Th [■'i.i }-\>,'\X I4ii^!;;:^:^:l^^:;:i^; ij."/'! ^r .:•. ^'^^;?^^'''i':::::'!^ '/■'li :n L'iiiiri SYSTEM OF GEOMETRY AND TRIGONOMETRY TOGETifER WITH A TREATISE OJV* SURVEriJ^TG; -REACHING VARIOUS WAYS OF TAKING THE SURVEY OP A FIELD ALSO TO PROTRACT THE SAME AND FIND THE AREA. LIKEWISE, RECTANGULAR SURVEYING: OB, AN ACCURATE METHOD OF CALCULATING THE AREA OF ANY FIELD ARITHMETICALLY, WITHOUT THE NECESSITY OF PLOTTING IT. TO THE WHOLE ARE ADDED, SEVERAL MATHEMATICAL TABLES, NECESSARY FOR SOLVING QUESTIONS IN TRIGONOMETRY AND SURVEYING ; WITH A PARTICULAR EXPLANATION OF THOSE TABLEJ^ AND THE MANNER OF USING THEM. COMPILED FROM VARIOUS AUTHORS, BY ABEL FLINT, A.BL ftFTH EDITION, WITH IMPORTANT ADDITIONS, BY GEORGE GILLET, SURVEYOR GENERAL OF THE STATE OF CONWECTlCUt. HARTPOllD : PITBLISHEP BY OLIVER D. COOKE & CO. 1825. district of Conneeticui, ss. BE IT REMEMBERED, That on the twenty-fifth day of Septcmbet, in the forty-third year of the Independence of the United States of America, OliTer D. Cooke & Co., of the said district, have deposited in this office the title of a book, the right whereof they claim as Proprietors, in the words following, to wit— " A System of Geometry and Trigonometry: together with a Treatise o». Surveying ; Teaching various ways of taking the Survey of a Field ; Also to Protract the same and find the Area. Likewise, Rectangular Surveying ; or, an Accurate Method of calculating the Area of any Field Arithmeticafly without the necessity of Plotting it. To the whole are added several Mathematical Tables, necessary for solving Questions in Trigonometry and Surveying ; with a particular explanation of those Tables, and the Manner of using them. Compiled from various Authors. By Abel Flint, A. M. Fifth Edition, with important Additions, By tJeorge Gillet, Surveyor General of the State of Connecticut." •^ In conformity to the Act of the Congress of the United States, entitled " An Act for the encouragement of Learning, by securing the copies of Maps, Charts, and Books, to the authors and proprietors of such copies, donns the times therein mentioned." R. I. INGERSOLL, Clerk of the District of Connecticut. A true copy of Record, examined and sealed by me, r r I r J R- 1- INGERSOLL, J ^!,'"\^S ^M^ ' ^terR of the Histrict of CmriMimt "fo-x^nx RECOMMENDATIONS HAVING perused, with some attention, the following Treatise on Surveying, in Manuscript, it appears to me to be estimable for its simplicity and perspicuity ; and, by excluding all matter but remotely connected with the main subject, and reducing the Tables of Log- arithms, of Logarithmic Sines, Tangents, and Secants, and of Difference of Latitude and Departure, without impairing their use, in their application to most cases which occur in common Surveying, and supplying any possible defect by a Table of Natural Sines, to com- prise, in the limits of a pocket volume, whatever is most essential and most useful in the Art, including the important modern improvement ot Rectangular Sur- veying ; and on the whole, particularly from the size of the volume, to be well adapted to general use. JOHN TREADWELL, Farmington, Sept. 20th, 1804. RECOMMENDATIONS. WE the subscribers have carefully perused a Trea-- tise on Surveying, prepared for the Press by the Rev. ;Vbel Flint of Hartford ; and find it worthy of the pub- lic patronage. Every thing not immediately necessary for the practical Surveyor has been excluded ; while it comprises all which is requisite in Field Surveying, both on the old and new plan ; elucidated and explained with a degree of conciseness and perspicuity not usually to be found in Treatises on the same subject. The Ma- thematical Tables are reduced to less than half the size occupied by others ; and any inconvenience which might result from such reduction, is obviated by the in- sertion of a Table of Natural Sines, not usually found in works of this nature. The Surveyor who shall own this will not be under the necessity of purchasing Gib- son, which is a more expensive work. ASHER MILLER, Surveyor General. GEORGE GILLET, Deputy Surveyor for Tolland County. MiDPLETOWN, Oct, 3, 1804. PREFACE. The following work is chiefly a compilation from other Books ; and but very little new is added, ex- cept a more full explanation, than has yet been published, of Rectangular Surveying, or the method of calculating the Area of Fields arithmC' tically, without drawing a plot of them and mea- suring with a Scale and Dividers, as has been the common practice ; and also a more particular ex- planation of the use of Natural Sines than is con- tained in most Mathematical Books. The Compiler has endeavoured to render this work so easy and intelligible that a Learner will require but little assistance from an Instructer, ex- cept with regard to the construction and use of Mathematical and Surveying Instruments. Before, however, he enters on the study of this Book he must be well acquainted with common Arithmetiq, with Decimal Fractions, and the Square Root; and he must also know the various characters or marks used in Arithmetic. A Surveyor will doubtless find many questions arise in the course of his practice, for the solution of which, no particular directions are here given ; nor is it possible to give directions for every case that may occur. In all practical Sciences much must be left to the judgment of the practitioner, who, if he is well acquainted with the general principles of his Art, will readily learn to apply those principles to particular cases. The primary design of this treatise is to teach common Field Surveying ; at the same time it con- tains the elements of Surveyiiig upon a larger PREFACE. Stale ; and the system of Geometry and Trigone metry with which it is introduced, with the Prob- lems for the mensuration of Superficies, as also the Mathematical Tables at the end, will be found use- ftil for many other purposes. It would be well, therefore, for those who do not intend to become practical Surveyors to acquaint themselves with what is here taught ; and with this view the fdllow- ing work is very proper to be introduced into Aca- demies, and those higher Schools which are design- ed to fit young men for active business in life. In- deed every person who frequently buys and sells land should learn to calculate the Contents of a field arithmetically; a knowledge which maybe acquired in a very little time, from the particular explanation here given of that method. Notwithstanding the many Books already pub- lished on the subjects here treated upon, it was thought a work of this kind was really wanted, and that if judiciously executed it would be useful. It is more particularly necessary at the present time in Connecticut;, as the Legislature of the State have lately enacted a I ^aw on the subject of Sur- veying, in consequence of which more attention must be paid to the Theory of that Art than has been common. These considerations induced the Compiler to select from various publications what appeared to him important; and to arrange the wnole in a method best adaptejd, in his view, for teaching that useful Art. How far he has succeeded in his en- deavours to simplify the subject, and render it easy to the Learner, must be submitted to the test of experience. Hartford, Conn. October, 1804j- P PEEFACE. A GENERAL VIEW OF THE CONTENTS OP THIS WOBK. The System of Geometry is divided into two parts. The first contains Geometrical Definitions respecting Lines, Angles, Superficies, &c. The second part contains a number of Geometrical Problems necessary for Trigonometry and Survey- ing. The System of Trigonometry is also divided into two parts : and teaches the solution of ques- tions in Right and Oblique angled Trigonometry, by Logarithms and also by Natural Sines. The Treatise on Surveying is divided into three parts. Part first treats of measuring Land, and is divided into three Sections. The first contains several Problems respecting Mensuration, and for finding the Area of various Right-lined Figures and Circles. The second Section teaches different methods of taking the Survey of Fields ; also to protract them, and find their Area in the manner commonly practised, and likewise by Arithmetical and Tri- gonometrical calculations, without measuring Di- agonals and Perpendiculars with a Scale and Di- viders ; interspersed with sundry useful rules and directions. The thu'd Section is a particular explanation and demonstration of Rectangular Surveyings or the method of computing the Area of Fields from the Field Notes, by Mathematical Tables, without the necessity of plotting the Field. To this Sec- tion is added a useful Problem for ascertaining the true Area of a Field which has been measured by a Chain too long or too short. PRSPAtfi. Part second treats of laying out Land in various shapes. Part third contains sundry Problems and Rules for dividing Land and determining the true Course and Distance of dividing Lines, or from one part of a Field to another. To this is added an Appen- dix concerning the Variation of the Compass and Attraction of the Needle ; also, a rule to find the difference between the present Variation, and that at a time when a Tract was formerly surveyed, in order to trace or run out the original lines. The Mathematical Tables, are a Traverse Ta- ble, or Table of Difference of Latitude and De- parture, calculated for every Degree and quarter of a Degree, and for any distance up to 50 ; a Ta- ble of Natural Sines calculated for every Minute ; -a Table of Logarithms comprised in four pages, yet sufficiently extensive for common use ; and a Table of Logarithmic or Artificial Sines, Tangents, and Secants, calculated for every 5 Minutes of a Degree. To these Tables are prefixed particular explanations of the manner of using them. GEOMETRY. GEOMETRY is a Science which treats of the properties of Magnitude. PART I. Geometrical Definitions. 1. A Point is a small Dot ; or, Mathematically considered, is that which has no parts, being of itself indivisible. 2. A Line has length but no breadth. 3. A Superficies or Surface, called also Area, has length and breadth, but no thickness. 4. A Solid has length, breadth, and thickness. 5. A Right Line is the shortest that can be drawn between two Points. Fis. \. G. The inclination of two Lines meeting one another, or the opening between them, is called an Angle. Thus at B. Fig. 1. is an Angle, formed by the meeting of the Lines AB and BC. 1. If a right Line CD. Fig. 2. fijlupon an- other Right Line AB, so as to incline to nei- ther side, bat make the Angles on each side equal, then those Angles are called Right Angles ; and the Line CD is said to be Per- pendicular to the other Line. B 10 GEOMETRY Fin. S. 8. An Obtuse Angle is greater than a Right Angle ; as ADE. Fig. 3. 9, An Acute Angle is less than a Right Angle ; as EDB. Fig. 3. Fii Koie. When three letters are used to express an Angle, the roidtlle letter denotes the angular Point. 10. A Circle is a round Figure, bounded by a Line equally distant from some Point, which is called the Centre. Fig. 4. 11. The Circumference or Periphery of a Circle is the bounding Line ; as ADEB. Fig. 4. 12. The Radius of a Circle is a Line drawn from the Centre to the Circumference ; as CB. Fig. 4. Therefore all Radii of the same Circle are equal. 13. The Diameter of a Circle is a Right Line drawn from one side of the Circumfer- ence to the other, passing through the Centre ; and it divides the Circle into two equal parts, tailed Semicircles ; as AB or DE. Fig. 5. 14. The Circumference of every Circle is supposed to be divided into 360 equal parts, called Degrees ; and each Degree into 60 equal parts, called Minutes ; and each Minute into 60 equal parts, called Seconds 5 and these into Thirds, &c Note. Since ail Circles are divided into the same number of Degrees, a Degree is not to be accounted a quantity of any determinate length, as so many inches or feet, &c. but is- always to be reckoned as being the 360th part of the Cir- cumference of any Circle, without regarding the bigness- of the Circle. 15. An Arch or Arc of a Circle is any part of the Circumfer- ence ; as BF or FD. Fig. 5 ; and is said to be an Arch of so many Degrees as it contains parts- of 360 into which the whoU Circle is divided. GEOMETRY 11 16. A Chord is a Right Line drawn from one end of au Arch to the other, and is the measure of the Arch ; as HG is the Chord of the Arch HIG. Fig, 6. Note. The Chord of an Arch of 60 degrees is equal in length to the Radius of the Circle of which the Arch is a part. 3 7. The Segment of a Circle is a part of a Circle, cut off by 1 Chord ; thus the space comprehended between the Arch HIG and the Chord HG is ■called a Segment. Fig. 6. 18. A Quadrant is one quarter of a Circle ; as ACB. Fig. 6. 19. A Sector of a Circle is a space contained between two Radii and an Arch less than a Semicircle; as BCD or ACD. Fig. 6. 20. The Sine of an Arch is a Line drawn from one end of the Arch, perpendicular to the Radius or Diameter drawn through the other end ; Or, it is half the Chord of double the Arch ; thus HL is the Sine of the Arch HB. Fig. 7. 21. The Sines on the same Diameter in- Af crease in length till they come to the Centre, iind so become the Radius. Hence it is plain that the Radius CD Fig. 7. is the greatest j. possible Sine, or Sineof 90 Degrees. 22. The Versed Sine of an Arch is that part of (he Diameter or Radius which is between the Sine and the Circumference ; thus LB is the Versed Sine of the Arch HB. Fig. 7. 23. The Tangent of an Arch is a Right Line touching the Circumference, and drawn perpendicular to the Diameter ; and is terminated by a Line drawn from the Centre through the other end of the Arch ; thus BK is the Tangent of the Arch BH. Fig. 7. JVote. The Tangent of an Arch of 45 Degrees is equal ic length to the Radius of the Circle of which the A-rch is a part. 14. The Secant of ann Arch is a Line drawn fioaa the Cenii 12 GEOMETRY. through one end of the Arch till it meets the Tangent ; thcfg CK is the Secant of the Arch BH. Fig. 7. 26. The Complement of an Arch is what the Arch wants of 90 Degrees, or a Quadrant ; thus HD is the Complement of the Arch BH. Fig. 7. 26. The Supplement of an Arch is what the Arch wants of 180 Degrees, or a Semicircle ; thus ADHis the Supplement of the Arch BH. Fig. 1. 27. The Sine, Tangent or Secant of the Complement of any Arch is called the Co-Sine, Co-Tangent, or Co-Secant of the Arch ; thus, FH is the Sine, DI the Tangent, and CI the Secant of the Arch DH ; or they are the Co-Sine, Co-Tangent, and Co- Secant of the Arch BH. Fig. 7. 28. The measure of an Angle is the Arch of a Circle coij- tained between the two Lines which form the angle, the angular Point being the Centre ; thus', the Angle HCB. Fig.l. is mea- sured by the Arch BH : and is said to contain so many Degrees as the Arch does. JSfote. An Angle is esteemed greater or less according to the opening of the Lines which form it, or as the Arch inter- cepted by those Lines contains more or fewer Degrees. Hence it may be observed, that the bigness of an Angle does not depend at all upon the length of the including Lines; for all Arches described on the same Point, and intercepted by the same Right Lines, contain exactly the same number of Degrees, whether the Radius be longer or shorter. 29. The Sine, Tangent, or Secant of an Arch is also the Sine, Tangent, or Secant of the Angle whose measure the Arch is. Fig. 8. ■ 30. Parallel Lines are such as are equally A, '. B distant from each other ; as AB and CD. Fig. 8. C' 31. A Triangle is a Figure bounded by Xhree Lines ; as ABC. Fig. 9. 3?. An Equilateral Triangle has its three side? equal in length to each other. Fig. 9. GEOMETRY. 1; Fig. 10. 33. An Isocles Triangle has two of its sides equal, and the other longer or shorter. Fig. 10, 34. A Scalene Triangle has three unequal sides. Fig. 11. 35. A Right Angled Triangle has one Right Angle. Fig. 12. Fisr. 11. Fig. If Fis:. 13. 36. An Obtuse Angled Triangle has one Obtuse Angle. Fig. 13. 37. An Acute Angled Triangle has all its Angles Acute. Fig. 9, er 10. 38. Acute and Obtuse Angled Triangles are called Oblique Angled Triangles, or simply Oblique Triangles ; in which the bottom Side is generally csdled the Base and the other two, Legs; 39. In a Right Angled Triangle the longest side is called the Hypothenuse, and the other two, Legs, or Base and Perpen- dicular. JVote. The three Angles of every Triangle being added to- gether will amount to 180 Degrees ; consequently the two Acute Angles of a Right Angled Triangle amount to 90 Degrees, the Rig;ht Angle being also 90. C u GEOMETRY. Fis;. 14 40. The perpendicular height of a Trian- gle is a Line drawn from one of the Angles to its opposite side ; thus, the dotted Line ID. Fig. 14. is the perpendicular height of the Triangle ABC. B JYote. This Perpendicular may be drawn from either of thp Angles ; and whether it falls within the Triangle, or on one of the Lines continued beyond the Triangle, is imma- terial. Fig. 15. 41. A Square is a Figure bounded by four equal sides, and containing four Right Angles. Ficr. 1.5. 42. A Parallelogram, or Oblong Square, is a Figure bounded by four sides, the opposite ones being equal and the Angles Right. Fig. 16. 43. A Rhombus is a Figure bounded by four equal sides, but has its Angles Oblique. Fisc. 17. Fig. 16. Fig. 17. 44. A Rhomboides is a Figure bound- d by four sides, the opposite ones being qual, but the Angles Oblique. Fig. 18. GEOMETRY. 13 45. The perpendicular height of a Rhombus or Rhomboides is a Line drawn from one of the Angles to its opposite side : thus, the dotted Lines AB. Fig. 17. and Fig. 18. represent the perpendicular height of the Rhombus and Rhomboides. Fig. 19. * 46. A Trapezoid is a Figure bounded by four sides, two of which are parallel though of unequal lengths. Fig. 19. and Fig. 20. ZIZX Fig. 20. JVofe. Fig. 19. is sometimes called a Right Angled Trape zium. 47. A Trapezium is a figure bounded by four unequal sides. Fig. 21. 48. A Diagonal is a Line drawn between two opposite Angles ; as the Line AB. Fig. 21. JC 49. Figures w:hich consist of more than four sides are called Polygons ; if the sides are equal to each other they are called regular Polygons, and are sometimes named from the number of their sides, as Pentagon, or Hexagon, a Figure of five or six sides, &c. ; if the sides are unequal, they are called irregulat Polygons. PART II. Geometrical Problems. Fig. 22, ■ PROBLEM I. To draw a lAne parallel to ^ another Line at any given distance ; as at the >.-- . ^: - Point D, to make a Line, parallel to the Line ' AB. Fig. 22. A^ -n-r-' ^ 16 GEOMETRY. With the Dividers take the nearest distance between the Point D and the given Line AB ; with that distance set one foot of the Dividers any where on the Line AB, as at E, and draw the Arch C ; through the Point D draw a Line so as just to touch the top of the Arch C. A more convenient way to draw parallel Lines is with ?i parallel Rule. Fig 23'. PROBLEM IL To bisect a given Line; .E to find the middle of it. Fii^. 23. ^ \ ^ ■:1{T> Open the Dividers to any convenient distance, more than half the given Line AB, and with one foot in A, describe an Arch above and below the Line, as at C and D ; with the same distance, and one foot in B, describe Arches to cross the former : lay a Rule from C to D, and where the Rule crosses the Line. as at E, will be the middle. Fig. 24. H PROBLEM III. To erect a Perpendicular from the end, or any part of a given Line. Fig. 24. > Open the Dividers to any convenient distance, as from D to A, and with one foot on the Point D. from which the Perpen- dicular is to be erected, describe an Arch, as AEG ; set off the same distance from A to E, and from E to G ; upon E and G describe two Arches to intersect each other at H ; draw a Line from H to D, and one Line will be perpendicular to the other. JVote. There are other methods of erecting a Perpendicular, but this is the most simple. GEOMETRY, ir PROBLEM IV. From a given Point, ^ as at (J, to drop a Perpendicular on a^ \^ s;iven Ldne AB. Fisr. 25. ^ F Fig. 25. C ' Gr B With one foot of the dividers in C describe an Arch to cut the gfiven Line in two places, as at F and G ; upon F and G describe two Arches to intersect each other below the Line as at D ; lay a Rule from C to D and draw a Line from C to the given Line. Perpendiculars may be more readily raised and let fall, by a small Square made of brass, ivory, or wood. Fig. 26. PROBLEM V. To make an Angle at E,^^ equal to a given Angle ABC. Fig. 26. "''^^I Open the dividers to any convenient distance, and with one foot in B describe the Arch FG ; with the same distance and one foot in E, describe an Arch fromH ; measure the Arch FG, and lay off the same distance on the Arch from H to I ; draw a Line through I to E, and the Angles will be equal. Fig. 27. PROBLEM VL To maJce an Acute Angle fqual to a given nnmber of Degrees^ suppose 36. Fig. 27. Draw the Line AB to any convenient length ; from a Scale of Chords take 60 Degrees with the dividers, and with one foot in B describe an Arch from the Line AB ; from the same Scale take the given number of Degrees, 36, and lay it on the Arch from C to D ; draw a line from B through D, and the Angle at B will be an Angle of 36 Degrees. D i8 GEOMETRY. Kg-.' 28. PROBLEM VII. To malce an Obtuse An- gle, suppose of 110 Degrees, fig. 28. Take a Chord of 60 Degrees as before, and describe an Arch greater than a Quadrant ; set off 90 Degrees from B to C, and from C to E set off the excess above 90, which is 20 ; draw a Line from G through E, and the Angle will contain 110 De- grees. JYote. In a similar manner Angles may be measured ; that is^ with a Chord of 60 Degrees describe an Arch on the an- gular Point, and on a Scale of Chords measure the Arch intercepted by the Lines forming the angle. / A more convenient method of making and measuring Angles is to use a Protractor instead of a Scale and Dividers. Fisr. 29. PROBLEM VIII. TomaheaTnangleoj Ihree given Lines, as BO, BL, LO. Fig. 29. Draw the Line BL from B to L ; from B, with the length ol the Line BO, describe an Arch as at ; from L, with the length of the Line LO, describe another Arch to intersect the former ; from draw the Lines OB and OL, and BOL will be the Triangle required. Fig. 30. PROBLEM IX. To make a Right Jingled Triangle, the Hypolhenuse and Angles being -7:iven, Fi^. 30. Sujipose the Hypothenuse CA 25 Rods or Chains, the angle GEOMETRY. id at C 35" 30' and consequently the Angle at A 54® 30'. Set JVote after the d9th Geometrical Definition. JVote. When degrees and minutes are expressed, they are distinguished from each other by a small cipher at the right hand of the degrees, and a dash at the right hand of the minutes ; thus 35° 30' is 35 degrees and 30 minutes. Draw the Line CB an indefinite length ; at C make an Angle of 35° 30' ; through where that number of Degrees cuts the Arch draw the Line CA 25 Rods, which must be taken from some Scale of equal parts ; drop a Perpendicular from A to B, and the Triangle will be completed. JVote. The length of the two Legs may be found by mea- suring them upon the same scale of equal parts from which the Hypothenuse was taken. Fi?. 31. PROBLEBI X. To make a Right An- gled Triangle, the Angles and one Leg being siven. Fior. 31. Suppose the Angle at C 33° 15', and the Leg AC 285. Draw the Leg AC making it in length 285 ; at A erect a Per- pendicular an indefinite length ; at C make an Angle of 33'^ 15' ; through where that number of Degrees cuts the Arch, draw a Line till it meets the Perpendicular at B. JYote. If the given Line CA should not be so long as the Chord of 60°, it may be continued beyond A, for the pur- pose of making the Angle. Fis. 32. PROBLEM XL To make a Right Angled Triangle, the Hypothenuse and one Leg being "iven. Fis- 32. B A 2a Suppose the Hypothenuse AC 40, and the Leg AB 28. Draw the Leg AB in length 28 ; from B erect a Perpendi- cular an indefinite length ; take 40 in the Dividers, and setting 20 GEOMETRY. one foot in A, wherever the other foot strikes the Perpendicular will be the point C. JYote, When the Triangle is constructed, the Angles may be measured by a Protractor, or by a Scale of Chords. Fig. 33. C PROBLEM XII. To make a Right Angled Triangle, the two Legs being given. Fig. 33. Suppose the Leg AB 38, and the Leg BC 46. Draw the Leg AB in length 38 ; from B erect a Perpendicu- lar to C in length 46 ; and draw a Line from A to C. Fig. 34. PROBLEM Xm. To make an Oblique Jingled Tri- angle, the Jingles and one Side being given. Fig. 34. Suppose the side BC 98 ; the Angle at B 45o 15'', the Angle at D 108O 30^ consequently the other Angle 26° IS''. Draw the side BC in length 98; on the Point B make an An- gle of 450 15'' ; on the Point C make an Angle of 26° 15'', and draw the Lines BD and CD. Fis. 35. PROBLEM XIV. To make an Oblique Angled Triangle, two Sides and an Angle op- posite to one of them being given. Fig. 35. let? Suppose the side BC 160, the side BD 79, and the Angle at C 290 9^ Draw the side BC in length 160 ; at C make an Angle of 290 9^, and draw an indefinite Line through where the Degrees cut the Arch ; take 79 in the dividers, and with one foot in B lay the other on the Line CD ; the point D will be the other Angle of the Triangle. GEOMETRY 21 D Fig. 36. PROBLEM XV. To make an Oblique'^ -^ Jingled Triangle, tivo Sides and their \^ — ^..N, contained Angle being given. Fig. 36. ^\%« i^e" aifp Suppose the side BC 109, the side BD 76, and the Angle at B lOlo 30'. Draw the side BC in length 109 ; at B make an Angle of 101° 30', and draw the side BDin length 76 ; draw a line from D to C and it is done. Fis. 37. PROBLEM Wis. 37. XVL To make a Square. Draw the Line AB the length of the proposed Square ; from B erect a Perpendicular to C and make it of the same length as AB ; from A and C, with the same distance in the dividers, de- scribe Arches intersecting each other at D, and draw the Lines AD and DC. Fig. 38. PROBLEM XVIL To make a Parallelo- p-am. Fig. 38. Draw the Line AB equai to ta , longest side of the Parallelo- gram ; on B erect a Perpendicular the length of the shortest side to C ; from C, with the longest side, and from A, with the shortest side, describe Arches intersecting each other at D, and draw the Lines AD and CD. E GEOMETRY. :>%r PROBLEM XVIII. To desaibe a Circle tvhich ehall pass through any three given Points, not lying in ^ a Right lane, as A, B, D. Fig. 43. :j^ Fig. 43. Draw Lines from A to B and from B to D ; bisect those Lines by Problem II. and the Point where the bisecting Lines inter sect each other, as at C, will be the centre of the Circle. PROBLEM XIX. To find the centre of a Circle. By the last Problem it is plain, that if three Points be any where taken in the given Circle's Periphery, the centre of the Circle may be found as there taught. Directions for constructing irregular Figures of four or more sides pay be found in the following Treatise on Surveying. TRIGONOMETRY. TRIGONOMETRY is that part of practical Geometry by which the Sides and Angles of Triangles are measured ; where- by three things being given, either all sides, or sides and Angles. a fourth may be found ; either by measuring with a Scale and Dividers, according to the Problems in Geometry, or more accurately by calculation with Logarithms, or with Natural Sines. Trigonometry is divided into two Parts, Rectangular and Oblique-angular. PARTI. RECTANGULAR TRIGONOMETRY. This is founded on the following methods of applying a Tri- angle to a Circle. Fis. 44. PROPOSITION I. In every Right Angled Triangle, as ABC, Fig. 44, it is plain from Fig. 7. compared with the Geometrical definitions to which that Figure refers, that if the Hypothenuse A AC be made Radius, and with it an Arch \ of a Circle be described from each end, BC will be the Sine of the Angle at A, and AB the Sine of the Angle at C ; that is, the Legs will be Sines of their oppo- site Angles. PROPOSITION If. If one Leg, AB, Fig. 45, be made Radius, and with it on the Point A an Arch be described, then BC, the other Leg, will be the Tangent and AC the Secant of the Angle at A ; and if BC be made Radius, and. an Arch be described with it on the Point C, then AB will be the Tangent and AC the Se- cant of the Angle at C ; that is, if one Leg-^ be made Radius the other Leg will be a Tangent of its opposite Angle, and the Hypothenuse a Secant of the same Angle, U TRIGONOMETRY. Thus, as different sides are made Radius, the other sides ac- quire different names, which are either Sines, Tangents or Se- cants. As the sides and Angles of Triangles bear a certain propor- tion to each other, two sides and one Angle, or one side and two Angles being given, the other sides or Angles may be found by instituting Proportions, according to the following Rules. Rule I. To find a side, either of the sides may be made Radius, then institute the following Proportion : As the name of the side given, which will be either Radius, Sine, Tangent or Secant ; Is to the length of the side given ; So is the name of the side required, which also will be either Radius, Sine, Tangent or Secant ; To the length of the side required. Rule II. To find an Angle one of the given sides must be made Radius, then institute the following Proportion : As the length of the given side made Radius ; Is to its name, that is Radius ; So is the length of the other given side ; To its name, which will be either Sine, Tangent or Secant Having instituted the Proportion, look for the corresponding Logarithms, in the Logarithms for nimibers for the length of the sides, and in the Table of Artificial Sines, Tangents and Se- cants, for the Logarithmic Sine, Tangent or Secant. Having found the Logarithms of the three given Terms, add together the Log. of the second and third Terms, and from their sum subtract the Log. of the first Term, the Remainder will be the Log. of the fourth Term, which, seek in the Tables and find its corresponding Number or Degrees and Minutes. See the Introduction to the Table of Logarithms ; which should be attentively studied by the Learner before he proceeds any further. JVote. The Logarithm for Radius is always 10, which is the Logarithmic Sine of 90o, and the Logarithmic Tangent ol 450. The preceding Propositions and Rules being duly attended to, the solution of the following Cases of Rectangular Tngono- metry will be easy. I TRIGONOMETRY Fig. 39. CASE I. 2Vie Angles and Hypothenuse given to find the Legs. Fig. 39. In the Triangle ABC, given the Hypothenuse AC 25 Rods or Chains ^ the Angle at A 35° 30^ : and consequently the Angle at C 54° 30'' : to find the Legs. Making the Hypothenuse Radius, the Proportions. will be : To find the Leg AB. As Radius - - iD.OOOno r Hyp. AC, 25 - - 1.39784 : : Sine ACB, 54° 30' 9.91069 : Leff AB, 20.35 1.30S63 To find the Leg BC. As Radius - • 10.00000 : Hyp. AC, 25 - - 1.39794 : : Sine CAB, 35° 30' 9.76395 : Leg BC, 14.52 11.16189 10.00000 1.16189 JVote. When the first Term is Radius, it may be subtracted by cancelling the first figure of the Sum of the other two Terms. Making the Leg AB Radius, the Proportions will be : To find the Leg AB. \s Secant CAB, 350 30^ Hyp. AC, 25 : Radius Leg AB, 20.35 To find the Leg BC. As Secant CAB, 35o 30' Hyp. AC, 25 : Tangent, CAB, 35o 30' Leg BC, 14.52 Making the Leg BC Radius, the Proportions will be To find the Leg AB. As Secant ABC, 540 30' Hyp. AC, 25 : Tangent ACB, 54° 30^ Leg AB, 20.35 To find the Leg BC. As Secant ACB, 54° 30' Hyp. AC, 25 : Radius Leg. BC, 14.52 The Logarithms of the four last Proportions being looked out, and added and subtracted according to the Rule, the result will be found to be the same as the two first Proportions. F ae TRIGONOMETRY By J^atural Sines. This Case may be solved by Natural Sines,* according to the following Proportions : As Unity or 1, is to the length ©f the Hypothenuse, so is the Natural Sine of the smallest Angle, to the length of the short- est Leg, Or, so is the Natural Sine of the largest Angle, to thfe length of the longest Leg. ' Or, which is the same thing, multiply the Natural Sines of the two Angles by the Hypothenuse, the Products will be the length of the two Legs. Example. Nat. Sine of 35° 30' Nat. Sine of 54° 30- 0.58070 0.81412 Hyp. 25 Hyp. 25 290350 407060 116140 162824 14.51750 20.35300 Leg BC 14.52 Leg AB 20.35 JVote, The thiid Decimal figure in the first Product being 7, the preceding figure may be called one more than it is. viz. 2. And whenever in any Product, &c. there are more places of Decimals than you wish to work with, if the one at the right hand of the last which you wish to retain is more than 5, add a Unit to the last, because a greater _ number than 5 is more than half. As the Table of Artificial or Logarithmic Sines, Tangents | and Secants, contained in this book, is calculated only for every 5 Minutes of a Degree, whenever any Question is to be solved where the Minutes cannot be found in that Table ; or where the length of the Hypothenuse is such a number as cannot be found in the Table of Logarithms for Numbers, the Question may be solved by Natural Sines as above taught. * See tlie Introduction to the Table of Natural Sines. I TRIGONOMETRY 2:7 CASE II. The Angles and one Leg given, to find the Hypothenuse and the other Leg, Fig. 40. Fi^, 40. 325 In the Triangle ABC, given the Leg AB 325, the Angle at A 330 W and the Angle at C 56^ 45^ : to find the Hypothenuse and the Leg BC. Making the given Leg Radius, the Proportions will be : To find the Hypothenuse As Radius, 10.00000 : Leg AB, 325 2.51188 ,: Sec. CAB, 33° 15' 10.07765 Hyp. 388.6 12.58953 To find the Leg BC. As Radius, 10.00000 : Leg AB, 325 2.511SS : : Tan. CAB, 33° 15' 9;81666 LegBC, 213.1 12,32854 JVote. Reject the first figure, w^hich is the same as subtract- ing Radius, and seek the numbers corresponding to the other figures. Making the Leg BC Radius, the Proportions will be ; To find the Hypothenuse As Tang. ACB, 56° 45^ Leg AB, 325 : Sect. ACB. 56° 45^ Hyp. 388.6 To find the Leg BC, As Tang. ACB, 56° 45' Leg AB, 325 : Radius LegBC, 213.1 Making the Hypothenuse Radius, the Proportions will be ; To find the Hypothenuse. As Sme BCA, 560 45' Leg AB, 325 ' : Radius Hyp. 388.6 To find the Leg BC. As Sine BCA, 56o 45' LegAB, 325 : Sine BAC, 330 15' Leg BC, 213. Xote. If the Leg BC had been given, instead of the Leg AB, the Proportions would have been the same mutatis mutan^ dis. By Natural Sines. To solve this Case by Natural cSines, institute the following Proportions ; as TRIGONOMETRY. To find the Hypothmuse. As the Natural Sine of the Angle opposite the given Leg, is to the length of the Leg, so is Unity or 1, to the length of the Hypothenuse. Or, which is the same thing, Divide the given Leg by the Natural Sine of its opposite Angle^ and the Quotient will be the Hypothenuse. To find the other Leg. As the Natural Sine of the Angle op- posite the given Leg, is to the length of the given Leg, so is the Natural Sine of the Angle opposite the other Leg, to the length of the other Leg. Example. Given Leg 325. Nat. Sine of 56° 45'', the Angle opposite the given Leg 0.83629. Nat. Sine of 33° 15^, the Angle op- posite the other Leg 0.54829. As 0.83629 : 325 : : 1 : 388.6 As 0.83629 : 325 : : 0.54829 : 213.07. CASE IIL The Hypothenuse and one Leg given, to find ike Angles and the other Leg. Fig. 41. " ^-4^ ^ In the Triangle ABC, given the Hypothenuse AC 50 and the Leg AB 40, to find the Angles and Leg BC. Making the Hypothenuse Radius, the Proportion to find. the Angle ACB will be : As Hyp. 50 - 1.69897 : Radius - - 10.00000 ::LegAB, 40 - 1.60206 11.60206 1.69897 Sine ACB, 53© 10' 9.90309 The Angle ACB being 530 10^the other is consequently 360 50^ TRIGONOMETRY. 29 Making the Leg AB Radius, tke Angle BAC may be found by the following Proportion ; As Leg AB, 40 - 1.60206 : Radius - - 10.00000 : : Hyp. 50 - - 1.69897 11.69897 1.60206 : Sec. BAC, 360 50^ 10.09691 The Angles being found, the Leg BC may be found by either f the preceding Cases. It is 30. By J^atural Sines. The Angle opposite the given Leg may be found by the fol- lowing Proportion ; As' the Hypothenuse is to Unity or 1, so is the given leg to the Nat. Sine of its opposite Angle. Or, which is the same thing. Divide the given Leg by the Hypothenuse, and the Quotient will be the Nat. Sine. Example. The Leg AB 40 divided by the Hypothenuse 50 quotes 0.80000 which looked in the Table of Nat. Sines, the nearest corresponding number of Degrees and Minutes will be found to be 53° 8^, the Angle ACB. JVote. The reason why the Angle as found by Nat. Sines differs 2 Minutes from the Angle as found by Logarithms, is that the Table of Logarithmic Sines, &c. contained in this book, is calculated only for every 5 minutes. By a Table of Logarithmic Sines, &c. calculated for every minute, the Angle will be found the same. J3y the Square Root. In this Case the required Leg may be found by the Square Root, without finding the Angles ; according to the following Proposition ; G 30 TRIGONOMETRY. In every Right Angled Triangle, the Square of the Hypo= Ihenuse is equal to the Sum of the Squares of the two Legs. Hence, The Square of the given Leg being subtracted from the Square of the Hypothenuse, the Remainder will be the Square of the required Leg. As in the preceding Example ; the Square of the Leg AB 40 is 1600 5 this subtracted from the Square of the Hypothenuse 50 which is 2500, leaves 900, the Square of the Leg BC, the Square Root of which is 30, the length of Leg BC as found by Tjogarithmg; CASE lY- Fk. 42. Tlie Legs given to find the Angles and Hij- foilunuse. Fig. 42 in the Triangle ABC, given the Leg AB 78.7 and the Leg BC 89 ; to find the Angles and Hypothenuse. Making the Leg AB Radius, the Proportion to find the Angk BAG will be ; As Leg AB, 78.7 1.89597 : Radius - « 10.00000 ; : Leg BC, 89 - 1.94939 11.94939 1.89597 Tang. BAC, 480 30^ 10.05342 The Angle ACB is consequently 41© 30'. Making the Leg BC Radius, the Proportion to find the Angle EGA will be the same as the above, mutatis mutandis. The Angles being found, the Hypothenuse may be found bv. CaseIL It is nearest II 9o TRIGONOMETRY . 31 By the Square Root, In this Case the Hypothenuse may be found by the Square Root, without finding the Angles ; according to the following Proposition. In every Right Angled Triangle, the sum of the Squares of the two Legs is equal to the Square of the Hypothenuse. In the above Example, the Square of AB 78.7 is 6193.693 the Square of BC 89 is 7921 ; these added make 14114.69 the Square Root of which is nearest 119. Sy JVatural Sines. The Hypothenuse being found by the Square Root, the Angles may be found by Nat. Sines, according to the preceding Case, Hyp, Leg. BC. Nat. Sine, 119) 89.00000 (74789 83 3 ... . 570 The nearest degrees and minutes cor- 476 responding to the above Nat. Sine are 48^ = 24^ for the Angle BAC. The difference 940 between this and the Angle as found by 833 Logarithms is occasioned by dividing by 119, which is not the exact length of the 1 070 Hypothenuse, it being a Fraction too much . 962 1180 1071 109 PART IL Oblique Trigonometry. The solution of the two first Cases of Oblique Trigonometi.'y depends on the following Proposition. In all Plane Triangles, the Sides are in proportion to each other as the Sines of their opposite Angles. That is, as the 33 TRIGONOMETRY. Sine of one Angle is to its opposite Side, so is the Sine of an- " other Angle to its opposite Side. Or, as one Side is to its oppo- site Angle, so is another Side to the Sine of its opposite Angle* Note. When an Angle exceeds 90° make use of its Supple- ment, which is what it wants of 180^. As the Sine of 90° is the greatest possible Sine, the Sine of any number of Degrees will be as much less as that number of Degrees exceeds 90, and will be the same as the Sine of the Sup- plement of that number of Degrees ; thus, the Sine of lOOo is the same as the Sine of SQo, and the Sine of 130C^- the same as the Sine of 50o, &c. CASE L The Jingles and one Side given, to find the dker Sides, Fis;. 47. 2(^0 In the Triangle ABC, given the Angle at B 48°, the Angle at G 72°, consequently the Angle at A 60°, and the Side AB 200, to find the Sides AC and BC. To find the Side AC. As Sine ACB, 72' - 9.97821 : Side AB, 200 - - 2.30103 : : Sine ABC, 43° - 8.87107 Side AC, 156 12.17210 9.97821 2.19389 To find the Side BC. As Sine ACB, 73"=" - 9.97821 , : Side AB, 200 - - 2.30103 » : : Sine BAC, 60° - 9.93753 1 Side BC, 182 12.32856 9.97821 2.26033 By JSTatural Sines. As the Nat. Sine of the Angle opposite the given Side is^^to the given Side, so is the Nat. Sine of the Angle opposite either of the required Sides to that required Side. TRIGONOMETRY. 3$ Given Side 200 ; Nat. Sine of 72°, its opposite Angle, 0.95115 ; Nat. Sine of ABC 48©, 0.74334; Nat. Sine ofBAC 60O, 0.86617. As 0.95115 : 200 : : 0.74334 : 156 As 0.95115 : 200 : : 0.86617 : 182. CASE II. Two Sides, and an Angle opposite to one of Ihem given, to find the other Angles and Side. AV. 48. In the Triangle ABC, given the Side AB 240, the Side BC ■200, and the Angle at A 46° 30' ; to find the other Angles and the Side AC. To find the ^iigle ACS. | As Side BC, 200 2.30103 : Sine BAG, 46° 30' g.SeO.'io :: Side AB, 240 2.38021 12.24077 2.30103 9.93974 Angle at A C 46° 30' 60 30 107.00 Sum of the three Angles Sum of two XSO" 107 Sine ACB, 60° 30' ■ I Angle at B 73 The Side AC will be found by Case I. to be nearest 253. JVbfe. If the given Angle be Obtuse, the Angle sought will be Acute ; but if the given Angle be Acute, and opposite a given lesser Side, then the Angle found by the operation may be either Obtuse or Acute. It ought therefore to be mentioned which it is, by the conditions of the question^ By Matural Sines^. As the Side opposite the given Angle is to the Nat. Sine of that Angle, so is the other given Side to the Nat. Sine of its opposite Angle. One given Side 200, Nat. Sine of 46^ 30'', its opposite Angle. 0.72537, the other given Side 240. As 200 : 0.72537 : : 240 : 0.87044=600 30". H u. TRIGONOMETRY CASE III. 2\vo Sides and their contained Angle given, f.o find the other Angles and Side. Fig. 49. 9^0 The solution of this Case depends on the following Propo- sition. In every Plane Triangle, as the sum of any two Sides is to their difference, so is the Tangent of half the sum of the two opposite Angles to the Tangent of half the difference between them. Add this half difference to half the sum of the Angles and you will have the greater Angle, and subtract the half dif- ference from the half sum and you will have the lesser Angle. In the Triangle ABC, given the Side AB 240, the Side AC 180, and the Angle at A 36° 40^ to find the other Angles and. Side. SideAB - 240 Al. - 240 AC - 180 AC - 180. Sum of the two Sides 420 Difference 60 The given Angle BAC 36° 40^, subtracted from 180°, leaves 143° 20^ the sum of the other two Angles, the half of which is 'no 40^ As the sum of two Sides, 420 - - 2.62325 : Their difference 60 ... 1.77815 : Tangent half unknown Ang. 71° 40' - 10.47969 : Tangent half difference, 230 20 The half sum of the two unknown Angles, The half difference between them. Add, gives the greater Angle ACB Subtract, gives the lesser Angle ABC The Side BC may be found by Case I or II, 12.25784 2.62325 9.63459 710 40 23 20 95 00 48 20 TRIGONOMETRY. Fig. 50. CASE IV. T'he three Sides given to find the An- gles. Fig. 50. A. i05 » B The solution of this Case depends Ofi the following Propo- sition. In every Plane Triangle, as the longest Side is to the sum of the other two Sides, so is the difference between those two Sides to the difference between the Segments of the longest Side, made by a Perpendicular let fall from the Angle opposite that Side. Half the difference between these Segments, added to half the sum of the Segments, that is, to half the length of the longest Side, will give the greatest Segment; and this half dif- ference subtracted from the half sum will be the lesser Seg- ment. The Triangle being thus divided, becomes two Right Angled Triangles, in which the Hypothenuse and one Leg are given to find the Angles. In the Triangle ABC, given the Side AB 105, the Side AC S5, and the Side BC 50, to find the Angles. Side AC - 85 AC - - 85- BC - 50 BC = - 50 Sum of the two Sides 135 Difference 35 As the longest Side AB, 105 Sum of the other two Sides, 135 : Difference between those Sides. 35 Difference between the Segments, 45 Half the Side AB Half the difference of the Segments Add, gives the greater Segment AD Subtract, gives the lesser Segment BD 2.02119 2.13033 1. 54407 3.67440 2.02119 1.65321 3e TRIGONOMETRY. Thus the Triangle is divided into two Right Angled Trian- gles, ADC and BDC ; in each of which the Hypothenuse and one Leg are given to find the Angles. To find the Angle DCA. As Hyp. AC, 85 - 1.92942 : Radius ... 10.00000 ; : Seg. AD, 75 - . 1.87506 11.87506 1.92942 Sine DCA, 61° 55' 9.94564 To find the Jingle DCB. As Hyp. BC, 50 - 1.69897 : Radius - . . 10.00000 : : Seg. BD, 30 - - 1.47712 : Sine DCB, 36° 50' 11.47712 1.69897 9.77815 The Angle DCA 61© 55^ suhtracted from 90O leaves the Angle CAD 28o 5^ The Angle DCB 36° 50'' subtracted from 90° leaves the An- gle CBD 530 10^. The Angle DCA 61© 55^ added to the Angle DCB 360 50^ gives the Angle i\CB 98© 45''. This Case maj' also be solved according to the following Proposition^ In every Plane Triangle, as the Product of any two Sides containing a required Angle is to the Product of half the sum of the three Sides, and the difference between that half sum and the Side opposite the Angle required, so is the Square of Radius to the Square of the Co-Sine of half the Angle re-, quired. Those who make themselves well acquainted with Trigono- metry will find its application easy to many useful purposes, particularly to the mensuration of Heights and Distances ; called Altimetry and Longimetry. These are here omitted, because, as this work is designed principally to teach the Art of common Field-Surveying, it was thought improper to swell its size, and consequently increase its price, by inserting any thing not particularly connected with that Art. It is recommended to those who design to be Surveyors to stVv*3y Trigonometry thoroughly ; for though a common field may be measured without an acquaintance with that Science, yet many cases will occur in practice where a knowledge of it will be found very beneficial ; particularly in dividing Land, and ascertaining the boundaries of old Surveys. Indeed no one who is ignorant of Trigonometry, can be an accomplished Surveyor. SURVEYING. SURVEYING is the Art of measuring, laying out, and di- viding Land. PART I. Measuring Land. The most common measure for Land is the Acre ; which contains 160 Square Rods, Poles or Perches ; or 4 Square Roods, each containing 40 Square Rods. The instrument most in use, for measuring the Sides of Fields, is Gunter's Chain, which is in length 4 Rods or 66 Feet ; and is divided into 100 equal parts, called Links, each containing 7 Inches and 92 Hundredths. Consequently, 1 Square Chain contains 16 Square Rods, and 10 Square Chains make 1 Acre. In small Fields, or where the Land is uneven, as is the case with a great part of the I^and in New-England, it is better to use a Chain of only two Rods in length ; as the Survey can be more accurately taken. SECTION I. Preliminary Problems. PROBLEM I. To reduce Ttvo Rod Chains to Four Ro<^ Chains, Rule. If the number of Two Rod Chains be even, take half the number for Four Rod Chains, and annex the Links if any : thus, 16 Two Rod Chains and 37 Links make 8 Four Rod Chains and 37 Links. But if the number of Chains be odd, take half the greatest even number for Chains, and for the remaining number add 50 to the Links : Thus, 17 Two Rod Chains and 42 Links m^e 8 Four Rod Chains and 92 Links. PROBLEM II. To reduce Tioo Rod Chains to Rods and DecinMl Parts. I 38 SURVEYING. Rule. Multiply the Chains by 2, and the Links by 4, vvhiclt will give Hundredths of a Rod : thus, 17 Two Rod Chains and 21 Links make 34 Rods and 84 Hundredths ; expressed thus, 34.84 Rods. If the Links exceed 25, add 1 to the number of Rods and multiply the excess by 4 : thus, 16 Two Rod Chains and 38 Links make 31.52 Rods. * PROBLEM HI. To reduce Four Rod Chains to Rods mnd Decimal parts. Rule. Multiply the Chains, or Chains and Links, by 4 ; the Product will be Rods and Hundredths : thus, 8 Chains and 64 Links make 34.56 Rods. ^Xote. The reverse of this Rule, that is, dividing by 4, will reduce Rods and Decimals to Chains and Links : thus, 105.12 Rods make 26 Chains and 2S Links. PROBLEM IV. To reduce Square Rods to Acres. RcLE. Divide the Rods by 160, and the Remainder by 40, if it exceeds that number, for Roods or Quarters of an Acre : thus, 746 Square Reds make 4 Acres, 2 Roods, and 26 Rods. PROBLEM V. To reduce Square Chains to .Aa-es. Rule. Divide by 10 ; or, which is the same thing, cut off' the Right hand figure : thus, 1460 Square Chains make 146 Acres ; and 846 Square Chains make 84 Acres and 6 Tenths. PROBLEM VI. 2 reduce Square Links to Acres. Hulk. Divide by 100000 : or, which is the same thing, cut off' the 5 Right-hand figures : thus, 3845120 Square Linksmakc 38 Acres and 45120 Decimals. J\^ole. When the Area of a Field, by which is meant its Superficial Con- tents, is expressed in Square Chains and Links, the whole may be consi- dered as Square Links, and the number of Acres contained in the Field, found as above. Then multiply the figures cut ofi" by 4, and again cut cfi" 5 figures, and you have the Roods ; multiply the figures last cut oft" by 40, and again cut off 5 figures, and you have the Rods. Example. How many Acres, Roods, and Rods, are there in 15Cs Sqaare Chains a,nd 3274 Square Links ? 15)63274 Square Links, 4 2)53096 40 21)23840 Jinsiaer. 15 Acres 2 Roods and 21 Rods. Problems for finding the Area of Right Lined Figures, and also of Circles. SURVEYING. 39 PROBLEM Vll. To find ihe .^ea of a Square or ParaU Idogram. Rule. Multiply the length into the breadth ; the Product will be the Area. PROBLEM VIIL To find the Area of a Rhombm or Shomboides. Rule. Drop a Perpendicular from one of the Angles to its. opposite Side, and multiply that Side into the Perpendicular; the Product will be the Area. :r PROBLEM IX. To find the Area of a Triangle^ Rule 1. Drop a Pei-pendicular from one of the Angles to its opposite Side, which may be called the Base ; then multiply the Base by half the Perpendicular, or the Perpendicular by half the Base ; the Product will be the Area. Or, multiply the whole Base by the whole Perpendicular, and half the Product will be the Area. Rule 2. If it be a Right Angled Triangle, multiply one of the Legs into half the other; the Product will be the Area. Or, multiply the two Legs into each other, and half the Pro- duct will be the Area. Rule 3. When the three Sides of a Triangle are known, the Area may be found Arithmetically, as follows : Add together the three Sides ; from half their Sum subtract each side, noting down the Remainders ; multiply the half Sum by one of those Remainders, and that Product by another Re- mainder, and that Product by the other Remainder ; the Square Root of the last Product will be the Area. Example. Suppose a Triangle whose three Sides are 24, 20, and 18 Chains. Demanded the Area. 24+20 + 18=62, the Sum of the three Sides, the half of which is 31. From 31 subtract 24, 20^ and 18 ; the three Re- mainders will be 7, 11, and 13. 