9-3!!468' 4 33 ■6,53,3 9-397846 4 36 ,0-602,54 .0-01.. 59 9-986X4. 52 5« 30 10 9-384940 5 42 -6,5060 9-398, ,5 5 44 ,0-60,885 ■0-0.3175 9-986825 50 30 3 12 9-385192 6 50 -6.4808 9-398383 6 53 ,060,6,7 .0-0.3,;. 6 3 9-986809 48 57 30 14 9'385445 7 59 -614555 9-39865, 7 62 .0-60.349 .0-0.3,06 1 7 . 9-980794 K 30 4 16 9-385697 8 67 -614303 9-3989,9 8 7, .0-60.08. 8 4 9-98677S U 00 30 18 9-385949 9 75 -6.4051 9-399,87 9 Ho .0-6008.3 .0-0,3238 9-9S6762 42 30 5 30 •20 9-386201 10 84 11 92 10 -6.3799 9-3994^^ 10 89 ,0-600545 ,0-600278 .0-0,3254 9-986746 40 55 9-386452 lO -6.3548 9-399722 11 98 ,0-0,3270 9-986730 (i 14 9-3867C4 12 ,00 10 •6,3296 9-399990 12 107 10-6000,0 ,0-0,3286 9-9867.4 36 54 30 W 9-3«6o^5 13 .09 10 •6,3045 9-400257 1.1 ,,6 ,0-599743 ,0-01330, 13 7 9-9S6699 H 30 7 ■m 9-387207 14 118 10 -6,2793 9-400524 14 ,25 ,o- 5994:^6 ,0-0,33,7114 7 9-986683 32 53 30 30 9-3S7458 IS ,16 10 -6,2542 9-40079, 15 ,33 10-599209 .0-0,3333; 15 8 9-986667 30 30 8 3^ 9-387709 16 134 10 6.229. 9-40,058 16 ,42 ,0-598942 ,0-0,3349 16 S 9-98665, •28 52 30 34 9-3879;9 17.42 10 6.204, 9-40 '3^5 17 ,5, ,0-598675 ,0-0,3365 17 9 9-986635 ■28 30 9 30 9-3'!?i.c 18 .50 .0 6., 790 9-40,59, 18 ,60 ,0-598409 ,0-0,338, 18 ,c 9-9866,9 24 51 30 39 9-38M1 19 159 .0 6, ,539 9-40,857 19 ,69 ,0-598143 ,0-0,3397 19,0 9-986603 •22 311 10 " 30 40 9-38S71, 20 .67 21 ,76 .0 6, ,289 9-402, 14 ■20 ,78 21 ,87 ,0-597876 ,0-0,34,3 20,, 21 ,, 9-986587 20 18 50 30 9-38S96' r^ 61,039 9-402390 10-5976,0 ,0-0,34:9 9-98657, II 41 9-3892., jM 18+ .0 6,0789 9-402656 |22 ,96 '°-597344 ,0-0,3445 22,2 9-986555 10 49 30 4(i 9-3S9+61I23 .92 10 0,0539 9-402922 ]23 205 ,0-597078 ,0-0,346, 23,2 9-986539 14 30 12 4.1 9-3?97ii|24 20 1 10 6,0289 9-403, .S7 |24 2,4 ,0-5962,3 ,0-0,3477 24,3 9-9S6523 12 48 30 50 9-38996025 209 10 6,0040 9-403453 125 222 ,0-596547 ,0-013493 25,3 9-986507 10 30 la i-l 9-3902,026218 .0 609790 9-4037,8 i2<>23. ,0-5,6282 ,0-0,3509 26,4 9-98649, s 47 30 ii 9-39°459;2' "7 .0 60954. 9-403983 r^' 240 ,0-596017 ,0-0.3525 27 ,4 9-986475 e 3(1 14 58 9-3^0708 28236 10 609292 9-404249 28 2+5 10-59575, .0-0.354. 28,5 9-986459 46 30 58 9-39-^957 29 244 .0 609043 9-4045 '4 29 258 10-595486 ,0-0,3557 29,5 9-986443 2 3:1 15_ 57 2 9-391^06 3025. .0 608794 9-404778 30 267 '0-5952.2 ,0-0,3573 .30,6 9-986427 3 58 30 9-39'4'i4 . 8 10" 608546 9-405043 • 9 ■°- 5-54957 ,0-013589 ' ■ 9-9864,, 16 4 9-39'703 2 ,6 ,0 608297 9-405308 2 ,7 10-594692 ,0-0,3605 9-986395 50 44 30 « 9-391951 3 25 10 608049 9-40;, 572 3 26 .0-594428 ,0-0,362, 3 2 9-986379 54 30 17 8 9-39i'99 4 3! .0 60780. 9-405836 * 35 ,0-594,64 .00,3637 4 2 9-986363 52 43 30 10 9- 39^447 5 4, 10 607553 9406.00 S 44 ,0-593900 ,0-0,3653 6 3 9-986347 50 3U 13 12 9-392695 6 49 10 607305 9-406364 6 52 ,0-593636 ,0-0.3669 6 3 9-98633, 49 4'-' 30 14 9-392943 7 57 .0 607057 9-406628 7 6, ,0-593372 ,0-0,3685 9-9863,5 -16 30 19 1« 9-393>9> 8 66 10 606809 9-406892 8 70 10-593,08 10-0,370. 8 4 9-986299 41 30 18 9-393438 9 74 10 606562 9-407,55 9 79 ,0-592845 .0-0137,8 9 5 42 30 20 30 20 22 9-393685 10 82 U 90 .0 6063.5 9-4074,9 10 87 11 96 10-59258. ,0-0,3734 10 5 11 6 9-986266 40 39 40 9-39393^ To" 6o6o58 9-407682 ,0-5923.8 ,0-0,3750 9-986250 21 24 9-394,79112 98 10 60582. 9-407945 12 105 0-592055 ,0-0,3766 12 6 9-9S6234 36 39° 30 2« 9-3944^.6;i:i ,06 10 605574 9-408208 13 .,4 0-59.792 ,0-013782 13 7 9-9862,8 » 3(1 22 28 9-394673 14 ,,4 10 6053.7 9-40847, 14 122 0-591529 ,0-0,3798 14 8 9-986202 32 an 30 30 9-3949,915 ,23 .0 60508, 9-408734 ;'5'3' 0-591266 ,0-0.38,4 15 8 9-986,86 30 30 23 32 9-395''-6'« '.r- .0 604834 9-408996 116 140 0-59,004 ,0-0,383, 16 9 9-986,69 2S 37 30 34 9-3954,2J17 ,40 10 604588 9-409259 17 149 0-59074, ,0-0,3847 17 9 9-986153 ■ia 30 24 3fi 9-395658 8 148 10- 604342 9-40952. 18 ,57 0-590479 .0-0,3863 18,0 9-986,37 24 36 30 38 9-395904 19 ,56 :o- 604096 9-409783 19 166 0-5902,7 0-0,3879! IP >o 9-986,2. 22 30 25 40 9-396150 20 164 31 .72 ,0- 603850 9-4,0045 1 20 ,75 21 ,84" 0-589955 0-0.3896 { 20 1, 9-986,04 20 35 9-396395 lo^ 60360c 9-4,0307 0-589693 o-o'39i2j 21 ,, 9-9S60S8 30 44 9-39664, 22 ,80 10- 603359 9-4,0569 22,92 0-58943, o-o,3,2X 22 ,2 9-9S6072 10 34 30 40 9-396886 23 .89 10- 6031.4 9-41083, 23 20, 0-589,69 0-OI3944 23 ,2 9-986056 M 30 27 48 9-397>32 24 .97 10- 602S68 9-4,1092 a 210 0-588908 0-0,3961 24 ,3 9986039 33 30 50 9-397377 25 205 10- 602623 9-4J>353 25 2.9 0-588647 0-0,3977 25,3 9-9S6023 10 30 28 32 9-39762, 26213 lo- 602379 9-4,1615 26227 0-588385 0-013993 26,4 9-986007 g 32 30 44 9-397866 27 22, o- 602,34 9-41,876 27236 0-588,24 0-0,4009 27,5 9-98599, 1) .It 29 M 9-39S11' 28 129 10- 601889 9-4,2137 8245 0-587863 0-014026 2R,5 9-985974 4 31 30 5S 9-398355 29 237 10- 60,645 9-4,2397 29 254 0-587603 0-0,4042 29,6 3-985958 ■i 30 SO 58 9-398600 W246 10-601400 9-4,2658 JO 262 0-587342 o-o,4os8| 301619-9859421 30 » // ? Cosine Paris Sfoant Cotang. Parts Tangt-.n» Coseo. |rHrt.s| Sine |ni.| 7.V 6- •_'■ ■ 1 TABLE eti LOG. SINES, CUSINES, Bcc. 0" 68"' 14^ T77 1 Sine ! Parts C 9-404179 23 186 10-595821 9-4.8616 23 .98 .0-58,384 ,0-0,4437 23.3 9-985563 30 42 48 9-404420 24 .94 .0-595580 9-4.8873 24 207 .0-58. .27 .0-0,4453 24 ,3 9-985547 12 18 an SO 9-404660 25 202 .0-595340 9-419130 25 2,5 .0580870 10-0,4470 25,4 9-985530 10 30 43 32 9-404901 26210 10-595099 9-419387 26 224 .0-5806,3 ,0-0,4486 2614 9-9S55.4 g 17 30 M 9-405141 272.8 .0-594859 94.9644 27 233 10-5S0356 ,0-0,4503 27,5 9-985497 t 44 50 9-4053S2 28 226] 10-594618 9-4.990. i-.'8 241 10-5S0099 .0-0,4520 28,5 9-985480 4 IB 30 58 9-405622 29234 .0-594378 9-420158 129 250 ,0-579842 10-0,4536 2916 9-985464 V 30 45 30 " 9-405862 .10 242 0-594.38 9-420415 30259 ,0-579585 ,0-0,4553 30,6 9-985447 1 15 9-406102 1 sl 0-593898 9-420671 1 8 10-579329 ,0-0,4570 9-985430 40 4 9-406341 2 .6 0-593659 9-420927 2 ,7 ,0-579073 10-0,4586 2 , 9985414 S6 14 ill 6 9-406581 3 24 .0-593419 9-4211 84 3 25 ,0-5788,6 10-0,4603 3 2 9-985597 i4 *1 » 9-40682C ♦ 32 0-593180 9-42.440 * 34 ,0-578560 ,0-0.46,9 4 2 9-985381 52 13* 30 m 9-407060 5 4c 0-592940 9-42.696 5 42 10-57S304 .0-0,4636 ' 3 9-985364 SO 30 48 12 9-407299 6 48 0-592701 9-42.952 fi 5. ,0-578048 ■ 0-0.4653 fi 3 9-985347 48 12 30 14 9-4075381 7 5;j 0-592462 9-422207 7 59 0-577793 .0-0.4670 7 4 998533c 46 30 49 111 9-407777 8 63 1 0-592223 9422463 s 6^; 0-577537 .0-0.4686 8 4 9-985-,>4 44 II 30 IB 9-408015 9 7. 0-59. 9S5 9-4:2718 9 76 0-577282 .00, 4703 9 5|9-9>*5297 30 &0_ »n 9-408254 .0 791 0-59.746 9-422974 |l» 85 1 0-577026 ,0-014720 10 6 9-985280 40 10 30 ■« 9-408492 n 87| 0-59150S 9-423229^ 11 93 0-57677. .0-014736! u 619-985264- 30 61 21 9-408731 12 95 0-591269 9-423484 12 .02 c-5765.6 ■0-014753 112 7 9-985247 36 30 21 9-408969 13 ,03 c-59103. 9-423739 13 .ic 057626, 10-014770 13 7 9-985230 34 30 52 2K 9-409207 14 .1. °-59C793 9423993 14 .19 0-576C07 .0-0.4787 14 8 9-985213 e j^i 30 9-409445 IS .18 0-590555 ^-424248 15 ,27 0-57575* 10-014803 15 8 9-985197 30 30 53 32 9-409682116 126 0-590318 9-4245'-- 3 IR 136 o"575497 10-014820 16 9 9-985.80 •28 7 JD 31 9-40992o|l7 134 0-590080 9-424757 17 144 o"575243 10-0.4837 17 10 9-985,63 26 64 3« 9-410157I8 142 0-589843 9-4250.. 18.5! 0-574989 10-014854 18,0 9-985,46 24 6 30 3S 9410395 19 .501 0-589605 9425265 19 .6. 0-574735 10-01487, 19 ,, 9-985,29 -22 30 y. 40 ,■4.0632 «0,5f 21 166 0-589368 9-4255.9 20 .70 Jl .78 0-57448, 20 ,, 21 ,2 9-985"3 9 985096 •20 18 6 9-410869 0-5S913. 9-425773 0-574227 .0014904 M II 9-4.1.06 M .74 0-588894 9-426027 22187 0-573973 100,492, 22,2 9-985079 16 4 » ir. 9-411343 2.> .82 0-588657 9-42628. *3 '95. =•5737.9 ,0-0,4938 23,3 9-985062 57 tn 9-4 0579 24 .90 0-58S42, 9-426534 »4 204 0-573466 ,0-0,4955 24 13 9-985045 12 3 «« 30 9-41.8.6 2J .93 0-588.84 9-426787 25 2,2 0-5732.2 10-0,4972 25 14 9-985028 10 30 h« .-.2 9-4.2052^6206! 9-4'228857 2i4| 0-587948 9-427041 2«220 0-572959 0-0.4989 26.5 9-98501' g 2 .10 il 0-5877.2 9-427294 27 229 0-572706 ,0-0,5005 27.5 9-984995 6 30 Kj 3I-. 9-4 125^4 is 222 0-587476 9-427547 28 237 0-572453 ,0-0,5022 28 ,6 9-984978 4 1 M .',8 9-4ii7'«29i;o 0-587140 9-4i78«' 29246 0-5722C0 .0-0,5039 29 16 9-98496, .J 30 flO 60 9-41299630 238 0-587C04 9-428052 30 254 o-57.94» .0^0,5056 30.7 9-984944 m. (1 /// 11'. ^ Co.ine ! Part, S«Tint CoUng. Parti T^igcrt Cowe. Part-. Sine 768 TABLE 08 LOG. SINES, COSINES, jco. jh on, 150 "/ // m. Sine Parts Cosec. Tangent Parts 1 Cotang. Secant Parts Cosine m. ^" ~0~ 9-417996 K.-587004 9-428052 10-571948 ,0-0,5056 9-984944 eo "Od 3U 2 9^413Z32 1" 8 10-586768 9-428305 1" 8 10-571695 ,0-015073 1" , 9-984927 53 311 1 * 9-413467 2 16 .0-586533 9-428558 2 ,7 .0-571442 10-015090 2 , 9-9849,0 56 J!. ia e 9-413703 3 23 10-5S6297 9-4288,0 3 25 10-57,190 10-0,5,07 3 2 9-984893 54 30 J » 9-41393!! 4 3, 10-586062 9-429062 4 33 .0-570938 ,0-0,5,24 4 2 9-9S4876 52 M 30 >o 9-414173J 5 39 .0-585827 9-429314 5 42 10-570686 ,0-0,5141 5 3 9984859 50 30 3 i-i 9-414408 6 47 10-585592 9-429566 6 50 10-570434 10-015158 6 3 9-984842 48 .-.7 311 u 9-414643 7 55 .0-585357 9-429818 7 59 10-570,82 10-015.75 7 4 9-984825 46 4 16 9-41487S S 62 .0-585.22 9-430070 8 67 10-569930 10-0,5192 8 5 9-984808 44 5(i lU 18 9-415111 9 70 .0-584888 9-430321 9 75 10-569679 10-015209 9 5 9-98479' 42 3(1 5 30 •20 9'4"5347 10 78 11 86 .0-584653 9'430573 10 84 11 92 10-569427 .0-569176 10-015226 .0 6 11 6 9-984774 38 fti 9-4-S5!i> 10-584419 9-430S24 ,0-015243 9-984757 ti 24 9-415815 12 94 .o-584'85 9-431075 12 100 10-568925 ,0-015160 12 7 9-984740 36 54 30 ■id 9-416049 13 lOI .0-58395. 9-431326 13 109 ,0-0,5277 13 7 9-984723 34 30 7 •28 9-416183 14 109 .0-583717 9-43'577 14 117 .0-568423 ,0-015294 14 8 9-984706 32 53 30 30 9-416517 15 117 .0-583483 9-431S28 15 125 10-568172 .0-0153., 15 9 9-984689 30 3U « 32 9-416751 16 125 10-583249 9-432079 16 134 10-567921 .0-0.5328 16 9 9-984672 . 52 m 34 9-416984 17 133 .0-583016 9-432329 17 14a .0-56767. .0-015345 17 ,0 9-984655 26 3(1 9 M 9-417217 18 140 .0-582783 9-432580 18 .50 10-567420 10-0.5362 18,0 9-984638 24 51 311 .» 9-417451 19148 .0-582549 9-432830 19 159 10-567170 .0-0.5380 19,, 9-984620 22 30 -^ 40 42 9-417684 20.56 21 164 .0-582316 9-433080 20 167 21 176 10-566920 .0-0.5397 20,, 21 ,2 9-984603 9-9845S6 18 50 9-417917 ,0-582083 9-43333' ,0-566669 10-015414 11 44 9-4>8i5o 22 171 10-58,850 9-433580 22 .84 .0-566420 10-0,543, 22,3 9-9S4569 16 49 30 40 9-418382 23 179 ,0-58,618 9-433830 23 192 .0-566.70 10-015448 2313 9-984552 14 30 12 48 9-418615 241.S7 ,0-58, 3«5 9-434080 24 20, .0-565920 ,00,5465 24.4 9-984535 ,2 48 311 50 9-41S847 25.95 io-58>,53 9-43433° 25 209 ,0-565670 10-0,5482 25 14 9-9.S45,8 10 30 13 52 9-419079 26 203 10-580921 9-434579 26217 ,0-565421 10-015500 2615 9-984500 8 47 30 54 9-419312 27 210 ,0-580688 9-434828 27 226 10-565172 ,0-0,55,7 2715 9-984483 a 14 56 9-419544 28 218 ,0-580456 9-435078 28 234 10-564922 10-0,5534 18 16 ./9S4466 4 46 3(1 58 9-419776 29226 ,0-580224 9-435327 29242 10-564673 ,0-015551 2917 9-984449 2 30 Ij 1 9-420007 30234 ,0-579993 9-435576 3025, 10-564424 10-01556S 30 17 9-984432 s» 58 45 9-420239 1 8 10-579761 9-435825 1 8 0-564175 10-0,5586 1 I 9-9844.4 16 4 9-420470 2 15 10-579530 9-436073 2 16 0-563927 10-015603 2 1 9-984397 56 44 30 6 9-420701 3 23 10-579298 9-436322 3 25 .0-563678 10-0.5620 3 1 9-9S4380 54 3(1 17 8 9-420933 4 31 10-579067 9-436570 4 33 ,0-563430 10-015637 4 2 9-984363 52 43 30 10 9 421164 5 38 10-578836 9-4368.9 5 41 ,0-563,8. .0-015655 5 3 9-984345 50 30 18 12 9-421395 6 46 10-578605 9-437067 6 49 10-562933 10-015672 6 3 9-984328 48 42 30 14 9-421626 7 54 10-578374 9-4373.5 7 58 10-562685 .0-0,5689 7 4 9-984311 46 30 19 10 9-421857 8 6. .0-578143 9-437563 « 66 .0-562437 .0-015706 8 5 9-984294 44 41 3U 18 9-422087 9 69 io-5779'3 9-437S.1 9 74 10-562.89 10-0,57241 9 5 9-984276 42 30 20 30 20 9-42231S 10 77 11 85 9-438059 10 Si 10-561941 10-0^74. .0-015758 10 6 ;: f 9-984259 40 411 3" 9-422548 10-577452 9438306 11 91 10-561694 9-984242 21 24 9-422778 .2 92 10-577122 9438554 12 99 10-56.446 .0-045776 12 719-984224 3« 39 30 i6 9-423008 13 100 10-576992 9-438S01 13 107 .0-561199 10-015793 13 8 9-98420- 34 30 n 2S 9-423238 14 108 10-576762 9-439048 14 1,5 10-560952 .0-0.58.0 14 8 9-984190 32 ■AH 30 30 9-423468 15,15 ,0-576532 9-439296 15 ,23 ,0-560704 10-0.5828 15 9 9-984172 30 30 23 32 9-423697 .6,23 ■0-576303 9-439543 16 132 0-560457 10-0,5845 16 9 9-984.55 •28 37 30 34 9-4239:^717 .51. .0-576073 9-439790 17 140 0-5602,0 ,0015863 17 ,0 9-984137 •26 24 36 9-424,56 18 138 .0-575844 9-440036 18 148 0-559964 .0-0,5880 18 10 9-9S4.20 21 3« 30 38 9-4243S6 19 146 .0-575614 9-440283 19 156 0-5597.7 ,0-0,5897 19 ,1 9-984,03 22 30 30 40 9-424615 20153 21 161 0-575385 9-440529 20 165 21 173 0-55947, 10-0.5915 20 12 21 12 9-984085 20 IL 9-424844 0-575.56 9-440776 0-559224 10-0.5932 9-984068 28 44 9-425073 M 169 .0-574927 9-44.022 22 181 0-55897S ,0-0,5950 2213 9-984050 Id 34 3CI 46 9-425301 23.76 .0-574699 9-44.268 23 ,89 0-558732 10-0,5967 23,3 9-984033 14 30 •-7 48 9-425530 « ,g4 ,0-574470 9-44,5,4 24 198 0-558486 10015985 24 14 9-9840.5 12 33 5(1 9-425758 25,92 10-574242 9-44,760 25 2C6 c-558240 ,0-0,6002 25 14 9-983998 10 30 28 52 9-425987 26 ,99 ,0-5740,3 9-442006 26 21.^ 0-557994 ,0-0160,9 2615 9-9S3981 H :i2 30 54 9-426215 27 207 10-573785 9-442252 27 2 22 0-557748 ,0-0,6037 27 16 9-983963 I, '3(1 29 56 9-426443 28215 0-573557 9-442497 28 230 0-557503 10-0,6054 28 16 9-983946 4 31 30 .58 9-426671 29i22 ,0-573329 9-442743 29239 0-557257 10-0,6072 2917 9-98392S 2 30 30 2 9-426899 30 230 '01573_>_£i Secant 9^4^988 Cotanj. 30247 ,0-557012 ,0-0,6089 30,7 9-9839.. 30 T77 ?• Cosine Parts Parta Tangent Co,;e<;. rart8 Sine ? 7T/ 74° 4" .W" 1 TABl.F. C,S 709 LOG. SlMiS, COblNKS, *.c. | I h -j.n IjC — 30" •?•! Sine 1 Parte 1 Cosec. Tangent Parta 1 Cotang. Secant Parts Cosine m Tn,\ v+26if9 y I10-573101 944^988 10-5570,,- ,0-0,6089 9-9839. 5a|"3ir| III 1 94i7-0.62.2 7 4 9-983788 4U 34 « 9-4i!i7. 8 60 ,0-57,283 9-444947 8 6s 10-555053 ,0-0,6230 8 5 9-983770 44 20 JO 8 9-4i89+^ 9 6!i ,0-57,056 9-4+5,91 9 73 ,0-554809 ,0-0,6248 9 5 9-983751 42 JO 35 9-429 'Tc 10 75 M 83 ,0-570830 9-445435 10 8. 11 89 ,0-554565 lC-0,6265 lu 6 U 6 9-983735 38 26 30 •2 9-42939 .0-570603 9-445679 .0-55431, ,0-0,6283 9-983717 3C 1 9-429623!:-^ 90 ,0-570377 9-445923 12 97 ,0-55+077 .0-0,6300 12 7 9-9S37OU JU 24 Ji> li 9-42984" 13 98 ,0-570,5, 9-446.57 1:; .06 10-553833 ,0-0,63,8 13 8 9-9S36S2 J4 30 37 s 943^^07, 14,05 .0-569925 9-4+64,, 14 ,,4 ■ 0-553589 ,0-0,6336 U 8 9-9S3664 23 jO 9-43°3o 15 I13I10-569699 9-4+665+ 15 ,22 ,0-5533+6 ,0-0,6353 15 9 9-983647 JO 30 38 a ■1 9-430527 16 no ,0-569473 9-44689S 16 ,30 ,0-553.01 .0-0,637, IG 9 9-983629 ■28 22 JO J •» 9'43^75^ 17 128 ,0-569248 9-447141 17 ,38 ,0-552859 ,0-0,6389 17,0 9-9836,1 -2U 30 i'J : c 9-43C978 18 ,35 10-569022 9-447384 18 ,46 ,0-5516,6 ,0-0,6406 18,, 9-9S3594 •24 21 JO 3 s 9-43-203 19 ,43 ,0-568797 9-447627 19.5+ ,0-551373 ,0-0,6+24 19ii 9-983576 -22 30 ~^ 4 943 "429 »0.5, 21 ,58 10-56857, 9-4478-0 20 .62 21 .7. .0-552,30 .0-0164+2 20.2 21 .2 9-9S355S 18 30 2 9-43i6;4 10-568346 9-4481,3 10-55,887 ,0-0,6+60 9-983540 41 4 4 9-431879 22 ,66 IO-563I1I 9-448356 22.79 ,0-55164+ ,0-0.6+77 22.3 9983523 10 lU W 4 B 9-4321C4 23 ,73 ,0-567896 9-448599 23 .87 10-55, +0, .0-0,6495 23.4 9-983505 14 JO 42 4 8 9-4323^9 24 181 .0-56767. 9-44884. 24 .95 10-55, ,59 ,0-0,65,3 24.4 9-983487 1-2 l(J 30 5 » 9-43^553 2S ,88 10-567447 9-449084 25203 .0-550916 ,0-0,653, 23.5 9-983+69 10 311 43 S i 9-432778 26 196 ,o-s672ii 9-449326 262.. ,0-550674 ,0-0.6548 26,5 9-983452 s 17 30 i 4 9-43300» 27203 .0-566998 9-449568 271.9 ,0-550432 .0-0,6566 27 ,6 9-983+3+ a JO 44 i 9-433226 28 2,0 ,0-566774 9-449810 28 227 ,0-550190 ,00,658+ 28 ,7 9-983416 ■t 10 JO J 8 9-43345> 29217 ,0-566549 9-450052 29235 .0-5+9948 ,0-0,6602 29,7 9-983398 •2 30 4S_ J 9-433675 30 226 ,0-566325 9-450294 10 2+4 '0-549706 10-0,66,9 30 ,8 9-983381 S7 58 1ft 9-433898 1 7 0-56.5,02 9-450536 1 8 ,0-549464 ,0-0,6637 I , 9-983363 <(i 9-434122 3 15 0-565878 9-450777 2 .6 10-549223 ,0-0,6655 2 I 9-983345 5fi 14 JO 9-434346 3 22 0-5*5654 9-45.0,9 3 24 0-54898, ,0-0,6673 3 1 9-983317 54 30 47 9-434569 4 30 0-56543, 945'26o 4 31 0-548740 ,0-0,669, 4 1 9-983309 02 .3 30 I 9-434793 5 37 j 0-565207 9-45'502 5 40 0-548498 ,0-0,6709 6 3 9-983291 50 M> 48 1 9-435°>6 6 44! 0-564984 9-45 « 743 6 48 0-548157 ,0-016727 6 4 9-983173 48 12 30 1 9-435239 7 52 0-56476. 9-45.984 7 56 0-5480.6 ,0-0,6744 7 4 9-983256 4U 30 49 1 9-435462 8 59 0-564538 9-452225 8 64 0-547775 ,0-0,6762 8 5 9-983238 44 1 1 30 1 9-435685 9 67 0-56+315 9-452465 9 72 0547535 ,0-0,6780 9 5 9-9832^0 4-2 30 51) t 9-435908 10 74 11 82 0-564092 9-452706 80 1 88 _oj+_7294 ,0-0,6798 10 6 11 7 9-983202 40 JO 9-43613. 0-563869 9*452947 0-547053 10-0,6816 9-983184 :,i 2i 9-436353 12 89 0-563647 9-453.87 2 96 o-5+6S,3 0-0.6834 12 7 9-983.66 ;to 9 10 W 9-436576 13 97 0-563424 9-453428 3 104 0-546572 0-0.6S52 13 S 9-983148 34 52 a 9-436798 14 ,04 0-563202 9-45366S 4 . 12 0-546332 0-0.6870 14 8 9-983,30 32 tj 30 30 9-437020 15 1,, 0-562980 9-453908 5 120 0-546092 0-0.6888 15 9 9-983,11 30 ?o &3 35 9-437242 ,18 0-5627^8 9-454148 6 .28 0-545852 0-016906 16 ,0 9-983094 -28 -/ 30 34 9-437464 7 ,16 0-562536 9-454388 7 ,36 0-5456,2 0-0,6924 17 ,0 5-983076 20 Ul 61 3e 9-437686 8.33 0-5623,4 9-454628 8 ,44 0-545372 0-0,6942 18,, 5-983058 (1 30 38 9-43-908 9 ,41 0-562092 9-454867 9 ,52 0-545133 0-0,6960 19,1 9-985040 .III a.t 40 JO 4' 9-43S.2, 20,48 21 ,56 0-56,871 9-455 'o- 20 ,60 21 ,68 0-5+4893 0-0,6978 20 ,2 21 13 9 9830^2 .■) 9-43835' 0-56,6+9 9-455346 0-54465+ 0-0,6996 J-983004 6(i 44 9-438572 22 163 0-56142S 9-455586 22,76 0-5444.4 0-0,70,4 22,3 9-982986 4 30 40 9438793 23 171 0-561207 9-455825 23 1S4 0-544,75 0-017032 23,4 9-981968 30 S7 4H 9-439014 24 178 0-560986 9-456064 24 192 0-543936 0-0,7050 24,4 3-982950 3 M) 50 9-439235 25 ,85 0-560765 9-456303 .5 100 0-543697 0-017068 25,5 y-9Si932 30 «R i! 9-439456 26 192 0-560544 9-456542 26 208 0-543458 0-0,7086 26 .6 /9S2914 2 10 ,V1 9-439677 27 2 00 0-560323 9-45678. 27 216 0-543219 0-0,7,04 27 16 /982896I 30 .'.!• 53 0-439897 28 207 0-560103 9-4570,9 28 224 0-542981 0-0, 7,12 28i7l ^ 3-982878 1 10 .'i7r|-„ • Co-iine Parts Secant Cotanj. Parts Tan-c:iit C08UO. Parts Sine "F —,7 74'^ 4" .Sli'" j TAbl.i: (58 LOG. SINES. COSINES, etc. |h 4ra IfjO ~(r Sine 1 Part. Cosec. T«^sent Part* 1 Cotang. Secant Parte 1 Cosine m" \~ 9'44°338| 10-559662 9-45749' ,10-542504 10-0.7.58 9-982)i+2 ("si 30 9-4405 5 S| '" 7 10-559441 9-457735 1" 8110-542265 .0-017.76 1" I 9-9S2S24 i.„ .10 1 9-440778 2 i;; .0-559222 9-457973 2 16 .0-542027 10-017195 2 1 9-9828C5 l:.(i .-!• 3a 9-440998! 3 21 10-559002 9-45i'2.i 3 24 10-54.789 10-0.72.; 3 2 9-982787 \i 31. 2 9-441218 4 29 .0-558782 9458449 4 32 10-54.55, ,0-0.723. 4 2 9-982769 .V2 5B 30 9-441438 5 36 10-558562 9-458687 5 39 ,0-541313 10-0.7249 * 3 9982751 50 311 a 9-441658 6 44 •0-558342 9-458925 6 47 10-541075 .0-0.7267 6 4 9-982733 W 67 30 9-44187: 7 5- 10-558,23 9-459163 ^ 55 .0-540837 ;o;o;7285 7 4 9-982715 1« 4 9-442096 8 58 .0-557904 9-459400 8 63 .0-540600 8 5 9-982696 44 .^)li 30 9-442316 9 65 10-557684 9-459638 9 7. .0-540362 .0-017322 9 5 9-982678 42 3U 6 30 •20 22 9-44'- 535 10 73 .0-557465 9-459875 10 79 11 87 .0-540.25 10-017340 10 6 11 7 9-982660 40 38 ii 9'442754 .0-557246 9-460.12 .0-5398S8 .0-0,7358 9-982642 e 24 9'442973 12 87 .0-557027 9-460349 12 95 .0-53965. 10-017376 12 7 9-982624 3(i 54 30 2d 9-443192 13 95 10-556808 9-460586 13 .03 .0-539414 ,0-0,7395 i3 8 9-982605 34 30 7 2S 9-443410 14 .02 10-556590 9-460823 14 110 10-539.77 .0-0.74.3 U 9 9-982587 3-2 53 30 30 9-443629 15,09 10-55637. 9-461060 16 118 10-538940 10-0,743. 15 9 9-982569 30 30 8 32 9-443847 16 1,6 .0-556153 9-46.297 16 .26 10-538703 .0-0.7449 16.0 9-98255' 28 52 30 34 9-444066 17 124 '0-555934 9-461533 117 .34 .0-538467 .0-017468 17.0 9-982532 •26 30 9 36 9-444284 18 .3. .0-5557.6 9-46.770 18 142 10-538230 10-017486 18 ,1 9-982514 •24 51 30 3S 9-444502 19.38 .0-555498 9-462006 |19 .50 10-537994 100.7504 1912 9-982496 •22 30 10 40 9-444710 20 146 21 .53 .0-555280 9-462242 20.58 .0-537758 .0-0.7523 20.2 21,3 9-982477 18 -. 9-444938 .0-555062 9-462478 21 166 10-537522 IO-0.754I 9-982459 11 44 9'445'55 22 .60 .0-554845 9-4627.5 22.74 10-537286 10-0.7559 2213 9-982441 JO 49 30 4fi 9'445373 23 .67 .0-554627 9-462950 23 18. .0-537050 ,0-0,7578 M14 9-9S2422 L4 30 12 48 9-445590 24 175 .0-5544.0 9-463186 24 189 .0-5368.4 10-017596 24 15 9-982404 12 48 30 50 9-445808 25 ,82 10-554.92 9-463422 25 197 .0-536578 10-017614 25,5 9-9823S6 10 3(1 l.j 52 9-446025 26 .89 ■0-553975 9-463658 26205 10-536342 10-017633 2616 9-982367 ^ 47 30 54 9-446242 27.96 .0-553758 9-463893 272,3 10-536107 ,0-017651 2716 9-982349 6 30 M 56 9-446459 28 204 10-553541 9-464.28 4S22. ■0-535872 ,0-017669 28 17 9-98233. 4 46 30 58 9-446676 29 21. '0-553324 9-464364 K9 229 10-535636 ,0-0,7688 29 18 9-9823.2 2 30 15 30 8 9-446893 30 2.8 IO-55J.07 9-464599 30 2,7 .0-53540. 10-017706 30 18 9-982294 58 1 30 1 9-447109 ' 7 .0-55289. 9-464834 1 8 .0535.66 10-017725 1 I 9-982275 16 J 9-447326 2 .4 .0-552674 9-465069 2 .6 .0-53493, ,0-0,7743 2 . 9-982257 44 30 a 9'447542 3 22 10-552458 9-465504 3 13 .0-534696 ,0-017761 3 2 9-982239 54 30 17 8 9-447759 4 29 .0-552241 9-465539 * 3' 10-534461 ,0-0,7780 4 2 9-982120 52 43 30 10 9-447975 5 36 .0-552025 9-465773 6 39 10-534217 ,0-0,7798 5 3 9-982202 50 30 18 12 9-448.91 6 43 10-551809 9-46600S « 4V .0-533992 ,0-0,78,7 6 4 9-982.83 48 42 30 14 9-448407 7 50 10-551593 9-466142 7 54 .0-533758 ,0-0,7835 ' 4 9-982,65 46 30 19 18 9-M8623 8 57 10-551377 9466477 8 62 10-533523 ,00,7854 8 5 9-9S2146 41 30 18 9-448838 9 64 .0-551.62 9-4667.. » 70 .0-533289 10-0,7871 9 6 9-981. 2S 4^2 3I> 20 30 20 9-449054 72 ' 79 .0550946 9-466945 !0 78 11 86 .0-533055 .0-0,7891 10 6 11 7 9-982.09 40 38 40 30 9-449269 10-550731 9-4671 79 10-532821 ,0-0,7909 9-98209. 21 24 9-449485 2 86 10-550515 9-467413 .9 93 10-532587 ,0-0,7928 12 7 9-982072 36 ;i9 30 26 9-44970C 3 93 0-550300 9-467647 13 .01 .0-532353 ,0-0,7946 13 8 9-982054 34 30 22 23 9-4499'5 4 ICO 0-550085 9-467880 14 .09 10-532120 .0-0.7965 14 9 9-982035 32 38 30 30 9-450.30 5 107 0-549870 9-46S..4 IS ,.7 ,0-53.886 0-0.7984 15 9 9-9820.6 30 311 23 32 9-450345 6 ..4 0-549655 9-468347 H.24 10-53.653 0-0.8002 16 10 9-98199S •28 37 30 34 9-450560 7 .22 0-549440 9-468581 17 132 ,0-53.4.9 0-0.802. 17i. 9-98.979 21J 311 24 36 9-450775 8 .29 0-549225 9-4688.4 18 .40 0-53.186 0-0.8039 ISli 9-98 ■1.61 24 3fi 30 38 9-450989 9 .36 0-5490.1 9-469047 19 148 0-530953 o;o.8o58 19.2 9-981942 22 30 25 40 9-45.204 .43 1 150 0-548796 9-469280 20 ,56 21 .63 0-530720 20 12 21,3 9-981924 20 35 30 9-45.418' 0-548582 9-469513 0-530487 0-0.8095 9-98,905 26 44 9-45.632' tt.57 0-548368 9-469746 22 171 0-530254 0-0.8114 2214 9-981886 le 34 30 40 9-45.846' !3 165 0-548.54 9-469979 23 .79 0-530021 0-0.8132 23 14 9-98.868 14 30 27 18 9-452060' !4 .72 0-547940 9-47021. 24.87 0-529789 0-0,8.5. 24.5 9-98. S49 12 Xi 30 50 9-452274' 5 .79 0-547726 9-470444 25.94 0-529556 0-0.8,70 25.6 9-98.830 10 30 28 52 9-452488' 6 .86 0-547512 9-470676 26202 0-519324 0-0.8188I-26 16 19-9818,21 6 32 30 54 9-452702' 7 .93 0-547298 9-470909 27 210 0-52909. 0-0.8207 2717 9-98179; 6 311 29 5« 9-4529.5' 8 200 0-547085 9-471.4. 2S21S 0-528859 0-0.8226 28.7 J-98.774 4 31 30 58 9-453129" 9 108 0-54687. 9-471373 29 226 0-528627 0-0.8244 2918 9-98.756 S 30 .10 6 9-4533423 2,5 .0-5466581 9-471605 3P 233 0-528395 0-0,8263 3U_I9 J-98.737 30 /// ^ Cosine ParU | Secant | Cotang. Parts Ta.igeiit Cohec. Parts Sine ^''\ 73° 4'- S-C- ~| TAHI F. G8 77« 1 LOG. SINES, i;OSINES, *c. 1 l" 6" \Cy° '" m Sine I Paits Coscc Tangent Parts Cotang. Secant Parts I Cosine •? ' " arj 7 9-4533+^1 .0-546658 9-47.605 10-528395 ,0-018163 9-9^,737 54 HiJ 9-453555! •' 7 .0 546445 9-47.837 1" 8 .0-518.63 .0-0,8282 i" 1 9-98,7,8 5S 311 61 4 9-453768 10-546231 9-472069 .0-527931 ,0-0,8300 2 , 9-98.700 50 2» 30 6 9-4539S1 10-5460.9 9-472300 .0-517700 10-0,83.9 3 2 9-98.68. 54 3ri 3.! 8 9-454194 4 28 10-545806 9-472531 .0-52746S ,0-0.8338 4 3 9-98.661 52 •-'8 30 10 9-45440- 5 35 '°-545593 9-472763 .0-527137 .0-0.8357 4 3 9-9«.643 50 :ni n ,i 0-454619 6 42 .0-54538. 9-472995 .0-517005 .0-0.8375 6 4 9-98,625 4S 27 30 14 0454832 7 49 .0-545.68 9-4732:6 .0-516774 .0-0.8394 7 4 9-98,606 40 3" 34 16 9-455044! 9 56 .0-544956 9-473457 .0-526543 .0-0.84.3 8 5 9-98,587 44 ai 30 18 9-4551561 9 63 9-455469'<' "O .c- 544744 9473688 .0-516312 .0-0,8431 y 6 9-98,568 42 3" 35 20 .0-54453, 9-4739'9 10-526081 ,00,845. 10 6 9-98,549 40 25 30 •M 9-45568111 78 .0-5443.9 9-474.50 11 84 .0-525850 .0-0,8469 1' 7 9-98.53. ■IS M 36 24 9-455893'2 85 .0-544107 9-47438. .0-5256.9 ,0-0,8488 12 8 998,5,2 30 •24 30 26 9-45610413 92 .0-543896 9474611 13 ICO .0525388 ,0-0,8507 13 819-98,493 34 3 8 .0-52.254 ,0-0.8848 I , 9-981152 4B 1 4 9-460108 2 14 0-539892 9-478975 2 15 ,0-52.025 .0-0.8867 2 I 9-98.133 58 U 30 e 9-4603.7 3 21 0539683 9-479203 3 13 .0-510797 .0-0. 8886 3 2 9-98, ..4 54 3(1 47 8 9-460527: 4 28 0539473 9-479432 >. }o .0-510568 ,0-0,8905 ♦ 3 9-98,095 V2 13 30 10 9-460736! 6 35 0-539164 9-479660 1 6 38 .0-510340 ,0-0,8914 S 3 9-98.076 50 30 48 12 9-460946^ 6 42 0-539054 9479889 1 <5 45 .0 520111 :o-o,i,.,43 6 4 9-98.057 43 12 3:l II 9-461155 7 49' 0-558845 9-4801.717 53 10-519883 .0-0.89-11 7 4 9-98.038 4(1 *' 1 49 10 9-4613641 8 56 0-538636 9-4S0345 8 6. .0-5.9655 ,o-o,89i, 8 5 19-98.0.9 i. 11 30 18 9-461573 9 6z 0-538427 9-480573 : 9 68 10 519427 .0-C.9CO0 9 6;9-9,'ioco .2 a« 3.1 20 22 9-461782 69 1 1 76 0-5381.8 9-48080. 10 76 .1 83 i£15'li99 10-51897, ,0-0,90,9 10 6 9-980,8. 40 10 9-461990 0-538010 '^s.UI^ .0-0,9039 9-98090. M 24 9-462i99li2 83! 0-53780. 9-48.-.?7|I2 9> 10-5.8743 ■ 0-0.9058 1'. 8 9-98094-. M u 31) 20 9-46240713 90 1 0-537593 9-48.4X4 |13 99 Jo;5>S5.6 ,0-011)077 13 i 9-980923 .34 3(1 .-.2 28 9-462616I14 97 0-537384 9-4817.1114 .c6 ,o*oiijcgc , 14 c) 9-980904 32 8 30 30 9-462824 15 .04 0-53-.76 9-48.939 15 1.4 ;o-5;8o6i o-o,g,,5ll5,.. 9-9808S5 30 30 .'.3 32 9-46303216 ... 1 0-536968 9-482.67 IS .2. .0-5,7833 ,0-0,9,34' 16"^ 9-980866 -28 7 30 34 9-463^0,17 ..8 0-536760 9-48239410 .29 .0-5.7606 0-0,9153 17 1, 9980847 -20 54 36 9-463448 IK .25 j 0-536551 9-48262. lb ii6 ■0-5.7379 0-0, 9, v, 18.1 9-980827 -21 e 30 38 9-46365619 .3 = 0-536344 9-482848 |19 144. .0-5,7,52 00,9, «! 19,2 9-980808 22 3» S.j *° 9463'!64: 20 ,39 21 .46^ 0-536156 9-483075 20 .5. .0-5.6925 0-0,92,, :?, 9-980789 -20 ft 9-464072 0-535928 9-483302' 21 .5, ,0-5,6698 0-019230 9-980770 .ifi U 9-46427922 153 0-53571. 9-483529 i*'^ >67 .0 ^.647, 0-0,9250122 ,419-980750 10 4 30 4« 9-464486123 ,60 o-S355'4 9-483755 !23 174 .0-5,6145 0-0,9269123 ,.,|5-,8o73i 0-0.9188 1 24 ,519-9807,2 ul 3.. ■'.7 4M 9-46469424 .67 1 0-535306 9-483982 !24 .82 .0-5,^0.8 12 a M SO 9-464901,25 .--4 1 0-535099 9-4841C8 25 ,89 ,0-5,5791 0-0,9307 25 ,6 9-980693 30 5R 52 9-465,o8j2f, .80' 0-534892 9-484435 h '97 10-515565 0-0,9317 I2C ,7 9-980673 'I 3 .» M 9-4653.527 18- 0-514685 9-48466. 27 105 ,0-5,5339 0-0.9346127 ,7 19-980654 ;<« .'.9 M 9-465522;J« 194 1 c-534478 9-48488- I28 1.1 ,0-5.5,13 0-0,9365 28,8 9-98063^ 4 1 M ; .in 9-46572929 201 j 53427. 9-485.13 129 220 ,0-5,4887 o-o,9384;29,9 99806,6 2 ,ip i;n s 9-46593530 208 0-534065 9-485339 •'O "7 ,0-51466, 0-0.9404130.9,9-980596 '^'^. Co.ine i Parts | Secant Cotang. 1 Parts "Tangent Cosec. j PurU j Sine ^■^\ 73° 4" 52- 1 772 TABLF. 68 LOG. SINES, COSINES, &c. ~ Ih yn, 17^ /// •? Sine Parts Cosec. Tangent Parts Cotang. Secant 1 Parts 1 Cohine in i4T ~o 9"+6593 .0-534065 9-485339 .0-5,466. ,0-0,9404 I9-980596 E2 30 •i 9-466142 I" 7 .0-533858 9-485565 ' " 7 10-5.4435 10-019423 1'. 9-980577 5n 30 1 4 9-46634* 2 14 .0-533652 9-48579. 2 .5 10-5,4209 10-0.9442 2 . 9-980558 511 59 30 c 9-4665, 3 20 •0-533445 9-4S6016 3 22 .0-5,3984 10-0.9462 3 2 9-980538 54 30 2 8 9-46676 4 27 .0-533239 9-486242 4 30 .0-513758 ,0-01948, 4 3 9-9805.9 52 5a 30 10 9-46696 5 34 10-533033 9-486467 5 37 .0-513533 ,0-0,9500 5 3 9980500 50 30 3 12 9-467173 6 41 .0-5328x7 9-486693 6 45 .0-5.3307 10-0,9520 6 4 9-9804S0 4M 57 30 u 9-467379 7 43 .0-53262. 9-486918 7 52 .0-5.3082 .0-0,9539 V 5 9-98046, 4li 4 10 9-46758 8 55 .0-5324.5 9-487143 8 60 10-5.2857 '0-0,9558 8 5 9-980442 44 56 30 18 9-467790 9 6. .0-5322.0 9-487368 9 67 .0-5.2632 ,0-0.9578 9 6 9-980422 42 30 6 30 ■i-i 9-467996 10 68 11 75 .0-532004 9-487593 9-4878.8 U 82 .0-512407 .0-0.9597 10 6 '1 7 9-980403 38 53 9-468202 10-55.798 |.0-5,2lS2 1-^^^ 9-980383 6 ■21 9 468407 12 82 .0-53.593 9-488043 12 90 .0-5. .957 10-0.9636 12 8 9-980364 M 34 30 ■iU 9-468612 13 89 10-531388 9488268 13 97 10-51.732 10-0.9656 13 8 9-980344 J4 30 7 28 9-46S8.7 14 96 .0-53. .83 9-488492 14 105 10-5. .508 .0-0,9675 14 9 9980325 32 53 30 30 9-469022 15 102 10 5J097!! 9-4887.7 15 112 .0-5.1283 10-0.9694 15 .0 9-980306 30 30 32 9-469227 16 109 .0-530773 9-48894. 16 .20 .0-511059 10-0197,4 16 ,0 9-9802S6 28 5-2 30 :u 9-469432 17 116 .0-530563 9-489166 17 127 .0-5,0834 10-0.9733 17 ,1 9-9S0267 20 30 9 3li 9-469637 18 123 10-530363 9-489390 18 135 .0-5.061C 10-019-53 18 ,2 0-9S0247 51 30 38 9-469842 19130 10-530.58 9-4896,4 19 142 ,0-510386 10-0J9772 19 ,2 9-9S022S 22 30 10 30 40 9-470046 20.37 2! ,43 10-529954 9-489858 20 ,50 21 ,57 ^5.0,62 ,0-509938 10-019792 20,3 21 ,4 ,-980208 20 60 9-470251 10-529749 9-490062 10-019811 9 980,89 II 44 9-470455 22.50 10-529545 9-490286 22 165 .0-5097.4 10-01983, 22,4 9-980.69 10 49 30 4(i 9-470659123 ,57 10-529341 9-490510 23 .72 .0-509490 10-0,9851 23,5 9-980.49 14 30 12 48 9-4708632* ,64 .0-529.37 9-490733 24 iSo 10-509267 10-0,9870 24,6 9-980.30 12 48 30 50 9-471067 25,7. .0-528933 9-490957 25 .87 .0-509043 10-0,9890 25,6 9 9801,0 30 13 52 9-471271 26.78 0-528729 9-491.80 26 .94 .0-508820 10-019909 26,7 9 98009, 8 47 30 54 9-47>^75 27.84 .0-528525 9-49.404 27 2C2 10-508596 10-019929 •27,8 9-98007, 8 30 14 5(1 9-471679 28 191 0-52S32. 9-49.627 28 209 .0-508373 10-0,9948 28 18 9-980052 4 4C 30 5S 9-47>8S2 29 198 .0-528. .8 9-49.850 29 2,7 .0-508.50 10-0.9968 29,9 9-980032 2 30 15 9 2 9-471086 30 205 0-5279.4 9-492073 a0 224 .0-507927 10-0,9988 30,9 99800,2 51 58 45 9-47^189 1 7 .0-527-11 9-492296 1 7 .0-507704 10-02C007 1 , 9979993 16 4 9-471492 t .3 .0-527508 9-4925.9 2 ,5 ,0-507481 10-020027 2 ] 9-9799V3 iti 44 30 1 9-472695 3 10 0-527305 9-492742 3 22 .0-50725S 10-020046 3 2 9-979954 51 30 17 8 9-4^2898 4 27 0-527.02 9-492965 4 30 ,0-507035 10-02 oc66 4 3 9-979934 5J 4.1 30 10 9-47310. 5 34 0-526899 9-493-87 5 37 .0-5068.3 10-0200i6j 5 3 9-9799,4 50 30 18 12 9-473304 6 40 0-526696 9-4954.0 6 44 ,0-506590 10-020,05 6 4 9-979895 48 42 30 14 9-473507 7 47 0-526493 9-493632 7 52 .0-50636S 10-020125 ' 5 9-979875 46 30 19 16 9-473710 8 54 0-526290 9-493854 1 « 59 ,0-506.46 10 020145 « 5 9-979S55 44 41 30 IS 9-4739>2 9 6. 0-5260S8 9-4940— j 9 66 .0-505923 10-020,64 U 6 9-979836 42 30 20 30 20 9-474115 10 67 11 74 0-525885 9-494299 U. 74 10-505701 10-020184 10 7 11 7 9-979816 '" 40 9-474317 0-525683 9-49452. 11 8. ,0-505479 10-020204 9-979796 21 24 9-4745 '9 12 81 0-52548. 9-494743 12 89 .0-505257 ,0-020224 12 8 9-979776 30 ■.vj 30 26 9-474721 13 88 0-525279 9-494965 13 96 ,0-505035 10-020243 13 9 9-979757 34 22 28 9-474923 14 94 0-525077 9-495186 14 ,03 .0-5048.4 10-020263 14 9 9979737 32 30 30 30 9-475'25 15 lol 0-524875 9-495408 15 ,1. .0-504592 10-020283 15 .0 9-979717 30 30 21! 32 9-475327 16 108 0-524673 9-495630 16 .18 ,0-504370 ,0-020303 16 I. 9-979697 2H 37 31) 31 9-475529 17 115 0-52447. 9-49585' 17 .26 10-504,49 10-020322 17 .. 9-979678 20 24 3li 9-475730 18 .22 0-524270 9-496073 18 .53 .0-503927 ,0-020342 18 .2 9979658 21 3li 3!l .18 9-475932 19 12S 0-52406S 9-496294 la 140 10-503706 ,0-020362 19.3 9-979638 30 4r 40 9-476133 20,35 21 141 0-525867 9-4965.5 20 .48 21 .55 .0-503485 10-020382 20,3 21.4 99796)8 18 30 9-476335 7^^667 9-496736 10-503264 10-020402 9-979598 2f; 41 9-476536 22.49 0-523464 9-496957 22 163 10-503043 10-02042, 22.5 9-979579 10 .-'4 30 40 9-476737 23 .55 0-525263 9-497178 23 .70 ,0-5028221 10-02044, ■23.5 9 979559 14 30 27 IS 9-476938 24 161 0-523062 9-497399 24 177 10-50260, ,0-02046, 24 16 9'979539 12 33 30 .Vl 9-477'39 25 .68 0-52286, 9-49-620 25,851 0-5023S0 ,0-02048, 25 ,6 9-979519 10 30 28 52 9-477340 26,75 0-522660 9-497S41 26 192 1 0-502159 0-02050, 26,7 9-979499 ^ 32 30 S4 9-477540 27 .Si 0-522460 9-4(1806. 27 200 0-50.939 0-02052, 27 ,8 9-979479 (i 30 2!) :.ti 9-477741 28 1 88 0-522259 9498282 28 207 0-50.718 .0-02054. 28,8 9-979459 1 31 3;i 5N 9-47794' 29.95 0-5:2059 9-498502 21)214 O-50149S 0-02056. 29.9 9979439 ■t .'iO 12 9-478142 10 202 0-521858 9-498722^ W 222 0-50,278 0-020580! 30 20 9-979420 n 1 :v) '" m Cosine Parts Secant Ccn,. plrtT Tangent Cosec. 1 Parts Sine m.j VV" 4" on- 3 TABLE n8 l.OG. SINES, COSINES. Sir.. j 1'' 10"- 17° 1 ' " m Sine i Parts 1 Cosec. TanijeHt Parts j Cotaiig. Secant Parts 1 Cosine -r^l -.uT l~ 9-47X14 10-52,858 9-498722 10-50.278 .0 -C2C5SO 19-979420 SO' 3U 1 ji) 1 2 9-47«34= I" 7 .0-52,658 9-498943 1 7 '0-501057 ic -020600 9-97940C lb 20 31 9-47854= 2 .3 .0-521458 9-499,63 a ,5 ,0-500837 -020620 a , 9-979380 ',/, 2y M 9-478742 3 20 .0-52,258 9499383 3 221,0-5006,7 ■020640 3 2 9-979360 ■A 3" 32 9-478942 * :6 [o'52i058 9-499603 4 29 10-500397 ■02c66o * 3 9-979340 ii 2B 30 9-479 '42 S 33 .0-520858 9-499822 5 36 10-500,78 -C206S0 5 3 9-979320 50 3C 3a 12 9-479542 6 40 .0-520658 9-500042 6 44 10-499958 -020700 6 4 9-979300 48 27 30 9*47954- 7 46 .0-520458 9-500262 7 5. ■0-499738 -020720 7 5J9-9792S0 Hi 30 34 9-47974< 8 57 .0-520259 9-50048, 8 58 .0-4995.9 -020740 8 5I9-979260 41 2C 30 9-479941 9 60 .0-520059 9 50070, 9 66 .0-499299 10 020760 9 619-979240 42 30 30 31) 94S0140 10 66 " 73 .0-5,9860 9-500920110 73 9-501,40 ill So .0-499080 .0 •020780 10 7 11 7 9-979220 40 26 9-480339 .0-5.966. !.o-49886o To 020800 9-979200 3(J 9-480539!!. «o 10-5.946. 9-50.359 12 88!, 0-49864, 10 020820 12 8 19-979,80 3U 24" 30 9-4S073S13 86 10-519262 9-501578 13 95110-498422 10 020840 13 919-979,60 3, 37 is 9-480937U 93 10-519C63 9-501797 |l4 102 1 10-493203 10 0!oS6o 14 ).948.55,;17 1.3 .0-5,8467 9-502453 17 ]24i|0-4v7547 10 020921 17 11 9-979079 2U 1 30 3!) 30 9-48.73' '8 ..9 .0-5.8269 9-502672 \lH 131 110-497328 10 020941 lis... ,,•979059 ■u 21 30 38 9-48193CI19 .26 .0-5.8070 9-502S91 ';19 ,39 10-497109 10 OJ0961 1 19 13 )-979039 j2 ; -!■ 40 40 4i _9 48M.Sj.20,3Z 9 ■.riiii\ii .39 10-5.787Z 9-503,09 20.46 21 ,53 ,0-49689, JO 020981 20 1; 1-9790,9 -an 20 .0-517673 9-50332S .0-496672 To^ 021001 21,4 9-978999 41 44 9-^325z5i22 146 ,0-5,7475 9-503546 22 .6.1.0-496454 10 02I021 2-.,, 5 9-978979 lu lu 30 4« 9-482723123 .52 10-517277 9-503764 j';3 .68 1.0-496236 .0 02,041 23'S]9-978959 14 ■ 311 42 48 948292 .'24 159 10-517079 9-503982 24 .75 ,o-496oi8 .0 02106, 24 16 '9-978939 12! la 30 30 9-483.1925 .66 .0-5,688, 9-504200 M 1S2 10-495800 10 021082 25.7 9-97ii9l8 43 ,9-4833 >6,26 .72 .0-5.66S4 9-504418 2fi .90 1.0-4955S2 .0 02,102 26.7 9 978So!( r 'I 30 W 9-4835.4127 .79 IO-5.6486 9-504636 ;-27 .97jio-495364 .0 02,.22 27.8 9-978878 44 Mi 9-4837.2128 .86 j c-5.6288 9-504854 28 204 .0-495146 .0 021.42 28 .9 9-978858 ■i 11; 31 (iS 9-483909;29 .92 0-5.609. 9-505072 ,29 212 ,10-494928 .0 02,162 29.99-978S38 2 ' 311 45 11 9-48410730 199 1 0-5.5893 9-5052^9 30219 .0-4947 11 12. O2II83 30 20 19-9788.7 49! 15 9-484304 ' 7 0-5.5696 9-505507 1 I 7 .0-494493 10 02,203 1 I 19-978797 »Hh.^, 4(! 4 9-48450. 2 .3 0-5.5499 9-505724 a .4[io-494276 .0 02,223 3 ,9-978777 56 1 14 30 li 9-484698 0-5.5302 9-505941 3 22,10-494059 ,0 02,243 3 2 9-97S757 54 1 30 <7 8 9-484895 4 26 0-5.5.05 9-506159 4 29 ,o-493«4' ,0 02,263 * 3 9-978737 52 13 30 10 9+85092 5 33 0-5.4908 9-506376 6 36 10-493624 ,0 02,284 6 3 9-9787.6 lu 48 12 9-485289 6 39 0-51471, 9-506593 a 43 10-493407 .0 02,304 6 4 9-97S696 48 12 30 14 9-485485 7 46 0-514515 9-5068,0 7 50 .0-493190 10 02.324 V 5 9-978676 40 30 49 1« 9-485682 8 52 0-5143,8 9507027 8 58 .0-492973 10 02.345 8 5 9-978655 41 11 30 li- 9485879 9 59 1 0-514,21 9-507243 9 65 ,0-492757 10 02,365 9 6 9-978635 42 30 30 22 9486075 10 651 11 72! 0-5,3925 9-507^60 10 11 11 79 10-492540 10 02,385 10 7 U 7 9-9786,5 40 38 lu 9-48627. 0-513729 9-507677 .0-492323 lo" 021406 9-978594 51 24 9-48646712 78 o-5'3533 9-507S93 12 87:10-492.07 10 02.426 12 8 9-978574 30 i) 30 20 9-486664113 85 0-513336 9-508110,13 94 .0-491890 .0 02,446 13 9 9-978554 31 30 .'.2 29 9-486860I14 91 0-513.40 9-508326 ,14 10. 1.0-491674 .0 021467 141019-978533 32 1! 30 30 9-487055J15 ,3 0-5,2945 9-508542 15 .08 .0-49145S O2.4S7 16 10 9-978513 30 30 :.3 3-2 9-487251)16 104 0-5,2749 9-508759 16 .13 .0-491241 0- 02.507 16,, 9-978493 ■28 7 30 H 9-487447,17 II. o-5'i553 9-508975 17 123 ■0-491025 0- 02,528 17 12 9-978472 ■2U 54 30 9-4876431I8 .17 0-5,2357 9-509191 18 ,30 .0-490809 0- 021548 18.219-9-8452 21 « 30 38 9-487838 19 .24 0-512162 9-509407 19.37 .0-490593 0- 02,569 19i3l9-f .843. 22 311 55 10 42 9-4S8O34J20 .31 9-48822921 137 0-5. .966 9-509622 20 .44 21 .51 1049037S 0- 02.589 20.4 21.4 9-97^4,1 20 5 0-5. .771 9-509838 .0-490.62 02.609 9-978391 50 44 9-488424,22 .44 0-51.576 9-510054 22 159 10-489946 0- 02,630 22.5 9-978370 10 4 30 4-1 9-4886. 9,-i3 .50 0-51,38, 9-5.0269 23 166 .0-48973. 0- 021650 23 ,6 9-978350 II 31J 67 18 9-4888.4124 .57 0-5, ,,86 9-510485 24 173 10-489515 0- 02:671 24.6 9-97S329 12 3 30 iO 9-489009« >63 0-5,0991 9-510700 25 ,80 10489300 02,69, 25.7 9-9-8309 lU 311 58 52 9-489204-26 .70 0-5,0796 9-5,09.6 26 ,87 10-489084 £,■ 02,712 26.8 9-978:88 8 2 3n -il 9-48939927 .76 o-5,c6c, 9-511131 27 195 .0-4S8S69 0- 021732 2718 9-9/8268 30 :•!» M 9-489593 28.83 0-5.C407 9-511346 28 202 10-488654 o- 021753 28,9 9-978247 4 1 30 •,H 9-489788 29 .89 9-511561 29 209 10-488439 0- 021773 29 20 9-97822- 2 1,0 12 9 489982 .0.96 0- 5 .'col 8 9-511776 30 2.6 0-021794 302019-9-8:06 11 '" ni Cosine Part.. Secant CotanR. Parts Tangrnt Cosec. ParU Sine m. 777 72= 4^ 4>S- 1 ■74 TABLK 68 LOG. SINES, COSINES, &o. ] l" ]-2"' 18<^ i rr/ m Sine 1 Parts Cosec. Tangent Parts 1 Cotang. Secant Parts] Cosine m V" "TT "jj" 9-48998 10-510018 9-51.776 ,0-488224 10 -02.794 J9-9782C6 »8,T;(r .w 2 9-49017 I" 6 10-509823 9-511991 1" 7 10-488009 10 -021814 1" . 9-978186 50 1 10 : 4 9-49037 2 13 10-509629 9-512206 2 .4 10-487794 10 ■021835 2 i!9-978.65 iii i an 30 6 9-490S6 3 19 10-509435 9-512420 3 21 10-487580 .0 •021855 3 2 9-978145 54 30 2 8 9-49075 4 26 10-509241 9-512635 4 28 10-487365 10 -02.876 4 3 9-978124 52 r,a 30 10 9-49095 5 32 .0-509047 9-512S50 5 36 13-487150 .0 -02.896 6 3 9-978104 50 30 3 12 9-49114 6 39 10-508853 9-513064 " 43 ,0-486936 10 •02.9.7 6 4 9-978083 48 -■•7 30 14 9-49134 7 45 10-508659 9-5.3278 7 50 ,0-486722 10 02.938 7 5 9-978062 46 34'35 .0-485865 1^ 022020 9-977980 6 U 9-492308 12 77 .0-507692 9-514349 12 85 .0-48565. 10 02204. 12 8 9-977959 36 .J4 30 28 9-492502 13 84 10-507498 9-514563 13 93 .0-485437 10 022C6. 13 9 9-977939 34 311 7 29 9-49269 14 90 .0-507305 9-5>4777 14 .00 .0-485223 10 022082 14 10 9-9779.8 32 5:t 30 30 9-49^S8i 15 96 .0-5071,2 9-514990 15 107 10-4S50.0 .0 022.03 15 10 9-977897 30 Ml 8 32 9-493.0S 16 ,03 .0-5069,9 9-5.5204 16 1.4 .0-484796 10 022123 16.1 9-977877 28 52 30 W 9-493273 17 109 10-506727 9-515417 17 .2. .0-484583 .0 022.44 17 12 9-977856 26 30 9 36 9-49346'' 18 116 ,0-506534 9-5.563. 18 .28 10-484369 .0 022.65 18 .2 9-977835 •24 51 30 38 9-493659 19 122 10-506341 9-5.5844 19 .35 10-484.56 .0 022. 85 19.3 9-977815 -22 30 10 30 40 12 9-493S5; 20 ,29 21 ,35 io-5c5i49 9-5.6057 20 .42 21 .50 .0-483943 10 C22206 20.4 21.4 9-977794 20 50 9-494044 ■0-505956 9-516271 .0-483729 10' 022227 9977773 II 44 9-494236 22 142 10-505764 9-516484 23 157 10-4835.6 10 022248 22.5 9-977752 16 49 30 46 9-494428 23 148 .0-505572 9-5.6697 •W.64 10-483303 10 02226S 23.6 9-977732 |.| 3(1 12 48 9-494621 24 155 10-505379 9-516910 24 .71 .0-483090 10 022289 2417 9-97771. 12 48 30 iO 9-494813 25 161 .0-505187 9-5'7'»3 25 178 10-482877 10 022310 2017 9-977690 10 30 IM 52 9-495005 26 168 10-504995 9-51733"; 26185 10-482665 10 02233. 26.8 9-977669 J, 47 30 54 9-495196 27 174 .0-504804 9-517548 17 .92 10-482452 JO 022352 27.9 9977648 U 50 9-495388 28 180 10-5046.2 9-517761 W,99 .0-482239 10 022372 28.9 9-977628 4 46" 30 58 9-495580 29 186 10-504420 9-517973 29206 10-482027 10 022393 29 20 9-977607 2 3(1 15 9-495772 30 193 10-504228 9-518186 ^0 2.4 10-48,8.4 10 0224:4 30 2 1 9-977586 «7 45 30 9-495963 1 6 ,0-504037 9-518398 1 7 10-48.602 10" 022435 1 I 9-977565 10 9-496154 2 13 .0-503846 9-5186.0 a 14 .0-48.390 10 022456 2 . 9-977544 56 44 30 9-496346 3 ,9! .0-503654 9-5.8822 3 2. .0-481178 10 022476 3 2 9-977524 54 30 17 9-496537 4 25 .0-503463 9-519034 4 28 0-480966 10 022497 4 3 9-977503 52 43 30 9-496728 5 32 .0-503272 9-519246 s 35! 0-480754 10 0225.8 5 3 9-977481 311 l« 9-496919 6 38 0-50308. 9-519458 6 42 0-480542 10 022539 6 4 9-977461 48 42 3IJ 9-497 1 10 7 44 0-502890 9-519670 7 49 0-480330 .0 022560 7 5 9-977440 46 36 lu 9-497301 8 5, 0-502699 9-5.9882 1 8 56 1 0-480118 .0 O225S. 8 6 9-977419 44 41 30 9-497492 9 57 0-502508 9-520094 9 63 0-479906 10 022602 9 6 9-977398 12 :io •2» 22 9-497682 10 63 11 70 0-502.27 9-520305 10 70 11 77 0-479695 022623 10 7 9-977377 9-977356 38 4l» 30 9-497873 9-5205,7 0-479483 kT 022644 21 21 9498064 12 76 ^•50.936 9-520728 12 84! 0-479272 .0 022665 12 8 9-977335 36 39 30 26 9-498254 1.-1 82 0-50.746 9-520939 i':' 9' 0-+79061 .0 0226S6 13 9 9-977314 34 30 22 28 9-498444 14 89 0-50.556 9-52. .51 14 98 0-47S849 10 022707 14 10 9-977293 32 38 30 30 9-498634 15 95 0-50.366 9-52.362 15 io5i 0-478638 10 022728 15 ?o 9-977272 30 30 23 32 9-498825 16 loi 0-501175 9-521573 16 ,12 0-478427 10 022749 16., 9-977251 28 37 30 34 9-499015 17 108 0-500985 9-521784 17 120 0-4782.6 17 12 9-977230 26 30 24 36 9-499-04 18 114 0-500796 9-52.995 18 .27 0-478005 .0- C2279. 18,3 9-977209 24 38 30 38 9-499394 lU 121 0-500606 9-522206 19.34 0-477794 0228.2 19.3 9-977.88 22 M 25 30 40 9-499584 20.27 21 ,33 0-500416 9-522417 20 14. 21 ,48 0-477583 10- 022833 20.4 21.5 9-977.67 20 35_ .10 9-499774 0-5C0226 9-522627 0-477373 10^ 022854 9-977146 26 44 9-499963 22 140 0-50C037 9-522838 22 .55 0-477.62 .0- 022875 2215 9-977.25 16 34 30 46 9-500153 2,1 146 0-499847 9-523048 ]23 .62 0-476952 10- 022896 23 16 9-977104 14 30 27 48 9-500342 24 ,52 0-499658 9-523259 j24 169 0-47674. 0- 0229.7 24 17 9-977083 12 :« 30 50 9-500531 20,59 0-499469 9-523469 25 .76 0-47653. 0- 022938 25 17 9-977062 10 30 28 52 9-500721 26,65 0-499279 9-523680 126 .83 0-476320 0- 022959 26 18 9-977041 n 32 30 54 9-500910 27 171 0-499090 9-523890 127 .90 0-476.10 0- 022980 27.9 9-977020 (i 30 20 56 9-501099 28 178 0-498901 9-524.00 28 .97 0-475900 0- 023001 28 20 9-976999 4 31 30 58 9-501288 29184 0-498712 9-5243. o 29 204 0-475690 0- 023022 29 20 9-976978 2 30 1(0 14 9-501476 30 190 0-498524 9-524520 JO 2 , 1 1 0-475480 0-023043 30 21 9-976957 3(1 777 „. Cosine j Paru| Secant Cotang. Parts 1 Tangent 1 Cosec. ParU 1 Sine m. / » .^,.--| UHi. SINES, COSINES, &c. j I" U'" 18° 1 /// Sine ! riru' C05CC. Tangent I Parts Cotang. Secant Part- 1 Cosine m r 1m 9'S'>'4" 10-4985:4 9524520 .0-475480 10-02304 9-976957 iel'W 1 m ■i 9-50.66 1" 6 10-498335 9-524730 •" 7 '0-475270 .0-023065 1" 1 9-976935 58 3(1 SI 4 9-5oi85< 2 12 .0-498246 9-524940 2 14 j. 0-4-5060 ;o;o2 3o86 9-9769.4 JO 2'.) 3U « 9-50204 3 19 10-497958 9-525.49 3 2.1.0-4:485. 9-976893 .'.4 31J M 9 9-50213 4 25 10-497769 9-525359 4 281.0-474641 !o-023;28 9-976872 32 20 30 111 9-5024K 5 3, 10-497581 9-525568 5 35 10-474432 10-023.49 9-976851 50 311 Xi 1-2 9-50260- « 3- 10-497393 9'5- 5778 6 42I10-474222 .0-023170 6 4 9-976830 18 27 M 14 9-50J79< y 44 10-497204 9-525987 7 49 10-474013 10-023192 7 5 9-976S08 4G JH 34 10 9- 502984 H 50 10-497016 9-526197 8 56 .0-473803 10-C23213 8 6 9-976787 44 •21; 30 18 9-503172 9 56 .0-496828 9-526406 9 63 '0-473594 10-023234 1 9 6 9-976766 42 w ■.u SO 9-503360 10 62 .1 69 10-496640 9-526615 10 70 !•! 77 10-473385 10-0232551 10 7 10-023277 ■' 8 9-976745 40 38 2ft 9-5035+S 10496452 9-526824 .0-473176 9-976723 :w M 9-50^35 12 75 .0-496265 9-527033 12 84 10-472967 10-023298! 12 9 9-976702 30 24 30 ! w 9-5039='3 i:< 81 10-496077 9-527242 lis 90 .0-472758 10-023319,13 9 9-9766S. 34 30 37 \-i» 9-504110 U 87 10-495890 9-527451 |14 97 10-472549 10-023340 j 14,0 9-97666C 3-2 23 30 30 9-50420S 15 ,4 .0-495702 9-577660 15 104 10-472340 .00233621 15,1 9976638 30 .10 98 m 9-504485 '« >oo ■0-495515 9-527868 16 ... 10-472132 .0-023383 16 1, 9-9766.7 '23 22 3« 34 9-504673 17 106 .0-495327 9-52S077 17 118 10-471923 10-02340+1 17 .2 9-976596 2C 30 3U 3(1 9-5C4S6CI8 1,2 10-495140 9-52S285 18 .25 10-471715 10-023426, 18 13 9-976574 -24 21 30 38 9-50504719 119 .0-494953 9-528494 19132 .0-47.506 10-023447 '9 13 9-976553 -22 30 40 40 9-505i34i2<' '»5 9-5054i'|2> >3' 10-494766 9-528702 20 139 21 .46 .0-47. 298^0-023468 20,4 21.5 9-976532 20 iL 30 1 43 .0-494579 9-5289.0 .0-47=^90 .0-023490 9-9765.0 41 44 9-505608,22 137 .0-494392 9-529.19 22 .53 .0-470SS. 10-02351. 22,6 9976489 10 30 40 9-5O5704;2-1 144 .0-494206 9-529327 i23 160 10-470673 ,0-023532 1-23 ,6 ;9-976468 14 42 48 9-50598.24 150 .0-494019 9-529535 |24 167 .0-470465 ■0-023554 j 24 17 9976446 1-2 18 30 M 9-5c6i6825 156 10-493832 9-529743 a 174 10-470257 .0-023575 25.8 9-976425 10 30 43 5-2 9-5c6354;2fi ,62 .0-493646 9-52995. 26 ,8. 10-4700+9 .0-023596 26.8 9-976404 H 17 30 Jl 9-506541127 169 .0-493459 9-530.58 i27 .88 .0-4698+2 .0-0236,8 27,9 9-976382 (J 311 44 .-,6 9-506727128 175 10-493273 9-530366 i«8 ,95 .0-469634 .0-023639 1 28 20 9-97636. J Ifi 30 38 9-506913J29 i«i|io-493o87 9-530574 |29 202 .0-469426 .0-023661 1292. 9-976339 ■2 311 i5_is| 9-507099:50 187 10-492901 9-53078.130209 .0-469219 .0-023682 30 2. 9-976318 «5 3H 15 — 9-5072851 1 6 10-492715 9-530989 ' 7 .0-4690., .0-02370+: I 1 9976296 46 9-50747,1 2 12 10-492529 9-53i'96i » '4 .0-46S804 10-023725 1 2 , 9-976275 iu U 30 9-507657I 3 18 10-492343 9-53.403 S 2. .0-+68597 .0-023746 3 2 9-976254 54 30 47 9-5078431 * 25 ■o-492>57 9-53'6.. 4 zS .0-468389 10-023768 * 3 9-976232 52 13 30 10 9-50802S 5 31 10-491972 9-53'«i8 5 34 .0-468.82 10-023789 5 4 9-97621, 50 30 48 II 9-508214 6 37 jio-491786 9-532025 6 4. 10-467975 10-0238,, 6 4 9-976189 48 12 30 14 9-508400 7 45 10-491600 9-532232 7 48 10-46776S ,0-023832 7 5 9-976168 10 .•id 49 ig 9 5085S5 8 49 10-491415 9"532439 « 55 10-467561 ,0-023854 8 6 9-976.46 44 11 30 18 9-50S770 9 55 10-49123C 9-532646 9 62 ■0-467354 .0-023875 9 6 9-976125 13 30 60 30 M 9-5089561 62 1 68 .0-49.044 .0-490859 ?:512^5_3 9-533059 10 69 11 76 .0-467.47 10-023897 10 7 11 8 9-976.03 1 10 9-509141 0-466^4. 10023919 9-97608. »i 24 9-509326 2 74 10-490674 9-533266 12 83 .0466734 10-023940 12 9 9-976060 M » 30 W 9 509511 3 80 10-490489 9-533472 IS 89 0-466528 10-023962 13 9 9-976038 31 :m) 52 2S 9-509696 4 86 .0-490304 9-533679 14 96 0-46632. 10-023983 U.o 9-9760.7 3-2 H 30 30 9.5C988C 5 92 .0-490120 9-533885 IS ,03 0-466115 0-02+00 5 15 .. 9975995 30 3(1 53 3-2 9-5100651 6 99 0-489935 9-534092 6 1.0 0-46590S 0-024026 16.2 9-975974 •28 7 30 34 9-51025C 7 105 0-489750 9-534298 17 ..7 0-465702 0-024048 17.2 9975952 ■20 311 ■'.4 30 9-510434 8 111 0-489566 9-534504 8 .24 0-465496 0-024070 18. 3 9-975930 24 K 30 38 9-510615 9 117 0-489381 9-534710 9 131 0-465290 0-024091 19.4 9975909 2-2 3(1 65 40 42 9-510803 iO 123 1 .29 0-489197 9-5349'6 JO 138 21 144 0-465084 o-46"4'87S 0-0241,3 20.4 21.5 5-975887 •20 5 9-510987 0-489013 9-535.22 0-024135 5-975865 AC 41 9-511172 "2 135 0-488828 9-535328 22 .5. 0464672 0-024156 22.6 5-975844 JH 4 30 4S 9-511356' '3 142 0-488644 9-535534 23 ,58 0-464466 0-024.78 23,7 5-975822 14 ,10 S7 48 9-511540' (4 148 0-488460 9-535739 24 .65 0-464261 0024200 24.7 5-975800 12 3 30 30 9-511724 5 154 0-488276 9-535945 25 172 0-464055 0-02422. 25.8 r975779 10 .10 88 M 9-511907 6 160 0-488093 9-536150 2r, .78 0-463850 0024243 26.9 r975757 8 2 3< 34 9-512091 7 166 0-487909 9-536356 27 186 0-463644 0-024265 27.9 >-975735 30 69 30 9-512275 8 171 0-487725 9-536561 28 193 0463439 0-024286 28 20 ■975714 4 1 30 38 9-512458 9 179 0-487542 9-536767 29 200 0-463233 0-024308 292. •975692 •1 10 m 1« 9-512642 185 0-487358 9-536972 JO 206 0-463028 0-024330 30 22 -975670 n n TTTj m. Cosine Parts Secant Cotang. Parts Tangent C'ospc. Sine ?^ 77, 71° 4" 4-1™ 1 776 TABLE 68 LOG. SINES, COSINES, &c. i" 16'" 19° "o~ ? Sine Parts 1 Cosec. Tangent Part. Cotang. Secant IPai-(s| Cosine 14 "Sir 9-511642 I10-487358 9-536971 .0-463018 I 0-014330 19-975670 30 ■2 9-512815 1" 6 10-487175 9-537177 1" 7 10-461813 I 0-014352 r 1 9-975648 3(1 I 4 9-5.3Q09 2 .1 .0-486991 9-537381 2 .4 .0-461618 . 0-014373 3 .,9-975627 511 69 30 9'5'3'9J 3 18 10-486808 9-537587 3 20 I'o-iitos ; 0-014395 3 119-975605 54 3(1 2 8 rsnvi 4 24 10-486615 9-53779^ 4 27 0-0244.7 ■» 319-975583 5-i 5(! 3n 10 9-513558 5 30 IO-+86441 9-537997 5 34 Io-l6i;o3 ; 0-014439 5 419-97556. 50 .«! 3 12 9-513741 5 36 10-486259 9-538202 6 4. .0-461798 . 0-02446.1 6 4 '9-975539 48 67 ao 1-1 9-513924 7 43 10-486076 9-538406 7 48 ■0-46.594 ' 0-024481 7 5i9-9755'8 4U 311 4 11) 9-514107 8 49 10-485893 9-5386.. 8 54 10-46.389 1 0-024504 8 6 9-975496 44 i6 30 IK 9-514189 9 55 10-48571. 9-5388.6 9 61 10-461184 . 0-014516 9 7 9-975474 4-2 3(1 '30 20 9-5.4471 10 61 11 67 .0-485518 9-539010 10 68 10-460980 1 0x2454^ 10 7 11 8 9-975451 9-975430 40 5S_ 30 9-514655 IO-485345 9-539114 11 -5 10-460776 I 0-014570 c ■M 9-514837 12 73 .0-485,63 9-539419 ,'2 81 110-460571 1 0-0-24592 12 9 9-975408 3G 64 30 ia 9-515019 13 79 .0-48498. 9-^39633 13 88110-460367 . 0-0246.4 13 9 9-975386 34 31 7 28 9 515101 14 85 10-4S4798 9-539837 ,'■» 95|'°-46o.63 . r 024635 14 ,0 9-975365 32 63 30 30 9-515384 15 9, 10-4846,6 9-540C4. 15 .01 [.0-459959 ■ 0-024657 15 11 9-975343 30 30 8 '^ 9-51556616 97 10-484434 9-540245 16 .09, .0-459755 1 0-014679 16 12 9-97531, -28 52 30 9-515748 17 103 10-484151 9-540449 17 1.6 110-45955. ' 0-014701 17,2 9-975299 ■21) 30 !> 30 9-515930 18 109 10-484070 9-540653 IS 121 10-459347 . 0-024723 18. 3 9-975177 -24 51 30 33 9-516. 11 19 115 10-483888 9-540857 il9 129 10-459.43 . 0-014745 19 ,4 '9-975155 22 30 10 30 40 9-516194 20 121 21 117 10-483706 9-54.06. 20 136 21 143 .0-458939 . 0-014767 20.5 9-975133 2115 19-9751,. 20 ill 9-516475 10-483515 9-541164 10-45X736 . 0-014789 II 44 9-5.6657 22 134 10-483343 9-541468 22 .50110-4585321. 0-01481. I -22 16 9-9-5,89 l(i 49 30 40 9-516838 23 140 10-483162 9-54.671 1-23 156 10-45S319 . 0-014833 -23 17 '9-975167 14 30 12 4S 9-517010 24 146 10-482980 9-54.875 |-« .63 10-458.15 . 0-014855 24 18 ^9-975'45 12 4!l 30 50 9-517101 25152 10-481799 9-541078 125 170 10-457921 . 0-024877 25 18 9-975.13 10 31' 13 32 9-5.73S1 26 158 10-4S161S 9-541181 t-26 177 10-457719 . 0-014899 I -26 19 19-975 ic, M 47 30 54 9-5>7564 27 164 10-482436 9-542485 |2' .84 9-5426SS |28 190 10-457515 . 0-014911 27 20 9-9750-9 II ,1(1 U 5li 9"5'7745 28 170 .0-482255 .0-4573.1 ( 0-01494; ' 28 20 ^9-97 505- 4 4(i 3(1 .58 9-517926 29.76 10-482074 9-542891 29 197 .0-457.09 . 0-014965 29 2 1 19-97 5c 3 i I'l I.', 17 9-5.8107:10 182 10-48.893 9-543094 30 104 .0-456906 1 0-0249S7 30 21 :9-975oi3 43 -h 9-5.8187 1 6 10-4817.3 9-543^97 1 7 .0-456703 1 0-025009 1 ■ |9'97499' 16 4 9-518468 2 .1 10-481532 9-543499 2 .3 .0-45650. I 0-025031 2 I 9-974969 .'.(■ 44 30 '' 9-518649 3 18 10-48.35. 9-543702 3 20 .0-456298 ■ 0-025053 3 1 9-974947 51 3(1 17 9-518819 4 24 10-481.71 9-543905 4 27 10-456095 . 0-025075 4 3:9-974915 52 43 30 Id 9 519010 6 30 10-480590 9-544.07 i 3+ .0-455893 . 0-025098 5 4 9-974903 50 30 IR 12 9-5.9.90 6 36 10-4S0810 9-5443.0 6 40 10-455690 . 0-025.10 6 4I9-9748S0 48 42 30 14 9-519371 7 41 10-4S0629 9-5445.1 7 47 10-455488 1 0-025.41 7 5 19-9748 58 4U 3(1 19 ll> 9-5'955r a 48 10-480449 9'5447>5 8 54 10-455285 1 0-025.64 8 6 '9-974836 +4 41 30 IS 9-519731 9 54 10-480269 9- 5449 '7 9 61 10-455083 1 0015,86 9 7I9-974S.4 12 3(1 20 20 9-51991. 10 601.0-480089 9-545. .9 10 67 10-45488. . 0-015108 10 7 '9-974791 lU 411 30 22 9-51009. U 661.0-479909 9-5453^1 U 74 10-454678 . 0-025230 H SI9-974770 z ~30 21 24 9-510171 12 71110-479729 9-545524 12 81 ,0-454476 1 0-025151 12 9I9-974748 :«i 30 26 9-510451 13 78 .0-479549 9-545716 13 87 ,0-454174 . 0-025275 131019-974715 34 30 22 28 9-520631 14 84 10-479369 9-545918 14 94 .0-454072 , 0-025297 14 10 19-974703 32 3(1 30 30 9-510810 15 90 10-479190 9-546.19 15 lOI .0-453S7. 1 0-025319 1511 9-9746S1 30 JO 23 32 9-520990 16 96 10-479010 9-546331 Ifi 108 10-453669 . 0-025341 16,2 9-974659 28 37 30 34 9-521169 17 .02 9-546533 17 1.4 10-453467 I 0-025364 17,3 9-974636 2(i 3(1 24 3(1 9-511349 18 108 10-4^8651 9-546735 .0-453165 I 0-0253S6 18,3 9-974614 24 3(i 30 33 9-51. 528 19 114 10-478472 9-546936 19 128 10-453064 1 0-025408 1914 9-974591 22 30 2.1 30 40 9-511707 30 120 .0-478295 9-547.18 9-547339 20 135 21 14, 10-451862 1 0-015430 20,5 21 16 9-9-4570 3.> 9-511887 21 126 .0-478.. 3 ■0-452661 I 0-025453 9-974547 2(J 14 9-5iio66j-2'2 131 10-477934 9-547540 2-2 148 10-451460 0-015475 22 16 9-974515 Hi 34 30 1(1 9-511145I-23 ,3S|io-4777;5 9-54774- •23 .55 10-451158 0015497 23,7 9-'y74503 14 3(1 27 48 9-qi24i4r>4 144110-477576 9"547945 24 161 10-452057 0-015519 24 18 9-97448. 12 33 311 50 9-?;26o:h>n .;o 10-477398 9-548144 25 .68 10-45,856 0-025541 25 ,8 9-974458 10 3(1 2^1 r,! V ;■:-••:■ V (,-'•. ^10-477119 9-548345 26.-5 .0-45.655 0-015564 26,9 9-974436 K 32 3fl .'.1 - / -'- ■■■•• 10-477040 9-548546 27 181 10-451454 0-025586 2720 9-9744.4 1) 311 2!l Sii 1 -, :- !"■; 10-476861 9-54874- ■2« 188 .0-45115; 0-015609 28 2 1 9-97439' 4 31 30 5^ '•., ,:.--"( .-( .0-476683 9-548948 ■29 .95 10-451053 0-015631 -29 2 1 9-974369 ■1 30 30 18 y ^zuq^.i'i 180 1 10-4-6 (105 9-549149 30 102 .0-450851 o;o2^6^ 30 22 9-97434- V 30 •' " m. Cosine | Parts | Seoaiit Cotans;. Parts Tangent Cosee. Ivu Sine 1^ "' 7l)° 4'' -i-J ■ 1 LOG. SINES, COSINES, Ac. l" IS™ 19" /// •? Sine 1 Paru Cosec. i Tangent Parts 1 Cotaiig. .S.-.-ai.t \Vmt l99'4U- 42; .-III "isr 9-5=349 5 ,0-476505 9-549,49 ,0-45085 ,0-025653; .10 2 9-52367 » 1" « ■0-476326 9-549349 1" 7 10-45065 ,o-02567« '" ' 'r97+3?t 5-^ 1 ,:i 3: 4 9-5^585 I 2 12 10-476,48 9-549550 2 ,3 .0-450450 ,0-025698 :,i, 1 -21. ;io 9-52403 3 ,8 10-475970 9-54975' 10-450249 10-02572 3 2 9-974279 .')! 30 32 8 9-52420 4 24 10-475792 9- 54995' 4 2- .0-450049 ,0-025-43 ■* 3 9-9:4257 0-2 1 21: 1 :io 10 9-52438 5 30 ,0-475614 9-550,52 5 33 .0-44984S ,0-02576, 5 4 9-974235 30 1 30 33 12 9-52456 ft 35 ,0-475436 9-550352 6 40 .0-449648 .0-025788 6 4 99742, 2 iH .'7 30 U 9-5H74 7 41 ,0-475258 9-5505521 7 47 .0-449448 ,0-0258,0 7 5 9-974,90 41) .•10 34 16 9-52492C 8 47 ,0-475080 9-550752 8 53 .0-449248 ,0-025833 8 6 9-974.67 II 26 30 13 9-52509 9 53 ,0-474903 9-550952 1 9 60 .0-449048 .0-02585, 9 7 9-974'45 1-2 30 35_ .10 20 r$^'5^7 10 59 ;1I 65 ,0-474725 9-55"53 10 66 '" 73 .0-448847 ,0-025878 10 7 9-974122 40 25 30 9'Si545'' ,0-474548 9-55'353 .0-448647 .0-025900 '11 8 9-974,00 36 24 9-525630112 71 '0-474370 9-55>552 '2 80 10-448448 .0-025923 12 9 9-974077 30 24 ,10 •20 9-525807I3 7-. 9-515984'* S3 10-474,93 9-55,75213 86 .0-44824S .0-025945 13. 9974055 34 30 37 Iho ic-4740,6 9-55'952 '-k 93 ,0-448048 .0-025968] 14 .0 9-974032 32 23 30 9-52616215 89 ,0-473838 9-552152 15 98 ,0-447848 10-025990 15 ,1 9-9-40,0 30 30 38 32 9-526339116 94 10-47366, 9-552351 16 ,06 10-447649 .0-0260,3 16,2 9-973987 ■IH 22 30 34 9-526;>6|17 100 ,0-473484 9-55255' 17, .3 10-447449 ,0-026035 17,3 9-973965 -20 30 3» 38 9-526693JI8 106 ,0-473307 9-552750 18 ,20 10-447250 ,0-026058 18. 3 9-973942 -24 21 30 36 9-52687o|l9 112 ,0-473,30 9-532950 19 ,26 .0-447050 10-026080 19.4 9-973920 22 30 40 40 42 9"5i7046 20 .,8 10-472954 9- 5 53 '49 20,33 '.1 140 .0-44685. .0-446652 10-026.03 20.5 21 .6 9-973897 ■20 20 9-5'-72i3 21 124 ,0-472777 9-553348 ,0-026.26 9-973875 41 U 9-527400:22 130 10-472600 9-553548 22 ,46 10-446452 ,0-026,48 22 .6 9-973852 10 19 30 4« 9-527576123 136 10-472424 9-553747 23 ,53 ,0-446253 ,0-026.7,; 23. 7 9973829 14 30 42 48 9-527753I24 142 10-472247 9-553946 24 .60 10-446054 .0-026,931 24, 8 9-97380- 1-2 18 30 JO 9-527929^25 148 ,0-47207, 9-554145 25 ,66 10-445855 10-0262.6 25 ,9 9-973784 10 30 43 5i 9-528. C526 i53]io-47i895 9-554344 :'8 '73 .0-445656 ,0-026239 26 19 9-973761 8 .7 30 ii 9-528281127 159 10-47,7,8 9-554543 |'7 '80 '0-445457 10-02626, 2720 9-973739 li 44 iO 9-52S45828 ,65 10-47,54; 9-55474' P" '86,10-445259 ,0-026284 28 2. 9-9737.6 4 16 .10 3S 9-52863429 17,110-47,366 9-554940 i'9 i93Jio-445o6o .0-026307 29 22 9-973694 2 30 4J 19 9-52S8iOi30 ,77 ,0-471,90 9-555'39 SO ,991,0-44486. .0-026329 30 22 9-973671 ftl 5M 15 30 9-5289861 1 61,0-47,0,4 9-555337 1 7 10-444663 ,0026352 1 I 9-973648 4C 4 9-529.6, a 12 10-470839 9-555536 2 13 .0-444464 ,0-026375 2 I 9-973625 3li !4 30 6 9-529337 3 '7 ,0-470663 9-555734 3 20 10-444266 ,0-026397 3 2 9-973603 31 .iO 47 « 9-529513 ,0-470487 9-555933 4 26 .o,M4o67 .0-026420 4 3 9-973580 5-i 13 30 10 9-5296S8 ,0-4703,2 9-556,3, 5 33 ,0-443869 .0026443 6 4 9-973557 30 30 48 12 9-529864 10-470136 9-556329 5 40 10-44367. 10-026465 1 6 5;o-973535 'in 12 30 14 9-530039 ,0-46996, 9-556527 7 46 .0-443473 .0-026488 7 5 9-973512 IC 31 49 10 9-53=2,5 ,0-469785 9-556725 8 53 .0-443275 .0-0265,, 8 6 9-973489 14 11 30 18 9-530390 9 52 ,0-4696,0 9-556923 9 59 .0-443077 ,o-0265-!4 9 7 9-973466 42 30 .".(1 lio" 2-2 9-530565 10 58 11 64 ,0-469435 9-55712, 10 66 U 72 .0-442879 ,0-026556 10 8 11 8 9-973444 40 ilL 30 9-530740 ,0-469260 9-5573'9 ,0-44268. .0-026579 9-973421 .it 21 9-5309,5-12 70 ,0-469085 9-5575'7 12 79 10-442483 .0-026602 12 9 9-973398 30 9 30 20 9-531090113 76 10-4689,0 9-5577'5 l.-l 86 10-442285 .0-026625 13,0 9-973375 31 30 r.2 2N 9-53'265l4 8, 10-468735 9-5579'3 14 92 .0-442087 .0-026648 14,0 9-973352 32 8 30 30 9-53,44015 87 .0-468560 9-558, ,0 15 99 .0-441890 ,0-026671 15., 9-973330 30 30 .-.3 3V 9-5316,416 93 10-468386 9-558308 16 ,05 .0-44.692 ,0-026693 16,2 9-973307 28 7 .30 34 9-53,78917 99 10-4682,. 9-558505 17 1,2 ,0-44.495 ,o-0267,6 17.3 r9"32S4 -2fl 54 3« 9-53,96318 ,05 .0-468037 9-558703 S,,9 .0-44.297 .0-026739 18 14 /97326. fi 30 38 9-532i38,'9'M .0-467862 9-558900 I 9 ,25 10441,00 ,0-026762 19.4 9-97323^ ■2-2 30 r.o 40 42 9-5323I2: 20 ,,7 21 ,23 10-467688 9-559097 20,32 21 .38 0-440903 ,0-02678; 20,5 21 .6 9-97321'; 20 9-532487 0-4675.3 9-559294 0-440706 0-026808 5-973.92 .VI 41 9-53266, 22 ,28 0-467339 9-55949' 22 ,45 0-440509 0-02683, 22,7 J-973169 lU 4 30 40 9-532?35 23 ,34 10-467,65 9-559688 1 23 ,52 0-4403,2 0-026S54 23 ,7 5-973,46 14 :>7 48 9-533CC9 24 ,40 .0-46699. 9-559885 24 .58 0-44.0,15 0-026876 24,8 5-973.24 3 30 30 9-533'83 25 ,+6 .0-4668.7 9-560082 25 ,65 0-4399,8 0-026899 25,9 5-973.01 10 30 .-.a 32 9-533357 26.52 10-466643 9-560279 26 .7, 0-43972, 0-026922 2620 5-973078 8 2 30 M 9-533S3' 27 158 ,0-466469 9-560476 27 .78 0-439524 0-026945 272, ^-973055 » 30 .'.!» 30 9-533704 28,64 0-466296 9-560673 28.8; 0-439327 0-026968 28 2, 5-973032 1 30 M 9-533878 29,69 0-466,22 9560869 29,9. 0-439,3, 0-02699, 29 22 5-973009 a (ill 20 9-534052 w ,7, ,0-4659481 9-56,066 1 10 ,98,10-438934 0-0270,4 30 23 5-972986 ' " i T (■.).in.- I'.irt, j S.rant | c;;unr| Pal-l. r-Ansruf Cos,.,-. !p,„-t^| .Sin,' i:^ 779 TABLE 68 una. SINES, COSINES., &c. 1' t>0"' 20° IT .?: Sine Parte i Cosec. Tangent Parte | Cotang. Secant Parte 1 Cosine 'm. '" 9-5,4052 1.0-465948 9-56.066 ,0-438934 027014 9-972986 to w 30 2 9-5341Jj1 '' 6|'0-465775 9-56,262! i" 7| .0-438738 JO 027057 1" I 19-972963 30 1 4 9'534i99 2 ..1.0-46560. 9-56,459 2 13 ,0-43854. .0 027060 2 2 I9-972940 M .v.* 30 9534572 3 .7 .0-465428 9-56,655 0-438345 ,0 027083 3 2:9-972917 34 2 8 9-53474S 4 23 10-465255 9-56,85. 4 26 0-438,49 .0 027.06 4 319-972894 52 68 30 10 9'534')'8 5 29 .0-4650S2 9-562048 •' 33 .0-437952 10 027129 5 49-972871 50 30 3 12 9-535092 6 34 ,0-464908 9-562244 6 39 0-437756 .0 027.52 6 519-972848 48 67 30 u 9-535^65 7 40 ,0-464735 9-562440 7 46 0-437560 .0 027.75 7 5 9-972825 40 30 4 l« 9-53543>' 8 46 9-562636 8 52 0-437364 10 027.98 8 6 9-972S02 44 56 30 18 9-5356,0 9 52 ,0-464390 9-562832 9 59 o-437'68 ,0 027222 9 7 9-972778 42 30 _5_ 20 22 9-535783 10 57 11 63 ,0-4642,7 9-56302S ,0 65, 11 72 0-436972 0-436776 .0 027245 10 8 11 8 9-972755 40 5i_ :i8 1 30 9\53 5956 .0-464044 9-563224 .0 02726* 9-972732 24 9-556129 12 69 .0-46387. 9-5634.9 12 78 0-43658. 10 02729. 12 9 9-972709 36,54 30 2« 9-5;630i 13 75 ,0-463699 9-5636.5 13 85 0456385 10 0273.4 13 10 9972686 34 .30 7 28 9-536474 14 80 ,0-463526 9-5638., 14 9. 0-436. S9 .0 027337 14 ,1 9-972663 32 [ 63 30 30 9-536646 15 86 10-463354 9-564006 15 9S 0-435994 10 027360 15,2 9-972640 30 1 3.. 8 32 9-5368,8 16 92 ,0-463.82 9-564202 16 104 0-435798 .0 027383 16,2 9-972617 28 52 30 31 9-53699, 17 98 ,0-463009 9-564397 17 ... 0-455603 10 027407 17.3 9-972593 20 30 » 3« 9-537163 18 .03 .0-462837 9564593 18 .,7 0-435407 .o C27430 18 .4 9-972570 24 51 30 38 9-537335 19 109 .0-462665 9-564788 19 .24 0-4352.2 .0 027453 19.5 9-972547 •22 30 ]0_ 40 9-537507 20 ,.5 21 ,21 .0-462493 9-564983 20 ,30 21 ,37 0-4350.7 10 C27476 20,5 21,6 9-972524 20 60 30 9-537679 .0-46232. 9-565.78 0-434822 To~ 027499 9-97250, II +4 9-53785' 22 ,26 ,0-462,49 9-565373 22 ,43 0-434627 10 22.7 9-972478 16 49 30 46 9-538023 23 .32 10-46,977 9-565568 23 ,50 0-434432 .0 027 5^6 23.8 9-972454 14 30 12 48 9-538194 24 .38 ,0-46,806 9-565763 24,56 0-434237 10 027569 24.8 9-97243, 12 48 30 50 9-538366 25 .44 ,0-461634 9-565958 25 163 0-434042 .0 027592 25.9 9-972408 10 30 11 32 '■"s^f 26 149 ,0-461462 9-566,53 26 ,70 0-433847 10 0276.5 •2620 9-972385 8 47 30 .'.1 27 ,55 ,0-46,29. 9-566348 27 176 0-433652 .0 027639 •27 2. 9-97236. 6 3.1 14 50 9-538880 28 .6. .0-46. .20 9-566542 28 183 0-433458 .0 027662 -28 22 9-972338 4 46 30 5S 9-539052 29 .67 .0-460948 9 566737 29 ,89 0-433263 .0 027685 29 22 9-9723,5 2 30 3fl ai 9-539223 30 .72 ,0-460777 9 566932 30,96 0-433068 .0 027709 3023 9-97229. 3* 58 _4£ 9 539394 I 6 .0-460606 9-567126 1 6 0-432874 ,0 027732 1 , 9-97226S 16 4 9539565 2 ,1 .0-460435 9-567320 a ,3 0-432680 10 027755 2 2 9-972245 56 44 30 9-539736 3 ,7 .0-460264 9-567515 » 19 0-432485 10 027779 3 2 9-97222, 54 3.1 17 8 9-539907 4 23 10-460093 9-567709 4 26 0-43229. .0 027802 4 3 9-972,98 52 43 30 10 9-540078 5 28 .0-459922 9-567903 6 32 0-432097 10 027825 5 4 9-972.75 50 30 18 12 9-540249 fi 34 10-45975' 9-568098 6 39 0-43,902 ,0 027849 6 5 9-972.5. 18 42 30 14 9-540420 7 40 ,0-459580 9-568292 7 45 0-43 170S ,0 027S72 7 5 9-972.28 46 30 19 I(S 9-540590 8 45 10-4594.0 9-5684S6 8 52 0-43.514 .0 027895 8 6 9-972.05 44 41 30 IS 9-54076. 9 5, 10-459239 9-568680 9 58 0-4J.320 .0 0279.9 9 7 9-97208. 42 30 2n__ 20 9-54093. 10 57 10-459069 9-568873 10 64 0-45. .27 .0 027942 10 8 9-972058 40 40 30 22 9-54.102 11 62 .0-458898 9-569067 11 7, 0-430933 To 027966 11 9 9-972034 38 30 21 24 9-541272 12 68 .0-458728 9-56926. 12 77 0-430739 .0 027989, 12 9 9-9720.. 30 39 30 26 9-541442 13 74 10-458558 9-569455 13 84, 0-430545 028012 1 13 .0 9-97.988 34 30 22 28 9-54. 613, i4 79 ■0-458387 9-569648114 90] 0-430352 028036: 14.. I9-97. 964 32 311 30 30 9-54178315 85 io-458217 9-569842115 97 1 0-430.58 .0 028059115.2 9-97.941 30 30 23 32 9-541953 16 9. .0-458047 9-570035 16 ,03 0-429965 10 028083 1 16 .2 9-971917 28 37 30 34 9-542.23 17 96 10-457877 9-570229 17 no .0-42977. .0 028.06] 17 13 9-9/1894 ■26 30 24 30 9-542293 18 102 ,0-457707 9-570422 Id 1.6 .o-429!;78 10 028130 18 .4 9-77 ■ 870 24 S(i 30 38 9-542462 19 108 .0-457538 9-5706.6 19 .23 .0-429384 ,0 028153 19.5 9-97,847 -22 30 25 30 40 42 9-542632 20 ,,3 21 1,9 ■0-457368 9-570809 20 129 21 .35 .0429.9. .0 028177 20.6 21 ,6 9-97.823 13 35 30 9-542802 10-457,98 9-57,002 10-428998 10 028200 9-97,800 20 44 9-54297. 22 ,25 10-457029 9-57,195 M.42 10-428805 .0 028224 22.7 9-97,776 16 34 30 48 9-54314, 23 130 io'456S59 9-57.388 23 .48 10-4286,2 10 028247 23 .8 9'97^753 14 30 27 48 9-5433.0 24.36 ,0-456690 9-57.58. 24 155 26,6, ,0-4284,9 .0 02827. 24.. 9 997.729 12 33 30 M 9-543480 25 ,42 .0-456520 9-571774 .0-428226 .0 028294 25,9 9-57,700 10 30 28 52 9-543649 26 ,+7 ,o-45635> 9-57.967 26 168 ,0-428033 10 0283.8 2620 9-97.682 8 32 30 54 9-543S.8 27 .53 .0-456.82 9-572.60 27 174 .0-427840 .0 028342 27 2, 9-97.658 6 30 29 06 9-5439^7 28 159 10-456013 9-572352 28 iS. ,0-427648 10 028365 28 22 9'97.63'; 4 31 30 58 9-544156 29 .64 .0-455844 9-572545 29 ,87 ,0-427455 028389 2923 9-97,6,. 2 30 30 2Z 9-54432 30 170 10-455675 9-572738 30 193 ,0-427262 .0-0284.2 30 23 9-97,588 30 777 ^ Cosine Parts Secant Cotang. Parte Tangent fosec. Parf» Sine >P 77/' fi't" 4^ ;W" 1 1,<)G. SINES, COSINES. J!u- I'h L'L"» 20° >//|m Sine j ParU Coiec. Tangent Parts Cotaiig. Secant j PartsI Cosine ■? .1' " -W]-o 9-5+4;iJi '0-455675 9-572738 .0-427262 .0-028412 9-97.588 38, 30 1 M 1 *■ 9-544494 '" 6 '0-4S55<:6 9-572930 1" 6 .0-427070 10-028436 r'119-971564 6S !■. :74| 8 45 !'°'4543i6 9-5742-61 8 51 '10-425724 .0-0286C2 8 6 9-97.398 44 2(i 30 18 9-545X4 1 9 5oI'°-454i57 9-5-4468 1 9 58 10-425532 10-028625 9 7 9-97.375 4; 30 :<5 20 9-54601 10 56 ill 61 iio-45-,989 9-5-4660 10 64 11 -0 .0-425340 10-028649 i;:: 9-97135. 41) If 9-S4'''7 1.0-453821 9-574852 .0-425148 10-028673 9-97.327 36 ■u 9-546347,12 67]ic-453653 9-575044112 77I10-424956 .C-028697|12 9 9-971303 Mi -.>4 JO ■m 9-546515'^ 7:, 10-453485 9-575236,13 83,10-424764 10-02S720 13.0 9-971280 14 30 n 9-546683l>* 78li°-4533'7 9-575427 M 89 10-424573 10-028744! Hi. 9-97.256 Si : 2a 10 HO 9-546851I5 84110-453149 9-575619 15 96I10-424381 10-028768 15 12 9-97.232 10 1 30 3H 9-547019I16 90110-452981 9-5758.0 1-6 .021.0-424.90 10-028792 16 13 9-971208 -2H 22 3U H 9-54718-117 95J10-452813 9-576002117 IC9I10-42399S .0-0288.5 1713 9-971185 ■ill , 30 39 3U 9-S4-354'lS 10. '10-452646 9-576.93 18., 5 1,0-423807 .0-028839 18 .4 9-97116, •24 21 30 IS 9-54752^-;>9 io7iio-452478 9-576385 19 ,21 .0-4236.5 .0-028863 llU 15 9-97.137 -2-i 30 40 40 9-5476S9 20 112 21 I ,3 10-4523.1 9-576576 20 .28 21 134 .0-423424 .0-028S87 20,6 2] 17 9-97. ..3 -io M 9-54785-' 10-452143 9-576767 .0-423233 10-02891. 9-971089 41 44 9-54^02422 123,10-451976 9-576959 122 14. 10-423041 .0-028934 22 17 9-971C66 m 19" 30 40 9-348i9>,23 129 [10-451809 9-577.50 23 147 10-422850 .0-028958 23 ,8 9-971042 14 3(1 42 49 9-54835924 134I10-451641 9-57734' •« "S3 10-422659 10-028982 24,9 9-971018 1-2 111 30 30 9-548526,25 140 10-451474 9-577532 25 .60 .0-422468 10-029006 25 20 9-970994 lu 111 43 5i 9-5486q3:26 145 10-451307 9-577723 26 ,66 .0-422277 10-029030 262, 9-970970 H 17 30 54 9-548860,27 151 10-45.140 9-577914 |27 173 10-422086 .0-029054; -27 2 1 9-970946 30 44 5(1 9-54902728 156 10-450973 9-5781C4 28,79 10-421896 ■ 0-029078,2822 9-970922 4 1« 30 is 9-54919329 162 10-450807 9-578295 29.85 10-421705 ■0-029102 2923 9970898 ■i 111 4i 10 23 9-54936030 168 ■0-450640 9-578486 30.92 ,0-421514 ■ 0-029.26 30 24 9970874 37 15 ~30 9-549527 1 6 .0-450473 9-578676 1 6 [10-42.324 10-029.50 9-970850 46 4 9-549693J 2 II .0-450307 9-578867 2 .3 10-421.33 .0-029.73 9-970827 .ii> 14 30 9 ^49860 3 ,7 10-450140 9-579057 3 .9 10-420943 .0-029.97 9-970803 54 311 47 8 9-550026 4 22 10-449974 9-579248 ♦ 25 .0-420752 ■0-029221 9-970779 5-2 13 10 10 9-550193 5 28 10-449807 9-579438 5 32 10-420562 10-029245 9-970755 50 30 48 li 9-550359 6 33 .0-44964. 9-579629 6 38 10-42037. 10-029269 9-970731 4S 12 30 14 9-550525 " 39 .0-449475 9-579819 7 44 10-420.81 10-029293 1 7 6 9-970707 l.i 30 4!) hj 9-550692 b 44 10-449308 9-58C009 8 5. 10-419991 ■ 0-029317 8 6 9-970683 44 11 30 Irl 9-550858 9 50 .0-449142 9-580199 9 57 .0-4.980. 10-02934. 9 7 9-970659 4-2 1(1 SO •^0 9-551024 10 55 .0-44S976 .0-448810 9-580389 .0 63 11 70 .0-419611 ■ 0-029365 10 8 11 9 9-970635 40 10 9-55M90 9-55'356 11 «. 9-5805-9 10-419421 ■0-0293S9 9-970611 Al 74 12 66 .0-448644 9-580769 il2 76 10-419231 0-029414112,0 9-970586 lU 9 30 ■i(i 9-55>52i 13 72 .0-448479 9-580959 jU 82 .0-4.904. 0-029438 i 13,0 j-970562 34 30 AJ ■IH 9-55'687 14 77 .0-448313 9-58.149 14 88 .0-4.885. 0-029462,14,. j-970538 1-2 8 :ki M 9-551853 15 8, .0-448.47 9-581339 15 95 .0-418661 0-029486 .5,2 3-970514 10 10 "l z\ 9-552018 16 88 .0-447982 9-581528 |l6 101 10-418472 0-0295,0 16,3 3-970490 ■2» J 9-552184 17 94 10-447816 9-58,718 ]17 107 10-418282 0-0295341 17 .4 3-970466 ■20 30 64 3G 9-552349 18 99 10-44765' 9-5819G- IK 114 .0-418093 0-029558 18,4 3-970442 1; 10 :i» 9-552515 19 105 10-447485 9-58209- |I9 120 .0-4.7903 0-029582! 19,5 3-9704.8 -2-2 10 65 40 9-5?268o 20 no 21 116 10-447320 9-582286 20 .26 a .33 10-4177.4 0-029606 20,6 -970394 '1 6 9-552845 .0-447.55 9-582476, .0-4.7524 0-029630 21 ,7 >-97037o ■iB 41 9-553010 22 121 .0 446990 9-582665 22 ,39 10-417335 0-029655 22,8 -970345 Hi 4 30 IC 9-553'76 23 127 .0-446824 9-582854 a ,45 .0-4.7146 0-029C79 23,8 -970321 14 10 67 48 9-55334' 24 .32 10-446659 9-583044 24 .52 .0-416956 0-029703 24 19 -970297 1-2 3 M 9-553506 25 138 10-446494 9-583233 25,58 10-4.6767 0-029727 25 20 -970273 ■ Kl S8 :••! 9-553670 2fi,43 10-446330 9-583422 26164 .0-416578 0-029751 2621 9-970249 , •> TO M 9 553835 27 149 10-446,65 9-583611 27 17. .0-4.6389 0-029776 27 22 9-970224 1; 111 M :,« 9-554000 m 154 10-446000 9-583800 28 .77 10-4.6200 0-029800 28 22 9-970200 1 1 :m -iH 9-554165 29 160 iO-445835 9-583989 29 .83 10-4160.. 0-029824 2923 9-970.76 .1(1 <;o 2« 9-554329 to 166 10-445671 9-584.77 )0 ,,0 10-415823 0-029S48I3O24I9-970152 :^_H (.■o.ifH- I'arU Sc-ant Coung. Part. Tangent Coaec. j Parte Sine ^1 Tr (iO^ 4^ 36- 1 TABLE H8 LOG. SINES, COSINES, &c. I'' _M'" 21 = -nr m Sine IV. 1 Cceo. Tangent ParU Cotang. 1 Seraiit j 1'miIs Co>inf m.j"'| "o~ ~ 9-55+3^9 110-445671 9-584-77 1 .. . 10-415823 ,0 0298481 9-970, 5. 36 60 :!i) ■I 9-55^H94 1" 5 10-445506 9-5-84366 1" 6 10-415634 ,0 029873 I- I 9-97012; .-.s 30 1 i 9-554658 2 11,10-445342 9-584555 2 13 10-415445 ,0 029897 1 2 2 9-970,0; M .■ill 3U a 9-55+S2Z i 16 10-445178 9-584744 3 19 10-415256 ,0 02992,] 3 2 9-97007., jj .111 2 8 9-554-9>'7 10-445013 9-584932 4 25 10-415068 ,0 029945 * 3 9-97005; .'.i ill i- III 9-S55'5' 10-444849 9-58512, 5 3, 10-4,4879 ,0 029970 5 4 9970C3C 50 3 \-l 9-5553"5 10-444685 9-585309 6 38 10-41469. ,0 029994 fi 5 9-970cct M '•>! ;!ti II 9-555+79 10-444521 9-585498 7 44 10-414502 IC 0300,8 7 6 9-9699S2 K 31! 4 111 9-555643 10-444357 9585686 8 50 10-414314 ,0 030043 8 7 9-969957 44 5(J .111 IS 9-555807 10-444193 9-585874 9 56 10-414.16 10 030067 9 7 9-969935 1-i 311 5 •ill 9-555971 10-444029 9-586062 10 63 ■0-4.3938 10 03009, 10 8 " 9 9-969909 40 .53 30 9'556i35 10-443865 9-586251 11 69 .0-4,3749 10^ 0301,6 ,-,6,884 '< il 9-556299 10-443701 9-586439 12 75 ,0-413561 10 030,40 12,0 996,860 3U 54 311 Mli 9-556+62 10-443538 9-586627:13 8. ,0-413373 10 030164 13,, 9-969836 31 30 7 •is 9-5566^6 "=■443374 9-586S15 14 88 .0-4. 3. 85 10 030189 14 ,, 19-9698,, 3'i 53 311 311 9-556739 10-443211 9-587003 15 94 10-412997 10 030213 9-969787 30 30 8 3-i 9-556953 10-443047 9-587190 16 100 10-412810 ,0 030238 16,3 9', 69762 -iS 52 :>n 31 9-557116 10-4,2884 9-58737S 17 106 10-412622 10 030262 17 14 9-969738 -ill 30 !» 3IJ 9-5572S0 10-442720 9-587566 IS 113 10-4,2434 10 030286 18,5 9-9697,4 ■u .Ill 3,S 9-557443 19 104 10442557 9-587754 '9 "9 ,0-4,2246 10 030311 19,5 ,-969689 ■ii 311 10 Jll 9-557606I2U 109 ,0-442394 9-587941 '^» '15 ,0-4,2059 10 212111 20.6 9-969665 ■in 60 :)ii u 9-55776921 115 10-442231 9-588129^1 ,31 .0-4, ,871 1~0^ 030360 21 ,7 9-969640 IS 30 11 J4 9-557931 22 120 10-442068 9-588316 22138 10-41,684 10 030384 22,8 9-9696,6 /() 49 :ni .10 9-558005 23 126 10-441905 9-588504 •23 144 10-41,496 10 030409 23,9 9-96959, 14 30 12 J.S 9-558258 24 ,3, 10-441742 9-58S691 24 150 10-41,309 10 030433 24,9 ,-,69567 i-i 4U 311 50 9-55i!4i' 23 137 10-441579 9-588S78 25 ,56 ,0-4, 1,22 10 0J0458 25 20 9-96,542 10 311 13 ■si 9-558583 26 .42 10-441417 9-5S9066 2fi ,63 10-410934 10 0304S2 26 2 I 9-9695,8 » 47 :iii :,\ 9-558746:27 147 10-441254 9-589253 27 169 1--41074-' 10 030507 27 22 9-969493 a 311 U M 9-558909 2S 153 10-441091 9-589440 «8.75 10-4,0560 10 030531 28 23 9-969469 4 41, :iii .',s 9-559071 29 158 10-440929 9-589627 J9 182 10-410373 10 030556 2923 9-969444 ■i 311 ],•» Zi 9-559134 ' 5 IO-.1.40766 9-5X9814 30 i8« 10-410186 10 0305S0 3024 9-969420 9-969395 35 45 5s| .-,0 9-559396 10-440604 9-590001 1 6 10-409999 to 030605 ' ' lU A 9-559558 2 11 ,0-440442 9-S90188 » 12 ,0-1098,2 10 030630 2 2 9-969370 M 44 0.1 9-559721 3 16 10-440279 9-590375 3 19 ,0-409625 10 030654 3 2 9-969346 .14 30 17 B 9-559883 4 22 10-440117 9-590562 4 25 ,0-409438 10 4 3 9-96932, 5i 43 :i(i 10 9-560045 5 27 10-439955 9-590748 5 3, 10-409252 10 0-0-0- 5 4 9-969297 •M 30 "!,i \l 9-560207 6 32 ,0-439793 9-590935 6 37 10-409065 10 030728 6 5 9-569272 JS 42 1 1 9-560369 7 38 10-439631 9-59,122 7 43 ic-408878 ,0 030753 7 6 9-969247 40 3P v.} Hi 9-560531 8 43 10-439469 9-591308 8 50 10-408692 ,0 030777 8 7 9-969223 44 41 Jll IS 9-560693 9 48 10-439307 9-591495 9 56 10-408505 10 030S02 9 7 9-969,98 4^2 30 20 ■ill 9-5608S5 9-56,016 10 54 11 59 10-439145 9-59168, 10 62 10-408319 '=. 030827 03085, 10 S n 9 9-969,73 40 40 10-438984 9-591867 ,0-408132 9-969,49 ■Jl •i\ 9-56M7g 12 65 ,0-438822 9-592054 12 74 ,0-407946 10 030876 12 ,019-969124 !3 ,1 9-969099 30 :)!! :iii •ill 9-561339 13 70 10-438661 9-592240 13 8, 10-407760 10 030901 34 30 22 ■is 9-56i50i|u 75 10-43S499 9-592426 14 87 10-407574 10 030925 u ,1 9-969075 Ii :i(i .111 ;iii 9-561662I15 g. 10-438338 9-592612 15 93 10-40738^ 10 030950 13,2 9-969050 30 30 ■iw .i-i 9-561824 ifi 86 10-438176 9-591799 16 99 10^407201 10 030975 16 13 9-969025 ■iS :i7 311 34 9-561935 17 91 10-438015 9-592985 17 105 10-407015 ,0 031000 17 14 9969000 ■iO 311 •-'1 ■K 9-562146 18 97 10-437854 9-593171 18 112 ,0-406829 10 031024 IS 15 ,-968976 -.4 :)(>■ :lii 3S 9-562307 19 102 10-437693 9-593356 19 ,18 ,0-406644 ,0 03,049 19 16 9-968,51 ■Ii 311 •2.-. JO 9-56246S 9-562629 ■211 108 21 113 10-437532 9-593541 20 ,24 21 130 10-406458 10 20 16 9-968926 21 .7 9-9689" ■'" 3.-. 10-437371 9-593728 ,0-406272 To^ 03,099 2fi J4 9-56179° ■22 ,19 10-437210 9-593914 22 136 10-406086 10 031123 22.8 9-968877 10 34 311 4li 9-562951 23 124 10-437049 9-594099 23 ,43 10-405901 10 031,48 23 19 9-968852 14 311 27 4S 9-563112 24 .29 10-436888 9-594285 24 149 ,0-405715 10 031,73 24 20 9-968S27 1-i 33 30 .'ill 9-563273 23 ,35 10-436727 9-594471 25,55 10-405529 10 031,98 25 20 9-968802 1. - — 28 ,Vi 9-563433 26 140 .0-436567 9-594656 26 161 ,0-405344 10 031223 26 21 9-963777 sia2 3(1 r,\ 9-563594 27 145 ,0-436406 9-594842 27 167 10-40515S 10 03.248 27 22 9-968751 6 30 2t) 3li 9-563755 28 151 io-436245 9-595027 ■28 174 .0-404973 10 03.271 2823 9-96S72S J :ti 30 .■iS 9-563915 •29 156 10-436085 9-595212 29 1 80 10-404788 10 03.297 29 24 9-968703 ■i 3(1 30 26 m. 9-564075 .iO 161 1 Pa.U 10-435925 Secant 9-595398 30 186 10-404602 10-031322 30 2 5 9-968678 :ui Cosiae Cotans,'. PartB Tangent Cosec. I'ai-ts Sine ^-i^^ (!8'^ 4" U"- i TAHLE fifi 78: LOG. SINES, COSINES, &c. Ih 0(> 21° / // m Sine 1 Parts 1 Cosec Tangent j P,ii-ts Cotang. Secant | Parts | Cosim- m. ' " 3i>~ 9-';6407Sl I.0-43592J 9595398 .0-404602 10-031322 "I9-968678 ii'iw .III 9-5642-i6| 1" 5 ,0-435764 9-595583 1" 6 .0-404417 .0-03.347 1" . 9-968653 .'iH 311 31 9-56439612 II 10-435604 9-595768 2 II 10-404232 .0-031372 2 2 y-968628 .lli 211 31) 9'56455 3 16 10-435444 9' 59 59 5 3 3 ,S 10-404047 10-031397 3 3 9-96S603 51 30 32 ?-5647. 4 21 ,o-4352S4 9-596.38 4 25 10-403S62 10-031422 •* 3 9-968578 :,i 2fl 30 9-56487 5 27 10-435124 9-596323 5 31 10-403677 10-031447 5 4 9-968553 :m 30 Xi 9 56503 6 32 10-434964 9-596508 6 37 .0-403492 10-031472 6 5 9-96852S ^537 .7 S9 0-428463 9-60404. 7 104 0-395959 0-032503 17 14 9-967497 -21i :ki 54 3a 9-571695 18 95 0-42S305 9-604223 8 no 0-395777 0-032529 I815 9-96747, 21 ti 30 J8 9-571852 19 100 0-428148 9-604406 9 116 0-395594 0-032554 19 16 ^-967446 ■!-i 30 S5 1 30 40 42 9-572CC9 20 105 21 no 0-427991 9-604588 20 .22 21 128 ' 0-395412 0-032579 20,7 996742, 18 1 .1 9-572166 0-427834 9-604771 0-395229 0-032605 21,8 9-967395 .-iG 44 9-5723^3 22 1,6 0-427677 9-604953 122 134: 0-395047 0-032630 22 ,9 9-96737C | ,r,| 1 30 V. 9- 572479 M 121 1 0-42752. 9-605135 23 140 1 0-394865 0-032656 23 20 9-967344 .-10 ■■.7 4S 9-57263624 126 0-427364 9-605317 24 ,46 1 0-394683 0-03268. 