SB 5flO 137 
 
 LO 
 OO 
 
O- 
 
 o 
 
 co 
 
 w 
 
Def lecfion Angles 
 
 t FYpm From From From From From 
 
 icmg.l Curve Tcmq. Curve Ton. Curve 
 Olj - EnW End End End Er?d End 
 
 O 000 4-35 000' 2 55' O'OO'jl'ss' 
 I 002 424: 005' 243 005 ' I'e 
 
 3 009 358t 0|4' 2 14/2 O235i O47y 
 
 4 0I5J 34-3 0ssy z |5T' O37^ OZ5' 
 
 5 0*22' 3*27 033' l37^ O55' OOO 
 
 6 O e 30'!3 09 O^sne' 
 
 9 IO3 208 l"35' 
 
 10 r IT' 4-s 
 
 0"55 
 
 25 OOO 
 
 'n A*<~. 
 &r- Co/o, 
 
info o/c/ track where 
 
 ou must- -So/v& 
 
 >ras, 
 
 ^replacing a ^ircuicir t^urve^ wihhouh changing 
 Hie length of Hhe line. 
 
 /Vp. of Spiri 
 
 50A--T 
 
 //>e follo 
 
 IOOA-IOON 
 
 // e /? e *v ///? < 
 
 This problem 
 
 fh<s n^w System /s founded u^> 
 , vvh/'/*> fh<s o/c/ ^Sysr&rr? is not 
 
 , 
 So. L mco/n 
 
CURVES 
 
 OF 
 
 CIVIL ENGINEERING. 
 
 THE TRANSITMAN'S POCKET 
 COMPANION. 
 
 CONTAINING INSTRUCTIONS FOR SURVEYS TO LOCATE 
 
 THE CENTER LINE OF ENGINEERING WORKS, 
 
 AND TABLES THAT ARE NEEDED 
 
 IN THE FIELD, 
 
 IN CONNECTION WITH 
 
 CIRCULAR, TRANSITION, AND VERTICAL CURVES. 
 
 PRICE, $2.50. 
 
 ARTHUR M. HAYNES, C.E. 
 
 M. iv'.'s. . 
 
 37 So. LINCOLN AVE., DENVER, COLO. 
 
 1903. 
 
- 
 
 y 
 
 
 Copyright, 1903, 
 
 by 
 ARTHUR M. HAYNES. 
 
 ROBERT DRUMMOND, PRINTER, NEW YORK. 
 
Deflecri-on Anqles 
 
 rom From From 
 3. Curve Tang. 
 
 orn rom from 
 Curve Tang, Curve 
 E.nd End End 
 
 End End j E-nd End End 
 
 ?35' OTOO' '55' CfOO I 35 
 24 Cf03' E'43y 2 005' fZZ 
 
 O OTOO' 4*35 OTOO '55 
 I CfOZ' 4*2-4 0*03' 2*43% 
 
 2 CfOS* 4- 12 0'07J4 Z*30* 
 
 3 008' 358 Cfl^ 2"^ 
 4 OTIS' 3*4-3 CT22J4 1*57* 
 
 5 0-22? 3*57 Cf33' I37X 2 
 
 6 GTSO' 3*O9 Cf45>i r ' 6* 
 
 7 0-40' 2T&0' 1*00' 0*52'/i 
 
 8 0*5 1*. 2*30 \'\6fc 0*27 
 
 9 1"03' 208' 1*33' O*OO* 
 
 10 TI7' I '45 
 
 11 r32' I'EI* 
 
 12 I" 4-8 055 
 
 13 2*O6 028 
 
 14 2*25 000 
 
 O5 
 B 00 
 
 One writer has furnished us a table of corrections to 
 apply to the more important functions, but it requires 
 .interpolation, and is confusing when taken with the 
 distractions of field-work. Another has given us volu- 
 minous tables for curve functions, for curves of integral 
 
 117655 3 
 
ROBERT DRUMMOND, PRINTER, NEW YORK. 
 
PREFACE. 
 
 OUR forefathers began laying out curves with loo-ft. 
 chords, because it was a little easier to do field-work 
 that way. In their practice the errors were not so seri- 
 ous as they now are, and their link chains made it more 
 difficult to measure arcs (or anything else) than with 
 steel tapes now used. 
 
 We have followed their example too long. This prac- 
 tice is responsible for countless shocking kinks in rail- 
 road curves that are covered up, whitewashed, and 
 unknown. The average transit party does not expect 
 to close on the P. T. closely when it had been previously 
 set according to tables. No matter how carefully they 
 may do their work they know there are errors in the 
 tables that will make fudging necessary. The method 
 is known to be inaccurate, and is made the excuse for 
 careless work. The errors have been characterized as 
 "inappreciable" or "negligible," but they are cumula- 
 tive and increase as the square of the degree ; have made 
 much trouble, and have thrown discredit upon the pro- 
 fession. 
 
 One writer has furnished us a table of corrections to 
 apply to the more important functions, but it requires 
 interpolation, and is confusing when taken with the 
 distractions of field-work. Another has given us volu- 
 minous tables for curve functions, for curves of integral 
 
 117655 3 
 
4 PREFACE. 
 
 degrees from i to 10. That work (Butts) has been 
 highly appreciated and ought to be in the hands of 
 every conscientious transitman, but it is limited to the 
 integral degrees i to 10, and only demonstrates the 
 impracticability of chord measurements. The mere 
 idea of measuring across a chord 100 feet and calling it 
 the length of the curve is revolting. The error for a 
 20 curve is a half of a foot. It might be excusable if it 
 resulted in ease and simplicity in doing the work. But 
 it results in difficulties and uncertainties. As one indi- 
 cation of the difficulties, there is not a curve shown on 
 any of the filed plats of surveys for irrigation canals in 
 Colorado. They aggregate 10,000 miles; some of them 
 cost a half million dollars, and are fine examples of 
 engineering, but their alinements are all attempted to 
 be shown by straight lines and angles because chord 
 measuring cannot be used on the sharp curves. The 
 excuse for this book is to advocate arc measurements. 
 
 A new table of i Curve Functions is here given, in 
 accordance with a new definition for "Degree of Curve," 
 which is found in the first paragraph of the text. With 
 measurements on the curve the table is exact for all 
 degrees. With measurements on chords, results are as 
 close with this table as with similar published tables. 
 So this table is prefectly applicable on work where the 
 errors of chord measuring is considered negligible. 
 Logarithms and tables of natural functions are not 
 given because they should not be used in the field. 
 Transit work is, or should now be, in trained hands, 
 which are supplied with such tables as those published 
 by Professor Jones, of Cornell University, by Von Vega, 
 or by the U. S. Geo. Survey. Special problems, too, are 
 considered as belonging in the classroom. 
 
 The subject of transition curves is made a prominent 
 feature. The discussion is much longer than necessary, 
 because there has been so much literature on the sub- 
 
PREFACE. 5 
 
 ject which has to be referred to. There seems to be no 
 other subject upon which engineers are so divided. 
 
 A section on vertical curves, too, is added, so that 
 the ground may be better covered, as indicated in the 
 title. While this subject applies especially to railroads, 
 it should be applied to city street grades much more 
 than it is. Street cars are unable to follow safely the 
 grades that are established by the city engineer, and 
 the unsightly appearance of sharp angles in street grades 
 is discreditable. 
 
 The engineer's practice is of two kinds: one of loca- 
 tion, the other of construction; one of planning, the 
 other of executing; one dealing only with nature, the 
 other with men, manufactured materials, and machines. 
 This work is to assist in the first-named practice ; in 
 the location of a center or base line, both horizontally 
 and vertically, from which all detail plans and measure- 
 ments may be made. A line which will pay due respect 
 to the inertia of moving objects and to civic aesthetics, 
 thus to ''make the dollars earn more interest." For 
 nature abhors an angle. 
 
 A. M. HAYNES. 
 
 DENVER, COLO., October, 1903. 
 
CONTENTS. 
 
 CHAPTER I. 
 
 CIRCULAR CURVES. 
 
 PAGE 
 
 1 . Definition of degree of curvature 9 
 
 2. Method of projecting curves on the ground 9 
 
 3. General definitions 10 
 
 CHAPTER II. 
 
 ALINEMENTS OF ENGINEERING WORKS. 
 
 4. Method of staking out 10 
 
 5. Transit points and plusses 1 1 
 
 6. Markings on stakes 1 1 
 
 CHAPTER III. 
 
 LINEAR MEASUREMENTS. 
 
 7. Tools 12 
 
 8. Manner of using 12 
 
 9. Slope measuring 13 
 
 10. Curve measuring 13 
 
 CHAPTER IV. 
 
 GENERAL DISCIPLINE. 
 
 11. Rules of conduct 14 
 
 12. Orders few and considerate 14 
 
 CHAPTER V. 
 
 ANGULAR MEASUREMENTS. 
 
 13. Transitmen should be relieved from discipline and manage- 
 
 ment 15 
 
 14. Care to be taken 15 
 
 CHAPTER VI. 
 
 TRUE MERIDIAN. 
 
 15. To obtain observations upon Polaris 16 
 
 CHAPTER VII. 
 
 FIELD WORK. 
 
 16. To stake out curves connecting tangents 17 
 
 17. Definitions of functions of curves 17 
 
 18. Plan of operations where curves predominate 18 
 
 7 
 
8 CONTENTS. 
 
 CHAPTER VIII. 
 
 TEANSITION CURVES. 
 
 19. Requirements for a system 19 
 
 20. Description to meet requirements 19 
 
 21. Selection of suitable curves 21 
 
 22. Deflection angles for spirals 22 
 
 23. Elements of spirals 23 
 
 24. Description not needed in practice 23 
 
 25. General equation and formulas 24 
 
 26. General deflection table . 25 
 
 CHAPTER IX. 
 
 PLATTING. 
 
 27. Duties of transitmen regarding same 26 
 
 28. Order of platting 27 
 
 29. Compound curves, special treatment 27 
 
 CHAPTER X. 
 
 TURNOUT CURVES. 
 
 30. Description 28 
 
 31. Complications to avoid 29 
 
 CHAPTER XI. 
 
 VERTICAL CURVES. 
 
 32. Definitions and description 30 
 
 33. Compensation for curves on grades 32 
 
 34. Vertical curves too little used 32 
 
 TABLES AND DIAGRAMS. 
 
 Table I. Differences in lengths of Arcs and Chords 34 
 
 II. Diagram. Sample transit notes 35 
 
 III. " Superelevation of Outer Rail 30 
 
 " IV. " Corrections in Chaining 40 
 
 V. Emergency Table for Determining Natural Func- 
 tions of angles 41 
 
 " VI. Curve Characteristics 43 
 
 " VII. Ordinates for Vertical Curves 44 
 
 " VIII. Azimuth of Polaris when at Elongation 44 
 
 " IX. Functions of a i Curve 45 
 
CURVES OF CIVIL ENGINEERING. 
 
 CHAPTER 
 
 CIRCULAR CURVES. 
 
 1. The Degree of a Curve is a term applied to circitlar 
 curves in a plane and is the change of direction in degrees 
 per one hundred feet; or, in other words, is the number 
 of degrees in an arc of the curve one hundred feet long. 
 
 The radius of a curve = 572Q ' 5 . 
 
 degree 
 
 The radius of a i curve = = 5729.57795. 
 
 7T 
 
 2. Circular curves are projected on maps by means 
 of their radii with the compass. On the ground 
 it is generally found necessary to make use of the geo- 
 metrical theorem that an arc subtends an angle on 
 the circumference equal to one half the angle at the 
 center subtended by the same arc. A transit is placed on 
 the curve (or circumference) and the curve is located in 
 loo-ft. arcs by turning angles for each arc equal to one 
 half the degree of the curve. The work can be commenced 
 and carried on at an unknown distance from the transit, 
 but it is generally required to begin at the transit so that 
 it may conform with a previously located tangent. 
 
 9 
 
IO CURVES OF CIVIL ENGINEERING. 
 
 When there is special reason for doing so, arcs of less 
 than TOO ft. can be located by deflecting angles pro- 
 portional to the length of arc measured. 
 
 It is bad practice to try to locate points on a curve 
 more than 60 from the transit, because one end of 
 the tape line is held on the curve, while the other end 
 describes an arc .with the tape as a radius, and the new 
 point being fixed on the curve, is at the intersection of 
 this arc with the line of colimation from the transit. 
 This angle of intersection is o at 180 from transit, and 
 is too acute for accuracy beyond 60 from transit. 
 
 Tt is impracticable to have the measuring line on the 
 curve. So it is placed on the chord in a straight line, 
 but the end is held back, distances given in Table I, 
 so that the result is the same as though actually 
 measured on the arc. 
 
 3. A curve of uniform degree in one direction is a 
 Simple Curve. Two or more curves in the same direction 
 connected, and with a common tangent at point of con- 
 nection, is a Compound Curve. If such curves are in 
 opposite directions they form a Reverse Curve. A Tangent 
 to a curve is a straight line which intersects it but does 
 not cross. 
 
 CHAPTER II. 
 
 ALINEMENT OF ENGINEERING WORKS. 
 
 4. Engineering works, such as railways, canals, 
 boulevards, dams, tramways, etc., are surveyed and 
 staked out with a line of stakes one hundred feet 
 apart and numbered consecutively, beginning with 
 station at one end of the work. Such points are 
 called stations; when it is necessary to have points 
 between two stations the distance is measured from 
 the last station and this distance is called a plus. The 
 
CURVES OF CIVIL ENGINEERING. I I 
 
 stake is marked the last station + the distance from 
 it in feet and tenths thereof. 
 
 5. At station and at other points along the line 
 where it is necessary to set up the transit, a hub is 
 driven flush with the ground and a tack put in the hub 
 to mark the exact point. The stake is driven in the 
 ground vertically one foot left, or if to be on a curve, 
 on the convex side of the curve and facing the hub. 
 Such points are called transit points, and the stakes to 
 the side are witness stakes, which have markings on the 
 back side as follows: 
 
 6. P. O. T., for a point on tangent. 
 
 P. R. C., for a point of reverse curve. 
 
 P. R. S., for a point of reverse spiral. 
 
 P. C. C., for a point of compound curve. 
 
 P. O. C., for a point on curve. 
 
 P. S., for a point at beginning of a spiral. 
 
 P. C., for a point at beginning of a circular curve. 
 
 P. T., for a point at beginning of a tangent. 
 
 P. I., for a point at intersection of tangents. 
 
 Sometimes the degree of the curves and the whole 
 alinemerit is indicated on the stakes from which any 
 one can take notes and plat the whole line. It is not 
 advisable to give to the public such information, and 
 friends of the enterprise do not need transit notes in 
 that form. Until late years such alinements have con- 
 sisted only of circular curves and tangents. But the 
 refinements of railway operation now demand that 
 rapidly moving heavy objects shall not pass directly from 
 tangents to sharp circular curves and back again but 
 must have their direction changed gradually over 
 transition curves. The transition curve has had a long, 
 hard birth, but it is now so easy to handle that it may 
 be introduced into the alinement of canals, roads , 
 streets, and where the only gain is in appearance. 
 
12 CURVES OF CIVIL ENGINEERING. 
 
 CHAPTER III. 
 
 LINEAR MEASUREMENTS. 
 
 7. All measurements should be made with a loo-ft. 
 steel tape, eleven steel marking pins, a hand level, 
 and a plumb bob. The work is done by a head 
 tapeman, rear tapeman, stake-marker, and axman, 
 all under the direction of the head tapeman, who re- 
 ceives his instructions from the transitman or assistant 
 locating engineer. The end of the tape is kept behind 
 and if plusses are to be taken the stake-marker drags 
 the tape ahead until the end is at the last station. 
 Then the head tapeman reads the plus and sets the point. 
 
 8. The rear tapeman should not be allowed to hold 
 his end of the tape at any plus stakes or hubs, but 
 should always remain at the last station point until 
 the next one ahead is set. This obviates the uncer- 
 tainty of mental calculations on the part of tapemen. 
 The tapemen do not handle stakes but fix the 
 points in the ground with the steel pins. The head 
 tapeman carries a range pole by which the transit- 
 man puts him on line when the steel pins are not visible. 
 The stake-marker drops a properly marked stake at 
 ^each pin. The tapemen check these markings by 
 calling out the numbers found on these stakes when 
 they make the measurement. The axman follows, 
 pulls up the pins and drives the stakes in their places. 
 
 The tapemen should work as close to the ground 
 as possible and thus avoid sags in the tape, wind, 
 swinging plumb bobs, irregular tension, mistaken 
 horizon and loss of time in trying to locate points 
 of plumb bobs. A tapeman who dislikes to stoop 
 is unreliable. Sometimes, in grass or brushy land 
 where the middle of the tape is supported, it is 
 
CURVES OF CIVIL ENGINEERING. 1 3 
 
 best to work from the tops of stakes if there be soil 
 to hold them firmly. Even plumb bobs may some- 
 times be used, and all work done in the air to avoid cut- 
 ting brush. But work in the air and plumbing down 
 by either tapemen or transitmen should be avoided 
 as much as possible. 
 
 9. When on a slope the rear tapeman ''lets out'" 
 the tape enough to give horizontal measurements and 
 when measuring on a chord of a curve "pulls in" the 
 tape enough to give arc measurements. The amounts 
 to give or take are shown in Table I and Diagram IV. 
 The rise or fall per 100 is noted with the hand level; one 
 tapeman uses the other as a level rod. They soon 
 learn where the graduations are on each man, though 
 he be riot marked. The correction is inappreciable, for 
 gentle slopes. When the slope becomes more than 6 per 
 hundred it becomes expedient to "break chain," using 
 not more than 50 ft. of the tape at one time, holding one 
 end up to horizontal and plumbing down. But the previ- 
 ous remarks regarding plusses should be borne in mind 
 and the rear end of the tape kept at the last station. 
 
 Table I is essentially the rear tapeman 's table. No 
 one else has any use for it except to know that the 
 tapemen use it properly. 
 
 10. The end of the tape should extend 0.5 beyond 
 the mark and the back of the tape graduated for 
 slope and chord measuring. Manufacturers are pre- 
 pared to furnish them, giving the graduations back 
 from the mark for the different slopes and ahead 
 from the mark for each degree of curve. The mov- 
 able clamped index point (Lallie's patent) should be 
 used on the tape to insure against the rear tapeman's 
 forgetfulness when on curves. If errors are thus made by 
 his forgetfulness it would be no more serious than if 
 made by the engineer's design, as has been >done for 
 a century. 
 
14 CURVES OF CIVIL ENGINEERING. 
 
 CHAPTER IV. 
 
 GENERAL DISCIPLINE. 
 
 11. Each man should attend strictly to his own 
 duties. Willingness to help others is an undesirable 
 qualification here. Few words should be the rule, 
 and distracting talk prohibited. When a signal or 
 instruction is given it should always receive a response 
 by motion of arms or saying "All right" when under- 
 stood. Rank goes with salary, and no two should have 
 the same" rank, so that it will be well understood 
 who controls movements when working in detach- 
 ments. They should work as one man. Shouting 
 indicates lack of skill. 
 
 12. Orders should be few as possible and in the 
 form of casual remarks or questions until it appears 
 that an assistant does not try to please. Then im- 
 perative orders become necessary; but they should 
 always indicate a condition that cannot long endure. 
 Keep watch for the one man who often disaffects the 
 whole party. No one man should be allowed, in peace, 
 to be habitually the last at breakfast or at work. The 
 men should be required to bunk together, and their 
 baggage limited to simple necessities. 
 
 Each assistant should feel sure of exact justice and 
 impartiality; that his comfort and welfare are given 
 careful consideration. If called upon to suffer hard- 
 ship and exposure, he is not to reason why, but feel that 
 it is unavoidable. Results are obtained by thought and 
 management, not by long hours and labor alone. The 
 day's work should be planned the evening before, and 
 started immediately after breakfast without any ques- 
 tions or confusion. Strict discipline is for the good of 
 all, and should be distasteful to none. 
 
CURVES OF CIVIL ENGINEERING. 1 5 
 
 CHAPTER V. 
 
 ANGULAR MEASUREMENTS. 
 
 13. The transitman should be relieved from the 
 discipline and management of the party as far as 
 possible, so that he [can give ^his undivided attention 
 to th'e mathematics of his work and the adjustments of 
 his instrument. A close record should be kept of the 
 azimuth (or corrected courses) of all tangents. If 
 they are true all his work must be correct unless there 
 be balancing errors, which is very improbable.' 
 
 He should commence with a true meridian, deter- 
 mined astronomically. Then, as he progresses with 
 his survey, he can check in the same way as often as 
 desired. The magnetic needle gives a rough check 
 and a very useful one because it is so easily and often 
 applied. He should be given every opportunity to 
 make complete ties with lines that may have been run 
 through the country before. If there be none, it may 
 be expedient to run one (without chaining), simply for 
 the purpose of checking azimuth. Angles are measured 
 to the nearest minute, so there is a possible allowable 
 error in azimuth equal to as many half minutes as 
 there are transit points, but such a possibility should 
 not be considered. It is the grossest carelessness to 
 allow the azimuth to go unchecked. 
 
 14. A complete* tie is illustrated in the sample transit 
 notes, top of page 37. The transitman should be given 
 vistas close to the ground when setting transit points, 
 so that he will not have to rely upon the head tapeman's 
 skill in plumbing down. The rear flag should always be 
 on the point last occupied by the transit. Otherwise the 
 angles will depend upon the work of the tapemen. 
 He should not be required to locate short spirals and 
 
1 6 CURVES OF CIVIL ENGINEERING. 
 
 should never be forced into short sights. If transit 
 hubs come near together on the line he should be given 
 time to fix sights upon distant objects, even if men 
 have to be sent to set such sights. 
 
 If chord measurements are used plusses for transit 
 points should be avoided as much as possible. Plusses on 
 curves cause errors, unless Table I is used. Such errors 
 become magnified if the back flag is not always on the 
 point last used by the transit. The transitman snould 
 be given large discretion in everything that pertains 
 to the accuracy of the transit work. Detailed' in- 
 structions relieve him of responsibility. The chief 
 is apt to be rusty and behind the times in transit work. 
 He may advise but should not crowd his ideas or assist- 
 ants upon the transitman. He only cares to have the 
 azimuth check first, and speed afterwards. 
 
 CHAPTER VI. 
 
 A TRUE MERIDIAN. 
 
 15. Is generally best obtained by means of the 
 eastern or western elongation of Polaris. This happens 
 twice a day at times in this country when it is not incon- 
 venient to make the observation after dark during 
 the seasons of field-w r ork. The elongation occurs 
 when the handle of the " Great Dipper" is due east 
 or west of Polaris. The exact time can be determined 
 by watching the star until it apparently ceases to 
 move and changes its direction. The true pole is then 
 between Polaris and the "Great Dipper," the angle 
 from Polaris being given in Table VIII. The cross 
 hairs may be illuminated by a common candle held 
 near the object glass. The transit holds the line until 
 daylight, when the result of the observation is secured. 
 The vertical angle to Polaris gives the latitude to be 
 used in the table. 
 
CURVES OF CIVIL ENGINEERING. 17 
 
 CHAPTER VII. 
 
 FIELD-WORK. 
 
 1 6. To locate a curve on the ground (either with 
 or without spirals) connecting two tangents, the tangents 
 should be run out to an intersection if practicable. 
 It is not necessary, but it promotes accuracy to work 
 from the point of intersection. The P. I. is also useful 
 as a permanent monument of the survey since it is 
 generally out of the way of grading operations which 
 destroy the rest of the line. 
 
 17. The shortest line from the P. I. to the curve 
 is the External Secant. From the P. I. to the ends of 
 the curve is the Tangent Distance, and between the ends 
 of the curve is the Long Chord. These three functions 
 of the curve are found in Table IX. 
 
 Even if the P. I. is not located on the ground this 
 tangent distance must be shown in the field-notes 
 before the platting is done. When the P. I. is located 
 {the station stakes being set up to the P. I.), the 
 transitman measures the whole angle. From Table IX 
 he takes the tangent distance corresponding to this 
 whole angle. If he is to put in transition curves he 
 adds the amount shown in the Table IX for the spiral 
 selected. This total he divides by the degree of curve 
 to be used which gives his tangent distance. He then 
 instructs the head tapeman to measure this distance 
 along the unmeasured tangent ahead and set the P. T. 
 While the party is doing this and returning, he checks 
 and completes his calculations for the curve. He sub- 
 tracts the tangent distance from the station of the P. I., 
 which gives him the station of the P. C. or P. S. This 
 
1 8 CURVES OF CIVIL ENGINEERING. 
 
 he has marked on a stake in his presence and sends the 
 party back to put it in, pulling up the stakes as they go. 
 
 He then moves his transit to the P. C. or P. S. and 
 runs in the curve. By adding the length of the curve 
 to the P. C. or P. S. he has the station of the P. T. first 
 set. This gives him a perfect check on the whole work. 
 The long chords are often useful in passing obstacles 
 that prevent measuring on the curve. If the P. I. is 
 not used as above described, a trial curve or curves 
 have to be first located. Then, noting how far to the 
 right or left the temporary P. T. is from the tangent 
 desired, he divides that distance by the sine of the 
 whole angle of the curve or curves run. This gives 
 him the distance the P. S. or P. C. has to be moved 
 along the first tangent to bring the P. T. on the second 
 tangent desired. This has been called the "butting 
 process." It is practicable only where the alinement 
 is easy and tangents predominate. l^ 
 
 1 8. To locate a long piece of crooked line, a prelim- 
 inary line has to be run, from which complete to- 
 pography notes are taken. An accurate contour map 
 is then prepared on a scale of about 200 ft. to one inch. 
 On this plat the locating engineer is able to project the 
 line for an economical location, and determine in the 
 office upon the position and character of all curves. It 
 then becomes the transitman's simple duty to put the 
 line on the ground. No attention is then paid to P. L's, 
 as they are usually out of reach in elevation if not in 
 horizontal distance on such lines. But their location 
 has to be known by the draftsman, and the transitman 
 should make his notes complete in this respect. When 
 the transit is on a P. O. C. the vernier should always 
 read when ranged to the P. C. 
 
CURVES OF CIVIL ENGINEERING. 19 
 
 CHAPTER VIII. 
 
 TRANSITION CURVES. 
 
 19. To be successful a system for placing transition 
 curves in railway tracks must be simple, flexible, trigo- 
 nometrical calculations avoided, and the work must be 
 easily recorded. The whole alinement of a tortuous 
 line should be easily shown on a scale of 1000 ft. to one 
 inch. The system should run automatically. It is not 
 difficult to make a special study of an individual curve 
 and, with time, fit it out with satisfactory easement 
 curves, but a plan for keeping a record of them and for 
 putting them in by wholesale has not been unanimously 
 accepted. Each railroad seems to have a plan of its 
 own. 
 
 Before transition curves were used the engineer had 
 to fix rules and give much attention to the ' ' run off ' ' of 
 the superelevation of the outer rail at the ends of curves. 
 With the advent of the transition curve the homely 
 term fortunately becomes obsolete. Transition curves 
 should not be made to fit the old ' ' run off. ' ' The lengths 
 of curves is unimportant in comparison with the con- 
 venience in handling them. 
 
 The economical length of a transition curve will not 
 admit of mathematical demonstration. It is a matter 
 of taste. The longer the better, if it fits the ground; 
 as long as the circular portion, is a rule that favors tran- 
 sit work and looks well. By bringing train speeds into 
 the problem and fixing lengths arbitrarily the require- 
 ments for a successful system cannot be met . 
 
 20.- So the plan here offered is to make transition 
 curves long enough, and their lengths and other func- 
 tions are made to vary with the main or circular curve ; 
 
2O CURVES OF CIVIL ENGINEERING. 
 
 that is, inversely as the degree. This property makes 
 it possible to tabulate all the dimensions of the com- 
 bined curves and of the individual spirals for i curves, 
 and all the calculation that is necessary is division by 
 the degree of curve. 
 
 Table IX not only gives the usual functions for a 
 i curve, but gives the same functions for the i curve, 
 combined with three different types of spirals a No. 5, 
 No. 9, and No. 14 which is believed to be all that are 
 ever needed in railway practice. They have unreason- 
 able dimensions for a i curve, but they are not expected 
 to be used with a i curve. When used with sharp 
 curves their dimensions, being divided by the degree 
 of curves, become manageable. Chords are 100 ft. long 
 for a i curve, but only 10 ft. long for a 10 curve, 25 ft. 
 long for a 4 curve, etc. The No. 5 consists of 5 chords, 
 No. 9 consists of 9 chords, No. 14 consists of 14 chords, 
 etc. They are always located by the same deflection 
 angles given on page 2 2 . 
 
 No. 5 is suitable for the easy curvature of ''prairie 
 roads," and No. 14 is designed for the sharp curva- 
 ture of mountain lines. These curves are "cubic par- 
 abolas practically," with a maximum curvature of i 
 when loo-ft. chords are used, and in all cases equal the 
 curvature of the main or central curve. By reference 
 to Table I it will be seen that the difference between 
 lengths of the chords and curves are truly negligible on 
 account of the short chords. Since there are no finite 
 arcs, chord measurements are used in this connection. 
 The No. 5 is " Searles spiral," and the No. 9 is used on 
 the Union Pacific Railway after Holbrook's plan. 
 They have the deflections figured so that the spiral 
 can be located from each chord-point. But it is seldom 
 convenient and never necessary to set the transit on 
 the middle portion of the spiral. It should not tax 
 the ingenuity of the transitman much to get around 
 
CURVES OF CIVIL ENGINEERING. 21 
 
 all obstacles by means of the dimensions given on page 
 23, though the general deflection table, page 25, will ac- 
 commodate the most exacting. 
 
 21. Selection. There is no necessity for a great 
 variety of spirals. On a given line of railroad the 
 variety of circular curves is generally small. The 
 maximum curves predominate, because the locating 
 engineer can generally save distance and total curva- 
 ture by using the sharpest curves allowable. On tor- 
 tuous mountain lines often 75% of the curves are of 
 maximum degree. So if a spiral be selected that is 
 suitable for the maximum degree of curvature, it may 
 be generally considered suitable for the whole line. 
 It may be unnecessarily long for some of the easier cur- 
 vature, but the objection (if it be an objection) is not 
 serious nor frequent, and the advantage of a system is 
 great. 
 
 Theoretically the longer the spiral the sharper the 
 central curve has to be. But since the longer spirals 
 are in connection with the easier curves that objection 
 is void. The theory that the length of " run off " should 
 vary as the degree of curve is false, because it rests 
 on the assumption that train velocity is as high on 
 sharp as on easy curves. A 6o-mile velocity requires 
 twice the superelevation and length of "run off" as a 42- 
 mile velocity, per Diagram III. So, when variation in 
 speed is considered, the old "run off" is often longer 
 on the easier curvature. 
 
 If a superelevation of more than 7 inches be prohibited 
 (which is customary) and if it be undesirable to have an 
 excessive load on the outer rail, it is undesirable to have a 
 velocity 
 
 of more than 30 miles per hour on a 12 curve. 
 '" " " 40 " " " " 6 30' " 
 
 tt it tt 5Q (t it tt tt 4 o 
 
 (( (I It /: ft (I It (( o (I 
 
 tl It it o (i it tt tl o tt 
 
22 CURVES OF CIVIL ENGINEERING. 
 
 This is apparent from Diagram III and probably gives 
 higher velocities than is practiced, or than is safe on 
 ordinary track. 
 
 A i curve is too easy anywhere. A i-J curve is 
 preferable and needs no easement, and may generally 
 be made to take the place of a 2. 
 
 The No. 5 spiral may be used on curves of less than 
 5, the No. 9 on curves from 4 to 9, the No. 14 on 
 curves from 7 to 14, making spirals between 100 and 
 200 ft. long. 
 
 22. DEFLECTION ANGLES. 
 
 No. 5 Spiral is located by the following deflection 
 angles : 
 
 From tangent end o 05', o 12^', o 23^', o 37^', o 55' 
 " curve " o 25', o 47*', i 6f, i 22*', i 35' 
 
 Whole angle, 2 30' 
 
 No. 9 Spiral is located by the following deflection 
 angles : 
 
 From tangent end 3', 7^', 14', 22%', 33', 45i'> 
 
 i o', i 16*', i 35' 
 From curve end 27', 52^', i 16', i 37i', 
 
 i 57', 2i 4 4', 2 30', 243i / . 2 55' 
 
 Whole angle, 4 30' 
 
 No. 14 Spiral is located by the following deflection 
 angles : 
 
 From tangent end 2', 5', 9^', 15', 22', 30 J', 40', 51', 
 i 3 f f i 17', i 32', i 48^, 2 6', 2 25'. 
 
 From curve end 28', 55', i 20^, i 45'. 2 08', 2 2 9 f, 
 2 50', 3 09', 3 26J', 3 43', 3 5*', 4 n*^4 35'- 
 
CURVES OF CIVIL ENGINEERING. 23 
 
 23. ELEMENTS OF INDIVIDUAL SPIRALS FOR A i c 
 CURVE. 
 
 For elements of spirals for other curves divide by the degree. 
 
 \ / 
 
 
 A 
 
 500 
 900 
 
 B 
 
 C 
 
 D 
 
 E 
 
 F 
 
 G 
 
 H 
 
 / 
 
 2 30 
 
 4 30 
 
 J 
 
 o r 
 
 o 55 
 i 35 
 
 No. 5 spiral. . . 
 No. 9 spiral. . . 
 
 499-95 
 899-74 
 
 8.00 
 24.86 
 
 183.3 
 316.9 
 
 183.2 
 315-9 
 
 66.7 
 133.6 
 
 250.0 
 449.9 
 
 2.55 
 7 . 20 
 
 No. 14 spiral. . 
 
 1400 
 
 1399- i 
 
 58.90 
 
 484.0 
 
 480.4 
 
 218.34 
 
 699.1 
 
 16.3 
 
 7 oo 
 
 2 25 
 
 Ordinates from tangent to each 100 ft. from P. S: 
 
 No. 5 Spiral 0.14, 0.73, 2.00, 4.40, 8.00. 
 
 No. 9 " .09, .4, 1.2, 2.6, 4.8, 7.9, 12.2, 17.8, 2 48. 
 
 No. 14 " .06, .29, .81, 1.74, 3.20, 5.29, 8.14, 11.86, 
 16.57, 22.38, 29.41, 37.78, 47-59. 5 8 -99- 
 
 24. Space is left in the table for inserting the ele- 
 ments of other spirals should the three given fail to 
 meet all requirements. The street railway people are 
 not fully provided for, because their needs are not under- 
 stood and they are wedded to a system of ordinates. 
 But with arc measurements they can lay out their 
 
24 CURVES OF CIVIL ENGINEERING. 
 
 sharp curves in the same way as do other engineers, as 
 they have not been able to do before. So this article 
 will be continued for the benefit of those who wish to 
 analyze and fix the tables for a special use, to accord 
 with individual tastes and opinions; about "run off" 
 for instance, which has been a live subject and may be 
 kept alive indefinitely. 
 
 25. THE GENERAL POLAR EQUATION 
 of this curve is 
 
 (r 2 r i \ 
 _. _j 1 ) w here 
 6 4 i2/ 
 
 a = first deflection angle from tangent (for first chord), 
 
 6 = any other deflection angle from tangent to chord 
 point, 
 
 r = number of chords distant (corresponds to radius 
 vector) . 
 
 The second differential coefficient of this equation is 
 
 2d 
 
 -, by which the first column in the table of deflections is 
 o 
 readily obtained. 
 
 Let N the number of a spiral, which corresponds 
 to the number of loo-ft. chords that are necessary to 
 make a maximum curvature of i at the end, then 
 
 N 
 Whole angle of spiral - 
 
 a 
 30 
 
 a 
 
 N + i , 
 
 5 ' 
 sin (2^' +5)'. 
 
CURVES OF CIVIL ENGINEERING. 
 
 Spirals increase tangent distances G +11 tan -J whole 
 angle. 
 
 Spirals increase external secants - . 
 
 cos -j whole angle 
 
 Thus figures relating to spirals are inserted in Table IX 
 
 26. GENERAL DEFLECTION TABLE. 
 (A table of coefficients.) 
 
 
 
 
 Different Positions of Transit. 
 
 
 
 
 i 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 
 p. s. 
 
 
 
 i 
 
 3i 
 
 7i 
 
 12* 
 
 19 
 
 26f 
 
 36 
 
 46* 
 
 58* 
 
 74 
 
 
 i 
 
 i 
 
 O 
 
 2 
 
 sri 
 
 io| 
 
 16* 
 
 24 
 
 32* 
 
 43 
 
 S4* 
 
 67* 
 
 
 2 
 
 *i 
 
 2 
 
 O 
 
 3 
 
 7* 
 
 13* 
 
 20* 
 
 29 
 
 38| 
 
 So 
 
 62^ 
 
 t/3 
 
 3 
 
 4* 
 
 4} 
 
 3 
 
 
 
 4 
 
 9* 
 
 i6J 
 
 2 4i 
 
 34 
 
 44l 
 
 57 
 
 g 
 
 4 
 
 7i 
 
 73 
 
 8* 
 
 4 
 
 O 
 
 5 
 
 i 
 
 19* 
 
 28^ 
 
 39 
 
 Sot 
 
 
 
 5 
 
 ii 
 
 "i 
 
 *oj 
 
 *i 
 
 .S 
 
 
 
 6 
 
 13* 
 
 224 
 
 32* 
 
 44 
 
 13 
 
 6 
 
 is* 
 
 16 
 
 15* 
 
 31 
 
 10* 
 
 6 
 
 
 
 7 
 
 Mi 
 
 2Si 
 
 36* 
 
 
 
 7 
 
 20 
 
 2i* 
 
 21 
 
 iQ* 
 
 1 6-4 
 
 12^ 
 
 7 
 
 
 
 8 
 
 I7t 
 
 28i 
 
 y 
 
 8 
 
 2 5i 
 
 27 
 
 27* 
 
 26 
 
 23* 
 
 IQ8 
 
 I4i 
 
 8 
 
 
 
 Q 
 
 iQi 
 
 
 9 
 
 31! 
 
 33* 
 
 34 
 
 33* 
 
 31 
 
 27* 
 
 22-^ 
 
 16* 
 
 Q 
 
 
 
 10 
 
 
 10 
 
 3i 
 
 405 
 
 4il 
 
 41 
 
 39* 
 
 36 
 
 3ii 
 
 25? 
 
 * 
 
 10 
 
 
 
 This is an actual table for a No. 29 spiral where a = i. 
 To use the table for any spiral multiply all the tabular 
 
 quantities by a ; or 3 . 
 
 That is, for a No. 5 spiral multiply the tabular quantities" 
 by 5', for a No. 9 spiral by 3', for a No. 14 by 2', etc. 
 
 The different positions of transit are shown thus , 
 from which read up for deflections toward the tangent 
 and down for deflections toward the curve. This 
 table is easily extended by use of the constant differences 
 which exist in the diagonal rows of figures parallel with . 
 These constant differences equal the number of rows 
 from . 
 
 Other interesting properties of this curve are ably- 
 presented by Torrance, Vial and Fulton in Vol. VII. 
 No. 2 Journal of the Western Society of Engineers. ' 
 
26 CURVES OF CIVIL ENGINEERING. 
 
 CHAPTER IX. 
 
 PLATTING. 
 
 27. The draftsman should plat the line under the 
 direction of the transitman. The transitman should 
 not lay his more or less perfect notes upon the drafts- 
 man's table and feel that he is through with them. 
 The draftsman should not handle the transit notes, 
 but they should be read to him, leaving him free to 
 watch his points and handle his tools, and allowing the 
 transitman to keep his books until full, and making 
 the notes continuous. With proper system a day's 
 work can thus be platted in half an hour. The chief of 
 the party has much to do with the draftsman directly, 
 and he should be careful that the draftsman does not 
 get a wrong idea of his position, that he may not think 
 that instrument-men are under his care, or that he is 
 independent of them. When lines do not come together 
 on paper as they do on the ground it is the transitman 1 s 
 duty to find the error with the draftsman's assistance, 
 and himself explain to the chief of the party. Much 
 confusion is caused by separating the field-work and 
 drafting both in camp and on maintenance work. 
 Draftsmen and fieldmen too often make trouble for 
 each other and the company. 
 
 The transitman should prepare a schedule from his 
 notes showing the courses and distances of all tan- 
 gents from P. I. to P. I., and on long chords of com- 
 pound curves. From this sheet the draftsman can 
 plat alone if the transitman is pressed for time. He 
 first draws a light, straight line through the center 
 of the roll of detail paper. A course is given to this line 
 corresponding to the general direction of the survey. 
 
CURVES OF CIVIL ENGINEERING. 2J 
 
 From this line all courses are taken by means of the 
 protractor and transferred with the triangle and straight- 
 edge or parallel rule to any part of the map desired. 
 
 28. When the lines are all platted as described in the 
 schedule then the tangents are scaled off from the P. I.'s, 
 and the centers of curves located. When transition 
 curves are used it is more convenient to draw the secant 
 lines and to locate the centers of curves on them by 
 scaling first from the P. I. the external secant to the 
 curve, then the radius to the center required. Then 
 draw the circular curves with the compass and the tran- 
 sition curves with the spiral rule. Write the station 
 and plus for each P. C., P. S., and P. T. in the radial 
 lines, and the angles and degrees between the radial 
 lines. Then, with the spring ^dividers and scale, locate 
 every even tenth station from 0. This is done only for 
 a check, and need not be inked in if there be crowding 
 of figures. If the work is done in the order named 
 any possible error in platting or calculating will be 
 detected. The transitman may then leave the work 
 to the draftsman and topographer. The line should 
 be inked in with vermilion water color, but the station 
 numbers should be left in pencil so their position may 
 be shifted if they be found to interfere with topography 
 notes. Letters and figures of all kinds should be made 
 to read from the southerly side of the plat. A simple 
 record of the spiral angle gives complete information 
 regarding the spiral. The number might be given, 
 but that would be twice the whole angle of the spiral 
 in degrees. 
 
 29. As has been intimated, when compound curves 
 with spirals are encountered, the long chords of curves 
 are platted instead of the tangents. Because tables can- 
 not then be used in determining tangent distances, so 
 it becomes a special problem quite complicated. First 
 the chord of the spiral is platted, then of the first cir- 
 
28 CURVES OF CIVIL ENGINEERING. 
 
 cular curve, then of the next circular curve or curves, 
 and finally of the last transition curve. 
 
 This method of platting also has to be used if the 
 
 locating engineer thinks there should be different kinds 
 of spirals at the two ends of a simple curve, or if a spiral 
 has to be located between two parts of a compound 
 curve. These complications ought to be avoided, and 
 can be with a little ingenuity. Compound curves can- 
 not be avoided, but connecting curves of great difference 
 in degree, necessitating a spiral, can be avoided by put- 
 ting in one or two additional P. C. C.'s. For those 
 
 . who disagree and have time for the confusing calcula- 
 tions use the No. 9 or No. 14 spirals. The chord-lengths 
 are made to correspond to the sharper curve; that is, 
 100 divided by the degree. A part is taken off from 
 the tangent end of the spiral proportional to the smaller 
 degree. That is if a 3 is connected with a 9 curve 
 three chords will be taken off the tangent end of the 
 No. 9 spiral. Here the complete deflection table is 
 necessary to turn deflections from the third-chord 
 point. The field-work is simple. The computations 
 for platting are by main strength and awkwardness 
 of latitudes and departures. 
 
 Convenience of platting should be considered in all 
 field-work. A large percentage of surveys are wasted 
 because they cannot be easily, intelligently platted. 
 
 CHAPTER X. 
 
 TURNOUT CURVES. 
 
 30. An ordinary standard-gage turnout from tan- 
 gent first makes an angle of about 2, then runs straight 
 1 6 ft. along the split rail, then there should be a true 
 circular curve to the wing of the frog, then a tangent 
 
CURVES OF CIVIL ENGINEERING. 29 
 
 for the full length of the frog, about 13 ft., and on to 
 clearance or to the next frog if it be a cross-over. The 
 lines of a frog are straight and rigid. This alinement 
 is further complicated by widening the gage on the 
 curve and at the point of frog. 
 
 So it is impractical to do this work with the transit. 
 The lead rail is located by ordinates from the main- 
 line rail. The whole angle of the lead-rail curve equals 
 the angle of the frog, minus the angle of the split rail. 
 The length of the curve depends upon the dimensions 
 of the frog, the split rail, and the pattern of rail. It is 
 quite simple to design a standard plan when all these 
 data are known. There would be only two or three 
 such plans for a large railroad system. Crotch' frogs 
 are generally prohibited. If used they break up the 
 lead into two curves with a tangent over the frog. Turn- 
 outs from curves are avoided if possible, but if unavoid- 
 able the standard plan may be used the same as if on 
 tangent. The transit work should begin at the P. I. 
 where the tangent passing the frog intersects the center 
 of main line. There turn the frog angle, run past the 
 frog, after which curves may be started as desired. 
 Tables cannot be used except for approximate work. 
 There are no practicable special problems. They are 
 all spoiled by the frog tangents, if not by the split rails. 
 
 31. The transitman should not be intimidated by 
 the mass of figures and formulas that are sometimes 
 used to illuminate this subject. The problems are all 
 quite simple and not different from those encountered 
 -elsewhere in curve location. For example, to stake 
 out the grading the turnout curves may be considered 
 ,as having a whole angle equal to the frog angle, and an 
 external secant equal to J gage. With these data enter 
 Table IX and find the degree and length of curve as 
 close to the truth as can be obtained by any special 
 turnout tables, or formulas, but only close enough to use 
 
30 CURVES OF CIVIL ENGINEERING. 
 
 in grading. Yard maps cannot be made until after 
 track laying, since rail- joints fix the location of switches. 
 Ill-founded theories] and formulas regarding turn- 
 outs has done much to take track-work out of the hands 
 of engineers. It has been one cause of the vexatious 
 reference to the difference between theory and practice . 
 There would be no difference if the engineer was left 
 to figure out his own special problems and understand 
 the foundation of all theories. Rules and tables are 
 dangerous in the hands of those unable to reproduce 
 them independently. 
 
 CHAPTER XI. 
 
 VERTICAL CURVES. 
 
 32, Vertical curves are laid out by vertical ordinates 
 from a horizontal line with the level. They are usually 
 very flat on railroads in comparison with horizontal 
 curves. The sharpest vertical curve allowed on at least 
 two prominent railroad main lines has a radius of 
 1 14, ooo ft. This accounts for the simple formulas and 
 definitions in this connection. 
 
 The curvature of vertical curves is designated by num - 
 bers in place of degrees. The Number of a Curve is 
 its change in its rate of grade, expressed in hundredths 
 of a foot, per hundred feet. For example, a No. 7 curve 
 changes its rate of grade .07 each successive 100 ft. 
 This .07 corresponds to the chord deflection in hori- 
 zontal curves. If the grade be assumed to run on the 
 loo-ft. chords of the curve the rate of grade on the first 
 chord from tangent will be changed in hundredths, 
 only one half the number of the curve, for the same rea- 
 son that the tangent deflections are half of chord deflec- 
 tions. But for all succeeding chords the rate of grade 
 
CURVES OF CIVIL ENGINEERING. 3! 
 
 changes as many hundredths as the number of the 
 curve. 
 
 The Whole Angle is designated by tenths of a foot 
 per hundred in place of degrees. For example, if a 0.8 
 grade intersects a +0.9 grade the angle formed will be 
 17 tenths. 
 
