" LIBRARY OF CONGRESS. %p..^T^ttp^i9]^ :fu UNITED STATES OF AMERICA. ELEMENTS SURVEYING, NAVIGATION, WITH DESCRIPTIONS OF THE INSTRUMENTS AND THE NECESSARY TABLES. BY CHAELES DAVIES, LL. D., AUTHOR OF ARITHMETIC, ALGEBRA, PRACTICAL MATHEMATICS FOR PRACTICAL MEN, ELEMENTS OF DESCRIPTIVE GEOMETRY, SHADES, SHADOWS, AND PER- SPECTITE, ANALYTICAL GEOMETRY, DIFFERENTIAL AND INTEGRAL CALCULUS. REVISED EDITION. NEW YOEK: PUBLISHED BY A. S. BARNES & CO., No. 51 JOHN-STREET. CINCINNATI: H. W. DERBY & CO., 1851. /. ^ DA VIE S' COURSE OF MATHEMATICS IBabies* iFivst Wessons in ^tiQmetic— For Beginners. Jiabies' ^ritjmetic— Designed for the use of Academies and Schools. I&ej to 3Bai)ics' 'Mtititmetic. Jiabies' Sanfbersitj ^ritt)mctic — Embracing the Science of Numbers and their numerous Applications. Ites to IBabies* sanibnsitj ^ritljmetic. 3iabies* IBlcmcntarw Sllficljra — Being an introduction to the Science, and form- ing a connecting hnk between Arithmetic and Algebra. 2&£2 to Babies' SElementnvs ^laefira. IBabiES' 3Slemcnts of ©EomettD and STrigonometrj, with Applications in Mensuration. — This work embraces the elementary principles of Geometry and Trigonometry. The reasoning is plain and concise, but at the same time strictly rigorous. Babies' 33'^actical lEatijematfcs for 33tractical iHSen — Embracing the Princi- ples of Drawing, Arcliitecture, Mensuration, and Logarithms, with Applications to the Mechanic Arts. Babies' 3Souraon's Algebra — Including Sturm's Theorem — Being an abridg- ment of the Work of M. Bourdon, with the addition of practical examples. Babies' Hcgcntrre's ©feometrj and SCrigonometrs — From the works of A. M. Legendre, with the addition of a Treatise on Mensuration of Planes and Solids, and a Table of Logarithms and Logarithmic Sines. Babies' Surbejing — With a description and plates of the Theodolite, Com- pass, Plane-Table, and Level ; also, Maps of the Topographical Signs adopted by the Engineer Department — an explanation of the method of surveying the Public Lands, Geodesic and Maritime Surveying, and an Elementary Treatise on Navigation. Babies' Bescriptibc CKeometrB — With its application to Spherical Projec- tions. Babies' S|)atres, Sljattotos, and llijteai? 33ei^sj)ectibe. Babies' ^nalstical fiSeometrj — Enjbi'acing the Equations of the Point and Straight Line — of the Oonio Sections — of the Line and Plane in Space ; also, the discussion of the General Equation of the second degree, and of Sub- faces of the second order. Babies' Btfferential and integral Calculus. 5 Entered according to Act of Congress, in the year one thousand eight hundred and (^ fifty-one, by Charles Davies, in the Clerk's Office of the District Court of the ^ United States for the Southern District of New York. J. p. JONES & CO., Stkbeoiypees. F. C. GUTIERBEZ, Pbimtee. S-3^7?/ PREFACE The Elements of Surveying, first publislied in 1830, was designed as a text-book for tlie pupils of the Military Academy, and in its preparation little regard was liad to the supposed wants of other institutions. The work, however, was received by the public with more favor than was anticipated, and soon became a lead- ing text-book in the Colleges, the Academies, and the higher grade of Schools. For the purpose of adapting it, more fully, to the sup- posed wants of these institutions many changes have been made, since its first publication, and the present edition will be found to differ, in many respects, from those which have preceded. It has been the intention to begin with the very ele- ments of the subject, and to combine those elements in the simplest manner, so as to render the higher branches of plane surveying comparatively easy. All the instru- ments needed for plotting have been carefully described ; and the uses of those required for the measurement of angles are fully explained. The conventional signs adopted by the Topographical Bureau, which are now used by the United States Engi- neers in all their Charts and Maps, are given in plates 5 and 6. Should these signs be generally adopted in the country, it would give entire uniformity to all maps and delinea- tions of the ground, and would establish a kind of lan- guage by which all the peculiarities of soil and surface could be accurately represented. IV PREFACE. A section lias also been added on Geodesy. This branch of Surveying is extensively applied in the Coast Survey, and now forms an important element of a practi- cal or scientific education. A full account is also given of the manner of survey- ing the public lands; and, although the method is simple, it has, nevertheless, been productive of great results, by defining, with mathematical precision, the boundaries of lands in the new States, and thus settling their titles on an indisputable basis. This method was originated by Col. Jared Mansfield, whose great acquirements in science introduced him to the notice of President Jefferson, by whom he was appointed surveyor- general of the North-Western Territory. May it be permitted to one of his pupils, and a gradu- ate of the Military Academy, further to add, that at the organization of the institution in 1812, he was appointed Professor of Natural and Experimental Philosophy. This situation he filled for sixteen years, when he withdrew from the Academy to spend the evening of his life in re- tirement and study. His pupils, who had listened to his instructions with delight, who honored his learning and wisdom, and had been brought near to him by his i^ind and simple manners, have placed his portrait in the public library, that the institution might possess an enduring memorial of one of its brightest ornaments and distin- guished benefactors. At the solicitation of several distinguished teachers, there is added, in the present edition, an article on Plane Sail- ing, most of which has been taken, by permission of the author, from an excellent work on Trigonometry and its applications, by Professor Charles W. Hackley. FiSHKiLL Landing, July, 1851. CONTENTS. BOOK I. SECTION I. PAGE. Of Logarithms, 9 Table of Logarithms, 11 Multiplication by Logarithms,. 15 Division by Logarithms, '. ^ _ 16 Arithmetical Complement, 17 SECTION IX. Geometrical Definitions, 19 Geometrical Constructions, 25 Description of Instruments, 25 Dividers, 25 Ruler and Triangle, 25 Scale of Equal Parts, 27 Diagonal Scale of Equal Parts, 27 Scale of Chords, 29 Semicircular Protractor, •_... 30 Sectoral Scale of Equal Parts, 30 Gunter's Scale, 32 Solution of Problems, 32 SECTION III. Plane Trigonometry, 38 Division of the Circumference, 38 Definitions of the Trigonometrical Lines, 39 Table of Natural Sines, 40 Table of Logarithmic Sines, 41 Theorems, 44 Solution of Triangles, 48 Solution of Right-Angled Triangles, , 54 Application to Heights and Distances, 55 VI CON-TENTS. BOOK II. PLANE SURVEYING. SECTION I. PAGE. Definitions, 64 Measurement of Lines and Angles, 66 Measures for Distances, 66 To Measure a Horizontal Line, 67 Measurement of Angles, 69 Of the Theodolite, 69 Verniers, 75 To Measure a Horizontal Angle with the Theodolite, 77 To Measure a Vertical Angle, 78 Measurements with the Tape or Chain, 79 Surveying Cross, 81 SECTION II. Area, or Contents of Ground, , 85 Of Laying out Land, 96 SECTION III. The Circumferenter, or Surveyor's Compass, 98 Surveying with the Compass, Definitions, etc., 99 Field Operations, 103 Traverse Table, 105 Of Balancing the Work, 109 Of the Double Meridian Distances of the Courses, 113 Of Finding the Area, 114 First Method of Plotting, 117 Second Method of Plotting, 117 Problems, 118 Offsets, 123 Of Supplying Omissions in the Field Notes, 124 To Determine the Angle between two Courses, ■. 186 Of Dividing Land, 127 SECTION IV. Method of Surveying the Public Lands, 131 Variation of the Needle, 134 Method of Ascertaining the Variations, 138 To Find the True Meridian with the Theodolite, 140 To Find the True Meridian with the Compass, 141 CONTENTS. Vli BOOK III. LEVELLING AND TOPOGRAPHICAL SURVEYING. SECTION I. PAGE. Of Levelling, 145 The Y Level, 147 The Water Level, ., 150 Levelling Staves, 151 Levelling in the Field, 153 Difference of Level between Tw^o Points, 153 Example, 154 Levelling for Section, 157 Plotting the Section or Profile, 158 SECTION II. Topographical Surveying, 159 Field Notes, 166 Plotting the Work, 167 BOOK lY. GEODESIC, TRIGONOMETRIC, AND MARITIME SURVEYING. SECTION I. Geodesic and Trigonometric Surveying, 173 Preliminary Reconnoissance and Establishment of Signals, 174 Measurement of a Base Line, 176 Triangulation, 178 Filling up the Survey, 181 Use of the Compass, 181 The Plane Table— Its Uses, 183 To Measure a Horizontal Angle, 185 To Determine Lines in Extent and Position, 185 Of Changing the Paper, 187 Reduction to the Centre,. 189 Spherical Excess, 190 Plotting the Triangulation, 192 The Circular Protractor, 192 To Lay off an Angle with the Protractor, 193 First Method of Plotting, 193 Second Method of Plotting, 194 Method of Chords, 195 To Layoff an Angle, 196 SECTION II. Maritime Surveying, '. 197 Vlll COITTENTS. BOOK V. OF NAVIGATION. SECTION I, PAGE. Definitions, 201 SECTION II. Of Plane Sailing, 205 SECTION III. Of Traverse Sailing, 207 Of Plotting, 209 SECTION IV. Parallel Sailing, 211 Middle Latitude Sailing, 214 Mercator's Sailing,. . '. 218 Mercator's Chart, 221 Line of Meridional Parts on Gunter's Scale, 222 ELEMENTS OP SURYEYMG. BOOK I. SECTION I. OF LOGAEITHMS. 1. The logarithm of a number is the exponent of the power to which it is necessary to raise a fixed number^ in order to produce the first number. TMs fixed number is called tlie base of tlie system, and may be any number except 1 : in tlie common system, 10 is assumed as tlie base. 2. If we form tbose powers of 10, wHcli are denoted by entire exponents, we shall have 10" =1 10' = 10, 10' = 1000 10' = 100, 10^ = 10000, &c., &c.. From tbe above table, it is plain, tbat 0, 1, 2, 8, 4, &c., are respectively the logarithms of 1, 10, 100, 1000, 10000, &c. ; we also see, tbat the logarithm of any number be- tween 1 and 10, is greater than and less than 1 : thus, log 2 = 0.301030. The logarithm of any number greater than 10, and less than 100. is greater than 1 and less than 2 : thus, log 50 = 1.698970. The logarithm of any number greater than 100, and less than 1000, is greater than 2 and less than 3 : thus, 10 ELEMENTS OF SURVEYING. [BOOK I. If tlie above principles be extended to otber numbers, it will appear, tbat the logarithm of any number, not an exact power of ten, is made up of two parts, an entire and a decimal part. The entire part is called the characteristic of the logarithm^ and is always one less than the number of places of figures in the given number. 3. The principal use of logarithms, is to abridge nu- merical computations. Let M denote any number, and let its logarithm be denoted by m ; also let N denote a second number whose logarithm is w; then, from the definition, we shall have, . 10"" = if (1) 10" = iV(2). Multiplying equations (1) and (2), member by member, we have, 10"' + " = MX N or, m + n=\og {MxN); hence. The sum of the logarithms of any two numbers is equal to the logarithm of their product. 4. Dividing equation (1) by equation (2), member by member, we have, m-n ^ ^^ 10 = j;t or, m — n = log -Tf- hence, The logarithm of the quotient of two numbers, is equal to the logarithm of the dividend diminished by the logarithm of the divisor. 5. Since the logarithm of 10 is 1, the logarithm of the product of any number by 10, will be greater by 1 than the logarithm of that number ; also, the logarithm of the quotient of any number divided by 10, will be less by 1 than the logarithm of that number. Similarly, it may be shown that if any number be mul- tiplied by one hundred, the logarithm of the product will be greater by 2 than the logarithm of that number ; and if any number be divided by one hundred, the logarithm of the quotient will be less by 2 than the logarithm of. that number, and so on. SEC, I] LOGARITHMS. 11 EXAMPLES, log 327 is 2.514548 log 32.7 " 1.514548 . log 3.27 " 0.514548 log .327 " 1.514548 log .0327 " 2.514548 From tlie above examples, we see, tliat in a number composed of an entire and decimal part, we may cbange the place of tlie decimal point without changing the deci- mal part of the logarithm; but the characteristic is dimin- ished by 1 for every place that the decimal point is removed to the left. In the logarithm of a decimal, the characteristic becomes negative, and is numerically 1 greater than the number of ciphers immediately after the decimal point. The negative sign extends only to the characteristic, and is written over it, as in the examples given above. TABLE OP LOGARITHMS. 6. A table of logarithms, is a table in which are writ- ten the logarithms of all numbers between 1 and some given number. The logarithms of all numbers between 1 and 10,000 are given in the annexed table. Since rules have been given for determining the characteristics of logarithms by simple inspection, it has not been deemed necessary to write them in the table, the decimal part only being given. The characteristic, however, is given for all numbers less than 100. The left hand column of each page of the table, is the column of numbers, and is designated by the letter N; the logarithms of these numbers are placed opposite them on the same horizontal line. The last column on each page, headed D, shows the difference between the loga- rithms of two consecutive numbers. This difference is found by subtracting the logarithm under the column headed 4, from the one in the column headed 5 in the same horizontal line, and is nearly a mean of the differ- ences of any two consecutive logarithms on this line. d^ 12 ELEMENTS OF SURVEYING. [BOOK I. To find^ from the table, the logarithm of any number. 7. If the number is less than 100, look on tlie first page of the table, in the column of numbers under N, until the number is found: the number opposite is the logarithm ought : ThuSj log 9 = 0.954243. When the number is greater than 100 and less than 1000. 8. Find in the column of numbers, the first three figures of the given number. Then pass across the page along a horizontal line until you come into the column under the fourth figure of the given number : at this place, there are four figures of the required logarithm, to which two figures taken from the column marked 0, are to be prefixed. If the four figures already found stand opposite a row of six figures in the column marked 0, the two left hand figures of the six, are the two to be prefixed ; but if they stand opposite a row of only four figures, you ascend the column till you find a row of six figures ; the two left hand figures of this row are the two to be prefixed. If you prefix to the decimal part thus found, the character- istic, you will have the logarithm sought: Thus, log 8979 = 3.953228 log .08979 = 2.953228 If, however, in passing back from the four figures found, to the column, any dots be met with, the two figures to be prefixed must be taken from the horizontal line di- rectly below : Thus, log 3098 = 3.491081 log 30.98 = 1.491081 If the logarithm falls at a place where the dots occur, must be written for each dot, and the two figures to be prefixed are, as before, taken from the line below: Thus, log 2188 = 3.340047 log .2188 = 1.340047 SEC. L] LOGARITHMS. 13 When the number exceeds 10,000. 9. The characteristic is determined by the rules already given. To find the decimal part of the logarithm : place a decimal point after the fourth figure from the left hand, converting the given number into a whole number and decimal. Find th^ logarithm of the entire part by the rule just given, then take from the right hand column of the page, under D, the number on the same horizontal line with the logarithm, and multiply it by the decimal part; add the product thus obtained to the logarithm al- ready found, and the sum will be the logarithm sought. If, in multiplying the number taken from the column Jj{, the 4^1^9.1 * part of the product exceeds .5, let 1 be added to the entire part; if it is less than .5, the decimal part of the product is neglected. EXAMPLE. I 1. To find the logarithm- of the number 672887. The characteristic is 5. ; placing a decimal point after the fourth figure from the; left, we have 6728.87. The decimal part' of the 'log'* 6728 is .827886', and the corres- ponding number in the column D is 65'; 'then 65x.87= 66.55, ' and since the decimal part exceeds ^ .5, we have 57 to be added to .827886, which gives .827943. Hence, log 672887 = 5.827943 Similarly, log .0672887 = 2.827943 The last rule has been deduced under the supposition that the difference of the numbers is proportional to the difference of their logarithms, which is suf&ciently exact within the narrow limits considered. In the above example, 65 is the difference between the logarithm of 672900 and the logarithm of 672800, that is, it is the difference between the logarithms of two numbers which differ by 100. We have then the proportion 100 : 87 : : 65 : 56.55, hence, 56.55 is the number to be added to the logarithm before found. 14 ELEMENTS OF SURVEYlNa. [BOOK I. To find from, the table the nwriber corresponding to a given logarithm. 10. Search, in tlie columns of logarithms for the decimal part of the given logarithm : if it cannot be found in the table, take out the number corresponding to the next less logarithm and set it aside. Subtract this less logarithm from the given logarithm, and annex to the remainder as many zeros as may be necessary, and divide this result by the corresponding number taken from the column marked D, continuing the division as long as desirable : annex the quotient to the number set aside. Point off, from the left hand, as many integer figures as there are units in the characteristic of the given logarithm increased by 1; the result is the required number. If the characteristic is negative, the number will be entirely decimal, and the number of zeros to be placed at the left of the number found from the table, will be equal to th,3 number of units in the characteristic diminished by 1. This rule, like its converse, is founded on the supposi- tion that the difference of the logarithms is proportional to the difference of their numbers within narrow limits. EXAMPLE. 1. Find the number corresponding to the logarithm 8.233568. The decimal part of the given logarithm is .233568 The next less logarithm of the table is .233504, and its corresponding number 1712. Their difference is - - - - 64 Tabular difference 253)6400000(25 Hence, the number sought 1712.25. The number corresponding to the logarithm 3.233568 is .00171225. 2. What is the number corresponding to the logarithm 2.785407? Ans. .06101084. 3. What is the number corresponding to the logarithm 1.846741? Aois. .702653. SEC. I.] LOGARITHMS. 15 MULTIPLICATIOIf BY LOGAEITHMS. 11. Wten it is required to multiply numbers by means of their logarithms, we first find from the table the loga- rithms of the numbers to be multiplied; we next add these logarithms together, and their sum is the logarithm of the product of the numbers (Art. 3). The term sum is to be understood in its algebraic sense; therefore, if any of the logarithms have negative characteristics, the difference between their sum and that of the positive characteristics, is to be taken ; the sign of the remainder is that of the greater sum. EXAMPLES. 1. Multiply 23.14 by 5.062. log 23.14 = 1.364363 log 5.062 = 0.704322 Product, 117.1347 . . . 2.068685 2. Multiply 3.902, 597.16, and 0.0314728 together. log 3.902 = 0.591287 log 597.16 = 2.776091 log 0.0314728 = 2.497936 Product, 73.3354 .... 1.865314 Here, the 2 cancels the + 2, and the 1 carried from the decimal part is set down. 3. Multiply 3.586, 2.1046, 0.8372, and 0.0294 together. log 3.586 = 0.554610 log 2.1046 = 0.323170 log 0.8372 = 1.922829 log 0.0294 = ^.468347 Product, 0.1857615 . . 1.268956 In this example the 2, carried from the decimal part, cancels 2, and there remains 1 to be set down. 16 ELEMENTS OF SURVEYINGf. [BOOK I. DIVISION OF JSrUMBEES BY LOGARITHMS. 12. When it is required to divide numbers by means of their logarithms, we have only to recollect, that the subtraction of logarithms corresponds to the division of their numbers (Art. 4). Hence, if we find the logarithm of the dividend, and from it subtract the logarithm of the divisor, the remainder will be the logarithm of the quotient. This additional caution may be added. The difference of the logarithms, as here used, means the algebraic differ- ence ; so that, if the logarithm of the divisor have a nega- tive characteristic, its sign must be changed to positive, after diminishing it by the unit, if any, carried in the sub- traction from the decimal part of the logarithm. Or, if the characteristic of the logarithm of the dividend is nega- tive, it must be treated as a negative number. EXAMPLES. 1. To divide 24163 by 4567. log 24163 = 4.383151 log 4567 = 3.659631 Quotient, 5.29078 . . 0.723520 2. To divide 0.06314 by .007241. log 0.06314 = 2.800305 log 0.007241 = 3.859799 Quotient, 8.7198 . . 0.940506 Here, 1 carried from the decimal part to the 3, changes it to 2, which being taken from 2, leaves for the cha- racteristic. 3. To divide 37.149 by :^;23.76. log 37.149 = 1.569947 log 523.76 = 2.719133 Quotient, 0.0709274 . 2.850814 SEC. I] LOGARITHMS. 17 4. To divide 0.7438 by 12.9476. log 0.7438 = 1.871456 log 12.9476 = 1.112189 Quotient, 0.057447 . . 2.759267 Here, the 1 taken from 1, gives 2 for a result, as set down. ARITHMETICAL COMPLEMENT. 13. Tlie Arithmetical complement of a logarithm is the number which remains after subtracting the logarithm from 10. Thus, 10 - 9.274687 = 0.725313. Hence, 0.725313 is the arithmetical complement of 9.274687. 14. We will now show that, the difference hetween two logarithms is truly found^ hy adding to the first logarithm the arithmetical complement of the logarithm to he subtracted^ and then diminishing the sum hy 10. Let a = the first logarithm, Z> = the logarithm to be subtracted, and c= 10 —5 = the arithmetical complement of b. Now the difference between the two logarithms will be expressed by a — h. But, from the equation c = 10 — h, we have c-10=-h, hence, if we place for — h its value, we shall have a — h = a + c—10, which agrees with the enunciation. When we wish the arithmetical complement of a loga- rithm, we may write it directly from the table, by subtract- ing the left hand figure from 9, then proceeding to the right, subtract each figure from 9 till we reach the last significant figure," which must be taken from 10: this will he the same as taking the logarithm from 10. 2 18 ELEMEITTS OF SURVEYING. [BOOK I. EXAMPLES. 1. From 3.274107 take 2.104729. By common method. By arith. comp. 3.274107 3.274107 2.104729 its ar. comp. 7.895271 Diff. 1.169378 Sum 1.169378 after sub- tracting 10. Hence, to perform division by means of tbe aritbmetical complement, we bave tbe following RULE. To the logarithm of the dividend add the ariilimetical com- plement of the logarithm of the divisor: the sum^ after sub- tracting 10, will be the logarithm of the quotient. EXAMPLES. 1. Divide 327.5 by 22.07. log 327.5 2.515211 log 22.07 ar. comp. 8.656198 Quotient, 14.839 . . . 1.171409 2. Divide 0.7438 by 12.9476. log 0.7438 .... 1.871456 log 12.9476 ar. comp. 8.887811 Quotient, 0.057447 . . . 2.759267 In tbis example, the sum of tbe characteristics is 8, from which, taking 10, the remainder is 2, 3. Divide 37.149 by 523.76. log 37.149 .... 1.569947 log 523.76 ar. comp. 7.280867 Quotient, 0.0709273 . . 2.850814 EC. 11] GEOMETRICAL DEFINITIONS. 1| 4. Divide 0.875 by 25. Ans. 0.035. 5. Divide 3.1416 by .944. Ans. 3.3279. 6. Divide 2756 by 327. Ans. 8.4281. 7. Divide 672859 by 0.09657. Ans. 6967580.64. SECTION II. GEOMETEICAL DEFINITIONS AND CONSTKUCTIONS. 1. Extension has tbree dimensions, length, breadtb, and thickness. 2. GrEOMETRY is the science which has for its object : 1st. The measurement of extension ; and 2dly. To dis- cover, by means of such measurement, the properties and relations of geometrical figures. 3. A Point is that which has place, or position, but not magnitude. 4. A Line is length, without breadth or thickness. 5. A Straight Line is one which lies in the same direction between any ■ two of its points. 6. A Broken Line is one made up of straight lines, not lying in the same direction. 7. A Curve Line is one which changes its direction at every point. The word line when used alone, will designate a straight line ; and the word curve, a curve line. 8. A Surface is that which has length and breadth without thickness. 20 ELEMENTS OF SURVEYING. [BOOK I, 9. A Plake is a surface, sucli, tliat if any two of its points be joined by a straight line, such line will be wholly in the surface. 10. Every surface, which is not a plane surface, or com- posed of plane surfaces, is a curved surface. 11. A Solid, or Body is that which has length, breadth, and thickness : it therefore combines the' three dimensions of extension. 12. An Akgle is the portion of a plane included be- tween two straight lines which meet at a common point. The two straight lines are called the sides of the angle, and the common point of intersection, the vertex. Thus, the part of the plane includ- ed between AB and AC is called an angle : AB and A are its sides^ and A its vertex. An angle is sometimes designated simply by a letter placed at the vertex, as, the angle A ; but generally, by three letters, as, the angle BA G or OAB^ — the letter at the vertex being always placed in the middle. 13. When a straight line meets an- other straight line, so as to make the adjacent angles equal to each other, each angle is called a right angle ; and the first line is said to be jperpendicu- lar to the second. 14. An Acute Angle is an angle less than a right angle. 15. An Obtuse Angle is an greater than a right angle. SEC. IT.] GEOMETRICAL DEFINITIONS. 21 16. Two straiglit lines are said to be parallel, wlien being situated in tlie same plane, they cannot meet, how far soever, either way, both of them be produced. 17. A Plane Figure is a portion of a plane terminat- ed on all sides by lines; either straight or curved. 18. A Polygon, or rectilineal fig- ure, is a portion of a plane terminat- ed on all sides by straight lines. The sum of the bounding lines is called the jperimeter of the polygon. 19. The polygon of three sides, the simplest of all, is called a triangle; that of four sides, a quadrilateral; that of five, a pentagon ; that of six, a hexagon ; that of seven, a heptagon ; that of eight, an octagon ; that of nine, an nonagon ; that of ten, a decagon ; and that of twelve, a 20. An Equilateral polygon is one which has all its sides equal ; an equiangular polygon, is one which has aU its angles equal. 21. Two polygons are mutually equilateral, when they have their sides equal each to each, and placed in the same order: that is to say, when following their bounding lines in the same direction, the first side of the one is equal to the first side of the other, the second to the second, the third to the third, and so on, 22. Two polygons are mutually equiangular, when every angle of the one is equal to a corresponding angle of the other, each to each. 23. Triangles are divided into classes with reference both to their sides and angles. 1. An which has its three sides equal. 22 ELEMENTS OF SURVEYING. [BOOK I. 2. An isosceles triangle is one wMcli tas only two of its sides equal. 8. A scalene triangle is one "vvkicli lias its three sides unequal. 4. An aciii&- wHcli lias its tliree acute. 5. A right-angled triangle is one wMdi has a right angle. The side opposite the right angle is called the hypothenuse^ and the other two sides, the hase and perpen- dicular. 6. An obtuse-angled triangle is one which has an obtuse angle. 24. There are three kinds of Quadkilaterals ; 1. The trapezium^ which has none of its sides parallel. 2. The trapezoid^ which has only two of its sides parallel. 8. The parallelogram^ which has its opposite sides parallel. SEC.II] GEOMETRICAL DEFINITIONS. 25. There are four kinds of Parallelograms: 23 1, The rJiomboid, which has no right angle. dJ 2. The rhombus , or lozenge, which is an ecLuilateral rhomboid. 3, The rectangle, which is an equian- gular parallelogram, but not equilateral. 4. The square, which is both equilat- eral and equiangular. A Diagonal of a figure is a line •\yhich joins the vertices of two angles not adjacent. EXPLANATION OF SIGNS. 26. The sign = is the sign of equality; thus, the ex- pression A = B, signifies that A is equal to B. 27. To signify that A is smaller than B, the expression A jB is used ; the smaller quantity being always at the vertex of the angle. 29. The sign + is called plus ; it indicates addition. 24 ELEMENTS OF SURVEYING. [BOOK I. SO. The sign — is called minus ; it indicates subtraction : Thus, A+B, represents the sum of the quantities A and B; A — B represents their difference, or what remains after B is taken from A ; and A — B+ 0, or A + C — B^ signifies that A and are to be added together, and that B is to be subtracted from their sum. 31. The sign X indicates multiplication : thus Ax B represents the product of A and B. The expression Ax {B-{- C— D) represents the product of J. by the quantity B+C—D. li A + D were to be multiplied by A — B-\- G, the product would be indicated thus; {A+D)x{A-B+Cl whatever is enclosed within the curved lines, being consid- ered as a single quantity. The same thing may also be indicated by a bar : thus, A + B+CxD, denotes that the sum of J., B and (7, is to be multiplied hj D. 82. A figure placed before a line, or quantity, serves as a multiplier to that line or quantity; thus, ^AB signi- fies that the line AB is taken three times ; ^A signifies the half of the angle A. 83. The square of the line AB is designated by AB~ ; its cube by AB . What is meant by the square and cube of a line is fully explained in Geometry. 34, The sign -y/ indicates a root to be extracted; thus, ■v/2 means the square-root of 2 ; -/ J. X B means the square- root of the product of A and B. SEC. II.] GEOMETRICAL CONSTRUCTIONS. 25 GEOMETRICAL CONSTRUCTIONS. 35. Before explaining the method of constructing geo- metrical problems, we shall describe some of the simpler instruments and their uses. DIVIDERS. 36. The dividers is the most simple and useful of the instruments used for drawing. It consists of two legs ha, he, which may be easily turned around a joint at h. One of the principal uses of this instrument is to lay off on a line, a distance equal to a given line. For example, to lay off on CD a distance equal to AB. For this purpose, place the forefin- ger on the joint of the dividers, and A\ B set one foot at A: then extend, with the thumb and other fingers, the ^' -^ — 2> other leg of the dividers, until its foot reaches the point B. Then raise the dividers, place one foot at (7, and mark with the other the distance GE : this will evidently be equal to AB. RULER AND TRIANGLE. 37. A Euler of convenient size, is about twenty inches in length, two inches wide, and a fifth of an inch in thick- 26 ELEMENTS OF SURVEYING. [BOOK I. ness. It should be made of a laard material, perfectly straight and smooth. The hypothenuse of the right-angled triangle, which is used in connection with it, should be about ten inches in length, and it is most convenient to have one of the sides considerably longer than the other. We can solve, with the ruler and triangle, the two following problems. I. To draw through a given point a line which shall be paral- lel to a given line. 38. Let be the given point, and AB the given line. Place the hypothenuse of the tri- o angle against the edge of the ruler, and then place the ruler and triangle , , on the paper, so that one of the sides of the triangle shall coincide exactly with AB: the triangle being below the line. Then placing the thumb and fingers of the left hand firmly on the ruler, slide the triangle with the other hand along the ruler until the side which coincided with AB reaches the point G. Leaving the thumb of the left hand on the ruler, extend the fingers upon the triangle and hold it firmly, and with the right hand, mark with a pen or pencil, a line through C: this line will be parallel to AB. IL To draw through a given point a line which shall he per- pendicular to a given line. 89. Let AB be the given line, and D the given point. Place the hypothenuse of the tri- angle against the edge of the ruler, as before. Then place the ruler and | triangle so that one of the sides of the triangle shall coincide exactly with the line AB. Then, slide the triangle along the ruler until the other side reaches the point I): draw through J) a right line, and it will be perpendicular to AB. SEC. II.] GEOMETRICAL CONSTRUCTIONS. 27 SCALE OF EQUAL PARTS. .1 .2 .n.U.B .6 .7 .8 .D7i 40. A scale of equal parts is formed by dividing a line of a given length into equal portions. If, for example, the line a6 of a given length, say one inch, be divided into any number of equal parts, as 10, the scale thus formed, is called a scale of ten parts to the inch. The line a&, which is divided, is called the unit of the scale. This unit is laid off several times on the left of the divided line, and the points marked 1, 2, 8, &c. The unit of scales of equal parts, is, in general, either an inch, or an exact part of an inch. If, for example, ah, the unit of the scale, were half an inch, the scale would be one of 10 parts to half an inch, or of 20 parts to the inch. If it were required to take from the scale a line equal to two inches and six -tenths, place one foot of the dividers at 2 on the left, and extend the other to .6, which marks the sixth of the small divisions: the dividers will then embrace the required distance. DIAGONAL SCALE OF EQUAL PARTS. M / / / / 1 / oa 1 / \ \ \ \ \ ] 08 \\ 1 /yi 1 1 1 1 07 \ \ \ \ \ \ M ' 06 MM'' '1 05 / W i ' ' ' or / 1 03 \ \ \ \ \ \ \ OZ \ \ I \\ \ \ 01 M / M , (i a.l .3.3.4.5.6.7. 41. This scale is thus constructed. Take ah for the unit of the scale, which may be one inch, -|, |- or f of an inch, in length. On ah describe the square ahcd. Divide the sides ah and dc each into ten equal parts. Draw af and the other nine parallels as in the figure. Produce ha to the left, and lay off the unit of the scale any convenient number of times, and mark the points 28 ELEMEN-TS OF SURVEYING. [BOOKI. 1, 2, 3, &c. Then, divide the line ad into ten equal parts, and through the points of division draw parallels to ah, as in the figure. Now, the small divisions of the line ah are each one- tenth (.1) of ah ; they are therefore .1 of ad, or .1 of ag or gh. If we consider the triangle adf, we see that the base df is one-tenth of ad, the unit of the scale. Since the distance from a to the first horizontal line above ah, is one-tenth of the distance ad, it follows that the distance measured on that line between ad and af is one-tenth of df: but since one-tenth of a tenth is a hundredth, it follows that this distance is one hundredth (.01) of the unit of the scale. A like dis- tance measured on the second line will be two hundredths (.02) of the unit of the scale ; on the third, .03 ; on the fourth, .04, &c. If it were required to take, in the dividers, the unit of the scale, and any number of tenths, place one foot of the dividers at 1, and extend the other to that figure between a and h which designates the tenths. If two or more units are required, the dividers must be placed on a point of division further to the left. When units, tenths, and hundredths, are required, place one foot of the dividers where the vertical line through the point which designates the units, intersects the line which designates the hundredths : then, extend the dividers to that line between ad and he which designates the tenths : the distance so determined will be the one required. For example, to take off the distance 2.34, we place one foot of the dividers at I, and extend the other to e: and to take off the distance 2.58, we place one foot of the dividers at p and extend the other to q. Eemark I. If a line is so long that the whole of it cannot be taken from the scale, it must be divided, and the parts of it taken fi-om the scale in succession. Eemark II. If a line be given upon the paper, its length can be found by taking it in the dividers and ap- plying it to the scale. SEC. II.] GEOMETRICAL CONSTRUCTIONS. 29 SCALE OF CHORDS. 42. If, "witli any radius, as AG^ we describe the quad- rant CZ), and then divide it into 90 equal parts, each part is called a degree. Through C, and each point of division, let a chord be drawn, and let the lengths of these chords be accurately laid off on a scale : such a scale is called a scale of chords. In the figure, the chords are drawn for every ten de- grees. The scale of chords being dnce constructed, the radius of the circle from which the chords were obtained, is known; for, the chord marked 60 is always equal to the radius of the circle. A scale of chords is generally laid down on the scales which belong to cases of mathematical instruments, and is marked cho. (l>.- To lay off, at a given point of a line, with the scale of chords, an angle equal to a given angle. 43. Let AB be the line, and A the given point. Take from the scale the chord of 60 degrees, and with this radius and the point ^ as a centre, describe the arc BC. Then take from the scale the chord of the given angle, say 30 de- "^ ^ grees, and with this line as a radius, and 5 as a centre, describe an arc cutting BG in G. Through A and G draw the hne AG, and BAG will be the required angle. 30 ELEMENTS OF SURVEYING. [BOOK I. SEMICIRCULAR PROTRACTOR. C A 44. This instrument is used to lay down, or protract angles. It may also be used to measure angles included between lines already drawn upon paper. It consists of a brass semicircle, ABO, divided to balf degrees. The degrees are numbered from to 180, both ways ; that is, from J. to ^ and from B to A. The di- visions, in the figure, are made only to degrees. There is a small notch at the middle of the diameter AB, which indicates the centre of the protractor. To lay off an a^igle with a Protractor. 45. Place the diameter AB on the line, so that the centre shall fall on the angular point. Then count the degrees contained in the given angle from A towards B, or from B towards J., and mark the extremity of the arc with a pin. Eemove the protractor, and draw a line through the point so marked and the angular point : this line will make with the given line the required angle. SECTORAL SCALE OF EQUAL PARTS. SEC. II.] GEOMETRICAL CONSTRUCTIONS. 31 46. The sector is an instrument generally made of ivory or brass. It consists of two arms, or sides, which, open by turning round a joint at their common extremity. There are several scales laid down on the sector : those, however, which are chiefly used in drawing lines and angles, are, the scale of chords already described, and the scale of equal parts now to be explained. On each arm of the sector, there is a diagonal line that passes through the point about which the arms turn : these diagonal lines are divided into equal parts. On the sectors which belong to the cases of English instruments, the diagonal lines are designated by the letter Jv, and numbered from the centre of the sector, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, to the two extremities. On the sectors which belong to cases of French instruments, they are de- signated, " Les parties egales," and numbered 10, 20, 30, 40, &c., to 200. On the English sectors there are 20 equal divisions between any two of the lines numbered 1, 2, 3, &c., so that there are 200 equal parts on the scale. The advantage of the sectoral scale of equal parts, is this — When it is proposed to draw a line upon paper, on such a scale that any number of parts of the line, 40 for example, shall be represented by one inch on the paper, or by any part of an inch, take the inch, or part of the inch, from the scale of inches on the sector : then, placing one foot of the dividers at 40 on one arm of the sector, open the sector until the other foot reaches to the corresponding number on the other arm : then lay the sector on the table without varying the angle. Now, if we regard the lines on the sector as the sides of a triangle, of which the line 40, measured across, is the base, it is plain, that if any other line be likewise meas- ured across the angle of the sector, the bases of the tri- angles, so formed, will be proportional to their sides. Therefore, if we extend the dividers from 50 to 50, this distance will represent a line of 50, to the given scale: and similarly for other lines. 32 ELEMENTS OF SURVEYING-. [BOOK I. Let it now be required to laj down a line of sixtj- seven feet, to a scale of twenty feet to tlie incli. Take one inch from tlie scale of inches: then place one foot of the dividers at the twentieth division, and open the sector until the dividers will just reach the twen- tieth division on the other arm : the sector is then set to the proper angle ; after which the required distance to be laid down on the paper is found by extending the divi- ders from the sixty-seventh division on one arm, to the sixty-seventh division on the other. gutter's scale. 47. This is a scale of two feet in length, on the faces of which a variety of scales is marked. The face on which the divisions of inches are made, contains, however, all the scales necessary for laying down lines and angles. These are, the scale of equal parts, the diagonal scale of equal parts, and the scale of chords, all of which have been described. SOLUTION OF PROBLEMS REQUIRING THE USE OF THE IN- STRUMENTS THAT HAVE BEEN DESCRIBED. I. At a given point in a given straight line, to erect a jperpen- dicular to the line. 48. Let A be the given point, and BC the given line. From A lay off any two distances, \L^ AB and AC, equal to each other. Then, from the points B and C, as centres, with a radius greater than BA, describe two arcs intersecting each B A (J other in D : draw AD, and it will be the perpendicular required. " j 11. From a given point without a straight line, to let fall a perpendicular on the line. 49. Let A be the given point, and BD the given line. SEC.IL] GEOMETRICAL CONSTRUCTIONS. 33 From the point J. as a centre, with a radius sufficiently great, describe an arc cutting the line BD in the two points B and D: then mark a point E^ equally dis- tant from the points B and i), and draAV AE : AE will be the perpendicular required. III. At a jpoint, in a given line, to make an angle equal to a given angle. 50. Let A be the given point, AE the given line, and IKL the given angle. From the vertex ^ as a centre, with any radius, describe the arc JX, terminating in the two sides of the angle. From the point J. as a centre, with a distance AE equal to KT, describe the arc ED; then take the chord LI, with which, from the point jE^ as a centre, describe an arc cutting the indefinite arc BE, in B; draw AB, and the angle EAB will be equal to the given angle K. IV. To divide a given angle, or a given arc^ into two equal parts. 51. Let G be the given angle, and AEB the arc which measures it. * From the points A and B as centres, describe with the same radius two arcs cutting each other in B: through D and the centre G draw GB : the angle AGE will be equal to the angle EGB, and the arc AE to the arc EB. V. Through a given point to draio a parallel to a given line, 52. Let A be the given point, and BG the given liiae. 34 ELEMENTS OF SURVEYUiTG. [BOOK I From J. as a centre, with a /'' e^ radius greater than the shortest distance from A to BG^ describe the indefinite arc ED : from the ^'' point jG' as a centre, with the same radius, describe the arc AF ; make ED = AF, and draw AD: then will AD be the parallel required. YI. Two angles of a triangle heing given, to find the third. 53. Draw the indefinite line DEF. At the point E, make the angle DEC equal to one of the given angles, and the angle GEH equal to the other : the re- maining angle HEF will be the third angle required. YII. To represent, on paper, a line of a given length, so that any number of its parts shall correspond to the unit of the 54. Suppose that the given line were 75 feet in length, and it were required to draw it on paper, on a scale of 25 feet to the inch. The length of the line 75 feet, being divided by 25, will give 3, the number of inches which will represent the line on paper. Therefore, draw the indefinite line AB, on which lay -i~£ off a distance A G equal to 3 inches : A G will represent the given line of 75 feet, drawn on the required scale. Ee^ark I. This problem explains the manner of repre- senting a line upon paper, so that a given number of its parts shall correspond to the unit of the scale, whether that unit be an inch or any part of an inch. When the length of the line to be laid down is given, and it has been determined how many parts of it are to SEC. II.] GEOMETRICAL CONSTRUCTIONS. 35 be represented on tlie paper by a distance equal to the unit of the scale, we find the length which is to be taken from the scale by the following RULE. Divide the length of the line hy the numher of parts which is to he represented hy the unit of the scale: the quotient will show the nuinher of units which is to he taken from ihe scale, EXAMPLES. 1. If a line of 640 feet is to be laid down on paper, on a scale of 40 feet to the inch ; what length must be taken from the scale ? 40)640(16 inches. 2. If a line of 357 feet is to be laid down on a scale of 68 feet to the unit of the scale, (which we will suppose half an inch), how many parts are to be taken ? i j 5.25 parts, or ( 2.625 inches. 3. A line of 384 feet is drawn on paper, on a scale of 45 feet to the inch ; what is its length on the paper ? Ans. 8.53 inches. Eemark II. When the length of a line on the paper is given, and it is required to find the true length of the line which it represents, take the line in the dividers and apply it to the scale, and note the number of units, and parts of a unit to which it is equal. Then multiply this number by the number of parts which the unit of the scale represents, and the product will be the length of the line. For example, suppose the length of a line drawn on the paper was found to be 3.55 inches, the scale being 40 feet to the inch : then, 3.55 X 40 = 142 feet, the length of the line. 36 ELEMENTS OF SURVEYING. "[BOOK I. VIII. Having given two sides and the included angle of a tri- angle, to describe the triangle. 55. Let the line ^=150 feet, and = 120 feet, be tlie given sides ; and J. = 80 degrees, the given angle : to de- scribe the triangle on a scale of 200 feet to the inch. Draw the indefinite line i)(r, and at the point D, make the angle ODH equal to 30 degrees : then lay off DG equal to 150, equal to three quarters of an inch, and DH equal to 120, equal to six tenths of an inch, and draw GH: DHG will be the required triangle. IX. The three sides of a triangle being given, to describe the triangle. 56. Let A, B and C, be the sides. Draw DE equal to the side A. From the point D as, 2, centre, with a radius equal to the second side B, describe an arc : from ^ as a cen- tre, with a radius equal to the third side (7, describe another arc inter- secting the former in F; draw DF and EF, and DFE will be the triangle required. X. Having given two sides of a triangle and an angle oppo- site one of them, to describe the triangle. 57. Let A and B be the given sides, and the given angle, which we will suppose is opposite the side B. Draw the indefinite line DF and make the angle FDH equal to the angle C: take DH= A, from the point i?j as a centre, with a radius equal to the other given side, B, describe an arc cutting DF in F; draw HF: then will DHF be the required tri- SEC. II.] GEOMETRICAL CONSTRUCTIONS. 37 If the angle G is acute, and tlie side B less tlian J., then the arc described from the centre E with the radius EF = B will cut the side DF in two points, F and 6^, lying on the same side of D: hence, there will be two triangles, DEF, and DEG, either of which will satisfy all the condi- tions of the problem. XL The adjacent sicks of a parallelogram^ with the angle which they contain, being given, to describe the parol- lelogram. 68. Let A and B be the given sides, and the given angle. Draw the line JDH, and jr/_ :^.jC; lay off BE equal to J. ; at / / ' the point B, make the angle ^Z /^ j£ EBF=0; take BF=B: de- A\ — i / scribe two arcs, the one from ^' ' F^ as a centre, with a radius FO = BE, the other from E, as a centre, with a radius EG = BF ; through the point G, where these arcs intersect each other, draw EG, EG ; BEGF will be the parallelogram required. XII. To find the centre of a given circle or arc. 59. Take three points, A, B, 0, any where in the cir- cumference, or in the arc: draw AB, BG; bisect these two lines by the perpendiculars, BE, EG: the point 0, where these perpendiculars meet, will be the centre sought. The same construction serves for making a circumference pass through three given points A, B, ' -^ (7, and also for describing a circumference, about a given triangle. 38 ELEMENTS OF SURVEYING. [BOOK I. PLANE TEIGONOMETRY. SECTION III. DEFINITIONS. — APPLICATION TO HEIGHTS AND DISTANCES. 1. In every plane triangle tliere are six parts : three sides and three angles. These parts are so related to each other, that when one side and any two other parts are given, the remaining ones can be obtained, either by geo- metrical construction or by trigonometrical computation. 2. Plane Trigonometry explains the methods of com- puting the unknown parts of a plane triangle, when a suf- ficient number of the six parts is given. 3. For the purpose of trigonometrical calculation, the circumference of the circle is supposed to be divided into 360 equal parts, called degrees ; each degree is supposed to be divided into 60 equal parts, called minutes; and each minute into 60 equal parts, called seconds. Degrees, minutes, and seconds, are designated respec- tively, by the characters ° ' ". For example, ten degrees, eighteen mimites^ and fourteen seconds^ would be written 10° 18' 14". 4. If two lines be drawn through the centre of the circle, at right angles to each other, they will divide the circumference into four equal parts, of 90° each. Every right angle then, as EOA, is measured by an arc of 90° ; every acute angle, as BOA^ by an arc less than 90° ; and every obtuse angle, as FOA^ by an arc greater than 90°. 5. The complement of an arc is what remains after subtracting the arc from 90°. Thus, the arc UB is the complement of AB. The sum of an arc and its complement is equal to 90°. 6. The supplement of an arc is what remains after subtracting the arc from 180°. SEC. I.] ' PLANE TRIGONOMETRY. 39 supplement of the arc AEF. The sum of an arc and its supplement is equal to 180°. 7. The sine of an arc is the perpendicular let fall from one extremity of the arc on the diameter which passes through the other extremity. Thus, BD is the sine of the arc AB. 8. The cosine of an arc is the part of the diameter in- tercepted between the foot of the sine and centre. Thus, OD is the cosine of the arc AB. 9. The tangent of an arc is the line which touches it at one extremity, and is limited by a line drawn through the other extremity and the centre of the circle. Thus, AG is the tangent of the arc AB. 10. The secant of an arc is the line drawn from the centre of the circle through one extremity of the arc, and limited by the tangent passing through the other extremi- ty. Thus, 00 is, the secant of the arc AB. 11. The four lines, BD, OD, AC, 00, depend for their values on the arc AB and the radius OA ; they are thus designated : sin AB for BD cos AB for OD tan AB for AQ sec AB for OC 12. If ABE be equal to a quadrant, or 90°, then EB will be the complement of AB. Let the lines ET and IB be drawn perpendicular to OE. Then, ET, the tangent of EB, is called the cotangent of AB ; IB, the sine of EB, is equal to the cosine of AB ; OT, the secant of EB, is called the cosecant of AB. In general, if A is any arc or angle, we have, cos J. = sin (90°-^) cot A = tan (90° - A) cosec A = sec (90° — A) 40 ELEMEN-TS OF SURVEYIN-G. [BOOK 13. If we take an arc, ABEF, greater than 90°, its sine will be FH ; OH will be its cosine ; A Q its tangent, and OQ its secant. But FH is tlie sine of tlie arc OF, wbicli is tbe supplement of AF, and OH is its cosine ; bence, the sine of an arc is equal to the sine of its supplement ; and the cosine of an arc is equal to the cosine of its supplement* Furtbermore, AQ is tbe tangent of tbe arc AF, and 0^ is its secant: GL is tbe tangent, and OL tbe secant of tbe supplemental arc GF. But since ^^ is equal to GL, and OQ to OL, it follows tbat, the tangent of an arc is equal to the tangent of its supplement; and the secant of an arc is equal to the secant of its supplement.* TABLE OF NATUEAL SINES. 14. Let US suppose, tbat in a circle of a given radius, tbe lengths of the sine, cosine, tangent, and cotangent, have been calculated for every minute or second of the quad- rant, and arranged in a table; such a table is called a table of sines and tangents. If tbe radius of tbe circle is 1, tbe table is called a table of natural sines. A table of natural sines, therefore, shows the values of the sines, co- sines, tangents, and cotangents of all the arcs of a quad- rant, which is divided to minutes or seconds. If the sines, cosines, tangents, and secants are known for arcs less than 90°, those for arcs which are greater can be found from them. For if an arc is less than 90°, its supplement will be greater than 90°, and the numerical values of these lines are the same for an arc and its sup- plement. Thus, if we know tbe sine of 20°, we also know the sine of its supplement 160° ; for tbe two are equal to each other. The Table of Natural Sines, beginning at page 63, of the tables shows the values of the sines and cosines only. * These relations are between the rmmerical values of the trigonometrical lines ; the algebraic signs, which they have in the different quadrants, are not considered. SEC. Ill] PLANE TRIGONOMETRY. 41 TABLE OF LOGARITHMIC SINES. 15. In this table are arranged the logarithms of the numerical values of the sines, cosines, tangents, and co- tangents of all the arcs of a quadrant, calculated to a ra- dius of 10,000,000,000. The logarithm of this radius is 10. In the first and last horizontal lines of each page, are writ- ten the degrees whose sines, cosines, &c., are expressed on the page. The vertical columns on the left and right, are columns of minutes. CASE I. To find, in the table, the logarithmic sine, cosine, tangent, or cotangent of any given arc or angle. 16. If the angle is less than 45°, look for the degrees in the first horizontal line of the different pages : when the degrees are found, descend along the column of minutes, on the left of the page, till you reach the number showing the minutes : then pass along a horizontal line till you come into the column designated, sine, cosine, tangent, or cotangent, as the case may be : the number so indicated is the logarithm sought. Thus, on page 87, for 19° 55', we find, sine 19° 55' ... . 9.532312 cos 19° 55' ... . 9.973215 tan 19° 55' .... 9.559097 cot 19° 55' ... . 10.440903 17. If the angle is greater than 45°, search for the de- grees along the bottom line of the different pages : when the number is found, ascend along the column of minutes on the right hand side of the page, till you reach the number express- ing the minutes: then pass along a horizontal line into the column designated tang, cot, sine, or cosine, as the case may be : the number so pointed out is the logarithm required. 18. The column designated sine, at the top of the page, is designated by cosine at the bottom ; the one designated tang, by cotang, and the one designated cotang, by tang. The angle found by taking the degrees at the top of the page, and the minutes from the left hand vertical column, is the complement of the angle found by taking the degrees 42 ELEMENTS OF SURVEYING. [BOOK I. at tlie bottom of tlie page, and tlie minutes from the riglit hand column on the same horizontal line with the first. Therefore, sine, at the top of the page, should correspond with cosine, at the bottom ; cosine with sine, tang with cotang, and cotang with tang, as in the tables (Art. 12). If the angle is greater than 90°, we have only to sub- tract it from 180°, and take the sine, cosine, tangent, or cotangent of the remainder. The column of the table next to the column of sines, and on the right of it, is designated by the letter D. This column is calculated in the following manner. Opening the table at any page, as 42, the sine of 24° is found to be 9.609313 ; that of 24° 01', 9.609597 : their difference is 284 ; this being divided by 60, the number of seconds in a minute, gives 4.73, which is entered in the column D. Now, supposing the increase of the logarithmic sine to be proportional to the increase of the arc, and it is nearly so for 60", it follows, that 4.73 is the increase of the sine for 1". Similarly, if the arc were 24° 20', the increase of the sine for 1", would be 4.65. The same remarks are applicable in respect of the column D, after the column cosine, and of the column D, between the tangents and cotangents. The column i), be- tween the columns tangents and cotangents, answers to both of these columns. Now, if it were required to find the logarithmic sine of an arc expressed in degrees, minutes, and seconds, we have only to find the degrees and minutes as before ; then, multiply the corresponding tabular difference by the sec- onds, and add the product to the number first found, for the sine of the given arc. Thus, if we wish the sine of 40° 26' 28". The sine 40° 26' ... . 9.811952 Tabular difference 2.47 , Number of seconds 28 . Product, 69.16 to be added 69.16 Gives for the sine of 40° 26' 28". 9.812021. SEC. III.] PLANE TRIGONOMETRY. 43 The decimal figures at the right are generally omitted in the last result ; but when they exceed five-tenths, the figure on the left of the decimal point is increased by 1 ; the logarithm obtained is then exact, to within less than one unit of its right hand place. The tangent of an arc, in which there are seconds, is found in a manner entirely similar. In regard to the co- sine and cotangent, it must be remembered, that they in- crease while the arcs decrease, and decrease as the arcs are increased ; consequently, the proportional numbers found for' the seconds, must be subtracted, not added. EXAMPLES. 1. To find the cosine of 3° 40' 40". The cosine of 3° 40' . . . 9.999110 Tabular difference .13 . Number of seconds 40 Product, 5.20 to be subtracted 5.20 Gives for the cosine of 3° 40' 40" 9.999105. 2. Find the tangent of 37° 28' 31". Ans. 9.884592. 3. Find the cotangent of 87° 57' 59". Ans. 8.550356. CASE II. To find the degrees, minutes^ and seconds answering to any given logarithmic sine, cosine, tangent, or cotangent. 19. Search in the table, in the proper column, and if the number is found, the degrees will be shown either at the top or bottom of the page, and the minutes in the side column either at the left or right. But, if the number cannot be found in the table, take from the table the degrees and minutes answering to the nearest less logarithm, the logarithm itself, and also the corresponding tabular difference. Subtract the logarithm taken from the table from the given logarithm, annex two 44 ELEMEISTTS OF SURVEYI]!^G, [BOOK I. ciphers to tlie remainder, and tlien divide tlie remainder by tlie tabular difference : the quotient will be seconds, and is to be connected with the degrees and minutes be- fore found : to be added for the sine and tangent, and subtracted for the cosine and cotangent, EXAMPLES. 1. Find the arc answering to the sine 9.880054 Sine 49° 20', next less in the table 9.879963 Tabular difference, 1.81)91.00(60". Hence, the arc 49° 20' 50" corresponds to the given sine 9.880054. 2. Find the arc whose cotangent is 10.008688 cot 44° 26', next less in the table 10.008591 Tabular difference, 4.21)97.00(23". Hence, 44° 26' - 23" = 44° 25' 37" is the arc answering to the given cotangent 10.008688. 3. Find the arc answering to tangent 9.979110. Am. 43° 37' 21". 4. Find the arc answering to cosine 9.944599. Ans. 28° 19' 45". 20. We shall now demonstrate the principal theorems of Plane Trigonometry. THEOEEM I. The sides of a plane triangle are proportional to the sines of their opposite angles. 21. Let ABC be a triangle ; then will OB : OA :: sin A : sin B. For, with J. as a centre, and AD equal to the less side BO, as a ra- dius, describe the arc BI: and with ^ as a centre and the equal radius -^ /?/// BO, describe the arc OL, and draw BE and OF perpen- dicular to AB: now BE is the sine of the angle A, and SEC. Ill] PLANE TRIGONOMETRY. 45 OF is the sine of B^ to the same radius AB or BC. But by similar triangles, AB '. BE :\ AG '. CF. But AB being equal to BG^ we have BG : sin J. : : AG : sin J5, or BG : AG :: sin A : sin B. By comparing the sides AB, AG, in a similar manner, we should find, AB : AG : : sin G : sin B. THEOEEM II. In any triangle, the sum of the two sides containing either angle, is to their difference, as the tangent of half the sum of the two other angles, to the tangent of half their difference. 22. Let A GB be a triangle : then will AB+AG : AB-AG : : tan ^{G+B) : tan \{G-B). With JL as a centre, and a A' radius AG, the less of the two given sides, let the semicircumfe- rence IFGE be described, meeting AB in I, and BA produced, in E. Then, 5^ will be the sum of the C"-- --'FGH sides, and BI their difference. Draw GI and AF. Since GAE is an outward angle of the triangle AGB, it is equal to the sum of the inward angles G and B (Bk. I., Prop. XXY., Cor 6). But the angle GIE being at the circumference, is half the angle GAE at the centre (Bk. III., Prop. Xyill.) ; that is, half the sum of the angles G and B, or equal to \{G-\-B). The angle AFG=AGB, is also equal to ABG+BAF; therefore, BAF= AGB- ABG. But, IGF=l{BAF) = ^^{AGB-ABG), or ^{G-B). With / and G as centres, and the common radius IG, let the arcs GB and IG be described, and draw the lines GE and IE perpendicular to IG. The perpendicular GE will pass through E, the extremity of the diameter lE^ 46 ELEMENTS OF SUR VE YI^-G. [BOOK I. since the right angle IGE must be inscribed in a semicircle. But GE is the tangent of CIE = 1{G+B)', and IH is the tan- gent of IGB^\{G-B\ to the common radius CI. But since the lines GE and IH are parallel, the tri- angles BHI and BGE are similar, and give the proportion, BE : BI :: GE : IH, or by placing for BE and BI, GE and IH, their values, we have AB + AG : AB-AG :: tan }{G+B) : tan i((7-^). GD-DB. THEOEEM III. In any plane triangle, if a line is draion from the vertical angle perpendicular to the base, dividing it into two segments : then., the whole base, or sum of the segments, is to the sum of the two other sides, as the difference of those sides to the differ- ence of the segments. 23. Let BA C be a triangle, and AD perpendicular to the base ; then will BG : GA + AB :: GA-AB For, AB" = BD~ + AD^' (Bk. IV., Prop. XL); and A0'' = D0' + AD'' by subtraction, AG~ — AB" = gd'-bb^. But since the difference of -?> J> C the squares of two lines is equivalent to the rectangle con- tained by their sum and difference (Bk. lY., Prop. X.), we have, AG^ - AB" = {A G+ AB) . {A G- AB) and GD^-DB~^{GD^DB). {GD-DB) therefore, {GD + DB).{GD-DB) = {AG +AB). {AG -AB) hence, GD + DB : AG+AB :: AG-AB : GD-DB. SEC. III.] PLANE TRIGONOMETRY. 47 THEOREM IV. In any right-angled plane triangle^ radius is to the tangent of either of tlie acute angles, as the side adjacent to the side opposite. 24. Let GAB be tlie proposed triangle, and denote the radius by R : then will ^ R : ioxi G :: AC : AB. ^^^ For, witb any radius as CD de- scribe the arc DH, and draw the tan- -^ gent DG. From, the similar triangles GDG and GAB, we have, OD : DG :: GA : AB; hence, R : tsin G :: GA : AB. By describing an arc with ^ as a centre, we could show in the same manner that, R : tan 5 : : AB : AC. THEOREM V. In every right-angled plane triangle, radiics is to the cosine of either of the acute angles, as the hypothenuse to the side adjacent. 25. Let ABC be a triangle, right-angled at B: then will, R : cos J. : : AG : AB. c For, from the point J. as a centre, with any radius as AD, describe the arc DF, which will measure the angle '^^ ~EF^ A, and draw DE perpendicular to AB: then will AE be the cosine of A. The triangles ADE and AGB, being similar, we have, AD : AE :: AG : AB: that is, R : cos J. : : AG : AB. Remark. The relations between the sides and angles of plane triangles, demonstrated in these five theorems, are 48 ELEMENTS OF SURVEYING. [BOOK I sufficient to solve all the cases of Plane Trigonometry. Of the six parts which make up a plane triangle, three must be given, and at least one of these a side, before the others can be determined. If the three angles only are given, it is plain, that an indefinite number of similar triangles may be constructed, the angles of which shall be respectively equal to the angles that are given, and therefore, the sides could not be determined. Assuming, with this restriction, any three parts of a triangle as given, one of the four following cases will al- ways be presented, I. When two angles and a side are given. II. "When two sides and an opposite angle are given. III. When two sides and the included angle are given. ly. When the three sides are given. CASE I. When two angles and a side are given. 26. Add the given angles together, and subtract their sum from 180 degrees. The remaining parts of the tri- angle can then be found by Theorem I. EXAMPLES. 1. In a plane triangle, ABG, there are given the angle J. = 58° 07', the angle B=2T 87', and the side J.5= 408 yards. Eequired the oth- er parts. GEOMETKICALLY. 27. Draw an indefinite straight line, AB, and from the scale of equal parts lay off AB equal to 408. Then, at J., lay off an angle equal to 58° 07', and at B an angle equal to 22° 87', and draw the lines AG and BG : then will ABG be the triangle required. The angle G may be measured either with the protractor or the scale of chords (Sec. II., Arts. 42 and 44), and will be SEC. III.] PLANE TRIGONOMETRY. 49 found equal to 99° 16'. The sides AG and BO may be measured by referring tbem to the scale of equal parts (Sec. II., Art. 40). We shall find ^ C= 158.9 and £C-= 351 yards. TRIGOKOMETRICALLY BY LOGARITHMS. To the angle . . . A = 5S° 07' Add the angle . . J5=22°87' Their sum, = 80° 44' taken from . . . 180° 00' leaves . . . . 99° 16', of which, as it ex- ceeds 90°, we use the supplement 80° 44'. To find the side BO. As sin 99° 16' ar. comp. 0.005705 : sin ^ 58° 07' 9.928972 : : AB 408 2.610660 : BO 351.024 (after rejecting 10) 2.545337. Eemark. The logarithm of the fourth term of a pro- portion is obtained by adding the logarithm of the second term to that of the third, and subtracting from their sum the logarithm of the first term. But to subtract the first term is the same as to add its arithmetical complement and reject 10 from the sum (Sec. I., Art. 13) : hence, the arith- metical complement of the first term added to the loga- rithms of the second and third terms, minus ten, will give the logarithm of the fourth term. To find the side A 0. As sin C 99° 16' ar. comp. 0.005705 sin B 22° 37' 9.584968 AB 408 2.610660 AO 158.976 2.201333 2. In a triangle ABO^ there are given A = 38° 25', ^ = 57° 42', and AB = 'iOO: required the remaining parts. Ans. C=83°53', ^(7=249.974, ^C= 340.04. 4 50 ELEMENTS OF SURVEYING. [BOOK I. CASE II. When two sides and an opposite 28. In a plane triangle, ABC, there are given AC= 216, (75= 117, the angle A = 22° 37', to find the other parts. are given. GEOMETRICALLY. 29. Draw an indefinite right line ABB' : from any point, as A, draw AC, making BAC= 22° 37', and make AC =216. With C as a centre, and a radius equal to 117, the other given side, describe the arc B'B; draw B'C and BC: then will either of the triangles ABC or AB'C, an- swer all the conditions of the question. TRIGONOMETRICALLY. To find the angle B. As BC 117 ar. comp. 7.931814 AC 216 2.334454 sin ^ 22° 37' 9.584968 sin B' 45° 13' 55", or ABC 134° 46' 05" 9.851236. The ambiguity in this, and similar examples, arises in consequence of the first proportion being true for either of the angles ABC, or AB'C, which are supplements of each other, and therefore, have the same sine (Art. 13). As long as the two triangles exist, the ambiguity will con- tinue. But if the side CB, opposite the given angle, is greater than AC, the arc BB' will cut the line ABB', on the same side of the point A, in but one point, and then there will be only one triangle answering the conditions. If the side CB is equal to the perpendicular Cd, the arc BB' will be tangent to ABB', and in this case also there will be but one triangle. When CB is less than the perpendicular Cd, the arc BB' will not intersect the base ABB', and in that case, no triangle can be formed, or it will be impossible to fulfil the conditions of the problem. SEC. Ill] Pl^ANE TRIGONOMETRY. 51 2, Given two sides of a triangle 50 and 40 respectively, and the angle opposite the latter equal to 32° : required the remaining parts of the triangle. Am. If the angle opposite the side 50 is acute, it is equal to 41° 28' 59" ; the third angle is then equal to 106° 81' 01", and the third side to 72.368. If the angle opposite the side 50 is obtuse, it is equal to 138° 31' 01", the third angle to 9° 28' 69", and the remaining side to 12.436. CASE III. When the two sides and their included angle are given. 30. Let ABC be a triangle ; AB, BG, the given sides, and B the given angle. Since B is known, we can find the sum of the two other angles : for A+G^1%0°-B, and, ^{A + C) = l{l^Q°-B). We next find half the difference of the angles A and G by Theorem II., viz., BG+BA : BG-BA :: tan ^(A+G) : tani(^-C), in which we consider BG greater than BA, and therefore A is greater than (7; since the greater angle must be op- posite the greater side. Having found half the difference of A and G, by add- ing it to the half sum, |( A + G\ we obtain the greater angle, and by subtracting it from half the sum, we obtain the less. That is, ^{A -f C) + ^{A -C) = A, and -l{A+G)-i{A-G)=G Having found the angles A and G, the third side AG may be found by the proportion, sin Jl : sin jB : : BG : AG. 52 ELEMENTS OF SURVEYING. [BOOK L EXAMPLES. 1. In the triangle ABC, let BG=54,0, AB = ^50, and the included angle B = 80° : required the remaining parts. GEOMETRICALLY. 81. Draw an indefinite right line BO, and from any point, as B, lay off a distance BG=b4S). At B make the angle CBA = 80° : draw BA, and make the distance BA = 4:50; draw AC; then will ABC he the required tri- angle. TRIGONOMETRICALLY. B0+ BA = 540 + 450 = 990 ; and BC-BA = 540 - 450 = 90. A+C= 180° -B= 180° - 80° = 100°, and therefore, i(^+(7)-i(100°) = 50°. To find ^{A - C). As BC+BA 990 ar. comp. 7.004365 : BC-BA 90 1.954243 t: tani(^+C) 50° 10.076187 : tan ^{A - C) 6° 11' 9.034795. Hence, 50° + 6° 11' = 56° 11' = ^!; and 50° -6° 11' = 43° 49' = a To find the third side A C. As sin C 43° 49' ar comp. 0.159672 sin ^ 80° 9.998351 AB 450 2.653213 AC 640.082 . 2.806236. 2. Given two sides of a plane triangle, 1686 and 960, and their included angle 128° 04' : required the other parts. Ans. Angles, 33° 34' 39" ; 18° 21' 21" ; side 2400. CASE IV. 82. Having given the three sides of a plane triangle, to find the angles. SEC. Ill] PLANE TRIGONOMETRY. 53 Let fell a perpendicular from the angle opposite tlie greater side, dividing the given triangle into two right- angled triangles : then find the difference of the segments of the base by Theorem III. Half this difference being added to half the base, gives the greater segment ; and, being subtracted from half the base, gives the less segment Then, since the greater segment belongs to the right-angled triangle having the greater hypothenuse, we have two sides and the right angle of each of two right-angled tri- angles, to find the acute angles. EXAMPLES. 1. The sides of a plane triangle being given ; viz., BG= 40, AG= 34, and AB = 25 : required the angles. GEOMETRICALLY. 33. With the three given lines as sides construct a tri- angle as in Prob. IX. Then measure the angles of the triangle either with the protractor or scale of chords. As BG That is, Then, And, TRIGONOMETRICALLY. AG-\-AB :: AG-AB 40 : 59 40 + 13.275 2 4Q- 13.275 o 59x9 = 26.6375= GD, = 13.3625 = BB. GB-BB, = 13.275. In the triangle BAG, to find the angle BAG. As AG 34 ar. comp. 8.468521 BG 26.6375 1.425493 sin J9 90° 10.000000 sin BAG 5r«84'40" 9.894014. 54 ELEMENTS OF SURVEYING. [BOOK I. In the triangle BAD, to find the angle BAD. AB 25 ar. comp. 8.602060 BD 13.3625 1.125887 sin Z> 90° 10.000000 sin BAD 32° 18' 35" .... 9.727947. Hence, 90° - DAG-^ 90° - 51° 34' 40" = 38° 25' 20" = C, and, 90°-5.4Z>=90°-32°18'35" = 57°41'25" = ^, and, BAD + DAG= 51° 34' 40" + 32° 18' 35" = 83° 53' 15" = A. 2. In a triangle, of wiiicli the sides are 4, 5, and 6, what are the angles ? Ans. 41° 24' 35"; 55° 46' 16"; and 82° 49' 09". SOLUTION OF EIGHT-ANGLED TEIANGLES. 34. The unknown parts of a right-angled triangle may- be found by either of the four last cases ; or, if two of the sides are given, by means of the property that the square of the hypothenuse is equivalent to the sum of the squares of the two other sides. Or the parts may be found by Theorems IV. and V. EXAMPLES. 1. In a right-angled triangle BAG, there are given the hypothe- nuse ^(7=250, and the base AG= 240: required the other parts. As BG AG sin A sin B To find the angle B. 250 ar. comp. 7.602060 240 2.380211 90° . . , 10.000000 73° 44' 23" 9.982271. But C= 90° - ^ = 90° - 73° 44'^3" = 16° 15' 37" : S ^C. Ill] PLANE TRIGONOMETRY. 65 Or C may he found from the proportion. As CB 350 ar. comp. 7.602060 AC 240 2.380211 R 10.000000 cos G 16° 15' 37" 9,982271. To find side AB hy Theorem IV. As E ar. comp. 0.000000 : tan G 16° 15' 37" 9.464889 : : AG 240 2.380211 AB 70.0003 1.845100. 2. In a riglit-angled triangle BAG, there are given AG =384:, and ^=53° 08': required the remaining parts. Ans. AB= 287.96; BG = 4:79.979 ; (7= 36° 52'. . APPLICATION TO HEIGHTS AND DISTANCES. L To determine the horizontal distance to a point which is in- accessible hy reason of an intervening river.* 35. Let G be the point. Measure along the bank of the river a hori- zontal base line AB, and select the -^^ stations A and B, in such a man- ner that each can be seen from the other, and the point G from both of them. Then measure the hori- . zontal angles GAB and GBA, with an instrument adapted to that purpose. Let us suppose that we have found AB = 600 yards, CA^ = 57°35', and GBA = 64:° 5V. The angle G= 180° -{A + B) = 57° 34'. To find the distance BG. As sin G 57° 34' ar. comp. 0.073649 : sin J. 57° 35' 9.926431 :i AB 600 2.778151 : BG 600.11 yards 2.778231. * Read, definitions, from 3 to 14. roaffes 64- and fiR. 56 ELEMENTS OF SURVEYING. [BOOK L To find the distance A G. As sin 57° 34' ar. comp. 0.078649 : sin 5 64° 51' 9.956744 :: AB 600 2.778151 : ■ AC 643.94 yards 2.808544. II. To determine the altitude of an inaccessible object above a given horizontal plane. FIRST METHOD. 36. Suppose D to be tlie inac- d cessible object, and BO the bori- ^^"'"'''"^S^. zontal plane from which the alti- „ =--r:.C^^ =:=-^/f^J^r tude is to be estimated : then, if \/' / /' \ ir, we suppose DG io be a vertical \ /y'>''' line, it will represent the required \ "<;'''' ' distance. ^ Measure any horizontal base line, as BA ; and at the extremities B and J., measure the horizontal angles GBA and GAB. Measure also the angle of elevation DBG. Then in the triangle GBA there will be known, two angles and the side AB\ the side BO can therefore be determined. Having found BO^ we shall have, in the right-angled triangle DBG^ the base BO and the angle at the base, to find the perpendicular DG, which measures the altitude of the point D above the horizontal plane BO. Let us suppose that we have found BA = 780 yards, the horizontal angle GBA = 41° 24'; the horizontal angle GAB =96° 28', and the angle of eleva- tion DBO= 10°43'. In the triangle BOA, to find the horizontal distance BO. The angle BOA = 180° - (41° 24' + 96° 28') = 42° 08' = 0. As sin 42° 08' ar. comp. 0.173369 sin J. 96° 28' . 9.997228 AB 780 2.892095 BO 1155.29 3.062692. SEC. Ill] PLANE TRIGONOMETRY. 57 In the right-angled triangle DBG, to find DC. As B ar. comp. 0.000000 ta.n DBG 10° 43' 9.277043 BG 1155.29 3.062692 DC 218.64 2.339735. Eemark I. It might, at first, appear, that the solution which we have given, requires that the points B and A should be in the same horizontal plane ; but it is entirely independent of such a supposition. For, the horizontal distance, which is represented by BA, is the same, whether the station A is on the same level with B, above it, or below it. The horizontal angles GAB and GBA are also the same, so long as the point G is in the vertical line DG. Therefore, if the horizontal line through A should cut the vertical line DG, at any point, as U, above or below C, AB would still be the hori- zontal distance between B and A, and AU, which is equal to A G, would be the horizontal distance between A and G. If at A, we measure the angle of elevation of the point D, we shall know in the right-angled triangle DAB, the base AB, and the angle at the base; from which the per- pendicular DB can be determined. 37. Let us suppose that we had measured the angle of elevation DAB, and found it equal to 20° 15'. First : In the triangle BA C, to find AG or its equal AB. As sin G 42° 08' ar. comp. 0.173369 sin ^ 41° 24' 9.820406 AB 780 2.892095 AG 768.9 2.885870. In the right-angled triangle DAB, to find DB. 3 B ar. comp. 0.000000 tan J. 20° 15' 9.566932 AB 768.9 2.885870 DB 283.66 . 2.452802. 68 ELEMENTS OF SURVEYING. [BOOK I. Now, since BO is less tlian B^, it follows that the station B is above the station A. That is, BB- BC= 283.66 - 218.64 = 65.02 = BC, which expresses the vertical dis- tance that the station B is above the station A. Eemark II. It should be remembered, that the vertical distance which is obtained by the calculation, is estimated from a horizontal line passing through the eye at the time of observation. Hence, the height of the instrument is to be added, in order to obtain the true result. SECOND METHOD. 88. When the nature of the ground will admit of it, measure a base line AB in the direction of the object B. Then measure with the instrument the angles of elevation at A and B. Then, since the out- ward angle BBC is equal to the ^um of the angles A and ABB, it follows that the an- j?!^^^^^^^s^^ gle ABB is equal to the difference of the angles of eleva- tion at A and B. Hence, we can find all the parts of the triangle ABB. Having found BB, and knowing the angle BBC, we can find the altitude BC. This method supposes that the stations A and B are on the same horizontal plane ; and therefore it can only be used when the line AB is nearly horizontal. Let us suppose that we have measured the base line, and the two angles of elevation, and (AB =975 yards, found J ^ =15° 86', [BBC = 27° 29'; required the altitude BC. SEC. Ill] PLANE TRIGONOMETRY. 59 First : ADB= DBC - ^ = 27° 29' - 15° 36' - 11° 53'. In the triangle ADB, to find BD. As sin J) : sin A :: AB 11° 53' ar. comp. 15° 36' 975 1273.3 0.686302 9.429623 2.989005 DB ■ 3.104930. the triangle DBG, to find DG. ar. comp. 27° 29' 1273 3 In As R : sin B DB 0.000000 9.664163 3.104930 687.61 : DG 2.769093. III. To determine the perpendicular distance of an object helow a given horizontal plane. 39. Suppose G to be directly over tlie given object, and A the point through, which the horizon- tal plane is supposed to pass. Measure a horizontal base line AB, and at the stations A and B conceive the two horizontal lines AG, BG, to be drawn. The oblique lines from A and B to the object are the hy- pothenuses of two right-angled triangles, of which AG, BG, are the bases. The perpendiculars of these triangles are the distances from the horizontal lines A G, BG, to the object. If we turn the triangles about their bases AG, BG, until they become horizontal, the object, in the first case, will fall at G', and in the second at G". Measure the horizontal angles GAB, GBA, and also the angles of depression G'AG, G"BG. 60 ELEMENTS OF SURVEYING. Let US suppose tliat we liave " AB =672 yards BAG =72° 29' found i ABG = 89° 20' C'AO = 27° 49' ^ C"BC= 19° 10'. First: in tlie triangle ABC, ihe^ horizontal angle ACB= 180" 49' = 68° 11'. [BOOK I. (^+5)=i8o°-iir To find the horizontal distance A 0. As sin 68° 11' ar. comp. 0.032275 sin ^ 39° 20' 9.801973 AB 672 2.827369 AC 458.79 ........ 2.661617. To find the horizontal distance BC. As sin G %8° 11' ar. comp. 0.032275 sin ^ 72° 29' 9.979380 AB 672 2.827369 BG 690.28 2.839024. In the triangle GA G\ to find GG'. As R ar. comp. 0.000000 tan C'^C 27° 49' 9.722315 AG 458.79 2.661617 GC' 242.06 2.383932. In the triangle GBG'\ to find GG". As R ar. comp. 0.000000 tan G"BG 19° 10' 9.541061 BG 690.28 2.839024 GG" 239.93 2.380085. Hence also, GG' - GG" = 242.06 - 239.93 = 2.13 yards, wliicli is the height of the station A above station B. SEC. Ill] PLANE TRIGONOMETRY. 61 PROBLEMS. 1. "Wanting to know tlie distance between two inacces- sible objects, wbicli lie in a direct level line from the bot- tom of a tower of 120 feet in height, the angles of depres- sion are measured from the top of the tower, and are found to be, of the nearer 57°, of the more remote 25° 30' : re- quired the distance between the objects. A71S. 173.656 feet. 2. In order to find the distance between two trees, A and B, which could not be directly measured be- cause of a pool which occupied the intermediate space, the distances of a third point from each of them were measured, and also the included angle ACB: it was found that, CB =672 yards, GA =588 yards, ^CS = 55°40'; required the distance AB. Ans. 592.967 yards. 3. Being on a horizontal plane, and wanting to ascer- tain the height of a tower, standing on the top of an in- accessible hill, there were measured, the angle of elevation of the top of the hill 40°, and of the top of the tower 51° ; then measuring in a direct line 180 feet farther from the hill, the angle of elevation of the top of the tower was 33° 45' ; required the height of the tower. Ans. 83.998. 4. Wanting to know the hori- zontal distance between two inac- cessible objects B and W, the fol- lowing measurements were made. ^^^^^^^g AB =536 yards BAW=4:0°16' WAB= 57° 4:0' ABB =42° 22' BBW= 71° 07'] required the distance BW. Ans. 939.527 yards. j62 ELEMENTS OF SURVEYI^-G. [BOOK I 5. Wanting to know the horizontal distance between two inacessible objects A and B, and not finding any station from which both of them could be seen, two points C and Z>, were chosen at a distance from each other, equal to 200 yards ; from the former of these points A could be seen, and from the latter B, and at each of the points C and I) a staff was set up. From a distance CF was measured, not in the direction BG, equal to 200 yards, and from B a distance BB equal to 200 yards, and the following angles taken, r AFC = 83° 00', BBE = 54° 30', viz. ]aCB-= 53° 30', BBC ^ 156° 25', [ACF = 54° 31', BEB = 88° 30'. Ans. AB=S4:5A67 yards. 6. From a station P there can be seen three objects. A, B and (7, whose distances from each other are known : viz., AB--= 800, AC= 600, and BO = 400 yards. Now, there are measured the horizontal an- gles. APC=?>%° 45' and BPC = 22° 30': it is required to find the three distances PA, PC, and PB. P ~ r PA = 710.193 yards. Ans. ipC = 1042.522 [p^ = 934.291. 7. This problem is much used in maritime survey- ing, for the purpose of locating buoys and sounding boats. The trigonometrical solution is somewhat tedious, but it may be solved geometrically by the following easy con- struction. SEC. III.] PLANE TRIGONOMETRY. 63 Let A, B, and G be the three fixed points on shore, and P the position of the boat from which the angles APO= 33° 45', GPB= 22° 30', and APB=6Q° 15', have been measured. Subtract twice APC=Q1° 30' from 180°, and lay off at A and C two angles, GAO^ A GO^ each equal to half the remainder =56° 15'. With the point 0, thus determined, as a centre, and OA or OC as a radius, describe the cir- cumference of a circle : then, any angle inscribed in the segment APG^ will be equal to 33° 45'. Subtract, in like manner, twice GPB=4:5°, from 180°, and lay off half the remainder = 67° 30', at B and G, de- termining the centre ^ of a second circle, upon the cir- cumference of which the point P will be found. The required point P will be at the intersection of these two circumferences. If the point P fall on the circumference described through the three points A, B, and (7, the two auxiliary circles will coincide, and the problem will be in- determinate. BOOK II. PLANE SUEYEYING. SECTION I. DEFINITIONS. — MEASUKEMENT OP ANGLES AND LINES. 1. Surveying-, in its most extensive signification, com- prises all tlie operations necessary for finding, 1st. The area or contents of any portion of the surface of the earth ; 2d. The lengths and directions of the bounding lines ; and, 3d. For making accurate delineations of the surface and bounding lines on paper. It is divided into two branches, Plane and Geodesic Surveying. 2. The radius of the earth being very large, the curva- ture may be neglected, when the survey is limited to small portions of the surface. This branch is called Plane Sur- veying. When the curvature is taken into account, as it must be in all extensive surveys, the method of measurement and computation is called Geodesic Surveying. 8. If at any point of the surface of the earth, regarded as a sphere, a plane be passed perpendicular to the radius, it will be tangent to the surface. Such a plane, and all planes parallel to it, are called horizontal planes. 4. A plane perpendicular to a horizontal plane, at a given point, is called a vertical plane. SEC. I] DEmfiTioifa. 65 5. All lines of Korizontal planes are called horizontal lines. 6. Lines "wMcli are perpendicular to a horizontal plane, are called vertical lines ; and all lines whicli are inclined to it, are called oblique lines. Thus, AB and DG are hori- jj^ zontal lines ; BG and AD are vertical lines ; and A G and BD are oblique lines. 7. The horizontal distance between two points, is the horizontal line intercepted be- tween the two vertical lines passing through those points. Thus, X>(7 or AB is the horizontal distance between the two points A and (7, or the points B and D. 8. A horizontal angle is one whose sides are horizontal; its plane is also horizontal. A horizontal angle may also be defined to be, the angle included between two vertical planes passing through the angular point, and the two objects which subtend the angle. 9. A vertical angle is one, the plane of whose sides is vertical. 10. An angle of elevation^ is a vertical angle having one of its sides horizontal, and the inclined side above the hor- izontal side. Thiis, in the last figure, BAG is the angle of elevation from A to O. 11. An angle of depression^ is a vertical angle having one of its sides horizontal, and the inclined side under the horizontal side. Thus, JDGA is the angle of depression from G to A. 12. An oblique angle is one, the plane of whose sides is oblique to a horizontal plane. 13. All lines, which can be the object of measurement, must belong to one of the classes above named, viz. : 1st. Horizontal lines : 2d. Vertical lines : 3d. Oblique lines. 66 ELEMENTS OF SURVEYING. [BOOK 11. 14. All the angles may also be divided into three classes, viz. : 1st. Horizontal angles : 2d. Vertical angles ; which, include angles of elevation and angles of depression : and 3d. Oblique angles, or those included by oblique lines. OF THE MEASUREMENT OF LINES AND ANGLES. 15. It has been shown (Bk. I., Sec. III., Art. 1), that at least one side and two of the other parts of a plane triangle must be given or known, before the remaining parts can be found by calculation. When, therefore, distances are to be found, by trigono- metrical calculations, two preliminary steps are necessary : • 1st. To measure certain lines on the ground : 2d. To measure such angles as may be necessary to de- termine the required parts. MEASURES FOR DISTANCES. 16. Any tape, rod, or chain, divided into equal parts, may be used as a measure ; and one of these equal parts is called the unit of the measure. The unit of a measure may be a foot, a yard, a rod, or any other ascertained distance. The measure in general use, is a chain of four rods or sixty-six feet in length ; it is called Gunter's chain, from the name of the inventor. This chain is composed of 100 links. Every tenth link from either end, is marked by a small attached brass plate, which is notched, to designate its number from the end. The division of the chain into 100 equal parts, is a very convenient one, since the divi- sions or links are decimals of the whole chain, and in the calculations may be treated as such. SEC. I] MEASUREMENT OF DISTANCES. 67 TABLE. 1 chain = 4 rods = 66 feet = 792 inclies = 100 links. Hence, 1 link is equal to 7.92 inches. 80 chains = 320 rods = 1 mile. 40 chains = | mile. 20 chains =.^ mile. 17. Besides the chain, there are needed for measuring, ten marking pins, which should be of iron, each about ten inches in length and an eighth of an inch in thickness. These pins should be strung upon an iron ring, and this ring should be attached to a belt, to be passed over the right shoulder, suspending the pins at the left side. Two staves are also required. Each of these should be about six feet in length, and have a spike in the lower end to aid in holding it firmly, and a horizontal strip of iron to pre- vent the chain from slipping off; these staves are to be passed through the rings at the ends of the chain. TO MEASURE A HORIZONTAL LINE. 18. At the point where the measurement is to be be- gun, place, in a vertical position, a signal staff, having a small flag attached to its upper extremity ; and place an- other at the point where the measurement is to be termi- nated. These two points are generally called stations. Having passed the staves through the rings of the chain, let the ten marking pins and one end of the chain be taken by the person who is to go forward, and who is called the leader, and let him plant the staff as nearly as possible in the direction of the stations. Then, taking the staff in ,his right hand, let him stand off at arm's length, so that the person at the other end of the chain can align it exactly with the stations : when the alignment is made, let the chain be stretched and a marking pin placed ; then measure a second chain in the same manner, and so on, until all the marking pins shall have been placed. When the marking pins are exhausted, a note should be made, that ten chains have been measured ; after which, the marking pins are to be returned to the leader, and the 68 ELEMENTS OF SUKVEYIN-Q. [BOOK IL measurement continued as before, until the wliole distance is passed over. It will be found desirable to fasten pieces of red cloth, to the heads of the marking pins, that they may be more readily found in thick grass, brushwood, &c. Great care must be taken to keep the chain horizontal, and if the slope of the ground be too great to admit of measuring a whole chain at a time, a part of a chain only should be measured: the sum of all the horizontal lines so measured, is evidently the horizontal distance between the stations. For example, in measuring the horizontal distance between A and C, we first place a staff at A and another at b, in the direction towards 0. Then slide up the chain on the staff at A until it becomes horizon- tal, and note the distance ah. Then remove the staves and place them at b and d : make the chain horizontal, and note the distance cd. Measure in the same manner the line fC; the sum of the horizontal lines ab, cd, fC, is equal to AB, the horizontal distance be- tween A and C. 19. The length of the chain should be compared, from time to time, with a standard kept for the purpose. To facilitate this comparison, let two stakes be driven in the ground, distant from each other one chain, and let nails be driven in the heads of the stakes to mark the ex- act length of the standard. Marks made upon the coping of a wall will answer the same purpose. If it is found that any line has been mea- sured with a chain, either too short or too long, the mea- sured distance may be corrected by the following pro- portion : As the length of the chain the length of the standard the measured distance the true distance. SEC. I] OF THE THEODOLITE. For the correction of areas we have this proportion, As the square of the length of the chain the square of the length of the standard, the area found the area required. MEASUREMENT OF ANGLES. 20. We come now to the measurement of angles, and for this purpose several instruments are used. The one, however, which affords the most accurate results, and which indeed can alone be relied on for nice or extensive opera- tions, is called a Theodolite. This instrument only will be described at present ; others will be subsequently explained. OF THE THEODOLITE. PI. 1. The theodolite is an instrument used to measure horizontal and vertical angles. It is usually placed on a tripod ABQ which enters by means of a screw the lower horizontal plate DJBJ^ and becomes firmly attached to the body of the instrument. Through the horizontal plate BU, four small hollow cylinders are inserted, which receive four screws with milled heads, that work against a second horizontal plate, FQ. The upper side of the plate BJE terminates in a curved surface, which encompasses a ball, that is nearly a semi-sphere, with the plane of its base horizontal. This ball, which is hollow, is firmly connected with the smaller base of a hollow conic frustum, that passes through the curved part of the plate DJS, and screws firmly into the curved part of the second horizontal plate FG. A hollow conic spindle passes through the middle of the ball, and the hollow frustum with which it is connect- ed. To this spindle, a third horiz;ontal and circular plate HI, called the limb of the instrument, is permanently attached. Within this spindle, and concentric with it, there is a sec- ond spindle, called the inner, or solid spindle. To this latter, is united a thin circular plate, called the vernier plate, 70 ELEMENTS OF SURVEYING. [BOOK II. wliicli rests on tlie limb of the instrument, and supports the upper frame- work. The two spindles terminate at the base of the spherical ball, where a small screw enters the inner one, and presses a washer against the other, and the base of the ball. On the upper surface of the plate FG, rests a clamp which goes round the outer spindle, and which, being compressed by the clamp-screw K^ is made fast to it. This clamp is thus connected with the plate FQ. A small cylinder a, is fastened to the plate FG : through this cylinder a thumb-screw L passes, and works into a small cylinder i, connected with the clamp. The cylinders h and a, admit of a motion round their axes, to relieve the screw L of the pressure which would otherwise be occasioned by working it. Directly above the clamp, is the lower telescope MK This telescope is connected with a hollow cylinder, which is worked freely round the outer spindle, by the thumb- screw P having a pinion working into a concealed cog- wheel, that is permanently fastened to the limb of the in- strument. By means of a clamp-screw Q^ the telescope is made fast to the limb, when it will have a common motion with the limb and outer spindle. The circular edge of the limb is chamfered, and is gen- erally made of silver, and on this circle the graduation for horizontal angles is made. In the instrument described, the circle is cut into degrees and half degrees ; the degrees are numbered from to 360. On the circular edge of the vernier plate, is a small plate of silver, called a vernier ; this plate is divided into 30 equal parts, and numbered from the line marked to the left. Two levels, at right angles to each other, are attached to the vernier plate by small adjusting screws ; one of the levels is seen in the figure. The vernier plate turns freely around with the inner spindle. It is made fast to the limb of the instrument by the clamp-screw S] after which the smaller motions are made by the tangent-screw T. There is a compass on the vernier plate, that is concentric with it, the use of which •will be explained under the head compass. SEC. I.] OF THE THEODOLITE. 71 The frame-work wliich supports the horizontal axis of the vertical semicircle UV and the upper telescope, with its attached level, rests on the vernier plate, to which it is made fast bj three adjusting screws, placed at the angu- lar points of an equilateral triangle. The vertical semi- circle UV, is called the vertical limb ; its motions are gov- erned by the thumb-screw Z, which has a pinion, that works with the teeth of the vertical limb. On the face of the vertical limb, opposite the thumb-screw Z, the limb is divided into degrees and half degrees : the degrees are numbered both ways from the line marked 0. There is a small plate resting against the graduated face of the verti- cal limb, called the vernier ; it is divided into 30 equal parts, and the middle line is designated by 0. On the other face of the vertical limb, are two ranges of divisions, commencing at the point, and extending each way 45°. The one shows the vertical distance of any object to which the upper telescope is directed, above or below the place of the instrument, in 100th parts of the horizontal distance: the other, the difference between the hypothenusal and base lines : the hypothenuse being sup- posed to be divided into one hundred equal parts : there- fore, by mere inspection, we can ascertain the number of links, which must be subtracted from every chain of an oblique line, to reduce it to a true horizontal distance. The supports of the upper telescope are called the wyes, and designated ys. Two loops, turning on hinges, pass over the telescope, and are made fast by the pins c and d] these loops confine the telescope in the F's. By withdrawing the pins, and turnilig the loops on their hinges, the telescope may be removed for the purpose of being reversed in position ; and in both situations, the tele- scope can be revolved in the F'5 about its axis. In the telescopes attached to the theodolite, are two principal lenses, one at each end. The one at the end where the eye is placed, is called the eye-glass, the other the object-glass. In order that the axis of the telescope may be directed to an object with precision, two spider's lines, or small 72 ELEMENTS OF SURVEYIJfG. [BOOK 11. hairs, are fixed at riglit angles to eacli other, and placed within the barrel of the telescope, and at the focus of the eye-glass. The vertical hair is moved by two small hori- zontal screws, one of which, / is seen in the figure ; and the horizontal hair, by two vertical screws, g and h. Before using the instrument it must be adjusted, that is, the parts must be brought to their proper relative positions : there are four principal adjustments. First adjustment. — To fix the intersection of the spider'a lines in the line of collimation or axis of the telescope. Having screwed the tripod to the instrument, extend the legs, and place them firmly. Then loosen the clamp- screw S of the vernier plate, and direct the telescope to a small, well-defined, and distant object. By means of a small pin t, on the under side of the telescope, slide the eye-glass till the spider's lines are seen distinctly ; then with the thumb-screw X, which forces out and draws in, the object-glass, adjust this glass to its proper focus, when the object, as well as the spider's lines, will be distinctly seen : after which, by the tangent-screw T and the thumb-screw Z, bring the intersection of the spider's lines exactly upon a well-defined point of the object. Having done this, revolve the telescope in the Yh half round, when the attached level mn, will come to the upper side. See, in this position, if the horizontal hair appears above or below the point, and in either case, loosen one, and tighten the other, of the two screws that work the horizontal hair, till the horizontal hair has been carried over half the space between its last position and the ob- served point. Carry the telescope back to its place ; di- rect again the intersection of the spider's lines to the point, and repeat the operation till the horizontal hair neither ascends nor descends, while the telescope is revolved. A similar process will arrange the vertical hair, and the line of collimation is then adjusted. Second adjustment. — To make the axis of the attached level of the upper telescope, parallel to the line of collimation. Turn the vernier plate, till the telescope comes directly SEC. I.] OF THE THEODOLITE. 