24 20 9-9673,9 1-2 3 30 JO 9-57279325 13' 1 0-427207 9-605500 2.'i,52 0-394500 0-032707 2521 ,•967293 ,.,j 3" 51 52 9-57295r. 26.37 0-427050 9-605682 26 .58 0-394318 0-032732 2622 9-967268 8 2 30 51 9-573106 27.42 0-426894 9-605S64 a? ,6+ 0-394.36 0-032758 2723 9-967242 (1 T,n 59 W. 9573263 28 147 0-426737 9-606046 28 .71 o-393')54 0-032783 2824 9-967217 4 1 30 is 9-5734'9 29 132 0-42658. 9-606228 29 .77 0-393772 0-032809 2925I9-96719. 9 3'i r.n £8 m. 9-573575 10 157I10-426425 9-606410 30 .831 0-393590 0032834 3025 9-967,66 n Cosine Parts 1 Secant Cotang. 1 Parts 1 Tangent | Cosec. 1 Parts 1 S,nc ( "?• fA' 4'' .T^" 1 782 TABLE 68 LOG. SINES, COSINES, :.c. | 1' -JS"' 22° 1 'o~ m. Sine Parts Cosec. Tangent Parts Cutang. Secant j Parte Cosine m. LI 9'573575 ,0-426425 9-6064,0 10-393590 ,0-032834 9-967,66 32 G3 30 2 9'5'/37;j '" 5 10-426268 9-60659, 1" 6 10-393409 .0-032860 1" 1 9-967140 se :vi 1 4 9-573888 2 10 10-426,12 9-606773 2 12 .0-393227 .0-032885 2 2 9-9671,5 5fl 59 30 8 9' 5 740+4 3 16 ,0-425956 9-606955 3 18 .0-393045 10-0329.. 3 3 9-967089 54 30 2 S 9-574200 4 21 10-425800 9-607,37 4 24 .0-392863 .0-032936 * 3 9-967064 52 58 30 10 9574356 5 26 10-425644 9-607318 5 30 .0-392682 ,0-032962 6 4 9-967038 50 3.J 3 l'2 9-57451^ 6 3, ,0-425488 9-607500 6 36 .0-392500 ,0-032987 6 5 9-9670,3 48 67 30 H 9-574668 7 36 10-425332 9-607681 7 42 .0-592319 10-033013 7 6 9-966987 46 30 4 16 9-5748x4 8 41 ■ .-5-425176 9-607863 8 48 .0-392,37 10-033039 8 7 9-96696, 44 56 30 18 9-574980 9 47 10-425020 9-608044 9 54 .0-39.956 10-033064 9 8 9-966936 42 30 — 'iO 9 575136 10 s^ " 57 .0-424864 9-608225 10 60 U 66 10-391775 ,0-033090 10 9 11 9 9-9669.0 40 53 9-57529" ,0-424709 9-60S407 10-391593 ,0-033116 9-966884 « 21 9-575447 12 62 ,0-424553 9-60S588 12 72 10-391412 ,0-033141 12,0 9-966859 36 54 30 ■iO 9-57560113 67 ,0-424398 9-608769 13 yS .0-39.231 10-033,67 13 ,1 9-966833 34 30 7 2S 9-j7575gl4 73 ,0-424242 9-608950 14 84 .0-39.050 ,0-033.92 14 ,2 9-966808 32 53 30 30 9-5759>3 15 7S ,0-424087 9-609131 15 90 .0-390869 .0-033218 15,3 9-966782 30 30 8 3i 9-576069 16 83 ,0-423931 9-6093,2 16 96 .0-390688 0-033244 16 14 9-966756 23 52 30 34 9-576224 17 88 ,0-423776 9-609493 17 ,03 .0-390507 0-033270 1714 9-966730 26 30 9 36 9-576379 18 93 ,0-42362, 9-609674 18 ,09 ,0-390326 .0033295 18. 5 9-966705 •24 51 30 3S 9-576534 19 99 ,0-423466 9609855 19115 .0-390.45 ,0-03332, 19.6 9-966679 -22 30 10 n 9-576689 20 ,04 21 109 , 0-423311 9-610036 20 ,2, 21 ,27 10-389964 10-033347 2017 21 .8 9-966653 18 50 30 9-576844 ,0-423156 9-6,02,7 .0-389783 0-033372 9-96662S u 44 9-576599 22 114 ,0-42300, 9-610397 22 ,33 .0-389603 ,0-033398 22,9 9 966602 10 49 30 40 9-577154 23 1,9 10-422S46 9-610578 23,39 ,0-389422 0-033424 23 20 9-966576 14 30 12 43 9-577309 24 .2+ ,0-422691 9-6,0759 24 ,45 10-38924, 0-033450 24 21 9-966550 12 48 30 50 9-577464 25 130 ,o'422536 9-6,0939 25,5, ,0-38906, 0-033475 25 21 9-966525 30 13 32 9-577618 26 nc IC-4223S2 9-611120 26 157 ,0-388880 10-03350, 2622 9-966499 's 47 1 30 54 9-57777327 140 ,0-422227 9-6,1300 27163 .0-388700 0-033527 2723 9-966473 30 U 50 9-577927 28 ,45 ,0-42207; 9-611480 M.69 10-388520 0-033553 28 24 9-966447 4 4G 30 59 9-578082 29,50 10-4219,8 9-6,1661 a»>75 .0-388339 0-033579 2925 9-96642. 2 15 30 a* 9-578236 30 ,55 10-421764 9-61,841 30 18, .0-388.59 0-033605 30 26 9-966395 32 53 ~30 9-5-8391 « 5 10-421609 9-6,202, TT 10-387979 0-033630 I 1 9-966370 16 4 9-57S':4^ 1 10 10-421455 9-6,2201 9 li 10-387799 0-033656 2 2 9-966344 50 44 30 6 9-578699 3 15 ,0-421301 9-612381 3 lg .0-3S76.9 0-033682 3 3 99663.8 54 30 17 fl 9-578853 4 20 10-421147 9-61256. 4 24 .0-387439 0-033708 * 3 9-966292 52 43 30 10 9-579008 8 26 10-420992 9-6,274. 6 30 .0-387159 0-033734 5 4 9-966266 50 30 10 12 9-579162 6 31 ,0-420838 9-6,2921 « 36 .0-387079 0-033760 6 5 9-966240 48 42 30 14 9-579316 7 36 10-420684 9-6,3,0, 7 42 .0-386899 0-033786 7 6 9-966214 40 30 19 10 9-579470 8 4, ,0-420530 9-61328. 8 48 .0-3867.9 0-033812 8 7 9-966,88 44 41 30 IH 9-579623 9 46 10-420377 9-613461 9 54 10-386539 0-033838 9 8 9-966,62 42 30 20 22 9-579777 10 5, U 56 ,0-420223 9-6.364, 10 60 11 66 .0-386359 0-033864 10 9 11 ,0 9-966136 40 38 40 30 9-57993- ,0-420069 9613S20 .0-386,80 0-033890 9-966,10 21 24 9-580085 12 6j ■0-419915 9-614000 12 72 .0-386000 0-033915 1210 9-966085 36 3U 30 20 9-580238 13 66 ,0-4,9762 9-6,4.80 13 7S .0-385820 0-03394, 13,1 9-966059 34 30 22 2S 9 580392 14 71 10-4,9608 9-6,4359 14 8+ .0-38564. 0-033967 14 12 9-966033 32 38 30 30 9-580545 15 77 10-4,9455 9-6,4539 15 90 .0-38546. 0-033993 15,3 9-966007 311 30 23 32 9-580699 16 82 ,0-4,930, 9-6147,8 16 96 .0-385282 0-034019 16,4 9-96598, ■28 37 30 34 9-5S0S52I7 87 ,0-4,9,48 9-6.4897 17 loi ,0-385.03 0-034045 17,5 9-96595"; -20 Ml 24 30 9-58100518 92 10-4, X995 9-6,5077 18 108 .0-384923 0-034071 18,6 9-965929 '24 ! 3R 1 30 33 9-58115819 97 ,0-4,8842 9-6,5256 19 114 ,0-384744 0-034098 19 17 9-965902 22 3'J 25 40 9-581312 20 ,02 2. ,07 10-4,8688 9-6.543, 9-6156,4 20 120 21 ,26 ,0-384565 0-034124 2017 21 18 9-965876 9-965850 I 35 30 9-581465 ,0-4,8535 10-384386 ,0-034,50 2G 44 9-58.6,8 22 ,12 ,0-418382 9-615793 22 132 ,0-384207 10-034.76 2219 9-965824 HI 34 ao 4« 9-581771 23 1,8 10-418229 9-615972 23 138 10-3S4028 ,0-034202 23 20 9-965798 14 30 27 4S 9-5S1924 24 ,23 10-418076 9-616,5, 24,44 ,0-383849 ,0-034228 24 2, 9-965772 12 33 M 30 9-582076 25 128 ,0-417924 9-6,6330 25,49 10-383670 10-034254 25 22 9-965746 10 30 28 32 9-582229 26 .33 ,0-417771 9-616509 26155 .0-38349. 10 0342S0 2623 9-965720 9 32 ao 31 9-582382 27 ,38 ,0-417618 9-6.6688 27 ,6, .0-3833.2 ,0-034106 2723 9965694 6 j 311 29 50 9-582535 M ,4-3 ,0-417465 96,6867 28 167 .0-383133 10-034332 28 24 9-965668 4 '31 30 53 9-582687 29 148 10-417313 9-6,7046 29 173 ,o-3S2o?4 ,0-034358 29 25 9-965642 2 3<1 30 30 9-582840 30 ,53 10-417160 9-617224 30 179 ,0-382776 '°:^34j8i C'ospc. 30 26 9-965615 30 / n •? Cosine Parts Secant Cotang. Parts Tangent P^rts Sine ^ ,777 67^' 4" OO"' 1 TABLE C3 " LOG. SINES, COSINES, .\.-. ,1, 30'' 2iJ° W Sine I'arts Cosec. Tangent Part« Cotang. 1 Secant Parts Cosine ii ' >■ 9-5X2S^c .0-417.60 9-617224 .0-3S2776 .0034385 9-9656.5 TiT ■so 2 9-58^99= '" 5 .0-4.7008 9-617403 1" 6 .0-382597 .0-0344. 1 ' , 9-965589 58 31 4 9-5»;'4 .04.6855 9-61758. 2 11 .0-3824,8 .0-034437 2 2 9-965563 50 2f 30 9-58329- 3 ,'5 .0-4.6703 9-617760 3 18 10-381140 .0-034463 3 3 9 965537 54 :t2 8 9-583440 .0-4.65;. 9-617939 4 24 10-381C6. ,0-034489 ■* 4 9-96551, 32 2a 10 10 9-5S360 5 ^5 .0-4.6399 9-618, .7 5 301.0-38,883 ,0-0345,6 5 4 9-9654S4 30 ;t;i 12 9'5-'3754 6 30 10-4.6246 9-6,8295 6 36 .0-38.705 ,0-034542 6 5 9965458 48 27 M 11 9-583906J 7 35 .0-4.6094 9-6.8i74 7 4^ .0-38.516 ,0-03+568 7 6 9-965431 10 :u 10 9-584058 8 40 .0-4.5941 9-6,8652 8 47 ,0-38,348 .0-034594 8 7 9-965406 41 2( JO 18 9-5S4210! 9 45 .0-4.5790 9-6,8830 « 53 10-38,170 .0-03461. 9 8 9-965379 42 3 3.-. 30 20 9-584361 10 50 11 56 .0-4.5639 9-619008 in 59 10-3S0991 .0-034647 10 9 1) ,0 9-965553 40 38 25 9-584513 .0-415487 9-6,9186 1. 65 10-3808,4 ic-034673 9-965327 J 30 24 9-5X4665 12 6, .0-415335 9-6,9364,12 7, ,0-380636 10-034699 12,, 9 96530, 3(1 2^ to ■111 9-sM>7 13 66 10-4.5.83 9-6.9543 [13 77 10-380457 .0-034726 13 ;. 9-965174 37 28 9-584968 14 71 .0-4.5032 9-6.9720 I14 83 ,0-380180 io-,-3475i U.i ,-965148 32 2:" 30 9-5S5.XO 15 76I10-4148S0 9-6.9S9S 15 90 ,0-380,02 ,0-034778 15,3 9-965111 30 38 32 9-585'-7:' 16 81 ,0-4.4728 9-620076 16 95 ,0-379924 ,0034805 16 .4 9-965195 28 22 30 34 9-5«54i3 17 86 ,0-4,4577 9-620154 17 loi .0-379746 ,0-03483, 17.5 9-965.69 M 39 M 9'585574 18 9, ,0-4.4426 9-610432 18 .07 .0-379568 ,0-034857 18.6 9-965.43 24 21 30 38 9585726 19 96 10-4.4274 9-610610 19, ,3 .0-379390 ,0-034884 19.7 9-9651.6 22 40 40 9-585S77 20 101 21 106 10-4.4.23 9-67.0787 20,, 9 2>,15 .0-379113 .0-0349,0 20 iS 21 .8 9-965090 18 20 9-586028 .0-4,3972 9 620965 .0-379035 10-034936 9965064 ~ 41 44 9-586179 22 II. .0-4,382. 9-61,141 22,30 .0-378858 .0-034963 22.9 9-965037 10 III 30 40 9-586331 23 I 16 ,0-413669 9-62,320 23 ,36 .0-37S680 .0-034989 23 20 9-9650.1 '3 t.' 4a 9-586482:24 I2T .0-4. 35. 8 9-62,497 24 ,41 .0-378503 10-0350.6 24 1, 9-964984 12 IH 30 30 9-58663323 126 .0-4.3367 9-61.675 25 ,48 .0-378315 io-o35,-4i 25 11 9 -9649 5 S 10 43 32 9-58678326 .3. .0-4132.7 9-61.85-1 2fi .54 .0-378.48 10-03 50.9 2613 9-964931 „ U 30 51 9-58693427 .36 10-4.3066 9-612019 •27 160 10-37797, 10-035095 2724 9-964905 u 3 44 3fi 9-5870S528 141 .0-4.29.5 9-621107 28 ,66 '0-377793 ,0-035,2, 2825 9-964879 4 10 30 58 9-587^3629 .46 9-58738630 ,5,_ 9-58753-' 1 5 .04.2764 9-621384 29 171 10-3776.6 10-035,48 2926 9-96485' 2 3 4J_ SI .0-4,26,4 9-611561 ■to 178 '0-377439 ,0-035,74 30 16 9 964816 29 3S 15 ,0-4,2463 9-611738 1 6 .0-377262 ,o-o352o. 1 J 9-964799 4>i 4 9-587688 2 ic 10-4113,2 9-6119,5 a ,1 .0-377085 10-035127 2 2 9-964773 50 14 30 fi 9-587838 3 ,5 10-412,62 9-613091 3 ,8 .0-376908 .0-035254 3 3 9-964746 54 31 47 8 9-587989 4 20 .0-4.20,1 9-613169 4 24 .0-37673, .0035280 4 4 9-96471C 13 30 10 9-588139 5 15 .0-41,861 9-613446 5 19 ,0-370554 ,0-035307 5 4 ^-964693 .')0 3. 48 12 9-588289 6 3c .0-4. .7.. 9-613623 - " ,0-376377 10-035334 6 5 9-964666 4H 12 30 14 9-588439 ' 35 .0-41.56. 9-6238CO 10-035360 7 6 9-964640 40 49 111 9588590 8 40 .0-4114,0 9623976 B 47 10-376014 ,0-035387 8 7 9-9646,3 1 1 30 18 9-588740 9 45 10-41 1260 9-624,53 9 53 ,0-375847 10-0354.3 9 8 9-964.87 12 31 51° 22 9-5S889C .0 50 '1 55 10-411110 9624330 10 59 11 65 ,0-375670 10-035440 10 9 9-96450C 40 38 10 9-589040 IC-410960 9-62450^ 10-375494 .0-035466 9-964534 jii 24 9-58919CJI2 60 10-4.08.0 9624683 12 7, .0-3753.7 .0-035493 12,, 9-9645'- Jli u 3f te 9-589340113 65 9-58948914 70 .0-4,0660 9-614859 13 76 .0-375141 10-035510 13 ,1 9-964480 31 3« .'.2 28 .0-4,05,, 9-615036 14 81 .0-374964 .0-035546 14 ,1 9-964454 8 10 30 9-589639I5 75 ,0-4,036, 9-6152,1 15 88 10-374788 ,0-035573 15,3 9-964417 III .'.3 32 9-5897S9'l6 80 .0-4.02.. 9-62C388 IB 94 10-3746,1 0-035600 16 .4 9-964400 -/8 7 to .H 9-58993817 85 10-4.0062 9-625565 17 ,00 10-374435 0-035626 17.5 9964374 ■u: a .14 Mi 9-59coX8!l8 90 10-4099121 9-62574, ,1H .c6 10-374159 0-035653 18 16 9-964347 ■i4 10 ;w 9-590237)9 95 10-4097631 9-6159.7 jl9 ..1I.0-374083I 0-035680 ly 17 9-964310 22 .-HI ■TT 40 9-590387,20 100 9-590556,21 105 .0-4096.3 9-61609, 1 20 1,8 21 ,13 ■P-3739°7 0-035706 20,8 21 .9 9-964194 ■"' A .0-409464 9-626169 'o-37373'l 0-035733 ;-964i67 3( s« 44 9-59068622 1 10 ,0-4093,4 9-616445 i2 ,19 ,0-373555 0-035760 2220 9-964240 !o 4 30 K 9-590835M .15 10-409165 9-61661. 23 135 .0-373379 0-035786 23 20 9-964114 14 3( fi7 4S 9-59098424 120 ,0-4090,6 9-616797 24 ,4, 1.0-373103 0-0358,3 24 2. 9-964.87 8 JO 30 9 59113325 125 ,0408867 9-626973 25 147 ,0-373017 0-035840 25 22 9-964.60 10 n M 52 9-;o.282l2« :3c 10-408718 9-627149 2fi .55 110-37185, 0-035867 2613 9-964>33| -/714 9-964'o6| 8 •i JO .'.4 /59'43';27 IJ5 .040X569 9627325 27 ,59 .0-371675 0-035894 6!, M /55>'5So,28 140 10-408410 9-6:750. 28.65 0-372499 0-035920 2815 9-964080 4 i .i" 1 ^« 9-591729129 I45;k.-4o827. 9-617676 29 .7. .0-371324 0-035947 29 26 9-964053 2 3< ...J ^ 9-59>878:30 1 50 |, 0-408 111 9-627851 30 .76 0-371.48 0-035974 3017 9-964016 m. Cosine j PnU 1 Secant CuUng. Parts Tangent Csec. Parts Sine m. "' 67" 4" 2M"' 784 TABLE (58 LOG. SINES, COSINES, S.e. | 1" ■^•" 23° 1 o" m Sine Parts Cosee. Tangent Parts i Cotang. Secant Parts Cosine m If, 9-591^7* 10-+08122 9-627852 10-372.48 10-03597+ 9-964026 2i 30 ■i 9-59202' '" 5 10-407973 9-628028 1" 6 .0-37.972 ,0-03600, 1" 1 9-963999 5a 30 1 4 9-592.76 2 ,0 10-407824 9-628203 2 .2 .0-37.797 ,0-036028 9-963972 00 &3 iO ti 9-592524 3 ,5 .o^407676 9-628379 3 17 1037.62. .0-03605+ 9-963946 54 30 '2 a 9-59'473 4 20 io^407527 9-628554 4 23 .0-37.446 .0-03608. 9-963919 5-2 08 JO 10 9^59262i 5 25 10-407379 9-6.8729 5 29 10-37.27. 10-C36.0S 9-963891 51 30 3 It 9-592770 6 30 10-407230 9-628905 6 35 .0-37,095 .0-036.35 9-965865 ,, 57 31 i-i 9^5929.S 7 35 10-407082 9-65.9080 7 4> .0-370920 ic-036.6. 9-963838 4ii 30 ■J 10 9-5930671 8 39 9-5932I5I 9 44 IO-+06933 9-629255 8 +7 .0-370745 ■0-036.S9I 8 7 9-9638.1 41 ou 30 IS 10-406785 9-629431 9 52 ,0-370569 .0-0362.6 9 8 9-96378+ 42 311 5 30 ■20 9-59336! 10 49 10-406637 9-629606 10 58 11 6+ .0-370394 10-0362+3 10 9 9-963757 40 55 9-593511 U 5+ 10-406489 9-629781 10-3702.9 ,0-036270 9-963730 (i n 9-593659 12 59 10-406341 9-629956 12 70 .0-37004+ ,0-036296 12,, I9-96370+ 30 54 30 ■iU 9-593307 13 6+ ■0-406193 9-630131 13 76 .0-369869 ,0-036323 13,2 9-963677 34 30 7 ■2li 9-593955 14 69 10-406045 9-630306 14 82 .0-36969+ .0-0363,0 14 .3 9-963650 3-2 53 30 :to 9-59+103 15 7+ 10-405897 9-630481 15 87 ,0-3695.9 .0-056377 IS ,3 9 963623 30 30 8 3-2 9- 5942 5 1 16 79 10-405749 9-630656 16 93 .0-369344 10-036+0+ 16 .4J9-963596 28 52 30 3J 9-594399 17 84 10-405601 9-630830 17 99 .0-369,70 .0-036+3. 17.5 9-965569 20 30 9 30 9-594547 18 89 10-405+53 9-63.005 ,0-568995 JO-036+58 18,619-563541 -24 51 30 38 9-594695 19 94 10-405305 9-63,180 19 HI ,0-568820 .0-056+S5 19,719-9635,5 -22 30 10 40 9-594842 20 99 10-405 15S 9-631355 20 ,,7 21 ,22 ,0-368645 10-0365.2 20,8 21,9 9-963488 20 50 30 9-594990 21 104 1&-+05010 9-631529 ,0-36847. .0-036559 9-96346. 11 44 9-595137 22 109 10-404563 9-63,70+ 22 128 ,0-368296 .0-056566 22 20 9-963+34 10 4» 30 46 9-595285 23 114 10-+0+715 9-63.S78 23 13+ ,0-368,22 .0-036593 23 2, 9-963+C7 14 30 12 43 9-59543^ 24 118 0-404568 9-632053 24 ,+0 ,0-567947 .003662. 24 22 9-965379 12 48 30 50 9-595580 25 123 0-404420 9-632227 25 ,+6 ,o-3«7773 .0-0366+8 25 22 9-963552 10 30 13 5-2 9-595717 26 128 0-404273 9-631+02 26,52 10-367598 ,0-036675 2623 9-965325 8 47 30 54 9-595S7427 133 i 0-404126 9-632576 27.57 10-367+2+ ,0-036702 27 2+ 9-965298 30 14 5U 9-596021 2S138 0-403979 9-632750 28 .63 10-367250 ,0-056729 2825 9-96517. 4 40 30 5S 9-596168 29 143 0-403S32 9-63292+ 28 169 10-367076 .0-036756 2926 9-965244 -2 30 15 33 9-596,15 in 14S 0-403685 9633099 30 175 10-36690, .0-036783 30 27 9-9632.7 27 45 9-596+62 ' 5 0-403538 9-633273 1 6 0-566727 ;^^6-87o i , 9-963,90 IG 4 9-596609 2 10 0-40339, 9-633447 2 12 0-566555 10-056857 2 2 !9-963>63 50 44 30 9-596756 3 15 0-4032+4 9-633611 3 17 0-366579 0-056865 3 5J9-963>35 54 30 17 s 9-596903 4 20 0-403097 9-633795 4 23 0-566205 10-036892 4 +9-963,08 .5-2 43 30 10 9-597050 5 2+ 0-402950 9-633969 6 29 0-56605, 10-0369,9 5 519-96308, 5U 30 18 1-2 9-597196 G 29 0-402804 9-634143 6 35 0-565857 0-0369+6 6 5 9-963054 48 42 10 14 9-597343 7 34 0-402657 9-6343.6 7 40 0-56568+ 0036973 7 6 9-963027 40 30 I'.) IU 9-597490 8 39 0-402510 9-634490 8 +6 0-5655,0 0-03700, 8 7 9-962999 14 41 30 18 9-597636 9 4+ 0-+02564 9-63466+ 9 51 0-565336 0-037028 y 8 9-96=971 12 30 •20 'IT •20 9-597783 10 49 11 54 _0302217 9-634838 10 58 11 6+ 0-365.62 0-037055 10 9 11 10 9-<;62<;4 5 9-9619.8 •18 40 9-597919 0-402071 9-63501, 0-56+989 0-037082 21 •24 9-598075 12 58 0-401925 0-635,85 12 69 0-56+815 0-037, ,0 12,, 9-962S9C 30 3!. 30 •28 9-598222 13 63 0-401778 y-635359 13 75 0-36464, 0-037,37 13 12 9-962863 34 30 22 •28 9-508368 0-401632 9-635532 14 8, 0-364468 0-037,6+ 14,3 9-962836 32 38 W 30 9-5985>4 15 73 0-401+86 9-635706 15 87 0-364294 0-057,9, 15 ,+ 9-962809 .10 30 23 3^2 9^59866o .6 78 c-4013+0 9-635879 16 92 0-36+.2, 0-0372,9 I615 /96278, 28 37 30 34 9-598806 1/ 83 0-40119+ 9-656052 17 98 0-3639+8 0-0372+6 17.519-961754 20 30 24 30 9-598951 18 88 0-+010+8 .,-636226 18,04 0-36377+ 0-057273 18, 6 19-96272- 24 3(|- 30 33 9-599098 19 93 -+00902 9-636399 1!) ,,0 0-56360, 0-03730, 19 ,7 9-962699 ■Ci 30 25 '30 40 9-59924+ 9-599390 20 98 0-400756 9-636572 20 ,16 21 ,2. 0-363418 0-363255 0-037518 20,819-962671 21 .919-962645 -20 35 -+00610 9-636745 0-037355 20 14 9-599536 22 107 0-400464 9-636919 22 .2- 0-3630S1 0-037383 2-22019-96261- 34 30 4C 9-599681 23 112 0-400319 9-637092 23 .33 0-362908 0-03-+IO 23 •_. '9-962 ^9^ <> 31! 2" 48 9-599817 24 I 17 0-400173 9-637265 24 .39 0-362735 0-037+3S 242219-96:562 33 30 50 9-599973 2;< fz 0-400027 9-637+38 25 .4+ 0-362562 0-03^+65 ■2.'.2 3 19 962535 10 311 •28 52 9^6ooii8 ■21; 127 0-399882 9-6376,, 26 .50 0-362389 0-05-+92 262+19-962508 H 32 30 54 9-600264 27 131 0-399736 9-657783 27 .56 0-3622,7 ,0-037520 2725 9-962+8C 1; ■111 2!l 50 9^600+09 28 136 0-399591 9-637956 28 .62 0-3620+4 ,0-057547 28 25 9962+53 4 31 3D 5" 9-60055+ ■29 141 0-399446 9-638,29 29 .68 0-561871 10-057575 2926 19-962+25 -2 30 30 34 9-600700 3(lj+6 0-39930C 9-63S302 « ,73 0-36,698 IO-057602 HO 27 9-962398 30 /// m. Cnsine Parts Sfoont Cotang- Parts 1 Tangent {■o«-c. 1 Parts Sine ^. T7/ tjtj" 41, OLJ-.r j TABLF. r>8 788 I.OG. SINES, COSINES. &c. -1 ,h a4m o:)o -| ■mT " .Sine 9 6co7c Parts Cosec. Tangent 1 Parts 1 Cotang. Secant Parts Cosine Im ['■■ ,0-399300 9-638302 ,0-36,698 ,o-c.376oi :9-962398 iilsTl 3I> ■I 9-6co84 '■' 5 ,0-399155 9-638475 1" 6 ,0-36,525 ,0-037630 1" . 9-961370 30 :ii 4 9-6C099C 2 10 1,0-3990,0 9-638647 2 ., 10-36.353 ,0 03-.657 2 2 9-961343 M -y .'III u 9-6oin .1 14 ,0-398865 9-63S820 3 17 10-361180 ,o-037&85 3 3 9-9623,5 54 30 M H 9'6oi28c 4 19 ,0-398720 9-638991 4 13 10-36,008 10-03-, 7,1 * 4 9-962188 52 -2 30 20 ■li 9-^°" 5° 9-602294 .0 48 " 53 10-397850 9-640027 10 57 U 63 ,0-359973 ,0-037877 .o-o37-,o5 10 9 9-962,23 40 38 •2:> .0-397706 9-640,59 .0-35980, 9-962095 3« ■n 9-602439 12 58 10-39756. 964037. .2 69 .0-359629 ,0-037,33 12.1 9-962067 3U 24 30 ■ill 9-602583 13 62 .0-397417 9-640544 13 74 .0-359456 io-037-,6o 13 .2 9-962040 34 30 37 M 9-602728 14 67 10-397272 9-640716 14 80 .0-359284 ,0-037988 14.3 9-9620,2 23 30 30 9-602872 IS 72 .0-397.28 9-640888 15 86 .0359. .2 ,0-0380,5 15.4 9-96,985 30 3« 3-2 9-603017 16 77 .0-396983 1-641060 .6 92 .0-358940 .0-038043 16. 5 9-96.957 -28 ■ii 30 34 9-603161 17 82 .0-396839 9-64.232 17 97 .0-358768 .0-03807, 17 .6 9-961929 -2« 30 ■19 3« 9-603305 18 87 .0-396695 9-64.404 |i8 .03 .0-358596 ,0-038098 18. 7 9-961902 -24 21 30 3H 9-603449 19 92 .0-39655. 9-641575 19 109 10-358425 .0-038.26 1917 9-961874 •1-i 3U ilL 40 4-2 9-603594 20 96 21 lOI .0-396406 9-641747 21) 1.5 9-64.9,9 2: .20 10-358253 ,0-038.54 20 .8 21.9 9-96,846 '" 20 30 9-6o37i8 .0-396262 10-358081 10-038181 9-96,8,9 11 41 9-603882 22 106 .0-396.18 9-64209, 2-2 ,26 10-357909 10-038209 2220 9-96.79, 111 l!l 30 4li 9-604026 23 ,11 .0-395974 9-6+2263 23 ,32 'O-357737 .0-038137 23 2. 9-96,763 Ij 30 42 4S 960417c 24 ,15 .0-395830 9-642434 24 .38 .0-357566 .0-038165 ■24 22 9-961735 1-2 18 30 .W 9-604313 25,20 .0-395687 9-642606 25 ,43 '0-357394 .0-038292 25 23 9-961708 10 30 4:» it 9-604457 26,25 '0-395543 9-642777 2.^ .4^ io-357223 .0-038320 26 24 9-961680 ^ 17 311 .'.4 9-60460, 27.3c .0-395399 9-64294,^137 1,5 10-357051 10-038348 2725 9-961652 ,; 44 3<1 9-6C4745 28,34 .0-395255 9-641.20 ki 160 10356880 10-038376 2826 y-96,624 4 Itf .30 3M 9-604888 29 .39 .0-395..-. 9-643292 19 '''6 10-356708 ,0-038403 2927 9-96,597 ■i 30 i:> SB 9-605032 SO ,44 .0-394968 9-64346, V^.7-~ ,0-356537 10 356366 ,003843. 30 ig 9-96,569 25 is 15 9-605,76 1 5 .0-394824 9-64363^ 1 6 10-038459 1 1 996,54, Hi 4 9-6053,9 2 .0 .0-39468. 9643806 !1 .. 10-356194 10-038487 2 1 996,5.3 3(i U 30 li 9605462 3 ,4 .0-394538 9-643977 » 17 10-350023 100385,5 3 3 9-961485 54 17 H 9-605606 4 .9 .0-394394 9-644.48 4 23 10-355S52 ,0-038542 « 4 9-96,458 5-2 13 10 9-605749 5 14 ,0 39425. 9-6443.9 5 28 ,0-355681 ,0-03X570 5 5 9 96.430 50 30 41) l'2 9-605892 6 19 .0-394108 9-644490 6 34 .0-3555.0 ,0-038598 6 6 9-90.402 48 12 30 14 9-606035 7 33 .0-393965 9-64466, 7 40' 0-355339 ,0-038616 7 7 9-96.374 40 4» lU 9-606.79 8 38 .0-39382. 9-644832 8 46 .0-355,68 ,0-038654 8 7 9-96,346 44 11 10 IH 9-606322 9 43 ■0-393678 9-645003 9 5, 0-354997 ,0-038682 9 8 9-96,3.8 .->() •20 9-606465 .0 48 11 52 '0-393535 9-645.74 lU 57 11 63 0-354826 ,0-038710 10 9 11 10 9-96.190 I J0_ 9-606608 10-393392 9-645345 0-354655 10-038737 9-96.163 .-.1 ■24 9-606751 12 57 .0-393249 9-6455.6 U 68 1 0-354484 10-038765 12 ,, 9-961235 ili 9 3U •20 9-606893 13 62 .0-393107 9-645687 13 74 0-3543,3 .0-038793 13 .2 9-96,207 34 30 V2 ■a 9607036 14 67 .0-392964 9-645857 14 80 o-354'43 ,0-03881, 14.3 9-961,79 32 8 .10 30 9-607179 15 7. .0-39282. 9646028 15 85 0-353972 .0-038849 15.4 9-961,5, 30 .10 .'il 3-2 9-607322 16 76 .0-392678 9-646199 6 9,1 0-353S0. .0-038877 IB. 5 9-961,23 7 30 34 9-607464 17 8. .0-392536 9-646369 " 97 1 0-35363. ,0-038905 17.6 9-96,095 -211 ■•t M 9-607607 18 86 .0-392393 9-646540 8 101 0-353460 .0-038933 18. 7 /96,c67 -24 6 30 M 9-607749 19 90 .0-39225. 9-046710 9 .081 0-353290 .0-03896, 19.8 /961039 •2-2 30 .)■. 4U 4-2 9607892 20 95 21 .CO .0-392.08 10-391966 9-64688. 20,. 4 0-353. .9 0-038989 20,9 21 10 9-96,0,, z r, 311 9-608034 9-6470?. 2: 119I 0-352949 0-0390,7 9-960983 nn 41 9-608177 22.05 ,0-39,823 9-647221 n .25 0-352778 0-039045 22 10 j-960955 Hi 4 311 411 9-608319 13 110 io-39i68i 9-647392 M.3. 0-351608 0-039073 23 2, 9-960917 u •■'7 4n 960846, 24 ,,4 .0-39.539 9-647562 M .37 0-351438 0-039101 24 22 9-960899 1-2 3 30 .VI 9-60S603 25 ,,9 .0-39.397 9-647733 25 .41 0-352267 0-039129 25 23 ^-96087, 10 .'i8 .V2 9-608745 26 ,24 .0-39.255 9-647903 26 .48 0352097 0-039157 2624 9-960843 „ 2 311 51 9-6'.g«S^ 27 ,28 .0-39... 3 9-648073 27,54 0-35.917 0-039.86 2725 9-9608,4 u 31' Ml .■.11 9-609029 28,33 .0-39097. 9-648143 28.59 0-35,757 0-0391.4 28 26 9-960786 4 1 3.1 .-.Hi 9-609171 29 .38 .0-390829 9-6484.3 29,65 0-35,587 0-039242 2917 9-960758 •2 311 9 609313 10 .43 10-39C687 9-648583 30 .7 1 0-3514.7 10-039270 3018 9-960730 Co,i„e Parte Si-cant CoUng. } Parte | TanKe„t Coaec. Parts Sine m. (i(i° 4" 2-1 "• TABLE 68 LCU. SINES. COSINES. &c. ] ,b 3e„. .4° ' "i?- Sine Farts 1 Cosec. Tangent Parts Cotang. Secant Parts' Cosne 5:ri „ 9'6o93i3 ,0-390687 9-648583 .0-351417 .0-039270 19-960730 2ft CO 311 i 9-609455 r 5 ,0-390545 9-648753 1" 6 .0-35.247 .0-03929S 1" . 9-960702 58 30 1 4 9-609597 2 9 .0-390403 9-648923 2 1, .0-351077 ,0-039326 2 2 9-960674 56 59 30 s 9609739 3 ■4 .0-39026, 9-649093 3 ,7 .0-350907 jo-039354 ^ 3 9-960646 a 3U 2 8 9609880 4 >9 ,0-390.20 9-649263 4 23 10-350737 ,0-039382 ♦ 4 9-9606.8 52 68 30 10 9-6,oo2z S 23 .0389978 9-649433 5 28 .0-350567 .0-03941, 5 5 9-960589 50 30 3 12 9-610164 6 28 .0-389836 9-649602 6 34 .0-35039S .0-039439 6 6 9-96056, 48 57 30 14 9-610305 7 33 .0-389695 9-649772 7 39 10-350228 .0-039467 7 7 9-960533 46 30 4 IG 9-6.0447 9-6.o;Sj 8 38 :o-389553 9-649942 8 45 ,0-350058 .0-039495 8 8 9-960505 44 56 30 18 9 4-i .0-389412 9-650,.. 9 5. ,0-349889 10-039523 9 8 9-960477 42 30 J_ 20 9-610729 10 47 '"•389271 9-6502S. 10 56 .o-3497'9 .0-039552 10 9 9-960448 40 55 30 22 9-6,087. 11 52 10-389.29 9-650450 11 62 .0-349550 .0-039580 11 .0 9-960420 38 30 6 24 9-6. .O.J 12 56 .0-388988 9-650620 12 68 ,0-349380 .0-039608 12,1 9-960392 36 54 30 ■ill 9-611.53 13 6. .0-3S8847 9-650789 13 73 .0-34921. .0-039636 13 12 9-960364 34 30 7 ■28 9-611294 14 66 .0-388706 9-650959 14 79 .0-34904. .0-039665 14.3 9-960335 32 53 30 9-6.1435 15 71 ,0-388565 9-65. .28 15 85 .0-348872 .0-039693 15.4 9-960307 30 30 8 32 9-611576 16 75 .0-388424 9-65.297 16 90 .0-34S703 .0-039721 16. 5 9-960279 28 52 3(1 34 9-611717 17 .0-388283 9-65.467 17 96 .0-348533 ,0-039750 17 .6 9960250 26 30 9 3(i 9-6. .858 IS 85 .0-3SS.42 9-65.636 13 .02 .0-348364 ,0-039778 18 17 9-960222 24 51 30 3H 9-61.999 19 10-38800. 9-65.805 19 .07 .0-348,95 ,o-0398c6 19,8 9-960,94 22 30 10 9-612140 20 21 9+ 99 ,0-387860 9-65.974 20,. 3 2, ,.8 .0-34S026 ,0-039835 20,9 21 20 9-960.65 20 50 9-6.2280 .0-387720 9-652.43 ,0-347857 .0-039863 9-960.37 1 1 44 9 61242. 22 .03 .0-387579 9-6523,2 22 .24 ,0-347688 ,0-03989. 22 2, 9-960109 49 30 46 9-6.1562 23 ,08 .0-387438 9-65248, 23 ,30 .0-3475.9 .0-039920 23 22 9-960080 30 12 48 9-612702 24 1,3 .0-387298 9-652650 24 ,35 .0-347350 ,0-039948 2423 9-960052 48 30 50 9-6.2843 23 i>7 .0-387,57 9-6528.9 25 ,4, .0-347.81 ,0-039976 25z3|9-96oo24 30 1.3 52 9-6.2983 26 .22 .0-3870.7 9-6529S8 26 .47 .0-3470.2 .0-040005 2624 9-959995 47 30 54 9-6.3124 27 .27 .0-386876 9-653.57 27 .52 .0-346S43 .0-040033 2725 9-959967 30 N 5li 9-613264 28 .32 .0-3S6736 9653326 88,58 .0-346674 .0-040062 28 26 9-959938 46 31) .'.8 9-6.3404 29 .36 10-386596 9653494 29 .64 .0-346506 .0-040090 2927 9-9599.0 30 4r 37 9-6.3545 30 111 10-386455 9-653663 30 .69 10-346337 10-040,, 8 30 2S 9-959882 23 45 30 9-6.3685 ~ 5 .0-3863,5 9653832 1 6 10-346168 ,0-040,47 1 1 9-959853 16 4 9-6.3825 2 9 ,0-386,75 9-654000 a I. .0-346000 10-040.75 2 2 9-959825 56 44 30 8 9-6.3965 3 14 :o-3S6o35 9-654,69 3 ,7 .0-34583. .0-040204 3 3 9-959796 34 30 17 8 9-614.05 4 '9 ,0-385895 9-654337 4 22 '0-3456*3 10-040232 4 4 9-959768 52 43 30 10 9-614245 5 23 10-385755 9-654506 » 28 .0-345494 .0-04026. 5 5 9-959739 50 30 18 12 9-6.4385 6 28 ,0-3856.5 9-654674 6 34 10-345326 .0-040289 6 6 9-9597.. 48 42 30 14 9-6I4525 7 3^ 10-385475 9-654843 7 39 .0-345157 .0-0403.8 7 7 9-959682 46 30 i9 10 9-6.4665 8 37 10-385335 9-6550,, S .^5 10 3449S9 .0-040346 e 8 9-959654 44 41 30 18 9-6.4804 9 42 ,0-385.96 9-655,79 9 so .0-34482. .0-040375 9 9 9-959625 30 20 ■.■0 ■2 9-6.4944 10 11 46 5' .0-385056 9-655348 10 56 .0-344652 .0-040404 10 .0 11 ,0 9-959596 40 38 40 9-6.5084 10-384916 9-6555,6 11 62 .0-344484 .0-040432 9-95956S 21 24 9-6.5223 12 56 10-384777 9-655684 12 67 ,0-3443,6 ,0-04046, 12,1 9'959539 30 39 30 26 9-6.5363 13 6. 10-3S4637 9-655852 13 73 .0-344.48 ,0-040489 13 .2 9-95951. 34 30 22 28 9-6.5502 14 65 0-384498 9-656020 14 78 .0-343980 ,0-0405,8 14.3 9-959482 32 3« 30 30 9-6.5642 15 70 0-384358 9-656,88 15 84 10-3438.2 0-040547 15,4 9-959453 30 30 23 32 9 6.5781 18 75 0-3842,9 9-656356 16 90 .0-343644 .0-040575 16,5 9-959425 28 37 30 34 9-6.592. 17 79 .0-384079 9-656524 17 95 ,0-343476 0-040604 17.6 9-959396 20 30 24 36 9-6.6060 18 84 0-383940 9-656692 18 ,01 .0-343308 0-040632 18,7 9-959368 24 36 ao 38 9-6.6.99 19 89 0-38380. 9-656860 19 .06 0-343.40 0-04066. 19 ,8 9-959339 22 30 25 40 42 9-6,6338 20 21 93 98 0-383662 9-657028 20 ..2 21 ..8 .0-342972 0-040690 20,9 21 20 9-959310 20 18 35 ""30 9-6,6477 0-383523 9-657.96 0-342804 0-0407. 8 9-959282 20 14 9-6,6616 22 °3 0-383384 9-657364 22 .23 0-342636 0-040747 22 2. 9-959253 16 34 311 46 9-6, 6755 23 07 0-383245 9-65753' 23 .29 0-342469 0-040776 23 22 9-959224 14 30 27 48 9-6.6894 24 ,2 0-383,06 9-657699 24 .34 0-34230. 0-040805 -24 23 9-959'95 12 33 30 50 9-5.7033 25 17 0-382967 9-657S67 25 .40 0-342.33 0-040833 25 24 9-959167 10 30 2R 5-2 9-6.7172 26 2 3, 0-382828 9-658034 26 146 0-34.966 0-040862 2625 9-959.38 9 32 311 54 9-6,7V 27 26 0-382689 9-658202 27 .5. 0-34.798 0-04089. 2726 9-959.09 6 30 20 51) •r6./45o 28 3' 0-382550 9-658369 28,57 0-34.63. 0-040920 28 27 9-959080 4 31 30 58 9-6.7588 29 35 0-3824.2 9-658537 29 162 0-34.463 0-040948 29 28 9-959052 2 30 :w 38 9-617727 Cosine 10 4° 0-382273 965870+ W .68 .0-341296 0-040977 30^9 9-959C23 30 rts Secant Cotaug. Parts Tangent Cosec. Parts Sine m. 05" 4" 22"' 1 TABLE G8 7S7 lAM. SIN '.S, CO ^0 SINES, \c. ,h 3t77'-7| , 10-382273 9-658704 1 1.0-34.296 10-040977 I9-959C23 22 37r 30 ■i 9-61-866 I" 5 .0-382,3+ 9-65887. I 1- 6 10-341129 .0-041006 l"i 9-958994 58 1 .01 31 4 9-6iXoo4l 2 9 10-38.996 9659039 2 , I .0-340961 10-C41035 2 2 9-958965 .50 j 2U .10 (i 9^6, 81431.1 ,4 .0-38.8,7 9659206 3 17 10-340794 .0-04.063 ■^ 3 9-958937 54 a> 8 9-618281 4 18 IO-3817I9 9-659373 4 22 .0-340627 .0-041092 * 4 9-9589^8 5-2 28 J) 10 9-6184191 5 23 10-38158. 9-659540 5 28 .0-340460 10-041.21 5 5 9-958879 50 30 33 It 9-6iS558|« 28 .o-3g,442 9-659708 fi 33 .0-340292 .0-041150 6 6 9-958850 48 27 30 14 9-61S696 7 3^ 9-618834 8 37 10-, 8. 304 9-65.875 7 39 ,0-340,25 10-041179 7 7 9-95882. 4l> 30 34 ro lo-, 81166 9-660042 8 44 .0-339958 10-041208 8 8 9-95S792 41 2(; 30 i« 9-618972 9 4> 10-381028 9660209 9 50 .0-33979, .0-04.237 9 9 9-958763 4-2 .'III 35 m 9-6191.0 10 46 10-380890 9-660376 10 56 .0-3,9624 .004.266 10 10 11 11 9-958734 40 38 iL 9-619248 11 50 .0-380752 9-660543 11 61 i°-339457 .0-041294 9-958706 36 ■ii 9-6.9386 12 55 10-380614 9-6607.0 li 67 ,0-339290 10-041323 12 12 9-958677 3li 24 30 ■ill 96. 9524 13 59 .0-380476 9-660877 13 72 .0-339123 10-041352 13 12 9-95SM 34 30 37 ■iH 9619662 14 64 .0-3803,8 9-661043 14 78 .0-338957 14 13 9-9586.9 32 23 311 30 9-619800 15 69 .0-380200 9-661210 15 83 .0-338790 10-04.410 15 14 9-958590 30 30 38 3i 9-619938 16 73 .0-380062 9-66.377 16 89 .0-338623 .0-041439 I615 9-95856. ■28 22 30 34 9-620076 17 78 .0-379924 9-661544 17 95 10-33S456 .0-04.468 17 16 9-958532 •26 30 3!) 30 9-620213 18 83 10-379787 9-66,7.0 18 100 .0-338290 10-04.497 18 17 9-958503 ■24 21 3« 9-620351 ly 87 .0-379649 9-661877 19 106 ,0-338,23 10-041526 19 18 9-958474 ?-2 30 40_ 40 9-620488 21 96 ■0-3795.^ 9-662043 20 111 '°-337957 10-041555 20,9 21 20 9-958445 •20 18 20 30 9620626 •0-379374 9-6622,0 2.117 10-337790 .0041584 9-958416 41 44 9-620763122 101 10-379237 9-662,76 22 ,22 10-337624 10-041613 22 21 9-958387 10 10 30 4(i 9-62090123 105 10-379099 9-662,43 |23 128 .0-337457 .0-041642 23 22 9-958358 14 311 4-.> 4S 9-62.038124 no 9-662709 24 133 ,0-33729, .0-04.67. 24 23 9-958329 .•2 18 30 50 9-621175 25,14 .0-378S25 9-662876 -25 139 ,0-337,24 10-041700 25 24 9-958300 10 30 43 5i 9-621313 26119 .0-378687 9-663042 126 145 ,0,36958 10-041729 2625 9-95827. y 17 30 54 9-62.450 27 124 10-378550 9-66320S !27 .50 ■0-336792 .0-041758 2726 9958242 30 44 50 9-621587 28 .29 .0-3784.3 9-663375 |28 ,56 ,0-336625 .0-041787 2827 9-9582.3 4 Id 30 5S 9-621724 29,33 .0-378276 9-66,541 29 161 ,0-336459 .0-04.8.7 2928 9-9,8.83 •2 311 45 39 9-62186. iOi38 ■0-378,39 9-66,707 30 167 ,0-336293 .0-041846 3C19 9958.54 " 10 3(1 9-621998 ' 5 10-378002 9-663873 1 6 o-„6,27 10041875 1 1 9-958.25 4fi 4 9-622135 2 9 10-37786, 9-664039 « II 0-3,596, 10-041904 2 2 9958096 .'Hi 14 30 11 9-622272 3 14 .o-3777^S 9-664205 3 ,7 0-335795 10-041933 1 3 9-958067 54 ail 47 8 9-622409 4 18 ,0-377591 9-66437. 4 12 0-335*29 10-041962 ■* 4 9-958038 5-2 13 30 10 9-622546 5 23 '0-377454 9-6645,7 6 28 0-335463 10-041991 5 5 9-9580C9 .50 30 48 II 9-622682 6 27 ,0-37-3.8 9-66470, 6 33 0-335297 0-042021 6 6 9-957979 48 12 30 n 9-622819 7 3:^ .0-377181 9^664869 7 39 ,0-335,3, 10-042050 7 7 9 957950 40 Ml 4!) Hi 9622956 8 36 10-377044 9-«5035 8 44 0-334965 0-042079 8 8 9-957921 44 11 30 IH 9-623092 9 4. .0-376908 9^66520o 9 50 0-, 34800 0-042108 9 9 9-957892 42 311 .-.0 •20 •« 9-623229 10 45 10-376771 .0-376635 9665366 9-665532 10 55 11 6, 0-3346,4 0-042137 10 10 9-957863 38 \0 9-623365 II 50 0-334468 0-042167 9-957833 ol" •24 9623502 12 54 10-376498 9665698 12 66 0-334302 0042196 12 1; 9-957804 36 y 30 •ill 9623638 13 59 10-376362 9665863 13 72 0-334,37 0-042225 13 13 9-957775 34 30 r,l W 9-623774 U 63 10-376226 9-666029 14 77 0-33397, 0-042254 14 14 9-957746 M 8 3<1 .W 9-62,9,, 15 68 10-376089 9-666.94 15 83 0-333806 0-042284 '5 .5 9-9577.6 M 311 .-■3 :« 9624047 16 72 "•375953 9-666360 16 88 0-333640 0-042313 16 16 9-957687 •2S 7 30 .14 9-624183 17 77 0-375817 9-666525 17 94 0-333475 0-042342 17 17 9-95765!* •26 30 .•.4 :«i 9-624319 IB 82 0-375681 9-666691 18 99 0-3,3309 0-042372 18 18 9-957628 •24 i 9-625406 26 ,,8 0-374594 9-668013 26 144 0-331987 0-042607 2625 9-957393 8 2 III '•1 9-625542 27 ,23 0-374458 9-668,78 27 149 0-531822 0-042656 2726 ;-957 364 3* ,0-372295 9-6708,3 13 71 .0-329187 .0-043.08 13.3 9-956892 34 30 7 •28 9-627840 63 .0-372160 9-670977 14 77 ,0-329023 .0-043. 38 14,4 9-956862 32 53 30 9-627974 67 .0-372026 9-67,142 15 82 ,0-328858 ,0-043167 15.5 9-956833 30 30 8 32 9-628109 72 .0-37189, 9-671306 16 88 ,0-328694 •0-043.97 16.6 9-956803 28 52 30 "A 9-628244 76 .0-37.756 9-67,470 17 93 .0-328530 ,0-043227 17.7 9-956773 20 30 9 30 9-628378 8, .0-37.622 9-671635 18 99 ,0-328365 .0-043256 18 18 9-956744 24 51 30 38 9-6285.3 19 ■^■S ■o-37>4«7 9-671799 19 104 ,0-32820, .0-0432S6 19.9 9-9567,4 22 30 10 30 40 9-628647 20 21 90 94 .0-37.353 9-671963 20 ,10 21 ,,; ,0-328037 .0-0433.6 20 20 21 2. 9-9566S4 -20 50 9-628782 .0-37.2,8 9-672127 ■0-327873 .0-043345 9-956655 II 44 9-6289.6 22 99 10-37,084 9-67229, 22 12. .0-327709 .c-043375 22 22 9-956625 16 49 30 40 9-629050 23 .0-370950 9-672455 23 126 .0-327545 .0-043405 23 23 9-956595 14 30 12 48 9-629185 24 I08 .0-370815 9-6726,9 24 .32 10-32738, 10-043434 2424 9-956;t;6 12 48 30 50 9-6293.9 25 ..2 .0-37068. 9-672783 25 ,37 10-3272.7 .0-043464 25 25 9-950536 10 30 13 5-2 9-629453 26 117 ,0-370547 9-672947 26,42 ,0-327053 .0-043494 2626 9-956506 8 47 30 54 9-629587 27 .0-370413 9-673II1 17 .48 ,0-326889 .0-043524 2727 9-956476 30 14 50 9-62972, 28 .26 10-370279 9-673274128 153 ,0-326726 0-043553 2828 9-956447 4 46 30 58 9-629855 29 .30 10-370.45 9-673438 39.59 .0-326562 0-043583 2929 9-956417 2 30 ~ «1 9-629989 30 ■11 4 .0-37001. 9-673602 30 ,64 .0-326398 ,0-0436.3 30 30 9-956387 19 45 9-630123 .0-369877 9-673766 1 5 1:0-3262341 0-043643 ~i T 9-956357 l(! \ 9-630257 9 .0-369743 9-673929 2 .. .0-326071 0-043673 2 2 9-956327 56 44 U 9-63039, n .0-369609 9-674093 3 .6 .0-325907 0-043702 3 3 9-956298 54 30 i7 8 9-630524 .8 .0-369476 9-674257 4 22 10-325743 0-043732 •« 4 9-956268 52 43 10 9-630658 22 .0-369342 9-674420 5 27 10-325580 0-043762 5 5 9-95623S 50 30 18 12 9-630792 27 10-369208 9-674584 « 33 10-325416 0-043792 6 6 9-956208 48 42 30 \i 9-630915 3' 10-369075 9-674747 7 38 10-325253 0-043S22 7 7 9-956178 46 30 19 Ifi 9-631059 36 0-36894. 9-6749" 8 44 .0-325089 0-043852 8 8 9-956,48 44 41 30 18 9-631192 40 9-675074 9 49 10-324926 9 9 9-9561,8 42 30 2(1 22 9-63.326 44 49 0-368674 9-675237 10 54 11 60 .0-324763 0-0439.1 10 10 11 .1 9-956089 40 40 39" 9-63.459 0-36854. 9-675401 .0-324599 0-043941 9-956059 21 24 9-63,593 53 0-368407 9-675564 12 65 .0-324436 0-043971 12 .2 9-956029 36 30 •26 9-631726 58 0-368274 9-675727 13 71 .0-324273 0-04400. 13 13 9-955999 34 30 22 28 9-63.859 62 0-368,4. 9-675890 14 76 .0-324, .0 0-04403, 14.4 9-955969 32 38 30 30 9-63.992 67 0-36800S 9-676053 15 82 .0-323947 0-04406. 15.5 9-955939 30 30 23 32 9-632,25 7" 0-367875 9-676217 16 87 .0-323783 0-04409. 16.6 9-955909 28 '\ 30 34 9-632259 75 0-36774. 9-676380 17 9^ .0-323620 0-044,2. 1717 9-955879 26 24 3(i 9-632392 go 0-367608 9-676543 18 98 ,0-323457 0-044,5, 18.8 9-955849 24 36 30 38 9-632525 84 0-367475 9-676706 19.03 .0-323294 0-044,8, 19.9 9-955819 •22 30 25 40 9-632658 20 21 89 93] _o-367342 9-676S69 20 109 21 ..4 .0-323,3, 0-0442 . 1 2020 212. IS 35 30 9-632790 0-367208 9-677032 .0-32296S 0-04424. 9-955759 26 44 9-632923 22 0-367077 9-677,94 22 .20 .0-322S06 0-044271 22 22 9-955729 16 34 30 4b 9-633056 23 ,02 0-366944 9-677357 23 .2 5 .0-322643 0-04430. 2323 9-955609 14 30 27 48 9^633,89 24 .07 0-3668.. 9-677520 24 ,3. .0-322480 0-04433. 24 24 9 955669 12 33 30 30 9-6333" 25 0-366678 9-677683 25.36 ,0-3223,7 0-04436, 2525 9-955639 10 30 28 52 9-633454 26 ,.6 0-366546 9-677846 2fi .41 io--!22.54 0-044391 2626 9-955609 8 32 30 54 9-633587 27 120 0-3664,3 9 67S00S 27 147 ,0-32,992 0-044421 27 27 9-955579 6 30 2!) r.ti 9-6337.9 28 '15 0-3662S, 9-678171 28 152 ,0-32,829 0-044452 2828 9-955548 4 31 58 9-633852 29 ,29 0-366.48 9-67S334 29 .58 .0-32.666 0-044482 29 29 9-955518 2 30 3(1 «z 9-633984 30 ■33 0-3660,6 9-678496 30 ,63 .0-32.504 0-044512 30 30 9-9 5 5485! "^ 30 /"// ^ Cosine J.a.8| Sec-ant | CoUng. Pa.-ts Tangent Cosec. Parts 1 Sine «4° 4'' 18'" 1 TAIU.E (is LOG. SINKS, COSINES, .'vr. 1" 4:?'" ij" Im 1 " Sinr Parts 1 Cosec-. Tangent 1 Parts Colang. Se,-ant 1 Parts Cosine m ■i'^ 9-63;98 t^ nc-5660,6 9-67X496 ,0-32,504 .0-0445 12 1 9-955488 18 Ttd 1 .111 1 1 9-6341, 7 I" 4 ,0-365883 9-678659 '" 5 ,0-52,34 ,00445421 1" 9-95545« 5a 31) :S3C 10 44 U 48 '"•364694 9-680,20 10 54 11 59 ,0-3,9880 'O-0448.4 11 ,, 9-955.86 *" l-± 9-63543 10-364562 9-680282 10-3,97,8 10044844 9-955,56 m 24 9-63557C 12 53 10-364430 9-680444 12 65 ,0-3,9556 ■0-C44874 12 ,2 9-955,26 30 24 311 20 9-635702 13 57 .0-364298 9-680606 13 70 ,0-319394 ,0-044904 13 ,3 9 955096 3-1 311 37 28 9-635834 14 61 10-364166 9-6S0768 14 76 ,0-319232 10 044935 14,4 9-955065 32 •23 v> 30 9-63596 15 66 ■0-364035 9-680930 15 8, 10-319070 10044965 15,5 9-955035 30 M 'I 9-636097 16 70 10-363903 9-68,092 16 86 .0-3,8908 10-044995 16,6 9-955005 28 22 30 9-636229 17 75 .0-36377, 9-68,254 17 92 ,0-3,8746 ,0-045026 17,7 9-954974 20 31) 39 30 9-636360 18 79 10-363640 9-68,4,6 18 97 ,0-3,8584 ,0-045056 18,8 9-954944 -24 21 30 ja 9-636492 19 83 ,0-363508 9-68,578 19 ,03 ,0-3,8422 ,0-045086 19,9 9-9549,4 ■<0 30 40 42 9-636623 20 88 21 92 10-363377 9-68,740 20 ,08 21 ,,3 ,0-3,8260 ,0-0451,7 20 20 21 2, 9-9548S3 21) 18 20 9-636754 ,0-363246 9-68,90, ,0-318099 10-045147 9-954S53 41 4^1 9-636886122 96 ■0-363, ,4 9-682063 22 ,,9 ,0-3,7937 10-045177 22 22 9954823 10 lit 30 4U 9-6370.723 .0, ,0-362983 9-682225 23 ,24 .0-3.7775 10-04520S 2323 9954792 14 30 42 48 9-637:4824 105 ,0-362852 9-682387 24 ,30 .0-3,76,3 .0-045238 24 24 9-954762 12 III 30 50 9-63728025 ,,c .0-362720 9-6S2548 M ,35 .0-3,7452 10-04526S 25 25 9-954732 10 30 43 52 9-63-'4..'^6 ,,4 .0-362589 9-682710 96.40 10-3,7290 10-045299 2626 9-95470, 8 17 30 54 9-63754227 ..9 .0-362458 9-68287, a; 146 10-317,29 ■0-045329 2727 9-95467, 44 50 9-63767328.23 ,0-362327 9-683033 28 ,5, 10-316967 ,0-045360 28 28 9-954640 4 If) 30 53 9-637804,29 127 ,0-362,96 9-683,94 29.57 ,0-3,6806 ,0-045390 2929I9-9546.O 2 30 4» 30 43 9-63793S 30 .3^ ' 4 ■0-362065 .0-36,934 9683356 30 162 10-3,6644 ■0-045421 30 30 9-954579 58 la 311 9-638066 96835,7 ' 5 ,0-3,6483 ,0-04545, I . 9-954549 4(; 4 9-63S197 2 9 .0-36,803 9-683679 a 1, 10-3,632, ,0-045482 2 2 9-9545.8 50 14 .«> 9-638328 3 13 .0-36,672 9-6S3840 3 ,6 .0-3,6,60 10-0455,2 3 3 9-954488 54 311 47 S 9638458 4 ,7 10-36,542 9-68400, 4 2, ■0-3,5999 ,0-045543 * 4 9954457 52 13 3,.| ro 9-638589 5 22 ,0-36,4,, 9-684,62 5 27 ,0-3,5838 10-045573 ■' 5 9954427 50 4« 12 9638720 6 26 ,0-361280 9-684324 6 32 10-315676 10-045604 6 6 9-954396 48 12 10 .1 9-63885. 7 30 ,0-361,49 9-6S4485 7 38 ,0-3155,5 .0-045034 7 7 9-954366 40 4!» ift 9-638981 8 35 ,0-36,0,9 9-684646 8 43 ,0-3,5354 10-045665 8 8 9-954335 14 II 10 IH 9-639112 9 39 ,0-360888 9-684807 9 48 .0-3.5.93 10-045695 9 9 ■) 954305I 42 30 SO 22 9-639242 10 43 11 48 ,0-360758 9-684968 10 54 11 59 .0-315032 ,0-045726 10 10 11 11 9-954274 3I 30 9-639373 ,0-360627 9-685,29 0-31487, ■0-045757 9-954243 SI 2J 9-639503 12 52 ,0-360497 9-685290 2 64 10-3,47,0 ,0-045787 12,2 99542.3 30 9 311 26 9-639633 13 ,6 0-360367 9-68545. 3 70 0-3,4549 ,0-0458,8 13,3 9-954,82 :m S2 2» 9639764 14 6, ,0-360236 9-6856,2 * 75 0-3,4388 0-045848 14 ,4 9954.52 32 H :io 30 9-639894 15 65 0-360.06 9-685773 5 So 0-3,4227 0-045879 13 ,5 9-954.2. JO S3 32 9-640024 16 69 0-359976 9-685934 6 86 0-3,4066 0-0439,0 16 ,6 9-954090 28 7 30 34 9-640154 7 74 0-359846 9-6S6095 7 9. 0-3.3905 0-045940 17 17 9-954060 20 311 S» 10 9-640284 8 78 0-3597,6 9-686255 8 96 0-3.3745 0-04597, 18, 8 1 ;-954029 24 6 311 3» 9-640414 9 82 0-359586 9-6864,6 9 ,02 3,3584 o-046oor. 19 19 J-953998 22 .10 S.) 42 9-640544 20 87 21 9, 0-359456 9-6S6577 9-686737 20 ,07 21 ,,3 0-3,3423 0-046012 2I2, 3-953968 20 5 9 64c 6 74 0-359326 0-3,3263 0-046C63 >-953937 Si; 41 9-640804 22 95 0-359.96 9-686898 2 ,18 0-3,3,02 0-046094 2222 ^-953906 10 4 10 40 9-64093423 ioo| 0-359066 9-687059 23 ,23 0-31294. 0-040,24 23 23 ^-953876 1^ •i7 1 48 9-64.C64 24 ,04 0-358936 9-6872,9 4 ,29 c-3,278. 0-046,55 24 24 )'953845 [2 3 ■"'i 50 964.194 25 ,09 0-358806 9687380 5 ,34 0-312620 0-046,86 25 25 9538.4 III :.« 52 /64.324 26 ,,3 0-358676 9-687540 6 ,39 0-3,2460 0-046217 2627 -953783 „ ._. 30 51 964145, 27 ..7 0-358547 9 68770, 7 .45 0-3,2299 0-046247 2728 -953753 30 S!) ill 9-64,583 28 ,22 0-3584-7 968786, 28 ,50 o-3,2i39 0-046278 28 29 -953722 4 1 311 in 9-64. 712I 29 ,26 0-358288 9-68802, 29 ,55 0-3. ,979 o-046-;o9 29 30 -95369, ; 3(1 (III ,«4 9-64,842 10 ,30 0-358,58 9-688,82 30 ,6, 0-046340 30^ -953660 -!^ Cosine Parti. Secant Cotang. Parts Tangent Cosec. Parts Sine ni. ~/" W 4'' l(i" 790 TABLE 68 LOG. SINES, COSINES. &c. | i" 44™ -26" '"im Sine Pai-ts Cosec. Tangent Parts Cotang. Secant Parts Cosine m. (7(1 9-641842 ,0-358,58 9-688182 ,0-3, ,8,8 0-046340 9-953660 16 30 ■2 9-641971 »" 4 ,0-358029 9-688342 '" 5 ,0-3, ,658 0-04637, 1" . 9-953629 311 1 9-642,0, 2 9 ,0-357899 9-688502 2 ,, ,0-3,, 498 0-04640, 2 2 9-953599 56 Oil 30 9-642230 3 ,3 ,0-357770 9-688663 3 ,6 ,0-3, .337 0-046432 ■* 3 9-953568 54 30 2 9-642360 4 ,7 ,0-357640 9-688823 4 2. ,0-3,1,77 0-046463 •* 4 9953537 52 08 30 10 9-642489 .0-357511 9-688983 5 27 .0-31,0,7 0-046494 5 5 9-953506 50 30 3 1-2 9-6426. S 6 26 .0-357382 9-689.43 6 32 ,0-310857 0-046525 6 6 9-953475 48 S7 30 U 9-642747 7 3° ,0-357253 9-689303 7 37 ,0-3,0697 0-046556 7 7 9-953444 46 ao 4 16 9-642877 8 34 ,0-357,23 9-089463 8 43 ,0-310537 0-046587 8 8 9-953413 44 30 30 IS 9-643006 9 39 10-356994 9-689623 9 48 .0-3.0377 0-0466,8 9 9 9-95338; 42 30 5 20 22 9-6+3>35 10 43 11 47 ,0-356865 9-689783 10 53 11 59 .0-3,02.7 0-046648 10 10 11 .1 9-953352 40 38 55 30 9-643264 10-356736 9-689943 .0-3.0057 0-046679 9-953321 G u 9643393 1-2 5, .0-356607 9-690.03 12 64 .0-309897 0-046710 12 ,2 9-953290 36 54 30 26 9-643522 13 56 10-356478 9-690263 13 69 ,0-309737 0-046-4, 13,3 9-953259 34 30 7 28 9-643650 14 60 ,0-356350 9-690423 14 75 10-309577 0-C46772 14,4 9-953228 32 53 30 30 9-643779 15 64 10-35622, 9-6905S2 15 80 .0-3094.8 0-046803 15,5 9-953197 30 30 8 32 9-643908 16 68 ,0-356092 9-690742 16 8; 10-309258 0046834 16 16 9-953,66 28 52 30 34 9-644037 17 73 10-355963 9-690902 17 9, ,0-309098 0-046S65 17 18 9-953'35 26 9 36 9-644165 18 77 .0-355835 9-691062 18 96 .0-308938 0-046896 18,9 9-953104 24 51 30 38 9-644294 19 82 10-355706 9-69122. 19 ,0, .0-308779 0-C46927 19 20 9-953073 22 30 10 40 9-644423 20 86 21 90 ■°-355577 9-6913S, 20 107 21 ,,2 .0-3086,9 0-04695S ■20 2, 21 J2 ^953042 20 50 9-644551 ,0-355449 9-69,540 ,0-308460 0-046989 9-953011 II 44 9-644680 22 94 ,0-355320 9-69.700 •22 ,,7 ,0-308300 c-047020 •2223 9-952980 16 ■49 30 46 9-644808 23 99 ,0355, 92 9-69.859 23 .23 .0-J08.4, 0-04705, 23 24 9-952949 14 12 48 9-644936 24 ,03 .0-355064 9-692019 24 128 ,0-30798, 0-0470S2 24 25 9-95291* 12 48 3(1 50 9-645065 ,0-354935 9-692,78 25 ,33 ,0-307822 , 0-047,, 4 ■2026 9952886 10 30 13 52 9-645193 26 ,,2 10-354807 9-692338 26,39 .0-307662 , 0-047145 •2627 9952855 J, 47 30 51 9-645321 27 116 10-354679 9-692497 27.44 ,0-307503 . 0-047176 ■2728 9-952824 (j 30 u 56 9-645450 28 120 ,0-354550 9-692656 28,49 ,0-307344 . 0-047207 2829 9-952793 4 4(< 30 58 9-645578 P9.24 .0-354422 9-692S.6 29,55 .0-307.84 . 0-047238 •2930 9-952762 30 }1_ '30 ftS 9-64570D •,(> ,29 .0-354294 .0-354,66 9-692975 30 .60 0-307025 , 0-047269 30 31 9-95273, 15 58 45 9-645834 > 4 9-693,34 1 5 ,0306866 , 0-047300 1 , 9-952700 16 4 9-645962 2 9 .0-354038 9693293 a I, ,0-306707 1 0-04733, 2 2 9-952669 56 44 30 6 9-646090 3 ,3 0-3539.0 9-693453 3 ,6 0-306547 , 0-047363 a 3 9952637 51 17 8 9-6462,8 4 ,7 0-353782 9-6936,2 4 2, 0-306388 , 0-047394 4 4 9-952606 52 4:1 30 10 9-646346 5 2, 0-353654 9-69377, 5 26 0-306229 1 0-047425 5 5 9-952575 50 30 18 12 9-646474 6 25 0-353526 9693930 6 32 0-306070 . 0-047456 6 6 9-952544 48 42 30 M 9-64660. 7 30 0-353399 9-094089 7 37 0-3059,, , 1-047488 7 7 9-9525,2 46 30 '30 ' '" 9-646729 8 34 0-35327. 9-694^48 8 42 0-305752 . 0-0475,9 8 8 9-95248, 44 41 18 9646857 9 38 o-353>43 9-694407 9 48 .0-305593 . 0-047550 9 9 9-952450 42 3(1 ■2(1 20 9-6469S4 9-647,12 10 42 •I 47 0-3530.6 9-694566 10 53 11 58 .0-305434 . 0-04758. U ,, 9-9524,9 40 40 0-352888 9-694724 0-305276 . 0-047613 9-95^387 21 24 9-647240 12 5, 0-352-60 9-694883 12 63 .0-305, ,7 . 0-047644 12,3 9-952356 :i« 39 30 26 9-647367 13 55 0-352633 9-695042 13 69 .o- 304958 . 0-047675 13 ,4 9-952325 34 3(1 22 28 9-647494 14 59 0-352506 9-69520, 14 74 0-304799 ' 0-047706 14 15 9-952294 32 38 30 30 9-647622 15 64 0-352378 9-695360 15 79 0-304640 1 0-047738 15 16 9-952262 30 30 2S 32 9-647749 16 68 0-35225. 9-6955,8 16 85 0-304482 . 0-047769 16,7 9-95223, 28 37 30 34 9-647877 7 7^ 0-352.23 9695677 17 901 304323 . 0-047800 17 i8 9-952200 30 24 36 9-648004 8 76 0-351996 9-695836 .8 95 1 0-304.64 . 0-047832 '.819 9952,68 24 30 to 38 9-648.3. 9 81 0-351869 9695994 19 10, 0-304006 . 0-047863 1920 9-95:137 22 30 2r, 40 9-64825S 20 85 21 89 0-35.742 9-696,5; ■20 106 21 ,,, 0-303847 ■ 0-047894 20 I, 2122 9-952.06 20 35 ~lo 9-648385 0-35.6.5 9-69631. ,0-303689 . 0-047926 9-952o:'4 26 41 9-6485.2 22 93 0-35,488 9-696470 22 ,,6 10-303530 . 0-047957 2223 9-952043 16 34 30 40 9-648639 23 98 0-35,36, 9-696628 33 ,22 .0-303372 . 0-047989 23 24 9-95201. 14 30 27 48 9-648766 24 .02 0-35.234 9-696787 24 .27 0-3032,3 1 0-048020 24 25 9-951980 12 33 30 ,V) 9-648893 25 ,06 0-351.07 9-696945 25 .32 .0-303055 , 0-04805, 2526 9-95.949 30 28 52 9-649020 26 ,,0 0-350980 9-697,03 26 .38 ,0-302897 1 0-048083 2627 9-95.9.7 (i 32 30 51 9-649,47 27 ,15 0-350853 9-697262 27 ,43 ,0-302739 . 0-0481,4 2728 9-95.886 6 30 2!» 9-649274 28 ,,9 0-350726 9 6974-0 28 148 .0-302580 . 0-048.46 28 29 9-95,854 4 31 30 58 9-649401 29 ,23 0-350599 9-697578 29 ,53 .0-302422 . 0-048.77 2930 9-95.823 2 311 30 ft6 9-64952- to ,27 0-350473 9-697736 10 ,59 10-302264 , 0-048209 30 3' 9 951791 .•«t '" ^ Cosiiie Parts Secant Cotang. Parts Tangent Cosec. Parts Si.ie ^ G;r 4^ 14" I TABLE 08 LOG. SINES, COSINES, ic. 1 ,h 4em ogo ] ' " \rn Sine j Part. 1 Cosec. Tangent Parli Cotang. Secant Parts I Cosine «n V" M\ 1 u 9-64951 10-350473 9697736 10-302164 10-048109 i9-95i79i 14 60 :ki! 2 9-649654 '" 4 ,0-350346 9-697894 1" 5 10-301106 .c-048140 1 ,19-951760 58 30 31 4 9-6+978 2 8 10-3502,9 9-698053 2 II 10-301947 .0-048171 2 219-95.718 5C 29 30 9-64990 3 ,3 ,0-350093 9698211 3 ,6 ,0-301789 .0-048303 ^ 3 9-951697 51 31) &i 8 9-650°?'( ,0-349966 9-698369 4 2, 10-301631 ■0-048335 9-95.665 52 28 *, 10 9- 6 50 16c 5 21 ,0-349840 9-698527 5 26 10-301473 .0-048366 5 c 9-95,634 50 30 :i3 12 9-65018, 6 25 10-349713 9-69S685 6 32 10-301315 .0-048398 6 6 9-95,602 4K 27 30 14 9-65041 7 29 ,0-349587 9-698843 7 37 10-301157 Jo;o48430 7 7 9-95,570 40 30 34 III 9-650539 8 34 10-34946, 9-69900. 8 42 10-300999 8 8 9-951539 4J •Hi M 18 9-650666 9 38 ,0-349334 9-699.59 9 47 10-300841 .c-048495 9 9 9-95.507 42 30 30 I 9*650792 10 42 11 46 10-34920S 9-6993,6 10 53 I. 58 10-300684 .0-048524 ID .. 9-95H76 40 38 25 9-6509,8 10-349C82 9-699474 10-300526 .0-048556 11 .2 9-95,444 ■Mi l24 9-651044 12 5, 10-348956 9-699632 12 63 .0-300368 .0-04S5S8 12.319-95.4.2 3C 24 30 1 m 9-65,.:-, 13 55 10-348829 9-699790 13 68 10-300210 10-048619 13.4 9-95,38, M 30 37 28 9-651297 14 59 .0-348703 9-699947 14 74 10-300053 10-04865. 14.5 9-95.349 32 23 30 30 9-651423 15 63 10-348577 9-700105 15 79 10-299S95 .0048683 15,6 9-951317 30 30 38 31 9-651549 16 67 10-34845. 9-700263 16 84 10-299737 .0-048714 16 .7 9-951186 28 22 30 W 9-651675 17 7, 10-348325 9-7C0420 17 89 ,0-299580 10-048746 17.8 9-951154 26 30 30 30 9-65 180C 18 76 ,0-348200 9-700578 18 95 ,0-299422 10-048778I I819I9-951221 24 21 30 38 9-651926 19 So ,0-348074 9-700736 19 100 10-299164 10-048809 1 1910 9-951I91 22 40 40 9-652052 20 84 21 88 ,0-347948 9-700893 20 105 10-299107 .0-048841 ■20 2. 2122 9-951159 20 20 30 9-652.78 ,0-347822 9-701051 21 1,0 io-i9>i949 ,0-048873 9-951.27 41 44 9-652304 22 92 10-347696 9-701208 j22 116 ,0-198791 .0-048904 2223 995.096 16 19 :io 46 9-652429 23 97 10-347571 9-70,365 23 ,2, .0-198635 ,0-048936 23,4 995.064 14 30 42 ! J8 9-652555:24 101 10-347445 9-70,523 24 ,26 10-198477 ■0-048968 24 25 995.032 12 18 30 1 50 9-652680125 .05 .0-347310 9-7016S0 l25 131 10-198310 .0-049000 25 16 9-95. oco 10 30 43 92 9-652806126 109 10-347194 9-701837 26 137 .0-198,63 .0-049032 2617 9-950968 g 17 30 34 9-65293127 113 10-347069 9-70,995 27 141 ,0-198005 .0-049063 27 28 9950937 30 44 56 9-653057,28 118 ,0-346943 9-702152 28 147 .0-197848 .0-049095 28 29 9-950905 4 16 30 5S 9-65318229 122 ,0-3468,8 9-702309 29 153 .0-29769. .0-049127 2931 9-950873 2 30 J5_47 9-653308I3O .26 ■0-346692 9-701466 !30 1,8 10-297534 10-049159 3032 9-950841 13 la 30 9-653433 1 4 ,0-346567 9-702623 ' 5 ,0-297377 10-049191 1 1 9950809 4e 9-653558 2 8 ,0-346442 9-702781 2 ,0 10-2972,9 .0-049112 2 2 9-950778 50 14 30 9-653683 3 12 10-346317 9-702938 3 ,6 .0-297061 ,0-049254 3 3 9-950746 54 47 9-653808 4 17 0-346192 9-703095 4 2, .0-196905 0-0492S6 * 4 9-950714 52 13 30 10 9'653934 5 2, 0-346066 9-703152 S 26 .0-29674S 0-0493,8 S 5 9-950682 50 31. 48 12 9-654059 6 25 0-345941 9-703409 6 31 .0-296591 0-049350 6 6 9-950650 49 12 30 14 9-C54184 7 29 0-345816 9-703566 7 37 .0-296434 0-049381 7 7 9-9506,8 46 30 4!) 1 le 9-654309 8 33 0-345691 9-703722 8 41 .0-296178 0-0494.4 8 9 9-950586 +1 ii 30 18 9-654434 9 37 10-345566 9-703879 9 47 .0-19611. 0-049446 9 .0 9-95^554 42 30 60 20 9-654558 10 42 11 46 10-345442 9-704036 9-704193" 10 52 '• 57 .0-195964 0-049478 10 ., 11 .2 9-950522 40 38 10 30 9-654683 °'3453'7 ,0195807 0-0495.0 9-950490 Al I24 9-654808 12 50 0-345,92 9-704350 12 63 ,029,650 0-049542 12.3 9-950458 30 9 30 1 20 9654933 13 54 0-345067 9 704506 13 68 .0-295494 0-049574 13,4 9-950426 34 30 sa yi» 9-655058 14 58 0-344942 9-704663 14 73 10-295337 0-049606 14.5 9-95°394 32 8 3ii :» 9-65518215 62 0-3448,8 9-704820 15 78 .0-295.80 0-049638 15 .6 9950362 30 30 .■.:i ;, .' : -'16 67 0-344693 9-704976 16 84 0-295024 0-049670 16. 7 9-950330 28 7 '17 71 0-344569 9-705133 17 89 0-294S67 0-049702 17 .8 9 930298 20 30 M MS 75 0-344444 9-705290 18 94 0-2947.0 0-049734I1819 9-950166 21 fi ' ' " ■■■■ '■' 79 0-344320 9-705446 19 99 0-294554 0-049766 1 19 10 9 950234 22 '11 30 ! 42 9655805 20 83 1 21 87 0-344,95 9-705603 20 104 21 no _0294W 0-294241 0-049798 j 201. 0049830121 11 9-950202 18 ft 30 9 6559^9 0-34407, 9-705759 9-950,70 ■'■(i 44 9656054 22 91 0-343946 9-7059,6 22, ,5 0294084 0-049862 2223 9-950,38 10 4 to \6 9-656178 23 95 0-343822 9-706072 23 ,20 0-293928 0-04989412325 9-950,06 14 30 57 48 9-656302 24 100 0-343698 9-706218 24 ,25 0-293772 04992612426 9-950074 12 3 30 30 9656426 23 104 0-343S74 9-706385 25 130 0-193615 0-049958 25 27 9-950042 10 30 .ilj 52 9-65655, 26 108 0-343449 9-70654, 26,36 10-193459 0049990 2628 9-950010 8 2 30 ! 54 9656675 27 1,1 0-34331; 9-706697 27 141 1 0-293303 0-050023 2729 9949977 30 sa ' -c 9 656799(28 116 0-343201 9-706854 28 146 0-293.46 0-050055 2830 9949945 4 1 30 1 '.8 9-656923-29 ,20 0-343077 9-7070,0 129 ,5, .0-292990 0-050087 2931 9-949913 2 30 fio_!4a 9-65704730 ,25 0-342953 9-707166 !30 ,57 .0-291834 Tangent Cosec. 3»3i 9-949881 ¥: 777 > // '^• Cosine ParU Senant Cotang. 1 Parts Parts Sine 63° 4" 12' 792 TABLE 68 LOG. SINES, COSINES. Ike. I" 48-" 27° ' " n» Sine Parts 1 Cosec. Tangent Parts Cotang. Secant Parts Cosine m «0 T' 9-657047 .0-342953 9-707.66 .0-292834 10-0501.9 9-94988. 12 VI 9-657171 '" 4 .0-342S29 9-707322 1" 5 13-292678 10-050.5. 1". 9-949549 38 30 1 9-657295 2 8 ■0-342705 9-707478 2 101.0-292522 10-050184 2 2 9-9498.6 56 Oil 30 9-657418 3 .2 .0-342582 9-707634 1 3 .6 10-292366 .0-0502.6 3 3 9-949784 54 30 2 9-657542 4 .6 .0-342458 9-70779C 4 I. .0-292210 .0050248 ■• 4 9-949752 5-2 58 3n 9-657666 5 2. .0-342334 9-707946 6 26 10-292054 10-050280 6 5 9-949720 50 30 S 9-65779° 6 25 10-3422.0 9-708.02 6 31 10-29.898 10-050312 6 6 9-949688 48 57 30 9-657913 7 29 .0-342087 9-708258 7 36 10-291742 10-050345 7 8 9-949655 46 30 4 9-658037 8 33 .0-341963 9-7084.4 8 42 .0-291586 .0-050377 8 9 9-949623 44 JB 30 9-658.6.] 9 37 .0-34.539 9-708570 9 47 .0-29.430 .0-050409 9,0 9-94959. 4-2 30 5 ■22 9-658^84 10 4. 11 45 .0-34.7.6 9-708726 10 52 I2 11 .0'29.274 10-050442 lOl, 11 .2 9-949558 40 55 9-658408 .0-34.592 9-708882 io-29..,8 .0-050474 9949526 « ■u 9-65853. 12 49 .0-341469 9-709037 .0-290963 .0-050506 12.3 9-949494 36 64 30 26 9-6586,5 13 53 .0-341345 9-709193 13 67 !0-290807 .0-050538 13 ,4 9-949402 34 30 7 •28 9-6587-/8 14 57 .0-3+,222 9-709349 14 73 .0-29065. 1005057. 14,5 9-949429 32 33 30 30 9-6589.M 15 62 .0-341099 9-709504 15 78 .0-290496 .0-050603 16 ,6 9-949397 30 30 g 3'2 9-659025 16 66 .0-340975 9-709660 16 83 .0-290340 10-050636 16,7 9949364 28 52 111 34 9-659.48 17 70 .0-340852 9-709816 17 88 .0-290. 84 .0-050668 17 ,8 9-949332 20 30 !) 36 9-65927. 18 74 .0-340729 9-70997. 18 93 .0-290029 .0-050700 18,9 9-949300 24 51 30 3S 9-659394 19 78 io'34o6c6 9-7.0.27 19 99 .0-289873 '0-050733 1921 9-949267 -22 30 10 40 9-659517 20 82 21 86 .0-340483 9-7.0282 20 .04 21 .09 10-289718 20 22 2123 9-949235 •20 18 50 9-659640 10-340360 9-7.0438 .0-2S9562 T^^oT^s 9-949202 11 H 9-659763 22 90 10-340237 9-7.0593 22 1.4 .0-289407 '0-050S30 2224 9-949.70 16 49 30 4li 9-659886 23 95 10-3401 14 9-710749 23 .,9 .0-28925. 10-050862 23 25 9-949.38 14 30 12 4H 9-660009 24 99 .0-33999. 9-710904 24 .25 .0-289096 10-050S95 ■24 26 9-949.05 12 48 30 60 9-660.32 25.03 .0-339868 9-71.059 25 .30 .0-28894. 10-050927 25 27 9-949073 10 30 13 .Vi 9-660255 26 .07 i°-339745 9-711215 •26 .35 .0-288785 10-050960 2628 9-949040 8 47 311 54 9-660378 27 ... .0-339622 9-711370 37 .40 .0-288630 10-050992 2729 9-949008 6 30 u 51) 9-660501 28., 5 10-339499 9-711525 28 ,45 10-288475 10-051025 2830 9-948975 4 46 30 5« 9660623 20 ..9 .0-339377 9-7. .68. 29.5. .0-288319 10-051057 293. 9-948943 1 311 1.-. 2 9660746 30 ,23 10-339254 9-711836 30.56 10-288164 .0-05.090 .0-05.122 30^ 9-948910 9-948878 11 46 9-66oS6q > 4 10-339.31 9 7.1991 ' 5 10-188009 Ifi 4 9-66099'. 2 i .0-339009 9-712.46 2 .0.0-287854 10-05. .55 2 2 9-948845 56 44 30 « 9-66. ..4 3 .2 .0338886 9-71230. I 3 .5 1.0-287699 ■0-051,88 3 3 9-948812 54 di 17 8 966.236 4 .6 .0-338764 9-712456 1 4 2, 10-287544 .0-05.220 •• 4 9-948780 52 43 30 10 9 66.359 5 20 .0-33864. 9-712611 S 26 .0-287389 10-051253 5 5 9948747 50 31 18 1-2 9 66.48. 6 24 .0-3385.9 9-712766 6 3. 10-287234 .0-05.285 6 7 9-9487.5 48 42 30 14 9-661603 7 28 10-338397 9-712921 7 36 .0-287079 0-05.3.8 7 8 9-9+8682 46 30 19 lli 9-661726 8 33 .0-338274 9-713076 8 4. .0-286924 .0-05.350 8 9 9-948650 44 41 30 18 9-66.848 9 37 .0-338.52 9-71323. 9 46 .0-286-69 .0051383 9 .0 9-9486.7 42 311 2(1 30 ■20 9-66.970 9-66:092 41 ' 45 .0-338030 9-7-3386 ;;;; .0-2S66.4 .0-05,416 10 1. 11 .2 9948584 9-948552 38 -^1 .0-337908 9-71354' 10-286459 .0-05,448 21 24 9-66i2.4 2 49 0-337786 9-7.3696 1-: 62 .0-286304 .0-05148. 12.3 9-9485,9 36 3!t 30 ■2li 9-662337 3 53 0-337663 9-7.3850 13 67 .0-286.50 10-0515.4 13 .4 9-948486 :n 30 22 48 9662459 * 57 0-33754' 9-714005 14 72 .0-285995 10-051546 14,5 9-948454 32 38 30 30 9-66258. 5 6. 0-3574.9 9-7.4160 15 77 .0-285840 15 16 9-94842, 311 30 23 32 9-662703 6 65 0-337297 9714314 16 83 .0^285686 10-051612 16 17 9-948388 28 37 30 34 9-662S25 7 69 0-337175 9-714469 17 88 .0-28553. 10-05,645 17 .8 9-948355 •26 24 3(i 9-662946 8 73 c-337054 9-714624 18 93 .0-285376 .0-05,677 18 .9 9-9*8323 ■24 38 m: 38 9-663068 9 77 10-336932 9-714778 19 98 .0-285222 .0-05.710 192. 9-948290 •22 30 2ft 40 9-663190 20 8. 21 85 10-3368.0 9-714913 20 :;3 21 .08 .0-285067 .0-051743 20 22 2123 9-948257 9-948224 20 35 9-6633.2 .0-336688 9-715087 .0-284913 .0-051776 2(i 44 9-663433 22 89 0-336567 9-715242 22 .14 =0284758 .c-051808 2224 9-948.92 ,6 34 30 46 9-663555 23 94 0-336445 9-715396 M 1191:0284604' 10-051S4. •2325 9-948.59 14 30 27 18 9-663677 24 98 .0-336323 9-71555' 24 .241.0-284449 .0-051874 24 26 9-948.26 12 33 30 ao 9-66379S 25 .02 10-336202 9'7'5705 25 ,29 10-284295 10-051907 25 27 9-948093 10 30 28 52 9-663920 2fi .06 0-336080 9-715860 26 134 10-284140 .0-051940 2628 ;-948o6o ^ 32 30 51 9-66404. 27 no o'335959 9-716014 27 139 .0-283986 10051972 ■2729 /948028 S 311 29 56 9-664.63 28 ..4 .0-335837 9-71616S 28 .44 10-283832 .0052005 283. 9-947995 4 31 30 W 9-664284 29 1.8 0-335716 9-7.6322 29 .50 10-283678 .0-052038 2932 9-947962 2 30 30 SO 9-664406 Cosi.-~ 30 .22 0-335594 9-7.6477 30 .55 .0-05207. 30_32 9-947929 30 ^-■1 Parts Secant Cotang. Parts Tangent Liisec. Parts Sine m. 777 ,..„. 1 TABLE 6S LOG. SINES, COSINES, &c. j !•• 5(l'" 27° 1" Sine Parts Cosec. Taneent Parts Cota„g. Secant Parts Cwine m '" V : 9-66,40f i°-335594 9-7.6477 .0-283523 .0-05207, 9-947929 xb IfT 9-664S1 '" 4 IO-33S473 9-7.663. 1" 5 .0-283369 .0-052.04 1" I 9-947896 58 30 SI 4 9'66+64!. 2 8 '°-33535i 9-716785 2 10 10-2832.5 .0-052.37 2 2 9-947863 50 2'J 30 9-664765 3 12 10-33523, 9-7.6939 3 ,5 10-283061 10-052170 3 3 9-947830 54 3C1 32 8 9-66489 4 16 ,0-335,09 9-7,7093 4 20 10-282007 10-052203 -1 4 9-94779:' 52 2H 3(1 10 9-66501. S 20 10-334988 9-717247 6 26 10-282753 10-052236 6 5 9-947764 50 311 33 12 9665133 6 24 .0-334867 9-7,740, 6 31 .0-282599 .0-052269 6 7 9-94773. 48 27 30 U 9-665254 7 28 10-334746 9-7.7555 7 36 10-282445 10-052302 7 8 9-947698 10 30 34 10 9-665375 8 32 ,0-334625 9-717709 8 4, ,0-28229. .0-052335 8 9 9-947665 44 2(; 30 18 9665496 9 36 10-334504 9-717863 9 46 10-282137 .0-052367 9 10 9-947633 42 30 35 20 9-66,6,7 10 40 .0-354383 9-71S017 10 5, .0-281983 .0-052400 10 11 9-9476CO 40 iL 30 22 9-665738 11 44 .0-334262 9-7.8,71 |ll 56 10-281829 10-052433 11 12 9-947567 38 30 30 2J 9-665S59 12 48 ,0-334,41 9-7.8325 Vi 61 .0-28.675 10-052467 1213 9-947533 30 24 30 20 9-665979 13 52 .0-334021 9-7,8479 13 67 .0-281521 .0-052500 13 14 9-947500 31 30 37 2S 9-666.60 14 56 ,0-333900 9-7,8633 14 72 .0-28.367 .0-052533 14 15 9-947467 32 23 30 30 9-66622, 15 60 .0-333779 9-7.8786 15 77 .0-281214 .0-052566 15 16 9-947434 30 30 :i« 32 9-666342 Ifi 64 ,0-333658 9-71S940 16 82 .0-281060 10-052599 16 18 9-947401 28 22 30 34 9-666462 17 68 .0-333538 9-7,9094 17 87 10-280906 10-052632 1719 9947368 20 30 :i!i 38 9-666583 18 72 ro-3334,7 9-7,9248 IS 92 .0-280752 .0-052665 I820 9-947335 24 21 30 38 9-666703 19 76 ,0-333297 9-7.9401 19 97 .0-280599 .0-052698 1921 9-947302 22 30 40 40 9-660824 20 80 21 84 =°-333.76 9-719555 20 102 21 108 10-280445 10-052731 20 22 2123 9-947269 20 20 30 9666944 ,o-333056 9-719708 .0-280292 10-052764 9-947236 n 44 9-667065 22 88 ,0-332935 9-719S62 221,3 10-280,38 10-052797 2224 9-947203 1!) 30 40 9667,85 23 92 , 0-3328, 5 9-720016 23 1.8 10-279984 10-052830 232, 9-947.70 30 4-2 48 9-667305 24 96 .0-332695 9-720169 24 ,23 .0-27983, 10-052864 24 26 9-947,36 18 30 50 9-667426 25 10, .0-332574 9-720322 25 128 .0-279678 .0-052S97 25 28 9-947.03 311 43 52 9-667546 26,05 .0-332454 9-720476 M133 10-279524 ,o-052930 2629 9-947070 17 30 54 9-667666 27 109 10-332334 9-720629 27 .38 10-27937, ,0-052963 2730 9-947037 30 *i "■' 9-6677S628 ,13 .0-332214 9-720783 28,43 10-2792,7 10-052996 28 3. 9-947004 Ifl 58 9-66-906 29 ,,7 ,0-332094 9-720936 29,48 10-279064 10-053030 2932 9-946970 2 30 4.1 30 51 9-668027 to ,21 ,0-331973 9-721089 30,54 10-2789.. 10-053063 30 33 9-946937 9 15 30 9-668147 1 4 10-331853 9-721243 ' 5 10-178757 10-053096 1 I 9-946904 4H 9-668267 2 8 10-331733 9-721396 1 «o io-»786o4 10-053129 2 2 9-946871 50 14 30 9-668386 3 12 .0-33.614 9-721549 3 15 10-17845. 10-053,63 3 3 9-946837 51 30 ■»7 9-668506 4 16 0-33.494 9-721702 ♦ 20 0-278298 10-053.96 * 4 9-946804 52 IS 30 9-668626 5 20 0-33.374 9-72.855 6 »5 .0-278145 .0-053229 6 6 9-94677. 50 30 411 9-668746 6 24 .0-33.254 9-722009 fl 30 .0-27799. 10-053262 6 7 9-946738 18 12 30 9-66S866 7 28 0-33.134 9722.62 7 36 0-27785S 10-053296 7 8 9-946704 40 .311 4!( 9-668986 8 32 0-33.0.4 9-7223.5 8 4. 0-277685 10-053329 8 9 9-94667. 44 1 1 30 9-669,0, 9 36 0-330895 9-722468 9 46 0-277532 .0-053362 9,0 9-946638 42 3(1 60 22 9-669225 10 40 11 44 0-330775 9-72262. 10 51 H 56 0-277379 10-053396 10 1 1 11 12 9-946604 40 lu 9-669345 0-33065, 9-722774 0-277226 10053429 9-94657. «1 21 9669464 0-330536 9-722927 12 61 0-277073 1213 9-946538 30 !) 30 2(i 9-6695S4 13 52 0-3304.6 9-723080 13 66 10-053496 13 14 9-946504 31 30 S2 28 9-669703 14 56 0-330297 9-723232 14 7. 0-276768 10-053529 14 .6 9-94647. 32 (! 30 30 9-669823 15 60 0-330177 9-723385 15 76 0-2766.5 10-053563 15 17 9946437 30 30 S3 32 9-669942 16 64 0-33C05S 9-723538 16 8. 0-276462 .0-053596 16 18 9-946404 2M r 30 .34 9-67006 1 il 68 0-329939 9-72369. 17 87 0-276309 .0-053629 1719 9-946371 W 30 /i4 .30 9-670,8, 18 72 0-3298,9 9-723S44 18 92 j 0-276,56 .0-053663 18 20 9-946337 21 1; 30 38 9-670300 19 76 0-329700 9-723996 19 97 1 0-276004 .0-053696 192, 9-946304 22 30 ft.i 40 9-6704,9 20 80 21 84 0-32958, 9-724.49 20 .02 21 .07 0-27585. .0-053730 20 22 2123 9-946270 ■io .1 30 1 4i 9-670538 0-329462 9-724302 0-275698 .0-053763 9-946237 ."ic Ui 9-670658 22 88 0-329342 9-724454 22 1.2 0-275546 .0-053797 2224 9-946203 10 4 30 40 9-670777 23 92 0-329223 9-724607 23 ..7 0-275393 .0-053830 23 26 9-946170 11 311 1,7 48 9-670896 24 96 0-329,04 9-724760 24 .22 0-275240 .0-053864 24 27 9-946136 12 3 30 50 9-67.0,5 25 ,00 0-328985 9-7249.2 25 ,27 0-275088 .0-053897 25 28 9-946103 10 311 .IH 52 9-67.134 2fl 104 0-328866 9-725065 26 .32 0-274935 .0-05393. 2629 9-946069 2 30 54 9-67,253 27 107 0-328747 9-7252.7 27 ,37 0-274783 .0-053964 2730 9-946036 1 30 &U 5tl 9-67 I37» 28 111 0-328628 9-725370 28.43 0-274630 10-053998 283, 9-946002 1 1 .10|5« 9-671490 29 ..5 0-32S5.0 9-725522 29 .48 0-274478 10-05403. 2932 9 945969 2 311 Trf) B2 9 67,609 30 .,9 o-3283_9, 9-725674 30 .53 0-274316 10-054065 3033 9-945935 {I ' " 1 m. Co,ine Part. 1 Srrant CotanK. Port. T.nKent Co,rv. "'• TF> -' - «. .... -| 79^ [ TABLE 08 r.OG. SINES, COSINES, iko. | I" .52"> 28- 'TT ta 1 Sine Parts 1 Cosec. Tangenl Parts Cotang. Secant Parts Cosine m «0 9-67160 .0-32839. 9-7256-/4 .0-274326 .0-05406 ^ 9-945935 ~a 30 2 9-67.72 '■' 4 .0-328272 9-725827 1" 5 ,0-274,73 ,0-054095 1" I 9-94590 5S 30 1 '1 9-67.84 2 8 .0-328.53 9-725979 9-726,3, 2 ,0 ,0-274021 .0-054.32 2 2 9-945868 51 og ■TO 6 9-67.96 3 12 .0-328035 3 ,5 .0-054,66 3 3 9-945834 54 2 8 967208 4 .6 10-3279,6 9-726284 10-2737,6 ,0-05420^ * 4 9-945800 52 J8 30 10 9-67220 5 20 .0-327797 9-726436 5 25 10-273564 10-054233 5 6 9-945767 50 30 3 1-2 9-67232 6 24 .0-327679 9-726588 6 30 .0-2734.2 10-054267 6 7 9-945733 48 57 3(1 It 9-67244C 7 28 .0-327560 9-726740 7 35 10-273260 10-054300 7 8 9-945700 4G 30 4 10 9-67255 8 32 .0-327442 9-726S92 8 40 .0-273.08 .0-054334 8 9 9-945666 44 5C 30 18 9-67267- 9 35 , 0-327323 9-727045 !) 46 10-272955 ■0-054368 9,0 9-945632 42 30 30 20 9-67279 10 39 11 43 ,0-327205 9-727197 10 5, 11 56 •0-272803 .0-054402 10 ,, n 12 9-945598 40 38 55 ~30 9-6729.4 ,0-327086 9-727349 .0-27265. .0-054435 9-945565 6 2-1 9-673032 12 47 .0-326968 9-72750, 12 6. .0-272499 .0-054469 12,3 9-94553. 30 54 30 W 9-67315^ 13 5. .0-326850 9-727653 13 66 .0-272347 .0-054503 13,5 9-945497 34 30 7 ■IS 9-673268 14 55 .0-326732 9-727805 14 7. 10-272.95 .0-054536 14 .6 9-945464 32 63 30 30 9-673387 15 59 .0-3266.3 9-727957 15 76 10-272043 10-054570 15,7 9-945430 30 30 8 32 9-673505 Ifi 63 10-326495 9-728.09 16 8. ,0-27.89. .0-054604 16,8 9-945396 25 52 30 34 9-673623 17 67 .0-326377 9-72826, 17 86 io-27.739 .0-054638 17,9 9-945362 -20 30 9 30 9-67374. 18 7. .0-326259 9-7284,2 18 9, .0-27,588 .0-054672 182019-945328 24 61 30 38 9-673859 19 75 10-326.4, 9-728564 [19 96 ,0-27.436 .0-054705 192,19-945295 22 30 10 4-2 9-6739-7 20 79 21 83 .0-326023 9-7287.6 21 ,06 .0-271284 .0-054739 2023 2124 9-94526. 20 50 9674095 .0-325905 9-728S68 .0-27. .32 .0-054773 9-945227 II 44 9-6742.3 22 87 .0-325787 9-729020 22 . . . .0-2709S0 10-054807 2225 9-945.93 10 43 30 4(1 9-674331 23 9, .0-325669 9-729.7, 23 ,.6 ,0-270829 ,0-054841 2326 9-945159 14 :«i 12 48 9-674448 24 95 .0-325552 9-729323 24 ,2, ,0-270677 .0-054875 2427 9-945.25 12 48 30 50 9-674566 25 99 .0-325434 9-729475 25 ,26 IO-2-,0525 .0-054908 25 28 9-945092 10 30 13 52 9-674684 26,03 .0-3253,6 9-729626 26 .32 10-270374 .0-054942,2629 9-945058 a •»7 30 54 9-674802 27 .06 ,0-325.98 9-729778 27 .37 .0-270222 ,0-054976 2730 9-945024 U 50 9-674919 28 .10 .0-3250S, 9-729929 98 .42 .0-270071 ,0-0550,0 283, 9-944990 4 4G 30 58 9-675037 29.. 4 10-324963 9-73008, W 147 ,0-2699,9 10-055044 2932 9-944956 2 30 15 30 B3 2 9-675.55 30 1.8 ■0-3^845 9-730233 30,52 .0-269767 ,0-055078 3034 9-944922 7 iL 9-6'7T^ 1 4 ,0-324728 9-730384 ' 5 10-2696,6 .0-055. .2 1 , 9-944SSS 16 4 9-6753901 2 8 9-675507 3 ,2 .0-3246.0 9-730535 2 10 ,0-269465 ■0-055,46 2 2 9-944854 50 44" 30 6 10-324493 9-730687 3 ,5 ,0-2693,3 .0-055.80 3 3 I9-944S20 30 17 8 9-675624 4 16 ,0-324376 9-730838 ♦ 20 .0-269.62 .0-0552,4 4 5 9*944786 43 30 10 9-675742 5 ,9 10-324258 9-730990 6 25 .0-2690.0 .0-055248 5 6 '9-944752 50 30 18 12 9-675859 6 23 ,0-324:41 9-731141 6 30 ,0-268859 .0-055282 6 7J9-9447.8 48 42 30 14 9-675976 7 27 ,0-324024 9-731292 7 35 .0-268708 .0-0553,6 7 8 19-944684 40 30 lu Ml 9-676094 8 3. ,0-323906 9-73 '444 .0-268556 .0-055350 8 99-944650 44 41 30 18 9-6762.. 9 35 ,0-323789 9-73>595 9 45 ,0-268405 .0-055384 9.09-9446.6 42 30 20 20 9-676328 10 39 11 43 m^3_672 9-73-746 10 50 11 55 ,0-268254 .0-0554.8 9-944582 40 4(1 9-676445 .0-323555 9-73.897 ,0-268.03 .0-055452 11 ,2 9-94454S 21 24 9-676562 12 47 .0-323438 9-732048 12 60 .0-267952 .0-055486 12.4 9-944514 30 30 30 20 9-676679 13 5. 10-32332. 9-732200 13 65 .0-055520 13.5 9-944480 34 30 22 23 9-676796 14 55 ,0-323204 9-732351 14 70 10-267649 ■0-055554 14.6 9-944446 32 38 30 30 9-6769.3 15 58 ,0-323087 9-732502 15 75 .0-267498! .0-055588 15.7 9-9444,2 30 30 23 32 9-677030 16 62 ,0-322970 9-732653 16 80 .0-267347 10-055623 16.8 9-944377 28 :i7 30 34 9-677.47 17 66 ,0-322853 9-732804 7 86 ,0-267.96 0-055657 17.9 ?-944343 '20 24 30 9-677264 18 70 10-322736 9-732955 8 9, .0-267045 0-05569. 3-944309 24 30 30 38 9-67738. 9 74 ,0-3226,9 9-733.06 9 96 .0-266894 0-055725 19 22 ?-944275 •22 30 25 30 40 42 9-677498 20 78 21 82 ,0-322502 9-733257 20 .0, .0-266743 0-055759 2023 2124 3-94424. 20 35^ 30 9-6776.4 ,0-322386 9-733408 21 ,06 0-266592 0-055793 -944207 26 44 9-67773. 22 86 ,0-322269 9-733558 22 I.. 0-266442 0-05582S 2225 •944,72 10 34 30 40 9-677848 23 89 ,0-322,52 9-733709 23 ,,6 0-266291 0-055S62 23 26 19-9441381 14 30 27 4S 9-677964 24 93 10-322036 9-733860 24 ,2. 0-266.40 0-055896 24 27 9-944104 1 12 33 30 50 9-67S081 25 97 .0-32.919 9-734011 25 ,26 0-265989 0-055930 25 28 S ■944070 10 30 28 52 9-678.97 26 10. .0-32.803 9-734'62 26 .3, 0-265838 0-055964 2629 9 -944036 g 32 30 54 9-67S3.4 27 10; 0-321686 9-7343'2 27 ,36 0-26568S 0-0559991 2-3. S -94400. 1. 30 29 50 9-678430 28 109 0-32.570 9-734463 28 ,4, 0-265537 0-056033 28,2 9 '941967 4 7 5 25 .0-2644S3 0-056273 5 6 9-943727 50 311 :« 12 0-679360 6 ^3 .0-320640 9-735668 6 30 .0-2643,2 0-056307 6 7 9-943693 48 27 ■i" n 9-679476 7 10-320524 9-735S18 7 35 10-2641S2 0-056342 7 8 9-943658 40 30 34 IC 9-679592 8 3' 10-320408 9-735969 8 40 10-26403. 0-056376 8 9 9-94362+ 44 2fi .10 JH 9-67970S 9 35 10-320292 9-736119 9 45 .0-26388. 0-0564,1 9.0 9-943589 4-2 30 ;to « 9-679S24 10 n 39 4^ 10-320.76 9-736269 10 50 11 55 .0-26373. 0-056445 lOl, 9-943555 38 ?.o 9-679940 10-320060 9-736420 ■0-2635S0 0-056479 11 ,3 9-94352. 31; ■J4 9-6S0056 12 46 10-319944 9-736570 12 60 ■0-263430 0-0565,4 12,4 9-943486 3li 24 .10 70 9 680172 13 5° 10-3.9828 9-736720 13 65 10-263280 0-056,48 1315 9-943452 34 30 37 it 9-6802S8 14 54 10-3.9712 9-736870 14 70 .0-263130 0-056583 14 16 9943417 32 23 .30 30 9-680403 15 58 .0-3.9597 9-73702. 15 75 .0-262979 0-056617 15,7 9-9433^3 311 30 38 3-1 9-6S0519 16 62 10-3. 94S1 9-73717' 16 8o|.o-262829| 0-056652 16 18 9-943348 ■28 22 30 Jl 9-6S0635 '7 66 .0-319365 9-737321 17 85 .0-262679 0-056686 1720 9-943314 20 30 39 30 9-680750 18 69 10-3.9250 9-737471 18 90 .0-262529 0-05672. 1821 9-943279 24 21 30 38 9-680866 19 73 10-3.9134 9-73762. 19 95 .0-262379 0-056755 19 22 9-943245 22 30 40 40 9-680982 20 77 9-737771 20 .00 .0-262229 0-056790 2023 9-9432.0 20 20 m 9-681097 21 8. '0-3>8903 9-737921 21 ,05 .0-262079 '> 0-056824 21 24 9-943176 IS 30 41 44 9-68.213 22 85 .0-3.8787 9-73807. 22 1.0 .0-26.929 . 0-056859 2225 9-943141 10 l» 30 41; 9-68.328 23 89 .0-3.8672 9-73822. 23 ..5 .0-26.779 , 0-056893 23 26 9-943107 14 30 42 48 9-68.443 24 93 .0-318557 9-738371 24 120 10-26.629 1 0-056928 24 28 9-943072 12 111 3U 50 9-68.559 25 97j.0-3.8441 9-73S521 25 .25 10-26.479 . 0-056963 2529 9-943037 10 30 43 52 9-68.674 26 .00 .0-3.8326 9-73867. 26 .30 ■o-26^329 . 0-056997 2630 9-943003 8 17 30 54 9-68.789 27 104 10-3182.1 9-73882. 27 135 10-261179 1 0057032 273. 9-942968 30 44 50 968.905 28 10-318095 9-73897. 28 140 0-057066 2832 9-942934 4 16 30 58 9-682020 29 1.2 10-3.7980 9-73912. WH5 ,0-260879 I 0-057101 2933 9-942899 2 30 4.'i 55 9-682.35 30 ..6 .0-3.7865 9-739271 30,50 10-260729 , 0-057136 30J4 9-942S64 5 30 9-6S225C 4 10-317750 9-739420 • 5 ,0-260580 ■ 0-057,70 1 I 9-942830 l(i 4 9-682365 8 .0-3.7635 9-739570 2 10 ,0-260430 1 0-057205 2 2 9-942795 14 30 G 9-682480 .1 .0-3.7520 9-739720 3 .5 .0-260280 1 0-057240 3 3 9-942760 30 47 8 9-682595 '5 .0-3.7405 9-739870 4 20 10-260130 1 0-057274 < 5 9-942726 52 13 .10 10 9-682-.0 '9 10-3.7290 9-740019 5 25 .0-25998. 0-057309 5 6 9-94269. 50 30 4K 12 9-682S25 1- 10-317175 9-740.69 6 30 .0-25983, . 0-057344 6 7 9-942656 48 12 3(1 14 9-68294C 27 10-3.7060 9-7403.9 7 35 .0-25968. 0-057379 7 S 9-94262. 40 30 4:1 10 9-6S3055 3' ■0-316945 9-740468 8 40 .0-259532 0-0574,3 8 9 9942587 44 11 30 18 9-683170 34 .0-3.6830 9-7406.8 9 45 ■0-259382 0-057448 9 10 9-942552 42 30 .-.1" ■fi 9-683284 38 42 .0-3.67.6 .0-3.660, 9-740767 10 50 11 55 ■ 0-259233 . 0-057483 10 ,, 11,3 9-9425.7 '" 10 9-6X3399 9-740917 ■0-259083 0-0575.8 9-942482 l> 9-6835.4 46 .0-3.6486 974. 066 12 60 .0-25S934 1 0-057552 12,4 9-942448 .10 9 ■iU 9-6X3628 5° 10-316372 9-7412.6 13 65 .0-258784 . 0-0575S7 13,5 9-9424.3 M 30 .'■■-' ■i8 9-683-43 54 10-316257 9-741365 14 70 ,0-258635 1 0-057622 14 ,6 9-942378 32 1! ■'" 30 96,^3858 57 ■0-3.6147 9-741514 15 75 10-258486 0-057657 15,7 9-942343 311 30 .-.3 il 9-683972 6. .0-316028 9-741664 16 80 10-255336 , 0-057692 16,9 9-942308 28 7 .111 34 9-684087 65 10-3159.3 9-741813 17 85 10-258.87 0057727 17 20 9-942273 20 30 ."i4 .30 9-684201 69 .0-3.5799 9-74.962 18 90 .0-258038 0-05776, 182. 9-942239 24 G (0 38 96843.5 73 .0-3,5685 9-742. .2 19 95 .0-257888 . 0-057796 19 22 9-942204 22 311 30 40 12 9 684410 76 .0-3.5570 9-74226. 20 .00 21 .05 10-257739 0-057831 ::: 9942169 18 5 9684 544 ■0-3.5456 9-742410 ,0-257590 0-057866 9-942.34 r.c II 9684658 -22 84 10-315342 9-742559 22 ..0 .0-25744. 0-057901 2226 9-942099 10 4 :i\ k. 9-684773 23 88 10-315227 9-742709 23 ..5 ,0-25729. 0-057936 23 27 9-942064 II 30 57 18 9-6848S7 24 92 .0-3.5.13 9-742858 24 120 ,0-257,42 0-05797, 24 28 9-942029 12 3 34) 50 968500. 25 96 10-3.4999 9-743007 25 .24 ,0-256993 0-058006 2529 9-94.994 10 30 oH rti 9-685.15 26 .00 .0-3.4885 9-743156 26 .29 10-256844 0-05804. 2630 9-94.959 H 2 20 51 9-685229 27 .03 .0-3.47-1 9-743305 27 .34 ,0-256695 0-058076 273. 9-941924 30 .in 511 9-685343 28 10-314657 9-7434 54 28 ,39 ,0-256546 0-058.., 2832 9941889 4 I .Tl 5« 9-685457 29 I . . 10-3.4543 9-743603 29,44 .0-256397 0-058.46 2934 9-941854 ■I 30 '-'U »g ■;-68 557i 30 "5 10-314429 9-743752 30_H9_ .0-256248 c^oj8.8j_ ■•'"3 5 9-94.8.9 m. 77/ '" ? Coiinc Parti Senai.t Cotanp. Farts Tangent Cnx-o. Parts Sine «!" " A^ 4' 796 TABLE G8 LOG. SINES, COSINES, &c. ] '.h 560. .>oo j 7>7 m Sine Parts Co.ec. Tangent | Parts Cotang. Secant Part. Cosine m ' " ~ 9-685,7 .0-314429 9'74375i .0-256248 .0-058,8. 9-94.8.9 "* CO 30 ■2 9-685685 1" 4 10-3.4315 9-74390, 1" 5 ,0-256099 10-058216 1 " 1 9-94.784 58 30 1 4 9-685799 2 8 .0-31420. 9-744050 2 .0 10-255950 .0-05S25. 2 2 9-94.749 50 69 30 11 9-6S5913 3 .1 10-314087 9-744,99 3 ,5 10-058286 3 4 9-94.714 54 30 2 8 9-686027 4 .5 .0-3.3973 9'744348 4 20 10-255652 .0-05832. " 5 9-94,679 52 58 30 10 9-686.4. 5 .9 .0-3,3859 9-744496 5 25 .0-255504 10-058356 6 6 9-941644 50 30 3 l-l 9-686254 6 23 10-3,3746 9-744645 6 30 ,0-255355 .0-05839, 6 7 9-941609 48 57 ao U 9-686368 7 26 ,0-3,3632 9-744794 7 35 .0-255206 ,0-058426 7 8 9-94'574 40 .30 4 10 9-686482 8 30 .0-3,35,8 9-744943 S 40 .0-255057 ,0-05846, 8 9 9-941539 44 50 30 l» 9-686595 9 34 .0-3,3405 9-745092 9 45 ,0-254908 10-058496 9 .1 9-941504 42 .-10 6 20 9-686709 10 38 11 42 ,0-3.329, 9-745240 9-745389 10 49 11 54 .0-05853. 10.2 11 .3 9 941469 40 38 55 9-686822 ,0-3,3,78 '^^, .0-05S567 9-941433 6 ■24 9-6S6936 12 46 .0-3.3064 9-745538 12 59 .0-254462 .0-058602 12.4 9-941398 36 54 30 20 9-687049 13 49 ,0-3,295, 9-745686 13 64 10-2543.4 ,0-058637 13,5 9-94,363 34 30 7 28 9-687.63 14 53 .0-3,2837 9-745835 U 69 .0-254,65 .0-05S672 14.6 9-941328 32 53 30 30 9-687276 15 57 ,0-3.2724 9-745983 15 74 .0-2540.7 ,0-058707 15 .8 994,293 30 30 8 32 9-687389 16 6. ,0-3.261. 9-746132 16 79 .0-253S6S .0-058742 16. 9 9-94.258 ■28 52 30 31 9-687503 17 64 .0-3,2497 9-74628. 17 84 ,0-2537.9 1720 9-94,222 -20 .30 !) 30 5-6876.6 18 68 .0-3.2384 9-746429 18 89 ,0-25357, .0-0588,3 I82. 9-941187 -24 51 30 38 9-687729 19 72 ,0-31227, 9-746577 19 94 ,0-253423 ,0-058848 1922 9-941.52 22 30 If 40 9-687843 9-687956 20 76 21 79 ,0-312,57 9-746726 20 99 21 ,04 10-253274 10-058883 2023 2125 9-94. ..7 20 50 .0-312044 9-746874 .0-253.26 10-058919 9-94,08, II 4^ 9-688069 22 83 10-31193. 9-747023 22 109 ,0-252977 10-05S954 2226 9-94,046 10 4!) 30 40 9-6S8.82 23 87 .0-3118.8 23 .,4 ,0-252829 ,0-058989 23 27 9-94,0,1 14 30 12 4.S 9-688295 24 9. 10-31,705 9-7473,9 24., 9 .0-2526S. 10059025 24 28 9-940975 12 4)! 3- 50 9-688408 25 95 10-31.592 9-747468 25 .24 .0-252532 10-059060 25 29 9-940940 10 30 13 5-2 9-6S852. 26 98 ,0-3. .479 9-7476.6 26 ,29 .0-252384 ,0-059095 2630 9-940905 8 47 30 5-1 9-688634 27 .02 .0-3. .366 9-747764 27.34 .0-252236 ,0-059,30 2732 9-940S70 C 3'l 14 50 9-688747 28 .06 10-311253 9-7479'3 28.39 10-252087 10-059166 2833 9-940834 4 40 30 58 9-6S8860 29 ..0 .0-3... 40 9-748061 29 144 .0-25.939 10-059201 2934 9-940799 2 30 1.3 30 57 9-688972 30 ..3 ,0-3. .028 9-748209 30 ii8 .0-25.79, 10-059237 3035 9-940763 3 45 ' 9-689085 1 4, 0-3109.5 9-748357 ' 5 10-25,643 .0059272 9-940728 30 10 4 9-689.98 2 7 0-3.0802 9-748505 2 10 .0-25,495 10-059307 2 2 9-940693 .56 44 30 C 9-6893., 3 I. o-,.o689 9-748653 3 15 .0-25.347 10-059343 3 4 9940657 54 30 17 8 9-689423 4 .5 0-310577 9-748801 4 20 0-25,199 10-059378 * 5 9 940622 52 43 30 10 9-689536 5 ,9 .0-3.0464 9-748949 5 25 0-25,05, 10-059414 5 6 9-940586 50 30 18 1-2 9-689648 6 21 0-3.0352 9-749097 6 30 0-250903 10-059449 6 7 9-94055, 48 42 30 14 9-68976. 7 26 0-3,0239 9"749245 7 34 0-250755 10059484 7 8 99405, 6 46 30 ll» 10 9-689873 8 30 0-3,0.27 9-749393 8 39 0-250607 10-059520 8 9 9-940480 44 41 30 18 9-6899S6 9 34 0-310014 9-74954' 9 44 0-250459 10-059555 9 ,, 9-940445 42 30 _ri 20 22 9-69009S 10 37 11 4. 0-309902 9-7496S9 10 49 U 54 0-2503,, 10-05959, 10 12 11.3 9-940409 40 40 9-690211 0-309789 9-749837 0-250,63 ,0-059626 9-940374 21 24 9-690323 12 45 0-309677 9-749985 12 59 0-2500.5 ,0-059662 12.4 9-940338 .30 ^i 30 20 9-690435 13 49 0-309565 9-750133 13 64 0-249867 .0-059697 13, 5 9-940303 3J 22 •2« 9-69054S 14 52 0-309452 9-75028. 14 69 0-2497,9 .0-059733 14 .7 9-940267 32 38 30 30 9-690660 15 56 0-309340 9-750428 15 74 0-249572 10-059769 15.8 9-940231 30 30 23 32 9-690772 6 60 0-309228 9-750576 16 79 0-249424 10-059S04 16 19 9-940.96 -29 37 30 34 9-690884 17 64 0-3091.6 9-750724 17 84 249276 10-059840 1720 9-94016C 26 30 24 30 9-690996 18 67 0-309004 9-750872 18 89 0-249.28 ■0-059875 I821 9-940.25 24 3G 30 38 9-69.. oS 19 71 0-308892 9-75,019 19 93 0-24S98. 10-0599., 1922 9-940089 -2-2 30 2.T ~3i7 40 42 9-691220 9-691332 20 75 21 79 0-308780 9-75,167 20 98 21 .03 0-24S833 10-059946 20 24 21 25 9-940054 9-9400,8 20 35 0-308668 9-751315 0-24S685 10-059982 2« 44 9-69.444 21 82 0-308556 9-75.462 22 108 0-24S538 io-c6co.8 2226 9-939982 16 34 30 40 9-691556 23 86 0-308444 9-75.610 23 .,3 0-248390 .0-060053 23 27 9-939947 14 30 27 4S 9-691668 24 90 0-308332 9-751757 24 .18 0-248243 10-060089 24 28 9-9399.1 12 33 30 50 969.780 25 94 9-751905 25.23 0-248095 10-060.25 2530 9939875 10 30 28 52 9-69.892 26 98 0-308108 9-752052 26 .28 0-247948 10-060160 2631 9-939840 8 32 .to 54 9-692004 27 .01 0-307996 9-752200 27 133 C-2478C0 10-060.96 2732 9-939804 6 30 2!) 50 9-692115 28.05 0-307885 9-752347 28.38 0-247653 10-060232 28 33 9939768 4 31 30 58 9-692227 29 108 0-307773 9-75H95 29 143 0-247505 10-C60267 2934 9-939733 1 .,0 3(1 sa q-692339 30 .12 0-30766. 9-751642 30 .48 0-247358 •0-060303 .3036 9-939697 30 777 ■?• Cosine Parts Secant Cotang. Parts 1 Tangent Cosec. Parts Sine m. .i(.- 4^ t"" 1 707 LOO. SINES. COSINES. &c. I" 58™ 29^ • " m Sine Pa.n 1 Cceo. Tangent | Parts Cotang. Secant Parts! Cosine ID " 9-69233 .0-30766. 