 If A = whole angle, N = number, 5 = external secant 
 in tenths, and L = length of curve in stations, then 
 
 and S=AL. 
 
 
 Approximate radius in inches on Plate A profile 
 
 T2 5 
 paper = -^-. 
 
 wi 
 
 By these formulas and Table VII the engineer plats 
 the grade line on the profile and calculates the eleva- 
 tion of grade for each station before going into the 
 field. The P. I.'s should be made at even stations, 
 and the ends of curve can usually be made at stations 
 without causing faulty grades. This greatly simplifies 
 the calculations which have to be tried and repeated 
 until the grade line is satisfactory. Straight grades 
 can usually be expressed with one decimal place, and 
 never more than two should be used, except when 
 compensating for curvature on maximum grades. 
 
 33. When laying a maximum grade, or where uniform 
 resistance is desired, the rate of grade should be made 
 less on curves than on tangents by the amounts shown 
 in column 8, Table VI. In the lower portions of such a 
 grade, where high velocities are admissible, and can be 
 had, compensation for curvature is unnecessary. But 
 where the velocity may fall to eight miles per hour curve 
 resistance should be fully compensated in the grade, so 
 that the resistance and velocity will be uniform. If 
 the velocity drops so the centrifugal force is lost the 
 
32 CURVES OF CIVIL ENGINEERING. 
 
 train "stalls." A maximum grade in a district is not 
 necessarily one of maximum ratio, but one which pro- 
 duces a maximum tractive power, where curves and 
 velocity are considered. It is desired to avoid enter- 
 ing the field so ably covered by the late A. M. Welling- 
 ton in his Economic Theory of Railway Location; but 
 that statement is necessary to support the new principle 
 advocated, viz. : 
 
 34. That more easy vertical curves should be intro- 
 duced into railway grades to supersede long, straight 
 grades which cause sharp summits and sags. Long, easy, 
 vertical curves, reversing in the middle of a hill, can be 
 used with great advantage, especially if the rate of grade 
 at the P. R. C. be not held down to the same rate allow- 
 able on a straight grade several miles long. '' Mo- 
 ment um " grades can be used nowhere to a better advan- 
 tage than at a P. R. C. of vertical curves. Curves are 
 more difficult to plot upon the profile, but they are well 
 worth the trouble. A large percentage of straight 
 grade generally causes sharper curves, which are very 
 objectionable in a grade line. This is for the same 
 reason that a sharper curvature gives larger percentage 
 of tangent in horizontal alinement. Establishing grade 
 is a capital service, where skill, time, and care are well 
 spent in projecting curves. 
 
TABLES 
 
 AND 
 
 DIAGRAMS. 
 
 33 
 
TABLE I. 
 
 DIFFERENCES IN LENGTHS OF ARCS AND 
 CORRESPONDING CHORDS. 
 
 "o 6 
 
 V > 
 
 F 
 
 Lengths of Arc. 
 
 100 
 
 90 
 
 80 
 
 70 
 
 60 
 
 50 
 
 40 
 
 30 
 
 20 
 
 10 
 
 1 
 
 .OOI 
 
 .OOI 
 
 .OOI 
 
 .OOI 
 
 
 
 
 
 
 
 2 
 
 .005 
 
 .004 
 
 .003 
 
 .002 
 
 .001 
 
 
 
 
 
 
 3 
 
 .Oil 
 
 .009 
 
 .006 
 
 .OO4 
 
 .002 
 
 .001 
 
 
 
 
 
 4 
 
 .020 
 
 .015 
 
 .010 
 
 .007 
 
 .004 
 
 .002 
 
 .001 
 
 
 
 
 5 
 
 .031 
 
 .023 
 
 .016 
 
 .Oil 
 
 .007 
 
 .004 
 
 .002 
 
 
 
 
 6 
 
 .045 
 
 033 
 
 .023 
 
 .015 
 
 .010 
 
 .006 
 
 .003 
 
 .001 
 
 
 
 7 
 
 .062 
 
 045 
 
 .031 
 
 .021 
 
 .013 
 
 .008 
 
 .004 
 
 .002 
 
 
 
 8 
 
 .081 
 
 59 
 
 .041 
 
 .028 
 
 .017 
 
 .010 
 
 .005 
 
 .002 
 
 
 
 9 
 
 .103 
 
 75 
 
 .053 
 
 .036 
 
 .022 
 
 .013 
 
 .006 
 
 .003 
 
 
 
 10 
 
 .127 
 
 093 
 
 .065 
 
 .044 
 
 .027 
 
 .016 
 
 .008 
 
 .003 
 
 .OOI 
 
 
 11 
 
 .154 
 
 113 
 
 .079 
 
 .053 
 
 033 
 
 .019 
 
 .010 
 
 .004 
 
 .OOI 
 
 
 12 
 
 .184 
 
 .134 
 
 .094 
 
 .063 
 
 .040 
 
 .022 
 
 .012 
 
 .005 
 
 .OOI 
 
 
 I3 o 
 
 .216 
 
 .158 
 
 . no 
 
 .074 
 
 .046 
 
 .027 
 
 .014 
 
 .006 
 
 .002 
 
 
 14 
 
 .250 
 
 .183 
 
 .127 
 
 .086 
 
 54 
 
 032 
 
 .016 
 
 .007 
 
 .OO2 
 
 
 15 
 
 .286 
 
 . 209 
 
 . 146 
 
 .099 
 
 .062 
 
 .036 
 
 .018 
 
 .008 
 
 .OO2 
 
 
 16 
 
 .324 
 
 .236 
 
 .166 
 
 . 112 
 
 .070 
 
 .041 
 
 .021 
 
 .009 
 
 .003 
 
 
 I7 o 
 
 .365 
 
 .266 
 
 .187 
 
 . 126 
 
 .079 
 
 . 046 
 
 .023 
 
 .010 
 
 .003 
 
 
 18 
 
 .409 
 
 .298 
 
 .209 
 
 .141 
 
 .088 
 
 051 
 
 .026 
 
 .Oil 
 
 .003 
 
 
 19 
 
 45 6 
 
 333 
 
 .233 
 
 .157 
 
 .098 
 
 .057 
 
 .029 
 
 .012 
 
 .OO4 
 
 
 20 
 
 507 
 
 370 
 
 .259 
 
 .174 
 
 . 109 
 
 .064 
 
 .032 
 
 .014 
 
 .004 
 
 
 25 o 
 
 .792 
 
 .580 
 
 .407 
 
 *73 
 
 .172 
 
 099 
 
 .051 
 
 .021 
 
 .OO6 
 
 
 30 
 
 1.136 
 
 .830 
 
 .580 
 
 39 
 
 245 
 
 .142 
 
 .072 
 
 .031 
 
 .OO9 
 
 .OOI 
 
 40 
 
 2.018 
 
 i .480 
 
 1 .036 
 
 695 
 
 435 
 
 .252 
 
 .130 
 
 .054 
 
 .Ol6 
 
 .002 
 
 50 
 
 3**44 
 
 2 . 270 
 
 1 .60 
 
 i .086 
 
 .686 
 
 393 
 
 . 200 
 
 .085 
 
 .025 
 
 .003 
 
 60 
 
 4.507 
 
 3.300 
 
 2.31 
 
 i-55o 
 
 .970 
 
 .564 
 
 ,290 
 
 .121 
 
 .036 
 
 004 
 
 100 
 
 12 .2l8 
 
 
 
 
 
 
 
 
 
 
 180 
 
 36.3 
 
 
 
 
 
 
 
 
 
 
 This table^was calculated by the following formula. 
 
 1 1459.1 6 X sin jf degree 
 
 ov , 
 degree; 
 
 34 
 
 erence = 100 
 
II. SAMPLE TRANSIT NOTES. 
 
*7an. 5 '03 
 STATION 
 
 DEF. 
 
 
 
 C.C. 
 
 M.C. 
 
 + 44 P.T. 
 9 
 
 255' 
 
 222' 
 
 
 
 N. 2020' E. 
 
 
 
 
 
 
 8 
 
 08' 
 
 
 Whole 
 Cir. Cur 
 
 Angle 
 'e 1612' 
 
 
 4- 94 P.S. 
 
 7 
 
 806' 
 
 517' 
 
 3 
 
 Spirals 
 Tots 
 
 900' 
 
 
 1 2512 / 
 
 6 
 
 217' 
 
 $ 
 
 is. 
 
 Tang. 
 
 288.7 
 
 
 4- 24 P.O. 
 5 
 
 135' 
 109' 
 
 A 
 
 CO ."ti 
 
 1 
 
 P.I. 286 H 
 
 - 62.7 not set 
 
 ^ 
 
 4 
 
 oe' 
 
 
 
 
 iM 
 
 f- 74 P.S. 
 3 
 
 
 
 
 
 ' 
 
 
 
 
 
 2 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 280 
 
 
 
 
 
 
 9 P.O.T. 
 
 
 
 
 
 N. SS^SO'V 
 
 8 
 
 
 
 
 N. 45 32'^E. 
 
 
 7 -f- 00 P.T. 
 
 255' 
 
 
 
 
 
 6 
 
 157' 
 
 
 
 
 
 5- 
 
 027' 
 
 ^2 
 
 J S 
 
 Whole 
 Cir. Cur 
 
 Angle 
 re 500' 
 
 
 + 75 P.S. 
 4 
 
 230' 
 
 Too' 
 
 "n 
 E M 
 
 h ^ 
 
 Spirals 
 Tot 
 
 900' 
 
 
 il 1400 / 
 
 + 50 P.O. 
 3 
 
 1 35' 
 
 l^' 
 
 s* 
 
 * * 
 
 Tang. 
 
 288.6 
 
 ^%/ 
 ^<J 
 
 2 . 
 
 014' 
 
 E 
 
 P.I. 274- 
 
 -13.6 
 
 \*%P 
 
 ^.yXc^P 
 
 4- 25 P.S. 
 
 
 
 
 
 
 
 
 
 
 270 
 
 
 
 
 N. 5932'E. 
 
 
 9 
 
 
 
 
 
 N. 4930': 
 
 -j- 40 P.T. 
 8 
 
 13Q' 
 118' 
 
 
 
 
 
 'V* 
 
 
 
 
 7 
 
 48' 
 
 <B 
 > 
 M 
 
 Whole ^ 
 Tang. 
 
 ngle 300' 
 150.1 
 
 
 6 
 
 18' 
 
 
 
 P.I. 266 
 
 -90.1 
 
 
 + 40 P.C. 
 265 
 
 
 
 
 
 
 
 
 
 
 
 
 
 N. 5632'E. 
 
 
Jan. 5 ''OS 
 STATION 
 
 DEF 
 
 
 
 C.C. 
 
 M.C. 
 
 4 
 
 
 
 
 N. 8929' E. 
 
 
 -f- 40 P.T. 
 3 
 
 435' 
 
 
 
 
 
 309' 
 
 
 
 
 
 2 4- 00 P.S. 
 
 1800' 
 
 
 Whole 
 Cir. Curv 
 
 Angle 
 e 3600' 
 
 
 1 
 
 1300' 
 
 CO 
 
 ti 1 
 
 Spirals 
 Tot 
 
 uW 
 
 
 1 50 OQ' 
 
 no 
 
 800' 
 
 g & 
 
 % 3 
 
 
 
 
 9 
 
 300' 
 
 O ^ 
 o g 
 
 Secant 
 
 61.00 
 
 
 4- 40 P.O. 
 
 8 
 
 225' 
 
 oV 
 
 P 
 
 Tang. 
 P.I. 31C 
 
 337.8 
 -f- 37.8 
 
 & 
 
 7+0 P.S. 
 
 
 
 
 
 S^P 
 
 ^Y<$> 
 
 6 
 
 
 
 
 1ST. 3929' E. 
 
 
 5-h 00 P.T. 
 
 135' 
 
 
 
 
 N. 2930'"E. 
 
 4 4- 00 P.S. 
 
 8ioH' ; 
 
 
 Whole 
 Cir. Cur\ 
 
 Angle 
 e 162l' 
 
 
 3 
 
 540^' 
 
 CO 
 
 ^ 1 
 
 Spirals 
 Tot* 
 
 500' 
 
 y&z 
 
 1 212l' 
 
 4- 50 P.O.C. 
 
 2 
 
 425^' 
 310^' 
 
 o P* 
 
 fc ^ 
 
 g 
 
 Ex. Sec. 
 
 20.7' 
 
 HifX 
 
 $?$* 
 
 1 
 
 040J4' 
 
 U * 
 
 ^ H 
 '{>. 
 
 Tang. 
 
 266.1 
 
 I 
 
 4- 73 P.O. 
 
 00 
 
 055' 
 005' 
 
 
 
 
 
 4 73P.R.C. 
 
 9 
 
 255 / 
 l4l' 
 
 
 
 
 
 
 
 
 4- 48 P.S. 
 
 8 
 
 1545' 
 13 C 50' 
 
 
 Cir. Cur\ 
 
 e 31 30' 
 
 
 7 
 
 950' 
 
 1 
 
 Spirals 
 Toti 
 
 900' 
 1 4030 / 
 
 
 6 
 
 5 50' 
 
 
 
 2 o 
 
 P.I. 296- 
 
 1-50 set 
 
 
 5 
 
 150' 
 
 oo 3 
 *fc 
 
 Tang. 
 
 320.8 
 
 4& 
 
 ^LJjfJPliu 
 
 4- 54.2 P.O. 
 4- 
 
 135' 
 32' 
 
 
 
 
 <^ b /c\* 
 
 %Y^' 
 
 4- 29.2 P.S.' 
 3 
 
 
 
 
 
 
 
 
 
 
 2 
 
 
 
 
 
 
 1 
 
 
 
 
 N. 2020' E. 
 
 
 DO 
 
 
 
 
 
 
 N. 1015' E. 
 
 4- 44 P.T. 
 
 
 
 
 
II. SAMPLE TRANSIT NOTES. 
 
 Lin 
 
 B 
 
 264+ 
 
 v/ 
 
 m. 
 
 * 
 
 * 
 
 266 + 30 
 
 25 +20, 
 
 
 248+12 
 
 jar 
 
 Ston 
 
 38 
 
III. SUPERELEVATION OF OUTER RAIL ON CURVES. 
 
 STANDARD GAUGE TRACK. 
 IN INCHES = DEGREE x VELOCITY 2 (IN MI.^PER H.) x .00065. 
 
 Superelevation for other gauges are proportional to gauge. 
 
 INCHES SUPERELEVATION 
 01 2345 67 
 
 39 
 
IV. DIAGRAM OF CORRECTIONS FOR MEASURING. 
 
 ON SLOPES ADD 
 
 TENTHS OF FOOT' 
 
 1 
 
 .4 A 
 
 ON CHORDS OF ARCS DEDUCT 
 
 TENTHS OF FOOT. 
 
 2 12 
 
 18 
 
 40 
 
TABLE V. 
 
 AN EMERGENCY TABLE FOR DETERMINING 
 NATURAL FUNCTIONS OF ANGLES. 
 
 Sine obtained directly from the table; 
 Cosine =sine of complement of angle; 
 
 sine 
 
 Tangent = or 
 cos 
 
 _ tangent distance for double the angle in Table IX. 
 lL57 2 9-6 I 
 
 ^ j. COS I 
 
 Cotangent = = ; 
 
 sine tang 
 
 becant = ; ; 
 
 Cosecant = ; 
 sine 
 
 Versine = i cosine ; 
 Coversine = i sine. 
 
 EXAMPLE. 
 
 Required sine of 
 
 From table 36 09^' =.59000 
 
 Correct to four decimal places. 
 41 
 
TABLE V. 
 NATURAL SINES. 
 
 Angle, 
 o / 
 
 Sine. 
 
 Dif. i'. 
 
 Angle. 
 
 / 
 
 Sine. 
 
 Dif. i'. 
 
 Angle. 
 
 f 
 
 Sine. 
 
 Dif. i'. 
 
 o 344 
 
 .01 
 
 .00029 
 
 20 29 
 
 35 
 
 .00027 
 
 42 5 1 
 
 .68 
 
 .00021 
 
 i 09 
 
 .02 
 
 * ' 
 
 21 06 
 
 .36 
 
 < i 
 
 43 38 
 
 .69 
 
 .OOO2I 
 
 I 43 
 
 03 
 
 t < 
 
 21 43 
 
 37 
 
 1 ' 
 
 44 26 
 
 .70 
 
 .OOO2I 
 
 2 174 
 
 .04 
 
 
 
 22 20 
 
 38 
 
 " 
 
 45 14 
 
 7 1 
 
 .00621 
 
 2 52 
 
 05 
 
 ' * 
 
 22 57 
 
 39 
 
 ' ' 
 
 46 034 
 
 72 
 
 .OOO2O 
 
 3 26J 
 
 .06 
 
 ' * 
 
 23 35 
 
 .40 
 
 ' ' 
 
 46 53 
 
 73 
 
 .OOO2O 
 
 4 01 
 
 .07 
 
 < c 
 
 24 124 
 
 .41 
 
 ' ' 
 
 47 44 
 
 74 
 
 .OOO2O 
 
 4 354 
 
 .08 
 
 (i 
 
 24 50 
 
 .42 
 
 .00026 
 
 48 354 
 
 75 
 
 .00019 
 
 5 10 
 
 .09 
 
 " 
 
 25 28 
 
 43 
 
 ' ' 
 
 49 28 
 
 .76 
 
 .OOOI9 
 
 5 44i 
 
 .10 
 
 * * 
 
 26 06 
 
 .44 
 
 ' ' 
 
 50 21 
 
 77 
 
 .OOOI9 
 
 6 19 
 
 .11 
 
 
 
 26 444 
 
 45 
 
 * ' 
 
 51 16 
 
 .78 
 
 .OOOlS 
 
 6 534 
 
 . 12 
 
 
 
 27 23 
 
 .46 
 
 
 
 52 ii 
 
 79 
 
 .00018 
 
 7 28 
 
 13 
 
 ** 
 
 28 02 
 
 47 
 
 
 
 53 08 
 
 .80 
 
 .OOOI7 
 
 8 03 
 
 .14 
 
 * * 
 
 28 41 
 
 .48 
 
 .00025 
 
 54 06 
 
 .81 
 
 .OOOI7 
 
 8 374 
 
 15 
 
 ' ' 
 
 29 24 
 
 .49 
 
 ' ' 
 
 55 05 
 
 .82 
 
 .OOOI7 
 
 9 124 
 
 .16 
 
 '* 
 
 30 oo 
 
 5 
 
 '* 
 
 56 06 
 
 83 
 
 .00016 
 
 9 47 
 
 17 
 
 * * 
 
 30 40 
 
 -5i 
 
 " 
 
 57 084 
 
 .84 
 
 .OOOl6 
 
 10 22 
 
 .18 
 
 * * 
 
 31 20 
 
 52 
 
 11 
 
 58 13 
 
 85 
 
 .OOOI5 
 
 10 57 
 
 .19 
 
 * * 
 
 3 2 oo 
 
 53 
 
 ' ' 
 
 59 19 
 
 .86 
 
 .OOOI5 
 
 II 32 
 
 . 2O 
 
 ' * 
 
 32 41 
 
 54 
 
 .00024 
 
 60 274 
 
 .87 
 
 .00014 
 
 12 074 
 
 .21 
 
 " 
 
 33 22 
 
 55 
 
 " 
 
 61 39 
 
 .88 
 
 .OOOI4 
 
 12 434 
 
 .22 
 
 .00028 
 
 34 034 
 
 56 
 
 11 
 
 62 52 
 
 .89 
 
 .OOOI3 
 
 13 18 
 
 23 
 
 * * 
 
 34 45 
 
 57 
 
 M 
 
 64 10 
 
 .90 
 
 .OOOI3 
 
 13 53 
 
 .24 
 
 ** 
 
 35 27 
 
 58 
 
 11 
 
 65 30 
 
 .91 
 
 .00012 
 
 14 29 
 
 25 
 
 11 
 
 36 094 
 
 59 
 
 .00023 
 
 66 56 
 
 .92 
 
 .OOOI I 
 
 15 4 
 
 .26 
 
 " 
 
 36 52 
 
 .60 
 
 " 
 
 68 26 
 
 93 
 
 .OOOII 
 
 15 40 
 
 .27 
 
 * * 
 
 37 354 
 
 .61 
 
 " 
 
 70 03 
 
 .94 
 
 .OOOIO 
 
 16 154 
 
 .28 
 
 " 
 
 38 IQ 
 
 .62 
 
 11 
 
 7i 48 
 
 95 
 
 .00009 
 
 16 514 
 
 .29 
 
 
 
 39 03 
 
 63 
 
 *' 
 
 73 45 
 
 .96 
 
 .00008 
 
 17 274 
 
 30 
 
 * * 
 
 39 474 
 
 .64 
 
 .OOO22 
 
 75 56 
 
 97 
 
 .00007 
 
 18 034 
 
 31 
 
 * * 
 
 40 324 
 
 65 
 
 ' ' 
 
 78 3i4 
 
 .98 
 
 .00006 
 
 18 40 
 
 32 
 
 " 
 
 41 18 
 
 .66 
 
 M 
 
 81 54 
 
 99 
 
 .00004 
 
 19 16 
 
 33 
 
 .00027 
 
 42 04 
 
 .67 
 
 " 
 
 90 oo 
 
 i .00 
 
 .00000 
 
 19 5 2 4 
 
 34 
 
 
 
 
 
 
 
 
 42 
 
TABLE VI. 
 CURVE CHARACTERISTICS. 
 
 
 
 For a i oo -Foot Arc. 
 
 
 Grade 
 
 
 D^> 
 
 
 
 Diff. in 
 
 of 
 
 Track 
 
 De- 
 gree. 
 
 Radius. 
 
 Middle 
 Ordi- 
 nate. 
 
 Quar- 
 ter Or- 
 
 dinate. 
 
 Tang. 
 Dis- 
 tance. 
 
 Chord. 
 
 of Rails 
 per 100 
 Feet. 
 
 alent 
 Re- 
 sist- 
 ance. 
 
 Gauge. 
 
 i 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 
 
 
 
 
 
 
 
 
 / // 
 
 i 
 
 11459.16 
 
 .109 
 
 .082 
 
 .44 
 
 100.000 
 
 .0410 
 
 0.015 
 
 4 8* 
 
 I 
 
 5729-58 
 
 .218 
 
 .163 
 
 .87 
 
 99.999 
 
 .0820 
 
 0.03 
 
 4 8 
 
 if 
 
 3819.72 
 
 .327 
 
 .245 
 
 I-3I 
 
 99-997 
 
 .1230 
 
 0.045 
 
 4 8* 
 
 2 
 
 2864.79 
 
 -436 
 
 .328 
 
 1.74 
 
 99-995 
 
 . 1640 
 
 0.06 
 
 4 8i 
 
 2* 
 
 2291 .84 
 
 -545 
 
 .408 
 
 2.18 
 
 99.992 
 
 . 2050 
 
 0.075 
 
 4 8f 
 
 3 
 
 1909.86 
 
 .655 
 
 .490 
 
 2.62 
 
 99.989 
 
 . 2461 
 
 0.09 
 
 4 8|- 
 
 si 
 
 1637 .02 
 
 .764 
 
 -573 
 
 3-05 
 
 99.985 
 
 .2871 
 
 0. 10 
 
 4 8* 
 
 4 
 
 I 43 2. "40 
 
 -873 
 
 -655 
 
 3-49 
 
 99 . 980 
 
 .3281 
 
 0. II 
 
 4 83- 
 
 S 
 
 1145-92 
 
 i . 090 
 
 .82 
 
 4.36 
 
 99.969 
 
 .4101 
 
 0.14 
 
 4 8* 
 
 6 
 
 954-93 
 
 1.309 
 
 .98 
 
 5.23 
 
 99-955 
 
 .4922 
 
 o. 16 
 
 4 8* 
 
 7 
 
 818.51 
 
 1-53 
 
 -15 
 
 6. 10 
 
 99.938 
 
 5742 
 
 0.18 
 
 4 8* 
 
 8 
 
 7l6. 20 
 
 i-75 
 
 -38 
 
 7.0 
 
 99.919 
 
 .6562 
 
 0. 20 
 
 4 8f 
 
 9 
 
 636.62 
 
 i .96 
 
 47 
 
 7-9 
 
 99.897 
 
 .7383 
 
 0. 22 
 
 4 9 
 
 10 
 
 572.96 
 
 2.18 
 
 .63 
 
 8.7 
 
 99.873 
 
 .8203 
 
 o. 24 
 
 4 9 
 
 II 
 
 520.87 
 
 2.40 
 
 .80 
 
 9.6 
 
 99.846 
 
 .9024 
 
 o. 26 
 
 4 9 
 
 12 
 
 477.46 
 
 2.62 
 
 -97 
 
 10.4 
 
 99. 816 
 
 .9844 
 
 0.28 
 
 4 9 
 
 13 
 
 440-74 
 
 2.84 
 
 13 
 
 ii.3 
 
 99.784 
 
 i .0664 
 
 0.30 
 
 4 9i 
 
 14 
 
 409.25 
 
 3-05 
 
 .29 
 
 12.2 
 
 99-750 
 
 1.1484 
 
 0.32 
 
 4 9* 
 
 15 
 
 381.98 
 
 3-27 
 
 .46 
 
 13.0 
 
 99.714 
 
 i . 2300 
 
 0.34 
 
 4 9* 
 
 16 
 
 358.10 
 
 3-49 
 
 .62 
 
 13-9 
 
 99.676 
 
 1.3124 
 
 0.36 
 
 4 9 
 
 18 
 
 3I8.3I 
 
 3-92 
 
 2.94 
 
 15-6 
 
 99-591 
 
 1.4766 
 
 0.38 
 
 4 9i 
 
 20 
 
 286.48 
 
 4-36 
 
 3.28 
 
 17.4 
 
 99-493 
 
 i .6406 
 
 0.40 
 
 4 9* 
 
 25 
 
 229.18 
 
 5-43 
 
 
 
 99. 208 
 
 
 
 
 30 
 
 190.99 
 
 6.51 
 
 
 
 98.864 
 
 
 
 
 35 
 
 163.70 
 
 7.6i 
 
 
 
 98.464 
 
 
 
 
 40 
 
 143.24 
 
 8.64 
 
 
 
 97.98i 
 
 
 
 
 50 
 
 114-59 
 
 10.75 
 
 
 
 96.856 
 
 
 
 
 60 
 
 95-49 
 
 12.80 
 
 
 
 95-493 
 
 
 
 
 180 
 
 31-83 
 
 31-83 
 
 
 
 63.66 
 
 
 
 
 Columns 7, 8, and 9 refer to standard gauge railroad track. 
 
 Column 5 is the distance of curve from tangent 100 feet from point of 
 tangency and equals half the chord deflection. 
 
 To find any radius not here shown, divide 5729.58 by the degree of 
 curvature. 
 
 To find radius of an old-style curve located witu IOO-IT;. cnords, add 
 07 X degree of curve to tabular quantity. 
 
 4? 
 
TABLE VII. 
 
 ORDINATES FROM TANGENT TO VERTICAL 
 CURVES FOR EACH 100 FEET FROM P. C. 
 
 6 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 fc 
 
 100 
 
 200 
 
 300 
 
 400 
 
 500 
 
 600 
 
 700 
 
 800 
 
 900 
 
 1000 
 
 IIOO 
 
 .60 
 
 1200 
 
 1300 
 
 Q . 
 
 1400 
 n c 
 
 2 
 
 .OI 
 
 .04 
 
 .09 
 
 .16 
 
 25 
 
 .36 
 
 49 
 
 .64 
 
 .81 
 
 .50 
 
 I.OO 
 
 1. 21 
 
 7 2 
 
 1.44 
 
 .04 
 I .69 
 
 9 
 1 .96 
 
 2* 
 
 .01 
 
 OS 
 
 .11 
 
 .20 
 
 .31 
 
 45 
 
 .61 
 
 .80 
 
 1. 01 
 
 1.25 
 
 i-5i 
 
 1. 80 
 
 2. II 
 
 2-45 
 
 3 
 
 .01 
 
 .06 
 
 .14 
 
 24 
 
 .38 
 
 54 
 
 74 
 
 .96 
 
 1. 21 
 
 1.50 
 
 1.81 
 
 2.16 
 
 2.53 
 
 2.94 
 
 3* 
 
 .02 
 
 .07 
 
 .16 
 
 .28 
 
 44 
 
 63 
 
 .86 
 
 .12 
 
 1.42 
 
 1.75 
 
 2.12 
 
 2.52 
 
 2.96 
 
 7 78 
 
 3-44 
 
 4* 
 
 .02 
 
 .09 
 
 .20 
 
 .36 
 
 .56 
 
 .81 
 
 .10 
 
 44 
 
 1.82 
 
 2.25 
 
 2.72 
 
 3.24 
 
 6 -o 
 3.80 
 
 3.92 
 
 4-41 
 
 5 
 
 03 
 
 .10 
 
 .22 
 
 .40 
 
 .62 
 
 .90 
 
 .22 
 
 .60 
 
 2.02 
 
 2.50 
 
 3-02 
 
 3.60 
 
 4.22 
 
 4-89 
 
 Si 
 
 03 
 
 .11 
 
 25 
 
 .44 
 
 .69 
 
 99 
 
 35 
 
 .76 
 
 2.23 
 
 2.75 
 
 3-33 
 
 3.96 
 
 4-65 
 
 5-39 
 
 6 
 
 03 
 
 .12 
 
 .27 
 
 .48 
 
 75 
 
 .08 
 
 47 
 
 .92 
 
 2.43 
 
 3-oo 
 
 3.63 
 
 4.32 
 
 5-07 
 
 5-38 
 
 6* 
 
 03 
 
 13 
 
 .29 
 
 52 
 
 .81 
 
 17 
 
 59 
 
 .08 
 
 2.63 
 
 3-25 
 
 3-93 
 
 4.68 
 
 5-49 
 
 6-37 
 
 7 
 
 .04 
 
 .14 
 
 31 
 
 .56 
 
 .87 
 
 .26 
 
 71 
 
 .24 
 
 2.83 
 
 3-50 
 
 4-24 
 
 5-05 
 
 5-91 
 
 6.86 
 
 7* 
 
 .04 
 
 IS 
 
 34 
 
 .60 
 
 93 
 
 35 
 
 .84 
 
 .40 
 
 3-04 
 
 3-75 
 
 4-54 
 
 5-40 
 
 6.34 
 
 7-35 
 
 8 
 
 .04 
 
 .16 
 
 .36 
 
 .64 
 
 .00 
 
 44 
 
 .96 
 
 56 
 
 3-24 
 
 4.00 
 
 4.84 
 
 5.76 
 
 6.76 
 
 7.84 
 
 8* 
 
 .04 
 
 .17 
 
 -38 
 
 .68 
 
 .06 
 
 53 
 
 .08 
 
 72 
 
 3-44 
 
 4-25 
 
 5.14 
 
 6.12 
 
 7.18 
 
 8.33 
 
 9 
 
 05 
 
 .18 
 
 .40 
 
 .72 
 
 .12 
 
 .62 
 
 .20 
 
 .88 
 
 3-64 
 
 4-50 
 
 5-44 
 
 6.48 
 
 7.60 
 
 8.82 
 
 9* 
 
 OS 
 
 .19 
 
 43 
 
 .76 
 
 .19 
 
 .71 
 
 33 
 
 3-04 
 
 3-85 
 
 4-75 
 
 5-75 
 
 6.84 
 
 8.03 
 
 9-3i 
 
 10 
 
 05 
 
 .20 
 
 45 
 
 .80 
 
 25 
 
 .80 
 
 45 
 
 3.20 
 
 4-05 
 
 5-oc 
 
 6.05 
 
 7.20 
 
 8-45 
 
 9.80 
 
 ii 
 
 .06 
 
 .22 
 
 49 
 
 .88 
 
 .40 
 
 .98 
 
 .69 
 
 3-52 
 
 4-45 
 
 5-50 
 
 6.65 
 
 7.92 
 
 9.29 
 
 10.78 
 
 12 
 
 .06 
 
 .24 
 
 54 
 
 .96 
 
 50 
 
 .16 
 
 94 
 
 3-84 
 
 4.86 
 
 6.00 
 
 7.26 
 
 8.64 
 
 10.14 
 
 11.76 
 
 13 
 
 .07 
 
 .26 
 
 59 
 
 .04 
 
 -63 
 
 34 
 
 3.i8 
 
 4.16 
 
 5-27 
 
 6.50 
 
 7-87 
 
 9.36 
 
 10.99 
 
 12.74 
 
 14 
 
 .07 
 
 .28 
 
 63 
 
 .12 
 
 75 
 
 52 
 
 3-43 
 
 4.48 
 
 5.67 
 
 7.00 
 
 8.47 
 
 O.IO 
 
 11.83 
 
 I3-72 
 
 15 
 
 .08 
 
 30 
 
 67 
 
 .20 
 
 .87 
 
 .70 
 
 3.6 7 
 
 4.80 
 
 6.07 
 
 7-50 
 
 9.08 
 
 0.80 
 
 12.67 
 
 14.70 
 
 16 
 
 .08 
 
 32 
 
 .72 
 
 .28 
 
 .00 
 
 .88 
 
 3-92 
 
 5-12 
 
 6.48 
 
 8.00 
 
 9.68 
 
 1.52 
 
 13.52 
 
 15-68 
 
 17 
 
 .OQ 
 
 34 
 
 -76 
 
 .36 
 
 .12 
 
 3-o6 
 
 4.16 
 
 5-44 
 
 6.88 
 
 8.50 
 
 10.28 
 
 2.24 
 
 14.36 
 
 16.66 
 
 18 
 
 .Op 
 
 .36 
 
 .81 
 
 .44 
 
 25 
 
 3-24 
 
 4.41 
 
 5.76 
 
 7.29 
 
 9.00 
 
 10.89 
 
 2.96 
 
 15-21 
 
 17.64 
 
 19 
 
 .10 
 
 .38 
 
 -85 
 
 52 
 
 37 
 
 3-42 
 
 4-65 
 
 6.08 
 
 7.69 
 
 9-50 
 
 11.49 
 
 3-68 
 
 16.05 
 
 18.62 
 
 20 
 
 .10 
 
 .40 
 
 .90 
 
 1. 60 
 
 2.50 
 
 3-6o 
 
 4-90 
 
 6.40 
 
 8.10 
 
 10.00 
 
 12.10 
 
 14.40 
 
 16.90 
 
 19.60 
 
 TABLE VIII. 
 AZIMUTH OF POLARIS WHEN AT ELONGATION. 
 
 3 
 
 1903. 
 
 1904. 
 
 1905. 
 
 1906. 
 
 1907. 
 
 1908. 
 
 1909. 
 
 1910. 
 
 1911. 
 
 rt 
 
 8 
 
 12 
 
 I" 14' 
 
 3 
 
 I4 ; 
 
 :-; 
 
 Ill', 
 
 :-; 
 
 S> 
 
 12' 
 
 11' 
 1 2' 
 
 4 
 8 
 
 i6 w 
 
 
 is 7 
 
 IS' 
 
 is' 
 
 14' 
 
 14' 
 
 14' 
 
 I3' 
 
 13' 
 
 1 6 
 
 20 
 
 ITi7' 
 
 I 7 / 
 
 I7' 
 
 16' 
 
 1 6' 
 
 16' 
 
 15' 
 
 IS 7 
 
 I 4 / 
 
 20 
 
 24 
 
 
 2?' 
 
 20' 
 
 2^ 
 
 ^ 
 
 I9' 
 
 
 i8 ; 
 
 i8 ; 
 
 24 
 
 3 
 32 
 
 1 26' 
 
 2 5 ' 
 
 2 5 ' 
 
 2 4 ' 
 
 2 4 ' 
 
 2 4 ' 
 
 2 3 / 
 
 23' 
 
 23' 
 
 30 
 
 32 
 
 34 
 
 1 28' 
 
 2 7 / 
 
 2 7 / 
 
 26' 
 
 26' 
 
 26' 
 
 2 5 ' 
 
 2 5 ' 
 
 25' 
 
 
 36" 
 
 i 3 o' 
 
 29' 
 
 2 9 ' 
 
 2 9 ' 
 
 28' 
 
 28' 
 
 2 7 ' 
 
 2 7 ' 
 
 2 7 ' 
 
 36 
 
 38 
 
 I32' 
 
 1 32' 
 
 o 31 ' 
 
 
 o ^j' 
 
 3o' 
 
 3t3'^ 
 
 2 Q ' 
 
 I2 9 ' 
 
 38 
 
 40 
 
 i 35' 
 
 1*34' 
 
 34' 
 
 I 34' 
 
 33' 
 
 i 33' 
 
 I32 / 
 
 32' 
 
 I32 
 
 40 
 
 
 i 3' 
 
 1*37' 
 
 o 37 ' 
 
 I 37' 
 
 
 i36' 
 
 i35' 
 
 35' 
 
 i34 
 
 42 
 
 44 
 
 1 41' 
 
 i 41' 
 
 40' 
 
 l 4 o' 
 
 39' 
 
 i39 / 
 
 i 3' 
 
 38' 
 
 i37 
 
 44 
 
 46 
 48 
 
 i45 / 
 i49 / 
 
 i44' 
 i 4 8' 
 
 i44 r 
 
 I 4 8' 
 
 I 43' 
 i47' 
 
 43' 
 47' 
 
 i 42 ' 
 IJ.46J 
 
 I 4 2' 
 
 i 4 6 / 
 
 i4S' 
 
 i 4 i 
 T45 
 
 46 
 48 
 
 50 
 
 i53' 
 
 i53' 
 
 I52' 
 
 I52 / 
 
 
 
 i5o' 
 
 I . 50' 
 
 i49 / 
 
 50 
 
 44 
 
TABLE IX. 
 
 TANGENT DISTANCES, LONG CHORDS, AND EX- 
 TERNAL SECANTS OF A ONE-DEGREE CURVE. 
 
 Also amounts to be added to same when No. 5, No. 9, 
 and No. 14 Spirals are to be used. 
 
 To find corresponding functions of any other curve divide 
 tabular number by degree of curvature. 
 
 Formulas used in construction of table: 
 
 Long chord = 2X5729.58X8^0, 
 Tangent =5729.58 Xtan a; 
 External sec = 5729.58 -i-cos 5729.58; 
 where a = J whole angle of curve. 
 
 With Metric System. 
 
 Using 20-meter chords, divide tabular quantities by five 
 times the proposed metric degree of curve for corresponding 
 quantities in metric measure. 
 
 This table is exact for arc measurements and is as accurate 
 as any table like it for the chord-measurement method for 
 laying out curves. 
 
 45 
 
IX. FUNCTIONS OF A ONE-DEGREE CURVE. 
 
 Whole 
 Angle. 
 
 Tangent 
 Distance. 
 
 Long 
 Chord. 
 
 External 
 Secant. 
 
 Whole 
 Angle. 
 
 1 
 
 50.0 
 
 100 .0 
 
 O . 22 
 
 1 
 
 2' 
 
 5I-67 
 
 103.3 
 
 0.24 
 
 2' 
 
 4'' 
 
 53-33 
 
 106 . 7 
 
 0.25 
 
 4' 
 
 6' 
 
 55-0 
 
 IIO.O 
 
 0,27 
 
 6' 
 
 8' 
 
 56.67 
 
 II3-3 
 
 0.28 
 
 8' 
 
 10' 
 
 58.33 
 
 116 .7 
 
 0.30 
 
 10' 
 
 12' 
 
 60 .00 
 
 I2O .O 
 
 0.31 
 
 12' 
 
 14' 
 
 61.67 
 
 123.3 
 
 0-33 
 
 14' 
 
 16' 
 
 63-33 
 
 126.7 
 
 0-35 
 
 16' 
 
 18' 
 
 65.00 
 
 130.0 
 
 0-37 
 
 18' 
 
 20' 
 
 66 .67 *o o ^ 
 
 133-3 
 
 0.39 v;; 
 
 20'' 
 
 22' 
 
 68.33 *"* 
 
 136.7 
 
 
 22 r 
 
 24' 
 
 7 - 00 ^ :: 5 
 
 140.0 
 
 -43 %~ " 
 
 24' 
 
 26' 
 
 71-67 a 
 
 143.3 
 
 0-45 a 
 
 26' 
 
 28' 
 
 73-34 J: - 
 
 146.7 
 
 0-47 | : r 
 
 28' 
 
 30' 
 
 75.00*8 
 
 150.0 
 
 0.49 * 
 
 30' 
 
 32 
 
 76.67.3. : 
 
 153-3 
 
 0.51 |: : 
 
 32' 
 
 34' 
 
 78.34^ 
 
 156.7 
 
 0-54 +> 
 
 34' 
 
 36' 
 
 8o.oo.S : s 
 
 160 .0 
 
 o . 56 -* s : 
 
 36' 
 
 38' 
 
 81.67 1^ _ 
 
 163-3 
 
 0.58 * 
 
 38' 
 
 40' 
 
 8 3 . 3 4! :: 
 
 166.7 
 
 0.60 ^" " 
 
 40' 
 
 42' 
 
 
 170.0 
 
 0.63 
 
 42' 
 
 44' 
 
 86!67 1 
 
 173-3 
 
 0.65 . 
 
 44' 
 
 46' 
 
 88. 34 1 s s 
 
 176.7 
 
 0.68 |"' 
 
 46' 
 
 48' 
 
 90.01 * 
 
 180.0 
 
 0.71 - 
 
 48' 
 
 50' 
 
 91.68^= = 
 
 183.3 
 
 o.73 ^ " 
 
 50' 
 
 52 
 
 93-34*8. [ 
 
 186.7 
 
 0.76 -g. 
 
 52 
 
 54' 
 
 95.01 3~ " 
 
 190.0 
 
 o.79 3"" 
 
 54' 
 
 5 6 ', 
 
 96. 68 .2: = 
 
 193-3 
 
 0.81 .S2 : = 
 
 56' 
 
 58' 
 
 98.34 *? 
 
 196.7 
 
 0.84 ""2 
 
 O-- - 
 
 58' 
 
 2 
 
 100 .01 *" 
 
 200 .0 
 
 0.87 *- 
 
 2 
 
 2' 
 
 101 .67 ' - 
 
 203.3 
 
 0.90 'g 
 
 2' 
 
 4' 
 
 103.34^ = 
 
 206.6 
 
 0.93 ^ = 
 
 4' 
 
 6' 
 
 105 .01 JH 
 
 210.0 
 
 0.96 c 
 
 6' 
 
 8' 
 
 I06.68|: : 
 
 213.3 
 
 0.99 |: s 
 
 8' 
 
 10' 
 
 108.35^ 
 
 216.6 
 
 I .02 " 
 
 10' 
 
 12' 
 
 no. 02 
 
 220 .0 
 
 I .06 
 
 12' 
 
 14' 
 
 1 1 1. 68 
 
 223.3 
 
 I .09 
 
 14' 
 
 16' 
 
 113-35 
 
 226.6 
 
 I .12 
 
 16' 
 
 18' 
 
 115.01 
 
 230.0 
 
 1 I 5 
 
 18' 
 
 20' 
 
 116.68 
 
 233.3 
 
 1 .19 
 
 20' 
 
 22' 
 
 118.35 
 
 236.6 
 
 1.23 
 
 22' 
 
 24' 
 
 I2O .02 
 
 240 .0 
 
 1.26 
 
 24' 
 
 .26' 
 
 121.68 
 
 243-3 
 
 1.30 
 
 26' 
 
 28' 
 
 123.35 
 
 246.6 
 
 i-33 
 
 28' 
 
 46 
 
IX. FUNCTIONS OF A ONE-DEGREE CURVE. 
 
 Whole 
 Angle. 
 
 Tangent 
 Distance. 
 
 Long 
 Chord. 
 
 External 
 Secant. 
 
 Whole 
 Angle. 
 
 2 30' 
 
 125 .02 
 
 250.0 
 
 1.36 
 
 2 30' 
 
 V' 
 
 126 .69 
 
 253-3 
 
 39 
 
 32' 
 
 34' 
 
 128.35 
 
 256.6 
 
 -43 
 
 34' 
 
 36' 
 
 130.02 
 
 260 .0 
 
 47 
 
 36' 
 
 38' 
 
 131.69 
 
 263.3 
 
 5 1 
 
 38' 
 
 40' 
 
 I33-36 
 
 266.6 
 
 -55 
 
 40' 
 
 42' 
 
 I35- 3 
 
 270.0 
 
 -59 
 
 42' 
 
 44' 
 
 136.70 
 
 273.3 
 
 1.63 
 
 44' 
 
 46' 
 
 138.36 
 
 276.6 
 
 1.67 
 
 46' 
 
 48' 
 
 140.03 
 
 280.0 
 
 1.71 
 
 48' 
 
 5 : 
 
 141.70 
 
 283.3 
 
 i75 
 
 S' 
 
 52 
 
 143.36 
 
 286.6 
 
 1.79 
 
 5*' 
 
 54' 
 
 I45-03 
 
 290.0 
 
 1.83 
 
 54' 
 
 56 ,' 
 
 146 . 70 
 
 293-3 
 
 1.88 
 
 56' 
 
 58' 
 
 148.37 
 
 296.6 
 
 i .92 
 
 58' 
 
 3 
 
 150 .04 
 
 300.0 
 
 i .96 
 
 3 
 
 2' 
 
 JS 1 -? 1 
 
 303.3 
 
 2 .OI 
 
 2' 
 
 4' 
 
 153.38 
 
 306.6 
 
 2 .05 
 
 4' 
 
 6' 
 
 155-04 
 
 309.9 
 
 2 .09 
 
 6' 
 
 8' 
 
 156.71 
 
 313.3 
 
 2.14 
 
 8' 
 
 10' 
 
 158.38 
 
 316.6 
 
 2 . 19 
 
 10' 
 
 12' 
 
 160.05 
 
 3I9-9 
 
 2 .24 
 
 12' 
 
 14' 
 
 161 .72 
 
 323.3 
 
 2 . 29 
 
 14' 
 
 16' 
 
 163.38 
 
 326.6 
 
 2.34 
 
 16' 
 
 18' 
 
 165.05 
 
 329.9 
 
 2.38 
 
 1 8' 
 
 20' 
 
 166.72 
 
 333.3 
 
 2.43 
 
 20' 
 
 22' 
 
 168.38 
 
 336.6 
 
 2.48 
 
 22' 
 
 24' 
 
 170.05 
 
 339-9 
 
 2.52 
 
 24' 
 
 26' 
 
 171.72 
 
 343-3 
 
 2-57 
 
 26' 
 
 28' 
 
 173-39 
 
 346.6 
 
 2 .62 
 
 28' 
 
 30' 
 
 175.06 
 
 349.9 
 
 2 .67 
 
 30' 
 
 32' 
 
 176.73 
 
 353-3 
 
 2 . 72 
 
 32' 
 
 3 < 
 
 178.40 
 
 356.6 
 
 2.77 
 
 34' 
 
 36' 
 
 180 .07 
 
 359-9 
 
 2.82 
 
 36' 
 
 38' 
 
 181.74 
 
 363.3 
 
 2.8 7 
 
 38' 
 
 40' 
 
 183.40 
 
 366.6 
 
 2.93 
 
 40' 
 
 42' 
 
 185.07 
 
 369.9 
 
 2.98 
 
 42' 
 
 44' 
 
 186.74 
 
 373-3 
 
 34 
 
 44' 
 
 46' 
 
 188.40 
 
 376.6 
 
 3.10 
 
 46' 
 
 48' 
 
 190.07 
 
 379-9 
 
 3.15 
 
 48' 
 
 50' 
 
 191.74 
 
 383-3 
 
 3.21 
 
 S' 
 
 5 ^ 
 
 193.40 
 
 386.6 
 
 3.26 
 
 52' 
 
 54' 
 
 !95-o7 
 
 389-9 
 
 3.32 
 
 54' 
 
 56' 
 
 196.74 
 
 393-3 
 
 3.38 
 
 56' 
 
 58' 
 
 198.41 
 
 396.6 
 
 3.44 
 
 58' 
 
IX. FUNCTIONS OF A ONE-DEGREE CURVE. 
 
 Whole 
 Angle . 
 