73 over two of tlie levelling screws, between the plates DE and FG. Turn these screws contrary ways, keeping them firm against the plate FG^ till the bubble of the level mn, stands at the middle of the tube. Then, open the loops, and reverse the telescope. If the bubble still stands in the middle of the tube, the axis of the tube is horizontal ; but if not, it is inclined, the bubble being at the elevated end. In that case, by means of the small vertical screws m and n, at the ends of the level, raise the depressed end, or de- press the elevated one, half the inclination ; and then, with the levelling screws, bring the level into a horizontal posi- tion. Eeverse the telescope in the Y's^ and make the same correction again ; and so on, until the bubble stands in the middle of the tube, in both positions of the tele- scope : the axis of the level is then horizontal. Let the telescope be now revolved in the y's. If the bubble con- tinue in the middle of the tube, the axis of the level is not only horizontal, but also parallel to the line of coUi- mation. If, however, the bubble recede from its centre, the axis of the level is inclined to the line of collimation, and must be made parallel to it by means of two small antagonistic screws, (one of which is seen at p,) which work horizontally. By loosening one of them, and tightening the other, the level is soon brought parallel to the line of collimation, and then, if the telescope be revolved in the F's, the bubble will continue in the middle of the tube. It is difficult to make the first part of this adjustment, while the axis of the level is considerably inclined to the line of collimation ; for, if the level were truly horizontal in one position of the telescope, when the telescope is re- versed, the bubble would not stand in the middle of the tube, except in one position of the level. This suggests the necessity of making the first part of the adjustment with tolerable accuracy ; then, having made the second with care, let the first be examined, and proceed thus till the adjustment is completed. Third adjustment. — To make the axes of the levels on the limb perpendicular to the axis of the instrument. This adjustment is effected, partly by the levelling 74 ELEMENTS OF SURVEYING. [BOOK II. screws, and partly by tlie thumb-screw Z. Turn the ver- nier plate, until the upper telescope •comes directly over two of the levelling screws, then turn them contrary ways, till the upper telescope is horizontal; after which, turn the vernier plate 180°, and if the bubble of the level remains in the middle of the tube, one line of the limb is horizon- tal. But if the bubble recede from the centre of the level, raise the lower, or depress the upper end, one -half by the levelling screws, the other by the thumb-screw Z^ till it is brought into a horizontal position. Turn the vernier plate again 180°, and if the level be not then horizontal, make it so, by dividing the error as before, and repeat the op- eration until the line of the limb is truly horizontal. Then turn the vernier plate 90°, and level as before. The limb ought now to be truly horizontal ; but lest the first horizontal line may have been changed, in obtaining the second, it is well to bring the telescope and level two or three times over the levelling screws, until an entire revolution can be made without displacing the bubble from the middle of the tube. As this can only be the case when the level revolves around a vertical line, it follows that the limb will then be horizontal, and the axis of the instrument vertical, and hence, the axes of the levels will be perpendicular to the axis of the instrument. Fourth adjustment, — To make the axis of the vertical limb perpendicular to the axis of the instrument Bring the intersection of the spider's lines of the upper telescope upon a plumb line, or any well-defined vertical object, and move the telescope with the thumb-screw Z: if the intersection of the spider's lines continue on the ver- tical line, the axis is horizontal. Or, the adjustment may be effected thus : Direct the intersection of the spider's lines to a well-defined point that is considerably elevated : then turn the vertical limb, until the axis of the telescope rests on some other well-de- fined point, upon or near the ground : reverse the tele- scope, and turn the vernier plate 180° ; now, if in elevating and depressing the telescope, the line of coUimation passes SEC. I.] VERNIERS. 75 througli the two points before noted, tlie axis is horizontal. If it be found, by either of the above methods, that the axis is not horizontal, it must be made so by the screws which fasten the frame-work to the vernier plate. There are two important lines of the theodolite, the po- sitions of which, are determined with great care by the maker, and fixed permanently. First, the axis of the in- strument is placed exactly at right angles with the limb and vernier plate ; and unless it have this position, the vernier plate will not revolve at right angles to the axis, as explained in the third adjustment. Secondly, the line of collimation of the upper telescope is fixed at right angles to the horizontal axis of the vertical limb. We can as- certain whether these last lines are truly at right angles, by directing the intersection of the spider's lines to a well- defined j)oint ; then removing the caps which confine the horizontal axis in its supports, and reversing the axis : if the intersection of the spider's lines can be made to cover exactly the same point, without moving the vernier plate, the line of collimation is at right angles to the axis. K the theodolite be so constructed that either of the y's admits of being moved laterally, so as to vary the angle between the horizontal axis and the line of collima- tion, these lines may be adjusted at right angles to each other, if they have not been so placed by the maker. The lower telescope being used merely as a guard, re- quires no adjustment, although it is better to make the axis, about which its vertical motions are performed, hori- zontal, or perpendicular to the axis of the instrument ; and this is easily effected by means of the two small screws k und Z, which work into the slide J.', that is connected with the horizontal axis. Having explained the methods of properly adjusting the theodolite, we will now explain the particular uses of its several parts, and the manner of measuring VERNIERS. 21. Before explaining the vernier, as applied to the the- odolite, we shall discuss the general theory of verniers. Y6 ELEMENTS OF SURVEYING. [BOOK 11. A Yernier is a contrivance for measuring parts of the equal spaces marked off on a given scale or limb. It is a graduated scale, so arranged, as to cover an ex- act number of equal spaces on the primary scale or liimh, to wMch. it is applied. It is divided into a ■ number of equal parts, greater by one tban tbe number of equal spaces which it covers on the hmb. The vernier may be applied to any scale of equal parts. The modes of its application are extremely various ; the principle, however, is the same in all, and may be illus- trated by a simple diagram. & 9 iO i1 fa 13 14- 1J Iff 17 18 a\ I I \ \ B C I ^ Let AB be any Iwib or scale of equal parts, one of which let us suppose equal to h. Let GD be a vernier^ equal in length to nine of these parts, and itself divided into ten equal spaces, each one of which is then equal to nine-tenths of h. The difference between a space on the limb and a space on the vernier, is therefore equal to one- tenth of h or x^o&. This is the least space that can be meas- ured by means of the vernier, and is called the hast count; hence, The least count of a vernier is equal to one of the equal divisions of the limb divided hy the number of spaces on the vernier. 22. The true reading of the instrument, for any position of the vernier, expresses the distance from the point where the graduation on the limb begins, marked 0, to the point of the vernier. In the diagram, that distance is ex- pressed by nine units of the scale, or 9. If, now, the vernier be moved till the division 1 coin- cides with the division 10 of the hmb, the point will have advanced along the limb a distance equal to j^S, and the reading will become 9 + ^^b. If we again move the vernier till the division 2 coincides with the di- vision 11 of the scale, the point will have advanced an additional distance, equal to ^b, and the reading becomes SEC. L] MEASUREMENT OF ANGLES. 77 9 + ^ob ; wlieii 3 coincides witli division 12, the reading will become 9 + x^o^, and so on, till finally, when the point 10 coincides with 19 of the sc^^le, the distance 9 will have been increased bj \%h^ and will become 10, as it should, since, in that case, the point will have been moved a whole space, and will coincide with the division 10 of the limb. Hence, the following rule for reading an instrument which has a vernier. Read the limb in the direction of the graduation up to the division line next 'preceding the point of the vernier ; this is called the reading on the limb. Look along the vernier till a dividing line is found to coincide with a line of the limb : multiply the number of this first line by the least count of the ver- nier : this is the reading on the vernier: the sum of these two readings is the reading of the instrument. 23. In the theodolite described, the limb is divided into half degrees, and 30 spaces on the vernier cover 29 spaces on the limb. Hence, the least count of this instrument is ^ of a half degree or 1'. Fig, 2, Plate 1, exhibits the vernier of the horizontal limb, and Fig. 3 the vernier of the vertical limb. TO MEASUEE A HORIZONTAL ANGLE WITH THE THEODOLITE. 24. Place the axis of the instrument directly over the point at which the angle is to be measured. This is ef- fected by means of a plumb, suspended from the plate which forms the upper end of the tripod. Having made the limb truly level, place the of the vernier at or 360° of the limb, and fasten the clamp- screw S of the vernier plate. Then, facing in the direc- tion between the lines which subtend the angle to be mea- sured, turn the limb with the outer spindle, until the tele- scope points to the object on the left, very nearly. Clamp the limb with the clamp-screw -S", and by means of the tangent screws L and Z, bring the intersection of the spider's lines to coincide exactly with the object. Having loosened the clamp-screw Q of the lower tele- scope MN^ direct it with the thumb-screw P to the 78 ELEMENTS OF SURVEYING. [BOOK II. same object at whicli the upper telescope is directed ; then tighten tlie clamp-screw Q. This being done, loosen the clamp-screw S of the vernier plate, and direct the telescope to the other object : the arc passed over by the point of the vernier, is the measure of the angle sought. The lower telescope having been made fast to the limb, will indicate any change of the position of the limb, should any have taken place ; and, as the accuracy of the mea- surements depends on the fixedness of the limb, the lower telescope ought to be often examined, and if its position has been altered, the limb must be brought back to its place by the tangent-screw L. It is not necessary to place the point of the vernier at the point of the limb, previously to^ commencing the measurement of the angle, but convenient merely ; for, whatever be the position of this point on the limb, it is evident that the arc which it passes over is the true mea- sure of the horizontal angle. If, therefore, its place be carefully noted for the first direction, and also for the sec- ond, the difference of these two readings will be the true angle, unless the point of the vernier shall have passed the point of the limb, in which case the greater reading must be subtracted from 860°, and the remainder added to the less. TO MEASURE A VERTICAL ANGLE. 25. We shall first explain the method of determining the index error. Having levelled the horizontal limb, di- rect the telescope to some distinctly marked object as the top of a chimney, and read the instrument. Reverse the telescope in the Y^s^ and turn the vernier plate»180°, and having directed the telescope to the same object, again read the instrument. If the two readings are the same, the limb is adjusted ; that is, the of the limb coincides with the of its vernier, when the axis of the telescope is parallel to the horizontal limb. When the reading found with the eye end of the tele- scope nearest the vernier, is greater than that obtained in the reversed position, the true elevation of the object SEC. I] PRACTICAL PROBLEMS. 79 whicli is equal to a mean of tlie readings, may be obtained bj subtracting half their difference from the first reading. If the first reading is less than the second, the half differ- ence must be added to the first. Hence, To find the index error^ take the reading of the limb ivhen the telescope is directed to a fixed object, first with the eye end of the telescope nearest the vernier, and then ivith the telescope and vernier plate both reversed. Take half the difference of these readings, and affect it with a minus sign if the first is greater, or a plus sign if the second is the greater ; this is equal to the index error. Let the operation be repeated several times, using dif- ferent objects, and a mean of the errors will be more cor- rect than the result of a single observation. 26. Having determined the index error, let the axis of the telescope be directed to any point either above or be- low the plane of the limb, and read the arc indicated by the of the vernier. To the arc so read apply the proper correction, if any, and the result will be the true angle of elevation or depression. The angle of elevation may be more correctly foimd by taking the elevation of the object, and repeating the obser- vation with the telescope and vernier plate reversed, and then taking a mean of the readings for the angle required. MEASUREMENTS WITH THE TAPE OR CHAIN ONLY. 27. It often happens that instruments for the measur- ment of angles cannot be easily obtained ; we must then rely entirely on the tape or chain. We now propose to explain the best methods of deter- mining distances, without the aid of instruments for the measurement of horizontal or vertical angles. I. To trace, on the ground, the direction of a right line, that shall be perpendicular at a given point, to a given right line. FIRST METHOD. 28. Let BG be the given right line, and A the given 80 ELEMENTS OF SURVEYING. [BOOK IL point. Measure from A, on tlie line BC, two equal distances AB, AC, one on each side of tlie point A. Take a portion of the chain ^ or tape, greater than AB, and B jl C place one extremity at B, and with the other trace the arc of a circle on the ground. Then remove the end which was at B, to 0, and trace a second arc intersecting the former at I). The straight line drawn through B and A will be perpendicular to BC at A. SECOND METHOD. 29. Having made AB= A C, take any portion of the tape or chain considerably greater than the dis- tance between B and 0. Mark the middle point of it, and fasten its two extremities, the one at B and the other at 0. Then, taking the chain by the middle point, stretch it tightly on either side of BC, and place a staff at B or JE: BAB will be the perpendicular re- quired. /\ THIRD METHOD. 80. Let AB be the given line, and C the point at which the per- pendicular is to be drawn. From the point C measure a distance CA A— equal to 8. With C as a centre, and a radius equal to 6, describe an arc on either side of AB : then, with J. as a centre, and a radius equal to 10, describe a second arc intersecting at E, the one before described : then draw the line EC, and it will be perpendicular to AB at a Eemark. Any three lines, having the ratio of 6, 8, and 10, form a right-angled triangle, of which the side corre- sponding to 10 is the hypothenuse. I SEC. I] SURVEYING CROSS. 81 FOURTH METHOD. 31. Let AD be tlie given riglit line, and D the point at which, the perpendicular is to be drawn. jf Take any distance on the tape ^ ^„.^-^ or chain, and place one extrem- -'^\ ity at i), and fasten the other at some point, as E^ between the two lines which are to form the right angle. Place a staff at E. Then, having stationed a person at i), remove the extremity of the chain and carry it round until it ranges on the line DA at A. Place a staff at A : then remove the end of the chain at A, . and carry it round until it falls on the line AE at E. Then place a staff at E; ADE will be a right angle, being an angle in a semicircle. •i 32. There is a very simple instrument, used exclusively in laying off right angles on the ground, which is called the SURVETIKG CROSS. PI. 2, Fig. 1. This instrument consists of two bars, AB and OD, permanently fixed at right angles to each other, and firmly attached at ..£^ to a pointed staff, which serves as a support. Four sights are screwed firmly to the bars, by means of the screws a, 5, c, and d. As the only use of this instrument is to lay off right angles, it is of the first importance that the lines of sight be truly at right angles. To ascertain if they are so, let the bar AB be turned until its sights mark some distinct object ; then look through the other sights, and place a staff on the line which they indicate : let the cross be then turned until the sights of the bar AB come to the same line : if the other sights are directed to the first object, the lines of sight are exactly at right angles. The sights being at right angles, if one of them be turned in the direction of a given line,, the other will mark the direction of a hne perpendicular to it, at the point where the instrument is placed. . 82 ELEMENTS OF SURVEYING. [BOOK II. El n. From a given point without a straight line, to let fall a perpendicular on the line. 83. Let C be tlie given point, and AB tlie given line. From C measure a line, as CA, to any point of the line AB. From A, measure on AB any distance as AF, and at F erect FF perpendicular to AB. ^^ ^' ^ .^ Having stationed a person at A, measure along tlie per- pendicular FF until the forward staff is aligned on the line AO: then measure the distance AF. Now, by similar tri- angles, we have, AF : AF :: AO : AB, in which all the terms are known except AB, which may, therefore, be found. The distance AB being laid off from A, the point B, at which the perpendicular CB meets AB, becomes known. If we wish the length of the perpen- dicular, we use the proportion, AF : FF :: AC : CB, in which all the terms are known, excepting CB: there- fore, CB may be determined. III. To determine the horizontal distance from a given point to an inaccessible object. FIRST METHOD. 84. Let A be an inaccessible object, and F the point from which the distance is to be measured. At F lay off the right angle AFB, and measure in the di- rection FB, any convenient dis- tance to B, and place a staff at B. Then measure from F, directly towards the object A, a distance FB of a convenient length, and at B lay off a line 1> BC perpendicular to FA. Measure along the line BO, C l::i -E SEC. L] PRACTICAL PEOBLEMS. 83 ■until a person at D shall range tlie forward staff on the line BA. Now, DF is known, being equal to the differ- ence between the two measured hues DB and GB. Hence, by similar triangles, BF : FG ■'. BE : FA, in which proportion all the terms are known, except the fourth, which may, therefore, be found. SECOND METHOD. 35. At the point F lay off FB perpendicular to the line FA, and measure along it any convenient distance, as FB. At B lay off the right an- gle FBB, and measure any dis- tance in the direction BB. Let a person at B align a staff on BA, while a second person at B ahgns it on BF: the staff will thus be fixed at G. Then measure the dis- tance BG. The two triangles BGB and GAF being similar, we have, BG : BB :: GF : FA, in which all the terms are known, except the fourth, which may, therefore, be found. THIRD METHOD. 36. Let B be the given point, and A the inaccessible object; it is required to find BA. Measure any horizontal base line, as BG. Then, having placed staves at B and G, measure any convenient dis- tances BB and GF, such that the points B, B, and A, shall be in the same right line, as also, the points F, G, and A ; then measure the diagonal lines BG and FB. 84 ELEMENTS OF SURVEYING. [BOOK II. Now, in tlie triangle BEG, tlie three sides are known, the^refore, tlie angle ECB can be found. In the triangle CDB, the three sides are also known, therefore the angle OBD can be determined. These angles be- ing respectively subtracted from 180°, the two angles ACB and -4.5(7 become known ; and hence, in the triangle ABO^ we have two angles and the included side, to find the side BA. lY. To find the altitude of an ohject, when the distance to the vertical line passing through the top of it is known. 87. Let CD be the altitude required, and A G the known distance. From A^ measure on the line AG^ any con- venient distance AB, and place a staff vertically at B. Then placing the eye at A, sight to the object D, and let the point, at which the line AD cuts the staff BE, be marked. Measure the distance BE on the staff; then. AB BE AG GD, whence CD becomes known. If the line AC cannot be measured, on account of in- tervening objects, it may be determined by calculation, as in the last problem, and then, having found the horizontal distance, the vertical line is readily determined, as before. SEC. IL] AREA OF LAND. 85 SECTION II. AREA OR CONTENTS OF GROUND. — LAYING OUT LAJ^D. 1. We come next to tlie determination of tlie area or superficial contents of ground. The surface of tlie ground being, in general, broken and uneven, it is impossible, without great trouble and ex- pense, to ascertain its exact area or contents. To avoid this inconvenience, it has been agreed to refer every sur- face to a horizontal plane : that is, to regard all its bound- ing lines as horLzontal, and its area as measured by that portion of the horizontal plane which the boundary lines enclose. For example, if ABCD were a piece of ground having an uneven surface, we should refer the whole to a horizontal plane, and take for the measure of the area that part of the plane which is inclu- ded between the bounding hori- zontal lines AB, BG, CD, DA. In estimating land in this manner, the sum of the areas of all the parts into which a tract may be divided, is equal to the area, estimating it as an entire piece : but this would not be the case if the areas of the parts had reference to the actual surface, and the area of the whole were calcu- lated from its bounding lines. 2. The unit of measure of a quantity is a quantity of the same kind regarded as a standard, and with which all quantities of that kind may be compared. For lines, the unit is a right line of a known length, as 1 foot, 1 link, 1 chain, or any other fixed distance. It has been already observed (Bk. II., Sec. L, Art. 16), that Gunter's chain of four rods or %& feet in length, and which is divided into 100 links, is the chain in general 86 ELEMEl^TS OF SURVEYING. [BOOK H use among surveyors. In measuring land, tlie length of this chain is generally taken for the unit of linear measure. 3. The unit of measure for surfaces is a square de- scribed on the unit of linear measure. Thus, 1 square foot, 1 square yard or 9 square feet. 1 yard = 3 feet. 1 chain = = 4 rods. 1 square chain, or 16 square rods. When, therefore, the linear measures of ground are feet, yards, rods, or chains, the superficial measures are square feet, square yards, squ.are rods, or square chains ; and the numerical expression for the area is the number of times which the unit of superficial measure is contained in the land measured. 4. An acre is a surface equivalent in extent to 10 square chains ; that is, equivalent to a rectangle of which one side is ten chains, and the other side one chain. One quarter of an acre is called a rood. Since the chain is 4 rods in length, 1 square chain eon- tains 16 square rods ; and therefore, an acre, which is 10 square chains, contains 160 square rods, and a rood con- tains 40 square rods. The square rods are called 'perches. 5. Land is generally computed in acres, roods, and perches, which are respectively designated by the letters A. B. P. SEC. 11] AREA OF LAND. 87 When tlie linear dimensions of a survey are cliains or links, the area will be expressed in square chains or square links, and it is necessary to form a rule for reducing this area to acres, roods, and perches. For this purpose, let us form the following TABLE. Miles. Acres. Eoods. Sq. Cliains. Perches. Sq. Links. 1 640 1 2560 4 1 6400.0 10.0 2.5 1.0 102,400 160 40 16 1 64,000,000 100,000 25,000 10,000 625 1 square mile = 6400 square chains = 640 acres. Kow, when the linear dimensions are links, the area will be expressed in square links, and may be reduced to acres by dividing by 100000, the number of square links in an acre : that is, by pointing off five decimal places from the right hand. If the decimal part be then multiplied by 4, and five places of decimals pointed off from the right hand, the figures to the left will express the roods. If the decimal part of this result be now multiplied by 40, and five places for decimals pointed off, as before, the figures to the left will express the perches. If one of the dimensions be in links, and the other in chains, the chains may be reduced to links by annexing two ciphers : or, the multiplication may be made without annexing the ciphers, and the product reduced to acres and decimals of an acre, by pointing off three decimal places from the right hand. When both the dimensions are in chains, the product is reduced to acres by dividing by 10, or pointing off one decimal place. From which we conclude; that, 1st. If links he multiplied hy links, the product is reduced to acres hy pointing off Jive decimal places from the right hand. 88 ELEMENTS OF SUEVEYING. [BOOK II. 2d. If chains he multiplied by links, the product is reduced to acres by pointing off three decimal places from the right hand. 8d. If chains be multiplied by chains, the product is reduced to acres by pointing off one decimal place from the right hand. 6. Since there are 16.5 feet in a rod, a square rod is equal to . 16.5 X 16.5 = 272.25 square feet. If tlie last number be multiplied by 160, we sliall have, 272.25 X 160 = 43560 = the square feet in an acre. Since there are 9 square feet in a square yard, if the last number be divided by 9, we obtain, 4840 = the number of square yards in an acre. PEOBLEM r. 7. To find the area of a piece of ground in the form of a square, rectangle, or parallelogram. Multiply the base by the altitude, and the product will express the area (Geom., Bk. IV., Prop. IV. and V.) 1. To find the area of the rectangular field ABCD. Measure the two sides AB, EG : let us suppose that we have found AB = 14 chains 27 hnks, and BG= 9 chains 75 links. Then, AB =14:11 links, BC= 975 links. ABXB0= 1391325 square links, = 13.91325 acres. 4 8.65300 roods, 40 26.12000 perches. Ans. ISA. SB. 26P. 2. "What is the area of a square field, of which the sides are each S3 ch. 81.? Ans. lOdA. IE. 29P. SEC. 11] AREA OP LAND. 89 3. What are tlie contents of a rectangular field, of wHcli tlie longer side is 49 ch. 27 1., and tlie shorter 38 ch. 71.? Ans. 187 A. 2R. IIP. 4. What are the contents of a fifeld in the form of a parallelogram, of which the base is 35 ch. 65 1., and alti- tude 61 ch. 4 1. ? Ans. 1%1A. 3R 33P. PROBLEM IL 8. To find the contents of a piece of land in the form of a triangle. FIRST METHOD. Measure either side of the triangle as BC^ and from the opposite angle A let fall a perpendicular AD, and measure this perpendicular ; then^ mul- tiply the base and perpendicular to- gether, and divide the product hy 2, the result will express the area of the triangle. Or^ the area is equal to the base multiplied by half the perpendicular^ or to the perpendicular multiplied hy half the base (Geom., Bk. lY., Prop. YL). 1. YiThat are the contents of a triangle whose base is 25 ch. 1 1, and perpendicular 18 ch. 14 1. ? • Ans. 22 A. 2E. 29P. 2. What are the contents of a triangle whose base is ? Ans. 7A. IB. 38P. SECOND METHOD. two sides and their included angle. Then, add together the logarithms of the two sides and the logarithmic sine of their included angle; from this sum subtract the logarithm of the radius, which is 10, and the remainder will he the loga- rithm, of double the area of the triangle. Find, from the table, 90 ELEMENTS OF SURVEYING. [BOOK II. the number answering to this logarithm^ and divide it ly 2 ; the quotient will he the required area (Geom. Mens., Prob. II., Case 2). 1, In a triangle ABC, suppose that we have found ^5=57.65 ck, A (7= 125.81 ch., and the included angle CAB=bT 25': required the area. Let the required area be designated by And log 2^- Q + log ^^57.65 . + log ^(7 125.81 ^ +log sin A 57° 25' loff B . . . = 6111.4 ) ; then, 1.760799 2.099715 9.925626 10 8.786140. = 8055.7 square chains. Ans. 805^. 2B. IIP. Eemark. In this example, the links are treated as de- cimal parts of the chain ; the result, therefore, is in square chains and decimal parts of a square chain. 2. What is the area of a triangle whose sides are 80 and 40 chains, and their included angle 28° 57' ? Ans. 29^. OB. IP. . THIRD METHOD. Measure the three sides of the triangle. Then, add them together and take half their sum. From this half sum subtract each side separately. Then, multiply the half sum and the three remainders together, and extract the square root of the pro- duct : the result will he the area (Geom. Mens., Prob. IL, Case 8). Or, after having obtained the three remainders, add together the logarithm of the half sum and the logarithms of the re- spective remainders, and divide their sum by 2 ; the quotient will be the logarithm of the area. 1. Find the area of a triangular piece of ground whose sides are 20, 80, and 40 chains. SEC. IL] AREA OF LAND. 91 BY riEST RULE. 20 45 45 45 80 -20 -80 -40 40 2)90 45- 25 1st rem. 15 2d rem. = half sum. Tiien, 5 3d rem. 45X25X15X5 = 84375: and -/MSTS = 290.4737 = tlie area. .. Am. 29A. OB. 8P. 2. What is the area of a triangle whose sides are 2569, 4900, and 5035 links? BY SECOOT) EULE. 2569 6252 6252 6252 4900 -2569 - 4900 - 5035 5035 3683 1st rem. 1352 2d rem. 1217 3d rem. 2 )12504 6252 = half sum. Then, log 6252 8.796019 log 3683 8.566202 log 1352 3.130977 log 1217 3.085291 2 )13.578489 Area in square links, 6155225 . . . 6.789244. Ans. 61A. 2B. 8P. PEOBLEM IIL 9. To find the area of a piece of land in the form of a trapezoid. Measure the two parallel sides, and also the perpendicular distance betiveen them. Add the two parallel sides together, and take half the sum ; then multiply the half sum hy the perpendicular, and the product will he the area (Geom., Bk. lY., Prop. Vn.) 92 ELEMENTS OF SURVEYING. [BOOK II 1. What is the area of a trapezoid, i \ of wliicli tlie parallel sides are 80 and / \ 49 chains, and the perpendicular distance / \ between them 16 ch. 60 l, or 16.60 chains ? '- ^ 30 + 49 = 79 ; dividing by 2, gives . . 89.5 multiply by 16.60 area in square chains 655.700. Ans. 65^. IB. IIP. 2. Eequired the contents, when the parallel sides are 20 and 82 ch., and the perpendicular distance between them 26 ch. Ans. 67^. 2i?. 16P. PROBLEM IV. 10. To find the area of a piece of land in the form of a quadrilateral. Measure the four sides of the quadrilateral^ and also one of the diagonals: the quadrilateral will thus he divided into two triangles, in loth of which all the sides will he known. Then, find the areas of the triangles separately, and their sum will he the area of the quadrilateral. 1. Suppose that we have measured J) the sides and diagonal AC, of the ^-^^l^ quadrilateral ABCD, and found ^^ ! ^ X,^ ^^=40.05 ch. CZ) = 29.87 ch., ^\. ^\ ?^ ^(7 = 26.27 ch. ^X) = 37.07 ch., ^^i^ and A(7=55ch.: ■« required the area of the quadrilateral. Ans. 101^. IP. 15P. Eemark. Instead of measuring the four sides of the quadrilateral, we may let fall the perpendiculars Bh, Dg, on the diagonal AC. The area of the triangle may then be determined by measuring these perpendiculars and the di- agonal AC. The perpendiculars are P^ = 18.95 ch., and P6 = 17.92 ch. SEC. II.] AREA OF LAND; 93 PKOBLEM V. 11. To find tlie contents of a, field having any number of sides. Measure the sides of the field and also the diagonals: the three sides of each of the triangles into which the field will he thus divided will then he known, and the areas of the triangles may then he calculated hy the preceding rules. Or, measure the diagonals, and from the angular points of the field draw perpendiculars to the diagonals and measure their lengths: the hase and perpendicular of each of the triangles will then he known. 1. Let it be required to determine tbe contents of tbe field ABODE, having five sides. Let us suppose that we liave mea- sured the diagonals and perpendicu- lars, and found, J. (7=: 36.21 ch., ^(7=89.11 ch., J5J = 4.08 ch., Dd=7.2Q ch., Aa = 4c.l9 ch. ; required the area of the field. Area of triangle ABG= 73.8684 square chains, area of " CD^= 141.9698 area of " ACE= 81.7399 area of ABODE =297.6776 Ans. 29A. 8B. IP. PROBLEM VI. 12. To find the contents of a long and irregular figure, bounded on one side by a straight line. Suppose the ground, of which the contents are required, to be of the form ABEeda, bounded on one side by the right line AE, and on the other by the curve edca. At A and E, the extremities of the right hne AE, erect the two per- pendiculars Aa, Ee, and on each of them measure the breadth of the land. 94 ELEMENTS OF SURYEYING. [BOOK II. Then divide tlie base into any convenient number of equal parts, and measure tlie breadth of the land at each point of division. Add together the intermediate breadths and half the sum of the two extreme ones: then multiply this sum hy one of the equal parts of the base line^ and the product will he the re- quired area very nearly (Mens. Prob. YI.) 1. The breadths of an irregular figure, at five equidis- tant places, being 8.20 ch., 7.40 ch., 9.20 ch., 10.20 ch., and 8.60 chains, and the whole length 40 chains, required the area. 8.20 4)40 8.60 10 one of the equal parts. 2 )16.80 8.40 mean of the extremes, 35.20 sum, 7.40 10 9.20 area 852.00 square ch. 10.20 35.20 sum. Ans. 35JI. 32P. 2. The length of an irregular piece of land being 21 ch., and the breadths, at six equidistant points, being 4.35 ch., 5.15 ch., 3.55 ch., 4.12 ch., 5.02 ch., and 6.10 chains: re- quired the area. Ans. 9^. 2R. SOP. 3. The length of an irregular piece of land is 80 ch., and the breadths at nine equidistant points are 5.75 ch., 6.12 ch., 4.80 ch., 5.09 ch., 3.87 ch., 5.17 ch., 6.00 ch., 8.94 ch., and 5.95 ch. : what is the area ? Ans. 40J.. SR UP. 4. The length of an irregular field is 39 rods, and its breadths at five equidistant places are 4.8, 5.2, 4.1, 7.3, and 7.2 rods: what is its area? Ans. 220.35 sq. rods. Eemark. If it is not convenient to erect the perpen- diculars at equal distances from each other, the areas of the trapezoids, into which the whole figure is divided, must be computed separately : their sum will be the re- quired area. SEC. II.] AREA OF LAND. 95 PROBLEM VII. 13. To find tlie area of a piece of ground in tlie form of a circle. Measure the radius AC: then multiply the square of the radius hy 8.1416 (Mens., Art. 15.). 1. To find tlie area of a circular piece of land, of wliicli tlie diameter is 25 cli. Ans. 49^. OR. 14P. PROBLEM VIIL 14. To find tlie contents of a piece of ground in tlie form of an ellipse. c Measure the semi-axes AE, CM Then multiply them together, and their jproduct ly 3.1416. 1. To find tlie area of an elliptical piece of ground, of wHcli tlie transverse axis is 16.08 cli., and tlie conjugate axis 9.72 cli. Ans. VIA. \R. 4P. Eemark I. Tlie following is tlie manner of tracing an ellipse on tlie ground, wlien tlie two axes are known. From C, one of the extremities of tlie conjugate axis as a centre, and AE lialf tlie transverse axis as a radius, describe tlie arc of a circle cutting AE in tlie two points F and 0- : these points are called the foci of the ellipse. Then, take a tape, the length of which is equal to AB, and fasten the two ends, one at the focus F, the other at the focus C Place a pin against the tape and move it around, keeping the tape tightly stretched: the extremity of the pin will trace the curve of the ellipse. Remark n. In determining the contents of ground, in the examples which have been given, the linear dimensions have been taken in chains and decimals of a chain. 96 ELEMENTS OF SURVETIITG. [BOOK II. If the linear dimensions were taken in terms of any otlier unit, tHey may be readily reduced to chains. For, a chain is equal to 4 rods, equal to 22 yards, equal to 66 feet. Hence, 1st. Hods may he reduced to chains and the decimal of a chain, hy dividing hy 4. 2d. Yards may he reduced to chains and the decimal of a chain, hy dividing hy 22. 8d. Feet may he reduced to chains and the decimal of a chain, hy dividing hy QQ. Eemaek III. If it is tliouglit best to calculate the area, witliout reducing the linear dimensions to chains, the re- sult can be reduced to acres : 1st. By dividing it hy 160 when it is in square rods (Art. 5). 2d. By dividing it hy 4840 when it is in square yards (Art. 6). 3d. By dividing it hy 43560 when it is in square feet (Art. 6). OF LAYING OUT LAND. 15, The surveyor is often required to lay off a given quantity of land, in such a way that its bounding lines shall form a particular figure, viz., a square, a rectangle, a triangle, &c. He is also often called upon to divide given pieces of land into parts containing given areas, or bearing certain relations to each other. The manner of making such divisions must always de- pend on a judicious application of the principles of geom- etry to the particular case. If, for example, it were required to lay out an acre of ground in a square form, it would first be necessary to find, by calculation, the side of such a square, and then to trace, on the ground, a figure bounded by four equal lines at right angles to each other. SEC. II.] LAYING OUT LAND. 97 PEOBLEM I. 16. To lay out a given quantity of land in a square form. Reduce the given area to square chains^ or square rods: then extract the square root, and the result will he the side of the required square. This square being described on the ground, will be the figure required. 1. To trace a square whicli stall contain IbA. OR. 12P. First, 15J[ = 60i^=2400P Add, 12P ; hence, IbA OR 12P=2412P; tlie square root of wMcli is 49.11. Therefore, if a squ.are be traced on tlie ground, of wliicli tlie side is 49.11 rods, it will be tlie required figure. 2. To trace a square wliicli shall contain 176J.. IR. 24:P. First, 176^ = 1760 square chains, 1R= 2.5 " hence, 24P= 1.5 " 176J- IP 24P= 1764 square chains : the square root of which is 42. Hence, if a square be traced on the ground, of which the side is 42 ch., it will be the required figure. PROBLEM XL 17. To lay out a given quantity of land in a rectangu- lar form, having one of the sides of the rectangle given. Divide the given area, reduced to square chains or square rods, by the given side of the required rectangle, and the quotient will be the other side. Then, trace the rectangle on the ground. 1, To lay off 240 acres in a rectangular form, one of the sides being given, and equal to 80 rods. First, 240J. = 2400 square chains = 88400 square rods. Then, 80)38400(480 rods ; which is the required side of the rectangle. 18. A great number of similar problems might be pro- posed. The solution of them does not, however, properly belong to surveying. The laying out of the ground, and 98 ELEMENTS OF SURVEYING. [BOOK II the tracing of lines, after tlie figure and area have been determined, are the only parts which appertain to a prac- tical treatise. The manner of tracing lines having been al- ready explained, it seems unnecessary to add the numerous examples often given under this head of the subject. SECTION III. SURVEYING WITH THE COMPASS. — DIVIDING LAND. 1. Before considering the principles involved in the method of surveying now to be explained, it will be ne- cessary to describe the instrument principally used in the field, and which is called THE CIRCUMFERENTER, OR SURVEYOR'S COMPASS. PI, 2, Fig. 2. This instrument consists of a compass-box DCE^ a magnetic needle, a brass plate AB^ from twelve to fourteen inches long, two plain sights, AF and BQ, one of which is more fally shown in Fig, 3 ; and a stand, which is sometimes a tripod, and sometimes a single staff pointed with iron at the lower end, so that it may be placed firmly in the ground. The open sights, AF and BO^ are placed at right an- gles to the plate AB^ and fastened to it firmly by the screws a and 5, In each sight there is a large and small aperture or slit ; the larger aperture being above the smaller in one of the sights, and below it in the other, A hair or thread of silk is drawn vertically through the middle of the large aperture, as shown in Fig. 8, The compass-box DGE is circular, and generally about six inches in diameter. At the centre is a small pin, on which the magnetic needle is poised. This needle, if al- lowed to turn freely around the point of support, will settle to a state of rest : the direction which it then indicates, is that of the magnetic meridian. SEC. Ill] WITH THE COMPASS. 99 In the interior of tlie compass-box, there is a graduated circle divided to degrees, and sometimes to half degrees : the degrees are numbered from the extremities of the di- ameter NS, both ways to 90°. The length of the magnetic needle is a little less than the diameter of the graduated circle, so that the needle can move freely around its centre, within the circle, and its positions be noted on the gi^aduated arc. The compass-box is turned about its centre, without moving the plate AB, by means of the milled screw L: it is fastened to the plate AB, by the screw P. In using the compass, it is important to ascertain the exact angle which may be included between the magnetic meridian and the direction that may be given to the line drawn through the eye and the sights AF and BG. To effect this, a small arc HI is described on the bar AB, having its centre at the centre of the compass-box. This arc is divided to degrees, and sometimes to the parts of a degree. A vernier is also used, which is permanently attached to the compass-box. When the point of this vernier coincides with the point of the graduated arc HI, the line of the compass-box marked NS, lies in the plane of the sights, Now, supposing the of the vernier to coincide with the of the arc HI, if the end of the needle does not stand at one of the lines of division of the gTaduated circle, let the whole degrees be read. Then, turn the compass-box by means of the screw L, until the needle points exactly to the line which marked the whole degrees : the space passed over by the of the vernier, shows the parts of a degree that are to be added to give the true reading. SURVEYESTG WITH THE COMPASS. 2. The line about which the earth revolves is called its axis; and the two points in which the axis meets the sur- face of the earth, are called the poles. 3. A plane passed through the axis is called a meridian 100 ELEMENTS OP SUEVEYING. [BOOK II. plane, and its intersection witli tlie surface is called a me- ridian line or a meridian. 4. All tlie meridians converge towards tlie poles, but they vary so little from parallelism witliin tlie narrow limits of surveys made with, the compass, that they may, without error, be regarded as parallel straight lines. 5. K a magnetic needle be suspended freely and allowed to settle to a state of rest, a vertical plane passed through its axis is called the plane of the magnetic meridian ; and its intersection with the surface of the earth is called the mag- netic meridian, or sometimes a North and South line. A line perpendicular to a North and South hne is called an East and West line. 6. A line traced or measured on the ground, is called a course; and the angle which this hne makes with the meridian passing through the -ivr point of beginning, is called the bearing. Thus, if we start from the point A, and measure in the direction AB. the line AB is the course, and the angle JSfAB is the bearing. When the course, like AB, falls between the north and east points, the bearing is read, north 46° east, and is written N. 46° E. When the course, like AC, falls between the north and west points, the bearing is read, north 80° west, and is written N. 30° W. When the course, like AF, falls between the south and east points, the bearing is read, south 70° east, and is writ- ten S. 70° E. When the course, like AB, falls between the south and west points, the bearing is read, south 70° west, and is written S. 70° W. A course which runs due north, or due south, is desig- nated by the letter N or S ; and one which runs due east, or due west, by the letter E or W. B ■yT E \ SEC. III.] WITH THE COMPASS. 101 7. If, after having passed over a course, the bearing is taken to the back station, this bearing is called the ha/ik sight^ or reverse hearing. 8. The perpendicular distance between the east and west lines drawn through the extremities of a course, is called the northing or southing^ according as the course is run to- wards the north or south. This distance is also called the difference of latitude^ or simply the latitude, because it shows the distance which one of the points is north or south of the other. Thus, in running the course from A to B^ AC \& the difference of latitude, c north. 9. The perpendicular distance be- W" tween the meridians passing through the extremities of a course, is called the de- parture of that course, and is east or west, according as the course lies on "" the east or west side of the meridian passing through the point of beginning. Thus, in running the course AB, CB is the departure, east. 10. It will be found convenient, in explaining the rules for surveying with the compass, to attribute to the lati- tudes and departures the algebraic signs, + and — . We shall, therefore, consider every northing as affected with the sign -f , and every southing as affected with the sign — , We shall also consider every easting as affected with the sign +, and every westing as affected with the sign -. 11. The meridian distance of a point is its perpendicular distance from an assumed meridian. Thus, if the distance be estimated from the meridian NS, BG will be the meri- dian distance of the point B. 12. The meridian distance of a line is the meridian dis- tance of its middle point, and is east or west, according as this point lies on the east or west side of the assumed me- 102 ELEMENTS OF SURVEYING. [BOOK II. ridian. Thus, FO drawn tliroTigli the middle point of AB, is the meridian distance of the line AB. The sign + will always be given to the meridian dis- tance of a point or line, when it lies on the east of the as- sumed meridian, and the sign — , when it lies on the west. 13. When a piece of ground is to be surveyed, we be- gin at some prominent corner of the field, and go entirely around the land, measuring the lengths of the bounding lines with the chain, and taking their bearings with the compass. It is not material whether the ground be kept on the right hand or on the left, and all the rules deduced for one of the cases, are equally applicable to the other. To preserve uniformity, however, in the language of the rules, we shall suppose the land to be always kept on the right hand of the surveyor. FIELD OPERATIONS. 14. Let ABCD be a piece of gTOund to be surveyed, A the point where the work is to be begun, and NS a meridian. On a sheet of paper, rule three columns, as follows, and head them stations, bearings, distances. Stations. Bearings. Distances. 1 N 311° w 10. 2 N" 62f ° E 9.25 3 S 36° E 7.60 4 S 451° W 10.40 Place the compass at J., and take the bearing to B, which is PAB: suppose this angle has been found to be 31^°. The bearing from ^ to 5 is then JST. 31^° W. En- i SEC. Ill] WITH THE COMPASS. 103 ter tiiis bearing in tlie field notes opposite station 1. Then measure the distance from A to B^ which we will suppose to be 10 ch., and insert that distance opposite sta- tion 1, in the column of distances. We next take the bearing from B to 0, N. 62f E., and then measure the distance BO— 9 ch. 25 1., both of which we insert in the notes opposite station 2. At station G we take the bearing to JD, S. 36° E., and then measure the distance CD = 7 ch. 60 1., and place them in the notes opposite station 3. At 1) we take the bearing to A, S. 45^° W., and mea- sure the distance DA = 10 ch. 40 1. We shall then have made all the measurements on the field which are neces- sary to determine the contents of the ground. 15. Eemark L The reverse bearing or back sight, from B to A, is the angle ABH- and since the meridians ISTS and HG are parallel, this angle is equal to the bearing NAB. The reverse bearing is, therefore, S. 31|-° E. The reverse bearing from G, is S. 62f ° W. ; that is, it is the angle IGB= QBG. And generally, a reverse hearing^ or hack sight, is always equal to (he forward hearing^ and differs from it in both of the letters by ivhich it is designated. 16. Eemark II. In taking the bearings with the com- pass, there are two sources of error. 1st. The inaccuracy of the observations : 2d. Local attractions, or the derange- ment which the needle experiences when brought into the vicinity of iron-ore beds, or any ferruginous substances. To guard against these sources of error, the reverse bearing should be taken at every station : if this and the forward bearing are of the same value, the work is proba- bly right ; but if they differ considerably, they should both be taken again. 17. Remark III. If the forward and back sights at the ' end of any course of the survey agree, it may be safely assumed, that no local attraction disturbs the needle at these points ; and hence, that the next foresight is also free from such disturbing causes. The error, therefore, from 104 ELEMENTS OF SURVEYING. [BOOK IL local attraction, wlien it arises, will first show itself in tlie difference between a true foresiglit and an erroneous back sight. When this difference appears, subtract the back sight from the foresight, and call the difference the correction for the next foresight. The correction will be positive when the foresight is the larger, and negative when it is less. Add this correction, with its proper sign, to the fore- sight of the next course, when the meridional and longitu- dinal letters of that course are both the same, or both dif- ferent from the foresight of the previous course, and sub- tract it when one of the letters is the same and the other different : the result will be the true bearing. The true bearing of any other course may be found by the same process. EXAMPLE. True Eoresiglits. Back Sights. Foresights of next Course. Foresights Corrected. 1. S 85° 10' W 2. N 16° 20' E 3. ]Sri7°25'W 4. S. 47° 18' E N 85° 05' E S18°20'W S 16° 10' E N48°10'W S 16° 15' W N 15° 25' W N 28° 16' E S 49° 15' W S16°20'W N17°25'W N 27° 01' E N50°07'W Note. — If there be no course in the survey in which the foreward and back sights agree, take the one in which they agree the nearest, and add half the difference of the bearings to the least, and treat the result as the true bearing. 18. Eemark IY. In passing over the course AB, the north- ing is found to be HB, and the departure, which is west, is repre- sented by AH. Of the course BG^ the northing is expressed by BG, and the departure, which is east, by GG. Of the course GD, the southing is expressed by GI, and the departure, which is east, by GF. Of the course DA^ the south- SEC. Ill] TRAVERSE TABLE. 105 ing is expressed bj KA, and tlie departure, which is west, by DK. It is seen frora the figure, that the sum of the northings is equal to HB -\-BG = HG -^ and that the sum of the southings is equal to CI-\r KA=PA=^ HG: hence, the sum of the northings is equal to the sum of the If we consider the departures, it is apparent that the sum of the eastings is equal to GC-{- CF= GF] and that the sum of the westings is equal to AH+ I)K= GF] hence also, the sum of the eastings is equal to the sum of the loestings. We therefore conclude, that when any survey is correctly made, the sum of the northings will be equal to the sum of the southings^ and the sum of the eastings to the sum of the westings. It would indeed appear plain, even without a rigorous demonstration, that after having gone entirely round a piece of land, the distance passed over in the direction due north, must be equal to that passed over in the direction due south ; and the distance passed over in the direction due east, equal to that passed over in the direction due west. Having now explained the necessary operations on the field, we shall proceed to show the manner of computing the contents of the ground. We shall first explain, THE TRAVERSE TABLE AND ITS USES. 19. This table shows the latitude and departure corres- ponding to bearings that are expressed in degrees and quarters of a degree from to 90°, and for every course from 1 to 100, computed to two places of decimals. The following is the method of deducing the formulas for computing a traverse table ; by means of these for- mulas and a table of natural sines, the latitude and depar- ture of a course may be computed to any desirable degree of accuracy. 106 ELEMENTS OF SURVEYING. [BOOK II. Let AD represent any course, and ^^ NAD = A CB, expressed in degrees and i minutes, be its bearing. Let AC he the j / unit of measure of the course, and also ^ the radius of the table of natural sines X < (Bk. L, Sec. IIL, Art. 14). Draw DU and a/-—^ CB parallel to NS, and AU perpen- i " dicular to AS. Then will DIJ be the ^ latitude, and AJE the departure of the course, and CB the co- sine, and AB the sine of the bearing. From similar triangles we have these proportions, AC : CB :: AD : DE, or 1 : cos of the bearing : : course : latitude, AC '. AB :: AD : AU, or 1 : sin of the bearing : : course : departure. Whence, lat. = course X cos of the bearing, dep. = course X sin of the bearing. We have then the following practical rule for compu- ting the latitude and departure of any course. Look in a table of natural sines for the cosine and sine of the bearing. Multiply each by the length of the course, and the first product will be the latitude, and the second will be the departure of the given course. EXAMPLES. 1. The bearing is 65° 89', the course 69.41 chains : what is the latitude, and what the departure? Natural cosine of 65° 89' 41231 Length of the course 69.41 Product, which is the Dif. of Latitude, 28.6184871. Natural sine of 65° 39' 91104 Length of the course 69.41 Product, which is the Departure . . 63.2352864. SEC. Ill] TRAVERSE TABLE. 107 2. The bearing is 75° 47', tlie course 89.75 chains : what is the latitude, and what the departure? Natural cosine of 75° 47' . 24559 Length of course 89.75 Product, which is the Dif. of Latitude, 22.0417025. Natural sine of 75° 47' 96937 Length of course 89.75 Product, which is the Departure . . 87.0009575. 20. In this manner the traverse table given at the end of the book has been computed. When the bearing is given in degrees aiid quarters of a degree, and the differ- ence of latitude and departure are required to only two places of decimals, they may be taken directly from the traverse table. If the bearing is less than 45°, the angle will be found at the top of the page ; if greater, at the bottom. Then, if the distance is less than 50, it will be found in the col- umn " distance," on the left hand page ; if greater than 50, in the corresponding column of the right hand page. The latitudes or departures of courses IN of different lengths, but which have the ^ same bearing, are proportional to the lengths of the courses. Thus, in the " figure, the latitudes AG, AO, or the de- partures GF, CB, are to each other as the courses AF, AB. S Therefore, when the distance is greater than 100, it may be divided by any number which will give an exact quotient, less than 100 : then the latitude and departure of the quotient being found and multiplied by the divisor, the products will be the latitude and departure of the whole course. It is also plain, that the latitude or departure of two or more courses, having the same bearing, is equal to the sum of the latitudes or departures of the courses taken sepa- rately. Hence, if we have any number greater than 100, as 614, we have only to recollect that, 610 -f 4 = 614 ; and also, that the latitude and departure of 610, are ten times n / E 108 ELEMENTS OF SURVEYIITG. [BOOK II. as great, respectively, as tlie latitude and departure of 61 : tliat is, equal to the latitude and departure of 61 mul- tiplied by 10, or with, the decimal point removed one place to the right. EXAMPLES. 1. To find the latitude and departure for the bearing Latitude' for 610 . . 530.90 Latitude for 4 . . 8.48 Latitude for 614 . . 534.38 Departure for 610 . . 300.40 Departure for 4 . . 1.97 Departure for 614 . . 302.37 In this example, the latitude and departure answering to the bearing 29|°, and to the distance 61, are first taken from the table, and the decimal point removed one place to the right : this gives the latitude and departure for the distance 610 ; the latitude and departure answering to the same bearing and the distance 4, are then taken from the table and added. 2. To find the latitude and departure for the bearing 62^°, and the course 7855 chains. Latitude for 7800 . 3602.00 Departure for 7800 . 6919.00 Latitude for 55 . 25.40 Departure for 55 . 48.79 Departure for 7855 . 6967.79 Latitude for 7855 . 3627.40 Eemaek. When the distances are expressed in whole numbers and decimals, the manner of finding the latitudes and departures is still the same, except in pointing off the places for decimals : but this is not difficult, when it is re- membered that the column of distances in the table, may be regarded as decimals, by removing the decimal point to the left in the other columns. 3. To find the latitude and departure for the bearing 47f °, and the course 37.57. Latitude for 37.00 . 24.88 Latitude for .57 . .38 Latitude for 37.57 . 25.26 Departure for 37.00 . 27.39 Departure for .57 . .42 Departure for 37.57 . 27.81 SEC. Ill] OF BALANCING. 109 OF BALANCING THE WORK. 21. The use of tlie traverse table being explained, we can proceed to compute tlie area of tlie ground. The field notes having been completed, rule a new table, as below, with four additional columns, two for latitude, and two for departure. Then find, from the traverse table, the latitude and de- parture of each course, and enter them in the proper col- umns opposite the station. Then add up the column of northings, and also the col- umn of southings : the two sums should be equal to each other. If they are not, subtract the less from the greater ; the remainder is called the error in latitude. This error takes the name of that column which is the less. For example, if the sum of the northings is less than the sum of the southings, the error is called, error in northing : but if the sum of the southings is less than the sum of the northings, the error is called, error in southing. We find the error for each particular course by the following pro- portion. As the sum of the courses Is to the error of latitude, So is each particular course To its correction. The error thus found may be entered in a separate col- umn ; after which add it to the latitude of the course when the error and latitude are of the same name, but subtract it when they are of different names. This will make the sum of the northings equal to the sum of the southings, and is called balancing the work. The northings and south- ings thus corrected are entered in columns on the right, under the head balanced. The eastings and westings are balanced in the same manner ; the difference between their sums being called error in departure. For an example, we will resume the one already con- sidered. no ELEMENTS OF SURVEYING. [BOOK IL Sta. Bearings. Distan- ces. LATITUDE. DEPARTURE. Cor. Lat. Cor. Dep. BALANCED. | N. + S. E. + W. N. + S. E. + W. 1 2 3 4 N 31io W N 62JO K S 360 E S 45iO W 10. 9.25 7.60 10.40 8.53 4.23 6.15 7.29 8.22 4.47 5.22 7.4i + 0.18 + 0.17 — 0.14 -0.19 + 0.02 -0.01 — 0.01 + 0.02 8.71 4.40 6.01 7.10 8.21 4.46 5.24 7.43 Sum of courses, 37.25 12.76 13 44 12.76 1269 12.63 12.63 13.11 13.11 12.67 12.67 Error in Northing . . . 0.68 0.06 Error in Westing. As 37.25 : 0.68 As 37.25 : 0.68 As 37.25 : 0.68 As 37.25 : 0.68 As 37.25 : 0.06 As 37.25 : 0.06 As 37.25 : 0.06 As 37.25 : 0.06 10 : 0.18 error in lat. of 1st course. 9.25 : 0.17 error in lat. of 2d course. 7.60 : 0.14* error in lat. of 3d course. 10.40 : 0.19 error in lat. of 4tli course. 10 : 0.02* error in dep. of 1st course. 9.25 : 0.01 error in dep. of 2d course, 7.60 : 0.01 error in dep. of 3d course. 10.40 : 0.02 error in dep. of 4tli course. 22. Remark I. In finding tlie error in latitude or de- parture, for a particular course, the last figure is sometimes doubtful : in which case it is best to mark it, as in the third proportion for error in latitude, and the first for er- ror in departure ; and then, if the figures taken do not balance the work, let each be increased or diminished by 1. 23. Eemark II. It has already been observed (Art. 18), that if the measurements on the field be correctly made, the sums of the northings and southings will be equal to each other, as also those of the eastings and westings. It is the opinion of some surveyors, that when the error in latitude or departure exceeds one link for every five chains of the courses, the field notes ought not to be relied on. This, perhaps, is a higher degree of accuracy than can be attained. The error, however, should always be made considerably less than one link to a chain. 24. The following is an example in which the latitude and departure of each course have been computed from the table of natural sines. SEC. Ill] OF BALANCING. Ill — Bearing.. Dut. Dif. ofLatitnde. Departure. Balanced. ] N. S. E. W. N. S. E. W. / N 45 65 W 63 ch. 36.81210 ■ 38.01149 36.65903 38.01149 2 N 4 50K 14.40 14.13513 6.26894 13.12813 6.26894 3 N 89 05 E 125.60 2.00800 125.48368 1.96126 126.49228 4 S 160W 11.80 11.16338 2.29688 12.11110 2.29688 5 S 7 40E 31.20 30.92101 4.16239 31.12138 4.16239 6 N 89 25 W 36.50 0.36139 35.49822 0.36139 35.49822 1 S 84 35 W 40. 3.11600 39.82120 3.80352 39.81260 8 S 14 35 W 21. 5.58264 20.24442 5.61385 20.24442 113.31662 112.04309 112.04309 136.91501 135.93221 135.91601 112.10986 112.10985 136.92361 136.92361 Instead of balancing by the metbod jnst explained, we divide eacb error by two. Now if we subtract half the error in southing from the column of northings, and at the same time add it to the column of southings, these two columns will exactly balance. In like manner, if we sub- tract half the error in easting from the column of westings, and at the same time add it to the column of eastings, these columns will also balance. The errors should be distributed in proportion to the lengths of the courses, but this may be done with sufficient accuracy without making the proportions. If any of the courses have been run over rough ground, the probability is that the errors belong to these courses, and they should be distributed among them. In this example we separate the half error in southing into the three parts .40700, .21302, and .04674, and subtract them respectively from the northings of courses 2, 1, and 3, and then place the northings in the balanced columns. For the southings we separate the half error into the four parts .40772, .20031, .03121, and .02752, and add them respec- tively to the southings of the courses '4, 5, 8, and 7. We then enter the southings in the balanced columns. As the error in easting is so small, we add half of it to the east- ing of course 3, and subtract half from the westing of course 7. 112 ELEMENTS OF SURVEYING. [BOOK IL OF THE DOUBLE MEEIDIAN DISTANCES OF THE COUESES. 25. After tlie work lias been balanced, tlie next thing to be done is to calculate the double meridian distance of each course. For this purpose, a meridian line is assumed, lying either wholly without the land, or passing through any point within it. It is, however, most convenient to take that meridian which passes through the most easterly or westerly station of the survey ; and these two stations are readily determined by inspecting the field notes. Having chosen the meridian, let the station through which it passes, be called tYiQ ^ principal station, and the course which begins at this point, the first course. Care, however, must he taken, not to confound this with the course which legins at station 1, and which is the first course that is entered in the field notes. It has already been remarked (Art. 10), that all de- partures in the direction east, are considered as plv:S, and all departures in the direction west as minus. 26. To deduce a rule for finding the double meridian distances of the courses. Let BO n represent any course, and AB the preceding Course ; also, let JD and j^ E be their middle points. Draw iXj: EH, CM, and DG, perpendicular to i |\. the assumed meridian NS. Draw | j i X^ also AI, EK, and BL, parallel to a\ -j:— -^~£|-\i5 NS. Then 2DG is the double me- | L_\ ridian distance of the course BC, and 2EH= IKO, is the double me- ^ ridian distance of the course AB. Now, 2DG = 2GK+2KL + 2LD; but 2KL = IL is the departure of the course AB, and 2LD = MG is the depar- ture of the course BC ; consequently, 2GB = 2 GK+ IL + MC; hence, the double meridian distance of a course, is equal to the double meridian distance of the preceding course SEC. Ill] DOUBLE MERIDIAN DISTANCES. 113 plus the departure of tliat course plus tlie departure of the course itself; if there is no preceding course, the first two terms become zero. We therefore have the following RULE. I. The double meridian distance of the first course is equal to its departure. II. The double meridian distance of the second course is equal to the double meridian distance of the first course^ plus its departure, plus the departure of the second course. III. The double meridian distance of any course is equal to the double meridian distance of the preceding course, plu^ its departure, plus the departure of the course itself 27. Eemark. It should be recollected that plus is here used in its algebraic sense, and that when the double me- ridian distance of a course and the departure which is to be added to it, are of different names, that is, one east and the other west, they will have contrary algebraic signs ; hence, their algebraic sum will be expressed by their dif- ference, with the sign of the greater prefixed to it. If the assumed meridian cuts the enclosure, the double meridian distances, estimated to the lefb, must be taken with the minus sign. The double meridian distance of the last course should be equal to the departure of that course. A verification of the work is, therefore, obtained by comparing this double meridian distance with the departure of the course. 28. To apply the above rule to the particular example already considered (Art. 21), rule a new table as below, in which are entered the balanced northings and southings, and the balanced eastings and westings. In this table there is but a single column for the dif- ferences of latitude, and a single column for the departures. The + sign shows when the difference of latitude is north, and the — sign when it is south. The + sign also shows when the departure is east, and the — sign when it is west. 8 114 ELEMENTS OF SURVEYING. [BOOK II. Sta. Bearings. Distances. Dif. Lat. Dep. D. M. D. 1 2^ 3 4 N 81i° W N 62f ° B S 86° E s 451-° W 10. 9.25 7.60 10.40 + 8.71 + 4.40 -6.01 -7.10 -5.24 + 8.21 + 4.46 -7.43 + 17.91 - 7.43 - 5.24 + 5.24 8.21 + 8.21 + 8.21 + 4.46 + 20.88 +20.88 + 4.46 - 7.43 + 17.91 We see, from inspecting the notes, tliat 2 is the most "westerly, and 4 the most easterly station. Either of them may, therefore, be taken for the principal station. Let us assume 2 for the principal station, and distinguish it by a star, thus *. Having done so, we enter the departure 8.21 in the column of double meridian distances, which gives the double meridian distance of the first course. The double meridian distances of the other courses are calculated ac- cording to the rule ; and as the last, opposite to station 1, is equal to the departure of the course, the work is known to be right. 29. Having shown the manner of computing the double meridian distance of each course, we shall now deduce a rule for finding the AEEA. Let us still consider the same example. We will first write the differences of latitude and the double meridian distances of the courses, in the following table. SEC. Ill] THE AREA. 115 Stations. Dif. of Latitude. D. M. D. Area. + Area. 1 + cB + 2ha 2cAB 2* + Bs + 2qp 2BsG 3 -yD + 2nh 2ms GD 4 -Df + 2ed 2cmDA It is evident, tliat cB multiplied by 2ha = cA^ will give double the area of the triangle cAB. But cB and la are both plus ; hence, the product will be plus, and must be put in the column of plus areas. Double the area of the triangle BsG^ is equal to Bs multiplied by 22'p, which product is also plus. The area of the trapezoid msGD is equal to yD = ms multiplied by nh (Geom., Bk. lY., Prop. YII., S.) ; hence, double the area is equal to yD into 2nh. But since yD is minus, and 2nh plus, it follows that the product will be negative ; hence, it must be placed in the column of nega- tive areas. Double the area of the trapezoid cADm, is equal to Df-=mc multiplied by 2de: but, since Df is negative and 2de positive, the product will be negative. It is now evident that the difference between the two columns is equal to twice the contents of the figure ABGD : and since the same may be shown for any other figure, we may write, for finding the areas, the following general RULE. I. Multiply the double meridian distance of each course by its northing or southing, observing that like signs in the multi- plicand and multiplier give plus in the product^ and that un- like signs give minus in the product. II. Place all the products which have a plus sign, in one column, and all the products which have a minus sign, in an- other. III. Add up the columns separately and take their difference : this difference will be double the area of the land. 116 ELEMENTS OF SURVEYIIfG. [BOOK 11. SO. We will now make tlie calculations in numbers. Having balanced tbe work, we can place it in tbe follow- ing table. Sta. Beanngs. rsst. Dif. Lat. Dep. D. M. D. Ares. + Area. 1 N 31iO W 10. + 8.71 -554 + 5.24 45.6404 2* N62JOE 9.25 + 4.40 + 8.21 + 8.21 36.1240 3 S 36° E 7.60 -6.01 + 4.46 + 20.88 125.4888 4 S45iOW 10.40 -7.10 -7.43 + 17.91 127.1610 81.7644 252.6498 81.7644 Area in square chains Dividing by 10 . , . Am. BjI. 2R. 7P. 22170.8854 85.4427 8.54427 4 2.17708 40 r . 7.08320 Observing in tbe field notes that station 2 is the most westerly point of the land, we assume the meridian wMcb passes through this point, as the one from which the me- ridian distances are to be calculated. We mark the prin- cipal station with a star. Opposite station 2, we enter, in the column of double meridian distances, headed D. M. D., the departure of the course from 2 to 3, which is the double meridian distance of that course, and plus. To this we add the departure of the course, and also the departure of the next course : their sum is the double meridian distance of the course from 3 to 4. To the last sum add the departure opposite station 3, and the minus departure opposite station 4 : their algebraic sum is the double meridian distance from 4 to 1. To the last sum add the last departure, which is minus, also the next departure which is likewise minus : this will give the double meridian distance of the course from 1 to 2, which is equal to its departure. Then forming the products, adding them together, ta- king their difference, and dividing it by 2, according to the rule, we obtain the contents of the ground. SEC. Ill] OF PLOTTING. OF PLOTTING. 117 81. It only remains to make a plot of the ground. For this purpose, draw any line, as NS, to represent the me- ridian passing through the princi- pal station ; and on this line take any point, as B, to represent that station. FIRST METHOD. Having fixed upon the scale on which the plot is to be made, lay off from B on the meridian, a distance Bs equal to the difference of latitude of the first course, and at s erect a perpendicular to the meridian, and make it equal to the departure of the first course : then draw BO^ which will be the first course. Through G draw a meridian, and make Cf equal to the difference of latitude of the second course, and through / draw a perpendicular /D, and make it equal to the depar- ture of the second course : draw GD, and it will be the second course. Lay down, in the same manner, the courses DA and ABj and the entire plot will be completed. SECOND METHOD, The work may be plotted in another manner, thus. At the principal station B^ lay off an angle equal to the bearing from B to (7, which will give the direction of BG. Then, from the scale of equal parts, make BG equal to the first course, this will give the station G. Through G draw a meridian, and lay off an angle equal to the bearing from G to i), and then lay off the course GD. Do the same for the bearing at D and the course DA ; also, for the bearing at A and the course AB^ and a 11! ELEMENTS OF SURVEYING. [BOOK 11. complete plot of tlie ground will thus be obtained. If the work is all right, the last line AB will exactly close the figure. This plot is made on a scale of 10 chains to an inch. 1. It is required to determine the contents and plot of a piece of land, of which the following are the field notes, viz. Stations. Bearings. Distances, 1 N 461° W 20 ch. 2 N 51|° E 13.80 8 E 21.25 4 S56°E 27.60 5 S 33i° W 18.80 6 N74i° W 80.95 CALCULATIOlSr. Sta- tiODB. Bearings. Dis. Dif. Lat. Dep. BALANCED. D.M.D. + AREA. + AREA. N + S E + W Lat. Dep. 1 N 46iO W 20 ch 13.T7 14.51 +13.88 -14.56 14.56 202.0928 2* N 51J0 E 13.80 8.54 10.84 +8.61 +10.81 10.81 93.0741 3 E 21.25 21.25 +21.20 42.82 4 S 5G0 E 27.60 15.44 22.88 —15.29 +22.82 86.84 1327.7836 5 S 33iO W 18.80 15.72 10.31 -15.63 -10.36 99.30 1552.0590 6 N 74iO W 30.95 8.27 29.83 +8.43 -29.91 59.03 497.6229 Sum of courses r32.4U 30.58 31.16 30.58 54.97 54.65 54.65 792.7898 2879.8426 792.7898 Erro innoi thing . . 0.58 0.32 Er or in We sting 2 )2087.0528 Jlns. 104.4 liJ 16P 1043.5264 Plot of the example. SEO. III.] PROBLEMS. 119 82. Eemakk. "When a bearing is due east or west, the error in latitude is nothing; the course must then be sub- tracted from the sum of the courses, and the remainder taken in balancing the columns of latitude. In the last example, the 3d bearing is due east, and the first term of the several proportions for error in latitude, was 132.40 — 21.25 = 111.15. In like manner, if a bearing is due north or south, the error in departure is nothing ; and the sum of the courses must be diminished by this course, before balancing the columns of departure. 2. Eequired the contents, and plot of a piece of land, of which the following are the field notes. Stations. Bearings. Distances. 1 S 34° W 3.95 ch. 2 S 4.60 3 S 36i° E 8.14 4 N 59i° E 3.72 5 N25° E 6.24 6 ]sri6° w 3.60 7 N65° W 8.20 Am. lOA. OB. bP. 3. Eequired the contents and plot of a piece of land, from the following field notes. Stations. Bearings. Distances. 1 S 40° W 70 rods 2 N45° W 89 3 N36° E 125 4 N 54 5 S 81° B 186 6 S 8°W 137' 7 W 130 Am. 201 A. SB. 33P. 120 ELEMENTS OF SURVETIN-G. [BOOK 11. 4. Eequired tlie contents and plot of a piece of land, from the following field notes. stations. Bearings. Distances. 1 S 40i° E 81.80 ck 2 N54° E 2.08 3 N 29i° E 2.21 4 N 28f ° E 85.35 5 N57° W 21.10 6 S 47° W 81.80 Ans. 92A. SB. 32P. 5. Eequired tlie area of a survey of wHcli the follow- ing are the field notes. Stations. Bearings. Distances. 1 N 42° E 5.00 ch. 2 East. 4.00 8 N 9° E 4.00 4 S 69° E 5.56 5 S 86° E 7.00 6 S 42° W 4.00 7 S 75° W 10.00 8 N 39° W 7.50 If, in this example, we assume 1 as the principal sta- tion, the double meridian distances will all be plus, and the positive area will exceed the negative. In balancing we shall find the error in southing to be .28 ch. and in westing .22 ch. The area is 13^. OR IIP. It should however be remarked, that in all the examples the answers may be slightly varied by distributing the corrections. 6. What is the area of a survey of which the following are the field notes. SEC. Ill] PROBLEMS. 121 Stations. Bearings. Distances. 1 N 75° 00' E 54.8 rods. 2 N 20° 30' B 41.2 3 East. 64.8 4 S 83° 30' W 141.2 . 5 S 76° 00' W 64.0 6 Nortli. 36.0 7 S 84° 00' W 46.4 8 N 63° 15' W 46.4 9 N 36° 45' E 76.8 10 N 22° 30' E 56.0 11 S 76° 45' E 48.0 12 S 15° 00' W 43.4 13 S 16° 45' W 40.5 1 In this survey 4 is the most easterly and 9 the most westerly station. The area is equal to 110^. 2B. 23P. It may vary a little, on account of the way in which the balancing is done. 7. What are the contents of a piece of land of which the following are the field notes? stations. Bearings. Distances. 1 S 75° W 13.70 ch. 2 S 20i° W 10.30 3 West. 16.20 4 N 33i° E 35.30 5 N76° E 16.00 6 South. 9.00 7 ]Sr84° E 11.60 8 S 531° E 11.60 9 S 36f ° W 19.20 10 S 22i° W 14.00 11 N 76f ° W 12.00 12 N15° E 10.85 13 N 161° E 10.12 122 ELEMENTS OF SURVEYING. [BOOK IL In this survey 4 is tlie most westerly station and 9 tlie most easterly. The area is llOA. 2R. 23P. The result may, however, as in the other examples, be slightly varied by the balancing. 8. What is the area of a survey of which the following are the notes? stations. Bearings. Distances. 1 S 46^ E 80 rods 2 S 5ir w 55.20 3 West. 85 4 N66° W 110.40 6 N 33i° E 75.20 6 S 74^° E 123.80 Arts 104^. \R. 16P. I. To determine the contents and houndary of a piece of land, hy means of offsets from the principal lines. 83. An offset is a line measured perpendicular to a course, and may lie either on the right or left of it. Let ABCDE be a piece of ground to be surveyed. Let us suppose it to be bounded on the west and north by a fence and road, and on the east and south by a creek or river. Assume as stations the prin- cipal points J., Bj G, D, and E. Take, with the compass, the bear- ings from A to B, from B to C^ from G to Z), from D to E, and from Eio A', and measure the dis- tances AB, BG, GD, BE, and EA. At convenient points of the course AB, as a, c, and f measure the offsets oh, cd, fg. Then, having measured these lines, as also the distances Aa, ac, cf, and fB, enough REO. Ill] PROBLEMS. 123 will be known to determine tlie area wMcli lies without tlie station line AB. The points 5, d and ^, of the fence which runs from A to B^ are also determined. Erect, in a similar manner, offsets to the other courses, and determine the areas which lie without the station lines. These several areas being added to the area within the station lines, will give the entire area of the ground. If the offsets fall within the station lines, the corres- ponding area must be subtracted from the area which is bounded by the station lines. II. To determine the hearing and distance from one point to another, when the points are so situated that one cannot he seen from the other. 34. Let A and G be the two points, and AB a meridian pass- ing through one. of them. From either of them, as A^ measure a course J.2, of a convenient length in the direction towards C, and take the bearing with the com- pass. At 2, take the bearing of a second course, and measure the distance to 3. At 3, take a third bearing and measure to 4. At 4, take the bearing to (7, and measure the distance from 4 to C. Then, the difference between the sum of the northings and the sum of the southings wiU be represented by AB, and the difference between the sum of the eastings and the sum of the westings by BO. The base AB, and the perpendicular BC of the right-angled triangle ABG, are then known. The angle at the base, BAG, is the bearing from J. to O ; or the equal alternate angle at G is the bearing from G to A, and the hypothenuse AG ib the distance. 35. Having measured the bearings and courses on the field, form a table, and find the base and perpendicular of the right-angled triangle, in numbers. 124 ELEMENTS OF SURVEYING. [BOOK II. Stations. Bearings. Distances. N. s. E. w. 1 Ner w 40cli 19.39 34.98 2 N42°W 41. 30.47 27.43 3 N12°E 16.10 15.75 3.35 4 N47°E 32.50 22.16 23.77 AB = 87.77 27.12 62.41 27.12 (7j5= 35.29 ch. Eemark. Had any of the courses run south, AB would have / been equal to the sum of the ^X northings, minus the sum of the J southings. 3I \ " To find the angle BAG, or the \ \ bearing from A to C. As radius : tan ^ : : AB : BO, or AB : BC :: B : tan A : that is. ^\^ Vi- A As AB 87.77 . ar. comp. : BO 35.29 : : B 8.056654 1.547652 10. : tan A 21° 54' 12" 9.604306 To find the distance AC. As sin A 21° 54' 12" ar. comp. : B : : BO 35.29 . , . . 0.428242 10. 1.547652 : ^C94.6 .... 1.975894 Hence, the bearing and distance are both found. OF SUPPLYING OMISSIONS IN THE FIELD NOTES. 36. The last problem affords an easy method of finding the bearing and length of one of the courses of a survey, SEC. Ill] PROBLEMS. 125 wlien tlie bearings and lengths of all the others are known. It may be necessary to use this method when there are obstacles which prevent the measuring of a course, or when the bearing cannot be taken. Indeed, two omissions may in general be supplied by calculation. It is far better, however, if possible, to take all the notes on the field. For, when any of them are supplied by calculation, there are no tests by which the accuracy of the work can be as- certained, and all the errors of the notes affect also the parts which are supplied. 1. In a survey we have the following notes stations. Bearings. Distances. 1 2 3 4 N 31i° W N 62f ° E Lost. S 45i° W 10 ch. 9.25 Lost. 10.40 What is the bearing and distance from station 3 to 4 ? ^^ ( Bearing, S 38° 62' E. ^* 1 Distance, 7.03 ch. 2. In a survey we have the following notes: stations. Bearings. Distances. 1 S 401" B 31.80 ch. 2 N54° B 2.08 3 Lost. Lost. 4 N 281° E 35.35 5 N57° W 21.10 6 S 47° W 31.30 What is the bearing and distance jfrom 3 to 4? ^^ (Bearing, N 34° 47' E. ' I Distance, 2.19 ch. 126 ELEMENTS OF SURVEYING. [BOOK II. III. To determine the angle included between any two courses^ when their bearings are known. 87. Let NS be a meridian passing through A. Let AB, AC, AH, AD, and AF, be five courses running from A. We readily deduce the following PRINCIPLES. ^(7 is N 26^ AH is N 65^ (7^5^=39° AB is N 46° E AG is N 26° W CAB = 12' When the meridional letters are alike, and those of depar- ture also alike, the difference of the hearings is the angle between the courses. When the meridional letters are alike, and those of depar- ture unlike, the sum of the bear- ings is the angle between the AGi& N 26° W AD is s m" w C4i> = 180°-92°=88° AC is N 26° W AF is S m° E CAi^=180°-40°=140° When the meridional letters are unlike, and those of depar- ture alike, the angle betiveen the courses is equal to 180°, minus the sum of the bearings. When the meridional letters are unlike, and those of depar- ture also unlike, the angle be- tween the courses is equal to the difference of the bearings taken from 180°. Eemark. The above principles are determined, under the supposition that the two courses are both run from the angular point. Hence, if it be required to apply them to SEC. Ill] OF DIVIDING LAND. 127 two courses run in tlie ordinary way, as we go around the field, tlie bearing of one of tliem must be reversed before the calculation for the angle is made. 1. The bearings of two courses, from the same point, are N 37° E, and S 85° W : what is the angle included between them? Ans. 132°. 2. The bearings of two adjacent courses, in going round a piece of land, are N 39° W, and S 48° W : what is the angle included between them? Ans. 87°. 3. The bearings of two adjacent courses, in going round a piece of land, are S 85° W, and N 69° W : what is the angle included between them? Ans. 154°. 4. The bearings of two adjacent courses, in going round a piece of land, are N 55° 30' E, and S 69° 20' E : what is the angle included between them? Ans. 124° 50'. OF DIVIDING LAND. 38. Fields are so variously shaped that it is difficult to give rules that will apply to all cases. It is by practice alone that facility is obtained in that branch of survey- ing relating to the division of estates. We shall add only a few examples that may serve as general guides in the application of the principles of Plane Geometry to such cases as may arise. I. To run a line from the vertex of a triangular field which shall divide it into two parts, having to each other the ratio of M to N. 39. Let ABG be any triangular field. Divide the side BC into two parts, such that (Geom., Bk. IV., Prob. 1.) BD I DC '.: m : w, ^ and draw the line AD: B D then will, ABD : DAG : : m : n. 128 ELEMENTS OF SURVEYING. [BOOK II. For, tlie two triangles ABD^ ADG having tlie same alti- tude are to each other as their bases (Geom., Bk. IV., P. 6, C): hence, the triangle is divided into parts having the ratio of m to n. II. To run a line parallel to one side of a triangular field, that shall form with the parts of the two other sides a triangle equivalent to the — part of the field. 40. Let OBA represent a triangular field and CA the side parallel to which the dividing line is to be drawn. On the side BC describe a semicircle : then divide BC at JD, so that BD '. BC '.: m : n. At D, erect the perpendicular BG to the diameter BO, and draw BG. Then, with ^ as a centre, and BG as a radius, describe the arc of a circle cutting BC at M Through E draw UF parallel to CA, and it will divide the triangle in the required ratio. For, (Geom., Bk. IV., P. 23.) BG^=BE' = BCxBD: „ o BD or, BE^ = BC''X jg^', whence, be"" '. BG" \: BD '. BC :: m : n. But, since the triangles BEF, BCA are similar, BE"" : BC" '.'. BEF : BCA. Wherefore, from equality of ratios, BEF : BCA : : m : n ; m and BEF=-xBGA. Eemark. The points E and F may easily be found by computation. For, since M^'^BCxBD, and BD = ~xBC, SEC. Ill] OF DIVIDING LAND. 129 BE'' = BG''x-',otBE we have In like manner BF= BA V — n = BG\f^. • EXAMPLE. Let it be required to divide tlie trian- gular field CAB, in whicli AG^'^ ch. AB = 11 ell. and GB — 1 ch. into two sucli parts that ABE shall be one-fourth of the whole field. In this case, we have m = 1, w = 4, and " ' hence, AE-- n ^42 4 ch. 50 1. and AB = b ch. 50 1. III. To run a line from a given point in the houndary of a piece of land, so as to cut off, on either side of the line, a given portion of the field. 41. Make a complete survey of the field, by the rules already given. Let us take, as an example, the field whose area is computed at page 118. That field contains lOAA IB 16P, and the following is a plot of it. Let it now be required to run a line from station A, in such a manner as to cut off on the left any part of the field; say, 26A 2B 31P. 130 ELEMEN-TS OF SURVEYING. [BOOK II. It is seen, by examining tlie field, that the division line will probably terminate on the course CD. Therefore, draw a line from A to G, which we will call the first closing line. The bearings and lengths of the courses AB, BO^ are always known ; and in the present example are found in the table on page 118 : hence, the bearing and distance from G to A, can be calculated by Art. 85: they are in this example, Bearing S 9° 28' E : Course 22.8 ch. Having calculated the bearing and length of the closing line, find, by the general method, the area which it cuts off: that area, in the present case, is 13A ^R 3P. It is now evident that the division line must fall on the right of the closing line AC^ and must cut off an area ACH, equal to the difference between that already cut off, and the given area : that is, an area equal 26.1 2R 31P given area, 13^1 2>R 2>P area already cut off, to . . . 12^ 3i? 28P. Since the bearing of the next course GD, and the bear- ing of the closing line AG are known, the angle AGD which they form with each other, can be calculated, and is in this example 80° 32°. Hence, knowing the hypothenuse AG, and the angle AGG at the base, the length AG of the perpendicular let fall on the course GD, can be found, and is 22.49 chains. Since the area of a triangle is equal to its base multi- plied by half its altitude, it follows, that the base is equal to the area divided by half the altitude. Therefore, if the area 12^ ZR 28P be reduced to square chains, and divided by 11.24^ chains, which is half the perpendicular A G, the quotient, which is 11.58 chains, will be the base GK Hence, if we lay off from G, on GI), a distance Gff, equal to 11.58 chains, and SEC. IV.] PUBLIC LANDS. 131 then run tlie line AH^ it will cut off from the land the re- quired area. Eemark I, If the part cut off by the first closing line, should exceed the given area, the division line will fall on the left of AG. Eemark II. If the difference between the given area and the first area cut off, divided by half the per- pendicular AG, gives ^ quotient larger than the course CD; then, draw a line from A to X>, and consider it as the first closing line, and let fall a perpendicular on DE. Remark III. When the point from which the divi- sion line is to be drawn, falls between the extremities of a course, dividing the course into two parts, con- sider one of the parts as an entire course, and the other as forming a new course, having the same bearing. The manner of making the calculation will then be the same as before. SECTION IV. PUBLIC LANDS — VARIATION" OF THE NEEDLE. 1. Soon after the organization of the present govern- ment, several of the states ceded to the United States large tracts of wild land, and these, together with the lands since acquired by treaty and purchase, constitute what is called the public lands, or public domain. Previous to the year 1802, these lands were parcelled out without reference to any general plan, in consequence of which the titles often conflicted with each other, and in many cases, several grants covered the same premises. In the year 1802, the following method of surveying the public lands, was adopted by Colonel Jared Mansfield, then surveyor-general of the North- Western Territory. 2. The country to be surveyed is first divided by meridians, six miles distance from each other ; and then 132 ELEMENTS OF SURVEYING. [BOOK II. again, by a system of east and west lines, also six miles from each other. The country is thus divided into equal squares, which are called townships. Hence, each township is a square, six miles on a side, and contains thirty-six square miles. 3. For the purpose of illustration, we have obtained from the general land offi.ce the accompanying map, which represents a considerable portion of the State of Arkansas. The principal meridian in this Survey is called the 5th meridian, and passes through the point of junction of the White river and the Mississippi. The principal base line, running east and west, intersects this meridian a little to the east of White river ; and from the meridian and base line, reckoned from this point of intersection, all the ranges of townships are laid off. For example, 1 North, will apply to all the townships lying in the first row north of the base line : 1 South, will apply to all the townships in the first row south of the base hne. Eange 1 East, will apply to all the townships lying in the first row, east of the 5th meridian : and range 1 West, will apply to all lying in the first row to the west of it. The small figures designate the rows of townships, reckoned north and south from the base line, and the ranges reckoned east and west from the 5th meridian. Thus, township 1 North, range 4 West, has its exact place designated, and may be immediately located. 4. The principal meridians, and the principal base lines are established by astronomical observation, and the lines of subdivision run with the compass. For convenience in making surveys, and for the purpose of designating particular localities, a state or large tract, is often divided into parts called "Districts." There are three such districts in the map before us, the boundaries of which are designated by the full dark lines. 5. Each township is divided into equal squares, by me- ridians one mile apart, and by east and west lines at the same distance from each other. Hence, each township is divided into 36 square miles, each one of which is called 134 ELEMENTS OF SURVEYING. [BOOK IL a section. The sections of a township are numbered from 1 to 36, beginning at the north-east angle, and each con- tains 640 acres. The diagram exhibits the 36 sections of a township. 6 5 4 3 2. 1-- 7 8 9 10 11 12 18 17 16 15 14 13 19 20 21 22 1 23 24 30 29 28 27 26 25 31 32 33 34 35 36 To describe a section accurately, we say, section num- ber 5, in township number 4 north, in range 3d west of a known meridian ; the one, for example, drawn through the mouth of White river. The description fixes precisely the place of the section. Go to the 3d range of townships, west of the known meridian, find township number 4 north, in this range, and lastly, section number 5 of that town- ship. The corners of the sections should be marked bj permanent corner-posts, or by lines blazed on trees. 6. The sections are divided into half sections, quarter sections, and even into eighths of sections. The following table shows the contents of a township, and its subdivi- sions : 1 township = 36 sections = 23040 acres. 1 section = 640 acres. i section = 320 acres. •^ section = 160 acres. \ section = 80 acres. SEC. IV.] VARIATION OF THE NEEDLE. 135 VARIATION OF THE NEEDLE. 7. The angle which the magnetic meridian makes with the true meridian, at any place on the surface of the earth, is called the variation of the needle at that place, and is east or west, according as the north end of the needle lies on the east or west side of the true meridian. 8. The variation is different at different places, and even at the same place it does not remain constant for any length of time. The variation is ascertained by comparing the magnetic, with the true meridian. 9. If we suppose a line to be traced through those points on the surface of the earth, where the needle points directly north, such a line is called the liiie of 7io variation. At all places lying on the east of this line, the variation of the needle is west ; at all places lying on the west of it, the variation is east. 10. The public is much indebted to Professor Loomis, for the valuable results of many observations and much scientific research, on the dip and variation of the needle, contained in the 39th and 42d volumes of Silliman's Journal. The variation at each place was ascertained for the year 1840 ; and by a comparison of previous observations and the application of known formulas, the annual motion, or change in variation, at each place, was also ascertained, and both are contained in the tables which follow. 11. If the annual motion was correctly found, and con- tinues uniform, the variation at any subsequent period can be ascertained by simply multiplying the annual motion by the number of years, and adding the product, in the algebraic sense, to the variation in 1840. It will be ob- served that all variations west are designated by the plus sign ; and all variations east, by the minus sign. The an- nual motions being all west, have all the plus sign. 136 ELEMENTS OF SURVEYING. [BOOK II 12. Our first object will be to mark tbe line, as it was in 1840, of no variation. For this purpose we sball make a table of places lying near this line. PLACES NEAE THE LINE OF NO VARIATION. Place. Latitude. Longitude. Variation. An. Motion. A Point. 40° 53' 80° 13' 0° 00' + 4'.4 Cleveland, 0. 41 31 81 45 -0 19 4.4 Detroit, Mich. 42 24 82 58 -1 56 4 Mackinaw. 45 51 84 41 -2 08 3.9 Marietta, 0. 39 30 81 28 -1 24 4.3 Charlottesville, Ya. 39 02 78 30 + 19 3.7 Charleston, S. C. 32 42 80 04 -2 44 1.3 At the point whose latitude is 40° 53', longitude 80° 13', the variation of the needle was nothing in the year 1840, and the direction of the line of no variation, traced north, was N 24° 35' west. The line of no variation, pro- longed, passed a little to the east at Cleveland, in Ohio — the variation there being 19 minutes east. Detroit lay still further to the west of this line, the variation there being 1° 66' east; and Mackinaw still further to the west, as the variation at that place was 2° 08' east. The course of the line of no variation, prolonged south- erly, was S 24° 35' E. Marietta, in Ohio, was west of this line — the variation there being 1° 24' east. Charlottesville, in Virginia, was a little to the east of it — the variation there being 19' west ; whilst Charleston, in South Carolina, was on the west, — the variation there being 2° 44' east. From these results, it will be easy to see about where the line of no variation is traced in our own country. 13. We shall give two additional tables: SEC. IV.] VARIATION OF THE NEEDLE. 137 PLACES WHERE THE VARIATION WAS WEST. Places. Latitude. Longitude. Variation. An. Motion. Angle of Maine. 48° 00' 67° 37' + 19° 30' + 8'.8 Waterville, Me. 44 27 69 32 12 36 5.7 Montreal. 45 31 73 35 10 18 5.7 Keesville, N. Y. 44 28 73 32 8 51 5.3 Burlington, Yt. 44 27 73 10 9 27 5.3 Hanover, N. H. 43 42 72 14 9 20 5.2 Cambridge, Mass. 42 22 71 08 9 12 5 Hartford, Ct. 41 46 72 41 6 58 5 Newport, E. I. 41 28 71 21 7 45 5 Geneva, N. Y. 42 52 77 03 4 18 4.1 West Point. 41 25 74 00 6 52 4 New York City. 40 43 71 01 5 34 3.6 Philadelpliia. 39 57 75 11 4 08 3.2 Buffalo, N. Y. 42 52 79 06 1 37 4.1 PLACES WHERE THE VARIATION WAS EAST. Places. Latitude. Longitude. Variation. An. Motion. Mouth, of Colum- 1 bia Eiver. j 46° 12' 123° 30' -2r 40' Unknown. Jacksonville, 111. 39 43 90 20 8 28 + 2'.5 St. Louis, Mo. 38 37 90 17 8 37 2.3 Nashville, Tenn. 36 10 86 52 6 42 2 Louisiana, at 29 40 94 00 8 41 1.4 Mobile, Ala. 30 42 88 16 7 05 1.4 Tuscaloosa, Ala. 33 12 87 43 7 26 L6 Columbus, Geo. 32 28 85 11 5 28 2 Milledgeville, " 33 07 83 24 5 07 2.4 Savannah, " 32 05 81 12 4 13 2.7 Tallahassee, El. 30 26 84 27 5 03 1.8 Pensacola, " 30 24 87 23 5 53 1.4 Logansport, Ind. 40 45 86 22 5 24 2.7 Cincinnati, 0. 1 39 06 84 27 4 46 3.1 138 ELEMENTS OF SURVEYING. [BOOK II. METHODS OF ASCERTAINIKG THE VARIATION". 14. The best practical metliod of determining the true meridian of a place, is bj observing the north star. If this star were precisely at the point in which the axis of the earth, prolonged, pierces the heavens, then, the intersection of the vertical plane passing through it and the place, with the surface of the earth, would be the true meridian. But, the star being at a distance from the pole, equal to 1° 30' nearly, it performs a revolution about the pole in a circle, the polar distance of which is 1° 30' : the time of revo- lution is 23 h. and 56 min. To the eye of an observer, this star is continually in motion, and is due north but twice in 23 h. 6Q min. ; and is then said to be on the meridian, Now, when it departs from the meridian, it apparently moves east or west, for 5 h. and 59 min., and then returns to the meridian again. When at its greatest distance from the meridian, east or west, it is said to be at its greatest eastern or western elongation. The following tables show the times of its greatest eastern and western elongations : EASTERN ELONGATIONS. Days. April. May. June. July. August. Sept. H. M. H. M. H. M. H. M. H. M. H. M. 1 18 18 16 26 14 24 12 20 10 16 8 20 7 17 56 16 03 14 00 11 55 9 53 7 58 13 17 34 15 40 13 35 11 31 9 30 7 36 19 17 12 15 17 13 10 11 07 9 08 7 15 25 16 49 14 53 12 45 10 43 8 45 6 53 WESTERN ELONGATIONS. Days. Oct. Nov. Dec. Jan. Feb. March. H. M. H. M. H. M. H. M. H. M. H. M. 1 18 18 16 22 14 19 12 02 9 50 8 01 7 17 56 15 59 13 53 11 36 9 26 7 38 13 17 34 15 35 13 27 11 10 9 02 7 16 19 17 12 15 10 13 00 10 44 8 39 6 54 25 16 49 14 45 12 34 10 18 8 16 6 33 SEC. IV.] VARIATION OF THE NEEDLE. 139 The eastern elongations are put down from tlie first of April to the first of October ; and the western, from the first of October to the first of April ; the time is computed from 12 at noon. The western elongations in the first case, and the eastern in the second, occurring in the daytime, cannot be used. Some of those put down are also invisi- ble, occurring in the evening, before it is dark, or after day- light in the morning. In such case, if it be necessary to de- termine the meridian at that particular season of the year, let 5 h. and 59 min. be added to, or subtracted from, the time of greatest eastern or western elongation, and the observ- ation be made at night, when the star is on the meridian. 