31X7=217; 217X11=2387; 2387x13=31031, the Square Root of which is 176.1, or 17 Acres 2 Roods and IT Rods. By Logarithms, As the Addition of Logarithms is the same as the Multipli- cation of their corresponding Numbers ; and as the Number answering to the one half of a Logarithm will be the Square Root of the Number corresponding to that Logarithm : it fol* lows. That if the Logarithm of the half Sum of the three Sides an,d the Logarithms of the three Remainders be added together. 40 SURVEYING. the Number corresponding to one half the Sum of those Lpg- arithnas will be the Area of the Triangle. The half Sum, 31 - - - 1.49136 The first Remainder, 7 - - - 0.84510 The second Remainder, 11 - - 1.04139 The third Remainder, 13 - - 1.11394 The Square of the Area, 31000 - Area 176 Square Chains 4.49179 2.24589 Rule 4. When two Sides of a Triangle and their contained Angle, that is, the Angle made by those Sides, are given, the Area may be found as iollqws : Add together the Logarithms of the two Sides ^nd the Lo- garithmic Sine of the Angle ; from their sum subtrafct the Lo- garithm of Radius, the Remainder will be the Logarithm of double the Area. Example. Suppose a Triangle one of whose Sides is 105 Rods and another 85, and the Angle contained between them 28^5^. Demanded the Area. One Side, 105 .... 2.02119 The other Side, 85 r - - 1.92942 Sine Angle, 28° 5' - - - - 9.67280 Subtract Radius Double Area, 4200 Rods Msiver. 2100 Rods. 13.62341 10.00000 3.62341 A^ete. Radius^may be subtracted by cancelling tlie Left-band figure of tlie Index, or subtracting 10, withoiit the trouble of setting down the Ci- phers. By J^atural Sines, Multiply the two given Sides into each other, and that Pro- duct by the Natural Sine of the given Angle ; the last Product will be double the Area of the Triangle. Nat. Sine of the Angle 28° 5' 0.47076 105 X 85=8925, and 8925 X 0.47076=4201 the double Area of the Triangle. PROBLEM X, Te find the Area of a Trapezoid'. SURVEYING. 41 KuLE. Multiply half the Sum of the two parallel Sides by the perpendicular distance between them, or the sum of the two parallel Sides by half the perpendicular distance, the pro- duct will be the Area. PROBIiEM XI. To find the Area of a Drapeziiim, or irre- gular Four Sided Figure. Rule. Draw a Diagonal between two opposite Angles, which will divide the Trapezium into two Triangles. Find the Area of each Triangle and add them together. Or, multiply the Diagonal by half the Sum of the two perpendiculars let fall upon it, or the Sum of the two perpendiculars by half the Dia- gonal, the product will be the Area. A'ofe. HTiere the length of the four Sides and of tj^e Diagonal is known, the Area of the two Triangles, into which the Trapezium is divided, may be calculated Arithmetically, according to Prob. IX. Rule 3. PROBLEM XII. To find the Area of a Figure containing more than Four Sides. Rule. Divide the Figure into Triangles, and Trapezia, by drawing as many Diagonals as are necessary, which Diagonals must be so drawn as not to intersect each other ; then find the Area of each of the several Triangles or Trapezia, and add them together ; the sum will be the Area of the whole Figure. J\^ote. A little practice will suggest the most convenient way of drawing the Diagonals ; but whichever way they are drawn, provided they do. not intersect each other, the whole Area will be found the same. PROBLEM XIII. Respecting Circles. Rule 1. If the Diameter be given the Circumference may be found by one of the following proportions : as 7 is to 22, or more exactly, as 113 is to 355, or in Decimals, as 1 is to 3. 14159, so is the Diameter to the Circumference. Rule 2. If the Circumference be given the Diameter may be found by one ot the following proportions : as 22 is to 7, or as 355 is to 113, or as 1 is to 0.31831, so is the Circumference to the Diameter. Rule 3. The Diameter and Circumference being known, multiply half the one into half the other, and the product will be the Area. Rule 4. From the Diameter only, to find the Area : multi- ply the Square of the Diameter by 0.7854, and the product will be the Area. Rule 5. From the Circumference only to find the Area ; K 42 SURVEYING. multiply the Square of the Circumference by 0.07958, and the product will be the Area. Rule 6. The Area being given to find the Diameter : divide the Area by 0.7854, and the Quotient will be the Square of the Diameter ; from this extract the Square Root, and you will have the Diameter. Rule 7, The Area being given to find the Circumference v. divide the Area by 0.07958, and the quotient will be the Square of the Circumference ; from this extract the Square Root, and Tou will have the Circumference. SECTION II. The following Cases teach the most usual methods of taking the Survey of Fields ; also, how to protract or draw a Plot oi' them, and to calculate their Area. JVbfe. The Field Book is a Register containing the length of the Sides of a Field, as found by measuring them with a Chain ; also the Bear- ings or Courses of the Sides, or the Quantity of the several Angles, a? found by a Compass or other instrument for that purpose ; together with such Remarks as the Surveyor thinks proper to make in the Field. CASE I. To survey a Triangular Field. Measure the Sides of the Field with a Chain, and enter their several lengths in a Field Book, protract the Field on Paper, and then find the Area by Prob. IX. Rule 1 . Or, without plot- '«ng the Field, calculate the Area by Prob. IX. Rule 3. Fig. 46=. FIE-LD BOOK. See Fig. 46. Chains. AB - - 20 BC - - 24 CA - - 18 To -find the Jlrea. Ch. L. BaseBC - - 24.00 HalfPerp. AD - 7.34 9600 SURVEYING; 960Q 7200 16800 Acres 17)61600 4 Roods 2) 46400 40 Rods 18) 56000 Acres Roods Rods Area 17 — 2 — 18.56 JVoie. When there are ciphers at the Right Hand of the Links, they may be rejected ; remembering to cut off a proper number of figures according to Decimal Rules. Observe, That in measuring witli a Chain, slant or inclined Surfaces, as the Sides of Hills, should be measured horizontally, and not on the Plane or Surface of the Hill ; otherwise, a sur- vey cannot be accurately taken. To effect this, the lower end of the Chain must be raised from the ground, so as to have the whole in a horizontal Line ; and the end thus raised must be directly over the Point where the Chain begins or ends, accord- ing as you are ascending or descending a Hill ; which Point may be ascertained by a Plummet and Line. CASE iL To suroey a Field in the form of a Trapezium,. Measure the several sides, and a Diagonal between two op- posite Angles ; protract the Field, and find the Area by Proe- tEM XI. Or, without protracting the Field, calculate the Area according to the JYote at the end of that Problem. Fig. 51, FIELD BOOK. See Fig. 51. 1-. Ch. h. AB ~ 27.50 BC ~ 11.70 West 160 Acres Roods Rods. 7. S. 36 30 W. 160 ^reallO — 2 — 23 8. N. 38 15 W. 136 Acres Roods ' Rods No. III. Rods. Area 744 — 3 — 28 1. S. 65040^ W. 49.7 2. s. 67 15 W. 34.5 No. 11. Ch.L. 3. s. 54 w. 17.9 1. N. 750 0^ E. 13.70 4. s. 20 w. 5.S 2. N. 20 30 E. 10.30 5. s. 7 30 E. 29.4 3. East 16.20 6. N. 83 E. 107.4 4. S. 33 30 W. 35.30 7. N. 5 50 W. 22. 5. S. 76 W. 16. 8. N. 18 30 w. 46. 6. North 9. Acres Rood Rods, 7. S. 84 W. 11.60 Area 34 — 1 — 19 42 SURVEYING. No. IV Rods. Rods. 1, N. 430 0' W. 12.44 16. .N. 18030^ W. 39. 2. N. 64 W. 8. 17. N. 86 5 E. 26.7 3. N. 52 w. 14.60 Acres Rood Rods 4. N. 37 5 w. 61.36 Area 48 • — 1 — 12 5. 6. N. N. 15 30 20 40 w. w. 21.76 44.60 No .VII. Ch. L. '7. N. 88 20 E. 167.60 1. N. 0045^ W. 9. 8. S. 34 40 E. 71.20 2. N. 19 30 W. 5.36 9. S. 75 W. 69.72 3. N. 23 W. 4.09 10. s. 55 W. 64.60 4. N. 41 35 W. 6.15 11. s. 25 W. 18.12 5. N. 3 W. 36.75 Acres Roods Rods. 6. S. 86 50 W. 13.33 ,B.rea 97 — 2 — 29 7. N. a 15 W. 17.65 I 8. N. 85 45 E. 12.56 1 No.V Rods. 9. S. 2 10 E. 8. 1 1. S. 11030^ W. 34.6 10. N. 86 45 E. 7.38 ' 2. s. 63 20 E. 93.6 11. S. 3 15 E. 13.20 3. N. 4 W. 34.9 12. N. 87 E. 29.92 4. S. 89 65 E. 40.1 13. N. 49 20 E. ^ 4.04 5. N. 5 20 W. 35.5 14. North 2.23 6. N. 69 40 W. 60. 15. N. 60 35 E. 6.50 7. S. 78 W. 30.6 16. S. 22 50 E. 17.94 8. N. 67 20 w. 1.2 17. s. 34 W. 3.50 9. S. 72 30 w. 10.4 18. s. 41 W. 3. 10. s. 66 55 w. 15.2 19. s. 22 60 W. 9.25 Acres Rood Rods, 20. s. 3 40 E. 2.64 Jlrca 41 — 1 — 34 21. s. 86 W. 2,50 22. s. 25 W. 14.50 No. VI , Rods. 23. s. 2 w. 5.38 1. S. 340 0^ E. 42.8 24. s. 10 E. 11.75 i 2. S. 29 E. 69.4 25. s. 86 W. 34.60 I 3. S. 64 50 W. 63. Acres Roods Rods 1 4. S. 25 E. 4. £r.ea 268 — 3 — ^ 1 5. 6. S. N. 66 30 25 W. W. 39. 4. 1 - No VIII. Rods " 7. S. 64 45 w. 32.2 1. S. 603O'' E. 19.1 8. N. 30 30 w. 18.3 2. S. 63 30 E. 14.36 9. N. 56 30 E. 34.5 3. S. 67 E. 10.68 10. N. 64 E. 12.5 4. N. 88 E. 13.3 11. N. 49 E. 14. 5. S. 31 30 W. 32.44 12. N. 26 10 w. 19.3 6. S. 31 55 W. 96.5 13. N. 21 w. 18.3 7. s. 33 25 W. 34.9 14. N. 44 10 w. 18. 8. s. 20 45 E. 3.68 15. N. 64 40 E. 30.5 9. s. 16 15 W. 64. SURVEYING. 53 10. N. 52O30' W. 12.8 21. N. 360 0^ E. 41.56 11. s. 45 W. 18.24 22. S. 68 E. 80.6 12. s. 69 W. 21.4 23. N. 44 30 E. 20.4 13. s. 12 40 W. 9.4 24. N. 2 30 W. 41. 14. s. 84 20 W. 9.5 25. N. 14 45 W. 62.32 15. N. 22 15 W. 24. 26. N. 16 W. 14.8 16. North 9.8 27. N. 1 45 W. 14.8 17. N. 29 15 W 30.6 28. N. 82 30 w. 99. 18. N. 44 26 W 21.8 19. N. 61 30 W 23.1 Acres Rood Rods 20. N. 41 W 10.8 Area 135 — 1 - - 15 CASE V. To survey a field from one station, at any place within the Field, from which the several Angles may be seen. Take the Bearing of the Angles, and measure their Distance from the Station. FIELD BOOK. See Fig. 61. Fig. 61. Ch. L, Station to A. N. 20OW. 8.70 B. N. 60 E. 10. C. N. 87 E. 11.40 D. S. 15 E. 10.50 E. S. 60 W. 12. F. N. 65 W. 8.78 To p'otract this Field. Draw a Meridian Line as N. S. From some point in that Line as a Centre lay off the Bearing and Distance to the several Angles, and draw Lines from one Angle to another, as AB, BC. ^'^ &c. N . CD, -54 SURVEYING, To find the Area. The Area may be calculated according to Prob. XII. by measuring Diagonals and Perpendiculars ; or more accurately according to Prob. IX. Rule 4. As the Bearing and Distance of the Lines from the Station lo the several Angles are knowrf, two Sides and their contained Angle are given in each of the Triangles into which the Plot !3 divided ; the Area may, therefore, be readily calculated by the Bule above referred to. J\''ote. As in the operation, the Logarithm of Radius is to be subtracted from the Sum of the other Logarithms, it may be done by rejecting the Left-hand figure, without the trouble of putting down the Ciphers and subtracting. Triangle aAB. Triangle aDE. aA, 8.70 - - 0.93952 aD, 10.50 - . 1.02119 aB, 10 - . 1.00000 aE, 12 . 1.07918 Sine AaB, 80° - . 9.99335 1.93287 Sine DaE, 75° - Doub. Area, 122 ^ 9.98494 Doub. Area, 85.7 2.08531 Triangle aBC. Triangle aEF. aB, 10 - 1.00000 aE, 12 . 1.07918 aC, 11.40 - . 1.05690 aF, 8.78 . 0.94349 Sine BaC, 27° aCD. 9.65705 1.71395 Sine EaF, 55° Doub. Area, 86.3 Triangle aFA. 9.91336 Doub. Area, 61.8 1.93603 Triangli aC, 11.40 - . 1.05690 aF,8.78 - . 0.94349 aD, 10.50 - . 1.02119 aA, 8.70 - . 0.93952 Sine CaD, 78° - aAB 9.99040 2.06849 Sine FaA, 45° - Doub. Area, 54 - 85.7 - 9.84948 Doub. Area, 117 1.73249 Triangle aBC - 51.8 aCD . 117. aDE - 122. aEF .. 86.3 aFA Vrea Vrea - 54. ... ,., Double J 516.8 s 25)84 SURVEYING. 55 84 4 Acres Roods Rods .irea 25 — 3 — 14.4 3)36 40 14)40 CASE VI. To survey a Field from some one of the .Angles, from which th^ others may be seen. From the stationary Angle take the Bearing and Distance to each of the other Angles, with a Compass and Chain. Fig. 59. FIELD BOOK. Sec Fig. 59. Ch. L. FG. N. 70O W. 14.60 FA. N. 50 W. 18.20 FB. N. 30 W. 16.80 FC. N. 10 w. 21.20 FD. N. 7 E. 16.95 i^E. N. 30 E. 8.50 To di'aw a Plot of this Field. Draw a Meridian Line to pass through the stationary Angle as at F. From the Point F, lay off the Bearing and Distance to the several Angles, and connect them by Lines, as FG, FA, FB, &c. The Area maybe calculated as taught in the preceding Case. 66 SURVEYING. CASE vn. To survey a Field from two Stations within the Field, provided the several Angles can be seen from each Station. Find the Bearing from each Station to the respective Angles ; and also the Bearing and Distance from one Station to the other. Fig. 62. FIELD BOOK. See Fig. 62, First Station. AC. N. 380 30^ E. AD. S. 69 E. AE. S. 69 W. AF. N. 63 W. AG N. 21 w. AH. North. Second Station. BC. S. 820 0^ E. BD. S. 17 E. BE. S. 2S W. BF. S. 49 W. BG. N. 76 W. BH. N. 24 W. Stationary Line AB. N. 14° E. 20 Chains. To protract this Field. At the first Station A, draw a Meridian Line and lay off the Bearings to the respective Angles ; draw the Stationary Line AB, according to the Bearing and Distance ; at B, draw a Me- ridian Line parallel to the other, and lay of the Bearings to the Angles, as taken from this Station ; from each Station draw Lines through the Degree which shows the Bearing of each Angle, as marked by the Protractor or Line of Chords, and the Points where those Lines intersect each other will be the An- gles of the Field. Connect those angular Points together by Lines, and those Lines will represent the several Sides of the Field. SURVEYING. Oi CASE VIII. To Sui'vey an inaccessible Field. Fix upon two Stations, at a convenient distance from the Field, from each of which the several Angles may be seen ; from each Station take the Bearing of the Angles ; and take the Bearing and Distance from one Station to the other. Fig. 67. FIELD BOOK. See Fig-. 67. Ah^ "H^3 S5 - s- Fh 'st Station. Second Station. AE. N. 90 15'' E., BE. N. 50O 0^ W AF. N. 16 E. BF. N. 29 15 w AG. N. 14 30 E. BD. N. 24 w AD. N. 39 E. BG. N. 21 30 w AH. N. 40 E. BH. N. 5 E. AC. N. 72 E. BC. N. 20 30 Ch. L. E. Stationary Distance AB, S. 88© 30^ E. 19.20. The directions given in the last Case for plotting the Field, will apply in this Case also ; and the Area in this and the pre- ceding Case may be calculated in the manner pointed out in Case IV. by dividing the Plot into Triangles and measuring Diagonals and Perpendiculars. Or the Sides may be found by Trigonometry, and the Area calculated Arithmetically, as already taught. 5& SURVEYING. CASE IX. To stiTvey a Field where the boundary Lines are very irregular^ vjithout noticing loith the Compass every small Bend. Fig, 68. Begin near one corner of the Field, as at A, Fig. 68. and measure to the next large Cor- ner, as B, in a straight Line ; noticing also the Bearing of this Line, From the Line take Offsets to the several Bends, at Right Angles from the Line ; noticing in the Field Book at what part ofM the Line they are taken, as at A 1, H 2, 1 3, B 4. Proceed in the same manner round the Field. In the Figure the dot- ted Lines represent the sta- tionary Lines, and the black Lines the Boundaries of the Field FIELD BOOK. Bearing and Distance, Offsets Bearing and Distance. Ofiisets Ch. L. Ch. L. Ch. L. Ch. L. AB. N, 85° 0' E. 11.20 0.56 EF. S. 57° 50' W. 8.20 0,40 at 6.40 1.40 at 1. 4 0.36 8.26 0.36 2.96 0.33 the end 0.36 5.88 the end 1. 12 BC. N. 70 20' E. 7.96 at 2.36 0.36 FG. S. 27° 40' E. 7.06 1.20 4.28 0.96 at 2. 0.24 the end 0.30 the end 0.16 CD. N. 62° 0' W. 4.68 GA. 3. 250 20' W. 6.48 at 4.34 0.30 at 3.80 0.80 the end U.40 DE, N. 110 10' w . 4.20 0.30 SURVEYING. 5^ To protract this Field. Draw the stationary Lines according to the directions in Case IT. From A make an Offset of 56 Links to I ; measure from A to H 540 Links and make the Offset H 2, 140 Links | measure from A to I 826 Links and make the Offset I 3, 36 Links ; at B make the Ofiset B 4, 36 Links. Proceed in the same manner round the Field, and connect the ends of the Off- sets by Lines, which will represent the Boundaries of the Field. To find the Area. Find the Area within the Stationary Lines as before taught ; then of the several small Trapezoids, Parallelograms and Trian- gles made by the stationary Lines, Offsets and boundary Lines, and add the whole together : thus, add 66 Links the Offset A 1 to 140 Links the Otiset H 2 and multiply their sum 196 by half 640 the length of the line AH, and the Product 52920 Square Links will be the Area of the Trapezoid AH 21 : again^' add 140 the Offset H 2 to 36 the Offset I 3 and multiply their Sum 176 by half 286 the length of the Line HI, and the pro- duct 25168 Square Links will be the Area of the Trapezoid HI 32. Proceed in the same manner to calculate the Area of ajl the Trapezoids, Triangles, &c. CASE X. To survey a Field by taking Onsets both to the Right and Left , thai is, within and without the Field, as occasion shall require, in consequence of the Stationary Lines crossing the boundary Lines : also, by Intersections, that is, taking the bearing of an inaccessible Corner from two Stations. The directions given in the preceding Case, together with the following Field Book, will show the Learner how to sur- vey a Field like the following, and also to protract it when sur- veyed. 60 SURVEYING. Fig. 69. FIELD BOOK. ,See U Fis:. 69. Offsets to the Left. Bearing and Distance. Offsets to the Right. Ch. L. Remarks. Ch. L. 1.12 3.40 1.25 Ch. L. AB. N. 88" 0' W. 22.12 at 4.25 7.40 13. A Tov/er bears from, A. N. 48° W., 0.45 BC, N. 27°45'W. 21.12 at 4.10 10.25 15. 1.20 1.15 From B the Tower bears N. 38° 30' E. C 1. S. 82° 15' E. 5.45 1, 2. N. 70 E. 13.25 2 D. N. 20 E. 3.36 From C go into the Field to 1, on account of some impediment on or near the boundary Line. At D, you get into another Corner of the Field. DF. S. 35O0'E. 15.15 E, an inaccessible Corner, bearsfromD. S. 65°30'E. 2.20 2.32 FA. S. 150 15' E. 15,10 at 1.20 7.45 12.25 0.36 E, the inaccessible Corner, bears from F N. 4" W. JVbfe. To draw a Tree, House, Tower, or any other remarkable object, in its proper place, in the Plot of a Field — From any two stations, while surveying the Field, take the bearing of the object , and the intersec- tion of the Lines, which represent the bearings, will determine the place of the object, in the same manner that the Tower is drawn in the Fi,a;ui-e. SURVEYING. 61 Tofaid the Area of the above Field. Find the Area within the stationary Lines, and then of the several small Trapezoids, &c. remembering to distinguish those without the stationary Ijines from those which are within. Subtract the Area of those within the stationary Lines from the Area of those without, and add the Remainder to the Area contained within the stationary Lines ; the sum will be the whole Area of the Field. SECTION in. Rectangular Surveying, or an accurate method of calculating the Area of a Field Arithmetically, from the Field Book, vdihout the necessity of protracting it and measuring with a Scale and Di- viders, as is commonly practised. I. Survey the Field in the usual method with an accurate Compass and Chain, and from the Field Book set down, in a Traverse Table, the Course or Bearing of the several Sides, and their length in Chains and Links, or Rods and Decimal parts of a Rod ; as in the 2d and 3d Columns of the following EXAMPLK. 6,'i SURVEYING. —■-*- -cCTaTOUic .™^- 1 1 2; ' ' 00 M 05 Wl fa- W M 1 M 5J CO ^ CO ^ ?! 1 ?! oa 00 s. - ^ 00 <^ p- "^ ■-< en (-« .0 ° c j^ W => *. 1;^ Ot j> w 1 *» » a- t(^ © W:- » I D- c >-> t- ^s K) J5 W . ^ Ul w 03 C5 ^ , -J 1-^ ->J M ►u 5> oco , CO hfe. tO! • io ^ Ha ■" • 1 W •-» tn Jl 00 • 1 OS 00 t« to « ts rf^ tp' : • 1 P P Ji.*. © w • • 1 CJ> 01 J5 UO <« ■<« to • • • 3) l(^ tl^O » c« *• •- to ts to to W rfi . >*>■ »f»-i r* t^ W 05 • • ^ "■» Qo' ^ 01 -n M -^ ■^J h-» ..A >^ to ^ to to 01 to j:^ to C3 In to CO to to to © to to 30 30 to 00 00 01 bO l»i en => 3> «1 (?5 • 5 tMj • — i gg^ 00 • 0' XI w -4 _o> 1 1 35 © fp to -i I-* <33 X Ml to P » ' T. ■vt »t • ^S- «5 3 • Cil >£>. NO «= -.-•^•raosc ^-™«. • , .. .. 19143.9019 Sum of South Areas 4245.4016 North Do, 2)14898.5003 Douhle Area of the Field Acres 744)92501 4 Roods 3)70004 40 Rods 28)00160 Acres Roods Rods 744 — 3 _ 28 SURVEYING. 63 2. Calculate by Right Angled Trigonomktrt, Case 1, or find by the Table of Difference of Latitude and Departure,* or by the Table of Natural Sines,| the northing or southing, easting or westing, made on each Course, and set them down against their several Courses, in their proper Columns, marked N. S. E. W. Js^ote. To determine whether the Latitude and Departure for any parti- cular Course and Distance are accurately calculated, square each of them ; and if they are right, the Sum of their Squares will equal the Square of the distance, for the following reason : the Latitude and De- parture represent the two Legs of a Right Angled Triangle, and the Distance the Hypothenuse ; and it is a Mathematical truth, that the Square of the Hypothenuse of any Right Angled Triangle is equal to the Sum of the Squares of the two Legs. 3. If the Survey has been accurately taken, the sum of the nortbmgs will equal the southings, and the eastings will equal the westings. If, upon adding up the respective Columns, these are foimd to differ very considerably, the Field should be again surveyed ; as some error must have been committed, either in taking the Courses or measuring the Sides. If the difference is small, a judicious, experienced Surveyor will judge from the nature of the ground or shape of the Field surveyed, where the mistake was most probably made, and will correct accord- ingly. Or, the northings and southings and the eastings and westings may be equalled by balancing them, as follows ; sub- tract one half the difference from that Column which is the largest, and add the other half to that Column which is the smallest ; and let the difference, to be added or subtracted, be divided among the several Courses, according to their length. In Example I. the upper numbers are the northings, &c. as found by a Table of Difference of Latitude and Departure, The several Columns being added, the northings are found to exceed the southings 47 Links, and the westings to exceed the eastings 24 Links. They may be balanced by taking 24 Links from the northings, and adding 23 Links to the southings ; and taking 12 Links from the westings, and adding 12 Links to the eastings. Take from the first Course of the northings 12 Links, from the second 7, and from the third 5 ; to the first southing add 7 Links, to the second 10, and to the third 6 : add to the first easting 3 Links, to the second 3, to the third 4, and to the * For an explanation of this Table, and the manner of using it, see tb^ remarks preceding the Table. t Bee the Remarks preceding the Table o-f Natural Sings. ^4 SURVEYING. iburth 2 ; take from the first westing 5 Links, from the secoud 4, and from the third 3. The lower numbers will then repre- sent the northings, &c. as balanced. 4. These Columns being balanced, proceed to form a De- parture Column, or a Column of Meridian Distances ; which shows how far the end of each Side of the Field is east or west of the station where the calculation begins. This Column is formed by a continual addition of the eastings and subtraction of the westings ; or by adding the westings and subtracting the eastings : See Example I. The first easting 20.74 is set for the first number in the De- parture Column ; to this add 24.38 the second easting, and it makes 45.12, for the second number; to this add 30.04 the third easting, and it makes 75.16, for the third number; to this add 9.56 the fourth easting, and it makes 84.72, for the fourth number ; the fifth Course being south, it is evident the Meri- dian Distance will remain the same, therefore, place against it the same easting as for the preceding Course; from this sub- tract 39.95, the first westing, and it leaves 44.77, for the sixth Course ; from this subtract 23.75, the second westing, and it leaves 21.02, for the seventh Course ; from this subtract 21.02 the last westing, and it leaves 0.0; to be set against the last Course, which shows that the additions and subtractions have been accurately made. For as the eastings and westings equal each other, it is evident that one being added and the other subtracted, there will in the end be no remainder. 5. The next step in the process is to form a second Depar- ture Column, the numbers in which show the Sum of the Me- ridian Distances at the end of the first and second, second and third, third and fourth Courses, &c. The first number in this column will be the first in the other Departure Column ; to which add the second number in that Column for the second in this : for the third add the second and third ; and for the fourth, the third and fourth ; and so on till the Column be completed. See Example I. The first number to be placed in the second Departure Co- lunm is 20.74 ; to this add 45.12, and it makes 66,86, for the second nimaber; to 45.12 add 75.16, and it makes 120.28,. for the third number; to 75.16 add 84.72, and it makes 159.88 for the fourth number ; to 84.72 add 84.72, and it makes 169.44 for the fifth number; to 84.72 add 44.77, and it makes 129.49 for the sixth number ; to 44.77 add 21.02, and it makes 65.79 for the seventh number; to 21.02 add 0.0, and it makes 21.02 for the eighth number. SURVEYING. 65 6. When the work is thus far prepared, multiply the several numbers in the second Departure column by the northings or southings standing against them respectively ; place the pro- ducts of those multiplied by the northings in the column of north areas, and of those multiplied by the southings in the co- lumn of south areas ; add up these two columns and subtract the less from the greater ; the remainder will be double the area of the field in square rods or square chains and links, whichever measure was used in the survey. Fig. 63. Demonstration of the preceding Rules. See Fig. 63. and Example 1. 51. ...VH The dotted line A 2 represents the northing, and the line 2 B the easting made by the first course ; these multiplied together^ that is, 77.15X20.74=1600.0910, which is double the area of the triangle A2B, as is evident from the Rule to find the area of a triangle, Prob. IX. Rule 1. This number is to be placed for the first number in the column of north areas. The line 3C represents the sum of the eastings made by the first and second courses, which is 45.12 the second number in the first departure column ; if to this you add 20.74 the length of the line 2B you have 65.86, which is the second number in the second depar- ture column, and which represents the sum of the two lines 3C and 26. These two lines with the line 2, 3 which represents the northing made by the second course, and the line BC, one of the sides of the field, form a Right Angled Trapezoid. Now^ by the rule to find the area of such a Trapezoid, See Prob. X. 65.86X31.66=2085.1276, double the area of the Trapezoid 2 BC 3. Place this product for the second number in the co- lumn of north areas. 66 SURVEYING. To the line 3C add CD 30.04, the easting made by the third course, and you have 75.16. which is the sum of the eastings made by the three first courses, and the third number in the first departure column. To this add 9.66, the easting of the fourth course, and you have 84.72, the length of the line IE, which represents the sum of the eastings made by the four first courses, and is the fourth number in the first departure column. These two, viz. the lines 3D 75.16 and IE 84.72, added to- gether make 159.88, the fourth number in the second departure column; which, being multiplied by 49.15, tke length of the line 3, 1 which represents the southing made by the fourth course, will give double the area of the Trapezoid 1 ED 3. The number thus produced is 7858.1 020^ which is to be placed for the first number in the column of south areas.. The fifth course being due south, it is evident the sum of the eastings will remain the same as at the end of the fourth course ; that is, the line 4F equals the line IE, which is 84.72. These added make 169.44, the fifth number in the second de- parture column. This, being multiplied by 54.10, the length of the line EF, which is the southing of the fifth course as cor- rected in balancing, and the same as the line 1, 4 — will give double the area of the parallelogram 1 EF 4, which is 9166.7040, the second number in the column of south areas. From the line AF 84.72 subtract 39.95, which is a west course, and it leaves 4G 44.77, the sum of the eastings, or the Meridian distance, at the end of the sixth course, and the sixth number in the first departure column. From this subtract 23.75 the westing made by the seventh course, and you have 21.02, the length of the line 511, which is the Meridian distance at the end of the seventh course, and the seventh number in the first departure column. The line 4G 44.77 added to the line SH. 21.02 make 65.79, the seventh number in the second departure column. This being multiplied by 32.21, the length of the line 4, 5 — which is the southing of the seventh course, will give double the area of the Trapezoid 4GH5, which is 2119- .0959, the third number in the column of south areas. The line H5, 21.02, is the westing of the last course, and the last number in the second departure column. This being multiplied by 26.65, the length of the line 5A, and the northing of the last course, produces 560.1830, which is double the area of the Triangle A5H, and the last number in the column of north areas. J^ote. It will be observed that against the third and sixth Courses there are no Areas ; the reason is, that these Courses being one e?i5t and tU« SURVEYING. 67 other west, there is no northing or southing to be multiplied into them : regard can therefore be had to them only in forming the Departure Co- lumns. By inspecting the Figure, and attending to the preceding illustrations, it will be seen that the three North Areas repre- sent double the Area of the Triangle A2B, the Trapezoid 2BC3, and the Triangle A5H, all of which are without the boundary lines of the field : also, that the three South Areas represent double the Area of the Trapezoid 3DE1, the Parallelogram 1EF4, and the Trapezoid 4GH5 ; and that these include not only the field but also what was included in the North Areas. There- fore the North Areas subtracted from the South, the remainder will be double the Area of the field, coatained within the black Jines. Additional Diredimvs and Explanations. The northings and southings may be added and subtracted instead of the eastings and westings ; then there will be two Latitude columns instead of Departure columns, and the num- bers in the second Latitude column must be multiplied into the eastings and westings, and you will have east and west Areas. When the coiirse is directly north or south, the distance must be set in the north or south column ; when east or west, in the east or west column. There will therefore sometimes be no number to be added to or subtracted from the number last set in the Latitude or Departure column ; then the number last placed in the column must be brought down and set against such Course ; as in Example L at the 5th Course. It may also sometimes be the case that there will be no number to multiply into the number in the second Latitude or Departure column ; then that number must be omitted, and against such Course there will be no Area as in Example I. at the 3d and 6th Courses. When the northings or southings, eastings or westings, be- ginning at the top, will not admit of a continual addition of the one and subtraction of the other, without running out before you get through the several Courses, you may begin at such a Course as will admit of a continual addition and subtraction ; and when you get to the bottom go to the top, and you will end in cipher as SURVEYING. at th€ Course next above that where you began; as inExAMPLt il. which begins at the 9th Course to add the eastings and sub- tract the westings. Example II. Courses. iDist. iRods N. S. W. lN.75O0'E. 2N. 2030E. 3 East 4 S. 33 SOW. 58.76 OW. e.North 6S. 84 OW. N. 6S15W. N. 3645 E. N.2230 E. S. 76 45 E. S. 16 OW. S. 16 45W. 54.814.21 4I.238.6i 64.8 141.2..... 64 i 36 36 ] 46.4 46.4 27.8 76.8 61.5 56 i51.7 48 ! 43.4 40.5 Idep. Col. !52.9i. • . 144.1 14. 64. 2dep. Col. North Areas \ 49 .46 .',21. '46, 9 . . 235.3 3341.26 158.5 302.611680.36 223.3 381.8 77.9 145.4 368.7' 62.1; 83.3 228.7 .'■ 83.3;166.6 i, 37.2 120.S 37.2 0.0 . . .! 46 . . .: 67.4 . . .114.1181.5 11.2 102,9 217 11.7 91.2191.1 37.2 46 113.4 Area 110 Acres, 2 Roods, 23 Rods, J^ote. In the above Example you might begin at the 4th Course to add the westings and subtract the eastinais ; or at the 6th Course to add the northings and subtract the southings : or at the 11th Course to add the southings and subtract the northings. So in every survey, some place may be found where you may begin to add and subtract, without run- ning out befor^ you get through all the Courses. When a field is very irregularly shaped, it will often happen that parts of the same Area will be contained in several differ- ent products in the columns of Areas ; but in the final result, one column being subtracted fi'om the other will leave what is Included within the boundary lines of the field. SURVEYING. 69 FfV. 64. Demonstratictn. See Fig. 64, and Ex- ample II. The Area standing against the 9th Coiu-se, which is where the calculation begins, is the Triangle I2K, all without the Field. The Area against the 10th Course is the Trapezoid 2KL35 also without the Field. The Area against the 11th Course is the Trapezoid 4ML3. This is a South Area, and contains a part of the Field and also part of the preceding North Area. The Area against the 12th Course is the Trapezoid 5NM45 part within and part Without the Field. The Area against the 13th Course is the Trapezoid 6AN5., part within and part without the Field. The Area against the 1st Course is the Trapezoid 6AB7, part within and part without the Field. This is a North Area, and to be ultimately subtracted from the South Areas ; but this includes a part of the preceding South Area, viz. tlte space nAso; it will, however, be seen hereafter that this same space is included in another South Area, This North Area contains also a part of the first North Area, viz. the space 6no7 ; but the same space is also included in another South Area. The Area against the 2d Course is also a North Area, and is , the Tx'apezoid 7BCS. This Trapezoid contains the space sBCx, without the Field ; the space osxw, within the Field ; and the space 7ow8, without the Field. But the space osxw will be contained in the next south Area ; and the space 7ow8, which was contained in the two first North Areas, will be con- tained in the next South Area. By examining the whole Figure in this manner, it will be ^een that the North Areas contain all without the Field that is R 70 SURVEYING. taken into the Calculation, and some of it twice over ; they also contain part of the Area within the Field. The South Areas contain all within the Field, and all without the Field that is contained in the North Areas. They also contain, twice over, so much of the Field as is included in any of the North Areas ; and likewise, twice over, that part without the Field which is contained twice in the North Areas. So that sub- tracting the North from the South Areas leaves double the Area of the Field. This method of calculating the Area of a Field by the Northings, Southings,Eastings, and Westings, divides the Field, with a certain quantity of the adjoining ground, into Right An- gled Trrangles, Right Angled Trapezoids, Parallelograms, or Squares, as may be seen by the Figures. It may therefore with propriety be called Rectangular Surveying. A Useful Problem. To find the true Area of a Field xvhieli has been measured by a Chain too long or too short. Calculate the Area as if the Chain was of a true length,, then institute the following Proportion : As the Square of the length of the true Chain ; Is to the Area, as found by the Chain made use of; So is the Square of the length of that Chain ; To the true Area of the Field. Example. Suppose a Field, measured by a Two Rod Chain 3 Inches too long, is found to contain 41 Acres 1 Rood and 33 Rods, what is the true Area t As the Square of 33 Feet, the true length of a Two Rod Chain ; Is to 41 Acres 1 Rood and 33 Rods ; So is the Square of 33 Feet 3 inches, the length of the Chain used in the Sur- vey; To 42 Acres and 13 Rods. 33 Feet=396 Inches. 396 X 396=156816 Square Inches. 41 Acres 1 Rood 33 Rods=6633 Rods. 33 Feet 3 Inches=399 Inches. 399 X 399=159201 square -» y\ f> fl p C 139201 X 6633—156316=6733 Rods. 6733-~l 60=42 Acres 13 Rods, the true Ai'ea. SURVEYING. ^ 71 PART II. Laying out Land. PROBIjEM I. To lay out any number of Acres in the form of a Square. « Annex 5 Ciphers to the number of Acres, which will turn them into Square Links, the Square Root of which will be the Side of the Square in Links. Example. It is required to lay out 810 Acres in the form of a Square. Jlnswer. Each Side of the Square must be 9000 Links, or 90 Chains. PROBLEM IL To lay out any number of Acres in the form of a Parallelogram, whereof one Side is given. Divide the number of Acres, when turned into Square Links, by the given Side ; the Quotient will be the Side required. Example. What must be the lomxest side of a Parallelogram, which is to contain 25 Acres, when the shortest side is 5 Chains and 50 Links 1 Jinswer. 2500000-r-650=4545 Links for the longest Side. PROBLEM III. To lay out any number of Acres in a Field^ 3, 4, 5, 6, SfC. times as long as it is broad. Divide the Acres, when turned into Square Links, by the proportion between the length and breadth ; the Square Root of the Quotient will be the shortest Side. Example. It is required to lay out 100 Acres 5 times as long as it is broad. Answer. 10000000-^-5=2000000 the Square Root of which is 1414 Links for the shortest Side, and the longest will be 7070 Links. PROBLEM IV. To make a Triangle which shall contain a given number of Acres, being confined to a certain Base. Double the given number of Acres, to which, annex 5 Ci- phers, and divide by the Base ; the Quotient will be the Per- pendicular in Links. Example. Upon a Base of 40 Chains to lay out 100 Acres in a Triangular form. Answer. 5000 Links or 50 Chains will be the length of the Perpendicular. 72 SURVEYING. The Perpendicular may' be erected from any part of the Base : Thus, the Triangle ABC. See Fig. 55. is the same as ABE, each containing 100 Acres. When the given Base is so situa- ted that a Perpendicular of suffi- cient length cannot be erected there- from, continue the Base as from B to D. Fig. 56. from which erect the Perpendicular DC, and complete the Triangle ABC, which will con- tain 100 Acres. ^, Fig. 56. ^.......fD PART III. Dividing Land. As different Fields are so variously, land many of them irre-r gularly shaped, and as they are required to be divided in many different proportions, it is difficult to give Rules which will ap* ply to particular cases. The business of dividing Land must therefore be left, in a great measure, to the skill and judgment of the Surveyor ; who, if he is well acquainted with Trigono- metry, and with measuring Land, will not find it difficult, after a little practice, to divide a Field in such a manner as shall be desired. If he has before him a plot of the Field, and knows the number of parts into which it is to be divided, and the pro- portion which each part. is to bear to the others, he will readily find out where the dividing Lines are to be drawn. A few Rules and Examples will be given for the general instruction of the Learner. PROBLEM I. To cut off any numhe^- of Aa-es from a Square, ■&r Parallelogram. SURVEYING. 73 Saj-^, as the whole number of Acres in the Field ; Is to the length of the Square or length or breadth of the Parallelo- gram ; So is the number of Acres proposed to be cut off; To their proportion of the length or breadth. PROBLEM II. To cut off any number of Acres by a Line proceeding from any Jingle of a Triangle. Measure the Base, or Side opposite the Angle from which the dividing Line is to be drawn ; Then say, As the number of Acres in the whole Triangle ; Is to the whole Base; So is the given numb'^r of Acres ; To their part of the Base. Fig. 67. Example. -See Fig. 67, In the Triangle ABC, which contains 48 Acres, it is required to cut off 18 Acres, by a Line proceeding from C to the Base AB, which is 40 Chains. As 48 : 40 : : 18 : 15 Lay 45 Chains on the Base from B to D, and draw the Line CD. The Triangle will then be divided as was proposed ; BCD containing 18 Acres. PROBLEM III. To take off any given number of Acres from a multangular Field. Fis. 65. ExABIPLE I. -See Fig. 65. Let ABCD, &c. be the Plot of a Field containing 11 Acres, from which it is required to cut off 5 Acres. Join two opposite Corners of the Field as D and G, with the R2 74 SURVEYING. tiine DG (which you may judge to be near the partition Line) and find the Area of the part DEFG, which, suppose, may want 140 Rods of the quantity proposed to be cut off. Mea- sure the Line DG, which, suppose to be 70 Rods ; divide 140 by 35 the half of^DG, and the Quotient 4 will be the length of a Perpendicular whose Base is 70 and the Area 140. Lay off 4 Rods from G to I, and draw the Line DI, which will be the dividing Line. Example II, See Fis. 60. Let ABCD, &c. be a tract of land to be divided into two equal parts, by a line from I to the opposite side CD ;A to iind arithmetically on what part of the line CD the dividing line IN will fall ; or to find the Distance CN. FIELD BOOK. AB. N. BG. S. CD. S. DE. S. EF, S. 19° 0' 77 27 52 15 30 E. E. E. W. E. Rods. lOS 91 115 58 7G GF. West GH. N. 36° 0' W. HI. North lA. N. 62 15 W. Acres Rood Rods Whole Area 152—1 — 25 Rod? 70.9 47 64.» 59 Find the Area of the part lABCI, according to Section IIL Page 57, as follows : set the Latitude and Departure of the three first Sides, lA, AB, and BC, in their proper colwnns, in a Tra- verse Table ; and place as much southing, viz. 109.1, equal to the line CK, and as much westing, viz. 71.7, equal to the line KI, as will balance the columns. This southing and westing will be the Latitude and Departure made by the line CI. The Area of lABCI will be found to be 8722 Rods, which is less SURVEYING. ■" 75 tiian half the Area of the whole Field by 3470 Rods, the quan- tity to be contained in the Triangle ICN. Find the bearinji and distance of CI by Right Angled Trigo- nometry, Case IV. as follows ; As CK, the southing of CT, 109 - . . _ . 2.03743 : Radius 10.00000 : : Kl, the westing of CI, 71.7 ------ 1.85552 11.85552 ' 2.03743 : Tangent Course S. 33° 20' W. 9.8180D As Sine Course 33° 20 - - - - - - - 9.73997 : Departure KI 71.7 - - 1.85552 :: Radius - - - - 10.00000 11.85552 9.73997 : Distance IC 130 ------- - 2.11555 J\fote. In this way the Course and Distance may be found from one Angle of a Field to another. Having found the line CI, divide 3470, the number of Rods to be contained in the Triangle ICN, by one half the line CI. viz. 65, the quotient will be the length of the Perpendicular PN, viz. 53.4. Now, by the bearings of CI and CD, it appears that they form an Angle of 60° 20^ ; wherefore, in the Triangle CPN are given the side PN 53.4, and the Angle at C 60° 20^ to find the Hjpothenuse CN. \s Sine. PCN 60O 20^ Side PN 53.4 : Radius Hyp. CN 61.5 9.93898 1.72754 10.00000 11.72754 9.93898 1.78856 Thus the dividing line must go from I to a point on the line CD, which is 61.5 Rods from C, The bearing and distance of 78 SURVEYING. this line may be found by the directions given above for finding the bearing and distance of the line CI. Or, they may be found by Oblique Trigonometry, Case III. Another Method oj finding the Distance CJV*. Having ascertained the Latitude and Departure of the line CI, set them down in a Traverse Table ; find the Latitude and Departure of the line CD, and place them m the Table ; the diiference-between the northing of the line IC, and the southing of the Line CD will be the southing of the line DI, viz. 6.6 ; and the sum of the eastings of those lines, as they are both easterly, will be the westing of the line DI, viz. 123.9. Pro- ceed to calculate the Area of the Triangle ICD, which will be found to be 6622 Rods, nearest. J^ote. As in this Triangle two sides and their contained Angle are given, the Area^nay be found by Prob. IX. Rule 4, Page 38. Having found the Area of this Triangle, proceed to find CN according to Prob. II. Page 73, as follows: As the Area of the Triangle ; Is to CD the Base ; So is the quantity to be contained in the Triangle ICN; To.CNits pro- portian of the Base. As 6522: 115: : 3470 : 61.2 A third method of finding the Distance CJV*. To the Logarithm of double the Area to be contained within the Triangle ICN add Radius; from this Sum subtract the Logarithmic Sine of the angle at C ; and from the Remamder sub- tract the Logarithm of the Side IC ; the last Remainder will be the Logarithm of the Side CN. The double Area of the Triangle ICN is 6940 ; the Angle at C is 60O 20^; the Side IC is 130. Double Area 6940 - - 3.84136 Radius - - - - 10.00000 13.84136 Sine ICN 60O 20' - - 9.9389S 3.90238 SURVEYING. 77 3.90238 Side TC 130 - . - 2.11394 Side CN 61.5 - - - 1.78844 .Yole. Radius may be added by placing a Unit before the Index of tte Logarithm for the double Area, without the trouble of setting down the Ciphers. By JVatural Sines. Divide the Double Area by the Natural Sine of the givejo Angle, and that quotient by the given Side ; the last Quotient will be the Side CN. Nat. Sine of the Angle at C 60° 20^ 0.86892 6940-~0. 86892=7986.92 7986.92-~l30=61.43 From the above the following general Rule may be drawn. To find the Side of a Trian0e when the Area is given, with one of the Sides and the Jingle contained between the given Side ajid the Side required. To the Logarithm of double the Area add Radius; from this Sum subtract the Logarithmic Sine of the given Angle, and from the Remainder subtract the Logarithm of the given Side; the last Remainder will be the Logarithm of the Side required. Or, By JVatural Sines: Divide the double Area by the Nat. Sine ol the given Angle, and that Quotient by the given Side ; the last Quotient will be the Side required. CONCLUDING REMARKS. Other methods of surveying Fields are taught by some authord on this subject. The preceding, however, will be found most useful in actual practice. Other instruments be- sides those mentioned in this Book are also sometimes used| such as the Plain Table, Semicircle, Perambulator, Theodov 78 SURVEYING. lite, &c. But of these instruments very little use is made in New-England ; and they are not often to be met with. For general practice none will be found more useful than a common Chain, and a Compass upon Rittenhouse's construction. A Surveyor should also provide himself with an Offset Staff, ten Links in length, and accurately divided into Links. This should be made of firm hard wood, and will be found very con- venient in taking Offsets, and also in measuring the Chain ; which should be often done, as from a variety of causes a Chain is liable to become inaccurate. It will be observed that in this Work there are no descrip- tions of Mathematical and Surveying instruments. The Com- piler omitted such descriptions from a belief that nothing which can be written on the subject will enable a person to under- stand them without an actual inspection of the instruments themselves, and some instruction from those acquainted with them. The general principles here taught may be applied to the surveying of Townships, Roads, Rivers, Harbours, &c. APPENDIX. CSF THE VARIATION OF THE COMPASS AND ATTRACTION OP THE NEEDLE. The Variation of the Compass is the number of Degrees that the Magnetic Needle points from the true North, either East or West. This differs in different places, and in the same place at different times. It is, at present, in Connecticut, a few degrees to the Westward. That is, the Needle points to the Westward of North, and is gradually approaching the true North. The following method of ascertaining the Variation, by the North Star, has been adopted by many Surveyors, as the most eligible to be practised on Land. It was communicated to the Compiler by Moses Warren, Jun. Esq. of Lyme, an experienced Surveyor, with permission to publish it. The Star commonly called the North Star, is not directly North but revolves round the Pole in a small circle, once in 24 hours. It cannot therefore be due North but twice in that period ; and that is within a very few minutes of the time when a Star, called Alioth, in the Constellation of Ursa Major, or the Great Bear, is directly over or under it. There is also another StEir nearly in an opposite direction from the Pole, called Gamma, in the Constellation of Cassiopeia. When these three Stars Text vertical the North Star is very near the Meridian ; and whc-a they are horizontal, it is at its greatest Elongation, that is, at its greatest distance East or West 6f the Pole, and on the same side as the Star in Cassiopeia. The Variation may be calculated when the Star is on the Meridian, or when at its greatest Elongation ; more accurately, however, at the latter period, because its motion being then neajjy verti- 80 APPENDIX. cal for some time gives the observer a better opportunity to complete his observation.* To find the Elongation of this Star in any Latitude, its Declina- tion must be known; that is, its distance North of the Equator. This being found, institute the foUovring Proportion : As Co-Sine of the Latitude ; Is to Radius ; So is Co-Sine of the Declination ; to Sine of the Elongation. The Declination of the North Star, January 1, 1810, was 8SO 17^ 28^^, and increasing at the rate of about 19 seconds and One half annually. The following Table Shows the Elongation, in several different Latitudes, for 5 years successively. It is calculated for the first of January in each year ; and in using it, if the time, when the Elongation is required, be past • the middle of the year, take it for the beginning of the next year. A Table showing the Elongation of the JVorth Star. Latitude. 