9-752642 .0-247358 10-060303 [9-939697 "2 "iio : ■n 9-693676 12 44 .0-306324 9-754409 12 59 ,0-24559, .0-C60733 12,4 9-939267 36 24 311 •20 9-693787 n 43 ,0-3062.3 9-754556 13 64 10-245444 10-C60769 13,5 9-93923, 30 :i7 ■iH 9693898 14 52 9-754703 14 69 ■0-245297 .0-060805 14,7 9-939195 32 23 311 30 9-694009 ■ 5 56 ,0-30599, 9-754850 15 73 .0-245.50 .0-06084, 15 ,8 9-939>59 30 30 38 Vi 9-694120 16 5, ■0-305880 9-754997 Ifi 78 .0-245003 ,0-060877 16,, 9-939.23 -28 22 30 34 9-694231 17 63 ,0-305769 9-755'44 17 83 .0-244856 .0-0609.3 17 20 9-939087 •28 30 39 38 9-694342 18 67 ,0-305658 9-75529' 10-244709 ,0-060948 1822 9-939052 •24 21 31V 3« 9-694453119 70 ,0-305547 9-755438 19 93 10-244562 ,0-060984 1923 9-9390.6 •22 W 4U 9-694564 20 74 21 78 ■0-305436 9-755585 20 98 21 ,03 10-2444.5 10-C6,020 2024 2125 9-938980 •20 20 9-694675 .0-305325 9-75573' 10-244269 ,0-06,056 9-938944 30 41 44 9-694786,22 8, 10-3052.4 9-75587S 22 .oS ■0-244.22 ,0-06,092 2226 9-938908 Hi lU 311 40 9-694897,2.-l 85 .0-305.03 9-756025 23., 3 ■0-243975 .0-06., 28 23 28 9-938872 14 30 4.' 4.S 9695007124 89 .0-3049,3 9-756172 24 ..8 .0-243828 10-061164 24 29 9-938836 12 18 30 30 9-69511825 93 .0-304882 9-7563,9 25 .22 10-24368, .0-061200 2530 9-938800 10 30 43 51 9-6952292S 97 .0-30477. 9-756465 26 ,27 ■0-243535 ,0-06,237 '26 3, 9-938763 „ 17 30 54 9-695339127 100 .0-304661 9-756612 V .32 10243388 .0-061273 2732 9-938727 y 44 .'lO 9-6954 50[28 104 .0-304550 9-756759 28,37 10-24324, .0-06.309 28 34 9-93869. 4 lo 3(1 5K 9-69556129 107 10-304439. 9-756905 2» 142 .0-243095 .0-06,345 2935 9-938655 •2 31' 4fl 59 2 9-69567.30 ... 0-304329 9-757052 30 ,47 10-242948 10-06,38, 3036 9-9386,9 1 58 15 9-695782 • 4 .0-304218 9-757199 I 5 10-242S0. .0-06,4.7 1 I 9-9385S3 4n 4 9-695892 2 7 '0-;04>o8 9-757345 2 10 10-242655 10-06.453 2 2 9-938547 50 14 311 8 9-696003 3 1. ,0-303997 9-75749* i ,5 .0-242508 ,0-06.489 3 4 9-9385^> 54 M 47 s 9-6961.3 4 ,5 0-303887 9-757638 4 ,9 10-242362 .0-06,525 * 5 9-938475 52 30 10 9-696223,3 .8| 303777 9-757785 5 24 .0-2422.5 .0-06.56, 5 6 9-938439 31 4!1 12 9-696334 6 22 1 0-303666 9-75793' 6 29 .0-242069 ,0-06.598 6 7 9-938402 48 12 311 14 9-696444 7 26 1 0-303556 9-758078 7 34 0-24.922 ,0-061634 7 8 9-938366 30 4;j IC 9-696554! 8 29 0-303446 9-758224 8 39 0-241776 ,0-061670 8,0 9-938330 44 11 311 18 9-6966641 9 13 1 0-303336 9-758371 9 44 0-241629 10-061706 9 1, 9-938294 *2 30 -'^ 20 9-696775 10 37 0-303225 9-758517 10 49 11 54 0-24,483 ,0-06,742 10 ,2 11,3 9-938258 40 10 9-696885 11 4° 0-3031,5 9-758663 0-241337 .0-06.779 9-93S221 .)l 24 9-696995 12 44 0-303005 9-7588,0 12 58 0-241.90 .0-06.8.5 1214 9-938,85 30 9 311 20 9-697,05 13 48 0-302895 9-758956 •.3 63 0-24.044 .0-06.85. 13 ,6 9-938.49 34 30 i2 21 9-6972.5 U 5, 0-302785 9-759102 14 68 0-240898 10-06. S87 14,7 9-938.13 32 « 311 30 9-697325 15 5; 0-302675 9-759248 16 73 0-240752 .0-06.924 15 18 9-938076 30 "i3 32 9-697435 16 59 0-302565 9-759395 16 78 0-240605 .0-06.960 16,9 9-938040 ■m 7 30 ■H 9-^97545 17 62 0-302455 9-75954. 17 83 0-240459 0-06.996 1720 9938004 20 ^ll 3« 9-697654 18 66 0-302346 9-759687 18 88 0-2403.3 0-062033 I822 /937967 24 6 311 38 9-69-764 19 70 0-302256 9-759833 19 93 0-240,67 0-062069 1 1923 9-93793" 22 31! ^ 40 9-697874 20 73 21 77 0-302,26 9-759979 20 97 21 .02 0-24002, 0-062,05 2024 2125 ?-937895 •7 4« 9-6983.324 88 1 0-30,687 9-760564 24 ,,7 0-239436 0-062251 24 29 ^-937749 12 3 30 50 9-69S423 25 ,2 0-30.577 9-7607,0 25 ,22 1 0-239290 0-062287 2530 r9377'3 10 30 "iH 52 9-698532 26 95 0-30.468 9-760856 ^ 127 0-239,44 0-062324 263, 5-937676 g 2 in 51 ,■698642 27 ,9 0-30.358 9-76.002 27 13. 0-238998 0-062360 2732 5-937640 n 30 VJ 50 9-698751 28 103 0-30.249 9-76., 48 28,36 0-23885, 0-062396 28 34 5-937604 4 1 311 r,H 9-6,886. 29 106 0-30. .39 9-761293 29 ,4, 0-238707 0-062431 2935 ) 937567 30 w 60 9-698970 30 no 0-30.030 9-76.439 30 146 0-23856, 0-062409 ,3036 ?-93753' '^ Cosine Part. Secant Coteng. Part. 1 Tiingent | Cowc. 1 Parts Sine m.| 798 TARI.F, (58 LOG. SINES, COSINES, S 20 72 21 76 ,0-298849 9-764351 20 97 .0-235648 10-063201 20 24 21 26 9-936799 -20 50 9-701259 .0-29874. 9-764497 21 ,02 ,0-235503 ,0-063238 9-936762 11 41 9-701368 22 80 .0-298632 9-764643 22 ,07 10-235357 ,0-063275 ] 2227 9-936725 16 49 30 46 9-701477 23 83 ■0-298523 9-764788 23 Ml ,0-2352,2 ,0-0633,,] 23 28 9-936689 14 30 12 48 9-701585 24 87 ,0-2984.5 9-764933 24 116 10-235067 10-063348 24 29 9-936652 1-2 48 30 50 9-701694I25 91 .0-298306 9-765079 25 ,2, ic-23492. .0-063385 253, 9-9366.5 10 30 13 32 9-701802 26 94 ,0-298.98 9-765224 26 126 .0-234776 ,0-063422 2632 9-936578 tl 47 30 54 9-701911 27 98 .0-29S089 9-765369 27 ,3, ,0-23463. 10-063458 2733 9-936542 6 u 50 9-702019 28 lOl ,0-29798. 9-7655'4 28 ,36 10-234486 .0-063495 28 34 9-936505 4 4G 30 5S 9-702127 29 105 .0-297873 9-765660 29 ,4, ,0-234340 .0-063532 2935 9-936468 2 30 15 30 I 30ro9 '0-297764 9-765805 30 145 ,0-234.95 .0-063569 3037 9-93643, S9 4.' 30 9-702344 CO 29-1^6 9-765950 ' 5 ,0-234050 .0-063606 1 , 9936394 16 t 9-702452 '0-I975** 9-766095 2 10 .0-233905 .0-063643 2 2 9-936357 56 44 30 8 9-702561 .0-297439 9-766240 3 ,4 .0-233760 0-C63680 3 4 9-936320 54 30 17 8 9-702669 io-29733> 9-766385 4 ,9 10-2336.5 .0-0637,6 4 5 9-936284 5-2 43 30 10 9-702777 ,0-297223 9-766530 S 24 ,0-233470 .0-063753 5 6I9-936247 50 30 18 12 9-702885 ,0-297,15 9-766675 6 29 ,0-233325 ,0-063790 6 7 9-9362.0 48 42 M 9-702993 ,0297007 9-766820 7 34 ,0-233,80 10-063827 7 9 9-936.73 4 ■Hi 9-70364, 13 47 10-296359 9-767690 3 63 0-2323,0 .0-064049 13.6 ;-93595' 34 30 22 •29 9 703749 14 50 10-29625, 9-767834 4 68 o-2;2,66 .0-064086 14 ,7 9-9359'4 32 38 30 30 9-703856 15 34 .0-296144 9-767979 5 72 0-23202, .0-064,23 15 ,8 9935877 30 30 23 32 9-703964 6 57 0-296036 9-768,24 6 -,7 0-23,876 10-064.60 16 20 9 935840 ■28 37 30 34 9-704072 7 61 ,0-295028 9-768269 7 82 0-23,73, 0-064.97 172, 9-935805 •26 30 24 36 9-704,79 8 64 0-29582. 9-7684,4 8 87 0-23,586 0-064234 18 22 9-935766 24 36 30 38 0-7O42ii7 9 68 0-2957,3 9-768558 9 92 0-23,442 0-06427, 1924 3935729 -22 30 25 30 42 9-/04395 20 72 21 75 0-295605 9-768703 - •0 97 0-23.297 0-064308 2025 3-935692 IS 35 30 9-704502 0-295498 9-768S4S 1 1 ,0, 0-23, .52 0-064345-1 21 26 3-935655 26 44 9^7046io 22 79 0-295390 9-768992 1 ■2 106 0-23,008 0-064382 2227 3-9356'S 16 34 30 4G r7047i7 23 83 0-295283 9-769.37 1 3 ,,l 0-230S63 0-0644,9 23 28 3-935581 14 30 27 48 9-704825 24 86 0-295,75 9-76928, 1 A ,,6 0-2307,9 0-064457 2430 3-935543 12 33 50 9-704932 25 90 0-295068 9-769426 1 5 ,2. 0-230574 0-064494 253, J-935506 IV 10 28 j-l 9-705040 26 93 0-294960 9-76957, 2 16 ,26 0-230429 0-06453, 26 32 3-935469 8 32 30 M 9-705147 27 97 0-294S53 9-7697,5 1 7 ,30 0-2302S5 0-064568 2733 3-935432 « 30 29 'M 9 705254 28 ,00 0-294746 V-769860 1 8,35 0-230,40 0-064605 28 35 3-935395 4 31 30 58 9-^05362 29 ,04 0-294638 9-770004 1 9 ,40 0-229996 0-064642 2936 3-935358 2 30 30 2 9-/05469 10 ,08 0-29453, 9-770.48 3 ,45 .0-229S52J 0-064680 3037 3-93^320 30 r77 ■? Cosine Parts Seea,it Cota.ig. Parts 1 Tangent | Cosec. Parts Sine m. ' " ^'d" .-i^' A,S'" 1 ABLl' V>S LOG. SINKS, COSINES, ic. | JiS .2m Jd" " f;ine Part 1 Cosfc. Tangent Parts Cotang. 1 Secunt P-irt* Cosine •? M 9-705469 I10-294531 9-770.48 229852 0-064680 9-935320 sa :ii) •i 9705576 r 4110-294424 9-770293 1" 5 .0 229707 0-0647,7 1" . 9-935283 58 311 31 4 9-705683 2 7|io-2943i7 9'770437 2 10 .0 229563 0-064754 2 2 9-935246 5(i -j;( JO 8 9-705790 3 11:10-294210 9-770582 3 .4 .0 2294.8 0-06479, 3 4 9-935209 51 3(1 32 8 9-705898 4 14I10-294102 9-770726 4 .9 to 119174 0-064829 4 5 9-935'7. 52 2(1 30 10 9-706005 5 t8 10-293995 9-770870 5 24 10 229.30 0-064866 5 6 9-935'34 50 30 33 12 9-706112 6 21 .0-2,3888 9-77,0.5 6 29 .0 228985 0-064903 6 7 9-935097 48 27 30 U 9-706219 7 ^5 .0-293781 9-77>i59 7 34 .0 22884. j-064940 7 9 9-935060 46 3(1 34 16 9-706326 8 28 .0-29367+ 9-771303 8 38 .0 228697 0-064978 8 10 9-935022 41 2(i 30 18 9-706433 9 3^ .0-293567 9-77,448 9 43 10 228552 0-0650,5 91, 9-934985 42 30 35 20 9-706539 10 36 39 .0-293461 9-771591 10 48 " 53 .0 228408 0-065052 10,2 U ,4 9-934948 40 25 9-706646 10-293354 9-77.736 .0 228264 0-065090 9-9349.0 3fi 24 9-706753 12 43 ,0-293247 9-77'8So 12 58 .0 228,20 0-065,27 12,5 9-934873 36 24 30 20 9-706860 13 46 .0-293140 9-772024 13 62 .0 227976 0-065,6, '13,6 9-934836 34 30 37 28 9-706967 14 50 .0-293033 9-772168 14 67 .0 227831 0-065202' 14 ,7 9-934798 32 23 30 30 9-707073 15 53 10-292927 9-772311 15 72 10 7t,C88 . 0-065239115,9 9-93476. 30 30 38 32 9-707180 16 57 10-292820 9-771457 16 77 117543 0-065277 16 10 9-934713 ■28 22 30 3A 9-707287 17 61 .0-292713 9-77260. 17 82 117399 ' 0-0653,4 172, 9-934686 -26 30 3» 30 9'707393 18 64 .0-292607 9-771745 18 86 .0 227255 . 0-06535, I822 9 934649 •24 21 30 38 9-707500 19 68 .0-292500 9-771889 19 91 .0 0-065389 1924 9-9346,, -22 30 40 30 40 9--076o6 20 21 71 75 10-292394 9-773033 20 96 21 10. .0 226967 I 0-065426 o^6l^ 2025 21 26 9-934574 20 18 20 30 9-707713 10-292287 9-773'77 To" 216823 . 9-934536 41 4J 9-707S19 22 78 .0-292.81 9-77331' 22 106 .0 226679 . 0-06550. 2227 9-934499 16 19 30 4C 9-707926 23 82 .0-292074 9-773465 23 ,10 10 226535 . 0-065539 23 29 9-934461 14 30 42 48 9-708032 24 85 .0-29.968 9-773608 24 ,,5 ,0 226392 . 0-065576 2430 9-934424 12 18 30 50 9-708139 25 89 .0-29.86. 9-773751 25 120 ,0 226248 . 0-0656,4 253, 9-934386 10 30 43 52 9-708245 26 9^ .0-29.755 9-773896 26 ,25 .0 226.04 > 0-06565, 2632 9-934349 g 17 30 5-1 9-708351 27 95 10-29.649 9-774040 27 ,30 .0 225960 . 0-065689 2734 9-9343.1 6 3U 44 56 9-708458 28 99 .0-29.542 9-774184 28 ,34 ,0 2258.6 , 0-065726 28 35 9-934174 4 IC 30 58 9-708564 29 103 .0-291436 9-774318 29,39 10 225672 , 0-065764 2936 9-934236 2 30 -■*£- " 30 3 2 9-708670 30 107 .0-29.330 9-774471 30 ,44 10 225529 , 0-06580, 3037 9-934199 57 58 15 9-708776 4 .0-29.224 9-774615 ' 5 io" 225385 , 0-065839 1 , 9-934.61 46 4 9-708882 7 . 0-29. US' 9-774759 t 10 10 22524. , 0-065877 2 3 9-934.23 56 14 30 6 9-708988 .0-29.0.2 9-774901 S ,4 ,0 125098 , 0-0659,4 3 4 9934086 54 30 47 8 9-709094, '4 .0-290906 9-775046 4 ,9 10 224954 ' 0-065952 4 5 9-934048 52 13 30 10 9-709200 18 .0-290800 9-77519° 5 24 ,0 2248,0 , 0-065989 5 6 9-93401, 50 30 48 12 9-709306 2, .0-290694 9-775333 6 29 10 224667 , 0-066027 6 8 9-933973 48 12 30 14 9-709412 ^5 .0-290588 9 775477 ' 3' ,0 224523 . 0-066065 7 9 9-933935 46 30 49 16 5-709518 28 .0-290482 9-775611 8 38 ,0 114379 ' 0-066,02 r933898 44 11 30 18 9-709624 31 .0-290376 9-775764 9 43 .0 224236 . 0-066,40 9,, 9933860 42 30 60 30 20 ■ti 9-709730 35 39 .0-290270 9-775908 10 48 '» 53 10 224092 . 0-066,73 10,3 11,4 9-933811 40 38 10 9-709836 .0-290164 9-77605, 7o" 223949 . 0-0662,6 9-933784 51 U 9-709941 4Z .0-290059 9-776.95 12 57 10 223805 1 0-066253 12,5 9-933747 36 9 30 21) 9-710047 46 .0-289953 9-776338 13 62 10 223662 . 0-06619, 13,6 9-933709 34 30 »2 28 9-710153 49 .0-289847 9-776481 14 67 1 -i 2235.8 1 0-066329 14 ,8 9-933671 .12 « 30 30 9-710259 S3 .0-28974. 9-776625 15 72 10 113375 • 0-066367 15.9 9-933633 30 30 S3 32 9-710364 56 .0-289636 9-776768 16 76 .0 223232 . 0-066404 16 20 9-933596 28 7 30 :h 9-710470 60 .0-289530 9-7769.2 17 8, 10 223088 I 0-066441 172. 9-933558 2(i 30 54' 3B 9-710575 9-710681 63 .0-289425 9-777055 IS 86 .0 222945 . 0-066480 I823 9 933520 24 (> 30 38 67 .o-2893'9 9-777199 19 9. .0 22280. . 0-0665.8 1924 9-933481 22 3(1 55 40 9-710786 20 21 70 74 .0-289^,4 9-777341 20 96 21 ,00 .0 222658 . 0-066555 2025 2126 9-933445 20 s 9-710892 ,0-289.08 9-777485 7o^ 2225,5 ' 0-066593 9-913407 5C 41 9-710997 22 77 .0-289003 9-777628 22 105 10 222371 . 0-00663. 22 28 9-933369 16 4 30 46 9-711103 23 81 10-288897 9-777771 23 ,.0 .0 222228 1 0-066669 23 29 9-933331 II 30 67 48 9-7. .208 24 8; ,0-288792 9-777915 24 ..5 .0 222085 ■ 0-066707 2430 9-933193 12 3 30 SO 9-711313 25 88 .0-2S8687 9-778058 25 ..9 .0 221942 0-066745 2532 9-933155 10 3(1 58 52 9-711419 26 92 .0-2885S. 9-778101 26 ,24 ,0 22.799 0-066783 2633 9-9332,7 „ 2 30 54 9-711514 27 95 .0-288476 9-778344 27 ,29 10 22.656 0-06682. 2734 9-933,79 1; 3(1 59 50 9-711629 28 99 .0-28837. 9-778488 28 ,34 10 22.5.1 0-066859 2835 9-933141 1 1 30 5» 9-711734 29 .0-288266 9-778631 29 ,3, 10 22.369 0-066896 2937 9-933,04 2 .111 CM « 9-711839 30 106 ,0-288.6, 9-778774 30 ,43 ,0-22.226 0066934 3P38 9-93J066 l> II 777 «?• Cosine Parts Secant Cotansf. Parts Tangent Cosec. Parts Sine ;^ .W° S"- 5()"' 800 TABLE S8 LOG. SINES, COSINES, &c. j 2*' 4,,, ;310 ] ~} m Sine Paris Cosec. Tangent Parts Ctang. Secant Parts Cosine m. r 1, T 9-7ii«3S .0-288.6. 9-778774 10-22.226 10 ■C66934 9-933066 ie ~m 30 •2 9'7ii944 I" 3 .0-288056 9-778917 >" 5 .0-22.083 ,0 -066972 r' I 9-933028 58 30 1 4 9-712050 2 7 .0-287950 9-779060 2 10 10-220940 -0670,0 2 3 9-932990 50 59 30 6 9-712155 3 10 .0-287845 9-779203 3 14 ,0-220797 -067048 3 4 9-932952 54 30 2 8 9-7.2260 4 14 .0-287740 9-779346 4 ,9 .0-220654 ■067086 •* 5 9-9329,4 52 58 30 10 9^7i2365 5 17 .0-287635 9-779489 5 24 .0-2205, ' •067124 5 6 9-932876 50 30 3 1-2 9-712+69 6 2. .0-28753. 9-779632 6 29 ZlTcfJ -067,62 6 8 9-932838 48 57 30 14 9-712574 7 24 .0-287426 9'779775 7 33 .0 •067200 7 9 9^932800 46 30 4 16 9-712679 8 28 .0-287321 9-779918 8 38 ,0^220082 .0 -067238 8 .0 9-932762 44 56 30 18 9-7i27«4 9 3. 9-780061 9 43 IO-2I9939 ,0 067276 9.. 9-932724 42 5 •20 9-712S89 10 35 11 38 .0-287.11 9-780203 10 48 11 52 iO-2.9797 .0 0673.5 10.3 11 14 9-932685 40 38 55 9-712994 .0-287006 9-780346 ,0-2,9654 To 067353 9-932647 6 •24 9-713098 12 42 .0-286902 9-780489 12 57 .0-2.95,. .0 06739, 12,5 9-932609 36 54 30 26 9-713203 13 45 .0-286797 9-780632 13 62 .0-2.936S .0 067429 13.7 9-93257. 34 .30 7 ■28 9-713308 14 49 .0-2S6692 9-780775 14 67 .0-2.9225 10 067467 14 ,8 9-932533 32 53 30 30 9-7134.2 15 52 .0-286588 9-7809.7 15 7, .0-219083 .0 067505 15.9 9-932495 30 30 8 3-2 9-7i35>7 16 56 .0-286483 9-78.060 16 76 10-2.S940 10 067543 1620 9-932457 -28 52 30 34 9-7.3621 17 59 10-286379 9-78.203 17 8. 10-2. S797 .0 06758. 17 22 9-9324.9 26 3( 9 36 9-713726 18 63 .0-286274 9-78.346 18 86 .0-2.8654 10 067620 18 23 9-932380 51 30 33 9-7.383. 19 66 .0-286169 9-78. 48S 19 90 10-2.85,2 .0 067658 19 24 9-932342 ■22 30 10 42 9-7.3935 20 70 21 73 10-286065 9-78.63. -20 95 21 .00 ,0-2,8369 .0 067696 2025 9-932304 18 50 9-7.4039 .0-28596. 9-78.774 .0-218226 To" 067734 2127 9932266 44 9-7 14.44 22 77 .0-285S56 9-78. 9'6 22 ,05 .0-2,8084 067772 2228 9^932228 16 49 30 46 9-7.4248 23 80 .0-285752 9-782059 23,09 0-2.794. 0678,. 2329 9-932.89 14 311 12 4» 9-714352 24 84 .0-285648 9-78220. 24 ,,4 0-217799 ,0 067849 2430 993215. 12 48 30 50 9-7.4457 2S 87 ■0-285543 9-782344 25,. 9 0-217656 067887 2532 9-932. .3 10 30 i:t 52 9-71456. 26 9, .0-285439 9-782486 26 ,24 0-2I75I4 ,0 067925 2633 9-932075 8 47 30 54 9-7.4665 27 94 10-285335 9-782629 27.29 0-217371 ,0 067964 2734 9-932036 6 30 14 56 9-7.4769 28 98 .0-28523. 9-782771 28 .33 0-2.7229 068002 2836 9-931998 4 46 30 08 9-7.4873 29.0. .0-285.27 9-7829.4 29 ,38 0-2.7086 ,0 06S040 1 29 37 9-93 '960 2 30 ■ — s ■i 9-7i497S!:!0 .051.0-285022 9-783056 30 ,43 0-2.6944 068079 3038 9-93.92. S5 53 45 9-715082 I 3.0-2849.8 9-783.99 ' 5 o-2,6So. 7o^ 068,17 9-93.883 16 9-7.5'86 2 7 .0-2848.4 9-78334. 2 9 0-2.6659 10 068,55 2 3 9-931845 56 44 30 6 9-715290 3 10 .0-2847.0 9-783483 3 .4 0-2.65,7 ,0 068.94 3 4 CC93.S06 54 30 17 8 9-7.5394 4 14 10-2S+606 9-783626 4 .9 0-2.6374 ,0 06S232 * 5 9-93.768 52 43 30 10 9-7>549« 5 .7 .0-284502 9-783768 5 24 0-2,6232 ,0 068270 5 6 5-93.730 50 30 18 12 9-7.5602 6 2. .0-284398 9-7839.0 6 28 0-216090 ,0 068309 6 8 9-93.69, 48 42 30 14 9-7.5705 7 24 .0-284295 9-784053 7 35 0-215947 .0 068347 7 9 9-93.653 46 30 19 18 9-7 • 5809 8 28 .0-284.9. 9-784195 8 38 0-2,5805 .0 068386 810 9-93,6,4 44 41 30 18 9-7i59n 9 31 .0-284087 9-7S4337 9 43 0-2.5663 .0 068424 9 .2 9-93,576 42 30 2 •028.915 9-7S73.9 10-212681 0-069234 9-9307t6 541 M 1 JO •i 9-7i8i«8 1 3 !0-2Xl8!2 9-78746. I" 5 IO-2.J539 0-069273 I'l 9-930727 5B 311 31 t 9-7i8z9i 2 7 .o-28.:c9 9-787603 2 9 10-212397 0-069312 9 3 y-930688 5<> •2!) 311 a 9-718394 3 10 10-281606 9--'<7745 3 .4 .0-212255 0069350 3 4 9 930650 54 30 .S2 8 9-718+97 4 14 10-281503 9-787886 4 19 10-212.14 0-0693S9 ♦ 5 9-93061. 52 2« 31) 10 9-718600 5 17 .0-281400 9-788028 6 24 10-211972 0-069428 5 6 9-930572 50 30 :« It 9-718703 6 20 10281297 9-788170 6 2S .0-2.1830 0069467 6 8 9930533 48 •-•7 30 14 9-718806 7 ^4 10-281194 9-7883.1 7 35 10-2116S9 0-069506 7 9 9-930495 4(1 3U 34 Iti 9-718909 8 ^7 10-281091 9-788453 8 38 .0-211547 0-069544 8 10 9-9304..6 44 26- 30 18 9-719011 9 3' 10-280989 9-788595 9 42 10211405 0-069583 9.2 9-930417 42 30 3S 311 40 9-7i9"4 10 11 34 38 10280886 9-788736 10 47 11 52 10-2.1264 0-069622 1013 11 14 9-930378 38 26 9-7'9i'7 .0-280783 9-788S78 0-069661 9-930339 36 •w 9-71932C 12 4' .0-280680 9-7890.9 12 57 10-2.0981 0-069700 12i6 9-930300 30 24 30 ■20 9-719422 13 44 .0-280578 9-78916. 13 61 .0-2.0839 0-069739 13.7 9-930262 34 30 37 •a 9-719515 14 48 10-280475 9-789302 u 66 10-21069S 0-069777 14 iS 9-930223 32 23 3U 30 9-719627 15 5- 10-280372 9-789444 15 71 .0-2.0556 0-069816 16 20 9-930184 30 30 38 32 9-719730 16 55 .0-280270 9-789585 16 75 .0-2104.5 0069855 I621 9-930145 •28 22 30 M 9-719833 i: 58 10-280167 9-789727 17 80 .0-2.0273 0-069894 17 22 9-930106 20 3.1 :m) 3U 9-7'9935 18 62 .0-280065 9-789S68 18 85 .0-2.0132 0-069933 I823 9-930067 24 21 30 38 9-720038 19 65 .0-279962 9-790009 19 89 .0-209991 ; 0-069972 1925 9-930028 -22 >ii 40 3U 40 42 9-720140 20 21 en .0-279860 9-790151 20 94 21 99 .0-209849 . 0-07001 1 20 26 2127 9-9299S9 20 2C 9-720242 .0-279758 9-790292 .0-209708 1 0-070050 9929950 41 +1 9-710345 22 75 .0-279655 9-790434 22 104 .0-209566 . 0-0700S9 2229 9-929911 10 10 30 40 9-720447 23 79 10-279553 9-790575 23 J08 .0-209425 . 0-070.28 2330 9-929S72 14 42 48 9-720549 24 10-279451 9-7907.6 24 ,13 .0-209284 . 0-070167 2431 9-929833 12 la 30 50 9-720652 25 86 .0-279348 9-790857 35 118 .c-209.43 1 0-070206 2532 9-929794 10 30 43 52 9-720754 26 89 .0-279246 9-790999 26 122 .0-209001 . 0-070245 2634 9-919755 8 17 30 54 9-720856 27 91 10-279.44 9-791140 S7 127 10-208860 I 0-070284 2735 9929716 44 50 9-720958 28 96 .0-279042 9-791281 28.32 10-2087,9 ' 0-070323 2836 9-929677 4 le 30 58 9-721060 29 99 .0-278940 9-791422 W>37 10-208578 . 0070362 2938 9-929638 2 311 45 30 7 9-72.162 30 ■°3 .0-278838 9-79.563 30 141 10-208437 I 0-070401 1 JO39 9-929599 58 15 30 9-721264 I 3 .0-278736 9-79.705 • 5 10-208295 1 0-070440 > ■ 9-929560 4(; 4 9-721366 3 7 .0-278634 9-79.846 » 9 10-208154 . 0-070479 2 3 9-92952. 50 u 30 9-721468 3 .0-278532 9-79.987 s 14 10-2080.3 1 0-070510 3 4 9-929482 .M 47 8 9-721570 4 >4 .0-278430 9-792.28 * .9 .0-207872 . 0-07055^ * 5 9-929442 52 i:{ 30 10 9-721672 S 17 .0-278328 9-792269 6 23 .0-20773. ' 0-070597 5 6 9-929403 50 3U 48 12 9-7i'774 6 20 10-278226 9-7924.0 6 28 .0-207590 . 0-070636 6 8 9-929364 4« 12 30 M 9-721876 7 J4 .0-278.24 9-79255. 7 33 .0-207449 ' 0-070675 7 9 9-919315 46 30 4U in 9-721978 8 ^7 .0-278022 9792692 8 38 .0-20730S I 0-070714 8 10 9-919186 14 11 30 18 9-722080 9 30 .0-277920 9-792S33 9 42 .0-207167 1 0-070754 9 12 9-929247 42 30 SO 30 22 9-722181 lU 11 34 37 .0-277819 9-792974 10 4- 10-207026 1 0-070793 10.3 9-929207 z 10 30 9-72228; 0-2777.7 9-793. .5 11 52 io-2c«885 ' 0-070832 II 14 9-929168 SI 24 9-7«385 12 4" 0-277615 9-793256 12 56 10-206744 . 0-07087. 12 16 9-929129 30 30 26 9-722487 13 44 .0-277513 9-793397 13 61 .0-206603 . 0-070910 13.7 9-929090 34 30 62 28 9-7"588 14 48 0-2774.2 9-793538 14 66 10-206462 1 0-070950 14 18 9-929050 32 8 30 30 9-722690 15 5' 0-2773.0 9-793679 15 70 10-206321 1 0-070989 15 20 9-92901. 30 30 S3 32 9-722791 16 55 0-277209 9-793819 16 75 10-20618. . 0-071028 I62. 9-918971 28 7 30 34 9-722893 17 58 .0-277.07 9-793960 17 80 10-206040 I 0-07.068 1722 9928933 20 S4 M 9722994 18 61 .0-277006 9-794.0. 18 84 .0-205899 . 0-07IIC7 18 24 9-918893 24 c 30 38 9-723096I19 54 0-276904 9-794242 19 89 .0-205758 . 0-07.146 1925 9-918854 •n 3(1 ftf. 42 9723197 20 21 68 7' .0276803 9-794383 30 94 21 98 .o-2o;6.7 1 0-07. .85 20 26 2128 9-928S15 20 3 9-723299 10-276701 9-794513 10-205477 . 0-071225 9-918775 50 44 9-723400 22 75 10-276600 9-794664 22,03 .0-205336 . 0-07.264 2229 9-918736 10 4 .10 4(i 9-723501 23 78 .0-276499 9-794805 23 108 .0205. 95 1 0-071304 2330 9-928696 14 Ml ft7 is 9-723603 24 82 .0-276397 9-794946 24 1.3 10-205054 1 0-07.343 343, 9928657 12 3 M 50 9-723704 2S 85 10276296 9-795086 25 1,7 .0-204914 . 0-07.382 2533 9-928618 10 30 AS 9-723805I26 89 10-276195 9-795117 26 .22 .0-204773 0-071422 2634 9-918578 8 2 HI 54 9-7239C6127 9^ .0276094 9-795367 27 .27 .0-204633 0-071461 2735 9-918539 8 9-7240071-28 95 10-275993 9-795508 28 ,3, .0-204492 0-07.501 28 37 9928499 4 1 ■' » 1 't 9-724109,29 98 10-275891 9-795649 29 .36 10-204351 0-071540 2938 9-928460 ■2 .'111 HO ' 8 9-72421030 102 .0-275790 9-795789 •■"> '4. .0-2042.1 0-071580 3039I9-928420 n (1 ' "!•?• Cnswr. 1 Parts | Secant Cotanp. 1 Part... [ Tungrnt Cosec. 1 PartB | Sine S^,^i 68' .;)" 62"' 1 802 TABLE 68 LOG. SINES, COSINES, arc. 2" S™ 32° / // Sine P.rti Cose*. Tangent Parts 1 Cotang. Secant Parts Cosine m "o~ 9-72421 10-275790 9-795789 .0-2042.. .C-C7.580 9-928420 S2 30 t 97243 ■ '" 3 .0-275689 9-795930 1" 5 .0-204070 .0-071619 r'119-928381 58 30 1 4 9-72441 a 7 .0-275588 9-796070 2 9 10-203930 10-071658 2 3 9-928342 56 sa 30 8 9"7i45' a 10 .0-275487 9-79621. 3 14 10-203789 10-071698 3 4 9-928302 54 30 2 8 9' 7246 M * 13 10-275386 9-796351 4 19 .0-203649 .0-071737 ■» 5 9-928263 52 5« 3« 10 9-72471 6 .7 10-275285 9-79649' 5 13 .0-203508 .0-071777 5 7 9-928223 50 3(1 3 12 9-7248if 6 20 .0-275.84 9-796632 6 18 ,0-203368 10-07.8.7 6 8 9-92S.83 48 57 30 14 9-724917 7 23 10-275083 9-796773 7 33 .0-203227 10-07.856 7 9 9-928.44 48 .30 4 l« 9-725017 8 27 .0-274983 9796913 8 37 10-203087 .0-07.896 8.. 9-928.04 +1 SB 30 1« 9-725118 9 30 .0-274882 9-797053 9 42 .0-202947 10-07.935 9,2 9-928065 4-2 30 i 30 22 9-725219 10 34 11 3, 10-27478. 9-797194 10 47 11 5. .0-202806 .0-07.975 10,1 U15 9-92S025 38 30 9-72532r 10-274680 9-797334 .0-202666 10-0720.5 9-927986 •i 24 9725420 12 40 10-274580 9-797475 12 36 ,0-202526 .0-072054 12.6 9-91-/946 36 64 *o 20 9-725521 13 44 10-274479 9-7976.5 13 6. ,0-202385 .0-072094 13 17 9-927906 34 30 7 28 9-725622 14 47 10-274378 9-797755 14 65 .0-202245 .0-072133 14.8 9-917867 32 53 30 30 9-725722115 50 10-274278 9-797895 15 70 .0-202.05 .0-072.73 15 10 9-927827 30 30 q 32 9-725823I16 54 10-274177 9-798036 16 75 .0-20.964 .0-0722.3 I61. 9-917787 28 52 30 34 9-725923 '7 57 10-274076 9-798176 17 79 10-20.824 .0-072252 17 22 9-917748 20 30 9 30 9-726024 18 61 10-273976 9-798316 18 84 .0-201684 .0-072292 18 24 9-917708 •i4 51 30 38 9-726124 19 64 .0-273875 9-798456 19 89 10-201544 .0-072332 1925 9-927668 22 30 10 30 40 42 9-726225 20 67 21 70 .0-273775 9-798596 20 93 21 98 .0-20.404 .0-07237. 20 26 9-927629 •20 50 9-726325 .0-273675 9-798737 .0-20.264 10-0724.. 21 28 9-927589 11 44 9-726426 22 74 10-273574 9-798877 22 103 10-201.23 .0-07245. 2229 9-917549 18 49 30 48 9-/26526 23 77 10-273474 9-799017 23 .07 .0-200983 .0-072491 2330 9-927509 14 30 12 48 9-726626 24 80 .0-273374 9-799'57 24 1,2 .0-200843 10-072530 2432 9-927470 12 48 30 10 9-726727 M 84 .0-273273 9-799297 25 ,,7 .0-200703 .0-072570 2533 9-917430 30 13 52 9-726827 26 87 10-273173 9-799437 26 .21 .0-200563 10-0726.0 2634 9-927390 e 47 30 54 9-726927 27 90 10-273073 9-799577 27 .26 10-200423 .0-072650 2736 9-927350 6 30 14 58 9-727027 28 94 10-272973 9-799717 28.31 10-200283 10-072690 2837 9-9273.0 4 46 30 58 9-727128 29 97 10-272872 9-799857 29136 10-200143 .0-072730 29 38 9-927170 2 30 \r, 9 2 9-727228 30 101 10-172772 9-799997 SO .+0 .0-100003 .0-072769 30 40 9-92723. 51 58 4ft 30 9-727328 I 3 .0-272672 9-800.37 I 5 ,0,99863 .0-072809 1 1 9-927,9. 16 4 9-727428 S 7 .0-272572 9-800177 » 9 'o- .99723 10-072849 S 3 9-92715, 56 44 30 8 9-727528 3 10 10-272471 9-800417 3 .4 •0--99583 .0-072889 3 4 9-927,,, 54 30 17 8 9-717628 ♦ -3 10-272371 9-800557 •♦ '9 .0-199443 .0-072929 * 5 9-92707, 52 43 30 10 9-727728 5 ,7 10-172271 9-800697 5 13 ,o-,993o3 .0072969 5 7 9-92703. 50 30 18 12 9-727828 6 20 10-272172 9-800836 » 28 .0-199.64 .0-073009 6 8 9-92699. 48 42 30 14 9-727928 7 23 .0-272072 9-S00976 7 33 10-199024 .0-073049 7 9 9-92695. 40 30 19 10 9-728027 6 27 10-271972 9-801116 8 37 ,o-,98884 .0-073089 811 9-9269.. 44 41 30 IB 9-728127 9 30 .0-27.873 9-801256 9 42 .0-198744 .0-073,29 9 12 9-92687. 42 30 20 20 9-728227 10 33 .0-27.773 9-80.396 10 46 .0-. 98604 .0-073.69 10.3 992683. 40 40 30 22 9-7283^7 " 37 .0-271673 9-80.535 11 5. .0-. 98465 .0-073209 11.5 9-92679. 38 30 21 24 9-728427 12 40 10-271573 9-80.675 12 5-6 .0-. 98325 .0-073249 12.6 9-926751 36 39 30 28 9-728526 13 43 10-271474 9-80.815 13 60 .0-.98.85 10-073289 13 17 9-9267.. 34 30 22 28 9-728626 14 47 10-27.374 9-801955 14 65 .0-.98045 .0-073329 14,9 9-92667. 32 3« 30 30 9-728726 15 50 10-271274 9-802094 15 70 .0-197906 .0-073369 15 20 9-92663, 30 30 23 32 9-728825 6 53 iD-271175 9-802234 IB 74 .0-. 97766 .0-073409 I621 9-92659, 28 37 30 34 9-72S925 7 56 .0-271075 9-802374 17 79 .o-,97626 .0-073449 1723 9-92655. '^6 24 38 9-729024 8 59 .0-2-0976 9-S02513 18 84 .0-. 97487 .0-073489 I824 9-926511 •24 3(i 30 38 9-729124 9 63 .0-270876 9-802653 19 88 10-197347 10-073529 1925 9-92647. 22 30 2{ 4a 9-729223 20 66 21 70 .0-270777 9-802792 20 93 21 98 ■ 0-. 97208 .0-073569 2027 21 28 9-92643. •20 30 30 9-729323 .0-270677 9-802932 .0-. 97068 ,0-073609 9-92639. 26 44 9-729422 22 73 .0-270578 9-803072 32 .02 .0-196928 ,0-073649 2229 9-92635. 16 34 30 40 9-729522 23 76 10-270478 9-803211 23 .07 IO-. 96789 0-073689 233, 9-9263.. 14 30 27 48 9-719621 24 80 .0-270379 9-803351 24 .12 10-196649 0-073730 2432 5-916270 12 33 30 JO 9-729720 25 83 10-270280 9-803490 25 1.6 10-. 965.0 0-073770 «33 9-926230 10 28 32 9-729820 26 86 10-270180 9-803630 26 .21 .0-. 96370 0-0738,0 2635 -926.90 g 32 30 ^4 9-729919 27 90 0-270081 9-8037691 27 126 .0-.9623, 0073850 2736 -926.50 (t 39 38 9-730018 ? 93 0-269982 9-803909 28 ,30 10-196091 0-073890 2838 -926.. 4 31 30 58 9-730117 29 96 0-269883 9-804048 29 .35 0-195952 0-073931 2939 -926069 2 30 30 LO 9-730217 iO 100 0-269784 9-804187 )0 .39 o-,958i3 0-07397. 3U40 -926029 30 '" ?: Cosme Parts Secant Cotang. Part« Tangent Cosec. Paxts Sine ?l^ 57° 3" 50'" 1 TA15LE C8 803 LOU. SINKS, COSINES, &c. S" 10'- 3-2° '" «?■ Sine jPwtsI Cosfc. Tangent Part. Cotang. Secant Parts 1 Cosine m. 1 ' ' W~ 9-73ci>- l.c-26,78 9-Sc4,S ,0 ,958, .0-07397 19-926029 son«r JO 1 9-73o3'« 1" ic-2696«4 9-80432 1" ,o-,9;67 ■ 0-0740, 9-925989 r,n i 31 4 975=4M « 7 .0-269585 9-804466 2 5 ,0-, 955341, 0-07405 2 9-925949 ;.i 2!» .10 6 9'7305'4 S re .0-169486 9-804605 3 ,4 .0-, 953951,007409 1 3 . 9-925908 S4 .1, 32 8 9-730613 ♦'1 .0-26938 9-804745 4 19 ,o-,9525 1 10-0741 31 4 9 9:5868 i-i •J« 30 10 9-73°7-i 5l« .026928* 9-804884 5 23 .o-,95,,6|.o-o74.7i| 5 " 9-925828 so 3. S3 » 9-7508. 1 «io ,0-269,85 9-805013 6 18 .0-.9497- ,0-0742, 6 8 99:5788 18 27 30 14 97309.0 7:3 10-269090 9-805,63 7 3: .o->9483- 10-074:5 7 r 9-9:5747 4(i 31 34 1« 973.009 826 .0-26899 9-805302 8 37 ,o-,9469i 10-07429 8 1 9-925707 44 -Mi 30 .8 9-73..0* 930 .o-^h8S9i 9-805441 « 4: ,0-, 94555 10-07433 9.2 9-9:5667 41 M no ■m 9-73. X06 103; II 36 I£2^Z94 9-805580 .« +6 '11 5, ,o-, 94420 .0-0743-4 lU 13 11 15 9-9256:6 40 26^ 38 ' 3U Ji 9-73.305 ,0-268695 9-8057,9 ,o-,9428 10-0744,4 9-9:5586 3C " 973.404 1240 ,0-2685,6 9-805859 [12 56 ,0-194,41 10-074455 12 16 9-9:5545 3« 24 30 20 9-73 '503 1343 ,0-268497 9-80599S 13 60 ,o-, 94001 ,0-074495 13 ,8 9-9:5505 U M 3? IS 9-73.602 1446 ,0-268398 9806,37 14 65 .0-, 93863 10-074535 14,9 1-9:5465 J-2 2:1 30 30 9-73.700 1549 ,o-:6830o 9-S06276 15 70 ■0-, 937:4 ,0-074576 15 20 99154:4 30 31 Sfl •2 9-73.799 16 53 ,0-26820, 9-8064,5 16 74 ,o-, 93585 10-0746,6 16 21 9-925384 28 22 30 M 9-73.897 1756 .0-268,02 9-806554 17 79 IO-, 93446 ,0-074657 1723 9-9:5343 26 30 39 w 9'73'99* 18 59 ,0-268004 9-806693 18 83 .0-, 93307 10-074697 18 24 9-9:5303 24 21 JO w 9-732095 1963 10-267905 9-806S32 ■ 9 88 ,o-,93,68 .0-074738 1926 9-925261 22 M 40 9-'3i.93 20 66 ,0-267807 9-80697, 20 93 .0^93019 .0-074778 2<,17 99:5::: 20 2« 30 i ■I 9-73"9» 21 69 .0-267708 9-8071,0 21 97 ,0-, 92890 ,0-0748,9 21 18 9-9:5,8, S 30 11 4 9-732390 22 73 ,0-2676,0 9-807249 22 ,02 .0-, 92751 ,0-074859 2230 9-915,4, (1 I!) 30 < n 9-7 3H.''9 2376 9-807388 -23 ,07 .0-, 926,1 10-074900 233, 9-92^.00 4 Ml 42 * H 9-73:587 2479 ,02674, 3 9-807527 94 ,,, .0-, 92473 .0-074940 2432 9-925-60 •2 IH 30 5 9-73:685 25 82 ,0-2673,5 9807666 25 ,,6 .0-. 9:334 .0-07498. 2534 9-925019 M 43 i 2 9-73:784 W%f, .o-2672,6 9-807805 2fi .2, ,o-,92,95 10-075021 2fi35 9-924979 8 17 30 J 4 9-73:881 2789 .0-267, ,8 9-807944 27.25 io-,92056 10-075062 2736 9-924938 ,l| 30 44 Is (1 9-732980 M91 ,0-267010 9-808083 28.30 io-,9,9,7 ,0-075,03 283? 9-9:4897 i W 30 |.. •- 9-733079 W95 ,0-266921 9-808222 ».3+ 10-19,778 10-075,43 2939 99:48 57 2 30 30 1 9-733.7- 3099 ,0-266813 9-80836, 30,39 io-,9,639 10-075 1S4 30 4o|'9 924816 4 ^ J5_ 8 ^«> » 9-733:75 ' 3 .0-266725 9-808^99 1 5 'C-.9.50. .0-075214 1 , 9-914776 J 4«l 9-733373 2 6 10-266627 9-808^38 t 9|io-,9,362 10-075265 2 3 9-9*4735 5 53 SI 9-7 34744 j 1652 0-265256 9-8,0580 6 74 0-, 89420 0-075836 16 22 J-924,64 -1 7 30 34 9-73484: '755 0-265.58 9-8,o-,S 7 79 o-,892S: 0-075876 1723 j-924,24 u M S4 * 9-734939 1 18 59 o-:65o6. 9-8,0857 8 83 0-, 89,43 0-0759,7 18 14 ^■9:4083 -l 6 JO .w 9-735037 I 96: c-264963 9-8,0995 9 88 0^,89005 0075958 19i6 )-9:4042 ■« 30 gfi 40 30 «/ 9-735.35 , J065 31 68 0-164S65 9-8.,>34' •0 92 _ 0-188866 0-075999 2027 2129 ■92AC01 If 6 .10 9-735:3: 1 0-164768 9-8. .272 2 o-,8872X 0-076040 •9:39"^ le M 14 9-735330 J2 72 0-164670 9-8, ,4,0 ■i 2 ,02 ,88590 0-07608, 2230 •9:39.9 10 4 10 4(i 9-735427 »75 0-164573 9-8. .549 = 3 ,06 0-, 88451 0-076,22 233, •9:3878 14 3" 67 *. 9'7355»5 M78 . 0-264475 9-8,1687 -i 4 , , , , 0,883,3 0-076,63 2433 •9:3837 vt :t 30 JO 9-7356:2 IS 82 . 0-264378 9-81,826 1 ^ ,,6 , o-,S8,74 0-076204 2534, 9:3796 1. .111 6n M 9-7357.9 26 85 . 0-26428, 9-8,1964 2 6,10 , 0-, 88036 0-076:45 2635 t, -9:3755 8 -i .W 4 9-7358.7 !27 88!. 0:64, 83 9-8,1,02 2 7 ,15 ,0-, 87898 0-076:86 "37 9 -9:37 4 r ?n fi» V, 9-7359'4l»89.|.o-:64o86 9-8,224, 2 «.:9.o-, 87759 0-076327 2«38|9 •9-3671 4 1 M SI 9-73601. ; 29 95 '.0-163989 0-8,2379 2 9 ,34l.o-.876i, > 0-0763681 29 39 |9-9236, 2 ; 30 RO 12 9-736109 |30 98|io-263«9i 9X12517 (30 ,39 10, 8748311 0-0764091304, 9-923,9. n n T77^ Co«inc iPart«] Srcant Cotang. j Part., j Tangent ) Cosec. 1 Parte Sine m .■^ 57' ;)" ^8"' I 8U4 LOG. SINES, COSINES, cvc. Oh |o.n 330 ' " m Sine Parts Cosec. Tangent Parts Cotang. Secant | Parts! Cosine m (id "oT 9-736109 10-263891 9-812517 ,0-187483 10-076409 9-92359. ^8 30 2 9-736206 ! '"3 10-263794 9-812656 1" 5 .0-187344 10-076450 I" 1 9-923550 59 30 1 4 9-736303 2 6 10-263697 9 812794 ,0-187206 ,0-07649, 2 3 9-923509 60 .'-)!• 30 9-736400 3 10 10-263600 9-8,2932 10-187068 10-076532 3 4 9-923468 54 30 2 s 9-736498 413 10-263501 9-813070 ,o-.8693c 10-076573 4 5 9-923427 52 58 .10 10 9-736595 S 16 10-263405 9-813209 10-186791 10-076614 5 7 9-923386 50 30 3 12 9-736692 019 10-263308 9-813347 ,0-186653 .0-076655 6 8 9-9^3345 48 t7 30 IJ 9-736789 7^3 ■0-2632.1 9-8,3485 7 32 ,0,865,5 ,0-076696 7 ,0 9-923304 41) 30 4 10 9-736886 826 .0-263,14 9-8,3623 8 37 10-186377 .0-076737 8 ,1 9-923263 44 5(i 30 18 9-736983 929 10-2630.7 9-813761 9 41 10-076778 9 12 9-923222 42 30 5 '30 22 9-737080 1032 11 36 10-262920 9-8,3899 10 46 11 51 ,0-186,01 .0-0768,5 10.4 11,5 9-923.81 ;"' 5.1 9-737'77 .0-262S23 9-814037 10-185963 10-076861 9-923.39 fi ■u 9-737274 1-2 39 10-262726 9-8,4,76 12 55 10-185824 ,0-076902 1217 9-923098 30 54 30 26 9-737371 1342 10-262629 9-814314 13 60 ,0-, 85686 .0-076943 13 18 9-923057 34 30 7 2S 9'737467 1445 10-262533 9-814452 14 64 ,0-185548 10-076984 14,9 9-923016 32 5a 30 30 9-737564 1548 10-262436 9-814590 15 69 ,0-1854.0 10-077025 152, 9-92297= 10 30 8 32 9-737661 1651 10-262339 9-814728 16 74 10-185272 10-077067 1622 9-92293; 28 S2 30 M 9-737758 1755 10-262242 9-814866 17 78 10-185134 10-077108 1723 9-922892 20 30 9 36 9-737855 I858 10-262145 9-815004 18 83 .0-184996 10-077149 I825 9-922851 24 51 30 38 9-73795' 1961 10-262049 9-815142 19 87 10-184858 10-077190 1926 9-9"8io 22 30 in 30 40 42 9-738048 20 64 2168 10-261952 9-815280 20 92 21 97 0-184720 10-077232 20 27 2129 9-922768 20 50 9-738145 10-261S55 9-815417 0-184583 10-077273 9-922727 11 44 9-738241 2271 10-261759 9-815555 22 ,01 0-184445 10-0773,4 2230 9-922686 IG 4» 30 40 9-738338 23 74 10-261662 9-815693 23 ,06 0-184307 10-077356 2332 9-922644 14 30 12 48 9-738434 2477 10-261566 9-81583. 24 1,0 0-184.69 10-077397 2433 9-922603 12 •)« 30 30 9-738531 -2081 10-261469 9-815969 25 ,15 c-184031 .0-077438 2534 9 922562 10 30 13 52 9-738627 2684 10-261373 9-816107 2d .20 0-183893 .0-077480 2636 9-922520 .s 41 30 5J 9-7387241278-/] 10-261276 9-816245 37 .24 0-183755 ,0-07752, 2737 9-922479 30 H 51) 9-738820 2890 10-261180 9-8.6382 28 .«9 .0-1836,8 10-077562 2838 9-922438 J ■10 30 53 9-7389'7 2994 0-261083 9-8.6520 9-8.6658 » '?3 .0 .33480 10-077604 2940 9-922396 2 30 r5 13 9-739013 0-260987 30,38 0-. 83342 10-077645 304. 9-922355 47 45 9-739109 > 3 10-26089, 9-8.6796 1 S 0-183204 10-077687 1 1 9-9223.3 IB 4 9-739206 2 6 0-260794 9-8,6933 2 9 0-183067 10-077728 2 3 9-922272 r.ii 44 30 <1 9-739302 3 10 0-260698 9-8.7071 3 14 0-. 82929 10-077769 3 4 9-922231 ''t 30 17 8 9-739398 413 0-260602 9-8.7209 4 .8 0-182791 10-077811 4 6 9-9221S9 52 a 30 10 9-739494 5 16 0-260506 9-817347 5 13 0-.S2653 10-077852 5 7 9-922148 50 30 13 12 9-73959° 6,9 0-260410 9-8,7484 « 27 0-1S2516 10-077894 fi 8 9-922106 18 42 JO 14 9-7396S7 7 22 0-260313 9-817622 7 32 0-182378 .0-077935 7 .0 9-922065 Jli 311 19 16 9-739783 826 0-260217 9-817759 8 37 0-182241 10-077977 8 ., 9-922023 44 41 30 IS 9-739879 929 0-260,2, 9-817897 9 4, 0-182103 10-078018 9,3 9-921982 42 ■M 20 30 20 9-739975. 9-740071 1032 1135 0-260025 9-818035 10 46 11 50 0-18,965 10-078060 10,4 11 15 9-921940 9-921S99 10 4(1 0-259929 9-8.8,72 0-181828 10-078101 21 24 9-740167 1238 0-259833 9-818310 12 55 0-18,690 10-078143 1217 9-921857 30 .-iy 30 2(i 9-740263 1342 0-259-37 9-818447 13 60 0-181553 10-078,85 13 18 9-921815 34 30 ■i-2 2H 9-740359 1445 _-25964. 9-818585 14 64 0-18, 41c 10-078226 14 19 9-921774 32 ;iii 30 Jll 9-740455 1548 0-259545 9-81S722 15 69 0-181278 .0-078268 1521 9-92,732 30 ..IP 'a .12 9-740550 1651 0-259450 9-818860 16 73 0-181,40 .0-078309 16 22 9-921691 28 ;'•/ 30 .11 9-740646 17 54 0-259354 9-818997 17 78 0-181003 .0-078351 1724 9-921649 20 30 04 .Hi 9-740742 IS57 0-259258 9-819135 s 82 0-1S0865 10-07S393 1825 9-92,607 -24 :in 30 3M 9-740838 19 6, 0-259.62 9-819272 9 87 0-180728 0-078434 1926 9-921566 22 ■'" 25 "30" 40 9-740934 2064I 0259066 9819410 20 92 21 96 0- 180590 0-078476 20 28 21 29 9921524 20 .10 9-741029 2167! 0-258971 9-819547 0-180453 0-0785,8 9-921482 2B II 9-741125 2270 0-25S875 9-819684 22 101 o;.8°3.6 0-078559 2231 9-921441 10 :u 1 30 4(> 9-741221 2374 0-258779 9-819822 23 105 0-07860, 2332 9-921399 n :«i 27 4S 9'74'3'6 2477 0-258684 9-819959 24 1.0 1 0-180041 0-078643 2433 9-92.357 12 33 .'.n 9-74>4'2 25 80 0-258588 9-820096 25 , 14 , 0-179904 0-07S685 2535 9-9213,5 10 30 28 .Vi 9-741508 2683 0-258492 9-S2'>2 34 26 1.9 0-179766 C-07S726 2636 9-92,274 K .-<2 30 .11 9-741603 27 86 0-258397 9-820371 27 124 0-179629 c-078768 2738 9-92,232 11 30 29 .Ki 9-741699 2S89 0-25S301 9 820508 28 128 0-1^9492 0-078810 2S39 9-921 19c 4 31 30 ••>« 9--'4i794 20 9)1 0-258206 9-820616 21. ,33 0-179354 0-078852 •2940 9-921.48 2 30 .SO 1« 9-'4i889 30 96 0-2581 1 1 9-820783 <0 137 0-179217 0-078893 3042 992 '.07 " 30 '/~ ": (;osinc 1 Parts 1 Secant Cotang. Paris Tangent | Coscc. i Parts Sine m. / // _ 56° fl" ^(>"' I TABLE 68 SOS -1. LOG. SINES. COSINK.S, «:c. | 1 4"' 33" 1 '" [m Sine Parts Coseo. Tange.it Parts 1 Cotang. Secant 1 Parts 1 Cosine 46 so" "~o 9-74>889 1 .0-258,., 9-8207S3 ,o-,792,7 .o-o78ii93 9-92, ,07 .10 •i 9-74>9«5 '"3 ,0-2580,5 9-820920 1" 5 ,0-, 79080 10-07S935 1" , 9-92,065 i.-l 311 31 4 9-742080 2 6 ,0-257920 9-82,057 2 9 '0-.7S943 ,0-078977 2 3 9-92.023 iU 'I'.l ;iu a 9"71i'76 3 9 .0-257824 9-821195 3 ,4 .0-, 78805 10-079019 3 4 9-920981 51 30 .-{2 8 9742271 4.3 .0-257729 9-821332 4 18 ,0-, 78668 10-07906. 4 6 9920939 ii in 30 10 9-7423(16 S16 .0-257634 9-821469 5 23 ,o-,7853. .0-079,03 5 7 9-920897 io :m 33 VJ 9-742462 6,9 .0-257538 9-82,606 6 27 ■0-, 78394 .0-079,44 6 8 9-920856 49 27 30 u 9-742557 7 22 .0-257443 9-82,743 7 32 .0-.7S257 10-079186 7 ,0 9-9208.4 10 311 31 10 9-742652 825 .0-257348 8 37 .0-.78.20 .0-079228 8 .1 9-920772 44 2(i 30 IS 9-742747 928 .0-257253 9-8220,7 9 4, 10-1779S3 10-079270 9.3 9-920730 4i SO 35 ao 9-742X42 1032 "35 .0-257,58 9-822.54 10 46 11 50 .0-, 77846 ^-079311 10-079354 10,4 11 .5 9-9206S8 40 2^ 9-742937 .0-257063 9-822292 .o-,777o8 9-920646 3G ■14 9-743=33 1238 .0-256967 9-822429 12 55 ,o-,7-57, 10-079396 12.7 9-920604 30 2i 30 M 9-743128 1341 .0-256872 9-822566 13 5y 10-177434 , 0-079438 13.8 9-920562 31 3U »7 IS 9-743223 U44 .0-256777 9-822703 14 64 10-177297 10079480 14 20 9-920520 3-i •Si 30 30 9-743318 154s .0-256682 9-822840 15 69 10-177160 10-079522 152, 9-920478 30 ■M 3e 31 9-743413 I65, 10-256587 9-822977 16 73 .0-. 77023 10-079564 I622 9-920436 ■i» '2'J 30 y-7435°8 1754 .0-256492 9-823. .4 17 78 .0-176886 .0-079606 1724 9-920394 •ili 30 3" 9-743602 18 57 10-256398 9-82325. 18 82 ,0-176749 .0-079648 I825 9-920352 24 ai 30 9-743697 i960 10-256303 9-823387 19 87 .0-079690 1927 9-9203. ■22 30 40 40 9-743792 20 63 2167 10-256208 9-823524 20 9, 21 96 .0-. 76476 .0-079732 20 28 21 29 9-920268 20 30 9-743887 .0-256, ,3 9-82366, .0-176339 .0-079774 9-920226 41 44 9-743982 2270 ,0-2560,8 9-823798 22 .o. .0-, 76202 .0-0798.6 223. 9-920.84 10 lu 30 4U 9-744077 2373 .0-255923 9-823935 23 lo; ,0-, 76065 .0-079859 2332 9-920,4, 14 3(1 42 48 9-744'7i 2476 10-255829 9-824072 24 no ,o-, 75928 .0-07990, 2434 9-920099 12 l)i 30 M 9-744266 2579 .0-255734 9-824209 26, ,4 10-17579, .0-079943 2535 9-920057 10 30 43 ii 9-74436> 2682 ,0-255639 9-824345 36,, 9 I0-, 75655 .0-0799S5 2636 9-9200,5 s 17 30 H 9-744455 27 86 .0-255545 9-824482 37 ,23 .o-,755,8 .0-080027 2738 9-9'9973 f, .,0 44 M 9-744550 38 89 ,0-255450 9-8246,9 io-,7538, .0-0S0069 28 39 9-9,993, 4 It; 30 iS 9-744644 2992 ,0-255356 9-824756 J9,3J ■0-, 75244 .o-cSo... 2841 9-919889 ■I 30 46 15 2 9-744739 3° 95 ,0-25526, 9-824893 80 137 IO-, 75,07 ,0-080,54 3042 9-9,9846 «5 '.s IL. 9-744833 1 3 .0-255.67 9S25029 1 5 '0-, 74971 10-0S0.96 1 , 9-9.9804 40 4 9-744928 2 6 ,0-255072 9-825,66 2 9 10-174834 .0-080238 2 3 9-9.9762 K u 30 a 9-745022 3 9 ,0-254978 9-825303 3 14 ,o-, 74697 ,0-080280 3 4 9-9,9720 51 30 47 8 9-745"7 4 13 .0-254883 9-825439 4 18 ,o-,7456. ,0-080323 4 6 9-9.9677 52 13 30 10 9-745211 5 16 0-254789 9-825576 5 23 ,0-174424 ,0-080365 5 7 9-9.9635 50 30 48 12 9-745306 6.9 .0-254694 9-8257.3 6 27 ,o-, 74287 .0-080407 6 8 9-9,9593 43 12 30 14 9-745400 7 22 0-254600 9-825849 7 32 ,o-,74,5, 10-080449 7.0 99,955, 10 30 4U 10 9-745494 825 0-254506 9-825986 8 36 ,0-1740,4 .0-080492 8 .. ;-9'9508 u U 30 IB 9-745589 928 0-2544,1 9-826,23 9 41 10-173877 .0-0S0534 9.3 9-9.9466 42 30 6U 30 20 22 9-745683 103. "35 0-254317 9-826259 45 1 50 10-173741 .0-080576 10,4 11 .6 9-919424 40 10 9-745777 0-254223 9-826396 10-, 73604 .0-0806,9 9-9.938. 61 24 9-745871 1238 0-254129 9-826532 ■^ 55 10-173468 ,0-08066, 12,7 r9'9339 30 u 30 2« 9-745965 1341 0-254035 9-826669 3 59 .0-.7333, 10-080703 13 ,8 /9'92y7 31 311 52 2S 9-746060 U44 0-253940 9-826805 4 64 10-173.95 10-080746 14 20 9-9.9254 3-i 11 30 30 9-746154 1547 0-253846 9-826942 5 68 .0-173058 .0-080788 IS21 9-9.92.2 30 3(1 53 32 9-746248 16 50 0-253752 9-827078 6 73 .0^.72922 .0-08083, I623 9-919.69 ■28 7 30 34 9-746342 '753 0-253658 9-8272.5 7 77 .0-172785 ,0-080873 1724 9-9.9.27 20 30 54 M 9-746436 18 56 0-253564 9-82735, 8 82 10-172649 ,0-0809,5 I825 99.9085 24 li 30 M 9-746530 i960 0-253470 9-827488 9 86 0,725,2 ,0-080958 1927 9-9.9042 ■ti 30 55 40 9-746624 9-746718 2063 2166 0-253376 9-827624 ' 9, 1 96 ,0-08,000 20 28 21 30 ,-9,9000 9-9.8957 20 5 0-253282 9-82776, • om7223~9 ^08,043 Mi 44 9-746812 2269 0-253.88 9-827897 ■ i 100 o-,72,o3 0-08,085 223, 5-9.89.5 ro 4 30 4a 9-746905 2372 0-253095 9-828033 - 3 ,05 0-, 71967 0-08,, 28 2332 9-9.8872 II 30 97 48 9-746999 2475 0-25300, 9-828,70 ■ 4 ,09 o-,7,830 0-081,70 3434 9-9,8830 1'^ 3 .10 30 9-747093 2.'>79 0-252907 9828306 • ■i ,,4 0-, 71694 0-08.2.3 2635 9-9,8787 10 30 5« 42 9-47.87 26 82 0-2528,3 9-S28442 ' ti ..8 0-171558 0-08.255 2«37 9-9,8745 H •> 30 .'.1 9-74728, 27 85 0-2527,9 9-828579 ' 7 .23 0-.7.42. 0-08.298 2738 9-9,8702 30 59 30 9-747374 2S88 0-252626 9-8287.5 ' H 127 0-.7.285 0-08,34, 28 39 ?-9'8659 ■1 1 30 3H 9-747468 2991 0-252532 9-82885. ■ 9 .32 0-.7..49 0-08,383 2B4, )-9.86.7 •; 30 80 \» 9-747562 30 94 0-252438 9^2ji98j^: 0,36 0-.710.3 0-08.426 1042 ,-9.8574 II n 1 II m. Co»ine Part.1 Seca„t Cotang. Parts Taiigcit Cosec. Part, Si.ie m. ^ :>«" .•(" 44" 1 50(i TABLli 68 LOG. SINES, COSINES, &c. ] 2h 16m 340 ____ 1 ,„ •?• Sine Parts Cosec. Tangent Parts J Jota-ng. Secant Parts Cosine m. '" T" ~r 9'74756i 10 252+3S 9-8289^.7 .0 171013 0-081426 J9-918574 ii "cii" 311 a 9-7+7655 '"3 10 252345 9-829i»4 5 .0 170876 0081468 l"i 9-9.8532 58 30 1 4 9-7+77+9 1 6 !0 252251 9-829260 9 .0 17074° 0-0815.1 2 3 9-918489 5(. 5!) JO fl 9-7+7842 3 9I10 252158 9-829396 '4 .0 170604 0-08.554 3 +9-918+46 54 30 u 8 9-7+7936 4 12 10 252064 9829532 18 .0 .70468 0-081596 4 69-9,8+0+ 52 511 30 10 9-7+8030 5 16 10 251970 9-829669 23 .0 170331 0-08.639 5 719-918361 50 311 3 12 9-7+8123 6.9 10 251877 9-829805 10 170.95 0-08.682 6 9l9-9'83i3 48 37 30 14 9-7+8216 7 22 10 2517S4 9-829941 32 .0 170059 0-08.724 7.0 9-9,8276 4« 30 4 16 9-7+8310 825 10 25.690 9-830077 36 .0 169923 0-081767 8 , I 9-9.8233 44 .■Mi 30 18 9-7+8+03 928 10 251597 9-830213 41 .0 169787 0-08.8.0 9.3 9-918,90 42 30 5 20 9-748+97 1031 113 + :o 251503 9-830349 45 50 .0 .6965. 0-08.853 10.+ 11 .6 9-9181+7 40 ft.-| 9-7+8590 10 251410 9-830+85 .0 .695,5 0-081895 9-9,8,05 6 i^ 9-7+8683 1237 10 251317 9-S3062. 54 .0 169379 0-081938 12.7 9-9,8062 30 54 30 20 9-7+8777 13 +0 10 251223 9-830757 59 .0 169243 0-081981 13 ,9 9-9,8019 34 30 7 28 9-7+8870 14+3 10 251130 9-830893 63 10 .69107 0-0X2024 14 20 9-917976 32 53 30 30 9-7+8963 15+7 10 251037 9-831029 68 10 16897. 0-082066 1521 9-917934 30 30 8 32 9-7+9056 16 50 10 2509+4 9-83.165 72 10 .68835 0-082109 I623 9-91789, •28 52 30 34 9-7+91+9 1753 10 250851 9-831301 77 10 168699 0-082152 17 2+ 9-9,7848 •28 30 » 36 9'7+9^43 18 56 10 250757 9-831+37 82 10 .68563 0-082195 1826 9-9,7805 24 51 30 38 9"7+9336 1959 10 25066+ 9-831573 86 10 168427 0-082238 1927 9-9,7762 ■22 30 10 30 40 9-7+9+29 2062 2165 10 250571 9-831709 20 21 91 95 10 168291 0-082281 2029 2130 9-9,7719 18 50 9-7+9522 To 250+78 9-8318+5 .0 ;68.55 0-08232+ 9-9,7677 M 44 9-7+9615 22 68 10 250385 9-83.98. 22 10 0-082566 223. 9-91763+ 16 49 30 46 9-7+9708 2372 10 250292 9-832117 23 104 10 .67883 0-082409 2333 9-917591 14 30 12 48 9-749801 2475 10 250199 9-832253 24 .09 .0 ■67747 0-082452 243+ 9-917548 12 48 30 50 9-7+9894 2578 10 250106 9-832389 as "3 10 16761. 0-082+95 3536 9-917505 10 30 13 52 9-749987 2681 10 250013 9-832525 S6 118 10 167+75 1 0-082538 2637 9-9.7+62 8 47 30 54 9-750079 27 8+ 10 2+9921 9-832660 w 112 10 .673+0 1 0-08258. 2739 9-917419 6 30 U 56 9-750172 2887 10 2+9828 9-832796 «8 127 .0 16720+ . 0-082624 28+0 9-9.7376 4 46 30 58 9-750265 3990 10 249735 9-8329,2 «9 '3' 10 .67068 . 0-082667 294. 9-917333 2 30 15 17 9-75035!* 3093 10 2+96+2 9-833068 ?£- 136 10 .66932 1 0-082710 30+3 9-9.7290 «3 45 9-75045' 1 3 To" 2+9549 9-833204 — .0 .66796 . 0-082753 9-9.72+7 k; 4 9-750543 2 6 10 249457 9'8-J333? 9 .0 ■66661 . 0-082796 2 3 9-91720+ 56 44 30 6 9-750636 3 9 10 249364 9-833475 '4 10 .66525 1 0-082839 3 + 9-9.716. 54 30 17 8 9-750729 4 12 10 2+9271 9-8336.. .8 10 ■66389 . 0-082882 4 6 9-9. 7118 52 43 30 10 9-750821 515 IC 249179 9-833747 23 10 .66253 1 0-082925 5 7 9-9.7075 50 30 18 12 9-75091+ 618 10 2+9086 9-833882 27 10 ■66118 . 0-082968 6 9 9-9.7032 48 42 M 14 9-751007 721 10 2+8993 9-83+0. 8 32 10 .65982 . 0-0X301 1 7 .0 9-9.6989 46 30 10 16 9-751099 825 10 2+8901 9834154 36 10 .658+6 . 0-083054 8.2 9-9,6946 44 41 30 18 9-751192 928 2+8808 9-834289 41 .0 .65711 1 0-083098 9.3 9-9.6902 42 10 20 30 '" 9-7^.28+ 1031 "34 10 2+8716 9-834425 45 50 .0 1655/5 1 0-083.4. 10.+ 11 .6 9-9.6859 40 in 30 9-75'377 10^ 2+8623 9-834561 To^ .65440 . 0-083.84 9-9.68.6 21 24 9-751+69 1237 10 2+853. 9-834696 54 .0 165304 . 0-083227 12.7 9-916773 36 3il 30 26 9-751561 '340 10 248439 9-834832 59 .0 .65.68 . 0-083270 13.9 9-9.6730 34 30 22 23 9-75165+ 14+3 10 2483+6 9-83+967 63 10 .65033 . 0-083313 14 20 9-9.6687 32 38 30 30 9-7517+6 15+6 10 2+825+ 9-835103 68 10 .64S97 . 0-083357 15 22 9-916643 30 30 a 32 9-751839 16+9 24816. 9-835238 72 10 .64762 . 0-083400 I623 9-9.6600 28 37 30 34 9-751931 1752 2+8069 9"835374 77 .0 .64626 1 0-083443 17 2+ 9-9.6557 20 311 24 311 9-752023 10 247977 9-835509 81 .0 .6449. . 0-083486 1826 9-91651+ 24 30 30 38 1959 247885 9-8356+5 86 .0 164355 1 0-083530 1927 9-916+70 22 30 25 40 9-752208 2062 247792 9-835780 20 21 90 95 10" .64220 . .64084 . 0-083573 2029 21 30 9-916427 20 35 30 9-752300 21 65 to 2+7700 9-8359.6 0-083616 9-9,6384 ■-•« 41 9-752392 2-168 2+7608 9-836051 22 99 10 163949 ' 0-083659 2232 9-9,6341 16 34 30 40 9-75HS4 3371 2+7516 9-836187 2S .0 .638.3 1 0-083703 2333 9-916297 14 30 27 48 9-752576 247+ 247424 9-836322 34 108 .0 .636.8 1 0-083746 2435 9-9,625+ 12 33 30 50 9-752668 9377 247332 9-836+58 25 113 .0 .63542 . 0-083789 2536 9-9.62.. 10 30 2« 52 9-752760 26 80 247240 9-836593 26 1.8 .0 163407 I 0-083833 36 37 9-9.6.6- a 32 30 54 9-752S51 27 83 10 2+7.48 9-836728 27 .22 .0 .63272 ■ 0-083876 2739 9-9.6.2+ c 30 ■Z'.) 56 9-7529++ 28 86 247056 9-836864 28 .27 .0 .63.36 1 0-083920 28 +0 9-9.608. 4 31 30 3S 9-753036 2989 10 2+696+ 9-836999 29 10 16300. 1 0-083963 29+2 9-9,6037 2 30 30 1 It 18 9-753128 C.«iiie 30 92 P-arts 246872 9-837.34 SO .36 10-162866 1 0-084006 3043 9-9,599+ 30 Secant Cotang. Parts Tangent Cosec. Parts Sine «? T77 5: ;... 1 TABLE 68 807 LOG. SINES, COSINES. Ice. Oh j3„, 340 Iff m Sine Partii Co«c. Tangent I'aits Cotang. Seoa,it Part5 Co»ii.e m f'f, ;*i)" 9-753128 IO-246872 9-837.34 |.o-. 62866 lO 084006 9-9.5994 «2 30 :iu 9-753120 ' " 3 10-146780 9-837270 1" 4 10-162730 10 084050 I" I 9-9.5950 68 30 SI 9-75J3'i 2 6 iO-246688 9-837405 2 9,10-162595 ,0 084093 2 3 9-9.5907 50 29 M 9' 7 5 3404 3 9 10246596 9-837540 3 13 lO- 161460 10 084137 3 4 9-9,5863 i4 30 ■x> 9'753495 4 12 10-146505 9-837675 4 18 ,0-, 62325 10 084.80 4 6 9-9.5820 S-2 2B .11) 10 9-753587 5.5 .0-246413 9-83781. 5 11 10 084224 8 7 9-915776 50 30 Xi 11 9-75?679 618 io-246321 9-837946 27 ■0-, 62054 10 084167 6 9 9-9.5733 48 27 .111 1 u 9-7S377I 721 .0-246229 9-83808. 7 3. ,0,619,9 10 0843.. 7 10 9-915689 4« 30 34 1 IB 9-75386^ 824 .0-246.38 9-8382,6 8 36 ,o-,6,784 10 084354 8 12 9-915646 44 20 30 IH 9'753954 927 10-246046 9838352 9 40 ,0, 6.648 ,0 084398 9.3 9-915601 4'i 30 35 !to 9-7 5401-6 9-754'37 1030 1134 .0-245954 9838487 10 45 11 49 10-1615,3 10 084441 10.5 11 ,6 9-9.5559 40 38 25 30 .10 M .0245863 9838622 10-16137S To 084485 9-9>55.5 Mi ?4 9-754«9 1237 .0-24577. 9-838757 12 54 ,o-,6,243 ,0 084518 1217 9-9.5472 M 24 HI JO 9-75^.320 1340 10-245680 9-838892 13 58 ,0-16, ,08 ,0 084571 13.9 99.5418 31 30 V JM 9-7544II 1443 10-245588 9-839027 14 63 ,0-160973 ,0 0846,5 14 20 9-9.5385 3-i 23 M 311 9-7S45°3 1546 .0-245497 9-839i6i 15 67 10-, 60838 10 084659 18 22 991534. 30 30 SH 3J 9-754595 16 49 .0-245405 9-839297 16 72 10-160703 10 084703 16 23 9-915297 •28 22 30 34 9-754686 1752 0-2453.4 9-839433 17 76 ,0-, 60567 ,0 084746 17 25 9-9.5254 Q6 JO 3'J 3e 9-754778 I855 0-245222 9-839568 18 8, ,0-160432 ,0 084790 18 26 9-9.5210 -24 21 30 38 9-754869 1958 0-24513 I 9-839703 19 85 ,0-160297 10 084834 1928 9-9.5.64 M 30 40 40 42 9-754960 2061 21 64 0-245040 9-839838 20 90 21 94 .0-160,62 .0 084877 80 29 2130 9-915,23 I 20 9-75505^ 0-244948 9-839973 ■0-, 60017 io" 08491, 9-915079 41 9-755'43 2267 0-244857 9-S40.08 22 99 ,0-159891 10 084965 2232 9-915035 Ifl 19 :ii) it 9-755134 2370 0-244766 9-840243 23 103 10-159757 ,0 085008 2333 9-914992 14 20 42 48 9-755316 2473 0-244674 9-840378 24 108 ,0-, 59621 10 085052 2435 9-9.4948 12 18 JO 50 9-7S54'7 25 76 0-244583 9-8405.3 25 III ■0-159487 10 085096 2536 9-914904 10 30 43 54 9-755508 2679 0-244492 9-840648 26 ,,7 10-159352 10 085140 2638 9-9.4860 » 17 :iii 54 9-755599 27 82 0-24440 J 9-840782 27 121 .0-1591,8 10 085.83 27 39 9-9148.7 a 30 14 M 9-755690 2885 0-244310 9-8409.7 28 ,26 10-, 59083 10 085227 2840 9-9.4773 4 16 m • 58 9-75578" 29 88 0-2442.9 9-84,052 at 130 .0-. 58948 ,0 085171 2942 9-914729 2 30 il_;i9 9-755871 309- 0-244.28 9-841.87 3C 135 10-158813 10 0853,5 3044 9-9,4685 «1 58 _I5 30 9-755963 1 3 0-244037 9841322 • 4 10-158678 To" 085359 1 1 9-914641 Ifi" 4 9-756054 2 6 0243946 9-84145- 2 9 IO-, 58543 10 085402 2 3 9-9.4598 50 14 1" I'r 9-756145 3 9 0-243855 9-841591 3 13 10-158408 ,0 085446 » 4 9-9.4554 54 30 *l i " 9-756236 4 12 0-243764 9-84.727 4 18 10-158273 10 085490 4 6 9-9,45,0 52 13 9-756327 515 0-243673 9-S4.86. S 12 10-158.39 10 085534 6 7 9-914466 50 30 48 1-2 9756418 618 0-243582 9-841996 6 27 10-158004 10 085578 6 9 9-9,4422 48 12 :iii 14 9-756509 721 0-24349. 9-842.3. 7 3. :o-, 57869 10 0S5611 710 9-9.4378 46 30 4'.l 10 9756600 824 0-243400 9-841266 8 36 .0-. 57734 .0 085666 8,2 9-9'4334 44 1 1 311 18 9-75669. 927 0-243309 9-841400 9 40 .0-157600 ,0 085710 9"3 9-9.4190 42 M .SO '" 9-756782 10 30 "33 0-2432.8 9-842535 10 45 11 49 .0-157465 10 085754 10.5 11 .6 9-9,4146 .„ 10 30 9-756872 0-243.28 9-842670 ,0-157330 To" 085798 9-9,4102 'il •24 9-756963 1236 0-243037 9-842805 12 54 .0-.57.95 ,0 0X5842 12.8 9-9.4.58 .HO 9 10 W 9-757054 IS 39 0-242946 9 841939 13 58 ,o-.57o6. ,0 C85886 13.9 9-9.4114 34 30 52 ■m 9-757144 1442 0-242856 9-843074 14 63 10-156916 ,0 085930 1421 9-914070 32 M 111 30 9-757235 1545 0-242765 9-843209 15 67 ,0-156791 ,0 085974 15 2 1 9-9,4026 30 30 .-.3 ! 32 9-757326 1648 0-242674 9-843343 16 72 ,0-, 56657 10 0860.8 I6i,» 9-9.3981 28 7 30 34 9-7S74>6 175. 0-142584 9-843478 17 76 10-, 56522 ,0 086062 1715 9-9.3938 20 30 .'.4 3« 9-757507 I854I 0-242493 9-8436.2 IS 81 .0-, 56388 10 086,06 I816 9-9,3894 24 6 w .U 9-757597 '9S7| 0-242403 9-843747 19 85 10-156153 .0 086,50 ,918 9-913850 22 30 55 30 40 45 9-7576X8 20 6o| 21 63 0-2423.2 9-843882 120 90 9-8440,6 [21 94 10-156, .8 ,0-155984 10 086,94 2019 213, 9-913806 9-9.3761 18 5 30 9-757778 0-242221 To" 086238 56 ** 9-757869 2266 0-141131 9-84415, 22 99 .0-. 55849 .0 086282 3231 9-9.3718 10 * 30 40 9'75795'; 23 6, 0-242041 9-844285 -23 ,03 ,0-1557,5 10 086326 2334 9-9.3674 14 30 »7 48 9-758050 2472 0-241950 9-844410 1-^4 ,03 ,0-, 55580 .0 0S6370 2435 9-9.3630 1-2 s 30 50 9-758140 25 76 0-241S60 9-844554 ■2.') 112 .0-. 5 5446 .0 0864,5 2537 9-913585 10 M 88 51 9-758230 2679! 0-24.770 9-844689 26 117 10-155311 10 086459 2638 9-9,354, 2 M M 9-75832. 27 82 1 0-241679 9-844813 I27 .1. ,0-155177 .0 086503 2740 9-9.3497 30 sa 50 9-7534.I 2985I .0-14.589 9-844958 [28 .16 I0'i5504i 10 086547 J84. 99. 3453 1 Sfl 5« 9-75850. M88 .0-241499 9-845091 29 .30 10-154908 10 086591 2943 99.3409 .10 «o 20 9-758591 3091 .0-241409 9-S45217 \30 135 .0-154773 IOOS6635 3044 9-9.3365 '" ": C'' 2U"' 3o° _ 1 7// m. Sine Parts 1 Cosec. Tangent Parts 1 Cotang | Secant Parts Cosine m. 40 (JO T 9'758S9' 24.409 9-845227 .0-. 54773 0086635 9-9.3365 30 •i 9-75S6Si '"3 24,3.9 9-84536. '" 4 ,r. 54639 0-086680 l"i 9 9,3320 5» 311 1 4 9 758772 2 6 .0 241228 9-845496 2 9 .0-. 54504 0-086724 2 3 9-9,3276 5« oa 311 6 9758S62 3 9 241,38 9-845630 3 ,; .0-. 54370 0-086768 3 4 9-9.3232 54 30 2 8 9-758952 4 .2 10 24.048 9-84576+ 4 .8 ,0-. 54236 0-0S6813 4 6 99.3.87 52 68 30 10 9-759042 5 .s .0 240958 9-845899 5 22 ,0-15410, . 0-086857 5 7 9-9.3143 50 30 3 12 9-759132 6.8 .0 24086S 9-846033 6 27 ,0-153967 , 0-086901 6 9 9-9.3099 48 37 11) U 9-759222 72. .0 14077S 9-846.68 7 3' ,0-153832 , 0-086945 7.0:9-9,3055 40 30 4 10 9-75931:' 824 .0 240688 9-8463C2 8 36 10-153698 0-086990 8.2 9-9'30>o 44 56 30 18 9-759402 927 .0 240598 9-846436 9 40 10-153564 I 0-087034 9,3 9-9.2966 42 30 ft 30 ■M 9-759492- 1030 'I 33 10 240508 9-8465-0 10 45 11 49 .0-153430 . 0-08707-^ ■ 0.5 11 16 9-9.2922 40 56 9-759582 To 240418 9 846705 .0-153295 . 0-087123 9-911877 ■n 9-759672 1236 10 240328 9-846839 12 54 .o-,53.6, 1 0-087.67 1218 9-912833 30 54 30 •20 9-759762 13 39 lO 240238 9-846973 13 58 ,0-153027 1 0-087212 13 .9 9-9.1788 34 30 7 28 9-75985^ 1442 .0 240.48 9-847. c8 14 63 ,0-152892 . 0-087256 14 2. 9-9.2744 32 8:i 30 30 9-759941 1545 .0 240059 9-847242 15 67 .0-152758 . 0-087300 15 22 9-9.2700 30 30 8 3^2 9-760031 I648 10 239969 9-847376 16 72 ,0-, 52624 1 °;o87345 16 14 9-912655 -28 52 30 (4 9-760.21 175. 10 239879 9-8475.0 17 76 .0-152490 . 1725 9-912611 2fi 30 9 36 9-760211 18 54 10 9-847644 18 80 ;°; 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Parts Tangent Cosec. Parts Sine 'm 777 ;)4° :)'' ns'" TAliLfc; 68 80? LOG. t.INE.S, COSINES, (kc. Jh 22'" 3.5° 1 if w ." Sine Parte Cosec. Tangent Parts C'otang. 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m 3« 9-76826. 1955 ,o-23,739 9-859799 19 84 10-. 40201 0-09.538 1929 9-908462 ■fl :'(i S.i 30 40 4S 9-768348 2058 21 61 10-23,652 9-859932 9-860C65 20 89 •21 93 10-14C06S 0-091584 2030 2132 9-908416 9-908,70 IS -30 9-768435 ,0-23,565 ,0-139935 0-091630 ,')C 44 9-768522 2264 ,0-23,478 9-860,98 122 97 ,o-„98o2 ,0-09,676 2234 9-908,24 111 4 30 4« 9-768609 2367 ,0-23,39, 9-86033, 23 ,01 ,o-,3.;669 ,0-09172, 2335 9-908279 13 .10 S7 l§ 9-768697 2470 10-231303 9-860464 24 106 10-139536 10-091767 2436 9-908233 1-2 3 .10 30 9-768784 2S73 ,0-23,216 9-860597 25 111 10-139403 10-09,8,3 2538 9-908187 10 30 .5R .Vi 9-76887. 2676 .0-23, ,29 9-860730 2fi ,,5 ,0-139270 ,0-09,859 2640 9-908.4. n 2 30 .'>) 9-768958 2779 ■0-23.042 9-860862 27 ,20 ,o-,39,38 ,0-09,905 2741 9-908095 n 30 .■••1 311 9-769045 28 81 ,0-230955 9-860995 28 124 ,0-139005 ,0-09195, 28 43 9-908049 4 1 3« 3H 9-769.32 2984 10-230868 9-86,128 2 30 9-770520 1543 10-219480 9-863151 15 66 10-136748 .0-092731 1513 9-907168 30 3U 8 32 9-770606 16 46 10-229394 9-863385 16 7, 10-1366.5 .0-092778 I615 9-907211 28 52 3.; 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Parts Tangent (;o»ec. Part. Sine ?• .S.1° a*- 34- 1 T\ni.K r>8 81 LOG. SINES, COSINES, Sec Oh .jc,"> aCi" w ^ Sine ParU Co»ec. Tangent Parts { Cotang. Secant Parts j Cosine 34 ;ni 9-77458« .0-2256,2 9869209 1.0-130791 10-094821 „ ;9-vo5i-9 .11) •i 9-774473 I" 3 10-225527 986934. '" 4 10-130659 .©•094868 1 2,9905.32 58 311 .11 4 9-774^5» 2 6 10-225442 9-869473 2 9 10-130527 .00949.5 2 3 9-905085 5( •2!1 .10 « 9^774644' 3 8 10-225356 9-X69605 3 13 10-. 30395 10-094962 3 5 9-905038 54 .'10 :)■-• 8 9-7747^9 4 II 10-22527. 9-S69737 4 .8 .0-. 30263 .0-095008 4 6 9-904992 5-2 211 :m 10 9-7748 14 5,4 10-225.86 9869869 5 22 .0-.3013. •0-095055 5 8 9-9.4945 50 .30 :t:t I'i 9-774X99 617 .0-225.01 9^87000. 6 2ft .0-. 29999 10-095102 6 9 9-904898 48 21 .10 14 9-774985 720 .0-2250.5 9-870.33 7 3' .o-,29867 10-095149 7 . 1 9-90485. 40 .30 :u lU 9-775070 823 10-224930 9-870265 « 35 .0-129735 10095196 8.3 9-904804 41 20 :«t 18 9-775155 925 10224845 9-870397 9 40 .0-129603 10-095243 9 .4 9-904757 4-2 311 X, Ml ■iO 9-77514° IO28 11 31 10^224760 9-870529 10 44 11 48 ■°-'2947 1 10-129339 ■ 0x95^89 10-095336 10.6 9-904711 411 25 9-775325 io^224675 9-87066. 11 17 9-904664 ■.w J4 9-775410 1-2 34 10-224590 9-870793 12 53 10-129207 10-0953S3J1219I9-9C46.7 3I> 24 :iii •ill 9-775495 ['•■»37 10^224505 9-870925 13 57 10-. 29075 .0-09 5430 j 13 20 9-904570 34 30 ■'7 is 9-775580 14 40 10^224420 9-871057 14 62 .0-. 28943 .0-095477 1422 9-904523 32 23 ,10 30 9-7-5665 •.542 10-224335 9-871189 15 66 .0-1288,1 IO-C95524 15 24 9-904476 30 .10 :tK 9-775750 I645 .0-224250 9-87132. Ifi 70 .0-.28679 10-09557. I625 9-904429 •28 22 .10 9-775835 1743 10-224165 9-871453 '7 75 .0-. 28547 10-0956.8 "727 9-904382 •20 30 M :ui 9-7759io I851 io-i24oSo 9-871585 18 79 10-.28415 .©•095665 I82S 9-9^4335 •24 21 .10 3S 9-776005 1954 .0-223995 9-87.7.7 19 84 10-128283 100957.2 1930 9-9C42XS n .30 ~ 41) 4-2 9-776090 2057 21 59 .0-223910 9-871849 •20 S8 21 9z .o-,28.5, ,0-, 28020 ■©•095759 •2031 21 33 9-90424' 20 18 20 30 9-776175 .0-223825 9-87.980 io^0958o6 9-904194 11 41 9-776259 2262 .0-223741 9-872. .2 22 97 .0-.27888 '0-095S53 2234 9-904,47 10 19 JO 4(i 9-776344 23 6s 10-223656 9-872244 23 .01 .0-127756 io^o959oo 23 36 9-904.00 M 30 42 48 9-776429 24 68 10-22357. 9-872376 24 106 .0-. 27624 10-095947 •2438 9-904053 VI 18 .10 SO 9-776514 2571 .0-223486 9-872508 25 ,,0 .0-127492 .0-095994 2539 9-904006 10 30 4.1 52 9-776598 2674 .0-223402 9-872640 26 ,,4 .0-127360 io-096©4i 2641 9-903959 17 :io 54 9-776683 2776 .0-2233.7 9-87277. 27 1.9 .0-. 27229 .©•096088 2742 9-9039.2 30 4i 5 4 10-. 26701 ■©•0962-7 1 2 9-903723 4(i 4 9-777106 1 J 6| 0-222894 9-873430 2 9 ,0-126570 ■0-096324 2 3 9-903676 5» 14 9-77719' 3 8 0-222809 9-873562 s 13 .0-126438 .0-09637. 3 5^9-903629 54 .30 J?" 8 9-777275 4 I I 0-222725 9-873694 4 lg .0-126306 .0-0964.9 4 69-90358. 3-2 i:< 10 9-777359 S14 0-222641 9-873825 5 21 10-126175 .0-096466 5 89-903534 50 30 4(i 1-2 9777444 617 0-222556 9-873957 6 26 .0-116043 .0-0965.3 6 919-903487 48 12 .10 14 9-777528 720 0-222472 9-874089 7 3. .0-12591. io-©9656o 7.1 [9-903440 46 30 49 1(1 9-777613 8 22 0-222387 9^8742:o 8 35 .0-115780 .0-096608 8,3,9-903392 44 II .10 18 9-777697 925 0-222303 9-874352 » 40 .0-125648 .0-096655 9.4 9-903345 4^2 30 50 •2-2 9-777781 1028 0-222219 9-874484 10 44 11 48 .0-.255.6 10-096702 10.6 9-903298 40 38 10 30 9-777866 11 31 0-222134 9-874615 .0-.23385 i©-09675o 9-903250 si' •24 9-7779;o 112341 0-222050 9-874747 12 53 .0-. 25253 io^096797 12.9 9-903203 30 » 30 ■M 9-778034 1 13 37 1 0-22,966 9-874879 13 57 .0-,25,2. ■©•096844 132. 9-903156 34 30 S2 ■28 9-778119 1440 0-22.88. 9-8750.0 14 6. '0-124990 ■©•©96X92 1422 9-903.08 3^2 » :i« 30 9-778203 1542 0-221797 9-875142 15 66 .o^i24858 .©•096939 15 24 9-903061 30 30 ,V» 3-2 9-778287 1645 0-22.7.3 9-875273 16 70 .0-124727 ■©•096986 I625 9-9030.4 •m 7 30 .14 9-778371 1748 9-875405 '7 75 10-124595 10 097034 9-902966 ■us 30 54 .Kj 9'778455 0-221545 9-875537 18 79 .0-, 24463 ■©•©97o8i I82S 9-902919 •24 li 30 ^18 9-778539 1953 0-22146. 9-875668 19 83 .0^. 24332 '0-097129 1930 9-902871 ■n 30 55 30 10 9-778624 2056 21 59 0-22.376 9-875800 20 88 21 92 .©•.24200 .0-097.76 2032 2133 9-902S24 '"' -4r 9-778708 0-12.292 9-87593, 10-124069 0-097224 9-902776 5C 44 9-778792 2262 9-876063 22 97 10-123937 0-09727. 2235 9-902-29 4 30 4t Cosec. 1 Parts Sine 1^ s;i" :)'' :i-2"' 1 812 TABLE 68 LOG. SINES, COSINES, &c. | 01, 2m™ 37" 1 TT " Sine Parts Cosec. Tanggnt j Parts Cotang. Seeant Part-s Cosine m «(l 9-779463 |io-220537 9-877,14 10-122886 0-C97651 9-902349 32 ■0 ■2 9'7;9';47 '"3 10-220453 9-877246 1 4 ,o-,22754 0-09760Q 1" 2 9-902301 58 30 1 4 9-779611 2 6 ;o-22«86 9-877377 2 9 .0-122623 0-097747 2 3 9-902253 -)6 59 31) « 9-775714 3 8 9-8775':9 3 .3 IO-.2249, 0-097794 3 5 9-902206 54 30 2 8 9-77979S 4 II IO-2202C7 9-8:7640 4 ,7 .0122360 0097842 4 6 9-902158 5-2 5« ,10 10 9 779882 5.4 10-2201 iS 987777. 5 22 10-122229 0-097890 5 S 9-902110 50 JO 3 V2 9779966 6.7 10-220034 9-877903 6 26 10-122097 0-097937 610 9-902063 48 57 Ml N 9-780049 7.9 10-219051 9-S78034 V 31 ,o-j2,966 0-097985 7 ,1 9-902015 46 30 i 1(> 9-780133 822 10-219867 9-878165 8 35 .o-,2,835 0-098033 8,3 9-901967 +4 5B 30 18 9-7802.6 925 .0-219784 9-878297 9 39 ,0-121703 0-098080 9,4 9-901920 42 30 5 ■20 1i 9'78°30o 1028 1131 .0-219700 9-878428 10 44 U 48 ,0-121572 0-098,28 10,6 U .8 9-901872 38 55 9-780384 IO-2I9616 9-878559 ,0-121441 0-098,76 9-901824 (i ■n 9-7?0467 12 3i 10-219533 9-87S691 12 52 ,0-121309 0-09S224 12,9 9-901776 36 54 JO ■ill 9-780551 1336 10-219449 9-S78S22 13 57 0-09827, 132, 9-901729 »1 30 7 9-780634 1439 .0-2I9366 9-878953 14 61 ,0-12,047 0-0983,9 1422 9-90,681 32 53 so 30 9-780718 1.547 .0-219282 9-8790S5 15 66 ,0-1209,5 0-098367 1524 9-90,633 30 30 8 32 9-78080. I645 10-219199 9-S79216 16 70 10-, 20784 0-0984,5 I625 9-901585 -28 52 .)» 34 0-780884 1747 10-219116 9-879347 17 74 ,0-120653 0-09S463 1727 9-90,537 ■26 30 9 30 9-780968 18 50 10-219032 9-879478 18 79 10-, 20522 0-0985,0 I829 9-901490 -24 51 .10 3S 9-78105. 1953 10-218949 9879609 19 83 .0-, 20391 1930 9-90,442 -2-2 30 10 30 40 9-781.34 2056 21 58 10-2. 8X?6 9-879-41 20 87 21 92 .0-, 20259 0-098606 2032 2133 9-90,394 -20 50 9-7812. 8 10-213782 9-879872 0-098654 9-90,346 II 44 9-78.301 226. .0-2,8699 9-SS0003 22 96 10-1,9997 , 0-098702 2235 99°'29S 16 40 30 4li 9-781384 2364 .0-2.8616 9-8S0134I43 lOI .0-119866 , 0-098750 2337 9-901250 14 30 12 48 9-781468 2467 10-218532 9-880^65 |34 ,05 .0-. 19735 . 0-098798 2438 9-90,202 1-2 48 30 50 9-78i55> 2570 .o-2i«449 9-880397 25 109 .0-1,9603 I 0-09S8+6 2540 9-901.54 10 311 13 3-2 9-781634 2673 io^ii8366 9880528 26 1.4 .0-119472 I 0-098894 2641 9-90,106 8 47 30 5A 9-7S.7.7 2775 .0-2.8J83 9-S80659 27 i.S .0-1,9341 , 0-098942 27 43l9-90'os8 6 14 5(i 9-781800 2878 10-2,8200 9-880790 18 .22 .0-1.9210 I 0-098990 2845 9-90,0,0 4 40 30 59 9-78.883 29 8. 10-2.8117 5-88092. ?a .27 ,0-1,9079 . 0-099038 2946 9-900962 •2 30 15 29 9-78.966 3083 .0-2.8034 9-88.05Z so ,31 .o-,,89+8 . 0-0990S6 30 48 9-900914 31 4.^. 30 9-782S49 "1 3 .0-217951 9-881.83 ' 4 .0-118817 ■ 0-099,3+ 1 2 9-900866 58 30 \G 4 9-782132 •2 6 10-2.786S 9-8813.4 2 9 .o-.,S686 1 0-099,82 2 3 9-9008.8 56 44 30 li 9-782215 3 S .0-2.77S5 9-88.445 3 ,3 .0-, 18555 ■ 0-099230 3 5 9-900770 54 .10 17 S 9-7S2298 4 I I IO-2I7702 9-88,577 ♦ .7 ,©-,,8423 1 0-099278 4 6 9-900722 32 43 30 10 9-78238. 5,4 .0-2.7619 9-88.708 5 22 10-118292 1 0-099326 5 8 9-900674 50 311 18 1'2 9-782464 6 17 10-2.7536 9-881839 6 26 io-,.8i6, I 0-09937+ 6 10 9-900626 48 42 30 14 9-782547 719 10 217453 9-881970 7 3> 0-..8030 . 0-099+22 7 11 9-900578 40 30 19 16 9-7S2630 10-217370 9882.0. 8 35 0-117899 . 0-09947, 813 9-900529 44 41 30 IS 9-7S27.3 925 10-217287 9-882232 9 39 0-. 17768 , 0-0995,9 9,4 9-900481 42 311 20 ■22 9-782796 10 28 1130 10-217204 9-882363 10 44 11 +8 o-,,7637 ■ 0-099567 10,6 9-9C043; z 411 9-782S79 0-2I7I2I 9-882494 0-1,7506 , 0-0996,5 9-900385 21 •24 9-78296. 1233 0-217039 9-882625 2 52 0-..7375 I D-099663 12,9 9-900337 ■M 3!) 30 ■2fi 9-7S3044 1336 0-216956 9-882756 3 57 0-. 17244 1 3-0997,1 1321 9-900289 34 30 22 •2.S 9-783117 1439 0-2.6873 9-882887 4 6, 0-.17113 I 3-099760 14 23 9-9C0240 32 38 30 30 9-7832.0 154. 0-2,6790 9-8830,8 5 65 0-116982 , 3-099808 15 24 9-900192 30 30 2:i 3-2 9-783292 1644 0-216708 9-883,48 6 70 0-1,6852 I 3-099856 1626 9-900,44 -28 37 30 34 9-783375 1747 0-216625 9-883279 7 74 0-1,672. , 3-099904 1727 9-90C096 26 30 24 3(i 9-783458 18 50 0-216542 9-S834.0 8 78 0-, 16590 I 3-099953 1829 9-900C47 -21 3li 30 38 9-783540 1952 0-216460 9-88354. 9 83 0-116459 ' 193. 9-899999 -22 30 2.5 40 9-783623 2055 21 58 0-216377 9-88,672 87 1 92 0-. 16328 1 3-100049 2032 2134 J- 8999 51 ■20 35 42 9-783705 0-216295 9-883803 0-1,6,97 r -100098 j-899902 2(; 44 9-783788 2261 0-2I62I2 9-883934 2 96 0-116066 K ■IC0146 2235 J-S9985+ lit 34 30 46 9-783870 2363 0-2.6130 9-88+065 3 100 0-. 15935 K -100194 2337 j-899806 14 30 27 48 9-783953 24 66 0-216047 9-884.96 4 105 0-. 15804 1 -IQO243 2439 ?-899757 12 33 3ir 50 9-784035 25 69 0-215965 9-88+326 5 109 0-115674 K -10029, 2540 ^899709 10 30 28 5-2 9-784. .8 2672 0-215882 9-884457 6 ,,3 0-115543 IC -100340 2642 j-899660 ,« 32 30 54 9-784200 2774 0-2,5800 9-884588 7 ,,8 0-115412 IC -,00388 2743 J-8996,2 6 30 2!t 51) 9-784282 28 77 9-8847.9 8 122 0-115281 K -,00436 28 45 ^-899564 4 31 30 58 V784365 2980 0-2I5635 9-88+850 9 ,26 0-115150 ,C -100485 2947 ^-899515 -2 30 :.(. JO 9-'84447 31.83 0-215553 9-884980 131 0-115020 I -100533 3048 ,-899467 ? 3(1 H «?• Cosiae Parts Secant Cotang. Parts Tangent Cosec. Part-8 Sine 52° 3' 30'^' TABLE G8 813 LOG. SINES, COSINES, &c. | .jh 3on. 37a TVi m Sine P«rti| Co«ec. Tangent Parts Cotang. Secant Parts Cosine m '" 35" "T 9-784447 10-215553 9-884980 '°-"5C20 10-. 00533 9-899467 ¥0 30 311 1 9-7845'-9 '"3 .0-2.54-1 9-8851,, 1" 4 ,o-..4889 .0-.C0582 1"2 9-8994,8 5M 30 31 \ 9-784611 2 5 .0-2.5388 9-S85242 ■•* 9 ,o-,.4758 ,o-,oc630 2 3 9-899370 56 -.'y 30 « 9-784694 3 8 .0-2,5306 9-885373 3 ,3 .0-1,4627 ,0-100679 3 5 9-89932, 54 30 :»2 8 9-784776 4 . 1 10-215224 9-885504 ,o-,,4496 10-, 00727 4 6 9-899273 '2H 3(1 10 9-784858 6.4 10-215142 9-885634 5 22 ,0-1,4366 10-100776 5 8 9-899224 50 30 ■x.\ VI 9-784941 6 16 ,0-215059 9-885765 6 26 ,o-,,4235 ,0-, 00824 6,0 9-899,76 48 27 3(1 14 9-785023 7.9 .0-214977 9-8S5896 7 30 ,0-1,4,04 ,o- .00873 7 ,. 9-899.27 48 30 31 10 9-785'05 .0-2,4895 9-886026 " 35 .0-1,3974 10-100922 8.3 9-899078 '-'0- 30 18 9-785187 9 25 .0-2.48,3 9-886157 9 39 ,o-,,3843 10-1C0970 9,5 9-899030 4-2 30 3.^ ■20 9-785^69 10 27 11 30 ,0-2,473. 9-886288 10 43 11 48 ,o-..37.2 10,6 11 ,8 9-89898, 40 •25 9-78535' .0-214649 9-S86+.9 .0-..358. 10-. 0.067 9-898933 36 •i\ 9-785+33 1233 .0-214567 9-886549 12 52 ,0-1,345, 10-.0..16 12,9 9-898884 ■M 24 3(1 •lU 9-7855'5 1336 ,0-214485 9-8866S0 13 57 ,0-101.65 132, 9-898835 30 37 •m 9-785597 1439 ,0-2,4403 9-8868.. 14 6, ,o-,,3.89 14 23 9-898787 3-2 23 3» 30 9-785679 154. 10-21432. 9-88694, 15 65 ,0-1.3059 .o-io.262 15 24 9-898738 30 30 38 32 9-785761 16 44 .0-2,4239 9-8S7072 16 70 ,0-.,2928 .0-1013. I 16 26 9898689 ■2« 22 30 34 9-785843 1747 ,0-2,4,5- 9-887202 17 74 ,0-1,2798 .0-10.359 1728 9-89864. 30 39 36 9-785925 18 49 ,0-2.4075 9-887333 18 78 ,0-1,2667 I0-.0.40S I829 9-898592 •24 21 30 38 9-786007 1952 10-213993 9-887464 19 83 .o-.,2536 10-10.457 193, 9-898543 ■li 30 40 40 44 9-786089 2055 2157 10-2139,, 9-887594 20 87 •21 9, 10-, 12406 .0-, 0.506 •2032 2134 9-898494 Is 2U 9-786,70 10-213S30 9-887725 ,0-, 12275 10-. 01554 9-898446 41 44 9-786252 2260 10-2,3748 9-887855 22 96 .o-,,2,45 10-.0.603 2236 9-898397 lu lU 30 4fi 9-786334 2363 .0-2.3666 9-887986 23 ,00 .o-.o,652 2337 9898348 14 30 42 9-786416 |24 66 .0-2.3584 9-888, ,6 24 ,04 Z-V,ml 10-10170, 2439 9-898299 1-2 IK 30 50 9-786497 25 68 10-213503 9-8S8247 25 ,09 ,0-11,753 ,0-, 0,750 204, 9-898250 10 30 43 3-2 9-786579 267, 10-213421 9-888378 26 ,13 ,0-,,,622 ,o-,oi79S 2642 9-898202 g 17 30 54 9-786661 "74 10-2,3339 9-888508 27.17 ,o-,,.492 ,0-, 0,847 2744 9-898x53 g 44 5C 9-786742 2877 ,0-2,3258 9-888639 28 122 io-.,i36, ,o-,o,896 2846 9-898.04 4 16° 30 5S 9-786824 29 80 ,0-2,3176 9-888769 29 126 10-111231 10-10,945 2947 9-898055 •2 4.^ 31 9-786906 30 82 ,0-2,3094 9-888900 30 ,30 ,o-,o,994 3048 29 58 3) 9-7869S7 1 3 0-2, 3013 9-889030 ' 4 ,0-110970 10- .02043 I 2 9-897957 46 4 9-787069 2 5 0-212931 9-889,6, 2 9 10-110839 ,0-102092 2 3 9897908 5« U 30 (i 9-78715° 3 8 0-2,2850 9-88929. 3 ,3 10-U0709 ,O-,02,4, 3 5 9-897859 54 3 4!) 1-2 9-787395 616 0-212605 9-8S9682 6 26 0-1,03,8 ,0-102288 6.0,9-8977.2 7., 9-897663 48 12 30 14 9-787476 7.9 0-212524 9-8898,3 7 30 o-,,o,87 ,0-, 02337 40 .10 49 10 9787557 822 0-212443 9-889943 8 35 o- 1 10057 ,0-102386 8,3 9-8976,4 1 1 30 IH 9-787639 924 0-2,236. 9-890074 9 39 0-109926 io-,02435 9,5 9-897565 30 ,V) ■20 9-787-20 9-78780. 1027 11 30 0-2.2280 9-890204 10 43 U 48 0-. 09796 ,0-, 02484 10 ,6 11 .8 9-8975.6 10 ,0-2.2.99 9-890334 0-, 09666 ,0-, 02533 9-897467 SI ■24 9-787853 1233 9-890465 12 52 0-109535 ,0-102582 1220 9-8974,8 8 30 2(i 9 787964 1:^35 'o-2;2036 9-890595 13 56 0-109405 ,o-,0263. 132. 9-897369 30 52 M 9-788045 1438 0-21,955 9-890725 14 6. 0-109275 .o-,0268o 14 23 9-897320 b 3« 30 9-788.27 1.54. 0-21,873 9-890856 15 65 o-,c9,44 ,0-102729 15 25 9-89727. 30 :;.\ 32 9-788208 I..43 o-2.,792 9-890986 16 69 o-,090,4 ,o-,o2778 1626 9-897222 28 7 3U 34 9-78S28S 1746 0-2. ,7,, 9-89,1,6 17 74 0-, 08884 ,0-,0282S 1728 9-897,72 54 3< 9-7883-0 I849 0-2,. 630 9-89,247 18 78 0-.08753 ,o-,02877 18 29 9-897,23 2"! •;" 30 3H 9-788451 195. o-.,,549 9-89.377 19 82 .0-. 02926 193. 9-897074 u:^ 40 9-788532 2054 2157 0-2,1468 9-89,507 20 87 21 ,. 0-.0S493 .0-102975 2033 21 34 9-897025 5 30 9-788613 0-2, .387 9-89,638 o-,c8362 ,0-103024 9896976 5n 44 9-788694 22 60 o-2.,3o6 9-!!9.7fi8 22 95 0-108232 ,0-103074 2236 9-896926 •1 30 4n 9-788775 -i3 62 9-89.S98 23 .00 0-, 08,02 10-103,23 2338 9-896877 30 57 48 9-78X856 2455 0-2, ,.44 9-892028 24 .04 i 0-, 07972 ,o-i03,72 ■2439 9-896828 3 30 M 9-788937 25 68 o-2,,o63 9-892,59 25 .08 0^.0784. ,0-,0322, •254. 9-896779 30 .^8 M 9-7890.8 267. 0-210982 9-892289 2fi .,3 o-.o-'7,I 2642 9-896729 2 30 SI 9-789099 2773 0-2.090. 9-8924,9 27 ..7 o-,o758. .0-. 03320 2744 9-896680 .sn W ,•789.80 2876 0-2,0820 9-892549 28 ,22 0-107451 .0.03369 2846 9-89663, 1 30 j« 9-78926. 2979 0-210739 9-892680 29 .26 .0-107320 ,o-,034.9 2948 989658, 3C az 9^789^5^ Cosine " 30 8. 10-210658 9-8,28,0 30,30. 10-1071,0 .0.03468 ^049 9-896532 Part- Secant Coung. ParU 1 Tang,nt Ccwr. Port* Sine If, .W ,-!'■ ilH'" 1 814 2"' LOG. SINES, COSINES, See. | 3-2" -38" 1 }7r m Sine 1 Parts Cosec. Tangent Parts Cotang. Secant Parts Cosine •Pi'"! ~(r\~o 9-7«934J 10-210658 9-892810 10-107190 .0-103468 9-896532 28 till 9-789423 1"3 10-210577 9-892940 1" 4 10-107060 .0-1035.7 1 ' 2 9-896483 5S .til '"! ■• 9-789504 2 5 10-210496 9-893070 2 9 10-106930 .0-.03567 2 3 9-896433 58 5!l 30 6 9-789584 3 8 10.2.0416 9-893200 3 13 10-106800 10-.036.6 3 5 9-896384 54 :95 I848 10-206805 18 78 0-100951 0-105854 18 30 9 894146 24 36 30 38 9-793275 1951 10-206725 9-899.78 0-100822 0-105904 1931 9894096 30 26 30 40 42 9-793354 9-793434 2053 2156 10-206646 9-899308 20 86 21 9, 0-100692 0-J05954 2033 21 35 9-894046 9-893996 20 35 30 10-106566 9-899438 0-100502 o- 106004 26 M 9-7935'4 2259 .0-206486 9-899568 22 95 0- 100432 0-106054 2237 9-893946 Is 34 1 30 40 9-793593 236l .0-206407 9-899697 23 99 0-.00303 0-106,04 23 5S 9-893896 30 27 48 9-793673 24 64 .0-206317 9-899827 24 .04 0-100173 0-.06.54 2440 9-893846 12 33 30 50 9-793752 24 67 .0-106248 9899957 25.08 0-. 00043 0-.06205 25 41 9 893795 10 ,30 28 52 9-793832 2669 .0-106.68 9-900087 26,11 0-099913 0-106255 12643 9-S93745 g 32 30 54 9-793911 2772 .0-206089 9-900216 27 ..7 0-099784 0-106,0512745 9-893695 8 30 2tt M 9-793991 28 74 10-106009 9-900346 28 111 0-C99654 0-. 06355 2847 9 893645 4 31 30 58 9-794070 29 77 .0105930 9-900475 29.25 0-099524 0-. 06405 2948 9-893595 ■i 30 30 1* 9794150 30 80 .0-105850 9-900605 30.30 0-C99395 .0-106456 .3050 9-893544 9 iO Cosine Parte Secant CotanK. Parts Tangent Cosec. Parti Sim 'm. ' " 5r 3" '_>(.•» 1 TABLE 68 LOO. SINES. COSINES, \c. ."- 34"' :!H" '"' m. Sine Parts C08CC. Tangent Parts Cotang. Si-cant I Parts Cosine m 1" W ~ 9 794'' 50 110-205850 9-9CC605 ' 10099595 ,o,c6456 „ 19-893544 26 30 .10 1 9-794219 \"3|io-20577i 9-900735 1" 4 ,0-099265 ,0-106506 9893494 58 30 31 1 9-794308 2 5 ,0-205691 9-900864 2 9 ,0099,36 10-106556 2 3 9-893444 :6 2!) 10 7 73 ,0-097192 ,o-,o73,2 1729 9-892688 •2« 30 .39 3« 9-795575 I847 ,0-204425 9902938 18 78 ,0-097062 ,0-, 07362 18 30 9-892638 •24 21 30 38 9795654 1950 ,0-204346 9-903067 |19 82 10096933 ,0-, 07413 1932 9-892587 n 30 40_ 30 40 9-795733 2053 2155 ,0-204267 9-903,97 20 86 ,0-096803 ,0- ,07464 2034 2' 35 9-891536 •20 20 30 9-795812 ,0-204188 9 903326 21 9, ,0-096674 10-107514 9-892486 41 44 9-795891 2258 10-204,09 9-903456 22 95 ,0096544 ,0-, 07565 2237 9-892435 16 19 w m 9-795970 23 60 10-204030 9-903585 23 99 ,0-096415 ,o-,o76i5 2339 9-892385 14 30 42 48 9-796049 2463 ,0-20395, 9-9037,4 24 ,04 ,0-096286 10-107666 2440 9-891334 11 18 M 30 9-79611: 25 66 ,0-203873 9-903844 25 108 ,0-096,56 0-1077,6 2542 9-892284 10 30 43 1^2 9-796106 26 68 .°:i°3794 9-903973 26 ,,2 ,0-096027 ,o-,o7767 2644 9-892233 g 17 so 34 9-796185 2771 9-904103 27 ,,7 10-095897 o-,078,8 •2745 9892,82 30 44 50 9-796364 28 74 ,0-203636 9-904232 M ,2, >o-o9;768 o-,o7868 2847 9^892,32 4 lU 30 58 9-796443 2976 10203557 9-904362 2l> ,15 10-095638 o-,079,9 •2949 989208, 2 30 45 »% 9-796511 3079 10-203479 9-904491 30,30 10-095509 0-107970 30^0 9-892030 zs 15 tv 1 9-796600 ' 3 ,0-203400 9-904620 « 4 ,0-095380 0-108020 989,980 58 30 K.K 4 9-796679 * 5 ,0-20332, 9-904750 9 9 10-095250 0-10807, 2 3 9-891929 5IJ 14 M 9-796757 3 8 ,0-203243 9-904879 3 13 10-095,2, O- 108 ,22 3 5 9-891878 34 30 47 8 9-796836 4 10 ,0-203,64 9-905008 '• <7 10-094992 o-,o8,73 ■» 7 5^2 13 30 10 9:96914 513 9-905138 » 12 ,0094862 0-.08223 5 8 9-891777 50 30 48 n 9-796993 6 16 10-103007 9-905267 6 26 ,0-094733 o-,o8274 6 ,0 9-89,726 48 12 30 14 9-797071 7 18 ,0-202928 9-905397 7 30 ,0-094603 0-, 08325 7 12 9-891675 40 30 49 111 9-797150 821 10-202850 9-905526 8 34 ,0-094474 0-108376 8,4 989, 624 44 1 1 30 18 9-797119 913 ,0-20277, 9-905655 9 39 ,0-094345 0-108427 915 9-89,573 4-2 30 sn W 9'797307 1016 1119 ,0-20269, 9-905785 10 43 11 47 ,0-0942,5 0-108477 10,7 9-89,523 38 10 j-797386 ,0-2026,4 9-905914 ^074"^ 0.08528 11 19 9-891472 fil •24 9-797464 1231 ,0-202536 9-906043 12 52 ,0-093957 o-,o8579 1220 9-89,42, 313 9 30 to 9-797541 1334 ,0-202458 9-906171 13 56 0-093828 0-108630 13 22 9-89,370 ■H 30 52 1» 9-797611 1437 ,0-202379 9-906302 14 60 0-093698 0-10868, 1424 9-89,319 32 « 30 30 9-797699 1539 10-202301 9-906431 15 65 ,0-093569 0-108732 1525 9-89,268 30 I 30 fi3 32 9-797777 16 42 ,0^202213 9-906560 16 69 0-093440 0-108783 16 27 9-89,2,7 28 7 30 34 9-79:856 1745 ,0-202,44 9-906690 •7 73 0-0933,0 0-108834 1729 9-89,166 20 30 54 30 9-797934 I847 ,0-202066 9-906819 18 78 ,0-09318, 0-108885 •«3' 9-8911,5 24 r; 30 38 9-798012 1950 ,0-20,988 9-906948 19 82 0-093052 o-,o8936 1932 9891064 -22 30 5.'. 40 9-798091 2052 ,0-201909 ,020,831 9"907o-'7 20 86 0-092923 0-, 08987 2034 2136 9-8910,3 9-890962 20 30 ~^ *i 9-79-^169 2155 9-907207 21 9, 0-092793 0-, 09038 50 \u 9-79«H7|m 58(10-201753 9907336(22 95 0-092664 0-, 09089 2237 9-S90911 lis t ,10 j VI 9-798315 lM6o[io20i675 9-907465 23 99 0-091535 0- ,09,40 2339 9-R90860 14 311 :<7 1 w 9-798403 !44 63|io-20i597 9-907594 24 ,03 0-092406 0-109191 244, 9-890800 12 s 30, JO 9:98482 M65^io-2oi5i« 9-90-723 -ih loS 0092277 ©•,09242 2541 9-890758 10 30 sn ' 37 9-798560 26 68 '10-20 1440 9-907853 2r. ,,2 ,0-092,47 o^,09293 2644 9-8907C7 n 2 30 .M 9-798638; 27 70 .020,562 9-907982 27 ,,6 10-0920,8 0-109344 2746 9-S90656 30 5» ;3« 9-798716 is 7,110-201284 9-908,,, 128 ,2, 10091S89 0-109395 2848 9-890605 4 1 M> W 9-798-94 w 76 io-2ono6 9-908240 ,29 ,25 ,0-091760 0, 09446 2949 9-890554 2 30 60 ,3« 9-798S72 130 78|ro-2oii28 9-908369 [30 ,29 ,o-o9,6„ 0-, 09497 305, 9-890503 ::'S Co«ine iPirt«! Se.-ant Cotang. 1 Part, j Tangent | Cosfc. Parts Sine l^TT.X 51° J)^ LM- 1 816 TABLE 63 LOG. SINES. COSINES, &c. 1 ^ 3g,„ 39° o" «?• Sine j Parti Cosec. Tangent Parts 1 Cotang. Secant Parts 1 Cosine m.' ' " 9-798S7» 10-20I12S 9-908369 uo-09.63, 10-IC9+97 9-890503 "zifuF .10 2 9-798950 '"3 IO-20I05C 9-908498 1" 4 10-09.502 10-109549 1" 2 9-890+5. 58 30 1 4 9-799028 2 5 10-200972 9-90S628 2 9 .0-09,372 .0-. 09600 2 3 9-890+00 21 5!t ■jti 6 9-799>o6 3 8 .0-200894 9-908757 3 13 ,0-09,243 .0-.0965. 3 5 9-J9C3+9 54 30 2 8 9 799>«4 4 10 .O-2O0S.6 9908886 4 17 '0-09.1.4 10-. 09702 4 7 9-89029S J2 r,fi y> 10 9-799^6^ 5.3 10-200738 9-909015 5 21 ,0-090985 10-. 09753 5 9 9-S902+7 50 30 .'J '5 9"799339 6.6 10-200661 9-909144 6 26 .0-090S56 .0-.09S05 6.0 9-890.95 48 f>l 30 14 9-7994'/ 7 iS 10-200583 9-909273 7 30 10-090727 .0-.09856 7 .2 9-890,++ 40 311 4 10 9'799495 8 2. .0-200505 9 909402 8 34 .0-090598 .0-109907 8.+ 9-890093 44 .'>i; 3(1 1* 9'799573 923110-200427 9-909531 9 38 .0-090+69 10-109958 9 It 9-8900+2 42 30 5 io 9-799651 10 26 11 28 .0-200349 9-909660 10 43 11 +7 .0-090340 10 1; 1119 9-889990 40 5.". 22 9-799728 10-200272 9 909789 10090211 10-. .og6. 9-889939 (i n 9-7998°6 123,1.0-200194 9-9099.8 12 52 10-C90082 10-1 10112 9-889888 30 54 30 20 9-799884 l;!33!io-2ooii6 9-910048 13 56 ■0-089952 ;°;;;°'64 1322 9-889S36 34 30 7 28 9-799961 14 30|io-2ooo38 9-910177 14 60 10-089S23 14 2+ 9-889785 32 53 30 9-800039 15381,0-199961 9-9,05(6 15 64 10-0S9694 Io-IIo266 15 26 9-88973+ 30 30 a n 9-800117 164.1,0-199883 9-9.0435 16 69 10-089565 10-110318 1627 9-8S9682 23 52 30 IJ 9-800195 1744 .0-199805 9-9.0,64 17 73 J°;o89-436 ,0-110369 1729 9-SS963. 