15. The following table exhibits the angle which the me- ridian plane makes with the vertical plane passing through the pole-star, when at its greatest eastern or western elon- gation: such angle is called the azimuth. The mean angle only is put down, being calculated for the first of July of each year: AZIMUTH TABLE. Year. Lat. 32° Azimuth. Lat. 34° Azimuth. Lat. 36° Azimuth. Lat. 38° Azimuth. Lat. 40° Azimuth Lat. 42° Azimuth. Lat. 440 Azimuth. 1851 1° 451' r48' 1° 501' 1° 53I' r 56f' 2° 001' 2° 041' 1852 1°45' 1° 47i' 1°50' 1° 53' 1° 561' 1° 59f' 2° 03|' 1853 1° 441' 1°47' 1° 49f' 1° 521' 1° 55|' 1° 591' 2° O31' 1854 l°44i' 1° 461' 1° 49i' 1°52' r 551' 1°69' 2° 02|' 1855 1° 431' 1° 461' 1° 48f' 1° 51f' l°54f' 1° 581' 2° 021' 1856 1° 43i' 1° 45f' 1° 481' r 511' l°54i' 1°58' 2° Olf 1857 1°43' 1° 45i' 1°48' 1° 50f' 1°54' 1° 571' 2° Oil' 1858 1° 42i' r 44|' r 471' 1° 501' 1° 531' 1°57' 2° OOf'l 1859 1°42' l°44i' 1° 47/ 1° 49f' 1°53' 1° 561' 2° 001' 1860 1° 41f ' 1°44' 1° 46J' 1° 491' 1° 521' r 56' 2° 00' 1861 1° 41i' r 431' 1° 461' 1°49' r 521' r 551' 1° 59r 140 ELEMENTS OF SURVEYING. [BOOK II, The use of tlie above tables, in finding tbe true meri- dian, will soon a,ppear. TO FIND THE TEUE MERIDIAN WITH THE THEODOLITE. 16. Take a board, of about one foot square, paste wliite paper upon it, and perforate it through the centre ; the diameter of the hole being somewhat larger than the diam- eter of the telescope of the theodolite. Let this board be so fixed to a vertical stafi", as to slide up and down freely : and let a small piece of board, about three inches square, be nailed to the lower edge of it, for the purpose of hold- ing a candle. About twenty-five minutes before the time of the great- est eastern or western elongation of the pole-star, as shown by the tables of elongations, let the theodolite be placed at a convenient point and levelled. Let the board be placed about one foot in front of the theodolite, a lamp or candle placed on the shelf at its lower edge ; and let the board be slipped up or down, until the pole-star can be seen through the hole. The light reflected from the paper will show the cross hairs in the telescope of the theodolite. Then, let the vertical spider's line be brought exactly upon the pole-star, and, if it is an eastern elongation that is to be observed, and the star has not yet reached the most easterly point, it will move from the line towards the east, and the reverse when the elongation is west. At the time the star attains its greatest elongation, it will appear to coincide with the vertical spider's line for some time, and then leave it, in the direction contrary to its former motion. As the star moves towards the point of greatest elonga- tion, the telescope must be continually directed to it, by means of the tangent-screw of the vernier plate ; and when the star has attained its greatest elongation, great care should be taken that the instrument be not afterwards moved. Now, if it be not convenient to leave the instrument in its place until daylight, let a staff, with a candle or small SEC. IV.] VARIATION OF THE NEEDLE. 141 lamp -apon its upper extremity, be arranged at thirty or forty yards from the theodolite, and in the same vertical plane with the axis of the telescope. This is easily effect- ed, by revolving the vertical limb about its horizontal axis without moving the vernier plate, and aligning the staff to coincide with the vertical hair. Then mark the point di- rectly under the theodolite ; the line passing through this point and the staff, makes an angle with the true meridian equal to the azimuth of the pole-star. From the table of azimuths, take the azimuth corres- ponding to the year and nearest latitude. If the observed elongation was east, the true meridian lies on the west of the line which has been found, and makes with it an angle equal to the azimuth. If the elongation was west, the true meridian lies on th§ east of the line: and, in either case, laying off the azimuth angle with the theodolite, gives the true meridian. TO FIND THE TEUE MERIDIAN WITH THE COMPASS. 17. 1. Drive two posts firmly into the ground, in a line nearly east and west ; the uppermost ends, after the posts are driven, being about three feet above the surface, and the posts about four feet apart : then lay a plank, or piece of timber three or four inches in width, and smooth on the upper side, upon the posts, and let it be pinned or nailed, to hold it firmly. 2. Prepare a piece of board four or five inches square, and smooth on the under side. Let one of the compass- sights be placed at right angles to the upper surface of the board, and let a nail be driven through the board, so that it can be tacked to the timber resting on the posts. 3. At about twelve feet from the stakes, and in the direction of the pole-star, let a plumb be suspended from the top of an inclined stake or pole. The top of the pole should be of such a height that the pole-star will appear about six inches below it ; and the plumb should be swung in a vessel of water to prevent it from vibrating. 142 ELEMENTS OF SURVEYING. [BOOK II. This being done, about twenty minutes before tbe time of elongation, place the board, to which the compass-sight is fastened, on the horizontal plank, and slide it east or west, until the aperture of the compass-sight, the plumb- line, and the star, are brought into the same range. Then if the star depart from the plumb-line, move the compass- sight, east or west, along the timber, as the case may be, until the star shall attain its greatest elongation, when it will continue behind the plumb-line for several minutes ; and will then recede from it in the direction contrary to its motion before it became stationary. Let the compass- sight be now fastened to the horizontal plank. During this observation it will be necessary to have the plumb-line lighted : this may be done by an assistant holding a candle near it. Let now a staff, with a candle or lamp upon it, be placed at a distance of thirty or forty yards from the plumb-line, and in the same direction with it and the com- pass-sight. The line so determined, makes, with the true meridian, an angle equal to the azimuth of the pole-star; and, from this line, the variation of the needle is readily determined, even without tracing the true meridian on the ground. Place the compass upon this line, turn the sights in the direction of it, and note the angle shown by the needle. Now, if the elongation, at the time of observation, was west, and the north end of the needle is on the west side of the line, the azimuth, plus the angle shown by the needle, is the true variation. But should the north end of the needle be found on the east side of the line, the elonga- tion being west, the difference between the azimuth and the angle would show the variation : and the reverse when the elongation is east. 1. Elongation west, azimuth . . 2" 04' North end of the needle on the west, angle 4° 06' Variation 6° 10' west. SEC. IV.] VARIATION OF THE NEEDLE. 143 2. Elongation west, azimuth . . 1° 59' North end of the needle on the east, angle 4° 50' Variation 2° 51' east. 3. Elongation east, azimuth . . 2° 05' North end of the needle on the west, ande 8° 30' Variation 6° 25' west. 4. Elongation east, azimuth . . 1° 57' North end of the needle on the east, angle 8° 40' Yariation 10° 37' east. Eemark I. The variation at West Point, in Septem- ber, 1835, was 6° 32' west. Remark II, The variation of the needle should al- ways be noted on every survey made with the compass, and then if the land be surveyed at a future time, the old lines can always be re-run. 18. It has been found by observation, that heat and cold sensibly affect the magnetic needle, and that the same needle will, at the same place, indicate different lines at different hours of the day. If the magnetic meridian be observed early in the morning, and again at different hours of the day, it will be found that the needle will continue to recede from the meridian as the day advances, until about the time of the highest temperature, when it will begin to return, and at evening will make the same line as in the morning. This change is called the diurnal variation^ and varies, during the summer season, from one-fourth to one-fifth of a degree. 19. A very near approximation to a true meridian, and consequently to the variation, may be had, by remember- ing that the pole-star very nearly reaches the true meri- dian, when it is in the same vertical plane with the star Alioth in the tail of the Great Bear, which lies nearest the four stars forming the quadrilateral. 144 ELEMENTS OF SURVEYING. [BOOK II. The vertical position can be ascer- tained by means of a plumb-line. To see the spider's lines in the field of the telescope at the same time with the star, a faint light should be placed near the object-glass. When the plumb-line, the star Alioth, and the north star, fall on the vertical spider's line, the horizontal limb is firmly clamped, and the telescope brought down to the horizon ; a light, seen through a small aperture in a board, i and held at some distance by an as- " sistant, is then moved according to signals, until it is cov- ered by the intersection of the spider's lines. A picket driven into the ground, under the light, serves to mark the meridian line for reference by day, when the angle formed by it and the magnetic meridian may be measured. ,5*=-. ~r" "v 6 BOOK III. LEVELLING AND TOPOGRAPHICAL SURVEnj^G. SECTION I. OF LEVELLING. 1. Levelling is tlie art of determining tlie relative dis- tances of points from the centre of the earth. 2. A line whose points are all equally distant from the centre of the earth, is called a line of true level, and a sur- face, all whose points are equally distant from the centre of the earth, as the surface of still water, is called a level surface. 3. One point is said to be above another, when it is farther from the centre of the earth; and this difference of distance from the centre, is called the difference of level be- tween the two points. 4. A straight line drawn tangent to a line of true level at any point, is a horizontal line, and is called a line of apparent level. Thus (PL 4, Fig. 1), if G is the centre of the earth and AEF a line of true level, ABD is a line of apparent level. This is the line of level determined by an instrument. The difference between the apparent and true level at any distant station _B, as determined from A, is BE, or the excess of the secant of the arc AE over the radius. 5. To find a general formula for computing this excess, we have (Geom. B. IV., Prop. XXX.) AB'^ = BE {BE + 2EG)] but since the arc AE is very small in comparison with the 10 146 ELEMENTS OF SURVEYING. [BOOK IIL radius of the eartli, tlie arc AE will not differ sensibly from tlie tangent AB ; tlie diameter 2JEC may, for the same reason, be taken for the secant {BE + 2EC) : hence, AH BUX2EC, or dividing by 2UG, BE= 2EG (1). If we take the mean diameter of the earth to be 7919 AE^" miles, formula (1) gives BE= WKTq (2) • lience, The departure of the apparent from the true level, starting from a given point, is equal to the square of the distance to the second point, divided hy the diameter of the earth. If in formula (2) you give to AE, in succession, every value from 1 chain to any given number of chains, (say 100), and reduce at the same time both terms of the frac- tion to inches, a table may be comjDuted as below. Table showing the differences in inches between the true and ap- parent level, for distances between 1 and 100 chains. Chains. Inches. Chains. Inches. Chains. Inches. Chains. Inches. 1 .001 26 .845 51 3.255 76 7.221 2 .005 27 .911 52 3.380 77 7.412 3 .011 28 .981 53 3.511 78 7.605 4 .020 29 1.051 54 3.645 79 7.802 5 .031 30 1.125 55 3.781 80 8.001 6 .045 31 1.201 56 3.925 81 8.202 Y .061 32 1.280 57 4.061 82 8.406 8 .080 33 1.360 58 4.205 83 8.612 9 .101 34 1.446 59 4.351 84 8.832 10 .125 35 1.531 60 4.500 85 9.042 11 .151 36 1.620 61 4.654 86 9.246 12 .180 37 1.711 62 4.805 87 9.462 13 .211 38 1.805 63 4.968 88 9.681 14 .245 39 1.901 64 5.120 89 9.902 15 .281 40 2.003 65 5.281 90 10.126 16 .320 41 2.101 66 5.443 91 10.351 17 .361 42 2.208 67 5.612 92 10.587 18 .405 43 2.311 68 5.787 93 10.812 19 .451 44 2.420 69 5.955 94 11.046 20 .500 45 2.531 70 6.125 95 11.233 21 .552 46 2.646 71 6.302 96 11.521 22 .605 47 2.761 72 6.480 97 11.763 23 .661 48 2.880 73 6.662 98 12.017 24 .Y20 49 3.004 74 6.846 99 12.246 25 .781 50 3.125 75 7.032 100 12.502 SEC. 1] THE Y LEVEL. 147 Observing tliat for AE— 80 chains = 1 mile, BE is equal to 8.001 inches, or about two-thirds of a foot, and since the differences of level vary as the squares of the dis- tances, we have the following easy rule for finding the cor- rection in feet. The correction for curvature^ in feet, is equal to two-thirds of the square of the distance in miles. INSTRUMENTS. 6. Before proceeding further in the discussion of the principles of levelling, we will describe some of the in- struments used, and first, THE T LEVEL. 7. A level is an instrument used to determine horizontal lines, and the difference of level of any two points on the surface of the earth. The part of the instrument shown in PL 4, Fig. 2, rests on a tripod, to which it is permanently attached at Z, HH is a horizontal brass plate, through which four levelling screws with milled heads are passed, and worked against a second horizontal plate OG. Two of these screws, K and ij are seen in the figure. aS' is a clamp-screw, which, being loosened, allows the upper part of the instrument to turn freely around its axis. Q is a tangent-screw, by means of which the upper part of the instrument is moved gently, after the clamp-screw S has been made fast. EE is a hori- zontal bar, perpendicular to which are the wyes, designat- ed Y's, that support the telescope LB. This telescope is confined in the Y's by the loops r, r, which are fastened by the pins p and p. The object-glass B, is adjusted to its focus by the screw X; the eye-glass L slides out and in freely. The screws f f work the slide which carries the horizontal hair ; and two horizontal screws, only one of which, a, is seen, work the slide that carries the verti- cal hair. CD is an attached spirit-level. The screw N elevates and depresses the Y, nearest the eye-glass. In some instruments this Y is elevated and depressed, by means of two screws at M and R. 148 ELEMENTS OF SURVEYING. [BOOK IIL Before using this level, it must be adjusted. The ad- justment consists in bringing the different parts to their proper places. The line of collimation is the axis of the telescope. With this axis, the line drawn through the centre of the eye- glass and the intersection of the spider's lines, within the barrel of the telescope, ought to coincide. FlEST ADJUSTMENT.* To fix the intersection of the spider's lines in the axis of the telescojye. Having screwed the tripod to the instrument, extend the legs, and place them firmly. Then loosen the clamp- screw S^ and direct the telescope to a small, well-defined, and distant object. Then slide the eye-glass till the spider's lines are seen distinctly ; after Avhich, with the screw -Z", adjust the object-glass to its proper focus, when the object and the spider's lines will be distinctly seen. Note now the precise point covered by the intersection of the spider's lines. Having done this, revolve the telescope in the Y's, half round, when the attached level CD will come to the upper side. See if, in this position, the horizontal hair appears above or below the point, and in either case, loosen the one, and tighten the other, of the two screws which work the horizontal hair, until it has been carried over half the space between its last position and the observed point. Carry the telescope back to its place ; direct again, by the screws at M and i?, the intersection of the spider's lines to the point, and repeat the operation, till the horizontal hair neither ascends nor descends while the telescope is revolv- ed. A similar process will arrange the vertical hair, and the line of collimation is then adjusted. Second adjustment. To make the axis of the attached level CD parallel to the line of colliraation. Turn the screw N^ or the screws M and i?, until the * This, and some of the following adjustments, are so similar to those of the theodolite, that they would not be repeated, but that some may use the level without wishing to study a more complicated instrument. SEC. L] THE Y LEVEL. 149 bubble of the level DO stands at the middle of the tube. Then open the loops, and reverse the telescope. If the bubble still stands at the middle of the tube, the axis of the level is horizontal ; but if not, it is inclined, the bubble being at the elevated end. In such case, raise the depress- ed, or depress the elevated end, by means of the screws M and h, half the inclination ; and then with the screw iV, bring the level to a horizontal position. Eeverse the teles- cope in the Y's, and make the same correction again ; and proceed thus, until the bubble stands in the middle of the tube, in both positions of the telescope; the axis of the level is then horizontal. * Let the telescope be now revolved in the Y's. If the bubble continues in the middle of the tube, the axis of the level is not only horizontal, but also parallel to the line of coUimation. If, however, the bubble recedes from the centre, the axis of the level is inclined to the line of collimation, and must be made parallel to it, by means of two small screws, which work horizontally ; one of these screws is seen at q. By loosening one of them, and tightening the other, the level is soon brought parallel to the line of col- limation ; and then, if the telescope be revolved in the Y's, the bubble will continue at the middle of the point of the tube. It is, however, difficult to make the first part of this adjustment, while the axis of the level is considerably in- clined to the line of collimation: for, allowing the level to be truly horizontal in one position of the telescope, after it is reversed, there will be but one corresponding position in which the bubble will stand at the middle of the tube. This suggests the necessity of making the first part of the adjustment with tolerable accuracy ; then, having made the second with care, re-examine the first, and proceed thus tin the adjustment is completed. Thirb adjustment. To make the level CD and the line of collimation perpendicular to the axis of the instruments or parallel to the horizontal har EE. Loosen the clamp-screw S, and turn the bar EE, until the level DG comes directly over two of the levelling 150 ELEMENTS OF SURVEYING. [BOOK IIL screws. By means of these screws, make tlie level CD truly horizontal. Then, turn the level quite round ; if, during the revolution, it continue horizontal, it must be at right angles to the axis of the instrument about which it has been revolved. But if, after the revolution, the level CD be not horizontal, rectify half the error with the screws at M and i?, and half with the levelling screws. Then place the bar EE over the other two levelling screws, and make the same examinations and corrections as before ; and proceed thus, until the level can be turned entirely around without displacing the bubble at the centre. When this can be done, it is obvious that the level DC and the line of collimation, are at right angles to the axis of the instru- ment about which they revolve ; and since the axis is care- fully adjusted by the maker, at right angles to the bar EE^ it follows, that the line of collimation, the level DC^ and the bar EE, are parallel to each other. The level is now adjusted. When used, however, it is best to re-examine it every day or two, as the work will be erroneous unless the instrument is accurately adjusted. THE WATER LEVEL. 8. The Water Level is an instrument that possesses the advantage of never requiring adjustment^ and also of being very cheap ; in fact, any ordinary workman may con- struct one. Having no telescope, it is impossible to take long sights, but for such work as is required to be done by the ordinary surveyor, it gives very good results. Two brass cups, G and i>, about four inches in diam- eter, and from four to five inches in height, are permanent- ly attached to a hollow brass tube of three feet long and half an inch in di- Q^ Fc ameter. The cups C*! 1^ are for the purpose ^ | ' of receiving the ends E and F of two bottles, the bottoms of which have been cut off. The bottoms may be cut off by tying a string round the bottles while heated. The ends are fixed in their places with putty. SEC. L] LEVELLING STAVES. 151 The projecting axis g works in a hollow cylinder h, which, forms the top of a stand. The tube, when the level is required for use, is filled with water (colored with lake or indigo), till it nearly reaches the necks of the bottles. After placing the stand tolerably level by the eye, with- draw both corks, and the surface of the water in the bot- tles will indicate a horizontal line in whatever direction the tube is turned. This level is well adapted to tracing con- tour lines as described in the next section. LEVELLING STAVES. 9. The levelling staves are used to determine the points at which a given horizontal line intersects lines that are perpendicular to the surface of the earth, and to show the distances of such points of intersection from the ground. The levelling staff is a necessary accompaniment to either of the levels described. Several kinds are used. One of the best, consists of a staff 12 or 15 feet long, and graduated to feet, tenths, and hundredths. A sliding vane is made to move up or down by a cord and pulleys, and on the vane is a vernier, by means of which the reading of the staff may be effected to thou- sandths of an inch. . AB represents a portion of the staff, DG the moveable vane^ with an opening EF^ through which the graduation on the staff is seen. F is the vernier of the vane, the being de- termined by the transverse line DG. To render this line more distinct, the vane is divided into four quarters, and the alternate ones are painted black, which, by their contrast with the white quar- ters, ^show the line DG distinctly. 10. Another variety of levelling staff is shown in PI. 4, Fig. 3. It is formed of two pieces, each about six feet long, one of which slides in a groove of the other, and bears a vane similar to that already described. It is grad- uated to feet, inches, and eighths of an inch. The line of 162 ELEMENTS OF SURVEYING. [BOOK III. sight of the telescope is always directed to the centre of the vane. When the line of sight is less than six feet from the ground, the staff is reversed, — the vane run up the staff, and the readings made by means of the reversed figures at the right, where they are cut by the lower line of the vane. When the line of sight is more than six feet from the ground, the staff stands as in the figure, the reading is then made at the line he, and the figures indicating the height, are found on the sliding part which carries the vane. The reading of the staff, as it now stands, is seven feet. 11. Another rod is sometimes used on which the figures are marked so plainly, that they may be read by the ob- server himself, without the aid of a vane ; thus avoiding errors through ignorance or negligence of the rodman. If the telescope used, inverts the object, the figures should be made inverted on the staff, so as to appear erect. Each of the rods described, has its advantages, and either one may be used according to the circumstances of the survey. 12. There is a method of testing the adjustments of the Y level, which ought not to be neglected, since all the re- sults depend on the accuracy of the instrument. The method is this: The level being adjusted, place it at any convenient point, as G (Fig. 4). At equal distances of about 100 yards, on either side, and in the same line with the level, place the levelling staves, CE, BF. Make the level horizontal with the levelling screws. Then, turn it towards either staff, as BF, and run the vane up or down, as required, until the intersection of the hairs strikes the centre : then make the slide fast, and note carefully the height of the vane. Turn the level half round, and do the same in respect of the staff CE. Let the telescope be now reversed in the Y's. Sight again to the staff BF, and note the exact height of the vane. Let the telescope be now turned half round, and the same be done for the staff CE. If the two heights last observed, are equal to those first noted, each to each, the line of collimation is perpendicular to the axis of the SEC. L] OF LEVELLING. 153 instrument, and if the bubble has, at the same time, pre- served its place at the middle point of the tube, the instru- ment is truly adjusted. For, had the line of coUimation b§en inclined to the axis of the level, it would, in the first instance, have taken the direction AF or Ad; and when turned half round, it would have taken the direction AU or Ab. The telescope being reversed in the Y's, and again directed to the staff BF, the line of collimation would take the direction Ad or AF, and when turned to the staff CF, it would take the direction Ab or AF: and the two distances BF, Bd, or (76, GE, can only be equal to each other when the line of col- limation falls on the horizontal line gf. LEVELLING IS THE FIELD. 13. The operation of levelling may be undertaken: 1st. For the purpose of determining the difference of level between two given points. 2d. For the purpose of obtaining a section or profile along a given line, as in the- reconnoissance for a line of railroad. 3d. For the purpose of determining the contour lines in a topographical survey, as described in the next section. DIFFERENCE OF LEVEL BETWEEN TWO POINTS. 14. When it is proposed to find the difference of level of any two objects, or stations, all levels made in the di- rection of the station at which the work is begun, are called, for the sake of distinction merely, back-sights ; and levels taken in the direction of the other station, fore- Before going on the field with the level, rule three columns, as below, and head them, stations, back-sights, fore-sights. 154 ELEMENTS OF STJRVEYIN-G. [BOOK II] FIELD NOTES. Stations. + Back-Sights. — Fore-Siglits. 1 2 3 4 10 11-6 6-8 3-9 3 4-9 8-3 Sums . . - - - HI -11 16-0 16-00 Dif. of level . . . . 15-11 EXAMPLE. Find the difference of level between any tiuo points^ as A and G (PI. 4, Fig. 5.) The level being adjusted, place it at any point, as B, as nearly in the line joining A and G as may be convenient. Place a levelling staff at Jl, and another at iV, a point lying as near as may be in the direction of G. Make the level horizontal, by means of the levelling screws ; turn the telescope to the staff at A^ and direct the person at the staff to slide up the vane until the horizontal line ah pierces its centre ; then note the distance Ah (equal to 10 feet in the present example), and enter it in the column of back- sights, opposite station 1. Sight also to the staff at iVJ and enter the distance Na, equal to 3 feet, in the column of fore- sights, opposite station 1. Take up the level, and place it at some other convenient station, as C, and remove the staff at A^ to M. Having levelled the instrument, sight to the staff at N^ and enter the distance Nd^ 11 feet 6 inches, in the column of back- sights, opposite station 2 : sight also to the staff at M^ and enter the distance Mf equal 0, in the column of fore-sights, opposite station 2. SEC. I.] OF LEVELLING. 155 Let tlie level be now removed to any other station, as Z>, and tlie staff at iVJ to some otlier point, as P. Let tlie distance Mg^ equal to 6 feet 8 inches, be entered in the column of back-sights, opposite station 3, and the distance P/i, equal to 4 feet 9 inches, in the column of fore-sights. Let the instrument be now placed at E^ and the distance Pm, equal to 3 feet 9 inches, and On^ equal to 8 feet 3 inches, be entered opposite station 4, in their proper columns. It is evident from the figure, that the difference of level NF^ between A and N^ is equal to the back-sight 6 J., dim- inished by the fore-sight aN] also that the difference of level between N and M is equal to the back-sight dN^ dim- inished by the foresight 0, and since each set of obser- vations is entirely independent of every other set, we may infer that the difference of level between two points as determin- ed hy one position of tlie level, is equal to the hack-sight^ dim- inished ly the fore-sight. If the fore-sight be greater than the back-sight, the difference will be affected with a minus sign, a result which shows that the second point is lower than the first. Generally, the difference of level betiveen any two points, detei^mined as above, is equal to the sum of the back- sights diminished by the sum of the fore-sights. If the result is plus, the second point is higher than the first ; if negative, it is lower. In the example given, the difference of level between A and G, is 15 feet 11 inches. 15. In the previous example, we did not regard the dif- ference between the true and apparent level. If it be ne- cessary to ascertain the result with extreme accuracy, this difference must be considered : and then, the horizontal distances between the level, at each of its positions, and the staves, must be measured, and the apparent levels dimin- ished by the differences of level; which differences can be found from the table. 156 ELEMENTS OF SURVEYING. [BOOK IIL THE FOLLOWIlsrG IS SUCH AN" EXAMPLE. Stat. Back-sts. Distances. Fore-st. Distances. Cor.back-sights Cor. fore-sts. 1 9-8 20 ch. 1-6 32 ch. 9-7.500 1-4.720 2 8-7 25 ch. 2-4 28 ch. 8-6.219 2-3.019 8 5-2 18 ch. 3-1 16 ch. 5-1.595 3-0.680 4 10-3 29 ch. 1-9 87 ch. 10-1.949 0-11.538 5 11-0 45 ch. 2-5 72 ch. 10-9.469 1-10.520 44-2.732 9-6.477 In this example, the first column shows the stations ; the second, the back-sights; the third, the distances from the level in each of its positions to the back staff; the fourth, the fore-sights ; the fifth, the distances from the level to the forward staff; the sixth and seventh, are the colamns of back and fore-sights, corrected by the difference of level. The corrections are thus made : — The difference of level in the table corresponding to 20 chains, is 5 tenths of an inch, which being subtracted from 9 feet 8 inches, leaves 9 feet 7.5 inches for the corrected back-sights; this is entered opposite station 1 in the sixth column. The dif- ference of level corresponding to 32 chains, is 1.280 inches, which being subtracted from the apparent level, 1 foot 6 inches, leaves 1 foot 4.720 inches for the true fore-sight from station 1. The other corrections are made in the same manner. The sum of the back-sights being 44 feet 2.732 inches, and the sum of the fore-sights 9 feet 6.477 inches, it fol- lows, that the difference, 34 feet 8.255 inches, is the true difference of level. 16. In finding the true from the apparent level, we have not regarded the effect caused by refraction on the apparent elevation of objects, as well because the refraction is different in different states of the atmosphere, as because the corrections are inconsiderable in themselves. 17. The small errors that would arise from regarding the apparent as the true level, may be avoided hy placing SEC. I.] OF LEVELLING. 157 the levelling staves at equal distances from the level. In such, case, it is plain, 1st, tliat equal corrections must be made in the fore and back-sights; and, 2dly, that when the fore and back-sights are diminished equally, the result, which is always the difference of their suras, will not be affected. This method should always be followed, if practicable, as it avoids the trouble of making corrections for the dif- ference of true and apparent level. The differences between the true and apparent level, being very inconsiderable for short distances, if only ordi- nary accuracy be required, it will be unnecessary to make measurements at all. Care, however, ought to be taken, in placing the levelling staves, to have them at as nearly equal distances from the level as can be determined by the eye ; and if the distances are unequal, let the next distances also be made unequal; that is, if the back-sight is the longer in the first case, let it be made proportionably shorter in the second, and the reverse. LEVELLING FOR SECTION". 18. Having decided upon the line along which a section is to be taken, let a permanent mark be made at the be- ginning of the line : this is called a hench-mark. A bench- mark is made by drilling a hole in a rock, or by painting upon a rock or fence, or sometimes by driving a stake in the ground, with its upper end marked by a nail-head. Bench-marks should be made from time to time along the line, to serve as checks, in case a re-survey should become necessary. The operations in the field are similar to those in the last example, and the field notes are kept in the same manner, except that a new column is added for bearings, when it is necessary to make a plot of the line of survey. The total distance of each point above or below the start- ing point may be computed, and written in a separate col- umn, paying particular attention to the signs. We annex an example, in witiich the heights are estimated in feet, and decimals of a foot. 15i ELEMENTS OF SURVEYING. [BOOK III. sta- tion. DiBtances in feet. B. Sight. F. Sight. Dif. between B. S. and F. S. Total Dif. of Level. REMARKS. 1 650 2.35 14.55 -12.20 - 12.20 Commenced at bench-mark A. 2 700 3.56 9.58 - 6.02 -18.22 3 750 10.34 6.21 + 4.13 - 14.09 4 650 14.55 0.25 + 14.30 + 0.21 5 600 9.98 1.67 + 8.31 + 8.52 6 650 3.62 14.54 - 10.92 - 2.40 B.M 1.23 13.45 - 12.22 - 14.62 Bench-mark on rock. 7 500 2.23 12.05 - 9.82 - 24.44 Terminating xABMon oak tree. 8 750 6.20 19.55 - 13.35 - 37.79 The fiftli column shows the diiference of level between any two consecutive positions of the levelling staff, and is found by subtracting the fore-sight from the corresponding back-sight, and giving to the remainder the proper sign. The sixth column shows the distance of each point above or below the bench-mark J., and is obtained by continual additions of the numbers in column 5. Thus, (- 12.20) -f (- 6.02) = - 18.22 ; (- 18.22) + 4.13 = - 14.09 ; and so on. It will be seen that the point of termination is 37.79 feet below the starting point. PLOTTING THE SECTION OR PROFILE. 19. The vertical distances being generally very small as compared with the horizontal distances, two different scales become necessary in plotting a profile. In order that the vertical distances may be fully exhibited in the plan, the scale used for them is much larger than is used for lines measured in a horizontal direction. This becomes absolutely necessary where long lines of profile, with a gentle slope, are to be plotted, as is always the case in the trial section of a railroad survey. "We shall illustrate the manner of plotting, by drawing the section determined by the field- notes just given. 20. Draw a horizontal line AK^ called a datum line, and SEC. II.] TOPOGRAPHICAL SURVEYING. 159 assume some point as A, to represent tlie point of begin- ning: lay off on tlie datum line, distances equal to tlie A 650 B 700 C 750 J) 650 (1) %v ^- '^^%^0€ (3) , JE, &c., tlius determined, erect perpendiculars, making them equal, on a scale of 25 feet to the inch, to the cor- responding differences of level taken from the field-book; through the points thus found, draw the irregular line APLM, and it will represent the surface of the ground along the line of level. The bench-mark, between stations 7 and 8, is not plotted, as it is supposed to be out of the line of the section, and no distances are measured to it. SECTION II. TOPOGRAPHICAL SURVEYING. 21. Besides the surveys that are made to determine the area of land and the relative positions of objects, it is fre- quently necessary to make minute and careful examinations for the purpose of ascertaining the form and accidents of the ground, and to make such a plan as will distinguish the swelling hill from the sunken valley, and the course of the rivulet from the unbroken plain. 160 ELEMENTS OF SURVEYING. [BOOK III 22. This brancb. of surveying is called Topography. In surveys made with a view to the location of extensive works, the determination of the slopes and irregularities of the ground is of the first importance : indeed, the examina- tions would otherwise be useless. 23. The manner of ascertaining these irregularities is, to suppose the surface of the ground to be intersected by a system of horizontal planes at equal distances from each other ; the curves determined by these secant planes, being lines of the surface, will indicate its form at the places of section, and, as the planes are nearer or more distant from each other, the form of the surface is more or less accu- rately ascertained. If such a system of curves be determined, and then pro- jected or let fall on a horizontal plane, it is obvious that the curves on such plane will be nearer together or farther apart, as the ascent of the hill is steep or gentle. If, therefore, such intersections be made, and the curves so determined be accurately delineated on paper, the map will give such a representation of the ground as will show its form, its inequalities, and its striking character- istics. 24. The subject divides itself, naturally, into two parts. 1st. To make the necessary examinations and measure- ments on the field ; and, 2d. To make the delineations on paper. For the former of these objects, the theodolite is the best instrument; the common level, however, will answer all the purposes, though it is less convenient. Before going on the field, it is necessary to provide a number of wooden stakes, about two feet in length, with heads. These stakes are used to designate particular points, and are to be driven to the surface of the ground. A nail should then be driven into the head of each of them, to mark its centre. 25. "We shall, perhaps, be best understood, by giving an example or two, and then adding such general remarks as SEC. IL] TOPOGRAPHICAL SURVEYING. 161 will extend tlie particular cases to all others that can occur. Let A (PL 4, Fig. 6), be the summit of a hill, the con- tour of which it is required to represent. At A, let a stake be driven, and let the axis of the theodolite, or level, be placed directly over the nail which marks its centre. From A, measure any line down the hill, as AB, using the telescope of the theodolite or level to arrange all its points in the same vertical plane. Great care must be taken to keep the measuring chain horizontal, for it is the horizontal distances that are required. At different points of this line, as a, 5, c, c?, &c., let stakes be driven, and let the horizon- tal distances J.a, aS, 5c, and cd^ be carefully measured. In placing the stakes, reference must be had to the abruptness of the declivity, and the accuracy with which the surface is to be delineated: their differences of level ought not to exceed once and a half, or twice, the distance between the horizontal planes of section. Having placed stakes, and measured all the distances along the line AB, run another line down the hill, as AG, placing stakes at the points e, / g, and A, and measuring the horizontal distances Ae, ef, fg, and gh. Run also the line AD^ placing stakes at «, Z, m, and n, and measuring the horizontal distances Ai, il, Im, and mn. Each line, AB, A C, AD, running down the hill from A, may be regarded as the intersection of the hill by a verti- cal plane ; and these secant planes are to be continued over all the ground which is to be surveyed. K the work is done with a theodolite, or with a level having a compass, the angles DAB and BAG, contained by the vertical se- cant planes, can be measured; if it is done with a level, having no needle, let any of the distances ae, hf, ai, hi, &c., be measured with the chain, and there will then be known the three sides of the triangles Aae, Abf, Aai, Ahl, &c. Let now, the difference of level of the several points marked in each of the lines AB, AD, AG, be determined. In the present example the results of the measurements and levelling, are — 11 » ELEMENTS OF SURVEYING. [BOOK IIL Line AB. Distances. Aa = 40 feet ah =50 " he =30 " cd =46 " Distances. Ae = 28 feet ef =45 " fg =55 " gh =49 " Distances. Ai = 25 feet il = 55 " Im =38 " mn = 48 " Line AC. Line J.i). Difference of Level. A above a 12 feet a above 5 8" h above c 9 " c above d 11 " Difference of Level. A above e 11 feet e above / 9 " / above ^ 12 " g above ^ 14 " Difference of Level. A above i 9 feet i above I 13 " Z above w 7 " m above n 14 " 30°. Angle CL4J5= 25°, AnglQ DAB ■ Tbese data are sufficient, not only to find the intersec- tions of horizontal planes with the surface of tbe bill, but also for delineating sucb curves of section on paper. Having drawn on tbe paper tbe line AB, lay off tbe angle BAG=2b°, and the angle BAD = ZO°. Then, from a convenient scale of equal parts, lay off tbe distances Aa, ah, he, cd, Ae, ef, fg, gh, Ai, il, Im, and mn. Let it be required that tbe borizontal planes be at a distance of eigbt feet from eacb otber. Since A is tbe bigbest point of tbe bill, and tbe difference of level of tbe points A and a, is 12 feet, tbe first plane, reckoning down- wards, will intersect tbe line traced on tbe ground from A to B, between A and a. Eegarding tbe descent as uniform, wbicb we may do for small distances without sensible error, we have this proportion ; as the difference of level of the points A and a, is to the horizontal distance Aa, so is 8 feet, to the horizontal distance from A to where the first SEC. II.] TOPOGRAPHICAL SURVEYING. 163 horizontal plane will cut the line from A to B. This dis- tance being thus found, and laid off from A to o, gives o, a point of the curve in which the first plane intersects the ground. The points at which it cuts the line from A to C, and the line from A to i), are determined similarly, and three points in the first curve are thus found. The graphic operations are greatly facilitated by the aid of the sector. Let it be borne in mind, that the descent from A to a, is 12 feet, and that it is required, upon the supposition of the descent being uniform, to find that part of the distance corresponding to a descent of 8 feet. Take the distance from A to a, in the dividers, and open the arms of the sector until the dividers will reach from 12 on the line of equal parts, on one side, to 12 on the line of equal parts, on the other. Then, without changing the angle, extend the dividers from 8 on one side, to 8 on the other; this will give the proportional distance to be laid off from A to o. Or, if the dividers be extended from 4 to 4, the proportional distance may be laid off from a to 0. If the distances to be taken from the sector fall too near the joint, let multiples of them be used ; as for in- stance, on the French sectors, let the arms be extended until the dividers reach from 120 on the one, to 120 on the other, then 80 or 40 will be the proportional numbers. Other multiples may be used, though it is generally more convenient to multiply by 10. 26. The second plane is to pass 8 feet below the first, that is, 16 feet below J., or 4 feet below a, a being 12 feet below A. Take the distance ah in the dividers, and ex- tend the sector, so that the dividers will reach from 8 to (the descent from a to 6 being 8 feet) 8, or fi-om 80 to 80 ; then, the distance from 4 to 4, or from 40 to 40, being laid off from a to ^, gives p, a point of the second curve. The difference of level between a and h being 8 feet, and the difference of level between a and ^ being 4 feet, the difference of level between 'p and h must also be 4 feet; hence, the third plane will pass 4 feet below 6, and 164 ELEMEITTS OF SURVEYING. [BOOK III. q, determined as above, is a point of the third curve, and so on. After having determined the points in which each contour line cuts the lines diverging from J., let the con- tour lines be drawn through them, so as to indicate the surface of the hill. The numbers (8), (16), &c., show the vertical distances of the respective planes below the point A. 27. Having drawn the horizontal curves, the next thing to be done is so to shade the drawing that it may represent accurately the surface of the ground. This is done by drawing a system of small broken lines, as in the figure, perpendicular in direction to the horizontal curves already described. In all topographical representations of undulat- ing ground, the lines of shading are drawn perpendicular to the horizontal curves. A profile along either of the diverging lines may be plotted by the rules already given (Art. 20.) The diagram shows the profile along the line AB. 28. The following example will illustrate the methods employed in making a topographical survey, where great accuracy is required. By means of a theodolite or level, range a line of stakes A, B, C, D, E^ kc, along one side, or through the middle of the ground to be surveyed, at equal and convenient distances from each other, say 50 feet apart. Mark, with a piece of red chalk, on each stake in this row, one of the letters of the alphabet. A, B, 0, D, B, &c., in their order. At A, range a line of stakes, perpendicular to AB, planting the stakes at intervals of 60 feet ; and mark them with the letters ^j ^j ^j &c., which are read A first, A second, A third, &c. SEC. II.] TOPOGRAPHICAL SURVEYING. 165 B E A 1 A A 3 A A 4 S B 1 B 2r B 3 b B B 4 c 1 c z (' 3 c a 4 S D 1 El B- D s a us B V 4 S E4 Ss At B, range a line of stakes also perpendicular to AE, and at distances of 50 feet from eacli other, and designate them ^j ^j -^> &c. Do the same at G, D, E, &c., until all the stakes are placed, dividing the area to be surveyed into squares of 50 feet on a side. The letters and figures should be plainly marked on a smooth face of each stake, for facility of reference. If this system of notation be fol- lowed, the stakes may be recorded without danger of con- fusion. The next operation is to determine the difference of level between each stake, and some fixed horizontal plane, which is called a ^lane of reference. If the sea is near, the plane of mean low water, may be taken as the plane of reference. If not, assume the horizontal plane, passing through the lowest point of the ground to be surveyed, and make a permanent bench-mark at the point of beginning. If the lowest point cannot be easily determined, assume such a plane of reference as shall pass quite below the low- est point of the ground. In the example, which we have taken for illustration, the stake -^» is at the lowest point, and let us assume the plane of reference to pass through that point. 166 ELEMENTS OF SIIRVEYIIfG. [BOOK IIL Set up the level at some convenient point, as a, take tlie reading of a levelling staff, set up at -^j and enter this reading as a back-sight. Then take the readings of the staff, at as many stakes as « can be reached from the posi- tion a of the level, entering them as fore-sights. Endeavor- ing to make the last reading as small as possible. At this last stake ^' drive a small peg for a bench-mark. Move the level to a second point b, and take a back- sight to the bench-mark (Gi), and fore-sights, to as many stakes as possible. The following is the form of a field- book, used in topographical levelling. FIELD NOTES. Back-sights. Fore-Sights. Difference Total dif.of level above E 3 Remarks. Object Reading Object Reading Object E3 Reading 0.000 E3 11.432 D3 1.211 -f 10.221 D3 10.221 C4 0.897 -F 0.314 C4 10.535 Check 10.535 C4 11.112 E2 5.281 + 5.831 E2 16.366 E4 6.154 — 0.873 E4 15.493 D4 6.001 -1- 0.153 D4 15.646 D2 1.182 + 4.819 D2 20.465 C3 2.917 — 1.735 C3 18.730 B5 6.080 — 3.163 B5 15.567 C5 0.921 -1- 5.159 C5 20.726 B4 0.113 -1- 0.808 B4 21.534 Check 10.999 B4 11.882 El 8.019 -f 3.863 El 25.397 21.534 B3 3.990 + 4.029 B3 29.426 Dl 4.118 — 0.128 Dl 29.298 C2 1.880 -1- 2.238 C2 31.536 A4 5.000 — 3.120 A4 28.416 A5 9.928 — 4.928 A5 23.488 D5 1.675 + 8.253 D5 31.741 E5 1.111 + 0.564 E5 82.305 A3 0.108 + 1.003 A3 33.308 CI 0.004 -f- 0.104 CI 83.412 Check 11.878 CI 11.149 B2 4.181 + 6.968 B2 40.380 33.412 Bl 2.008 + 2.173 Bl 42.553 A2 0.817 + 1.191 A2 43.744 Check 10.832 43.744 A2 10.102 Al 4.332 -i- 5.770 Al 49.514 Check 5.770 49.514 SEC. II.] TOPOGRAPHICAL SURVEYING. 167 If we subtract the first fore-sight (D3), from the back- sight (E3), the difference, entered in the column headed difference^ is evidently the height of (D3), above the plane of reference through (E3); and we accordingly enter it under the column headed total diff. of level, as well as in the column of differences. If we subtract the fore-sight (C4) from the fore-sight (D3), the difference, entered in the column of difference, is evidently the height of (C4) above (D3); if we now add this difference to the previous total, we shall find the height of (C4) above (E3). Subtracting the fore-sight (E2) from the back-sight (C4), we get the dif- ference of level between (E2) and (04) which, added to the previous total, gives the height of (E2), above the stake (E3). In subtracting the fore-sight (E4) from the fore-sight (E2), we find a negative result which shows that (E4) is below (E2). We enter, then, this difference with its neg- ative sign, and to get the total, we subtract this difference from the previous total, and so on. As a check on the accuracy of our computation, sub- tract the fore-sight (C4) from the back-sight (E3), and the difference will give the height of (C4), above the plane of reference. Again, subtract the fore-sight (B4) from the back-sight (C4), and add the remainder to the height of (C4,) and we shall find the height of (B4), which should agree with the height found under the heading, total diff. of level; and so on for each time the level is moved. PLOTTING THE WORK. 29. Draw, on a piece of paper, a straight line AW. From a scale of equal parts, set off distances AB, BG, &c., each to. represent 50 feet. Erect perpendiculars at each of the points A, B, 0, &c., and then set off the distan- ces from A to 2, from 2 to 3, &g., each to represent 50 feet; and through the points 2, 3, 4 and 5, draw parallels to AB. These, by their intersections with the lines drawn through A, B, (7, &c., will determine the position of the stakes, 4' ^' &c.: and write in red ink on the plot, the 168 ELEMEN-TS OF SURVEYING. [BOOK IIL height above the plane of reference of each stake, taken from the column of total differences in the field-book. Let us sup- pose that the horizontal planes are to be taken at distances of 6 feet. We may find the points in which the contour 19.5 / \l7 , ^ 33.-5 1 428,4 ,5 \-'^ 40,4 / J / 21,5 X .«/ / ■^) 1 C D K 331- 29,3 / / / / / 30,5 / / / 1 f 1 15.6 / / , J/ /' J 16,4./ / 0,0 ) \\\ 1.^.5 / \ lines intersect the lines at right angles, by the previous method, or perhaps still better, let the Surveyor take the plot thus commenced into the field, and by the eye trace the contour lines on the map. If we note where the lines at right angles cut fences, roads, streams, &c., we can, by joining the points, obtain a plot of the ground. 80. The contour lines may be found as follows : Set up the level at a, and observe that the back-sight, to the stake, placed at (.^3), gave a reading of 11.432. Depress the vane equal to the distance between the horizontal secant planes, that is, 6 feet, which is done by placing it. at the reading 5.432. Then direct the rodman, by signals up or down the hill, till the horizontal hair of the telescope coin- cides with the horizontal line of the vane. The foot of the staff is then 6 feet above the first point. Let a stake, marked 6, be driven here, and direct the rodman around the hill, until a second position shall be found, when the SEC. II.] TOPOGRAPHICAL SURVEYING. 169 horizontal liair of the telescope will cut the vane, and drive there another stake, marked 6 ; and so on, until a sufficient number of stakes have been driven to determine the curve (6). Then, let the line of stakes, marked 6, be surveyed with the compass and chain, and plotted. Other contour lines may be found in a similar manner, 31. We will add another example for determining the contour of an undulating piece of ground (PL 4, Fig. 7,) by means of horizontal sections. Let rows of stakes DA^ HE^ IF^ &c., be driven at intervals, depending upon the required accuracy of the survey, and let / g, h, &c., be stakes driven along the lines, at such points as will best show the accidents of ground. Determine as before the difference of level between each stake, and some fixed point, and then determine where the contour lines cut the lines AD, JEH, &c., by the rules already laid down. After the stakes are all placed, and the distances meas- ured, let the differences of level of all the points so desig- nated be found. In the present example, the results of the measurements are, Ft. Ft. Ft. Ft. Ft. Aa =80 AE= 100 EF= 100 FG = 100 GD=100 ab =60 Ef =105 Fi = 74 Gm= 96 Bq = 76 he =90 fg = 85 ik =115 mn = 76 qs = 85 cd =55 gh = 71 M = 60 np = 76 St = 127 dD = bO hH= 74 II = 86 pL = 87 tG = 47 Of the Levelling. Line AD. Line EH. Line FI. Line ai. Line BG. Ft. Ft. Ft. Ft. Ft A above a 5 ^below J. 3 i^'below E 2 6^belowi^l ^below6^2 a '' bQ ^above /9 i'^ above ^ 3 G above m 2 jS above q 3 b " c 7 / " ^3 i " Z;5 w " wl q "52 C below d 2 g '' hi k '' 12 n '' p2 S " ^3 d above Z) 4 hhelovfUS I below IB p below Z 4 t below (75 The heights of the points are here compared with each other, two and two. Before, however, we can conceive 170 ELEMENTS OF SURVEYING. [BOOK III. clearly their relative lieiglits, we must assume some one point, and compare all the others with it. Let the point A be taken. The height of Ft. Ft. J. above a 5 ^ above/ 12 J. above ^ 13 J. above j9 11 A ' I 11 A A " c 18 A A " d 16 A A ' i)20 A A ' E 3 A g 15 h 16 ^13 F 5 i 8 A " Z 15 A " / 12 ^ " (^ 6 A " m 8 ^ " w 9 A " L 7 A " B 8 A " q 11 A " s 13 A " t 16 J.nd of J. above (7, 11 feet. This being done, a mere inspection shows us the high- est and lowest points, as also the relative heights of the others, reckoning upwards or downwards. Let them be now written in the order of their heights above the lowest point, which is D. The difference of level between A and D being 20 feet, if the difference of level of each of the points below J., be taken from 20 feet, the remainder will be the height above D. Arranging them in their order, we have Ft above D 2 " D 4 " D 4 " D 4: " D 5 " D 5 ^above D 7 " D 7 " X> 7 " D 8 " D 8 " D 9 A above I). Ft. 1 2) above D 9 9 " D 9 G " X> 9 n " Dll i " D12 m " Z>12 ^abovei^l2 X>14 D15 DVl 20 feet. In this example, the plane of reference is assumed through D, the lowest point of the ground ; and the secant planes are taken 3 feet apart. 82. The manner of shading the map, so as to indicate the hills and slopes, consists in drawing the lines of shad- ing perpendicular to the horizontal curves, as already ex- plained. These shading lines are drawn close together, when the slope is abrupt, and further apart, as it grows more gentle. Fig. 7 indicates the method of shading. SEC. II.] TOPOGRAPHICAL SURVEYING. 171 83. Wlien the plane of reference is so chosen that the points of the work fall on different sides of it, all the re- ferences on one side are called positive, and those on the other, negative. The curves having a negative reference are distinguished by placing the minus sign before the number ; thus — ( ). 34. In topographical surveys, great care should be taken to leave some permanent marks, with their levels written on them in a durable manner. For example, if there are any rocks, let one or more of them be smoothed, and the vertical distance from the plane of reference marked there- on: or let the vertical distance of a point on some promi- nent building, be ascertained and marked permanently on the building. Such points should also be noted on the map, so that a person, although unacquainted with the ground, could by means of the map, go upon it, and trace out all the points, together with their differences of level. 35. Besides representing the contour of the ground, it is often necessary to make a map which shall indicate the cultivated field, the woodland, the marsh, and the winding river. For this, certain characters, or conventional signs, have been agreed upon, as the representatives of things, and when these are once fixed in the mind, they readily suggest the objects for which they stand. Those which are given in Plates 5 and % have been adopted by the Engineer Department, and are used in all plans and maps made by the United States Engineers. It is very desirable that a uniform method of deline- ation should be adopted, and none would seem to be of higher authority than that established by the Topographi- cal Bureau. It is, therefore, recommended, that the con- ventional signs given in Plates 5 and 6, be carefully studied and uniformly followed. BOOK IV. GEODESIC, TEIGONOMETEIC AND MAEITIME SUEYEYING. SECTION I. GEODESIC AND TEIGONOMETRIO SURVEYnTG. 1. When a large extent of territory, or a long line of sea-coast is to be surveyed, it becomes necessary to con- sider tbe curvature of tbe eartb's surface; tbis brancb of surveying is called Geodesic surveying. 2. Extensive geodesic operations prove tbat tbe eartb is an oblate spberoid, tbe sbortest diameter of wbicb coin- cides "witb tbe terrestrial axis, and all of wbose meridians, are equal ellipses. Tbe meridian lines, bowever, differ so little from tbe circumferenc* of circles, tbat tbey may be taken for tbem, except wben great accuracy is required. Tbe eartb, will, tberefore, in tbe following pages, be re- garded as a perfect spbere. 8, Tbe operations necessary to tbe successful execution of a Geodesic Survey, require tbe minutest attention, and wben performed, numerous corrections are to be applied to tbe measured lines and angles, on account of tbe various causes of error incident to sucb operations. To investigate tbose causes of error, and to deduce rules for correcting tbe errors, in all cases, would far exceed tbe limits of an elementary treatise. We sball, tberefore, attempt notbing more tban a brief outHne of tbe operations SEC. L] TRIANGTJLATION. 173 of a trigonometric survey, with, tlie application of some of the more important corrections. 4. It may be observed tliat most of the operations de- scribed in this section, are equally applicable, whether we regard the area surveyed as plane or spherical : in either case, the basis of an accurate survey, is an extensive sys- tem of triangulation. 6. After having made a preliminary examination or re- connaissance of the territory to be surveyed, suitable stations are selected at the most prominent points, and these points are marked by staves or signals. A hase line is then measured. The lengtb of the base will, in general, depend upon the magnitude of the survey, and each, extremity is marked by a signal. The next step is the triangulation. At each extremity of the base, the angles between the base, and the lines drawn to each of the visible signals, are carefully meas- ured by means of a theodolite. The sides of the triangles thus obtained, serve as nqw bases upon which, other trian- gles may be formed, and so on, until the entire area is covered by a net-work of triangles. 6. This system of triangles is called the primary system, and the operation of forming them is called the primary triangulation. Within the primary triangles, and depending upon them, a system of smaller triangles is formed in the same manner, called the secondary system ; and if the extent or importance of the work should demand it, the secondary may be sub-divided into tertiary triangles. Having completed the triangulation, the characteristics , of the surface, such, as roads, streams, villages, boundaries, &c., are filled in by means of the compass, plain table, or some of the methods abeady explained. After the field work is completed, the triangles, when regarded as spherical, are reduced by applying the formula for spherical excess, hereafter explained, and other neces- sary corrections, and thus the whole work is plotted upon paper. 174 ELEMENTS OF SURVEYIlfG. [BOOK IV. PRELIMIlSrARY EECONKOISSANCE AND ESTABLISHMENT OF SIGNALS. 7. Before commencing a trigonometrical survey, an ex- amination of the entire territory should be made for the purpose of selecting a location for the base line, and proper points for stations ; this examination should be more or less elaborate, according to the nature and extent of the survey. The proper distribution and combination of the trian- gles, so as to adapt them to the survey in hand, require great judgment and care, and but few rules can be given for the selection of trigonometrical points. Those points should, in general, be chosen in such a manner, that they may be distinctly visible from each other, and so that the triangles formed, by uniting them, may be as nearly as possible equilateral. It is easily seen, that a triangle which has an obtuse or a very acute angle, will experience a greater change of form for a given error, than one which is nearly equilate- ral ; and since the accuracy of each triangle depends upon the preceding ones, it is further evident, that the introduc- tion of a single ill-conditioned triangle, might vitiate the whole survey. Except in extreme cases, no angle, less than 80°, should be used, and even angles of 30° should not be admitted when the locality can be so chosen as to prevent it. The base is usually much shorter than the sides of the primary triangles ; these sides, however, should be increased as rapidly as is consistent with the above remarks. 8. The accompanying diagram will illustrate the man- ner of increasing the sides without introducing ill-con- ditioned triangles. Having measured the base AB, and the requisite angles, the triangles ABG and ABD, may be de- termined, and the line i) (7 computed; with Z>(7 as a base, the triangles JDCU and BGF are formed, and thence JERF, and JSGF, in which the sides are much greater than the base AB. SEC. I.] SIGNALS. 175 j)^ J— I s.'^c In tliis manner tlie sides may be increased to any de- sirable extent. An ordinary map of the country, or a sketch made witli tbe pocket compass, will be of material assistance in making a proper distribution of the stations. 9. The stations are marked by signals, which may be constructed in a great variety of ways, depending upon the locality of the stations, and the lengths of the sides of the triangles. Sometimes a signal has to be raised above the level of the adjacent country, in which case it is constructed of timbers, and upon the apex, is placed a vertical staff, bear- ing a flag. The exact trigonometrical point is determined by a plumb-line, suspended from the apex of the signal. A temporary signal may be constructed with three or four pieces of scantling framed and traced, as shown in the annexed figure, with a short pole projecting from the apex. The plumb determines the point B, which is the exact trig- onometrical point over which the theodolite is to be placed. Where the sides of the trian- gles are not very great, a pole, planted ver- tically, and surmounted by a flag, will an- swer as a signal. In order to distinguish the different signals, the which they bear, should be different from each other. They may be formed by arranging stripes of white and 176 ELEMEl^TS OF SURVEYING. [BOOK IV. red, according to some pre-arranged plan, and tlie flags of tlie different stations should be entered in a book. For tbe purpose of future reference, tbe trigonometrical point, at each station, as B, should be indicated by a permanent mark. If the point falls upon a rock, a hole may be drill- ed to show the locality; or if not, a mark-stone may be sunk under the point, deep enough to be beyond the reach of accident. A record of the monument should be pre- served, together with its reference to some of the perma- nent objects in the neighborhood. In order to render the signals visible from the distant stations, polished tin plates are sometimes attached to the signal-post, so as to reflect the sun towards the stations at certain hours of the day. The Drummond-light has also been used to show very distant stations. A light may also be produced that can be seen at a distance of 60 or 70 miles, by placing a ball of lime about a quarter of an inch in diameter, in the focus of a parabolic reflector, and heat- ing it intensely by a stream of oxygen gas, directed by a blow-pipe, through a flame of alcohol. If obstacles, as trees, and under-brush intervene, vistas have to be opened along the lines, from station to station. MEASUEEMENT OF A BASE LINE. 10. The measurement of a base line on which the ac- curacy of the entire survey depends, is one of the most difi&cult operations of geodesic surveying, and one, for the successful accomplishment of which, art and science have been strongly taxed. The selection of a proper site for a base line, forms one of the first objects of the prehminary reconnaissance. It should, if possible, be fixed on an open plain. It must be so chosen, that the surrounding signals may be distinctly seen from its extreme points ; and hence, those signals which mark points of the adjacent triangula- tion, should be selected with reference to the base. The length of the hase^ should, in a measure, depend upon the magnitude of the survey, though circumstances seldom admit its being taken more than 6 or 8 miles in length. SEC. I] BASE LINE. 177 11. Different instruments iiave been used for measuring base lines, such, as steel chains, glass, platinum and deal rods ; and more recently, a combination of rods, of differ- ent metals, so adjusted, that the apparatus maintains an in- variable length at all temperatures. This last mentioned apparatus, has been much improved, and most successful!}^ used by Prof. Bache, in the Survey of the United States Coast. 12. In minor surveys, where the base line does not much exceed 1000 or 2000 feet, sufficient accuracy may be attained by the use of wooden rods. To render the rods less susceptible of change, from moisture, they should be saturated with, boiling oil, and covered with, a thick coat- ing of varnish. The ends of the rods should be protected by metallic caps, which prevent their wearing, and insure a more per- fect contact. When the rods are prepared for use, they should be carefully compared with some standard measure, and from time to time this comparison should be repeated, in order to detect any minute change of length, should sucb change take place. 13. The following method of measuring a base line of 1000 or 2000 feet, may be rendered very accurate. Having decided upon the direction of the base, and measured it carefully, two or three times with a chain, let a theodolite be planted at one end of the line, and direct- ed upon a flag, planted at the other. Then, by means of the vertical limb, let a row of pickets be driven along the base, taking care to plant them at a distance from each other, equal to the length of one of the deal rods. Then, plant in the place of each picket, a vertical post, 6 or 8 inches in diameter, and projecting a sufficient distance above the surface of the ground. If necessary, let the posts be steadied by heaping about them, earth or stones. Next, with the assistance of a spirit-level, let each post be sawed off, so as to bring their tops to the same horizontal 12 17i ELEMENTS OF SURVEYING. [BOOK IV. plane, and by means of the theodolite, let a line be marked on the top of each post, in the direction of the base. This line will determine the direction in which the rods are to be placed, and the contact of the ends must all be on this line. The contact of the rods should be made with great care, so as to avoid moving the rod already established ; and this will be more readily done, when three rods are used. The measurement should be repeated two or three times to guard against error, 14. If the nature of the ground does not admit of the posts being brought to a level, let them, by means of the theodolite, be brought into an oblique plane AB, and after B having measured, as before, the line AB, determine accu- rately the difference of level between the points A and ^, equal to BG: then, from the right-angled triangle ABC, we should find the horizontal distance AC =^ V A^ — BC^. 15. In very extensive surveys, the base should be several miles in length, and the apparatus for measurement, as well as the operations on the field, become more complicated. For a full description of a very perfect hase apparatus, and the method of using it, the reader is referred to Prof. Bache's pamphlet, on the subject — ^the details of the descrip- tion would exceed our limits. TRIANGULATION. / 16. The theodolite is generally used for measuring the angles of a trigonometric survey. The extent of the survey,, and the standard of accuracy to which the results are re- quired to conform, must determine the size and perfection of the instrument to be employed. The angles of the pri- mary triangles of the United States Coast Survey, are meas- iired with theodolites, whose horizontal circles are 24 or 80 SEC. L] TRIANGULATION. 179 inclies in diameter; and to eliminate as mucli as possible, every source of error, great numbers of operations are made on eacli station, tbe readings being made on different points of the arc. Usually from 40 to 60 observations are made for each angle — one measurement, with the telescope direct, and one with it reverted, constituting a complete observa- tion. With these precautions, it has been found that the error in a primary triangle (where the sum of its three an- gles has been compared with 180°), has fallen much with- in 3 seconds. The error of 3 seconds has been adopted as the highest admissible limit of error. 17. Observations are also made at the principal stations upon the pole-star, and other stars near the pole, for the purpose of determining the angle, made by the sides of the triangle with the meridian. In minor surveys, and in a secondary triangulation, the operations are much less elabo- rate ; still, every precaution is to be taken to insure the greatest attainable accuracy. As a general rule, all the an- gles of every triangle, should be measured, if possible. 18. To illustrate the manner of carrying on a minor triangulation, let us refer to the plan of the harbor [plate 6], in which AB is the measured base, C, D, E, &c., tri- angulation points, at which signals have been erected. Commence the triangulation at A^ the west end of the base ; and for convenience in plotting, it would be well to make the line, passing through the point, and 180" parallel, in each position of the instrument, to the base AB. Having brought the of the vernier to the of the limb, clamp the vernier plate, and direct the upper teles- cope to the signal at B, and clamp the limb. Enter the observation as in the following table: OBSERVATION AT STATION A. Name of Station. Vernier I. Vernier II. Mean. Station B 00° 00' 00" 00' 00" 00° 00' 00" Station E 72° 24' 55" 25' 5" 72° 25' 00" Station G 138° 34' 56" 35' 4" 138° 35' 00" &c. &c. &c. &c. 180 ELEMENTS OF SirRYETIIfG. [BOOK IV. Having recorded tlie reading of tlie first vernier, and tlie minutes and seconds of the second vernier, unclamp tlie vernier plate, and direct tlie telescope to tlie station at E, and record both verniers, as before. Again unclamp the vernier plate, and direct the telescope on the signal at G; and then read and record, as before. Having determined the angles subtended by all the signals visible from J., let the theodolite be removed to B. Bring the of the vernier I to 180° on the limb, and direct the telescope on the signal at A — the line (0°, 180°) will then be parallel to its first position, and the limb may be clamped. Eead now the angles to the signals at J., E, (7, &c., and record as before. If the theodolite is now removed to the station E, the line (0°, 180°), may be made parallel to its first position, by adding 180° to the reading of the first vernier, from A to E^ and then directing the telescope on the signal at A. The line (0°, 180°), will thus be made parallel to AB, and the reading may be made and recorded as before ; and so on until all the stations have been visited, and the an- gles measured. From the field records, the angles BAE, EAO, ABEj EBG^ ko,.^ may be easily deduced, the whole may be plotted on paper, or the several sides may be com- puted trigonometrically. It may be observed that the line (0°, 180°), has been made parallel to the hase line at each station ; where great accuracy is required, this cannot be done, since a single reading is insufficient to give the angle. The angle is then determined, as directed in the previous article, or by means of the principle of repetition. 19. To illustrate this principle of repetition, suppose the of the vernier to coincide with the of the limb, and the telescope to be directed, from the station ,4, upon one of the objects, as the signal at B. Clamp the limb, and unclamp- ing the vernier plate, direct the telescope on the second ob- ject, as the signal at E. If we now clamp the vernier plate, and unclamping the limb, direct the telescope on the signal at B, the line (0°, 180°), of the limb, will make with AB, an angle equal to BAE. Again clamp the limb, SEC. I.] TRIAITGULATION-. 181 and unclamping tlie vernier plate, direct tlie telescope on the signal at E. The reading will evidently be equal to twice the angle BAE^ and if we repeat the operation, the reading will be three times the angle, and so on. After ten repetitions, if we add 360° each time the of the vernier passes the of the limb, the final reading will be ten times the angle BAE^ affected with the joint errors of the ten observations, and one-tenth of this will be the read- ing required, to a greater degree of accuracy than could probably be attained by a single observation. 20. The method of reading angles, by this mode, is as follows : Angles at station A, between signals B (left), and E , c, and d. TO LAY OFF AN ANGLE WITH THE PEOTRACTOR. 39. Let its centre be placed over the angular point, and the diameter passing through and 180°, on the given line. Turn the screw that works the index, until the of the vernier, coincides with the division corresponding to the given angle; then let the angular brass pieces be turned down; the points dotted by the steel pins will show the direction of the required line. If this line does not pass through the angular point, the pins are out of place, and must be adjusted. FIRST METHOD OF PLOTTING. 40. Suppose it were required to make the plan of the harbor on a scale of 450 yards to an inch. Divide the length of the base line AB^ which we will suppose equal to 1140 yards, by 450, and the quotient 2.53 will express the length which is to represent the base line on the paper (Bk. I., Art. 54.) Draw an indefinite line AB, to represent the base, and having chosen any point, as A, for the first station, lay off 2.53 inches to JB. The other extremity of the base line will thus be determined. 13 194 ELEMENTS OF SURVEYING. [BOOK lY. Then, place tlie circular protractor at A, and lay off tlie angle BAJS, and then the angle UAG. . Next, place the protractor at B, and lay off the angles ABE and EBO. The intersection of the lines AE and BE will determine the station E. Let the protractor be then placed at this point, and all the angles of station E, laid down. The point G, where EG intersects AG, and the point 0, where EC intersects BO, will then be found. By placing the protractor at G and G, we can deter- mine the points I) and E, when the place, on the paper, of all the stations will be known. To unite the work done with the compass, spread the compass-notes before you, and draw through A a line to represent the meridian. This line makes an angle of 12° with the course AE. Then, lay off from the scale the distances Aa, Ab, Aq, Ac, Ad, Ae, and at the several points erect perpendiculars to AE. Lay off on these perpendiculars the lengths of the offsets, and the curve traced through the points so deter- mined, will be the margin of the lake. At E, draw a parallel to the meridian through A, and lay down the course Eff, which makes an angle of 50° with the meridian. Then, lay down the several distances to the offsets, and draw the offsets and lay off their lengths. Do the same for the course HI, and all the compass-work will be plotted. The work done with the plane-table (Art. 28), is united to the work done with the theodolite, by simply placing the line AN on the paper of the plain-table, upon the line AN", drawn on the plot of the triangulation. SECOND METHOD OF PLOTTING. 41. Place the centre of the protractor near the centre of the paper, and draw a line through the points and 180°. This line will have the same position with the cir- cular protractor that the base line AB had with the limb of the theodolite. SEC. I] METHOD OF CHORDS. 195 Lay off then from the point an arc equal to the direc- tion from A to JS, also an arc equal to the direction AG, and through the centre point, and the points so determined, draw lines. Lay off in succession, in a similar manner, the directions taken at all the stations ; and through the centre point, and the points so determined, draw lines, and designate each by the letters of the direction to which it corresponds. Now, since all the lines drawn on the paper have the same position with the circular protractor, as the corresponding lines on the ground have with the limb of the theodolite, it follows that each direction wiU be parallel to its corres- ponding line upon the ground. Hence, any line may be drawn parallel to that passing through and 180°, to represent the base line AB. Having drawn such a line, and marked a point for the station A, lay off the length of the base, and the extremity will be the station B. Through A and B, so determined, draw parallels re- spectively to the lines corresponding to the directions A^ and BE, and the point of intersection will determine station K Through B and U draw parallels to the lines which correspond to the directions BO, GE, and their point of intersection will determine station C. Through G and E draw lines parallel to the lines corresponding to the direc- tions GE and ED, and the point of intersection will de- termine D. In a similar manner we may determine the stations F and G. METHOD OP CHORDS. 42. Let us first prove that the chord of a given arc is equal io the sine of half the arc loith double the raditts. Let BAF be any given angle, and AR a line bisecting it. Let '^Sh^ 3<<^ '' DC he the chord of the arc GD, X%^ — ''X^' described with a given radius, ji:^^^^^'^^\ X_ and HF parallel to GD, the sine A Q F of half the given angle, to a radius AF== 2 AG. 196 ELEMENTS OF SURYETIlfG. [BOOK lY. Since AF=2AC we have, from similar triangles, HF= 2KG, but DC= 2KG, hence HF= CD. TO LAY OFF AN ANGLE. 48. To avoid, as far as possible, / the use of fractions, let us suppose )^^ ^-^-X^ the radius of the table of natural /"'■'O'^r'''^^ \'^ sines to be 1 ten^ or 10 inches. .^^^^"^^ \ \;_ Take from a scale 5 equal parts, with which as a radius, from the centre J., describe an arc CD. Take from the table the natural sine of half the arc, and remove the decimal point one place to the left; the residt will express the sine of the arc to the radius 10, or the chord of half the arc to the radius 5. From the same scale, take this sine in the dividers, and from C, as a centre, describe an arc cutting CD in D ; draw AD, and CAD will be the angle required. This is the most accurate of all the methods of laying off an angle, and it may also be applied advantageously to the second method of plotting, thus : Draw a fine straight line, generally in the direction of the meridian or of the base line of the survey ; and also a line exactly perpendicular to it. From the point of intersection, as a centre, with a radius of 5 equal parts of the scale, describe the circumference of a circle cutting the straight lines in the points marked and 90°. To lay off an angle, as for instance, the angle 14° 29'. The half of it is 7° 14' 30", the natural sine of which is 0.126005, or 1.26 to the radius of 10 inches. Set off from to &, as in the figure, this distance taken from the scale, and through the two points &, 5, thus determined, draw a straight line. This line should pass through the centre, and will make with the line (0, 0) the angle 14° 29' ; and any line on the paper drawn parallel to it, will make with the line (0, 0) the same angle. The further application is obvious. SEC. II.] MARITIME SURVEYING. 197 SECTION II. MARITIME SURVEYIlSra. 44. When, in connection with a trigonometrical survey on shore, a harbor is to be surveyed for the purpose of ascertaining the channels, their depth and width, the posi- tions of shoals, and the depth of water thereon, other means must be used, and other examinations made in ad- dition to those already referred to. Let buoys be anchored on the principal shoals and along the edges of the channel, and using any one of the lines already determined as a base, let the angles subtended by lines drawn from its extremities, to the buoys respectively, be measured with the theodolite. Then, there will be known in each triangle the base and angles at the base, from which the distances to the buoys are easily found ; and hence, their positions become known. Having made the soundings, and ascertained the exact depth of the water at each of the buoys, several points of the harbor are established, at which the precise depth of the water is known ; and by increasing the number of the buoys, the depth of the water can be found at as many points as may be deemed necessary. 45. If a person with a theodolite, or with any other in- strument adapted to the measurement of horizontal angles, be stationed at each extremity of the base line, it will not be necessary to establish buoys. A boat, provided with an anchor, a sounding line, and a signal flag, has only to throw its anchor, hoist its signal flag, and make the sound- ing, while the persons at the extremities of the base line measure the angles ; — ^from these data, the precise place of the boat can be determined. 46. There is another method of determining the places at which the soundings are made, that admits of great 19'8 ELEMENTS OF SURVEYING. [BOO'E: IV. despatch, and wliidi. if the observations are made with- care, affords results sufl&ciently accurate. Having established, trigonometrically, three points which can be seen from all parts of the harbor, and having pro- vided a sextant, let the sounding be made at any place in the harbor, and at the same time the three angles subtend- ed by lines drawn to the three fixed points, measured with the sextant. The problem, to find, from these data, the place of the boat at the time of the sounding, is the same as example 6, page 62. It is only necessary to measure two of the angles, but it is safest to measure the third also, as it affords a veri- fication of the work. The great rapidity with which angles can be measured with the sextant, by one skilled in its use, renders this a most expeditious method of sounding and surveying a harbor. The sextant is not described, nor are its uses explained in these Elements, because its construction combines many philosophical principles, with which the Surveyor cannot be supposed conversant. 47. There is yet another method of finding the sound- ings, which, although not as accurate as those already ex- plained, will, nevertheless, afford results approximating nearly to the truth. It is this ; — ^Let a boat be rowed uni- formly across the harbor, from one extremity to the other of any of the lines determined trigonometrically. Let soundings be made continually, and let the precise time of making each be carefully noted. Then, knowing the length of the entire line, the time spent in passing over it, as also the time of making each of the soundings, we can easily find the points of the line at which the several soundings were made ; and hence, the depth of water at those points becomes known. 48. If a person stationed on shore with a theodolite, takes the bearing of the boat, at every second or third sounding, determined by hoisting a flag, it will fix the positions of the SFC. II.]" MARITIME SURVEYING. 199 soundings witli great accuracy. Soundings may thus be made along any number of known lines, and a comparison of the depths found on different lines, at or near their points of intersection, will show with what degree of ac- curacy the work has been done. Sounding-lines should be made of strong cord, and di- vided into feet or fathoms, by different colored rags or other marks. The lead is shaped like the frustum of a cone, with the base J5, hollowed out, to hold some grease. The land or mud of the bottom adheres to the grease, and thus shows the na- ture of the bottom, which should be en- tered in the field-book, and laid down upon the map. As the cord is liable to change its length, it should be com- pared from time to time with some standard. In tide-waters, the exact time of each sounding is to be noticed, and an assistant should note the height of the tide at regular in- tervals, upon a tide-guage. The tide-guage is permanently placed at some convenient point of the harbor, and its point is referred by means of a spirit-level, to some fixed bench-mark, on a level with mean low-water mark, to which all the soundings must be reduced. 49. Having plotted the work done with the theodolite, as also the outline of the harbor traced with the compass, it remains to delineate the bottom of the harbor ; and this is done by means of horizontal curves, which have already been used to represent broken or undulating ground. Let the plane of reference be taken through low-water mark, or to coincide with the surface of the water at low tide. The accuracy with which the bottom of the harbor is to be delineated, will guide us in fixing the distance be- tween the horizontal planes of section. The first horizontal plane should be passed at a dis- tance below the shallowest point that has been sounded, equal to the number of feet fixed upon for the distance between the planes of section; and the curve, in which it 200 ELEMENTS OF SURVEYIITa. [BOOK lY. intersects tlie bottom of tlie harbor determined as in Book in. Sec, II. And similarly, for the other horizontal planes of section. Having thus delineated the bottom of the harbor, and noted on the map the distance of each intersecting plane below the plane of reference, let such lines be drawn as will indicate the channels, shoals, sunken rocks, and direc- tion of the current. In the example given in plate 6, soundings have been made in three directions from the sand-bar in the harbor, and also from the rocky shore across to the light-house.. BOOK V. OF NAYIGATION. SECTION I. DEFINITIONS. 1. "We have given, in tlie preceding parts of this -work, various applications of Plane Trigonometry. We propose, in this Book to explain the best methods of determining the place of a ship at sea. This application of Trigonom- etry constitutes the science and art of Navigation. 2. There are two methods of determining the place of a ship at sea. 1st. When a ship departs on her voyage, if we note her courses and the distance sailed, we may, at any time, by means of Plane Trigonometry, determine her place, very nearly. 2d. By means of observations on the heavenly bodies, and the aid of Spherical Trigonometry, we may determine with great accuracy, the place of the ship. This method is called Nautical Astronomy. The first part of Navigation, viz., the cases which can be solved without the aid of observations on the heavenly bodies, wiU be alone treated of. 8. The earth is nearly spherical. For the purposes of Navigation it may be considered as perfectly so. It re- volves round one of its diameters, called the axis, in about twenty-four hours. 4. The great circle, whose poles are the extremities of the axis, is called the equator. The poles of the equator 202 ELEMENTS OF SURVEYING. [BOOK V. are called the poles of the earth — one is called the north pole, and the other the south pole. 5. The circumference of every great circle which passes through the poles, cuts the equator at right angles, and is a meridian circle. Every place on the surface of the earth has its own meridian ; but for the purposes of Geography and Navigation, all the meridians are reckoned from a par- ticular meridian, which is called the first meridian. The English have fixed on the meridian of the Greenwich Ob- servatory, for the first meridian. 6. The longitude of any place is the arc of the equator, intercepted between the meridian of that place and the first meridian, and is east or west, according as the place lies east or west of the first meridian. 7. The difference of longitude of two places is the arc of the equator included between their meridians ; this arc is equal to the difference of longitudes when they are of the same name, and to the sum of the longitudes, when they are of different names.' 8. The latitude of a place is its distance from the equator, measured on the meridian of the place, and is north or south according as the place lies north or south of the equator. 9. The small circles drawn parallel to the equator, are called parallels of latitude. The arc of any meridian inter- cepted between the parallels passing through any two places, measures the difference of latitude of those places; this difference is found by subtracting the less latitude from the greater, when the latitudes are of the same name, and by adding them when they are of different names. 10. The sensible horizon of any place is an imaginary plane, supposed to touch the earth at that place, and to be extended indefinitely. A plane passing through the centre of the earth, and parallel to the sensible horizon, is called the rational horizon. The north and south line, is the intersection of the plane of the meridian circle with the sensible horizon, and the line which is drawn perpendicular to this, is called the east and west line. SEC. 1] NAVIGATION. 203 11. The course of a ship, at any point, is the angle which her track or keel makes with the meridian. So long as the course is unchanged, the ship would sail in a straight line, if the meridians were truly parallel ; but as the meridians bend constantly toward the pole, the direction of her path is continually changing, and she moves in a curve called the rhumb line. The course of a ship is indicated by the mari- ner's compass. 12. The marin- er's compass consists of a circular card, whose circumfer- ence is divided into thirty-two equal parts called points ; each point being subdivided into four parts, called quar- ter points. To the under side of this card a slender bar of mag- netized steel, called a needle, is permanently attached. The direction of the needle corresponds to the diameter NS. The diameter EW, at right angles to NS, is intended to indicate the east and west points. The points of the compass are thus read : be- ginning at the north point, and going east, we say, north and hy east, north north east, north east and by north, north east; and so on, round the compass, as indicated by the letters. The card being permitted to turn freely on the pin, on which it is poised, as a centre, the line NS will always indicate the true magnetic meridian, but this, as we have seen in (Bk. II., Sec. 7-14), is not the true meridian, and hence, the variation must always be allowed for. On the interior of the compass box, in which the card swings, are two marks a and b, which lie in a line passing through the centre of the card, and the compass box is so 204 ELEMENTS OF SURVEYING. [BOOK V. placed tliat this line sliall be parallel to tlie keel of tlie ship. Consequently, if & be placed towards tbe bow of the vessel, the point which it marks on the card will show the compass course, for the line NS is always on the magnetic meridian, and EW" is east and west. The course is gene- rally read to quarter points, and as a quadrant contains eight points, each point is equal to 90° -r- 8 = 11° 15' ; and a quarter point = 11° 15'H-4=2° 48' 45". The table of Khumbs, after the Traverse Table, shows the degrees in each course, to quarter points. 13. A ship's rate of sailing is determined by means of an instrument, called the %, and an attached line called the log line. The log is a piece of wood in the form of a sector of a circle, the rim of which is loaded with lead, so that when it is heaved into the sea it assumes a vertical position. The log line is so attached as to hold the log square against the water, that it may not be drawn along after the ship as the line unwinds from the reel, by the ship's forward motion. The time in which the log line unwinds from the reel, is noted by a sand-glass, through which the sand passes in half a minute ; that is, in the one hundred and twentieth part of an hour. For convenience, the log line is divided into equal parts, marked by knots, and each part is equal to the one hun- dred and twentieth part of a nautical or geographical mile*. Now, since half a minute is the one hundred and twen- tieth part of an hour, and each knot indicates the one hun- dred and twentieth part of a mile, it follows that the mem- ber of knots reeled off while the half minute glass runs out, wiU indicate the rate of the ship's sailing per hour. * A geograpliical mile is one minute, or one-sixtieth of a degree, measured on tlie equator. Taking the diameter at 7916 English miles, the geographical mile will be about 6079 feet ; that is, one-sixth greater than the English mile, which is 6280 feet. SEC, II.] PLANE SAILING. 205 SECTION II. OF PLANE SAILING. 14. Let tlie diagram EPQ represent a por- tion of the eartli's sur- face, P the pole, and EQ the equator. Let AB be an J rhumb line, or track described by a ship in sailing from A to B. Conceive the path of the ship to be divided into very small parts, and through the points of division draw meri- dians, and also the parallels of latitude 1% c'c, d'd, e'e, and B'B: a series of triangles will thus be formed, but so small that each may be considered as a plane triangle. In these triangles, the sum of the bases Ah' + he' + cd' -f de' + e/= AB', which is equal to the difference of latitude between the points A and B. Also, h'h + c'c + d'd + e'e +fB = BB', which is equal to the distance that the ship has departed from the meridian AB'P, and is called the departure in sailing from A to B. Therefore, the distance sailed, the dif- ference of latitude made, and the departure, may be represented by the hypothenuse, the base and perpendicular of a right- angled triangle, of which the angle op- posite the departure is the course. When any of the four parts above- named are given, the other two can be determined. This method of determining the place of a ship reduces all the elements to the parts of a plane triangle, and hence is called plane 206 ELEMEN"TS OF SURVEYIITG. [BOOK V. EXAMPLES. 1. A ship from latitude 47° 30' N. has sailed S. W. by S. 98 miles. What latitude is she in, and what departure has she made ? Let G be the place sailed from, CB the meridian, and BOA the course, which we find from the table of rhumbs to be equal to 33° 45' ; then A will be the dis- tance sailed, equal to 98 miles. Also, AB will be the departure, and CB the differ- ence of latitude. Then by the formulas for the solution of right angled triangles, A As radius ar. c. : cos G 33° 45' : : AG 98 0.000000 9.919846 1.991226 GB 81.48 1.911072 As radius ar. c. 0.000000 : sin G 33° 45' 9.744739 :: GA 98 1.991226 AB 54.45 1.735965 Latitude left 47° 30' N. Dif lat. = 81.48 miles = 81.48 minutes = 1° 22' S. In latitude 46° 08' Departure, 54.45 miles. 2. A ship sails 24 hours on a direct course, from lat- itude 38° 32' N. till she arrives at latitude 36° 56' K The course is between S. and E. and the rate 5^ miles an hour. Required the course, distance, and departure. Lat. left 38° 32' K 24 X 5i = 132 miles = distance. In lat. 36° 56' Diflf. 1° 36' = 96 miles. As dist. 132 ar. c. 7.879426 : diff. lat. 96 1.982271 : : radius 10.000000 : cos course 43" 20' 9.861697 As radius ar. c. 0.000000 : dist. 132 2.120574 : : sin course 43° 20' 9.836477 dep. 90.58 1.957051 SEC. Ill] TRAVERSE SAILING. 207 Hence, tlie course is S. 43° 20' E,, and the departure 90.58 miles east. 3. A ship sails from latitude 3° 52' S. to latitude 4° 30' N,, the course being N. "W. by W. ^W. : required the dist- ance and departure. Ans. Dist. 1066 miles; dep. 939.2 miles W. 4. Two points are under the same meridian, one in lat- itude 52° 30' K, the other in latitude 47° 10'/ N. A ship from the southern place sails due east, at the rate of 9 miles an hour, and two days after meets a sloop that had sailed from the other : required the sloop's direct course, and distance run. Ans. Course S. 53° 28' E.; dist. 537.6 miles. 5. If a ship from latitude 48° 27' S., sail S. W. by W. 7 miles an hour, in what time will she reach the parallel of 50° south ? Ans. 23.914 hours. SECTION III OF TRAVERSE SAILING. 15. When a ship, in going from one place to another, sails on different courses, it is called Traverse Sailing. The determination of the distance and course, from the place of departure to the place of termination, is called compounding or loorking the traverse. This is done by the aid of the *' Traverse Table," which has already been explained, and the method of working the traverse, is in all respects simi- lar to that adopted in the Prob. of Art. 34, page 123. EXAMPLES. 1. A ship from Cape Clear, in lat. 51° 25' N"., sails, 1st, S. S. E. i E. 16 miles ; 2d, E. S. E. 23 miles ; 3d. S. W. by W. i W. 36 miles ; 4th, W. f K 12 miles ; 5th, S. E. by E. \ E. 41 miles : required the distance run, the direct course, and the latitude. 208 ELEMENTS OF SURVEYING. [BOOK V. We first form tbe table below, in wbicli we enter tlie courses, from tbe table of rhumbs, omitting the seconds, and tben enter tbe latitudes and depart- ures, taken from tlie tra- verse table, to tbe nearest quarter degree. Thus, in taking tbe latitude and departure for 25° 18' we take for 25^°. The dif- ference of latitudes gives tbe line AG, and tlie dif- ference of departures the line GF. TEAVERSE TABLE. Courses. Dist's. Diflf. of Latitude. Departure. No Angle. N. s. E. w. 1 2 3 4 5 S. S. E.iE. . . E. S. E S. W. by W. i W. W. fN S. E. by E. i E. . 25° 18' 67° 30' 61° 52' 81° 33' 59° 03' 16 23 36 12 41 1.77 1447 8'.80 17.04 21.12 6.83 21.25 35.14 31.71 11.87 1.77 61.43 1.77 63.22 43.58 43.58 Diff. 59.66 19.64 Latitude left Difference of latitude 59. 51° 25' K miles = 1° 00' S. In latitude 60° 25' K SEC. Ill] TRAVERSE SAILING. 209 Then, by formulas for the solution of right-angled tri- angles, we have. As AG, diff. lat. ar. c. 8.224317 As sin course ar. c. .504995 departure 19.64 1.293141 : radius 10.000000 radius, 10.000000 : : departure 19.64 1.293141 : tang course 18° 13' 9.517458 distance 62.83 1.798136 Therefore the direct course is S. 18° 13' E., and the distance 62.83 miles. OF PLOTTING. 16. There is yet another method of finding the direct course and distance, much practiced by seamen, although it does not afford a high degree of accuracy. It is a method by plotting, which requires the use of a mariner's scale and a pair of dividers. One of the scales marked on the mariner's scale, is a scale of chords, commonly called a scale of rhumbs, being divided to every quarter point of the compass ; and there is also a second scale of chords divided to degrees. Both of these scales are constructed in reference to the same common radius, so that the chords on the scale of rhumbs correspond to those on the scale of marked chords. The manner of using the scales will appear in plotting the last example. To construct this traverse, describe a circle with a radius equal to the chord of 60° and draw the meridian N/S. Then take from the line of rhumbs the chord of the first course 2-j points, and apply it from S to 1, to the right of NS, since the course is southeasterly, and draw Al ; take, in like manner, the chord of the second course, 6 points, from ;S' to 2, and lay it off also to the right of the meri- dian line. Apply the chord of the third course, 5^ points, from S to 3, to the left of the meridian ; the fourth course, 7i points from iV to 4, to the left of NS, this course be- ing northwesterly ; and, lastly, apply the chord of the fifth course, 5] points, from S to 5, to the right of N/S, and join all the lines as in the figure. 14 210 ELEMENTS OF SURVEYING. [BOOK V. In the direction Al, lay off the distance AH= 16 miles from a scale of equal parts, and through the extremity H, draw HG parallel to A2, and lay off HC= 23 miles. Draw CD parallel to ^3, and lay off CD =36 miles ; then draw DE parallel to J.4, and lay off 12 miles ; and lastly, draw EF parallel to J.5, and lay off 41 miles, and F will be the place of the ship. Hence, we conclude that AF is the dist- ance made good, and GAF is the course. Applying, then, the distance AF to the scale of equal parts, we find it equal to 62f miles ; and applying the chord Sa to the scale of chords, we find the course GAF = 18i°. 