 Tangent 
 Distance. 
 
 Long 
 Chord. 
 
 External 
 Secant. 
 
 Whole 
 Angle. 
 
 4 
 
 200.08 
 
 399-9 
 
 3-49 
 
 4 
 
 2' 
 
 201.75 
 
 403-3 
 
 3.55 
 
 2' 
 
 4' 
 
 203.42 
 
 406 .6 
 
 3.6l 
 
 4' 
 
 6' 
 
 205 .09 
 
 409.9 
 
 3.67 
 
 6' 
 
 8' 
 
 206.76 
 
 4i33 
 
 3-73 
 
 8' 
 
 10' 
 
 208.43 
 
 416 .6 
 
 3-79 
 
 10' 
 
 12' 
 
 2IO . IO 
 
 419.9 
 
 3-85 
 
 12' 
 
 14' 
 
 211.77 
 
 423-3 
 
 3-92 
 
 14' 
 
 16' 
 
 213-43 
 
 426.6 
 
 3.98 
 
 16' 
 
 18' 
 
 215.10 
 
 429.9 
 
 4.04 
 
 18' 
 
 20' 
 
 216.77 
 
 433-3 
 
 4. 10 
 
 20' 
 
 22' 
 
 218 .44 
 
 436.6 
 
 4. 16 
 
 22'. 
 
 24' 
 
 22O . II 
 
 439-9 
 
 4. 22 
 
 24' 
 
 26' 
 
 221 .78 
 
 443-2 
 
 4.28 
 
 26' 
 
 28' 
 
 223.45 
 
 446 .6 
 
 4.35 
 
 28' 
 
 30' 
 
 225 . 12 
 
 449-9 
 
 4.42 
 
 30' 
 
 32' 
 
 226.79 
 
 453-2 
 
 4.48 
 
 32' 
 
 34' 
 
 228.46 
 
 456.6 
 
 4-55 
 
 34' 
 
 36' 
 
 230.13 
 
 459-9 
 
 4 .62 
 
 36' 
 
 38' 
 
 231 .80 
 
 463.2 
 
 4.69 
 
 38' 
 
 40' 
 
 233-47 
 
 466.6 
 
 4.76 
 
 40' 
 
 42' 
 
 235.14 
 
 469.9 
 
 4.82 
 
 42' 
 
 44' 
 
 236.81 
 
 473-2 
 
 4.89 
 
 44' 
 
 46' 
 
 238.48 
 
 476.6 
 
 4.96 
 
 46' 
 
 48' 
 
 240.15 
 
 479-9 
 
 5-3 
 
 48' 
 
 5' 
 
 241 .81 
 
 483.2 
 
 5.10 
 
 50' 
 
 52' 
 
 243.48 
 
 486.5 
 
 5-17 
 
 5 2/ 
 
 54' 
 
 245 -IS 
 
 489.9 
 
 5-24 
 
 54' 
 
 I*' 
 
 246.82 
 
 493-2 
 
 5-3i 
 
 56' 
 
 #' 
 
 248.49 
 
 496.5 
 
 5-38 
 
 58' 
 
 5 
 
 250. 16 
 
 499-9 
 
 5-46 
 
 5 
 
 a' 
 
 251-83 
 
 503-2 
 
 5-53 
 
 2' 
 
 4' 
 
 253-50 
 
 506.5 
 
 5.60 
 
 4' 
 
 6' 
 
 2 55- i 7 ^ 
 
 509-9 
 
 5-68 ^ 
 
 6' 
 
 8' 
 
 256.84 I- 
 
 5I3-2 
 
 5-75 6 
 
 8' 
 
 10' 
 
 258.51 -g 
 
 5*6-5 
 
 5' 8 32 
 
 10' 
 
 12' 
 
 260.18 , 
 
 5*9-9 
 
 5-9o| 
 
 12' 
 
 14' 
 
 261.85 < 
 
 523-2 
 
 5 -98 & 
 
 14' 
 
 16' 
 
 263.52 
 
 526.5 
 
 6.06 g 
 
 16' 
 
 18' 
 
 265.19 o- 
 
 529.8 
 
 6.13^ 
 
 18' 
 
 20' 
 
 266.86 
 
 533-2 
 
 6.21 ^ 
 
 20' 
 
 22' 
 
 268.53 3 
 
 536.5 
 
 6.293 
 
 22' 
 
 24' 
 
 270.20 ^ 
 
 539-8 
 
 6.37 
 
 24' 
 
 26' 
 
 271.87 
 
 543-2 
 
 6.45 
 
 26' 
 
 28' 
 
 273-54 
 
 546.5 
 
 6.53 
 
 28' 
 
 48 
 
IX. FUNCTIONS OF A ONE-DEGREE CURVE. 
 
 Whole 
 Angle. 
 
 Tangent 
 Distance. 
 
 Long 
 Chord. 
 
 External 
 Secant. 
 
 Whole 
 Angle. 
 
 5 30' 
 
 275.21 
 
 549-8 
 
 6.61 
 
 5 30' 
 
 32' 
 
 276 88 
 
 553-2 
 
 6.69 
 
 32' 
 
 34' 
 
 278 56 
 
 S5 6 -5 
 
 6.77 
 
 34' 
 
 36; 
 
 280.23 
 
 559-8 
 
 6-85 
 
 36' 
 
 38' 
 
 281 . 90 
 
 5 6 3-2 
 
 6-93 6 
 
 38' 
 
 40' 
 
 283-57 
 
 566.5 
 
 7-0x5 
 
 40' 
 
 42' 
 
 285.24 
 
 569-8 
 
 7-o 9 . 
 
 42' 
 
 44' 
 
 286.91 
 
 573-2 
 
 7 J 7 co! 
 
 44' 
 
 46' 
 
 288.58 
 
 576.5 
 
 7-25 o 
 
 46' 
 
 48' 
 
 290.25 
 
 579-8 
 
 7-34 
 
 48' 
 
 50' 
 
 291.92 
 
 583-1 
 
 7-43 | 
 
 50' 
 
 5 2 ' 
 
 293-59 
 
 586.5 
 
 
 52' 
 
 54 
 
 295 . 26 
 
 589.8 
 
 7 .60 
 
 54' 
 
 56' 
 
 296.93 
 
 593-1 
 
 7.68 
 
 56' 
 
 S 8 
 
 298 .60 
 
 596.5 
 
 7-77 
 
 58' 
 
 6 
 
 300 . 28 
 
 599-8 
 
 7-85 
 
 6 
 
 2' 
 
 301 -95 
 
 603.1 
 
 7-94 
 
 2' 
 
 4' 
 
 303-63 
 
 606.5 
 
 8.03 
 
 4' 
 
 6' 
 
 305-30 'o 
 
 609.8 
 
 8.12 
 
 6' 
 
 8' 
 
 306.97 1 
 
 613. i 
 
 8.21 
 
 8'- 
 
 10' 
 
 308.6413 
 
 616 .4 
 
 8.30 
 
 10' 
 
 J2 7 
 
 3 10 3 1 -a 
 
 619.8 
 
 8-39 
 
 12' 
 
 14' 
 
 311.98 C 
 
 623.1 
 
 8.48 
 
 14' 
 
 16' 
 
 3*3-66 .0 
 
 626 .4 
 
 8-57 
 
 16' 
 
 18' 
 
 3J5-33 2 
 
 629.7 
 
 8.66 
 
 r8' 
 
 20' 
 
 317.00 E 
 
 633-1 
 
 8-75 
 
 20.' 
 
 22' 
 
 318.67 5 
 
 636.4 
 
 8.84 
 
 22' 
 
 24' 
 
 320.34 < 
 
 639.7 
 
 8-94 . 
 
 24' 
 
 26' 
 
 322 .01 
 
 643.1 
 
 9-03 
 
 26' 
 
 28' 
 
 323.68 
 
 646 .4 
 
 9-13 5zi 
 
 28' 
 
 3' 
 
 325.35 
 
 649-7 
 
 9-23 1 
 
 30' 
 
 32' 
 
 327.02 
 
 653-0 
 
 9-32 $ 
 
 32 
 
 34 
 
 328.70 
 
 656.4 
 
 9.42 
 
 34' 
 
 36' 
 
 330.37 
 
 659-7 
 
 9-52 S 
 
 36' 
 
 38' 
 
 332-04 
 
 663.0 
 
 9 .62 N 
 
 38' 
 
 40' 
 
 333.71 
 
 666.3 
 
 9.7i | 
 
 40' 
 
 42' 
 
 335-39 
 
 669.7 
 
 ' 9.81 * 
 
 42' 
 
 44' 
 
 337-o6 
 
 673.0 
 
 9.91 
 
 44' 
 
 46' 
 
 338.73 
 
 676.3 
 
 IO .OO 
 
 46' 
 
 48' 
 
 340.40 
 
 679.6 
 
 IO . IO 
 
 48' 
 
 50' - 
 
 342.08 
 
 $83-0 
 
 IO . 2O 
 
 5 0/ 
 
 52' 
 
 343-75 
 
 686.3 
 
 10.30 
 
 52 ^ 
 
 54' . 
 
 345-42 
 
 689.6 
 
 10.40 
 
 54 
 
 56' 
 
 347-io 
 
 692 .9 
 
 10.50 
 
 56 
 
 58' 
 
 348.77 
 
 696.3 
 
 10 .60 
 
 58' 
 
IX. FUNCTIONS OF A ONE-DEGREE CURVE. 
 
 Whole 
 Angle. 
 
 Tangent 
 Distance. 
 
 Long 
 Chord. 
 
 External 
 Secant. 
 
 Whole 
 Angle. 
 
 7 
 
 350-44 
 
 699.6 
 
 10 . 71 
 
 7 
 
 2' 
 
 352.ii 
 
 702.9 
 
 io.il 
 
 2' 
 
 4' 
 
 353.78 
 
 706 . 2 
 
 10 .91 
 
 4' 
 
 6' 
 
 355-45 
 
 79-5 
 
 II .01 
 
 6' 
 
 8' 
 
 357-12 
 
 712.9 
 
 II . II 
 
 8' 
 
 10' 
 
 358.8o 
 
 7l6 . 2 
 
 11.22 
 
 10' 
 
 12' 
 
 360.47 
 
 7 T 9-5 
 
 11.32 
 
 12' 
 
 14' 
 
 362 .14 
 
 722.8 
 
 n-43 
 
 14' 
 
 16' 
 
 363-82 
 
 726 . 2 
 
 IJ -53 
 
 16' 
 
 18' 
 
 365-49 ^ 
 
 729-5 
 
 ii . 64 
 
 18' 
 
 20' 
 
 367-I7 5 
 
 732-8 
 
 n-75 
 
 20' 
 
 22' 
 
 368.84^ 
 
 736.1 
 
 ii .85 
 
 22" 
 
 24' 
 
 370.51 .b 
 
 739-5 
 
 ii . 96 
 
 24' 
 
 26' 
 
 372.19 
 
 742.8 
 
 12 .07 
 
 26' 
 
 28' 
 
 373-86 
 
 746.1 
 
 12 .18 
 
 28' 
 
 3; 
 
 375-54 ; 
 
 749-4 
 
 12 .29 
 
 30' 
 
 32' 
 
 377-21 ^ 
 
 752.8 
 
 12 .40 
 
 32' 
 
 34' 
 
 378-88 ^ 
 
 756.1 
 
 12 . 51 
 
 34' 
 
 36' 
 
 380. 56 ^ 
 
 759-4 
 
 I2 -63 ^ 
 
 36' 
 
 38' 
 
 382.23 
 
 762.8 
 
 12.74 6 
 
 38' 
 
 40' 
 
 383-91 
 
 766.1 
 
 12.85^ 
 
 40' 
 
 42' 
 
 385.58 
 
 769-4 
 
 I2. 9 6| 
 
 42' 
 
 44' 
 
 387-25 
 
 772.7 
 
 13.08 
 
 44' 
 
 46' 
 
 388.93 
 
 776.1 
 
 13-19 o 
 
 46' 
 
 48' 
 
 390.61 
 
 779-4 
 
 13-30 o 
 
 48' 
 
 50' 
 
 392.28 
 
 782.7 
 
 13.41 -d 
 
 50' 
 
 52' 
 
 393-95 
 
 786.0 
 
 13.53 3 
 
 52' 
 
 54' 
 
 395-62 
 
 789.4 
 
 13.64 
 
 54' 
 
 56' 
 
 397-30 
 
 792.7 
 
 13.76 
 
 56' 
 
 58' 
 
 398.97 
 
 796.0 
 
 13.88 
 
 58' 
 
 8 
 
 400 .65 
 
 799-4 
 
 13.99 
 
 8 
 
 2' 
 
 402.33 
 
 802.7 
 
 14. 10 
 
 2' 
 
 4' 
 
 404.00 
 
 806.0 
 
 14.22 
 
 4' 
 
 6' 
 
 405.67 -- 
 
 809.3 
 
 14.34 
 
 6' 
 
 8' 
 
 407-35 g 
 
 812.6 
 
 14.46 
 
 8' 
 
 10' 
 
 409.03 -g 
 
 816.0 
 
 14.58 
 
 10' 
 
 12' 
 
 410.70 -a 
 
 819-3 
 
 14.70 
 
 12' 
 
 14' 
 
 412.38^ 
 
 822.6 
 
 14.82 
 
 14' 
 
 16' 
 
 414 .06 
 
 825.9 
 
 14.94 
 
 i6' 
 
 1 8' 
 
 415-74 d 
 
 829.3 
 
 15 .06 
 
 18' 
 
 20' 
 
 417.41 5 
 
 832.6 
 
 15.18 
 
 20' 
 
 22' 
 
 419.08 ? 
 
 835.9 
 
 15-30 
 
 22' 
 
 24' 
 
 420.76 < 
 
 839.2 
 
 15-43 
 
 24' 
 
 26' 
 
 422 .44 
 
 842.6 
 
 J 5-55 
 
 26' 
 
 2.8' 
 
 424 . IT 
 
 845-9 
 
 T 5 -67 
 
 28' 
 
 50 
 
IX. FUNCTIONS OF A ONE-DEGREE CURVE. 
 
 Whole 
 Angle. 
 
 Tangent 
 Distance. 
 
 Long 
 Chord. 
 
 External 
 Secant. 
 
 Whole 
 Angle. 
 
 8 30' 
 
 425.79 
 
 849.2 
 
 15.80 
 
 8 30' 
 
 32' 
 
 427.47 
 
 852.5 
 
 15-93 
 
 32' 
 
 34' 
 
 429.I5 
 
 855-8 
 
 16 .06 
 
 34' 
 
 36' 
 
 430.83 
 
 859.2 
 
 16. 19 
 
 36' 
 
 38' 
 
 432.50 
 
 862.5 
 
 16 .31 
 
 38' 
 
 40' 
 
 434.17 
 
 865.8 
 
 16.43 
 
 40' 
 
 42' 
 
 435.85 
 
 869.1 
 
 16.56 
 
 42' 
 
 44' 
 
 437-53 
 
 872.5 
 
 16.69 
 
 44' 
 
 46' 
 
 439.20 
 
 875.8 
 
 16.81 
 
 46' 
 
 48' 
 
 440.88 
 
 879.1 
 
 16.94 
 
 48' 
 
 50' 
 
 442.55 
 
 882.4 
 
 17.07 
 
 50' 
 
 5*' 
 
 454-23 
 
 885.7 
 
 17 .20 
 
 52' 
 
 54' 
 
 455-90 
 
 889. I 
 
 17-33 
 
 54' 
 
 56' 
 
 437-5S 
 
 892.4 
 
 17.46 
 
 56' 
 
 58' 
 
 459.26 
 
 895-7 
 
 J 7-59 
 
 58' 
 
 *> 
 
 450.93 
 
 899 .0 
 
 17.72 
 
 9 
 
 2' 
 
 452 .60 
 
 902.3 
 
 17-83 
 
 2' 
 
 4' 
 
 454.28 u^a 
 
 905-6 
 
 17.97 "> 
 
 4' 
 
 6' 
 
 455^6 o*. 
 
 909 .0 
 
 18.10 d 
 
 6' 
 
 8' 
 
 457-64* 
 
 912.3 
 
 18.26 * : 
 
 8' 
 
 io' 
 
 459-32 : 
 
 9I5-7 
 
 i8. 3 8.1 : 
 
 10' 
 
 12' 
 
 4f i .00 w 
 
 919.0 
 
 18.52 & 
 
 12' 
 
 14' 
 
 4^2.68 .0: 
 
 922.4 
 
 18.65 J3: 
 
 14' 
 
 16' 
 
 4^4.36 ? 
 
 925-7 
 
 18.79 
 
 16' 
 
 18'. 
 
 4^6.04 & 
 
 929.0 
 
 18.93 ^r 
 
 18' 
 
 20' 
 
 467-71 g. 
 
 932.3 
 
 19 .06 S; 
 
 20' 
 
 22' 
 
 469.39 < 
 
 935-6 
 
 19.19 < 
 
 22' 
 
 24' 
 
 471-07 
 
 939-o 
 
 *9'33 
 
 24' 
 
 26' 
 
 472.75 
 
 942.3 
 
 19.49 
 
 26' 
 
 28' 
 
 474.42 
 
 945-6 
 
 19.62 
 
 28' 
 
 3' 
 
 476.10 
 
 948.9 
 
 J 9-75 
 
 30' 
 
 3^' 
 
 477-78 
 
 952.2 
 
 19.89 
 
 32' 
 
 34' 
 
 479.46 
 
 955-5 
 
 20.03 
 
 34' 
 
 36' 
 
 481 .13 
 
 958.9 
 
 20. 17 
 
 36' 
 
 38' 
 
 482.81 
 
 962 . 2 
 
 20.31 
 
 38' 
 
 40' 
 
 484 . 49 
 
 965.5 
 
 20.45 
 
 40' 
 
 42' 
 
 486.17 
 
 968.9 
 
 20.59 
 
 42' 
 
 44' 
 
 487.84 
 
 972.2 
 
 20.74 
 
 44' 
 
 46' 
 
 489.52 
 
 975-5 
 
 20.88 
 
 46' 
 
 48' 
 
 491 . 20 
 
 978.8 
 
 21 .02 
 
 48' 
 
 5' 
 
 492.88 
 
 982.1 
 
 21 . l6 
 
 5' 
 
 52' 
 
 494.56 
 
 985-4 
 
 21.30 
 
 S^' 
 
 54' 
 
 496.24 
 
 988.7 
 
 21.45 
 
 54' 
 
 56' 
 
 497.92 
 
 992.0 
 
 21.59 
 
 56' 
 
 58' 
 
 499 .60 
 
 995-3 
 
 21 74 
 
 58' 
 
 51 
 
IX. FUNCTIONS OF A ONE-DEGREE CURVE. 
 
 Whole 
 Angle. 
 
 Tangent 
 Distance. 
 
 Long 
 Chord. 
 
 External 
 Secant. 
 
 Whole 
 Angle. 
 
 10 
 
 501 .28 
 
 998.7 
 
 21 .89 
 
 1O 
 
 2' 
 
 502.96 
 
 IOO2 .O 
 
 22 .04 
 
 2 f 
 
 4' 
 
 504.64 
 
 1005 .4 
 
 22.18 
 
 4' 
 
 6' 
 
 506.32 
 
 I008.-7 
 
 22.33 
 
 6' 
 
 8' 
 
 508.0 
 
 IOI2 .O 
 
 22.48 
 
 8 7 
 
 10' 
 
 509.68 
 
 IOI5.3 
 
 22 .63 
 
 10' 
 
 12' 
 
 5H-36 
 
 1018. 7 
 
 22.78 
 
 12' 
 
 14' 
 
 5*3-04 
 
 IO22 .O 
 
 22.93 
 
 14' 
 
 1 6' 
 
 514-72 
 
 I02 5-3 
 
 23.08 
 
 16' 
 
 1 8' 
 
 516 .40 
 
 1028.6 
 
 23.23 
 
 18' 
 
 to' 
 
 518.08 
 
 1031 .9 
 
 23-38 
 
 20' 
 
 22' 
 
 5I9-76 
 
 1035.3 
 
 23-53 
 
 22' 
 
 24' 
 
 52i -44 
 
 1038.6 
 
 23.69 
 
 24' 
 
 26' 
 
 523-12 
 
 1041 . 9 
 
 23.84 
 
 26' 
 
 28' 
 
 524.80 
 
 1045.2 
 
 23.99 
 
 28' 
 
 30' 
 
 526.48 
 
 1048.5 
 
 24.14 
 
 30' 
 
 32/ , 
 
 528.16 
 
 1051 .8 
 
 24.30 
 
 32; 
 
 34 
 
 529.84 xAo 
 
 1055-2 
 
 24-45 
 
 34 
 
 36 
 
 53I-52 o- 
 
 1058.5 
 
 24.60 ^ 
 
 36' 
 
 38' 
 
 533-20 
 
 1061.8 
 
 24-75 6. 
 
 38' 
 
 40' 
 
 534- 88 4= 
 
 1065 . i 
 
 24.91 * 
 
 40' 
 
 4V 
 
 536. #6 cc 
 
 1068 .4 
 
 25.06 |- 
 
 42' 
 
 44' 
 
 538.4.4 : 
 
 1071.7 
 
 25.22 c& 
 
 44' 
 
 46' 
 
 540.CJ2 t 
 
 1075 .0 
 
 25-37 c: 
 
 46' 
 
 48' 
 
 541.60 
 
 1078.4 
 
 25.54 *p 
 
 48' 
 
 50' 
 
 543-29 ?- 
 
 1081 . 7 
 
 25.70 *" 
 
 50' 
 
 52 
 
 544-97 < 
 
 1085 .0 
 
 25-86^ 
 
 52' 
 
 54' 
 
 546.65 
 
 1088.4 
 
 26.02 
 
 54 
 
 56' 
 
 548.33 
 
 1091.7 
 
 26.18 
 
 56' 
 
 58' 
 
 550.02 
 
 1095.0 
 
 26.34 
 
 58' 
 
 11 
 
 55I-70 
 
 1098.3 
 
 26 . ^o 
 
 11 
 
 2' 
 
 553.38 
 
 noi .6 
 
 26.66 
 
 2' 
 
 4' 
 
 555-o6 
 
 1105.0 
 
 26.83 
 
 4 r 
 
 6' 
 
 556.74 
 
 1108.3 
 
 26 .99 
 
 6' 
 
 8' 
 
 558.43 
 
 mi .6 
 
 2 7- I 5 
 
 8' 
 
 to' 
 
 560.11 
 
 1114.9 
 
 27- 3 1 
 
 10' 
 
 12' 
 
 561.80 
 
 1118.3 
 
 27.47 
 
 12' 
 
 14' 
 
 563-48 
 
 II2I .6 
 
 27.64 
 
 14' 
 
 16' 
 
 565-16 
 
 1124.9 
 
 27 . 80 
 
 i6 f 
 
 18' 
 
 566.84 
 
 1128 . 2 
 
 27.97 
 
 18' 
 
 20' 
 
 568.53 
 
 H3I.5 
 
 28.14 
 
 20 r 
 
 22' 
 
 570.22 
 
 II34.8 
 
 28.30 
 
 22 7 
 
 24' 
 
 571-9 
 
 ; 1.138.1 
 
 28.47 
 
 24' 
 
 26' 
 
 573.58 
 
 1141.4 
 
 28.64 
 
 26' 
 
 28' 
 
 575-26 
 
 1144.7 
 
 28.80 
 
 28' 
 
IX. FUNCTIONS OF A ONE-DEGREE CURVE. 
 
 Whole 
 Angle. 
 
 Tangent 
 Distance. 
 
 Long 
 Chord. 
 
 External 
 Secant. 
 
 Whole 
 Angle. 
 
 11 3' 
 
 576.95 
 
 1148 .0 
 
 28.97 
 
 11 30' 
 
 32' 
 
 578 . 63 
 
 1151.4 
 
 29.14 
 
 32' 
 
 34' 
 
 580.32 
 
 ri 54-7 
 
 29.31 
 
 34' 
 
 36' 
 
 582 .00 ^os 
 
 1158.0 
 
 29.48 
 
 36' 
 
 38' 
 
 583.69 |: 
 
 1161.3 
 
 29.65 
 
 38' 
 
 40' 
 
 585-37 g 
 
 1164.6 
 
 29.82 
 
 40' 
 
 42' 
 
 587.05 ' : 
 
 1168.0 
 
 30.00 
 
 42' 
 
 44' 
 
 588.73^ 
 
 1171 .3 
 
 30.17 
 
 44' 
 
 46' 
 
 590.42 - 
 
 1174.6 
 
 30.34 
 
 46' 
 
 48' 
 
 592.io 2| 
 
 1177.9 
 
 30.51 
 
 48' 
 
 50' 
 
 593-79 
 
 1181.2 
 
 30.68 
 
 50' 
 
 52' 
 
 595-47 S: 
 
 1184.6 
 
 30.85 
 
 5 2/ 
 
 54' 
 
 597.16 < 
 
 1187.9 
 
 31.02 
 
 5 < 
 
 56' 
 
 598.84 
 
 II9I .2 
 
 31 . 2O 
 
 56 
 
 58' 
 
 600.53 
 
 II94-5 
 
 31-37 
 
 58' 
 
 12 
 
 602 .21 
 
 II97.8 
 
 3I-56 
 
 12 
 
 2' 
 
 603.89 
 
 I2OI . 2 
 
 31-73 
 
 2' 
 
 4' 
 
 605.58 
 
 1204 . 5 
 
 3L9I 
 
 4' 
 
 6' 
 
 607 . 27 
 
 1207 .8 
 
 32.09 u^a 
 
 6' 
 
 8' 
 
 608.96 
 
 I2II . I 
 
 32.27 6. 
 
 8' 
 
 .10' 
 
 610 .64 
 
 I2I4.4 
 
 32.45 -g 
 
 10' 
 
 12' 
 
 612.32 
 
 I2I7.7 
 
 
 12' 
 
 14' 
 
 614.01 
 
 1221 .O 
 
 32 .81 & 
 
 14' 
 
 1 6' 
 
 615.70 
 
 1224.3 
 
 33-00 JD: 
 
 16' 
 
 1 8' 
 
 617.38 .Ac* 
 
 1227.6 
 
 33.18 ^^ 
 
 1 8' 
 
 20' 
 
 619.07 6- 
 
 1230.9 
 
 33-35 |," 
 
 20' 
 
 22' 
 
 620.76 Ij 
 
 1234.3 
 
 33-53 < 
 
 22' 
 
 24' 
 
 622 .45 .-. 
 
 1237.6 
 
 33-71 
 
 24' 
 
 26' 
 
 624.13 
 
 1240.9 
 
 33.89 
 
 26' 
 
 28' 
 
 625.82 |- 
 
 1244.2 
 
 34.07 
 
 28' 
 
 3' 
 
 627.50 *? *r 
 
 1247-5 
 
 34.26 
 
 30; 
 
 32' 
 
 629.19 aft 
 
 1250.9 
 
 34.44 
 
 32 
 
 34' 
 
 630.87 ^ 
 
 1254.2 
 
 34.62 
 
 34 
 
 36' 
 
 632-56 < 
 
 1257.5 
 
 34.80 
 
 3 
 
 38' 
 
 634.24 
 
 1260.8 
 
 34-99 
 
 38' 
 
 40' 
 
 635-93 
 
 1264. I 
 
 35.18 
 
 40' 
 
 42' 
 
 637.62 
 
 1267.4 
 
 35-36 
 
 42' 
 
 44' 
 
 639-3 
 
 1270.7 
 
 35-55 
 
 44' 
 
 46' 
 
 640.09 
 
 1274.0 
 
 35-73 
 
 46' 
 
 48' 
 
 642.68 
 
 I2 77-3 
 
 35-92 
 
 48' 
 
 5' 
 
 644.37 
 
 1280.6 
 
 36.12 
 
 5' 
 
 52' 
 
 646 .06 
 
 1284.0 
 
 36.31 
 
 52' 
 
 54' 
 
 647-75 
 
 1287.3 
 
 36.5 
 
 54 
 
 56' 
 
 649.44 
 
 1290 .6 
 
 36.69 
 
 56 
 
 58' 
 
 651-13 
 
 1293.9 
 
 36.88 
 
 58' 
 
 53 
 
IX. FUNCTIONS OF A ONE-DEGREE CURVE. 
 
 Whole 
 Angle. 
 
 Tangent 
 Distance: 
 
 Long 
 Chord. 
 
 External 
 Secant. 
 
 Whole 
 Angle. 
 
 13 
 
 652.81 
 
 1297.2 
 
 37.07 
 
 13 
 
 2' 
 
 654-50 
 
 1300.5 
 
 37.26 
 
 2' 
 
 4' 
 
 656. 19 
 
 1303-8 
 
 37-45 
 
 4' 
 
 6' 
 
 657.88 
 
 1307.1 
 
 37-64 
 
 6 7 
 
 8' 
 
 659-57 
 
 1310.4 
 
 37.83 
 
 8' 
 
 10' 
 
 661 .25 
 
 !3i3.7 
 
 38.03 
 
 10' 
 
 12' 
 
 662 .94 
 
 1317.0 
 
 38.22 
 
 12' 
 
 14' 
 
 664-63 
 
 1320.4 
 
 38.41 
 
 14' 
 
 16' 
 
 666 .32 
 
 1323.7 
 
 38.60 
 
 16' 
 
 18' 
 
 668.01 . . 
 
 O O\ 
 
 1327.0 
 
 38.80 
 
 18' 
 
 20' 
 
 669 . 70 6, 
 
 !330-3 
 
 39-00 ^ 
 
 20 7 ' 
 
 22' 
 
 671-395" 
 
 J 333.6 
 
 33.19^ 
 
 22' 
 
 24' 
 
 673.08!, 
 
 1336.9 
 
 39-391 
 
 24' 
 
 26' 
 
 674.77c&' 
 
 1340.2 
 
 39-59;^ 
 
 9# 
 
 28' 
 
 676.46^. 
 
 1343-5 
 
 39-79^ 
 
 28' 
 
 3o' 
 
 678.15^ 
 
 1346.8 
 
 39-99^ 
 
 30' 
 
 32' 
 
 679.84 
 
 1350-2 
 
 40 . 19 N *- 
 
 32' 
 
 34' 
 
 681.53^ 
 
 1353.5 
 
 40-3955 
 
 34' 
 
 36' 
 
 683.22^- 
 
 1356.8 
 
 40.59^ 
 
 36' 
 
 38' 
 
 684.91 
 
 1360.1 
 
 40.79 
 
 38' 
 
 40' 
 
 686.60 
 
 1363-4 
 
 40.99 
 
 40' 
 
 42' 
 
 688.29 
 
 1366.7 
 
 41.19 
 
 42' 
 
 44' 
 
 689.98 . 
 
 1370.0 
 
 .41-39 
 
 44' 
 
 46' 
 
 691 .67 
 
 J373-3 
 
 4L59 
 
 46' 
 
 48' 
 
 693.36 
 
 1376.6 
 
 41 .80 
 
 48' 
 
 50' 
 
 695-05 
 
 J379-9 
 
 42 .00 
 
 50' 
 
 52' 
 
 696.74 
 
 1383-3 
 
 42 . 20 
 
 52' 
 
 54' 
 
 698.43 
 
 1386.6 
 
 42.40 
 
 54' 
 
 56' 
 
 2fOO . 12 
 
 1389.9 
 
 42 .61 
 
 56' 
 
 58' 
 
 ^OI .8l 
 
 1393-2 
 
 42.82 
 
 58' 
 
 14 
 
 703.5I 
 
 1396.5 
 
 43.03 
 
 14 
 
 2' 
 
 705.20 
 
 1399.8 
 
 43.24 
 
 2' 
 
 4' 
 
 706 .89 >" o*4 
 
 1403.1 
 
 43-44 ,^4 
 
 4' 
 
 6' 
 
 708.58 6 ( ; 
 
 1406 .4 
 
 43.65 . M 
 
 6' 
 
 8' 
 
 710.27 ~ " 
 
 1409.7 
 
 43-86^:: 
 
 8 X 
 
 to' 
 
 7"- 97 |: = 
 
 1413.0 
 
 44.07 ^ 
 
 10' 
 
 12' 
 
 7i3.66c& 
 
 1416.4 
 
 44.27 ;a : : 
 
 I2 X 
 
 14' 
 
 715-36^: : 
 
 1419.7 
 
 44-48^ 
 
 14' 
 
 1 6' 
 
 717.05 ^oo H 
 
 1423.0 
 
 44.7o^ : = 
 
 1 6' 
 
 18' 
 
 718.74 aas 
 
 1426.3 
 
 44.91 trZo 
 
 18' 
 
 20' 
 
 720.43^ 
 
 1429.6 
 
 45.12 g 
 
 20' 
 
 22' - 
 
 722.12 ^ ! 
 
 1432.9 
 
 45-33<" : 
 
 22' 
 
 24' 
 
 723.81 
 
 1436.2 
 
 45-54 
 
 24' 
 
 26' 
 
 725.50 
 
 1439.5 
 
 45-75 
 
 26' 
 
 2g' 
 
 727.20 
 
 1442 .8 
 
 45-97 
 
 28' 
 
 54 
 
IX. FUNCTIONS OF A ONE-DEGREE CURVE. 
 
 Whole 
 Angle. 
 
 Tangent 
 Distance 
 
 Long 
 Chord. 
 
 External 
 
 Secant. 
 
 Whole 
 Angle. 
 
 14 30' 
 
 728 .90 
 
 1446. I 
 
 46.18 
 
 14 30' 
 
 32' 
 
 730-59 
 
 1449-5 
 
 46 .40 
 
 3^' 
 
 34' 
 
 732 .28 
 
 1452 .8 
 
 46 .61 
 
 34' 
 
 36' 
 
 733-98 
 
 1456.1 
 
 46.83 
 
 36' 
 
 33' 
 
 735- 6 7 
 
 1459-4 
 
 47.04 
 
 38' 
 
 40' 
 
 737-37 
 
 1462.7 
 
 47-25 
 
 40' 
 
 42' 
 
 739.06 
 
 1466 .0 
 
 47-46 
 
 4=' 
 
 44' 
 
 740.76 
 
 1469.3 
 
 47-68 
 
 44' 
 
 46' 
 
 742.45 
 
 1472.6 
 
 47.90 
 
 46' 
 
 48' 
 
 744-15 
 
 1475-9 
 
 48.12 
 
 48' 
 
 5' 
 
 745 - 8 4 
 
 1479.2 
 
 48.34 
 
 5' 
 
 52' 
 
 747-54 
 
 1482.5 
 
 48.56 
 
 S^' 
 
 54' 
 
 749- 2 3 
 
 1485.9 
 
 48.78 
 
 54' 
 
 56' 
 
 750-93 
 
 1489.2 
 
 49 .00 
 
 56' 
 
 58' 
 
 752 .62 
 
 1492.5 
 
 49.22 
 
 58' 
 
 15 
 
 754.3 2 
 
 1495.8 
 
 49.44 
 
 15 
 
 2' 
 
 756.02 
 
 1499.1 
 
 49.68 
 
 2' 
 
 4' 
 
 757-7 1 Aont 
 
 1502.4 
 
 49-90 ^^^ 
 
 4' 
 
 6' 
 
 759-40 6 ^ ^ 
 
 I 55-7 
 
 5" I 3 
 
 6' 
 
 8' 
 
 761 . 10 
 
 1509 .0 
 
 5-34: : 
 
 8' 
 
 10' 
 
 762.80 J_ , 
 
 i5 I2 -3 
 
 SO-SS'g 
 
 10' 
 
 12' 
 
 764.49'd" " 
 
 I5I5-6 
 
 50.77 &= = 
 
 12' 
 
 14' 
 
 766.18 fc. 5 
 
 1518.9 
 
 51.00* 
 
 14' 
 
 16' 
 
 767. 88 - 
 
 1522 . 2 
 
 51.23^- : 
 
 16' 
 
 1 8' 
 
 769-58 OOH 
 
 I 5 2 5-5 
 
 1:1 AC; ^^^" 
 
 S* 'T-J W 0*C 
 
 18' 
 
 20' 
 
 _ !- i> 
 771.28.3 
 
 1528.8 
 
 51.67^ 
 
 20' 
 
 22' 
 
 772.983- 
 
 1532.1 
 
 5i9o<- - 
 
 22' 
 
 24' 
 
 774-68 
 
 1535.4 
 
 52.14 
 
 24' 
 
 26' 
 
 776.37 
 
 1538.7 
 
 52.37 
 
 26' 
 
 28' 
 
 778.07 
 
 1542.0 
 
 5 2 .60 
 
 28' 
 
 3' 
 
 779-77 
 
 1545.3 
 
 52.82 
 
 3' 
 
 32' 
 
 781.47 
 
 1548.6 
 
 53-05 
 
 32 
 
 34' 
 
 783-17 
 
 i55i-9 
 
 53-30 
 
 34' 
 
 36' 
 
 784.86 
 
 1555-2 
 
 53-53 
 
 36' 
 
 38' 
 
 786.56 
 
 1558-5 
 
 53.75 
 
 38' 
 
 40' 
 
 788.26 
 
 1561.8 
 
 53-97 
 
 40' 
 
 42' 
 
 789.96 
 
 1565-1 
 
 54-20 
 
 42' 
 
 44' 
 
 791 .66 
 
 1568.4 
 
 54-43 
 
 44' 
 
 46' 
 
 793-35 
 
 i57 J -7 
 
 54.67 
 
 46' 
 
 48' 
 
 795-05 
 
 i575-o 
 
 54-90 
 
 48' 
 
 SO'' 
 
 796.75 
 
 1578.3 
 
 55-J3 
 
 5' 
 
 S^' 
 
 798.45 
 
 1581.6 
 
 55-36 
 
 S^' 
 
 54' 
 
 800 . 15 
 
 1584.9 
 
 55-6o 
 
 54 
 
 56' 
 
 801 .85 
 
 1588.2 
 
 55-84 
 
 56 
 
 58' 
 
 803.55 
 
 i59i.5 
 
 56-08 
 
 58' 
 
IX. FUNCTIONS OF A ONE-DEGREE CURVE 
 
 Whole 
 Angle. 
 
 Tangent 
 Distance. 
 
 Long 
 Chord. 
 
 External 
 Secant. 
 
 Whole 
 Angle. 
 
 16 
 
 805.25 
 
 1594.8 
 
 56.3 1 
 
 16 
 
 2' 
 
 806.95 
 
 1598.1 
 
 56.55 
 
 2' 
 
 4' 
 
 808.65 
 
 1601 .4 
 
 56.80 
 
 4' 
 
 6' 
 
 810.35 
 
 1604. 7 
 
 57.03 
 
 6' 
 
 8' 
 
 812 . 05 
 
 1608 .0 
 
 57.27 
 
 8' 
 
 10' 
 
 813.75 
 
 1611.3 
 
 57-5 
 
 10' 
 
 12' 
 
 815-45 
 
 1614 .6 
 
 57-74 
 
 12' 
 
 14' 
 
 817.15 
 
 1617.9 
 
 57-98 
 
 14' 
 
 16' 
 
 818.85 
 
 l62I .2 
 
 58.22 
 
 16' 
 
 18' 
 
 820 55 
 
 1624.5 
 
 58.46 
 
 18' 
 
 20' 
 
 822 .25 4 
 
 1627.8 
 
 58-70 
 
 20' 
 
 22' 
 
 823.95 6 
 
 1631 .1 
 
 58.95 
 
 22' 
 
 24' 
 
 825.65 
 
 1634.4 
 
 59.20 
 
 24' 
 
 26' 
 
 827.35 1 
 
 1637.7 
 
 59-43 
 
 26' 
 
 28' 
 
 820.06 'a 
 a: 
 
 1641 .O 
 
 59.67 
 
 28' 
 
 3o' 
 
 830.76 
 
 1644.3 
 
 59-9 1 
 
 30' 
 
 32' 
 
 832.46 ^ 
 
 1647 -6 
 
 60 . 16 
 
 32' 
 
 34' 
 
 834-16 . .5 
 
 1650.9 
 
 60.40 ^4 
 
 34' 
 
 36' 
 
 835.86--- 
 
 1654.2 
 
 60.65 
 
 36' 
 
 38' 
 
 S37.56:| 
 
 J657-5 
 
 60 .90 ^ : - 
 
 38' 
 
 40' 
 
 839.27?. 
 
 1660.8 
 
 61 . 14 ^ 
 
 40' 
 
 42' 
 
 840. 97 |T 
 
 1664. i 
 
 6l -39|< : " 
 
 42' 
 
 44' 
 
 842 .67 t^ 
 
 1667 .4 
 
 61 .64 v. 
 
 44' 
 
 46' 
 
 844. 3 7^0 . 
 
 1670.7 
 
 61.89^^ 
 
 46' 
 
 48' 
 
 846 . 07 6 6 -t 
 
 1674 .0 
 
 62 . 14 oi t^vc' 
 
 48' 
 
 50' 
 
 847-78^ 
 
 1677-3 
 
 02 .38 ^ 
 
 50' 
 
 52' 
 
 849.483- 5; 
 
 1680.6 
 
 62 .63 <T 
 
 52' 
 
 54' 
 
 851. 18^ | 
 
 1683.9 
 
 62.88 
 
 54' 
 
 56' 
 
 852.88 
 
 1687.2 
 
 63-13 
 
 56' 
 
 58' 
 
 854.59 j 
 
 1690.5 
 
 63.38 
 
 58' 
 
 17 
 
 856.30 
 
 1693.8 
 
 63-63 
 
 17 
 
 2' 
 
 858.00 o 
 
 1697.1 
 
 63.88 
 
 2' 
 
 4' 
 
 859.70 
 
 1700 .4 
 
 64.13 
 
 4' 
 
 6' 
 
 861.41 5 
 
 1703-7 
 
 64-38 
 
 6' 
 
 8' 
 
 863.11 
 
 1707.0 
 
 64.64 
 
 8' 
 
 10' 
 
 864.82 
 
 1710.3 
 
 64 . 90 
 
 10' 
 
 12' 
 
 866.52 
 
 1713.6 
 
 65.16 
 
 12' 
 
 14' 
 
 868.23 
 
 1716.9 
 
 6s .42 
 
 14' 
 
 16' 
 
 869.93 
 
 i 7^o . 2 
 
 65.68 
 
 16' 
 
 18' 
 
 871.64 
 
 1723- 4 
 
 65-93 
 
 18' 
 
 20' 
 
 873-35 
 
 1726.7 
 
 66.18 
 
 20' 
 
 22' 
 
 875-05 
 
 1730.0 
 
 66.43 
 
 22' 
 
 24' 
 
 876.76 
 
 1733-3 
 
 66.68 
 
 24' 
 
 26' 
 
 878.46 
 
 1736.6 
 
 66.95 
 
 26' 
 
 28' 
 
 880. 17 
 
 1739-9 
 
 67.23 
 
 28' 
 
 56 
 
IX. FUNCTIONS OF A ONE-DEGREE CURVE. 
 
 Whole 
 Angle. 
 
 Tangent 
 Distance. 
 
 Long 
 Chord. 
 
 External 
 Secant. 
 
 Whole 
 Angle. 
 
 17 30' 
 
 881.88 
 
 *743-2 
 
 67.47 
 
 17 30' 
 
 3 2 ' 
 
 883.58 
 
 1746.5 
 
 
 3 2 ' 
 
 34' 
 
 885.29 . . 
 
 1749.8 
 
 68.00 
 
 34' 
 
 36' 
 
 886.99 a ? 
 
 *753-* 
 
 68.25 
 
 36' 
 
 38' 
 
 888.70 c. 
 
 1756.4 
 
 68.50 
 
 38' 
 
 40' 
 
 890.41 -g 
 
 *759-7 
 
 68.77 
 
 40' 
 
 42' 
 
 892 .11 - 
 
 1763.0 
 
 69.03 
 
 42' 
 
 44' 
 
 893.82 * 
 
 1766.2 
 
 69-30 
 
 44' 
 
 46' 
 
 895.53 : 
 
 I769-5 
 
 69-56 
 
 46' 
 
 48 r 
 
 897.24 ?<>. 
 
 1772.8 
 
 69.82 
 
 48' 
 
 50' 
 
 898:95 3R 
 
 1776.1 
 
 70.09 
 
 5' 
 
 52' 
 
 900.66 ?- 
 
 1779.4 
 
 70.36 
 
 52' 
 
 54' 
 
 902-37 "*' 
 
 1782.7 
 
 70.63 
 
 54' 
 
 56' 
 
 904.08 
 
 1786.0 
 
 70.90 
 
 56 
 
 58' 
 
 905-79 
 
 1789.3 
 
 71.17 
 
 58' 
 
 18 
 
 907.49 
 
 1792.6 
 
 7* -42 
 
 18 
 
 2'* 
 
 909 . 2O 
 
 1795-9 
 
 71.68 
 
 2' 
 
 4' 
 
 910.91 4 
 
 1799.2 
 
 7*-95 
 
 4' 
 
 6' 
 
 912 .62 
 
 1802 .5 
 
 72.22 iA 4 
 
 6' 
 
 8' 
 
 9*4-33 & 
 
 1805.8 
 
 7 2 .49 -_ f 
 
 8' 
 
 TO' 
 
 916.03 ** 
 
 1809. I 
 
 72 . 76 ^ 
 
 10' 
 
 12' 
 
 9*7-74 $ 
 
 1812 .4 
 
 73 . 03 ^.^ 
 
 12' 
 
 14' 
 
 9*9-45 fc 
 
 I8I5.7 
 
 73.30^ " 
 
 14' 
 
 16' 
 
 921 . 16 
 
 1819.0 
 
 73.58 fe: . 
 
 16' 
 
 18' 
 
 922.87 
 
 1822.2 
 
 73.86^ 
 
 18' 
 
 20' 
 
 924.581 - 
 
 1825-5 
 
 74.12 ^^ 
 
 20' 
 
 22' 
 
 926 . 29 I2T J2 
 
 1828.8 
 
 74.40?, , 
 
 22' 
 
 24' 
 
 928.00^ 
 
 1832.1 
 
 74.67^ 
 
 24' 
 
 26' 
 
 929.71 -a : 
 
 I835.4 
 
 74.94 
 
 26' 
 
 28' 
 
 931-42^ 
 
 1838.7 
 
 75.22 
 
 28' 
 
 30' 
 
 933.13 ^~ 
 
 1842 .0 
 
 75-49 
 
 30' 
 
 32' 
 
 934.84 c ~4 
 
 1845-3 
 
 75-76 
 
 3 2/ 
 
 34' 
 
 936.55 * W 6 
 
 1848.6 
 
 76.03 
 
 34' 
 
 36' 
 
 938.26 -0: ^ 
 
 1851.9 
 
 76.30 
 
 36' 
 
 38' 
 
 939- 98 < 
 
 1855.2 
 
 76-58 
 
 38' 
 
 40' 
 
 941-69 
 
 1858.5 
 
 76.87 
 
 40' 
 
 42' 
 
 943.40 J5 
 
 1861.8 
 
 77 *5 
 
 42' 
 
 44' 
 
 945 * * 
 
 1865.1 
 
 77-43 
 
 44' 
 
 46' 
 
 946.82 
 
 1868.4 
 
 77-7o 
 
 46' 
 
 48' 
 
 948.53 
 
 1871.7 
 
 77.98 
 
 48' 
 
 50' 
 
 950.25 3 
 
 1875-0 
 
 78.26 
 
 50' 
 
 52' 
 
 95L96 
 
 1878.3 
 
 78.55 
 
 52' 
 
 54'. 
 