20 30 « 30 9-800272 18 47 IO-.99728 9-9.0693 18 77 10-.. 0421 183. 9-S89579 24 51 30 38 9-8C0350 1950 10-. 99650 9-9.0822 19 82 I0-089J78 10-110472 1932 9-889528 •22 30 \0 40 9-800427 2052 2155 . 0-195 j73 9-9,095, 20 86 21 90 ■0-089049 10-110523 2034 21 36 9-889+77 20 5(1 4-2 9-800505 .0-. 99495 9-911080 10-088920 10-1.0575 9-889+25 11 u 9-800582 2257 10-1994.8 9-9. .209 ■22 95 10-088791 .o-.,o626 22 38 9-88937+ 10 4y 30 4(i 9-800660 2;( 00 .0-199340 99. .338 -23 99 10-0S8662 10-110678 2339 12 18 9-»oo737 2462 .0-199263 9-911467 24 ,03 10-0SS533 10-1,0729 244, 9-88927, 12 4« 30 9-S00815 2565 .0-199.85 9-911596 ■25 107 10-088404 10-1,078, 2543 9-8892,9 10 ■i' 13 2 9-800892 2667 9-91,725 -26 ,.2 ,0-088275 10-..0832 2644 9-889,68 f, 47 30 4 9-800969 2770 .0-.9903. 9-91.853 27 1.6 in-088147 ,o-,,o8S4 2746 9-8891,6 6 30 U (i 9801047 2873 10-.9S953 9-911982 28 ,20 10-088018 ,0-1,0936 2848 9-S8906+ 4 4t> 30 8 9-801.24 2975 10-198876 9-912111 29 ,25 10-0878S9 .0-110987 2950 9-8890,3 30 )5 a 7 9-S01201 30 7X 10-198799 9-912240 30,29 10-087760 10-U1039 305, 9-8S896, 23 45 •2 9-801279 "TT ,0-. 98721 9-9.2369 10-0S763. 10-1.1090 I J 9-8889,0 58-i;r| 16 4 9-801356 2 5 .0-1986+4 9-912498 3 9 10-087502 .0-1.11+2 2 3 9-888858 56 44 6 9-801433 3 8 10-.9S567 9-9.2627 3 ,3 10-087373 io-,i,,94 3 5 9-888806 30 17 S 9-801511 4.0 10-19S489 9-912756 4 ,7 10-087244 10-1.1245 ♦ 7 9888755 52 43 9-801588 513I10-198412 9-9.2885 5 2, 10087. .5 .0-1.1297 5 9 9-8S8703 50 30 l» 2 9-S0.66S 6,5 10-19S335 9-913014 6 26 ,0-086986 10-11.349 6,0 9-88865, 48 42 30 4 9-801742 7i8 9-913.43 7 30 10-086857 .0-111400 7 ,2 9-8S8600 4U 30 19 8 9-S01819 821 10-198181 9-9.3271 8 34 10-086729 .0-111452 8 ,4 9-S885+8 44 41 30 8 9-801896 923 10-.98104 9-9.3400 9 39 10-086600 10-11 1504 9.6 9-S88+96 42 20 • 30 2 9-801973 10 26 11 28 .0-. 98027 9-9.3529 10 43 11 47 10-086471 .0-111556 10.7 11 19 9-888+++ 9-888393 40 40 2 9-802051 10-197949 9-913658 .0-086342 10-111607 21 • 4 9-802118 123. 10-197872 9-9.3787 2 5, 10-086213 lo-, 11659 122. 9-8883+, 30 31." 30 1 6 9-802205 1333 10-197795 9-9139.6 13 56 10-086084 13 22 9-88S289 34 ■22 -i s 9-802282 1436 10-197718 9-914044 14 60 .0-0S5956 io-M,763 14 24 9888237 32 3(t 30 3 9-802359 1538 10-197641 9-9.4173 5 64 .0-085827 ,o-i,.8,5 15 26 9-888,85 30 30 2:t 3 2 9-802436 I641 .0-197564 9-914302 6 69 .0-0S5698 ,o-,,,S66 16 28 9-888,3+ -28 37 30 3 4 9-802512 1743 10-.974S8 9-9.4431 7 73 .0-085569 ,o-,,,9,8 1729 9-88S082 28 30 24 3 9-802589 1 8 46 10-. 97411 9-914560 » 77 10-0854+0 ,o-,..97o I83, 9888030 24 36- 30 3 3 9-802666 1948 10-197334 9-91468S 9 82 10-0853.2 1933 9-88797S 22 30 2,5 4 30 4 9-802743 205, 2154 10-197257 9-914817 20 86 21 90 .0-085183 0-1.2074 2035 21 36 9-887926 20 1 X, 1 2 9-802820 10-197180 9-9.4946 10-08505+ 0-112126 ^-88787+ 18 30 2t; • 4 9-802897 •22 57 .0-197.03 9-915075 22 94 10-08+925 0-U2178 22 38 9-8S7822 16 34 30 4 6 9-802974 2359 .0-197026 9-915203 23 99 0-084797 0-1.2230 23 +0 ^-887770 14 30 27 4 8 9-803050 24 62 .0-. 96950 9-915332 24 .03 0-0S4668 O-T 12282 2442 J-8877.8 12 33 30 5 9-803127 25 64 0-196S73 9-915+61 25 ,07 00S4539 0-112334 25+3 ?-S87666 10 1 30 2fi 5 2 9-803204 20 67 0-196796 9915590 6 ,,2 00844.0 o-,,2386 26+5 ,•8876,4 «l 32 30 5 4 9-80318. 2769 0-.967.9 9-9,5718 7 ..6 00S+2S1 0-11243S 27+7 -887562 30 2!» 5 li 9-803357 2872 0-196643 9-915847 8 ,20 0-08+153 0-1.2490 28+8 -887510 31 30 5 9 9-803434 2974 0-196566 9-915976 9 .24 0-0S+02+ 0-..2542 2950 -S87458 3(1 :ti) 3 3 9-803511 30 77 0-.96489 9-916.04 .29 0-083896 0-, 12594 so 51 ■8S7406 30 i] CosiQe ParU Secant Cota,.,. Purts Tangent Coscc. Parts Sine ^ '" .00'^ 3h ^>o,. J T.ARij- ns 817 LOG. SINES, COSINES, &c. li" ;j8'' 39^ _ZI" Sine i Parts Cosec. T«„gent Partj j;ctang. 1 Se,.a„t IPon. Cosine m. 30 M) „ Q-S0351I 1 10-796489 9-916,04 10 083S96 0-112594 9-8874cb 22 M •2 9^So3 587 1"3 10-1964,3 9-916233 1" 4 ,0 083767 0-, ,2646 \" 2 9-887354 .',s 311 n 4 9^Sc^664 1 a 5 10-196336 9-916362 2 9 10 °83638 0-112698 2 3 9-887302 M •.;9 30 ti 9'8o574o 1 3 8 10-196260 9-916491 S ,3 10 0-112750 3 5 9-887250 H 30 32 H 9-803817 ! 4io 10-196183 9-916619 ■• >7 10 08338° CI-1I2S02 •• 7 9-887,98 rn 28 ao 10 9'8o3g93 513 10-196107 9-916748 5 2, 10 083252 0-112854 5 9 9-887,46 00 30 33 1-2 9-803970 6,5 10-196030 9-916877 6 26 10 083123 0-112907 6,0 9-887093 4S -.27 30 H 9^So4046 718 10-195954 9-917005 7 30 ,0 0S2995 0-112959 7 ,2 9-88704, 40 30 34 10 980+113 820 10-195877 9-917134 8 34 ,0 082866 8 14 9-886989 J4 -.'(i 30 IK 9SC4199 923 ,0,9580, 9-9'7262 9 39 ,0 082738 0-1,3063 916 9-886937 42 30 :ij •20 9^8o4276 1025 ,0-195724 9 9'739> 10 43 11 47 ,0 082609 0-113, ,5 1017 11 19 9-886885 3S 25 9-804352 10-195648 9-917520 ,0 0824S0 0-1,3,68 9-886832 36 ■n 9-804428 1230 ,0-195572 9-917648 12 5, ,0 082352 0-1,3220 122, 9-886780 3(i 24 30 •211 9-804505 1333 ,0-195495 9-917777 13 56 ,0 082223 1 0-113272 1323 9-886728 34 30 37 •2.M 9-804581 1435 ,0-195419 9-917906 14 60 ,0 082094 1 0-113324 14 24 9-886676 3'2 23 30 30 9-S04657 1538 ,o-, 95343 9-918034 15 64 ,0 081966 0-113377 1526 9-886623 30 30 38 3^2 9-804734 lfi40 ,0195266 9-918163 16 69 10 081S37 1 0-113429 1628 9-88657, ■2H 22 30 9-804810 1743 10-195190 9-91S291 17 73 JO 08,709 1 0-113481 1730 9-8865,9 ■20 30 39 9-S04886 18 46 ,o-,95i,4 9-91S420 18 77 JO 081580 1 0-113534 1831 9-886466 ■21 21 30 3'i 9-S0496Z 1948 ,o-, 95038 9-918548 19 81 ,0 08,452 1 0-113586 1933 9-8864,4 ■22 30 4(l_ 40 4-2 9-805039 205, 2153 ,o-,9496. 9-9,8677 20 i„ 21 90 IZ 08,323 , O-.I363S 2035 2137 9-886362 ■20 20 9-805115 ,0-, 94885 9-9,8805 08,195 ' 0-113691 9-886309 41 44 9-805 191 2256 ,0-194809 9-9,8934 22 94 ,0 081066 1 0-1137.53 2238 9-886257 Hi 19 311 4« 9-805267 2358 ,0-194733 9-9,9063 23 99 ,0 0S0937 1 0-113796 2340 9-8S6204 14 30 42 4S 9-805343 2461 10-194657 9-9,9,9, 24 .03 10 080809 I O-I13S48 2442 9-886,52 12 18 30 ,',0 9-805419 25 63 10-194581 9-9,9320 25 107 10 0806S0 1 0-113901 2544 9S86099 10 30 43 '1-2 9-805495 26 66 ,0-194505 9-919448 26 111 ,0 0S0552 I 0-1,3953 26 4 5 9-886047 H 17 30 54 9-805571 27 68 0-194429 9-9'9577 27 I Hi IC 0S0423 1 0-, 14005 2747 9-8S5995) 30 44 5G 9-805647 2871 0-194353 9-919705 28 120 10 0S0295 1 0-114058 9-885942 •1 l(i 30 .'iS 9-S05723 2973 0-194277 9-919834 29 124 ,0 080166 1 0-114110 2950 9-885890 2 ].?" 45_ 39 9805799 3076 0-19420, 9-919962 30 ,29 ,0 080038 1 0-I14I63 30 52 9-885837 ai 9-805875 1 3 0-194125 9-92009, ' 4 To 079909 1 o-l ,42,6 1 2 9-885784 46 4 9-805951 « 5 194049 9-920219 « 9 10 079781 I o-i 14268 2 4 9-885732 .Vi 14 30 fi 9-806027 3 8 0-193973 9-920348 3 .3 10 079652 1 0-1,432, 3 5 9-885679 54 30 47 S 9-806103 4 10 0-193897 9-920476 ♦ '7 10 079524 I 0-II4373 9-885627 5-2 13 30 10 9-806.79 513 0-193821 9-920604 5 21 10 079396 1 0-..4426 5 ; 9-885574 50 30 48 VI 9-806254 6.5 0-.93746 9-920733 6 26 10 079267 1 0-114478 6 11 9-885522 t " ' 30 M 9-806330 7,8 o-,93670 9 920861 7 30 10 079139 , 0-114531 7 12 9-885469 30 4!l lU 9-806406 820 0-193594 9-9^0990 8 34 10 079010 1 0-114584 814 9-8854,6 14 1 1 30 l« 9806482 923 0-193518 9-921118 9 39 10 078882 r 0-114636 916 9-885364 Vi 30 no_-io 9-806557 1025 1128 0-, 93443 9-921247 10 43 11 47 10 078751 r 0-114689 1018 9-8853,, .10 10 30 ■2-2 9-806633 0-, 93367 9-92,375 To" 078625 1 0-1,4742 9-S85258 ul ■24 9-806709 1230 0-193291 9-921503 12 51 ,0 078497 I 0-114795 1221 9-SS5205 30 9 30 •2Ci 9-806785 1333 0-193215 9-921632 13 55 ,0 078368 , 0-114847 1323 9-885,53 ■H 30 .'.•.• •2K 9-806860 1435 0-193140 9-92,760 14 60 ,0 078240 , 0-114900 1425 9-885,00 .12 a 30 30 9-806936 1538 0-193064 9-92,889 15 64 ,0 078,1, , o- 114953 15 26 9-885047 30 30 r.3 3-2 9-8070,, 16 40 0-192989 9-9220,7 16 68 ,0 077983 1 0-115006 1628 9-S84994 •2S 7 30 31 9807087 1743 0-192913 9-922,45 17 73 ,0 077855 ■ 0-115058 1730 9-884942 •211 30 .'.4 :«i 9-807,63 I845 0-192837 9-922274 18 77 ,0 077726 1 0-115,,, 18 32 9-SS4889 ■21 30 38 9-807238 1948 0-192762 9-922402 |19 8, ,0 077598 , 0-1,5,64 1933 9-SS4836 Tl 30 30 1» 9-807314 2050 2153 0-192686 9-922530 20 86 21 90 ,0 077470 I o-,,52i7 2035 2137 9-884783 •20 r. 9807389 0-19261 1 9-922659 To" 077341 1 0-115270 9-884730 :,r, 41 9807465 2255 0-192535 9-922787 22 94 ,0 0772,3 , 0-1,5323 2239 9-884677 111 4 30 40 9-807540 2358 10-192460 9-922915 23 98 ,0 0770S5 , 0-115375 2340 9884625 14 .10 .'.V 9-8076,5 24 60 10-192385 9-923044 24 103 ,0 076956 , 01,5428 2442 9-884572 P2 3 30 y 80769, 25 63 ,0-192309 9-923172 25 107 ,0 076828 , o-,,548. «44 9-884519 10 30 :.8 9-807766 26 6, ,0-, 92234 9-923300 26 111 ,0 076700. 0-115534 2646 9-884466 , 2 30 9-80784^ 27 68 ■0-192158 9-923429 27 116 ,0 076571 ■ 0-115587 2748 9-884413 11 30 .i!) 9-807917 2870 .0-192083 9-923557 28 120 10 076443 0-115640 2849 9-884360 4 1 30 .'iK 9-80799* 2973 10-192003 9-923685 29 124 ,0 076315 0-1,5693 295. 9-884307 2 .30 lil) «0 9-808067 3076 ,0-19,933 9-9238,4 30 128 ,0-076,86 0-115746 3053 9884254 ' "l" Comne Port, Sc-nnt Cotanj;. Parts Tange7,t" " CoM-c~. Parts Si„e m. TTi 50'^ :\" i>0'" 1 ei8 FABLK 68 LOG. SINES, COSINES, &c. n 21. 40'" 40° '" ?• Sine P.^ _Cose<,J Tangent Part^ Cotang. Secant Parts! Cosine »7^' ^ 9-8o«o67 191933 9-923814 ,0-076,86 10 .,5746 J9-884254 20I (.-0 3CI i 9-808143 «"3 19,857 9-923942 4 ,0-076058 10 ■'5799 1" 2 9-88420. 58 1 30 1 9-8oS2i8 2 5 ,0 ,91782 9-924070 9 ,0-075930 10 ,.5852 2 4 9-S84.48 50 ."i!! .'III « 9-808293 3 8 10 ,91707 9-924.98 >; ,0-075802 .0 ,.5905 3 5 9-884095 54 30 2 9-808368 4 10 10 191632 9-924327 ,0-075673 .0 ..5958 4 7 9-8S4042 5-2 5)i 31 10 9-S0S++4 513 10 ,91556 9-9^4455 21 ,0-075545 .& . .60.. S 9 9 883989 50 30 .■» ,. 9-808,. 9 615 10 .9,48, 9-9245S3 261,0-0754,7 .0 116064 6.. 9-883936 48 57 30 N 9-8o8«4 7,8 10 191406 9-924711 30 .0-0752S9 10 .,6,17 7 12 9-883883 4I> 30 4 9-808669 820 10 ,9133, 9-924840 34 .0-075.60 JO 1 1617. 8.4 9-883829 41 Sli 18 9-808744 923 .5.256 9-924968 38 .0-075032 ro ■.■.^27.^ 9.6 9-883776 42 30 5 •20 9-S08S.9 9-808S94 1025 1128 10 ,9.1s. 9-925096 43 .0-074904 .0 ..6277 1018 9-88372, 40 55 30 To" ,91,06 9-925224 10-074776 10" 1.6330 1119 9-883670 (> u 9-S08969 12 30 ,9,03. 9-925352 5' 10-074648 ,.6383 122. 9-8836.7 3(1 54 30 ■Ui 9 809044 1333 ,0 .90956 9-92548. 56 .0-0745.9 ,0 .,6436 1323 9-883564 34 30 1 7 ■2M 9-S09119 U35 10 190881 9-925609 60 .007439. 10 ..6490 1425 9-8835.0 3-2 53 1 30 9-S09194 15 38 10 190S06 9-9^5737 64 .0-074263 ..6543 15 27 9-883457 30 3( a n 9-809269 16 40 .9073. 9-925865 68 .0-074.35 ,.6596 1628 9883404 -28 52 30 M 9-S09344 1743 ,c 190656 9-925993 73 .0-074007 ,.6649 1730 9-88335. -20 30 9 3ti 9-809419 I845 10 190581 9-926.22 77 .0-073878 .0 116703 18 32 9-883297 -24 51 .10 34 9-809494 1948 10 .90506 9-926250 8, 10-073750 .0 116756 1934 9-883244 -2-2 30 10 Vt 9-809,69 2050 10 '9°43' 9-926378 1-20 85 ,0-073622 10 ,16809 •2035 9-883,9. -20 50 ^w 4-2 9-809643 2153 To" '9°357 9-926506 21 90 ,0-073494 10 H6S63 2137 9-883.37 18 ~3i7 1 1 44 9-S09718 2255 ,0 .90282 9-926634 J2 94 .0-073366 .0 ,169,6 22 39 9-883084 16 4!) 30 40 9-809793 2358 ,0 .90207 9-926762 23 98 ,0-073238 .0 ,16969 2341 9;88303' 14 30 12 48 9-809868 2460 ,0 .90.32 9-926890 24 102 10-073. 'o .0 ..7023 2442 1-2 4« 30 50 9-809943 2563 10 190057 9-9270.9 M 107 10-07298, 10 .,7076 2544 9 882924 10 311 13 5-2 9-8,00,7 2665 ,0 .89983 9-927147 26 ... .0-072853 10 ,17,29 2646 9-88287. 8 47 3U 54 9-810092 27 6S 10 ,89908 9-927275 27 "5 10-072725 .0 ,,7,83 2748 9-8828,7 tj 30 14 ..« 9-810167 2870 ,0 .89833 9-927403 M 120 10-072597 .0 ,,7236 28 50 9-SS2764 4 46 i8 9-8,024, 29 73 10 .89759 9-927531 29 124 10-072469 ,17290 2951 9-8827.0 -2 15 «1 9-8103,6 30 75 10 189684 9-927659 SO ■ 28 10-07134" .0 "7343 3053 9-882657 xa 45 30 9-810390 I 2 ,0 .89610 9-9^7'87 T" 4 .0-072213 To ■■7397 9-882603 lli 4 9-810465 2 5 ,0 ■89535 9-027915 2 9 .0-072085 .0 ..7450 2 4 9-S82550 .56 44 30 « 9-8,0540 3 7 ,0 .89460 9-928043 3 '3 .0-07.957 .0 1.7504 3 5 9-S82496 54 30 17 g 9-8,0614 4 10 10 .89386 9-9.- 8. 7 1 ♦ .7 .0-07.829 .0 "7557 4 7 9-882443 .5-2 43 30 10 9-810689 5 12 ,0 .893.. 9-928.-99 5 21 ,0-07,70. .0 ..76.. 5 9 9-882389 .50 30 18 1-2 9-8,0763 6.5 ,0 .89237 9-9^84^7 6 26 .0-07.573 .0 ..7664 61. 9-882336 48 42 30 14 9-8,0838 7,7 ,0 .89. 62 9-928555 7 30 .0-07.445 .0 "77'8 713 9-882282 40 30 19 lU 9-810912 10 .89088 9-9286S4 8 34 10 ..777. 814 9-882229 44 41 30 18 9-8.0986 922 ,0 .89014 9-9288.2 8 38 10-07.. 88 .0 1,7825 9 16 9-8S2175 4-2 30 20 •20 9-8., 061 9-8,1,35 1025 1127 ,0 ,88939 9-928940 10 11 43 47 .0-07.060 10 ,,7879 10 18 11 20 9-S82.2. 40 40 ,0 ,88865 9-929068 .0-070932 To ..7932 9-882068 21 24 1230 ,0 ,88790 9-929.96 12 5- 10-070804 .0 ..79S6 122. 9-8820.4 Mi 39 30 •2>) 9-8,, 284 1332 ,0 ,88716 9-929324 13 55 .0-070676 10 ..8040 13 23 9-8S.960 31 30 22 ■28 9-8. .35S 1435 ,0 .88642 9 929452 14 60 .0-070548 .0 ..S093 1425 9-8S.907 3-2 3H 30 30 9-81,433 1537 10 .88567 9-929580 15 64 ic-070420 10 ..8.47 15 27 9-88.853 30 311 23 32 981 150-7 1 6 40 10 .88493 9-929708 16 68 10-070292 .0 ..820. I629 9-88.799 -28 ■'L 311 34 9-8,158, 1741 10 .S84.9 9-929836 17 73 ,0-070,64 .0 .,8254 1730 9-88.746 -20 24 JO 9-81,655 I845 ,0 .8834; 9929964 18 77 ,0-070036 10 ..8308 18 32 9-88,692 -24 3(i 30 38 9-8. 1730 1947 ,0 .88Z70 9-930092 19 8. 10069908 .0 ..8362 1934 9-88,638 •ti 30 25 30 40 9-S..804 2050 2152 10 .88.96 9-930220 20 21 85 90 10-0697S0 .0 ..84.6 2036 2138 9-8S1584 ■20 :f5 -1^ 9-8.1878 To .88.22 9-930348 ,0-069652 .^ ..S470 9-88,530 2« 44 9-811952 2255 10 188048 9-930475 22 94 .0-069525 .0 "8 5^3 ■22 39 9-88.477 III :<4 30 46 9 8.2026 •2357 ,0 ,87974 9-930603 23 98 .0-069397 .0 "8577 234, 9-88.423 14 27 48 9-8 12, 00 2460 10 ,87900 9-93073. 24 .0-069269 .0 ..863. -2443 9-88.369 1-2 33 30 50 <, 8,2.74 ■2562 10 ,87826 9-930859 25 .07 10-069.4. .0 ..86S5 2545 9-88,3.5 10 30 2« .5-2 9-812248 2665 10 ,8775^- 9-930987 26 ... .0-0690.3 .0 "8739 26 47 9-8S.26. s 32 30 54 9-812322 2767 10 ,87678 9-93.1,5 27 "5 .0-068885 .0 "S793 2748 9-88.207 30 29 50 9-812396 28 70 ,0 187604 9-931243 28 ..9 .0-068757 ,0 ..8S47 2850 9-88. .53 4 31 .30 58 9-8.2470 2972 10 18753° 9-931371 29 •24 ,0-068629 ,0 11890. 29 5^ 9-88. 099 •i 30 :io 42 9-812544 30 74 io-,874';6 9-93,499 j30 128 .0-06850. .0-..8954 3054 9-881046 30 '" •? Cosine Parts Secunt Cotang. 1 Parts Tangent Cosec. Parts j Si.ie ^Pl 49° ;}" 11 _J TAIU.F. (18 819 LOG. SINES, COSINES, &<:. | •jx 42'" 40" 1 '"Im 1 ■• Sine l'a.-t»| Cose.-. Tai.ge.it I'hi-Us I CoUllj;. Secant I'aits Cnsine m 18 :m 3.. 1 9^!ii2544 10-.S7456 9-931499 .0-06850, .0-1.8954 19-881046 30 -i 9-812618 l"2 .0-. 87382 9-93.627 '" 4 .0-068373 ■0-1.9008 1"2 9-880992 .')» 30 31 4 9-81:692 2 5 .0-. 87308 9'93>755 2 9 10-068245 .0-1.9062 2 4 9-8S0938 .'.11 21) 30| U 9-812766 3 7 IO-. 87234 9-9318S3 3 13 .0-068.17 10-1.9. .61 3 5 9-880884 .'i-l 30 32 8 9-812840 4 .0 10. 87160 9-932010 4 17 10-C67990 ■0-119170' 4 7 9-880830 .'12 2H 30 in 9-812914 5 12 .0-1S70S6 9-932138 5 2. 10-067862 ,o-,.9224 5 9 9-880776 .'»■ 311 33 1-2 9-812988 615 10-187012 9-932266 6 26 10-067734 ■0-..9278 611 9-880722 18 •-•7 30 n 9-813062 7 17 .0-.S693S 9-932394 7 3° .0-067606 ■0-1,9333 7 .3 9-880667 10 30 34 IB 9-813135 820 .0-186865 9932522 8 34 .0-067478 .o-.,9387 8 14 9-8806,3 11 -J(.- 30 13 9-813209 9 22 .0.8679. 9-932650 9 38 .0-067350 ■0-..944. 9.6 9-880559 1-2 30 35 30 !" 9-813783 1024 1127 .0-. 86717 9-932778 10 43 11 47 .0-067222 ,0-. 19495 10.8 9-880505 38 2.-, 9'8i3i57 .0-. 86643 9-932906 .0-067094 .01. 9549 11 20 9-880451 M ■n 9813430 1229 .0-.S6570 9'933033 12 51 10-066967 .0-1,9603 1222 9-880397 30 24 10 ■20 9813504 1.332 10-1S6496 9-933.61 13 55 .0-066839 .0-1,9657 13 24 9-880343 31 30 37 ■28 9-813578 ,434 10-186422 9-933289 14 60 .0-0667.. .o-,,97,. 1425 9-880289 32 23 30 30 9-8,3651 1537 .0-.S6349 9-9334'7 IS 64 .0-066583 ,o-..9766 15 27 9-880234 30 30 3R 32 9-813725 16 39 10-186275 9-933H5 16 68 .0-066455 ■o-,,9820 16 29 9-S-8o,8o 23 22 30 3J 9-813799 1742 .0-18620. 9-933672 17 72 .0-066328 .0-1.9874 1731 9-880,26 ■10 30 3!) 3« 9-813872 IS 44 .0-.86.28 9-933800 18 77 .0-066200 ,0-119928 I832 9-880072 U 30 3« 9-813946 1947 .0-. 86054 9-933928 19 8. 10-066072 10-. 19982 1934 9-8SC018 -2-2 30 4U W 42 9-814019 2049 21 5. .0-18598. 9-934056 20 85 21 89 10-065944 .0-. 20037 2036 2138 9-879963 -20 2(» 30 9-814093 10-185907 9-934184 .0-0658.6 .0-.2009. 9-879909 41" 41 9-814166 2254 lo^. 85834 9-9343.1 22 q4 .0-065689 10-120145 2240 9-879855 10 1:1 30 4e 9-814240 2.-) 56 .0-185760 9'934439 23 98 10-06556. ■ o- 120200 2342 9-87980. 11 30 12 49 9-814313 2459 .0-.S5687 9-934567 24 .C2 .0-065433 10-. 20254 24 43 9-879746 1-2 Itl M 50 9-814387 25 6. .0-185613 9-934695 25 .06 10-065305 .0-120308 2545 9-879692 10 30 43 52 9-814460 2664 .0-. 85540 9-934821 86 11. .0-065178 10-120363 2647 9-879637 H 17 30 51 9-814533 27 66 .0-185467 9-934950 ■n 115 10-065050 IO-. 20417 2749 9-879583 ti .30 44 riii 9-814607 2869 .0-185,393 9-935078 28 ..9 .0-064922 .0-.2047. 2851 9-879529 4 l(i .10 3r, 44 9-8.636. 2254 .0-183639 9-938.42 22 94 10-061858 .o-,2,78i 2240 9-8782,9 10 30 i« 9-8.6434 2356 .0-.S3566 9-938270 23 98 .0-06.730 10-12.836 2342 9-878,64 14 3U 57 48 9-8.6507 2458 IO-. 83493 9-938398 24 102 :o-o6i6o2 .0-12189. 2444 9878,09 12 3 50 9-8.6579 256. .0-18342. 9-938525 25 106 .0-06.475 10-121946 2546 9-S78054 10 30 58 52 9-8.6652 2663 10. 83348 9-938653 28 111 10-06.347 .0-.2200. 2647 9-877999 H 2 30 51 9-8.6725 27 66 .0-183275 9-938780 27 115 .0-06.220 .C-122055 2749 9-877945 f 30 5<» 5« 9-8.6798 28 68 .O^l83202 9-938908 28 ..9 .0-06.092 .0-122I.O 285. 9-877890 4 1 30 M 9-8.6870 2970 .0.83.30 9-939035 29 .23 .0-060965 .O-.22.65 2953 9-877835 •2 30 m M 9-8.6943 3023 .©■i83057 9-939.63 30^£28 10-060837 .0-.22220 3055 9-877-, So TIT m. Co«;.>e Part- .Srriiiit Cotang. Parts Tangent Co,ee. Parts Sine ^ 77; 49° ah Ki'" 1 TABLR 68 LOG. SINES, COSINES, &.-. 2h 44.n 4lo IT ? Sine I'arts Cosec. Tangent I'arts | Cotang. Secant Parts 1 Cosine in. (id 9-816943 10-183057 9-939,63 10-060S37 ,0-, 22220 9-87-780 16 M i 9-817016 l"2 IO-1S29S4 9-93929, 1" 4 .0-060709 10- 122275 1" 2 9-87-, 7^5 51 30 1 4 9-Si7oS8 2 5 10-1829,2 9-93941812 8 10-0605S2 ,0-122330 2 4 9-877670 5i; .in 30 C 9-8.7.61 3 7 10-182839 9-939S46 1 3 13 .0-060454 ,0-122385 3 5 9-877615 04 2 8 9 ^T-n 4 10 10-182767 9-9:!';673 4 17 10-060327 10-122440 4 7 9-877560 5-2 s» 30 10 9-8.7306 5 12 10-182694 9-939S01 f. 21 .0-060199 to-122495 5 9 9-877505 50 311 3 12 9-8.7379 fi ,4l>0-lS2621 9-93992S « ^5 10-060072 10-122550 6,, 9-877450 4S ■^7 30 IJ 9-8.7451 7 17 ,0-182549 9-94C056 7 30 10-059944 10-122605 7.3 9-877395 111 30 < l(J 9-8.7514 8.9 ,0-182476 9-940183 8 34 10-059S17 10-1:2660 815 9-877340 44 5(; 30 IH 9-8.7596 9 22 ,0-182404 9-940311 9 38 10-059689 ,0-1227,5 916 9-8772S5 4 2 30 5 ■20 9-817668 10 24 10-182332 9-940439 iO 42 10-059561 10-122770 10 18 9-87723C 40 5j 30 2-2 9-8.774. 1127 ,0-182259 9-940566 11 47 ,0-059434 ,0-122825 11 20 9-877.75 :i8 ~io 6 ■n 9-S.78.3 1229 io-,82,87 9-940694 12 51 ,0-059306 10-122880 12 22 9-877,20 3(j 54 30 26 9-8.7886 1332 ,o-,82,i4 9-940821 .3 55 10-059179 10-122935 13 24 9-877065 31 7 US 9-8.7958 1434 10-182042 9-940949 14 59 ,0-05905, 10-122990 14 26 9-877010 3-2 D-i 30 30 9-818030 .536 .o-,Si97o 9-94.076 15 64 ,0-058924 IO-, 23046 15 27 9-876954 30 311 8 3'2 9-818.03 16 39 10-18,897 9-941204 16 68 10-058796 ,0-, 23101 1629 9-876899 -2» 52 30 34 9-8.8,75 1741 io-,SiS25 9-941331 17 7 = 10-058669 ;o;;^3.56 173, 9-876844 -26 3(1 !) 30 9-818247 I843 10-181753 9-941459 18 76 10-058541 1833 9-876789 •24 51 30 38 9-818320 1946 ,0-18:680 9-941586 19 Si 10-058414 10-123266 1935 9-876734 -2-2 30 10 40 9-81830, 20 48 215, 10-, 81608 9-941713 20 85 21 89 ,0-058287 10-123322 2037 2138 9-876678 18 50 9-818464 10-181536 9-94184, 10-058159 10-123377 9-876623 II 44 9-818536 225, 10-181464 9-94,968 22 93 .0-058032 10-123432 2240 9-876568 Hi 4!) 30 4li 9-8.8609 23 5* >o-,S,39, 9-942096 23 98 10-057904 .0-123487 2342 9-876513 14 30 12 4» 9-8.8681 2458 10-181319 9-942223 24 ,02 10-057777 10-123543 2444 9-876457 1-2 4H 30 50 9-818753 356, 10-18,247 994235, 25 106 10057649 10-.23598 2546 9-876402 10 30 13 5-2 9-S18825 2«63 .o-,8,,75 9-942478 26 1,0 10-057522 ,0-123653 2648 9-S76347 8 47 30 54 9-818897 2765 .o-,8,,03 9-942606 27 ,,5 10-057394 ,0-, 23709 2749 9-876291 6 U 50 9-8.8969 28 68 10-18103, 9-942733 28 .,9 10-057267 ,o-,23764 28;, 9-S76236 4 4C 3(1 5S 9-8. 904. 2970 ,0-, 80959 9-94286, 29 123 •0-057,39 10-123819 2953 9-S-61SJ •2 3,1 10 AS 9-819113 30 72 10-180SS7 9-941988 .30 127 0-057012 10-123875 305519-876125 IS 5S 45 9-819185 1 2 ,0-1808,5 9-943115 • 4 0-056S85 10-, 23930 1 2 9-876070 IG 4 9-S19257 » 5 >o-, 80743 9-943H3 2 8 0-056757 ,o-.239S6 2 4 9-S76014 .)(i 44 30 9-819329 3 7 io->8o67i 9"943370 3 ,3 0-056630 .0-124041 3 6 9-875959 54 31 17 B 9-819401 4 ,0 10-180599 9-943498 4 17 0-056502 10-124096 4 •> 9-875904 0^2 43 30 9-8.9473 6,2 .o-,8o527 9-943625 0-056375 10-124152 5 9 9-S7584S 50 3 1 111 9-819545 614 10-180455 9-94375» 6 25 0-056248 10-124207 6,1 9-875793 48 42 30 14 9-819617 7 17 ,o-,8o38; 9-943880 7 30 0-056120 ,0-124263 713 9-875737 40 30 10 10 9S19689 8,9 ,o-,8o3,. 9-944007 8 34 0-055993 8,5 9S756S2 44 41 30 Id 9-8.976. 922 IO-, 80239 9'944i35 9 38 0-055865 10-124374 9-875626 42 30 20 ■20 9-S19832 1024 ,o-,So,68 9-944262 10 42 0-055738 10-124429 10 ,9 9-87557. 40 40 30 ■22 9-8.9904 1116 ,0-180096 9-9443S9 11 47 0-055611 0-124485 11 20 9-875515 38 30 21 '24 9-819976 U19 ,0-180024 9'9445'7 12 5. 0-055483 0-12454, 1222 9-S75459 3li 3!) 30 ■2ti 9-820048 1331 10-179952 9-944644 13 55 0-055356 0-124596 13 24 9-875404 34 30 22 ■28 9-Szo,20 1*34 10-179880 9'94477. 14 59 0-055229 0-124652 14 26 9875348 3-2 38 30 30 9-820,9, 1536 10-179809 9-944899 15 64 0-05510J 0-124707 15 28 9-875293 30 30 23 3^2 9-820263 16 38 ,0-179737 9-945026 6 68 0-054974 0-124763 16 30 9-875237 •28 37 30 31 9-820335 174" lo-, 79665 9-945.53 7 7'- 0-054847 0-124819 173. 9-S75.S1 211 30 >4 3lj 9-820406 I843 io-i7<;594 9-94528. 8 76 0-054719 0-124874 18 33 9-S75126 ■24 3G 30 3S 9-820478 1946 IO-I79J22 9-945408 9 8, 0-054592 0-124930 1935 9-875070 ■22 30 25 40 9-820550 2048 2,50 ,0- ,79450 9-945535 20 85 0-054465 0-124986 2037 21 39 9-875014 ■20 IS 35 30 9-82062. 10-179379 9-945663 21 89 0-054337 0-125042 9-874958 26 44 9-820693 2253 IO-, 79307 9-945790 22 93 0-054210 0-125097 2241 9-874903 lU :i4 .10 40 9-820764 23 c: 10-179236 9-9459.7 23 98 0-054083 0-125153 2343 9-874847 14 311 27 4S 9-820836 2457 10-179,64 9-946045 24 ,02 0-053955 0-125209 2445 9-874791 1-2 3;i 30 SO 9-820907 25 60 10-179093 9-946172 25 ,06 0-053828 0-125265 2546 9-874735 10 30 28 52 9-S20979 2662 10-17902, 9-946299 26 1,0 0-053701 0-125320 2648 9-874680 S 32 30 54 9-82,050 2765 10-178950 9-946427 27 115 0-053573 0-125376 2750 9-8746H 9-874568 e 30 20 5li 9-821122 2867 .0-178878 9-946554 28 119 0-053446 0-125432 2852 4 .'tl 30 5« 9-82,193 2969 10-178807 29 123 0-053319 0-, 25488 2954 9-874512 ■i 3(1 30 TIT 46 9-82,265 •<0 7-- 10-. 78735 9-946S08 10 127 0-053,92 0-125544 3056 9-874456 30 Cosine Parts Secant Cotang. Parts Tangct Cosec. Parts Sine ^1 777 48'' ;!" 14'" ^ T.Afil.K ()8 821 LOG. SINES, COSINES, *c. j ._,„ 4,;.., 4 1 , It m. Sine I'arts Cosec. TanK.-„t I'arte Cotang. Seca,it ! Parts Cosine "?- ' " :)(F ~ 9-S2I26; .0-.7S735 9-9+68C8 ,0-053,92 .0 115544 9-87+456 14 M) :i(l .^ 9-X21336 1" 2 .0-.7S664 9-9+6936 1' 4 10-053064 .0 .15600 I" 2 9-87++00 .'jS 30 :il 4 9^ Si 1407 a 5 .o-,-S593 9-9+7063 2 8 ,0-052937 10 115656 2 4 9-87+344 M 2fl .III li 9 821479 3 7 io-.785^' 9-9+7190 3 '3 10-052S.0 .0 115712 3 6 9-87+2X8 .14 30 M H 9^ 82 If 50 4 10 IO-.7S450 9-9+7318 4 >7 10-052682 .0 .25768 4 7 9-874232 r,-i 28 jii 10 9-82,62. 5,i I0-. 78379 9-9+7+45 5 2. 10-052555 ^0 .15813 5 9 9-87+. 77 so 30 an 1-2 9-82169, «M .0-, 78307 9'947572 A 25 10-052+2S 10 .25879 6 .1 9-87+12. 48 27 M 1^ 982,76+ 7 •? .0-.7S136 9-9+7699 7 30 10-052301 .0 '15935 ' 13 9-87+065 4li 30 M Iti 9-82.835 8.9 .c-.78.65 9-9+7827 s 34 10-052173 10 .25991 815 9-87+009 14 20 St 16 9-82.906 92, ,0-. 7 8094 9-947954 9 38 10 .260+7 H 17 9-873953 4-2 30 311 !" 9-S2.977 9-S21049 1024 1126 10-17S013 9-9+808, 10 4^ 47 .^05.919 10-051792 10 1261C+ 1019 11 21 9 873896 40 25 .0-.7795, 9-948208 .0^ 126160 9-8738+0 Mi ■23 9-S22I20 HI28 ,0-177880 9-948335 12 5' 10-05.665 10 .161.6 12 22 9-873784 31! 24 111 ■ili 9-S22.9. 133, io-.',78o9 9-9+8+63 13 55 10-051537 .0 126272 13 24 9-873728 34 30 M •28 9-822262 1433 >o-. 77738 9-9+8590 14 59 10-051410 10 126328 14 26 9-873672 3-2 23 30 9-822333 1036 .o-,-7667 9-9+87.7 15 64 10-05.283 10 1263S+ 15 28 9-8736,6 30 30 3H 3-2 9-S22404 16 38 ,o-, 77596 9-9488++ 16 68 .0-05. .55 10 .26+40 16 30 9-873560 ■28 22 30 34 9-822475 17+0 ,o-, 77525 9-9+8972 17 72 .c-051028 10 116496 1732 9873504 ■2(i 30 .(il 3Ci 9-8225+6 I843 .0-17745+ 9-9+9099 18 76 10-050901 10 ,16,52 18 3+ 9-873448 ■24 21 311 3S 9-8226,7 ins .0-. 77383 9-9+9226 19 8. 10-05077+ 10 .26609 1936 9-87339' ■22 30 to 30 40 9-822688 OT47 2150 .0-. 773.1 9-949353 20 21 85 89 10-0506+7 10 ,26665 2037 2139 9873335 I 20 9821759 .0-.772+. 9-9+9480 10-050520 10^ 12672. 9-873279 41 44 9-822830 2252 .0-177,70 9-9+9608 22 93 10-050392 .0 ,16777 22+1 9-S73223 in lU 30 4S 9-82290. 2355 .0-177099 9-949735 23 98 .0-050265 .0 126834 23+3 9-873.66 1 1 30 42 4H 9-822972 2457 .0-.7702S 9-9+9262 24 102 .0-050.38 10 .26890 2445 9-873.10 ]-i in 30 30 9-823043 255, ,0-, 76957 9-9+9989 25 106 .0-0500.. 10 1269+6 25+7 9-873054 10 30 43 5-2 9-823. .4 -M62 .0-1768S6 9-95CI.6 26 . .0 .0-0+988+ 10 .27002 26+9 9-S7299S 8 17 34 9-813.85 2764 io-,76S.5 9-9501+3 27 . .+ I0-0+9757 10 ,27059 2750 9-872941 30 44 50 9-823255 28 66 .0-. 767+5 9-95037. 28 .19 .0-0+9629 ,0 .27.15 28 52 9-S72SS5 4 '30 30 5S 9-813326 2969 ,0-, 766-4 9-950+9S 29 .13 .0-049502 ,0 127,7. 2954 9-872829 •2 45 vt 9-813397 307, ,o-.766o3 9-950615 30 IIL .0-0+9375 10 .17228 3056 9-872772 13 30 9-823468 1 2 .0-. 76531 9-950752 4 .o-c+92+8 io^ 127284 1 2 9-S727.6 40 4 9-823539 a 5 .o-,7fM6, 9-950879 8 10-0+9 12, 10 ,2734, 2 + 9-872659 5C U 30 c 9-823609 3 7 .0-.7f.39' 9-95.006 13 10-C+899+ .0 1^7397 3 6 9-S72603 54 30 47 8 ,•813680 * 9 10-. 76520 9-9;ii33 17 10-0+8867 .0 127+53 4 8 9-S72547 =■2 13 3« 10 9-813751 5 12 10-1762+9 9-95.16. 2. 10-04S739 10 ,27510 S 9-872+90 50 30 48 1-2 9-81382. 614 .o-.76,79 9-95. 38S 15 10-04S612 10 ,27566 6,; 9-87243+ 4i 12 14 9-823892 7.6 .0-176.08 9-95'5i5 30 .0-048+85 .0 ,27623 713 9-8-2377 4(i 30 4!) lli 9-825,63 81, 10-176037 9-95.6+2 34 .0-0+8358 10 127679 815 9-872321 44 II 30 in 9-824033 9ai 10-175967 9-951769 38 10-0+S231 10 127736 9 17 9-87226+ 4-2 30 fiO •20 9-824.04 lOij II 16 10-17.896 9-951896 4^ 47 10-0+8104 10 12779- 10,9 II2, 9-S72208 10 38 10 9-824174 9-952013 10-0+7977 10 1278+9 9-872151 51 ■24 9-814145 13 18 ;:■;?- 5 9-951150 5> 10-0+7S50 10 127905 1223 9-872095 30 a 30 ■2li 9-8143.5 1330 Io-I;5685 9-951177 55 10-0+7723 10 127962 1325 9-872038 34 30 ■2H 982+386 1433 ,o-,756,+ 9-952+05 59 !0-c4759i; 10 1280.0 1426 9-87,981 3^2 8 30 9-824456 1535 .0-, 75544 9-951531 6+ ioc+7+68 ,0 12S07; 152819-871925 30 30 .'>3 3-2 9-824527 IB 37 ,0-. 75+73 9-951659 68 10-0+73+. 10 .28.32 16 30 9-S7.868 ■2S 7 30 34 9-824597 17+0 .0-. 75+03 9,52786 72 io-c+72,4 10 .28189 1732 9-871811 28 30 .■)4 3li 9-S24668 I842 .o-.7533i 9-952913 76 10-0+70S7 10 .282+5 18 3+ 9-87.755 -24 fi 30 :« 9-824738 '944 .0-. 7 5262 9-9530+0 80 10-C+696C 10 .28302 1936 9-87.698 2-2 «o -l.'l • '" 9-824S08 2047 2149 .0-.75.91 10, 75121 9-953167 20 85 89 io-c+6833 '^ .28359 T2-8+-15 2038 21+0 9-S7.6+, 20 ~J0 9-8^4879 9-953^94 10C46706 9-87.585 .-.(i 44 9824949 225, ,0 ,75051 9-953+2. 22 93 10-046579 10 128+72 22+1 9-S7.528 10 4 311 411 9-8150.9 2354 10-17+98, 9-9535+8 23 97 ,0-046+52 .0 128529 33+3 9-871+7. 14 3< •"■7 411 9-815090 24,6 ,0-17+91° 9953675 24 10-04632. .0 ,28586 24 + 5 9-S71+14 I'i 'f 30 W 9-815,60 2558 ,0-, 7+840 9-953802 25 .06 10-046. 98 10 ,28642 25+7 9S7.358 10 M .•|H .V2 9-815130 26 6, ,0-17+770 9-953929 26 110 .0-0+607. .0 ,28699 26+9 987.30. 8 '2 30 .VI 9-825500 2763 ,0-17+700 9-954056 27 11+ ,0-0+59++ .0 12S756 2751 9-8; 1244 3U M .'il> 9''»S37i. 28 66 ,0-17+629 9-95+183 28 1,8 10-0+5817 .0 128S.3 28 55 9-8- 1 187 4 1 30 .'m 9-825441 29 68 IO-I7+S59 9-95+3.0 29 ,23 io-c+5690 .0 128S70 •2955 9-871130 '2 30 i;o 55 9 8255.. ■W^i 10-17++89 9954+37 30 ,27 10-0+5563 .0 ,18927 3057 9-871073 Tit r C.,.inc Ports Se.-ont Cotan«. 1 1' r.s Ta.,|.,-„t Coscr. Port, Sine ?-"'| 4 HO .^h ,._,,., J 822 TABLE (>8 LOG. SINES, COSINES, .\c. 1 2" 48'" 42° 1 m. Sine Parts Cosec. Tangent Parts Cotang. Secant Parts Cosine 12 (iO 9-«^-55>' io^,744>i9 9-954437 ,0-045563 ,0 ,28927 9-87.073 mi 2 9-82S58' 1"2 10-174419 9-954564 1" 4 ,0-045436 10 ,28983 1"2 9-87.0.7 58 30 1 •1 9-825651 2 5 ,0-174349 9-95469, 2 8 10-045309 10 ,29040 2 4 9-870960 60 59 30 a 9-825721 3 7 10-, 74279 9-954819 3 .3 10-045181 ,0 129097 3 6 9-870903 54 30 ■J 8 9-8^579' ♦ 9 io^i74209 9-954946 4 17 ,0-045054 10 129154 4 8 9-870846 52 58 JO 10 9-82586, 6 12 10-, 74139 9'955073 5 2, 10-044927 10 12921, 6 ,0 9-870789 50 30 3 12 9-825931 614 10-174069 9-955200 6 25 ,0-044800 10 ,2926s 6 1, 9-870732 48 57 30 N 9-826001 7,6 IO-I73999 9-955327 7 30 ,0-044673 10 129325 7,3 9-870675 46 30 4 10 9-82607, 8,9 ,0-173929 9-955454 8 34 10-044546 10 129382 8,5 9-8706.8 44 5(i 30 18 9-826,^, ,0-173859 9-95558, 9 38 10-044419 10 ,29439 9.7 9-87056. 42 30 9 '." 9^8262., IO23 1126 .o-,73789 9-955708 10 42 11 47 10 ,29496 10,9 11 21 9-870504 40 5,> 9-826281 ,o-,737,9 9'955*>35 ,0-044,65 10^ ■29553 9-870447 6 •u 9-82635, 12 28 ,0-, 73649 9-95596" 12 5, 10-044039 10 .29610 1223 9-S70390 36 54 30 ■16 9-82642, 133- 10-, 7357c 9956088 13 55 10-043912 10 .29667 1325 9-870333 34 3(1 7 ■I* 9-826491 14 33 ,0-173509 9-9562,5 14 59 10-043785 ,0 129724 U27 9-870276 32 5.-) 3(1 9-826561 .535 ,0-173439 9-956342 15 63 ,0-043658 ■0-, 29782 15 29 9-8702,8 30 3(1 8 3-2 9-826631 16 37 ,0-173369 9-956469 16 68 ,0-043531 ■0,29839 16 30 9-870,6, 28 52 30 3J 9-826701 1740 ,0-173299 9-956596 17 72 10-043404 ,0 ,29896 1732 9-870,04 26 30 9 30 9-826770 I842 10-173230 9-956723 18 76 10-043277 ,0 ,29953 18 34 9-870047 •24 51 3(1 38 9-826840 1944 io-,73i6c 9-956850 19 80 10-043150 .30010 1936 9-869990 -22 3(1 10 40 9-826910 2047 2149 ,0-173090 9-956977 20 85 21 89 10-043023 ,0 n£0_6^ 20 38 21 40 9-869933 9-869S75 50 9-826980 ,0-173020 9-957,04 10-042896 lo" ,30.25 li 4-1 9-827049 225, ,.-,7295, 9-95723, 22 93 10-042769 10 ,30,82 2242 9-8698,8 49 3(1 40 9-S27119 2354 ,0-172881 9-957358 23 97 10-042642 JO ,30239 2344 9-86976. 14 3(1 1-2 48 9-827189 2456 ,0-1728,1 9-9574!>5 24 ,02 10-0425,5 ,0 ,30296 2446 9-869704 12 41! 30 50 9-827158 2558 10-172742 9-957612 25 ,06 ,0-042388 ,0 '30354 2548 9-869646 10 3(1 13 5-2 9-827328 26 6, ,0-, 72672 9-957739 26 110 ,0-04226, ,0 1304,, 2649 9-869589 8 47 30 51 9-827398 2763 ,0-172602 9-957866 27 ,14 ,0-042,34 10 ,30468 275. 9-869532 6 30 14 50 9-827467 2865 ,0-, 72533 9-957993 28 1,8 ,0-042007 ,0 ,30526 28 53 9-869474 4 n\ 30 5S 9-827537 2068 ,0-172463 9-958120 29,23 ,0-04,880 ■30583 2955 9-8694,7 •2 3(1 15 ft9 1 9-827606 Sll 70 ,0-172394 9-958247 30 ,27 ,0-04,753 ,0 .30640 30 5- 9-869360 11 45 9-827676 1 2 10-, 72324 9-958373 1 4 0-041627 To ,30698 ' ^ 9-869302 IG 4 9-827745 2 5 10-172255 9-958500 1 8 ■0-041500 10 ■30755 2 4 9-869245 56 44 30 9-8278,5 3 7 ,0-172,85 9-958627 3 ,3 10-04,373 10 ,308.2 3 6 9-869,88 54 30 17 8 9-827884 4 9 .o-,72i,6 9-958754 4 ,7 ,0-04,246 ,0 ,30870 4 8 9-869,30 52 4;< 30 10 9-827954 5 12 .0-, 72046 9-95888, 5 21 ,0-0411,9 10 ,30927 610 9-869073 50 30 1« 1-2 9-828023 6,4 ,o-,7,977 9-959008 6 25 ,0'040992 10 130985 612 9-8690,5 48 42 30 14 9-828093 7,6 10-17,907 9-959'35 7 30 ,0-040865 10 13,042 7,3 9-86895S 46 30 19 10 9S28162 8,9 io-,7,838 9-959262 8 34 ,0-040738 10 .3. .00 8,5 9-868900 44 41 30 18 9-82823, 921 .o-,7,769 9-959389 9 38 ,0-04061, 10 ■3"^57 9,7 9-868843 42 30 20 30 •20 9-82830, 1023 11 26 ,o-, 7,699 9-9595,6 10 42 11 47 10-040484 10 .312.5 10,9 112. 9-868785 40 W_ IO-, 71630 9-959642 ,0-040358 To .3,272 9-86S728 21 •24 9-82"8439 122S I0-,7I56. 9-959769 12 5, 10-040231 10 13.330 1223 9-868670 36 3!) 3(1 •26 9-828509 133c , 0-17, 49, 9-959S96 13 55 10-040104 10 .3,388 13 25 9-8686,2 34 30 22 •28 9-828578 1433 10-, 71422 9-960023 14 59 10-039977 10 ■3 "445 14 27 9-868555 32 3B 30 30 9-828647 15 35 io-,7,353 9-960,50 15 63 10-039850 ,0 ,3,503 1529 9-868497 30 30 23 32 9-8287,6 16 37 ,o-,7,284 9-960277 16 68 10-039723 10 ,3,560 163. 9-868440 28 37 30 34 9-828786 1-40 10-, 712, 4 9-960404 17 71 10-039596 10 13,6.8 1733 9-868382 26 24 36 9-828855 I842 10-171,45 9-960530 18 76 10-039470 10 .3,676 1835 9-868314 •24 30" 30 38 9 828924 1944 9 960657 19 80 'O-039343 10 ,3,733 1936 9-S68267 22 26 40 9-828993 ■2046 ,0-171007 9 960784 20 85 ,0-039216 10 ,3,791 203s 9-868209 •20 35 ~3(r 42 9-829062 21 4, 10-170938 9-960911 21 89 10-039089 To 13,849 2140 r>-868i5i 30 26 44 9-829,3. 225, 10-170869 9-96,038 22 93 10 ,3,907 2242 9-S68093 34 30 46 9-829200 23 53 10-, 70800 9-96,165 23 97 ,0-038835 10 ,31964 2:144 9-868036 30 27 48 9-S29269 •2455 10-170731 9-961292 24 ,02 ,0-038708 10 132022 3446 9-867978 3:» 3C 50 9-829338 ■25 5S ,o-, 70662 9-961418 26 106 10-03S582 10 ,32080 2548 9-867920 30 28 52 9-829407 26 6c ,0-170593 9-961545 26, 10 10-038455 ,0 ,32,38 2650 9-867862 32 30 54 9-829476 •2762 10-170524 9-96,672 27 ,14 10-038328 10 ,32,96 2752 9-867804 30 29 56 9-829545 2865 ■0-170455 9-96,799 •28,, 8 ,0-03820, 10 ,32253 28 54 9-867747 .-tl 30 58 9-829614 2967 JO-, 70386 9-96,926 ■29 ,23 ,0-038074 10 ,323,, 2956 9-867689 30 30 SO 9-829683 3060 ,0-, 70317 9-962052 30 ,27 10-037948 ,0-, 32369 3058 9-86763, »0 TIT •? (;osine | Parts Secant Cotang. Parts Tangent Cosec. Parts •? TTJ 4 7° -A^ 10"' 1 LOG. SINES, COSINK.s, &c. ■2" -,0"> 42" '" ■? Sine Faru CoKc. Ta„ge..t Parts Cotang. Sec-ant Parts Cosine n> ~T7? at) CI 9-8z96»3 .0-. 70317 9-91)2052 .0037948 '0-. 3^369 9-S6765. lb W :u) ■I 9829752 1"2 10-. 70248 9-962.79 '" 4 10-037821 lo^i 32427 1"2 9-867573 58 .10 :6332o 9-9'-3447 10 42 11 46 10^056680 10-132949 10 19 II2. 9-86705. .'" 25 9-830440 10-169560 10-036553 10-133007 9-S66993 Mi '^1 9-850509 H27 10-169491 9-963574 12 51 10-036426 10-. 33065 1223 9-866935 3ti 24 : 31 9-832901 1739 0-167099 9-968009 17 72 ,0-03,991 .0-135,08 1735 9-864892 •20 30 54 311 y-832969 I84, 0-.6705. 9-968,36 18 76 .0-03.864 o-i3„67 I835 9-864833 •24 l> 311 3n 9-835057 1943 0-. 66963 9-968263 19 80 0-03.737 0-, 35226 1937 9-864774 Tt .10 55 40 9-833105 21.45 0-. 66895 9-96X389 20 84 0-03.6.1 0-. 35284 2039 9-8647.6 '20 5 30 4.1 9-833.73 2148 0-. 66827 9-968516 21 89 0-031484 0-135343 2I4. 9-864657 18 ~3cr «6 41 9-833241 22 50 0-. 66759 9-968643 22 93 0-05.357 0-I35402 2243 9^864598 III 4 30 Id 9-833509 •23 52 0-.66691 9-968769 23 97 0-05.25. 0^135461 2345 /S64559 14 311 57 4n 9-833377 2455 10. 66625 9-968896 24 .0. 0-03.104 ©•135519 2447 9^864481 3 M 50 9-833444 2557 .0-166556 9-969023 25 106 0-030977 0-. 35578 2549 9-864422 10 30 58 ii 9-833512 2659 .0-.66488 9-969.49 26 1 .o 0-03085, 0-155657 265.19-864365 H •> :iii 11 9-853580 276. 10-166420 9969276 27 1.4 0-030724 10-155696 27 53 19-864304 (i 30 5!) SO 9-833648 2864 10-166352 9-969403 0-030597 0-155755 285519-864245 4 1 30 .18 9-8337.6 29 65 .0-. 66284 9-969529 29 .22 .0-03047. 10-1358.4 2957 9-864.86 •2 30 on M 9-833783 30 68 .o-.6fi2.7 9-969656 to .27 .0-030344 .0-135875 3059 9-864127 1 II m. Conine Part. Se4-jint C„t«„K. Parts Ta„g,-„t Coser. Parts 1 Sine ^^1 47° a" 8" J TABLE 68 LOG. SINES, COSINES, &c. Oh 52'" 43° 1 /// m Sine Parts Cosfc. Tangent I Parts _Cotang. Secant Parts Cosine m- ' " 1 IT "o" 9-833783 10 1662.7 9-969656 .0 030344 10-135873 9-864,27 T vo 30 ■2 9-833851 1" 2 10 166149 9-969783 r 4 10 030217 .0-, 35931 1"2 9-864069 5S 30 1 ^ 9-833919 2 4 10 16608. 9-969909 2 8 10 030091 ,o-i359()o 2 4 9-S64010 60 5!1 30 B 9-833986 3 7 10 .660.4 9-970036 3 13 10 029964 ,0- 1 36049 3 6 9-863951 51 30 2 s 9-834^054 4 9 10 .65946 9-970.62 4 17 10 029S3S .0-. 36108 4 8 9-863S92 5-2 S8 30 10 9-8341" 5 II 10 .65878 9-9702S9 5 21 10 02971, ■o-,36,67 5 10 9-863833 50 30 3 \! 9-834189 613 10 1658,, 9-9704.6 6 15 10 029584 .0-. 36226 6 12 9-863774 48 57 3(1 II 9-834157 7 16 10 165743 9-970542 7 30 10 029458 .0-. 36285 7,4 9-863715 40 30 4 ll> 9-834325 81S 10 165675 9-970669 8 34 10 02933, IO-. 36344 8,6 9-863656 44 56 3(1 IH 9-834392 9 20 10 .65608 9-970796 9 38 10 029204 .0-136403 9,8 9-863597 4^2 311 r, ■20 9-S34460 10 22 10 .65540 9-970922 10 41 10 029078 10-136462 10 20 9-863538 40 55 ^M ■tl 9-8345-7 ','^5 10" ■65473 9-97.049 11 46 10" 02895, 10-136522 11 22 9-863478 38 30 G ■;i 9-834S95 10 .65405 9 971175 12 51 .0 028825 .o-,3658i 12 24 9-863419 36 54 3(1 •Hi 9-83+662 1329 10 .65338 9-971302 13 55 .0 028698 10-136640 1326 9-863360 34 30 7 ■iS 9-S34730 U31 10 .65270 9-971429 14 59 .0 C2857, 10-, 36699 14 28 9-863301 3-2 53 30 30 9-S34797 1534 10 .65203 9-971555 15 65 .0 028445 .0-136758 1530 9-S63242 30 30 8 3-2 9-834865 1636 10 .65.35 9-971682 16 68 10 018318 .0-1368.7 16 32 9-863183 -28 52 30 M 9-834932 1738 10 .65068 9-971808 17 72 10 .0-. 36876 1733 9-863124 -20 30 9 3C 9-834999 I84I 10 .6500. 9-971935 18 76 10 02S065 .0-, 36936 I835 9-S63064 24 51 30 38 9-835067 1943 10 164933 9-972062 19 80 10 017938 10-136995 1937 9-863005 -2-2 30 10 W 9-835134 2045 2147 10 164866 9-9721S8 20 21 84 .0 .0-, 37054 2039 214, 9-862946 -20 IS 50 9-835201 To" .64799 9-972315 lo" 0276S5 10-. 37. .3 9-862887 11 ■ii 9-835269 2249 10 16473. 9-972441 22 93 .0 017559 10-137173 2243 9-862827 10 4!) 3(1 n 9-S35336 2352 10 .64664 9-972568 23 97 ,0-137232 2345 9-862768 14 30 12 ^H 9-S35403 2454 10 164597 9-972695 24 ni 027305 10-137291 2447 9-862709 1-2 48 30 r,u 9-835471 2556 10 .64529 9-972821 25 .05 027179 10-137350 2549 9-862650 10 30 !.•) .12 9-S35538 2658 10 164462 9-972948 26 .10 :o 027052 10-137410 2651 9-862590 8 47 30 Ji 9-S35605 2761 10 .64395 9-973074 27 114 026926 ,0-137469 2753 9-862531 3(1 14 :.(; 9-835672 2863 10 164328 9-97320. 28 >i8 10 026799 .0-137529 28 55 9-862471 4 40 30 =1 9-835739 2965 10 16426, 9-973317 2J 122 10 026673 .0-, 37588 2957 9-862412 •2 30 15 30 S3 9-835807 30 68 10 164,95 9-97345+ 30 126 10 026546 .0-. 37647 3" 59 9862353 7 45 9-835874 1 2 w 164126 9-973581 ~ 4 lo" 026419 .0-. 37707 9-862293 16 J 9-S35941 2 4 10 .64059 9-973707 12 S 10 026293 .0-, 37766 2 4 9-S62234 50 44 30 (1 9-836008 3 7 10 163992 9-973834 3 '3 10 026166 .0-I37S26 3 6 9S62174 51 3(1 17 ri 9-836075 4 9 10 163925 9-973960 4 17 10 026040 4 8 9-862115 5-2 4:t 30 10 9-836-41 5ll 10 .63S58 9-974087 5 10 0259,3 10-137945 5 10 9-862055 50 30 18 1-2 9-836209 6.3 10 ,6379. 9-974113 6 15 10 015787 .0-. 38004 612 9-86,996 43 42 30 II 9-836276 7 16 10 163724 9-974340 7 30 10 025660 .o-.3So64 714 9-861936 40 30 19 10 9-836343 818 10 163657 9-974466 8 34 015534 .o-,38,23 8 16 44 41 30 IH 9-S36410 920 10 163590 9-974593 9 38 10 025407 ,0-. 38.83 9,8 9-861817 4-2 30 20 ■20 9-836477 IO22 1125 10 16-^523 9-9747x0 10 11 41 46 10 025280 .0-138242 10 20 II22 9-S6175S 38 40 9-836544 10 .63456 9-974846 025154 ,o-, 38302 9-86, 69S 21 •21 9-836611 1227 10 .63389 9-974973 12 51 10 025027 io-,3S362 1224 9-86,638 30 39 30 ■21 ; 9-836678 1329 10 163322 9-975099 13 55 024901 .0-.3842, 13 26 9-861579 31 30 22 ■28 9-836745 143. 10 ,63255 9-975226 14 59 024774 .o-,384S. 14 28 9-861519 3-2 38 30 3(1 9-836812 1533 10 .63188 9-975351 15 63 10 024648 ,0-138541 1530 9-86,459 30 311 2.1 32 9-836S78 16 36 10 163122 9-975479 16 68 02452, IO-. 38600 16 32 9-86,400 ■28 37 30 31 9-836945 1738 10 163055 9-975605 17 72 024395 .O-.3S660 1734 9-861340 •20 30 1 24 3li 9-837012 18 40 10 162988 9-975731 18 76 02426s 10-.38720 I836 9-86,280 ■24 3.1 1 311 3S 9-837079 1941 10 16292. 9-975S5S 19 80 10 024,42 10-138779 19 38 9-86122: •22 .>,-, 2.-> ^0 12 9-837146 ■2045 2147 10 .62854 9-975985 20 21 84 89 10 024015 10-138839 20 40 2142 9-861161 ■20 35 30 9-837212 ro 1627SS 9-976111 0238S9 i^^8^ 9-86,101 2(i n 9-837279 2249 10 16272. 9-976238 22 93 023762 10-13S959 2244 9-861041 10 34 31 Ki 9-837346 •23 52 10 .62654 9-976364 23 97 023636 10-139019 2346 9-860981 11 3(1 27 IS 9-S37412 24 54 10 .625SS 9-97649. 24 101 023509 ,0-139078 24 48 9-860922 \-> 33 30 r,(i 9-837479 2556 10 .6252. 9-9766.7 25 105 023383 ,0-139,38 •2550 9-860862 10 30 2(1 9-S37546 2658 10 .62454 9-976744 2fi no 023256 2652 9-860802 ({ 32 .1(1 r.i 9-S376.2 2760 10 .6238S 9-976870 27 114 .0 023130 ;o-!]9258 2754 9-860742 3(1 2i) M 9-837679 2863 10 .6232. 9-976997 28 iiS 10 023003 10-139318 28 56 9-S60682 4 31 3(1 r>n 9-837746 2965 10 .62254 9-977.23 29 122 10 022877 10-139378 2958 9-860622 •2 30 :to 5% 9-8,78.2 3067 io-i62iSS 9-977250 iO 126 10 022750 ■0-139438 306019-860562 30 777 m. Cosine P^-U Se.-.int Cotang. Parts T mgpiit Cosec. Parts Sine pi -1 __l TABLE 08 LOG. SINES, COSINES, &c. 1 «'• 54"' ' 4:3° 1 ■M ? Sine I'arti Conrc. Tangent Parte | Cotanff. Secant Parts 1 Coaine m 311 9-837812 10-161. 88 9-977150 I10-022750 ,0-, 39438 9-860562 M 7 9-837879 1"2 10161111 9-977377 • 4 10-012613 .0-.3949S 1" 2 9-860502 .',K 311 SI 4 9'X37945 « 4 .0-162055 9-977503 2 8 10-012497 ,0-139558 ,0-139618 2 4 9-S60++1 .■-.c. 2!) 311 (1 9-83«o'i 3 7 io^.6,988 9-977630 3 13 10-021370 3 6 9-860382 jl 30 32 ,S 9-838C-8 •» 9 .O^l6l922 9-977756 4 17 10-0222+< 10-139678 4 8 9-860312 .1-2 28 m 10 9-838145 S II .o-,6,855 9-977881 6 21 IO-022II1 10-I3973S S 10 9-S60261 M .-.0 Xi 1'^ 9-838211 8'3 10-161789 9-9:8009 fi 25|ic-02.99, .0-. 39798 6 12 9-860202 4S 27 .11) It 9-838178 715 10161712 9-978135 7 30 10-021865 10-139858 714 I9-S60.+2 4a 34 III 9-838344 817 10-161656 9-978262 8 34 10-021738 10-13991S 8 16 19-860082 41 20 ,1C IH 9838410 9 20 10-161590 9978388 9 38 .0-02.6.2 .0-139978 918 9-860022 4-i 30 .),■> '." 9-838477 10 22 I 124 io-,6.523 919785.5 10 42 11 46 10-021485 10-14C038 ,0-1+0098 IO20 11 22 9-859962 40 S,! 9-838543 .o^.6,+57 9-9786+1 10021359 9-859902 3(; ■21 9-838610 1227 .o^i6i390 9-97S768 12 51 10-02,232 10-1+0,58 1224 9-859842 M 24 .10 •2B 9-838676 13 29 .o^i6,324 9-97889+ 13 55 .0-02,106 .0-1+02,9 1326 9-85978. J4 30 37 •AS 9-838742 1431 io^,6,i58 9-979021 14 59 .0-010979 ,0-, 40279 UiS 9-859721 3-2 23 .10 9-838808 1333 10-161192 9-9791+7 15 63 .O-OI0S53 .0-1+0339 1030 9-85966, 3C 30 •M 3-2 9-838875 I835 .o-i6,,i5 9-979174 16 67 .0-010726 10-1+0399 9-S5960, •28 22 :w .11 9-838941 1737 TO-16.059 9-979400 17 72 10-0206cO 10- ,+0+59 173+ 9-85954. 2li .10 39 .Ki 9-839007 I84O 10-160993 9-979527 18 76 .0-020+73 10-140520 I836 9-8594S0 -21 21 .10 .1H 9-839073 1942 10-160927 9-979653 19 80 10-020347 10-140580 ,0-140640 1938 9-859+20 22 30 40 40 9-839140 9-839206 2044 21 46 10-160860 9-979780 20 84 21 89 10-020220 20+0 2142 9-859360 IS 30 10-160794 9979906 10-020094 10-140700 9-859300 41 41 9-839272 22+8 10-160718 9-980033 22 93 10-019967 .o-,+o76. 224+ 9-859239 III 10 30 411 9-839338 2351 .0-160662 9-980.59 23 97 .0-01984. ,0-1+0811 2346 9-859,79 14 30 42 4« 9-839404 2453 .o-,6o596 9-980186 24 101 IO-OI97I+ io-,+o88. 2448 9-859,19 12 18 :io :io 9-839470 2555 10-. 60530 9-9S0411 55,05 10-019588 10-1+09+1 2550 9-859058 III 30 43 5i 9-839536 2fi57 10-160+64 9-9S0538 26 1,0 .00.9462 ,0-141002 2652 9-858998 » 17 .10 51 9-839602 2760 .0-160398 9-980665 27 ,,4 .0-019335 io-,+,o63 2754 9-858937 C 44 ^li 9-839668 2862 10-160332 9-98079, 28 118 10-019209 10-,+, ,13 2856 9-858877 4 \ii 30 .OS 9-839734 29 6+ 10-160266 9-98c9.» U 122 10-0. 90S2 io-,+i,83 2958 9-8588,7 2 111 _4»_ 5S 2 9-839800 30 66 10-160200 9-981044 30 ,16 .0-0.8956 10-, +.2++ 3060 9-858756 s 15 9-839866 1 2 .0-160,34 9-981171 ' 4 .0-0,8829 10- .+,30+ 1 2 9-85S696 46 4 9-839932 2 4 10-160068 9-981297 3 g ,0-0,8703 .o-,+,365 2 4 9-858635 5li 14 311 9-839998 3 7 10-160002 9-98.424 3 ,3 10-0,8576 10-,+, +15 3 6 9-858575 .M 30 <; H 9-840C64 4 9 10-159936 9-98.550 4 17 10018450 .o-,4,486 4 8 9-85S514 .52 13 10 9-840130 5 11 .0-159870 9-98.677 5 21 .0-0,8323 ,o-,4,5+6 5,0 9-858+54 .10 30 4» IV 9-S4C196 6.3 10-159804 9-981803 6 25 ,0-018,97 ,o-,+,6o7 6,2 9-858393 4S |o 30 II 9-840262 715 .0-159738 9-98.929 7 29 ,0-0,807, 7i + 9-858332 10 A 1 49 Hi 9-840328 817 10-159671 9-982056 8 34 .0-0,7944 ,o-.+,7i8 8,6 9-S5S272 +1 I 1 30 IS 9-840393 920 0-159607 9-982182 9 38 ,0-0,78,8 ,o-,4,789 9,8 9-85S2., 42 311 .10 ■ii 9-840459 10 22 1124 0-1595+1 9-981309 10 42 U 46 ,0-0,769. 10-14,849 10 20 1122 9858,5. '" 10 9-840525 0-159475 9-982435 ,00,7565 10-1419,0 9-858090 »l 21 9-840591 1226 0-159409 9-982562 12 51 10-017438 io-,4,97. 12.'.+ 9-858029 30 9 311 20 9-840657 i3 29 0-1593+3 9-981688 13 55 ,0-017312 ,0-142032 13 26 9-857968 31 30 .V2 •AS 9-840722 1431 0-159278 9-982814 14 59 10-0,7,86 10-142092 U28 9-857908 .12 » 30 30 9-840788 1533 0-159212 9-98194, 5 63 ,0-017059 .0- ,42,53 1530 9-857X47 30 30 13 Tl 9-840854 If, 35 0-159,46 9-983067 16 67 ,0-0,6933 10-142214 16 32 9-857786 ■28 7 30 31 9-8409 '9 1737 0-159081 9-983194 7 72 ,0-0,6806 10-142274 1734 9-857726 211 .■>) .HI 9-840985 18 39 0-159015 9-983320 8 76 ,0-0,6680 .0-.42335 18 36 9-857665 24 1) 30 :« 9-84.05. 1942 0-158949 9-983447 9 80 ,0-0,6553 o-,423r;8 1938 9-857604 •22 30 .-..-. 10 9-8+11.6 2044 2146 0-158884 9-983573 20 84 21 88 10-0,6427 ,0- ,42457 20+0 21+1 9-857543 20 .1 1/ 9-84.. 82 o-,588i8 9-983699 0-0,630, ©-,425,8 9-857482 W II 9-841247 2248 0-158753 9-983826 22 93 0-0,6.74 o-,+2578 22+5 9-857421 111 •1 311 III 9-841313 2351 0-158687 9-983952 23 97 0-0,6048 0-142639 23+6 ;-85736. 14 30 .-.7 in 9-841378 24 53 0-158622 9-984079 24 101 0-0,592, 0-142700 24+8 3-857300 12 3 311 30 9841444 2*55 0-. 58556 9-984205 25 105 0-0,5795 0-142761 255, 3-857239 10 30 ,-.(1 r,i 9-841509 2657 0-158+91 9-984331 26109 0-0.5668 0-142822 2653 3-857.78 tt 2 30 .51 9-841575 2759 '0-158425 9-984458 27 ,14 0-0,5542 0-142883 2755 3-857. .7 .111 .-.:) :,o 9-841640 286l 10-158360 9-984584 28 118 0-0,54,6 0-142944 28 57 3-857056 I 1 111 1 :,H 9-841:06 2064 10-158294 9-9847,1 29 122 0-0,5289 0-143005 -2959 3856995 2 30 W ls« 9-84.77. •1066 10-158229 9 9S4S37 iO 126 n-0,5.63 o-i43o6f .10 6, 3-856934 '.'il'°l.^'l'"il I'url, Si-L-ant Coun?. l';.rt» Tange.it COMCC. Part. Sine ^ 777 LOG. SINES, COSINES, Nc. | 2'' 30'" 44° 1 /// " Sine Part, Cosec. Tangrnt Parts Cotang. Secant Parts Cosine » 1 II 9'84'77' 10-158229 9-984837 0-015163 ,o-,43o66 9-856934 4 "Sir :vt ■I 9-841837 !" 2 ,0-158.63 9-984964 1" 4 0-0.5036 ,o-,43,27 I"2 9-856873 58 30 I J 9-841902 a 4 .0-.58C98 9-985090 2 8 0-0.49,0 10-143,88 2 4 9-856812 50 69 30 9-84.967 3 7 10-158033 9-985216 3 ,3 0-0,4784 10-143249 3 6 9-85675- 54 30 2 8 9-842033 * 9 >o; 157967 9-985343 -» 17 0-0,4657 J0-, 433,0 4 8 9-856690 5-2 58 30 10 9-842098 5 II 9-985469 5 2, 0-01453, 10-14337. 5 10 9-S56629 50 30 3 12 9-84^163 6 13 ,0-, 57837 9-985596 6 25 0-0,4404 10-143432 6 12 9-856568 48 67 30 IJ 9-842229 715 10-15777, 9-985722 7 29 0-0,4278 ,0-, 43493 7,4 9-856507 4(-. 3(1 4 1« 9-842294 817 .0-, 57706 9-985848 8 34 0-0,4152 ■0-143554 816 9-856446 44 5B 30 18 9-842359 920 ,o-,57fi4. 9-985975 9 38 0-0,4025 ,o-,436,6 9 ,8 9-856384 4-2 30 30 •20 9-842424 10 22 1124 .0-, 57576 9-986,0. 10 42 U 46 0-0,3899 .0-. 43677 10 20 U 22 9-8563^-3 40 60 9-842490 ,0-1575,0 9-986228 0-013772 ■0-, 43738 9-856262 6 •2J 9-842555 1226 ,0-157445 9-986354 12 5, 0-013646 '0-143799 1224 9-85620, 36 54 30 ■if, 9-842620 13 28 .0-1573S0 9986480 13 55 0-0,3520 ,0-, 43860 1327 9-856140 34 3(1 7 •2S 9-842685 1430 ,0-1573,5 9-986607 14 59 0-0,3393 ,0-143922 14 29 9-856078 3-2 53 30 30 9-842750 1533 10-, 57250 9-986733 15 63 0-013267 '0-143983 153, 9-856017 30 3(1 8 3-2 9-8428.5 I635 10-157,85 9-986860 16 67 0-013,40 ,0-. 44044 I633 9-855956 -28 62 30 34 9-842S80 1737 ,0-157120 9-986986 17 7^ 0-0,30,4 10-. 44106 1735 9-855895 •26 30 9 36 9-842946 18 39 ,0-, 57054 9-987, ,2 18 76 0-0,2888 10-144,67 18 37 9-855833 -24 51 30 38 9-8430., 1941 ,0-156989 9-987239 19 80 0-0,276, .0-144228 I939I9-855772 -2-2 30 ID 10 9-843076 2043 2146 ,0-, 56924 9-987365 20 84 21 88 0-0,2635 .o-,44289 204, 2' 43 9-85571, -20 6U 9-84314. ,0-156859 9-98749 ■ 0-0,2509 10-144351 9-855649 11 AA 9-843206 2248 ,0-156794 22 93 0-0,2382 ,0-144412 2245 9-855588 16 49 30 40 9-843271 2350 ,0-, 56729 9-987744 23 97 0-0,2256 ,0- ,44474 234719-855526 14 30 12 48 9-843336 2452 ,0-156664 9-98787. 24 ,0, 0-0,2129 ,0-, 44535 2449 9-855465 1-2 4)1 30 50 9-84340. 2554 ,0-, 56599 9-987997 26 ,05 0-012C03 .0-. 44596 25 5,. 9-855404 10 .K, 13 52 9-843466 2656 ,0-156534 9-988.23 26 ,09 0-011877 .0-144658 2653 9-855342 8 4; 30 54 9-843530 2759 ,0-156470 9-988250 27 ,14 0-01,750 ,0-1447,9 27559-855^8. a 30 14 50 9-843595 28 61 10-, 56405 9-988376 28 ,18 0-0,, 624 10-14478, 28579-8552.9 4 4(; 30 58 9843660 2963 ,0-, 56340 9-988503 2» 122 0-01.497 10-144842 29599-855158 •2 30 15 57 9-843725 3065_ ,0-, 56275 9-988629 10 ,26 , 0-01,37, 10-144904 30 6i|9-8<;5cq6 3 45 9-843790 1 2 ,0-, 56210 9-988755 1 4 I 0-0,1245 10-144965 1 2 9-855035 16 4 9843855 2 4 ,o-, 56,45 9-988882 2 8 , o-oiiiiS 10-145027 2 4 9-854973 51i 44 30 9-843919 3 6 0-15608, 9-989008 3 ,3 , 0-0,0992 10-1450S9 3 6 9-8549.. 54 30 17 8 9-843984 4 9 ,o-,56o,6 9-989,34 4 ,7 , 0-0,0866 0-.45.50 4 8 9-854850 52 43 3(1 10 9-S44049 5 II o-'5595> 9-98926. 5 2, I 0-0,0739 0-,+52,2 5 10 985478S 50 30 l» 1-2 9-8441,4 fii3 0-155886 9-989387 6 25 , 0-0.06,3 0-145273 6,2 9-854727 48 42 30 14 9-844,78 7,5 0-155822 9-9895,3 7 29 1 0-0,0487 0-I4533S 7,4 9-854665 40 3(1 13 Hi 9-844243 8,7 0-155757 9-989640 8 34 , 0-0,0360 0-145397 8 16 9-854603 44 41 Ml IH 9-844308 9,9 0-155692 9-989766 9 38 > 0-0,0234 0-145458 9,9 9-854542 42 3(1 20 20 9-844372 IO21 1124 0-155628 9-989893 42 1 1 46 I 0-145520 IO21 1123 9-854480 38 411 9-844437 0-155563 9-990019 0-009981 0-14558^ 9-8544,8 21 ■24 9-844502 1226 0-155498 9-990145 2 5, 1 0-009855 0-145644 1225 9-854356 36 31) 30 ■2li 9-844566 1328 0-155434 9-990272 3 55 1 0-0C9728 0-145705 13 27 9-854295 34 3(1 22 28 9-S4463, 1430 0-155369 9-990398 4 59 I 0*009602 0-145767 14 29 9-854233 3^2 3)1 30 30 9-S44696 1532 0-155304 9-990524 5 63 1 0-009476 0-145S29 153, 9-854,7. 3U 3(1 23 32 9-S44760 1634 0-, 55240 9-990651 6 67 I 0-009349 0-145891 1633 9-854.09 ■28 37 30 34 9-844825 1737 0-, 55.75 9-990777 7 72 I 0-009223 0-145953 •735 9-854047 •26 30 24 31i 9 S44889 18 39 o-,55,i. 9-990903 8 76 I 0-009097 0-146014 18 37 9-853986 •24 3(i 30 38 9-844954 1941 o-,55046 9-991030 9 80 , 0-008970 0-146076 1939 9-853924 22 3(1 2S_ 10 9-8450. 8 2043 2145 0-, 54982 9-991156 JO 84 , 0-0O8S44 0-146138 ■20 4 1 21 43 9-853S62 •20 3.-. 9-S45083 o-,549"7 9-991283 21 88 I 0-0087,7 o- ,46200 9-853800 2(; 44 9-845,47 2247 0-154853 9-991409 M 93 . 0-00859. 0-146262 2245 9853738 hi ■J4 30 46 9-8452,, 2349 0-154789 9-99'5!5 n 97 ' D-008465 0-146324 2347 9-853676 14 3(1 27 48 9-845276 2452 0-154724 9-99.662 24 ,0, , 0-00833S 0-1463S6 2449 9-8536.4 1-2 3,-t ;« 50 9-845340 2554 0-154660 9-991788 25 105 1 0-0082.2 0-146448 255. 9-85355= 10 3( 2K 52 9-845405 2656 0-154595 9-991914 6 109 1 D-00S0S6 0-146510 26 54 ;-853490 3-J 3(1 54 9-845469 2758 0-15453, 9992041 7 114 1 0-007959 0-146572 2756 9-8534=8 '<. 30 211 5(i 9-845533 28 60 0-154467 9-99-167 8 1 iS , D-007833 0-146634 28,8 9-853366 4 :u 3!l 58 9845598 29621 0-, 544,-2 9-992293 9 ,22 1 0-007707 0-146696 2960 9853304 ■2 311 :to S8 9-845662 3O64 0-, 54338 9-992420 126 1 D-007580 o-l46-:(:X 30 62 9-8^3=4= i 31) C(.si.,e Pa,-ts| Secant Cocang. | Parts Tangeot Cosec. ParU Sine 1 - - ..... 1 TABLE 08 825 LOO. SINES, COSINES, &c. ^,h 58'" 44° _ "1 w m. Sine Part? Coiec,_ Tangent I'a.t,! Cotanc;, Secant | Parts Co,ine m '2 30 9-S+;66a .0 ■54338 9-992420 .0 007580 10 146758 9-853242 .10 ■i 9-S+S726 1" 2 .0 154^74 9-992546 '" 4 .0 001454 .0-.46820I r'2 9-853,80 M 311 M .1 9-845790 2 4 .0 154210 9-992672 2 8 .0 007328 .0-146882 2 4 9-853, ,8 r,n •2'.) .10 ti 9845855 3 6 10 '54'45 9-992799 3 ,3 .0 007201 .0-. 46944 3 6 9-853056 ,',4 .'10 :u X 9-845919 4 8 10 .5408. 9-992925 4 ,7 .0 007075 .0- .47006 4 8 9-852994 fri 28 30 10 9-S45983 6.0 10 1540.7 9-993051 A 2, .0 006949 .0-. 47069 5.0 9-852931 .-io 30 33 15 9-846047 6 13 .0 '53953 9-993,78 6 25 10 006822 io-,47.3.| 6.2 9-852869 .|H •-•7 .10 H 9-846... 7'5 10 153889 9-993304 7 29 .0 006696 .0-147.93 7,5 9-852S07 411 :<4 111 9-8+6.75 817 .0 .53825 9-993430 8 34 .0 006570 .0-147255 8,7 9-852745 44 2»i 30 l« 9-846240 9.9 .0 153760 9-993557 9 38 .0 006443 10-1473.7 9,9 9-8526S3 4-i .10 3,i .H) OT 9-846504 1123 .0 .53696 9-993683 9-993810 10 42 11 46 ,0 0003.7 ,0-, 47380 102. 1123 9-S52620 4(1 2.1 9-S46368 10 '5363^ 10 006.90 .0-147442 9-852558 36 21 9-846431 1226 .0 .53568 9-993936 12 5, 10 006064 10-147504 1225 9-852496 :<(] 24 w ■iO 9-846496 l.-i28 .0 153504 9-994062 13 55 10 005938 .0-.47566 13 2-? 9-852434 M .10 37 •is 9-846560 1430 10 .53440 9-994.89 14 59 ,0 005S.1 10-147629 14 29 9-85237, 3-2 23 .10 .10 9846624 1532 10 .53376 9-994315 15 63 10 C05685 10-147691 153. 9-852309 3(1 311 38 .« 9-846688 16 34 .0 15331^ 9-99444, Ifi 67 ,0 005559 10-.47753 1633 9-852247 22 .n 9-846752 1736 .0 .53248 9-994568 17 72 ,0 005432 10-.47816 '7 35 9-852,84 -in .1(1 3') 30 9-8468.6 18 38 .0 .53.84 9-994694 18 76 ,0 005306 10-.47878 I837 9-852122 ■21 21 30 38 9-846880 1940 .0 .53120 9-994820 19 80 ,0 10-14794, 1940 9-852059 ■M 30 40 30 40 9-846944 2042 2145 10 .53056 9-994947 20 84 21 88 .0 005053 10-148003 20 42 2144 9-851997 III 20 9-847008 To" .52992 9-995073 To" 004927 10-148066 9-85.934 41 41 9-84707. 2247 .0 152919 9-995,99 22 93 .0 004801 .0-148128 2246 9-85,872 hi U> 40 9-847135 2,-i49 .0 .52865 9-995326 23 97 .0 004674 10-148,90 2348 9-85.8.0 II .10 42 4« 9-847199 245. .0 ,5280, 9-995452 24 .0. 10 004548 io-,48253 2450 9-85,747 \i 111 30 .',0 9-847^63] 25 53 10 .5^737 9-995578 26.05 ,0 004422 io-,483i5 2552 9-851685^0 30 43 r,t 9-»473^-7 2655 10 .52673 9-995705 26 .05 ,0 004295 ,o-,48378 2654 9-85.622 K 17 30 ^^ 9''*-t"39' 2758 .0 ,52609 9-99583, 27 ..+ ,0 004169 ,0-148441 2756 9-85.559 i, 44 M 9'847454 2s6o 10 .52546 9-995957 28 .,8 ,0 004043 10-148503 2858 9-85.497 1 If; 30 58 9-8475'S 2962 10 .52482 9-996084 29 122 10 003916 . 0-148566 29 60 9-85.434 ■; 30 45^ .V) 59 9-84758^- 3064 10 .524.8 9-9962.0 30 .26 To" 003790 10-.4862S 30 62 9-85.372 1 l.-i 9-847646' .^ 15^354 9-996356 I 4 003664 10-14S691 I r 9-85.309 4H 9-847709 2 4 .0 .5229. 9-996463 2 8 ,0 003537 .0-148754 2 4 9-85.246 ,•,11 u 30 9'847773 3 6 .0 .52227 9-996589 3 ,3 ,0 0034,, , 0-1488, 6 3 6 9-851124 .',, .10 47 s 9-847836 4 8 .0 J 5^-1 64 9-996715 4 ,7 ,0 003285 ,0- ,48879 4 8 9-851.21 ri-i 13 30 10 9-84-9CC 5.1 .0 9-996842 5 2, 10 003,58 ,0- ,48942 5 .0 9-85.058 ,',0 30 48 fl 9-847964 6.3 .0 .52036 9-996968 6 25 003032 10-149004 6.3 9-850996 IS 12 3fl II 9-848027 715 ;° 151973 9-997094 7 29 10 002906 10-149067 715 9-850933 Ki 30 49 10 9-S4809. 8.7 ,5.909 9-997221 M 34 ,0 002779 .0-149,30 8.7 9-850870 II 11 .10 IM 9 848155 9.9 .0 15.845 9-997347 9 38 ,0 002653 ,0- ,49,93 9,9 9-850807 n 30 50 30 '"' 9-S482,8 9-S4S282 1021 1123 L° 15.782 9-997473 ■ 42 n 46 7^ 002527 .0-.49255 II23 9-850745 '" 1(1 30 .5,7,8 9-997600 002400 .o-,493,8 9850682 Bl ■11 9-848345 1225 10 .5,655 9-997726 12 5, .0 002274 ,0-14938, 1225 9-8506.9 3li 9 30 ■a-i 9-848409 13 28 10 15.591 9-997852 13 55 .0 002,48 .0-149444 13 27 9-850556 34 30 l>2 m 9-848472 1430 10 .5.528 9-997979 14 59 .0 C0202. 10-. 49507 14 29 9-850493 .n R .HI M 9-848535 ..^ 32 .0 .5.465 9-998105 15 63 ,0 001S95 .0-.49570 153, 9-85043C .1(1 30 .-.3 :u 9-848599 •«34 10 .5140. 9-99823, 16 67 ,0 001769 10-. 49632 16 34 9-850368 -2S 7 ■Kl ■;4 9-848662 1736 .0 ■51338 9-998358 17 72 ,0 00,642 .0-149695 1736 9-850305 ■11; .u :m 9-848-26 18 38 .0 ,5.274 9998484 18 76 10 00 , 5 . 6 .0-149758 18 38 9-850242 i> r, .Vl .IS 9-848789 1940 .5.2.. 9-998610 19 80 ,0 00.390 .0-.4982. 1940 9-850179 T2 30 .'..'i 10 w 9-848852 2043 2145 ,5.. 48 9-998737 9-998863 7.11 10 00.263 10-. 49884 2042 2144 9-850116 •'" ~30 9-8489.6 To" .51084 iT 00. .37 .0-149947 9-S50053 Sfi II 9-848979 2247 .0 .5.02. 9-998989 22 93 ,0 00101 1 10-. 50010 2246 9-849990 III 4 :io 10 9-849042 2349 10 .50958 9-999116 23 97 ,0 000884 .0-. 50073 2348 9-849927 14 31) S7 Is 9-849.C6 245, 10 ,50894 9-999242 24 10, 10 000758 .0-. 50136 2450 9-849864 It 3 :io .•,0 9-849169 2,553 .0 .5083. 9-999368 25 ,05 .0 000632 .0-. 50.99 2552 9-84980, 10 30 SH .Vi 9-849232 2655 10 .50768 9-999495 26 .09 C00505 .0-150262 2654 9-849758 H 2 30 .',1 9-849295 2757 I'J .50705 9-99962. 27 ..4 10 000379 .0-, 50326 2756 9-S49674 II 30 ftn .VI 9-849359 28 60 10 ,5064. 9-999747 28 ,,g .0 000253 ,o-, 50389 28 59 9-84961. 1 1 .10 .•,H 9-849422 2962 .0 .50578 9-999874 29 .22 .0 GOO. 26 .0-. 50452 296, 9-849548 ■2 30 IH) 60 m. 9-849485 3064 10 1505.5 30 ,26 .0-000000 ,o-,505,5 .3063 9-849485 ^■ {•o.inc Pf.rt» Scant (-..,a„K. Parts Tnll^•rnt i'ttfCC. Pnr;.| Sine 4;.° ~ 3'' 0™' 1 82S TABI.I- f)9 LOG. OK Tin; syUAKi; OK THE Sl.NE* OF HALF Till; AllC. 0" 1° 2° 0' 15' 30' I 45' 0' ! 15' 1 30' 1 45' 0' 1 15' 30' oMo'" , Oh 0- 0" I'" Oh 2m 01. 3... 01. 4... 01. 3... 1 01. «". 1 01. 7." 01. 8." ' 0'. i}'- ^ 5- 5- 6- 6 1 6- 6- 16- 6- 4-67757 27963 63.8. 3S8168 07550 23385 36774 4837.158600 67751 le 1-12127 4-69193 28684 63662 5-88530 07839 I 23626 36980 48552158761 6-895 1 30 '•7»333 4-70605 29399 64141 5-S88S90S127 23866 37,86 48732 58921 6 8 040 2 45 I-07552 4-71995 30108 646,7 5-89247108414 24106 37392 48912 5908. 68.84 3 1 2-31539 4-73363 30S.. 65090 5-89604I 08700 24345 37597 49092 59241 6S328 4 15 2-;i92i 4-74710 31509 65561 5-89959' 08985 24583 37802 49271 59401 68471 ft 30 i'67757 4-76036 32201 66029 5-90313109270 2482, 38006 49450 59560 6S615 ti 45 2-SI.47 4-77342 66495 5-90665109553 2505S 38209 49628 59719 6875S 7 2 ^•9-7451 4'7S629 33569 66958 5-9.016,09836 25294 38412 49807 59878 6890. H U, 5-02976 4-79897 MliL 674.9 5-9.366; ini.7 25530 386.5 49984 60036 69044 J' M 3-12127 4-81147 34916 67877 5-9, 7'4, .039S 25765 50.62 60.94 1 69. 86 10 45 3-204.06 4-82379 3558- 68333 5-9206. .0677 ' 25999 39019 50339 60352 69328 II :t 3-27963 4-83594 36242 68787 5-92406 ,0956126233 39220 505.6 60509 69470 12 15 3-349'6 4-84792 36897 6923S 5-92750I 1.234 '26466 39421 50692 60666 696.2 13 30 3-41353 4-85973 37548 69687 5-93093! .15.. 26699 39622 50868 60S23 69754 14 45 347345 4-87139 38.94 70.33 5-93434 11787 2693. 3982. 5.044 60980 69895 15 4 3-5295' 4-88290 3S835 70578 593774 '2063 27162 4002. 5.219 6.136 70036 l(i 15 3-58217 4-89425 3947.171020 5-94. .3 12337 27393 4C220 5 "394 6.292 17 30 3-63182 4-90546 40103 171460 5-94450I 126.. 27623 404.8 51568 6.448 703.8 l» 45 3-67S7S 4-9'653 40730 1 7.897 ^947861 ,2883 27S52 406.6 51743 6,604 70458 1!) 5 3-72333 4-9^745 41352 72332 5-95.2. 13155 28081 '^^ 5i9'6|6,759 70598 20 15 3-76571 4-93824 4.971 72766 5-95454 13426 28309 4.011 52090 6.914 70738 21 30 3-8o6i2 4-94890 425S4 73'97 595786 13696 28537 4.208 52263 62068 7087S 22 45 3-S4473 4-95943 43 "94 73626 5-96.17 .3966 28764 4.404 52436 62223 7.017 23 (i 3-88.69 4-96983 43799 74052 5-96447 14234 Z8991 4.600 52608 62377 71157 24 15 3-91715 4-9801. 44400 74477 5-96775 14502 29217 41795 52780 62531 7.296 25 30 3-95122 4-99027I 44997 74900 5-97.02 14769 29442 4.990 52952 62684 71435 2« 45 3-98400 5-0003. 4559° 75320 5-97428 15035 29667 421S5 53124 62838 71573 27 5 401559 5-0.024 46179 75739 5-97753 15300 29S91 42379 53295 6299. ■>>: 15 4-04607 5-02005 46764 76.56 5-98076 .5564 30114 42573 53466 63143 7185c 30 30 4-0755i| 5-02976 47345 76570 5-98399 .5828 30337 42766 .3636 63296 7.9SS 46 4-1040015-03935 47922 76983 5-98720 16091 30560 42959 53806 63448 72125 31 8 4-13157 5-04885 48495 77394 5-99040 16353 3078. 43151 53976 63600 72263 32 15 4-1583° 5-05824 49065 77802 5-99358 16614 3.003 43343 54146 63752 72400 33 30 4-1S+23 5-06753 49631 78209 5-99676 16874 3.223 43534 54315 63903 72537 34 45 4-20941 5-07672 50.93 78614 5-99992 17134 31444 43726 54484 64054 72674 35 9 4-21388 5-0858. 50752 79017 6-0030S 17393 3.663 439,6 54652 64205 I72S 11 3■•■ 0'- \3-" 30' 1 45' 0' 15' 1 30' 45' 0- 16' Oh 21 n • . Ol, 1,;.., OM7"'|0i' IH"' 01. !».,. 0^(1". 6- 6- |6- r T r 7' T \ T »' 760Z8 S3584 90535 6-96970 02960 ^8564 ,3827 ,8790 23483 27936 32,7, (1 15 76.59 83704 1 90646 6-97073 03057 08654 .3912 ,8870 23559 28008 32240 1 30 76290 83825 |9°757 6.97.76 03'53 08745 .3997118950 23635 2S0S0 32309 2 45 76+^1 839+5 1 9°868 6-97279 03249 08835 .4082 .9030 237" 28,53 32377 3 I -•^ss^ S4065 90979 6-97382 03345 .4.67 ,9.., 23787 28225 32446 4 76683 84.85 9.089 6-97485 03441 090.5 1+252 ,9,91 2S297 32515 : 85256 92079 6-98405 04300 .50.. .9908 2+5+3 289+3 33.30 14 4ft 77979 85374 92,89 698506 04395 099,0 ,5095 19987 246,8 29014 33198 15 4 78108 85492 92298 6-98608 04490 09999 '5'79 2C066 2+693 290S6 33266 I'i Ift 78^-36 856.0 92407 6-98709 045S5 ,0088 ,5262 20,45 2476S 29'57 3333+ 17 30 7S364 85728 925,6 6988.. 04680 10,77 153+6 20225 2+843 29228 33+02 III 45 78492 85846 92624 6-989.2 04774 ,0265 15+30 20304 249,8 29299 33+70 19 6 7S620 85963 92733 6-99013 04869 .0354 15513 20383 24993 29371 33538 "Sir 15 7 8 748 86080 92841 6-991.4 04963 10443 •5597 20461 25068 29442 33606 •21 30 78S75 86,97 92950 6-992,4 05057 .56S0 20540 25,43 295,3 33673 22 45 79002 863,4 93058 6-993,5 05,5, ,06^9 '5763 206,9 252,7 29584 337+1 23 6 79129 S643. 93,66 6-994,6 05245 .0708 ,5846 20698 25292 29655 33809 24 15 -9256 S6548 93274 6-995,6 05339 ,0796 .5930 20776 25366 29726 33876 25 30 793«3 86664 93382 6-996.6 05+33 10S84 .60,3 20855 25441 29797 339+4 2(; 45 795<>9 86781 93489 6-99717 05527 .0972 .6096 20933 25515 29S67 3+01, 27 7 79636 86S97 93597 6998.7 05620 .1060 16. 78 25590 29938 3+079 2H 15 79762 870.3 93704 6-Q99,7 057,+ .,148 ' ,6261 ' 2,090 25664 30009 34146 29 30 87.29 938,2 7-000,7 05807 .1235I.6344I2..68 25738 30079 342,3 30 45 80014 87244 939'9 7-co,i6 05901 .,323 .6427 21246 258,2 30,50 3+28. 31 8 80.39 87360 94026 7-002.6 05994 114,1 16509 2,325 25886 30220 3+3+8 32 15 80265 87475 94'33 7-003.5 C6087 ,.498 .6592 2,403 25960 30291 34415 33 30 80390 8759. 94239 7-00415 C6.80 .15S6 ,6674 2,48, 26034 3036,, 34482 34 45 805.5 87706 94346 7-005,4 06273 .,673 16756 2,55s 26108 3043, 3+549 35 9 80640 87821 94453 7-006.3 06366 ..760 .6839 2,636 26182 30501 346,6 30 15 80764 87935 94559 7-007,2 06458 1,847 ,6921 2,7,4 26256 30572 3+68 3 37 30 80889 S8050 94665 7-008., 0655, "934 .7003 2.792 26330 30642 3+750 31! 45 8.0.3 88,65 9477 > 7-009,0 06643 ,202, 1 1708512,869 26403 307.2 3+8.7 34884 39 40 10 8. .37 88279 94877 7-0.009 06736 .2,c8 ,7,67 21947 26477 30782 15 8126. 88393 94983 7-01107 0682S 12,95 17249 22024 26550 30852 3+950 41 30 8.38s 88507 95089 7-0.206 06920 ,733' 22102 26624 30922 35017 42 45 8.509 88621 95 '94 7-01304 070,3 12368 i74'2 22179 26697 30992 35084 43 1 1 8.632 88735 95300 7-0.403 07105 '2455 1 749-1 22256 26771 3.062 35150 44 15 8.756 88848 95405 70.50. 07,96 '2 5+1 17574, 22333 '26844 31,3, 35217 45 30 8,879 88962 95510 7-0,599 072S8 .2627 17657 224,, 269.7 3.20, 35283 4(i 45 82002 89075 956.5 7-0,697 07380 '27' + 17738 22488 26990 3127' 35350 47 12 82.24 89. 88 95720 7-0,795 07472 ,28001,7820122565 27063 3'3+o 35+16 411 15 82247 8930.1 95825 7-0.802 107563 .2886 1 .790. 1 22642 27,37 3,4,01 35482 49 30 82369 89414 95930 7-0.990 07655 ,2972 ,7982 [227.9 272,0 31+79 355+9 "Tio 45 82492 89527 96034 7-02088 07746 .3058 ,8063 122795 27282 3 '5+9 356.5 51 13 8:6.3 S9639 96.39 702185 .3144 ,8.44122872127355 3,6,8 3568. 52 15 8^735 89752 96243 702282 07928 13229 ,8225 1 22949 27428 3,687 35747 53 30 82857 89864 96347 702379 080,9 13315 ,8306 23025 27501 3.757 35813 51 45 82979 89976 96451 7-02476 08,, 13401 ,8387 23,02 27573 3,826 35879 55 14 83.00 90088 96555 7-02573 0820. 13486 .846S 23,78 27646 3,895 35945 56 15 83221 90200 96659 7-02670 08292 13572 18548 23255 27719 3,964 360.. 57 30 8534* 90312 96763 7-02767 08383 '3657 ,8629 23331 27791 32033 36077 58 «fi hit> 90423 9686) 7-02864 08473 .J -42 .8709 23407 127864 36,43 59 830 TABLE 09 I>00. SINi; SQUARE 5° 6° 7° 8° 30' 45' 01. 22'" '0'' 23'" 0' 15' 1 30' 0i'25'"|0i'2(i'" 45' 0' 1 15' 1 30' 45' 0' „1, 24"' 0" 27"' 0i'2K"'|0i'2!»'"l0i'30" 01' 31'" 01' 32'" d (i 36209 40067 43760 7- |7- 7- 47302 : 50706 53980 7- >7- 571351 60179 63,20 65964 687.7 1,1 36274 40129 43820 47360I 50761 5V034 57.87 60229 63,68 660,, 68762 1 :i() 36340 40192 43SS0 4741^,508.7:54087 57238 6=279 63216 66057 6SS07 2 4.1 36406 40255 43941 47476 1 50872 ,54.41 57290 60329 63264 66103 68852 3 I 36471 403.8 44001 47533 50928 54 '94 57341 60378 633,2 66150 68897 4 15 36537 40380 44061 47591 50983 54247 57393 60428 63360 66.96 68942 5 3(t 36602 40443 4412. 47649 5.039 54301 57444 60478 6340S 66243 68987 li 4ft 36668 40506 44181 47707 5.094 543 54 57496 60527 63456 66289 69032 7 2 36733 40568 44241 47764 5 > '49 '54407 57547 60577 63504 66336 69077 8 15 3679S 4063. 4430. 4782, 5.205 1 5446. 57598 60627 63552 66382 69,22 9 36864 40693 4436. 47879 512601545.4 57650 60676 63600 66429 69,67 TiT 45 36929140756 44420 47936 5'3'5 54567 57701 60726 63648 66475 692,2 11 5 36994 40X.8 44480 47994 5>37o 54620 57752 60775 63696 6652, 69257 12 15 37°59 408S0 44540 4S05, 51426 54673 57804 60825 63744 66568 69302 13 :«t 37124 40943 44600 48.09 5.48. 54727 57855 60874163792 66614 69347 14 15 37189 41005 44659 48.66 5-536 547 So 57906 60924 I 63839 66660 69392 15 4 37^54 4.067 44^19 48223 5'59> 54833 57957 60973 63887 66701, 69437 Ifi 15 373>V 41129 44779 482S0 5.646 54886 58C08 6.022 63935 66753 694S. 17 30 37384 4119. 44838 48337 51701 54939 58060 61072 63983 66799 69526 18 45 37449 41253 44S98 48395 5.756 54992 58... 61 .2. 64030 66845 A9i7i 19 ~T"u 375 '4 4>3i5 44957 48452 5181. 55045 58,62 6. .70 64078 6689, 696,6 20 15 37579 41377 450.6 48509 51866 55097 58213 6,220 64,26 66937 69660 21 ■M 37643 4'439 45076 48566 51921 55 '50 58264 6,269 64.73 66983 69705 22 45 37708 4.50. 45135 48623 5'975 55203 583.5 613,8 67029 69750 23 6 3777i 4.563 45194 48680 52030 55256 58366 61367 64269 67075 69794 24 15 37»37 4.625 45254 4S737 52085 55308 584.6 6,4,7 643,6 67,2, 69839 25 30 37902 4.686 45313 48794 52140 5536. 58467 6,466 64364 67,67 69883 20 45 37966 41748 45372 48850 52194 554'4 585.8 615,5 644,, 672,3 6992S 27 7 38030 4543" 48907 52249 55467 58569 6,564 64458 67259 69972 28 15 38095 4187. 4'933 45490 48964 52304 555>9 i!^- 6,6,3 64506 6^305 700,7 29 ■M 38159 45549 4902. 52358 55572 5X670 61662 64553 6735. 7Co6, 30 45 38223 4.994 45608 49077 52413 55624 58721 6171, 6460, 67397 70,06 31 8 382S8 42056 45667 49134 52467 55677 58772 6,760 64648 67443 70.50 32 15 38352 421.7 45726 4919. 52522 55729 58823 61S09 64695 674S9 70.95 33 30 38416 42.74 45785 49247 52576 55782 58873 61S5S 64743 67535 70239 34 45 38480 42240 45844 49304 5263. 55834 58924 61907 64790 67580 70283 35 9 38544 4230. 45903 49360 52685 55887 58974 61955 64837 67626 70328 3f; 15 38608 42363 45962 494 '7 52739 5';939 59025 62004 64885 67672 70372 37 30 38672 42424 46020 49473 52794 55992 59075 62053 64932 677,7 704.6 38 45 38736 424S5 46079 49530 52848 56044 59.26 62,02 64979 67763 7046. 39 lo" 10 38800 42546 46138 49586 52902 56096 59176 62151 65026 67809 70505 15 38S63 42607 +6,96 49642 52956 56,48 59227 62199 65073 67X54 70549 41 30 38927 42668 46255 49699 53011 56201 59277 62248 65.20 67900 70593 42 45 38991 42729 46313 497 55 53065 56253 59327 62297 65,67 67946 7063S 43 11 39°54 42790 46372 498.1 53'>9 56305 59378 6234s 652.4 6799. 706S2 44 15 39118 4285, 46430 49867 53'73 56357 59428 62394 6526, 6S037 70726 45 30 39,82 429.2 46489 49923 53227 56409 59478 62442 65308 6S082 70770 46 45 39^5 42973 46547 49979 53281 5646, 59529 6249. 65355 6S.28 ^°l'i 47 12 39309 43034 46605 5^,036 53335 565 '3 59579 62540 65402 68. 73 70S58 48 15 39372 43°95 46664 1 50092 53389 56565 59629 625SS 65449 6S219 70902 49 30 3943 5 43155 46722 50.48 53443 56617 59679 62636 65496 68264 7=946 "50" 45 39499 432.6 467S0 50204 53497 56669 59729 62685 65543 6S309 70990 51 13 39562 43277 46838 50259 5355° 5672, 59779 62733 65590 6S355 71034 52 15 39625 43337 46896 503" 5 53604 56773 59829 627S2 65637 68400 7.078 53 30 59688 43398 46955 50371 53658 56825 59879 62830 65683 68445 7. .22 54 45 3975' 43458 47013 50427 53712 56876 59929 62878 65730 6849, •'.166 55 H 39815 435'9 47071 50483 53765 56928 59979 62927 65777 68536 ,1210 (>(> li 39878 43579 47129 50539 53819 56980 60029 62975 65824 685S. 7'2S4 57 30 39941 43639 47187 50594 53873 57032 60079 63023 65870 68627 7.298 68 45 40004 43700 47245 50650 53926 57083 _5°'i9. 63071 I65917 68672 _7il4. 68 S.r. l' 2" 3" 4' 5" «' 7' 8 !)' 10' 11' 12- 13' 14' 15' 1 1). 04. I'iuu 4 9 13 17 1' :6 3° 34 3» 43 47 5' 55 6° H 1 I). 45. I'lirts 36 9 11 15 18 II 14 27 30 33 36 37 42 4; 1 TABLE 09 881 I.O«. SINE SQUAKK 1 8^ 9^ 10° 15' 3(f 45' 0' 15' 1 30' 45' 0' 15' 1 30' ( 45' .. 0" 33 ' (»'' 34' (]^t.V 0'' 3ti" 0" 37' 1 Ol' 38" Ol- 3!)" n'' 40' 01' 4K 0''4'i'"|0''43' 7- |7- 7- -,. |7- .. 7- 7" 7- [7- o' m'^i 73974:76487 7S929 8.303 836,5 85S66 8S059 90.98 92286 94324 l.i 71429 74016 76528 78969 8 1 342 83653 85903 88095 90234 92320 943 57 1 I 30 71473 74059 76569 79009 81382 83691 85940 88131 90269 92354 9439. 2 45 71516 74101 76610 79049 8142. 83729 88. 67 90304 92389 94424 3 1 7,560 74.43 76652 79089 8.459 83767 860H 88203 90339 92423 94458 4 15 7,604 74.?6 76693 79129 8,498 83804 86050 882 39 90374 92457 9449' 5 :*o 7164)! 74228 76734 79.69 81537; 83842 860S7 SS276 90409 92492 94525 6 ■45 7,691 7427.176775 79209 81576 83880 S6124 88312 90445 1 92526 94558 7 2 (» 7>7j5 743.31768.6 79249 S161S 839.8 86161 S8348 90480 I 92560 94592 8 15 71778 74355176857 79289,81634 83956 8619S S8383 905,5 92595 94625 9 30 71S22 74398 76898 79329 S1693 83994 86235 884.9 90550 92629 94659 Ti 45 71866 74440 76940 79369 84032 86272 88455 90585 92663 94692 II 3 71909 74482 7698. 79409 8.771 84070 86309 8849. 90620 92697 94726 12 15 71953 74524 77012 79449 81810 84107 86346 88527 90655 92751 94759 13 30 7.996 74567 77063 79489 81S48 84.45 86382 88563 90690 92766 94792 14 45 72040 74609 '77104 79529 81887 S4.83 86419 88599 90725 92800 94826 15 4 7^083 7465. 77.45 79568 8 1926 S422. 86456 88635 90760 92834 94859 l«i 15 72.26 74693 77186 79608 8. 965 842 58 86493 88671 90795 92868 94892 17 30 72170 74735 77227 79648 82003 84296 86530 S8707 90830 92902 94926 1» 45 722.3 74777 77267 79688 82042 84334 86566 S8742 90865 92936 94959 IH 5 ^2257 74819 77308 79728" 82081 84372 86603 88778 90900,92970 94992 20 15 72300 74861 77349 79767 82119 84409 86640 88814 90935 1 93005 95026 21 30 72343 74904 77390 79807 82,58 84447 1 86676 88850 90970 1 93039 95059 22 45 72387 74946 7743 > 79847 82197 84484 86713 88SS5 9.C05 93073 95092 23 G 72430 74988 77472 79S86 82235 84522 86750 88921 91039 93107 95'26 24 15 72473j75°30 775.3 79926 S2274 84560 86786 88957 91074 93.41 95'59 25 30 72,16 75072 77553 79966 S2313 84597 S6823 88993 91,09 93'75 95.92 2(i 45 72560 75.14 77594 80005 82351 84635 S6860 S9C28 91.44 93209 95225 27 7 72603 75.55 77635 80045 82390 84672 86896 89064 9. .79 ,93243 95259 28 15 72646 75.97 77676 80085 82428 847.0 S6933 89. 00 9.2.4I93277 95292 29 :«» 72689 75239 777.6 80124 S2467 1 84747 86969 89.35 9.248 1 93311 95325 Ito" 45 72732 75281 77757 80164 82505 84785 87C06 89.71191283193345,95358 31 8 72775 75323 77798 80203 82544 84822 87042 89207 9.3.8 V3379 9539. 32 15 7281S 75365 77838 S0243 82582 84860 87079 89242 9.353 934'3 95424 33 30 7286, 75407 77879 80282 8262. 84897 87115 89278 9.3S7 93447 95458 34 45 72904 75448 77920 80322 81659 84935 87.52 893.4 91422 93480 9549. 35 » 72947 75490 77960 8036, 82698 84972 87.88 89349 9 '457 93 5 '4 95524 3K 15 72990 75532 78001 80401 82736 85010 87225 89385 91492 93548 95557 37 30 73°33 75574 78041 80440 82774 85047 87261 89430 9.526 93582 95590 38 45 73076 75615 78082 80480 82813 85084 87298 89456 91561 936,6 95623 39 10 73.19 75657 78122 805,9 82851 Ii7l2- 87334 89491 91596 93650 95656 40 15 73.62 75699 78.63 80558 82889 85159 8737. 89527 91630 03684 95689 41 30 7320; 75740 7S203 S0598 82928 85196 87407 89562 9,665 937'7 95722 42 45 73248 75782 78244 80637 82966 85234 87443 S9598 9,699 9375' 95755 43 II 7329. 75824 78284 80677 83004 8527. 87480 89633 9'734 937S5 957S8 44 15 73334 75865 7X325 80716 83043 85308 875.6 89663 91769 938.9 9582. 45 30 ^")i"7 7590- 78365 80755 83081 8 5 346 87552 89704 9.803 93852 95854 4fi 45 7H'9 75948 78405 S0794 83119 85383 875S9 89740 91838 93886 95887 •17 li -1462 75990 78446 80834 83.57 85420 87625 89775 91872 93920 95920 4« 15 -3^C5 7603, 7S4.86 80873 8,196 85457 87661 89810 ,91907 193954 95953 49 :u) 76073 78526 809.2 83234 85494 87697 89846 9.941 93987 95986 50 45 -•,syo 76.. 4 7S567 80951 83272 85532 87:'34 89881 91976 94021 960.9 51 13 :'3633 76,36 78607 80991 83310 85569 87770 89916 920.0 94055 96052 52 15 716-6 76.97 78647 8,030 83348 85606 87806 89952 9204 s 94088 96085 53 :«o 73718 76239 78688 8,069 833S6 85643 87842 89987 92079 94.22 96,18 54 45 73761 76280 78728 81108 83424 85680 87878 90022 92114 94.56 96150 85 14 73803 7632. 7876S 81147 83462 857.7 S79.5 90057 92,48 94.89 96183 5B 15 73846 76363 78808 S1186 83501 85754 8795. 90093 92,83 94223 96216 S? 30 73889 76404 7S848 8.225 «3539 85791 87987 90128 922.7 94257 96249 58 45 7393' 7644; 78889 8,264 83577 85829! 88023 90163 922;. 1 94290 962S2 59 s*.-. r r 3' 4" a' c r b w w w n' \y u' is' 1 I) 4( I'iirts 1 6 9 II 14. 17 lO 23 26 19 32 34 37 40 43 1 I>. 33 I'liris 247 9 II 13 IS iS 20 22 24 20 29 31 33 1 TABLE no I.r)U SINU SyUARK 1 12° 13° :«• 0' 1 15' 30' 45' 0' 15' 1 30' 45^ 0' ">' . Oi'44-j 0'' 45"' 0''4(i'" 01. 47m (l"4«'"loi'49"'|Oi'50'" 01' 0)'" 01. 02'" 0l'53".|(ti>54'' 9. 7-9 \' 8-0 1 S'o 8-0 |8-o 80 8- 8- 1 8-1 9 J 63146 J7-982604 0,63,, 2024S 38469156312 73792 090922 07717 24190 +0352 15 S3474 y982925 01945 20555 38770 56606 74080 091205 07995 24462 406.9 1 30 63801 17-983245 02259 10862 39070 569CO 74368 09,487 08272 24734 40886 2 •l.'i 64129 7-983565 02572 2,168 39370 5719+ 7+656 091770 085+9 25006 41152 3 1 6+457 7-983885' 028S6 21475 39670 574S8 7+9+4 092052 08826 25277 +1+.9 4 ij 64784 7-984206 03199 21781 39970 57782 75232 092334 09102 25549 41685 5 30 65,,, 7-9S4526 03512 +0270 58076 75520 092617 09379 25S20 +1952 f, 45 6,-439 7-984846 03825 22394 40570 58370 75808 092899 09655 2609, +2218 7 2 65766 7-985166 04137 22700 40870 58665 76095 09318, 09932 26363 424S4 8 i,'. 66C93 17-985485 04450 23006 41169 58957 76383 093463 10209 26634 42750 43c 16 a 1»' 311 66420 [7'9858o5 04763 23312 41469 59250 76670 093744 10485 26905 45 66746 I7-9S6124 05075 23617 41768 59543 76958 094026 10761 27,76 43282 11 3 n 67C73 |7-9«6443 05388 23923 42067 59S36 772+S 094308 11037 27+47 43557 12 15 67399 7-986762 0570c 24229 42367 60129 77532 09+589 1131 + 2771S 43814 13 30 6772617-087082 06012 1+534 42666 60422 778.9 09487, 11590 279S9 44080 14 45 68052 7-987400 6S378 7-987719 06324124839 +2965 60715 78.06 095,52 11865 2S259 4+3+5 15 4 06636 25.45 43264 6,008 78393' 095+33 12,+, 28530 44611 11; 15 6i'704 7-988038 06947 25450 43562 6.30, 7868010957.+ J2+,7 28SCO 44876 17 30 69030 7-9SS357 0,259 25755 43861 61593 78967 095995 12693 29071 1 451+2 18 45 65355 [7-988675 07571 26060 44159 6,886 79253 096276 12968 29341 +5+07 10 5 69681 17-988994 07882 26365 44458 62.78 79540 096557 I32++ 296.1 45672 20 15 70006 7-989312 08.93 26669 4+756 62470 79826 096S3S 13519 45937 21 30 70332 7-989630 08505 26974 45055 62763 801,3 097119 '379+ 30152 46203 22 45 70657 7-989948 088.6 2727S 45353 63055 80399 097399 1+069 30422 4646S 23 6 70982 7-990266 09127 27583 4565. 63347 80685 097680 ■+3+5 30692 46732 24 15 71 ;o7 7-990583 09438 27887 45949 63638 80971 097960 14620 30961 46997 2S 30 71632 7-990901 09748 28191 46247 63930 81257 098241 14S95 31231 47262 2fi 45 71956 17-991219 10059 28495 46544 64222 8. 5+3 098521 15169 31501 +7527 27 7 722S1 7-991536 10370 28799 46S42 64513 8.828 09880, 15444 31770 +7791 2f! 15 72606 7-991853 10680 29103 47139 64S05 82114! 099081 ■5719 320+0 +8056 2!) 30 A» 72930 7-992171 10990 1 29407 47437 65096 1 82400 j 099361 15993 32309 48320 45 73^-54 7-992+88 1,300 297.0 47734 65387 82685 099641 .6268 32579 +8585 31 R 73578 7-992805 11611 30014 4803. 65679 82970 1 099921 16542 328+S +88+9 32 15 73902 7-99312. 11920 30317 48328 65970 83256 100200 .68.7 33117 49113 33 30 74226 7-993+38 .2230 3062. 48626 66261 83541. 100480 17091 33386 1+9377 34 45 7455° 7-993755 12540 30924 48922 6655, 83826 .00759 17365 33655 49641 :i5 9 7tS73 7-994071 12850 31227 49219 66842 84111 1 101039 17639 3392+ 49905 3B 15 75197 7-994387 I3'59 3 "53° 49516 67,33 84396,101318 17913 3+193 50169 37 30 75520:7-994704 .3469 31S33 49813 67424 84681 ,0,597 18.87 34461 50+33 3!) 