2. A ship sails from a place in latitude 24° 32' N., and runs the following courses and distances, viz., 1st, S. W. by "W. dist. 45 miles ; 2d, E. S. E. dist. 50 miles ; 3d, S. W. dist. 30 miles ; 4th, S. E. by E. dist. 60 miles ; 5th, S. "W. by S. i W. dist. 63 miles : required her latitude, and the direct course and distance from the place left to the place arrived at, and the construction of the traverse. ^^^ j Lat. 22° 3' N., course S. ^^' I Dist. 149.2 miles. 3. A ship from lat. 28° 32' K has run the following courses, viz., 1st, N. W. by N. 20 miles ; 2d, S. W. 40 miles ; 8d, N. E. by E. 60 miles ; 4th, S. E. 55 miles ; 5th, W. by S. 41 miles ; 6th, E. N. E. 66 miles : required her lat- itude, the distance made good, and the direct course, also the construction of the traverse. Ans. Dist. 70.2 miles, course E. 4. A ship from lat. 41° 12' N. sails S. W. by W. 21 miles ; S. W. i S. 31 miles ; W. S. W. i S. 16 miles ; S. I E. 18 miles ; S. W. i W. 14 miles ; then W. i N. 30 miles: required the latitude, the direct course, and the distance. ^^ ( Lat. 40° 05', course S. 52° 49' W. ■ iDist. 111.7 miles. 5. A ship runs the following courses, viz.: 1st, S. E. 40 miles; 2d, N. E. 28 miles; 3d, S W. by W. 52 miles ; 4th, N. W. by W. 30 mHes ; 5th, S. S. E. SEC. IV.] PARALLEL SAILIN-G. 211 8Q miles; 6tli, S. E. by E. 58 miles: required the direct course, and distance made good. ^^ ( Direct course S. 25° 59' E., or S. S. E. a E., nearly, ' (Distance 95.87 miles. 6. A ship sails, 1st, N. W. by W. i W. 40 miles; 2d, K W. by i K, 41 miles ; 3d, N. by E. 16.1 miles ; and 4tli, K E. i E. 32.5 miles : required the distance made, and the direct course. Ans. Course, 21° 54' West of North. Dist. 94.6 miles. These examples will, perhaps, suffice to illustrate the principles of plane sailing. The longitude, made on any course, cannot be deter- mined by these methods, for this being the arc of the equator intercepted between two meridians, cannot be found under the supposition that the meridians are parallel. The most simple case of finding the difference of lon- gitude is when the ship sails due east or due west : this is called Parallel Sailing. SECTION IV. PARALLEL SAILING. 17. The entire theory of parallel sailing is comprehend- ed in the following proposition, viz.: The cosine of the latitude of the parallel^ is to radius^ as the distance run to the difference of longitude. Let IQR represent the equa- tor, and FDN any parallel of latitude : then, CI will be the radius of the equator, and EF the radius of the paralleL Suppose FD to be the dis- tance sailed, then the differ- ence of longitude will be meas- ured by IQ, the arc intercept- ed on the equator. Then, 212 ELEMENTS OF SURVEYING. [BOOK V. since similar arcs are to eacli other as their radii (Geom., Bk. v., Prop. 14), we have, iJF '. CI :: dist. FD : diff. long. IQ. But FF is the sine of PF, or cosine of FI, the latitude: and CI is the radius of the sphere : hence, cos lat. : i? : : distance : difp. longitude. 18. If we denote by D the distance between any two meridians, measured on the parallel whose latitude is L ; a/nd by D' the distance between the same meridians meas- ured on the parallel whose latitude is L', the arcs are similar, and we shall have (Geom,, Bk. Y., Prop. 14), cos L : D : : cos L' : D', that is, cos L : cos L' : : D : B'. Hence, when the longitude made on different parallels is the same, the distances sailed are proportional to the cosines of the parallels of latitude. 19. By referring to Th. Y., Bk. I., we see that in any right-angled triangle B : cos angle at base : : hyp. : base, or Gos F : E :: FC : FC ; and by comparing this with the propor- tion, cos lat. : i? : : dist. : diff. long ; we see, that if in a right-angled triangle the angle at the base be made equal to the latitude of the parallel, and the base to the distance run ; then, the hypothenuse will represent the difference of longitude. It follows therefore, that any problem in parallel sail- ing, may be solved as a simple case of plane sailing. For, if we regard the latitude as the course, the distance run as the base, the difference of longitude will be the hypo- thenuse of the corresponding right-angled triangle. SEC. lY.] PARALLEL SAILING. 213 EXAMPLES. 1. A ship from latitude 53° 56' K, longitude 10" 18' E., has sailed due west, 236 miles : required her present longitude. By the rule As cos lat. 63° 56' . ar. c. . .230087 : radius 10.000000 : : distance 236 . . . . . 2.372912 : diff. long. 400.8 .... 2.602999 Long, left . . 10° 18' E. Diif. long. = -^ degrees = 6° 40' W. Long. . . 3° 38' E. 2. If a ship sails B, 126 miles from the North Cape, in lat. 71° 10' IST., and then due N., till she reaches lat, 73° 26' IST. ; how far must she sail W. to reach the meri- dian of the North Cape ? Here the ship sails on two parallels of latitude, first on the parallel of 71° 10', and then on the parallel of 73° 26', and makes the same difference of longitude on each parallel. Hence, by Art. 18, As cos lat. 71° 10' arith. comp. 0.491044 : distance 126 . . 2.100371 : : cos lat. 73° 26' . . 9.455044 : distance 111.3 . . 2.046459 3. A ship in latitude 32° K sails due E. till her dif- ference of longitude is 384 miles : required the distance run. Ans. 325.6 miles. 4. If two ships in latitude 44° 30' N., distant from each other 216 miles, should both sail directly S. till their distance is 256 miles, what latitude would they arrive at? Ans. 32° 17' N. 214 N'AVIGATION. [BOOK V. 5. Two ships in the parallel of 47° 54' K, have 9° 35' difference of longitude, and they both sail directly S., a distance of 836 miles: required their distance from each other at the parallel left, and at that reached. Am. 385.5 miles, and 479.9 miles. SECTION V. MIDDLE LATITUDE SAILING. 20. Having seen how the longitude which a ship makes when sailing, on a parallel of latitude may be determined, we come now to examine the more general problem, viz., to find the longitude which a ship makes when sailing upon any oblique rhumb. There are two methods of solving this problem, the one by what is called middle latitude sailing, and the other by Mercator's sailing. The first of these methods is confined in its application, and is moreover somewhat inaccurate even where applicable ; the second is perfectly general, and rigorously true ; but still there are cases in which it is advi- sable to employ the method of middle latitude sailing, in preference to that of Mercator's sailing. It is, therefore, proper that middle latitude sailing should be explained, especially since, by means of a correction to be hereafter noticed, the usual inaccuracy of this method may be rectified. Middle latitude sail- ing proceeds on the supposition that the de- y^ '^VXX'S^^^ parture or sum of all the meridional distan- ces, h% c'c, did, &c., from to T, is equal to the distance M'M between the meridians passing through and T, measured on the parallel of lati- tude equally distant from and T. SEC. v.] MIDDLE LATITUDE SAILING. 215 The middle latitude is half the sum of tlie two extreme latitudes, if they are both of the same name, and half their difference, if they are of contrary names. The supposition above becomes very inaccurate when the course is small, and the distance run great ; for it is plain that the middle latitude distance will receive a much greater acces- sion than the departure, if the track OT cuts the successive meridians at a very small angle. The principal approaches nearer to accuracy as the angle of the course increases, because then as but little ad- vance is made in latitude, the several component depart- ures lie more in the immediate vicinity of the parallel M'M. But still, in very high latitudes, a small advance in lat- itude makes a considerable difference in meridional dist- ance ; hence, this principle is not to be used in such lat- itudes, if much accuracy is required. By means, however, of a small table of corrections, con- structed by Mr. Workman^ the imperfections of the middle latitude method may be removed, and the results of it ren- dered in all cases accurate. This table we have given at the end of this work. 21. The rules for middle latitude sailing may be thus deduced. We have seen, in the first case of plane sailing, that if a ship sails on an oblique rhumb from to T, that the hypothenuse OT will represent the distance ; OT' the difference of latitude, and T'T^ the depart- ure. Now, by the present hypothesis, the departure T'T is equal to the middle parallel of latitude between the meridians of the places sailed from and arrived at : so that the difference of longitude of these two places is the same as if the ship had sailed the distance T'T on the mid- dle parallel of latitude. The determination of the differ- ence of longitude is, therefore, reduced to the case of par- allel sailing: for, T'T now representing the distance on the parallel, if the angle T'TO' be made equal to the latitude of 216 NAVIGATION. [BOOK V. that parallel, we shall have, by the last case, the difference of longitude represented by the hypothenuse O'T. We therefore have the following theorems: I. In the triangle O'TT', cos O'TT' : TT' : : B : T0'\ that is, cos mid. lat. : departure : : R \ diff. longitude. II. In the triangle O'TO sin 0' : OT : : sin : O'T] that is, since sin 0' = cos O'TT' cos mid. lat. : distance : : sin. course : diff. longitude. III. In the triangle OTT', we have B : tangent : : OT' : TT' ; comparing this with the first proportion, and observing that the extremes of this are the means of that, we have OT' : O'T :: cos O'TT' : tang 0; that is, diff. lat. : diff. long. : : cos mid. lat. : tang course. These three propositions comprise the theory of mid- dle latitude sailing ; and when to the middle latitude sail- ing, the proper correction, taken from Mr. Workman's table, is applied, these theorems will be rendered accurate. In the table of pages 93 and 94, the middle latitude is to be found in the first column to the left. Then, along the horizontal Hue, and under the given difference of lat- itude, is inserted the proper correction to be added to the middle latitude to obtain the latitude in which the meri- dian distance is accurately equal to the departure. Thus, if the middle latitude be 37°, and the difference of latitude 18°, the correction will be found on page 94, and is equal to 0° 40'. EXAMPLES. 1. A ship, in latitude 51° 18' N., longitude 22° 6' W., is bound to a place in the S. E. quarter, 1024 miles dis- tant, and in lat. 37° N. : what is her direct course and dis- SEC. v.] MIDDLE LATITUDE SAILING. 217 tance, as also the clijBference of longitude between the two places ? Lat. from 51° 18' K Lat. to 87° N. Sum of latitudes . Mid. lat. . . . . 88° 18' . 44° 9' Diff. lat. 14° 18 = 858 miles. As distance 1024 : radius : : diff. lat. 858 6.989700 10.000000 2.933487 cos course 33° 5' 9.923187 Cos mid lat 44° 9' ar c 0.144167 : tang course 33° 5' 9.813899 : : diff. lat. 858 2.933487 diff. long. 779 2.891553 In this operation the middle latitude has not been cor- rected, so that the difference of longitude here determined is not without error. To find the proper correction, look for the given middle latitude, viz., 44° 9', in the table of corrections, the nearest to which we find to be 45° ; against this and under 14° diff. of lat, we find 27' ; and also, under 15° we find 31', the difference between the two being 4' ; hence, corresponding to 14° 18' the correction will be about 28'. Hence, the corrected middle latitude is 44° 37', therefore, Cos corrected mid. lat. 44° 37' ar. comp. 0.147629 : tang, course 33° 5' . . 9.813899 : : diff. lat. 858 . . . 2.933487 diff. long 785.3 . 2.895015 2. A ship sails in the IST. "W. quarter, 248 miles, till her departure is 135 miles, and her difference of longitude 310 miles : required her course, the latitude left, and the lat- itude come to. ) Course K 32° 59' W. ; Lat. left 62° 27' K; lat. in 65° 55' K 3. A ship, from latitude 37° N., longitude 9° 2' W., having sailed between the N. and W., 1027 miles, reckons that she has made 564 miles of departure : what was her direct course, and the latitude and longitude reached? . (Course K 38° 19' W., or K W. nearly; ' I Lat. 51° 18' K ; long. 22° 8' "W. 218 NAVIGATION. [BOOK V. 4. Required tlie course and distance from the east point of St. Michael's, lat. 87° 48' K, long. 25° 13' W., to the Start Point, lat. 50° 13' K, long. 3° 38' W. ; the middle latitude being corrected by Workman's table, Ans. Course K 51° 11' B. ; dist. 1189 miles. mercatoe's sailing. 22. It has already been observed, that when a ship sails on an oblique rhumb, the departure, the difference of latitude, and the distance run, are truly represented by the sides of a right-angled triangle. Thus, if a ship sails from A to B, the departure B'B will represent the sum of all the very small meridian distances, or elementary departures, b'b, p"_p, &c. ; the difference of latitude AB will re- present, in like manner, the small dif- ferences of latitude Ab\ h'p\ &c. ; and the hypothenuse AB, will express the sum of the distances corresponding to these several differences of latitude and departure. Each of these elements is supposed to be taken so small, as to form on the surface of the sphere a series of triangles, differing insensibly from plane triangles. Let ABB' be a triangle, in which the angle A repre- sents the course, AB' the difference of latitude, B'B the departure, and AB the distance run. Produce the side AB to C, until CC shall be equal to the difference of longitude of the two extremities of the course : then, for the sake of distinction, we call AB' = the proper difference of latitude, AC = the meridional difference of latitude, and we are now to explain the manner of constructing a table, called a table of meridional parts, which will furnish the meridional differences of latitude, when the ^proper differ- ences are known. Let Ah'h represent one of the elementary triangles ; h'h will then be one of the elements of departure; and AV the corresponding difference of latitude. Now, as Vh is a small arc of a parallel of latitude, it is to a portion of the SEC. v.] MERCATOR'S SAILIlfG. 219 equator containing an equal number of degrees, as the co- sine of its latitude is to radius (Art. 17). This similar portion of the equator, is the difference of longitude be- tween h' and h. Suppose, now, that Ah' is prolonged to p', making p'p equal to the difference of longitude between h and h' : then W : pp' : : cos lat. I'h : R (Art. 17.) But, by similar triangles, we have W : pp' : : Ah' : Ap', and consequently, proper lat. Ah' : mer. dijff. of lat. Ap' : : cos lat. hh' : 1. Denoting the proper difference of latitude by d, the meridional difference of latitude by D, the latitude of h'h by Z, and the radius by 1, which is, indeed, the radius of the table of natural sines, we shall have c? : Z) : : cos Z : 1, which gives D — d secant I, since ^ = sec. I. ' cos I K then, we know the latitude I of the beginning of a course, and the proper difference of latitude d of the ex- tremity of the course, we can easily find the meridional latitude D corresponding to that course. The determination of AC which represents the meri- dional difference of latitude, involves the determination of all the elementary parts, on which it depends. If d be taken equal to 1', we shall have from the equation above D=V sec. ?, or D = sec. 1, it being understood that I expresses minutes or geographi- cal miles. From this equation, the value of D^ corresponding to every minute of ?, from the equator to the pole, may be calculated ; and from the continued addition of these, there may be obtained, in succession, the meridional parts cor- responding to 1', 2', 3', 4', &c., of proper latitude, and when registered in a table, they form a table of meridional parts, given in all books on Navigation. The following may serve as a specimen of the manner in which such a table may be constructed, and, indeed, of the manner in which the first table of meridional parts was 220 NAVIGATION. [BOOK V. actually formed by Mr. Wriglit, tlie proposer of this valu- able metliod. Mer. pts. of V - nat. sec. 1'. Mer. pts. of 2' = nat. sec. 1' + nat. sec. 2'. Mer. pts. of 3' = nat. sec. 1' + nat. sec. 2' + nat. sec. S'. Mer. pts. of 4' = nat. sec. 1' + nat. sec. 2' + nat. sec. 8' + &c. Hence, by means of a table of natural secants we have Nat. Sees. Mer. Pts. Mer. pts. of 1' = 1.000000 = 1.0000000 Mer. pts. of 2' = 1.0000000 + 1.0000000 = 2.0000002 Mer. pts. of 3' = 2.0000002 + 1.0000004 = 8.0000006 Mer. pts. of 4' = 3.0000006 + 1.0000007 = 4.0000013, &c. There are other methods of construction, but this is the most simple and obvious. The meridional parts thus de- termined, are all expressed in geographical miles, because in the general expression D = l' sec. 2, 1' is a geographical mile, 23. Having thus formed the table of meridional parts, if we find from it, the meridional parts corresponding to the latitudes of the place left and the place arrived at, their difference will be the meridional difference of lat- itude, or the line AC in the diagram. The difference of longitude denoted by CO may then be found by the fol- lowing proportion. I. As radius is to the tangent of the course, so is the meri- dional difference of latitude to the difference of longitude. But if the departure be given instead of the course, then, II. As the proper difference of latitude is to the departure, so is the meridional difference of latitude to the longitude. Other proportions may also be deduced from the diagram. EXAMPLES. As an example of Mercator's or rather Wright's, sailing, let us take the following : 1. Eequired the course and distance from the east point of St. Michael's to the Start point: the latitudes being 87° 48' N., and 50° 13' K, and the longitudes 25° 13' W., and 3° 38' W. SEC. v.] MERCATOR'S CHART. Start Point, lat. 50° 13' K St. Michaers, lat. 37° 48' K Proper difference of lat. 12° 25 60 Mer. pts. 8495 Mer. pts, 2453 Mer. diflf. 1042 _ Diff. oflong. 21° 35' Diff. in miles 745 60 Diff. in miles 1295 Now, let us suppose that we liave sailed from A to B: we shall tlien know AB' equal proper diflf. lat. = 745 miles ] AC = meridional diff. of lat. = 1042; and 0'0 = the difference of lon- gitude equal to 1295 miles. It is re- quired to find the course B'AB, and the distance AB. For the Course. As AC 1042 6.982132 : radius 10.000000 :: CC 1295 3.112270 : tang. A 51° 11' E. 10.094402 For the Distance. As cos A 51° 11' 0.202850 : AB' 745 2.872156 : : radius 10.000000 AB 1189 3.075006 2. A ship sails from latitude 37° N. longitude 22° 56' W., on the course N. 33° 19' E. : till she arrives at 51° 18' N. : required the distance sailed, and the longitude ar- rived at. Am. Dis. 1027 miles ; long. 9° 45' W. MEEOATOR's CHART. 24. Mercator's Chart is a Map constructed for the use of Navigators. In this chart all the meridians are repre- sented by straight lines drawn parallel to each other, and the parallels of latitude are also represented by parallel straight lines drawn at right-angles to the meridians. The chart may be thus constructed. Draw on the lower part of the paper a horizontal line to represent the parallel of latitude which is to bound the southern portion of the chart. From a scale of equal parts, corresponding in size 222 NAVIGATION. [BOOK V. to the extent of tlie map to be made, lay off, on this line, any number of equal distances, and tbrongli the points draw a series of parallels to represent the meridians. Then draw a line on the side of the map, and for the second parallel of latitude, find from the table of meri- dional parts the meridional difference of latitude corres- ponding to the degrees between the first and second par- allel, and lay off this distance for the interval between the two parallels. Then find the meridional difference between the second and third, and lay it off in the same way for the third parallel, and so on, for the fourth, fifth, &c. A place whose latitude and longitude are known, may be laid down in the same manner; for it will always be determined by the intersection of the meridian and parallel of latitude. If the chart is constructed on a small scale, the divisions on the graduated hues, may be degrees instead of minutes ; and the meridians and parallels may be drawn only for every fifth or tenth degree. We have already seen (Art, 23), that the meridional difference of latitude bears a constant ratio to the difference of longitude, so long as the course remains unchanged : and hence we see that on Mercator's chart, every rhumb will be represented by a straight line, LINE OF MERIDIONAL PARTS ON GUNTER's SCALE. 25. This scale corresponds exactly with the table of me- ridional parts, excepting, that in the table, the circle is divid- ed to minutes, while the scale is divided only to degrees. A scale of equal parts is placed directly beneath the scale of meridional parts ; if the former corresponds to divisions of longitude, the latter will represent those of latitude. Hence, a chart may be constructed from those scales, by using the scale of equal parts for the lines of longitude, and the scale of meridional parts for those of latitude. A TABLE OF LOGARITHMS OF NUMBERS FEOM 1 TO 10,000. N. Log. N. Log. N. Log. N. Log. I 0-000000 26 1-414973 ■ 5i 1 -707570 76 1 880814 2 o-3oio3o 27 i.43i364 52 1 •716008 77 I 886491 3 0-477121 28 1.447158 53 I 724276 78 1 892095 4 0-602060 29 1.462898 54 1 782394 79 I 897627 5 0-698970 3o 1-477121 55 I 740868 80 I 908090 6 o-778i5i 81 1-491862 56 I 748188 8x 1 908485 7 0-845098 32 i.5o5i5o tl \ 755875 82 I 918814 8 0-908090 33 i.5i85u 768428 83 1 919078 9 0-954243 34 1-531479 59 1 770852 84 1 924279 10 I -000000 85 1.544068 60 1 778151 85 1 929419 ,1 I -041393 36 i.5563o8 61 1 785330 86 I 934498 12 I-079I8I i- 118943 37 1-568202 62 1 792892 87 1 989519 944483 i3 38 1-579784 63 1 799341 88 I 14 1.146128 39 1-591065 64 1 806181 89 I 949390 i5 1-176091 40 1-602060 65 1 812918 90 1 954243 i6 1-204120 41 1-612784 66 1 819544 91 1 959041 n I -230449 42 1-628249 tl \ 826075 92 I 968788 i8 1-255273 48 1-688468 882509 93 1 968483 19 1-278754 44 1-643453 69 1 838849 94 I 978128 20 i-3oio3o 45 1-653213 70 1 845098 95 1 977724 21 1-322219 46 1-662758 71 1 851258 96 I 982271 22 1-842423 47 1-672098 72 I 857383 97 I 986772 23 1.861728 48 1-681241 73 I 868323 98 I 991226 24 I-3802II 49 1-690196 74 I 869282 875061 99 I 995635 25 1.397940 5o 1-698970 75 1 100 2 000000 Remark. In the following table, in the nine right hand columns of each page, where the first or leading figures change from 9's to O's, points or dots are introduced in- stead of the O's, to catch the eye, and to indicate that from thence the two figures of the Logarithm to be taken from the second column, stand in the next line below. A TABLE OF LOGARITHMS FROM 1 TO 10,000. N. ' 2 3 4 5 6 7 8 9 D. 100 000000 0434 0868 i3oi 1734 2166 2598 3029 3461 3891 432 lOI 4321 4751 5i8i 5609 6o38 6466 6894 7321 7748 8174 428 102 8600 r.il & 9876 •3oo •724 1147 1570 1993 24i5 424 io3 012837 4100 4521 4940 536o 5779 6197 6616 n 104 7033 745i 7868 8284 X 9116 3252 9532 3664 9947 •36i •775 io5 021189 53o6 i6o3 2016 2428 4075 4486 4896 All io6 5715 6125 6533 6942 7350 7757 8164 8571 8978 408 :o^ 9384 033424 Til •195 •600 1004 1408 1812 2216 2619 3021 404 4227 8223 4628 5029 543o 5830 6230 6629 7028 400 109 7426 7825 8620 9017 9414 9811 •207 •602 •998 396 no 041393 1787 2182 2576 Itsl 3362 3755 4148 4540 8830 3^ III 5323 5714 6io5 64o5 V,ll 7664 8o53 8442 112 9218 053078 9606 mi •3§o •766 1538 1924 2309 2694 386 ii3 3463 423o 46x3 4996 5378 5760 6142 6524 382 114 6905 7286 7666 8046 8426 8§o5 9i85 9563 3333 9942 •320 379 ii5 060698 io75 1452 1829 2206 2582 2958 3709 4o83 376 116 4458 4832 5206 558o 5953 6326 6699 7071 7443 78i5 372 \\l 8186 8557 8928 6640 9668 ••38 •407 •776 1145 i5i4 ^S 071882 225o 2617 3352 3718 4085 445 1 4816 5i82 119 5547 5912 6276 7004 7368 7731 8094 8457 8819 363 120 079181 9543 3i44 9904 35o3 •266 •626 Til 1347 1707 2067 2426 36o 121 082785 3861 4219 4934 5291 9198 6004 357 122 636o 6716 7071 7426 7781 8i36 8490 8845 tf, 355 123 9905 093422 •258 •611 »963 i3i5 1667 2018 2370 2721 35i 124 3772 4122 4471 4820 5169 55i8 5866 62i5 6562 349 125 6910 7257 7604 7951 8298 8644 5S 9335 9681 ••26 346 126 100371 0715 1059 i4o3 1747 2091 2777 3119 3462 343 IS 38o4 4146 4828 5169 8565 55io 585: 6191 6531 687, 340 7210 7549 7888 8227 8903 9241 9579 9916 •253 338 129 110590 0926 1263 1599 1934 2270 2605 2940 3275 3609 335 i3o 1 13943 4277 461 1 4944 5278 56ii 5943 6276 9586 6608 6940 333 i3i 7271 7603 7934 8265 8595 8926 9256 9915 •245 33o I32 120574 0903 I23l i56o 1888 2216 2544 2871 3198 6456 3525 328 i33 3852 4178 45o4 483o 5i56 5481 58o6 6i3i 6781 325 i34 7io5 7429 7753 8076 8399 8722 9045 9368 9690 ••12 323 i35 i3o334 o65d 0977 1298 1619 1939 2260 258o 2900 3219 321 i36 3539 3858 4177 4496 4814 5i33 545 1 5769 6086 64o3 3i8 137 6721 7037 7354 7671 7987 83o3 8618 8934 9249 9064 3i5 138 •194 •5o8 •822 1136 i45o 1763 2076 2389 2702 3i4 139 3327 3639 3951 4263 4574 4885 5,96 5507 58i8 3ii 140 I46I28 6438 6748 7o58 7367 7676 79B5 8294 86o3 8911 309 Ui Jlii 9527 9835 •142 •449 •756 io63 1370 1676 1982 307 142 2594 2900 32o5 35io 38i5 4120 4424 4728 5o32 3o5 143 5336 5640 5943 6246 6549 6852 7154 7457 7759 8061 3o3 144 8362 8664 8965 9266 9567 9868 •168 •469 •769 1068 3oi 145 i6i368 1667 1967 2266 2564 2863 3i6i 3460 3758 4o55 299 146 4353 465o 4947 5244 5541 5838 6i34 6430 6726 7022 297 U7 7317 7613 7908 8203 8497 1434 8792 9086 9380 9674 tl 295 148 170262 o555 0848 1141 1726 2019 23ll 26o3 293 149 3i86 3478 3769 4060 435i 4641 4932 5222 55i2 58o2 291 i5o 176091 638i 6670 S 7248 7536 7825 8ii3 8401 8689 1 558 289 i5i 181844 9264 9552 •126 •4i3 S? •985 3839 1272 287 l52 2129 4075 24i5 2700 2985 5825 3270 4123 4407 285 1 53 4691 5259 5542 6108 6391 6674 6956 7239 283 1 54 7521 7803 8084 8366 8647 8928 9209 9490 9771 ••5i 281 i55 190332 0612 & 3^ i45i 1730 2010 2289 2567 2846 279 1 56 3i25 3403 4237 45i4 4792 5069 5346 5623 278 1 57 a 6176 6453 6729 70o5 7281 7556 7832 8107 8382 276 1 58 8932 9206 9481 9755 ••29 •3o3 •577 •85o 1124 274 159 201397 1670 1943 2216 2488 2761 3o33 33o5 3577 3848 272 N. I 2 3 4 5 6 7 8 9 D. A TABLE OF LOGARITHMS FROM 1 TO 10,000. N. j I 2 3 4 5 6 7 1 8 9 D. 1 60 204120' 4391 4663 4934 5204 5475 5746 6016 6286 6556 271 161 6826: 7006 gSiD 9783 7365 7634 7904 8173 8441 8710 8979 9247 269 162 ••5i •319 •586 •853 1121 i388 1654 1921 267 i63 212188; 2454 2720 2986 3252 35i8 3783 4049 43i4 4579 266 164 4844; 5109 5373 5638 5902 6166 6430 6694 6957 7221 264 i65 7484, 7747 8010 8273 8536 8798 9060 9323 9585 9846 262 166 220108 0370 o63i 0892 ii53 1414 1675 lilt 2196 2456 261 167 2716 2976 5309! 5568 3236 3496 6342 4oi5 4274 6858 4792 5o5i 259 168 5826 6084 6600 71.5 7372 7630 258 169 7887J 8144 8400 8657 8913 9170 9426 9682 9938 •■93 256 170 230449 0794 0960 I2l5 1470 1724 1979 2234 2488 2742 254 171 5^23! 5781 35o4 3757 4011 4264 4517 4770 5o23 5276 253 172 6o33 6285 6537 6789 7041 7292 7544 7795 252 173 8046 8297 8548 8799 9049 9299 9550 9800 ••5o •3oo 25o 174 240549 0799 1048 1297 1 546 179D 2044 2293 2541 2790 249 175 3o3S 3286 3534 3782 4o3o 4277 4525 4772 5019 5266 248 176 55i3 5759 6006 6252 6499 6745 6991 7237 7482 7728 246 177 7973 8219 8464 8709 8954 1395 9198 9443 9687 Its •176 245 178 25o420 0664 0908 ii5i 1638 1881 2125 2610 243 179 2853 3096 3338 358o 3822 4064 43o6 4548 4790 5o3i 242 180 255273 55i4 5755 5996 6237 6477 6718 6958 7198 3g? 241 181 7679 7918 o3io 8i58 07^? 8637 8877 9116 9355 9594 III 182 260071 o548 1025 1263 i5oi 1739 1976 4346 2214 1 83 245 1 2688 2925 3162 3399 3636 3873 4109 4582 237 184 4818 5o54 5290 5525 5761 5996 6232 6467 6702 6937 235 1 85 7172 7406 7641 7875 8110 8344 8578 8812 9046 9279 234 186 95i3 9746 9980 •2l3 •446 •679 •912 1144 1377 1609 233 187 271842 2074 4389 23o6 2538 2770 3ooi 3233 3464 3696 3927 232 188 4i58 4620 485o 5o8i 53ii 5542 5772 6002 6232 23o 189 6462 6692 6921 7i5i 7380 7609 7838 8067 8296 8525 229 190 278754 8982 9211 9439 9667 9895 2169 •123 •35i •578 •806 228 191 281033 1261 1488 1715 1942 2396 2622 2849 3075 227 192 33oi 3527 3753 Itll 42o5 443i 4656 4882 5107 5332 226 193 5557 5782 6007 6456 6681 6905 7i3o 7354 7578 225 194 7802 8026 8249 8473 8696 8920 9143 9366 ffi 9812 223 195 290035 0257 0480 0702 0925 1147 i369 1591 2o34 222 196 2256 2478 2699 2920 3i4i 3363 3584 38o4 4025 4246 221 197 4466 4687 4907 5127 5347 5567 5787 6007 6226 6446 220 198 6665 6884 7104 7323 7542 7761 7979 8198 8416 8635 219 199 8853 9071 9289 9507 9725 9943 •161 •378 .595 •8i3 218 200 3oio3o 1247 1464 i68i 4059 2114 233i 2547 2764 2980 217 201 3ig6 3412 3628 3844 4275 4491 6639 4706 4921 5i36 216 202 535i 5566 5781 5996 6211 6425 6854 7068 7282 2l5 203 7496 7710 7924 8137 835i 8564 8778 8991 9204 9417 2l3 204 9630 9843 ••56 •268 •481 •693 •906 1118 i33o 1 542 212 205 311754 1966 2177 2389 2600 2812 3o23 3234 3445 3656 211 206 3867 4078 4289 4499 4710 4920 5i3o 5340 555i 5760 210 207 5970 6180 6390 6599 7018 7227 7436 7646 7854 209 208 8o63 B272 8481 8689 9106 9314 9322 9730 9938 20a 209 320146 o354 o562 0769 0977 1184 1391 1598 i8o5 2012 207 210 322219 2426 2633 2839 3046 3252 3458 3665 3871 4077 206 211 4282 4488 4694 4899 6930 5io5 53io 55i6 5721 5926 6i3i 2o5 212 6336 6541 6745 7155 g? 7563 7767 7972 8176 204 2l3 838o 8583 8787 8991 9194 9601 9805 •••8 •211 203 214 33o4i4 0617 0819 1022 1225 1427 i63o i832 2o34 2236 202 2l5 2438 2640 2842 3044 3246 3447 3649 385o 4o5i 4253 202 216 4454 4655 4856 5o57 5257 5458 5658 5859 6059 6260 201 217 6460 6660 6860 7060 7260 7459 7659 7858 8o58 8257 200 218 8456 8656 8855 9054 9253 945 1 9650 9849 ••47 •246 199 219 340444 0642 0841 1039 1237 1435 i632 i83o 2028 2225 198 N. I 2 ' 4 5 6 7 8 9 D. 15 A TABLE OF LOGARITHMS FROM 1 TO 10,000. N. 1 I 2 3 4 5 6 7. 8 9 D. 220 342423 2620 4785 3oi4 3212 3409 36o6 38o2 3999 4196 607 197 221 4392 6353 4589 4981 5178 % 5570 5766 5^62 i?6 222 6549 6744 6939 7135 7525 7720 79i5 8uo 195 223 83o5 85oo 8694 8889 9083 9278 9472 9666 9860 ••54 194 224 350248 0442 o636 0829 1023 1216 1410 i6o3 1796 1989 3916 193 225 2i83 2375 2568 2761 2954 3i47 3339 3532 3724 193 226 4108 43oi 4493 4685 4876 5o68 5260 5452 5643 5834 192 227 6026 6217 6408 6599 6790 6981 7172 7363 7554 7744 191 228 7935 8125 83i6 85o6 8696 8886 9076 9266 9456 9646 190 229 9835 361728 ••25 •2l5 •404 0593 •783 •972 1161 i35o 1539 189 230 1917 2io5 2294 2482 2671 2859 3048 3236 3424 188 23l 36i2 38oo 3988 4176 4363 455i 4739 4926 5ii3 53oi 188 232 5488 5675 5862 6049 6236 6423 6610 86? •5i3 6983 7169 187 233 7356 7542 7729 791D 8101 8287 8473 8845 9o3o 186 234 9216 9401 9587 9772 "& •143 •328 •698 •883 i85 235 371068 1253 1437 1622 1991 2175 236o 2544 2728 184 236 2912 4932 3280 3464 3647 383i 401 5 4198 4382 4565 184 237 4748 5ii5 5298 5481 5664 5846 6029 6212 6394 1 83 238 6577 ttt 6942 7124 7306 7488 7670 7852 8o34 8216 182 239 8398 8761 8943 9124 9306 9487 9668 9849 ••3o 181 240 38021 1 0392 0573 0754 0934 iii5 1296 1476 1 656 1837 181 241 2017 2197 2377 2557 2737 2917 3097 3277 3456 3636 180 242 38i5 3995 4174 5964 4353 4533 4712 4891 5070 5249 5428 179 243 56o6 5785 6142 6321 6499 6677 6856 7034 8811 7212 178 244 7390 7568 7746 7923 8101 8279 8436 8634 8989 178 245 9166 9343 9520 9698 9875 ••5 1 •228 •4o5 •582 •759 177 246 390935 1112 1288 1464 1641 1817 1993 2169 2345 2521 176 247 4452 2873 3048 3224 3400 3575 \t\ 3926 4101 4277 176 248 4627 4802 4977 5i52 5326 5676 5850 6025 175 249 6199 6374 6548 6722 6896 7071 7245 7419 7592 7766 174 25o 397940 8.14 8287 8461 8634 8808 8981 9154 9328 95oi 173 25l 9674 9847 ••20 • 192 •365 •538 •7.1 *883 Jo56 1228 173 252 401401 1573 1745 1917 2089 2261 2433 26o5 2777 2949 172 253 3l2I 3292 3464 3635 3807 3978 4i'49 4320 4492 4663 171 254 4834 5oo5 5.76 5346 5517 5688 58D8 6029 6199 6370 171 255 6540 6710 6881 8749 7221 7391 756i 7731 7901 8070 170 256 8240 8410 8579 8918 9087 9237 9426 9764 169 257 9933 •102 •271 •440 :5 •777 •946 1114 1283 i45i 169 258 411620 1788 1956 2124 2461 2629 43o5 2796 2964 3i32 168 259 33oo 3467 3635 38o3 3970 4i37 4472 4639 4806 167 260 414973 5i4o 5307 5474 5641 58o8 ^n^o 6141 63o8 6474 167 261 6641 6807 6973 8633 7i3o If. 7306 7472 7638 7804 7970 8i35 166 262 83oi 8467 8964 9129 9295 9460 9625 9791 i65 263 9956 •121 •286 •616 •781 •945 mo 1275 1439 1 65 264 421604 1788 1033 1% 5371 2261 2426 25go 2754 2918 3082 164 265 3246 3410 3574 5?34 4o65 4228 4392 4555 4718 164 266 4882 5o45 5208 5697 586o 6023 6186 6349 1 63 267 65n 6674 6836 6999 7161 7324 7486 7648 781 1 7973 9591 162 268 8i35 8297 li^ 8621 8783 Ifi 9106 9268 9429 162 269 9752 9914 •236 •398 •720 •881 1042 i203 161 270 43 1 364 i525 i685 1846 2007 2167 2328 2488 2649 2809 161 271 2969 3i3o 3290 3450 36io 3770 3930 5526 4090 4249 4409 160 272 4569 4729 4888 5048 5207 5367 5685 5844 6004 1 59 273 6i63 6322 6481 6640 6798 8384 §s 7II6 S?J 7433 7592 274 7751 7909 8067 9648 8226 8701 9017 9175 275 9333 9491 9806 ?S •122 •279 •437 •594 •752 1 58 276 440909 1066 1224 i38i 1695 i852 2166 2323 1 57 277 2480 2637 B 2950 45i3 3io6 3263 3419 3576 3732 3889 .57 278 4045 4201 4669 4825 4981 6537 5i37 5293 5449 1 56 279 56o4 5760 6071 6226 6382 6692 6848 7003 1 55 N. ^ 2 3 4 5 6 7 8 9 D. A TABLE OP LOGARITHMS FROM 1 L TO 10,000. t N. I 2 3 4 5 6 7 8 9 D. 280 J447i58 73i3 7468 7623 7778 7933 8088 8242 8397 8552 1 55 281 8706 8861 90i5 9170 9324 9478 9633 9787 9941 21 1 54 282 :45o249 o4o3 0557 0711 0865 1018 1172 .326 .479 .54 283 1786 1940 2093 3247 2400 2553 2706 2859 3o.2 3.65 1 53 284 33i8 3471 3624 3777 3930 4082 4235 4387 4540 4692 1 53 285 4845 4997 5i5o 53o2 5454 56o6 5758 5910 6062 6214 .52 286 6366 65i8 6670 6821 6973 8638 7276 8789 7428 7579 773. 1 52 287 7882 8o33 8184 8336 8487 9995 8940 9091 9242 .5. 288 9392 9543 9694 9845 •146 •296 •447 •597 •748 .5i 289 460898 1048 1 198 1348 1499 1649 1799 1948 2098 2248 i5o 290 462398 2548 2697 2847 2997 3 146 3296 3445 35o4 5o85 3744 i5o 291 3893 4042 4191 4340 4490 4639 4788 4936 5234 149 292 5383 5532 568o 5829 5977 6126 6274 7756 6423 6571 6719 .49 293 6868 7016 7164 73i2 7460 7608 ^8^ 8o52 8200 148 294 8347 8495 8643 8790 8938 9?f^ 9233 9527 9675 148 2gD 9822 9969 •116 •263 •410 .557 2025 •704 •85. •998 1.45 147 296 471292 1438 1 585 1732 1878 2171 23.8 2464 26.0 146 297 2756 2903 4362 lltl 3195 4653 3341 3487 3633 nil 538. 407. 146 298 4216 4799 6252 4944 5090 5526 146 299 567. 58i6 5962 6107 6397 6542 6687 6832 6976 145 3oo 477121 7266 741 1 8999 7700 7844 7989 8i33 8278 8422 145 3oi 8566 8711 8855 9143 9287 9431 9575 9719 9863 144 3o2 480007 oi5i 0294 0438 o582 0725 0869 .0.2 ..56 27I? 144 3o3 1443 1 586 1729 1872 2016 2159 2302 2445 2588 143 3o4 2874 3oi6 3,59 33o2 3445 3587 3730 3872 40.5 4.57 143 3o5 43oo 4442 4585 4727 4869 Son 5i53 5295 5437 5579 142 3o6 5721 5863 6oo5 6147 6289 643o 6572 67.4 6855 6997 142 3o7 7.38 7280 7421 7563 7704 7845 7986 8127 8269 84.0 141 3o8 855i 8692 8833 lut 9114 9255 9396 9537 9677 98.8 141 309 9958 ••99 •239 •520 •661 •801 •941 io8i .222 140 3io 491362 i5o2 1642 1782 1922 2062 2201 2341 2481 2621 140 3ii 2760 2900 3o4o 3.79 3319 3458 IX 3737 3876 40.5 139 3l2 4i55 4294 4433 4572 4711 485o 5.28 5267 5406 139 3i3 5544 5683 5822 5960 ?3? 6238 6376 65.5 6653 6791 139 3i4 6930 7068 7206 7344 7621 7759 7897 8o35 8.73 .38 3i5 83ii 8448 8586 8724 8862 8999 9137 9275 9412 9550 .38 3i6 9687 9824 9962 ••99 •236 •374 •5u •648 •785 •922 .37 3i7 5oio59 1 196 1333 1470 1607 1744 1880 20.7 2.54 229. 3655 137 3i8 2427 2564 2700 2837 2973 3109 3246 3382 35.8 i36 3.9 3791 3927 4o63 4199 4335 4471 4607 4743 4878 5o.4 i36 320 5o5i5o 5286 5421 5557 5693 5828 5964 6099 6234 6370 .36 321 65o5 6640 6776 6911 7046 7.81 7316 7451 8934 772. .35 322 7856 7991 8126 8260 8395 853o 8664 8799 9068 i35 323 9203 9337 9471 9606 9740 9874 •••9 •.43 •277 •4.1 .34 324 5io545 0679 o8i3 0947 1081 I2l5 1 349 1482 .6.6 ,750 .34 325 1 883 2017 2l5l 2284 2418 255i 2684 28.8 295. 3o84 i33 326 3218 335i 3484 3617 3750 3883 4016 4149 4282 4414 .33 327 4548 4681 48i3 4946 5079 52II 5344 5476 5609 5741 i33 328 5874 6006 6139 6271 64o3 6535 6668 6800 6932 7064 8382 l32 329 7.96 7328 7460 7592 7724 7855 7987 8119 825i l32 33o 5i85i4 8646 8777 8909 9040 9171 93o3 9434 9566 9697 i3i 33i 9828 9959 ••90 •221 •353 •484 •6i5 •745 •876 .007 i3i 332 52II38 in 1400 i53o 1661 1792 1922 2o53 2.83 23.4 i3i 333 2444 2705 2835 2966 3o?6 3226 3356 3486 36.6 .30 334 3746 3876 4006 4i36 4266 4396 4526 4656 4785 49.5 i3o 335 5o45 5i74 5304 5434 5563 69^5 582 2 595. 6081 62.0 129 336 6339 6469 6727 6856 7114 7243 7372 750. 129 337 763o 7759 9045 8016 8145 8274 9559 8402 853 1 8660 8788 '.It 338 89.7 9'74 9302 9430 9687 98.5 9943 ••72 339 o3o2oo o328 0456 o584 0712 0840 0968 1096 1223 i35i 128 N. I 2 3 4 ' 1 6 7 8 9 ~b7 A TABLE OF LOGARITHMS FROM 1 TO 10,000. N. 1 I 2 ^ 4 5 6 7 8 9 D. 340 531479 1607 1734 1862 1990 2117 2245 2372 25oo 2627 128 341 2754 2882 3009 3i36 3264 3391 35i8 3645 3772 3899 127 342 4026 41 53 4280 4407 4534 4661 4787 4914 5o4. 5167 127 343 5294 5421 5547 5674 6937 58oo 5927 6o53 6180 63o6 6432 126 344 6558 66«5 681 1 7063 7189 8448 73i5 7441 7567 7693 126 345 7819 7945 8071 8197 8322 8574 8699 8825 8931 126 346 9076 9202 9327 9432 9578 9703 9829 99^4 ••79 •204 125 347 540329 1579 0455 o58o 0705 o83o 0955 1080 1205 i33o J 454 125 34S 1704 1829 1953 2078 22o3 2327 2452 2576 2701 125 349 2825 2950 3074 3199 3323 3447 3571 3696 3820 3944 124 35o 544068 4192 43i6 4440 4564 4688 4812 4936 5o6o 5i83 124 35i 5307 543 1 5555 5678 58o2 5925 6049 6172 6296 6419 124 352 6543 6666 6789 6913 7o36 8267 7159 7282 74o5 ??g 7652 123 353 7775 7898 8021 8144 8389 85i2 8635 8881 123 354 9003 9126 9249 0473 9371 9494 9616 9739 9861 9984 •106 123 355 55.0228 o35i 0595 0717 0S40 0962 1084 1206 1328 122 356 i45o 1072 1694 I8I6 1938 2060 2181 23o3 2425 2547 122 357 2668 2790 291 1 3o33 3i55 3276 3398 3519 3640 3762 121 358 3883 4004 4126 4247 4368 4489 4610 4731 4852 4973 121 359 5094 52i5 5336 5457 5578 5699 5820 5940 6061 6182 121 360 5563o3 6423 6544 6664 6785 6905 7026 7146 7267 8469 7387 120 36i 7507 7627 8829 7748 7868 7988 8108 8228 8349 8589 120 362 8709 8948 9068 9188 9308 9428 9548 9667 9787 120 363 9907 ••26 •146 •265 •385 •5o4 •624 •743 •863 •982 119 364 56II0I 1221 i34o 1459 1578 I6g8 18.7 1936 2o55 2174 119 365 2293 2412 253i 2630 2769 2887 3oo6 3i23 3244 3362 119 366 3481 36oo 3718 3837 3955 4074 4192 43ii 4429 4548 119 367 4666 4784 4903 502I 5.39 5257 5376 5494 56i2 5730 118 368 5848 5966 6084 6202 6320 6437 6555 6673 6791 6909 118 369 7026 7144 7262 7379 7497 7614 7732 7849 7967 8084 118 370 568202 83i9 8436 8554 8671 8788 8905 9023 9140 9257 117 371 9374 9491 9608 9723 9842 9939 ••76 •193 •309 •426 117 372 570343 0660 0776 0893 1010 1 1 26 1243 1359 1476 1592 117 373 1709 1825 1942 2038 2174 2291 2407 2523 2689 2755 116 374 2872 2988 3io4 3220 3336 3452 3568 3684 3800 39,5 n6 375 4o3i 4147 4263 4379 4494 4610 4726 4841 4957 5072 116 376 5i88 53o3 5419 5534 565o 5765 588o 5996 6111 6226 u5 377 6341 6457 6572 6687 6802 6917 7o32 7147 7262 7377 ii5 378 7492 7607 8868 7836 8983 795i 8066 81S1 8295 8410 8325 ii5 379 8639 8754 9097 9212 9326 9441 9555 9669 114 380 579784 t% ••12 •126 •241 •355 •469 •583 •697 •811 114 38i 580925 ii53 1267 i38i \U\ 1608 1722 1 836 1950 114 382 2o63 2177 2291 2404 25i8 2745 2858 2972 3o85 114 383 3199 33i2 3426 3539 3652 3763 3879 3992 4io5 4218 ii3 384 433i 4444 4557 4670 4783 4896 5009 5l22 5235 5348 ii3 385 5461 5574 5686 5799 5912 6024 6137 6250 6362 6475 ii3 386 6587 6700 6812 6925 7037 7149 8272 7262 7374 8496 7486 8608 7599 112 387 7711 7823 8944 7935 8047 8160 8384 8720 112 388 8832 9o56 9167 9279 9391 95o3 96i5 9726 9838 112 389 9950 ••6i .173 i284 •396 •507 •619 •730 •842 •953 112 390 591065 1176 2288 1287 1399 i5io 1621 1732 1843 1955 2066 III 391 2177 2399 25io 2621 2732 2843 2954 3064 3i75 III 392 3286 3397 35o8 36i8 3729 3840 3930 4o6i 4282 III 393 4393 45o3 4614 4724 4834 4945 5o35 5i65 5276 5386 IIO 394 5496 56o6 5717 6817 5827 5937 6047 6137 6267 6377 6487 110 I'^l 6597 6707 6927 7037 7146 7256 8353 7366 7476 7586 IIO 396 -,695 8791 7805 79'4 8024 8i34 8243 8462 8572 8681 IIO m 8900 9009 9119 9228 9337 9446 9556 9665 9774 109 398 9883 9992 •JOI •210 •319 •428 •537 •646 •755 •864 109 399 600973 10S2 1191 1299 1408 i5i7 1625 1734 1843 1951 109 N. I 2 3 4 5 6 7 8 9 "dT A TABLE OF LOGARITHMS FROM 1 TO 10,000. N. I j 2 3 4 5 6 7 8 9 D. 400 602060 l^ \ III] 2386 2494 2603 2711 2819 2928 3o36 io3 401 3i44 3469 3577 4658 3686 3794 3902 4010 4118 108 402 4226 4334 ! 4442 455o 4766 4874 4982 6?66 5x97 108 4o3 53o5 54i3 ; 5521 5628 IS? 5844 5951 6o5g 6274 108 404 63Si 6489 ■ 6396 6704 6919 7026 8098 7133 8203 7241 7348 8419 107 4o5 7455 7562 1 7669 7777 7884 8954 7991 83i2 107 406 8526 8633 1 8740 8847 9061 9167 9274 938 X 9488 107 407 9394 9701 1 9808 9914 ••21 •128 •234 •341 •447 •554 107 408 610660 0767 0873 0979 1086 1192 2254 1298 i4o5 i5ii 1617 2678 106 409 1723 1829 1936 2042 2148 236o 2466 2572 106 410 612784 2890 2996 3io2 3207 33i3 3419 3525 363o 3736 106 411 3842 3947 ' 4o53 41 59 4264 4370 4475 4581 4686 4792 106 412 4897 5oo3 ' 5io8 52i3 5319 5424 5329 5634 5740 5845 io5 4i3 5950 6o55 j 6160 6265 6370 6476 658i 6686 6790 6895 io5 414 7000 8048 7io5 1 7210 73i5 7420 7325 2S 7734 7839 7943 8989 103 4i5 8i53 1 8207 8362 8466 8571 8780 8884 io5 416 9093 9198 9302 9406 95u 9615 9719 9824 9928 ••32 104 417 620136 0240 0344 0448 0332 o656 0760 0864 0968 1072 104 418 1176 1280 1384 1488 1592 1693 im 1903 2007 2110 104 419 2214 23i8 2421 2523 2628 2732 2939 3o42 3146 104 420 623249 3353 3456 3559 3663 3766 3869 3973 4076 4179 io3 421 4282 4385 4488 4391 4695 4798 4901 5004 5x07 5210 io3 422 53i2 54i5 53i8 5621 5724 5827 5929 6o32 6x35 6238 io3 423 6340 6443 6546 6648 6751 6853 6956 7o58 8082 7x61 7263 8287 9308 io3 424 7366 7468 8491 7571 7673 7773 7878 8900 7980 8x85 102 423 8389 8593 8695 8797 9002 9104 9206 102 426 9410 9512 9613 971 5 9817 9919 ••21 •123 •224 •326 102 427 630428 o53o o63i 0733 0835 0936 io38 1 139 1241 i342 102 428 1444 1545 1647 1748 1849 1951 2052 2i53 2255 2356 lOI 429 2457 2559 2660 2761 2862 2963 3064 3i65 3266 3367 lOI 430 633468 4578 3670 3771 3872 It 4074 4175 4276 tilt 100 431 4477 4679 4779 4880 5o8i 5x82 5283 100 432 5484 55S4 5683 5783 5886 5986 6087 6187 6287 6388 100 433 6488 6588 6688 6789 6889 6989 7089 7.89 8190 7290 It 100 434 7490 7390 7690 7790 7890 ^^88 8090 8290 99 435 8489 8589 8689 8789 8888 9088 9188 9287 9387 99 436 94S6 9586 9686 9785 9885 9984 ••84 •i83 •283 •382 99 437 438 640481 o58i 0680 0779 0879 0978 1077 1177 1276 2267 1375 99 1474 1373 1672 1771 1871 1970 2069 3o58 2x68 2366 99 439 2465 2563 2662 2761 2860 2959 3x56 3235 3354 99 440 643453 3551 365o 3749 3847 3946 4044 4143 4242 4340 98 441 4439 4537 4636 4734 4832 4931 5029 5127 5226 5324 98 442 542-2 5521 5619 lv,i 58x5 59,3 6011 6110 6208 63o6 98 443 6404 6302 6600 6796 6894 6992 7089 7187 7285 98 444 7383 7481 7579 7676 7774 7872 l$t 8067 8i65 8262 98 445 836o 8458 8555 8653 8750 8848 9043 9140 9237 97 446 9335 9432 953o 9627 9724 9821 IVl ••16 •ix3 •2x0 97 447 65o3o8 o4o5 0502 0399 0696 0793 0987 1084 ix8x 97 448 1278 1375 1472 1569 1666 1762 2826 1956 2o53 2x5o 97 449 2246 2343 2440 2536 2633 2730 2923 3019 3xi6 97 450 653213 3309 34o5 35o2 3598 3695 3791 4754 3888 3984 4080 96 45 1 4177 5i3S 4273 4369 4465 4562 4658 485o 4946 5o42 96 452 .5235 533 1 5427 5523 56x9 5715 58io 6^64 6002 96 453 6098 6194 6290 6386 6482 6577 6673 5?S? 6960 96 454 70^6 7152 8202 7343 7438 8393 7534 7629 7820 7916 8870 96 455 801 1 1 8107 8298 8488 8584 8679 8774 95 456 8965 9060 9155 9230 9346 9441 9536 9631 9726 9821 95 457 9916, ••11 •106 •201 •296 •391 1339 •486 •58i •676 •771 95 458 660865 0960 io55 ii5o 1243 1434 i529 2475 1623 1718 95 459 i8i3| 1907 2002 2096 2191 2286 238o 2569 2663 Jl N. 1 I 2 3 4 5 6 7 8 9 D. A TABLE OF LOGARITHMS FROM 1 TO 10,000. N. I 2 3 4 5 6 7 8 9 D. 460 662753 2852 2947 3o4i 3i35 3230 3324 34i8 35i2 3607 94 461 3701 3795 3889 3983 4078 4172 4266 436o 4454 4548 94 462 4642 4736 483o 4924 5862 5oi8 5lI2 5206 5299 5393 5487 94 463 558 1 5675 5769 5956 6o5o 6143 6237 633 1 6424 94 464 65i8 6612 6705 6799 6892 6986 7079 7173 7266 7360 94 465 8386 7546 7640 8572 7733 7826 7920 8oi3 8106 8.99 8293 93 466 8479 8665 8739 8852 8945 9038 9i3i 9224 93 % 9317 9410 95o3 9596 9689 97S2 9875 9967 ••60 •I 53 93 670246 0339 043 1 o524 0617 0710 0802 0895 0988 1080 93 469 1.73 1260 i35S i45i 1 543 i636 1728 1821 19:3 2005 93 470 672098 2190 2283 2375 2467 2560 2652 2744 2836 2929 92 47 » 302I 3u3 32o5 3297 3390 3482 3574 3666 3708 385o 92 472 3942 4o34 4126 4218 43 10 4402 4494 4586 4677 4769 92 473 4861 4953 5o45 5i37 5228 5320 54.2 55o3 5395 5687 92 474 5778 5d7o 5962 6o33 6145 6236 6328 6419 65ii 6602 92 475 6694 6785 6876 6968 7059 7.5i 7242 7333 7424 8336 7516 91 476 g°? 7698 7789 7881 7972 8o63 8i54 8245 8427 91 477 8609 8700 8791 8882 8973 9064 9i55 9246 9337 91 47 rf 9428 9519 9610 9700 979' 9882 9973 ••63 •I 54 •245 9> 479 68o336 0426 o5i7 0607 0698 0789 0879 0970 1060 u5i 91 480 681241 i332 1422 i5i3 i6o3 1693 1784 1874 1964 2o55 90 43 1 2145 2235 2326 2416 25o6 2596 2686 2777 2867 2957 90 482 3 047 40? 3227 3317 3407 3497 3587 3677 3767 3857 90 483 3947 4845 4935 4127 4217 4307 4396 4486 4576 4666 4756 90 484 0O2D 5.14 5204 5204 5383 5473 5563 5652 % 485 5742 5^3 1 5921 6010 6100 6279 6368 6458 6547 486 6636 6726 681D 6904 6994 7o83 7172 7261 81 53 735. 7440 89 487 488 7529 8420 7618 7707 7796 7886 8776 7975 8064 8242 833 1 89 85o9 8098 8687 8865 8953 9042 9i3i 9220 89 489 9309 9398 9486 9575 9664 9753 9841 9930 ••19 •107 89 490 690196 0285 0373 0462 o53o 0639 0728 0816 0905 0993 ll 491 loSi 1170 1258 1 347 1435 1524 1612 2583 1789 1877 492 1965 2o53 2142 2230 23i8 2406 2494 2671 2759 88 493 2847 2935 38i5 3o23 3iu 3199 3287 3375 4234 3463 355 1 3639 88 494 3727 3903 3991 4078 4i66 4342 443o 4517 88 495 46o5 4693 4781 4868 4936 5o44 5i3i 5219 5307 5394 88 496 5482 5569 5657 5744 5832 5919 6007 6094 6182 6269 87 4l^ 6356 6444 653 1 66i8 6706 6793 6880 6968 7055 8014 87 7229 8101 7317 7404 749' 7578 8449 7663 7752 7839 7926 87 499 8i88 8275 8362 8535 8622 8709 8796 8883 87 5oo 698970 9057 9144 9231 93.7 9404 9491 9578 9664 975i 87 5oi 9«38 9924 "ii •«98 •184 •271 »358 •444 •53 1 •617 87 502 700704 0790 0877 0963 io5o n36 1222 1 309 1395 2258 1482 86 5o3 i568 i6d4 1741 1827 1913 1999 2086 2172 2344 86 5o4 243. 20.7 26o3 2689 2775 2861 2947 3o33 3ii9 32o5 86 5o5 329. 3377 3463 3549 3635 3721 38o7 3893 3979 4o65 86 5o6 4i5i 4236 4322 4408 44q4 4579 4665 4751 4837 4922 86 507 5oo8 5094 5179 6o35 5265 5350 5436 5522 5607 5693 5778 86 5o8 5864 5949 6120 6206 6291 6376 6462 6547 663 a 85 509 6718 6803 6888 6974 7059 7144 7229 73i5 7400 7485 85 5io 707570 8421 7655 7740 7826 791 1 7996 808 1 8166 825i 8336 85 5ii 85o6 859. 8676 8761 8846 8931 9015 9100 9185 85 5l2 9270 9355 9440 9524 S 9694 9779 9863 9948 ••33 85 5i3 710U7 0963 0202 0287 0371 0540 0625 0710 V,% 0879 85 5i4 1048 Il32 1217 i3oi 1 385 1470 1554 1723 84 5i5 1807 2?S \l\l 2060 2144 2229 23i3 2397 2481 2566 84 5i6 265o 2902 2986 3070 3i54 3238 3323 3407 84 ^;^ 3491 3575 365, 3742 3826 3910 4^33 4078 4162 4246 84 433o 4414 IS? 458i 4665 4749 4916 5ooo 5o84 84 519 5167 525 1 5418 55o2 5586 5669 5753 5836 5920 84 N. I 2 3 4 5 6 7 8 9 1)7 A TABLE OF LOGARITHMS FROM 1 TO 10,000. N. I 2 3 4 5 ' 7 ' 8 1 9 D. 1 520 716003 6087 6170 6254 6337 642! 65o4 6588 6671 1 6754 -^1 521 6838 6921 7004 7088 8oo3 7254 7338 7421 7504 1 7587 8253 8336 1 8419 sal 522 7671 7754 8668 7920 8086 8169 83: 523 85o2 8585 8731 8834 8917 9000 9083 9165 9248 83 1 524 9331 9414 : 9497 9380 9663 9745 9828 9911 9994 ^^77 83; 523 720159 0242 i 0323 0407 0490 0573 o655 0738 0821 \ 0903 83 i 526 09S6 1068 11 5i 1233 i3i6 1393 1481 i5o3 , 1646 i 1728 82, 527 1811 1893 1 1975 2038 2140 2222 23o5 2387 2469 : 2552 82: 528 2634 2716 2798 2881 2963 3045 3127 3209 3291 3374 82 j 529 3456 3538 3620 3702 3784 3866 3948 4o3o 4112 4194 82 53o 724276 4358 4440 4522 4604 4685 4767 4849 4931 5oi3 82 1 53 1 5095 5.76 , 5258 5340 5422 5303 5585 5667 5748 583o 821 532 59.2 5993 ! 6075 61 56 6238 6320 6401 6483 6564 6646 82! 533 6727 6S09 1 6890 6972 7053 7'34 7216 7297 7379 8191 7460 81; 534 754. 7623 ' l-joi 7783 7866 7948 ^2'9 8110 8273 81 535 8354 8435 ' 85i6 8597 8678 8739 8841 8922 9003 9084 81 536 9165 9246 9327 9408 '4i 9570 965i 9732 9813 9893 81 537 9974 ••55 ••36 •217 •378 •459 •540 1 ^62 1 •702 81 538 730782 o863 0944 1024 iio5 1186 1266 i347 i 1428 i5o8 81 539 \589 1669 1730 i83o 1911 1991 2072 2l52 ! 2233 23.3 81 540 732394 2474 2555 2635 2715 2796 2876 2956 i 3o37 3117 80 54. 3197 327S 3358 3438 35i8 3398 3679 3759 3839 39.9 80 542 3999 4079 4160 4240 4320 4400 4480 456o 1 4640 4720 80 1 043 4800 4bao 4960 5o4o 5l20 5200 5279 5359 ; 5439 55i9 80 544 5599 5679 0739 5838 5918 5998 6078 6137 1 6237 63.7 80 545 6397 6476 6556 6635 6715 6795 6874 6934 1 7034 7ii3 801 546 7193 7272 l^'z 7431 75., 7390 7670 8463 7749 1 7829 7908 791 547 79^7 8067 8146 8225 83o5 8384 8343 8622 8701 iV' 548 8781 8860 8939 9018 9097 9177 9256 9335 9414 9493 79 549 9372 965i 9731 9810 9889 9968 ••47 •126 •2o5 i284 79; 550 740363 0442 0521 0600 0678 0757 o836 0915 0994 1073 79! 55i Il52 i23o ■i3o9 i388 1467 .546 1624 1703 1782 i860 79 552 1939 2018 2096 2175 2234 2332 2411 2489 2568 2647 79 i 78! 553 2725 2804 28a2 2961 3o39 3823 3ii8 3196 3273 3353 343. 554 35io 3588 1 3667 3745 3902 3980 4038 4i36 1 42i5 78 1 555 4293 4371 i 4449 4328 4606 4684 4762 4840 4919 1 4997 781 556 5075 5i53 1 523i 5309 5387 5465 5543 t 5621 5699 1 5777 78! s 5855 5933 ! 6011 6ob9 6167 6245 6323 6401 6479 i 6556 78 6634 6712 6790 6868 6945 7023 7101 7179 7256 7334 8o33 8110 78 559 7412 7489 7307 7643 7722 7800 7878 7955 78 56o 748188 8266 8343 8421 8498 8576 8653 1 8731 8808 1 8885 77 56 1 8963 9040 9118 9193 9272 9350 9427 9304 9582 1 9639 77 i 562 9736 9814 989. 9968 ••45 •123 •200 •277 •354 ! '43 1 771 563 75o5o8 o586 0663 0740 0817 0894 0971 1048 II25 j 1202 771 564 1279 1356 1433 i5io 1 587 1664 1741 1818 1895 1972 77 555 2048 2123 : 2202 2279 2356 2433 2309 2380 2663 1 2740 77 1 566 2816 2893 ! 2970 3o47 3i23 3200 3277 ; 3353 343o 1 35o6 77! 567 3583 3660 3736 38i3 3889 3966 4042 ! 4119 4195 1 4272 77 568 4348 4425 45oi 4578 4654 4730 4807 4883 4960 5o36 76 569 5lI2 5189 5265 5341 5417 5494 5570 5646 5722 I 5799 76 570 755875 6636 5951 6027 1 6io3 6180 6256 6332 6408 6484 j 656o 76 57. 6712 6788 1 6864 6040 7016 7092 7168 7244 ' 7320 76 572 7396 7472 1 7548 1 7624 7700 7775 785i 7927 8oo3 i 8070 761 573 8,55 8230 1 83o6 ' 8382 8458 8533 8609 1 8685 : 8761 [ 8836 76 1 574 8912 8988 1 9063 ! 9139 9214 9290 9366 j 9441 1 9517 I 9592 76 1 575 g663 9743 ' 9819 : 9894 1 9970 ••43 •121 i ^196 ! '272 ' •3i-i 75 576 760422 0498 1 0373 j 0649 0724 0799 0875 [ 0950 ! 1025 IIOI 73 %l 1.76 i25i ■ i326 1402 1477 1532 1627 1702 1 1778 i853 75 1928 2oo3 1 2078 2i53 2228 23o3 2378 2453 2529 2604 3278 3353 75 579 2679 2754 I 2829 2904 2978 3o53 3128 32o3 75 1 N. I j 2 3 1 4 5 6 7 8 9 -1 10 A TABLE OF LOGARITHMS PROM 1 TO 10,000. N. ■ 1 ' 3 1 4 5 6 7 8 9 D. 58o 76342^ 35o3 3578 3653 3727 38o2 3877 3952 4027 4101 75 58i Ant 425i 4326 4400 4475 455o 4624 4699 4774 4848 75 582 4923 499S 5072 5.47 3221 5296 5370 5443 5320 5594 75 583 5669 5743 ! 58i8 5892 5966 6041 6ll3 6190 6264 6338 74 584 641 3 6487 6562 6636 6710 6785 6859 6933 7007 7082 74 585 7i56 7230 7304 7379 7453 7527 7601 8342 7675 7749 7823 8564 74 586 78y8 8638 7972 8046 8.20 8194 8268 8416 8490 74 587 8712 8786 8860 89J4 9008 9082 9i56 923o 93o3 74 588 9^77 945i 9525 9599 9673 9746 9820 9894 9968 ••42 74 589 770115 0189 0263 o336 0410 0484 0557 o63i 0705 0778 74 590 770852 0926 ??S 1073 1 146 1220 1293 1367 1440 i5i4 74 59. 1087 1661 1808 i88i 1955 2028 2.02 2175 2248 73 592 2322 2393 2468 2542 26i5 2688 2762 2835 2908 2981 73 593 3o55 3128 3201 3274 3348 3421 3494 3567 3640 3713 73 594 3786 386o 3933 4006 4079 4.32 4223 4298 4371 4444 73 595 4517 4390 4663 4736 4809 4882 4955 5o28 5ioo 5173 73 596 5246 5319 5392 5465 5538 56io 5683 5756 5829 5902 73 597 5974 6047 6120 6193 6263 6338 641 1 6483 6556 6629 73 598 6701 6774 6846 6919 6992 7064 7137 7209 7282 7334 8079 73 599 7427 7499 7572 7644 7717 7789 7862 7934 8006 72 600 778i5i 8224 8296 8368 844. 85i3 8585 8658 8730 8802 72 601 8S74 8947 9019 9091 9i63 9236 9308 9380 9432 9524 72 602 9396 9669 9741 9813 9885 9937 ••29 •lOI •.73 •245 72 6o3 780317 0389 0461 o533 o6o3 0677 0749 0821 0893 0965 72 604 1037 1109 ii8i 1253 i324 1396 1468 1540 1612 1684 72 6o5 1755 1827 1899 1971 2042 2114 2i86 2258 2329 2401 72 606 2473 2544 2616 2688 2759 283 1 S 2974 3o46 3ii7 72 607 3189 3260 3332 3403 4^89 3546 3689 3761 3832 7! 608 3904 3975 4046 4118 4261 4332 44o3 4475 4546 7> 609 4617 4689 4760 483 1 4902 4974 5o45 5ii6 5187 5259 71 610 785330 5401 5472 5543 56i5 5686 5757 5828 5899 5970 71 611 6041 6112 6i83 6254 6325 6396 6467 6538 6609 6680 71 612 675. 6822 6893 6964 7035 7106 7177 7248 7319 7390 7' 6i3 7460 IH' 7602 7673 7744 7815 8522 7885 8593 7936 8027 8098 71 614 8168 8239 83io 838i 8451 8663 8734 8804 71 6i5 8875 8946 9016 9087 9157 9228 9299 9369 9440 g5io 7« 616 9581 9631 9722 9792 9863 9933 •••4 0.74 •144 •2l5 70 617 790285 o336 0426 0496 o567 0637 0707 0778 1480 0848 0918 70 618 0988 1039 1 1 29 1199 1269 1 340 1410 1330 1620 70 619 1691 1761 1 83 1 1901 1971 2041 2111 2l8l 2252 2322 70 620 792392 2462 2532 2602 2672 2742 2812 2882 2952 3022 70 621 3092 3i62 323i 33oi 3371 3441 33II 358i 3631 3721 70 622 3790 386o 3930 4000 4070 4139 4209 4279 4349 4418 70 623 4488 4558 4627 4697 4767 4836 4906 4976 5043 5ii5 70 624 5i85 52 34 5324 53q3 5463 5532 56o2 5672 5741 58ii 70 625 588o 5949 6019 6088 6i58 6227 6297 6366 6436 65o5 69 626 6574 6644 6713 6782 6852 6921 6990 7060 7129 7198 69 627 7268 7337 7406 7475 8167 8858 7545 76.4 7683 8374 7752 7821 7890 69 628 7960 8029 8236 83o5 8443 83i3 8582 69 629 865i 8720 1% 8927 8996 9065 9134 9203 9272 69 63o 799341 9409 9478 9547 9616 9685 9754 9823 9892 9961 69 63 1 800029! 0098 0167 0236 o3o5 0373 0442 031 1 o38o 0648 69 632 0717 0786 o854 0923 0992 io6i 1129 1 198 1266 1335 69 633 1404I 1472 i54i 1609 2293 1678 1747 i8i5 1884 1952 2021 69 634 2089 2i58 2226 2363 2432 25oo 2568 2637 2705 tl 635 2774 2842 2910 2979 3047 3ii6 3.84 3252 3321 3389 636 3457 3525 3594 3662 3730 3798 3867 3935 4616 4oo3 4071 68 til 4139 4208 4276 4344 4412 4480 4548 4685 4753 68 482, 4889 5o25 5093 5i6i 5229 5297 5365 5433 68 639 55oi 5569 5637 5705 5773 5841 5908 5976 6044 6112 68 N. I 2 3 4 5 6 1 7 ~8~ 9 "dT A TABLE OF LOGARITHMS FROM 1 TO 10,000. 11 N. I 2 3 4 ' ' 7 8 9 D. "640 806180 6248 63i6 6384 645 1 65i9 6587 6655 6723 l§ 68 641 6858 6926 6994 7061 7129 7197 7264 8008 7400 68 642 7535 7603 7670 8346 7738 7806 7873 7941 8076 68 643 8211 8279 84.4 8481 8549 8616 8684 8731 8818 67 644 8886 8953 9021 9088 9i56 9223 9290 9358 9425 9492 67 645 9360 9627 9694 9762 9829 9896 9964 ••3 1 .•98 •i65 67 646 810233 o3oo 0367 0434 o5oi o569 0636 0703 0770 0837 67 647 0904 0971 ,039 1 106 1173 1240 i307 1374 1441 i5o8 67 648 1575 1642 1709 1776 1843 1910 2579 1977 2044 2111 2178 67 649 2245 23l2 2379 2445 25l2 2646 2713 2780 2847 67 65o 812913 2980 3o47 3X14 3i8i 3247 33i4 338i 3448 35i4 67 65i 358i 3648 37.4 3781 3848 3914 3981 4048 4114 4181 67 652 4248 43i4 438 1 4447 45i4 458. 4647 47 >4 4780 4847 tl 653 49J3 4980 5o46 5ii3 5179 5246 53i2 5378 5445 55ii 654 5578 5644 5711 5777 5843 59.0 5976 6042 6109 6.75 66 655 ■ 6241 63o8 6374 6440 65o6 6373 6639 X 6771 6838 66 656 6904 6970 7o36 7102 7169 7235 7301 7433 8160 66 657 7565 S292 8338 7764 7830 & 7962 8028 8094 66 658 8226 8424 8490 8622 8688 8754 8820 66 659 8885 8951 9017 9083 9149 92i5 9281 9346 9412 9478 66 660 819544 9610 9676 9741 9807 9873 & •»»4 ••70 •i36 66 661 820201 0267 o333 0399 0464 o53o 0661 0727 0792 66 662 o858 2233 0989 1033 1120 1186 1231 i3i7 i382 1448 66 663 i5i4 1645 17IO 2364 1775 1841 1906 1972 2037 2103 65 664 2168 2299 2952 2430 2495 2 560 2626 2691 2756 65 665 2822 2887 3oi8 3o83 3.48 32l3 3279 3344 3409 65 666 3474 3539 36o5 3670 3735 38oo 3865 %: 3996 406 1 65 667 4126 4I9I 4256 4321 4386 445 1 45i6 4646 47II 65 668 4776 4841 4906 5556 4971 5o36 5ioi 5i66 523i 5296 536i 65 669 5426 5491 5621 5686 5751 58i5 5S8o 5945 6010 65 670 826075 6140 6204 6269 6334 6399 6464 6528 6393 6658 65 671 6723 6787 6852 6917 6981 7046 7111 7175 7240 73o5 65 672 673 7369 8oi5 7434 -8080 7495 7363 762-8 .7692.. -7-737 -78.21 7886 7951 8395 65 64 8144 8209 8853 8273 8338 8402 8467 853 1 674 8660 8724 8789 X. 8982 9046 9III 9175 9239 64 675 9304 9368 9432 9497 9625 9690 9754 9818 9882 64 676 9947 ••n ••75 •139 •204 •268 •332 •396 •460 •525 64 677 83o589 o653 0717 0781 0845 ;s 0973 1037 1102 n66 64 678 i23o 1294 i358 1422 i486 i6i4 1678 1742 1806 64 679 1870 1934 1998 2062 2126 2189 2253 2317 238i 2445 64 680 832509 2573 lf,l 2700 2764 2828 2892 2956 3593 3o2o 3o83 64 681 3.47 321 1 3338 3402 3466 3530 3657 3721 64 682 3784 3848 39.2 3975 4o39 4io3 4166 423o 4294 4357 64 683 4421 4484 4548 461 1 4675 §?? 4802 4866 4929 5564 4993 64 684 5o56 5l20 5i83 5247 53io 5437 55oo 5627 63 685 5691 5754 5817 588 1 5944 6007 6071 6i34 6197 6830 6261 63 686 6324 6387 6451 65i4 6577 6641 ^]of 6767 6894 63 687 8219 7020 7083 7146 7210 7273 7336 8o3o 7462 8093 7325 63 688 7652 7715 ml 7841 lit 7967 8i56 63 689 8282 8345 8471 8597 8660 8723 8786 63 690 838849 89.2 8975 9o38 9101 9164 $11 9280 Hi 9352 941 5 63 691 9478 9541 9604 9667 9729 9792 9981 ••43 63 692 840106 0169 0232 0294 0357 0420 0482 0608 0671 63 693 0733 0796 s 0921 0984 1610 1046 1109 1172 1234 1297 63 694 1350 1422 1985 2047 1547 1672 1735 1797 i860 2347 63 695 2II0 2172 2235 2297 2360 2422 2484 62 696 2609' 2672 3233 32q5 2734 2796 2859 2921 3544 2983 3046 3io8 3170 62 697 698 3357 3420 3482 36o6 3669 3731 3793 62 3855 X 3980 46oi 4042 4104 4i66 4229 4291 4353 441 5 62 699 4477 4664 4726 4788 485o 4912 4974 5o36 62 N. 1 2 3 4 5 6 7 8 9 'K 12 A TABLE OF LOGARITHMS FEOM 1 TO 10,000. N. I 2 3 4 a 1 6 7. 8 9 D. 700 84509S 5i6o 5222 5284 5346 5408 5470 5532 5594 5656 62 701 5718 5780 5842 5904 5966 6028 6ogo 6i5i 62i3 6275 62 702 6337 6399 6461 6523 6585 6646 6708 7326 6770 6832 6894 62 703 6955 7573 8i8q 7017 7079 7141 7202 7264 7388 7449 8066 75ii 62 704 7634 & 7758 7819 7881 8497 7943 8004 8138 62 705 8231 8374 8989 8435 8559 8620 8682 8743 62 706 88o5 8866 .8928 9542 905i 9112 9174 9235 9297 9358 61 Vol 9419 85oo33 9481 9604 9665 9726 9788 9849 991 1 9972 6i 0093 oi56 0217 0279 o34o 0401 0462 0324 o585 61 709 0646 0707 0769 o83o 0891 0952 ioi4 1075 ii36 1197 61 710 851258 l320 i38i 1442 i5o3 1 564 1625 1686 1747 1809 61 711 IX ;g! 1992 2o53 2114 2175 2236 2297 2358 2419 61 712 2602 2663 2724 2785 2846 2907 2968 3029 61 7i3 3090 3i5o 32U 3272 3333 3394 3455 35.6 3577 3637 61 714 3698 3759 3820 388i 3941 4549 4002 4o63 4124 4i85 4245 6i 7i5 43o6 4367 4428 4488 4610 4670 4731 4792 4852 61 716 5l!g 4974 5o34 5095 5i56 5216 5277 5337 5398 5459 61 ]\l 5580 5640 5701 5761 6366 5822 5882 5943 6548 6oo3 6064 61 6124 6i85 6245 63o6 6427 6487 6608 6668 60 719 6729 6789 685o 6910 6970 7o3i' 7091 7152 7212 7272 60 720 857332 7393 7453 75i3 7^74 7634 7694 If, 78.5 9018 7875 8477 9078 60 721 7935 7995 8097 8o56 8116 8176 8236 8297 60 722 8537 8657 8718 8778 8838 8898 •i58 60 723 9i38 9198 9258 9318 9370 9978 9439 9499 9619 9679 •278 60 724 9739 86o338 9799 9859 9918 ••38 ••98 •218 60 725 0398 0458 o3i8 0578 0637 0697 0757 0817 0877 60 726 oq37 0996 io56 1116 1176 1236 1295 i355 I4i5 1475 60 727 728 1 534 1594 1 654 1714 23lO 1773 i833 1893 1952 2012 2072 60 2l3l 2191 2787 2231 2370 243o 2489 2549 2608 2668 60 729 2728 2847 2906 2966 3o25 3o85 3144 3204 3263 60 730 863323 3382 3442 35oi 356i 3620 368o 3739 3799 3858 59 73. 3917 3977 4570 4o36 4096 4i55 4214 4274 4333 4392 4452 59 732 4DII 463o 4689 4748 4808 4867 4926 4985 5o45 59 733 5io4 5i63 5222 5282 5341 5400 5459 55i9 5578 5637 59 734 5696 6287 5755 58i4 5874 5933 6524 5992 6583 6o5i 6110 6169 6228 59 735 6346 64o5 6465 6642 6701 6760 6819 59 736 6878 6937 7526 6996 7055 7114 7173 7232 8468 7350 ?» 59 ]U 7467 7585 8.74 7644 8233 7703 7762 7821 7939 59 8o56 8ii5 8292 83 5o 8409 8527 8586 59 739 8644 8703 8762 8821 8879 8938 8997 9o56 9114 9173 59 740 869232 9290 9349 9408 9466 9525 9584 9642 9701 9760 59 741 9818 9877 9935 9994 ••53 •ill •170 •228 •287 •345 742 870404 0462 0321 0579 0638 a 0755 o8i3 0872 :s 743 t'3 1047 1 106 1164 1223 i339 ITol If, 1456 58 744 i63i 1690 1748 1806 1 865 2040 ?£ 58 745 2i56 22l5 2273 233i 2389 2448 2564 2622 58 746 2739 2797 2855 2913 2972 3553 3o3o 3o88 3.46 3204 3262 58 ?s 3321 3379 3437 4018 3495 36ii 3669 2727 3785 3844 58 3902 3960 4076 4134 4192 425o 43o8 4366 4424 58 749 4482 4540 4598 4656 4714 4772 4830 4888 4945 5oo3 58 750 875061 5iio 569S 5i77 5235 5293 535i 5409 5466 5524 5582 58 75i 5640 5756 58i3 5871 5929 5987 6045 6102 6160 58 752 6218 6276 6333 6391 6449 65o7 6564 6622 6680 6737 58 753 6795 6853 6910 6968 7026 7083 7141 7199 7256 7314 58 754 7371 7429 7487 7544 7602 7659 7717 8292 7774 7832 7889 58 755 8522 8004 8062 8119 8177 8234 8349 8407 8464 57 756 8579 8637 8694 8752 q325 8809 8866 8924 9^55 9039 57 757 9096 9153 9211 9268 9383 9440 9497 96.2 ^■7 758 9669 9726 9784 9841 9898 & ••i3 ••70 •127 j "185 57 759 880242 0299 o356 o4i3 0471 o585 0642 0699 0756 57 N. I , I 3 1 4 5 6 7 8 9 D. A TABLE OF LOGARITHMS FEOM 1 TO 10,000. 13 N. I 2 3 4 5 6 7 8 9 D. 760 880814 0871 0928 0985 1042 1099 ii56 I2l3 1271 i328 57 761 i385 1442 1499 1 556 i6i3 1670 1727 1784 1841 .898 57 762 1955 2012 2069 2126 2i83 2240 2297 2354 2411 2468 57 763 2325 258i 2638 2695 3264 2752 2809 2866 2923 3548 3o37 57 7^4 3093 3i5o 3207 3321 3377 3434 3491 4059 4625 36o5 57 765 366 1 3718 3775 3832 3888 3945 4002 4n5 4172 57 766 4229 4285 4342 4399 4455 4D12 tu 4682 4739 5303 57 ]U 4795 4852 4909 496D 5022 5078 5i92 5248 57 536i 5418 5474 5531 5587 5644 5700 5757 58i3 5870 57 769 5926 5983 6039 6096 6i52 6209 6265 6321 6378 6434 56 770 886491 6547 6604 6660 6716 % 6829 6885 6942 6998 56 771 7034 71U 7167 7223 7280 85i6 7449 73o5 736 1 56 772 7617 7674 7730 11% 7842 7898 8011 8067 8123 56 773 8179 8236 8292 8404 8460 8573 8629 8685 56 774 8741 8797 8853 8909 8965 9021 9077 9134 9190 9246 56 775 9302 9358 9414 9470 9D26 9582 9638 9694 9730 9806 56 776 9862 9918 9974 ••30 ••86 •141 •'97 •233 •365 56 777 890421 0477 0533 o589 0645 0700 0756 0812 0924 56 778 T, io35 1091 1 147 i7o5 I203 JS i3i4 1370 1426 1482 56 779 1593 1649 1760 1872 1928 1983 2039 56 780 892095 2i5o 2206 2262 23i7 2373 2429 2484 2540 2595 56 "^^^ 265i 2707 2762 2818 2873 2929 3^40 3o4o 3096 3i5i 56 782 3207 3262 33i8 3373 3429 3484 3595 365i 3706 56 783 3762 38i7 3873 3928 3984 4039 4593 4094 4130 42o5 4261 55 784 43i6 4371 4427 4482 4538 4648 4704 4759 4814 55 ■^L^ 4870 4925 4980 5o36 5091 5146 5201 5257 53i2 5367 55 786 5423 5478 5533 5588 5644 ss 5754 5809 5864 5920 55 787 5975 6526 6o3o 6o85 6140 6195 63o6 636i 6416 6471 55 788 658i 6636 6692 6747 6802 6857 6912 s 7022 55 789 7077 7i32 7187 7242 7297 7352 7407 7462 7572 55 790 897627 7682 823i & 7792 7847 7902 7957 8012 t^l 8122 55 791 8176 8341 8396 8451- 85o6 856 1 8670 55 792 8725 8780 8835 8890 8944 8999 9054 9109 9164 9218 55 793 9273 9328 9383 9437 9547 9602 9656 971 1 9766 55 794 9821 9875 9930 9983 ••g4 0695 •203 •258 •3l2 55 795 900367 0422 0476 o53i o586 0640 0749 1295 0804 0859 55 796 0913 °tl 1022 1077 ii3i 1 186 1240 1 349 1404 55 797 1458 1 567 1622 1676 1731 1785 1840 1894 1948 54 798 2oo3 2057 2112 2166 2221 2273 2329 2873 2384 2438 2492 3o36 54 799 2547 2601 2655 2710 2764 2818 2927 2981 54 800 903090 3 144 3199 3253 3307 3361 3416 3470 3524 3578 54 80 1 3633 3687 3741 3795 3849 3904 3958 4012 4066 4120 54 802 4174 4229 4283 4337 4391 4443 4499 4553 4607 5i48 4661 54 8o3 4716 4770 4824 4878 4932 4986 5o4o 5094 5202 54 804 5256 53io 5364 5418 5472 5526 558o 5634 5688 5742 54 8o5 5796 585o 5904 5958 6012 6066 6119 6658 6173 6227 6281 54 806 6335 6389 6443 6497 6551 66o4 6712 6766 6820 54 l°l 6874 6927 6981 7519 7035 7089 7626 7143 7196 7250 73o4 7358 54 808 7411 7465 8002 7573 7680 7734 7787 7841 8378 7895 54 809 7949 8o56 8110 8i63 8217 8270 8324 8431 54 8io 908485 8539 8592 8646 8699 8753 8807 8860 8914 8967 54 811 9021 9074 1 9128 9181 9235 9289 9342 9396 9930 9449 95o3 ^J 812 9556 9610 9663 9716 9770 9823 9877 9984 ••37 53 8i3 910091 0144 0197 0731 025i o3o4 o358 041 1 0464 03i8 0571 53 814 0624 0678 0784 o838 0891 0944 Sg io5i 1 104 53 8i5 1.58 1211 1264 .317 i37i 1424 1477 1 584 1637 53 816 1690 1743 1797 i85o 1903 1956 2009 2o63 2116 2169 53 817 818 2222 2275 2328 238i 2435 2488 2541 2594 2647 3178 2700 53 2753 2806 2859 2913 2966 3019 3072 3i25 323i 53 819 3284 3337 3390 3443 3496 3549 3602 3655 3708 8 3761 9 53 N. 1 I 2 3 4 5 6 7 14 A TABLE OF LOGAEITHMS FEOM 1 TO 10,000. N. I 2 3 4 5 6 7 8 9 D. 820 9i38i4 2^2 3920 3973 4026 4079 4i32 4184 4237 4290 53 821 4343 4449 45o2 4555 4608 4660 4713 4766 4819 53 822 4872 4925 4977 5o3o 5o83 5i36 5189 5241 5294 5347 53 823 5400 5453 55o5 5558 56ii 5664 5716 5769 5822 5875 53 824 5927 5980 6o33 6o85 6i38 6191 6243 6296 6349 6401 53 825 6434 65o7 6559 6612 6664 6717 6770 6822 6875 6927 53 826 6980 7033 708D 7138 7190 7243 7295 7348 7400 7433 53 827 7D06 7558 761 1 7663 8188 7716 7768 7820 gj? 7925 85o2 52 828 8o3o 8o83 8i35 8240 8293 8345 8450 52 829 8555 8607 8659 8712 8764 8816 8869 8921 8973 9026 52 83o 919078 9i3o 9183 9235 9287 9340 9392 9444 9496 9549 52 83 1 9601 9653 9706 9758 9810 9862 9914 9967 ••19 ••71 52 832 920123 0176 0228 0280 o332 o384 0436 0489 o54i 0593 52 833 0645 a 0749 0801 o853 0906 0958 lOIO 1062 1114 52 834 1166 1270 l322 1374 1426 1478 i53o i582 1634 52 835 1686 1738 1790 23lO 1842 1894 1946 Itil 2o5o 2102 2i54 52 836 2206 2258 2362 2414 2466 2570 2622 2674 52 837 838 2725 2777 2829 2881 2933 2985 35o3 3o37 3089 3i4o 3192 52 3244 3296 3348 3399 345i 3555 3607 3658 3710 52 839 3762 38i4 3865 3917 3969 4021 4072 4124 4176 4228 52 840 924279 433 1 4383 4434 4486 4538 4589 4641 4693 4744 52 841 479(3 4848 s? 4951 5oo3 5o54 5io6 5i57 ??;? 5261 52 842 5312 5364 5467 55i8 5570 5621 5673 5776 52 843 5828 5879 5931 5982 6o34 6o85 6137 6188 6240 6291 5i 844 6342 6394 6445 6497 6548 6600 665 1 6702 6754 68o5 5i 845 6857 6908 6939 7011 7062 7114 7165 7216 7268 7319 5i 846 7370 7422 7473 7524 a 7627 7678 7730 7781 7832 5i 847 7883 7935 7986 8o37 8140 9191 8242 8293 8345 5i 84B 8396 8447 8498 8549 8601 8652 8703 8754 88o5 8857 5i 849 8908 8959 9010 9061 9U2 9163 9215 9266 9317 9368 5i 85o 929419 9470 9521 9572 9623 9674 9725 9776 9827 2S? 5i 85i 9930 9981 *<»32 ••83 •i34 •i85 •236 •287 •338 5i 852 930440 0491 o542 0592 0643 0694 0745 0796 0847 0898 5i 853 0949 1000 io5i 1102 ii53 1204 1254 i3o5 i356 1407 5i 854 1458 1 509 i56o 1610 1661 1712 1763 1814 1 865 1915 5i 855 1966 2017 2068 2118 2169 2220 2271 2322 2372 2423 5i 856 2474 2324 2575 2626 2677 2727 2778 2829 3335 2879 2930 5i 857 2981 3o3i 3o82 3i33 3i83 3234 3285 3386 3437 5i 858 3487 3538 3589 3639 3690 3740 3791 3841 3892 3943 5i 859 3993 4044 4094 4145 4195 4246 4296 4347 4397 4448 5i 860 934498 4549 4599 4650 4700 4751 4801 4852 4902 4953 5o 861 5oo3 5o54 5io4 5x54 52o5 5255 53o6 5356 5406 5457 5o 862 5507 5558 56o8 5658 5709 5759 5809 5860 5910 5960 5o 863 6011 606 1 6111 6162 6212 6262 63i3 6363 6413 6463 5o 864 6514 6564 6614 6665 6715 6765 68i5 6865 6916 6966 5o 865 7016 7066 7117 7167 7217 7267 7317 7367 7418 7468 5o 866 7518 7568 7618 7668 8169 7718 8219 lltl 7819 8320 7869 8370 7919 7969 5o 867 8019 8069 8119 8420 8470 5o 868 8520 8570 8620 8670 8720 8770 8820 8870 8920 8970 5o 869 9020 9070 9120 9170 9220 9270 9320 9369 9419 9469 5o 870 939519 9569 9619 9669 9719 0218 9769 9819 9869 9918 9968 5o 871 940018 0068 ou8 0168 0267 o3i7 o367 0417 0467 5o 872 o5i6 o566 0616 0666 0716 0765 o8i5 o865 09.5 0964 5o 873 I0I4 1064 1114 ii63 I2l3 1263 i3i3 i362 1412 1462 5o 874 i5ii i56i 1611 1660 I7I0 1760 1809 1855 1909 24o5 1958 5o 875 2008 2o58 2107 2157 2207 2256 23o6 2355 2435 5o 876 25o4 2554 2603 2653 2702 2752 2801 285i 3^96 2950 5o 877 3ooo 3049 3593 3148 3198 3247 3297 3346 3445 59 878 3495 3544 3643 s 3742 X 3841 3890 4384 3939 ^ 879 3989 4o38 4088 4137 4236 4335 4433 59 N. 1 I , i 3 4 5 6 7 8 9 D. A TABLE OF LOGARITHMS FROM 1 TO 10,000. 15 N. I 2 3 4 5 6 1 7 8 9 D. 88o 944483 4532 458 1 463 1 4680 4729 4779 1 4828 4B77 4927 49 88 1 4976 5o25 3074 5i24 5173 5222 5272 5321 5370 5419 49 882 5469 55i8 5567 56i6 5665 5715 5764 ! 58i3 5862 39,2 49 883 5961 6010 6039 6108 6157 6207 6236 63o3 6354 64o3 49 884 6452 65oi 655i 6600 6649 6698 6747 7238 6796 6845 6^94 49 885 6943 6992 7041 7090 7140 7189 7287 7336 7385 49 886 7434 7483 7532 8022 758i 763o 7679 7728 7777 7826 7875 ■ 49 887 7924 7973 8070 8119 8168 8217 8266 83i5 8364 49 888 841 3 8462 85ii 856o 8609 8657 8706 8755 8804 8853 49 889 8902 8951 8999 9048 9097 9146 9195 9244 9292 9341 49 890 949390 9439 9488 9536 9585 9634 9683 973 1 9780 9829 49 891 9«7S 9926 9975 ••24 «»»73 •121 •170 •219 •267 •3i6 49 892 930365 0414 0462 o5n o56o 0608 0637 0706 0754 oSo3 49 893 o85i 0900 0949 0997 1046 1095 1143 1192 1240 1289 49 894 i338 1 386 1435 1483 i532 1 580 1629 1677 1726 1773 ii 895 1823 1872 1920 1969 2017 2066 2114 2i63 22U 2260 896 23o« 2356 2403 2453 2502 255o 2399 2647 2696 2744 48 897 2792 2841 2809 2938 2986 3o34 3o83 3i3i 3i8o 3228 48 898 3276 3325 3373 3421 3470 35i8 3566 36i5 3663 3711 48 899 3760 38o8 3856 3905 3953 4001 4049 4098 4146 4194 48 900 954243 4291 4339 4387 4435 4484 4532 438o 4628 4677 48 901 4725 4773 ! 4821 4869 4918 4966 5oi4 5o62 5iio 3i58 48 902 3207 5255 I 53o3 535I 5399 5447 5495 5543 5592 5640 48 903 5688 5736 5784 5832 5880 5928 5976 6024 6072 6120 48 904 6168 6216 6265 63 1 3 6361 6409 6457 65o5 6553 6601 48 ^05 6649 6697 6745 6793 6840 6888 6936 6984 7032 7080 48 906 7120 7176 7224 7272 7320 7368 7416 7464 75i2 7539 48 907 ^^o"? 7655 7703 775i 8229 7799 7847 7894 7942 8421 7990 8o38 48 908 8086 8i34 8181 8277 8323 8373 8468 8316 48 909 8564 8612 8659 8707 8755 88o3 885o 8898 8946 8994 48 910 959041 9089 9137 9185 9232 9280 9328 9375 9423 9471 48 911 9518 9566 9614 9661 9709 9737 9804 9852 9900 9947 48 912 9995 ••42 ••90 •i38 •l83 •233 •280 •328 •376 •423 48 9i3 960471 o5i8 o566 o6i3 0661 0709 0756 0804 o85i 0899 48 914 0946 0994 1 041 1089 1 563 ii36 ii84 I23l nS i326 1374 47 9i5 1421 It's i5i6 1611 1 658 1706 1801 1848 47 916 1895 1990 2o38 2085 2l32 2180 2227 2275 2322 47 9'7 2369 2417 2464 25ll 2559 2606 2653 2701 2748 2795 47 9.8 2843 2890 2937 2985 3o32 3079 3i26 3i74 3221 3268 47 919 33i6 3363 3410 3457 35o4 3552 3399 3646 3693. 3741 47 920 963788 3835 3882 3929 3977 4024 4071 4118 4i65 4212 47 921 4260 4307 4354 4401 4448 4495 4542 4590 a 4684 47 922 4731 4778 4825 4872 4919 4966 5oi3 5o6i 5i55 47 923 5202 3249 5296 5343 lu: 5437 5484 553i 5578 5625 47 924 5672 5719 5766 58i3 5907 6376 5q34 6001 6048 6095 47 923 6142 6189 6658 6236 6283 6329 6423 6470 6317 6564 47 926 6611 6705 6752 6799 6845 6892 6939 6986 7033 47 ^2^ 7080 7127 7173 7220 7267 73i4 736i 7408 7454 7301 47 7548 7595 7642 7688 7735 7782 7829 7875 7922 & 47 929 8016 8062 8109 8i56 8203 8249 8296 8343 8390 47 930 968483 853o 8576 8623 8670 8716 8763 8810 8856 8903 47 931 8950 8996 9043 9090 9i36 9i83 9229 9276 9323 9369 47 9? 9416 9463 9309 9356 9602 9649 9695 9742 9789 9*^35 47 933 9882 2S 9973 ••21 ••68 •ii4 •161 •207 •254 •3 00 47 934 970347 0440 0486 o533 0579 0626 0672 ;s? 0765 46 93d 0812 o858 0904 0951 0997 1044 1090 1137 1229 46 936 1276 l322 1369 I4i5 1461 i5o8 1 554 i6oi 1647 1693 46 $1 1740 1786 i832 1879 1925 1971 2018 2064 2110 2157 46 2203 2249 2295 2342 2388 2434 2481 2527 2573 2619 46 939 2666 2712 2758 2804 285i 2897 2943 2989 3o35 3oS2 J6 N. I 2 3 4 5 6 7 8 9 -1 16 A TABLE OP LOGAKITHMS FROM 1 TO 10,000. N. I 2 3 4 5 6 7 8 1 9 D. 940 973128 3174 3220 3266 33i3 3359 34o5 3451 3497 3543 46 941 S; 3636 3682 3728 3774 3820 3866 4374 39^9 4oo5 46 942 4097 4143 4189 4235 4281 4327 4420 4466 46 943 45i2i 4558 4604 465o 4696 5i56 4742 4788 4834 4880 4926 46 944 49721 5oi8 5o64 5iio 5202 5248 5294 5340 5386 46 945 5432: 5478 5524 5570 56i6 5662 5707 5753 5799 5845 46 946 589.: 5937 5983 6029 648a 6075 6121 6167 6212 6258 63o4 46 947 635oi 6396 680S; 6854 6442 6533 6579 6625 6671 6717 6763 46 948 6900 6946 6992 7037 7083 7129 7175 7220 46 949 7266; 7312 7358 7403 7449 7495 7541 7586 7632 7678 46 950 977724' 7769 7815 7861 It, 7952 8409 7998 8043 8089 8i35 46 95i 8181 8226 8272 83i7 8454 85oo 8546 8591 46 952 8637! 8683 8728 8774 8819 9275 8865 89.1 8956 9002 9047 46 953 9093 9 1 38 9184 9230 9321 9366 9412 9457 95o3 46 954 9548 9594 9639 9685 1 9730 9776 982. 9867 99' 2 9958 46 955 980003 0049 0458; o5o3 0094 0140 oi85 023 1 0276 0322 0367 0412 45 956 o549 0594 0640 o685 0730 0776 0821 0867 45 957 0912 0957 ioo3 1048 1 1093 1.39 1184 1229 1275 l320 45 958 iJyo 1411 1456 i5oi 1 i547 1592 i637 1 683 1728 1773 45 959 I8I9 1864 1909 1934 2000 2045 2090 2i35 2181 2226 45 960 982271 : 2310 2362 2407 1 2452 2497 2543 2588 2633 2678 45 961 2723 2769 2814 2859 2904 2949 2994 3 040 3o85 3i3o 45 962 3175; 3220 3265 33ro 3356 3401 3446 3491 3536 358i 45 963 3626: 3671 3716 3762 38o7 3852 3897 4392 3987 4o32 45 964 40771 4122 4167 4212 4257 43o2 4347 4437 4482 45 965 4527 4572 4617 4662 4707 4752 4797 4842 4887 4932 5382 45 966 4977 5o22 5067 5lI2 5,57 5202 52.17 5292 5337 45 967 5426: 5471 55.6 5561 56o6 5651 5696 574. 5786 5830 45 968 5875 5920 5965 6010 6o55 6100 6144 6189 6234 6279 45 969 6324 6369 64i3 6458 65o3 6548 6593 6637 6682 6727 45 970 986772 6817 686 1 6906 6951 6996 7040 7085 7i3o 7175 45 971 7219 7264 8202 7353 7398 7443 7488 7532 7577 7622 8068 45 972 7666 77 1 1 7800 7845 f^l 7934 838i 7979 8425 8024 45 973 8ii3: 8i57 8247 8291 8470 85i4 45 974 8559 8604 8648 8693 9 1 38 8737 8782 8826 8871 X 8960 45 975 9005 9049 9094 9i83 9227 9272 93i6 94o5 45 976 9450 9494 9539 9583 9628 9672 97'7 9761 9806 9850 44 977 978 9895 9939 9983 ••28 ••72 •1.7 •161 •206 •25o •294 44 990339 o383 0428 0472 o5i6 o56i o6o5 o65o S^ 0738 44 979 0783 0827 0871 0916 0960 1004 1049 1093 1182 44 980 991226 1270 i3i5 1359 i4o3 1448 1492 1536 i58o 1625 44 981 1669 17.3 1758 1802 1846 1890 1935 '979 2023 2067 44 982 2111 2i56 2200 2244 2288 2333 2377 2421 2465 25o9 44 983 2554I 2598 2642 2686 2730 2774 2S19 2863 2907 3392 3833 44 984 2995 3o39 3o83 3127 3n2 3216 3260 3304 3348 44 985 3436 3480 3524 3568 36i3 3657 3701 3745 3789 44 986 3877 3921 3965 4009 4o53 4097 4537 4141 4i85 4229 4273 44 987 43.7 4361 44o5 4449 4493 458i 4625 4669 47i3 44 988 4757 4801 4845 4889 4933 4977 5021 5o65 5io8 5i52 44 989 5196 5240 5284 5328 5372 5416 5460 55o4 5547 5591 44 990 995635 5679 5723 5767 58ii 5854 5898 5942 5986 6o3o 44 991 6on4 6117 6161 62o5 624Q 6293 6337 638o 6424 6468 44 992 65i2 6555 6599 7037 6643 6687 6731 6774 6818 6862 6906 44 993 6949 6993 7080 i 7124 7168 7212 7255 7299 7343 44 994 7386 7430 7474 7517 i 756i 76o5 8041 7648 7692 7736 7779 44 995 7823 7867 7910 7954 7998 8o85 8129 8172 8216 44 996 III 83o3 8347 8390 8434 8477 8521 8564 8608 8652 44 997 8739 8782 8826 8869 8gi3 9348 8g56 9000 9043 9087 44 998 oi3i 9174 9218 9261 93o5 9392 9435 9479 99'3 9522 44 999 9565 9609 9652 9696 9739 9783 9826 9870 9957 43 N. 1 , 1 3 1 4 5 6 7 8 9 D. i TABLE OF LOGAEITHMIC SINES AND TANGENTS FOE ETEET DEGREE AND MINUTE OF THE QUADEANT. Eemaek. The minutes in the left-liand column of eacli page, increasing downwards, belong to the degrees at the top ; and those increasing upwards, in the right-hand column, belong to the degrees below. 18 (0 DEGEEES.) A TABLE OF LOGAEITHMIC M. Sine D. Cosine D. Tang. D. Cotang. 1 0-000000 10-000000 0-000000 Infinite. 60 6-463726 5017-17 000000 -00 6-463726 5017-17 2934-83 13-536274 S 2 764756 2934-85 000000 • 00 764756 235244 3 940847 2o82-3i 000000 ■ 00 940847 2082-3l 059153 s 4 7-065786 i6i5-i7 i3i9-68 1115.75 000000 .00 7-065786 1615.17 12-934214 837304 758122 5 162696 000000 .00 162696 i3io-6o 1115-78 852-54 55 6 241877 9-999999 •01 241878 54 7 308824 966-53 852-54 999999 .01 308825 6331^3 53 8 366816 999999 •01 366817 52 9 417968 762-63 999999 999998 -01 417970 463727 762-63 582o3o 5i 10 463725 689-88 -01 689-88 536273 5o II 7-5o5ii8 629-81 9-999998 • 01 7-5o5i2o 629-81 12.494880 457091 s 12 542906 579-36 536-41 999997 .01 542909 579-33 i3 577668 999997 999996 .01 577672 536-42 422328 47 U 609853 499-38 -01 609857 499-39 390143 36oi8o 46 i5 639816 467-14 999996 -01 639820 467-15 45 i6 667845 438-81 999995 -01 667849 438-82 332i5i 44 ;? 694173 4i3-72 999995 -01 694179 413-73 3o582i 43 718997 391-35 999994 ■01 719004 391-36 g??S 42 19 742477 371-27 999993 -01 742484 371-28 41 20 764754 353-15 999993 -01 764761 351^36 235239 40 21 '■&i 336-72 9-999992 •01 7-785951 8061 55 336^73 12-214049 193845 39 38 22 321-75 999991 -01 321^76 23 825451 3o8-o5 999989 -01 825460 3o8-o6 174540 i56o56 37 24 843934 2^3 -S -02 843944 295-49 36 25 861662 -02 861674 283-90 138326 35 26 878695 273-17 263-23 999988 -02 878708 273-18 121292 34 S 895085 999987 -02 895099 263-25 104901 33 910879 IS:?? 999986 -02 910894 254-01 089106 32 29 Q26119 999985 •02 926134 245-40 073866 3i 3o 940842 237-33 999983 -02 940858 237-35 059142 3o 3i 7-955082 229-80 9-999982 '02 7-955100 229-81 12.044900 It 32 968870 222-73 999981 •02 968889 222-75 o3iiii 33 982233 216-08 999980 -02 982253 2i6-io 017747 27 34 995198 209-81 999979 -02 995219 209-83 203^92 004781 26 35 8-007787 203-90 198-31 999977 999976 -02 8-007809 020045 11.992191 979955 968055 25 36 020021 -02 198-33 24 37 031919 043501 193-02 188.01 999975 -02 031945 103-05 23 38 999973 -02 043527 i88-o3 956473 22 39 054781 183-25 999972 -02 054809 183-27 945191 21 40 065776 178.72 999971 •02 o658o6 178-74 934194 20 41 8-076500 086965 174-41 "SSS -02 8-076531 174^44 11.9234.69 9i3oo3 \l 42 170-31 •02 086997 170^34 43 097183 166-39 162-6.5 999966 •02 097217 166-42 002783 892797 8feo37 n 44 107167 999964 •03 107202 162^68 16 45 1 16926 159-08 155-66 099963 •o3 116963 159-10 155-68 i5 46 1 26471 999961 •o3 126010 873490 14 47 48 i358io 152-38 999959 999958 ■o3 i3585i i52-4i 864149 i3 144953 149-24 •o3 144Q96 153952 149-27 855004 12 49 153907 146-22 999956 •o3 146-27 846048 II 5o 162681 143-33 999954 •o3 162727 143-36 837273 10 5i 8-171280 140-54 9-999952 •03 8-171328 140-57 11.828672 I 52 179713 137-86 999950 -03 ;ss ;r5:^2 820237 53 187985 135.29 999948 •o3 811964 8o3844 7 54 196102 i32.8o 999946 •o3 196156 132-84 6 55 204070 i3o-4i 999944 • o3 204126 i3o-44 795874 788047 5 56 2 1 1895 128-10 999942 •04 211953 128-14 4 57 219581 125-87 999940 •04 219641 125-90 ?» 3 58 227134 123-72 999938 ■04 227195 123-76 2 59 234557 121-64 999936 .04 234621 121-68 765379 I 60 241855 119-63 999934 • 04 241921 119-67 758079 Cosine D. Sine Cotang. D. Tang. mT (89 DEGREES.) SINES AND TANGENTS. (1 DEGEEE.) 19 M. Sine D Cosine D. Tang. D Cotang. 8-241855 119 63 9-999934 04 8-241921 119 67 11-758070 60 I 249033 256094 117 68 999932 04 249102 1x7 ll 750898 tl 2 ii5 80 999929 04 256i65 ii5 743835 3 263042 ii3 98 999927 04 263ii5 114 02 736885 57 4 269881 112 21 999925 04 269956 112 25 730044 56 5 276614 283243 110 5o 999922 04 276691 no 54 723309 55 6 108 83 999920 04 283323 108 87 716677 54 7 289773 107 21 999918 04 289856 107 26 710144 53 8 296207 io5 65 999915 04 296292 io5 70 703708 52 9 302546 104 i3 9999 '3 04 3o2634 104 18 697366 5i 10 308794 102 66 999910 04 308884 102 70 691116 5o II 8-314904 101 22 9-999907 04 8-3i5o46 lOI 26 11-684954 678878 672886 S 12 321027 ^ 82 999905 04 321122 99 87 i3 327016 47 999902 999899 04 327114 333025 98 5i 47 U 332924 97 14 o5 97 19 666975 46 i5 338753 95 86 999897 o5 338856 95 90 661144 45 i6 344504 94 60 999894 o5 344610 94 65 655390 44 \l 35oi8i 93 38 lllIVs o5 350289 355895 36i43o 93 43 6497" 43 355783 92 ;? o5 92 24 644105 42 19 36i3i5 ?; 999885 o5 §5 08 638570 41 20 366777 90 999882 o5 366895 95 633io5 40 21 8-372171 88 80 9.999879 o5 8-372292 88 85 11-627708 ll 22 377499 87 72 999876 o5 382889 87 77 622378 23 382762 86 67 999873 o5 86 72 617111 37 24 387962 85 64 999870 o5 388092 393234 85 70 611908 36 25 393101 84 64 999867 o5 84 70 606766 35 26 398179 83 66 999864 o5 398315 83 71 601685 34 3 4o3i99 82 71 999861 o5 403338 82 76 596662 33 4o8i6i 81 ll 999858 o5 4o83o4 81 82 591696 32 29 4i3o68 80 999854 o5 4i32i3 80 91 586787 3i 3o 417919 79 96 999851 06 418068 80 02 581932 3o 3i 8-422717 ?? 2I 9-999848 06 8-422869 427618 79 14 11-577131 29 32 427462 999844 06 78 3o 572382 28 33 432156 77 40 999841 06 4323i5 77 45 567685 2 34 436800 76 57 999838 06 436962 441 56o 76 63 563038 35 441394 75 77 999834 06 75 83 558440 25 36 445941 74 99 999831 06 446110 75 o5 553890 24 37 450440 74 22 999827 06 45o6i3 74 28 549387 23 38 454893 73 46 999823 06 455070 73 52 544930 540319 22 39 459301 72 73 999820 06 459481 72 79 21 40 463665 72 00 999816 06 463849 72 06 536i5i 20 41 8-467985 71 29 9-999812 06 8-468172 71 35 11-531828 ;§ 42 472263 70 60 999809 06 472454 ^ 66 527546 43 476498 69 91 999805 06 485o5o f, 523307 519108 17 44 480693 tl 24 999801 06 U 16 45 484848 59 999797 07 65 514950 5io83o i5 46 488963 67 94 999793 07 489170 493250 68 01 14 a 493040 67 3i 9997^6 07 67 38 506750 i3 497078 66 tl 07 497293 66 76 502707 12 49 5oio8o 66 999782 07 501298 505267 66 i5 498702 II 5o 5o5o45 65 48 999778 07 65 55 494733 10 5i 'tX 64 89 9-999774 07 8-509200 513098 64 96 1 1 - 490800 486902 I 52 64 3i & 07 64 39 53 516726 63 75 07 516961 63 82 483o39 7 54 52o55i 63 19 999761 07 SSS 63 26 479210 475414 6 55 524343 62 64 999757 07 62 72 5 56 528102 62 999753 07 528349 62 18 47i65i 4 ll 531828 61 58 999748 07 532080 61 65 467920 3 535523 61 06 999744 07 535779 6i i3 464221 2 59 539186 60 55 999740 07 54^084 60 62 46o553 I 60 542819 60-04 999735 07 60-12 456916 Cosine D. Sine Cotang. D. Tang 16 (88 DKGREES.) 20 (2 DEGEEES.) A TABLE OF LOGAEITHMIC M. Sine D. Cosine | D. Tang. D. Cotang. 8-5428I9 60 -04 9-999735 -07 8-543084 60-12 11-456916 60 I 546422 59-55 999731 •07 550268 59-62 453309 u 2 tmii 59-06 58-58 999726 ::i 59-14 449732 3 999722 553817 58-66 446183 u 4 557054 58-11 999717 .08 557336 58-19 57-73 442664 5 56o54o 57-65 999713 .08 560828 439172 55 6 563999 57-19 999708 .08 564291 57-27 54 I 567431 56-74 999704 .08 567727 56-82 53 570836 56-30 999699 •08 571137 56-38 428863 52 9 574214 55.87 sa -08 574520 lit 425480 5i 10 577566 55-44 -08 577877 422123 5o II 8-580892 55-02 9-999685 -08 8.58i2o8 55-10 11-418792 8 12 584193 54-60 999680 -08 584514 54-68 415486 i3 587469 54-19 999675 -08 I'^.lt 54-27 4i22o5 47 14 590721 53-79 999670 .08 53-87 408949 46 i5 593948 53-39 999665 -08 594283 53-47 4o25o8 45 i6 597152 53-00 999660 -08 597492 53-08 44 17 6oo332 52-61 999655 -08 600677 52-70 399323 43 18 603489 606623 52-23 999650 -08 6o3839 606976 52-32 396161 42 19 51-86 999645 .09 5i-94 51.58 393022 3^9906 41 20 609734 5i-49 999640 .09 610094 40 21 8-612823 51-12 9-999635 -09 8.613189 51-21 1 1-38681 1 39 22 615891 618937 50-76 999629 •09 616262 5o-85 383738 38 23 5o-4i 999624 •09 619313 5o.5o 380687 37 24 621962 5o-o6 999619 -09 622343 5o-i5 377657 36 25 624965 49-72 999614 .09 625352 49-81 374648 35 26 627948 49-38 999608 •09 628340 49-47 371660 34 11 63091 1 49-04 999603 .09 63i3o8 49-13 48-80 368692 33 633854 48-71 999597 •09 634256 365744 862816 32 29 636776 48-39 ^lU ••09 637184 48-48 3i So 639680 48-06 .09 640093 48-16 359907 3o 3i 8-642563 47-75 9-999581 •09 8.642982 645853 47-84 11-357018 29 32 645428 47-43 999575 .09 47-53 354147 2§ 33 648274 47-12 999570 -09 648704 47-22 351296 27 34 65iio2 46-82 999564 .09 65i537 46-91 348463 26 35 653911 46-52 999558 .10 654352 46 -6i 345648 25 36 656702 46-22 999553 .10 657149 659928 46-3i 342851 24 ll 659475 45.92 999547 • 10 46-02 340072 23 662230 45-63 999341 .10 662689 45-73 3373.1 22 39 664968 45.35 999535 -10 665433 45-44 334567 21 40 667689 45-06 999529 -10 668160 45.26 331840 20 41 8-670393 44-79 9-999524 -10 8-670870 44-88 11-329130 ll 42 673080 44-5i 999518 -10 673563 44-61 326437 43 675751 44-24 999512 -10 676239 44-34 323761 17 44 678405 43-97 999506 -10 tfs 44-17 32II00 16 45 681043 43.70 999500 -10 43-80 3 1 8456 i5 46 683665 43.44 9994o3 999487 -10 684172 43-54 3i5828 14 s 686272 43-18 -10 686784 43-28 3i32i6 i3 688863 42.92 42.67 999481 -10 689381 43 -o3 810619 12 49 691438 999475 -10 694029 42-77 3o8o37 11 5o 693998 42.42 999469 -10 42-52 3o547i 10 5i 8-696543 42-17 9-999463 • 11 8-697081 42-28 "la I 52 699073 41-92 999456 - 1 1 699617 42 -o3 53 701589 41-68 999450 -II 702139 tit 297861 I 54 704090 41-44 999443 • 1 1 704646 295354 55 706577 41-21 999437 -II 707140 41-32 292860 5 56 709049 40-97 999431 - 1 1 709618 41-08 200382 287917 285465 4 57 711507 40-74 4o-5i 999424 - II 712083 40.85 3 58 713952 999418 -11 714534 40.62 2 59; 71,6383 40.29 999411 • 1 1 716972 40.40 283028 I 60 718800 40.06 999404 -11 719396 40-17 280604 Cosine D. Sine Cotang. D. Tang. M. (8Y DEGREES.' SINES AND TANGENTS. (3 DEGREES.) 21 M. Sine D. Cojiue D. Tang. 1 ^- 1 Cotang. 8.718800 40.06 9-999404 '^ 8.719396 40-17 39.95 11-280604 60 1 721204 39-84 999398 • 1 1 721806 278.94 ^2 2 723595 39.62 999391 .11 724204 39-74 275796 58 3 720972 728337 39-41 999384 . 1 1 726588 39.52 273412 57 4 nil 999378 .11 728959 39.30 271041 56 5 730688 999371 11 73.3.7 3^:8? 38.68 268683 55 6 733027 38-77 999364 .12 733663 266337 54 I 735354 38-57 999337 .12 735996 264004 53 737667 38-36 999350 .12 7383.7 38.48 26.683 52 9 739969 38-i6 999343 •12 740626 38.27 259374 5i 10 742209 37-96 999336 •12 742922 33.07 257078 5o II 8-744536 37-76. 9.999329 ■12 8.745207 37.87 11.254793 8 12 746802 37-56 999322 • 12 747479 37-68 252021 i3 749055 37-37 9993 1 5 .12 749740 37.49 250260 47 •4 751297 37-17 999308 ■12 731989 37-29 24801 1 46 i5 753528 36-98 999301 •12 754227 37.10 245773 45 i6 755747 36-79 999294 999286 .12 756453 36-92 243547 44 17 707955 36-61 .12 758668 36-73 241332 43 i8 76oi5i 36-42 999279 .12 760872 36-55 239128 42 19 762337 36-24 999272 .12 763o65 36-36 236935 41 20 76451 1 36 -06 999265 .12 765246 36-18 234754 40 21 8-766675 35-88 9.999257 .12 8-767417 36-00 11.232583 g 22 768828 35-70 999250 .13 769578 35.83 23o422 23 770970 35-53 999242 .13 771727 35.65 228273 37 24 773I0I 35-35 999235 .i3 773866 35.48 226134 36 25 773223 35.18 999227 •i3 775995 35.31 224oo5 35 26 777333 35-01 999220 .i3 7781 14 35.14 221886 34 S 779434 34-84 999212 .i3 780222 Itll 219778 33 78x524 34-67 999205 .13 782320 217680 32 29 7836o5 34-51 999 '97 .i3 784408 34.64 . 215592 3i 3o 785675 34-31 999189 .13 786486 34-47 2i35i4 3o 3i 8-787736 34-18 9.999181 .i3 8-788554 34-31 11.211446 ll 32 789787 34-02 999174 .i3 790613 34-15 209387 33 791828 33-86 999 1 66 .i3 792662 IfM 207338 27 34 793809 33-70 999158 .i3 794701 205299 26 35 793881 33.54 999 1 00 .i3 796731 33-68 203269 20124a 25 36 797894 33-39 33.23 999142 .i3 798702 33-52 24 ll &,l 999134 .i3 800763 33-37 199237 23 33.08 999126 .i3 802765 33-22 197235 22 39 803876 32.93 0991 18 .i3 804758 33-07 195242 21 40 8o5802 32-78 999"° .i3 806742 32-92 193258 20 41 8-807819 32-63 9.999102 .i3 8-808717 32-78 U.191283 189317 I^ 42 809777 32.49 ^X •14 810683 32-62 43 811726 32.34 ■14 812641 32-48 187309 n 44 8i366-r 32.19 32-05 999077 -14 814589 32-33 185411 16 45 815599 999069 -14 816529 til 183471 i5 46 817022 31.91 999061 -14 818461 181539 14 s 819436 31-77 999053 -14 820384 31-91 179616 i3 821343 31-63 999044 •14 822298 31-77 177702 12 i9 823240 til 999036 -14 824205 31-63 173897 II 5o 825i3o 999027 -14 826103 3i.5o 10 5i 8-8270II 31-22 9.999019 -14 8-827992 31-36 11.172008 I 52 828884 3i-o8 999010 -14 829874 31.23 170126 53 830749 30.95 999002 -14 831748 3i.io 168252 7 54 832607 30.82 &l -14 8336i3 30.96 30.83 166387 6 55 834456 30.69 -14 835471 164529 5 56 836297 30.56 998976 ■14 837321 30.70 162679 4 ll 838i3o 30-43 998967 -i5 839163 30.57 160837 3 58 839956 3o-3o 998958 -i5 840998 30.45 159002 2 59 841774 30.17 998950 -i5 842825 30-32 157175 1 60 843585 30-00 998941 -i5 844644 30-19 155356 Cosine D. Sine Cotang. D. Tang. M. 22 (4 DEGEEES.) A TABLE OF LOGARITHMIC M. Sine D. Cosine D. Tang. D. Cotang. 8-843585 3o-o5 9-998941 •i5 8.844644 30-19 11-155356 60 I 845387 29-92 998932 .i5 846455 30-07 153545 ^ 2 847183 29-80 998923 .i5 848260 29-95 i5i74o 3 848971 29-67 998914 .i5 85oo57 29-82 ;i§?g 57 4 85o75i 29-55 998887 .i5 85 1 846 29-70 56. 5 852525 29-43 .i5 853628 29-58 146372 55 6 ' 854291 29-31 .i5 855403 29-46 144597 54 7 856049 29-19 998878 .i5 857171 29-35 142829 141068 53 8 857801 28-^4 998869 .i5 858932 860686 29-23 52 9 859546 998860 .i5 29-11 i393i4 5i 10 861283 998851 .i5 862433 29-00 137567 5o II 8-863014 28-73 9-998841 .15 8.864173 28-88 11.135827 49 12 864738 28-61 998832 .i5 865906 28-77 134094 48 i3 866455 28 -5o 998823 .16 867632 28-66 132368 47 U 868i65 28-39 28-28 998813 ■ 16 869351 28-54 1 30649 46 i5 869868 998804 .16 871064 28-43 128936 45 i6 871565 28-17 itii .16 872770 28-32 127230 44 I? 873255 28-06 .16 874469 28.21 125531 43 i8 874938 27-95 998776 .16 876162 28-11 123838 42 19 876615 27-86 998766 .16 877849 28-00 I22l5l 41 20 878285 27-73 998757 .16 879529 27-89 120471 40 21 8-879949 27-63 9-998747 •16 8.881202 27-79 11.118798 39 38 22 881607 27.52 998738 .16 882869 27-68 ii7i3i 23 883258 27-42 998728 •16 884530 27-58 115470 37 24 884903 886542 27-31 998718 •16 886 1 85 27.47 ii38i5 36 25 27-21 998708 .16 887833 27.37 112167 35 26 888.74 27-11 ?& .16 889476 27.27 110524 34 27 889801 27-00 .16 891 11 2 27-17 108888 33 28 891421 26-90 26-80 998679 .16 892742 27-07 107258 32 29 893035 998669 •17 894366 26-97 26-87 105634 3i 30 894643 26-70 998659 •17 895984 104016 3o 3i 8-896246 26-60 9.998649 •17 8-897596 26-77 11.102404 29 32 807842 26-51 998639 •17 899203 26-67 100797 28 33 899432 26-41 998629 •17 900803 26-58 099197 27 34 901017 26-31 998619 •17 902398 26-48 097602 26 35 902596 26-22 998609 •17 905570 26-38 096013 25 36 904169 26-12 998599 •17 26-29 094430 24 ll 905736 26-03 998589 •17 907147 26-20 092853 23 907297 25-93 998578 •17 908719 910285 26-10 091281 089715 22 39 908853 25-84 998568 •'7 26-01 21 40 910404 25-75 998558 •17 911 846 25-92 20 4i "US? 25-66 9-998548 •n 8-913401 25-83 11.086599 It 42 25-56 998537 .17 914951 25-74 o85o49 43 9l5022 25-47 998527 .17 916495 gi8o34 25-65 o835o5 17 44 9i655o 25-38 998516 .18 25-56 081966 16 45 918073 25-29 998506 .18 919568 25-47 080432 i5 46 919591 25-20 998495 998485 • 18 921096 25-38 078904 077381 14 47 921 io3 25-12 .18 922619 25-30 i3 48 922610 25 -o3 998474 .18 924136 25-21 075864 12 49 924112 24-94 998464 .18 925649 25-12 074351 II 5o 925609 24-86 998453 .18 927156 25-03 072844 10 5i 8-927100 24-77 9-998442 • 18 8-928658 24-95 11-071342 t 52 928587 24-69 998431 .18 93oi55 24-86 069845 068353 53 930068 24-60 998421 • 18 931647 24-78 I 54 93 1 544 24-52 998410 .18 933 1 34 24.70 066866 55 93301 5 24-43 998388 .18 934616 24-61 065384 5 56 934481 24-35 .18 936og3 24-53 063907 4 57 935942 24-27 998377 .18 937565 24-45 062435 3 58 937398 24-19 998366 .18 939032 24-37 060968 059506 o58o48 2 59 938850 24-11 998355 .18 94o4q4 24-30 I 60 940296 24- o3 998344 .18 941932 24-21 1 Cosine D. Sine Cotang. D. Tang. 1 "mT (85 DEGREES.) SINES AND TANGENTS. (5 DEGREE.) 23 M. Sine D. Cosine D. Tang. D. Cotang. 8-940296 941738 24-o3 9-998344 19 8-941952 24-21 II -058048 60 23 94 998333 '9 943404 24 i3- 056596 S 2 943174 23 87 998322 19 944852 24 o5 o55i48 3 944606 23 79 998311 19 946295 947734 23 97 053705 57 4 946034 23 7' 998300 19 23 ^2 052266 56 5 947456 23 63 998289 19 949168 23 o5o832 55 6 948874 23 55 998277 19 950597 23 -i 049403 54 7 950287 23 48 998266 19 952021 23 66 047979 046559 53 8 951696 23 40 998255 19 953441 23 60 52 9 953100 23 32 998243 19 954856 23 5i 045144 5i 10 954499 23 25 998232 19 956267 23 44 043733 5o II 8.955894 23 17 9.998220 19 8-957674 23 37 11-042326 8 12 957284 23 10 998209 19 959075 23 It 040925 039527 i3 958670 23 02 ??^1S 19 960473 23 47 U 960052 22 t 19 961866 23 14 o38i34 46 i5 961429 22 998174 19 963255 23 07 036745 45 i6 962801 22 80 998163 19 964639 23 00 o3536i 44 '7 964170 22 73 998151 19 966019 22 g 033981 43 18 965534 22 66 998139 998128 20 968766 22 032606 42 19 966893 22 59 20 22 79 o3i234 41 20 968249 22 52 9981 16 20 970133 22 71 029867 40 2l 8-969600 22 44 9-998104 20 8-971496 22 65 ii-o285o4 S 22 970947 22 38 998092 998080 20 972855 22 57 027145 23 972289 22 3i 20 974209 22 5i 025791 ll 24 973628 22 24 998068 20 975560 22 44 024440 25 974962 22 17 998056 20 976906 22 37 023094 021752 35 26 976293 22 10 998044 20 978248 22 3o 34 11 977619 22 o3 998032 20 979586 22 23 020414 33 978941 21 97 998020 20 980921 22 17 019079 32 ?9 » 21 23 998008 20 982251 22 10 017749 016423 3i 3o 21 997996 20 983577 22 04 3o 3i 8-982883 21 77 9-997985 20 8-984899 21 97 ii-oi5ioi ll 32 984189 21 70 997972 20 986217 21 013783 33 985491 21 63 997959 20 988842 21 84 012468 ll 34 ISI 21 57 ^]IU 20 21 78 0IU58 35 21 5o 21 990149 21 71 00985 I 008549 25 36 989374 21 44 997922 21 991451 21 65 24 ll 990660 21 38 997910 1 997807 997885 21 992750 21 58 007250 005955 23 991943 21 3i 21 994045 21 52 22 39 993222 21 25 21 995337 21 46 004663 21 4o 994497 21 19 997872 21 996624 21 40 003376 20 41 8.995768 21 12 9-997860 21 8.997908 21 34 11-002092 :? 42 997036 998299 21 06 V,]IU 21 999188 21 27 000812 43 21 00 21 9-000465 21 21 10-999535 17 44 999560 20 q4 997822 21 001738 21 i5 998262 16 45 9-000816 20 87 997809 21 oo3oo7 21 S 996993 i5 46 002069 20 82 997797 997784 21 004272 21 995728 14 47 oo33i8 20 76 21 005534 20 97 994466 i3 48 004563 20 70 997771 21 006792 20 §5 993208 12 49 oo58o5 20 64 997758 21 008047 009298 20 991953 II 5o 007044 20 58 997745 21 20 80 990702 10 5i 9-008278 20 52 9-997732 21 9-010546 20 74 10-989454 988210 I 52 oogSio 20 46 997719 21 oAir, 20 68 53 010737 20 40 997706 21 20 62 986969 I 54 01196a 20 34 997680 22 014268 20 56 985732 55 oi3i82 20 29 22 oi55o2 20 5i 984498 5 56 014400 20 23 997667 22 016732 20 45 983268 4 a oi56i3 20 17 997654 22 017959 20 40 982041 3 016824 20 12 ■ 997641 22 019183 20 33 980817 2 59 oi8o3i 20 06 997628 22 o2o4o3 20 28 l]& I 60 019235 20-00 997614 22 021620 20-23 Cosine D. Sine 1 Cotanff. D. Tang. (84 DEGREES.) 24 (6 DEGREES.) A TABLE OF LOGARITHMIC M. Sine D. Cosine D. Tang. D. Cotang. 9-019235 20-00 9-997614 .22 9-021620 20-23 10-978880 60 I 020435 19-95 19-89 997601 .22 022884 20.17 977166 ll 2 02i632 997588 .22 024044 20.11 975956 3 022825 19-84 997574 •22 025231 20-06 & 57 4 024016 19-78 997561 .22 026455 20-00 56 5 025203 19-78 997547 .22 027655 028852 19-95 972845 55 6 026386 19-67 997534 .23 ;?:§? 971148 54 7 027567 19-62 997520 .28 080046 968763 53 8 028744 19-57 997507 .23 081287 19-79 52 9 029918 i9-5i 997498 997480 • 28 082423 19-74 967575 5i 10 081089 19-47 -23 088609 19-69 966891 5o u 9-o32257 19-41 9-997466 -28 9-084791 19-64 10-965209 s 12 o3342i 19-86 997432 -23 035969 19-58 964081 i3 034582 19-30 997489 997425 -23 087144 19-53 962856 47 U 035741 19-25 -23 088816 19-48 961684 46 i5 086896 19-20 99741 1 -23 089485 19-48 9605 1 5 45 i6 088048 I9-I5 997897 -23 04065 1 19-38 959349 44 17 089197 19-10 997888 -23 04i8i3 19-33 ■958187 43 i8 040842 19-05 & -23 042978 19-28 » 42 19 041485 18.99 -28 044180 19-23 41 20 042625 18-94 997341 -28 045284 19-18 954716 40 21 9-048762 18.89 9-997827 •24 9-046434 19-13 10-953566 U 22 044895 18-84 997818 • 24 047582 048727 19-08 952418 23 046026 18-79 », •24 19-08 951273 37 24 047154 18-75 •24 049869 o5ioo8 18-98 9501 3 1 36 25 048279 18-70 997271 ■24 18-98 18.89 ?g§S 35 26 049400 i8-65 997257 -24 o52i44 34 S o5o5i9 o5i635 18-60 997242 -24 058277 18.84 946728 33 18-55 997228 -24 054407 18-79 32 29 052749 i8-5o 997214 •24 055535 18-74 944465 3i So 053859 18-45 997199 -24 056659 18-70 943341 3o 3 1 9-054966 18-41 9-997185 -24 9-057781 18-65 10.942219 3 32 056071 i8-36 997170 -24 058900 18-69 941100 33 057172 i8-3i 997156 •24 060016 18-55 989984 988870 27 34 058271 18-27 997141 •24 061180 18.51 36 35 059867 18-22 997127 •24 062240 18.46 987760 25 36 060460 18-17 997112 •24 063348 18.42 986652 24 13 o6i55i i8-i3 997098 •24 064453 18.37 935547 33 062689 18-08 997088 .25 065556 18.33 934444 22 39 068724 064806 i8-o4- 997068 .25 066655 18.28 933345 21 40 17.99 997053 .25 067752 18.24 982248 20 41 9-065885 17-94 9.997089 .25 9-068846 18.19 18. i5 10.981154 ^9 42 066962 17.90 997024 .25 069988 980062 18 43 068086 17.86 997009 .25 071027 18-10 928073 927887 «7 44 069107 17.81 996994 .25 072118 18-06 16 45 070176 17.77 996979 .25 078197 18-02 926808 i5 46 071242 17.72 996964 ■25 074278 17-97 925722 14 s 072806 17-68 996949 .25 075356 17-03 924644 i3 078866 17-63 996984 .25 076482 17-89 923568 12 49 074424 \llt 996919 .25 o775o5 17-84 922495 1 1 5o 075480 996904 .25 078576 17-80 921424 10 5i 9-076533 17.50 9.996889 .25 9-079644 17-76 10-920356 ? 52 077588 078681 17-46 996874 .25 080710 17-72 919290 53 17-42 996858 .25 081778 17-67 918227 7 54 079676 080719 17-38 996843 .25 082888 17-63 917167 6 55 17.33 996828 .25 088891 17-59 916109 5 56 081759 17.20 17-25 996812 .26 084947 17-55 9i5o53 4 ll IMI 996707 .26 086000 17-5. 914000 3 17.21 996782 .26 087050 17-47 912950 2 59 084864 \IM 996766 .26 088098 17-43 IVolll I 60 085894 996751 .26 089144 17-38 Cosine D. Sine Cotang. D. Tang. 'm7\ (83 DEGREES.) SINES AND TANGENTS. (7 DEGREES.) 25 M. Sine D. Cosme D. Tang. D. Cotang. 9-085894 17.13 9-996751 • 26 9-089144 17-38 10.910856 60 I 086922 17-09 996735 -26 090187 091228 17 -34 9008.3 908772 It 2 087947 17-04 996720 .26 17 -3o 3 088970 17-00 996704 .26 092266 17 •27 907734 57 4 089990 16-96 996688 .26 093302 17 -22 906698 56 5 091008 16-92 i6-88 16.84 996673 .26 094336 17 :;? 905664 55 6 7 092024 093037 996657 996641 • 26 .26 & 17 17 904633 9o36o5 54 53 8 094047 16-80 996625 .26 097422 098446 17 •3 902578 52 9 095o56 16-76 996610 .26 17 901554 5i 10 096062 16-73 996594 .26 099468 16 •99 900532 5o II 9-097065 16-68 9-996578 -27 9-100487 16 95 "•1« ii 12 098066 16-65 996562 -27 101 5o4 16 ^7 i3 099065 16-61 996546 .27 I025i9 16 897481 S U 100062 16-57 996530 ■27 103532 16 84 896468 i5 ioio56 16.53 996514 .27 104542 16 80 895458 45 i6 102048 16-49 996498 .27 io555o 16 76 894450 44 :i io3o37 16-45 996482 .27 106556 16 72 893444 43 io4o25 16-41 996465 •27 107559 16 s 892441 42 •9 io5oio 16-38 l& •27 io856o 16 891440 4x 20 105992 16-34 ■27 109559 16 61 890441 40 21 9-106973 i6-3o 9-996417 ■27 9-110556 16 58 10-889444 888449 39 38 22 107901 16-27 996400 ■27 iii55i 16 54 23 108927 16-23 996384 •27 112543 16 5o 887457 37 24 I 0900 I 1 10873 16-19 16-16 996368 •27 II3533 16 46 886467 36 25 996351 •27 1 1452 1 16 43 884493 35 26 11.842 16-12 996335 •27 ii55o7 16 S 34 27 II 2809 16-08 996318 •27 116491 16 883500 882528 33 28 113774 i6-o5 996302 .28 117472 16 32 32 29 1 14737 16-01 996285 .28 1 1 8452 16 ll 881548 3i 3o 115698 15-97 996269 .28 119429 16 880571 3o 3i 9-116656 15-94 9-996252 .28 9-120404 16 22 10-879596 878623 ll 32 117613 ti; 996235 .28 122348 16 18 33 1 18567 996219 .28 16 i5 877652 27 34 1 19319 15-83 996202 .28 I233I7 16 1 1 876683 ' 26 35 120469 i5-8o 996185 .28 124284 16 07 875716 ! 25 36 121417 15-76 996168 .28 125249 16 04 874751 ^ 24 ll 122362 15-73 996151 .28 126211 16 01 873789 I 23 872828 : 22 i233o6 15-69 996134 .28 127172 i28i3o i5 97 39 124248 15.66 996117 .28 i5 94 871870 1 21 40 125187 15-62 996100 .28 129087 i5 91 870913 20 41 9-126125 \tu 9-996083 •29 9-130041 i5 87 10.869959 ;? 42 127060 996066 •29 i3o994 i5 84 869006 43 127993 i5-52 996049 ■29 131944 i5 81 868o56 17 16 44 128925 \l:il 996032 •29 132893 133839 i5 77 867107 45 129854 996015 •29 i5 74 866161 i5 46 130781 15-42 & •29 134784 i5 71 865216 14 47 131706 ;l:S •29 135726 i5 67 864274 i3 48 i3263o 995963 •29 136667 i5 64 863333 12 49 i3355i i5-32 995946 ■29 137605 i5 61 862395 861458 II 5o 134470 15.29 995928 •29 138542 i5- 58 10 5i 9-135387 15.25 9-995911 •29 9-139476 i5- 55 io.86o524 I 52 i363o3 l5.22 995894 •29 140409 i5- 5i i& 53 137216 15.19 995876 .29 i4i34o i5- 48 1 6 54 i38i28 i5.i6 995859 • 29 142269 i5- 45 85773. 55 139037 I5.I2 995841 •29 143196 i5- 42 856804 5 56 139944 i4o85o 15.09 995823 •29 144121 i5- ll 855879 4 u i5.o6 995806 -29 145044 i5- 854956 3 141754 i5-o3 995788 -29 145966 i5- 32 854034 2 59 142655 i5-oo 995771 •29 146885 i5- 29 853ii5 I 60 143555 14-96 995753 •29 147803 i5-26 852197 Cosine D. Fine 1 1 Cotang. ! D. 1 Tang. M. j 26 (8 DEGREES.) A TABLE OF LOGAEITHMIC M. Sine D. Cosine D. Tang. T>. Cotang. 