 953 -67 
 
 1881.6 
 
 78.84 
 
 54' 
 
 56' 
 
 955-39 
 
 1884.9 
 
 79-*3 
 
 56' 
 
 58' 
 
 957-10 
 
 1888.2 
 
 79.40 
 
 58' 
 
 57 
 
IX. FUNCTIONS OF A ONE-DEGREE CURVE. 
 
 Whole 
 Angle. 
 
 Tangent 
 Distance. 
 
 Long 
 Chord. 
 
 External 
 Secant. 
 
 Whole 
 Angle. 
 
 19 
 
 958.81 
 
 1891 .4 
 
 79.67 
 
 19 
 
 2' 
 
 960.52 
 
 1894.7 
 
 79-95 
 
 2> 
 
 4' 
 
 962.23 
 
 1898.0 
 
 80 . 24 
 
 4' 
 
 6' 
 
 963-95 
 
 1901 . 2 
 
 80.52 
 
 6' 
 
 8' 
 
 965.67 
 
 1904.5 
 
 80.80 
 
 8' 
 
 10' 
 
 967.38 
 
 1907 .8 
 
 81 .09 
 
 10' 
 
 12' 
 
 969. 10 
 
 1911 . i 
 
 8i.37 
 
 12' 
 
 14' 
 
 970.82 
 
 1914.4 
 
 81.66 
 
 14' 
 
 16' 
 
 972.53 
 
 1917.7 
 
 81.95 
 
 16' 
 
 i$ f 
 
 974.24 
 
 1921 .0 
 
 82.23 
 
 18' 
 
 20' 
 
 10 Qv TJ- 
 
 975-95 
 
 1924 . 2 
 
 82.52 
 
 20' 
 
 22' 
 
 977.66: : 
 
 I927-5 
 
 82 .80 
 
 22' 
 
 24' 
 
 979-38- 
 
 1930 .8 
 
 83.09 
 
 24' 
 
 26' 
 
 981.09.^: : 
 
 1934.0 
 
 83-38 
 
 26' 
 
 28' 
 
 982.81 & 
 
 1937-3 
 
 83-67 
 
 28' 
 
 30' 
 
 984- 53 & : 
 
 1940.6 
 
 83.97 
 
 30' 
 
 32' 
 
 986.24 r~* 
 
 1943-9 
 
 84.26 
 
 32' 
 
 34 
 
 987.96 3 
 
 1947.2 
 
 84-55 
 
 34' 
 
 36' 
 
 989-675. . 
 
 !95 -5 
 
 84 84 *r> O* *t 
 
 36' 
 
 38' 
 
 99*-39< 
 
 1953-8 
 
 85.13 6 _ W 
 
 38' 
 
 40' 
 
 993 - 11 
 
 I 957- 1 
 
 85.43S"~ 
 
 40' 
 
 42' 
 
 994.83 
 
 1960.4 
 
 85-72 | : , 
 
 42' 
 
 44' 
 
 996.55 
 
 1963 .6 
 
 86.oi 
 
 44' 
 
 46' 
 
 998 . 26 
 
 1966 .9 
 
 86.30 fc. . 
 
 46' 
 
 48' 
 
 999.98 
 
 1970.2 
 
 B6v6--5^u 
 
 48' 
 
 50' 
 
 1001 . 70 
 
 1973-5 
 
 86.90 "^ 
 
 50' 
 
 52' 
 
 1003.42 
 
 1976.8 
 
 87-20^, : 
 
 52' 
 
 54' 
 
 1005.13 
 
 1980. i 
 
 87.50^ 
 
 54' 
 
 56' 
 
 1006.85 
 
 1983-3 
 
 87.80 
 
 56' 
 
 58' 
 
 1008 . 56 
 
 1986.6 
 
 88.10 
 
 58' 
 
 2O 
 
 1010.3 
 
 1989.9 
 
 88.39 
 
 2O 
 
 2' 
 
 IOI2 . I 
 
 1993.2 
 
 88.69 
 
 2' 
 
 4' 
 
 IOI3.8 ^j 
 
 1996.5 
 
 88.99 
 
 4' 
 
 6' 
 
 IOI5-5 6- 6 
 
 1999.7 
 
 89.29 
 
 6' 
 
 8' 
 
 1017.3 " ^ 
 
 2003 .0 
 
 89.59 
 
 8' 
 
 10' 
 
 1018.9 |= 4 
 
 2006 .3 
 
 89.89 
 
 10' 
 
 12' 
 
 1020.6 <n w 
 
 2009 .6 
 
 90.19 
 
 12' 
 
 14' 
 
 1022 .3 J3: J5 
 
 2012 .9 
 
 90.49 
 
 14' 
 
 16' 
 
 1024.0 ^l q 
 
 2Ol6 . I 
 
 90.80 
 
 16' 
 
 18' 
 
 iO2c; .7 S,^ S 
 
 ' cV^-R 
 
 2OI9 .4 
 
 91 . 10 
 
 18' 
 
 20' 
 
 1027.5 5^ 
 
 2O22 . 7 
 
 91.40 
 
 20' 
 
 22' 
 
 1029.2 < 
 
 2026 . o 
 
 91.70 
 
 22' 
 
 24' 
 
 1031 .0 
 
 2029.3 
 
 92 .00 
 
 24' 
 
 26' 
 
 1032.7 
 
 2032.5 
 
 92.30 
 
 26' 
 
 28' 
 
 1034.4 
 
 2035.8 
 
 92 .61 
 
 28' 
 
 58 
 
IX. FUNCTIONS OF A ONE-DEGREE CURVE. 
 
 Whole 
 Angle. 
 
 Tangent 
 Distance. 
 
 Long 
 Chord. 
 
 External 
 Secant. 
 
 Whole 
 Angle. 
 
 20 30' 
 
 1036.1 
 
 2039.1 
 
 92 .92 
 
 20 30' 
 
 32' 
 
 1037.8 
 
 2042 .4 
 
 93-23 
 
 32' 
 
 34' 
 
 1039-5 
 
 2045-7 
 
 93-53 
 
 34' 
 
 36' 
 
 1041.3 
 
 2049 .0 
 
 93-84 
 
 36' 
 
 38' 
 
 1043.0 
 
 2O52 . 2 
 
 94-15 
 
 38' 
 
 40' 
 
 1044.7 
 
 2055-5 
 
 94.46 
 
 40' 
 
 42' 
 
 1046.3 
 
 2058.8 
 
 94-77 
 
 42' 
 
 44' 
 
 1048 .0 
 
 2O62 . I 
 
 95-o8 
 
 44' 
 
 46' 
 
 1049.7 
 
 2065 .4 
 
 95-40 
 
 46' 
 
 48' 
 
 1051-5 
 
 2068.6 
 
 95-7 1 
 
 48' 
 
 So' 
 
 1053-3 
 
 2071.9 
 
 96.02 
 
 5 ^ 
 
 $*' 
 
 1055.0 
 
 2075.2 
 
 96.34 
 
 52' 
 
 54' 
 
 1056.7 
 
 2078.5 
 
 96.66 
 
 54' 
 
 56' 
 
 1058.4 
 
 2081 .7 
 
 96.97 
 
 56' 
 
 58' 
 
 IO6O . 2 
 
 2085 .O 
 
 97.28 
 
 58' 
 
 21 
 
 1061 .9 . 
 
 2088.3 
 
 97.58 
 
 21 
 
 2' 
 
 1063 .6 
 
 2091 .6 
 
 97.90 
 
 2' 
 
 4' 
 
 1065.3 . 
 
 2094.9 
 
 98.22 
 
 4' 
 
 6' 
 
 1067.0 1 *? 
 
 2098. i 
 
 98.54 ^c-,4 
 
 6' 
 
 8' 
 
 1068.8 d : : 
 
 2101 .4 
 
 98.85 -. : 
 
 8' 
 
 10' 
 
 I0 7o.5^ 
 
 2104.7 
 
 99.16^ 
 
 10' 
 
 12' 
 
 1072.2.*: : 
 
 2IO8 .O 
 
 99-47 -i=: : 
 
 12' 
 
 1.4' 
 
 1073. 9 co 
 
 2III . 2 
 
 99 -78 co 
 
 14' 
 
 16' 
 
 1075.7.0= = 
 
 2II4.5 
 
 100.09 J5: : 
 
 16' 
 
 18' 
 
 I0 77-4 *p;j 
 
 2II7.8 
 
 IOO . 42 o f^o 
 
 18' 
 
 20' 
 
 o 
 
 1079. 1 t- 
 
 2121 . I 
 
 100.75 *^ 
 
 20' 
 
 22' 
 
 1080.8^, : 
 
 2124.4 
 
 IOI .06 *d: : 
 
 22' 
 
 24' 
 
 1082. 5<r " 
 
 2127.7 
 
 101.38* 
 
 24' 
 
 26' 
 
 1084.3 
 
 2131 .0 
 
 101 . 70 
 
 26' 
 
 28' 
 
 1086 .0 
 
 2134.2 
 
 IO2 .02 
 
 28' 
 
 30' 
 
 1087 .8 
 
 2*37-5 
 
 102.35 
 
 30; 
 
 32' 
 
 1089.5 
 
 2140 .8 
 
 102 .67 
 
 32 
 
 3 < 
 
 IO9I . 2 
 
 2144.1 
 
 103 .00 
 
 34 
 
 36 
 
 I 093 r O 
 
 2147.4 
 
 103.32 
 
 36 
 
 38' 
 
 1094.7 
 
 2150 .6 
 
 103.64 
 
 38' 
 
 40' 
 
 1096 .4 
 
 2153-9 
 
 103.97 
 
 40' 
 
 42' 
 
 1098. I 
 
 2157.2 
 
 104.30 
 
 42' 
 
 44' 
 
 1099.9 
 
 2160 .4 
 
 104.62 
 
 44' 
 
 46' 
 
 noi .6 
 
 2163.7 
 
 104.94 
 
 46' 
 
 48' 
 
 1103.3 
 
 2167 .0 
 
 105.27 
 
 48' 
 
 5 ; 
 
 1105.1 
 
 2I7O . 2 
 
 IO5 .60 
 
 5 ; 
 
 52 
 
 1106 . 9 
 
 2173-5 
 
 105.93 
 
 52 
 
 54' 
 
 1108.6 
 
 2176.8 
 
 106 . 26 
 
 54 
 
 56' 
 
 1110.3 
 
 2l8o .O 
 
 106 .60 
 
 56' 
 
 58-' 
 
 III2 .O 
 
 2183.3 
 
 106 92 
 
 & 
 
IX. FUNCTIONS OF A ONE-DEGREE CURVE. 
 
 Whole 
 Angle. 
 
 Tangent 
 Distance. 
 
 Long 
 Chord. 
 
 External 
 Secant. 
 
 Whole 
 Angle. 
 
 22 
 
 1113.7 
 
 2186.6 
 
 IO7 .2 
 
 22 
 
 2' 
 
 1115.4 
 
 2189 .9 
 
 107.5 
 
 2' 
 
 4' 
 
 III7.2 ^ 2193 . 2 
 
 107.9 
 
 4' 
 
 6' 
 
 IIl8.9 ^ 2196.4 
 
 108.2 
 
 6' 
 
 8' 
 
 1120 .6 ^ 2199 . 7 
 
 108.6 
 
 8' 
 
 10' 
 
 1122.3 * 
 
 2202 .9 
 
 108.9 
 
 10' 
 
 12' 
 
 1124.0 '5. 
 
 22O6 . 2 
 
 109.3 
 
 12' 
 
 14' 
 
 1125 .8 C 2209 . 5 
 
 109 .6 
 
 14' 
 
 16' 
 
 1127.5 2212.7 
 
 no .0 
 
 16' 
 
 18' 
 
 1129.2 2216.0 
 
 o ! 
 
 110.3 
 
 18' 
 
 20' 
 
 
 2219.3 
 
 no .6 
 
 20' 
 
 22' 
 
 II32.7 | 
 
 2222 .6 
 
 110.9 
 
 22' 
 
 24' 
 
 II34-5 
 
 2225.8 
 
 111.3 
 
 24' 
 
 26' 
 
 II36.2 
 
 2229 . I 
 
 in .6 
 
 26' 
 
 28' 
 
 II38.0 
 
 2232 .4 
 
 112 .O 
 
 28' 
 
 3 0/ 
 
 H39-7 
 
 2235.6 
 
 112.3 
 
 3' 
 
 32' 
 
 1141 .3 
 
 2238.9 
 
 112 .6 
 
 32' 
 
 34 r 
 
 1143.0 ^&* 
 
 2242 . I 
 
 113.0 
 
 34' 
 
 36' 
 
 1144.8 -_ , 
 
 2245.4 
 
 113-3 ^ d z 
 
 36' 
 
 38' 
 
 1146.6 ~ 
 
 2248 . 7 
 
 II3-7 6. : 
 
 38' 
 
 40' 
 
 1148 .4 .: ; 
 
 o<~ 
 
 2252 .0 
 
 114-0^" " 
 
 40' 
 
 42' 
 
 1150 . i co 
 
 2255.3 
 
 114 . 3 .; ^ 
 
 42' 
 
 44' 
 
 1151 .80:: 
 
 2258.5 
 
 114.6 co 
 
 44' 
 
 46' 
 
 1153 .6 U-, Tj-10 
 
 2261.8 
 
 II5.,0: = 
 
 46' 
 
 48' 
 
 ii55-3 S 
 
 2265 . i 
 
 II5.3 o t vq 
 
 48' 
 
 5o; 
 
 1157.0 -d * 
 
 2268.3 
 
 11$. J " 
 
 50' 
 
 
 II58.83J 2 " 
 
 2271 . 6 
 
 1 16 . o o- ^ 
 
 52' 
 
 54' 
 
 1160 . 5 
 
 2274.9 
 
 116.4^ 
 
 54' 
 
 56' 
 
 1162.3 
 
 2278. 2 
 
 116. 7 
 
 56' 
 
 58' 
 
 1164.0 
 
 2281.5 
 
 117.0 
 
 58' 
 
 23 
 
 1165.7 
 
 2284.7 
 
 117.4 
 
 23 
 
 2' 
 
 1167.4 
 
 2288.0 
 
 117.7 
 
 2' 
 
 4' 
 
 ii$9 . i * 
 
 2291 . 2 
 
 118.1 
 
 4' 
 
 6' 
 
 1190.9 c 
 
 2294.5 
 
 118.4 
 
 6' 
 
 8' 
 
 11^2.6 ^ 
 
 2297.7 
 
 118.7 
 
 8' 
 
 10' 
 
 H74.3 -g, 
 
 2301 .0 
 
 119.1 
 
 10' 
 
 12' 
 
 1176 .0 co 
 
 2304.3 
 
 119.4 
 
 12' 
 
 14' 
 
 1177.8 ,0 
 
 2307.5 
 
 119.7 
 
 14' 
 
 1 6' 
 
 1179.6 
 
 2310.8 
 
 I2O . I 
 
 16' 
 
 18' 
 
 Il8 i.3 | 
 
 2314.0 
 
 120.5 
 
 i8 7 
 
 20' 
 
 1183.0 g 
 
 2317.3 
 
 120 . 9 
 
 20' 
 
 22' 
 
 1184.8 < 
 
 2320 .6 
 
 121 . 2 
 
 22' 
 
 24' 
 
 1186.5 
 
 2323-8 
 
 121 .6 
 
 24' 
 
 26' 
 
 1188.3 
 
 2327.1 
 
 I2I-9 
 
 26' 
 
 28' 
 
 1190 .0 
 
 2330.4 122.3 
 
 28' 
 
 60 
 
IX. FUNCTIONS OF A ONE-DEGREE CURVE. 
 
 Whole 
 Angle. 
 
 Tangent 
 Distance. 
 
 Long 
 Chord. 
 
 External 
 Secant. 
 
 Whole 
 Angle. 
 
 23 30' 
 
 1191.7 
 
 2333-6 
 
 122 .6 
 
 23 30' 
 
 32' 
 
 II93-5 2336.9 
 
 123.0 
 
 32; 
 
 34' 
 
 1195.2 2340.2 
 
 123-3 
 
 34 
 
 36' 
 
 1197.0 
 
 2343-5 
 
 123-7 
 
 36' 
 
 38' 
 
 1198.7 
 
 2346.7 
 
 I24.O 
 
 38' 
 
 40' 
 
 I2OO .4 
 
 2349.9 
 
 124.4 
 
 40' 
 
 42' 
 
 I2O2 . 2 
 
 2353.2 
 
 124.7 
 
 42' 
 
 44' 
 
 1203.9 
 
 2356.4 
 
 125.0 
 
 44' 
 
 46' 
 
 1205.7 
 
 2359-7 
 
 125.4 
 
 46' 
 
 48' 
 
 1207.4 
 
 2363-0 
 
 125.8 
 
 48' 
 
 50' 
 
 1209.1 4 
 
 2366 . 2 
 
 126 . 2 
 
 50' 
 
 52' 
 
 1210.9 
 
 2369 . 5 
 
 126.5 
 
 52' 
 
 54' 
 
 1212 .6 
 
 2372.7 
 
 126 .9 
 
 54' 
 
 56' 
 
 I2I4.4 -g 
 
 2376.0 
 
 127 .2 
 
 56' 
 
 58' 
 
 I2I6.I 
 
 2379.2 
 
 127 .6 
 
 58' 
 
 24 
 
 03 
 1217.9 fc 
 
 2382.5 
 
 128.0 
 
 24 
 
 2' 
 
 1219.6 
 
 2385-8 
 
 128.3 
 
 2' 
 
 4' 
 
 I22I.4 N ' 
 
 2389.1 
 
 128.7 
 
 4' 
 
 6' 
 
 I223.I ^ 
 
 2392.3 
 
 129 .O ^G"'* 
 
 6' 
 
 8' 
 
 1224.9 j: T3 
 
 2395-6 
 
 129 .4 6- - 
 
 8' 
 
 10' 
 
 1226 .6 "g 
 
 2398.8 
 
 129.8 J 
 
 10' 
 
 12' 
 
 1228.3 -a 3 
 
 2402 . I 
 
 130.1 .: : 
 
 12' 
 
 14' 
 
 I230.I u 
 
 2405.3 
 
 130.5^ 
 
 14' 
 
 16' 
 
 1231.8-2^ 
 
 2408 .6 
 
 130.8^ = 
 
 16' 
 
 18' 
 
 1233-5 OM4 
 
 2411 .8 
 
 131 * 2 1; 25 
 
 18' 
 
 20' 
 
 I2 35 -3 " "*6 
 
 2415.1 
 
 131 .6 _ M 
 
 20' 
 
 22' 
 
 1237- I 5 
 
 2418.4 
 
 132.05: - 
 
 22' 
 
 24' | 1238.8^ 2 
 
 2421 .6 
 
 132.3 ' 
 
 24' 
 
 26' 
 
 1240.5 
 
 2424.9 
 
 132,7 
 
 26' 
 
 28' 
 
 1242.2 g 
 
 2428 . i 
 
 J 33- I 
 
 28' 
 
 30' 
 
 1244.0 r 
 
 2431.4 
 
 133-5 
 
 30' 
 
 32' 
 
 1245.7 o 
 
 2434-7 
 
 133-8 
 
 32' 
 
 34' 
 
 1247.5 -a 
 
 2437-9 
 
 134-2 
 
 34'. 
 
 36' 
 
 1249-3 3 
 
 2441.2 
 
 134.6 
 
 36; 
 
 38' 
 
 1251 .0 
 
 2444.4 
 
 i35-o 
 
 38' 
 
 4' 
 
 1252.7 
 
 2447.7 
 
 135-4 
 
 40' 
 
 42' 
 
 I2 54-5 
 
 2451.0 
 
 135-8 
 
 42' 
 
 44' 
 
 1256.3 
 
 2454.2 
 
 136.2 
 
 44' 
 
 46' 
 
 1258.0 
 
 2457-5 
 
 136-5 
 
 46' 
 
 48' 
 
 1259-7 
 
 2460 . 8 
 
 136.9 
 
 48' 
 
 5' 
 
 1261 .4 
 
 2464 .0 
 
 137.2 
 
 5 0/ 
 
 52' 
 
 1263 2 
 
 2467.3 
 
 137-6 
 
 52/ , 
 
 54' 
 
 1265 .O 
 
 2470.5 
 
 138.0 
 
 54 
 
 56' 
 
 1266 . 7 
 
 2473.8 
 
 138.3 
 
 56 
 
 58' 
 
 1268.5 
 
 2477.0 
 
 138.7 
 
 58' 
 
 61 
 
IX. FUNCTIONS OF A ONE-DEGREE CURVE. 
 
 Whole 
 Angle. 
 
 Tangent 
 Distance. 
 
 Long 
 Chord. 
 
 External 
 Secant. 
 
 Whole 
 Angle. 
 
 25 
 
 1270 . 2 
 
 2480 . 2 
 
 I 39- 1 
 
 25 
 
 2 f 
 
 1272 .0 
 
 2483-5 
 
 J 39-5 
 
 2' 
 
 4' 
 
 1273-7 
 
 2486.7 
 
 139-9 
 
 4' 
 
 6' 
 
 I2 75-5 
 
 2490 .0 
 
 140.2 
 
 6' 
 
 8' 
 
 1277.2 
 
 2493.2 
 
 140 .6 
 
 8' 
 
 10' 
 
 1278.9 
 
 2496.4 
 
 141 .0 
 
 10' 
 
 12' 
 
 1280 . 7 
 
 2499.7 
 
 141 .4 
 
 12' 
 
 14' 
 
 1282 .4 
 
 2502.9 
 
 141 .8 
 
 14' 
 
 16' 
 
 1284.2 
 
 2506 . 2 
 
 142 . 2 
 
 16' 
 
 18' 
 
 1286.0 
 
 2 509-5 
 
 142 .6 
 
 18' 
 
 20' 
 
 1287 . 7 10 o4 
 
 2512.7 
 
 142 .9 
 
 20' 
 
 22' 
 
 I28 9-5 c- . 
 
 2516.0 
 
 143-3 
 
 22' 
 
 24' 
 
 1291 . 2 X" " 
 
 2519.2 
 
 
 24' 
 
 26' 
 
 I293.0rt 
 
 2522.5 
 
 144.0 
 
 26' 
 
 28' 
 
 1294.8 == 
 
 
 144.4 
 
 28' 
 
 3o' 
 
 1296 . 5 . , 
 
 2529 .O 
 
 144.8 
 
 3 O/ 
 
 32' 
 
 I2 9 8.3^Voo 
 
 2532.3 
 
 145.2 
 
 32' 
 
 34' 
 
 1300.0 M CJ 
 
 2535-5 
 
 145.6 
 
 34' 
 
 36' 
 
 1301.8^^ 
 
 2538.8 
 
 146 .0 "> <*;* 
 
 36' 
 
 38' 
 
 
 2542.0 
 
 146.4 6. . 
 
 38' 
 
 40' 
 
 1305.2 
 
 2545-2 
 
 146.8^ 
 
 40' 
 
 42' 
 
 1307.0 
 
 2548.5 
 
 147-2-g: : 
 
 42' 
 
 44' 
 
 1308.7 
 
 255J-7 
 
 147 .6 <n 
 
 44' 
 
 46' 
 
 1310 . 5 
 
 2555-o 
 
 148.0,0: : 
 
 46' 
 
 48' 
 
 1312.2 
 
 2558-2 
 
 148 .4 TjT- 
 
 48' 
 
 
 
 
 CS t^O 
 
 
 5' 
 
 1314.0 
 
 2561.4 
 
 148.8^ - 
 
 50' 
 
 52 ', 
 
 1315.7 
 
 2564-7 
 
 149.2 ^: : 
 
 52' 
 
 54' 
 
 1317 . 5 
 
 2567.9 
 
 149.6 " 
 
 54' 
 
 56' 
 
 1319.2 
 
 2571.2 
 
 150.0 
 
 56' 
 
 58' 
 
 1321.0 
 
 2574-4 
 
 150.4 
 
 58' 
 
 2 
 
 1322.8 
 
 2577-7 
 
 I 57 
 
 26 
 
 2' 
 
 1324.5 >Ao4 
 
 2581 .0 
 
 151.1 
 
 2' 
 
 4' 
 
 1326.3 
 
 2584.2 
 
 I 5 I -5 
 
 4 f 
 
 6' 
 
 1328.1 55- = 
 
 2587-5 
 
 i5i-9 
 
 6' 
 
 8' 
 
 1329.8-3 
 
 2590.7 
 
 152.3 
 
 8' 
 
 10' 
 
 I 33 I -5 : : 
 
 2593-9 
 
 152.7 
 
 10' 
 
 12' 
 
 J 333-2 g. , 
 
 2597.2 
 
 i53.i 
 
 12' 
 
 14' 
 
 i335-o-" ^ 
 
 2600 .4 
 
 J 53-5 
 
 14' 
 
 16' 
 
 1336.7 6*? 
 
 2603.7 
 
 
 16' 
 
 18' 
 
 1338. 5|3 
 
 2607 .0 
 
 154.3 
 
 18' 
 
 20' 
 
 1340.3 |: : 
 
 26lO . 2 
 
 154.7 
 
 20' 
 
 22' 
 
 1342.0 ' 
 
 2613.5 
 
 
 22' 
 
 24' 
 
 1343-8 
 
 26l6.8 
 
 J 55-5 
 
 24' 
 
 26' 
 
 1345-6 
 
 262O .O 
 
 155 .9 
 
 26' 
 
 28' 
 
 1347-4 
 
 2623 . 2 
 
 156.3 
 
 28' 
 
IX. FUNCTIONS OF A ONE-DEGREE CURV 
 
 'E. 
 
 Whole 
 Angle. 
 
 Tangent 
 Distance. 
 
 Long 
 Chord. 
 
 External 
 Secant. 
 
 Whole 
 Angle. 
 
 26 30' 
 
 I349- 1 
 
 2626 .4 
 
 156.7 
 
 26 30' 
 
 32' 
 
 I350-9 
 
 2629.7 
 
 I57-I 
 
 32' 
 
 34' 
 
 l35 2 -7 
 
 2632.9 
 
 157-5 
 
 34' 
 
 36' 
 
 1354-4 
 
 2636 . I 
 
 157-9 
 
 36' 
 
 38' 
 
 KSS 6 - 2 
 
 2639.4 
 
 158.3 
 
 38' 
 
 40' 
 
 1357-9 
 
 2642 .6 
 
 158.7 
 
 40' 
 
 42' 
 
 1359-7 
 
 2645.9 
 
 I59- 1 
 
 42' 
 
 44' 
 
 !36i.5 
 
 2649. J 
 
 159-5 
 
 44' 
 
 46' 
 
 1363.2 
 
 2652.4 
 
 160 .0 
 
 46' 
 
 48' 
 
 1365-0 
 
 2655.6 
 
 160 .4 
 
 48' 
 
 5 0/ 
 
 1366.7 4 
 
 2658.9 
 
 160.8 
 
 50' 
 
 5 2 ' 
 
 1368.5 
 
 2662 .2 
 
 161 . 2 
 
 52' 
 
 54' 
 
 1370-2 
 
 2665 .4 
 
 161.6 
 
 54' 
 
 56' 
 
 i372.o -3 
 
 2668.7 
 
 162 .0 
 
 56' 
 
 58' 
 
 1373-8 
 
 2671.9 
 
 162 .4 
 
 58' 
 
 27 
 
 K) 
 
 1375-5 * 
 
 2675.1 
 
 162.8 
 
 27 
 
 2' 
 
 1377-3 * 
 
 2678.4 
 
 163.2 
 
 2' 
 
 4' 
 
 1379.0 * 
 
 2681.6 
 
 I6 3.6^ 4 
 
 4' 
 
 6' 
 
 1380.8 AdR 
 
 2684.9 
 
 164.0 
 
 6' 
 
 8' 
 
 1382.6 c : ; 
 
 2688.1 
 
 164.5!- : 
 
 8' 
 
 10' 
 
 1384.4^ ^ 
 
 2691 .3 
 
 164. 9g 
 
 10' 
 
 12' 
 
 1386.2-^ 
 
 2694 .6 
 
 165. 3 -a' : 
 
 12' 
 
 14' 
 
 1388.0^ 
 
 2697.8 
 
 165.7^. 
 
 14' 
 
 16' 
 
 13*6*7-* 
 
 2701 . i 
 
 166.1 - - 
 
 1 6' 
 
 18' 
 
 i39i.5]^4 
 
 2704.3 
 
 166.5-- 25 
 
 18' 
 
 20' 
 
 1393-2 j^d 
 
 2707.5 
 
 166 .9 ^d 
 
 20' 
 
 22' 
 
 1395-03: Jz: 
 
 2710 .8 
 
 167. 4<~ : 
 
 22' 
 
 24' 
 
 1396.7^ g 
 
 2714.0 
 
 167.8 
 
 24' 
 
 26' 
 
 J 398-5 i| 
 
 2717.2 
 
 168.2 
 
 26' 
 
 28' 
 
 1400.3 ^ 
 
 2720.4 
 
 168.6 
 
 28' 
 
 30' 
 
 1402.0 ^ 
 
 2723.6 
 
 169 .0 
 
 30' 
 
 32' 
 
 1403.8 ? 
 
 2726.8 
 
 169.4 
 
 32' 
 
 34' 
 
 J 405.6 ^ 
 
 2730.0 
 
 169.8 
 
 34' 
 
 36' 
 
 I 47-3 ^ 
 
 2733-3 
 
 170.3 
 
 36' 
 
 38' 
 
 1409. i 
 
 2736.5 
 
 170.7 
 
 38' 
 
 40' 
 
 1410.8 
 
 2739.8 
 
 171.1 
 
 40' 
 
 42' 
 
 1412 .6 
 
 2743.0 
 
 171.6 
 
 42' 
 
 44' 
 
 1414.4 
 
 2746.3 
 
 172 .0 
 
 44' 
 
 46' 
 
 1416 . i 
 
 2749-5 
 
 172.4 
 
 46' 
 
 48' 
 
 1417.8 
 
 2752.7 
 
 172.9 
 
 48' 
 
 5 : 
 
 1419.6 
 
 2756.0 
 
 !73-3 
 
 5' 
 
 5* 
 
 1421.4 
 
 2759.2 
 
 173.7 
 
 52' 
 
 54 
 
 1423.1 
 
 2762 .5 
 
 174.2 
 
 54' 
 
 56' 
 
 1424.9 
 
 2765.8 
 
 174.6 
 
 56' 
 
 58' 
 
 1426.7 
 
 2769 .0 
 
 175-0 
 
 58' 
 
 63 
 
IX. FUNCTIONS OF A ONE-DEGREE CURVE. 
 
 Whole 
 Angle. 
 
 Tangent 
 Distance. 
 
 Long 
 Chord. 
 
 External 
 Secant. 
 
 Whole 
 Angle. 
 
 28 
 
 1428.5 
 
 2772.2 
 
 J 75-4 
 
 28 
 
 2 f 
 
 I430-3 
 
 2775-5 
 
 175-8 
 
 2' 
 
 4' 
 
 1432.0 
 
 2778.7 
 
 176.3 
 
 4' 
 
 6' 
 
 1433-8 
 
 2782 .0 
 
 176.7 
 
 6' 
 
 8' 
 
 1435-6 
 
 2785-2 
 
 177.2 
 
 8' 
 
 10' 
 
 1437-4 
 
 2788.4 
 
 177.6 
 
 10' 
 
 12' 
 
 1439.2 
 
 2791.7 
 
 178.0 
 
 12' 
 
 14' 
 
 1441 .0 
 
 2794.9 
 
 178.5 
 
 14' 
 
 16' 
 
 1442.7 
 
 2798.1 
 
 178.9 
 
 16' 
 
 18' 
 
 1444-5 
 
 2801.3 
 
 179-3 
 
 jS f 
 
 20' 
 
 1446.2 4 
 
 2804. 5 
 
 179.7 
 
 . 20' 
 
 22' 
 
 1448.0 ^ 
 
 2807.8 
 
 l8o.2 
 
 22' 
 
 24' 
 
 1449.7 ^ 
 
 2811 .0 
 
 180.6 
 
 24' 
 
 26' 
 
 i45 J -5 "g 
 
 2814. 2 
 
 iSl.O 
 
 26' 
 
 28' 
 
 1453-3 
 
 2817.5 
 
 181.5 
 
 28' 
 
 3o' 
 
 I 455- 1 | 
 
 2820 . 7 
 
 181 .9 
 
 30' 
 
 32' 
 
 1456.9 
 
 2824 .0 
 
 182.3 
 
 ;t 32' 
 
 34' 
 
 1458.7 - -o 
 
 2827 . 2 
 
 182.8 . . . 
 
 34' 
 
 36' 
 
 1460.5 ;?* 
 
 2830.5 
 
 183.2 $$t 
 
 36' 
 
 38' 
 
 1462. 3- ^ 
 
 2833-7 
 
 183-7^: : 
 
 38' 
 
 40' 
 
 1464.0 
 
 2836.9 
 
 184.1 -^ 
 
 4o' 
 
 42' 
 
 1465- 8 : 
 
 2840 . 2 
 
 184.6-^ : 
 
 42' 
 
 44' 
 
 1467.6 g. 
 
 2843-4 
 
 185-0^ 
 
 44 7 
 
 46' 
 
 1469.3 ooo 
 
 2846.6 
 
 185. 4 : : 
 
 46' 
 
 48' 
 
 I47 1 -* 4 
 
 2849.8 
 
 l8 5-9^22 
 
 48' 
 
 5o' 
 
 1472.9^** 
 
 2853.0 
 
 186.3^ 
 
 50' 
 
 52' 
 
 1474. 7 3 : , 
 
 2856.3 
 
 186.7^ 
 
 - 52' 
 
 54' 
 
 i47 6 -5 -5 
 
 2859.5 
 
 187.2 
 
 54' 
 
 S^' 
 
 '478-3 | 
 
 2862.7 
 
 187.6 
 
 56 
 
 58' 
 
 1480.0 co 
 
 2866.0 
 
 188.1 
 
 58' 
 
 29 
 
 1481.8 1 
 
 2869.2 
 
 188.5 
 
 29 
 
 a' 
 
 1483-6 ^ 
 
 2872.5 
 
 189 .0 
 
 2' 
 
 4' 
 
 1485-4 a 
 
 2875-7 
 
 189.4 
 
 4' 
 
 6' 
 
 1487.1 ^ 
 
 2878.9 
 
 189.9 
 
 6' 
 
 8' 
 
 1488.9 < 
 
 2882.1 
 
 190.3 
 
 8' 
 
 10' 
 
 1490.7 
 
 2885.3 
 
 190.7 
 
 10' 
 
 12' 
 
 1492.5 
 
 2888.5 
 
 191 .2 
 
 12' 
 
 14' 
 
 1494.3 
 
 2891.8 
 
 191 .6 
 
 14' 
 
 16' 
 
 1496 .0 
 
 2895 .O 
 
 192 . i 
 
 16' 
 
 18' 
 
 1497.8 
 
 2898.2 
 
 192.5 
 
 18' 
 
 20' 
 
 1499.6 
 
 2901 .4 
 
 193.0 
 
 20' 
 
 22' 
 
 1501 .4 
 
 2904 . 6 
 
 193-5 
 
 22' 
 
 24' 
 
 1503-2 
 
 2907.9 
 
 193-9 
 
 24' 
 
 26' 
 
 1505-0 
 
 2911 . i 
 
 194.4 
 
 26' 
 
 28' 
 
 1506.7 
 
 2914.3 
 
 194.8 
 
 28' 
 
 64 
 
IX. FUNCTIONS OF A ONE-DEGREE CURVE. 
 
 Whole 
 Angle. 
 
 Tangent 
 Distance. 
 
 Long 
 Chord. 
 
 External 
 Secant. 
 
 Whole 
 Angle. 
 
 29 30' 
 
 1508.5 
 
 2917.5 
 
 195-3 
 
 29 30' 
 
 32' 
 
 I5I0.3 
 
 2920 .8 
 
 195.7 
 
 32; 
 
 34' 
 
 1512 .0 
 
 2924.0 
 
 196.2 
 
 34 
 
 36' 
 
 I5I3.8 . . 
 
 2927.2 
 
 196 .6 
 
 36 
 
 38' 
 
 1515-6"** 
 
 2930.5 
 
 197.1 
 
 38' 
 
 40' 
 
 1517.4^= = 
 
 2933.7 
 
 197-5 
 
 40' 
 
 42' 
 
 1519.2-3 
 
 2937.0 
 
 198 .0 
 
 42' 
 
 44' 
 
 1521.0-*: : 
 
 2940 . 2 
 
 198.4 
 
 44' 
 
 46' 
 
 1522 . 7 ^ 
 
 2943.4 
 
 198.9 
 
 46' 
 
 48' 
 
 1524.5 = = 
 
 2946 .6 
 
 199.3 
 
 48' 
 
 
 O GO Tf 
 
 
 
 
 50' 
 
 1526.3 C i-' rr> 
 
 2949.8 
 
 199.8 
 
 5 
 
 52' 
 
 1528.0 '^R 
 
 2953.0 
 
 200.2 
 
 52 ^ 
 
 54' 
 
 1529.8?, : 
 
 2956.3 
 
 200.7 
 
 54 
 
 56' 
 
 1531 .6 "^ 
 
 2959.5 
 
 2OI . I 
 
 56 
 
 58' 
 
 1533.4 
 
 2962 .7 
 
 2OI .6 
 
 58' 
 
 30 
 
 1535.2 
 
 2965.9 
 
 2O2 . I 
 
 30 
 
 2' 
 
 1537.0 
 
 2969.1 
 
 2O2 .6 
 
 2' 
 
 4' 
 
 1538.8 
 
 2972.3 
 
 203.0 . . 
 
 4' 
 
 6' 
 
 1540.6 ^_ 
 
 2975.6 
 
 203.5 ^^^ 
 
 6' 
 
 8' 
 
 1542.4 
 
 2978.8 
 
 203. 9^3 : 
 
 8' 
 
 10' 
 
 
 
 1544.2 z 
 
 2982 .0 
 
 204.4^3 
 
 10' 
 
 12' 
 
 1546.0 -g 
 
 2985.3 
 
 204.9 :r : 
 
 12' 
 
 14' 
 
 1547-8 *a 
 
 2988.5 
 
 205.3^ 
 
 14' 
 
 16' 
 
 1549.6 t 
 
 2991.7 
 
 205 .8 z : 
 
 16' 
 
 18' 
 
 1551.4 
 
 2994.9 
 
 206.3 "3 itv? 
 
 18' 
 
 20' 
 
 1553.2 t^s 
 
 2998. i 
 
 206.8,3 w 
 
 20' 
 
 22' 
 
 1554.9,6- 
 
 3001.3 
 
 207.2 5j : = 
 
 22' 
 
 34' 
 
 1556.7^ ^ 
 
 3004.5 
 
 207.7 
 
 24' 
 
 26' 
 
 
 3007.7 
 
 208.1 
 
 26' 
 
 28' 
 
 1560. 3 1" 
 
 3010.9 
 
 208.6 
 
 28' 
 
 30' 
 
 1562 .1 jr: 
 
 3014.1 
 
 2t>9.1 
 
 3; 
 
 32' 
 
 1563 ,9 ^09 . 
 
 3017-3 
 
 209.5 
 
 32 
 
 3 < 
 
 *565-7 5- 
 
 3020.5 
 
 2IO .O 
 
 z i 
 
 36' 
 
 1567-4^ , 
 
 3023.8 
 
 2IO .5 
 
 3 6 
 
 38' 
 
 1569.23=5 
 
 3027.0 
 
 211 .O 
 
 38' 
 
 40' 
 
 2 
 1571.0 
 
 3030.2 
 
 2II.5 
 
 40; 
 
 42' 
 
 1572.8 
 
 3033.4 
 
 212 .0 
 
 42' 
 
 44' 
 
 1574.6 
 
 3036.6 
 
 212 .4 
 
 44' 
 sf 
 
 46' 
 
 1576.4 ^ 
 
 3039.9 
 
 212 .9 
 
 46' 
 
 48' 
 
 1578.2 ^ c 
 
 3043.1 
 
 213.4 
 
 48' 
 
 50', 
 
 1580.0 5 
 
 3046.3 
 
 213.9 
 
 5' 
 
 52' 
 
 1581.8 < 
 
 3049.5 
 
 214.4 
 
 52 ' 
 
 54' 
 
 1583.6 
 
 3052.8 
 
 214.8 
 
 54' 
 
 56' 
 
 1585.4 
 
 3056.0 
 
 215.3 
 
 56 
 
 58' 
 
 1587.2 
 
 3059-2 
 
 215.8 
 
 5 8 
 
 65 
 
IX. FUNCTIONS OF A ONE-DEGREE CURVE. 
 
 Whole 
 
 Angif. 
 
 Tangent 
 Distance. 
 
 Long 
 Chord. 
 
 External 
 Secant. 
 
 Whole 
 Agnle. 
 
 31 
 
 1588.9 
 
 3062 .4 
 
 216.3 
 
 31 
 
 2' 
 
 1590.7 
 
 3065.6 
 
 216.8 
 
 2' 
 
 4' 
 
 1592.5 
 
 3068.8 
 
 217.3 
 
 4' 
 
 6' 
 
 1594.3 
 
 3072.0 
 
 217.7 
 
 6' 
 
 8' 
 
 1596.1 
 
 3075-2 
 
 218.2 
 
 8* 
 
 10' 
 
 1597-9 
 
 3078.4 
 
 218.7 
 
 10' 
 
 12' 
 
 1599-7 
 
 3081.6 
 
 219 . I 
 
 I2 7 
 
 14' 
 
 1601 . 5 
 
 3084.8 
 
 219 .6 
 
 14' 
 
 16' 
 
 1603.3 
 
 3088.0 
 
 220 . I 
 
 16' 
 
 18' 
 
 1605.1 
 
 309L3 
 
 22O . 6 
 
 18' 
 
 20' 
 
 1606 .9 
 
 3094.5 
 
 221 . I 
 
 20' 
 
 22' 
 
 1608.7 
 
 3097.7 
 
 221.6 
 
 22 X 
 
 24' 
 
 1610.5 
 
 3100 .9 
 
 222 . I 
 
 24' 
 
 26' 
 
 1612.3 
 
 3104.1 
 
 222 . 5 
 
 26' 
 
 28' 
 
 1614 . i 
 
 3 I0 7-3 
 
 223.0 
 
 28' 
 
 30' 
 
 1615.9 
 
 3110.5 
 
 223.5 
 
 3' 
 
 32' 
 
 1617.7 
 
 3113-7 
 
 224 .O 
 
 3 2 ' 
 
 34 
 
 l6 *9-5 ^4 
 
 3116.9 
 
 224.5 ^4 
 
 34' 
 
 36 
 
 1621.3 
 
 3120.1 
 
 225 .0 
 
 36' 
 
 38' 
 
 1623.1 jO: : 
 
 3123.3 
 
 225.5 = - 
 
 38' 
 
 40' 
 
 1624.9 13 
 
 3126.5 
 
 226 .0 15 - 
 
 40' 
 
 42' 
 
 1626 . 7 'Br : 
 
 3129.7 
 
 226.5 '& : 
 
 42' 
 
 44' 
 
 1628. 5^ m 
 
 3132.9 
 
 227.0^ 
 
 44' 
 
 46' 
 
 1630.3 ~ : 
 
 3136.2 
 
 227.5 " " 
 
 46' 
 
 48' 
 
 1632.1 J 
 
 vo v, O 
 
 3139-4 
 
 228.0^! 
 
 48' 
 
 5 0/ 
 
 1633.9^*- 
 
 3142.6 
 
 228.4^ 
 
 50' 
 
 52/ , 
 
 1635 7 ^ : 
 
 3I45-8 
 
 228. 9^ : : 
 
 52' 
 
 C A 
 
 1637-5 
 
 3149.0 
 
 229.4 
 
 54' 
 
 56' 
 
 1639-3 
 
 3i5 2 -2 
 
 229.9 
 
 56; 
 
 58' 
 
 1641 .1 
 
 3I55-4 
 
 230.4 
 
 
 32 
 
 1642 .9 
 
 3158.6 
 
 230.9 
 
 32 
 
 2 f 
 
 1644.7 
 
 3161.8 
 
 231.4 
 
 2 f 
 
 4' 
 
 1646.5 
 
 3165.0 
 
 231.9 
 
 4' 
 
 6' 
 
 1^8-8.3 
 
 3168.2 
 
 232.4 
 
 6' 
 
 8' 
 
 1650. i 
 
 3i7i-4 
 
 33 2 .9 
 
 8' 
 
 10' 
 
 1651.9 
 
 3174.6 
 
 233-4 
 
 10' 
 
 12' 
 
 1653.7 
 
 3177.8 
 
 233-9 
 
 I2 7 
 
 14' 
 
 l6 55-5 
 
 3181 .0 
 
 234-4 
 
 14' 
 
 16' 
 
 1657-3 
 
 3184.2 
 
 234.9 
 
 16' 
 
 18' 
 
 1659.1 
 
 3187.4 
 
 235-4 
 
 18' 
 
 20' 
 
 1660. 9 
 
 3190.6 
 
 235.9 
 
 20' 
 
 22' 
 
 1662 . 7 
 
 3193.8 
 
 236.4 
 
 22' 
 
 24' 
 
 1664.5 
 
 
 236.9 
 
 24' 
 
 26' 
 
 1666.3 
 
 3200. 2 
 
 237.4 
 
 26' 
 
 28' 
 
 1668.1 
 
 3203.4 
 
 237-9 
 
 28' 
 
IX. FUNCTIONS OF A ONE-DEGREE CURVE. 
 
 Whole 
 Angle. 
 
 Tangent 
 Distance. 
 
 Long 
 Chord. 
 
 External 
 Secant. 
 
 Whole 
 Angle. 
 
 32 30' 
 
 1669.9 
 
 3206 . 6 
 
 238.4 
 
 32 30' 
 
 3*' 
 
 1671.7 
 
 3209.8 
 
 238.9 
 
 32' 
 
 34' 
 
 1673.5 
 
 3213.0 
 
 239-4 
 
 34' 
 
 36' 
 
 1675.3 
 
 3216.2 
 
 239.9 
 
 36' 
 
 38' 
 
 1677.1 
 
 3219-4 
 
 240.5 
 
 38' 
 
 40' 
 
 1679 .O 
 
 3222 .6 
 
 241 .O 
 
 40' 
 
 4*' 
 
 1680.8 
 
 3225.8 
 
 24L5 
 
 42' 
 
 44' 
 
 1682.6 
 
 3229.0 
 
 242 .0 
 
 44' 
 
 46' 
 
 1684.4 
 
 3232.2 
 
 242.5 
 
 46' 
 
 48' 
 
 1686.2 
 
 3235.4 
 
 243-0 
 
 48' 
 
 5 0/ 
 
 1688.1 
 
 3238-6 
 
 243-5 
 
 5o; 
 
 52' 
 
 1689.9 
 
 3241.8 
 
 244.0 
 
 
 54' 
 
 1691.7 
 
 3245-0 
 
 244.6 
 
 54' 
 
 56' 
 
 1693-5 
 
 3248.2 
 
 245- 1 
 
 56' 
 
 58' 
 
 1695.3 
 
 325L4 
 
 245-6 
 
 58' 
 
 33 
 
 1697.2 
 
 3254.6 
 
 246.1 
 
 33 
 
 2 f 
 
 1699.0 
 
 3257.8 
 
 246.6 
 
 2' 
 
 4' 
 
 1700.8 
 
 3261 .0 
 
 247 .2 ... 
 