45 758+4 7-995020 13778 32135 50109 677.4 680C4 8+965 ,0,876 ,02156 18461 3+730 50696 3!l 1(» 76,67 7-995336 .4087 32J38 50405 85250 1S734 3+999 50960 40 15 76490 7-995652 ,4396 3274" 50702 68295 85534 102434 1900S 35267 5,223 41 30 76813 7-995968 ,4705 33043 50998 68585 858.9 102713 1928. 35535 51+87 42 45 77135 7-996283 15014 33345 51294 68875 86103 102992 19555 35S0+ 51750 43 11 77+58:7-996599 153^3 33648 51590 69.65 86387 103271 19828 36072 520.3 44 15 777S0 7-996914 15631 33950 51S86 69455 S6671 103549 20102 36340 52277 45 30 7S103 7-997230 15940 34252 52182 69745 S6956 103S28 20375 36608 525+0 40 45 78425 7-997545 ,6248 3+55+ 52477 70034 87239 104106 20648 36876 1 52803 47 1-2 787+7 7-997S60 .6557 3+856 52773 70324 87523 10+385 20921 37144 53066 4a 15 3(7 79069 7-998175 16865 35 '57 5306S 706.3 j 87807 104663 2.. 94 37+12 I5332S 40 79391 7-998490 17173 35459 53364 70903 8809. 1 10494. 2. +67 37679 53591 50 45 79713 7-998804 17+81 35760 53659 71,92 88374 105219 2.739 379+7 5385+ 51 13 80035 7-999119 .7789 36062 53954 71481 88658 105+97 382.5 5+117 52 15 80356 7-9994.33 ,8097 36363 5+249 7.770 889+1 '05775 22285 38482 5+379 53 30 8067S 7-y997+« 1S404 36664 5+5+4 72050 72348 89214 106053 22557 38750 54642 54 45 80999 8-000062 1S712 36965 5+839 89508 106330 22829 39017 5+904 55 14 U 81320 8-000376 19019 37266 55134 72637 S9791 106608 23102 39284 55166 5(J 15 81641 8-000690 19326 37567 55428 72926 90074 ,06885 23373 39551 55+29 57 30 81962 800,004 19634 37868 55723 732.5 90357 107163 23645 398.8 5569. 5H 45 82283 8-00.3.8 1 ■994> 38169 560.8 73503190639 107++1 239.8 40085 5>153 50 Sec. I' -r 3" 4" 5" 0- T »' 9" 10" IT 12" 13' 14' 15' D. 324. Parts I2 43 65 X6 108 130 151 173 194 116 138 259 281 302 3?.4 D. 2«4. Piiru 18 35 53 70 88 106 123 141 158 176 ,94 2,, 2:9 246 264 FAHLK W) 838 I.OO. SINK syUAKt .5'' _1S'„ 14^ 1G° 0' I.V 3(1' 4.V " 0' 1 U^ 30 45' 0' 1 15'" — 0'' 55" Oi'Sfi" 0"&7"' oi^58^ 0'' 59" ,iM,^| IM." Ih.j,,, 1''3"' 11.4,,, 1 ih,v„ «. Si 8- 8-2 8-2 8-2 !8-2 8-2 8 2 8- |8-5 Il' (i 56215 71788 ,87085 02. .2 ,6879 3'395 45669 59:08 735'9 287... C0488 l.'l 5647- 72046 ■87337 02360 .7.23 3'635 45905 59940 -574S 28733' C07.0 1 :w 56738 72303 .87590 02608 ■7367 3'875 46.4, 60172 73976 287560 CC93, 2 *:> 57COO 72560 ,87842 02856 ,76., 321.5 46376 60404 74204 287784 0,,52 3 1 57262 72X17 18S095 03.04 ■7854 3 = 354 466,2 6c6;6 7445 = 288C09 0,373 4 1.-. 575=4 7307+ ,88347 0335 = 3 = 594 46848 60867 74660 288233 0,594 5 :«» 577!i5 7333' .88599 03600 ,8342 3=833 47083 61099 74888 =88458 0,8,5 ti j.i 5S0+6 73588 |8»85> 03848 ,8585 33073 473"9 6,33, 751.6 02035 7 2 (1 5830S 73844 189104 04095 ,8829 333' = 47554 6.562 75344 288906 02256 tl 1.-. 11569, 58830 74101 189356 j 04343 ,9072 3155=147790 61794 62025 1557 = 7 5 SCO 289131 0^4:7 9 M 74357 .896081 0459. .93.6 33791 1 48025 289355; 02698 10 45 59091 74614 ■89859104838 '9559 34030 48260 62257 76027 289579 029,8 1 1 3 () 5935= 74870 .90... ,05086 .9802 34269 48495 62488 76=55 289803 03.39 12 Ift 596.; 7 5 '=6 .90363105333 20045 34508 48730 627.9 76483 290027 03359 13 :to 59«7+ 75382 .906.5 05580 202S8 34747 48965 6295. 767,0 290251 03580 14 4.^ 60135 75639 ■9C866 05827 2053, 34986 49=00 63182 76938 290475 038C0 15 4 U 60396 .91.18 06074 20774 35==5 4943 5 634,3 77.65 290699 C4021 l(i l.i 60656 76150 ■9,369 06322 21017 35464 49670 63643 7739= 290922 04241 17 30 609,7 76406 ' 19,620 06569 2,263 35703 49905 63875 77620 291146 C4^6, 111 4.-> 61177 76662 191872 06816 = '5°3 3594' 36,80 S0140 64.06 77847 291370 C4681 19 20 :. 6.438 76,.8 192.23 07062 = ■745 50374 64337 78074 29,593104901 1.-. 61698 77174 ■9=374 07309 2,988 364.8 50609 64567 78301 29,817105.2, 21 ■Ml 6,95X 774=9 .92625 07556 22230 36656 50843 64798 785=8 292040 05341 22 4ft 62218 776S5 192876 07803 = =473 36895 5,078 65029 78755 292264 05561 23 fi (! 62478 77940 .93.27 08049 2 = 715 37133 5,3.2 65=59 789S2 292487 0578. 24 15 62738 78,95 ■93378 08296 22957 3737= ' 5^547 65490 79=09 2927,0 o6co. 25 :ii) 62998 78451 1936=9 08542 23100 376,0 5.78.; 6:720 79436 =9=933 06221 2(i 4.1 63258 78706 .93879 087S8 = 344= 37848 5=° 15 65951 79662 =93.57 06440 27 7 <• 63518 78961 194130 09035 23684 3S086 52249 66,8. 79889 293380 06660 2H 15 63778 79=. 6 .94381 092S. 23926 38324 5248 J 664,, 293603 06880 21) :w 64037 7947" '94631 09527 24,68 38562,527.7 66642 80342 293826 07099 "30" 45 64297 79726 ,9+88. 09773 244,0 388001 5195. 66872 80569 294049 073.9 31 8 t) 64556 79981 1951321.00,9 =465 = 39038 53^85 6-.02 80795 294272 07538 32 15 6+8,6 80235 1.95382., 0265 24893 39=75 53419 6733* 8,02, 294494 07757 33 :«o 65075 80490 .9563=! 105 1 J = 5'35 395^3 53653 6755* 8.248 =947.7 07977 34 45 65334 80745 .95882 .0757 = 5377 3975' 53886 6779= 8.474 294940 08.96 35 9 (1 65593 80999 196132 11003 256.8 39988 54120 68022 8. 700 295.62 084,5 3fi 15 65852 81254 ,96382 ..248 25860 40226 543 54 6825, 8,926 295385 086,4 37 : = 875 = 43070 57'5^ 7,004 84635 29805, .,260 49 69213 84554 199625 '4435 28993 43307 57384 71234! 84860 1 298273 . .478 M) 45 694^1 84807 199874 .4680 29234 43S43 576,7 7.462 850S6 298495 ..696 Al 13 69729 8506, 14925 =9474 43780 57849 7169, 853.. =987.7 "9'5 S2 15 69986 853,4 200372 .5,69 29714 44016 58082 7i9'9 85536 29893S 12.33 Xi 311 - -44 85567 200621 15414 =995 5 44252 583.4 72.48 8576. 299,60 .235. 54 45 S58,, 2C0869 .5658 30195 44489 58547 7=377 85986 =99381 1=569 5» It II -'--59 86070- 2011,8 .5902 30435 44725 58779 72606 862.. 299603 .2787 56 15 710,- 86 -,26, 20.366 ,6,47 30675 44961 590 ■■ 7 = 834 S6436 =998=4 .3005 57 30 86579 20.6,5 ,639, 309.5 45'97 59=44 73061 86661 30C046 .3223 58 4A 71531 86832 1 201863 ,66,5 31155 45433 59476 7 3 = 9' 86886 300267 13441 5!t Set-. r 2 3' 4" 5' ti' 7' H' 'J' lO' 11' 12'" 13' 14' 1.')' 1 I). 2r;0. 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Jh^o. 8-4 8-4 8-4 8-4 8- 8-5 8-5 8-5 8-5 |8-5 85 1) 1) 46467 5-568 68524 79340 490019 00564 10979 21266 3.429 4147c 51392 h'l 466531 57752 68706 7952c 490196 00/39 1.151 21436 3>597'4'636 5'556 1 M 4 47398 58486 69431 80235 490903 01437 .184. 22118 32270 41301 522.3 5 30 47584158670 69612 49.080 01612 .20.3 22288 31438 42467 51377 (i ir, 47770158853 69793 80593 491256 01786 12186 2245S 32606 42633 51542 7 •2 U 47956 |59°37 69975 80772 49'433 0196, ,2358 22628 31774 41799 52706 H lo 48.42 |C9220 70.56 80951 491609 02135 1253c 22798 32942 42965 52870 9 IT. :to 48327 ; 594C4 70337 8. .30 491786 02309 12702 22968 33"' 43'3' 53034 45 48513-59587 70518 81308 491962 02483 12874 2313S 33178 43197 53198 11 :i (» 48699 59771 70699 8.487 492139 02658 13047 23308 33446 43463 53362 1-2 1.-. 48885 59954 70S80 8.666 491315 02832 .3119 23478 33614 43629 53516 13 :(ii 49070 60137 7.06. 8.S44 492492 03006 '339' 23648 33781 43795 53690 14 4.-, 49256 60320 7.241 82023 492668 03180 '3563 2381S 33950 43961 53854 1;^ 4 49442 60504 7.422 82201 492844 03354 '3735 239S8 34118 44127 540.8 1(1 1,-. 49617 60687 7.603 823S0 493021 03528 13906 24.58 341S6 44193 54182 17 :jo 49813160870 7.784 82558 493'97 03702 1407S 24328 34454 44459 54346 Hi 4.-. 4999S 6.053 7.964 82737 493373 03876 14250 14498 3461. 44614 545°9 19 5 501 84 6.236 7i'45 82915 493549 04050 14422 24667 34789 44790 54673 20 l.'l 50369 6.4.9 72326 83093 493715 04224 '4594 24837 34957 44956 54837 21 :f() 5°554 61602 72306 83271 493901 04398 14766 25007 35124I45121 55001 22 ■JS 50740 6.783 72687 83450 494077 04572 '4937 25176 35292 45287 55.64 23 H 5C925 6,968 72868 83628 494153 04746 15109 25346 35459 45453 5531S 24 l.'l 5. ..0 62.50 73048 83806 494429 04919 152S1 i55'5 35617 45618 5549' 23 :m 5'=9; 61333 73228 83985 494605 05093 '5451 15685 35795 45784 55655 2(; 4.') 5I4S0 625.6 73409 84.63 4947S1 05267 15624 15854 35962 45949 55S.9 27 7 '• 5.666 62699 735S9 8434- 494957 05441 ■5795 26024 36129 461.5 55982 2H l.'l 5.851 6288. 73769 845.9 495133 05614 ■^967 26.93 36297 462S0 56.46 29 "So 72^ 63064 7395° 84697 495308 05788 16.38 26363 36464 46445 56309 311 i.'i 52221 63247 74130 84875 495484 05961 163.0 26532 36631 46611 56471 31 H n 52406 63429 743.0 85053 495660 06135 16481 26701 36799 46776 56636 32 l.'l 5^59' 636.2 74490 8523' 495835 06308 16652 26S7. 36966 46941 56799 33 :«) 5^775 63794 7467. 85408 496011 06482 16824 27040 37'33 47.07 56963 34 l.'l 52960 63976 74851 85586 496,87 06655 16995 27209 37300 47272 57.26 35 9 (t 53>i5 64.60 7503' 85764 496362 06829 17166 17378 37468 47437 57189 3(i l.'l 5333° '6434' 752.. 85941 496538 07002 '7338 27548 37635 47602,57452 37 :t(i 53515 64524 7539' 86. .9 496713 07175 17509 177'7 37802 I 47767 1 57615 3K 4.'i 53699 64706 7557> S6297 496889 07349 17680 778?7 27886 37969 12911 57779 39 10 53884164888 '7575. 86475 497064 07511 18055 38.36 48097 57941 ~m l.'l 54068 j 65070 7593° 86652 497139 07695 18022 2822+ 38303 48262 58.05 41 ■M) 54^53 65252 76. .0 86830 497415 07868 1S.93 18393 38470 48417 5826? 12 4.'i 54437 : 65434 76290 87007 497590 0S041 .8364 28562 38637 4S591 5843 ■■ 43 1- 54622 65617 76470 X7.85 497765 08214 ■8535 28731 38804 48757 58594 44 l.'l 54806 [65799 76649 37362 49:'94i C8387I 18706 28899 3S971 48922 5S757 4."i rtii 54991 6598. 76829 87540 498116 08560 ,8877 29068 39' 37 49087.58910 4li 4.'i 55>75: 66,62 77009 87-.7 49819T 087331 19048 29237 39304 49152,59083 47 12 55359:66344 7'.88 87894 498466 08906 1.91. 9 29^o6 39471 49417 59246 4H l.'l 555441*6526 7736S 880721498641 09079 I 19390 19575139638549581 59408^ 49 :tii 557^8 66708 77547 8S249 4988.6 09252119560 ^9743 39804 49746 59571 ,iO 4.1 559'j' 66890 77717 88426149899. 09425 19731 299.2 3997' 499" 59714 51 1.1 '' mS i*" ■/-, iK'; 1 I>. n;i. I'Hrt, ,, 21 V. 44 55 <•<; :6 Sy v8 .09 .20 .5. i4» .53 "H | sne TABLE 69. lOO. SINK SQUARK 0" '22° ■23" ■24^ 30'" 8 15' 1 30' 1 45' 0- 1 15' 1 30' ! 4ft' li'32'" |l''33'"l li'34'"lr'35'" 0' 15' li'28"' li'2!)'"|l''30"'|l''3I"' li'3(i'" li'37"' li'3H"' S-5 «-5 8-5 8-5 8- 8-6 8-6 |8-6 8-6 8-6 |8-6 o' ()' 6119S 70X90 80471 89944 59931. 08573 '7734 126795 35758 44625 1 53399 16 61360 7105, 80630 90101 599466 08726 17885 26945 35906 44772 5354; ■M) 6,5.3 7,211 80789 902 5 8 59962. 088S0 18037 27095 36055 44919 53690 4,-1 6,685 7,372 80948 90415 599776 09033 18189 27245 36203 I 45066 I 53836 1 853 81424 90886 600242 09494 .8644 27695 36649 45507 54272 4ft 62334 720,4 81582 91042 600397 09647 .8796 27845 36797 45654 54417 2 62497 72,74 8.74. 91199 600552 .8947 27995 36946 4580, 54562 1ft SO 62659 7^3 34 X1S99 9,356 600707 09954 19099 28.45 37094 45947 54707 62S21 72495 91512 600862 10107 19251 28295 37242 46094 54S53 4ft 62983 72655 822^6 9.669 601016 10260 19402 28445 37391 4624. 54998 3 63.4; 72S,5 82375 91826 60,17, 10413 '9554 28595 37539 463SS 55.43 Ift 63307 72975 82533 9,982 60,326 10566 19705 28745 37687 46534 55288 30 63469 73136 8269. 92139 60148. 10720 19857 28895 37835 46681 55433 4S 63631 73296 82850 92296 60,636 10873 29044 37984 46828 55578 4 63793 73456 83008 92452 60179: U026 20160 29194 38132 46974 55723 16 63955 736,6 83166 92609 601945 ■1.79 20311 29344 38280 47121 55868 30 64,17 73776 83325 92765 602.00 1.332 20462 29494 38428 47267 1 56014 45 64279 73936 li4il 8364, 92922 602255 ..485 2c6,4 29643 38576 474 '4 56.59 ^ 5 6444, 74096 93078 602410 .1638 20765 29793 38724 47560 56304 15 64603 74256 83799 93234 602564 1179. 20916 29943 38872 47707 56448 30 64765 744.6 83957 9339' 602719 1.944 21067 30092 39020 47853 56593 4ft 64926 745-6 84.15 93547 602873 12096 21219 30242 39.68 4XC00 56738 6 65088 74736 84273 93703 603028 12249 21370 30391 393.6 48146 56883 15 65250 74896 84431 93860 603.82 12402 21521 30541 39464 48293 57028 30 654,2 75056 84589 94016 603337 ■2555 21672 30690 39612 48439 57'73 2C 45 65573 752'5 84747 94172 603491 12708 21823 30X40 39760 48585 573.8 27 7 65735 75375 84905 94328 603646 12861 21974 30989 39908 48731 57462 28 15 65896 75535 85063 94484 603800 13013 22.25 31139 40056 48878 57607 57752 29 30 66058 75695 85221 94641 603955 13166 22276 31288 40203 49024 45 662,9 75854 85379 94797 604.09 133.9 22427 3,438 40351 49170 57896 31 8 66381 76014 85537 94953 604263 1347. 22578 3'587 40499 49316 580+1 32 1ft 66542 76.73 85695 95.09 6044,8 13624 22729 31736 40647 49463 58186 :i3 30 66704 76333 S5S53 95265 604572 13776 22880 31886 40794 49609 58330 34 45 66865 76493 86010 9542. 604726 13929 23031 32035 40942 49755 58475 35 ') 67027 76652 86168 95577 604880 .408. 23182 32184 41090 49901 58620 3« 15 67188 768,2 86326 95732 605035 .4234 23333 32333 41237 50047 58764 37 30 67349 76971 86483 95888 605,89 .4386 23484 32482 41385 50193 58909 311 4i 675,0 77130 86641 96044 605343 14539 23634 32632 4.532 50339, 50485 59053 30 40' 10 67672 77290 86799 96200 605497 14691 23785 3278. 59198 15 67833 77449 86956 96356 605651 14844 23936 32930 1.828 50631 59342 41 30 67994 77609 87.14 965.2 605805 ,4996 24087 33079 41975 50777 594X6 42 45 68,55 77768 8727, 96667 605959 15148 24237 33228 42.23 50923 5963. 43 11 68316 77927 8-429 96823 606113 15301 24388 33377 42270 51069 59775 44 15 6X477 780S6 875S6 96979 606267 15453 24539 33526 42417 5.215 599.9 45 30 68639 78246 87743 97.34 606421 .5605 24689 33675 42565 51360 6CC64 4<> 45 68880 78405 87901 97290 606575 •5757 24840 33824 42712 5.506 60208 47 I'J 6896, 78564 88058 97446 606729 15910 24990 33973 42859 5.652 60352 4B 15 69,2, 78723 88216 9760, 606883 607036 .6062 25.41 34.22 43007 51798 60496 4» 30 69282 78882 97757 T6IT? 25291 34271 431541 5«943 6064, 50 45 69443 79041 88530 97912 607.90 16366 25442 344'9 43301 52089 60785 51 13 69604 79200 886x7 9806S 607344 16518 25592 34568 43449 52235 60929 52 15 69765 79359 88845 1 98223 607498 16670 25742 347 '7 43596 52380 61073 5S 30 69926 795'8 X9002 98379 60765. .6822 25893 34866 43743 52526 61217 54 45 70087 79677 89159 98534 607S05 .6974 26043 350.5 43890 52672 6.361 55 14 70257 79836 89316 98689 607959 17126 1 26194 35.63 44037 52817 6.505 5(; 15 70408 79995 89473 98845 608.. 2 17278 1 26344 35312 44184 52963 61649 57 30 70569 80,54 89630 99000 60S266! 17430 1 26494 1 35461 44331 53108 61793 5« 45 70729 80313 89787 99155 608419 1 17582 1 26644 1 35609 44478 53254 6.037 b'J Sec. 1' 2 3- 4- 5" C T 8' 9' 10' 11' 12" 13' U' 15' D. Ifi2 Farts ii 22 r- 43 54 ^5 7* S* 97 >oS .19 .50 140 .51 .62 1>. 145 Parts 10 19 29 39 4X 58 68 77 S7 97 106 116 126 13s H'J | TABLE 69 fe37 l.OO. SINE SQUAUE 1 240 1 20^ •45;_ 0' IS' 30- 4S' 0' 15' 30' 45' 0' Id' _I^ ,1, 33„, I1.40' l"4l~ lh 40,,, Ih4:,„, 11-4^ V' 45™ I" 4(i"' ,„47„, Ti^4H'" li'4!l"' 8-7 X^6- 8-6 8-6 S-6 X- 8-7 87 8-7 8-7 8-7 It 62081 70674 79'77 87595 6,5,27 0+.76 •2343 20+31 28+39 36371 44?26 II IS 62J15 70816 79318 87734 696065 0+3.3 12+79 20565 28572 36502 44356 1 ■Kl 62369 70958 79459 87974 696203 0+450 ,26,+ 2069, 3663+ 4-H86 2 4,1 62S13 79600 880.3 6,634. 04586 12750 2S838 36765 446.7 :« 1 n 62657 71243 7974' 88.53 696+79 0+723 ,2885 20967 28970 36896 44747 4 l.i 62801 713S5 7988-- 8S292 6966.8 0+860 13020 21,0, 29103 37028 44877 5 :»n 62945 80023 8S432 696756 0+996 ,3,56 21235 29236 37'59 45C07 li 43 63088 71670 80164 8857. 6968,+ 05133 1329' 2,36, 29368 3729. 45 '37 7 i 6r-3^ 7.8.2 80305 88710 697032 05270 13+26 2,503 29501 37422 45268 R 15 633-6 7'955 80445 80586 88S50 697.70 05+06 13562 2,637 29634 37554 45398 45528 !l III 63520 72097 88989 6,730s 05543 ,3697 2,771 29-66 376S5 4.'> 63663 72239 80727 X9129 697445 05679 .3832 21905 298,9 378.6 45658 1 1 :i (1 63807 7238, 80868 89268 697583 058.6 13967 2203, 30032 37948 45788 I-.' l.i 63951 72523 8.C08 89407 69772, 05952 .+ 102 22173 3016+ 38079 + 59.8 I.H : 6+238 72808 8,290 89686 6,7,97 06225 '4373 22++0 30+29 383+, +6,78 15 4 11 6438. 72950 8.430 S9825 698.35 06362 14508 2257+ 30562 38+73 +6308 Ifi l.i 645'- 5 73092 8.57. S9964 698273 06+98 ,46+3 22708 3069+ 3860+ 46438 17 :«) 6+668 73134 8,7,, 90103 698+.0 06635 14778 228+, 30827 38735 46568 HI 4S 648,2 733:-6 818521,0242 6985+8 0677. ,+9,3 22975 30959 38866 +6698 l!l .i '•49 51 735'** 8,993; 9038. 6,8686 0690S 150+S 23109' 31092 38997 46828 211 l:. 65099 73-^60 82.33 ,0520 6,8823 07044 .5.83 23242 3 '22+ 39128 46958 21 :t(i 652+2 73X02 82274 ,0660 6,8,6. 07.80 .5318 23376 3.356 39259 47087 22 4.'. 653S6 7 3944 824.4 90799 699099 07316 15453 235,0 3.489 3939' 47217 23 f> 1) 655:9 74086 82555 90938 699237 07453 15588 236+3 3.62. 39522 47347 24 i.'> 65672 74217 8269; 9.077 69937+ 07589 15723 23777 3'753 39653 47477 25 »• 65816 74369 82835 9.2.6 6,95.2 07725 .5858 23,,, 3.8S6 3978+ 47607 2»! 4 A 65959 7451' 82976 9'355 6996+9 07861 15993 2+044 320.8 399'5 47736 27 7 « 66;d2 74653 831.6 9H93 699787 07998 .6,27 24.78 32,50 +00+6 +7866 2(( 15 662+5 74'95 83256 91632,699924 0813+ 16262 243" 32282 40.77 47996 29 :3i) :«o 66389 74936 83397 91771 70C062 08270 16397 24445 32+.+ 40308 +8,26 4"> 665,2 75078 83537 919.0 700,99 oX+06 16532 24578 32547 40438 48255 31 fl n 66675 75220 83677 92049 700337 OS 5+2 16667 247,2 32679 40569 48385 32 1.-. 66SIS 7536. 838.7 92,88 700474 08678 ,680, 24845 40700 48515 33 :3 62395 70006 77547 850,9 92423 799760 0703. 14239 2,382 28464 30 54841 62523 70132 77672 85.43 92545 799882 07,52 .4358 21501 28581 22 45 54970 62650 70259 77797 85266 92668 800003 07273 .4478 21619 28699 23 6 55099 62777 70385 77922 85390 92791 800,25 07393 '4597 2173S 288.6 24 15 55227 62905 705.. 78047 85,14 929,4 800247 075.4 .47.7 21856 2S934 25 30 55356 63032 70637 78.72 8563X 93037 800368 07635 .4836 21975 29051 2 634.4 7,0,6 78547! 860,0 193405 800733 07996 08, ,7 .5.9s 2233c 29403 2!l 30 30 55870 6354. 71,42178672 86134 93527 800855 .53.4 22449 2952, 45 55998 63669 7,268178797 86257 93650 800976 08237 '5434 22567 29638 31 8 56,27 63796 7,394,78922 86381 93773 80,098 08358 .5553 22685 29756 32 15 56255 63923 71520 79047 86505 93895 80,2,9 0847S .5672 22804 29873 3.3 30 56383 64050 7,646 '79.72 86629 940,8 80,34, 0859S .5792 22922 29990 34 45 565,2 64,77 7.772 79296 86752 94140 80,462 087,9 .59" 23040 30,07 35 9 56640 64305 7.898 7942. 86S76 94263 80,584 08839 .603, 23.59 30225 3(! 15 56768 64432 72024 79546 87000 94386 80,705 08960 ,6,50 23277 30342 37 30 56897 64559 72,50 7967. 87.23 94508 So, 827 09080 ,6269 23395 30459 :m 45 57025 j 64686 72276 79796 87247 94631 80,948 09200 16388 235,3 30576 uT \0 57.53 M.3 72402 79920 87370 94753 S02070 0932, ,6508 23632 30694 15 57282 64940 72527 80045 87494 94876 802,91 0944. ,6627 237^0 308,1 41 30 57410 65067 72653 87618 94998 8023,2 0956, ,6746 23S68 30928 12 45 57538 65,94 72779 80294 8774. 95121 802434 096S2 ,6865 23986 3.C45 43 11 57666 6532, 72905 804,9 87865 95243 802555 09802 16985 24,04 31162 H 15 57794 65448 73031 80544 87988 95365 802676 09922 17104 24223 31279 45 30 57923 65575 73.57 80668 88,, 2 95488 802798 ,0042 17223 2434. 31396 41! 45 5805, 65702 73282 80793 I8S235 95610 802919 ,0,62 .7342124459 3.5.3 47 12 58,79 65829 73408 809,8188359 95733 803040 j 10283 17461 24577 3.63, 48 l£ 58307 65956 66083 73534 8,042 ! 88482 9S855 803161 ! 10403 17580 I 24695 17699124813 3.74S 4!l 7>0 30 5843 5 73660 81,67 88606 95977 8032S3 ,0523 31S65 45 58563 662J0 73785 8,29, 88729 96099 803404 ,0643 17818 2493, 3,982 51 13 5869. 66336 739.. 8,4,6 88852 96222 803525 ,0763 ,7938 25049 32099 52 15 588,9 66+63 74037 8,540' 88976 96344 803646 ,0883 18057 25.67 322,6 53 M 58947 66590 74.62 8,665 89099 96466 803767 ,1003 ,8,76 25285 32332 54 45 59075 667,7 74288 8,789 X9222 96588 803888 11123 ,8295 25403 32449 hn 14 59203 66844 744 '3 8,9,4 89346 967.. 804010 11243 ,84,4 25521 32566 .-.(! 15 59331 66970 74539 82038 89469 96833 804131 1,363 .8533 25639 32683 57 :r n' lo iv 12" 13- \r 15' 1 I). 129. Tarts 9 17 ;6 34 43 52 60 69 78 86 95 103 iij 121 129 J>. 1'7. Pans 8 .6 23 3, 39 47 5S f'^ 70 78 8'^ 94 'c> ,09 ,,7 .J T.MU.F. 60 I.OO. SINE SQCARK 1 ■,i'>' 31° a^'^ 3:r 15' :«•' 1 45' .J'' 15' 30' 45' 0' 15' ] 30' 45' 0' •-'"I- .2h .I,.. I '2>> a"' .Jh 4n, •21-5". 21' 6™ 21. 7"- 2l'8"> 2h 9m .11, ion. 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S 3367 50259 57094 1 38-0 70590 77:54 3864 904.9 896922 337 !_ 09770 2ft 30 6532 3482 5°374 57:07 3983 7070: 77365 3974 90528 897030 3479 09876 311 4:. 66+8 3598 50488 573:0 4095 708,3 4083 90637 897'37 3586 09982 ai » II 6164 37<3 50603 57434 4207 709:5 77586 4'93 90746 897:45 3693 .0088 32 i:. 6?8i 3828 57547 4320 7.036 77697 4303 90854 897353 3800 ,0,94 aa aa 6997 3944 508^^ 57660 443: 71148 77807 44,2 90963 89746. 3907 ,030 ai i.i 7"3 4059 5°945 5"774 4545 71:59 779.8 4522 9,072 897569 40.4 10407 a.'i •1 II -»3o 4'74 5,060 57887 4657 7>370 78028 4632 9, ,8, 897677 4,21 IC513 aii In 7346 428, 5 "74 58000 4769 7.48: 78,39 474' 9,289 897785 4:28 1C619 a? ao -46^ 4405 5,288 58, ,4 4882; 71593 78249 485. 9.398 897892 4334 .0725 311 4.1 757S 4520 5,403 58:^7 4,94171705^ 78360 4960 91507 89SC00 444' 1CS31 3!! \\rT 7694 463 s 58340 5,06 718,6 78470 507019,6,5 898,08 4548 K..;37 "40 IS -811 4750 s'fip 58453 5219 7,927 7858, 5.79 1 917:4 8982,6 4655 11043 41 an 7917 4865 5'745 58,67 533" 72039 7869, 5289,9,833 8983:4 4762 1,149 42 4.'. 80+3 49811 51859 5S680 5443 72,50 78S02 5398 1 9.941 S98431 4869 ,1255 43 1 1 11 S1S9 S096 51973 58793 5555 7226, 789,2 550819:050 898539 ♦976 1,361 M l.'i S375U21I 52CS8 5S906 566817:373 79022 5617,92,58 898647 5083 ..467 I.'. ao 839- 1 51-6 52202 590,9 5780,7:484 79.33 57:7 9::67 1898754 5,90 .15^3 u; 4.'. 8507 j 544. 5'-3'6 59132 ■5852 7:595 79:43 5836,92376:898862 5:96 116-9 n 12 II '•'M 555'': 5^43° 59246 6co4 , 7:706 79353 5946 ! 92484 1 8.;8970 5403 ..785 4H l.'i a-39l5*7i 5^544 59359 6>'6 7'-8.8 79464 6055; 9:593! 8990-7 55,0 11891 41, air g8;5i57(f6 5'265X 59V72 16227 7:9:9179574 6164 9x70,1899,85 5617 11997 50 4". 8971 5901 52771 59585 6341 173040179684 6274 928,01899293 57:3 51 la II 908716016 52886 59698. 6453 l-3'5>! 79795 6383 9:9,81899400 583° 122c 9 52 i.> 9203 6131 5300c 59S,, 6565! 73:6: 179905 6492 1 93027 I89950S 5937 ,231; 53 .'III 9319 6246 53114 57924 ,6677 173374! 800,5 6002193,351899615 6044 124:1 54 4. 943; 636,, 55228 60037 6789173485 Xoi25 6711 93244! 899723 6.50 12526 55 II 9;;i 6476! 53342 6c,5C 690, ; 73596 80235 68:' 19335:189983, 6257 12632 :,r, I.I 9''*'7 6591 53456 60263 70,3 73707 80346 69301934001 899918 6364 ,273s 57 :io 9-83 6706 53570 60376 7115 738,8 80456 7039 93569 .,00046 64-0 ,2844 5)1 4.1 9899 6821 i 53*84 60489.7237 739:9 80566 -148 930-7 900,53 65" 1295c .'i!l .s«. r •_•- .r 4- :,■ ic 7 II. 111;. 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Sl.NE SQUARi; 33° 34° 35" 15 30' 49' *L. 15' 30' 45' 0' 15' 30' 45' 2'' 13" 2h 14" 2i,j5„ 21. 16n 2h jjr, 8-9 2'' 18" Oh 19m 2h20" 2h2|n 2h 22" 2>.2*" ?-9 8-9 8-9 8-9 8-9 89 8-9 8-9 |8-9 d •3055 19377 25648 3:87. 38045 50251 562S4 6227, 682,3 74". rt 15 .3.6. ,9482 ^575^ 3 '974 38,47 44273 5035' 56384 62370 683.2 742C9 1 ■Ml ■ 3267 .9587 25960 26065 32077 38250 44375 50452 56484 62470 684,0 74307 2 •43 13373 >969' 3218, 38352 44476 50553 56584 62569 68509 74405 3 1 13478 .9796 32284 38455 44578 50654 56684 62668 74502 4 la 13,84 1990 1 26169 32387 38557 38660 44680 50755 56784 62768 68706 74600 5 .•1(» 13690 20006 26273 32490 4478. 508^6 56S84 62867 68805 7469S (> •13 '3795 2011: 26377 32593 38762 44883 5°957 56984 62966 68903 74796 7 2 (1 13901 20216 2648. 32697 38864 44984 5,058 57085 63066 69002 74894 8 13 14007 I4IIZ 20321 26585 32800 38967 450S6 5,158 57185 63165 69.0, 74992 IF :t(i 20425 26689 32903 39069 45188 5 '259 572S5 63264 69.99 7 5090 43 142 1 8 20530 26793 33006 39171 45289 5,360 57385 63364 69298 75187 1 1 :< (• 14324 20635 ^6897 33109 39274 4539' 51461 57485 63463 69396 75285 12 15 14429 20740 33212 39376 45492 5.562 57585 63562 69495 75383 13 :«> '4-535 20844 27104 333'6 39479145594 5.662 6366. 69593 75481 14 4.-. 14640 20949 27208 334'9 39581 45695 5.763 57785' 63761 69692 7557S 15 4 14746 21054 27312 33522 39683 45797 5.864 63860 69790 75676 l(i 13 .4852 21159 27416 33625 39785 45898 51965 57985 63959 69889 75774 17 30 ■4957 2,263 27520 33728 398SX 46000 52065 58085 64058 699S7 75872 1)1 45 .5063 21368 27624 3383. 39990 4610. 52.66 58185 64.57 70086 75969 19 3 .5. 68 21473 27728 33934 40C92 46203 52267 58284 j 64257 70.84 76067 20 13 15274 i>577 27832 34037 40194 46304 52367 58384 64356 70282 76165 21 ■M •5379 27935 34140 40297 46406 52468 58484 64455 7038, 76262 22 43 15484 28039 34243 40399 46507 52569 58584 64554 70479 76360 23 n 15590 21891 28143 34346 40501 46609 52669 58684 64653 70578 76458 24 13 15695 21996 28247 34449 40603 46710 52770 58784 64752 70676 76555 25 :f() 1580, 22100 28351 3 + 552 40705 4681. 52871 58884 6485. 70774 76653 2« 43 15906 22205 28454 34655 40S07 46915 52971 58984 64950 70873 76750 27 7 16012 22310 2S558 34758 409.0 47014 53072 59083 65050 70971 76848 2« 13 16117 22414 28662 34861 410.2 47115 53172 59183 65149 65248 71069 76946 2!» IM) 16222 22519 28766 34964 41.14 47217 53273 59283 71 168 1 77043 -30- 43 .6328 22623 28869 35067 412,6 47318 53373 59383 65347 71266' 7^.4, 31 i) (1 16+33 22728 1 28973 35170 4.3'8 47419 53474 59482 65446 7.364 '77238 32 13 16538 22832 29077 35272 4,420 47521 53574 59582 65545 7.462 77336 33 :tii 16644 22937 29,80 35375 4,522 47622 53675 59682 65644 7,561 77433 34 43 16749 23041 29284 35478 41624 47723 53775 59782 65743 71659 7753. M !l 16854 23.46 29388 3558' 4.726 47824 53876 5988. 65842 71757 77628 3li 13 16959 23250 2949, 356X4 41828 47926 53976 59981 65941 7185s 77726 37 ;ti) 17065 ^3354 29595 35787 41930 48027 54077 6008. 66040 71953 77823 3K 43 17170 ^3459 29698 35889 42032 48.28 48229 54177 60. So 66.38 72052 77921 3!l Id II '7»75 ^3563 29802 35992 42.34 54278 60280 66237 72150 780.8 13 17380 23668 29905 36095 42236 48330 54378 60380 66336 72248 78. 16 41 :«» 17486 23772 30009 3619S 42338 4S432 54479 60479 66435 72346 782,3 42 43 ■759' 23876 30113 36300 42440 48533 54579 60579 66534 72444 783,1 43 1 1 17696 239S. 302.6 36403 42542 48634 54679 60679 66633 72542 78408 44 13 17801 24085 30320 36506 42644 48735 54780 60778 66732 72641 78505 45 ■M) 17906 24.89 30423 36608 42746 48836 54880 60878 6683. 72739 78603 4(i 43 18011 24294 30527 367 1 1 42848 48937 54980 60977 66929 72837 78700 ■)7 12 n 18116 24398 30630 368,4 42950 49038 55081 6.077 67028 72935 'll'' 4K 13 1S221 24502 30734 369,6 43052 49139 55181 61.77 67.27 73033 18895 40 ~ftO 3(. 'S327 24606 30837 37019 43153 49241 55281 61276 67226 73,31 78992 43 18432 24711 30940 37122 43255 49342 55382 6.376 67325 73229 79089 51 i:i .8537 248.5 31044 37224 43357 49443 55482 6.475 67423 73327 79187 52 15 18642 24919 3 "47 37327 43459 49544 55582 6.575 67522 73425 79284 33 30 .S747 25023 31251 37430 43561 49645 55682 6,674 67621 73523 7938. 34 43 18852 25127 3'354 37532 43662 49746 55783 61774 67720 7362, 79479 55 u n 1S957 25232 3'457 37635 43764 49847 558S3 6.873 67818 737.9 79576 .'M. 13 ,9062 ^5336 3.56. 37737 43866 49948 55983 61973167917 738.7 79673 a? :w ,9167 25440 3.664 37840 43968 50049 56083 62072 68016 739.5 79770 58 45 19272 ^5544 3.767 37942 44069 1 50150 56183 62171 I68114 74013 7986X 50 Sec. 1-2' 3 4 (i 7 H » 10 II' 12 13' 14' 13' D. 103. I'arts 7 14 21 ;8 5S 4: 49 ^f' ^1 7° 77 84 91 98 1C5 I>. 117. I'mis 6 ,5 19 zh -,2 59 i5 5; 5S e-, -I -S 84 91 97 TAni.R 69 841 LOG. 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S.C35 86836 9259618-998314 03990 09626 .5211 20776 26192 3.769 37207 II .1 8. .30 86932 92691 18-998409 04c 8 5 09720 '53"4 2CS69 26384 3.S60 37298 12 lA 81117 87029 92787 8-998504 04179 098.3 .5407 2096. 26475 3.95' 37388 13 .'(I) 8.314 87.25 9288318-998599 04273 09907 .55CO 11053 26567 31042 3/478 14 4.", 8.411 8721. 91978 ;S-998694 04367 '5593 11,45 26658 3='3> 37569 15 4 (• 8.5.8 873. 8 93074 8-998789 04462 .0094 .56S6 21237 26750 32224 37659 Hi 15 8.6.5 874.4 93.7018-998883 04556 .0.87 '5778 2.330 26842 3=3.5 37749 17 3(1 875.0 93165 J8-99S978 C4650 ,028. .587. 2,422 26933 32405 37839 IH 45 S.809 8:606 93361 18999073 047+4 .0374 15964 2,5.4 27025 3=496 3-930 l!l 5 81906 S7703 93456 8-999.68 04S38 ,0468 16057 2,606 271.6 3 = 587 38C10 'W 15 81003 87799 9355218-999263 04933 .056. 16150 2.698 27208 32678 38. .0 21 3(1 81.CO 87895 93647 8-999358 05017 .0654 16243 2,79' 27299131769 381C0 22 45 81.97 8799' 93743 18-999453 0511. .0748 ■6335 2,883 2739'l3=86o 38=9. 23 «; II 81194 93838 8999547 051.5 ,0842 .6428 2,975 27481 1 32951 3838' 24 15 8139. 88.84 93934 8 999642 05309 ,0935 .652. 22067 =7574! 3304' 3847. 25 :t(i 81488 88180 94019 8-999737 05403 ,,029 ,66,4 11159 276651 33.32 3856. 2fi 45 81585 88376 94125 8-999832 05497 ,6706 27756 33==3 3865. 27 7 11 S16S1 88472 94220 8 999917 05591 1,2.5 16799 22343 =7848 333 '4 3874. 2K 15 817-9 1 88568 94316 900C021 05685 11309 ,6893 JJ435 27939 33405 38831 2!» ~3?r 81875 88665 944.. 9-OC0.16 05780 ..402 ,6985 22527 2803. 1 33495 38922 ~W 45 8297118876. 94507 9-0002.. 05874 ,.496 ,7077 226.9 2S.22 33586 390.1 31 8 (1 83069 88857 94602 9000305 0596S ,.589 .7.70 227.. 282.3 33677 39.01 32 15 83.66 88953 94697 9-000400 06062 .,682 .7263 22803 28305 33768 39.91 33 3il 83163 89049 94793 '9-000495 06,56 .1776 '7355 22895 28396 33858 39282 :m 45 83359 1 89.45 94S88 9-000590 06250 ,,869 .7448 22987 284S8 3 3949 3937= 35 » (I 83456,89141 94984 9 000684 06344 ,,962 '754' 23079 28579 34040 39462 3(; 15 ''55';i 89337 95079 9-000779 06438 ,2055 ■7633 23171 28670 34.30 3955= :«7 :4. 900.536 07.89 1 .18011 .S374' 23907 294CO 3485; 40171 45 :i(i 84413 90:01 95937 9-001630 07183 ,2895' ,8467 23999 19492 34946140362 4(i 45 S4510 90197 '96031 9-001725 07377 .2988 1 18559 24091 29583 35037 40451 47 12 11 84617 9"59)I96>^7 9-0'"*"9 0747' .308. j ,8652 24181 29674 35.27 40541 4« 15 84713 190489 9622'- 9-°o'9'4 07564 .3.74! .8-44 '24274 29765 35--'8 4063= 4!) -^ 84810 9058519631719-001008 07658 ,32671 ,8837 14366 29856 35308 40722 511 45 X49C6 9068. 1964.3 9-001.03 0775* 13361 1 1S919 24458 29948 35399 408.2 41 13 85003 J 90777 j 96508 ,9-002197 07846 ,34541 1902. 24550 50039 35489 40901 52 15 85100 90872 9660319-001191 07940 '3 547 i 19 "4 24642 30.30 35580 40991 A3 M> 85.96:90968 96698 9-C01386 08033 13640 1 19106 24733 3011. 35670 4.081 54 15 85193 91064 96793 9-C0248. 08.17 '3733 1 19=99, -4825 30311 3576, 4. .71 55 U n 85389 91.60 968889-001575 0812. 13826 1 1939. ; 249.7 30403 I358S' 4.16. 56 15 S5486 91256 96983:9-001670 08315 139.9 1 ,9484 15009 30495 '■ 3594= 4'35' 57 3)1 85581 9.352 970799x02764 08408 .4011 ; .9576 151CO 30586 36032 4.44. 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' 557^0 61J42 66279 7.480 76646 8,77s 86875 9.938 96968 9705, 3!l 40 10 n Ts^ 50550 55858 6.150 66366 7.566 76732 8,863 86959 92022 15 45194 50639 55946 66453 7.653 76818 8,94s 87044 92,06 97.35 41 30 453«3 5072-! 56034 61305 66540 7.739 76903 82033 87128 92,90 972,8 4-.' 45 45473 50816^ 56.22 6.393 66627 76989 82, ,8 871.3 92274 97502 43 11 45562 5090c j 562.. 6.4S0 667,4 7. 911 77075 82203 87298 91358 97385 1 44 15 4,652 50994 ' 56199 6.568 6680. 7.998 77.61 82289 87382 9=441 97469 45 30 4574' 51CS2 1 56387 61655 1 66888 1 72085 77147 82374 87467 92526 97552 4li 45 45830 51171 1 56475 6.-43 66974 72.7. 77331 82459 87551 926,0 97656 47 12 4592c 51260 1 56563 161830 1 67061 1 72257 774.8 82544 87636 91694 97719 4(t 15 46009 515481 5665. 1 6. 9. 8 j 67.48 1 71343 77504 82629 S772, 91778 1 97803 4» 5(^ 30 46098 5'437 1 567391620.51 67135 72430 77589 "17.4 87805 92S62 97886 45 46187 51516 56827 62093 67311 725,6 77675 82«oo 87890 92946 97970 31 13 46277 5.6,4! 569.5 1 62.80 67409 72602 77761 82885 S7975 93030 98053 52 15 ♦6566 5.705 57003 62267 67496 72689 77846 82970 88059 93114 98.37 33 :«) 46455 5.791 5709. 62355 67583 71775 77931 8J055 88144 93,98 98220 fi4 45 46544 51S80 57»79 62442 67669 7286. 78018 83.40 88228 93282 98303 .•„5 II )l 466J4 5.969 57167 62530 67756 71947 7S.03 831*5 88313 93366 98387 3fi 15 46725 5i°57 57355 6i6i7| 67843 73':34 781S9 833.0 8S397 9345° 1 9847c 37 *l 46812 52.46 57443 62704,679301 73.20 7S175 83395 88482 93534 98554 38 45 4690. 511351 5753.|62792j68o_r7| 73206 78360 834S0 88 5^^|_936ii^aj_ 986,7 50 Se,'. 1-2* 3' 4- 5' (i' 7' «' !» 10 1 1 ' 12 13' 14 lo' I>. !in. I'^irts 6 II i8 24 -,o -,6 4J 48 <;4 fio 66 -: -S S4 90 n. 111. P..it- 6 II 1- zz 2? -,4 V) 1^ ^c ^*^ h: ^' -5 7S '^4 TABLK 60 843 LOO. SINE syi'ARli 41 30- 42= 43° 440^ 0' s. 4o' 0- 1 15' 1 30' 1 45' *•!_ 1.^30' 45- 2»'46" [2'' 47"' 2h48™ 21' 49'"! 2'' 50"' 21-51"' 2h 52"' 2>'53"'|2l'54"' 2'' 55'" 9' 21' Mi"' 9' 9"' 9' 91 19-1 91 9> 9'' 9"> 9> o' o" C,S-20 03:06 08658 13579: "8468 23325 28.5. 32946 377.. 42446 47 ■ 5 ' n 15 098804:03788 0S74. 13661 18549 23405 18131 33^26 37790 42524 47229 1 30 098887:03871 08823 '3742 18630 13486 1S31. 33105 37869 42603 473C7 •> 45 0989-0 C3954 0S905 .3824 18711 13567 18391 37.85 37948 42682 473S5 3 1 099c 54 04037 08987 13906 18791 13647 18471 33265 38028 4276c 47463 4 15 099137 04120 09070 13987 18873 13718 18551 33344 38.07 42839 47542 5 M C99220 : 04202 09.52 14069 18955 13809 28632 33424 38.86 429 IS 47620 fl 45 099304 04285 09234 14151 19036 13889 18711 33504 38165 42996 47698 7 2 099387 04368 09316 14231 19117 13970 18791 33583 38344 43075 47776 H 15 0994701 04451 °9398 14314] 19198 24051 18871 33663 33742 3S413 3X502 43232 47854 479-- ,77 :«) °99553l°4533 0948. .43961 19279 24.31 28952 45 099637104616 09563 14477, .9360 24212 29032 33822 38581 433" 4fo,o 1 1 :i 099720 04699 09645 14559 '944« 24291 19111 33901 38660 433^9 48088 \-2 15 099803 04781 09717 1464. '9523 24373 19191 3398. 38739 43468 48,66 13 :«) 099886 04S64 09809 14722 19604 24454 29272 34061 388,j 43546 4S244 U 45 C99970 04947 09891 .4804 19685 24534 29353 34.40 38898 43625 48322 lo 4 (1 IC0053 05030 09974 14886 .9766 246.5 29433 34220 38977 43703 4840. u; 15 .00.36 05112 10055 ,4967 .9847 24695 295'3 34299 39056 43782 484:^9 17 :<(i IC0219 05.95 I0220 .5049 .9928 24776 29593 34379 39'35 43860 48557 III 45 .00303 05277 15.30 24856 29673 34458 39214 43939 48655 10 5 (1 .C0386 05360 10301' .5212 20090 24937 29753 34538 39293 440.8 4S7.3 ■M 15 1C0469 ] C5443 103841 15193 20171 150.7 19833 346.7 39372 44096 4879- •-'1 .10 .C0552 °SSi5 .04661 15375 20151 25098 29913 34697 3945> 44 '74 48869 ■-'■J 45 .00635 05608 10548 15457 20333 25.78 29993 34776 39530 44253 48947 23 K .00718 056,. 10630 15538 10414 25259 30073 34856 39609 44331 49025 •-'4 IS 100801 <'5773 107.2 .5620 20495,25339 3o>53 34935 39688 44410 49. C2 •J5 :«o .00885 05856 .0794 15701: 20576 25420 30233 35015 39766 44488 49 -So 2(1 45 .0C968 05938 108771 15783 ■20657 25500 303-3 35094 39845 44S67 49258 -'7 7 •• .0105. 06021 10959; i58%;20738 2558' 30393 35'74 39924 44645 49336 ■JH 15 ,o..34 06103 11041 ! 15946,20819115661 30472 35253 4C003 44724 494,4 2!( .'Ml 10.2.7 c6i86 11123 1 16027110900125742 30552135332 4C0S2 44802 49492 ~30 45 101300 06269 112051 16109 1 20981 25822 30631 35411 40161 448SC 49^1- 31 » n .0.383 06351 11287 1 1619c, 21062 '15902 307.1 1 35491 40140 44959 49 64 8 32 15 .0.466 06434 11369] 16272 '21 143 125983 30791,35571 40319 45037 49726 33 30 .01549 06516 .14511 16353121214 26063 30S71 35650 40398 451.6 49804 3-1 45 10.632 06599 11533 .6434 2.305 26,44 30951 35729 40477 45 '94 49S82 35 » 10.7.5 io668. ..614 .65,6!ii385 26224 31031 35809 40556 45272 4996c ■Mi 15 .0.798 :o6:-64 11696 16597 j 21466 26305 31111 35888 40634 4535' 5CC33 37 30 .0.88. C6846 11778 16679 21547 26385 31191 35967 40713 45429 50115 311 45 .01964 IC6929 11860 16760 11628 16465 3.27. 36047 40792 45507 SO'93 3:1 10 .02047 I 0701 ■ 1.942; 16841,21709 26546 3'35i 36116 40871 45586 5027. "41^1 15 .02.30^07093 12C14 .6913 1.790 26626 3'43> 36105 40950 45664 5'=349 41 :«o .02213 lo7'76 11106 17004 21871 26706 3.5.. 36185 4.019 5<427 42 45 .02296 107258 11188 17086 [21951 16787 3>59' 36364 41107 4582^ 505c 5 43 M 101379 0734. 11170 17167 21033 26867 3.670 36443 41186 45899 50582 44 15 102462 j 07423 12352 17248 22113 26947 3.750 36523 4.265 45977 5c 66c 45 30 102545 07506 12434 17330 21194 27028 31830 36602 4' 344 46056 5C73i> 41; 45 .02628107588 12515 .74" 21175 27.08 31910 36681 41423 46. 3i 50816 47 \i 102711 j 07670 '2597 17491 11356 31990 36761 4>Soi 462.2 5cl.'94 41) 15 102-94; 07753 12679 17574 21437 27168 ,1069 36840 4.580 4629c il^' ' 41! :«i 102877 07835 12761 17655:22517 27349 31149 36919 4.659 46369 5,^49 "^ii 1 45 102960,079.7 .2843 .7736 22598 274*9 31119 36998 4.738 46447 51,27 51 13 103043 1 oScoo 12925 17818 21679 27509 31309 37077 4.8.6 46525 5.205 52 15 .031261 08082 13006 17899 22759 27589 32388 37'57 4'895 46603 5.282 53 30 103109:08164 ■3088 17980 22840 27670 32468 37236 4'974 46681 51360 54 45 10329 1 j 08247 13170 18061 1192. 27750 31548 j 37315 46760 5.438 55 14 .03374 08319 .3251 18143 23001 17830 316271 37394 42.3. 46838 5.5>6 511 15 .03457 1 0841 1 '3334 18224 23083 179.0 32707137474 412.0 469.6 57 .'iO 103540:08494 ■34'5 .8305 23163 27990 32787:37553 41188 46994 5,671 511 45 ..•,3^23 085-6 > 3497 18386 23244 1807. 32867 1 37632 42367 47073 5'749 5!l " SeT.-i- 2~S-^4^"5'~ 5- r II !»■ 10- 11 12 13' 14' 15' 1 n. «3. r>ir«s 5 i< ,6 zi zf. 5, 19 44 ^0 SS f'l bb 7'- 77 «3 1 1. 7H. I'.ru , K ,f. ., :f ;, -,6 4: 4" v'- ^ ^: Hi< -, -« | 8f4 TABLE 69 LOO. SINE SQUARK 440 45° 40^ 470 15' 30- 45- 0' 15' 1 30' 45' 0' !■'' 1 30' i 45- a' s^o;- 21>5H"' 21.59... ■31, 0". 31, in, 3^2". 31' 3"> 3" 4'" 3I' 5"' 3h6„j 31,7™ SI- H'" 9' 91 9-. 9'' 9-'7 9'7 9' 9-. 8 9' 919 9- 9-20 o' o" 5.826 56473 6.090 65679 0240 4775 79278 3756 S8207 263, ,97028 '399 15 51904 56550 6. .67 65756 03,6 4X48 79553 3830 8828. 2704 •97'°' '47= 1 30 5,982 56627 6,244 65832 0392 49=4 79428 3905 88355 2778 '97'74 '545 2 45 52059 56704 6,320 65908 0467 4999 79503 3979 88429 285. '97=47 .6.7 3 1 5J>37 5678. 6,397 65984 0545 5074 79578 4054 88503 =9=5 .973=0 .690 4 15 522.5 56»59 6,474 66060 06,9 5 '49 79652 4.28 88576 2998 '97595 .762 5 : 61934 665,8 ,073 560, 80,0. 4574 89020 3439 197832 2198 11 3 5^758 57399 620.0 66594 "49 5676 80,76 4648 89094 35"=, '97905 2270 12 IS 52836 57476 62087 66670 >==5 575> 8025, 47=3 89168 3586 .97977 = 345 13 30 529.3 57553 57630 62,6+ 66746 1300 5827 803 = 5 4707 8924. 3659 .98050 24,6 14 45 5299. 62240 66822 .376 590= 804CO 487. 803.5 3733 ,98.23 2488 15 4 53068 57707 623,7 66898 ,45= 5977 80475 4946 89389 3806 ,98.96 2561 10 I& 53146 57784 61393 66974 •5=7 6052 80550 5020 89465 3879 ,98269 2633 17 30 53=35 5786. 62470 67051 ,603 80624 5094 89557 5955 .98342 2706 IH 45 555°> 57938 62547 67. = 7 67203 .679 6203 "6^8 S0699 5,68 896,, 4026 4.00 .984.5 2778 10 20 5 55578 58015 62623 1754 80774 5=43 89684 .98488 2S5, 15 55456 58092 62700 67279 ,830 6353 80849 53'7 89758 4'75 ,9856, =9=5 21 30 55535 58.69 62776 67355 ,905 6428 80923 539' 89S32 4246 198634 =996 22 45 536.1 58246 62853 6743, ,98. 6503 80998 5465 89906 4320 ,98707 3068 23 (1 53688 58323 61929 67507 2057 65:8 8,073 5540 89980 4395 ,98780 314. 24 15 55766 58400 63006 67583 2.32 6653 8, ,47 56.4 90055 4466 ,98853 32.3 25 :m 55843 58477 63082 67659 2208 6729 5688 90127 4540 .98926 3285 20 45 539=' 58554 63,59 67735 2283 6804 8,297 576 = 9020, 46.3 198998 3358 27 7 53998 5863. 65 = 35 678,, =359 6879 8,371 5836 90=75 4686 199071 3450 28 15 30 54076 58708 633,= 67887 =455 6954 8,446 59" 5985 90348 4855 199144 150J_ 557? 2!» 54'53 58785 65388 67963 25.0 7029 8,52, 90422 199217 45 54=3' 58862 63465 68039 2586 7,04 8,595 6059 90496 4906 199290 5648 31 n 54308 58959 6354' 68, ,5 266, 7'79 6,33 90570 4979 ,99363 3,20 3.' 15 54385 590.6 636,8 68,9, =757 7=54 8,744 6207 90643 5055 ,99436 379= :<3 30 54463 59095 65694 68267 28,2 73=9 8,8.9 628, 90717 5.26 ,99508 5865 34 45 54540 59.70 6577. 68343 2888 7404 8,894 6356 9079, 5'99 ,9958, 5937 ;« !» 546.8 59=47 63847 684,9 2963 7479 8,968 6430 90864 5272 ,99654 40,0 3ff 15 54695 595=4 63924 68495 3039 7554 82043 6504 90938 5546 •997=7 4082 37 30 5477 = 5940. 64000 6857. 3, ,4 7629 82, ,7 6578 9,0,2 54'9 ,99800 4' 54 3B 45 54850 59477 64076 68647 3,90 7704 82,92 6652 9,085 549= .99872 4= = 7 30 10 549=7 595 54 64.55 68723 3265 7779 82266 6726 91,59 5565 .99945 4=99 40 15 55005 5965' 64229 68799 334. 7854 8=34' 6800 9.233 5659 2000 1 8 437' 41 :«t 55082 59708 64306 68875 34,6 79=9 824,6 6874 9.306 57,2 2CC09. 4444 42 45 55'59 59785 64382 6895. 549' 8C04 82490 6948 9.380 5785 200,64 4"6 43 II 55=57 59862 6445S 69027 5567 8079 82565 7023 9'454 585S 2C0236 4588 44 16 555H 59959 64535 69.03 3642 8,54 82639 7097 9.527 595' 2C0309 4661 45 30 5559" 600.5 6461, 69.78 57.8 8229 8=7.4 7'7' 9.60, 6004 200382 4755 40 46 55468 64687 69=54 3793 8304 82788 7=45 9,674 6078 20045s 4S05 47 :2 55546 6o°69 64764 69330 3869 8379 82863 75'9 9 '748 6,5, 200527 4878 411 15 55623 60246 64S40 69406 3944 8454 82937 2121 7467 9,822 6224 6297 2006.-0 4950 5C22 411 50 30 55700 60323 64916 69482 40,9 85 = 9 830.2 9,895 45 55778 60399 64993 69,58 4095 8604 83086 754' 9,969 6370 =00745 5094 51 IS 55855 60476 6=069 69634 4,70 8679 83.6. 76,5 92042 6443 2008,8 5,67 42 15 5593 = 60553 6} '45 69709 4246 8754 85 = 55 7689 92.. 6 65,7 20089. 5 = 59 53 :\n 56009 60630 6-2i2 69785 45=' S829 83309 7763 92.90 6590 2C0963 53" 54 45 56087 60707 6j^.,8 6986, 4596 8904 83384 7857 92263 6663 201036 5383 55 U 56.64 60783 65374 69937 447 = 8979 85458 79" 9=337 6736 20,, 09 .5456 5H 15 5624. 60860 65450 700,3 4547 9054 83533 7985 924.0 6809 10, ,8. 55=8 67 30 563.8 60937 65;=7 70089 4622 9,28 83607 8059 92484 6882 201254 56CO 5fl 45 56396 6.014 1 65603 70,64 4698 9203 83682 8,33 9=557 6955 201327 5672 6» Sec. 1' 2- 3 4' 5' (i' 7' »' 3' 10 11' 12' 13 14' 15' i D. 7R. Parts 5 lo i6 2. 26 31 -,6 41 47 ^t S7 «= (■^ 71 78 1 1). 72. Partr, 5 ,0 ,4 ,, 24 ^') 'A '",« 4', 4* ^^ sS 62 67 7- | TAB IF. 6f) 84r, 1.00. SINK StilJAKK 470 48'^ 49° ». 15' 1 -.W 1 15' 0' -_L-1 3(1' 1 45' 0' '3'' 17' 1 :«.' 1 45- 3''!l"''i3i'IO"' 3» 11' 31^12" 3i> 13" 31. Um|;)l,|.v; 3I' It!' |3''lll'"l3'' l!l' 9-2 ,9-2 l9-2 92 9-2 I92 J9-2 92 92 92 192 0' «! 05745 ico64i 14358 18627 228701 27089! 31284 3 54 54 39600 43722 14782. 1.'. 05817 |, ,,36; .4429 18698 22941 27159 3'353 35523 39669 4379' 4788, 1 'M> 05889, 1C207 145CI .8768 23C11 27229 3.423 35593 39738 1 43859 47957 •-' ■>:, 05961 1 10279 i >457i 18839 23082 273'^-o 3'493 35662 39807 1439^8 1 48025 3 1 06033 10351 1 14643 .89.0 23152 273701 3'5o2 3573' 39876 [43996 148094 4 1.-. 06105 1 '04^-3! >47>5 18981 23223 27440I 3.632 35«co 39944 44065 48-62 5 :io 06178 ,0494 147S6 .9052 23293 275.0 3.702 35870 40013 44'33 48230 6 4.-. 06250 10566 14S57 19123 23364 27580 3.772 35939 4C082 44202 48298 7 •." » 06322 10638 14929 19194 23434 27650 3.841 3600S 40151 44270; 48366 \r, 06394 1 '07 10 15C00 .9265 23505 27720I 319" 36077 40220144339,48434 » M 064661 107S1; 15071 .9336 23575 27790 3.9S0 36.47 40289144407 48502 4". 06538 10853 15.42 .9406 23646 27860 32050 362.6 40358 44476 : 485-0 1 1 3 l> c66io i 10925 .52.4 '9477 237.6 27930 32120 36285 40426 44544 i 48638 \> l.'i C6682 .0996 15285 .9548 23786 280CO 32. S9 36354 1 40495! 446.2 [48706 lit :ki 06755 1106S ■5356 19619 23857 28070 32259 36423 4C 564 446S1 : 48774 14 4.". 06827 ..140 '54»7 .9690 23927 28.40 32329 36493 1 40633 1 44749 48842 15 4 06S99 '5499 .976, 23998 282101 32398 36562 40702144818 4X9IU Hi 1.-. C697, ,.283 15570 ,9831 24068 28280 1 32468 3663. 40770:44886 48978 17 30 07043 "355 1564, 19902 24.39 28350 32537 36700 40839,44954149046 l!l 4.-. 07115 ,1426 15712 '9973 24209 28420 32607 36769 40908 145023 |49"4 1!« i U 07.87 i.49li 15784 20044 24279 28490 32676 36839 40977 145091 !49'82 lA 07259 11570 '5855 201,5 24350 28560 32746 36908! 41046 145160149250 ■-•l :«) °"15' 1164. ,5926 20,86 24420 28630 328.6 36977 41114 45228 493 '8 22 15 07403 ..7,3 '5997 20256 2449. 28700 32S85 37046 |4"83 45296 I493S6 23 C 07475 11785 16068 20327! 2456. 28770 32955 37'15|4'252 45365 49454 24 15 °7547 ,,856 16.40 20398 2463. 28S40 33024 37'84!4'32. 45433 49522 25 31) 076,9 1,928 162,1 20469 24702 289.0 33094 37254 4.389 45501 49590 21; 45 0769, 11999 .6282 20539 24772 28980 33'63 37323 41458 I45570I49658 ^•7 7 t» 07763 ,2071 '6353 206,0 24842 ' 29050 33233 37392 41527 45638 49726 2lt 15 078,5 12142 ,6+24 2c68i 249.3 29120 33302 37461 4-5^5 4^-06149794 2!l :44 >742o 2.670 125896 30C98 34275 38428 42557 46662 50744 43 11 II 089,5 132,51 .7491 2,74' 15967 30168 34344 38497 1 42625 46730 508,2 44 15 08987 .3287 1.7562 2,8,2 26037 30237 344'4 38566 42694 46798 50880 45 :«o 09058 '33581 ,7633 2,882 26,07 30307 34483 38635 42763 1 46867 50948 46 45 09,30 13430 17704 21953 26177 30377 34552 3S704 42831 46935 5,015 47 12 09202 1350, '7775 22024 ' 26247 30447 34622 38773 42900 47003 5,083 4)1 15 09274. '3573, 17846 17917 22094 1 26318 305.7 34691 38842 42968 47071 5"5> til :iii 09346 ,3644 22.65J263XS 30586 3476,1 38911 43037 47 '40 5.2,9 w7 45 094181 13715 17988 22235126458 30656 34830 38980 43106147208 5.287 Al 13 09490 13787 18059 22306 '26528 30726 34899 39049 43174 I47276 5'354 52 15 09561 .3858 ,8130 22376 26598 30796 34969 39"8 43243 47344 5.422 ■'.3 :v) r,9633 .3930 ,8201 22447 26668 30865 35038 39187 433" 474'2 5.490 54 45 09705 ,4001 18272 22518 26739 30935 3 5 '07 39255 43380 '47480 5-558 5A U 09777 ,4072 18343 22588 1 26809 1 31005 35'77 39324 43448 47549 5.626 5A 15 09849 14144 18414 226591 26879 3'075 35246 39393 435«7 476'7 51693 57 :«) 09920 14215 18485 22729 26949 3 "44 353>5 39462|43585l47685;5i76i| 58 4.1 09992 1 ,4287 i 18556 22800 1 27019 31214 35385 3953' 143654 147753 l5'82S 51* .->*.. 1' 2 3' 4' ft- tr T 8- !» 10- ir IJ- 13- 14- !»' 1 \>. li. I'iirc, 5 10 14 19 14 29 34 ,« 43 4li 53 58 62 67 7» 1 j I>. HH. I'urt* 4 9 ,3 ,8 23 ,7 ,. 36 40 4S ^0 54 59 *! *8 ) 94G TABLE GJ) I.OO. SINE SQUAKK 50° |__ 5P 52° ». ' 15' 1 30^ 45' 15' 1 30' 1 45' 0' 1 15' 1 so- 3" 20"' |3'' 21 ■"'a" 22" 3'' 23'" ^•2^ 3I' 25'" 31. 26'" 1 31. 27"' 3b 28"' la.' 29"' 13" 30n 9-2 |9-2 l9-2 92 9-2 9'i 9-2 |9-2 9-2 9-2 9-2 d 51897,55949 59978 639S5 67969 71930 75870:79788 83684 8755S 9.4.2 lA 51964 156016 60045 6405. 68035 7-996 75936 79853 83749 87623 9.476 :«) 52031 1 56083 60. .2 64.18 68.0,172062 76C0. 799.8 838.3 87687 9,540 45 52100 56.5. 60.79 64.84 68,77 72.28 76067 79983 83878 87752 9.604 1 52.67 562.8 60246 6425, 68234 72.94 76,32 80048 83943 878,6 91668 Ij 52235 56285 603.3 643,8 68 300 72260 76.97 80 1,3 840C8 87880 9.732 :«» 52303 56353 60380 643S4 68366 71325 76263 80.78 84072 S7945 9.796 4ft 52360 56420 60-M7 64451 68432 7239. 76328 80244 84.38 88009 9,860 2 (t 52438 564S7 60514 645.7 6849S 72457 76394 80309 S4202 8S073 91924 15 52506 56555 60580 64584 68564 72523 76459 ! 80374 84266 88,38 91988 ily 52573 56622 60647 6+650 6863, 72589 76525 1 80439 8433. 88202 92052 45 5264, 56689 607.4 647.7 6S697 72654 76590 80504 84396 88266 92, 16 :t 52709 56756 6078, 64783 68764 76655 80569 8446. 88331 92,80 15 52776 56824 60848 64850 68829 72786 7672. 80634 84525 88395 92244 .to 52844 5689. 609.5 649.6 68S95 72852 76786 80699 84590 S8459 92308 45 52912 56958 ' 60982 64983 6896, 729.7 76852 80764 84655 88524 92372 4 52979 57025] 61049 65049 69027 729S3 769.7 80829 847.9 1*8588 92436 15 53°47 57093 6. ..6 65.16 69093 73049 76982 80894 847S4I 88652 j 92500 W 53"5 57.60 6..82I651S2 69160 73. "5 77048 80959 S4849 887.7 92564 45 55.82 57227 6.249)65249 69226 73180 771.3 8.024 849.3 S878, 92627 1!» 5 II 53250 57294 613.6 65315 69292 73246 77.78 8.089 84978 l88i7 9269, ^20" Ift 533"7 57362 6,383 65382 69358 733'2 77244 8, .54 85042 88909 92755 21 30 533S5 57429 6.450 65448 69424 73378 77309 8.2,9 85.07 88974 928,9 22 45 53453 57496 6,5,7 655.4 69490 73443 77374 81284 85,72 S9038 928S3 23 (> 53520 57563 6,583 65581 69556 73509 77440 8.349 85236 89,02 92947 21 15 53588 57630 6,650 65647 69622 73575 77505 8,4.4 85301 89,67 930,, 25 30 53655 57698 6,717 657,4 69688 73640 77570 8.479 85366 89231 93075 2« 45 53723 57765 6.784 65780 69754 73706 77636 8.544 85430 89295 93'39 27 7 53790 57832 6.85. 65847 69820 1 73772 7770, 8,609 85495189359 93203 2« 15 30 53858 57899 57966 6.9.7 659,3 69886 li^iZ. 77766 8,674 85559 89423 93266 2!t 53926 6.984 65979 69952 73903 7783218,739 85624 89488 93330 45 53993 58033 1 6205. 66046 700,8 73969 77897 8,803 85688 89552 93394 31 8 5406. 58101 62. .8 66, ,2 70084 74034 77962 8,868 85753 896,6 93458 3J 15 54.28 58.68 62.84 66,79 70150 74100 78028 8,933 858,8 89680 93522 33 30 54.96 58235 6225. 6624^ 70216 74166 7S093 8,998 85882 89745 93586 34 45 5426J 58302 623.8 6631. 70282 7423. 78,58 82063 S5947 89809 93650 35 !♦ 5433> 58369 62385 6637S 7034S 74297 78223 82128 860, , 89873 937.3 30 15 5439S 58436 62452 66444 70414 74362 1 78289 82.93 86076 89937 93777 •■(7 30 54466 58503 62518 665.0 70480 74428 78354 82258 86140 9000, 9384, 3» 45 54533 58570, 62585 66577 70546 74494 784.9. 82323 86205 1 90065 93905 39 10 5460. 58637 62652 6664, 706,2 745 59 784S4 82388 86269 90.30 93969 "io" 15 54668 58705 627.8 667.0 70673 74625 78550 82452 S6334 90194 94033 41 30 54735 5«772 62785 66776 70744 7469. 786,5 86398 902 58 94096 42 45 54803 58839 62852 66842 708,0 74756 78680 82582 86463 90322 94160 43 II 54870 58906 629.8 66908 70876 74822 7S745 82647 86527 903S6 94224 44 15 54938 5X973 62985 66975 70942 74S87 78810 827.2 86592 90450 94288 45 3(» 55005 59040 63052 6704. 71008 74953 78876 82777 86656 905,4 9435. 46 45 55073 59107 631,8 67107 71074 750.8 7894. 82842 8672. 90579 944.5 47 I'i (t 55.40 59.74 63,85 67.74 71,40 75084 79006 82906 867S5 90643 94479 48 15 55208 59241 63252 67240 71206 75.49 79071 8297. 86850 1 90707 1 94543 49 30 55275 1 59308 633.8 67306 71272 75^.5 79.36; 83036 86914 9077, 94607 "so" 45 5534 59375 63385 67373 71338 75^-8. 79202 '83.0. 86979; 90835! 94670 jl i:> 554.0 59442 63452 67439 71404 75346 79267 83.66 87043 j 90899 94734 52 15 5 5477 59509 635.8 67505 7.469 754.2 79332 1 83230 87.08 90963 94798 53 30 55545 59576 63585 67571 71535 7.60. 75477 79397 1 83295 87.72 ; 9,027 94S6. 54 45 556.2 59643 63652 67638 75 543 79462 1 83360 8723619,09, 94925 55 (4 55679 597.0 637.8 67704 7.667 7560S 79527183425 S730. i9,,55l949S9 50 15 55747 59777 637S5 67770 7'733 75674 79593 1 83490 8736519.2.9195053 57 30 558.4 59844 63852 67836 7.799 75739 79658 83554 8743019. 284;95i. 6 58 45 55881 599.1 639,8 67902 7.865 75805 79723^3619 S7494I9134S 1 05180 5» S.'C. r 2' 3' 4' o'o- "f a 9 10 I r u ' 13' 14 15- 1 U. fin- r.irts 4 9 13 18 23 27 32 36 41 45 50 54 59 63 68 . j ». 64. 1'J"> 4 V n 17 2> 26 30 -4 3S 43 47 51 53 60 64 1 TABLE 69 847 1 LOO. SINE SgUAKK 1 52^ 53° ^. Jl 55'-^ O'J 15'. 45 llj"'^ ■•Xl' 1 45- 0' 1 15' 1 30- _i5'_ :,^,3,„: ;jl, 5.J.,. 1 ;{1, :(;(... 3i'34"'|3"35-' 3'' 3(!'" 31' 37'" 13" 3)1"' 3"3»"' 3i'4()"'|3i'41"' i. 9- 9- |9-3 9-3 9-3^ 9-3 93 9-3 9-3^ '„l ^'5 (»' 95^44 299055102845 066.5 .0364 14094 17803 2.492 25.6. 28811 32442 \:> 953^7 2991 iS 02908 066-8 10427 '4'55 17864 21553 28872 32502 1 :m 9557- 299 1S2 0297. 06740 .0489 .4217 17926 2.6.4 25283 28933 32562 2 45 95455 299245 1 01034 C6803 .055. .4279 .7988 2.676 25344 28993 32623 3 1 96.35 29994. 103727 07492 ..236 .4961 1X665 21350 26015 29660 33286 14 45 9619S 300004 j 03790 07554 "299 15023 18727 124,, 26075 2972, 33346 15 4 96262 300068 1 C3853 076.7 1. 361 15085 .8788 22471 26136 297S1 33407 l« 15 96326 300.3. 03915 07679 1.423 15.461.8850 »2533 26197 29842 33467 17 :ti) 96389 30CI94 03978107742 11485 .52081 18911 12595 26258 299CI 33527 1» 45 96453 300157 10404. ,07804 11 547 .5270 1 .8973 12656 263.9 263S0 29961 30024 335S7 33648 lit ft 965.6 300321 ,04104 07867 ..6.0 15332 '9035 117.7 15 96580 300384 [04.67 07930 ..672 15394 .9096 12778:2644, 30084 337C8 21 ;w 96644 300447 ,04230 07992 ..734 15456 .9158 22S40I 26502 30,45 33768 22 45 96707 3005.CJ 04293 08055 1.796 15518 192.9 2290, 26563 30205 33828 23 « 1) 96-71 300574 1043561 08.. 7 .1858 .55*0 .928.1 12962 26624 30266 33889 24 15 96S34 300637 1 04418 08.80 .1920 15641 .9342 »3023 26684 30316 33949 25 :w 96S98 300700. 04^.8. 08242 11983 •5703 '9404 130S4 26745 30387 34C09 2« 45 9696, 300763 04544 08305 12045 .5765 19465 13.46 25go6 30447 34069 27 7 97025 300826 1 04607 08367 12.07 .5827 .9527 13207 26S67 3050S 34.29 2(1 15 97088 300889 1 04670 08430 12169 15888! .9588 13268 26928 30568 3-t'90 2!l 30 97.52 300953 1 04733 08492 .223. '5951 1 19650 13329126989 30029 3425c 31) 45 97i«5 30.016 04796 08555 12294 13390 27049 30689 343.0 31 » 1) 97^79 301079 04858 12356 16074 19773 i345'l27.io 30750 34370 32 15 97342 3c 1.42 0492. ' 08680 .24.8 16.36 .9834 135.2 27.71 308,0 34430 33 :«t 97406 30.205 04984 08742 12480 .619? .9896 23574 27232 30871 34490 34 45 97469 301268 05047 08805 12542 16260 19957 13635 27293 30931 34551 35 9 97533 301332 05.10108867 .2604 .632, 200.9 13696 27354 30992 346., 3li 15 97596 301595 05172 08929 .2666 .6383 20080 23757 274.4 3,052 3467. 37 :t(i 97660 30.458:05235108992 .2729 16445 2014. 238.8 27475 3.113 3473. 31! 45 97-23 30.52. 05298 1 09054 12791 .650S 10203 1 23879 27536 31.73 3479' 3!) 10 (1 97-87 301584.0536. 09. 17I .2853 .6568:20264 13940 27597 3,234 3485, 40 15 9-850 30.647 05423 09.79 .2915 .6630 20326 1400. ^7657 3,294 349,2 41 .'Ml 979'4 30.7.0 05486 09242 •2977 16692 20387 14062 31355 34972 42 45 9797:^ 30.773 05549 09304 13039 16754 20449 24124 27779 314.5 35032 43 II 1) 9804 . 30.836 056.2 09367 .310. .6S15 205,0 24.85 27840 31475 35'-92 44 15 98104 301900 05674 09429 13.63 16877! 2057, 14246 2790. 31536 35.52 45 :(ii 98.67 301963 05737 0949. 13225 .6939120633 14307 27961 31596 352.2 in 45 98231 302026 , 05800 09554 13287 17C01 1 20694 24368 18022 3.657 15272 47 12 II 98294 3020S9 05863 096.6 '3349 .7062 ' 20756 14429 28083 3'7'7 35332 411 15 9S358 302152 '05925 09679 '34" 17124I20817 24490 28J44 3.778 41t M 98421 302215 05988 09741 •3473 ,7186120878 2455' 28104 3,838 35452" 50 45 98485 302278 0605. 09803 '3535 17247 20940 246.2 28265 3,898 355'3 51 i:i 98548 302341 06.14 09866 13597 17309 ;;o62 24673 28,26 3.959 35573 52 1.'. 98611 302404 06176 09928 13659 '737. 24734 18386 320.9 35633 53 .'((I 98675 302467 ] 06239 09990 13722 ■7431 21.24 24795 28447 32080 35693 54 45 98738 302530,06302 10053 .3784 .7494 2.185I24S56 28508 32140 35753 55 14 98801 302593 06364 .0..5 .3S46 17556I2.246 24917 28568 35813 5i; 15 98865 302656 ! 06427 10,771.3908 .76.S 2.308! 24978 28629 3226° 35873 57 3« 98928 3027.9106490 10240 1 .3970 '7679 121369 125039 2 8 690 3232. 35933 5)1 45 98992 302782 1 06552 10302 1 .4032 .774' 2143.i25.co 28751 3238, • 35993 5!) s«:. r r 3- 4' 5' ti* 7' n' f 10' ir 12" 13 14-Y5 -■ 1 1). 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S3°57 S6406 89738 1 3053 6352 399633 2899 6148 0938. 2598 31 8 76364 79747 83. .3 8646, 89793 3>o8 6406 399688 »953 6202 09435 265. 32 15 76420 79803 83.69 865.7,89849 3.63 646. 399742 3008 6256 0948S 2705 33 30 76477 79859 83225 86573 89904 32.8 65,6 399797 3062 6310 09542 2758 34 45 76533 799-6 83281 86629 1 89959 3^74 057. 399852 3. .6 6364 09596 28.2 35 9 76590 79972 83337 86684 1 900.5 3329 6626 399906 3.70 6418 09650 2865 :u: 15 766+f. 180028,83392 86740 90070 3384 668. 59996. 3225 6472 09703 2919 37 30 76703 1 8C084 8344S 86795 90.25 3439 6735 4CC0.5 3279 6526 0975- 2972 38 45 76759 1 80.40 83504 8685. 90.8. 3494 1 6790 4CC070 3333, 6580 098,, 3!» "40 10 768,6180.97 83560 86907 90236 3549 16845 400.24 3387 6634 09864 3079 15 76872 I 80253 836.6 86962 90292 3604 6900 400179 3442 6688 099. S 3,32 41 30 76929180309183672 870.8190347 3659 6955 400233 3496 6742 09972 3.86 42 45 769S5' 80365 83728 87074 , 90402 3 7. 4 1 7009 400288 3550 6796 3-=39 43 11 7:042 ,8042. 1 83784 87.29 '90458 ,3769 7064 400342 3604 6850 IC079 3^93 44 15 7-098 80478 '83840 87185,905.313824 7.19 400397 3659 6904 10.33 3346 43 30 7-155 S0534 83896 S7240 90568 j 3879 7.74 40045. 37.3 6958'. 0.87 3399 4(1 45 772.. 80590,85952 87296,906:4(393417228 400506 3767 7012 .0240 3453 47 12 77268 80646 1 84007 87351 90679: 3989 7283 400560 382. 7066 ] 10294 3506 4)1 15 77324 80702 : 84063 8-407 90734 4045] 733S 400615 3875 7i2oiic348 3560 4!) 30 77380 180-58, 84' .9 87463 90790:4100 7393 400669 3930 7174! '040. 16^ 45 774371808.5:84.75 87518 90845 I4. 55 7447 400724 39S4 7228 ,0455 3666 51 13 77493 , 8087. ,8423. 87574 90900, 42.0 7502 400778 4038 728. 10509 3720 52 15 77550 80927,84287 87630,90956,4263 7557 400833 4092 7335 10562 3773 53 30 77606 80983 84343 87685 9.0.. I4310 76.2 400887 4146 7389 .0616 3827 54 45 77663 8.039 84398 8774' 9'o66 4375 7666 400942 420. 74431 '0670 3880 55 14 777.918.095184454 87796, 9'iJ' ,443° 772. 400996 4225 7497 1 .0723 3933 5B 15 77775 !8m5' 84510 87852 1 9.. 77 4485 7776 401051 4309 755' '0777 39S7 57 .10 77832,8.208 84566 8790V 9123214540 7831 40.. 05 ,4363 7605 .0830 404c 5(1 4.5 778S8 8.264 84622 8-962 ' 9. 2S7 4595 -88? 401159 441717659! 10884 4^9" 5!) Srt. 1- 2- 3' 4' y H- 7 H a 10 11 12- 13 14 15' n. .17. rViiN 4 X ■■ 15 19 2, 27 -io 34 3« 4^^ 4^ 49 SI ■;- 1 D. .S4. IW., 3 7 ,o H .8 2. 24 »8 3= ".^ W 4= 4* 49 '4 ] 800 TABI.F. 69 U)(i. SINK SQUAKi; 61° 6 15' 2° 630 64° _!: 15' 30' 45' 0' 30' ! 45' 0- 1 15' 30' 45' 41, isn, 0' 4h Ifin. 4'' 5" 9-4. 41, cm 41, 7„. 41. 8". 41. gm| 41, 10m [41. 11... 41, 12m 1 41. 13'" 4h|4n ?-4 9-42 9-42 9-42 9-4 9-43 9 4 9-4 9-4 9-4 9-4 «' 4147 j 17340 0517 3679 6825 29955 1 3070 36170 39255 42325 45379 484.9 lo 4200 1 17393 0570 373' 6877 30007 1 3122 36222 39306 42376 45430 48470 1 3(1 4-53 ('7446 0623 3784 6929 30059, 3174 36273139358 42427 4548. 48520 2 4/1 43071 "7499 0676 3836 6982 301111 3226 36325 39409 4247 8 45532 4857' 3 1 4360 17552 0728 3S89 7034 30163 1 3277 36376 39460 42529 45583 48622 4 1» 17605 0781 394' 7086 30215 3329 36428 395.' 42580 45633 48672 5 30 4467 17658 CS34 3994 7.38 30267 33S1 364-9 39563 4263. 45684 48723 ti 46 4510 177II 0887 4046 7191 303.9 3433 3653. 39614 42682 45735 48773 7 •i tl 4573 .7764 0940 4099 7243 30371 3484 36582 39665 4=733 45786 48824 8 15 4627 .78. 7 0992 4152 7^95 30423 3536 36634 397.6 42784 45836 4J874 !« 3(1 4680 1C45 4204 7347 30475 3588 366S5 1 3976S 42835 45887 48925 "nr 4f> 4733 17924 1098 4»57 7400 30527 3640 36737 398.9 42886 45938 48975 11 3 (1 47>!7 17977 4309 7452 30579 3691 3678S 39870 42937 45989 49026 12 .5 4S40 18030 i»03 4362 7504 3063, 3743 36840 3992' 42988 46039 490-6 13 30 4893 18083 1256 44'4 7556 30683 3795 36891 39973 43039 46090 49127 14 45 4946 18.36 1309 4467 7609 30735 3X47 36943140024 43090 46141 49 '77 15 4 5000 18189 1362 45'9 7661 30787 3898 36994 4C075 4314' 46192 49228 k; 13 5053 18242 1414 457^ 7713 30839 3950 37046 40126 43.92 46242 49278 17 30 5.06 18295 1467 4624 7765 30891 4002 37097 40177 43243 46293 493=9 IH 45 5 5.60 .S348 ■ 520 4^ 47 = 9 78.7 30943 4054 37 149 1 40229 1 43294 46344 49379 III 5»'3 1840 1 '573 7870 30995 4.05 37200 [40280 143345 '46394 49430 20 15 S266 18454 .625 4782 7922 31047 4'57 37252 40331143396146445 49480 21 30 5319 18507 1678 4834 7974 31099 4209 37303 40382 43446 46496 49530 22 45 5373 "8560 .731 4886 8026 31151 4260 37354 40433 43497 46546 4958. 23 « 5426 .86,3 .784 4939 8079 31203 43.2 37406 40485 43548 46597 49631 24 15 5479 18666 1836 4991 813. 3.155 4364 37457 40536 43599 4664.S 49682 25 30 5532 18718 .889 5044 8183 3.307 44.5 37509 40587 43650 46699 4973 = 26 45 5586 .877. 1942 5096 8235 3.35914467 37560 40638 43701 46749 49783 27 7 5639 j 18824 1994 5 '49 8287 3.4.1 I4519 376..I406S9 43752 468C0 49833 28 15 5692 5745 18S77 2047 5201 8340 3.463 457° 3766314074. 43803 46851 498S3 20 30 '18930 2100 5»54 8392 3.5.5 4622 377.4 1 40791 43854 46901 49934 "30" 45 579S1 18983 2152 5306 8444 3.567 4674 37766 \ 40843 43905 46952 49984 31 « 5852 1 19036 2205 5358 8496 3.618 4725 37817 40894 43956 47003 50035 32 15 5905! 19089 2258 5411 8548 31670 4777 37S69 40945 44007 47053 50085 33 30 5958 19142 5463 8600 31722 4829 37920 40996 44057 47.04 50.36 34 45 6011 19195 5516 S653 3'774 48S0 3797. 4.047 44108 47155 50186 35 t) 606+ 19248 2416 5568 8705 3.826 4932 38023 I41C39 44'59 47205 50236 31! Ifl 6118 19301 2469 562. 8757 31878 4984 38074141.50 44210 47256 50287 37 3l. 6171 19354 2521 5673 8809 3.930 5035 38.25 4.20. 44261 47306 50337 311 45 6224 1 19407 2574 5725! 8861 l'^± 5087 38i77'4i252 44312 ] 47357 50387 3!) 10 6-77 1 '9460 2627 5778 8913 32034 5.39 38228 4.303 44363 47408 50438 4(1 15 633^1 19513 2679 5830 8966 32085 5190 38280 4.354 44414 47458 50488 41 30 6384I.9566 2732 5882 90,8 32.37 5242 3833. 4.405 44465 47509 50539 42 45 6437 19618 2784 5935 9070 32189 5293 38382 4.456 445. 5 47160 50589 43 11 6490 .967. ^837 5987 9122 3224. 5345 38434 1 4.507 44566 4:610 5C639 44 15 ''543 19724 2890 6040 9 '74 32293 5397 38485 ] 4.559 ! 44617 47661 50690 45 .10 6596 ■9777 2942 6092 9226 3^345 5448 38536 41610 44668 477" 50740 ■U\ 45 6649 19830 2995 6.44 927S 32397 5500 38588 4.66. 447.9 47762 50790 47 \i f)702 ' 19883 3048 6197 9330 32449 555. 38639 4.7.2 44770 478.3 50841 411 15 .10 67561 19936 3100 '^=49 9382 32500 5603 3869, 4.763 4482. 47863 508_9' 'i» 6809! 19989 3.53 630. 9434 32552 5655 38742 4.8.4 44871 I47914 5o9^. 45 6862 1 20042 3205 6354 9487 32604 5706 38793 4.865 44922 47964 50992 51 13 6915 20094 3258 6406 9539 32656 5758 38844 4.9.6 44973 48015 51042 52 15 6968 20147 33" 6458 959' 32708 5809 38896 4.967 45024 48065 51092 &3 30 7021 3363 65.. 9643 3^759 5861 38947 420.8 45075 48116 5. '43 54 4A 7074 2o»53 34.6 6563 9*95 3X8.1 5912 38998 42069 45.25 48167 51'93 55 14 7127 20306 3468 6615 9747 32863 5964 39050 42120 45.76 482.7 5.243 5fi 15 7I8I 20359 352 1 6668 9799 32915 6016 39.01 42.72 45227 48268 5.294 57 30 7234 20411 3574 6720 985. 32967 6067 39.52 42223 45278 1 483 18 51344 5ri 45 72S7 20464 3626 6772 9903 33018 ' 61 19 39204^42274 45329148369 5 '394 59 ~ .Sec. r-i* 3 4^'i5 i&~rV^W\V~\V~ 3-r4-ia- a .VI. I'arls 3 7 >■ '4 >!i I' 15 ^8 3^ 35 39 4^ 46 49 53 1 1). SO. I'jJts 3 7 ic 15 17 ao X3 17 JO 31 -.7 4c 43 47 jo j TABM'. Of) 8r,i I, no. SINK SQL'ARK " " ' 64^ G5^ ^.„^^ 1 a. 15' 1 SO' 45'_ 0' 1 IS' 30 1 45' 0' 1 15' 1 30' 1 46' 4M7'"|4M!I" 4''li»'" 4hgom 4"21'" 4h 2-2". '41. 23"' 4l> 24'"| 4I' 25"" 4!" ar.'"' 4'' 27°' 9-4 [9-4 I9-4 9-4 '9-4 94 '9-4 9-4 1 9 4 9-4 9-4 (1 51445 1 5445, 5745' 60433 63400 66353:69193 722,8 75.'« 78026 ; 809.9 16 51495 1 54505 57501 60483163450166403:69341 72266 75,77 78074 [80957 1 30 51546: 54555 5755' 60532 (65499 [66452 69390 713.5 :^5ii5 78,221 81C05 2 •15 51596 54605 57601 60582 63548 66501 169439 72363 75174 78, 7o| 8,053 3 1 (t 51646 54655 5765' 60631 1 63598 66550 [69488 724.1 75311 782,8 8,, 0, 4 l.> 5.696 5+^06 57700 60681 636+7 66599169537 72461 1 7537. 78267 81149 5 :«i 51746 54756 57750 60730 63696 66648 1 69586 72509 754'9 783.5 8, ,97 (! 4.'> 51797 54806 57800 60780 63746 66697 69635 72558 75467 78363 8,245 7 3 51847 1 54856 608-.9 63795 66746169683 72606 755-6 7841,18,293 >i !■'■ 51897 1 54906 579:0 608791638441 66795 ■69-31 72655 1 75564 78459 8,5+1 !f :i(i 5 '94^ 1 54956 57949 60929 63894166844,6978. 727041756.1 78507, 8,388 10 4'. 51998^ 55006 57999 60978 63943 66S93I 6983c 72752 7566, 78555(8,436 1 1 :i (1 52048 55056 58049 6,028 63992 6694.2 ' 69879 7280, 75709 78604! 8,484 12 15 5.09S 55106 58099 610.7 64041 66992 1 69927 72849 75757 7865218,532 i:< .'ID 52.4S 55156 58.+S 6.127 6409. 67041 69976 72898 75806 787001 8,580 14 45 52199 55206 61176 64140 67090170025 71947 75854 78748 8,628 15 4 II 52249 55256 5824S 61226I64189 67139 70074 71995 75902 78796 [8.6-6 III !5 52299 55306 58298 61275 [64139 67.88 70123 73044 7595.! 78844! 8,724 17 30 5^349 55356 58347 61325 6428S 67137 70171 73092 75999 78892 8,77, HI 45 52400 55406 ^8397 6,5-4! 64557 67286 70220 73 >4. 760+7 7894018,8,9 l!l 5 52450 55456 5«447 61424 64386 67335 70269 73.89 76096 78988:8,86- 20 15 525001 55506 58497 61473 64456 67384 703 IS 73138 76,44 79036; 8,915 21 :to 5i55>^i 55556 58546 61523 64485 67433 70J66 73186 76,92 79085 8,963 22 45 52600, 55605 58596 61572 64534 67482 70415 73335 7624, 79133 820,, 23 6 5^651, 55655 58646 61622 164583 6753. 70464 73384 76289 79181 82059 24 15 52701 1 55-05 '5?695 61671 64633 6.580 705.3 75431 76337 79229 82107 25 :«() 5^751155755 5«745 61721 64682 67629 70562 7348. 76386 79177 82154 2fi 45 52801155805 58795 6,770 64731 67678 70610 73519 76434 79315 82202 27 7 5^851 55»55 58845 61820 647S0 67727 70659 73578 76482 79373 82250 2H 13 52902] 55905 58894 6.869 64830 1 67776 70708 75626 7653. 79411 82298 20 .III 5^95^ 55955 58944 6.9.8 64879! 67815 70757 736,5 76579 79469 82346 30 45 53002 56C05 58994 6,968 64,28 6-874 70806 •3713 76627 795.7 82394 31 It 53052 56055 59043 620.7 64977 67913 70854 73771 76675 79565 1 8244. 32 15 56,05 59093 62067 65026 67971 70903 73820 76.24 796.3 82489 33 :5^ 60135 63104 66059 68999 7,926 74838 77737 80621 83493 54 45 54205 57202 60185 63154 66108 69048 71974 74886 777S5 80669 83540 56 14 54^55 57^5^ 60235 63203 66,57 69097 72023 7493 5 77833 80-.7I 83588 51; 15 54305 57302 60284 65252 66206169146 74983 77881 80765 83636 57 SO 54355 57351 60334 63301 66255169,95 72,20 75032 77919 808,3 83684 5(1 45 54405 574'S 60383 6335. 66304 69:4., -2,6, 75080 _77978 8086, 8373. 59 Se,; r 2- r"4- 5- «• 7" R- 9' 10^ 11' 12' T 3' U' 15' n. :,n. I'.,rls ^ 7 lo 15 17 10 :-, n 3^ -, ,- 40 45 4- ^0 1 1). IK. r..rn 5 6 10 n >ft "9 '-» if' ^9 3^ 35 3* 4^ 4S 4« J 852 TABLE 69 LOG. SINE SQUAKIi 67° 68° 1 69° 0' 15' 30' J 45' 0' 15_ 4" 33- 30^1 ji^\_iy_J_\o' \ 30- 4i'28'"l4M9"' 41>»»'"|4I'3I" 41,32^ 4l>34'" 4"35'" 4''3«"'|4''37" 4*' 38'" 9-4 |9-4 |9-4 l9-4 94 9' 95 95 95 V5 95 (1 83779186635189478 92307 95113 497926 007.6 03492 06256 09007 11745 15 83827 1S66S3 89525 91354 95.70 497973 00762 03539 06301 09053 11790 1 :i(i 83S74 86730 89572 9240. 952.7 4980.9 00809 03585 06348 i C9098 ,,836 2 ■15 S3922 86778 89620 92448 95164 49S066 00855 0363. 06394 09144 ,,881 3 1 (1 83970 86825 89667 91495 9531' 498112 00901 03677 06440 09 190 11917 4 15 840.7 86873 89714 92542 95357 498159 1 00948 03723 06486 09235 1.972 :to 84065 869,0 89761 91589 95404 498106 CC99+ 03769 06531 09281 t; 45 84,13 86968 89S09 92636 95451 498152 0,040 038.5 06578 09327 ,2063 7 2 8416. 87015 89S56 92683 95498 498199 0,087 03862 06624 0937J ,2,09 K 15 84208 87062 89903 itni. 95545 498345 01133 05908 06669 09418 11154 it ■M) 84156 87110 89950 91778 95591 498392 0.179 03954 067,5 09464 122CO IF ■15 84304 S7157 89998 92825 95638 49S438 01226 040C0 0676. 09510 12245 1 1 ;i (1 «435. 87205 90045 92872 956S5 498485 0,272 040:16 06807 09555 12291 12 15 84399 87252 90092 91919 95731 498532 0.3.8 04092 06853 0960, 11336 13 :io 84447 87300 90139 92966 95778 498578 0.365 04.38 06899 09647 ■ 2382 14 »5 84494 87347 90186 930.2 95825 498625 0,4,, 04.84 06945 09692 12427 15 4 84542 87395 90234 93059 95871 498671 01457 04231 0699. 09738 11473 Ifi 15 84590 87442 9028. 93106 95919 498718 01504 04277 07037 09784 125,8 17 M 84637 87489 90328 93153 95965 498764 01550 04323 07083 09S30 12564 Itt 45 S4685 87537 90375 _932oo 96012 4988.. 0,596 04369 07.28 09875 ,2609 III a 84733 87584 90423 93147 96059 498857 0.643 044.5 07.74 09921 Ifoo 'W 15 84780 87632 90470 93194 96.06 498904 0,689 04461 07220 09967 21 :m 84828 87679 90517 93341 96.52 498951 0,735 04507 07266 HIT, 45 84S75 87726 90564193388 96199 I49S997 0,782 04553 07311 10058 1. 1791 23 6 (1 84923 87774 90611 93435 96246 499044 0,828 04599 07358 24 15 8497, X7821 90658 93482 96293 499090 01874 04645 07404 10149 ! 12882 25 :{0 85018 87869 90706 93519 96339 499«37 0,92, 04691 0745c 10195 ,2927 26 45 85066 87916 90753 93576 96386 499183 0,967 04738 07495 .0140 11973 27 7 851 14 87963 90800 93623 96433 499130 02013 04784 07541 .0286 130.8 2)1 15 85161 88011 90848 i 93670 96480 499176 04830 07587 10332 ,3064 2!» 30 85109 88058 90S94 93717 96526 499313 02106 04876 07633 10377 ,3,09 "30" 45 85256 88106 9094. 93764 96573 499369 |C2. 52 04922 07679 1042 3 ■3154 31 K 8 5 304 88.53 90989 938.1 96620 4994.6 02.98 04968 07725 10469 13200 32 15 85352 88200 9.036 93858 96666 499462 02245 05014 07771 105,4 13145 33 .• 4'' 41"' 41, 42m 41, 4:,. 4M4'"' 4'' 45"' 41, 4,i,„ 4h 47,,, 4h4nm|4i,4,,,„ ., 9-5 9-5 95 9-5 9 5 9-5 9-5 (9-5 9"5 9'5 9'5 fli o' 14470 •7183 19883 21570 25245 17908 30559 33'97 358:3 3X437 4,040 l.-> >45'S .7::g 19927 2:6.5 25290 27952 30603 3324' 35867 384S. I4.C83 1 30 14561 ■7-73 .9972 22659 25334 27997 50647 33285 55,10 38524 4.. 26 2 4.-> .46C6 .73'S 200.7 1:704 25379 28041 3069. 33329 35954 58568 + ..69 1 14651 ■7363 20062 22749 25423 28085 30735 33372 35998 586,. 41213 4 In .4696 1-408 20107 12794 25468 281:9 30779 33416 36041 38655 41:56 :»(• '474'- '7453 20.52 2:838 25512 308:3 33460 36085 58698 4.299 li 4.1 H-S7 .7498 20.97 1:883 25557 28:i8 30867 33504 36.:, 38742 4.-4: 7 J M85Z '7543 1024: 22928 25601 :8:6: 30,11 33548 56.72 38785 4.3S6 )l 1.-. .4*78 '7588 ■7633 20287 1:97: 25645 2S306 30,55 33592 362.6 38828 414:9 9 :«) .4915 2033, 130.71:5690 28351 50999 33635 56:60 4.472 ~W i.'i .4968 .7678 20376 2306: 15734 28395 51043 33679 56303 38915 4'5.5 11 3 15014 '7724 2042. :3.o6 25779 28439 3.087 33723 36347 38959 4.559 15 1505, .7769 20466 23151 25813 28483 3.13. 33767 3639. 3900: 41602 l.'t :i(t 15104 .78.4 205.1 13195 25S68 285:8 3"75 338" 36434 59046 4.645 14 4j 15149 '7859 20556 :3:40 25912 3.:., 33854 56478 39089 4.688 15 4 I) ";i95 .7904 20600 23285 25957 :86,6 31:63 3389S 3652. 39.32 4.73' l«> 15 15:40 17949 20645 133:9 i6coi 28660 31307 33942 56565 39.76 4.775 17 M 15285 '7994 :o69o »3374 26045 28704 3'35' 33986 36609 392.9 4.81a It) 45 '=330 .8039110735 23419 260,0 2S749 3'395 34030 34074 36652 39265 4-86. To 5 ■ 5376 18084 20780 23463 26.34 18793 3<439 36696 39306 41904 15 154:1 .8.:9 208:5 23508 26179 28S37 5.483 34"7 36740 39349 41948 21 M 15466 .S174 20869 23552 26223 28881 3.527 34.6. 56783 39393 4.991 22 45 15511 18:19 209.4 23597 26:67 28,26 3>57' 34205 568:7 39436 42034 23 fi It M557 .8:64 20959 23642 163.2 2X970 3.6.5 3+249 36S70 39480 42077 24 15 1560: .8309 2.004 23686 26356 290.4 5.65, 34293 36914 39523 4:120 25 30 15647 .8354 2.049 2373' 16401 29058 3.703 34336 36957 39566 4:164 2(i 45 ■ 56,: 18399,2.094 23775 26445 29.02 3 '747 34380 37COI 3,6.0 42207 27 7 '5737 '8444 :..38 23820 26489 19146 31791 34424 37045 39653 42250 20 15 ■5783 18489 211S3 23865 26534 19.91 3.835. J446S_ 3-088 59697 42293 29 "3(7 .to ■ 58:8 .8534 2122S 23909 26578 29235 31879 345" 37132 39740 42336 45 ■5873 .8579 21273 23954 26625 19279 3'923 34555 37'75 39783 42379 31 8 (I .59'S .8624 213.7 23998 26667 29323 5.967 34599 372.9 39827 4:4:3 32 15 15963 .8669 21362 14043 26711 29367 34643 3726: 59870 4:466 33 30 .600, .87.4 2.407 240S7 26756 2,41. 33055 346X7 37306 399.3 4:509 34 45 16054 .8759 2.452 24.3: 26800 2,456 3 •099 34730 37350 39957 42552 .•|5 n 16099 .SS04 2.497 24'77 26844 2,5CO 32'43 34774 37393 40000 42595 3)i 15 16144 .8849 14::. 26889 29544 52.87 348.8 37437 40045 42638 :t7 30 ■ 6,8, .8894 2.586 24:66 26933 2,588 52251 34862 37480 40087 42681 3il 45 10 16:55 .8939 2163. 243.0 26977 29632 32275 34905 37524 40.30 42725 ■39 i6:go .S984 2.676 M3 5 5 2-022 19676 323-9 34949 37567 40.73 4:768 10 15 163:5 .90:9 2.720 24400 27066 29721 32363 34993 576.. 402.7 4:81. 41 :io .6370 19074 2.765 24444 271.0 29765 52407 35037 37654 40260 4:S.;4 42 45 ■ 6415 .9. .9 24489 27'55 29809 3245' 35080 576,8 40304 4:8,7 43 II 16460 .9164 2.855 24533 27.99 19855 32495 35'24 3774' 40347 42940 (4 15 .6506 .9209 2.S99 24578 27244 29897 32538 35.68 37785 40390 4:983 45 .10 16551 19254 2.944 246:: 27288 19941 5:582 352.. 578:8 40434 430:7 46 45 16596 19299 21989 24667 27332 29985 52626 35255 37872 40477 43070 47 12 16641 '9344 2:034 247 II 27376 30029 52670 35299 379.5 40520 43'13 48 15 .6686 .9389 1 22078 24756 27421 30074 327»4 35343 y?i^i 40563 43'56 43199 49 liO 1673, 19433 t2»'23 24800 17465 JC..8 32758 35386 3S0CI 40607 45 ■6777 '9478 22168 24845 27509 30162 32802 35430 38046 40650 43:42 51 1.3 168:: '9523 222.3 14889 27554 30206 3:846 35474 3808, 406,3 43285 W 15 16S67 ,9568 22257 24934 17598 30250 52890 355.7 38'33 40737 43328 53 30 ,691: 196.5 14978 27642 30:94 32934 3556. 38.76 407S0 43371 .14 45 16957 .9658 21347 25023 27687 30338 52,78 35605 38220 4rS:3 434'4 5S 11 i7f^o: 19703 2239. 15067 2773' 3038: 53021 35648 38263 40866 4345S 5« 15 17047 '9-48 22436 25. .2 27775 30426 33065 35692 38507 40,. 435'^' .".7 .30 1709: '9793 2:48. 15.56! 17M9 30470 53.09 35736 38 3 50 40953 43 544 r.8 45 J 7. 37 19838 225:5125201 2-864 30514' 33'53 35779 38394 40996 43.8. .19 S^.. r 2 3- 4- »• «- r H- 9- 10- ir 1-.' 13- 14- I.-.' ] n 45. IVis 5 6,.: ., .8 z, 14 27 30 51 5^ 39 4- 45 1 n. 13. I'lru 1 6 , 11 14 I- lo 23_26 29 32 3 5 37 4-^^ 43 1 H?,i TABLE 69 LOO. SINE SQUARE 1 72- 73^ 74° 75° 30' 43' 0' 15' 1 30' ; 45' 0' 15' 30' 46' C i. 41' 50' |41'51" 4I. 52" 4h'53'' " 9-5 4'' 54" 41' 55" 4^5«n 41, 57m 4^5jr 4^^^ 5'' 0" 9-5 9*5 rV 95 95 9'5 95 9'5 9-5 9'5 o' 45630 4620S 48775 5>33o 53874 56406 5S916 61435 63933 66419 68S94 15 43673 4625. 4S818 5.373 539.6 56448 58968 6.477 63974 6646c 6S935 1 :(i) 43716 46294 4886, 5.4.5 53958 56490 59010 6.5.9 640,6 66502 •2 ■13 43759I46337 48903 5.458 5400. 56532 59052 6,560 64057 66543 690I8 3 I 43802 1 46380 48946 5.500 54043 56574 59094 6.602 64099 66584 69059 4 l.i 4384? 46423 4S989 5>543 54085 566.6 59.36 6,6+4 64140 66626 69,00 3 :«) 43XS8 46466 49031 5.585 54.27 56658 59177 6 685 64,82 66667 69,4, n 4.) 4393' 46508 49074 5.628 54.70 56700 592.9 6. 27 64223 66708 69,82 7 2 43974 4655, 491.6 5.6-0 542.2 5674-' 59261 6.769 64265 66750 69223 il 13 44017 46594 49.59 5.7.3 54254 567S4 59303 64306 6679. 6926, .•{II 44061 46637 49102 51755 1 54296 56826 59345 61852 64348 66832 69306 10 •13 44104 U^fiiio 49244 5'797 54339 56869 59387 6.894 64389 66874 69347 11 3 44147 1 46723 49287 51S40 543S. 569.1 59429 61935 64431 669.5 693S8 12 13 44.9-1 46766 49330 51882 54423 56953 5947. 6.977 64472 66956 69429 13 :fo 44233 46808 49372 5'5^5 54465 56995 595.2 62019 64514 66998 69470 l4 45 44276146X^1 49415 5.967 54508 57037 59554 62060 64555 67039 695.1 15 i 443 '9 146894 49458 52010 54550 57079 59596 62102 64597 67080 69552 Ifi 13 44362 46937 49500 52052 54592 57.21 59638 62.44 64638 67121 69593 17 .30 44405 46980 49543 52095 54634 57.63 59680 62,86 64680 67,63 69635 111 43 4444S 4449' 47022 49586 52.37 54677 57205 59722 62227 64721 672C4 69676 l.'l 47065 49628 52.79 547.9 57247 59764 62169 64763 67245 697,7 "aiT Id 44534 47.08 4967. 52222 5476. 57289 59806 62311 64804 67287 69758 21 30 44577 47'5i 497 > 3 52264 54803 57J3I 59847 62352 64846 6732S 69799 22 43 44620 47'94 49756 52307 54846 57373 59889 62394 64887 67369 69840 23 6 .1 44663 47^37 49799 52349 154888 57415 5993. 62435 64929 674,0 6988, 24 13 44706 47279 4984. 5239' 54930 57457 59973 62477 64970 67452 69922 26 :to 44749 47322 49884 52434 54972 57499 6001 5 625.9 6,011 67493 69963 26 43 4479- 47565 49926 52476 550.4 5754. 6C056 62560 65053 67534 70c 04 27 7 44835 47408 49969 52519 55057 57583 60098 62602 65094 67576 70045 2» 15 448-8 1 474,, 500.2 52561 55099 57625 60.40 62644 65.36 676,7 70087 2!l ao 44921 47493 50054 52603 55.41 57667 60182 62685 65.77 67658 70128 30 43 44964 47536 50097 52646 551S3 57709 60224, 62727 652.9 67699 70,69 31 8 45007 47579 50139 52688 55225 5775' 60266 1 62769 65260 6774. 32 13 45050 47622 5C1K2 5273. 5526H 57793 60307 628,0 65302 677S2 7025, .■(3 ■M 45093 47664 50224 52773 553.0 57835 60349 62852 65343 67823 70292 34 45 45135 47707 50267 528.5 55352 57877 60391 62893 65384 67S64 70333 35 9 45.78 47750 503.0 52858 55394 579.9 60433 62935 6,426 67905 70374 3(i 13 45221 47793 50352 52900 55436 5796. 60475 62977 6,467 67947 70415 3/ 30 45264 47835 50395 52942 55479 58003 605.6 630.8 6,509 679S8 70456 3K 43 45307 47878 50437 52985 5552. 58045 605,8 63060 63,0, 3^550 68029 70497 3a To (1 45350 I47921 50480 53027 55563 58087 606C0 65592 68070 70538 40 15 45393 47964 50522 53070 55605 58.29 60642 63143 65633 68,12 70579 41 30 45436 48006 50565 53. .2 55647 58,7. 60684 63185 65674 68,53 42 43 45479 48049 50608 53.54 55689 5S2.3 60725 63226 657.6 68,54 7c66° 43 11 45 5^^ 4S092 50650 53.97 55732 58255 60767 63268 65757 68235 70702 44 13 45565 48.35 50693 53239 55774 58297 60809 63309 65799 68277 70743 43 30 4560S 48177 50735 5328. 558.6 58339 6085, 63351 65840 683,8 70784 40 43 45651 48220 50778 53324 55858 5838' 60892 63393 65881 68359 70S25 47 1-2 45694 48263 50820 53366 559CO 58423 60934 63434 65923 684CO 70866 4fl 15 45737 48305 50863 53408 55942 58465 60976 63476 65964 6844, 7CS07 49 "5(1 30 45779 48348 50905 5345. 55984 58507 6.018 635.7 66005 684S2 70948 43 45822 48391 5094S 53493 56027 58549 61059 63559 66047 68 5 24 70989 31 13 45865 48434 50990 53535 56069 5859. 61 .0. 63600 66cS8 68565 7.030 52 13 45908 48476 5.033 535-8 56... 