9.143555 14-96 9-995753 ■3o 9-147803 i5-26 10-852197 60 I 144453 14-93 995735 -3o 148718 i5 23 85x282 li 2 145349 14-90 14-87 995717 -3o 149632 i5 20 85o368 3 146243 995699 -3o i5o544 i5 17 840456 57 4 i47i36 14-84 995681 -3o i5i454 i5 14 848546 56 5 148026 14-81 995664 -3o 152363 i5 II 847637 55 6 149802 14-78 995646 -3o 153269 i5 08 846731 54 7 14-75 995628 -3o 154174 i5 o5 845826 53 8 i5o686 14-72 995610 •3o 155077 i5 02 844923 52 9 i5i569 14-69 ^9559. -3o 155978 14 11 844022 5i lo i5245i 14-66 995573 •3o 156877 14 843123 5o II 9-153330 14-63 9-995555 -3o 9-157775 14 93 10-842225 8 12 1 54208 14-60 995537 -3o 158671 14 ^7 841329 840435 i3 i55o83 14-57 995519 -3o 159565 14 47 U ;g?s 14-54 995501 -3i 160457 14 84 839543 838653 46 i5 14-51 995482 -3i i6i347 14 81 45 i6 157700 14-48 995464 -3i 162236 14 79 i^r. 44 I? 158569 159435 14-45 995446 -3i i63i23 14 76 43 i8 14-42 995427 -3i 164008 14 73 835992 42 19 i6o3oi 14-39 14-36 995409 -3i 164892 14 70 835io8 41 20 161 164 995390 -3i 165774 14 67 834226 40 21 9-162025 14-33 9-995372 -31 9-166654 14 64 10-833346 ^I 22 162885 i4-3o 995353 .31 167532 14 61 832468 23 163743 14-27 995334 .31 168409 14 58 83i59i 11 24 164600 14-24 995316 .3i 169284 14 55 830716 25 165454 14-22 995297 • 31 170157 14 53 829843 828971 35 26 i663o7 14-19 14-16 995278 -3i 171029 14 5o 34 27 167159 168008 995260 -3i 171899 14 47 828101 33 28 14-13 995241 •32 172767 14 44 827233 32 29 168856 14-10 995222 -32 173634 14 42 826366 3i 3o 169702 14-07 995203 -32 174499 14 39 825501 3o 3i 9-170547 i4-o5 9-995184 -32 9-175362 14 36 10-824638 3 32 171389 14-02 995165 •32 176224 14 33 823776 33 172230 13-99 995146 -32 177084 14 3i 822916 27 34 173070 13-96 995127 •32 177942 14 28 822058 26 35 36 173908 174744 i3-94 13-91 13-88 995108 995089 ■32 •32 \fJM 14 14 25 23 821201 820345 25 24 37 175578 995070 •32 i8o5o8 U 20 IX% 23 38 176411 13-86 995o5i •32 i8i36o 14 17 22 39 177242 13-83 c)95o32 •32 182211 14 i5 817789 21 40 178072 i3-8o 995oi3 •32 i83o59 14 12 816941 20 41 9-178900 13-77 9-994993 •32 9-183907 14 09 10-816093 ;i 42 XI?, 13-74 994974 -32 184752 14 07 8:5248 43 13-72 994955 -32 185597 186439 14 04 8i44o3 n 44 181374 13-69 13-66 994935 -32 14 02 8i356i 16 45 182196 994916 994896 -33 187280 i3 ? 812720 811880 i5 46 i83oi6 13-64 -33 188120 i3 14 47 183834 i3.6i 994877 -33 188958 i3 ,3 811042 i3 48 1 8465 1 '.tU 994857 -33 189794 i3 810206 12 49 185466 994838 • 33 190629 i3 89 8of538 II 5o 186280 13-53 994818 • 33 191462 i3 86 10 5i 9.187092 i3-5i 9-994798 ■33 9-192294 i3 ^4 10-807706 I 52 187903 i3-48 994779 •33 193124 i3 81 806876 53 188712 13-46 994759 •33 ,93953 i3 79 806047 1 54 189519 190325 13-43 994739 • 33 194780 i3 76 8o522o 6 55 13-41 994719 •33 195606 i3 74 804394 5 56 i9ii3o 13-38 994700 -33 196430 i3 71 803570 4 57 19.933 13-36 994680 -33 XI i3 69 802747 3 58 192734 13-33 994660 -33 i3 66 801926 2 59 193534 i3.3o 994640 • 33 198894 i3. 64 801106 I 60 194332 13.28 994620 •33 199713 i3 61 800287 Cosine D. Sine 1 Cotans:- D. Tang. _i^-_ (81 DEGREES.) SINES AND TANGENTS. (9 DEGEEE.) 27 M. Sine D. Cosine D. Tang. D. Cotang. 9.194332 13-28 9.994620 -33 9- 199713 i3-6i 10-800287 60 I 195120 195925 13-26 994600 -33 200529 201345 13-59 ]%ll 59 2 i3-23 994580 -33 13-56 58 3 196719 I3-2I 994560 •34 202 1 5g 13-54 797841 57 4 197D11 198302 i3-i8 994540 •34 202971 i3-52 797020 796218 56 5 i3-i6 994519 •34 203782 13-49 55 6 19909 1 i3-i3 994499 •34 204592 .3-47 795408 54 I 199879 I3-II 994479 •34 205400 13-45 794600 53 200666 i3-o8 994459 994438 ■34 206207 13-42 793793 52 9 20i45i i3-o6 •34 207013 i3-4o 792987 5i 10 202234 13-04 994418 •34 207817 13-38 792183 5o II 9-2o3oi7 I3-0I 9.994397 ■34 9-208619 13-35 10-791381 8 12 203797 12-99 994377 • 34 209420 13-33 7^9780 788982 i3 204577 12-96 994357 •34 210220 i3-3i 47 U 205354 12-94 994336 •34 211018 13-28 46 i5 2o6i3i 12-92 ,2-§9 994316 •34 2ii8i5 13-26 788185 45 i6 206906 994295 •34 212611 13-24 787389 78659! 44 17 207679 12-87 994274 -35 2i34o5 I3-2I 43 18 208452 12-85 994254 -35 214198 13-19 785802 42 19 209222 12-82 994233 -35 214989 13-17 78501 1 41 20 209992 12.80 994212 -35 215780 i3-i5 784220 40 21 9.210760 2Il526 12-78 9-994191 • 35 9-216568 13-12 10-783432 3q 22 12-75 9941 7 1 -35 217356 i3-io 782644 38 23 2I229I 2i3o55 12-73 9941 5o -35 218142 i3-o8 781858 u 24 12.71 994129 -35 218926 i3.o5 781074 25 2i38i8 12-68 994108 • 35 219710 i3-o3 780290 35 26 214579 215338 12-66 994087 -35 220492 13-01 779508 34 27 12-64 994066 -35 221272 12-99 778728 33 28 =:s?i 12-61 994045 -35 222052 12-97 777948 32 2g 12.59 994024 -35 222830 12-94 777170 3i 3o 217609 12.57 994oo3 •35 2236o6 12-92 776394 3o 3i 9-218363 12-55 9-993981 -35 9-224382 12-90 12-88 10-775618 11 32 219116 12-53 993960 -35 225i56 774844 33 219868 12. 5o liZ -35 225929 12-86 774071 27 34 220618 12-48 -35 226700 12-84 773300 26 35 22i367 12-46 -36 227471 772529 25 36 2221l5 12-44 993875 -36 228239 12-79 771761 24 37 222861 12-42 993854 -36 229007 12-77 12-75 770993 23 38 223606 12.39 993832 -36 229773 770227 22 39 224349 12.37 993811 -36 23o539 12.73 768698 21 40 225092 12.35 993789 • 36 23l302 12.71 20 41 9.225833 12-33 9-993768 •36 9-232065 12.69 10-767935 ;? 42 226573 12. 3i 993746 •36 232826 12.67 767174 43 227311 12.28 993725 • 36 233586 12.65 766414 \i 44 228048 12.26 993703 •36 234345 12.62 765655 45 228784 12.24 993681 -36 235io3 12.60 764897 i5 46 229518 12.22 993660 •36 235859 12.58 764141 i4 8 230252 12.20 993638 • 36 2366i4 12.56 763386 i3 230984 12.18 993616 •36 237368 12-54 762632 12 49 23I7I4 12-16 993594 •37 238i2o 12-52 761880 11 5o 232444 12-14 993572 ■37 238872 12-50 761128 10 5i 9-233172 12-12 9-993550 • 37 9-239622 12-48 10-760378 I 52 233899 234625 12-09 993528 •37 240371 12-46 %t 53 12-07 993506 ■37 241 118 12-44 1 54 235349 236073 12 -oS 993484 • 37 24i865 12-42 758i35 6 55 12.03 993462 •37 242610 12-40 757390 5 56 236795 12-01 993440 .37 243354 12-38 756646 4 57 58 2375i5 XI. 99 993418 -37 244097 244839 12-36 755903 3 238235 11.97 993396 •37 12-34 755161 2 59 238953 11.95 993374 •37 245579 12-32 754421 I 60 239670 11-93 993351 • 37 246319 12-30 753681 i Cosine 1 D. Sine Cotang. D. Tang. ^ (80 DEGREES.) 28 (10 DEGREES.) A TABLE OF LOGARITHMIC 'm. Sine D. Cosine D. Tang. D. Cotang. 9-239670 11-93 9.993351 .37 9-2463.9 I2-3o 10 -753681 60 I 240386 l\t 993329 -37 247057 12.28 752943 s 2 241101 993307 -37 247794 12-26 752206 3 241814 11-87 993285 -37 248530 12-24 75.470 57 4 242526 11-85 993262 -37 249264 12-22 7507.36 56 5 243237 11-83 993240 •37 ISfo 12-20 750002 55 6 243947 11-81 993217 -38 12-18 749270 54 7 244656 11-79 993195 -38 25.461 \l.,l 748539 53 8 245363 11-77 993172 ■38 25219. 747809 52 9 246069 11-75 993149 • 38 252920 I2-I3 747080 5i 10 246773 11-73 993.27 -38 253648 12-11 746352 5o II 9-247478 11-71 9-993.04 -38 9-254374 12^09 10-745626 S 12 24S181 11-69 99308. -38 235.00 12-07 744900 i3 248883 ;::S 993059 993o36 •38 255824 12-05 744176 47 14 249583 -38 256547 i2-o3 743453 46 i5 2502S2 11-63 9930.3 -38 257269 12-01 742731 45 i6 250980 25.677 I. -61 992990 ■ 38 2587.0 12-00 742010 44 17 11-50 992967 -38 11-98 74.290 43 i8 202373 11-58 992944 -38 259429 11-96 740571 42 19 253067 11-56 992921 •38 260.46 n-94 739854 41 20 253761 11-54 992898 •38 260863 II^92 739.37 /,o 21 9-254453 11-52 9-992875 •38 9-26.578 l\X 10-738422 It 22 255144 I. -50 992852 •38 262292 737708 23 255834 11-48 sss -39 263oo5 11-8^ ?af 11 24 256523 11-46 -39 2637.7 ii^85 25 25721. 11-44 992783 •39 264428 ii^83 735572 35 26 mis 11-42 992759 •39 265.38 ii^8i 734862 34 11 11-41 992736 •39 265847 ..■79 ..-78 734153 33 259268 11-39 9927.3 -39 266555 733445 32 29 259951 11-37 992690 .39 26726. 11-76 f.iii 3i 3o 260633 11-35 992666 •39 267967 11-74 3o 3i 9-26i3.4 11-33 9-992643 • 39 9-26867. 11^72 "t• Cotang. o-5l2642 6..2 9-975670 ^ 9.536972 6-84 10.463028 60 5 1 3009 6 XX 975627 73 537382 6-83 4626.8 It 2 5i3375 6 XX 975583 H 537792 6-83 462208 3 5i374i 6 xo 97DD39 73 538202 6-82 461798 57 4 514107 6 09 975496 ^^ 53861 X 6-82 46.389 56 5 514472 6 09 973432 73 539020 6-8x 460980 55 6 514837 6 08 975408 73 539429 6-8x 460371 54 7 5i5202 6 08 975363 '^l 539S37 6-80 460163 53 8 5 1 5566 6 07 975321 73 540245 6-80 459755 52 9 5 1 5930 6 07 975277 73 540653 6-79 499347 408939 5i 10 516294 6 06 973233 73 54x061 6-79 5o II 9 -516657 6 o5 9.975x89 ^^ 9.54x468 6-78 10-458532 8 12 517020 6 05 973x43 73 54x875 6-78 458x25 i3 517382 6 04 975x01 ^^ 542281 6-77 457719 47 U 517745 6 04 975057 73 542688 6-77 4573.2 46 i5 518107 6 o3 9750,3 73 543094 6-76 456906 45 i6 518468 6 03 974969 74 543499 6.76 45650 X 44 I? 518829 6 02 974923 74 543903 6-75 436095 43 i8 519190 6 ox 974880 74 5443x0 6-75 455690 455285 42 19 519551 6 01 974836 74 544715 6-74 41 20 519911 6 00 974792 74 545xx9 6.74 454881 40 21 9-520271 6 00 9.974748 74 9-545524 6-73 xo- 454476 39 22 52063 1 5 99 974703 74 543928 6.73 454072 38 23 520990 5 99 974659 74 54633 X 6.72 453669 453263 37 24 521349 5 98 9746x4 74 546735 6-72 36 25 521707 5 98 974570 74 547x38 6.7X 452862 35 26 522066 5 97 974525 74 547540 6-7X 402460 34 27 522424 5 96 974481 74 548345 6-70 432057 33 28 522781 5 96 974436 74 6-70 45x655 32 29 523.38 5 95 974391 74 548747 6-69 45x253 3i 3o 523495 5 95 974347 75 549149 6-69 45o85i 3o 3i 9-523852 5 94 9-974302 75 9.549550 6-68 10 .450400 11 32 524208 5 94 974257 75 549951 6-68 450049 33 524564 5 93 9742x2 V 55o352 6-67 449648 11 34 524920 5 93 974x67 ^^ 550752 6-67 449243 35 525275 525630 5 92 974x22 75 551132 6-66 448848 25 36 5 91 974077 75 55x552 6-66 448448 24 u 520984 526339 5 91 974082 75 55x932 6-65 448048 23 5 90 973987 75 552351 6-65 447649 22 39 526693 5 90 973942 73 552750 6-65 447250 2X 40 527046 5 89 973897 75 553.49 6-64 446851 20 41 9-527400 5 89 9-973852 75 9-553548 6-64 X 0.44645 2 19 42 527753 5 88 973807 75 553946 6-63 446054 18 43 528x05 5 88 973761 75 554344 6.63 445656 17 44 528458 5 87 9737x6 76 55474X 6.62 445259 16 45 528810 5 87 973671 76 555x39 6.62 44486 X i5 46 529161 5 86 973625 76 555536 6.6x 444464 14 8 5295x3 5 86 973580 76 555933 556329 6-61 444067 i3 529864 5 85 973535 76 6-60 44367 X 12 49 53o2x5 5 85 973489 76 556725 6-6o 443275 II 5o 53o565 5 84 973444 76 557X2X 6.59 442879 10 5i 9-53o9x5 5 84 9-973398 76 9-5575x7 6-59 xo. 442483 2 52 53x265 5 83 973332 76 5579x3 6-5o 442087 53 53x6x4 5 82 973307 76 5583o8 6-58 441692 I 54 53x963 5323x2 5 82 97326X 76 558702 6-58 44x298 55 5 8x 9732x5 76 559097 6-57 440903 5 56 532661 5 81 973169 76 55949. 6.57 44o5o9 4401 i5 4 57 533009 5 80 973124 76 559885 6.56 3 58 533357 5 80 973078 76 560279 6.56 439721 2 59 533704 5 7Q 973o32 77 560673 6.55 439327 I 60 534052 5.78 972986 77 56io66 6.55 438934 Cosine D. Sine D. Cotan^. D. Tang. M. (70 DEGREES.) 38 (20 DEGREES.) A TABLE OF LOGAEITHMIC M. Sine D. Cosine D. Tang. D. Cotang. 9 -534032 5.78 9-972986 •77 g-56io66 6-55 10-438934 60 I 534399 5.77 972940 •77 561459 6-54 438541 5o 2 534745 5.77 972894 •77 56i85i 6-54 438149 58 3 535092 535438 tVe 972848 •77 562244 6-53 437756 u 4 972802 •77 562636 6-53 437364 5 535783 5-76 972755 •77 563028 6-53 436972 436581 55 6 536129 5-75 972709 972663 •77 563419 6-52 54 I 536474 5-74 •77 563811 6-52 436189 53 5368 1 8 5-74 972617 •77 564202 6-51 435798 52 9 537x63 5-73 972570 •77 564592 6.5i 435408 5i 10 537507 5-73 972524 •77 564983 6.5o 435017 5o II 9-537851 5-72 9.972478 •77 9-565373 6.5o 10-434627 49 12 538194 5-72 972431 -78 565763 6.49 434237 48 i3 538538 5-71 972385 .78 5661 53 6.49 433847 47 14 538880 5.71 972338 .78 566542 6.49 433458 46 i5 539223 5-70 972291 -78 566932 6.48 433068 45 i6 539565 5-70 972245 ■^l 567320 6.48 432680 44 I? 539907 5-69 972198 ■''I 567709 6.47 432291 43 i8 540249 ?:S 972131 ■^^ 568098 6.47 431902 42 19 540590 972105 -78 568486 6-46 43iDi4 41 20 540931 5-68 972058 -78 568873 6.46 431127 40 21 9-541272 5-67 9-972011 -78 9.569261 6.45 io-43o73g 39 3§ 22 54i6i3 5-67 971964 •7^ 569648 6.45 43o352 23 541953 5-66 971917 •t 570035 6.45 429965 37 24 542293 5-66 971870 •7^ 570422 6-44 429378 36 25 542632 5-65 971823 -78 570809 6-44 429191 35 26 ItSVo 5-65 971776 -78 571195 6-43 428805 34 11 5-64 971729 •79 571581 6-43 428419 33 543649 5-64 971682 •79 571967 6.42 428033 32 29 543987 544325 5-63 971635 ■79 572352 6.42 427648 3i 3o 5-63 971588 •79 572738 6.42 427262 3o 3i 9-544663 5-62 9-971540 ■79 9-573123 6.41 10-426877 11 32 545000 5-62 971493 •79 573507 6.41 426493 33 545338 5-6i 971446 •79 573892 6.40 426108 27 34 545674 5-6i 971398 •79 574276 6.40 425724 26 35 54601 1 5-60 97I3D1 •79 574660 6.39 425340 25 36 546347 5.60 97i3o3 •79 575044 6.39 424056 424573 24 U 546683 5-59 971256 •79 575427 6.39 23 547019 971208 •79 57D810 6.38 424190 22 39 547354 971161 •79 576193 6.38 423807 21 40 547689 5^58 971113 •79 576576 6.37 423424 20 41 9-548024 5-57 9-971066 .80 9-576908 577341 6.37 io-423o4i ;? 42 548359 548693 til 971018 -80 6.36 422659 43 970970 -80 577723 6-36 422277 n 44 549027 5-56 970922 -80 578104 6-36 421896 16 45 549360 5-55 970874 -80 578486 6-35 42i5i4 i5 46 549693 5-55 970827 -80 578867 6-35 421133 14 S 550026 5-54 970779 -80 579248 6-34 420752 i3 55o359 5-54 970731 -80 579629 6.34 420371 12 49 550692 5-53 970683 -80 58ooog 6.34 419991 II 5o 551024 5-53 970635 • 80 58o389 6.33 419611 10 5i 9-55i356 5-52 9-970586 .80 9.580769 6.33 io-4i923r I 52 551687 552018 5-52 970538 .80 581149 6.32 4i885i 53 5-52 970490 -80 58i528 6-32 418472 7 54 552349 5-5i 970442 -80 581907 6-32 418093 6 55 552680 5.5i 970394 -80 582286 6-31 417714 5 56 553010 5-5o 970345 -81 582665 6.31 417335 4 57 553341 5-50 970297 -81 583043 6.3o 416957 3 58 553670 5-49 970249 -81 583422 6-3o 416578 2 59 554000 5-49 970200 -81 583800 6-29 416200 I 60 554329 5-48 970152 -81 584.77 6-29 415823 Cosine D. Sine 1 D. Cotaiig. D. Tang. M. (69 DEGREES.) SINES AND TANGENTS. (21 DEGEEES.) 39 M. Sine D. Cosine D. Tang. D. Cotang. 9-554329 5-48 9-970152 81 9 •5841 77 6-29 io-4i5823 60 I 554658 5.48 970103 81 584555 6 29 415445 u 2 554987 5.47 970055 81 584982 585309 6 28 4i5o68 3 5553 1 5 5-47 970006 8i 6 28 414691 57 4 555643 5.46 969957 81 585686 6 27 414814 56 5 555971 5.46 969909 8i 586062 6 27 418088 4i856i 55 6 556299 5.45 969860 81 586489 6 27 54 7 556626 5.45 96981 1 81 5868 1 5 6 26 4i3i85 53 8 556953 5-44 969762 81 58?566 6 26 412810 52 9 557280 5-44 969714 81 6 25 412484 5i 10 557606 5.43 969665 81 587941 6 25 412059 5o II 9.557932 5.43 9-969616 82 9-5888i6 6 25 10-411684 ii 12 558258 5.43 969567 82 588691 6 24 411809 i3 558583 5-42 969518 82 589066 6 24 410984 4io56o 47 14 558909 5.42 969469 82 589440 6 23 46 i5 559234 5-41 969420 82 589814 6 28 410186 45 i6 559558 5-41 969370 82 590188 6 23 409812 44 I? 559883 5-40 969321 82 590562 6 22 409488 43 i8 560207 5-40 969272 82 590935 6 22 409065 42 19 56o53i 5.39 969223 82 591808 6 22 408692 41 20 56o855 5.39 969173 82 591681 6 21 408819 40 21 9.561178 5-38 9-969124 82 9-592054 6 21 10-407946 407574 ^1 22 56i5oi 5.38 969075 82 592426 6 20 23 561824 5.37 969025 82 592798 6 20 407202 37 24 562146 5-37 5-36 968976 82 598170 6 19 406829 36 20 562468 968926 83 598542 6 \l 406458 35 26 562790 5-36 968877 83 598914 6 406086 34 27 563II2 5.36 968827 88 594285 6 18 405715 33 28 563433 5.35 968777 88 594656 6 18 405344 32 ?9 563755 5-35 968728 88 595027 6 17 404978 3i 3o 564075 5.34 968678 83 595898 6 17 404602 3o 3i 9.564396 5.34 9-968628 88 9-595768 6 11 iO'4o4232 29 28 32 564716 5-33 968578 88 596188 6 408862 33 565o36 5.33 96S528 88 596508 6 16 408492 27 34 565356 5.32 968479 88 596878 6 16 408122 26 35 565676 5-32 968429 83 597247 6 i5 402753 25 36 5663:4 5.31 968379 83 597616 6 i5 402884 24 ^7 5.31 968829 83 nut 6 i5 4o20i5 23 38 566632 5.31 968278 83 6 14 401646 22 39 566951 5.30 968228 84 598722 6 14 401278 21 40 567269 5-3o 968178 84 599091 6 18 400909 20 41 9.567587 5.29 9-968128 84 9-599459 6 18 io-4oo54i [I 42 567904 5.29 968078 ^^ 599827 6 18 400173 43 5682 2 2 5.28 968027 84 600194 6 12 399806 \l ^ 568539 5.28 967977 84 600062 6 12 899438 45 568856 5.28 967927 84 600929 6 II 398704 i5 46 569172 5.27 967876 84 601296 601662 6 II 14 47 56948S 5.27 967826 84 6 11 898888 i3 48 569804 5.26 967775 84 602029 602895 602761 6 10 897971 12 P 570120 5.26 967725 84 6 10 897605 II 5o 570435 5.25 967674 84 6 10 397289 10 5i 9.570751 5-25 9-967624 84 9-608127 608498 6 09 10-396878 1 52 571066 5-24 967573 84 6 09 896507 53 57x380 5-24 967522 85 608808 6 2 356142 I l^ 571695 5.23 967471 85 604228 6 895777 5d 572009 572323 5-23 967421 85 604588 6 08 3954.2 5 56 5-23 967870 85 604953 6o53i7 6 07 895047 4 s 572636 5-22 967819 85 6 07 894688 3 572950 5.22 967268 85 6o5682 6 07 894818 2 59 573263 5.21 967217 85 606046 6 06 398954 I 60 573D75 5.21 967166 85 606410 6-o6 393590 Cosine D. Sine 1 dT Cotang. D. Tang. mT (68 DEGREES.) 40 (22 DEGREES.) A TABLE OF LOGARITHMIC M. Sine D. Cosine D. Tang. D. Cotang. ^ 5?3888 5.21 9-967166 .85 9^606410 6.06 10 •393590 60 I 5.20 9671 i5 • 85 606773 6 06 393227 59 2 574200 5.20 967064 .85 607137 6 o5 392863 58 3 574512 5.19 967013 -85 607500 6 o5 392500 57 4 574824 5.19 966961 -85 607863 608225 6 04 392137 56 5 575i36 5.19 5.i§ 966910 -85 6 04 391775 55 6 575447 966809 966808 • 85 6o8588 6 04 391412 54 7 575758 5-18 -85 608950 609312 6 o3 391050 53 8 576069 ^'7 966756 • 86 6 o3 390688 52 9 576379 5.17 966705 -86 609674 6 o3 390326 389964 5i 10 576689 5.16 966653 • 86 6ioo36 6 02 5o II 'i]tl 5.16 9-966602 ■86 9^6io397 610759 6 02 10-389603 s 12 5.16 966550 •86 6 02 389241 388880 i3 577618 5.i5 966499 • 86 611120 6 01 47 14 577927 5-i5 966447 •86 611480 6 01 388520 46 i5 578236 5-14 966395 • 86 611841 6 01 388159 45 16 578545 5. ,4 966344 • 86 612201 6 00 387799 387439 44 17 578853 5-13 966292 • 86 6i256i 6 00 43 18 579162 5.13 966240 • 86 612921 6 00 387079 42 19 579470 5-13 966188 -86 613281 5 99 386719 41 20 ^19111 5.12 966136 • 86 6i364i 5 99 386359 40 . 21 9 -580085 5.12 9-966085 • 87 9-614000 5 98 10-386000 39 22 580392 5. II 966033 •87 614359 614718 5 98 385641 38 23 580690 5. II 965981 .87 5 98 385282 37 24 58ioo5 5. II 965928 965876 -87 6i5o77 5 97 384023 384565 36 25 58i3i2 5.10 •87 61 5435 5 97 35 26 58i6i8 5.10 965824 -87 615793 6i6i5i 5 97 384207 34 ^l 581924 5.09 965772 -87 5 96 383849 33 28 582229 582535 5.09 965720 •87 6i65o9 5 96 383491 32 29 1:2 965668 -87 616867 5 96 383i33 3i 3o 582840 9656 1 5 •87 617224 5 95 3S2776 3o 3i 9-583145 5.08 9-965563 • 87 9-617582 5 95 10-382418 29 32 583449 5.07 96551, •87 617939 5 95 382061 28 33 583754 5.07 965458 .87 618295 5 94 381705 27 26 34 584058 5.06 965406 -87 6i8652 5 94 38i348 35 584361 5.06 965353 • 88 619008 5 94 380992 25 36 584665 5.06 965301 • 88 619364 5 93 38o636 24 37 584968 5.o5 965248 • 88 619721 5 93 380279 23 38 585272 5.o5 965195 • 88 620076 5 93 379568 22 39 585574 5.04 965143 -88 620432 5 92 21 40 585877 5.04 965090 -88 620787 5 92 379213 20 41 9-586179 5.o3 9-965037 • 88 9-621142 5 92 io^378858 '9 42 586482 5.o3 964984 • 88 tiini 5 91 378503 18 43 586783 5.o3 ^64031 964879 964826 • 88 5 91 378148 17 44 587085 5.02 • 88 622207 5 90 377793 16 45 587386 5-02 • 88 622561 5 90 ^J7439 377085 i5 46 587688 5-01 964773 • 88 622915 5 % i4 47 587989 5-01 964719 • 88 623269 5 376731 i3 48 588289 5.01 964666 .89 623623 5 89 376377 12 49 588590 5.00 964613 -89 623976 5 89 376024 n 5o 588890 5.00 964560 • 89 624330 5 88 375670 10 5i '1^;?5 4-99 9-964507 .89 9 •624683 5 88 io^3753i7 I 52 4-99 964454 .89 625o36 5 88 374964 53 pa 4-98 964400 .89 625388 5 87 374612 I 54 964347 .89 625741 5 87 374259 55 590387 4.98 964294 .89 626093 5 87 373907 56 590686 4-97 964240 -89 626445 5 86 373555 s 590984 4-97 964187 • 89 626797 5 86 373203 591282 ill 964133 .89 627149 5 86 372851 59 591580 964080 .89 627501 5 85 372499 37214S 60 591878 4-96 964026 • 89 627852 5 85 Cosine D. Sine D. Cotan^. D. Tang. "m7 (67 DEGREES.) SINES AND TANGENTS. (23 DEGREES.) 41 M. Sine D. Cosine D. Tang. D. Cotang. o g. 591878 4.96 9-964026 ~^ 9-627852 5-85 10-372148 60 I 592176 4-95 963972 .89 62S203 5-85 371797 S 2 592473 4-95 &,l .89 628554 5-85 371446 3 592770 4-93 -90 62S905 5-84 371095 57 4 593067 4.94 96381 1 -90 629255 5-84 370745 56 5 593363 4-94 963757 • 90 629606 5-83 370394 55 6 093659 4-93 963704 -90 629956 5-83 370044 54 7 593953 4-93 963650 • 90 63o3o6 5-83 369694 53 8 594231 4-93 963596 .90 63o656 5-83 369344 52 9 094547 4-92 963542 -90 63ioo5 5-82 368993 5i 10 594842 4.92 963488 .90 63i355 5-82 368645 5o II 9.595137 4-91 9-963434 -90 9-631704 5-82 10-368296 % 12 595432 4-91 963379 .90 632053 5-81 367947 i3 595727 4-91 963323 -90 632401 5-81 367399 47 14 696021 4-90 963271 -90 632750 5-81 367230 46 10 0963 1 5 4-90 963217 .90 633098 5-80 366902 45 i6 596609 596903 4-89 963 1 63 .90 633447 633795 5-8o 366553 44 '7 4-89 963io3 .91 5-8o 366205 43 i8 597196 4-89 g63o34 • 91 634143 5-79 365857 42 19 597490 4-88 962999 .91 634490 5-79 365510 41 20 597783 4-83 962945 -91 634838 5-79 365i62 40 21 9-598075 4-87 9-962890 962836 •91 9-635x85 5-78 io-3648i5 39 22 59S368 4-87 -91 635532 5-78 364468 38 23 598660 4-87 962781 -91 635879 5-78 364I2I 37 24 598932 4-86 962727 .91 636226 5-77 363774 36 20 599244 4-86 962672 • 91 636572 5-77 363428 35 26 599336 4-85 962617 •91. 636919 5-77 363o8i 34 n 599327 4-85 962362 • 91 637265 5-77 362735 33 28 600118 4-85 962308 .91 63761 1 5-76 362389 32 ?9 600409 4-84 962453 -91 637956 638302 5-76 362044 3i 3o 600700 4-84 962398 .92 5-76 361698 3o 3i 9-600990 4-84 9-962343 -92 9-638647 5.75 io-36i353 ?? 32 601260 4-83 962288 .92 638992 5-75 361008 U 601570 4-83 962233 .92 639337 5-75 36o663 27 U 601860 4-82 962178 .92 639682 5-74 36o3i8 26 35 602 1 5q 4-82 962123 .92 640027 5-74 359973 25 36 602439 4-82 962067 .92 640371 5-74 339629 24 .^T 602728 4-8i 962012 .92 640716 5-73 359284 358940 23 *38 6o3oi7 4-8i 961957 .92 641060 5-73 22 39 6o33o5 4-8i 961902 -92 641404 5-73 358596 21 40 603594 4-8o 961846 -92 641747 5-72 358233 20 i 4i 9-6o3882 4-8o 9-961791 -92 9-642091 642434 5-72 10-357909 42 604170 4-79 961735 -92 5-72 357566 18 43 604437 4-79 961680 -92 642777 5-72 357223 17 44 604740 V.l 961624 •93 643120 5-71 356880 16 43 6o5o32 961569 -93 643463 5-71 336537 i5 46 6o53i9 4-78 96i5i3 •93 643806 5-71 356.94 U 47 6o56o6 4-78 961438 •93 644148 5-70 355852 i3 48 605892 4-77 961402 .93 644490 644832 5-70 355510 12 49 606179 4-77 961346 •93 5-69 355i68 " i 00 606465 4-76 961290 -93 645174 354826 10 5i 9-606751 4-76 9-961235 .93 9-645516 5.69 10-354484 I 52 607036 4-76 961179 961123 •93 645857 5.69 354143 53 607322 4-75 -93 646199 i:§ 353801 7 54 607607 4-75 961067 -93 646540 353460 6 55 607892 4-74 961011 -93 646881 5.68 353119 5 56 608177 4-74 960955 -93 647222 5-68 352778 il 608461 4-74 960899 -93 647562 5.67 352438 58 608745 4-73 960843 .94 647903 5.67 352097 l^ 609029 4-73 960786 -94 648243 5-67 351737 6o 609313 4-73 960730 .94 648583 5-66 35.417 Cosine 1 D. Sine D. Cotan?. D. Tang, i M. (66 DEGREES.) 42 (24 DEGREES.) A TABLE OF LOGARITHMIC M. Sine D. Cosine D. Tang. D. Cotang. 9-6o93i3 4-73 9-960730 94 9-648583 5-66 10-351417 60 I 609597 72 960674 94 648923 5 66 351077 f? 2 609880 72 960618 94 649263 5 66 350737 3 610164 72 960561 94 649602 5 66 350398 35oo58 57 4 610447 71 96o5o5 94 649942 5 65 56 5 610729 71 960448 94 65o28i 5 65 3497 '9 55 6 611012 70 960392 960335 94 65o62o 5 65 349380 54 I 611294 70 94 650959 5 64 349041 53 611576 70 960279 94 65i297 5 64 348703 52 9 6ii858 69 960222 94 65i636 5 64 348364 5i 10 612140 69 960165 94 651974 5 63 348026 5o II 9-612421 '& 9-960109 95 9-652312 5 63 10-347688 s 12 612702 960052 95 652650 5 63 347350 i3 612983 68 959995 95 652988 5 63 347012 47 46 14 613264 67 959938 95 653326 5 62 346674 i5 613545 67 959882 95 653663 5 62 346337 45 i6 6i3825 67 959825 95 654000 5 62 346000 44 17 6i4io5 66 959768 95 654337 5 61 345663 43 18 614385 66 9597 1 1 95 654674 5 61 345326 42 19 614665 66 959654 95 655011 5 61 344989 41 20 614944 65 959596 95 655348 5 61 344652 40 2? 9-6i5223 65 9-939539 95 9-655684 5 60 10-344316 ?? 22 6i55o2 4 65 959482 95 656020 5 60 343980 23 615781 64 959425 95 656356 5 60 343644 37 24 616060 64 959368 95 656692 5 59 343308 36 25 6i6338 64 959310 96 657028 5 59 342972 35 26 616616 63 959253 96 657364 5 59 342636 34 27 616894 4 63 959195 96 657699 5 M 342301 33 28 617172 . 62 09.38 96 658o34 5 341966 32 29 617400 62 959081 96 658369 5 58 34i63i 3i 3o 617727 62 959023 96 658704 5 58 341296 3o 3i 9-618004 4 61 9-958965 96 9-659039 5 58 10-340961 29 32 618281 4 61 958go8 958850 96 659373 5 57 340627 28 33 6i8558 61 96 659708 5 57 340292 339958 S 34 618834 60 958792 96 660042 5 57 35 619110 60 958734 96 660376 5 57 339624 25 36 619386 60 958677 96 660710 5 56 339290 24 37 619662 59 958619 96 661043 5 56 338957 23 38 619938 59 958561 96 661377 5 56 338623 22' 39 620213 59 9585o3 97 661710 5 55 338290 337957 21 40 620488 58 958445 97 662043 5 55 20 41 9-620763 58 9-958387 97 9-662376 5 55 10-337624 \l 42 621038 57 958329 97 662709 5 54 3369^8 43 62i3i3 4 57 958271 97 663042 5 54 n 44 621587 57 958213 97 663375 5 54 336625 16 45 621861 56 9581 54 97 663707 5 54 336293 i5 46 622135 4 56 958096 97 664039 5 53 335961 14 47 622409 4 56 958o38 97 664371 5 53 335629 i3 48 622682 4 55 957979 97 664703 5 53 335297 12 49 622956 4 55 ?^??63 97 665o35 5 53 334965 1 1 5o 623229 4 55 97 665366 5 52 334634 10 5i 9-623502 4 54 9-957804 97 9-665697 5 52 io.3343o3 I 52 623774 54 957746 98 666029 5 52 333971 53 624047 54 957687 957628 98 666360 5 5i 333640 7 54 624319 53 98 666691 5 5i 333309 6 55 624591 53 957570 98 667021 5 5i 332979 332648 5 56 624863 53 95751 I 98 667352 5 5i 4 U 625i35 52 957452 98 667682 5 5o 3323i8 3 625406 52 957393 98 668013 5 5o 331987 2 59 625677 625948 52 957335 98 668343 5 5o 33i657 33i328 I 60 4-5i 957276 98 668672 5-5o Cosine D. Sine D. Cotangr. D. Tang. M. (65 DEGREES.) SINES AND TANGENTS. (25 DEGREES.) 43 M^ Sine D. i Cosine D. 1 T;mg. D. ! Cotang. 9.625948 4-5i 9.957276 .93 9.668673 5-50 ' io-33i327 60 I 626219 4-5i 957217 957.58 .98 669002 5-49 330998 330668 U 2 626490 4-5i .98 669332 5-49 3 626760 4-5o 957099 .98 669661 5-40 33o339 57 4 627030 4-5o 957040 .98 669991 5-48 330009 56 5 627300 4-5o ,5698> .98 670320 5-48 329680 55 6 627570 4.49 l&l •99 670649 5-48 329351 54 7 627840 4.49 •99 670977 5-48 329023 328694 53 8 628109 628378 4-49 956803 •99 67.306 5-47 52 9 4-48 956744 •99 671634 5.47 328366 5i 10 628647 4.48 956684 •99 671963 5-47 328037 5o II 9-628916 4-47 9.956625 •99 9.672291 5-47 10-327709 a 12 629185 4-47 956566 •99 672619 5.46 32738. i3 629453 4-47 9565o6 •99 672947 5-46 327053 47 46 14 629721 4-46 956447 •99 673274 5-46 326726 i5 629989 4-46 956387 •99 673602 5.46 326398 45 i6 630257 4.46 956327 •99 673929 5.45 326071 44 n 630324 4-46 956268 •99 674257 5.45 325743 43 iS 630792 4-45 956208 J. 00 674584 5.45 325416 42 «9 631039 4-45 956148 1 .00 6749.0 5-44 325090 41 20 63i326 4-45 956089 1. 00 675237 5.44 324763 40 21 9-631393 4-44 9.956029 1. 00 9.675564 5.44 10-324436 ii 22 63 1 859 632123 4-44 955969 1. 00 675890 5-44 324110 23 4-44 gss 1. 00 676216 5.43 323784 37 24 632392 4-43 1. 00 676543 5.43 323457 36 25 632638 4-43 955789 1. 00 676869 5.43 323.3. 35 26 632923 4-43 955729 1. 00 677194 5-43 322806 34 27 633189 4-42 955669 1.00 677520 5-42 322480 33 28 633434 4-42 955609 1. 00 677846 5-42 322.54 32 29 633719 4-42 955548 1. 00 678.71 5.42 32.829 3i 3o 633984 4-41 955488 1. 00 678496 5.42 32i5o4 3o 3i 9-634249 4-41 9.955428 1. 01 9-678821 5.4. 10-321179 29 32 634514 4-40 955368 I. 01 679146 5.41 320854 28 33 634778 4-40 955307 1. 01 679471 5.41 320329 27 34 633042 4.40 955247 J. 01 679795 5.41 320205 26 35 6353o6 4-39 955i86 1. 01 680120 5.40 319880 25 36 635570 4-39 955126 I. 01 680444 5.40 319556 24 '^ 635834 til 955o65 1. 01 680768 5.40 319232 23 636097 955oo5 1. 01 681092 5.40 22 39 636360 4-38 954944 954883 I. 01 6814.6 5.39 3 18584 21 40 630623 4-38 I -01 681740 5.3^ 318260 20 41 9-636886 4-37 9.954823 I-OI 9-682063 5-39 10.317937 19 42 637148 4-37 954762 I-OI 682387 5-3o 3176.3 18 43 6374.1 4-37 954701 l-OI 682710 5-38 3.7290 17 44 637,673 4-37 954640 I-OI 683o33 5-38 316967 16 45 637935 4-36 954579 934318 I-OI 683356 5-38 3.6644 i5 46 6384^8 4-36 1.02 683679 5-38 3i632i 14 47 4-36 954457 1-02 684001 5.37 3.5999 i3 48 638720 4-35 954396 1-02 684324 5.37 3.5676 12 49 638981 4-35 954335 1.02 684646 5.37 3.5354 II 5o 639242 4-35 954274 1.02 684968 5.37 3.5o32 ID 5i 9 -639503 4-34 9.954213 1.02 9-685290 5.36 io.3i47io 1 52 639764 4-34 954152 1.02 6856.2 5.36 3.4388 53 640024 4-34 954090 1.02 685934 5.36 3.4066 7 54 640284 4-33 954029 1-02 686255 5.36 3.3745 6 55 640544 4-33 953968 1.02 686577 686898 5.35 3 1 3423 5 56 640804 4-33 ^g23 1.02 5.35 3.3.02 4 57 641064 4-32 1.02 687219 5.35 3.2781 3 58 641324 4-32 953783 1.02 687540 5.35 3.2460 2 59 641584 4-32 953722 i.o3 687861 5.34 3i2i39 3ii8i8 I 60 641842 4-3i 953660 i.o3 688182 5-34 Cosine D. Sine D. Cotang. D. Tansr. M. (64 DEGREES.) 4A (26 DEGREES.) A TABLE OF LOGAEITHMIC M. Sine D. Cosine D. Tang. D. Cotang. 9-641842 4-3i 9-953660 i-o3 9-688182 5-34 io-3ii8i8 60 I 642101 4 3i 953599 i-o3 688502 5 34 311498 ll 2 642360 4 3i 953537 i-o3 688823 5 34 311177 3 642618 4 3o 953475 1-03 689143 5 33 3 10857 57 4 642877 4 3o 953413 1-03 689463 5 33 3 1 0537 56 5 643 1 35 4 3o 953352 i-o3 689783 5 33 310217 55 6 643393 643650 4 3o 953290 i-o3 690103 5 33 309897 54 7 4 29 953228 I -03 690423 5 33 309577 53 8 643908 4 29 953166 i-o3 690742 5 32 309258 308938 52 9 644165 4 29 28 953104 i-o3 691062 5 32 5i 10 644423 4 953042 i-o3 691381 5 32 308619 5o II 9-644680 4 28 9-952980 1-04 9-691700 5 3i io-3o83oo 49 12 644936 4 28 952918 952855 1-04 692019 5 3i 307981 48 i3 645193 4 27 1-04 692338 5 3i 307662 47 14 645450 4 27 902793 1-04 692656 5 3i 307344 46 i5 645706 4 27 952731 1-04 692975 5 3i 307025 45 i6 645962 4 26 952669 1-04 693293 5 3o 306707 44 17 646218 4 26 952606 1-04 693612 5 3o 3o6388 43 i8 646474 4 26 952544 1-04 693930 5 3o 306070 42 19 646729 4 25 952481 1-04 694248 5 3o 3o5752 41 20 646984 4 25 952419 1-04 694566 5 29 3o5434 40 21 9-647240 4 25 9-952356 1-04 9-694883 5 29 io-3o5ii7 ll 22 647494 4 24 952294 1-04 695201 5 29 304799 23 647749 4 24 952231 1-04 695518 5 29 304482 37 24 648004 4 24 952168 i-o5 695836 5 29 304164 36 25 648258 4 24 952106 i-o5 696153 5 28 3o3847 35 26 648512 4 23 952043 i-o5 696470 5 28 3o353o 34 27 648766 4 23 931980 I -05 696787 5 28 3o32i3 33 28 649020 4 23 951917 I -05 697103 5 28 302897 3o258o 32 29 649274 4 22 951854 i-o5 697420 5 27 3i 3o 649527 4 22 95179' I -05 697736 5 27 302264 3o 3i 9-649781 4 22 9-951728 I -05 9-698053 5 27 io.3oig47 U 32 65oo34 4 22 95i665 i.o5 698369 5 27 3oi63i 33 650287 4 21 951602 i-o5 69868D 5 26 3oi3i5 27 ¥. 65o539 4 21 951539 i-o5 699001 5 26 IZlll 26 35 650792 4 21 951476 i-o5 699316 5 26 25 36 651044 4 20 951412 i-o5 699632 5 26 3oo368 24 37 65 1 297 4 20 951349 1-06 699947 5 26 3ooo53 23 38 65 1 549 4 20 951286 1-06 700263 5 25 299737 22 39 65 1800 4 19 951222 I -06 700578 5 25 299422 21 40 652052 4 >9 951159 1-06 700893 5 25 299107 20 41 9-6523o4 4 ;? 9-951096 95io32 1-06 9-701208 5 24 10-298792 ;§ 42 652555 4 1-06 701523 5 24 298477 43 652806 4 18 950968 1-06 701837 5 24 298163 17 44 653o57 4 18 $x I -06 702152 5 24 297848 16 45 6533o8 4 18 1-06 702466 5 24 297534 i5 46 653558 4 '7 950778 1-06 702780 5 23 297220 14 47 653So8 4 17 950714 1-06 703095 5 23 296905 i3 48 654059 4 '7 95o65o 1-06 703409 703723 5 23 296591 12 49 654309 4 16 95o586 1-06 5 23 296277 II 5o 654558 4 16 95o522 1-07 704036 5 22 295964 10 5i 9-654808 4 16 9-950458 1-07 9-7o435o 5 22 10-295650 I 52 655o58 4 16 950394 95o33o 1-07 704663 5 22 295337 53 655307 4 i5 1-07 704977 5 22 295023 7 54 655556 4 i5 950266 1.07 705290 5 22 294710 6 55 655805 i5 950202 1-07 7o56o3 5 21 294397 294084 5 56 656o54 14 95oi38 1-07 705916 5 21 4 57 656302 14 950074 1-07 706228 5 21 293772 3 58 656551 14 950010 1-07 706541 5 21 293459 2 59 656799 i3 ms 1-07 706854 5 21 293,46 I 60 657047 4-i3 1-07 707166 5-20 292834 Cosine D. Sine D. Cotang. D. Tang. M. (63 DEGREES.) ,.1 SINES AND TANGENTS. (27 DEGREES.) 45 M. Sine D. Cosine D. Tang. D. Cotang. 9-657047 4-i3 9-949881 1-07 9.707166 5-20 10.292834 60 I 657295 4-i3 949816 1-07 707478 5.20 292522 11 2 637542 4-12 949752 1-07 707790 5.20 292210 3 tUlT, 4-12 949688 1-08 708102 5.20 291898 57 4 4-12 949623 i-o8 708414 5.19 291586 56 5 658284 4-12 949558 I -08 708726 5.19 291274 55 6 658531 4ii 949494 I -08 709037 5-19 290963 54 I 658778 4-u 949429 I -08 709349 5-19 290651 53 659025 4-11 949364 I -08 709660 5.10 5.1S 290340 52 9 639271 4-10 949300 i-o8 709971 290029 5i 10 639317 4-10 949235 i-o8 7x0282 5-18 289718 5o II 9.659763 4-10 9-949170 I -08 9.710593 5.18 10-289407 ii 12 660009 4-09 949105 I -03 710904 5-i8 289096 288785 i3 660255 4-09 949040 1.08 7ii2i5 5.18 47 14 66o5oi 4-09 948975 I -08 7II525 5.17 288475 46 i5 660746 4-oq ^IS? I -08 7II836 5.17 288164 45 i6 660991 4-o8 1.08 712146 5.17 287854 44 '7 661236 4-o8 948780 1-09 712456 5.17 287544 43 i8 661481 4-o8 948715 1-09 712766 5.16 287234 42 19 661726 4-07 948650 1-09 '.llVsl 5.16 286924 41 20 661970 4-07 948584 1-09 5.16 286614 40 21 9-662214 4-07 9-948519 1-09 9.713696 5.16 10-286304 ^2 22 662459 4-07 948454 1-09 714003 5-16 285995 38 23 662703 4-o6 948388 I -09 714314 5.i5 285686 37 24 662946 4- 06 948323 1-09 714624 5.i5 285376 36 23 663190 4-o6 948257 1-09 714933 5.i5 285067 35 26 663433 4-o5 948192 1-09 713242 5.i5 284758 34 27 663677 4-o5 948126 1-09 7i555i 5.14 284449 33 28 663920 4-o5 948060 1-09 7i586o 5.14 284140 32 29 664163 4-o5 947995 I-IO 716168 5.14 283832 31 3o 664406 4-04 947929 I-IO 716477 5.14 283523 3o 3r 9-664648 4-04 9-947863 I-IO 9.716785 5.14 10-283215 It 32 664891 4-04 947797 I-IO 717093 5.i3 282907 33 665 1 33 4-o3 947731 I-IO 717401 5.i3 282599 27 34 665375 4-o3 947665 I-IO 717709 718017 718325 5.i3 282291 26 35 665617 4-o3 947600 I-IO 5.i3 281983 25 36 665839 4-02 947533 I-IO 5.i3 281670 H 37 666100 4-02 947467 I-IO 718633 5.12 281367 23 38 666342 4-02 947401 I-IO 718940 5.12 281060 22 39 666583 4-02 947335 I-IO 719248 5-12 280752 21 40 666824 4-01 947269 I-IO 719555 5.12 280445 20 41 9-667065 4-01 9.947203 I-IO 9.719862 5.12 io.28oi38 \l 42 667303 4-01 947136 I - n 720169 720476 720783 5. II 279831 43 667546 4-ox 947070 I-II 5. II 279524 17 44 667786 4-00 947004 III 5-11 279217 16 45 668027 4-00 946937 946871 I-II 721089 5. II 278604 i5 46 668267 4-00 I-II 721396 5-11 14 s 668306 3-99 946804 I-II 721702 5.10 278298 i3 668746 3-99 946738 I-II 722009 7223i5 5.10 277991 12 49 668986 3-99 946671 I-II 5.10 277685 II 5o 669225 3-99 946604 I-II 722621 5.10 277379 10 5i 9-669464 3-98 9-946538 I-II 9.722927 5.10 10-277073 9 52 669703 3-98 946471 I-II 723232 5.09 276768 8 53 669942 3-98 946404 I-II 723538 5.09 276462 7 54 670181 3.97 946337 I-II 723844 5.09 276136 6 55 670419 3-97 946270 I-I2 724149 5.09 275851 5 56 670658 3-97 946203 I - 12 724434 t:i 275546 4 57 670896 3-97 946 1 36 I-I2 ]IUH 275241 3 58 671134 3-^6 946069 I-I2 5.08 274935 2 59 671372 3.96 946002 I-I2 725369 5.08 274631 I 60 671609 3.^6 945935 I-I2 725674 5.08 274326 Cosine D. Sine D. Cotanar. D. Tang. M. (62 DEGREES.) 46 (28 DEGREES.) A TABLE OF LOGARITHMIC M. Sine D. Cosine D. Tang. D. Cotang. o 9-671609 3.96 9-945985 945868 I-I2 9-725674 5-08 10-274826 60 I 671847 8 95 1-12 725979 5-08 274021 u 2 672084 8 95 945800 1-12 726284 5.07 278716 3 672821 8 95 945788 1-12 726588 5-07 278412 57 4 672558 3 95 945666 I-I2 726892 5.07 278108 56 5 672795 678032 3 94 ?gl? I-I2 727197 5.07 272808 55 6 3 94 I-I2 727501 5-07 272499 54 7 678268 3 94 945464 1-18 727805 5.06 272195 53 8 6785o5 8 94 945896 I-l3 728109 5-06 271891 52 9 678741 8 98 945828 i-i3 728412 5-06 271588 5i 10 678977 3 93 945261 1-18 728716 5-06 271284 5o II 9-674218 8 93 9-945198 1-18 9-729020 5-06 10-270980 S 12 674448 3 92 945'?5 1-18 729828 5-o5 270677 i3 674684 3 92 945o58 1-18 729626 5-o5 270874 47 U 674919 675155 8 92 944990 1-18 729929 5-o5 270071 46 i5 8 92 944922 1-13 780233 5-o5 269767 45 i6 675890 8 91 944854 1-18 780535 5-o5 269465 44 17 675624 3 91 944786 i-i3 780888 5-04 269162 268859 43 18 675859 3 91 944718 i-i3 781141 5-04 42 19 676094 3 91 944650 i-i8 731444 5-04 268556 41 20 676828 3 90 944582 I-I4 731746 5.04 268254 40 21 9-676562 3 90 9-944514 1-14 9-782048 5-04 10-267952 ll 22 676796 3 90 944446 1-14 782851 5-03 267649 23 677080 3 ^ 944377 I-I4 782653 5-o3 267347 37 24 677264 8 944309 1-14 782955 5-08 267045 36 25 677498 3 f 944241 1-14 788558 5-08 266748 35 26 6777^1 3 944172 I-I4 5-08 266442 34 27 677964 8 88 944104 I -14 788860 5-02 266140 33 28 678197 8 88 944036 1-14 784162 5-02 265888 32 29 678480 3 88 948967 1-14 784468 5-02 265587 3i 3o 678668 3 88 948899 1-14 784764 5-02 265236 3o 3i 9-678895 3 87 9-948880 I-I4 9-735o66 5-02 10-264934 ?l 32 679 > 28 8 87 948761 I -14 785867 735668 5-02 264688 33 679860 3 87 948693 i-i5 5-01 264882 27 34 679592 3 87 943624 i-i5 735969 5-01 264081 26 35 t£U 3 86 943555 i-i5 786269 5-01 268781 25 36 3 86 948486 i-i5 786570 5-01 268480 24 37 680288 3 86 943417 i-i5 786871 5-01 268129 23 38 68o5i9 3 85 948848 i-i5 787171 5-00 262829 22 39 680750 8 85 948279 i-i5 787471 5-00 262529 21 40 680982 8 85 948210 i-i5 737771 5-00 262229 20 41 9.681218 8 85 9-948141 i-i5 9-738071 5-00 10-261929 It 42 681448 3 84 943072 i-i5 788871 5-00 261629 43 681674 3 84 943008 i-i5 788671 4-99 261829 17 44 681905 3 84 • 942934 i-i5 788971 4-99 261029 16 45 682185 3 84 942864 i-i5 789271 4-99 260729 i5 46 682865 3 88 942795 i-i6 789570 4-99 260480 14 s 682595 8 88 942726 1-16 789870 4-99 260180 i3 682825 8 88 942656 i-i6 740169 4-99 259881 12 49 688055 3 88 942587 i-i6 740468 4-98 259532 5o 688284 3 82 942517 i-i6 740767 4-98 259238 10 5i 9-6835i4 3 82 9-942448 i-i6 9.741066 4-98 io-258g34 I 52 688743 3 82 942378 i-i6 741865 4-98 258635 53 688972 3 82 942808 i-i6 741664 4-98 258336 I 54 684201 3 81 942289 i-i6 741962 4-97 258o88 55 684430 3 81 942169 I -16 742261 4-97 257789 5 56 684658 3 81 942099 i-i6 742559 4-97 257441 4 57 684887 685ii5 3 80 942029 1-16 742858 4-97 257142 3 58 3 80 ■ 941959 I -16 7481 56 4-97 256844 2 59 685348 3 80 941889 1-17 743454 4-97 256546 I 60 685571 3-80 941819 1-17 748752 4-96 256248 Cosine D. Sine D. Cotang. I). Tang. 1 M. | (61 DEGREES.) SINES AND TANGENTS. (29 DEGREES.) 47 M." Sine D. Cosine D. Tang. D. Cot;ing. j 9.685571 3.80 9-941819 1-17 9'743752 4-96 10-236248 60 I 685799 3-79 94.749 1-17 744o5o 4-96 255950 59 255632 58 2 686027 3-79 941679 I-I7 744348 4-96 3 686254 3-79 941609 I-I7 744645 4-96 255355 1 57 4 686482 3-79 3-78 94.539 1-17 744943 4-96 255o57 56 5 686709 941469 1-17 745240 4-96 234760 55 6 686936 3-78 941398 1-17 745538 4-95 254462 54 I 687163 3-78 941328 I-I7 745835 4-95 254.65 53 687389 3-78 941258 1-17 746.32 4.95 253868 52 9 687616 3-77 941187 1.17 746429 4-95 253571 5i 10 687843 3-77 941 1 17 1. 17 746726 4-93 253274 5o II 9.688069 3-77 9-941046 1-18 9-747023 4.94 10-252977 49 12 688293 3-77 940975 i-i8 7473.9 4.94 232681 48 i3 688521 3-76 940905 940834 I -18 747616 4-94 232384 47 H 688747 3-76 1-18 747913 4-94 232087 46 i5 688972 3-76 940763 1-18 748209 4-94 25.791 45 i6 689.98 3-76 940693 i-i8 7485o5 4.93 25.495 44 17 689423 3-75 940622 1-18 748801 4-93 230903 25o6o7 43 i8 689648 3-75 94055 I 1-18 749097 4-93 42 19 689873 3-75 940480 1. 18 7493q3 749689 4-93 41 20 690098 3-75 940409 i-i8 4-93 25o3.i 40 21 9-690323 3-74 9-940338 i-i8 9-749985 4-93 .0-2500.5 39 22 690548 3-74 940267 i-i8 750281 4-92 249719 38 23 690772 3-74 940.96 1-18 750576 4-92 249424 37 24 690996 3-74 940125 I -19 750872 4-92 249128 248833 36 25 691220 3-73 940054 1-19 731.67 4-92 35 26 691444 3.73 939982 I -19 751462 4-92 248538 34 27 691668 3.73 9399.1 1-19 751757 4-92 248243 33 28 69.892 3-73 939840 1-19 752052 4-91 247948 32 29 6921.5 3-72 939768 1-19 752347 4-91 247653 3i 3o 692339 3-72 939697 1-19 752642 4-91 247338 3o 3i 9-692562 3-72 9-939625 1-19 9-752937 4-91 10-247063 U 32 692785 3-71 939554 1-19 753231 4-91 246769 33 693008 3.71 939482 1-19 753526 4-91 246474 11 34 69323. 3.71 9394.0 1-19 753820 4.90 246180 35 693453 3.71 939339 1-19 7541x5 4.90 245885 23 36 693676 3-70 939267 1-20 754409 4-90 245591 24 37 693898 3-70 939.95 1-20 754703 4-90 243297 23 38 694120 3-70 939123 1-20 754997 4-90 245oo3 22 39 694342 3-70 93S980 1-20 f5lH t% 244709 2444x5 21 40 694564 3-69 1-20 20 41 9-694786 3-69 9 -938908 1-20 9-755878 4-89 10-244.22 42 695007 3.69 1-20 756172 756465 4-89 2 ^3828 43 695229 tu 938763 1-20 4-89 243535 17 44 695450 938691 1-20 756759 4-89 243241 16 45 69567. 3-68 938619 1-20 757052 4-89 2429.48 242655 i5 46 695892 3-68 938547 1-20 757345 4.88 14 s 696.. 3 3-68 938475 1-20 757638 4-88 242362 i3 696334 3.67 938402 I-2I 757931 ^i^o 242069 12 f^ 696554 3-67 938330 1-2. 758224 4-^? 241776 24x483 1 1 5o 696775 3-67 938258 I-2I 7585x7 4.88 10 5i 9-696995 3.67 9-938.85 I-2I 9-7588x0 4.88 10-241190 9 52 6972.3 3-66 938. .3 I-2I 759.02 4-87 240898 8 53 697433 3-66 938040 1-21 ]i^f, 4-87 240605 7 54 697654 3-66 937967 I. 21 4-87 24o3.3 6 55 697874 3-66 937895 I-2I 759979 4-87 240021 5 56 698094 3-65 937822 I-2I 760272 4-87 239728 4 ll 6983.3 3-65 937749 I-2I 760564 4-87 , 239436 3 58 698532 3-65 937676 I-2I 760856 4-86 239144 2 ^ 69875. 3-65 937604 I-2I 761 148 4-86 238352 I 60 698970 3.64 937531 I-2I 761439 4-86 23856. Cosine D. Sine D. Cotans:. D. Tansr. ~m7 (60 DEGREES.) 48 (30 DEGREES.) A TABLE OF LOGARITHMIC M. Sine D. Cosine I ). Tang. D. Cotang. 9-698970 3-64 9-937531 I 21 9-761439 4-86 10-238561 60 I 699189 3 64 937458 I 22 76173. 4-86 238269 u 2 699407 3 64 937385 I 22 762023 4-86 237977 3 699626 3 64 937312 1 22 762314 4-86 237686 57 4 699844 3 63 937238 I 22 762606 4-85 237394 56 5 700062 3 63 937165 I 22 762897 763 1 88 4-85 237103 55 6 700280 3 63 937092 I 22 4-85 2368.2 54 7 700498 3 63 937019 I 22 763479 4-85 236521 53 8 700716 3 63 llXt \ 22 763770 4-85 236230 52 9 700933 3 62 22 764061 4-85 null 5i 10 70ii5i 3 62 936799 I 22 764352 4-84 5o II 9-701368 3 62 9-936725 I 22 9-764643 4-84 10-235357 § 12 701585 3 62 936652 I 23 764933 4-84 235067 i3 701802 3 61 936578 I 23 765224 4-84 234486 47 U 702019 3 61 9365o5 I 23 765514 4-84 46 i5 702236 3 61 936431 I 23 7658o5 4-84 234195 45 i6 702452 3 61 936357 I 23 766095 4-84 233905 44 17 702669 3 60 936284 I 23 766385 4-83 2336.5 43 18 702885 3 60 936210 I 23 766675 4-83 233325 42 19 7o3ioi 3 60 936i36 I 23 766965 4-83 233o35 41 20 7033x7 3 60 936062 I 23 767255 4-83 232745 40 21 9.703533 3 59 9-935988 I 23 9-767545 4-83 10-232455 12 22 703749 3 59 935914 I 23 767834 4-83 232.66 23 703964 3 59 935840 I 23 768124 4-82 23.876 37 24 704395 3 59 935766 I 24 768413 4-82 23.587 36 25 3 it 935692 I 24 768703 4-82 23.297 35 26 704610 3 935618 I 24 &: 4-82 23.008 34 27 704825 3 58 935543 I 24 4-82 230719 33 28 29 7o5o4o 705254 3 3 58 58 935469 1 935396 I 24 24 769570 769860 4-82 4-8i 23o43o 23oi4o 32 3i 3o 705469 3 57 935320 1 24 770148 4-8i 22q852 3o 3i 9-705683 3 57 9-935246 I 24 9-770437 4-8i 10.229563 ^? 32 705898 3 57 935.71 I 24 770726 4-8i 229274 228985 28 33 7061 12 3 57 935097 I 24 7710.5 4-8i 27 34 706326 3 56 935022 I 24 77i3o3 4-8i 228697 26 35 706539 3 56 934948 I 24 77.592 4-8i 228408 25 36 706753 3 56 934873 I 24 77.880 4-8o 228.20 24 37 706967 3 56 934798 I 25 772.68 4-8o 227832 23 38 707 1 So 3 55 934723 I 25 772457 4-8o 227543 22 39 707393 3 55 934649 I 25 772745 4-80 227255 21 40 707606 3 55 934574 I 25 773o33 4-8o 226967 20 41 9.707819 3 55 9.934499 I 25 9-77332. 4-8o 10.226679 ;? 42 708032 3 54 934424 I 25 773608 4-79 226392 43 708245 3 54 934349 I 25 773896 774184 4-79 226104 \i 44 708458 3 54 934274 I 25 4-79 2258.6 45 708670 3 54 934.99 1 934123 I 25 774471 4-79 225529 i5 46 708882 3 53 25 774759 4-79 22524. 'i 47 709094 3 53 934048 I a5 775046 4-79 224954 i3 48 709306 3 53 933073 I 25 775333 4-79 224667 12 49 709518 3 53 933898 I 26 77562. 4-78 224379 II 5o 709730 3 53 933822 I 26 775908 4-78 224092 10 5i 9-709941 3 52 9-933747 I 26 9-776195 4-78 io.2238o5 I 52 710153 3 52 933671 I 26 776482 4-78 2235.8 53 7io364 3 52 933596 1 26 776769 777053 4-78 22323. 7 54 710575 3 52 933520 I 26 4-78 222945 6 55 710786 3 5i 933445 I 26 777342 4-78 222658 5 56 710997 3 5i 933369 I 26 777628 4-77 222372 4 11 711208 3 5i 933293 I 26 777915 4-77 222085 3 711419 3 5i 933217 1 26 778201 4-77 22.799 2 59 711629 3 5o 933141 I 26 778487 4-77 22.5.2 I 60 711839 3-50 933066 I 26 778774 4-77 22.226 Cosine D. Sine T ). Cotaner. D. Tang. |M. (59 DEGREES.) SINES AND TANGENTS. (31 DEGREES.) 49 M. Sine D. 1 Cosine D. Tang. D. Cotang. 9.7U839 3-5o 9 -933066 1-26 9-778774 4-77 10-221226 60 I 712030 3-5o 932990 1-27 779060 4-77 22og4o It 2 712260 3.5o 932^38 1-27 779346 4-76 220654 3 712469 3-49 1-27 779632 4-76 220368 j 57 1 4 712679 3-49 932762 1.27 7799'8 4-76 220082 56 5 712889 3-49 932685 1-27 780203 4-76 219797 55 6 I 71-3098 7i33o8 3-49 3-49 lilts 1-27 1-27 780489 780775 4-76 4-76 219511 219225 218940 54 53 713517 3-48 932457 1-27 781060 4-76 52 9 713726 3-48 932380 1-27 781346 4-75 218654 5i 10 713935 3-48 932304 1-27 781631 4-75 218369 5o II 9-714144 3-48 9-932228 1-27 9-781916 4-75 10-218084 49 12 714352 3-47 93-3 i5i 1-27 782201 4-75 217799 48 i3 714561 3-47 932075 1-28 782486 4-75 2,75.4 47 14 714769 3-47 931998 1-28 782771 4-75 217229 46 i5 71497a 3-47 931021 931843 1-28 783o56 4-75 216944 45 i6 7i5i86 3-47 1-28 783341 4-75 216659 44 I? 715394 3-46 931768 1-28 783626 4-74 216374 43 i8 7i56o2 3-46 931691 1-28 783910 4-74 216090 42 19 715809 3-46 931614 1-28 784195 4-74 2i58o5 41 20 716017 3-46 93 1 537 1.28 784479 4-74 215521 40 21 9-716224 3-45 9.931460 1-28 9-784764 4-74 io-2i5236 11 22 716432 3.45 93 1 383 1-28 785048 4-74 214952 23 716639 3.45 93i3o6 1-28 785332 4-73 214668 u 24 716846 3-45 93 1 229 1-29 7856 I 6 4-73 214384 25 717053 3.45 93ii52 1-29 785900 4-73 214100 35 26 717259 3-44 931075 1.29 786184 4-73 2i38i6 34 27 717466 3-44 930998 1-29 786468 4-73 213532 33 28 717673 3-44 930921 930843 1-29 786752 4-73 213248 32 2g 717879 3-44 1-29 787036 4-73 212964 3i 3o 718085 3-43 930766 1-29 787319 4-72 212681 3o 3i 9-718291 3.43 9-930688 1-29 9.787603 4-72 10-212397 29 28 32 718497 3-43 930611 1-29 787886 4-72 212114 33 718703 3-43 93o533 1-29 788170 4-72 2ii83o 27 34 718909 3.43 93o456 1-29 788453 4-72 211547 26 35 719114 3-42 930378 1-29 788736 4-72 211264 25 36 719320 3.42 93o3oo 1-30 789019 4-72 210981 24 37 71952D 3-42 930223 I -30 789302 4-71 210698 23 38 719730 3-42 930145 i-3o 789585 4-71 2io4i5 22 39 719935 3-41 930067 1-30 789868 4-71 2IOl32 21 40 720140 3-41 929989 i-3o 790i5i 4-71 209849 20 4i 9-720345 3-41 9-929911 929833 1-30 9-790433 4-71 10-209567 \l 42 720549 3-41 i-3o 790716 4-71 209284 43 720754 3-40 929755 1. 30 790999 4-71 209001 17 44 720958 3-40 929677 i-3o 791281 4-71 208719 16 45 721162 3-40 929599 1-30 791563 4-70 208437 i5 46 721366 3-40 929321 i-3o 791846 4-70 208154 14 47 721570 3-40 929442 i-3o 792128 4-70 207872 i3 48 721774 3.39 929364 i-3i 792410 4-70 207590 12 f^ 721978 3-39 929286 i-3i 792692 4-70 207308 II 5o 722181 3-39 929207 1-31 792974 4-70 207026 10 5i 9-722385 3-39 9-929129 i-3i 9-793256 4-70 10-206744 9 52 722588 3.39 929050 i-3i 793538 4-69 206462 8 53 722791 3-38 IZI i-3i 793819 4-69 206I8I 7 54 722994 3-38 1-31 794101 4-69 205899 6 55 723197 3-38 928815 i.3i 794383 4-69 2o56i7 5 56 723400 3-38 928736 i-3i 794664 4-69 205336 4 ^o 723603 3.37 928657 i-3i 794945 4-69 2o5o55 3 58 7238o5 3-37 928578 i-3i ]& 4-68 204773 2 59 724007 3.37 928499 i-3i 204492 I 6o 724210 3-37 928420 i-3i 795789 4-68 2042 1 1 1 Cosine D. Sine D. Cotang. D. 1 Tang. (58 DEGREES.) 50 (32 DEGREES.) A TABLE OF LOGARITHMIC M. Sine D. Cosine D. Tang. D. Cotang. 9-724210 3.37 9-928420 1-32 9-795789 4-68 10-204211 60 I 724412 3.37 928342 1-32 tTr 4-68 203930 ii 2 724614 3-36 928263 1-32 4-68 203649 3 724816 3-36 928183 1-32 796632 4-68 203368 u 4 725017 3-36 928104 1-32 7969:3 4-68 203087 5 725219 3-36 928025 1-32 797194 4-68 202806 55 6 725420 3-35 927946 1-32 797473 4-68 202525 54 7 725622 3-35 927867 1-32 797755 4-68 202245 53 8 725823 3-35 927787 927708 1-32 798036 4-67 201964 52 9 726024 3-35 1-32 7983:6 4-67 20:684 5i 10 726225 3-35 927629 1-32 798596 4-67 20:404 5o II 9-726426 3.34 9-927549 1-32 9-798877 4-67 IO-20II23 % 12 726626 3-34 927470 :-33 799:57 4-67 200843 i3 726827 3-34 927390 :-33 799437 4-67 200563 47 46 U 727027 3.34 927310 1-33 799717 ttl 200283 i5 727228 3.34 927231 1-33 799997 2oooo3 45 i6 727428 3-33 927.51 1-33 800277 4-66 199723 44 \l 727628 3-33 927071 1-33 800557 4-66 199443 43 727828 3-33 926991 1-33 8oo836 4-66 I98884 42 19 728027 3-33 9269.1 1-33 8o:::6 4-66 41 20 728227 3-33 926831 1-33 80:396 4-66 198604 40 21 9-728427 3-32 9-926751 1-33 9-801675 80:955 4-66 10-198325 39 38 22 728626 3-32 926671 1-33 4-66 198045 23 728825 3-32 926591 1-33 802234 4-65 197766 37 24 729024 3-32 9265ii 1-34 8o25i3 4-65 197487 36 25 729223 3-3i 926431 1-34 802792 4-65 197208 35 26 729422 3-3i 92635: :-34 803072 4-65 196928 34 27 729621 3-3i 926270 :-34 8o335i 4-65 196649 33 28 729820 3-3i 926:90 :-34 8o363o 4-65 196370 32 29 730018 3-3o 926::o 1-34 803908 4-65 196092 3i 3o 730216 3-3o 926029 1-34 804:87 4-65 1958.3 3o 3i 9-7304.5 3-3o '■??§§ 'Ji 9-804466 4-64 10-195534 11 32 7306.3 3-3o 804745 4-64 195255 33 730811 3-3o 925788 1-34 8o5o23 4-64 194977 27 34 73:009 3-29 925707 1-34 8o53o2 4-64 194698 26 35 73.206 3-29 925626 1.34 8o558o 4-64 194420 25 36 73.404 3-29 925545 1-35 8o5859 4-64 194.41 24 37 73.602 3-29 925465 :-35 806:37 4-64 193863 23 38 73.799 3-29 925384 1-35 8064: 5 4-63 193535 22 39 73.996 3-28 9253o3 1-35 806693 4-63 193307 21 40 732193 3-28 925222 :-35 806971 4-63 193029 20 41 '■&'^ 3-28 9-925:41 :-35 9-807249 4-63 10-19275: '9 42 3-28 925o6o :.35 807527 4-63 :92473 :8 43 732784 3-28 924979 924897 1-35 807805 4-63 :92:95 17 44 732980 3-27 1-35 808083 4-63 191917 16 45 733.77 3-27 9248:6 1-35 8o836: 4-63 :9:639 i5 46 733373 3-27 924735 1-36 8o8638 4-62 :9:362 14 47 733569 3-27 924654 :-36 8089:6 4-62 :9:o84 :3 48 733760 3-27 924572 :-36 809:93 4-62 190807 :2 49 733961 3-26 924491 1-36 809471 4-62 190529 II 5o 734.57 3-26 924409 1-36 809748 4-62 190252 10 5i 9-734353 3.26 9-924328 1-36 9-8:0025 4-62 :o- 189975 I 52 734549 3-26 924246 1-36 8:o3o2 4-62 : 89698 53 734744 3-25 924:64 1-36 8io58o 4-62 189420 7 54 ?MS 3-25 924083 ■ :-36 8:0857 4-62 189:43 6 55 3-25 92400: 1-36 8::i34 4-6: 188866 5 56 735330 3-25 9239:9 1-36 8::4io 4-6: 188590 4 57 735525 3-25 923837 1-36 8::687 4-61 i883:3 3 58 7357.9 3-24 923755 1-37 8::964 4-6i i88o36 2 59 7359.4 3.24 923673 1.37 8:2241 4-61 187759 187483 I 60 736109 3.24 923591 1-37 8:25:7 4-61 Cosine D. Sine D. Cotanar. D. Tang. IT (5Y DEGREES.) SINES AKD TANGENTS. (33 DEGREES.) 51 M. Sine D. Cosine D. Tang. D. Cotang. 9.736109 3.24 9.923591 1.37 9-812517 4-bi 10-187482 60 I 7363o3 3 24 923509 1.37 812794 4 61 187206 59 186930 ! 58 2 736498 3 24 923427 1.37 813070 4 61 3 ?S£ 3 23 923345 1.37 813347 8i3623 4 60 186653 a 4 3 23 923263 1.37 4 60 186377 5 737080 3 23 923181 1.37 813899 814175 4 60 186101 55 6 737274 3 23 923098 1.37 4 60 185825 54 7 737467 3 23 923016 1.37 8,4452 4 60 185548 53 8 737661 3 22 922^51 1.37 &14728 4 60 185272 52 9 ?as 3 22 \:U 8i5oo4 4 60 184996 5i 10 3 22 922768 815279 4 60 184721 5o II 9.738241 3 22 9.922686 1.38 9.815555 4 59 10-184445 g 12 738434 3 22 922603 1.38 8i583i 4 59 184169 183893 i3 738627 8 21 922520 1.38 816107 4 59 47 U 738820 3 21 922438 1.38 8i6382 4 59 i836i8 46 i5 739013 3 21 922355 1.38 8 16658 4 59 183342 45 i6 739206 3 21 922272 1.38 816933 4 59 183067 44 n 739398 3 21 922189 1-38 817209 4 59 182791 43 i8 ]^Ts 3 20 922106 1-38 817484 4 59 i825i6 42 19 3 20 922023 1-38 l\illl 4 it 182241 41 20 739975 3 20 921940 1.38 4 181965 40 21 9.740167 3 20 9.921857 1.39 9-8i83io 4 58 10-181690 ll 22 740359 3 20 921774 1.39 8i8585 4 58 i8i4i5 23 74o55o 3 19 921691 1.39 818860 4 53 181140 37 24 740742 3 19 921607 1.39 819135 4 58 180865 36 25 740934 3 19 921524 1.39 819410 4 58 180590 35 26 741 1 25 3 19 921441 1.39 819684 4 58 i8o3i6 34 27 74i3i6 3 ;? 921357 1.39 819959 4 58 180041 33 28 741 5o8 3 921274 1.39 820234 4 58 179766 32 29 741699 3 18 921190 1.39 82o5o8 4 57 179492 3i 3o 741889 3 18 921107 1.39 820783 4 57 179217 3o 3i 9.742080 3 18 9.921023 1.39 9.821057 4 57 10-178943 3 32 742271 3 18 'au 1.40 821332 4 57 178668 33 742462 3 17 1-40 821606 4 57 178394 S 34 742652 3 17 920772 1.40 821880 4 57 178120 35 742842 3 17 920688 1.40 822154 4 57 177846 25 36 743o33 3 17 920604 1.40 822429 4 57 177571 24 37 743223 3 17 920520 1.40 822703 4 57 177297 23 38 743413 3 16 920436 1-40 822977 4 56 177023 22 39 743602 3 16 920352 1.40 823250 4 56 176750 21 40 743792 3 16 920268 1.40 823524 4 56 176476 20 41 9.743982 3 16 9.920x84 1-40 9.823798 4 56 10-176202 ;? 42 7441 7 I 3 16 920099 920015 1.40 824072 4 56 175928 43 744361 3 i5 1.40 824345 4 56 175655 u 44 744550 3 i5 919846 1. 41 '& 4 56 175381 45 744739 744928 3 i5 1. 41 4 56 175107 i5 46 3 i5 919762 1. 41 825166 4 56 174834 14 47 745117 3 i5 1. 41 825439 825713 4 55 174561 i3 48 745306 3 14 919593 1. 41 4 55 174287 12 49 745494 3 14 919508 1.41 825986 4 55 174014 11 5o 745683 3 14 919424 1. 41 826259 4 55 173741 10 5i 9-745871 3 14 9.919339 1. 41 9-826532 4 55 10.173468 I 52 746059 3 14 919254 1. 41 826805 4 55 173195 53 746248 3 i3 919169 • 919085 1. 41 827078 4 55 172922 I 54 746436 4 i3 1. 41 827351 4 55 172649 55 746624 3 i3 1. 41 827624 4 55 172376 5 56 746812 3 i3 Vhll 1-42 827897 4 54 172103 4 57 746999 747187 3 i3 1.42 828170 4 54 '7'^^S 3 58 3 12 918745 1.42 828442 4 54 I7i558 2 59 747374 3 .12 918659 1.42 828715 4 54 171285 I 60 747562 3.12 918574 1.42 828987 4.54 171013 Coaine D. Sine D. Cotang. D. Tang. mT 18 (56 DEGREES.) 52 (34 DEGEEES.) A TABLE OF LOGARITHMIC M. Sine D. Cosine D. Tang. D. Cotang. 9-747562 3-12 9-918574 918489 1-42 9 -828987 4-54 10-171013 60 I 747749 3-12 1-42 829260 4-54 170740 u 2 748123 3-12 918404 1-42 829532 4-54 170468 3 3.U 9i83i8 1-42 829805 4-54 ,70195 57 4 748310 3-II 918233 1-42 830077 4-54 169923 56 5 748497 3-II 918147 1-42 83o349 4-53 169651 55 6 748683 3-u 918062 1-42 83o62i 4-53 169379 54 7 748870 3-11 917976 917891 1-43 830893 4-53 ,69107 53 8 749056 3.10 1-43 83ii65 4-53 168835 52 9 749243 3-10 917805 1-43 831437 4-53 168563 i 5i 10 749429 3-10 917719 1-43 831709 4-53 16829, 1 5o II 9-749615 3.10 9-917634 1-43 9-831981 4-53 10-1680,9 4o 12 749801 3-10 917548 1.43 832253 4-53 167747 167475 48 i3 749987 3-09 917462 1.43 832525 4-53 2 14 750172 3-09 917376 1.43 832796 4-53 167204 i5 75o358 3.09 917290 1-43 833o68 4-52 45 i6 75o543 3.09 917204 1.43 833339 4-52 166661 44 17 750729 3^:^^ 917118 1-44 833611 4-52 ,66389 166,18 43 i8 750914 917032 1-44 833882 4-52 42 19 751284 3-o8 916946 916859 1-44 834154 4-52 ,65846 41 20 3.08 1-44 834425 4-52 165575 40 21 9-751469 3-o8 9-916773 1-44 'IS 835238 4-52 io-i653o4 11 22 75i654 3.08 916687 1-44 4-52 ,65o33 23 751839 752023 3-o8 916600 1-44 4-52 ,64762 37 24 3.07 9i65i4 1-44 835509 4-52 164491 36 25 752208 3.07 916427 1-44 835780 4-5i 164220 35 26 752392 3.07 916341 1-44 836o5i 4-5i \iin 34 27 732576 752760 3.07 916254 1-44 836322 4-5i 33 28 3.07 916167 1-45 836593 4-5, 163407 32 29 752944 3.06 916081 1-45 836864 4-5i i63i36 3i 3o 753128 3-o6 915994 1-45 837134 4-5i 162866 3o 3i 9-753312 3-o6 9-915907 1-45 9-8374o5 4-5i 10-162595 li 32 753495 3-o6 9,5820 1-45 837675 4-5i ,62325 33 753679 3-06 915733 1-45 837946 4-5, 162054 ?6 34 753862 3-05 915646 1-45 838216 4-5i 16,784 35 734046 3-o5 9.5559 1-45 838487 4-5o ,6,5,3 25 36 754229 3-05 915472 1-45 838757 4-5o ,61243 24 37 754412 3.o5 915385 1-45 839027 4-5o 160973 23 38 754595 3-o5 915297 1-45 & 4-5o 160703 22 39 754778 3-04 915210 1-45 4-5o 160432 21 40 754960 3-04 9i5i23 1-46 839838 4-5o 160,62 20 41 9-755x43 3-04 9-9i5o35 1-46 9-840108 4-5o 10-159892 11 42 755326 3-04 914948 1-46 840378 4-5o 159622 43 755508 3-04 914860 1-46 840647 4-5o 159353 17 44 7556go 3-04 914773 1.46 840917 4-49 159083 i588i3 ,6 45 755872 3-03 914685 1.46 841187 4-49 ,5 46 756o54 3-o3 914598 1-46 841457 841726 4-49 158543 14 47 756236 3.o3 914510 1-46 4-49 158274 i3 48 756418 3 -03 914422 1-46 841996 4-49 i58oo4 12 49 756600 3-03 914334 1-46 842266 4.49 157734 II 5o 756782 3-02 914246 1-47 842535 4-49 157465 10 5i 9.756963 3-02 9-9141^8 1-47 9-842805 4-49 10-157,95 2 52 757144 3-02 914070 1-47 843074 4-49 156926 53 757326 3-02 913982 1-47 843343 4-49 ,56657 7 54 757507 3-02 913894 1-47 843612 til ,56388 6 55 757688 3-01 913806 1-47 843882 i56,,8 5 56 ]t& 3-01 913718 1-47 844i5i 4-48 ,55849 4 u 3-01 9i363o 1-47 844420 4-48 ,55580 3 758230 3.01 913541 1-47 844689 844958 4-48 j553,i 2 59 7584U 3-01 913453 1-47 4-48 ,55042 I 60 758591 3.01 913365 1-47 845227 4.48 154773 Cosine D. Sine D. Cotang. D. Tang. 1 M. | (55 DEGREES.) StN-ES AXD TANGENTS. (35 DEGREES.) 53 M. Sine D. Cosine 1 >_ Tang. D. Cotiing. j 1 9.753591 3-01 9.913365 1 47 845496 845764 4-48 10-154773 60 I 758772 3-00 913276 I 47 4-48 I 54504 is 2 758952 3.00 913187 I 48 4-48 154236 3 759132 3-00 913099 I 48 846033 4-48 I53698 57 4 759312 3-00 9i3oio I 48 846302 4-48 56 5 759492 3-00 912922 I 48 846570 4-47 1 53430 55 6 739672 2-99 912833 I 48 846839 4.47 i53i6i 54 7 759852 2-99 912744 I 48 847107 847376 4-47 152893 53 8 760031 2-99 9.2655 I 48 4-47 152624 52 9 7602 I I 2-99 912566 I 48 847644 4-47 152356 5i 10 760390 2-99 912477 I 48 847913 4-47 152087 5o II 9-760369 2-98 9-912388 I 48 9.848181 4-47 io-i3i8i9 it 12 760748 2-98 912299 I 49 848449 4-47 i5.55i i3 760927 2-98 912210 I 49 848717 848986 4-47 i5i283 47 14 761 106 2.98 912121 I 49 4-47 i5io.4 46 i5 761285 2-98 9i2o3i I 49 849254 4-47 1 50746 45 i6 761464 2.98 91 1942 I 49 849522 4-47 130478 44 n 761642 2.97 91.853 I 49 849790 4-46 i5o2io 43 i8 761821 2.97 911763 I 49 850038 4-46 1^9 42 19 761999 2-97 91 1674 I 49 85o325 4-46 41 20 762177 2.97 9ii584 I 49 800593 4-46 149407 40 21 9.762356 2-97 9.911495 I 49 9-850861 4-46 10-149139 39 22 762534 2.96 911405 I 49 851129 4.46 14887 1 38 23 ?62889 2.96 9ii3i5 I 5o 851396 4-46 148604 37 24 2.96 911226 I 5o 831664 4-46 148336 36 23 763067 2.96 9III36 I 5o 85i93i 4-46 148069 35 26 763245 2.96 91 1046 I 5o 832199 4-46 147801 34 27 763422 2.96 910936 I 910866 I 5o 852466 4-46 147534 33 28 763600 2.95 5o 852733 4-45 147267 32 29 763777 2.95 910776 I 5o 853001 4-45 146999 3i 3o 763934 2.95 910686 I 5o 853268 4-45 146732 3o 3i 9-764131 2.95 9.910596 I 5o 9.853535 4-45 10-146465 ll 32 764308 2-95 9io5o6 I 5o 853802 4-45 146198 33 764483 2-94 9io4i5 I 5o 854069 854336 4-45 145931 27 34 764662 2-94 910325 I 5i 4-45 143664 26 35 764838 2-94 910235 I 5i 854603 4-45 145397 i45i3o 25 36 765oi5 2-94 910144 I 5i 854870 4-45 24 ll 765191 2-94 910054 I 5i 855i37 4.45 144863 23 765367 2-94 909963 I 5 1 855404 4-43 144596 22 39 765544 2.93 909873 I 5i 855671 4-44 144329 21 4o 765720 2.93 909782 I 5i 855938 4-44 144062 20 4i 9.765896 2.93 9.909691 I 5i 9-856204 4-44 10-143796 \t 42 766072 2-93 909601 I 5i 856471 4-44 143529 143263 43 766247 2.93 909510 I 5i 856737 4-44 17 16 44 '^^Ai'l 2.93 909419 I 909328 I 5i 857004 4.44 142996 142730 45 766598 2.92 52 857270 4-44 i5 46 766774 2.92 909237 I 52 857537 4-44 142463 14 47 766949 2.92 909146 I 52 837803 4-44 142 197 i3 48 767124 2-92 909055 I 908964 I 52 838060 4.44 141931 I 41 664 12 ! 49 767300 2-92 52 858336 4.44 II i 5o 767475 2-91 908873 I 52 858602 4-43 141398 10 1 '' 9-767649 2.91 9.908781 I 52 9-858868 4-43 io.i4ii32 t ^-' 767824 2.91 908690 I 52 839134 4-43 140866 53 ]Ul^ 2.91 908599 I 52 859400 4-43 140600 7 ^4 2.91 908307 I 52 859666 4-43 i4o334 6 1 55 768348 2.90 908416 I 53 859932 4-43 140068 5 56 768522 2.90 908324 I 53 860198 4-43 139802 4 57 768697 2.90 908233 I 53 860464 4.43 139536 3 58 768871 2.90 908141 I 53 860730 4-43 139270 2 59 769045 2.90 » ; 53 860995 4.43 139005 I 60 769219 2.90 53 861261 4-43 i3§739 1 Cosine D. Sine I X Cotang. D. Tang. ^ (54 DEGREES.) 54 (36 DEGREES.) A TABLE OF LOGARITHMIC M. Sine D. Cosine 1 I ). Tang. D. Cotang. 9-769219 Ill 'Z'^&l ; .53 9-861261 4-43 10-138739 60 I 769393 • 53 861527 4-43 138473 u 2 769566 2.89 907774 I 53 861792 4-42 138208 3 769740 2.89 907682 I 53 862058 4-42 137942 u 4 769913 2-89 907590 I 53 862323 4-42 137677 5 770087 907498 1 53 862389 4-42 137411 55 6 770260 2-88 907406 I 53 862854 4-42 137146 136881 54 I 770433 2-88 907314 I 54 863 1 19 863385 4-42 53 770606 2-88 907222 I 54 4-42 i366i5 52 9 770779 2-88 907129 I 54 863650 4-42 136350 5i 10 770952 2-88 907037 I 54 863915 4-42 i36o85 5o II 9.771125 2-88 9-906945 I 906852 I 54 9-864180 4-42 10-135820 8 12 771298 2-87 54 864445 4-42 135555 i3 771470 2-87 906760 I 906667 I 54 864710 4-42 135290 47 14 771643 2.87 54 864975 4-41 135025 46 i5 771815 2.87 906575 I 54 865240 4-41 134760 45 i6 771987 2.87 906482 I 54 8655o5 4-41 134495 44 \l 772159 2.87 906389 I 55 865770 4-41 134230 43 772331 2-86 906296 I 55 866035 4-41 133965 42 19 772003 2-86 906204 1 I 55 866300 4-41 133700 41 20 772675 2-86 906111 I 55 866564 4-41 133436 40 21 9-772847 773018 2-86 9-906018 I 55 9-866829 4-41 10-133171 ^1 22 2-86 905025 I 905832 I 55 '£]^l 4-41 132906 23 773190 2-86 55 4-41 132642 37 24 773361 2-85 905739 I 905645 I 55 867623 4-41 132377 36 25 773533 2-85 55 867887 4-41 132II3 35 26 773704 2-85 905552 I 55 868x52 4-40 131848 34 27 773875 2-85 905459 I 55 868416 4-4o I3i584 33 28 774046 2-85 905366 I 56 868680 4-40 i3i32o 32 29 774217 2-85 905272 I 56 868945 4-40 i3io55 3x 3o 774388 2-84 905179 I 56 869209 4-40 130794 3o ■ 3i 9-774558 2-84 9-9o5o85 I 56 9-869473 4-40 io.i3o527 It 32 774729 2-84 904992 I 904898 I 56 869737 4.40 130263 33 774899 2-84 56 870001 4-40 \l^ 11 34 775070 2-84 904804 I 56 870265 4.40 35 775240 2-84 9047 1 1 I 56 870529 4-40 1 2947 1 25 36 775410 2-83 904617 I 56 870793 871057 4-40 129207 24 37 775580 2-83 904523 I 56 4.40 128943 23 38 775750 2-83 904429 I 904335 I 57 871321 4.40 128679 22 39 775920 2-83 57 871585 4.40 1 28415 21 40 776090 2-83 904241 I 57 871849 4.39 I28i5i 20 41 9-776259 2-83 9-904147 I 57 9-872112 4-39 10-127888 \i 42 776429 77659§ 2-82 904053 I 57 872376 4-39 127624 43 2-82 903959 ' I 903864 I 57 872640 4-39 127360 \i 44 776768 2-82 57 872903 4-39 127097 45 776937 777106 2.82 903770 I 57 873167 4-39 126833 i5 46 2-82 903676 1 57 873430 4-39 126570 14 8 777275 2-81 9o358i I 57 ©^ 4-39 i263o6 x3 777444 2-81 903487 I u 4-39 1 26043 X2 49 777613 2-81 903392 I 874220 4-39 125780 II 5o 777781 2-81 903298 I 58 874484 4-39 1255x6 10 5i 9-777950 2-81 9 -903203 I 58 9-874747 4-39 10-125253 i 52 778119 2-81 903 1 08 I 58 875010 4-39 1 24990 53 778287 2-8o 9o3oi4 I 58 875273 4-38 124727 I 54 778455 2.80 902919 1 902824 I 58 875536 4-38 124464 55 778624 2-8o 58 875800 4-38 124200 5 56 778792 2-80 902729 I 58 876063 4-38 X 23937 123674 4 u 778960 2-80 902634 I 58 876326 4-38 3 779128 2-80 902539 I 59 876589 4-38 1234II 2 59 779295 2-79 902444 I 59 876851 4-38 123x49 I 60 779463 2-79 902349 I 09 877114 4-38 122886 Cosine D. Sine 1 E Tang. D. Cotang. M. (53 DEGREES.) SmES AND TANGENTS. (37 DEGREES.) 55 M. Sine D. Cosine I ). Taug. D. Cotaiig. i 9-779463 2-79 9-902349 I 902253 I V 9-877114 4-38 10-122886 60 I 779631 2 79 59 877377 4 38 122623 u 2 779798 2 79 902158 I ^9 877640 4 38 122360 3 ?32?g 2 79 902063 I ^9 l]^ 4 38 122007 57 4 2 79 901967 I 901872 I 59 4 38 121835 56 5 780300 2 78 59 878428 4 38 121572 i 55 . 6 780467 2 78 901776 1 Q01681 I ^9 8789^3 4 38 i2i3o9 54 7 780634 2 78 ^9 4 37 121047 1 53 8 780801 2 78 901585 I ^9 879216 4 37 120784 ! 52 9 780968 2 78 901490 I 59 879478 4 37 120322 5i 10 781134 2 78 901394 I 60 879741 4 37 120239 5o u 9.781301 2 9-901298 I 60 9 -880003 4 37 10.119997 S 12 781468 2 901202 I 60 880265 4 37 119735 i3 781634 2 901 106 I 60 880528 4 37 119472 47 14 781800 2 901010 I 60 880790 8810D2 4 37 IIQ2I0 1 46 i5 781966 2 900914 I 900818 I 60 4 37 II 8948 45 i6 782132 2 ?2 60 88i3i4 4 37 1 1 8686 44 17 782298 2 900722 I 60 881576 4 37 118424 43 i8 782464 2 76 900626 I 60 881839 37 118161 42 19 782630 2 76 900529 I 900433 I 60 882101 4 ll 1 17899 41 20 782796 2 76 61 882363 4 1 1 7637 40 21 9.782961 2 76 9-900337 I 61 9.882625 4 36 10.117375 ll 22 783127 2 7^ 900240 I 61 882887 4 36 117113 23 783458 2 75 900144 I 6i 883148 4 36 116852 37 24 2 75 900047 I 6i 883410 4 36 1 16590 36 25 783623 2 75 is??: ; 61 883672 4 36 116328 35 26 783788 2 75 61 883934 4 36 116066 34 11 783953 2 75 899757 I 6i 884196 884457 4 36 ii58o4 33 7841 18 2 75 899660 I 61 4 36 115543 32 29 784282 2 74 899564 I 61 884719 4 36 115281 3i 3o 784447 2 74 899467 I 62 884980 4 36 Il5020 3o 3i 9.784612 2 74 9-899370 I 62 9-885242 4 36 10-114758 ll 32 784776 2 74 899273 I 62 8855o3 4 36 114497 33 784941 2 74 899176 I 62 885765 4 36 II4235 ll 34 785io5 2 74 62 8S6026 4 36 113974 35 785269 2 73 62 886288 4 36 113712 25 36 785433 2 73 898884 I 62 886549 4 35 ii345i 24 ll 785597 2 73 898787 I 62 886810 4 35 113190 23 785761 2 73 898689 I 62 887072 4 35 112928 1 1 2667 112406 22 39 785925 2 73 898592 I 62 887333 4 35 21 40 786089 2 73 898494 I 63 887594 4 35 20 41 9-786252 2 72 9-898397 I 63 9-887855 4 35 10-112145 :i 42 786416 2 72 898299 I 63 8881 16 4 35 111884 43 786579 2 72 898202 I 63 888377 4 35 111623 17 44 786742 2 72 898104 I 63 888639 4 35 iii36i 16 45 786906 2 72 898006 I 63 888900 4 35 111 100 i5 46 787069 2 72 897908 I 63 889160 4 35 110840 14 47 787232 2 71 897810 I 63 889421 4 35 110579 i3 48 1?^?? 2 71 897712 I 63 889682 4 35 iio3i8 12 49 2 71 897614 I 63 889943 4 35 110057 II 5o 787720 2 71 897516 I 63 890204 4 34 109796 1 10 1 5i 9-787883 2 71 9-897418 I 64 9-890465 4 34 10-109535 I 52 788045 2 71 897320 I 64 890725 4 34 109273 53 788208 2 71 897222 I 64 890986 4 34 109014 1 54 788370 2 70 897123 1 I 64 891247 4 34 108733 6 55 788532 2 70 897025 i I 64 Iglill 4 34 108493 5 56 ■7^8694 2 70 806926 1 I 64 4 34 108232 i 4 u 788836 2 70 896828 I 64 892028 4 34 107972 3 789018 2 70 896729 I 64 892289 4 34 107711 2 59 789180 2 70 896631 I 64 892549 4 34 107431 I 60 789342 2.69 896532 I 64 892810 4-34 107190 Cosine D. Sine 1 D. Cotang. D. Tanar. IT (52 DEGREES.) 56 (38 DEGEEES.) A TABLE OF LOGAEITHMIC M. Sine D. Cosine I ). Tang. D. Uotang. o 9.789342 2 69 9-896532 I 64 9-892810 4-34 10-107190 106930 60 1 789504 2 69 896433 I 65 893070 4-34 U 2 789665 2 69 896335 I 65 893331 4-34 106669 3 789827 2 69 896236 1 65 893591 893851 4.34 106409 u 4 789988 2 69 896137 1 65 4.34 106149 5 790149 2 tl 896038 I 65 8941 1 1 4-34 105889 55 6 79o3io 2 » ; 65 894371 4-34 105629 105368 54 7 790471 2 68 65 894632 4-33 53 8 790632 2 68 895741 I 65 894892 895152 4-33 io5io8 52 9 790793 2 68 895641 I 65 4-33 104848 5i 10 790954 2 68 895542 I 65 895412 4-33 104588 5o II 9-79iii5 2 68 9-895443 I 66 9-895672 4-33 10.104328 8 12 791275 2 67 895343 I 66 895932 4-33 104068 i3 791436 2 67 895244 I 66 896192 896452 4-33 io38o8 47 14 791596 791757 2 67 895145 I 66 4-33 103548 46 ID 2 67 895045 I 66 896712 4-33 103288 45 i6 791917 2 67 894945 1 894846 I 66 896971 4-33 io3o29 44 11 792077 2 67 66 897231 4-33 102769 43 792237 2 66 894746 I 66 897491 897751 4-33 102509 42 19 792397 2 66 894646 I 66 4-33 102249 41 20 792557 2 66 894546 I 66 898010 4-33 101990 40 21 9-792716 2 66 9-894446 I 67 9.898270 4-33 10.101730 38 22 792876 2 66 894346 I 67 898530 4-33 101470 23 793o35 2 66 894246 I 67 898789 4-33 101211 37 24 793195 793354 2 65 894146 I 67 '& 4-32 100951 36 25 2 65 894046 I 67 4-32 100602 100432 35 26 793514 2 65 893946 I 893846 I 67 899568 4-32 34 27 793673 2 65 67 899827 4.32 100173 33 28 793832 2 65 893745 I 67 900086 4-32 099914 32 29 793991 2 65 893645 I 67 900346 4-32 099654 3i 3o 7941 5o 2 64 893544 1 67 900605 4-32 099395 3o 3i 9 -794308 2 64 9-893444 I 68 9 - 900864 4-32 io.099i36 098876 3 32 794467 2 64 893343 I 68 901124 4-32 33 794626 2 64 893243 I 68 901383 4.32 098617 27 34 794784 2 64 893142 I 68 901642 4-32 098358 26 35 794942 2 64 893041 I 68 901901 4-32 098099 2'5 36 795101 2 64 892940 I 892839 I 68 902160 4.32 097840 ?4 u 795259 2 63 68 902419 4-32 097581 23 795417 2 63 Zi^ ; 68 902679 902938 4-32 097321 22 39 795575 2 63 68 4-32 097062 21 40 795733 2 63 892536 1 68 903197 4-31 096803 2'0 41 9-795891 2 63 9-892435 I 69 9-903455 4-31 10-096545 ;? 42 796049 2 63 892334 I 69 903714 4-3i 096286 43 796206 2 63 892233 I 69 903973 4-3i 095768 ]i 44 796364 2 62 892133 I 69 904232 4-3i 45 796531 2 62 892030 I 69 904491 904750 4-31 095509 i5 46 796679 2 63 891029 I 891827 I 69 4-3i 095250 14 « 796836 2 62 69 9o5oo8 4-3i 094992 i3 796993 797 1 5o 2 63 891726 I 69 905267 4-3i 094733 12 49 2 61 891624 I 69 905526 4-3i 094474 11 5o 797307 2 61 891523 I 70 905784 4-3i 094216 10 5i 9.797464 2 61 9-891421 I 70 9-906043 4-31 10.093957 2 52 797621 2 61 891319 1 70 9o63o2 4-3i 093698 53 797777 2 61 891217 1 70 9o656o 4-3i 093440 I 54 797934 798091 2 61 891115 I 70 9068 1 Q 4-3i 093181 55 2 61 891013 1 70 907077 4-3i 092923 5 56 798247 2 6i IX I 70 907336 4-31 092664 4 57 798403 2 60 70 907594 907852 4.31 092406 3 58 798560 2 60 890707 1 8qo6o5 I 70 4-3i 092148 2 59 798716 2 60 70 908111 4-3o 091889 i 60 798872 2.60 89o5o3 I 70 908369 4-3o 091631 Cosine D. Sine I ). Cotang. D. Tang. 1 M. 1 (51 DEGREES.) SINES AND TANGENTS. (39 DEGREJES.) 57 M. j Sine • D. Cosine D. Tang. D. Cotang. 9.79S872 2-6o 9-890503 1-70 9-908369 908628 4-3o 10-091631 60 I 799028 2-6o 890400 I-7I 4-3o 091372 ll 2 799 '84 2-6o 890298 I-7I 908886 4-3o 091114 3 799339 2-59 890195 1-71 909144 4-3o 090856 u 4 799493 2.59 ii^ 1-71 909402 4-3o 090398 5 7996D1 2.59 1-71 909660 4-3o 090340 55 6 799806 2-59 1-71 909918 4-3o 090082 54 7 799962 8001 17 2-59 889785 I-7I 910177 4-3o 089823 53 8 2.59 889682 I-7I 910435 4-3o 089365 52 9 800272 2-58 889579 1-71 910693 910951 4-3o 089307 5i 10 800427 2-58 889477 1-71 4-3o 089049 5o M 9-800582 2-58 9-889374 1-72 9.9II209 4-3o 10-088791 § 12 800737 2-58 889271 1-72 911467 4-3o 088533 i3 800892 2-58 889168 1-72 911724 4-3o 088276 47 14 801047 2-58 889064 888961 1-72 911982 4-3o 088018 46 i5 801201 2-58 1-72 912240 4-3o 087760 45 i6 8oi356 2.57 888858 1-72 912498 912756 4-3o 087502 44 ;j 8oi5ii 2-57 888755 1-72 4-3o 087244 43 80 1 665 2.57 888651 1-72 9i3oi4 4-29 086986 42 19 801819 2.5J 888548 1-72 913271 4-29 086729 41 20 801973 2-57 888444 1-73 913529 4-29 086471 40 21 9-802128 2.57 9-888341 1.73 9-913787 4-29 io-o862i3 u 22 802282 2-56 888237 1.73 914044 4-29 085936 23 802436 2-56 888134 1.73 914302 4-29 083698 37 24 802589 2-56 888o3o I ••73 914360 4-29 085440 36 25 802743 2-56 887926 887822 1.73 914817 4-29 o85i83 35 26 802897 2-56 1.73 915075 4-29 084925 34 27 8o3o5o 2-56 887718 1.73 915332 4-29 084668 33 28 803204 2-56 887614 1-73 915590 4-29 084410 32 ^ 803357 2-55 887510 1-73 915847 4-29 ■ 084153 3i So 8o35ii 2-55 887406 1-74 916104 4-29 083896 3o 3i 9 -803664 2-55 9 -887302 1-74 9-916362 4-29 10-083638 ll 32 803817 2-55 887198 1-74 916619 4-29 o8338i 33 803970 2-55 887093 1-74 916877 4-29 o83i23 27 ¥ 804123 2-55 88690Q 1-74 917134 4-29 082866 26 35 804276 2-54 886885 1-74 917391 4-29 082609 25 36 804428 2-54 886780 1-74 917648 4-29 082352 24 i^ 804581 2-54 886676 1-74 917905 til 082095 081837 23 804734 2-54 886571 1-74 918163 22 39 804B86 2-54 886466 1-74 918420 4-28 o8i58o 21 4o 8o5o39 2-54 8S6362 1-75 918677 4-28 o8i323 20 4j o-8o5f9i 2-54 g. 886257 1.75 9-918934 4-28 10-081066 :i 42 805343 2-53 886i52 1-75 919191 4-28 080809 43 805493 2-53 886047 1.75 919448 4-28 o8o552 \i 44 8o5647 2-53 885942 1.75 919705 4-28 080295 45 803799 2-53 885837 1-75 919962 4-28 o8oo38 i5 46 805931 2-53 885732 1.75 920219 4-28 079781 14 47 806 I o3 2-53 885627 1-75 920476 4-28 079524 i3 48 806254 2-53 885522 1-75 920733 4-28 079267 12 49 806406 2-52 885416 1-75 920Q90 4-28 079010 11 5o 806557 2-52 8853 1 1 1.76 921247 4-28 078753 10 5i 9-806709 2-52 9-885205 1.76 9-92i5o3 4-28 10-078497 ? 32 806860 2-52 885100 1.76 921760 4-28 078240 53 80701 1 2-52 884^^9 1.76 922017 4-28 077983 7 54 807163 2-52 1.76 922274 4-28 077726 6 55 807314 2-52 884783 1-76 922530 4-28 077470 5 56 807465 2-5l 884677 1.76 922787 4-28 077213 4 il 807615 2-5l 884572 1-76 923044 4-28 076956 3 58 807766 2-5r 884466 1.76 923300 4-28 076700 2 59 807917 2-5l 884360 1-76 923557 4-27 076443 I 60 80S067 2-51 884254 1-77 9238i3 4-27 076187 Cosine D. Sine D. Cotang. D. Tang. "mT (50 DEGREES.) 58 (40 DEGREES.) A TABLE OF LOGARITHMIC M. Sine D. Cosine D. Tang. D. Cotang. 9.808067 ^.5i 9.884254 1-77 9-9238.3 4-27 10.076187 60 I 808218 2.5l 884148 1-77 924070 4-27 075980 58 2 8o8368 2.5l 884042 1.77 924327 4-27 075673 3 8o85i9 2.5o 883936 ' 883829 1.77 924583 4-27 075417 57 4 808669 2.5o 1.77 924840 4-27 075160 56 5 808819 2.5o 883723 883617 1.77 925096 4-27 074904 55 6 808969 2.5o 1.77 925352 4-27 074648 54 I 8091 19 2.5o 883510 1-77 925609 925865 4-27 074891 53 809269 2.5o 883404 1-77 4-27 074135 52 9 809419 2.49 883297 1-78 926.22 4-27 078878 5i 10 809569 2-49 883191 1.78 926378 4-27 078622 5o 11 9.809718 2-49 9-883084 1.78 9-926634 4-27 10.078866 a 12 809868 2-49 882977 1.78 926890 4-27 078110 i3 810017 2-49 882871 1.78 927147 4-27 072853 47 14 810167 2-49 882764 1.78 927403 4-27 072597 46 i5 8io3i6 2.48 882657 1.78 927659 9279.5 928171 4-27 072841 45 i6 810465 2.48 882550 1-78 4-27 072085 44 \l 810614 2-48 882443 1.78 4-27 071829 43 810763 2.48' 882336 1-79 928427 4-27 071573 42 19 810912 2.48 882229 1-79 928683 4-27 07.3.7 41 20 811061 2-48 882l2i 1-79 928940 4-27 071060 40 21 9.811210 2.48 9.8820.4 1.79 9.929196 929452 4-27 10.070804 32 22 8ii358 2-47 88.907 1.79 4-27 070548 38 23 8ii5o7 2-47 881799 1-79 929708 4-27 070292 070086 37 24 8ii655 2-47 881692 88.584 1.79 929964 4-26 36 25 81 1804 2-47 1-79 980220 4-26 069780 069525 35 26 811952 2-47 88.477 1-79 930475 4-26 34 27 812100 2-47 88.369 1.79 930731 4-26 069269 33 28 812248 2-47 88.26. 1.80 930987 931243 4-26 32 29 812396 2.46 88.153 1.80 4-26 3i 3o 812544 2.46 881046 1.80 931499 4-26 o685oi 3o 3i 9-812692 2-46 9 -880^8 1.80 9-931755 4-26 10.068245 29 32 812840 2-46 1.80 932010 4-26 067990 28 33 812988 2.46 880722 1.80 932266 4-26 067734 27 34 8i3i35 2-46 880613 1-80 932522 4-26 067478 26 35 8i3283 2-46 88o5o5 1.80 932778 4-26 067222 25 36 8i343o 2.45 880397 1.80 933o33 4-26 066967 24 37 813578 2.45 880289 1-81 933289 4.26 0667 1 1 23 38 813725 2.45 880180 1.81 933545 4-26 066455 22 39 813872 2.45 880072 1.81 933800 4-26 066200 21 40 814019 2-45 879963 1. 81 934o56 4-26 065944 20 41 9-814166 2-45 9.879855 1. 81 9-934311 4-26 .0.065689 ;i 42 8i43i3 2-45 879746 1. 81 934567 4-26 065433 43 814460 2-44 879637 1.8. 934823 4-26 o65i77 17 44 814607 2-44 879529 1. 81 935078 4-26 064922 064667 16 45 8.4753 2-44 879420 1. 81 935333 4-26 i5 46 814900 2-44 87931. 1.8. 935589 4-26 06441 1 14 s 8 1 5046 2-44 879202 1.82 935844 4-26 0641 56 i3 815193 2.44 8789^4 878§75 1.82 936.00 4-26 068900 12 49 815339 81 5485 2-44 1.82 936355 4-26 063645 J I 5o 2-43 1.82 936610 4-26 068890 10 5i o-8i563i 2-43 9-878766 1.82 9-936866 4-25 10.068184 I 52 815778 2-43 878656 1.82 937121 4-23 062879 53 815924 2-43 878547 1.82 937376 4-25 062624 1 54 816069 816216 2-43 878438 1.82 937682 4-25 062868 6 55 2.43 878328 1.82 987887 4-25 062118 5 56 8i636i 2-43 878219 1.83 988142 4-25 06 1 858 4 57 8i65o7 2-42 878109 1.83 988898 938653 4-25 061602 3 58 1 8.6652 2-42 877999 877800 877780 1.83 4-25 061847 2 59 I 816798 2.42 1.83 988908 4-25 061092 060887 I 60 [ 8.6943 2-42 1.83 989168 4-25 ° 1 Cosine 1 D. 1 Sine 1 D. Cotang. D. Tang, i M. | (49 DEGRE ES.) SINES AND TANGENTS. (41 DEGKEES.) 59 M. Sine D. Cosine D. Tiiug. D. Cotiing. 9.816943 2-42 9-877780 1-83 9-939163 4-25 10-060837 60 I 817088 2-42 1-83 939418 4-20 o6o582 u 2 817233 2.42 1-83 939673 4-25 060327 3 817379 2-42 877450 1-83 939928 4-25 060072 57 4 817524 2.41 877340 1-83 940183 4-25 059817 56 5 817668 2-41 877230 1-84 940438 4-25 059562 55 6 817813 2-41 877120 1-84 940694 4-25 059306 54 I 817958 2-41 877010 1-84 940949 4-25 059051 53 8i8io3 2-41 8767^^ 1-84 941204 4-25 058796 52 9 818247 2-41 1-84 941458 4-25 058542 5i 10 818392 2-41 1.84 941714 4-25 058286 5o II 9-818536 2.40 9-876568 1-84 9-941968 4-25 io.o58o32 a 12 8i868r 2-40 876457 1-84 942223 4 25 057777 057522 i3 818825 2-40 876347 1-84 942478 4-25 47 i4 l^ 2-40 876236 1-85 942733 4-25 057267 46 i5 2-40 876125 1-85 942988 4-25 057012 45 i6 819257 2.40 876014 1-85 943243 4-25 056757 44 'I 819401 2.40 875904 1-85 943498 4-25 o565o2 43 i8 819045 2.39 875793 1-85 943702 4-25 056248 42 19 819689 2-39 875682 1-85 944007 4-25 055738 41 20 819832 2-39 875571 1-85 944262 4-25 40 21 9-819976 2.39 9-875459 875348 1.85 9-944517 4-25 10-055483 ll 22 820120 2-39 1-85 944771 4-24 055229 23 820263 J -39 875237 1-85 945026 4-24 054974 37 24 820406 lit 875126 1-86 945281 4-24 05446^ 36 25 82o55o 875014 1-86 945535 4-24 35 26 820693 2-38 874903 1-86 945790 4-24 054210 34 U 820836 2-38 l]X 1.86 946045 4-24 053955 33 820979 2-38 1.86 946299 946004 4-24 053701 32 29 821122 2-38 874568 1.86 4-24 053446 3i 3o 821265 2-38 874456 1.86 946808 4-24 053192 3o 3i 9-821407 2.38 9-874344 1.86 9.947063 4-24 10-052937 052682 il 32 82i55o 2-38 874232 1-87 947318 4-24 33 821693 2.37 874121 1-87 947572 4-24 052428 11 34 821835 2.37 874009 873896 1-87 947826 4-24 052174 35 821977 2.37 1-87 948081 4-24 051919 25 36 822120 2-37 873784 1-87 948336 4-24 o5i664 24 U 822262 2.37 '& 1-87 948090 4-24 o5i4io 23 822404 2-37 1-87 948844 4-24 o5ii06 22 39 82 2546 2.37 873448 1-87 949353 4-24 050901 21 40 822688 2-36 873335 1.87 4-24 050647 20 4i 9.822830 2-36 9-873223 ;:S 9-949607 4-24 10 -050393 o5oi38 \l 42 822972 2-36 873110 949862 4-24 43 823114 2-36 &l 1-88 950116 4-24 049884 17 44 823255 2-36 1 .88 950370 4-24 049630 16 45 823397 2-36 872772 1-88 950625 4-24 049375 i5 46 823539 2.36 872659 1-88 ?S?]? 4-24 049121 048867 14 8 823680 2.35 872547 1.88 4-24 i3 823821 2-35 872434 1.88 95i388 4-24 048612 12 P 823963 2.35 872321 1-88 901642 4-24 048358 11 5o 824104 2-35 872208 1.88 951896 4-24 048104 10 5i 9.824245 2-35 9-872095 1.89 9-952i5o 4-24 10-047850 9 52 824386 2-35 871081 871868 1.89 952405 4-24 047595 8 53 824027 824668 2-35 1.89 imt 4-24 047341 7 54 2-34 871755 1-89 4-24 047087 046833 6 55 824808 2-34 87 I 641 1.89 953167 4-23 5 «^ , 824949 2-34 871528 1-89 953421 4-23 046579 4 u 825090 2-34 871414 1-89 953675 4-23 046325 3 825230 2-34 871301 1-89 &I 4-23 046071 2 ^ 825371 2-34 871187 1.89 4-23 045817 I 6o 8255II 2-34 871073 1-90 954437 4-23 045563 1 Cosine D. Sine D. Cotang. D. Tang. "mT (48 DEGRE ES.) 60 (42 DEGREES.) A TABLE OF LOGARITHMIC M. Sine D. Cosine ] X Tang. D. Cotaug. 9-8255II 2-34 9-871073 I .90 9-954437 4.23 10-045563 60 I 82565: 2 33 870960 I 90 954691 4-23 045309 o45o55 ll 2 825791 825931 2 33 870846 I 90 954945 4-23 3 2 33 870732 I 90 955200 4-23 044800 u 4 826071 2 33 870618 I 90 955454 4-23 044546 5 826211 2 33 870504 I 90 955707 4-23 044298 55 6 826351 2 33 870390 I 90 955961 4-28 044039 043785 54 7 826491 2 33 870276 I 90 956215 4-28 53 8 826681 2 33 870161 I 90 956469 956723 4-28 o4853i 52 9 826770 2 32 870047 1 91 4-28 043277 5i 10 826910 2 32 869933 I 91 956977 4-23 048028 5o II 9-827049 2 32 9-869818 I 91 9-957231 4-23 10.042769 o425i5 49 12 827189 2 32 869704 I 91 957485 4-23 48 i3 827328 2 32 869589 1 91 957739 4-23 042261 47 U 827467 2 32 869474 I 91 957993 958246 4-23 042007 46 i5 827606 2 32 869360 I 91 4-23 041754 45 i6 827745 827884 2 32 869245 I 91 958500 4-28 o4i5oo 44 17 2 3i 869130 I 91 958754 4-28 041246 43 i8 828023 2 3i 869015 I 92 959008 4-28 040992 42 19 828162 2 3i 868000 I 92 959262 4-23 040788 41 20 828301 2 3i 868785 I 92 959516 4-23 040484 40 21 9-828439 828578 2 3i 9-868670 I 92 9-959769 960023 4-28 10-040281 39 38 22 2 3i 868555 I 92 4-23 089977 23 828716 2 3i 868440 I 92 960277 4-23 089728 37 24 828855 2 3o 868324 I 92 960531 4-28 089469 089216 088962 36 25 828993 2 3o 868209 I 868093 I 92 960784 4-23 35 26 829131 2 3o 92 961088 4-23 34 27 829269 2 3o ^j,t ; 93 961 291 4-28 088709 088455 33 28 829407 2 3o 93 961545 4-23 32 29 829545 2 3o 867747 I 93 961799 962052 4-28 088201 3i 3o 829683 2 3o 867631 I 93 4-23 087948 3o 3i 9-829821 2 29 9-867515 I 93 9-962806 4-28 10-037694 11 32 829959 2 29 867399 I 867283 I 93 962560 4-28 087440 33 830097 830234 2 29 93 962818 4-28 037187 27 34 2 29 867167 I 93 968067 4-23 036988 26 35 83o372 2 29 867051 I 93 968820 4-23 086680 25 36 83o5o9 2 29 866935 I 866703 I 94 968574 4-23 036426 24 37 83o646 2 29 94 968827 4-23 036178 23 38 830784 2 li 94 964081 4-23 08566^ 22 39 830921 2 866586 I 94 964335 4-23 21 40 83io58 2 28 866470 I 94 964588 4-22 035412 20 41 9-831195 2 28 9-866353 i 94 9-964842 4-22 io.o35i58 ;? 42 83i332 2 28 866237 I 94 965095 4-22 084905 43 831469 2 28 866120 I 94 965349 4-22 03465 1 \i 44 83 1 606 2 28 866004 I 95 965602 4-22 084898 45 831742 2 28 865887 I 95 965855 4-22 084145 i5 46 831879 832015 2 28 865770 I 95 966105 4-22 083891 14 s 2 27 865653 I 95 966862 4-22 033638 i3 832152 2 27 865536 I 95 966616 4-22 033384 12 49 832288 2 27 865419 I 95 966869 967.28 4-22 o33i3i II 5o 832425 2 27 865302 I 95 4-22 082877 10 5i 9-832561 2 27 9-865x85 I 95 9-967876 4-22 10-082624 i 52 832697 2 27 865o68 I 95 967629 4-22 082871 53 832833 2 27 864950 I 864833 I 95 ^'d 4-22 082117 7 54 832969 833 1 o5 2 26 96 4-22 081864 6 55 2 26 864716 I 96 968389 4-22 081611 5 56 833241 2 26 864598 1 864481 I 96 968643 4-22 081357 4 11 833377 2 26 96 968896 4-22 o3iio4 3 833512 2 26 864363 I 96 969149 969403 4-22 o8o85i 2 59 833648 2 26 864245 I 96 4-22 o3o597 I 60 833783 2.26 864127 I 96 969656 4-22 080844 Cosine D. Sine 1 D. Cotang. D. Tang. "mT (47 DEGREES." SINES AND TANGENTS. (43 DEGREES.) 61 M. Sine D. Cosine D. Tang-. D. Cotang. 9.833783 2-26 9-864127 1.96 9-969656 4-22 io-o3o344 60 I 833919 2 25 864010 1.96 969909 4 22 o3oo9i 029838 ll 2 834034 2 25 863892 1-97 970162 4 22 3 834189 2 25 863774 1.97 970416 4 22 029584 57 56 4 834325 2 25 863656 1.97 970669 4 22 029331 5 834460 2 25 863538 1.97 970922 4 22 029078 55 6 834595 834730 2 25 863419 1-97 971175 4 22 028825 54 I 2 25 863301 1.97 971429 4 22 028571 53 834865 2 25 863 1 83 1-97 971682 4 22 0283 1 8 52 9 834999 835i34 2 24 863o64 1-97 971935 4 22 028065 5i 10 2 24 862946 1-98 972188 4 22 027812 5o II 9.835269 2 24 9-862827 1.98 9-972441 4 22 10-027559 8 12 835403 2 24 862709 1.98 972694 4 22 027306 i3 835538 2 24 862590 1.98 972948 4 22 027052 2 U 835672 2 24 862471 1.98 973201 4 22 026799 i5 835807 2 24 862353 1.98 973454 4 22 026546 45 i6 835941 2 24 862234 1.98 973707 4 22 026293 44 17 836075 2 23 862115 1-98 973960 4 22 026040 43 i8 836209 2 23 861996 1-98 974213 4 22 025787 42 19 836343 2 23 861877 1.98 974466 4 22 025534 41 20 836477 2 23 861758 1.99 974719 4 22 025281 40 21 0.836611 2 23 g.86i638 1-99 9.974973 4 22 IO-025027 ii 22 836745 2 23 86i5i9 1-99 975226 4 22 024774 23 836878 2 23 861400 1-99 975479 4 22 024521 37 24 837012 2 22 861280 1-99 975732 4 22 024268 36 25 837146 2 22 861161 1-99 975985 4 22. 024015 35 26 837279 2 22 86 I 041 1-99 976238 4 22 023762 34 11 837412 2 22 860922 860802 1-99 976491 4 22 023509 33 837546 2 22 1.99 976744 4 22 023256 32 29 837679 2 22 860682 2.00 976997 977250 4 22 o23oo3 3i 3o 837812 2 22 86o562 2-00 4 22 022750 3o 3i 9^^7945 2 22 Q. 860442 2.00 9-9775o3 4 22 10-022497 11 32 838078 2 21 86o322 2-00 977756 4 22 022244 33 8382II 2 21 860202 2-00 978009 4 22 021991 11 34 838344 2 21 860082 2-00 978262 4 22 021738 35 838477 2 21 859^42 2-00 9785i5 4 22 021485 25 36 838610 2 21 2-00 978768 4 22 021232 24 3? 38 838742 2 21 859721 2.01 979021 4 22 020979 23 838875 2 21 859601 2.01 979274 4 22 020726 22 39 839007 2 21 859480 2-01 979527 4 22 020473 21 40 839140 2 20 859360 2-01 979780 4 22 020220 20 4i 9-839272 2 20 9.559239 2.01 9.980033 4 22 10-019967 ]l 42 839404 2 20 859119 858998 858877 858756 2-01 980286 4 22 OI9714 43 839536 2 20 2-01 980538 4 22 019462 17 44 839668 2 20 2-01 980791 4 21 019209 16 45 839800 2 20 2-02 981044 4 21 018956 i5 46 839932 2 20 858635 2-02 981297 981550 4 21 018703 14 47 840064 2 '9 858514 2-02 4 21 018450 i3 48 840196 2 •9 858393 2-02 981803 4 21 018197 12 P 840328 2 19 858272 2-02 982056 4 21 017944 017691 II 5o 840459 2 19 858i5i 2-02 982309 4 21 10 ^' 9-840591 2 19 9-858029 857908 2-02 9.982562 4 21 10-017438 I 52 840722 840854 2 19 2-02 982814 4 21 01 7 1 86 53 2 19 857786 2-02 983067 4 21 016933 7 54 840985 2 ;§ 857665 2-o3 983320 4 21 016680 6 55 841116 2 857543 2-03 983573 4 21 016427 5 56 841247 2 18 857422 2.03 983826 4 21 016174 4 II 841378 2 18 857300 2.03 984079 4 21 015921 3 84i5o9 2 18 857178 2-03 984331 4 21 015669 2 ^ 841640 2 18 857056 2-o3 984584 4 21 oi54i6 I 6o 841771 2-l8 856934 2 -03 984837 4-21 oi5i63 Cosine D. Sine D. Cotanar. D. Tang. M. (46 62 (44 DEGREES.) A TABLE OF LOGARITHMIC M. Sine D. Cosine D. Tang. D. Cotang. 9-841771 2.18 '■St 2-03 9.984837 4-21 io-oi5i63 60 I 841902 2 -18 2-o3 985090 4-21 014910 014657 u 2 842033 2 856690 2-04 985343 4-21 3 842163 2 856568 2-04 985596 4-21 014404 57 4 842294 2 856446 2-04 985848 4-21 oi4i52 56 5 842424 2 856323 2-04 986101 4-21 013899 55 6 842555 2 856201 2-04 986354 4-21 013646 54 I 842685 2 856078 2.04 986607 4-21 013393 53 842815 2 855^33 2-04 986860 4-21 oi3i4o 52 9 842946 2 2-04 9871 12 4-21 012888 5i 10 843076 2 85571 1 2-05 987365 4-21 012635 5o II 9-843206 2 9-855588 2-05 9-987618 4-21 10-012382 49 12 843336 2 855465 2-05 987871 4-21 012129 48 i3 843466 2 855342 2-o5 988123 4-21 011877 s i4 843595 2 855219 2-05 988376 4-21 011624 i5 843725 2 855096 2-o5 988629 4-21 011371 45 i6 843855 2 854073 854850 2-05 988882 4-21 oiin8 44 \l 843984 2 2-05 989134 4-21 010866 43 8441 14 2 854727 2-06 989387 4-21 oio6i3 42 , 19 844243 2 854603 2-06 989640 4-21 oio36o 41 20 844372 2 854480 2-06 989893 4-21 010107 40 21 9 -844502 2 9-854356 2-06 9-990145 4-21 10-009855 S 22 844631 2 854233 2-06 9903^8 4-21 009602 23 844760 844889 84501 8 2 854109 2-06 4-21 009349 37 36 24 2 853986 2-06 990903 4-21 008844 25 2 853862 2-06 99II56 4.21 35 26 845147 2 853738 2-o6 991409 4-21 008338 34 27 845276 2 853614 2-07 991662 4.21 33 28 845405 2 853490 2-07 991914 4-21 008086 32 29 845533 2 853366 2-07 992167 4-21 007833 3i 3o 845662 2 853242 2-07 992420 4-21 007580 3o 3i 9-845790 2 g-853ii8 2.07 9-992672 4-21 10.007328 11 32 845919 2 852Q94 852869 852745 2.07 992925 4-21 007075 33 846047 2 2.07 993178 4-21 006822 27 34 846175 2 2.07 993430 4.21 006570 26 35 846304 2 852620 l:°J> 993683 4.21 oo63i7 25 36 846432 2 852496 993936 4-21 006064 24 !S 846560 2 852371 2.08 994189 4-21 oo58ii 23 846688 2 852247 2.08 994441 4-21 005559 22 39 846816 2 852122 2-08 994694 4-21 oo53o6 21 4o 846944 2 851997 2-o8 994947 4-21 oo5o53 20 4i 9-847071 2 9.851872 2.08 9.995199 4-21 10-004801 ;i 42 847199 2 851747 2.08 995432 4-21 004548 43 847327 2 85i622 2.08 995705 4-21 004295 17 44 847454 2 85 1 497 2.09 995957 4-21 004043 16 45 847582 2 85i372 2-09 996210 4-21 003790 i5 46 847709 847836 2 85i246 2-09 996463 4-21 003537 14 S 2 85II2I 2-09 996715 4-21 003285 i3 847964 2 fX 2-09 996968 4-21 oo3o32 12 49 848091 2 2-09 997221 4-21 002779 002527 II 5o 848218 2 850745 2-09 997473 4-21 10 5i 9-848345 2 9.850619 850493 2.09 9.997726 4-21 10-002274 I 52 848472 2 2-10 997979 4-21 002021 53 848599 2 85o368 2-10 4-21 001769 ooi5i6 I 54 848726 2 850242 2-10 998484 4-21 55 848852 2 85oii6 2-10 998737 4-21 001263 5 56 848979 2 849990 2-10 998989 4-21 OOIOU 4 U 849I06 2 849864 2-10 999242 4-21 060758 3 849232 2 849738 2-10 999495 4-21 ooo5o5 2 59 849359 2 84961 1 2-10 999748 4-21 000253 I 60 849480 2-II 849485 2-10 10.000000 4-2! 10-000000 Cosine D. Sine D. Cotan^. D. Tang. M. | (45 DEGREES.) A TABLE OF NATUEAL SINES. 63 M Deg. 1 Deg. 2 Deg. 3 Deg. 1 4 Deg. M 60 S. C. S. S. U. S. ^9-85 S. C. S. S. C.S. S. C.S. 00000 Unit. 01745 03490 l^lt 05234 99863 06976 99756 I 00029 I -0000 01774 oi8o3 99984 o35i9 o5263 99861 07005 99754 59 2 00058 I -0000 99984 03548 99937 05292 99860 07034 99752 58 3 00087 I -0000 oi832 99983 03577 99936 o532i 99858 07063 99750 57 4 00116 I • 0000 01862 99983 o36o6 99935 o535o 99857 07092 99748 56 5 00145 I -0000 01891 99982 03635 99934 05379 o54o8 99855 07121 99746 55 6 00175 I -0000 01920 99982 o3664 99933 99854 07i5o 99744 54 7 00204 I -0000 01949 01978 99981 03693 99932 05437 99852 07179 99742 53 8 00233 I-OOOO 99980 03723 99931 05466 99851 07208 99740 52 9 00262 I -0000 02007 99980 03752 99930 05495 99849 07237 99738 5i 10 00291 I. 0000 02036 99979 °^78i 99929 05524 99847 07266 99736 5o II oo32o 99999 02c- "^ 99979 o38io 99927 05553 99846 07295 99734 ^? 12 00349 00378 99999 0209^ 99978 03839 99926 05582 99844 07324 99731 i3 99999 02123 99977 03868 99925 o56ii 99842 07353 99729 47 U 00407 99999 02l52 99977 03897 99924 o564o 99841 07382 9Q727 46 ID 00436 99999 02181 99976 03926 99923 00669 99839 0741 1 99725 45 i6 00465 99999 022II 99976 03955 99922 05698 99838 07440 99723 44 17 00495 99999 02240 99975 03984 99921 05727 99836 07469 99721 43 i8 oo524 99999 99998 02260 02298 99974 0401 3 99919 99918 05756 99834 07498 99719 99716 42 19 00553 99974 04042 05785 99833 07527 41 20 oo582 99998 02327 99973 04071 99917 o58i4 99831 07556 99714 40 21 006 1 1 99998 02356 99972 04100 99916 o5844 99829 07585 99712 ll 22 00640 99998 02385 99972 04129 99915 05873 99827 07614 99710 23 00669 00698 99998 02414 99971 04159 99913 05902 99826 07643 99708 37 24 99998 02443 99970 04188 99912 05931 99824 07672 99705 36 25 00727 99997 02472 99969 04217 99911 05960 99822 07701 99703 35 26 00756 99997 025oi 99969 99968 04246 99910 05980 99821 07730 99701 34 u 00785 99997 o253o 04275 99909 06018 99819 07759 07788 99699 33 00814 99997 02560 99967 o43o4, 99907 06047 99817 99696 32 29 00844 99996 02589 99966 04333 99906 06076 99815 07817 99694 3i 30 00873 99996 02618 99966 04362 99905 o6io5 99813 07846 99692 3o 3i 00902 99996 02647 99965 04391 99904 06134 99812 07875 99689 It 32 00931 99996 02676 99964 04420 99902 06 1 63 99810 07904 99687 33 00960 99995 02705 99963 04449 04478 99901 06192 99808 07933 99685 2 34 00989 01018 99995 02734 99963 06221 99806 07962 99683 35 99995 02763 99962 04507 99098 o625o 99804 07991 99680 25 36 01047 99995 02792 99961 04536 99897 06279 99803 08020 99678 24 37 01076 99994 02821 99960 04565 99896 o63o8 99801 08049 99676 23 38 oiio5 99994 02850 99959 04594 99894 06337 99799 08078 99673 22 39 oii34 99994 02879 02908 99959 04623 99893 06366 99797 08107 99671 21 40 J0II64 99993 99958 04653 99892 06395 99795 o8i36 99668 20 41 OU93 99993 02938 99957 04682 99890 06424 99793 o8i65 99666 19 42 01222 99993 02967 99956 047 1 1 mil 06453 99792 08194 99664 18 43 0I25l 99992 02996 99955 04740 06482 99790 08223 99661 \l 44 01280 99992 1 o3o25 99954 04769 99886 o65ii 99788 08252 99659 45 oi3o9 99991 o3o54 99953 04798 99885 o654o 99786 08281 99657 i5 46 01338 99991 o3o83 99952 04827 99883 06569 99784 o83io 99654 14 47 01367 99991 03lI2 99952 04856 99882 06598 99782 08339 08368 99652 i3 48 01396 99990 o3i4i 99951 04885 99881 06627 99780 99649 12 49 01425 99990 o3i70 99950 04914 99879 99878 06656 99778 08397 99647 II 5o 01454 99989 o3igQ 99949 04943 06685 99776 08426 99644 10 5i 01483 99989 03228 99948 04972 99876 06714 99774 08455 99642 9 52 oi5i3 99989 03257 99947 o5ooi 99875 06743 99772 08484 99639 8 53 01542' 99988 03286 99946 o5o3o 99873 06773 99770 o85i3 99637 7 54 01371 .99988 o33i6 99945 o5o59 o5o88 99872 06802 99768 08542 99635 6 55 01600 999871 03345 99944 99870 o683i 99766 08571 99632 5 56 01629: 99987^ 03374 99943 o5u7 o5i46 ?9869 06860 99764 08600 99630 4 11 01658 99986 o34o3 99942 99867 06889 06918 99762 08629 08658 99627 3 01687 99986 03432 99941 o5i75 99866 99760 99625 2 59 01716 99985 03461 99940 o52o5 99864 06947 99758 08687 99622 -4 "M" C.S. S. C.S. S. C.S. S. C.S. S. C. S. S. 89 Deff. 88 Deg. 87 Deg. i 86 Deg. 1 85 Deg. 64 A TABLE OF NATURAL SINES. M 5 Deg. 6 Deg. 1 Deg. 8 Deg. 9 Deg. M S. C. S. S. 0. S. S. C. S. S. C. S. S. .0 S. 08716 99619 10453 99452 12187 99255 18917 99027 15643 98769 60 I 08745 99617 10482 99449 12216 99251 18946 99028 15672 98764 59 2 08774 99614 io5ii 99446 12245 99248 13975 99019 15701 98760 58 3 08803 99612 10 540 99443 12274 99244 14004 99015 15780 98755 57 4 o883i 99609 10569 99440 12802 99240 14033 990 1 1 15758 98751 56 5 08860 99607 10597 99487 12881 99287 14061 99006 15787 98746 55 6 08889 08918 99604 10626 99434 12860 99233 14090 99002 i58i6 9874. 54 7 99602 io655 9943 1 12889 99280 14119 14148 98998 15845 98787 53 8 08947 99599 10684 99428 12418 99226 98994 15873 98782 52 9 08976 99596 10713 99424 12447 99222 14177 98900 15902 98728 5i 10 09005 99594 10742 99421 12476 99219 99215 14205 989^6 1 598 1 98728 5o II 09034 99591 10771 99418 12504 14284 ^8982 11$^ 98718 49 12 09063 99588 10800 99415 12533 99211 14268 ,8978 98714 48 i3 09092 99586 10829 99412 12562 99208 14292 98973 16017 98709 47 14 ogi2i 99583 io858 99409 12591 99204 14820 98969 16046 98704 46 i5 09i5o 99580 10887 99406 12620 99200 14349 98965 16074 98700 45 i6 09179 99578 10916 99402 12649 99197 14378 98961 i6io3 98695 44 ',1 09208 99575 10945 99899 12678 99193 99189 14407 98957 16182 98600 43 09287 99572 10973 99396 12706 14436 98953 16160 98686 42 19 09266 99570 11002 99393 12735 99186 14464 98948 16189 16218 98681 41 20 09295 99567 iio3i 99890 12764 99182 14493 98944 98676 40 21 09324 99564 '■ 1 1060 99886 12798 99178 14522 98940 16246 98671 39 22 09353 99562 11089 99888 12822 99175 i455i 98986 i62-'5 98667 88 23 09382 99559 iiiiS 99380 12851 99171 14580 98931 16804 98662 37 24 0941 1 99556 1 1 147 99377 12880 99167 14608 98927 16333 98657 36 25 09440 99553 I1I76 99374 12908 99168 14687 98923 1 636 1 98652 35 26 09469 99551 ii2o5 99370 12987 99160 14666 98919 16890 98648 34 27 0949B 99548 11234 99867 12966 99156 14695 98914 16419 98648 33 28 09D27 99545 11263 99864 12995 99152 14728 98910 16447 98688 32 29 09556 99542 11291 99860 18024 99148 14752 98906 16476 98688 3i 3o 09535 99540 Il320 99357 i3o53 99144 14781 98902 i65o5 98629 30 .31 09614 99537 11849 11878 99354 i3o8i 99141 14810 98897 16533 98624 29 28 32 09642 99534 99351 i3iio 99187 14838 98893 16562 98619 33 09671 9953. 1 1407 99847 18189 99188 14867 98889 1659. 98614 27 34 09700 99528 1 1436 99844 I3i68 99129 99125 14896 98884 16620 98609 26 35 09720 09758 99526 II465 99341 18197 14925 98880 16648 98604 25 36 99523 11494 99337 18226 99122 14904 98876 16677 98600 24 37 09787 99520 11523 99334 13254 99.18 14982 16706 98595 23 38 09816 99517 ii552 99331 18288 99114 i5oii 98867 16784 98590 22 39 09845 99514 ii58o 99327 I33I2 99110 1 5040 98863 16763 g8585 21 40 09874 9951 1 1 1609 ii638 99824 13841 99106 15069 98858 16792 98580 20 41 09903 99508 99820 18870 99102 1 5097 98854 16820 98575 19 18 42 09932 99506 1 1667 99817 18899 99098 i5i26 98849 16849 98570 43 09961 995o3 1 1696 99314 18427 99094 i5i55 98845 16878 98565 17 44 09990 99500 11725 99810 18456 ITol] i5i84 9^^4' 16906 98561 16 45 10019 99497 II 754 99807 13483 l5212 98886 16985 98556 i5 46 10048 99494 1 1783 99808 i35i4 99088 i524i 98882 16964 98551 14 3 10077 99491 11812 99800 13543 99079 99075 15270 98827 16992 98546 i3 10106 99488 1 1 840 99297 18572 15292 98828 17021 98541 12 49 I0I35 99485 U898 99293 i36oo 99071 15327 98818 i7o5o 98536 II 5o 10164 99482 99290 99286 18629 99067 15356 98814 17078 98581 10 5i 10192 99479 11927 i8658 99068 15385 98809 17107 17186 98526 9 52 10221 99476 1 1956 99283 13687 99059 99055 15414 98803 98521 8 53 I025o 99473 1 1985 99279 18716 15442 98800 17164 98516 7 54 10279 99470 12014 99276 18744 9905 1 '^A'^' 98796 17198 98511 6 55 io3o8 99467 12043 99272 18773 99047 i55oo 98701 9^787 17222 98506 5 56 10337 99464 12071 99269 99265 18802 99043 '^^^9 17250 98501 4 ll 10366 99461 12100 i388i 99039 99085 15557 98782 17808 98496 3 10395 99458 12129 99262 18860 1 5586 98778 98491 2 59 10424 99455 12158 99258 13889 9908 1 1 i56i5 98773 17886 98486 I M C. 8. S. C. S.' C. S. S. C. S. S. "cTsT S. 8i Deg. 83 Deg. 82 Deg. 81 Deg. 80 Deg. A TABLE OF NATURAL SINES. 65 M 10 Deg. 11 Deg. 12 Deg. 13 Deg. 14 Deg. 60' S. C. S. S. 1 908 1 C. S. S. C.S. S. C. S. S. C.S. 17365 "98487 ^I63 20791 978,5 ^2495 97437 24,92 97o3o •i 17393 98476 19109 98157 20820 97809 22523 9743o 24220 97023 59' 2 17422 9847. 19138 98152 20848 97803 22552 97424 24249 970,5 58: 3 1745. 98466 19167 98146 20877 97797 22580 97417 24277 97008 ^^l ■4 17479 98461 19195 98140 20905 9779' 22608 97411 243o5 9700, 56! 5 17508 98455 19224 98135 20933 97784 22637 97404 24333 96994 551 6 17537 98450 19252 98.29 20962 97778 22665 97398 24362 96987 54 7 17565 98445 19281 98124 20990 97772 22693 97391 24390 96980 53' 8 1759/, 98440 19309 98118 21019 97766 22722 97384 24418 96973 52 i 9 17623 98435 19338 98,12 21047 97760 22750 97378 24446 96966 5i| 10 17651 9S430 19366 98107 21076 97754 22778 97371 24474 96959 5o 11 17680 98425 19395 98101 21104 97748 22807 97365 245o3 96952 49 12 17708 98420 19423 98096 21132 97742 22835 97358 2453, 96945 48 i3 17737 98414 19452 98090 21161 97735 22863 9735, 24559 96937 47 1 4 17766 98409 19481 9S084 21189 97720 22892 97345 24587 96930 46 i5 17794 98404 19509 98079 21218 97723 22920 97338 246,5 96923 45 i6 17823 98399 19538 98073 21246 97717 22948 97331 24644 969,6 44 17 17852 983^i 19566 98067 21275 9771 1 22977 97325 24672 96909 43 |8 17880 98389 19595 98061 2i3o3 97705 23oo5 973i8 24700 96902 42 19 17909 98383 19623 98056 2i33i 97698 23o33 973,1 24728 96894 41 20 17937 98378 19652 98050 2i36o 97692 23062 97304 24756 96887 40 21 17966 983-;3 19680 98044 2i3S8 97686 23090 97298 24784 96880 ^ 22 17995 98368 19709 98039 21417 97680 23ii8 97291 248,3 96873 23 18023 98362 19737 98033 21445 97673 23 146 97284 24841 96866 ll 24 i8o52 9S337 19766 98027 21474 97667 23,75 97278 24869 96858 25 18081 98352 19794 98021 2l502 9766, 23203 97271 24897 9685, 35 26 18109 98347 19823 980,6 2i53o 97655 2323, 97264 24925 96S44 34 27 i8i38 9834. 19851 98010 21559 97648 23260 97257 24953 96837 33 28 18166 98336 19880 98004 21587 97642 23288 97251 24982 96829 32 29 18195 9833. 19908 97998 2,6,6 97636 233,6 97244 25o,o 96822 3i 30 18224 98325 19937 97992 21644 97630 23345 97237 25o38 968,5 3o 3i 18252 98320 19965 97987 21672 97623 23373 97230 25o66 96807 29 32 18281 983 1 5 19994 97981 2,701 97617 2340, 97223 25094 96800 28 33 i83o9 983x0 20022 97975 21729 97611 23429 23458 97217 25,22 96-793 11 34 18338 983o4 2005l 97969 2,758 97604 97210 25,5, 96786 35 18367 98299 20079 20108 97963 2,786 97598 23486 97203 25,79 96778 25 36 18395 98294 97958 218,4 & 235,4 97196 97189 25207 96771 24 a 18424 98288 2oi36 97952 21843 23542 25235 96764 23 18452 98283 20165 97946 2,87, 97579 2357, 97182 25263 96756 22 39 18481 98277 20193 97940 2,899 21928 97573 23599 97176 2529, 96749 2, 30 i85o9 18538 98272 20222 97934 97566 23627 97,69 25320 96742 20 41 98267 202§0 97928 21956 97560 23656 97162 25348 96734 19 42 18567 98261 20279 97922 21985 97553 23684 97155 25376 96727 ,8 43 18595 98256 2o3o7 979,6 220,3 97547 237,2 97148 25404 96719 17 44 18624 98250 20336 979,0 22041 97541 23740 97141 25432 96712 ,6 45 18652 9824^ 2o364 97905 22070 97534 23769 97134 25460 96705 i5 46 18681 98240 20393 97899 22098 97528 23797 97,27 25488 96697 14 47 48 18710 98234 20421 97893 22,26 97321 23825 97,20 255,6 96682 i3 18738 98220 2o45o 97887 22,55 975,5 23853 97113 25545 12 49 18767 98223 20478 9788, 22,83 97508 23882 97,06 25573 96675 II 5o 18795 98218 2o5o7 97875 222,2 97502 239,0 97,00 256o, 96667 10 5i 18824 98212 2o535 97869 22240 97496 97489 23938 97093 25629 96660 9 52 18852 98207 20563 97863 22268 23966 97086 25657 96653 8 53 1 888 1 98201 20592 97857 22297 97483 23995 97079 25685 96645 7 54 18910 98196 20620} 97851 22325 97476 24023 97072 25713 96638 6 55 18938 98190 20649I 97845 22353 97470 24o5i 97065 25741 96630 5 56 18967 98185 20677 97839 22382 97463 24079 97058 25769 96623 4 57 18995 98,79 20706 97833 22410 97457 24108 97o5i 25798 966,5 3 58 19024 98174 20734 97827 22438 97450 24136 97044 25826 96608 2 59 19052 C. S. 98168 1 S. 20763 97821 22467 97444 24164 97037 25854, 96600 c. s. I s. Zj C. S. S. c.s. S. C.S. S. 79 Deg. 78 Deg. 1 77 Deg. 76 Deg. "75 ] Deg. A TABLE OF NATUEAL SINES. M 15 Beg. 16 Beg. 11 Beg. 1 18 Deg. 19 Deg. M S. iC.S. 25882 96593 25910 96585 S. C. S. S. 1 c. s. r s. C. S. S. 1 s.c. 27564 96126 29237 9563o'! 30902 95106 32557 94552 "60 I 27592 96118 29265 95622 j 30929 95097 32584' 94542 '59 2 25938 96578 27620 96110 29293 956i3 30985 95088 3261 2^ 94533 58 3 25966 96570 27648 96102 29321 o56o5 95079 32639' 94523 57 4 25994 1 96562 27676 96094 29348 95506 31012 95070 32667 94514 56 5 26022 96555 27704 96086 29376 95588 31040 95061 32694 94504 55 6 26o5o 1 96547 27731 96078 29404 95579 31068 95o52 32722 94495 54 I 26079 ' 96540 27759 96070 29432 95571 31095 95043 32749 94485 53 26107 96532 27787 96062 29460 95562 31123 95o33 32777 94476 52 9. 26i35 96524 27815 96054 29487 95554 3n5i 95024 32804 94466 5i 10 26163 ' 96517 27843 96046 2951 5 95545 ! 31178 95oi5 32832 94457 5o II 26191 96509 27871 96037 29543 95536 3 1 206 95006 3 2859 1 04447 49 12 26219 96502 27899 96029 29571 95528 3x233 94997 32887 94438 48 i3 - 26247 96494 27927 96021 29599 29626 95519 31261 94988 32914 94428 47 14 26275 96486 27955 96013 95511 31289 94979 32942 94418 46 1 5 263o3 96479 27983 96005 29654 95502 3i3i6 94970 32969 94409 45 i6 2633 1 96471 28011 95997 29682 95493 95485 3 1344 94961 32997 94399 44 17 26359 96463 28039 95989 29710 31372 94952 33024 94390 43 i8 26387 96456 28067 95981 29737 95476 3i399 94943 33o5i 94380 42 19 26415 96448 28095 95972 29765 95467 31427 94933 33079 94370 41 20 26443 96440 28123 95964 29793 95459 3 1 454 94924 33 1 06 94361 40 21 26471 96433 28i5o 95956 29821 95450 31482 94915 33 1 34 94351 3^ 22 26500 96425 28178 95948 29849 95441 3i5io 94906 33i6i 94342 23 26528 96417 28206 95940 29876 95433 3i537 l'& 33189 94332 37 24 26556 96410 28234 95931 29904 95424 3i565 33216 94322 36 25 26584 96402 28262 95923 29932 95415 31593 94S78 33244 9431 3 35 26 26612 96394 28290 95915 29960 95407 31620 94869 33271 94303 34 27 26640 96386 283 18 95907 29987 95398 95389 31648 94860 33298 94293 33 28 26668 96379 28346 95898 3001 5 31675 94851 33326 94284 32 29 26696 9637. 