 4' 
 
 6' 
 
 1702 .7 ^ ^^ 
 
 3264.2 
 
 247-7 ""* 
 
 6' 
 
 8' 
 
 1704.5 ; - 
 
 3267.4 
 
 248.2 6, : 
 
 8 X 
 
 10' 
 
 1706. 3 ~ : 
 
 3270.6 
 
 248. 7 -a 
 
 10' 
 
 12' 
 
 1708.1 * 
 
 3273.8 
 
 249.2-5= = 
 
 12' 
 
 14' 
 
 1709. 9 'ST : 
 
 3277.0 
 
 249.7^ 
 
 14' 
 
 16' 
 
 C/2 
 
 1711.7 
 
 3280.2 
 
 250. 3 : : 
 
 1 6' 
 
 18' 
 
 I 7 I 3-5 ^_ : : 
 
 3283.4 
 
 250.8 
 
 1 8' 
 
 20' 
 
 1715-3 j 
 
 3286.6 
 
 251-3-0 
 
 20' 
 
 22' 
 
 1717.1 ***- 
 
 3289.8 
 
 251.83= = 
 
 22' 
 
 24' 
 
 1718.9 *c: : 
 
 3293.0 
 
 252.3 
 
 24' 
 
 26' 
 
 1720.8 Y 
 
 3296.2 
 
 252.8 
 
 26' 
 
 28' 
 
 1722 .6 
 
 3299.3 
 
 253-3 
 
 28' 
 
 3 0/ 
 
 1724.4 
 
 3302.5 
 
 253-9 
 
 30' 
 
 32' 
 
 1726.2 
 
 3305.7 
 
 254-4 
 
 32 
 
 34' 
 
 1728.0 
 
 3308.9 
 
 255.0 
 
 34 
 
 36' 
 
 1729.9 
 
 33 12 . i 
 
 255.5 
 
 36 
 
 38' 
 
 I73L7 
 
 3315.3 
 
 256.0 
 
 38' 
 
 40' 
 
 1733.5 
 
 3318.5 
 
 256-5 
 
 40' 
 
 42' 
 
 1735.3 
 
 3321.7 
 
 257.0 
 
 42' 
 
 44' 
 
 1737.2 
 
 3324.9 
 
 257.5 
 
 44' 
 
 46' 
 
 
 3328.1 
 
 258.0 
 
 46' 
 
 48' 
 
 1740.8 
 
 3331-2 
 
 258.5 
 
 48' 
 
 50' 
 
 1742.6 
 
 3334-4 
 
 259.1 
 
 5' 
 
 I*' 
 
 1744.4 
 
 3337-6 
 
 259.6 
 
 52 ', 
 
 54'. 
 
 1746.2 
 
 3340.8 
 
 260.2 
 
 54' 
 
 56' 
 
 1748 .0 
 
 3344-0 
 
 260.7 
 
 56' 
 
 58' 
 
 1749.9 
 
 3347-2 
 
 261 .3 
 
 58' 
 
 67 
 
IX. FUNCTIONS OF A ONE-DEGREE CURVE. 
 
 Whole 
 Angle. 
 
 Tangent 
 Distance. 
 
 Long 
 Chord. 
 
 External 
 Secant. 
 
 Whole 
 Angle. 
 
 34 
 
 I75L7 
 
 3350.4 
 
 261.8 
 
 34 
 
 2' 
 
 1753.6 
 
 3353-6 
 
 262 .4 
 
 2' 
 
 4' 
 
 1755.4 
 
 3356.8 
 
 262 .9 
 
 4' 
 
 6' 
 
 1757.2 4 
 
 3360.0 
 
 263.5 
 
 6' 
 
 8' 
 
 1759-0 ^ 
 
 3363.1 
 
 264.0 
 
 8' 
 
 10' 
 
 1760.8 g 
 
 3366.3 
 
 264.5 
 
 10' 
 
 12' 
 
 1762.7 "g 
 
 3369.5 
 
 265 . I 
 
 12' 
 
 14' 
 
 1764.5 
 
 3372.7 
 
 265.6 
 
 14' 
 
 16' 
 
 1766.3 
 
 3375-9 
 
 266 .2 
 
 16' 
 
 18' 
 
 1768.1 ^ 
 
 3379-0 
 
 266.7 
 
 18' 
 
 20' 
 
 1769.9 o 
 
 3382.2 
 
 267.2 
 
 20' 
 
 22' 
 
 i77i-7 
 
 
 267.8 
 
 22' 
 
 24' 
 
 1773.6 ^ 
 
 3388^6 
 
 268.3 
 
 24' 
 
 26' 
 
 1775-4 
 
 3391-8 
 
 268.9 
 
 26' 
 
 28' 
 
 1777.2 
 
 3395-0 
 
 269.4 
 
 28' 
 
 30' 
 
 1779.0 
 
 3398.1 
 
 269.9 
 
 30' 
 
 32' 
 
 1780.9 
 
 3401.3 
 
 270.5 
 
 32' 
 
 34' 
 
 1782.7 ^4 
 
 3404.5 
 
 270.0 
 
 34' 
 
 36' 
 
 1784.5 
 
 3407-7 
 
 271 .6 iA4 
 
 36' 
 
 38' 
 
 I786.3|= = 
 
 3410.9 
 
 272.1 ^ _ H 
 
 38' 
 
 40' 
 
 1788.2 * 
 
 3414.0 
 
 272 .6 2 
 
 40' 
 
 42' 
 
 1790. I :: 
 
 3417.2 
 
 273.2 .: : 
 
 42' 
 
 44' 
 
 I79L9 g- - 
 
 3420.4 
 
 273-7 & 
 
 44' 
 
 46' 
 
 
 3423.5 
 
 274.3 gs r 
 
 46' 
 
 48' 
 
 1795^12$ 
 
 3426.7 
 
 274.8^o H 
 
 48' 
 
 5 ; 
 
 1797.4^" 
 
 3429.9 
 
 275.3 "^ 
 
 5; 
 
 52' 
 
 1799.2^: : 
 
 3433-1 
 
 275. 9S: : 
 
 52 
 
 54' 
 
 1801 . i 
 
 3436.3 
 
 276. 4< 
 
 54' 
 
 56' 
 
 1803.0 
 
 3439.4 
 
 277.0 
 
 56' 
 
 58' 
 
 1804.8 
 
 3442.6 
 
 277.5 
 
 58' 
 
 ,35 
 
 1806. 6 
 
 3445 - 8 
 
 278.1 
 
 35 
 
 2' 
 
 1808.5 4 
 
 3449-0 
 
 278.6 
 
 2' 
 
 4' 
 
 1810.3 
 
 3452.1 
 
 279.2 
 
 4' 
 
 6' 
 
 1812 . i 
 
 3455-3 
 
 279.7 
 
 6' 
 
 8' 
 
 1813-9 -g 
 
 3458.5 
 
 280.2 
 
 8' 
 
 10' 
 
 1815.7 
 
 346i.7 
 
 280.8 
 
 10' 
 
 12' 
 
 1817.6 g 
 
 3464.9 
 
 281.3 
 
 12' 
 
 14' 
 
 1819.4 * 
 
 3468.0 
 
 281.9 
 
 14' 
 
 16' 
 
 1821.3 * 
 
 347 1 - 2 
 
 282.4 
 
 16' 
 
 18' 
 
 1823.1 
 
 3474-4 
 
 283.0 
 
 18' 
 
 20' 
 
 1824.9 3 
 
 3477-6 
 
 283.6 
 
 20' 
 
 22' 
 
 1826.8 
 
 3480.8 
 
 284.1 
 
 22 r 
 
 24' 
 
 1828.6 
 
 3484.0 
 
 284.7 
 
 24' 
 
 26' 
 
 1830.4 
 
 3487.1 
 
 285.2 
 
 26' 
 
 28' 
 
 1832.3 
 
 3490.3 
 
 285.8 
 
 28' 
 
 68 
 
IX. FUNCTIONS OF A ONE-DEGREE CURVE. 
 
 Whole 
 Angle. 
 
 Tangent 
 Distance. 
 
 Long 
 Chord. 
 
 External 
 Secant. 
 
 Whole 
 Angle. . 
 
 35 30' 
 
 1834.1 
 
 3493-5 
 
 286.4 
 
 35 30' 
 
 3*' 
 
 1836.0 
 
 3496.6 
 
 286.9 
 
 32' 
 
 34' 
 
 I837-8 4 
 
 3499-8 
 
 287.5 
 
 34' 
 
 36' 
 
 1839.7 
 
 3503-0 
 
 288.0 
 
 36' 
 
 38' 
 
 1841-5 & 
 
 3506.2 
 
 288.6 
 
 38' 
 
 40' 
 
 1843-3 'S 
 
 3509.3 
 
 289.2 
 
 40' 
 
 42' 
 
 1845-2 
 
 35*2.5 
 
 289.7 
 
 42' 
 
 44' 
 
 1847.0 1* 
 
 
 290.3 
 
 44' 
 
 46' 
 
 1848.9 
 
 35i8l8 
 
 290.8 
 
 46' 
 
 48' 
 
 1850.7 4 
 
 3522.0 
 
 291.4 
 
 48' 
 
 5' 
 
 1852.5 
 
 3525-2 
 
 292 .0 
 
 50' 
 
 5*' 
 
 1854.3 3 
 
 3528.4 
 
 292 .6 
 
 52' 
 
 54' 
 
 1856.2 
 
 3531 . 5 
 
 293.1 
 
 54' 
 
 56' 
 
 1858,0 
 
 3534-7 
 
 293-7 
 
 56' 
 
 58' 
 
 1859.9 
 
 3537-9 
 
 294-3 
 
 58' 
 
 36 
 
 1861.7 
 
 354i.i 
 
 294.9 
 
 36 
 
 2' 
 
 1863.6 
 
 3544-3 
 
 295-5 
 
 2' 
 
 4' 
 
 1865.4 
 
 3547-4 
 
 296.0 
 
 4' 
 
 6' 
 
 1867.3 " 
 
 3550-6 
 
 296.6 ^<>j 
 
 6' 
 
 8' 
 
 1869.2 g 
 
 3553-8 
 
 297 . 1 o- . 
 
 8' 
 
 10' 
 
 1870.9 13 
 
 3557-0 
 
 2 97-7^ " 
 
 10' 
 
 12' 
 
 1872.8 
 
 356o.2 
 
 298.3 .h- - 
 
 12' 
 
 14' 
 
 1874.6 & 
 
 3563-3 
 
 298. 8 c&" " 
 
 14' 
 
 16' 
 
 1876.4 
 
 3566.5 
 
 299. 4J5: : 
 
 1 6' 
 
 18' 
 
 1878.3 5 
 
 3569-6 
 
 3OO.O J>0 H 
 
 1 8' 
 
 20' 
 
 1880. i " 
 
 3572.8 
 
 3 ' 6 * 
 
 20' 
 
 22' 
 
 1882. o: ? 
 
 3576.0 
 
 301 .2 :: : 
 
 22' 
 
 24' 
 
 1883.8* < 
 
 3579-1 
 
 3 I -7 < 
 
 24' 
 
 26' 
 
 1885.74= 
 
 3582.3 
 
 302.3 
 
 26' 
 
 28' 
 
 .i88 7 . 5 
 
 3585.5 
 
 302.9 
 
 28' 
 
 3; 
 
 1889. 3 I s 
 
 3588.6 
 
 303.5 
 
 30' 
 
 
 1891 . 2 ^ " 
 
 3591.8 
 
 304.0 
 
 32 
 
 !*' 
 
 1893.0 $? 
 
 3594-9 
 
 304.6 
 
 34 
 
 36' 
 
 1894.85, 6 
 
 3598.1 
 
 305.2 
 
 36 
 
 38' 
 
 1896.7 <" 2 
 
 3601.3 
 
 305-8 
 
 38' 
 
 40' 
 
 1898.5 4 
 
 3604.4 
 
 306.4 
 
 40' 
 
 4 2/ 
 
 1900.4 ^ 
 
 3607.6 
 
 307.0 
 
 42' 
 
 44' 
 
 1902.2 
 
 3610.7 
 
 307.5 
 
 44' 
 
 46' 
 
 1904.1 IJ ? 
 
 3613-9 
 
 308.1 
 
 4 | 
 
 48' 
 
 1905.9 o 
 
 3617.1 
 
 308.7 
 
 48' 
 
 5' 
 
 1907.8 
 
 3620.2 
 
 309.3 
 
 5' 
 
 S^' 
 
 1909.6 < 
 
 3623.4 
 
 309.9 
 
 52 / 
 
 54' 
 
 1911.5 
 
 3626.5 
 
 310.4 
 
 5 i 
 
 56' 
 
 1913.3 
 
 3629.7 
 
 311.0 
 
 56' 
 
 58' 
 
 1915.2 
 
 3632 .8 
 
 3H.6 58' 
 
IX. FUNCTIONS OF A ONE-DEGREE CURVE. 
 
 Whole 
 Angle. 
 
 Tangent 
 Distance. 
 
 Long 
 Chord. 
 
 External 
 Secant. 
 
 Whole 
 Angle. 
 
 37 
 
 1917.1 
 
 3636.0 
 
 312.2 
 
 37 
 
 a' 
 
 1919 .O 
 
 3639 - 1 
 
 312.8 
 
 2' 
 
 4' 
 
 1920 .8 
 
 3642.3 
 
 313.4 
 
 4' 
 
 6' 
 
 1922.7 ? 
 
 3645.5 
 
 314.0 
 
 6' 
 
 8' 
 
 i 9&4 . 5 6 
 
 3648.6 
 
 314.6 
 
 8' 
 
 10' 
 
 1926.4 -j 
 
 3651-8 
 
 3I5. 2 
 
 10' 
 
 12' 
 
 1928.3 
 
 3654.9 
 
 315.8 
 
 12' 
 
 14' 
 
 1930.1 tw 
 
 3658.1 
 
 316.4 
 
 14' 
 
 16' 
 
 1932.0 
 
 3661.3 
 
 3I7-0 
 
 16' 
 
 18' 
 
 1933.8 
 
 3664.5 
 
 317.6 
 
 18' 
 
 20' 
 
 1935-7 ^ 
 
 3667.6 
 
 318.1 
 
 20< 
 
 22' 
 
 1937.6 : 3 
 
 3670.8 
 
 318.7 
 
 22' 
 
 24' 
 
 1939-4- < 
 
 3673.9 
 
 3*9-3 
 
 24' 
 
 26' 
 
 1941 .3 & 
 
 3677.1 
 
 3J9-9 
 
 26' 
 
 28' 
 
 1943.1 co 
 
 3680 . 2 
 
 320.5 
 
 28' 
 
 30' 
 
 1945.0 J : 
 
 3683.3 
 
 321.1 
 
 3o' 
 
 32' 
 
 1946.9124 
 
 3686.5 
 
 321.7 
 
 32' 
 
 34' 
 
 1948.7 3 H . 
 
 3689.6 
 
 322.3 
 
 34' 
 
 36' 
 
 1950.6^ 
 
 3692.8 
 
 322.9 A j 
 
 36' 
 
 38' 
 
 1952. 4<f -3 
 
 3695-9 
 
 323-5 d. : 
 
 38' 
 
 40' 
 
 1954-3 I 
 
 3699.1 
 
 324- I 5" 
 
 40' 
 
 42' 
 
 1956.2 
 
 3702.2 
 
 324. 7 1:: 
 
 42' 
 
 44' 
 
 1958.0 ^ 
 
 3705.5 
 
 325.3^ 
 
 44' 
 
 46' 
 
 1959-9 4 
 
 3708.6 
 
 325.9,0: = 
 
 46' 
 
 48' 
 
 1961.7 a 
 
 37II.8 
 
 326.5 r*\o N 
 
 48' 
 
 50' 
 
 1963.6 | 
 
 37M.9 
 
 327.I """ 
 
 50' 
 
 52' 
 
 1965-5 
 
 3718.0 
 
 327.7^: : 
 
 52' 
 
 54' 
 
 1967.3 
 
 3721.2 
 
 328. 3^ 
 
 54' 
 
 56' 
 
 1969 . 2 
 
 3724.5 
 
 328.9 
 
 56' 
 
 58' 
 
 I97I.O 
 
 3727.6 
 
 329-5 
 
 58' 
 
 38 
 
 1972.9 
 
 3730.7 
 
 330.2 
 
 38 
 
 2' 
 
 1974.8 
 
 3733-8 
 
 330.8 
 
 2' 
 
 4' 
 
 1976.6 ^^^ 
 
 3737-0 
 
 331-4 
 
 4' 
 
 6' 
 
 1978.5 > 
 
 3740.1 
 
 332.o 
 
 6' 
 
 8' 
 
 1980.3,0: : 
 
 3743.3 
 
 332.6 
 
 8' 
 
 10' 
 
 1982 . 2 'd 
 
 3746.4 
 
 333-2 
 
 10' 
 
 12' 
 
 1984.0 -g," : 
 
 3749-5 
 
 333.8 
 
 12' 
 
 14' 
 
 1985.9^ 
 
 3752.7 
 
 334.5 
 
 14' 
 
 16' 
 
 1987- 72 : : 
 
 3755-8 
 
 335- 1 
 
 16' 
 
 18' 
 
 1989-6 ?n 
 
 3759-o 
 
 335-7 
 
 18' 
 
 20' 
 
 to u-j O 
 I99I.5 cj^t^ 
 
 3762.2 
 
 336.3 
 
 20' 
 
 22' 
 
 1993 -4 ?: : 
 
 3765.3 
 
 336.9 
 
 22' 
 
 24' 
 
 1995. 3^ 
 
 3768.5 
 
 337-5 
 
 24' 
 
 26' 
 
 1997.1 
 
 3771.6 
 
 338.i 
 
 26' 
 
 28' 
 
 1999.0 
 
 3774-8 
 
 338.7 
 
 28' 
 
 70 
 
IX. FUNCTIONS OF A ONE-DEGREE CURVE. 
 
 Whole 
 Angle. 
 
 Tangent 
 Distance. 
 
 Long 
 Chord. 
 
 External 
 Secant. 
 
 Whole 
 Angle. 
 
 38 30' 
 
 2OOO .8 
 
 3777-9 
 
 339-3 
 
 38 30' 
 
 32' 
 
 2OO2 . 7 
 
 3781.1 
 
 339-9 
 
 32' 
 
 34' 
 
 2004.5 
 
 3784.2 
 
 340.6 
 
 34' 
 
 36' 
 
 2006.4 4 
 
 3787-4 
 
 341.2 
 
 36' 
 
 38' 
 
 2008 .3 
 
 3790.5 
 
 341.8 
 
 38' 
 
 40' 
 
 2OIO . 2 
 
 3793-7 
 
 342.4 
 
 40' 
 
 42' 
 
 2012. I *g 
 
 3796.8 
 
 343-o 
 
 42' 
 
 44' 
 
 2014.0 
 
 3800 .0 
 
 343-7 
 
 44' 
 
 46' 
 
 2015.8 C 
 
 3803.1 
 
 344-3 
 
 46' 
 
 48' 
 
 2017.7 - 
 
 3806.2 
 
 344-9 
 
 48' 
 
 50' 
 
 2019.6 " 
 
 3809.4 
 
 345-5 
 
 50' 
 
 5*' 
 
 2021.5 
 
 3812.5 
 
 346.1 
 
 52' 
 
 54' 
 
 2023.4 5 
 
 3815-7 
 
 346.8 
 
 54' 
 
 56' 
 
 2025.3 
 
 3818.9 
 
 347-4 
 
 56' 
 
 58' 
 
 2027 .2 
 
 3822.0 
 
 348.0 
 
 58' 
 
 39 
 
 2O29 .O 
 
 3825.1 
 
 348.6 
 
 39 
 
 2' 
 
 2030.9 
 
 3828.2 
 
 349-3 
 
 2' 
 
 4' 
 
 2032 .8 ... 
 
 3831.4 
 
 349-9 ^ . . 
 
 4' 
 
 6' 
 
 2034. 7' ^H 
 
 3834-5 
 
 350.5""? 
 
 6' 
 
 8' 
 
 2036.6 ,o : : 
 
 3837-7 
 
 351-2 c, 5 
 
 8' 
 
 10' 
 
 2038.4-3 
 
 3840.8 
 
 35i. 8-g 
 
 10' 
 
 12' 
 
 2040.3 -a : : 
 
 3843-9 
 
 352. 4 -a : = 
 
 12' 
 
 14' 
 
 2042.2^ 
 
 3847-1 
 
 353.1^ 
 
 14' 
 
 16' 
 
 2044. i : : 
 
 3850.2 
 
 353- 7- : : 
 
 16' 
 
 18' 
 
 2046. o||| 
 
 3853.4 
 
 354.3 ^2 
 
 18' 
 
 20' 
 
 2047 -8 N ^^ 
 
 3856.5 
 
 354- 9-d 
 
 20' 
 
 22' 
 
 2049.7 S: : 
 
 3859-6 
 
 355- 5< : : 
 
 22' 
 
 24' 
 
 2051 .6 1 
 
 3862.8 
 
 356.2 
 
 24' 
 
 26' 
 
 2053-5 
 
 3865-9 
 
 356.8 
 
 26' 
 
 28' 
 
 2055.4 
 
 3869.1 
 
 357-5 
 
 28' 
 
 30' 
 
 2057.2 
 
 3872.2 
 
 358.1 
 
 30' 
 
 32' 
 
 2059.1 4 
 
 3875-3 
 
 358.7 
 
 32' 
 
 34' 
 
 2061 .0 
 
 3878.5 
 
 359-4 
 
 34 
 
 36' 
 
 2062.9 j 
 
 3881.6 
 
 360.0 
 
 36' 
 
 38' 
 
 2064.8 13 
 
 3884-7 
 
 360.7 
 
 38' 
 
 40' 
 
 2066.6 '& 
 
 3887.9 
 
 361.3 
 
 40' 
 
 . 42' 
 
 2068.5 
 
 3891.0 
 
 362.0 
 
 42' 
 
 44' 
 
 2070.4 ^ 
 
 3894.2 
 
 362.6 
 
 44' 
 
 46' 
 
 2072.3 
 
 3897-3 
 
 363-3 
 
 46' 
 
 48' 
 
 2074.2 *- 
 
 3900.4 
 
 363-9 
 
 48' 
 
 50' 
 
 2076.0 ^ 
 
 3903.5 
 
 364-5 
 
 50' 
 
 52' 
 
 2077.9 
 
 3906.6 
 
 365-2 
 
 52 
 
 54' 
 
 2079.8 
 
 3909.8 
 
 365-8 
 
 54 
 
 56' 
 
 2081 . 7 
 
 3912.9 
 
 366.5 
 
 56 
 
 58' 
 
 2083.6 
 
 3916.0 
 
 367.1 
 
 =;8' 
 
IX. FUNCTIONS OF A ONE-DEGREE CURVE. 
 
 Whole 
 Angle. 
 
 Tangent 
 Distance. 
 
 Long 
 Chord. 
 
 External 
 Secant. 
 
 Whole 
 Angle. 
 
 4O 
 
 2085 . 4 
 
 3919.2 
 
 367.7 
 
 4O 
 
 2' 
 
 2087.3 
 
 3922.3 
 
 368.4 
 
 2' 
 
 4' 
 
 2089 . 2 
 
 
 369.0 
 
 4? 
 
 6' 
 
 2091 . I 
 
 3928.6 
 
 369.7 
 
 6' 
 
 8' 
 
 2093.0 
 
 3931-7 
 
 370.3 
 
 8' 
 
 10' 
 
 2094.9 
 
 3934-8 
 
 371.0 
 
 10' 
 
 12' 
 
 2096.8 
 
 3937-9 
 
 371-6 
 
 12' 
 
 14' 
 
 2098.7 
 
 3941.0 
 
 372.3 
 
 14' 
 
 16' 
 
 2100.6 
 
 3944-2 
 
 372.9 
 
 1 6' 
 
 18' 
 
 2IO2 .5 
 
 3947-3 
 
 373.6 
 
 18' 
 
 20' 
 
 2104.3 
 
 3950-5 
 
 374-2 
 
 20'. 
 
 22' 
 
 2IO6. 2 *?< 
 
 3953.6 
 
 374-9 
 
 22' 
 
 24' 
 
 2I08.I "g 
 
 3956.8 
 
 375-5 
 
 24' 
 
 26' 
 
 2IIO.O 
 
 3959-9 
 
 376.2 
 
 26' 
 
 28' 
 
 2111.9 J 
 
 3963.0 
 
 376.8 
 
 28' 
 
 3' 
 
 2H3.7 ^ 
 
 3966.1 
 
 377-5 
 
 30' 
 
 32' 
 
 2II5.6 ^ 
 
 3969.2 
 
 378.1 
 
 32' 
 
 34' 
 
 2117.5 l ? > 
 
 3972.4 
 
 378.8 ... 
 
 34' 
 
 36' 
 
 2119.4,: .3 
 
 3975.5 
 
 379.4 100 ? 
 
 36' 
 
 38' 
 
 2121.3^' 
 
 3978.6 
 
 380.1 c,. : 
 
 38' 
 
 40' 
 
 2123. 2 1, : 
 
 3981 .8 
 
 380.8^ 
 
 40' 
 
 42' 
 
 2125.1? . 
 
 3984.9 
 
 381. 4 &- = 
 
 42' 
 
 44' 
 
 2127 .0 <~V 
 
 3988.1 
 
 382. !< 
 
 44' 
 
 46' 
 
 2128.9 o<? 
 
 3991.2 
 
 382.7^ = 
 
 46' 
 
 48' 
 
 2130.8 $ 
 
 3994.3 
 
 383.4 ^^^ 
 
 48' 
 
 50' 
 
 2132. 7 I 5 1 
 
 3997-4 
 
 384. i ^ ; 
 
 50' 
 
 52' 
 
 2134. 6^ 15 
 
 4000.5 
 
 
 52' 
 
 54' 
 
 2136.5 -a 
 
 4003.7 
 
 385^ 
 
 54' 
 
 56' 
 
 2138.4 ? 
 
 4006 .8 
 
 386.0 
 
 56' 
 
 58' 
 
 2140.3 
 
 4009 . 9 
 
 386.7 
 
 58' 
 
 41 
 
 2142.2 ^ 
 
 4013.1 
 
 387.4 
 
 41 
 
 2 
 
 2144.1 
 
 4Ol6 . 2 
 
 388.1 
 
 2' 
 
 4' 
 
 2146.0 i 
 
 4019.3 
 
 388.7 
 
 4' 
 
 6' 
 
 2147.9 < 
 
 4022.5 
 
 389.4 
 
 6' 
 
 8' 
 
 2149.8 
 
 4025.6 
 
 390.0 
 
 8' 
 
 10' 
 
 2151.7 
 
 4028. 7 
 
 390.7 
 
 10' 
 
 12' 
 
 2153.6 
 
 4031 .8 
 
 391.4 
 
 12' 
 
 14' 
 
 2155.5 
 
 4034.9 
 
 392.0 
 
 14' 
 
 16' 
 
 2157.4 
 
 4038.0 
 
 392.7 
 
 1 6' 
 
 18' 
 
 2159-3 
 
 4041 . 2 
 
 393.4 
 
 18' 
 
 20' 
 
 2l6l .2 
 
 4044-3 
 
 394.1 
 
 20' 
 
 22' 
 
 2I63.I 
 
 4047-4 
 
 394.8 
 
 22' 
 
 24' 
 
 2165 .O 
 
 4050.5 
 
 395-4 
 
 24' 
 
 26' 
 
 2166 . 9 
 
 4053.6 
 
 396.1 
 
 26' 
 
 28' 
 
 2168.8 
 
 4056.7 
 
 306.7 
 
 28' 
 
IX. FUNCTIONS OF A^ ONE-DEGREE CURVE. 
 
 Whole 
 
 Angle. 
 
 Tangent 
 Distance. 
 
 Long 
 Chord. 
 
 External 
 Secant. 
 
 Whole 
 Angle. 
 
 41 30' 
 
 2170.7 
 
 4059.8 
 
 397-4 
 
 41 3' 
 
 32' 
 
 2172.6 
 
 4062 . 9 
 
 398.1 
 
 32' 
 
 34' 
 
 2174.5 
 
 4066 .0 
 
 398.8 
 
 34' 
 
 36; 
 
 2176.4 
 
 4069 . 2 
 
 399-5 
 
 36' 
 
 
 2178.3 
 
 4072.3 
 
 400.2 
 
 38' 
 
 40' 
 
 2180.3 
 
 4075-4 
 
 400.9 
 
 40' 
 
 42' 
 
 2l82 . 2 
 
 4078.5 
 
 401 .6 
 
 42' 
 
 44' 
 
 2184. I 
 
 4081 .6 
 
 4O2 . 2 
 
 44' 
 
 46' 
 
 2186. o 
 
 4084.7 
 
 402.9 
 
 46' 
 
 48' 
 
 2188.0 
 
 4087.9 
 
 403.6 
 
 48' 
 
 5 0/ 
 
 2189.9 4 
 
 4091 .0 
 
 404.3 
 
 5' 
 
 5 2/ 
 
 2191.8 " 
 
 4094.1 
 
 405.0 
 
 52' 
 
 54' 
 
 2193-7 * 
 
 4097.2 
 
 405.6 
 
 54' 
 
 56' 
 
 2195-6 -g 
 
 4100.3 
 
 406.3 
 
 56' 
 
 58' 
 
 2197-5 
 
 4103.4 
 
 407.0 
 
 58' 
 
 42 
 
 2199.4 " 
 
 4106.6 
 
 407.7 
 
 42 
 
 2' 
 
 2201.3 ^ 
 
 4109.7 
 
 408 .4 
 
 2' 
 
 4' 
 
 2203.3 
 
 4112.8 
 
 409.0 
 
 4' 
 
 6' 
 
 2205.2 ?>*- 
 
 4115.9 
 
 409.7 ^i 
 
 6' 
 
 8' 
 
 2207 . 1 jg: Ig 
 
 4119.0 
 
 410.4^- . 
 
 8' 
 
 10' 
 
 22O9 .O 'rt 
 
 4122 . i 
 
 4 ii. i 
 
 10' 
 
 12' 
 
 2210.9 'Sr 
 
 4125.2 
 
 411. 8 |:: 
 
 12' 
 
 14' 
 
 2212.9^ 
 
 4128.3 
 
 412.500 
 
 14' 
 
 16' 
 
 2214.8 2* 
 
 
 JH ^ 
 
 iff 
 
 18' 
 
 2216.7 "5 . 
 
 4134.5 
 
 4i3.8^t 
 
 1 8' 
 
 20' 
 
 2218. 6^'S- 
 
 4I37-7 
 
 414.5^- 
 
 20' 
 
 22' 
 
 2220.5 j: 
 
 4140 .8 
 
 415.25= s 
 
 22' 
 
 24' 
 
 2222.5 < 5 
 
 4I43-9 
 
 4I5-9 
 
 24' 
 
 26' 
 
 2224.4 
 
 4147.0 
 
 416.6 
 
 26' 
 
 28' 
 
 2226 .3 w 
 
 4150.1 
 
 4I7-3 
 
 28' 
 
 30' 
 
 2228.2 
 
 4I53-2 
 
 418.0 
 
 3' 
 
 32' 
 
 2230.2 
 
 4156 .3 
 
 418.7 
 
 32' 
 
 34' 
 
 2232 . i R 
 
 4I59-4 
 
 419.4 
 
 34' 
 
 36' 
 
 2234.0 ; 
 
 4162.5 
 
 420 . i 
 
 36' 
 
 38' 
 
 2235.9 < 
 
 4165 .6 
 
 420 .8 
 
 38' 
 
 40' 
 
 2237.8 
 
 4168.7 
 
 421.5 
 
 40' 
 
 42' 
 
 2239.8 
 
 4171.8 
 
 422 . 2 
 
 42' 
 
 44' 
 
 2241.7 
 
 4174.9 
 
 422.9 
 
 44' 
 
 46' 
 
 2243.6 
 
 4178.0 
 
 423.6 
 
 46' 
 
 48' 
 
 2245-5 
 
 4181 . i 
 
 424.3 
 
 48' 
 
 5 0/ 
 
 2247.4 
 
 4184.3 
 
 425.0 
 
 5' 
 
 52' 
 
 2249.4 
 
 4187 .4 
 
 425.7 
 
 52' 
 
 54 - 
 
 2251.3 
 
 4190.5 
 
 426.4 
 
 54' 
 
 56' 
 
 2253.2 
 
 4193.6 
 
 427.1 
 
 56' 
 
 58' 
 
 2255.1 
 
 4196.7 
 
 427.8 
 
 58' 
 
 73 
 
IX. FUNCTIONS OF A ONE-DEGREE CURVE. 
 
 Whole 
 Angle. 
 
 Tangent 
 Distance. 
 
 Long 
 Chord. 
 
 External 
 Secant. 
 
 Whole 
 Angle. 
 
 43 
 
 2257.0 
 
 4199.8 
 
 428.5 
 
 43 
 
 2' 
 
 2259.0 
 
 4202 .9 
 
 429.2 
 
 2' 
 
 4' 
 
 2260 . 9 
 
 4206.0 
 
 429.9 
 
 4 ; 
 
 6' 
 
 2262 .8 
 
 4209. I 
 
 430.6 
 
 
 8' 
 
 2264 . 7 
 
 4212 . 2 
 
 431-3 
 
 8' 
 
 to' 
 
 2266 .6 
 
 4215.3 
 
 432.0 
 
 10' 
 
 12' 
 
 2268.6 
 
 42l8 .4 
 
 432.7 
 
 12' 
 
 14' 
 
 2270.5 
 
 4221 .5 
 
 433-5 
 
 14' 
 
 16' 
 
 2272 .4 
 
 4224.6 
 
 434-2 
 
 16' 
 
 18' 
 
 2274.3 
 
 4227.7 
 
 434-9 
 
 18' 
 
 **' 
 
 2276 . 2 
 
 4230.8 
 
 435-6 
 
 20' 
 
 22' 
 
 2278 . 2 
 
 4133-9 
 
 436.3 
 
 22' 
 
 24' 
 
 2280.1 
 
 4237.0 
 
 437-o 
 
 34' 
 
 26' 
 
 2282 .0 
 
 4240 . i 
 
 437-8 
 
 26' 
 
 28' 
 
 2283.9 
 
 4243.2 
 
 438.5 
 
 28' 
 
 30' 
 
 2285.8 
 
 4246 . 2 
 
 439- 2 
 
 30' 
 
 32' 
 
 2287.7 
 
 4249-3 
 
 439-9 
 
 32' 
 
 34' 
 
 2289.6 ^ ; 4 
 
 4252.4 
 
 440.7 . . . 
 
 34' 
 
 36' 
 
 2291 -5 ""'^H 
 
 4 2 55 5 
 
 441.4 "><*;: 
 
 36' 
 
 38' 
 
 2293. 4|- . 
 
 4258.6 
 
 442.1 e z . 
 
 38' 
 
 40' 
 
 2295.5 rt 
 
 4261 .7 
 
 442. 8 ~ 
 
 40' 
 
 42' 
 
 2297 .6 'g,- : 
 
 4264 .8 
 
 443 5 = : 
 
 42' 
 
 44' 
 
 2299-5^ 
 
 4267.9 
 
 444 . 2 CG 
 
 44' 
 
 46' 
 
 2301. 4 - 
 
 4271 .0 
 
 445 -0^ : = 
 
 46' 
 
 48' 
 
 2303-3 4$ 
 
 4274.1 
 
 445-7 ;? 
 
 48' 
 
 5' 
 
 23 5.2 ^ **" 
 
 4277.2 
 
 446.4^ M 
 
 5o; 
 
 5 2/ 
 
 2307.2 j : : 
 
 4280.3 
 
 447.1 j: : 
 
 
 54' 
 
 2309.1 ? 
 
 4283.4 
 
 447-8^ 
 
 54' 
 
 56' 
 
 2311.0 
 
 4286.5 
 
 448.6 
 
 56' 
 
 58' 
 
 2312.9 
 
 4289 .6 
 
 449-3 
 
 58' 
 
 44 
 
 2314-9 
 
 4292.7 
 
 450.0 
 
 44 
 
 2' 
 
 2316.8 
 
 4295.8 
 
 450-7 
 
 2' 
 
 4' 
 
 2318.8 
 
 4298.9 
 
 
 4' 
 
 6' 
 
 2320.7 
 
 4302.0 
 
 452.2 
 
 6' 
 
 8' 
 
 2322.7 
 
 4305 - 1 
 
 452.9 
 
 8' 
 
 10' 
 
 2324.6 
 
 4308.1 
 
 453-6 
 
 10' 
 
 12' 
 
 2326 .6 
 
 4311.2 
 
 454-3 
 
 12' 
 
 14' 
 
 2328.5 
 
 4314.3 
 
 455-1 
 
 14' 
 
 16' 
 
 2330-5 
 
 43*7-4 
 
 455-8 
 
 16' 
 
 18' 
 
 2332.4 
 
 4320.5 
 
 456.5 
 
 18' 
 
 20' 
 
 2334-3 
 
 4323-5 
 
 457-3 
 
 20' 
 
 22 X 
 
 2336.3 
 
 4326.6 
 
 458.0 
 
 22 X 
 
 24' 
 
 2338.2 
 
 4329.7 
 
 458.8 
 
 24' 
 
 26' 
 
 2340.2 
 
 4332.8 
 
 459-5 
 
 26' 
 
 28' 
 
 2342.1 
 
 4335 -Q 
 
 460.3 
 
 28' 
 
 74 
 
IX. FUNCTIONS OF A ONE-DEGREE CURVE. 
 
 Whole 
 Angle. 
 
 Tangent 
 Distance. 
 
 Long 
 Chord. 
 
 External 
 Secant. 
 
 Whole 
 Angle. 
 
 44 30' 
 
 2344.0 
 
 4338.9 
 
 461 .O 
 
 44 30' 
 
 32' 
 
 2346.0 
 
 4342 .0 
 
 461.8 
 
 32' 
 
 34' 
 
 2347v9 
 
 4345 - 1 
 
 462.5 
 
 34' 
 
 36' 
 
 2349-8 
 
 4348.2 
 
 463.3 
 
 36' 
 
 38' 
 
 2351-8 
 
 435 J -3 
 
 464 .0 
 
 38' 
 
 40' 
 
 2353-7 
 
 4354-4 
 
 464.7 
 
 40' 
 
 42' 
 
 2355-7 
 
 4357-5 
 
 465.5 
 
 42' 
 
 44' 
 
 2357- 6 
 
 4360.6 
 
 466.2 
 
 44' 
 
 46' 
 
 2359- 6 
 
 4363-7 
 
 467.0 
 
 46' 
 
 48' 
 
 2361.5 
 
 4366.7 
 
 467.7 
 
 48' 
 
 50' 
 
 2363-5 
 
 4369.8 
 
 468.4 
 
 50' 
 
 52' 
 
 2365-5 
 
 437 2 -9 
 
 469.2 
 
 52' 
 
 54' 
 
 2367-4 
 
 4376.0 
 
 469.9 
 
 - 54' 
 
 56' 
 
 2369.4 
 
 4379-0 
 
 470.7 
 
 56' 
 
 58' 
 
 237I-3 
 
 4382.1 
 
 471.4 
 
 58' 
 
 45 
 
 2373-3 
 
 4385-2 
 
 472.1 
 
 45 
 
 2' 
 
 2375-3 
 
 4388.3 
 
 ' 472.8 
 
 2' 
 
 4' 
 
 2377-2 t& + 
 
 4391-4 
 
 473-6 . . . 
 
 4' 
 
 6' 
 
 2379.2.-. M 
 
 4394.5 
 
 474-3 ^ H 
 
 6' 
 
 8' 
 
 2381.2^: : 
 
 4397-6 
 
 475-1 js : 
 
 8' 
 
 10' 
 
 2383.il 
 
 4400 .6 
 
 475-8-g 
 
 10' 
 
 12' 
 
 2385- * " : 
 
 4403.7 
 
 476.6-g=: 
 
 12' 
 
 14' 
 
 2387.0^ 
 
 4406 . 8 
 
 477-3^ 
 
 14' 
 
 16' 
 
 2389.0^- 
 
 4409.9 
 
 478. i- : 
 
 16' 
 
 18' 
 
 o oo oo 
 
 2390'9 M NXA 
 
 ui v, O 
 
 4413.0 
 
 478.8^ 
 
 18' 
 
 20' 
 
 2392.9^ 
 
 4416 .0 
 
 479-6-d 
 
 20' 
 
 22' 
 
 2394.95: : 
 
 4419.0 
 
 480. 43 : : 
 
 22' 
 
 24' 
 
 2396. 8^ 
 
 4422.1 
 
 481.1 
 
 24' 
 
 26' 
 
 2398.8 
 
 4425.2 
 
 481.9 
 
 26' 
 
 28' 
 
 2400 . 7 
 
 4428.3 
 
 482.7 
 
 28' 
 
 30' 
 
 2402.7 
 
 4431-3 
 
 483-4 
 
 30; 
 
 32' 
 
 2404.7 
 
 4434-4 
 
 484.2 
 
 32 
 
 34' 
 
 2406 .6 
 
 4437-5 
 
 485.0 
 
 3 i 
 
 36' 
 
 2408.6 
 
 4440 . 5 
 
 485-7 
 
 36 
 
 38' 
 
 2410.5 
 
 4443-6 
 
 486.5 
 
 38' 
 
 40' 
 
 2412.5 
 
 4446 . 7 
 
 487.2 
 
 40' 
 
 42' 
 
 2414.5 
 
 4449 - 8 
 
 488.0 
 
 42' 
 
 44' 
 
 2416 .4 
 
 4452.8 
 
 488.8 
 
 44' 
 
 46' 
 
 2418.4 
 
 4455-9 
 
 489.5 
 
 46' 
 
 48' 
 
 2420.3 
 
 4459-0 
 
 490.3 
 
 48' 
 
 50' 
 
 2422.3 
 
 4462 . i 
 
 491 .0 
 
 50' 
 
 52 : 
 
 2424-3 
 
 4465.1 
 
 491.8 
 
 52 
 
 54'. 
 
 2426 . 2 
 
 4468.2 
 
 492.5 
 
 54 
 
 56' 
 
 2428.2 
 
 4471-3 
 
 493-3 
 
 56 
 
 ; 58' 
 
 2430.1 4474-4 
 
 494.1 
 
 58' 
 
 75 
 
IX.- FUNCTIONS OF A ONE-DEGREE CURVE. 
 
 Whole 
 Angle. 
 
 Tangent 
 Distance. 
 
 Long 
 Chord. 
 
 External 
 Secant. 
 
 Whole 
 Angle. 
 
 46 
 
 2432.1 
 
 4477-5 
 
 494-8 
 
 4G 
 
 2' 
 
 2434.1 
 
 4480 . 6 
 
 495-6 
 
 2' 
 
 4' 
 
 2436.0 
 
 4483.6 
 
 496.3 
 
 4' 
 
 6' 
 
 2438.0 
 
 4486.7 
 
 497.1 
 
 6' 
 
 r 
 
 2439.9 
 
 4489.8 
 
 497-9 
 
 8' 
 
 10' 
 
 2441.9 
 
 4492.8 
 
 498.7 
 
 10' 
 
 12' 
 
 2443.9 
 
 4495-9 
 
 499-5 
 
 12' 
 
 14' 
 
 2445.8 
 
 4498.9 
 
 5o-3 
 
 14' 
 
 16' 
 
 2447.8 
 
 4502 .0 
 
 501 .0 
 
 16' 
 
 18' 
 
 2449.7 
 
 4505.1 
 
 501.8 
 
 18' 
 
 20' 
 
 2451-7 
 
 4508. i 
 
 502.6 
 
 20' 
 
 22' 
 
 2453-7 
 
 4511.2 
 
 503.4 
 
 22' 
 
 24' 
 
 2455-7 
 
 45*4.3 
 
 504-2 
 
 24' 
 
 26' 
 
 2457.6 
 
 45*7-3 
 
 504.9 
 
 26' 
 
 28' 
 
 2459.6 
 
 4520.4 
 
 505.7 
 
 28' 
 
 30' 
 
 2461 .6 
 
 45 2 3-4 
 
 506.5 
 
 3' 
 
 32' 
 
 2463.6 
 
 
 507-3 
 
 32' 
 
 34' 
 
 2465-5 A o,4 
 
 4529.6 
 
 508.0 
 
 34' 
 
 36' 
 
 2467.5 
 
 4532.6 
 
 508.8 ^** 
 
 36' 
 
 38' 
 
 2469- 5 : : 
 
 4535-7 
 
 509-6 6, : 
 
 38' 
 
 .40' 
 
 247 I -5l . 
 
 4538.8 
 
 510.4* 
 
 40' 
 
 42' 
 
 2473.51" " 
 
 4541.8 
 
 5 II. 2. |: = 
 
 42' 
 
 44' 
 
 2475-4 g. - 
 
 4544-9 
 
 512 .0 co 
 
 44' 
 
 46' 
 
 2477. 4 ^ a " H 
 
 4548.0 
 
 512 .7 ,0= 5 
 
 46' 
 
 48' 
 
 2479- 4 ~o 
 
 455i.o 
 
 5*3-5 ^^ 
 
 48' 
 
 50' 
 
 2481.4.?*" 
 
 4554.1 
 
 5*4-3 s*t 
 
 50' 
 
 52 
 
 2483.45= = 
 
 4557-2 
 
 515 . i tfs = 
 
 52' 
 
 54' 
 
 2485.4 
 
 4560.2 
 
 515 .9 
 
 54' 
 
 56' 
 
 2487-3 
 
 4563.3 
 
 516.6 
 
 56' 
 
 58' 
 
 2489.3 
 
 4566.4 
 
 5*7-4 
 
 58' 
 
 47 
 
 2491.3 
 
 4569-4 , 
 
 518.2 
 
 47 
 
 2' 
 
 2493.3 
 
 4572.4 
 
 519.0 
 
 2' 
 
 4' 
 
 2495.3 
 
 4575-5 
 
 519.8 
 
 4' 
 
 6' 
 
 2497.3 
 
 4578.5 
 
 520.6 
 
 6' 
 
 8' 
 
 2499.2 
 
 4581.6 
 
 521.4 
 
 8' 
 
 10' 
 
 2501 .2 
 
 4584.6 
 
 522 . 2 
 
 10' 
 
 12' 
 
 2503.2 
 
 4587-7 
 
 5 2 3 "O 
 
 12' 
 
 14' 
 
 2505.2 
 
 4590.7 
 
 523.8 
 
 14' 
 
 16' 
 
 2507.2 
 
 4593-8 
 
 524.6 
 
 16' 
 
 18' 
 
 2509.1 
 
 4596.8 
 
 5 2 5.4 
 
 18' 
 
 20' 
 
 2511 . I 
 
 4599-9 
 
 526 . 2 
 
 20' 
 
 22' 
 
 25I3.I 
 
 4602 . 9 
 
 527.0 
 
 22' 
 
 24' 
 
 25*5. i 
 
 4606 .0 
 
 527.8 
 
 24' 
 
 26' 
 
 2517.1 
 
 4609 . o 
 
 528.6 
 
 26' 
 
 28' 
 
 2519.1 
 
 4612 . i 
 
 529-4 
 
 28' 
 
 76 
 
IX. FUNCTIONS OF A ONE-DEGREE CURVE. 
 
 Whole 
 Angle. 
 