1820 1821 1822 1823 1824 380 20 5^ 34^^ 20 5/7// 20 4^39^'' 20 4/ 13^^ 20 3/47'^ 39 2 7 23 2 6 54 2 6 25 2 5 59 2 5 33 40 2 9 12 2 8 41 2 8 14 2 7 46 2 7 20 41 2 11 11 2 10 40 2 10 12 2 9 44 2 9 18 42 2 13 10 2 12 39 2 12 11 2 11 43 2 11 16 43 2 15 22 2 14 51 2 14 22 2 13 54 2 13 26 44 2 17 33 2 17 4 2 16 34 2 16 5 2 15 37 * The following Figure exhibits a view of the relative situation of these Stars as they appear, when in a horizontal position : or when the North Star is in its greatest Eastern Elongation. The Great Bear. Cassiopeia- * Aliotb Pole( North StSr Ganima ^ APPENDIX. Si "The Elongation for the Latitude of the observation being- calculated, or taken from the above Table, proceed to find its range, according to the following directions ; Take a pole 18 or 20 feet in length; to the end of it fasten a small line ; raise it to an elevation of 45° or 50° ; and support it by two crotches of suitable height to keep it firm in its place. At the end of the line, near the ground, fasten a weight of half a pound cr more, which should swim in water to prevent the air from moving the line. Southward of the line, fix a Compass sight, or other piece of metal or wood, with a narrow, perpendicular aperture at a convenient height from the ground, say about 2 or 2 1-2 feet ; and let it be so fixed that it can be moved a small distance East or West at pleasure. Let an as- sistant hold a light either NE or NW.of the line, nearly as high as the range from the sight to the North Star, in such a position that the line may be plainly seen ; then, (the three Stars above mentioned being parallel or nearly so with the Horizon) move the sight-vane East or West, until through the aperture, the line is seen to cut the Star ; and continue to ob- serve, at short intervals, till the Star is seen at its greatest Elongation. Let a lighted candle be placed in an exact range with the sight-vane and line at the distance of 20 Rods or more, which should stand perpendicularly, be made fast, extinguished, and left till morning. Then the sight-vane, the line, and the candle, will be the range of Elongation, which observe accu- rately with a Compass ; and if the Elongation be East and the Tariation West, the former must be subtracted from the latter ; and if they are both West they must be added, anil their differ- ence or sum will be the true Variation. OF THE ATTRACTION OF THE NEEDLE. It is well known that any iron substance has an influence upon the magnetic Needle, attracting it one way or the other from the point where it would settle, were there no such attraction. A surveyor should therefore be careful to see that no iron is near the compass when taking a bearing. But as the Earth ic certain spots contains, near its surface, iron or other minerals which attract the Needle, it will frequently happen that it will point wrong. To ascertam whether this is the case, the sur- veyor, at each station, should take a back view of the one last left ; and if he finds that the compass does not reverse truly, he S 62 APPENDIX. may be sure, provided the compass be accurately graduated and placed horizontally, that he either made a mistake at the last station, or that in one or the other of the stations, the Needle was attracted from the true point. When he finds a place where he suspects there is an attraction, he should go a few rods backward or forward, and see whether the Needle points differently. In this way he may prevent mistakes in his field notes, by putting down a wrong course. To take back sights is particularly necessary in running long lines, and laying out new lands, where the Needle is the only thing to guide the sur- veyor. By practice and experience a knowledge will be acquired on this subject, and with regard to many other things in surveying, which cannot be taught by books ; and after all the directions which can be written, the practitioner will frequently find oc- casion for the exercise of his own judgment. A Rule to find the difference between the 'present variation of the Compass, and that at a time when a Tract was formerly sur- veyed, in order to trace or run out the original lines. Go to any part of the premises where any two adjacent cor- ners are known ; and if one can be seen from the other, take their bearing ; which, compared with that of the same line in the former survey, shows the difference, But if one corner cannot be seen from the other, run the line according to the given bearing, and observe the nearest distance between the line so run and the corner ; then work by the following proportion : As the length of the whole line, Is to 57.3 degrees,* So is the said distance, To the difference of variation required. Example. Suppose it be required to run a line, which, some years ago, bore N, 45° E., distance 20 chains, and in running this line by the given bearing, the corner is found 20 links to the left hand ; what is the present bearing of this line ? * 57.3 degrees is the Radius of a circle (nearly) in such parts as the cir- cumference contains 360. APPENDIX. 83 Ch. Deg. As 20 : 57.3 : : 100 20 2000 1146.0 60 2000)68760(34 Minutes. Answer — 34 Minutes to the left hand is the allowance re- quired, and the line in question bears N. 44© 26^ E. The compiler of this work acknowledges himself under ob- ligations to George Gillett, Esq. Surveyor General of the state of Connecticut, for the following illustrations, remarks, and miscellaneous questions, considering them Ciilculated to be use- ful to the learner, and the practical surveyor. They came to hand too late to be inserted in their proper places, in the body of the work, and are here put together in the Appendix. Remarks on the Irregularities of the Magnetic Needle. By a statute of this state, applicants for the appointment of County Surveyor are required to be well skilled in point of science in the theory of the most approved methods of survey- ing lands. It is also as necessary that they should be as well skilled in practical surveying. A practical knowledge must be acquired by experience, and no one can have a thorough know- ledge of correct practice without being made acquainted with the imperfections and irregularities of the Magnetic Needle. It is supposed, by most people, that this instrument, in all places, points directly to the Poles of the earth, and that it re- mains as permanent as the Poles themselves — an infallible guide.* This is a mistaken idea. A fevv remarks on this sub- * There is one line around the globe on which there is no variation. The general course of this line, on this side of the globe, is from northwest to southeast, but is crooked and irregular iii its course. According to Dr. Holly's chart, made in 1700, the line of no variation crossed the meridian of London in 55® South latitude — crcssed the equator in 17° W. longi- tude — ^fiom thence, by various windings, to the island of Bermuda, fro;u 84 APPENDIX. ject will here be offered, and some facts respecting it will be stated. Notwithstanding the great utility derived from the Magnetic thence nearly a west course until it struck the continent near Charles- ton, in South Carolina. This line is not stationary, but is ever varying its position ; and, notwithstanding the irregularity of its courses, it never crosses itself. About 1756, another variation chart was made, when it was found that the line had fallen so far to the ^vest that it struck the con- tinent near the coast of Florida. On the east side of this line, the Magnetic Needle points to the west of north, and on the west side it points to the east of north, and a regular increase of either east or west variation is found from it, depending on the course that is taken. The line of no variation now runs through Pennsylvania, and not far from Norfolk, in Virginia. When the Connecticut Western Reserve was surveyed into townships, the variation at that place was easterly from one to two degrees. In 1813, at New-Orleans, the variation was easterly, about eight or nine degrees. In 1701, at Philadelphia, the variation was westerly, eight degrees and a half. In 1794, at the same city, the west variation had diminished to one degree and a half, which proves that the progress of the line of no variation had been from west to east. In 1813, by observations at this city, it was found that the west variation had increased to about two or three degrees. By a series of observations, commenced at Hebron in Connecticut, by the writer of this, in 1805, and continued to 1813, it was found that the west variation during that period increased more than half a degree. The result of these obser- vations agree with those at Philadelphia, that there had been a retrograde motion of the Needle. Since 1313, the west variation has diminished, or certainly it has not increased. The west variation at Hebron is now (1825) a few minutes more than five degrees. In 1580, at London, the Magnetic Needle pointed eleven degrees and a half to the east of north, which proves that the line of no variation was east of that place. The east variation diminished until 1657, when the line of no variation arrived there and soon passed by ; of course west variation began, and continued to increase until 1806, when it exceeded twenty-four degrees. The line of no variation must have had a rapid progress through the At- lantic and through a great part of the United States, to have arrived at Charleston in 1700, and at the coast of Florida in 1756. The present bear- ing of all old lines in this state prove that there has been a considerable de- crease of west variation since the first surveys were made ; which also proves that the progress of the line of no variation, in the United States, has, for a long time, been from west to east. How far the line of no variation pro- gressed westward in the interior of this country before it turned, no one can tell. It is unaccountable how the west variation in London should increase, while at Philadelphia it was diminishing, when both places are on the same side of the line of no variation. The variation of the Needle has long been a subject of much perplexity. Observations have been made in abundance. Many facts have been ascertained, but the diflSculty is, they are not reducible to system. The polarity of the Magnetic Needle, with its variations anel irregularities, is a hidden mystery, which is never to be searched out by man. It is sufficient in itself, without any other evidence, to cause the reflecting Jiiind to wonder at, admire, and adore the wisdom, knowledge, and power of HIM who planned and directs it. APPENDIX. 85- Keedle, it cannot be relied on where great accuracy is requiredp on account of the irregularities to which it is subject, such as its annual motion in variation, its diurnal motion, and, what is attended with greater difficulty, its local attraction. When an ©Id course is given to renew a line, it cannot be depended on, en account of the difference in variation between the time of the first running and the renewal of it. No annual rate can be fixed on for the variation of the Mag- netic Needle, as its motion is much more rapid in some years than in others. By observations made at London during a pe- riod of more than two hundred years, it appears that in some years the motion of the Needle was rapid, in others, but little would be discovered, and, in some years, the motion was retro- grade. There is no regularity in its motion in any place. Another difficulty in retracing a line from an old course or from one recently given is, that it is often found that two com- passes do not make the same course. It was well known to the celebrated Rittenhouse, that his compasses did not all agree, or make the same course, and he never was satisfied as to the rea- son of it. It has also been ascertained that different Needles do not point alike at the same place. French writers, on Mag- netism, have latel}' treated on this subject. Two compasses may differ a quarter of a degree or more or less, when no de- fect can be discovered in either- A survey may be taken as correctly with one as with the other. The question then natu- rally arises, which of the two is right ? The answer is, both are right ; neither of them points directly to the Poles of the earth, except on the line of no variation. All that can be said of them is, that one has a greater variation than the other, and that which has the least cannot have the preference^. The di- urnal motion of the Magnetic Needle is another defect in it. As the sun rises in the forenoon, and the earth becomes heated, it has an effect on the unknown something which gives polarity to the Needle, and turns the north end of it to the west. la. the afternoon and night following, it returns to its position,. For several years, the writer of (bis made observations with Rittenhouse's compass, to ascertain the diurnal motion ; and in the summer season usually found about a sixth part of a degree.. In the winter, but little or none could be discovered. The di- urnal motion of the Needle has been known in Europe about a century.* The local attraction is an irregularity to which the Magnetic Needle is subject. These are found oftener in hilly, ' The diurnal motion is mentioned in Dr. Williams' History of Verniont, S3 ae APPENDIX. broken lands, filled with ledges, than in level, feasible land, where there are no ledges. As attractions are out of sight, they i^iust be searched out, as before directed in this work, by locaL experiment. They often amount to a quarter, a half, and some-i times to a whole degree or more. The writer of this has kno wn^ a difference of more than five degrees within a distance of fortyl rods. When an old line is to be renewed where the bounds are lost, the circumstances attending the case must govern. These may be various, such as giving the lots on each side of the line and contiguous thereto, their full width or quantity, or by dividing the overplus or the wantage, as the case may happen. It would be difficult to mention all the circumstances which may govern, or which may serve as evidence in such cases. After all, the Magnetic Needle is the best guide that has ycl been discovered, and it cannot be dispensed with in land survey- ing ; but the surveyor who is best acquainted with it, will make as little use of it as he can. In small surveys, where one angle may be seen from another, the quantity of each angle may be taken by an instrument constructed for that purpose, vvithout the use of the Magnetic Needle ; and the sides may be measured, and one side, no matter which, may be made a meridian, and from that meridian courses may be calculated for the other sides, and the survey may be calculated by the rules of rectangular survejing. This method has been recommended by theorists, and the ingenuity displayed in the invention, together with the correctness of it, so far as it is practicable, must be acknow-- ledged ; but in larger surveys, it cannot be introduced to prac- tice, on account of the obstructions which intervene between the angular point and the termination of two contiguous lines which contain the angle : in such cases, the danger in taking the quantity of an angle will be greater than that of the Magnetic Needle. If in every town in the state, a meridian line was established by the motion of the heavenly bodies, and such meridians were X>erpetuated by durable monuments, whenever a survey was to be taken in the vicinity of a meridian, a surveyor might set his compass on it and note the variation found, and that variation should be inserted in the deed or in whatever writing or instru- ment by which the land is conveyed and made a record; this would assist a surveyor at an}"^ future period in retracing those lines, by setting his compass on the same meridian and allowiHg the same variation that was allowed when the survey was made. This would tend greatly to the security of landed property, and APPENDIX, ^7 perhaps would be the best remedy for the variation of the Mag. uetic Needle, and for the difference between two compasses which differ, that can be invented. On Practical Surveying. It would be no easy matter to describe all the different mev thods which may be taken in different cases, in taking the field- work of a survey. Only one case will be given here, which is represented by the following figure. See Fig, 1. Fig. 1. The survey was begun J th 2, at the corner numbered 1. The corner numbered 2 was in a pond. The course and distance were / xjT^. taken from 1 to jn, then from u\ to 11. The angle at 2 was a right one, of course there was a right angled triangle, wherein ^ the angles and hypothe- ^ iiuse were given, to find the sides ml and In. From n to 3, the course t2^^^ and distance were taken "'~-^. .''' on the line. The next '^ ** line ran through a thicket in a swamp, where nothing could bt done correctly. Courses and distances were taken from 3 to s,. thence to a-, thence to 4, and the course and distance of the line 3 — 4 were calculated by a traverse from those courses and dis- tances. At the angle 5, a tree stood on a high bluff of ledges, inaccessible on either line terminating at that point. The course from 4 to 5 was taken at 4. Next, the course and dis- tance were taken from 4 to a, and from a the course was taken tO' 5. Next, the course and distance were taken from a to 6, and from 6 the course was taken to 5. Two oblique triangles, with the angles and one side in each, were given to find the sides 4-^—5 and 5 — 6. The closing line ran through thick Ijushes and water, and the course and distance were taken on the dotted as APPENDIX. Une to the line 1 — 2, at a point twenty rods from 1 . The course and distance of 6 — 1 were calculated accoirdingly. Whenever a line runs through or over a place where it Is difficult to take either course or distance correctly,if, by taking u traverse around at a Utile distance, the surveyor can have level, clear land, and then calculates his course and distance by the traverse, he will be more likely to ascertain the true course and distance than by continuing on the line. Directions for running Lines. Many people suppose that a surveyor at the beginning of a Jine, by intuition or by some magic art, can set his compass di- rectly to the terminating point, whatever obstructions may in- , tervene, and that he needs no assistants ; but this is a mistaken 1 idea. In running a line of considerable length, a surveyor should have two assistants to carry the chain, and two to carry flags, in whose ability and correctness he can confide, and a fifth ^ to use &n axe. If the surveyor is not furnished with such a set! of assistants, his employer need not place too much, confidence in his work. The flag staves should be as much as two and a half inches in diameter, or what would be better, two stripes _ of a board of that width and seven or eight feet in length. If* they are not so wide, they cannot be seen through the sights of t,he compass, at any great distance. On one end of each staff, a red flag of" a yard in length should be wound tight, and not left to hang loose and flutter in the wind. Red will be seen quicker through bushes than any other colour, and the brighter the co- lour the better. Being thus manned and equipped, at the be- ginning of the line, he must set his compass as near the true line as he can, or, what would be better, he may set up one of {he flags at the place of beginning, and go forward as far as he can have a fair view of the back flag, there set his compass on his random line, and send the other assistant as^far forward as he can conveniently see the flag. When each flag is clearly seen through the sights of the compass, the back flag must bo brought up and placed where the compass stood. In this naan-. ner, he must proceed on his random line, taking care each time he sets his compass to turn the sights to the back flag. Great care must be taken to keep these flags perpendicular ; also, the surveyor must keep the staff and the sights of his compass per- peadicuUir. A little leaning of the flags, or turning the sights APPENDIX. 88 of the compass from a perpendicular, will make a crooked line. In looking through the sights of the compass to the flags, the surveyor must look as near the ground as he can, and, when practicable, the flag should be turned down, on account of the danger of being leaned when kept up. All obstructions, such as bushes, brush, &c. must be cleareil away. The random line must be measured, and at convenient distances, perhaps at every twenty rods, stakes must be set di- rectly in it. Every stake must be numbered, that no mistake may be mede in calculating, to set them in the true line. If, in the course of the random line, the Magnetic Needle does not traverse as at first, or traverse alike at different places, no re- gard must be paid to it — the two flags must direct the course ; neither should the surveyor be turned aside or terrified by the cry of either of the parties, You are wrong,You are wrong, (for he will most certainly hear it,) but he must continue his random line, until turning at right angles either to the right or to the left, aS the case may be, he will exactly strike the bound, or the point where a bound is to be erected ; there he may stop, and mea- sure the distance from the termination of it to the bound. Then, having the length of the random line and the distance to the true bound, he has the less of a right angled triangle, the hy- pothenuse will be the length of the true line ; also, the angle contained between the tree and the random line must be added to or subtracted from the course of the random line, (as the case'may happen,) which will give the course of the true line. Suppose the whole length of the random line is 2G0 rods, and the distance from the termination of it to the bound is 90 links, the calculation for setting the stakes on the true line may be made thus : — As the whole distance is to 90 links, so is 180, or any other 20 rods stake, t& the distance that such stake is to be moved. The answer is, the first stake is to be moved 9 links, the second 18 links, and so adding 9 links at each stake until the whole are moved at right angles from the random on the true line. Most of the crooked lines and consequent disputes and law-suits between farmers have arisen for the want of this care and attention. When a long line is to be run over a number of ridges and through intervening valleys, it should first be run and established from one ridge to another, and the intermediate spaces in the valleys may be taken afterward. By taking long sights there will be less danger of turning from a straight line. In all cases., the forward flag should be carried as far as it can be distinctly ^en, unless it is at the termination of a line. 98 APPENDIX, On keeping up Bounds. fl As the Magnetic Needle cannot be relied on in renewing lost boundaries, it is of the first importance that good, substantial bounds be made and kept up. In divisions or distributions of lands, erery surveyor ought to see that such bounds are erected. I; It is his business to see them made, and such bounds ought to be f described in deeds, or in the ins^truments by which the lands are Conveyed, and to be made a part of the record. By proper care and attention to this part of the business, almost an endless train of disputes may be prevented. Highways are attended j: with more difficulties of this kind than the location of any other! divisions of real estate. In laying highways, it is the custom ' to lay the centre lines, and order them to be of a certain width. In taking surveys of roads, stakes are usually set at the angles. When the roads are made, all these stakes are lost, and the tra- velling path is often built on one side of the centre ; but the bounds are lost, and after a tew years have elapsed, it is utterly impossible to tell where the road was laid. Surveyors who are employed on such business ought to de- scribe the angles, or as many as is practicable, in such a manner that the road may afterward be found. The follozieing Survey of a Road may serve as an Example. Beginning at a point on the centre of an old road, (here dcr scribe what road,) 14 rods westerly of the range of the west end of J. T.'s house, thence running S. 17° E. 84 rods 10 links to a point bearing West, 54 links from the S. W. corner of a large rock ; thepce, S. 5° E. 77i rods, to a point 77 links east of the centre of a large white-oak tree ; thence, S. 7° 30'' W. G7 rods 20 links, to a point bearing West 7 rods 10 links, from a perpendicular crevice in a rock. Enough of the survey is given to serve as an example. DIRECTIONS FOR USING THE COMPASS, AND CONCERNING ATTRAC- TIONS OF THE NEEDLE. In all cases the surveyor ought to set his compass at leasjt twice on each line, even if he has a fair view of the whole length of it. When there are local attractions, and no two places are found on the same line where the compass has the same tra- APPENDIX. 01 \revse, the surveyor should take a medium and enter in his field book, noting such courses, as he may still have occasion to cor- rect them in his calculations. If in such cases he is at a loss what course to enter in his field hook, and suspects that some minutes may be added to, or subtracted from the course he enters in his book, let him prefix to such courses the sign of addition or subtraction as the case may be, which will often assist him in balancing his surveys. CONCERNING DRAWIJVG A MAP OF A FIELD. When a map is to be made of a multangular piece of land, whether a calculation or division is to be made from it, the sur- veyor should measure across the lot in some central place at least once, and in more places if convenient and the case may I'equire it. .By cross measures, the map will be made more correct. The surveyor should not be afraid of wearing his chain by measuring too much. When a survey is to be calcu- lated by plotting, it should not be laid on a scale less than ten rods to an inch. REMARKS ON BALANCING A SURVEY. In every survey which is accurate, the sum of the Northings will equal that of the Southings, and the Eastings will equal the Westings ; but this is not always an infallible proof that ,the survey is accurate, for two errors may be committed, one exactly to balance the other, which no rule will detect ; but such cases do not often occur. In a survey of one hundred acres, whatever may be the number of the angles, the differ- ence between the two columns of Latitu.de and those of Depar- ture, ought not to exceed a rod for each, but to come within these limits if possible. If in such a survey either of the differences should exceed a rod, where the land is valuable and easily surveyed, it would be better to take a re-survey, or so far as to detect the error. Some authors have given rules for balancing surveys, which are indiscriminately applied to every line in the survey, which presupposes thvt a proportional error must have been commit- ted on each and all, both in courses and distances, when in al- most every survey, a part of the lines are on land so level and so clear from obstructions of any kind, that if the surveyor and c'hainmen attend to their business, they will not be likely to m APPENDIX. commit much error on them ; while other lines, on other parts of the same survey, are attended with so many difficulties, that when they have done their best, it will scarcely be possible for them to avoid some error, and the surveyor who takes the survey will best judge on what lines the errors were committed, and whether they are in the courses or in the distances. In all cases the corrections should be made on the lines containing the errors. When the errors are in the courses they should be corrected, and when the errors are in the distances, the cor- rection should be in them : or the corrections may be in both courses and distances as the surveyor may judge proper. When a course is northwesterly and southeasterly, or north- easterly and southwesterly, if the correction of it increases the latitude and diminishes the departure, or if it diminishes the latitude and increases the departure, so as to bring the differ- ences to an even balance, it is good evidence that the course contains some error. On Redangular Surveying. Rectangular Surveying is a name given to the method here treated of, by the late Governor Treadwell. A more appropriate name could not have been given ; for, the whole survey is reduced to right lined figures, such as triangles, trapezia, squares, and parallelograms. It is simply- multiplying the latitudes by the longitudes from a meridian from which the survey is calculated. The calculations are made from a meridian, drawn, either at the eastern or at the western extremity of the map. All the spaces lying between the field and the meridian from which the survey is calculated, and between the parallels of latitude of the northern and southern extremities of it, are included in the calculation. Parallels of latitude are drawn from each angle to the meridian, which are called meridian distances. In forming the column of meridian distances, when the meri- dian is drawn at the eastern extremity, the westings are added and the eastings are subtracted. When the meridian is drawn at the western extremity, the eastings are added, and the west- ings are subtracted. The meridian distances proceeding from each end of a Une, are added together, to form the column of double mean dis- tances, which the compiler of the foregoing work has called second departure column. The whole is illustrated by the following figure. See Fig. 2. APPENDIX. &3 Directions for calculaiing meridian distances by several methods ; iils H o CO en ta CO o n 3 CO 05 :^ 3 «l -1 CO fe 8' o ~1 CS S h3 OJ g g to CO OD -J ;::; 8 O O S § i CO •05 g ^ s^ s CD o CO o P ss 11 ^ C3 11 feSg CO >- coa 8^1 05 ».. 05 m 05 00 ES fis 8§ cs J^ 03 en CO a 05 o -J g 8 en o lb. en o OS 2 en 00 05 s 05 ••a > CO Cn 00 ^ ta 423 11623 3351 CO > CO — to W 05 00 CO 09 S _^ a T 94 APPENDIX. m Fig. 2. Meridian Dis- J^ tances, and Double Mean Distances, are more proper terms or names for the eighth and ninth columns, than first Departure, and se- cond Departure. The meaning of x the term Meridian Distance is the dis- tance made from any Meridian. It is not very essen- tial by what names the columns are called, as names have no effect on the final result. This survey is calculated from the meridian of the first sta- tion. To form the first column, marked at the top, Merid. Dist., set the easting 16.90 against the first station into the column, which is the meridian distance of 2, or the distance from 2 to 1 ; to this number add the next easting, and they make 22.11, the meridian distance of 3 ; to this number add the next east- ing, and they make 80.07, the meridian distance of 4 ; from this number, subtract the first westing, and 73.82 remains, the meridian distance of 5 ; from this number, subtract the next westing, and 70.33 remains, the meridian distance of 6, or the westing of the closing line. Subtract the last westing, and 00.00 remains. This is on the principle of going around a circle. Next, form the column of double mean distances by adding two opposite sides of the different figures. Set the first Merid. Dist. into the column. To the first meridian distance, add the second, and they make 39.01, the double of the figure 23ns. To the second, add the third, and they make 102.18, the double of the figure 34m». To the third, add the fourth, and they make 153.89, the double of the figure 45aw. To the fourth, add the fifth, and they make 144.15, the double of the figure 56as. To the fifth, add the sixth, and they make 70.33. APPENDIX. 9d The second column, marked at the top, Merid. Dist., is commonly called the Pennsylvania method. Only one column is used in finding the meridian distances, but the operation and final results are the same as that when two columns are used. This method is not so easily explained to the learner, but is preferable in practice only because an error may be com- mitted in forming the column of double mean distances which may not be discovered, but in this method an error cannot be committed without being detected. To form this column, set the first easting 16.90 in the upper place, and add it to itself and they make 33.80 ; to this number, add the next easting, and they make 39.01 ; add the same easting again, and they make 44.22 ; to this number, add the last easting, and they make 102.18 ; add the same easting again, and they make 160.14 ; from this number, subtract the first west- ing, and 153.89 remains ; subtract the same westing again, and 147.64 remains ; from this number, subtract the second westing, and 144.15 remains ; subtract the same westing again, and 140.66 remains ; from this number subtract the last westing, and 70.33 remains ; subtract the same westing again, and 00.00 remains. The upper numbers in this column are the same as the double mean distances which stand against them. For the remainder of the process in finding the areas, pro- ceed as before taught in this work. The north area against the first station is the double of the triangle 12*; that against the second, is the double of the figure 23ms ; that against the third, is the double of the figure 34«i» : the south area against the fourth station, is the double of the figure 45am ; that against the fifth, is the double of the figure 56za ; that against the sixth, is the double of the triangle 6I0. The three north areas all lie without the field, and are bound- ed north on the line to4. The three south areas contain all within, and all without the field, which is included in the calcu- lation. It is obvious then that when the less is subtracted from the greater, the contents of the field will remain. Another column may be formed as the eleventh in this ex- ample, which, for distinction, is here called half departure. It contains half the sum of the numbers in the double mean column. These numbers when multiplied by their respective northings or southings, give the simple areas of the different figures. This method is preferable in practice, as the multi- plications are greatly diminished. When the last decimal in the double mean distance is an odd number, a unit may be taken m APPENDIX. off, and take half the remainder rather than annex another de - chnal. Perhaps this would not make the difference of a rod in a survey of one hundred acres, or the odd numbers in the last place of decimals may be balanced by sometimes adding a unit. If the numbers are diminished a trifle, it may be remarked; that, on account of the uneven surfaces, there is danger of making the distances too much rather than falling short of the true measure. To plot the foregoing Field from the several Latitudes and JVEeridian Distances, without the use of the protractor, or the line of Chords. First, set the northing of the first line from 1 to s ; set the northing of the second line from s to n ; set the northing of the third line from b to m ; set the southing of the fourth line from mto a; set the southing of the fifth line from a to z; next, from these points, draw parallels of latitude perpendicular to the meridian ; then, on these parallels of latitude, set the me- ridian distances of the several stations from sto 2, 16.90 ; from n to 3, 22.11 ; from m to 4, 80.07 ; from a to 5, T3.82 ; from z. to 6, 70.33. From one of these last points to another, draw the boundary lines of the field, and if the plan does not per- fectly close, it is because some error was committed in the process, or the scale ^as incorrect. In practical surveying, it is next to an impossibility in any case, to work so accurately that the survey will exactly close without some correction. The difference between the two columns of latitude, and the two columns of departure, are the legs of a right angled triangle, the hypothenuse of which will be the distance which the sur- vey will fail of closing. These differences, as before taught in this work, must be balanced, and the column of meridian distances must be formed by the numbers as balanced. When the survey is balanced, and this method of plotting is taken, the parallels of latitude must be laid down according to the balancing, and the map will perfectly close. When the courses and distances are corrected according to . the balancing, they will form a survey which will contain no ejror. N. B. Great care must be taken to keep the latitudes paral- lel and perpendicular to the meridian. The better to effect this, a meridian line may be laid on each side of a sheet^ or a kalf sheet of paper, as the occasion may require. APPENDIX. 97 The follmving Survey is calculated from a meridian running- through the map : of course, part of the meridia?!, distances are east, and part are tvest. See Fig. 3. Fig. 3. Ko. Courses 1N60000'E Dist. Rods N. S. 20.00 10.00 2 S.30 OOE. 40.00! 134.64 3.8.70 00W.i70.00 23.94 4n.30 OOW, 40.00 34.641 ^N.74 OOFJ5O.42 13.94! W. 17.32 17.32IE 34.64E, 20.00 48.46 65.78 54.64E, 74,64 E. 8.86 E. 56.92 W 20.00 76.92 W 96.92W 48.46,W 00.00 173.20 1892.73' 212. lOl 2664.50 675.53 173.20 5444.86, 173.20 2)5271. A. Q. R. 160)2635(16 1 35 160 1035 960 T3 75 98 APPENDIX. The column of meridian distances in this eiample is formed by adding twice, and subtracting twice against each station, as in the Pennsylvania method. Set the first easting in the upper place, which is the distance from a to 2, being east meridian distance ; add it to itself, and it makes 34.64 ; to this number, add the next easting, and they make 54.64, east meridian dis- tance from a to m ; add the same easting again, and they make 74.64 ; from this number, subtract the first westing, and there remains 8.86 east meridian distance from i to s. As the first westing canndt be subtracted again, the last east meridian dis- tance, 8.86, must be subtracted from the first westing ; this crosses the meridian, and gives 58.92 west meridian distance in the lower place. Having crossed the meridian, the westings must now be added, and the eastings subtracted. To the 56.92 in the lower place, add the last westing, and they make 76.92 west meridian distance from r to u; add the same westing again, and they make 96.92 ; from this number, subtract the easting of the closing line, and there remains 48.46 west meridian distance, from v to 1, or the easting of the closing line; subtract again, and 00 00 remains. Having com- pleted the column of meridian distances, next' multiply the upper number against each station, by its northing or southing, and set the products on the east side of the meridian, in their respective columns of north or south areas ; but on the west side of the meridian, the order is reversed ; the north products are setinfJhe column of south areas, and the south products are set in the column of north areas. The north area against the first station, is the figure 2z\a; the south area against the second station, is the figure mnia ; the south area against the third station, is the figure sxie ; the south area against the fourth station, is the figure mver, made by the northing of the fourth line ; the south area against the last station, is the figure v5rl. The foregoing columns of meridian distances might have been commenced, by setting the first easting in the lower place^ and the additions and subtractions, made as before directed, and the last subtraction would end in 00.00 at the upper place, against the first station. In this case, as there would be no upper number against the first station, there would be no product in either column of areas against it. The east meri- dian distance against the second station would extend no further east than the third station, and the meridian distance against the third station, would be on the west side of the meridian ; and the meridian distances, against the fourth and fifth stations, WQuld extend as much farther west, as the easting of the fiyst line., APPENDIX, 0^ The products against the second, fourth, and fifth stations.^ would be set in the column of south areas, and that against the third station, on account of its being on the west side of the meridian, would be placed in the column of north areas, and would be subtracted from the footing of the south areas. When a survey is calculated from a meridian running through the map, it is always best to set the first departure in the lower place, as it saves one multiplication^ On Distributing Estates. A farm is to bfe distributed among a number of heirs. A survey is made, and the difference between the columns of lati- tude, and between those of departure, are two rods for each. The survey is balanced, and calculated arithmetically, and is found to contain two hundred acres. The surveyor next draws his map, by which the divisions are to be made, according to the courses and distances. The plan does not close by nearly two rods and three-quarters. He next corrects the lines, and makes the map close as well as he can ; and when the divisions are made, they may not agree with the first calculation by two or three acres, or more. Should the map be drawn as before directed, by the meridian distances and the latitudes as balan- ced, it would close, and would be in exact conformity to the calculation made arithmetically. If the divisions are made arithmetically, without the use of the scale and dividers, the calculations must be made according to the balancing, or the divisions will not agree with the first calculation. It will be acknowledged by every experienced surveyor, that it is a difiicult matter to make the amount of a considerable number of divisions agree with the whole, when calculated by itself. It is the common practice in distributions, to make the di- visions with scale and dividers ; this method will answer very well provided the map is drawn on a large scale. The following is a useful rule in dividing lands, when any quantity is to be added to, or taken fi*om, a division in the form of a triangle. Having the area, the contained angle, and one side of a tri- angle given, to find the adjoining side, including the angle. 100 APPENDIX. Rule. To the sine of the given angle, or its supplement if obtuse, add the logarithm of the given side ; subtract radius from this sum, and subtract the remainder from the logarithm of the double area, the last remainder will be the logarithm of the side required. In taking a survey, go around with the sun, not that you can work more correctly, or that it will have any effect in calcula- ting, but when you put your courses and distances on your map they will follow around with the lines, from the left to the right. Wherever you begin, set your compass on the angle and cause a stake or a flag-staff to be erected at the next. When your line runs over a hill, cause a stake to be erected at each end of it, and take your station on the top of the hill, directly between them. If bushes obstruct the sight, make an offset, or set your compass a little distance from the line, from whence you may see the back flag, and cause the forward flag or stake to be set against the bound in a direction with the compass and the back flag. When the line is measured, measure the distance from the flag to tiie bound, and calculate your true course by Trigo- nometr}'. If your next line is of such a distance that you can- not see through the whole length of it, run as near the true line as you can, and if you do not exactly strike the bound, measure the distance from the termination of your random line, and calculate your course as before directed, or if you can dis- cover a tree standing near the termination of your line, take the course and distance to that, thence to the bound, and calcu- late your true course and distance. By practice and experience, a method for taking courses will soon become familiar, in all cases. In measuring bills and in- clined surfaces, the horizontal distances must be taken. A plummet should be suspended from the end of the chain, when it is levelled. Where hills are very steep, the surveyor should assist the chainmen, and when the best is done in levelling and plumbing the chain, judgment must frequently be called mto exercise. Even when rises and descents are easy, there is dacjger of making too much measure. In such cases, chainmen often make allowances, but the surveyor would do better to keep them to close measure, and from the shape of the ground judge himself what allowances ought to be made. If he is ex- perienced in his business, he will form a more correct judgment APPENDIX. 101 than inexperienced chainmen. Particular care must be taken that the chain is carried on a straight line, and that, it is well straightened. When a tally is ended, and the hinder chainman brings up the sticks, they must be counted. When on counting the sticks it is discovered that one is lost., the chainmen should not leave the chain and go back to find it. but, from the last mark, should measure back to the point where the tally began, to see whether one chain is lost from their mea- sure. Many blunders in this way have been left undetected by not taking this care. A careful accurate chainman never lost a stick or miscounted a tally. Young surveyors should practice much for their own instruction, and should make correct practice familiar, before they offer their services. It is as necessary that they should spend some time in acquiring a practical knowledge, as it is that they should spend any time in acquiring a knowledge of theory, A young surveyor should bear in mind that if he is detected in one error ia the beginning of his practice, it will be more to his disadvantage than to be detected in two when he shall be well established. If an error is committed in a survey, it is not against the surveyor provided he detects and corrects it, but if he cannot detect and correct his own errors, that is suffi- cient evidence of his deficiency in point of knowledge and skill. Form of a Field Book, Beginning at a murstone at the southwest corner, Rods Links 40 00 to a white -oak tree., 30 00 to a heap of stones, 60 00 to a maple tree, 36 00 to a pine tree, 40 00 to a spruce tree, 70 12 to the place of beginning. When a survey is calculated by chains and links, the numbers are less than when it is calculated by rods and decimal parts. Every method by which the numbers are diminished is an im provement. In a hilly country, the two-pole chain is prefera- ble and is more commonly used, because it can be levelled better. Hills are often found so steep that even th,e Iwo-pole cbgirv cannot be levelled,, 1. N. 250 00'' E. 2. N. 10 00 E. 3. N. 76 00 E. 4. S. 10 00 W. 6. s. 5 00 W. 6. s. 85 05 W. 103 APPENDIX. MISCELLANEOUS. When a survey is calculated by chains and links, and the con- tents stand in acres and decimal parts of an acre, it may be mul- tiplied by the price of an acre, and the product will be the amount. Example. A piece of land, 12 chains and 25 links in length, and 10 chains and 26 links in breadth, is sold for ^20 25, per acre ;— what is the price of it ? Length 12.25 Breadth 10.25 6125 2450 1225 Acres and decimal parts 12.55G26 Price of an acre 20.25 6278125 2511250 2511250 Answer ^254,26.40625 The writer of these pages knows not who invented the fol- lowing rules for finding contained angles. For plainness, none of the kind exceeds them. N fi90 F 1 When the first letters are alike, and the two n' 4.4 w' • ^^^^ ^^^ unlike, add the degrees of both courses J together, which gives the contained angle. Q 790 F 1 When the two first and the two last letters are V a*! f' f" ^'^'^®' subtract one course from the other, and J the remainder will be the contained angle. }When the two first letters are unlike, and the two last alike, add both courses together, and sub- tract their sum from 180, the remainder will be the contained angle. 'I When the two first and the two last letters are N. 570 W. i unlike, subtract one course from the other, the S. 25 E. I remainder from 180, and the remainder will be J the contained angle. Application of the above Rules. Two courses are given, viz. N. 67° W. and N. 28° E. to find APPENDIX. 103 the angle. — Suppose yourself standing at the point where these courses meet. Reverse the letters oi" the first course, and they will stand thus, S. 670 E. } The third rule applies in this N. 28 E. I case. When the quantity of any angle in a survey is wanted, the preceding course must be reversed ; then both courses will run from the same point. Converging of Meridians. The breadth of a degree of longitude in any parallel of latitude is to the breadth of a degree upon the equator, as the Co-sine of that Lat. is to Radius. R. : 60 Miles : : Co-sine of the Lat. : the breadth of a degree on that Lat. As Radius - 10.00000 Is to 60 Miles, - - 1.77815 So is Co-sine Lat. 60O 9.69897 11.47712 10.00000 To 30 Miles - 1.47712 MISCELLANEOUS QUESTIONS. 1. At a certain point I took the elevation of a tower 30 15' — then measured toward the tower on an angle of depression 70 333 feet to a level with the base of the tower, when I took the elevation again 8°. — Required the height of the tower and the distance from the second place of observation to the base ; also how much higher the land was at the place of the first ob- servation than at the second. Am Height, - - - 99.6 feet. Distance required, - 708.6 feet. Difference in the height of land, 40.58 feet. 2. Two persons made observations on the altitude of a me- teor, both being on the same side of it, and in a vertical plane passing through it. The distance of their stations were 200 rods apart, and at one the angle of elevation was 36° 25^, at the other 32° 50', and at the last the outer limb of the meteor 104 APPENDIX. subtended an angle of 2^. — Required the distance from the last place of observation, also the height and diameter of it. M, Q. R. Answer. — The distance, 5 .. 3 .. 60 Height, 3 .. .. 70 Diameter, 1 8 feet 2 inches. 3. Fx'om tlie top of a steeple 165 feet high, the angle of depression of Che nearest bank of a river is 11° 15', that of the opposite bank is 6° 15'. Re- quired the width of the river. .insw. 41.13 rods. 4. What length of cart-tire will it take to band a wheel 5 feet in diameter ? .Snsw. 15 feet 8 1-2 inches. 5. A gentleman laid out a garden in a circle, containing one acre, one quarter, and one rod, with a gravelled v/alk on the outer side of it within the circle which took up twelve rods of ground. What is the diameter of the circle, and what is the width of the walk ? ^nsw. The diameter 16 rods — Width of the walk 4 feet. 6. Neptune laid out 1000 square miles of the surface of the sea in a circle, and sold to Aeolus all that part of It which lies without a concentric circle of one third of the diameter. What is the diameter, and how much was sold ? .Snsw. The diameter 35.68 miles. The quantity sold 888.92 square miles. 7. A Farmer laid out an elliptical orchard, the longest diameter of which was 30 rods, and the shortest was 20 rods, and surrounded the same with a wall two feet thick, within the figure. What is the quantity within the wall, and how much is covered by it ? d. Q, R. Jinsio. Within the wall 'i .. 3 ..22 Covered by the wall, 9.3 rods. 8. From a point in an equilateral triangle, I measured the distances to each corner, and found them 20, 28, and 30 rods. Required the area and the length of the sides.* - .?- Q. R. Answ. The Area 5 .. 