28374 95890 30043 95380 31703 94842 33353 94274 3i 3o 26724 96353 28402 95882 30071 95372 31730 94832 33381 94264 3o 3i 26752 96355 28429 95874 30098 95363 3i758 94823 33408 94254 29 32 26780 96347 28457 95865 30126 95354 31786 94814 33436 94245 28 33 26S08 96340 28485 95857 30154 95345 3i8i3 94805 33463 94235 11 34 26836 96332 285i3 95849 30182 95337 31841 94795 33490 94225 35 26864 96324 28541 95841 30209 95328 3 1 868 94786 33518 94215 25 36 26892 96316 28569 95832 30237 95319 31896 94777 33545 94206 24 37 26920 9630.8 28597 95824 30265 95310 31923 94768 33573 94196 23 38 26948 96301 28625 95816 30292 95301 3i95i 94758 33600 94186 22 39 26976 96293 28652 95807 3o32o 95293 31979 94749 336?I 94176 21 40 27004 96285 28680 95799 30348 95284 32006 94740 33655 94167 20 41 27032 96277 28708 95791 30376 95275 32034 94730 33682 94157 19 18 42 27060 96269 28736 95782 3o4o3 95266 32061 94721 33710 94147 43 27088 96261 28764 95774 3043 1 95257 32089 94712 33737 94137 17 44 27116 96253 28792 95766 3o45q 95248 32116 94702 33764 94127 16 45 27144 96246 28820 95757 30486 95240 32144 94693 33792 94118 i5 46 27172 96238 28847 95749 3o5i4 90231 3217. 946S4 33819 94108 14 47 27200 96230 28875 95740 30542 95222 32199 94674 33846 94098 33874 94088 i3 48 27228 96222 28903 95732 30570 95213 32227 94665 12 49 27256 96214 28931 95724 30597 95204 32254 94656 33901 94078 II 5o 27284 96206 28959 95715 30625 95195 32282 94646 33929 94068 10 5i 27312 96198 28987 95707 3o653 95 1 §6 32309 94637 33956J 94o58 9 52 27340 96190 29015 95698 30680 95177 32337 94627 339831 94049 8 53 27368 96182 29042 95690 30708 95168 32364 94618 34011! 94039 7 54 27396 96174 29070 95681 30736 95159 32392 94609 34038 94029 6 55 27424 96166 29098 95673 30763 95i5o 32419 94599 34065 94019 5 56 27452 96158 29126 95664 30791 95142 32447 t&To 34093 94009 4 57 27480 96150 29154 95656 30819 95i33 32474 34120 &l 3 58 27508 961421 29182 95647 30846 95124 32502 94571 34147 2 59 M 27536 96134 29209 C. S. 95639 S. 30874 C. S. 95ii5 S. 32529 94561 34175s 93979 C. S. 1 s. 1 C. S. S. 74Deff. 1 7BBeg. 1 72 Beg. nBeg. 1 70 Deg. A TABLE OF NATURAL SINES. r i 20 Deg. 21 Beg. 22 Deg. 23 Deg. 24 Deg. M M i iS. C.S. S. C.S. S. C.S. 92718 S. 39073 C.S. 92o5o S. -4-^74 C.S. 34202 93969 l^f-^ 93358 ?^4^i 9,355| 60 i I 34229 93959 35864 93348 37488 92707 39,00 92039M 40700 9,343 §1 2 34207 93949 35891 93337 37015 92697 39.27 92028 1 40727 9,33i 3 34284 93939 359,8 93327 37342 92686 39,53 920, 6| 40753 9,3,9 57: 4 343x1 93929 30945 93316 37069 92675 39,80 92005 j 40780 9,307 56: 5 34339 93919 30973 93306 37090 92664:; 39207 9,994; 40806 91295 55] 6 34366 93909 36000 93295 37022 92653 39234 91982 40833 9,283 54! I 34393 93899 36027 93285 37649 92642 ! 39260 9,971 40860 9,272 53 1 34421 93889 36o54 93274 37676 92631 39287 9,959 40886 9,260 52; 9 34448 93879 36081 93264 37703 92620 393,4 91948 409,3 9,248 5i 10 34475 93S69 36108 93253 37730 92609 39341 91936' 4og3q 9,236 5o II 345o3 ^3859 36i35 93243 37757 92598 39367 39394 91925 40966 9,224 s 12 34530 93849 36162 93232 37784 37811 9^^^I 9,914 40992 9,2,2 i3 34557 93839 36190 g3222 92576 39421 91002 9,89, 410,9 9,200 47 i4 34584 93829 36217 93211 37838 92565 39448 4,045 91,88 46: i5 34612 93819 36244 93201 37865 92554 39474 91879 41072 9, ,76 45 i6 34639 93809 36271 93190 93180 37892 92543 3950, 9,868 41098 91,64 44 17 34666 93799 36298 37919 92532 39528 9,856 41,25 9, ,52 43 34694 93789 36325 93169 37946 92521 39555 9,845 4ii5, 9,, 40 42 19 34721 93779 36352 93 1 59 93148 37973 925,0 3958f 9,833 41178 9, ,28 41 20 34748 93769 36379 37999 92499 39608 91822 41204 9, ,,6 40 21 34775 93759 36406 93i37 38026 92488 39635 9,810 4123, 9,, 04 ^ 22 34803 93748 36434 93127 38o53 92477 3966, 9 '799 41257 9,092 91080 23 34830 93738 36461 93n6 38o8o 92466 39688 917S7 4,284 S 24 34857 93728 36488 93106 f.'V 92455 397,5 9,775 4,3io 9,068 20 34884 93718 365i5 93095 38i34 92444 3974, 91764 4,337 9,o56 35 26 34912 93708 36542 93084 38i6i 92432 39768 9,752 4,363 91044 34 27 34939 93688 36569 93074 38i88 92421 39795 9,741 4,390 9,032 33 28 34966 36596 93o63 382i5 92410 3q82 2 91729 91718 41416 9,020 32 29 34993 93677 36623 93o52 38241 92399 39848 41443 91008 3i 30 35021 93667 36650 93042 38268 92388 39875 91706 4,469 90996 3o 3i 35048 93657 36677 93o3i 3S295 92377 39902 l\lli 4,496 90984 29 32 35075 93647 36704 93020 38322 92366 39928 4,522 90972 28 33 35io2 93637 36731 93010 f^.^i 92355 39955 91671 4,549 90960 27: 34 35i3o 93626 36758 92999 38376 92343 39982 91660 4,575 90948 26; 35 35i57 936i6 36785 92988 38403 92332 40008 91648 4,602 90936 25 36 35i83 93606 36812 92978 38430 92321 4oo35 9,636 41628 90924 24 S 352II 93596 36839 92967 38456 92310 40062 9,625 4,655 909,1 23 12^ 93585 36867 92956 38483 92299 400S8 916,3 4168, a 22 39 93575 36894 92945 38510 92287 4o,i5 9,60, 41707 21 40 35293 93565 36921 92935 38537 92276 40141 9,590 4,734 90875 20 41 35320 93555 36948 92924 38564 92265 40168 9,578 4,760 90863 % ^l 35347 93544 36975 92913 \lV' 92254 40195 9,566 41787 9o85i 43 35375 93534 37002 92902 92892 38617 92243 4022, 9,555 418,3 90839 17 44 35402 93524 37029 38644 9223, 40248 9,543 41840 90826 16 45 35429 93514 37056 38671 92220 40275 9,531 41866 90814 i5 46 35456 935o3 37083 92870 38698 92209 4o3o, & 41892 90802 14 47 35484 93493 37110 92859 3^7?5 92IQ8 40828 41919 90790 i3 48 355II 93483 37137 92849 ^I'^^l 92186 40355 91496 9,484 41945 90778 12 49 35538 93472 37164 Q2838 f.V^- 92175 4o38, 41972 90766 11 5o 35565 93462 37191 92827 38800 92164 40408 91472 41998 90753 10 5i 35592 93452 37218 92816 38832 92,52 40434 9,461 42024 90741 I 52 35619 93441 37245 92805 38859 92,4, 4046, 9,449 42o5i 90729 53 35647 93431 37272 92794 38886 92i3o 40488 91437 42077 907,7 1 54 35674 93420 37299 92784 389,2 92, ,9 4o5i4 9,425 42,04 90704 6 55 35701 93410 37326 92773 38939 92,07 4004, 91414 42, 3o ?a 5 56 35728 93400 37353 92762 38966 t% 40567 91402 42,56 4 57 35755 93389 37380 92751 38993 40094 9,390 42,83 90668 3 58 35782 & 37407 92740 39020 92073 4062, 9,378 42209 90655 2\ 59 M 358io 37434 C.S. 92729 S. 39046 C.S. 92062 S. 40647 9,366 _42235 90643 C.S. S. C.S. S. C.S. s. 69 Deg. 68 Deg. 67 Deg. 1 66 Deg. 1 65 Deg. 1 19 A TABLE OF NATURAL SINES. M 25 Deg. 26 Deg. 27 Deg. 28 Deg. 29 Deg. M S. C. S. S. c. s. S. C. S. S. C. S. ^s'^ C. S. 42262 9063 1 43837 89879 89867 S? 89101 46947 88295 48481 87462 60 I 42288 90618 43863 89087 46973 88281 485o6 87448 58 2 423i5 90606 4388g 439.6 89854 4545x 89074 46999 88267 48532 87434 3 42341 90594 8984X 45477 89061 47024 88254 48557 87420 57 4 42367 90582 43942 89828 455o3 89048 47o5o 88240 48583 87406 56 5 42394 90569 43968 89816 45529 89035 47076 88226 48608 8739X 55 6 42420 90557 43994 89803 45554 89021 47101 88213 48634 87377 54 7 42446 90545 44020 89790 45580 89008 47127 88199 48659 87363 53 8 42473 90532 44046 89777 45606 S??5 47153 88i85 48684 87349 87335 52 9 42499 90520 44072 89764 45632 47178 88x72 48710 5i 10 42525 90507 44098 89752 45658 88968 47204 88x58 48735 8732X 5o II 42552 90495 44124 89739 45684 88955 47229 88144 48761 87306 49 12 42578 90483 441 5x 89726 45710 88942 47255 88i3o 48786 87292 48 i3 42604 90470 44177 89713 45736 88928 47281 88117 4881 1 87278 47 14 4263 1 90458 44203 89700 45762 88915 47306 88io3 48837 87264 46 i5 42657 90446 44229 89687 45787 88902 47332 88089 48862 87250 45 i6 42683 90433 44255 89674 458? 88888 47358 88075 48888 87235 44 \l 42709 90421 4428X 89662 45865 88875 47383 88062 48913 87221 43 42736 90408 44307 89649 88862 47409 88048 48938 87207 42 19 42762 i:lt 44333 89636 45891 88848 47434 88034 48964 87193 41 20 42788 42815 44359 89623 459x7 88835 47460 88020 48989 87178 40 21 90371 44385 89610 45942 88822 47486 88006 49014 87164! 39! 22 42841 90358 44411 89597 45968 88808 47511 87993 49040 87i5o 38 23 42867 90346 44437 89584 45994 88705 47537 87979 49065 87136 37 24 42894 90334 44464 8957, 46020 88782 47562 87963 49090 87121 36 25 42920 90321 44490 89558 46046 88768 47588 87951 49116 87107 35 26 42946 90309 445x6 89545 46072 88755 47614 87937 49141 87093 34 11 42972 90296 90284 44542 89532 46097 88741 47639 47665 87923 49166 87079 33 gs 44568 895,9 46x23 88728 87909 49192 87064 32 29 90271 44594 89506 46149 88715 47690 87896 87882 49217 87o5o 3i 3o 43o5i 90259 44620 89493 46x75 88701 47716 49242 87036 3o 3i 43077 90246 44646 89480 46201 88688 47741 87868 49268 87021 29 32 43x04 90233 44672 89467 46226 88674 47767 87854 49293 87007 28 33 43i3o 90221 44698 89454 46252 88661 47793 87840 49318 86993 27 34 43 1 56 90208 44724 89441 46278 88647 47818 87826 49344 86978 26 35 43182 90196 44750 89428 46304 88634 47844 87812 49369 86964 25 36 43209 90183 44776 89415 46330 88620 47869 47895 87798 87784 49394 86949 24 37 43235 90171 44802 89402 46355 88607 4941? 49445 86935 23 38 43261 90x58 44828 89389 46381 88593 47920 87770 86921 22 39 43287 90146 44854 89376 46407 88580 47946 87756 49470 86906 21 40 433 1 3 90133 44880 89363 46433 88566 47971 87743 49495 86892 20 41 43340 90120 449061 89350 46458 88553 47997 87729 87715 49521 86878 19 42 43366 90108 44932! 89337 46484 88539 88526 48022 49546 86863 18 43 43392 90095 44958! 89324 46510 48048 87701 49571 86849 17 44 43418 90082 44984I 8931. 46536 885 1 2 48073 87687 49596 86834 16 45 43445 90070 45oio 89298 46561 88499 48099 87673 49622 86820 i5 46 43471 90057 45o36 89285 46587 88485 48124 87659 49647 868o5 14 47 43497 90045 45062 89272 46613 88472 481 5o 87645 49672 86791 i3 48 43523 90032 45o88 89259 89245 46639 88458 48175 87631 49697 86777 12 49 43549 43575 90019 45ii4 46664 88445 48201 87617 49723 86762 II 5o 90007 45 1 40 89232 46690 88431 48226: 87603 49748 86748 10 5i 43602 89994 45x66 892x9 46716 88417 48252 87589 48277I 87575 49773 86733 9 52 43628 89981 451921 89206! 46742 88404 49798 86719 8 53 43654 89968 452x8 89193 89x^0 46767 88390 483o3 87561 49824 86704 7 54 43680 89956 45243 46793 46819 88377 48328 87546 49849 86690 6 55 43706 89943 45269 45295 89167 88363 48354 87532 49874 86675 5 56 43733 89930 89x53 46844 88349 48379 87518 49899 86661 4 57 43759 43785 89918 453 2 X 89140 46870 88336 48405 87504 49924 86646 3 58 89005 45347 89127 46896: 88322 48430 87490 49950 86632 2 59 438 1 1 89§92 45373 89x14 46921 883o8 48456 87476 49975 86617 I -M C. S. S. c. s. 1 s. C. S. S. C. S. S. C. S.' S. 64 Deff. 1 63 Deg. 62 Deg. 1 61 Deg. 1 60 Deg. 1 A TABLE OF NATURAL SINES. 69 M 30 Beg. 31 Beg. 32 Deg. 83 Deg. 34 Beg. M 60 S. C.S. S. 5x504 C.S. 857.7 S. C.S. S. C. S. S. C.S. 5oooo 866o3 52992 84805 54464 83867 55919 82904 I 50025 86588 5x529 85702 53017 84789 54488 8385. 55943 82887 U 2 5oo5o 86573 86559 5x554 85687 53o4. 84774 545.3 83835 55968 82871 3 50076 5x579 85672 53066 84759 54537 838,9 55992 82855 57 4 5oioi 86544 5 1 604 85657 5309. 84743 5456. 838o4 56oi6 82839 56 5 50126 86530 5x628 85642 53.15 84728 54586 83788 56040 82S22 55 6 5oi5i 865x5 5x653 85627 53.40 84712 54610 83772 56o64 82806 54 3 50176 86501 51678 856.2 53.64 84697 54635 83756 56o88 82790 53 5020I 86486 51703 85597 53.89 8468 X 54659 83740 56. .2 82773 52 9 50227 86471 5x728 85582 53214 84666 54683 83724 56.36 82757 5r 10 50252 86457 5.753 85567 53238 84650 54708 83708 56.60 82741 5o II 50277 86442 5.778 8555. 53263 84635 54732 836g2 56.84 82724 49 12 5o3o2 86427 5i8o3 85536 53288 846x9 54756 83676 56208 82708 48 i3 5o327 86413 5x828 8552. 533.2 84604 54781 83660 56232 82692 47 U 5o352 86398 5x852 855o6 53337 84588 54805 83645 56256 82675 46 i5 5o377 86384 5x877 85491 5336. 84573 54829 83629 56280 82659 45 i6 5o4o3 86369 51902 85476 53386 84557 54854 836.3 563o5 82643 44 \l 50428 86354 5.927 8546. 534.. 84542 54878 83597 56329 82626 43 50453 86340 5X932 85446 53435 84526 54902 83581 56353 56377 826.0 42 19 50478 86325 5x977 8543. 53460 845.1 54927 83565 82593 41 20 5o5o3 863x0 52002 85416 53484 84495 5495. 83549 5640. 82577 40 21 5o528 86295 8628X 52026 85401 53509 84480 54975 83533 56425 8256i 39 22 5o553 52o5i 85385 53534 84464 54999 835x7 56449 82544 38 23 50578 86266 52076 85370 53558 84448 55024 83 5o. 56473 82328 37 24 5o6o3 8625x 52IOI 85355 53583 84433 55048 83485 56497 5652. 823X1 36 23 50628 86237 52x26 85340 53607 84417 55072 8346q 82495 35 26 5o654 86222 52x5x 85325 53632 84402 55097 83453 56545 82478 34 27 50679 86207 52x75 853.0 53656 84386 55.2. 83437 56569 82462 33 28 50704 86x92 52200 85294 53681 84370 55.45 8342. 56593 82446 32 29 50729 86x78 52225 85279 53705 84355 55.69 834o5 566.7 82429 3x 3o 50754 86x63 5225o 85264 53730 84339 55194 83389 5664. 824.3 3o 3i 50779 86x48 52275 85249 53754 84324 552x8 83373 56665 82396 2Q 32 50804 86x33 52299 85234 53779 84308 55242 83356 56689 82380 28 33 50829 86x19 52324 852.8 53804 84292 55266 83340 567.3 82363 27 34 5o854 86x04 52349 852o3 53828 84277 5529X 83324 56736 82347 26 35 50879 86089 52374 85.88 53853 84261 553x5 833o8 56760 82330 25 36 50904 86074 gs 85.73 53877 84245 55339 55363 83292 56784 823.4 24 ll 50929 86059 85x57 53902 84230 83276 568o8 till] 23 50954 86045 52448 85.42 53926 84214 55388 83260 56832 22 39 50979 86o3o 52473 85x27 53951 84198 84182 55412 83244 56856 S2264 21 40 5 1 004 860 X 5 52498 85x12 53975 55436 83228 56880 82248 20 41 5io29 86000 52522 85096 85o8. 54000 84167 55460 832.2 56904 8223X ;? 42 5io54 85985 52547 54024 841 5. 55484 83x95 56928 82214 43 5io79 85970 52572 85o66 54049 84.35 55509 83x79 83.63 56952 82198 82.81 17 44 5iio4 85956 52597 85o5i 54073 84.20 55533 56976 16 45 51129 85941 5262X 85o35 54097 84.04 55557 83x47 57000 82x65 i5 46 5u54 85926 52646 85020 54122 84088 55581 83i3x 57024 82148 14 s 5ii79 II 5267X 85oo5 54146 84072 556o5 83xx5 57047 82X32 i3 5i2o4 52696 84989 541 7 1 84057 55630 lit 5707X 82. x5 X2 i^ 51229 52720 84974 54x95 84041 55654 57095 82098 82082 II 5o 5i254 85866 52745 84959 84943 54220 84025 55678 83o66 57119 57.43 10 5i 5x279 85851 52770 54244 84009 55702 83o5o 82065 9 8 52 5i3o4 85836 52794 84928 54269 83994 55726 83o34 57.67 82048 53 5i329 85821 528x9 849.3 84897 54293 83978 55750 83oi7 57.9. 82032 7 ^^ 5i354 858o6 52844 54317 83962 55775 83oo. 572.5 820x5 6 55 5x379 85792 52869 84882 54342 83946 55799 82985 57238 i:??? 5 56 5i4o4 85777 52893 84866 54366 83930 55823 82969 57262 4 ^2 51429 85762 52918 8485. 54391 t£ 55847 82953 57286 8.965 3 58 51454 85747 52943 84836 54415 5587X 82936 573.0 81949 2 5g M 5x479 C.S. 85732 S. 52967 84820 54440 C.S. 55895 82920 57334 C. S. 8x932 s. "M C.S. S. s. C.S. S. 59 Depr. 58 Beg. 57 Beg, i 56 Deg. 1 55 Deg. 70 A TABLE OF NATURAL SINES. 1 M 85 Deg. 86 Deg. 37 Deg. 88 Deg. 89 Deg. S. 1 c. s. 57358; 81915 S. G. S. S. C. S. S. C. S. S. C. S. M 58779 80902 60182 79864 6,^ 7880. 62932 Tnis 60 I 5738 8.899 58802 80885 6o2o5 79846 61589 78783 62955 77696 59 2 5740; 8.882 58826 80867 60228 79829 61612 78765 62977 77678 58 3 5742^ 8.865 58849 8o85o 6o25i 7981. 6i635 78747 63ooo 77660 57 4 57453 8.848 58873 80833 60274 79793 6.658 78729 63022 77641 56 5 57477 8.832 58896 808.6 60298 79776 6168. 78711 63045 77623 55 6 57501 8i8i5 58920 80799 6o32i 79758 61704 78694 63o68 77605 54 7 57524 8.798 58943 80782 60344 79741 61726 78676 63090 77586 53 8 57548 81782 58967 80765 60367 79723 61749 78658 63. .3 77568 52 9 57572 81765 58990 80748 60390 79706 6.772 78640 63.35 77550 5i 10 57596 1 81748 590.4 80730 60414 79688 61795 78622 63,58 77531 5o n 576,9 57643 1 8173. 59037 807.3 60437 79671 61818 78604 63 1 80 773.3 49 12 i 8.714 59061 80696 60460 79653 6.841 78586 63203 77494 48 i3 57667 8.698 59084 80679 60483 79635 61864 78568 63225 77476 47 14 57691 8168. 59.08 80662 6o5o6 79618 61887 78550 63248 77458 46 i5 577.5 81664 5913. 80644 60529 79600 61909 78532 6327. 77439 45 i6 57738 8.647 59.54 80627 6o553 79583 ■61932 785.4 63293 77421 44 17 57762 8.63. 59,78 806,0 60576 79565 61955 78496 633.6 77402 43 18 57786 81614 5920. 80593 60599 79547 61978 78478 63338 77384 42 19 578.0 'sMl 59225 80576 60622 79530 62001 78460 6336. 77366 41 20 57833 59248 8o558 60645 79512 62024 78442 63383 77347 40 21 'A^^ 8.563 59272 8o54i 60668 79494 62046 78424 63406 77329 li 22 5788. 8 1 546 59295 8o524 60691 79477 62069 78405 63428 77310 23 57904 8i53o 593.8 8o5o7 607,4 79459 62092 78387 6345. 77292 37 24 57928 8i5i3 59342 80489 60738 79441 62, ,5 78369 63473 77273 36 25 57952 81496 59365 80472 6076, 79424 62i38 7835. 63496 77255 35 26 57976 81479 59389 80455 60784 79406 62160 78333 635,8 77236 34 27 57999 81462 59412 80438 60807 79388 62183 783.5 63540 77218 33 28 58023 8.445 59436 80420 6o83o 79371 62206 78297 63563 77199 32 29 58047 81428 59459 80403 6o853 79353 62229 78279 63585 77.8. 3i 3o 58070 81412 59482 8o386 60876 79335 6223, 78261 636o8 77.62 3o 3i 58094 81395 59506 8o368 60899 79318 62274 78243 63630 77144 29 32 D8i,8 81378 59529 8o35, 60922 79300 79282 62297 78225 63653 77.25 28 33 58.41 8.36. 59552 80334 60945 62320 78206 63675 77107 27 34 58.65 8.344 59576 8o3i6 60968 79264 62342 78.88 63698 77088 26 35 58.89 81327 59399 80299 60991 79247 62365 78.70 63720 77070 23 36 58212 8i3.o 59622 80282 6.0,5 79229 62388 78,52 63742 77o5. 24 ll 58236 8.293 59646 80264 6io38 79211 62411 78,34 63765 77033 23 58260 81276 59669 80247 6.06. 79193 62433 78.. 6 63787 77014 22 39 58283 81259 59693 8o23o 6.084 79176 62456 78098 638.0 76996 21 40 58307 81242 597.6 80212 61.07 791 58 62479 78079 63832 76977 20 41 58330 8.225 59739 80,95 6.i3o 79,40 62502 78061 63854 76959 \i 42 58354 81208 59763 80.78 6.. 53 79,22 62J24 7S043 63877 76940 43 58378 81.91 59786 80.60 6.. 76 79,05 62547 78025 63899 7692. 17 44 5840. 8. .74 59809 80,43 6.. 99 79087 62570 78007 63922 76903 16 45 58425 8.. 57 59832 80.25 61222 79069 62592 77988 63944 76884 i5 46 58449 8.140 5o856 80.08 6.245 79o5i 62615 77970 68966 76866 14 47 58472 81123 59879 8009, 6.268 79033 62638 77952 68989 76847 i3 48 58496 8.106 59902 80073 6129, 790,5 62660 77934 6401. 76828 12 49 585 19 81089 59926 8oo56 6.3.4 789L 62683 779.6 64033 768.0 I . 5o 58543 81072 59949 8oo38 6.337 62706 77897 64056 76791 .0 5i 58567 8io55 59972 80021 6.36o 78962 62728 77879 64078 76772 9 52 58590 8.o38 59995 8ooo3 6.383 78944 6275. 7786, 64100 76754 8 53 586 1 4 8.02. 60019 79986 6.406 78926 62774 77843 64123 76735 7 54 58637 81004 60042 79968 61429 78908 62796 77824 64145 76717 6 55 5866. 80987 6oo65 7995. 6145. 7889, 628.9 77806 64167 76698 5 56 58684 80970 60089 79934 61474 78873 62842 77788 64190 76679 4 u 58708 80953 60, .2 799,6 6.497 78855 62864 77769 64212 76661 3 5873. 80936 6oi35 79899 6.520 78837 62887 77751 64234 76642 2 59 M 58755 80919 S. 60, 58 7988, S. 6 1 543 78819 S. 62909 c."s. 77733 S. 64256 C. S. 1 76623 S. 1 M C. S. C. S. C. S. i 54 De^. 1 53 Deg. 1 52 Deg. 51 Deg. 1 50 Deg. 1 A TABLE OF NATURAL SINES, M 40 Deg. 41 Deg. 42 Deg. 1 43 Deg. 44 D^cf. M 60 S. C. S. S. 656o6 1 C. S. ' 75471 S. C.S. S. C.S. bgm |C.S. 71934 64279 76604 66913 743x4 68200 73i3S I 64301 76586 60628 75452 66935 74295 68221 73116 69487 71914 59 2 64323 76567 65650 75433 66956 74276 68242 73096 69508 71894 58 3 64346 76548 65672 70414 66978 74256 68264 73076 69529 71873 37 4 64368 76530 65694 75395'! 66999 74237 68285 73o56 69549 71853 56 5 64390 765 II 65716 75375![ 67021 74217 683o6 73o36 69570 ^ 71833 55 6 64412 76492 i 65738 70356 67043 74198 68327 73016 69O91 ! 7l8l3 54 7 64435 76473 65739 75337 67064 74178 68349 72996 696.2 i 71192 53 8 64457 76455 65781 75318 67086 74159 68370 72976 69633; 71772 52 9 64479 76436 658o3 75209 70280 67107 74139 68391 72957 69654 71732 5i 10 64501 XI 65825 67129 74120 68412 72937 69675 71732 5o II 64324 65847 75261 67i5i 74100 68433 72917 72897 69696 69717 71711 S 12 64546 76380 60869 75241 67172 74080 68455 71691 i3 64568 7636i 65891 75222 67194 74061 68476 72877 69737 71671 47 14 64590 76342 65913 75203 67210 74041 68497 72807 69758 7i65o 46 i5 64612 76323 65935 75184 67237 74022 68018 72837 69779 7i63o 45 i6 64635 76304 65956 75i65 67258 74002 68539 72817 69800 71610 44 n 64657 76286 65978 75i46 67280 73983 68561 72797 69821 71590 43 i8 64679 76267 66000 75126 67301 73963 68582 72777 69842 71569 42 19 64701 76248 66022 75107 67323 73944 686o3 72757 69862 71549 41 20 64723 76229 66044 75088 67344 73924 68624 72737 69883 69904 71529 40 21 64746 76210 66066 75069 67366 73904 68645 72717 7i5o§ ll 22 64768 76192 66088 75o5o 67387 73885 68666 72697 69925 71488 23 64790 76173 66109 75o3o 67409 73865 68688 72677 69946 71468 37 24 64812 76154 661 3 1 7501 1 67430 73846 68709 72657 69966 71447 36 25 64834 76135 66 1 53 74992 67452 73826 68730 72637 69987 71427 35 26 64856 76116 66175 74973 67473 73806 68751 72617 70008 71407 34 ^l 64S78 76097 66197 66218 74953 67495 73787 68772 72597 70029 71386 33 28 64901 76078 74934 67516 73767 68793 72577 70049 71366 32 29 64923 76059 66240 74915 67538 73747 68814 72557 70070 71343 3i 3o 64945 76041 1 66262 74896 67509 73728 68835 72537 70091 71325 3o 3i 64967' 76022 66284 74876 67580 73708 68857 68878 72517 70112 7i3o5 S 32 64989* 76003 663o6 74857 67602 73688 72497 70i32 71284 33 65oii 759841 66327 74838 67623 73669 68899 72477 70153 71264 2 34 65o33 75965 66349 74818 67645 73649 68920 72457 70174 71243 ^35 65o55 75946 66371 74799 67666 73629 68g4i 72437 70193 71223 25 36 65077 75927, 66393 74780 67688 73610 68962 72417 70213 71203 24 37 65o99 t0^ 66414 74760 67709 73090 68983 72397 70236 71182 23 38 65l22 66436 74741 67730 73570 69004 72377 70237 71162 22 39 65J44 75870! 75851 66458 74722 67752 73551 69025 72337 70277 71141 21 40 65i66 66480 74703 67773 73531 69046 72337 70298 71121 20] 41 65:88, 75832 66501 74683 67795 73511 69067 72317 70319 71100 42 65210 758.3i 66523 74664 67816 73491 69088 72297 70339 71080 6 1 43 65232 75794) 66545 74644 67837 73472 69109 72277 7o36o 71009 17 44 65254 75775; 66066 74625 67859 73452 69130 72257 7o38i 71039 16 45 65276: 75756! 66588 74606 67880 73432 69151 72236 70401 71019 13 46 65298' 75738' 66610 74586 67901 73412 69172 72216 70422 70998 14 47 65320 75719 66632 74567 67923 73393 69193 72196 70443 70978 i3 48 65342 ?SJ 66653 7454s 67944 73373 69214 72176 70463 70937 12 49 65364 66675 74528 67965 73353 69235 72i56 70484 70937 70916 II 5o 65386, 75661 66697 74509 as 73333 69256 72i36 7o5o5 10 5i 654o8 75642: 66718 74489 73314 69277 72116 70525 70896 I 52 6543o 75623i 66740 74470 68029 73294 69298 72095 70546 70875 53 654021 7 5604 1 66762 7445 1 68o5i 73274 69319 72070 70567 70855 7 54 65474J 755851 66783 7443: 68072 73254 69340 72055 70587 70834 6 55 65496 75566 66800 74412 68093 73234 69361 72035 70608 70813 5 56 1 655i8 75547' 66827 74392 68ii5 732i5 69382 72015 70628 70793 4 ll ! 65540 755281 66848 74373 68i36 73195 69403 71990 70649 70772 3 f i 65562 730091 66870 74353 68107 73175 69424 71974 70670 70752 2 59 ! 65584 75490 66891 74334 68179 73i55 69445 71954 70690 70731 I 60 i 656o6 C. S. 75471 S. 66913 74314 68200 73i35 69466 C.S. 71934 S. 707 1 1 C.S. 70711 S. C. s. 1 S. C. S. S. 49 1 eg. 1 48 Deg. 1 47 Deg. 1 46 Deg. ! 45 Deg. 1 travetjst; taklf. a p B § iDeg. iDeg. 1 Deg. 1 Lat. Dep, 0.00 Lat. Dep. ~o:oi Lat. Dep. 1.00 1.00 1.00 0.01 2 2.00 0.01 2.00 0.02 2.00 0.03 2 3 3.00 0.01 3.00 0.03 3.00 0.04 3 4 4.00 0.02 4.00 0.03. 4.00 0.05 4 5 5.00 0.02 5.00 0.04 5.00 0.07 5 6 6.00 0.03 6.00 0.05 6.00 0.08 6 7 7.00 0.03 7.00 0.06 7.00 0.09 7 8 8.00 0.03 8.00 0.07 8.00 0.10 8 9 9.00 0.04 9.00 0.08 9.00 0.12 9 10 10.00 11.00 0.04 0.05 10.00 11.00 0.09 0.10 10.00 11.00 0.13 0.14 10 if 11 12 12.00 0.05 1 12.00 0.10 12.00 0.16 12 13 13.00 0.06 1 13.00 0.11 13.00 0.17 13 14 14.00 0.06 14.00 0.12 14.00 0.18 14 15 15.00 0.07 15.00 0.13 15.00 0.20 15 16 16.00 0.07 16.00 0.14 16.00 0.21 16 17 17.00 0.07 17.00 0.15 17.00 0.22 17 18 18.00 08 18 00 0.16 18.00 0.24 18 19 19.00 0.08 19.00 0.17 19.00 0.25 19 20 20.00 0.09 20.00 0.17 20.00 0.26 20 21 21.00 0.09 21.00 0.18 21.00 0.27 21 22 22.00 0.10 22.00 0.19 22.00 0.29 22 23 23.00 0.10 1 23.00 0.20 23.00 0..S0 23 24 24.00 0.10 24.00 0.21 24.00 0.31 24 25 25.00 0.11 25.00 0.22 25.00 0.33 25 26 26.00 0.11 26.00 0.23 26.00 0.34 26 27 27.00 0.12 27.00 0.24 27.00 0.35 27 28 28.00 0.12 28.00 0.24 28.00 0.37 28 29 29.00 0.13 29.00 0.25 29.00 0.38 29 30 30.00 0.13 30.00 0.26 30.00 0.39 30 31 31.00 0.14 31.00 0.27 31.00 0.41 31 32 32.00 0.14 32.00 0.28 32.00 0.42 32 33 33.00 0.14 83.00 0.29 33.00 0.43 33 34 34.00 0.15 34.00 0.30 34.00 0.45 34 35 35.00 0.15 35.00 0.31 35.00 0.46 35 36 36.00 0.16 36.00 0.31 36.00 0.47 36 37 37.00 0.16 37.00 0.32 37.00 0.48 37 38 38.00 0.17 38.00 0.33 38.00 0.50 38 39 39.00 0.17 39.00 0.34 39.00 0.51 39 40 41 40.00 41.00 0.17 0.18 40.00 0.35 0.36 40.00 41.00 0.52 0.54' 40 41 41.00 42 42.00 0.18 42.00 0.37 42.00 0.55 42 43 43.00 0.19 43.00 0.38 43.00 0.56 43 44 44.00 0.19 44.00 0.38 44.00 0.58 44 45 45.00 0.20 45.00 0.39 45.00 0.59 45 46 46.00 0.20 46.00 0.40 46.00 0.60 46 47 47.00 0.21 47.00 0.41 47.00 0.63 47 48 48.00 0.21 48.00 0.42 48.00 0.63 48 49 49.00 0.21 49.00 0.43 49.00 0.64 49 50 50.00 0.22 50.00 0.44 50.00 0.65 50 1 .2 Dep. 891 Lat. Deg. Dep. Lat. Dep. Lat. 1 89^ Deg. 1 I 89i Deg. TRAVERSE TAHLE. 9. iDeg. k Deg. IDeg. 1 1 Lat. Dep. Lat. Dep. Lai. 1 Dep. 51 Troo 0.22 51.00 0.45 51.00 "0767 ^ 52 52.00 0.23 52.00 0.45 52.00 0.68 52 53 53.00 0.23 53.00 0.46 53.00 0.69 53 54 54.00 0.24 54.00 0.47 54.00 0.71 54 55 55.00 0.24 55.00 0.48 55.00 0.72 55 56 56.00 0.24 56,00 0.49 56.00 0.73 56 57 57.00 0.25 57.00 0.50 57.00 0.75 57 58 58.00 0.25 58.00 0.51 57.99 0.76 68 59 59.00 0.26 59.00 0.51 58.99 0.77 59 60 60.00 0.26 6C.00 0.52 59.99 0.79 60 61 61.00 '0.27 61.00 0".53" 60.99 0.80 61 62 62.00 0.27 62.00 0.54 61.99 0.81 62 63 63.00 0.27 63.00 0.55 62.99 0.82 63 64 64.00 0.28 64.00 0.56 63.99 0.84 64 65 65.00 0.28 65.00 0.57 64.99 0.85 65 66 66.00 0.29 66.00 0.58 65.99 0.86 66 67 67.00 0.29 67.00 0.58 66.99 0.88 67 68 68.00 0.30 68.00 0.59 67.99 0.89 68 69 69.00 0.30 69.00 0.60 68.99 0.90 69 70 71 70.00 71 .00 0.31 0.31 70.00 71.00 0.61 69.99 0.92 0.93 70 71 0.62 70.99 72 72.00 0.31 72.00 0.63 71.99 0.94 72 73 73.00 0.32 73.00 0.64 72.99 0.96 73 74 74.00 0.32 74.00 0.65 73.99 0.97 74 75 75.00 0.33 75.00 0.65 74.99 0.98 75 76 76.00 0.33 76.00 0.66 75.99 0.99 76 77 77.00 0..34 77.00 0.67 76.99 l.Cl 77 78 78.00 0.34 78.00 0.68 77.99 1.02 78 79 79.00 0.34 79.00 0.69 78.99 1.03 79 80 81 80.00 0.35 0.35 80.00 81.00 0.70 0.71 79.99 80.99 1.05 80 81 81.00 1.06 82 82.00 0.36 82.00 0.72 81.99 1.07 82 83 83.00 0.36 83.00 0.72 82.99 1.09 83 84 84.00 0.37 84.00 0.73 83.99 1.10 84 85 85.00 0.37 85.00 0.74 84.99 1.11 85 86 86.00 0.38 86.00 0.75 85.99 1.13 86 87 87.00 0.38 87.00 0.76 86.99 1.14 87 88 88.00 0.38 88.00 0.77 87.99 1.15 88 89 89.00 0.39 89.00 0.78 88.99 1.16 89 90 91 90.00 91.00 0.39 90.00 91.00 0.79 89.99 90.99 1.18 1.19 90 91 0.40 0.79 92 92.00 0.40 92.00 0.80 91.99 1.20 92 93 93.00 0.41 93.00 0.81 92.99 1.22 93 94 94.00 0.41 94.00 0.82 93.99 1.23 94 95 95.00 0.41 95.00 0.83 94.99 1.24 95 96 96.00 0.42 96.00 0.84 95.99 1.26 96 97 97.00 0.42 97.00 0.85 96.99 1.27 97 98 98.00 0.43 98.00 0.86 97.99 1.28 98 99 99.00 0.43 99.00 0.86 98.99 1.30 99 100 100.00 0.44 Lat. 100.00 Dep. 0.87 Lat. 99.99 Dep. 1.31 100 i .2 o Dep, Lat. 89! Deg. 89A Deg. 39i Deg. TRAVF.RSE TABiE. 1 1 Deg, H Deg. 11 Deg. 1 11 Deg. 1 Lat. Dep. 6702 Lat. D^p. Lat. 1 Dop. ■ Lat. Dep. 1.00 1.00 0.02 1.00 0.03 1.00 ~~0Ai3 2 2.00 0.03 2.00 0.04 2.00 0.05 2.00 0.06 3 3.00 0.05 3.00 0.07 3.00 0.08 3.00 0.09 3 4 4.00 0.07 4.00 0.09 4.00 0.10 4.00 0.12 4 5 5.00 0.09 5.00 0.11 5.00 0.13 5.00 0.15 5 6 6.00 0.10 G.OO 0.13 6.00 0.16 6.00 0.18 6 7 7.00 0.12 7.00 0.15 7.00 0.18 7.00 0.21 7 8 8.00 0.14 8.00 0.17 8.00 0.21 8.00 0.25 8 9 9.00 0.16 9.00 0.20 9.00 0.24 9.00 0.28 9 10 10.00 0.17 10.00 0.22 10.00 11.00" 0.26 10.00 0.31 10 11 H.OO 0.19 il.OO 0.24 0.28 10.99 0.34 11 12 12.00 0.21 12.00 0.26 12.00 0.31 11.99 0.37 12 13 13.00 0.23 13.00 0.28 13.00 0.34 12.99 0.40 13 14 14.00 0.24 14.00 0.31 14.00 0.37 13.99 0.43 14 15 15.00 0.26 15.00 0.33 14.99 0.39 14.99 0.46 i5 16 16.00 0.28 16.00 0.35 15.99 0.42 15.99 0.49 16 17 17.00 0.30 17.00 0.37 16.99 0.45 16.99 0.52 17 18 18.00 0.31 18.00 0.39 T7.99 0.47 17.99 0.55 18 19 19.00 0.33 19.00 0.41 18.99 0..50 18.99 0.58 19 20 21 20.00 I 0.35 1 20.00 21 .00 0.44 0.46 19.99 0.52 0.55 19.99 0.61 20 21.00 0.37 20.99 20.99 0.64 21 22 22.00 0.38 21.99 0.48 21.99 0.58 21.99 0.67 22 23 23.00 0.40 22.99 0.50 22.99 0.60 22.99 0.70 23 24 24.00 0.42 23.99 0.52 23.99 0.63 23.99 0.73 24 25 25 . 00 0.44 24.99 0.55 24,99 0.65 24.99 0.76 25 26 2G.00 0.45 25.99 0.57 25.99 0.68 25.99 0.79 26 27 27.00 0.47 26.99 59 26.99 0.71 26.99 0.83 27 28 28.00 0.49 27.99 0.61 27.99 0.73 27.99 0.86 28 29 29.00 0.51 28.99 0.63 28.99 0.76 28.99 0.89 29 30 31 30.00 0.52 29.99 30.99 0.65 29.99 30.99 0.79 29.99 30.99 0.92 30 31.00 0.54 0.68 0.81 0.95 31 32 32.00 0.56 31.99 0.70 31.99 0.84 31.99 0.98 32 33 ■ 32 . 99 0.58 32.99 0.72 32.99 0.86 32.98 1.01 33 34,33.99 0.59 33.99 0.74 33.99 0.89 33.98 1.04 34 35 34.99 0.61 34.99 0.76 34.99 0.92 34.98 1.07 35 36 ^5.99 0.63 35.99 0.79 35.99 0.94 35.98 1.10 35 37 36.99 0.05 36.99 0.81 36.99 0.97 36.98 1.13 37 38 37.99 0.66 37.99 0.83 37.99 0.99 ' 37.98 1.16 38 39 38.99 0.68 38.99 0.85 38.99 1.02 138.98 ! 1.19 39 40 41 39.99 40.99 0.70 39.99 0.87 39.99 40.99 1.05 1.07 39.98 40.98 , 1 .22 40 "41 0.72 40.99 0.89 1 25 42 41.99 0.73 41.99 0.92 41.99 1.10 41.98 1 28 1 42 43 42 . 99 0.75 42.99 0.94 42.99 1.13 42.98 1.31 43 44 43.99 0.77 43.99 0.96 43.99 1.15 43.98 l.b4 44 45 44.99 0.79 44.99 0.98 44.99 1.18 44.98 1.37 45 46 45.99 0.80 45.99 1.00 45.99 1.20 45.98 1.40 46 47 46.99 i 0.82 46.99 1.03 46.99 1.23 46.98 1.44 47 48 47.99 0.84 47.99 1.05 47.98 1.26 47.98 1.47 49 49 48.99 0.86 48.99 1.07 48.98 1.28 48.98 1.50 49 50 49.99 0.87 49.99 1.09 49.98 _1-31. 49.98 Dep. 1.53 50 5 a .2 Dep. Lat. Dep. Lat. Dep. Lat. Lat. 89 Deg. 881 Deg. 881 Deg. 88iDeg. TRAVERSE TABLE. 1 3 ? "51 iDeg. U Deg. H Deg. 1| Deg. D s Lat. Dep. Lat. Dep. 1.11 Lat. Dep. Lat. Dep. 50.99 0.89 50.99 .=)0.98 nr34 "50.W 1.56 51 52 51.99 0.91 51.99 1.13 51.98 1.36 51.98 1..59 52 53 52 99 0.92 52.99 1.10 52 . 98 1.39 52.98 1.62 53 54 53 99 0.94 53.99 1.18 53 . 98 1.41 53.97 1.65 54 55 54 99 0.96 54.91' 1.20 54.98 1.44 54.97 1.68 55 56 55.99 0.98 55.99 1.22 55.98 1.47 55.97 1.71 56 57 56.99 0.99 56.99 1.24 56 m 1.49 56.97 1.74 57 58 57.99 1.01 57.99 1.27 h7 . 98 1.62 57.97 1.77 58 59 58.99 1.03 58.99 1.29 58.98 1.54 58.97 1.80 59 60 61 59.99 1.05 59.99 1.31 59.98 1.67 69.97 1.83 60 60.99 1.06 60.99 60.98 1.60 60.97 1.86 61 62 61.99 1.08 61.99 1.35 61.98 1.02 61.97 1.89 62 63 62.99 1.10 62.99 1.37 62.98 1.65 62.97 1.92 63 64 63.99 1.12 63.98 1.40 63.98 1.68 63.97 1.95 64 65 64.99 1.13 64.98 1.42 64.98 1.70 64.97 1.99 65 66 65.99 1.15 65.98 1.44 85.98 1.73 05.97 2.02 66 67 66.99 1.17 66.98 1.46 66.98 1.75 66.97 2.05 67 68 67.99 1.19 67.98 1.48 67.98 1.78 67.97 2.08 68 69 68.99 1.20 68.98 1.51 68.98 1.81 68 97 2.11 69 70 71 69.99 70.99 1.22 69.98 1..53 69.98 1.83 69.97 2.14 70 71 1.24 70.98 1..55 70.98 1.86 70.97 2.17 72 71.99 1.26 71.98 1.57 71.98 1.88 71.97 2.20 72 73 72.99 1.27 72.98 1.59 72.97 1.91 72.97 2.23 73 74 73.99 1.29 73.98 1.61 73.97 1.94! 73.97 2.26 74 75 74.99 1.31 74.98 1.64 74.97 1.961 74.97 2.29 75 76 75.99 1.33 75.98 1.66 75.97 1.99 75.96 2.32 76 77 76.99 1.34 76.98 1.68 76.97 2.02 76.96 2.35 77 78 77.99 1.36 77.98 1.70 77.97 2.04 77.96 2.38 78 79 78.99 1..38 78.98 1.72 78.97 2.07 78.96 2.41 79 80 81 79.99 80.99 1.40 79.98 80.98 1.75 79.97 2.09 79.96 2.44 80 1.41 1.77 80.97 2.12 80.96 2.47 81 82 81.99 1.43 81.98 1.79 81.97 2.15 81.96 2.50 82 83 82.99 1.45 82.98 1.81 82.97 2.17 82.96 2.53 83 84 83.99 1.47 83.98 1.83 83.97 2.20 83.96 2.57 84 85 84.99 1.48 84.98 1.85 84.97 2.23 84.96 2.00 85 86 85.99 1..50 85.98 1.88 85.97 2.26 85.96 2.63 86 87 86.99 1.52 86.98 1.90 86.97 2.28 86.96 2.66 87 88 87.99 1.54 87.98 1.92 87.97 2.30 87.96 2.69 88 •89 88.99 1.55 88.98 1.94 88.97 2.33 88.96 2.72 89 90 91 89.99 1.57 89.98 1.96 1.99 89.97 2.36 89.96 2.75 ' 2.78 90 91 90.99 1.59 90.98 90.97 2.38 90.96 92 91.99 1.61 91.98 2.01 91.97 2.41 91.98 2.81 92 93 92.99 1.62 92.98 2.03 92.97 2.43 92.96 2.84 93 94 93.99 1.64 93.98 2.05 93.97 2.46 93.96 2.87 94 95 94.99 1.66 94.98 2.07 94.97 2.49 94.96 2.90 95 96 95.99 1.68 95.98 2.09 95.97 2.51 95.96 2.94 96 97 96.99 1.69 96.98 2.12 96.97 2.. 54 96.95 2.96 ; 97 98 97.99 1.71 97.98 2.14 97.97 2.57 97.95 2.99 98 99 98.98 1.73 98.98 2.16 98.97 2.59 98.95 3.02 99 100 Q 99.98 1.75 1 99.98 2.18 99.97 2.62 99.95 3.05 |lO0 Dep. ,L... Dep. Lat. Dep. 88X Lat. Deg. Dep. Lat. \i 89 Deg. 881 Deg. 1 8Bi Deg. li JQ TRAVERSE TABLE. 1 r 2Deg. 2^ Deg. 2i Deg, 21- Deg. m 1 Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 1.00 0.03 1.00 0,04 1.00 0.04 1.00 0.05 1 2 2.00 0.07 2.00 0.08 2.00 0.09 2.00 0.10 2 3 ! 3.00 0,10 3.00 0.12 3.00 0,13 3.00 0.14 3 4 4.00 0.14 4.00 0.16 4.00 0.17 4.00 0.19 4 5 5.00 0.17 5.00 0.20 5.00 0,22 4.99 0.24 5 8 6 6.00 0.21 6.00 0.24 5.99 0.26 5,99 0.29 6 7 7.00 0.24 6.99 0.27 6.99 0.31 6,99 0.34 7 8 7.99 0.28 7.99 0.31 7.99 0.35 7.99 0.38 8 9 8.99 0.31 8.99 0.35 8.99 0,39 8.99 0.43 9 10 9.99 0.35 9.99 0.39 9.99 0,44 S.99 0.48 10 if 11 10.99 0.38 10.99 0.43 10.99 0,48 10.99 0.53 12 11.99 0.42 11.99 0.47 11.99 0.52 11.99 0.58 12 13 12.99 0.45 12.99 0.51 12.99 0.57 12.99 0.62 13 14 13.99 0.49 13.99 0.55 13.99 0.61 13.98 0.67 14 15 14.99 0.52 14.99 0.59 14.99 0.65 14.98 0.72 15 16 15.99 0.56 15.99 0.63 15.99 0.70 15.98 0.77 16 17 16.99 0..39 16.99 0.67 16.98 0.74 16.98 0.82 17 18 17.99 0.63 17.99 0.71 17.98 0,79 17.98 0.86 18 19 18.99 0.66 18.99 0.75 18.98 0.83 18.98 0.91 19 20 19.99 0.70 19.98 0.79 19.98 0.87 19.98 0.96 20 21 20.99 0.73 20 . 98 0.82 20.98 0.92 20.98 1.01 21 22 21.99 0.77 21.98 0.86 21.98 0.96 21.97 1.06 22 23 22.99 O.bO 22 . 98 0.90 22.98 1.00 22.97 1.10 23 24 123.99 0.84 23.98 0.94 23.98 1.05 23.97 1.15 24 25 24.98 0.87 24.98 0.98 24.98 1.09 24.97 1.20 25 26 25. OH 0.91 25.98 1.02 25.98 1.13 125.97 1.25 26 27 26.98 0.94 26.98 1.06 26.97 1.18 26.97 1.30 27 28 127.98 0.98 27.98 1.10 27.97 1.22 27.97 1.34 28 29 128.98 1.01 28.98 1.14 28.97 1.26 28.97 1..39 29 30 1 29.98 1.05 29.98 1.18 29.97 1.31 29.97 1.44 30 31 31 30.98 1.08 30.98 1.22 30.97 1.35 130.96 1.49 32 31.98 1.12 31.98 1.26 31.97 1,40 31.96 1..54 32 33 32.98 1,15 32.97 1,30 32.97 1,44 32.96 1.58 33 34 33.98 1.19 33.97 1.33 33.97 1.48 33.96 1.63 34 35 34.98 1.22 34.97 1.37 34.97 1.53 34.96 1.68 35 36 35.98 1.26 35.97 1.41 35.97 1.57 35.96 1.73 36 37 36.98 1.29 36.97 1.45 36.96 1.61 36.96 1.78 37 38 37.98 1.33 37.97 1.49 37.96 1,66 37.96 1.82 38 39 38.98 1,36 38.97 1.53 38.96 1,70 38.96 1.87 39 40 41 39.98 40.98 1.40 1.43 39.97 1,57 39.96 1.75 39.95 1.92 40 ^41 40,97 1.61 40.96 1.77 40.95 1.97 42 41.97 1.47 41,97 1.65 41,96 1.83 41.95 2.02 42 43 42.97 1.50 42.97 1,69 42,96 1.88 42.95 2.06 43 44 43.97 1.54 43.97 1,73 43.96 1.92 43.95 2.11 44 45 44.97 1,57 44.97 1.77 44.96 1,96 44.95 2.16 45 46 45.97 1.61 45.96 1,81 45.96 2.01 45.95 2.21 46 47 46.97 1,64 46.96 1,85 46.96 2,05 46.95 2.25 47 48 47.97 1,68 47.96 1.88 47.95 2,09 47.95 2.30 48 49 48.97 1.71 48.96 1.92 48.95 2.14 48.94 2.35 49 50 149.97 1.74 49.96 1^ 49.95 2.18 49.94 2.40 _50 © s 8 Dep Lat. Dep. Lat, Dep. Lat. Dep. Lat. 5 88 1 3eg. 871 Deg. 87| Deg. 87i Deg. TRAVERSE TABLE. 1 "5l 2 Deg. 2i Deg. 2^ Deg. 21 Deg. 111- Lat. Dep. Lat. Dep. 1- " Dep. Lat. Dep. 50.97 1.78 50.96 2.00 50.95 2.22 50.94 2.45 52 51.97 1.81 51.96 2.04 51.95 2.27 51.94 2.50 52 53 52.97 1.85 52.96 2.08 52.95 2.31 52.94 2.54 I 53 54 53.97 1.88 1 53.96 2.12 53.95 2.36 j 53.94 2.59 54 65 54.97 1.92 1 54.96 2.16 54.95 2.40 54.94 2.64 55 56 55.97 1.95 il 55.96! 2.20 55.95 2.44 55.94 2.69 ! 56 57 56.97 1.99 , 56.96 1 2.24 56.95 2.49 56.93 2.73 57 58 57.96 2.02 i 57.96 2.28 57.94 2.53 57.93 2.78 58 59 58.96 2.06 58.95! 2.32 58.94 2.57 58.93 2.83 59 60 61 59.96 2.09 59.95 j 2.36 59.94 2.62 2.66 59.93 2.88 60 -61 60.96 2.13 60,95 2.39 60.94 60.93 2.93 62 61.96 2.16 61.951 2.43 61.94 2.70 61.93 2.97 62 63 62.96 2.20 62.95 1 2.47 62.94 2.75 62.93 3.02 63 64 63.96 2.23 63.95! 2.51 63.94 2.79 63.93 3.07 64 65 64.06 2.27 64.95: 2.55 164.94 2.84 64.93 3.12 65 66 65.96 2.30 65.95! 2. .59 165.94 2.88 65.92 3.17 66 67 06.96 2.34 66.95 2.63 66.94 2.92 66.92 3.21 67 68 67.96 2.37 67.95 2.67 67.94 2.97 67.92 3.26 68 69 68.96 2.41 68.95 2.71 68.93 3.01 68.92 3.31 69 70 71 69.96 2.44 69.95 1 2.75 69.93 3.05 69.92 3.36 70 71 70.96 2.48 70.95 2.79 70.93 3.10 70.92 3.41 72 71.96 2.51 71.94 2.83 71.93 3.14 71.92 3.45 72 73 72.96 2.55 72.94 2.87 72.93 3.18 72.92 3.50 73 74 73.95 2.58 73.94 1 2.91 73.93 3.23 73.91 3.55 74 75 74.95 2.62 74.94 2.94 74.93 3.27 74.91 3.60 75 76 75.95 2.65 75.94 2.98 75.93 3.31 75.91 3.65 76 77 76.95 2.69 76,94 3.02 76.93 3.36 76.91 3.70 77 78 77.95 2.72 77.94 3.06 77.93 3.40 77.91 3.74 78 79 78.95 2.76 78.94 3.10 78.92 3.45 78.91 3.79 79 80 81 79.95 2.79 79.94 3.14 79.92 3.49 79.91 3.84 3.89 80 81 80.95 2.83 80.94 3.18 80.92 3.53 80.91 82 81.95 2.86 81.94 3.22 81.92 3.58 81.91 3.93 82 83 82.95 2.90 82.94 3.26 82.92 3.62 82.90 3.98 83 84 83 . 95 2.93 83.94 3.30 83.92 3.66 83.90 4.03 84 85 84.95 2.97 84.93 3.34 84.92 3.71 84.90 4.08 85 86 85.95 3.00 85.93 3.38 85.92 3.75 85.90 4.13 86 87 86.95 3.04 86.93 3.42 86.92 3.79 86.90 4.17 87 88 87.95 3.07 87.93 3.45 87.92 3.84 87.90 4.22 88 89 88.95 3.11 88.93 3.49 88.92 3.88 88.90 4.27 89 90 91 89.95 3.14 89.93 3.53 89.91 3.93 89.90 4.32 90 91 90.95 3.18 90.93 3.57 90.91 3.97 90.90 4.37 92 91.94 3.21 91.93 3.61 91.91 4.01 91.89 4.41 92 93 92.94 3.25 92.93 3.65 92.91 4.06 92.89 4.46 93 94 93.94 3.28 93.93 3.69 93.91 4.10 93.89 4.51 94 95 94.94 3.32 94.93 3.73 94.91 4.14 94.89 4.56 95 96 95.94 3.35 95.93 3.77 95.91 4.19 95.89 4.61 96 97 96.94 3.39 96.93 3.81 96.91 4.23 96.89 4.65 97 98 97.94 3.42 97.92 3.85 97.91 4.27 97.89 4.70 98 99 98.94 3.46 98.92 3.89 98.91 4.32 98.89 4.75 99 100 99.94 3.49 99.92 3.93 99.91 4.36 99.88 _4.8^ 100 s a .2 Q T .1 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 88 1 )eg. 871 Deg. 8^ Deg. 87^ Deg. TKAVEKSE TABLE. c % 3 ? 1 3Deg. 3i Deg. 3^ Lat. Deg. Dep. j 31 Deg. f Lat. Dep. Lat. Dep. Lat. Dep. 1 1.00 0.05 1. 00 0.06 1.00 0.06 1.00 ""oToe" 1 2 2.00 0.10 2.00 0.11 2.00 0.12 2.00 0.13! 2 3 3.00 0.16 3.00 0.17 2.99 0.18 2.99 0.20' 3 4 3.99 0.21 3.99 0.23 3.99 0.24 3.99 0.26' 4 5 4.99 0.26 4.99 0.28 4.99 0.31 4.99 0.33 5 6 5.99 0.31 5.99 0.34 5.99 0.37 5.99 0.39 fi 7 6.99 0.37 6.99 0.40 6.99 0.43 6.99 0.46 7 8 7.99 0.42 7.99- 0.45 7.99 0.49 7.98 0.52 8 9 8.99 0.47 8.99 0.51 8.98 0..'i5 8.98 0.59 9 10 11 9.99 0,53 9.98 0.57 9.98 0.61 9.98 0.65 10 11 10.98 0.58 10.98 0.62 10.98 0.67 10.98 0.72 13 11.98 0.63 11.98 0.68 11.98 0.73 11.97 0.78 12 13 12.98 0.68 12.98 0.73 12.98 0.79 12.97 0.85 13 14 13.93 0.73 13.98 0.79 13.97 0.85 13.97 0.92 14 15 14.98 0.79 14.98 0.85 14.97 0.92 14.97 0.98 15 16 15.98 0.84 15.97 0.91 15.97 0.98 15.97 1.05 16 17 16.98 0.89 16.97 0.90 16.97 1.04 16.96 1.11 17 18 17.98 0.94 17.97 1.02 17.97 1.10 17.96 1.18 18 19 18.98 0.99 18.97 1.08 18.96 1.16 18.96 1.24 19 ■20 21 19.97 1.05 19.97 1.13 19.96 1.22 19.96 1.31 20 20.97 1. 10 20.97 1.19 20.96 1.28 20.96 1.37 21 22 21.97 1.15 21.96 1.25 21.96 1.34 21.95 1.44 22 23 22.97 1.20 22.96 1.30 22.96 1.40 22.95 1..50 23 24 23.97 1.26 23.96 1.36 23.96 1.47 23.95 1.57 24 25 24.97 1.31 24.96 1.42 24.95 1.53 24.95 1.64 25 26 25.96 1.36 25.96 1.47 25.95 1.59 25.94 1.70 26 27 26.96 1.41 26.96 1.53 26.95 1.65 26.94 1.77 27 28 27.96 1.47 27.95 1.59 27.95 1.71 27.94 1.83 28 29 28.96 1.52 28.95 1.64 28.95 1.77 28.94 1.90 29 30 31 29.96 1.57 29 . 95 1.70 29.94 1.83 29.94 1.96 2.03 30 31 30.96 1.62 30.95 1.76 30.94 1.89 30.03 32 31.96 1.67 31.95 1.81 31.94 1.95 31.93 2.09 32 33 33.95 1.73 32.95 1.87 32.94 2.01 32.93 2.16 33 34 33.95 1.78 33.95 1.93 33.94 2.08 33.93 2.22 34 35 34.95 1.83 34.94 1.98 34.93 2.14 34.92 2.29 35 36 35.95 1.88 35.94 2.04 35.93 2.20 35.92 2.35 36 37 36.95 1.94 36.94 2.10 36.93 2.26 36.92 2.42 37 38 37.95 1.99 37.94 2.15 37.93 2.32 37.92 2.49 38 39 .38.95 2.04 38.94 2.21 38.93 2.38 38.92 2.55 39 40 41 39.95 2.09 39.94 2.27 39.93 2.44 39.91 2.62 40 40.94 2.15 40.93 2.32 40.92 2.. 50 40.91 2.68! 41 1 42 41.94 2.20 41.93 2.38 41.92 2.56 41.91 2.75 42 43 42.94 2.25 42.93 2.44 42.92 2.63 42.91 2.81 43 44 43.94 2.30 43.93 2.49 43.92 2.69 43.91 2.88 44 45 44.94 2.36 4-1.93 2.55 44.92 2.75 44.90 2.94 45 46 45.94 2.41 45.93 2.61 45.91 2.81 45.90 3.01 46 47 46.94 2.46 46.92 2.66 46.91 8.87 46.90 3.07 47 48 47.93 2.51 47.92 2.72 47.91 2.93 47.90 3.14 48 49 48.93 2.56 48.92 2.78 48.91 2.99 48.90 3.20 49 50 " i .2 a 49.93 2.62 49.92 2.83 49.91 3.05 49.89 3.27 _^ Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. J .2 Q 87'Deg. 86J Deg. 86i Deg. m\ Deg. TRAVERSE TABLK. [■■ — 3 Deg. 3i Deg. ■y. Deg, CI Deg. C B 1 Lat. Dep. Lat. Dep. 1 J^at. Dep. Lat. Dep. 51 '50.93 i 2.07 50.92 2.89 : 50.90 3-11 "50^89 3.34 61 52 51.93 2.72 51.92 2.95 51.90 3.17 51.89 3.40 52 53 52.93 2.77 52.91 3.00 .52.90 3.24 52.89 3.47 53 54 53.93 2.83 .53.91 3.06 53.90 3.30 53,88 3.53 54 55 54.92 2. 88 54.91 3.12 54.90 3.36 54.88 3.60 55 56 55 . 92 2.93 55.91 3.17 155.90 3.42 55.88 3.66 50 57 56.92 2.98 66.91 3.23 56.89 3.48 .56.88 3 73 57 58 57.92 3.04 57.91 3.29 57.89 3.54 57.88 3.79 58 59 58.92 3.09 58.91 3.34 58.89 3.60 58.87 3.86 59 60 59.92 3.14 59.90 3.40 59.89 3.66 59.87 3.92 60 61 ,6U.92 3.19 60.90 3.46 60.89 3.72 60.87 3.99 61 62 61.92 3.24 61.90 .3.51 3.57 161.88 3,79 61.87 4.05 62 63 62.91 3.30 62.90 [62.88 3.85 62,87 4.12 63 64 63.91 3.35:; 63.90 3.63 63.88 3.91 63.86 4.19 64 65 64.91 3.40 1 64.90 3.69 64.88 3.97 64. S6 4.25 65 60 65.91 3.45 65.89 3.74 65.88 4.03 65.86 4.32 66 07 66.91 3.51 66.89 3.80 66.88 4>09 66.86 4.38 67 68 67.91 3.56 67.89 3.86 67.87 4.15 67.85 4.45 68 69 68.91 3.61 68.89 3.91 68.87 4.21 68.85 4.51 69 70 71 69.90 3.66 ij 69.89 3.72 i! 70.89 3.97 69.87 4.27 4.33 69.85 70.85 4.58 70 71 70.90 4.03 70.87 4.64 72 71.90 3.77 71.88 4.08 71.87 4.40 71.85 ,4.71 72 73 72.90 3.82 72.88 4.14 72.86 4.46 72.84 4.77 73 74 73.90 3.87 73.88 4.20 73,86 4.52 73.84 4.84 74 75 74 . 90 3.93 74.88 4.25 74.86 4,58 74,84 4.91 75 7n 75.90 3.98 75.88 4.31 75.86 4.64 75,84 4.97 76 77 76.89 4.03 76.88 4.37 76.86 4,70 76.84 5.04 77 78 77.89 4.08 77.87 4.42 77.85 4.76 77,83 5.10 78 79 78.89 4.13 78.87 4.48 78.85 4.82 78,83 5.17 79 80 81 79.89 80.89 4.19 4.24 79,87 4.54 79.85 4.88 79,83 5.23 80 81 80.87 4.. 59 80.85 4.94 80,83 5.30 82 81.89 4.29 81.87 4.65 81.85 5.01 81,82 5.36 82 83 82.89 4.34 82.87 4.71 82,85 5,07 82,82 5.43 83 84 83.88 4.40 83.86 4.76 83.84 5,13 83.82 5.49 84 85 84.88 4.45 84.86 4.82 84.84 5.19 84.82 5.56 85 86 85.88 4.50 85.86 4-88 85,84 5,25 85.82 5.62 86 87 86.88 4.55 86.86 4.93 86.84 5,31 86.81 5.69 87 88 87.88 4.61 87.86 4.99 87.84 5,37 87.81 5.76 88 89 88.88 4.66 88.86 5,05 88.83 5.43 88.81 5.82 89 90 91 89.88 4.71 89.86 5.10 89.83 90.83 5.49 89.81 5.89 90 "9T 90.88 4.76 90.85 5.16 5.56 90.81 5 . 95 92 91.87 4.81 91.85 5.22 91.83 5.62 91.80 6.02 92 93 92.87 4.87 92.85 5.27 92.83 5.68 92.80 6.08 93 94 93.87 4.92 93.85 5.33 93.82 5.74 93.80 6.15 94 95 94.87 4.97 94.85 5.39 94.82 5.80 94.80 6.21 95 96 95.87 5.02 95.85 5.44 95.82 5.86 95.79 6.28 96 97 96.87 5.08 96.84 5.50 96.82 5.92 96.79 6., ^4 97 98 97.87 5.13 97.84 5.56 97.82 5.98 97.79 6.41 98 99 98.86 5.18 98.84 5.61 98.82 6.04 98.79 6.47 99 100 8 s a 99.86 5.23 99.84 5.67 99,81 6.10 99.79 6.54 100 Dep. Lat. Dep. Lat. Dep. Lat. Dop. Lat. 1 87 1 )eg. 861 Deg. SGi Deg. 86i Deg. 10 TRAVERSE TABLE. 1 4 Deg. 4iDeg. H Deg. 41 Deg. 9 1 Lat. Dep. Lat. Dep.. Lat, Dep. Lat. Dep. ~^l 1.00 0.07 1.00 0.07 1.00 0.08 1.00 0.08 2 2.00 0.14 1.99 0.15 1.99 0.16 1.99 0.17 3 2.99 0.21 2.99 0.22 1 2.99* 0.24 2.99 0.25 .3 4 3.99 0.28 3.99 0.30 1 3.99 0.31 3.98 0.33 4 5 4.99 0.35 4.99 0.37 1 4.98 0.39 4.98 0.41 5 6 5.99 0.42 5.98 0.44 5.98 0.47 5.98 0.50 6 7 6.98 0.49 8.98 0.52 6.98 0..55 6.97 0.58 7 8 7.98 0.56 7.98 0.59 7.98 0.63 7.97 0.06 8 9 , 8.98 0.63 8.98 0.67 8.97 0.71 8.97 0.75 9 10 11 9.98 0.70 9.97 0.74 9.97 0.73 0.86 9,97 0.83 10 11 10.97 0.77 10.97 0.82 10.97 10,96 0.91 12 11.97 0.84 11.97 0.89 11. qe 12.96 0.94 11,96 0.99 12 13 12.97 0.91 12.96 0.96 1.02 12.96 1.08 J3 14 13.97 0,98 13.96 1.C4 13.96 1.10 13.95 1.16 14 15 14.96 1.05 14.96 1.11 14.95 1.18 14.95 1.24 15 16 15.96 1.12 15.96 1.19 15.95 1.26 15.95 1.32 16 17 16.96 1.19 16.95 1.26 16.95 1.33 16.94 1.41 17 18 17.96 1.26 17.95 1.33 17.94 1.41 17.94 1.49 18 19 18.95 1.33 18.95 1.40 18.94 1.49 18.93 1..57 19 20 21 19.95 1.40 19.95 1.48 1.56 19.94 1.57 19.93 1.66 20 21 20.95 1.46 20.94 20.94 1.65 20.93 1.74 22 21.95 1.53 21.94 1.63 21.93 1.73 21.92 1.82 22 23 22.94 1.60 22.94 1.70 22.93 1.80 22.92 1.90 23 24 23.94 1.67' 23.93 1.78 23.93 1.88 23.92 1.99 24 25 24.94 1.74 24.93 1.85 24.92 1.96 24.91 2.07 25 26 25.94 1.81 25.93 1.93 25.92 2.04 26.91 2,15 26 27 26.93 1.88 26 . 93 2.00 26.92 2.12 26.91 2,24 27 28 27.93 1.95 27.92 2.08 27.91 2.20 27.90 2,32 28 29 28.93 2.02 28.92 2.15 28.91 2.28 28.90 2,40 29 30 31 29.93 2.09 29.92 2.22 "2730 29.91 2.35 29.90 2.48 30 31 30.92 2.16 30.91 30.90 2.43 '30.89 2.57 32 31.92 2.23 31.91 2.37 31.90 2.51 31.89 2.65 32 33 32.92 2.30 32.91 2.45 32.90 2.59 32.89 2.73 33 34 33.92 2.37 33.91 2.52 33.90 2.67 33.88 2.82 34 35 34.91 2.44 34.90 2.59 34.89 2.75 34.88 2.90 35 36 35.91 2.51 35.90 2.67 35.89 2.82 35.88 2.98 36 37 36.91 2.58 36.90 2.74 38.89 2.90 36.87 3.06 37 38 37.91 2.65 37.90 2.82 37.88 2.98 37.87 3.15 38 39 38.90 2.72 38.89 2.89 38.88 3.06 38.87 3.23 39 40 41 39.90 40.90 i 2.79 39.89 2.96 39.88 3.14 39.86 3.31 40 41 1 2.86 40.89 3.04 40.87 3.22 40.86 3.40 42 41.90 1 2.93 41.88 3.11 41.87 3.30 41.86 3.48 42 43 42.90 3.00 42.88 3.19 42.87 3.27 42.85 3.56 43 44 43.89 ': 3.07 43.88 3.26 43.86 3.45 43.85 3.64 44 45 44.89 3.14 44.88 3.33 44.86 3.53 44.85 3.73 45 46 45.89 3.21 45.87 3.41 45.86 3.61 45.84 3.81 46 47 46.89 3.28 46.87 3.48 46.86 3.69 46.84 3.89 47 48 47.88 3.35 47,87 3.56 47.85 3.77 47.84 3.97 48 49 48.88 8.42 48.87 3.63 48.85 3.84 48.83 4.06 49 _50 1 49.88 3.49^ 49.86 3,71 49.85 3.92 49.83 4.14 J>0 c i Dep. Lat. Dep. Lat. Dep. 1 Lat. Dep. Lat. 86 Deg. 85i Deg, 85i Deg. 85i Deg. TRAVERSE TABLE. 11 5 n 4 Dog. 4i Deg. ^Deg. 4| Deg. s ? 51 Lat. Dep. Lat. 1 Dep. Lat. Dep. Lat. Dep. 50.88 3.56 150.86 3.78 50.84 4.00 50.82 4.22 52 51.87 3.63 :\ 51.86 .3.85 51.84 4.08 51.82 4.31 52 53 52.87 3.70 1 52.85 3.93 52.84 4.16 52.82 4.39 53 54 53.87 3.77 11 .53.85 4.00 53.83 4.24 53.81 4.47 54 55 54.87 3.84 , 54.85 4.08 54.83 4.32 54.81 1 4. 55 55 56 55.86 3.91 , 55.85! 4.15 .55.83 4.39 55.81 4.64 56 57 56.86 3.98 i 56.84 4.22 56.82 4.47 56.80 1 4.72 57 58 57.86 4.05: 57.84 4.30 57.82 4.55 57.80 4.80 58 59 58.86 4.12 :[ 58.84 4.37 58.82 4.63 58.80 4.89 59 60 61 59.85 4.19 4.26 59.84 4.45 59.82 4.71 59.79 4.97 60.79, 5.05 60 61 60.85 60.83 4.. 52 60.81 4.79 62 61.85 4.32 i; 61.83 4.59 61.81 4.86 61.79 5.13 62 63 62.85 4.39 ii 62.83 4.67 62.81 4.94 62.78 5.22 63 64 63.84 4.46 1 63.82 4.74 63.80 5.02 63.78 5.30 64 65 64.84 4.53 1 64.82 4.82 64.80 5.10 64.78 5.38 65 66 65.84 4.60 65.82 4.89 65.80 5.18 65.77 5.47 66 67 66.84 4.67 1 66.82 4.97 66.79 5.26 66.77 5.55 67 68 67.83 4.74 67.81 5.04 07.79 5.34 67.77 5.63 68 69 68. S3 4.81 i 68.81 5.11 68.79 5.41 68.76 5.71 69 70 71 69.83 70.83 4.88 69.81 5.19 69.78 5.49 69.76 5.80 70 71 4.95 1! 70.80 5.26 70.78 5.57 70 . 76 5.88 72 71.82 5.02 1; 71.80 5.34 71.78 5.65 71.75 5.96 72 73 72.82 5.09 72.80 5.41 72.77 5.73 72.75 6.04 73 74 73.82 5.16 1,73.80 ■ 5.48 73.77 5.81 73.75 6.13 74 75 74.82 5.23 74.79 5.56 74.77 5.88 74.74 6.21 7.5 76 75.81 5.30 75.79 5.63 75.77 5.96 75.74 6.29 76 77 76.81 5.37 ' 76.79 5.71 76.76 6.04 76.74; 6.38 77 78 77.81 5.44 77.79 5.78 77.76 6.12 77.73 6.46 78 79 78.81 5.51 178.78 5.85 78.76 6.20 78.73 6.54 79 80 81 79.81 5.58 (79.78 ! 80.78 5.93 79.75 6.28 79.73 6.62 SO Si 80.80 5.65 6.00 80.75 6.36 80.72 6.71 82 81.80 5.72 181.78 6.08 81.75 6.43 81.72 6.79 82 83 82.80 5.79 : 82.77 6.15 82.74 6.51 82.71 6.87 83 84 83.80 5.86 83.77 6.23 83.74 6.59 83.71 6.96 84 85 84.79 5.93 84.77 6.30 84.74 6.67 84.71 7.04 85 86 85.79 6.00 85.76 6.37 85.73 6.75 85.70 7.12 86 87 86.79 6.07 86.76 6.45 85.73 6.83 86.70 7.20 87 88 87.79 6.14 87.76 6.52 87.73 6.90 87.70 7.29 88 89 88.78 6.21 88.76 6.60 88.73 6.98 88.70 7.37 89 90 91 89.78 6.28 89.75 i 6.67 i 90.75 1 6.74 89.72 7.06 89.69 7.45 90 91 90.78 6.35 90.72 7.14 90.69 7.54 92 91.78 6.42 91.75 1 6.82 1 91.72 7.22 91.68 7.62 92 93 92.77 6.49 92.74 6.89 92.71 7.30 92.68 7.70 93 94 93.77 6.56 93.74 6.97 93.71 7.38 93.68 7.78 94 95 94.77 6.63 94.74 7.04 94.71 7.45 94.67 7.87 95 96 95.77 6.70 95.74 1 7.11 i 95 . 70 7.53 95.67 7.95 96 97 96.76 6.77 96.73, 7.19 96.70 7.61 96.67 8.03 97 98 97.76 6.84 97.73 1 7.26 97.70 7.69 97.66 8.12 98 99 98.76 6.91 98.73 7.34 98.69 7.77 98.66 8.20 99 100 1 99.76 6.98 99.73: 7.41 99.69 7.85 99.66 8.28 100 Dep. 86 1 Lat. Dep. Lat. Dep. 851 ] Lat. Dep. Lat. 1 fisi Deg. Oeg. 85^ Deg. 12 TRAVERSE TABLE. 5 Deg. 5i Deg. 5-1 Deg. 5JDeg. j r Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. S I 1.00 0709" 1.00 0.09 1.00 0.10 0.99 0.10 1 2 1.99 0.17 1.99 0,18 1.99 0.19 1.99 0.20 2 3 2.99 0.26 2.99 0.27 2.99 0.29 2.98 0.30 3 4 3.98 0.35 3.98 0.37 3.98 0.38 3.98 0.40 4 5 4.98 0.44 4.98 0.46 4.98 0.48 4.97 0.50 f. 6 5.98 0.52 5.97 0.55 5.97 0.58 5.97 0.60 6 7 6.97 0.61 0.97 0.64 6.97 0.67 6.96 0.70 7 8 7.97 0.70 7.97 0.73 7.06 0.76 7.96 0.80 8 9 8.97 0.78 8.96 0.82 8 96 0.86 8.95 0.90 9 10 9.96 0.87 9.96 0.92 9.95 0.96 9.95 1.00 Ji 11 10.96 0.96 10.95 1.01 10.95 1.05 10.94 1.10 111 12 11 . 95 1.05 11.95 1.10 11.94 1.15 11.94 1.20 12 .; 13 12.95 1.13 12.95 1.19 12.94 1.25 12.93 1.30 13, 14 13.95 1.22 13.94 1.28 13.94 1.34 13.93 1.40 14; 15 14.94 1.31 ! 14.94 1.37 14.93 1.44 14.92 1..50 15 i 16 15.94 1.39 1 15.93 1.46 15.93 1.53 15.92 1.60 16 17 16.94 1.48 1 16.93 1.56 16.92 1.63 16.91 1.70 17 13 17.93 1..57i 17.92 1.65 17.92 1.73 17.91 1.80 18 19 18.93 1.66 1 18.92 1.74 18.91 1.82 18.90 1.90 19 20 19.92 1.74! ~lT83"; 19.92 1.83 19.91 1.92 19.90 20.89 2.00 20 2\ 21 20.93 20.91 1.92 20.90 "STOT 2.10 22 21.92 1.92: 21.91 2.01 21.90 2.11 21.89 2.20 22 23 22.91 2.00 22.90 2.10 22.89 2.20 22.88 2.30 23 24 23.91 2.09 23 . 90 2.20 23.89. 2.30 1 23.88 2.40 24 25 24.90 2.18 24.90 2.29 24.88 2.40 24.87 2.50 25 26 25.90 2.27 25.89 2.38 25.88 2.49 25.87 2.60 26 27 20. 90 2.35 26.89 2.47 26.88 2.59 26.86 2.71 27 28 27.89 2.44 27.88 2.56 27.87 2.68 27.86 2.81 28 29 28.89 2.53 28.88 2.65 28.87 2.78 28.85 2.91 29 30 31 29.89 2.61 29.87 2.75 " 2.84 29.86 2.88 29.85 3.01 30 30.88 2.70 30.87 30.86 2.97 30.84 3.11 31 32 31.88 2.79 31.87 2.93 31.85 3.07 31.84 3.21 32 33 32.87 2.88 32.86 3.02 32.85 3.16 32.83 3.31 33 34 33.87 2.9C 33.86 3.11 33.84 3.26 33.83 3.41 34 35 34.87 3.05 34.85 3.20 34.84 3.35 34.82 3.51 35 36 35.86 3.14 35 . 85 3.29 35.83 3.45 35.83 3.61 36 37 36.86 3.22 36.84 3.39 36.83 3.55 36.81 3.71 37 38 37.86 3.31 37.84 3.48 37.83 3.64 37.81 3.81 38 39 38.85 3.40 38.84 3.57 .38.82 3.74 38.80 3.91 39 40 39.85 40.84 3.49 3.57 39.83 3.66 39.82 3.83 3.93 39.80 4.01 40 41 40.83 3.75 40.81 40.79 4.11 42 41.84 3.66 41.82 3.84 41.81 4.03 41.79 4.21 42 43 42.84 3.75 42.82 3.93 42.80 4.12 42.78 4.31 43 44 43.83 3.83 43.82 4.03 43.80 4.22 43.78 4.41 44 45 44.83 3.92 44.81 4.12 44.79 4.31 44.77 4.51 45 46 45.82 4.01 45.81 4.21 45.79 4.41 45.77 4.61 46 47 46.82 4.10 46.80 4.30 46.78 4.. 50 46.76 4.71 47 48 47.82 4.18 47.80 4.39 47.78 4.60 47.76 4.81 48 49 48.81 1 4.27 48,79 4.48 48.77 4.70 48.75 4.91 49 50 49.81 I 4.36 49.79_ 4.58 49.77 4.79 49.75 JAL _50 Dep. ', Lat. Dep. Lat. Dep. Lat, Dep. Lat. 1 s 85 Deg. 841 De,ir. m Deg 84^ Deg. TRAVKIiSK TABLl- 13 51 5 Deg. 5i Deg. H Deg. Lat. Deg-. C Lat. Dep. Lat. Dep. Lat. Dep. DepT; i 5."lT 61 50.81 4.44 50.79 4.67 50.77 4.89 50.74 52 51.80 4.53 51.78 4.76 51.76 4.98 51.74 5.21 52 53 52.80 4.62 52.78 4.85 52.76 5.08 62.73 5.31 5,. 54 53.79 4,71 53.77 4.94 53.75 5.18 .53.73 5.41 5; 65 .'■>1.V9 4.79 54.77 5.03 54.75 5.27 .54.72 5.51 i 5:. 56 55.79 4.88 55.77 5.12 55.74 5.37 .55.72 5.61 i 5ii 57 56.78 4.97 56.76 5.22 56.74 5.46 5«.71 5.71 57 58 57.78 5.06 57.76 5.31 57.73 5.56 57.71 5.81 58 59 58.78 5.14 .58.75 5.40 58.73 5.65 58.70 5.91 59 60 61 59.77 5.23 59.75 5.49 59.72 60.72 5.75 59.70 6.01 60 60.77 5.32 60.74 5.58 5.86 60.69 6.11 61 62 61.76 5.40 61.74 5.67 61.71 5.94 61.69 6.21 62 63 62.76 5.49 62.74 5.76 62.71 6.04 62.68 6.31 63 64 63.76 5.58 63.73 5.86 63.71 6.13 63.68 6.41 64 65 64.75 5.67 64.73 5.95 64.70 6.23 64.67 6.51 65 66 65.75 5.75 65.72 6.04 65.70 6.33 65.67 6.61 66 67 66.75 5.84 66.72 6.13 66.69 6.42 66.66 6.71 67 68 67.74 5.93 67.71 6.22 67.69 6.52 67.66 6.81 68 69 68.74 6.01 68.71 6.31 68.68 6.61 68.65 6.91 69 70 71 69.73 6.10 69.71 6.41 69.68 6.71 69.65 7.01 70 70.73 6.19 toTto" 6.50 70.67 6.81 70.64 7.11 71 72 71.73 6.28 71.70 6.59 71.67 6.90 71.64 7.21 7-/ ^3 72.72 6.36 72.69 6.68 72.66 7.00 72.63 7.31 7S 74 73.72 6.45 73.69 6.77 73.66 7.09 73.63 7.41 74 75 74.71 6.54 74.69 6.86 74.65 7.19 74.62 7.51 75 76 75.71 6.62 75.68 6.95 75.65 7.28 75.62 7.61 76 77 76.71 6.71 76.68 7.05 76.65 7.38 76.61 7.71 77 78 77.70 6.80 77.67 7.14 77.64 7.48 77.61 7.81 78 79 78.70 6.89 78.67 7.23 78.64 7.57 78.60 7.91 79 80 81 79.70 80.69 6.97 79.66 7.32 79.63 7.67 79.60 8.02 80 7.06 80.66 7.41 80.63 7.76 80.59 8.12 81 82 81.69 7.15 81.66 7.50 81.62 7.86 81.59 8.22 82 83 82.68 7.23 82.65 7.59 82.62 7.96 82.58 8.32 83 84 83.68 7.32 83.65 7.69 83.61 8.05 83.58 8.42 84 85 84.68 7.41 84.64 7.78 84.61 8.15 84.. 57 8.52 85 86 85.67 7.. 50 85.64 7.87 85.60 8.24 85.57 8.62 86 87 86.67 7.58 86.64 7.96 86.60 8.34 86.. 56 8.72 87 88 87.67 7.67 87.63 8.05 87.59 8.43 87.56 8.82 88 89 88.66 7.76 88.63 8.14 88.59 8.53 88.55 8.92 89 90 91 89.66 7.84 89.62 8.24 89.59 8.63 89.55 9.02 90 90.65 7.93 90.62 8.33 90.68 8.72 90.54 9.12 91 92 91.65 8.02 91.61 8.42 91.58 8.82 91.54 9.22 92 93 92.65 8.11 92.61 8.51 92.57 8.91 92.53 9.32 93 94 93.64 8.19 93.61 8.60 93.57 9.01 93.53 9.42 94 95 94.64 8.28 94.60 8.69 94.56 9.11 94.52 9.52 95 96 95.63 8.37 95.60 8.78 95.56 9.20 95.52 9.62 96 97 96.63 8.45 96.59 8.88 96.55 9.30 96.51 9.72 97 98 97.63 8.54 97.59 8.97 97.55 9.39 97.51 9.82 98 99 98.62 8.63 98.59 9.06 98.54 9.49 98.50 9.92 99 100 1 Q 99.62 8.72 99.58 9.15 99.54 9.58 99.50 10.02 100 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. J 85 1 )eg. 84iDeg. 84i Deg. 84i Deg. 20 14 TRAVERSE TABLE. 6D ... 64 Deg. 6iDeg. H Deg. O 3 P 1 Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. ~T 0.99 0.10 0.99 0.11 0.99 0.11 0.99 0.12 2 1.99 0.21 1.99 0.22! 1.99 0.23 1.99 0.24 2 3 2.98 0.31 2.98 0.33 2.98 0.34 2.98 0.35 3 4 3.98 0.41 3.98 0.44 3.97 0.45 3.97 0.47 4 5 4.97 0.52 4.97 0.54 4.97 0.57 4.97 0.59 5 6 5.97 0.63 5.96 0.65 5.96 0.68 5.96 0.71 6 7 6.96 0.73 6.96 0.76 6.96 0.79 6.95 0.82 7 8 7.96 0.84 7.95 0.87 7.95 0.91 7.94 0.94 8 y 8.95 0.94 8.95 0.98 8.94 1.02 8.94 1.06 9 10 11 9.95 10.94 1.05 9.94 1.09 9.94 1.13 1.25 9.93 1,18 1.29 10 11 1.15 10.93 1.20 10.93 10.92 12 11.93 1.25 11.93 1.31 11.92 1.36 11.92 1.4J 12 13 12.93 1.36 12.92 1.42 12.92 1.47 12.91 1..53 13 14 13.92 1.46 13.92 1.52 13.91 1.59 13.90 1.65 14 15 14.92 1.57 14.91 1.63 14.90 1.70 14.90 1.76 15 16 15.91 1.67 15.90 1.74 15.90 1.81 15.89 1.88' 16 17 16.91 1.78 16.90 1.85 16.89 1.92 16.88 2 00 i 17 18 17.90 1.88 17.89 1.96 17.88 2.04 17.88 2.12 1 18 19 18.90 1.99 18.89 2.07 18.88 2.15 18.87 2.23 i 19 20 19.89 2.09 19.88 2.18 19.87 2.26 19.86 2.35! 20 21 20,88 2.20 20.88 2.29 20.87 2.38 20.85 2.47 21 22 21.83 2.30 21.87 2.40 21.86 2.49 21.85 2.59 22 23 22.87 2.40 22.86 2.50 22.85 2.60 22.84 2.70 23 24 23.87 2.51 23.86 2.61 23.85 2.72 23.83 2.82 24 25 24.86 2.61 24.85 2.72 24.84 2.83 24.83 2.94 25 26 25.86 2.72 25.85 2.83 25.83 2.94 25.82 3.06 26 27 26.85 2.82 26.84 2.94 26.83 3.06 26.81 3.17 27 28 27.85 2.93 27.83 3.05 27.82 3.17 27.81 3.29 28 29 28.84 3.03 28.83 3.16 28.81 3.28 28.80 3.41 29 30 '31 29.84 3.14 29.82 3.27 29.81 3.40 29.79 3.. 53 30 30.83 3.24 30.82 3.37 30.80 3.51 30.79 3.64 1 31 1 32 31 82 3.34 31.81 3.48 31.79 3.62 31.78 3.76 32 33 32.82 3.45 32.80 3.59 32.79 3.74 32.77 3.88 33 34 .33.81 3.55 33.80 3.70 33.78 3.85 33.76 4.00 34 35 34.81 3.66 34.79 3.81 34.78 3.96 34.76 4.11 35 36 35.80 3.76 35.79 3.92 35.77 4.08 35.75 4.23 36 37 36.80 3.87 36 . 78 4.03 36.76 4.19 36.75 4.35 37 38 37.79 3.97 37.77 4.14 37 . 76 4.30 37.74 4.47 38 38.79 4.08 38.77 4.25 38.75 4.41 38.73 4.. 58 39 40 39.78 4.18 39.76 4.35 39.74 4.53 39,72 4.70 4.82 40 41 41 40.78 4.29 40.76 4.46 40.74 4.64 40.72 42 41.77 4.39 41.73 4.57 41.73 4.76 41.71 4.94 42 43 42.76 4.49 42.74 4.68 42.72 4.87 42.70 5.05 i 43 44 43.76 4.60 43.74 4.79 43.72 4.98 43.70 5.17, 44 45 44.75 4.70 44.73 4.90 44.71 5.09 44.69 5.29 45 46 45.75 4.81 45.73 5.01 45.70 5.21 45.68 5.41 1 46 47 46.74 4.91 46 . 72 5.12 46.70 5.32 46.67 5.52 47 48 47.74 5.02 47.71 5.23 47.69 5.43 47.67 5.64 48 49 48.73 5.12 48.71 6.34 48.69 5.55 48.06 5.76 49 50 49.73 5.23 49.70 5.44 49.68 5.66 49.65 5.88 _50^ ■s Dop. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 1 " Q 84 Deg. 83.1 Deg. 831 Deg. 83i Deg.- 5 TRAVERSE TABLK. 15 1 ~51 6Deg. 6i Deg. 61 Deg 61 Deg. p I 51 Lat. Dep. Lat. Dep. Lat 50.67 Dep. Lat. Dep. 50.72 5.33 50.70 5.55 5.77 50.65 5.99 52 51.72 5.44 51.69 5.66 51.67 5.89 51.64 6.11 52 53 52.71 5.. 54 52.68 5.77 .52.66 6.00 52.63 6,23 53 51 .53.70 5.64 \53.68 5.88 53.65 6.11 53.63 6.35 54 5:5 .54.70 5.75 54.67 5.99 54.65 6.23 54.62 6.46 55 56 .55.69 5.85 55.67 6.10 55.64 6.34 1 55.61 6.58 56 57; 56.69 5.96 56.66 6.21 56.63 6.45 56.60 6.70 57 58 ! 57.68 6.06 57.66 6.31 57.63 6.57 67.60 6.82 58 59 58.68 6.17 58.65 6.42 .58.62 6-68 58.59 6.93 59 _fiO 59.67 6.27 59.64 6.53 59.61 6.79! 59.. 58 7.05 60 "61 61 60.67 6.. 38 60.64 6.64 50.61 6.91I 60.58 7.17 62 61.66 6.48 61.63 6.75 61.60 7.02 61.57 7.29 62 63 62.65 6.59 62.63 6.86 62.60 7.13! 62.. 56 7.40 63 64 63.65 6.69 63.62 6.97 63.59 7.25, 63.56 7.52 64 65 64.64 6.79 64.61 7.08 64.58 7.36 64.55 7.64 65 66 65.64 6.90 65.61 7.19 65.58 7.47 1 65.54 7.76 66 67 66.63 7.00 66.60 7.29 66.57 7 58 66.54 7.88 67 68 67.63 7.11 67.60 7.40 67.56 7.70 67.53 7.99 68 69 68 . 62 7.21 68 . 59 7.51 68.56 7.81 68.52 8.11 69 70 69.62 7.32 69.58 7.62 69.55 7.92 69.51 8.23 70 71 "71 70.61 7.42 70.58 7.73 70.54 8.04 70.51 8.. 35 72 71.61 7.53 71., 57 7.84 71.. 54 8.15 71.50 8.46 72 73 72.60 7.63 72.57 7.95 72.. 53 8.26 72.49 8.58 73 74 73.. 59 7.74 73.50 8.06 73.. 52 8.38 73.49 8.70 74 75 74.59 7.84 74.55 8.17 74.52 8.49 74.48 8.82 75 76 75.58 7.94 75.. 55 8.27 75.51 8.60 75.47 8.93 76 77 76.58 8.05 76.54 8.38 76.51 8.72 76.47 9.05 77 78 77.57 8.15 77.. 54 8.49 77.50 8.83 77.46 9.17 78 79 78.. 57 8.26 78.53 8.60 78.49 8.94 78.45 9.29 79 80 81 79.56 8.36 79.53 8.71 79.49 80.48 9.06 79.45 9.40 80 81 80.56 8.47 80.52 8.82 -9:17 80.44 9.52 82 81.. 55 8.57 81.51 8.93 81.47 9.28 81.43 9.64 82 83 82.55 8.68 82.51 9.04 82.47 9.40 82.42 9.76 83 84 83.54 8.78 83.50 9.14 H3.46 9.51 83.42 9.87 84 85 84.53 8.88 84.. 50 9.25 84.45 9.62 84.41 9.99 85 86 85.53 8.99 85.49 9.36 85.45 9.74 85.40 10.11 86 87 86.52 9.09 86.48 9.47 86.44 9.85 86.40 10.23 87 88 87.52 9.20 87.48 9.58 87.43 9.96 87.39 10.34 88 89 88.51 9.30 88.47 9.69 88.43 10.08 88.38 10.46 89 90 91 89.51 9.41 89.47 9.80 89.42 10.19 89.38 10.58 90 91 90.50 9.51 90.46 9.91 90.42 10.30 90.37 10.70 92 91.50 9.62 91.45 10.02 91.41 10.41 191.30 10.81 92 93 92.49 9.72 92.45 10.12 92.40 10.. 53 '92.36 10.93 93 94 93.49 9.83 93.44 10.23 93.40 10.64 193.. 35 11.05 94 95 94.48 9.93 94.44 10.34 94.39 10.75 : 94.. 34 11.17 95 96 95.47 10.03 95.43 10.45 95.38 10.87 95.33 11.28 96 97 96.47 10.14 96.42 10.56 96.38 10. 9S 96.33 11.40 97 98 97.46 10.24 97.42 10.67 97.37 11.09 97.32 11.52 98 99 98.46 10.35 98.41 10.78 98.. 36 11.21 98.31 11.64 99 100 99.45 10.45 99.41 10.89 99.36 11.32 99.31 11.75 100 g 1 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. If. 84 Deg. 831 Deg. 83| Deg. 83i Deg. a 16 TRAVERSE TABLE. 5 1 P 1 7Deg. 7i Deg. 71 Deg 71 Deg, 1 Lat. Dep. Lat. 0.99 Dtp. Lat. Dep. Lat. Dep. 0.99 0.12 0.13 0.99 0.13 0.99 0.13 "Y 2 1.99 0.24 1.98 0.25 1.98 0.20 1.98 0,27 2 3 2.98 0.37 2.98 0.38 2.97 0.39 2.97 0.40 3 4 3.97 0.49 3.97 0.50 3.97 0.52 3.96 0,54 4 5 4.96 0.61 4.96 0.63 4.96 0.65 4.95 0,67 5 6 5.96 0.73 5.95 0.76 5.95 0.78 5.95 0,81 6 7 6.95 0.85 0.94 0.88 6.94 0.91 6.94 0,94 7 8 7.94 0.97 7.94 1.01 7.93 1.04 7.93 1.08 8 9 8.93 1.10 8.93 1.1 1- 8.92 1.17 8.92 1.21 9 10 11 9.93 10.92 1.22 9.92 1.26 9.91 1.31 9.91 1.35 10 1.34 10.91 1.39 10.91 1.44 10.90 1,48 11 12 il.9i 1.46 11.90 1.51 11.90 1.57 11.89 1,62 12 13 12.90 1.58 12.90 1.64 12.89 1.70 12,88 1,75 13 14 13.90 1.71 13.89 1.77 13.88 1.83 13.87 1.89 14 15 14.89 1.83 14.88 1.89 14.87 1.96 14.86 2.02 15 16 15.88 1.95 15.87 2.02 15.86 2.09 15.85 2,16 161 17 16.87 2.07 16.86 2.15 16.85 2.22 16.84 2,29 17 18 17.87 2.19 17.86 2.27 17.85 2.35 17.84 2.43 18 19 18.86 2.32 18.85 2.40 18.84 2.48 18,83 2.56 19 20 21 19.85 2.44 i 19.84 2.52 19.83 2.61 19,82 2.70 20 21 20.84 2.56 20.83 2.65 20.82 2.74 20.81 2.83 22 21.84 2.68 21.82 2.78 21.81 2.87 21,80 2.97 22 23 22.83 2.80 22.82 2.90 22.80 3.00 22.79 3.10 23 24 23.82 2.92 23.81 3.03 23.79 3.13 23.78 3.24 24 25 24.81 3.05 24.80 3.15 24.79 3.26 24,77 3.37 25 26 25.81 3.17 25.79 3.28 25.78 3.39 25.76 3.51 26 27 20.80 3.29 26.78 3.41 26.77 3.52 26.75 3.64 27 28 27.79 3.41 27.78 3.53 27.76 3.65 27.74 3.78 28 29 28.78 8.53 28.77 3,66 28.75 3.79 28.74 3.91 29 30 29.78 3.06 29.76 3.79 29.74 3.92 29.73 4,05 30 31 30.77 3.78 30.75 3.91 30.73 4.05 30.72 4.18 31 32 31.76 3.90 31.74 4.04 31.73 4.18 31.71 4,32 32 33 32.75 4.02 32.74 4.16 32.72 4.31 32.70 4,45 33 34 33.75 4.14 33.73 4.29 33.71 4.44 33.69 4,58 34 35 34.74 4.27 3'1.72 4.42 34.70 4.57 34.68 4,72 35 36 35.73 4.39 35 .7 1 4.54 35 . 69 4.70 35.67 4,85 36 37 36.72 4.51 36.70 4.67 36 . 68 4.83 36.66 4.99 37 38 37.72 4.C3 37.70 4.80 37.67 4.96 37.65 5,12 38 ^ 38.71 4.75 38.69 4.92 .38.67 B.09 38,64 5.26 39 40 41 39.70 40.70 4.87 5.00 39 . 68 5.05 39.66 40.65 5.22 .39,63 5.39 40 41 40.67 5.17 5.35 40.63 5.. 53 42 41.09 5.12 41.66 5.30 41.64 5.48 41,62 5.66 42 43 42.68 5.24 42.66 5.43 42.03 5.61 42.61 5.80 43 44 43.67 5.30 43.65 5.55 43.62 5.74 43.60 5.93 44 45 44.67 5.48 44.64 5.68 44.62 5.87 44.. 59 6.07 45 46 45 . 66 5.61 45.63 5.81 45.61 6.00 45.58 6.20 46 47 46.65 5 . 73 46.62 5.93 46.60 6.13 ; 46.57 6.34 47 48 47.64 5.85 47.62 6.06 47.59 6.27 47.. 56 6.47 48 49 48.63 5.97 48.61 6.18 48.58 6.40 1 48.55 6.61 49 50_ c Q 49.63 6.09 49.60 6.31 49.57 _6.53^ 49.54 6.74 _50 Dep, Lat. Dep. Lat. Dep. Lat. Dep. Lat. 1 .2 P 83 Deg. 821 Deg. 821 Deg. m Deg. Til AVERSE TABLE. 17 7Deg. n Deg. n Deg- 7$ Deg. 1 "51 Lat. Dep. Lat. Dep. Lat, Dep. Lat. Dep. 50,62 6.22 50.59 6.44 .50.56 6.66 "50:53^ 6.88 52 51. Gl 6.34 51.58 6.56 51,56 6,79 51.53 7.01 1 .52 1 53 52.60 6.46 ,52.58 6.69 ,52,55 6,92 52.52 7.15 531 54 53.60 6.58 53,57 6.81 53.54 7.05 .53.51 7.28 54 55 54.59 6.70 54,56 6.94 54.53 7.18 54.50 7.43 55 56 55.58 6,82 55,55 7,07 55.52 7.31 55.49 7.55 56 57 56.58 6.95 56 , 54 7.19 56.51 7.44 56.48 7.69 57 58 57.57 7.07 57.54 7.32 57.50 7,57 57.47 7.82 58 59 .53.56 7.19 58.53 7.45 58.50 7.70 58.46 7.96 59 60 61 59.55 7.31 59.52 7.57 59.49 7.83 59.45 8.09 60 60.55 7.43 60.51 7.70 60.48 7,96 60.44 8.23 61 62 61.54 7.56 61.50 7.82 61.47 8,09 61.43 8.3H 62 63 62.. 53 7.68 62.50 7.95 62.46 8.22 62.42 8.50 63 64 63.52 7.80 63.49 8.08 63.45 8.35 63.42 8.63 64 65 64.52 7.92 64.48 8,20 64.44 8.48 64.41 8.77! 65 66 65.51 8.04 05.47 8,33 65.44 8,61 65.40 8.90 1 66 67 66 50 8.17 66.46 8.40 66.43 8,75 66.39 9 . 04 1 67 68 67.49 8.29 67.46 8.58 67.42 8.88 67.38 9. It 68 69 68.49 8.41 68.45 8.71 68.41 9,01 68.37 9.30 69 70 71 69.48 8,53 69.44 8.83 69,40 9.14 69.36 9.44 70 70.47 8,65 70.43 8.96 70.39 9.27 70.35 9.57 71 72 71.46 8.77 71,42 9.09 71.38 9.40 71.34 9.71 72 73 72.46 8.90 72.42 9.21 72 38 9.. 53 72.33 9.84 73 74 73.45 9.02 73.41 9.34 73,37 9.66 73.32 9.98 74 75 74.44 9.14 74.40 9.46 74,36 9,79 74.31 10,11 75 76 75.43 9.26 75.39 9.59 75,35 9.92 75.31 10,25 76 77 76.43 9.38 I 76.. 38 9,72 76.34 10.05 76.30 10,38 77 78 77.42 9.51 77.38 9.84 77,33 10.18 77.29 10.52 78 79 78.41 9.63 78.37 9.97 78,32 10.31 78.28 10.65 79 80 81 79.40 9.75 79.36 10.10 79.32 8073T 10.44 79.27 10.79 80 81 80.40 9.87 80.35 10.22 10.57 80.26 10,92 82 81.39 9.99 81. .34 10,35 81.30 10.70 81.25 11.06 82 83 82.38 10.12 82,34 10,47 82.29 10.83 82.24 11.19 83 84 83.37 10.24 83.33 10.60 83.28 10.96 83.23 11.33 84 85 84.37 10.36 84.32 10.73 84.27 11.09 84.22 11.46 85 86 85.36 10.48 85.31 10.85 85.26 11.23 85.21 11.60 86 87 86.35 10.60 86.30 10.98 86.26 11.36 86.21 11.73 87 88 87.34 10.72 87.30 11,11 87.25 11,49 87.20 11.87 88 89 88.34 10,85 88.29 11.23 88.24 11.62 88.19 12.00 89 90 ^1 89.33 10 97 89.28 11.36 89.23 11.75 89.18 12.14 90 90.32 11,09 90.27 11,48 90.22 11.88 90.17 12.27 91 92 91.31 11,21 91.26 11.61 91.21 12.01 91.16 12,41 92 93 92.31 11.33 92.26 11.74 92.20 12.14 92.15 12.54 93 94 93.30 11.46 93.25 11.86 93.20 12.27 93.14 12.68 94 95 94.29 11.58 94.24 11.99 94.19 12.40 94.13 12.81 95 96 95.28 11.70 95.23 12.12 95.18 12.53 95.12 12.95 1 961 97 96.28 11.82 96.22 12.24 96.17 12.66 96.11 13,08 97 98 97.27 11.94 97.22 12.37 97,16 12.79 97.10 13.22 98 99 98.26 12.07 98.21 12.49 98,15 12,92 98.10 13.35 99 100 5 99.25 12.19 99.20 12.62 99.14 13.05 99.09 13.49 100 1 .2 Q Dep. Lat. Dep, Lat, Dep. Lat. Dep. Lat. 83 1 3eg. 821 Deg. 82^ Deg. 82i Deg. 18 TRAVERSE TABLE. 8 Beg. iii Deg. 8-k Deg. 8J Deg. a 9 Lai. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 1 0.99 0.14 0.99 0.14 ~o:m' 0.15 0.99 0.15 ~T 3 1.98 0.28 1.98 0.29 1.98 0.30 1.98 0.30 2 3 2.M7 0.42 2.97 0.43 2.97 0.44 2.97 0.46 3 4 3.9G 0..56 3.96 0.57 3.96 0.,59 3.95 0.61 4 5 4.95 0.70 4.95 0.72 4.95 0.74 4.94 0.76 5 6 5.94 0.84 5.94 0.86 5.93 0.89 5.93 91 6 7 6.93 0.97 6.93 1.00 6.92 1.03 6.92 1.06' 7 8 7.92 1.11 7.92 1.15 7.91 1.18 7.91 1 22 8 9 8.91 1.25 8.91 1.29 8.90 1.33 8.90 1.37 1 9 10 9.90 1.39 9.90 1.43 9.89 1.48 9.88 1.52 1 10 M 10.89 1.53 10.89 1..58 10.88 1.63 10.87 1.67 11 12 J 1.88 1.67 11.88 1.72 11.87 1.77 11.86 1.83 12 13 12.87 1.81 12.87 1.87 12.86 1.92 12.85 1.93 13 14 13.86 1.95 13.86 2.01 13.85 2.07 13.84 2.13 14 15 14.85 2.09 14.85 2.15 14.84 2.23 14.83 2.28 15 16 15.84 2.23 15.84 2.30 15.82 2.36 15.81 2.43 16 17 16.83 2.37 16.83 2.44 16.81 2.51 16.80 2.59 17 IS "17.82 2.51 17.81 2.58 17.80 2.66 17.79 2.74 18 19 18.82 2.64 18.80 2.73 18.79 2.81 18.78 2.89 19 20 19.81 2.78 19.79 2.87 19.78 2.96 19.77 3.04 20 " 21 21 20 . 80 2 . 92 20.78 3.01 20.77 3.10 20.76 3.19 22 21.79 3.06 21.77 3.16 21.76 3.25 21.74 3.35 22 23 22.78 3.20 22.76 3.30 22.75 3.40 22.73 3.50 23 24 23.77 3.34 23.75 3.44 23.74 3.55 23.72 3.65 24 2.5 24.76 3.48 24 . 74 3.59 24.73 3.70 24.71 3.80 25 20 25.75 3.62 25.73 3.73 25.71 3.84 25.70 3.96 26 27 26.74 3.76 26.72 3.87 ,26.70 3.99 26.69 4.11 27 28 27.73 3.90 27.71 4.02 27.69 4.14 27.67 4.26 28 29 1 28 . 72 4.04 28.70 4.16 28.68 4.29 28.66 4.41 29 30 29.71 4.18 29.69 4.30 4.45 29.67 4.43 29.65 4.56 30 3Y 30.70 4.31 30.68 30.66 4.58 30.64 4.72 31 32 1 31.69 4.45 31.67 4.59 31.65 4.73 31.63 4.87 32 33 132.68 4.59 32.66 4.74 32.64 4.88 32.62 5.02 33 34 33.67 4.73 33.65 4.88 33.63 5.03 33.60 5.17 34 35 34.66 4.87 34.64 5.02 34.62 5.17 34.-59 5.32 35 36 35.65 5.01 35.63 5.17 35.60 5.32 135.58 5.48 36 37 36.64 5.15 36.62 5.31 36.. 59 5.47 36.57 5.63 37 38 37.63 5.29 37.61 5.45 37.58 5.62 37.56 5.78 38 39 38.62 5.43 38.60 5.60 38.57 5.76 ,38.55 5.93 39 40 139.61 5.57 39-59 40.f>8 5.74 39.56 5.91 .39.53 6.08 40 41 41 40.60 5.71 5.88 40.55 6.06 40.52 6.24 42 41.59 5.85 41.57 6.03 41.54 6.21 41.51 6.39 42 43 42.. 58 5. 93 42.56 6.17 42.53 6.36 42.50 6.54 43 44 43.57 6.12 43.54 6.31 43.52 6.50 43.49 6.69 44 45 44.56 6.26 44.53 6.46 44.51 6.65 44.48 6.85 45 46 45.55 6.40 45.52 6.60 45.49 6.80 45.46 7.00 46 47 46.54 6.54 46.51 6.74 46.48 6.95 146.45 7.15 47 48 47.53 6.68 47.50 6.89 47.47 7.09 47.44 7.30 48 49 48.52 6.82 48.49 7.03 48.46 7.24 48.43 7.45 49 50 49.51 6.96 49.48 7.17 49.45 7.39 49.42 7.61 50 J Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. i S .2 P 82 1 Deg. 811 Deg. 81,^ Deg. an Deg. TKAVERSE TABLE. 19 - 8 Dcg. m Deg. H Deg. &J Dog. 3 Tat: Dep. 1 Lat. Dep. Lat. Dep. Lat. Dep. "51 "50750" 7.10 "30:4^ 7.~32 50.44 7.54 50.41 7.76 51 52 51.49 7.24 51.46 7.46 51.43 7.69 51.39 7.91 52 53 52.48 7.33 52.4.5 7.61 52.42 7.83 52.38 8.06 53 54 53 . 47 7.. 52 53.44 7.75 53.41 7.98 ,53.37 8.21 54 55 54.46 7.65 .54.43 7.89 54.40 8.13 54.36 8.37 55 56 55.46 7.79 55.42 8.04 55.38 8.28 55.35 8.52 56 57 56.45 7.93 56.41 8,18 56.37 8.43 56., 34 8.67 57 58 57.44 8.07 57. W 8.32 57.36 8.57 57.32 8.82 58 59 .58.43 8.21 58.39 8.47 .58., 35 8.72 58.31 8.98 59 60 .59.42 8.35 59. 38 8.61 59.34 8.87 59.30 9.13 60 61 60.41 8.49 60.37 8.75 60.3.3^ 9.02 60.29 9.28 61 62 61.40 8.63 61.36 8.90 61.32 9.16 61.28 9.43 62 63 62.39 8.77 62.35 9.04 62.31 9.31 62.27 9.58 63 64 63.38 8.91 63.34 0.18 63.30 9.46 63.26 9.74 64 65 64.37 9.05 64.33 9.33 64.29 9.61 64.24 9.89 65 66 65.36 9.19 65 . 32 9.47 65.28 9.76 05.23 10.04 66 67 6f..33 9.32 66.31 9.61 66.26 9,90 66.22 10.19 67 68 67.. 34 9.46 67.30 9.76 67.25 10.05 67.21 10.34 68 69 68.33 9.60 68.29 9.90 68.24 10.20 68.20 10.50 69 70 71 69.32 9.74 69.28 10.04 69.23 10.35 69.19 10.65 70 70.31 9.88 70.27 10.19 70.22 10.49 70.17 10.80 71 72 71.30 10.02 71.25 10.33 71.21 10.64 71.16 10.95 72 73 72.29 10.16 72.24 10.47 72.20 10.79 72.15 11.10 73 74 73.28 10.30 73.23 10.62 73.19 10.94 73.14 11.26 74 75 74.27 10.44 74.22 10.76 74.18 11.09 74.13 11.41 75 78 75.26 10.. 58 75.21 10.91 75.17 11.23 75.12 11.56 76 77 76.25 10.72 76.20 11.05 76.15 11.38 76.10 11.71 77 7S 77.24 10.86 77.19 11.19 77.14 11. .53 77.09 11.87 78 79 7S.23 10.99 78.18 11.34 78.13 11.68 73.08 12.02 79 80 81 79.22 11.13 79.17 11.48 79.12 11.82 79.07 12.17 80 81 80.21 11.27 80.16 11.62 80.11 11.97 80.06 12.32 8-Z 81.20 11.41 81.15 11.77 81.10 12.12 81.05 12.47 82 83 82.19 1 1 . 55 82.14 11.91 82.09 12.27 82.03 12.63 83 84 83.18 11.69 83.13 12.05 83.08 12.42 83.02 12.78 84 85 84.17 11.83 84.12 12.20 84.07 12.56 84.01 12.93 85 86 85.16 11.97 85.11 12.34 85.06 12.71 85.00 13.08 86 87 86.15 12.11 86.10 12.48 86.04 12.86 8.5.99 13.23 87 88 S7.14 12.25 87.09 12.63 87.03 13.01 86.98 13.39 88 89 88.13 12.39 88.08 12.77 88.02 13,. 16 87.96 13.54 89 90 31 89.12 12.53 89.07 90.06 12.91 89.01 13.30 88.95 89.94 13.69 90 91 90.11 12.66 13.08 90.00 13.45 13.84 92 91.10 12.80 ' 91.05 13.20 90.99 13.60 90.93 14.00 92 93 92.09 12.94 92.04 13.34 91.98 13.75 91.92 14.15 93 94 93.09 13.08 ' 93.03 13.49 92.97 13.89 92.91 14.30 94 95 94.08 13.22 i 94.02 13.63 93.96 14.04 93.89 14.45 95 96 95.07 13.36 95.01 i3.78 94.95 14.19 94.88 14.00 96 97 96.06 13.50 96.00 13.92 95,93 14.34 95.87 14.76 97 98 97.05 13.64 196.99 14.06 96,92 14.49 96.86 14.91 98 99 98.04 13.78 ! 97.98 14.21 97.91 14.63 97.85 15.06 99 100 Q 99.03 13.92 98.97 14.35 93.90 14.78 98.84 15.21 100 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. i (5 82 [)cg. 811 Deg-. 8H Deg. 8U Deg. 20 TRAVEKSE TABLE. 2 f 1 9Deg. 9i Deg. H Deg. n Deg 5 Lat. 0.99 Dep. Lat. Dep. Lat. Dep. Lat. Dep. 0.16 ~0:99" 0.16 0.99 0.17 0.99 0.17 1 2 1.98 0.31 1.97 0.32 1.97 0.33 1.97 0.34 2 3 2.96 0.47 2.96 0.48 2.96 0.50 2.96 0.51 3 4 3.95 0.63 3.95 0.64 3.95 0.66 3.94 0.68 4 5 4.94 0.78 4.93 0.80 4.93 0.83 4.93 0.85 5 6 5.93 0.94 5.92 0.96 5.92 0.99 5.91 1.02 6 7 6.91 1.10 0.91 1.13 6.90 1.16 6.90 1.19 7 8 7.90 1.25 7.90 1.29 7.89 1.32 7.88 1.35 8 9 8.89 1.41 8.88 1.45 8.88 1.49, 8.87 1.52 9 10 9. 88 1.56 9.87 1.61 9.86 1.65 9.86 1.69 10 11 10.86 1.72 10.86 1.77 10.85 1.82 10.84 1.86 11 12 11.85 1.88 11.84 1.93 11.84 1.98 11.83 2.03 1 2 13 12.84 2.03 12.83 2.09 12.82 2.15 12.81 2.20 13 14 13.83 2.19 13.82 2.25 13.81 2.31 13.80 2 .37 14 15 14.82 2.35 14.80 2.41 14.79 2.48 14.78 2.54 15 16 15.80 2.50 15.79 2.57 15.78 2.64 15.77 2.71 161 17 16,79 2.66 16.78 2.73 16.77 2.81 16.75 2.88 1 17! 18 17.78 2.82 17.77 2.89 17.75 2.97 17.74 3.05 18 19 18.77 2.97 18.75 3.05 18.74 3.14 18.73 3.22 19 20 19.75 3.13 19.74 3.21 19.73 3.30 19.71 3.39 20 21 20.74 3.29 20.73 3.38 20.71 3.47 20.70 3.. 56 "21" 22 21.73 3.44 21.71 3.. 54 21.70 3.63 21.68 3.73 22 23 22.72 3.60 22.70 3.70 22.68 3.80 22.67 3.90 23 24 23.70 3.75 23.69 3.86 23.67 3.96 23.65 4.06 24 25 24.69 3.91 24.67 4.02 24.66 4.13 24.64 4.23 25 26 25.68 4.07 25.66 4.18 25.64 4.29 25.62 4.40 26 27 26.67 4.22 26.65 4.34 26.63 4.46 26.61 4.57 27 28 27.66 4.38 27.64 4.50 27.62 4.62 27.60 4.74 28 29 28.64 4.54 28.62 4.66 28.60 4.79 28.58 4.91 29 30 31 29.63 4.69 29.61 4.82 29.59 4.95 29.57 5.08 5.25 30 31 30.62 4.85 30.80 4.98 30.57 5.12 30.55 32 31.61 5.01 31.58 5.14 31. .56 5.28 31.54 5.42 32 33 32.59 5.16 32.57 5.30 32.55 5.45 32.52 5.59 33 34 33.58 5.32 33.. 56 5.47 33.53 5.61 33.51 5.76 34 35 34.57 5.48 34.54 5.63 .34.52 5.78 34.49 5.93 35 36 35.56 5.63 35.. 53 5.79 35.51 5.94 35.48 6.10 36 37 36.54 5.79 36.62 5.95 36.49 6.11 .36.47 6,27 37 38 37.53 5.94 37.51 6.11 37.48 6.27 37.45 6.44 38 39 38.52 6.10 38.49 6.27 38.47 6.44 38.44 6.60 39 40 41 39.51 40.50 6.26 6.41 39.48 40.47 6.43 39.45 6.60 39.42 6.77 40 41 6.59 40.44 6.77 40.41 6.94 42 41.48 6.57 41.45 6.75 41.42 6.92 41.39 7.11 42 43 42.47 6.73 42.44 6.91 42.41 7.10 42.38 7.28 43 44 43.46 6.88 43.43 7.07 43.40 7.26 43.36 7,45 44 45 44.45 7.04 44.41 7.23 44.38 7.43 44.35 7.62 45 46 45.43 7.20 45.40 7.39 45.37 7.59 45.34 7.79 46 47 46.42 7.35 46.39 7.55 46.36 7.76 46.32 7.96 47 48 47.41 7.51 47.38 7.72 47.34 7.92 47.31 8.13 48 49 48.40 7.67 48.36 7.88 48.33 8.09 48.29 8.30 49 50^ 49.38 7.82 49.35 8.04 49.32 8.25 49.28 8.47 50 1 ft 1 Dep. Lat. Dep. Lat. Dep. Lat. Dop. Lat. 81] Oeg. 801 Deg. 801 Deg. 80i Dog. 21 i 51 9 Beg. 94 Deg. H Deg. 91 Deg. a Lat Dep. 7.98 Lat. Dep. ~8T20 i-"atr Dep. Lat. Dep. 50.37 "50734 JoJiO 8.42 50.26 8.64 51 52 51.36 8.13 51.32 8.36 51.29 8.58 51.25 8.81 52 53 52.35 8.29 52.31 8.52 52.27 8.75 52.23 8.98 53 54 53.34 8.45 53,30 8.68 .53 . 26 8.91 53.22 9.14 54 55 54.32 8.60 54.28 8.84 ,54.25 9.08 .54.21 9.31 55 56 55.31 8.76 55.27 9.00 .55.23 9.24 55.19 9.48 56 67 56.30' 8.92 56.26 9.16 56.22 9.41 56.18 9.65 57 58 57.29 9.07 57.25 9.32 57.20 9.57 57.16 9.82 58 59 58.27 9.23 58.23 9.48 .58.19 9.74 .58.15 9.99 59 60 59.26 9.39 59.22 i 9.64 ,59.18 9.90 59.13 10.16 60 61 60.25^ 9.. 54 60.21 I 9.81 60.16 10.07 60.12 10733 61 62 61.24 9.70 61.19 9.97 61.15 10.23 61.10 10.50 62 63 62.22 9.86 62.18 10.13 62.14 10.40 62.09 10.67 63 64 63.21 10.01 63.17 10.29 63.12 10.56 63.08 10.84 64 65 64.20 10.17 64.15 10.45 64.11 10.73 64.06 11.01 65 66 65.19 10.32 65.14 10.61 65.09 10.89 65.05 11.18 66 67 66.18 10.48 66.13 10.77 66.08 11.06 66.03 11.35 67 68 67.16 10.64 67.12 10.93 67.07 11.22 67.02 11.52 68 69 68.15 10.79 68.10 11.09 68.05 11.39 68.00 11.69 69 70 71 69.14 10.95 69.09 11.25 69.04 11.55 68.99 11.85 12.02 70 71 70.13 11.11 70.08 11.41 70.03 11.72 69.97 72 71.11 11.26 71.06 11.57 71.01 11.88 70.96 12.19 72 73 72.10 11.42 72.05 11.73 72.00 12.05 71.95 12.36 73 74 73.09 11.58 73.04 11.89 72.99 12.21 72.93 12.53 74 75 74.08 11.73 74.02 12.06 73.97 12.. 38 73.92 12.70 75 76 75.06 11.89 75.01 12.22 74.96 12.. 54 74.90 12.87 76 77 76.05 12.05 76.00 12.38 75.94 12.71 75.89 13.04 77 78 77.04 12.20 76.99 12.. 54 76.93 12.87 76.87 13.21 78 79 78.03 12.36 77.97 12.70 77.92 13.04 77.86 13.38 79 80 79.02 12.51 78.96 12.86 78.90 13.20 78.84 13.55 80 81 81 80.00 12.67 79.95 13.02 79.89 13.37 79.83 13.72 82 80.99 12.83 80.93 13.18 80.88 13.53 80.82 13.89 82 83 81.98 12.98 81.92 13.34 81.86 13.70 81.80 14.06 83 84 82.97 13.14 82.91 13.50 82.85 13.86 82.79 14.23 84 85 83.95 13.30 83.89 13.66 83.83 14.03 83.77 14.39 85 86 84.94 13.45 84.88 13.82 84.82 14.19 84.76 14.. 56 86 87 85.93 13.61 85.87 13.98 85.81 14.36 85.74 14.73 87 88 86.92 13.77 86.86 14.15 86.79 14.. 52 86.73 14.90 88 89 87.90 13.92 87.84 14.31 87.78 14.69 87.71 15.07 89 90 88.89 14.08 88.83 14.47 88.77 14.85 88.70 15.24 90 91 91 89.88 14.24 89.82 14.63 89.75 15.02 89.69 15.41 92 90.87 14.39 90.80 14.79 90.74 15.18 90.67 15.58 92 93 91.86 14.55 91.79 14.95 91.72 15.35 91.66 15.75 93 94 92.84 14.70 92.78 15.11 92.71 15.51 92.64 15.92 94 95 93.83 14.86 93.76 15.27 93.70 15.68 93.63 16.09 95 96 94.82 15.02 94.75 15.43 94.68 15.84 94.61 16.26 96 97 95.81 15.17 95.74 15.59 95.67 16.01 95.60 16 43 97 98 96.79 15.33 96.73 15.75 96.66 16.17 96.58 16.60 98 99 97.78 15.49 97.71 15.91 97.64 16.34 97.57 16.77 99 100 s a 1 98.77 15.64 98.70 16.07 98.63 16.50 98.56 16.93 100 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. Q 81 Deg. 801 Deg. 80^ Deg. 80i Deg. 22 TRAVERSE TABLE. p 10 1 Lat. "DepT lOi Deg. 10^ Deg. 10| Deg. i Lat. Dep. Lat. Dep. Lat. Dep. 1 "oTos' 0.17 "0798 1)718 "OAiS q7i8 "6798" 0.19 1 2 1.97 0..35 1.97 0.36 1.97 0.36 1.96 0.37 2 3 2.95 0.52 2.95 0.53 2.95 0.55 2.95 56 3 4 1 3 . 94 0.69 3.94 0.71 3.93 0.73 3.93 0.75 4 5 4 . 92 0.87 4.92 0.89 4.92 0.91 4.91 0.93 5 6 i 5.91 1.04 5.90 1.07 5.90 1.09 5.89 J. 12 6 7 6.89 1.22 6.89 1.25 6.88 1.28 6.88 1.31 8 7.88 1.39 7.87 1.42 7.87 1.46 1 7.86 1.49 8 9 8.86 1.56 8.86 1.60 8 . 85 1.64 8.84 1.68 9 10 9.85 1.74 9.84 1.78 9.83 10.82 1.82 9.82 1.87 10 11 11 [10.83 1.91 10.82 1 .96 2.00 10.81 2.05 12 11.82 2.08 11.81 2.14 11.80 2.19 11.79 2.24 12 13 i 12.80 2.26 12.79 2.31 12.78 2.37 12.77 2.42 13 14 13.79 2.43 13.78 2.49 13.77 2.55 13.75 2.61 14 1.5 14.77 2.60 14.76 2.67 14.75 2.73 14.74 2.80 15 16 15.76 2.78 15.74 2.85 15.73 2.92 15.72 2.98 16 17 16.74 2.95 16.73 3.03 16.72 3.10 16.70 3.) 7 17 18 17.73 3.13 lV.71 3.20 17.70 3.28 17.6'8 3.36 18 19 18.71 3.30 18.70 3.38 18.68 3.46 18.67 3.54 19 20 21 19.70 20.68 3.47 3.65 19.68 3.56 3.74 19.67 3.64 19.65 20763' 3.73 3.92" 20 21 20.66 20.65 3.83' 22 21.67 3.82 21.65 3.91 21.63 4.01 21.61 4.10 22 23 22.65 3.99 22 . 63 4.09 22.61 4.19 22 . 60 4.29 23 24 23.64 4.17 23.62 4.27 23.60 4.37 23 . .58 4.48 24 2.5 24.62 4.34 24.60 4.45 24.58 4.56 24.56 4.66 25 26 25.61 4.51 25.59 4.63 25.56 4.74 25.. 54 4.85 26 27 26.59 4.69 26.57 4.80 26.. 55 4.92 26.153 5.04 27 28 27.57 4.86 27.55 4.98 27.. 53 5.10 27.51 5.22 28 29 28.56 5.04 28.. 54 5.16 28.51 5.28 28.49 5.41 29 30 29.54 5.21 29.52 5.34 29.. 50 5.47 29.47 5 . 60 30 31 30.. 53 5.38 30.51 5.52 30.48 5.65" .30.46 " 5.78 3l 32 31.51 5.56 31.49 5.69 31.46 5.83 31.44 5.97 32 33 32.. 50 5.73 32.47 5.87 32.45 6.01 32.42 6.16 33 34 33.48 5.90 33.46 6.05 33.43 6.20 33.40 6.34 34 3.5 34.47 6.08 34.44 6.23 34.41 6.38 34.39 6.. 53 35 36 35.45 6.25 35.43 6.41 35.40 6.56 35.37 6.71 36 37 36.44 6.42 36.41 6.58 36.38 6.74 36.. 35 6.90 37 38 37.42 6.60 37.39 6.76 37.36 6.92 37.33 7.09 38 39 38.41 6.77 .38.38 6.94 38.35 7.11 38.32 7.27 39 40 41 39.39 6.95 39.36 7.12 39.33 7.29 39.30 7.46 40 41 40.38 7.12 40.35 7.30 40.31 "7747 40.28 7.65 42 41.36 7.29 41.33 7.47 41.30 7.65 41.26 7.83 42 43 42.35 7.47 42.31 7.65 42.28 7.84 42.25 8.02 43 44 43.33 7.64 43.30 7.83 43.26 8.02 43.23 8.21 44 45 44.32 7.81 44.28 8.01 44.25 8.20 44.21 8.39 45 46 45.30 7.99 45.27 8.19 45.23 8.38 45.19 8.. 58 46 47 46.29 8.16 46.25 8.36 46.21 8.57 46.18 8.77 47 48 47.27 8.34 47.23 8.. 54 47.20 8.75 47.16 8.95 48 49 48.26 8.51 48.22 8.72 48.18 8.93 48.14 9.14 49 50 49.24 8.68 49.20 8.90 49.16 9.11 49.12 9.33 50 i s ~8 .2 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 80 1 Deg. 791 Deg. 791 Deg. 79i Deg. TtiAVEKSE lARLE. 23 3 10 Deg. m Deg. lOi Deg. 101 Deg. O 1 9 ~5T Lat. Dep. Lat. Dep. Lat. Dcp. Lat. Dep. TT 50.23 8.86 50.19 9.08 50.15 9.29 .50.10 9.51 52 51.21 9.03 51.17 9.25 51.13 0.48 51.09 9.70 52 53 52.19 9.20 52.15 9.43 .52.11 9.66 52.07 9.89 53 54 53.18 9.38 53.14 9.61 53.10 9.84 .53.05 10.07 54 65 54.16 9.55 54.12 9.79 54.08 10.02 .54.03 10.26 55 56 55.15 9.72 55.11 9.96 55.06 10.21 55.02 10.45 56 57 56.13 9.90 56.09 10.14 56.05 10.39 56.00 10.63 57 58 .57.12 10.07 ,57.07 10.32 .57.03 10.57 ,56.98 10.82 58 59 58.10 10.25 .58.06 10.50 ■58.01 10.75 57.96 11.00 59 60 59.09 1 10.42 59.04 1 10.68 59.00 10.93 .58.95 59.93 11.19 60 ~61 61 60.07 110.59 60.03' 10.85 .59.98 11.12 11.38' 62 61.06 i 10.77 61.01 11.03 60.96 11.30 60.91 11. .56 62 63 62.04 10.94 61.99 ' 11.21 61.95 11.48 61.89 11.75 63 64 63.03 11.11 62.98 1 11.39 62.93 11.66 62.88 11.94 64 65 64.01 11.29 63.96 11.57 63.91 11.85 63.86 12.12 65 66 65.00 11.46 64.95 11.74 64.89 12.03 64.84 12.31 66 67 65.98 11.63 65.93 11.92 65.88 12.21 65.82 12.50 67 68 66.97 11.81 66.91 12.10 66.86 12.39 66.81 12.68 68 69 67.95 11.98 67.90 12.28 67.84 12.57 67.79 12.87 69 70 71 68.94 12.16 68.88 12.46 68.83 12.76 68.77 13.06 70 75 69.92 12.33 69.87 1 12.63 69.81 12.94 69.75 13.24 72 70.91 12.50 70.85 i 12.81 70.79 13.12 70.74 13.43 72 73 71.89 12.68 71.83 '' 12.99 71.78 13.30 71.72 13.62 73 74 72.88 12.85 72.82 i 13.17 72.76 13.49 72.70 13.80 74 75 73.86 13.02 73.80 13.35 73.74 13.67 73.68 13.99 75 76 74.85 1 13.20 74.79 13.52 74.73 13.85 74.67 14.18 76 77 75.83 13.37 75.77 13.70 75.71 14.03 ; 75.65 14.36 77 78 76.82 13.54 76.76 13.88 76.69 14.21 76.63 14.55 78 79 77.80 13.72 77.74 14.06 77.68 14.40 77.61 14.74 79 80 81 78.78 13.89 78.72 14.24 78.66 14.. 58 78.60 14.92 80 81 79.77 14.07 79.71 14.41 79.64 14.76 79.58 15. if 82 80.75 14.24 80.69 14.. 59 80.63 14.94 80.50 15.29 82 83 81.74 14.41 81.68 14.77 81.01 15.13 81.54 15.48 83 84 82.72 14.59 82.66 14.95 82.59 15.31 82.53 15.67 84 85 83.71 14.76 83.64 15.13 83.. 58 15.49 83.51 15.85 85 86 84.69 14.93 84.63 15.30 84.56 15.67 84.49 16.04 86 87 85.68 15.11 85.61 15.48 85.54 15.85 85.47 16.23 87 88 86.66 15.28 86.60 15.66 86.53 16.04 8'3.46 16.41 88 89 87.65 15.45 87.58 15.84 87.51 16.22 87.44 16.60 89 90 91 88.63 89.62' 15.63 88.56 16.01 88.49 16.40 88.42 16.79 16.97 90 91 15.80 89., 55 16.19 89.48 16. 5S 89.40 92 90.60 15.98 90.53 16.37 90.46 16.77 90.39 17.16 92 93 91.59 16.15 91.52 16.55 91.44 16.95 91.37 17.35 93 94 92.57 16.32 92.. 50 16.73 92.43 17.13 92.35 17.53 94 95 93.56 16.50 93.48 16.90 93.41 17.31 93.33 17.72 95 96 94.54 16.67 94.47 17.08 94.39 17.49 94.32 17.91 96 97 95.53 16.84 95.45 17.26 95.38 17.68 95.30 18.09 97 98 96.51 17.02 96.44 17.44 96.36 17.86 96.23 18.28 98 99 97.50 17.19 97.42 17.62 97.34 18.04 97.26 18.47 99 100 T s 98.48 17.36 98.40 17.79 98.33 18.22 98.25 18.65 100 .2 Q 1 Dcp. Lat. Dep. 1 Lat. Dep. Lat. Dep. Lat. 80 Deg. 79i Deg. 79j Deg. 79i Deg. 24 TRAVERSE TABLE. I 11 Deg. lU Deg. Hi Deg. Ill Deg. ? ? 1 Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. ~Y 0.98 0.19 0,98 0.20 0.98 0.20 0.98 nr.20- 2 1.96 0,38 1,96 0.39 1.96 0.40 1.96 0.41 2 3 2.94 0.57 2,94 0.59 2,94 0.60 2.94 0.61 3 4 3.93 0.76 3,92 0.78 3,92 0.80 3.92 0.82 4 5 4.91 0,95 4,90 0.98 4,90 1.00 4.90 1.02 5 6 5.89 1,14 5,88 1.17 5.88 1.20 5.87 1.22 6 7 6.87 1,34 6,87 1.37 6.86 1.40 6.85 1.43 7 8 7.85 1.53 7,85 1.56 7.84 1.59 7.83 1.63 8 9 8.83 1,72 8,83 1.76 8,82 1,79 8.81 1.83 9 10 9.82 1.91 9,81 1.95 9,80 1.99 9.79 2.04 10 11 11 10.80 2.10 10,79 2.15 10.78 2.191 10.77 2.24 12 11.78 2.29 11,77 2.34 11,7-6 2.39 11.75 2.44 12 13 12.76 2.48 12,75 2.54 12,74 2.59 12.73 2.65 13 14 13.74 2.67 13.73 2.73 13.72 2.79 13.71 2.85 14 15 14.72 2.86 14.71 2.93 14.70 2.99 14.69 3.06 15 16 15.71 3,05 15.69 3.12 15.68 3.19 15.66 3.26 16 17 16.69 3,24 16.67 3.32 16.66 3.39 16.64 3.46 17 18 17.67 3,43 17.65 3.51 17.64 3.. 59 17.62 3.66 18 19 18.65 3,63 18,63 3.71 18.62 3.79 18.60 3.87 19 20 19.63 20.61 3,82 4,01 19.62 3.90 -4TT0- 19.60 3.99 19.58 4.07 20 21 30,60 20.. 58 4.19 20 . 50 4.28 ' 21 22 21.60 4,20 21,58 4.29 21.56 4.39 21.54 4.48 23 23 22.58 4,39 22,56 4.49 22.54 4.. 59 22.52 4.68 23 24 23.56 4,58 23,54 4.68 23.52 4.78 23.50 4.89 24 25 24.54 4.77 24,52 4.88 24.50 4.98 24.48 5.09 25 26 25.52 4.96 25,50 5.07 25.48 5.18 25.46 5.30 26 27 20.50 5.15 26,48 5.27 26.46 5.38 26.43 5.. 50 27 28 27.49 5.34 27.46 5.46 27.44 5,58 27.41 5.70 28 29 28.47 5.53 28,44 5.66 28.42 5,78 28.39 5.91 29 30 29.45 5.72 29,42 30,40 5.85 6.05 29,40 5.98 29.37 6.11 30 31 30.43 5.92 30,38 6.18 30.35 6.31 31 32 31.41 6.11 31,39 6.24 31,36 6.38 31.33 6.52 32 33 32.39 6-30 32,37 6.44 32.34 6.58 32.31 6.72 33 34 33.38 6.49 33.35 6.63 33.32 6.78 33.29 6.92 34 35 34.36 6.68 34.33 6.83 34.30 6.98 34.27 7.13 35 36 35.34 6.87 35.31 7.02 .35.28 7.18 35.25 7.33 36 37 36.32 7.06 36.29 7.22 36.26 7.38 36.23 7.53 37 38 37.30 7.25 37.27 7.41 37.24 7.58 37.20 7.74 38 39 33.28 7,44 38.25 7.61 38.22 7.78 38.18 7.94 39 40 39.27 7,63 39,23 7,80 39.20 7.97 39.16 8.15 40 41 41 40.25 7.82 40,21 8,00 40.18 8.17 40.14 8 .35 42 41.23 8.01 41,19 8,19 41.16 8.37 41.12 8.55 42 43 42.21 8.20 42.17 8.39 42.14 8.57 42.10 8.76 43 44 43.19 8.40 43.15 8.58 43.12 8.77 43.08 8.96 44 45 44.17 8.59 44.14 8.78 44.10 8.97 44.06 ■9.16 45 46 45.15 8.78 45.12 8.97 45.08 9.17 45.04 9.37 46 47 46.14 8.97 46.10 9.17 46.06 9.37 46.02 9.57 47 48 47.12 9.16 47.08 9.36 47.04 9.57 46.99 9.78 48 49 48.10 9.35 48.06 9.. 50 48.02 9.77 47.97 9.98 49 1 49.08 9,54 49.04 Lat. Da^. 49.00 9.97 48.95 10.18 50 Dep. Lat, Dep. 781 Dep. Lat. Dep. Lat. i 79] Deg, '8^ Deg. 78i Deg, TKAVEKSE TABLE. 25 a § 51 11 Deg, Hi Def, 11^ Deg. Ill Deg. ~51 Lat. 1 Dep. Lat. Dep. Lat. Dep. 1 Lat. 1 Dep, 50,06 9.73 50,02 9.95 49.98 10.17 49.93 10.39 52 51.04 9.92 51,00 10.14 50.96 10.. 37 1 50,91 10.59 52 53 52.03 10.11 51,98 10.34 51,94 10.57 51,89 10.79 53 51 53.01 10.30 52.96 10.. 53 62.92 10.77 52.87 11.00 54 55 53.99 10.49 53.94 10.73 53.90 10.97 53.85 11.20 55 56 54.97 10.69 54.92 10.93 64.88 11.16 54.83 11.40 56 57 55.95 10.88 55.90 11.12 55.86 11.36 55.81 11.61 57 58 56 . 93 11.07 56.89 11.32 56.84 11.56 56.78 11.81 58 59 57.92 11.26 57.87 11.51 57.82 11.76 57.76 12.01 59 60 6'l 58.90 11.45 .58 . 85 59.83 11.71 58.80 11.96 58.74 12.22 60 ~6l 59.88 11.64 11.90 59.78 12.16 59 . 72 12.42 63 60.86 11.83 60.81 12.10 60.76 12.36 60.70 12.63 62 63 61.84 12.02 61,79 12.29 61.74 12.56 61,68 12.83 63 64 62.82 12.21 62.77 12.49 62.72 12.76 62,66 13.03 64 65 63.81 12.40 63,75 12.68 63.70 12.96 63,64 13.24 65 66 64.79 12.59 64,73 12.88 64.68 13.16 64.62 13.44 66 67 65.77 12.78 65,71 13.07 65.66 13.36 65,60 13.64 67 68 66.75 12.98 66,69 13.27 66.63 13.56 66.58 13.85 68 69 67.73 13.17 67,67 13.46 67.61 13.76 67,55 14.05 69 70 71 68.71 13.36 68,66 13.66 68.59 13.96 68,53 14.25 70 69.70 13.55 69,64 13.85 69.57 14.16 69,51 14.46 71 72 70.68 13.74 70,62 14,05 70.55 14.35 70.49 14.66 72 73 71.66 13.93 71.60 14,24 71.53 J 4. 55 71.47 14.87 73 74 72.64 14.12 72.58 14.44 72.51 14.75 72.45 15.07 74 75 73.62 14.31 73.56 14.63 73.49 14.95 73.43 15.27 75 76 74.60 14.50 74.54 14.83 74.47 15.15 74.41 15.43 76 77 75.59 ! 14.69 75.52 15.02 75.45 15.35 75 39 15.68 77 78 76.57 14.88 76.50 15.22 76.43 15.55 76.37 15.88 78 79 77.55 15.07 77.48 15.41 77.41 15.75 77.34 16.09 79 80 81 78.53 15.26 15,46 78.46 1 15.61 78.39 15.95 78.32 16.29 80 79.51 79.44 15.80 79.37 16.15 79.30 16.49 TT 82 80.49 15,65 80,42 16.00 80.35 16.35 80.28 16.70 82 83 81.48 15,84 81,41 16.19 81.33 16.55 81.26 IB. 90 83 84 82.46 16.03 82,39 16.39 82.31 16.75 82.24 17.11 84 85 83.44 16,22 83,37 16.58 83.29 16.95 83.22 17.31 85 86 84.42 16,41 84.35 16.78 84.27 17.15 84.20 17.51 86 87 85.40 16.60 85.33 16.97 85.25 17.35 85.18 17.72 87 83 86.38 16.79 86.31 17,17 86.23 17.54 86.16 17.92 88 89 87.36 16.98 87.29 17,36 87.21 17.74 87.14 18.12 89 90 91 88.35 17.17 88.27 17,56 88.19 17.94 88.11 18.33 90 89.33 17.36 89.25 17,75 89.17 18.14 89.09 18.53 91 92 90.31 17.55 90.23 17,95 90.15 18.34 90.07 18.74 92 93 91.29 17.75 91.21 18.14 91.13 18.54 91.05 18.94 93 94 92.27 17.94 92.19 18,34 92.11 18.74 92.03 19.14 94 95 93.25 18.13 93.17 18.53 93.09 18.94 93.01 19.35 95 96 94.24 18.32 94.16 18.73 94.07 19.14 93.99 19.55 96 97 95.22 18.51 95.14 18.92 95.05 19.34 94.97 19.75 97 98 96.20 18.70 96.12 19.12 96.03 19.54 95.95 19.96 98 99 97.18 18.89 97.10 19.31 97.01 19.74 96.93 20.16 99 100 98.16 19.08 98.08 19.51 97.99 19.94 97.90 20.36 lOOf Dep. Lat. Dep. Lat. Dep, Lat. Dep. Lat. 1 79 Deg. 781 Deg. 78|Deg. m Deg. 26 TRAVERSE TABLE. 1 12Deg 12i Deg. m. Deg. 124 Deg. K Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 3 r 0.98 0.21 ~0798" 0,21 0.98 0,22 0,98 0,22 1 2 1.96 0.42 1.95 0.42 1.95 0.43 1.95 0.44 2 3 2.93 0.62 2.93 0.64 2.93 0.65 2,93 0.66 3 4 3.91 0.83 3.91 0.85 3.91 0,87 3.90 0.88 4 5 4.89 1.04 4.89 1.06 4.88 1,08 4.88 I.IO 5 6 5.87 1.25 5.86 1.27 5.86 1.30 5,85 1.32 6 7 6.85 1.46 6.84 1.49 6.83 1,52 6.83 1.54 7 8 7.83 1.66 7.82 1.70 7.81 1,73 7,80 1.77 8 9 8.80 1.87 8.80 1.91 8.79 1.95 8,78 1.99 9 10 9.78 2.08 9.77 2.12 9.76 2,16 9,75 2.21 10 11 in.7G 2.29 10.75 2.33 10.74 2.38 10.73 2,43 11 12 11.74 2.49 11.73 2.55 1 1 . 72 2.60 1 1 , 70 2.65 12 13 12.72 2.70 12.70 2.76 12.69 2.81 12,68 2,87 13 14 13.09 2.91 13.68 2.97 13.67 3,03 13.65 3,09] 14 15 . 14.67 3.12 14.66 3.18 14.64 3.25 14,63 3,31 15 16 15.05 3.. 33 15.64 3.39 15.62 3,40 15.61 3.. 53 1 16 17 16.63 3.. 53 16.61 3.61 16.60 3.68 16.58 3.75! 17 18 17.61 3.74 17.59 3.82 17. .57 3,90 17.. 06 3.97 ! 18 19 18.53 3.95 18.57 4.03 18.55 4.11 18.. 53 4.19 19 20 19.56 4.16 19.54 20.52 4.24 19.53 4.33 19,51 20,48 4.41 ! 20 21 20 . 54 4.37 4.46 20 . 50 4.5.5 4,63 21 22 2 1 . 52 4.57 21.50 4.67 21.48 4.76 21.46 4,86 23! 22.. 50 4.78 22.48 4.88 22.45 4.98 22.43 5,08 23 24 123.48 4.99 23.45 5.09 23.43 5.19 23.41 5.30 24 25 24.45 5.20 24.43 5.30 24.41 5.41 24,38 5.. 52 25 26 25.43 5.41 25.41 5.52 25. 3S 5.63 25,36 5,74 26 27 26.41 5.61 26.39 5.73 26.30 5.84 26.33 5,96 27 28 27.. 39 5.82 27.36 5.94 27.34 6.06 27.31 6,18 28 29 28 . 37 6.03 28 . 34 6.15 28.31 6.28 28.28 6.40 29 30 29.34 6.24 29.32 .30.29^ 6.37 6.. 58 29.29 6.49 29,26 6 . 62 30 31 30.32 6.45 ,30.27 6.71 30,24 6,84 31 32 31.30 6.65 31.27 6.79 31.24 6.93 31,21 7,06 32 33 32.28 6.86 32 . 25 7.00 32 . 22 7.14 32.19 7,28 33 34 33.26 7.07 33.23 7.21 33.19 7.36 33,16 7.50 34 35 34.24 7.28 .34.20 7.43 ,34.17 7,. 58 134.14 7.72 35 36 35.21 7.48 35.18 7.64 35.15 7.79 135,11 7,95 36 37 , 36.19 7.69 36.16 7.85 36.12 8,01 136,09 8,17 37 38 137.17 7.90 37.13 8.06 37.10 8,22 i 37,06 8,39 38 39 38.15 8.11 38 . 1 1 8.27 38.08 8 44 138,04 8,61 39 40 39.13 8.32 39.09 40:07^ 8.49 39.05 8,66 8,87 i 39.01 8.83 9.05 40 41 41 40.10 8.52 8.70 40.03 39.99 42 4[.08 8.73 41.04 8.91 41.00 9.09 40,96 9.27 42 43 142.06 8.94 42.02 9.12 41,98 9.31 41.94 9.49 43 44 143.04 9.15 43.00 9.34 42.96 9.. 52 42.92 9.71 44 45 144.02 9.36 43.98 9.55 43.93 9.74 43,89 9.93 45 46 44.99 9.56 44.95 9.76 44.91 9,96 U4.87 10.15 46 47 45.97 9.77 45.93 9.97 45.89 10,17 45.84 10.37 47 48 46.95 9.98 46.91 10.18 46.86 10,39 '46.82 10,. 59 48 49 47.93 10.19 47.88 10. lO 47.84 10,61 47.79 10.81 1 49 50 48.91 10.40 48.86 10.61 48.81 10.82 48.77 11,03 1 50 1 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat, 1 Q 78 Deg. 771 Deg. 771 Deg, 77i Deg. TRAVERSE TABLE. 27 "5i 12 Deg. 12i Deg. 12i Deg. 12| Deg. Lat. 1 Dup. 49.89 'To. (30 Lat. ; Dep. Lat. Dep. Lat. Dep. 49.84 1 10.82 49.79 ! 11.04 49.74 11.26 52 50.86, 10.8] 50.82 11.03 50.77 11.25 50.72 11.48 i 52} 53 51.84 1 11.02;! 51.79 1 11.25 151.74 11.47 51.69 11.70 .53 54 .52.82' 11.23 .52.77 : 11.46 152.72 11.69 52.67 ! ll.L'2 '. 54 | 55 53.80 , 11.44 .53.75 11.67 1 53.70 11.90 .53.64 '•■ 12.14 I 55 1 56 .54.78 ; 11.64 54.72 1-11.88 54.67 12.12 .54.62 12.36 1 5ti 57 55.75 1 11.85 .55.70 12.09 155.65 '12.34 II 55.. 59 12..'}8 i 67 5S 56.73 1 1,2.06 56.68 12.31 56.63 ; 12.55 II 56.67 12.80 58 59 57.71 12.27 57.66 12.52 57.60 l".i.77 II 57.55 13.02 1 59 58.69 1 12.47 53.63 12.73 .59.61 12.94 1 58.58 ■59.55 12.99 58.52 13.24! 60 59.67 12.68 13.20 59.50 13.46 1 61 6-2 60 , 65 12.89 60.59 i 13. 16 160.53 13.42 60.47 13.68 i 62 G:j 61.62 13.10 61.57 ; 13.37 61.51 13.64 61.45 13.90 1 63 64 62.60 13.31 62.54 i 13.58 .62.48 13.85 62.42 14.12 64 65 63.58 13.51 63.52 13.79 63 .46 14.07 63.40 14.35 65 66 fi4.56 13.72 64.50 14.00 164.44 14.29 64.37 14.57 06 67 6 5.. 54 13.93 65.47 I 14.22 ; 65.41 14.50 65.35 14.79 67 6S 65.51 14.14 66.45 14.43 166.39 14.72 60.32 15.01 68 69 67.49 14.35 67.43 14.64 67.36 14.93 67.30 15.23 69 70 tiS.47 14.55 68.41 69.38 14.85 15.06 [68.34 69.32 15.15 68.27 15.45 15.67 70 71 69.45 14.76 15.37 69.25 T2 70.43 ' 14.97 70.36 15.28 70.29 15.58 70.22 16.89 72 73 71.40 ' 15.18 71.34 15.49 71.27 15.80 71.20 16.11 73 74 72. 3S: 15.39 72.32 15.70 72.25 16.02 72.18 16.33 74 75 73.36 1 15.59 73.29 15.91 73.22 16.23 73.15 16.55 75 76 74.34 j 15,80 74.27 16.13 74.20 16.45 74.13 16.77 76 77 75.32 1 16.01 75.25 16.34 75.17 16.67 75.10 16.99 77 78 76.30 1 16.22 76.22 16.55 76.15 16.88 76.08 17.21 78 79 77.27 ! 16.43 77.20 16.76 77.13 17.10 77.05 17.44 79 80 81 78.25! 16.63 78.18 79.16 16.97 78.10 79.08 17.32 78.03 17.66 80 81 79.23 16.84 17.19 17.. 53 79.00 17.88 82 80.21 17.05 80.13 17.40 80.06 17.75 75.98 18.10 82 83 81.19 17.26 81.11 17.61 81.03 17.96 80.95 18.32 83 84 82.16 17.46 82.09 17.82 82.01 18.18 81,93 18.54 84 85 83.14 17.67 83.06 j 18.04 j 82.99 18.40 82.90 18.76 85 86 84.12 17.88 84.04 i 18.25 1 83.96 18.61 83.88 18.98 86 87 85.10 18.09 85.02 18.46 84.94 18.83 84.85 19.20 87 88 86.08 18.30 86.00 18.67 85.91 19.05 85.83 19.42 88 89 87.06 18.50 86.97 18.88 86.89 19.26 86.81 19.64 89 90 91 88.03 18.71 87.95 88.93 19.10 87.87 19.48 19.70 87.78 19.86 90 91 89.01 18.92 19.31 88.84 88.76 20.08 92 89.99 19.13 89.91 19.52 89.82 19.91 89.73 20.30 92 93 90.97 19.34 90.88 19.73 90.80 20.13 90.71 20.52 93 91 91.95 19.54 91.86 : 19.94 1 91.77 20.35 91.68 20 . 75 94 95 92.93 19.75 92.84 20.16 92.75 20.56 92.66 20.97 95 96 93.90 19.96 93.81 ! 20.37 93 . 72 20 . 78 ( 93.63 21.19 9fi| 97 94.83 20.17 94.79 1 20.58 1 94.70 20.99 1 94.61 ' 21.41 ! 97 98 95.86 20.38 95.77 '20.79 I 95.68 ' 21.21 95.58 21.63 1 98 99 96. N4 20.. 58 96.75 121.01 96.65 21.43 96.56 i 21.85 1 99 100 c 5 97.81 20.79 97.72 i 21.22 97.63 121.64 97.53 122.07 |100 Dep. 1 Lat. Dep. 1 Lat. Dep. 1 Lat. Dep. Lat. | 78 1 )ecr. \ 771 Deg i 77A Deg. 77il 3eg. Q i 28 TrwVVFESE TABLE. 13 Deg. 134 Deg. 131 Deg. I3.f Deg. Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep, ~i 0.97 0.23 ~1)T97 0.23 0.97 0.23 0.97 0,24 ~l 2 1.95 0.45 1.95 0.46 1.95 0,47 1.94 0,48 2 3 2.92 0.67 2.92 0.69 2.92 0,70 2.91 0,71 3 4 3.90 0.90 3.89 0.92 3.89 0,93 3.89 0,95 4 5 4.87 1.12 4.87 1.15 4.86 1.17 4.86 1,19 5 6 5.85 1.35 5.84 1.38 5.83 1,40 5.83 1,43 6 7 6.82 1.57 0.81 1.60 6.81 1,63 6.80 1,66 7 » 7.80 1.80 7.79 1.83 7.78 1,87 7.77 1,90 8 y 8.77 2.03 8.76 2.06 8.75 2,10 8.74 2,14 9 10 11 9.74 2.25 9.73 2.29 9.72 2,33 9.71 2,38 2,61 10 11 10.72 2.47 10.71 2.52 10.70 2,57 10.68 12 11.69 2.70 11.68 2.75 11.67 2,80 11.66 2.85 12 13 12.67 2.92 12.65 2.98 12.64 3,03 12.63 3.09 13 14 13.64 3.I01 13.63 3.21 13.61 3,27 13.60 3.33 14 15 14.62 3.37; 14.60 3.44 14,59 3,50 14.57 3.57 15 16 15.59 3.00' 15.57 3.67 15.56 3,74 15.54 3.80 16 17 16.57 3.821 10.55 3.90 16.53 3,97 16.51 4.04 17 IS 17.54 4.0.T! 17.52 4.13 17.50 4,20 17.48 4,28 18 19 18.51 4.27! 18.49 4.35 18.48 4.44 18.46 4,52 19 20 21 19.49 20.46 4.501 4.72' 19.47 4.58 19.45 4.67 1 19.43 4,75 20 20.44 4.81 20.42 4.90 20.40 4,99 21 22 21.44 4.95 21.41 5.04 21.39 5,14 21.37 5,23 22 23 22.41 5.17 22.39 5.27 22.36 5,37 22.34 5.47 23 24 23.38 5.40 23.36 5.50 23.34 5,60 23.31 5.70 24 26 24.36 5.62 24.33 5.73 24.31 5,84 24.28 5.94 25 26 25.33 5.85 25.31 5.96 25,28 6.07 25.25 6.18 26 27 20.31 6.07 26.28 6.19 26.25 6.30 26.23 6.42 27l 28 27.28 6.30 27.25 6,42 27.23 6,. 54 27.20 6,66 28 29 28.26 6.52 28.23 6.65 28,20 6,77 28.17 6.89 29 30 31 29.23 30.21 6.75 29.20 6.88 29,17 7,00 29 . 14 7.13 30 6.97 30.17 7.11 30,14 7,24 30.11 7.37 31 32 31.18 7.20 31.15 7.33 31,12 7,47 31.08 7.61 32 33 32.15 7.42 32.12 7.56 32,09 7,70 32.05 7.84 33 34 .33.13 7.65 33.09 7.79 33,06 7,94 33,03 8.08 34 35 34.10 7.87 34.07 8.02 34,03 8.17 34.00 8.32 35 36 35.08 8.10 35.04 8.25 35,01 8.40 34.97 8.56 36 37 36.05 8.32 36.02 8.48 35,98 8.64 35.94 8,79 37 38 37.03 8.55 36.99 8.71 36,95 8,87 36.91 9,03 38 39 38.00 8.77 37.96 8.94 37,92 9.10 37.88 9,27 39 40 41 38.97 9.09 9.22 38.94 9.17 9.40 38,89 9.34 9.57 38.85 9,51 40 41 39.95 39.91 39.87 39.83 9,75 42 40.92 9.45 40.88 9.63 40.84 9.80 40.80 9.98 42 43 41.90 9 67 41.86 9.86 41.81 10.04 41.77 10,22 43 44 42.87 9.90 42.83 19.08 42.78 10,27 42.74 10,46 44 45 43.85 10.12 43.80 10.31 43.76 10.51 43.71 10.70 45 46 44.82 10.35 44.78 10.54 44.73 10.74 44.68 10.93 46 47 45.80 10.57 45.75 10.77 45,70 10.97 45.65 11.17 47 48 46.77 10.80 46.72 11.00 46,67 11.21 46.62 11.41 48 49 47.74 11.02 47.70 11.23 47.65 11.44 47.60 11,65 49 50 48.72 11.25 48.67 11.46 48,62 11.67 48.57 11,88 ^0 1 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat, 1 5 77 Deg. 761 Deg. 761 Deg. 76i Deg. TRAVERSE TABLE. 29 51 13 Deg. 13i Deg. 13-i Deg, 131 Deo. s ? 51 Lat. Dep. Lat. Dep. Lat. Dep, Lat. Dep. 49.69 11,47 49.64 11.69 49,. 59 11.91 49.54 12.12 52 50.67 11,70 50.62 11.92 50.. 56 12.14 .50.61 12.36 52 53 51.64 11.92 51.59 12.15 51.54 12.37 51.48 12.60 53 54 52.62 12.15 .52.66 12.38 .52.51 12.61 52.45 12.84 54 55 53.. 59 12.37 53.. 54 12.61 63.48 12.84 .53.42 13.07 55 56 54.56 1 12.60 54.51 12.84 54.45 13.07 54.40 13.31 5C 57 55.541 12.82 55.48 13.06 .55.43 13.31 .55.37 13., 55 57 68 50.51 13.05 56.46 13.29 .56.40 13.. 54 56 34 13.79 58 59 57.49 13.27 .57.43 13.52 57.37 13.77 67.31 14.02 59 60 58.46 13. .50 58.40 13.75 58.34 14.01 .58.28 14.26 60 "61 59.44 13.72 59.38 13.98 59.31 "14.24 59.25 14.. 50 61 62 60.41 13.95 60.35 14.21 60.29 14.47 60.22 14.74 62 63 61.39 14.17 61.32 14.44 61.26 14.71 61.19 14.97 63 f;4 62.36 14.40 62.. 30 14.67 62.23 14.94 62.17 15.21 64 65 63.33 14.62 63.27 14.90 63.20 15.17 63.14 15.45 65 66 64.31 14.85 64.24 15.13 64,18 15.41 64,11 15.69 66 67 65. 2S 15.07 65.22 15.36 65,15 15.64 65,08 15.93 67 68 6f..26 15.30 66.19 15.59 66,12 15,87 €6,05 16.16 68 69 67.23 15.52 67.16 15.81 67,09 16,11 67,02 16.40 69 70 71 68,21 15,75 68.14 16,04 16.27 68.07 16.34 16.57 16.81 17.04 67,99 16.64 70 "71 69.18 15.97 69.11 69.04 68,97 16.88 72 70.15 16.20 70.08 16. .50 70.01 69.94 17,11 72 73 71.13 16,42 71.06 16.73 70.98 70.91 17.35 73 74 72.10 16.65 72.03 16.96 71.96 17.28 71.88 17.59 74 ,75 73.08 16.87 73.00 17.19 72.93 17,50 72.85 17.83 75 76 74.05 17.10 73.98 17.42 73.90 17,74 73.82 18.06 76 77 75.03 17.32 74.95 17.65 74.87 17,98 74.79 18.30 77 78 70.00 17.55 75.92 17.88 75,84 18,21 75.76 18.. 54 78 79 70.98 17.77 76.90 18.11 76.82 18,44 76.74 18.78 79 80 81 77.95 18.00 77,87 78.84 18.34 18. ".57' 77.79 78.76 18,68 77.71 78,68 19.01 19.25 80 81 78.92 18.22 18,91 82 79.90 18.45 79.82 18.79 79.73 19.14 79.65 19.49 82 83 80.87 18.67 80.79 19.02 80.71 19.38 80.62 19.73 83 84 81.85 18.90 81.76 19.25 1 81.68 19.61 81.. 59 19.97 84 85 82 . 82 19.12 82.74 19.48 ' 82.65 19.84 82.. 56 20.20 85 86 83.80 19.35 83.71 19.71 83.62 20-08 83.54 20.44 86 87 81.77 19.57 84.68 19.94; 84.60 20.31 84.51 20.68 87 88 85.74 19,80 85.66 20.17 85 . 57 20.54 85.48 20.92 88 89 86.72 20.02 86.63 20.40 i 86.. 54 20.78 86.45 21.15 89 90 91 87.69 88.67 20.25 87.60 88.58 20,63 20.86 ' 87.51 88.49 21.01 21.24 87.42 88.39 21.39 21.63 90 91 20.47 92 89. P4 20.70 89.55 21.09 89.46 21.48 89.36 21.87 92 93 90.62 20.92 90. .52 21.32 90.43 21.71 90.33 22.10 93 94 91.59 21.15 91.. 50 21.. 54 91.40 21.94' 91.31 22.34 94 9r. 92.. 57 21,37 92.47 21.77 92..38i22.18| 92.28 22.58 95 96 93 . 54 21.60 93.44 22.00 93..35 122.41 1 93.25 22.82 96 97 94.51 21.82 94.42 22.23 ; 94.32 22.64 1 94.22 23.06 97 98 95.49 ■>.2.05 95.39 22.46 95.29 22.88 1 95.19 23.29 98 99 96.46 22.27 96.36 22.69 96.26 23.11 96.16 23.53 99 100 8 c at .2 Q 97.44 22.50 97.34 22,92 97.24 23.34 97.13 23.77 100 Dcp. -•i Dep, T.rj Dep. Lat. 1 Dep. Lat. 5 77 Deg. 76} Deg. j 76i Deg, 76} Deg. 21 30 TRAVERSE TABLE. .Oe. [ 14iDeg. Uk Deg. 1 141 Deg. 3 Lat.| Dep. Lat. Dep. Lat. Dep. Lat. Dep. ~o79T' ~0"."2T 0.97 0.25 ~'o:w 0.25 0.97 0.25 ~~i 2 1.94 0.48 1.94 0.49 1.94 0.50 1.93 0.51 2 3 2.91 0.73 2.91 0.74 2.90 0.75 2.90 0,76 3 , 4 3.88 0.97 3.88 0.98 3.87 1.00 3.87 1,02 4 5 4.85 1.21 4.85 1.23 4.84 1.25 4.84 1,27 5 6 5.82 1.45 5.82 1.48 5.81 1.50 5.80 1.53 6 7 6.79 1.69 6.78 1 72 6.78 1.75 6.77 1.78 7 8 7.76 1.94 7.75 1.97 7.75 2.00 7.74 2.04 8 9 8.73 2.18 8.72 2.22 8.71 2.25 8.70 2.29 9 10 11 9.70 10.67 2.42 2.66 9.69 2.46 2.71 9.68 2.50 2.75 1 9.67 2.55 2.80 10 11 10.66 10.65 10.64 12 11 . 04 2.90 11.03 2.95 11.62 3.00 11.60 3.06 12 13 12.61 3.15 12.60 3.20 12.59 3.25 12.57 3.3) 13 14 13.58 3.39 13.57 3.45 13.55 3.51 13.. 54 3.. 56 14 15 14.55 3.63 14.54 3.69 14.. 52 3.76 14.51 3.82 15 16 15.52 3.87 15.51 3.94 15.49 4.01 15.47 4.07 16 17 16.50 4.11 16.43 4.18 16.46 4.26 16.44 4.33 17 18 17.47 4.35 17.45 4.43 17.43 4.51 17.41 4 . 58 18 19 18.44 4.60 18.42 4.63 18.39 4.76 18.37 4.34 19 20 21 19.,41 4.84 19.38 4.92 19.36 5.01 5.26 19.34 5.09 20 21 20.38 5.08 20.35 5.17 20.31 5,. 35 22 21.35 5.32 21.32 5.42 21.30 5.51 21.28 5.60 22 23 22.32 5.56 1122.29 5.81 ,23.26 5.66 22.27 5.76 22 . 24 5.86 23 2t 23.99 5.91 23.24 6.01 23.21 6,li 24 25 24,26 6.05 24.23 6.15 24.20 6.26 24.18 6.37 25 26 25.23 6.29 25.20 6.40 25.17 6.51 25.14 6,62 28 27 26.20 6.53 26.17 6.65 26.14 6.76 26.11 6,87 27 28 27.17 6.77 27.14 6.89 27.11 7.01 27.08 7,13 23 29 2S.14 7.02 28.11 7.14 28.08 7.26 28.04 7,33 29 30 31 29.11 30.08 7.26 7.50 29. OS 7.38 29.04 7.51 29.01 7.64 7.'8y 30 31 30.05 7.63 30.01 7.76 29.93 32 31.05 7.74 31.02 7.88 30.98 8.01 30.95 8.15 32 33 32.02 7.98 31.93 8.12 31.95 8.26 31.91 8.40 33 34 32.99 8.23 32.95 8.37 32 . 92 8.51 32.83 8. 60 34 35 33.96 8.47 .33 . 92 8.62 33.89 8.76 33.85 8.91 35 36 .34.93 8.71 34.89 8.86 34.85 9.01 34.81 9.17 36 37 35.90 8.95 35.86 9.11 35.82 9.26 .35.78 9.42 37 38 36.87 9.19 36.83 9.35 36.79 9.51 36.75 9.67 38 39 37.84 9.44 37.80 9.60 37.76 9.76 37.71 9.93 39 40 3S.81 9.68 33.77 9.85 38.73 10.02 38.63 10.18 40 41 33.78 9.92 39.74 10.09 39.69 10.27 39. "65 10.44 41 42 4'J.75 10.16 40.71 10.34 40.66 10.52 40.62 10.69 42 43 41.72 10.40 41.68 10.58 41.63 10.77 41.. 58 10.95 43 44 42.69 10.64 42.65 10.83 42.60 11.02 42.-55 11.20 44 45 i 43.66 10.89 43.62 11.08 43.57 11.27 43.52 11.46 45 46 144.63 11.13 44.58 11.32 44.53 11.52 44.48 11.71 46 47 45.60 11.37 45.55 11.57 45.. 50 11.77 45.45 11.97 47 48 46 . 57 11.61 46 . 52 11.82 48.47 12.02 46.42 12.22 48 49 47.54 11.85 I 47.49 12.06 47.44 12.27 47.39 12.48 49 50 i i .2 Q ,48.51 12.10 48.46 12.31 48.41 12.52 48.35 12.73 50 Dep, 1 Lat. Dep. iLa.. Dag. Dep. Lat. Dep. Lat. 1 3 76 Deg. ^H Deg. 15\ Deg. TRAVERSE TABLE. 31 1' 51 14 Deg. 14i Deg. 141 Deg. 141 Deg. 1 Lat. Dep. Lat. Dep. Lat. 49.38 Dep. Lat. Dep. T2T98 49.49 12,34 49.43 12.55 12.77 49.32 52 50.46 12.58 50.40 12.80 50.34 13.02 .50,29 13.24 52 53 51.43 12.82 51.37 13.05 51.31 13.27 51.25 13.49 53 54 52.40 13.06 52.34 13.29 52.28 13. ,52 52,22 13.75 54 55 53.37 13.31 53.31 13.54 53.25 13,77 .53.19 14,00 55 56 54.34 13.55 54.28 13.78 54.22 14,02 .54.15 14,26 1 561 57 55.31 13.79 .55.25 14.03 .55.18 14.27 .55.12 ! 