 Tangent 
 Distance. 
 
 Long 
 Chord. 
 
 External 
 Secant. 
 
 Whole 
 Angle. 
 
 47 3' 
 
 2521 .O 
 
 4615.1 
 
 530.2 
 
 4:7 3 0' 
 
 32' 
 
 2523.0 
 
 4618.2 
 
 53LO 
 
 32' 
 
 34' 
 
 2525-0 
 
 4621 .2 
 
 53L8 
 
 34' 
 
 36' 
 
 2527 .0 
 
 4624.3 
 
 532.6 
 
 36' 
 
 38' 
 
 2529.0 
 
 4627.3 
 
 533-4 
 
 38' 
 
 4' 
 
 2531.0 
 
 4630.4 
 
 534-2 
 
 40' 
 
 42' 
 
 2533.0 
 
 4633.4 
 
 535-0 
 
 42' 
 
 44' 
 
 2535.0 
 
 4636.5 
 
 535-8 
 
 44' 
 
 46' 
 
 2537.0 
 
 4639.5 
 
 536.6 
 
 46' 
 
 48' 
 
 2539.0 
 
 4642 .6 
 
 537-4 
 
 48' 
 
 5' 
 
 2541.0 4 
 
 4645-6 
 
 538.2 
 
 5 0/ 
 
 52' 
 
 2543.0 
 
 4648.7 
 
 539-0 
 
 52 ! 
 
 54' 
 
 2545.0 
 
 4651.7 
 
 539-8 
 
 54 
 
 56' 
 
 2547-0 -3 
 
 4654-8 
 
 540.6 
 
 56' 
 
 58' 
 
 2549.0 . 
 
 4657.8 
 
 54L4 
 
 58' 
 
 48 
 
 CO 
 
 255 1 - K 
 
 4660 .9 
 
 542.3 
 
 48 
 
 2' 
 
 2553-0 * 
 
 4663.9 
 
 543-1 
 
 2' 
 
 4' 
 
 2555-0 o 
 
 4667 .0 
 
 544-0 . . . 
 
 4' 
 
 6' 
 
 2557.0 ^<* 
 
 4670.0 
 
 544.8 ""*;? 
 
 6' 
 
 8' 
 
 2559-0 |s : 
 
 4673-1 
 
 545- 6 0; = 
 
 8' 
 
 10' 
 
 2561.0*2 
 
 4676 . i 
 
 546. 4-g 
 
 10' 
 
 12' 
 
 2563 -o-a : 
 
 4679.1 
 
 547. 2 -a : : 
 
 12' 
 
 14' 
 
 2565-0^ 
 
 4682.2 
 
 548.0^ 
 
 14' 
 
 1 6' 
 
 2567.0^ 
 
 4685.2 
 
 548.9-5= = 
 
 16' 
 
 18' 
 
 
 4688.2 
 
 549-7^25 
 
 18' 
 
 20' 
 
 257 1 - jpd 
 
 4691.3 
 
 55-5-;g_ _ H 
 
 20' 
 
 22' 
 
 2573-o^: * 
 
 4694.3 
 
 
 22' 
 
 24' 
 
 2575-0^ "g 
 
 4697.3 
 
 552.2 
 
 24' 
 
 26' 
 
 2577-0 
 
 4700.4 
 
 553-o 
 
 26' 
 
 28' 
 
 2579.0 g 
 
 47 3.4 
 
 553-8 
 
 28' 
 
 3' 
 
 2581.0 *> 
 
 4706.4 
 
 554-6 
 
 30; 
 
 32' 
 
 2583-0 ^ 
 
 4709.5 
 
 555-4 
 
 32 
 
 34' 
 
 2585-0 
 
 47 I2 -5 
 
 556.2 
 
 34 
 
 36' 
 
 2587.0 3 
 
 47^.5 
 
 557-0 
 
 36' 
 
 38' 
 
 2589.0 
 
 4718.6 
 
 557-9 
 
 38' 
 
 40' 
 
 2591 .0 
 
 4721.6 
 
 558.7 
 
 40' 
 
 42' 
 
 2593-0 
 
 4724.6 
 
 559-5 
 
 42' 
 
 44' 
 
 2595-0 
 
 4727.6 
 
 560.3 
 
 44' 
 
 46' 
 
 2597-1 
 
 4730.7 
 
 561.2 
 
 46' 
 
 48' 
 
 2599.1 
 
 4733-7 
 
 562.0 
 
 48' 
 
 50' 
 
 2601 . 
 
 4736.8 
 
 562.8 
 
 5' 
 
 52' 
 
 2603. 
 
 4739-8 
 
 563-6 
 
 52 ', 
 
 54' 
 
 2605. 
 
 4742.8 
 
 564-4 
 
 54 
 
 56' 
 
 2607 . 
 
 4745-9 
 
 565-3 
 
 56 
 
 58' 
 
 2609. 
 
 4748.9 
 
 566.1 
 
 58' 
 
IX. FUNCTIONS OF A ONE-DEGREE CURVE. 
 
 Whole 
 Angle. 
 
 Tangent 
 Distance. 
 
 Long 
 Chord. 
 
 External 
 Secant. 
 
 Whole 
 Angle. 
 
 49 
 
 26ll .2 
 
 4752.0 
 
 566.9 
 
 49 
 
 2' 
 
 2613 .2 
 
 4755-0 
 
 567-7 
 
 2' 
 
 4' 
 
 2615.2 
 
 4758'. 
 
 5 68.6 
 
 4' 
 
 6' 
 
 2617.2 
 
 4761 .0 
 
 569-4 
 
 6' 
 
 8' 
 
 2619 . 2 
 
 4764. i 
 
 57-3 
 
 8' 
 
 10' 
 
 2621 . 2 
 
 4767.1 
 
 57 1 - 1 
 
 10' 
 
 12' 
 
 2623.3 
 
 4770.1 
 
 572.0 
 
 12' 
 
 14' 
 
 2625.3 
 
 4773-1 
 
 572.8 
 
 14' 
 
 16' 
 
 2627.3 
 
 4776.2 
 
 573-6 
 
 16' 
 
 1 8' 
 
 2629.3 
 
 4779-2 
 
 574-5 
 
 i8 r 
 
 20' 
 
 2631.3 4 
 
 4782.3 
 
 575-3 
 
 20' 
 
 22' 
 
 2633.4 
 
 4785-3 
 
 576.2 
 
 22' 
 
 24' 
 
 2635.4 | 
 
 4788.3 
 
 577-o 
 
 24' 
 
 26' 
 
 2637.4 - 
 
 4791.4 
 
 577-9 
 
 26' 
 
 28' 
 
 2639.4 . 
 
 4794.4 
 
 558.7 
 
 28' 
 
 30' 
 
 2641.4 ^ 
 
 4797-4 
 
 579-5 
 
 30' 
 
 32' 
 
 2643.5 
 
 4800.5 
 
 580.4 
 
 32' 
 
 34' 
 
 2645-5 5 
 
 4803.5 
 
 581.2 . . . 
 
 34' 
 
 36' 
 
 2647.5 xAoR 
 
 4806 . 5 
 
 582.1 IOCV 2 
 
 36' 
 
 38' 
 
 2649.5 |: ? 
 
 4809 .6 
 
 582.9^, ; 
 
 & 
 
 40' 
 
 2651.5-3 ^ 
 
 4812.6 
 
 583-8^ 
 
 40' 
 
 42' 
 
 2653.6-*: 
 
 4815.6 
 
 584. 6. g: : 
 
 42' 
 
 44' 
 
 2655.6* 
 
 4818.6 
 
 585.5^ 
 
 44' 
 
 46' 
 
 2657 .6 ,0 = 
 
 4821.7 
 
 sWvs'l; = 
 
 46' 
 
 48' 
 
 2659.6 <^<^^ 
 
 4824.7 
 
 587 .2 oq e> 
 
 48' 
 
 So' 
 
 2661 .6 ' M 
 
 4827.7 
 
 588.!^" 
 
 50' 
 
 $*' 
 
 2663. 7 5. ; 
 
 4830.7 
 
 588.95= = 
 
 52' 
 
 54' 
 
 2665.7 ^ * 
 
 4833-8 
 
 589- 7 < 
 
 54' 
 
 56' 
 
 2667.7 -g, 
 
 4836.8 
 
 590.6 
 
 56' 
 
 58' 
 
 2669.7 < 
 
 4839.8 
 
 59i-4 
 
 58' 
 
 5O 
 
 2671.7 <~ 
 
 4842.9 
 
 592.3 
 
 5O 
 
 2' 
 
 2673.7 ^ 
 
 4845-9 
 
 593-2 
 
 2' 
 
 4' 
 
 2675.8 * 
 
 4848.9 
 
 594-0 
 
 4 r 
 
 6' 
 
 2677.8 S 
 
 4852.0 
 
 594-9 
 
 6' 
 
 r 
 
 2679.8 
 
 4855-0 
 
 595-8 
 
 8' 
 
 10' 
 
 2681.9 
 
 4858.0 
 
 596.7 
 
 10' 
 
 12' 
 
 2683.9 
 
 4861 .0 
 
 597-6 
 
 12' 
 
 14' 
 
 2686.0 
 
 4864.0 
 
 598.4 
 
 14' 
 
 16' 
 
 2688.0 
 
 4867. 
 
 599-3 
 
 16' 
 
 18' 
 
 26^0. i 
 
 4870. 
 
 600. i 
 
 18' 
 
 20' 
 
 2692 . i 
 
 4873- 
 
 601 .0 
 
 20' 
 
 22' 
 
 2694. i 
 
 4876. 
 
 601 .9 
 
 22' 
 
 24' 
 
 2696 . 2 
 
 4879. 
 
 602 .7 
 
 24' 
 
 26' 
 
 2698.2 
 
 4882 .2 
 
 603.6 
 
 26' 
 
 28' 
 
 27OO .3 
 
 4885.2 
 
 604.4 
 
 28' 
 
 78 
 
IX. FUNCTIONS OF A ONE-DEGREE CURVE. 
 
 Whole 
 Angle. 
 
 Tangent 
 Distance. 
 
 Long 
 
 Chord. 
 
 External 
 Secant. 
 
 Whole 
 Angle. 
 
 50 30' 
 
 2702.3 
 
 4888.2 
 
 605-3 
 
 50 30' 
 
 32' 
 
 2704.3 
 
 4891 . 2 
 
 606 . 2 
 
 32' 
 
 34' 
 
 2706 .4 
 
 4894 . 2 
 
 607 .O 
 
 34' 
 
 36' 
 
 2708 .4 
 
 4897.2 
 
 607.9 
 
 36' 
 
 38' 
 
 2710.5 
 
 49OO . 2 
 
 608.8 
 
 38' 
 
 4' 
 
 2712.5 
 
 4903.2 
 
 609.7 
 
 40' 
 
 42' 
 
 27M.5 - 
 
 4906 . 2 
 
 610 . 6 
 
 42' 
 
 44' 
 
 2716.6 c 
 
 4909.2 
 
 611.5 
 
 44' 
 
 46' 
 
 2718.6 
 
 4912.2 
 
 612.3 
 
 46' 
 
 48' 
 
 2720.7 | 
 
 p, 
 
 49I5-2 
 
 613-2 
 
 48' 
 
 5' 
 
 2722 . 7 ^ 
 
 4918 . 2 
 
 614. i 
 
 50' 
 
 52' 
 
 2724.8 
 
 4921.3 
 
 615 .0 
 
 52' 
 
 S4' 
 
 2726.8 <? 
 
 4924.3 
 
 615.8 
 
 54' 
 
 56' 
 
 2728.8 | 
 
 4927-3 
 
 616.7 
 
 56' 
 
 58' 
 
 2730.9 1" 
 
 4930-3 
 
 617.6 
 
 58' 
 
 51 
 
 2732.9 < 
 
 4933.3 
 
 618.5 
 
 51 
 
 2' 
 
 2734-9 
 
 4936.3 
 
 619.4 
 
 2' 
 
 4' 
 
 2737.0 
 
 4939-3 
 
 620.3 . 
 
 4' 
 
 6' 
 
 2739.0 
 
 4942.3 
 
 621.2 l ":r 
 
 6' 
 
 8' 
 
 2741 . 1 "> c>4 
 
 4945-3 
 
 622 .0 c : - 
 
 8' 
 
 10' 
 
 2743.1 | = : 
 
 4948.3 
 
 622. Q-g 
 
 10' 
 
 12' 
 
 2745.1- 
 
 495J-3 
 
 623.8-^= 
 
 12' 
 
 14' 
 
 2747. 2. : - 
 
 4954-3 
 
 624. 7< 
 
 14' 
 
 16' 
 
 2749.2 & 
 
 4957-3 
 
 625.6,5= = 
 
 16' 
 
 1 8' 
 
 275J-3.C: : 
 
 4960.3 
 
 626.4 ^ " 
 
 ^ W 00 00 
 
 18' 
 
 20' 
 
 2753-3 2S2. 
 
 4963-3 
 
 627- 3-d 
 
 20' 
 
 22' 
 
 2755-3 3R 
 
 4966.3 
 
 628.233- = 
 
 22' 
 
 24' 
 
 2757-4;^ s 
 
 4969.3 
 
 629 . 1 
 
 24' 
 
 26' 
 
 2759-4<T " 
 
 497 2 -3 
 
 630.0 
 
 26' 
 
 28' 
 
 2761.5 
 
 4975-3 
 
 630.8 
 
 28' 
 
 3' 
 
 2763.6 
 
 4978.3 
 
 631-7 
 
 3o' 
 
 32' 
 
 2765.6 j 
 
 4981.3 
 
 632.6 
 
 32' 
 
 34' 
 
 2767.7 o 
 
 49 8 4- 3 
 
 633.5 
 
 34' 
 
 36' 
 
 2769.8 * 
 
 4987-3 
 
 634.4 
 
 36' 
 
 38' 
 
 2771.8 * 
 
 4990-3 
 
 635-3 
 
 38' 
 
 40' 
 
 2773.9 c& 
 
 4993-3 
 
 636.2 
 
 40' 
 
 42' 
 
 2775.9 
 
 4996.3 
 
 637-1 
 
 42' 
 
 44' 
 
 2778.0 
 
 4999-3 
 
 638.0 
 
 44' 
 
 46' 
 
 2780. I 
 
 5002.3 
 
 638.9 
 
 46' 
 
 48' 
 
 2782.2 
 
 5005.3 
 
 639.8 
 
 48' 
 
 5' 
 
 2784.2 < 
 
 5008.3 
 
 640.7 
 
 50' 
 
 5 2 
 
 2786.3 
 
 50H-3 
 
 641 .6 
 
 52' 
 
 54' 
 
 2788.4 
 
 5014-3 
 
 642.5 
 
 54' 
 
 56' 
 
 2790.4 
 
 5 OI 7-3 
 
 643-4 
 
 56' 
 
 58' 
 
 2792-5 
 
 5020 .3 
 
 644-3 
 
 58' 
 
 79 
 
IX. FUNCTIONS OF A ONE-DEGREE CURVE. 
 
 Whole 
 Angle. 
 
 Tangent 
 Distance. 
 
 Long 
 Chord. 
 
 External 
 Secant. 
 
 Whole 
 Angle. 
 
 52 
 
 2794.5 
 
 5023.3 
 
 645.2 
 
 >2 
 
 2' 
 
 2796.6 
 
 5026.3 
 
 646. I 
 
 2' 
 
 4' 
 
 2798.6 
 
 5029.3 
 
 647.0 
 
 4' 
 
 6' 
 
 2800.7 4 
 
 5032 . 3 
 
 647.9 
 
 6' 
 
 8' 
 
 2802.7 
 
 o 
 
 5035-3 
 
 648 . 8 
 
 8' 
 
 10' 
 
 2804.8 5z 
 
 5038.3 
 
 649-7 
 
 10' 
 
 12' 
 
 2806.8 1J 
 
 504L3 
 
 650.6 
 
 12' 
 
 14' 
 
 2808.9 '& 
 
 5044-3 
 
 651 . 5 
 
 14' 
 
 16' 
 
 28ll .O VH 
 
 5047.3 
 
 652.4 
 
 16' 
 
 18' 
 
 28I3.I <~ 
 
 5050-3 
 
 653-3 
 
 18' 
 
 20' 
 
 2815.2 ^ ^ 
 
 5053.3 
 
 654.3 
 
 20' 
 
 22' 
 
 2817 .3 ?o 4J 
 
 5056.3 
 
 655 2 
 
 22' 
 
 24' 
 
 2819. 3 1' ^ 
 
 5059-3 
 
 656.1 
 
 24' 
 
 26' 
 
 2821 .4 'g 
 
 5062.3 
 
 657.0 
 
 26' 
 
 28' 
 
 2823.5 ja : 
 
 5065.3 
 
 658.0 
 
 28' 
 
 3' 
 
 2825.5 &. 
 
 5068.3 
 
 658.9 
 
 3' 
 
 32' 
 
 2827 .6 ^ -r 
 
 507L3 
 
 659.8 
 
 32' 
 
 34' 
 
 2829.7 H.O 4 
 
 5074.3 
 
 660.7 . . . 
 
 34' 
 
 36' 
 
 2831.7,5*0 
 
 5077.3 
 
 66 1 .6 "'*'* 
 
 36' 
 
 38' 
 
 2833.8^: fc 
 
 5080.3 
 
 662.5 o. : 
 
 38 
 
 40' 
 
 2835.9 ' -| 
 
 5083.3 
 
 663.5-3 
 
 40' 
 
 42' 
 
 2837.9 co 
 
 5086.3 
 
 664. 4 5 = 
 
 42' 
 
 44' 
 
 2840.0 J5 
 
 5089-3 
 
 665.3^ 
 
 44' 
 
 46' 
 
 2842.1 
 
 5092.3 
 
 666 .3 - : 
 
 46' 
 
 48' 
 
 2844.2 S" 
 
 5095-3 
 
 667-2 ^^^ 
 
 48' 
 
 50' 
 
 2846.3 ; 
 
 5098.3 
 
 668.1^ H 
 
 50' 
 
 52' 
 
 2848.4 <! 
 
 5 IOI -3 
 
 669.0^= s 
 
 52' 
 
 54' 
 
 2850.4 
 
 5 I0 4-3 
 
 670 .0 
 
 54' 
 
 56' 
 
 2852.5 
 
 5 I0 7-3 
 
 670.9 
 
 56' 
 
 58' 
 
 2854.6 
 
 5110.2 
 
 671.8 
 
 58' 
 
 53 
 
 2856.7 
 
 5113.2 
 
 672.7 
 
 53 
 
 2' 
 
 2858.8 t ^4 
 
 5116.2 
 
 673-6 
 
 2' 
 
 4' 
 
 2860.8 . M 
 
 5119.2 
 
 674.6 
 
 4' 
 
 6' 
 
 2862.9 : : 
 
 5122 . 2 
 
 675-5 
 
 6' 
 
 8' 
 
 2865.0-3 
 
 5 I2 5-i 
 
 676.4 
 
 8' 
 
 10' 
 
 2867. 1 'J. 5 : 
 
 5128.1 
 
 677-3 
 
 10' 
 
 12' 
 
 2869.2 * tH 
 
 5131 . i 
 
 678.2 
 
 12' 
 
 14' 
 
 2 87 1- 3^V^> 
 
 5134. i 
 
 679.1 
 
 14' 
 
 16' 
 
 2873.4 ^S- 
 
 5 I 37- 
 
 680. i 
 
 16' 
 
 18' 
 
 2875.5^^ 
 
 5140 .0 
 
 681.0 
 
 18' 
 
 20' 
 
 2877.S3- : 
 
 5142.9 
 
 682.0 
 
 20' 
 
 22' 
 
 2879.6^ 
 
 5 J 45-9 
 
 682.9 
 
 22' 
 
 24' 
 
 2881.7 
 
 5148.9 
 
 683.8 
 
 24' 
 
 26' 
 
 2883.8 
 
 5151-8 
 
 684.8 
 
 26' 
 
 28' 
 
 2885.8 
 
 5J54-8 
 
 685.7 
 
 28' 
 
 80 
 
IX. FUNCTIONS OF A ONE-DEGREE CURVE. 
 
 Whole 
 Angle. 
 
 Tangent 
 Distance. 
 
 Long 
 Chord. 
 
 External 
 Secant. 
 
 Whole 
 Angle. 
 
 53 30' 
 
 2887.9 
 
 5157.8 
 
 686.7 
 
 53 30' 
 
 32' 
 
 2890.0 
 
 5160.8 
 
 687.6 
 
 32' 
 
 34' 
 
 2892 . I 
 
 5163.7 
 
 688.6 
 
 34' 
 
 36' 
 
 2894.2 xA^4 
 
 5166.7 
 
 689.5 
 
 36' 
 
 38' 
 
 2896.3 6 
 
 5 l6 9-7 
 
 690.5 
 
 38' 
 
 40' 
 
 2898. 4*' 
 
 5172.6 
 
 691.4 
 
 40' 
 
 42' 
 
 2900.5 * : 
 
 5175 .6 
 
 692.4 
 
 42' 
 
 44' 
 
 2902 .6 jg" 
 
 5178.6 
 
 693.3 
 
 44' 
 
 46' 
 
 2904-7 5- : 
 
 
 694.3 
 
 46' 
 
 48' 
 
 2906.8 ^^ 
 
 5184.5 
 
 695-2 
 
 48' 
 
 50' 
 
 2908.9 
 
 5187.4 
 
 696. i 
 
 50' 
 
 S^' 
 
 2911.0^* 
 
 5190.4 
 
 697.1 
 
 52' 
 
 54' 
 
 2913.1 3= s 
 
 5I93.4 
 
 698.0 
 
 54 
 
 56' 
 
 2915.2 
 
 5196.3 
 
 699 .0 
 
 56 
 
 58' 
 
 
 5*99-3 
 
 700 .0 
 
 58' 
 
 54 
 
 2919.4 
 
 5202.3 
 
 700.9 
 
 54 
 
 2' 
 
 2921.5 
 
 5205.3 
 
 701.9 
 
 2' 
 
 4' 
 
 2923.6 
 
 52O8 . 2 
 
 702.8 
 
 4' 
 
 6' 
 
 2925.7 
 
 5211 . 2 
 
 703.8 ^j 
 
 6' 
 
 8' 
 
 2927 .8 
 
 5214.2 
 
 704.7 0; - 
 
 8' 
 
 10' 
 
 2929.9 
 
 52I7.I 
 
 705.713 
 
 10' 
 
 12' 
 
 2932.0 
 
 5220.1 
 
 706.6.*: : 
 
 12' 
 
 14' 
 
 2934.1 
 
 5223.1 
 
 707 .6 co 
 
 I 4 f 
 
 1 6' 
 
 2936.2 
 
 5226 .O 
 
 708.5,= = 
 
 16' 
 
 1 8' 
 
 2938.3 . . 
 
 5229.0 
 
 709.5 J 
 
 18' 
 
 20' 
 
 2940.4 ^- 
 
 5232.0 
 
 710.5 ^ ~ M 
 
 20' 
 
 22' 
 
 2942.51: : 
 
 5235.0 
 
 711. 4 |= : 
 
 22' 
 
 24 
 
 2944. 6 ~ 
 
 5237.9 
 
 712.4 
 
 24' 
 
 26' 
 
 2946.7.*: : 
 
 5240.9 
 
 7I3.4 
 
 26' 
 
 28' 
 
 2948.8 co 
 
 5243.9 
 
 7 J 4.3 
 
 28' 
 
 3' 
 
 2950.9^ : 
 
 5246.8 
 
 715.3 
 
 3' 
 
 32' 
 
 2953.0^2 
 
 5249.8 
 
 716 .3 
 
 32; 
 
 34' 
 
 2955.2 3 
 
 5252.8 
 
 717.2 
 
 34 
 
 36' 
 
 2957. 3I- s 
 
 
 718.2 
 
 3 o 
 
 38' 
 
 2959. 4<" " 
 
 5258^ 
 
 719.2 
 
 38' 
 
 40' 
 
 2961.5 
 
 5261 .6 
 
 720 . i 
 
 40' 
 
 42' 
 
 2963.6 
 
 5264.6 
 
 721.1 
 
 42' 
 
 44' 
 
 2965.8 
 
 5267.6 
 
 722 .1 
 
 44' 
 
 46' 
 
 2967.9 
 
 5 S 70.5 
 
 723.1 
 
 46' 
 
 48' 
 
 2970.0 
 
 5273.5 
 
 724.0 
 
 48' 
 
 5' 
 
 2972.1 
 
 5276.5 
 
 725.0 
 
 5 0/ 
 
 52' 
 
 2974.2 
 
 5279.5 
 
 726 .0 
 
 $ 2 ', 
 
 54' 
 
 2976.4 
 
 5282.4 
 
 727.0 
 
 
 56' 
 
 2978-5 
 
 5285.4 
 
 728.0 
 
 56' 
 
 58' 
 
 2980 . 6 
 
 5288.3 
 
 728.9 
 
 58' 
 
 81 
 
IX. FUNCTIONS OF A ONE-DEGREE CURVE. 
 
 Whole 
 Angle. 
 
 Tangent 
 Distance. 
 
 Long 
 Chord. 
 
 External 
 Secant . 
 
 Whole 
 Angle. 
 
 55 
 
 2982.7 
 
 529I-3 
 
 729.9 
 
 55 
 
 2' 
 
 2984.8 
 
 5294.2 
 
 73-9 
 
 2' 
 
 4' 
 
 2987 .0 
 
 5297.2 
 
 731-9 
 
 4' 
 
 6' 
 
 2989.1 4 
 
 5300.1 
 
 732. -9 
 
 6' 
 
 8' 
 
 2991.2 
 
 5303-I 
 
 733-8 
 
 8' 
 
 10' 
 
 2993.3 * 
 
 5306.0 
 
 734-8 
 
 10' 
 
 12' 
 
 2995.4 . 
 
 5309-0 
 
 735-8 
 
 I2 f 
 
 14' 
 
 2997.6 
 
 53 11 -9 
 
 736.8 
 
 14' 
 
 16' 
 
 2999-7 
 
 53 J 4-9 
 
 737-7 
 
 16' 
 
 18' 
 
 3001.8 
 
 53I7-8 
 
 738.7 
 
 18' 
 
 20' 
 
 3003.9 ^o 
 
 5320.8 
 
 739-7 
 
 20'. 
 
 22' 
 
 3006.0 6 _ 
 
 
 740.7 
 
 22 r 
 
 24' 
 
 3008.2 K~ J5 
 
 5326.7 
 
 74L7 
 
 24' 
 
 26' 
 
 3 IO -3 I? 
 
 5329 V .6 
 
 
 26' 
 
 28' 
 
 3012.4 : 
 
 5332.6 
 
 743-6 
 
 28' 
 
 30; 
 
 3014.5 S: 
 
 5335-5 
 
 744-6 
 
 30' 
 
 
 3016.6 ^ 
 
 5338.5 
 
 745-6 
 
 32' 
 
 34 J 
 
 3018.8 ~? 
 
 534L4 
 
 746.6 ^4 
 
 34' 
 
 36' 
 
 3020.9^*6 
 
 5344.4 
 
 747-6 . 
 
 36' 
 
 38' 
 
 3023. o|: J 
 
 5347-3 
 
 748.6^: 
 
 38' 
 
 40' 
 
 3025.1 1 
 
 5350.2 
 
 749.6^ j 
 
 40' 
 
 42' 
 
 3027.3 to 
 
 5353-2 
 
 750. 6 |r ' 
 
 42' 
 
 44' 
 
 3029.4 .0 
 
 5356.1 
 
 751-6 . 5 
 
 44' 
 
 46' 
 
 3031.5 r 
 
 5359-1 
 
 752 .6 ^ w ^ 
 
 46' 
 
 48' 
 
 3033.7 o 
 
 5362.0 
 
 753.6 ci^oo 
 
 48' 
 
 5o; 
 
 3035-8 : 
 
 5365-0 
 
 754-6^ : = 
 
 5 0/ 
 
 
 3037-9 < 
 
 5367.9 
 
 
 52' 
 
 54' 
 
 3040.0 
 
 5370.9 
 
 75^6 
 
 54 
 
 56' 
 
 3042.2 
 
 5373-8 
 
 757-6 
 
 56' 
 
 58' 
 
 3044-3 
 
 5376.8 
 
 758.6 
 
 58' 
 
 56 
 
 3046.5 
 
 5379-7 
 
 759-6 
 
 56 
 
 2 f 
 
 3048.6 ^4 
 
 5382.7 
 
 760.6 
 
 2 ' 
 
 4' 
 
 3050.8 . M 
 
 5385-6 
 
 761.6 
 
 4' 
 
 6' 
 
 3052.9^" K 
 
 5388.6 
 
 762.6 
 
 6' 
 
 8' 
 
 3055.1 -j^ _ 
 
 5391-5 
 
 763.6 
 
 8' 
 
 10' 
 
 3057-2'^" : 
 
 5394-4 
 
 764.6 
 
 io r 
 
 12' 
 
 3059-2 g. .- 
 
 5397-4 
 
 765:6 
 
 12' 
 
 14' 
 
 3061. 4^00 
 
 5400.3 
 
 766.7 
 
 14' 
 
 16' 
 
 3063.6 MC^g. 
 
 5403-2 
 
 767.7 
 
 16' 
 
 18' 
 
 3065.8 *- 
 
 54o6.2 
 
 768.7 
 
 18' 
 
 20' 
 
 3067.9^- = 
 
 5409.1 
 
 769-7 
 
 20' 
 
 22' 
 
 3070.0 
 
 5412.0 
 
 770.7 
 
 22' 
 
 24' 
 
 3072.2 
 
 5415 .0 
 
 771.7 
 
 24' 
 
 26' 
 
 3074.4 
 
 54I7-9 
 
 772.8 
 
 26' 
 
 28' 
 
 3076.5 
 
 5420 . 8 
 
 773-8 
 
 28' 
 
IX. FUNCTIONS OF A ONE-DEGREE CURVE. 
 
 Whole 
 Angle. 
 
 Tangent 
 Distance. 
 
 Long 
 Chord. 
 
 External 
 Secant. 
 
 Whole 
 Angle. 
 
 56 30' 
 
 3078.6 
 
 5423.7 
 
 774-8 
 
 56 30' 
 
 32' 
 
 3080.8 
 
 5426.7 
 
 775-8 
 
 32' 
 
 34' 
 
 3082.9 
 
 5429.6 
 
 776.8 
 
 34' 
 
 36' 
 
 3085.1 t*4 
 
 5432.5 
 
 777-9 
 
 36' 
 
 38' 
 
 3087.3 ^ ^ 
 
 5435-5 
 
 778.9 
 
 38' 
 
 40' 
 
 3089. 4 2" 
 
 5438.4 
 
 779-9 
 
 40' 
 
 42' 
 
 3091 .6 g. - 
 
 544L3 
 
 780.9 
 
 42' 
 
 44' 
 
 3093. 8 '|T 
 
 5444.3 
 
 782.0 
 
 44' 
 
 46' 
 
 3095.9 fc : - 
 
 5447-2 
 
 783-0 
 
 46' 
 
 48' 
 
 309S.o-^ 
 
 5450.1 
 
 784.0 
 
 48' 
 
 50' 
 
 3100.1 i%$ 
 
 5453-1 
 
 785.0 
 
 5' 
 
 52' 
 
 3102- 3-c 
 
 5456.0 
 
 786.0 
 
 52' 
 
 54' 
 
 3104. 4^ : = 
 
 5458.9 
 
 787.0 
 
 54' 
 
 56' 
 
 3106 .6 
 
 5461.9 
 
 788.1 
 
 56' 
 
 58' 
 
 3108.7 
 
 5464.8 
 
 789.1 
 
 58' 
 
 57 
 
 3110.9 
 
 5467.8 
 
 790.1 
 
 57 
 
 2' 
 
 
 5470.7 
 
 791.2 
 
 2' 
 
 4' 
 
 3115-2 
 
 5473-6 
 
 792.2 
 
 4' 
 
 6' 
 
 3 II 7-4 
 
 5476.6 
 
 793.2 ">*+ 
 
 6' 
 
 8' 
 
 3119.6 6 
 
 5479-5 
 
 794.3 d- : 
 
 8' 
 
 io' 
 
 3121.7 -2 
 
 5482.4 
 
 795-3^ 
 
 10' 
 
 12' 
 
 3123.9 
 
 5485.3 
 
 796.3.*: : 
 
 12' 
 
 14' 
 
 3126.0 
 
 5488.3 
 
 797-4^ 
 
 14' 
 
 16' 
 
 3128.2 ,0 
 
 5491.2 
 
 798.4J3-- : 
 
 16' 
 
 18' 
 
 3130.4 ? 
 
 5494-1 
 
 799-5 <*.^. 
 
 18' 
 
 20' 
 
 3132.5 >?^ 
 
 5497.0 
 
 wocco 
 800.5 
 
 20' 
 
 22' 
 
 
 5499-9 
 
 80 1 . 5 d: : 
 
 22' 
 
 24' 
 
 3i36.'82~3 
 
 5502.8 
 
 802. 6 < 
 
 24' 
 
 26' 
 
 
 5505-8 
 
 803.6 
 
 26' 
 
 28' 
 
 3141 .2 C& 
 
 5508.7 
 
 804.7 
 
 28' 
 
 30' 
 
 3143.3!' 
 
 5511 .6 
 
 805.7 
 
 30; 
 
 32' 
 
 3145.5 M CO* 
 
 55*4.6 
 
 806.7 
 
 32 
 
 34' 
 
 3147.6 S3" 
 
 5517 . 5 
 
 807.8 
 
 i 34 
 
 36' 
 
 3149-85, 
 
 5520.4 
 
 808.8 
 
 36 
 
 38' 
 
 3152. o<f -g 
 
 5523.4 
 
 809 .9 
 
 : 38' 
 
 40' 
 
 3154.2 
 
 5526.3 
 
 810.9 
 
 40' 
 
 42' 
 
 3156.4 
 
 5529.2 
 
 811 .9 
 
 42' 
 
 44' 
 
 
 5532.1 
 
 813.0 
 
 44' 
 
 46' 
 
 3160.7 <5 
 
 5535.o 
 
 814.0 
 
 46' 
 
 48' 
 
 3162.9 
 
 5538.0 
 
 815.1 
 
 48' 
 
 50' 
 
 3165.1 | 
 
 5540.9 
 
 816.1 
 
 5 0/ 
 
 52' 
 
 3167.2 
 
 5543-8 
 
 817.2 
 
 52 / 
 
 54' 
 
 3169.4 
 
 5546.7 
 
 818.2 
 
 
 56' 
 
 3171.6 
 
 5549-7 
 
 819.3 
 
 56' 
 
 58' 
 
 3I73-8 
 
 5552.6 
 
 820.3 
 
 58' 
 
 83 
 
IX. FUNCTIONS OF A ONE-DEGREE CURVE. 
 
 Whole 
 Angle. 
 
 Tangent 
 Distance. 
 
 Long 
 Chord. 
 
 External 
 Secant. 
 
 Whole 
 Angle. 
 
 58 
 
 3176.0 
 
 5555-5 
 
 821.4 
 
 58 
 
 2' 
 
 3178.2 
 
 5558.4 
 
 822.4 
 
 2' 
 
 4' 
 
 3180.4 
 
 5561.3 
 
 823.5 
 
 4' 
 
 6' 
 
 3182.6 4 
 
 5564.2 
 
 824.6 . 
 
 6' 
 
 8' 
 
 3184.8 
 
 5567.1 
 
 825.6 ^S 
 
 8' 
 
 10' 
 
 3186.9 55. 
 
 5570.0 
 
 826. 7g: 
 
 io r 
 
 12' 
 
 3189.1 *g 
 
 5573-0 
 
 827.713 
 
 12' 
 
 14' 
 
 3I9L3 $ 
 
 5575-9 
 
 828.8-^: 
 
 14' 
 
 16' 
 
 3193-5 -3 
 
 5578.8 
 
 829.9^ 
 
 16' 
 
 ft' 
 
 3r95-7 ^ 
 
 
 831.0!= 
 
 18' 
 
 20' 
 
 3197.8 . .< 
 
 5584.6 
 
 832.0^5 
 
 20'. 
 
 22' 
 
 3200.0 j? ^ 
 
 5587 . 5 
 
 S33.i^ M 
 
 22' 
 
 24' 
 
 3202.2 ^ : 5 
 
 5590.4 
 
 834-15= 
 
 24' 
 
 26' 
 
 3204. 4g 
 
 5593-3 
 
 835-2^ 
 
 26' 
 
 28' 
 
 3206 .6 'p. : 
 
 5596.2 
 
 836.2 
 
 28' 
 
 3 2' 
 
 3208.7 . 
 
 5599-1 
 
 837.3 
 
 30' 
 
 
 3 2 1 o . 9 ^ c , 
 
 5602 .0 
 
 838.3 
 
 32' 
 
 : 34; 
 
 3213-1 d? 
 
 5604.9 
 
 839.4 
 
 34' 
 
 36 
 
 32i5-3^6 
 
 5607.8 
 
 840.5 
 
 36' 
 
 * 38' 
 
 3217-5^= * 
 
 5610.7 
 
 841.6 
 
 38' 
 
 40' 
 
 3219.7 4 
 
 5613-6 
 
 842.7 
 
 40' 
 
 42' 
 
 3221.9 m 
 
 5616.6 
 
 843-8 
 
 42' 
 
 44' 
 
 3224.1 .0 
 
 5619 . 5 
 
 844.9 
 
 44' 
 
 46' 
 
 3226.3 ? 
 
 5622.4 
 
 845-9 
 
 46' 
 
 48' 
 
 322*. 5 1 
 
 5625.3 
 
 847.0 
 
 48' 
 
 5 0/ 
 
 3230.7 3 
 
 5628.2 
 
 848.1 ^i 
 
 50' 
 
 52' 
 
 3232.9 <: 
 
 5631. i 
 
 849-2 6. . 
 
 52; 
 
 54' 
 
 3235.! 
 
 5634-0 
 
 850. 3g~ 
 
 
 56' 
 
 3237-3 
 
 5636-9 
 
 851 .4 * 
 
 56' 
 
 58' 
 
 3239.5 
 
 5639-8 
 
 852.4 := 
 
 58' 
 
 59 
 
 3241-7 
 
 5642.7 
 
 853.5 !- : 
 
 59 
 
 2' 
 
 3243.9 ^4 
 
 5645.6 
 
 854 ' 6 O\ fOOO 
 
 2' 
 
 4' 
 
 3246.1 H 
 
 5648.5 
 
 855.6 
 
 4' 
 
 6' 
 
 3248. 3 = 
 
 565L4 
 
 856.73, - 
 
 6' 
 
 8' 
 
 3250.5^ 
 
 5654.3 
 
 857- 8<" " 
 
 8' 
 
 10' 
 
 3252. 7 '^ 
 
 5657.2 
 
 858.9 
 
 10' 
 
 12' 
 
 3254.9 g. 
 
 5660 . i 
 
 860.0 
 
 12' 
 
 14' 
 
 3257-1^ 
 
 5663.0 
 
 861.1 
 
 14' 
 
 16' 
 
 3259.3 ^ 
 
 5665.9 
 
 862.2 
 
 16' 
 
 18' 
 
 3261.5 *- 
 
 5668.8 
 
 863.3 
 
 18' 
 
 20' 
 
 3263.75= 
 
 5671-7 
 
 864.4 
 
 20' 
 
 22' 
 
 3266.0 
 
 5674.6 
 
 865.5 
 
 22' 
 
 24' 
 
 3268.2 
 
 5677.5 
 
 866.6 
 
 24' 
 
 26' 
 
 3270.4 
 
 5680.4 
 
 867.7 
 
 26' 
 
 28' 
 
 3272.6 
 
 5683.3 
 
 868.8 
 
 28' 
 
 84 
 
IX. FUNCTIONS OF A ONE-DEGREE CURVE. 
 
 Whole 
 
 Angle. 
 
 Tangent 
 Distance. 
 
 Long 
 Chord. 
 
 External 
 Secant. 
 
 Whole 
 Angle. 
 
 59 30' 
 
 3274.8 
 
 5686.2 
 
 869.9 
 
 59 30' 
 
 32' 
 
 3277.0 
 
 5689.1 
 
 871.0 
 
 32' 
 
 34' 
 
 3279.2 
 
 5691.9 
 
 872.1 
 
 34' 
 
 36' 
 
 3281.4 2 
 
 5694.8 
 
 873.2 
 
 36' 
 
 38' 
 
 3283-6 6 
 
 5697.7 
 
 874.3 
 
 38' 
 
 40' 
 
 3285-8 i 
 
 5700.6 
 
 875.4 
 
 40' 
 
 42' 
 
 3288.0 % 
 
 5703.5 
 
 
 42' 
 
 44' 
 
 3290.2 w 
 
 5706.4 
 
 877*6 
 
 44' 
 
 46' 
 
 3292.4 
 
 5709.3 
 
 878.7 
 
 46' 
 
 48' 
 
 3294.7 ^ 
 
 5712.2 
 
 879.8 
 
 48' 
 
 5' 
 
 3296.9 
 
 57I5- 1 
 
 880.9 j 
 
 50' 
 
 52' 
 
 3299.1 3 
 
 57 J 7-9 
 
 882.0 6 
 
 52' 
 
 54' 
 
 330L4 
 
 5720.8 
 
 883.1 2 
 
 54' 
 
 56' 
 
 3303.6 
 
 5723-7 
 
 884.2 g 
 
 56' 
 
 58' 
 
 3305.8 
 
 5726.6 
 
 885.3 
 
 58' 
 
 6O 
 
 33o8.o 
 
 5729-6 
 
 886.4 & 
 
 6O 
 
 2' 
 
 33 IO -3 
 
 5732.5 
 
 887.5 oo 
 
 2' 
 
 4' 
 
 3312.5 -.o4 
 
 5735.4 
 
 888.6 . .^ 
 
 4' 
 
 6' 
 
 3314.7 6- - 
 
 5738.2 
 
 889.7 "/^ 
 
 6' 
 
 8' 
 
 3316. 9|zr - 
 
 574 1 - 1 
 
 890.9^= < 
 
 8' 
 
 10' 
 
 3319- I |: : 
 
 5744.0 
 
 892.0^, 
 
 10' 
 
 12' 
 
 3321. 3c 
 
 5746.9 
 
 893-1^ 
 
 12' 
 
 14' 
 
 3323-5 c: : 
 
 5749.8 
 
 894.2 g. 
 
 14' 
 
 1 6' 
 
 3325-7 ">qvo 
 
 5752.7 
 
 895.4^^ 
 
 16' 
 
 18' 
 
 3328.0 ZZ^ 
 
 5755-5 
 
 896. 5 ^06 
 
 18' 
 
 20' 
 
 3330.2^^ 
 
 5758.4 
 
 897.65= r 
 
 20' 
 
 22' 
 
 3332. 4f ' 
 
 5761 .3 
 
 898.7 ' 6 
 
 22 
 
 24' 
 
 3334-7 
 
 5764.2 
 
 899.8 * 
 
 24' 
 
 26' 
 
 3336.9 
 
 5767.1 
 
 901.0 
 
 26' 
 
 28' 
 
 3339-1 
 
 5769-9 
 
 902.1 J| 
 
 28' 
 
 30' 
 
 3341.4 
 
 5772.8 
 
 903.2 J5 
 
 30' 
 
 32' 
 
 3343-6 ? 
 
 5775-7 
 
 904.3 o, 
 
 32 
 
 34' 
 
 3345-9 6 
 
 5778.6 
 
 905.4 s 
 
 34' 
 
 36' 
 
 3348.1 * 
 
 
 906.6 ^ 
 
 36' 
 
 38' 
 
 3350-3 | 
 
 5784.3 
 
 907.7 ^ 
 
 38' 
 
 40' 
 
 3352-6 
 
 5787-2 
 
 908.8 
 
 40' 
 
 42' 
 
 3354-8 
 
 579o.i 
 
 910.0 
 
 42' 
 
 44' 
 
 3357 - 1 - 
 
 5793-0 
 
 911.1 
 
 44' 
 
 46' 
 
 3359-3 * 
 
 5795-9 
 
 912.2 
 
 46' 
 
 48' 
 
 336i.5 
 
 5798.7 
 
 9 J 3-3 
 
 48' 
 
 s; 
 
 3363.8 ? 
 
 5801 .6 
 
 9 J 4-5 
 
 5' 
 
 
 3366.0 
 
 5804.5 
 
 915.6 
 
 52 ', 
 
 54' 
 
 3368.3 
 
 5807.4 
 
 916.7 
 
 54 
 
 56' 
 
 3370.5 
 
 58lO. 2 
 
 917.9 
 
 56 
 
 58' 
 
 3372-8 
 
 58I3.I 
 
 919.1 
 
 58' 
 
IX. FUNCTIONS OF A ONE-DEGREE CURVE. 
 
 Whole 
 Angle. 
 
 Tangent 
 Distance. 
 
 Long 
 Chord. 
 
 External 
 Secant. 
 
 Whole 
 Angle. 
 
 61 
 
 3375-0 
 
 5816.0 
 
 92O . 2 
 
 61 
 
 2' 
 
 3377-3 
 
 5818.9 
 
 921.3 
 
 2' 
 
 4' 
 
 3379-5 
 
 5821.7 
 
 922.5 
 
 4' 
 
 6' 
 
 
 5824.6 
 
 923.6 
 
 6' 
 
 8' 
 
 3384-0 : 
 
 5827.5 
 
 924.8 
 
 V 
 
 10' 
 
 3386.2 * 
 
 5830.3 
 
 925.9 
 
 10' 
 
 12' 
 
 3388.5 g 
 
 5833.2 
 
 927.0 
 
 12' 
 
 14' 
 
 3390.7 
 
 5836.0 
 
 928.2 
 
 14' 
 
 16' 
 
 3393-0 g 
 
 5838.9 
 
 929.4 
 
 16' 
 
 18' 
 
 3395-2 
 
 5841.8 
 
 930.5 
 
 18' 
 
 20' 
 
 3397-5 o 
 
 5844.7 
 
 931.6 . . 
 
 20'. 
 
 22' 
 
 3399-8 ^ 
 
 5847 . 6 
 
 932.8 ' - 
 
 22' 
 
 24' 
 
 3402.0 Jj 
 
 5850-4 
 
 933-9;- = 
 
 24' 
 
 26' 
 
 3404-3 
 
 5853.3 
 
 935 - 1 -3- 
 
 26' 
 
 28' 
 
 3406.5 
 
 5856.2 
 
 936.3-^ : 
 
 28' 
 
 30' 
 
 3408.8 
 
 5859.0 
 
 937-4? 
 