1 ..33 Length of each side 45 rods. 9. Required the dimensions of a parallelogram, containing one acre and a. half, bounded by 64 rods of fence. Answ. 12 by 20 rods. 10. The area of a parallelogram is five acres one quarter and thirty-five rods, and the diagonal is forty-three rods. Required the length of the sides. Ansio. 35 by 25 rods. 11. Required the dimensions of a parallelogram containing twenty-six acres one quarter and twenty-four rods, when the length exceeds the breadth by fifty-two rods. Ansiv, 44 by 96 rods. 12. Required the dimensions of a parallelogram containing 250 acres, when the sides are in the proportion of 7 to 3. Ansio. 130.93 by 305 1-2. 13. The state of Connecticut contains a little upwards of 4828 square miles, or 3,090,000 acres, including rivers, harbours, creeks, roads, &c. if this quantity of land is laid in a square, what will be the length of each side? M. Q. R. Answ. 69 .. 1 .. 75.11 JVote. In the Preface, it is observed that the Traverse Table in this book h calculated for any distance up to 50. After the Preface was printed, it was thought best to extend that Table to 70. The table of Logarithms is filso much more extensive, than is noticed in the Preface. * This may be solved geometrically. I ERRATA. Appendix page 89, line 22, for "less" read legs. « " 94 line 25, for "from 2 to 1" read/rom 2 to 3244 3264 3284 330J 332c 3345 3365 S38fi 3405 3425 21* 5 344i 346. ) 3486 350f 3526 3546 3566 3586 3606 3626 21 - 364C 366( ) 3686 370e 3726 3746 3766 3786 3806 3826 218 3846 386( ) 3885 390. . 3925 3945 3965 396c 400c 4025 219 4044 406- ! 4' 84 410' I 41-24 4143 4163 418i 4203 4223 NO. 1 2 3 4 i 5 6 1 7 8 9 A TABLE OF LOGARITHMS. No. 2200—2800. Log. 34ii42— 44716. ( NO. 1 2 3 4 . 5 6 7 1 8 i 9 1 220 34242 34262 34282 34301 34321 34341 34361 34380 34400 3442CJ 221 4439 4459 4479 4498 4518 4537 4557 4377 4396 4616 i22 4635 4655 4674 4694 4713 4733 4753 4772 4792 4811 223 4830 4850 4869 4889 4903 4928 4947 4967 4986 5005 224 5025 5044 5064 5083 5102 5122 5141 3160 5180 619£ 225 5218 5238 5257 5276 5295 5315 5334 5353 5372 5392 226 5411 5430 5449 5468 5488 5507 3526 5545 55641 6583 227 5603 5622 5641 5660 5679 5698 5717 3736 3735 3774 228 5793 5813 5832 5851 5870 5889 5908 5927 5946 5966 229 230 5984 6003 6021 6211 6040 6229 6059 6078 6097 6116 6133 6154 6173 6192 6248 6267 6286 6305 6324 6342 231 6361 6380 6399 6418 6436 6455 6474 6493 6311 6530 232 6549 6568 6586 6605 6624 6642 6661 6680 6698 6717 233 6736 6754 6773 6791 6810 6829 6847 6866 6884 6903 234 6922 6940 6959 6977 6996 7014 7C33 7051 7070 7088 235 7107 7125 7144 7162 7181 7199 7218 7236 7234 7273 236 7291 7310 7328 7346 7365 7383 7401 7420 7438 7457 237 7475 7493 7511 7530 7548 7666 7585 7603 7621 7638 238 7658 7676 7694 7712 7731 7749 7767 7785 7803 7822 239 240 7840 7858 7876 7894 7912 7931 8112 7949 7967 7985 8003 8166j 8184 8021 8039 8057 8075 8093 8130 8148 241 8202 8220 8238 8256 8274 8292 8310 8328 83461 8364 242 8382 8399 8417 8433 8453 8471 8489 85071 8525J &543 243 8561 8578 8596 8614 8632 8650 8668 8686 87031 8721 244 8739 8757 8775 8792 8810 8828 8846 8863 88811 8899 245 8917 8934 8952 8970 8987 9005 9023 9041 9038; 9076 246 9094 9111 9129 9146 9164 9182 9199 9217 9233! 9252 247 9270 9287 9305 9322 9340 9358 9375 9393 9410 9428 248 9445 9463 9480 9498 9515 9533 9550 9568 9585 9602 249 9620 9637 9655 9672 9690 9707 9881 9724 9742 9739 9777 99151 99331 9950 250 9794 9811 9829 9846 9863 9898 251 9967 9985 40002 40019 40037 40054 40071 40088:40106:40123 02611 02781 0295 232 4D140 40157 0175 0192 0209 0226 0243 253 0312 0329 0346 0364 0381 0398 0'415 04321 0449 0466 254 0483 0500 0518 0535 0552 0569 0588 0603J 0620 0637 255 0654 0671 0688 0705 0722 0739 0756 0773! 0790 0807 256 0824 084l 0858 0875 0892 0909 0926 0943 0960 0976 257 0993 1010 1027 1044 1061 1078 1095 1111 1128 1145 258 1162 1179 1196 1212 1229 1246 1263 1280 1296 1313 259 260 1330 1347 1363 1380 1397 1414 1430 1447 1 1464 1481 1497 1514 1531 1547 1564 1581 1597 1614! 1631 1547 261 1664 1881 1697 1714 1731 1747 1764 1780 1797 1814 262 1830 1847 1863 1880 1896 1913 1929 1946 19631 19791 263 1996 2012 2029 2045 206? 2078 2095 2111 2127 2144 264 2160 2177 2193 2210 2226 2243 2259 2275 2292 2308 265 ■2325 2341 2357 2375 2390 2406 2423 2439 2455 2472 266 2488 2504 2521 2537 2553 2570 2586 2602 2619 2635 267 2651 2667 2684 2700 2716 2732 2749 2765 2781 2797 268 2813 2830 2846 2862 2878 2894 2911 2927 29431 2959! 26e 270 2975 2991 3008 3169 3924 3040 3056 3217 3072J 3088: 3104 3120 3136 3152 3185 3201 3233: 3249 3263 3281 271 3297 3313 3329 3345 3361 3377 3393 3409 3425 3441 272 3^157 3473 1 3489 3505 3521 3537 3553 3569 3584 3600 273 3616 3632 36481 3664 3680 3696 3712 3727 3743 3759 274 3775 3791 3807 3823 3838 3854 3870 3886 3902 3917 275j 3933 394? 3965 3981 3996 4012 4028 4044 4059 4075 27f 4091 410- 4122 4138 4154 4170 4185 4201 4217 4232 ,27' n 4248 4264 4279 4293 4311 4326 43^12 4358 4373 4389 27f i 4404 442C 4436 4451 4467 4483 4498 4514 4529 4545 Hi ) 456C 457e 4592| 4607 4623 4638 4654 4669 4685 4700 no 1 2 i 3 4 5 6 7 8 p A TABLE OF LOGARITHMS. No. £800—3400. Log. 44716—53148. \ so ■28f 1 2 44747 3 4 5 6 1 7 8 9 44856 44716 44731 44762 44778 44793 44809 44824 44840 ■281 4871 48S6 4902 4917 4932 4948 4933 4979 4994 5010 •282 5025 5040 5056 507] 5086 5102 5117 5133 5148 5163 283 .5179 5194 5209 5225 6240 5255 5271 5286 5301 5317 284 5332 5347 6362 5378 5393 5408 5423 5433 5454 5469 285 5484 6500 5515 5530 5545 5561 5576 5531 5606 5621 28fi 5637 5652 5637 5682 5697 5712 5728 5743 5758 5773 287 5788 5803 5813 5834 5849 5834 5879 5894 5908 5924 288 5939 5954 5963 598^ 6000 6015 6030 6045 6060 6076 289 290 6090 6105 6120 6135 6150 6165 6180 6135 8210 6225 6240 6255 6270 6285 6300 6315 6330 6:345 6359 6374 291 6389 6404 6419 6434 6449 6464 6479 6434 6509 6523 292 6538 6553 6568 6583 6598 6613 6627 6642 6657 667^ 29E 6687 6702 6716 6731 6746 6761 6776 6790 6805 682C 294 6835 6850 6864 687f* 6894 6909 6323 6938 6953 6967 295 3982 6997 7012 7026 7041 7056 7070 7085 7100 7114 296 7129 7144 7159 7173 7188 7202 7217 7232 7246 7261 297 7273 7290 7305 7319 7334 7349 7363 7378 7392 7407 233 7422 743S 7451 7435 7480 7494 7503 7524 7538 7553 299 ;300 7567 7712 7582 7538 7311 7756 7625 7640 7654 7669 7813 7683 7698 7727 7741 7770 7784 7799 7828 7842 301 7857 7871 7885 7900 7914 7929 7943 7958 7972 798q 302 8001 8015 8029 8044 8058 8073 8087 8101 8116 8I3C 303 8144 8159 8173 8187 8202 8216 8230 8244 8259 8273 304 8287 8302 8316 8330 8344 8359 8373 8387 8401 8416 305 8430 8444 8458 8473 8487 8501 8515 8530 8544 8558 306 8572 8586 8601 8615 8829 86-13 8657 8671 8686 870C 307 8714 8728 8742 8756 8770 8785 8799 8813 8827 8841 308 8855 8869 8883 8837 8911 8926 8940 8954 8968 8982 309 310 8996 9010 3024 9164 903S 9178 9052 9066 9080 9220 9094 9108 9122 9136 9150 9192 9206 9234 3248 9262 311 9276 9290 9304 9318 9332 9346 9360 9374 9388 9402 312 9415 9429 9-143 9457 9471 9485 3499 3513 9527 9541 313 9554 9568 9582 9593 9810 9624 9638 9651 9665 9679 314 9693 9707 9721 9734 9743 9762 9776 9790 9803 9817 315 9831 9845 9859 9872 9888 9900 9914 9927 3941 9955 316 9969 9982 9996 50010 50024 50037 50051 5?j85 50079 50092 317 50106 50120 50133 0147 0161 0174 0188 0202 0215 0229 318 0-243 0256 0270 02S4 0297 0311 0325 0338 0352 0365 319 320 0379 0393 0406 0542 0420 0556 0433 0569 0447 0461 0598 0474 0488 0501 0515 0529 0583 0610 0623 0637 321 0651 0334 0378 0391 0705 0718 0732 0745 0759 0772 322 0786 0799 0813 0823 0840 0853 0866 0880 0893 0907 3-23 0920 0934 0947 0931 0974 0987 IC-Ol 1014 1028 1041 324 1055 lOGS 1081 1005 1108 1121 1135 1148 1162 1175 325 1188 1203 1215 1228 1242 1255 1268 1282 1295 1308 i'>6 1322 1335 "1348 1362 1375 1388 1402 1415 1428 1441 327 1455 1468 1481 1495 1508 1521 1534 1548 1561 1574 328 1587 1601 1614 1627 1640 1654 1637 1680 1693 1706 329 330 1720 1733 1746 1759 1891 1772 1786 1799 1812 1825 1838 1851 1865 1878 1904 1917 1930 1943 1957 1970 331 1983 1996 2009 2022 2035 2048 2031 2075 2088 2101 332 2114 2127 2140 2153 2166 2179 2192 2205 2218 2231 333 2244 i'257 2270 2284 2297 2310 2323 2336 0349 2362 334 2375 2388 2401 i414 2427 2440 2453 2466 ^9 2492 '^Sj 2504 2517 2530 2543 2556 2539 2582 2595 2608 2621 336 2634 2647 2360 2673 2686 2699 2711 2724 1737 2750 337 2763 2776 2789 2802 2815 2827 2840 2653 ifS66 2879 338 i>892 2905 2917 2930 29431 2956 2969 2982 2991 3007 339 3020 3033 3046 3058 3071 4 3084 3097 3110 7 3122 3135J NO. d 1 2 3 5 6 8 1 9 1 10 A TABLE OF LOGARITHMS. No. 3460—4000. Log. 53148—60206." | NO. 340 1 2 3 4 5 6 7 8 53250 9 53148 63161 53173 53186 63199 53212 53224 53237 53263 341 3275 3288 3301 3314 3326 3339 3362 3364 3377 3390 -3i9. 3403 3415 3428 3441 3453 3466 3479 3491 5504 3517 343 3529 3542 3655 3567 3580 3593 3605 3618 3631 3643 344 3656 3668 3681 3694 3706 3719 3732 3744 3757 3769 345 3782 3794 3807 3820 3832 3845 3857 3870 3882 3895 346 3908 3920 3933 3945 3958 3970 3983 3995 4008 4020 347 4033 4045 4058 4070 4083 4095 4108 4120 4133 4145 348 4158 4170 4183 4195 4208 4220 4233 4246 4258 4270 349 350 4283 4407 4296 4419 4307 4320 4332 4345 4357 4370 4382 4394 4432 4444 4456 4469 4481 4494 4506 4518 351 4531 4543 4555 4568 4580 4593 4605 4617 4630 4642 352 4654 4667 4679 4691 4704 4716 4728 4741 4753 4765 353 4777 4790 4802 4814 4827 4839 4851 4864 4876 4888 354 4900 4913 4925 4937 4949 4962 4974 4986 4998 5011 355 5023 6035 6047 5060 5072 5084 5096 5108 5121 6133 356 5145 5157 5169 5182 5194 6206 5218 6230 5242 5255 357 5267 5279 5291 6303 5315 5328 5340 5352 5364 5376 358 5388 5400 5413 5426 5437 5449 5461 6473 5485 5497 359 360 5509 5630 5622 6642 6534 5546 6666 5558 5670 5582 6594 5606 5618 6654 6678 5691 6703 6715 5727 5739 361 5751 5763 5775 5787 5799 5811 6823 6835 5847 5859 362 5871 6883 5895 5907 5919 6931 6943 5965 6967 5979 363 5991 6003 6015 6027 6038 6060 6062 6074 6086 6098 364 6110 6122 6134 6146 6158 6170 6182 6194 6205 6217 365 6229 6241 6253 6265 6277 6289 6301 6312 6324 6336 366 6348 6360 6372 6384 6396 6407 6419 6431 6443 6455 367 6467 6478 6490 6502 6514 6526 6638 6549 6561 6573 368 6586 6697 6608 6620 6632 6644 6656 6667 6679 6691 369 370 6703 6714 6832 6726 6844 6738 6750 6761 6773 6891 6785 6797 6808 6820 6855 6867 6879 6902 6914 6926 371 6937 6949 6961 6972 6984 6996 7008 7019 7031 7043 372 7054 7066 7078 7089 7101 7113 7124 7136 7148 7159 373 7171 7183 7194 7206 7217 7229 7241 7252 726^ 7276 374 7287 7299 ■7310 7322 7334 7345 7357 7368 7380 7392 376 7403 7415 7426 7438 7449 7461 7473 7484 7496 7507 376 7519 7630 7542 7563 7666 7576 7588 7600 7611 7623 377 7634 7646 7657 7669 7680 7692 7703 7715 7726 7738 378 7749 7761 7772 7784 7795 7B07 7818 7830 7841 7852 379 38C! 7864 7978 7875 7887 8001 7898 7910 7921 7933 7944 7955 7967 7990 8013 8024 8036 8047 8058 8070 8081 381 8092 8104 8115 8127 8138 8149 8161 8172 8184 8195 382 8206 8218 8229 8240 8262 8263 8274 8286 8297 8309 383 8320 8331 8345 8354 8365 8377 8388 8399 8410 8422 384 8433 8444 8466 8467 8473 8490 8501 8512 8524 8535 385 8546 8557 8569 8580 8591 8602 8614 8625 8636 8647 386 8659 8670 8681 8692 8704 8715 8726 8737 8749 8760 387 8771 8782 8794 8805 8816 8827 8838 8850 8861 8872 388 8883 8894 8906 8917 8928 8939 8950 8961 8973 8984 389 390 8995 9006 9017 9028 9140 9040 9061 9062 9073 9084 9095 9106 9118 9129 S151 9162 9173 9184 9195 9207 391 9218 :9229 9249 9251 9262 9273 9284 9295 9306 9318 392 9329 9340 9.351 9362 9373 9384 9395 9406 9417 9428 393 9439 9450 9461 9472 9483 9494 9506 9517 9528 9539 394 9650 9561 9572 9583 9594 9605 9616 9627 9638 9649 395 9660 9671 9682 9693 9704 9715 9726 9737 9748 9759 396 9770 9780 9791 9802 9813 9824 9835 9846 9857 9868 397 9879 9890 9901 9912 9923 9934 9945 9956 9966 9977 398 9988 9999 60010 60021 60032 60043 60054 60065 60076 60086 399 NO. 60097 60108 0119 0130 0141 0162 0163 0173 0184 0195 1 2 3 4 5 6 7 8 9 / A TABLE OF LOGARITHMS. II No. 4000—4600.- Log. 60206—66276. | NO. 1 2 3 4 5 6 7 8 9 400 60206 60217 80228 60239 60249 60260 60271 60282 60293 60304 401 0314 0325 0336 0347 0358 0369 0379 0390 0401 0412 402 0423 0433 0444 0455 0466 0477 0487 0498 0609 052C 403 0531 0541 0552 0563 0574 0584 0595 0606 0617 0627 404 0638 0649 0660 0670 0681 0692 0703 0713 0724 0735 405 0746 0756 0767 0778 0788 0799 0810 0821 0831 0842 406 G853 0863 0874 0885 0895 0906 0917 0927 0938 0948 407 0959 0970 0981 0991 1002 1013 1023 1034 1045 1055 408 1066 1077 1087 1098 1109 1119 1130 1140 1151 1162 409 410 1172 1189 1289 1194 1300 1204 1215 1321 1225 1236 1342 1247 1352 1257 1268 1374 1278 1310 1331 1363 411 1384 1395 1405 1416 1426 1437 1448 1458 1469 1479 412 1490 1500 1511 1521 1532 1642 1553 1663 1574 1684 413 1595 1606 1616 1627 1637 1648 1658; 1669 1679 1690 414 1700 1711 1721 1731 1742 1752 1763 1773 1784 1794 415 1805 1815 1826 1836 1847 1857 1868 1878 1888 1899 416 1909 1920 1930 1941 1951 1962 1972 1982 1993 2003 417 2014 2024 2034 2045 2055 2066 2076 2086 2097 2107 418 2118 2128 2138 2149 2169 2170 2180 2190 2201 2211 419 420 /'2221 2325 2232 2242 2252 2263 2273 2377 2284 2387 2294 2397 2304 2315 2335 2346 2356 2366 2408 2418 421 2428 2439 2449 2459 2469 2480 2490 2500 2511 2521 422 2531 2542 2552 2662 2572 2583 2693 2603 2613 2624 423 2634 2644 2655 2665 2675 2685 2696 2706 2716 2726 424 2737 2747 2757 2767 2778 2788 2798 2808 2818 2829 425 2839 2849 2859 2870 2880 2890 2900 2910 £32] 2931 426 2941 2951 2961 2972 2982 2992 3U0Z 3012 3022 3033 427 3043 3053 3063 3073 3083 3094 3104 3114 3124 3134 428 3144 .3155 3165 3176 3185 3195 3205 3215 3225 3236 429 430 3246 3256 3266 3276 3286 3296 3306 3317 3327 3337 3347 3357 3367 "3377 3387 3397 3407 3417 3428 3438 431 3448 3458 3468 3478 3488 3498 3608 3518 3628 3538 432 3.548 3558 3568 3579 3589 3599 3609 3619 362S 3639 433 3649 3659 3669 3679 3689 3699 3709 3719 372S 3739 434 3749 3759 3769 3779 3789 3799 3809 3819 382£ 3839 435 3849 3859 3869 3879 3889 3899 3909 3919 392£ 3939 436 3949 3959 3969 3979 3988 3998 4008 4018 4028 4038 437 4048 4058 4068 4078 4088 4098 4108 4118 4128 4137 438 4147 4157 4167 4177 4187 4197 4207 4217 422' 4237 439 44a 4246 4345 4256 4266 4276 4286 4296 4395 4306 4316 4326 4335 4434 4355 4365 4375 4385 4404 44141 4424 441 4444 4454 4464 4473 4483 4493 4603 4513 4525 4532 442 4542 4552 4562 4572 4582 4691 4601 4611 462: 4631 443 4640 4650 4660 4670 4680 4689 4699 4709 471S 4729 444 4738 4748 4758 4768 4777 4787 4797 4807 4816 4826 445 4836 4846 4856 4865 4876 4885 4896 4904 4914 4924 446 49.33 4943 4953 4963 4972 4982 4992 5002 5011 5021 447 6031 6040 5050 5060 6070 5079 6089 5099 5108 6118 448 51 2P 5137 5147 5167 5167 5176 5186 5196 620S 6215 449 450 5225 5234 5244 T341 6254 5263 5360 5273 6283 5292 5302 5312 5321 5331 6350 5369 6379 5389 5398 6408 451 .541 P 5427 5437 5447 5456 5466 6476 6486 6495 5604 452 5514 5523 5532 5543 6552 5562 6571 5581 5591 5600 453 561C 5619 5629 6639 5648 5658 5667 5677 5686 5696 454 570e 5715 5725 5734 5744 5753 5763 5772 5782 5792 455 580; 5811 5820 6830 5839 5849 5858 5868 5877 5887 456 589t 5906 5916 6926 5935 5944 5954 5963 6973 5982 457 5992 6001 6011 6020 6030 6039 6049 6068 6068 6077 458 608- 6096 6106 6115 6124 6134 6143 61,53 6162 6172 45S \'0 6181 6191 6200 6210 6219 6229 6 6238 6 6247 7 6257 6266 1 2 3 4 8 9 12 A TABLE OF LOGARITHMS. Nn 4f00 ^(^ Log 6627 5 71600 1 VB NO. 460 1 2 3 4 5 6 7 86332 66342 8 66351 9 66276 66285 66295 66304 66314 66S23 66361 461 6370 6380 6389 6398 6408 6417 6427, 6436 6445 6455 462 6464 C474 6483 6492 6502 6511 65211 6530 6539 6549 463 6558 6567 6577 6586 6596 6605 6614, 6624 6633 6642 464 6652 6661 6671 6680 6689 6699 6708 6717 6727 6736 465 6745 6755 6764 6773 6783 6792 68011 6811 6820 6829 466 6839 6848 6857 6867 6876 6885 6894 6904 6918 6922 467 6932 6941 6950 6960 6969 6978 6987 6997 7006 7016 468 7025 7034 7043 7052 7062 7071 7080 7089 7099 7108 469 470 7117 7127 7136 7145 7154 7164 7256 7173 7182 7191 7201 7210 7219 7228 7237 7247 7265 7274 7284 7293 471 7302 7311 7321 7330 7339 734R 73571 7367 7376 7385 472 7394 7403 7413 7422 7431 7440 7449 1 7459 7468 7477 473 7486 7495 7504 7514 7523 7532 7541 7650 7560 7569 474 7578 7587 7596 7605 7614 7624 7633| 7642 7651 7660 475 7669 7679 7688 7697 7708 7715 7724 7733 7742 7752 476 7761 7770 7779 7788 7797 7806 7815 7825 7834 7843 477 7852 7861 7870 7879 .7888 7897 7906 7916 7925 7934 478 7943 7952 7961 7970 7979 798S 7997 8006 8015 8024 479 480 8034 8124 8043 8052 8061 8070 8079 8088 1 8097 8106 8115 8133 8142 8151 8160 8169 8178 8187 8196 8205 481 8215 8224 8233 8242 8251 8260 8269 8278 8287 8296 482 8305 8314 8323 8332 8341 8350 8359 8368 8377 8386 483 8395 8404 8413 8422 8431 8440 8449 8458 8467 8476 484 8485 8494 8502 8511 8520 8529 8538 8547 8556 8565 485 8574 8583 8592 8601 ■8610 8619 8628 8637 8646 8655 486 8664 8673 8681 8690 8699 8708 8717 8726 8735 8744 487 8753 8762 8771 8780 8789 8797 8806 8815 8824 8833 488 8842 8851 8860 8869 8878 8886 8895 8904 8913 8922 489 490 8931 8940 8949 8958 8966 8975 ~9C6l 8984 8993 9002 9011 9099 9020 9028 9037 9046 9055 9073 9082 9090 491 9108 9117 9126 9135 9144 9152 9161 9170 9179 9188 492 9197 9205 9214 9223 9232 9241 9249 9258 9267 9276 493 9285 9294 9302 9S11 9320 9329 9338 9346 9355 9364 494 9373 9381 9390 9399 9408 9417 9425 9434 9443 9452 495 9461 9469 9478 9487 9496 9504 9513 9522 9531 9539 496 9548 9557 9566 9574 9583 9592 9601 9609 9618 9627 497 9636 9644 9653 9662 9671 9679 9688 9697 9705 9714 498 9723 9732 9740 9749 9758 9767 9775 9784 9793 9801 499 500 9810 9819 9827 9914 9836 9845 9854 9862 9871 9880 9888 9897 9906 9923 9932 9940 9949 9968 9966 9975 501 9984 9992 70001 70010 70018 70027 70036 70044 70053 70062 502 70070 70079 0088 0096 0105 0114 0122 0131 0140 0148 503 0157 0165 0174 0183 0191 0200 0209 0217 0226 0234 504 0243 0252 0260 0269 0278 0286 0295 0303 0312 0321 505 0329 0338 0346 0355 0364 0372 0381 0389 0398 0406 506 0415 043,4 0432 0441 0449 0458 0467 0475 0484 0492 507 0501 0509 0518 0526 0535 054^ 0552 056] 0569 0578 508 0586 0595 0603 0612 0621 0629 0638 0646 0655 0663 509 510 0672 0680 0689 0697 0706 0714 0723 0808 0731 0740 0749 0757 0766 0774 0783 0791 0800 0817 0825 0834 511 0842 0851 0859 0868 0876 0885 0893 0902 0910 0919 512 0927 0935 0944 0952 0961 0969 0978 0986 0995 1003 513 1012 102C 1029 1037 1046 1054 1063 1071 1079 1088 514 1096 1105 1113 1122 1130 1139 1147 1155 1164 1172 51.'i 1181 118£ 1198 1206 1214 1223 1231 1240 1248 1257 51 f 1265 127J 1282 1290 1299 1307 1315 132^ 1332 1341 51' 1349 135' 1366 1374 1383 1391 1399 1408 1416 1425 51f 1432 144 145C 145& 1466 147a 1483 1492 1500 1509 51J ) 151' 152. J 1533 1542 1550 155S 1567 1575 1584 1592 1 1 2 3 4 5 6 7 8 9 A TABLE OF LOGARITHMS, IS ' No. 5200—5800. Log. 71600—76^13, | NO.I 1 1 ' 520,71600,71609 2 71617 3 4 5 1 6 7 8 71667 9 716-25 71634 71642 71630 71659 71675 52r 1684 1692 1700 1709 1717 1725 1734 1742 1730 1759 522i 1767 1775 1784 1792 1800 1809 1817 1826 1834 1842 523 1850 1858 1867 1875 1883 1892 1900 1908 1917 1925 524 1933 1941 1950 1958 1966 1975 1983 1991 1999 2008 525 2016! 2024 2032 2041 2049 2057 2066 2074 2082 2090 526 2099 2107 2115 2123 2 J 32 2140 2148 2156 2165 2173 527 2181 2189 2198 2206 2214 2222 2230 2239 2247 2265 528 2263 2272 2280 2288 2296 2304 2313 2321 2329 2337 529 530 2346 2354 2362 2444 2370 2452 2378 2387 2393 2477 2403 2411 2419 2428 2436 2460 2469 2485 2493 2501 531 2509 2518 2526 2534 2542! 25501 2558 2567 2575 2583 532 2591 2599 2607 2616 26241 2632] 2640 2648 2656 2666 533 2673 2681 2689 2697 2705 2713! 2722 2730 2738 2746 534 2754 2762 2770 2779 2787 2795' 2803! 2811 2819 2827 535 2835 2843 2852 2860 2868 2876i 2884 2892 2900 2908 2989 536 2916 2925 2933 2941 2949 2957 2965 2973 2981 537 2997 3006 3014 3022 3030 3038 3046 3054 3062 3070 538 3078 3086 3094 3102 3111 3119 3127 3135 3143 3151 539; 3159 5401 3239 3167 3175 ^255 3183 3263 3191 3272 3199 3207 3215 3223 3231 3247 3280' 3288 3296 3304 3312 541 : 3320 3328 3336 3344 3352 3360 3368 3376 3384 3392 5421 3400 3408 3416 3424 3432 3440 3448 3456 3464 3472' 543 34801 3488 3496 3504 3512! 3520 3528 3536 3544 3552 3632 ,544! 3560| 3568 3576 3584! 35921 3600 3608 3616 3624 545' 3640! 3648 3666 36641 36721 3679 3687 3695 3703 3711 546] 3719 3727 3735 3743 3751 3759 3767 3775 3783 3791 547 3799 3807 3815 3823 3830 3838 3846 3854 3862 3870 5481 3878 3886 3894 3902 3910 3918 3926 3933 3541 3949 549; 3957 550 4036 3965 3973 4052 3981 3989 4068 3997 4005 40J3 4092 4020 4028 4044 4060 4076 4084 4099 4107 551 4115 4123 4131 4139 4147! 4155 4762 4170 4178 4186 552 4194 4202 4210 4218 4225 4233 4241 4249 4257 4266 553 4273 4280 4288 4296 ^304 4312 4320 4327 4335 4343 554 4351 4359 4367 4374 4382 4390 4398 4406 4414 4421 555, 4429 4437 4443 4453 446? 4468 4476 4484 4492 4500 556 4507 4515 452;J 4531 4J39 4547 4334 4662 4570 4578 557 4586 4593 4601 46091 4617 4624 4632 4640 4648 4656 558 4663 4671 4679 4R57 4695 4702 4710 4718 4726 4733 559 4741 560 4819 4749 4757 "5834 4764 4842 4772 4780 4788 4796 4803 4811 4827 4850 4858 4865 4873 4881 4889 561 1 4896 490* 4912 4920 4927 4935 4943 4950 4958 4968 562 4974 4981 4989 4997 5003 6012 3020 6028 6035 5043 563 5(^1 5059 5066 5074 3082 5089 5097 5105 5113 5120 564! ol28i 5136 5143 5151 5159 5166 3174 5182 5189 5197 565! 52051 5213 5220 5228 3236 5243 3251 5259 5266 5274 566 5282 5289 5297 5305 5312 5320 5328 5335 5343 5351 567' 5358! 5366 5374 5381 5389 3397 5404 3412 5420 3427 568 1 5435 5442 5450 5458 5465 5473 5481 5488 5496 5504 569; 5511 5519 570 5587J 5595 5526 5603 5534 5542 5549 5357 5565 5572 5580 5610 5618 5626 3633 5641 5648 5656 571 5664 5671 5679 5686 5694 6702 5709 5717 5724 5732 572 5740 5747 5755 5762 5770 3778 5785 5793 6800 5808 573 5815 5823 5831 5906 3838 3846 6833 6861 5868 5S76 3884 574 5891 5899 5914 5921 5929 5937 6944 6952 5959 575 5967 5974 5982 5989 5997 6005 6012 6020 6027 6035 576 6042 6050 6057 6065 6072 6080 6087 6095 6103 6110 6185 577 6118 6125 6133 6140 6148 6155 6163 6170 6178 578 6193 6200 6208 6215 6223 6230 6238 6245 6253 6260 .!>79 KO. 6268 6275 6283 6290 6298 6305 6313 6320 6328 6335 1 1 2 3 4 5 6 7 8 9 14 A TABLE OF LOGARITHMS. No. 6800— 6460. Log. '?(}it4JS— 80618. | HO. Oil 2 3 1 4 5 6 7 8 1 9 580 76543176350 76358 763651 76373 76380 76388 76395 76403 7641C 581 6418 6425 6433 64401 6448 6456 6462 6470 6477 6485 582 6492 6500 6507 6516 6522 6630 6637 6545 6562 6569 583 6567 6574 6682 6689 6597 6604 6612 6619 6626 6634 584 6641 6649 6666 6664 6671 6678 6686 6693 6701 6708 585 6716 6723 6730 6738 6745 6763 6760 6768 6775 6782 586 6790 6797 6805 68121 6819! 6827 6834 6842 6849 6856 587 6864 6871 6879 6886 6893 6901 6908 6916 6923 6930 588 6938 6945, 6953 6960 6967 6975 6982 6989 6997 7004 589 590 7012 7019 7026 7093; 7100 7034 7041 7048 7122 7066 7063 7070 7078 7085 7107 7116 7129 7137 7144 7161 591 7169 7166' 7173 7181 7188 7195 7203 7210 7217 7226 592 7232 7240' 7247 7264 7262 7269 7276 7283 7291 7298 593 7305 7313 7320 7327 7335 7342 7349 7367 7364 7371 594 7379 7386 7393 7401 7408 7416 7422 7430 7437 7444 595 7452 7459 7466 7474 7481 7488 7495 7603 7510 7517 696 7525 7532 7539 7546 7554 7561 7668 7676 7583 7690 597 7597 7606 7612 7619 7627 7634 7641 7648 7666 7663 598 7670 7677 7685 7692 7699 7706 7714 7721 7728 7735 599 600 7743 7760 7767 7764 7772 7779 7786 7793 7801 7873 7808 7815 7822 7830 7837 7844 7851 7869 7866 7880 601 7887 7896 7902 7909 7916 7924 7931 7938 7945 7952 602 7960 7967 7974 7981 7988 7996 8003 8010 8017 8026 603 8032 8039 8046 8063 8061 8068 8075 8082 8089 8097 604 8104 8111 8118 8125 8132 8140 8147 8164 8161 8168 606 8176 8183 8190 8197 8204 8211 8219 8226 8233 8240 606 8247 8264 8262 8269 8276 8283 8290 8297 8305 8312 607 S319 8326 8333 8340 8347 8365 8362 8369 8376 8383 8455 608 83SO 8398 8406 8412 8419 8426 8433 8440 8447 B09 610 8462 ^69 8540 8476 8647 8483 8554 8490 8497 8504 8512 8619 8526 8533 8561 8569 8676 86a3 8590 8597 611 8604 8611 8618 8625 8633 8640 8647 8654 8661 8868 612 8676 8682 8689 H696 8104 8711 8718 8726 8732 8739 613 8746 8753 8760 8'W 8774'. «781 8789 8796 8803 8810 614 8817 8824 8831 8838 «845| 8852 8869 8866 8873 8880 616 8888 8896 8902 8909 8^16! 8923 8930 8937 8944 8951 616 8958 8965 8972 8979 89861 8993 9(K)0 9007 9014 9021 9092 617 9029 9036 9043 9U6U 9057 1 "3064 9071 9078 9086 618 9099 9106 9113 9120 9127 1 91iH 9141 9148 9155 9162 619 620 9169 9176 9183 9190 9197 1 9204 nil 9281 9218 9225 9232 9295 9302 9239 9246 9263 9260 9267 1 9274 99,88 621 9309 9316 9323 9330 9337 9344 9351 96&e 9365 9372 62? 9379 9386 9393 9400 9407 9414 9421 9428 <1435 9442 623 9449 9466 9463 9470 9477 9484 9491 9498 95t« 9511 m4 9518 9625 9632 9539 954(] 955a 9560 9567 9574 ^581 625 9688 9696 9602 9609 96K 962a 963(J 9637 9644 965rt 69.6 9657 9664 9671 9678 968£ 9691ii 969!J 970b 9715 972C 697 9727 9734 974] 9748 9754! 9761 976fc 9775 9785 , 9789 69,8 9796 9803 9810 9817 9824! 9831 983- 9844 9851 9858 629 m 9865 9872 9879 9886 9893: 990C 990i 99ia 9921 » 9927 9934 9941 9948 9955 9962 996£ 99U 9982 998S 9996 fiSl 80003 8001(1 80017 8002^ 80030 8003'- 80044 80061 8005t 60065 639 (X)72 0079 008S 0092 0099 OlOC 01 la 0121 012' 0134 63? 014(1 0147 0164 016; 0168 017£ 0182 018i 019f ) 0202 634 0209 0216 022£ 022S 023f ) 024S 0251 025- 0264 (.0271 m 0277 0284 0291 0296 (mt > 0312 031!: 082£ 033i , 0339 63( 034^ 03,5fl 035f 0366 037i I 0381 0381 039a 040( ) 0407 637 0414 0421 042f 043^ 044 044? 046£ 0462 046f 0475 638 0482 048£ 049e 0502 050< ) 05ie 0523 063C 063e 0543 639 0550 0567| 056^ I 057C 057' 068^ 069] 6 0596 0604 [ 0611 9 NO J- 0' 1 1 1 2 3^ 4 6 7 6 A TABLE OF LOGARITHMS. 15 -VT^m^r^m. Log. 8661 §—34510. 1 NO. 1 1 2 3 4 5 6 " 7 8 9 640 80618,80625180632 80638 80645 80652 80659 86665180672 80679 641 0686 0693 0699 0766 0713 0720 0726 0733 0740, 0747 642 0754 07601 0767 0774 0781 1 0787 0794 0801 0808; 0814] 643 0821 0828 0835 0841 0848 0855 0862 0869 0875 0882 644 0889 0895 0902 0909 0916 0922 0929 0936 0943 0949 645 0956 0963 0969 0976 0983 0990 0996 1003 1010 1017 646 1023 1030 1037 1043 1050 1057 1064 1070 1077 1084 647 1090 1097 1104 1111 1117 1124 1131 1137 1144 1151 648 1158 1164 1171 1178 1184 1191 1551 1258 1198 1204 1211 1218 649 1224 1^1 '1238 1245 1266 1271 1278 1285 650 1291 1298 "1305 1311 1318; 1325 1331 1 1338 1345 1351 651 1358 1365 1371 1378 1385 1391 1398 1405 1411 1418 652 1425 1431 1438 1445 1451 1458 1465 1471 1478 1485 653 1491 1498 1505 1511 1518 1525 1531 1538 1544 1551 654 1558 1564 1571 1578 15&i 1591 1598, 1604 1611 1617 655 1624 1631 1637 1644 1551 1657 1664i 1671 1677 1684 656 1690 1697 1704 1710 17171 1723 1730, 1737 1743 1750 657 1757 1763 1770 1776 1783 1790 1796 1803 1809 1816 658 1823 1829 1836 1842 1849 1856 1862 1869 1876 1882 659 660 1889 1895 1902 1908 1915 1921 "1987 1928 1935 1994 2000 1941 1948 1954 1961 1968 1974 1981 2007 2014 661 2020 2027 2033 2040 2046 2053 2060 2066 2073 2079 662 2086 2092 2099 2105 2112 2119 2125 2132 2138 2145 663 2151 2158 2164 2171 2178 2184 2191 2197 2204 2210 664 2217 2223 2230 2236 2243 2249 2266 2263 2269 2276 665 2282 2289 2295 2302 2308 2315 2321 2328 2334 2341 666 2347 23.54 2360 2367 2373 2380 2387 2393 2400 2406 667 2413 2419 2426 2432 2439 2446 2462 2458 2465 2471 668 2478 2484 2491 2497 2504 2510 2617 2523 2530 2536 669 670 2543 2549 2556 2620 2562 2569 2676 2682 2688 2653 2595 2601 2607 2614 2627 2633 2640 2646 2659 2666 671 2672 2679 2685 2692 2698 2706 2711 2718 2724 2730 672 2737 2743 2750 2766 2763 2769 2776 2782 2789 2795 673 2802 2808 2814 2821 28271 2834 2840 2847 2863 2860 674 2866 2872 2879 2885 2892 2898 2905 2911 2918 2S24 675 2930 2937 2943 2950 2966 2963 2969 2976 2982 2988 576 2995 3001 3008 3014 3020 3027 3033 3040 3046 3052 677 3059 3065 3072 3078 3086 3091 3097 3104 3110 311T 678 3123 3129 3136 3142, 3149 3155 3161 3168 3174 318i 679 680 3187 3193 3257 3200 3264 3206: 32131 3219 3270 3276; 3283 3225 3289 3232 3238 3296 3302 3245 3251 3308 681 3315 3321 3327 3334 3340i 3347 3353 3359 3366 3372 682 3378 3385 3391 3398-3404! 3410 3417i 3423 3429 3436 683 3442 3448 3455 3461 3467 3474 3480] 3487 3493 3499 3563 684 3506 3612 3518 3525 3581 3537 3544: 3650 3656 685i 3569 3575 3582 3588 36941 3601 3607 3613 3620 3626 686 3632 3639 3645 3651 3668 3664 3670 3677 3683 3689 687 3696 3702 3708 3715: 3721 3727 3734 3740 3746 3753 688 3759 3765 3771 3778i 3784 3790 3797 3803' 3309 3816 689 690 3822 3885 3828 3891 3835 3897 3841 1 3847 3904 3910 3863 3916 3860 3923 3866| 3872 3929! 3936 3879 3942 691 3948 3954 3960 3967 3973 3979 3985 3992 3998 4001 692 4011 4017 4023 4029; 4036 4042 4048 4065 4061 4067 4130 693 4073 4080 4086 4092 4098 4105 4111 4117 4123 694 4136 4142 4148 4155 4161 4167 4173 4180 4186 4192 595 4198 4205 4211 4217 4223 4230 4236 42421 4248 4255 696 4261 4267 4273 4280i 4286 4292 4298 4305 4311 4317 697 4323 4330 4S36 4342 4348 4354 4361 4367 4373 4379 698 4386 4392 4398 4404: 4410 4417 4423 4429 4435 4442 699 4448 4454 1 4460 4466; 4473 4479 5 4485 6 4491 7 4497 4504 9 2 3 4 8 16 A TABLE OF LOGARITHMS. No. 7000—7600." Log. 845 l(i— 88(1)8 l' NO.I 1 2 1 3 4 1 5 1 6- 1 7 : 8 i 9 700 845 IC 84516 84522 84528 84535,84541 84547, 8456384569 84566 701 4572 4578 4584 4590 4597 4603 4609 46151 462li 4628 702 4634 4640 46461 4652 4658 4665 4671 4677j 4685! 4689 7031 4696 4702 4708 4714 4720 4726 4733 4739 4745 4751 704 4757 4763 4770 4776 4782 4788 4794 4800 4807 4813 705 4819 4825 4831 4837 4844 4850 4856' 4862 4868 4874 706 4880 4887 4893 4899 4905 4911 4917 4924 4930 4936 707 4942 4948 4954 4960 4967 4973 4979 4985 4991 4997 708 5003 5009 5016 6022 5t)28 6034 5040 50461 6062 5058 6120 709 710 5065 5071 5077 5083 6089 5095 5101 5107| 6114 6126 5132 5138 6144 5150 6156 6163 6169 .6175 6181 711 5187 6193 5199 5205 5211 5217 5224 5230 5236 6242 712 6248 6254 5260 5266 5272 6278 5285 52911 5297 5303 713 5309 5315 5321 6327 5333 5339 5345 6352 5368 5364 714 5370 5376 5382 5388 5394 5400 6406 5412 5418 6425 715 5431 5437 5443 5449 5455, 6461 5467 6473 6479 5485 716 5491 5497 5603 5509 5516 6622 5528 5534 6540 5546 717 5552 5558 5564 .5570 5576 5582 5588 5594 56001 6606 718 5612 5618 6626 5631 6637 5643 6649' 6655 5661 5667 719 720 5673 5679 6685 5691 5697 6703 6763 5709 5715 5769 3776 57211 5727 5733 5739 5745 5751 5757 67811 6788 721 5794 6800 5808 5812 5818 6824 5830 6836 6842 6848 722 5854 6860; 5866 5872 5878 5884 5890 6896 6902 5908 723 5914 6920 6926 6932 5938 5944 5950 5966 6962 6968 724 5974 5980 5986 5992 5998 6004 6010 6016 6022 6028 725 6034 6040 6046 6052 6058 6064 6070 6076 6082 6088 726 6094 6100 6106 6112 6118 6124 6130 6136 6141 6147 727 6153 6159 6165 6171 6177 6183 6189 6195 6201 6207 728 6213 6219 6225 6231 6237 6243 6249: 6256 6261 6267 729 730 6273 6279 6285 6291 6297 6303 6308 6368 6314J 6320; 6326) 6332 6338 6344 6350 6356 6362 6374 6380' 6386 731 6392 6398 6404 6410 6415 6421 6427i 6433 6439 6445 732 6451 6457 6463 6469 6476 6481 64871 6493 6499] 6504 733 6510 6516 6522 6528 6534 6640 6546i 6662 6558! 6564 734 6570 6576 6581 6587 6593 6599 6605' 6611 6617 6623 735 6629 6635 6641 6646 6652 6658 6664 6670 6676 6682 7Sfi 6688 6694 6700! 6705 6711 6717 6723 6729 6735' 6741 737 6747 6763 6759 6764 6770 6776 6782 6788 6794| 6800 7S8 6806 6812 6817 6823 6829 6836 6841 6847 6853 6859 739 740 6864 6923 6870 6876 6882 6941 6888 6894 6900 6906 6911J 6917 6929 6935 6947 6953 6958 6964 6970 6976 741 6982 6988 6994 6999 7005 7011 7017 7023 7029 7035 749. 7040 7046 7052 7058 7064 7070 7076 7081 7087 7093 743 7099 7105 7111 7116 7122 7128 7134 7140 7146 7151 744 7157 7163 7169 7176 7181 7186 7192 7198 7204 7210 7i5 7216 7221 7227 7233 7239 7245 7251 7256 7262 7263 746 7274 7280 7286 7291 7297 7303 7309 7315 7320 7326 747 7332 7338! 7344 7349 7356 7361 7367 7373 7379 7384 748 7390 7396 7402 7408 7413 7419 7425 7431 7437 7442 749 750 7448 7454 7460 7466 7471 7477 7483 7489 7547 7496 7500 7506 7512 7518 7523 7629 7636 7641 7552 7658 751 7664 7570 7576 7581 7587 7693 7599 7604 7610 7616 752 7622 7628 7633 7639 7646 7651 7656 7662 7668 7674 T53 7679 7685 7691 7697 7703 7708 77141 7720 7726 7731 754 7737 7743 7749 7764 7760 7766 7772 ,7777 7783 7789 755 7795 7800 7806 7812 7818 7823 7829 7836 7841 7846 756 7852 7858 7864 7869 7876 7881 7887 7892 7898 7904 767 7910 7915 7921 7927 7933 7938 7944 7950 7965 7961 758 7967 7973 7978 7934 7990 7996 8001 8007 8013 801.8 769 8024 8030 8036 8041 8047 8053 8058 8064 8070 8076 9 ko. 1 [ 2 3 4 5 6 7 8 A TABLE OP LOGARITHMS. 17 N 0. 7600—8200. Log 88081—91381. 1 NO. 1 2 , 3 1 4 5 1 6 7 1 8 1 9 76088081 88087 88093 38098 88104 88110 88160' 88121i88127!88133l 761 8138 8144 8150 8156 8161 8167 8173 81781 8184 8190 762 8196 8201 8207 8213 8218 8224 82301 8235: 8241 8247 763 8252 8253 8264 8270 8275 8281 8287, 8292 8298 8304 764 8309 8315 8321 8326 8332 8338 8343 8349 8355 8360 765 8366 8372 8377: 8383 8389 8395 8400 8406 8412 8417 766 8423 8429 8434, 8440 8446 8451 8457 8463 8468 8474 767 8480 8485 8491 8497 8502 8508 8513 8519 8525 8530 768 8536 8542 8547 8553 8559 8564 8570 8576 85811 8587! 769 770 8593 8649 8598 8655 8604 8660 8610 8666 8615 8672 8621 8677 862> 8683 8632 8689 8638 8694 8643 8700 8756 771 8705 8711 8717 8722 8728 8734 8739 8745 8750 772 8762 8767 8773 8779 8784 8790 8795 8801 8807 8812 773 8818 8824 8829 8835 8840 8843 8852 8857 8863 8868 774 8874 8880 8885- 8891 8897 8902 8903 8913 8919 8925 775 8930 8936 8941 8947 8953 8958 8964 8969 8975 8981 776 8986 8992 8997 9003 9009 9014 9O20 9025 9031 9037 777 9042 9048 9053 9059 9064 9070 9076 081 087 092 778 9098 9104 9109 9115 9120 9126 9131 137 143 148 779 9154 9159 9165 9170 9176 9182 9187 193 193 iOi 260 315 780 9209 9215; 9221 S226 9232 9237 9243 248 254 781 9265 9271 927S 9282 9287 9293 9298 304 310 782 9321 9326 9332 9337 9343 9348 9354 360 365 371 783 9376 9382 9387 9393 9398 9404 9409 415 421 426 784 9432 9437 9443 9448 9454 9459 9465 470 476 481 785 9487 9492 9498 9504 9509 9515 9520 626 531 537 786 9542 9548 9553 9559 9564 9570 9575 581 586 592 787 9597 9603 9609 9614 9620 9625 9631 636 642 647 788 9653 9658 9664 9669 9675 9680 9636 691 697 702 789 9708 9713 9719 9724 9730 9735 9741 746 752 757 790 9763 '97681 9774 9779 9785 9790 9796 801 807 812 791 9818 9823 9829 9834 9840 9845 9851 856 862 867 922 792 9873 9878 9883 9889 9894 9900 9905 911 916 793 9927 99331 9938 9944 9949 9955 9960 966 971 977 794 9982 9988' 9993 9998 90004 90009 90015 90020 90026 90031 795 90037 90042 '90048 90053 0059 0064 0069 0075 0080 0086 796 0091 0097 0102 0108 0113 0119 0124 0129 0135 0140 797 0146 0151 0157 0162 0168 0173 0179 0184 0189 0195 798 0200 0206 0211 0217 0222 0227 0233 0238 0244 0249 0304 799 0255 0260 0266 0271 0276 0282 0287 0293 0298 800 0309 0314 0320 0325 0331 0336 0342 0347 0352 0358 801 0363 0369 0374 0380 0385 0390 0396 0401 0407 C412 802 0417 0423 0128 0434 0439 0445 0450 0455 0461 0466 803 0472 0477 0482 0488 0493 0499 05(J4 0509 0515 0520 804 0526 0531 0536 0542 0547 0553 0558 0563 0569 0574 805 0580 0585 0590 0596 0601 0607 0612 0617 0623 0828 606 0634 0639 0644 0650 0655 0660 0606 0671 0677 0682 807 0687 0693 0698 0703 0709 0714 0720 0725 0730 0736 808 0741 0747 0752 0757 0763 0768 0773 0779 0784 0789 0843 809 0795 0800 0806 0811 0816 0822 0827 0832 0838 810 0849 0854 0859 0865 0870 0875 0881 0886 0891 0897 811 0902 0907 0913 0918 0924 0929 0934 0940 0945 0950 312 0956 0961 0966 0972 0977 0982 0988 0993 0998 1004 813 1009 1014 1020 1025 1030 1036 1041 1046 1052 1057 814 1062 1068 1073 1078 1084 1089 1094 1100 1105 1110 815 1116 1121 1126 1132 1137 1142 1148 1153 1158 1164 816 1169 1174 1180 1185 1190 1196 1201 1206 1212 1217 1270 817 1222 1228 1233 1238 1243 1249 1254 1259 1265 818 1275 1281 1286 1291 1297 1302 1307 1312 1318 1323 819 132« 1334 1339 1344 1350 1355 1360 1365 1371 1376 NO. i 1 2 3 4 5 i 6 ' 8 9 16 A TABLE OF LOGARITHMS. No. "8200—8800. Log. 91381— 94448. f NO.I 1,2 3 4 5 6 , 7 8 9 820,9138191387,91392 91397 91403 91408 9141391418 91424 91429 821 1434 1440 1445 1450 1455 1461 1466! 1471 1477 1482 822 1487 1492 14S8 1503 1508 1514 1519! 1524 1529 1535 823 1540 1545 1661 1556 1661 1566 1672: 1577 1582 1587 824 1593 1598 1603 1609 1614 1619 1624t 1639| 1635 1640 825 1645 1651 1656 1661 1666 1672 1677' 16821 1687 16931 826 1691 1703 1709 1714 1719 1724 1730i 17351 1740 17451 827 1751 1756 1761 1766 1772 1777 1782 17871 1793 17981 828 1803 1808! 1814 1819 1824 1829 1834 1840! 1845! 1850| 829 830 1855 1861 1866 1918 1871 1876 1882 1887 1892 1897! '^O^j 1908 1913 19241 1929 1934 1939 1944 1950 19651 831 1960 1965 1971 19761 1981! 1986 1991 19971 2002j 2007 832 2012 2018 2023 2028 2033! 2038 2044 2049 2064: 2069 833 2065 2070 2076 2080 2086! 2091 2096 2101 2106! 2111 834 2117 2122 2127 2132 2137 2143 2148 2153 2158i 2163 835 2169 2174 2179 21841 2189 2195 2200 2203» :i21D! 2215 836 2221 2226 2231 2236 2241 2247 2252 2267^ 2262| 2267 837 2273 2278 2283 2288' 2293 2298 2304 23091 2314! 2319 838 2324 2330 2335 2340 2345 2350 2356 2361, 2366 2371 839 840 2376 2381 2387 2392 2397 2443 2449 2402 2454 2407 2412 2459 2464 2418: 24231 2428 2433 2488 2469 2474 841 2480 2485 2490 2496 2500 2605 2511 2516 2521' 2526 842 2531 2536 2542 2547 2552 2557 2662 2667 2672 2578 843 2583 2588 2593 2698 2603 2609 2614 2619 2624 2629 844 2634 2639 2645 2650 2655 2660 2665 2670 2675 2681 845 2686 2691 2696 2701 2706 2711 2716 2722 2727 2732 846 2737 2742 2747 2752 2758 2763 2768 2773 2778 2783 847 848 2788 2793 2799 2804 2809 2814 2819 2824 2829 2834 2840 2845 2850 2856 2860 2865 2870 2875 2881 2886 849 850 2891 2896 2901 2906 2911 2916 2921 2927 2932 29371 2942 2947 2952 2957 2962 2967 2973 2978 2983 2988! 851 2993 2998 3003 3008 3013 3018 3024 3029 3034: 3039 852 3044 3049 3054 3059 3064 3069 3075 3080 3085 3090 853 3095 3100 3106 3110 3115 3120 3125 3131 3136 3141 854 3146 3151 3156 3161 3166 3171 3176 3181 1 3186 3192 855 3197 3202 3207 3212 3217 3222 3227 3232: 3237 3242 856 3247 3252 3258 3263 3268 3273 3278 3283! 3288 3293 857 3298 3303 3308 3313 3318 3323 3328 3334! 3339 3344 858 3349 3354 3359 3364 3369 3374 3379 3384j 3389 3394 859 860 3399 3404 3455 3409 3414 3420 3465 3470 3425 3430 3435 1 3440 3445 3450 3460 3475 3480 34851 3490 3495 861 3500 3505 3510 3515 3520 3526 3631 3536! 3541 3546 862 863 3551 3556 3661 3566 3571 3576 368L 3586: 3591 3596 3601 3606 3611 3616 3621 3626 3631 3636! 3641 3646 864 36511 3656 3661 3666 367 r 3676 3682 3687' 3692 3697 865 3702; 3707 3712 3717 3722 3727 3732 3737 3742 3747 866 37521 3767 3762 3767 3772 3777 3782 3787i 3792 3797 867 3802, 3807 3812 3817 3822 3827 3832 3837! 3842 3847 868 3852 3857 3862| 3867 3872; 3877 3882 3887; 3892 3897 869 3902 3907 3912 3917 3922 3927 3932 3937; 3942 3947 870 3952 3957 3962 3967 3972; 3977 3982 3987 3992 3997 871, 4002 4007 4012 4017 4022: 4027 4032 4037 4042: 4047 872i 4052 4057 4062 4067 4072 4077 4082 4086 4091! 4096 873; 4101 4106 4111 4116 4121 4126 4131 4136 41411 4146 874 4151 4166 4161 4166 417a 4176 4181 4186 4191 4196 875 42011 4206 4211 4216, 4221 4226 4231 4236 4240 4246 876 4250| 4255 4260 4265! 4270 4275 4280 4286 4290 4296 877 878 4300i 4305' 431(1 43151 4320 4325 4330^ 4335 4340 4345 4349i 4354 4359 4364! 4369 4374 4379! 4384 4389 4394 4438 4443 879 4399' 4404 4409 4414! 4419 4424 4429 4433 NO. 1 2 3 1 4 ^5_ 6 1 7 8 9 A TABLE OP LOGARITHMS. 1^ TRSTssiKv-glwJ: Log . 94448—97313. | NO. 1 j 2 1 3 4 5 16. 7" 8 1 9 880 94448 g4453'94458'94463 94468 94473!9447894483 94488,94493 881 4498 4503' 4507' 4512 4517 4522 4527 4532 45371 4542 882 4547 4552; 4557; 4562 4567 4571 4576 4581 4586; 4591 883 4596 4601 4606 4611 4616 4621 4626 4630 4635J 4640 884 4645 4650 4655 4660 4665 4670 4675 4680 46851 4689 885 4694 4699 4704 4709 4714 4719 4724 4729 4734 4738 886 4743 4748 4763 4758 4763 4768 4773 4778 4783 4787 887 4792 4797 4802 4807 4812 4817, 4822 4827 4832 4836 888 4841 4846 4851 4856 4861 4866 4871 4876 4880: 4885 889 890 4890 4895 4900 4949 4905 4910 4915 4919 4963 4968 4924 4973 4929. 4934 4939 4944 4954 4959 49781 4983 891 4988 4993 4998 5002 5007 5012 6017 5022 50271 5032 892 5036 5041 5046 5051 5056 50611 5066 5071 5075; 5080 893 5085 5090 5095 5100 5105 5109 5114 5119' 51241 5129 894 5134 5139 5143 5148 5153 5158 5163 51681 5173, 5177 895 5182 5187 5192 5197 5202 5207 5211 5216 5221 5226 896 5231 5236| 5240 5246 5250 5255 5260 5265 5270 5274 897 5279 6284! 5289 5294 5299 6303 5308 5313 5318 5323 898 5328 5332 5537 5342 5347 5352 5357 6361 5366 5371 899 6376 5381 6386 5390 5395 5400 5405 5410 5416 5419 900 5424 5429 5434 5439 5444 5448 5453 5458 1 5463 5468 901 5472 5477: 5482 5487 5492 5497 5501 5506 6511 5516 902 5521 5525' 5530 5535 5540 5545 5650 5554: 5559 5564 903 5569 5574: 5578| 5583 5588 5693 5698 6602 5607 5612 904 5617 56221 56261 5631 5636 5641 5646 6660 5655 5660 905 5665 5670 56741 5679 5684 5689 5694 5698 5703 5708 906 5713 5718! 57221 5727 5732 5737 5742 6746 5751 5756 907 5761 5766i 5770 5775 5780 5785 5789 5794 5799 5804 908 5809: 5813 6818i 5823 5828 5832 5837 5842 5847 5852 909 5856 5861 5866; 5871 5875 6880 5885 5890 5895 5899 910 5904; 5909 5914i 5918 5323, 5928 5933 5938 5942 5947 911 5952| 5957 5961! 5966 5971 5976 5980 5985 5990 5995 912 5999i 6004; 6009| 6014, 6019 6023 6028 6033 6038 6042 913 6047' 6052 6057| 6061' 6066 6071 6076 6080 6085 6090 914 6095 6099 6104! 6109 6114 6118 6123 6128 6133 6137 916 6142 6147 61521 6156 6161 6166 6171 6175 6180 6185 916 6190 6194 6199 6204 6209 6213 6218 6223 6227 6232 917 6237 6242 6246; 6251 6266 6261 6265 6270 6275 6280 918 6284 6289 62941 6298 6303 6308 6313 6317 6322 6327 919 6332 6336 6341 6346 6350. 6356 6360 6365 6369 6374 920 6379 6384 63881 6393 6398, 6402 6407 6412 6417 6-121 921' 6426 6431 6435 6440 6445 6450 6454 6459 6464 6468 922 6473 6478 6483 6487 6492 6497 6501 6506 6511 6515 923 6520 6525 6530 6534 6539 6644 6548 6553 6558 6562 924 6567 6572 6577 6581 6586 6691 6596 6600 6605 6609 925' 6614 6619 6624 6628 6633 6638 6642 6647 6652 6656 926 6661 6666 6670 6675 6680 6685 6689 6694 6699 6703 927 6708 6713 6717 6722 6727 6731 6736 6741 6745 6750 928 6755 6759 6764 6769 6774 6778 6783 6788 6792 6797 929; 6802 6806 6811 6816 6820 6825 6830 6834 6839 6844 930 6848 6853 6858 6862 6867 6872 6876 6881 6886 6890 931 6895 6900 6904 6909 6914 6918 6923 6928 6932 6937 932 6942 6946 6951 6956 6960 6965, 6970 6974 6979 6984 933 6988 6993 6997 7002 7007 70111 7016 7021 7025 7030 934 7035 7039 7044 7049 7053 70681 7063 7067 7072 7077 935 7081 7086 7090 7095^ 7100 71041 7109 7114 7118 7123 936 7128 7132 7137 7142 7146 71511 7155 7160 7165 7169 937 7174 7179 7183 7188 7192 7197 7202 7206 7211 7216 938 7220 7225 7230 7234 7239 7243 [ 7248 7253, 7267 7262 939 7267 7271 7276 7280 7285. 7290. 7294 7299, 7304, 7308 No.l 1 1 1 2 .| 3 1 4 1 5 1 6_^ 7 19 19 ZQ A TABLE OP LOGARITHMS. "Nd."9400~l(X)00. Log. 97313—9 9996. NO., . 1 i 2 I 3 , 4 5_|_^,_2 L_l^_ 940 97313 97317 97322 97327 97331 97336 97340 97345 97350 97354 941 7359i 7364; 7368! 7373i 7377 7382 7387 7391 7396 7400 942 7405^ 7410' 7414' 7419 7424 7428 7433 7437 7442 7447 943 7451' 74561 7460! 7465: 7470 7474 ■ 7479 7483 74881 7493 944 7497' 7502' 7606! 7511 7516 7520 7525 7529 7534} 7539 945 7643 7548' 7552: 7567' 7562 7566 7571 7575 7580 7585 946 7589 7594 7598 7603 7607 7612 7617 7621 7626 7630 947 7635 7640 7644 7649 7653 7658 7663 7667 7672 7676 948 7681 7685 7690 7695 7699 7704 7708 7713 7717} 7722 949 7727 7731 7736: 7740; 7745 7749 7754 7759 7763] 776j 950 'iTTO'rm 1782 ~7786i 7791 ~7795 7800 7804 78091 7813 951 7818 7823 7827' 7832 7836 7841 7845 7850 7855: 7859 962 7864 7868 7873 7877: 7882 7886 7891 7896 7900i 7905 953 7909: 7914 7918 7923' 7928 7932 7937 7941 79461 7950 954 79561 7950 7964 7968! 7973 7978 7982 7987 7991! 7996 955 8000| 8005 8009 8014; 8019 8023 «Q28 8032 8037! 8041 956 8046' 8050 8055 8069 8064 8068 8073 8078 8082J 8087 957 80911 8096 8100 8105' 8109 8114 811^ 8123 8127 8132 958 8137 8141 8146 8150 8155 8159 8164 8168 81731 8177 959 8182! 8186 8191, 8195 8200 8204 8209 8214 8218 ; 822 3 980 6227! "8232 "8236''8241!'"8245 "8250 8254 8259 8263 "8268 961 8272! 8277 8281 8286! 8290 8295 8299 8304 8308; 8313 962 8318i 8322 8327 8331 ! 8336 8340 8345 8349 8354] 8358 963 8363; 8367 8372 8376' 8381 8385 8390 8394 8399! 8403 964 8408; 8412 8417 8421' 8426 8430 8435 8439 8444: 8448 965 8453 8457 8462 8466' 8471 8475 8480 8484 8489' 8493 966 8498 8502 8507 8511; 8516 8520^ 8525 8529 8534; 8538 967 8543 8647 8552 85561 8661 8666 8570 8574! 8579] 8583 968 8588 8592 8597 86011 8605 8610 8614 8619 8623i 8628 969 - 8632 8637 8641 ■ 8646; 8650 8655 865 9 8664 8668 ! 8673 970 8677 "8682 "8686 8691! 8695 8700 8704 8709 8713! 8717 971 8722 8726 8731 8735: 8740 8744 8749 8753: 8758! 8762 972' 8767 8771 8776 8780 8784 8789 8793 8798' 88021 8807 973 8811 8816 8820 8826) 8829 8834 8838 8843: 8847| 8851 974 8866; 8860 8866 8869 8874 8878 8883 8887, 8892; 8896 8905; 8909 89141 8918 8923 8927 8932; 89361 8941 8949 8954 8958| 8963 8967 8972 8976i 8981! 8985 8994 8998 90031 9007 9012 9016 9021' 9026 9029 047j 052 056 061 065i 0691 074 092' 096 100| 105 149 193 238 976 8900 976 8946 977 8989 978; 9034 979: 9078 Jlrtificial Sines, Tangents, and Secants. 2 1 Mi Sine , C. Sine Degree. 0.0000010.00000 5 7.16270] 00 10 46373 00 15, 63982' 00 20' 76475, 9.99999 25, 86166i 99 30 940841 98 35 8.00779 9.99998 0657S 11693 16-268 20407 24186 C. Sine! Sine Tang. ,C.Tang, Secant. iC. Sec.i M O.OOOOOI Infinite 7. 16270! 12. 83730 46373 63982 76476 86167. 94086! 53627 36018 23524 13833 05914 10,000001 Infinitel 60 00 12.83730; 65 00 53627, 50 8.0078111.99219 06581 i 1169S| 16273 20413 241921 93419 88304 83727 79587 75808 C.Tan?.! Tana 36018' 45 23525' 40 13834' 35 05915 30 10.0000211.99221 25 03 04 05 06 07 C. Sec. 93422 20 88307 i 15 83732 10 79593! 6 75814 Secant M 89 Degrees. 1 Degree. M Sine i C. Sine; Tan?. C.Tang.i Secant. C. Sec. M 8.241861 9.99993i 8,2419211.75808 27661 30879 33875 36678 39310 41792 92! 276691 91 i 30888! 89 33886 j 88 366891 87 1 39323 85 41807 72331 69112 66114 63311 60677 58193 10.00007 08 09 11 12 13 15 11.75814: 60 72339' 55 69121! 50 66125 45 63322 40 60690' 35 58208 30 8.44139, 4636& 48485 50505 52434 54282 9.99983 8.44156 11.55844 ia00017ill. 558611 25 82' 46385 536151 18| 53634 20 80 48505 51495 20! 51515 15 78 50527 49473 22' 49495 10 76' 52459 47541 24! 47566 5 74 54308 45692 26i 45718 C. Sine' Sine C .Tang. I Tang. | C. Sec! Secant.! M 88 Degrees. 2 Degrees. Ml Sine C. Sine; Tang. C.Tang.| Secant , C. Sec. | M 9.99974 8.54308 11.45692* 10.00026|ll.45718!"60 22 Artificial Sines, Tangents, and Secants. 3 Degrees. .| M Sine C. Sine Tang. C.Tang. Secant 8.71940 1 1.28060, 10.0006C C. Seel M] C 8.7188C 9.99940 11.28120 60 5 7306S 37 73132, 2686{ 63, 26931 55 1( 74226 3^ 74292, 25708 66 25774 60 IS 75353 30 75423 24577 70 24647 45 2( 7645] 26 76525: 23475 74 2354E 40 25 77522 2i 77600: 2240( 77. 22478 35 30 78567 19 78649; 21351 8.79673 11.20327 81 10.-0008S ! 21433 30 35 8.79588 9.99915 11.20412 25 40 80585. 11 80674 19326 89 19415 20 45 81560, 07 816531 18347 93 18440 15 50 82513' 03 82610! 1739C 97 17487 10 55 83446 98898 83547' 16452 102! 16554 5 60 84358 894 84464 15536 106 ! 15642 1 Secant Ivi Ml G. Sine Sine C.Tang.' Tang. IC. Sec. 86 Degrees. 4 Degrees. M Sine C. Sine Tang. C.Tang. Secant C. Sec. fll 8.84358 9.99894 8.84464 11.16536 10.00106 11.15642 60 5 85252 890 8536E 14637 110 14748 65' 10 86128 885 8624£ 13757 115 13872 50 15 86987 880 87106 12894 120 13013 45 20 87829 876 87953 12047 124 12171 40 25 88654 671 88783 11217 129 11346 3,7 30 89464 866 89598 8.90399 10402 134 10536 30 25 35 8.90260 9.89861 11.09601 10.00139 11.09740 40 91040 856 91185 08815 144 08960 20 45 91807 851 91957 08043 149 C8193 15 50 92561 845 92716 07284 155 07439 "1 55 93302 840 93462 06538 160 06698 5 60 94030 834 Sine 94195 05805 166 05970 C. Sec. Secant M! C. Sine C.TangJ: Tang. 85 Degrees. | Degrees. g ftl Sine 1 C. Sine' Tang, j C.Tang. Secant jC. Sec W Oj 8.94030 9.99834 8.94195 11.05805,10.00166 11.05970, 6Q 5 94746 829 94917 05083 171 05254 55 10 95450 823 95627 04373 177 04550 50 15 961431 817 96325 03675 183 03857 45 20 968251 812 97013 02987 188 03175 40 25 97496 806' 97691 02309 194 02504 35 30 98157 800 98358 01642 200 01843 30 25 35 8.98808 9.99794 1 8.99015 11.00985 10.00206 11.01192 40 99450 787 99662 00338 213 00560 20 45 9.00082 781 9.00301 10.99699 219 10.99918 15 60 .. 00704 775 00930 99070 225 99296 10 65 01318 768 01550 98450 232 98682 5 60 01923 761 02162 97838 239 98077 M "Ml C. Sine Sine C.Taiig. Tang. C. Sec. Secant 84 Degrees. 1 Artificial Sines, Tangents, and Secants. 23 6Degrees. Mj Sine C. Sine Tang. C.Tang. Secant | C. Sec. M 9.01924 9.99761 9.0216210.9783810.0023910.98076 60 02520 03109 03690 04263 04828 05386 755 7481 741! '734! 727 1 720: 02765 03361 03949 04528- 05101 05666 97235 96639 96051 95472 94334 245 352 259 2661 273 280, 97480 55 96891 50 96310 45 95737 40 95172 35 94614; 30 9.05937 06481 07018 07548 08072 08589 9.99713 9.06224 10.93776 10.00287 10.94063| 25 705 i 698i 6901 683: 675: 06775 07320 07858 08389 08914 93225 295 92680 302 92142 310 91611 3171 91086 325i 935191 20 92982! 15 92452 91928 91411 C. Sine Sine C.Tana;. Tan?. C. Sec. Secant M 83 Degrees. 7 Degrees. M "0 5 10 15, 2o: 25 30 Sine I C. Sine; Tang. jC.Tang. Secant C. Seel M 9.08589| 091011 096061 10106 10599 11087 11670 10.00325 10.91411 60 333, 90899, 55 9.99675 9.0891410.91086 667| 09434 90566 669 1 09947 900531 341 ' 90394; 50 661 10454 89546] 349| 89894 45 643 10956 89044, 357; 89401: 40 635 11452 885481 3651 88913i 35 627 11943! 880571 373 88430 30 t;. 120471 12619 129851 13447! 13904! 143561 9.99618i 9.12428:10.87572 610! 12909' 87091 602! 133841 86616 6^1 13864! 86146 5841 14320! 85680 575' 14780! 86220 10.00382 10.87963 25 390, 87481! 20 398: 4071 416: 4251 87015! 15 86563' 10 86098: 5 85644' M C.Sine Sine C.Tang.' Tang. iC. Sec' Secant i M 82 Degrees. 8 Degrees. M Sine | C. Sine| Tang. , C.Tang. | Secant |C. Sec.! JM 9.995761 "9. 14780 10.86220, 1000425 ,1085644 ! ~60 9.14356 14803! 15245 15683; 16116: 16545 16970 566 557 548 539 530 520i 9.17391 178071 182201 18628| 19033 194331 15236 84764 434 15688 84312 443 16135 83865 452 16677 83423 461 17016 82984 470 17450 82560 480 85197! 55 84765! 50 843171 45 838841 40 83455 35 83030 30 9.99611 9.1788010.82120 10.00489 10.82609 25 501 492 482 472 462 M C. Sine 18306 81694 499 82193 18728 81272 508 81780 19146 80854 518 81372 19561 80439 528 80967 19971 80029 538 C. Sec. 80567 Secant C.Tang. Tang. 81 Degrees. ^4 Artificial Sines, Tangents, and Secants. 9 Degrees. | M Sine C. Sine Tang. C.Tang. 10.80029 Secant C. Sec. M 60 9.19433 9.99462 9.19971 10.00538 10.80567 5 19830 452 20378 79622 548 80170 55 10 20223 442 20782 79218 558 79777 50 15 20613 432 21182 78818 568 79387 45 20 20999 421 21578 78422 579 79001 40 25 21382 411 21971 78029 589 78618 35 30 21'761 400 22361 9.22747 77639 600 78239 30 35 9.22137 9.S9390 10.77253 10.00610 10.77863 25 40 22509 379! 23130 76870 621 77491 20 45 22878 368 23510 76490 632 77122 15 50 23244 357 23887 76113 643 76756 10 55 23607 346 24261 75739 654 76393 5 60 23967 335 24632 75368 665 76033 M C. Sine Sine C.Tang Tang. 'C. Sec. Secant M 80 Degrees. 