14.51 i 57| 5S 56.28 14.03 .56.22 14.28 56.15 14. .52 56.09 14,77 581 59 57.25 14.27 57.18 14.52 57.12 14.77 57.06 15,02 ! 591 60 61 58.22 14.52 .58.15 14.77 16,02 .58.09 15.02 .58.02 58.99 15,28 60 61 69.19 14.76 59.12 59 . 06 15.27 15,. 53 62 60.16 15.00 60.09 15,26 60.03 15.52 .59 . 90 15.79 62 63 61.13 15.24 61.06 15.51 60.99 15.77 60.92 16.04 63 64 62.10 15.48 62.03 15.75 61.96 16.02 61.89 16.29 64 65 63.07 15.72 63.00 16,00 62 . 93 16.27 62.86 16.. 55 65 66 64.04 15.97 63.97 16.25 63.90 16.53 63.83 16.80 66 67 65.01 16.21 64.94 16.49 64.87 16.78 64.79 17.06 67 68 65.98 16.45 65.91 16.74 65.83 17.03 65.76 17.31 68 CO 66.95 16.09 66.88 16,98 66.80 17,28 66.73 17.57 69 70 71 67.92 16.93 67.85 17.23 67.77 17.53 17.78 67.69 68.66 17.82 70 68.89 17.18 68.82 17.48 68 . 74 18.03 71 72 69.86 17.42 69.78 17.72 69.71 18.03 69.63 18.33 72 73 70.83 17.66 70.75 17.97 70.67 18.28 70.. 59 18.59 73 74 71.80 17.90 71.72 18.22 71.64 18.. 53 71.56 18.84 74 75 72 77 18.14 72.69 18.46 72.61 18.78 72., 53 19.10 75 76 V3 74 18.39 73.66 18.71 73.58 19.03 73,. 50 19., 35 76 77 74.71 18.63 74.63 18.95 74.. 55 19.28 74.46 19.60 77 78 75.68 18.87 73,60 19.20 75.52 19.. 53 75.43 19.86 78 79 76.65 19.11 76.57 19.45 76.48 19.78 76.40 20.11 79 80 81 77.62 78.. 59 19.35 77.. 54 19.69 77.45 20.03 77.. 36 78.33 20.37 20.62 80 81 19.60 78.51 19.94 78.42 20,28 82 79.56 19.84 79.48 20,18 79.. 39 20,. ^3 79.30 20.88 82 83 80.. 53 20.08 80.45 20,43 80.36 20,78 80.20 21.13 83 84 81.50 20.32 81.42 20,68 81.32 21,03 81.23 21.39 84 85 82.48 20.56 82.. 38 20,92 82.29 21.28 82.20 21,64 85 86 83.45 20.81 83.35 21,17 83.26 21.53 83.17 21.90 86 87 84.42 21.05 84.32 21.42 84.23 21.78 84.13 22.15 87 88 85.. 39 21.29 85.29 21.66 85.20 22.03 85.10 22.41 88 89 86.36 21.53 86.26 21.91 86.17 22.28 86.07 22.66 89 90 91 87.33 21.77 22.01 87.23 22.15 22.40 87.13 22.. 53 87.03 22,91 90 91 88.30 88.20 88.10 22.78 88.00 23,17 92 89.27 22.26 89.17 22.65 89.07 23.04 88.97 23,42 42 93 90.24 22.. 50 90.14 22.89 90.04 23.29 89.94 23,68 1 93 94 91.21 22.74 91.11 23.14 91.01 23. .54 90.90 23.93 1 94 95 92.18 22.98 92.08 23.38 91.97 23.79 91.87 24.19 1 95 96 93.15 23.22 93.05 23-63 92.94 24.04 92.84 24.44 1 96 97 94.12 23.47 94,02 23.88 93.91 24.29 93.80 24.70 97 98 95.09 23.71 94.98 24.12 94.88 24.. 54 94,77 24.95 i 98 99 96.06 23 95 95.95 24.37 95.85 24.79 95,74 25.2! ' 99 100 97.03 24.19 96.92 24.62! 96.81 25.04 96.70 25.46 ,190 s c Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. , c Q 76 Deg. 75| Deg 75^ Deg. 75iDeg TRAVERSE TABLE. 15 Deg. 15^ Deg. 15i Deg. 15i Deg. Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 1 0.97 0.26 0.96 0.26 0.96 0.27 0.96 0.27 1 2 1.93 0.52 1.93 0..53 1.93 0.53 1.92 0.54 2 3 2.90 0,78 2.89 0.79 2.89 0.80 2.89 0.81 3 4 3.86 1.04 3.86 1.05 3.85 1.07 3.85 1.09 4 5 4.83 1.29 4.82 1.32 4.82 1.34 4.81 1.36 5 6 5.80 1.55 5.79 1.58 5.78 1.60 5.77 1.63 6 7 0.76 1.81 6.75 1.84 6.75 1.87 6.74 1.90 7 8 7.73 2.07 7.72 2.10 7.71 2.14 7.70 2.17 8 9 8.69 2.33 8.68 2.37 8.67 2.41 8.66 2.44 9 10 9.60 2.59 9.65 2.63 9.64 2.67 9.62 2.71 2". 99 10 11 11 10.63 2.85 10.61 2.89 10.60 2.94 10.59 12 11.59 3.11 11.58 3.16 1 1 . 56 3.21 11, .55 3.26 12 13 12.56 3.36 12.54 3.42 12.53 3.47 12,51 3.53 13 14 13.52 3.62 13.51 3.68 13.49 3.74 13.47 3.80 14 15 14.49 3.88 14.47 3.95 14.45 4.01 14.44 4.07 15 16 15.45 4.14 15.44 4.21 15.42 4.28 15.40 4.34 16 17 16.42 4.40 16.40 4.47 16.38 4.54 16.36 4.61 17 18 17.39 4.06 17.37 4.73 17.35 4.81 17.32 4.89 18 19 18.35 4.92 18.33 5.00 18.31 5.08 18.29 5.16 19 20 19.32 5.18 5.44 19.30 20.26 5.26 19.27 5.34 19.25 5.43 5. "70 20 21 21 20.28 5.52 20.24 5.61 j 20.21 22 21.25 5.69 21.23 5.79 21.20 5.88 1 21.17 5.97 22 23 22.22 5.95 22.19 6.05 22.16 6.151 22.14 6.24 23 24 23.18 6.21 23.15 0.31 23.13 6.41 23.10 6.51 24 2o 24.15 6.47 24.12 6.. 58 24.09 6.68' 24.06 6.79 25 26 25.11 6.73 25.08 6.84 25.05 6.95 1 25.02 7.06 26 27 126,08 6.99 26.05 7.10 26.02 7.22 25.99 7.33 27 28 27.05 7.25 27.01 7.36 26.98 7.48 26.95 7.60 28 29 28.01 7.51 27.98 7.63 27.95 7.75 27.91 7.87 29 30 31 28.98 7.76 28 . 94 7.89 28 . 9 1 8.02 28.87 8.14 8.41 30 31" 29.94 8.02 29.91 8.15 29.87 8.28 29.84 32 30.91 8.28 30.87 •8.42 30. H4 8.55 30.80 8.69 32 33 31.88 8.54 31.84 8.68 31.80 8.82 31.76 8.90 33 34 32.84 8.80 32 . 80 8.94 32.76 9.09 32.72 9.23 34 35 33 . 8 1 9.06 33.77 9.21 33.73 9.35 33.69 9.5'1 35 36 34.77 9.32 34 . 73 9.47 34.69 9.62 31 . 65 9.77 36 37 35.74 9.. 58 35 . 70 9.73 35 . 65 9.89 35.61 10.04 37 38 36.71 9.84 36.66 10.00 36.62 10.16 36.. 57 10.31 38 39 37.67 10.09 37.63 10.26 37 . 58 10.42 37.. 54 10.59 39 40 33.64 10.35 38.59 1 10. .52 3S.55 10.69 To:96- 3S . 50 3;».46 10.86 11.13 10 41 41 39.60 1 10.61 39.56 1 10.78 39 . 5 1 42 40.57 1 10.87 40.. 52 11.05 40.47 11.22 40.42 11.40 42 43 41.53 j 11.13 41.49 11.31 41.44 11.49 41.39 11.67 43 44 42.50 1 11.39 42.45 11.57 42.40 11.76 42.35 11.94 44 45 43.47 1 11.65 43.42 11.84 43.36 12.03 143.31 12.21 45 46 44.43 11.91 44.38 12.10 44.33 12.29 44.27 12.49 46 47 1 15.40 ' 12.16 145.35 12.30 45.29 12.56 45.24 12.76 47 48 46.36 i 12.42 46.31 12.63 46.25 12.83 46.20 13.03 48 49 47.33 1 12.68 i 47.27 12.89 47.22 13.09 47.16 13.30 49 50 48.30 j 12.94 : 48.24 13.15 48.18 13.36 Lat, 48.12 13.57 50 i s s c .2 Dep. 1 Lat. jl Dep. 1 Lat. Dep. Dep. Lat. 75 Deg. 74! Deg. 74. Deg. 74i Deg. TRAVERSE TjVBLE. 33 2 5. 1 5T 15 Dcg. 15i Deg. 15i Deg. 151 Deg. i 5j Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 49.26 T3726" 49.20 13.41 49.15 13.63 49.09 13.84 52 50.23 13.46 50. J7 13.68 50 . 1 1 13.90 .50.05 14.11 52 53 51.19 13.72 51.13 13.94 51.07 14.16 51.01 14.39 63 54 .52.16 13.98 52.10 14.20 .52.04 14.43 51.97 14.60 54 55 53,13 14.241 53.06 14.47 .53.00 14.70 .52.94 14.93 ■ 65 56 54.09 14.49 54.03 14.73 53.96 14.97 63.90 i 15.20 56 57 55.06 14.75 54.99 14.99 54.93 15.23 .54.86 15.47 57 58 56.02 15.01 55.96 15.26 55.89 15.. 50 .55.82 15.74 58 59 .56.99 15.27 56.92 15.52 56.85 15.77 56.78 1 16.01 59 60 61 57.96 15.53 57.89 15.78 57.82 58 . 78 16.03! 16.30 i 57.75 1 16.29 60 "61 58.92 15.79 58.85 16.04 58.71 i 16. .56 62 59.89 16.05 59.82 16.31 59 . 75 16.57 59.67 16.83 62 63 60.85 16.31 60.78 16.57 60,71 16.84 60.63 I 17.10 63 64 61.82 16.56 61.75 16.83 61.67 17.10 CI. 60 ! 17.37 64 65 62.79 16.82 62,71 17.10 62.64 17.37 62.. 56 17.64 65 66 63.75 17.08 63.68 17. 3S 63.60 17.64 03.52 17.92 66 67 64.72 17.34 64.64 17.62 64.56 17.90 64. 4S 18.19 67 63 65.68 17.60 65.61 17.89 65.53 18.17 65.45 18.40 68 69 66.65 17.86 66.57 18.15 66.49 18.44 66.41 18.73 69 70 71 67.61 18.12 67.54 18.41 67.45 18.71 67.37 19.00 70 71 68.58 18.38 68.. 50 18.68 68.42 18.97 68.33 19.27 72 69.55 18.63 09.46 18.94 69.38 19.24 69.30 1 19.54 72 73 70.51 18.89 70.43 19.20 70.35 19.51 70.26 19.82 73 74 71.48 19.15 71.39 19.46 71.31 19.78 71.22 20.09 74 75 72.44 19.41 72.36 19.73 72.27 20.04 72.18 20..% 75 76 73.41 19.67 73.32 19.99 73 . 24 20.31 73,15 20.63 76 77 74.38 19.93 74.29 20.25 74.20 20.58 74.11 20.90 77 78 75.34 20.19 75.25 20.. 52 75.16 20.84 75.07 21.17 78 79 76.31 20.45 76.22 20.78 76.13 21.11 76.03 21.44 79 80 81 77.27 20.71 77.18 21.04 77.09 21.38 77.00 21.72 80 81 78.24 20.96 78.15 21.31 78.05 21.65 77.96 21.99 82 79.21 21.22 79.11 21.. 57 79.02 21.91 78.92 22.26 82 83 80.17 21.48 80.08 21.83 79.98 22.18 79.88 22.53 83 84 81.14 21.74 81.04 22.09 80.94 22.45 80.85 22.80 84 85 82.10 22.00 82.01 22.36 81.91 22.72 81.81 23.07 85 86 83.07 22.26 82.97 22.62 82.87 22.98 82.77 23.34 86 87 84.04 22.52 83.94 22.88 83.84 23.25 83.73 23.62 87 88 85.00 22.78 84.90 23.15 84.80 23.. 52 84.70 23.89 88 89 85.97 23.03 85.87 23.41 85.76 23.78 85.66 24.16 89 91 86.93 23.29 86.83 23.67 86.73 24.05 86.62 24.43 90 91 87.90 23.55 87.80 23.94 87.69 24.32 "87758 24.70 92 88.87 23.81 88.76 24.20 88 . 65 24.59 188.55 24.97 92 93 89.83 24.07 89.73 24.46 89.62 24.85 89.51 25.24 93 94 90.80 24.33 90.69 24.72 90.58 25.12 90.47 25.52 94 95 91.76 24.59 91.65 24.99 91.54 25.39 91.43 25.79 95 96 92 73 24.85 92.62 1 25.25 92.51 25.65 92.40 126.06 96 97 93.69 25.11 93.58 25.51 93.47 25.92 93.36 26.. 33 97 98 94.66 25.36 94.55 25.78 94.44 26.19 94.32 26.60 98 99 95.63 25.62 95.51 26.04 95.40 26.46 95.28 26.37 99 100 i i 96.59 Dep, 25.88 36.48 26.30 96.36 26.72 96.25 27.14 100 1 ^ Lat. Dep. Lat. Dep. Lat, Dep. Lat. 75 Deg. 741 Deg. 74^ Deg. 74iDcg. 34 TRAVEKSE TABLE. 1 16 Deg. 164 Deg. 161 Deg. 161 Deg. 3 ? L... Dep. Lat. Dep. Lat. Dep, Lat. Dep. 0.96 0.28 0.96 0.28 0.96 ~0 28" 0.96 0.29 2 1 93 0.55 1.92 0.56 1.92 6.57 1.92 0.58 2 3 2.88 0.83 2.88 0.84 2.88 0.85 2.87 0.85 3 4 3.85 1.10 3.84 1.12 3.84 1.14 3.83 1.15 4 5 4.81 1.38 4.80 1.40 4.79 1.42 4.79 1.44 5 6 5.77 1.65 5.76 1.68 5.75 1.70 5.75 1.73 6 7 6.73 1.93 0.72 1.96 6.71 1.99 e.70 2.02 7 8 7.69 2.21 7.68 2.24 7.07 2.27 7.66 2.31 8 9 8.65 2.48 8.64 2.. 52 8.63 2.. 56 8.62 2 . 59 9 10 11 9.01 2.76 9.60 2.80 9.. 59 2.84 9.58 2.88 10 10.57 3.03 10., 56 3.08 10.55 3.12 10.. 53 3.171 ll! 12 11.54 3.31 11.52 3.36 11.51 3.41 11.49 3.46 12 13 12.. 50 3.58 12.48 3.64 12.46 3.69 12.45 3.75 13 14 13.40 3.86 13.44 3.92 13.42 3.98 13.41 4.03 14 15 14.42 4.13 14.40 4.20 M..38 4.26 14.36 4.32 15 16 15.38 4.41 15.36 4.48 15.34 4.54 15.32 4.61 16 17 16.34 4.69 16.32 4.76 16.30 4.83 16.28 4.90 17 18 17.30 4.96 17.28 5.04 17.26 5.11 17.24 5.19 18| 19 18.26 5.241 18.24 5.32 18.22 5.40 18.19 5.48 19 20 19.23 5.51 19.20 5.60 19.18 5.68 19.15 5.76 6.05 20 21 21 20.19 5.79 20.16 5.88 20.14 5.96 20.11 22 21.15 6.06 21.12 6.16 21.09 6.25 21.07 6.34 22 23 22 . 1 1 6.34 22.08 6.44 22.05 6.53 22.02 6.63 23 24 23.07 6.62 23.04 6.72 23.01 6.82 22.98 6.92 24 25 24.03 6.89 24.00 7.00 23.97 7.10 23.94 7.20 25 26 24.99 7.17 24.96 7.28 24.93 7.38 24.90 7.49 26 27 25.95 7.44 25.92 7.. 56 25.89 7.67 25.85 7.78 27 28 20.92 7.72 20.88 7.84 26.85 7.95 20.81 8.07 28 29 27.83 7.99 27.84 8.11 27.81 8.24 27.77 8.36 29 30 28.84 8.27 28.80 8.39 28.76 8.52 28.73 8.65 30 31 29.80 8.. 54 29 . 76 8.67 29.72 8.80 29.68 •8.93 31 32 30.76 8.82 .30.72 8.95 30.68 9.09 30.64 9.22 32 33 31.72 9.10 31.68 9.23 31.64 9.37 31.60 9.51 33 34 32.68 9.37 32.64 9.51 32.60 9.66 32.56 9.80 34 35 33.64 9.65 33.60 9.79 33.56 9.94 33.51 10.09 35 36 34.61 9.92 34.56 10.07 34.52 10.22 34.47 10.38 36 37 35.57 10.20 35., 52 10.35 35.48 10.51 35.43 10.66 37 38 36.53 10.47. 36.48 10.63 36.44 10.79 36.39 10.95 38 39 37.49 10.75 37.44 10.91 37.39 11.08 37.35 n.24 39 40 41 38 . 45 11.03 38.40 11.19 38.35 39.31 11.36 38.30 11. .53 40 41 39.41 11.30 ' 39.36 11.47 1 1 . 64 39.26 11.82 42 40.37 1 1 . 58 40.32 11.75 40.27 11.93 40.22 12.10 42 43 41.33 11.85 41.28 12.03 41.23 12.31 41.18 12. ,39 43 44 42.30 12.13 42.24 12.31 42.19 12., 50 42.13 12.68 44 45 43.26 12.40 43.20 12.59 43.15 12.78 43.09 12.97 45 46 44.22 12.68 44.16 12.87 44.11 13.06 44.05 13.26 46 47 45.18 12.95 45.12 13.15 45.00 13.35 45.01 13.55 47 48 46.14 13.23 46.08 13.43 46.02 13.63 45,96 13.83 48 49 47.10 13.51 47.04 13.71 46.98 13.92 46.92 14.12 49 50 48.08 13.78 48.00 13.99 47.94 14.20 47.88 14.41 50 T Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 74 Deg. 731 Deg. 731 Deg. 73i Deg. s TRA.VERSE TABLE. 35 o 3 ? 51 16 Deg. WiDeg. 16 i Dsg 161 Deg. P .51 ^LaT' Dop. LatT' Dep. Lat. Dep. Lat. 48T84 Dep. 14". 70 49.02 14.06 48.96 14.27 48.90 T4r4T 52 49.99 14.33 49.92 14.. 55 49.86 14.77 49.79 14.99 5-Z 53 50.95 14.61 50.88 14.83 .50.82 15.05 1 50 . 75 16.27 53 64 51.91 14.88 51.84 15.11 51.78 15.34! 51.71 15.56 5.i 55 52.87 15.16 .52.80 15.39 52.74 15.62' 52.67 15.85 5.n 56 .=^3.83 15.44 .53.76 15.67 .53.69 15.90 63.62 16.14 6i:i 57 54.79 15.71 .54.72 15.95 .54.65 16.19 .54.. 58 16.43 58 ,55.75 15.99 55.68 16.23 .55.61 16.47 55.. 54 16.72 ,58 59 56.71 16.26 .56.64 16.51 56.57 16.76 66 . .50 17.00 59 60 57.68 16.54 57.60 16.79 57.-53 17.04 57.45 17.29 60 61 .58.64 16.81 58.56 17.07 .58.49 17.32 58.41 17.. 58 61 62 59.60 17.09 .59.. 52 17.35 59.45 17.61 69.37 17.87 62 63 60.56 17.37 60.48 17.63 60.41 17.89 60.33 18.16 63 64 61.52 17.64 61.44 17.91 61.36 18.18 61.28 18.44 64 65 62.48 17.92 62.40 18.19 62.32 18.46 62.24 18.73 65 66 63.44 18.19' 63.. 36 18.47 63.28 18.74 63.20 19.02 66 67 64.40 18.47 64.32 18.75 64.24 19.03 64.16 19.31 67 68 65.37 18.74 65.28 19.03 65.20 19.31 65.11 19.60 68 69 66.33 19.02 66.24 19.31 66.16 19.60 66.07 19.89 69 70 71 67.29 19.29 67.20 68.16 19.. 59 67.12 19.88 67.03 20.17 70 71 68.25 19.57 19.87 68.08 20 . 1 7 67.99 20.46 72 69.21 19.85 69.12 20.15 69.03 20.45 68 . 95 20.76 72 73 70.17 20.12 70.08 20.43 69.99 20.73 69.90 21.04 73 74 71.13 20.40 71.04 20.71 70.95 21.02 70.86 21.33 74 75 72.09 20.67 72.00 20.99 71.91 21.30 71.82 21.61 76 76 73.06 20 . i/5 72.96 21.27 72.87 21.59 i 72.78 21.90 76 77 74.02 21.22 73.92 21.55 73.83 21.87 i 73.73 22.19 77 78 74.98 21. .50 ■54.88 21.83 74.79 22.15 74.69 22.48 78 79 75.94 21.78 75.84 22.11 75.75 22.44 ' 75 . 65 22.77 79 80 -81 76.90 22.05 76.80 22.39 76.71 22.72 |76.61 23.06 80 81 77.86 22.33 77.76 22.67 77.66 23.01 ,77.56 28.34 82 78.82 22.60 78.72 22.95 78.62 23.29 ,78.52 23.63 82 83 79.78 22.88 79.68 23.23 79 . 58 23.. 57 179.48 23.92 83 84 80.75 23.15 80.64 23.51 80.. 54 23.86 180.44 24.21 84 85 81.71 23.43 81.60 23.79 81.50 24.14 ;81.39 24.50 85 86 82.67 23.70 82.56 24.07 82.46 24.43 i 82.35 24.78 86 87 83.63 23.98 83.52 24.35 83.42 24.71 83.31 25.07 87 88 84.59 24.26 84.48 24.62 84.38 24.99 184.27 25.36 88 89 85.55 24.53 85.44 24.90 85.33 25 . 28 i 85.22 25.65 89 90 91 80.51 24.81 86.40 25.18 86.29 25.56 j86.18 87.14 25.94 26.23 90 91 87.47 25.08 87.36 25.46 87.25 25.85 92 88.44 25.36 88.32 25.74 88.21 26.13 188.10 26.51 92 93 89.40 25.63 89.28 26.02 89.17 26.41 189.05 26.80 y3 94 90. CS 25.91 90.24 26.30 90.13 26.70 90.01 27.09 94 93 91.32 26.19 91.20 26.. ^^8 91.09 26.98 90.97 27.38 95 96 92.28 26.46 92.16 26.86 92.05 27.27 191.93 27.67 96 97 93.24 126.74 93.12 27.14 93.01 27.55 1 92.88 27.95 97 98 94.20 27.01 94.08 27.42 93.96 27.83 93.84 28.24 98 99 95.16 27.29 95.04 27.70 94.92 28.12 94.80 28.. 53 99 100 i .2 Q 96.13 27.56 96.00 27.98 Lat. 95.88 28.40 95.76 28.82 100 ~i c C Dep. Lat. Dep. Dep. La.. Dep. Lat. ' 74 Deg. 73} Deg. 73^ Deg. j 7^i Deg. 36 TKAVKRSE TABLE. p CD 17 Deg. 17i Deg. m Deg. 171 Deg. a 9 Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 0.96 0.29 0.95 0.30 0.95 0.30 0.95 0.30 2 1.91 0.,58 1.91 0.59 1.91 0.60 1.90 0,61 2 3 2.87 0.88 2.87 0.89 2.86 0.90 2.86 0.91 3 4 3.83 1.17 3.82 1.19 3.81 1.20 3.81 1.22 4 5 t.78 1.46 4.78 1.48 4.77 1..50 4.76 1.52 5 6 5.74 1.75 5.73 1.78 5.72 1.80 5.71 1.83 6 7 6.69 2.05 6.69 2.08 6.68 2.10 6.67 2 13 8 7.65 2.34 7.64 2.37 7.63 2.41 7.62 2.44 8 9 8.61 2.63 8.60 2.67 8.. 58 2.71 8.57 2.74 9 10 11 9.55 10.52 2.92 9.55 2.97 9.54 3.01 9.52 3.05 10 11 3.22 10.51 3.26 10.49 3.31 10.48 3.35 12 11.48 3.51 11.46 3.56 11.44 3.61 11.43 3.66 12 13 12.43 3.80 12.42 3.85 12.40 3.91 12.. 38 3.96 13 14 13.39 4.09 13.37 4.15 13.35 4.21 13.33 4.27 14 15 14.34 4.39 14.33 4.45 14.31 4.51 14.29 4.57 15 16 15.30 4.68 15.28 4.74 4.81 15.24 4.88 16 17 16.26 4.97 16.24 5.04 16!21 5.11 16.19 5.18 17 18 17.21 5.26 17.19 5.34 17.17 5.41 17.14 5.49 18 19 18.17 5..'^.6 18.15 6 63 18.12 5.71 18.10 5.79 19 20 21 19.13 5.85 19.10 .5.93! 15.23! 19.07 20.03 C.Ol 6.31 19.05 6.10 20 21 "20 . 08 6.14 20.06 20.00 6.40 22 21.04 fi.43 21.01 6 52 i 20.98 6.62 20.95 6.71 22 23 21.99 6.72 21.97 e,.8'4| 21.94 6.92 21.91 7.01 23 24 22 . 95 7.02 2.;. 92 7.12 22.89 7.22 22.86 7.32 24 20 23.91 7.31 23.88 7 41 23.84 7.. 52 23.81 7.62 25 26 24.86 7.60 24.83 7.71 24.80 7.82 24.76 7.93 26 27 25.82 7.89 25.79 8.01 2rj.75 8.12 25.71 8.23 27 28 ■Zf> . 7s 8.19 26.74 8.30 26.70 8.42 26.67 8.54 28 29 27.73 8.48 27.7') 8.60 27.66 8.72 27.62 8.84 29 3(1 31 28 . 69 29.65 8.77 9.06 28.65 29.61 8.90 28.61 29 . 57 9.02 28.57 9.15 30 31 9.19 9.32 29.. 52 9.45 32 30.60 9.36 30.56 9.49 30.. 52 9.62 30.48 9.76 32 33 31. .56 9.65 31.. 52 9.79 31.47 9.92 31.43 10.06 33 34 ?2.5l 9.94 32.47 10.08 32.43 10.22 32.38 10.37 34 35 S3. 47 10.23 33.43 10.38 33 . 38 10.52 33.33 10.67 35 36 34.43 10.53 34.. 38 10.68 34.33 10.83 34.29 10.98 36 37 35.38 10.82 35.34 10.97 35.29 11.13 35 24 11.28 37 38 36.34 11.11 36.29 11.27 36.24 11.43 30.19 11.58 38 39 .37. :W 11.40 37.25 11.57 37.19 11.73 37.14 11.89 39 40 41 ,38.25 11.09 38.20 11.86 12.16 .38.15 12.03 38.10 12.19 40 41 39.21 11.99 39.16 39.10 12.. 33 39.05 12.50 42 40.16 12.28 40.11 12.45 40.06 12.63 40.00 12.80 42 43 41.12 12.57 41.07 12.75 41.01 12.93 40.95 13.11 43 44 42. OS 12.86 42.02 13.05 41.96 13.23 41.91 13.41 44 45 43.03 13.16 42.98 13.34 42.92 13.53 42.86 13.72 45 46 43.99 13.45 43.93 13.64 43.87 13.83 43.81 14.02 46 47 44.95 18.74 44.89 13.94 44.82 14.13 44.76 14.33 47 48 45.90 14.03 45.84 14.23 45.78 14.43 45.71 14.63 48 49 46.86 14.33 46.80 14.. 53 46.73 14.73 46.67 14.94 49 50 i 47.82 14.62 47.75 14.83 47.69 15.04 47.62 115.24 50 1 5 Dsp. Lat. Dep. _ Lat. Dep. Lat. Dep, 1 Lat. 73 Deg. 721 Deg. 72| Deg. 724 Deg. TKAVERSE TABLK. 37 1 51 17 Deg. 17i Deg. IT^ D.g. 171 De„.. 9 Lat. Dep.l Lat. 48.71 Dep. Lat. 48 JH D.P., 15.34 Lat. Dep. 43.77 14.91 15.12 48.57 15.. 55 51 52 49.73 15.20 49.66 15.42 49.59 15.64 49.. 52 16.85 52 53 50.68 15.50 50.62 15.72 50 . 55 15.94 50.48 ; 16. 16 ■ 53 54 51.64 15.79 51.. 57 16.01 5 1 . 50 16.24 51.43 16.46 , 54 55 52.60 16.08 .52.53 16.31 52.45 16.54 .52.38 i 16.77 ; ,55 56 53.55 16.37 53.48 16.61 .53.41 16. 84^ .53.33 1 17.07 1 56 57 54.51 16.67 54.44 16.90 .54.36 17.14 54.29 17.33 1 57 58 .55.47 16.96| 55.39 17.20 .55.32 17.44 .55.24 17.68 53 59 56.42 17.25 1 50.35 17.. 50 56.27 17.74 56.10 17.99 59 _6U 61 57.38 17. .541 57.30 17.79 57.22 18.04 57.14 18.29 1 60 18.60 1 61 58.33 17.33 58.26 18.09 5S.18 18.34 58.10 6-Z .59.29 18.13 59.21 18.39 59.13 18.64 59.05 18.90 ! 62 63 60.25 18.42! 60.17 18.68 GO. OS 18.94 GO. 00 19.21 63 64 61.20 18.71 61.12 j 18.98 61.04 19.25 1 60.95 19.51 64 65 62.16 19.00; 62.08 i 19.28 61.99 19.55 61.91 19.82 65 66 63.12 19.30' 63.03 19.57 62.95 19,35 62.86 20.12 66 67 64.07 19.59 ' 63.99 19.87 63.90 20.15 63.81 20.43 67 68 65.03 19.88; 64.94 20.1.6 64.85 20.45] 64.76 20.73 68 69 65.99 20.17; 65.90 20.46 65.81 : 20.75 65.72 21.04 69 70 71 6B.94 20.47 I 66.85 20.75 66.76 , 21.05 66.67 21.34 21.65 70 71 '67.90 20.76 67.81 21.05 ^07. 71 21.35 67.62 72 68.85 21.05 68.76 21.35 68.67 21.65 68.57 21.95 72 73 09.81 21.34, 69.72 21.65 69.62 21.95 69.52 22.26 73 74 70.77 21.64 70.67 21.94 70.58 22.25 70.48 22., 56 74 75 71.72 21.93 71.63 22 . 24 71.53 22.. 55 71.43 22.86 75 76 72.68 22.22 72.58 22.. 54 72.48 22.85 72.38 23.17 76 77 73.64 22.51 73.. 54 22.83 73.44 23.15 73.33 23.47 77 78 74.59 22.80 74.49 23.13 74.39 23.46 74.29 23.78 78 79 75.-55 23.10 75.45 23.43 75.34 1 23.76 75.24 24.03 79 80 76.50 23.39 76.40 23.72 76.30 24.06 76.19 24.39 ' 80 TI 77746- 23.68 77.30 24.02 77.25 24.36 77,14! 24.69 81 82 78.42 23.97 78.31 24.32 78.20 24.66 78.10 25.00 82 83 79.37 24.27 79.27 24.61 79.16 25.96 79.05 25.30 83 84 80.33 24.56 80.22 24.91 80.11 25.26 80.00 25.61 84 85 81.29 24.85 81.18 25.21 81.07 25.56 80.95 25.91 85 86 82.24 25.14 82.13 25.50 82.02 1 25.86 81.91 26.22 86 87 83.20 25.44 83.09 25.80 82.97 , 26.16 82.86 26 . 52 1 87 1 88 84.15 25.73 84.04 26.10 83.93 26.46 83.81 26.83 88 89 85.11 26.02 85.00 26.39 84.88 26.76 84,76 27.13 89 90 91 86.07 26.31 85.95 26.69 '85.83 27.06 85.72 27.44 ■27.74 90 91 87.02 26.61 86.91 26.99 ; 86.79 27.36 86.67 92 87.98 26.90 87.86 27.28 '87.:'4' 27.66 87.62 28.05 92 93 88.94 27.19 88.82 27.58 88.70 27.97 88.57 i 23.35 | 93 94 89.89 27.48 89.77 127.87 89.65 28.27 89.53 ' 28.66 94 95 90.85 27.78 90.73 28.17 90.60 28. .57 90.48 128.96 95 96 91.81 28.07 91.68 28.47 91.56 28.87 91.43 129.27 96 97 92.76 28.36 92.64 28.76 92.51 29.17 92.38 129.57 97 98 93.72 28.65 93.59 29.06 93.40 29.47 93.33:29.88 1 98 99 94.67 23.94 94.55 29.36 94.42 29.77 94,29 30,18 99 100 s 95.63 29.24 .95.50 29.65 95.37 1 30,07 95,24 1 30,49 100 Dep. Lat. Dep. Lat. Dep. 1 Lat. jDep. 1 Lat, 1 73 Deg. m Deg. 72i Deg. 72iDeg, 38 TRAVERSE TABLE. 5 1 18 Deg. 18i Deg. 18| Deg. 181 Deg. f r Lat. Dep. Lat. Dep. Lat. Dep. Lat. 0.95 Dep. 0.32 0.95 0.31 0.95 0.31 1 0.95 0.32 2 1.90 0.62 1.90 0.63 1.90 0.63 1.89 0.64 2 3 2.85 0.93 2.85 0.94 2 84 0.95 2.84 0.96 3 4 3.80 1.24 3.80 1.25 3 79 1.27 3.79 1.29 4 5 4.76 1.55 4.75 1.57 4.74 1.59 4.73 1.61 5 6 5.71 1.85 6.70 1.88 5.69 1.90 5.68 1.93 6 7 6.66 2.16 6.65 2.19 6.64 2.22 6.63 2.25 7 Si 7.61 2.47 7.60 2.51 7.. 59 2.54 7.58 2.57 8 9 8.56 2.78 8.55 2.82 8.. 53 2.86 8.52 2.89 9 10 1 9.51 11 1 10.46 3.09 3.40 9.50 10.45 3.13 3.44 9.48 10.43 3.17 3.49" 9.47 10.42 3.21 10 3. ,54 ! li 12 11.41 3.71 11.40 3.76 11.38 ? 81 11.36 3.86 i 12 1.3 12.36 4.02 12.35 4.07 12.33 4 12 12.31 4.18 13 14 13.31 4.33 13.30 4.38 13.28 4.44 13.26 4. .50 [ 14 15 14.27 4.64 14.25 i 4.70 14.22 4.76 14.20 4.82 15 16 15.22 4.94 15.20 5.01 15.17 5.08 15.15 5.14 10 17 16.17 5.25 16.14 5.32 16.12 5.39 16.10 5.46 17 18 17.12 5.56 17.09 5.64 17.07 5.71 17.04 5.79 18 19 18.07 5.87 18.04 5.95 18.02 6.03 17.99 6.11 19 20 19.02 6.18 18.99 19.94 6.26 18.97 6.35 18.94 19.89 6.43 1 20 1 '21 19:97 6.49 6.58 19.91 6.66 ~6.75 21 22 120.92 6.80 20.89 6.89 20.86 6.98 20.83 7.07 22 23 121.87 7.11 21.84 7.20 21.81 7.30 21.78 7.39 23 24 '22.83 7.42 22.79 7.52 22.76 7.62 22 . 73 7 71 24 25 23.78 7.73 23 . 74 7.83 23.71 7.93 1:23.67 8.04' 25 26 24.73 8.03 24.69 8.14 24.66 8.25 24.62 8.36 26 27 25 . 68 8.34 25 . 64 8.40 25.60 8.57 25.57 8.68 27 28 26.63 8.65 26.59 8.77 26.55 8.88 26.51 9.00 1 28 i 29 127.. 58 8.96! 27.54 9.08 27.50 9.20 27.46 9.32 29 30 128.53 9.27i 28.49 29.44 9.39 28.45 9.52 9.84 28.41 29.35 9.64 3C 31 31 29.48 9.58 9.71 29.40 9.96 32 30.43 9.89 30.39 10.02 30.35 10.15 30.30 10.29 1 32 1 33 31.38 10.20 31.34 10.33 31.29 10.47 31.25 10.61 33 ! 34 .32.34 10.51 32.29 10.65 1 32 . 24 10.79 32.20 10.93 34 35 33.29 10.82 33.24 10.96 1 33.19 11.11 .33.14 11.25 35 36 34.24 11.12 34.19 11.271 34,14 11.42 34.09 11.57 36 37 35.19 11.43 35.14 11.59 35.09 11.74 35.04 11.89 37 38 36.14 11.74 36.09 11.90 36.04 12.06 35.98 12.21 38 39 37.09 12.05 37.04 12.21 36.98 12.37 36.93 12.54 39 40 38.04 12.36 37.99 12.53 37.93 12.69 37.88 '38.82 12.86 40 1 41 38.99 12.67 38 . 94 12.84 38.88 13.01 13.18 41 42 39 . 94 12.98 39.89 13.15 39.83 13.33 39.77 13.. 50 42 43 40.90 13.29 40.84 13.47 40.78 13.64 40.72 13.82 43 44 41.85 13.60 41.79 13.78 41.73 13.96 41.66 14.14 44 45 142.80 13.91 42.74 14.09 42.67 14.28 42.61 14.40 45 46 43.75 14.21 43.69 14.41 43.62 14.60 43.56 14.79 46 47 144.70 14.52 44.64 14.72 44.57 14.91 44.51 15.11 47 48 45.65 14.83 45.59 15.03 45.52 15.23 45.45 15.43 48 49 46.60 15.14 46.54 15.35 46.47 15.55 46.40 15.75 49 50 47.55 1 15.45 1 47.48 JJ>.66_ 47.42 15.87 47.35 16.07 50 i Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. c 5 l| 72 Deg. 711 Deg. 7HI )eg. 7U Deg. TRAVKRSE TABLF. 2 i 51 18 Deg. 18i Deg. 18^ Deg. 1 181 Deg. Lat. Dep. Lat. Dep. Lat. j Dep. ,"l6Tl8" j-La,. 48 .29 Dep. 16.39 18.50 15.76 48.43 i 15.97 Us.. 36 52 49.45 16.07 49.38 16.28 49.31 1 16.50 ! 49.24 16.71 62 53 50.41 16.38 1 50.33 16.60 50.26 ' 16.82 50.19 17.04 53 54 51.36 16.69 ]51.28 16.91 ,51.21 1 17.13 51.13 17.36 54 55 '52.31 17.00 52.23 17.22 .52.16 1 17.45 52.08 17.68 55 66 53.26 17.30 53.18 17. .54 153. 11 17.77 53.03 18.00 56 57 54.21 17.61 54.13 17.85 54.05 18.09 i 53.98 18.32 57 58 55.16 17.92 55.08 18.16 65.00 18.40 1 54.92 18.64 j 58 59 .56.1] 18.23 .56.03 18.48 55.95 i 18.72 | 55.87 18.96 1 59 GO 61 57.06 18.54 56.98 18.79 56.90 ' 19.04 56.82 19.29 _60 58.01 18 85 57.93 I 19. 10 57.85 19.36 57.76 19. 6f 61 62 .58.97 19.16 .58.88 1 19.42 58.80 19.67 58.71 19.93' 62 63 59.92 19.47 59.83 19.73 59.74 , 19.99 59.66 20 . 25 : 63 61 60.87 19.78 60 . 7S 1 20 . 04 60.69 20.31 60.60 20 . 57 i 64 65 61.82 20.09 61.73 20.36 61.64 20.62 61.55 20.89 : 05 66 62.77 20.40 62.68 1 20.67 62.59 I 20.94 62.50 21.22 ; 66 67 63.72 20.70 63.63 20.98 63.54 121.26 63.44 21.54 ! 67 68 64.67 21.01 64.58 21.30 64.49 21.58 64.39 21.86 1 68 69 65.62 21.32 65.53 ! 21.61 65.43 21.89 65 . 34 22.18 ; 69 70 71 66.57 21.63 66.48 21.92 66.38 22.21 66.29 22.50 1 70 22.82 ! 71 67.53 21.94 67.43 22.23 67.33 22.53 67.23 72 68.48 22.25 68.38 22.55 68.28 22.85 ! 68.18 23.14 72 73 69.43 22.56 69.. 33 22.86 69.23 23.16 1 69.13 23.47 1 73 | 74 70.38 22.87 70.28 23.17 70.18 23.48 1; 70.07 23.79 t 74 1 75 71.33 23.18 71.23 23.49 71.12 23.80 : 71.02 24.11 75 76 72.28 23.49 72.18 23 . 80 72.07 24.12 i 71.97 24.43 76 77 73.23 23.79 73.13 24.11 73.02 24.43 72.91 24.75 77 78 74.18 24.10 74.08 24.43 73.97 24.75 73.86 25.07 78 79 75.13 24.41 75.03 24.74 74.92 25.07 74.81 25.39 79 80 81 76.08 77.04 24.72 75 . 98 25.05 75.87 25.38 75.75 76.70 25.72 1 80 26.04 i 81 25.03 76.93 25.37 76.81 25.70 82 77.99 25.34 77.88 25.68 77.76 26.02 77.65 26.. 36' 82 83 78.94 25.65 78.83 25.99 78.71 26.34 78.60 26.68 83 84 79.89 25.96 79.77 26.31 79.66 26.65 79.54 27.00 1 84 85 80.84 26.27 80.72 26.62 80.61 26.97 80.49 27.32 85 86 81.79 26.58 81.67 26.93 81.56 27.29 81.44 27.64 86 87 82.74 26.88 82.62 27.25 82.50 27.61 82.38 27.97 87 88 83.69 27.19 83.57 i 27.56! 83.45 27.92 83.33 28. 2Q 88 89 84.64 27.50 84.52 ' 27.87 i 84.40 28.24 84.28 28.61 89 90 91 85.60 86.55 27.81 28.12 85.47 128.18! 85.35 28.56 85.22 28.93 90 29.25; 91 86.42 I 28.50 ! 86.30 28.37 86.17 92 87.50 28.43 87.37 1 28.81 87.25 129.19 Si'. 12 29.57 j 92 93 88.45 28 . 74 88.32 1 29.12 88.19 29.51 88.06 29.89 93 94 89.40 29.05 89.27 ! 29.44 ! 89.14 \ 29.83 89.01 30.22 1 94 95 90.35 29.36 90.22 29 . 75 1 90.09 1 30.14 89.96 30.54 ; 95 96 91.30 29.67 91.17 30.06 1 91.04 30.46 170.91 30.86 96 97 92.25 29.97 92.12 30.38: 91.99 30.78 91.85 31.18 97 98 93.20 30.28 93.07 30.69' 92.94 31.10 92.80 31.50 98 99 94.15 30.59 94.02 31.00; 93.88 31.41 93.75 31.82. 99 100 1 95.11 30.90 94.97 Dep. 31.32 :| 94.83 31.73 94.69 32.14 100 Dep. Lat. Lat. ! Dep. Lat. Dep. Lat 8 72 1 )eg. 71} Deg. \ 71iDeg. 7U Deg. 1 b 40 TRAVFRSE TABLE. B 19 Deg. 19i Deg. 19i Deg. 191 Deg. B Lat. 0.95 Dep. "oTsF Lat. Dep. Lat. Dep. Lat. Dep, 0.94 0.33 0.94 0..33 0.94 0.34 I 2 1.89 0,65 1.89 0,66 1.89 0.67 1.88 0.68 2 3 2.84 0.98 2.83 0,99 2.83 l.UO 2 82 1.01 3 4 3.78 1.30 3.78 1..32 3.77 1.34 3.76 1,35 4 5 4.73 1.63 4.72 1,65 4.71 1.67 4.71 1,69 5 6 5.67 1.95 5,66 1,98 5.66 2.00 5.65 2,03 fi 7 6.62 2.28 6,01 2,31 6.60 2.34 6.59 2,37 7 8 7.56 2.60 7,55 2,64 7.54 2.67 7.53 2,70 8 9 8.51 2.93 8.50 2.97 8.48 3.00 8.47 3,04 9 10 9.46 3.26 9.44 10.38 3.30 9.43 3.34 9.41 3,38 10 11 10,40 3,58 3.63 10.37 3.67 10.35 3,72 11 12 11.35 3.91 11. .33 3,96 11.31 4.01 11.29 4,06 12 13 12.29 4.23 12.27 4.29 12.25 4,34 12.24 4.39 13 14 13.24 4., 56 13.22 4.62 13.20 4.67 13,18 4.73 14 15 14.18 4.88 14,16 4.95 14,14 5,01 14,12 5.07 15 16 15.13 5.21 15,11 5.28 15,08 5,34 15,06 5,41 16 17 16.07 5.-53 16,05 5.00 16,02 5,67 16,00 5,74 17 18 17.02 5.86 16.99 5.93 16,97 6,01 16,94 6,08 18 19 17.96 6.19 17.94 6.26 17,91 6.34 17.88 6.42 19 20 21 18.91 6.51 18.88 6.59 18,85 6.68 18,82 6.76 20 21 19.56 0.84 19.83 6.92 19.80" 7,01 19,76 7.10 22 20,80 7.16 20.77 7.25 20.74 7.34 20.71 7.43 22 23 21,75 7.49 21.71 7.. 58 21.68 7.68 i' 21.65 7.77 23 24 22.69 7.81 22 . 66 7.91 22,62 8.01 22.-59 8.11 24 25 23.64 8.14 23,60 8,24 23,57 8.35 23.53 8.45 25 26 24.-58 8.46 24,55 8,-57 24.51 8.68 24.47 8.79 26 27 25.. 53 8.79 25,49 8,90 25.45 9.01 25.41 9.12 27 28 26,47 9.12 26,43 9,23 26.39 9.35 26.35 9.46 28 29 27.42 9,44 27.38 9,-56 27.34 9.68 27.29 9.80 29 30 28.37 9,77 28,32 9,89 28.28 10.01 28.24 10.14 30 31 29.31 10,09 29,27 10,22 29.22 10,35 29.18 10.48 3i 32 30.26 10,42 30,21 10,55 30,16 10,68 30.12 10.81 32 33 31.20 10.74 31,15 10,88 31,11 11,02 31.06 11.15 33 34 32.15 11.07 32,10 11,21 .32,05 11,35 32.00 11.49 34 35 33.09 11,39 33,04 1 1 , 54 32.99 11,68 32.94 11.83 35 36 34.04 1 1 , 72 33,99 11.87 33.94 12,02 33.88 12.17 36 37 34.98 12,05 34,93 12.20 34.88 12,35 34.82 12.50 37 38 35.93 12,37 35.88 12.-53 35.82 12,68 35.76 12.84 38 39 36.88 12,70 36.82 12.86 36.70 13.02 .36.71 13.18 39 40 37.82 13,02 37.76 38.71 13.19 37.71 13.35 13.69 37.65 13.-52 40 41 4f 38.77 13,35 13.-52 38.05 38.59 13.85 42 39.71 13,*7 39,65 13.85 39.59 14.02 39.53 14.19 42 43 40.66 14.00 40.60 14.18 40,-53 14.35 40,47 14.. 53 43 44 41.60 14.32 41.. 54 14.51 41,48 14.69 41,41 14.87 44 45 42.55 14,65 42.48 14.84 42,42 15.02 42,35 15.21 45 46 43.49 14,98 43.43 15.17 43,36 15.36 43,29 15.-54 46 47 ! 44,44 15,30 44.37 15.-50 44.-30 15.69 44,24 15.88 47 48 145.38 15,63 45.32 15.83 45,25 16.02 45.18 16.22 48 49 46.33 15.95 46.26 16,15 46.19 16.36 46.12 16.56 49 50 47.28 16.28 47.20 16,48 47.13 16^,^ 47.06 16.90 50 c 1 Dep. Lat. Dep. Lat. Dep. Lat. Dep, Lai. 1 71 1 )eg. ■ 70.1 Deg. 70il Deg. 70i Deg. TRAVERSE TABLE. 41 a i 51 19 Deg. 191 Deg. 19^ Dog. 19| Deg. K P '51 Lat. 1 Dep. Lat. Dep. Lat. Dop. Lat. Dep. 48.22 16.60 48.15 T6."8r 48.07 17.02 48.00 17.23 52 49.17 16.93 49.09 17.14 49.02 17.36 48,94 17.57 52 53 .50.11 17.26 50.04 17.47 49.96 17.69 49.88 17.91 53 54 51.06 17.58 .'SO. 98 17.80 .50.90 18.03 1 .50.82 18.25 54 55 52.00 1 17.91 j 51.92 18.13 51.85 18.36 51.76 18.-59 .55 56 52.95 18.23! 52.87 18.46 .52.79 18.69 52.71 18.92 57 53.89 18.. 56, 53.81 18.79 53.73 19.03 -53.65 19.26 57 58 .54.84 18.88 54.76 19.12 1 .54.67 19.36 -54.-59 19.60 58 59 55.79 19.21 55 . 70 19.45! .55.62 19.69 55 . 53 19.94 59 60 61 50.73 19.. 53 56 . 65 19.78 56.56 57 . 50 20.03 20.36 .56.47 20 . 27 60 61 57 . 68 19.86 57.59 20.11 -57.41 20.61 62 58.62 20.19 .58.-53 20.44 58.44 20.70 58.35 20 95 62 63 59.-57 20.51 59.48 20.77 59.39 21.03 59 . 29 21.29 63 64 60.51 20.84 60.42 21.10 60.33 21.36 60.24 21.63 64 65 61.46 21.16 61.37 21.43 01.27 21.70 61.18 21.96 65 66 62.40 21.49 62.31 21.76 62.21 22.03 62.12 22.30 66 67 63.35 21.81 63.25 22 . 09 63. iO 22.37 63.06 22 . 64 67 68 64.30 22.14 64.20 22.42 64.10 22 . 70 64.00 22.93 68 69 65.04 22.40 65.14 22.75 65.04 23.03 64.94 23.32 69 <0 71 66.19 22.79 66.09 23 . 08 65.93 23.37 65.88 66.82 23 . 65 70 71 67.13 23.12 07.03 23.41 66 . 93 23.70 23.99 72 08.08 23.44 67.97 23.71 67.87 24.03 67.76 24.33 72 73 69.02 23.77 68 . 92 24.07 03.81 24.37 68.71 24 . 67 73 74 69.97 24.09 69.86 24.40 09.76 24.70 69.65 25.01 74 75 70.91 24.42 70.81 24 . 73 70.70 2'.. 04 70.. 59 25.34 75 76 71.86 24.74 71.75 25.06 71.64 25.37 1 71. .53 25.63 76 77 72.80 25.07 72.69 25.39 72.-58 25 . 70 72.47 26.02 77 78 73.75 i 25.39 73.84 25.72 73.. 53 26.04 73.41 26.36 78 79 74.70; 25.73 74.-58 26.05 74.47 26.37 74.35 26 . 70 79 80 81 75.64 26.05 75.-53 26.38 75.41 26 . 70 75.29 27.03 80 81 76.59 26.37 76.47 26 . 70 76.35 27.04 76 .24 27.37 82 77.53 26.70 77.42 27.03 77.30 27.37 77.18 27 . 7 1 82 83 78.48 27.02 78.36 27.36 78.24 27.71 78.12 23.05 83 84 79.42 27.35 79.30 27.69 79.18 23.04 79.06 23 . 39 84 85 80.37 27.67 80.25 28.02 80.12 23.37 80.00 23 . 72 85 86 81.31 28.00 81.19 28.35 81.07 23.71 80.94 29.06 86 87 82.26 28.32 82.14 28 . 63 82.01 29.04 1 81.88 29.40 87 88 vS3.21 28.65 83.08 29.01 92.95 29.37 1 82.82 29 . 74 88 89 84.15 28.98 84.02 29 . 34 83 . 90 29.71 , 83.76 30.07 89 90 91 85.10| 29.30 84.97 29.67 84.84 30.04 84.71 30.41 90 91 86.04! 29.63 85.91 30.00 85.78 30.38 85.65 30.75 92 86.99 29.95 86.86 30 . 33 86.72 30.71 86.-59 31.09 92 93 87.93,30.28 87.80 30.66 87.67 31-04 37.. 53 31.43 93 94 88.88 1 30.60 88.74 30.99 188.6I 31.38 88.47 31.76 94 95 89.82 30.93 89.69 31.32 189.-55 31.71 1 89-41 32.10 95 96 90.77 31.25 90.63 31.65 90.49 .32.05 90.35 32.44 96 97 91.72 31.58 91. .58 31.98 91.44 32.38 91.29 1.32.78 97 98 92.66 31.91 92.-52 32.31 92.38 32.71 92.24 33 . 1 2 98 99 93.61 33.23 93.46 32.6'! 93.32 i 33.05 93.18 .33.45 99 100 T Q 94.55 32.56 94.41 32.97 94.26 33., 38 Lat. 94.12 Dep. 33^ Lat. J 1 Dep. Lat. Dep. Lat. Dep. 71 Deg. 701 Deg. 70i Deg. 70i Deg. 42 TRAVERSE TABLE. 20 Deg. m Deg. 201 Deg. 201 Deg. i 1 Lat. 0.94 1 Dep. Lat. Dep. Lat. Dep. Lat. Dep. " 0.35 0.34 0.94 0..35 0.94 0.35 0.94 2 1.88 0.68 1.88 0.69 1.87 0.70 1.87 0.71 3 2.82 1.03 2.81 1.04 2.81 1.05 2.81 1.06 3 4 3.76 1.37 3.75 1.38 3.75 1.40 3.74 1.42 4 5 4,70 1.71 4.69 1.73 4.68 1.75 4.68 1.77 5 6 5.64 2.05 5.63 2.08 5.62 2.10 5.61 2.13 6 7 6.58 2.39 6.67 2.42 6.56 2.45 6.55 2.48 7 8 7.52 2.74 7.51 2.77 7.49 2.80 7.48 2.83 8 9 8.46 3.08 8.44 3.12 8.43 3.15 8.42 3.19 9 10 11 9.40 3.42 9.38 10.32 3.46 9.37 3.50 9.35 3.. 54 10 11 10.34 3.76 3.81 10.30 3.85 10.29 3.90 12 11.28 4.10 11.26 4.15 11.24 4.20 11.22 4.25 12 13 12.22 4.45 12.20 4.50 12.18 4.55 12.10 4.61 13 14 13.16 4.79 13.13 4.85 13.11 4.90 13.09 4.96 14 15 14.10 5.13 14.07 5.19 14.05 5.25 14.03 5.31 15 16 15.04 5.47 15.01 5.. 54 14.99 5.60 14.96 6.67 16 17 15.97 5.81 15.95 5.88 15.92 5.95 15.90 6.02 17 18 16.91 6.16 16.89 6.23 16.86 6.30 16.83 6.38 18 19 17.85 6.50 17.83 6.. 58 17.80 6.65 17.77 6.73 19 20 18.79 6.84 18.76 6.92 18.73 7.00 •18.70 7.09 20 21 19.73 7.18 19.70 7.27 19.67 7.35 19.64 7.44 21 22 20.67 7.52 20.64 7.61 20.61 7.70 20.. 57 7.79 22 23 21. G] 7.87 21.58 7.96 21. .54 8.05 21.51 8.15 23 24 22.55 8.21 22 . 52 8.31 22.48 8.40 22.44 8 . 50 24 25 23.49 8.55 23.45 8.65 23.42 8.76 23.38 8.86 25 26 24.43 8.89 24.39 9.00 24.35 9.11 24.31 9.21 26 27 25.37 9.23 25.33 9.35 25.29 9.46 25.25 9.57 27 28 26.31 9.58 26.27 9.69 26.23 9.81 26.18 9.92 28 29 27.25 9.92 27.21 10.04 27.16 10.16 27.12 10.27 29 30 28.19 1 10.26 28.15 10.38 28.10 10.51 28.05 10.63 30 31 29.13 10.60 29.08 10.73 29.04 10.86 28.99 10.98 31 32 30 . 07 10.94 30.02 11.08 29 . 97 11.21 29.92 11.34 32 33 31.01 11.29 30.96 11.42 30.91 11.56 30.86 11.69 33 34 31.95 11.63 31.90 11.77 31.85 11.91 31.79 12.05 34 35 .32.89 11.97 32.84 12.11 32 . 78 12.26 32.73 12.40 35 38 33.83 12.31 .33 . 77 12.46 33.72 12.61 33.66 12.75 36 37 .34.77 12.65 34.71 12.81 34.66 12.96 34.60 13.11 37 38 35.71 13.00 35.65 13.15 35 . 59 13.31 35 , 54 13.46 38 39 36.05 13.34 30 . 59 13.50 36.. 53 13.66 .36.47 13.82 39 40 37.59 13.68 37. .53 13.84 37.47 14.01 37.41 14.17 40 "^41 38 . 53 14.02 38.47 14.19 38.40 14.36 38.34 14.53 41 42 39.47 14.36 39.40 14.. 54 39.34 14.71 39.28 14.88 42 43 40.41 14.71 40.34 14.88 40.28 15.06 40.21 15.23 43 44 41.35 15.05 41.28 15.23 41.21 15.41 41.15 15.59 44 45 42.29 15.39 42 . 22 15. .58 42.15 15.76 42.08 15.94 45 46 43.23 15.73 43.16 15.92 43.09 16.11 43.02 16. .30 46 47 44.17 16.07 44.09 16.27 44.02 16.46 43.95 16.65 47 48 45.11 16.42 45.03 16.61 44.96 16.81 44.89 17.01 48 49 46.04 16.76 45.97 16.96 45.90 17.16 45.82 17.36 49 50 Q 46.98 17.10 46.91 17.31 46.83 17.51 46.76 17.71 50 c £ Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 70 Deg. 691 Deg. en Deg. 69i Dog TUAVEKSK TAliLK. 43 '51 20 Deg. 20i Dog, 201 Deg. 201 Deg. 2 "51 Lat. Dep. Lat, Dep. T7,65 Lat. 1 Dep. Lat, 4776T Dep. 47.92; 17,44 | 47 35 47.771 17.86 18.07 52 48.86 1 17.79 j 48.79 18.00 43,71 18.21 i 48,63 18.42 52 53 49.801 18.13 49.72 IS. 34 49.64; 18.56 1 49.56 18,78 53 54 50.74 18.47 50.66 18.69 t .50.58 1 18.91 1 .50.50 19.13 54 53 51. 6S 18.81 j 51.60 19.04 51.. 52 19,26 1 51.43 19.49 55 5G ,52.62 19.15 .52.54 19.38 .52.45 19.61 1 52.37 19.84 66 57 ,53.56 i 19.. 50 53,48 19.73 53.39 19.96 1 .53,30 20.19 57 5S .54.50 19.84 54.42 20.07 54.33 20.31 ; 54.24 20.55 58 59 55.44 j 20.18 5 5.. 35 20.42 55 . 26 20.66 1 55.17 20 . 90 59 60 fil 5n.3S : 20.. 52 7>7T:V2 ' 20.86 56.29 20.77 56.20 .57.14 21.01 21.36 56,11 21.20 21.61 60 61 57.23 21.11 57,04" 6-2 5.S.23 21.21 .58.17 21.46 .58.07 21,71 57,98 21.97 62 0:5 59.20, 21.. 55 59.11 21.81 59.01 22,06 58,91 22 . 32 63 r,i 60.14 1 21.89 60,04 : 22,15 1 59.95 22.41 59,85 22.67 64 r,.-, 6 1 . OS ^ 22 . 23 60.98 j 22.50 60.88 22.76 60.78 23.03 65 Ofi 62.02' 22.57 61.92 22.84 61.82 23.11 61,72 23.38 66 67 62.98 22.92 62.86 23.19 62.76 23.46 1 62.65 23.74 67 G8 63.90 123.26 63,80 23,54 63.69 23.81 63.59 24.09 68 6'J 64.84 1 23.60 64.74 23.83 64,63 24.16 64,52 24.45 69 70 71 65.78 23.94 66.72 1 24.28 65.67 66.61 24.23 65.57 24.51 65.46 24.80 70 71 24,5? 66.50 24.86 66.39 25.15 72 67.66 i 24.63 67.55 24.92 67.44 25.21 67.33 25,51 72 73 68.60 i 24,97 68.49 25,27 68.38 25.57 68.26 25,86 73 74 69.54 : 25.31 69.43 25.61 69.31 25.92 69,20 26,22 74 75 70.48 25.65 70.36 25.96 70.25 26,27 70,14 26.57 75 76 71.42 . 25.99 71.30 26.30 71.19 26,62 71.07 26.93 76 77 72.36 ' 26.34 72.24 26.65 72.12 26.97 72,01 27.28 77 78 73 . 30 ; 26 . 68 73.18 27.00 73.06 27.32 72,94 27.63 78 79 74.24:27.02 74.12 27.34 74.00 27.67 ! 73,88 27,99 79 80 81 75.18 1 27.36 76.12 1 27.70 75.06 27.69 28.04 74,93 128,02 74,81 75 . 75 28,34 80 75.99 75,87 28.37 28,70 81 82 77.05 23.05 76.93 28.38 76.81 28 . 72 76.68 29.05 82 83 77.99 ! 28.39 77.37 28.73 77.74 29,07 77.62 29.41 83 84 78 . 93 j 28 . 73 78.81 29.07 78.63 29.42 78 . 55 29.76 84 85 79.87 29.07 79.75 29.42 79.62 29,77 79.49 30.11 85 86 80.81 29.41 80.68 29.77 80,55 30.12 80,42 30.47 86 87 81.75 29 . 76 81.62 30.11 81,49 30,47 181,38 30.32 87 88 82.69 30.10 82 . .56 30.46 82,43 30,82 182.29 31,18 88 89 83.63 30.44 83.. 50 30.80 S3, 36 31.17 83,23 31,-53 89 90 91 84.57 30.73 84.441 31,15 84,30 31,52 84,16 31,89 90 91 85.51 31.12 85.-38 31,50 85,24 31,37 135,10 32.24 92 85.45 31.47 86.31 31,84 86.17 32,22 86.03 32.59 92 93 87.39, 31.81 87.25 32.19 87.11 .32.57 86.97 32.95 93 91 8S.33' 32.15 88.19 32.. 54 88 . 05 32.92 87,90 133.30 94 95 89.27 32.49 89.13 32.88 88.98 33.27 188,34 33 . 66 95 95 90.21 ; 32.83 90.07 33.23 89.92 1 33.62 89,77 34.01 96 97 91.15 133.18 91.00 33 . 57 90.86 33.97 90.71 34.37 97 9S 93.09' 33.. 52 91.94 ,33.92 91.79134.32 91.64 34.72 98 99 93.03 33.86 92.88 34.27 92.73 34.67 92.. 58 35.07 99 10_0 .1 : 93.97. 34,20 93.82 34,61 93.67 1 35,02 93.51 35.43 100 c 1 "" ' Dep. i 70 Lat. Dep. Lat. Dep. j Lat, Dep. Lat. Deg. ..1 Deg. 69 i Deg 69i Deg 44 TRAVKKSE TAI5LE. 21 Deg. 21i Deg. 211 Deg. 21i Deg. Lat. Dep. 1 Lat. Dep. "0.36 Lat. Dep. Lat. Dep. 0.93 0.36 1 0.93 0.93 0.37 0.93 0.37 2 1.87 0.72 1.86 0.72 1.86 0.73 1.86 0.74 2 3 2.80 1.08 2.80 1.09 2.79 1.10 2.79 1.11 3 4 3.73 1.43 3.73 1.45 3.72 1.47 3.72 1.48 4 6 4.67 1.79 4.66 1.81 4.65 1.83 4.64 1 .85 5 6 5.60 2.15 5.59 2.17 5.58 2.20 5.57 2.22 6 7 6.54 2.51 6.52 2.54 6.51 2.57 6,50 2.59 7 8 7.47 2.87 7.46 2.90 7.44 2.93 7.43 2.96 8 9 8.40 3.23 8.39 3.26 8.37 3.30 8.36 3.34 9 111 9.34 3.58 9.32 3.62 9.30 3.67 9.29 3.71 4.08 10 11 10.27 3.94 10.25 3 . 99 10.23 4.03 10.22 )2 11.20 4.30 11.18 4.35 11.17 4.40 11.15 4.45 12' 13 12.14 4.66 12.12 4.71 12.10 4.76 12.07 4.82 13 14 13.07 5.02 13.05 5.07 13.03 5.13 13.00 5.19 14 ir, 14.00 5.38 13.98 5.44 13.96 5.. 50 13.93 5.56 15 ic 14.94 5.73 14.91 5.80 14.89 5.86 14.86 5.93 16 17 15.87 6.09 15.84 6.16 15.82 6.23 15.79 6.30 17 18 16.80 6.45 16.78 6.52 16.75 6.60 16.72 6.67 18 19 17.74 6.81 17.71 6.89 17.68 6.96 17.65 7.04 19 ^ 18.67 7.17 18.64 7.25 18.01 7.33 1 8.. 58 7.41 20 21 19.61 7.53 i 19.57 7.61 19. .54 7.70 19.50 7.78 21 22 20.54 7.88 20.50 7.97 20.47 8.06 20.43 8.15 22 23 21.47 8.24 21.44 8.34 21.40 8.43 21.36 8.. 52 23 24 ] 22.41 8.60 22.37 8.70 22.33 8.80 22.29 8.89 24 25 23.34 8.96 23.30 9.06 23.26 9.16 23.22 9.20 25 26 24.27 9.32 24.23 9.42 24.19 9.53 24.15 9.63 20 27 25.21 9.68 25.16 9.79 25.12 9.90 25.08 10,01 27 28 20.14 10.03 20.10 10.15 26.05 10.26 26.01 10 38 23 29 27.07 10. ,39 27.03 10.51 26.98 10.63 26.94 10.75 29 30 31 28.01 10.75 27.96 10.87 11.24 27.91 11.00 27.86 28.79 11.12 11.49 30 31 28.94 11.11 28. 8t. 28.84 11.36 32 29.87 11.47 29.82 11.60 29.77 11.73 29.72 11.86 32 33 30.81 11.83 30.76 11.96 30.70 12.09 .30.65 12.23 33 34 31.74 12.18 31.69 12.32 31.63 12.46 31. .58 12.60 34 35 32.68 12.54 32.62 12.69 32 . 56 12.83 32.51 12.97 35 36 33.61 12.90 33.. 55 13.05 33.50 13.19 33.44 13.34 36 37 34.54 13.26 34.48 13.41 34.43 13.56 34.37 13.71 37 33 35.48 13.62 35.42 13.77 35.36 13.93 35.29 14.08 38 39 36.41 13.98 36 . 35 14.14 36.29 14.29 36.22 14.45 39 40 41 37.34 33.28 14.33 37.28 14.50 37.22 14.66 37.15 14.82 40 41 14.69 38.21 14.86 38.15 15.03 38.08 15.19 42 39.21 15.05 39.14 15.22 39.08 15.39 39.01 15.56 42 43 40.14 15.41 40.08 15. .58 40.01 15.76 39.94 15.93 43 4-1 41.08 15.77 41.01 15.95 40.94 .16.13 40.87 16.30 44 45 42.01 16.13 41.94 16.31 41.87 16.49 41.80 16.68 45 46 42.94 16.48 42.87 10.67 42.80 16.86 42.73 17.05 46 47 43. S8 16.84 43.80 17.03 43.73 17.23 43.65 17.42 47 48 44.81 17.20 44.74 17.40 44.66 17.59 44.58 17.79 48 49 45.75 17. .56 45.67 17.76 45.59 17.96 45.51 18.16 49 50^ 40.68 17.92 46 ^6£ 18.12 46.52 18.33 46.44 Dep. 68i 18.53 _50 1 .2 Dep. Lat. Dep. Lat. Dep. Lat. Lat. Deg. 69 Deg. 68^ Deg 1 08i Deg. TKAVEKSE TABLE. 45 5 9 '51 21 Oeg. 2Ii Deg. 21i Deg. 211 De.. 1 Lat. 47.61 Dep. Lat. 1 Dep. 47.53 ! 18.48 Lat. 1 Dep. Lat. Dep. 18.28 47.45 j 18.69 47.37 18.90 "51 52 4S.55 i 18.64 48.46 ! 18.85 48. .38 19.06 48.30 19.27 52 53 49.48 i 18.99 1 49.40 ; 19.21 49.31 |19 42 49.23 19.64 ' 53 54 50.41 i 19.35 1 50.33 19.57 50.24 ! 19.79 50.16 20.01 .5' 55 51.35 ; 19.71 ! 51.26 ! 19.93 51.17 ^20.16 51.08 20.38; 5. 58 52 28 [20.07 .52.19 20.30 .52. 10 120.52 .52.01 20.75 1 Ri^.l 57 53 21 20.43 53.12 20.66 .53.03 20.89 52 . 94 21.12 1 57! 58 54.15 120.79 .54.06 ! 21.02 53.96 121.26 .53.87 21.49 58 59 55.08 i 21.14 54.99 '21.38 54.89 21.62 .54.80 21.86 59 CO 61 56.01 56.95- 21.50' 55.92 ! 21.75 55.83 21.99 55.73 22.23 60 61 21.86 56.85 i22.11 5G.76 22.36 56.66 22.60 fi2 57.88 22.22: 57.78 22.47 57.69 22 . 72 57.59 22.97 62 63 58.82 22.58 : 58.72 22.83 58 . 62 23.09 ! .58 . .52 23.35' 63 64 .59.75 22.94 59.65 23.20 59.55 23.46 159.44 23 . 72 64 65 60.68 23.29 60.. 58 23.56 60.48 23.82 160.37 24.09 65 6G 61.62 23.65-01.51 23.92 61.41 24.19 ji 61.30 24.46 ' 66 67 62.55 124.01 1 62.44 24.28 62.34 24.56 1162.23 24.33 ; 67 68 63.48 124.37 163.38 24.65 63.27 24.92 f|63.16 25.20 63 69 64.42 124.73!: 64.31 125.01 64.20 25.29 <\ 64.09 25.57 1 69 70 '71 65.35 25.09; 65.24 25.37 65.13 25.66 '65.02 25.94 70 6h.28 25.44 1 66.17 25.73 66.06 26.02: 65.95 26.31 71 72 67.22 125.80 67.10 26.10 66.99 26.39 1, 66.87 26.68 i 72 73 68.15 '26.16 68.04 26.46 67.92 26.75 !i 67.80 27.05 1 73 74 69.08 26.52 68.97 26.82 68.85 27.12 1168.73 27.42 1 74 75 70.02 26.88 69.90 27.18 69.78 27.49 i 69.66 27.79 75 76 70.95 27.24 70.83 27.55 70.71 27.85 70.59 28.16 1 76 77 71.89 27.59 71.76 27.91 71.64 28.22 i! 71.52 28.53 77 78 72.82 27.95 72.70 28.27 72.57 28.59 !i 72.45 28.90 78 79 73.75 28.31 73.63 28.63 73.50 28.95 li 73.38 29.27 79 SO -81 74.69 28.67 74.56 75.49 29.00 74.43 29.32 74.30 '75.23 29.64 80 75.62 29.03 29.36 75 . 36 29.69 30.02 ! 81 82 76.55 29.39 76.42 29 . 72 76.29 30.05 ,!76.16 30 . 39 1 82 83 77.49 29.74 77.36 30.08 ll 77.22 30.42 i! 77.09 30.76 1 83 84 78.42 30.10 78.29 30.44 ii 78. 16 30.79 ' 78.02 31.13 1 84 85 79.35 30.46 79.22 30.81 79.09 31.15 i 78.95 31.50 I 85 86 80.29 30.82 80.15 131.17 80.02 31.52 79.88 31.87 86 87 81.22 31.18 81.08 31.53 80.95 31.89 80.81 32.24 87 88 82.16 31 54 82.02 31.89 81.88 32.25 81.74 32.61 88 89 83.09 31.89 82.95 32.26 82.81 32.62 182.66 32.98 89 90 91 84.02 32.25 83.88 1 32.62 83.74 32.99 183.59 33 . 35 90 "91 84.96 [32.61 ■84.81 32.98 84.67 33.35 ,84.52 33.72 92 85.89 .32.97 1 85.74 33.34 85.60 33.72 '85.45 34.09 92 93 86.82 33.33 li 86.68 33.71 86.-53 34.08 186.33 34.46 93 94 87.76 33.69 187.61 34.07 187.46 34.45 87.31 34.83 94 95 88.69 34.04 88.. 54 34.43 188.39 34.82 i 88.24 35.20 95 96 89.62! 34.40 89.47 34.79 89.32 35.18 li 89.17 35.57 96 97 90.56 34.76 90.40 35.16 90.25 35.55 190.09 35.94 97 9S 91.49 35.12 91.34 : 35.52 91.18 135.92 i| 91.02 36.31 98 99 92.42 35.48 92.27 , 35.88 92.11 136.28 i| 91.95 36.69 ' 99 100 ■s 5 93.36 35.84 93.20 36.24 93.04 36.65 ll 92.88 37.06 ilOO Dop. Lat. Dep. 1 Lat. Dep. Lat. Dep. Lat. C3 69 Deg. 68J Deg. ' 68i Deg. 68J Deg. 22 46 TRAVERSE TABLK. 3 55' 22 Deg. 224 Deg. 22^ Deg. 221 Deg. D 1 i P Lai. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 1 0.93 0.37 0.93 0.38 0.92 0..38 0.92 0.39 2 1.85 0.75 1.85 0.76 1.85 0.77 1.84 0.77 2 3 2.78 1,12 2.78 1.14 2,77 1.15 2.77 1.16 3 4 3.71 1.50 3.70 1.51 3,70 1.53 3.69 1.55 4 5 4.64 1.87 4.63 1.89 4,62 1.91 4.61 1.93 5 6 5.56 2.25 5.55 2,27 5.. 54 2.30 5.53 2 , 32 6 7 6,49 2.62 6.48 2,65 6.47 2.68 6.40 2.71 7 8 7.42 3.00 7.40 3.03 7,39 3,06 7.38 3,09 8 9 8.34 3.37 8.33 3.41 8.31 3.44 8.30 3,48 9 10 9.27 3.75 9.26 3.79 9 . 24 3.83 9.22 3.87 10 if 11 10.20 4.12 10.18 4.17 10.16 4.211 10,14 4,25 12 1 11.13 4.50 11.11 4.54 11,09 4.59 11.07 4,64 12 13 12.05 4.87 12.03 4.92 12.01 4.97 11.99 5.03 13 14 12.98 5.24 12.96 5.30 12.33 5.36 12.91 5.41 14 15 13.91 5.62 13.88 5.08 13.86 5.74 13.83 5.80 15 16 14, S3 5.99 14.81 6.06 14,78 6.12 14.76 6.19 16 17 15.76 6.37 15.73 6,44 15,71 6.51 15.68 6,57 17 18 16,69 6.74 16.66 6.82 16.63 6.89 16.60 6,96 18 19 17.62 7.12 17.59 7.19 17.55 7.27 17.52 7,35 19 20 21 18.54 7.49 18.51 7.57 18,48 7.65 18.44 7.73 20 19.47 7.87 19,44 7.95 19,40 8.04 19.37 8,12 21 22 20.40 8.24 20,36 8.33 20.33 8.42 20.29 8.51 22 23 21.33 8.62 21,29 8,71 21.25 8.80 21.21 8.89 23 24 23.25 8.99 22,21 9,09 22.17 9.18 22.13 9.28 24 25 23,18 9.37 23.14 9,47 23.10 9.57 '123.05 9.67 25 26 24,11 9.74 24.08 9.84 24.02 9.95: 23.98 10.05 26 27 25.03 10.11 24.99 10.22 24.94 10.33 11 24.90 10.44 27 2S 25.96 10.49 25.92 10.60 25.87 10.72 i| 25.82 10.83 28 20 26.89 10.86 26.84 10.98 26.79 11.10 126.74 11.21 29 30 27.82 11.24 27.77 11.36 27 . 72 11.48 27.67 11.60 30 31 28.74 11.61 28.69 11.74 28.64 11.86 28.59 11.99 31 32 29.67 11.99 29 . 62 12.12 29.56 12.25 29,51 12.37 32 33 00,60 12.36 30,54 12.50 30.49 12.63 30.43 12.76 33 34 3 1.. 52 12.74 31,47 12.87 31.41 13,01 131.35 13.15 34 35 32,45 13,11 32.39 13.25 32.34 13,39 32.28 13.53 35 36 33.38 13.49 33.32 13.63 33 . 26 13.78 33.20 13.92 36 37 34.31 13.86 34.24 14.01 34.18 14,16 34,12 14.31 37 38 35.23 14.24 35.17 14.39 35.11 14,54 35.04 14.70 38 39 36.16 14.61 36.10 14.77 36.03 14,92 35.97 15.08 39 40 37.09 14.98 37.02 15,15 36.96 15.31 .36.89 15.47 40 41 41 38.01 15.36 37.95 15.. 52 37.88 15.69 37.81 15.86 42 38.94 15.73 38.87 15.90 33.80 16.07 38.73 16.24 42 43 39.87 16.11 39.80 16.28 39.73 16.46 39,65 16.63 43 1 44 40.80 16.48 40.72 16.66 40 . 65 16.84 40.58 17.02 44 45 41.72 16.86 41.65 17.04 41. .57 17.22 41.. 50 17.40 45 46 42.65 17.23 42 , 57 17.42 12.50 17.60 42.42 17.79 46 47 43.58 17.61 43,50 17.80 43.42 17.99 43.34 18.18 47 48 ! 44.50 17.98 44.43 18.18 44.35 18.37 44.27 18.56 48 49 1 45.43 18.36 45.35 18.55 45.27 18.75 45.19 18.95 49 50 46.36 18.73 46.28 18.93 46.19 19,13 46.11 19.34 50 1 .2 Q I 1 Q Dep. Lat. Dep. Lat, Dep. Lat. Dep. Lat. 68 Dog. 67J Deg. 67i Deg. 67i Deg. TRAVERSE TABLE. 4? s. 1 ? 61 22 Deg. 221 Deg. 1 221 Deg. 1 221 Deg. 1 Lat. Dep. 47.29 19.10 Lat. Dep. Lat. Dep. Lat. Dep. 47.20 19.31 47.12 19.. 52 47.03 19.72 ! 52 48,21 : 19.48 48.13 19.69 48.04 19.90 47.95 20.11 1 52 53 49.14 19.85 49.05 20.07 48.97 20.28 48. «8 20.50 53 54 50.07 120.23 49.93 20.45 49.89 20.66 49.80 20.88 54 55 ! 51.00 i 30.60 50.90 ! 20.83 .50.81 21.05 .50.72 21.27 j 5;. 56 1 51.92 1 20.98 51.83 1 21.20 51.74 21.43 51.64 21.66 5(j 57 ,62.85 21.35 52.76 21. .58 52.66 21.81 52.. 57 ?.2.04 67 58 53.78 1 21.73 53.68 21.96 53.59 22.20 .53.49 22.43 58 59 154.70! 22.10 54.61 22.34 .54.51 22.58 .54.41 22.82 69 60 55.63 122.48 55.. 53 22.72 55.43 56 . 36 22.96 23.34 55.33 1 23.20 60 61 61 56.. 56 1 22.85 56.47 23.10 56.25 23.. 59 62 57.49 23.23 57.38 23.48 1 57.28 23.73 57.18 23.98 62 63 58.41 23.60 58.31 23.85 58.20 24.11 58.10 24.36 63 64 59.34 23.97 .59.23 24.23 59.13 24.49 59.02 24.75 64 65 60.27 24.35 60.16 24.61 60.05 24.87 59 . 94 25.14 65 66 61.19 24.72 61.09 24.99 60.98 25.26 60.87 25.52 66 67 62.12 25.10 62.01 25.37 61.90 25.64 61.79 25 . 9 1 67 68 63.05! 25.47 62.94 25.75 62.82 26.02 62.71 26.30 68 69 63.98 125.85 63.86 26.13 63 . 75 26.41 63.63 26.68 69 70 71 64.90 26.22 64.79 26.51 64.67 65.60 26.79 27.17 64.55 27.07 70 71 65.83 26.60 65 . 7 1 26.88 65.48 27.46 72 66.76 26.97 66.64 27.26 66 52 27.55 66.40 27.84 72 73 67.68 27.35 67.56 27.64 67.44 27 . 94 67.32 28.23 73 74 68.61 27.72 68.49 28.02 68.37 28.32 68.24 28.62 74 75 69.54 28.10 69.42 28.40 69.29 28.70 69.17 29.00 75 76 70.47 28.47 70.34 28.78 70.21 29.08 70.09 29.. 39 76 77 71.39 28.84 71.27 29.16 71.14 29.47 71.01 29.78 77 78 72.. 32 29 . 22 72.19 29.53 72.06 29.85 1 71.93 30.16 78 79 73.25 29.59 73.12 29.91 72.99 3). 23 72.85 ,30.. 55 79 80 81 74.17 75.10 29.97 74.04 30.29 30.67 73.91 30.61 73.78 30.94 80 SI 30.. 34 74.97 74.83 31.00 74.70 31.32 82 76.03 30.72 75.89 31.05 75.76 31.38 75.62 31.71 82 83 76.96 31.09 re. 82 31.43 76.68 31.76 70.54 32.10 83 84 77.88 31.47 77.75 31.81 77.61 32.15 77.46 32.48 84 85 78.81 31.84 78.67 .32.19 78.53 32.53 78.39 32.87 85 86 79.74 32.22 79.60 32.56 79.45 32.91 79.31 33.26 86 87 80.60 32.59 80.. 52 32 . 94 80.38 .33.29 180.23 33.64 87 88 81.59 32.97 81.45 33.. 32 81.30 33.68 81.15 34.03 88 89 82.52 33.34 82.37 33.70 82.23 34.06 182.08 34.42 89 90 91 83.45 33.71 83.30 34.08 83.15 34.44 1 83 . 00 34.80 35.19 90 91 84.37 34.09 34.22 34.46 84.07 34.82 ! 83.92 92 85.30 34.46 85.15 34.84 85.00 35.21 184.84 35.58 92 93 86. 23 1.34. 84 86.08 1 35.21 85.92 35 . 59 1 85 . 76 35.96 93 94 87.16 35.21 87.00 35.59 86.84 35.97 86.69 36.35 94 95 88. 08 1.35. 59 87.93 35.97 87.77 36.35 87.61 36.74 95 96 89.01 135.96 88.85 36.35 88.69 3">.74 88.. 53 37.12 96 97 89.94] 36.34 89.78 36.73 89.62 37.12 189.45 137.51 1 97 93 90.86 136.71 90.70 37.11 90..54 137.50 90.38 1 37.90 i 98 99 91.79 137.09 91.63 37.49 '91.46 37.89 :91.30 38.28 1 99 100 92.72 37.46 92.. 55 37.86 92 .39_j 38.27 ; 92.22 38.6^ , 100 ! §• 1 c 1 5 Dep. Lat. Dep. j Lat. Dep. Lat. Dep. Lat. 5 5 68 Deg. 671 Deg. C7i Deg. 67J Deer. 48 TRAVKKSE TABLE, o 23 Deg. 23i Deg. 23^ Deg. 231 Deg. r Lat. Dcp. Lat. Dcp. Lat. Dep, L«. Dep. 0.40 1 0.92 0.39 0.92 0.39 0.92 0.40 0.92 2 1.84 0.78 1.84 0.79 1,83 0.80 1.83 0.81 2 3 2.76 1.17 2.76 1.18 2,75 1.20 2.75' 1.21 3 4 3.68 1.56 3.68 1.58 3.67 1.59 3.66 1 1.61 1 5 4.60 1.95 4.59 1.97 4.. 59 1.99 4.58! 2.01 5 6 5.52 2.34 5.51 2., 37 5.50 2.39 5.491 2.42 6 7 6.44 2.74 6.43 2.76 6.42 2! 79 6.41 1 2.82 7 8 7.36 3.13 7.35 3.16 7.34 3.19 7,32 3.22 8 9 8.28 3.52 8.27 3.55 8.25 3.59 8.24 3,62 9 10 9.20 3.91 9.19 10.11 3.95 '4.34 9.17 10.09 3.99 4.39 9.15 10.07 4.03 4.43 10 11 11 i 10.13 4.30 12 111.05 4.69 11.03 4.74 11.00 4.78 10.98 4.83 12 13 11.97 5.08 11.94 5.13 11.92 5.18 11,90 5.24 13 14 i 12.89 5.47 12.86 5.. 53 12.84 5.58 12,81 5.64 14 15 13.81 5.86 13.78 5.92 13.76 5.98 13.73 6,04 15 16 14.73 6.25 14.70 6.32 14.67 6.38 14.64 6.44 16 17 15.65 6.64 15.62 fi.71 15.59 0.78 15.. 56 6.85 17 .18 16.57 7.03 16., 54 7.11 10.51 7.18 16.48 7.25 18 19 17,49 7.42 17.46 7., 50 17.42 7,58 17.39 7.65 19 20 21 18.41 7.81 18.38 7.89 18.. 34 7.97 18.31 8.05 20 ~21 19.33 8.21 19.29 8.29 19.2-^ 8.37 19.22 8.46 22 20.25 8.60 20.21 8.68 20.18 8.77 20,14 8.86 22 23 '21.17 8.99 21.13 0.08 21.09 9.17 21.05 9.26 23 24 '22.09 9.?8 22.05 9.47, 22.01 9.. 57 21.97 9.67 24 25 123.01 9.77 22.97 9.87 22.93 9.97 22.88 10.07 25 26 23.93 10.16 23.89 10.26 23.84 10.37 23.80 10.47 26 27 24.85 10.. 55 24.81 10.66 24.76 10.77 24,71 10.87 27 28 25.77 10.94 25 . 73 11.05 25.68 11,16 25 . 63 11.28 28 29 26.69 11.33 26.64 11.45 26.. 59 11.56 26.. 54 11.68 29 30 31 27.62 28.54 11.72 27.. 56 11.84 27.51 28.43 11.96 12.36 27 . 46 12.08 30 12.11 28.48 12.24 28.37 12.49 31 32 29.46 12.. 50 129.40 12.63 29 . 35 12.76 29.29 12.89 32 33 30 . 38 12.89 30.32 13.03 30.26 13.16 30.21 13.29 33 34 31.30 13.28 31.24 13.42 31.18 13., 56 31.12 13.69 34 35 32.22 13.68 32.16 13.82 32.10 13.96 32.04 14.10 35 36 33.14 14.07 33.08 14.21 33.01 14.. 35 32.95 14.. 50 36 37 34.06 14.46 34.00 14.61 33 . 93 14.75 33.87 14.90 37 38 34.98 14.85 34.91 15.00 34.85, 15.15 34.78 15.30 38 39 35.90 15.24 35.83 15.39 35.77 15.. 55 35.70 15.71 39 40 41 36.82 37.74 15.63 36.75 37 . 67 15.79 16.18 36 . 68 37 . 60 15.95 36.61 "37.-53 16.11 16., 51 40 41 16.02 16.35 42 38.66 16.41 38.59 16.58 38 . 52 16.75 38.44 16.92 42 43 39.58 16.80 39.51 16.97 39.43 17.15 39.36 17.32 43 44 1 40.50 17.19 40.43 17.37 40 . 35 17. .54 40.27 17.72 44 45 141.42 17. .58 41.35 1 17.76 41.27 17.94 41.19 18.12 45 46 ' 42.. 34 17.97 42.26^ 18.16 42.18 18.34 142.10 18.53 46 47 43 . 26 18.36 43.18 18. .55 43. 10 18.74 143.02 18.93 47 48 44.18 18.76 44.10 18.95 44.02 : 19.14 43.93 19.33 48 49 45.10 19.15 1145.02 19.34 44.94 i 19,54 44.85 1'».73 49 50 46.03 1 19. .54 45.94 19.74 45.85 19 .94 : 45 . 77 20.14 50 1 i ' Dep. Lat. Dep. j Lat. Dcp. Lat, Ij Drp. Lat. 67 Dog jl 661 Deg. 66i Deg, 1 66ii Dog. TRAVERSE TA.ULE. 2 23 Deff. 23i Deg. 23| Deg, 231 Lat. Deg. Lat. Dep. Lat. Dep. Lat, Dep. Dep. 46.95 19.93 46.86 20. i3 46 . 77 20.34 46.68 20.. 54 61 52 47.87 20.32 47.78 20 . 53 47.69 20.73 47,60 20.94 , 52j 53 48.79 20,71 48.70 20.92 48.60 21.13 48.51 21.35 53 54 49.71 21.10 49.61 21.52 49.52 21.53 49.43 [21.75 ! 54] 55 50.63 21.49 50.53 21.71 50.44 121.93 50,34 22.15 55 56 51.. 55 21.88 51,45 22.11 51.36 ! 22.33 51,26 22.55 56 57 52.47 22.27 52.37 22.50 52.27 22.73 52.17 22.96 57 5S 53.39 22.66 53.29 22.90 53.19 23.13 53.09 23.36 58 59 54.31 23.05 54.21 23.29 54.11 23.53 .54.00 23.76 59 60 61 55 . 23 23.44 55.13 23.63 55.02 23.92 54.92 24,16 60 56.15 23.83 56.05 24. OS 55.94 24.32 .55.83 124,57 j 61 1 62 57.07 24.23 56.97 24.47 .56.86 24.72 .56.75 24.97 1 62] 63 57.99 24.62 57.88 24.87 57.77 25.12 .57.66 25 . 37 63 64 58.91 25.01 58.80 25.20 .58.69 25.52 58.58 25,73 64 65 59.83 25.40 59 . 72 25 . 66 59.61 25 . 92 59.. 50 26.18 65 66 60.75 25.79 60.64 26.05 60 . 53 26.32 60.41 26.. 58 1 66 67 61.67 26.18 61.56 20.45 61.44 20.72 61.33 26.93 67 6S 62.59 26.57 62.48 26.84 62.36 27.11 62.24 27.39 68 69 63.51 26.98 63.40 27.24 63.28 27.51 63.16 27.79 89 70 71 64.44 65.36 27.35 64.32 27.63 64.19 27.91 64.07 23.19 28.59 70 71 27.74 65.23 28.03 65 . 1 1 23.31 64.99 72 66.28 28.13. 66.15 28.42 66.03 23.71 65.90 29.00 72 73 67.20 28.. 52 67.07 23.82 63.95 29.11 66.82 29.40 73 74 68.12 28.91 67.99 29.21 67.86 29.51 67.73 29.30 74 75 69.04 29.30 68.91 29,61 68,78 29.91 68.65 30.21 75 76 69.99 29.70 69.83 30.00 69.70 30.30 69.-56 30.61 76 77 70.88 30.09 70 . 75 30,40 70.61 30.70 70.43 31.01 77 78 71.80 30,48 ^.67 30,79 71.53 31.10 71.39 31.41 73 79 72.72 30.87 72.53 31.18 72.45 31.50 72.31 31.82 79 80 81 73.64 31.26 73.50 31.58 73.36 31.90 73.32 32.22 30 81 74.. 56 31.65 74.42 31.97 74.23 32.30 74.14 .32.62 82 75.48 32.04 75.34 32.37 75.20 32.70 75.06 33.03 S3 83 76.40 32.43 76.26 32 . 76 76.12 33.10 75.97 33.43 33 84 77.32 32.82 77.13 33,16 77.03 33.49 76,89 33.83 34 85 78.24 33.21 78.10 33.55 77.95 33.89 77,80 34.23 85 86 79.16 33.60 79.02 33.95 73.87 34.29 78 . 72 34.64 86 87 80.08 33.99 79.93 34.34 79.78 34.69 79 . 63 35.04 87 83 81.00 34.33 80.85 34.74 80.70 35.09 80.55 35.44 88 89 81.92 34.78 81.77 35,13 81.62 35.49 81.46 35.84 89 90 91 82.85 35,17 82.69 35.53 82.54 35.89 82.33 36.25 90 9! 83.77 35.56 83.61 35.92 83.45 36.29 83.29 36.65 93 84.69 35.95 84.53 36.33 84.37 135.63 84.21 37.05 92 93 85.61 36.34 85.45 36,71 85.29: 37.08 85,12 37.46 93 94 86. .53 36.73 86.37 37.11 86.20' 37.48 86.04 37.86 '■ 94 95 87.45 37.12 87.29 37.50 87.12 37.88 86.95 33.26 1 95 96 88.37 i 37.51 88.20 37.90 88.04! 33.28 87.37 38 . 66 96 97 89.29 1 37.90 89.12 33.29 88.95 .38.68 88.79 39.07 97 98 90.21 t 38.29 90.04 33.68 89.87 39.03 89.70 39.47 98 99 91.13 •' 33.68 90.96 39.03 90.79 39.48 90.62 .39.87 99 100 1 a 92.05 .39.07 Dep. Lat. 91.88 39.47 91.71 |39.87 91.53 40,27 100 Dep. Lat, Dep. 1 Lat. Dep Lat. 1 3 67 Deg. 66| Deg. 66i Deg. 6Gk Deg. 60 TRAVERSE TABLE. '~1 24 Deg. 24i Deg. 241 Deg. 241 Deg. O 1 p 1 Lat. 0.91 Dep. Lat. Dep. Lat. Dep. Lat. Dep. 0.41 0.91 -0741 0.91 0.41 0.91 0.42 2 1.83 0.81 1.82 0.82 1.82 0.83 1.82 0.84 2 3 2.74 1.22 2.74 1.23 2.73 1.24 2.72 1.26 3 4 3.65 1.63 3.65 1.04 3.64 1.66 3.63 1.67 4 5 4.57 2.03 4.56 2.05 4.55 2.07 4.54 2.09 5 6 5.48 2.44 5.47 2.46 5.46 2.49 5.45 2.51 6 7 6.39 2.85 6.38 2.87 6.37 2.90 6.36 2.93 7 8 7.31 3.25 7.29 3.29 7.28 3.32 7.27 3.35 8 9 8.22 3.66 8.21 3.70 8.19 3.73 8.17 3.77 9 10 11 9.14 10.05 4.07 4.47 9.12 4.11 9.10 4.15 9.08 4.19 10 11 10.03 4.52 10.01 4.56 9.99 4.61 12 10.96 4.88 10.94 4.93 10.92 4.98 10.90 5.02 12 13 11.88 5.29 11.85 5.34 11.83 5.39 11.81 5.44 13 14 12.79 5.69 12.76 5.75 12.74 5.81 12.71 5.86 14 15 13.70 6.10 13.08 6.16 13.65 6.22 13.62 6.28 15 16 14.62 6.51 14.. 59 6.57 14.56 6.64 14.53 6.70 16 17 15.. 53 6.92 15.50 6.98 15.47 7.05 15.44 7.12 17 18 16.44 7.32 16.41 7.39 16.38 7.46 16.35 7.. 54 18 19 /7.36 7.73 17.32 7.80 17.29 7.88 17.25 7.95 19 20 21 18.27 8.13 18.24 8.21 18.20 8.29 18.16 8.37 20 21 19.18 8.54 19.15 8.63 19.11 8.71 19.07" 8.79 22 20.10 8.95 20.06 9.04 20.02 9.12 19.98 9.21 22 23 21.01 9.35 20.97 9.45 20.93 9.54 20.89 9.63 23 24 21.93 9.76 21.88 9.86 21.84 9.95 21.80 10.05 24 25 22.84 10.17 22.79 10.27 22.75 10.37 22.70 10.47 25 26 23 . 75 10.. 58 23.71 10.68 23.66 10.78 23.61 10.89 26 27 24.67 10.98 24.62 11.09 24.57 11.20 24.52 11. .30 27 28 25.. 58 11.39 25.. 53 11. .50 25.48 11.61 26.43 11.72 28 29 26.49 11.80 26.44 11.91 26.39 12.03 26.34 12.14 29 30 31 27.41 12.20 27.35 12.32 27.30 12.44 27.24 12., 56 30 31 28,32 12.61 28.26 12.73 28.21 12.86 28.15 12.98 32 29.23 13.02 29.18 13.14 29.12 13.27 29.06 13.40 32 33 30,15 13.42 30.09 13.55 30.03 13.68 29.97 13.82 33 34 31.06 13.83 31.00 13.96 30.94 14.10 30.88 14.23 34 35 31.97 14.24 31.91 14.38 31.85 14.51 31.78 14.65 35 36 32.89 14.64 32.82 14.79 32.76 14.93 32.69 15.07 36 37 33.80 15.05 33.74 15.20 33.67 15.34 lf)3.60 15.49 37 38 34.71 15.46 34.65 15.61 34.58 15.70 .34.51 15.91 38 39 35.63 15.86 35.56 16.02 .35.49 16.17 35.42 16.33 39 40 36.54 16.27 36.47 16.43 36.40 16.59 36.33 16.75 40 41 37.46 16.68 37.38 16;84 37.31 17.00 37.23 17.16 41 42 38 . 37 17.08 38 . 29 17.25 38.22 17.42 38.14 17.58 42 43 39.28 17.49 39.21 17.60 39.13 17.83 .39.05 18.00 43 44 40.20 17.90 40.12 18.07 40.04 18.25 39.96 18.42 44 45 41.11 18.30 41.03 18.48 40.95 18.66 40.87 18.84 45 46 42.02 18.71 41.94 18.89 41.86 19.08 41.77 19.26 46 47 42.94 19.12 42.85 19.30 42 . 77 19.49 42.68 19.68 47 48 43.85 19.52 43.70 19.71 43.68 19.91 43.. 59 20.10 48 49 44.78 19.93 4^4.68 20.13 44.. 59 20.32 44.50 20.51 49 50 g c a 45.68 20.34 45.59 20.. 54 45.50 20.73 45.41 20.93 50 Dep. Lat. Dep. Lntr Dep. 651 Lat. Deg. Dep. Lat. S 66 1 )eg. 65| Deg. 65^ Deg. TRAVEUSE TABLE. 51 2 24 Deg. Lat. Dep. 1 51 52 53 54 55 46.59 47 . .50 48.42 49.33 .50.24 20.74; 21.15 i 21.56 21.96 22.37 24i Deg. Lat, I Dep. 77 7S 79 81 82 S3 84 85 85 87 88 89 9J) 91 92 93 94 95 I 96 97 98 99 100 .07 23 .99 , 23 .90 24 ■ll\^ .73 24" .64 25 ..55 25 ,47 I 26 .33 I 26 ,29 25 46, 47, 48, 49. 50, 78,151, 18 ; 51. 59 1.52, 00 .53. .40 |l54, 81 ii 55, 22 n 56, 62 ■ 57. 03 Us. 44 59, ij.f ! fill .84 ' 60 . 25 I 6 1 .21 27 .12 27.66 ; 62 ,03 23.06 I 62 ,95 23. 86 23 78 29 69 ' 29 60 30 52 30 43 30 34 31 26 31 17 i 32 OS 32 47 63. 83 :j 64. 65. 66. 67. 20.95 21.36 21.77 22.18 22.. 59 23.00 23.41 23.82 24.23 24.64 24i Deg. Lat. Dep, 00 132, 91 I 33, 82 I 33, 74 3t, 65 34, 56 134, 48 35. 39 35, 31 36, 22 36. 13 37 05 37 96 , 37 87 ' 33 79 , .38 70 :39 61 ; 39 53 '39 44 40 35 '40 25.05 25.46 25.88 26.29 26.70 27.11 27.52 37.93 28.34 23.75 29.16 29.57 29.98 30.39 30.80 31.21 31.63 32.04 32.45 32.86 35 76 17 57 98 39 79 20 01 42 'i 83, 83 : 84. 23'! 85, 64 I 86. 05 : 87, 45 , 88 86 ! 89, 27 J 90, 67 I 91, 33.27 33.68 34.09 34.. 50 34.91 35.32 35 . 73 36.14 36.55 36.96 97 ,37.38 88 37.79 79 ; 38.20 71 33.61 62 39.02 53 ! 39.43 44 139.84 35 40.2.5 26 40.66 18 41.07 Dep, Lat, I Dep. Lat. 66De2 65| Deg, 46.41 47.32 48.23 49.14 50.05 50.96 51.87 .52.78 53.69 54.60 55.51 56.42 57.33 .58.24 59.15 60.06 60.97 61.88 62.79 63.70 64.61 65.52 66.43 67.34 68.25 69.16 70.07 70.98 7 1. 89 72.80 73.71 74.62 75.. 53 76.44 77.35 78 26 79.17 80.08 80 99 81.90 82.81 83.72 84.63 85.54 86.45:39 87.36 ! 39 88.27 140 89.18 40 90.09 141 91.00 41, 24J Deg. Lat. Dep. 46.32 47.22 48.13 49.04 49 . 95 50.86 51.76 52.67 53.58 54.49 55.40 56.30 57.21 .58.12 59.03 59.94 60.85 61.75 62.66 63.57 Dep. Lat. 65* Deg. 64.43 65.39 66.29 67.20 68.11 69.02 69.93 70.84 71.74 72.65 i 73 . 56 74.47 75.38 76.28 77.19 78.10 79.01 i 79.92 80.82 :81.73 i 82 . 64 83 . 55 84.40 185.37 186.27 187.18 88.09 89.00 89.91 90,81 21.35 21.77 22.19 22.61 23.03 23.44 23.86 24.28 24.70 25.12 25 . 54 25.96 28.38 26.79 27.21 27.63 28.05 28.47 28.89 29.31 29.72 30.14 30.. 56 30.98 31.40 31.82 32.24 32.66 33.07 .33.49 33.91 34.33 34.75 35.17 35.59 36.00 36.42 36.84 37 26 37.68 33.10 38.. 52 38.94 39.35 39.77 40.19 40.61 41,03 41.45 41,87 Dep. Lat 65^ Deg. S2 TRAVERSE TABLE. 25 Deg. 25i Deg. 25hDeg. 251 Deg. T Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 0.91 0.42 o.so 0.43 0.90 0,43 0.90 0.43 2 l.Sl 0.85 1,81 0.85 1.81 0,86 1.80 0.87 2 3 2.72 1.27 2.71 1.28 2.71 1,29 2.70 1.30 3 4 3.63 1.69 3.62 1.71 3.61 1.72 3.60 1,74 4 5 4.53 2.11 4.52 2.13 4.51 2.15 4.50 2.17 5 6 5.44 2.54 5.43 2.. 56 5,42 2,. 58 5.40 2,61 6 7 6.34 2.96 0..33 2,99 6,32 3.01 6.30 3.04 7 8 7.25 3.38 7.24 3,41 7,22 3.44 7.21 3. 48 8 9 8.16 3.80 8,14 3.84 8.12 3.87 8.11 3.91 9 10 9.06 4.23 9,04 4.27 9.03 9.93 4.31 9.01 4.34 4.78 10 11 11 9.97 4.65 9,95 4.69 4.74 9.91 12 10.88 5.07 10,85 5.12 10.83 5.17 10.81 5.21 13 1 11.78 5.49 11,70 5,55 11.73 5.60 11.71 5.65 13 14 12. b9 5.92 12.66 5.97 1:^.64 6.03 12.61 6.08 14 1.5 1 13.59 6.34 13.57 6.40 13.54 6.46 13.51 6., 52 15 IH j 14. ."50 6.76 14.47 6.83 14.44 6.89 14.41 6.95 16 17 15.41 7.18 15.38 7.25 15.34 7.32 15.31 7.39 17 18 16.31 7.61 16.28 7.68 16.25 7.75 16.21 7.82 18 19 17.22 8.03 17.18 8.10 17.15 8.18 17.11 8,25 19 20 21 18.13 19.03 8.45 18.09 8.53 18.05 8.61 18.01 18.91 8.69 9.12 20 21 8.87 18r99 8.96 18.95 -9:04" 19.94 9.30 19.90 9. 33 19.86 9.47 19.82 9.56 22 23 20.85 9.72 1 20.80 9.81 20.76 9,90 20.72 9.99 23 24 21.75 10.14 21.71 10.24 21.66 10. ,33 21.62 10.43 24 25 22.66 10. .57 22.61 10.66 22.56 10.76 22.52 10.86 25 20 23.56 10.99 23.52 11.09 23.47 11.19 23.42 11.30 26 27 24.47 11.41 24.42 11.52 24.37 11.62 24.32 11,73 27 28 25.38 11.83 25.32 11.94 25.27 12.05 25.22 12,16 28 29 26.28 12.26 26,23 12.37 26.17 12. 4S 26.12 12.60 29 30 27.19 12.68 27,13 12.80 27.08 12.92 27.02 13.03 30 31 28.10 13.10 28.04 13.22 27.98 13.35 1 27.92 13.47 31 32 29.00 13.52 28.94 13.65 28.88 13.78 28.82 13.90 32 33 29.91 13.95 29.85 14.08 29.79 14.21 29.72 14.34 33 34 30.81 14.37 30.75 14.. 50 30.69 14.64 .30.62 14.77 .^4 :iF 31.72 14.79 31.66 14.93 31.59 15.07 31,. 52 15.21 35 3f. 32.63 15.21 32.56 15,36 32.49 15.50 32,43 15.64 36 37 33.53 15.64 33.46 15,78 33.40 15.93 33.33 16.07 37 38 34.44 16.06 34.37 16.21 .34.30 16.36 34,23 16.51 38 39 .35.35 16.48 35.27 16.64 35.20 16.79 35,13 16.94 39 40 3fi.25 16.90 36.18 17.06 36.10 17.22 .36.03 17.38 40 41 37.16 17.33 37.08 17.49 37.01 17.65 36,93 17.81 41 42 38,06 17.75 37.99 17.92 37.91 18.08 37,83 18.25 42 43 38.97 18.17 38,89 18.34 38.81 18.51 38.73 18.68 43 44 39.88 18.60 39,80 18.77 39.71 18.94 .39,63 19.12 44 45 40.78 19.02 40,70 19.20 40,62 19.37 40,. 53 19.. 55 45 46 41.69 19.44 41,60 19.62 41,. 52 19.80 41.43 19.98 46 47 42.60 19.86 42.51 20.05 42,42 20.23 42.33 20.42 47 48 43.50 20,29 43,41 20.48 43,32 20.66 43.23 20.85 48 49 44.41 20,71 44.32 20.90 44.23 21.10 44.13 21.29 49 60 45.32 21.13 45.22 21.33 45.13 21,53 45.03 21.72 50 j Distance.! Dep. Lat. Dep, Lat. Dep. Lat. Dep. Lat. 1 65 Deg. 64| Deg. 64i Dog. 64i Deg. TRAVERSE TAT!I,E. 53 i 25 Deg. 25i Deg, 25 i Deg. 231 Deg. s Id Lat. Dep. Lat. 46.13 Dep, Lat. Dep. Lat. Dep, 46.22 21.55 21.75 46.03 21.90 45.94 "22TT0" 52 47.13 21.98 47,03 22.18 46.93 22.39 40.84 22.. 59 52 53 48.03 22.40 47,94 22.61 47.84 22.82 47,74 23.03 53 54 48.94 22.82 48.84 23.03 48,74 23.25 48.64 23.40 54 55 49.85 23.24 49.74 23.46 49.64 23.68 49.-54 23 . 89 55 56 50 . 75 23,67 50.05 23.89 50.. 54 24 . 1 1 .50.44 24.. 33 50 57 51.66 24.09 51.55 24,31 51,45 24.54 51.34 24.70 57 58 52 . 57 24.51 52.46 24,74 52,35 24.97 .52.24 25.20 58 59 .53.47 24.93 53.30 25,17 53,25 25.40 53.14 25 . 63 59 60 PI .54.38 25.36 54.27 25.59 .54.16 25.83 54.04 26.07 00 01 .55.28 25,78 55.17 26.02 55.00 26.20 54.94 1 26.50 02 .56.19 26.20 .56,08 26,45 55.96 a<-\pj 55,8 i •ZF.9k 6? 63 57.10 26.62 .56.98 26.87 56,80 ^-7 12 ;.0 . 7'1 '.7 .J7, G3l 64 .58.00 27.05 .57.89 27.30 .57.77 27.55 -57.64 27.80 64 65 ,58.91 27,47 58.79 27.73 58 . 07 27.98 .58.. 55 28.24 65 66 .59.82 27.89 59.69 28.15 59.57 28.41 59.45 28.07 66 67 60 . 72 28. 32. 60.60 28.58 00.47 28.84 60.35 29.11 67 68 61.63 28.74 61.50 29.01 01.38 29.27 61.25 29.. 54 68 69 62.-54 29.10 02.41 29.43 02.28 29.71 62.15 29.98 69 70 "71 63.44 29.58 63,31 29.80 63.18 64.08 30.14 03.05 30.41 30.85 70 71 64.35 30.01 64,22 30,29 30.. 57 63.95 72 65.25 30.43 65,12 30.71 64.90 31.00 64.85 31.28 72 73 66.16 30,85 66.03 31.14 65.89 31.43 65.75 31,71 73 74 67.07 31.27 60.93 31. .57 66.79 31.86 60.65 32.15 74 75 67.97 31.70 07.83 31.99 67,09 32.29 67.. 55 .32.58 75 76 68.88 32.12 08.74 32.42 68,60 32.72 68.45 33.02 76 77 69.79 32.54 69.64 32.85 69.50 33.15 69 . 35 33.45 77 78 70.69 32.96 70 . 55 33.27 70.40 33 . .58 70.25 33.89 78 79 71.60 33.39 71.45 33,70 71.30 34.01 71.16 34.32 7S 80 81 72.. 50 33.81 72.36 73.26 34.13 72.21 34.44 34.87 72.06 72,96 34,70 35,19 80 81 73.41 34.23 34.55 73.11 82 74.32 34,65 74.17 34.98 74.01 35.30 73.80 35.02 82 83 75.22 35.08 75.07 35.41 74.91 35.73 74.76 38.06 83 84 76.13 35.50 75.97 35.83 75.82 36.16 75.66 36,49 84 85 77.04 35.92 76.88 36.20 76,72 30,-59 76.56 36,93 85 86 77.94 36.35 77,78 36.08 77,62 37,02 77.46 37.30 86 87 78.85 36,77 78.69 37.11 78,. 52 37-45 78.35 37.80 87 88 79.76 37,19 79.59 37,54 79.43 37.88 79.26 38.23 88 89 80.66 37,61 80.50 37,96 80.33 38-32 80.16 38.07 89 90 91 81.57 38,04 81.40 38.39 81.23 38.75 81.06 39.10 39.53 90 91 82.47 38.46 82.31 38.82 82.14 39.18 81.96 92 83.38 38.88 83.21 39.24 83.04 39.01 82.86 39,97 92 93 84.29 39.30 84.11 39.67 83,94 40.04 83.76 40.40 93 94 85.19 39,73 85.02 40.10 84.84 40.47 84.67 40,84 94 95 86.10 40,15 85.92 40.52 85.75 40.90 85,57 41,27 9^5 96 87.01 40.57 86.83 40.95 80.05 41.. 33 86,47 41,71 96 97 87.91 40.99 87.73 41.38 87.55 41.70 87,37 42,14 97 98 88.82 41.42 ,88.64 41.80 88.45 42.19 88,27 42.. 58 98 99 89.72 41.84 89.54 42.23 89.36 42,02 89,17 43,01 99 1^ i Q 90.63 42,26 90.45 42.66 90,26 43.05 90,07 43.44 100 Dep. Lat, Dep. La.. Dep, Lat. Dep. Lat. i 65 Deg. 641 Deg. 64i Deg. 64} Deg. 54 TRAVKRSE TABLE. 1 1 26 Deg. 264 Deg. 26 h Deg. 261 Deg. 1 «■ 3 Lat. Dep. Lat. Dep. Lat. 1 Dep. Lat. Dep. r 0.90 44 "O'.W 0.44 0.89 1 0.45 1 0.89 0.45 i 1 2 1.80 0.83 1.79 0.88 1.79 0.89 1.79 90 2 3 2.70 1.32, 2.69 1.33 2.68 1.34 2.63 1.35 3 4 3.60 1.75 3.. 59 1.77 3.. 53 1.78 3.. 57 I.80' 4 5 4.49 2.19 4.48 2.21 4.47 2.23 4.46 2 . 25 1 5 6 1 5.39 2.63 5.38 2.65 5.37 2.68 5.38 2.70! 6 7 1 6.2!) 3.07 6.28 3.10 6.26 3.12 6.25 3.15 7 81 7.19 3.51 7.17 3.54; 7.16 3.57 7.14 3.60 8 9! 8.09 3.95 8.07 3 . 93 ! 8.05 4.02 8.04 4.05 9 10 1 8.99 4. 38 8.97 4.42 8.95 4.46 8.93 4.. 50 10 11 11 9.89 4.82 9.87 4.87 i 9.84, 4.91 9.82 4.9.) 12 10.79 5.26 10.76 5.3! 10.74 5.35 10.72 5.40 12 13 11.68 5.70 11.66 5.75 11.63! 5.80 11.61 5.85 13 14 12.. 58 6.14 12.53 6.19 J 2. 53 6.25 12.. 50 6.30 14 15 13.4S 6.58 13.45 6.63 13.42 6.69 13.39 6 . 75 15 16 14.38 7.01 14.35 7.08 14.32 7.14 14.29 7.20 16 17 15.28 7.45 15.25 7.. 52 15.21 7.59 15.13 7.65 17 18 16.18 7.89 16.14 7.96 16.11 8.03 16.07 8.10 18 19 17.03 8.33 17.04 8.40 17.00 8.48 16.97 8.. 55 19 20 21 17.98 8.77 17.94 8.85 17.90! 8.92 17.86 18.75 9. GO 9.45 20 21 18.87 9.21 18.83 9.29 18.79 9.37 22 19.77 9.64 19.73 9.73 19.09 9.82 19.65 9.90 22 23 20.67 10.08 20.63 10.17 20.. 58 10.26 20.. 54 10.35 23 24 21.. 57 10.52 21.52 10.61 21.48 10.71 21.43 10.80 21 25 22.47 10.96 22 . 42 11.06 22.37 11.15 22., 32 11.25 25 26 23.37 11.40 23 . 32 11.50 23.27 11.00 23.22 11.70 26 27 24.27 11.84 24.22 11.94 24.16 12.05 124.11 12.15 27 28 25.17 12.27 25.11 12.38 25.06 12.49 125.00 12.60 28 29 26.06 12.71 , 26.01 12.83 25 . 95 12.94 125.90 13.05 29 30 26.96 13.15 26.91 13.27 26.85 13.39 ! 26.79 1 3.. 50 30 31 27.86 13.59 27.80 13.71 27.74 13.83" 127.68 13.S5 TT 32 28.76 14.03 28.70 14.15 28.64 j 14.28 28.. 58 14.40 32 33 29.66 14.47 29.60 14.60 29.. 53 ! 14.72 129.47 14.85 33 34 1.30.56! 14.90 30.49 15.04 30.43 i 15.17 ! 30.36 15.30 34 35 131.46 1 15.34 31.39 15.48 31.32 1 15.62 31.25 15.75 35 36 32.36 15.78 .32 . 29 15.92 32.22 16.06 32.15 16.20 36 37 33.26 1 16.22 .33.18 16.36 33.11 16.51 33.04 16.65 37 38 34.15 i 16.66 34.08 16.81 34.01 16.96 33.93 17.10 33 39 35.05 17.10 34.98 17.25 34.90 17.40 34.83 17.55 39 40 35.95 j 17.53 35.87 i 17.69 35.80 ! 17.85 .35.72 36.61 18.00 40 41 136.85, 17.97 36.77 1 18.13 36.69 1 18.29 1 18.45 41 42 37.75 18.41 37.67 18. .58 37. .59 I 18.74 37.51 i 18.90 42 43 33.65 18.85 38.57 19.02 .38.48 ! 19.19 38.40 i 19.35 43 44 39.55 19.29 39.46 19.46 39.38 19.63 39.29 1 19.80 44 45 40.45 19.73 40.36 • 19.90 40.27 I 20.08 40.18 20.25 45 46 41.34 20.17 41.26 20.35 41.17 1 20.53 41.08 20.70 46 47 42.24 20.60 42.15 20.79 42.06' 20.97 41.97 121.15 47 48 43.14:21.04 43.05 21.23 42.96 121.42 42.86 i 21.60 48 49 44.04 21.48 43.95 21.67 43.85 21.86 43.76 1 22 . 05 49 50 4^ ,94 121.92 44.84 22.11 44.75 22.31 44.65 1 22.50 50 i 5 Dep. 1 Lat. Dep. Lat. Dep. Lat. Dep. Lat. i .2 64 Deg. 631 Deg. 63i Deg. 63t Deg. TRAVERSE TABLE. 55 ~5\ 26 Deg. 26i Deg. 26i Deg. 263 Deg. "51 Lat. 1 Dep. Lat. Dep. Lat. Dep. 45T64 ^776 Lat. Dep. 22796 45.84 22.33! 45.74 "22.56 46 .54 52 46.74 22.80! 46.64 23.00 46.54:23.20 46.43 1 23.41 52 53 47.64 23.23 1 47.53 23.44 1 47.43 1 23.65 47. 33 23.83 53 54 4S.53 23.67 48.43 23.88 48.33 24.09 48 22 24.31 54 55 49.43 1 24.11! 49.33 24.33 49.22 1 24. .54 49.11 24.76 55 56 50.33 24.. 55, 50.23 1 24.77 50. 12 24.99 50.01 25.21 56 57 51.23 24.99 51.12 25.21 51.01 25 43 50.90 25.66 57 58 .52.13 25.43 .52.02 25.65 51.91 25 68 51.79 26.11 58 59 53.03 125.86 .52.92 26.09 52.80 26.33 52.69 26.-56 59 60 ~6T 53.93 26.30 53.81 i 26.54 53.70 26 77 .53.. 58 27.01 60 54.83 ; 26.74 .54.71 1 26.98 54.59 27.22 54.47 27.46 61 62 .55.73 ' 27.18 55.61 : 27.42 .55.49 27.66 55.36 27.91 62 63 56.63 27.62 56.50 '. 27.86 .56.33 23.11 " 56.26 ' 23.36 63 64 57.. 52 2S.06 57.40 ! 28.31 .57.28 1 23.56 ,, 57.15 : 23.81 64 65 58.42 , 28.49 .58.30 123.75 .53.17 1 29.00 j' 58.04: 29.26 65 66 59.32 i 28.93 59.19 i 29.19 59.07 29.45 58.94; 29.71 66 67 60.22 29.37 60.09 i 29.63 59.96 29.90 1 59.83 • 30.16 67 68 61.12 29.81 60.99 30.03 60.86 30.34 j] 60.72 30.61 63 C9 62.02,30.25 61.88 30.52 61.75 30.79 61.62, CI. 03 ! 69 1 70 71 62.92 30.69 62.78 ! 30.96 62.65 31.23 |! 62.51 j 31.51 1 70 j 63.81 i 31.12 63.68 ; 31.40 63.. 54 31.68 63.40 131.98 i 71 72 64.71 31. .56 64.57,31.84 64.44 32.13 64.29 33.41 73 1 73 65.61 : 32.00 65.47 1 33.29 65.-33 32.57 65.19 .32.86 73 74 66.51 32,44 66.37) 32.73 66.23 33.03 ; 66.08 , 33.31 33.46 1 66.97: 33.76 74 75 67.41 I 32.88 67.27! 33.17 67.12 75 76 68.31 f 33.32 68.16 1 33.61 68.01 133.91 i! 67.87 34.21 76 77 69.21 ; 33.75 69.06 ; 34.06 63.91134.36 63.76 34.66 j 77 78 70.11 34.19' 69.96 34.50 69.80 1 34.80 69.65 35.11 78 79 71.00 34.63 70.85' .34.94 70.70 35.25 70..55 135.56 79 80 81 71.90 : 35.07 72.80 : 35.51 71.75] 35.38 71.59 35.70 71. 44i 36.01 80 73.33' 36.46 ! 81 72.65 1 35.83 72.49 36.14 82 73 . 70 35 . 95 73.54 1 36.27 73.38 36.. 59 73.22 36.91 82 83 74 . 60 36 . 38 74.44! 36.71 74.28 37.03 74.12 ! 37.36 83 84 75 . 50 36.82 75.34137.15 75.17 37.48 !j 75.01 1 37.81 84 85 76.40 37.26 76. '-43 .37.59 76.07 37.93 ■' 75.90' 38.26 85 86 77.30 37.70 77.13 .33.04 76.96 .38.37 11 76.80 1 .33.71 86 87 78.20 38.14 78.03 33.48 77.86 38.82 77.69 ! 39.16 87 88 79.09 38.. 58 78.92 38.92 78.75 39.27 78.,53: 39.61 88 89 79.99 39.01 79.82 1 39.36 79.65 j 39.71 79.48 40.06 89 90 91 80.89 39.45 80.72 I 39.81 80.54; 40.16 80.37, 40.51 i 90 1 81.79 39.89 81.62 140.25 81.44:40.60 81.26 40.96 : 91 92 82.69 40.33 82.51 1 40.69 il 82.33 41.05 Ij 82.15 41.41 t 92 93 83.59 40.77 83.41 41.13! 83.23! 41.50 i: 83.05 4L.8G | 93 94 84.49 41.21 84. 31 J 41. 58 i! 84. 12 141.94 83.94 42.31 i 94 95 85.39 41.65 85.20 42.021 85.02:42.39 84.83 42.76: 95 96 86.28 42.08 86.10 42.46 !' 85.91 i 42.83 85.73 43.21 96 97 87.18 42.. 52 87.00 42.901:86.81 43.28 n 86.62 43.66 97 93 88.08 42. 9S ,87.89 43.341' 87.70 43.73 !! 87.51 44.11 93 99 88.98,43.40 88.79,43.79 188.60,44.17 188.40 44.56 99 100 i 89.88 ; 43.84 89.69] 44.23 ll 89.49 44.63 1 89.30 , 45.01 100 Dep. I Lat. Dep. Lat. Dep. Lat. Dep. 1 Lat. | § | 1 3 r 1 s 64 Deg. 631 Deg. 1 63| Deg. 1 63iDeg. S j 66 TEAVEKSE TABLE. o p p § 1 27 Deg. 27i Deg. 27| Deg, 271 Deg. "~1 Lat. Dep. Lat. Dep. Lat. ~0T89 Dep. Lat Dep. 0.89 0.45 0.89 0.46 0,46 0.88 0.47 2 1.78 0.91 1.78 0.92 1.77 0,92 1.77 0.93 2 3 2.67 1.36 2.67 1.37 2.66 1,39 2.65 1.40 3 4 3.. 56 1.82 3.. 56 1.83 3.. 55 1,85 3.54 1.86 4 5 4.45 2.27 4.45 2.29 4.44 2,31 4.42 2.33 6 6 5.35 2.72 6.33 2.75 6.32 2.77 5.31 2.79 6 7 6.24 3.18 6.22 3.21 6.2) 3.23 6.19 3.26 7 8 7,13 3.63 7.11 3.66 7.10 3.69 7.08 3.72 8 9 8.02 4.09 8.00 4.12 7.98 4.16 7.96 4.19 9 10 11 8.91 9.80 4.54 8.89 4.58 8.87 4.62 8.85 4.66 5.12 10 11 4.99 9.78 5.04 9.76 5.08 9.73 12 10.69 5.45 10.67 5.49 10.64 6.. 54 10.62 5.. 59 12 13 11. .58 5.90 11.56 5.95 11.53 6.00 11. .50 6.05 13 14 12.47 6.36 12.45 6.41 12.42 6.46 12.39 6.52 14 15 13.37 6.81 13.34 6.87 13.31 6.93 13.27 6.98 15 16 14.26 7,26 14.22 7.33 14.19 7.39 14.16 7.45 16 17 15.15 7.72 15.11 7.78 15.08 7.85 15.04 7.92 17 18 16.04 8.17 16.00 8.24 15.97 8.31 15.93 8..3S 18 19 16.93 8.63 16.89 8.70 16.85 8.77 16.81 8.85 19 2^ 21 17.82 9.08 9.. 53 17.78 9.16 17.74 9.23 17.70 9.31 20 ~21 18.71 18.67 9.62 18.63 9.70 18.58 9.78 22 19.60 9.99 19.56 10.07 19.51 10.16 19.47 10.24 22 23 20.49 10.44 20.45 10.53 20 . 10 10.62 20.35 10.71 23 '^4 21.38 10.90 21. .34 10.99 21.29 11.08 21.24 11.17 24 25 22.28 11.35 22.23 11.45 22.18 11.54 22.12 11.64 25 26 23.17 11.80 23.11 11.90 23.06 12.01 23.01 12.11 20 27 24.06 12.26 24.00 12.36 23.95 12.47 23.89 12.57 27 28 24.95 12.71 24.89 12.82 24.84 12.93 24.78 13.04 28 29 25.84 13.17 25.78 13.28 25.72 13.39 25.66 13.50 29 30 31 26.73 13.62 26.67 13.74 14.19 26.61 13.85 26.55 13.97 30 31 27.62 14.07 27.56 27.. 50 14.31 27.43 14.43 32 28.51 14.53 28.45 14.65 28.38 14.78 28.32 14.90 32 33 29.40 14.98 29.34 15.11 29.27 16.24 29.20 15.37 33 34 30.29 15.44 30.23 15.57 30,16 15.70 ,30.09 15.83 34 35 31.19 15.89 31.12 16.03 31.05 16.16 30.97 16.30 35 36 32.08 16.34 32.00 16.48 31.93 16.62 31.86 16.76 36 37 32.97 16.80 32.89 16.94 32.82 17.08 32.74 17.23 37 38 .33.86 17.25 33.78 17.40 33.71 17.55 .33.63 17.69 38 39 34.75 17.71 34.67 17.80 34.. 59 18.01 34.51 18.16 39 40 41 35.64 18.16 35.. 56 18.31 18.77 35.48 18.47 35.40 18.62 40 41 36.53 18.61" 36.45 36.37 18.93 36.28 19.09 42 37.42 19.07 37 34 19.23 37.25 19.39 37.17 19.56 42 43 38.31 19.52 .38.23 19.69 38.14 19.86 38.05 20.02 43 44 39.20 19.98 39.12 20.15 39.03 20.32 38.94 20.49 4-4 45 40.10 20.43 ,40.01 20.60 39.92 20.78 39.82 20 . 95 45 46 10.99 20.88 i 40.89 21.06 40.80 21.24 40.71 21.42 46 47 41.88 21.34 :41.78 21.52 41.69 21.70 41.59 21.88 47 48 42.77 21.79 42.67 21.98 42,58 22.16 42.48 22.35 48 49 4.]. 66 22.25 ; 43.56 22.44 43,46 22.63 43.36 22.82 49 50 § s s .2 a 44.55 22.70 44.45 22.89 44,35 23.09 44.25 23.28 _50 1 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 63] :»eg. 62| Deg. 621 Deg. 62i Deg. TRAVERSE TABLE. £7 a 3 ? "51 1 27 Deg. 21i Deg. .m Dog. 271 Deg. c 3 "sT Lat. Dep. Lat. 1 Dep. Lat. Dep. Lat. Dep. 45.44 23.15 45.34 23.35 45.24 23.55 45.13 23775" 52 46.33 23.61 46.23 23,81 46,12 24.01 46,02 24.21 52 53 47.22 24.06 47.12 24,27 47,01 24.47 46,90 24.68 53 54 48.11 24.52 48.01 24.73 47,90 24.93 47.79 25.14 54 55 49.01 24.97 48.90 25.18 48.79 25.40 48.67 25.61 55 56 49.90 25.42 49.78 25.64 49; 67 25.86 49,56 26.07 56 57 50 . 79 25.88 50.67 26.10 50.56 26.32 .50.44 26. .54 57 1 58 51.68 26.33 51.56 26.56 51.45 26.78 51.33 27.01 58 59 52.57 26.79 52.45 27.01 .52.33 27.24 52.21 27.47 59 60 61 53.46 27.24 53.-34 27.47 .53.22 27.70 .53.10 27.94 60 61 54.35 27.69 54.23 27.93 54.11 28.17 53 . 98 28.40 62 55.24 28.15 55.12 28.39 54.99 23.63 .54.87 28.8? 62 63 .56.13 28.60 .56.01 28.85 55.88 29.09 55.75 29.33 63 64 57.02 29.06 56.90 29.30 56,77 29.55 56,64 29.80 64 65 57 92 29. M 57.79 29.76 157,66 30.01 57.52 30.26 65 66 .58.81 29 . 96 .58.68 30.22 158.54 30.48 58.41 30.73 66 67 .59.70 30.42 59.50 30.68 59.43 30.94 59.29 31.20 67 68 60.59 30.87 60.45 31.14 60.32 31.40 60.18 31.68 68 69 61.48 31.33 61.34 3J.59 61.20 31.86 61.06 32.13 69 70 71 62.37 31.78 62.23 32.05 62.09 32.32 61.95 32.59 33.06 70 71 63.26 32.23 6?. 12 32.51 62.98 32.78 62.83 72 64.15 32.69 64.01 32.97 63.86 .33.25 63.72 33.52 72 73 65.04 33.14 64.90 33.42 64,75 33.71 64.60 33 . 99 73 74 65.93 33 . 60 65.79 33.88 65,64 34.17 65.49 34.46 74 75 66.83 34.05 66.68 .34.34 66.. 53 34.63 66.37 34.92 75 76 67.72 34.50 67.57 34.80 67.41 35,09 67.26 .35.39 76 77 68.61 34.96 68.45 35.26 68.30 35.55 68.14 35.85 77 78 69.50 .35.41 69.34 35.71 69.19 36.02 69.03 36.32 78 79 70 . 39 35.87 70.23 36.17 70.07 36.48 69.91 36.78 79 80 81 71.28 36.32 71. 12 72.01 36.63 70.96 36.94 70,80 37.25 80 81 72.17 36.77 37.09 71,85 37.40 71.68" 37.71 82 73.06 37.23 72.90 37.. 55 72.73 37.86 72.. 57 38.18 82 83 73.95 37.68 73.79 38.00 73 . 62 38.33 73.45 38.65 83 84 74.84 38.14 74.68 38.46 74.51 38,79 74.34 39.11 84 85 75.74 38.59 75.57 33.92 75.40 39.25 75.22 39.. 58 85 86 76.63 39.04 76.46 39.38 76.28 39.71 76.11 40.04 86 87 77.52 39.. 50 77.34 39.83 77.17 40.17 76.99 40.51 87 88 78.41 39.95 78.23 40.29 78.05 40.63 77.88 40.97 88 89 79.30 40.41 79.12 40.75 78.94 41.10 78.76 41.44 89 90 91 80.19 40.86 SO. 01 41.21 79.83 41. .56 79.65 41.91 90 91 81.08 41.31 80.90 41.67 80.72 42.02 80.53 42.37 92 81 ,97 41.77 81.79 42.12 81.60 42.48 81.42 42.84 92 93 82.86 42.22 82.68 42.58 82,49 42.94 82.30 43.30 93 94 83.75 42.68 83.57 43.04 83.. 38 43.40 83.19 43 . 77 94 95 84.65 43.13 84.46 43.50 84.27 43.87 84.07 44.23 95 96 85.54 43.. 58 85.35 43.96 85.15 44.33 84.96 44.70 96 97 86.43 44.04 86.23 44.41 86.04 44.79 85.84 45.16 97 98 87.32 44.49 87,12 44.87 86.93 45.25 86.73 45.63 98 99 88.21 44.95 88.01 45.33 87,81 45.71 87.61 46.10 99 100 ^9.10 Dep. 45.40 88.90 45.79 88.70 46,17 88.50 46.56 100 1 Lat. Dep. Lat. Dep, Lat. 1 Dep. L.. 63 Deg. 621 Deg. 62_l Deg. 62i Deg. 58 TKAVERSE TABLE. 1 28 Deg. 28i Deg. 1 28i Deg. 281 Deg. a 1 1 Lat. Dep. Lat. 0.88 Dep. Lat. Dep. LatT Dep. 0.48 1 0.88 0.47 0.47 0,88 0.48 0.88 2 1 . 77 0.94 1.76 0.95 1,76 0.95 1.75 0.96 2 3 2.65 1.41 2.64 1.42 2.64 1.43 1 2.63 1.44 3 4 3.. 53 1.88 3.52 1.89 3.. 52 1.91 3.. 51 1.92 4 5 4.41 2.35 4,40 2.37 4,39 2.39 4.38 2.40 5 6 5.30 2.82 5.29 2.84 5.27 2,86 5.26 2.89 6 7 6.18 3.29 6.17 3.31 6.15 3.34 6.14 3.37 7 8 7.06 3.76 7.05 3.79 7.03 3.82 7.01 3.85 8 9 7.95 4.23 7.93 4,26 7.91 4.29 7.89 4.33 9 10 8.83 4.69 8.81 4.73 8.79 4.77 8.77 4.81 10 11 9.71 5.16 9.69 5.21 9.67 5.25 9.64 5.29 11 12 10.60 5,63 10.57 5,68 10.55 5.73 10.52 5.77 12 13 11.48 6,10 11.45 6.15 11.42 6.20 11.40 6.25 13 14 12.36 6,57 12.33 6.03 12.30 6.68 12,27 6.73 14 15 13.24 7.04 13,21 7.10 13.18 7.16 13.15 7.21 15 16 14.13 7.51 14.09 7.57 14.06 7.63 14.03 7.70 16 17 15.01 7.98 14.98 8.05 14,94 8,11 14.90 8.18 17 18 15.89 8.45 15.86 8.52 15.82 8,59 \' 15,78 8.66 18 19 16.78 8.92 16.74 8.99 16.70 9,07 16,66 9.14 19 20 21 17.66 18.54 9.39 9.86 17.62 18.50 9.47 9.94 17.58 9,54 ' 17. .53 10.02: 18.41 9.62 20 18.46 10.10 21 22 19.42 10.33 19.. 38 10.41 19.33 10.50 ; 19.29 10.. 58 22 23 20.31 10.80 20.26 10.89 20.21 10.97 20.16 11.06 23 24 21.19 11.27 21.14 11. .36 21.09 11,45 ,21,04 11.. 54 24 25 22.07 11.74 22.02 11.83 21.97 11.93 21.92 12.02 25 26 23.96 12.21 22 . 90 12.31 22.85 12.41 22 . 79 12.51 26 27 23.84 12.68 23.78 12.78 23.73 12.88 23.67 12.99 27 28 24.72 13.15 24.66 13.25 24.61 13.36 24.. 55 13.47 28 29 25.61 13.61 25.55 13.73 25.49 13.84 25.43 13.95 29 30 31 26.49 27.37 14.08 14.55 26.43 14.20 26.36 27.24 14.31 14,79 26.30 27.18 14.43 14.91 30 31 ! 27.31 14.67 32 28.25 15.02 28.19 15.15 28.12 15.27 28.06 15.30 32 33 29.14 15.49 29.07 15.62 29.00 1 15.75 28.93 15.87 33 34 30 . 02 15.96 29.95 16.09 29.88 16.22 29.81 16.35 34 35 30.90 16.43 30.83 16.57 30.76 16.70 30.69 16 83 35 36 31.79 16.90 31.71 17.04 31.64 17,18 31.56 17.32 36 37 32.67 17.37 32.59 17.51 32 . ^^2 17.65 32.44 17.80 37 38 33.55 17.84 133.47 17.99 33.39 18.13 .33.. 32 18.28 38 39 34.43 18.31 1,34.35 18.46 34.27 18.61 34.19 18.76 39 40 41 35.32 36.20 18.78 19.25 i 35.24 18.93 19, 4f 35.15 36". 0« 19,09 19,. 5 6 35,07 35.95 19.24 19.72 40 41 36.12 42 37.08 19.72 37.00 19.88 36.91 20 . 04 36.82 20.20 42 43 37.97 20.19 37.88 20.35 37.79 20,52 37.70 20,68 43 44 38. S5 20.66 38.76 20.83 38 . 67 20.99 38.. 58 21.16 44 45 39.7-3 21.13 39.64 1 21. .30 39.. 55 21.47 3 J. 45 21.64 45 46 40.62 21.60 40.52 21.77 40.43 21.95 40.33 22.13 46 47 4I..50I 22.07 41.40 22.25 41.30 22.43 4i.21 22-61 47 48 42.38 ; 22.53 42.28 22.72 42.18 22.90 42.08 23.09 48 49 43.26 123.00 43.16 23.19 43,06 23.. 38 42.96 23.57 49 50 44.15'! 23.47 44.04 23.67 43,94 23.86 43.84 24.05 _50 i 5 Dep. 1 Lat. Dep. Lat. Dep, Lat. Dep. Lat 5 5 62 Deg. 61| Deg. ei^Deg. dH Deg. TRAVERSE TACtK. *^ 1 28 Deg. m Deg. 28iDeg. 1 281 Deg. 5 § 'tl Lat. 1 Dep. ! Lat. 1 Dep. Lat. Dep. Lat. Dep.! 45.03 1 23.94; 44.93 124. 14 44.82 1 24.34! 44.71 24.133 1 52 45.91 124.41 U5.81 1 24.C1 j 45.70 24.811 45.. 59 25.01 52 53 46.80 24.88 i 46.69 [25.09 46.58 ' 25.29 1 46.47 25.49 53 54 47. 68! 25. 35 47. 57; 25. 56^1 47. 46 0577 47.34 25.97 54 55 48. . 56 ! 25.82 48.45 1 26.03 1; 48.33 26 .24 48.22 26.45 5.^ .56 49.45 26.29 49.33 ! 26.51 '! 49.21 26.72; 49.10 26.94 56 .57 ,50.33 26.76 50.21 26.98 1 .50.09 27.20 1 49.97 127.42 57 58 51.21 ' 27.23 51.09 27.45 1 50.97 27.68 li 50.85 127.90 58 59 52.09 27.70 51.97 27.93 1 51.85 28,15 1, 51,73 28.38 59 60 52. 9S "53.86 28.17 ;. 52. 85 28.40 i ,52.73 28.63!: 52.60 ! 28,86 60 -6T 28.64 .53.73 28.87! 53.61 20.11 1 53.48 29.34 54.74 29.11 54.62 29.35 154.49 29.58 54.36 29.82 62 63 55.63 i 29.58 55.i=i0 1 29.82 i .55.37 30.06 i 55.23 30.30 63 64 56.51 130.05': 56.38 30.29 56.24 30., 54 56.11 30.78 64 65 57.39 1 30.52 157.26 30.77 57.12 31.02 50.99 31.26 65 66 .58.27 i 30.99 i .58.14 31,24 .58.00 31.49 .57.86 31.75 66 07 59.16 31.45 ■ 59.02 31.71 58.88 31.97 58.74 32.23 67 68 60.04 31.92 59.90 .32.19 69.76 32.45 59.62 32.71 68 69 60.92 ; 32.39 160.78 32 . 60 60 . 64 32.92 60.49 33.19 69 70 61.81 132.86 61.60 .33.13 61.52 33.40 33.88 61.37 33.67 34.15 70 71 71 ;62T69 ; 33..33 62.54 33.61 62.40 62.25 72 63.57 i 33.80 63.42 34.08 63.27 .34.36 63.12 34.63 72 73 64.46 1 .^.27 64.30 34.55 64.15 34.83 64.00 35.11 73 74 65.34 34.74 ;| 65.19 35.03 65.03 35.31 64.88 35.59 74 75 66.22 i 35.21 i; 66.07 35.. 50 65.91 1 35.79 05.75 36.07 75 76 67.10 35.68 1 66.95 35.97 66.79 136.26 66.63 36.50 70 77 67.99! 36.15:1 67.83 30.45 67.67 136.74 67.51 37.04 77 78 63.87 36.62 68.71 36.92 68..55 137.22 68.38 37.. 52 78 79 69.75 37.09,1 69.59 37.39 69.43 37.70 69.26 38.00 79 80 81 70.64 37.. 56 70.47 37.87 70,31 138,17 1 70.14 38.48 80 81 71.52 38.03 71.35 38.34 71.18 33 . 65 : 71.01 38.96 82 72.40 : 38.. 50 72.23 38.81 72.06 39.13 171.89 39.44 82 S3 73.28 1 38.97 73.11 39.29 72.94 39,60 72.77 39.92 88 84 74.17 ' 39.44 73.99 39.70 73.82 40.08 173.64 40.40 84 85 75.05 I 39.91 74.88 40.23 74.70 40,. 56 74.52 40.88 85 86 75.93 40.37 75.76 40.71 75 58 41.04 75.40 41.36 86 87 76.82:40.84 76.64 41.18 76.46 41.51 76.28 41.85 87 88 77.70 i 41.31 77.52 41.65 77.34 41.99 !77.15 I42..33 88 89 78.58 141.78 78.40 42.13 178.21 42.47 ,78.03 142.81 89 90 91 79.47 142.25 79.28 42.00 79.09 42.94 1 78.91 ! 43.29 79.78:43.77 90 91 80.35 42.72 80.16 43.07 79.97 43.42 92 81.23 43.19 81.04 43.55 80.85 43.90 180.66 ! 44.25 92 93 82.11 43.66 81.92 44.02 81.73 44.38 ' 81.54 '44.73 93 94 83.00 44.13 82.80 44.49 82.61 i 44.85 82.41 45.21 94 95 83.88 44.60 i! 83.68 44.97 83.49 45.33 83.29 45.69 95 96 S4.76 145.07!! 84.57 145.44 1184.37 45.81 '84.17 46.17 96 97 85.65 45..54I 85.45 45.91 85.25 1 46.28 85.04 46.66 97 98 86. .53 46.01 i! 86.33 j 46.39 || 86. 12 146.76 185.92 47.14 98 99 87.41 46.48 :| 87.21 , 46.86 i! 87.00 | 47.24 ; 86.80 47.62 99 J 00 83.29 46.95 1; 88.09 47.33 ;; 87.88 . 47.72 1 87.67 ,48.10 Dep. ! Lat. 100 1 1 <^ 5 Dep. j Lat. Dep. : Lat. Dep. ! Lat. 62 Deg. 1 1 61| Deg. eii Deg. 6U Deg, TRAVERSE TABLE. 1 CD 29 Deg. 1 294 Deg. 29i Deg. 291 Deg. s 1 Lat. -0787 Dep. Lat. Dep. Lat. Dep. Lat. Dep. 0.48 0.87 0.49 0.87 0.49 1 0,87 0.,50 2 1.75 0.97 1.74 0.98 1.74 0.98 1 1,74 0.99 3 2.62 1.45 2.62 1.47 2.61 1 1,48 2,60 1.49 3 4 3.. 50 1.94 3.49 1.95 3.48 1,97 3,47 1,98 4 5 4.37 2.42 4.36 2.44 4.35 2,46 4,34 2,48 5 6 5.25 2.91 1 5,23 2.93 5.22 2.95 5.21 2,98 6 7 6.12 3.391 6.11 3.42 6.09 3,45 6,08 3,47 7 8 7.00 3.88 j 6.98 3.91 6.96 3.94 6.95 3.97 8 9 7.87 4.36 1 7.85 4.40 7.83 4.43 7,81 4.47 9 10 if 8.75 9'.02 4.85 1 5.33 1 8 . 72 9.00 4.89 8.70 4,92 6.42 8,68 4.90 10 5.37 9.. 57 9,55 5.46 11 12 10.50 5.82 10.47 5.86 10.44 5.91 10,42 5.95 12 13 11.37 6.30 1 1 1 . 34 6.35 11.31 6.40 11,29 6.45 13 14 12.24 6.79 12.21 6.84 12.18 6.89 12.15 6.95 14 15 13.12 7.27 13.09 7.33 13.06 7.39 13.02 7.44 : 15 16 13.99 7.76 13.96 7.82 13.93 7.88 13.89 7,94; 16 17 14.87 8.24 14.83 8.31 14. SO' R.37 14.76 8,44 1 17 IS 15.74 8.73 15.70 8.80 15.67 8.86 15,63 8.93 18 19 16.62 9.21 16.58 9.28 16.54 9.36 16.50 9.43 19 20 21 17.49 18.37" 9.70 10. LS' 17.45 "is. 32 9.77 10.26 17.41 18.28' 9.85 10.34 17.36 9.92 20 18.23 10.42 21 22 19.24 10.67 i 19 19 10.75 19.15 10.83 19.10 10.92 22 23 20.12 11.15 : 20.07 11.24 20.02 11.33 19.97 11.41 23 24 20.99 11.64 20.94 11.73 20.89 11.82 20.84 11.91 24 25 21.87 12.12 21.81 12.22 21.76 12.31 21.70 12.41 25 26 22 . 74 12.60 22.68 12.70 22.63 12.80 22.57 12.90 26 27 23.61 13.09 23 . 56 13.19 23.50 13,30 23.44 13.40 27 28 24.49 13.57 24.43 13.68 24.37 13.79 24.31 13.89 28 29 25.. 36 14.06 25.30 14.17 25.24 14.28 25.18 14.39 29 30 26.24 14.. 54 20.17 14.06 26.11 14.77 26.05 14.89 I 30! "31 27.11 15.03 27.05 1,5.15 26.98 15.27 26.91 15.38 31 32 27.99 15.51 27.92 15.64 27.85 15.76 27.78 15. 8M 32 33 28.86 16.00 28.79 16.12 28.72 16.25 28 . 65 16.38 33 34 29 . 74 16.48 29 . 66 16.61 29.59 16. r4 29 . 52 16.87 34 35 30.01 16.97 30 . 54 17,10 30.46 17.23 .30.39 17.37 35 36 31.49 17.45 31.41 17.59 31.33 17.73 31.26 17.86 , 36 I 37 32.36 17.94 32 . 28 18.08 32.20 18.22 32.12 18.36 37 38 33.24 18.42 33.15 18.. 57 33 . 07 18.71 32.99 18.86 38 39 34.11 18.91 34.03 19.00 33.94 19.20 33.86 19.35 39 40 41 .34.98 .35 . 86 19.39 19.88 34.90 3"5 . 77 19.. 54 20.03 34.81 19.70 34.73 19.85 40 41 35.68 1 20.19 35.60 20.34 42 36.73 20 . 36 36 . 64 20.. 52 36.55:20.68 36.46 20.84 42 43 37.61 20.85 37., 52 21.01 37.43 121.17 37.33 21.34 43 44 .38.48 21.33 38.39 21.50 38.30 21.67 38.20 21.83 44 45 .39.36 21.82 39.26 21.99 39.17 22.16 39.07 22.. 33 45 46 140.23 22.30 40.13 22.48 1 40.04 22.65 39.94 22.83 j 46 47 1 4 1 . 1 1 22 . 79 41.01 22.97 40.91 23.14 40.81 23.32 1 47 48 41.98 23.27 1 41.88 23.45 41.78 23 . 68 41,67 23.82 48 49! 42.86 23.70 1 42.75 23.94 42,65 24.13 42,54 24.31 49 50 1 43.73 24 '.24 43.62 24.43 43.. 52 24.62 43.41 24,81 50 1 1 i Dep. j Lat. Dep. Lat. Dep. Lat. Dop. Lat, .2 61 Deg. 1 601 Deg. 60J Deg. 60i Deg. TRAVERSE TABLE. 61 r _ 29 Deg. 29i Deg. 29^ Deg, 291 Deg. 1 1 Lat. Dep. Lat. Dep. Lat, Dep. Lat. Dep, IT 44.61 24.73 44.50 24.92 44,39 25.11 44.28 25T3T ~51 52 45.48 25.21 45.37 25.41 45.26 25.61 45.15 25,80 52 63 46.35 25.69 46,24 25.90 46.13 26.10 46.01 26 . 30 53 54 . 47.23 26.18 1 47.11 26.39 47.00 26.59 46.88 26,80 5.) 55 1 48.10 26. G6 47.99 26.87 47.87 27.08 47,75 27,29 55 5fl 48.98 27.15 48.86 27.36 48.74 27.. 58 48.62 27,79 56 57 49.85 27.63 49.73 27.85 49.61 28.07 49.49 28. 2S 57 5S 50 . 73 28.12 50.60 28 . 34 50.48 28.56 50.36 23.78 58 59 51.60 28.60 51.48 28.83 51.35 29.05 51.22 29. 2S 59 60 fil .52.48- 53.35 29.09 29.57 52.35 29.32 52.22 29.55 30.04 52.09 52.96 29.77 60 61 .53.ii2 29.81 .53.09 30 . 27 62 54.23 30.06 54.09 30.29 53.96 30.. 53 53.83 30.77 62 63 55.10 30.54 1 54.97 30.78 54.83 31.02 54.70 31.26 63 G4 55.98 31.03 55.84 31.27 55.70 31.52 55.56 31.76 64 65 56.85 31.51 ! 56.71 31.76 56.57 32.01 56.43 32.25 65 00 57.72] 32.00 1 57.. 58 32.25 57,44 32.50 .57.30 32.75 06 67 .58.60 1 32.48 j .58.46 32.74 .58.31 32.99 58.17 33.25 67 68 .59.17! 32.97 59.33 33.23 59.18 33.48 59.04 33.74 68 69 60.35 33.45' 60.20 33.71 60.05 33.98 ,59.91 34.24 69 70 TI 61.22 33.94, 34.42 ; 61.07 34.20 60.92 ,34.47 60.77 61.64 34,74 70 71 62.10 61.95 .34.69 61.80 34.96 35.23 72 62.97 34.91 62.82 35.18 62.67 35,45 62.51 35.73 72 73 63.85 35.39 63.69 35.67 63.54 35.95 63.38 36.22 73 74 64.72 35.88 64.56 36.16 64.41 36.44 64.25 36.72 74 75 65.60 36.36 65.44 36.65 65.28 36.93 65.11 37.22 75 76 66.47 36.85 66.31 37.14 66.15 37.42 65.98 37.71 76 77 67.35 37.33 07.18 37.62 67.02 37,92 66.85 38.21 77 7S 68.22' 37.82 68.05 38.11 67.89 38,41 67.72 38.70 78 79 69.09 38.30 68.93 38.60 68.76 38.90 68.59 39.20 79 80 81 69.97 70.84 38.78 69.80 39.09 39.58 69.63 39.39 69.46 39.70 80 39.27 70.67 70.. 50 39.89 70.32 40.19 82 71.72 39.75 71.54 40.07 71.37 40.38 71.19 40,69 82 83 72 . 59 40.24 72.42 40.56 72.24 40.87 72.06 41,19 83 84 73.47 40.72 73.29 41.04 73.11 41,36 72.93 41.68 84 85 74.34 41.21 74.16 41.53 73.98 41,86 73.80 42.18 85 86 75.22 41.69 75.03 42,02 74.85 42.35 74.67 42.67 86 87 76 . 09 42.18 75.91 42.51 75.72 42.84 75 . 53 43.17 1 87 88 76.97 42.63 76.78 43.00 76.59 43.33 76.40 43.67 1 88 89 77.84 43.15 77.65 43.49 77.46 43.83 77.27 44.16 1 89 90 91 78.72 43.63 78.52 79.40 43.98 78.33 79.20 44.32 44.81 78.14 M.66 90 91 79.-59 44.12 44.46 79.01 45.16 92 80.46 44.60 80.27 44.95 80.07 45.30 79.87 45,65 i 92 93 81.34 45.09 81.14 45,44 80.94 45 . 80 80,74 46.15 93 94 82.21 45 . 57 82.01 45.93 81.81 46.29 81,61 46.64 94 95 83.09 46.06 82.89 46.42 82.68 46.78 82.48 47.14 95 96 83.96 46.. 54 83.76 46.91 83.55 47.27 83.35 47.64 96 97 : 84.84 47.03 84.63 47.40 84.42 47.77 84.22 48.13 97 ■98 185.71 1 47.51 85.50 47.88 85.29 148.26 85,08 48.63 98 99 86.59 48.00 86.38 48.37 86.17 48.75 85,95 49.13 99 100 1 .2 Q '87.46 148.48 87.25 48,86 Lat, 87.04 149.24 86,82 49.62 100 Dep. 1 Lat. Dep. Dep. Lat, Dep. Lat, i" 61 Deg. 601 Deg. 60^ Deg. 60i Deg, .2 Q 23 62 TIIAVERSE TABLE. 30 Deg. 30i Deg. 30^ Deg. 301 Deg. f 1 Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 0.87 0..50 0.86 0.50 0.86 0.51 0.86 0.51 2 1.73 1.00 1.73 1.01 1.72 1.02 1 1.72 1.02 2 3 2.60 1.50 2.59 1.51 2.58 1.52 1 2.58 1.53 3 4 3.46 2.00 3.46 2.02 3.45 2.03 3.44 2.05 4 5 4.33 2.50 4.32 2.52 4.31 2.54 4.30 2.56 5 6 5.20 3.00 5.18 3.02 5.17 3.05 5.16 3.07 6 7 6.06 3.50 6.05 3.53 6.03 3.55 6.02 3.58 7 a 6.93 4.00 6.91 4.03 6.89 4.06 6.88 4.09 8 9 7.79 4.50 7.77 4.53 7.75 4.57 7.73 4.60 9 10 11 8.66 5.00 8.64 5.04 8.62 5.08 8.59 5.11 10 M 9.53 5.50 9.. 50 5.54 9.48 5.58 9.45 5.62 12 10.39 6.00 10.37 6.05 10.34 6.09 10.31 6.14 12 13 11.26 6.50 11.23 6.55 11.20 6.60 j 11.17 6.65 13 14 12.12 7.00 12.09 7.05 12.06 7.11 12.03 7.16 14 15 12.99 7.50 12.96 7.56 12.92 7.61 12.89 7.67 15 16 13.86 8.00 13.82 8.06 13.79 8.12 13.75 8.18 16 17 14.72 8.50 14.69 8.56 14.65 8.63 14.61. 8.69 17 18 15.59 9.00 15.55 9.07 15.51 9.14 15.47 9.20 18 19 16.45 9.50 16.41 9.57 16.37 9.64 10.33 9.71 19 20 21 17.32 10.00 17.28 10.08 17.23 18.09 10.15 10.66 17.19 10.23 20 21 18.19 10.50 18.14 10.58 18.05 10.74 22 19.05 11.00 19.00 11.08 18.96 11.17 18.91 11.25 22 23 19.92 11.50 19.87 11.59 19.82 11.67 19.77 11.76 23 24 20.78 12.00 20.73 12.09 20.68 12.18 20.63 12.27 24 25 21.65 12.50 21.60 12.59 21.54 12.69 21.49 12.78 25 26 22.52 13.00 22.46 13.10 22.40 13.20 22.34 13.29 26 27 23.38 13.50 23.32 13.60 23.26 13.70 23.20 13.80 27 28 24.25 14.00 24.19 14.11 24.13 14.21 24.06 14.32 28 29 25.11 14.50 25.05 14.61 24.99 14.72 24.92 14.83 29 30 31 25.98 15.00 25.92 15.11 25.85 15.23 25.78 15.34 30 31 26.85 15.50 26.78 15.62 26.71 15.73 26.64 15.85 32 27.71 16.00 27.64 16.12 27.57 16.24 27.. 50 16.36 32 33 28.. 58 16.50 28.51 16.62 28.43 16.75 28.36 16.87 33 34 29.44 17.00 29.37 17.13 29.30 17.26 29.22 17.38 34 35 30.31 17.50 30.23 17.63 30.16 17.76 30.08 17.90 35 36 31.18 18.00 31.10 18.14 31.02 18.27 30.94 18.41 36 37 32.04 18.50 31.96 18.64 31.88 18.78 31.80 18.92 37 38 32.91 19.00 32.83 19.14 .32.74 19.29 .32.66 19.43 38 39 33.77 19.50 33.69 19.65 33.60 19.79 33.52 19.94 39 40 IT 34.64 20.00 34.55 20.15 34.47 20.30 34.38 20.45 40 41 35.51 20.50 35.42 20.65 35.33 20.81 .35.24 20.96 42 36.37 21.00 36.28 21.16 36.19 21.32 36.10 21.47 42 43 37.24 21. .50 37.14 21.66 37.05 21.82 36.95 21.99 43 44 38.11 22.00 .38.01 22.17 37.91 22.33 37.81 22.. 50 44 45 38.97 22.50 38.87 22.67 .38.77 22.84 38.67 23.01 45 46 39.84 23.00 39.74 23.17 39.63 23., 35 39.. 53 23.52 46 47 40.70 23.50 40.60 23.68 40.50 23.85 40.39 24.03 47 48 41.57 24.00 41.46 24.18 41.36 24.36 41.25 24.. 54 48 49 42.44 24.50 42.33 24.68 42.22 24.87 42.11 25.05 49 50 43.30 25.00 43.19 25.19 43.08 25.38 42.97 25.56 50 a Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 60 1 yog. 691 Deg. 59\ Deg. 59J Deg. TRAVERSE TABLE. 63 ■ 1 30 Deg. 30i Deg. 30i Deg. 30 J Deg. O a P 51 Lat. Dep. Lat. D'ep. Lat. Dep. Lat. Dep. 44.17 25.50 44.06 25.69 43.94 25.88 43.83 26.08 52 45.03 26.00 44.92 26.20 44.80 26.39 44.69 26.59 52 53 45.90 26.50 45.78 26.70 45.67 26.90 '45.55 27.10 53 54 46.77 27.00 46.65 27.20 46.53 27.41 46.41 27.61 54 55 47.63 27.50 47.51 27.71 47.39 27.91 47.27 28.12 55 56 48.50 28.00 48.37 28.21 48.2r> 28.42 48.13 28.63 56 57 49.36 28.50 49.24 28.72 l49.ll 28.93 48.99 29.14 57 58 50.23 29.00 50.10 29.22 1 49.97 29.44 49.85 29.65 58 59 51.10 29.50 50.97 29.72 50.84 29.94 50.70 30.17 59 60 61 51.96 3U.00 51.83 30.23 51.70 30.45 51.56 30.68 60 61 52.83 30.50 52.69 30.73 .52.-56 30.96 52.42 31.19 62 53.69 31.00 53.56 31.23 53.42 31.47 53.28 31.70 62 63 54.56 31.50 54.42 31.74 54.28 31.97 54.14 32.21 63 64 55.43 32.00 55.29 32.24 55.14 32.48 55.00 32.72 04 65 56.29 32.50 56.15 32.75 56.01 32.99 55.86 33.23 65 66 57.16 33.00 57.01 33.25 .56.87 33.50 56.72 33.75 66 67 58.02 33.50 57.88 33.75 .^7.73 34.01 57.58 34.26 67 68 58.89 34.00 58.74 34.26 58.59 34.51 .58.44 34.77 68 69 59.76 34.50 59.60 34.76 59.45 35.02 59.30 35.28 69 70 71 60.62 35.00 60.47 35.26 60.31 35.53 60.16 35.79 70 61.49 35.. 50 61.33 35.77 61.18 36.04 61.02 36.30 TI 72 62.35 36.00 62.20 36.27 62.04 36.54 61.88 36.81 72 73 63.22 36.50 63.06 36.78 62.90 37.05 62.74 37.32 73 74 64.09 37.00 63.92 37.28 63.76 37.. 56 63.60 37.84 74 75 64.95 37.50 64.79 37.78 64.62 38.07 64.46 38.35 75 76 65.82 38.00 65.65 38.29 65.48 38.57 65.31 38.86 ! 76 1 77 66.68 38.50 66.52 38 . 79 66.35 39.08 G6.17 39.37 77 78 67.55 39.00 67.38 39.29 67.21 39.59 67.03 39.88 78 79 68.42 39.50 68.24 39.80 68.07 40.10 67.89 40.39 79 80 81 69.28 40.00 69.11 40.30 68.93 40.60 68.75 40.90 80 70.15 40.50 69.97 40.81 69.79 41.11 69.61 41.41 81 82 71.01 41.00 70.83 41.31 70.65 41.62 70.47 41.93 82 83 71.88 41.. 50 71.70 41.81 71.. 52 42.13 71.33 42.44 83 84 72.75 42.00 72.56 42.. 32 72.38 42.63 72.19 42.95 84 85 73.61 42.50 73.43 42.82 73.24 43.14 73.05 43.46 85 86 74.48 43.00 74.29 43.32 74.10 43.65 73.91 43.97 86 87 75.34 43.50 75.15 43.83 74.96 44.16 74.77 44.48 87 88 76.21 44.00 76.02 44.33 75.82 44.66 75.63 44.99 88 89 77.08 44.50 76.88 44.84 76.08 45.17 76.49 45.51 89 90 91 77.94 45.00 77.75 45.34 77.55 45.68 77.35 46.02 90 78.81 45.50 78.61 45.84 78.41 46.19 78.21 46.53 91 92 79.67 46.00 79.47 46.35 79.27 46.69 79.07 47.04 92 93 80.54 46.50 80.34 46.85 180.13 47.20 79.92 47.55 93 94 81.41 47.00 81.20 47.35 180.99 147.71 80.78 48.06 94 95 82.27 47.50 82.06 47.86 i; 81.85 48.22 81.64 48.57 95 96 83.14 48.00 82.93 48.36 .82.72 48.72 82.50 49.08 96 97 84.00 48.50 83.79 48.87 ;l 83.58 49.23 83.36 49.60 97 98 84.87 49.00 84.66 49.37 84.44 49.74 84.22 50.11 98 99 85.74 49.60 85.52 49.87 85.30 50.25 85.08 50.62 99 100 86.60 50.00 86.38 50.38 86.16 50.75 85.94 51.13 100 1 .2 Dep. Lat. Dep. [ Lat. Dep. Lat. Dep. Lat. c 60 Deg. 59i Deg. 69i Deg. 59i Deg. 64 TRAVERSE TABLE, 2 i 31 Deg. 3U Deg. 3lh Deg. • 31 1 Deg. O 3 Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 1 0.86 0.51 0.85 ~0T52" 0.85 0.52 "oTss" 0..53 ~T 2 1.71 1.03 1.71 1.04 1,71 1.04 1.70 1.05 2 3 2.57 1.55 2.56 1.56 2.56 1.57 2.55 1..58 3 4 3.43 2.06 3.42 2.08 3.41 2.09 3.40 2. JO 4 5 4.29 2.58 4.27 2.59 4.26 2.61 4.25 2.63 5 6 5.14 3.09 5.13 3.11 5.12 3.13 5.10 3.16 6 7 6.00 3.61 5.98 3.63 5.97 3.06 5.95 3.68 7 8 6.86 4.12 6.84 4.15 6.82 4.18 6.80 4.21 8 9 7.71 4.64 7.09 4.67 7.67 4.70 7.65 4,74 9 10 U 8.57 9.43 5.15 8.55 5.ly 8., 53 5.22 8.50 5.26 10 5.67 9.40 5.71 9.38 5.75 9.. 35 5.79 11 12 10.29 6.18 10.26 6.23 10.23 6.27 10.20 6.31 12 13 11.14 6.70 11.11 6.74 11.08 6.79 11.05 6.84 13 14 13.00 7.21 11.97 7.26 11.94 7.31 11.90 7.37 14 15 12.56 7.73 12.82 7.78 12.79 7.84 12.76 7.89 1 15 j 16 13.71 8.24 13.68 8.30 13.64 8.36 13.61 8.42 16 1 17 14.57 8.76 14.53 8.82 14.49 8.83 14.46 8.95 17 18 15.43 9.27 15.39 9.34 15.35 9.40 15.31 9.47 IS 19 16.29 9.79 16.24 9.86 16.20 9.93 16.16 10.00 19 20 17.14 10.30 17.10 10.. 38 17.05 17.91 10.45 17.01 10,52 20 21 18.00 10.82 17.95 10.89 10.97 17.86 11.05 ~2T 22 18.86 11.33 18.81 11.41 18.76 11.49 18.71 11.58 22 23 19.71 11.85 19.66 11.93 19.61 12.02 19.56 12.10 23 24 20.57 12.36 20.52 12.45 20.46 12.54 20.41 12.63 24 25 21.43 12.88 21. .37 12.97 21.32 13.06 '21.26 13.16 25 26 22.29 13.39 22.23 13.49 22.17 13.58 22.11 13.68 26 27 23.14 13.91 23.08 14.01 23.02 14.11 22.96 14.21 27 28 124.00 14.42 23.94 14.53 23.87 14.63 23.81 14.73 28 29 24.86 14.94 24.79 15.04 24.73 15.15 ,24.06 15.26 29 30 25.71 26.57 15.45 25.65 15.50 25.. 58 15.67 125.51 15.79 30 15.97 26.. 50 16.08 26.43 16.20 126.36 16.31 31 32 27.43 16.48 27.36 16.60 27.28 16.72 S27.21 16.84 32 33 28.29 17.00 28.21 17.12 28.14 17.24 128.06 17.37 33 34 29.14 17.51 29.07 17.64 23.99 17.76 128.91 17.89 ■M 35 30.00 18.03 29.92 18.16 29 . 84 18.29 29.76 18.42 35 36 30.86 18.. 54 30.78 18.68 .30.70 18.81 130.61 18.94 36 37 31.72 19.06 31.63 19.19 31.55 19.33 131.46 19.47 37 38 32.57 19.57 32.49 19.71 32.40 19.85 132.31 20.00 38 39 33.43 20.09 33.34 20.23 33.25 20.38 J33.16 20.52 39 .40 41 34.29 20.60 34.20 20.75 34.11 20.90 [34.01 21.05 40 35.14 21.12 35.05 21.27 34.96 21.42 1 34.86 21.57 41 42 36.00 21.63 35.91 21.79 35.81 21.94 35.71 22.10 42 43 36.86 22.15 36.76 22.31 30.66 22.47 36.. 57 22.63 43 44 37.72 22.66 37.62 22.83 37.. 52 22.99 37.42 23.15 44 45 138.57 23.18 38.47 23.34 38.37 23.51 38.27 23.68 45 46 139.43 23 . 69 39.33 23.86 39.22 24.03 39.12 24.21 46 47 40.29 24.21 40.18 24.38 40.07 24.. 56 39.97 24.73 47 48 41.14 24.72 41.04 24.90 40.93 25.08 140.82 25.26 48 49 142.00 25.24 41.89 25.42 41.78 25.60 41.67 25.78 49 50 ! 42.86 25.75 42.75 25.94 42.63 26.12 142.52 26.31 50 ..1 Q Dep. 59] Lat. 3eg. Dep. Lat. Dep. Lat. Dep. Lut. 1 .2 P 581 Deg. 5Qh Deg. 58k Deg. TRAVERSE TABLE 65 2 g 31 Deg. 3U Deg. 31^ Deg. 311 Deg. 1 "51 Lat. Dcp. Lat. Dep. Lat. Dep. Lat. Dep. 26.84 43,72 26.27 43.60 26.46 43.48 26.05 43.37 52 44.57 26.78 44.46 26.98 44.34 27.17 44.22 27.36 52 53 45.43 27.30 45.31 27.49 45.19 27.69 45.07 27.89 53 54 46.29 27.81 46.17 28.01 46.04 28.21 45.92 28.42 54 55 47.14 28.33 47.02 28.53 46.90 28.74 46.77 28.94 55 56 48.00 28.84 47.88 29.05 47.75 29.26 47.62 29.47 56 57 48.86 129.36 48.73 29.57 48.60 29.78 48.47 29.99 57 58 49.72 ; 29.87 49.58 30.09 49.45 30.30 49.32 30.. 52. 58 69 50.57 130.39 50.44 30.61 50.31 30.83 .50.17 31.05 59 60 61 51.43 30.90 51.29 31.13 51.16 31.35 31.87 51.02 31.57 60 61 52.29 31.42 .52.15 31.65 52.01 51.87 32.10 62 53.14 31.93 53.00 32.16 .52.86 32.39 52.72 32.63 62 63 54.00 32.45 53.80 32.68 53.72 .32.92 53.57 33.15 63 64 .54.86 32.96 54.71 33.20 .54.57 33.44 .54.42 33.68 64 65 55.72 33.48 55.. 57 33.72 55.42 33.96 55.27 34.20 65 66 56.57 33.99 56.42 34.24 .56.27 34.48 56.12 34.73 66 67 57.43 34.51 57.28 .34.76 57.13 35.01 56.98 35.26 67 68 58.29 35.02 58.13 35.28 57.98 35.53 57.82 35.78 68 69 59.14 35.54 58.99 35.80 58.83 36.05 58.67 36.31 69 70 71 60.00 36.05 59.84 36.31 59.68 36.57 59.52 36.83 70 71 60.86 36.57 60.70 36.83 60.54 37.10 60.37 37.36 72 61.72 37.08 61.55 37.35 61.39 37.62 61.23 37.89 72 73 62.57 37.60 62.41 37.87 02.24 38.14 62.08 38.41 73 74 63.43 38.11 63.26 38.39 63.10 38.66 62.93 38.94 74 75 64.29 38.63 1 64.12 38.91 63.95 39.19 63.78 39.47 75 76 65.14 39.14 39.66 64.97 39.43 64.80 39.71 64.63 39.99 76 77 66.00 65.83 39.95 65.65 40.23 65.48 40.. 52 77 78 G6.86 40.17 66.08 40.46 66.51 40.75 66.33 41.04 78 79 67.72 40.69 67.54 40.98 67.36 41.28 G7.18 41.57 79 80 81 68.57 41.20 68.. 39 41.50 68.21 41.80 68.03 42.10 80 81 69.43 41.72 69.25 142.02 69.06 142.32 68.88 42.62 82 70.29 42.23 70.10 142.54 69.92 42.84 69.73 43.15 82 83 71.14 42.75 70.96 43.06 70.77 43.37 70.58 43.68 83 84 72.00 43.26 71.81 43.58 71.62 43.89 71.43 44.20 84 85 72.86 43.78 72.67 44.10 72.47 44.41 72.28 44.73 85 86 73.72 44.29 73.. 52 44.61 73.33 44.93 73.13 45.25 86 87 74.57 44.81 74.. 38 45.13 74.18 45.46 73.98 45.78 87 88 75.43 45.32 75.23 45.65 75.03 45.98 74.83 46.31 88 89 76.29 45.84 76.09 46.17 75.88 46.50 75.68 46.83 89 90 91 77.15 46.35 76.94 77.80 46.69 76.74 47.02 76.. 53 47.36 90 91 78.00 46.87 47.21 77.59 47.55 77.38 47.89 92 78.86 47.38 78.65 47.73 78.44 48.07 78.23 48.41 92 93 79.72 47.90 79.51 48.25 79.30 48.59 79.08 48.94 93 94 80.. 57 48.41 80.36 48.76 80.15 49.11 79.93 49.47 94 95 81.43 48.93 81.22 49.28 81.00 49.64 80.78 49.99 95 96 82.29 49.44 82.07 49.80 81.85 50.16 181.63 50.52 96 97 83.15 49.96 82.93 50.32 82.71 50.68 182.48 5:. 04 97 98 84.00 50.47 83.78 50.84 83.56 51.20 183.33 51.57 98 99 84.86 .50.99 84.64 51.36 84.41 51.73 84.18 52.10 99 100 85.72 1 51.50 85.49 51.88 85.26 52.25 85.04 62.62 100 J i Dep. 1 Lat. Dep. Lat. Dep. Lat. Dep. Lat. 59 De?. 581 Deg. 58i Deg. 58} Deg. 66 TRAVERSE TABLE. 32 Deg. 32i Deg. 32i Deg. 321 Deg. E 3 r Lat, Dep. Lat. Dep. Lat. Dep. Lat. Dep. 1 "0.85" 0.53 0.85 0.53 0.84 0.54 0.84 0.54 2 1.70 1.06 1.69 1.07 1.69 1.07 1.68 1.08 2 3 2.54 1.59 2.54 1.60 2.53 1.61 2.52 1.62 3 4 3.39 2.12 3.38 2.13 3.37 2.15 3.. 