 3o' 
 
 32' 
 
 3411.1 
 
 5861.9 
 
 938. 6 : : 
 
 32' 
 
 34' 
 
 3413.3 ^.& + 
 
 5864-8 
 
 939-7 ?5od 
 
 34' 
 
 36' 
 
 34I5.6 6 ^ " 
 
 5867-6 
 
 940.9 ^ 
 
 36' 
 
 38' 
 
 
 5870.5 
 
 942.1 ^: : 
 
 38' 
 
 40' 
 
 3420.1 |, , 
 
 5873.3 
 
 943-2 
 
 40' 
 
 42' 
 
 3422. 4 ~ " 
 
 5876.2 
 
 944-4 
 
 42' 
 
 44' 
 
 3424.6 : : 
 
 5879.1 
 
 945 5 
 
 44' 
 
 46' 
 
 3426. 9 ^H c* 
 
 5882.0 
 
 946.7 
 
 46' 
 
 48' 
 
 3429-1 * 
 
 5884.8 
 
 947-9 
 
 48' 
 
 50' 
 
 343.1. 4 -* 
 
 5887.7 
 
 949-o 
 
 50' 
 
 52' 
 
 3433- 7 < : : 
 
 5890.6 
 
 950.2 
 
 52' 
 
 54' 
 
 3435-9 
 
 5893 .4 
 
 95 J -3 
 
 54' 
 
 56' 
 
 3438.2 
 
 5896.3 
 
 952.5 
 
 56' 
 
 58' 
 
 3440 . 5 
 
 5899.1 
 
 953-6 
 
 58' 
 
 62 
 
 3442.7 
 
 5902 .0 
 
 954.8 
 
 62 
 
 2' 
 
 3445-0 4 
 
 5904.8 
 
 956.0 . . . 
 
 2' 
 
 4' 
 
 3447-2 
 
 5907-7 
 
 957.2 l ? 
 
 4' 
 
 6' 
 
 3449-5 
 
 59io.5 
 
 958.3 o": = 
 
 6' 
 
 8' 
 
 3451-8 -g 
 
 59*3-4 
 
 959.5^ 
 
 8' 
 
 10' 
 
 3454-1 
 
 5916 . 2 
 
 960.7 -^: : 
 
 10' 
 
 12' 
 
 3456.4 
 
 59i9.i 
 
 961.9^ 
 
 12' 
 
 14' 
 
 3458.6 - 
 
 592L9 
 
 963.1,0: : 
 
 14' 
 
 16' 
 
 3460.9 o> 
 
 5924.8 
 
 
 16' 
 
 18' 
 
 3463.2 
 
 5927-6 
 
 965.4^^ 
 
 18' 
 
 20' 
 
 3465.5 ^ 
 
 5930.5 
 
 966 .6 J : : 
 
 20' 
 
 22' 
 
 3467-8 
 
 5933-3 
 
 967.8 ' 
 
 22' 
 
 24' 
 
 3470.0 
 
 5936.1 
 
 969.0 
 
 24' 
 
 26' 
 
 3472.3 
 
 5939-0 
 
 970.1 
 
 26' 
 
 28' 
 
 3474-6 
 
 5041 -8 
 
 071 -3 
 
 28' 
 
IX. FUNCTIONS OF A ONE-DEGREE CURVE. 
 
 Whole 
 Angle. 
 
 Tangent 
 Distance. 
 
 Long 
 Chord. 
 
 External 
 Secant. 
 
 Whole 
 Angle. 
 
 02 30' 
 
 3476.9 
 
 5944-7 
 
 972.5 
 
 62 30' 
 
 32' 
 
 3479-2 
 
 5947-5 
 
 973-7 
 
 32' 
 
 34' 
 
 348i.5 
 
 5950-4 
 
 974-9 
 
 34' 
 
 36' 
 
 3483.8 ^^ + 
 
 5953-2 
 
 976.0 
 
 36' 
 
 38' 
 
 3486.0 6 
 
 5956.1 
 
 977-2 
 
 38' 
 
 40' 
 
 3488. 3 * : 
 
 5958.9 
 
 978.4 
 
 40' 
 
 42' 
 
 3490.6 g. 
 
 596i.8 
 
 979-6 
 
 42' 
 
 44' 
 
 3492. 9 - ' 
 
 5964.7 
 
 980.8 
 
 44' 
 
 46' 
 
 3495-2 g. . 
 
 5967-5 
 
 982 .0 
 
 46' 
 
 48' 
 
 3497 5 " H 
 
 5970.4 
 
 983.1 4 
 
 48' 
 
 5o' 
 
 3499.7 2 
 
 5973-2 
 
 984.3 
 
 50' 
 
 S*' 
 
 3502.0^ 
 
 5976.1 
 
 985-5 2 
 
 52' 
 
 54' 
 
 3504- 2^ = 
 
 5978.9 
 
 986.7 a . 
 
 54' 
 
 56' 
 
 3506.5 
 
 598i.8 
 
 987-9 1 
 
 56' 
 
 58' 
 
 3508.8 
 
 5984.6 
 
 989.1 
 
 58' 
 
 63 
 
 35 11 - 1 
 
 5987-4 
 
 990.3 
 
 63 
 
 2' 
 
 3513.4 
 
 5990.3 
 
 991.5 H 
 
 2' 
 
 4' 
 
 35*5-7 
 
 5993-1 
 
 992.7 . .3 
 
 4' 
 
 6' 
 
 35*8. o 
 
 5996.0 
 
 993-9 c - < 
 
 6' 
 
 8' 
 
 35 2 o.3 
 
 5998.8 
 
 995- i : 
 
 8' 
 
 10' 
 
 3522.6 
 
 6001 .6 
 
 996. 3.|- 
 
 10' 
 
 12' 
 
 3524.9 
 
 6004 .4 
 
 997- 5 
 
 12' 
 
 14' 
 
 3527-2 
 
 6007 . 2 
 
 998.7 fcs 
 
 14' 
 
 , 16' 
 
 3529'5 
 
 6OIO . I 
 
 999-9^ 
 
 16' 
 
 18' 
 
 3531-8 
 
 6OI2 .9 
 
 IOOI . I ^06 
 
 18' 
 
 20' 
 
 w? O> "* 
 
 3534-1 ; H 
 
 6015.8 
 
 1002.3^= 4 
 
 20' 
 
 22' 
 
 3536. 4: : 
 
 6018. 6 
 
 1003.5 d 
 
 22' 
 
 24' 
 
 3538.7l3 
 
 6021 .4 
 
 IOO4.7 
 
 24' 
 
 26' 
 
 3541. O.b: : 
 
 6024 . 2 
 
 1006. o * 
 
 26' 
 
 28' 
 
 3543-3^ 
 
 6027 .0 
 
 1007.2 Jo, 
 
 28' 
 
 30' 
 
 3545-6 |V 
 
 6029.9 
 
 1008.4 o 
 
 30' 
 
 32' 
 
 3547-9 H-4 
 
 6032 . 7 
 
 1009.6 ^ 
 
 32' 
 
 34' 
 
 3550. 2 $ 
 
 6035.6 
 
 1010.8 
 
 34' 
 
 36' 
 
 35.52.5?- - 
 
 6038.4 
 
 IOI2 . I ^g 
 
 36' 
 
 38' 
 
 3554- 8T " 
 
 6041 .3 
 
 IOI3.3 < 
 
 38' 
 
 40' 
 
 3557-1 
 
 6044 . i 
 
 IOI4.5 
 
 40' 
 
 42' 
 
 3559-4 
 
 6047 .0 
 
 IOI5.7 
 
 42' 
 
 44' 
 
 356i.7 
 
 6049 8 
 
 1016 .9 
 
 44' 
 
 46' 
 
 3564-0 
 
 6052 . 6 
 
 1018.2 
 
 46' 
 
 48' 
 
 3566.3 
 
 6055.5 
 
 1019 .4 
 
 48' 
 
 50' 
 
 3568.7 
 
 6058.3 
 
 IO2O .6 
 
 5 ,' 
 
 52' 
 
 357 1 - 
 
 6o6l .2 
 
 IO2I .8 
 
 52 
 
 54' 
 
 3573-3 
 
 6064.0 
 
 1023.0 
 
 54' 
 
 56' 
 
 3575-6 
 
 6066 . 9 
 
 1024.3 
 
 56 
 
 58' 
 
 3577-0 ! 
 
 6069 . 7 
 
 1025.5 
 
 58' 
 
 87 
 
IX. FUNCTIONS OF A ONE-DEGREE CURVE. 
 
 Whole 
 Angle. 
 
 Tangent 
 Distance. 
 
 Long 
 Chord. 
 
 External 
 Secant. 
 
 Whole 
 Angle. 
 
 64 
 
 3580.2 
 
 6072.5 
 
 1026.7 
 
 64 
 
 2' 
 
 3582.6 
 
 6075.3 
 
 1027.9 
 
 2' 
 
 4' 
 
 3584.9 
 
 6078.1 
 
 IO29 . 2 
 
 4' 
 
 6' 
 
 3587.2 4 
 
 6081 .0 
 
 1030.4 
 
 6' 
 
 8' 
 
 3589.5 6 
 
 6083.8 
 
 1031.7 
 
 8' 
 
 10' 
 
 3591-8 * 
 
 6086.6 
 
 1032.9 
 
 10' 
 
 12' 
 
 3594-2 . 
 
 6089.4 
 
 I034.I 
 
 12' 
 
 14' 
 
 3596.5 tg 1 
 
 6092 . 2 
 
 1035.4 14' 
 
 16' 
 
 3598.8 - 
 
 6095 .0 
 
 1036.6 
 
 16' 
 
 18' 
 
 3601.1 ^ 
 
 6097.8 
 
 1037.9 
 
 18' 
 
 20' 
 
 3603.4 *| 
 
 6100. 7 
 
 I039.I * 
 
 20' 
 
 22' 
 
 3605.7 ^ 
 
 6103.5 
 
 1040.3 6 
 
 22' 
 
 24' 
 
 3608.1 13 ^ 
 
 6106.3 
 
 I04I.6 ^ 
 
 24' 
 
 26' 
 
 3610.4 -g, ' 
 
 6109.2 
 
 1042 .8 * 
 
 26' 
 
 28' 
 
 3612.8 ^ 
 
 6112 .0 
 
 1044.1 '5. 
 
 28' 
 
 
 o 
 
 
 
 
 30' 
 
 3615-1 X 
 
 6114.8 
 
 1045.3 1 
 
 30' 
 
 32' 
 
 3617.5 % 
 
 6117.6 
 
 1046.5 co 
 
 32' 
 
 34' 
 
 3619.8 .* + 
 
 6120.4 
 
 1047.8 . . % 
 
 34' 
 
 36' 
 
 3622 .1 "?? M 
 
 6123.2 
 
 1049 .0 "* CT & 
 
 36' 
 
 38' 
 
 3624.5^2 
 
 6126.0 
 
 I0 5-3 6. < 
 
 38' 
 
 40' 
 
 3626.8^ '% 
 
 6128.9 
 
 1051 .5 - 
 
 40' 
 
 42' 
 
 3629. 2 
 
 6131.7 
 
 1052.7!: 
 
 42' 
 
 44' 
 
 
 6i34.5 
 
 1054. o & 
 
 44' 
 
 46' 
 
 3633.82 t 
 
 6137.3 
 
 1055.2.0: 
 
 .46' 
 
 48' 
 
 3636.2 M o 
 
 vo ^ O 
 
 6140. i 
 
 1056.5 9 y? 
 
 48' 
 
 50' 
 
 3638.^ ' *~~ 
 
 6143.0 
 
 1057.7 * 
 
 50' 
 
 52' 
 
 3640.9?^| 
 
 6145.8 
 
 1059. o|: | 
 
 52' 
 
 54' 
 
 3643.2 -"jp 
 
 6148.6 
 
 IO6O.2 -H 
 
 54' 
 
 56 : 
 
 3645.5 
 
 6151.4 
 
 I06I.5 .^ 
 
 56' 
 
 58' 
 
 3647.9 | 
 
 6154.2 
 
 IO62.7 & 
 
 58' 
 
 65 
 
 3650.2 t; 
 
 6157.0 
 
 1063.9 <~ 
 
 65 
 
 2 f 
 
 3652.6 * . 
 
 6159.8 
 
 
 2' 
 
 4' 
 
 3654.9 ^2 
 
 6162.6 
 
 1066.4 
 
 4' 
 
 6' 
 
 3657-3 3,6 
 
 6165.4 
 
 1067.7 | 
 
 6' 
 
 8' 
 
 3659.6 ^ 
 
 6168.2 
 
 1068.9 
 
 8' 
 
 10' 
 
 3661.9 1 
 
 6171 .0 
 
 1070. 2 
 
 10' 
 
 12' 
 
 3664.3 cc 
 
 6173.8 
 
 1071 .4 
 
 I2 X 
 
 14' 
 
 3666.7 1 
 
 6176.6 
 
 1072.7 
 
 14' 
 
 16' 
 
 3669.0 1? 
 
 6179.4 
 
 1073.9 
 
 16' 
 
 18' 
 
 367L3 o 
 
 6182.2 
 
 1075.2 
 
 18' 
 
 20' 
 
 3673.6 5 
 
 6185.1 
 
 1076.5 
 
 20' 
 
 22' 
 
 3676.0 << 
 
 6187.9 
 
 1077.7 
 
 22' 
 
 24' 
 
 3678.3 
 
 6190 . 7 
 
 1079.0 
 
 24' 
 
 26' 
 
 3680.6 
 
 6193-5 
 
 1080 . 3 
 
 26' 
 
 28' 
 
 3683.0 
 
 6196 . 3 
 
 1081.6 
 
 28' I 
 
 88 
 
IX. FUNCTIONS OF A ONE-DEGREE CURVE. 
 
 Whole 
 Angle. 
 
 Tangent 
 Distance. 
 
 Long 
 Chord. 
 
 External 
 Secant. 
 
 Whole 
 Angle. 
 
 65 30' 
 
 3685-4 
 
 6199. I 
 
 1082 .9 
 
 65 30' 
 
 32' 
 
 3687.7 
 
 6201 .9 
 
 1084.2 
 
 32' 
 
 34' 
 
 3690.1 . . . 
 
 6204.7 
 
 1085.5 
 
 34' 
 
 36' 
 
 * 10 O> ^ 
 
 3692.4 
 
 6207.5 
 
 1086.7 
 
 36' 
 
 38' 
 
 3694-8 o- s 
 
 6210.3 
 
 1088.0 
 
 38' 
 
 40' 
 
 3697- 2 -g 
 
 6213.2 
 
 1089.3 
 
 40' 
 
 42' 
 
 3699- 5 'PT : 
 
 6216 .O 
 
 1090 .6 
 
 42' 
 
 44' 
 
 37oi. 9*2 
 
 6218.8 
 
 1091 .9 
 
 44' 
 
 46' 
 
 3704. 2- - 
 
 6221 .6 
 
 1093.1 
 
 46' 
 
 48' 
 
 3706.6^1 
 
 6224 .4 
 
 1094.4 
 
 48' 
 
 50' 
 
 3709.0 
 
 6227 . 2 
 
 1095.7 * 
 
 50' 
 
 52' 
 
 37II-32: : 
 
 6230.0 
 
 1097.0 . 
 
 52' 
 
 54' 
 
 3713-7^ 
 
 6232 .8 
 
 1098.3 
 
 54' 
 
 56' 
 
 3716.1 
 
 6235.6 
 
 1099.6 *g 
 
 56' 
 
 58' 
 
 3718.5 
 
 6238.4 
 
 IIOO.Q "S, 
 
 C/2 
 
 58' 
 
 6O 
 
 3720.8 
 
 6241 .2 
 
 I IO2 . 2 
 
 66 
 
 2' 
 
 3723-2 
 
 6244.0 
 
 H03.5 X 
 
 2' 
 
 4' 
 
 3725-5 
 
 6246.8 
 
 IIO4.8 
 
 4' 
 
 6' 
 
 3727-9 * 
 
 6249.6 
 
 I I O6 .O ^ C"Td 
 
 6' 
 
 8' 
 
 3730-3 c 
 
 6252.3 
 
 II0 7-3 6. 3 
 
 8' 
 
 10' 
 
 3732.7 * 
 
 6255.1 
 
 iio8.6ST 
 
 10' 
 
 12' 
 
 3735-1 .b 
 
 6257.9 
 
 1109.9 .*?. 
 
 12' 
 
 14' 
 
 3737-5 
 
 6260.7 
 
 I I I I . 2 " 
 
 14' 
 
 16' 
 
 3739-8 & 
 
 6263.5 
 
 III2.5| : 
 
 16' 
 
 18' 
 
 3742.2 ^ 
 
 6266.3 
 
 III3 .8 ^ 
 
 18' 
 
 20' 
 
 3744.6 ^f 
 
 6269 . I 
 
 oo 
 III S- I T- 4 
 
 20' 
 
 22' 
 
 3747-0 6. -e 
 
 6271 .9 
 
 IIl6 .4 r^; M 
 
 22' 
 
 24' 
 
 3749. 4^- < 
 
 6274.7 
 
 1117. 7< 1 
 
 24' 
 
 26' 
 
 375 I -7l. 
 
 6277.5 
 
 III9.I J 
 
 26' 
 
 28' 
 
 3754.1'J-- 
 
 6280.2 
 
 1120.4 .h 
 
 28' 
 
 30' 
 
 3756. 5|: 
 
 6283.0 
 
 1121.7 ? 
 
 30' 
 
 32' 
 
 3758.9 ^vo . 
 
 6285.8 
 
 1123.0 ^ 
 
 32' 
 
 34 
 
 3761.3 H^J 
 
 6288.6 
 
 1124.3 
 
 34' 
 
 36' 
 
 3763-7^^ 
 
 6291 .4 
 
 II2 5- 6 ^ 
 
 36' 
 
 38' 
 
 3766.0^: 2 
 
 "^ rt 
 
 6294.1 
 
 1126 .9 d 
 
 *^ 
 
 38' 
 
 40' 
 
 3768.4 
 
 6296 .9 
 
 1128.2 
 
 40' 
 
 42' 
 
 3770.8 W 
 
 6299.7 
 
 1129.5 
 
 42' 
 
 44' 
 
 3773-2 ,0 
 
 6302.5 
 
 1130.8 
 
 44' 
 
 46' 
 
 3775-6 ? 
 
 63 5-3 
 
 1132.2 
 
 46' 
 
 48' 
 
 3778.0 | 
 
 6308.1 
 
 II33-5 
 
 48' 
 
 50' 
 
 3780.4 
 
 6310.9 
 
 1134.8 
 
 50' 
 
 52 
 
 3782.8 < 
 
 6313.7 
 
 1136.1 
 
 52' 
 
 54 
 
 3785-2 
 
 6316.5 
 
 H37-4 
 
 54' 
 
 56' 
 
 3787-6 
 
 6319.2 
 
 1138.8 
 
 56' 
 
 58' 
 
 3790.0 
 
 6322.0 II40.I 58' 
 
IX. FUNCTIONS OF A ONE-DEGREE CURVE. 
 
 Whole 
 Angle. 
 
 Tangent 
 Distance. 
 
 Long 
 
 Chord. 
 
 External 
 Secant. 
 
 Whole 1 
 Angle. 
 
 67 
 
 3792.4 
 
 6324-8 
 
 1141.4 
 
 67 
 
 2' 
 
 3794-8 
 
 6327.5 
 
 1142.7 
 
 2' 
 
 4' 
 
 3797-2 
 
 6330.3 
 
 1144 .0 
 
 4' 
 
 6' 
 
 3799-6 2 
 
 6333.I 
 
 1145.4 
 
 6' 
 
 8' 
 
 3802 .0 o 
 
 
 1146.7 
 
 8 r 
 
 10' 
 
 3804.4 5 
 
 6338.6 
 
 1148 .0 
 
 10' 
 
 12' 
 
 3806.8 . 
 
 6341 .4 
 
 1149.4 
 
 12' 
 
 14' 
 
 3809.2 
 
 6344.2 
 
 1150.7 
 
 14' 
 
 16' 
 
 3811.6 1 
 
 6346.9 
 
 1152 .0 
 
 16' 
 
 18' 
 
 3814.0 a 
 
 6349.7 
 
 IJ 53-4 
 
 18' 
 
 20' 
 
 3816.4 ?! 
 
 6352.5 
 
 1154.7 -04 
 
 20' 
 
 22' 
 
 3818.8 * 
 
 6355-3 
 
 1156 .0 6. 
 
 22' 
 
 24' 
 
 3821.2 ^< 
 
 6358.1 
 
 1157.4^" 
 
 24' 
 
 26' 
 
 3823.6 
 
 6360.8 
 
 H58.7.1 : 
 
 26' 
 
 28' 
 
 3826.0 w 
 
 6363.6 
 
 
 28' 
 
 30' 
 
 3828.4 t 
 
 6366.3 
 
 Il6l .4 J5: 
 
 30' 
 
 32' 
 
 3830-9 4 
 
 6369.1 
 
 1162.7 oo 
 
 32' 
 
 34' 
 
 3833-3 :*4 
 
 6371.8 
 
 1164.1 "'* 
 
 34' 
 
 36' 
 
 3835-7 "?S M . 
 
 6374.6 
 
 1*65.4^ 
 
 36' 
 
 38' 
 
 3838. i < 
 
 6377-3 
 
 1166 . 7 <T 
 
 38' 
 
 40' 
 
 3840.5^ *g 
 
 6380.1 
 
 ri68.i 
 
 40' 
 
 42' 
 
 3843.0-5, ;a 
 
 6382.8 
 
 1169 .4 
 
 42' 
 
 44' 
 
 3845.4^ * 
 
 6385.6 
 
 1170.8 
 
 44' 
 
 46' 
 
 3847.8-2 a 
 
 6388.4 
 
 1172.1 
 
 46' 
 
 48' 
 
 3850.2 2" o 
 
 6391.2 
 
 H73-4 
 
 48' 
 
 50' 
 
 3852.6^ 
 
 6394.0 
 
 1174.8 
 
 50' 
 
 52' 
 
 3855.1 TS ds-tf 
 
 6396.7 
 
 1176 . i 
 
 52' 
 
 54' 
 
 3857- 5^ 
 
 6399.5 
 
 H77-5 
 
 54' 
 
 56' 
 
 3859-9 
 
 6402 .3 
 
 1178.8 
 
 56' 
 
 58' 
 
 3862.3 | 
 
 6405 . I 
 
 i 180 . 2 
 
 58' 
 
 68 
 
 3864.7 < 
 
 6407 .9 
 
 1 1 8 1 . 6 
 
 68 
 
 2' 
 
 3867.1 ,0 
 
 6410. 7 
 
 1183 . o 
 
 2' 
 
 4' 
 
 3869.6 <^4 
 
 6413-5 
 
 1184.3 ^d4 
 
 4' 
 
 6' 
 
 3872.0 ^ c - 
 
 6416 . 2 
 
 1185.7 - M 
 
 6' 
 
 8' 
 
 3874.4 ^^ 
 
 6419 .O 
 
 1187 .0 ^- = 
 
 8' 
 
 i a' 
 
 3876.8 <| 
 
 6421.7 
 
 1188.4^ 
 
 10' 
 
 12' 
 
 3879.3 ^ 
 
 6424.5 
 
 1189.7^ : 
 
 12' 
 
 14' 
 
 3881.7 fc 
 
 6427.2 
 
 II9I . I JH_ 
 
 14' 
 
 16' 
 
 3884.2 
 
 6429.9 
 
 1192 .4 \ 
 
 16' 
 
 18' 
 
 3886.6 2 
 
 6432 .6 
 
 1193 . 8 46e o 
 
 18' 
 
 20' 
 
 3889.0 -| 
 
 6435-4 
 
 1195.2 jgj 
 
 20' 
 
 22' 
 
 3891-5 < 
 
 6438-1 
 
 1196 . 5 < ' " 
 
 22 r 
 
 24' 
 
 3893-9 
 
 6440 . 9 
 
 1197.9 
 
 24' 
 
 26' 
 
 3896.4 
 
 6443-7 
 
 1199.2 
 
 26' 
 
 28' 
 
 3898.8 
 
 6446.4 
 
 1200.6 
 
 28' 
 
 90 
 
IX. FUNCTIONS OF A ONE-DEGREE CURVE. 
 
 Whole 
 Angle. 
 
 Tangent 
 Distance. 
 
 Long External 
 Chord. Secant. 
 
 Whole 
 Angle. 
 
 68 30' 
 
 3901.2 
 
 6449.2 
 
 1202 .0 
 
 68 30' 
 
 32' 
 
 3903-7 
 
 6452.0 
 
 1203.3 
 
 32' 
 
 34' 
 
 3906.1 
 
 6454.7 
 
 1204.7 
 
 34 
 
 36' 
 
 3908.5 4 
 
 6457-5 
 
 I2O6 . I 
 
 36' 
 
 38' 
 
 3910.8 ^ 
 
 6460 . 2 
 
 1207.5 
 
 38' 
 
 40' 
 
 39I3-4 * 
 
 6463.0 
 
 1208.9 
 
 40' 
 
 42' 
 
 39I5-9 S 
 
 6465.7 
 
 I2I0.3 
 
 42' 
 
 44' 
 
 3918.3 
 
 6468.5 
 
 I2II .6 
 
 44' 
 
 46' 
 
 3920.7 o 
 
 647L3 
 
 1213.0 
 
 46' 
 
 48' 
 
 3923.2 o- 
 
 6474.0 
 
 1214-4 ^4 
 
 48' 
 
 5' 
 
 3925.6 -g2 
 
 6476.8 
 
 1215.8 d ~ 
 
 So' 
 
 5^' 
 
 3928.0 -a^ 
 
 6479.5 
 
 1217.2 ^ 
 
 52' 
 
 54' 
 
 3930.5 <? 
 
 6482.3 
 
 1218. 6 -3 
 
 54' 
 
 S6' 
 
 3932.9 
 
 6485 .0 
 
 I22O.O 'a : 
 
 56 
 
 58' 
 
 3935-4 7 
 
 6487.8 
 
 1221.4 2 
 
 58' 
 
 09 
 
 3937-9 f 
 
 6490 .6 
 
 1222.8 ^ 
 
 69 
 
 2' 
 
 3940-4 4 
 
 6493.3 
 
 1224. 2 06 a 
 
 2' 
 
 4' 
 
 3942.8 .3 . 
 
 6496. i 
 
 1225.6 >TJ H 
 
 4' 
 
 6' 
 
 3945-3 ^ 
 
 6498.8 
 
 1227.0 "'^ 
 
 6' 
 
 8' 
 
 
 6501 .6 
 
 1228.4^0 
 
 8' 
 
 10' 
 
 3950. 2 ^ 
 
 6504-3 
 
 1229. 8-g 
 
 10' 
 
 12' 
 
 3952. 7 , 
 
 6507.1 
 
 1231.2-% 
 
 12' 
 
 14' 
 
 3955 - 1 w 
 
 6509.8 
 
 1232.6^ 
 
 14' 
 
 1 6' 
 
 3957-6^ 
 
 6512 .6 
 
 1234. o 
 
 16' 
 
 1 8' 
 
 3960 . o M ' ? 
 
 6515 . 3 
 
 I2 35-4 
 
 18' 
 
 20' 
 
 3962.5^ [ 
 
 6518.0 
 
 1236.8^0* 
 
 20' 
 
 22' 
 
 3965-0^^, 
 
 6520.8 
 
 1238.23^ 
 
 22' 
 
 24' 
 
 3967. 4 J< 
 
 6523-5 
 
 1239.6 ^ 
 
 24' 
 
 26' 
 
 3969-9 13 
 
 6526.3 
 
 1241.0 g^ 
 
 26' 
 
 28' 
 
 3972.3 | 
 
 6529.0 
 
 1242.4 J6." 
 
 28' 
 
 30' 
 
 3974-8 * 
 
 653I-7 
 
 1243.8 |: 
 
 3' 
 
 32' 
 
 3977-3 ^4 
 
 6534.5 
 
 1245.2 t^oo 
 
 32' 
 
 34' 
 
 3979-7 *" 
 
 6537-2 
 
 1246.6 ^ 
 
 34' 
 
 36' 
 
 3982.2 g 
 
 6540 .0 
 
 1248.0 ;g^ 
 
 36' 
 
 38' 
 
 3984.6 3^ 
 
 6542.7 
 
 1249.4 <<" 
 
 38' 
 
 40' 
 
 3987.1 3J, 
 
 6545-4 
 
 1250.8 
 
 40' 
 
 42' 
 
 3989.6 * 
 
 6548.2 
 
 1252 .2 
 
 42' 
 
 44' 
 
 3992-0 
 
 6550-9 
 
 1253.6 
 
 44' 
 
 46' 
 
 3994-5 6 
 
 6553.7 
 
 1255-0 
 
 46' 
 
 48' 
 
 3997-0 
 
 6556-4 
 
 1256.4 
 
 48' 
 
 So; 
 
 3999-5 | 
 
 6559-I 
 
 1257.9 
 
 50' 
 
 
 4002 . o 
 
 6561.9 
 
 1259.3 
 
 52' 
 
 54' 
 
 4004 . 5 
 
 6564.6 
 
 1260 . 7 
 
 54 
 
 56' 
 
 4007 . o 
 
 6567.4 
 
 1262 . 2 
 
 56 
 
 58' 
 
 4009.5 ! 6570.1 
 
 1263 .6 
 
 58' 
 
 91 
 
IX. FUNCTIONS OF A ONE-DEGREE CURVE. 
 
 Whole 
 Angle. 
 
 Tangent 
 Distance. 
 
 Long 
 Chord. 
 
 External 
 Secant. 
 
 Whole 
 Angle. 
 
 70 
 
 4011 .9 
 
 6572.8 
 
 1265 .0 
 
 70 
 
 2' 
 
 4014.4 
 
 
 1266.4 
 
 2' 
 
 4' 
 
 4016.9 
 
 6578^3 
 
 1267.8 
 
 4' 
 
 6' 
 
 4019.4 
 
 6581 .0 
 
 1269.3 
 
 6' 
 
 8' 
 
 4021 . 9 
 
 6583.7 
 
 1270.7 
 
 8' 
 
 IP' 
 
 4024.4 
 
 6586.4 
 
 1272 . I 
 
 10' 
 
 12' 
 
 4026.9 
 
 6589.1 
 
 1273-5 
 
 12' 
 
 14' 
 
 4029.4 -g 
 
 6591.9 
 
 1275.0 
 
 14; 
 
 16' 
 
 4031.9 *a 
 
 6594.6 
 
 1276 .4 
 
 
 18' 
 
 4034.4 "2 
 
 6597.3 
 
 1277.9 
 
 18' 
 
 20' 
 
 4036.8 ^ 
 
 6600.0 
 
 1279.3 
 
 20' 
 
 22' 
 
 4039-3 2 
 
 6602 .7 
 
 1280.7 
 
 22' 
 
 24' 
 
 4041.8 *- 
 
 6605.5 
 
 1282 . 2 
 
 24' 
 
 26' 
 
 4044 . 3 ? 
 
 6608.2 
 
 1283.6 
 
 26' 
 
 28' 
 
 4046.8 
 
 6610 . 9 
 
 I285.I 
 
 28' 
 
 30' 
 
 4049 3 
 
 6613.6 
 
 1286.5 
 
 3 0/ 
 
 32' 
 
 4051.8 
 
 6616.3 
 
 1288.0 
 
 32 7 
 
 34' 
 
 4054.3 . . . 
 
 6619 .0 
 
 1289.4 
 
 34' 
 
 36' 
 
 4056.8 ^^M 
 
 6621.8 
 
 1290.8 f j 
 
 36' 
 
 38' 
 
 4059-3;: s 
 
 6624.5 
 
 1292.3 6 : : 
 
 38' 
 
 40' 
 
 4061 .8 *3 
 
 6627 . 2 
 
 1293 . 7 ^ 
 
 40' 
 
 42' 
 
 4064. 4 : = 
 
 6629 . 9 
 
 1295. 2- : : 
 
 42' 
 
 44' 
 
 4066.9^ 
 
 6632 .6 
 
 1296 .6 cc 
 
 44' 
 
 46' 
 
 4069. 4. 2 : = 
 
 6635.4 
 
 1298 . I J3: s 
 
 46' 
 
 48' 
 
 4071 .9 ^ ^ 
 
 6638.1 
 
 1299.5 g % 
 
 48' 
 
 50' 
 
 4074.45^ 
 
 6640.8 
 
 1301.0^^ 
 
 50' 
 
 52' 
 
 4076.9?: - 
 
 6643.5 
 
 
 52' 
 
 54' 
 
 4079. 4^ 
 
 6646.2 
 
 1303-9^ 
 
 54' 
 
 56' 
 
 4081 .9 
 
 6649 .0 
 
 1305.3 
 
 56' 
 
 58' 
 
 4084.4 
 
 6651.7 
 
 1306.8 
 
 58' 
 
 71 
 
 4086.9 
 
 6654.4 
 
 1308.3 
 
 71 
 
 2' 
 
 4089.5 j 
 
 6657.1 
 
 1309.7 
 
 2' 
 
 4' 
 
 4O92 .O 
 
 6659.9 
 
 I3II . 2 
 
 4' 
 
 6' 
 
 4094.5 52 
 
 6662.6 
 
 I3I2.6 
 
 6' 
 
 8' 
 
 4097.0 | 
 
 6665.3 
 
 I3I4.I 
 
 8' 
 
 10' 
 
 4099.5 
 
 6668.0 
 
 I3I5.6 
 
 10' 
 
 12' 
 
 4102 .0 o 
 
 6670. 7 
 
 I3I7.0 
 
 12' 
 
 14' 
 
 4104.6 o 
 
 6673.4 
 
 I3I8.5 
 
 14' 
 
 16' 
 
 4107.0 2 
 
 6676.1 
 
 1320.0 
 
 16' 
 
 18' 
 
 4109.5 
 
 6678.8 
 
 I32I.4 
 
 18' 
 
 20' 
 
 4112 . I << 
 
 6681.5 
 
 1322 .9 
 
 20' 
 
 22' 
 
 4114.6 
 
 6684.2 
 
 1324.4 
 
 22' 
 
 24' 
 
 4117.2 
 
 6686.9 
 
 1325.8 
 
 24' 
 
 26' 
 
 4119.7 
 
 6689.6 
 
 I327.3 
 
 26' 
 
 28' 
 
 4122 . 2 
 
 6692.3 ' 1328.8 28' 
 
IX. FUNCTIONS OF A ONE-DEGREE CURVE. 
 
 Whole 
 Angle. 
 
 Tangent 
 Distance. 
 
 Long 
 Chord. 
 
 External 
 Secant. 
 
 Whole 
 Angle. 
 
 71 30' 
 
 4124.7 
 
 6695.0 
 
 1330.3 
 
 71 30' 
 
 32' 
 
 4127.3 
 
 6697.7 
 
 I33L8 
 
 3 2/ 
 
 34' 
 
 4129 .8 
 
 6700 .4 
 
 1333.2 
 
 34' 
 
 36' 
 
 4132.4 ^4 
 
 6703.1 
 
 1334.7 
 
 36' 
 
 38' 
 
 4134.9 6 : 
 
 6705.8 
 
 1336.2 +** 
 
 38' 
 
 40' 
 
 4137.4 fc" 
 
 6708.5 
 
 1337.7 ^ : : 
 
 40' 
 
 42' 
 
 4140.0 ^ 
 
 6711 .2 
 
 1339 . 2 ^ 
 
 42' 
 
 44' 
 
 4142.5 '& : 
 
 67I3-9 
 
 1340. 6 = : 
 
 44' 
 
 46' 
 
 4I45-0 fcu , 
 
 6716.6 
 
 1342 - IC L . 
 
 46' 
 
 48' 
 
 4147 .6 " M " a 
 
 6719.3 
 
 
 48' 
 
 5o; 
 
 4150. i 2 
 
 6722 .O 
 
 H 00 O 
 
 I345.I ^odo- 
 
 5o' 
 
 
 4152.7 ^* 
 
 6724.7 
 
 ' I 346.6, d 
 
 52 ,' 
 
 54' 
 
 4155-2 5= = 
 
 6727.4 
 
 1348.13= = 
 
 54' 
 
 56' 
 
 4157-8 
 
 6730.1 
 
 1349.6 
 
 56 
 
 58' 
 
 4160.3 
 
 6732.8 
 
 I 35 I - 1 
 
 58' 
 
 72 
 
 4162 .8 
 
 6735.5 
 
 1352.6 
 
 72 
 
 2' 
 
 4165.4 
 
 6738.2 
 
 I354.I 
 
 2' 
 
 4' 
 
 4167.9 
 
 6740.9 
 
 1355-6 
 
 4' 
 
 6' 
 
 4170.5 * 
 
 6743.6 
 
 
 6' 
 
 8' 
 
 
 6746.3 
 
 1358*6 
 
 8' 
 
 10' 
 
 4I75-6 
 
 6749.0 
 
 1360.1 
 
 10' 
 
 12' 
 
 4178.1 
 
 675 J .7 
 
 1361.6 
 
 ia' 
 
 14' 
 
 4180.7 eg 
 
 6754.4 
 
 1363-1 
 
 14' 
 
 16' 
 
 4183.2 j> 
 
 6757-1 
 
 1364.6 
 
 16' 
 
 18' 
 
 4185.8 o 
 
 6759.8 
 
 1366.1 
 
 18' 
 
 20' 
 
 4188.4 <oa . 
 
 6762.5 
 
 1367.6 ^j 
 
 20' 
 
 22' 
 
 4I9LO |: 5 
 
 6765.1 
 
 I369.I O'. ; 
 
 22' 
 
 24' 
 
 4193.5 -3 < 
 
 6767.8 
 
 1370.65 
 
 24' 
 
 26' 
 
 4196.1 .53. 
 
 6770.5 
 
 1372.2^. . 
 
 26' 
 
 28' 
 
 4198.6 & 
 
 6773.2 
 
 J373-7C& 
 
 28' 
 
 30' 
 
 4201 .2 : 
 
 6775.9 
 
 1375.2 0= 5 
 
 30; 
 
 32' 
 
 4203.8 J^4 
 
 6778.6 
 
 1376.7 ^^^ 
 
 32 
 
 34' 
 
 4206.3 jf^- 
 
 6781.3 
 
 1378. 2^ M S 
 
 34 
 
 36' 
 
 4208.9 TJ j 
 
 6784.0 
 
 
 36 
 
 38' 
 
 4211 .4 ^ ,-H 
 
 6786.7 
 
 1381. 3<f " 
 
 38' 
 
 40' 
 
 4214.0 -a 
 
 6789.3 
 
 1382.8 
 
 40' 
 
 42' 
 
 4216.6 ^ 
 
 6792 .0 
 
 1384.3 
 
 42' 
 
 44' 
 
 4219.1 
 
 6794.7 
 
 1385-8 
 
 44' 
 
 46' 
 
 4221.7 ^ 
 
 6797.4 
 
 1387-4 
 
 46' 
 
 .48' 
 
 4224.2 - 
 
 6800. i 
 
 1388.9 
 
 48' 
 
 50' 
 
 4226.8 ? 
 
 6802.7 
 
 1390.4 
 
 50' 
 
 52' 
 
 4229.4 
 
 6805 .4 
 
 i39i-9 
 
 52 ' 
 
 54' 
 
 4231.9 
 
 6808.0 
 
 1393.4 
 
 
 56' 
 
 4234.5 
 
 6810.7 
 
 i395.o 
 
 56' 
 
 58' 
 
 4237-1 
 
 6813.4 
 
 1396-5 
 
 58' 
 
 93 
 
IX. FUNCTIONS OF A ONE-DEGREE CURVE. 
 
 Whole 
 Angle. 
 
 Tangent 
 Distance. 
 
 Long 
 Chord. 
 
 External 
 Secant. 
 
 Whole 
 Angle. 
 
 73 
 
 4239.7 
 
 6816. I 
 
 1398.0 
 
 73 
 
 2' 
 
 4242.3 
 
 6818. 8 
 
 1399 . 5 
 
 2' 
 
 4' 
 
 4244.8 
 
 6821.5 
 
 1401 . i 
 
 4' 
 
 6' 
 
 4247.4 
 
 6824.2 
 
 1402 .6 
 
 6' 
 
 8' 
 
 4250.0 
 
 6826.8 
 
 1404. 2 
 
 8'' 
 
 10' 
 
 4252.6 
 
 6829.5 
 
 1405.7 
 
 10' 
 
 12' 
 
 4255 . 2 
 
 6832.2 
 
 1407-3 
 
 12' 
 
 14' 
 
 4 2 57 7 
 
 6834.9 
 
 1408.8 
 
 14' 
 
 iff 
 
 4260.3 
 
 6837-5 
 
 1410 .4 
 
 16' 
 
 18' 
 
 4262 .9 
 
 6840.2 
 
 1411.9 
 
 18' 
 
 20' 
 
 4265.5 4 
 
 6842.8 
 
 1413.5 ^ . . 
 
 20' 
 
 22' 
 
 4268.1 
 
 6845.5 
 
 1415 .0 >0<> 
 
 22' 
 
 24' 
 
 4270.7 
 
 6848.2 
 
 1416. 6: : 
 
 24' 
 
 26' 
 
 4273.3 i 
 
 6850 . 9 
 
 1418.1- 
 
 26' 
 
 28' 
 
 4275-9 -~ 
 
 6853.5 
 
 1419 -7 -a- : 
 
 28' 
 
 30' 
 
 4278.5 < 
 
 6856.2 
 
 1421. 2 < 
 
 30' 
 
 32' 
 
 4281.1 
 
 6858.9 
 
 1422 .8 <-2 : - 
 
 32' 
 
 34' 
 
 4283.7 . .;? 
 
 6861 .6 
 
 1424.3 J'J 
 
 34' 
 
 36' 
 
 4286.3 ^ a ^ 
 
 6864.3 
 
 1425 .9 N 
 
 36' 
 
 38' 
 
 4288. 9 k d r ; 
 
 6866.9 
 
 1427. 4|: : 
 
 38' 
 
 40' 
 
 4291.5-3 ^ 
 
 6869.6 
 
 1429.0 
 
 40' 
 
 42' 
 
 4294.1 .: 
 
 6872.3 
 
 1430.6 
 
 42' 
 
 44' 
 
 4296.702 
 
 6874.9 
 
 1432.1 
 
 44' 
 
 46' 
 
 4299.3 ,0 = 
 
 6877.6 
 
 1433-7 
 
 46' 
 
 48' 
 
 4301 .9 <? 4 
 
 6880.2 
 
 1435-2 
 
 48' 
 
 5' 
 
 4304.5 ss: 
 
 6882.9 
 
 1436.8 
 
 50' 
 
 5 2/ 
 
 4307.1 ? : fc 
 
 6885.5 
 
 1438.4 
 
 52' 
 
 54' 
 
 4309.7^ *g 
 
 6888.2 
 
 1439-9 
 
 54' 
 
 56' 
 
 4312.3 -a 
 
 6890 . 9 
 
 I44L5 
 
 56' 
 
 58' 
 
 4314.9 < 
 
 6893.6 
 
 1443.0 
 
 58' 
 
 74 
 
 4317-6 i 
 
 6896.3 
 
 1444.6 
 
 74 
 
 2' 
 
 4320.2 
 
 6899 .0 
 
 1446.2 
 
 2' 
 
 4' 
 
 4322.9 j 
 
 6901 .6 
 
 1447.8 ^? 
 
 4' 
 
 6' 
 
 4325-5 
 
 6904.3 
 
 1449-3,: : 
 
 L 6' 
 
 8' 
 
 4328.1 
 
 6906 . 9 
 
 14 CQ . 9 ^ 
 
 "15 
 
 r"p s' 
 
 10' 
 
 4330.7 
 
 6909.6 
 
 JH ^ 
 
 io r 
 
 12' 
 
 4333-4 
 
 6912 . 2 
 
 1454.1 < 
 
 12' 
 
 14' 
 
 4336.0 
 
 6914.8 
 
 1455- 7^ : 2 
 
 ?j 14' 
 
 16' 
 
 4338.6 
 
 6917.5 
 
 1457.2 9 t 
 
 16' 
 
 18' 
 
 4341.2 
 
 6920. I 
 
 1458. 8^ a 
 
 18' 
 
 20' 
 
 4343-8 
 
 6922 .8 
 
 1460.4^- = 
 
 20' 
 
 22' 
 
 4346.5 
 
 6925-5 
 
 1462 .0 
 
 22' 
 
 24' 
 
 4349 - 1 
 
 6928.2 
 
 1463.6 
 
 24' 
 
 26' 
 
 435*-7 
 
 6930.8 
 
 1465.2 
 
 26' 
 
 28' 
 
 4354-3 
 
 6933-5 
 
 1466.8 
 
 28' 
 
 94 
 
IX. FUNCTIONS OF A ONE-DEGREE CURVE. 
 
 Whole 
 Angle. 
 
 Tangent 
 Distance. 
 
 Long 
 Chord. 
 
 External 
 Secant. 
 
 Whole 
 Angle. 
 
 74 30' 
 
 435 6 -9 
 
 6936.1 
 
 1468 .4 
 
 74 30' 
 
 32' 
 
 4359-6 
 
 6938.8 
 
 1470 .0 
 
 S^' 
 
 34' 
 
 4362.2 
 
 6941.5 
 
 1471.6 
 
 34' 
 
 36' 
 
 4364.9 ,A^4 
 
 6944.1 
 
 1473.2 . 
 
 36' 
 
 3*' 
 
 4367-5 c. , M 
 
 6946.8 
 
 1474-8 "*2 
 
 38' 
 
 4C/ 
 
 437 - 1 S" 
 
 6949.4 
 
 1476.4;!" = 
 
 40' 
 
 42' 
 
 4372.8 g. . 
 
 6952 .O 
 
 1478.0-3 
 
 42' 
 
 44' 
 
 4375 -4 c&" " 
 
 6954.7 
 
 1479. 6 -gr : 
 
 44' 
 
 46' 
 
 4378.1 ; - 
 
 6957-3 
 
 1481.2 < 
 
 46' 
 
 48' 
 
 4380.7^,^ 
 
 6960 .O 
 
 1482. 8 =.= 
 
 48' 
 
 50' 
 
 4383-3 jj 
 
 6962 .6 
 
 <N q -<t 
 1484 -4 ^ Ov o 
 
 So' 
 
 52' 
 
 4386.0^ 
 
 6965 . 2 
 
 1486.0 T- 
 
 52' 
 
 54' 
 
 4388.6^ = 
 
 6967.9 
 
 1487.6^= = 
 
 54' 
 
 56 
 
 4391.2 
 
 6970.5 
 
 1489 . 2 
 
 56' 
 
 58' 
 
 4393-9 
 
 6973-2 
 
 1490.8 
 
 58' 
 
 75 
 
 4396.5 
 
 6975.9 
 
 1492.4 
 
 75 
 
 2' 
 
 4399-2 
 
 6978.6 
 
 1494.0 
 
 2' 
 
 4' 
 
 4401-8 4 
 
 6981.2 
 
 1495.6 
 
 4' 
 
 6' 
 
 4404.5 - 
 
 6983.9 
 
 1497-3 
 
 6' 
 
 8' 
 
 4407.1 ,c 
 
 6986.5 
 
 1498.9 
 
 8' 
 
 10' 
 
 4409.8 -g 
 
 6989. I 
 
 J 5oo.5 
 
 id* 
 
 12' 
 
 4412.5 
 
 6991 .8 
 
 1502 . i 
 
 12' 
 
 14' 
 
 44i5.i ? 
 