58633 61.43 63642 66,30 68606 33 30 4595' 485.9 5.075 53620 56.53 5S675 611S, 6;b83 66,71 68647 7, ,,2 34 43 45994 48,62 5.1.8 53661 56195 587.. 61226 63725 662.2 68688 71153 33 14 n 46037 48604 5.. 60 53704 56237 58758 6.268 63767 66254 68730 7,194 5fi 15 46080 [48647 5.203 53747 56279 58800 613.0 63.s'o8 6629, 6877. 71235 37 30 46123 48690 5.245 53789 56321 5S842 6.352 63850 66336 688.2 7.276 3Ji 46 46166 I48752 5. 288 53S3.I 56363 58884! 61393 6389. 6637S 68S53I 7.3.7 59 .Ser. r'-2' 3 4 3' (i- 7" »' !•' 10" H' 12' 13' U' 13' 1 D. 43. I';,.!.-. -5 6 <) ,2 14 1- 2o 15 i6 29 ~,2 -,5 ',7 ^o 45 1 TABI.K 6!) too. SINE squakl: j 75° 76^ -,-- 77° 15' 1 30' ft"!-' I,*' 2"' •«.V SI'S"- o-_ 15' 30' 45' 15' 30' •J.V o" 1 1" fl" 4'" r,<' 5- 5" B'" fii, 7,,, .ii' 0'" .i^O"- 51. 10". 9-S l9-S 95 9-5 95 9"5 95 rl 9-5 95 ]9'5 tl II 7i;>i> 73811 76253 78684 81 104 835'3 85911 88299 90676 95042195398 1.1 " ' i99 73852 76294 78724 81144 83553 85,5. 88339 907.6 93082 95437 1 »ll -14.40 73893 76334 78765 81185 83593 8599. 88379 90755 93.21 95477 ■J 4.1 -14S1 73933 1 76375 78805 81225 83633 86031 S8+,8 90795 93.61 95516 3 1 (I!-is;j: 759741 764>5 78846 8.265 83673 8607, 88+58 90834 93200 95555 4 -iS^! j-4<"5 76456 7S8S6 81305 837.3 86111 88+98 90874 93239 9 5594 .■. : 71727 |74'78| 76618 79048 81466 83874 86270 88656 9.032 93397 95751 9 Ml 7176SI 74219 76659 79088 81506 839.4 863.0 88696 9107. I93436 95790 T 4". 71809 7+260 76700 79128 8.5+6 83954 86350 88736 9.1.1 93475 95829 1 1 3 1) 71850 7+300 767+0 79-69 815S- 83994 86390 88775 91.50 93 5 '4 9586S 12 l.i 71891 7434' 76781 79209 81627 84034 86430 88815 i9"90 93 5 54 95907 13 30 71932 74382 7681. 79250 81667 8+074 86470 88855 91229 93593 95946 14 45 71973 74423 {76862 79290 8.707 841,4 86,09 88894 91269 93632 95986 l.i 4 72013 74463176902 79330 81747 84154 86549 88934 91308 93672 96025 Hi 15 7205+ 7+50+76943 79371 81788 84.94 86589 88974 91348 93711 96064 17 80 72095 74545 76983 794" 81828 84234 86629 89013 93750 96,03 U< 4o 72136! 74586 77024 79451 1 81868 IS427+ S6669 89053 1 91427 93790 96.42 96,8, 19 20 .■ 72177 1746261 77065 79492181908 843.4 (86709 89093 9.466 93829 16 722I« 174667 177205 79532 819+8 843541867+8 89132 9.506 93868 96220 21 ;«» 72*59 7+708 77146 79573 8.989 8+39+ 8678S 89,72 9 '545 93907 962,9 22 4.-> -2300 74748 77186 79613 82029 8+434 86828 89212 9.584 93947 96299 23 « 723+1 74789! 77227 79653 82069 8447+ 86868 89251 91624 93986 96338 24 l.i -2382 74830 77267 79694 82109 845.+ 1 86908 8929, 9.663 94025 96377 2.i 3I» 72423 74871 77308 79734 82,49 X+ 5 5+186947 89330 9.703 94065 964,6 2(1 4.1 72+63 174911 77348 79774 82.89 84594 S6987 89370 9.7+2 94104 96455 27 7 72504174952 798.5 82230 8+63+187027 S94.0 9.782 94143 1 96494 2K ■ •1 725+5 1 7+993 77429 79855 82270 84674 87067 89449 9.821 94.82196533 2ri W :«> 72586 1 75033 77470 79895 82310 84714 87107 89489! 9.86. 94222 96,72 in 7262717507+ 77510 79936 82350 84754 87.46 89529 1 91900 9426. ,966., 31 8 72668 75>'5! 7755' 79976 82390 84794 S7186 89568 9.939 94300 966,0 32 l.i 72709 75'56! 7759' 80016 82430 8+834 87226 89608 9.979 94339 '96689 33 30 72750 75'96 77632 80057 82470 8487+ 87266 89647 92018 94379 96729 34 4,i 72791 75237, 77672 80097 825.1 84913 87306 896S7 92058 94418,96768 :(.-. » 72831 75278 '77713 80137 8255. 8+953 87345 89727 1 92097 94457 96S0- 3« 1.5 72872 75318 1 77754 80178! 82591 84993 87385 89766192.37 94496 968+6 37 30 72913 75359 1 77794 802.8 1 82631 85033 87425 89806 92.76 94536 96885 3^ 4.-. -295+1 75400 1 77834 80258 1 82671 85073 87465 89845 1 922.51 94575 1 96924 3'l 10 72995 175440 ,77875 80298 ^2711 85113 87504 89885192255 94614 96963 -^ l,i 73036 {75481 779'5 80339 82751 85-53 87544 89925 1 92294 94653 97002 41 :«) 75076' 75522 77956 80379 82791 85,93 87584 89964 92354 94693 9704, 42 4.'i -3II7. 75562 77996 S04.9 82832 85233 87624 90C04 192373 94732 97080 43 II 73158] 75603 78037 80460 82872 85273 X7663 9C0+3 924.2 94771 97.19 44 l.i 73199 75644 78077 80500 82912 85313 87703 9C0S3 92452 94810 97158 4.i 30 73240 75684 78.18 80540 82952 85353 87743 90.22 92491 94850 97'97 4*> i^ 73»8. 75725 78.58 80581 82992 85393 87783 90.62 92531 94889 97236 47 \i 73321 75766 78199 8062. 85433 87822 90202 92570 94928 97275 4H l.i "lo 73362 75806 7829 8066. 83072 85473 87862 902+1 9260919+96719-^31 + 4!) 73403 758+7 78279 8070. 83777 S5513 87902 9028. 92649 95006 973,3 4» 73444 75887 78320 S0742 85552 87942 90320 92688 95046 97392 f,\ IS -3485 7 59=8 78360 807S2 85592 8798. 90360 92728 9,085 97432 .■■.2 l.i 73526 75969 78401 80822 85652 S802. 90399 92-6- 95124 97471 .i3 :».) 73566 76009 -8441 80862 S5672 8S06, 90+39 ,2806 95163 97,10 .i4 4.1 -3607 76050 78482 80903 85712 88. 0. 90478 9:8+6 95202 97549 hf. 14 73648 7609, 7S522 8c 94 3 85:'52 881 + 905.8 92S85 9,242 9-5R8 .i« l.i 73689 76131 78563 809S3 85-92 S81S0 905^8 9292+ 95281 9-627 •i7 30 73730 76172 786c, 81023 85832 88220 90597 9296+ 9,320 9-666 .iH 4» 73770 76212 78644 8,064 83+73 1 858-2 88259 90637,93003 953';9-9-705 .'>0 ^< ... V 'J 3' 4' .V r. r H- '• 10 II Iv 13' II I.'>' I>. 41. I'..rt, 5 5 !! II 14 i6 I', :: 24 17 r^ r, ;S l" 4' 1 I> 3». I'.iri, 5 ; 8 10 IS IS iS ;i :i 26 J9 >" 11 1* 39 1 H56 TABLE 69 l-OG. SINi; SQUARE j 78 °' 79° 80° n. 0' J15'_ 30' 45' 0' 15' 30' 45' 5'' 19'" 0' 15' 30' 5'' 22'" 51, Ivm fti' 13"- 5M4™ 5'' 15"' jh |g,„ 5I' 17"' 5I' ■20'" 51,91". 9' 9-6 96 9-6 9-6 96 9-6 96 76~ 9-6 -6— 597744 C0078 02403 04717 09315 1,598 1387^ 16135 18388 20632 l.i 597783 00117 02442 04756 07059 09353 ,,636 13909 16173 .8426 20669 1 30 597822 00156 02480 04794 07098 09391 11674 13947 16210 .S463 120706 2 45 59786. 00.95 02519 04833 07136 09429 , ,7,2 13985 .6248 .850. 20744 3 1 597900 00234 02558 0487, 07174 09467 11750 14023 .6285 .8538 207S. 4 15 597939 [C0273 02596 04910 07213 09505 1406, 16323 .8576 208.8 5 30 597978 1 003 1 1 02635 04948 07251 09544 1,826 14098 ,636, .86,3 20855 e 45 02674 04986 07289 09582 11864 14136 .6398 .865. 20S93 7 2 U 598056 00389 05025 07327 09620 11902 14174 .6436 .8688 20930 H 15 598095 0042S 02751 07366 09658 11940 14212 16474 18725 ^9_^ 21C05 "lo 30 59S133I 00467 027S.; 05,02 07404 09696 11978 14250 .65,. 18763 45 59Si72[ 00505 02S28 05140 07442 09734 12016 14287 16549 18800 21C42 11 3 59S211 100544 02867 05,79 0748, 09772 lie 54 14325 .6586 18838 21079 12 15 598250^00583 02905 052,7 075,9 098.0 12092 14363 .6624 18875 21116 13 :m 598289 00622 02944 05256 07557 09848 .2.30 14401 .6662 18913I21154 14 45 598328! 00661 02982 05294 07595 09886 .2.68 14438 ,6699 18950121,9, 15 4 598367100699 0533^ 07634 09925 .2205 14476 ,6737 18987 2122S Hi 15 598406 C0738 03060 05371 07672 09963 12243 14514 16774 ,9025! 2.266 17 30 598445 00777 03098 05409 077,0 12281 14552 16812 .906212.303 IK 45 598484 |co8 16 03,37 05448 07748 .0039 12319 14589 16850 19.00 21340 2,377 10 20 5 598523100854 03175 05486 07787 10077 1^357 14627 16887 19137 15 598562 00893 03214 055-5 07825 10. .5 12395 ,4665 16925 19175 2,415 21 :v) 59S601J 00932 03253 05563 07863 10153 1^433 14703 ,6962 ,92,2 21452 22 45 598640 00971 0329, 0560. 0790, 10,91 12471 14740 1 7000 19249 2,489 23 6 598679 1 01009 03330 05640 07940 10x29 12509 14778 17037 192S7 2,526 24 15 598718:01048 03368 05678 07978 ,0267 .25471.4816 17075 19324 2.564 25 3(1 59S757 01087 03407 05717 080,6 10305 12585 14854 17113 19362 21601 20 4o 598796 01126 03446 05755 08054 10343 12622 14891 17150 19399 2,638 27 7 598834 01164 03484 05794 08093 1038. 12660 14929 17188 19436 2.675 2H 15 598873 1 01203 °35^3 05832 08131 10420 12698 .4967 17225 .9474I 217,2 20 30 598912 01242 0356, 05870 08169 1 '0458 12736 15005 17263 19511 [21749 30' 45 598951 I01281 03600 05909 08207 10496 12774 15042 17300 19549 21787 31 8 598990] 01319 03638 05947 08246 10534 12812 150S0 17338 195S6 2,824 32 15 599029 01358 03677 05986 08284 10572 12850 .5.18 17376 ,962312,86, 33 3!l 599068 1 01397 037.6 06024 08322 10610 128S8 15155 17413 ,966, 21899 34 45 599107 [01436 03754 06062 08360 10648 12926 15193 17451 19698 2.936 35 9 599146 01474 °3793 06101 08398 106S6 12963 15231 1748S 19736 2.973 30 15 599i85'oi5i3 03831 06,39 08437 10724 13001 15269 17526 19773 37 30 599224 [01552 03870 06,77 08475 10762 13039 15306 17563 22047 3)1 45 599262 01591 03908 062,6 085,3 .o8co ,3077 15344 1760. 19848 22085 30 10 2fi^" 51, 27... 51, .2am 5''2!)'"l5i'.30™ .'i^Sl'" 51^^32™ 5'' XV" 9-6 9-6 9-6 9.6 9-6 9-6 9-6 9-6 76~ 9-6 9-6 o' o' 2lS6, 25089 = 7303 29507 31701 33886 3606, 38226 403S3 42529 44666 lA 22902 25.26 = 7339 =9543 3>738 33922 36097 38263 40418 42565 44702 1 »» 22939 25.63 27376 29580 31774 11958 36133 38299 40454 4260. 4473- '.! 45 »^977 25200 =74- 3 29617 3.8.. 31995 36,69 38115 40490 42636 J44773 1 1 25014 ^5^37 27450 29653 3.847 14031 36206 38371 405:6 42672 J448"8 4 15 23051 25274 27487 29690 3.884 34067 36242 38407 40562 42708 44844 3 : 43 24015 26234 28443 30642 32831 35011 37.8. 3914= 41495 43635 45-67 31 A 1) 24052 2627. 28479 30678 3=867 35047 37=17 39378 41529 43670 45802 32 13 240X9 26308 28516 30715 3=904 35083 37253 394.4 41564 43706 45818 3.3 311 24.26 26345 = 8553 30751 32940 35120 37289 39449 41600 41741 45S7I 34 43 24.64 2638. 28590 30788 3=977 35156 37325 39485 4,636 43777 459'^9 33 11 2420. 264.8 286.6 30824 33013 35.92 37361 39521 41672 438.3 45944 :«( 13 24238 26455 28663 3086, 33049 35228 37397 39557 4,707 43848 45980 37 30 24275 26492 28700 30898 33086 35=65 37434 39591 4.741 43884 460.5 31) 4'i 243.2 26520 28736 10934 33.22 351oi| 17470 39629 4.779 439.9,46050 3!l fo H149 26566 28773 1 30971 31159 35337 37506 •^5 4.8,5 43955 4"67S^ 4ir 13 243S6 26603 288.0 31007 11>95 35373 3754= 39701 4,850 4399. 46.2. 41 30 24421 26639 28845 31044 11=31 35409 17578 39737 4.886 44026 46157 42 43 24460 26676 28883 31080 33268 35446 376.4 19771 4.922 44062 46.92 43 11 '4497 *67.3 28920 31. .7 33304 3548= 37650 3980S 4.958 44097 46228 41 13 -4'; 14 26750 28957 31153 33341 35518 37686 39844 41993 44.33 4626, 43 30 »4';7" 26787 28993 31.90 33377 35554 377« = 39880 42029 44.69 46298 tli 43 2,6c8 26824 29030 3.226 33413 35590 37758 399.6 42065 44=04 46334 47 l_' 2464, 26861 29067 3.263 33450 356=7 17794 3995 = 4210. 44'4o| 46369 4H 13 24682 26898 29.03 3.300 33486 35663 37830 39988 42136 44275 1464^5 4!) W 2+7>9 26934 19140 3.336 335== 15699 17866 40C14 42.72 44311 1 46440 ts 24756 2697. =9'77 31373 31559 15735 37902 40060 422c 8 44146 464-6 A! n 24-91 27008 29213 3.409 13595 15771 17938 400,6 42243 44-82 465.. »2 13 24830 27045 29250 3.446 13631 35808 17974 40131 42279 444.7 465.16 5S .to 24867 27082 29287 3.4S2 33668 15844 380.0 40167 4=1' 5 44453146582 114 43 2 49r.4 27l>9 29323 31519 13704 35S80 38046140203 4 = 15. 44489146617 63 14 24941 27155 =936013.555 33740 35916 3808214^239 423S6 44524 46651 .3(i 13 24978 2719= =919-'|3>59= 33777 3595= 38..8UC275 4=422 ^4560 46688 57 .10 250.5 27229 29433 13.628 33813 35988 3815414^311 4245S 44591 46-21 511 43 '\^V- 2-7266 29470 '1.665 11840 36025! 38190140347 42491 4463. 46-'S9 .3!! -_^--^ _^^^. __-_--_. _^„__^^ IJ- |3~ li' 13' 1 1) :i7. IVir.s I s 7 lo i; i; 1- :- :i z^ zj z<) v- 14 17 1 l» .1.. I'i.iiH : i; - >= '4 i'' 'T J" • -, ;'■' -K r 11 V, 1 85R TABLE » 9 c LOG. 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'843 23634 254.8 27.93 2896, 3072, 24 15 ,2799 14630 .6453 18267 20074 2.873 23664 25447 27223 30751 25 M 12830 14660 16483 'I'n 20104 2.903 23694 25477 27252 29020 30780 26 45 7 » 12860 1 469 1 165.3 "f'i 20134 2.933 23724 25507 27282 29049 30809 27 12891 '472. 16544 "o"! 20,6+ 2,963 23753 25536 273" 29079 30838 28 15 12922 '4752 16574 .8388 20194 21993 23783 25566 27341 29.08 30868 2!) 30 12952 14782 .6604 .84.8 20224 22023 238.3 25596 ^27370 29137 30897 W 45 129S3 14813 .6634 18448 20254 22052 23843 25625 27400 29167 309?6 31 8 13013 14843 16665 .8479 20284 22082 23872 25655 27429 2^9^ 30955 32 15 30 13044 14873 16695 .8509 203.4 22.12 23902 25685 27459 29226 30985 33 13074 14904 'i'^l .S539 20344 22142 23932 257'4 27488 29255 3.0,4 34 45 .3.05 '4934 16756 .8569 20374 22172 23962 25744 275.8 29284 3,043 35 9 15 13136 13166 .4965 16786 'IP^ 20405 23992 25773 27547 29314 3fi ■4995 16816 18629 20435 22232 24021 25803 27577 29343 3,, 02 37 30 45 '1'97 15026 .6846 .8659 20465 22262 24051 25833 27606 29373 3, ,3, 38 13227 1,-056 16877 18690 20495 22292 2408 j_ 25862 27636 29402 3.. 60 39 40 10 1325X 13288 150S6 .6907 18720 20525 22322 241.1 25892 27665 2943. 31189 15 15117 .6937 .8750 20555 2235. 24140 25922 27695 29461 312,9 41 .'to 13319 '5 '47 16967 .8780 20585 2238. 24170 25951 27724 29490 31248 42 45 II '3349 15.78 ,6998 .88.0 206.5 22411 24200 2598. 27754 295.9 3'277 43 13380 15208 ■ 7028 .8840 20645 2244. 24230 26010 27783 29549 3,306 44 3(1 45 13411 .523S .7058 18870 20675 22471 24259 26040. 27813 29578 31335 45 13441 15269 17089 .8901! 20705 22501 24289 26070 27842 1 29607 31365 4G '3472 .5299 11719 .8931 20735 22531 24319 26099 27872 29637 3 '394 47 12 13502 .5330 17149 18961 20765 22560 24349 26.29' 2790, 29666 3.423 4« '3533 15360 17179 .8991 20795 22590 24378 26,58 2793' 29695 3'452 49 30 45 .» I.I '3563 .5390 .7210 .902. 22620 1 24408 26,88 27960 29725 31482 lo- •3594 13624 ■5^55 '542' .7240 1905. 20855 22650 24438 1 262.8 27990 29754 3'5" st ',1*1' .7270 .9081 20885 22680 24468 26247 280J9 29783 3.540 A2 .5481 17300 19111 209.5 22710 24497 26:71 28049 29813 3.569 53 30 13055 45 15716 .55.2 '733' 19141 20945 22740 24527 26306 28078 29842 31598 54 15542 .736. 19172 20975 22769 24557 26336 28.08 29871 3.628 55 It 13746 '5573 '739' .9202 21004 22799 24586 26366 28,37 29901 1 31657 5(i .5603 1 7421 19232 21034 22X29 24616 26395 28,66 29930 3.686 57 30 n8c7 •5633 '7452 19262 21064 22859 24646 26425 28,96 29959 3'7'5 5(1 45 -FJll 15664 .7482 19292 2.C94I22889 24676 26454 28225 20989 31744 59 Src. 1- 2- 3- 4' 5' «' V If :«.. I'an, 2 4 6 X .c ,1 ,4 ,6 ,8 20 22 24 26 28 30 | 8<;2 TABLE 69 LOO. SINE SQUABK 94° 95^ 96° 97° _i- 30' 45' 0' 1 15' 30' 45' 0' 15' :w' 45' 0' ,;!, ,8". fihjgm ,jh2(|."lf,l<21"' if'-li"' fih .23n, if' 24'" (jh 25". CI. 2«nT Ch 27.., fih 2i|i. ~, ", 9-7 '9-7 9-7 |9-7 19-7 9-7 9-7 l9-7 9-7 97 9-7 u (i 3 '774 3352" 35162 36994 387,9 40437 42,47 43849 45544 47232 489,2 Id -,.So3 3355' 35291 37023 38748 40465 42175 43878 45573 47260 48940 1 30 3,83z 33580 35320 37051 38777 40494 411C4 43906 4560, 472SS 4896S 2 •(.> 3.X6. 33609 35349 37081 38805 40523 42232 43934 45629 473'6 48996 3 1 1) 31890 33638 3537- 37110 38S34 4055, 43161 1 43963 45657 47 344 49024 4 l,i 31920 33667 35406 1 37138 38863 40580 42289 [43991 45685 47372 49052 5 :<(* 3 '949 33696 35435 37,67 38892 40608 42317 440,9 457'3 47400 49080 C 40 31978 33725 35464 37,96 38920 40637 42346 44048 45742 47428 4910S 7 2 31007 3 3754 35493 37225 38949 40665 42374 44076 45770 47456 49,36 8 l.i 32036 337X3 35522 37254 38978 40694 40722 42453 4243, 44104 45798 47485 49164 -To- :t() 32066 33812 3555> 37282 39C06 44,32" 45826 475'3 49,92 4,-> 32095 33S4. 35580 373" 39035 4075, 42460 44'6, 45854 4754' 49219 ll 3 32124 33S70 35609 37340 39063 40780 42488 44,89 45883 47569 49247 12 1.-. 3-'53 33899 35638 37369 39092 40808 425,6 44217 459" 47597 49275 13 :w 32,82 33928 35667 37397 3912, 40837 42545 44246 45939 47615 49303 14 43 32211 33957 35696 37426 39'49 4086; 42573 44274 45967 47653 49331 15 4 32241 33986 35724 37455 39,78 40894 42601 44302 45995 4768, 49359 l(i 15 32270 34015 35753 374S4 39207 40922 42630 44330 46023 47709 49387 17 .•to 32299 34044 357ii2 375'3 39235 4095, 42658 443 59 46051 47737 494.5 18 45 32328 34073 35811 37541 39264 39293 4C979 42687 427.5 44387 46080 47765 49443 lu 20 o 3^357 34102 35840 37570 4,008 444.5 46,08 47793 4947' 15 32386 34'3i 35869 37599 39321 4,036 42744 44443 46,36 47821 49499 21 30 3M'5 34160 35898 37628 39350 4,065 42772 44472 46,64 47S49 49526 22 45 3^445 34189 35927 3-656 39379 4,093 42800 44500 46,92 47877 49554 23 U 3H74 34118 35956 37685 39407 4>,22 42829 44528 46220 47905 49582 24 15 3^503 34148 359S5 37714 39436 4"5o 42857 44557 46249 47933 496,0 25 30 32531 34277 360.3 37743 39465 4,179 42885 44585 46277 47961 49638 20 45 3256. 34306 36041 37772 39493 4,107 419,4 44613 46305 47989 49666 27 7 32590 34335 36071 37800 39522 4.236 42942 4464, 46333 480,7 49694 28 15 32619 34364 36,00 37829 3955' 4,264 4197, 44670 4636, 48045 49722 2!l :»o 32649 34394 36,29 37858 39579 4,293 42999 44698 46389 '48073 49750 30 45 32678 34422 36,5s 37887 39608 43027 44726 46417 48,0, 49778 31 H 32707 3445" 36,87 379-5 39636 4,350 43056 44754 46445 48,29 49805 32 15 32736 34479 362,6 37944 39665 4,378 43084 44783 46473 48.57 49833 33 30 32765 34509 36244 37973 39694 4,407 43, ,2 448" 46502 48,85 49861 34 45 32794 34537 36273 38002 39722 4'435 43,4, 44839 46530 482.3 49889 35 9 32S23 34567 36301 38030 3975' 4,46+ 43,69 44867 46558 4S14, 49917 ■m; 15 32852 34590 36331 38059 39779 4'-492 43198 44896 46586 48269 49945 37 30 32882 34625 36360 38088 39808 4,51. 43126 44924 466,+ 48297 49973 38 45 io 329U 34654 36389 38.. 7 39837 39865 4' 549 4,578 43254 43283" 44952 46642 48325 50000 5002S 39 40 52940 346S2 364,8 38,45 44980 46670 48353 15 32969 347 '• 36447 38.74 39894 41606 433" 45009 46698 4838, 50056 41 30 32998 34740 36475 38203 39911 4,635 43339 45037 46727 48409 50084 42 45 33017 34769 36504 38231 3995' 4.663 43368 45065 46755 48437 50,11 43 II 33056 34798 36533 38260 399«o 4,691 43396 45093 46783 48465 50,40 44 15 33085 34827 36562 38189 40008 4,720 43424 45'2i 468,, 48493 50,68 45 30 33"4 34856 3659, 383,8 40037 4 '749 43453 45150 46839 4852. 50,95 46 45 33'43 34885 36620 38346 40065 4'777 434S. 45.78 46867 48549 50223 47 12 33-73 349'4 366+8 38375 40094 4,805 43509 45206 46895 48577 5015, 48 15 30 33202 34943 34972 36677 38404 ^.13_ 40,5, 4.834 43538 45 = 34 46923 4S605 50279 49 3323' 36706 38432 4.861 43566 45262 4695, 48633 50307 50 45 33160 35001 36735 3846, 40180 4.89' 43594 4519, 46979 4866, 50335 51 13 33289 35030 36764 38490 401^^8 419,9 43623 453'9 47007 48689 50362 52 15 333>8 35°59 36793 385.9 40237 41948 4365. 45347 47036 487.7 50390 53 30 33347 3S°88 36S2. 38547 40266 41976 43679 45375 47064 48745 50418 54 45 33376 35"7 36850 38576 40294 42005 43708 45403 47093 48773 50446 55 14 33405 35M6 36S79 38605 40323 42033 43736 45432 47,20 48800 50474 50 15 33434' 35'75 36908 38633 4035, 41062 43764 45460 47.48 48828 50502 57 30 33463 I 35204 36937 38661 40380 41090 43793 45488 47,76 4S856 50529 5H 45 33492! 35233 36966 3869, 404081411,8 4382,1455,6 47204 48884 50557 59 Sec. r 2' 3' 4' 6' V V 8' 0" 10" 11 12" 13' 14' 13' | r». 2 «. P». ts 1 . 6 7 9 ' '3 '5 '7 ,9 10 11 2t 26 » 8 1 r.Ani.K 69 Rirt l.oa. SINK sgUARE 97-^ 1 98^ 1 99= ^ 15^ 80' 1 45' 15' 1 30' 45' 0' 15' SO' 45 i^ 6b3on,!ci.3l"' (;h :<.>„, vy 33"^ rfi 34'" tji< 35"' «!> 36'" ,;l, ;,7,., 6'" -AW" 6X 3!)"- '~ ' 97 9-7 9-7 9'7 9-7 9"7 9-7 97 9'7 9 7 1 50585 52251 53909 55560 57*03 5S840 60469 62091 63706 65314 669,4 lA 5C.613I ,22-8 53936 55587 57*3' 58867 60496 62118 63733 65340 6694, 1 3t» 50641 j 513061 5396+ 556.5 57*58 58894 60523 62145 63760 65367 6696S 2 45 50669 5Z534 5399' 55642 57*85 58921 60550 62172 63786! 65,94 66994 1 3 1 50696 52361 54019 55670 573'3 58949 60577 62,99 63813 65421 6-.2, 4 la 50724 52389 5+047 55697 57340 58976 60604 62226 63840 65+4716704- 6 •JO 5°75=' 5J4'7 5+07+ 557*+ 57367 59003 6063. 6**53 6386- 65+7+ 67C7+ « 4.-. 50780 5*444 54102 5575* 57395 59030 6065, 62280 63894 6550. 67101 7 ■> 50808 5H7* 54.29 55779 574** 59057 60686 62307 63921 655*7 6-127 8 \b 5CS35 50863 C25C0I 5+>57 55807 57449, 59085 6071, 623,4 63948 65554 671 H U ' 'm 5*5*71 54.84 55834 57477 59.12 60740 62361 6397+ 65581 67180 10 ih 5089. 5*555 54212 55862 57504 59'39 60767 62388 64001 6560S 67207 II 3 50919 5*585 54240 55889 5753' 59166 60794 62415 64028 65634 67*3+ \l l.~> 509+7 52611 5+*67 559.6 57558 59'93 60821 6244* 6+055 65661 67260 13 30 5°9:4 526,8 5+*95 5 5944 575X6 59221 60848 62468 64082 65688 67287 14 45 51C02 52666 5+3** 5597. 576'3 59*48 60875 62495 64108 65714 673'; 15 1 51030 52694 5+350 55999 576+0 59*75 60902 62522 6413, 65741 6:340 11; 15 51058 52721 5+377 56026 57668 59302 60929 62549 64162 65768 67367 17 30 S1085 5*749 5++05 56054 57695 593*9 60956 62576 64.89 65-95 67393 18 45 "FIT 51113 527-6 5+43* 560S1 "767^8" 577** 59356 60983 62603 642,6 6,821 67420 10 20 ' 51141 52804 54+60 57750 593S4 61010 62630 64243 65X4S j 67446 J 5 5.169 52832 5+487 56136 57777 594" 610,8 62657 64269 65875 674-3 21 .Ml 5"97 52859 5+5 "5 56163 57S04 59+38 61065 62684 64296 6590. 67+99 22 45 51124 5*887 5+5+3 56.9. 5783' 59+65 6.092 6271. 643*3 65928 67526 23 8 51252 5*9'5 5+570 562.8 57859 59+9* 611,9 62738 64350 65955 67553 24 15 51280 52942 5+598 56245 57886 595.9 6,, 46 62765 64377 6598. 67579 25 ;)0 5.308 52970 5+6*5 56*73 579'3 595+7 6.173 6279* 64403 66008 67606 2t) 45 5' 535 52998 54653 56300 5794' 595741 6.200 628.9 64430 66035 676,2 2; 7 5«363 53025 54680 56328 57968 5960,161227 62845 6«57 66061 67659 21) 15 30 5'39' 53°53 54708 56355 57995 5962816.254 62872 644X4 66c88 67685 20 51419 53081 547 3 5 56382 58022 59655I61281 62899 645" 661.5 677.2 •M 45 5>447 53108 5+763 56410 58050 59682,61308 62926 6+537 66141 67739 31 H 5 ■4.7+ 53-36 5+790 56+37 58077 59710I6.335 62953 64564 66168 67765 32 15 51502 53.64 548.8 56465 58.04 59737 61362 629X0 64591 66195 6779* 33 :«i 5'53° 53>9" 5+8+5 5649* 58131 59764 61389 63007 64618 66221 67818 34 45 5M58 53*'9 5+873 565,9 58159 5979' 6:4,6 63034 64645 66248 67845 35 9 5'585 53246 5+900 5654- 58186 5981 8 6,443 6306, 64671 66275 67871 3fi 15 51613 53*74 549*8 565:'4 58213 598+5 61470 63088 64698 66302 67898 :«7 31 » 51641 5330* 5+955 56602 58*41 59872 6.497 631,5 647*5 66328 67924 3H 45 51669 533*9 54983 56629 58268 59900 6.524 63,4. 64752 66355 6795, 30 To 5,696 53357 550.0 566561 58295,59927 6155. 631681 64778(66382 67977 ~4(» 1? 5'7H 53385 55038 56684 583** 5995+ 6.578 63195 64805 ' 66408 68004 41 :fo 5'75i 534'* 55065 567.1 58350 5998' 61605 63222 64832,66435 680,1 42 45 5'779 53440 55093 56738 58377 6cooX 61632 63249 64859 66462 68057 43 II 51807 53+67 55.20 56766 58404 60035161659 63276 64886 66488 68084 44 15 5"835 53+95 55.48 56793 5843. 60062161686 63303 6+912 665.5 68110 45 :to 5.863 535*3 55'75 56820 58459 6C089I617.3 63330 64939 6654. 68.37 4ti 45 51890 5355° 55*03 56848 58486 601.7 63357 64966 66568 68163 47 12 51918 53578 55*30 56875 585'3 60.44 6;'67 63384 64993 66595 68190 40 15 ii946_ ^05 55*58 56903 5S540 60171 6.794 63410165019 6662. 682,6 40 :to 5 '974 53633 55*85 56930 5856S "6^7^ 6182! 63437 650+6 66648 68243 6f> 45 52C01 53661 553'* 56957 58595 60225 61848 63464 65073 66675 68169 51 .J 52029 53688 553+0 56985 58622 60252 6.875 63491 65100 6670. 68206 62 15 52057 53716 55367 570.2 58649 60279 6.902 635.8 65126 66728 683^2 53 30 1,1084 537+3 55395 57039 58676 60306 6.929 635+5 65.53 66755 68349 t4 4A 5»1F2 5377' 554** 57067 58704 603,3 61956 6357* 65180 6678, 68375 54 14 II 52140 53799 55450 57094 5873' 60,6. 61983 63598 65*07 6W08 68402 5« 15 52.67 53826 55477 57.2. 58758 60388 62010 63625 65*33 66834 68428 57 30 5»'95 53854 155505 57 '49 58785 60415 6*037 63652 65260 66861 68455 •''" 45 52223 53881 I5553* 57.76 588.3 60442 1 62064 63679 65*87 66888 68481 i» S«-. r 2' 3' A' V 6' r H- !)• 10' 11' \1' V.V 14' IS' D.n. I'.fi- z 4 5 7 9 11 1^ .4 P* i8 JO 2J »3 13 j; 8fi4 TARI.E 69 LOO. siNi; hiCiUAKi: ] 100° 101° 102= 0' IS' 30' 1 45' 0' 15' 1 30' 45' _0^|_15' 30' «'■ 40" CMl" 6'' 42'" 1 61- 43" (>i' 44" (i''45"'Ui'46"' (}<■ 47" «'• 48"' «!' 4,1" C^oO" 9'7 9-7 9-7 l9-7 9-7 97 97 97 9 7 97 9'7 (t 6S508 70094 7.674 73246 748.2 7637, 77922 79467 8.005 82536 8406. IS 68534 70,21 71700 73273 74838 76397 7794S 79+93 8,03, 82562 S4086 ;{ii 68,61 7<:J47 71726 73299 74864 76423 77974 795.9 8,056 82587 84... 4.'i 6S587 70174 7.753 73325 74890 76448 78000 79544 8,082 826,3 84.37 1 (1 686.4 70200 7>779 7335" 749.6 76474 7S026 79570 8. ,07 8263S l.'l 6S640 1 70226 71805 73377 74942 76500 78051 79596 8. .33 82664 8^187 .•to 68667 7C253 71S32 73403 74968 1 76526 78077 7962, 8,159 82689 84212 4."i 68693 j 70279 7,858 73430 74994 76552 7S103 79647 81184 827.4 84238 2 6S720|703°5 71884 73456 75020 1 76578 78,29 79673 81210 82740 84263 l.i 68746 7033^ 70358 7,910 73482 75046(76604 78.55 1 79698 8,235 81261 84289 6S773 71936 73508 75072 76630 78180 79724 S^ 843.4 ~i 68905 70490 72068 73639 75202 76759 7S309 79852 81389 82918 8444. 4 II 6S932 705.6 72094 73665 7522S 76785 78335 79878 8,414 82943 84466 15 6895S 70543 72120 7369, 75254 76811 78361 79904 8.440 82969 8449'. 17 1 ;tii 68985 70569 72146 737'7 75280 76837 78387 79929 81465 82994 845.6 18 45 6 (1 6901 1 70595 72173 73743 75306 75332 76863 784.2 79955 8149. 83020 84542 84567 I!) 20 69038 70612 72199 73769 768S9 78438 7998. 81516 83045 15 69064 70648 72225 73795 75358 769.5 78464 8.542 83071 84592 21 :to 69090 70674 7225, 7382, 75384 76940 78490 80032 8.567 83096 84618 22 45 69,17 70701 72278 73847 754.0 76966 785.5 80058 8,593 84643 23 « 69143 70727 72304 73874 75436 76992 7854. 80083 816, » 83.47 8466S 24 15 69,70 70753 72330 73900 75462 770.8 78567 80109 8,644 83.72 S4694 25 IM 69,96 70780 72356 73926 7548S 77044 78593 80,34 8.669 83,98 847.9 21! 45 69223 70806 72382 73952 755.4 77070 786,8 80,60 8,695 83225 S4744 27 7 69149 70832 724C9 73978 75540 77096 78644 80,86 8,72, 83248 84770 28 15 69276 70S59 72435 74004 75566 77.22 78670 802,, 8,746 83274 84795 2!l M) 69301 70SS5 72461 74030 75592 77.47 78696 80237 8.772 83299 84820 30 45 69329 70911 72487 74056 756.8 77.73 7S72, 80263 8.797 83325 84845 31 8 II 69355 70938 725.4 74082 75644 77.99 78747 80288 8,823 83350 8487. 32 15 69381 70964 72540 74.08 75670 77225 78773 803,4 8,848 83375 84896 33 :t(i 69408 70990 72566 74135 75696,7725. 78799 80340 8,874 8340, 84921 34 45 69434 71017 72592 '4.61 75722 77277 78824 1 S0365 8,899 83426 84947 35 !l 69461 71043 72618 74 = 87 75748 77303 78850 80391 8,925 83452 84972 36 15 69487 71069 72645 74213 75774 77328 78S76 80416 8,950 83477 84997 37 :ii) 69514 71096 72671 74239 758ro 77354 78902 SC442 8,976 S3502 85022 38 45 6y£4^ 69566 71 122 72697 74265 75S26 77380 78927 1'0468 82001 8352SI 85048 3U lU 7.148 72723 74291 75852 77400 78953 80493' 82027 83553 85073 40' 15 69595 7.175 72749 743.7 75S78 77432 78979 80519 82052 83519 8 5098 41 :«i 696.9 71201 72775 74343 75904 77458 79005 80544 82078 83604 85.23 42 45 69646 71227 72S02 74369 75930 77483 79030 80570 82,03 83629 85149 43 1 1 II 69672 7.^53 72828 74395 75956 77509 79056 80596 82,29 836,5 85.74 44 !5 69698 7.280 72854 74421 759S2 77535 79082 S0621 82,54 83680 85.99 45 Ml 69725 71306 72880 74447 7600S 7756. 79.07 80647 82180 83705 85224 4(i 45 6975. 7'33- 72906 74473 76034 77587 79.33 80672 82205 8373. 85250 47 |-.> 69778 71359 72933 74500 76060 77613 79'59 8069S 8223. 83756 85275 48 15 30 69804 7.385 69S31 7x4. I 72959 74526 76085 77638 79,84 S0724 S0749 82256 837S2 833C0I 4il 72985 74552 76. .1 77664 792,0 82282 83807 85326 .50 45 6985- 71437 73011 7457S 76.37 77690 79236 80775 82307 S3832 8535' 51 13 69883 71464 73037 74604 76163 777.6 79262 80799 82333 83858 85376 52 15 69910 71490 73063 74630 76,89 77742 79287 80826 82358 83883 S5401 53 30 69936 71516 73090 74656 76215 7776S 793.3 ^152 82384 83908 85427 54 45 69962 71543 73.16 746S2 76241 77793 79339 80S77 82409 83934 85452 55 U 69989 7.569 73.42 74708 76267 778.9 79364 S0903 82434 83959 85477 5(; 15 70015 7>595 74734 76293 77845 79390 80928 82460 83985 85502 ■'"7 30 70042 7.62. 73'94 74760 763,9 7787. 794,6 80954 8248s 840,0 1 85528 58 45 70068 71648 73120 74786 76345 77897 79442 809S0 84035 1 85553 5!( Sec. 1' 2 3' 4- 5' 6' T ST 9' 10' U' 12' 13' U 15' 1 I) -16. I'.irts J 3 5 7 9 lo 12 14 IS 17 19 ^' " ^4 i* 1 TARI.K GO I,()G. 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I» •9474 2083. 22,82 23527 24865 26198 27524 28844 30158 3.466 32768 36 15 .9496 20853 22204 23549 24888 26220 27546 28866 30.80 3.488 32789 37 ■Ml 19519 20876 22227 23571 249.0 26242 27568 28888 30202 31509 3)i 45 UT (1 19542 20899 22249 23594 249:2 26264 27590 289,0 30224 31531 32833 39 40 19564 20921 22272 236,6 24954 26286 276,2 2S932 30245 31553 32854 15 19587 2C944 22294 23639 24977 26309 27634 28954 30267 31575 32876 41 3(1 .96,0 20966 223,7 2366, 24999 26331 27656 28976 30289 3.596 32898 42 45 ■ 9632 20989 22339 23683 25021 26353 27678 28998 30311 3.6.8 32919 43 11 19655 210. 1 22362 23706 25043 26375 27700 29020 30333 31640 32941 44 15 .9678 21034 22384 23728 25066 26397 27722 29042 30355 3.662 32963 45 30 19700 2.056 22406 23750 25088 264,9 27744 29064 30377 3.683 32984 4C 45 '97M 21079 22429 23773 25. ,0 2644, 27767 29086 30398 31705 33006 47 12 .9746 21 103 22451 23795 25132 2646, 27789 29,07 30420 3.727 33027 4(1 lA ,9768 2.^ ^^474 238.7 25.55 26486 27811 29129 30442 3 '749 33049 49 30 .9791 »II47 22496 25X40 25.77 2650X 2783312915, 30464 1 31770 33071 50 45 19814 2.169 225,9 23862 25199 26530 27855 29.73 30486 3,792 33092 51 13 .9S36 2.192 2254, 23884 2522, 26552 27877 29.95 30507 3,8,4 33114 52 15 .9859 212.4 22564 23907 25243 26574 27899 292.7 30529 31835 33'35 53 :«) .9881 2.237 22586 23929 25266 26596 27921 29239 3055' 31857 33 '57 54 45 .9904 2.259 22609 23951 25288 266,8 27943 2926. 30573 3.8S0 33'79 56 14 .9927 [2.282 22631 23974 25310 2664, 27965 29283 30595 3.90. 33200 5C 15 .9949.2.304 22653 23996 »5332 2666, 27987 29305 30617 3.922 33222 57 30 .9972 1 2.327 22676 24018 25355 26685 280C9 29327 30638 3 '944 33244 511 45 19995 i ^'350 22698 2404. I 25377 26707 280,. 2 1349 30660 31966 33265 5!) St-c. r 2' 3' 4' 5' (J' T 8' !»' 10' 11' 12' 13' 14' 15" I.. 23. l>ar,H, 5 5 6 8 9 , . „ ,4 . 5 -7 ■« =c « 2, TABLE 69 LOO. SINE SQUARE 111° _ _ 11-° 113^ e 15' 30' 1 45' 0' 15' 30' 45' (C 15' 1 30' 45' T" 25"' 7"26- 7^27"' 7" 28"' 71, 29n, 71, 301. 7., 3|,„ 7h 30m 7" 33-17' .11" 71- 35" 9-8 9-8 ^ 9-8 9-8 9-8 9-8 9-8 9-8 9-8^ 9-8 9-8 33^87 35867 37.48 38414 39693 40956 42213 44710 45949 Ift 33308 34601 35889 37.70 38445 397.4 40977 42234 43485 44730 45970 30 33330 34623 35910 37.9. 38466 39735 40998 41155 43506 44751 4599° 45 3335^- 34644 35931 37212 38487 39756 4.0.9 42276 43517 44771 46011 1 33373 34666 35953 37134 38508 39777 41040 42297 43548 44793 46031 15 33395 34687 3 5974 3725": 38530 39798 4.06, 423.8 43568 448.3 46052 :4 39.86 4045. 42965 44212 45454 46690 3fi 15 34085 35375 36658 37935 39207 40472 4.731 42986 44133 45475 4671. 37 30 34107 1 35396 36679 37957 39228 40493 41753 43006 44154 45495 46731 3H 45 34.28 354.7 36701 37978 39149 39270 405.5 41774 43027 44175 455.6 46751 3!) Wn 34150 35439 36711 37999 40536 4.795 43048 44195 45537 46771 40 15 3417. 35460 36743 38020 39191 40557 418,6 43069 443.6 45557 46793 41 30 34.93 35481 36765 38042 393.3 40578 4.837 43090 44337 45578 468.4 42 45 34214 35503 367S6 38063 39334 40599 4.858 43111 44358 45599 46834 43 II 34136 35515 36807 38084 39355 40620 43.31 44378 456.9 46S54 44 15 34157 35546 36829 38.05 39376 4064. 41900 43.51 44399 45640 46875 45 30 34179 35567 36850 38.27 39397 40662 41910 43.73 44420 4566, 46895 46 45 34300 35589 36871 3S.48 394.8 40683 4.941 43.94 44441 4568, 46916 47 12 34311 356.0 36893 38.69 39439 40704 41961 431.5 44461 45702 46937 48 ift 34343 35631 i!2!± 36935 38190 38Z., 39460 40715 4,983 43135 44481 46957 49 30 34365 35653 39481 40746 42004 43256 44503 45743 46978 50 45 34386 35675 36957 38133 395.3 40767 42015 43177 44513 45764 46998 81 13 34408 35696 3697S 38154 395=4 40788 42046 4329S 44544 45784 470,9 52 15 34419 357.7 36999 3S175 39545 40809 42067 43319 44565 45805 47039 53 :v) 3445' 35739 37021 38296 39566 40830 42088 433;o 44586 45S26 47060 54 45 34471 35760 37042 383.8 39587 4085. 42.09 43360 44606 45S46 470S0 6S 14 n 34494 35781 37063 38339 39608 40872 41130 44617 45S67 47.01 of! 15 345'5 35803 37084 38360 39619 40893 41150 43401 44648 45887 47111 57 30 3453/ 35814 37106 3838. 39651 409.4 42,7. 43413 44668 4590S 47.41 58 46 34558 35846 37.17 3840a 39671 40933 42192 43444 44689 45919 59 Se.-. 12 3' 4- 5' «" 1' B' O" 10' U' 12' 13' 14' 15' 1 P. -21. I'.trts 13467 « ,0 ,1 ,3 ,4 15 17 ,8 JO 1. 1 tabi.e m LOO. SINK SQUAKE 1 114° 0' 1 !»' JO' 1 45- 115' ll6° 0' 1 15' 30' 4.V 0' 1 15' 1 30' 7" 30™ I?" 37"' 7''3B"'l7"3!»'" 7" 40-1 7'' 41 "1 7'' 42" 71. 43,,, 71. 4 4...|7h4sn 7h 4,j„, 8. 9-8 ■9-8 9'8 9-8 9-8 |9-S 9-8 |9-8 98 j9-8 9-8 +7i83U84>°'49fi3- 50848 52058 53263 5+46.] 55654 56841 58022 59.98 li-i 47203] 4843' 49653 5086S 52078 53283 54481 55674 56S6. 58042 592.7 : 47408 4S635 49856 l5'°7l 52280 53483 54680 55872 57058 5S238 594.3 11 3 47429148655149876 51091 52300 53503 54700 55892 57078 58258 59432 12 iTi 47449 ; 4867" i 49896 5IIII 52320] 53523 54720 559'2 57097 58277 59452 13 3i 52721 53923 551.8 56308 5749' 5S669 59842 33 30 47879 49103 50322 5'535 52742 53943 55.38 56327 575" 5S6S9 59S61 34 45 47900 49124 50342 5'555 52762 53963 5S'58 56347 5753. 58709 5988. 35 9 (» 47920 49144 50363 5'575 527S2 53982 55.78 56367 57550 58728 59900 3f. Ifi 4794" 49.65 50383 5'595 52S02 j 54C02 55.97 56387 57570 58748 59920 37 :io 47961 49185 50403 5.6.5 52822 t 54022 552.7 56406 57590 58767 59939 311 45 iO 4-98. 49205 1 50423 t 51655 52842 1 54042 55237 56426 57609 58787 59959 3» 4:; 48002 49226 504441 51656 52862 1 54062 55257 56446 57629! 58806 59978 15 4S022 49246150464 5 '676 52882 1 54082 55277 56466 57649 58826 59998 41 30 48043 49266 ! 50484 5.696 52902 54102 55297 56485 57668 58846 600.7 42 45 48063 49287 50504 51716 52922! 54122 553'7 56505 576S8 58S65 60037 43 II 480S4 49307 50525 5.736 52942154142 55336 56525 57708 58885 60056 44 15 48104 49327 50545 5'756 52962 54162 55356 56545 57727 58904 6C075 45 30 48125,493481 50565 5'777 52982 54.82 55376 56564 57747 58924 60095 40 45 48145 1 49368 1 50585 5'797 53002 54202 55596 56584 57767 58944 60.. 4 47 12 48166,49388150605 5.8.7 53022 54222 554'6I 56604 57786 58963 60,34 4H 15 48186 '494091 50626! 51837 53042 54242 55436 1 56624 57806 58983 60153 4!» 30 48207 ] 49429 1 50646 1 51857 53062 542621 5 545 5, 56645 57826 59C02 60173 50 45 48227 ,494491 50666 1 51877 53082 54282, 554751 56663 57«45 59022 60,92 61 13 48247 49470 50686 51897 53.02 5+302 j 55495 1 566S3 57865 5904. 60211 r.2 15 48267 49490 50707 51918 53.23 54322 555'5| 56703 57885 5906. 6023, 63 30 ^8288 49510 50727 51938 55.43 543421 55535 56722 57904 59080 6025. 54 45 48308 49531! 50747 |5'958 53,63 54362 55555 56742 57924 59100 60270 66 14 48329 4955' 1 50767 |5'978 53.83 5438. 55575 56762 5-944 59.20 60290 m: 15 48349 14957' 1507881 51998 483-0 149592' 50808] 52018 53203 54401 1 55594 56782 57963 59139 60309 67 "»n 53223 544211556.4,56801 57983159159 60328! AH «:> 4''>70 49612 50828 1 5203? 53241 5444. : 55634 56S21 58003 59178 60,48 A!l 1) .'M, V. r : 3 4 4 1 - X T H- 9 " i|- li> n IJ 13 14- 15- S70 TABLE n.9 LOO. SINE SQUARIi 110° 117° 118° 119° 4ft' 0' 16' 30' 46' 0' 18' 30' 45' 0' 15' 7''47^ 71. 48- 71, 40- 7" so- Thftlm 9-8 71, 52,n 71, 53,,, 7"64". 7'' 55" 7"5«'" 7h57m 9-8 9-8 9-8 9-8 9-8 9-8 9-8 ^8 9-8 i9'8 o' 60367 6,532 62690 63843 64990 66,31 67167 68397 69522 70641 7'7S4 15 60387 6.55. 62709 63861 65009 66,50 66169 67286 68+16 69540 70659 71773 30 60406 61570 62728 638S1 65028 67305 68435 69559 70678 7i'9' 45 6o+a6 6,590 62748 63900 650+7 66188 67324 68454 69578 70697 7,8,0 1 60445 6,609 62767 639,9 65066 66107 673+2 68+72 69597 70715 71828 15 6C465 6,628 62786 1 63938 650S5 66126 67561 68491 69615 70734 71847 ■M) 60484 6,6+8 62805 63958 6510+ 66245 67380 685,0 69634 70752 7.865 45 60504 61667 62825 63977 65.23 66264 67399 68529 69653 70771 7,884 2 60513 616S6 62844 63996 65142 66283 67+18 68547 69671 70790 7.902 15 6054Z 6056Z 61706^ 61725 62863 640.5 65.61 66302 67437 68566 69690 70808 7.92. 71939 ir 30 62882 64034 65,80 6632, 67+56 '^^4 69709 70827 45 60581 6,7+4 62902 64053 65199 66340 67475 69727 70845 71958 8 60601 61764 62921 6+073 651,8 66559 67493 6862-' 69746 70864 71976 15 60620 6,783 62940 6+092 65158 66378 675.2 68641 69765 71995 30 60640 6,802 62959 6+11, 65^-57 66397 67531 68660 69783 70901 72013 45 60659 6,822 62979 64.50 65176 664,6 67550 68679 69^01 70910 71031 4 60678 6,84, 62998 641+9 65295 66435 67569 68698 69821 70938 71050 15 60698 61860 630.7164.68 655,+ 66454 67588 68716 69859 70957 72069 31) 607.7 61880 63036 1 64.87 65333 66+72 67607 68735 69S58 70975 72087 45 60757 6.899 65056 6+107 65551 66+9. 67625 6^6^ 68754 69877 70994 71.06 72.14 4r 5 60756 61918 65075 6+216 65371 665,0 6S773 69895 71012 15 60776 61938 65094 6+245 65390 66529 67665 6879, 69914 7103. 71.43 30 60795 6,957 63. .3 6+264 65+09 665+8 67682 688,0 69933 7.050 71.6. 22 45 60814 6,976 65.32 64283 65+28 66567 6770. 68829 6995, 71068 71.79 23 6 60834 6,995 65.52 64302 65447 66586 67710 688+8 69970 71087 71.98 24 15 60853 620,5 63.7. 6+321 65+66 66605 67739 68866 69989 71105 721.6 25 30 60873 62034 63.90 6434c 65+85 6662< 6775; 68885 -C007 71124 72235 20 45 60892 62053 65209 64560 65504 566+3 67776 6890+ 70026 71143 72253 27 7 6091 1 62073 65228 64379,65523 66662 67795 6S923 700+5 71161 72272 28 15 60931 62092 652+8 64398 6554^ 6668. 678.4 689+1 70063 71180 72290 29 30 :m) 60950 62,,, 65267 644.7 65C6, 66700 67833 68960 70082 7,198 72309 45 60970 62.3. 652S6 64+36 65580 667.9 67852 68979 70,0, 7,117 72327 31 n 60989 62.50 65505 64455 65^99 06738 67870 6X998 70, ,9 7.235 72346 32 15 6100S 62,69 633^5 64474 656. 8 65757 678S9 690,6 70. 5 S 71254 72364 33 31) 61018 62.89 63344 64+93 65657 61/75 67908 69035 70157 7.272 72383 34 45 61047 62208 63365 6+512 65656 66794 67927 69054 70.75 71291 72401 35 9 61067 62227 63382 64532 65675 668,3 67946 69073 70194 7.3.0 72420 3« 15 6. 1 9. V:< 4 5 6 8 9 10 11 1 '4 '5 '7 18 9 TAR LI- G9 S71 LOO. SINK SQUARE 119° 120^ 121'^ ll >> ■ .ft' 8. 30' 45' 0' 1ft' 30 45^ 0' 1 15' 30' 4^'" l|i'7'" 0_ 7''5H"':7'»i<"' 9-8 9-8 SM)- 81. in, U"2'" 9-8 8''3"' IIM- !8>'5"' 9-S J9-8S 8'' «"■ )|l. gin (I" !("! 9-8 9«8 9-S7 9-88 9-88 ^^ 9-88 o' n 7»862 73964 75061 76153 77238 83.9 79394,0463 '527 1 2585 3639 4686 IS 72881 73983 75080 76171 77256 8337 79411 10481 ■545 2603 3656 4704 1 30 72899 74001 75098 76.89 77274 8355 79429 0499 .562:262. 3674 472. 2 46 72917174019 75116 76207 77293 8373 79447 05.6 ■ 580 263S 3691 4738 3 1 729^6 74038 75134 7622s 7731' 8391 79465 0534 ■598 2656 3709 4756 4 l.i 72954 74056 75152 76243 77329 8408 79483 0552 .6.5 2673 3726 4773 5 :in 72973 i 74074 75171 7626. 77347 8426 79501 0570 1633 269, 3744 479' 6 4:, 72991 7+093 75189 762S0 77365 8444 79519 0587 .65, 2709 376, 4S08 7 S (1 75009 74111 75207 76298 77383 8462 79536 0605 ,668 2726 3778 4826 8 l.j 71028 74':'9 75225 76316 77401 8+80 79554 0623 .686 2744 3716 1 4843 •1 :io 73046 I7414S 75244 76334 77419 8498 79572 064. .704 TjeT 38.314860 "TTT «.-. -3C65 74>66 75262 76352 77437 S5.6 79590 0658 2779 383. 4S78 1 1 3 (1 73083 1 74184 75280 76370 77455 8534 79608 0676 ■739 2796 3848:4895 12 15 74202 75298 76389 77473 8552 79626 0694 ■757 28.4 3S66 4913 13 :<() 73120 74221 75316 76406 77491 8570 79644 0712 ■774 2832 3S8, 4930 14 4r, 73'38 74239 75335 76425 77509 85S8 7966. 0729 ■792 2849 390 ' 4947 1ft 4 73'57 74257 75353 76443 77527 8606 79679 0747 .S.o 2867 39'8 4965 Hi IS 73>75 74176 75371 7646. 77545 S624 79697 0765 .827 28S4 3936 4982 17 311 73>93 74194 75389 76479 77563 S642 79715 0783 .8+5 2902 3953 4999 HI 4:< 73^1^ 743>i 75407 76497 7758. 8660 79733 0800 .863 '92° 397- 5"'7 111 5 73^30 7433' 75426' 76515 77599 8678 79751 oS.S iS?o 2937 398S 5034 •Jd l.i 7 3H9 74349 75444 76533 77617 8696 7976S 0836 .898 2955 4cc6 50S2 21 311 73267 74367 75462 76551 77635 87.3 79786 OS 54 .9.6 2972 4023 5069 22 45 732S5 74386 75480 76569 77653 8731 79804 087. 193312990 404, 50S6 23 C 73304 74404 75498 76588 77671 8749 79822 0889 .95. 3007 40581 5,04 24 1.-. 733" 74422 75517 76606 77689 8767 79840 0907 ■969 3025 4076 5.2. 2ft 3(1 73340 74440 75534 76624 77707 8785 79858 0925 ,986 3042 4093 5.38 20 4.) 73359 74459 75553 76642 77725 8S03 79875 0942 2004 3060 4.., 5.56 27 7 <• 73377 74477 75571 76660 77743 882. 79893 0960 2021 3078 4,28 5173 2H 1ft ~30 73396 74495 US 76678 77761 8839 79911 0978 _203_9_ J£2i 4146 5.9. 2!) 734H 745.4 76696 77779 8857 79929 0996 2057 3i^3 4,63 5208 3(1 4.') 7343^ 74532 75626 76714 77797 8875 79947 .0.3 2074 3.30 4.8, 52-5 31 8 7345' 74550 75644 76732 77815 79965 .03. 2092 3.48 4.98 5243 32 1ft 73469 74568 75662 76750 77833 89.1 79982 1049 21,0 3,65 42,5 5260 33 3(1 73487 74587 75680 76769 77851 77869 8928 80000 ■067 2,27 3,83 4235 5277 34 4ft 73506 74605 75699 76787 8946 8C018 .08+ 2.45 3200 4250 5295 3ft ;i (1 ^3524 74623 75717 76805 77887 8964 8C036 , .02 2.63 32,8 4268 3K 1ft 73';43 74641 75735 76823 77905 8982 80054 . .20 2.80 3235 4285 ':530 3; 3(t 7356. 74660 75753 76841 77922 9CC0 8C071 1137 2.98 3253 4303 5347 38 4ft 7!5'9 74678 75771 76859 77941 9018 8C089 '155 22.6 2233 327. 3288 4320 5364 3.'> 40 73598 74696 75789 76877 77959 9056 So 107 1173 4338 5382 1ft 73616 74715 75808 76895 77977 9054 80 1 2 5 1 .191 225. 3306 4355 5399 41 3(» 73634 74733 75826 76913 77995 9072 80.43 1208 2268 3323 4372 54^6 42 4ft 73653 74769 75844 76931 780.3 90S9 80.60 1226 2286 3341 4390 5434 43 1 1 (1 73671 75862 76949 7803. 9107 80.78 .244 2304 3358 4407 5451 44 1ft 7-/'89 74788 75880 76967 78049 9125 80.96 .261 231. 3376 4425 5468 4ft 30 73708 74806 75898 76986 78067 9143 802,4 1279 2339 3393 4442 54S6 4<; 4ft 73726 74824 75917 770C4 78085 916. 1297 2357 341. 4460 5503 47 12 73744 74842 75935 77022 78.03 9.79 80249 .3.5 2374 342S 4477 5520 48 Ift 73763 74861 75953 77040 78.2. 9.97 80267 1332 2392 3446 4495 5538 40 30 737S1 74879 75971 77058 78,39 9215 87285 1350 2409 3463 1 45,2 5555 iVI 4ft 73799 74897 75989 77076 78157 9233 80303 .368 2427 348. 4529 5572 61 13 738'8 749 '5 76007 77094 78.75 9251 8032, 1385 2445 3498 4547 5590 62 Ift 73836 74934 76026 77112 78.93 9268 80338 .403 2462 35.6 4564 5607 ftS :«» 73854 74952 76044 77130 782.. 9286 80356 .42. 2480 3533 4582 5624 64 4ft 73873 74970 76062 77148 78229 9304 80374 .438 2497 3551 4599 5642 56 14 73891 74988 76080 77166 78247 9322 80392 .456 2515 3568 46,7 5659 50 Ift 73909 75007 76098 77184 78265 9340 804,0 ■474 2533 3586 4634 5677 •'•>7 30 73928 75015 76116 77202 78283 9358 80427 1491 2550 3604 4651 5694 58 4ft ^w^ 75043 76.34 77220 78301 9376 80445 1509 2568 362, 4669 5711 ftW Sr.-. r r 3- 4- ft- «• 7' 8' !»• 10' ll* 12' 13' 14' 1ft ~1 1) IK. r..n 1 1 4 5 6 7 » '"^ '■ 'i '3 '4 '6 <7 iX 1 TABLE (59 LOG. SINE SQUARU | _ 12'i^ 123^ 124° 125 SO- _i?L 0- 16' 1 30' 1 45' 0' 15' j 30' 45' J.. 8'' 10-" «|'ii"> 81. 12... ()i, I,-}... fih 14m 8'' 15"' ,)1, Ign, ,ji, |7„,l8i. 1(1". HI. Ip... 81' 20"' 9-8 9-8 9'8 9-8 9-8 9 u 98 9 ly-S 9-8 9'8 (i 85719 86765 87797 8S823 S9844 90S60 9.870 92875 93874 94S69 95858 15 85746 86783 87S14 88 840 8986. 90876 9I887 93S91 94S85 95874 1 30 85763 86S00 8783. S8857 S987S 90893 9.903 929OS 93908 941)02 95891 2 -15 85781 86817 87848 88R74 89895 90910 9.920 92925 939241940.8 95907 3 1 S579S S6834 87S66 S8S9, 899.2 90927 91937 92942 93941 194935 95924 4 15 858. 5 S6852 878S3 88908 89929 90944 91954 92958 93957 94951 95940 5 :)o 85832 86S69 87900 88925 89946 90961 919 I 9*975 93974 94968 95956 6 45 8-86" 86886 879.7 8S943 S9963 90978 9.987 92992 93991 94984 95973 7 2 86903 87934 S8960 89980 90995 92004 93008 94007 9500. 95989 8 15 IS. 86920 8795' 8S977 899_9I 9.0.. 9202. 93025 94024 950.7 96006 » 30 85902 86938 87968 8S994 900.4 9.028 92038 93042 1 94040 95034 96022 -nr 45 85919 86955 S7986 S901. 90031 9.045 92054 93058 1 94057 95050 96039 11 3 85936 86972 88003 89028 90048 91062 9207. 93075 94074 95067 96055 12 15 85954 86989 88020 89045 90065 9.079 920S8 93092 94090 950S3 9607. 13 30 8597r 87007 88037 89062 9008. 91096 92.05 93.08 94107 95ICO 96088 14 45 Sr,;ii8 i 8702+ 88054 89079 9009S 9. ..3 92.22 93125 94.23 95116 96.04 15 4 9 86co6 1 87041 88071 89096 90. .5 9,129 92.38 93,42 94.40 95133 96.2. 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SINK syUARK ] 141"^ 14£ H3° 144° 45- •J" 2?" »i'28"'l9''2!l" 30' 45- 0' 15' 1 30' 1 46' 0' 16' ». •J'' 30'" !)1'31" ,ji, 32." 91'33"'|U''34"'|U''3S"' ft" 3r;"' 91, ;,7,„ 99 9'9 99 99 9.9 99 9-9 19-9 9-9 99 |9-9 () 506X5 5' 3+0 5.990 52636 53177 539'3 54545 55171 55795 56413 5-026 l.-> 5C696 5'35' 5200. 52647 5318:' 53914 54555 55181 55805 56413 57036 1 311 50707 5.362 52012 52657 53298 53934 54566 55'93 55815 56433 57046 2 45 5'^7>« 5'373 52013 52668 53309 53945 54576 55103 55816 56443 57057 3 1 t) 50729 5.384 52034 51679 53 3 "9 53955 54587 55114 55836 56454 57067 4 15 50740 5 '395 5.045 52689 5333=^ 53966 54597 155114 55846 56464 57077 5 :<(! 5075' 5.405 51c 5 5 52700 5324» 53977 54608 55135 55857 564-4 57087 ti •1.-, 50762 5.4.6: 52c66 527.1 5335' 53987 546.8 55145 55867 56484,57097 7 2 5°773 5.427152077 52722 53362 53998 54629 55155 55877 56495 57107 8 ia_ SojH 5.438 1 520X7 srii 53371 ii?^ ^4639 i5_i^ 55888 56505.157118 » :i() 50795 5.449 5i°9« 51743' 53383 54019 54650 55176 55898 56515 '57128 111 4.-> 5oSc6 51460 52109 51754 53394 54029 54660 551S7 55908 56515; 57138 1 1 3 50817 51471 52.20 52764] 53404 54040 54671 155197 55919 56536 57148 12 15 50828 5.48.15^.31 51775 53415 54050 546S1 1 55307 55919 56546 57158 13 :«) 50838 5.492 I 52.41 52786 54415 5406. 54692:553.8 55939 56556 57169 14 4.1 50S49 5.503 52152 52796 53436 54071 54702 55318 55950 56566 57179 15 4 50860 51514 52.63 51807 53447 54082 547 '3 55339 55960 56577,57189 Hi 15 50871 51525 52174 52S.8 53457 54093 54713 55349 55970 56587 57199 17 :«) 50881 5.536 52184 52829 53468 54103 54734 55359 55981 56597 57209 IK 45 J0893 S'5+7 5^>95_ 51839 53479 54114 54744 55370 5 599' 56607 572.9 ly 5 50904 5«557 52206 51850 53489 54124 54754 55380 5600. 56618 57119 20 15 50915 50926 5.568 522.7 52861 53500 54135154765 55390 5601 1 56628 57240 21 :«» 51579 52228 5287. 535" 54'45 54775 55401 56022 5663S 57250 22 45 50937 51590 51138 52882 53511 54.56 54786 554.1 56032 56648 57260 23 6 50948 51601 52249 52893 53531 54166 54796 55422 56042 56659 57270 24 15 5°959 5.6.2 52260 52903 53541 54177 54S07 55431 56053 56669 57280 25 30 50970 5.622 5227. 52914 53553 54187 54817 55442 '56063 56679 57290 2« 45 50980 5>633 52281 51915 53564 54198 54828 53*53 '56073 56689 57301 27 7 50991 51644 52292 51936 53574 54209 54838 55463, 56084 5(639 57311 2H 15 5IOC2 51655 1 52303 52946 53585 54219 54849 55422.1 56094 56710 57311 2ft 30 51013 5.666)52314 mr. ii^i 54230 54859 55484 56.04 56710,57331 3l(' 45 51024 5.677 5^314 54240 54870 55494 56114 56730 57341 31 8 5'°35 5'687 5-335 52978 53617 5415' 54S80 55505 56115 56740 57351 32 15 51046 51698 52346 51989 53617 54161 54890 55515 56135 56751 57361 33 M 5'057 51709 52357 53000 53638 54171 54901 55525 56145 56761 57371 34 4.> 51068 5.710 52367 53010 53649 54282 54911 55536 56156 5677- 57381 35 ft 5'079 5'73> 5-37S 5302. 53659 54193 54911 55546 56166 56:8. 57391 3(i 15 51090 5174^151389 53032 53670 54303 54931 55556 56176 56791 57402 :»7 30 51101 5.751' 514C0 53042 53680 543 '4 54943 55567 561S7 56802 57411 3(1 45 5"" 5.763; 51410 53053 53691 54314 54953 55577 56197 568.2 57411 3ft 10 51122 51774 5141' 53064, 53702 54335154964 55588 56207 56822 57433 40 15 5"53 5.785 51431 53074 53711 54345 54974 55598 562.7 56831 57443 41 30 5"44 5.796 52443 1 53085 53723 54356 54984 55608 5622S 56841 57453 42 45 5";.' 5.806,52453! 53096 53733 54366 54995 55619 56238 56S53 57463 43 11 51.66 ii8i7| 52464 53"^6 53744 34377 55005 55619 56248 56863 1 57473 H 15 51177 51828 , 51475 <,3ii7 1 53755 54387 550.6 55639 56258 56873 ' 5:'483 45 30 5.188 5.83, 52486 53'i8, 53765 54398 55026 55650 56269 56S83 57493 4K 45 5. .99 5.850 52490 53'38 537/6 54408 55037 55660 56279 56894, 57503 47 12 512.0 51861 52507 53.49 53786 544'9 55047 55670 56289 56904; 57513 411 15 30 51220 51871 5.88Z .25,8 53.60' 53797 54419 55057 55681 1 56300 56914 157524 49 5.231 '.'5191 53>70, 53807 54440 55068 55691 56310 56924157534 50 46 51242 5.89J 52539 53.81 1 538.8 54450 55078 55701 56320 56934 1 57544 51 13 5>M3 5.904 52550 53.92 53829 5446. ,55089 55711 56330 56945 I 57 554 62 IS 5.264 5.915 51561 53202; 53839 5447' ,55099 55722 56341 56955 57564 53 30 5'i75 51926, 51571 532.3' 5,850 54482 551.0 55733 56351 56965 1 57574 54 4ft 5.286 5.9,6 51581 53224 1 53860 54492 55120 55743 1 56361 56975157584 55 14 5'»97 519+71 51593 53134; 53871 54503 55'3o 55753 5637' 56985 57594 r.i! 15 ,-.308 51958] 52604I 53245 5388. 545'3 1 55'4' 55764156381 56996 57605 57 30 5.3.8 51069, 526.4' 53256 53892 545141 55<5' 55774; 56391 57OC6 5:6.5 5H _ '•'* 5'329 5.980 52625:53266 539' 3 54534' 55'62 55784 564'! 570.6 '57625 -,, s.-.-. r 2- 3- 4' 5' 6' r ar »• lo' ir i2' \x i IV 1 n. 10. funs I I 1 3 3 4 5 s 6 7 7 8 9 •; '° 1 TABLF. 69 LOG. SINE SQUARE i __U4°_ 145° 140° 147° 30' 45^ 0' la' 30' 1 45' 0' 15' 1 30' 1 45' .JL_ "yi^ss"' 9'' SO"- yh40n, 9h41n, yi. 4-2'" 1 !)!' 43'" 91, 44,,, siMS'^lsMe-^'uM?'" 9h 4(i„, 3. 9-9 99 99 9-9 9*9 9-9 9-9 i9'9 |99 9-9 9'9 57635 58239 5S839 59434 60025 606,, 61,93 1 61770 1 62342 62910 63474 1ft 57645 58249 5SS49 59444 60035 60621 6,202 6.779 62352 62920 63483 30 57655 58259 58859 59454 60044 60630 6,212 6,789 62361 62929 63495 4ft 57665 58269 58869 59464 60054 60640 6,222 6,798 6237, 62939 63502 1 U 57675 58279 58879 59474 60064 60650 6,231 61808 62380 62948 635,, U 57685 5S289 58889 59484 60074 60660 6124. 618,8162390 62957 6352, :v> 57696 58299 58899 59493 60084 60669 6,250 6,827 62399 62967 63530 •15 57706 58309 58909 59503 60093 60679 6,260 6.837 62409 62976 63539 2 57716 583.9 58919 595.3 60103 606S9 6,270 61S46 62418 629S6 63549 15 577^6 5832 58929 595^3 59533 601,3 60699 6,279, 61856 62428 1 62995 635.8 -T^ ■M 57736158340 58938 60123 60708 6,289 61865 62437 63C05 63567 4ft 57746 5S350 58948 59543 60,33 607,8 6.299 61875 62447 630,4 63577 11 3 n 57756 5836c 58958 59553 60,42 60728 61308 6,885 62456 63023 63586 I ft 57766 58370 5S96S 59563 60152 60737 61318 6,894 62466 63033 63595 :to 57776 5S380 58978 59572 60162 60747 61328 61904 62475 63042 63605 4A 57786 58390 58988 59582 60172 60757 6. 33716.913 62485 63052 636,4 4 57797 5S400 58998 59592 60182 60767 6,347 6,923 62494 6306, 63623 Ift 57807 584,0 59008 59602 60,91 60776 6.357 61932 62504 63070 63633 3i) 578'7 58410 59018 596,2 6020, 60786 6,366 6,942 625.3 630S0 63642 45 ft (f 578^7 58430 59028 59622 6021, 60796 ^3lt 6.95. 62523 63°.<9 6365, 57837 58440 59038 59632 60221 60805 6,385 6,96, 62532 63059 6366, Ift 57847 58450 59048 5964, 60230 608,5 6.395 6,970 62542 63,08 63670 30 57857 5S460 59058 5965. 60240 60825 6,405 6,980 6255, 631,8 63679 45 57867 58470 59068 5,66, 60250 60834 614,4 6,990 6256, 63,27 63689 6 <• 57S77 ^8480 59078 5967, 1 60260 60844 61424 6.999 62570 63136 63698 15 578S7 58490 590S8 5968, 60270 60854 6,434 62009 62579 63.46 63707 30 57897 5S500 59097 59691 60279 60864 6,443 620,8 62589 63,55 C37.7 20 4ft 57907 585.0 59,07 59701 60289 60873 61453 62028 62598 63165 63726 27 7 579«7 58520 59,17 59710 60299 60883 6,462 62037 62608 63.74 63735 28 15 57928 58530 59127 59720 60309 60893 61472 62047 626,7 63.83 63745 29 30 57938158540 59'37 59730 60318 60902 6,482 62057 62627 63193 63754 30 45 57948 58550 59147 59740 6032S 609,2 6149, 62066 62636 63202 63763 31 8 57958 58560 59'57 59750 60338 60922 6,501 62076 62646 632., 63773 32 1ft 57968 58570 59.67 59760 60348 6093, 6,5,, 62085 62655 6322, 63782 33 30 57978 58580 59.77 59769 60357 6094. 6,520 62095 62665 63230 6379. 34 45 57988 58590 59187 59779 60367 6095, 6,530 62,04 62674 63240 63S01 35 !) 57998 58600 59.97 59789 60377 60960 6,539 62,14 62684 63249 638,0 3fi Ift 58C08 586,0 59207 59799 60387 60970 6.549 62,23 62693 63258 638,9 37 30 58018 58620 59216 59809 60396 60980 61559 62,33 62703 6326S 63S28 38 45 58028 58630 59226! 598.9 60406 60990 6,568 62142 627,2 63277 63838 39 10 58038 58640 59236 J59S28 60416 60999 6.578162152 62721 "6li;7 40 15 58C4S 58650 59246 59838 60426 6,009 6,587 62,6, 6273, 63296 63S56 41 30 5S05S 58660 59256 59848 60436 610.9 6,597 62,7, 62740 63305 63866 42 4ft 58C68 58670 59266 59858 60445 61028 61607 62180 62750 633.5 63875 43 II 58078 58680 59276 5986S 60455 61038 6,6,6 62190 62759 63324 638S4 44 Ift 5S089 5S690 ^9286 59878 60465 6104S 61626 622CO 62769 63333 63894 45 30 5S099 5S700 59296 59887 60475 6.057 6,635 62209 62778 63343 63903 4« 4ft 58,09 58709 59306 59897 60484 61067 6,645 622,9 62788 63352 639,2 47 12 58.19 587.9 593.5 59907 60494 6,077 6.655 62228 62797 63362 63922 48 1ft 30 58,19 58729 59325 599.7 60504 6,086 6,664 62238 62807 6337. 63931 49 5S139 58739 59335 59927 -6^1^ 61096 61674 622471628,6 63380 63940 50 45 58149 5S749 59345 59937 60523 6,106 61683 62257 62825 63390 63949 51 13 58159 58759 59355 59946 60533 6,1,5 6,693 62266 62835 65399 63959 52 15 58,69 5S769 59365 59956 60543161,25 6,703 62276 62844 63408 63968 53 30 58.79 58779 59375 59966 60553 6, ,35 6,712 62285 62854 634.8 63977 64 4ft 58,89 5S789 59385 59976 60562 6,, 44 6,722 62295 61863 63427 639S7 55 14 58.99 58799 59395 59986 60572 61154 6,73. 62304 62S73 63436 63996 5(; 15 58Z09 58 809 59405 59995 60582 61,64 6,741 62314 63446 64005 57 3(1 582,9 5S819 59414 60C05 60591 61,73 6175. 62323 6289, 63455 64014 58 45 58x20 58829 59424 60015 6060, 6,183 61760 62333 6290. 63465 64024 69 Sec. 1- 2- 3- 4- 5' 6' V 8' 9" 10' 1 T 12' 13' 14' IS' D. 10. l-.r.,s ,1x3345567 7 S 9 -o TABLE ()9 861 LOG. SINE 8QU.\UK <)° 147° 148 u 8. :m 30' 45' ^0^ JIl\ 30' 45' 0' r !»' »V 45' V-oO" 9" 51"' „i, ft,>"i it'' 53'" 91^54, „ V^'l^ •fi' 5fi"' .,h57m »^ 58"' M" 59-" 99 9-9 99 99 99 9'9 q-9 99 99 99 99 » 64033 64588 65,38 65683 66124 6676, 67293 6782, 68344 68S63 6937S lA 64042 64597 65147 65692 66233 66770 67302 67830 6S353 68872 69386 1 30 64052 64606 65.56 65701 66242 66779 673.. 67839 68362 6S8S0 69395 2 45 6406, 64615 65165 657.0 66251 667S8 673^0 67S47 68 370 68889 69403 3 1 64070 64624 65'74 65719 66260 66707 67329 67856 68379 68898 694,2 4 I.i 64079 64634 65. S3 65729 66269 66S06 67337 67865 68388 68906 69420 5 »• 64089 64645 65192 65738 6617S 66S14 67346 67874 6S396 689.5 69429 45 64099 64652 65202 65747 66287 66823 67355 67882 68405 68923 69437 7 2 64107 6466. 65211 65756 66196 66832 67364 6789, 684,4 6S932 69446 11 13 64U6 646-0 65220 65765 66305 6684. 67373 67900 6S42J 6S941 69454 9 10 30 64.26 "646S0 65229 657741663.4 66850 67382 67909 6S431 68949 69463 4.'i 64,35164689 65238 65783 I 66323 66859 67390 679,7 68440 68958 6947, 1 1 3 64144.64698 65247 65792 1 66332 66868 67399 67926 6S44S 68966 694S0 12 1.-. 64154 64707 65256 65801 6634, 66877 67408 67935 68457 68975 69488 13 :iii 64163 647.6 65265 658.0 66350 66886 674,7 67943 68466 68984 69497 14 4.'V 64172 647^6 65'-74 658.9 66359 66895 67426 6795^ 6S474 68991 69506 15 4 6418, 64-35 65284 65828 6636S 66903 67434 6796. 68483 69001 695,4 10 15 64.9. 64744 65293 65837 66377 669.2 67443 67970 68491 69009 69523 17 :<(! 64200 64753 65302 65846 66386 6692, 67452 67978 68500 69018 69531 IK 45 64209 6476Z 653 ■■ 65855 66395 66930 1 6746. 67987 68509 69027 69540 69548 ~20 5 642.8 64771 65320 65864 66404 66939 67470 67996,68518 69035 15 64228 6478. 65329 65873 664,3 66948 67479 68005 68526 69044 69557 21 :<() 64237 64790 65338 65882 66422 66957 67487 68013 68535 69052 69565 22 45 64246 64799 65347 6589, 6643, 66966 67496 63021 68544 6906, 69574 23 fi 6415; 64808 65356 65900 66440 66974 67505 6803, 68552 69069 69582 24 15 64265 648.7 65566 65909 66449 66983 67514 68040 6856, 69078 6959, 25 3(1 64274 64827 65375 659 iS 66458 6699, 67523 68048 68570 69087 69599 2(i 45 642S3 64836 65384 65927 66466 6700. 67531 68057 68578 69095 69608 27 7 64292 64845 65393 65936 66475 670,0 67540 68066 68587 69104 69616 2(1 15 64302 64854 65402 65945 66484 67019 67549 6S074 68596 691.2 69625 20 30 643,1 64863 654.. 65954 66493 67028 67558 68083 68604 6912. 69633 'M* 45 64320 64873 65420 65963 66502 67037 67567 68092 686,3 69,29169642 31 « 64329 648S2 65429 65972 665,, 67045 67575 6S10, 68622 69,38 69650 32 15 64359 64891 65438 65981 66520 67054 67584 68109 68630 69,47 69659 33 30 64348 649C0 65447 65990 66529 67063 67593 68, ,8 68639 69,55 69667 34 45 64357 64909 65456 65999 66538 67072 67602 68,27 68648 69,64 69676 35 9 II 64366 6+9,8 65466 66008 66547 6708, 676,0 68,36 68656 69,72 69684 30 13 64375 64927 65475 660,8 66556 67090 676,9 68,44 68665 69181 69693 37 30 64385 64936 65484 66027 66565 67099 67628 68,53 68673 69189 69701 3« 45 64394 64946 65493 6603; 66574 67,08167637 68681 69198 697,0 3!l 10 64403 64955 65502 66044 66583 67, ,6 67646 68,70 J6S69, 69206 69718 ~W 15 64413 64964 655,1 66054 66592 67.25 67654 68,79 68699 69215 69727 41 30 64422 64973 65520 66063 6660, 67.34 67663 6X,88 68708 69224 69735 42 45 64431 64982 65529 66072 66609 67143 67672 68,96 68717 69232 60744 43 II 64440 6499 1 65538 66081 66618 67.52 6768, 68205 68715 6924. 69752 44 15 64449 65001 65547 66089 66627167.6, 67690 681,4 68734 69249 69760 45 30 64459 65010 65556 66098 66636 67,69 67698 68223 68741 69258 69769 4G 45 64468 65019 65565 66,08 66645 67,78 67707 6823. 68751 69266 69777 47 12 64477 65028 65575 661,7 66654 1 67187 677,6 68240 68760 69275 69786 40 64486 65037 65584 66,16 66663167,96 67725 68149 6S768 69284 69-94 4(» 60 30 64495 65046 65593 66.35 66672167205 67733 68157 68777 69291 69803 45 64505 65055 65602 66.44 [6668. 1672,4 67742 68166 6S786 6930, 69S,, 51 13 64514 65065 656.. 66,53166690 67223 6775' 68175 68794 69309 69820 52 15 64523 65074 65620 66,62 66699 6713. 67760 68283 68803 693,8 69828 53 r«i 64532 65083 65619 66,70 66708 67140 67768 68292 688,1 69326 69837 54 45 6454^ 65092 6;638 66,79 667,7 67249 67777 6830, 68820 69135 69845 55 U 64551 65.0- 65647 66,88 66725 67258 677S6 683,0 68829 69343 69854 50 15 64560 65110 65656 66197 66734 67167 67795 683.8 68837 69352 69861 57 30 64569 65,19 65665 66106 66743 67176 67803 68327 68846 6,;6o]69«7. 5(1 45 6457S 65.29 65674 66215 66751 672S4 678,2 68,16 6885 s 69369 U9879 5!l S.T. 1- 2- 3- 4- 5- (i- r H- »' !(»• 11' \r Kf II IV 1>. 9 I'arU . 1 2 2 3 4 4 < 5 6 7 7 S s ,; 8S2 TABLE 69 LOO. SINE SQUARE 0- 130'' .aL 151° J 62° j^ 1 15' 30' 0- 1 15' 1 so- 45' 0' 15' , 3C lOi'O-llOM" 10i'2'"|10''3" lo" 4" 10'' 5- 10" G" 10" 7m Vo" 8-" lOhflmllohlO" 9-9 1 9-9 99 9'9 9-9 99 99 99 99 99 9-9 6 69888 70393 70894 7-39" 7.883 7237. 72855 73334 73808 74279 1 74744 i/> 69896 70401 70902 71399 7.89. 72379 72863 73342 73816 74286 74752 1 :w 69905 70410 709 1 1 7.408 7.9C0 72387 7287, 73349 73824 74294 74760 2 45 699.3 70418 70919 7,416 7.908 72395 72879 73357 73832 74302 74768 3 1 69921 70427 70927 71424 71916 72403 72887 73365 73840 j 743.0 74775 4 15 69930 70435 70936 7.432 71924 724J1 72895 73373 7384S 743.8 74783 5 'M 69938 70443 70944 7.440 7.932 72420 72903 73381 73855 1 74325 7479. «! 45 69947 70452 70952 71449 7.940 72428 72911 73389 73863 74333 74798 7 2 69955 70460 7096. 7'457 7.949 72436 729,9 73397 7387: 7434. 74S06 8 15 69964 70469 70969 7.465 7.957 -Zriil 72927 73405 73879 74349 74S14 i) :«) 69972 70477 70977 71473 7,965 72452 72935 73413 73887 74356 74822 nr 45 699X. 70485 70986 7.487 7.973 72460 72943 7342. 73895 74364 74829 1 1 3 70494 70994 7i4>'9 71981 7246S 7295, 73429 73903 74372 74837 12 15 69997 70502 l7>002 7'497 7,989 72476 72959 73437 /3910 74380 74S45 13 311 70006 70510 71010 71306 71997 72484 72967 73445 739.8 7438S 74852 14 45 70014 70519 71019 7'514 72006 72492 1 72975 73453 73926 74395 74860 15 4 70023 70527 71027 71522 720,4 72500172983 7346. 73934 74403 74868 16' 15 70031 70535 71035 71531 72022 72508 72991 73468 73942 744'. 74876 17 SO 70040 70544 7.044 71539 72030 72516 72999 73476 73950 744.9 74883 18 45 70048 70552 7.052 71547 72038 72525 73007 73484 73958 74426 7489. 1» 20 5 » 70057 7056, 7.060 71555 72046 72533 73015 73492 73965 74434 74899 15 70065 70569 71069 71564 72054 7254. 73023 73500 73973 74442 74906 21 :<(> 70073 70577 71077 71572 72063 72549 7303. 73508 7398. 74450 749.4 22 45 70082 705S6 7.085 71580 72071 72557 73039 735,6 73989 -4458 74922 23 6 70090 70594 71093 7.588 72079 72565 73°47 73524 73997 74465 74929 24 15 70099 70602 7.102 71597 72087 72573 73055 73532 74005 74473 74937 25 30 70107 706II 71. .0 71605 72095 72581 73063 73540 74013 7448. 74945 2(; 45 70116 70619 7Ui8 716.3 72103 72589 73071 73548 74020 74489 749:3 27 7 70124 70627 7.126 7.62. 72111 72597 73°79 73556 74028 74496 74960 28 15 70132 70636 70644 7>i35 7.629 72,20 72605 73087 73563 74036 74504 7496S 2!) 30 70141 7H43 7.63S 72128 72613 73095 7357. 74044 745>2 74976 "30" 45 70149 70653 71151 7,646 72136 7262, 73.03 73579 74052 74520 74983 31 8 70158 7066, 71160 7,654 72144 72629 73111 73587 74060 74528 74991 32 15 70166 70669 71168 7,662 72152 72637 731.9 73595 74067 74535 74999 3S 30 70175 70678 7.176 7,670 72160 72645 73,27 73603 7407 s 74543 75006 34 45 70183 70686 71184 7,679 72,68 72654 73.35 736.. 74083 7455. 75014 35 9 70191 70694 71.93 71687 72,76 72662 73142 73619 7409. 74559 75022 3f! 15 70200 70703 71695 72,85 72670 73150 736" 74099 74566 75029 37 30 70208 70711 71^09 7,703 72,93 72678 73158 736^^ 74.07 74574 75037 38 45 70217 7.2.8 7171. 7220. 72686 73166 73643 74. .4 74582 75045 3:' 10 70225 70728 7.226 7.720 72209 72694 73174 73650 74122 74590 75053 I0 15 70233 70736 7.234 7.728 72217 72702 73182 73658 74130 74597 75060 41 30 70242 70744 7.242 7.736 72225 72710 73190 73666 74138 74605 75068 42 45 70250 70753 7.251 7.744 72233 72718 73198 73674 74.46 746.3 75076 43 11 70259 70761 71259 7.752 72241 72726 73206 73682 74.54 74621 75083 14 :5 70267 70769 71267 7.761 72249 72734 73214 73690 74,61 7462S 75091 45 30 70276 :o77!i 71275 7.769 72258 72742 73222 7369S 74.69 74636 75099 46 45 702S4 70786 71284 71777 72266 72750 73230 73706 74'77 74644 75.06 47 12 70292 70794 7,292 71785 72274 72758 73238 73714 74185 74652 7511'C 48 15 70301 70803 71300 7.793 72282 72766 72774 73246 73254 73729 74193 74658 75122 75129 4!) "so" 30 70309 708.1 7,30s 71801 72290 74200 74667 45 703,8 70819 7.3.7 718,0 72298 72782 7326a 73737 742^^1! 74675 75137 51 13 703,6 70828 7'3»5 71818 72306 72790 73270 73745 742,6 74683 75.45 52 15 70334 70836 7'333 7,826 72314 72798 73278 1 73753 1 74214 74690 75.52 53 M} 7°343 70844 7'34' 71834 72322 72806 73286 1 73761 74232 74698 75.60 54 45 7035; 70853 7.350 71842 7233. 728,4 73294 73769 74239 74706 75.68 ftS 14 70360 70861 71358 7185. 72339 72823 73302 73777 74247 747.3 ■5:7; )fi 15 70368 70S69 7.366 7.859 72347 72831 733.0 73785 74255 7472. ■S.83 5V 30 70376 7087S 7>374 7,867 72355 72839 733.8 73792 74263 74729 7519. 58 4« 70385 70886 1 71383 7187s 7_236^ 72.47 73326 1 73800 7427. 74737 75.98 5U Sec. l-2'3- 1" 5" (i- 7" r !l 10- 11- 12' 13" 14' 15' 1 D R. Hurts 1,1133445556778 1 883 LOG. SINK SQUARE 152' 133^ 134° I 153° s. 4ft' 0' 15' ] 30' 1 4.1' (/ 1ft' 30' 4ft' 0' 15' lOMl" 10M2'° 10M3" lOi'U^'lOi'lS" 10M6'" I0M7'" io"ia" 10M9" U,l,20n. 10h2l" 99 99 9-9 9-9 99 9-9 |9-9 9-9 99 99 9-9 II 7i68 74685 1.1 4 U 753Z8 75784 -6236 76683 77.16 77564 77999 78418 78854 7917s 79691 i« 15 753J6 7S791 76243 76690 77.33 77571 78006 78436 78861 79182 79699 1; ■M 75343 75799 7615. 76698 77.4' 77579 78013 78441 78868 79289 79705 IH 4.5 5 » 71ili 75359 75S07 76»,8 76705 77.48 77.55 77586 78020 78450 78457 78875 79196 79712 I'J 75814 76166 767.3 77593 78027 788S2 79303 797.9 20 1,1 753"*. 75811 76173 76720 77.63 7760. 78034 78464 78889 793.0 79716 21 30 7537+ 75810 7618, 76727 77170 77608 78042 7847. 78896 793.7 79733 22 4.1 7538* 75837 76288 767,5 77177 776,5178049 78478 78901 79314 79740 23 C 753li9 7584s 76196 76741 77185 77622 1 78056 78485 789.0 7933. 79747 24 15 75397 75851 76303 76750 77.91 77630 78063 78491 7S917 79138 79754 25 30 75405 75860 76,., 76757 77.99 77637 78070 7S5C0 78914 79345 79761 20 45 754" 75867 763.8 76765 77107 77644 78078 78507 7893. 79351 79768 27 7 75420 75875 76126 76771 771.4 77652 7S085 785.4 7X9,8 79359 79775 28 15 754^7 75882 76333 76779 7712. 77659 78092 78511 78945 79366 7978. 2i» 30 75435 75890 76341 76787 77666 78099 78518 78951 79373 79788 30 45 75443 75897 763+8 76794 77116 77673 78106 78535 78959 79379 79795 31 » 75450 75905 76355 76802 77143 7768, 78. .4 78541 78967 79386 79S02 .■«2 1.1 75458 75911 76,63 76809 7715. 77688 78.2. 78549 78974 79393 79809 83 75465 75920 76370 768.6 77158 77695 78128 78556 78,8. 79400 79816 4.1 7 5473 75918 76378 76824 77165 77701 78.35 78563 78988 79407 79823 35 3 (1 7548' 75935 76385 76S3. 77171 777,0 78.41 7857. 78995 794.4 798,0 3«; 1.1 754!i!f 75943 76393 76839 77180 777'7 78149 78578 79001 79421 79816 37 30 75496 7595° 76400 76846 77187 77714 78.57 78585 79009 79418 79841 38 4o lU 75504 755" 7595S 76408 76415 76853 77194 7-73. 78164 78591 790.6 7943 5 79850 39 75965 76S6, 77301 77739 78.7. 78599 79023 79441 79857 15 755'9 75973 76421 76868 77309 77746 78.78 78606 79030 79864 41 30 75516 75980 76430 76875 773.6 77753 78185 786.1 79037 79456 79871 42 4.1 75534 75988 76438 76883 77314 77760 78.91 78610 79044 79878 43 II 75541 75995 76445 76890 7733" 77768 78200 78627 7905. 79470 79885 44 15 7 5549 76003 76451 1 76898 77338 77775 78107 78h,4 ^ 79477 79892 4.1 30 75557 76011 76460 76905 77346 77781 78114 78643 79484 79898 46 45 75564 76018 76467 769.1 77789 7821. 78649 79072 7949' 79905 47 14 » 75571 76016 76475 76910 77360 77796 78228 7865b 79079 79498 79912 48 U 7S580 76033 76481 76917 77367 -7804 778.. 78115 .8663 78670 79086 79505 799.9 411 'ftiT 30 75587 7604. 76490 76934 77375 78143 79093 79511 79916 4ft 75595 76048 76497 76942 77381 778,8 78250 78677 79.00 795 «9 7993 3 51 75601 76056 76505 76949 77389 77'!i5 78157 786S4 79.07 795*5 79940 .12 Ift 756.0 76063 765.1 76957 77397 778,3 7S164 78691 791.4 79531 79946 S.t 30 756.8 76071 76510 76964 77840 7817. 78698 79,21 79539 7995 3 .'>4 46 75615 76078 76527 7697. 774". 7784- 78178 78705 79.18 79546 79960 5.1 14 75633 76086 76514 76979 77419 77854 78186 787.1 79>15 79553,7996- 61; 15 75640 76093 76541 76986 77416 7786. 78191 787.9 7914J 79560 1 79974 A7 30 7sH* 76,0, 76549 1 76993 77411 77869 78300 78727 79.49 7956717998. »n 45 li^SS 76557, 7-001 77440 778-6 78307 78^34179.56 70574 179988 .VI Soc. r 2' 3' 4' 8' (;■ 7 tf !»■ 10' 11' i-*' \y ir u* U. 7. I'afU o I I a . 3 3 4 4 5 5 6 6 7 7 TABLE fiO LOO. SINK SQUAHK | 13 ,0i.22n, 3° 156° 157° 158° _! 45' 0' 1 15' 1 _3»L 45' 0' 15' 10l.2!»'" 30- 45' 0' ,01.23- 9"9 10I.24"' 9-9 0i'25"> 0i'2C"' IO"27'" 9-9 101.28". 10'>30'" 101.31"' ,01.32". 9"9 9-9 99 99 99 9-9 99 99 o' o' 79995 80404 80809 81209 8,606 8,998 82385 82769 83.48 835.3 83893 lA 800UI 8041, 80816 81216 8,6,2 82004 82392 8^775 83.54 83529 83899 1 3(( 80008 X04.7 80822 III? 8,6,9 820,, 82398 83.60 83535 8^°' 2 45 80015 80424 80829 8.625 820,7 82405 82788 83167 83541 3 1 S007.2 80431 80836 lull 8,632 82024 824,, 82754 83173 83547 839,8 4 15 80029 80438 80842 81243 8.639 82030 824,7 82801 83,79 83554 83924 5 30 80036 80444 80849 8,249 8,645 82037 S2424 82807 83186 83560 83930 t; ■15 80043 80451 80856 8,256 8.652 82043 82430 828,3 83,9. 83566 83936 7 2 S0049 80458 80862 8,262 S.658 82050 82437 82S20 83,98 8357. 8394. 8 15 80056 S0465 80869 8,269 8,665 82056 82443 82826 83204 83579 I39J4 "To ;*(> 80063 80472 80876 8,276 8,67, 82063 82450 82832 832,, 83585 4r> S0070 80478 808S3 81282 8,678 82069 82456 82839 83217 83593 8396, 1 1 3 80077 804S5 80889 8,289 8,684 S2076 82462 82845 83223 83597 83967 12 15 80084 80492 80896 8.296 8,69, 82082 82469 8285, 83229 S3603 83973 13 30 80090 80499 80903 8. 302 8.698 820S9 82475 82857 83236 836,0 83979 14 45 80097 80505 80909 8,309 8,704 82095 82482 82864 83242 836,6 8398. 15 4 80104 80512 80916 8,3.5 8,7,, 82,02 8248S 82870 83248 83622 8399. lU 15 80111 80519 80923 8,322 8,7,7 82,08 82494 82877 83254 83628 S3997 17 3(1 80118 80526 80929 81329 8,724 82,, 4 82501 82883 83261 83634 84003 Hi 45 80,25 80533 80936 81335 8,730 82,2, 82507 82889 83.67 83640 840,0 1!) 5 80.3. 80539 80943 8,342 81737 82,27 825,4 82896 83.73 83647 840,6 20 13 80138 S0546 80949 8.348 8,743 82,34 82902 83280 83653 84022 21 30 80145 80553 80956 8>355 8,750 82,40 82526 82908 83286 83659 84028 22 45 S0152 80560 80963 81362 8,756 82,47 8^533 829,5 83292 83665 84034 23 C 80159 80566 80970 8,368 8.763 82,53 82539 82921 83298 8367, 84040 24 15 80166 80573 80976 81375 81770 82,60 82546 82927 83305 83678 84046 25 30 80172 80580 80983 8,382 8,776 82,66 82552 82934 833,, 83684 84052 2(i 45 80179 80587 80990 8.388 8,783 82173 82558 82940 833>7 83690 84058 27 7 80186 80593 80996 8.395 8.789 82179 82565 82946 833.3 83696 84065 2K __15 30 80193 80600 8,003 8140. 8,796 8257. 82953 83330 83702 8407, 2!) 80200 80607 8,0.0 81408 8,8o2 82192 82 57 8 82959 83336 S3708 84077 :573 8.965 82353 82737 83116 83492 83862 8+229 53 14 80377 807S2 81,83 8,580 8,972 82360 82743 83,23 83498 83869 84.35 5t; 15 803S3 80789 81.89 8.586 81978 82366 82750 83129 835<^4 8387s 8424, 37 30 80390 80795 81,96 S.593 8,985 82373 82756 83>35 835,0 8388, 58 45 80397 80802 8,203 8,599 8,99, 82379 82762 83142 83516I83SS7 8^253 5» 1 S«. r 2- 3- 4- 5- C- 7' ir U'10'll-|2-|3' 14-13' 1 j D. 7. 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Part. oiiii2i»«lJ3334 1 888 TABLR GO LOO. SINE SQUAKli j 166° 167" 169° 0' lli'lo" 30' 48' 0' 15' 30' 1 45' 0' 15' ll''13" 30' 11'' 14 _45'_ ■11''15' llhC ll"?" HI'S' 11'' ft" IIMO' IIMI 11M2" ,9-9 l9'9 9-9 9'9 9'9 99 99 9-9 9'9 9'9 9'9 93958 941S1 94399 9461 = 94S22 950=7 95229 954=6 95619 95807 9599= IS 93962 94184 94402 94616 94825 95031 95232 954=9 95622 95811 95995 1 31) 93966 94188 94406 94619 948=9 95034 95=35 9543= 956=5 958.4 95998 2 45 93970 94192 94409 94623 94832 9503S 95=39 95436 956=8 95817 9600. 3 1 93973 94'95 944'3 94626 94836 9504, 95242 95439 95631 958=0 96004 4 15 93977 94199 94417 94630 94839 95044 95=45 9544= 95635 95823 96C07 5 30 93981 94202 94420 94633 94!-'43 95048 95=48 95445 95638 95826 9601c ti 45 93984 94206 94424 94637 94846 95051 95=5= 95448 9564. 958=9 96015 7 2 939S8 9+210 944=7 94641 9+850 95054 95=55 9545= 95644 95832 96016 H 15 9399^ 94213 9443' 94644 94853 95058 95=59 95455 95647 95835 95838 96019 -TTT ao 93996 94217 94434 94648 94856 95061 95=6= 95458 95650 96022 45 93999 94221 94438 94651 94860 95065 95265 95461 95654 95842 9602, II 3 94C03 94224 94442 94655 94863 95068 95=68 95465 95657 95845 96028 12 15 94007 9422S 94445 9465S 94867 95071 95=7= 95468 95660 95848 9603, 13 30 94011 9423, 94449 94662 94870 95075 95=75 95471 95663 95851 96034 14 45 94014 94^35 9445= 94665 94874 95078 95=78 95474 95666 95854 96037 15 4 94018 94-39 94456 94669 94877 95081 95=8= 95478 95669 95857 96040 k; 15 94021 ] 94243 94460 94672 94881 95085 95=85 95481 95673 95860 96043 17 30 94025 94246 94463 94676 9488+ 95088 95=88 95484 95676 95S63 96047 IK 45 94029 94250 94467 1 94679 94S87 95092 95292 95487 95679 95866 96050 19 5 94033 94^54 94470 94683 94891 95095 95=95 95491 956S2J95S69 96053 20 15 94037 94^57 94474 94686 94894 95098 95=98 95494 95685 95872 96056 21 30 94040 94261 94477 94690 94898 95102 95301 95497 956S8 95876 96059 22 45 94044 94265 94481 94693 94901 95105 95305 95500 95692 95879 96062 23 C 94048 9426S 94485 94697 94905 95108 95308 95503 95695 95882 96065 24 15 94051 94^7^ 94488 94700 94908 95 1 12 95311 95507 95698 95885 96068 25 30 94055 94^75 9449= 94-04 949" 95115 95315 95510 95701 95888 96071 20 45 94059 94279 94495 94707 949 '5 95118 95318 95513 95704 95S91 96074 27 7 94063 94283 94499 94711 949 '8 95.22 953=1 95516 95707 95894 96077 2H 15 94066 94286 94502 947 '4 949== 95 '=5 953=4 955=0 957^ 95714 95897 96080 20 30" 94070 94290 94506 94718 949=5 95129 95328 955=3 9590^ 96083 "iiiT 45 94074 94294 94510 947=1 949=9 9513= 95331 95526 95717 95903 960S6 31 8 () 94077 94=97 945 '3 947=5 9493= 95135 95334 955=9 95720 95906 96089 32 15 94081 94301 94517 947 = 8 94935 95139 95338 9553= 957=3 95909 96092 33 30 94085 94305 94520 9473= 94939 95141 95341 95536 95726 95912 96095 34 45 94088 94308 945=4 94735 9494= 95 HS 95344 95539 957=9 95916 96098 35 9 94092 94312 945 = 7 94739 94946 95'49 95347 9554= 9573= 959.9 9610, •Mi 15 94096 94315 94531 9474= 94949 95 '5= 95351 95545 95736 95922 96,04 37 30 941CO 943 '9 94535 947461 94953 95155 95354 95548 95739 959=5 96107 3(1 45 9A22.1. 943 = 3 "4538 94749 1 94956 94959 95159 95357 9555= 9574= 95928 961,0 3!) 40 10 94107 94326 9454= 9475= 95162 9536. 95555 95745 95931 96,13 15 94I1I 94330 94545 94756 94963 95.65 95364 95558 9574S 95934 961,6 41 30 94' '4 94334 94549 94759 94763 94966 95169 95367 95561 95751 95937 961,9 42 45 94118 94337 945S = 94970 95172 95370 95564 95754 95940 96,22 43 11 94122 94341 94556 94766 94973 95'75 95374 95568 95757 95943 961=5 44 15 94125 94344 94559 94770 94976 95179 95377 95571 95761 95946 96,28 45 30 94129 94348 94563 9477 3 94980 95182 95380 95574 95764 95949 96131 40 45 94>33 9435 = 94566 94777 94983 951S5 95383 95577 95767 9595 = 96134 4/ 12 94136 94355 94570 94780 94987 95189 95387 95580 95770 95955 96137 4(; 15 94140 94359 94362 94573 94784 94991 9y'9± 95390 95584 95773 95958 96140 4!» 50 30 94 '44 94577 947S7 94993 95195 95393 95587 95776 95961 96,43 45 94147 94366 9458. 9479' 94997 95199 95396 95590 95779 95965 96,46 51 13 94151 94370 94584 94794 95000 952C2 95400 95593 9578 = 95968 96,49 52 15 94'55 94373 945SS 94798 95C04 95205 95403 95596 95786 9597' 96.52 53 30 94 '58 94377 94591 94801 95007 95=09 95406 95600 95789 95974 96,54 54 45 94162 94381 94595 94805 95010 9.2.2 95410 95603 9579= 95977 96.57 55 U 94166 94384 9459S 94808 ;50'4 9i"5 954'3 95606 95795 95980 96,60 5(1 15 94170 9438S 94602 9481= 95017 95/19 95416 95609 95798 95983 96,63 57 30 941731 9439' 94605 94815 95021 95222 954'9 95612 95801 95986 96,66 511 45 94.77I 94395 94609 94819 95024 1 95-'=S 954=3 956.5! 9_5_8o£t 95989 96.69 5!) S«-. 1" 2' 3' 4" 5' «■ 7' «" »■ 10' 11' 12' 3- 14 15- D.3 Parts , , . , , z z z a i 3 3 3 | TABLC G9 liOe. SINE SyUAKE 1 \ leo" 170° 171^ ~4.V mm;... SO' 1 45' __?'_ ll"21"'!ll''22". 4,V 0' 1 15' 1 30' lli>l8'"llIM9- llh.20m l|i'24'"llli'2.i"',ll''2«"'lli'27'" 99 l9-9 99 99 99 9-9 9-9 99 99 99 9 9 o' i> 96172 96349 96521 96688 96852 97012 97.67 973.S 9746; 97608 97747 l.i 96175 9635- 9*5^3 9669, 96855 97014 97,70 9732. 97468 97611 97749 1 3() 96,78196354. 96526 96694 96S5S 970,7 97,72 97323 97470 976.3 97752 2 4A 961S1 96357 96529 96697 96860 97020 97'75 97326 974:'3 976.5 977 54 3 1 96. 84 96360 96532 96699 96S63 97022 97.77 97328 97475 976,8 97756 4 ;■> 96,87 96363 96535 96702 96S66 ! 97025 97.80 9733. 97477 97620 97758 S 30 96,90 96366 96538 96705 96868 97027 97.82 97333 97480 97622 97761 u 4.-. 96,93 96369 96540 96708 96871 97^3° 97.85 97336 97482 97625 197763 7 2 96,96 96372 96543 967,, 96874 97033 97.87 97338 97485 97627 97765 R V, 96199 96,75 96546 96713 1 968-6 1 97035 97.90 97341 1 97487 97629 97767 •1 :m 96202 96377196,49 967,6 96879 ' 9/038 97.93 97343 97489 97632 97770 "iF 4:, 96205 96380196552 96719 96882 97040 97.95 97346 97492 97634 97772 1 1 :» 96208 96383 1 9655+ 96722 96884 97043 97.98 97348 97494 97636 97774 12 i.-i 962,, 96386196557 96724 96887 97046 97200 9735' 97497 97639 97776 l.i :«) 962,+ 96389 [96560 96727 96890 97048 97203 97353 9749919764. 97779 u 4.-. 962,7 96392,96563 96730 96S92 9705, 97205 97355 97501 1 97643 9778. m 4 96120 96395 96566 96733 96895 97054 97208 97358 97504,97646 97783 ifi l.i 96223 96398 96569 96735 96898 97056 97210 97360 97506,97648 97786 17 M 96226 96401 9657, 9673S 96900 97059 97213 97363 97509 1 97650 97788 i« 4.-. 96229 96403 965-4 96741 96903 9706, 972,5 97365 975" 97653 97790 97792 19 20 a II 96232 96406 1 96577 96743 96906 97064 9721S 97368 975'3 97655 IS 96234 96409 96580 96746 96908 97067 97220 97370 975,6 97657 97795 21 .•(1) 96237 964,2 96583 96749 969,, 97069 97223 97373 ,75,8 97660 97797 22 J.J 96240 964,5196585 96752 969,4 97072 97226 97375 9752' 97662 97799 2.) t; i> 96243 964,8196588 96754 969,6 97074 97228 97378 97523 97664 9780, 24 ]-> 96246 96421 '96591 96757 969,9 97077 97131 97380 97525 97667 97804 2.i m 96249 1 96424 96593 96760 96922 97079 97233 97383 97528197669 97806 2fi _ 4.5 96252196426 96597 96763 96924 97082 97236 97385 97530 9767. 97808 27 96255 ,96429196599 96765 96927 97085 97238 97387 97532 97673 97810 2H ~"iti7 96258 962— 96432 I 96602 96768 9677. 96930 97087 97241 97390 97535 97676 978.3 97815 29 96435 96605 96932 97090 97243 97392 97537 97678 4.-. 