36 2.16 4 5 4.24 2.65 4.23 2.67 4.22 2.69 4.21 2.70 5 6 5.09 3.18 5.07 3.20 5.06 3.22 5.05 3.25 6 7 5.94 3.71 5.92 3.74 5.90 3.76 5.89 3.79 7 8 6.78 4.24 6.77 4.27 6.75 4.30 6.73 4.33 8 9 7.63 4.77 7.61 4.80 7.59 4.84 7.57 4.87 9 10 11 8.48 5.30 8.46 5.34 8.43 5.37 8.41 5.41 10 9.33 i 5.83 9.30 -5.W 9.28 5.91 9.25 5.95 11 12 10.18 6.36 10.15 6.40 10.12 6.45 10.09 6.49 12 13 11.02 6.89 10.99 6.94 10.96 6.98 10.93 7.03 13 14 11.87 7.42 11.84 7.47 11.81 7.52 11.77 7.57 14 15 12.72 7.95 12.69 8.00 12.65 8.06 12.62 8.11 15 16 13.57 8.48 13.53 8.54 13.49 8.60 13.46 8.66 16 17 14.42 9.01 14.38 9.07 14.34 9.13 14.30 9.20 17 18 15.26 9.54 15.22 9.61 15.18 9.67 15.14 9.74 18 19 16.11 10.07 16.07 10.14 10.02 10.21 15.98 10.28 19 20 16.96 10.60 16.91 10.67 16.87 10.75 16.82 10.82 20 21 17.81 11.13 17.76 11.21 17.71 11.28 17.66 11.36 21 22 18.66 11.66 18.61 11.74 18.. 55 11.82 18.50 11.90 22 23 19.51 12.19 19.45 12.27 19.40 12.36 19.34 12.44 23 24 20.35 12.72 20.30 12.81 20.24 12.90 ;1 20. 18 12.98 24 25 21.20 13.25 21.14 13.34 21.08 13.43 21.03 13.52 25 26 22.05 13.78 21.99 13.87 21.93 13.97 21.87 14.07 26 27 22.90 14.31 22.83 14.41 22.77 14.51 22.71 14.61 27 28 23.75 14.84 23.68 14.94 23.61 15.04 23.55 15.15 28 29 24.59 15.37 24.. 53 15.47 24.46 15.58 24.. 39 15.69 29 30 25.44 15.90 25.37 16.01 25.30 16.12 25.23 16.23 30 31 26.29 16.43 26.22 16.54 26.15 16.66 26.07 16.77 31" 32 27.14 16.96 27.06 17.08 26.99 17.19 26.91 17.31 32 33 27.99 17.49 27.91 17.61 27.83 17.73 27.75 17.85 33 34 28.83 18.02 28.75 18.14 28.68 18.27 28.60 18.39 34 35 29.68 18.55 29.60 18.68 29.52 18.81 29.44 18.93 35 36 30.53 19.08 30.45 19.21 30.. 36 19.34 30.28 19.48 36 37 31.38 19.61 31.29 19.74 31.21 19.88 31.12 20.02 37 38 32.23 20.14 32.14 20.28 32.05 20.42 31.96 20.56 38 39 33.07 20.67 32.98 20.81 32.89 20.95 32.80 21.10 39 40 33.92 21.20 33.83 21.34 33.74 34.58 21.49 33.64 21.64 40 41 41 34.77 1 21.73 34.67 21.88 22.03 34.48 22.18 42 35.62 22.26 35.52 22.41 35.42 22.57 35.32 22.72 42 43 36.47 22.79 36.37 22.95 36.27 23.10 .36.16 23.26 43 44 37.31 23.32 37.21 23.48 37.11 23.64 37.01 23.80 44 45 38.18 23.85 38.06 24.01 37.95 24.18 37.85 24.. 34 45 46 39.01 24.38 38.90 24.55 38.80 24.72 38.69 24.88 46 47 3D. 86 24.91 39.75 25.08 39.64 25.25 39.53 25.43 47 48 40.71 25.44 40.59 25.61 40.48 25.79 40.37 25.97 48 49 41.55 25.97 41.44 26.15 41.33 26.33 41.21 26.51 49 50 42.40 26.50 42.29 26.68 42.17 26.86 42.05 27.05 _50 6 1 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 1 58 1 )eg. 571 Deg. 67iDeg. 51 \ Deg. TKAVERSE TABLE. 67 i 51 32 Deg. 32i Deg. 32i Deg. 32J Deg. Lat. Dep. 1 Lat. Dep. Lat. 43". Of Dep.| "27.401 Lat. Dep. 27.03 43.13 27.21 42789 27,. 59 1 52 44.10 27.56 1 43.98 27.75 43.86 27.94' 43.73 28.13 52 53 4^1.95 28.09 44.82 28.28 44.70 28.48 ' 44.58 28.67 53 64 45.79 28 . 62 45.67 28.82 45.54 29.01 ; 45.42 29.21 54 55 46 . 64 29.15 !| 46.51 29,35 46.39 29.55 46.26 29,75 55 56 47.49 29.68 i; 47.. 36 29.88 47.23 30.09 47.10 30.29 5fi 57 48.34 30.21 ![ 48.21 30.42 48.07 30.63 47.94 30.84 57 58 49.19 30.74 |j 49.05 30.95 48.92 31.16 48.78 31.38 58 59 50.03 31.27 49.90 31.48 49.76 31.70 49.62 31.92 59 60 CI 50 . 88 31.80 ; 32.. 33 : 50.74 32.02 50.60 32.24 50.46 32.46 33.00 60 61 51.73 51.59 32.55 51.45 32.78 51.30 62 52.58 32.85 i! 52.44 33.08 52.29 33.31 52.14 33.54 62 63 53.43 33.38, 53.28 33.62 53.13 33.85 52.99 34.08 63 64 54.28 33.91 54.13 34.15 53.98 34.39 53.83 34.62 64 65 55.12 34.44 54.97 34.68 .54.82 34.92 54.67 35.16 65 60 55.97 34.97 1 55.82 35.22 55.66 35.40 .55.51 35.70 66 67 .56 . 82 35.50 56.66 1 35.75 56.51 36.00 56.35 36.25 67 68 57.67 36.03 157.51 1 36.29 57.35 36.. 54 57.19 36.79 68 69 58.52 36..56i|58.36! 36.82 58.19 37.07 58.03 37.33 69 fi .59.36 60.21 37.09 ! 59.20 37.35 37.62 1 60.05 1 37.89 59.04 37.61 58.87 37.87 70 71 59.88 38.15 59.71 38.41 72 61.06 38.15 : 60.89 1 38.42 60,. 78 38.69 60.. 55 38.95 72 73 61.91 38.68 '161.74 138.95 61.57 39.22 61.40 39.49 73 74 62.76 39.21 62.58 i 39.49 62.41 39.76 62.24 40.03 74 75 63.60 39 . 74 63.43 i 40.02 63.25 40.30 163.08 40.57 75 76 64.45 40.27! 64.28 40.. 55 64.10 40.83 63.92 41.11 76 77 65.30 40.80 1 65.12 41.09 64.94 41.37 64.76 41.65 77 78 66.15 41.33 1 65.97 41.62 65.78 41.91 6^.60 42.20 78 79 67.00 41.86' 66.81142.10 66.63 42.45 1 66.44 42.74 79 80 81 67.84 68.69 42.39 42.92 67.66 I 42.69 68.50 1 43.22 67.47 68.31 42.98 67.28 43.28 80 81 43.52 16S.12 43.82 82 69 . .54 43.45 69.35! 43.76 '69.16 1 44.06 ' 68.97 44.36 82 83 70 . 39 43.98 70.20 1 44.29 70.00 ! 44.60 ; 69.81 44.90 83 84 71.24 44.51 1 71.04i 44.82 70.84 145. 13 170.65 45.44 84 85 72.08 45.04 71.89 45.36 171.69 145.67 ! 71.49 45.98 85 86 72.93 45.57 72.73; 45.89 i 72.53 46.21 72.33 46.52 86 87 73.78 46.10 73.. 58 46.42 173.38 46.75 73.17 47.06 87 88 74.63 46.63 74.-42 46.96 174.22 47.28 74.01 47.61 88 89 75.48 47.16 75.27 47.49 75.06 47.82 74.85 48.15 89 90 91 76.32 77.17 47.69 48 .22' 76.12 1 48.03 76.96 i 48.56 175.91 148.36 75.09 176.53 48.69 90 91 176.75 48.89 49.23 92 78.02 48 . 75 77.81 1 49.09 77.59 49.43 i 77.38 49 77 92 93 78.87 49.28 78.65 ; 49.63 78.44 49.97 178.22 .50.31 93 94 79.72 49.81 79.-50! 50.16 179.28 50.51 79.06 50.85 94 95 80.56 50.34 1 80.34 .50 . 69 80.12 151.04 i 79.90 51.39 95 96 81.41 50.87 1 81.19 51.23 180.97 1 51.58 '80.74 51.93 96 97 82.26 51.40 1:82.04 51.76 181.81 ! 52.12 1 81.58 .52.47 97 98 83.11 51.93 1 82.88 52.29 82.65 152.66 182.42 53.02 98 99 83.96 .52.46 83.73 52.83 83.50 53.19 183.26 53.56 99 1,00 84.80 52.99 Lat. 84.57 53.36 184.34 1 Dep. 53.73 84.10 54.10 100 s i .5 d i Dep. 1 " Dep. fLat. Lat. Dep. Lat. i 58] Deg. 571 Deg. 57i Deg. 57i Deg. 68 TRAVERSE TABLE. o 1 33 Deg. 33k Deg. 33i Deg. 331 Deg. Lat. Dep. Lat. Dep. 'l.V Dep. Lat. Dep. ~0756 f 0.84 0.54 0.84 0.55 0.83 0.55 0,83 2 1.68 1.09 1.67 1.10 1.67 1.10 1.6G 1.11 2 3 2.52 1.63 2.51 1.64 2.50 1.C6 2.49 1.67 3 4 3.35 2.18 3.35 2.19 3.34 2.21 3.33 2.22 4 5 4.19 2.72 4.18 2.74 4.17 2.76 4.16 2.78 5 6 5.03 3.27 5.02 3.29 5.00 3.31 4.99 3.33 6 7 5.87 3.81 5.85 3.84 5.84 3.86 5.82 3.89! 7 8 6.71 4.36 6.69 4.39 6.67 4.42 6.65 4.44 8 9 7.55 4.90 7.53 4.93 7.50 4.97 7.48 5.00 9 10 11 8.39 5.45 8.30 9.20 5.48 6.03 8.34 9.17 5.52 8.31 9.15 5.56 10 6.11 11 9.23 5.99 6.07 12 10.06 6.54 10.04 6.58 10.01 6.62 9.98 6.67 12 13 10.90 7.08 10.87 7.13 10.84 7.18 10.81 7.22 13 14 11.74 7.62 11.71 7.68 11.67 7.73* 11.64 7.78 14 15 12.53 8.17 12.54 8.22 12.51 8.28 12.47 8.33 15 16 13.42 8.71 13.38 8.77 13.34 8.83 13.30 8.89 IB 17 14.26 9.20 14.22 9.32 14.18 9.38 14.13 9.44 17 18 15.10 9.80 15.05 9.87 15.01 9.93 14.97 10.00 18 VJ 15.93 10.35 15.89 10.42 15.84 10.49 15.80 10.56 1 19! 20 16.77 10.89 16.73 10.97 16.68 11.04 11.59 16.63 11.11 20 21 17.61 11.44 17.56 11.51 17.51 17.46 11.67 21 22 18.45 11.98 18.40 12.06 18.35 12.14 18.29 12.22 22 23 19.29 12.53 19.23 12.61 19.18 12.69 19.12 12.78 23 24 20.13 13.07 20.07 13.16 20.01 13.25 19.96 13.33 24 25 20.97 13.62 20.91 13.71 20.85 13.80 20.79 13.89 25 26 21.81 14.16 21.74 14.26 21.68 14.35 21.62 14.44 26 27 22.64 14.71 22.58 14.80 22.51 14.90 22.45 15.00 27 28 23.48 15.25 23.42 15.35 23.35 15.45 23.28 15.56 28 29 24.32 1.5».79 24.25 15.00 24.48 16.01 24.11 16.11 29 30 31 25.16 16.34 25.09 16.45 25.02 16.56 24.94 16.67 17.22 30 31 2G.00 16.88 25.92 17.00 25.85 17.11 25.78 32 26.84 17.43 26.76 17.55 26.68 17.66 26.61 17.78 32 33 27.68 17.97 27.60 18.09 27.52 18.21 27.44 18.33 33 34 28.51 18.. 52 28.43 18.64 28.35 18.77 28.27 18.89 34 3S 29.. 35 19.06 29.27 19.19 29.19 19.32 29.10 19.44 35 36 30.19 19.61 30.11 19.74 30.02 19.87 29.93 20.00 36 37 31.03 20.15 30.94 20.29 30.85 20.42 .30.76 20.. 55 37 38 31.87 20.70 31.78 20.84 31.69 20.97 31.60 21.11 38 39 32 71 21.24 32.62 21.. 38 32.. 52 21.53 32.43 21.67 39 40 41 33.55 21.79 33.45 21.93 33.36 34.19 22.08 .33.26 22.22 40 34.39 22.33 34.29 22.48 22.63 34.09 22.78 41 42 35.22 22.87 35.12 23.03 35.02 23.18 34.92 23.33 42 43 36.06 23.42 35.96 23.58 35.86 23.73 35.75 23.89 43 44 36.90 23.96 36.80 24.12 36.69 24.29 36.. 58 24.45 44 45 37.74 24.51 37.63 24.67 37.. 52 24.84 37.42 25 00 45 46 3S.58 25.05 38.47 25.22 38.36 25.39 38.25 25.. 56 46 47 39.42 25.60 39.31 25.77 39.19 25.94 39.08 26.11 47 48 40.28 26.14 40.14 26.32 40.03 25.49 39.91 26.67 48 49 41.09 26.69 40.98 26.87 40.86 27.04 40.74 27.22 49 50 41.93 27.23 41.81 27.41 41.69 27.60 41.57 27.78 50 Q Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. i c 57 Deg. 56J Deg. 56i Deg. 56i Deg. travkkse table. 51 33 Deg. 33i Deg. 33^ Deg. 331 Deg. i 51 Lat. Dep. Lat. Dep: 27.96 Lat. 42.53 Dep. 28: 15 Lat. DepT 42.77 27.78 42.65 42.40 28.33 62 43.61 28.32 43.49 28.51 43.36 28.70 43.24 28. S9 52 53 44.45 28.87 44.32 29.06 44.20 29.25 44.07 29.45 63 54 45.29 29.41 45.16 29.61 45.03 20.80 44.90 130.00 54 55 46.13 29.96 46.00 30.16 45.86 30.36 45 . 73 : 30 . 56 55 56 46.97 30.. 50 46.83 30.70 46.70 30.91 46. 56131. 11 56 57 47.80 31.04 47.07 31.25 47.53 31.46 47.39 ! 31.67 57 5S 48.64 31.59 48.50 31.80 48.. 37 32.01 48,23 ! 32.22 58 59 49,48 32.13 49.34 32.35 49.20 32.56 49.06 132.78 59 60 61 50.32 32.68 .50.18 32.90 50.03 33.12 49.89 1 33.33 60 51.16 .33.22 51.01 138.45 .50.87 33.67 Ij 50.72 1 33. .S9 61 62 .52.00 33.77 51.85 33.99 51.70 34.22 .51. .55 134.45 62 63 52.84 34.31 .52.69 : 34.. 54 52.53 34.77 |i 52.38 35.00 63 64 53.67 34.86 53.52; 35.09 ,53 . 37 35.32 53.21 135.56 64 65 54.51 35.40 54.36 i 35.64 54.20 35.88 54.05 i 36.11 65 66 .55.35 1 35.95 1 55.19 i 36.19 55.04 36.43 54.88 136.67 66 67 56.19 136.49 56.03 136.74 55.87 36.98 65.71 i 37.22 67 68 57.03 i 37.04 56.87 37.28 56.70 37.53 : .56.54 37.78 68 69 57.87 j 37.58 57.70 37.83 57.54 38.08 1 .57.37 38.33 69 70 71 58.71 38.12 58.54 38.38 .58.37 38.64 58.20 38.89 1 39.45! 70 71 59.55 38.67 59.38 38.93 59.21 39.19 .59.03 72 60.38 39.21 60.21 39.48 60.04 39 . 74 59.87 40.00 i 72 73 61.22 39.76 61.05 40.03 60.87 40.29 i 60.70 '40.56 1 73 74 62.06 40.30 61.89 40.57 61.71 40.84 61.53! 41. Ill 74 75 62.90 40.85 62.72 41.12 62.. 54 41.40 62.36 41.67 75 76 63.74 41.39 63.. 56 41.67 63.38 41.95 63.19 1 42.22 76 77 64.58 41.94 64.39 42.22 64.21 42.. 50 64.02 142.78 77 7S 65.42 42.48 65 . 23 42.77 65.04 43.05 64.85 143.33 78 79 66.25 43.03 66.07 43.32 65.88 43.60 65.69 143.89 79 80 81 67.09 67.93 43.57 66.90 43.86 66.71 44.15 66.52 144.45 80 44.12 67.74 44.41 67.54 44.71 67.35 45.00 ~8l 82 68.77 44.66 68.58 44.96 68.38 46.26 68.18 45.56 82 83 69.61 45.20 69.41 45.51 69.21 45.81 69.01 46.11 83 84 70.45 45.75 70.25 46.06 70.05 46.36 69.84 46.67 84 85 71.29 46.29 71.08 46.60 70.88 46.91 70.67 47.22 85 86 72.13 46.84 71.92 47.15 71.71 47.47 71.51 47.78 86 87 72.96 47.38 72.76 47.70 72.55 48.02 72.34 148.33 87 88 73.80 47.93 73.59 48.25 73.38 48.57 173.17 148.89 88 89 74.64 48.47 74.43 48.80 74.22 i 49.12 [74.00 49.46 89 90 91 75.48 49.02 49.56 75.27 76.10 49.35 49.89 76.05! 49.67 ! 74.83 .50.00 90 76.32 75.88 i 50.23 1 75.66 50.56 91 92 77.16 .50.11 76.94 .50.44 76.72 1 50.78 i 76.50 51.11 92 93 78.00 50.65 77.77 50.99 77.65 51.33 ; 77.33 51.67 93 94 78.83 51.20 78.61 i 51.54 78.39 51.88 1 78.16 52.22 94 95 79.67 51.74 79.45 52.09 79.22 52.43 : 78.99 62.78 95 96 80.51 52.29 80.28 52.64 80.05 52.99 ; 79.82 63.33 96 97 81.35 52.83 81.12 ,53.18 80.89 63.64 180.65 53.89 97 98 82.19 53.37 81.96 53.73 81.72 54.09 81.48 54.45 98 99 83.03 53.92 82.79 54.28 82.55 54.64 182.32 55.00 99 100 1 .2 83.87 1 54.46 183.63 .54.83 83.39 ,55.19 j 83.15 55.66 100 Dep. 1 Lat. D,p. Lat. Dep. ■ Lat. Dep. Lat.- I 57 Deg. 561 Deg. 56^ Deg. 56i Deg. 1; 70 TRAVERSE TABLE. 1 34 Deg. 34i Deg. 34^ Deg, 341 Deg. E' Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 1 0.83 0.56 0.83 0.56 0.82" 0.57 0. 82 0,.57 1 2 1.66 1.12 1.65 1.13 1.65 1.13 1.64 1.14 2 8 2.49 1.68 2.48 1.69 2.47 1.70 2.46 1.71 3 4 3., 32 2.24 3.31 2.35 3.30 2,27 3.29 3,28 4 5 4.15 2.80 4.13 3.81 4.12 2,83 4.11 2.85 5 6 4.97 3.36 4.96 3.38 4.94 3,40 4.93 3.42 6 7 5.80 3.91 5.79 3.94 5.77 3.96 5.75 3.99 7 8 6.63 4.47 6.61 4.50 6.59 4.. 53 6.57 4.56 8 9 7.46 5.03 7.44 5.07 7.42 5.10 7.39 5.13 9 iO 8.29 5.59 8.27 5.63 8.24 5.66 8.22 5.70 6.27 10 11 11 9.13 6.15 9.09 6.19 9.07 6.23 9.04 12 9.95 6.71 9.92 6.75 9.89 6.80 9.86 6,84 12 13 10.78 7.27 10.75 7.32 10.71 7.36 10.68 7,41 13 14 11.61 7.83 11.57 7.88 1 1 . 54 7.93 11.50 7.98 14 1ft 12.44 8.39 12.40 8.44 12.36 8.50 12.32 8.. 55 15 16 13.26 8.95 13.23 9.00 13.19 9.06 13.15 9.12 16 17 14.09 9.51 14.05 9.. 57 14.01 9.63 13.97 9.69 17 IH 14.93 10.07 14.88 10.13 14.83 10.20 14.79 10.26 18 19 15.75 10.62 15.71 10.69 15.66 10.76 15.61 10.83 19 20 16.58 11.18 16.53 11.26 16,48 11.33 16.43 11.40 20 21 17.41 11.74 17. .36 11.82 17,31 11.89 17.35 11.97 21 22 18.24 12.30 18.18 12.38 18.13 12.46 18.08 12.54 22 23 19.07 12.86 19.01 12.94 18.95 13.03 18.90 13.11 23 24 19.90 13.42 19,84 13.51 19.78 13.59 19.72 13.68 24 25 20.73 13.98 20,66 14.07 20.60 14,16 30.54 14.25 25 26 21.55 14.54 21.49 14.63 21.43 14.73 21.36 14.82 26 27 22.38 15.10 22.32 15.20 22.25 15.29 22.18 15,39 27 28 23.21 15 66 23.14 15.76 23.08 15.86 23.01 15,96 28 29 24.04 16.22 23.97 16.32 23 . 90 16.43 23.83 16.53 29 30 24.87 16.78 24.80 16.88 24.72 35.55 16.99 17.56 24.65 17,10 17,67 30 31 31 25.70 17. .33 25.03 17.45 25.47 32 26.53 17.89 26.45 18.01 36.37 18.12 26.29 18.24 32 33 27.36 18.45 27.28 18,57 37.30 18.69 27.11 18,81 33 34 28.19 19.01 38.10 19.14 38.03 19.26 27.94 19,38 34 35 29.02 19. .57 28.93 19.70 38.84 19.82 28.76 19.95 35 36 29.85 20.13 29.76 30.26 29.67 20.39 29.58 20.52 36 37 30.67 20.69 30,58 30.83 30.49 20.96 30.40 21,09 37 38 31.. 50 21.25 31.41 31.39 31.32 21.52 31.22 21.66 38 39 32.33 21.81 32.24 31.95 32.14 33.09 32.04 22.23 39 40 33.16 23.-37 33.06 32.51 .33.97 33.79 22.06 32.87 22.80 40 41 .33.99 22.93 33.89 33.07 23.23 33.69 23.. 37 41 42 34.82 i 23.49 34.73 33.64 34.61 33.79 34.51 23.94 42 43 35.65 24.05 35.54 34.20 35.44 24.36 35.33 24.51 43 44 36.48 24.60 36.37 24.70 36.36 24.92 36.15 25.08 44 45 37.31 25.16 37.30 25.. 33 37.09 35.49 36.5,7 25.65 45 46 38.14 25.72 38.03 25.89 37.91 26.05 37.80 26.22 46 47 38.96 26.28 38.85 1 36.45 38.73 26.62 38.02 [26.79 47 48 39.79 26.84 39.68,27.01 39.56 27.19 39.44 37.36 4S 49 40.62 1 27.40 40.. 50 [27.68 40.38 27.75 40.26 27.93 49 50 41.45 1 27.96 41.33 128. 14 41.31 28.32 41.08 38.50 50 6 ' 1 Dep, 1 Lat. Dep. 1 Lat. Dep. Lat. Dep. Lat. s 56] Deg. 551 Deg. 55A Deg. 5=4 Deg. Xn A VERSE TABLE. 71 D 34Deg. 34i Deg. Mi Deg. 34J Deg, 2 3 Lat. j Dep. Lat. [ Dep. Lat. 1 Dep. Lat, 1 Dep. "51 42.28 28.52 42.16 28.70 42.03:28.89 41.90 29.07 'Jl 52 43.11 29.08 42.98 {29.27 42.85 29.45 42.73: 29.64 52 53 43.94 29.64: 43.81 ^29.83 43.68 .30.02 43.. 55 30.21 53 54 44.77 30.20 44.64 i 30.39 44.50 30.59 44.37 30.78 54 55 45.60 30.76 1 45.40 30.95 45.33 31.15 45.19 31.35 55 56 46.43 31.31 46.29 31.52 146.15 31.72 46.01 31.92 56 57 47.26 31.87 47.12 32.08 46. 9S 32.29 40.83 32.49 57 58 48.08 32.43 ': 47.94 ' 32.64 !i 47.80 i 32.85 47.06 1 33.00 58 59 48.91 32.99 48.77 33.21 48.62 33.42 48.48^33.03 59 60 49.74 33.55 1 49.60 33.77 49.45 33.98 49.30 34.20 60 61 50.57 34.11 50.42 34.33 50.27 34.55 .50.12 34.77 ^ 62 51.40 34.67 1 51.25 34.89 51.10 35.12 50.94 35.34 62 63 52.23 35.23 52.08 35.46 51.92 35.68 51.70 35.91 63 64 53.00 35.79 52.90 36.02 52.74 36.25 52.59 30.48 64 65 53.89 36.35 53 . 73 36 . 58 53.57 36,82 53.41 1 37.05 65 66 54. 72. 36. 9P 54.55:37.15 .54.39 [37.38 54.23 1 37.02 60 67 55.55 37.46 .55.38 i 37.71 55.22! 37.95 55.05| 38.19 07 68 56.37 38.03 56.21 1 38.27 56.04! 38.. 52 .55.87! 38.76 08 69 57.20 38.58 1 57.03 1 38.83 56.86 1 39.08 50.09 39.33 69 70 58.03 39.14 57.86 39.40 57.69 ' 39.65 57.52 39.90 70 71 58.86 39.70 58.69 39.96 58.51 140.21 58.34 40.47 71 72 59.69 40.26 1 59.51 40. .52 59.34 140.78 59.16 41.04 72 73 60.52 40.82 60.34(41.08 60.10 41.35 59.98 41.61 73 74 61.35 41.38 61.17 41.65 60,99 41.91 60.80 42.18 74 75 62.18 41.94 61.99 42.21 61.81 142.48 61.62 42.75 75 76 63.01 42.50; 62.82 42.77 62.63 43,05 62.45 43.32 70 77 63.84 43.06 1 63.65 43.34 63.46 43.61 63.27 43.89 77 78 64.66 43.62 64.47 143.90 64.28 44.18 1 64.09 44.46 78 79 65.49 44.18. 05.30 44.46 65.11 44.75 64.91 : 45.03 79 80 81 66.32^44.74 67.15 45.29' 66.13 ;45.02 65.93 : 45.31 65.73 45.60 06.55 40.17 80 81 66.95 45.59 66.75 45.88 82 67.98 45.85 67.78 46.15 67.58 1 46.45 07.37:40.74 82 83 68.81 [46.41 ' 68.61 146.71 68.40 47.01 t 68.20 47.31 83 84 69.64 (46.97 69.43 47.28 69.23 47.58" 69.02 47.88 84 85 70.47 47.53 70.26 47.84 70.05 48.14 69.84 148.45 85 86 71.30 48.09 71.09 48.40 70.87 48.71 70.66! 49.02 80 87 72.13 48.65 71.91 48.96 71.70 49.28 71.48 49.59 87 88 72.96 49.21 72.74 49.53 72.52 49.84 72.30:50.10 88 89 73.78 149.77 73.57 50.09 73.35 50.41 73.13 50.73 89 90 "91 74.61 50.33 75.44 i 50.89 74.39 \ 50.65 ; 74.17 50,98 : 73.95! 51.30 90 91 75.22 51.22 i 75.00 j 51.54 ! 74.77! 51.87 92 76.27 51.45 76.05 ' 51.78 175.82' 52.11 1 75.59 1 52.44 92 93 77.10 52.00 76.87 52.34 ! 76.64 1 52.68 70.41 ! 53.01 93 94 77.93 52.56 77.70 , 52.90 i 77.47 53.24 1 77.23! 53.58 94 95 78.76 i 53.12 78.53 53.47 78.29 53.81 ; 78.00 54.15 95 96 79.59 53.68 79.35 54.03 79.12 54.37 78.88 '54.72 90 97 80.42 154.24 80.18 : 54.59 79.94 54.94 |( 79.70 i 55.29 97 98 81.25 i 54.80 81.01 1.55.15 80.70 55.51 1:80.52 1 ,55.86 98 99 82.07 55.36 81.83 55.72 81.59 .56.07 |i 81.34 i 56.43 99 lOO Q 82.90 55.92 82.66 56.28 82.41 56.64 82.16 1 57.00 100 g .1 Dep. Lat. Dep. Lat. Dep. Lat. Dep. j Lat. 56 Deg. 551 Deg. 55i Deg. 55J Deg. 72 TRAVEKSB TABLE. 1 9 35 Deg. 354 Deg. 35i Deg. 35i Deg. Lat. Dep. Lat. Dep. Lat. Dep. 0.58 Lat. Dep. 1 0.82 0.57 0.82 0.,58 0.81 0.81 "0^58" 1 2 1.64 1.15 1.63 1.15 1.63 1.16 1.63 1.17 2 3 2.46 1.72 2.45 1.73 2.44 1.74 3.43 1.75 3 4 3.28 3.29 3.27 3.31 3.26 3.32 3.35 2.34 4 5 4.10 2.87 4.08 2.89 4.07 2.90 4.06 2.93 5 6 4.91 3.44 4.90 3.46 4.88 3.48 4.87 3.51 7 5.73 4.01 5.73 4.04 5.70 4.06 5.68 4.09 7 8 6.55 4.59 6.53 4.63 6.51 4.65 6.49 4.67 8 9 7.37 5.16 7.35 5.19 7.33 5.23 7.30 5.26 9 10 "ll 8.19 5.74 8.17 5.77 8.14 5.81 6.39 8.12 5.84 6.43 10 11 9.01 6.31 8.98 6.35 8.96 8.93 12 9.83 6.88 9.80 6.93 9.77 6.97 9.74 7.01 12 13 10,65 7.46 10.63 7.50 10., 58 7.55 10.55 7.60 13 U 11.47 8.03 11.43 8.08 11.40 8.13 11.36 8.18 14 15 12.29 8.60 12.25 8.66 12.21 8.71 12.17 8.76 15 16 13.11 9.18 13.07 9.33 13.03 9.29 12.99 9.35 16 17 13.93 9.75 13.88 9.81 13.84 9.87 13.80 9.93 17 18 14.74 10.32 14.70 10.39 14.65 10.45 14.61 10.52 18 19 15.56 10.90 15.. 53 10.97 15.47 11.03 15.42 11.10 19 20 31 16.38 11.47 16.33 11. .54 16.28 11.61 lfi.23 17.04 11.68 '12.27 20 21 17.20 12.05 17.15 13.12 17.10 12.19 22 18.02 12.62 17.97 13.70 17.91 12.78 17.85 12.85 22 23 18.84 13.19 18.78 13.37 18.73 13.36 18.67 13.44 23 21 19.66 13.77 19.60 13.85 19.54 13.94 19.48 14.02 24 25 20.48 14.34 20.42 14.43 20.35 14.53 i: 20.29 14.61 25 26(21.30 14.91 21.33 15.0' 21.171 15.10 21.10 15.19 26 27 22.12 15.49 32.05 15.58 21.98 1 15.68 i21.91 15.77 37 28 22.94 16.06 22.87 16.15 22.80 16.26 122.72 16.36 28 29 23.76 16.63 23.68 16.74 23.61 16.84 i 33.54 16.94 29 30 24.57 17.21 24.. 50 25.32 17.81 34.42 17.42 1 34.35 17.53 30 ■ 31 25.39 17.78 17.89 25.24 18.00 |25.16 18.11 31 32 ! 26.21 18.35 26.13 18.47 26.05 18.58 125.97 18.70 33 33 27.03 18.93 26.95 19.05 36.87 19.16 36.78 19.28 33 34 27.85 19.50 27.77 19.63 27.68 19.74 '37.59 19.86 34 35 28.67 20.08 38.58 20.20 28.49 20.33 128.41 20.45 35 36 29.49 20.65 29.40 20.78 29.31 20.91 1 29.22 21.03 36 37 30.31 21.22 30.22 21.35 30.13 31.49 30.03 21.62 37 38 i 31.13 21.80 31.03 21.93 30.94 22.07 30.84 23.20 38 39 1 31.95 22.37 31.85 22.51 31.75 23.65 '31.65 23.79 39 40} 32.77 41 33.. 59 33.94 32.67 33.48 23.09 23.66 33.56 33.38 33.33 33.81 32.46 33.27 23.37 23.95 40 41 23.. 53 42 34.40 34.09 34.30 24.24 34.19 34.39 134.09 24.54 42 43 35.22 24.66 35.12 24.83 35.01 34.97 1 34.90 25.12 43 44 36.04 25.24 35.93 35.39 35.82 35.55 35.71 25.71 44 45 36.86 25.81 36 . 75 35.97 36.64 36.13 36.. 52 26.29 45 46 i 37.68 26.38 37.57 36.55 37.45 36.71 137.33 26.88 46 47 38.. 50 26.96 II .38.38 27.13 38.26 37.29 138.14 27.46 47 48 39.32 27.. 53 39.20 37.70 39.08 27.87 38.96 28.04 48 49 40.14 28.11 40.02 28.28 39.89 28.45 i39.77 38.63 49 50 40.96 28.68_ 40.83 38.86 40.71 29.04 140.58 29.21 50 a a Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. (5 55 1 >eg. 54} Deg. 544 Deg. 54i Deg. TJlAVEltSE TABLE. 73 1 51 35 Deg. 35i Deg. 35i Deg. 351 Deg. 9 Lat. Dep. Lat. Dep. Lat. 1 Dep. Lat, Dep. 41.78 29.25 41.65 29.43 41.52^29.62 41., 39 29.80 i 51 52 42.60 29.83 42.47 30.01 42.33 130.20 42.20 30.. 38 .52 53 43.43 .30.40 43.28 30.59 43.15 130.78 43.01 30.97 53 54 44.23 30.97 44.10 31.17 43.96 31.36 43.82 31.55 54 55 45.05 31.55 44.92 31.74 44.78 31.94 44.64 32.13 1 55 56 45.87 32.12 45.73 32.32 45.. 59 132.52 45.45 32.72; 50 57 46.69 32.69 46.. 55 32.90 46.40 33.10 46.26 33.,30i 57 58 47.51 33.27 47.37 33.47 47.22 33.68 47.07 33.89 i ,58 59 48.33 33.84 48.18 34.05 48.03 34.26 47.88 34.47 59 60 61 49.15 34.41 49.00 .34.63 48.85 34.84 35.42 48.69 49.51 35.05 60 35.64" 61 49.97 .34.99 49.82 35.21 49.66 62 50.79 35.56 50.63 35.78 50.48 36.00 Ij 50.32 .36.22 i 62 63 51.61 36.14 51.45 36.36 51.29 36.58 i| 51.13 36. 8i 63 64 52.43 36.71 52.27 36.94 .52.10 37.16 51.94 37.39 64 65 53.24 37.28 53.08 37.51 .52.92 37.75 52.75 37.98 65 66 54.06 37.86 53.90 38.09 53.73 38.33 :| 53.56 38.56 66 67 54.88 38.43 54.71 ,38.67 54.55 38.91 j.54.38 39.14 ' 67 68 55 . 70 39.00 55.53 39.55 55.36 39.49 55.19 39.73, 68 69 56.52 39.58 56.35 39.82 56.17 40.07 156.00 40.31 i 69 70 71 57.34 40.15 57.16 .57.98 40 40 40.98 56.99 '57.80" 40.65 .56.81 40.90 70 58.16 40.72 41.23 57.62 141.48 71 72 .58.98 41.30 58.80 41.. 55 .58.62 41.81 .58.43 1 42.07 72 73 59.80 41.87 59.61 42.13 '59.43 42.39 59 . 24 42.65 73 74 60 . 62 42.44 60.43 42.71 60.24 42.97 60.06 43.23 74 75 61.44 43.02 61.25 43.29 61.06 43.55 60.87 43.82 i 75 1 76 62.26 43.59 62.06 43.86 61.87 44.13 61.68 44.40 76 77 63.07 44.17 62.88 44.44 '62.69 44.7] 62.49 144.99 77 78 63.89 44.74 63.70 45.02 63.50 45.29 63.30 j 45.57 78 79 64.71 45.31 64.51 45.59 64.32 45.88 64.11 46.16 79 80 81 65.53 45.89 65.33 66.15 46.17 46 . 75 65.13 46.46 64.93! 46.74' 80 65.74 47.32 > 81 66.35 46.46 65.94 47.04 82 67.17 47.03 66.96 47.33 66.76 47.62 66.55 '47.91 | 82 83 67.99 47.61 67.78 47.90 67.. 57 48.20 67.36 I 48.49 1 83 84 63.81 48.18 68.60 48.48 68.39 48,78 68 . 1 7 49.08 t 84. 85 69.63 48.75 69.41 49.06 69.20 49.36 08.98 49.66 85 86 70.45 49.33 70.23 49.63 70.01 49.94 69.80 50.25 1 86 87 71.27 49.90 71.05 50.21 170.83 50.. 52 70.61 50.83 87 88 72.09 50 47 71.86 50.79 71.64 51.10 71.42 51.41 88 89 72.90 51.05 72.68 51.37 72.46 51.68 72.23 .52.00 89 90 91 73.72 51.62 73.50 51.94 73.27 74.08 .52.26 73.04 52.58 90 91 74.54 ,52.20 74.31 52.-52 52.84 173.85 53.17 92 75.36 52.77 75.13 53.10 74.90 53.42,174.66 53.75 92 93 76.18 .53.341 75.95 53.67 75.71 54.01 ' 75.48(54.34 93 94 77.00 53.92 76.76 54.25 76.. 53 54.. 59 76.29 1 54.92 94 95 77.82 ,54.49 77.58 54.83 77.34 55.17 77.10 55.50 95 96 78.64 55.06 78.40 .55.41 78.16 55.75 77.91 56.09 96 97 79.46 55.64 79.21 .55.98 7S 97 56.33 78.72 56.07 97 98 80.28 .56.21 80.03 56.. 56 79.78 56.91 79.53 57.26 98 99 81.10 56.78 80.85 57.14 80.60 57.49 80.35 157.84 99 A22 1 ■a 81.92 57.36 81.66 57.71 81.41 58.07 81.16 ' 58.42 Dep. Lat. 100 Dep. Lat. Dep. Lat. Dep. L«.i 55 Deg. 54} Deg. 54i Dog. 54i Deg. 3 74 TRAVERSE TABLE. CO 1 s 1 ti6 Deg. 36i Deg. 36A Deg. 361 Deg. C 3 P 1 Lat. Dep. ~^8T] 0.69 Lat. Dep. Lat. Dep. Lat. Dep. 0.81 0.59 0.80 0..59 0.80 0.60 2 1.62 1.18 1.61 1.18 1.61 1.19 1.60 1 20 2 3 2,43 1.76 2.42 1.77 2.41 1.78 2.40 1.79 3 4 3.24 2.35 3.23 2.37 3.22 2.38 3.20 2.39 4 5 4.05 2.94 4.03 2.96 4.02 2.97 4.01 2.99 5 6 4.85 3.53 4.84 3.55 4.82 3.57 4.81 3.59 6 7 5.66 4.11 5.65 4.14 5.63 4.16 5.61 4.19 7 8 6.47 4.70 6.45 4.73 6.43 4.76 6.41 4.79 8 9 7.28 5.29 7.26 5.32 7.23 5.35 7.21 5.3S 9 10 11 8.09 5.88 6.47 8.06 5.91 8.04 5.95 8.01 5.98 10 11 8.90 8.87 6.50' 8.84 6.54 8.81 6.58 12 9.71 7.05 D.68 7.10 9.65 7.14 9.61 7.18 12 13 10. .52 7.64 10.48 7.69 10.45 7.73 10.42 7.78 13 14 11.33: 8.23 11.29 8.28 11.25 8.33 11.22 8.38 14 15 12.14 ! 8.82 12.10 8.87 12.06 8.92 12.02 8.97 15 16 12.94! 9.40 i 12.90 9.46 12.86 9.52 12.82 9.57 16 17 13.75 1 9.99 13.71 10.05 13.67 10.11 13.62 10.17 17 18 14.56 10.58 14.. 52 10.64 14.47 10.71 14.42 10.77 18 19 15.37 j 11.17 15.32 11.23 15.27 11.30 15.22 11.37 19 20 21 10.18 11.76 16.13 11.83 16.08 16.88 11.90 12.4'9 16.03 11.97 20 21 16.99 12. .34 16.94 12.42 16.83 12.56 22 17.80 12.93 17.74 13.01 17.68 13.09 17.63 13.16 22 23 18.61 i 13.52 18.55 13.60 18.49 13.68 18.43 13.76 23 24 19.42 14.11 19.35 14.19 19.29 14.28 19.23 14.36 24 25 20.23 1 14.69 20.16 14.78 20.10 i4.87 20.03 14.96 25 26 21.03 15.28 20.97 15.37 20.90 15.47 20.83 15.56 26 27 2i.84 : 15.87 21.77 15.97 21.70 16.06 21.63 16.15 27 28 22.05 116.46 22.58 16.56 22.51 16.65 22.44 16.75 28 29 23.46 i 17.05 23.39 17.15 23.31 17.25 23.24 17.35 29 30 ~3l 24.27 1 17.63 24.19 17.74 18.33 24.12 17.84 18.44 24.04 17.95 30 31 25.08 18.22 25.00 24.92 24.84 18.55 32 25.89 1 18.81 25.81 18.92 25.72 19.03 25.64 19.15 32 33 26.70 1 19.40 26.61 19.51 26.53 19.63 26.44 19.74 33 34 27.51 1 19.98 27.42 20.10 27.33 20.22 27.24 20.34 34 35 28.32,20.57 28.23 20.70 28.13 20.82 28.04 20.94 35 36 29.12 21.16 29.03 21.29 28.94 21.41 28.85 21.54 36 37 29.93 21.75 29.84 21.88 29.74 22.01 29.65 22.14 37 38 30.74 22.34 30.64 22.47 30.55 22.60 30.45 22.74 38 39 31.55 22.92 31.45 23.06 31.35 23.20 31.25 23.33 39 40 32.36 23.51 32.26 23.65 32.15 23.79 32.05 23.93 24". .53 40 4T 33.17 24.10 33.06 24.24 32.96 24.39" 32.85 42 33.98 24.69 33.87 24.83 33.76 24.98 33.65 25.13 42 43 34.79 25.27 34.68 25.43 34.57 25.58 34.45 25.73 43 44 35.60 25.86 35.48 26.02 35.37 26.17 35.26 26.33 44 45 36.41 26.45 36.29 26.61 36.17 26.77 36.06 26.92 45 46 37.21 27.04 37.10 27.20 36.98 27.36 36.86 27.52 46 47 38.02 27.63 37.90 27.79 37.78 27.96 37.66 28.12 47 48 38.83 28.21 38.71 28.. 38 38.59 28.55 38.46 28.72 48 49 39.64 28.80 39.52 28.97 39.39 29.15 39.26 29.32 49 _50 Q 40.45 29.39 40.32 29.57 40.19 29.74 40.06 29.92 50 1 s Dop. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 54 Deg. 5311 3eg. 53iDeg. 53i Deg. TEAVKESE TABLE. 75 3 9 51 36 Deg. 36i Deg. 36i Deg. 361 Deg. 1 ? "51 Lat. Dep. Lat. Dep. Lat. 1 Dep Lat. 1 Dep. i41.26 29.98 I41.13 30.16 41,00 30.34 40.86:30.51 52 42.07 30.66 i 41.94 30.75 41.80 30.93 41.67 31.11 52 53 42.88 31.15 '42.74 31.34 42.60 31.53 42.47 i 31.71 53 54 43.69 31.74 143.55 31.93 43.41 132.12 43.27 [32.31 54 55 '44.50 32.33 ■; 44.35 32.52 144.21 132.72 44.07 1 32.91 6,5 5fi 45.30 32.92 45.16 33.11 45.02 ,33.31 j 44.87 133.51 57 46.11 33.50 145.97 33.70 45.82 j 33.90 45.67 1 34.10 57 58 46.92 34.09 46.77 34.30 '46.62 ! 34.50 )l 46.47 134.70 58 59 47.73 .34.68 47.58 34.89 : 47.43 ,35 09 i! 47.27 135.30 59 61 48.54 35.27 Ij 48.39 .35.48 : 48.23 35.69 j 48.08 j 35.90 60 61 49.35 35.85 i49. 19 36.07 ; 49.04 36.28 48.88 36.50 6-^ 50.15 36.44 1:50.00 36.66 49.84 36.88 49.68 37.10 62 63 50.97 37.03 50.81 37.25 50.64 37.47 50.48 37.69 63 64 51.78 37.62 j 51.61 37.84 51.45 38.07 51.28 38.29 64 65 52.59 38,21 ' 52.42 38.44 52.25 3S.66 52.08 38.89 65 66 .53.40 38.79 | 53.23 39.03 ! 53.05 39.26 62.88 39.49 66 67 54.20 '• 39.. 38 j 54.03 39.62 53.86 39.85 53.68 40.09 67 68 55.01 : 39.97 154.84 40.21 54.66 40.45 64.49 40.69 69 69 55.82:40.56 55.64 40.80 55,47 41.04 55.29 41.28 69 70 71 56.63 41.14 57.44 41.73 50.45 41.39 56.27 41.64 56.09 41.88 42.48 70 71 57.26 41.98 57.07 142.23 66.89 72 58.25 42.32 ii 58.06 42.57 57.88 142.83 57.69 43.08 72 73 59.06 42.91 ;| .58.87 43.17 58.68 43.42 58.49 43.68 73 74 59.87 43.50 r 59.68 43.76 59.49 44.02 59.29 44.28 74 75 60.68 44.08: 60.48 44.35 60.29 44.61 60.09 44,87 75 76 61.49 44.671 61.29 44.94 61.09 45.21 60.90 45.47 76 77 62.29 45.26 62.10 45.53 61.90 45.80 61.70 46.07 77 78 63.10 45.85 62.90 46.12 62.70 46.40 62.50 46.67 78 79 63.91 46.43 63.71 46.71 63.. 50 46.99 63.30 47.27 79 80 81 64.72 47.02 64.52 47.30 64.31 47.69 64.10 47,87 80 81 65.53 47.61 i 65.32 47.90 65.11 48.18 64.90 48.46 82 66.34:48.20; 66.13 48.49 65.92 48,78 65.70 49.06 82 83 67.15 48.79 66.93 49.08 66.72 49.37 66.60 49.66 83 84 67.96 49.37: 67.74 49.67 67.. 52 49.97 67.31 50.26 84 85 68.77 ,49.96 68.55 .50.26 68.33 50.56 68.11 60.86 85 86 69.58 50.55 69.35 50.85 69.13 51.15 68.91 51.46 86 87 70.38 51.14 70.16 51.44 69.94 I 51.75, 69.71 52.05 87 88 71.19 ,51.73 70.97 52.04 70.74 52.34 70.51 52.65 88 89 72.00 52.31 71.77 52.63 71.54 52.94 71.31 53.25 89 90 91 72.81 52.90; 72.58 73.39 53.22 72.35 53.53 72.11 .53.86 90 -91 73.62 53.49 .53.81 73.15 54.13 72.91 ,54.45 92 74.43 54.08 74.19 54.40 73.95 54.72 73.72 55.05 92 93 75.24 1.54. 66 75.00 54.99 74.76 55.32 74.52 55.64 93 94 76.05 55.25 i 75.81 55.. 58 75.56 55.91 75.32 50.24 94 95 76.86 1 55.84 76.61 56.17 76.37 56.51 76.12 56.84 95 96 77.67! 56.43 i| 77.42 .56.77 77.17 67.10 76,92 57.44 96 97 78.47 ,57.02 1 78.23 57.36 77.97 57.70 77,72 58.04 97 98 79.28 157.60 79.03 .57.95 78.78 58,29 78,52 .58.64 98 99 80.09 5S.19i 79.84 58.54 79.68 58.89 79 32 59.23 99 100 80.90 ,58.78 I 80.64 59.13 80.39 59.48 80.13 59.83 Lat. 100 5 1 1 Dep. 1 Lat. 54 Deg. 1 Dep. Lat. Dep. Lat. Dep 531 Deg. 53iDeg. 53J Deg. 76 TRAVERSE TABLK. 3 37 Deg. 37^ Deg. 37i Deg. 371 Deg. Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 0.80 0.60 0.80 0.61 0.79 0.61 0.79 0.61 1 2 1.60 1.20 1.59 1.21 1.59 1.22 1.58 1.22 2 3 2.40 1.81 2.39 1.82 2.38 1.83 2.37 1.84 3 4 3.19 2.41 3.18 2.42 3.17 2.43 3.16 2.45 4 5 3.99 3.01 3.98 3.03 3.97 3.04 3.95 3.06 5 6 4.79 3.61 4.78 3.63 4.76 3.65 4.74 3.67 6 7 5.59 4.21 5.57 4.24 5.55 4.26 5.53 4,29 7 8 6.39 4.81 6.37 4.84 6.35 4.87 6.33 4.90 8 9 7.19 5.42 7.16 5.45 7.14 5.48 7.12 5.51 9 10 7.99 6.02 7.96 6.05 7.93 6.09 7.91 6.12 10 11 11 8.78 6.62 8.70 6.66 8.73 6.70 8.70 6.73 12 9.. 58 7,22 9.. 55 7.26 9.. 52 7.31 9.49 7.35 12 13 10.33 7.82 10.35 7.87 10.31 7.91 10.28 7.90 13 14 11.18 8.43 11.14 8.47 11.11 8.52 11.07 8 . 57 14 15 11.98 9.03 11.94 9.08 11.90 9.13 11.86 9.18 15 j 16 12.78 9.63 12.74 9.68 12.69 9.74 12.65 9.80 lo! 17 13.58 10.23 13.53 10.29 13.49 10.35 13.44 10.41 17 18 14.38 10.83 14.33 10.90 14.28 10.96 14.23 11.02 18 19 15.17 11.43 15.12 11.50 15.07 ll.i>7 15.02 1 1 . 63 19 20 15.97 12.04 15.92 12.11 15.87 16.66 12.18 15.81 12.24 20 j 21 16.77 ! 12.64 16.72 12.71 12.78 16.60 12.80 21 22 i 17.57; 13.24 17.51 13.32 17.45 13.39 17.40 13.47 22 23, 18.37 13.84 18.31 13.92 18.25 14.00 18.19 14.03 23 24 19.17 14.44 19.10 14.53 19.04 14.61 18.98 14.69 24 25 [ 19.97 15.05 19.90 15.13 19.83 15.22 19.77 15,31 25 26 ! 20.76 15.65 20.70 15.74 20.63 15.83 20.56 15.92 26 27 21.56 16.25 21.49 16.34 21.42 16.44 21.35 16.. 53 27 28 22.33 16.85 22.29 16.95 22.21 17.05 22.14 17.14 2S 29 23.16 17.45 23.08 17.55 23.01 17.65 22.93 17.75 29 30 31 23.96 24.76 18.05 23.88 18.16 23.80 18.26 23 . 72 18.37 30 31 18.06 24.08 18.76 24.59 18.87 24.51 18.9.^ 32 25.. 56 19.26 25.47 19.37 25.39 19.48 25.30 19.59 33 33 i 20.35 19.80 26.27 19.97 26.18 20.09 26.09 20.20 33 34 1 27.15 20.46 27.06 20.58 26.97 20.70 26.88 20.82 34 35 1 27.95 21.06 27.86 21.19 27.77 21.31 27.67 21.43 35 36 28.75 21.67 28.66 21.79 28.56 21.92 28.46 22.04 30 37 29.55 22.27 29.45 22.40 29.35 22.132 29.26 22.65 37 38 30.35 22.87 30.25 23.00 30.15 23.13 30.05 23.26 33 39 31.15 23.47 31.04 23.01 30.94 23.74 30.84 23.88 39 40 41 31.95 24.07 31.84 24.21 31.73 32 53 24.35 24.96 31.03 24.49 40 41 32.71 24.67 32.64 24.82 32.42 25.10 42 33.54 25.28 33.43 25.42 33 32 25.57 33.21 i 25.71 42 43 34.34 25.88 34.23 26.03 34.11 26.18 34.00 '20.33 43 44 35.14! 20.48 35.02 26.63 34.91 26.79 34.79 26.94 44 45 35.94 27.08 35.82 27.24 35.70 27.39 35..58I27..55 45 40 36.74 27.68 36 . 02 27.84 36.49 28.00 36.37! 28.16 1 46 1 47 37.. 54 28.29 37.41 28.45 37.29 28.61 37.16:28.77 1 47 1 48 38 . 33 28.89 38.21 29.05 .38.08 29.22 37.95 29.39 48 49 39.13 29.49 39.00 29.66 38.87,29.83 38.74 30.00 49 50 i 1 39.93 30.09 39 . 80 30.26 39.67 30.44 39 . 53 30.61 _50 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 1 .2 S3 Deg. 521 Deg. 52i Deg. 52i Dog. TRAVERSE TABLE. 77 51 37 Deg. 37i Deg. 37i Deg. 371 Deg. 5 p Lat. Dcp. Lat. Dep. Lat. Dep. Lat. Dep. i 40.73 30.69 40.60 30.87 40.46 31.05 40, .33 131.22 51 1 52 41.53 31.29 41.39 31.48 41.25 31.60 41.12 31.84 52 53 42.33 81.90 42.19 32.08 42.05 .32.26 41,91 32.45 53 54 43.13 32.50 42.98 32.69 42.84 32.87 42,70 33.00 54 55 43.92 33.10 43.78 33.29 43 . 63 33.48 43,49 33 . 67 55 56 44.72 33.70 44.58 33.90 44.43 34.09 44.28 34.28 56 57 45.52 34.30 45.37 34.50 45.22 34.70 45.07 34.90 57 58 46.32 134.91 40.17 .35.11 46.01 35.31 45.86 35.51 58 59 47.12! 35.51 46.96 35.71 46.81 35 . 92 46.65 36.12 59 60 61 47.92 36.11 47.76 36.32 47.60 36 . 53 37.13 47.44 36.73 60 48.72 36.71 48.. 56 36.92 48.39 48.23 37.. 35 "61 62 49.. 52 37.31 49.. 35 37.53 49.19 37.74 49.02 37.96 62 63 50.31 37.91 50.15 38.13 49.98 38.. 35 49.81 38.57 63 64 51.11 38.. 52 50 . 94 38.74 50.77 38.96 .50.60 39.18 64 65 51.91 39,12 51.74 39.34 51.57 39.57 51.39 39.79 65 66 52.71 39.72 52.54 39.95 52.36 40.18 52.19 40.41 06 67 53.51 ] 40.32 .53.33 40.55 53.15 40.79 .52.98 4i.02 67 68 .54.31 140.92 54.13 41.16 53.95 41.40 .53.77 41.63 08 69 .55.11 i41..53 .54.92 41.77 54.74 42.00 .54.56 42.24 69 70 "71 O5.90 42.13 55.72 42.37 .55.. 53 .56.33 42.61 43.22 .55.35 42 86 43.47 70 71 .56.70 42 . 73 56 . 52 42.98 56.14 72 57.50 43.33 ,57.31 43.. 58 57.12 43.83 56 . 93 44.08 72 73 58.30 43.93 58.11 44.19 57.91 44.44 .57.72 44.69 73 74 59.10 44.53 58.90 44.79 .58.71 45.05 58.51 45.30 74 75 59.90 45.14 59.70 45.40 59 . 50 45.66 59.30 45.92 75 76 00.70 45.74 60.. 50 46.00 60.29 46.27 60.09; 48.-53 i 76 8 77 61.49 46.34 61.29 46.61 61.09 46.87 60.88 47.14! 77 1 78 G2.29 46.94 62.09 47.21 61.88 47.48 61.67 47.75 i 78 79 63.09 47.. 54 62.88 47.82 62.67 48.09 62.46 48.37 i 79 80 81 63.89 148. 15 64.89 48.75 63.68 64.48 48.42 49 .03 63.47 64.26 48 , 70 49.31 63.26 48.98 i 80 49.59 i 81 64.05 82 65.49 49.35 65.27 49.63 1 65.05 49.92 64.84 .50.20 1 82 83 66.29 49.95 66.07 |,50.24i 65.85 5.-0.53 65.63 .50.81 83 84 67.09 50.55 66.86 .50.84 66.64 51.14 66.42 51.43 84 85 67.88 51.15 67.66 51 .45 67.43! 51.74 67.21 .52.04 85 86 68.68 51.76 68.46 .52.06 08.23 .52.35 68 . 00 52.65 86 87 69.48 52.36 09.25 .52.66 69.02 .52.96 68.79 .53.26 87 88 70.28 .52.96 70.05 53.27 69.82 .53.. 57 69 . .58 .53.88 88 89 71.08 53. .56 70.84 53.87 70.61 54.18 70.37 54.49 89 90 91 71.88 54.16 72.68 .54.77 71.64 72.44 54.48 71.40 .54.79 71.16 .55.10 90 .55.08 72.20 .55.40 71.95 ,55.71 91 92 73.47: 55.37 73.23 55.69 72.99 56.01 72.74 .56.32 92 93 74.27; 55.97 74.03 56.29 73 . 78 56.61 73.. 53 56.94 93 94 75.07' 56.57 74.82 56.90 74.58 57.22 74.. 32 .57., 55 94 95 75.87! 57.17 75.62 57.50 75.37 57.83 75.12 .58.16 9.5 96 76.67 57.77 76.42 58.11 76.16 58.44 75.91 .58.77 96 97 77.47 : 58.38 77.21 .58.71 76.96 59.05 76.70 59.39 97 98 78.27,58,98 78.01 59.32 77.75 59.60 77.49 60.00 98 99 79.06 S .59.. 58 78.80 ' .59.92 78.. 54 60.27 78.28 60.61 99 100 1 "5 79.86 : 60.18 79.60 60.53 79.34 60.88 79,07 1 61.22 100 Dep. 1 Lat. Dep. Lat. Dep. Lat. Dcp. Lat, 1 53 1 )e|r. 521 Deg. 1 1 52^ Deg. 52^ Deg. 24 78 TRAVERSE TABLE. 5 3 p T 38 Deg. 38i Deg. 38J Deg. 38i Dtg. J 1 Lat. Dep. Lat. Dep. Lat. Dep. Lat. D«p. 0.79 0.62 0.79 0.62 0.78 0.62 0.78 '~0'.63" 2 1.58 1.23 1..57 1.24 1.57 1.24 1.56 1.25 2 3 2.36' 1.85 1.86 2.35 1.87 2.34 1.88 3 4 3.15! 2.46 3! 14 2.48 3.13 2.49 3.12 2.50 4 1 5 3.94' 3.08 3.93 3.10 3.91 3 11 3.90 3.13 5I G 4.73 j 3.69 4.71 3.71 4.70 3.74 4.68 3.76 S 7 5. .52, 4.31 5.50 4.33 5.48 4.36 5.46 4.38 7 8 6.30 4.93 6.28 4.95 6.26 4.98 6.24 5.01 S 9 7.09 1 5.54 7.07 5.57 7.04 5.60 7.02 5.63 9 10 7.88 6.16 7.85 6.19 7.83 8.61 6.23 7.80 6.26 10 "TT 8.67 6.77 8.64 6.81 6.85 8., 58 6.89 i 11 12^ 9.46 7.39 9.42 7.43 9.39 7.47 9.36 7.51 12 13 : 10.24 8.00 10.21 8.05 10.17 8.09 10.14 8.14 13 14 11.03 8.62 10.99 8.67 10.96 8.72 10.92 8. 70 14 15! 11.82' 9.23 11.78 9.29 11.74 9.34 11.70 9.39 15 16 i 12.61 i 9.85 12.57 9.91 12.52 9.96 12.48 10.01 16 17 13.40 1 10.47 13.35 10.52 13.30 10.58 13.26 10.64 17 18 14.18 1 11.08 14.14 11.14 14.09 11.21 14.04 11.27 18 19 ,14.97 11.70 14.92 11.76 14.87 11.83 14.82 11.89 19 _20 15.76 i 12.31 15.71 12.38 15.65 12.45 15.60 12.5?. 20 21 16.55 12.93 16.49 13.00 16.43 j 13.07 16.38 13.14"! 21 22 17.34 13.54 17.28 13.62 17.22! 13.70 17.16 13.77 1 22 23 18.12 ' 14.16 18.06 14.24 18.00 14.32 17.94 14.40 23 24 18.91 , 14.78 18.85 14.86 18.78 14.94' 18.72 15.02 24 25 19.70 15.39 19.63 15.48 19.57 15.56 r 19. .50 15.65 25 26 20.49 ; 16.01 20.42 16.10 20.35 16.19 : 20.28 16.27 26 27 21.28 1 16.62 21.20 16.72 21.13 16.81 l'21.06 16.90 27 28 22.06 1 17.24 21.99 17.33 21.91 17.43!i21.84 17.. 53 28 29 22.85 17.85 22 . 77 17.95 22.70 18.05 i 22.62 18.15 29 30 23.64 18.47 23.56 18.57 23.48 18.68 j 23.40 18.78 30 31 124.43 19.09 24.34 19.19 24.26 19.30 24.18 19.40 31 32 25.22 i 19.70 25.13 19.81 25.04 19.92 24.96 20.03 32 33 26.00 20.32 25.92 20.43 25.83 20.54 1 25.74 20.66 33 34 26.79 20.93 26.70' 21.05 26.61 21.17 1 26. .52 21.28 34 35 27.58,21.55 27.49 : 21.67 27.39 i 21.79 1 27.30 21.91 35 36 28.37 : 22.16 28.27 1 22.29 28.17 i 22.41 1 28.08 22.. 53 36 37 [29.16 1 22.78 29.06 22.91 28.96 23.03 28.86 23.16 ; 37 38 129.94 1 23.40 29.84 23.. 53 29.74 23.66 ' 29.64 23.79 1 38 39 130.73 124.01 30.63 24.14 30.52 24.28 , 30.42 24.41 1 39 40 31.52; 24.63 41 : 32.31 125.24 31.41 24.76 31.30 1 24.90 ,31.20 25.04 1 40 25.66 41 32.20 25.38 32.09 ! 25.. 52 t 31.98 42 ' 33.10; 25.86 32.98 26.00 32.87 26.15 i 32.76 26.29 42 43 33.88 26.47 33.77 26.62 33.65 26.77 33.53 26.91 43 44 34.67 27.09 34.55 27.24 34.43 27.39 134.31 27., 54 ' 44 45 35.46 27.70 35.34 27.86 35.22 28.01 35.09 28.17 45 46 36.25 28.. 32 36.12 128.48 36.00 28.64 35.87 28.79 46 47 37.04 28.94 36.91 29.10 36. 7S 29.26 36 . 65 29.42: 47 48 37.82 29.. 55 .37.70 29.72 37.57 29.88 37.43 30.04 48 49 38.61 30.17 38.48 30.34 38.35 30.50 38.21 30.67 ; 49 50 39.40 30.78 39.27 30.95 39.13 31.13 38.99 31.30 50 '8 e .2 Dep. Lat. Dep. Lat. Dep, Lat. Dep. Lat. ;i 52 Deg. 5U Deg. 5H Deg. 5U Deg. 1 "i is 1 TRAVKKSE TABLE. 79 o 5.' I 51 38 Deg. 38J Deg. 384 Deg. 381 Deg. ! ^ Lat. Dep. Lat. [ Dep. Lat. Dep. Lat. 39.77 Dep. 3 40.19 31.40 40.05 31.57 39.91 31.75 3J.92 51 52 40,98 32.01 40.84 .32.19 40.70 32.. 37 40.65 32.. 55 52 53 41.76 32.63 41.62 32.81 41.48 32.99 41. .33 33.17 53 54 42.55 33.25 42.41 33.43 42.26 33.62 42.11 33.80 i 641 55 43.34 33.86 43.19 34.05 43.04 34.24 42.89 [ 34.43 .551 5fi 44.13 34.48 43.98 .34.67 43.83 34.86 43.67 , 35.05 I 561 57 44.92 35.09 44.76 35.29 44.61 35.48 44.45 35.68! •" 58 45.70 35.71 45 . 55 .35.91 45 . 39 36.11 45.23 36 . 30 1 58 1 59 46.49 36.32 46.33 36.. 53 46.17 36.73 46.01 36.93 59 60 «1 47.28 36.94 47.12 37.15 46.96 37.35 37.97 46.79 37.. 56 38.18 60 61 48.07 37.66 47.90 37.76 47.74 47.57 «2 48.86 38.17 48.69 38.38 48.. 52 ;i8.60 48.35 38.81 62 fi3 49.64 38.79 49.47 39.00 49.. 30 39.22 49.13 39.43 63 fi4 50.43 39.40 50.26 39.62 .50.09 39.84 49.91 40.06 64 65 51.22 40.03 51.05 40.24 50.87 40.46 50 . 69 40.68 65 66 52.01 40.63 51.8:1 40.86 51.65 41.09 51.47 41.31 66 67 62.80 41.25 52.62 41.48 .52.43 41.71 52.25 41.94 i 67 6S 63.58 41.86 .53.40 42.10 53.22 42.33 .53.03 42.56 i 68 69 54.37 42.48 54.19 42.72 54.00 42 . 95 .53.81 43.19 , 69 70 71 55.16 43.10 .54.97 43.34 .54.78 43.. 58 44.20 54., 59 43.81 70 55.95 43.71 .55.76 43.96 ,55.57 55.37 44 44 71 72 56.74 44.33 56.54 44.57 56.35 44.82 .56.15 45 07 72 73 57.52 44.94 57.33 45.19 57.13 45.44 50.93 45.59 73 74 58.31 45.56 58.11 45.81 57.91 46.07 .57.71 46.32 74 75 59.10 46.17 58.90 46.43 58.70 46.69 .58.49 46.94 1 75 76 59.89 46.79 59.68 47.05 59.48 47.31 59.27 47.57 1 76 77 60.68 47.41 60.47 47.67 60.26 47.93 60 05 48.20 1 77 /8 61.46 48.02 61.25 48.29 61.04 48.56 60 83 48.82 j 78 7ft 62.25 48.64 62.04 48.91 61.83 49.18 61.61 49.45 I 79 80 81 63.04 49.25 62.83 49.53 : 62.61 49.80 62.39 63.17 ,50.07 1 80 63.83 49.87 63.61 50.15 63.39 59.42 50.70 81 82 64.62 50.48 64.40 50 . 77 i 64.17 51.05 63.95 51.33 82 83 165.40 51.10 65.18 51.38 64.96 51.67 64.73 1 51.95 83 84 66.19 51.72 65.97 .52.00 65.74 52.29 65.51 52.. 58 84 85 66.98 52.33 66 . 75 .52.62 !! 66.52 .52.91 66.29 53.20 85 86 67.77 .52.95 67.. 54 53.54 11 67.30 53.. 54 67.07 53.83 86 87 68.56 .53.56 68. .32 53.86 i 68.09 54.16 67.85 54.46 87 SR 69.34 54.18 69 . 1 1 54.48 ij 68.87 54.78 68.63 55.08 88 89 70.13 54.79 69.89 .55.10 ! 69.65 .55.40 69.41 ,55.71 89 90 91 70.92 55.41 70.68 .55.72 ,70.43 .56.03 70.19 70.97 .56.. 33 90 91 71.71 56.03 71.46 56.34 71.22 56.65 5C.96 92 72 . 50 56.64 72.25 .56.96 72.00 .57.27 71.75 57.58 92 93 73.28 57.26 73.03 57.58 72.78 57.89 72.53 .58.21 93 94 74.07 57.87 73.82 58.19 73.57 58.52 73.31 58.84 94 95 74,86 .58.49 74.61 58.81 74.35 59.14 74.09 .59.46' 95 96 75.65 59.10 75.39 59.43 75.13 59.76 74.87 60.09 [ 96 97 76.44 .59.72 76.18 60.05 75.91 60.38 75.65 60.71 ! 97 98 77.22 60.. 33 76.96 60.67 76.79 61.01 76.43 61.34 98 99 78.01 60.95 77.75 61.29 77.48 61.63 77.21 61.97 99 100 78.80 61.57 78.53 61.91 78.26 62.25 77.99 62.69 1 00 £ c 1 .2 Dep, Lat. Dep. Lat. jl Dep. 1 Lat. Dep. Lat. 52 Deg. 5i| Dog. 5UDeg. 1 1 5UDeg. 80 TRAVERSE TABLE. a 1 39 Deg. 39J Deg. 39 i Deg. 39^ Deg. Lat. Dep. Lat. Dep. Lat. Dep, Lat. Dep. 0.78 0.63 0.77 0.63 "oTtt" 0,64 0,77 0.64 2 1.55 1.26 1.55 1.27 1.54 1,27 1..54 1.28 2 3 2.33 1.89 2.32 1.90 2.31 1,91 2,31 1.92 3 4 3.11 2.52 3.10 2.53 3.09 2.54 3,08 2.56 4 5 3.89 3.15 3.87 3.16 3.86 3,18 3,84 3.20 5 6 4. 66 i 3.78 4.65 3.80 4.63 3.82 4.61 3.84 6> 7 5.44' 4.41 5.42 4.43 5.40 4.45 5.. 38 4.48 7 8 6.22 5.03 6.20 5.06 6.17 5.09 6.15 5.12 8 9 G.99 5.60 6.97 5.69 1! 6.94 .5.72 6.92 5.75 9 10 li 7.77 6.29 6.92 7.74 6.33 7.72 6.36 7.69 6,39 10 11 8.55 8.52 6.96 i 8.49 7.00 8.48 7.03 12 9.33 7.55 9.29 7.59 9.26 7.63 9.23 7.67 12 13 1 10.10 8.18 10.07 8.23 110.03 8.27 9.99 8.31 13 14 i 10.88 8.81 10.84 8.86 10.80 8.91 10.76 8.95 14 1.5 11.66 9.44 11.62 9.49 11.57 9.. 54 11. .53 9.59 15 If) 1'^.43 10.07 12.39 10.12 12. .35 10.18 12.30 10.23 16 17 13.21 10.70 13.16 10.76 13.12 10.81 13.07 10.87 17 18 13.99 11.33 13.94 11.39 13.89 11.45 13.84 11.51 18 19 14.77 11.96 14.71 12.02 14.66 12.09 14.61 12.15 19 20 21 15.54 12.59 15.49 12.65 15.43 12.72 15.38 12.79 20 21 16.32 13.22 16.26 13.29 t 16.20 13.36 16.15 13.43 22 17.10 13.84 J7.04 13.92 16.98 13.99 16.91 14.07 22 23 17.87 14.47 17.81 14.55 17.75 14.63 17.63 14.71 23 24 18.65 15.10 18.59 15.18 18., 52 15.27 18.45 15.35 24 25 J9.43 , 15.73 19.36 15.82 19.29 1 15.90 19.22 15.99 25 26 20.21 1 16. 3R 29.13 16.45 20.06 16.54 19.99 16.63 20 27 20.98 j 16.99 20. 9i 17.08 20.83 17.17 20.76 17.26 27 23 21.70 i 17.62 21.68 17.72 21.61 17.81 21.. 53 17.90 28 29 22.54 1 18.25 22.46 18.35 22.38 18.45 22.. 30 18.54 29 30 -31 23.31 1 18.88 23.23 18.98 23.15 19.08 23.07 23.83 19.18 30 31 21.09 19.51 24.01 19.61 23.92 19.72 19.82 32 24.87 20,14 24.78 20.25 24.69 20.35 24.60 20.46 32 33 25.65 20.77 25.55 20.88 25.46 20.99 25 . 37 21,10 33 34 26.42 21.40 26.33 21.51 26.24 21.63 26.14 21,74 34 35 27.20 I 22.03 27.10 22.14 27.01 22.26 26.91 22,38 35 36 27.98 122.66 27.88 22 . 78 27.78 22.90 27.68 23,02 3.6 37 28.75 i 23.23 28.65 23.41 28.55 23.53 28.45 23.66 37 38 29. .53, 23. 91 29.43 24.04 29.32 24.17 29.22 124.30 38 39 30.31 ,24. .54 30.20 24.68 30.09 24.81 29.98 24.94 39 40 41 31.09 25.17 30.98 25.31 30.86 25.44 26.08 30.75 25.. 58 40 41 31.86 25.80 31.75 25.94 31.64 31,52 26.22 42 .32.64 26.43 32 , 52 26 . .57 32.41 26 . 72 32.29 26.86 43 43 33.42 27.00 33.30 27.21 33.18 27.35 33.06 27.. 50 43 44 34.19 127.^9 34.07 27.84 33.95 27.99 .33.83 28.14 44 45 .34.97 128.32 34.85 28.47 34.72 28.62 34.60 28.77 45 46 35.75 [28.95 35 . 62 29.10 35.49 29.26 35.37 29.41 46 47 36.. 53 29.58 1 30.40 29.74 36.27 29.90 36.14 30.05 47 48 37.30 30.21 37.17 30.37 37.04 30.. 53 36.90 30.69 48 49 38. OS 30.84 37.95 31.00 37.81 31.17 37.67 31.33 49 50 1 Q 38.86 31.47 38.72 31.64 38., 58 31,80 38.44 31.97 50 s c 5 Dep. L... Dep. Lat. Dep. Lat. Dep. Lat. 51 Deg. 1 50|I )eg. son :>og. 50i I 3eg. TRAVEJiSK TARLE. 81 o 5" P 61 39 Deg. 39J Deg. 39i Deg. 391 Deg. s ? 51 Lat. 1 Dep. Lat. Dep. Lat. 39.35 Dep. Lat. Dep. 139.63, 32.10 39.49 32.37 .32.44 39.21 32.61 62 ; 40.411 32.72 40.27 32.90 40.12 33.08 39.98 33.25 52 53 41. 19133. 35 41.04 33.53 40.90 33.71 40 . 75 33.89 53 54 141.97 1 33.98 41.82 34.17 41.67 34.35 41.52 34.. 53 54 55 43.74 1 34 61 i 42.59 134.80 42.44 1,34.98 42.29 35.17 55 56 43.52; 35.24 43.37 35.43 43.21 35.62 43.06 35.81 56 57 44. .30, 35.87 44.14 36.06 43.98 36.26 43.82 36.45 57 58 45.07 36.50 44.91 36.70 44.75 36.89 44.59 37.09 58 59 45.85 37.13 45.69 37.33 45.53 37.53 45.36 37.73 59 60 61 48.63 47.41 37.76 46.46 37.96 46.30 38.16 46.13 38.37 60 61 38.39 47.24 38.60 47.07 38.80 46.90 39 .'01 62 48.18 39.02 48.01 39.23 47.84- 39.44 47.67 39 . 65 62 63 48.96 39.65 48.79 39.86 48.61 40.07 48.44 40.28 63 64 49.74 40.28 49.56 40.49 49.38 40.71 49.21 40.92 64 65 ,50.51 40.91 50,34 41.13 .50.16 41.35 49.97 41.56 65 66 51.29 41.54 51.11 41.76 50.93 41.98 50.74 42.20 06 67 52.07 42.16 51.88 42.39 51.70 42.62 51.51 42.84 67 68 52.85 42.79 52.66 43.02 ,52,47 43.25 52.28 43.48 08 69 53.52 43.42 .53.43 43.66 53.24 43.89 53.05 44.12 69 70 71 .54.40 55.18 44.05 54.21 44.29 .54.01 44.53 45.16 63.82 .54.59 44 . 76 45.40 70 71 44.68 54.98 44.92 .54.79 72 55 . 95 45.31 55.76 45.55 55.. 56 45.80 55.36 46.04 72 73 56.73 45.94 56.53 46.19 56,33 46.43 56.13 46.68 73 74 57.51 46.57 57.31 46.82 57.10 47.07 56.89 47.32 74 75 68.29 47.20 58.08 47.45 57.87 47.71 .57.66 47.06 75 76 59.06 47.83 58.85 48.09 .58.64 48.34 .58.43 48.60 76 77 59.84 48.46 59.63 48.72 59.42 48.98 59.20 49.24 77 78 60.62 49.09 60.40 49.35 60.19 49.61 59.97 49.88 78 79 61.39 49.72 61.18 49.98 60.96 50.25 60.74 50.52 79 80 81 62.17 50.. 35 61.95 50.62 51.25 61.73 62.60' 50.89 61.51 51.16 80 -81 62.95 50.97 "62.73 51.52 62.28 51.79 82 63.73 51.60 63.50 51.88 63.27 52.16 63.04 52.43 82 83 64.. 50 52.23 64.27 52,51 64.04 62.79 63.81 53.07 83 84 65.28 52.86 65.05 53,15 64.82 .53.43 64.58 63.71 84 85 66.06 .53.49 65.82 53,78 65.. 59 54.07 65.35 64.35 85 86 66.83 54.12 1 66.60 54.41 66.36 54.70 66.12 .54.99 86 87 67.61 54.75 07.37 55.05 67.13 55.34 66.89 .55.63 87 88 68.. ^9 55.38 68.15 55.68 67.90 65.97 67.66 66.27 88 89 69.17 56.01 68.92 .56.32 68.67 56.61 68.43 56.91 89 90 91 69.94 56.64 1 69.70 56.94 69.45 70.22 57.26 69.20 67., 55 90 91 70.72 57.27 1 70.47 57.68 57.88 69.96 58,19 92 71.50 57.90- 71.24 58.21 70.99 58.52 70.73 58.83 92 93 72.27 68 . 53 : 72.02 .58.84 71.76 59.16 71.50 .59.47 93 94 73.05 59.16' 72.79 59.47 72.53 59.79 72.27 60.11 94 95 73.83 59.79 j 73.57 60.11 73.30 60.43 73.04 60.76 95 96 74.61 60.41 1 74.34 60.74 74.08 61.06 73.81 61.39 90 97 75.38 61.04 75.12 61.37 74.85 61.70 74.68 62.03 97 98 76.16 61.67 75.89 62.01 75.62 62.34 75.35 62.66 98 99 76.94 62.30 76.66 62.64 76.39 62.97 76.12 63.30 99 100 i .2 77.71 62.93 77.44 63.27 77.16 63.61 76.88 63.94 100 s 5 Q Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 51 Deg. 501 Deg. 50i Deg. 50i Deg. 82 TRAVERSE TABLE 1 40 Deg. m Deg. 40i Deg. 40.1 Deg. ? 1 Lat. 1 Dpp. 1 Lat. Dep. Lat. Dep. Lat. Dep. 0T65 0.76 0.65 0.76 0.65 0.76 2 1.53 1.29 1.53 1.29 1..52 1.30 1.52 1.31 2 3 2.30 1.93 2.29 1.94 2.28 1.95 2.27 1.96 3 4 3.06 2,57 3.05 2.58 3.04 2.60 3.03 2,61 4 5 3.83 3.21 3.82 3.23 3.80 3.25! 3.79 3.26 5 6 4.60 3.80 4.58 3.88 4.. 56 3.90 1 4,55 3-92 6 7 5.36 4.50 5.34 4.52 5.32 4.55 5,30 4.57 7 8 6.13 5.14 6.11 5.17 6.08 5.20 6.06 6.22 8 9 6.89 5.79 6.87 5.82 6.84 5.84 6.82 5.87 9 10 11 7.66 6.43 7.07 7.63 6.46 7.60 6.49 7.14 7.58 8.33 6,53 7,18" 10 11 8.43 8.40 7.11 8.36 12 9.19 7.71 9.16 7.75 9.12 7.79 1 9.09 7.83 12 13 9.96 8.36 9.92 8.40 9.89 8.44 1 9.85 8,49 13 14 10.72 9.00 10.69 9.05 10.65 9.09 I 10.61 9,14 14 15 j 11.49 9.64 11.45 9.69 11.41 9.74 11.36 9,79 15 16 12.26 10.28 12.21 10.34 12.17 10.39 12.12 10.44 16 17 13.02 10.93 12.97 10.98 12.93 11.04! 12.88 11.10 17 18 13.79 11.57 13.74 11.63 13.69 11.69 : 13.64 11.75 18 19 14. .55 12.21 14.50 12.28 14.45 12.34 14.39 12.40 19 20 15.32 12.86 15.26 12.92 15.21 12.99 15.15 13.06 20 21 16.09 13.50 16.03 13.57 15.97 13.64 15,91 13.71 21 22 16.85 14.14 16.79 14.21 16.73 14.29 16,67 14.36 22 23 17.62 14.78 17.55 14.86 17.49 14.94 17.42 15.01 23 24 18.39 15.43 18.32 15.51 18.25 15.59! 18.18 15.67 24 25 19.15 16.07 19.08 16.15 19.01 16.24 18.94 16.32 25 2R 19.92 16.71 19.84 16.80 19.77 16.89 19.70 16.97 26 27 20 . 68 17.36 20.61 17.45 20.53 17. ,54 20.45 17.62 27 28 21.45 18.00 21.37 18.09 21.29 18.18 21.21 18.28 28 29 22.22 18.64 22.13 18.74 22.05 18.83 21.97 18.93 29 30 31 22.98 19.28 22.90 23.66 19.38 22.81 19.48 20.13 22.73 23.48 19.. 58 '20.24 30 31 23 . 75 19.93 "20703 23.57 32 24.51 20 . 57 24.42 20.68 24.33 20.78 24.24 20.89 32 33 25.28 21.21 25.19 21.32 25.09 21,43 25.00 21.54 33 34 20.05 21.85 25.95 21.97 25.85 22.08 25.76 22.19 34 35 26.81 22.50 26.71 22.61 26.61 22.73 26.51 22.85 35 30 27.58 23.14 27.48 23.26 27.37 23.38 27,27 : 23.50 36 37 28.34 23.78 28.24 23.91 28.13 24.03 28,03 24,15 37 38 29.11 24.43 29.00 24.55 28.90 24.68 28,79 j 24.80 38 39 29.88 i 25.07 29.77 25.20 29.66 25.33 29,54 1 25,46 39 40 30.64 25.71 30.53 25.84 30.42 25.98 ,30,30 i 26 , 1 1 40 41 31.41 126.35 31.29 26.49 31.18 26.03 31,06 ! 26,76 41 42 32.17; 27.00 32.06 27.14 31.94 27.28 31,82 27.42 42 43 32.94 I 27.64 32.82 27.78 32.70 27.93 132,58 28.07 43 44 33.71 28.28 33.58 28.43 33.46 28.58 33.33 28.72 44 45 34.47 28.93 34.35 29.08 34.22 29.23 t 34,09 ' 29.. 37 45 46 35.24 29.57 35.11 29.72 34.98 29.87 34,85 30.03 46 47 36.00 30.21 35.87 30.37 35.74 30.52 35,61 ! 30.68 47 48 36.77 1 30.85 36.64 31.01 36.50 31.17 36,36 ! 31.33 48 49 ' 37.54' 31.50 37.40 31.66 37.26 31.82 37,12 31.99 49 50 j 38.30 1 32.14 ^.16 32.31 38.02 32,47 37,88 ,J^2.64 _5J e It i5 Dep. 1 Lat. Dep. Lat. Dep. Lat. Dep. 1 Lat. 50 Deg. 49J Deg. 49i Deg. m Deg. TRAVERSE TABLE. 83 3 40 Deg. 40i Deg. 40h Deg. 401 Deg. Lat. Dep. Lat. Dep. Lat. 38.78 Dep. Lat. 38.64 Dep. 39.07 32.78 33.92 32.95 .33.12 33.29 51 52 39.83 33.42 39.69 33.60 39.54 33.77 ,39.39 33.94 .52 53 40.60 ' 34.07 40.45 34.34 40.30 34.42 40.15 ,34.60 53 51. 41.37 34.71 41.21 34.89 41.06 35 . 07 40.91 35 . 25 i 54 55 42.13 3.',. 35 41.98 35 . 54 41.82 35.72 41.67 35.90 , .55 56 42.90 36.00 42.74 36.18 42.. 58 36.37 42.42 36.-55 1 56 57 43.66 36 . 64 43 . 50 36.83 43.34 37.02 43.18 ' 37.21 57 58 44.43 37.23 44.27 37.48 44.10 37.67 43.94 37.86 58 59 45 . 20 37.92 45.03 33.12 44.86 3«..32 44.70 33.51 59 f.O 45 . 96 38.57 45 . 79 38 . 77 45.62 138.97 45.45 39.17 60 ■ P,[ 46.73 39.21 46.56 39.41 46 . 33 1 39 . 62 46.21 39.82 61 62 47.49 39.85 47.32 40.06 47.15 40.27 46.97 40.47 62 63 48.26 40.50 48.08 40.71 47.91 40 . 92 47.73 41.12 63 64 49.03 41.14 48.85 41.35 48.67 41.56 48.48 41.78 64 65 49 . 79 41.78 49.61 42.00 49.43 42.21 49.24 42.43 65 66 50.56 42.42 50.37 42.64 .50,19 42.86 50.00 43.08 66 67 51.32 43.07 51.14 43.29 50.95 43.51 50.76 43 . 73 67 6S 52.09 43.71 51.90 43.94 51.71 44.16: 51.51 44.39 68 69 52.86 44.35 52.66 44.53 .52.47 44.81 j .52.27 45.04 69 70 71 .53 . 62 45.00 53.43 45.23 53.23 .53.99 45.46 : 53.03 45.69 70 .54.39 45 . 64 54.19 45.87 46.11 i ,53.79 46.35 71 72 55.16 46.28 .54.95 46.52 ,54.75 46.76 i 54., 54 47.00 72 73 ! 55.92 46.92 55.72 47.17 .55.51 47.41 55.30 47.65 73 74 .56.69 47.57 56.48 47.81 56.27 48.06 1 56.06 48., 30 74 75 57.45 48.21 57.24 48.46 57.03 48.71 56.82 48.96 75 76 58.22 48.85 58.01 49.11 5? . 79 49.36 57.57 49.61 76 77 .58.99 49.49 .58.77 49.75 58.55 .50.01 ,58.33 50.26 77 78 59.75 .50.14 59,. 53 .50.40 59.31 ,50.66 59.09 50.92 73 79 60.. 52 50.78 60.30 51.04 60.07 51.31 .59.85 51., 57 79 80 81 61.28 51.42 61.06 51.69 60.83 '6i.59 51.96 .52.61 60.61 ,52.22 80 62.05 .52.07 61.82 52 . 34 61.36 52.87 81 82 i 62 . 82 52.71 62.59 .52.98 62.35 .53.25 62.12 53.53 32 83 1 63.58 .53.35 63.35 53.63 63.11 .53.90 62.88 .54.18 83 84 1 64.35 53 . 99 64.11 .54.27 63.87 54.. 55 63.64 54.83 84 85 65.11 54.64 64.87 .54.92 64-63 ,55.20 64.39 55.48' 85 1 86 65.88 ,55.28 65.64 55.57 65- 39 55.85 65.15 56.14 86 87 66.65 55.92 66.40 56.21 66.16 56 . .50 65.91 56.79 87 88 67.41 56 . 57 67.16 .56 . 86 66.92 57.15 66.67 .57.44 i'8 89 68.18 57.21 67.93 57 . ,50 67.68 57.80 67.42 58.10 89 90 "91 68.94 57.85 68.69 69.45 58.1.5 68.44 58.45 68.18 58 . 75 90 69.71 58.49 58.80 1 69.20 59.10 68.94 59.40 91 92 70.48 59.14 70.22 59 . 44 1 69.96 59.75 69.70 60.05 92 93 71.24 59.78 70.98 60.09 70.72 60.40 70.45 60.71 93 94 72.01 60.42 71.74 60.74 71.48 61.05 71.21 61.36 94 95 72.77 61.06 72.51 61.33 72.24 61.70 71.97 62.01 95 93 73.54 61.71 73.27 62.03 73.00 62., 35 72.73 62.66 96 97 74.31 6-2.35 74.03 62.67 73.76 63.00 73.48 63.32 97 1)8 1 75.07 62.99 74.80 63.32 74.52 63.65 74.24 63.97 98 99 i 75.84 63 . 64 75.56 63.97 75.28 64.30 75.00 64.62 99 l.)0 76.60 64.28 76.32 64.61 76.04 64.94 75.76 Dep. 65.23 100 g c "to O 9 s Dep. Lat. Dep. Lat. 1 Dep. Lat. Lat. 5 50 Deg. 491 Deg. 49 h Deg. 49i Deg. 84 TRAVERSE TABLE. 5 i 1 41 Deg. 4U Deg. 4U Deg. 411 Deg. i 1 Lat. 1 Dep. Lat. Dep. 0.C6 Lat. Dep. Lat. Dep. 0.67 0.75 1 0.6fi 0.75 1 0.75 0.66 0.75 2 1.51 : 1.31 1.50 1.32 1..50 1.33 1.49 1.33 2 •3 2.26 1.97 2.26 1.98 2.25 1.99 2.24 2.00 3 4 3.02 2.62 3.01 2.64 3.00 2.65 2.98 2.66 4 5 3.77 3.28 3.76 3.30 i 3.74 3.31 3.73 3.33 5 6 4.53 : 3.94 4.51 3.90 4.49 3.98 4.48 4.00 6 7 5.23; 4.50 5.26 4.62 5 . 24 4.64 5.22 4.66 7 8 6.04 1 5.25 6.01 5.27 5 99 5.30 5.97 5.33 8 9 6.79 5.90 6.77 5.93 6.74 5.96 6.71 5.99 9 10 7.55 6.56 7.52 6.59 7.49 6.63 7.46 6.66 10 11 8.30 7.22 8.27 7.25 8.24 7.29 8.21 7.32 11 12 9.06 7.87 9.02 7.91 8.99 7.95 8.95 7.99 12 13 9.81 8.53 9.77 8.57 9.74 8.61 9.70 8.06 13 14 10.57 9.18 10.53 9.23 10.49 9.28 10.44 9.32 14 15 11,32 9.84 11.28 9.89 11.23 9.94 11.19 9.99 15 16 12.08 10., 'iO 12.03 10.55 11.98 10.60 11.94 10,65 16 17 12.83 11.15 12.78 11.21 12.73 11.26 12.68 11.32 17 18 13.58 11.81 13.53 11.87 13.48 11.93 13.43 11.99 1.8 19 14.34 12.47 14.28 12.. 53 14.23 12.59 14.18 12.65 19 20 15.09 13.12 1 15.04 13.19 14.98 13.25 14.92 13.32 20 21 15.85 13.78 1 15.79 13,85 15.73 13.91 15.67 13.98 2l 22 16.60 14.43 1 16.54 14.51 16.48 14.58 16.41 H.65 22 23 17.36 15.09 17.29 15.16 17.23 15.24 17.16 15.32 23 24 18.11 15.75 ' 18.04 15.82 17.97 15.90 17.91 1 15.08 24 25 18.87 , 16.40 18.80 16.48 18.72 16.57 18.65 16.65 25 26 19.02; 17.06 19.55 17.14 19.47 i 17.23 1 19.40 17.31 26 27 20.38 .. 17.71 20.30 17.80 20.22 1 17.89 20.14 17.98 27 28 21.13 18.37 21.05 18.46 20.97 1 18. .55 20.89 18.64 28 29 21.89 19.03 21.80 19.12 21.72 1 19.22 21.64 19.31 29 30 22.64 19.68 22.56 19.78 22.47 1 19.88 22.38 19.98 30 31 23.40 20.34 23.31 20.44 23.'22 20.54 23 . 13 20.64 3! 32 24.15 20.99 24.06 21.10 23.97 21.20 23.87 21.31 32 33 24.91 21.65 24.81 21.76 24.72 21.87 24.62 21.97 33 34 25.66 22.31 25.56 22.42 25.4i5 22.. 53 25.37 22 . 64 34 35 26.41 22.06 26.31 23.08 26.21 23.19 26.11 23.31 35 36 27.17 23.62 27.07 23.74 26.96 123.85 26.86 23.97 36 37 27.92 124.27 27.82 24.40 27.71 24.. 52 27.60 24.64 37 38 28.68 ,24.93 28.57 25.06 28.46 25.18 28.35 25.30 38 39 29.43 25.59 29.32 25.71 29.21 25.84 29.10 25.97 39 40 30.19 26.24 30.07 26 . 37 29.96 26.50 29.84 26.64 40 41 30.94 26.90 30.83 127.03 "30.71 27.17 .30.59 27 . SO 41 42 31.70 27. .55 31. .58 t 27.69 31.46 27.83 31.33 27.97 42 43 32.45 28.21 32.33 [28.35 32.21 28.49 .32.08 28.63 43 44 33.21 28.87 33.08 ! 29.01 32.95 29.16 32.83 29.30 44 4ft 33.96 29.. 52 33.83 1 29.67 33.70 29.82 33.57 29.97 45 46 34.72 ,30.18 34.-58 30.33 34.45 30.48 34.32 30.63 46 47 35.47 130.83 35.34 30.99 35 . 20 31.14 35.06 31.30 47 48 36.23 31.49 36.09 31.65 35.95 31.81 35 . 8 1 31.96 48 49 36.98 32.15 36.84 32.31 36.70 32.47 36.56 32.63 49 50 i 37.74 32.80 37.59 32.97 3V.45 33.13 37.30 33.29 50 c B Dep. 1 Lat. Dep. Lat. Dep. Lat. Dep. Lat. 49 Deg, 48J Deg. m Dog. 48i Deg. TRAVKRSE TABLE. 85 3 41 Deg, 4U Deg. 1 41i Deg. 411 Deg. Lat. Dep. Lat. Dep. Lat. Dep, Lat. Dep. ? 33.49 33.46 .38.34 33.63 .38.20 33,79 ,33.05 33.96 "51 52 39.24 34.12 39.10 34.29 33 . 95 34.46 33 . 79 34.63 .52 1 53 40.00 34.77 39.85 34.95 39.69 35.12 39.-54 35,29 .53! 54 40 . 75 35.43 40.60 35.60 40.44 35.78 40.29 35,98 1 .541 55 41.51 36. OS 41,35 36 . 26 41.19 36.44 41,03 36 . 62 55 56 42.26 36.74 42.10 36.92 41.94 37.11 41,78 37.29 56 57 43.02 37.40 42.85 37.58 42.69 37.77 42.. 53 37.96 57 53 43.77 38.05 43.61 38.24 43.44 38.43 43.27 38 . 62 58 59 44.. 53 38.71 44.38 38.90 44.19 39.09 44.02 39.29 59 61 45.28 39.36 45.11 1 39.56 44.94 39.76 44.76 39.95 60 61 46 . 04 40.02 45.86 1 40,22 45.69 40.42 45.51 40.62 62 46.79 40.68 46.61 1 40.88 46.44 41.08 46.26 41.23 62 63 47.55 41.33 47.37 1 4L.,54 47.18 41,75 47.00 41.05 63 64 48.30 41.99 48. 12 142.20 47.93 42.41 47.75 42.62 64 65 49.06 42.64 48.87 ' 42.86 48.68 43,07 48.49 43.28 65 66 49.81 43.30 49.62 43.. 52 49.43 43 , 73 49.24 j 43.95 66 (57 50.57 43.96 50.37 i44,l8 50.18 44,40 49.99 1 44.61 67 68 5 1 . 32 44.61 51.13 i 44.84 .50.93 45,08 50.73 45.28 68 69 52.07 45.27 51.88 45.49 51.63 45.72 51.48 45.95 69 70 71 52.83 45.92 52 , 63 46.15 .52.43 46.38 47.05 52.22 46.61 47.28 70 "71 .53.58 46.58 53.38 46.81 .53.18 .52.97 72 .54.34 47.24 54.13 47.47 .53.92 47.71 53.72 47.94 72 73 55.09 47.89 54.88 48.13 54.67 48.37 .54.46 48.61 73 74 .55.85 48.55 55.64 48.79 55.42 49.03 55.21 49.28 74 75 56.60 49.20 .56.39 49.45 ,56.17 49.70 .55.95 49.94 75 76 57.36 49.86 57.14 50.11 56.92 .50.. 36 56 . 70 .50.61 76 77 58,11 50,52 .57.89 50.77 .57,67 51.02 57.45 51.27 77 78 58.87 51.17 58 . 64 51.43 ,58,42 51.68 ,58,19 ,51,94 78 79 59.62 51.83 59.40 52.09 59,17 .52.35 58,94 52.60 79 80 81 60.38 .52.48 60.15 52.75 53.41 ,59,92 60,67 53.01 59,68 53.27 80 61.13 53,14 60.90 53.67 60,43 53 . 94 81 82 61.89 .53.80 61.65 54.07 61.41 .54.33 61,18 .54.60 82 83 62.64 54.45 62.40 .54.73 62.16 ,55,00 61,02 55.27 83 84 63.40 55.11 63.15 55.38 62.91 55.66 62,67 .55.93 84 85 64.15 55.76 63.91 .56.04 63.66 56.32 63.41 56 . 00 85 86 64.90 .56.42 64.66 56.70 64.41 56.99 64.16 57 . 27 86 87 65.66 57.08 65.41 57.36 65.16 57 . 65 ' 64.91 .57.93 87 88 66.41 .57.73 66.16 58 . 02 65.91 58.31 i 65 . 65 ,58 . 60 88 89 67.17 58.39 66.91 58.68 66.66 58.97 66.40 1 59.26 89 90 91 67.92 59.05 67.67 59.34 67.41 59.64 60.30 67.15 1 59.93 67.89 60.60 90 91 68.68 .59.70 68.42 60.00 68.15 92 69.43 1 60.36 69.17 60.66 68.90 60.96 68.64 61.26 92 93 70,19 i 61.01 69.92 61.32 69,65 61,62 69.38 1 61.93 93 94 70,94:61.67 70.67 61.98 70,40 62,29 70.13 1 02.59 i 94 1 95 71.70 62.33 71.43 62.64 71,15 62.95 70.88 ; 63.26 | 95 1 96 72.45 62.98 72.18 63.30 71.90 63.61 71.62 63.92 96 97 73.21 63.64 72.93 63.96 72.65 64.27 72.37 64.59 97 98 73.96 64.29 73,68 64.62 73.40 64.94 73.11 65.26 I 98 99 74.72 64.95 74.43 65,28 74.15 65.60 73.86 65.92 99 100 1 3 75.47 65.61 75,18 65.93 74.90 66.26 74.61 66.59 100 1 3 Der Lat. Dep. Lat. Dep. Lat. D.p. Lat. 49 Deg. 481 Deg. 48J Deg. 48i Deg. 86 TKAVERSE TABLE. 1 s ? 1 42 Deg. m Dog. 42i Deg. ~ 42| Deg. 3 Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 0.74 0.67 "oTt^ 0.67 0.74 0.68 0.73 0,68 r 2 1.49 1..34 1.48 1.34 1.47 1.35 1.47 1.36 2 3 2.23 2.01 2.22 2.02 2.21 2.03 2.20 2.04 3 4 2.97 2.68 2.96 2.69 2.95 2.70 2.94 2 . 72 4 5 3,72 3.35 3.70 3.36 3.69 3.38 3.67 3.39 5 6 4.46 4.01 4.44 4.03 4.42 4.05 4.41 4.07 6 7 5.20 4.68 5.18 4.71 5.16 4.73 5.14 4.75 7 8 5.95 5.35 5.92 5.. 38 5.90 5.40 5.87 5.43 8 9 6.60 6.02 6.66 6.05 6.64 6.08 6.61 6.11 9 10 7.43 6.69 7.40 6.72 7.37 6.76 7.34 8.08" 6.79 7,47 10 11 11 8.17 7.36 8.141 7.4U 8. 11 7.43 12 8.92 8.03 8.88 8.07 8.85 8.11 8.81 8,15 12 13 9.66 8.70 9.62, 8 , 74 9.. 58 8.78 9.. 55 8.82 13 14 10.40 9.37 10.36 1 9.41 10.32 9.46 10.28 9,. 50 14 15 11.15 10.04 11.10 10.09 11.06 10.13 11.01 10.18 15 16 11.89 10.71 11.84! 10.76 11.80 10.81 1 1 . 75 10.86 10 17 12.63 11.38 12.58 i 11.43 12.. 53 11.48 13.48 11. .54 17 18 13.38 12.04 13.32 12.10 13.27 12.16 1 13.22 12.22 18 19 14.12 12.71 14.06 12.77 14.01 12.84 13.95 12.90 19 20 14.86 13.38 14.80 1. 57.54 13.45 14.75 15.48 13.51 14.19 14.69 1.5". 42 13.58 20 21 21 15.61 14.05 14.12 14,25 22 16.35 14.72 16.28 14.79 16.22 14.86 16.16 14,93 22 23 17.09 15.39 17.02 15. 4C 10.96 15.54 16.89 15.01 23 24 17.84 16.06 17.77 16.14 17.69 16.21 17.62: 16.29 24 25 18.. 58 16.73 18.51 16.81 18.43 16.89 18.36; 16.97 25 26 19.32 17.40 19.U5 17.48 19.17 17.57 19.09 ! 17.05 26 27 20.06 18.07 19.99 18.15 19.91 18.24 19.83 18.33 27 2S 20.81 18.74 20.73 18.83 20 . 64 18.92 20.. 56 19,01 28 29 21.55 19.40 21.47 19.. 50 21.38 19.59 21.30 19,09 29 30 22.29 20.07 22.21 20.17 22.12 20.27 22 . 03 20,30 30 31 23.04 20.74 22.95 20.84 22 .'86 20.94 22.76 21,04 ' 3r 32 23.78 21.41 23.69 21.52 23 . 59 21.62 23.. 50 21,72 32 33 24.. 52 22.08 24.43 22.19 24.. 33 22.29 24.23 22,40 33 34 25.27 22 . 75 25 . 1 7 22.86 25.07 22.97 24.97 23.08 34 35 26.01 23.42 25.91 23.53 25.80 23.65 25.70 23 . 76 35 36 26.75 24.09 26.65 24.21 26.-54 24.32 26.44 24,44 36 37 27 50 24.76 27.39 24.88 27.28 25.00 27.17 25,12 37 38 28.24 25.43 28.13 25.. 55 28.02 25.07 27.90 25 , 79 38 39 28.98 26.10 28.87 26.22 28 , 75 26.35 28 . 64 26,47 39 40 41 29.73 26.77 27.43 29.61 30.35 26.89 27.57 29.49 27.02 27.70 29.37 27,15 27,83 40 41 30.47 30 . 23 30 . 1 1 42 31.21 28.10 31.09 28.24 30.97 28.37 30.84 28,51 42 43 31.96 28.77 31.83 28.91 31.70 29.05 31. .58 1 29.19 43 44 32.70 29.44 32.57 29.58 32.44 29.73 ,32.31 29.87 44 45 33.44 30.11 33.31 30.26 33.18 30.40 33.04 .30.55 45 46 34.18 30.78 34.05 30.93 33.91 31.08 33.78 31.22 46 47 34.93 31.45 34.79 31.00 34.65 31.75 134.51 131.90 47 48 35.67 32.12 35 . 53 32.27 35.39 32.43 j 35 . 25 ! 32 . 58 48 49 36.41 32.79 36.27 32.95 .36.13 33.10 ,35,98 i 33.26 49 50 37.16 33.46 37.01 Dep. 33.62 36.86 33.78 36 . 72 33,94 Lat. _50^ 1 14 5 Dep. Lat. Lat. Dep. Lat. Dep, 48 Deg. 471 Deg. 47iDeg. m Deg. TRAVEKSE TABLE- 87 5 X 42 Deg. 42k Deg. 42i Deg. 421 Deg. 51 3 Lat Dep. Lat. Dep. Lat. Dep. Lat. Dep. TT 37.90 34.13 37.75 34.29 37.60 34.46 37.45 34.63 52 j 38.64 34.79 38.49 34.96 38.34 35.13 38.18 35.30 52 53 '39.39 35.46 39,23 35.64 39.08 35.81 38.92 35.93 53 54 140.13 30.13 39,97 36.31 39.81 36,48 39.65 36.66 54 55 40.87 36.80 40,71 36.98 40.55 37,16 40.39 37.. 33 55 56 41.63 37.47 41,45 37.65 41.29 37,83 41.12 38.01 56 57 42.36 38,14 42,19 38.32 42.02 38.51 41.86 38,69 57 58 43.10 38.81 42,93 39.00 42.76 39.18 42.69 39,37 58 59 43.85 39.48 43,67 39.67 43.50 39.86 43.32 40.05 59 60 -6T 44.59 40,15 44,41 40.. 34 44.24 40.. 54 44.06 40 . 73 60 61 45.33 40,82 45.15 41.01 44.97 41.21 44.79 41.41 63 46.07 41,49 45.89 41.69 45,71 41.89 45.53 42.09 62 63 46.82 42,16 46.63 42.36 46,45 42.56 46.26 42.76 63 64 47.58 42,82 47.37 43.03 47,19 43,24 47,00 43.44 ■ 64 65 48.30 43,49 48.11 43 . 70 47,92 43.91 47.73 44.12 65 66 49.05 44,16 48.85 44,38 48,66 44.. 59 48.47 44.80 66 67 49.79 44.83 49.59 45.05 49,40 45.26 49.20 45.48 67 68 50.53 45.50 50.33 45.72 .50.13 45.94 49.93 46.16 68 69 51.28 46,17 51.07 46,39 .50.87 46.62 50.67 40.84 69 70 71 52.02 46,84 51.82 47,07 51.61 47.29 51.40 47.-53 48.19 70 71 52.76 47,51 52,56 47,74 52.35 47.97 53.14 72 .53.51 48,18 53.30 48.41 .53.08 48.64 53.87 48.87 73 73 54.25 48,85 .54,04 49.08 53.82 49.i:'2 153.61 49.55 73 74 54.99 49,52 .54,78 49.76 54.56 49.99 154.34 .50.33 74 75 .55.74 50.18 55.52 50.43 55,30 50.67 i 65,07 .50.91 75 76 56.48 .50.85 56.36 51.10 .56.03 51.34 55.81 51.59 76 77 57.22 51.52 57.00 51,77 56 , 77 62.02 56.. 54 52.27 77 78 57,97 .52.19 57.74 53,44 57,51 .52.70 .57.28 52.95 78 79 58.71 52.86 58.48 .53,12 58,24 53.37 .58.01 53.63 79 80 81 59.45 .53.-53 .59,22 53.79 58.98 [54.05 i 58.75 54,30 80 81 GO. 19 54,20 59.96 ,54.46 59.72 54.72 59.48 54.98 82 60.94 54,87 60.70 55.13 60.46 55.40 ; 60.21 55.66 82 83 61.68 55,54 61.44 55.81 61.19 56.07 60.95 56.. 34 83 84 62.42 56,21 62.18 56.48 61.93 .56.75 61.68 67.02 84 85 63.17 56,88 62,92 57.15 62.67 57.43 62.42 57.70 85 86 63.91 57,. 55 63.66 57.82 63,41 58.10 63.15 68.38 86 87 64.65 58.21 64,40 .58.50 64,14 58.78 ,63.89 59.06 87 88 65.40 58.88 65,14 59.17 64.88 59.45 164.62 59.73 88 89 66.14 59.55 65.88 59.84 65.62 60,13 i 65.-35 60.41 89 90 91 66.38 60.22 66.62 60.51 66.35 60,80 66.09 61.09 90 91 67.63 60.89 67.36 61.19 67.09 61.48 66.82 61.77 92 68.37 61.56 68.10 61.86 67.83 .62.15 67,-56 63.45 92 93 69.11 62.23 68.84 62.53 68.57 62.83 68.29 63.13 93 94 69.86 162.90 69.. 58 63.20 69.30 63,51 169.03 63.8] 94 95 70.60 63.57 70.32 63.87 70.04 64,18 ; 69,76 64,49 95 96 71.34 64.24 71.06 64.55 70.78 64,86 170.49 65,16 96 97 72.08 64.91 71.80 65.22 71.52 i 65.53 71,23 65.84 97 98 72.83 65.57 72.54 65.89 72.25 66.21 71.96 66.52 98 99 73.57 66.24 73.28 66,56 72.99 66,88 72.70 67.20 99 100 s 74.31 66.91 74.02 67.24 73.73 67,56 73.43 67,88 100 Dep, Lat, Dep. Lat. Dep, Lat. Dep, Lat, 8 V. p 48 Deg. 471 Deg. 47i Deg. 47i Deg. TRAVERSE TA.ELE. 1 43 Deg. 43i Deg. 43i Deg. 431 Deg. 1 a Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 0,73 0.68 0.73 0.69 0.73 0.69 0.72 0.69 2 1.46 1.36 1.46 1.37 1.45 1.38 1.44 1.38 2 3 2.19 2.05 2.19 2.06 2.18 2.07 2.17 2.07 3 4 2.93 2.73 2.91 2.74 2.90 2.75 2.89 2,77 4 5 3.66 3.41 3.64 3.43 3.63 3.44 3.61 3.46 5 6 4.39 4.09 4.37 4.11 4.35 4.13 4.33 4.15 6 5.12 4.77 5.10 4.80 5.08 4.82 5.06 4.84 7 8 5.85 5.46 5.83 5.48 5.80 5.51 5.78 5.53 8 9 6.58 6.14 6.56 6.17 6.. 53 6.20 6.50 6.22 9 10 7.31 6.82 7.28 6.85 7.25 6.88 7.22 6 92 10 11 8.04 7.50 8.01 7.54 7.98 7.57 7.95 7.61 11 12 8.78 8.18 8.74 8.22 8.70 8.26 8.67 8.30 12 13 9.51 8.87 9.47 8.91 9.43 8.95 9.39 8.99 13 14 10.24 9.55 10.20 9.59 10.16 9.64 10.11 9.68 14 15 10.97 10.23 10.93 10.28 10.88 10.33 10.84 10.37 15 16 1 1 , 70 10.91 11.65 10.96 11.61 11.01 11.56 11.06 16 17 12.43 11.59 12.33 11.65 12.33 11.70 12.28 11.76 17 18 13.16 12.28 13.11 12.33 13.06 12.39 13.00 12.45 18 19 13.90 12.96 13.84 13.02 13.78 13.08 13.72 13.14 19 20 21 14.63 13.64 14.57 13.70 14.51 13.77 14.45 13.83 20 15.36 14.32 "15^30 14.39 15.23 14.46 15.17 14.52 21 22 16.09 15.00 13.02 15.07 15.96 15.14 15.89 15.21 22 23 16.82 15.69 16.75 15.76 16.68 15.83 16.61 15.90 23 24 17.55 16.37 17.48 16.44 17.41 16.52 17.34 16.60 24 25 18.28 17.05 18.21 17.13 18.13 17.21 18.06 17.29 25 26 19.02 17.73 18.94 17.81 18.86 17.90 18.78 \7.9a 26 27 19.75 18.41 19.67 18 50 19.59 18.59 19.50 18.67 27 28 20.48 19.10 20.39 19.19 20.31 19.27 20.23 19.36 28 29 21.21 19.78 21.12 19.87 21.04 19.96 20.95 20.05 29 30 '31 21.94 20.46 21.85 20.56 21.76 20.65 21.67 20.75 30 22.67 21.14 22.58 21.24 22.49 21.34 22.39 21.44 31 32 ' 23.40 21.82 23.31 21.93 23.21 22.03 23.12 22.13 32 33 24.13 22.51 24.04 22.61 23.94 22.72 23.84 22.82 33 34 24.87 23.19 24.76 23.30 24.66 23.40 24.56 23.51 34 35 25 . 60 23.87 25.49 23.98 25 . 39 24.09 25.28 24.20 35 36 •^6.. 33 24.55 26.22 24.67 26.11 24.78 26.01 24.89 36 37 27.06 25.23 26.95 25.35 26.84 25.47 26.73 25.59 37 38 27.79 25.92 27.68 26.04 27.56 26.16 27.45 26 . 28 38 39 28.. 52 26.60 28.41 26.72 28.29 26.85 28.17 26.97 39 40 41 29.25 27.28 29.13 29.86 27.41 29.01 27.53 28.89 27.66 40 '41 29.99 27.96 28.09 29.74 28.22 29.62 28.35 42 .30.72 28.64 30 . 59 28.78 30.47 28.91 30.34 29.04 42 43 31.45 29.33 31.32 29.46 31.19 29.60 31.06 29.74 43 44 32.18 30.01 32.05 30.15 31.92 30.29 31.78 30.43, 44 45 32.91 30.69 32.78 30.83 32.64 30.98 .32.51 31.12 ! 45 46 .33.64 31.37 33.51 31.52 33.37 31.66 33.23 31.81 46 47 34.37 32.05 34.23 32.20 34.09 32.. 35 33.95 32.50 47 48 35.10 32.74 34.96 .32.89 34.82 33.04 34.67 33.19 48 49 35.84 33.42 35.69 33.57 35.. 54 33,73 35.40 .33.88 49 50 36.. 57 34.10 36.42 34.26 36.27 34.42 36.12 34.. 58 50 1 .2 Q Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 5 47 Deg. 46| Deg. 46i Deg. 46\ Deg. TRAVERSE TABLE. 89 p ~5l 43 Deg. 43i Deg. 43i Deg. 433 Deg. 1 51 Lat. Dep. Lat. 1 Dep. Lat. Dep. Lat. 36.84 Dep. 37.30 34.78 37.15 34.94 36.99 35.11 35.27 52 38.03 35.46 37.88 35.63 37.72 35.79 37.56 35 . 96 52 53 38.76 36.15 38.60 36.31 38.44 36.48 38.29 36.65 53 5i 39.49 36.83 39.33 37.00 39.17 37.17 39.01 37.. 34 54 55 40.22 37.51 40.06 37.69 .39.90 37.86 39.73 38.03 55 56 40.96 38.19 40.79 38.37 40.62 38.55 40.45 .38.72 56 57 41.69 38.87 41.. 02 39.06 41.35 39.24 41.17 39.42 67 58 42.42 39.. 56 42.25 39.74 42.07 39.92 41.90 40.11 58 59 43.15 40.24 42.97 40.43 42.80 40.61 42.62 40.80 59 60 61 43.88 44.61 40.92 43.70 41.11 43.52 44.25 41.30 41.99 43.34 41.49 60 61 41.60 44.43 41.80 44.06 42.18 62 45.34 42.28 45 . J 6 42.48 44.97 42 . 68 44.79 42.87 62 63 46.08 42.97 45.89 143.17 | 45 . 70 43.37 45,51 4 3.. 57 63 64 46.81 43.65 46.62 43.85 46.42 44.05 46.23 44.26 64 65 47.54 44.33 47.34 44.. 54 47.15 44.74 46.95 44.95 65 G6 48.27 45.01 43.07 45 . 22 47.87 45.43 47.68 45.64 66 67 49.00 45.69 48.80 45.91 48.60 46.12 1 48.40 46.33 67 68 49 . 73 46.38 49.53 4 6.. 59 49.33 46.81 49.12 47.02 68 69 50.46 47.06 .50.26 47.28 .50 . 05 47.50 49.84 47.71 69 70 71 51.19 51.93 47.74 48.42 .50.99 47.96 "48.65 .50.78 48.18 50.57 51.29 48.41 70 71 51.71 51.50 48.87 49.10 72 .52 . 66 49.10 52.44 49.33 52.23 49.56 52.01 49.79 72 73 53.39 49.79 53.17 '50.02 .52.95 .50.25 52 . 73 50.48 73 74 .54.12 .50.47 53.90 .50.70 53.68 50.94 .53.45 51.17 74 75 54.85 51.15 54.63 51.39 54.40 51.63 54.18 51.86 75 76 55.58 51.83 55.36 52 . 07 55.13 .52.31 .54.90 52.55 76 77 56.31 52.51 56.08 52.76 55.85 53.00 55.62 53 . 25 77 78 57.05 53.20 56.81 53,44 56.58 53 . 69 56.34 53 . 94 78 79 57.78 53.88 57.. 54 54.13 57.30 54.38 57.07 54.63 79 80 81 58.51 54 . 56 58.27 .54.81 .58.03 .58.70 .55.07 55 . 76 57.79 .58.51 .55.32 56.01 80 81 59.24 55.24 59.00 55.. 50 82 59.97 55 . 92 59.73 56.18 59.48 56.45 59.23 56.70 82 83 60 . 70 56.61 60.45 50.87 60.21 ,57.13 ,59.96 57.40 83 8-i 61.43 57.29 61.18 57.56 60.93 57.82 60.68 58.09 84 85 62.17 57.97 01.91 58.24 61.66 .58.51 61.40 58 . 7.S 85 86 62.90 .58.65 62.64 58.93 62.38 59.20 ! 62.12 59.47 86 87 63.63 59.33 63.37 59.61 63.11 ,59.89 1 62.85 60.16 87 88 64.36 60.02 64.10 60 . 30 63.83 60 . .58 63.. 57 60.85 88 89 65.09 60.70 64.82 60.98 64.56 61.26 64.29 61. .54 89 90 91 65.82 01.38 65.55 61.67 65.28 61.95 1 65.01 62.24 90 91 66 . 55 62.06 '66.28 62.35 66.01 162.64 65.74 62.93 92 67.28 162.74 67.01 63.04 66.73 63.33 66.46 63.62 92 93 68.02 63.43 67.74 63.72 67.46 64.02 j 67.18 1 64.31 93 94 68.75 64.11 68.47 64.41 68.19 64.71 167.90 65.00 94 95 69.48 64.79 69.20 65.09 168.91 65.39 •68.62 65 . 69 95 96 70.21 , 65.47 69.92 65.78 69 . 64 66.08 1 69 . 35 66.. 39 96 97 70.94 66.15 70.65 66.46 70.36 66.77 70.07 67.08 97 98 71.67 66.84 71.37 67.15 71.09 67.46 70.79 67.77 98 99 72.40 67.52 72.11 67.83 71.81 68.15 71.51 68.46 99 100 1 1 3 73.14 68.20 72.84 68.52 72.54 08.84 72.24 69.15 100 1 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 47 Deg. 46} Deg. 1 46i Deg. 46J Deg. 90 TRAVERSE TABLE. g ? 1 44 Deg. 444 Deg. 44i Deg. 44J Deg. 45 Deg. p 3 Lat. Dep. Lat. Dep. Lat. 0.71 Dep. "oTto Lat. Dep. "o?n Lat. Dep. 0.72 0.69 0.72 0.70 0.71 0.71 0.71 I 2 1.44 1.39 1.43 1.40 1.43 1.40 1,42 1.41 1.41 1.41 3 2.16 2.08 2.15 2.09 2.14 2.10 2.13 2.111 2.12 2.12 3 4 2.88 2.78 2.87 2.79 2.85 2.80 2.84 2.821 2.83 2.83 4 5 3.60 3.47 3.. 58 3.49 3.5V 3.50 3.55 3.. 52 3.54 3.. 54 5 6i 4.32 4.17 4.30 4.19 4.28 4.21 4.26 4.22! 4.24 4.24 fi 7 5.04 4.86 5.01 4.88 4.99 4.91 4.97 4.93i 4.95 4.95 8 5.75 5.56 5.73 5., 58 5.71 5.61 5.68 5.63, 5.66 5.66 8 9 6.47 6.25 6.45 6.28 6.42 6.31 6.39 6.. 34 6.36 6 . 36 9 10 11 7.19 6.95 7.64 7.16 7. '88 6.98 7.13 7.01 7.71 7.10 7.04 7.74! 7.07 7.07 7.78 10 7.91 7.68 7.85 7.81 7.78 12 8.63 8.34 8.60 8.37 8.56 8.41 8.52 8.45i 8.49 8.49 12 13 9.35 9.03 9.31 9.07 9.27 9.11 9.23 9.I5I 9.19 9.19 13 14 10.07 9.73 10.03 9.77 9.99 9.81 9.94 9.86! 9.90 9.90 14 15 10.79 10.42 10.74 10.47 10.70 10.51 10.65 10.561 10.61 10.61 15 16 11.51 11.11 11.46111.16 12.18 11 .86 11.41 11.21 11.36 11.26! 11.31 11.31 16 17!l2.23 11.81 12.13 11.92 12.07 11.971 12.02 12.02 17 18 12.95 12.50 12.89 12.56 12.84 12.62 12.78 12.671 12.73 12.73 18 19 13.67 13.20 13.61 13.26 13.. 55 13.32 13.49 13.381 13.43 13.43 19 20 21 14.39 15.11 13.89 14.59 14.33 13.96 14765 14.26 14.02 14.20 14.081 14.14 14.8.5 14.14120 14.85:21 15.04 14.98 14 72 14.91 14.78i 22 15.83 15.28 15.76 15.35 15.69 15.421' 15. 62 15.49 15.56 15.56|22 23 16.54 15.98 16.47 16.05 16.40 16.12.116.33 16.19 16.26 16.2623 24 17.26 16.67 17.19 16.75jll7.12 16.82 '17.04 16.90 16.97 16.97 24 25117.98 17.37 17.91 17.44 17.83 17.52 17.75 17.60 17.68 17.83125 26|I8.70 18.06 18.62 18.14 18.54 18.22| 18.46 18.30 18.38 18.38126 27119.42 18.76 19.34 18.84 19.26 18.92 19.17 19.01 19.09 19.09127 28 20.14 19.45 20.06 19.54 19.97 19.63 19.89 19.71 19.80 19.80128 29|20.8fi 20.15 20.77 20.24 20.68 20.33 20.60 20.42 20.51 2O.51I29 30 121.. 58 31122.30 32 23.02 20.84 21.49 20 . 93 21.40 22.11 21 .03 21.31 21.73 22.02 21.12 21.21 21.21 30 21.92 31 21.53 22.21 21.63 21.82121.92 22.23 22.92 22.33 22.82 22.43,22.73 22.53 22.63 22.63 32 33 23.74 22.92 23.64 23.03 23.54 23.13 23.44 23.23 23.33 23., 33! 33 34124.46 23.62 24.35 23.72 24.25 23.83:24.15 23.94 24.04 24.04134 35 25.18 24.31 25.07 24.42 24.96 24.53,24.86 24.64 24.76 24.75135 36 25.90 25.01 25.79 25.12 25.68 25. 23 1 25.67 25.34 25.46 25.46!.36 37 26.62 25.70 26.50 25.82 26.39 25.93:26.28 26.05 26.16 26.16 37 38 27.33 26.40 27.22 26.. 52 27.10 26.63126.99 26 . 75 26.87 26.87 38 39 28 . 0.1 27.09 27.94 27.21 27.82 27.341 27.70 27.46 27.58 27.58 39 40 41 28.77 29.49 27.79 28.65 27.91 28.53 28.04 28.41 28.74 29.12 28.16 28.28 28 . 28 28.99 40 41 28.48 29.37 28.61 29.24 28.86 28.99 43 SO. 21 29.18 30.08 29.31 29.96 29.44 29.83 29.57 29.70 29.70 42 43 30.93 29.87 30.80 30.00 30.67 30.14 30. .54 30.27 30.41 30.41 43 44 31.65 30.56 31.52 30.70 31.38 30.84 31.25 30.98 31.11 31.11 J.4 45 32.37 31.26 32.23 31.40 32.10 31.54131.96 31.68 31.82 31,82 45 46 33.09 31.95 32.95 32.10 32.81 32.24 32.67 32.38 32.53 32.53 46 47 33.81 32.65 33.67 32.80 33.52 32.94133.38 33.09 33.23 33.23!47 48 34.. 53 33.34 34.38 .33.49 34.24 33.64 34.09 33.79 .33.94 33.94148 49 35 . 25 34.04 3.0.10 34.19 34.95 .34.341 34.80 34.50 34.65 34.65149 50'35.97 34.73 35.82 34.89 35.66 35.05^35.61 Let, 1 Dep. 35.20 Lat. 35.36 Dep. 3^3^ Lat. 50 1 s 1 .2 q Dcp. Lat. Dep. 1 Lat. Dep. 46 Deg. 451 Deg. 45h Deg. 451 Deg. 45 Deg. travt:rse tablr. 91 5' 41 Deg. 44i D.g. 1 1 1 44i Deg. 441 Deg. 45 Deg. 1 g ' Lai. j Dep. Lat. ' Dep. 51 36.69 3.-). 13 36.. 53 3.5.591 Lat. Dep. Lat.| Dep. Lat. , Dep. g 36.38 35.75 136.22 35.90 36.06 36.06 51 | 5-i37.-ir36.13 37.25:36.29 37.09 36.451 36.93 36.61 36. 77136. 77 52 53,35.12 36.32 37.93 36. 9Si 37.80 37.15! 37.64137.3137.48 37.48 S3 5413^.84 37.51 38. 6S 37.68; 38.52 37.85 38.35 33.02 38.18l3S.18l 54 5.5I39. 56 33,21 39. 4U 38.3S!;39.23 38.55 39.06 38.72 38.89|38.89! 55 5(;;40.23 3S.90 40.11 39.08 139.94 39.25 39.77:39.42 39.60 39.60 56^ 57:41.00^39.60 40.83:39.77;j40.66 39.95 40.48:40.13 40.31 40.31! 57 5341.72 40.29 41 .55.40. 47| 41 .37 40.65 41.19 40.83 41.01 41.0li 58 59-42.44l40.9S, 42. S6!41. 17 42.08 41 . 35 41. 90141. .54 41.72 41.72 59 60 43. 1 6:41 .6S 42.93j41 .871142.79 42.05 42.61 42. 24 42.43142. 431 60 fi i 143 . s'N'42 .37,43. 69 42 . 57!i43 5i 42.76 43.32142.94 43.13143.13! 61 6244.61(43.07' 44.41143.26 !44 22 43.46 44. 03143. 66 43.84 43.84 62 634.5.32 43.76 45. 13143. 96!;44 03 44.16 44.74:44.3.5 44.55:44.55, 63 64 46.0-1 44. 46!;45. 84144. 66ii45. 65 44.86 45. 45!45. 06 ,45.25:45.251 64 65146.76 45.15 46. 56|45. 36:46 36 45.56 46.16145.76145.96145.961 65 66147.48 45. S5: 47. 28146. 051147. 07 46.26 46. 87!46.46'46. 67146. 671 66 67 43.20 46.54 47.99|16.75;:47.79 46.96|47.58;47.17:47.38i47.38| 671 68 43.92 47.24 48. 7 1147. 45 48.. 50 47. 661148. 29l47.87:;48. 08:48. 081 38 | 69 49 . 63 47 . 93 49 .42i43 . 15,49 . 2 1 48. 36i;49.00;4S. 58 ,48.79:48.79 49.06:149.71 49.28, :49. 50, 49. 50 69 7U 5J.35 43.63! 50. 14 43.85' 49.93 70 7 h5 1 . 07 49 . 32 50 . 86j49 . 54, 50 . 64 49.76:50.42:49.98 50.20150.20 71 72 :5 1 . 79 50 .02 5 1 . 571 50 . 24 5 1 . 35 50. 47!:51.13!50. 69 150.91150. 91 72 73 ;.52 .51 50 . 7 1 ' 52 . 29150 . 94^ 52 . 07 51.17i:5l.84'51.39 51.62l51.62i 73 74 53.23 51.40 53.01151.64! 52.78 5 1.87 •.52.. 55 52.10 52.33 52.33; 74 7.5.53.95 52.10,153.72152.33' 53.49 .52.571.53.26:52.80 .53.03.53.03' 75 76:54.67 52. 79i:54. 44153. 031 .54.21 53.27:53.9753.51 53.7453.741 76 77|.55.39.53.49!'55.16 53 . 73; 54.92 53.97 54.63 54.21 54.45.54.45: 77 78156.11 .54. 131155.87 .54.43: 55.63 .54.67 55.39 .54.91 55.15:55.151 78 79!56.33 54.83|:56.59 55.13,156.35 55.37 56. 10 55. 63;:55. 86 55. sol 79 S0J57.55 55.57!|.57.30 8l'.53.27 56.27j]58.02 55.82! 57.06 56.07 56. 8156. 32 .56.57 56.57: SO 56.77 57.52 57.03 .57.23 57.28! 81 56.52! 57.77 82153.99 56.96158.74 57.22! .58.49 57.47,58.24 57.73 57.98 57.98 82 83;59.71 57.66:59.45 57.92! 59.20 58.18 58.95 58.43 58.6958.69 83 84!60.42 58.351,60. 17 .58.61 59.91 58 . 88 59 . 66 59 . 14' .59 . 40 59 . 40 84 85161. 14 59.05 60.89 59.31 60.63 59.58,60.37 59.84 60.10 60.10 85 86!61.S6 5).74:61.60 60.01 61.34 60.28 61.08 60.55 60.81 60.81 86 S7J62.58 60.44 62.32 60.71 62.05 60.98 61.7961.25 61. .5261. 52 87 83|63.30 61.13,63.03 61.41 62.77 61.68 62.50 61.95 62.23 62.23 88 89:64.02 61.82163.75 62.10 63.48 62.33163.2162.66 62.93 62.93] 89 9^' 64.74 62. .52:64. 47 62.80 64.19 63. 08J.63. 92163.36 63.6463.641 90 9l|65.46 63.211:65.18 63.50 64.91 63.78 64.63 64. 07 '64. 35164. 351 91 92166. 18 63.91! 65.90 64.20jl65.62 64.48165.34 64.77 65.05 65.05 92 93:66.90 64.60,66.62 64.89ii66.33 65. 13! 66.05 65.47 65.7665.76 93 94|67.62 65.30!:67.33 65.59 67.05 65.89|66.76!66.18 66.47l66.47 94 95[68. 34 65.991,68.05 66.29 67.76 66. 59, ,67. 4 7, 66. 88 67.18 67.18 95 96:69. r6 66.69' 68.76 66.99 68.47 67.29 68.18 67.59 67.88 67.88! 9^ 97:69.73 67.3S:69.43167.69 69.19 67.99 68.39 bS. 29 68.59 68.591 97 9=^:70.50 68.03:70.20,68.33 69.90 68.69 69.60 68.99 69.30 69.301 98 99i71.21 68.77! 70.91 169.08 70.61 69. 39!!70. 31, 69. 70 70.00 70.00' 99 100J71. 93 69.47 t ' Dep. ' Lat. j71. 63 69.78 71.33 70.09'171.02;70.40 ,70.71 70.711100 Dep. : Lat. Dep. Lat. Dep. Lat. Dep. Lat. g 1 46 Deg. 45| Deg. i 45 i Deg. !«» Deg. 45 Deg. 1 1. 92 A TABLE OF RHUMBS. THE DEGREES, MINUTES, AND SECONDS, THAT EVERY POINT AND QUARTER POhN'T OF THE COMPASS MAKES WITH THE MERIDIAN. N byE. N.N.E. N.E.byN. N.E. N.E.byE. E.N.E. E. by N. East. ITH, |PtS. qr. 1 1 3 N. by W. 1 1 1 1 1 2 3 N.N.W. 2 2 1 2 2 2 3 N.W. by N. 3 3 1 3 2 3 3 N.W. 4 4 1 4 2 4 3 N.W.byW. 5 6 1 5 2 5 3 W.N W. 6 6 1 6 2 6 3 W. by N. 7 7 1 7 2 7 3 West. 8 n ^ jf |PU . qr. 2 48 45 1 5 37 30 2 8 26 15 3 11 15 1 14 3 45 1 1 16 52 30 1 2 ]9 41 15 1 3 22 30 2 2J 18 45 2 1 28 7 30 2 2 30 53 15 2 3 33 45 3 3j 33 45 3 1 39 22 30 3 2 42 11 15 3 3 4.5 4 47 48 45 4 1 ,50 37 30 4 2 53 26 15 4 3 56 15 5 59 3 45 5 1 61 52 30 5 2 64 41 15 5 3 67 30 6 70 18 45 6 1 73 7 30 6 2 75 56 15 6 A 78 45 7 81 33 45 7 1 84 22 30 7 2 87 11 15 7 3 90 8 U SOUTH. i S. by E. S.S.E. S.E. by S. S.E. S.E. byE. E.S.E. E. by S. East. S. byW. S.S.W. S.W. by S S.W. S.W. by W W S.W. W. by S. West WORKMAN S TABLE, FOR CORRECTING THE MIDDLE LATITUDE. 93 Mid. j l.at. 30 40 50 60 70 80 90 100 110 o o '' ' / ' / / / / 15 02 03 04 06 09 \l 15 19 23 16 02 03 04 OG 09 12 15 18 22 17 02 03 04 06 08 11 14 17 21 IS 02 03 04 06 08 11 14 17 20 19 02 03 04 06 07 10 13 16 19 2) 02 03 14 06 07 09 12 15 18 21 02 03 C4 06 07 09 12 15 18 22 t2 03 04 06 07 09 12 15 17 23 C2 03 04 06 07 09 12 15 17 24 02 03 04 06 07 09 11 14 10 25 02 03 04 05 07 09 11 14 16 26 02 03 04 05 07 09 11 14 16 27 02 03 04 05 07 08 11 14 16 28 02 03 04 05 06 08 10 13 15 29 02 03 04 05 06 08 10 13 15 30 02 03 04 05 06 08 10 13 15 31 02 03 04 05 06 08 10 13 15 32 02 03 04 05 06 08 10 13 15 33 02 03 04 05 06 08 10 13 15 34 02 03 04 05 06 08 10 13 15 35 02 03 04 05 06 08 10 13 15 36 02 03 04 05 06 08 10 13 15 37 <2 03 04 05 06 08 10 13 15 38 02 03 G4 05 06 08 10 13 15 39 02 03 04 05 06 08 10 13 15 40 02 03 04 05 06 08 10 13 15 41 02 03 04 05 06 08 10 13 15 42 02 03 04 05 06 08 10 13 15 43 02 03 04 05 07 09 11 14 16 44 02 03 04 05 07 09 11 14 16 45 02 03 04 05 07 09 11 14 16 46 02 03 04 05 07 09 11 14 16 47 02 03 04 05 07 09 11 14 16 48 02 03 04 05 07 09 11 14 16 49 02 03 04 05 07 09 11 14 17 50 02 03 04 05 07 09 11 14 17 51 02 03 04 05 07 09 11 14 17 52 02 03 04 05 07 09 12 15 18 53 02 03 04 06 07 09 12 15 18 54 02 03 04 06 08 10 13 16 19 55 02 03 04 06 08 10 13 16 19 56 02 03 04 06 08 10 13 16 20 57 02 03 04 06 08 11 14 17 20 58 02 03 04 06 09 11 14 17 21 59 02 03 04 06 09 12 15 18 22 60 02 03 04 06 09 12 15 19 23 61 02 03 05 07 09 12 15 19 23 62 02 03 05 07 09 12 16 20 24 63 02 04 05 07 09 13 16 20 24 64 02 04 06 08 09 13 17 21 25 65 02 04 06 08 10 13 17 21 25 66 02 04 06 08 10 14 18 22 20 67 02 04 06 08 11 15 18 23 27 68 02 04 06 08 11 15 19 24 28 69 02 05 06 09 12 16 20 25 30 70 03 05 06 09 13 17 21 26 31 71 04 06 07 09 13 18 22 27 33 72 04 06 08 10 14 19 23 29 35 25 94 WOUKMAN'S TABLE, FOR CORRECTING THE MIDDLE LATITUDE. Mid" Lat. 120 130 1 140 150 160 170 180 190 1 200 o O / o / O / O / O / O / o / / / 15 27 31 35 40 45 51 58 1 06 I 14 16 26 30 34 38 43 49 56 1 03 1 11 17 25 28 32 37 42 48 54 1 01 1 08 18 24 27 31 36 41 i 46 52 58 1 06 19 23 26 30 34 40 1 45 50 56 1 03 20 22 25 29 33 38 i 43 48 54 1 00 21 21 25 29 33 37 { 42 47 53 58 22 20 24 23 32 36 ! 41 46 51 56 23 20 24 28 32 36 40 45 50 55 24 19 23 27 31 35 39 44 48 53 25 19 23 27 31 35 39 43 47 52 26 19 22 26 30 34 38 42 47 52 27 19 22 26 30 33 38 42 46 51 28 18 21 25 29 33 37 41 46 51 29 18 21 25 29 32 36 41 45 50 30 18 21 25 28 32 36 41 45 50 31 18 21 25 28 32 36 41 45 50 32 18 21 25 28 31 36 41 45 50 33 18 21 24 27 31 35 40 44 49 34 18 21 24 27 31 35 40 44 49 35 18 21 24 27 31 35 40 44 49 36 18 21 24 27 31 35 40 44 49 37 18 21 24 27 31 35 40 44 49 38 18 21 24 27 31 36 40 45 50 39 18 21 25 28 32 36 41 45 50 40 18 22 25 28 32 36 41 45 50 41 18 22 25 28 32 37 41 45 50 43 18 22 26 29 33 37 42 46 51 43 19 23 26 30 34 38 42 46 51 44 19 23 27 30 34 38 43 47 52 45 19 23 27 31 35 39 43 47 52 46 19 23 27 31 35 39 44 48 53 47 20 23 27 31 35 40 44 49 54 48 20 23 27 31 35 40 45 50 55 49 21 24 28 32 36 41 45 51 57 50 21 24 28 32 36 41 46 52 58 51 21 24 28 32 37 42 47 53 59 52 22 25 29 33 37 42 48 54 1 00 53 22 25 29 33 38 43 49 55 1 01 54 23 26 30 34 39 44 50 56 1 02 55 23 26 30 35 40 45 51 57 1 03 56 24 27 31 3(> 41 46 52 58 1 04 57 24 28 32 37 42 48 U 54 1 00 1 oe 58 25 29 33 38 44 50 55 1 02 1 08 59 26 30 34 39 45 51 57 1 04 1 IC 60 27 31 35 40 46 52 59 1 06 1 13 61 27 31 36 41 47 54 1 01 1 08 1 15 62 28 32 37 42 49 56 1 03 1 10 1 18 63 29 33 39 44 51 58 1 05 1 12 1 21 64 29 34 40 46 53 1 00 1 07 1 14 1 24 05 30 35 41 48 55 1 02 1 09 1 17 1 27 66 31 37 43 50 58 I 05 1 12 1 21 1 31 67 33 38 45 53 i 00 1 07 1 16 1 25 1 35 68 34 40 48 55 1 02 1 10 1 19 1 30 1 39 69 36 42 50 58 1 05 1 13 1 23 1 34 1 4-1 70 38 44 52 1 00 1 08 1 17 1 28 1 39 1 50 1 71 40 46 55 1 03 1 12 1 22 1 32 1 44 1 50 1 72 42 49 58 1 06 1 16 1 27 1 38 1 50 2 04 1 TABLE or MERIDIONAL PARTS. 95 yrros 1 1- r^ 30 1 40 50! 60 70| 83 90| lOO llo| 120| 13C] 60 120 180 24( 300 361 421 482 542 603 664 725 787 1 1 61 121 181 241 301 362 422 483 543 604 665 721 788 2 2 62 122 182 242 302 363 423 484 544 605 666 727 789 3 3 63 123 183 243 303 364 424 485 545 606 667 728 790 4 4 64 124 184 244 304 365 425 486 546 607 668 729 791 5 5 65 125 185 245 305 366 420 487 547 608 669 730 792 6 6 66 126 186 246 306 367 427 488 548 609 670 731 793 7 7 67 127 187 247 307 368 428 489 549 610 671 732 794, 8 8 68 128 188 248 308 369 429 490 550 611 672 734 795 9 9 69 129 189 249 309 370 430 491 551 612 673 735 796 10 10 70 130 190 250 310 371 431 492 552 613 664 736 797 11 11 71 131 191 251 311 372 432 493 553 614 675 737 798 12 12 72 132 192 252 312 373 433 494 554 615 676 738 799 13 13 73 133 193 253 313 374 434 495 555 616 677 739 800 14 14 74 134 194 254 314 375 435 496 556 617 678 740 801 15 15 75 135 195 255 315 376 436 497 557 618 679 741 802 16 16 76 136 196 256 316 377 437 498 558 619 680 742 803 17 17 77 137 197 257 317 378 438 499 559 620 681 743 804 18 18 78 138 198 258 318 379 439 500 560 621 682 744 805 19 19 79 139 199 259 319 380 440 501 561 622 683 745 806 20 20 80 140 200 260 320 381 441 502 562 623 684 746 807 21 21 81 141 201 261 321 382 442 503 563 624 685 747 808 22 22 82 142 202 262 322 383 443 504 564 625 687 748 809 23 23 83 143 203 263 323 384 444 505 565 626 688 749 810 24 24 84 144 204 264 324 385 445 506 567 627 689 750 811 25 25 85 145 205 265 325 386 446 507 568 628 690 751 812 26 26 86 146 206 266 326 387 447 508 569 629 691 752 813 27 27 87 147 207 267 327 388 448 509 570 631 692 753 815 28 28 88 148 208 268 328 389 449 510 571 632 693 754 816 29 29 89 149 209 269 330 390 450 511 572 633 694 755 81? 30 30 90 150 210 270 331 391 451 512 573 634 695 756 818 31 31 91 151 211 271 332 392 452 513 574 635 696 757 819 32 32 92 152 212 272 333 393 453 514 575 636 697 758 820 33 33 93 153 213 273 334 394 454 515 576 637 698 75y 821 34 34 94 154 214 274 335 395 455 516 577 638 699 760 822 35 35 95 155 215 275 336 396 456 517 578 639 700 761 823 36 36 96 156 216 276 337 397 457 518 579 640 701 762 824 37 37 97 157 217 277 338 398 458 519 580 641 702 763 825 38 38 98 158 218 278 339 399 459 520 581 642 703 764 826 39 39 99 159 219 279 340 400 460 521 582 643 704 765 827 40 40 100 160 220 280 341 401 461 522 583 644 705 766 82S 41 41 101 161 221 281 342 402 462 523 584 645 706 767 829 42 4-2 102 162 222 282 343 403 463 524 585 646 707 768 830 43 43 103 163 223 283 344 404 464 525 586 647 708 769 831 44 44 104 164 224 284 345 405 465 526 587 648 709 770 832 45 45 105 165 225 285 346 406 466 527 588 649 710 77 i 833 46 46 106 166 226 286 347 407 467 528 589 650 711 772 834 47 47 107 167 227 287 348 408 468 529 590 651 712 773 835 48 48 108 168 228 288 349 409 469 530 591 652 713 774 836 49 49 109 169 229 289 350 410 470 531 592 653 714 775 837 50 50 110 170 230 290 351 411 471 532 593 654 715 777 838 51 51 111 171 231 291 352 412 472 533 594 655 716 778 839 52 52 112 172 232 292 353 413 473 534 595 656 717 779 840 53 53 113 173 233 293 354 414 474 535 596 657 718 780 841 54 54 114 174 234 294 355 415 476 536 597 658 719 781 842 55 55 115 175 235 295 356 416 477 537 598 659 720 782 843 56 56 116 176 236 296 357 417 478 538 599 660 721 783 844 57 57 117 177 237 297 358 418 479 539 600 661 722 784 845 58 58 118 178 238 298 359 419 480 540 601 662 723 785 846 59 59 119 179 239 299 360 420 481 541 602 663 724 786 847 96 TABLE OF MERIDIONAL PARTS. M. 1 140| 150| 160| 170| 180| ]90| 20O| 2lo| 220| 230| 24o 250| 260| 270 848 910 973 1035 1098 1161 1225 1289 1354 1419 1484 1550;iG16|1684 1 850 911 974 36 99 63 26 90 55 20 85 51 18 85 2 851 913 975 37 1100 64 27 91 56 21 86 52 19 86 3 852 914 976 38 01 65 28 92 57 22 87 53 20 87 4 853 915 977 39 02 66 29 93 58 23 88 54 21 88 5 854 916 978 41 03 67 30 95 59 24 90 56 22 89 6 855 917 979 42 05 68 32 96 60 25 91 57 2-3 90 7 856 918 980 43 06 69 33 97 61 26 92 58 24 91 8 857 919 981 44 07 70 34 98 62 27 93 59 25 93 9 858 920 982 45 08 71 35 99 63 28 94 60 28 94 10 859 921 983 1046 1109 1172 1236 1300 1364 1430 1495 1561 1628 1695 11 860 922 984 47 10 73 37 01 66 31 96 62 29 96 12 861 923 985 48 11 74 38 02 67 32 97 63 30 97 13 862 924 986 49 12 75 39 03 68 33 98 64 31 98 14 863 925 987 50 13 76 40 04 69 34 99 65 32 99 15 864 926 988 51 14 77 41 05 70 35 1500 67 33 1700 16 865 927 989 52 15 78 42 06 71 36 02 68 34 01 17 866 928 990 53 16 79 43 07 72 37 03 69 35 03 18 867 929 991 54 17 81 44 08 73 38 04 70 37 04 19 868 930 993 55 18 82 45 10 74 39 05 71 38 05 20 869 931 994 1056 1119 1183 1246 1311 1375 1440 1506 1572 1639 1706 21 870 932 995 57 20 84 48 12 76 41 07 73 40 07 22 871 933 996 58 21 85 49 13 77 43 OS 74 41 08 23 872 934 997 59 22 86 50 14 79 44 09 75 42 09 24 873 935 998 60 23 87 51 15 80 45 10 77 43 11 25 874 936 999 61 25 88 52 16 81 46 11 78 44 12 26 875 937 1000 63 26 89 53 17 82 47 13 79 45 13 27 876 938 !001 64 27 90 54 18 83 48 14 80 47 14 28 877 939 1002 65 28 91 55 19 84 49 15 81 48 15 29 878 941 1003 66 29 92 56 20 85 50 16 82 49 16 30 879 942 1004 1067 1130 1193 1257 1321 1386 1451 1517 1583 1650 1717 3i 880 943 05 68 31 94 58 22 87 52 18 84 51 18 32 882 944 06 69 32 95 59 24 88 53 19 85 52 20 33 883 945 07 70 33 96 60 25 89 55 20 86 53 21 34 884 946 08 71 34 98 61 26 90 56 21 88 54 22 35 885 947 09 72 35 99 62 27 92 57 22 89 56 23 36 886 948 10 73 36 1200 64 28 93 58 24 90 57 24 37 887 949 11 74 37 01 65 29 94 59 25 91 58 25 38 888 950 12 75 38 02 66 30 95 60 26 92 59 26 39 889 951 13 76 39 03 67 31 96 61 27 93 60 27 40 890 952 1014 1077 1140 1204 1268 1332 1397 1462 1528 1594 1661 1729 41 891 953 15 78 41 05 69 33 98 63 29 96 62 30 42 892 954 16 79 42 06 70 34 99 64 30 97 63 31 43 893 955 18 80 44 07 71 35 1400 65 31 98 64 32 44 894 956 19 81 45 08 72 36 01 67 32 99 66 33 45 895 957 20 82 46 09 73 38 02 68 33 1600 67 34 46 896 958 21 84 47 10 74 39 03 69 35 01 68 35 47 897 959 22 85 48 11 75 40 05 70 36 02 69 36 48 898 960 23 86 49 12 76 41 06 71 37 03 70 38 49 899 961 24 87 50 13 77 42 07 72 38 04 71 39 50 900 962 1025 1088 1151 1215 1278 1343 1408 1473 1539 1605 1672 1740 51 901 963 26 89 52 16 80 44 09 74 40 06 73 41 52 902 964 27 90 53 17 81 45 10 75 41 08 75 42 53 903 965 28 91 54 18 82 46 11 76 42 09 76 43 54i 904 966 29 92 55 19 83 47 12 77 43 10 77 44 55 905 968 30 93 56 20 84 48 13 79 44 11 78 46 56 90G 969 31 94 57 21 85 49 14 80 46 12 79 47 57 907 970 32 95 58 22 86 50 15 81 47| 13 80 48 58 908 971 33 96 59 23 87 52 16 82 481 14 81 49 59i 909] 972 34 97 601 24 88 53 18 83i 49 1 15 82i 50 TABLE OF MERIDIONAL PARTS. 97 M.| 280| 290| 30o| Sio] 320| 330| 34o| 350| 36o| 370| 380| 39o| 40O| 41o| Oi 7511 1819 1888 1958 >028 2100 2171 2244 23181 2393 2468 2545 2623 2r02| 1 ^-\ 21 90 59 30 01 73 46 19 94 70 46 24 03 21 53 22 91 60 31 02 74 47 20 95 71 48 25j 04 3 55 23 92 62 32 03 75 48 22 96 72 49 27 06 4 56 24 93 63 33 04 76 49 23 98 73 50 28 07 5 57 25 94 64 34 05 78 50 24 99 75 51 29 OS 6 58 26 95 65 35 07 79 52 25 2400 76 53 31 10 7 59 27 96 66 37 OS 80 53 27 01 77 54 32 11 8 60 29 98 67 38 09 81 54 28 03 78 55 33 12 9 61 30 99 69 39 10 82 55 29 04 80 57 34 14 10 1762 1831 1900 1970 2040 2111 2184 2257 2330 1 2405 2481 2558 2636 2715 11 64 32 01 71 41 13 85 58 32 06 82 59 37 16 12 65 33 02 72 43 14 86 59 33 08 84 60 38 18 13 66 34 03 73 44 15 87 60 34 09 85 62 40 19 14 67 35 05 74 45 16 88 61 35 10 86 63 41 20 15 68 37 06 76 46 17 90 63 37 11 87 64 42 22 16 69 38 07 77 47 19 91 64 38 13 89 66 44 23 17 70 39 08 78 48 20 92 65 39 14 90 67 45 24 18 72 40 09 79 50 21 93 66 40 15 91 68 46 26 19 73 41 10 80 51 22 94 68 42 16 92 69 48 27 20 1774 1842 1912 1981 2052 2123 2196 2269 2343 2418 2494 2571 2649 2728 21 75 43 13 83 53 25 97 70 44 19 95 72 50 29 22 76 45 14 84 54 26 98 71 45 20 96 73 51 '31 23 77 46 15 85 56 27 99 72 46 22 98 75 53 32 24 78 47 16 86 57 28 2200 74 48 23 99 76 54 33 25 80 48 17 87 58 29 02 75 49 24 2500 77 .-■S5 35 26 81 49 18 88 59 31 03 76 50 25 01 .-78 57 36 27 82 50 20 90 60 32 04 77 51 27 03 80 58 37 28 83 52 21 91 61 33 05 79 53 28 ,04 81 59 39 29 84 53 22 92 63 34 07 80 54 29 '05 82 61 40 30 1785 1854 1923 1993 2064 2135 2208 2281 2355 2430 2506 2584 2662 2742 31 86 55 24 94 65 37 0. 82 56 . 32 08 85 63 43 32 87 56 25 95 66 38 10 83 .58 33 09 86 65 4.4 33 89 57 27 97 67 39 11 85 ■59 34 10 88 66 46 34 90 58 28 98 69 40 13 86 60 35 12 89 67 47 35 91 60 29 99 70 41 14 87 61 37 13 90 69 48 36 92 61 30 2000 71 43 15 ^.88 63 38 14 91 70 50 37 93 62 31 01 72 44 1^ 90 64 39 15 93 71 51 38 94 63 32 02 73 45 17 91 65 40 17 94 73 52 39 95 64 34 04 75 46 19 92 66 42 18 95 74 54 40 1797 1865 1935 2005 2076 .147 2220 2293 £368 2443 2519 2597 2675 2755 41 98 66 36 06 77 49 21 95 69 44 21 98 76 56 42 99 68 37 07 78 50 22 96 70 45 22 99 78 58 43 1800 69 38 08 79 51 24 97 71 47 23 2600 79 59 44 01 70 39 10 80 52 25 98 73 48 24 02 80 60 45 02 71 41 11 82 53 26 99 74 49 26 03 82 62 46 03 72 42 12 83 55 27 2301 75 51 27 04 83 63 47 05 73 43 13 84 56 28 02 76 52 28 06 84 64 48 06 75 44 14 85 57 30 03 78 53 30 07 86 66 49 07 76 45 15 86 58 31 04 79 54 31 08 87 67 50 1808 1877 1946 2017 2088 2159 2232 2306 2380 2456 2532 2610 2688 2768 51 09 78 48 18 89 61 33 07 81 57 33 11 90 70 52 10 79 49 19 90 62 35 08 83 58 35 12 91 71 53 11 80 50 20 91 63 36 09 84 59 36 14 92 72 54 13 81 51 21 92 64 37 11 85 61 37 15 94 74 55 14 83 52 22 94 65] 38 12 86 62 38 16 95 75 56 15 84 53 24 95 67 39 13 88 63 4C 17 96 76 57 16 85 55 25 96 68 41 14 89 64 41 19 98 78 58 17 86 50 26 97 69 42 16 9C 66 4S 2C 9S 79 59 18 S7 fi7j 27 98| 70i 43 17 91 6' 441 21 270C 80 98 TABLE OF MERIDIONAL PARTS. M.|420|430|440| 450 46o| 470| 480I 49-3| 5i)-3 -5"lo 520 530 ■540 550! 2782 286312946 30)0 3116 3203 329213382:3474 3569 3665 3764|33G5;39fi8 | 1 83 64 47 31 17 04 9'.^l 84! 76 70 67 65 67 70 2 84 66 49 33 18 06 ■ 95] 85 78 72 68 67 68 71 3 86 67 50 34 20 07 96 87 79 74 70 69 70 73 4 87 69 51 36 21 09 98 88 81 75 72 70 71 75 5 88 70 53 37 23 10 99 90 82 77 73 72 73 77 6 90 71 54 38 24 12 3301 91 84 78 75 71 75 78 ? 91 73 56 40 26 13 02 93 85 80 77 75 77 80 8 92 74 57 41 27 14 03 94 87 82 78 77 78 82 9 94 75 58 43 29 16 05 96 88 83 80 79 80 84 10 2795 2877 2960 3044 3130 3217 3306 3397 3490 3585 3681 3780 3882 3985 11 97 78 61 46 31 19 08 99 92 86 83 82 83 87 !2 98 80 63 47 33 20 09 3400 93 88 85 84 85 89 13 99 81 64 48 34 22 11 02 95 90 86 85 87 91 14 2801 82 65 5U 36 23 12 03 96 91 88 87 89 92 ]5 02 84 67 51 37 25 14 05 98 93 90 89 90 94 16 03 85 68 53 39 26 16 07 99 94 91 90 92 96 17 05 86 70 54 40 28 17 08 3501 96 93 92 94 98 18 06 88 71 55 42 29 19 10 03 98 95 94 95 99 19 07 89 72 57 43 31 20 11 04 99 96 95 97 4001 20 2809 2891 2974 3058 3144 3232 3322 3413 350G 3601 3598 3797 3899 40O3 21 10 92 75 60 46 34 24 14 07 02 99 99 M-i\ 05 22 11 93 76 61 47 35 25 16 09 04 3701 3800 02 06 23 13 95 78 63 49 37 26 17 10 06 03 02 04 08 24 14 96 79 64 50 38 28 19 12 07 04 04 06 10 25 15 97 81 65 52 40 29 20 14 09 06 or-, 07 12 2f) 17 99 82 67 53 41 31 22 15 10 07 07 09 14 27 18 2900 83 6S 55 42 32 23 17 12 09 09 11 15 28 20 02 85 70 56 44 34 25 18 14 11 11 13 17 29 21 03 86 71 57 45 35 27 20 15 13 12 14 19 30 2822 2904 2988 3073 3159 3247 3337 3428 3521 3617 3714 3814 3916 4021 31 24 06 89 74 60 48 38 30 23 18 16 16 18 22 32 25 07 91 75 62 50 40 31 25 20 17 17 19 24 33 26 08 92 77 63 51 41 33 26 22 19 19 21 28 34 28 10 93 78 65 53 43 34 28 23 21 21 22 28. 35 29 11 95 80 66 54 44 36 29 25 22 22 25 29 36 30 13 96 81 68 50 46 37 31 26 •24 24 26 31 37 32 14 98 83 69 57 47 39 32 28 26 26 28 33 38 33 15 99 84 71 59 49 40 34 30 27 27 30 35 39 34 17 3000 85 72 60 50 42 36 31 29 29 32 37 40 2836 2918 3002 3087 3173 3262 3352 3443 3537 3633 3731 3 31 3933 4038 41 37 19 03 88 75 63 53 45 39 34 32 32 35 40 42 39 21 05 90 76 65 55 47 40 36 34 34 37 42 43 40 22 06 91 78 66 56 48 42 38 36 36 38 44 44 41 24 07 93 79 68 58 50 43 39 37 3S 40 45 45 43 25 09 94 81 69 59 51 45 41 39 39 42 47 46 44 26 10 95 82 71 61 53 47 43 41 41 44 49 47 45 28 12 97 84 72 62 54 48 44 42 43 45 51 48 47 29 13 98 85 74 64 56 50 46 44 44 47 52 49 48 31 14 3100 87 75 65 57 51 47 46 46 49 54 50 2849 2932 3016 3101 3188 3277 3367 3459 3553 3649 3747 3848 3951 4056 51 51 33 17 03 90 78 68 60 55 51 49 49 52 58 52 52 35 19 04 91 80 70 62 56 52 50 51 54 60 53 54 36 20 05 92 81 71 64 58 54 52 53 56 61 54 55 37 21 07 94 83 73 65 59 55 54 54 58 63 55 56 39 23 08 95 84 74 67 61 57 55 56 59 65 56 58 40 24 10 97 86 76 68 62 59 57 58 61 67 57 59 42 26 11 98 87 78 70 64 60 59 60 63 69 58 60 43 27 13i3200 89 79 71 66 62 60 61 64 70 59 62 44 29' I4I 01 90 «1 73 1 67' 64 62 fi:^ 66 72 TABLE OF MERIDIONAL PARTS. 99 M. 560 570 58^1 590 60O| 61o| 620| 630| 640| 65o| 66o| 670| 680, (i.^jcj 4074 4183 429414409 452T 4649 477514905 5039 5179,5324 5474 5631 5795 | 1 76 84 96 11 29 51 77 07 42 81 26 77 33 97 2 77 86 98 13 31 53 79 09 44 84 28 79 36 5800 3 '/9 88 4300 15 33 55 81 12 46 86 31 82 39 03 4 81 90 02 17 35 57 84 14 49 88 33 84 42 06 5 83 92 04 19 37 60 86 16 51: 91 36 87 44 09 6 85 94 06 21 39 62 88 18 53 93 38 89 47 li 7 86 95 08 23 41 64 90 20 55 95 41 92 50 14 8 88 97 09 25 43 66 92 23 58 98 43 95 52 17 9 90 99 11 27 45 68 94 25 60 5200 46 97 55 20 10 4092 4201 4313 4429 4547 4670 4796 4927 5062 5303 5348 5500 5658 5823 11 94 03 15 31 49 72 98 29 65 05 51 02 60 25 12 95 05 17 33 51 74 4801 31 67 07 53 05 63 28 13 97 07 19 34 53 76 03 34 69 10 56 07 66 31 14' 99 OS 21 36 55 78 05 36 71 .12 58 10 68 34 15 4101 10 23 38 57 80 07 38 74 14 61 13 71 37 16 03 12 25 40 59 82 09 40 76 17 63 15 74 39 17 04 14 27 42 62 84 11 43 78 19 66 18 76 42 18 05 16 28 44 64 87 14 45 81 22 68 20 79 45 19 08 18 30 46 66 89 16 47 83 24 71 23 82 48 20 4110 4220 4332 4448 4568 4691 4818 4949 5085 5226 5373 5526 5085 5851 21 12 21 34 50 70 93 20 51 88 29 76 28 87 54 22 13 23 36 52 72 95 22 54 90 31 78 31 90 56 23 15 25 38 54 74 97 24 56 92 34 80 33 93 59 24 17 27 40 56 76 99 26 58 95 36 83 36 95 02 25 19 29 42 58 78 4701 29 60 97 38 85 39 98 65 26 21 31 44 60 80 03 31 63 99 41 88 41 5701 68 27 22 32 46 62 82 05 33 65 5102 43 90 44 04 71 28 24 34 47 64 84 07 35 67 04 46 93 46 06 74 29 26 36 49 66 86 10 37 69 06 48 95 49 09 76 30 4128 423S 4351 4468 4588 4712 4839 4972 5108 5250 5398 5552 5712 5879 31 30 40 53 70 90 14 42 74 11 53 >401 54 15 82 32 32 42 55 72 92 16 44 76 13 55 03 57 17 85 33 33 44 57 74 94 18 46 78 15 58 06 59 20 88 34 35 46 59 76 96 20 48 81 18 60 08 62 23 91 35 37 47 61 78 98 22 50 83 20 63 11 65 25 94 36 39 49 63 80 4600 24 52 85 22 65 13 67 28 96 37 41 51 65 82 02 26 55 87 25 67 16 70 31 99 38 42 53 67 84 04 28 57 90 27 70 18 73 34 5902 39 44 55 69 86 06 31 59 92 29 72 21 75 36 05 40 4146 4257 4370 4488 4608 4733 4861 i994 5132 5275 5423 5578 5739 5908 41 48 59 72 90 10 35 63 96 34 77 26 80 42 11 42 50 60 74 92 12 37 65 99 36 80 28 83 45 14 43 52 62 76 94 14 39 68 5001 39 82 31 86 47 17 44 53 64 78 95 16 41 70 03 41 84 33 88 50 19 45 55 66 80 97 18 43 72 05 43 87 36 91 53 22 46 57 68 82 99 20 45 74 08 46 89 38 94 56 25 47 59 70 84 4501 23 47 76 10 48 92 41 96 58 28 48 61 72 86 03 25 50 79 12 51 94 43 99 61 31 49 62 74 88 05 27 52 81 14 53 97 46 5602 64 34 50 4164 4275 4390 4507 4629 4754 4883 5017 5155 5299 5448 5604 5767 5937 51 66 77 92 09 31 56 85 19 58 5301 51 07 70 40 52 08 79 94 11 33 58 87 21 60 04 54 10 72 43 53 70 81 96 13 35 60 90 23 62 06 56 12 75 46 54 72 83 98 15 37 62 92 26 65 09 59 15 78 48 55 73 85 99 17 39 64 94 28 67 11 61 17 81 51 56 75 87 4401 19 41 66 96 30 69 14 64 20 83 54 57 77 89 03 21 43 69 98 33 72 16 66 23 86 57 58 79 91 05 23 45 7114901 35 74 19 69 25 89 60 59 81 92 07 25 47 73 i 03 37 76' 21 71' 28 92 6Z 100 TABLE OF M ERIDIONAL PARTS M. 70O| 710| 720| 730| 740( 750| 760| 770| 780| 790] 80O| 8io| 820l 8:)o\ 015366 6146i6335 6534 6746 6970 7210 7467 7745 8046] 8375 8739 0145 9606 1 65: 49 38 38 49 74 14 72 49 51 81 45 53 14 2 73 52 41 41 53 78 18 76 54 56 87 52 60 22 3 75 55 45 45 57 82 22 81 59 61 93 58 67 31 4 78 58 48 48 60 86 27 85 64 67 98 65 74 39 5 81 61 51 52 64 90 31 90 69 72 8404 71 82 47 6 84 64 54 55 68 94 35 94 74 77 10 78 89 55 7 86 67 58 58 71 97 39 98 78 83 16 84 96 64 8 89 70 61 62 75 7001 43 7503 83 88 22 91 9203 72 9 92 73 64 65 79 05 47 07 88 93 27 97 11 81 10 5995 6177 6367 6569 6782 7009 7252 7512 7793 8099 8433 8804 9218 9689 11 98 80 71 72 86 13 56 16 98 8104 39 10 25 97 12 6001 83 74 76 90 17 60 21 7803 09 45 17 33 9706 13 04 86 77 79 93 21 64 25 OS 15 51 23 40 14 14 07 89 80 83 97 25 68 30 13 20 57 30 48 23 15 10 92 84 86 6801 29 73 35 17 25 63 36 55 31 16 13 95 87 90 04 33 77 39 22 31 69 43 62 40 17 16 98 90 93 08 37 81 44 27 36 74 49 70 48 18 19 6201 94 96 12 41 85 48 32 41 80 56 77 57 19 22 05 97 6600 15 45 89 53 37 47 86 63 85 65 20 6025 6208 6400 0603 6S19 7049 7294 7557 7842 8152 8492 8869 9292 9774 21 28 11 03 07 23 52 98 62 47 58 98 76 9300 83 22 31 14 07 10 26 56 7302 66 52 63 8504 83 07 91 23 34 17 10 14 30 60 06 71 57 68 10 89 15 9800 24 37 20 13 17 34 64 11 76 62 74 16 96 22 09 25 40 23 17 21 38 68 15 80 67 79 22 8903 30 17 26 43 26 20 24 41 72 19 85 72 85 28 09 38 26 27 46 30 23 28 45 76 23 89 77 90 34 16 45 35 28 49 33 27 31 49 80 28 94 82 96 40 23 53 44 29 52 36 30 35 53 84 32 98 87 8201 46 30 60 52 30 6055 6239 6433 6639 6856 7088 7336 7603 7892 8207 8552 8936 9308 9861 31 58 42 37 42 60 92 40 08 97 12 58 43 76 70 32 61 45 40 46 64 96 45 12 7902 18 64 50 83 79 33 64 49 43 49 68 7100 49 17 07 23 71 57 91 88 34 67 52 47 53 71 04 53 22 12 29 77 63 99 97 35 70 55 50 56 7-5 08 68 26 17 34 83 70 9407 9906 30 73 58 53 60 79 12 62 31 22 40 89 77 14 15 37 76 61 57 63 83 16 66 36 27 45 95 84 22 24 38 79 64 60 67 8r 20 71 40 32 51 8601 91 30 33 39 82 68 63 70 9C 24 75 45 37 56 07 98 3fc 42 40 6085 6271 6467 6674 0894 7128 7379 7650 7942 8262 8614 9005 9445 9951 41 88 74 70 77 98 32 84 54 48 67 20 12 53 60 42 91 77 73 81 6901 36 88 59 53 73 20 18 61 69 43 94 80 77 85 05 40 92 64 58 79 32 25 69 78 44 97 83 80 88 09 45 97 68 63 84 38 32 77 87 45 6100 87 83 92 13 49 7401 73 68 90 44 39 85 9996 40 04 90 87 95 17 53 06 78 73 95 51 40 93 10005 47 00 93 90 99 20 57 10 83 78 8301 57 53 9501 10015 4S 09 96 94 0702 24 61 14 87 83 07 63 60 09 10024 49 12 99 97 06 28 65 19 92 89 12 69 67 17 10033 50 0115 0303 6500 6710 6932 7169 7423 7697 7994 8318 8676 9074 9525 10043 51 IH 00 04 13 36 73 27 7702 99 24 82 81 33 10052 52 21 09 07 17 40 77 32 06 8004 29 88 88 41 10061 53 24 12 11 20 43 81 36 11 09 35 93 96 49 10071 54 27 15 14 24 47 85 41 16 14 41 8701 9103 57 100«0 55 3( 19 17 28 51 89 45 21 20 47 07 10 G5l 10089 50 33 22 21 31 55 94 49 25 25 52 14 17 73 10(199 57 3( 25 24 35 59 98 54 30 30 58 20 24 8l!l0108 58 41 28 28 38 63 '[7202 58 35 35 04 26 31 89|l(ll 18 59 4; 32 31 42 66 1 06 63 40 40 69 33 38 98 10127] I'lale 1 Plate 1 Hate 'i ~~^ ^y^/. .^ Pfcite Plate 5. .J cJ J ■J J J ■i^^^'^-^j Fl<)us:>lie.l L. "Vine yard S - ■*. „ 44. 'i i^t ;* * » =4. ^ ^ i -, » «i ^ % % 4 DETAILS OF LEAVES i < S i i ) > M 5 $ i V 5 I I M 1 i i i ! i 5 i , 1 i $ 5 $ S i - :'Ocik fA'^cods '"^Kk^^r Heath m©^ps. &i, RPike road ^\/\/\/VVV"ooden Fence Ay\/y\^- _Conujioiiioad_^^___ ^7W. J/r/J/zTi/ /'/"■/,■ /',/////>■!/ //!/■ f'l//l/l/i/l /luUrri/ //■/• J/m-Miv (mif //■/■// (•rmrrtf r„ur/ /A'U.yr (7/wr/, ./>/ iy//,/,/r JJk. /Ji/,ir//,;/ Forfff Owalri/ Jhusr J//// f/ri.s-/ /)(>. Saw Do. Sua/ii /h>. ,'/' St,'nr /><: or ri};>,/ Tri//fii<»iifri'r/i/ /'ri/it O A' I \ ^igT PmiOu-tmu Sr XT. ,U, ,v ,,,,,,,,1 U^ 00 Direction of the cuixpnt Jtucks souietiuies iiaTe ¥? Anihorag-p J^ for Ships Huoys Rocks .ihcivs * , ' ("hainiel-^ "niaiks — n^a I Haffjonrs C3C it4icki> soiuetiDies h i ■1^ i