10 Degrees. M Sine C. Sine Tang. C.Tang. Secant C. Sec. M 60 9.23967 9.99335 9.24632 10.75368 10.00665 10.76033 5 24324 324 25000 75000 676 75676 55 10 24677 313 25366 74635 687 75323 60 15 25028 301 25727 74273 699 74972 45 20 25376 290 26086 73914 710 74624 40 25 25721 278 26443 73557 722 74279 35 30 26063 267 26797 73203 733 73937 30 25 35 9.26403 9.99255 9.27148 10.72852 10.00745 10.73597 40 26739 243 27496 72504 757 73261 20 45 27073 231 27842 721581 769 72927 15 50 27405 219 28186 718141 781 72595 10 55 2773.1 207 28527 71473! 793 72266 5 60 28060 195 28865 71135 Tang. 806 71940 M M C. Sine Sine C.Tang. C. Sec. Secant 79 Degrees. nBegrees. M Sine C. Sine 9.99195 Tang. C.Tang., Secant C. Sec. M 9.28060 9.28865 10.71135 10.00805 10.71940 60 5 28384 182 29201 70799 818 71616 55 10 28705 170 29535 70465 830 71295 50 15 29024 157 29866 70134 843 70976 45 20 29340 145 30195 69805 855 70660 40 25 29654 132 30522 69478 868 70346 35 30 85 29966 9.30275 119 30846 69154 881 70034 30 25 9.99106 9.31168 10.68832 10.00894 10.69725 40 30582 093 31489 68511 907 69418 20 45 30887 080 31806 68194 920 69113 15 50 31189 067 32122 67878 933 68811 10 55 31490 054 32436 67564 946 68510 5 60 M 31788 040 32748 67252 960 68212 C. Sine Sine C.Tang. Tang. IC. Sec. Secant M| 78 Degrees. | .Mrtijicial Sines, Tangents, and Secants. 25 ^ 12 Degrees. . M Sine C. Sine Tang. jC.TangJ Secant 9.32747110.67253 10.00960 C. Sec.| M 9.31788 9.99040 10.682121 60 6 32084 99027! 33057 669431 00973 67916 65 10 32378 99013 33365 66635 00987 67622 50 15 32670 99000' 33670 66330; 01000 67330 45 20 32960 98986 33974 66026 01014 67040 40 25 33248 98972' 342761 65724 01028 66752 35 30 33534 98958 345761 65424 9.34874! 10.66126 01042 66466 30 25 35 9.S3818 9.98944 10.01056 10.66182 40 34100 98930 35170 64830 01070; 65900 20 45 34380 98916 35464 64536 01084! 65620 16 50 34658 98901 35757 64243 01099! 65342 10 55 34934 98887 36047 63953 01113 65066 5 60 36209 98872 36336 63664 01128 64791 M -M C. Sine Sine C.Tang. Tang. C. Sec. Secant 77 Degrees. 13 Degrees. \ Mi Sine C. Sine Tang. 9.36336 C.Tang. Secant 10^1128 C. Sec; Mi 9.36209 9.98872 10.63664 10.64791 60 5 35482 98858 36624' 63376 01142 64518 55 10 35752 98843 36909| 63091 01157 64248 50 15 36022 98828 37193; 62807 01172 63978 45 20 36289 98813 37476i 62524! 01187 63711 40 25 36555 98798 37758 62244 01202 63445 35 30; 36818 98783! 38035! 61965 9.98768' 9.38313 10.61687 01217 63182 30 35 9.37081 10.01232 10.629191 25 40 37341 98733! 38589 61411 012471 62659! 20i 45 37600 98737 38863 611371 01263! 62400 15 60 a785S 98722 89136 60864; 01278 62142 10 55 38113 98706 39407 60593 01294 61887 5 60 38368 98690 39677| 60323 013101 61632] O] M C. Sine Sine iC.TangJ Tang. ;C. Sec! Secant 1 M] 76 Degrees. | 14 Degrees. | M Sine C. Sine Tanar. |C. Tang,' Secant :C. Sec.j Mj 0, 9.38368 9.98690 9.39677| 10.60323 10.01^10 10.61632 60 6 38620 98875 39945' 60055; 01323, 61380 55 10 38371 98659 40212; 59783 01341 61129 50 15 39121 98643 40478 595221 013571 60879 45 20 39369 98627 40742 59253; 01373, 60631 40 25 39615 98610 41004 589981 01390, 60385 35 301 89860 98594 9.98678 41266 58734} 01406, 601401 30; 35! 9.40104 9.41526 10.58474 10.01422 i0.59896i 25 40 40345 98561 41784 532161 01439; 596551 20 45 40586 98545 42042 57958 014551 59414 15 5C 40325 98528 42297 57703 01472 591751 10 55; 41063 98511 42552 574481 01489 58937 6 60' 41300 98494 Sine 42805: 67195; 01508 58700 C.Tang.l Tang. iC. Sec.l Secant "m M C. Sine 75 Degrees. \ 36 Artificial Sines, Tangents, and SecanU, 15 Degrees. , M Sine 9.41300 I C. Sine Tang. C.TangJ Secant 10.5719610.01506 C. Sec. M i 9.98494 9.42805 10.58700 60 5 41535 98477 43057 56943 01523, 58465 66 10 41768' 98460 *43308 56692 01540 58232 50 15 42001 98443 43558; 56442 01557 67999 45 20 42232 98426 43806i 56194 01574 67768 40 25 42462 98409 44053: 56947 01591 57538 35 30 42690 98391 44299 65701 01609 57310 10.67083 SO 26 35 9.42917 9.98374 9.44544 10.66456! 10.01626 40 43^143 98356 44787 56213 01644 56867 20 45 43368 98338 46029 54971 01662 66632 16 50 43591 98320 45271 64729 01680 66409 10 55 43813 98302 46511 64489 01698 66187 5 60 44034 98284 45750 C.Tang. 54250 01716 66966 M M C. Sine Sine Tang. IC. Sec. Secant 74 Degrees. 16 Degrees. M Sine C. Sine Tang. 1 C.Tang. Secant C. Sec. M 9.44034 9.98284 9.45750 10.54250 10.01716 10.66966 60 5 44253 98266 45987 54013 01734 55747 55 10 44472 98248 46224 63776 01752 65523 60 15 44689 98229 46460 63540 01771 65311 45 20 44905 98211 46694 63306 01789 56096 40 25 45J20 98192 46928 63072 01808 54880 36 30 46334 98174 47160 62840 01826 64666 30 25 36 9.45547. 9.98155 9.47392; 10.62608 10.01845 10.54453 40 457581 98136 47622 623781 01864 64242 20 45 45969J 98117 47852 62148 01883| 64031 15 60 461 78J 98098 48080 61920 019021 53822 10 65 46386| 98079 48307 61693 01921 63614 .6 60 465941 98060 48534 51466 01940 53406! O] M C. Sine! Sine C.Tang. Tang. C. Sec. Secant i MJ 73 De grees. | 17 Degrees. | Mi Sine C. Sine Tang. C.Tang. Secant 9.98060 9.4863410.51466 10.01940 C. Seci M. 9.46594 10.634061 60 6 46800 98040 48759 51241 : 01960 53200; 55j 10 47005 98021! 48984! 51016 01979 62995 50 15 47209 980011 49207 50793 01999 52791 45 20 / 47412 97982| 49430 50570 020181 52688 40 25 47613 97962^ 496521 50348 02038 52387 35 30 47814 979421 49872 50128! 02058 9.50092 10.49908 '10.02078 52186 30 35 9.48014 9.97922 10.51986 25 40 48213 97902 50311 49689 02093, 51787 20 45 48411 97882 505291 49471 02118! 51589 15 5a 48608 97861' 50746; 49254 02139! 51392 '§ 65 48803 97841 50962 49038 02159' 61197 60 48998 97821 51178 48822 r Sine C.Tang. Tang. 02179 51002 "M M C. Sine C. Sec. Secant 72 Decrees. I Artificial Sines, Tangents, and Secants. ^T 18 Degrees. , M Sine 1 C. Sine; Tang. C.Tang. Secant C. See.; Ml 9.4899a 9.97821. 9.6117810.4882210.02179 10.51002 SO! 5 49192 97800, 61S92 48608 02200 50808 551 10 49385 97779j 51606 48394; 02221 60615. 50 60423 45 15 49677 97759] 51819 48181 02241 20 49768 97738 62031] 47969 02262 50232 4€ 25 49968 97717i 52242 • 47758 02283 60042 35 30 50148] 97696| 62452 47548- 02304 49852 30j 35 9.50336 9.97674 9.62661 10.47339 10.02326 10.49664 25| 40 60523, 97653 52870, 47130. 02347 4a477, 20 45 50710! 976321 53078 46922] 02368 492901 15 SO 50896 97610 63285, 46716| 02390 49104] 10 65 51080 97589, 534921 465081 02411 48920 5 60 61264 97567] 53697! 46303; 02433 Sine C.Tang. Tang. iC. Sec, 48736j M' C. Sine Secant \ M 71 Degrees. 19 Degrees. IVI| Sine | C.Sine, Tang. C.Tang. Secant 10.46303 10.02433 C. Sec. M 60 9.51264i 9.97567 9.53697 10.48736 5 51447 97545 53902 46098 02455 48553 55 10 61629 97523 64106 45894 02477 48371 50 15 61811 97501 64309 45691 02499 48189 45 20 61991 97479 54512 45488 02521 48009 40 25 62171 97457 54714 45286 02543 47829 35 30 52350 97435 54916 46085 02565 47660 SO 25 20 35 9.52527 9.97412 9.55115 10.44885; 10.02588 10.47473 40 62705 97390j 55315 44685 02610 47295 45 52881 97367 55514 44486 02633 47119 15 50 53066 97344 55712 44288 02656 46944 10 55 63231 97322 55910 44090 02676 46769 5 60 5S405 972991 56107 43893 02701 C. Sec. 46595 M M C. Sine Sine C.Tang Tang. Secant 70 Degrees. 20 Degrees. M| Sine C. Sine Tang. C.Tang. Secant C. See.j Ml 9.97299 9.56107 10.4389310.0270110.46595] 6oi 0; 9.53405 51 63578 97275 56303 43697 1 02725; 46422 55 10 63751 97252 66498] 43502; 02748 46249 60 15 53922 97229] 56693 43307, 02771 46078 45 20 54093 97206' 56887 43113 02794 46907 49 25 64263 97182 57081 42919 02818 45737 35 30^ 54433 97159 57274 42726 02841 45667 .30 25 3£ 9.54601 9.97135 9.57466 10.42534110.02865 10.45399 40 54769 97111! 57658 42342] 02889 45231 20 4fi 54936 970871 57849] 42151 0291S 45064 15 5C 55102 97063] 58039 41961 02937 44898 10 5i 55268 97039] 58229: 41771 0296] 44732 5 601 55433 97015[ 58418) 41682 Sine C.Tang. Tang. 0298S C. Sec 44567 M M C. Sine 1 Secant 69 Degrees. | 2S Ariijicial Sines, Tangenfa, and Sedanis. 21 Degrees. | m Sine C. Sine Tang. C.Tang. Secant C. Sec. M ». 55433 9.97015 9.68418 10.41582 10.02985 10.44567 60 5 55597 96991 58606 41394 03009 44403 55 10 55761 96966 58794 41206 03034 44239 50 15 55923 96942 58981 41019 03058 44077 4^ 20 56085 96917 69168 40832 03083 43915 40 25 56247 96893 69354 40646 03107 43753 36 30 56408 96868 9.96843 59540 40460 03132 43592 3Q 35 9.56568 9.59725 10.40276 10.03157 10.43432 26 40 56727 968181 69909 40091 03182 43273 20 46 56886 967931 60093 39907 03207 43114 15 50 57044 96767' 60276 39724 03233 42956 1? 56 67201 96742 60459 39541 03258 42799 I 60 57358 96717 60641 39359 03283 42642 M M C. Sine Sine C.Tang.' Tang. 'C. Sec.l Secant 68 Deg;rees. 22 Degrees. M| Sine C. Sine Tang. C.Tang. Secant C. Sec. M 60 9.57358 9,96717 9.60641 10.39359 10.03283 10.42642 5 57514 96691 60823 39177 03309 42486 56 10 57669 96665 61004 38996 03335 42331 50 15 57824 96640 61184 38816 03360 42176 45 20 67978 96614 61364 38636 03386 42022 40 25 58131 96588 61644 38456 03412 41869 35 30 58284 96562 61722 9.61901 38278 03438 10.03465 41716 10.41564 SO 25 35 9.68436 9.96535 10.38099 40 58588 96509 62079 37921 03491 41412 20 45 68739 96483 62256 37744] 03517 41261 15 50 68889 96456 62433 37567 03644 41111 10 55 59039 96429 62609 37391 03571 40961 5 60 59188 96403 62786 37216 03597 Tang. C. Sec. 40812 Secant M Ml C. Sine Sine C.Tang. 67 De grees. grees. ' 23 De M Sine C. Sine Tang. C.Tang. Secant C. Sec. 60 9.59188 9.96403 9.62785 10.37215 10.03597 10.40812 6 59336 96376 62961 37039 03624 40664 55 ■10 59484 96349 63135 36865 03651 40516 50 15 59632 96322 63310 36690 03678 40368 45 20 59778 96294 63484 36516 03706 40222 40 25 59924 96267 63657 36343 03733 4D076 3S 30 35 60070 96240 63830 36170 03760 39930 30 25 9.60215 9.9621^ 9.64003 10.35997 I0.037b8 10.39785 40 60359 96185 64176 35826 03815 39641 20 4a 60503 96157 64346 35654 03843 39497 15 m 60646 96129 64517 36483 03871 39364 10 55 60789 96101 64688 35312 03899 39211 5 60 60931 96073 64858 35142 03927 39069 M C. Sine Sine C.Tang. Tang. C. Sec. Secant 1 M| 66 Degrees. 1 ^Iriificial SineSf Tangents^ and Secants, 29 24 Degrees. | M Sine 4 9.60931 ::, Sine Tang. C.Tang. Secant C 0.03927 10 Sec ^M 9.96073 9.64358 10.35142 : .39069 60 5 61073 96045 65028 34972 03955; 38927 55 10 61214! 96017 65197 34803, 03983 38786 60 15 61354| 959S8 65366 34634' 040121 38646 45 20 614941 95960 65535 34465; 04040! 38506 40 2,5 616341 95931 :€5703' 342971 040691 38366 35 30 61773| 95902 658701 34130. 04098] 38227 SOj 9.958731 9.66038 10.33962 10.04127 10.SS089 25] 35 9.61911 40 62049 95844 66204 33796 04156 ST951 20 45 62186 95815 66371| 33629! 04185 37814 15 60 62323 95786 66537 33463 04214 37677 10 65 62459| 95757; 66702' 332981 04243 37541 5 60 62595I C. Sine' 95728! 66S671 331331 Sine C.Tang. Tang. 04272 C. Sec. 37405 Secant M 65 Degrees. 25 Degrees. { M Sine 1 C. Sine Tang. 1 C.Tang. 9.95728 9.66867 10.33133 Secant C 10.04272 1 . Sec.i M 9.62595 3.37405 60 6 62730; . 95698 67032i 32988 04302; 37270! 65 U ' 62865' 95668 67196; 32804 04332 37135' 50 15 I 62999! 95639 67360| 32640 04381 1 S700l! 45 2( ! 63133 95609 67524 32476 043911 36867: 40 2a ' 63266 95579 67687 32313 04421 36734 35 30 63398 95549 67850 32150 9.95519 9.63012 10.31983 ■04451 36602; 30 10.04481 la 36469: 25 35 9.63551 4C ' 63662 95488! 681741 31826 04512; 36338| 20 45 ; 63794 95458 68336,- 31664 04542 36206 15 oC 639241 95427 68497 31503 04573! 36076' 10 5a , 64054 95397 68658 31342 04603| 35946! 5 6C ' 64184 ii C. Sine 95366 68318 31182 04634J C. Sec' 358 16 1 Sine C.Tang. Tang. Secant 1 M a 64 Degrees. 26 Degrees. [ Sine i C. Sine Tang. C.Tang. Secant C. Sec.j M ( ) 9.64184 9.95366 9.6881810.31182 10.0463410.35816; 60 , ) 64313 95335J 68978 31022 04665 35687 55 i( ), 64442; 95304 69133; 30862 04696 35558 50 L i 645711 95273 69298| 30702 04727 35429 45 2( 1 64693! 95242 694571 30543 04758 1 35302 40' o 5 64S26' 95211! 69615 30385 04789 1 35174 35 3( ) 64953 95179| 69774' 30226 9.95148 9.69932 10.30068 04821 1 35047; 30 10.04852 10.349211 25 3 5 9.65079 4 65205 9511t ) 70089, 2991 J ; 048841 34795 20 4 5 65331 9508^ 1 702471 2975S 04916' 34669 16 5 65456 9505s I 70404; 29596 049481 34544 10 6 5! 65580 950201 70560 29440 04980! 34420 5 « 0' 65705 94988| 707171 29283 Sine 1 C.Tang. Tang^ 05012 34295 _2 31 a II C. Sine C, Sec! Secant 63 Degrees. 30 Artificial Sines, Tangents, and Secmts> 27 Degrees. f M Sine 1 C. Sine 9.94988 Tang. C.Tang.i Secant i 9.70717 10.29283 10.05012' D. Sec.| MJ 9.65705 10.34296 60 6 65828 94956 70873 29127 05044 34172 55. 10 65952 94923 7:.028 28972 05077 34048 60 15 66075 94891 71184 28816 05109 33926 45 20 66197 94858 71339 28661 05142 33803 40 25 66319 94826 71493 28507 05174 33681 35 30 66441 94793 71648 28352 05207 33569 SO 35 9.66562 9.94760 9.71802 10.28198 10.05240 10.33438i 25 1 40 66682 94727 71955! 28045J 05273 33318 201 45 66803 94694 72109; 27891 05306 33197 16 1 60 66922 94660 72262| 27738 05340 33078 10 55 67042 94627 72415| 27585 05373 82958 5 60 67161 94593 72567' 27433J 05407] 32839 m C.Sine Sine C. Tang. Tang. C. Sec' Secant M 62 Degrees. 28 Degrees. M Sine 1 C. Sine; Tang. C.Tang. 9.94593, 9.72567 10.27433 Secant 10.05407 C. Sec, Ml 9.67161' 10.32839; 60 { 5 67280i 94560 72720 27280 05410 32720l 661 10 67398! 94526 72872{ 27128 05474 32602 50 15 67515| 94192 73023! 26977 05603 32485 45 20 67633 94453 73175 26825 05642 32367 40 25 67750 94424 73326 26674 06676 32250 35 30 67866 94390 73476 26524 10.26373 05610 32134 30 35 9.67982 9.94356 9.73627 10.05645| 10.32018 26 40 68098 94321 73777 26223 05679! 31902 20 45 68213 94286 73927 26073 05714 31787 15 50 68328 94252 74077 25923 05748 31672 10 65 68443 94217 74226 25774 05783 31557 o 60 68557 94182 74375 25625 Tang. 05818 S1443 M M! C. Sine Sine IC.Tang. C. Sec! Secant 61 Degrees. \ 29 De grees. [ Mj Sine | C. Sine Tang. C.Tang. Secant C. Sec.| M 9.66557 9.94182 9.74375:10.25625,10.05818 10.31443 60 5 68671 94147 74524 254761 05853 31329 55 10 68784 94112 74673 26327 05888 31216 50 15 68897 94076 74321 25179 05924 31103 45 20 69010 94041 74969 25031 05959 30990' 40 25 69122 94005 75117 24883 06995 ■308781 35 SO 69234 93970 75264 24736 06030 10.06066 S0766| 30 85 9.69345 9.93934! 9.75411 10.24589 10.30655! 25 4C 69456 93898 75558 24442 06102 305441 20 4h 69567 93862 75705 24295 06138 30433| 15 W 69677 93826 75852 24148 06174 303231 10 bl 69787 93789 75998 24002 0621] 30213 6 60 69897 93763 76144 23856 06247 30103 p M C. Sine Sine C.Tang Tang. C. Sec. Secant M >. 60 Degrees. ' Jtrtijicial Sines, Tangents, and Secants, S I 30 Degrees. , M Sine C. Sine Tang. C.Tang; Secant. C. Sec.| Mj G 9.69897 8.93753 9.76144 10.23856 10.06247 10.30103 60 5 70006 93717 76290 23710 0628S 29994 55 10 70115 93680 76435 23565 06320 29885 50 15 70224 93643 7658C 2342C 06357 29776 45 20 70332 93606 76725 23275 06394 29668 40 25 70439 93569 76870 23130 06431 29561 35 30 70547 93532 77015 22985 06468 29453 30 "23 35 9.70654 9.93495 9.7715910.22841 10.06505 10.29346 40] 70761 93457 77303 22697 06543 29239 20 45 70867 93420 77447 22553 06580 29133 15 60 70973 93382 77591 22409 06618 29027 10 55 71079 93344 77734 22266 06656 28921 5 60 71184! M C. Sine! 93307 77877 22123 06693 28816 M Sine C.Tang. Tang. C. Sec. Secant 59 Degrees. | 31 De grees. M; Sine C. Sine Tang. C.Tang. Secant. C. Sec. M 9.71184 9.93307 9.77877 10.22123 10.06693 10.28816 60| 5| 71289 93269 78020 21980 06731' 28711 55 10 713931 93230 78163] 21837 06770] 28607 50 15 71498 931C2 78306 21694 06808 285021 45 20| 71602 93154 78448 21552 06846 28398 40 25, 71705 93115 78590 21410! 068S5 28295 35 30' 71809 93077 9.93038 78732 21268 06923 281 91 30 35 9.71911 9.78873 10.21126:10.06962]l0.28089 25| 40, 720141 92999 79015 20985 07001 27986 20 45\ 72116 92960 79156 20844 07040 27S84' 15 501 72218' 92921 79297 20703 07079 27782 10 55l 72320 92881 79438 20562 07119 27680] 5 60l 72421' 92842 Sine 79579 C.Tang. 20421 07158 27579' M C. Sine Tang. C. Sec. Secant. M 58 De grees^___ ;rees. 32 be, M Sine [ C. Sine Tang. C.Tang. Secant C. Sec. M 9.72421, 9.92842 9.79579 10.20421 10.07158 10.27579 60 5 72522 92803 79719i 20281; 071971 27478 56 10 72622 92763 79860 20140i 07237 273781 50 15 72723 92723 80000 20000 07277 27277 45 20 72823 92683 80140 19860 07317 27177 40 25 729221 92643 80279 19721 07357 27078 35 30 35 73022 9.731211 92603 9.92563 80419 9.80558 19581 10.19442 07397 26978! 301 10.07437 10.26879' 25 40 73219 92522 80697] 19303 07478 26781! 20 45l 73318' 92482 80836 19164 07518 26682] 15 50 73416] 92441 80975 19025 07559 26584 10 55 73513' 92400 81113 18887 07600 264871 5 €0 73611 I^ri C. Sine 92359 Sine 81252 18748 07641 C. Sec. 263891 01 C.Tang. Tang. Secant 1 Ml 57 Degrees. .. „ 1 ^S2 *^rUJicial Sines, Tangents, and Secants. 33 Degrees. i n-j M Sine C. Sine Tang. C.Tang. Secant C. Sec. M 60 9.73611 9.92359 9.81252 10.18748 10.07641 10.26389 6 73708 92318 81390 18610 07682 26292 55 10 73805 92277 81628 18472 07723 26195 50 15 73901 92235 81666 18334 07765 26099 45 20 73997 92194 81803 18197 07806 26003 40 25 74093 92152 81941 18059 07848 25907 35 30 35 74189 9.74284 92111 82078 17922 07889 25811 30 9.92069 9.82216 10.17785 10.07931 10.25716 25 40 74379 92027 82352 17648 07973 25621 20 45 74474 91985 82489 17511 08016 25526 15 50 74568 91942! 82626 17374 08058 26432 10 55 74662 91900 82762 17238 08100 25338 6 60 M 74756 91857 Sine 82899 17101 08143 25244 M C. Sine C.Tang. Tang. C. Sec. Secant 56 Degrees. | 34 Degrees. | M Sine C. Sine Tang. | C.Tang. Secant C. Sec. M| 9.74756 9.91857 9.82899 10.17101 10.08143 10.25244 60 5 74850 91815 83035 16965 08185 25150 55 10 74943 91772 83171 16829 08228 25057 50 15 75036 91729 83307 16693 08271 24964 46 20 75128 91686 83442 16558 08314 24872 40 25 75221 91643 «3578 16422 08357 24779 35 30 75313 91599 83713 16287 08401 24687 30 25 35 9.75405 9.91556 9.83849 10.1615110.08444 10.24595 40 75496 91512 83984 16016 08488 24504 20 45 75587 91469 84119 15881 08531 24413 15 50 75678 91425 84254 16746 08575 24322 10 00 75769 91381 84388 15612 08619 24231 6 60 75859 91336 84523 15477 Tang. 08664 24141 M C. Sine Sine C.Tang. C. Sec' Secant M 55 De jrees. grees. 35 De M Sine C. Sine Tang. C.Tang., Secant C. Sec. M 9.75859 9.91336 9.84523 10.15477 10.08664 10.24141 60 5 75949 91292 84657 15343 08708 2405] 56 10 76039 91248 84791 15209 08752 23961 50 15 76129 91203 84925 15075 C8797 23871 45 20 76218 91158 85059 14941 08842 23782 40 25 76307 91114 85193 14807 08886 23692 35 30 76395 91069 85327 14673 08931 23605 30 35 9.76484 9.91023 9.85460 10.14540 10.08977 10.23516 25 40 76572 90978 85594 14406 09022 23428 20 45 76660 90933 85727 14273 09067 23340 15 50 76747 90887 85860 14140 09113 23253 10 55 76835 90842 85993 14007 09158 23165 5 60 M 76922 90796 8612a 13874 09204 23078 C. Sine Sine C.Tang. Tang. iC. Sec. Secant M 54 Degrees. ^ \ Jtrtificial Sines, Tangents, and Secariits. 33 3S^ Degrees. Sine 9.76922 77009 '77095 77181 77268 77353 77439 C. Sine 9.90796 90750 90704 90657 90611 90565 90518 9.77524 9.90471 776091 90424 77694: 77778j 778621 77946 Tang. C.Tang. Secant iC. Sec. M 9.86126 86259 86392 86524 86656 86789 86921 10.1337410.0920410, 13741 09250 13608 09296 13476 09343 13344 09389 132111 09435 13079; 09482 23078 60 22991 66 22305 50 22819 45 22732' 40 22647 35 225611 30 90377 90330 90282 90235 Ml C. Sine Sine 9.87053,10.12947 10.09529 87185 12815 09576 873171 12683, 09623 874431 12552 09670 87580; 12420 09718 877111 12289 0976, 10.22476 25 22391 20' 22306 15 22322 10 22136; 5 22054 C.Tang.' Tang. C. Sec. Secant I M 53 Degrees . 37 Degrees. Ml Sine 9.77946 78030 78113 78197 78280 78362 78445 9.78527 78609 77691 78772 78853 789341 C. Sine, Tang. iC.Tang.l Secant ,C. Sec.i M 9.90235 90187 90139 90091 90043 89995 89947 89849 89801 89752 89702 89653 9.87711110.12289 10.0976510.220541 60 21970 65 21687 50 21803 45 21720 40 21638 35 21555 SO 87843 87974 88105 88236 88367 88498 121571 12026 11895 11764 11633 115(B 098131 09861 09909! 09957 10005! 100531 9.88629 10. 1 1371 110.10102 10.21473 88769 88890 89020 89151 89281 112411 11110 10980 10849 10719 10151 I 10199 10248! 10298J 103471 21391 21309 21228 21147 210661 C. Sine! Sine IC.Tang.l Tang. IC. Sec.: Secant I M 62 Degrees. 38 Degrees. Sine I C. Sinej Tang^jC.Tang. Secant C. Sec.j M 60 9.78934 79015 79095' 791761 79256. 79335! 79415 9.89653 896041 895541 895041 894351 89405| S93541 9.8928110.10719 10.10347 10.21066 20985 20905 20824 20744 20385 205S5 89411 10589 10396 89541 10459 10446 89671 10329 10496 89801 10199 10545 89931 10069 10595 90061 09939 10646 9.79494 9.893041 9.90190 10.09810 10. 10696 10.205061 79573, 892541 90320 09680 10746- 20427^ 796521 892031 90449! 09551 107971 20348 797311 89152 90578 09422 108481 20269 79809, 89101 90708 09292 108991 20191 79887 89050 | 90837 1 09163 _J^^\_J^\^ C. Sine! Sine C.Tang. Tang. IC. Sec. i Secant 51 D egrees. 8 55! 5() 45 40| 35 i J10| 25^ 20] 15 10 3 _oi mI — « 34 .Artificial Sines, Tangents, and Secants^ 39 Degrees. "" M Sine C. Sine Tang. C.Tang., Secant) C. Sec. M 60 9.79887 9.89050 9.90837 10.09163 10.10950 10.20113 6 79965 88999 90966 09034 11001 20035 55 10 80043 88948 91095 08905 11062 19957 60 16 80120 88896 91224 08776 H104 19880 45 20 80197 88844 91353 08647 11156 19803 40 25 60274 88793 91482 08618 11207 19726 35 30 80351 88741 91610 08390 10.08261 11259 19649 30 35 9.80428 9.88688 9.91739 10.11312 10.19572 25 40 80504 886361 91868 08132 11364 19496 20 45 80580 88584' 91996 08004 11416 19420 15 50 80656 88531' 92125 07875 11469 19344 10 55 80731 88478 92253 07747 11522 19269 5 60 M 80807 C. Sine 88425 Sine 92381 07619 11575 19193 M C.Tang. Tang. C. Sec. Secant 50 Degrees. 40 Degrees. M Sine C. Sine Tang. jC.Tang. Secant C. Sec. M| 9.80807 9.88425 9.92381 10.07619 10.11575 10.19193 66 5 80882 88372 92510 07490 11623 19118 55 10 80957 88319 92638 07362 11681 19043 50 15 81032 88266 92766 072S4 11734 18968 45 20 81106 88212 92694 07106 11788 18894 40 25 81180 88158 93022 06978 11842 18820 35 30 81254 88105 93150 06850 11 895 18746 30 25 35 9.81328 9.88050 9.93278 10.0672210.11950 10.18672 40 81402 87996 93406 06594 12004 18598 20 45 81475 87942 93533 06467 12053 18525 15 50 81549 87887 93661 06339 12113 18451 10 55 81622 87833 93789 06211: 12167 18378 5 60 81694 87778 93916 060S4 Tang. 12222 18306 M M C. Sine Sine C.Tang. C. Sec.l Secant 49 Degrees. 41 Degreielt 1 M Sine C. Sine Tang. 9.93916 C.Tang., Secant C. Sec. M 9.81694 9.87778 10.06084 10.12222 10.18306 60 5 81767 87725 94044 06956 12277 18233 65 10 81839 87668 9417] 05829 12332 18161 SO 15 8191] 8761S 9429£ 05701 12381 18089 45 20 8198f 87557 94426 0557-^ 12443 J8017 40 26 82055 87501 9455^ 05446 12499 17945 36 30 82126 87446 94681 05319 12554 17874 10.17802 30 25 35 9.82198 9.87390 9.94808 10.05192 10.12610 40 82269 87334 94936 05065 12666 17731 20 45 8234C 87277 95062 04938 12723 17660 15 6C 8241C 87221 95190 04810 12779 17590 10 5i 8248] 87164 95317 04683 12836 17519 6 6C ) 8255 87107 96444 04556 12893 17449 M M' C. Sine Sine C.Tang Tang. IC. Sec. Secant I 48 Degrees. _ \ Artificial Sines, Tangents, and Secants. 35 42 Degrees. | M\ Sine C. Sine Tang. C.Tang. Secant. C. Sec. 10.17449 IVI 60 6 9.82551 9.87107 9.95444 10.04556 10.12893 5 82621 87050 95571 04429 12950 17379 .W 10 82691 86993 95698 04302 13007 17309 60 15 82761 86936 95825 04175 13063 17239 45 20 8-2830 86879 95952 04048 13121 17170 40 25 82899 86821 96078 03922 13179 17101 35 30 82968' 86763 96205 03795 13237 17032 30 15 85 9.83037: 9.86705 9.96332 10.03668 10.13295 10.16963 40 83106J 8S647 96459 03541 13353 168941 20] 45 831741 86589 96586 03414 13411 16826 15 60 83242i 86530 96712 03288 13470 16758 10 55 83310! 86472 96839 03161 13528 16690 6 60 833781 86413 96966 03034 13587 16622 Ml C. Siael Sine iC.Tang.! Tang. IC. Sec. Secant i Ml 47 Degrees. ! 43 Degrees. M Sine | C. Sine; Tang. iCTan^. Secant. C. Sec. M 9.833781 9.86413 9.96966, ia03034 10.13587,10.16622 60i 5 83446 86354: 97092 02908 13646 16554 65 10 83513 86295| 97219 02781 13705 16487: 50 15 83581 86235; 97345 02655 13765 164191 45 20 83648 86176, 97472 02528 13824 16352 40 25 83715 881161 97598 02402 13884 16285 35 30 83781 86056j 97725 02275 13944 162191 30, So 9.83848 9.85996 9.9785110.02149 10.1400410.161521 25' 40 83914 85936 979781 02022! 14064 16086 20 45 83980 85876 98104 01896 14124 160-20 15 50 84046 85815 98231 01769 14185 15954 10 -55 84112 857541 98357 01643 14246 15888 a 60 84177 85693 98484 01516 14307 15823 M! C. Sinel Sine 'c.Tang. Tang. 1 C. Sec. Secant, i M>. 46 D egrees. agrees. 44 D M| Sine } C. Sine Tang. C.Tang.; Secant C. Sec. M Oi 9.84177 9.85393, 9.98484 10.01516 10.14307 10.15823 60 5 84-242} 85632: 98610 01390: 14368 15758 55, 10 84308 85571: 98737; 01263 14429 15692 50 15 84373' 85510: 98863| 011371 14490 15627 45 20 64437 85448 98989 OlOllj 14562 15563 40 25 84502 85386 99116 003841 14614 154981 35 ,30 84566 85324 99242 00758 14676 10.14738 15434! 30 35 9.84630' 9.852621 9.99368'10.00632 10.15370! 25 40 846941 8520C 99495 00505 1480C 15306! 20 45 84758| 8513- 99621 0037£ 14863 152421 15 6( 84822 85074 99747 0025J 14926 15178, 10 55| S4885 85012 9987< 00126 14988 15115 5 60] 84949 8494E 10.00000 10.00000 15051 1 150511^ C. Seel Secant ! M, Mi C. Sinel Sine IC.Tang Tang. 45 D egrees. ^ { ^Q TRAVERSE TABL£. Ill, A Traverse Table, or Table of Difference of Latj- TUDE AND Departure, calculated for degrees and quarters of degrees, and for any distance up to 100 Rods, Chains, &c. ; by which the northings and southings, eastings and westings made in a Survey may be found. JVote. Northings and southings are called Difference of Latitude, or simply Latitude ; eastings and westings are called Departure, Meridian Dis- tance, or Longitude. Explanation of the Table. To find the Latitude and Departurcf or Worthing, Sj-c. for any Course and Distance. If the Course be less than 450, look for it at the top, but If more than 45° at the bottom of the page, and look for the Dis- tance in the right or left hand column ; against the Distance, ^"hd directly under or over the Course, stand the norUiing, &c. in whole numbers and decimals. If the Course be less than 45°, the northing or southing will be greater than the easting or westing; but if more than 450. the easting or westing will be the greatest. When the Distance exceeds 100, take any two or more num- bers, which, added together, will equal the Distance, and find the Latitude and Departure for each of those numbers ; add the several Latitudes together and the sum will be the whole Latitude ; and so for the Departure. And when the Distance is in Chains and I^inks, or whole numbers and decimals, find the Latitude, &c. for the Chains or whole numbers, and then for the Links or decimals, remembering to remove the decimal point in the Table further to the left, according to the given "decimal. Examples. J. Required the Latitude and Departure for 45 Rods, on a Course JV. 150 15^ W. Under 15° 15^ and against 45 is 43.42 for the northing, and 11-. 84 for the westing. 2. Required the Latitude and DepaTtute for 1 20 Rods, on « Course S. Sgo 30^ J5. TRAVERSE TABLE. 37 Take one third of 120 which is 40 ; against this number, over 58« 30' is 29.90 for the Latitude and 34.11 for the De- parture. These muhiplied by 3 give G2.70 for the Southing and 102.33 for the Easting. 3. Required the Latitude and Departure for 37.36 Rods or 37 Chains and 36 Links, on a Course JV. 26** 46' E. For 37. Lat. 33 04 Dep. 16.65 0.36 .32 .16 37.36 33.36 16.81 Northing 33.36 Easting 16.81 Xote. When the Minutes are not 15, 30, or 45, the Northings, &c. must ISe calculated by Natural Sines, or by Ti'igonometry. 38 TRAVERSE TABLE. Ed "ft)ei. i'i)eg. ibeg. 9. Lat.lDep. Lat. Dep. Lat. Dep. 1 l.OOj 0.00 1.00 0.01 1.00 0.01 1 2 2.00i 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 0.06 4 5 5.00 0.02 5.00 0.04 5.00 0.07 5 6 6.0a 0.03 6.00 0.05 6.00 0.08 6 7 7.00i 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 9.00i 0.04 9.00 0.08 9.00 0.12 9 10 11 10.00: 0.04 11.00 0.05 10.00 0.09 10.00 0.i3 0.14 16 11 11.00 0.10 11.00 12 12.00' 0.05 12.00 0.10 12.00 0.16 12 13 13.00: 0.06!! 13.00 0.11 13.00 0.17 13 14 14.00 0.06 114.00 0.12 14.00 0.18 14 15 15.00 0.07 jl5.00 0.13 15.00 0.20 15 18 16.00 0.07 116.00 0.14 16.00 0.21 16 17 17.00 0.07 17.00 0.15 17.00 0.22 17 18 18.00 0.08 18.00 0.16 18.00 0.24 18 19 19.00 0.08 19.09 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 2222.00 O.lOi 22.00 0.19 22.00 0.29 22 23 23.00 0.10123.00 0.20 23.00 0.30 23 2424.00 0.10! 24.00 0.21 24.00 0.31 24 25 25.00 0.11125.00 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 3030.00 0.13 30.00 0.26 30.00 0.39 30 3131.00 0.14 31.00 0.27 31.00 0.41 31 32 32.00 0.14132.00 0.28 32.00 0.42 32 33 33.00 0.14,33.00 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 0.31 135.00 0.46 35 36 36.00 0.16 36.00 0.31 136.00 0.47 36 37 37.00 0.16 37.00 0.321137.00 0.48 37 38 38.00 0.17 38.00 0.33 38.00 0.50 38 39 39.00 0.17139.00 0.34 39.00 0.51 39 4040.00 0.17 40.00 0.35 40.00 0.52 40 4141.00 0.18 41.00 0.36 41.00 0.54 41 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 0.20l 46.001 0.40| 46.00 0.601 46 47 47.00 0.21 47.00 0.41 47.00 0.62 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 0.651 50 Dep. Lat. Dep. Lat. Dep. Lat. tg 89|Deg. 89iDeg. 89iDeg. Q TRAVERSE TABLE. 3Sf 5 iDeg. iDeg. |Deg. 5 51 Lat. 51.0C Dep. 0.22 Lat. Dep. Lat. Dep. 51.00 0.67 51 51.00 0.45 52 52.00 0.23 52.00 0.45 52.00 0.68 62 53 53.00 0.23 53.00 0.46 53.00 0.69 53 64 54.00 0.24 54.00 0.47 54.00 0.71 64 55 55.00 0.24 55.00 0.48 55.00 0.72 55 56 56. C6 0.24 56.00 0.49 56.00 57.00 0.73 56 57 57.0C 0.25 57.00 0.50 0.75 67 58 58.0C 0.25 58.00 0.51 57.99! 0.76 58 59 59.C(. 0.26 59.00 0.51 58.991 0.77 59 60 61 60.0C 61.CC 0.26 60.00 0.52 59.99I 0.79 60.991 0.80 60 61 0.27 61.00 0.53 62 62.0C 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 65.0C 0.28 65.00 0.57 64.991 0.85 66 66 66.CC 0.29 66.00 0.58 65.99! 0.86 66 67 67.0C 0.29 67.00 0.58 66.99; 0.88 67 68 68.0C 0.30 68.00 0.59 67.99' 0.89 68 69 69.0C 0.30 69.00 0.60 68.99, 0.90 69 70 71 70.0C 71.00 0.31 70.00 0.61 69.99 0.92 70 71 0.31 71.0o! 0.62 70.99 0.93 72 72.0C 0.31 72.00' 0.63 71.99 0.94 72 73 73.00 G.32 73.OO1 0.64 72.99 0.96 73 74 74.00 0.32 74.00 0.65 73.99 0.97 74 75 75.0C 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 77.0C 0.34 77.00 0.67 76.99 1.01 77 78 78.CC 0.34 78.00 0.68 77.99 1.02 78 79 79.0t 0.34 79.00 0.69 78.99 1.03 '9 80 80.C1 0.35 80.00 0.70 79.99 1.05 80 81 81.CC 0.35 81.00 0.71 80.99 1.06 81 82 82.00 0.36 82.00 0.72 81.99 1.07 82 83 83.tt 0.36 83.00 0.72 82.99 1.09 83 84 84.a 0.37 84.00 0.73 83.99 1.10 84 86 85.0C 0.37 85.00 0.74 84.99 1.11 85 86 86.CC 0.38 86.00 0.75 85.99 LIS 86 87 87. (A 0.38 87.00 0.76 86.99 1.14 87 88; 88.U C.38 88.00 0.77 87.99 L15 88 891 sg.ot 0.39 89.00 0.78 88.99 i.iei 89 90 90.0C 0.39 90.00 0.79 89.99 1.18 90 91 91.0C 0.40 91.00 0.79 90.99 1.19; 91 92! 92.0C 0.40 92.09 0.80 91.99 1.20 92 93 93.CC 0.41 93.00 -0.81 92.99 1.22 93 94' 94.0C 0.41 1 94.00 0.82 93.99 1.23 94 95 95.0C 0.41 95.00 0.83 94.99 1.24 95 96, 96.0C 0.42 96.00 0.84 95.99 1.26 9« 97 97.0C 0.42 97.00 0.85 96.99 1.27 97 1.28 98 98 98.0C 0.43 98.00 0.86 97.99 99 99.0C 0.43 99.00 0.86 98.99 1.30 99 100 lOO.OC 0.44 100.00 0.87 99.99 1.31 100 ■♦-J Dep. Lat. Dep. Lat. Dep. Lat.i CO Q 89|Deg. 89iDeg. 1 89peg.| 5 40 TRAVERSE TABLE. o 1 1 Deg. H Deg. 1 i Deg. l|Deg.| 2 So' <-► 1 Lat. Dep. 0.02 Lat. 1.00 Dep. 0.02 Lat. Dep. 0.03 Lat. 1.00 Dep. 0.03 1.00 1.00 2 2.00 0.03 2.0(? 0.04 2.00 0.05 2.00 0.06 2 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 6.00 0.11 5.00 0.13 6.00 0.16 6 6 6.00 0.10 6.00 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 0.26 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 11.00 0.22 10.00 0.26 10.00 0.31 10 11 11.00 0.19 0.24 11.00 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 15 16 16.00 0.28 16.00 0.35 15.99 0.42 1.6.99 0.49 16 17 17.00 0.30 17.00 0.37 16.99 0.45 16.99 0.62 17 18 18.00 0.31 18.00 0.39 17.99 0.47 17.99 0.56 18 19 19.00 0.33 19.00 0.41 18.99 0.60 18.99 0.68 19 20 20.00 0.35 0.37 20.00 21.00 0.44 0.46 19.99 20.99 0.52 19.99 20.99 0.61 20 21 21 21.00 0.55 0.64 22 22.00 0.38 21.99 0.48 21.99 0.68 21.99 0.67 22 23 23.00 0.40 22.99 0.60 22.99 0.60 22,99 0.70 23 24 24.00 0.42. 23.99 0.52 2.S.99 0.63 23.99 0.73 24 26 25.00 0.44 24.99 0.55 24.99 0.65 24.99 0.76 2£ 26 26.00 0.45 26.99 0.57 26.99 0.68 25.99 0.79 26 27 27.00 0.47 26.99 0.59 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 0.61 28.99 0.63 28.99 0.76 28.99 0.89 29 30 31 30.00 0.52 29.99 0.66 - 29.99 G.79 29.99 0.92 30 31.00 0..54 30.99 0.68 30.99 0.81 30.99 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 33.9S 1,0< S4 35 34.99 0.61 34.99 0,76 34.99 0.92 34.98 1,07 35 36 35.99 0.63 36.99 0.79 35.99 0.94 35.98 I.IC 36 37'36.99 0.65 36.99 0.81 36.99 0.97 36.98 l.U 37 38i37.99 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 38.98 L19 39 40 39.99 0,70 39.99 0.87 39.99 1.05 39.98 1.22 40 41 41 40.99 0.72 40.99 0.89 40.99 1.07 40.98 1.2S 42141.99 0.73 41.99 0.92 41.99 1.10 41.98 1.2f 42 43142.99 0.75 42.99 0.94 42.99 1.13 42.98 1.3 43 44143.99 0.77 43.99 0.96 43.99 1.15 43.98 1.3< 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 46.98 1.40 46 4746.99 0.82 46.99 1.03 46.39 1.23 46.98 1,4; 47 48 47.99 0.84 47.99 1 06 47.98 1.26 47.98 1.47 48 49 48.99 0.86 48.99 1.07 48.98 1.28 48.98 1,5C 49 60 49.99 0.87 Lat. 49.99 1.09 Lat. 49.98 Dep. 1.31 49.98 1,53 60 en Q "S Dep. Dep. Lat. Dep. Lat. Q |89 Deg. 88|Deg. Upeg. 88iDeg. TRAVERSE TABLE. 41 d p. 51 1 Deg. 1^ Deg. HDeg. 11 Deg. CO 51 Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 50.99 0.89 50.99 1.11 50.98 1.34 50.98 1.56 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 1.16 52.6-8 1.39 ,52.98 1.62 53 54 W.99 0.94 53.99 1.18 53.98 1.41 ,53.97 1.65 54 55 54.99 0.96 54.99 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 56.98 1.49 56.97 1.74 57 58 57.99 1.01 57.99 1.27 57.98 1.52 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 1.57 59.97 1.83 60 61 60.99 1.06 60.99 1.33 60.98 1.60 60.97 1.86 6'i 61.99 1.08 61.99 1.35 61.98 1.62 61.97 1.89 62 63 62.99 1.10 62.99 1.37 62.96 1.65 62.97 1.92 63 64 63.99 1.12 63.98 1.40 63.98 1.68 63.97 1.96 64 65 34.99 1.13 64.98 1.42 64.98 1.70 64.97 1.99 65 66 65.99 1.15! 65.98 1.44 65.98 1.73 65.97 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 69.93 1.53 39.98 1.83 69.97 2.14 70 1.24 70.98 1.55 70.98 1.86 70.97 2.17 71 n 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 7E 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 1.96 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 7b 77.99 1.36 77.98 1.70 77.97 2.04 77.96 2.38 78 79 78.9S 1.38 78.98 1.72 78.97 2.07 78.96 2.41 79 SO 81 79.96 80.99 1.40 79.98 1.75 79.97 2.09 79.96 2.44 80 1.41 80.98 1.77 80.97 2.12 90.96 2.47 81 8:i 81.96 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 63.96 2.57 84 So 84.98 1.48 84.98 1.85 84.97 2.23 84.96 2.60 85 86 85.96 1.50 85.98 1.88 85.97 2.25 85.96 2.63 86 87 86. 9£ 1.52 86.98 1.90 86.97 2.28 86.96 2.66 87 88 87.9S 1.54 87.98 1.62 87.97 2,30 87.96 2.69 88 89 88.96 1.55 88.98 1.94 38.97 2.33 88.96 2.72 89 90 91 89.99 90.96 1.57 89.98 1.96 89.97 2.36 89.96 2.75 90 91 1.59 90.98 1.99 .90.97 2.38 90.96 2.78 92 91.99 1.61 91.98 2.01 91.97 2.41 91.96 2.8] 92 93 ■)2.96 1.62 92.98 2.03 92.97 2.43 92.96 2.8' 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 94.9fc 2.9C 95 96 95.99 1.68 95.98 2.09 95.97 2.51 95.9e 2.9' 96 97 96.96 1.69 96.98 2.12 96.97 2.54 96.9c 2.96 97 98 97.96 1.71 97.98 2.14 97.97 2.57 97.9c 2.99 9P 99 98.9t 1.73 98.98 2.16 98.97 2.59 98.9,= 3.02 9fl 100 5 99.9t 1.75 99.98 2.18 99.9- Dep. 2.62 99.9c Dep 3.0£ IOC en Dep Lat. Dep. Lat. Lat. Lat. 89 Deg. 88|Deg. 1 88iDej?. SSiDeg a 10 42 TRAVERSE TABLE. t 00 ] J 2 Dog. 2iDeg 2iDeg 1 ^^ ^^^- di Lat Dep. 0.03 Lat iDep Lat .IDep Lat . Dep. ."■ l.OC 1.00 0.0< I i.ool 0.04II i.ool 0.05I ll 2 2.0C 0.07 2.00 O.Of 2.0{ D 0.0£ 2.00 0.10 2 9 3.0C O.IC 3.00 0.12 3.0( ) 0.1£ 3.00 0.14 3 A 4.0C 0.1^ 4.0f O.Ifi 4.0( } o.r 4.00 0.19 4 £ 5.0C 0.17 5.0C 0.20 5.0( ) 0.22 4.99 0.24 5 6 6.00 0.2] 6.0f 0.24 6.9S ) 0.26 5.95 ) 0.29 6 7 7.00 0.24 6.99 0.27 6.9J ) 0.31 6.9£ 0.34 7 0.38 8 0,43 9 8 7.99 0.28 7.99 0.3] 7.9E 0.35 7.9£ . J) 8.99 0.31 8.99 0.35 8.9E 0.39 8.9£ i(J 11 9.99 10.99 0.35 0.38 9.99 0.39 9.9£ 0.44 9.9£ 0.48 10 10.99 0.43 10.99 0.48 10.99 0.53 11 12 11.99 0.42 11.99 0.47 11.99 0.52 11.99 0.58 12 la 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.S8 0.72 15 16 15.99 0.56 15.99 0.63 15.99 0.70 15.18 0.77 16 17 16.99 0.6S 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 0.96 20 1.01 21 5>0 21 19.99 20.99 0.70 19.98 0.79 19.98 20.98 0.87 19.98 20.98 0.73 20.98 0.82 0.92 22 21.99 0.77 21.98 0.86 21.98 0.96 21.97 1.06 22 23 22.99 0.80 22.98 0.90 22.98 1.00 22.97 1.10 23 24 23.99 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 25.98 0.91 25.98 1.02 25.98 1.13 -25.97 1.25 28 27 26.98 0.94 26.98 1.06 26.97 1.18 26.97 1.30 27 28 27.98 0.98 27.98 1.10 27.97 1.22 27.97 1.34 28 29 28.98 1.01 28.98 1.14 28.97 1.26 28.97 1.39 29 30 31 29.98 30.98 1.05 29.98 1.18 1.22 29.97 30.97 1.31 29.97 1.44 30 1.49 31 1.08 30.98 1.35 30.96 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 3-4.96 1.68 353 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 ].7S 37 38 J7.98 1.33 37.97 1.49 37.96 l.fifi 37.96 1.82 3S 39 38.98 1.36 38.97 1.53 38.96 1.70 38.96 1.87 39 40 41 39.98 1.40 1.43 39.97 40.97 1.57 1.61 39.96 1.75 1.77 1 39.95 40.95 1.92 40| 40.98 40.96 1.97 4ll 42 41.97 1.47 41.97 1.65 41.96 1.83 41.95 2.02 42I 43 42.97 1.50 42.97 1.69 42.96 l.RS 42.95 2.06 43" 44 43.97 1.54 43.97 1.73 43.96 1.92 43.95 2.11 44| 2.16 455 45 44.97 1.57 44.97 1.77 44.96 1.96 44.95 46 45.97i 1.61 46.96 1.81 45.96 2.01 45.95 2.21 46| 47 46.97 1.64 16.96 1.85 46.96 2.05 46.^5 2.25 47| 2.30 48'' 48 47.97 1.6g 47.96 1.88 17.95 2.09 ■ 47.96 49 48.97 1.71 48.96 1.92 48.95 2.14 18.94 2.35 49, 2.40 50 50 m 49.97 1.74 49.96 1.96 49.95 2.18 ' 49,94 Dep. Dep. Lat. Dep. Lat. Dep. Lat. ] Lat. ^• 88 beg. 1 87|Deg. B7iDeg. •< 37iDeg.Q| TRAVERSE TABLE. 5 51 2Deg. 2iDeg 2i Deg. 21 Deg. o Cfi' 51 Lat. Dep. Lat. Dep. 2.00 Lat. Dep. Lat. Dep. 50.97 1.78 50.96 50.95 2.22 50.94 2.46 62 51.97 1.81 51.96 2.04 51.95 2.27 51.94 2.50 52 bS 52.97 1.85 52.96 2.08 52.95 2.31 52.94 2.. 54 53 54^53.97 1.88 53.96 2.12 53.95 2.36 53.94 2. .59 54 55; 54. 97 1.92 54.96 2.16 54.95 2.40 54.94 2.64 56 56 55.97 1.96 55.96 2.20 56.95 2.44 55.94 2.69 66 57i56.97 1.99 56.96 2.24 56.95 2.49 56.93 2.73 67 58;67.96 2.02 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 59.96 61 60.96 2.09 2.13 59.95 2.36 59.94 60.94 2.62 59.93 2.88 60 60.95 2.39 2.66 60.93 2.93 61 6261.96 2.16 61.95 2.43 61.94 2.70 61.93 2.97 62 6362.96 2.20 62.95 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 64.96 2.27 64.95 2.55 64.94 2.84 64.93 3.12 66 66 65.96 2.30 65.95 2.59 65.94 2.88 65.92 3.17 66 8766.96 2.34 66.95 2.63 66.94 2.92 66.92 3.21 67 6867.96 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 2.48 69.95 2,75 69.93 3.05 69.92 3.36 70 71 70.96 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 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 76.93 3.31 75.91 3.65 76 77 76.95 2.68 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. in 78.92 3.45 78.91 3.79 79 80 81 79.95 2.79 2.83 79.94 80.94 3.14 3.18 79.92 80.92 3.49 79.91 3.84 3.89 80 81 80.95 3.53 80.91 82 81.95 2.86 81.94 3.22 81.92 3.58 81.91 8.93 82 S3 82.95 2.90 82.94 3.26 82.92 3.62 82.90 3.98 8.3 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 35.9^ 3.75 85.90 4.13 S(i 87 86.95 3.04 86.93 3.42 80.92 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 90.95 3.14 89.93 3.53 89.91 3.93 89.90 4.32 90 01 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 4.4C 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 4.5C 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 ■*-» Q 99.94 3.49 99.92^ 3.93 Dep.] Lat. 99.91 4.36 99.88 4.80 100 to Q Dep. Lat. Dep. Lat. Dep. Lat. 88 De^. 87fDe£. 871 Deg. 87iDeg. 44 TRAVERSE TABLE. p. 1 3 Deg. II 31 Deg. H Deg. 3fbeg. Lat. Dep. Lat. 1.00 Dep. Lat. Dep. Lat. Dep. 1.00 0.05 0.06 1.00 0.06 1.00 0.06 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 6 6 5.99 0.31 5.99 0.34 5.99 0.37 5.99 0.39 6 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 8.98 0.51 8.98 0.56 8.98 0.69 9 10 9.99 0,52 9.98 0.67 9.98 0.61 0.67 9.98 0.65 10 11 11 10.98 0.58 10.98 0.62 10.98 10.98 0.72 12 11.98 0.63 11.98 0.68 11.98 0.73 11.97 0.78 Is 13 12.98 0.68 12.98 0.73 12.98 0.79 12.97 0.85 13 14 13.98 0.73 13.98 0.79 13.97 0.85 13.97 0.92 14 15 14.98 0.79 14.98 0.86 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 0.96 16.97 1.04 16.96 1.11 17 18 17.98 0.94 1 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 21.96 1.44 22 23 22.97 1.20 22.96 1.30 22.96 1.40 22.95 1.60 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 1.63 24.95 1.64 25 26 25.96 1.36 25.96 1.47 25.95 1.59 25.94 1.70 26 27 26.86 1-41 26.96 1.53 26.95 1.65 26.94 1.77 27 28 27.96 1.47 r27.95 1.69 27.95 1.71 27.94 1.83 28 29 28.96 1.52 128.95 1.64 28.95 1.77 28.94 1.90 29 30 31 29.96 30.96 1.57 ;29.95 1 . . . 1.70 29.94 1.83 29.94 30.93 1.96 30 31 1.62 30.95 1.76 30.94 1.89 2.03 32 31.96 1.67 31.95 1.81 31.94 1.96 31.93 2-09 32 33 32.95 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 2.2£ 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 40.94 2.09 39.94 '40.93 2.27 39.93 2.44 39.91 2.62 40 41 2.15 2.32 40.92 2.50 40.91 2.68 42 41.9^^ 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 2.8] 43 44 43.94 2.30 43.93 2.49 43.92 2.69 43.91 2.88 44 45 44.94 2.36 44.93 2.55 44.92 2.75 44.90 2.9-3 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 2.87 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 CO 49.93 2.62 Lat. ^49.92 2.83 49.91| 3.05 Dep. [Lat. 49.89 3.27 50 Dep. Dep. Lat. Dep. Lat. 87 Deg. ;86f Deg. 86iDeg. 86lD€g. TRAVERSE TABLE. 46 TRAVERSE TABLE. 5 4Deg. H Deg. 41 ■ Deg. 4| Deg. 5 CO 03 • Lat.lDep. Lat. Dep. Lat.JDep. i Lat. Dep. 1 I.OOJ 0.07 1 l.OC 0.07, i I.OOI 0.08 1.00 0.03 I 2 2.00i 0.14 ! 1.99 0.15: 1.99 0.16 1.99 0.17 3 2.99 0.21 : 2.99 0.221 2.99 0.24 2.99 0.25 S 4 3.99 0.28 3.99 0.30 i 3.99 0.31 3.98 0.33 4 5 4.99 0.35 4.99 0.37,: 4.98 0.39 4.98 0.41 5 6 5.99 0.42 5.98 0.441 5.98 0.47 5.98, 0.50 6 7 6.98 0.49 6.98 0.52i: 6.98: 0,55 6.97 0.58 7 8 7.98 0.56 7.98 0.59 : 7.98 0.63 7.97 0.66 8 9 8.98 0.63 8.98 0.67 1 8.97 0.71 8.97 0.75 9 10 9.98 0.70 0.77 9.97 0.74 9.97 0.78 9.97 0.83 10 111 10.97 10.97 0.82 !l0.97 0.86 10.96 0.91 11 1211.97 0.84 11.97 0.89 '11.96 0.94 11.96 0.99 12 1312.97 0.91 12.96 0.96 |-12.96| 1.02 12.96 1.08 13 14l 13.97 0.98 13.96 1.04 !13.96! 1.10 13.95 1.16 14 15' 14.96 1.05 14.96 1.11 114.951 1.18 14.95 1.24 15 1615.96 1.12 15.96 1.19|il5.95] 1.26 15.95 1.32 16 1716.96 1.19 16.95 1.26! 16.951 1.33 16.94 1.41 17 18 17.96 1.26117.95 1.331:17.94 1.41 17.94 1.49 16 19;i8.95 1.33,118.95 1.40'; 18.94; 1.49 18.93 1.57 19 2019.95 2l'20.95 1.40''l9.95 1 1.46i 20.94 1.481 19.94| 1.57 1.56' 20.941 1.65 19.93 1.66 20 20.93 1.74 21 2221.95 1.53|21.94 1.63' 21.93! 1-73 (21.92 1.82 22 2322.94 1.60! 22.94 1.70,22.93! 1.80 ;22.92 1.90 23 24'23.94 1.67li23.93 1.78:!23.93 1.88 ,23.92 1.99 24 ,25124.94 1.74i,24.93 1.85 24.92 1.96 24.91 2.07! 25 26 25.94 1.81 25.93 1.93125.92 2.04 [25.91 2.15; 26 27 26.93 1.88,1 i26.93 2.00 26.92 2.12 |26.91 2.241 27 2827.93 1.951:27.92 2.08 27.91 2.20 127.90 2.321 28 29,28.93 2.02! 128.92 2. 15| 28.911 2.28! 128.90 2.40; 29 3029.93 2.09 29.92 2.22 29.91 2.35 29.90 30.89 2.48 2.57 30 31 3ll30.92 2.16 30.91 2.30 30.90 2.43 32 31.92 2.23 31.91 2.37 31.901 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 3433.92 2.37 33.91 2.52; 33.90! 2.67 133.88 2.82 34 3534.91 2.44 34.90 2.59; 34.89 2.75'i34.88 2.90J 35 3635.91 2.51 35.90 2.67 35.89 2.82:35.88 2.98 36 37,36.91 2.58 36.90 2.74 36.89 2.90;l36.67 3.06! ST 38 37.91 2.65 37.90 2.82 37.88 2.98, 37.87 3.15! 38 S9'38.90 2.72J 38.89 2.89 38.88 3.06, 38.87 3.231 39 40.39.90 2.79 39.89 40.89 2.96; 39.86 3.14 3.04 40.87 3.22' 39.86, 3.31 40.86 3.40 _4Q 41 4l|40.90 2.86 42 41.90 2.93! 41.88 3.1141.871 3.30 41.86 3.48 42 43:42.90 3.00! 142.88 3.19 42.87' 3.37 42.85 3.56 43 4443.89 3.071:43.88 3.26 43.861 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 3.2ll 45.87 3.41 45.86 S.61| 45.84 3.81 45 47 46.89 3.28|i46.87 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 49,48.68 3.42 48.87 3.63 43.85 3.84 48.83 4.06 49 60 49.68 3.49 49.86 3.71J '49.85 8.92 49.83 4.14 50 -s '^ Dep. Lat. Dep. Lat.JDep. Lat. Dep. Lat. 86 Deg. 86|DegJl85^Deg.l 85iDeg.| -4 TRAVERSE TABLE. 4/ ;-,; 4 Deg. j 4' Deg. 4i Deg.jj 4J Deg. a r- Lat. Dep. Lat. Dep.' Lat. Dep. j Lat.jDep. 5 «-•• 51 50.88 3.56 50.86 3.78 50.84 4.00/50.821 4.22 51 52 51.87 3.63 51.86 3.85 51.84 4.08 i51.82; 4.31 52 53 52.87 3.70 52.85 3.93 52.84 4.16 52.82! 4.39 53 54 53.87 3.77 53.85 4.00 53.83 4.24 53.81i 4.47 54 55 54.87 3.84 54.85 4.08 54.83 4.32I 54.811 4-55 55 66 55.86 3.91 55.85 4.15 55.83 4.39 55.8II 4.64^ 56 57 56.86 3.98 56.84 4.22 56.82 4.4?! 56.80 4.721 57 58 57.86 4.05 57.84 4.30 57.82 4.55 57.80 4.80; 68 59 58.86 4.12158.84 4.37 58.82 4.63 58.80; 4.89 59 6059.65 4.19|59.84 4.45 59.82 4.71 |59.79i 4.97 60.81 4.7916O.79: 5.05 60 61 61 60.85 4.26 60.83 4.52 62 61.85 4.32 61.83 4.59 61.81 4.86 61.79 5.13 62 63 62.85 4.39 62.83 4.67 62.81! 4.94 62.78 5.22: 63 64 63.84 4.46 63.82 4.74 63.80; 5.02 163.78 6.30 64 65,64.84 4.53 64.82 4.82 64.80 5.10.64.78 5.38! 65 66 65.84 4.60 65.82 4.89 65.80 5.18 165.77 5.47 66 67 66.84 4.67 66.82 4.97 66.79 5.26 66.77 6.55^ 67 68 67.83^ 4,74 67.81 5.04 67.79 5.34 67.77 5.63 681 69 68.83| 4.81 68.81 5.11 68.79i 5.41 68.76 5.71! 691 70 69.831 4.88 69.81 5.19 j69.78 5.49 69.76 5.80 70 7170.83! 4.95 70.80 5.26 70.78 5.57 !70.76 5.88 71 72 71.82 5.02 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 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 75| 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 5.781:77.76 6.12 77.73 6.46 78 79 78.81 5.51 78.78 5.85i78.76 6.20 78.73 6.54 79 80 79.81 8180.80 5.58 79.78 5.65 80.78 5.93 79.75 6.28 79.73 6.62; 80 6.00 80.75 6.36 80.72' 6.71I 81 82 81.80 5.72 81.78 6.08 81.75 6.43;!81.72 6.79- 82 83 82.80 5.79 82.77 6.15i 82.74 6.51il82.71 6.87 83 84 83.80 5.86 83.77 6.23i 83.74 6.59i|83.7i; 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 8786.79 6.07 86.76 6.45 86.73 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 8988.78 6.21 88.76 6.60 88.73 6.98 88.70 7.37 89 90,89.78; 6.23 89.75 1 1 6.67 89.72 7.06 89.69 7.45 90 9190.78 6.35 90.75 6.74' 90.72 7.14 90.69 7.54 91 92 91.78 6.42 91.75' 6.82 91.72 7.22! 91.68 7.62 921 93 92.77 6.49 92.741 6.89 92.71 7.3o! 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 7.11 95.70 7.53' 95.67 7.95 96 97 96.76 6.77 96.73 7.19 96.70 7.6II 96.67 8.03 97 98 97.76 6.84 97.73 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| 100199.76 6.98 99.73 7.41 99.69 7.85 99.66 8.28 100 ^ JDep. •XI Lat. [pep. Lat.j'Dep. Lat. JDep.; Lat. ^ \ ■ ^ Ql 86 Deg.ii863Deg.'85]Deg. laSiDeg. Qj 48 TRAVERSE TABLE. 2i 5 Deg. 5i beg.i 5i Deg. 1 6;^ Deg. »-<• Gf3 . ^ ' 'l r* Lat. Dep. 1 Lat. Dep. Lat.l Dep. ; Lat. Dep. 00 1 1.00 0.091 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 0.36 ! 3.98 0.37 3.98 0.38 3.98 0.40 4 5 4.98 0.44 j 4.98 0.46 4.98 0.48 4.97 0.50 5 6 5.98 0.52' 5.97 0.55 5.97 0.58 5.97 0.60 6 7 6.97 0.61 6.97 0.64 6.97 0.67 6.96 0.70 7 a; 7.97 0.70 7.97 0.73 7.96 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 1 1 0.87 9.96 0.92 9.95 0.96 9.95 1.00 10 ll!l0.96| 0.96 10.95 J.Ol 10.95 1.05 10.94 1.10 11 1211.95 1.05 11.95 1.10 11.94 1.16 11.94 1.20 12 1312.95 1.13 12.95: 1.19 12.94 1.25| 12.93 1,30 13 1413.95 1.22 13.94, 1.28 13.94 1.34 13.93 1.40 14 15 14.941 1.31 14.94; 1.37 14.93 1.44 14.92 1.60 15 16 15.94; 1.39 16.93 1.46 16.93 1.53 15.92 1.60 16 1716.94] 1.48 16.93 1.56 16.92 1.63 16.91 1.70 17 1817.93 1.57 17.92; 1.65! 17.92 1.73 17.91 1.80 18 19 18.93 1.66 18.92; 1.74 18.91 1.82 18.90 1.90 19 20,19.92 1.74 19.92i 1.83 19.91 1.92 19.90 2.00, 20 2120.92 1.83 20.91 1.92 20.90 2.01 20.89 2.10 21 22 21.921 1.92 21.911 2.01 21.90 2.11i 21.89 2,201 22 2322.91 2.00 22.90 2.10 22.89 2.20: 22.88 2.30' 23 2423.91 2.09 23.90 2.20 23.89 2.301 23.88 2.401 ^ 35 24.90 2.18 24.90 2.29 24.88 2.401 24.87 2.50 25 26 25.90 2.27 125.89: 2.38 25.88 2.49; 26.87 2.60! 26 27 26.90 2.35 126.89^ 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; 28.86 2.91 29 30 30;29.89 2.6i; 29.87; 2.75 29.86 2.88| 29.85 3.01 31'30.88 2.70'30.87 2.84 ! 30.86 2.97 30.84 3.11; 3l| 32;31.83 2.79:i31.87i 2.93 31.85 3.07: 31.84 3.21 32 33^32.87 2.88 132.86! 3.02 32.85 3.16132.83 3.31 33 34^33.87 2.96 33.86; 3.11 33.84 3.26 33.83 3.41 34 35!34.87 3.05 34.86; 3.20 34.84 3.35 34.82 3.51 35 36'35.86 3.14 35.85: 3.29 35.83 3.45 35.82 3.61 36 37136.86 3.22 36.841 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 3S 39J38.85 3.40 38.841 3.57 38.82 3.74 38.8C 3.91 39 40 4039.85' 3.49 39.831 3.66 39.82 3.83 39.80 4.01 41 40.84 3.57 40.83J 3,75 40.81 3.93 40.79 4.11 41 42'41.84i 3.66 41.82| 3.84 41.81 4.031 41.79 4.21 42 43;42.84i 3.75:142.82 3.93 42.80 4.12 ;42.7g 4.31 43 44:43.83 3.83i:43.82 4.03 43.80 4.22 '43.78 4.41 44 45 44.83 3.92'i44.81 4.12 44.79 4.31 44.77 4.51 45 46'45.82 4.01ij45.81 4.21 45.79' 4.41 :45.77 4.61 46 47 46.82 4.10146.80 4.30 46.781 4.50 46.76 4.71 47 48|47.82 4.18|47.80 4.39 '47.78 4.60 47.76 4.81 43- 49148.81 4.271,48.79 4.48:48.77 4.70 146.75 4,91 49 50 49.81 4.36 49.79 Dep. 4.58 49.77 4.79 J49.75 6.01 Lat. 50 CO Dep. Lat. Lat. Dep. Lat. Dep. 85 Deg. 843 Peg. 84iDeg. 84iDeg. TRAVERSE TABLE. 49 51 5Deg. 5iDeg. H Deg. 5 J Deg. 5 CO 51 Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 50.81 4.44 50.79 4.67 50.77 4v89 50.74 5.11 52 51.80 4.53 51.78 4.76 51.76 4.98 51.74 5.21 52 53 52.8C 4.62 52.78 4.85 52.76 5.08 52.73 5.31 5S 54 53.79 4.71 53.77 4.94 53.75 5.18 53.73 ,5.41 54 55 54.79 4.79 54.77 5.03 54.75 5.27 54.72 6.51 55 56 55.79 4.88 55.77 5.12 55.74 5.37 55,72 5.61 56 57 56.78 4.97 56.76 5.22 56.74 5.46 56.71 6.71 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 5.75 5.85 59.70 6.01 60.69 6.11 60 61 60.77 5.32 60.74 5.58 60.72 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 64i63.76 5.58 63.73 5.86 63.71 6.13 63.68 6.41 64 65 1 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 70.67 6.71 69.65 7.01 70 70.73 6.19 70.70 6.50 6.81 70.64 7.11 71 72 71.73 6.28 71.70 6.59 71.67 6.90 71.64 7.21 72 73 72.72 6.36 72.69 6.68 72.66 7.00 72.63 7.31 73 74 73.72 6.45 73.69 6.77 73.66 7.09 73.63 7.41 74 75 74.71 6.54 7469 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 6.97 7.06 79.66 7.32 79.63 80.63 7.67 79.60 a02 80 80.69 80.66 7.41 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 82.581 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 8.5.67 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 R.S2 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. 5t! 8.63 89.55 9,02 90 90.65 7.93 90.62 8.33 90.58 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 9.011 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 99.62 8.72 99.58 9.15 99.54 9.58 1 Lat.l 1 99.50 10.02 100 CO Dep. Lat. Dep. Lat. Dep. Dep.| Lat. cc Q 85 Deg.l 84fbeg.| 84iDeg.