96264 9643S 9660S 96774 96935 97091 97246 97395 97540 97680 978,7 31 II II 96267 9644, 966,, 96776 96938 97093 97248 97397 97542 97683 978.9 32 l.i 962-0 96444 966,3 96779 96940 97098 97251 97400 97544 97685 97822 33 :(ii 96273 96447 966,6 96782 96943 97 'oo 97253 97402 97547 97687 97824 31 4.i 96276 96449 966,9 96784 96946 97.03 97256 97405 97549 97690 97826 3.i 9 11 96279 96452 ' 96622 96787 96948 97105 97258 97407 97552 97692 97828 3t l.i 9628, 96455^96625 96790 96951 97108 97261 97409 97554] 97694 97830 37 311 ,6284 96458 96627 96792 96954 97111 97263 974.2 97556197697 97833 3'l 4.i 9628- 9646, 1 96630 96795 96956 971,3 97266 97414 97559 1 97699 1 97835 3.1 "SlT «l II 96290 96464196633 96798 96959 97, ,6 97268 974.7 9756' 1977011 97837 l.i 96293 96467 96636 9680, 96962 97.18 9727. 974.9 97563 197703 97839 41 :504' 96672 96836 96996 97.5* 97303 9745' 97594 97733 97868 .'>4 4i 96334196506 96675 96839 96999 97154 97306 97453 97596 97736 97870 ;.& 14 II 96,37196509 96677 968+. 97001 97157 97308 97456 97599 97738 97873 5li l.i 96540 965,2 96680 96844 97004 1 97 1 59 973'. 97458 97601 1 97740 97875 .i7 ?,tl 96,43 96515 96683 96S47 1 97006 97,62 973.3 97460 97603 1 97742 97877 .ill 4.i 96546 ,/i5,8 96686 96849 197009, 97 '65 973.6 97463 1 97606 1 97745 '9'879 ,VI .s.r. 1' 2' y r y r 7' h- •.>■ lo- ir 12- ur u* i.i' 1 U. 3. r,rt« o , . , 1 1 2 2 1 » 2 5 3 3 1 TABLE 69 LOG. SINE SQUARE 1 172° 173° 174° 0' _'5L 30- 1 45' "L- 15' 1 30' 1 45' 0' 1 15' 1 SO' 11 "2n'" 111' 29" lli'30"':ll''31"' l,h3.2„ l|i'33'":i|i'34'"!lli'35- ii''3(;'":ii''37"'iii''38" 99 9'9 9'9 99 99 99 9-9 l9-9 99 9-9 9"9 97SSZ 980.3 98.38 98260 98378 98492 98602 98707 98S09 98906 15 978S4 9S014 98,40 98262 98380 98494 98604 98709 988,0 98908 9900. 30 97S86 98C16 98.42 98264 98382 98496 98605 987., 988.2 9S909 99002 45 97S8g 98018 98.44 98266 983S4 98498 98607 98713 98S.4 9S9.. 99004 I 97890 98020 9S.46 9S268 9S386 98500 98609 987.4 988.5 989.2 99005 15 gy^gs 980J3 98149 98270 9838S 9850. 986.. 987.6 9S8.7 98914 99007 HO 97ii95 9S025 98.51 98272 98390 98503 986.3 987.8 988.9 989.6 9900S 45 97«97 98017 98.53 98274 98392 98505 986.4 98719 98S10 989.7 99010 2 97899 98029 98.55! 98276 98394 98507 986.6 98721 98822 98919 99011 15 979°' 98031 98.57 '9827S 98396 98509 9S618 98723 9S824 98920 99013 30 97904 98033 98,59198280 98398 985., 98620 98725 9S825 98922 990.4 ~nr 45 97906 98036 98,6, 9S282 98400 985.3 9862. 98726 98827 98923 990.6 11 3 97908 9803S 98,63 98284 98402 985.4 98623 98728 98829 98925! 990.7 15 97910 98040 98.65 982S6 98403 985.6 98625 98730 98830 98926 . 99019 13 30 979:2 98041 9 97934 98063 98.88 98308 98424 98537 98644 98749 98848 99035 24 15 97936 98065 98.90 98J.0 98426 98539 98646 98750 98850 98945 99037 25 30 97939 98067 98.92 983.2 98428 98540 98648 98752 9885. 98947 99038 2fi 45 97941 98069 98.94 983.4 98430 98542 98650 98753 98853 98948 99040 27 7 n 979+3 98.96 983.6 98432 98544 98652198755 98855 98950 9904, 28 15 97945 98074 98.98 983.8 9S434I 98546 98653 1 98757 98856 9895. 99043 2!< 30" 9791-7 98076 98320 98436 98548 98655 98759 9S858 98953 99044 30 45 97949 98078 98202 98322 98438 98549 j 98658 98760 98860 98955 99046 31 a 9795=^ 98080 98204 98324 98440 9855' 98659 98762 98S6. 98956 99047 32 15 97954 98082 98206 98326 9844: 98553198660 98764 9SS63 98958 99048 33 30 97956 98084 98208 98328 98443 98555 98662 98765 98864 98959 99050 34 45 97958 98086 982.0 98330 98445 98557 98664 98767 98866 9896. 99052 35 » 97960 98088 982.2 98332 98447 9855S 98666 98769 9S868 98962 99053 36 15 97962 98090 982.4198334 98449 98560 98667 98770 98S70 98964 99054 :<7 30 97965 9S092 98216 98336 9845. 98562 98669 98772 9887. 98965 99056 38 45 97967 9S2.8 98338 98453 1 98564 98455 98566 986., 98774 98872 9S967 99057 3H ~40 10 97969 98097 98220 98340 98673198775 98874 98969 99059 15 9797. ,98099 98222 98342 98456 1 98568 98674 98777 98876 98970199060 41 30 97973 98'°' 98224 98343 9845' '98569 98676 98779 98877 98972199062 42 45 97975 9S103 98226 98345 98460 98571 9S678 98781 98S79 198973 99063 43 11 97977 98105 9822a 98347 9S462 98573 9S680 98782 9888. 9S975 99065 44 15 ,7980 98,08 98230 98349 98464 98575 9868, 98784 9S882 98976 99066 45 3(1 97982 98109 98x32 98351 98466 98577 98683 98786 98884 19897SI 99068 4« 45 97984 98,,, 98234 98353 98468 98579 98685 98787 98885 98979 99069 47 12 97986198113 98236 98355 98470 98580 98687 98789 98887 19898, 19907, 48 15 97988 I9SM; 97990 981 17 98238 98357 98472 98582 98688 98690 98791 98888 1 9S982 1 99072 4!) ~5?r 30 98240 98359 98473 98584 98792 98890 98984 99074 46 97993 98.20 98242 9836. 98475 98586 98692 98794 98892 98985 99075 51 13 97995 98.22 98244 98363 98477 9S588 98694 98796 98893 98987 99076 52 Is 97997 98.24 98246 98365 98479 98589 98695 98797 98895 98989 9907S 53 30 97999 98126 98248 98367 9848. 9859. 98697 98799 98896 98990 99079 54 45 98001 98128 98250 98369 98483 98593 98699 98800 98898 98992 99081 55 14 98003 98,30 98,7, 98485 98595 9870, 9S802 98900 1 98993 99082 5C 15 98006 9S.32 98254 j 98373 98487 98596 98702 98804 9890,198995 99084 57 3« 98008 98.34 98256 98375 98488 98598 98704 j 98805 98903 1 98996 99085 58 45 98CIO 9S.36I 98258 1 98376 98490_ 98600 98706 1 98807 98904 i 9899S 99087 59 S.-C. 1" 2" 3' 4 5 (i' 7" «' 9' 10' 11" 12- 13- 14' 15' 1 '■"■"■■°°° •■-• 1 TABLE 69 LOO. SINE SQUARE 174" ' 46' m° 176^ i;?" ■. 0- 15' 3(.' 45' 0' 1 15' 1 30' 45' 0' 1 15' 11 "SO"' 1 IMO"' ll'-Jl" 111.42"' IIMS'" ll"44"'ll''45"''lli'4fi'" llh47„. I1M8'"II'>4!»"> 9-9 9-9 9-9 99 9'9 99 9-9 99 99 9-9 99 o' n 99088 99'73 99=54 9933° 99402 9947' 99535 99595 99651 9970= 99750 15 99089 99'74 99=55 9933' 99404 9947 = 99536 99596 9965. 99703 19975' 1 30 99091 99176 99256 99333 99405 99473 99537 99597 99652 99704 9975' 3 45 9909: 99-77 99=57 99334 99406 99474 99538 99598 99653 99705 9975 = 3 1 99094 99.78 99=59 99335 99407 99475 99539 99599 99654 99706 99753 4 15 99095 99.80 99260 99336 99408 99476 99540 99600 99655 99706 99754 5 30 99097 99.8. 9926. 99337 99409 99477 9954' 996CO 99656 99707 997 54 6 4:> 99098 99183 99263 99339 994" 99478 9954= 9960. 99657 99708 99755 7 > 99100 99.84 99264 99340 994.2 99479 99543 99602 99658 99709 99756 8 .to 99'°' 99185 99265 9934' 9934= 994 '3 9948' 99544 99603 99604 99659 997'° 997" ?9"57 99757 9 10 99103 99.87 99267 99414 99482 99545 99659 45 99104 99.88 99268 99344 99415 99+83 99546 99605 99660 997.1 99758 11 : 99105 99.89 99269 99345 994 '6 99484 99547 99606 99661 997.1 99759 12 15 99107 99.9. 99270 99346 994 '8 99485 99548 99607 99662 997 '3 99760 13 ■M 99ioS 99.92 99272 99347 994.9 99486 99549 99608 99664 99714 99760 14 ir, 99 "o 99'93 99 = 73 99349 99420 99487 99550 99609 99664 99715 9976. 15 4 99111 99'95 99=74 9935° 994=' 99488 9955' 996.0 99665 997' 5 9976= 16 15 99.13 99.96 99276 9935' 99422 99489 9955 = 996.. 99666 997'6 99763 17 SO 99114 99>97 99=77 9935 = 994=3 99490 99553 996.2 99666 99717 99763 18 45 ft 9911S 9_?i99. 99200 99=79 99353 99355 99424 99492 _??154 99555 996.3 99667 997.8 99764 19 99117 99280 99426 9-967^ 99668 997.9 99765 20 16 99.18 99202 992X1 99356 994=7 99494 99556 996.5 99669 99719 99765 21 30 99.10 99203 99282 99357 99428 99495 99557 996.6 99670 99720 99766 22 45 99.21 99204 99283 99358 994=9 99496 99558 996'7 9967. 99721 99767 23 6 99.13 99206 99285 99360 99430 99497 99559 996.8 99672 99722 99768 24 15 99.24 99207 99286 9936. 9943' 99498 99560 996.8 99673 997=3 99768 2J 30 99.25 99208 99287 99362 9943 3 99499 9956. 996.9 99673 997=3 99769 26 45 99.27 992.0 99288 99363 99434 995CO 99562 99620 99674 997=4 99770 27 V 99.28 992.. 99290 99364 9943 5 9950. 99563 9962. 99675 997=5 9977' 28 15 99.30 992.2 9929. 99366 99436 99502 99564 99565 99622 99676 997=6 9977' 29 99.3. 99214 99292 99367 99437 995°3 996=3 99677 997=7 9977 = ■30- 46 99.32 99215 99294199368 99438 99504 99566 99624 99678 997=7 99773 31 8 99'34 992.6 99=95 99369 99439 995°5 99567 996 = 5 99679 997=8 99773 32 15 99'3S 99118 99296 9937° 99440 99506 99568 99626 99680 997=9 99774 33 30 99'37 992.9 99=97 9937 = 99442 995°7 99569 99627 99680 99730 99775 34 4^ 99'39 99220 99298 99373 99443 99509 99570 99628 9968. 9973' 99776 36 9 99140 99222 993C0 99374 99444 995.0 9957' 99629 99682 9973' 99776 3fi 1.1 9914. 99223 993°' 99375 99445 995" 9957 = 99630 99683 9973 = 99777 37 30 99.42 99224 993°3 99376 99446 995.2 99573 9963' 99684 99733 99778 3R 45 99'44 99226 99227 99304 99378 99447 9903 99574 9963. 99685 99686 99734 99779 39 40 10 99'4S 99305 99379 99448 99 5 '4 99575 99632 99734 99779 15 99.46 99228 99306 99380 99450 995 '5 99576 99633 996S6 99735 99780 41 .Vt 99.4S 99230 99308 9938. 9945' 995.6 99577 99634 99687 99736 9978. 42 45 99149 99231 99309 99382 9945 = 995'7 99578 99635 99688 99737 99781 43 11 991 5 1 99232 99310 99384 99453 99518 99579 99636 J996S9 99737 99782 <4 15 99152 99-34 993" 99385 99454 995.9 99580 99637 99690 99738 99783 45 SO 99' Si 99=3 5 993.2 99386 99^55 995=0 99581 99638! 9969' 99739 99784 46 45 99 1 S 5 99236 993'4 99387 99456 9952.1 99582 99639 [99692 99740 99784 47 It 991,6 99238 1993.5 99388 99457 99522 [99583 99640 1 99692 9974' 99785 48 15 99>s8 99 = 39 993''' 99389 99459 99523 99584199641 i 99693 9974' 99786 49 So 99'>9 99240 993 iS 9939' 99460 99524 99585 1996421 99694 9974= 99786 60 46 99,60 99=4= 993 '9 9939= 9946. 99525 99,86 '99642 99695 99743 99787 61 1* ,9.62 99243 993=" 99393 99462 995=6 ,99587 j 99643 , 99696 99744 99788 62 ir> 99.6, 99244 99311 99394 99463 995=7 ,99588199644, 99697 99744 99788 53 30 9916; 99246 99323 99395 99464 995=9 99589 99645199697 99745 99789 64 ».-. r,9,6fi 99H7 993=4 99397 99465 99530 99590 99646 99698 99746 99790 6ft 14 ,9.67 9924S' 99325 99398 99466 9953' 9959' 99647 99699 99747 99790 r,fl lA ,916, 99250199326 99399 99467 9953 = 9959= 99648 99700 99748 9979' 67 *l 99170 9925.199328:99400 99469 99533 99593 99649 9970. 99748 9979= 58 45 99'7^ 99=5=1993=919940' 99470 99534 1 99594 99650 1 99702 99749 99793 59 S.C. r 2' s' 4' 5' ri' T B' •»• 10" 11 i',>' 13 ir i.i' l>. 1. I'.Ils OOUOOOOIII 1 1 1 1 I 892 TABLE I-OO. SINE SQUARE 79° 177° 178^ 30' 1 45' 0' _U,' 1 30' ll''33'"'lli'54" 45' 0' IS' »0' 45' lli'SO" Ili'Sl" 11 '■52" lli'55" ll>'5(i" 1 l-iT^ IP' 58" 111' SO-" 9"9 99 9-9 9-9 !9'9 99 9-9 99 9" 9 (1 99793 99833 99868 99899 99926 99948 99967 99981 9999Z 9-999998 1.-. 99794 99833 99868 99899 99926 99949 99967 999S2 99992 9'9999?8 30 99795 99834 99S69 9990G 99926 99949 99967 999S2 99992 9999998 45 99795 99834 99869 99900 99927 99949 99968 99982 99992 9999998 1 99796 99S35 99870 99901 99927 99950 99968 99982 99992 9-999998 Ij 99797 99S36 99870 99901 99928 99950 99968 99982 99992 9-999998 »() 99797 99S36 99871 99902 99928 99950 99969 99983 99993 9 999998 4J 9979S 99837 99871 99902 99928 9995' 99969 99983 99993 9 999998 2 99799 99838 9987'- 99903 99929 9995' 99969 99983 99993 9-999998 lr> 99799 99838 998731 99903 1 99929 9995 > 99969 99983 99993 9999998 :)0 998CO 99839 99873 99903 1 99930 99952 99970 99983 199993 9-999998 4."> 99S0. 99839 99874 99904 99930 99952 99970 99984' 99993 9-999998 3 99S01 99840 99874 99904 99930 99952 99970 99984 99993 9-999999 l."« 99802 9984, 99875 99905 9993' 99953 99970 99984 99993 9-999999 :7 99941 9996, 99977 99989 1 99996 10-cooooo 40 15 99821 99857 99S89 999,8 99942 9996, 99977 99989 99996 10-000000 30 99821 99858 99890 999,8 99942 99962 99977 99989 99996 lo-ooooco 45 99822 99858 99890 999,8 99942 99962 99978 99989 99997 lo-oocooo II 99822 99859 99S91 999,9 99943 99962 99978 99989 99997 10-000000 15 99823 99859 99891 99919 99943 99963 99978 95990 99997 lo-ooocco 30 99S24 99860 99892 99920 99943 99963 99978 99990 99997 lo-oooooc 45 99824 99860 99892 99920 99944 99963 99979 99990 99997 lo-cooooo 1-2 99S25 9986, 99893 99920 99944 99964 99979 9999° 99997 lO-COOOCO 15 99826 99862 99893199921 99944 99964 99979 99990 99997 10-000000 30 99826 99862 99894 9992, 99945 99964 99979 99990 99997 lo-ooooco 45 99827 99863 99894 99921 99945 99964 99979 99990 99997 lo-ococoo 13 99827 99863 99895 99946 99965 99980 99991 99997 10-000000 15 99828 99S64 99895 999-3 99946 99965 999S0 99991 99997 10-ocoooo 30 99829 99S64 99896 999-3 99946 99965 999S0 99991 99997 10-000000 45 99829 99865 99896 99923 99947 99966 99980 99991 99998 10-000000 55 U 99S30 99X65 99897 99947 ,9966 999S, 99991 99998 10-ooooco 5fi 15 99831 99866 99897 99924 99947 99966 9998' 99991 99998 10-ooooco 57 30 9983. 99866 99898 99948 99966 999X1 99991 99998 lo-oooooo W 45 9983^ 99867 99868 99915 99948 99,67 99981 99992 99998 lo-oococo 69 1 '" 1 S93 L()(i.\l3 0-525 0-533 0-551 0-565 0-580 0-594 0-610 0-626 0-643 u M 0-471 0483 0495 0-507 0-5,9 0-532 0-546 0-559 0-574 0-588 0-604 0-610 34 rt.'i 0-456 0-467 0-480 0-501 0-51410-526 0-540 0-553 0-567 0-581 0-597 3.5 M 0-440 0-450 0-46, i 0-471 0-484 0-495 0-5=8 0-510 0-533 0-54S 0-560 0-575 3« :t7 0-414 0-434 0-445 1 0-455 0-466 0-478 0-4X9 0-50, 0-514 0-516 0-540 0-553 37 :tit 0-408 0-4I8 0-418 j 0-438 0-449 0-460 1 0-47, 0-482 0-494 0-507 0-519 0-531 33 :«» o:v)± 0-402 0-4,1 1 0-411 0-432 o-Mi 1 0-453 0-464 0-4-5 0-487 0-499 0-5.1 J9 UT "•377 0-386 0-396 0-405 0-415 0-425 1 0-435 0-447 0-457 0-468 0-480 0-491 411 41 0-361 0-371 0-380 c-389 0-398 0-408 0-4,8 0-428 0-438 0449 0-460 0-472 41 42 0-547 °-355 0-364 0-371 0-382 0-391 0-4CO 0-4,0 0-420 0-431 0441 0-452 42 Ct 0-33, 0-340 0-34810-356 0-365 0-374 0-383 0-393 0-401 0-411 0-411 0-433 4:1 44 0-3.6 0-324 0-331 lc-340 0-349 0-357 0-366 0-375 0-384 0-394 0-404 0-4:4 44 4.'i 0-301 0-309 0-3,6 0-324 o-3;3 0341 1 0-349 0-358 0-367 0-376 0-385 C-39S 4.5 4n 0-286 0-293 0-3C, 0-3.8 0-3,6 0-324 0-332 0-341 0-349 0-358 0-36,- 0-576 4t! 47 0-271 0-278 0-2X5 '>-^9'- 0-300 0-308 ,0-315 0-313 0-331 0-340 0-349 0-358 47 48 0-255 0-162 0-169 0-276 0-184 0-291 C199 0306 0-3,4 0-311 0-331 0-339 4H 49 CV240_ 0-247 0-154 0-260 0-167 0-175 k-i8i 0-289 0-297 I0-30S 0-3,1 o-;i. 49 :■()' 0225 0-131 0-138 0-144 0-25, 0-158 c-165 0-171 0-279 Ol87 0-194 0-301 ■so .'.1 0-109 0-2,6 0-221 0-228 0-235 0-141 o-»48 0-155 0-262 0-169 0-176 0-184 SI .52 0-.94 0-200 0-206 1 0-2,2 0-2,8 0-215 : 0-131 0138 0-244 0-15, 0-258 0-165 62 .5.1 0-178 0-184 0-190 0, 96 0-202 o-ioX 0-1,4 0-227 0-133 0-140 0-147 63 .54 0-162 0-168 0-173 °"'79 0,85 0-191 0-197 0-203 0-109 0-121 c-128 64 .55 0-146 0-152 0-157 0-162 o-,68 0-174 o''79 0-185 0-191 0-197 0-1C4 c-iio ftfl hV, 0-130 o'35 0-140 0-146 015, 0,56, o-.6^ 0-168 0-I73 0-179 o-,85 0,91 r>K .57 0-114 o-i,8 o-]lt\l-\?, 0-134 0-.39 10-144 0-150 0-155 o-,6c 0,66 o-,7i 67 .511 0-097 o-ioo 0-116 o-iiij 0-116 0-131 0-137 0-141 0,48 0-153 ,511 .59 ocgo 0-062 0-084 0-089 1 00,4 0-071 1 0-076 0-098 o-,03'o-,oS 0-085 0090 0113 0-094 Ollg 0-113 0-1 iS _o^4 S9 0-067 0-0X0 0-099 0-104 0-109 01 14 00 •■1 0045 1 ° C4V 0-053 : "Oj* 0-062 0-066 C-071 0-075 o-cXo 0-0X5 0-089 0094 r.l <;•.' 3-017 1 0-^31 0-O3J 0-039 0-04} 0-047 ' o-ori 0. .6,0-060 0-C65 0-C69 0-07^ B2 894 TABLE 70 1-OOAlUTII.MS FOR COMPUTINO THE REDUCTION TO THE MERIDIAN, AT SEA. Part I. Latitude and Declination of the same name. Lut. ~0« Declination. ;;; 12= 0-974. 1.^° 14^ IS" lfi° \r 18° 1 vr 20° 21° 22 = •23 = 0-938 0-904 0-873 0-844 o-8i6 0-789 0-764 740 0-717 0-695 0-673 ~0° 0-972 0-936 0-90Z 0-871 0-841 0-813 0-787 761 0-737 0-7.4 0-69. 1 1-051 1-009 0-970 0-934 0-900 0-868 0-839 0-811 784 0-758 0-734 0-710 2 1-097 1-049 1-007 0-967 0-931 0-897 0-866 0836 807 0-7S1 0-755 0-730 3 I-I47 1-094 1-047 1-004 V^J 0-928 0-895 o;863 833 0-804 0-777 0-751 4 1-204 I-I45 1-092 1-045 0-962 0-925 859 0-829 0-801 0-773 6 1-270 I -20 I 1-142 1-089 1-042 0-999 0-959 0-922 888 0-856 0-825 0-797 C, 1-348 1-267 1-199 1-139 1-086 1-039 0-995 0-956 9.9 0-884 0-852 0-S21 7 '•345 1-264 1-196 .■136 1-083 1-035 0-992 0-915 0-880 0-848 8 ~nr 1-342 1-261 1-193 1-133 1-080 988 _o^948_ 0-911 0876 !t 1-339 1-258 .■.89 ~i^7I^ 1-076 028 0-984 0-944 0-906 10 ■-336 1-254 1.85 1-125 072 1-023 0-980 0-939 U 1-332 1-250 121 1-067 0-975 12 .-328 1-246 ■77 1-116 1-063 13 1-323 242 1-172 rl'st 14 1-319 1-237 1-.67 1-106 15 1-314 1232 1.62 Hi 1-332 .-308 1-226 17 1-250 1-328 .•303 18 1181 ,-246 • -32, 1!) 20 1-121 I-177 1-242 1-319 •20 1-067 I-I16 1-172 1-237 1-314 21 1-019 1-063 l-l 12 1-167 1-232 1-308 22 0-975 I-OI4 1-058 i-io6 1-162 1-226 1-303 23 0-934 0-970 I-OC9 1-052 I-lOl 1-156 1-221 1-297 24 25 0-897 0-929 0-965 1-004 1047 1-095 1-151 1-2.5 1-291 23 26 0-861 0-890 0-924 0-959 0-998 1-041 1-090 1-144 1-208 !-202 21) 27 0-828 0-856 0-886 0-918 0-953 0-992 1-035 1-083 1-13S 1-278 27 28 0-797 0-823 0-S50 0-880 0-912 0-947 0-986 1-028 1-076 1-131 .•195 1-27. 28 1 2!) "So" 0-767 0-791 0-8.7 0-844 0-874 0-906 0-940 0-979 1-021 1-069 1-.24 1-1S8 21»| 0-739 0-761 0-785 0-811 0-838 0-867 0-934 0-972 1-014 1-062 1-117 31) ai 0-712 0-733 0-755 0-779 0-804 0-831 o-86o 0-892 0-926 0-965 1-007 1-055 31 32 0-686 0-706 o'726 0*748 0-772 0-797 0-824 0-853 0-885 0-919 0-957 0-999 32 3:1 0-661 0-679 0-699 0-720 0-742 0-765 0-790 0-817 0-846 0-877 0-911 0949 33 M 0-636 0-654 0-672 0-692 0-734 0-757 0-782 0-809 0:838 0-869 0-903 SI 33 0-612 0-630 0*647 0-665 0-685 0-705 0-727 0-750 0-774 0-829 0-86. 33 36 0-590 0-606 0-622 0-640 0-6,8 0-677 0-697 0-719 0-742 0-766 0-792 0-S21 3a 37 0-568 0-583 0-598 0-615 0-632 0-650 0-669 0-689 0-710 0-733 0-758 0-784 S7 38 0-546 0-560 0-575 0-591 0-607 0-624 0-642 0-661 0-681 0-702 0-724 0-749 38 39 0-525 0-538 0-552 0-530 0-567 o-5?2 0-599 0-6,5 0-633 0-652 o'672 0-693 0-715 39 40 0-504 0-517 0-544 0-559 0-574 0-590 0-607 0-624 0-643 0-662 0-683 40 41 0-484 0496 0509 0-522 0-536 0-550 0-565 0-5S1 0-597 0-615 0-6.3 0-653 41 42 0-464 0-47 5 °'*ll 0-500 0-5.3 0-527 0-541 0-556 0-572 0-588 0-605 0-623 42 43 0-444 0-455 0-466 0-478 0-49. 0-504 0-5.7 0-532 0-546 0-562 0-578 0-595 43 44 0-424 0-45 5 0-446 0-457 0-+69 0-482 0-494 0-508 j 0-522 0-536 0-552 0-568 44 45 0-405 0-415 0-426 0-436 0-448 0-460 1 0-472 0-484 0-498 0-511 0-526 0-541 43 4t; 0-3X6 0-395 0-405 0-4.6 0-427 0-438 0-449 0-46. 0-474 0-487 0-501 0-515 40 47 0367 0-376 0386 0-396 0-406 0-4.6 0-42-' 0-439 0-451 0-463 0-476 0-490 •17 1 48 0-348 0-357 10-366 0-375 0-385 0-395 0-406 0-417 0-428 0-440 0-452 0-465 48 49 0-33710-346 flJSS 0-365 0-374 0-384 0395 0-405 0-4.7 0-428 0-440 49 50 0-310 0-318 0-327 0-315 0-344 0-354 0-363 0-37310-383 0-394 0-405 0-4.6 50 51 0-291 0-299 0-307 0316 0-324 0-333 0-342 0-351 0-361 0-371 0-381 0-392 51 SS 0-273 0-280 0-296 0-304 0-312 0-330] 0-339 0-349 0-359 0-369 52 53 0-254 0-261 0-269 0-276 0-284 0-292 0-300 0-309 0-317 0-326 0-336 0-346 53 54 0235 0-242 0-249 0-257 0-264 0-X71 0-279 0-287 0-296 0-304 0-313 0-322 54 55 0-2I6 0-223 1 0-230 o'-'f 0-244 0-251 0-258 0-266 0-274 0-282 0-291 0-299 55 56 0197 0-204 0-2IO 0-225 0-230 0-237 0-245 0-252 0-260 0-268 0-277 58 57 0178 0184 ' 0-190 0-197 0203 0-210 o-2i6 0-223 0-231 0-238 0-246 0-254 57 58 0-159 0164 |o-i7o 0-176 0-183 0-189 0-195 0-201 0-209 0-2l6 0-223 0-231 58 59 0139 0-145 o-'SO 0-156 O-.62 o-i68 0-174 0-.80 0-.87 0-194 0-20I 0-208 59 60 0II9 0-125 0-Y30 0-135 0-141 0.47 0-153 0-159 0-.65 0-171 0-178 0-185 (iO 61 0099 0-104 i 0-109 0115 o-i;o 0-125 0-131 0-137 0-.43 0-149 0-155 0-161 (il «'J 0079 0-084 o-oSS 0-093 0-099 0-104 o-iio 0-I15 0-120 0-126 0-132 0-.3S (;2 TABLE 70 LOGAKITHMS j FOR COMPUTING THE REDUCTION TO THE MERIDIAN, AT SEA. Part I. Latitude and Declination of the same name. 1 Dkc LI NATION. .at. ■ - - - - . Lai. I-M 25' 1 26° 1 27" 1 28° 29° 1 33° 31° 32° 33° 34° 35° 0°' 0-652 0-632 0-613 0-594 0-575 0-SS7 1 0-539 0-522 0-505 0-489 0-472 O-4S6 ^ 1 0-670 0-649 I 0-629 0-609 0-590 0-571 ,0-553 0-535 0-5.8 0-501 ! 0-484 0-457 1 2 0-688 0-666 0-645 0-625 0-605 0-586 0-567 0-548 0-530 0-513 0-496 0-478 2 3 0-707 0-684 0-662 0-641 0-621 i 0-601 0-58. 0-562 0-543 0-525 0-508 0-490 3 4 0-727 0-703 , 0-680 0-65S ' 0-637 0-616 0-596 1 0-576 0-557 0-538 0-520 0-5021 4 5 0-747 0-723 0-699 0-676 0-654 0-632 06. 1 0-591 0-571 0-551 0-532 o-5<4 i 6 0769 0-743 0-718 0-694 0-67. 0-649 0-627 0-606 0-5S5 0-565 0-545 0-526! 6 7 0-793 0-765 0-739 0-714 0-689 0-666 0-644 0-622 o-6oi 0-5S0 0-559 0-539 ! ' 8 0-817 0-78S 0-760 0-734 0-709 0-6S4 0-661 i 0-63S 0-6i6 0-595 0-574 0-553 ^ 9 0-844 0S.3' 0-783 0-755 0-729 0704 ' 0-679 ! 0-655 0632 0-610 0-589 0-567 1 9 10 0-872^ 0-839 0-808 0-778 0-750 0-724 0-6 8" 0-673 0-649 "0-626 0-604' "0-5S2 I 10 1 11 0-902 0-S67 0-834 o-,^o3 0-773 0-745 0-718 0-692 0-667 0-643 ! 0-620 0-597 11 12 0-935 0-897 0-862 0-829 0-797 0767 0-739 0-712 0-6S6 0-661 0-637 0-613 12 13 0-970 0-930 0-892 0-857 0-823 0-791 0-761 0-733 0-706 0-680 0-654 0-630 13 14 I -010 0-965 0-924 0-8S6 0-850 08.7 0-785 0-755 0-726 0-699 0673 0647 14 IS I -OS? 1-004 09 59 0-918 0-8S0 0-S44 o-Su 0-779 0-749 0-720 0-692 0665 15 16 I-IOI I -047 0-Q98 0-953 0-911 0-S74 o-S;S 0-804 0-772 0-742:0-713 0-685 16 17 1-157 I 096 I -04 1 0-992 0947 0-905 o-f''67 0-831 0-797 0-765 0-735 0-705 17 18 1-222 I -151 1-0S9 1-035 0-9S6 0-940 0-S9S 0-S60 0-824 0-790 0-758 0-727 18 19 '•^97 I-216 I-I45 .-0S3 I 029 0-980 0-934 ' 0S91 0-853 0-S17 0-782 0750 19 20 1-291 I-2'O 1-138 1-076 1-022 0-973 0-927 0-8S4 0-S46 "0-809" 0-774-i 20 SI 1-285 1-203 1-131 1-069 I -01 5 0965 0-919 0-S77 1 0-S3S o-Soo i 21 22 1-278 1-.96 I -124 I -061 1-007 0-957 0-911 0-868 0-829! 22 23 1-271 I-.89 1-1.7 1-054 0-999 0-949 0-903 0-860 23 24 1-264 1-1S2 1-109 1-046 0-991 0-941 0-894 1 24 25 1-256 i-'73 I-IOl I -03S 0-983 0933 25 26 1-248 1-165 1 -092 1 029 0-974 ; 26 27 1-239 I -1 56 1-0S3 1-020 27 28 1-230 1-147 1 -074 28 29 1-264 ' 1-22 1 .-.38|_29_ "niT 1-1^2 t-256 T^l 30 31 1-109 I -1 74 1-248 3] 32 1-046 l-ioi 1-166 1-29 32 33 0-991 1-03S 1093 I-I57 1-230 33 S4 0-941 0-9S3 1-030 1-04 1-147 I -22 I 84 35 0-S95 ovn 0-974 1-075 1-138 I-2I2 35 36 0-S52 0-886 0-924 0-965 1-0.2 1-065 '-'28 I 202 36 37 0-812 0-843 0-877 0-914 0-955 l-002| 1-055' i-"8 1-191 37 38 0-775 0-803 o-,^34 0-867 0-904 0-945 : 0-992 I -045 1-107 I -181 38 39 0-740 0-765 0-793 0-823 0-857 0-894 : 0-935 0-9S2 1 034 1-097 1 •■'7o 39 40 0-706 0-730 "0-755" 0-783 0-S.4 0-S47' 1 0-883 0-924 0970 1-023 ! 1-086 7^8 40 41 0-673 0-696 0-719 0-745 0773 0803 0-836 : 0-872 0-914 6-958 ! 1-0.2 1-075 41 42 0-642 0-663 0-6S5 0-709 0-734 0-762 0-792 : 0-825 0-S61 0-901 : 0-947 I -000 42 1 43 0-613 0-632 0-653 0-675 0698 0-723 0-751 0-781 0-813 0-849 0-889 0-934 43 44 0-5S5 0602 0-621 0-642 0-664 0-687 1 0-712 ,0-739 0-769 0-801 1 0-837 0-877 ■14 4S 0-557 0-574 0-591 0610 0631 0-652 1 0-675 °'7oo 0-727 0-756 ! 0-789 0-825 45 46 0-530 0-546 0-562 0-580 1 0-599 0619 0-640 ; 0663 0687 0-714 0-744 0-776 46 47 0504 o-5'9 0-534 0-551 ' 0-56S 0-587 , 0-607 0-628 o-6;o 0-675 0-701 0-731 47 48 0478 0492 0507 1 0-522 \ 539 ,0-556 0-575 0594 0-615 0-637 0-662 0-688 48 >9 .50 0-453 0428 _^o-466 0-480 0-494 0-510 0-526 a;54j; 0-56. 0-58. 0497 1 0-513 ; 0-530 0-548 0-601 0-624 0-648 0-610 49 SO ■^0-440 -0-453 ' 0-467 ro-4S2 0567 1 0-588 ' 51 0403 ,0-415 0-427 • 0-440 1 0-454 0468 0-483! 0-499 0-516 0-534:0-553 0-573 51 52 0-379 0-390 0-402 , 0-4.4 0-427 0-440 0454 ; 0-469 0-4S5 0-501 1 0-519 0-538 52 53 0-356 0-366 0377 0-388 0-400 ,0-413 0-426 0-440 0-454 0-470 1 0-4S6 0-504 53 54 0332 0-342 0-352 0-363 0374 •0-3S6 0-398 0-4.1 0-425 0-439 ! 0-455 0-471 54 55 0-308 0-3.8 0-328 0-338 0-348 0-359:0-371 0-383 o-3.,6 0-410 ; 0-424 0-438 55 56 0-285 0-294 0-303 o-3'3 0-322 0-3.33 0-344 0-356 0-368 0-380 I 0-394 0-408 5G 57 0-262 0-270 0279 0-288 0-297 0-307 1 0-317 0-328 0-340 0-352 0-364 0-377 57 58 o-23« 0-246 0-254 0-26J 0-272 0-2-Si 1 0-291 0-301 0-3.2 0-323 0-335 0-347 58 59 0-2.5 0-222 0-230 0-238 0-247 0-255 0-264 ; 0-274 0-284 0-295 0-306 0-317 59 -Lo- 0-I9I o-igS" 0205 0-2.3 0-22I 0230 0238 0-247 0-257 0267 0277 0-288" "eo ci 0-168 0-174 .81 0-.8S 0196 0204 0-212 0-220 0-229 0-238 1 0-248 0-258 61 6S 0-144 0-150 157 0.64 171 I7S OIS6 j 0-194 0202 0-229 62 LOGARITHMS i FOR COMPUTING THE REDUCTION TO THE MERIDIAN, AT SKA. | I'art II. Latitude and Declination of co«ft-ffry Niinies. Lat, Declikaticv. 0° " 1^ 2° 3° 4° 5° 1 C° r 8= 9° 10" 11° I. at. 0" '•359 1-279 1-212 1-153 i-ioi 1-055 1-012 1 .-360 1-280 1-213 1-154 1-056 1-014 0-975 3 1-360 1-281 1-213 1-155 1-103 1-057 1-015 0-976 0-941 S 1-360 1-281 1-213 1-155 1-104 .-058 1-016 0-977 0-942 0-909 4 1-360 1-280 1-213 1-155 I -104 1-058 1-016 0-978 0-943 0-910 0-879 5 • 359 1-280 1-213 1-155 1-104 j;o58 1-016 0-978 0-943 0-910 o-88o 0-851 6 279 .■213 1-155 1-104 1-058 0-979 0-943 0-911 0-880 0-852 0-825 7 I- 1 54 1-103 1-058 .016 0-978 0-943 0-911 0-881 0-851 0-825 0-800 B '53 1-057 1016 0-978 0-943 0-911 0-85210-825 0-800 0-776 8 9 .-056 1-015 0-977 0-943 0-8S0 0-852 0-825 1 0-800 0-776 0-754 9 1(1 °55 1-014 0-976 0-942 0-910 0-880 0-852 0-825 0-800 0-776 0-754 0-732 1 10 II 0-975 0-941 0-909 0-879 0-851 0-825 0-800 0-776 0-754 0-732 0-711 1 11 12 o 974 0-939 0-907 0-878 0-850 0-824 0-799 0-775 0-753 0-732 0-711 0692 ' 12 i:( o 938 0-906 0-876 0-849 0-823 0-798 0-775 0-752 0-731 0-691 0-672 13 u o 904 0-875 0-847 0-821 0-797 0-774 0-751 0-730 0-710 0-69I 0-672 0-654 14 15 o 873 0-846 0-820 0-795 0-772 0-750 0-729 0-709 0-690 0-671 0-653 0-636 15 Ki o 844 o-8i8 0-794 0-771 0-749 0-728 0-708 0-689 0-670 0-653 0-635 0-6,9 16 17 o 816 0-792 0-769 0-747 0-726 0-706 0-687 0669 0-651 0-634 0-617 0-602 17 IK o 789 0-767 o'745 0-724 0-705 0-686 0-668 0-650 0-633 0-617 o-6o. 0-586 18 1!) o 264_ o'743 0-722 0-703 0-684 0-666 0-648 0-632 0-6.5 0-600 0-584 0-570 0-554 19 20" ~^ 74° 0-720 0-700 0-682 0-664 0-630 0-614 0-598 0-583 0-568 21 o 717 0-698 0-679 0-661 0-644 o-6iS o-6i2 0-596 0-581 0-567 0-553 0-539 1 22 o 695 0-676 0-659 0-642 0-625 0-609 0-594 0-579 0-565 0-551 0-537 0-524 22 23 o 673 0-656 0-639 0-613 0-607 0592 0-577 0-563 0-549 0-535 0-522 0-509 '23 24 o 65. 0-636 0-621 0-604 0-589 0-575 0560 0-547 0-533 0-520 0-508 0495 24 25 o 631 0-616 0-601 0-586! 0-572 0-558 0-544 0-531 0-5.8 0-505 0-493 0-481 25 •-'« o 613 0-598 0-583 0-569 0-555 0-541 0-528 0-515 0-503 0-491 0-479 0-467 2»; 27 o 594 0-579 0-565 0-551 0-538 0-525 10-512 0-500 0-488 0-476 0-465 0-454 27 211 o 575 0-56. 0-548 0-535 0-522 0-509 0-497 0-485 0-473 0-462 0-45. 0-440 28 2fl o 557 0-544 0-531 0-5.8 0-506 0-494 0-482 0-470 0-459 0-44S 0-437 0-427 29 Ifo" '^ 540 0-527 0-514 0-502 0-490 0-478 0-467 0-456 1 0-445 0-434 0-425 0-414 30 :ti o 521 0-510 0-498 0-486 0-463 0-452 0-431 0-421 0-401 31 :<2 o 505 0-493 0-482 0-470 0459 0-448 0-438 o-4^7 0-417 0-407 0-397 0-388 32 3:t o 489 0-477 0-466 0-455 0-444 0-434 0-423 0-413 0-403 0-394 0-384 0-375 33 34 o 472 0-46. 0-450 0-440 0-429 0-419 0-409 0-399 0-390 0-380 0-371 0-362 34 .•t.-i o 456 0-445 0-43 5 0-424 0-414 0-405 0-395 0-386 0-376 0-367 0-358 0-349 35 :«; o 440 0-429 0-419 0-4CO 0-390 10-381 0-372 0-363 0-3 54 0-345 0-337 •Mi 37 o 4*4 0-414 0-404 0-395 0-385 0-376! 0-367 0-358 0-350 0-341 0-333 0-324 a7 .-ill o 408 0-399 0-389 0-380 0-371 0-362 1 0-353 1 0-345 0-336 0-328 0-320 0-312 3li JUL - i93 577 0-384 0-365 0-357 0-348 0-34010-331 0-323 o-3'5 0-302 0-307 0299 0-287 39 40 0-368 0-360 0-351 0-342 c-334 0-326 1 0-3.8 0-310 0-294 41 o 362 0-353 0-345 0-336 0-328 0-320 0-312 0-304 0-297 0-289 0-2S2 41 42 o 347 0-338 0-330 0-322 0-314 0-306 0-299 0-291 0-284 0-276 0-269 0-262 42 43 o 33' 0-323 0-315 0-308 0-3C0 0-292 0-2S5 0-278 0-270 0-265 0-256 0-249 43 44 o 3.6 0-308 0-301 0293 0-286 0-279 0-264 0-257 0-250 0-243 0-237 44 4r, o 301 0-294 0-286 0-279 0-272 0-265 0-258 0-251 0-244 0-237 0-23. 0-224 45 4fi o 286 0-279 0-271 0-264 0-257 0-251 0-244 0-237 0-231 0-224 o-2i8 0-21 , 4fi 47 o ^7' 0-264 c-257 0-250 0-243 1 °-i37 0230 0-224 0-217 0-211 0-205 o-,98 47 48 o ^55 0-249 0-242 0-235 0-229 1 0-223 o-2i6 0-210 0-204 10- 19S 0191 0-185 4.S 4!l o ^40 0-234 0-227 0-221 0-215 0-208 0-202 0-196 0-190 lo 184 0-.7X 0-172 4a .'.(1 ~^ 225 0-219 0-212 o-2o6 0-200 0-194 0-.S8 0-182 0-176 0-171 0-165 0-159 .51) ;>! o 209 0-203 0-197 0-191 0-185 0-180 0-174 0-.68 0-163 0-157 0-151 0-145 51 .V.' o '94 0-188 0-182 0-17* 0-171 o-]% 0-.60 0-.54 0-149 0-143 0-138 o-,32 52 53 o '73 0'172 0-167 0-161 0-156 0-145 0-140 0-134 01 19 0-124 o-,i9 63 51 c 162 0-157 0-I5I 0-146 0-141 °o'\ll 0-130 0-125 0-115 o-iio 0-105 51 A5 o ■46 0-141 o;j36 0-131 0-125 0-115 o-iio 0-105 0-101 0-096 0-09. 55 50° 30° i 21° 1 22"^ 1 -23' '"o' 0-974 0-938 0-904 0-873 0-8441 0-816 0-789 0-764 0-740 0-7,710-695 0-673 "o' 1 °'93» 0-906 0-87S 0-846 0-818 0-792 0-767 0-743 0-720 0-698 1 0-676 0-656 I 1 0-907 0-876 0-847 0820 0-794 0-769 0-745 0-722 0-700 0-679 0-659 0-639 2 3 0-878 0-849 0821 0-795 0-771 0-747 0-724 0703 0-682 0-66, 0-642 0-623 3 4 0-850 0-S23 0-797 0-772 0-749 0-726 0-705 0-684 0-66+ 0-644 0-625 0-607 4 0-82+ 0-798 0-774 0-750 0-728 0-706 0-6S6 0-666 0-646 0-628 0-609 0-592 5 G 0-799 0-77S 0-751 0-729 0-708 0-687 0-66S 0-64* ' 0-630 0-6,2 0-594 0-577 6 7 0-776 0-752 0-730 0-709 0-689 0669 0-650 0-63-. 0-6,4 0-596 0-579 0-563 7 8 ■^"753 0-731 0-710 0-690 0-670 0-65, 0-633 0-6,5 0-598 0-58, 0:565 0-549 8 » 0-752 0-691 0-67. 0-653 0-634 o-6,8 0-6,7 0-600 0-583 0-567 0-537 0-535 9 10 -w 0-711 0-691 0-672 0-653 0-635 0-60, 0-584 0-568 0-553 0-522 II 0-692 0-672 0-654 0-636 0-6,9 0-602 0-586 0-570 0-554 0-539 0-524 0-509 II 12 0673 0654 0-636 0-6,9 0-603 0-5S6 0-57, 0-555 0-540 0-525 0-5,, 0-497 12 13 0-654 0-637 0-620 0-603 0-587 0-571 0-556 0-54, 0-527 0-5,'. 0-498 0-485 13 14 0-636 0-620 0-603 0-587 0-572 0-557 0-542 0-527 0-513 0-499 0-486 0-473 14 IS 0-6,9 0-602 0-587 0-572 0-557 0-542 0-528 0-5,4 0-500 0-487 0-474 0-46, 15 k; 0-603 0-5S7 572 0-557 0-542 0-528 0-5,5 0-501 0-488 0-475 0-462 0-449 Iti 17 0-586 0-571 0-557 0-5+2 0-528 0-5,5 0-50. 0-488 0-475 0-463 0-450 0-438 17 IK 0-571 0-556 0-542 0-528 0-5,5 0-50, 0-488 0-475 0-463 0-451 0-438 0-426 IB I!) °s;5 0-541 0-527 oj_,4_ 0-50, 0-488 0-475 ^461 0-45. 0-439 c-427 0-4,5 I."* •211 0-540 0-527 0-513 0-500 0-488 0-475 0-463 0-45, 0-439 0-427 0-4,6 0-404 2(1 21 0-525,0-512 0499 0-487 0-475 0-462 0-45. 0-439 0-427 0-4.6 0-405 0-393 21 22 0-511 0-49X 1 0-486 0-4-4 0-462 0-450 0-438 0-427 0-4,6 0-405 0-394 0-3X3 2-J 2:1 C497 0-485 I 0-472 0-46, 0-449 0-426 0-4.5 0-404 0-393 0-383 23 84 0-483 0-471 0-459 0-448 0-437 0-425 0-414 0-404 0-393 0-3S2 0-372 0-^62 21 sa 0469 0-458 0-446 0-435 0-424 0-41J 0-403 0-392 0-382 0-372 0-36, 0-351 28 M 0-456 0-445 0-434 0-423 0-4,2 0-402 0-39, 0-38, 0-371 0-36, c-35. 0-341 26 27 0-432 0-421 0-4.0 0-400 0-390 0-380 0-370 0-360 0-350 0-340 0-331 27 «H 04,9 0-419 0-408 0-398 0-388 0-37S 0-368 0-359 0-349 0-339 0-330 0-320 ?n 2!» 0-416 0403 0-406 0-396 0-384 0-386 0-374 0-376 0-367 0-357 0-347 0-336 0-327 0-329 1 0-320 0-310 2» 0-394 0-364 0-355 0-346 0-3,8 0309 0-300 "30 31 039. 0-381 0-372 0-362 0353 0-344 0-335 0-326 0-3,7 0-30S 0-299 0-290 3! :« 0-378 0-369 0-359 0-350 0-34, 0-332 0-323 0-3,5 0-306 0-297 0-289 0-2S0 32 :« 0366 0-356 0-347 0-338 0-330 0-321 0-3,2 0-304 0-295 0-2S7 0-278 0-270 33 :u "■353 0-3-W 0-335 0-327 0-3,8 0-310 0-301 0-293 0-285 0-276 0-268 0-160 34 :j3 0-341 0-332 0-324 0-3,5 0-307 0-298 0-290 0-282 0-274 0-266 0-25S 0-250 3S .Mi 0328 0-320 0-312 0-3-3 0-295 0-287 0-279 0-27,10-263 0-256 0-248 0-240 36 .■«7 0-3.6 0-308 0-300 0-292 0-284 0-276 0-268 0-260 0-253 0-245 0-237 0-230 37 :»« 0304 0-296 0-288 0-280 0-272 0-265 0-257 0-250 0-242 0-235 0-227 JH au 0-291 0-284 0276 0-26, 0-261 0-254 0-246 0-239 0-231 0-224 0-217 0-210 39 4U 0279 0-.-2 0-264 0-257 ; 0-250 0-242 0-235 0-22S 0-22, 0-214 0-207 ~'W "40 41 0-267 0-260 0-252 0-245 0-238 0-231 0-224 0-2,7 0-2,0 0-203 0-.96 c-188 41 12 0255 0-247 0-240 0-233 0-227 0-220 0-2,3 0-206 0-199 0,92 o-,86 c-,78 12 43 0-242 0-235 0-228 1 0-222 1 0-215 o-2o8 0-202 o-,95 o-,88 o-,82 o-,75 o-,-)8 13 44 230 0-223 0-216 1 0-210 0-203 0-197 o-,90 o-,84 o-,77 o-,7i 0-164 G-ij8 44 45 0-217 0-21I 0-2041 0-198 1 0-192 0-185 0-179 0-173 o-,66 0-.60 0-154 0-147 4t 4C 0-205 0-198 0-192 0-186 0-180 O-.74 0-167 o-,6, 0-155 0,49 0-143 0,36 46 47 0-192 0-186 0-180 0-174 0-168 o-,6l 0-156 o-,i;o 0-.44 0.38 0-132 o-,26 47 411 c-179 0-173 0-168 0-162 0-156 o-,50 0-144 o-,38 o-,32 o-,27 0-,2l o-"5 48 4'J 0-167 0161 0-155 0-149 0-144 0-.38 o-,32 o-,26 0-,2, o-,,5 0-.09 c-,04 ■I9 .'Ml 01 54 0-148 0-142 0-137 1 0-131 ! 0126 1 o-,2c o-"5 0,09 o-,04 0-C98 0-C93 'to 61 C14& 0-135 0-130 o-,24 1 0-1,9 0-1,3 ;o-,o8 0-.03 0-097 0-092 0-086 0-081 51 .'.2 r.-I27 0-122 0-117 o-iii 1 o-io6 0-101 0-096 0-090 0-0S5 o-c8o 0-C75 0069 52 S3 0-114 O-iOg 0-103 o-oe>8 0-093 0-08S o-o^3 0-078 O-073 0-068 0-1)63 0-058 63 ri4 o-ioo 0-095 0-090 0-085 0-080 0-075 0-070 0-065 o-c6o 0-055 0-05, 0046 64 65 0-086 0-081 0-076 0-072 0-067 0-062 1 0-057 0-C52 0-C48 0-C43 0-038 0-033 55 .'iU 0-072 0-067 0-063 0-058 i 0-053; 0-049 10-044 0-039 0-035 0-030 0-025 0-C2I 58 .'■7 0-057 0-053 0-048 0-044 ! 0-039 1 0-035 0-030 0-026 0-017 o-coS ft7 .'iK O-043 0-038 0-034 1 0-030 0-025 10021 ln-017 0-0,3 0-CC8 0-003 1 9-999 9995 6H S!l C-C28 0-019! 0-0.5 9V96 999^ 9988 9-998 9-994 9-99015-985 9^98^ 59 "60 (;() C-C12 |o-oo8 0-00^ 1 v-OOO 9-984 9-980 9-97619-97. 1 9*967 (ii 9-996 1 9-992 9-989 ,9-985 1 9-98. t 9977 '9-973 9-969 9965 9-961 1 9-957 9-953 «l 62 9-980 1 9-976 ; 9-973 j 9-909 I 9-965 9W*" 1 yys? 9-954 .,-950 9-9461 9-94; 19-938 62 896a LOGARII'H.MS FOR COMPUTING THE REDUCTION TO THE MERIDIAN, AT SEA. Part II. Latitude and Declination of contrary Names. Declination. Lat. Lat. 24° 1 25° 26° 27° 28° 29° 30° _31° 32° 33° 040 35° 0° 0-652 ' 0-632 0-613 0-594 0-S75 0-557 0-539 0-522 0-505 0-489 0-472 0-456 0° 1 0-636 0-617 0-598 0-579 0-56. 0-544 0-526 0-510 0-493 0-477 0-461 0-445 1 2 0620 0-601 0583 0-565 0-548 0-53' 0-514 0-498 0482 0-466 0450 0-435 2 3 0-605 o-5«7 0569 0-551 0-535 0-518 0-502 0-486 0-470 0-455 0-439 0-424 3 4 o-5Sy , 0-572 0-555 0-538 0-522 0506 0-490 0-474 0-459 0-444 0-429 0-414 4 5 0-574 ,0-558 0-541 0-525 0-509 0494 0-478 0-463 0448 0-433 0-419 0-404 5 6 0-560 0-544 0-52S 0-512 0-497 0-482 0-467 0-452 0-437 0-423 0-409 0-395 6 7 0-546 0-531 0-515 0-500 0-48S 0-470 0-456 0-441 0-427 0-413 0-399 0-385 7 8 0-533:0-518 0-503 0-488 0-473 0-459 0-445 0-431 0-417 0-404 0-390 0-376 8 9 0-520 0-506 0-491 0-476 0-462 0-448 0-434 0-421 0-407 0-394 0-380 0-367 9 10 0-507 ' 0-493 0-479" 0-465 0-451 0-437 0-424 0-411 0-397 0-3X4 0-371' 0-358 !° 11 0-495 ■ 0-481 0-467 0-453 0-440 0-426 0-413 0-401 0-387 0-375 0-362 0-349 11 1-2 0-483 0-469 0-455 0-442 0-429 0-416 0-403 0-391 0-378 0-366 0353 0-341 12 Pi 0-471 0-457 0-444 0-431 0-418 0-406 0-393 0-381 0-368 0-356 0-344 0-332 13 H 0-459 ' 0-446 0-433 0-421 0-408 0-396 0-384 0-372 0-359 0-347 0-335 0-323 14 15 0-448 0-435 0-422 0-410 0-398 0-386 0-374 0-362 0-349 0-338 0-326 0-315 15 16 0-436 0-424 0-412 0-400 0-3S8 0-376 0-364 0-353 0-341 0-330 0-318 0-307 16 17 0-425 0-413 0-402 0-390 0-378 0-366 0-355 0-344 0-332 0-321 0-309 0298 17 18 0-414 0-403 0-391 0-380 0-368 0-357 0-346 0-335 0-323 0-312 0-301 0-290 18 19 0-404 0-392 0-381 0-370 0-358 0-347 0-336 0-326 0-314 0-303 0-292 0-282 19 20" 0-393 0-382 0-371 0-360 0-349 0^338 0-327 0-317 0-306 0-295 0-2S4 0-274 20 21 0-383 0-371 0-361 0-350 0-339 0-329 0-318 0-308 0-297 0-2S6 0-276 0-266 21 22 0-372 0-361 0-351 0-340 0-330 0-320 0-309 0-299 0-2S8 0-278 0-268 0-25S 22 23 0-362 0-35I 0-341 0-330 0-320 0-310 0-300 0-289 0-279 0-270 0-260 0-250 23 24 0-351 0-341 0-331 0-32I 0-311 0-301 0-291 0-281 0-271 0-262 0-252 0-242 24 25 0-341 0-331 0-321 0-311 0-301 0-292 0-282 0-272 o;262 0-253 0-243 0-234 25 26 0-331 0-322 0-312 0-302 0-292 0-283 0-273 0-264 0-254 0-245 0-235 0-226 26 27 0-321 0-312 0-302 0-292 0-283 0-274 0-264 0-256 0-246 0-237 0-227 0-218 27 28 0-311 0-302 0-292 0-283 0-274 0-265 0-256 0-248 0-238 0-229 0-219 0-2.0 28 29 0-301 0-292 0-282 0-274 0-265 0-256 0-247 0^239 ^-229 0-221 29 so" 0-291 0-282' 0-273 0-265 0-256 0-247 0-238 0-230 0-221 "0^213" 0-204 0-195 30 31 0-281 0-272 0-263 0-255 0-246 0-238 0-229 0-221 0-212 0-204 0-196 0-187 31 32 0-271 0-263 0-254 0-246 0-237 0-229 0-221 0-213 0-204 0-196 0-1S7 0-179 32 33 0-261 0-253 0-245 0-237 0-228 0-220 0-212 0-204 0-195 0-1S7 0-179 0-171 33 34 0-252 0-244 0-236 0-228 0-220 0-2I2 0-203 0-195 0187 0-179 0-171 0-163 34 35 0-242 0-234 0-226 0-218 0-210 0-203 0-194 0-186 0-178 0-170 0-162 0-155 35 36 0-232 0225 0-217 0-209 0-201 0-194 0-186 O-I7S 0-170 0-162 0-154 36 37 0-222 0-215 0-207 0-I99 O-I91 O-.S4 0-176 0-169 0-161 0-153 0-145 o-\]l 37 38 0-212 0-205 0-197 0-190 0-182 0-175 0-167 0-160 0-152 0145 0-137 0-130 38 39 0-202 0-195 0-187 0-180 0-173 0-166 0-158 0-152 0-143 0-.36 0129 0-122 39 40 0-192 "0-185' 0-178 0-171' 0-164 0-157' 0-150' 0-143 0135 0-J28 0-121 0-114 40 41 0-182 0-175 0-168 0-162 0-155 0-148 0-141 0-134 0-127 0-120 0-1.3 0-.06 41 42 0-172 0-165 0-158 0-152 0-145 0-138 0-131 0-125 0-118 o-ii I 0-104 0-097 42 43 O-I61 0-155 0-148 0-142 o-'35 0-129 0109 0-102 0-095 0-08S 43 44 0-151 0-144 0-.38 0-132 0-126 O-II9 0-M3 01 06 o-ioo 0-093 0-086 0-079 44 45 0-141 0-134 o-,28 0-122 0-116 o-uo 0-103 0097 0-090 0-0S4 0-077 0-071 45 46 0-131 0-124 0-118 0-112 o-io6 o-ioo 0-094 0-087 0-081 0-074 0-06S 0-062 46 47 0-120 0-114 0-108 0-102 0-096 0-090 0-0S4 0-078 0-071 0-065 0-058 0-053 47 48 0-109 0-103 0-098 0-092 0-086 o-oSo 0-074 0-068 0-062 0-056 0-049 0-043 48 49 0-098 0-092 0087 0-082 0-075 0-070 0-064 0-058 0-052 0-046 0-040 0-034 49 5ir 0-087 0-081 0-076 0-071 0-064 0-059 0-054 0-048 0-042 0-036 0-030 0-024 50 51 0-076 0-070 0-064 o-o6o 0-054 0-049 0-043 0-037 0-032 0-026 0-020 0-0.4 5'. 52 0-064 0-059 0-053 0-048 0-043 0-038 0-032 0-027 0-021 0-016 0-010 0-004 52 53 0-052 0-048 0-042 0-037 0-031 0-027 0-021 0-016 o-oio 0-005 o-ooo 9-994 53 S4 0040 0-036 0-031 0-026 0-020 0-015 0010 0-005 9-999 9-994 . 9-989 9984 54 55 0-028 0024 0-019 0-014 0-009 0-003 9-998 9 994 9-988 9983 9-978 9973 55 56 0-0.6 001 1 0-006 0-OO2 9-997 9-992 9-987 9-9S2 9-977 9-972 9-967 9-962 56 57 0-003 9-999 9-994 9-990 9-9S5 9-980 9-975 9-970 9-965 9-961 9-955 995' 57 5S 9-990 9986 9-9S1 9-977 9-973 9-968 9963 9-958 9-953 9-949 9-944 9-939 58 59 9-977 9-973 9-968 9-964 9960 9-956 9-950 9-946 9-941 9-937 9-932 9-927 59 60 9963 9959 9-955 9-95' 9-946 9943 9-937 9-933 9-928 9-924 9920 9-915 60" 61 9-948 9-945 9-941 9-937 9-932 9-929 9-924 9-920 9-915 9-911 9-907 9-902 61 "-' 9-934 9930 9-926 9-923 9-9.S 9-914 9910 9-906 9-898 9-894 9-889 ••'-' TARLR 71 8?7 1.0(}AR1TH.MS lOR CO.MPI'TINO THi: COUKECTION OK THIC LATITUDK BV ACCOLNT. Pakt I. Observations on the same side Itolli of tlie .Meridian and of the Prime Vertical. Azimuths. 8° 1 10° 1 12° 1 14° „jo 1 ,„o , .2JO 1 2-2° 1 84° 26° 1 28° 30° 32° 31° 12 9-106: j 1 1 14 9-316 1 1 lli 9-5^'49-.6; 1 IH 9-43C9- = 3«Vo5 5 i 1 1 2(1 9-+64 9-29c,vii6:8-9;5 ■It 9-490 9-329 '9-172 19-010 8-829 24 9-5" V359 9'»'5 9-071,8-918 8-744 •J« 9-52,S 9-383 '9-248 9..68-9S1 8-836 ".i 9- 543;9-+°3 19-^75 9-152 9-029 8-902 I8-762 :w 9'S55 9'4'9 9-^97 9-.82I9-068 8-953 i8-S3- 8 6,5 3-.- 9'5*59'435:9"3'^ 9-206 9-.c« 8-993 I8-S84 8-766 ;m 9-5-5 9-446 19-332 9 5«3;9-457 19-346 9 590.9 467 9-359 9-227 9-126 9-02718-926 8-821 8-707 ae 9-245 9-. 48 9-05518-96. 8-865 fl*5 8-653 :«8 9-260 9-. 68 9-079,8-99' 8-90. 8«09 8-7..L._ 40 9'5909'475 9-37° 9-274 9-185 9-099,9-016 8-932 8-847 8-75818-662 42 9-6029-483 9-379 9286 9-11819-038 8-959 8-879 8-79718-710 8-6.7 44 9-6089-490 9-389 9 297,9-214 9'6i3,9'497 19-397 9-308 !9-226 9-'34;9-o57 8-9S2 8-907 S-8308-751 8-667 8-576 4(i 9-149 9-075 9-003 8-93. 8-859 8-785 j.S-708 18-626 8-5371 4H 9-6179-503,9-404 9-317 9-237 9. 6» '9-050 9-C2. 8-953 8-8858-8.5 8-744 8-668 8-589 .VI 9 622I9-508I9-411 9-325 9247 9-'74 9-'05 9-038 8-972 8-907:8-842 S-775 8-70518-632 52 9-6269-513 9-418 9-333 9-256 9-. 8519-. .8 9053 8-990 8-927 8-865 8-802 8-737 i8-670 .'■4 9-62919-518 9'6539-523 9-42419-340 9-265 9-.95 9129 9-067 9-006 8946 8-886 8-826 8-76518-702 .id- 9-429 ;9-347 9-27! 9-205 9-141 9-079 9-020 8-962 8-905 8-848 8-790 8-73> all 96369-527 9-6399-53' 9'435 9'354 9-2S, 9-214 9-151 9-C91I9034 8-978 8-923 8-868 8-8.3 8-757 «<) 9-440 9-360 9-222,9-160 9-102 9046 8-992 '8-939 8-886 8-834 jS-78. G2 9-6,^2 9-535 9-4449-365 9-449 9-37' 9-295 9-23019-169 9-112 9-058 9-C05 8-954 8-903 8-853 |8-8o2 «i4 9-645 9-539 9-301 9-237,9-178 9-122 9069 9-0.8 I8-968 S-919I8-S70 18-822 6n 9-648 9-542 9'453 9-376 9-307 9-244 19- '86 9. 3. 9-079 9-029 8-98. 8-933 18-887 |8-840 68 9-651 9-545 9-457 9-381 9-313 9-25. 9'94 9-140 9-089 9040 8-993 8-947 8-902 8-857 "II 9-653 9-549 9-461 19- 386 9-319 9-258 9-2C, 9-'48 9-099 9-05. 9-005 8-960 I8-916IS-873 TT 9-656 9-552 9-465 '9-390 9-324 9264 9-208 9-. 56 9-270 9-2.5 9-164 9-107 7^ 9-016 8-972 18-930 J8-887 74 9-658 9-555 9-469 9-395 9 329 9-1.6 9-070 9-026 8-98418-94218-902 7'! 9661 9-55S 9-473 9 399 9-334 9-275 9-222 9. 7. 9-124 9-079 9-036 8-995 18-959 '8-9.5 711 9-663 9-56. 9-476 19-403 9-339 9-281,9-228 9-. 78 9-132 9-088 9-046 9-co6|s-966 18-928 11(1 9-665 9-564 9-4809-408 9-344 9-287 ,9-234 9-185 9. 40 9-097 9055 9-0.6J8-977 ,8-940 «2 9-667 9-567 9-483 9 4'2 9-349 9-292 9-240 9- 192 9-'47 9-.05 9-065 9-026 S-98S|8-952 til 9-67C 9-569 9-487 I9-416 9-353 9-297 9-246 9-199 9-'55 9-1.3 9-073 9-035 8-999,8-963 KB 9-6-2 9-572 9-490 19-420 9-358 9-302 9-252 9-205 9-162 9-121 9-082 9-045 9-009 8-974 INI 9-674 9-575 9-493 9-423 9-362 9-307:9-257 9-21. 9-169 9'. 28 9-090 9-0549-019 8-985 'M 9-676 3(;° 9-5^8 9-496 !9'427 40° j 4-2° 9-366 9-3.29-263 9-2'8 9-'75 921^ 9-098 9-062 I9-02S 8-995 .•«l° 44° 4(i° 1 4HO 50° 3-2° 54° 46° 38° 1 «(l° 1 62° "wF i^ 8-567 8-492 |8-4o8 8-314 ! i 1 1 .if; 8-670 8-606 8-538 8-464 8-381 8-288 1 j .Ml 8 700 8-640 8-5778-5.0 8-437 8-35618-264 1 (id 8-726 8-671 8-6.2I8-551 8-485 8-4.3 |8-333 8-242 1 (12 S-750 8-698 8-643 8-587 8-526 8-46. [8-39. 8-3'2 8-22. 1 (14 8-773 8-723 8-671 I8-618 8-563 8-503 Is-AAO 18-370 8-292 i (i(; 8-793 8-745 8-69718-647 8-595 8-54o;s-482|8-4.9 8-3508-2731 BH 8-8i2|8-766|8-72o|8-673 8-624 8-573,8-5208-462 8-40. S-332 S-256 7" 8-829|8-786[8-74»ls-697 8-651 8-603 8-551 8-501 8-444 8-383 8-316 8-240 1 72- 8-84618-804 [8-762 8-719I8-676 8-631 J8-584 8-535 I8-483 8^1 8-367 8:i5T:FII7,| 74 8-861 S-Kii 8-781 I8-740 8-698 8-656 8-612 8-566 8-518 8467 8-4.2 8-353 8-287 1 7B 8-8768-837 8-798 8-759 8-719 8 679 '8-638 8-595 i8-550 8-503 I S-453 8-398 l8-34< S-27C 7'i 8-8908-852 8-8.5 8-777 8-739 I8-701 ,8-661 8-621 8-579 18-535 , 8-489 8-439 i8-38< 8-328 «n 8-903l«-867 8-83. 8-794 8-758 8-721 8-684 8-645 '8-606 8- 564 8-52. 8-476 8 427 8-375 «2 8-916,8-881 '8-846 8-8ii;8-776 8- 740 8-705 8668 8-631^8-591 8-55. 8-509 S-464 S-416 H4 8-928l8-894;«-86o 8-826 8-793^8-759 8-7:4 8690 ,8-654 :8-6i7 8-579 8-540 8-498 8-454 IIV S-940I8-907 '8-874 8-841 |8-8o9 '8-776 8-743 '8-7>o :8-676 8-641 S-605 8-568 8-520 S-488 HII 8-9518-91918-887 8-856 18-824 18-793 '8-761 18-729 ,8-697 8-664 8630 8-595 8-5^8 8-520 «« 8 9638931 8-9CC 8-86, 8-839-8-809 I8-778 8-748 8-717 S-685 8-653 8-620 I8-585 8-550 TABLE 71 LOGARITHMS FOR COMPUTING THE CORRKCTION OF THE LATITUi:)E BV ACCOUN?. Part II. Observations on difterent sides either of the Meridian or of the Prime Vertical I — 3'= 10° 12° J^ .6°i 18° 20° 22° 1 24° 1 20° 1 2 8°| 30° J^L^i 8° 9-977 10 9931 9-879 1 12 9-897 9-840 9-797 14 9-870 9-810 9-764 9-728 16 9-849 9-786 9-737 j-699 9-667 IH 9-83. 9766 9-7,5 9-674 9-64, 9-613 2lt 9-8.8 9-749 9-696 9654 9-619 9-589 9-564 22 9-806 9-735 9-680 9-636 9-599 9-568 9-542 9-519 2» 9-795 9-7^2, 9-666 9 620 9-582 9-550 9-522 9-498 9-476 26 9-7X6 9-7,2 9-654 9-606 9567 9-534 9-505 9-480 9-457 9-437 28 9-778 9 702 9-643 9-594 9-554 9-519 9-489 9-463 9-440 9*418 9399 30 9-771 9-693 9-633 1 9-583 9-542 9-5°6 9-47"; 9-448 j-424 9-402 9-382 9^364 32" 9-764 9-686 9-624 9-573 9-530 9-494 9-46. 9-434 9-409 9-386 9-366 19-347 rw 34 9-758 9-678 9-6,6 9-564 9-520 9-483 9-450 9-421 9-395 9-372 9-351 933, 9-313 9-296 •■Mi 9753 9-672 9-608 9-555 9-511 9-473 9-439 9-410 9-383 9-359 9-337 9-316 9298 9-280 38 9-74819-666 9-60, 9-547 9-502 9-463 9-419 9-399 9-371 9-346 9-324 9-303 9-283 9-265 40 y743J9-66o 9-594 9-540 9-494 9 454 9-419 9388 9-360 9-335 9-311 9-290 9-270 9-251 42 9-739,9-655 9588 9-533 9-486 9-446 9-410 9-378 9-350 9324 9-30^ ri-ii 9-257 9-238 44 9-73519-650 9-583 9-527 9-479 9-438 9-402 9-369 9-340 9-313 9-28, [9-266 9-245 9-«5 40 9731 9-646 9-578 9-521 9-473 9-431 9-394 9-36, 9-331 9303 9-27J 9-25S 9-233 9-213 48 9728 9642 9-573 9-5>5 9-466 9-424 9-386 9-352 9-312 9-294 9-Z6S 9-244 9-2x2 9-201 50 52 9-725 9-638 9-568 9-510 9-460 9-417 9-379 9-344 ou. 9-2S5 9-249 ^^34 9224 9-211 9_^9. 9-179 9-7219-634 9-7189-630 9-563 9-504 9-454 9-410 9371 9*337 9-305 9-276 9-201 54 9-559 9-499 9-449 9-404 9-365 9-329 9-297 9-267 9-240 9-215 9-. 91 9-i68| 66 9-7,59-626 9-555 9-495 9-443 9398 9-358 9-322 9-289 9-259 •/23, 9-205 9-181 9-158 5(1 9-7,39-623 9-551 9-490 9-438 9-392 9352 9-315 9-282 9-251 9-223 9-196 9-171 9-148 60 9-7,c!9-620 9-547 9-486 9-433 9-387 9-346 9-309 9-275 9-243 9-2,5 9-187 9162 9-138 02 ^707-9-617 9-543 9-481 9-428 9-381 9-340 9-302 9-268 9-236 9-206 9179 9-153 9-128 G4 ^•7059-613 9-539 9-477 9-423 9-376 9-334 9-296 9-26, 9-22S 9-198 9-170 9-144 9-1.8 66 9-707.9-6IO 9-536 9-473 9-419 9-371 9-3*8 9-289 9254 9-221 9-191 9-162 9-135 9-109 08 9-700,9-607 9-531 9-469 9-414 9-366 9-322 '■2-^ 9-247 9-2,4 9-183 9-154 9-126 9' 100 70 72 9-698 9605 9-529 9465 9-410 9-361 9-317 9-207 19-175 9-145 9-117 9-108 9-090 9-6959602 9-525 9-461 9405 9356 9-31. 9-271 9-234 9-200 9-167 9-137 9-^ 74 9-6939-599 9522 9-457 9-401 9-351 9-306 9-265 9-228 9-193 9-, 60 9-129 9-100 9-072 70 9-69,9-596 9-JI9 9-453 9-396 9-346 9301 9259 9-221 9-, 86 9-152 9-121 9091 9-062 78 9-6899-594 9-516 9450 9-392 9-341 9-295 9-253 9-215 9-179 9-145 9-113 9-082 9-053 80 9-6879-59' 9-5" 9446 9-388 9-336 9-290 19-247 9-208 9-172 9137 9-105 9-074 9-044 82 9-6859-588 9509 9-442 9384 9-332 9-285 9-241 9-202 9-165 913° 9096 9-065 9-034 84 9-6829-586 9-506 9-438 9-379 9-327 9-279 9236 9 ,95 9-157 9-122 9-088 9-056 9-025 8fi 9-6809583 9-503 9-6789-580 9.500 9-435 9-375 9-322 9-274 9-230 9-189 9-150 9-114 9080 '9047 9-015 118 9-43' 9-371 9-317 9-268 9-224 9-, 82 9-143 9-,o6 9-071 19-037 9-005 90 9-6769-578 9-496 9-427 |9- 366 9-312 9-265 9-2,8 52^ 9-136 9-098 9-062 19028 ;8-995 58° j 00° 1 02° 36° 38° 40° 4->° 1 44° 40° 1 48° 1 50° 54° 50° 36' 9-2641 1 ; " 38 9-248|9-i3i 40 9-234I9-2.7 ,9-201 I 42 9-2109-202 9-186 9-171 44 9-2069-.89 9-172 9-15619 '4cl 1 46 9 '93,9-'75 9 ,58 9-141 9 '\>|9 no 48 9MSi;9-i62 9* '45 9127 9-1119095 9 079' 50 9-,699-,5o|9-,32 9-114 9 097 9-08019 9o83Vo66!9 064 9-049 52 9-158 9-138,9, ,9, 9, 01 050 9-034,9-018 54 9i47 9-i26|9-io7|9-og8 9-070 9-052)9 035 9-019 19-002 8986 1 56 9-,36J9-,i5 9-09519-076 9-057,9-039 9 9-004 8-987 8-970 8 954 58 9-,25'9-io4 9C83J9-063 [9-044 9-02519 007 8-989 8-972 8-955 8 938 8-92, 60 9-,i5J9-093 9-072 9-05, 19-032 I9 0,2 ,8 994 8-975 8-957 8-939 8 921 8-904 8-886 62 9 J059-083 9-060 9-03919-0,9,8-99918 9-028 ,9-007 I8-986 8 9-016,8-994 18-973 8 980 8-96, 8-942 8-924 1^ 905 8887 8-869 |8-85, 04 9 09419-071 9-049 966 8-947 8-927 8-908 » 889 8-870 8851 8-832 06 9-0849-061 9-038 953 8933 8-913 8-893 18 873 8-853 8-834 8-814 B8 9074'5-c5o 9-027I9CC4I8 982 8 96018-939 8-918 8-898 8-877 l8-857]8-836 8 gi6 8-9C TAIU.F. 71 I.OOARITHMS FOR LO.MPI'TIN^i THK CdRKECTION OF Till: I.ATITUDIO BV ACC'.'JM I'aut II. (continued.) Observations on rfi'/^crew* sides eiflier of tiie Meridian or of tiic Prime Vertical. AZIMUIHS. ;«r UK" -^ 42" 44° { 4«° 48° j on" 1 !i2° 1 r.4° 5«° j .".H" BO" ^ 70° 9-065 9-040 9-OI6 8-991 8-9708-948 8-926 J8-904I8-8S3 8-862 8-848 8-8,9 8-798 8-776 n 9-005 8-98. 8-958 8-935 8-9i2l8-89u!8 868I8-846 8-824 8-802 74 904519019 8-994 8-969 8-94518-9" 8-898 8-875 ;8-853 8-83° 8-807 8-784 8-7608-737 7B 9035'90o8i8-983 8-9S7 8-933 8-909 18-885^8-86. !s-837 8-8,3 8-790 8-766 ;8-74.| -717 711 9-025;8-998|«-971j8-946|S-9i0S-895]8-870[8 846'8-i!j'|8-797 9-oi5,8-987 8-960 8-933 18-907 8-88. 8-S56 8-831 8-805 ;8-78o 8-772 |8-747 18-72. -691 Kit 8-754 8-728 '8-70. -674 8.! 9-oo5i8 976 8948 |8-9^. 18-894 8-868 I8-841 18-8.5 8-789 8-762 8-99518 965 8-937 ;8-909 .8-88. 18-854 8-826 :8-799 8-772 8-744 S-725I8-708I8 680 •65, St 8-7.6:8-68718-658, -62S at 8-98418-954 8-9.5 8-896 8-867 (8-839 8-8i.|8-7!*=':8 754 8-725 8-696 18-666 18-635 18-603 88 8-974:8-943 8-913 8-883 S-853 8-824 ,8-795 8-765 ,8-736 8-706 8-675 8-643 8-6., 8-577 M 8-06318-931 8-9oo|8-869 8-839 ;8-8o9 18-778 8-748 8-7,7 I8-685 8-6538-6208-5858-550 TABLE 7'. LOGAKITILMS 1 FOR COMPUTING THE EQUATION OF EQUAL ALTITUDES 1 Interval. L.K.A. Log. IJ InicTval. 4" .30"' Log A. Log. B. Inlerval Log. A. L,>g. U I"a0" 2 2-/ 25 22809 22499 23300 71, aon. 2-2032 2-458 1 1 ar, 2722 22810 4 .35 2 24^9 23323 7 35 22055 2-4645 1 40 2719 2-2823 4 40 2-2479 23(46 7 40 2-1998 2-4690 1 45 2,15 22S31 4 45 22469 23370 7 45 2 1980 24755 1 50 2711 2-2S38 4 50 22459 233y4 7 50 2-1963 2-48.4 1 ir, 2707 2-2846 4 55 2-2449 23418 7 55 2-1945 2-4876 2 270,5 2-2854 5 2-2438 23444 8 2 1928 2-493« 2 5 2699 22863 5 5 2 2428 23470 8 5 2 1910 2 5004 -2 10 2695 22V72 5 10 2-2417 23t9-' H 10 21892 25070 ■2 15 2690 2-2882 5 15 2 2406 2 3524 8 15 21874 25141 •2 20 2685 2-2891 5 20 22394 a3';52 8 20 2 1855 2 521 1 2 -J 5 2-2. 8j 2-2902 5 25 2 23«3 23581 8 25 rlsf 25286 2 .-}.. 2 2f7S 2-2912 5 30 22371 23610 8 .30 25360 2 :i5 22,69 22924 5 35 22359 2 3'>4l 8 35 2-,79S 2 5439 2 40 22664 2-2935 5 40 22347 2-367, 8 40 2-1778 25518 2 45 ^ 2658 22947 5 45 22334 23703 8 45 2 1758 25602 2 50 2 2652 22950 5 50 22322 23735 8 50 2.738 2-5685 '2 55 2 2646 2641 2-2Q72 5 55 22309 22297 23768 23802 8 55 9~0 21718 i577_6_ 2-58u8 2 2985 22998 l> 2 ,697 .-) 5 26.34 G S 2-22S3 2 3S37 9 5 2-1677 25963 3 10 2628 2-3012 n 10 22271 2-3»73 9 10 2.656 26.63 .-( 15 2621 2-3027 6 15 2-2.'57 2 39 rt 15 2 1635 2 6,64 .3 20 26.4 23042 fi 20 22244 2 39+7 9 20 2 1613 26273 .3 25 2'<)7 23058 6 25 22230 23986 •J -.'5 2 1592 2-6384 5 .-iO 2600 23073 6 .30 22il6 24024 9 30 2,570 26499 .1 .-iS 2592 23090 G 35 2 2202 24065 'J 35 2157 266,9 .1 40 2585 23105 6 .10 22187 24106 !) 40 215^5 26744 3 45 2577 23124 6 45 2-2,73 2-4149 !> 45 2 1502 26874 .3 50 2569 23141 6 50 22,58 241 2 9 50 2 14,80 27011 .3 55 22561 23.59 6 55 22143 24^37 9 55 2 1457 27154 4 22553 23177 7 22127 24283 10 2 1433 2-7303 4 5 22544 23,96 7 5 2il.2 24330 10 5 2 1409 2-74()0 4 10 2 2536 23216 7 10 22096 2 437'< 10 10 213S6 27626 4 15 2-2527 23236 7 15 |2-2oSo 244^6 10 15 2 1361 27801 4 20 22518 2 (257 7 20 22064 24178 10 2ii 21337 2-7084 4 25 22509 2-3278 7 2-. '2'2fi.|S 2.i';3i 10 25 2 .312 2.S076 1 TABLE 7.1 THIi LOGARITHAIIC DIFFEKENCK n (Bi,ioFneter, 30 iiicl.e». FalirenliiMt's Tl.crm.Hiieter, 90=.) i: Horizontal I'arillaK. 1 •of >«T. Corr. for ' of Par. | 6y 53 1 54' 1 55' 1 50' | 57' 1 5«' I 57^l9Mo 9'29 9108 9°65 9044 9022 j 9001 50 19 21 21 it 0,9,52!y,3. 9109 9087 9066 9044 9022 9001 8979 I ~i r, 13 10 9'33 9111 9089 9067 9045 9023 9001 8979 8957 10 4 7 7 '5 •'0 9114 9091 9069 9047 9024 9002 8979 8957 8935 20 8 II iJ 30 9095 9072 9049 9026 9C04 8981 S958 8935 8912 30 12 13 15 2C 40 9°75 9052 9029 9006 89S3 8960 8937 8913 8S90 40 16 17 20 50 9. _,-6 1 9032 1 9009 8986 8962 1 8939 89.5 8892 18868 50 n 11 11. 11 23 1'"^ , Alt. 5" 6° 7" 8' 14° 25° 34 ' 42' 51° G4° m>' Sub 17 13 1 1 9 7 9 1113 15 '7 18 . -U (JO 90 , , 9 7 5 4 I hu Logaritlimic Difference is not given in this Table for altitudes ies.s tlinn 3°, lun;ir observalion ought not to be employed with very low aUitucle;,. TAni.K 7;J 901 THi; L,()(iARilH.MI(; DIKKICRH.VCIO ( Haromeler. ;«) incl.ea. Kaliienheil's Tli.TriiDii.fler, 60°.) 3> A pp. Alt JIorizontHl lanillax. "of l'..r. Corr. for"ofl'ar.«u/,. 1 &»■ 1 .54' 1 f.o' 1 ftO' ; 67' on' d!»' 1 60' 1 CI' Z\i'\j-\ JLl«- 10 o 9-99 t 9-99 ; 999 1 999 9-99 9'99 999 999 999 ll I) 9037,9013,8989 8965 1 8941 89'7 >894 8870 8846 2 3 4 lu 9018 18993 18969 1 8945, 8921 8896 8872 8824 10 4 5 6 6 7 g 20 8998 189741 8949; 89:5 '890° 8875 885. 8802 20 X 9 "o .2 :m 8979 8954 8929 89C4J 8879 8854 8850 87S0 :to 12 '3 '4 15 .6 .7 40 8960 8935 8909 8884 8859 8833 8S08 8758 40 17 .8 .8 ■9 20 ho Ml S9J2 89. S 88891886418838 8812 8787 8765 8735 ~0 21. ^ 24 3 il 3 26 4 .smA. 1! II 8 89) 8S69 8843 1 88.7 S79. 8739 871 - III S90, 8876 8850 8823 1 8797 877. 8744 87. 8 869J III 4 5 6 7 9 ■^1) 8883 1 8857 8830 880318776 S750 8723 1 8696 S669 20 9 11 12 .3 13 311 886418837 88.0 8783:8756 8729 8702 8675 8647 ;to ■3 14 15 .6 17 18 HP. 41) 8845 188.8 8790 8763 8735 870? 8680 8653 40 18 '9 21 23 53' M 8826 18799 877. 8743 I 87.5 8687 8659 863. 8604 60 il 21 21 26 27 2i 5 ii 1) 880718779 18751 8723 1 S694 8703 S674 8666 lliT 8610 8582 I 3 4 in 878818760 8731 8645 86.7 8588 8 560 10 5 6 7 8 8 .0 2 4 •211 876918740 87.. 8682 8653 S624I 8595 8566 8538 20 1 1 12 13 .5 3 6 ;in 8-501872.18691 8662 1 8633 8603 8574 854s 85.6 30 15 16 17 .7 18 20 4 X 411 873. S70. 8672 8642 1 8612 8582 8 53 8523 8494 40 2. 13 24 ^5 6 9 ."ill 87.2IS6S2 8652 862218592 8562 hiL 8502 S472 ,50 21 26 ii 28 3 21. 4 21 5 7 .3 S693 I 8662 "86ir 860. 857. 854. 8510 84S0 8450 I 2 111 S674 S643 86.2 85S. S55. 8520 8489 8458 8428 10 5 6 7 8 9 10 815 '.'(1 86,5 8624 8592 856. 8530 8499 8468 8437 8406 20 1 1 12 >3 >4 .6 !» 17 'Ml 8636 S604 S573 8541 8510 8478 8447 84,6 8384 30 .6 17 .8 •9 20 21 411 S61- S5S5 S553I852. 8490 8458 8426 8394 8362 40 21 22 »3 *4 15 17 .'ill ^;9S:s^66 8533:850. M^ illL 8405 8373 834° GO 27 IL 21 2 3^ 3 IL 4 11 5 11 II 8579,8546185.4 848. 8449 84.6 8384 835. 83.8 "IT 1 ll) 8560:852-8+94 846. 842S 8395 8363 8330 8297 10 5 7 8 9 10 20 854.18508 8474 844. 8408 8375 834. 8308 8275 20 II '3 '4 '5 <7 :vi 8522 84S9 8455 S42. 8 388 8354 8320 8253 30 17 ■ 8 '9 23 40 8503 8469 1 8435 840. 8367 8333 8299 8266 8232 40 ^3 *4 25 26 17 28 ■)0 84S4IS450 84.6 8347 83'3 «278 8244 8210 .50 28 il 3' il 33 34 Id 846518431 8396 I§f 8327 8292 8257 8223 X.88 ~~0~ 1 2 3 T ^6- 10 8447 84. 2 8377 8342 8 30 7 8271 8236 820. 8.66 10 6 7 8 9 12 20 8428 8392 8357 82S6 825. 82,5 8180 8.45 20 12 '3 '4 15 ',6 18 ;io 8409 83-'3 8338 8302 8266 3230 8,95 8.59 30 18 >9 »3 24 40 8390 8354 83.8 8282 8246 82.0 8.74 8138 8.01 40 24 15 26 28 30 .'.0 8371 833s S299 8262 8226 S.89 8.53 8. .6 8080 .50 Jl 31 33 il 35 36 ui'li »353 83. 6 S279 8242 8205 8.69 Y^ 8095 8058 (T 1 J 4 -J -J III 8334 8297 8260 8222 8.85 8.48 8... 8074 So 3 7 10 6 7 9 12 20 8278 8240 8203 8.65 8.28 8090 8053 8015 20 .2 '4 15 \°(, 17 '9 »ll 8297 8259 8221 8,83 8,45 8.07 8069 803. 7994 30 >9 20 2. »3 »4 14 40 8278 8240 820. 8.63 8.25 1 8087 8048 8010 7972 40 25 »7 28 »9 31 .^0 W 82S9 822.|8.82;8i43 8.05] 8066 8028 7989 7950 .50 32 *l 5 2l 4 21 5 Ji 7 HP. 8240 18201 8162 8.24 808518046 X007 7968 7929 (T 10 8222 Is. 83 8143 8104 8065 8025 7986 7947 7907 10 7 8 9 "i 'J (il 20 8203 : 8164 8124 8084 8045! 8005 7965 7926 7886 20 13 .4 .6 17 18 :tii 8.8,18.45 8.05 8065 802517985 7945 7905 7865 30 20 2. 23 24 15 27 2 4 :« 7 41 9 .5.1 40 8.66 1 8126 8085 8045 Sees 1 7964 79^4 7884 7843 40 = 7 28 30 31 34 .'ill 8.47 [8107 8066 8025 798517944 7903 1 7863 1 7822 .50 34 21:11 Ji 21. 40 IB~ "8.2918088 80+7 8co6 7965 , 7924 78821 7X4.1 7800 '! 3 4 5 7 III 8..0 8069 8027 7986 7945 i 7903 7862 17820! 7779 10 7 X 10 '4 2(1 8092 8050 1 8008 79^7 7925 7883 784. 7S00I7758 20 >4 '5 «7 Is '9 f!l.3 3(1 8073 803.17989 7947 7905 7863 7?2I 7779 7736 .10 24 »5 18 71.5 411 8055 80.2! 7970 1 7927 7885 7842 78CO 7758 7715 40 28 30 31 34 36 U .8 .Ml i:i 8036! 7993 1 7950 1 7908 7865^822 7779 7737 7694 .50 ^ 21 -22 i£ il B20 So. 8 7974 1793! | 7888 7845 780/. 7759 7715 {T^ 3 4 7 III 7999 7956 79.217869 7825 7782 773« 7695 7651 10 7 9 '3 '5 2(1 •981 7937 7893 7849 7805 7762 -718 7674 7630 20 '5 16 .7 '9 10 22 .■(11 '8 7«74 7830 7786,7741 7697 17653 7609 :iii 24 »5 27 28 30 411 -944 j 7899 7855 78.0 1 7766 ■77*' 7677 763^ 75X8140 30 3' 33 34 36137 r>o 7926 788. 17836 779' 1 7746 1 7701 7656 76.. 7567I f>o 37 : 3° 3i' 42 SI" (i4'' IMI^ 1 Smr". Alt. ft" IP 1" 8° 9° • 1^ la'' 14° 1 B 30'= •'"''• 17 13 11 9 7 9 '1 n '5 '7 '8 i ."4. 15 u 9 7 5 4 3 » ' | 002 TABLE 73 THE LOOARITH.MIC UIFFEKENCE ( Barometer 30 ii ntal P cl.M. FalirrBhei''. Tlierm.miMer, 60°) A,, p. All. ilor.K. rillnx. "of Corr. for " of Par. ,ub 53' 54' 55' i 5«r| 57' 6f!' 1 BiC BO' ! fir Piir 0' ^'!il ff_ ^ JIT .5-; ^ 9-<)i 999 9-99 9-99 9'99 999 9*99 999 9-99 20 7907 7862 7817 777J 7726 7636 759' 7545 4 6 8 10 7SS9 7843 7798 775^ 7707 7661 76,5 7570 75=4 10 8 12 '4 •5 20 7871 7825 7779 7733 7687 764, 7595 7549 75°3 20 15 17 10 21 = 3 ,„/,. :fo 7851 7806 7760 7714 7667 762. 7575 75^9 7482 30 = 3 =5 28 =9 34 40 7«34 77S8 7741 7694 7648 760. 7554 7508 7461 4!) 3' 33 36 37 39 iiO 78,6 7769 77^^ 7674 7628 758' 7534 7487 ! 7440 50 39 4i 44 45 46 H.P. i\ (1 7798 7750 7703 ■7656 7608" 756, 75'4 746617419 ~F 5 6 8 10 7779 773^ 7684 7636 7589 754' 7493 7446 7398 10 8 '4 16 ■20 7761 7713 7665 76,7 7569 7521 7473 74^5 17377 20 16 iS 21 22 =4 53' .w 7743 7695 ,646 7598 7550 7501 7453 7405 i735(' 30 =4 16 29 30 3= 40 77^5 7676 7628 7579 7530 748' 7433 73«4 733« 40 3= i 34 37 39 41 22~o" 7707 7689 765S 7609 2i*!2. 7462 7413 73^4^73'5 50 41 14= ^ 46 7 48 8 1 2 2 4 7639 7 59° 7540 749' 7442 1 739^ 7343 1 7*94 ~~ir 2 10 7671 7621 757 > 752' 7471 7422 737i 73=3 17=73 10 8 10 ■3 15 17 ^ I 20 7653 7602 755^ 7502 745^ 7402 7352 7=5 = 20 '7 18 = 3 = 5 :ti) 7635 75S4 7534 7483 7433 7383 7331 7^82 7=3 = 30 = 5 = 7 30 3 = 34 5 9 40 76,7 7566 75 '5 7464 74'4 7363 7312 726, 7211 40 34 35 39 40 4= « II 23~0 7598 7547, 7496 7445 7394 7343 7292 7=4' 7190 50 4= _4= ii 5 49_ 11 9 7 13 8 .4 9 16 75X> 75-9 7478 7426 7375 73 = 3 7272 7221 7.69 10 7563 75i> 7459 7407 7356 7304 7252 7200 7 '49 10 9 10 '4 '5 '7 20 •'545 7493 744' 7389 7336 7284 7232 7180 7128 20 17 '9 = 3 =4 26 ;to 75^7 74^4 7422 7370 7317 7265 7212 7160 7107 30 26 28 3' 33 35 40 7509 7456 7403 735' 7298 7=45 7192 714017087 40 35 37 40 4= 44 50 749' 7473 743i 7385 7^79 7226 7173 7'i9 7066 -C46 60 ^ 5° 5 Jl 7 Ii 9 iT-Ji 7420 7366 73'3 7^59 7206 7'53 7099 10 7455 7402 7548 7294 7240 7187 7'33 7079 10 9 II '4 16 18 20 743S 7384 733<^ 7:175 7221 7167 7"3 7059 7005 20 18 20 = 3 = 5 = 7 30 7420 -365 7^57 7202 7148 7093 7039 69S4 30 27 29 33 34 36 40 7402 7347 7^93 7238 7183 7128 7074 7019 6964 40 36 38 4= 44 46 r.o 25 (. 7384 7329 7274 7219 7'''4 7 '09 7054 6999 6944 M 46 48 11 5 7 55 9 7367 7311 7256 7200 7 '45 7090 7°34 697916923 2 10 7349 7293 723S 7.82 7126 7070 7014 6959 6903 10 9 II '5 17 19 20 733> 7275 7219 7163 7 107 .'705 1 6995 6939 6883 20 '9 20 24 26 28 ; 73'4 7258 7201 7145 7088 703^ 6975 6919 6862 M 28 30 34 36 38 40 7296 7240 7.83 7126 7069 1 7012 6956 6S99 6842 40 38 40 44 45 48 50 7279 7^^^ 7'65 7'07 705016993 693616879 6822 5:1 48 49 £ 53 6 55 8 57 9 2li"n 7261 7204 7146 7089 7031 16974 6>,.6' 6859 6S02 10 7244 7.86 7128 7070 7013 6955 6897 6839 678, 10 9 12 '5 17 IS 20 7226 7168 7110 7052 6994 6936 687S 6S20 6761 20 '9 21 27 29 :«» 7209 7150 7092 7034 6975 6917 6858 68co 674. 30 = 9 31 35 37 39 HP. *o 7191 7'33 7074 7015 6956 6898 68 39 67S0 6721 40 39 41 45 47 49 •iO' 50 7174 JILL 7056 6997 6938 1 6878 68,9 6760 6701 50 49 51 51 6 57 8 Jl 27^17 7156 7°97 703X' 6978 6919 6859 6Sco 674016681 " H 4 h> 7-39 7079 7020 6960 69C0 6840 6781 6721 1 6661 10 10 .2 14 16 18 20 1' J 20 7062 7C02 6942 6SS2 AS22 6761 670. 664, 20 ,0|22 24 26 28 30 2 4 m 710J 7044 6984 6923 6863 6803 6742 66S2 6621 30 30 1 3-' '34 36 38 40 3 6 40 7087 7027 6,66 6905 6844 6784 5723 6662 ] 66c2 40 40 42 44 46 48 5° 4' S 50 7070 7009 6948 6887 6765 6704 6643,6582 50 5' ii 55 57 21 60 5 10 28 7053 l'»99i '^93° 6869 6X07 6746 6684 6623 16562 II ~o| 2 4 6 8 10 r. n 10 7036 6974 6912 685, 6789 6727 6665 6604 6542 10 10 12 '4 16 18 21 7 15 20 701S 6956 6894 6832 6770 670S 6646 658+16,22 20 ^3 = 5 27 29 31 K'17 30 7001 6939 6877 6814 6752 6690 6627 656516503 30 3' 33 35 37 39 42 !» 19 40 6,S4 6922 6859 6796 6734 667, 66og 6545 1 6+83 40 42 44 46 48 50 5= 50 6967 6904 684. 6718 6715 665' 6589 65=^ M 3 50 jl 5 5 iz. 59 61 ioO 6950 68«7 6823 6760 6697 6633 6570 6507 6443 I) 2 4 "6^ ~T 77 10 69-, 3 (6869 6806 6742 6678 66.5 65;, 6488 6424 10 1 1 '3 '5 '7 «9 21 20 6916 6852 6788 6724 6660 6596 6532 6469 6405 20 21 = 3 = 5 28 30 3 = 30 6S99 6835 6771 6:06 6642 6578 65,4 6449 6385 30 3= 34 3^ 39 4' 43 40 6882 68 1« 6753 6688 6624 6559 6495 6430 j 6366 40 43 45 47 49 52 54 50 6X6. CSoo 1735 6671 65o6 654, 6476 ^64J' 634^ 50 54 56 58 60 63 6_5 SuiiN \h. 5" fi" 7" «° 14° 25' 34 42" 51" (if 00" | Si,m'> Alt. 5' (r 7" tC 0' 11° 12" 14° 1 B° W- ««(.. 17 1', II 9 7 9 II >-> 15 ^^ ■>* 1 '"*• 15 i> 9 7 '-, 4 3 ^- " TABLE 73 no? TIIK LOOAKiril.MIC DIKFEHKNCi; | (H^nimeler, »0 iiici.e.'.. Kahieiilieit . ■llie.m..nieln-, 50°.) 1 All. Iloriiontiil \'.,n,\Ux. "of Corr. for '/ of I'«. ,uh •"5 63' 1 W 1 65' 1 6(i' 1 ft7' 1 w 1 r.!t' 60' ( or l>,ir -£.1^ lilFjL 1 8' i 10 ii 9"99 9'99 |999 999 l9'99 999 |9-99 999 1 9-99 1 1 1 30 6M 6-83 1 67.)! 6653 I6588 6522 1 6457 6592 6327 J 1 4 6 9- " 10 6831 6766 6700 6635 16569 6504 6439 637316308 10 ,1 '3 l'5 '7 iti*. 20 68.5 6749 6683 6617 655' 6485! 6420 6354I628S 20 22 *4 26 *9 13' 33 .10 6798 673216665 6599 I 6533 1 6467 640, 6335 I 6269 31) 33 35 37 !+* 4-1 w 6781 6714:664816581 165,5 6449 1 6382 63,6 1 6249 40 +4 46 +9 51 |53 56 H.I'. w> 6764 6697 ; 6630 1 6564 1 6497 1 6430 1 6363 1 6^96 [ 6230 50 56 58 |6o 62 ii 66 &:«' »1 6747 ! 6680 6613 6546 6479 64,216344 62771 62, J 1 2 1 4 "7 9 ,1 10 6731 6663 6596 j 6528 646, 6393 [6326 6258 6,9, 10 '■|>3 16 18 *3 20 6714 66461 65791 6511 6+43 6375 I6307 6240 6,72 20 *3|*5 *7 *9 3* 34 l|2 :«) 6697 6629 1 6561 6493 64^5 6357 1 6289 6339; 6270 6221 6153 :io 3+1 36 38 41 +3 +6 23 40 6681 6612 j 654+1 64-6 6407 6202 6,34 411 46,48 50 5* 55 57 3l 5 50 6664 1 6596 1 6527 1 6458 6389 652,16252 6, 8316, ,5 50 11 11. 62 64 ii ii 4 6 32 6648 1 6579 1 65 10 j 6441 6372,6303,62341616516096 2 5 7 9 ,, 51 8 10 6631 1 6562 1 6493; 6423 6354 6285162,516,4616077 10 , 1 '+ 16 18 *3 *i',o 20 6615 , 65451647s 1 6406 6336 6267 16,97! 6,27! 6058 20 *3 *5 28 30 3* 35 7 11 :«i 6598^6528 6458 6388 63,8 624916,7916109,6039 :«t 35 37 40 4* ++ 47 H,3 4(t 658216512:6441,637, 630, 623, I 6,60 1 6090 ' 6020 40 47 49 5* 54 56 59 » ,4 50 6565 6495 6424 [6354 6283' 6213 1 6,42 1 6071 1 6toi 50 11 6, il ii ii 21 xTT 6549:6478,6407,6336 6265 6195 6124, 6055 5982 5 7 9 12 ■ 6533 6461 '6390 63,9 624S 1 6,77 |6ic6[ 603+ ; 5963 10 12 '4 17 19 *4 •JO 6516 6445 : 6373 6302 6230] 6,59 6087 60,6 5944 20 *4 26 29 31 33 36 :^^' 6^97 6223 6148 6074 ^'^°° 5926 5851 mi 5759 50 (I 62 ii 5 7 7* _74 sTT 635s 6^-80 6206 6,3> - 6057 1 5982 590s 1 5833 10 6339 626416189 6. ,5 6040, 5965 5890 58.5 5740 10 ,2 1 '5 '7 22 *5 20 6323 6248 6.73 6098 6023 5948 587^ 5797 37** 20 '5! *7 30 3* 35 38 :)i» 6307 6232 6)56 6081 6006 5930 5855 5779 5704 ■M) 38 40 43 +5 48 5^ ■10 6292 6216 6,40 6064 5989 59'3 5837 5761 5686 40 50 53 55 58 61 63 TiO 6276 '62C01 6124! 6048 597' 1 5895! 5819 15743 5667 50 il 66 1?. 7' 74 76 :(K 6260 6183 1 6107 1 6031 5954 j 5878158021 57»5 5938 5861 5784 570S 5649 o" "X 5 8 10 t 13 10 62.^ '6167! 609. 6014 563, 10 •3! '5 18 20 ^5 26 20 6228 6152 : 6075 1 5998 592, 5844 5767! 5690 56,3 20 26 28 3' 33 36 39 II. P :(o 6213 : 6136! 6058 j 5981 5904 5827 1 5749 5672 5596 .-to 39! 4> 44 46 49 5* liV 40 6,,7 1 6,20 1 6042 5964 5887 58091 573^ 5654 5577 40 5*1 5+ 57 59 62 65 r.ii 618, 1 6,04^6026 1 5948 5870 1 579^15714 5637 1111 50 ii ^ 70 11 21 "S 97 Tm' — " 608816009 5931 5853! 577515697 56,9 5 5+' 1 3 5 JO '3 r 2 10 6,50 6072 1 5993 59'5 5837 5758 5680 560, 55*3 10 'V 16 ,8 2, *3 26 2 i 20 6,35 60561 5977 5899 5820 574. '5662 5584 5505 20 26 29 V 3+ 37 39 :♦ 5 MO 6, ,9 60.0^596, 5882 5803 5724' 5645 5566 5+87 HO 39! +* 45 47 50 53 ^ 7 40 6,4 6024 5945 5866 5787 1 5-07 5618 5 549 5469 40 Ill f 5S 6, 63 66 5! 9 50 6088 ^09 5993 59^915850 57701 5690 1 5611 553' 1 545*1 50 66 12. 3 11 5 7+ 8 77 19. •3 7 '3 ;t.. 59'3I5833 5753 56-'3 15594 5 5 '4 5+34 0' ~o 10 6058 5977 1 5897 58,7 5737 5657 5577 5496 54:6 10 •3 16 '9 11 *4' *7 '.'(► 6042 5962, 588, 5801 572, 5640 5560 5479 5399 20 *7 29 n 35 37 i 40 ;io 6027 5946 5«66 5785 5704 5623 5543 5+6* 538, :♦ 16 '9 22: *5 *7 :.'o ^9S< 5«6, 5787 5705 5622 5540 545*1 5376 5*94 20 27 30 33 36 38 + ' :i Horizonlal Panillix. " of Corr. for " of I'ijr, sub. T^ A|,p. Par. "-^ Alt. 53' 1 «4' 55' .56' 37' 1 5»' 1 59' I CO' 111' 0- 2" 4' B" 8" 1 10" 0.= o 9-99 999 999 9-99 9-99 9-99 999 9'99 9'99 ! Id" o' 5891 5X08 57*4 564. 5558 5474 5391 5308 5**5 31 6 8 " '4 ««6. 10 5876 5793 5709 5625 554* 5458 5375 5*91 5207 10 14 17 19 22 25 28 20 586, 5777 5694 56,0 55*6 544* 535S 15*74 5190 20 28 3'l34 36 39 14* II. P. .HO 5847 5762 5678 5594 55.0 54*6 534* 5*57 5'73 30 ■^^ 45148 5° 53J56 S3 40 5832 5747 5663 5578 5494 5410 53*5 5241 5.56 40 56 59 62 65 50 5817 i731 i64L 5563 5478 5393 53°9 5**4 ilil 50 IL li 76 21. iiii ,' , 41 5802 5717 5632 5547 5462 5377 5*9* 5207 5122 3 8 II 14 10 5787 570* 56.7 553* 5446 536. 5276 5.9. 5105 10 '4 '7 20 *3 26 28 2 3 20 5773 5687 5602 5516 543 > 5345 5260 5174 5089 20 28 3' 34 37 4° 143 3 4 30 5758 5672 5587 5501 5415 53*9 5*43 5.58 5072 30 43 46 49 5' 54157 4 6 40 5744 5658 5571 5485 5399 53'3 5**7 5141 5°55 40 57 60 63 66 69 7* 5 7 50 57^9 5643 5556 5470 5384 5*97 5211 5124 5038 50 .75_ 78 81 _83_t86 fi 8 42 57>4 5628 5541 5455 5368 5281 5-95 5108 ~^ ~ 3 -e 9 '4 7 It » 10 10 5700 56,3 55*6 5439 535* 5266 5'79 5092 5005 10 '4 20 *3 26 29 " 211 5686 5599 55>i 54*4 5337 5*5° 5163 5°75 4988 20 29 3* 35 38 4' 44 '3 30 5671 5584 5496 5409 53** 5*34 5 '47 5°59 497* 30 44 47 49 5* 55 58 40 5<'57 5569 5482 5394 5306 5218 5'3i 5°43 4955 4(1 58 61 64 67 73 50 5643 illl 5467 5379 5^9' 5203 5027 493") 50 11 2i 21 6 82 9 TT 15 iTlT 5628 554° 545* 5363 5*75 5187 5°99 5010 4922 (1 3 10 56.4 5526 5437 5349 5260 5171 5083 4994 49°6 10 '5 18 21 *4 26 30 20 5600 5511 54** 5334 5*45 5,56 5067 4978 4S90 20 3° 32 35 38 4' 45 ■M 5586 5497 5408 5319 5*3° 5141 5051 496* 4873 3(1 45 47 5° 53 56 60 4(1 557* 5482 5393 5304 5214 5125 5036 4946 4S57 40 60 63 65 68 71 75 50 5558 5468 I 5378 5*89 5199 5110 5020 493° 484. 50 7; 21. 81 il 87 ll 44 5544 5+54 5364 5*74 5.84 5094 5004 49 '4 48*5 3' -T 9 "12 '5 10 553° 5439 5349 5*59 5169 5079 4989 4899 4809 10 '5 lis 21 *4 27 3° 20 5516 54*5 5335 5*45 5154 5064 4973 4883 4793 20 3°' 33 36 39 4* 45 30 5502 5411] 5320 5230 5139 5048 4958 4867 4777 30 45i48 5' 54 57 61 40 5488 5397|53°6 5215 5124 5033 494* 485. 4760 4(1 61 64 67 73,76 60 H74 5460 5369 5*77 5200 5109 5094 5018 4W 49" 4836 4744 50 °i 3 82 }1 9 iil^ 45 5.86 5003 4820 47*8 12 '5 10 5446 5355 5263 5171 5080 49S8 4896 4S04 47'3 10 I5'i8 21 *4 *7 31 20 5433 5341 5*49 5157 5065 4973 4881 4789 4697 20 3' 34 37 40 43 46 30 54'9 53*7 5*35 5142 5050 4958 4866 4774 4681 30 46 49 5* 55 58 62 40 54=5 5313 5220 5.28 5°35 4943 485. 4758 4666 40 62 65 68 74 '77 50 539* 5*99 5113 49*8 483s 4743 4650 50 77 80 83 87 90 -2i. 1F"o 5378 5285 5'9* 5099 5006 49'3 ^S^ 47*7 4634 ~ 3 -6 9 12 ;;5 10 5365 5*71 15178 5085 499* 489S 4805 47'* 4619 10 '5 ■9 *5 28 20 5351 5258 5.64 5071 4977 4884 479° 4697 4603 20 31 34 37 40 44 47 II. P. 30 5338 5*44 5150 5°57 4963 4S69 4775 46X2 4588 3(1 47 5° 53 56 59 63 61 ' 40 53*4 5*3° 5;36 5042 4948 4854 4760 4666 457* 40 63 66 69 7* 75 78 50 53" 5*'7 5028 4934 484° 4745 4651 I4557 50 ]l T 85 -T 9 91. '3 94 16 « 5298 5203 5 "09 5014 4920 1 4825 473' 4636 4542 J 10 5284 5190 5095 5000 4906 4811 4716 46*1 45*7 10 16 '9 *5 28 3* 3 20 5271 5176 508. 4986 489. 4796 4701 4606 4511 20 32 35 38 44 48 5 30 5*58 5163 506S 497* 4877 4782 4687 4592.4496 30 48 5' 54 56 60 64 6 40 5*45 5149 5°54 4959 4S63 4768 4672 4577 4481 40 64 66 70 73 76 So 50 5*3* 5.36 5040 4945 4849 4753 4658 456214466 50 80 IL 86 il 11 ^ II 48-0 5218 51*3 502714931 4835 4739 4643 4547 445' 3 6 10 '3 16 III 5206 5109 5013 4917 4821 47*5 4629 4533 4436 10 16 '9 22 26 29 3* >3 20 5'93 5096 5000 4903 4807 4711 4614 4518 4421 20 32 35 39 4* 45 48 9 H 30 5. So 5083 4986 4890 4793 4696 : 46C0 4503 4406 30 48 5* 55 58 6i 65 40 5.67 5070 4973 4876 4779 468214585 4488,459' 40 65 67 7' 74 78 81 50 5 '54 5°57 4960 4862 4765 4668 1 457 1 4474,4376 ."iO Si il 87 90 2l± 97 16 «9 "o 5141 [5044 4946 4849 4751 4654 1 4556 4459 4361 3 -6" 10 '3 III 512815031 4933 4835 4738 4640 454* 4444 ' 434" 10 16 '9 *3 26 29 33 ;.'0 5.16 5018 4920 4822 47*4 4626 4528 44301 433* 20 33 36 39 42 46 49 30 5103 5005 4907 4809 4710 4612 4514 44'6l43'S 49 5* 56 59 6* 66 40 5091 4992 4894 4795 4697 4598 I4500 44°* ! 4303 40 66 69 7* 75 79 82 50 5078 J4979 48811478* 4683 4585 1 4486 4387 1 4*89 50 82 85 89I92 95 98 1 Si.n's Alt. .5° V,° 7° R° 14° 25° 34° 42° 51° «4° !I0° Stiii'»Alt. i-.° « 7°«°«' II' 12° \-V' H° W° unh. 17 13 II 9 7 9 11 13 15 17 18 jnA. 15 11 9 7 5 4 3 * ' ° 1 T.ABI.R 7;{ on.-, Till'; I-OCiAIUTllMli: niFKKKKNCIv | ( Il«nimi'td-, :t(» iiic^i.es. Kalireiilii'il'.> Tliermoineter, :^{^°.) i Apr- Horizontal Fiirallnx. | 'cf Corr. (or " of far ni/.. ]T^ | Alt. 53' 54- 1 55- 1 6H- | 57' 1 SH' | 6!)' | (io- 1 nr Par. ^[rj 4- B' 1 li'l 10 -Z 3 _ 999 9-99 ,9-99 J9-99 ]9-99 19-99 J9-99 j 9-99 ; 9-99 — 1- - 60° (1 5C65 4966 4867 4769 4670 [4571 447* 4373 14*74 3 7 >o ,3 16 10 5°53 4954 4«55l4755 4656! 4557 4458 43 59 1 4260 10 16 a, *6; 3° 33 ,«4. 2(1 5040 494' 48421 474* 4643 ! 4544 4444 4345 ' 4*4^ 20 33 36 40 43' 46 5° »l) J028 4928 : 4829 , 4729 4630 4530 443° 433' 4*3' 30 5°|53 56 60 63 67 II. P. 40 5016 4916 4816 47.6 4616 45.6 4417 43'7 4*'7 40 67 70 73 77; 8c 83 53' 50 5££i 4903 ! 4803 1 47031 4603 1 4503 4403 4303 I4203 ,"10 ll!»L yo| 93! 97 100 51 4991 14S9 1 4790146901459° 445*9 4389 4*89 4'8S ^ir ^3 -l--Tl,-77' I 10 4979 :48:-»l 4778! 4677 4577 4476 4376 4*75 i4'74 10 17 *3 *6: 3°| 34 ." ' 2(1 4967 4ii66 14765 4664 4564 4463 4362 4261 14160 20 34 37 40 43: 47 50 ■'• 4 SO 4954 4853 475^ 465 > 455° 4449 4348 4*47 4'46 30 5° 54 57! 60: 64' 6- 4 5 74! 78: 8,| 84 ;: 6 40 4942 4841 4740 4639 4537 443° 4930 48291477.7 1 4626 4524 1 4423 4335 4*34 4'33 40 67 71 50 4321 4220I4119 50 il 88 ^i_2ll^'i^ '7' ^8 .VJ (1 49i8i48i6 4715 !46i?:45'> i44'0!43o8 4106 4105 3 7| '°l '+1 '■' H 10 lo 4906 1 4804 4702 46CO 1 4499 4397 4*95 4'93 409. 10 17 *4 *7j 3'| 34 ,, ,, 2(1 4S94 4792 4690 4588 4486 4384 428. 4'79 4°77 20 34 37 4.] 44 48 5'' MO 4S82 47S0 4678 4575 4473 437> 4268 4.66 4064 30 51 54 58' 6.1 65I 68 40 4871 4768 4665 4563 4460 4358 4*55 4'53 4050 40 68 72 7 51 79' 82; 8b „ ,, so 4859 4756 4653 4550 4448 4345 4*4* 4'39 4036 50 86 89 _93]_96i_99io2 ,:,, 53 4847 1 4744 4641 14538 4435 433* 4**9 4.26 4°*3 3 7 'o; '4' '7 , 10 4835 473'- 4629 45*6 44** 43 "9 42.6 4113 4009 10 .7 *4 *7! 3'| 34 1 . 20 4874 4720 4617 4513 4410 4306 4203 4099 3996 20 34 39 41 451 48 5* 2 3 :o; .4; '7 « 8 10 476614661 4557 445* 4348 4*43 4'39 4034 393° 10 *4! *«! 3'i 35 7 '- 20 4755 4650 4545 4440 4336 4*31 4126 4021 39'7 20 35 139 4* 45 49 52 H .1 *l 4743 4638 4533 44*8 4324 4219 4114 4009 3904 30 5* 56 59 63 66| 7o»l'3 40 473^ 4627 45** 4417 43" 4*06 4101 3996 389' 40 70 74 77 8. 84J SS 5« 4721 46.5 45'o| 4405 I 4*99 '4194 408^ 3983 3878, 50 88 11 Jl ji\]2i^ 6T~0 4709 -^6^^ 4498 14393 1428714182 4076 397' 3865 ~o 3 7 "! 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"•' 8t 8 ' 89 ^'■■^' 30 4676 457o| 4464 14358 14251 [4145 4039 3933 38*7 30 53 57 6. 40 4665 4559)445* 4346 4*4°i 4'33 4027 39*0 3S.4 40 7. 74 78 flO 4654 4548 444' 1433414*28 4121 40'4!39°8 380, 50 i2_ 9* 4 _96|_99 u^ io6| 1 , _ J 56 4643 4536 44*9! 43231 4216 4109 4C03 3895 1?^ "(T 7 ..: .4I .8 .. , 10 4632 14525 [4418 4311 ! 4104 4097 399° 3883 3776 10 .8 *5 *» 3*^ 36 :,;, 20 4622 j 4514 1 4407 1 43CO 4192 ; 4085 3978 3871 3763 20 36 39 43 « ^8! ]\ ;' t 30 46ii|4503!4396|4288|4i8iJ4073 3966 3858 375' 30 54 57 61 40 4600 [4492, 438 5 14277 4169 4062 3954 3846; 3739 40 72 75 79 8*: 86; 9°l,i!6| 50 458914481 43-3 42661 4158 4050 39421 3834137*6 50 9° 931 97j'°''04'°8 7 7 1 57 4578 1 447° 1 4361 1 4254 1 4146 1 4038 ! 3930 1 3822 1 37 14 (j" °! 4 7f'"'i '4' '8 ills 10 4568 4460 4351 ,4243 4135 1 4027 3918 1 3810 3702 10 18 '22 25 29 32 36 9I9 2(» 45 58 '4449, 4341 ,4^3^ 4'24]4°'5 39°7 , 3798 369° 20 36:40 43 47 5'| 54 30 4547 1 4439 , 433° ! 4^1' 1 4' ■ ^ 4004 3895 ; 3786 3678 30 54 58 6.1 65' 69' 73 40 4537,4428 43>9 4i'0!4'0'l 399^ 3883 , 3774 3666 40 73:76 80 83 87, 9. II. P. 50 4526 44^ 43o8_| 4199; 4090 4;ir44a7 4297 ' 4'8"^8 , 4079 398, 1,872 13763 13654 m 91 ,941 98 .02 105 109 SI 1 SH 3969; 38601 3751 3642 (T oj 41 7 ~l~ri:T8,. 10 4506 4396 4287: 4177 14068] 3958 13849 '3739 363° 10 i8'22l 25' 29' 33' 37 ' . 20 4496I43S6 4276 4166 4057 3947 1 3837 3728:3618 20 37 1 40 44; 48 5' 55 : - 30 4485! 4375:4^66 415614046 3936 3826 37.6 1 3606 30 55 59 621 66 7° 73 -J 4 4(1 4475 4365 '4^55 '4'45 [4035 3925I38.5 3-05 3595 40 73 177 8,1 84' 88 92 4 6 50 4465 1 4355 4^44 4'34i 4024 39'4 3803 3693 3583 50 91:_21_22I£lifZiIf ;; , ;ll 4405 '4294 4182 4071 3960 3848 •.--8 I-.626 ,;,4 .V) 9; 06 icr 104 ic8 1 1 1 Ml,', All. ft" (f V n' u" 2.1" 31" 42° 51° " 4° !lo'° 1 Smri. Alt. ft" (P T «" H" 1 1° 12° I4» IH^ 30'1 1 <../,. 1- n II 1) 7 II n ■' '" 'S 1 •'"''• (? (I ') 7 > 4 3 2 1'^ no6 TAELE 73 THK LOGARITHMIC DIFKERKNCIi } (lJi.rometer, 30 iricliea. Fahrenheit's Thermometer, 50".) ^^1 A pp. Alt. Horizontal I'ar-.illax. "of 1'i.r. Corr. for" of l'»r. tub. .53' 1 54' 55' 1 66' 1 67' 1 58^ 5!)' 1 6»' 61'" JYr^ Jl^" 8' ^ 10- 9'99 |9'99 9'99 9'99 1 9'99 9'99 9'99 1999 9-99 i (JO 4395,4184 4172 406. 3949 3838 3726 36.5 3503 4 7 11 15 19 .«ui. 10 43S6 4^74 4.62 4051 3939 3827 37'5 3604 3491 10 '9 22 26 30 33 37 H.P. 20 4376,4264 4152 4040 3928 3817 3705 3593 348. 20 37 4' 45 48 5-\ 56 ty 30 4366 4254 4142 4030 391S 3806 3694 3582 3470 30 56 60 63 67 7' 75 40 4357 4^45 4132 4020 3908 3796 3683 357' 3459 40 75 79 82 86 901 94 ^ 50 4347 4135 4'^^ 4010 3898 3785 3673 3560 3448 50 9± 97 4 lOI 105 109,1 12 2 3 «1 4331* 4225 4113 4000 3S87 3775 3662 3549 3437 ~7l^ 10 4328 42.6 4103 399° 3877 3764 3652 3539 3426 10 19 13 26 30 34 38 20 4319 4206 4093 398Q 3S67 3754 364, 3528 3415 20 38 4' 45 49 53 57 5 SO 4310 4>97 4084 3970 3S57 3744 363, 351S 3405 30 57 60 64 68 71! 76 c 40 4301 4.87 4074 3961 3847 3734 362. 3507 3394 40 76 79 _83 87 9'| 95 7 AO 4291 4282 4178 4.68 4064 4055 JiiL 394' j837_ 3827 3714 36,0 -3497 3383 50 IL ^ 106 iio!n3 ■51 '9 3600 34S6 3373 4 "1 10 4173 4"45 393' 3818 3704 3590 3476 3362 10 19 ^3 27 30 34 20 4264 4150 4036 3922 3808 3694 3580 3466 3352 20 38 41 46 53 M.P. 30 4155 4141 4027 3912 3798 3684 3570 3456 3342 30 57 61 65 68 72 : 4001 3767 3650 3533 34'7 3300 31S5 1(» '9 -i 27 3' 35, 19 20 4109 3992 387! 3758 364' 35H 3407 3291 3'74 20 39 43 4" 5' 54 59 .30 4101 3984 3867 3750 3633 35,6 3398 328. 3164 30 59 62 66 70 74 78 111'. 40 4093 3976 3858 374' 3624 3507 3389 3272 3'55 40 78 82 86 90 94 98 53' 50 4085 I'll! 3S50 3733 36,5 3498 3380 3if'3 3146 50 98 102 106 209 "3 "7 66 4077 3959 IhT 3714 liST 1^ 337' 3254 3136 4 8 16 20 1 10 4069 395' 3833 37.6 3598 34S0 3363 3245 3127 10 20 14 17 3' 35 40 2 20 406, 3943 3825 3708 3590 3472 3354 3236 3118 20 40 43 47 5' 55 59 3 30 4053 3935 3817 3699 3463 3345 3227 3110 30 59 63 67 7' 75 79 4 40 4"45 3917 3809 369. 3573 3455 3337 3219 3101 40 79 83 86 90 94 98 A 50 4038 3919 3801 ,683 3565 3446 lEi 3210 3092 50 98 4 106 8 ~I2 1.4]. .8 l6| 2C 6 7 lT~n 4030 39- 3793 1677 3556 [3438 3320 3201 3083 ~ir 10 4023 3904 3785 3667 3548,3430 33" 3193 3074 10 20 24 2S 32 36 4c 55 59 K 6 20 4015 3896 3778 3659 3540 3422 3303 3184 3066 20 40 43 47 51 9 - 30 4008 3889 3770 365. 353^ 34'4 3195 3,76 3057 30 59 63 67 75 79 40 4000 388. 3762 3643 3514 3405 3286 3167 3048 40 79 83 87 9' 95 99 H.P. 50 3993 3874 3755 3747 3635 3516 3397 3278 3'59 3040 50 99 103 4 107 III "5"9 16 20 Bl' «H 3985 3866 362S 3508 3389 3270 3150 3031 8, 12 10 3978 3859 3739 3620 3501 338' 3262 3142 3023 10 20 24, 28i 32 44 48! 51 36 4c i 20 3971 3852 373^ 36,3 3493 3373 3^54 3134 3015 20 40 56; 6c 2 30 3964 3844 37^5 3605 3485 3366 3246 3126 3007 30 60 64 68 71 84 88 92 76| 8c 40 3957 3S37 3717 35981 3478 1 3358 3238 31.8 2998 40 80 96,100 4 50 SI 1950 3830 3710 3590 347013350 3230 3"o 2990 ■50 KC l04lloSill2 11612c 6 r, 3943 3823 3703:3583 3462 1 3342 3222 3102 2982 4 8| 12 .6 20 lo 3936 3S<6 3695 3575 3455 3335 3215 3095 1974 10 20 24 2S 32 36 40 7 20 3929 3809 3688 3568 3448] 33^7 3207 3087 2966 20 40 44 481 52 56 60 8 .30 3922 3802 368.1 3561 34401532013199 3079 2959 30 60 64 68l 72. 76 80 9;? 40 39'5 379 5 3674 3554 3433l33'i|3'92 3071 2951 40 So 84 881 92; 96I.0. 50 3909 37S8 3'''67l3 54'^ 3426 1 3305 I31S4 jo6_4_ _2 943_,_ 50 ioT|io5'ic9'ii3 117I120 Si.i,\ Alt. 5 ()" 7 li 14 " 25' 31 42 51" 04" !)0 ' 1 Siai's Alt. 5 (>" r It" 0° 1 1' 12" 14° 1 rao" suL 17 i-i 11 9 7 9 n n 15 17 18 1 »"/-. IS 11 9 7 5 4 3 ^ > <-' 1 THK I.OOAKITll.MIC 1)1 FFKUKNCK j (B..r,>,„eter, :tOi..c lies. ralUz Fahrei>l,eii'» TI.eiinomfier, aO^.) _ 1 A,.p. Hjri«,ntal P 1 "oC l'..r. Corr. fur " of I'ar. , lb. |5 r.s |'s4' 55- 5C' ] 57' 1 5a' 1 50' (irt- 1 61- o-l-Jr-W il 10 ., 9>j ■./99 9'99 999 999 [999 9-99 9 99 999 70 (t 3902 37«' 3660 3539 34>8 3198 3'77 3056 2935 4 8 .2 16 20 10 3S9S 3774 3653 353» 34" ! 