| 841 Deg. Q 12 50 TRAVERSE TABLE. o CO 6Deg. 61 Deg. 6i Deg. 6^ Deg. 9 CO Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 1 0.99 0.10 0.99 0.11 0.99 0.11 0.99 0.12 1 2 1.99 0.21 1.99 0.22 1.99 0.23 1.99 0.24 2 3 2.98 0.31 2.98i 0.33 2.98 0.34 2.98 0.35 3 4 3.98 0.41 3.981 0.44 3.97 0.45 3.97 0.47 4 S 4.97 0.52 4.97| 0.54 4.97 0.57 4.97 0.59 5 6 5.97 0.63 5.96i 0.65 5.96 0.68 5.96 0.71 6 7 6.96 0.73: 6.961 0.76 6.96 0.79 6.95 0.82 7 R 7.96 0.84 7.95: 0.87 7.95 0.91 7.94 0.94 8 9 8.95 0.94 8.95 0.98 8.94 1.02 8.94 1.06 9 10 11 9.95 1.05 9.94 1.09 9.94 1.13 9.93 1.18 10 11 10.94 1.15 10.93 1.20 10.93 1.25 10.92 1.29 12 11.93 1.25' 11.93 1.31 11.92 1.36 11.92 1.41 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 17 1ft 17.90 1.88 17.89 1.96 17.88 2.04 17.88 2.12 18 19 18.90 1.99 18.89 2.07 18.88 2.15 18.87 2.23 19 20 19.89 21 20.88 2.09 19.88 2.18 19.87 2.26 19.86 2.35 20 21 2.20 20.88 2.29 20.87 2.38 20.85 2.47 22 21.88 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 '24.851 2.72 24.84 2.83 24.83 2.94 25 26 25.86 2.72i25.85i 2.83 25.83 2.94 25.82 3.06 26 27 26.85 2.82 26.84, 2.941 126.83 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 ■ 31 30.83 3.24! {30.82 3.37! '30.80 3.51 30.79 3.64 32 31.82 3.3431.81; 3.48131.79 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 3.66i34.79| 3.8l| 34.78 3.96 34.76 4.11 35 36 35. 8C 3.76 35.79 3.92 135.77 4.08 35.75 4.23 36 37 36. 8C 3.87 36.78 4.03 136.76 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 39 38.79 4.08 38.771 4.25 38.75 4.41 38.73 4.58 39 40 39.78 4.18 39.76J 4.35 139.74 4.53 39.72 ■40.72 4.70 40 41 41 40.78 4.29 140.76; 4.46; 40.74 4.64 4.82 42 41.77 4.39 i41.75! 4.57! 41.73 4.76 41.71 4.94 4<3 43 42.76 4.49 42.74! 4.681 42.72 4.87 42.70 5.05 43 44 43.76 4.60i43.74 4.79,43.72 4.98 43.70 5.17 41 45 44.75 4.70i44.73' 4.90; 44.71 5.09 44.89 5.29 45 4b 45.75 4.81 45.73; 5.011:45.70 5.21 45.68 5.41 46 47l46.7< 4.91 46.72! 5.12 i46.7(J 5.32 46.67 5.52 47 48 47.74 5.02 !47.7i: 5.25 ,47.69 6.43 147.67 5.64 48 4i) 48. 7J .5.12 48.71: 5.3^ 48.69 5.55 ;48.66 6.76 49 SL 49.73 5.2.S 49.70! 6.44 49.68 5.66 49.65 5.88 50 <-> CO Q 1 Dep.i Lat. 4-J CO Dep Lat Dep. Lat. Dep, Lat. 84 Deg. IsSfDeg. 83iDeg SSiDeg. TRAVERSE TABLE. 51 P. 6Deg. 6i Deg. 6 i Deg. 6iDeg. o «-t- 51 Lat. Dep. Lat. Dep. 60.70 5.55 Lat. Dep. Lat. Dep. 50.72 5.33 50.67 5.77 50.65 5.99 51 52 51.72 5.44 51.69 5.66 51.67 5.89 51.64 6.111 52 53 52.71 5.54 52.68 5.77 52.66 6.00 52.63 6.23 53 54 53.70 5.64 53.68 5.88 53.65 6.11 53.63 6.35 54 55 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 55.61 6.58J 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 57.60 6.82' 58 59 58.68 6.17 58.65 6.42 58.62 6.68 58.59 6.93 59 60 59.67 6.27 59.64 6.53 60.64 6.64 59.61 6.79 59.58 7.05! 60 61 60.67 6.38 60.61 6.91 60.58 7.17 61 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.Sb 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 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 J67.55 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 71 69.62 7.32 69.58 7.62 70.58: 7.73 69.55 70.54 7.92 69.51 8.23 70 8.35 71 70.61 7.42 8.04 70.51 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 73.56! 8.06 73.52 8.38 73.49 8.70 74 75 74.59 7.84!j74.55i 8.17 74.52 8.49 74.48 8.82, 75 76 75.58 7.94;j75.55' 8.27 75.51 8.60 75.47 8.93 76 77 76.58 8.05 176.54' 8.38 76.5! 8.72 76.47 9.05 77 78 77.57 6.15 177.54 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 80.52: 8.82 79.49 9.06 79.45 9.40 80 80.56 8.47 80.46 9.17 80.44 9.52 81 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 8.78i83.50; 9.14 83.46 9.51 83.42 9.87 84 85 84.53 8.88 184.50 9.25 84.45 9.62 84.41 9.99 85 86 85.53 8.99 85.49 9.36 85.45 9.74 85.4C 10.11 86 87 86.52 9.09! 86.48: 9.47 86.44 9.85 86. 4C 10.23 87 88 87.52 9.20J 87.48 9.58 87.43 9.96 87.3S 10.34 88 89 88.51 9.30i 88.47 9.69 88.43 10.08 88.3S 10.46 89 90 91 89.51 9.41 89.47j 9.80 9.51 90.46 9.91 89.42 10.19 89.38 10.58 90 10.70 91 90.50 90.42 10.30 90.3- 92 91.50 9.62^91.45 10.02 91.41 10.41 91.36 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 93.35 11.05 94 95 94.48 9.931 94.^14 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 10.98 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 98.4110.78 98.36 11.21 98.31 11.64 98 100 99.45 10.45 99.41110.89 99.36 11.32 99.31 11.75|100 • Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat \i 84 Deg. SS^Deg. 83iDeg. 83iDeg. t i>2 TRAVERSE TABLE. o 7 Deg. 'J\ Deg. 7i Deg. 7J Deg. C p. Lat. Dep. Lat.JDep. Lat, Dep, Lat. Dep. 1 0.99 0.12 0.99| 0.13 0.99 0.13 0.99 0.13 1 2 1.99 0.24 1.98! 0.25 1.98' 0.26 1.98 0.27 2 3 2.98 0.37 2.98 0.38 2.97 0.39 3.97 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 S 6 5.96 0.73 5.95 0.76 5.95 0.78 5.95 0.81 6 7 6.95 0.85 6.94 0.88 6.94 0.91 6.94 0.94 7 j 8 7.94 0.97 7.94 1.01 7.93 1.04 7.93 1.08 8 9 8.93 1.10 8.931 1.14 8.92 1.17 8.92 1.21 9 10 9.93 1.22 9.92 1.26 10.91 1.39 9.91 1.31 9.91 1.35 10 11 11 10.92 1.34 10.91 1.44 10.90 1.48 12 11.91 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 16 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 18.841 2.481 18.83 2.56 19 20 21 19.85 2.44 2.56 19.84 2.52 19.83 2.61 19.82 2.70 20 21 20.84 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 21.801 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 25.781 3.39 25.76 3.51 26 27 26.80 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 3.53 28.77 3.66 28.75 3-.79 28.74 3.91 2S 30 31 29.78 3.66 29.76 3.79 30.75 3.91 29.74 3.92 4.05 29.73 4.05 30 31 30.77 3.78 30.73 30,72 4.18 32 31.76 3.90 31.74 4.04 31.73 4.18 .?1.71 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 33.691 4.58 34 35 34.74 4.27 34.72 4.42 134.70' 4.57 34.68: 4.72 35 36 35.73 4.39 35.71 4.54 |35.69 4.70 35.67' 4.85 36 37 36.72 4.51 36.70 4.67 i36.68 4.83 36.66; 4.99 37 38 37.72 4.63 37.70; 4.80 i37.67 4.96 37.65i 6.12 38 39 38.71 4.75 38.69i 4.92 38.67 6.G9 38.64 6.26 39 40 39.70 4.87 39.68 5.05 40.67 5.17 39.66 5.22 40.65 6.35 39.63 5.39 40 41 41 40.70 5.00 40.63 5.53 42 41.69 5.12 41.66 6.30 |41.64| 5.48 41.621 5.66 42 43 42.68 5.24 42.661 6.43 142.63 6.61 42.61! 5.80 43 44 43.67 6.36 43.65' 5.55 43.62 5.74 43.60 5.93i 44 45 44.67 5.48 44.64 5.68 44.62; 5.87 44.59' 6.07| 45 45.58 6.201 46 46:45.66 5.61 45.63 6.81 45.61; 6.00 4746.66 5.73 46.62 5.93 46.60' 6.13 46.57 6.34; 47 48147.64 5.85 47.62 6.06 47.59; 6.27 47.56; 6.47 48 49 48.63 5.97 48.61 6.18 48,58i 6.40 48.55; 6.61 49 60 49.63 6.09 49.60| 6.31 49.57! 6.53 49.54| 6.74 50 3 Dep. Lat. Dep.l Lat. Dep.' Lat. Dep.l Lat. 00 83 Deg. l823Deg. 821 Deg. 82il Peg. 5 TRAVERSE TABLE 51 50.62 52 51.61 53 52.60 54 53.60 55 54.59 56 55.58 57 66.58 58 57.67 59 58.56 60 59.55 61 60.65 62 61.54 63 62.63 64 63.52 65 64.52 66 65.51 67 66.60 68 67.49 69 68.49 7069.48 71 70.47 72 71.46 73 72.46 74 73.45 75 74.44 76 75.43 77 76.43 78 77.42 79 78.41 80 79.40 .43 160.51 .56 161.50 .68 [62.50 .80 J63.49 .92; 64.48 .04: 65.47 .17166.46 .29j 67.46 .41 1 68.45 .53169.44 7060.48 7.96 82 61.47 8.09 95 62.46 8.22 08 63.45 8.35 20|64.44 8.48 33 165.44 8.61 46 166.43 8.75 60.44i 8 61.43 8 62.42: 8 63.42 8 64.41 8 65.40 8 66.39i 9 67.38. 9 68.37 9 69.36! 9 9190.32 11.09 9291.31 11.21 93 92.81 11.35 94 93.3011.46 95 94.29 11.58 96 95.28 11.70 97 96.28 11.82 98 97.27 11.94 99 98.2612.07 100 99.2512.19 90.27 91.26 92.26 93.25 94.24 11.48 11.61 11.74 11.86 11.99 95.23112.12 96.22112.24 97.22112.37 98.21 12.49 99.20 12.62 ^ Dep.l Lat. Dep. Lat.| Dep. Lat 90.22 11.88 91.21 12.01 92.20 12.14 93.20 12.27 94.19 12.40 95.1812.53 96.17 12.66 97.16 12.79 96.15 12.92 99.14 13.05 P I 83 Peg. 82|Deg.'82jDeg. 90.1712.271 91 91.1612.41 92 92.1512.54 93 93.1412.68 94 94.1312.81 95 95.12 12.95 96 96.11 13.08 97 97.10 13.22J 98 98.1013.35 99 99.091 13.49 100 iDep.! Lat.j 82'Deg.|Q 54 TRAVERSE TABLE. 5 8 Deg. 8i Deii., 8i Deg.j 8f Deg. ) 1 Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 0.99 0.14 0.99 0.14 0.99 0.15 0.99 0.15 2 1.98 0.28 1.98 0.29 1.98 0.30 1.98 0.30 2 3 2.97! 0.42 2.97 0.43 2.97 0.44; 2.97 0.46 3 4 3.961 0.56 3.96 0.57 3.96 0.69; 3.96 0.61 4 5 4.95; 0.70 4.96 0.72 4.96 0.74 4,94 0.76 5 6j 6.941 0.84 5.94 0.86 5.93 0.89 5.93 0.91 6 7| 6.93! 0.97 6.93 1.00 6.92 1.03 6.92 1.06 7 81 7.92| 1.11 7.92 1.15; 7.91 1.18 7.91 1.22 8 9 8.911 1.25 8.91 1.29 8.90 1.331 8.90 1.37 9 10 9.90 1.39 9.90 1.43 9.89 1.48j( 9.88 1.52 10 11110.89 1.53 10.89 1.68 10.88 1.63110.87 1.67 11 1211.881 1.67|11.88 1.72 11.87 1.77111.86 1.83 12 1312.871 1.81 112.87 1.87|12.86 1.92 12.85 1.98 13 14 13.86! 1.95 113.86 2.01 13.86; 2.07 13.84 2.13 14 15I4.85i 2.09 114.85 2.15 14.84 2.22 14.83 2.28 15 16 15.84 2.23 15.84 2.30;il5.82! 2.36 15.81 2.43 16 17 16.83i 2.37 16.83 2.44|16.8l| 2.61 16.80 2.59 17 18 17.82; 2.51 17.81 2.58; 17.80 2.66 17.79 2.74 18 1918.821 2.64 18.80 2.73 18.79 2.81 18.78 2.89 19 2019.811 2.78 19.79 2.87; 19.78 2.96 19.77 3.04 20 2120.80 2.92 20.78 3.01 20.77 3.10 20.76 3.19 21 22 21.791 3.06 21.77 3.16121.76 3.25 21.74 3.35 22 23 22.78: 3.20 22.761 3.30122.75 3.40 22.73 3.50 23 2423.771 3.34 23.75' 3.44; 23.74 3.65 23.72 3.65 24 25 24.76^ 3.48; 24.74; 3.59:24.73 3.70 24.71 3.80 25 26 25,75j 3.62 25.73; 3.T:3,.25i71; 3.84 25.70! 3.96 26 27 26.74; 3.76 26.72; 3.87 26.701 3.99 26.69! 4.11 27 28 27.73, 3.90 27.71i 4.02 27.69; 4.14 27.67i 4.26 28 -29 28.72! 4.04 28.70 4.16, 28.681 4.29 28.66 4.41 29 30 29.71! 4.18 29.69| 4.30| 29.67 1 1 4.43 29.65 4.66 30 31 3130.70; 4.31 !30.68i 4.45 30.66 4.58 30.64 4.72 32 31.69 4.45 31.67 4.69 31.66 4.73 31.63 4.87 32 33 32.68 4.59 32.66 4.74 32.64 4.88 32.62 6.02 33 34 33.67 4.731 33.65 4.88 33.63 5.03 33,60 5.17 34 35 34.66 4.87' 34.64 6.02 34.62 5.17 34.59! 5.32 35 36 35.65 5.01 35.63 5.17 36.60 6.32 35.58! 5.48 36 37 36.64 5.15:36.62 5.31 36.59 5.47 36.57 5.63 37 38 37.63 5.29137.61 6.46 37.58! 6.62 37.56 5.78 38 39 38.62, 5.43 138.60 6.60:38.571 5.76 38.56 5.93 39 40 39.61j 5.S7|:39.59 4140.60 5.71 40.58 6.74 39.561 5.91 6.88 40.55 6.06 39.53 6.C8 40 41 40.52 6.24 42 41.591 5.85' 41.57 6.03 41.54 6.21 41.61 6.39 42 43 42.68 6.98 42.56 6.17 42.53 6.36 42.60 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 44.61 6.65, 44.48 6.85 45 46 45.65, 6.40; 45.52 6.60 45.49 6.80i45.46 7.00 46 47 46.54 6.54 46.51 6.74 46.48 6.96ll46.45 7.15 47 48 47.63; 6.68; 47.50 6.89 47.47: 7.09;!47.44 7.30 48 4948.62! 6.82; 48.49 7.03;48.46; 7.24i|48.43 7.45 49 60 5 49.511 6.96i49.48 Dep.! Lat.liDep. 7.17 Lat. 49.45 7.39! ! 49.421 7.61 50 1 1 Dep.! Lat. 1 Dep.; Lat. 82 Deg.li81fDeg. 81iDeg.l SliDeg. Q TRAVERSE TABLE. 0| ®^*S' 81 Deg. 8i Deg. 8f Deg. 5' on Lat.lDep. Lat. Dep. Lat. Dep. Lat. Dep. siWsc 7.10 50.47 7.32 50.44 7.54 50.41 7.76 51 52 51.4S 7.24 51.46 7.46 51.43 7.69 51. .39 7.91| 52 53 52.48 7.38 52.45 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 8,21j 54 55|54.46 7.65 54.43 7.89 54.40 8.13 54,36 8.371 55 5655.46 7.79 55.42 8.04 55.38 8.28 55.35 8.52! 56 57;56.46 7.93 56.41 8.18 56.37 8.43 66.34 8.67i 57 58 57.44 8.07 57.40 8.32 57.36 8.57 57.32 8,82, 58 59,58.45 8.21 58.3£ 8.47 58.35 8.72 58.31 8.981 59 6059.42 6160.41 8.35 159.38 8.61 59.34 8.87 59.30 9.13 60 9,28! 61 8.49 '60.37 8.75 60.33 9.02 60.29 6261.40 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 9.18 63.30 9.46 63,26 9.74! 64 65,64.37 9.05 64. 3£ 9.33 64.29 9.61 164.24 9.89 65 66,65.36 9.19 65.32 9.47 65.28 9.76 165.23 10.04 66 6766.35 9.32 66.31 9.61 66.26 9.90 66.22 10.19 67 6867.34 9.46 67.30 9.76 67.25 10.05 67.21 10.34! 68 6968.33 9.60 68.29 9.90 68.24 10.20 68.20 10.50 69 7069.32 7170.31 9.74r69.28 1 9.88170.27 10.04 69.23 10.35 69.19 10.65 70 71 10.19 70.22 10.49 70.17 10.80 7271.30 10.02: 71.25 10.33 71.21 10.64 71.16 10.95 72 7372.29 10.161 72.24 10.47 J72.20 10.79 !72. 15 11.10 73 74*73.28 10.3073.22 10.62.l73.19 10.94 73.14 11.26 74 75174.27 10.44!; 74. 22 10.76! 74.18 11.09 74.13 11,41 75 76;75.26 10.58ii75.21 10.91! 75.17 11.23 75.12 11.56 76 77 76.25 10.72li76.20 11.051 76.15 11.38 76.10 11.71 77 78 77.24! 10. 861 77.19 11.19 77.14 11.53 77.09 11.87 78 79 78.23 10.99 78.18 11.34 78.13 n.68 78.08 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 n.97 80.06 12.32 82 81.20 11.41 81.15 11.771 81.10 12.12 81.05 12.47 82 83 82.19 11.55 '82.14 11.91 82.09 12.27 82.03 12.63 83 84!83.18 11.69 83.13 12.05' 183.08 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 ll.97j85.ll 12.34 85.06 12.71 85,00 13.08' 86 87 86.15 12.11186.10 12.48' 86.04 12.86 8.5.99 13.23 87 88 87.14 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 91 89.12 12.53 89.07 90.06 12.91i 1 89.01 13.30 88.95 89.94 13.69! 90 13.841 91 90.11 12.66 13.06: 90.00 13.45 92 91.10 I2.80: 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 13.08 193.03 13.49, 92.97 13.89:92.91 14.30 94 95 94.08 13.22 94.02 13.63! 93.96 14.04: !93.89 14.45' 96 96 95.07 13.36 95.01 13.78 94.95 [4.19!94.88 14.60 96 97 96.06 13.50] 96.00 13.92 '95.93 14.34 95.87 14.76 97 98 97.05 13.641196.99 14.06 96.92 14.49 ,96.86 14.91! 98 99 98.04 13.78' 97.98 14.21 97.91 14.63: 97.85ll5.06' 99 100 CO 99.03 Dep. 13.92 98.97 14.35 98.90 Lat. Dep. 14.78 i 98.84 15.21 lOOj Lat. ! Dep. Lat. Dep. Lat.l M 82 DegJ 81fDeg.l'81iDeg.ll 81 J Deg, =5 56 TRAVERSE TABLE. o 9 Deg. 1 9i Deg. 9i Deg. 9| Deg. o r Lat. Dep.? Lat.lDep. Lat. 0.99 Dep, 0.17 Lat. Dep. CO 1 1 0.99 0.16 0.991 0.16 0.99 0.17 2 1.98 0.31 1.971 0.32 1.97 0.33 1.97 0.34 2 3 2.96 0,47 2.96' 0.48 1 2.96 0.50 2.96 0,51 J 4 3.95 0.63 3.95 0.64'! 3.95 0.66i 3.94 0.68 i 5 4.94 0.78 4.93 0.80 4.93 0.83 4.93 0.85 5 6 5.93 0.94 6.92 0.96 6.92 0.99 5.91 1.02 6 7 6.91 1.10 6.91 L13 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 Ji 9 8.89 1.41 8.88 1.45 8.88 1.49 8.87 1,52 9 10 11 9.88 1.56 9.87: 1.61 10,86 1.77 9.86 10.85 1.65 9.86 10.84 1,69 1.86 10 11 10.86 1.72 1.82 1211.85 1.88 11.84 1.93 11.84 1.98 11.83 2.03 12 1312.84 2.03 12.83' 2.09 12.82 2.15 12.81 2.20 13 14 13.83 2.19 13.82! 2,26 13.81 2.31 13.80 2.37 14 1514.82 2.35 14.80] 2.41 1' 14. 79 2.48 ,14.78 2.54 15 1615.80 2.60 15.791 2.571 15.78 2.641,15.77 2.71 16 17 16.79 2.66 16.78' 2.73116.77 2.81116.75 2.88 17 1817.78 2.82 17,77! 2.89l|17.75 2.97:17.74 3.05 18 19 18.77 2.97 18.75i 3.05 18.74 3.14:;18.73 3.22 19 20|19.75 2l!20.74 3; 13 3.29 19.74 3.21 |19.73 20.71 3.30 3.47 19.71 3.39 20 20.73 3.38 20.70 3.56 21 22:21.73 3.44 21.71 3.64 21,70 3.63! 21.68 3.73 22 23 22.72 3.60 22.70 3.70 22.68 3.80' 22.67 3.9C 23 2423.70 3.75 23.69 3.86 23.67 3.96 23.66 4.06 24 25^24.69 3.91 24.67 4.02 ,24.66 4.13 24.64 4.22 25 2625.68 4.07, 25.66 4.18 i25.64 4.29 25.62 4.4C 26 27 26.67 4.22 26.65 4.34 26.63 4.46 26.61 4.57 27 28 27.66 4.381 27.64 4.50 i27.62 4.62 27.60 4.74 28 29 28.64 4.64 28.62 4.66 28.60 4.79 28.68 4.91 29 3029.63 3l'30.62 4.69 29.61 30.60 4.82 29.59 30.57 4.95 5.12 ;29.57 30.55 5.08 30 31 4.85' 4.98 5,25 32 31.61 5.01 31.68 5.14 31.66 5.28 31.6'^ 6,42 32 33 32.59 5.16' 32.57 5.30 32.56 5.45i 32.52 5,59 33 3433.58 5.32!|33.56 6.47 33.53 5.61 33,51 6.76 34 3534.57 5.48i!34.54 6.63 34.52 5,78 34,49 5.93 35 3635.56 5.63; 35.63 6.79 35.51 6.94 35.48 6.10 36! 37 36.64 5.79 36.52 5,95 36.49 6.111136.47 6.27 37 38 37.53 5.94 37.511 6.11 37.48 6.27 137.45 6.44 38 39 38.52 6.10 38.49 6.27 38.47 6.44 138.44 6.60 39 40:39.51 6.26 39.48 6.43 39.45 40.44 6.60 6.77 39.42 6.77 40 41 42 4ll40.50 6.41 40.47 6.59 40.41 6.04 4241.48 6.57 41.45 6.75 41.42 6.92 41.39 7.11 4342.47 6.73 43.AA 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 4746.42 7.35 46.39 7.65 46.36 7,76ii46.32 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 60 49.38 7.82 49.35 8.04 49,32 8.26 49.28 8.47 60 CO Q Dep. Lat. Dep. Lat. Dep, Lat. Dep. Lat. CO 81 Deg. SOfDeg. '80^ Deg. SOtDeg. TRAVERSE TABLE. 9? IJeg.j ^ Qi 9 Deg. I 9^ Deg. 9f Deg Lat. Dep. r Lat. srso 6251, 53,52, 64 53, 55 54, 56'55, 57 56, 58;57, 5958. 60,59. ereo, 62|61, 63;62, 64;63, 66'64, 66;65. 6766, 6867, 69'68, 70:69. 7.98 8.13 8.29 8.45 8.60 8.76 8.92 9.07 9.23 9.39 50.34 51..^2 52.31 53.30 54.28 55.27 56.26 67.25 58.23 59.22 9.54 9.70 9.86 21|10.01 2010.17 19|l0.32 18:10.48 16:10.64 1510.79 1410.95 60.21 61.19 62.18 63.17 64.15 65.14 66.13 67.12 68.10 69.09 Dep. Lat. Dep. Lat.Dep. f 8.20 8.36, 8.52, 8.68 8.84 9.00 9.161 9.32 9.48 9.64 50.30 51.29 52.27 53.26 54.25 55.23 56.22 57.20 58.19 59.18 8.42;!50, 8.58! i51, 8.75 i52, 8.91 53, 9.08 :54. 9.24 165, 9.41 56, 9.57 57, 9.74 158, 9.90|59, 9.81 9.97 i0.13 10.29 10.45 10.61 10.77 10.93 11.09 11.25 60.1610.07,60 61.1510.23161. 62.14 10.40 !62, 63.12 10.56 '63, 64.11 10.73 65.09 10.89 66.08 11.06 67.07 11.22 68.05 11.39 69.0411.55 26 8.64' 51 25 8.8li 52 23 8.98 53 22 9; 14 54' 21 9.31 55' 19, 9.48, 56* 18 9.65 57! 16' 9.82, 58, 15' 9.99, 59 13 10.16 60. 1210.33! 61 1010.60! 62 09 10.67i 63^ 0810.84: 64 06 11.01 1 65 0511.18 66 0311.351 67 02)11.52] 68 0011.69| 69 99 11.85 70 81 80.00: 12.6!- 82 80.99 )i;.83 8381.9SI2.9S 84 83.^7 ia.l4 35 c3.95 13.30 8684.94 13.45 87 85.93 13.61' 88,'66.92:i3.77 89:87.90' 13.92 9088.8914.08 79.95 13.02 80.93 13.18 81.92113.34 82.91]13.50 S3.89|13.66 84. 88! 13. 82' 85.87|13.98 86.86!14.15 87.84'l4.31 88.S3! 14.47. 79.89 13 80.88 13 81.8613 82.85 13 83.83 14 84. g2 14 85.61 14 86.79 14, 87.78 14. 88.77 14 '^.97 12.02 170.96 12.19 71.95 12.36 72.93 12.53 73.92 12.70 74.9012.87 75.89 13.04 76.87 13.21 77.86 13.38 78.84 13.55 ,37i|79.8313.72 ,53 80.82 13.89i ,70; 81.80 14.061 ,86 82.79 14.23| 03 83.77 14.39i .19 84.76 14.56] 36 85.74 14.73' 52' 86.73 14.90! 69; 87.71 15.07j 85; 88.70 15.24' ^ Dep.i Lat. Dep.' Lat. Dep. Lat. ^ I 81 Peg. 80|Deg. SOjDeg. Dep. Lat.l^J SOJDeg.P 58 TRAVERSE TABLE, 5 10 Deg. 1 lO^Deg. lOiDeg. lOfDpg. -'1 Lat. Dep.j Lat. Dep. ; Lat. Dep. Lat. Dep. 1 0.981 0.17, 0.98 0.18 0.98 0.18 0.98 0;i9 1 2 1.97 0.35 1.97 0.3^ 1.97 0.36 1.96 0.37 2 3 2.95 0.52 2.95 0.531 2.95 0.65 2.96 0.56 3 4 3.94' 0.691 3.94 0.71 3.93 0.731 3.93 0.75 4 5 4.92 0.87 1 4.92 0.89 4.92 0.91 4.91 0.93 5 G 5.91 1.04 5,90 1.07 5.90 1.09 5.89 1.12 6 7 6.89 1.22: 6.89 1.25 6.88 1.28 6.88 1.31 7 8 7.88 1.39 7.87 1.42 7.87 1.46 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 10.82 1.96 9.83 1.82 9.82 1.87 10.81 i 2.05 10 11 11 10.83 1.91 10.82 2.00 12 11.82 2.08 11.81 2.14 ll.SOi 2.19] 11.79; 2.24 12 13 12.80 2.26 12.79 2.31 12.78! 2.37; 12.77: 2.42 13 14 13.79 2.431 13.78i 2.49 13.77 2.65 13.75: 2.61 14 16 14.77J 2.60^ 14.76j 2.67 14.76 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.O.; 16.72 3.10 16.70 3.17 17 18 17.73 3.13 17.71' 3.20 17.70 3.281 17.68' 3.36 18 19 18.71 3.30 18.70 3.38 18.68 3.461 18.67J 3.54 19 20 21 19.70 3.47 3.65 19.68 3.56 19.67 3.64 19.65 3.73 20 21 20.68 20.66 3.74 20.65 3.83' 20.63! 3.92| 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 4.37j 23.68 4.48 24 25 24.62 4.34 24.601 4.45:24.58 4.56; 24.56 4.66 25 26 25.61 4.61 25.69| 4.63 25.56 4.741 25.54 4.85 26 27 26.59 4.69 26.57' 4.S0 26.65 4.921 26.53 5.04 27 28 27.57 4.86 27.55 4.98 ^7.53 5.101 27.51 5.22 28 29 28.56 5.04 28.54 5.16'28.&V 5.28 28.49 5.41 29 30 81 29.54 5.21 29.62 6.34 29.60| 5.47 30.51 6.52'30.48| 5.65 29.47 5.60 3<3.46 6.78 30 31 30.53 5.38 32 31.51 6.56 31.49 5.69 31.46: 6.83 31. 4t 5.97 32 33 32.50 5.73 32.47 6.87 32.45: 6.01 32.42! 6.16 S3 34133.43 6.90 33.46 6.05 33.43' 6.20| 33.401 G.u 34 35 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 6.66 35.37 6.71 36 37 36.44 6.42 36.41 6.58 36.38! 6.74136.35 6.90 37 38 37.42 6.60 37.39 6.76 37.36! 6.92 37.33 7.09 38 89 38.41 6.77 :38.3S 6.94 38.35 7.11 38.32 7.27 39 40 39.39 6.95 39.36 7.12 39.33 7.29 39.30 140.28 7.46 40 41 41 40.38 7.12 40.35, 7.30' 40.31 7.47 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 41 45 44.32 7.81 '44.28 8.0L 44.25 8.20 44.21 8.39 45 46 45.30 7.99 46.27, 8.19''45.23 8.38 45.19 8.58 46 47 46.29 8.16 46.26; 8.36! 46.21 8.57 46.18 8.77 47 48 47.27 8.34 '47.23' 8.54'47.2C 8.75 147. 16 8.95 48 49 48.26 8.51 48.22 8.72't48.18 8.93 148.14 9.14 49 5C CC 49.24 8.68 '49.20: 8.9C jDep. Lat » 49.1fi 9.11 49.12 9.33 50 CO Q Dep. Lat. Dep. Lat. Dep. Lat. 80 Deg. ;79iDeg 79iDeg. 79lDeg. TRAVERSE TABLE. 59 51 10 Deg. 10{Deir. lO^Dej:. lO|Deg. c Lat. 50.23 Dep. Lat. Dep. 50.191 9.08 Lat. Dep. Lat. Dep. r" 9.51 51 8.86 50.15 9.29 50.10 52 51.21 9.03 5L17, 9.25 51.13 9.48 51.09 9.70 52 53 52.19 9-20 52-15' 9.43 52.il 9.66 52.07 9.89 53 54 53.18 9,38 53.14 9.61 53.10 9.84 53.05 10.07 64 55 54.16 9.55 54.12 9.79 54.08 10.02 54.03 10.26 65 56 55.15 9.72 55.11 9.96 55.06 10.21 55.02 10.45 56 57 56.13 9.90 56-09110.14 56.05 10.39 56.00 10.63 57 58 57.12 10.07 57.07:10.32 57. C3 10.57 56.98 10.82' 68 59 58.10 10.25 58.06 10.50 58.01 10.75 57.96 11.00 59 60 61 59.09 10.42 5C-04 10.68 60.0310.85 59.<}0 59.98 10.93 58.95 11.19 60 11.38^ 61 60.07 10.59 11.12 59.93 62 61.06 10.77 61.0111.03 60.96 11.30 60.91 11.56 62 63 62.04 10.94 61.9911.21 61.95 11.48 61.89 11.75 63 64 63.03 11.11 62.9811.39 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 64.9511.74 64.89 12.03 64.84 12.31 66 67 65.98 11.63 65.9311.92 66.8? 12.21 65.82 12.50 67 68 66.97 11.81 66.91 12.10 6b.S6 12.39 66.81 12.68 68 69 67.95 11.98 67.90 12.2b 67.84 12.57 67.79 12.87 69 70 71 68.94 69.92 12.16 68.88 12.46 69.8712.63 68.83 69.81 12.76 68.77 13.06 "0^ 13.24 71 12.33 12.94 69.75 72 70.91 12.50 70.85 12.81 70.79 13.12 70.74 13.43 72 73 71.89 12.68 71.8312.99 71.78 13.30 71.72 13.62 73 74 72.88 12.85 72.82 13.17 72. 7o 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 13.20 74.79 13.52 74.73 13.85 74.67 14.18 76 77 75.83 13.37 75.77113.70 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 77.8C 13.72 77.74 14.06 77.68 14.40 77. 6J 14.74 79 80 81 78.78 13.89 78.72 14.24 79.71 14.41 78.66 79.64 14.58 78.60 14.92 80^ 15.11 81 79.77 14.07 14.76 79.58 82 80.75 14.24 80.69 14.59 80.63 14.94 80.56 15.29 82 83 81.74 14.41 81.6814.77 81.61 15.13 81.54 15.46 83 84 82.72 14.59 82.6614.95 82.59 15.31 82.63 15.67 84 85 83.71 14.76 83.6415.13 83.38 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 85.6n5.48 85.54 15.85 85.47 16.23 87 88 86.66 15.28 86.6015.66 86.5,? 16.04 86.46 16.41i 88 89 87.65 15.45 87.58|l5.84 87.61 16.22 87.44 16.60 89 90 91 88.63 15.63 88.66.16.01 89.55il6.19 88.49 16.40 88.42 89.40 16.791 90 16.97 91 S9.62 15.80 89.48 16.58 92 90.60 15.98 190.53 16.37 90.46ll6.77 90.39 17.16 92 93 91.59 lo.lS 91.52 16.55 91.44 16.95 91.37 17.35 93 94 92.57 16.32 92.50 16.75 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 95.4517.26 95.38 17.68 95.30 18.09| 97 98 96.51 17.02 96.4417.44 96.36 17.86 S6.28 18.28) 98 99 97.50 17.19 97.42 17.621 97.34 18.04 97.26 18.47' 99 100 • 98.46 17.36 98.40 17.79J 98.33 18.22 98.25 18.65 100 Lat. ^ Dep. Lat. Dep. Lat. Dep. Lat. Dep. s 80 Deg. 79iDeg.| 79iDeg.| 79iDeg.p 1 60 TRAVERSE TABLE, So t-f- 11 Deg.|lUDeg. lliDeg, ll|Deg.| si Lat.Dep.j Lat, Dep. Lat, Dep.' Lat. ^ CO Dep. T* 1 0.981 0.19 0.98 O.So'i 0.98 0.20 0.98 0.20 1 2 1.96 0.38 1.96 0.39 1.86 40 L96 0.41 2 0.61 8 3 2.84 0.57 2.94 0.59 2,94 0.60 2.84 4 3.93 0.76, 3.92 0.78 3.92 0.80 3.92 0,S2 4^ 5 4.91 0.95' 4.90 0.98 4.90 1.00 1 4.80 1.02 5 6 5.89 1.14 5.88 1.17 1 5.88 1.20il 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 1.79,1 8.81 1.83 9 10 9.82 1.91 9.81 1.95j 9.80 1.99 ! 9.79 2.04 10 11 10.80 2.10 10.79 2.15 10.78 2.19 10,77 2.24 11 1211.78 2.29 11.77 2.34' 11.76 2.39: 11.75 2.44 12 1312.76 2.48 12.75 2.54! 12. 74 2.59' 12.73 2.66 13 M 14 13.74 2.67 13.73 2.73113.72 2.79^ 13.71 2.85 15 14.72 2.86 14.71 2.93; 14.70 2.99' 14.69 3.C6 15 16115.71 3.05 15.69 3.1215.68 3.19 15.86 3.26' 16 1716.69 3.24 16.67 3.3216.66 3.39 16.64 3.46| 17 1817.67 3.43 17.65 3.51 il7.64 3.59; 17.62 3.66! 18 19 18.65 3.63 18.63 3.71 18.62 3.79 18.60 3.871 19 20 19.63 3.82 119.62 1 3.90 19.60 3.99; 19.58 4.07J 20 21 20.61 4.01 20.60 4.10 !20.58 4.19' 20.56 4.28 21 22 21.60 4.20 21.58 4.29 21.56 4.39"21.54 4.48 22 23 22.58 4.39 22.56 4.49 22.54 4.59 22.55 4.68: 23 24,23.56 4.58 J23.54 4.68 '23.52 4.78: 23.50 4.89 24 25 24.64 4.7:j24.52 4.88 24.50 4.98: 24.48 5.09 26 26125.52 4.96 '25.50 5,07 '25.48 5.18: 25.46 6.30 26 27 26.50 5.15 '26.48 5.27 '26.46 6.38' 26.43 6.50; 27 28:27.49 5.34 !27.46 5.46 27.44 6.58 27.41 5.70I 28 29J28.4T 5.5328.44 5.66 28.42 5.78 28.39 6.91| 29 6.11 30 30 29,45 5.72J!29.42 5. §5 29.40 5.98 29.37 3! 30.43 5.92,30.40 6.05 'ao.ss 6.18' 30.35 6.31 31 32 31.41 6.1l!31.39 6.24 31.36 6.38 31.33 6.52 32 6,72' 33 33 32.39 6.30; '32.37 6.44I 32.34 6.58 32.31 34 33.38 6.49j;33.35 6.63 33.32 6.7.8 33.29 6.92: 34 35134.36 6.68 134,33 6.83 34.30 6.98 34.27 7.13 35 36 35.34 6.87 35.31 7.C2 35.28 7.18 '35.25 7.33 36 37 36.32 7.06 36.29 7.22 36.26 7.38 136.22 7.53' 37 7.74; 38 7.94 39 38 37.30 7.25 37.27 7.41 37.24 7.58 37.20 39 38.28 7.44 38.25 7.61 i 38,22 7.78 38,18 40 39.27 7.63 39.23 7,80 39.20 7.97; 39.16 i 8.15 40 41*40.25 7.82 40.21 8.C0 40.18 8.17 40.14 8.35 41 4241.23 8.01 41.19 8.19' 41.16 8,37 41.12 8.65 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 8.58i43.12 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 45.16 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 9.67 47 4847.12 9.16 47.08 9.36| 47.04 9.57"46.99 9.78 48 49 48.10 9.35 48.06 9. 66] 48.02 9.77147.97 9.98 49 10.18 60 6049.08 1 9.64 49.04 9.75: 49,00 9.97 48.95 CO Deg. Lat.! Dep. 783 Lat. Dep. Lat.iiDep. I! Lat.L* 1 OQ s 79 Deg. Deg, 78^1 Deg.l 781] Jeg. 21 TRAVERSE TABLE. G^ TRAVERSE TABLE. o 12 Deg.l 1 12iDeg. 12iDeg. ] - Lat. ' Dep. L2f Deg.] 5-5 En* 1 Lat. Dep. Lat. Dep. Lat.lDep.'i r" 0.98 0.21 0.98 0.21 0.98' 0.22 0.98' 0.221 J 2 1.96 0.42 1.95 0.42 1.95! 0.43 1.95 0.441 2 3 2.93 0.62 2.93 0.64 2.93I 0.65 1 2.93 0.66 3 4 3.91 0.83 3.91 0.85! 3.91, 0.87 { 3.90i 0.88 4 5 4.89 1.04 4.89 I.O61 4.88 1.08 4.88' 1.10 5 6 5.87 1.25 6.86 1.27' 5.86 1.30, 5.85! 1.32 6 7 6.85! 1.46 6.84 1.49 6.83, 1.521 6.83 1.54 7 8 7.83 1.66 7.82 1.70! 7.81! 1.73 1 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 10.73^ 2.431 11 11110.76 2.29^ 10.76 2.33 10.74 2.38 1211.74 2.49ill.73 2.65 11.72 2.60, 11.70 2.65i 12 1312.72 2.70il2.70 2.76 12.69 2.81 12.68 2.87' IS 1413.69 2.91:113.68 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 16 16 15.65 3.33 15.64 3.39 15. K 3.46' 15.61 3.53 16 17 16.63 3.5316.61 3.61 16.60 3.68 16.58 3.75 17 18 17.61 3.741 17.59 3.82 17.57 3.90: 17.56 3.97 18 1918.58 3.95 18.57 4.03 18.55 4.11, 18.531 4.19: 19 20 19.56 4.16! 19.54 4.24 19.53i 4.33 1 19.61 4.41 1 20 2120.54: 4.37 20.52 4.46 2O.6O' 4.55 20.48 4.63! 21 2221.52' 4.57 21.50] 4.67 21.48 4.76 21.46' 4.86 22 23 22.50! 4.78 22.481 4.88 22.45^ 4.98 22.431 6.08 23 24 23.48] 4.99 23.45 5.09 23.43 5.19 23.41 6.30 24 25 24.451 5.20 24.43' 5.30 24.41 5.41 24.38 5.62 25 26 25.431 6.41 25.4l| 5.52 25.38 5.63 25.361 6.74 26 27 26.41 5.61 26.39 5.73 26.36 5.84 !26.33 6.96 271 2827.39 5.82 27.36' 6.&4 27.34 6.06 '27.31! 6.18 28| 2928.37 6.03 28.34! 6.15 28.31 6.28 28.281 6.40 29| 30 29.34 6.24 29.32! 6.37 29.29; 6.49 29.26 6.62 30 3130.32 6.45 30.29 6.58 30.27i 6.71 30.24 6.84 31 3231.30 6.65 31.27, 6.79 31.24| 6.93 31.21 7.06 32 3332.28: 6.86 32.25' 7.00 32.22' 7.14 132.19^ 7.28 331 34 33.26! 7.07 33.5i3' 7.21 33.19 7.36 33.16 7.50 341 35 34.24! 7.28 34.20 7.43 34.17 7.68 34.14 7.72 35 36 35.21' 7.48 35.18 7.64 35.15 7.79 35.ll! '-^Si 36 37 36.19 7.69 36.16 7.86 36.12 8.01 36.09' 8.17' 37 38 37.17 7,90 37.13 8.06 37.10: 8.22 37.06 8.39 38 39 38.15' 8.11 38.11 8.27 38.081 8.44 38.04 8.6I1 39 40 39.13! 8.32 39.09 8.49 39.05; 8.63 39.01 8.83: 40 4140.10^ 8.52 40.071 8.70 40.03! 8.87,39.99 9.05^ 41 42 41.08' 8.73 41.04! 8.91 41.00^ 9.09 |40.96l 9.27^ 42 43 42.06 8.94 42.02: 9.12 41.93 9.31 I41.94| 9.49i 43 4443.04 9.15 43.00' 9.34 42.96 9.52 42.92! 9.71! 44] 46144.02 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 44.87 10.15: 46 47 45.97, 9.77 45.931 9.97 45.89 10.17 45.84 10.37 47 4846.95! 9.98 46.91|10.18 46.86 10.39 46.82 10.69 48 4947.9310.19 47.88110.40 47.8410.61 47.79 10.81! 49 50 48.9110.40 48.86 10.61 48.81 10.82 |48.77H.03i 50 ^ Dep.' Lat.' Dep. Lat. Dep. Lat. JDep.; Lat. ^J M !_ to s 1 78 Deg.i77|Deg. 77iDeg.i|77iDeg. S | TRAVERSE TABLE. H on 51 12 Deg. T2iDeg. 121 Deg. 12fDeg. Lat. Dep. 5 51 Lat. Dep. Lat.lDep. 49.&4I10.82 Lat. Dep. 49.89Jl0.60 49.79 11.04 49.74 11.26 52 50.86llO.81 oO.Siiill.OS 50.77 11.25 50.72 11.48 52 53 51.84!ll.02 51.7911.25 51.74 11.47 51.69 11.70 53 54|52.82|11.23 '52.77'll.46 52.72 11.69 52.67 11.92 54 55 53.80|11.44 ^53.75111. 67 53. 7C 11.90 i53.64 12.14 55 56154.78:11.64 i54.72ill.88 54.67 12.12 54.62 12.36 56 57 55.75!ll.85 58|56. 73 12.06 155.70 12.09 55.65 12.34 155.59 12.58 57 |56.68 12.31 56.63 12.55 56.57 12.80 58 59 57.7112.27 57.66 12.52 57.60 12.77 57.55 13.02 59 60 58.69jl2.47 58.63 12.73 58.58 12.99 58.5213.24 60 61 59.67'l2 68 59.61 12.94 59.55 13.20 59.5013.46 61 62 60.6512.89 160.59 13.16 60.53 IJ.42 160.4713.68 62 63 6L62 13.10 61.57 13.37 61.51 13.64 61.45 13.90 63 64'62.60 13.31 62.54 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 64.56 13.72 64.50 14.00 6^1.44 14.29 64.37 14.57 66 67 65.54 13.93 65.47 14.22 65.41 14.50 65.35 14.79 67 68 66.5114.14 66.45 14.43 66.39 14.72 66.32! 15.01 68 69 67.49 14.35 67.43 14.64 67.36 14.93 67..30 15.23 69 70 71 68.47 14.55 11.76 68.41 14.85 68.34 69.32 15.15 68.27^15.45 69.2515.67 70 71 69.45 69.38!l5.06 15.37 72 70.43 14.97 70.36:15.28 70.29 15.58 70.2215.89 72 73 71.40 15.18 71.3415.49 71.27 15.80 71.2016.11 73 74 72.38 15.39 :72.32il5.70 72.26 16.02 72.1816.33 74 75 73.36 15.59 [73.29 15.91 73.22 16.23j 73.15 16.55 75 76 74.34 15.80 74.27 16.13 74.2c 16.45; 74.13:16.77 76 77 75.32 16.01 75.25 16.34 75.17 16.67175.10 16.99 77 78 76.30 16.22 76.22 16.55 76.16 16.88 !76.08 17.21 78 79 77.27 16.43 77.20 16.76 77.13 17.10 i77.05]l7.44 79 80 78.25 16.63 .78.18 16.97 78.10 17.32 78.0317.66 80 81 79.23 16.84 79.18 17.19 79.08 17..53 79.00:17.88 81 82 80.21 17.05 80.131 17.40 80.06 17.75 79.9818.10 82 83 81.19 17.26 8l.llll7.61 81.03 17.96 SO.95! 18.32 83 84 82.16 17.46 82.09 17.82 82.01 18.18 i81.93'18.54 84 85 83.14 17.67 83.06 18.04 82.99 18.40 I82.90il8.76 85 86' 84. 12 17.88 84.04 18.25 83.96 13.61 ;83.88'1S.98 86 87!85.1G 18.09 85.02 18.46 84.94 18.83 i84.85 19.20 87 88 86.08 18.30 86.00 13.67 85.91 ■9.65 85.83 19.42 88 89 87.06 18.50 86.97 18.88 86.89 19.26 86.8119.64 89 90 88.03 91 89.01 18.71 18.92 87.95 88.93 19.10 87.87 88.8^ 19.48 !S7.78:19.86 19.70|88.76!20.08 90 91 19.31 92 89.99 19.13 89.91 19.52 89.82 19.91 !89.73j20.30 92 93 90.97 19.34 90.88 19.73 90. SO iJ.13 '90.71:20.52 93 94 91.95 19.54 91.86 19.94 91.77 20.35 191.68:20.75 94 95 92.92 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 93.6321.19 96 97 94.88 20.17 94.79 20.58 94.70 20.99 94.6II2I.4I 97 98 95.86 20.38 95.77 20.79 95.68 21.21 ,95.58:21.63 98 99 96.84 20.58 96.75 21.01 96.65 21.43 96.56:21.85 99 100 IS 97.81 Dep. 20.79 Lat. 97.72 Dep. 21.22 97.63 Dep. 21.64 9T.53 22.07 100 03 Lat. Lat. Dep. J Lat. 78 Deg. 77f Deg. 77iDeg.i 77iDeg. Q u TRAVERSE TABLE. o 1 13 Deg. IS^Deg. ISfDeg. 133 Deg. 5? CD <-^ 1 Lat. 0.97 Dep. 0.23 Lat. Dep. 0.97 0.23 Lat.JDep. 0.97^ 0.23 Lat. Dep. 0.97 0.24 2 1.95 0.45 1.95 0.46 I.95I 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 1.191 6 6 5.85 1.35 5.84 1,38 1 5.83 1.40 5.83 1.43! 6 7 6.82 1.57 6,81 1.60 1 6.81 1.63 6.80 1.66 7 8 7.80 1.80 7.79 1.83 7.78 1.87 7.77 1.90 8 9 8.77 2.02 8.76 2.06 8.75 2.10 8.74 2.14 9 10 9.74 2.25 9.73 2.29 9.72 2.33 • 9.71 2.38 21 11 10.72 2.47 10.71 2.52 :10.70 2.57 10.68 2.61 11 12 11.69 2,70 11.68 2.75 !ll.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 .3.15 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 3.67 15 16 15.59 3.60 15.57 3.67 16,56! 3.74 15.54 3.80 16 17 16.57 3.82 16.55 3.90 16.53 3.97 I6.51! 4.04] 17 18 17.54 4.05 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' 4.52I 19 20 21 19.49 4.50 4.72 19.47 4.58 20.44 4.81 19.45 4.67 19.43 4.75 20.40, 4.99 20 21 20.46 20.42 4.90 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 6.47 23 24 23.38 5.40 23.36 5.60 23,34 6.60 23.31; 5.70 24 25 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 26.31 6.07 26.28 6.19 26.25 6.30 26.23, 6.42 27 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 29.23 6.75 29.20, 6.88 30.17 7.11 29.17 30,14 7.00 29.14 7.13 30.1l| 7.37 30 31 31 30.21 6.97 7.24 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 32,09j 7.70 32.051 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 34.07i 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 38.05 8.32 36,02 8.48 35.98i 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 S7.92t 9.10 37.88: 9.27 39 40 38.97 9,00 38.94, 9.17 38.89 9.34 38.85 9.51 40 4139.95 9.22 39.9li 9.40 39.87' 9.57 39.83 9.75 41 42 40.92 9.45 40.88, 9.63 40.84' 9.80 40.80 9.88 ^ 43 41,90 9.67 41.86 9.86 41.8l| 10.04 41.7710.22 43 44 42.87 9.90 42.83 10.08 42.7810.27 42.74 10.46 44 45 43,85 10.12 43.80 10.31 43,7610,51 43.71 10.70 46 46 44.82 10.35 44.78,10.54 44.7310.74 44.6810.93 46 47 45.80 10.57 45.75 10.77 45.7010.97 45.6511.17 47 48 46.77 10.80 46.7211.00 46.67jll,21 46.62!ll.41 48 49 47.74 11.02 47.7011.23 47.65|11.44 47.60|11.65 49 50 5 48.72 11.25 48.67lll.46 48.62 11,67 48.57 11.88 50 Dep. Lat. Dep.l Lat. Dep. Lat. Dep. Lat, 77 Deg. k^Deg. 76iDeg. 76iDeg. TRAVERSE TABLE. 6i (_, 13Deg. ISfDeg 13iDeg..l3|Deg. 66 TRAVERSE TABLE. 5 14 Deg.^ 14iDeg.|| 14iDeg. M^Deg. to' Lat.j Dep.j Lat. Dep. Lat. Dep. Lat. Dep.j 1 0.97 0.24' 0.97 0.25' 0.97 0,25 0.97 0.25 ij 2 1.94 0.48: 1.94 0.49. 1.94 0.50 1.93 0.61 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 £ 6 5.82 1.45 5.82 1.48 5.81 l,50|i 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| 9.68 2.50 9.67 2.55 10 10.66 2.71 10.65 2.75 10.64 2.80 11 12 11.64 2.90 11.63 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 3.31 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 3.69i 14.52 3.76J 14.51 3.82 15 16 15.52 3.87 15.51 3.941 15.49 4.011 15.47 4.07 16 17 16.50 4.11 16.48 4.18i 16.46 4.26! 16.44 4.33 17 18 17.47 4.35 '17.45 4,43 i 17.43 4.51:17.41 4.581 18 19 18.44 4.60 i 18.42 4.68' 18.39 4.76 18.37 4.841 19 20'19.41 4.84 19.38 4.92: 19.36 5.01' 19.34J 5.091 20] 2120.38 5.08 20.-35 5.I7I 20.33 5.26 20.31 5.351 21 22 21.35 5.32 121.32 6.42 21.30 5.61 21.28 5.6OI 22 2322.32 5.56 i22.29 6.66 22.27 5,76!l22.24 6.S6i 23 24 23.29 5.8l!^23.26 6.9li 23.24 6.01 23.21 6.11 24 25124.26 6.05 24.23 6.15 24.20 6.26124.18 6.37 25 26'25.23 6.29 25.20 6.40 25.17 6.51!125.14 6.62 26; 27j26.20 6.53 26.17 6.65 26.14 6.76|l26.11 6.87! 27 2827.17 6.77 127.14 6.89 27.111 7.01]127.08 7.I3I 28 29 28.14 7.02 l28.ll 7.14 28.081 7.26 '28.04 7.38; 29 3029.11 IM 29.08 7.38' 29.041 7.51 29.01 7.64; 30 1 3130.08 7.50 I3O.O5 7.63 30.0lt 7,76 '29.98 7.89' 31 32 31.05 7.74 i31.02 7.88 30.98J 8.01 :30.95 8.15; 32 3332.02 7.98;l31.98| 8.12 3I.95I 8.26131. 91 8.40 33 34,32.99 8.23132.95', 8.37 32.921 8.51I '32.88 8.66 34 35,33.96 8.47^33.921 8.62133.89' 8.76^33.85! 8.91 35 36 34.93 8.71 ,34.891 8.86 34.85' 9.01 !34.81 9.17 36 37 35.90 8.95 ,35.861 9.11 35.821 9.26 |35.781 9.42! 37 38;36.87 9.19 36.831 9.35 36.79| 9.51 36.75 9.671 38 39137.84 9.44 37.80i 9.60 37.76 9.76 37.71 9.93I 39 40 38.81 9.68 38.771 9.85 38.73 10.02 :38.6810.18 40 41|39.78 9,92 39.7410.09 39.69 10.27 |39.65'l0.44! 41 4240.75 10.16 140.71 10.34 40.66ll0.52 i40.62!l0.69' 42 4341.72 10.40' '41.68 10.68 41.63il0.77 141.5810.95 43 42.55:11.20 44 44 42.69 10.64" 42.65 10.83 42.6C 11.02 45 43.66 10.89; 143.62 11.08 43.57 11.27 43.5211.46 45 46 44.6i: 11.13 I44.5B 11.32 44.63 11.52 4^1.4811.71 46 47 45.60 11.3' j45.5511.67 45.5C 11.77 45.45,11.97 47 48 46.67 11.61 46.52 11.82 46.4' 12.02 46.4212.22 48 49i47.5411.85'|47.49,12.06 47.44 12.27 47.39 12.48 49 5 -•- 48.5lll2.10 48.4612.31 - 1 11 1 48.41 12.52 48.3512.73 60 ; Dep .JLat .|Dep.|Lat. Dep Lat. Dep.| Lat ^ 7C DegJ753DBg. ll75fDeg. 75iDeg TRAVERSE TABLE. 6? a So" 51 14 Deg. HiDeg.j Hi Deg. 1 45 Deg. 2 So Lat. Dep. Lat. Dep. Lat. Dpe. Lat. Dep. 49.49 12.34 49.43 12.55 49.38 12.77 49.32 12.98 51 52;50.46 12.58 50.40 12.80 50.3413.02 50.29 13.24 52 53i51.43 12.82 51.37 13.05 51.31113.27 51.25 13.49 53 5452.40 13.06 62.34 13.29 52.28113.52 52.22 13.75 54 55i53.37 13.31 53.31 13.54 53.25113.77 53.19 14.00 55 56,54.34 13,55 54.28 13.78 54. 22 1 14. 02 54.15 14.26 56 57,55.31 13.79 55.25 14.03 55. is; 14.27 55.12 14.51 57 58 56.28 14.03 56.22 14.28i 56.15,14.52 56.09 14.77 58 5957.25 14.27 57.18 14.52: 57.12tl4.77 57.06 15.02 59 60 58.22 1 6159.19 i4.52j 58,15 14.77| 58.09 15.02 59.06'l5.27 58.02 15.28 60 61 14.76: 59.12 15.021 58.99 15.53 6260.16 15.00 60.09 15.251 60.03115.52 i59.96 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; 61.9616.02 61.89 16.29 64 65 63.07 15,72 63.00 16.00 62.9316.27 j62.86 16.55 65 66 64.04 I5.97i 63.97 16.25 63.90 16.53 63.83 16.80 66 67 65.01 16.21 6494 16.49 64.87 16.78 164.79 17.06 67 68 65,9S 16.45 65.91 16,74 65.83 17.03 |65.76 17.31 68 69:66,95 16.69' 66.88 16.98 66.80 17.28 166.73 17.57 69 70|67.92 71'68.89 16.93| 67.85 17.23 67.77 17.53 68.7417.78 67.69 17.82 70 71 17.18' 68.82 17.48 68.66 18.08 72:69.86 17.42! 69.78 17.72 69.7118.03 169.63 18.3S 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 18.8^ 74 io,72.77 18.14; 72.68 18.46 72.61 18.78 72.53 19.10 75 76|73.74 18.39 73.66 18.711 73.58 19.03 73.50 19.35 76 77174.71 18.63 74.63 18.95: 74.55 19.28 74.48 19. 6C 77 78 75.68 18.87 75.60 19.20: 75.52 19.53 75.43 19.86 78 79 76.65 19.11 76.57 19.45 i76.48 19.78 76.40 20.11 79 80 81 77.62 19.35 77.54 19.69| 77.45 20.03 19.94! 78.4220.28 77.36 20.37 80 81 78.59 19.60 78.51 78.33 20.62 82 79.56 19.84 79.48 20. 18ii79.39 20.53 79.30 20.88 82 83 80.53 20.08| 80.45 20.43! 80.36 20.78 80.26 21.13 83 84 81.50 2O.32I 81.42 20.681 81.32 21.03 81.23 21.39 84 85 82.48 20.56! 82.38 20.92 82.29 21.28 182.20 21.6-^ 85 8683.45 20.81 83.35 21.17 83.26 21.53 83.17 21.90 86 87|S4.42 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 8986.36 21.53 86.26 21.91' 86.17 22.23 86.07 22.68 89 90 87.33 91 88.30 21.77J 87.23 22.15, 87.13|22.53 88.10,22.78 87.03 22.91 90 91 22.011 68.20 '22.40 86.00 23.17 92 89.27 22.26: 89.17 22.65 89,07 23.04 88.97 23.42 92 93 90.24 22..50i 90.14 22.89 90.04 23.29 89.94 23.68 93 94 91.21 22.741 91.11 23.14 91.01 23.54 90.90 23.93 94 95 95 92.18 22.98' 92.08 2-3.381 91.97 23.79 91.87 24.19 96 93.15 23.22 93.05 23.63! 92.9424.04 92.84 24.44 96 97194.12 23.47, 94.02 23.88i 93.9124.29 93.80 24.70 97 98 95.09 23.711 94.98 24.12 94.88 24.54 94.77 24.95 98 99 96.06 23.951 95.95 2i.37j 95.85 24.79 95.74 25.21 99 100 CO 5 97.03 24.19 96.92 24.62 96.81 ;25.04 Dep.! Lat. 96.70 25.46 100 CO Q Dep. Lat. Dep. Lat.l Dep. Lat. 76 Deg. 75|Deg.| 75iDeg. 75iDeg. m TRAVERSE TABLE. s 1 15 Deg. IS^Deg.j ISiDeg. laiDe?. 5 on' ■ irt- 1 Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 0.97 0.26 0.96 0.26 0,96 0.27 0.96 0.27 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 L04 3.86 1.05 3.86 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 6.80 1.55 6.79 1,58 6.78 1.60 5,77 1.63 6 7 6.76 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 11 9.66 2.59 9.65 10.61 2.63 9.64 2.67 9.62 2.71 10 11 10.63 2.85 2.89 10.60 2.94 10.59 2,99 .12 11.59 3.11 11.58 3.16 11.66 3.21 11.56 3.26 12 13 12.56 3.36 12.54 3.42} 12,63 3.47 12.51 3.63 13 14 13.62 3.62 13.61 3.681 13.49 3.74 13.47 3.80 14 15 14.49 3.88 14.47 3.95i 14,45 4,01 14,44 4.07 15 16 15.45 4.14 15.44 4.21 16,42 4.28 16.40 4.34 16 17 16.42 4,40 13.40 4.47 16.38 4„54 16.36 4.61 17 18 17.39 4.66 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 6.16 19 20 21 19.32 6.13 19.30 6.26 19,27 5.34 19.25 6.43 20 21 20.28 5,44 20.26 5..62 20.24 6,61 20.21 5.70 22 21.26 5.69 21.23 6.79 21.20 5.88 21.17 5.97 22 23 22.22 6.95 22.19 6.05 22.16 6.16 22.14 6.24 23 -24 23.18 6.21 23.15 6.31 23.13 6.41 23.10 6.61 24 25 24.15 6.47 24.12 6.58 24.09 6.68 24.06 6.79 25 26 25.11 6.73 aj.08 6.84 26.05 6.95 26.02 7.06 26 27 26.08 6.99 26.06 7.10 26.02 7.22 25.99 7.33 27 28 27.06 7.25 27.01 7.36 26.98 7.48 26.95 7.60 28 29 28.01 7,61 27.98 7.63 27.95 7.75 27.91 7.87 29 30 31 28.98 7.'?6 28.94 7.89 28.91 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 30.84 8,56 30.80 8.69 32 33 31.88 8.54 31.84 8.B8 31.80 8.82 31.76 8.96 33 34 32.84 8.80 32.80 8.94 32.76 9.09 32.72 9.23 34 35 33.81 9.06 33.77 9.21 33.73 9.36 33.69 9.60 35 36 34.77 9,32 34.73 9.47 34.69 9.62 34.65 9.77 36 ■37 35.74 9.68 35.70 9.73 35,65 9.89 35.61 '-O.O-: 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 38 40 38.64 10.35 38,69 10.52 38.55 10.69 38,50 10.86 40 41 39.60 10,61 39,56 10.78 39.51 10.96 39,46 11.13 41 ,42 40.57 10,87 40.52 11.05 40.47 11.22 40,42 11.40 42 43 41.53 11.13 41.49 11.31 41.44 11.49 41.39 11.67 43 44 4^50 11.39 42.45 11.67 42.40 11,76 42,35 11.94 44 45 43.47 11,65 43.42 11.84 43.36 12,03 43,31 12.2] 45 46 44.43 11.91 44.38 12.10 44.33 12.29 44,27 12.49 46 47 45.40 12.16 45.36 12.36 45.29 12.56 46,24 12.76 47 48 46.36 12.42 146.31 12.63 46.25 12.83 46.20 13.03 48 49 47.3S 12,68 ;47.27 12.89 47.22 13.09 47.16 13.30 49 :60 48.30 12,94 148.24 13.15 48.18 13.36 48.12 13.67 60 Dep. Lat, iDep. Lat, Dep. Lat. Dep. Lat. en 5 75 Deg. ' 74iDeg .74fDeg. 74iDeg. TRAVERSE TABLE TRAVERSE TABLE. TRAVERSE TABLE. 71 p. 51 16 Deg. le^Deg. 16i Deg. le^Deg. 51 Lat. Dep. Lat. Dep. Lat. 48.90 Dep. 14.48 Lat. Dep. 14.70 49.02 14.06 48.96 14.27 48.84 5ii 49.99 14.33 49.92 14.55 49.86 14.77 49.79 14.89 55 5ii 50.95 14.61 50.88 14.83 50.82 16.05 50.75 15.27 Bf. 54 51.91 14.88 51.8415.11 51.78 15.34 51.71 15.56 M 55 52.87 15.16 52.80 16.39 52.74 15.62 52.67 15.85 5.^. 56 53.83 15.44 53.76 15.67 53.69 15.90 53.62 16.14 56 57 54.79 15.71 54.72 15.95 54.65 16.19 54.58 16.43 57 58 55.75 15.99 55.68 16.23 55.61 16.47 55.64 16.72 58 69 56.71 16.26 56.64 16.51 56.57 16.76 56.50 17.00 59 60 61 57.68 16.54 57.60 16.79 67.53 17.04 57.46 17.29 17.58 60 61 68.64 16.81 58.56 17.07 58.49 17.32 58.41 62 59.60 17.09 59.52 17.35 59.45 17.61 59.37 17.87 62 6S 60.56 17.37 60.48 17.63 60.41 17.89 60.33 18.16 63 64 61.52 17.64 61.44ll7.91 61.36 18.18 61.28 18.44 64 65 62.48 17.92 62.40il8.19 62.32 18.46 62.24 18.73 65 66 63.44 18.19 63.3618.47 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 19.57 67.20 19.59 67.12 19.88 20.17 67.03 67.99 20.17 20.46 70 71 68.25 68.16 19.87 68.08 72 69.21 19.85 69.12 20.15 69.03 20.45 68.95 20.75 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 20.95 72.96 21.27 72.87 21.59 72.78 21;90 76 ■77 74.02 21.22 73.92 21.55 73.83 21.87 73.73 22.19 77 78 74.98 21.50 74.88 21.83 74.79 22.15 74.69 22.48 78 79 75.94 21.78 75.84 22.11 75.75 22.44 75.66 22.77 79 80 81 76.90 22.05 22.33 76.80 22.39 22.67 76.71 22.72 76.61 77.56 23.06 80 77.86 77.76 77.66 23.01 23.34! 8l| 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 79.48 23.92 83 84 80.75 23.15 80.64 23.51 80.54 23.86 80.44 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 82.35 24.78 86 87 83.63 23.98 83.52 24.35 83.42 24.71' 83.31 26.07 87 88 84.59 24.26 84.48 24.62 84.38 24.99 84.27 25.36 88 89 85.55 24.53 85.44 24.90 85.33 25.28 85.22 25.66 89 90 91 86.51 24.81 86.40 25.18 25.46 86.29 25.56 86.18 87.14 25,94 26.23 90 91 87.47 25.08 87.36 87.25 25.85 92 88.44 25.36 88.32 25.74 88.21 26.13, 88.10 26.51 92 93 89.40 25.63 ,89.28 26.02 89.17 26.4ll 89.06 26.80 93 94 90.36 25.91 00.24 26.30 90.13 26.70' 90.01 27.09 S4 95:91.32 26.19 91,20 26.58 91.09 26.98' 90.97 27.38 95 96 92.28 26.46 92.16 26.86 92.05 27.27 91.93 27.67 96 97 93.24 26.74 93.12 27.14 93.01 27.55: 92.88 27.95 97 98 94.20 27.01 94.08 27.42 93.96 27.&3 93.84 28.24 98 99 95.16 27.29 95.04 27.70 94.92 28.12' 94.80 28.53 99 100 96.13 27.56 96.00 27,98 95.88 28.40 95.76 28.82J100 CO Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 1 ^• 1 CO 74 Deg. 73^Deg. 73^1 Deg.l 73^1 I>eg. «| n TRAVERSE TABLE. o TTC eg. IT^Deg. IT^Deg. 17fDeg. CO en 1 Lat. 0.96 Dep. Lat. Dep. Lat. i Dep. Lat. Dep. 0.29i 0.95: 0.30 0.95 0.30 0.95 0.30 1 2 1.91 0.58 1.91 0.59 1.91 0.60 1.90 0.61 2 3 2.87 0.83! 2.87 0.89 2.86 0.90 2.86 0.91 3 4 3.83 1.17: 8.82 1.19 3.81 1.20 3.81 1.22 4 5 4.78 1.46 4.78: 1.48 4.77 1.50 4.76 1.52 6 6 5.74 1.75 5.73 1.78 5.72 1.80 5.71 1.83 6 7 6.69 2.05i 6.691 2.08 6.68 2.10 6.67 2.13 7 fi 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 9.56 '2.92 9.55 2.97 9.54 3.01 9.52 3.05 IQ 10.52 3,22! 10.51 3.26 10.49 3.31 10.48 3.35 12 11.48 3,51 11.46 S.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 15.26 4.81 15.24 4.88 16 17 16.26 4.97 16.24 6.04 16.21 5.11 16.19 6.18 17 18 17.21 5.26 17.19 5.34 17.17 5.41 17.14 5.49 18 19 18.17 5.56 18.15 5.63 18.12 5.71 18.10 5.79 19 20 19.13 5.85 19.10 5.93 19.07 6.01 19.05 6.10 20 21 21 20.08 6.14 20.06 6.23 20.03 6.31 20.00 6.40 2'i 21.04 6.43 21.01 6.52 20.98 6.62 20.95 6.71 22 2a 21.99 6.72 21.97 6.82 21.94 6.92 ;21.91 7.01 2? 24 22.95 7.02 22.92: 7.12 22.89 7.22 i22.86 7.32 24 25 23.91 7.31 23.881 7.41 23.84 7.52 [23.81 7.62 25 26 24.86 7.60 24.83] 7.71 24.80 7.82 124.76 7.9a 26 27 25.82 7.89 l25.79| 8.01 25.75 8.12 25.71 8.2s 27 38 26.78 8.19 26.74J 8.30 26.70 8.42 26.67 8.54 28 29 27.73 8.48 i''i7.70| 8.60 i27.66 8.72 27.62 8.84 2.9 30 28.69 S129.65 8.77 l28.65i 8.90 1 |28.61 9.02 28.57 9.15 31 9.06 :29.6l': 9.19 29.57 9.32 29.52 9.45 32 30.60 9.36 30.56, 9.49: '30.52 9.62 30.48 9.76 32 33131.56 9.65 :31.52| 9.79|31.47 9.92 31.43 10.06 33 34:32.51 9,94 ;32.47 10.08:32.43 10.22 32.38 10.37 34 35 33.47 10.23 33.43 10. 38 i '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 3735.38 10.82 |35.34 10.97! 33.29' 1 1. 13| 135.24 11.28 37 38j36.34 11.11 36.29 11.27136.2411.43 36.19 11.68 3S 39|37.30 11.40 37.25 11.57; 37.19jll.73 37.14 11.89 39 40 41 38.25 11.69 138.20 11.86 38.15|12.03 i39.16Jl2.16 39.1o!l2.33 38.10 39.05 12.19 41 39.21 11.99 12.50 42 40.16 12.28 J40.llil2.45; 40.06 12.63 40.00 12.80 42 43 41.12 12.57 l41.07|12. 75 41.01 12.93 40.95 13.11 43 44 42.08 12.86 '42.02 13.05 41.96il3.23 41.91 13.41 4^1 46 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 13.74 [44.89 13.94 ;44.82 14.13 44.76 14.33 47 48 48 45.90 14.03 45.84 14.23 !45.78 14.43 45.71 14.63 49 46.86 14.33 46.80] 14.53 46.73 14.73 46.67 14.94 49 60 .22 47.82 Dep. 14.62 47.75 14,83 Dep. Lat. 47.69 15.04 Lat. 47.62 Dep. 15.24 _50 m Lat. Dep. Lat. 73 ] Deg. 72|Deg. 72iDeg. 72iDeg. Q TRAVERSE TABLE. 74 TRAVERSE TABLE. 5 18 Deg. ISfDeg. IsfDeg. 18|Deg. S' 1 Lat. 0.95 Dep. 0.31 Lat. Dep. Lat. Dep. Lat. 1 Dep. 0.95 0.31 0.95! 0.^ O.gsi 0.32 1 2 1.90 0.62 1.90l 0.63 1.90: 0.63 1.89i 0.64 2 3 2.85 0.93 2.851 0.94 2.84: 0.95 2.841 0.96 3 4 3.80 1.24 3.80i 1.25 3.79' 1.27 3.79! 1.29 4 5 4.76 1.55 4.75; 1.57 4.74 1.69 4.731 1.61 5 6 5.71 1.85 5.70 1.88 5.691 1.90 5.63 1.93 6 7 6.66 2.16 6.65 2.19 6.64i 2.22 6.63 2.25 7 8 7.61 2.47 7.60 2.51 7.59! 2.54 7.581 2.57 8 9 8.56 2.78 8.55 2.82 8.53 2.86 8.52 2.89 9 10 9.51 3.09 9.50 3.13 9.48; 3.17 10.43 3.49 9.47 10.42 3.21 3.54 10 11 11 10.46 3.40 10.45 3.44 12 11.41 3.71 11.40 3.76 11.38 3.81! 11.36 3.86 12 13 12.36 4.02 12.35 4.07 12.33 4.I2I 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 4.70 14.22 4.76; 14.20 4.82 16 16 15.22 4.94 15.20 5.01 15.17 5.08i 15.15 5.14 16 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 17.071 5.71 17.04 5.79 18 19 18.07 5.87 18.04 5.95 18.021 6.03 17.99 6.11 19 20 21 19.02 6.18 6.49 18.99 6.26 19.94 6.58 118.97 6.35! ! — : — 1 119.91 6.66' 18.94J 6.43 19.89| 6.75 20 21 19.97 22 20.92 6.80 20.89 6.89 120.86 6.98! 20.83 7.07 22 23 21.87 7.11 21.84 7.20 21.81 7.30i 21.78, 7.39 23 24 22.83 7.42 22,79 7.52122.76: 7.62| 22.73 7.71 24 25 23.78 7.73 23.74 7.831 i23.71i 7.93 23.67; 8.04 25 26 24.73 8.03 2469 8.14; 124.66 8.25 24.62 8.36 26 27 25.68 8.34 25.64 8.46' 125.60: 8.57 25.57! 8.68 27 28 26.63 8.65 26.59 8.77 26.55 8.88 26.51 9.00 28 29 27.58 8.96 27.54 9.08 127.50, 9.20 27.46 9.32 29 30 28.53 9.27 28.49 9.39 128.45 9.52 28.41 9.64 30 31 29.48 9.58 29.441 9.71 29.40 9.84 29.35' 9.96 31 32 30.43 9.89 30.39 10.02 130.35 10.15 30.30 10.29 32 33 31.38 10.20 31.34 10.33 131.29 10.47 31.25 10.61 33 34 32.34 10.51 32.29 10.65 132.24 10.79 32.20 10.93 34 35 33.29 10.82 33.24 10.96 33.19 11.11 33.14 11.25 35 36 34.24 11.12 34.19 11.27 34.1411.42 34.09 11.67 36 37 35.19 11.43 35.1411.59 35.0911.74 36.0411.89 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 41 38,04 38.99 12.36 12.67 37.9912.53 1 38.9412.84 37.93 12.69 '38.88 13.01 37.8812.86 40 41 38.82 13.18 42 39.94 12.98 39.89,13.15 39.83 13.33 39.7713.50 42 4340.90 13.29 40.84113.47 40.78 13.64 40.72 13.82 43 44 41.85 13.60 41.79 13.78 '41.73 13.96 41.6614.14 44 45 42.80 13.91 42.74;i4.09; 42.67 14.28 42.61 14.46 45 46 43.75 14.21 43.69:14.41! 43.62 14.60 43.56 14.79 46 47 44.70 14.52 44. 64' 14.72! i44.57 14.91 44.5115.11 47 4S!45..65 14.83 45.59il5.03 45.52 15.23 45.4515.43 48 49146.60 15.14 46.54il5.35 146.47 15.55 46.401 15.75 49 60 47.55 Dep. 15.45 Lat. 47.4! Dep i 15.66 !47.42 15.87 47.35 18.07 50 . Lat. Dep. Lat. Dep. Lat. CO Q 72 Deg. n^Deg. 7HDeg. |71iDeg. TRAVERSE TABLE. ■76 TRAVERSE TABLE. 19 Deg. T9iD^ 19iDeg." 19^Deg.| 00 Lat. Dep. Lat. Dep. Lat. Dep, Lat. Dep. 1 0.95 0.33 0.94 0.33 0.94 0.33 0.94 0.34 1 2 1.89 0.66 1.89 0.66 1.89 0.67! 1.88 0.68 2 3 2.84 0.98 2.83 0.99 2.83 1.00 2.82 1.01 S 4 3.78 1.30 3,78 1.32 3.77 1.34 3,76 1.36 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 6 7 6.62 2.28 6.6i: 2,31! 6.60 2.34 6.59 2.37 7 8 7.56 2.60 7,65 2.64 7.54 2.67! 7.53 2.701 8 9 8.51 2.93 8,50 2.971 8.48 3.00 8.47 3.041 9 10 11 9.46 10.40 3,26 9.44 10,38 3.30j 9.43 10.37 3.34 3.67 9.41 10.35 3.38| 10 3.72 11 3.68 3.631 12 11.35 3.91 11,33 3.96 jll.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 14113.24 4.66 13.22i 4.621 i 13.20 4.67 13.18 4.73! 14 16] 14. 18 4.88 14.16 4.95 14.14 5.01 14.12 6.07! 15 16 15.13 5.21 15.111 5.28 15.08 5,34 16.06 5.41! 16 17 16.07 5.53 16.05: 6.60 16.02 6.67 16.00 5,74| 17 18 17.02 6.86 I6.99| 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 19.86 6.51 6.84 18.88 19.83 6,69 6,92 18.85 6.68 18.82 6,76j 20 19.80 7.01 19.76 7,10l 21 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 7,68 21.68 7.68 21.66 7,77 23 24!22.69 7.8IH22.66 7.91 22.62 8.01 22.59 8,11 24 25 23.64 8.14i|23.60 8.24 23,57 8.36 23.53 8,45 25 2624.68 8.46:i24.55 8.67 24.61 8.681 124.47 8.79 26 27:25.53 8.79:i25.49i 8.90 25.45 9.01125.41 9.12 27 28 26.47 9.12!26.43i 9.23 26.39 9.35126.36 9.46 28 2927.42 9.44J27.38 9.56 27.34 9.681 !27.29 9.80: 291 3028.37 9.771 128.32 ji 9.89 28.28 10.01 128.24 H).14 30 3129.31 lO.O9ll29.27 10.22 I29.22 10.35 29.18 10,48 31 32I3O.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 35i33.09 11.39,33.04 11.64 ,32.99 11,68 32.94 11.83 35 36,34.04 11.72133.99 11.87i33.94 12.02 33.88 12.17 36 37:34.98 12.06: 34.93 12.20 |34.88 12.35 34.82 12.50 37 3835.93 12.3735.88 12.63 '35.82 12.68 35.76 12.84 38 3936.88 12.70 36.82 12.86 136.76 13,02 36.71 13.18 39 40J37.82 41 38.77 13.02 13.35 37.76 13.19 37.71 13.36; 37.66 13.62 40 38.71 13.52 38.65 13.69 38.59 13.86 41 42 39.71 13.67 39.65 13.85 i39.59 14.02 39.63 14.19 42 43 40.66|14.00ii40.60il4.18 ;40.53 14.36! 40.47 14.63 43 44 41.60! 14.32 41.54il4.51 41.48 14.69 41.41 14.87 44 4542.65114.65 l42.48114.84 42.42 15.02 42.36 16.21 45 46 43.49! 14.98 43.43:15.17 |43.36 15.36 43.29 16.54 46 47 44.44:15.30 i44.37l5.50 44.30 15.69] 44.24 16.88 47 48 45.3815.63 45.3215.83 45.25 16.02! 45.18 16.22 48 49 46.33.15.93 46.26 16.15 46.19 16.36: 46.12 16.56 49 5047.28' 16.28 '47.20 16.48 i 1 : I 47.13 16.69 47.06 16.90 50 tg !Dep.[Lat. JDep.i Lat. Dep. Lat. Dep. Lat. CO 5 71 Deg. ^703Deg. 70iDeg,l 70iDeg. TRAVERSE TABLE. IQiDegJ 193Deg. Lat.Dep. 48.0017.23 51 48.94 17.57 49.88 17.91 50.82 18.25 51.76 18.59 !52.71 18.92 53.65 19.26 54.59 19.60 55.5319.94 59 66.47120.27 60 .29; 63 .63 64 65' 70 85.65 30 86.5931 87.5331 88.47 31 89.4132 90.3532 91.29 32 92.24 33 93.18 33 94.1233 ^ Dep. Lat. ,Dep. Lat.j S I 71 Peg. I70 3 Peg. 701 Peg. Pep. I Lat. 70 'Peg. 87 91 92 93 94 95 96 97 98 99 100 78 TRAVERSE TABLE. s ft- 1 20 Ueg. 20-1 Des;. 