3290 3.69 3049 Z928 10 24 28 32 36 40 ,ub 20 38X9 376'< 3647 3526 34.4 3283 3.62 304. 2920 2(1 40 44 48 52 56 6i 30 ,SS2 3.01 3640 35<9|S398 3276 3'55 3034 29.3 30 6. 651 69 73 77 81 40 -,S-6 3/55 3*^33 3512 3391 3269 3.48 3027 2905 40 8. 85 89 93 97 .0. 64) 3S69 3V4)i 362b 3384 314' 3019 2898 50 101 105 109 "3 1.7 .21 TT'o 3863 3741 3620 3498 3377 3255 3133 3012 2890 oi 4 8 "72 .6 IZ 10 3857 3735 36,3 3492 3370 324S 3i^7|3'-o5 2883 10 20 24 18 32 37 4. i 1 2.1 3851 3729 3607 3485 3363 3242 3.20 299S 2876 20 4' 45 49 53 57 6. 2 1 :m 5X4+37" 36UI 3479 3357 3235 3113 2991 2869 30 61 65 69 73 77 8. 3 2 40 3S38 37.6 3594 3472 3350 3228 3.0612984 2862 40 8. 85 _89 93 98 102 4 1 2 ftO 3S88 j466_ 3343 1 3221 3*^99 1 2977 2hi 30 in2 ic6 "4 1.8 .22 •] 5 "72"^ 3826 370+ 3581 3459 3 3 37 |3'- 14 3092 1 2970 2848 2^"^ ~8 .2 .6 ^0 (J 4 10 3820 369» 3575 3453 3330 3»^8 3085 2963 284. 10 24 29 33 37 41 7 4 20 38 14 1 3692 3569 34+7 33^4 3202 3079 '2., 5 7 2834 20 4. 45 49 53 57 61 « 5 3(1 3808 36S6 3563 344" 33.8 3'95 3073 2950 2827 30 61 65 69 78 82 915 40 3803 3A80 3557 3434 33'* 3189 3066 2943 2S2. 40 82 86 90 94 98 102 .50 3-97 3674 liil 3428 13£1 3. 82 3060 2937 28.4 50 102 106 11 M_9 111 ::« «i 3791 1 j658 3545 3422 3299 3176 3053 Z930 280- "~F 4 8 .2 ~6 10 37»5 3662 3539 34.6 3^93 3.70 3047 ■ 2924 zSo. 10 20 25 29 33 37 41 'iO 37S0 3*^57 3533 3410 32S7 3.64 304. 29,8 2794 20 4> 45 49 53 57 62 3(1 37 4 ,651 3528 3404 328, 3.58 3°35 2911 2-88 : 3385132591 3'33i 3C=7 2SS. 2756 263c 2(1 42 46 i" 54 59 63 >i|4 M 3633 3S07 3381 3255 3129 j 3003 2877 275' 16; ^ 3(1 63I 67 71 76 80 84 '■> 4 4U 3629 3403 3377 3251 3125 2999 2873 2:47 262. 4(1 ?4 88 92 97 .0. .05 so 362_5 3499 33-3 J147 3'2'h-995 2R68 2742 2616 50 10; 109 ■>3 122 .26 79 362, 3495 3369 3243 311612990 2864! 2738 "1677 "(T c i * ~il ~i? 21 10 36,7 349' 3365 3239 3.13 1 2986 2860 2-34 2608 10 2 25 29 34 5" *2 20 36,4 3488 336. 3235 3 '09 1 2982 2X56 2730 2604 20 42 46 5': 59 *? 30 3"'o 3484 3358 323' 3105 I 2979 2852 2726 2600 30 6 6- 7 7« ; 8c X4 ■;;: ; -,6o; 1 3480 3354 3228 ,,c, 2975 2848 »-'22 2596 40 84, 87 93 97 jic '05 so ' 3603 1 3477 1 3350 1 3"4l 3097 1 197> 1 »844 2 7^8 i 2 59J^ AO 1C5I11C 114 11! I122 .26 s,...'. AU. 5° IP 7° a" 14° 23' 34° 42° 51° 04° !M)° 1 Slur-. Alt. !," r 7° 11° it" 1 r 12° 14° 18° 30° 1 1 ,;l, ,-,;,,.) 7 9 '■ '3 >S .7 •! 1 ..,/,, .51157,432 ' <: 1 TABLE 73 THt; hOGARITHfJIC DIFFERENCE (Barometer, 30 inches. Fal.reiil.eit's Thermometer, 60°.) J A,, p. Alt. lorizontal Parallax. "of Par. Corr. for " of Par. .u*. •^1 "s-f 54' 55' 5C 1 57' _^ 59' 1 r;o' 1 61' 0' r ^ 6-|8' W ^ 999 999 9-99 9-99 9-99 9-99 9-99 1999 19*99 80 3600 3473 3347 3220 3094 2967 2840 2714,2587 10 3596 3470 13343 3217 3090 2963 2S37 2710 ^584 10 20 3593 3467 3340 3213 3087 2960 2833 2707 20 «<4. 30 3590 3463 3337 3210 3083 1 2956 283° 2703 2576 3(( ! 40 3587 3460 3333 3206 3080 1 2953 2826 2699 ^573 40 50 358+ 3457 333° 3203 3076 2949 2823 2696 28,912692 2569 50 H.l'. 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J 7670 753' 739ft 47 4(1 9.68 8973 8787 860S 8437 827. 8. .2 7959 ■/it, 7667 7 5-8 7J94 48 4f» 9,65 8970 8784 S6os 843; 8269 8110 7956 7808 -665 75^6 739= 49 5H 916, S967 1 S78, 8602 843, 8266 17^ 7954 Wi- 7662 75=4 7390 "50" 51 9158 S964 8778 8599 8428 8263 8,04 795' 7803 7660 75" 7387 51 52 9'55 896. 8775] 85,6 8415 8,02 7949 7^58 75'9 7385 52 53 9152 8957 8772 1 85,4 S422 8258 809, 794ft 7798 7^55 "5'7 7383 5;» 54 9.48 8954 8769 859. 8420 82 55 80,7 7944 779*^ 7^5 3 r5'5 738. 54 55 9'4S 895' 8766 8588 84.7 82521 8094 794' 7794 7651 75'3 7379 55 6« 9142 8948 8763 8,85 84M r87S0| 809. 7939 779' 764S 75.0 73-ft :>r, 57 9.38 8,45 8760 8582 8411 8747 80x9 7936 7-89 7646 ^508 -3"4 57 58 9' 35 8,42 87',; 8579 8409 8244 8086 7934 7786 7644 7506 -772 :<« 5a 9132 8919 8754 8576 R406 8742 8084 793' 7-S4 7^4' 75=. 7'i7'^ ."W 60 9.2« 8935 875- 8573 8403 inn 808^ 79=9 7782 7639 7toi ^,6« lilt TABLE 74 PROPORTIONAL LOGARITHMS sec 1. n.) h in 0''35''lo''3(Flo^37°' h „,| h J h m h m h n h in h m sec "" 0^33 0°34' 0°3B'|0''39'l0°40' 0°41' 0°42' 0°43 0°44' 7368 7238 7..2I6990 6871 6755 6642 653. 6425 6320 6218 6, ,8 7365 7236 7..0 16988 6S69 6753 6640 6530 6423 6318 62.6 1 7363 7^34 7108 6986 6867 6751 6638 6528 63.7 62,5 6.15 2 736. 7232 7106 U984 6865 6749 6637 6527 6I20 63.5 62,3 61.3 3 7359 7229 7 104 1 6982 6863 6747 6635 6525 64.8 63.3 62.. 4 7357 7227 71021 6980 6861 6745 6633 6523.64.6 63.2 6210 6. 10 5 7354 7225 6978 6859 6743 663. 652. 64.4 63,0 6208 6.08 r, 735^ 7223 7098 6976 6857 6742 6629 65-,9 64.2 6308 6206 6.07 7 735° 7221 7°95 6974 6855 6740 6627 65.8 64.. 6306 6205 6.05 It 1341 7219 7093 6972 6853 6738 6625 65.6 1 6409 6305 6203 6103 9 "To" 7346 7217 7091 6970 6851 673616624165,416407 6303 6201 6.02 10 7343 7215 7089 6968 6849 6734 6622 65.2] 6405 630. 6200 6,00 II 7341 7212 7087 6966 6847 6732 6620 6510 [6404 6300 6,98 6099 l> 7339 7210 7085 6964 6845 6730 6618 6509 I 6402 6298 6.96 6097 13 7337 7208 7083 1 6962 6728 6616 6507 6400 6296 6194,6095 14 7335 7206 708, 6960 68^1 6726 66.4 6505 6398 6294 6.93 609+ 15 7333 7204 7079 6958 6839 6724 6612 6503 6397 6293 6.9. 6092 IK 7330 7077 6956 6S38 6723 66.1 650, 6395 629. 6,89 6090 17 732S 7200 7075 6954 6836 6721 6609 6500 6393 6289 6.88 6089 IH 73.6 7.98 7073 ^£11 _6834i_67_.9 6607 649i 639. 6288 6.86 6087 19 "20" 73^4 7.96 7071 6950 6832 6717 6605 6496 6390 6286 6,84 60S 5 20 21 73" 7'93 7069 6948 6830 67.5 6603 6494 6388 6284 6.83 6084 21 22 7320 7191 7067 6946 6828 6713 660. 6492 6386 6282 6181 6082 22 23 73>7 7.89 7065 6944 6826 6711 6600 649. 6384 6281 6,79 6080 23 24 73>5 7.87 7063 6942 6824 6709 6598 6489 6383 6279 6,78 6079 24 24 7313 7.85 706, 6940 6822 6707 6596 6487 6381 6277 6.76 6077 25 2« 7311 7.83 7°59 6938 6820 6706 6594 6485 *379 6276 6174 6076 26 27 7309 7181 7057 6936 6818 6704 6592 6484 6377 6274 6.73 6074 27 28 73°7 7'79 7054 6934 6816 6702 6590 6482 6376 6272 6.7. 6072 28 29 ■w 7304 7177 7052 6932 6814 6700 6589 6480 6374 6270 6,69 607. 29 7302 7175 7050 6930! 6812 6698 6587 647S 6372 6269 6,68 6069 30 31 7300 7172 7048 6928! 6810 6696 6585 6476 6370 6267 6.66 6067 31 32 7298 7170 7046 6926 6809 6694 6 8 6475 669 6265 6,64 6066 32 33 7296 7.68 7044 6924 6807 66^2 68. 6473 6367 626^ 6163 6064 :« 34 7294 7166 7042 6922 6805 6691 6579 647. 6365 6262 6,61 6063 34 35 7291 7.64 7040 6689 6578 6469 6363 6260 6159 6061 36 3(; 7^89 7162 7038 eT 68cl 6687 6576 6467 6362 6259 6.58 6059 36 37 7287 7160 7036 6916 6799 6685 6574 6466 6360 6257 6.56 605S 37 38 7285 7.58 7034 6914 6797 6683 6572 6464 6358 6255 6.54 6056 38 39 7283 7.56 7032 ^9'^ 6795 6681 6570 6462 6357 6254 6.53 6055 39 40 7281 7-54 7030 69.0 6793 6679 6568 6460 6355 6252 6.5. 6053 40 41 7279 7.52 7028 6908 6791 6677 6567 6459 6353 6250 6,50 605, 41 42 7276 7>49 7026 6906 6789 6676 6565 6457 635. 6248 6.48 6050 42 43 7274 7<47 7024 6904 6787 6674 6563 6455 6350 6247 6,46 6048 43 44 7272 7145 7022 6902 6785 6672 6561 6453 6348 6245 6.45 60+6 44 45 7270 7>43 7020 6900 6784 6670 6559 645. 6346 6243 6,43 6045 45 46 7268 7141 7018 6898 6782 6668 6557 6450 6344 6242 6.41 6043 46 47 7266 7'39 7016 6896 6780 6666 6556 6448 6343 6240 6,40 6042 47 48 7264 7>37 7014 689+ 6778 6664 6554 6446 6341 6238 6.38 6040 48 4n 7261 7.35 7012 6892 6776 6662 6552 6444 6339 6237 6136 6038 49 "50" 7^59 7133 7010 6890 6774 6661 6550 6443 JJ^ ^^ 6135 6037 50 51 7257 7131 7Co8 6888 6772 6659 6548 644. 6336 6233 6,33 6035 51 82 7255 7129 7006 6886 6770 6657 6547 6439 6334 623. 6.71 603; 52 53 7^53 7126 7004 1 6884 6768 6655 6545 6437 6332 6230 16. 3D 6032 S3 54 7^5- 7124 7C02 68S2 6766 6653 6543 6435 6331 6228 6,28 6030 54 55 7249 7122 7000 6880 6764 665, 654. 6434 6329 6226 6126 6029 55 5C 7246 7120 6998 6878 6762 6649 6539 6432 6327 6225 6125 6027 56 57 7244 7118 6996 6877 6761 6648 6538 6430 6525 6223 6123 6025 67 R8 7. .6 6994 6875 6759 6646 6536 6428 6324 622. 6.2. 6024 58 59 7140 7114 6992 6873 6757 6644 6534 6427 63« 6220 1 6123 6022 M «0 7238 7112 6990 687. 6755 6642 6532 6425 6320 62.8:6.i816o2.| d T.Aiii.r. 7i. 913 i'UOI'OKflONAI, I.OU.VIUTII.MS «ecT h mt h n,l h n.1 h ml h m\ 0°45'10^4G'|0°47'|0''48'IO°49'| h n> ll B h B h . h .,„ „, „ „1 "" a' 50' ft-'ftl' 0'52 0''53'|0''M'j0'.-.4 rSS "" 6oz. 5,25 583- 1 5740 1 565'! 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S'>53 14 5997 5902 5809 57,8 5629 554' 5456 5371 5290 5209 5129 5051 15 5995 5900 5807 57.6 5627 5 54° 5454 537° 5288 5207 S.28 5050 It; 5993 5S98 5806 57'5 5626 5538 545 3 5369 5287 5200 5'i7 5049 17 599^ 5897 5804 57'3 5624 5537 545- 5368 52S5 5205 5>i5 5C48 III _5990_ 5895 i!£I 57'^ ^62^ J^l6_ 545° 5366 5284 5203 5'i4 5°46 lit 5988 5S94 5S0. 571C 562, 5534 5449 5365 5183 5202 5'i3 5°45 20 59»7 5S92 5800 5709 5620 5533 5447 5364 528, 5201 5122 5044 21 22 5985 5S91 5798 5707 56,8 553' 5446 5362 5280 5'99 5120 5042 22 23 5984 58S9 5796 5706 56,7 553° 5444 536' 5179 5.98 5"9 5C41 23 24 5982 5888 5795 5704 56,5 5528 5443 5359 5177 5197 5. .8 5040 24 2A 598. 5886 5793 5703 5614 5517 5441 5358 5276 5'95 51.6 5°39 25 2(i 5979 5884 5791 5701 56,2 5515 5440 5357 5175 5 '94 5"5 5°37 2t; 27 5977 58S3 5790 5700 56,, 5514 5439 5355 5173 5'93 5"4 5036 27 2K 5976 588. 5789 5698 56,0 5513 5437 5354 5171 5191 5112 5°35 211 2a 59:4 58S0 i787 jhL 5 60S 552. i43i 5351 ii91 5... 5033 2» :«) 5973 5878 5786 5695 1 5607 5510 5435 535' ii6i" 5.89 5"° 5032 1i() 31 597" 5877 5784 5694 5605 55.8 543 3 535° 526S 5.87 5.08 5031 31 3> 5969 5875 5783 5692 5604 55'7 5431 5348 5266 5186 5.07 5030 32 33 596h 1 5874 596t ! 5«7X 57S1 569, 5601 55.6 543° 5347 5265 5.85 5.06 5028 33 34 57S0 5689 5601 S5'4 54'-9 5346 5264 5183 5105 5027 34 3.1 5965 5870 5778 5688 15599 55'3 5428 5344 5262 5,82 5103 5026 :f. 3«> 5963 5869 5777 5686 5598 55" 5426 5343 526. 518. 5102 5025 3«; 37 596, 5867 5775 5685 5596 5510 5415 5341 5260 5'79 5101 5023 37 31) 5960 5866 5774 5683 5595 5508 5413 534° 5258 5178 5099 5022 38 3!) 595^ 5864 5772 5682 5594 55°7 54" 5339. 5157 5'77 ifii 5°!' 311 41) 5957 1^ 5771 l6l^ 559^ 5505 5421 5337 5x56 5>75 5°97 5019 lo" 41 5955 586. 5769 5679 559' 5 5"4 54'9 5336 5154 5'74 5°95 50.8 41 4-2 5954 5860 5768 5677 S5«9 15503 54.8 5335 5153 5'73 5094 5017 42 43 5951 5858 5766 5676 5588 5501 54'6 5333 5151 5'7' 5°93 5016 43 44 595° 5856 5764 5674 5586 5500 54'5 5331 5150 5170 5092 5014 44 ■tri 5949 5855 5763 5673 5585 5498 54'4 533' 5»49 5169 5090 5013 45 41) 5947 5853 576. 5671 5583 5497 54.2 5319 5248 5168 5089 5012 4(; 47 5946 385'- 5760 56T0 5582 5495 54" 5328 5246 5166 508X 5010 47 48 5944 5850 5758 5669 5580 5494 5409 5326 5145 5165 5086 50C9 48 43 594J 5849 5667 5579 5493 54°8 5315 _5^4 516415085 5008 40 60 594' 1 5847 5755 -^ 5577 549' 54°7 53»4 5242 5.62 5084 5007 50 SI 5939 5846 5754 5664 5576 549° 54°5 53" 5241 5.6, 5082 5005 51 .'.2 5938 5S44 575^ 566; 5575 5488 5404 5321 5»39 5,60 508, 5004 52 53 593b 5842 575' ;66, 5573 5487 5402 53'9 5238 5. 58 S080 50f:3 53 54 5935 584. 5749 5660 5571 5486 5401 53'8 5137; 5<57 5079 5002 54 5S 5933 5839 5748 5658 5570 54S4 540° 53>7 5135 5156 5077 5CCC 55 56 593' 5«38 5746 5657 5569 5483 5398 53'5 5»34 5 '54 5°76 4999 5t! 67 5930 58-/ 5745 5655 5567 548. 5397 53'4 5133 5'53 5075 14998 57 5fl 5928 5835 5743 5654 5566 5480 5395 53'3 5 = 3' S'i- 5073 499<- All 59 59-- 5S33 574^ 5652 55^4 5478 5394i53" 5230 5150:5072 4995 5!) (JO |592s|,«-,ij ^-40 565. 55«3 5477 53')3,53'<' 5"9l 5'49;5°7!i49')4| «" | su TABLi; 7t PROPORTIOHAI, LOGARITHMS ■ ., „. h „,! h ..I h ml h o. h „! h .„, /.ml h ml 1, nl h mi h ml 1. n. see )/' U''ari»°68'|0'^59'| ll^l'lL l°2'il°3' 104-j ,0 5-| ,OB.| I";' joffl 1°9 "' ,994,4918 4844 477' 4699 "4^' 4559 4491 44-4 4357 4292 42281 4164 4993 49 '7 4*43 4770 4698 4628 4558 449° 4422 4356 4291 4227 4163 1 4991 I4916 4842 4769 4697 4626 4557 4489 44-' 4355 4290 4225 4162 2 4990 '49 1 5 484' 4768 4696 4625 4556 4488 4420 4354 4289 422414161 4989 49'3 4839 4766 4694 4624 4555 4486 44,9 4353 4288 4223 4160 4988 4912 4838 4765 4693 4623 4554 «S5 44,8 435^ 4287 422214159 4986 49" 48-'7 4764 4692 4622 4552 4484 44'7 435' 428c 4221 14158 4985 491014836 4763 4691 462. 455' 44«.? 4416 4350 42S4 422^ 4157 4984 4908 4834 4762 4690 4619 4550 44»2 44'5 4348 4283 4219 4156 498} 4907! 4S33 4760 46S9 4618 4549 44S' 44'4 4347 4282 42.8 4.55 "To" 4981 4906 4832 4759 4688 46.7 4548 448° 4412 4346 4281 14217 4 '54 -fir 4980 4905 4831 4758 4686 4616 4547 44781^" 4345 4280 4216 4>53 4979 4903 4830 4757 4685 46.5 4546 447- 441° 4344 4279 4=15 4152 'r 4977 4902 4828 4756 4684 46,4 4544 4476 4409 4343 4278 1 42.4 4151 4976 49°' 4827 4754 46S3 4612 4543 4475 44°8 4342 4277 42'3 4150 4975 4900 4826 4753 4682 46.1 454- 4474 44°7 434' 4276 4212 4149 4974 4898 4825 475^ 4680 46.0 454' 4473 4406 434° 4275 42" 4'47 4972 4897 4823 475' 4679 4609 454° 447* 44° 5 4339 4274 4146 497' 4896 4822 4750 4678 4608 4539 447' 4404 4338 4273 42C9 4'45 4970 4895 4821 4748 4677 4607 4537 4469 4402 4336 427' 4144 "20" 4969 W4 4820 4747 4676 4605 4536 4468 4401 4335 4270 1 4206 4'43 "2() 4967 4892 4819 4746 4675 4604 4535 4467 44°° 4334 4269 4205 4142 4966 489, 4817 4745 4*73 4603 4534 4466 '4399 4333 4268 4204 4141 22 23 4965 4890 4816 4744 4672 4602 4533 4465 4398 4332 4267 4203 4140 23 24 4964 4889 481S 4742 4671 460. 453^ 4464 4397 433' 4266 4202 4139 24 25 4962 4887 4814 474' 4670 4600 453' 4463 4396 433° 4265 4201 4.38 25 2C 4961 4886 4812 4740 4669 4599 45^9 4462 4395 4329 4264 4200 4'37 2fi 27 4960 4885 4811 4739 4668 4597 4528 4460 4394 4328 4263 4199 4136 27 28 4-959 4884 48.0 4738 4666 4596 45^-7 4459 4392 432714262 4198 4'35 2lt 29 4957 4882 4809 4736 4665 4595 liii _445i 439' 43261426, "97 4'34 29 30 4956 4881 4808 4735 ^66^ 4594 45^5 4457 439° 4325 4260 4196 4'33 30 31 4955 4880 4806 4734 466, 4593 45^4 4456 4389 4323 4259 4'95 4132 31 32 4953 4879 4805 4733 4662 459^ 45^3 4455 4388 43»2 4257 4194 4131 32 33 495^ 4877 4804 473^ 4660 4590 4522 4454 4387I4321 42561 4193 4130 33 34 495' 4876 4803 4730 4659 4589 4520 4453 14386 4320 4255 4192 4129 34 35 4950 4875 4801 47^9 4658 4588 45 '9 445' 4385 43'9 4254 4190 4.28 35 3ti 4949 4874 4800 4728 4657 4587 45.8 4450 4384 43'8 4253 4.89 4127 36 37 4947 4872 4799 47^7 4656 4586 45'7 4449 4383 43'7 4252 4188 4126 37 38 4946 4871 '4798 4726 4655 4585 4516 4448 438' 43-6 4251 4'S7;4'25 38 39 4945 4870 1 4797 47H 4653 4584 45'5 4447 438° 43'5 _42 4076 j 40.5 1 3954 3895 3836 3778 37*1 3664 3609 3554 3499 3446 25 2« 4.0751 4014 1 3953 3894 3835 3777 37*° 3663 3608 3553 3498 3445 26 27 4074 4013 3952 3893 3834 3776 37 >9 5663 3607 355* 3497 3444 27 2fl 407JI4012 395' 3892 3833 3775 57.8 3662 3606 355' 3496 3443 28 29 4071 '4°" 3950 3949 389, 3890 3S32 38i7 3774 37'7 3661 3605 ilil J496 Jill 29 4071 4010 3773 37.6 3660 3604 3549 3495 344' 39 .■ 37'4 3658 3602 3547 3493 3439 32 :t3 4^68 4007 3946 3887 3828 377° 37'3 5657 360. 3546 349* 3438 33 M 4067 4006 3945 3886 3827 3769 37'* 3656 3600 3545 349' 3438 34 •Xi 4066 4005 3944 3885 3826 3768 37" 3655 3599 3544 349° 3437 35 3f 406, 4CO4 3943 3884 3X25 3768 3710 3654 3598 3544 3489 3436 3ri ••17 4064 4C03 394* 3883 3S24 3767 3709 3653 3598 3543 3488 343 5 37 HI! 4063 4002 394' 3882 3S23 3766 3708 365* 3597 354* 3488 3434 3K 39 4062 1 4001 3940 388, i^ 3765 3708 3651 1 3596 354' J481 iljl 3fl liT 4061 1 4000 3939 7877 T8l7 376413707 3650 3595 354° 3486 343* 49" 41 4060 3999 3938 3879 3820 3-'63[37o6 3649 3594 3539 3485 343' 41 42 4059 3998 3937 3878 3820 376* 37°5 3649 3593 3538 3484 343' 42 43 4057 3997 3936 3877 38.9 3761 1 3704 3648 359* 3537 3483 343° 43 44 40^6 399^13935 3876 38,8 3760,3703 3647 359' 3536 348* 34*9 44 4.'i 4"55 3995, 3934 3875 38.7 3759 137°* 3646 359° 3535 348. 34*8 45 4 3872 3814,3756,3699 3643 3587 3533 3479 34*5 ((I 4!l 40SJ_ 3990 13930 3S71 3813 1 3755! 3*^98 |3fi4J 35S6 Jill 3478 34*4 49 :>li 40S'-. 139891 ir,!,, 3870 38.2 375413697 3641 T^ 353' 3477 34*3 "50 .il 4049 3988 1 39:8 3S6, 3R1. 3"53 3696 3640 3585 3S3° 3476 34*3 51 .■•2 4048 39''7i39i7 3868 38.0 375* 3695 3639 3584 3 5*9 3475 34** »2 53 404- 39S6 h9i<^ 3809 375' 36,4 3638 3583 35*» 3474 34* ' 53 a* 4046 398513925 3808 3750 3693 3«37 3582 35*7 3473 34*0 54 M 4045 39»4 39M 3807 3749 3692 3636 358. 3526 3472 34'9 55 .■.« 4044 3983 1 3923 3806 3748 3692 363, 35S0 35*5 347' 34'8 5(i 57 4043 )9»i I 3911 3805 3747 ,69,13635 3579 35*5 3471 34'7 57 51! 4042 3981 3921 3804 3746 3690, 3634 3578 3524 3470 ,4.6 5n a:i 4041 1 5980! 3920 3803 174 5 36S, 3633 357- 35^^469 34. U 5!l ••" 4-4" 39"9| 3/19I 3'"'o ,802 13745 |3''S8|3';3'- "■'■■•"■■■""■■'i i;o Pl() rAR».E 7i PROPORTIONAL LOGARITHMS ~" h m li in h ml h ml h n.{ h m 1°24' r25'|l°2G'|l''27 n n h m h mi ), n h ml 1. ni sec %>' l''22' i°23 1-28 1°29 1°30' P31 1°32 ,"33 "' 34'5 3362 3310' 3259 1 3208 3158 3108 3059 3010,1962 2915 1 I286S 3414 i36i 3309 1 3258] 3207 3'57 3107 3058 3009 2961 2914 2867 1 J4'3 3360 330813257 3206 3.06 3°57 3009 296, 2913 I2866 2 3411 3359 J307 13256! 3205 3105 3056 3008 2960 2912 12866 3 3411 3358 3306 3^55 3204 3105 3056 3007 =959 2912 1=865 4 3410 33S8 3Jo6 3^54 ,203 3104 3°55 3006 2958 2911 12864 r. 3409 3357 3305 3^53 3203 3.03 3°54 3005 2958 2910 2863 1; 340S 3356 3304 3^53 3202 3102 3°53 3005 =957 2909 2862 7 3407 3355 3303 3252 320. 3IOI 3052 3004 2956 2909 2S62 8 340713354 33£1 3^5' 3=°° 315° 3'°' 3°5= 3C03 =955 =9°8 2861 9 To" 3406 3353 3250 3199 3149 3100 3051 3002 1 2954 2907 2860 Id 3405 3352 3300 3^49 31981 3148 3099 3050 3001 =954 2906 =859 1 1 3404 335" 3300 1 324S 3'98|3>48 309S 3049 3C01 =953 2905 12859 12 3403 335" 3299 3^7 3197 3 '47 3°97 3048 3000 = 95= 2905 285S 13 3402 3350 3298 3^47 3,96 3.46 3097 3047 =999 = 95' 2904! 2857 14 3401 3349 3^97 3246 3'95 3'45 3096 3047 1 2998 =950 2903 2856 15 34CO 3348 3296 3^45 3>94 3144 3°95 5046 2997 =95° 2902 2855 l 2997 2949 2901 2855 17 3399 3346 3^94 3243 3"93 3>43 3093 3°44 2996 2948 2901 2854 18 4r 3398. 3345 3344 3^94 3=4= 3'9= 3 '4= 3°9= 3043 2991 =947 2900 2853 19 3397 3^93 3241 3191 3141 3091 3043 =994 2946 11^1 Ts^T 20 21 3396 3344 3292 3241 3190 3140 3091 3042 2993 2946 289S 2852 21 22 3395 3343 329. 3240 3J89 3139 3090 3041 =993 1 =945 2898 285, 22 23 3394 334^ 3239 3.38 3089 3040 2992 1 2944 '!97 2850 23 24 .3393 334' 3289 3238 3188 3.38 3088 3039 2991 1 2943 2896 2S49 24 25 3393 3340 328S 3=37 3187 3'37 3087 3038 2990 2942 2895 2848 25 2« 3391 3339 328-8 3=36 3186 3136 3087 3038 2989 2942 2894 2848 26 27 339' 3338 3287 3236 3.85 3'35 3086 3037 2989 2941 2894 2847 i;7 28 339° 3338 3286 3=35 3184 3 '34 3085 3036 2988 12940128931 2846 28 29 3389 3337 3^85 3=34 3183 3'33 3084 3035 2987129391289212845 29 30 3388 3336 3284 3=33 3183 3'33 3083 3034 2986 2939 289. 2845 31) 31 3387 3335 3283 3=3= 3.82 3'3= 3082 3°34 2985 1 293812890,2844 31 32 33S6 3334 3282 3=3' 3.8. 3082 3°33 2985,2937:2890 2843 82 33 3386 3333 3282 3=3' 3180 3130 3081 3032 29841=9361=889 2842 33 :u 5385 333^ 328. 3=3° 3'79 3129 3080 1 3031 2983 ,2935 12888 284. 3-1 35 3384 3331 3280 3229 3178 3.28 3079 303c 2982 2935 1 2887 2S4, 35 36 33S3 333' 3279 3228 3.78 3.28 3078 3030 2981 2934 2887 2S4CI 36 37 3382 3330 3278 3227 3'77 3127 3078 3029 298, =933 2886 2839 37 38 3381 33^9 3277 3226 3>76 3,26 3077 3028 2980 =93 = 7885 2S38 38 39 3380 33^8 3^76|3^^5 3175 3125 3076 3027 =979 =93' 'S 2858 39 40 40 3379 33^7 3276,3225 3'74 3124 3°75 3026 =978 2931 =837 41 3378 3326 3175 3224 3'73 3124 3074 3026 =977 =93° 2883 2836 41 42 3378 33^5 3^74 1 3"3 3'73 3'=3 3073 3025 =977 =9=9 2882 2835 42 43 3377 3325 3273 3222 J172 3122 3073 3024 2976 2928 2881 2835 43 44 3376 33H 3272 3221 3171 3121 3072 3023 =975 = 9=7 2880 2834 44 45 3375 33^3 3271 3220 3170 3120 3071 3022 =974 =9=7 28S0 2833 45 46 3374 3322 3170 3^- '9 3.69 3119 3070 3022 =973 2926 2879 2832 46 47 3373 33^' 3270 3219 3168 3119 3069 3021 =973 =9=5 287S 283. ■17 4!! 3372 3320 3269 32,8J3>68 3118 3069 3020 = 97= =9=4 2877 283. 48 49 3371 |33>9 3268 3117 3068 3019 = 97' = 9=3 2876 28 30 2829 49 ■sr 3371 33'9 3267 3216 3166I3116J3067 30, S 2970 =9=3 2876 50 SI 3370 33.8 3266 3='5 3,65 3"5 3°66 30,8 2969 2922 2875 2828 51 »2 33'7 3265 3214 3164 3 1 14 1 3065 3017 2969 2921 2S74 2828 52 A3 3368 33,6 3264 3214 3.63 311413064 30,6 2968 2920 2873 2827 53 54 3367 33'5 3264 3213 3.63 3113 3064 30.5 2967 2920 =873 2S26 54 65 3366 33'4 3263 3212 3162 3112 3063 3014 2966 29.9 2S72 2825 55 »6 3365 33'3 3262 3211 3.61 3'" 3062 3°'3 2965 29.8 2871 2824 56 57 3365 33'3 3261 3210 3160 3110 3061 1 3013 2965 2917 2870 2824 57 58 3364 3312 3260 3209 3159 3109 306013012 2964 29,6 2869 2S25 58 59 3363 33" 3-59 3209 3158 3109 3060 301 1 12963 29.6 2S69 28-;2 59 tiO 3362 3310 3259 3208 3.58' 3108 3059 1 3010 12962 2915 2868 2«2 I 1 tC 1 TABI.K 7i PROPORTIONAL l.OUARIl .'I.MS si;.' k ml 1. ml h in k m h m h „< 1, m K m' h ml h m h m h m sec. /, l<>34'il»36',l<'S8' i°37' rsff r3tni°40' l''4l' 1042' 11° 43' 1°44' l''4,V „ iS2i 2775 2730 1685 2640 2596 2553 25.0 2467 1 2424 2382 234. 1 2811 2775 2729 268412640 2596 255212509 2466 ; 2424 2382 2340 I U 2820 2774 2728 2683 2639 '595 '55' !"io8 2465 2423 1381 '339 2 ^ 28,9 1 1773 2728 2683 2638 '594 '55' 2507 2465 2422 2380 '339 ,'( 4 2818 277' 2727 2682 2637 '593 1550 2507 2464 242. 2380 2338 4 ft 2818 277' 2726 268. 'Pi '593 '549 2506 2463 242. '379 '337 A r, 2817 277' 2725 2681 2636 '59' 2548 2505 2462 2420 2378 2337 1; 7 2S16 277012725 2680 2635 259. '548 2504 2462 j 2419 2378 2336 7 n 28M 2-.69 2724 2679 2634 2590 '547 2504 2461 ,2419 '377 '335 H !) 281, 28.4 2769 2723 2678 2678 2634 2590,2546 ^503_ 2502 2460124.8 2376 »375 '335 '334 9 10 2768 J7" 2633 2589 '545 2460 24.7 1 1 2813 2767 2722 2677 2632 2588 '545 2502 '459 24.7 '375 '333 1! 12 2766 2676 2632 2588 '544 250. '458 2416 '374 '333 12 13 2811 2766 2720 1675 2631 '587 '543 2500 '457 2415 '373 '33' 13 14 2811 2765 2719 2675 j 2630 25S6 2543 '499 '457 2414 '373 233. 14 Id 2810 2764 2719 2674 2629 2585 2542 '499 2456 2414 2372 '33' I A 1« 2809 2763 2718 2673 I2629 2585 2541 2498 '455 24.3 2371 2330 in 17 2S08 2763,27.7 2672 1 2628 2584 2540 2497 '455 24.1 2371 2329 17 IH 2808 2762 j 2716 2672 2627 2583 1 2540 '497 '454 2412 232S 18 l!» 28071276112716 2671 I2626 £581^539 '496 H5i 241 1 2369 232S 1!) 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'577 '533 2490 244S 2405 2364 2322 27 28 2SC0 '754 2709 2664 2620 2576 '53' 2489 '447 2405 '363 2322 28 29 1799 1753 1 '708 2663 26.9 '575 2489 2446 '404 2362 2321 2!» 30 2798 *753!'707 2663 1 2618 '574 '53' 2488 ; 2445 2403 2362 2320 "30" 31 2798 2752 2707 2662 2618 '574 '53° 2487 '445 2403 236. 2319 31 32 279/ 2751 2706 2661 26.7 '573 2530 24S7 '444 2402 2360 23.9 32 33 2796 2750 2705 2660 2616 1572 2529 2486 '443 2401 '359 2318 33 34 »795 2750 2704 2660 26,5 157' 2528 2485 '443 2400 '359 '3'7 34 lio »795 '749 2704 2659 26.5 2571 2527 2484 2442 2400 2358 '3'7 3n ■M '794 2748 2703 2658 26.4 2570 2527 2484 '44' '399 '357 2316 3r> 37 '793 '747 2702 2657 26.3 2569 2526 2483 2440 2398 '357 2315 37 3H 2792 j 2747 2637! 26.2 256911525 2482 '44° 2398 2356 23.5 38 3!» 2792 2746; 2701 '656126.2 2568:2525 2482 '439 '397 '355 2314 3U 40 2791 ; 2745 1*700 2655 2611 1 2567 12524 248. 2438 2396 '355 '3'3 40 41 2790 j 2744 '699 2654; 26.0 ,2566,25231 2480 1438 2396 '354 '3>3 41 42 2789 i '744 '698 2654 : 2610 2566 , 2522 2480 2788 ! 2743 1 '6,.l 1 2653 1 2609 I 2565 2522 2479 »437 '395 '353 2312 42 43 1436 '394 '353 231 1 43 44 '788 1274* 2697I2651 2608:256412521 2478 2436 '394 2352 23.. 44 4.-. 2787] 2741 2696 2652 2607 ] 2564 2520,2477 »435 '393 235.123.0 45 4l 4!) '784: '738 2693,1649,260412561 2517 "474 '43'l'39° 2348! '307 4!» AH X783 12738 1692 I2648 j 2604! 2560 15'7 11474 '43> 1*389 234812306 50 .11 2782 2737 2692 , 2647 ; 2603 1 2559 25.6 2473 243. {2389 234- 'I06 fil S2 2781 2736 2691 264612601:2558 25-5 1 '47' 2430 2388 '346 '3C5 A3 A.1 2-8, 2735 2690 '2646; 2601 12558 2514 2472 14'9>387 2346 2304 «» U 2780 273s 1 '68, 264512601:2557 2514! '471 1419 1 2387 2345 2304 A4 .V. '779 2734; '689 2644,2600 2556 25'3 '470 242S 2386 '344i'3<'3 fVS Afi 277S 2733 '688 '643 2599 '556 25 i2 24-0 2417 2385 234412302 A6 57 2778 273', '687 2643 2599 '2555 25.2 2469 2426 1384 2343 23f 2 ■'■7 AH 2777 2731 2686 2642 ^ 2598 2554 2511 2468 2426; 2384 123421 130T 58 n» 2776 1-31 , 26x6, 2641 i :i;9- 2553 'i; i^ ' '46- ' 24' ^ 2383 1 234 i | 2 ^cr A!) tiO -.-^ 2-3" :6S5 -.640 2596 2553 25"^ U^- 24.-4 2182, ;,4i 'a^c i;n HTS TABLE 74 PROPORTIONAL LOGARITHMS sec. 1. m h m 1. ml h ,„| h ml L ml i. ml h n. h m h m . n,l h » aec 1''46' 1°47' i°4i; jr4y' i°5o'|i"5rir52'|i"53' 1°54' 1°55' l°56'|r57' "' 2300 2259 22.8 1217812139 2099 2061 I2022 .984 1946, 1908 1871 "99 2258 2218 2178I213S12099 2060 2021 19S3 ■945 1 ■9°7 .870 1 :l298 2257 2217 2177 '2137 12098 2059 2021 .982 ■944 ; '9°7 1870 2 2298 "57 2216 2176 2137 209S 2059 2020 .982 1944 1906] 1869 3 2297 2256 22l6 2176 2,36 2097 2058 2019 .98. 1943 i 1906 j 1868 4 2296 "-55 2215 2175 2'35 2096 2057 2019 1980 '943 1905 186S 6 2296 2255 22 J4 2174 "35 2096 2057 2018 .980 1942 1904 1867 6 2295 2*54 2214 2174 2134 2095 2056 2017 '979 194 < .904 .867 7 2294 2^53 2213 2173 "33 2094. 2055 2017 '979 1 ,4 I 1903 1 1866 8 "94 2172 2111 2094 2055 2016 .978 1941 19£l|l!!l 9 2293 TIJT 2212 2172 213212093 2054 2016 '977 ■939 1902 .865 10 2292 2251 22II 2171 2132 2092 2053 2015 '977 '939 1901 1S64 11 2291 2251 2210 2170 2131 2092 2053 20>4 1976 1938 1901 .863 12 2291 2250 2210 2170 2130 2091 2052 2014 '975 1900 1863 13 2249 2209 2,69 2090 2051 2013 '975 '937 1S99 1S62 14 2289 2249 2208 2,69 2129 2C90 2051 '974 1936 .899 .862 15 2289 2248 2208 2168 2128 2089 2050 2012 1973 J936 1898 1861 16 2288 2247 2207 2i67 2128 2088 2050 2011 '973 ■935 1898 i860 17 22S7 224.7 2206 2167 2127 2088 2049 2010 1972 '934 1S97 i860 18 2287 2246 2206,2166 2>26 2087 2048 20:0 '972 '934 .896 1859 19 2286 2245 2205 2.65 2126 20S6 2048 2^°9 I971 ■933 If^ .858 -20" 2285 2245 2204 2.65 2125 2086 2047 2009 '97° ■933 ,895 .858 21 22 2285 2244 2204 2164 2124 2085 2046 2008 1970 1932 1S94 .857 22 23 22S4 "43 2203 2163 2124 2084 20+6 2007 1969 1931 1894 ■ 857 23 24 2283 2243 2,63 2123 2084 2045 2007 1968 1931 1893 1856 24 25 2283 2242 2202 2.62 2083 2044 2C06 1968 1930 .893 ■855 25 2(! 2241 2201 2161 2122 20S3 2044 2005 1967 1929 1892 .855 26 27 2281 2241 2200 2l6l 2I2I 2082 2043 2005 1967 1929 1891 .854 27 28 2281 2240 22CO 2160 2120 2081 2042 2004 1966 1928 .891 .854 28 29 2280 "39 2199 2159 2120 2081 2042 2C03 1965 1927 1890 29 "30" 2279 2239 2198 2159 2II9 2080 2041 2C03 .965 1927 1889 78^ 30 31 2279 2238 2198 2.58 2118 2079 2041 2002 ,964 1926 1889 1852 31 32 2278 2237 "97 2157 2118 2079 2040 2001 .963 ,926 18S8 .85. 32 33 2277 2237 2,96 2157 2II7 2078 2039 2001 1963 1925 1888 1850 33 34 2276 2235 2.96 2.56 2I16 2077 2039 2000 .962 1924 1887 1850 34 35 2275 2235 2195 2155 2I16 2077 2038 2000 196, '9-4 1886 .849 35 3(; "75 2^35 2194 2155 2II5 2076 2037 1999 1961 1923 1886 .849 36 37 2274 2234 2194 2154 2114 2075 2037 1998 i960 1922 .885 ,848 37 38 2274 2233 2193 2153 2II4 2075 2036 I99S i960 .922 .S84 1847 38 3n 2273 «33_ 2.92 "53 21.3 2074 2231 ■997 '959 ,92. 1884 1847 3;» 40 2272 2232 2192 2152 2II3 "73 2035 .996 1958 1921 1883 .846 40 41 2231 2191 2151 2073 2034 ,996 1958 1920 1883 1846 41 42 2271 2231 2190 2151 2III 2033 "995 '957 1919 1882 1S45 42 43 2270 2230 215c 21II 2071 2033 1994 1956 1919 i88i .844 43 44 2270 2229 2189 "49 2110 2071 2032 1994 1956 .9.8 1881 .844 44 4o 2269 2229 2188 2149 2.09 2070 2032 '993 '955 .9.8 1880 1843 45 4« 2268 2228 2iS8 214S 2IC9 2070 '993 '955 1917 18-9 1842 46 47 2268 2227 2. 87 2147 2.08 2069 2030 '99- '954 1916 1879 .842 47 48 2267 2227 2186 2147 2107 2068 2030 '99' '953 1916 .878 ,84, 48 4!) 2166 2226 2186 «i46 2c68 2029 '99' '953 1915 1878 .8+1 49 50 2266 2225 2.85 2145 2106 2067 2028 1990 1952 1914 i877l>S4° "jiT 61 2265 2225 2.84 2145 2105 2066 2028 19S9 '95' 1914 1S76 1839 51 52 2264 2224 2.84 2144 2,05 2066 2027 ,989 '95' 1913 1876 1S39 52 53 2264 2223 2.83 2143 2104 2065 2026 ,988 1950 1912 .875 ■sss Xi 54 2263 2223 2182 2143 2103 2064 2026 .987 1950 1912 187s '»38 64 55 2262 2182 2:42 2103 2064 2025 .987 ■949 1911 .874 '837 55 56 2262 2221 2181 2»41 2063 2024 .986 .948 1911 1S73 1836 6«i 57 2261 2220 21S0 2141 2101 2062 2024 1986 1948 1910 .873 ■S36 5- 68 2260 2220 2 1 So 2140 2IOI 2062 2023 .9S5 1947 1909 .8721.835 58 69 2260 2219 2179 2139 2100 2061 2023 19S4 1946 1909 1871! iSi4 5<>| BO 2259 22,8l2,78 -'39 2099 2061 2022 19841 1946! i9o8|;87i .834 j CO | TABLE 7i 019 PROPORTIONAL LOGARITHMS Mel h nl k m! ll HI h m h ml h a h ml h m' h IT h n ll Bl h a h m '~ ••/ r»«'|i°f!)' 2°0' 2°1' 20 2' j 2" 3' 2° 4' 1 2° 5' 1 2° «• 207' 2°8' rv 2°10' II 1834 ■797 .76. '715 ,689 ,654 ,6,9 .584 '549 «5^5 ,48, '447 ,4,3 » .833 '797 ,760 ,724 ,688 ,653 ,6,8 ,583 ,548 ,5,4 ,480 1446 ,4,3 \ Is" ,796 ,760 ,724 ,688 ,652 ,6,7 ,582 .548 ,5,4 '479 ,446 '■4'* 2 '795 '759 1723 ,687 ,652 ,6,7 ,582 '547 ■5'3 '479 ■445 ■4^* 3 Isi' '795 '758 ,687 ,65, ,6,6 ■ 58, '547 ,5,2 ■478 '445 '4" 4 ,83. '794 ,758 ,722 ,686 ,65, .6,6 .58, ,546 15,2 ,478 '444 ,4,0 5 1830 ■794 '757 ,72, .686 ,650 ,6,5 ,580 ,546 ,5,, '477 ■443 ,4,0 6 1830 '793 '757 ,72, ,685 ,650 ,6,4 ,580 '545 ,5,, '477 '443 ■409 7 1819 1791 ,756 ,720 ,684 ,649 ,6,4 '5-9 1544 15,0 ,476 '44* ,409 H .828 1 1791 ,7.9 168+ ,64s ,6.3 ,578 '544 15,0 J476 '44* ,408 9 "To" i8z8 '79' '755 ,7,9 ,6S3 ,648 ■6.31,578 '543 1509 '475 144, ,408 10 1827 ■79' '754 ,7,8 ,683 ,647 '6,2 ,577 '543 ,508 ■474 ,44, ,407 11 1827 '79° ■754 ,7,8 |, 682 ,647 16,2 '577 ,542 ,508 ■474 ,440 ,407 12 1826 ,789 '753 '7'7 16S, ,646 ,6,, 1576 .542 ,507 ■473 ,440 ,406 13 .825 ,789 '75^ ,7,6 ,68, ,645 .6.0 '575 '54' ,507 ■473 ■439 ,405 U .825 ,788 '75» ,7,6 ,6So ,645 .6.0 '575 '540 ,506 ■47* ■438 ,405 15 1824 1787 '75' ■7'5 ,680 ,644 .609 '574 ,540 ,506 ■47* ■438 1404 18 .823 ,787 '75' ,7.5 ,679 ,644 .609 '574 ■539 ,505 ,471 ■437 ,404 17 1823 ,786 ,750 ,7,4 ,678 ,643 ,6o8 '573 '539 ,504 ,470 ■437 1403 III 1822 ,786 J749. ,7,3 ,678 ,642 .607 ■573 ,538 ,504 ■470 ■436 ,403 19 20 .822 .785 '■49 ,7,3 ,677 "76^ .607 ,572 ■ 538 ,503 ,469 ,436 ,402 20 21 ,82.1,785 ,748 ,677 ,54' .606 '57' ■5«7 ,503 ,469 ■43 5 1402 21 22 ,820 .784 1748 ,7,2 ,676 ,64, 1606 ■57^ ■536 ,502 1468 ■434 ,40, 22 23 ,S»o 1783 '747 ,7,, ,675 1640 ,60s ,570 ,536 .502 ,468 '434 ,4CO 23 2* .8,9 .783 ,746 ,7,, ■675 ,640 .605 ■ 570 '535 ,50, ,467 ■43 3 '4°° 24 2» .819 .782 ,746 ■7'0 1674 ,639 1604 .569 ■535 ,500 1466 '433 '399 25 26 1818,1781 '745 '709 ,674 1638 ,603 ,569 ■534 ,500 ,466 '43* ■399 2fi 27 ,8,7 .78. '745 '709 ,673 ,638 .603 ,568 ■534 '499 ■465 '43* ,398 U7 28 ,8.71,780 ,744! 1708 1673 ,637 1602 ,567 '533 '499 ,465 ,431 ,398 2B •-'!» .8,61.780 ,743! '708 .672 ,637 ,602 ,567 '53^ '498 ■464 '43 ■ '397 2!l :«() .8i6l .-779 •743 '707! '671 ,636 .60, ,566 ,532 1498 '464 ,430 '397 30 : ■497 ,463 ■4*9 ,396 31 .1.' ■8.4 1778 '74* ,706 .670 ,635 ,6oo ,565 ■53^ ,496 ,463 '4*9 '395 32 33 iS,4 .777 ,741 ,705 .670 ,634 '599 ,565 ■530 ,496 ,46* 1428 '395 33 :m ,8,3 1777 ,740 1705 .669 .634 '599 ,564 ,529 ■495 ,46, 1428 ■394 34 35 ,8,1 ,776 1740 ,704 .668 ■633 ,598 ,563 ,529 '495 ,46, '4*7 '394 35 30 ,8,2 '775 '739 1703 ,668 1633 ,598 ,563 ,528 '494 ,460 '4*7 '393 3fi 37 .8, , '775 '739 1703 ,667 ,632 '597 ,562 ,528 ■494 ,460 ,426 '393 37 311 18,, '774 .73S ,702 ,667 ,63, ,596 ,562 '5*7 ^493 '459 ,426 '39* 38 30 •10 ,8,0 1774 '737 ,702 ,666 ■596 ,56, ■527 1 ^493 '459 ■4*5 '39* 30 ■809 1.773 '737 ,70, "^^5 16^ '595 ,560 ■ 526 ■49* -^ ■4?4 '39' 40 41 1809 "772 .736 17CO ,665 ,630 "595 ,560 ■5*5 ■49' '457 '4*4 1390 41 42 ,8c8 ,772 .736 ,700 ,664 ,6291 ,594 ,559 '5*5 '49' '457 ■4*3 ■39^ 42 43 1808 '77' '735 ,699 ,664 162SJ ,593 '559 ■5=4 '49° ,456 '4*3 ,389 43 44 ,807 ■77' '734 ,69, ,663 '628I ,593 .5S8 ,524 '49° ,456 ,4** 13R9 44 4.7 1S06 1770 '734 ,698 1663 ,6271 ,592! ,558 ■5*3 '489 ■455 ,422 ,388 45 40 i8c6 ,769 '733 1697 1662 ,627! ,592 '557 '5*3 ,489 '455 142, ,388 \f. 47 1805 1769 '733 '«97 ,661 .6261 159, ,556 ,522 ,488 ■454 1420 ,387 47 48 ,805,1768, 1731. 1696 '66' ,626 ,59, ,556 ,521 ,487 '454 ,420 .387 48 49 ,8041,768 .73,1.6961,660 ,625! ,590 '555 ,52, ,487 _H53 14,9 Jl'^ 49 50 ,8031,767 ,73,11695 ,660 ,6241,589 '555 ,520 ,486 '45* ,419 13S6 50 51 ,803 1766 '730 1 '694 ,659 ,6241,589 '554 ,520 ,486 '45*1 ■4'8 '385 51 :..' ,802' 1766 ,730 ,694 ,658 ,623 ,588 '554 ,519 14S5 ■45'! ■418 ,384 52 .'.:j i8ci , ,765 17291,693 ,658 ,623, ,588 '553 ,5,8 ,485 ■45' 14,7 ,384 53 .-.4 ,80,, 1765 ,7281 ,693 1657 ,621 ,5871,551 ,5,8 ,4f<4 1450 14,7 ,383 54 (>.■> iSool 1764 , 728 i, 692 '657 ,62,' ,586 ,551 ,5.8 ,48, 1450 ,383 55 .j« ,8cO|,763 ,727 ,69, ,656 ,62, ,586 '55' ■5'7 ,483 ■449 ,382 5r> 57 '799 -763 '7»7 ,69, ,655 ,6201,585 '55' ,5,6 ,482 '449 1382 57 .'•8 .798 .762 ,726 ,690 .655 ,620 .585 '55° ,^6 • 482 .448 '■^V 58 .>» .798 .76, '7J5 ,600 1654. .6,9 ,584 ,550 ■5'5 ,48, ■447 ,38, 50 mt ,797' -•'61 ,-251 10891 ,6541 1019 ,,;84l ,5491 ,5,5 ,4ki M47 1413 ! I38r> fio TABLV. 74 PliOPOirriON>tl, LOGARITHMS 1 sec. 20^r 2° 12° 2° 13" h m 2° 14' 2° is" 2°16" 2=17' 2° is" 2°1!" 2° 20" 2°2r « 8PC. // 2 3 4 6 C 7 !» .380 '379 '379 ■378 '378 •377 ■377 ,376 .376 '375 •347 .346 1346 •345 •345 •344 •344 •343 •343 134Z 1314 1314 >3'3 '3'3 1312 1311 1310 1310 1309 1282 12S1 12S1 1280 1279 1278 1277 •277 1249 1249 1248 1248 1247 •H7 .246 1245 1245 1217 1217 1216 1216 1215 121; 1214 1214 1213 .2.3 ii86 ::■: ■i 1182 1181 1181 1 1 54 '•53 ••53 1152 1152 1151 1151 1150 1150 ••49 1123 1122 1 120 tI20 III9 III9 III8 II18 1091 1091 109U 1090 10S9 ICS9 1088 1088 1087 1087 io6i 1060 1059 .059 1058 J058 1057 ::p ,os6 1030 1029 1029 102S 1028 1027 1026 1026 10 12 13 IS l323 '313 1321 1321 1292 1292 .291 .29. 1290 .289 1288 1288 l»87 1287 1286 1285 iil: .283 tl82 1260 1260 i»59 .258 1258 •157 JI57 1256 1256 Iiz8 1227 1227 1226 1226 1225 .225 1224 .224 1223 1219 I2I8 ,.96 ..96 ••95 "94 '•94 "93 ••93 1 192 1 192 ,■9. 1191 1 190 1 190 ..89 Wll ..87 i'>86 .164 .164 ;;si .162 1161 ..6. 1 160 •'6° • 1^9 ••59 .■58 1. 58 ••57 iiii • •55 1 1 54 • ■54 "33 1132 1132 1131 1130 1 1 30 1129 1129 1128 1128 1127 1 127 1126 1126 112s 1125 1 124 "i^ 1123 1099 1099 1098 JC97_ • 097 1096 .096 IC95 IC95 .094 IC93 •093 ■ 092 IC9I 1320 1319 '3'7 B •315 '3'5 1314 •155 1254 1254 '153 •153 1251 1251 1250 '24? ic66 1065 .065 .064 1064 1063 ,063 1062 :o62 ICDI ic6i T.\EI,F, 7i 921 PROPORTIONAL LOGAUITHM3 etc. 2° 23" 2° 24" 1, n,{ h .»{ 1. m h m h m h m h .1. ml h mi ^ n. lec. 2" 25' 2° 2G' 12° 27' 2°28'j2°2!)' 2° 30' 2° 31' 2032' 2° 33 2° 34' 0999 0969 0939 0909 0880 08501082. 0792 0763] 0734 0706 0678 1 0999 1 0969 0939 0909 0879 0850 0820 0791 0762 0734 0705 0677 2 0998 1 0968 0938 0908 0879 0849 0820 0791 0762 0733 0705 0677 3 099S 0968 0938 0908 0878 0849 08.9 0790 0762 0733 0704 0676 4 0997 0967 0937 0907 0878 0848 08.9 0790 0761 0732 0704 0676 5 0997 0967 0937 0907 0877 0S48 0818 0789 0761 0732 0703 0675 fi 0996 0966 0936 1 0906 0877 0847 08.8 0789 076010731 0703 0675 7 0996 0966 0936 0906 0S76 0S47 0817 0788 0760 0731 0702 0674 R 0995 0965 0935 0905 0876 0846 0817 078S 0759 °73° 0702 0674 9 0995. 0994 09651 0935 1 0905 0875 0846 0816(0787 0759 °730 070a 0673 0964 0934 1 0904 087510845 0816 0787 0758 0729 0701 0673 10 II 099+ 0964 0934 0904 0874 0845 0815 0787 0758 0729 0701 0672 11 12 0993 0963 0933(0903 0874 1 0844 0815 0786 07S7 0729 0700 0672 12 13 0993 0963 0933,0903 087310844 0786 "757 0728 0700 067, 13 U C992 0962 0932 0902 0873 0843 0814 0785 0728 0699 0671 14 15 099: 0962 0932 0902 0872 0S43 0814 07S5 0756 0727 0699 0670 15 l« 0991 0961 0931 0901 C872 084210813 0784 0755 0727 0698 0670 \l) 17 0991 0961 0931 0901 0S7. 0842 1 08.3 0784 0755 0726 0698 0669 17 Ifl 0990 1 0960 0930 0900 087. 0841 0812 0754 0726 0697 0669 IH 1!) 0990 1 0960 1 0930 C9C0 0870 084. 0812 0783 0754 0725 0697 of 69 l'( -w 0989 0959 0929 0899 0870 0840 0811 1 0782 °753 0725 0696 0668 "20 21 0989,0959 0929 0899 0869 0840 081 1 07S2 0753 0724 0696 0668 21 22 0988 0958 0928 0898 0869 0839 0810 C781 0752 0724 0695 0667 22 r.i C988 0958 0928 0898 0868 0839 0810 078110752 0723 0695 0667 23 24 C987 0957 0927 0897 0868 o?38 0809 0780 0751 0723 0694 c666 24 24 0987 0957 0927 0897 0867 0838 0809 0780 0751 0722 0694 0666 2ft 2K 0986 0956 0926 0896 0867 0837 0808 0779 0750 0722 0693 0665 2(i 27 0986 09561 0916 0896 0866 0837 0808 0779 0750 0721 0693 0665 27 88 C985 0955 0925 0895 0866 0836 0807 0778 0750 0721 0693 0664 2H 29 0985 095510925 0895 0865 0836 0807 0778 ■^749 0720 0692 066+ 20 i«r 0984 0954 '0924 0894 0865 0835 o8r6 0777 0749 0720 0692 0663 "sir :ii C984 10954 0924 0894 0864 0835 0806 0777 0748 0720 0691 0663 31 32 0983 0953 0923 0893 086+ 0834 0805 0776 0748 0719 069, 0662 32 Xi 0983 0953 0923 0893 0863 0834 0805 0776 0747 0719 0690 C662 33 :m 0982 0952 0922 0892 0863 0833 0804 0775 0747 0718 0690 0662 34 3o 0982 0952 0922 0892 0862 0833 0804 °775 0746 0718 0689 0661 35 3« 0981 0951 0921 0891,0862 0833 0803 0774 0746 0717 0689 0661 36 37 0981 0951 0921 0891 0861 0S32 0803 0774 0745 0717 0688 0660 37 :ui 09S0 0950 0920 0890 0861 0832 0802 0773 0745 0716 0688 oofto 38 .•w 0980, 0950 1 0920 0890 0860 083, 0802 0773 _o744|.2Zil 0687 0659 3:( 40 IF 0979 1 0949 j 0919 0889 0S60 083. 0801 io773 0744 0715 0687 I0659 41 0979 1094910919 0859 0830 0801 0772 °743 0715 06S6 0658 41 42 0978 1 0948 0918 0888 0859 0830 0801 0772 °743 0714 0686 o6s8 42 43 0978,0948 0918 0888 0858 0829 0800 0771 0742 0714 0685 0657 43 44 097710947 0917 0887 0858 0829 0800 0771 0741 0713 0685 0657 44 4.'. 0977 I 0947 0917 0887 0857 0828 0799 0770 0741 0713 0685 0656 45 4r. 09761094610916 0857 0818 0799 0770 0741 0712 0684 0656 4S 47 0976 [ 0946 1 0916 0886 0856 0827 0798 0769 0740 0712 0684 0655 47 4H °975 0945 l°9'5 0885 0856 0827 0798 0769 074010711 0683 0655 4U 43 0975 1 0945 1 0915 0885 0855 0826 0797 0768 0739I0711 0683 0655 49 AO 0974 1 0944 1 0914 im -58T7 0826 1 0797 0768 0739 1 0711 0682 0654 50 Al 0974 '0944] 09 14 0884 0855 0825 0796 0767 0739 0710 0682 0654 51 S2 097310943,0915 0883 1 0854 0825:0796 0767 1 0738 0710 06S1 0653 52 fi3 0973 0943 0913 088310854 0824,0795 0766 1 0738 0709 0681 C653 53 A4 0972 J0942 0912 08S2I 0853 0824 0795 0766 0737 0709 c6So 0652 54 S.i C972 0942 ,0912! 0882 10853 0823 0794 0765 0737 o7il'o6So|o65i 65 5fi C971 I0941 0911 I0881 C852 1082310794 0765 073* 0708 '0679' 0651 50 97 0971 : 0941 1 091 1 088. 0852 : 0822 1 0793 1 0764 0736 i 0707 1 0679 1 C651 57 Ml 0970^0940 0910 0880 1 0851 ' 0821 1 0793 0764 0735 JC707 0678 IC650 68 ft't 0970 0940 091c 1 0880 0851 0821 [0792 10763 0735 0706 0678! 0650 59 mi o'M 0939IC9C9 0880 0850 c82i 1 0792,0763 1 0734 0706 |c678, '649 ifj 022 TABLE 7i PROPORTIONAL I/>OARlTHMS wc h n •L k > n ti t nl h . n h n h n Ih .|h W" m\ h ^ h ml h •^ see " 2° 36 2° 36 2° 37 2° 38 2° 39 2=40 2° 41 2° 42 2-43 '2° 44 2° 46 2°4t 0649 0621 0594 0566 °539 0512 0484 045S 043 0404 0378 0353 0649 0621 °593 0566 0538 0511 0484 0457 0430 1 0404 0377 035 064! 0621 °593 0,65 0538 0511 0484 0457 043c 0403 °377 °35 064S 0620 0592 0565 0537 0510 0483 0456 043c 0403 0377 035c 0648 0620 0592 0564 °537 0510 0483 0456 0429 0402 0376 035c 0647 06.9 0591 0564 0536 0509 0482 °455 0429 0402 0376 0349 0647 0619 0591 0563 0536 0509 0482 0455 0428 C402 °375 0349 0646 0618 0590 0563 0^36 050S 048. 0454 0428 0401 °375 0349 0646 0618 0590 0I2 ^535 0508 048, 0454 0427 C401 0374 0348 0645 06.7 0590 0535 0507 0480 0454 0427 0400 °374 0348 10 0645 ^6T7 0589 ^562: °534 0507 0480 °453 0426 0400 0373 °347 1 1 0644 0616 05S9 056, °534 0507 0479 °453 0426 0399 °373 0347 12 0644 0616 0588 056. °533 0506 0479 0452 0426 0399 °373 0346 13 0643 06,5 05S8 056c °533 0506 0479 0452 0425 0399 0372 0346 14 0643 06.5 0587 0560 0532 0505 0478 0451 0425 0398 0372 0346 15 0642 06,5 0587 °559 0532 0505 0478 0451 0424 0398 0371 °345 IB 0642 06,4 0586 °559 0531 0504 047710450 0424 0397 037, 0345 17 064, 06,4 0586 0558 0531 0504 0477 0450 0423 °397 0370 0344 18 0641 c6,3 0585 0558 0531 0503 0476 0450 0423 0396 0370 0344 19 064 ■ 0613 058^ PHI 0530 0503 0476 0449 £422 0396 0370 ^343 "2(1 0640 0611 0584 °557 0530 0502 0475 0449 0422 '=395 0369 °343 "20" 21 0640 0612 058+ °557 0529 0502 0475 0448 0422 0395 0369 0342 21 22 0639 061, 0584 0556 0529 0502 C475 0448 0421 0395 0368 0342 22 23 0639 0611 0583 0556 0528 0501 0474 0447 0421 0394 0368 0342 23 34 06^8 0610 0583 °555 0528 0501 0474 1 0447 0420 0394 0367 0341 24 25 0638 0610 0582 °555 0527 0500 0473 0446 0420 0393 0367 0341 25 26 0637 0609 0582 °554 0527 0500 0473 0446 0419 0393 0366 0340 26 27 0637 0609 05S, °554 0526 0499 0472 0446 0419 0392 0366 0340 27 28 0636 0608 0581 °553 0526 0499 0472 0445 04.8 0392 0366 °339 28 2t) 0636 0608 0580 °553 0526 0498 °47i 0445 0391 0365 °339 29 3» 0635 0608 -^ 0552 0525 0498 0471 0444 ^^ 039, 0365 °339 -w 31 C635 0607 "S79 0552 0525 0497 0471 0444 C417 0391 0364 0338 31 32 0634 0607 0579 0551 0524 0497 0470 0443 04,7 0390 0364 0338 32 33 0634 0606 °579 0551 0524 0497 0470 "443 0416 0390 0363 °337 33 34 0634 0606 05-8 0551 0523 0496 0469 0442 0416 0389 0363 0337 34 35 0633 0605 0578 0550 0523 0496 0469 0442 0415 0389 0363 0336 35 3fi °633 0605 0577 otto 0522 0495 0468 0442 0415 0388 0362 0336 36 37 0632 0604 0577 0549 0522 0495 0468 0441 0414 0388 0362 0336 37 38 0632 0604 0576 0549 0521 0494 0467 0441 0414 0388 0361 °335 ■is 3U 063, 0605 0576 0548 05^1 0494 0467 0440 04H 0387 036- 0335 39 40 40 063, 060, °575 0548 0521 0493 0466 0440 0413 0387 0360 0334 41 0630 0602 0575 °547 0520 0493 0466 0439 0413 0386 0360 °334 41 42 0630 0602 0574 0547 0520 0493 0466 0439 0412 0386 °359 °333 42 43 0629 0602 0574 0546 0519 0492 0465 0438 0412 0385 °359 °333 43 44 0629 0601 0573 0546 0519 0492 0465 0438 041 1 0385 °359 0332 44 45 0628 0601 0573 0546 0518 0491 0464 0438 041 1 0384 0358 0332 45 4f> 0628 0600 0573 0545 05.8 0491 0464 C437 0410 0384 0358 0332 46 47 0627 0600 0572 0545 0517 0490 0463 0437 0410 0384 ■=357 C331 47 48 0627 0599 0572 0544 0517 0490 0463 0436 0410 0383 °357 0331 48 49 0627 0599 0571 °544 0489 0462 0436 0409 0409 ^ 03^ 0356 0^30 0330 49 5(1 50 S6l6 0598 0571 °543 0516 0489 0462 0435 51 0626 0598 0570 0543 05,6 0489 0462 0435 0408 03S2 0356 0329 51 62 0625 0597 0570 0542 0515 0+88 0461 0434 0408 038, °355 0329 52 53 0625 0597 0569 0542 0515 0488 04^ I 0434 0407 038. 0355 0329 53 54 0624 0596 0569 0541 0514 0487 046c 0434 0407 0381 °354 0328 54 55 0624 0596 P56g 054. 0514 04S7 0460 °433 0406 0380 °354 0328 SS 6« 0623 0596 S568 0541 0513 U486 =459 0433 0406 0380 0353 0327 56 57 0623 °595 0568 0540 0513 □486 =>459 0432 0406 0379 0353 0327 57 58 0622 0595 0567 0540 0512 0485 D45S 0432 0405 0379 0352 0326 58 o9 0622 0594 0567 0539 0512 C485 D45S C431 0405 0378 0352 0326 fin *n 0621 1 0594 0566 0539 05.2 C4»4 C458 1 D431 0404 0355 D326 60 TAIU-F. 74 023 PHOPOKTIONAI, l^GARITHMSl •ec l> n. h ml h „,l h m h m h »■ k ml h n,' h m h .1 2^ft7"|2^5)rj h F.. sec "' J- 47 2^4K'|2-'49' rTM- 2^51' 2 52' '°53'|2°54' 2°55' 2°6«i' 5'J' "' 0326 i^To];-::; 0248 0223 0197 0172 1^7" 0122 OC98 C073 OC49I CC24 „ 1 D32S 0199 0273 0248 0222 0197 0172 0147 0122 C097 C073 C048 C024 1 2 032510299 °^73 0247 0222 0197 0171 0,46 0121 0097 0072 0048 C023 2 3 0324 1 0298 0^73 0247 0221 0196 0171 0146 OI2I 0096 0072 0047 0023 3 4 0324 029* 02^2 02+6 0221 0,96 0171 0,46 0121 0096 0071 0047 4 5 0323 0297 0272 0246 0221 0195 0170 0145 0120 0096 0071 0046 C022 6 a 0323 0297 0271 0246 0220 0195 0170 0145 0120 0095 0071 OC46 0022 B 7 0322 0297 0271 0245 0220 0194 0169 0144 01 19 0095 0070 0046 C021 7 H 0322 0296 0270 0245 0219 0194 0109 0144 01 19 0094 0070 0045 C021 H !l °3^^ 0^96 02'0 0244 0219 0194 0169 0143 0119 0024_ 0069 1 0045 1 OC2 1 !( 10 0321 0295 0270 0244 0218 0193 ^768" omT 0118 0093 0069 1 0044 1 C020 Id II 0321 0295 0269 0244 0218 0193 0168 0143 0118 0093 0068 1 C044 1 C020 II 12 0320 0294 0269 0243 0218 0192 0167 0142 01 17 CO93 oc68 0044 COI9 12 i:« 0320 0294 0268 0243 0217 0192 0167 0142 0117 0092 C068 C043 JOI9 13 14 0319 0294 1 0268 0242 0217 0192 0166 0141 0117 0092 0067 0043 COI8 U 15 0319 0293 0267 0242 0216 0191 0166 0141 0116 C091 co57 C042 0018 IS 16 0319 0293 o2£7 0241 0216 0191 0166 0141 01 16 0091 0066 0042 0018 1« 17 03.8 0292 1 0267 1 0241 0216 0190 0165 0140 OMS 0091 0066 0C42 OC17 17 IK 03.80292 0266 0241 0215 0190 0.65 0140 0090 cc66 C041 0017 IH 19 0317 1 0291 0266 0240 0.89 0,64 °'39 0114 ^090 _oo65^ 0041 0016 19 •20 03"7 029' 0265 0240 0214 0.89 0164 013910114 OC89 C065 0C40 CO16 20 21 031610291 0265 0239 0214 0,89 0.63 0139 0.14 0064 0040 0016 21 22 03.6 0Z90 0264 0239 0213 0188 0163 0138 0113 0089 0064 C040 CO15 22 23 0316 0290 026+ 0238 0213 0188 0163 0138 OII3 0088 0064 0039 0015 23 24 0315 0289 0264 0238 0213 0187 0162 0137 0112 0088 C063 C039 COI5 24 26 0315 0289 0263 0238 0212 0187 oi6z 0137 0112 0087 0063 0038 0014 25 20 C314 0288 0x63 0212 0186 0161 0136 01 12 0087 0062 0038 0014 2fi 27 0314 0288 0262 0237 0211 0186 0161 0136 OlII 0087 0062 0038 28 0313 0288 0262 0236 0211 0186 0161 0136 0111 0086 C062 COI3 2B 29 0313 0287 0261 0210 01X5 0160 0135 0110 0086 C061 0037 2!) 30 0313 0287 ^I6T 0^35 0210 0185 0160 0135 Olio 0085 0061 "S^ 0012 :m 3! 0312 0286 0261 0235 0210 0.84 0159 0134 Olio 0085 C060 C036 C0I2 31 32 0312 0286 0260 0235 0209 0184 0159 0134 0109 0084 cc6o C035 0011 32 :« 0311 0285 0260 0234 0209 0184 0158 0134 0109 OC84 0060 0035 001 1 XI :i4 0311 0285 0259 0234 0208 0.83 015S 0133 0108 0084 0059 0035 COIO 34 35 031010285 0259 0233 0208 0183 0158 0133 0108 «83 0059 0034 COIO 35 36 03.0! 0284 0258 0233 0208 0182 0157 0132 0107 0083 0058 0034 COIO :« 37 0310 0284 0258 0232 0207 0182 0157 0132 Q107 0082 C058 0033 0CC9 37 :«) 0309 0283 0258 0232 0207 oi8i 0156 0131 0107 0082 C057 0033 00c 9 38 3!» 0309 0283 0^57 0232 0206 0181 0.55 0'3' 0106 C082 0057 o°33 cou8 3» 40 0308 TliT 0257 0231 ■^I^ 0181 0156 0131 -^TZb 0081 CO 57 0032 ccc8 40 41 0308 0282 0256 0231 0205 0180 0155 0130 0105 0081 0056 0032 ocoS 41 42 030710282 0256 0230 0205 0180 0155 0.30 0105 cc8o 0056 0031 OC07 42 43 0307 0281 025s C230 0205 0179 0154 0.29 0105 008010055 0031 0007 43 44 0306 0281 0255 0230 0204 0179 0154 0129 0104 0080 0055 0031 OC06 44 46 0306 0280 0255 0229 0204 0179 0153 0129 0104 0079 0055 0030 OC06 46 4t; 0306 0280 0254 0229 0203 0178 0153 0128 0103 0079 0054 0030 0006 4i 0300 1 0274 ■'■'M»j 0223 1 0197 ■ ..1-2 0147 i,122 ,009810073 0049 0024 000.,. K., 924 ABBREVIATIONS ADOPTED IN ADMIRALTY CHARTS. ABUllliVIATIONS ADOPTED IN THE ADMIRALTY CHARTS, WITH EXPLANATORY NOTES. But'- B'- C. - C.G. Cuth. Ch. Chan. Clieq. Col"- Cr.. E.D. Fl« L*- Fms. Ft. • G. . G"-- H. - H"-- Ho. H-- - Anchornift. - Bay. a buoy) Black. - Battery. - Bank. - Cape. - Coast Guard. - Cathedral. - Church. ■ Chotinei. Chequered. - Coloured, - Creek. - Kxitttence Doubt- ful. • Floating Light. - Fathoms. • Feet or Foot, : GrL ■Hour.' ■ Heai. ■ HowK. ■ Harbour. J a buoy) Nuritnntal. Sliip^s. 1- - Kii. L. - General Abbreviations. H.W. - High Water. I Hiyh Water. W.W.V.hi'.i FallSf \ Chauye. I. . - Islarnl. ■ IsUnubi. ■ K'io/.s. ■ Lake. ■ Latitmle. ./"yhi""' ■ „ Alternalinii. ■ „ Fixed and Flashing. ■ „ Fixed. • ,, Flashing. ,f Inter iniHent. ■ „ Occulting. ■ „ Bevohing. V- F. L'- Kl. V- lut. TV Uoc. I.' Rev. L.W, m. (near » liglit) Auul. Ma^" - Magazine. Mag*^' - Magnetic. ni n. (near s light) Mii Mt. - Mountain. Np. • Neaps. Mde. Obs" Spot Olservalioi Soot + P. - - Port. P D. - P.,.sition doui ful. V'- ■ ■ Peak. P'- - - Point. D. ar i buoy) Rett, . . Beef. ■ Bock, ■ Sound. (n ar a lluht) Secooda, ■ Shoal. • Springs. - Strait. • Teleqra/ih. "■ . Varialnm. ■ Village (near s light) Visible. ■ (near » buoy) Vertical Sinpet OrTi:n IN ADMTHAI.TY rnAI?TS. 925 All iii-i^'lits ore eiven in fe.-! nl.ovi; IIii;li Wiitci Dr.linnry Springs, nnil in pliuM where there it no tiilc. iil.ine the level uf llie sc;i. ri"'-''i:eplion3 to this (jeneral nil* ara Hated on the lille of the eharr.) All hea i'liis. inchiding the ilireitinr. of winds soil ciirrentj, are mapnelic. except when otli(r»i>e expres^ed. Bearings of li;;hl8 bjc given a« jrrf«/r<.m neaicard, und n<^ from ihe li;;hts The natiirn'. fciile, or the propirion which the Chart scale bcara to the conh (ohtained hy redueiiig the numher of feet in the minme of laiitiide to inches. Hud lijvidiiig the product by the scale), is repn scntcd thus ■^^■ A eub)e'„ length is assumed to lie e4ual to lOU fathoms ; it is the 10th purt of a »^.» Suu/iiliui/.s upon Foreiyn C/iarh are tiprrsseii thug : — An.iran (Faden) = 6-223 Enoli^h feet, or l-0',7 English faihoim (Metre) = 3-28 0-547 (,Fav») = 175 „ „ 1 0^9 (Vadem) = 5-575 .. r 0929 „ = 5 yt-s .. ,. o 9X4 (Brii-se) = 5329 „ „ o-8b8 „ „ Chilian Dani-h aud N',rwc-iau Dutch (European) „ (Ka^t Indian) Knnch ttaliai. Ja|,ane-o P..nugu,-S8 Gennau (Meirc) = 3-2M „ „ 0-547 ., - '-zS o 547 (riithom) = 6coo „ „ 1000 „ ., CBraoa) = 6oj( „ „ 1-000 (Mitre) = 3 2S1 „ „ 0547 Hussiin, Sasliine or Fuihom (Ca) = 6000 „ „ 1-000 ^ „ iSpanish (liraza) = 5-492 ^ » 0-915 •. <• Swedish (K.nnn) = 5-843 „ ,. 0'974 ., „ United States (Futlioni) = 6-ooo ., „ 1000 „ The Duteh Elle, the Spanish, Portuguese, aud Italian MeOo, nad also the Frmch ifitre, are i leuticul. CnABACTFBISTICS MARKED AOilNST LifilirS OS THE AdUIISALTJ- ClIARTS. F, Fixed. A continuous steady light. Yu Flashing. Showing a tingle flash. (ip. Fi.. Group flisbing. Showing groups of two or more flashes iu succession (not neeemarily of tha same colojr), separated by eclipse.s. F. & Fl. Fixed ai:d fliishing. Fixed light varied by a Hngle white or coloured flash, which may Le prc-ceded and followed by a short edipse. F. & Gp. Fl. Fixed and group Hashing. The same as the preceding, but with groups of flashes. Rkt. Revolving. Light gradually increasing to full effect, then decreasing to eclipse. [At short distances and in clear ueather a faint continuous light may be ohserred.] (Vt. Occulting. A Bfoady light with, at regular intervals, one sudden and total eclipse. Op. Occ. Gronp occulting. A steady light with, at regular intervals, groups of two or more sudden and total eclipses. Thr note attached to lievoli'ing lights is in some cases applicable. Alt. Alternating. Lights of different colours (generally red and white) alternately, without any intervening eclipse. The distance the Lights are visible is calculated from « height of 15 feet abore the sea al H.W. lit.-ve-sels belonging to the Trinity Ilonse, Loudon, are c. loured red,ha.ie tlieir Name painted on their sides carry a Ball at vaii, niasl-head, fire a gun if a ship is slari.iing imo dacecr, and sound either a Gom; or Fo,■ 1/ A.V, page U tndicaUi. t HBHiviATioKS ft1opt«l lu Admiralty charts, p. 924, 925 A bbreriations, p. 10, not* • ill Table lU explanation, p. 397 ADrolboJ, no cliange of teuiijer. of water on, 1038 Acfe'cration, Table 23, explan. p. ■109 .367 Acute, 86, p. 24 A.Jjnsting screws, caution, «7 Adjnstir.g compavsep, 332 Professor Airy on, 238 Adjustments of the sextant, 499 Admiralty ice chart, 1052 charts, abbreriations adopted In, 924, 925 A.lventure, H.M.S. p. 373, note Agoof tide, 919 necessary for height, 935 Alry's projection of great circl-' on chart, 388 Alceste, log, p. 367, 372, note Altitude, def. 206 circles of, 427 apparent and true, •M2 parallels of, 430 changes of, 669 aorrection of, p, 230 obserring the moon's, 540 a star's, 641 rciluction of, for change of place. OTH till :'.-!7 I'l. i!B3 Dur-anxle, 666.ic. from the uximuth, 66H, &.c. on the prime vertical, 664,*'*. and hoar-angle. Table 2n, exjilau. p. 411 Tables 43, 44, explan. p. 41.'> chat gc of, to and, 661. &c. change of, at a glTen azimuth, 670, Ac. Table 46, explan. p. 416 do. and rariathn of do. p. 200 Alti'ndoi, obserring at .-e.i, 487,534 ■ In. wi'h"lia«'l'.-'.'ri'^..,i or die-, 538 obserrerl from opposite poii the horizon, 636, 511 a «t of, error of inrcrvaU, ! of stara, afford a check <>i DR. as ul«> on a misUke i Ainbiguoiu case, pla p. 50a A'cplitiide, def. 446 p. 41» linn. 41 ral>Ul»9A,avpUl affiMifed bv refra' tain errors, 8SS to compute the, 887 alogies or trigon. canons, 162 rules for working by logs. 166 alngy, 43 chor, angles for recovering a lost, to l,iy off. at a point, »5 find, p. 314, note t Angles to measure and lay off, 106, 107 Animalciilffi colour the sea, p. 372, Annatom, bearings required, p. 375, Annftaire d€s Afar^s^ p. 335, note • -Antarctic circle, 211 A"r, Pulo, p. 382 .Apparent Altitude, 432 dip, 2't6 Table 30, explan. p. 411 distance, 848 (2), and 850 time, def. 474 tintol , 605 Approximate, note on term, p. 61 are often preferable, p. 273, note Approximate Doub. Alt .advantage of the method in practice. Pref. vi has been found convenient, p. 263, Appro: 306 diould be w te Lunar, principle, p. 302, r enough in general, 843, p. IS a check against error in the rigorous process, p. 304, note t affords the angles at both bodies, p. 314, note t Arago, tcrreatr. refr. 536 Arc, def. so to convert into time, 8T0 Table 17, explan. p. 408 •quare of, to find, p. 418, Tab. 56 la the limit of the sum of the chords, p. 120, note of sextant, to teat, 498 Arctic circle, 211 Arithmetic complemeat, 63 Lieut, p. 396 , of the lead, 3M IS, p. 380 (10) stand for, 519 -Assumption, solution by, p. fil, note Astronomical bearings, 903 : dav, 480 Astronomy, Nautical Spherics applied to, p. 62A-64A .Athos, Mt. example, 394 Augmentation, ))semid. 440 Table 42, explan. p. 416 .Australia dews, p. 368 Awash, sj-mbol of, p. 399 (1) Axiom, 112 Azimuth, def. 444 ; how measured, 441 to find, from tbe alt. 673 from the hour-angle, 675 from the hour-angle and alt. 676 from change of alt. 677 tiibles Burdwood and Davis, in- di/ Jrperiitence, 733 n, 728 by the moon. 743 by a planet, 742 Drffr. o/ drprnth-iice, 745 When neither altitude is near mcridluii, 746 the simplest case, 760 by the son, 7S1 by the moon, 765 by a star. 753 by a planet, 75i D-gr 0/ rfrprn Ja/ic, 771 Ivorys method. 757 correctinn of lat., p. 266 THWc7I.cxplan. p. 428 ll.;i:/r'/fn'b...li.«,7.'>9 one alt. near tlie murid. 761 ,• the I not at the feinit Instant. 764 aelthcr nit. near the merid. 746 tbcgeiieralor rigorous proces.s,77l i)*^r. of drffwlaiiu by any o D.R., abbrcv. of dead reckoning, 203 Drift of a current, 290 Ducom, Court d' Obtervalioiu AViu- tiquet,j>. 256, note Du Petit Thouors, M., p. IOC, note t, 1038 D'Urville. M., voyage, 1035 Dutch feet, p. 38o (3) paUlls, p. 380 (4) ■•*. n page Is Indkatei. Fisher, remark on 191, note on observing the Imzydiscof tba sun, p. 195. note on lunitr ohserv. p. 361, note rit:'.iuy. Capt., additions to the sex> Eclipse, 466 Keliptic, 46S Elevation ol affects place of 205, 446 (2), 546 affects refraction, p. 414, note effect of, on altitude, 559 time of rising and setting. 326 638 ID amplitude, 446 (I), Entire correction, 907, 951 Hpacts, Table 14, explan. p 407 Equal alts. 796 at sea, 798 ; on shore, 803 equation of, 797 logs, tor computing do.. Table 72, explan. p. 428 Equal corr. for change of refract. 810 Eciuation of time, 476 to reduce. 683, 684, p. 208 A table of. Table 62, cxpLiu. p. 4; 1 Equator, def. 182 days and nights equal on, 182 celestial, 425 Equatorial instrument, p. 177, note Iviuiangulor triangles, 148 l:quilateral, 87 Iviuiuoctial, 182 Equinox, 463 Ericsson's lead, p. 163 Error, Total, of compass, 907, p. 334 Errors, effects of, in any computation. See D'gree of Dfj>e»daiir^ in the case, p. 52 of the D.R. p. 352 of the time at sea, 973, 98t KsUblishment of the Vort, vulgar, 921 correct, 923 is an interval, 937 Estimate angles, useful to be able to, 492 Evolution, 70 I'Al.ros, Captain, p. 105. noto I .^-jee Is. water clear, 1032-3 Keet, no. of in a sea mile, 186, p. 104, note, and Table 64A lio. of, sobtouding 1', Table », explan. p. 387 Danish, Dutch, &c, p. 380 I'igiiie, useful to refer to, in the mind, 167(3) the, la the ground of the mathe- matical solution, p. 61 (3> shewing deduction of lat. from, mor. alt. 462 showing deduction of mean time from a star's hoor-anglo, 472 shewing di'iluction of mean time from the sun's hour-angle, 478 or liigit, the last, S6 Figures of different t^nek^ 390 usoil In tahia, Tref. p Til and viil rint meridiouii, 191 aiul p. ;i96 p. ssl, Foreign charts, soundings how ex- pressed on, p. 925 measures, p. 37:-, 380 Forging ahead or astern, 96d Fractions, p. 1 decimal, p. 6 to convert vulgar intodccimal, 32 Fuel, how symbolised, jlse b, p. 401 8 of dip. 536 lical mile. p. 379 ; Table 64A , 1' f I'. 21 : problems, p. 24 T ,,,.,„s.p. 33 p. 192, note X Glasses, sand, 266 should be often examiued, 267 Globe, def. 90 principle of rectifying, p. 161, Graves, Capt., p. 266, note Great circle, def. 336, p. 56A Great circle sailing. 3311, p, 62a places on same side of eciuator .845 Airy's method ( Davis star azimuth tables, use of in projecting, p. 136 (iodfroy's chart and diagram, 38» Towson's diagram and table, 347 Oreat*'st common nuiutiire, 8, note Greek letters for stars, 666 vloh I ,481 > Und, without chroD. 676 by chroo. 676 refer to in crossing Faoiflc Ocna, pp. 364 and 406, notes M T., correcUon of, for 2d dlff. ol lunar dlsL Table 67, p. 419 ind log. 266, note liratte, 642, p. 178 «, sound of, from splitting of Ice, 1048 r's eeiUe . deacrlbed r*30 GKNEHAT- INDEX. s prefixed op ' j>,' vrncn pagt Hail, Capt. B.. observ. of the SPa horizon, observ. of planets, p. 356, Band lead. 399 Hartiiup, Mr., p. 179, note Heather on mathematical ments, p. 32, Height of eye, 205, 446 and 546 ileight of land may be found by tri.il. p. 388, note is reckoned from H.W. p. 388 of tide, comput. of. 934 Horschel, Sir J., p. 169, note f planet, p. 169, note f Hewett, Capt., rating chron. at sea, p. 294. note High land, finding ship's dist. from. 2117 High water, to find time of, roughly, 936, nearly, 933 Home. Sir Ev., 1034, p. 369 Horizon, sea, or visible, 204, Table 8 apparent places of. changes with temperature, 208 from a boat. 538 place of do. in a fog, p. 1 91, note eallr ,536 undulation of, indicates extrar dinary refractions, p. 196, not' refraction of. affected by slion &c., p. J96, note* rational, 421 : distance of, p. 3t and 45 Horn semicircle, or protractor, 108 useful in laying down points, 368 Horsburgh, pp. 351, 355. notes instance of fallacious agreement of lunar and chronom. p, 351, Hour-angle, def. 467 to find, from mean time, 609 of the sun, 609 by Spherics, p. 63a Huur-angle, of the moon, 612 of a star, 611 from the alt. 613 the merid. 622 m passing the prime vertical, i T;Lble 29, explan. p. 411 it rising and setting. 620 chart, 1052 Islands, a danger. 1052 taken for Innd, 1045 danger of landing on, p. 363 (6) near. 1052 yields fresh water, 1034 (5), p. 369 ght and i but not a Imbros, Mt.. an example, ; Index of a logarithm, 57 to mnasure, by the horizon, by the sun, 496 (2) des and tide tables, p. 340, Instruments of navigation, p. 63 nautical astron. p. 178 for drawinggeometrical figures, 91 See Heather on p. 32 Interpolation, 50 note on mental, p. 215 for second differences, p. 214 of sid. T. to turn to M.T. 603 in a double alt not to be cor- rected for change of long. p. Inverse proportion, 52 Involution, 66 Iron, hard and soft, 237 meguetised by induction. 237 transient magnetism of, 237 permanent magnetism of, 237 used in adjusting compasses, 240 upright, 241 horizontal radially. 242 horizontal tangentially, 243 ,243, Flindera" bar,": I inadju Irradiation, 712 Islands, small, appearance different a high and low water, 1060 Tsosce'es triangle, 87 Ivory's refract, p. 412, note method of double alt. 757 Johnson, A. C, on Lat. and Lc Journal, ship's, 403 to 413 suggestions on, 413 ex. of man-of-war's, 413 Jupiter, planet, p. 170, note K.A. and decl. to reduce, observed by day, p. 3r)6, long., by (satellites of), KERGgELEN', Voyage, 1047 KilomHre, Table 37, esphui. p. ^ King, Capt., p. 351, note Knot, 260 Krusenstern, Admiral, p. 375 his Memoirs quoted, 1058 La Caii ,542 ing the, 1029 when approaching. 1033 when to be set, 4iJ8 indications of,'1035 last point mentioned (Table 10\ position of given, p. 389 Latitude, def. 184 how deduced from the mer. alt. 462 is measured in miles, 186. .ste Spheroidal Tables, 64a diiT. of, 188-9 is determined absolutely, 680 importance of, p. 243, note ral methods in this work, p. 213, account, or dead reckoning, 954 errors of D.R. 964 in a double alt. p. 260, note Finding by obs- rmtion, by Mer. alt. 681 Latitude by Mer, ait. Degr. of D^pmSani by Reduction to the meridian, p. 249, p. 63a by the sun, 699 by the moon, or star, or a pla- net, 703 not near noon. See Doub'e AU. p. 255, Degr. of Depfndanc, «i>4 by equal alts, near noon, 732 do. not near noon, 746 by Circummeridional alts, by the son, 706 by a star, pole star, or a plauef 713-717 by Double Altitude, p. 255 Dpgi: of Depet.danc^ 730 by Alt. of the Pole Star, 717 an(5 p. 277 Latitudes and Longitudes i Lazarev, M., 547 Lead, 397, &c. ; Massey's, 402 rate of descent of hand, 397 Lead-line, 399 when re-measured should be wet, 399, note League, 199 Lecky's danger-angle tables, p. 143 Leeway, 202 to correct the course f vays , th« log-board, 407 Leg of an angle, 81, p. 56A Lighthouses, painted, p. 390, note Lights, to make, p. 365, note remarks on. pp. 403, 404 Lights, how shown on Admiralty charts, p. 92.5 Limits of obs. and methods, p. 51 Log, ship's journal. heaving 265 259, 263; wetted when measured, 26 D find the number corresponding to place the index, 58 Logarithmic difference, Table 73, explanation, p. 428 to correct for bar. and therm. Table 73 to compute the, p. 429 Logarithmic sines, cosines, &c. to half minutes, Table 68, explanation, p. 424 derivation of these quantiticgi, from the log. sine, p. 426 sines to ten seconds. Table 67, explan. p. 424 Logarithms, 56, tkc. arithmetical operations, by, P4,& e. practical suggestions in u^ing, 60 number oi places to be used, fiit remarks on an abuse of, p. 215, reasons for the number of pla.-oM given, Pref. viii uses In trigonometry, 165 ofnumbers,TabIe64,explan.p -I'.'J Log. sine, to convert into a prupnr- tional log. p. 430 subtracting, use of log. secant, &€.. p. 49, note square. Table 69 ; expl.in-.- p. 426, same as h>,T. ritude def. J91 mrii" be reckoned either E.orW. : I GENKKAL IXI)i;X. 93J gki'.brit III Index it/tr lo Ihl i t pi-j).f fit t'j/ ■ p' ichtn fagt is tnjicafed. Longitnile, liow mcnsurctl, 193 dlfl. of, 194, 195 l8 deteimincil relatively only, 826 hy account orDcail Reckoniug.Of'5 is more correctly kept in low lats. 967 ocrrectiou by Table 1, p. 378* should be uiarkea on chart lor timcof observation, 1U07 by lunar, p. 301 by the moon's alt. 864 . 23/ metboaiaUax of, p. 182, note case or box for, p. 188, note • nu'thods of increasing eflicicncy, caution against tormenting, p. 183,11 ,491 may produce errors, 499 Bhallow water, variation of compa^ affected in, p. 72, and note Ship, how umguetised, 244 magnetic forces of, 245 BUip'ii journal, p. 154-157 all matters relating to ship's place inserted, 412 Ship*s change of place, how affects 3(5) altitude, 548 Shoal patch, how symboiise Tracks, figures of different, 390 Ti-aiii d€ GdodAsie, p. 151, note Transit, dcf Transit of 453 :peditions, deter- minations of longitude from, notes on pp. 393, 395 Traverse, to work a, 287 Traverse sailing, 286 Traverse Table 1, explan. p. 377 use of, in proportioning, p. 379 in right-angled triangles, p. 378 in reducing measures, p. 379, 380 in correcting longitude, p. 378a Triangle, 87 Trigonometrical canon, U Trigonometry, terms of, pp propositions of, p. 45 rules for use of, 163 spherical, p. 55A-64A ; plane, 50a Tropic, 210 Tropical year, 465, and note 'J'roughton's circle, p. 185, note caution against tormenting the sextant, p. 183, note True alt. to reduce to app. 657 course to reduce to compass, 225-230, p. 169 Tube, plain, of sextant, use of, 543 rwiliglit, 4d4 ,150-157 TKD States' exploring expe- dition, 209, 547. 1U54 height of waves, 547 telegraphic determinations oi longitude, notes tu pp. 332-395 change of, in England, chartof, 219, p.7I affected by ground in azimuth, on the meridia from short double a from equal altitudes, 897 on the prime vertic from altitude, 900 from time, 902 by astronomical bearing, 9U3 remarks on the term "Variation,* 907 to correct courses and bearings for, 221, p. 159 Variations, daily and 12-hourIy, Table 21, explan. p. 408 Venus, period, p. 169, note* observed by day, p. 366, 311 iiracy in luu declination, to reduce, 593 R.A. to reduce, 692 determinations from transit of, pp. 393-395 Vernier, 494 Versts, p. 369 (12) Vertex of the great circle, 344 Vertical danger-angle, Lecky's tables, p. 143 Vessels, in a sea, acquire a tendency to move ahea Navigation of the Atlantic Ocean, by Capt. A. B. Becher, R.N., with an account of the Winds, Weather and Currents found therein throughout the year (with Charts) (1892). 5 Navigation of the Indian Ocean, China and Australian Seas, by Capt. A. B. Becher, R.N, with an account of the Winds-, Weather, and Currents found tlierein throughout tlie year (with Charts) (ISGi) 5 Chart of the Sulina Branch of the Danube (European Commission of the Danube), sutvejed by Kobe't Hansford," Surveyor of the Commisaion, under the direction of C. A. Hartley, Engineer in Chief (showing 45 nautical miles of the Hiver from Sulinal, size 10 ft. X 2 ft 3 in. (1860) 20 SAIL-MAKING. Remarks on Rigging Ships with Flat Surface Sails, by Lieut. William CongaUon, R.N.R. (1365) 2 SALVAGE. Salvage Operations. The floating of H.M. Battleship "Howe." Illustrated by 23 plans and photogta.phs,hy Rear-Admiral G. T. H. Boy'esjate Flarj-Cnjitain H.M.S. "Anson" (10001 ... ' 5 How Ships are Lost, and How to Save Life and Property at Sea (Illustrated), by ir. p. B. Kn«ser (1877) 1 SEAMANSHIP. Under Square Sail, by O.^.r. Wdher, (1898) 2 Under the Red Ensign; or, "Going to Sea," by niomas Gr,nj (1892) ... 1 6 SEXTANTS. Course and Position by Sextant Observations of two known 0\3\ectS,hy I^t--Cvl. English, late R.E G Captains' and Officers' Bridge or Poop Companion. Tables for finding the distance of an object at sea by inspection (without the use of pencil or paper), at the same time giving the distance the ship will go wide of the object before getting to it, and tVe course to steer to obtain a required distance. The a^ove gives, with the aid of a compass only, the distance of a moving ship from any fixed object. By A. Hiitteroih 2 6 Stars and Sextants. Star Distance Tables for facilitating the use of Lord EUenbornugh's method of Correctin? the Centring and Total Errors of Sextants at Sea, by John Ahner Spriqqe, Wm. Fraser Doak, M.A.. F.R.A.S., T. Charltnn Hxtdsou, B.A., F.R.A.S., of H.M. Nautical Almanac Ofice, AdmiraUy, and Arthur S. Cox, B.Sc.,A.B.C.S 2 6 SHIPPING. Historical Notes on Shipping, by p. I. /..„(,<•, Ji/,7.xY..l (1S79) 1 o 9 List of Nautical Works published by J. D. POTTER. SIGNALS. 8. d. Signal Cards— British System, with riatca, cont'iiuini,' Instructions for Sema- phoring by Day, and wiili the Morse Code by Day or Night, together with the principal " Urfjent " Light or Sound Signals, in accordance with the New Code. Also, Sheet of New Code Flags (34 Flags, coloured). Compiled by J. Whitly Dixon (Retired Captain, Roijal Navy). (Size, 24.i x 19i) 1 6 Ditto ditto mounted on thick card 2 SPEEDS. Speed and Consumption of Steam-Ships, with Algebraic Formula for Economical Speed, and Rules for calculating th-) alterations in Draught and Trim corresponding to Chasgej in Displacamint, and for using the Hydrometer to estimate those duo to Differences in the Specific Gravity of lh.> Wnlir ; fjr use in the Royal Navy and Mercantile Marine; by J. P. Kit(/ii!Cft, Jlfi. \' ' Licit. R X i;.. AsiM.ln.-^t.N.A., M.R.U.S.I., Tounjcr Brother of the Tr, . s. ... i U Speed Tables, for finding the distance run in a given time at : iveen the limits of 10 to ISknots, by J. D. Macpherson (Pacific Stc.i... : .^... Co.) ... 1 STAKS. The Bearings of the Principal Bright Stars of greater declination than 23" mirth or 23" south ; also those of the Moon and Planets when similarly situated, by .1. C. ./../i«sn„, /;.Y. (Published by request) 3 Pole-Star Latitude: a Method of Finding the Latitude from an Altitude of the Pole Star, by Dartiton Hutlon (Master Mariner), B.A., M.Inst.C.E 1 Position-Line Star Tables. A new and simple method of fixing ship's position by observations of stars near Meridian and Prime Vertical without logarithmic calculation, by //. J3. (VH..f(,ti„, fl. .v. .5 Tables for Facilitating the Determination of the Latitude and Time at Sea by Observations of the Stars, by tiear-Admiral c. Shadweil, f.r.s. 2 6 A Handbook for Star Double Altitudes, by A. C. Johnson, R.N., with directions for selecting the Stars 2 6 See also SoxtantS. STABILITY. A New Theory of the Stability of Ships, second edition, revised and enlarged, (with 28 diagrams), by ^U/. /. C'oujjer (18'J'J) 2 SURVEYING. Practical Nautical Surveying and the Handicraft of Navigation, by Com. T. A. Hull, ll..\. 3 O Practical Observations on Surveying (on determining the Position of a Vessel when Sounding), by Commander l\ F. Shurtland, R.N. 1 TIDES. Moxly's Theory of the Tides, with numerous diagrams by Capt.J.F.Ruthi'cn.F.R.a.S. 2 O Tide Charts of the English and Bristol Channels and entrance of the Thames, c-omipilud liucn the Admiralty Tide Tables, Uy Alijenwn Ilcber I'ercy, lato Lieut. Knyal Navy 5 The Direction and Rate of the Tidal Streams at every Hour, for 48 Localities between the Nore and Scllly Isles, compiled from Admiralty Sourei-8 only, l,y K. //.,... -..i Cu«i„s 2 Twelve Charls of the Tidal Streams of the Channel Islands and Neighbouring French Coasts, by v. WimurcZ t'liiii'i-' -i o io List of Nautical Works published by J. D. POTTER. TIDES-co»f»,»e(;. 6. d. The General Direction of the Tidal Streams In the North Sea for every Hour "before" and "after," and at High Water, Dover, compiled by Com. G. K. Uandij, R.N.R., from Official Publications (on one sheet, size 23 by 17 inches) 1 The Universal Tidal Ready Reckoner, calculated by Capt. w. E. Hutchinson, i 6 The North Sea, Its Physical Chai-acterislics, Tides, Currents and Fisheries, by W. H. -ineeler, M.Intsf.C.E. 2 6 The Currents on the South -Eastern Coasts of Newfoundland and the Amount of Indraught into the Largest Bays on the South Coast, from Invesiigations of the Tidal and Current Survey in the Season of 1903, by W. Bell D ncson, M.A , D.Sc, F.R.S.C, M Inst C.E., Supeii7ite7vle>,t Published by order of the Minister of Marine and Fishfrics, Ottawa ... ... ... ^o chayje. The Currents in the Gulf of St. Lawrence, including the Anticosti Region, Belle Isle, and Cabot Straits, coudcnsed from the Reports of the Snriey ol Tides and Currents for tlie Seasons of 1894, 1895, and 1896. Published liy order of the Miuister rf Ma. ine and Fifheries, Ottawa Xo charge. The Currents at the entrance of the Eay of Fundy and on Ihe Steam- ship Routes in or approaching Southern Nova Scotia, from investi- gations . f the Tidal and Current Survey in the Season of 190i, by Tl'. Bell Dawson, M.A., D.Sc, F.R.S.C , M.Iiist.C.E., Superintendent. Published by the Department of Marine and Fisheries, Ottawa, Canada ... ... ... ... Nu charge. The Currents in Belle Isle Strait, from Investigations of the Tidal and Current Survey in the Seasons of 1894 and 1906. By W. Bell Daivson, M.A., D.Sc, F.R.S.C, M.Inst.C.E., Siiperijitendent. Published by the Department of Marine and Fisheries, Ottawa. Canarla ... ... ... ... ... ... ... No charge. Tables of Hourly Direction and Velocity of the Currents and Time of Slack Water in the Bay of Fundy and its Approaches as far as Cape Sable. From investigations of the Tidal and Lurrent Survey in the seasons of 1S,U4 and 1907. By W. Bell Daieson, U.A., D.Sc., M.Dist.C.E., Superin- tenderit. Published by the Department of Marine and Fisheries, Ottawa, Canada No charge. See also Time. TIME. How to Find the Time at Sea in less than a Minute, being a New and Accurate Method, with specially adapted Tables, by A. C. Johnson, R.N. 2 6 Time, Tide, and Distances. A handy book of reference for the Shipowner, Underwriter, or Traveller. Contains the World's Time compared with Greenwich ; the Tides round the British Coasts and those from Bergen via the Eastern Route to Japan with that at London Bridge; approximate Distances from Home Ports to Home and Foreign Ports (over 13,000 references) ; and a Speed and Distance Table for Bates of Speed from 8 to 21 knots for distances up to 14,000 nautical mi\fs,hy J. McEirdy,R.N.R 15 Time-Altitudes for Expediting the Calculation of Apparent-Time, &.C.,hj A. C.Johnson, R.N. 4 The Blue Coat Boys' Clock. A dial showing the simultaneous time of day at all parts of the earth's sui-face, size 20 X 17 inches ... ... ... ... ... ... 5 C See also Azimuths, ClironoiDeters, Tides, WINDS. The True Direction and Velocity of Wind, observed from Ships while Sailing, by James N. Miller (Member of the Liverpool Polytechnic Society), with Table for Indicating the True Direction of the Winds at Sea (1870) 6 The Wind in its Circuits: with the explanation of the Origin and Cause of Circular Storms and Equinoctial Gales j illustrated with numerous Diagrams and a Chart of the Prevailing Winds of the World for Spring and Summer, by Lieut. R. U. Armit, R.N. (1S70) 7 6 See also Meteorology. t HOWAHD COLLINS'S SINGLE-HANDED DIVIDEHS. Specially Designed for Navigators. The advantages of these Single-handed Dividers are that tlioy can bo picked up from the table by one hand alone, and the logs opened or closed by the finger and thumb of the same hand, without any other assistance wliatever. Navigators are thus enabled to work, and retain in position, the parallel ruler with one hand, while distances are being measured with the other. It is needless to say that this enables much time to be saved in laying off courses and distances, a matter for consideration in these days of steamers travelling a mile in less than two-and-a-half minutes. The joint itself is of an entirely new form, being made a round ball. This is found to be a great advantage, and the best form for rolling between the thumb and fore-finger when " stepping " distances ; as for instance, in measuring fifty miles by the legs being set to ten miles of the chart scale. Tliese Dividers are of the best make in German-silver, price 7s. 6d. per pair in cardboard box, and with special cleat and screws for fixing to the chart-room bulk-head to hold them when not in use. " None seem to be quite on a level of excellence with these." — Merchant Service Review. " The price is certainly a reasonable one." — The Shipping World. B. d. BRASS DIVIDERS 6-iuch, 2/6; 8-inch 3 6 FIELD'S PARALLEL RULERS. Boxwood 21-inch, 18/; 21-inch, IT) ; IS-inch, 11/; 15-inch 8 Ebony 21-inch, 21/ ; 21-iuch, 18/ ; 18-inoh, U/; 15-inch 11 e INCORRECT CHARTS. SPECIAL BOARD OF TRADE OFFICIAL NOTICES TO SHIPOWNERS. NOTICE TO SHIPOWNERS AND AGENTS. The attention of the Board of Trade has frequently boon oillcd to cases in which British vessels have been endangered or wrecked through Masters attempting to navigate them by means of antiquated or otherwise defective Charts. The Board of Trade desire, therefore, to direct the especial attention of Shipowners and their Servants and Agents to Iho necessity of seeing that the Charts taken or sent on board thoir Ships are corrected down to the time of sailing. Neglect to supply a Ship with i)roper Charts will bo brought prominently before the Court of Inquiry in the event of a wreck occurring from tbatcanse. The Oflicial Catalogue of Charts, plans and sailing directions, published by the Admiralty (iMncd annually in March), can be obtained free of charge on application to the Chart Agency, 146, Minoried, London, E.G., or from anv of the sub-agoncics at the Homo or Foreign Ports. Sfafniinif, ithov'ivij flic vvinhiT of Nriv BrUixh Adiinraltij Churh Pvhlished, Corrections made to the Chart Flates, and Quantities Printed, for the' years 1885, 1890, 1895, 1900, and 1906. 1885 1890 1895 1900 1905 New Chart Plates Engi iived andPubliphed 54 76 114 102 110 Chart Plates Improved by Additional Flans 32 10 34 30 36 Chart Plates Improved by Corrections and Additions 186 130 163 224 196 Corrections Made to the Chart Plates 2,750 4,750 5,300 4,520 5,320 Minor Corrections at the hands of the Draughtsmen 29,800 37,270 30,0f6 35.50 60,499 Total Number cf Charts Printed 272,115 297,120 312,638 580,207 689,930