26^Deg, 20jDeg. 2 1 Lat. 0.94 Dep. 0.S4 Lat. 0.94 Dep, 0.35 Lat. 0.94 Dep. 0.35 Lat. 0.94 Depi 0.35 2 1.88 0.68 1.88 0.69 1.87 0.70 1.87 0.71 2 3 2.82! 1.031 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 6.62 2.10 : 5.61 2.13! 6 7 6.58 2.39, 6.57 2.42 6.56 2.45 I 6.55 2,48 7 6 7.52 2.74, 7.51 2.77 7.49 2.80 7.48 2.831 g 9 8,46 3.08; 8.44 3.12 8,43 3.15 8.42 3,19 9 10 11 9.40 3,42, — 1 — ! 10.34! 3,76 9,38 3.46 9.37 3.50 9,35 3.54 10 10,32 3,81 10.30 3.85 10.29 3.90 11 12 11,281 4.10 11,26 4.15 11.24 4.20 11.22 4,25 12 13 12.221 4.45 12.20 4.50 12.18 4.55 12.16 4,61: IS 14 13,16: 4.79 13.13 4.86 13.11 4.90 13.09 4.96 14 15 14,10i 5.13 14.07 5.19 14.05 6.25 14.03 5,311 15 1615.04! 5.47 15,01 5.54 14.99 5.60 14.96 5.67 K iri5.97i 5.81 15.95 5.88 15.92 6.95 15.90 6,02 17 1816.91; 6.16 16,89 6.23 16.86 6.30 16.83 6.36 18 19 17.851 6.50 17,831 6.58 17.80 6.65 17.77 6.73 19 20 21 18.79 6.84! 18,76 6.92 18.73 7.00 18.70 7.09 20 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 2321.61: 7.87121.58 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 2523.49: 8.55 23.45 8.65 23.42 8.76 23.38 8.86 25 2624.43! 8.89 24.39 9.00 24.36 9.11 24.31 9.21 26 2725.37 9.23 25.33. 9.36 26.29 9.46 25.26 9.57 27 28 26.311 9.58 26.27 9.69 26.23 9.81 26.18 9.92 28 29 27.25i 9.92 27.21 10.04 27.16 10.16 27.12 10.27 29 30 28.19 10.26 28. 15i 10.38 28. 10 10.51 28.06 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 3331.01 11.29 30.96 ll.*i 30,91 11,56 30,86 11.69 33 3431.95 11.63 31.9011.77 3i.86 11.91 31.79 12,05 34 35 32.89 11.97 32.84 12.1] 32.78 12.26 32.73 12,40 35 36 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 35.7113.1)0 35.65|18.15 36.69 13.31 35.54 13.46 38 3936.65 13,34 36.59 13.50 36.53 13.66 36.47 13.82 39 40!37.59 13.68 37.53! 13.84 37.4? 14.01 37.41 14.17 40 4138.53 14.02 38.47 14.19 38.40 14.36 38.34 14.53 41 42 39.47 14,36 39.4014.54 39.34 14.71 39.28 14.88 42 43 40.4114.71 4G.34il4.8s 40.28 16.06 40.21 15.23 43 4441.35 15.05 41.28,16.28 41.21 15.41 41.15 15.59 44 45 42.29 15.39 42.22:15.68 42.16 15.76 42.08 15.94 45 46 43.2315.73 42.16:15.92 43.09 16.11 43.02 16.30 46 47 44.17 16.07 44.09il6.27 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 46.0416.76 45,97116.96 46.90 17.16 45,82 17.36 49 5046.9817.10 46.91117.31 46.83 Dep. 17,51 46.76 17,71 50 ^ Dep.' Lat. en Dep,l Lat. Lat. Dep.| Lat. ,70 Deg.i 693 Deg. 69iDeg.| 69lDeg. s TRAVERSE TABLE. so TRAVERSE TABLE, t3 21 Deg. 21iDeg. 21^Deg. 21 4^ Deg. 2 1 I Lat. Dep. Lat. Dep. Lat. Dep. Lat.jDep. 0.93 0.37 0.93 0.36 i 0.93 0.36 0.93 0.37 2 1.87 0.721 1.86 0.72 1.86 0.73 1.86 0.74 2 3 2.80 1.081 ! 2.80 LOS- 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 i 4.66 L81 4.66 1.83 4.64 1.85 5 6 5.60 2.15 1 5.59 2.17 6.58 2.20 5.57 2.22 6 7 6.54 2.61 1 6.52 2.64 6.51 2.57 6.50 2.69 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 10 9.34 3.68 9.32 3.62 9.30i 3.67 9.29 3.71 10 11 10.27 3.94 10.251 3.99 10.231 4.03 10.22 4.08 11 12 11.20 4.30 11.18| 4.35 11.17; 4.40 11.16 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 13.051 5.07 13.03] 6.13 13.00 6.19 14 15 14.0iD 5.38! 13.98! 6.44 13.9(81 6.50 13.93 5.66 15 16 14.04 6.73 14.91 5.80 14.891 5.86 14.86! 5.93 16 17,15.87 6.09 15.841 6.16 15.82: 6.23 15.79! 6.30 17 18 16.80 6.45 16.78 6.52 I6.75! 6.60 16.72 6.67 18 19|17.74] 6.81 117.711 6.89 17.68| 6.96 17.66 7.04 19 2018.671 7.17 {18.64! 7.25 18.61J 7.33 18.58 7.41 20 21 19.6l| 7.53 19.67i 7.61 19.54! 7.70 19.50 7.78 21 22'20.54j 7.88 20.50' 7.97 20.47! 8.06 20.43 8.15 22 23 21.47' 8.24 21.44i ^.34 21.40: 8.43 21.36 8.52 23 24 22.41; 8.60 22.371 8.70 22.33: 8.80 22.291 8.89 24 25 23.34; 8.96 23.30; 9.06 23.26| 9.16 23.22! 9.26! 25] 26 24.271 9.32 24.23i 9.42 24.191 9.53 24.15! 9-63 26 27 25.21i 9.68 ,25.16i 9.79 25.12! 9.90 25.0810.01 27 28 26.1410.03 26.10:10.15 26.05! 10.26 26.0110.38 28 29 27.0710.39 27.0310.51 26.98 10.63 26.94^10.75! 29] 30 31 28.0110.75 27.961 10.87 27.91 11.00 28.84 11.36 27.86 11.12| 30 11.49 31 28.9411.11 28.8911.24 28.79 32 29.87;11.47 29.82:11.60 29.77111.73 29.72 11.86 32 33 30.8ljll.83 30.7611.96 30.7012.09 30.65 12.23 33 34 31.7412.18 31.6912.32 31.6312.46 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 1 12.90 33.55 13.05i 33.50 13.19 33.44 13.341 36 37 34.5413.26 34.4813.41' 34.43 13.56 34.37 13.71 37 38 35.48;13.62 35.4213.77: 35.3613.93 35.29 14.08: 38 39 36.41il3.98 ;36.35 14.14136.2914.29 36.22!14.45; 39 40 37.3414.33 37.28il4.60: 37.22,14.66 38.1515.03 37.15 14.82 40 38.0815.191 41 41 38.28] 14.69 38.2114.86 42 39.2l!l5.05 39.14il5.22i39.08il5.39 39.0l|l6.56| 42 43 40.14 15.41 40.08 15.58 140.0115.76 39.9415.931 43 44 41.08! 15.77: 41.01: 15.95 140.94; 16. 13i 40.8716.30 44 45 42.01 16.13:|41.94 16.31 41,87 16.49 41.80'16.68' 45 46 42.9416.48il42.87;l6.67: 42.8016.86 42.73 17.05' 46 47 43.88 16.841 i43.80:i7.03 43.73il7.23 43.65 17.42 47 48 44.81 17.20 |44. 74] 17.40 44.6617.69 44.58 17.79 48 49 45.75 17.56 45.67 17. 76| 45.59!l7.96 45.5118.16 49 50 46.68 17.92 46.6018.12! 1 i 46.52 18.33 46.4418.53 50 en Q Dep. Lat. Dep.l Lat.' Dep. Lat. Dep. Lat. to Q 69 Deg. 68 3 Deg. i aS^Deg. 68iDeg. TRAVERSE TABLE. 81 {-,21 Deg.21iDeg.;i21^Deg. r*j Lat. Dep. ] Lat. Dep. ! Lat. Dep. 47.63 18.48 I4S.46 18.85 49.40 19.21 50.33 19.67 51.26 19.93 52.19 20.30 53.1220.66 .54.06 21.02 54.99 21.38 55.92 21.73 47.45 18. 48.38 19. 49.31 19. 50.24 19. 61.17 20. 62.10 20. 63.03 20. 53.96 21. 54.89 21. 65.83 2L ,21peg. Lat. Dep. 69 47.37 06 48.30 : 42;, 49.23: 79i;50.16: 60 61 56.95;21.86 62 57.88 22.22 63 58.82'22.58 64 59.75 22.94 63 60.68 23.29 66 61.62 23.65 67 62.55 24.01 68 63.48 24.37 69 64.42 24.73 70 65.85 25.09 7166. 72 67. 73 68. 74 69, 75 70. 76 70. 77 7L 7872. 79.7S, 80 74. 81 tZ 82 76. 83 77. 84,78. 85 79. 86 80. 87 81. 68 82. 89 83. 90 84. .28 26.44 ,22 26.80 ,15 26.16 ,08 26.52 ,02 26.88 ,95 27.24 89 27.59 ,82 27.93 ,75 28.31 ,69 28.67 ,62 29.03 55 29.39 ,49 29.74 ,42 30.10 35 30.46, 29 30.82 22 31.18 i 16 31.54 09 31.89 0232.25 9184.96 32.61 92 85.89 32.97 93 86.82 33.33 94 87.76 33.69 95 88.69 34.04 96 89.62 34.40 97 90.56 34.76 98 91.49 35.12 99 92.42 33.48 100 93.36 35.84 ♦: iDep.t Lat. .2 84.8^32.98 86.7433.34 86.68 33.71 87.6134,07 88.54134.43 89.47!34.79 90.40 35.16 91.34!33.52 92.27i35.88 93.20J36.24 ]73.36 29.69l ] 76.29 30.05 i [77.22 30.42|i 178.16 30.79!! 79.09 31.1511 180.02 31.52! 180.95 31. 89 1: !61.8832.23;i: 182.81 32.62, i| |83.7432.99;|i 184.67 33.35 185.6033.72 186.53 34.08 87.46 34.45 '88.39 34.82 89.32 35.18 90.25 35.56 91.18 35.92 92.11 36.28i 93.04 36.65j ! Dep.' Lat. .87; 86 ;.24| 87, 1.61 i 88 :.98 89 1.36 90 Q 69 Deg.i68£Deg. 'eS^Deg. 84,62 33.' 185.45 S4.( !86.38 34.^ |87.31 34.( 188.2435.5 |89.17 35.i 90.09 35.J 91.02 36.J 91.95 36.{ 92.88 37.C 98 99 100 16 Dep. Lat. TBAVERSE TABLE TRAVERSE TABLE, 84; TRAVERSE TABLE. o s r* 23 Deg. 23iDeg. j23|Deg.l|23aDeg. 0' Lat. Dep. Lat. Dep. ;Lat. Dep. i: Lat. Dep. 1 0.92 0.39 0.92] 0.39 j 0.92 0.40 1 0.92 0.40 1 2 1.84| 0.78 1.84| 0.79 1 1.S3 0.80 1.88 0.81 2 3 2.76 1.17 2.76i 1.18 i 2.75 1.20; 2.75 1.21 3 4 3.68 1.66 3.681 1.68 3.67 1.59 3.66 1.61 4 6 4.60| 1.95 4.691 1.97 1 4.59 1.99 4.58 2.01 6 6 6.52! 2.34 5.611 2.3711 6.60 2.39: 6.49 2.42 7 6.44 2.74 6.43| 2.76 1 6.42 2.79 6.41 2.82 7 8 7.36, 3.13 7.35 3.16|i 7.34 3.19 7.32 3.22 8 9 8.281 3.52 8.27 3.56 i 8.26 3.69; i 8.24 3.62 9 10 11 9.20 8.91 10.13' 4.30 9.19 3.96 10.11 4.34 9.17 ,10.09 3,99 4.39 9.15 4.03 Id 11 10.07 4.43 1211.05 4.69 ll.OSi 4.74 11.00 4.78 1.0.98 4.83 13 13 11.97 5.08 11.941 6.13 11.92 6.181)1.90 6.24 13 1412.89 5.47 12.861 6.631 12.84 6.58! 12.81 5.64 U 15 13.81 6.86 13.78: 6.92! 13.76 6.98j 13.73 6.04 15 16! 14.731 6.25i 14.70! 6.32 14.67 6.381 14,64 6.44 16 17 16.65 6.64i 15.62 6.71. 15.69 6.781.15.56 6.85 17 18 16.67 i 7.03| 16.54 7.11 16.61 7.18116,48 7.25 18 19 17.49 7.42 17.46 7.501117.42 7,68 17.39 7,65 19 20j 18.41 2119.33 7.81 8.21 18.38 7.89 19.29; 8.29 1 18.34 7.97 18.31 8,05 20 21 i 19.26 8.37 19.22 8,46 22 20.25 8.60 20.21; 8.681 20.18 8.7-7 20.14 8,86 22 23 21.17^ 8.99 21.13 9.08! 21.09 9.17 21,05 9.26 23 24 22.091 9.38. 22.05, 9.47 22.01 9.67 21,97 9.67 24 25 23.01 9.77 22.97 9.87:^22.93 9.97 22,88 10,07 25 26 23.93 10.16 23.89 10.26123.84 10.37 23,80! 10.47 26 27,24.86 10.56 24.81 10.66! 24.76 10.77 24.7110.87 27 28 25.77 10.94 25.7311.05 25.68 11.16 26.6311.28 28 29 26.69; 11.33 26.64 11.45| 26.59 11.66 26.64ill.68 29 SO 31 27.62ill.72 1 28.6412.11 27.66 11.84:27.51 11.96 27.46 12.08 28,37 12,49 SO SI 28.48 12.24 I28.43 12.36 32 29.4612.60 29.40 12.63 [29.35 12.76 29,29:12.89 32 33 30.38 12.89 30,32,13.031130.26 13.16 30.2113.29 SS 34 31.3013.28 31.24|13.42!!31.18 13.,56 31,1213,69 34 35 32.22,13.68 32.16,13.82 32.10 13.96 32.04; 14. 10 35 S6 33.14114.07 33.08 14.21:33.01 14.35 32.9514,50 36 37 34.06114.46 34.00 14.61 !33.93 14.75 33.8714,90 87 S8 34.98|l4.86 34.91 15.001 34.86 15.15 34.7816,30 88 39 35.90115.24 35.83 16.39,' 135.77 15,55 36,70 15,71 39 40 36.82 15.63 36.76 16.79 36.68 15.96 36.61 16.11 40 41 37.74 16.02 37.67 16.181 |S7.60 16.36 37.6316,61 41 42 38.66116.41 38.59 16.58138.52 16.75 38.4416.92 42 43 44 39.68116.80 40.60117.19 39.51 16.97; 39,43 17.37:40.35 17.16 17,54 39,36!l7.32 40.2717.72 43 44 40.43 45 41.42117.58 41.36 17.76 141.27 17.94 41.1918.12 45 46 42.34 17.97 42.26 18,16,42.18 18.34 42,10:18.53 46 47i 43.26 18.36 43.18 18.55; 43.10 18,74 43.02! 18.93 47 48 44.18,18.76 44.1018.96 44.02 19.14 43.9319.33 48 49 49 45.10119.16 45.02 19.34! 144.94 19.54 44.85:19,73 6Q 46.03 Dep^ 19.64 46.94 19.74 I45.85 1 19.94 45.77 20.14 60 Dep. Lat. Dep. Lat. Dep. Lat. ■s 67 Peg. m^Veg. iee^Peg.l 66iDeg.S| TRAVERSE TABLE. 85 t:j|23 Deg 3G TRAVERSE TABLE, c «-»■ 1 24 Deg. 24J^Deg. r24^Deg. 24^ Deg, 2 So* 1 Lat. Dep. Lat. Dep. Lat. Dep. Lat, Dep. 0.91 0.41 0.91 0.41 0.91 0.41 0,91 0.42 9 1.8f 0.81 1.82 0.82 1.82 0.83 1.82 0.84 9 8 2.74 1.22 2.74 1.23 2.73 1.24 2.72 1,26 3 4 3.65 1.63 3.65 1.64 3.64 1.66 3.8£ 1.67 4 ,5 4.57 2.03 4.56 2.05 4.56 2,07 4.64 2,0£ 6 6 5.48 2.44 3.47 2.46 6.46 2.49 5.45 2,51 6 7 6.39 2.85 6.38 2.87 6.37 2,90 6.36 2,9S 7 R 7.31 3.25 7.29 3.29 7.28 3.32 7.27 3.55 fi 9 8.22 3.66 8.21 3.70 8.19 3,73 8.17 3,77 P 10 11 9.14 10.05 4.07 4.47 9.12 4.11 9.10 10.01 4,16 4,56 9.08 4,19 10 10.03 4.52 9.9& 4,61 11 19 10.96 4.88 10.94 4.93 10.92 4,98 10.90 5,02 19 13 11.88 6.29 11.85 5.34 11.83 6,39 11.81 5,44 1.S 14 12.79 6.69 12.76 6.75 12,74 6.81 12.71 5,86 14 15 13.70 6.10 13.68 6.16 13.66 6.22 13.62 6,28 15 18 14.62 6.51 14.59 6.57 14.56 6.64 14.53 6.70 16 17 15.53 6.92 15.60 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 17.36 7.73 17.32 7.80 17.29 7,88 17.25 7.95 19 20 91 18.27 19.18 8.13 ia24 19.15 8.21 8.63 18.20 19.11 8.29 8.71 18.16 19,a7 8,37 20 21 8.54 8.79 99 20.10 8.95 20.06 9.04 20.02 9.12 19.98 9,21 29 93 21.01 9.35 20.97 9.45 20.93 9.64 20.89 9,63 '23 94 21.93 9.76 21.88 9.86 21.84 9,95 21.50 10,05 24 95 22.84 10.17 22.79 10.27 22.75 10.37 22.70 10.47 95 96 23.75 10.58 23.71 10.68 23.66 10.78 23.61 10.89 26 97 24.67 10.98 24.62 11.09 24.57 11.20 24.52 11.30 27 98 26.58 11.39 25.56 11.50 25.48 11,61 25.43 11.72 28 99 26.49 11.80 26.44 11.91 26.39 12,03 26.34 12.14 29 80 27.41 12.20i 27.35 12.32 27.30 28.21 12.44 12.86 27.24 28.16 12.56 12.98 30 31 31 28.32 12.61 28.26 12.73 32 29.23 13.02 29.18 13.14 29.12 13.27 29,06 13,40 39 33 30.15 13.42 30.09 13.66 30.03 13.68 29.97 13.82 33 34 31.06 ia.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 14.66 35 3fi 32.89 14.64 32.82 14.79 32.76 14.93 32.69 15.07 3fi 37 33.80 15.05 33.74 16.20 33.67 15.34 33.60 15,49 37 38 34.71 15.46 34.65 13.61 34,68 15,76 34,61 15.91 38 39 39 35.63 15.86 35.66 16.02 35,49 16.17 35.42 16,33 40 36.54 16.27 36.47 37.38 16.43 16.84 36.40 37,31 16,69 17,00 36.33 37,23 16.75 17.16 40 41 37.46 16.68 41 49 38.37 17.08 38,25 17.26 38.22 17,421 38,14 17,68 42 43 39.28 17.49 39.21 17.66 39.13 17.83] 39.05 18.00 4% 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 4« 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 43.76 19.71 43.68 19.91 43.59 20.10 4£( 49 44.76 19.93 44.68 20.13 44.69 20.32 44.50 20.51 49 30 s 46.68 Dep. 20.34 Lat. 45.59 20.64 45.50 Dep. 20.73 Lat, 45.41 20.93 5Q CD 5 Dep. Lat. Dep. 65^1 Lat, )eg. 66 Deg.l 65|DegJ 65^1 )eg. TRAVERSE TABLE. sy o 24 Deg. 24iDeg.] 24iDeg.| 242Deg. (-»■ SI r- Lat. Dep. Lat. Dep. Lat. Dep. Lat. 46.32 Dep. 21.35 51 46.59 2a 74 46.50 20.95 46.41 21.15 52 47.50 21.15 47.41 21.36 47.32 21.56 47.22 21.77 52 53 48.42 21.56 48.32 21.77 48.23 21.98 48.13 22.19 ,53 54 49.33 21.96 49.24 22.18 49.14 22.39 49.04 22.61 .54 65 50.24 22.37 50.15 22.59 50.05 22.81 49.95 23.03 56 56 51.16 22.78 51.06123.00 50.96 23.22 50.86 23.44 56 57 52.07 23.18 51.97l23.41 51.87 22.64 51.76 23.86 57 58 52.9S 23.59 52.88 23.82 52.73 24.05 52.67 24.28 58 59 53.90 2400 53.79 24.23 53.69 24.47 53.58 24.70 59 60 61 54.81 55.73 24.40 54.7124.64 55.62 25.05 54.60 24.88 54.49 25.12 25.54 60 61 24.81 .55.51 25.30 55.40 62 56.64 25.22 56.53 25.46 56.42 25.71 56.30 26.96 62 63 57.55 25.62 57.44 25.83 57.33 26.13 57.21 26.38 63 64 58.47 26.03 58.35 26.29 58.24 26.54 58.12 26.79 64 65 59.38 26.44 59-26 26.70 59.15 26.96 59.03 27.21 65 66 60.29 26.84 60.1827.11 60.06 27.37 59.94 27.63 66 67 61.21 27.25 61.09 27.52 60.97 27.78 60.85 28.05 67 68 62.12 37.66 62.00 27.93 61.88 28.20 61.75 28.47 68 69 63.03 28.06 62.91 28.34 62.79 28.61 62.66 28.89 69 70 71 63.95 28.47 63.8228.75 64.74|29.16 63.70 29.03 63.57 64.48 29.31 70 71 64.86 28.88 64.61 29.44 29.72 72 65.78 29.28 65.65 29.57 65.52 29.86 65.39 30.14 72 73 66.69 29.69 66.5629.98 66.43 30.27 66.29 30.56 73 74 67.60 30.10 67.47 30.39 67.34 30.69 67.20 30.98 74 75 68.52 30.51 68.38j30.80 68.25 31>10 68.11 31.40 75 76 69.43 30.91 69.29 31.21 69.16 31.52 69.02 31.82 76 77 70.34 31.32 70.21 31.63 70.07 31.93 69.93 32.24| 771 78 71.26 31.73 71.12 32.04 70.98 32.35 70.84 32.66! 781 79 72.17 32.13 72.03 32.45 71.89 32.76 71.74 33.07 79 80 73.08 32.54 72.94 32.86 72.80 33.18 72.65 33.49 80 81 74.00 32.95 73.85 33.27 73.71 33.59 73.56 33.91 81 82 74.91 33.35 74.76 33.68 74.62 34.00 74.47 34.33 82 83 75.82 33.76 75.68 34.09 75.53 34.42 75.38 34.75 83 84 76.74 34.17 76.59 34.50 76.44 34.83 76.28 35.17 84 85 77.65 34.57 77.50 34.91 77.35 35.25 77.19 35.59 85 86 78.56 34.98 78.41 35.32 78.26 35.66 78.10 36.00 86 87 79.48 35.39 79.32 35.73 79.17 36.08 79.01 36.42 87 88 80.39 35.79 80.24 36.14 80.08 36.49 79.92 36.84 88 89 81.31 36.20 81.15 36.55 80.99 36.91 80.82 37.26 89 90 91 82.22 36.61 82.06 36.96 81.90 37,32 81.73 37.63 38.10 90 91 83.13 37.01 82.97'37.38 82.81 37.74 82.64 92 84.05 37.42 :83.88i37.79 83.72 38.15 83.55 •38.52 92 93 84.96 37.83 84.79 38.20 84.63 38.57 84.46 38.94 93 94 85.87 38.23 185.71 38.61 85.54 38.98 85.37 39.35 94 95 86.79 38.64 86.62 39.02 86.45139.40 86.27 39.77 95 96 87.70 39.05 87. 53 139.43 87.36139.81 87.18 40.19 96 97 88.61 39.45 188.44 39.84 88.2740.23 88.09 40.61 97 98 89.53 39.86 89.35 40.25 89.1840.64 89.00 41.03 98 99 90.44 40.27 90.26 40.66 90.09;41.05 89.91 41.45 99 100 ■4-> CO 91.35 Dep. 40.67 91.18 4L07 91.00 41.47 90.81 41.87 100 CO Lat. Dep. Lat. Dep. Lat. Dep. Lat. Q 66 Deg 65^Deg. 65|Deg 65] Dei., jo) -TRAVERSE TABLE. TRAVERSE TABLE. 5-j25 Deg. 25^Deg.|;25iDeg. 253Deg. q .22 21 .13 21 .03:22 ;.9422 .85 23 1.75 23 .66'24 .57124 .4724 .33 25 .55 46. ,98 47. ,40 47. ,82 48. ,24 49, ,67! 50. ,09 51. ,51 i 52. ,93 53, ,36 54. Lat. Dep. I Lat. Dep. Lat.Dep. Lat.Dep 61 55.28 25.78 62 56.19 26.20 63 57.10126.62 64 58.00 27.05 13 21.75 03 22.18 94122.61 84123.03 7423.46 6523.89 5524.31 46^24.74 36125.17 27125.59 65 58.91 66|59.82 67160.72 68j61.63 28.74 69 62.54129.16 70.63.44129.08 27.47 27.89 28.32 7164, 72|65. 73,66. 74'67, 7567, 76,68, 7769, 78 70, 7971, 80 72, 35 30.01 25 30.43 1630.85 0731.27 97 31.70 88;32.12 7932.54 69132.96 60:33.39 ,50j33.81 .41^34.23 .32 34.65 .2-2 35.08 .13 35.50 .04 35.92 .9436.35 .85136.77 .7637.19 1.6637.61 .57 I 38.04 SI '82.47 38.46 02 83.38 38. 8S 93 84.29 39.30 94:85.19 39.73 95|86. 10 40.15 96 87.01 40.57 97 87.9140.99 9888.8241.42 99l89.72!41.84 100,90.63 42.26 ^ I Dep. I Lat. 55.17i26.02 56.0826.45 56.98i26.87 57.89127.30 58.79 59.69 60.60 61.50 62.41 63.31 30.29 30.71 31.14 31.57 67.8331.99 68.74:32.42 69.64|32.85 70..55i33.27 71.45 33.70 72.36 34.13 73.26 34.55 74.17 34.98 75.07i35.41 75.97i35.83 76.88 36.28 64.08 64.99 65.89 66.79 67.69 68.60 45.94i22, 46.8422. 47.74I23, 48.64{23 49.54123, 50.44,24. 51.34|24 52.24j25 53.14 25 54.04|26 54.94:26. '55.8426. 156.74:27, i57.64'27, 58.55:28, !59.45|28, 160.35,29, '61.2529, 162.16 29, 63.05 30 30.57; 31.00; 31.43 31.86 32.29 32.72 69.50133.15 70.40 33.58 ,71.30 34.01 72.21 34.44 77.78 78.69 79.59 36.68 37.11 37.54 73.11 74.01 74.91 75.82 76.72 77.62 78.52 ,16 51 .59 52 ,031 53 .46! 54 .89i 55 ,33! 56 ■ .76 57 .20! 58 .63 59 .07J 60 [50I 61 .94: 62 .37 63 ,80' 64 ,24i 65 ,67i 66 Hi 67 ,54| 68 ,98' 69 ,41' 70 '."si: 71 .28; 72 .71 73 .15 74 .58 75 ;.02 76 1.45 77 1.89 78 :.32 79] 1.76 80 34.87 35.30 35.73 36.16 36.59 37.02 37.45 80.5037.96 81.40 38.39 82.31^38.82 83.2139.24 84.1139.67 85.02 40.10 85.92!40.52 86.8340.95 87.73 41.38 88.64 41.80 89.54 42.23 90.45;42.66 79.43'37.88 80.33 38.32 81.23 38.75 72.9635.19; 73.8635:62: 74.76 36.06 75.66 36.49 76.56 36.93 77.46 37.36 78.36 37.80 79.26 38.23 80.16 38.67 81.06 39.10 87] 82.14 39, 83.04 39, 83.94 40, 84.84 40, 85.75 40, 86.65 41. 87.55 41, 88.45 42, 89.36 42, 90.26 43, 18 81. 61 82. 04 83. 47 84. 90 85, 33 86, 76 87, 19 88, 62 89, 05i90, 96 39.53 86 39.97 76 40.40 67 40.84 57 41,27 47 41.71 37 42.14 27 42.58, 17 43.01 07 43.44 Q 65 Peg. Dep. I Lat. Dep. Lat. Dep.! Lat 643 Deg. 64] Peg. 1164^ Peg. iQ 90 TRAVERSE TABLE. 26 Deg. 26iDeg.|26iDeg. Lat. Dep. Lat.'Dep.j Lat. Dep 0.90 0.44 1.80 0.88 2.70 1.32 3.60 51 4.49 6 5.39 7| 6.29 8, 7.19i 3.51 9 8.09, 3.95 10, 8.991 4.38 1.75 2.19 2.63 3.07 0.89 1.79 2.68 3.58 4.47 5.37 6.26 7.16 8.05 8.95 9.84 10.74 11.63 12.63 13.42 14.32 15.21 16.11 21 18.87; 9.21 2219.77 9.64 23 20.67 10.08 2421.57 10.52 25 22.47 10.96 26 23.37 11.40 27 24.27 11.84 28 25.17 12.27 29 26.06:12.71 30 26.9613.15 31 27.86113.59 32 28.7614.03 33 29.66] 14. 47 3430.5614.90 35 31.46:15.34 36 32.3615.78 37 33.26116.22 38 34.1516.6S 39'35.05|17.10 40!35.95| 17.53 4r36.85a7.97l!: 4237.75 18.41 43 38.65 18.85!: 44 39.5519.29 45 40.45 19.73 I 46 41.34 20.17j| 47 42.24 20.60;i 48 43.14 21.04:1 49 44.04 21.48:: 50:44.94 21. 92ii 18.79 19.69 20.58 121.48 '22.37 123.27 24.16 25.06 25.96 26.85 13.39 4.91 9.82 5.35 10.72 5.80i 11.61 6.25' 12.50 6.69| 13.39 7.14 14.29 7.59 15.18 8.03 16.07 8.48 16.97 8.92 17.86 9.371 9.82: 10.26; 10.71 11.15; 11.601 12.051 12.49 12.94 36.69 37.59 38.48 ; 39.38 40.27 41.17 '42.06 i 42.56 143.85 44.76 ^ Dep.l Lat. Dep.: Lat. P'64DegJ633Deg. 13.83 14.28 14.72': 15.17 15.62 16.06 16.51 16.96 17.40 17.85 18.29 18.74 19.19 19.63 20.08 20.53 20.97 21.42 21.86 22.31, 4,95 11 5.40' 12 5.85 13 6.301 14 6.75; 15 7.20 16 7.65 17 8.10 18 8.55 19 9.00 20 9.45 21 9.90 22 10.35 23 10.80 24 11.25 25 11.70 26 12.15 27 12.60 28 13.05 29 13.50, 30 13.951 31 14.40 32 14.85 33 15.30 34 15.75 35 16.20 36 16.63 37 17.10 38 17.55 39 18.00; 40 I 36.61 37.51 38.40 39.29 40.18 41.08 41.97 42.86 43.76 44.65 Dep. Lat. Dep. Lat 45 41 ,90 42 ,35 43 ,80 44 25 45 70 46 15, 47 60 48 63|Deg.l63}Peg.P TRAVERSE TABLE. n TRAVERSE TABLE. o 27 Deg. 27^Deg.| 27iDeg.j 27^ Deg. r-r- K Lat, Dep. Lat. Dep, Lat. Dep. Lat. 'Dep. ~1 0.89 0.45 0.89 0,46 0.89 0.46 0.88' 0.47 1 2 1.78 0.91 1.7S 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 3.65 1.85 3,54 1,86 4 5 4.45 2.27 4.45 2.29 4.44 2.31 4,42' 2,33 5 el 5.35 2.72 5.33 2.75 5.32 2.77 5,31 2.79 6 t 6.24 3.18 6.22 3.21 6.21 3.23 6.19 3.26 7 8 7.13 3.63 7.11 3.66 7.10 3.69 7.08i 3.72 8 9 8.02 4.09 8.00 4.12 7.98 4.16 7.96 4.19 9 10 8.91 4.64 8.89 4.68 8.87 4.62 8.85! 4.66 10 11 11 9.80 4.99 9.78 5.04 9.76 5.08 9.73 6,12 12; 10.691 5.45 10.67 5.49 10.64 5.54 10.62 5.69 12 13[11.58| 5.90 11.56 6.95 11.53 6.00 11.50 6,05 13 1412.47; 6.36 12.45 6.41 12.42 6,46 12.39 6.52 14 15 13.37 6.81 113.34 6.87 13.31 6.93 13.27 6.98 15 1614.26 7.26 14.22 7.33 14.19 7.39 14.16 7.45 16 1715.15 7.72 15.11 7.78 15.08 7.86 15.04 7.92: 17 1816.04 8.17 i 16.00 8.24 15.97 8.31 15.93 8.38! 18 19,16.93' 8.63 16.89 8.70 16.85 8.77 16.81 8.86 19 2017.82 9.08 17.78 9.16 17.74 9.23 17.70 9.31 20 21 18.7li 9.53 18.671 9.62 18.63 9.70 18.58 9.78 Ti 2219.60 9.99 19.56 10.07 19.51 10.161 19.47 10.241 221 23 20.4910.44 20.4510.53 20.40' 10.621 20.35'l0.7ll 2S| 24,21.38 10.90 21.3410.99 21.291L08 21.24 11.17; 24 25'22.28 11.36 22.23 11.45 22.1811.54 22.12 11.641 25 2623.17 11.80 23.1111.90 23.06112.01 23.01 12.11 26 27 24.0612.26 124.0012.36 23.9512.47 23.89 12.671 27 2824.9512.71 24.8912.82 24.84!l2.93 24.78 13.04 28 29125.84 13.17 ,25.78 13.28 25.7213.39i 25.66 13.50 29 3026. 7313.62 3l'27.62!l4.07 126.6713.74 1 '27.5614.19 26.61 13.85 26.55 13.97 30 27.50 14.31 27.43 14.43 31 32'28.5L14.53 '28.45 14.65ll28.38 14.78 28.32 14.90 32 3329.40 14.98 29.34 15.1i;;29.27 15.24 29.20 15.37 33 3430.29l5.44 30.23 15.57l30.16 15.70 30.09 15.83 34 35 31.1915.89131.1216.031131.0516.16 30.97 16.30 35 36 32.0816.34 ,32.0016.48; :31.93 16.62 31.86 16.76 36 37i32.97l6.80 '32.8916.94 '32.8217.08 32.74 17.231 37 3833.8617.25 33.78 17.40 33.71 17.55 33.63 17.69 38 39|34.75l7.71 34.67ll7.86 134.69 18.01 34.51 18.16 39 4035.64l8.16 35.66 18.31 135.48 18.47 35.40 36.28 18.62 40 19.091 41 41 36.53! 18.61 36.45 18.77 36.37 18.93 4237.42 19.07 137.34 19.23 37.2619.39 37.17 19.661 42 43 38.31 19.52 138,23 19.69; 38.14 19,86 38.05 20.02 43 44'39.20 19.98 39.12 20. 15' 139.03 20.32 38.94'20.49 44 45 40.10 20.43 40.01 20.60 139,92:20.78 39.82 20.95 45 46 40.99 20.88 40.89 21.06 l40.8021.24 40.7121.42, 46 47I4I.88 21.34 41.78 21.52 141.6921.70 41.5921.88' 47 48 42.77 21.79 142.67 21.98 i42.58la2.16 42.48,22.36! 48 49143.66 22.25 143.56 22.44 43.46 22.63 43.3622.82 49 50 44.65 22.70 44.46 22.89 44.35 23.09 44.26 2S.28 50 CO Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 63 Deg, 62|Deg. |62iDeg. 62iDeg. TRAVERSE TABLE. M TRAVERSE TABLE. 5 1 28 Deg. 28-iDeg. 28^Deg.j 283 Deg. 1 ^1 Lat. 0.88 Pep. 0.47 Lat. Dep. Lat. Dep. Lat. j Dep. 01 0.88 0.47 0.88 0.48 0.88'i 0.48 l| 2 1.77 0.94 1.76 0.95 1.76 0.96 l,75i 0.96 2 3 2.65 1.41 2.64; 1.42 2.64 1.43 2.631 1.44 3 ; 4 3.63 1.88 3.621 1.89 3.52 1.91 3.51 1.92 4 5 . 6 4.41 2.35 4.40 2.37 : 4.39 2.39 4.38! 2.40 6 5.30 2.82 5.29i 2.84 i 5.27 2.86 5.261 2.89 6 7 6.18 3.29 6.111 3.31 : 6.16 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 7.96 4.23 7.93 4.26 : 7.91i 4.291 7.89 4.33 9 10 10 8.83 4.69 8.81 4.73 1 8.79 4.77! 8.77 4.81 11 9.71 6.16 9.69 5.21 1 9.67 6.25| 9.64 5,29 11 12 10.60 6.63 10.67 5.68 10.56 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 6.67 12.33 6>63 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 7.67 14.06! 7.63 14.03; 7.70 16 17 16.01 7.98 14.98 8.05 14.94| 8.11 14.90' 8.18 17 18 15.89 8.46 15.86 8.52 15.82 8.59 15.78 8.66 18 19 16.78 8.92 16.74 8.99 16.701 9.07 16.66 9.14 19 20 21 17.66 9.39 9.86 17.62 9.47 18.50 9.94 17.68! 9.54 17.53 9.62 I 20 18.54 18.4610.02 18.41 10.10 21 CJCi 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 28 2^1 24 21.19 11.27 21.14 11.36:21.09 11.46 21.04 n.64 ,25 22.07 11.74 22,02 11.83[ 21.97 11.93 21.92 12.02 25 26 22.96 12.21 22.90 12.31 22.85 12.41 22.79 12.61 26 27 23.84 12.68 25.7812.78 ;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 29 25.61 13.61 26.56 13.73 26.49 13.84 25.43 13.95 SO 26.49 14.08 26.43 14.20 26.36 14.31 26.30 14.43 30 31 27.37 14.56 27.3114.67 27.2414.79 27.18 14.91 81 32 28.25 15.02 28.19 15.16 28.1215.27 28.06 15.39 32 33 29.14 16.49 29.07 16.62 129.00 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 30.7616.70 30.6916.83 35 36 31.79 16.90 31.71 17.04 31.64 17.18 31.5617.32 36 37 32.67 17.37 32.59 17.61 32.52 17.65 32.44 17.80 37 38 33.56 17.84 33.47 17.99 33.39 18.13 33.3213.28 38 39 34.43 18.31 34.3518.46 34.27 18.61 34.19 18.76 39 40 ,40 36.32 18.78 35.24J 18.93 35.1519.09 35.07 19.24 41 36.20 19.26 36.1219.41 36.03 19.56 35.95 19.72 41 42 37.08 19.72 37.0019.88 36.91 20.04 36.82 20.20 42 43 37.97 20.19 37.88 20.35 37.79 20.62 37.7020.68: 43 44 38.85 20.66 38.76 20.83 38.67 20.99 38.58 21.16 44 45 39.73 21.13 39.64 21.30 39.55 21.47 39.45 21.64 45 46 40.62 21.60 40.52 21.77 140.43 21.95 40.3322.13 46 47 41.50 22.07 41.4022.25 141.30 22.43 41.21 22.61 47 48 42.38 22.53 42.2822.72 142.18 22.90 42.08 23.09 48 49 43.26 23.00 43.1623.19 I43.O6 23.38 42.96 23.67 49 50 44.15 23.47 44.04 23.67 I43.94 23.86 43.84 24.06 60 s Dep.' Lat. Dep.: Lat. Dep. Lat. Dep.' Lat. ^ 00 62 Deg, eiJDeg. ClxDeg. 61i Deg. «i TRAVERSE TABLE a^ 28iDeg.]|28f Deg.i ^ (-,28Deg. ||28iDeg. 5145J 62 45.1 53 46.i 54,47. 56!48. 56l49. 57i60.i 68 51. 69 j 52.1 6052. 81l71.52l38.0S 82j72.40'38.50 83 73.28;38.97 84.74. 17i39.44 85 75.05l39.91 86 7S.93l40.37 87 76.82!40.84 88 77.70 41.31 89 78.58|41.78 90 79.47i42.25! 9i8O.35i42.72 92 81.23143. 19 93 82.1143.66 94 83.00 44.13 95 83.88144.60 96 84.76 45.07 97 85. 65 145. 64 98 86.53 46.01 99 87.41 46.48 100 88.29;46.95 80.16l43.07( 81.04 43.65 81.92.44.02 82.80 44.49 83.68 44.97 84.57 45.44 85.45 46,91 86.33 46.39 87.21 46.86 88.09 47.33 82.6114485 83.49 46.33 84.37|45.81 85,25 46,28 86.12 46.76 87.00|47.24 87.88 47.72 79.78 43.77 91 80.66 44.25 92 8U54i44.73 93 82.41:45.21 94 83.29|45.69 96 84. L7 [46.17 96 85,0446.^ 97 85.92 47.14 98 86.80 47.62 99 87.67i48.10 100 4J Dep. Lat.; Dep. Lat. Dep. Lat. iDep.l Lat. ^j .2 ' . '\ - , - .S2 P ! 62 Peg.! 61f Peg. lei^Deg. '61 j Peg. P 96 TRAVERSE TABLE. 5 m' 1 29 Deg.| 29iDe«;. 29^Deg.! 29iDeg. "i? Lat. 0.87 Dep.| Lat. Dep. Lat. Dep. Lat. Dep. 03 0.48 0.87 0.49 0,87 0.49 0,87 0.60 1 2 I.75I 0.97 1.74 0,98 1.74 0.98 1.74 0.99! 2 3 2.62 1.45 ! 2,62 1,47 2.61 1.48 2.60 1.49 • 3 4 3,50i 1,94 1 3.49 1.95 3.48 1.97 3.47 1.98 4 5 4.37: 2.42 1 4.36 2.44 4.35 2.46 4.34 2.48 5 6 6.25! 2.91 1 6.231 2.93 6.22 2.95 ' 5.21 2.98 6 7 6.12 3.39 6.11 3.42 6.09 3.45 6.08 3.47 7 8 7.OO1 3.88 1 6.98 3.91 6.96 3.94 6.95 3.97 8 9 7.87i 4.36 1 7.85 4.40 7.83 4.43 7.81 4.471 9 10 11 8.75 4.86 i 8.72 5.33 9.60 4.89 8.70 4.92 8.68 4.96; 10 9.62 5,37 9.57 6.42 9.65 5.46 11 12 10.50 5.82 10.47 5,86 10.44 5.91 10,42 5.95i 12 13 11.37 6.30 11.34 6.35 11.31 6,40 11.29 6.45I 13 14 12.24 6.79 12.21 6.84 12.18 6.89 12.16 6.95' 14 IS 13.12 7.27 13.09 7.33 13,06 7.39 13.02 7.441 15 16 13.99 17114.87 7.76 13.96 7.82 13.93 7.88 13.89 7.94 16 8.241 14.83 8.31 14.80 8.37 14.76 8.44 17 18il5.74] 8.73! 15.70 8.80 15.67 8.86 15.63 8.931 18 19ll6.62i 9.21i 16.58 9.28 16.54 9.36 16.50 9.43 19 20 21 17.49 9.701 17.45 9.77 17.41 9.85 17.36 10.34 18.23 9.92 20 10.42 21 18.3710.18; 18.32 10.26 18.28 22 19.2410.67! 19.19 10.75 19.15 10.83 19.10 10.92 22 23 20.12ill.l5j20.07;il.24 20.02 11.33 19.97 11.41 23 2420.991 11.64i 20.94 11.73 20.89 11.82 20.84 11.91 24 25J21.87 12.12; 21. 8112.22 21.76 12.31 21.70 12.41 26 26 22. 74! 12. 60! 22.6812. 70 22.63 12.80 22.67 12.90 26 27 23.61 13.09' 23.5613. 19 23.60 13.30 23,44 13.40 27 2824.49; 13.57 24.43,13.68 24.37 13.79 24.31 13.89 28 29125.36! 14.06 25.30 14.17 25.24 14.28 26.18 14.39 29 3e26.24|14.54 26,1714.66 26.11 14.77 26.06 14.89! 30 3127.1115.03 27.0515.15 26.98 15.27 26.91 15.38i 31 3227.99 15.51 27.92 15.64 27.85 15.76 27.78 15.88 32 3328,86116.00 28.79 16,12 28.72 16,25 28,66 16.38 sa 34 29,74! 16.48! 29.66 16.61 29.59 16.74 29.52 16.87 34 35 30.61 I6.97I 30.54 17. IG 30.46 17.23 30.39 17.37 36 36 31.49 17.45' 31.41 17.66 31.33 17.73 31.26 17.86 36 37 32,36il7.94; 32.28 18.08 32.20 18.22 32.12 18.36 37 38 33.24118.42 33. 15! 18.67 33.07 18.71 32.99 18.86 38 39i34.1lil8.9L34.03|19.66 33.94 19.20 33.86 19.35 39 40 34,98 19.39; 34.90|19.64 34,81 19.70, 34.73 1 19.86 40 4i35.86i9.88i36.77l2O.03 35,68 20,19 35.60 29.34 41 42 36.73!20.36 36.64 20.52 36,65 20.68 3^.46 20.84 42 43 37,6l!20.85 37.52121.01 37.43121. 17 37.33 21.34 43 44 38.48]21,33 38.39i21.50 3S.30J21.67i 38.20 21.83 44 45 39.3621.82 39.26;21.99 39,17i22,16 39.07 22.33, 45 46 40.23122.30 40.13'22.4S 40.04 22,65 39.94 22.83 46 47 4I.lli22.79 41.0li22.97 40.91 23.14 40.81 23.32 47 48 41.9823.27 41.88i2S.45 41.78 23.63 41.67 23.82 48 49 42.86123.76 42.75!23.94 42.65 24.13 42.64 24.31! 49 6043.73 24.24 43.62i24.43 43.52 24.62 43.41 24.8l| 60 "« Dep.| Lat. Dep.! Lat. Dep. Lat. Dep.l Lat. CO Q 161 Deg.i603Deu. eOfDeg.l 60]Deg. Q TRAVERSE TABLE. — 29 Deg. 2935:Deg.!29^Deg. 29|Deg, 51 44.6i;24.73 52 45.48 25.21 53 46.35 25.69 54 47.23 26.1«| 55 48.10 26.-66, 56 48.98 27.15' 5749.85 27.63 58 50.73 28.12! 59 51.6028.60 60 52.48 29.09! T*-\ Lat.lDep. Lat.,Dep.j Lat.Dep. Lat. Dep. r^ 61i53, 6254. 63 55. 64 55, 65 56, 66 57, 67 58. 68 59. 69 60. 70 61. 35:29.57| 23 30.06 10 30.54 98 31.03 8531.51 72 32.00 60 32.48! 4732.97! 35 33.45 22 33.94 44.50:24.92 45.37 25.41 46.2425.90 47.11 26.39 47.99 26.87 48.8627.36 49.73 27.85 50.60 28.34 51.48 28.83 52.35 29.32, 53.22;29.8li 54.09 30.29 54.97 30.78 55.8431.27 56.7131.76; 57.58 32.25 58.4632.74' 59.33 33.23: 60.20 33.71 61.07 34,20 44.39 25.11 45.26'25.61 46.1326.10 47.0026.59 47.87 27.08 48.74 27.58 49.61128.07 50.48 28.56 51.3529.05 52.2229.55 7162.10 34.421 7262.97 34.91 73 63.85 35.39 74 64.72 35.88 75 65.60 36.36" 76 66.47 36.85, 77 67.35'37.33 78'68.22;37,82' 79 69.09:38.30 80;69.97!38.78 81[70.8439, 8271.7239, 83 72.59'40, 84: 73.47:40. 8574.34;41. 86j 75.22141. 87]76.09'42. 88,76.97:42. 89,77.8443. 90 78.72 43. 9I79.59I44. 9280.4644.1 93 81.34 45.1 94 82.21 !45.i 9583.09'46.( 96183.9646.1 971848447.1 S8,85.7147., 9986.59'48.( 100!87.46'48. .1 I 39.58 40.07; 40.56 4L04 27:70.67 7.5 71.54 24 72,42 72 73.29 21 74.1641.53 69| 75.03 42.02 18, 75.9iJ42.51, 66 76.78:43.00: isl 77.65|43.49: 63:; 78. 52 43. 98 61.80 34.96 62.67 35.45 63.54 35.95 64.41 36.44 65.28 36.93 66.15 37.42 67.02 37.92 67.89 38.41 68.76 38.90 69.63 39.39 70,5039.89 71.37 40.38 72.2440.87 73,11 41.36 73.98 41.86: 74.85 42,35 75.72 42.84 76.59'43.33 77,4643.83 78,33'44,32 44.28[25.; 45,15 25,1 46.0126.; 46.8826.! 47,7527.: 48.62 27.' 49.49|28,; 50.3628,' 51.22,29.; 52.09,29.' 52.9630,27 61 53.8330.77 62 54.70 31.26 63 55.56 31.76! 64 56.4332.25 57.30 32,75 58.17 33.25 59.04 33.74 59.9113424 60.77:34.74 Dep. I Lat. 61 Deg. Dep. I Lat. 602 Peg. Dep. I Lat. 60.fDe£. 81 Dep. I Lat. ^^ _co eoiDeg.Q 9S TRAVERSE TABLE. s 30 Deg.| 30^Deg.| 30iDeg. 30|Deg. GJ CD 1 Lat. 0.87 Dep. 0.50 Lat. 0.86 Dep. 0.60 Lat. Dep, 0.51 Lat. 0.86 Dep. 0.51 on 0.86 1 2 1.73 1.00 1.73 1.01 1.72 1.02 1.72 1,02 g 3 2.60 1.50 2.59 1.51 2.68 1.62 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 2.64 4.30 2.56 6 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 8 6.93 4.00 6.91 4.03 6.89 4.06; 6.88 4.09 8 9 7.79 4.50 7.77 4.63 7.75 4.57! 7.73 4.60 9 10 8.66 5.00 8.64 6.04 8.62 5,08; 8.59 6,11 10 lli 9.53! 5.50 9.50 S.54 9.48 5.58: 9.45 6.62 11 12110.39 6.00 10.37 6.05 10.34 6.09 10.31 6.14 12 13ill.26: 6.50 11.23 6.55 11.20 6,60 11.17 6,65 13 1412.12| 7.00 12.09 7.05 12.06 7.11 12.03 7.16 14 1512.99! 7.50 12.96 7..T6 12.92 7.61 12.89 7.67 15 1613.86 8.00 13.82 8.06 13.79 8.12 13.76 8.18 16 17 14.72: 8.50 14.69 8.56, i 14.65 8.63 14.61 8.69 17 1815.59! 9.00 15.55 9.07! 15.51 9.14 15.47 9.20 18 19,16.45 9.50 16.41 9.67 16.37 9.64 16.33 9.71 19 20 17.32| 10.00 17.28 lO.Oa 17.23 18.14 10.58 1I8.O9 10.15 10.66 17.19 18.05 10,23 20 2118.1910.50 10,741 21 22: 19.05' 11.00 19.00 11.08 !18.96 11.17 18.91 11.25! 22 23! 19.92! 11.60 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 21.6012.59 21.54 12.63|;21.49 12.78 25 26122.52 13.00 22.46; 13.10 22.40 13.20 22.34 13.29: 26 27123.33,13.50 23.32! 13.60 23.26 13.70:23.20113.80: 27 28.24.25' 14.00 24. 19 [14. 11 24.13 14.21 24.06 14.32J 26 29125.11! 14.50 26.05^4.61 24.99 14.72 24.9214.83! 29 30 25.98| 15.00 26.9215.11 25.85 15.23 25.78 15.34' 30 :| 3126.8515.50 26.7816.62 26.71 15.73 '26.64 15.85 31 32;27.7lil6.00 27,6416.12 27.57 16.24 27.50!l6.36! SO 33 28.5816.50 28.51 16.62 28.43!l6.75 28.36'l6.87 33 34 29.44 17.00 29.37 17.13 29.30117.26 29.2217.38 34 35'30.31 17.50 30.23! 17.63 3(3. 16; 17.76 30.0817.90 35 86 31.18 18.00 31.10 18.14:31.02 18.27 30.9418.41 3R .37 32.04 18.50 31.96 18.641 131. 88 18.78 31.8018.92 37 38 32.91 19.00 32.83 19. 14| 132.74 19.29 32.66 19.43 .«?8 39 33.77 19.60 33.69 19.65] i33.60 19.79 33.52;19.94 39 40 34.64 20.00 34.55 35.42 20. 15j {34.47 20.30 20.81 34.38 20.45 40 4J 35.51 20.50 20.65 35.33 35.2420.96 41 42 36.37|21.G0 36.28 21.16 !38.19 21.32 36.10:21.47 42 43 37.24J21.50 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 22.60 38.87 22.67 38.77 22.84 38.67123.01 45 46 39.84 23.00 39.74 23.17 39.63 23.35 39.53 23.52 46 47'j40.70 23.50 40.60 23.68 40.60 23.85 40.39 24.03 47 48 41.57 24.00 41.46 24.18 41.38 24.36 41.25 24.54 48 49 42.44 24.50 42.33 24.68 42.22 24.87 42.1125.05 49 60 43.30 25.00 43.19 26,19 43.08 Dep. 25.38 Lat. 42.97 25.56 Dep.l Lat, 50 U3 m s Dep. Lat. Dep. Lat. 60 Deg. 59|Deg. 59iDeg.l 59lDeg. Q TRAVERSE TABLE. 9d ©30 Deg. r*i Lat. Dcp 5r44.17 5245.03 5345.90 5446.77 55 47.63 56 48.50 57 49.36 58 50.23 59 51,10 6051.96 25.60 26.00 26.50 27.00 27.50 28.00 28.50 29.00 29.50 30.00 6152, 62 53. 63 54, 64 55. 65 56, 6657, 67 58. 68 58. 69 59. 70,60. — i — 7161, 72 62. 73 63. 74:64. 7564. 76165. 30.50 31.00, 31.50 32.00 32.50 33.00: 33.50 34.00 34.50 35.00 88 76 9178. 9279. 9380. 9481. 95 82. 96(83. 97184. 84. 35.50 36.00 36.50 37.00 37.50 38.00 38.50 39.00 39.50 40.00' 40.50 41.00 41.60 42.00 42.60 43.00 43.50 44.00 44.50 45.00 45.50! 46.00; 46.50J 47.00 j 47.50! 48.00| 48.501 49.00 49.50| 50.00 Dep. Lat. 60 Des SO^Deg. Lat. Dep. 44.06 44.92 45.78 46.65 47.51 48.37 49.24 50.10 50.97 51.83 52.69 53.56 54.42 55.29 56.15 57.01 57.88 58.74 59.60 60.47 61.33 62.20 63.06 63.92 64.79 65.65 66.52 67,38 68.24 69.11 69.97 70.83 71.70 72.56 73.43 74.29 75.15 76.02 76.88 77.75 78.61 79.47 80.34 81.20 82.06 82.93 83.79 84.66 85.52 86.38 SOiDeg. Lat. Dep, .94 45.841 46.35| 46.85 47.35 47.86 48.36 48.87 49.37! 49.87! 50.38! Dep. Lat. I 59|Deg.i Dep. I Lat. 59iDeg. 30|Deg, Lat. Dep 43.83 44.69 45.55 46.41 47.27 48.13 48.99 49.85 50.70 51.56 52.42 53.28 54.14 55.00 55.86 56.72 57.58 58.44 59.30 60.16 61.02 61.88 62.74 63.60 64.46 65.31 66.17 67.03 67.89 68.75 69.61 70.47 71.33 72.19 73.05 73.91 74.77 75.63 76.49 77.35 78.21 79.07 79.92 80.78 81.64 82.50 83.36 84.22 85.08 85.94 26.08 26.59 27.10 27.61 28.12 28.63 29.14 29.65 30.17 30.68 31.19 31.70 32.21 32.72 33.23 33.75 34.26 34.77 35.28 35.79 36.30 36.81 37.32 37.84 38.35 38.86 39.37 39.88 40.39 40.90 41.41 41.93 42.44 42.95 43.46 43.97 44,48 44.99 45.51 46.02 46.53 47.04 47.55 48.06 48.57 49.08 49.60 50.11 50.62 51.13 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 Dep. Lat. oQj-Deg.p 2"00 TRAVERSE TABLE, Is CO 31 Deg. 31iDeg. 31^ Deg. 31|Deg. 5 on Lat. Dep. Lat. i Dep. Lat. Dep. Lat. Dep. 1 0.86 0.61 0.85i 0.52 0.85 0.62 8.85 0.53 1 2 1.71 1.03 1.7l! 1.04 1.71 1.04 1.70 1.05 2 3 2.67 1.56 2.56 1.66 2.56 1.67 2.65 1.58 3 4 3.43 2.06 3.42; 2,08 3^1 2.09 3.40 2.10 4 6 4.29 2.58 4.27 1 2.59 4.26 2.61 4.25 2.63 6 6 5.14 3.09 5.13! 3.11 5.12 3.13 5.10 3.16 6 7 6.00 3.61 5.981 3.63 5.97 3.66 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 7.69! 4.67 7.67 4.70 7.66 4.74 . 9 10 11 8.57 9.43 6.15 6.67 8.561 5.19 8.53 5.22 8.50 5.26 10 9.40 6.71 ! 9.38 6.76 9.35 5.79 U 12 10.29 6.18!l0.26; 6.23 10.23 6.27 10.20 6.31 12 13 11.14 6,70 11.11 6.74 11.08 6.79 111.05 6.84 13 14 12.00 7.21 11.97! 7.26 11.94 7.31 11.90 7.37 14 15 12.86 7.73 12.82j 7.78 12.79 7.84 12.76 7.89 15 16 13.71 8.24 13.68 8.30 13.64 8.36 13.61 8.42 16 17 14.57 8.76 14.63 8.82 14.49 8.88 14.46 8.95 17 18 15.43 9.27 15.39 9.34 : 15.35 9.40 15.31 9.47 18 19 16.29 9.79 16.24 •9.86 16.20 9.93 16.16 10.00 19 20 17.14 10.30 17.1010.38 17.95110.89 17.05 17.91 10.45 10.97 17.01 17.86 10.52 11.06 20 21 21 18.00 10.82 22 18.86 11.33 18.81111.41 18.76 11.49 18.71'11.58 22 23 19.71 11.85 19.6611.93 !l9.61 12.02 19.56112.10 23 24 20.57 12.36 20.5212.45 !20.46 12.54; 20.41 12.63 24 25 21.43 12.88 21.3712.97 21.32 13.06; 21.26 13.16 25 26 22.29 13.39 22.2313.49 22.17 13.58! 22.11 13.68 26 27 23.14 13.91 23.08 14.01 23.02 14.llll22.96 14.21 27 ,28 24.00 14.42 23.94 14.53! 23.87 14.631123.81 14.73 28 29 24.86 14.94 24.79 15.C4i 24.73 16.15 24.66 15.26 29 30 25.71 15.45 25.65 15.66| 25.58 26.50 16.08! !2€.43 15.67 25.51 16.20 26.36 15.79 16.31 SO 31 31 26.57 15.97 82 27.43 16.48 27.3616.601:27.28 I6.72! 27.21 16.84 32 33 28.29 17.00 28.21 17.12 !28. 14 17.24 28.06 17.37 S3 34 29.14 17.51 29.07 17.64 28.99 17.76 !28.91 17.89 34 35 30.00 18.03 i29:92 18.16! 29.84 18.29 129.76 18.42 35 36 30.86 18.54 30.78 18.68' 30.70 18.81 130.61 18.94 36 37 31.72 19.06ll31.63 19.19 31.55 19.33 !31.46 19.47 37 38 32.57 19.57 32.49 19.71! S2.40 19.85 ,32.31120.00 38 39 33.43 20.09! !33.34 20.23: S3.25l20.38 |33.16|20.62 39 40 34.29 20.60! 34.2020.75 34.11 35.05 21.27 34.96 20.90: 34.01 21.05 34.86 21.57 40 41 41 35.14 21.121 21.42 42 36.00 21.63ii35.9121.79i 35.81 21.94: 35.71 22.10 42 43 36.86 22.15i!36.76 22.31 36.66 22.47! 36.5722.63 43 44 37.72 22.66il37.62 22.83! 37.52 22.99' 37.42 23.15 41 45 38.57 23. 1 8': 138.47 23.34! 38.37|23.51 38.27i23.68 45 46 39.43 23.69!i39.33 23.86 39.22124.03 i39.12|24.21 46 47 40.29 24.211 [40.18 24.38 40.071 24.56; 39.97 24.73 47 j 48 41.14 24. 72||41.04 24.90 40.93] 25.081 40.82'25.26 48 49 42.00 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 42.62j26.31 60 — — .2 Dep. Lat. Dep. Lat. Dep. Lat. 1 Dep. 1 Lat. 4.J 59 Deg. ; 58fDeg. 58iDeg.| SSiDeg. TRAVERSE TABLE. 16i m' 61 31 Deg. 31iDeg. Sl^Deg. 31gDeg. ES' 51 Lat. 43.72 Dep. Lat. Dep. Lat. Dep. 26.65 Lat. 43.37 Dep. 26.27 43.60 26.46 43.48 26.84 62 44.57 26.78 44.46 26.98 44.34 27.17 44.22 27.36 62 US 45.43 27.30 45.31 i?7.49 45.19 27.69 45.07 27.89 53 64 46.29 27.81 46.17 28.01 46.04 28.21 45.92 28.42 64 65 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 66 67 48.86 29.36 48.73j29.67 48.60 29.78 48.47 29.99 67 58 49.72 29.87 49.58l30.09 49.46 30.30 49.32 30.52 68 59 50.57 30.39 50.44 30.61 50.31 30.83 50.17 31.05 69 60 61 51.43 52.29 30.90 51.29131.13 i 62.1531.66 51.16 31.35 61.02 31.57 60 61 31.42 52.01 31.87 51.67 32.10 62 53.14 31.93 53.00:32.16 52.86 32.39 62.72 32.63 62 63 54.00 32.45 53.86'32.68 53.72 32.92 63.57 33.15 63 64 54.86 32.96 54.71:33.20 64.57 33.44 54.42 33.68 64 65 56.72 33.48 56.57 '33. 72 55.42 33.96 56.27 34.20 65 1 66 56.57 33.99 66.42[34.24 56.27 34.48 56.12 34.73 66 67 57.43 34.51 67.28134.76 67.13 36.01 56.98 36.26 67 68 58.29 35.02 58.13i35.28 57.98 35.53 57.82 36.78 66 69 59.14 35.64 58.99135.60 58.83 36.05 68.67 36.31 69 70 60.00 36.05 69.84 36.31 69.68 36.67 59.52 36.83 37.36 70 71 71 60.86 36.67 60.70 36.83 60.54 37.10 60.37 79. 61.72 37.08 61.55;37.35 61.39 37.62 61.23 37.89 72 73 62.57 37.60 62.4137.87 62.24 38.14 62.08 38.41 73 74 63.43 38.11 63.26J38.39 63.10 38.66 62.93 38.94 74 75 64.29 38.63 64:l2!38.9i 63.95 39.19 63.78 39.47 76 76 65.14 39.14 64.97'39.43 64.!-0 39.71 64.63 39.99 76 77 66.00 39.66 66.83 39.95 65.65 40.23 65.48 40.62 77 78 66.86 40.17 66.68 40.46 66.51 40.76 66.33 41.04 78 79 67.72 40.69 67.54 40.98 67.36 41.28 67.18 41.57 79 80 81 68.57 69.43 41.20 68.39 41.50 68.21 41.80 68.03 68.88 42.101 801 41.72 69.25 42.02 69.06 42.32 42.62 81 8?, 70.29 42.23 7040 42.64 69.92 42.84 69.73 43.15 82 83 71.14 42.75 70.96 43.06 70.77 4S.37 70.58 43.68 83 84 72.00 43.26 71.81 43,68 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 8fi 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 46.78 87 88 75.43 45.32 76.23:45.65 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|46.69 1 77.80147.21 76.74 47.02 76.63 77.38 47.36 90 91 78.00 46.87 77.59 47.56 47.89 99. 78.86 47.38 78.66l47.73 76.44 48.07 78.23 48.41 92 93 79.72 47.90 79.61:48.26 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 f-1. 22 49.28 81.00 49.64 80.78 49.99 95 96 82.29 49.44 82.07 49.80 t81-85 50.16 81.63 60.62 96 97 83.15 49.86 82.93|50.32 182.71 50.68 82.48 51.04 97 98 84.00 60.47 83. 78 150.84 83.56 61.20 63.33 51.57 98 99 84.86 60.99 84.64|51.36 84.41 51.73 84.18 62.10 99 100 85.72 Dep. 51.50 Lat. 85.49 Dep. 61.88 86.26 62.25 86.04 52.62 100 to P Lat. Dep. Lat. Dep. Lat. 59. Deg SS^Deg. 58^Deg. 58^Det;. 102 TRAVERSE TABLE, So' 1 32 Deg. 32iDeg.| 32^Deg.| 32peg.| 2 ES' ft- 1 Lat. 0.85 Dep. Lat. Dep. Lat. Dep. Lat, Dep. 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 L68 1.08 2 a 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 b 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 « 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 6.37 8,41 5.41 10 11 9.33 6.83 9.30 5.87 9.28 5.91 9.25 5.95 12 10.18 6.36 10.15 6.40 10.12 G.45 10.09 6.49 12 la 11.02 6.89 10.93 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 16 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 8.6S 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 9.741 181 19 16.11 10.07 16.07 10.14 16.02 10.21 15.98 10.28i 19 1 20 21 16.96 17.81 10.60 16.91 10.67 16.87 10.75 16.82 10.82 20 21 11.13 17.76 11,21 17.71 11.28 17.66 11.36 22 18.66 11.66 18.61 11.74 18.56 11.82 18.50 11.90 221 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 20.18 12.98 24| 26 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 21.8V 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 31 25.44 15.90 25.37 16.01 25.30 16.12 25.23 16,23 30 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 26.9S 17.19 26.91 17.31 32 3327.99 17.49 27.91 17.61 27.83 17.73 27.75 17.85 33| 34:28.83 18.02 28.76 18.14 28.68 18.27 28.60 18,39 34 3529.68 18.55 29.60 18.68 29.52 18.81 29.44 18.93 35 36I30.3S 19.08 30.46 19.21 30.36 19.34 30.28 19.48 36 37131.38 19.61 31.29 19.74 31.21 19.88 31.12 ?,0.02 37 38J32.23 20.14 32.14 20.28 32.05 20.42 31.96 20.56 38 39i33.07 20.67 32.98 20.81 32.89 20.95 32.80 21.10 39 40 33.92 21.20 33.83 34.67 21.34 33.74 21.49 33.64 21.64 40 41 41 34.77 21.73 21.88 34,58 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 36.16i23.26 43 4437.31 23.32 37,21 23,48 37.11 23.64 37.01 J23.80 44 46 38.16 23.85 38.06 24,01 37.96 24.18 37.85 24.34 45 46 39.01 24.38 38.9C 24.55 38.80 24.72 38.69 24.88 46 47 39.86 24.91 39.75 26.08 39.64 25.25 39.63 25.43 47 48:40.71 25,44 40,59 25.61 40,48 25.79 40.37l25.97 48 49|41.55 25,97 41.4-3 26.15 41.33 26.33 41.31126.51 49 60 42.40 26.50 42,29 26.68 42.17 26.86 42.05i27.05 50 CO Q Dfep. Lat. Dep. Lat, Dep, Lat, Dep. Lat. P 58 De-. i573Deg. 57^Deg. ST^Deg. TRAVERSE TABLE. 104 TRAVERSE TABLE. 33 Deg. 33iDeg. 33peg. 33|Deg. I Lat. Dep. Lat. Dep. Lat. 0.83 Dep. 65 Lat. Dep. 1 0.84 0.54 0.84 0.55 0.83 0.56 2 1.68 1.09 1.67 1.10 h67 1.10 1.66 1.11 2 S 2,52 1.63 2.51 1,64 2.50 1.66 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 6 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 4.3S 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 8.39 5.45 8.36 5.48 8.34 5.52 8.31 5.56 10 11 9.23 5.99 9.20 6.03 9.17 6.07 9.15 6.11 11 1210.06 6.54 10.04 6.58 10.01 6.62 9.98 6.67 12 1310.90 7.08 10.87 7.13 10.84 7.18 10.81 7.22 13 1411.74 7.62 11.71 7.68 11.67 7.73 11.64 7.781 14| 15 12.58 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 8,83 113.30 8.89 16 1714.26 9.2« 14.22 9.32 14.18 9.38 I14.I3 9.44 17 1815.10 9.80 16.05 9.87 15.01 9.93 14.97 10.00: 181 19 15.93 10.35 15.89 10.42 15.84 10.49 15.80 10.56i 19| 20|16.77 10.89 16.73 10.97 16.68 11.04 [16.63 11.11 20 21 21:17.61 11.44 17.56 11.51 17.51 11.59 17.46 11.67 22! 18.45 11.98;'18.40'12.06 18.35 12.14 il8.29 12.22 22 23119.29 12.53! 19.23 12.61 19.18 12.69 il9.12 12,78| 23 24 20.13 13.07! 20.07 13.16 20.01 13.26 19.96 13.33 24 ^ 20.97 13.62;!20.9ri3.71 20.85 13.80 :20.79 13.89 25 26 21.81 14.16! 21.74 14.261 21.68 14.36 21.62 14.44! 26 27 22.64!l4.71i[22.5814.80| 22.51 14.90 ;22.45 15.00 27 28,23.48 15.25' 23.42 15.351 23.35 15.45 23.28 15.56 28 29 24.32 15.79,24.25 15.90| 24.18 16.01 24.11 16.11 29 80 25.16 16.34 25.09 16.45 25.02 16.56 24.94 25.78 16.67 30 31 26.00 16.88 '25.92 n.OO' 25.85 17.11 17.22: 31 32!26.84 17.43i;26.76 17.55' 26.68 17.66 26.61 17.78: 32 SS 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 35!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 30.86 20.42 30.76 20.56; 37 38:31.87:20.70!'31.78 20.84l;31.69 20.97 31.60 21.11 38 39:32.7l'21.24; 32.62 21.38' 32.52 21.53 32.43 21.67 39 40!33.55'21,79! 33.45 21.93' 33.36 1 1 li , |l 22.08 33.26 22.22 40 4l'34.39!22.33!!34.29;22.48l;S4.19 22.63 34.09 22.78 41 42'35.22|22.87:l35.12:23.03 35.02 23.18i'34.92 23.33 42 43,36.06 23.42' 135.96:23.58 35.86 23,73; 35.75 23.89 43 4436.90 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 46:38.58 25.05 38.4725.22 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 48,40.26 26.14 40.14 26.32 40.03 26.49 39.91 26.67 48 49',41.09 26.69 40.98 26.87 '40.86 27.04 40.74 27.22 49 60 41.93 27.23 41.8127.41 41.69 27.60 41.57 27.78J 601 1^ Dep.l Lat. Dep. Lat. Dep. Lat. Dep. Lat. 00 67 Deg. 56fDeg. 66iDeg. l56iDeg. Q TRAVERSE TABLE. 105 7159. 72 60. 73 61. 74,62, 76 62. 76 63, 77'64. 78i65, 79 66, 80 67, 55 38.67 38 39.21 22 39.76 06 40.30 90 40.85 74 41.39 58 41.94 ,42 42.48 ,25 43.03 .09 43.57 8167.93 44.12 82 68.77 44. 83 69.61 45.20 84 70.45 43.75 85 71.29 46.29 86 72.13 46.84 87 72.96 88 73.80 89 74.64 90; 75.48 47.38 47.93 48.47 49.02 33iDeg. 33|Deg.| Q 59.38 38.93 60.21 39.48 61.05 40.03 61.89 40.57 62.72 41.12! 63.56 41.67 64.39 42.22 65.23 42.77 66.07 43.32 66.9043.86 59.2139.19 60.04 39.74 60.87 40.29 61.7140.64 62.54 41.40 63.38 41.95 64.21 42.60 65.04 43.05 65.88 43.60 66.7144.15 59.03 39.45 71 59.87 4O.0OJ 72 60.70 40.56 73 61.63 41.111 74 62.36 41.671 75 63.19 42.22! 76 64.02 42.78| 77 64,86 43.331 78 65.69 43.89| 79 66.52 44.45 8350.00 90 9l!76.32 49.56 92; 77. 16 50.11 93,78.00!50.65 94|78.83 51.20 95,79.67 51.74 9680.51 9781.35 98182.19 99,83.03 100 83.87 52.29 52.83 53.37 53.92 54.46 76.1049.89! 76.94 50.44 77.77 50.99 78.61 61.64 79.45 62.09 80.28 52.64 81.12 63.18 81.96 53.73 '82.79 54.28 183.63 54.831 75,8850.23 76.7250.78 77.55 51.33 78.3951.88 79.22 52.43 80.05 52.99 80.89 53.54! 81.72 54.09 82.55 54.64, i83.39 56,19 75.66 50. 76.50 51, 77.3351, 78.16,52, 78.99 52, 79.82153, 80.65153, 81.48 54. 82.32 55, 83,15 55. Dep. Lsit. Dep. Lat. Dep.i Lat. Dep. I Lat. Q 57 Peg 56jDeg. 56»Deg. 20 ' 56j^Deg. IQ^ TRAVERSE TABLE. P. en «-^ 1 34 Deg.| 34iDeg. ^ 34^Deg. 343Ueg.| 5 Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 0.83 0.56 0.83 0.56 0.32 0.57 0.82 0.57 l| 3 1.66 1.12 1.65 L13 1.65 1.13 1.64 L14 2 3 2.49 1.68 2.48 L69 2.47 1.70 2.46 L71 3 4 3.32 2.24 3.31 2.25 3.30 2.27 3,29; 2.28 4 5 4.15 2.80 4.13 2.81 4.12 2.83 4.III 2.85 6 6 4.97 3.36 4.96 3.38 4.94 3.40 4.93| 3.42 6 7 5.80 3.91 6.79 3.94 5.77 3.96 6.75' 3.99 7 8 6.63 4.47 6.61 4.50 6.59 4.53 6.57 4.56 8 9 7.46 6.03 7.44 6.07 7.42 5.10 7.39 5.13 9 10 8.29 5.69 8.27 5.63 8.24 6.66 8.22 5.70 10 ,11 12 9.12' 6.15 9.09 6.19 9.07 6.23 9.04' 6.27 11 9.95 6.71 9.92 6.75 9.89 6.80 9.86 6.84 12 1310.78i 7.27 10.76 7.32 10.71 7,36 10.68 7.41 13 1411.61' 7.83 11.67 7.88 n.54 7.93 11.60 7.98 14 1512.44 8.39 12.40 8.44 12.36 8.50 12.32 8.55 15 1613.26; 8.95 13.23 9.00 13.19 9.06 13.15 9.12 16 i7jl4.09l 9.51 14.05 9.57 14.01 9.63 13.97 9.69 17 1814.92 10.07 14.88 10.13 14.83 10.20 14.79 10.26 18 19:15.7510.62 16.71 10.69 15.66il0.76 15.61 10.83 19 20' 16.58 11,18 ,2l'l7.4111.74 16.53 11.26 11.82 16.4811.33 17.31|11.89 16.43 11.40 17.25 11.97 20 21 17.36 '22 18.24' 12.30 18.18 12.38 18.1312.46 18.08 12.54! 22 2319.0712.86 19.0lil2.94 18.9613.03 18.9013.11 23 2419.9013.42 19.8413.61 19.78 13.59 19.72 13.68 24 25 20.73 13.98 20.6614.07 20.6014.16 20.54 14.25 25 26 21.55 14.64 21.49 14.63 21.4314.73 21.36 14.82 26 27,22.3815.10 22.32 15.20 22.25 15.29 22.18 15.39 27 28'23.2115.66 23.1416.76 23.08 16.86 23.01 15.96 28 29|24.04 16.22 23.97 16.32 23.90!l6.43 23.83 16.53 29 30,24.8716.78 24.8O! 16.88 24.7216.99 24.65 17.10 30 3l26.70'l7.33 26.62|l7.45 25.55! 17.56 25.47 17.67 31 32 26.63l7.89 26.4518.01 26.3718.12 26.29 18.24 32 33 27.36i 18.45 i27.2818.67 27.2018.69 27.1118.81 33 34J28. 19 19.01 28.10|19.14 28.02 19.26 27.94 19.38 34 35j29.02 19.67 28.9319.70 28.84 19.82 28.76 19-95 35 36 29.85,20.13 37 30.67 20.69 129.7620.26 29.67 20.39 29.68 20.52 36 30.6820.82 30.49 20.96 30.40 21.09 37 38|31.50,21.25i 31.41 21.39 31.32 21.52 31.22 21.66! 38 39|32.33 21.81 32.24:21.95 32.14 22.09 32.04 22.23I 39 .4C 33.16 22.37 33.06|22.51 32.97 22.66 132.87 22.80| 40 41 33.99122.93 33.89 23.07 33.79 23.22 133.69 23.37! 41 45 34.82 23.49; 34.7223.64 34.61 23.79 j34.51 23.94! 42 4£ 35.65 24.05 35.64 24.20 35.44 24.36 '35.33 24.51' 43 44 36.48 24.60! 36.37 24.76 36.26 24.92 !36. 15 25.08' 44 46 37.31 25.161:37.20 25.33 37.09 25.49 36.97 25.65 45 46 38. 1425.721 '38.02 25.89 37.91 26.05 137.80 26.22 46 47|38.96 26.28' 38.85 26.45 38.7326.62 i38.62 26.79; 47 ,45 S 39.79 26.84! ,39.68 27.01 39.56 27.19 39.44 27.36 48 4£ 40.62l27.40 140.50 27.58 40.38 27.75 40.2627.93 49 6( ) 41.45 27.96 Dep. Lat. 41.3328.14 1 41.21 28.32 41.08 28.60 50 Dep.! Lat. Dep. Lat. Dep. Lat. CO S., 56 Deg. 553De;.^ 55i|Deg. 55,iDeg. TRAVERSE TABLE. 10^ '34 Deg. j34|Deg. Lat. Dep. | Lat. Dep 5142.28 62:43.11 63;43,94 54,44.77 65 45.60 56146.43 57;47.26 58;48.08 59i48.91 60 49.74 6150.57 6251.40 63 52.23 64 53.06 65i53.89 66 54.72 67,55.56 68 56.37 6957.20 70; 58.03 7158.86 28.52 29.08 29.64 30.20 30.76 31.31 31.87 32.43 32.99 33.55 34.11 34.67 35.23 35.79 36.35 36.91 37.46 38.03 38.58, 39.14 39.70 40.26 40.82 41.38 72 59.69 73 60; 52 74 61,35 75 62.18 41.94 76 63.0142.50 77 63.84143.06 78 64.66143.62 79 65.49144. 18 80 66.32l44.74 91 75.4450.89 92 76.27 51.45 93 77.10 52.00 94 77.93 52.56 95 78.76 53.12 96 79.59 53.68 97 80.42 54.24 98 81.25 54.80 99 82.07 55.36 100 82.90 55.92 2 . Uep.i Lat. Dep. I Lat.| Dep. Lat. Dep. Lat Q 56 Peg. 553Deg. 55jDeg.ll55|Deg.p 108 TRAVERSE TABLE. 2 GO 35 Deg. 35iDeg. 35|Deg.| 3531^ Ed Lat. Dep, Lat. Dep. Lat. Dep, Lat. Dep. 1 0.82 0.57 0.82 0.58 0.81 0.58 0.81 ase 1 2 1.64 1.15 1.63 1.15 1.63 1.16 1.62 L17 2 3 2.46 1.72 2.45 1.73 2.44 1.74 2.43 1.75 3 4 3.28 2.29 3.27 2.31 3.26 2.32 3.26 2.34 4 5 4.10 2.87 4.08 2.89 4.07 2.90 4.06 2.92 6 6 4.91 3.44 4.90 3.46 j 4.88 3.48 4.87 3.51 6 7 5.73 4.01 5.72 4.04 1 5.70 4.06 5.68 4.0S 7 8 6.55 4.59 6.53 4.62 6,51 4.65 6.49 4.67 8 9 7.37 5.16 7.35 5.19 1 7.33 5.23 7.30 6.26 9 lOj 8.19 11 9.01 5.74 6.31 8.17 5.77 8,14j 5.81 8.12 5.84 10 8.98 6.36 ' 8.96 6.39 8.931 6.4S 11 12 9.83 6.88 9.80 6.93 ! 9.77 6,97 9.74; 7.01 12 1310.65 7,46 10.62 7.50 10,68! 7.65 10.65; 7.6t 13 1411.47 8.03 111.43 8.08 11.40; 8.13 11.361 8.U 14 15:12.29 8,60 ! 12,25 8.66 12.211 8.71 12.17 8.76 > 16 1613.11 9,18 13.071 9,23 13.03! 9.29 12.99 9.3t 16 17 13.93 9.75 13,88! 9,81 13.84 9.87 13.80 9.9f 17 18 14.7410.32 14.70 10.39 14,6510.45 14.61 10.55 - 18 19 15.56! 10.90 15,5210.97 15.47 11.03 il6.42 ll.K > 19 20 16.38 11.47 il6.33;il.54 !16.28|lL61,!l6.23 11,66 20 2i 17.20 12.05 'l7.1512.12 17.1012.19! 17.04 12.2' 21 22118.0212.62 17.9712.70 17.91 12.78, 17.85 12. 8£ 22 2318.8413.19 118.7813.27 18.7213,36118.67 13,44 23 2419.6613.77 19.6013.85 19,54 13,94! 19,48 14.0S 24 25 20.481 14,34 20.42 14.43 20.35 14.52 j20.29 14.6] 26 26 21,30: 14.91 21.2315.01 21.17 15.10 21.10 15. IS 26 27 22.12 15.49 22.0515.58 21.98 15.68^21.91 15.7- 27 28 22.94 16.06 22.8716.16 22.80il6.26 22.72 16.36 28 29 23,7616.63 i23,68 16.74 23.6116.84 23.64 16.94 I 29 30 24,5717,21 24.6017.31, ,24.42 17.42 124.35 17.6f: 30 31 25.391 17.78 25,3217.89 25.24il8.G0' 26.16 18.11 31 3226.2118.35 26.1318.47 !26.05'18.58 25.97 18. 7C >| 32 33 27.0318,93 26.95 19.05 !26.87'19.16 26.78 19.28 i S3 34 27,8519.50 27.77 19.62 127.6819.74 27.59 19.86 ►1 34 35,28.67 20.08 28.58 20.20 128.49^20.32 !28.41 20.45 36 36129.49 20.65 29.40 20.78 129,31 i20.91!29,22 21.03 36 37130.31 21.22 30.22 21.35 30.1221.49 !30.03!21.62 37 38 31.13 21.80 31.03 21.93 30.94l22.07ii30.84,22.2C 38 39 31,95 22,37 31.85 22.61 31.75 22.66H31.65 22.79 39 40 41 32,77 33,69 22.94 23.62 32.67 23,09 33.48 23.66 32.66 23.231 i32.46i23.37 '.'. .ii. ,„| 40 33.38 23.81 !33.27!23.9S 41 42 34,40 24.09 34.30 24.24 34.19 24.39.34.09,24.54 42 43 35,22 24.66 35.12 24.82 35.0124.97 34.90 25.12 43 44 36,04'25.24 35.93 25.39 36.82 25.55 135.71 25.71 44 45 36.86^25.81 36.75 25.97 36.64I26.13136.52 26.29 46 46'37.68 26.38 37.57 26.65 37.45!26.7i:i37.33 26.88 46 47i38.S0|26.96 38.38 27.13 38.26 27.291 i38.14.27.46 47 48i39.32 27.53 39.2027.70 39.08 27.87i 38.96|28.04 48 49 40.14 28.11 40.02 28.28 39.89 28.46 39w7i28.63 49 66 40.96 Dep. 28.68 40.8328.86 40.71 29»04| 40.58j29,21 60 Lat. Dep. Lat. Def>. Lat.l Dep.! Lat. ^ 55 DegJ'543Deg.' 54|I )eg.'^54iDeg. a TRAVERSE TABLE. 109 P. 35 Deg. 35peg. 35iDeg. 35|Deg. 09 51 Lat. 41.78 Dep. 29.25 Lat. Dep. Lat. Dep. Lat. Dep. 41.65 29.43 41.52 29.62 41.39 29,80 51 52 42,60 29.83 42.47 30.01 42.33 30.20 42.20 30,3E 52 53 43.42 30.40 43.28 30.59 43.15 30.78 43.01 30.97 63 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 4478 31.94 44.64 32,12 55 56 45.87 32.12 45.73132.32 45.59 32.52 45.45 32,72 66 57 46.69 32.69 46.55132.90 46.40 33.10 146.26 33,30 67 5fi 47.51 33.27 47.37 33.47 47.22 33.68 147.07 33,89 68 59 48.33 33.84 48.18 34.05 48.03 34.26 ;47.88 34,47 69 60 61 49.15 34.41 49.00 34.63 48.85 34,84 48.69 35,05 60 61 49.97 34.99 49.82 35.21 49.66 35,42 49.51 35,64 62 50.79 35.56 50.63:35.78 50.48|36.00'i60.32 36,22 62 63 51.61 36.14 51.45:36.36 51.29 36.53 |51.13 36.8] 63 64 52.43 36.71 52.27'36.94 52.1037.16Sl5I.94 37.39 64 65 53,24 37.28 53.0837.61 52.9237.75 52.75 37.98 65 66 54.06 37.36 53.90;38.09 53.73,38.33':53.56 38.56 66 67 54.88 38.43 54.71 38.67 5455!38.9ljl5438 39.14 67 68 55.70 39.00 55.53 39.25 55.36|39.49|l55.19 39.73 68 69 56.52 39.58 56.35 39.82 56.17 40,07 '56.00 40.31 69 70 57.34 40.15 57.16 40.40 56.99 40,65 56.81 40.90 70 71 71 58.16 40.72 57.98 40.98 57.80 41,23 57.62 41.48 72 58.98 41.30 58.80 41.55 58.02 41,81 58.43 42.07 72 73 59.80 41.87 59.61 42.13 59.43 42,39 69.24|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 75 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 4471 62.49 44.9E 77 78 63.89 44.74 63.70 45.02 63.50 45.29! ;63.30 45.57 78 79 64.71 45.31 64.51 45.59 64.32 45.83 6411 46.16 79 80 65.53 45.89 65.33 46.17 65.13 46.46 64.93 46.74 80 81 66.35 46.46 66.15 46,75 65.94 47.04 65.74 47.32 81 82 67.17 47.03 66.96 47.33 66,76 47.62 166.55 47.91 82 83 67.99 47.61 67.78 47.90 67.57 48.20 167.36 48.49 8.? 84 68.81 48.18 68.60 48.48 68.39 48.78 68.17 49.08 84 85 69.63 48.75 69.41 49.06 69.20149.36 68.98 49.66 85 86 70.45 49.33 70.23 49.63 70.01 49.94 69.80 50.25 86 87 71.27 49.90 71.05 50.21 70.83 50.52 70.61 60.83 87 «8 72.09 50.47 71.86 50.79 71.64 51.10 71,42 51.41 88 89 72.90 51.05 72.68 61.37 72.46 51.68 72.23 62,00 89 90 91 73.72 74.54 51.62 52.20 73.50 51.94 73.27 52.26 73.04 52,58 90 74.31 52.52 74.03 52.84 73.85 53,17 91 92 75.36 52.77 75.13 53.10 7490'53.42 7466 53,75 92 93 76.18 53.34 75.95 53.67 75.715401 75.48 54.34 93 94 77.00 53.92 76.76 54.25 76.535459 76.29 54.92 94 95 77.32 54.49 77.58 54.83 77.3455.17 77.10 55.50 95 S6 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 78.97 56.33 78.72 56.67 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 57.84 99 iOO • Q 81.92 Dep, 57.36 81.66 Dep. 57.71 81.41 Dep. 58.07 81.16 58.42 100 wmam Lat. Lat. Lat. Dep.l Lat, )eg. 55 Deg. 542Deg. 54^Deg. 5411 19 110 TRAVERSE TABLE. q 1 36 Deg.aeiDeg. Se^Deg. 36 J Deg. 5 55 T Lat, 0.81 Dep. 0.59 Lat, 0.81 Dep. 0.59 Lat. 0.80 Dep. 0.59 Lat. Dep, 0.80 0.60 2 1.62 1.18 1.61 1.18 1.61 1.19 1.60 1.20 'f. a 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 ft 5 4.05 2,94 4.03 2.96 4.02 2.97 4.01 2.99 h 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 1,73 8 9 7.28 5.29 7.26 5.32 7.23 5.35 1 7.21 5,38 9 10 8.09 5.88 8.06 6.91 8.04 5.95 1 8.01 5.98 10 11 11 8.90 6.47| 8.87 6.50 8.84 6.54 8.81 6.58 12 9.71 7.05 9.68 7.10 9.65 7.141 9.61 7,18 12 la 10.52 7.64 M).48 7.69 10.45 7.73J 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 8.821 12.10 8.87 12.06 8.92 12.02 8.97 15 16j 12.94 9.40| 12.90 9.46 12.86 9.52 12.82 9.57 16 1713.75 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 15.37111.17 15.32 11.23 15,27 11.30 15.22 11.37 19 20 21 16.18 11.76 12.34 16.13 16.94 11.83 16.08 16.88 11.90 16.03 11.97 20| 16.99 12.42 12.49 16.83 12.56 21 22 17.8012.93 17.74 13.01 17.68 13.09. 17.63 13.16 22 ■23 18.61|13.52 18.55 13.60 18.49 13.68j 18.43 13.76 28 24 19.4214.11 19.35 14.19 19,29 14.28 19.23 14.36 24 25 20.23; 14.69 20.16 14.78 20.10 14.87 20.03 14.96 25 26;21.03 15.28 20.97 15.37 20.90 15.47 20.83 16.56 26 27121.8415,87 21.77 15.97 21.70 16.06 21.63 16.15 27 28 22.65,16.46 22.58 16.56 22.51 16.65: 22.44 16.75' 28 29 23.46 17.05 23.39 17.15 23.31 17.25 23.24 17.35, 29 39 24.27 17,63 24.19 17.74 24.12 17.84 24.04 17.95J SO 31 25.08 18.22 25.00 18.33 24.92 18.44 24.84 18.55 31 3225.89 18.81 25.81 18.92 25.72 19.03 25,64 19.15 32 33 26.70 19.40 ;26.61 19.51 26.53 19.63 26.44 19.74 33 34 27.51 1 19.98 127.42 20.10 27.33 20.22 27.24 20.34! S4 35 28.32,20,57 28.23 20.70 28.13 20.82 28.04 20.94 35 86129.12 21.16 29.03 21.29 28.94 21.41 28.85 21.54 S6 37:29.93!21.75 29.84 21.88 29.74 22.01 29.65 22.14 S7 38 30.74 22,34 30.64 22.47 30.55 22.60 30.45 22.74 SB 39'31.55 22,92 31.45 23.06 31.35 23.20 31.25 23.33 3«) 40 32.36 23,51 32.26 23.65 32.15 23.79 33.05 23.93 40 41 33.17 24.10 33.06 24.24 32.96 24.39 32.85 24.53 41 4233.98 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 26.45 136.29 26.61 36.17 26.77 36.06 26.92 45 4637.21 27.94 37.10 27.20 36.98 27.36 36.86 27.52 46l 47138.02 27,63 37.90 27.79 37.78 27.96 37.66 28.12 47 48 38.83 28,21 38.71 28.38 38.69 28.55 38.46 28.72 48 49!39,64 28^0 39.62 28.97 39.39 29.15 39.26 29.32 49 50 40.45 Dep. 29.39 Lat, 40.32 29.57 Lat. 40.19 Dep. 29.74 Lat. 40.06 Dep. 29,92 Lat, 50 '4,3 cn Dep. 64 Deg. 53|Deg. oSiDeg. 53] Deg. TRAVERSE TABLE- ^-,36 Deg.i 36xDeg. .36iDeg.j 36f Deg.j ^ Lat.jDep. Lat.lDep. Lat. Dep. Lat. Dep 5141. 52 42, 53 42. 54 43. 55 44. 56 45. 5746. 58 46. 59 47. 60,48. 2629.98' 07130.56 88131.15 6931.74: 50 32.33;; 30 32.92;: I1I33.5O 92134.09 73134.68 54:35.27 61 49.35'35.85 62 50.1636.44 63 50.97 37.03 6451.78 37.62 65 52.69 38.21 66 53.4038.79 67 542039.38 68 55.0139.97 69 55.82;40.56 70,56.63141.14 1.07' 49.1 1.66|,49.J ■.25i50.i '.84| 51.. 1,44 52.1 1.03 53.( 1.62 53.: 1.21: 64.1 1.80 55.. .39 66.: 30.341 30.93 31.53 32.12 32.72 33.31 33.90 34,50i 35.09 35.69 40.86 30.. 41.67 31. 42.47 31. ,43.27 144.07 ,44.87 45.67 :46.47 '47.27 :48.08 32.: 8165.5347.61 82 66.S4'48.20 83 67.1548.79 84 67.96i49.37 85 68.77 49.96 86 69.58 50.55 87 70.38 51.14 88 71.19 51.73 89 72.00 52.31 90 72.8152.90 9173.62,53.49 92 74.43;54.08 93 75,24 54.66 94 76.05 55.25 95 76.8655.84 96 77.67156.43 97 78.4757.02 98:79.28 57.60 99 80.09,68.19 100:80.90 58.78 57.26 41.98 58.06;42.57i 58.87I43.I7 59.68l43.76 60.4S|44,35 61.29:44.94 62.10145.53 62.90 48.12 63.7146.71 64.52|47,30 65.32147,90 66.13!48,49 66.93|49.08 67.74149.67 68.55 50.26 69.35 50.85 70.1651.44 70,97 52,04 71.77 52.63 72.5863.22 73.39 53,81 74.1954.40 75,00 54,99 75,8155,58 76,6156,17 77.42 56.77 78,23 57,36 79,03 57.95 79,84 58.54 80.64 59.13 57.07 57.88 58.68 42,23 42,83 43.42 56.89 57.69 58.49 59.49 44.02 59.29 60.09 60.29 61.09 61.90 62.70 63.50 64.31 65,11 65.92 66.72 67.52 68.33 69.13 69.94 44.61 45.21 60.90|45. 46.80 61,70 46. 46.40 46.99 47.59 .30[ 59 .90| 60 :.5oi 61 .10, 62 .69 1 63 1.291 64 1.891 65 .49 66 1.09 67 1.691 68 69 62.50 63. .30 64.10 48,18 48.78 49.37 49,97 50,56 51,15 51.75 70. 74152.34 71,54152.94 72,35 53u63 j 54.13 i 54.72 55,32 55.91 56-51 57.10 57.70 58.29 79.58 68,89 80.39 59.48 75 47! 76 07i 77 67 78 27 79 87 80 64.90 65.70 66.50 67.31 68,11 68.91[61, 69,71j52, 70.51152, 71,3l|53. 72.11163. Dep,| Lat. |Dep.| Lat. Dep, Lat. 1 Dep.' Lat 83 26' 84 86' 85 46' 86 05: 87 65 88 25 89 85 90 1.46 91 i,06 92 ..64 93 1.24 94 1.84 95 .44 96 1.04 97 1.64 98 .23 99 ,83 100 54 Peg. l53^Deg. 53xDeg.ii53JDeg,Ct TRAVERSE TABLE, 32.74 33.54 34.34 35.14 35.94 36.74 37.54 38.33 39.13 39.93 24.6 25.28 25.88 26.48 27.08 27.68 28.29 28.89 29.49 30.09 Dep. Lat. 53 Deg. 32.64124.82 33.43|25.42 34.23:26.03 35.02i26.63 35.82'27.24 36.6227.84 37.41 38.21 39.00 39.80 28.45 29.05 29.66 30.26 Dep. Lat 523Deg. 32.5324.96 33.32 25.57 34.1126.18 34.9126.79 35.70 27.39 36.49 28.00 37.29,28.61 38.08l29.22 38.87129.83 39.6730.44 Dep.' Lat. 52iDeg. 32.4225.10 33.21125.71 34.0026.33 26.94 27.55 28.16 28.77 29.39 30.00 30.61 Dep. Lat.Lj I m 52iDeg.p TRAVERSE TABLE. US 37^Deg. 37iDeg. 37|Deg ! 40.73 141.53 [42.33 143.13 ,43.92 56 44.72 5745.52 5846.32 59 47.12 60 47.92 61 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 30. S9 31.29 31.90 32.50 33.10 33.70 34,30 34.91 35.51 36.11 36.71 37.31 37.91 38.52 39.12 39.72 40.32 40.92 41.53 42.13 42.73 43.33 43.93 44.531 45.14 45.74 46.34 46.94 47.54 48.15 48.75 49.35 49.95 50.55 51.15 51.76 52.36 52.96 53.56 54.16 54.77 55.37 55.97 56.57 57.17 57.77 58.38 58.98 59.58 60.18 Dep. Lat. 53 Peg. Lat. 40.60 41.39 42.19 42.98 43.78 44.58 45.37 46.17 46.96 Dep. 4'*.76 36.32 48.56 49.35 50.16 50.94 51.74 52.54 53.33 54.13 54.92 55.72 56.52 57.31 58.11 58.90 59.70 60.50 61.29 62.08 62.88 63.68 42.98 43.58 44.19 44.79 46.40 46.00 46.61 47.21 47.82 48.42 64.48 65.27 66.07 66.86 67.66 68.46 69.25 70.05 70.84 71.64 72.44 73.23 74.03 74.82 75.62 76.42 77.21 78.01 78.80 79.60 30.87 31.48 32.08 32.69 33.29 33.90 34.50 35.11 35.71 36.92 37.53 38.13 38.74| 39.34 39.95' 40.55' 4L16i 41.77i 42.37 Lat.Dep. 40.46B1.05 41.2531.66 42.05l32.26 42.84132.87 43.63 33.48 44.43l34.09 45.22|34.70 46.0135.31 46.81 35.92 47.60 36.53 49.03 49.63 50.24 50.84 51.46 52.06 52.66 53.27 53.87 64.48 56.33 43.22 57.i2l4S.83 55.08 55.69 56.29 56.80 57.50, 68.11! 58.71' 59.32 ».92 60.53 Dep. Lat, 52|Deg. 64.2649.31 65.0549.92 65.85 50.53 66.b4l5i.l4 67.4Si5L74 68.23 52.35 69.0252.96 69.82|53.57 70.61154.18 71.40 54.79 Lat, 56.14 56.93 57.72 58.51 59.30 60.09 60.88 61.67 62.46 63.26 64.05 64.84 65.63 66.42 67.21 68.00 68.79 69.58 70.37 71.16 Dep 43.47 44.08 44.69 45.30 45.92 46.53 47.14 47.75 48.37 48.98 49.59 60.20 50.81 51.43 52.04 52.65 53.26 53.88 54.49 66.10 51 52 53 64 65 56 67 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 52iDeg lU TRAVERSE TABLE. o 1 38 Deg. 38iDeg.| 38^Deg. 38iDeg. 5 en 1 Lat. 0.79 Dep. 0.62 Lat. 0.79 Dep, 0.62 Lat. 0.78 Dep. 0.62 Lat. 0.78 Dep. 0.63 2 1.58 1.23 1.57 1.24 1.67 1.24 1.56 1.25 2 3 2.36 1.85 2.36 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 5 3.94 .'?,08 3.93 3.10 3.91 3.11 3.90 3.13 5 6 4.73 3.69 4.71 3.71 4.70 3.74 4.68 3.76 6 7 6.52 '4.31 5.50 4.33 6.48 4.36 5.46 4.38 7 8 6.30 4.93 6.28 4.95 6.26 4.98 6.24 5,01 8 9 7.09 5.54 7.07 6.67 7.04 6.60 7.02 6.63 9 10 11 7.88 8.67 6.16 6.77 7.85 8.64 6.19 6.81 7.83 8.61 6.23 6.86 7.80 8.68 6.26 10 11 6.89 12 9.46 7.39 9.42 7.43 9.39 7.47 9.36 7.61 12 13 10.24 8.00 10.21 8.06 10.17 8.09 10.14 8.14 13 14 11.03 8.62 10.99 8.67 10.96 8.72 10.92 8.76 14 15 11,82 9.23 11.78 9.29 11.74 9.34 11.70 9.39 15 16 12.61 9.85 12.57 9.91 12,52 9.96 12.48 10.01 16 17 13.40 10.47 13,36 10,62 13,30 10.58 13.26 10.64 17 18 14.18 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 16.76 12.31 15.71 12.38 16.65 12.45 16,60 12.52 20 21 16.65 12.93 16.49 13.00 16.43 13.07 16.38 13.14 21 22 17.34 13.54 17.28 13.62 17.22 13.70 17.16 13.77 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 16.S9 19.63 15.48 19.67 15.56 19.50 15.65 25 26 20.49 16.01 20.42 16.10 20.3* 16.19 20.28 16.27 26 27 21.28 16.6S 21.20 16.72 21.13 16.81 21.06 16.90 27 28 29 22.06 22.85 17.24 21.99 17.33 51.91 17.43 21.84 22.62 17.53 18.15 28 17.85 22.77 17.96 22.70 J 8.06 29 30 31 23.64 24.4S 18.47 23.56 18.57 19.19 23.48 2426 18.68 19.30 23.40 24.18 18.78 19.40 30 19.09 24.34 31 32 25.22 19.70 ^.13 19.81 26.04 19.92 24.96 20.03 32 33 26.00 20.32 26.92 20.43 26.83 20.64 25.74 20.66 33 34 26.79 20.93 26.70 21.05 26.61 2U17 26.62 21.28 34 35 27.68 21.65 '27.49 21.67 27.39 21.79 27.30 21.91 36 36|28.37 22.16 ,28.27 22.29 28.17 22.41 28.08 22.53 36 87 29.16 22.78 129.06 22.91 28.96 23.03 28.86 23.16 37 38 29.94 23.40 129,84 23.63 29.74 23.66 29.64 23.79 38 39 30.73 24.01 ISO.63 24.14 30.62 24.28 30.42 24.41 39 40 31.52 24.63 31.41 24.76 31.30 24.90 31.20 25.04 40 41 32.3] 26.24 132.20 26.38 32.CS 26.62 31.98 25.66 41 42 33.10 25.86 32.98 26.00 32.87 26.15 32.76 26.29 42 43 33.88 26.47 33.77 26.62 33.65 26.77 33.63 26.91 43 44 34.67 27.09 34.65 27.24 i34.43 27.39 34,31 27.54 44 46 35.46 27.70 36.34 27.86 36.22 28.01 36,09 28.17 45 46 36.25 28.32 36.12 28.48 36.00 28.64 35.87 28.79 46 47 37.04 28.94 36.91 S9.10 36,78 29,26 36.65 29.42 47 48137.82 29.55 37.70 29.72 37,67 29,88 37.43 30.04 48 49138.61 30.17 38.48 30.34 38.36 30,50 38.21 30.67 49 50J39.40 30.78 Lat. 39.27 30.95 39,13 Dep, 31,13 38.99 31.30 Lat, 50 In Dep. Dep, Lat. Lat. Dep, s 52 Deg. '51|Deg. 51^ Deg. &U Deg. s TRAVERSE TABLE. 16 TRAVERSE TABLE. CD 1 ,39 Deg. 39iDeg. 391 Deg. 39|Deg. Lat 0.78 Dep. 0.63 Lat iDep. Lat. 0.77 Dep. Lat. 0.77 Dep. 0.64 0.77 0.63 0.64 2 1.56 1.26 1.55 1.27 1.54 1.27 1.54 1.28 2 a 2.33 1.89 2.32 1.90 2.3] 1.91 2.31 1.92 3 4 3.11 2.52 3.10 2.53 3.09 2.64 3.08 2.56 4 5 3.8£ 3.15 3.87 3.16 3.86 3.18 3.84 3.20 5 6 4.66 3.78 4.65 3.80 4.65 3.82 4.61 3.84 6 7 5.44 4.41 5.42 4.43 5.40 4.45 6.38 4.48 7 8 6.22 5.03 6.20 5.06 6.17 6.09 6.15 6.12 S 9 6.99 5.66 6.97 6.69 6.94 .').72 6.92 .5.75 9 iO 7.77 6.29 7.74 6.33 7.72 6.36 7.69 6.39 10 11 11 8.55 6.92 8.52 6.96 8.49 7.00 8.46 7.03 12 9.33 7.55 9.29 7.59 9.26 7.63 9.23 7.67 12 13 10.10 8.18 10.07 8.23 10.03 8.27 9.99 8.31 13 14 10.88 8.81 10.84 8.86 10.80 8.91 10.76 8.95 14 15 11.66 9.44 11.62 9.49 11.67 9.54 11.53 9.59 15 16 12.43 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 11.61 18 19 14.77 11.96 14.71 12.02 14.66 12.09 14.61 12.15 19 20 15.54 12.59 13.22 15.49 16.26 12.65 15.43 12.72 13.36 15.38 16.15 12.79 13.43 20 21 21 16.32 13.29 16.20 22 17.10 13.84 17.04 13.92 16.98 13.99 16.91 14.07 22 23 17.87 14.47 17.81 1455 17.76 14.63 17.68 14.71 23 24 18.65 15.10 18.59 15.18 18.52 15.27 18.45 15.35 24 25| 19.43 15.73 19.36 16.82 19.29 15.90 19.22 16.99 25 26|20.21 16.36 20.13 16.45 20.06 16.54 19.99 16.63 26 27|20.98il6.99 20.91 17.08; 20.83 17.17 20.76 17.26 27 28 21.7617.62 21.68 17.72: 21.61 17.81 21.53 17.90 28 29 22.5418.25 22.46 18.35! 22.38 18.46 22.30 18.54 29 30 23.31118.88 23.23 18.98 19.61 23.15 19.08 19.72| 23.07 23.83 19.18 301 31 24.091 19.51 24.01 23.92 19.82 31 32'24.87|20.14 24.78 20.25 24.69 20.35 24.60 20.46 32 33 25.65 20.77 25.65 20.88 25.46 20.991 26.37 21.10 33 34 26.42l21.40 26.33 21.51 26.24 21.63 26.14 21.74 34 35 27.20 22.03 27.10 22.14 27.01 22.26 26.91 22.38 85 36'27,98 22.66 27.88 22.78 27.78 22.90l 27.68 23.02 36. 3728.7523.28 23.65 23.41 28.65 23.63 28.45 23.66 37 38 29.5323.91 29.43 24.04 29.32 24.17 29.22 24.30 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 25.311 30.86 25.44 26.08 30.75 25.58 26.22 40 41 31.86 25.80 31.75 25.94 31.64 31.52 42 32.64 26.43 32.52 26.57 32.41 26.72 32.29 26.86 42 43 33.42 27.06 33.30 27.21 33.18 27.35 33.06 27.60 43 44 34.19 27.69 34.07 27.84 33.96 27.99 33.83 23.14 44 45 34.97 28.32 34.85 28.47 34.72 28.62 34,60 28.77 45 46 35.76 28.95 35.62 29.10 35.49 29.26 35.37 29.41 46 47 36.53 29.68 36.40 29.74 36.27 29.90 36.14 30.05 47 4ft 37.30 30.21 37.17 30.37 37.04 30.53 36.90 30.69 48 49 38.08 30.84 37.95 31.00 37.81 31.17 37.67 31.33 49 50 ♦J Q 38.86 31.47 Lat. 38.72 Dep. 31.641 1 Lat. 38.58 J1.80 38.44 Dep. 31.97 5D Dep. Dep. Lat. Lat.j 51 Deg. 1 50fDeg.l 50iDeg.|l 501 Deg. If il TRAVERSE TABLE. IS TRAVERSE TABLE. • 40 Deg. 40iDeg. 40iDeg. 40|Deg.| P. I Lat. Dep. Lat. Dep, Lat. 0.76 Dep. 0.65 Lat, 0,76 Dep. 0.65 1 0.77 0.64 0.76! 0,65 2 1.53 1.29 1,53 1.29 1.52 1.30 1.62 1.31 2 3 2.30 1.93 2,29 1,94 2.28 1.95 2.27 L96 3 4 3.06 2,67 3.05 2.68 3.04 2.60 3.03 2.61 4 6 3.83 8.21 3.82 3.23 3.80 3.25 3.79 3.26 5 6 4.60 3.86' 4,68 3.88 4.66 3.90 4.55 3.92 6 7 S.36 4.50! 5,34 4.52 6:32 4,55 6.30 4.67 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 6.82 6.84 5.84 6.82 5.87 9 10 7.66 6.43; - ,| 7,63 6.46 1 8,40 7,1L 7.60 8.36 6.49 7.14 7.58 1 8.33 6.53 7.18 10 11 11 8.43 7.07 12 9.19 7.71 9.16 7.75 9.12 7,79 1 9.09 7.83 12 13 9.96 fi.36 9,92 8.40 9.89 8,44 9.85 8.49 13 14 10.72! 9.00 110.69 9.06 i 10.66 9.09i 10,61 9.141 141 16 11.49' 9.64 11.45i 9.69 11.41 9.74: 11,36 9.79 15 16 12.2C!l0.28 :12.2i:i0.34 12.17 10,39: 12.12 10.44 16 17 13.02 10.93 113.9710.98 J12.93 11,04 12,88 11.10 17 18'l3.79, 11.57 il3..74'll. 63 Il3.69 11,69 13,64 11.75 18 19 14.53 12.21 ;14.60 12.28 14.45 li;.34 14,39 12.40 19 20 15.32112.86116.26:12.92 21116.09113.60 il6.03 13.57 15.21 15.97 12.99 15.15 13.64 15.91 13.06 20 21 13.71 22116.8614.14 16.7914.21 16.73 14.29' 16.67 14.36 22 23117.62 14.78^17.5514.86 17.49 14.94' 17.42 15.01 23 24il8.39 15.43 18.32 16.51 18.25 15.59| 18.18 15.67 24 25I19.15 16.07 19.08 16.15 19.01 16.241 18.94 16.32 25 2619.92 16.71 i 19.84 16.80 19.77 16.89 19.70 16.97 26 27,20.68117.36 120.6117.45 20.53 17.54 20.45 17.62 27 28l21.45il8.C0 21.37 18.09 21.29 18.18 21.21 18,28 28 29i22.22il8.64 22.1318.74 22,06 18.83 21.97 18.93 29 30 31 22.98jl9.28i22.90,19.38 23.75 19.93 '23.66'20.03 22,81 19.48 :22.73 23.48 19.58 20.24 30 31 23.67 20.13 32 24.61 20.67 '24.42 20.68 24.33 20.78 24.24 20.89 32 33 25.28 21,21 23.19 21.32 25.09 21.43 25.00 21.54 33 34 26.05 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 36 27.58 23.14:27.48 23.26:27.37 23.38 27.27 23.50 36 37 28.34 23.78 128.24 23. 91j 28.13 24.03 28.03 24.15 37 38 29.11:24.43 ;29.00 24.55: 28.90 24.68 28.79 24.80 38 39 29.88 25.07 |29.77 25.20 29.66 25.33 29.54 25,46 39 40 30.64j25.7r'S0.53 25.84 30.42 25.98 :30.30 26.11 40 41 4131.4126.36 31.29 26.49 31.18 26.63 ■31,06 26. 7S 42 32.17;27.00 32,06 27,14j 31.94 27.28 31,82 27.42 42 43 32.9427.64 32.82 27.781 32.70 27.93 32.58 28.07 43 44 33.7128.28 33.68 28.43 33.46 28.58 33,33 28.72 44 46 34.47:28.93 34,36 29.08 34,22 29.23: 34.09 29.37 46 46,33.24,29.57 35.11 29.72 |34,98 29.87 34.85 30.03 46 47j36.00i30.21 35.87 30.37| 35.74 30.52^35.61 30.68 47 48 36.77lS0.85 36.6431.03j!S6,60 31,17 36.36 31.33 48 49 37.5431.50 37.4031.66 37.26 31,82 i37,]2 31.99 49 50 38.30 32.14 38.16 32,31 38.02 32.47 37.88 32.64 50 Dep, Lat. Dep. Lat. Dep. Lat, Dep. Lat. 60 Deg. 49|Deg. 49^ Deg. 49lDeg. TRAVERSE TABLE. 120 TRAVERSE TABLE. 5 1 41 Deg. 41iDeg. 41iDeg. 41|Deg. 55 Lat. 0.75 Dep. 0.66 Lat. Dep. Lat. Dep. Lat. Dep. 0.75 0,66 0.75 0.66 0.76 0,67 1 9. 1.51 1.31 1..50 1,32 1.60 1.33 1.49 1.33 2 3 ?,.2fi 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 3.9,8 3.76 3.30 3.74 3.31 3.73 3.33 5 6 4.53 3.94 4.51 3.96 4.49 3.98 448 4.00 ti 7 5.28 4.59 6.26 4.62 5,24 4.64 6.22 4.66 '; 8 B.04 6.25 6.01 5.27 5.99 5.30 5.97 6.33 8 < 9 6.79 5.90 6.77 5.93 6.74 5.96 6.71 6.99 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 S 12 9.06 7.87 9.02 7.91 8.99 7.96 8.95 7.99 12 ; 13 9.81 8..53 9.77 8.57 i 9.74 8.61 9.70 8,66 13 . 14 10.57 9.18 10.53 9.23 I1O.49 9.28 10.44 9.32 14 i 15 11.32 9.84 11.28 9.89 111.23 9.94 H.19 9.99 16 : Ifi 12.08 10.50 12.03 10.55 !ll.98 10.60 11.94 10.65 16 ,17 12.83 11.15 12.78 11.21 I12.73 11.26 12.68 11.32 17 i 18 18.58 11.81 13.53 11.87 i 13.48 11.93 13.43 11.99 18 ; 19 14.34 12.47 14.28 12.53 14,23 12.59 14.18 12.65 19 20 . 21 15.09 15.85 13.12 13.78 15.04 13.19 14.98 13.25 14.92 13.32 20 21 15.79 13.85 15.73 13.91 15.67 13.98 ' 22 16.60 14.43 16.54 14.51 16,48 1468 16.4114.65 22 ; 23, 17.36 15.09 17.29 15.16 17.23 15.24 17.16ll5.S2 23 24 18.11 15.75 I8.04| 15.62 17.97 15.90 17.9115.98 24 25 ia87 16.40 18.80116.48 18.72 16.57 18.65ll6.66 2i. 26 19.62 17.06 119.551 17. 14 '19.47 17,23 19.40 17.31 2b , 27 20.38 17.71 ,20.30117.80 20.22 17.89 20.14 17.98 27 28 21.13 18.37 21.05il8.46 20.97 18,65 20,89 18.64 S8 23 21.89 19.03 ,21.80119.12 21.72 19.22 21.64 19.31 29 30 31 22.64 19.68 22.56|19.78 |22.47 19.88 22.38 1 19.98 30 31 23.40 20.34 23.3120.44 !23.22 20.54 23. is|20.64 ^2 24.15 20.99 !24.06 21.10 23.97 21.20 23.87|21.3] !*> 33 24.91 21.65 24.81-21.76 |24.72 21.87 i24.62l21.97 33 34 25.66 22.31 25.56122.42 |25.46 22.63 i25.37i22,64 34 35 26.41 22.96 26.31 23.08 |26.2l!23.19 26.1l!2S.3] 35 3tt ?7.17 23.62 27.07 '23. 74 126.96 23.85 :26.86 23.97 36 37 27.92 24.27 27.82 24.40| 127. 71 24.52 ?7.60 24.64 37 3« 28.68 24.93 28.67 25.061 28.46 25.18 28.35 25.30 38 39 29.43 25.59 29.32i25.71 29.21 25.84129.10 25.97 39 • 40 ll 30.19 30.94 26.24 26.90 30.0726.37 30.83l27.03 29.86 26.50 29.84 26.64 40 30.71 27.17 30.59 27.30 41 42 31.70 27.55 31..58 27.69 31.46 27.83 31.33 27,97 42 43 32.45 28.21 32.33 28.35 32.21 28.49 f32.08i28.63 43 44 33.21 28.87 33.08 29.01 32.95 29.16 32.83 29.30 44 45 33.96 29.62 '33.83 29.67 133.70 29.82 133.67 i29.97 45 46 34.72 30.18 34.58 30.33 34.45 30.48 34.32|30.63 46 47 35.47 30.83 35.34 30.99 35.20 31.14 35.06 31.30 47 48 36.23 31.49 36.09 31.65 35.96 31.81 35.81 31.96 48 49 36.98 32.15 36.8432.31 36.70 32.47 36.56 32.63 49 bO 37.74 Dep. 32.80 Lat. 37.6932.97 1 Dep. Lat. 37.46 33.13 37.3033.29 Dep.' Lat. 60 CO S: Dep. Lat. o 49 Deg. 481 D«g. 48^Deg.|i48jDeg.| TRAVERSE TABLE. 121 41 De". ;41|Deg. 41^Deg. 41|Deg. ,-, 7~ ' 55' Lat. Dep.; r" ^ Dep. I Lat. Dep. Lat.' Dep. Lat. jDep. I Lat. £ J49 DesrHH^Pp.: 4S;, Dpg. '48^l3eg. 23 123 TRAVERSE TABLE, E5' 42 Deg. 42fDeg. j42^Deg. 423 Ueg. Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 1 0.74 0.67 0.74 0.67 0.74 0.68 0.73 0.68 1 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 4.44 403 4.42 4.05 4.4) 4.07 6 7 5.20 4.68 5.18 4.71 5.16 4.73 5.14 4.75 7 s' 5.95 5.35 5.92 5,38 5.90 5,40 6.87i 5.43 8 9 6.69 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 8.14 7.40 6.11 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 14 10.40 9.37 10.36 9.41 10.32 9.46 10.28 9.50 1511.16 10.04 11,10 10.09 11.06 10.13 ill.Ol 10,18 15 1611.89 10,71 11,84 10.76 11.80 10.81 111. 75] 10.86 16 17112.63 11,38 12.58 11.43 12.53 11.48 il2.48lll.54 17 18113.38 12.04 13.32 12.10 13.27 12.16 113.2212.22 18 19 14.12 12.71 14.06 12.77 14.01 12.84 13.9512.90 19 20:14.86 13.38 14.80 13.45 14.75 13.61 14.69 13.68 20 21I15.6I 14,05 15.54 14.12 15.48 14.19 15.42' 14.25 21 2216.35 14.72 16.28 14.79 16.22 14.86 16.1614.93 22 23117,09 15.39 17.02 15.46 16.96 15.54 16.89' 15.61 23 24 17.8416.06 17.77 16.14 17.69 16.21 17.6216.29 24 2518.5816.73 18.51 16.81 18.43 16.89 j 18.36 16.97 25 26:19.3217.40 19.25 17.48 19.17 17.57 19.09 17.65 26 27i20.06 18.07 19.99!i8.15: 19.91 18.24 19.8318.33 27 28.20.8lll8.74 20.73' 18.83i 20.64 18.92 20.56 19.01 28 29 21,5519.40 21.47 19.50 21.38 19.59 21.30 19.69 29 30 22,29 20.07 31 23.04'20.74 22,21 22.95 20.17 22.12 22.86 20.27 20.94 22.03 20.36 22.76 21.04 30 31 20.84 32:23.78|21.41 23.6921.52 23.5921.62 23.50,21,72 32 33;24.52,22.08 24.43I22.I9 24.33'22.29 24.23 22.40 33 34 25.2722.75 25.17 22.86 25.07 22.97 24.97 23.08 34 35 26.0123.42 .25.9123.53 25.8023.65 125,70 23.76 35 36 26.75 24.09 26.65 24.21' 26.54 24.32 i26.44 24.44 36 37 27.50 24.76 27.39 24.88 27.28 25.00 i27.17 25.12 37 38 28.24 25.43 28.13 25.55 28.02 23.67 127.90 25. 79 38 39 28.98 26.10 28.8726.22 28.75 26.35 128.6426.47 39 40;29. 73 26.77 1 1 29.6126.89 29.49 27.02 '29.37 27. 15 40 4130.4727.43 30.3527.57 30.23 27.70 30.1127.83: 41 4231.2128.10 '31.0928.24 30.97 28.37 ,'30.84 28.51; 42 43 31.96 28.77 31.8328.91 31.7029.05 31.58 29.19' 43 4432.7029.44 32.57 29.58 32.4429.73 '32.31 29.87' 44J 45'33.44 30.11 33.31 30.26 33.18 30.40 133.04 30.55 45 46 34.1830.78 34.05 30.93 33.91 31.08 33.7831.22 46 47 34.93 31.45 34.7931.60 34.65 31.75 34.51 31.90. 47 48:35.67 32.12 35.53 32.27 35.39 32.43 35.25 32.58 48 49 36.41 32.79 36.27 32.93 36.1333.10 35.9833.26 49 50 37.16 33.46 37.01,33.62 36.8633,78 36.7233.94 50 ■4^ Dep.l Lat. Dep. Lat. Dep,' Lat. Dep. Lat. 48 Deg. 473 Deg. 47^Deg. :47fDeg. Q TRAVERSE TABLE. 124 TRAVERSE TABLE. o 43 Deg. 43iDeg. 43^Deg. 433Deg. d s Lat. Dep. Lat. Dep. Lat. Dep. 1 Lat. Dep. ¥ 1 0.73 0.68 0.73 0.69 0.73 0.69 0.72 0.69 1 2 1.46 1.36 1.46 1.37 1 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 6 6 4.39 4.09 4.37 4.11' 4.35 4.13! 4.33 4,15| 6 7 6.12 4.77 6.10 4.801; 5.08 4.82 5.06 4,84; 7 8 5.85 5.46 5.83 5.481 5.80 6.51 5.78 6.53 8 9 6.58 6.14 6.56 6.171 6.53 6.20 i 6.60 6.22 9 10 7.31 6.82 7,28 6.851: 7.25 6.88' 7.22 1 6.92 10 11 8.04 7.50 8.01 7.54 7.98 ' 1 7.57 7.95! 7.61 111 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 9.59i 10.16 9.64 lO.llI 9,68 14 15 10.97 10.23 10.93 10.281 10.88 10.33 10.84 10,37 15 16 11.7010.91; 11.65 10.961 11.61 11.01 n.56tll.06 16 17 12.43,11.59! 12.38 11.65 12.33 11.70 12.28 11.76 17 18 13.1612.28 13.11 12.33 13.06 12.39 13.00 12.45 18 19 13.90112.961,13.84 13.02 13.78 13.08 13.7213.14 19 20 14.63 13.641 14.57 13.70 14.51 13.77 14.4513.83 20 21 15.36 14.321 15.30 14.39! 15.23 14.46 15.17 14.52 21 2216.09 15.00 16.02116.07 16.% 15.14 15.8915.21 22 23 16.82 15.69; 16.75 15.76 ItJ.eS 15.83 16.6115.90 23 24! 17.55 16.37 17.48 16.44 17.41 16.52 17.3416.60 24 25 18.28 17.05,18.2117,13 18.13 17.21 18.06 17.29 25 26 19.02 17.73 18.94 17.81 18.86 17.90 18.78 17.98 26 27 19.76 18.41 19.67 18.50 19.-^9 18.59 19,dO-i« g? 27" 28 20.48 19. IQ 20.39 19.19 20.31 19.27 20.23 19.36 281 29 21.21.19.78; 21.12 19.87 21.04 19 96 20.95 20,05 291 30 21,94j20,46| 21,85 20.56, 21,76 20.65 21.67 20.75 30 31 22.67'21.14! 22.58 21.24 22.49 21.34 22.39 21.44 31 32 23.4021.82 23.31 21.93 23.jil 22.03 23.12 22.13 32 33 24,13 Z2-.51. 24.04 22.61 23.94 22.72 23.84 22.82 33 34j24.87 23.19 24.76 23.30 24.66 23.40 24.56 23.51 34 35125.60 23.87 25.49 23.98 25,39 24.09 25.28 24.20 35 36 26.33 24.55 26.22 24.67 26. li 24.78 26.01 24.89 36 3727.06 25.23, 26.95 25.35 26.84 25.47; 26.73 25.59 37 3827.79 25.92 27.68 26.04 27.56 26.16' 27.45 26.28 38 39 28.52 26.60 28.4126.72 28.29,26.85 28.1726.97 39 40 29.25 27.28 29.13 27.41 29.01|27.53; 28.89 27.66 40 41 29.99 27.96 29.86 28.09 29.74 28.22 29.6228.36 "il 42i30.72 28.64! 30.5928.78 30.47 28.91 30.34 29.04 42 4331.45 29.33 31.32 29.46 31.19 29.60 31.06 29.74 43 44132.18 30.01 32.05 30.15 31.92 30.29 31.7830,43 44 45 32.9130.69 32,7830.83 32.6430.98 32.5131.12 45 4633.6431.37 33.5131.52 33.37 31.66 33.23 31.81 46 47 34.37 82.05 34.2332.20 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 35.5433.73 35.40 33.88 491 60 36.57 34.10 ;36.42 34.26 36.27 34.421 36.12 34.58 50 CO St! Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. ^^ 47 Deg.''463Deg. 46i Deg. 46^ Deg. B TRAVERSE TABLE. 126 TRAVERSE TABLE. TRAVERSE TABLE. 128 NATURAL SINES. IV, A Table of Natural Sines, calculated to five places of figures, for every J)Iinute. Natural Sines are Decimals bearing the same proportion to Unity or 1 that the Sine of the corresponding number of Degrees and Minutes bears to Radius or Sine of 90°. That is, 1 is assumed as the Nat. Sine of 90°, and the Table calculated accordingly. Explanation of the Table. To find the JValural Sine of any number of Degrees and Minutes. U the degrees be less than 45, look for them at the Top of the Columns, and for the Minutes at the left-hand ; but if more than 45, look for them at the Bottom, and for the Minutes at the right-hand ; under or over the Degrees and against the Minutes will be the Natural Sine required. The reverse of this will give the Degrees and Minutes cor- responding to any Natural Sine. To calcfidate the JVorthing or Southing, ^c. for any Course and Distance, by JYat. Sines. Find the Nat. Sine and Co-Sine of the Course, and into each of these multiply the Distance ; the Products will be the Lati- tude and Departure required. Example. Required the Latitude and Departure for 6 Chains aiid 22 Links, on a Course JV. 38° 27' W. Nat. Sine of 380 27', 0.62183 Nat. Co-Sine 0.78315 6.22 6.22 124366 124366 373098 3.8677826 jin^wer. Northing 4.87 156630 156630 469890 4.8711930 Westing 3.87 A TABLE OF NATURAL SINES. 130 A TABLE OF NATURAL SINES. M 5Deg. f 6 Deg. jTD eg- 8 Deg. 9 Deg. M 60 N. S.iN.CS ^I\. S. N.CS.iN. S.jN.CS N. S. N.CS N. S.|N.CS C 08716 99619 10453 99452!l2187 99255813917 99027 15643 98769 1 74S 17 482 49 216 51 946i 23 672 64 59 2 774 - 14 511 46 245 49 975 19 701 60 58 3 803 12 540 09 569 43 274 44 14004 15 730 55 67 4 831 40 302 40 033 11 758 51 56 5 860 07 597 37 331 37 061 06 787 46 55 6 889 04 626 34 360 33 090 02 816 41 64 7 918 02: 655 31 389 30 11998998 845 37 53 8 947 99599,' 684 28 418 26 148 94 873 32 58 9 976 96 713 24 447 22 177 to 902 28 61 10 09005 94) 742 21 476 19 205 86 931 23 50 11 034 9I| 771 18 504 15 234 82 959 18 49 12 063 88 800 15 533 11 263 73 988 14 48 13 092 86 829 12 562 08 292 73 16017 09 47 14 121 83 858 69 591 04 320 69 046 04 46 15 150! 80 887 06 620 00 349 65 074 00 45 44 1609179;99o78 10916;99402 12649 99197 1437898961 16103 98696 17 208 75 945 99399 678 93 407 57 132 90 43 18 237 72 973 96 706 89 436 53 160 86 42 19 266 70 11002 93 736 86 464 48 189 81 41 20 295 67 031 90 764 82 493 44 218 76 40 21 324 64 060 86 793 78 622 40 246 71 39 22 353 62 089 83 822 75 551 36 275 67 38 23 382 59 118 8(H 851 71 580 31 304 62 37 24 411 56 147 77 880 67 608 27 333 57 36 25 440 53 176 74 906 03 637 23 361 52 36 26 469 51 206 70 937 60 666 •19 390 48 34 27 498 48 234 67 966 56 695 14 419 43 33 28 527 45 263 64 995 52 723 10 447 38 32 29 556 42 291 60 13024 48 752 06 476 33 31 30 585 40 320 57 063 44 781 02 505 29 30 29 31 09614 99537U 1349 99354 13081 99141 14310 98897 16533 98624 32 642 34 378 51 110 37 838 93 66i 19 2S 27 33 671 31 407 47 139 33 887 89 591 14 34 700 28 436 44 168 29 896 81 .620 09 26 35 729 26 465 41 197 26 926 80 64S 04 25 36 758 23 494 37 226 22 954 76 677 00 24 37 787 20 523 34 254 18 9S2 71 700 98595 23 38 818 17 552 31 283 14 15011 67 734 90 22 39 845 14 580 27 312 10 040 63 763 85 21 40 S74 11 609 24 341 06 069 58 792 80 20 41 903 08 638 20 370 02 097 54 820 75 19 42 932 06 667 17 39999098 126 49 849 70 18 43 961 03 696 14 427 94 155 45 878 66 17 44 990 00 725 10 456 91 184 41 906 61 16 45 10019 99497 754 07 485 87 212 36 935 56 15 46 10048 99494 1178399303 1351499083: 15241 9883^ 27 16964 98551 14 47 077 91 812 00 543 79 270 992 46 13 48 106 88 840'99297 572 75 292 23 17021 41 12 49 135 85 889 93 600 71 327 18 050 36 11 50 164 82 898 90 629 67 356 14 078 31 10 51 192 79 927 86 658 63 386 09 107 26 9 52 221 76 956 83 687 59 414 05 136 21 8 53 250 73 985 79 716 55; 442 00 164 16 7 54 279 70 12014 76 744f 511 471 98796 193 11 6 55 308 67 043 72 7731 47] 500 91 222 06 5 56 337 64 071 69 802i 4S| 529 87 250 01 4 57 366 61 100 65 831 1 39 557 82 279 98496 3 58 395 58 129 62 8601 35! 686 78 308 91 2 59 M 424 N.CS 55 158 58 8891 3l| 615 73 336 86 N. S. I M N. s.! N.CS. N. S. N.CS.N. Sj n.cs.In. s.sn.cs.I 84 Deg.j 83 Deg.i 82 Deg4' 81 1 )eg.i BO E )eg. A TABLE OF NATURAL SlNES. 131 M 10 Deg.,n Deg.j 12 Deg. 13 Deg. 14 Deg. iV. s. 17365 N.CS'iN. S. N.CS N. S.,N.CS N. S. N.CS N. S. N.CS M 60 98481 19081 98163 2079197815 22495'97437 24192 97030 1 393 76i 109 57 820 809 623 430 220! 023 59 2 432 71 138 52 848 803 552 424 249 015 58 3 451 66' 167 46 877 797 580 417 277 008 57 4 479 6I3 195 40 905 791 608 411 305 001 66 5 508 551 224 35 9331 784 637 404 333 96994 65 6 537 60, 252 29 962 778 665 398 362 987 54 7 565 45 281 24 990 772 693 391 390 980 63 8 594 40 309 18 21019 766 722 384 418 973 52 9 623 35 338 12 047! 760 750 378 446' 966 51 10 651 30 366 07 076i 754 778 371 474S 969 50 11 680 25 395 01 104 748 807 366 503; 952 49 12 708 201 423 98096 132' 742 835 358 531 946 48 13 737 14 452 90 1611 735 863 351 5591 937 47 14 766 093 481 84 189' 729 892 345 587 930 46 15 794 04| 509 79 218 723 920 338 615 923 45 16 17823 98399,19538'98073 21246 97717*22948 275 71 If 977 97331 24644 96916 ~44 17 852 94 566 67 325 672 909 43 18 880 89 595 61 303 705^23005 318 700 902 42 19 909 83 633 56 331 698 033 311 728 894 41 20 937 78 652 50 360 692 062 304 756 887 40 21 966 73 6S0 44 388 686 090 298 784 880 39 22 995 68 709 39 417 680 118 291 813 873 38 23 18023 62 737 33 445 673 146 284 841 866 37 24 052 57 766 27 474 667 175 278 869! 858 36 25 081 52 794 21 602 661 203 271 897 851 35 26 109 47 823 16 530 655 231 264 925 844 34 27 138 41 851 10 559 648 260 257 953 837 33 28 166 36 880 04 587 642 288 251 982 829 32 29 195 31 90897998 616 636 316 244 25010 822 31 .30 31 224 25 937| 92 644 21672 630; 345 97623 23373 237 038 815 30 29 1.8252 98320'19965 97987 97230 25066 96807 32 281 15 994; 81 701 617 401 223 094 800 28 33 4509 10200221 75 729 611 429 604J 458 217 122 793 27 34 338 04 051! 69 758 210 151 786 26 35 367 98299 079 63 786 593 486 203 179 778 25 36 395 94 108 58 814 692 514 196 207 771 24 37 424 88 136 52 843 585 542 189 235 764 23 38 452 83 165 46 871 579 571 182 263 756 22 39 481 77 193 40 899 573 599 176 291 749 21 40 509 72 222 34 928 666 627 169 320 742 20 41 538 67 250 28 956 560 656 162 348 734 19 42 567 61 279 22 985 553 684 165 376 727 18 43 595 56 307 16 22013 547 712 148 404 719 17 44 624 50 336| 10 041 541 740 141 432 712 16 45 1:6 652 45 364! 05 070 534 769 ^3797 134 460 705 15 14 1868198240 20393 97899 22098 97528 97127 25488 96697 47 710 34 421 93 126 521 825 120 516 690 13 48 738 29 450 87 155 615 853 113 545 682 12 49 767 23 478 81 183 508 882 106 673 676 11 SO 795 18 507! 75 212 602 910 10(y 601 667 10 51 824 12 535 69 240 496 938 093 629 660 9 52 852 07 563! 63 2681 489 966 086 657 653 8 53 881 01 592! 57 2971 4835 995 079 685 645 7 54 910 98196 6201 51 325 476'24023 072 713 638 6 55 938; m 649| 45- 353 470 051 065 741 630i 5 56 9671 85 677 39; 382 463 079 058 769 623! 4 57 9951 79 706 33^ 410 457 108 051 798 6I5I 3 58 190241 74 7341 27; 438 450 136 044 826 6081 2 59 052| 68 7631 21 467 444 164 037 854 600 1 m N.CSIN. S. N.CS'isi. S.N.CS'N. S.JN.CS'N. S. N.CS N. S. M^ 79 Deg. 78 Deg.i77 Deg.'76 Deg.»75 Deg. _l 133 A TABLE OF NATURAL SINES. 15 Deg.|16 Deg.| 17 Deg.jlS Deg.| 19 Deg. Mn. S. N.CS In. s.in.cs N. S. N.CS N. S. N.CS N. S.IN.CS j M 25882 96593 27564 96126 29237 9563030902 95106 32557 94562 60 1 910 585 592 118 265 622 929 097 584 542 59 2 938 678 620 110 293 613 957 088 «12 633 58 3 966 570 648 102 321 605 985 079 639 523 57 56 55 4 994 562 676 094 348 596 31012 070 667 514 5 26022 555 704 086 376 588 040 061 694 504 6 050 547 731 078 404 579 068 062 722 495 64 53 7 079 540 759 070 432 571 096 043 749 485 8 107 532l 787 062 460 562 123 033 777 476 52 9 135 624 815 064 487 554 151 024 804 466 51 10 163 517 843 046 515 545 178 015 832 457 50 11 191 509 871 037 543 536 206 006 859 447 49 12 219 602 899 029 571 528 233 94997 887 438 48 13 247 494 .927 021 599 519 261 988 914 428 47 14 275 486 955 013 626 511 289 979 942 418 46 45 44 16 303 479 983 006 654 502 316 970 969 409 16 2633i 96471 28011 95997 29682 95493 31344 94961 32997 94399 17 359 463 039 989 710 485 372 952 33024 390 43 18 387 456 067 981 737 476 399 943 051 380 42 19 415 448 095 872 765 467 427 933 079 370 41 20 443 440 123 964 793 459 454 924 106 361 40 21 471 483 160 956 821 450 482 915 134 351 39 22 500 425 178 948 849 441 510 906 161 342 38 23 528 417 206 940 876 433 537 897 189 332 37 24 556 410 234 931 904 424 565 888 216 322 36 26 584 402 262 923 932 415 593 878 244 313 35 26 612 394 290 915 960 407 620 869 271 303 34 27 640 386 318 907 987 398 648 860 298 293 S3 28 668 379 346 898 30015 389 675 851 326 284 32 29 696 371 374 890 043 380 703 842 353 274 SI 30 724 363 402 882 071 372 730 832 381 264 30 29 31 26752 96356 28429 95874 30098 95363S31758 94823 33408 94254 32 780 347 467 865 126 354 786 814 436 245 28 S3 808 340 485 857 154 345 813 805 463 235 27 34 836 332 513 849 182 337 841 795 490 225 26 -35 864 324 641 84] 209 328 868 786 518 215 25 36 892 316 669 832 237 319 896 777 546 206 24 87 920 308 597 824 265 310 923 768 573 196 23 38 948 301 625 816 282 301 951 758 600 186 22 39 976 293 662 807 320 293 979 749 627 176 21 4027004 286 680 799 348 284^32006 740 655 167 20 41 032 277 708 791 376 275 034 730 «82 157 19 42 060 269 736 782 403 266 061 721 710 147 18 43 088 261 764 774 431 267 089 712 737 137 17 44 116 253 792 766 459 248 116 702 764 127 16 46 46 144 246 96236 820 757 486 240 144 693 792 118 94108 15 14 27172 28847|95749 30514 95231 32171 94684 33819 47 200 230 876 740 542 222 199 674 846 098 13 48 228 222 903 732 570 213 227 666 874 088 12 49 256 214 931 724 697 204 254 656 901 078 11 60 284 206 959 715 626 195 282 646 929 068 10 51 312 198 967 707 653 186 309 637 956 058 9 52 340 190 29015 698 680 177 337 627 983 049 « 53 368 182 042 690 708 168 364 618 34011 039 7 54 396 174 070 681 736 159 392 609 038 029 6 56 424 166 098 673 763 160 419 599 065 019 6 66 452 158 126 664 791 142 447 590 093 009 4 57 480 150 154 656 819 133 474 580 120 93999 3 58 508 142! 182 647 846 124 502 571 147 989 o -59 636 134 209 639 874 115 629 561 175 979 1 M N.CS N. S. N.CS nTsT N.CS N. S. N.CS N. S. N.CS N. S. 1m 74 Deg. 73 Deg. 72 ] Deg. 171 Deg. 70 Deg. A TABLE OP NATURAL SINES. m 20 Deg. 21 Deg. 9 10 11 12 13 14 J5 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 ~3i 32 33 34 35 36 37 38 39 40 N.CS N. S. N.C8 34202 93969 35S37 93358 229 959 864 348 257 949 891 33 " 284 939 918 327 311 929 945 31o 339 919 973 3O0 366 909 360U0 21».> 393 899 027 285 421 889 054 274 26 25i 22 DegT23 Deg.,24 Deg. 443 879 081 475 869 108 503 859 135 243 530 849 162 232 557 839 190 222 584 829 217 211 012 819 244 ! 201 34639 93809 36271 93190 666 694 721 748 775 803 830 857 884 912 939 966 993 35021 35048 075 102 130 157 183 211 239 266 293 411 320 42 347 431 375 441 402 45! 429 4635456 47 484 48] 511 49 538 50 565 511 592 799 298 180 739 325 169 779 352 159 769 379 148 759 406 137 748 434 12 738 461 .V. S. N.CtJ IN". S. N.CS { N. S. N.CS 37461 92718 390739205040674 91355 488 707 100; 039t 700 343 515 687 127 028; 727 331 542 686 153| 0161 753 319 5691 675 180 005; 780 307 C.S5' 664 20791994- 806 293 022: 653 234' 982; 833 283 649' 642 260 971 860 272 676; 6-31 237 959 836 260 703: 620 314 948 913 248 730' 609 341 936c 939 236 757; 698 367 925 966 224 784| 587 394i 914; 992 212 811i 576 421 90241019 200 838: 565 443, 891 045! 188 865 554 474 879 072 176 37892 92543,39501 91888 41098 91164 919i 532 528 856 125 152 946i 52L 655 845, 151 140 9731 510; 581 8335 178 128 728 488 lib 106 999 j 499 608; 8225 204 116 38026) 488^ 6351 810'; 231 104 0o3' 477 661 ! 799 o57 092 619 647 674 701 728 755 782 59! 810 ."mJn.csIn. s. 718 515 095 708 542 084 698 569 074 688 596 063 677 623- 052 667 650 042 93657 36677 93031 647 704 O20 637 731 010 626 758 92999 616 785 988 606 812 978 596 839; 967 585 867 956 575 894! 945 565 S21 935 555 948 924 544 975: 91'3 534 37002 902 524 029. 892 514 056 881 93503 37083 92870 493, 110 859 483^ 137 849 472 164 838 4S2, 191 827 452| 218 816 441 j 245 805 4311 272 794 38295 92377 39902-91694;41496 90984 322' 366 928' 683] 522 972 3491 355 9551 671| 549 960 376| 343 982 660 575 945 403 332.40008 648J 602 936 O8O; 466: 688 1071 455' 715 1341 444 741 787^ 284 080 775.; 310 068 764< 337 056 161, 432 768! 752i 363 044 188 421 795 74U 390 032 215' 410 822! 729J 416- 020 241' 399 848i 718? 443 008 268 388 875! 7061 469 90996 M 60 59 58 57 56 55 64 53 52 51 50 49 48 47 46 _45 44 43 42 41 40 39 33 37 36 35 34 S3 32 31 30 430 321I 035 456 310) 062 483 2995 088 510 28"! 115 537 276' 141 564 2651 198 591 264i 195 617 243i 221 644 231| 248 671 220 . 27J> 33898 92209-40301 725 193"; 328 752 186i 355 778 175' 381 164 1 403 152! 434 141i 461 420 410' 400 389 379 368 636j 628i 924 625 655 911 613: 681 i 899 601] 707i 887 590j 734: 875 6781 760 863 666] 7871 651 655: 613 639 543j 840 826 _53i; 666; 814 9151914189290802 805 832 859 886 130i 483 293 784 9121 119; 514 326 773 939 107j 541 353 762' 9661 0961 567 380 751 993 085; 594 407 74039020 073i 621 434 729 046 082 647 508 919 496} 946 484' 972 472i 993 461.42024 449, 437 425 4i4 402 390 378 366 N.CS N. S. N.CS'N. S.'iN.CSlN. S.I N.CS 051 077 104 130 156 183 209 235 790 778 766 753 741 729 717 704 692 680 668 655 643 NTs? 29 28 27. 2Q 25* 2< 23' 22' 21^ 20 19 18 17 16 if 14 13 12 11 10: M 69 Deg.i68 Deg.67 Deg,;66 DegJ65 Deg.i 36 131 A TABLE OF NATURAL SINES. 25 Deg j26 Deg 27 Deg,|28 Deg. 29 Deg, 5r~ilN7^!^?7^NXis N. S. N.CSiN. S.N.CS n'/'sTnTcs 45399 8910M6947 88295 425 087i 973 281 451 074 999 477 061 47024 503 048 050 529 035 554 021 580 0081 606 8899 632' 881] 16 42683 90433,44255 89674s458I3 B8888M7358 88075 709 4215 281 736 408| 307 762: 396? 333 788 3831 359' 815i 3711 385' 841 3583 411 8&7 346i 437 383 062 409 048 434, 034 460: 020 662) 839 875 649J 865 8621 6361 891, 848| 6231 917' 835; 610 942 822| 466 006|49014 597 968 808| 584- 994 7958 24 894 3341- 464 571-46020 782| 662 965 25 920 32 li 490 558i 046 768S 588 951 KAid f\ia tckS at a qq-v 511 87993 537 97« 26 946 309 516 545 072 7553 614 937 27^ 972 296 542| 532? 097: 74l| 639 923 28 999 284 568' 5195 123 72^ 665 909 29 43025 271 594 606; 149 715! 690 896 30 051 259 1 620 493/ 175 701 ? 716 3143077 90246|44646 89480^46201 8868sk7741 87868 32 104 233S 672! 467| 226; 674] 767 854 33 130 221, 698,' 454) 252; 661:- 793 840 34 156 35 182 36 209 37 235 38 261 287 313 340 366 392 418 445 2083 7241 196| 7501 183s 776j 1711 802! 168 148| 133 120 108' 095 441 278 647> 818 428 304 634! 844 Am 330 620,? 869 402' 355 607i 895 39 40 41 42 43 44 45 464347190057,45036 47 497 045] 06; 6231 032 549' 019 675 007 602 89994 628| 981 654| 968! 680j 956 706 943 733 759 785 811 826 812 798 784 770 756 743 729 715 701 687 673 48481 506 532 557 583 608 634 659 684 710 735 761 1301 786 811 837 862 48888 913 938 964 989 xM.CS M 87462! 60 448; 59 434; 58 4201 57 406: £6 3911 55 377 64' 363 349 335 321 306 292 278 264 250 87235 221 207 193 178 164 150 136 121 107 093 079 064 050 036 040 065 090 116 141 166 192 217 242 49268 293 318 344 369 394 419 445 470 495 521 546 671 596 622 87659 49647,86805 645= 672! 791 631; 697! 777 617] 723 603' 748 589^ 773 575j 798 56! 824 546! 849; 632: 874' 518 899 924i 950 975 504 490 476 87021 007 86993 978 964 949 935 921 906 892 878 863 849 834 820 762 748 733 719 704 690 675 661 646 632 1 617 53 52 51 50 49 48 47 46 45 44 43, 42 41 40 39 38 37 36 35 34; 33 32 31 30 "29 28 27 26 26 24 23 22 21 20 19 18 17 16 14 13 12 11 10 9 8 7 I 4 3 2 1! N. ;l^. n.cs n. s.rrn 64 Peg. 83 Deg. 62 Peg. 61 Peg. 60 Peg. A TABLE OF NATURAL SINES, 135 30 Deji. 31 Deg. 32 Deg, M N. s. N.rs r- 25 50000 025 050 076 101 126 151 86603 588 573 559 544 530 515 176 501 2011 486 227,1 471 252! 457 277 442 302 427 327 413 352 398 377 384 86369 354 340 16 50403 428 453 478 503 528 553 678 603 628 654 679 704 729 754 50776 804 829 854 879 904 929 954 979 51004 029 054 079 104 129 51164 179 204 229 264 279 304 329 364 379 404 429 454 479 8614S 62275 85-i49 63754 84324 N.CS 325 310 296 281 266 251 237 2"i2 207 192 178 163 51604 529 55^ 5'h 60-4 628 65[ 67' 70l Kb 758 77 f- 80i 828 862 87 6190ii 927 652 977 52002 026 051 076 101 126 151 175 200 225 250 X.r 8 ?v S.lN^Ci 8'5717 52992 84806 70253017 789 687 041 1 774 672 066 759 091 743 115 728 140: 712 164' 697 85476 5338(i 84567 461 J 411 542 446f 436 626 431| 460! 511 416J 484| 495 401! 5091 480 385j 6341 464 370i 558 i 448 3S5i 583: 433 340' 607! 417 325! 632 402 310f 656 386 294} 681 1 370 279' 705 355 264 730i Sii iJ3 299 234 779| 308 119 324 218j 8041 292 104 349 203| 8281 277 089- 374 188| 8631 26 J 074 399 1731 877 245 059 423 157; 902| 230 045 448 142'; 926; 214 030 473 127' 961 198 015 498 ll?i 975 182 000 522 096^54lX)0' 167 85985 547 081 j 024 161 970» 57« 066! 049 135 „„^, ..^ ««- wu 956 657 05l| 073 120 533 163 976 181 941 621 035 ; 097 104 ; 567 14 7 57000 165 85926 52646 85020 54122 84088;6558i 83131 57024 82148 911 671 005. 146 072i 605 115 047 132 896 696 84989; 171 057? 630! 098 071 115 881 720 974r 195 041- 654 082 096 098 866 745 S59( 220 026; 678: 066 119 082^ 851 770 943j 244 009- 702] 050 143 065 33 Deji 54854 83613 56305 878 697. 329 902| 581' 353 927! 565» 377 9611 649; 401 9761 533; 425 999 617i 449 55024 601? 473 048 485! 497 072 469. 521 097 463 545 121 437 569 145 421; 593 169 405 617 194 389 641 82643 626 610 693 677 561 544 528 511 495 478 462 446 429 413 55218 83373 56665 82396 242i 356; 689^ 380 266! 340 713. 363 a9r 324) 736- 347 315 308; 760 330 339 292 784 314 363 276 808 297 S88i 260t 832 281 412: 244 856 264 436 228 880 248 460, 212 904 231 484 195 928 214 509, 179 952 198 836 794 9284 269 83964 726 034 167 048i o 821 819 913! 293 978 750! 017 191 032; 7 806 844 792 869 882 342 946 N 317 S62 773 001 215 0151 799 82985 238 81999 777 893 866 366 930 823i 969 262, 982 762 918 851 391 016 847| 953 286| 965 747 943 836? 416 899 871 936 310l 949 732 967 820[ 440 883 896i 920 334: 932 iN.C> N, S N ( S|N. S. W.CS:N. S. 5P O 5.^ I)pg.i57 Deg.^56 Peg. 55 Deg. J3e A TABLE OF NATURAL SINES^. M 35 Deg.!36 Deg.\ 37 Deg." 38 Deg,|39 Ueg.j M N. S.N.CSjN. S. N.CS.'N. S.,N.CS,,N. S. N.CS* N. S.,N.CS| 57358 81915'58779;80902;60I82 79864 6I.566'78801 62932,777151 60 1 881 899i 802' 885v 205 846 589 783 955 6961 69 2 405 882 826' 867] 228; 829 612 765* 977 678| 58 3 429 866 849 850? 261; 811 635 848 873 833; 2741 793 658 747 63000 660 57 4 453 729: 022 641 56 5 477 832 896| 816- 298i 776. 681 711 045 623 55 6 501 815 820 799J 321 758! 704 694 068 605 54 7 524 798i 943 7823 344; 741? 726 676 090 686 63 8 548 782 967 765, 367 723 749' 658 113 568 52 9 572 765 990 748; 390 706 772' 6401 135 650 61 10 596 748-59014 730 414 688 7951 622^ 158 631 50 11 619 731 037 713! 437 671 818| 604 180 613 49 12 643 714 061 696i 460 653 8411 686 203 494 48 13 667 698 084 6791 483 635 8641 568 225 4761 47 14 691 681 108 662! 506 618 887 550 248^ 458| 46! 15 715 664 131 644' 629 600' 909 ^ 532 271 439| 45] 16 57738 81647S59164, 80627160563 79583 61932 7851463293 7742li 44] 17 762 631S 178 6101 576 585 956 496, 316 402 43 18 786 6141 201 593| 599 6473 978; 4781 338! 384 42 19 810 5972 226 676 622 530:!62001l 4605 361 366 41 20 833 580' 248 55S? 645 512s 024i 442^ 383 347 40 21 857 563j 272 641 668 4945 046: 424, 406! 329 39 22 881 546 295 624 69 li 477S 069 405 428 3101 38] 23 904 530i 318 507 714 459| 092 387s 451 292 37 24 923 613' 342 489 738 441| 115 369, 473 273 36 25 952 496i 365 472 761 4242 138 351 496 255 36 26 976 479i 389 465S 784 406| 160 38^ 183 333 518 236i 34] 27 999 462 412! 438? 807 316 540 218 33 28 580231 4455 436| 420^ 830 37ii 206 297 563 199 32 29 047 428^ 4591 4031 853 35^ 229 279 585 181 31 30 "31 070 412 482 58094 81396 69508 386) 876 335] 251 261 608 ,636^8 162 30 29 80368?60899 ; 79318i62274 78243 77144 32 118 378 629 3511 922| 3005 297 225; 653 125 28 33 141 361 552 334? 945 282 320 206 675 107 27 34 165 344 576 316f 968 264 342 18Sl 698 088 26 35 189i 327. .599 299:- 991 247 365 170? 720 070 25 36 212 310' 622 282;:61015 229 388 152| 742 051 24 37 2361 293- 646' 264? 038 211 411 134| 766 033 23 38 260; 276 669i 247" 061 193 433 lief 787 014 22 39 283i 259 693 230J 0841 176 466 098| 810 76996 21 40 307 242 716 212? 107| 158 479 079|'i 832 977 20 J 330 354 225 739 195 1531 122 znc> 524 061 854 ^ 04S 877 959 i 19 940 18 208 763 178 •'43 378 191 786 160° 176! 105 647 fcp2T 899 921! 17 44 401; 174 809 143 199| 087 670l^007l 922 903' 16 4S ^46 47 425 157 832; 125 222i 069 592 77988' 944 77970 63966 884 15 76866 14 68449 8114069856 80108 61245 79051 62615 472 123- 879, 091 268i 033 638 952. 989 847| 13 48 496 106 e02i 073 291 1 015 660 934,"64011 828i 12 49 519;" '089 926 056 314 78998 683 916 033 8io! 11 50 543' 072; 949: 038 337: 980 706 897 056 791 1 10 51 667 0553 9721 021 3601 962 728! 879 078 7721 9' 52 590 038' 995i 003 383 944 751! 861 100 754 8 53 614 02160019 79986 406 926 774 843 123 735 7 54 637 004 042 968- 429 908 796 824 145 717 6 55 66180987i ,065 951. 451 891 819 808 167 698 5 S6 684 970] 089; 934? 474 873 842 788 190 679 4 S7 708 9531 112; 916; 497 855 864 769 212 661 3 58 ^31 936] 135i 899j 520 837 887 751 234 642 2 59 M 755 N.CS 919] 158' 881-; 543 819 909 733 256 623 N. S. I M N. S.fN.CS.iN. S.jN.OS N. S. n.cs|n. s. N.CS. 54 Deg.!63 DegA52 Deg. 61 Deg. [so Deg. 1— a^^MB A TABLE OP NATURAL SINES. 1S7 40 Deg. N. S. N.CS 64279 301 323 346 368 390 412 435 457 479 501 524 546 568 690 612 M 1 2 3 4 5 6 7 6 9 10 11 12 IS 14 \5 16 17 18 19 20 21 22 23 24 25' 26 27 28 29 30 '3164967 321 989 33:65011 34 033 76604 586 64633 657 679 701 723 746 768 790 812 834 856 878 901 923 915 76304165956 286j 978 267166000 248 022 055 077 099 122 144 166 i88 210 232 264 276 41 Deg7T2 Peg. } 43 Deg.l 44 Peg? N. S. . N.CSN. S . N.CSiJV. S. N. Cs|n. S.|N.CS 65606 628 567 650 648 530 511 492 473 455 436 417 398 380 361 342 323 7547166913 229 210 192 173 154 135 116 097 078 059 04l' 044 066 088 109 131 153 175 197 218 240 262 76022 66284 003! 306 75984^ 327 965 349 946 371 9271 393 908 414 8891 436 87M 458 85lj 480 832| 501 813 523 794] 545 7751 566 756' 588 74314)68200 295j 221 2761 242 256; 264 237 285 217 306 198 327 178! 349 159; 370 139i 391 120j 412 100! 433 0801 455 061? 476 041j 497 022; 518 74002 68539 73983. 561 963) 682 944] 603 924] 624 904 645 685! 666 865i 688 846r 709 826) 730 806) 751 787j 772 767 793 7471 814 72S 835 73135 69466 116-, 487 096i 608 076; 529 056' 549 036 670 016 591 729961 612 9761 633 957? 654 937 917 71934 914 894 873 853 833 813 792 772 752 732 711 691 671 46 66298 47; 320 481 342 364 386 408 430 452 474 496 518 540 562 584 606 75738=66610 719 632 699 653 680 675 661 697 642 623 585 666 718 740 604 762 783 806 547 827 528( 848 609i 870 490) 891 4711 913 N. S. N.CS 74586 67901 567 923 548" 944 528i 965 509 987 489 68008 470, 029 451; 051 431: 072 412; 093 392 115 373 136 353 157 334 179 314 200 N. s. nTcs 73412 69172 393' 193 373 214 353 236 333 256 SM; 277 294' 298 274 319 254 340 234 361 215 382 195 403 175 424 156 445 135 466 N. S.'N.CS 675 696 897j 717 877, 737 . . _ 857^ 758' 650 837- 779 630 1 72817 69800 71610 797i 821 590 777^ 8421 569 767; 862 649 737i 883! 529 717:4 9041 608 6971 9251 488 677 946 j 468 6571 966! 447! 637- 987; 427 61T70008i 407^ 597 029 386 577l 049! 366 557j 070 345! 5373 091 325 i 72517 70112 71305! 497, 132; 284 477 153! 264 467i 1741 243 437^ 1951 223 4175 215' 203 3971 2361 182 357J 277 337 298 3171 319, .^ 297I 339 080 277 360! 059 257J 381; 039 236; 401! 019 72216 70422 70998 196' 443 9781 176' 463 957 156 484 937 136 606 916 116, 525 896 095 546 875 075 667 855 055 687 834 035 608 813 015 628 793 71995 649 772 974 670! 752 954 690 731 934 711 711 nT^'n.csn. s. '52 141 121 100 60 59 58 67 56 65 54 63 62 51 49 48 47 46 J5 44 43 42] 4ll 40^ 39' 38 37; 36 35' 34 33, 32 ! 31 ;_30 i 29 28 27 26 25 24 23 21 20 19 18 17 16 J5 14 13 12 10 9 8 7 € 3 2 49 Peg. 48 Pe g.i47 Peg. 4 6 Peg..45Deg._ m 6A8 019 408 619 Wi :l;l >'h\\i < ;'■ i;i-»:i-rt; i':^% i; m ■('i. }\^''i' ■<:!) ! '' > '. I.