 6994.4 
 
 I 53-7 
 
 14' 
 
 16' 
 
 4417-8 ^ 
 
 6997.0 
 
 1505-4 
 
 1 6' 
 
 18' 
 
 4420.5 2" 
 
 6999-7 
 
 1507.0 
 
 18' 
 
 20' 
 
 4423.1 ^^^ 
 
 7002.3 
 
 1508.6 ^ j 
 
 20' 
 
 22' 
 
 4425.8^: | 
 
 7005 .0 
 
 1510.2 6- . 
 
 22' 
 
 24' 
 
 4428.4- < 
 
 7007 .6 
 
 1511.8^^ " 
 
 24' 
 
 26' 
 
 443i.i-a : 
 
 7010.2 
 
 J 5iS.sl : s 
 
 26' 
 
 28' 
 
 4433-8^ 
 
 7012 .8 
 
 ISIS- leg 1 " " 
 
 28' 
 
 3 ! 
 
 4436. 4 -2 : 
 
 7015-4 
 
 1516. 7 |: = 
 
 30' 
 
 32' 
 
 4439.1 ^4 
 
 7018.0 
 
 1518.3 
 
 32' 
 
 3 
 
 4441 .7 '^^^ 
 
 7020.7 
 
 1520.0 roa S 
 
 34' 
 
 36 
 
 4444- 4 ?- fc 
 
 7023.3 
 
 1521.65. . 
 
 36' 
 
 38' 
 
 4447- 1 <" *g 
 
 7026 .0 
 
 i5 2 3-3<" " 
 
 38' 
 
 40' 
 
 4449 7 
 
 7028.6 
 
 1524-9 
 
 40' 
 
 42' 
 
 4452.4 
 
 7031.2 
 
 1526.5 
 
 42' 
 
 44' 
 
 4455-0 
 
 7 33.9 
 
 1528 . 2 
 
 44' 
 
 46' 
 
 4457-7 : 
 
 7036.5 
 
 1529.8 
 
 : 46' 
 
 48' 
 
 4460 .4 ^ 
 
 7039.2 
 
 !53i-5 
 
 ; 48' 
 
 5 ; 
 
 4463.1 | 
 
 7041 .8 
 
 i533.i 
 
 s: 
 
 52' 
 
 4465.8 
 
 7044.4 
 
 J 534.7 
 
 52' 
 
 s - 
 
 4468 .4 
 
 7047.1 
 
 1536.4 
 
 54' 
 
 5 o 
 
 4471 .1 
 
 7049.7 
 
 1538-0 
 
 56' 
 
 58' 
 
 4473-8 
 
 7052.3 
 
 T 539-7 
 
 ' 58' 
 
 95 
 
IX. FUNCTIONS OF A ONE-DEGREE CURVE. 
 
 Whole 
 Angle. 
 
 Tangent 
 Distance. 
 
 Long 
 Chord. 
 
 External 
 Secant. 
 
 Whole 
 Angle. 
 
 76 
 
 4476.5 
 
 7055-0 
 
 I54L4 
 
 76 
 
 2' 
 
 4479.2 
 
 7057-6 
 
 1543-0 
 
 2' 
 
 4' 
 
 4481 .8 
 
 7060 . 2 
 
 1544.7 
 
 4' 
 
 6' 
 
 4484.5 
 
 7062.8 
 
 1546.3 
 
 6' 
 
 8' 
 
 4487.1 
 
 7065.4 
 
 1548 .0 
 
 8' 
 
 10' 
 
 4489.9 
 
 7068.1 
 
 1549-7 
 
 10' 
 
 12' 
 
 4492 .6 
 
 7070.7 
 
 I55I-3 
 
 12' 
 
 14' 
 
 4495-3 
 
 7073-3 
 
 1553-0 
 
 14' 
 
 16' 
 
 4498 .0 
 
 7075-9 
 
 1554-7 
 
 16' 
 
 18' 
 
 4500.7 
 
 7078.5 
 
 1556.3 
 
 18' 
 
 20' 
 
 4503-4 4 
 
 7081 . 2 
 
 1558.0 
 
 20' 
 
 22' 
 
 4506.1 
 
 7083.8 
 
 J 559-7 
 
 22' 
 
 24' 
 
 4508.8 1 
 
 7086 .4 
 
 1561.3 
 
 24' 
 
 26' 
 
 45 I]C -4 - 
 
 7089.0 
 
 1563-0 
 
 26' 
 
 28' 
 
 45i4.i 
 
 7091 .6 
 
 1564-7 
 
 28' 
 
 30' 
 
 4516.9 < 
 
 7094.2 
 
 1566.4 
 
 30' 
 
 32' 
 
 4519.6 a 
 
 7096 .8 
 
 1568.1 
 
 32' 
 
 34' 
 
 4522.3 U 
 
 7099.4 
 
 1569 . 8 
 
 34' 
 
 36' 
 
 4525.0 ^4^ 
 
 7102 .0 
 
 1571.4^? 
 
 36 
 
 38' 
 
 4527' 7 : '5 
 
 7104.6 
 
 1573- l|: = 
 
 38' 
 
 40' 
 42' 
 
 4530.4^ ^ 
 4533. 2 - = 
 
 7107.3 
 7109.9 
 
 1574- 8 -g 
 
 1576. 5 ft : : 
 
 40' 
 42' 
 
 44' 
 
 4535-9^ 
 
 7112.5 
 
 1578.2^ 
 
 44' 
 
 46' 
 
 4538.6^: 
 
 7115.1 
 
 1579.8^= 5 
 
 46' 
 
 48' 
 
 4541-3 3^ <4 
 
 7117.7 
 
 ^81.5 SSI- 
 
 48' 
 
 5o; 
 
 4544.0 3" 
 
 7120.4 
 
 1583.2^ 
 
 5 ,' 
 
 
 4546.8^ & 
 
 7123.0 
 
 1584- 9S : : 
 
 52' 
 
 54' 
 
 4549- 5 < "g 
 
 7125.6 
 
 1586.6 
 
 54 
 
 56' 
 
 4552.2 'a 
 
 7128.2 
 
 1588.2 
 
 56 
 
 58' 
 
 4554-9 ^ 
 
 7130.8 
 
 1589.9 
 
 58' 
 
 77 
 
 4557-6 ^ 
 
 7133.5 
 
 1591.6 
 
 77 
 
 2' 
 
 4560.3 
 
 7136.1 
 
 1593-3 
 
 2' 
 
 4' 
 
 4563.0 *- 
 
 7138.7 
 
 1595-0 
 
 4' 
 
 6' 
 
 4565.7 
 
 7I4L3 
 
 1596.7 
 
 6' 
 
 8' 
 
 4568.4 
 
 7143.9 
 
 1598.4 
 
 8' 
 
 10' 
 
 4571-2 
 
 7146.5 
 
 1600. I 
 
 10' 
 
 12' 
 
 4573-9 
 
 7149.1 
 
 1601.8 
 
 12' 
 
 14' 
 
 4576.6 
 
 7151 . 7 
 
 1603.5 
 
 14' 
 
 16' 
 
 4579-3 
 
 7 T 54.3 
 
 1605 . 2 
 
 16' 
 
 18' 
 
 4582 .0 
 
 
 l6o6 .9 
 
 18' 
 
 20' 
 
 4584.8 
 
 7159.5 
 
 1608. 6 
 
 20' 
 
 22' 
 
 4587.5 
 
 7162 . i 
 
 1610.3 
 
 22' 
 
 24' 
 
 4590.3 
 
 7164.7 
 
 1612 .0 
 
 24' 
 
 26' 
 
 4593-0 
 
 7 J 67-3 
 
 1613.7 
 
 26' 
 
 28' 
 
 4595-7 
 
 7169.9 
 
 1615.4 
 
 28' 
 
 96 
 
IX. FUNCTIONS OF A ONE-DEGREE CURVE. 
 
 Whole 
 Angle. 
 
 Tangent 
 Distance. 
 
 Long 
 Chord. 
 
 External 
 Secant. 
 
 Whole 
 Angle. 
 
 77 30' 
 
 4598.5 
 
 7*72.5 
 
 1617 . I 
 
 77 30' 
 
 32' 
 
 4601 . 2 
 
 7i75.i 
 
 1618.8 
 
 32' 
 
 34' 
 
 4604.0 
 
 7177.7 
 
 1620.5 
 
 34' 
 
 36' 
 
 4606.7 ^^4 
 
 7180.3 
 
 l622 . 2 
 
 36' 
 
 38' 
 
 4609.5 6 _ j 
 
 7482.9 
 
 1624.0 
 
 38' 
 
 40' 
 
 4612 . 2 J" 
 
 7185.5 
 
 1625.7 
 
 40' 
 
 42' 
 
 4615.0!^ . 
 
 7188.1 
 
 1627.5 
 
 42' 
 
 44' 
 
 46l7.7l" " 
 
 7190.7 
 
 1629 . 2 
 
 44' 
 
 46' 
 
 4620.5 ^ : 
 
 7I93-3 
 
 1630.9 
 
 46' 
 
 48' 
 
 4623.3^; 
 
 7195.9 
 
 1632.7 
 
 48' 
 
 50' 
 
 4626 .O > H 
 
 7198.5 
 
 1634.4 
 
 50' 
 
 S^' 
 
 4628.8^* 
 
 7201 . i 
 
 1636.1 
 
 52' 
 
 54' 
 
 4631- 5 3j : : 
 
 7203.7 
 
 1637.9 
 
 54' 
 
 56' 
 
 4634.2 
 
 7206.3 
 
 1639.6 
 
 56' 
 
 58' 
 
 4637.0 
 
 7208.9 
 
 1641.3 
 
 38' 
 
 78 
 
 4639-7 
 
 7211.5 
 
 1643.0 
 
 78 
 
 2' 
 
 4642 .5 
 
 7214.1 
 
 1644 .8 
 
 2' 
 
 4' 
 
 4645.2 
 
 7216.7 
 
 1646.5 ^.^ 
 
 4' 
 
 6' 
 
 4648 .0 
 
 7219.3 
 
 1648.3 t - 
 
 6' 
 
 8' 
 
 4650,8 
 
 7221.9 
 
 1650.0 j: : 
 
 8' 
 
 10' 
 
 4653-5 
 
 7224.4 
 
 1651-7 g 
 
 10' 
 
 12' 
 
 4656.3 
 
 7227.0 
 
 1653. 5 -a : : 
 
 12' 
 
 14' 
 
 4659.0 
 
 7229.6 
 
 1655.2^ 
 
 14' 
 
 16' 
 
 4661.8 
 
 7232.2 
 
 1657. o^ = 
 
 16' 
 
 18' 
 
 4664.6 
 
 7234-8 
 
 '658.7;- So 
 
 18' 
 
 20' 
 
 ~* iA <> 4 
 4667.4 
 
 7237-3 
 
 1660.5 -a 
 
 20' 
 
 22' 
 
 4670.2^: : 
 
 7239-9 
 
 1662. 3^^ : 
 
 22' 
 
 24' 
 
 4673.0-3 
 
 7242.5 
 
 1664 . o 
 
 24' 
 
 26' 
 
 4675.7^ : 
 
 7245.0 
 
 1665.8 
 
 26' 
 
 28' 
 
 4678 . 5 c/2 
 
 7247.6 
 
 1667.5 
 
 28' 
 
 3; 
 
 4681. 3 I 55 
 
 7250.2 
 
 1669.3 
 
 30' 
 
 32' 
 
 4684.1 ^J 
 
 7252.8 
 
 1671 .0 
 
 32' 
 
 34' 
 
 4686.9 3;: 
 
 7255.4 
 
 1672.8 
 
 34' 
 
 36' 
 
 4689.6;^ 
 
 7258.0 
 
 1674.5 
 
 36' 
 
 38' 
 
 4692 .4 <j" 
 
 7260.6 
 
 1676.3 
 
 38' 
 
 40' 
 
 4695.2 
 
 7263.2 
 
 1678. I 
 
 40' 
 
 42' 
 
 4698.0 
 
 7265.8 
 
 1679.9 
 
 42' 
 
 44' 
 
 4700.8 
 
 7268.3 
 
 1681.7 
 
 44' 
 
 46' 
 
 4703.6 
 
 7270.9 
 
 1683.4 
 
 46' 
 
 48' 
 
 4706.4 
 
 7273-5 
 
 1685.2 
 
 48' 
 
 5' 
 
 4709 . 2 
 
 7276.1 
 
 1687.0 
 
 5' 
 
 5^' 
 
 4712.0 
 
 7278.7 
 
 1688.8 
 
 52' 
 
 54' 
 
 4714.8 
 
 7281.3 
 
 1690 .6 
 
 54' 
 
 56' 
 
 4717.6 
 
 7283.9 
 
 1692.3 
 
 56' 
 
 58' 
 
 4720.4 
 
 7286.5 
 
 1694. i 
 
 58' 
 
 97 
 
IX. FUNCTIONS OF A ONE-DEGREE CURVE. 
 
 Whole 
 Angle. 
 
 Tangent 
 Distance. 
 
 Chord. 
 
 External 
 Secant. 
 
 Whole 
 Angle. 
 
 79 
 
 4723- 1 
 
 7289 . 
 
 1695.9 
 
 79 
 
 2' 
 
 4725-9 
 
 7291 . 6 
 
 1697.7 
 
 2' 
 
 4' 
 
 4728.7 
 
 7294.1 
 
 1699.5 
 
 4' 
 
 6' 
 
 4731-5 
 
 7296.7 
 
 1701.3 
 
 6' 
 
 8' 
 
 4734-3 
 
 7299.2 
 
 1703.0 
 
 8' 
 
 10' 
 
 4737- 1 
 
 7301.8 
 
 1704 . 8 
 
 10' 
 
 12' 
 
 4739-9 
 
 7304.3 
 
 1706 . 6 
 
 I2 f 
 
 14' 
 
 4742.7 
 
 7306.9 
 
 1708 .4 
 
 14' 
 
 16' 
 
 4745-5 
 
 7309-5 
 
 I7IO . 2 
 
 16' 
 
 18' 
 
 4748.3 
 
 7312.0 
 
 1712 .0 
 
 18' 
 
 20' 
 
 4751-2 
 
 7314.6 
 
 1713.7 . . . 
 
 20' 
 
 22' 
 
 4754.0 
 
 7317 . 2 
 
 I7I5-5 ^ C '- 
 
 22^ 
 
 24' 
 
 4756.9 
 
 73J9-8 
 
 
 24' 
 
 26' 
 
 4759-7 ^ 
 
 7322 . 3 
 
 1719.1^ 
 
 26' 
 
 28' 
 
 4762.5 .fa 
 
 7324.9 
 
 I72O .9 ,|H : , 
 
 28' 
 
 3' 
 
 4765.3 < 
 
 7327.4 
 
 I 7 22. 7 f 
 
 30' 
 
 32' 
 
 4768.2 
 
 733o.o 
 
 1724.5,^ 
 
 32' 
 
 34' 
 
 4771 .0 ^ 
 
 7332.5 
 
 
 34' 
 
 36' 
 
 4773.8 lAor- 
 
 7335' J 
 
 I728.I "'* 
 
 36' 
 
 38' 
 
 4776.6 6, ^ 
 
 7337-6 
 
 1729. 9| : - 
 
 38' 
 
 40' 
 
 4779-4-a' ^ 
 
 -9340.2 
 
 I73L7 
 
 40' 
 
 42' 
 
 4782. 2-g: 
 
 7342.8 
 
 1733.5 
 
 42' 
 
 44' 
 
 4785- IC 
 
 7345-3 
 
 1735.3 
 
 44' 
 
 46' 
 
 4787. 9& 
 
 7347-9 
 
 I737- 1 
 
 46' 
 
 48' 
 
 4790.7 22 4 
 
 7350.4 
 
 1738.9 
 
 48' 
 
 50' 
 
 4793.6 S3J: 
 
 7353-0 
 
 1740.8 
 
 50' 
 
 52' 
 
 4796 .4 ^g, 
 
 7355-5 
 
 1742.6 
 
 52' 
 
 54' 
 
 4799. 2<T | 
 
 7358.1 
 
 1744.4 
 
 54' 
 
 56' 
 
 4802.0 ', 
 
 736o.6 
 
 1746.2 
 
 56' 
 
 58' 
 
 4804.9 ^ 
 
 7363-2 
 
 1748.0 
 
 58' 
 
 8O 
 
 4807.7 f. 
 
 7365.8 
 
 1749.9 
 
 8O 
 
 2' 
 
 4810.5 N 
 
 7368.4 
 
 I75L7 u . < ^ 4 
 
 2' 
 
 4' 
 
 4813.3 5 
 
 7370.9 
 
 
 4 f 
 
 6' 
 
 4816.2 5 
 
 7373-5 
 
 1755.4 6. i 
 
 6' 
 
 8' 
 
 4819.0 
 
 7376.0 
 
 1757.2:: 
 
 8' 
 
 10' 
 
 4821 .9 
 
 7378.5 
 
 1759. o|: : 
 
 10' 
 
 12' 
 
 4824.7 
 
 7381.1 
 
 1760 . 8 M 
 
 12' 
 
 14' 
 
 4827.6 
 
 7383-6 
 
 1762.6,0: : 
 
 14' 
 
 16' 
 
 4830.4 
 
 7386.2 
 
 1764.5 4"?^ 
 
 16' 
 
 18' 
 
 4833-3 
 
 7388.7 
 
 1766.3 "^ 
 
 18' 
 
 20' 
 
 4836.2 
 
 7391.2 
 
 1768. 2|= : 
 
 20' 
 
 22' 
 
 4839.0 
 
 7393-8 
 
 1770.0 
 
 22' 
 
 24' 
 
 4841.9 
 
 7396.3 
 
 1771.9 
 
 24' 
 
 26' 
 
 4844.8 
 
 7398.9 
 
 J773-7 
 
 26' 
 
 28' 
 
 4847.6 
 
 74oi .4 
 
 1775.6 
 
 28' 
 
IX. FUNCTIONS OF A ONE-DEGREE CURVE. 
 
 Whole 
 Angle. 
 
 Tangent 
 Distance. 
 
 Long 
 Chord. 
 
 External 
 Secant. 
 
 Whole 
 Angle. 
 
 80 30' 
 
 4850.5 
 
 7404.0 
 
 1777-4 
 
 80 30' 
 
 32' 
 
 4853 .4 
 
 7406.5 
 
 1779-3 
 
 32' 
 
 34' 
 
 4856.2 
 
 7409.1 
 
 1781.1 
 
 34' 
 
 36' 
 
 4859.1 ^^4 
 
 74H.6 
 
 1783.0 
 
 36' 
 
 38' 
 
 4862.0 . 
 
 7414.2 
 
 1784.8 
 
 38' 
 
 40' 
 
 4864. 8 : : 
 
 7416.8 
 
 1786.7 
 
 40' 
 
 42' 
 
 4867.7*8. , 
 
 74I9-3 
 
 1788.5 
 
 42' 
 
 44' 
 
 4870.6$- ' 
 
 #42 I. 9 
 
 1790.4 
 
 44' 
 
 46' 
 
 4873.4 . : 
 
 7424.4 
 
 1792.2 
 
 46' 
 
 48' 
 
 4876.3^ a 
 
 7427.0 
 
 1794.1 
 
 48' 
 
 5' 
 
 4879.2 ^S 
 
 7429.5 
 
 1796.0 ^ 
 
 50' 
 
 5 2 ' 
 
 4882.0^ 
 
 7432.1 
 
 1797.9 
 
 5*' 
 
 54' 
 
 4884. 9 2= : 
 
 7434-6 
 
 1799.7 g 
 
 CA 
 
 56' 
 
 4887.8 
 
 7437-2 
 
 1801.6 - 
 
 56' 
 
 58' 
 
 4890.7 
 
 7439-7 
 
 1803.5 . 
 
 58' 
 
 81 
 
 4893.6 
 
 7442.2 
 
 1805.4 < 
 
 81 
 
 2' 
 
 4896.5 
 
 7444-7 
 
 1807.3 & 
 
 2' 
 
 4' 
 
 4899.3 
 
 7447-2 
 
 1809.1 
 
 4' 
 
 6' 
 
 49O2 . 2 
 
 7449-8 
 
 1811 .0 . . * 
 
 6' 
 
 8' 
 
 4905.1 
 
 7452.3 
 
 1812.9 ^| 
 
 8 7 
 
 10' 
 
 4907.9 
 
 7454-8 
 
 1814. 8^T 
 
 10' 
 
 12' 
 
 4910.8 
 
 7457-4 
 
 1816.7 $ 
 
 12' 
 
 14' 
 
 4913.7 
 
 7459-9 
 
 1.818,5$- 
 
 4' 
 
 16' 
 
 4916.6 
 
 7462.4 
 
 1820.4 g- 
 
 1 6' 
 
 18' 
 
 49190 
 
 7464.9 
 
 1822.3 ^4 
 
 1 8' 
 
 20' 
 
 4922.4 in0 ? 
 
 7467.5 
 
 1824.2 ^^ 
 
 20' 
 
 22' 
 
 4925-35= = 
 
 7470.0 
 
 1826.0 2' ^ 
 
 22 7 
 
 24' 
 
 4928.2* 
 
 7472.5 
 
 1827.9^ -g 
 
 24/ 
 
 26' 
 
 493 1 -*.*: : 
 
 7475-1 
 
 1829.8 -a 
 
 26' 
 
 28' 
 
 4934.0 c& 
 
 7477-6 
 
 1831.7 \ 
 
 28' 
 
 30' 
 
 4936.9^= = 
 
 7480.1 
 
 1833.6 t 
 
 30; 
 
 32' 
 
 4939.8 555 
 
 7482.6 
 
 1835.5 i 
 
 32 
 
 34' 1 
 
 4942.7 $ 
 
 7485.1 
 
 1837.4 3 
 
 34 
 
 36' 
 
 4945-6;d 
 
 7487.7 
 
 J839-3 < 
 
 36 
 
 38' 
 
 4948.5? : : 
 
 7490.2 
 
 1841 .2 
 
 38' 
 
 40' 
 
 495 1 -4 
 
 7492.7 
 
 1843.1 
 
 40' 
 
 42' 
 
 4954-3 
 
 7495-2 
 
 1845 .0 
 
 42; 
 
 44' 
 
 4957-2 
 
 7497-7 
 
 1846 .9 
 
 44 
 
 46' 
 
 4960 . 2 
 
 7500.2 
 
 1848.8 
 
 46' 
 
 48' 
 
 4963.1 
 
 7502.7 
 
 1850.7 
 
 48' 
 
 50' 
 
 4966 . o 
 
 7505.3 
 
 1852.6 
 
 5; 
 
 52' 
 
 4968.9 
 
 7507.9 
 
 1854.5 
 
 52 
 
 54' 
 
 497 J -9 
 
 75*0.4 
 
 1856.4 
 
 54 
 
 56' 
 
 4974-8 
 
 75 12 9 
 
 1858.3 
 
 56 
 
 58' 
 
 4977-7 
 
 75*5-4 
 
 1860.2 
 
 58' 
 
 99 
 
IX. FUNCTIONS OF A ONE-DEGREE CURVE. 
 
 Whole 
 Angle. 
 
 Tangent 
 Distance. 
 
 Long 
 Chord. 
 
 External 
 Secant. 
 
 Whole 
 Angle. 
 
 82 
 
 4980.6 
 
 75 J 7-9 
 
 1862.2 
 
 82 
 
 2' 
 
 4983.6 
 
 7520.4 
 
 1864.1 
 
 2' 
 
 4' 
 
 4986.5 
 
 7522.9 
 
 1866.0 
 
 4' 
 
 6' 
 
 4989.4 
 
 
 1867.9 
 
 6' 
 
 8' 
 
 4992.4 
 
 7527-9 
 
 1869.8 
 
 8' 
 
 10' 
 
 4995-3 
 
 7530.4 
 
 1871.8 
 
 10' 
 
 12' 
 
 4998.3 
 
 7532.9 
 
 1873.7 
 
 I2 r 
 
 14' 
 
 5OOI . 2 
 
 7535-4 
 
 1875.6 
 
 14' 
 
 16' 
 
 5004.2 
 
 7537-9 
 
 1877.6 
 
 16' 
 
 18' 
 
 5007.1 
 
 7540.4 
 
 1879-5 
 
 i8 r 
 
 20' 
 
 5010 .0 ^ a 4 
 
 7543-o 
 
 1881 .5 
 
 20' 
 
 22' 
 
 5 OI 3-o i 
 
 7545-5 
 
 1883.4 4 
 
 22 A 
 
 24' 
 
 5015.95- - 
 
 7548.0 
 
 1885.3 6 
 
 24' 
 
 26' 
 
 5018.9 'g 
 
 7550.5 
 
 1887.3 fc 
 
 26' 
 
 28' 
 
 5021.8'Br : 
 
 C/3 
 
 7553-o 
 
 1889.2 *g 
 
 28' 
 
 30' 
 
 5024.7 - - 
 
 7555-5 
 
 1891 . 2 , 
 
 30' 
 
 32' 
 
 5027. 7 *" 
 
 7558 .0 
 
 1893.1 & 
 
 32' 
 
 34' 
 
 5030.6 
 
 7560.5 
 
 1895.1 o 
 
 34' 
 
 36' 
 
 5033-6^^- 
 
 
 l897 - N 
 
 36' 
 
 38' 
 
 5036.55: : 
 
 7565.5 
 
 1899.0 ^C/g 
 
 38' 
 
 40' 
 
 5039.5 
 
 7568.0 
 
 1900.9 ^ **> 
 
 40' 
 
 42' 
 
 5042.4 
 
 7570-5 
 
 1902.9-3 
 
 42' 
 
 44' 
 
 5045-4 
 
 7573-o 
 
 1904.8-^: 
 
 44' 
 
 46' 
 
 5048.4 
 
 7575-5 
 
 1906.8^ 
 
 46' 
 
 48' 
 
 505 1 -3 
 
 7578.o 
 
 1908. 7 
 
 48' 
 
 5' 
 
 5054-3 
 
 7580.6 
 
 I9I0.7 2ln 
 
 5 0/ 
 
 52' 
 
 5057.3 
 
 7583.1 
 
 1912.63. h 
 
 52' 
 
 54' 
 
 5060 . 2 
 
 7585.6 
 
 1914 .6 <J" ^ 
 
 54' 
 
 56' 
 
 5063.2 
 
 7588.1 
 
 1916.5 I 
 
 56' 
 
 58' 
 
 5066 . I 
 
 7590.6 
 
 1918.5 
 
 58' 
 
 83 
 
 5069 . I 
 
 7593-1 
 
 1920.5 
 
 83 
 
 2' 
 
 5072.1 ^4 
 
 7595-6 
 
 1922.5 T 
 
 2' 
 
 4' 
 
 5075.1 c - 
 
 7598.1 
 
 1924.4 
 
 4' 
 
 6' 
 
 5078. o : = 
 
 7600.5 
 
 1926.4 5 
 
 6' 
 
 8' 
 
 5081 .0-3 
 
 7603 . o 
 
 1928.4 < - 
 
 8' 
 
 10' 
 
 5084. og" : 
 
 7605.5 
 
 1930.4 
 
 10' 
 
 12' 
 
 5087 .0 g. 
 
 7608 .0 
 
 1932.4 
 
 12' 
 
 14' 
 
 5089. 9 xVo 
 
 7610.5 
 
 1934.4 
 
 14' 
 
 16' 
 
 5092.9 VC^ 
 
 7613.0 
 
 1936.3 
 
 16' 
 
 18' 
 
 5095.9^^ 
 
 7615.5 
 
 1938.3 
 
 1 8' 
 
 20' 
 
 5098. 93j : : 
 
 7618.0 
 
 1940.3 
 
 20' 
 
 22' 
 
 5101.9 
 
 7620.5 
 
 1942.3 
 
 22' 
 
 24' 
 
 5104.9 
 
 7623.0 
 
 1944.3 
 
 24' 
 
 26' 
 
 5107.8 
 
 7625.5 
 
 1946.3 
 
 26' 
 
 28' 
 
 5110.8 
 
 7628.0 
 
 1948.3 
 
 28' 
 
 100 
 
IX. FUNCTIONS OF A ONE-DEGREE CURVE. 
 
 Whole 
 Angle. 
 
 Tangent 
 Distance. 
 
 Long 
 Chord . 
 
 External 
 Secant. 
 
 Whole 
 Angle. 
 
 83 30' 
 
 51*3-8 
 
 7630.4 
 
 1950.3 
 
 83 30/ 
 
 3*; 
 
 5116.8 
 
 7632.9 
 
 1952.3 
 
 32' 
 
 34' 
 
 5119.8 
 
 7635 4 
 
 1954.3 
 
 34' 
 
 36' 
 
 5122.8 
 
 7637.9 
 
 1956.3 
 
 36' 
 
 38' 
 
 5*25.8 
 
 7640.4 
 
 1958.3 
 
 
 40' 
 
 5128.8 
 
 7642.9 
 
 1960.3 
 
 . 4 o r 
 
 42' 
 
 5*3*-9 
 
 7645.4 
 
 1962.3 
 
 42' 
 
 44' 
 
 5*34-9 
 
 7647.8 
 
 1964.3 
 
 44/ , 
 
 46' 
 
 5*37-9 
 
 7650.3 
 
 1966.3 
 
 
 48' 
 
 5140.9 
 
 7652.8 
 
 1968.3 
 
 48' 
 
 So; 
 
 5*43-9 4 
 
 7655.3 
 
 I970-3 
 
 5 0/ 
 
 
 5146.9 
 
 7657.8 
 
 1972.3 H 
 
 *2' 
 
 54' 
 
 5*49-9 j 
 
 7660.3 
 
 1974.4 6 
 
 54' 
 
 56' 
 
 5*52-9 -3 
 
 7662.8 
 
 1976.4 ^ 
 
 56' 
 
 58' 
 
 5*55-9 
 
 7665.3 
 
 1978.4 g 
 
 58' 
 
 84 
 
 5*58.9 < 
 
 7667.8 
 
 1980.4 </? 
 
 84 
 
 2' 
 
 5161.9 
 
 7670.2 
 
 1982.4 j: 
 
 2' 
 
 4' 
 
 5165.0 . .5 
 
 7672.7 
 
 1984.5 <? 
 
 4' 
 
 6' 
 
 5168 .0 ^ ^ 
 
 7675.2 
 
 1986.5 5 
 
 6' 
 
 8' 
 
 5*7*-o: 5 
 
 7677.6 
 
 1988.5 ^5 
 
 8' 
 
 10' 
 
 5*74.015 ^ 
 
 7680.1 
 
 1990. 5|- ^ 
 
 10' 
 
 12' 
 
 5*77-*-a : 
 
 7682.6 
 
 
 12' 
 
 14' 
 
 5180.1 co 
 
 7685.1 
 
 1994. 6. |: 
 
 *4' 
 
 16' 
 
 5*83- *Ja : 
 
 7687.6 
 
 1996.6 tt 
 
 1 6' 
 
 18' 
 
 5186.2 jrt 4 
 
 7690.0 
 
 1998.6,0: 
 
 18' 
 
 20 1 
 
 5189.2 sr 
 
 7692.5 
 
 2000. 7 ^ H 
 
 20' 
 
 22' 
 
 5I92.2:g : 
 
 7695.0 
 
 2002 . 7 -d 'jg 
 
 22' 
 
 24' 
 
 5*95-3^ *g 
 
 7697 5 
 
 2004. 7 ^ : ^ 
 
 24' 
 
 26' 
 
 5*98.3 
 
 7699.9 
 
 2006.8 .b 
 
 26' 
 
 28' 
 
 5201.4 b 
 
 7702.4 
 
 2008.8 c& 
 
 28' 
 
 30' 
 
 5204.4 '~ 
 
 7704.8 
 
 2010.9 
 
 3' 
 
 32' 
 
 5207.4 ^ 
 
 7707-3 
 
 2012.9 
 
 32' 
 
 34' 
 
 5210.5 T ^- 
 
 7709.8 
 
 2015.0 ^ 
 
 3< 
 
 36' 
 
 5213-5 3 
 
 77*2-3 
 
 2017.0 ^ 
 
 
 38' 
 
 5216.6 
 
 7714.8 
 
 2019 . I 
 
 38' 
 
 40' 
 
 5219.6 
 
 77*7-2 
 
 2O2I . I 
 
 40' 
 
 42' 
 
 5222 . 6 
 
 7719.7 
 
 2023.2 
 
 42' 
 
 44' 
 
 5225.7 
 
 7722.1 
 
 2O25 . 2 
 
 44' 
 
 46' 
 
 5228.8 
 
 7724.6 
 
 2027.3 
 
 46' 
 
 48' 
 
 5231-9 
 
 7727.0 
 
 2029.3 
 
 48' 
 
 50' 
 
 5234.9 
 
 7729 5 
 
 2031.4 
 
 50' 
 
 52' 
 
 5238.0 
 
 7732.0 
 
 2033.4 
 
 52' 
 
 54' 
 
 5241 .0 
 
 7734-4 
 
 2035-5 
 
 54 
 
 56' 
 
 5244.1 
 
 7736.9 
 
 2037.6 
 
 56 
 
 58' 5247.2 
 
 7739-3 
 
 2039.6 
 
 58' 
 
 101 
 
IX. FUNCTIONS OF A ONE-DEGREE CURVE. 
 
 Whole 
 Angle. 
 
 Tangent 
 Distance. 
 
 Long 
 Chord. 
 
 External 
 Secant. 
 
 Whole 
 Angle. 
 
 85 
 
 5250.2 
 
 7741-8 
 
 2041.7 
 
 85 
 
 2' 
 
 5253 . 3 
 
 7744.2 
 
 2043-7 
 
 2' 
 
 4' 
 
 5256 .4 
 
 7746.7 
 
 2045 -8 
 
 4' 
 
 6' 
 
 5 2 59 5 "t 
 
 7749-1 
 
 2047.9 
 
 6' 
 
 8' 
 
 5262 .6 
 
 7751-6 
 
 2O5O.O H 
 
 8' 
 
 10' 
 
 5265.6 ^ 
 
 7754.1 
 
 2O52 . I 
 
 10' 
 
 12' 
 
 5268.7 | 
 
 7756.5 
 
 2054.1 ^ 
 
 12' 
 
 14' 
 
 5271.8 
 
 7759.0 
 
 2056.2 
 
 14' 
 
 16' 
 
 5274.9 
 
 7761.4 
 
 2058.3 * 
 
 16' 
 
 18' 
 
 5278.0 - 
 
 7763-9 
 
 2060.4 
 
 1 8' 
 
 20' 
 
 5281.0 ^ c . j 
 
 7766.4 
 
 2062 .5 
 
 20'- 
 
 22' 
 
 5284.1 ^ 
 
 7768.8 
 
 2064.6 ^^ 
 
 22' 
 
 24' 
 
 5287.2*- ^ 
 
 7771 .3 
 
 2066 .7 -; 3 
 
 24' 
 
 26' 
 
 5290.3 g 
 
 7773-7 
 
 2068. 8g : 
 
 26' 
 
 28' 
 
 5293.4^ : 
 
 7776.1 
 
 2070.9 % 
 
 28' 
 
 30' 
 
 5296.4 c: 
 
 7778.6 
 
 2073 .0 c& 
 
 30' 
 
 32' 
 
 5299.5^ 
 
 7781.0 
 
 2075 . I o: 
 
 32' 
 
 34' 
 
 5302.6 2- 
 
 7783.5 
 
 2O77 . 2 ^-oo * 
 
 34' 
 
 36' 
 
 5305.7^*0 
 
 7785.9 
 
 2079.3^6 
 
 36' 
 
 38' 
 
 5308.8^= fc 
 
 7788.4 
 
 2081 .4 13: ^ 
 
 38' 
 
 40' 
 
 5311.9 4 
 
 7790.8 
 
 2083.5 -| 
 
 40' 
 
 42' 
 
 5315.0 cc 
 
 7793-2 
 
 2085.6 co 
 
 42' 
 
 44' 
 
 5318.1 ,0 
 
 7795-7 
 
 2087.7 J5 
 
 44' 
 
 46' 
 
 5321.2 fl 
 
 7798.1 
 
 2089.9 
 
 46' 
 
 48' 
 
 5324.3 J 
 
 7800.6 
 
 2092.0 S 
 
 48' 
 
 50' 
 
 5327.4 : 
 
 7803.1 
 
 2094. i 
 
 50' 
 
 52' 
 
 5330.5 < 
 
 7805.5 
 
 2096 . 2 
 
 52' 
 
 54' 
 
 5333.6 
 
 7808.0 
 
 2098.3 
 
 54' 
 
 56' 
 
 5336.7 
 
 7810.4 
 
 2100.5 
 
 56' 
 
 58' 
 
 5339.8 
 
 7812.8 
 
 2IO2 .6 
 
 58' 
 
 86 
 
 5342.9 
 
 7815-3 
 
 2104.7 
 
 86 
 
 2' 
 
 5346.0 
 
 7817-7 
 
 2106. 8 . ^ . 
 
 2' 
 
 4' 
 
 5349.1 xAd4 
 
 7820. 2 
 
 2109 .0 ^ ** 
 
 4' 
 
 6' 
 
 5352. 2 ^ ^ 
 
 7822.6 
 
 2III .26.. 
 
 6' 
 
 8' 
 
 
 7825.0 
 
 2113-3^ " 
 
 8' 
 
 10' 
 
 5358.51, : 
 
 7827.4 
 
 2115 .4 -^ : = 
 
 10' 
 
 12' 
 
 536i .6 ^ 
 
 7829.8 
 
 2117 . 5 w 
 
 12' 
 
 14' 
 
 5364.8 fc- - 
 
 7832.3 
 
 2119 . 7 : - 
 
 14' 
 
 16' 
 
 5367.9Xo^ 
 
 7834.7 
 
 2 121 .8 ^^^ 
 
 16' 
 
 18' 
 
 5371.0 m 
 
 7837.1 
 
 2124.0 ^^^ 
 
 18' 
 
 20' 
 
 5374.2^ 
 
 7839-5 
 
 2126. I J : : 
 
 20' 
 
 22' 
 
 5377-3< : : 
 
 7842 .O 
 
 2128.2 
 
 22' 
 
 24' 
 
 5380.5 
 
 7844.4 
 
 2130.4 
 
 24' 
 
 26' 
 
 5383-6 
 
 7846.8 
 
 2132.5 
 
 26' 
 
 28' 
 
 5386.8 
 
 7849. 2 
 
 2T34-7 
 
 28' 
 
 102 
 
IX. FUNCTIONS OF A ONE-DEGREE CURVE. 
 
 Whole 
 Angle . 
 
 Tangent 
 Distance. 
 
 Long 
 Chord. 
 
 External 
 Secant. 
 
 \Vhole 
 Angle. 
 
 86 30' 
 
 5389-9 
 
 7851.6 
 
 2136.9 
 
 86 30' 
 
 32' 
 
 5393-0 
 
 7854.0 
 
 2139.0 
 
 3 2/ 
 
 34' 
 
 5396.2 ^ 4 
 
 7856.5 
 
 2141 . 2 
 
 34' 
 
 36' 
 
 5399-3 . 
 
 7858.9 
 
 2143-3 
 
 36' 
 
 38' 
 
 5402.5*: : 
 
 7861.4 
 
 2145-5 
 
 38' 
 
 40' 
 
 5405. 6 ^ _ 
 
 7863.8 
 
 2147-7 
 
 40' 
 
 42' 
 
 5408. 8 ;a- - 
 
 7866.3 
 
 2149.8 
 
 42' 
 
 44' 
 
 5412.0 ^ 
 
 7868.7 
 
 2152.0 
 
 44' 
 
 46' 
 
 5415 . 2 <"" 
 
 7871.1 
 
 2I54.I 
 
 46' 
 
 48' 
 
 5418.3 || 4 
 
 7873.5 
 
 2156.3 
 
 48' 
 
 50' 
 
 5421 .4 " ^ 
 
 7875 -9 
 
 2158.5 
 
 5' 
 
 52' 
 
 5424.6?: = 
 
 7878.3 
 
 2160.6 4 
 
 52' 
 
 54' 
 
 5427.7 
 
 7880.8 
 
 2162.8 ^ 
 
 54' 
 
 56' 
 
 5430.8 
 
 7883.2 
 
 2165.0 X 
 
 56' 
 
 58' 
 
 5434.0 
 
 7885.6 
 
 2167.2 *g 
 
 58' 
 
 87 
 
 5437-2 
 
 7888.0 
 
 2169.4 $ 
 
 87 
 
 2' 
 
 5440.4 
 
 7890.4 
 
 2171.6 
 
 2' 
 
 4' 
 
 5443-5 
 
 7892.8 
 
 2173-8 ^ 
 
 4' 
 
 6' 
 
 5446.7 
 
 7895 2 
 
 2176.0 
 
 6' 
 
 8' 
 
 5449-9 
 
 7897-6 
 
 2178.1 ^XTJ 
 
 8' 
 
 10' 
 
 5453-0 
 
 79OO .O 
 
 2180.3 ^ : ^ 
 
 10' 
 
 12' 
 
 5456.1 
 
 7902.4 
 
 2182 .5 
 
 12' 
 
 14' 
 
 5459-3 
 
 7904.8 
 
 2184 .6 .fc: 
 
 14' 
 
 16' 
 
 5462.5 
 
 7907.2 
 
 2186.8 c& 
 
 16' 
 
 18' 
 
 5465-7 
 
 7909.7 
 
 2189.0^: 
 
 18' 
 
 20' 
 
 5468.9 10 ? 
 
 79I2.I 
 
 2191 .2^^"] 
 
 20' 
 
 22' 
 
 5472. I J: : 
 
 7914.5 
 
 2193 .4 *d^ ^ 
 
 22' 
 
 24' 
 
 5475-3- 
 
 7916.9 
 
 2195 .6 <j* ^ 
 
 24' 
 
 26' 
 
 5478. 5. |:: 
 
 79I9-3 
 
 2197.8 
 
 26' 
 
 28' 
 
 5481 .7 g 
 
 7921.7 
 
 22OO.O <^ 
 
 28' 
 
 3o; 
 
 5484.9 jir : 
 
 7924.1 
 
 22O2 . 2 " 
 
 30; 
 
 
 5488.1 t5 
 
 7926.5 
 
 2 2 04 . 4 N t- 
 
 32 
 
 34' 
 
 5491-3 $ 
 
 7928.9 
 
 22O6.6 ^ 
 
 34' 
 
 36' 
 
 5494- 5 , . 
 
 793L4 
 
 2208.8 ^ 
 
 36; 
 
 38' 
 
 5497- 7 f " 
 
 7933-8 
 
 2211 .O 
 
 38' 
 
 40' 
 
 5500.9 
 
 7936.2 
 
 2213.3 
 
 40' 
 
 42' 
 
 5504-1 
 
 7938.6 
 
 2215-5 
 
 42' 
 
 44' 
 
 5507-3 
 
 7941.0 
 
 2217.7 
 
 44' 
 
 46' 
 
 
 7943-4 
 
 222O .O 
 
 46' 
 
 48' 
 
 55I3-7 
 
 7945-8 
 
 2222 . 2 
 
 48' 
 
 5' 
 
 5516.9 
 
 7948.2 
 
 2224.4 
 
 5' 
 
 5^' 
 
 5520.2 
 
 7950.6 
 
 2226 .6 
 
 52 ^ 
 
 54' 
 
 55 2 3 -4 
 
 7953-o 
 
 2228.8 
 
 
 56' 
 
 55 2 6.6 
 
 7955-4 
 
 2231.1 
 
 56' 
 
 58' 
 
 
 79^7.8 
 
 2233 .3 
 
 5 8 ' 
 
 103 
 
IX. FUNCTIONS OF A ONE-DEGREE CURVE. 
 
 Whole 
 Angle. 
 
 Tangent 
 Distance. 
 
 Long 
 Chord. 
 
 External 
 Secant. 
 
 Whole 
 Angle. 
 
 88 
 
 5533-0 
 
 7960.2 
 
 2235-5 
 
 88 C 
 
 2' 
 
 5536.3 
 
 7962 .6 
 
 2237-7 
 
 2' 
 
 4' 
 
 5539-5 
 
 7965.0 
 
 2239.9 
 
 4' 
 
 6' 
 
 5542.7 
 
 7967.4 
 
 2242 . 2 
 
 6' 
 
 8' 
 
 5545-9 
 
 7969.8 
 
 2244.4 H 
 
 8 / 
 
 10' 
 
 5549-1 
 
 7972.2 
 
 2246.7 1 
 
 10' 
 
 12' 
 
 5552.4 
 
 7974-6 
 
 2248.9 - 
 
 12' 
 
 14' 
 
 5555-6 
 
 7977-o 
 
 22.51.2 . 
 
 14' 
 
 16' 
 
 5558.9 
 
 7979-4 
 
 2253.4 03 
 
 16' 
 
 18' 
 
 5562.1 
 
 7981.8 
 
 2255-7 
 
 18' 
 
 20' 
 
 5565-3 
 
 7984.1 
 
 2258.0 "5 
 
 20-: 
 
 22' 
 
 5568.6 ? 
 
 7986.5 
 
 226o . 2 ^ d/J 
 
 22' 
 
 24' 
 
 5571-8 6 
 
 7988.9 
 
 2262 . 5 o : j 
 
 24' 
 
 26' 
 
 5575- 1 ~ 
 
 7991-3 
 
 2264.7,, 
 
 26' 
 
 28' 
 
 5578.3 4 
 
 7993-7 
 
 2267 .0 .h. 
 
 28' 
 
 30' 
 
 5581.5 < 
 
 7996.1 
 
 2269.3^ 
 
 30' 
 
 32' 
 
 5584.8 
 
 7998.5 
 
 2271 .7 : 
 
 32' 
 
 34' 
 
 5588.0 5 
 
 8000.9 
 
 2273.8 94 
 
 34' 
 
 36' 
 
 5591-3 iAo 
 
 8003.3 
 
 2276 .1 - 
 
 36' 
 
 38' 
 
 5594-5 6. ^ 
 
 8005.7 
 
 2278.4?: * 
 
 38' 
 
 40' 
 
 5597-8- < 
 
 8008.0 
 
 2280.7 | 
 
 40' 
 
 42' 
 
 5601. i. gs 
 
 8010 .4 
 
 2283.0 ^ 
 
 42' 
 
 44' 
 
 5604.3 w 
 
 8012.8 
 
 2285.2 % 
 
 44' 
 
 46' 
 
 5607 .6 o: 
 
 8015.2 
 
 2287.5 X 
 
 46' 
 
 48' 
 
 5610 . 8 u?oc . 
 
 8017.5 
 
 2289.8 
 
 48' 
 
 5 0/ 
 
 5614.1 3^ 
 
 8019.9 
 
 2292 . i ! 
 
 50' 
 
 52' 
 
 
 8022 .3 
 
 2294.4 < 
 
 52' 
 
 54' 
 
 5620. 6 <" ^ 
 
 8024. 7 
 
 2296.7 
 
 54' 
 
 56' 
 
 5623-9 , 
 
 8027 . i 
 
 2299 . o 
 
 56' 
 
 58' 
 
 5627.1 w 
 
 8029.5 
 
 2301 .2 
 
 58' 
 
 89 
 
 5630.4 
 
 8031.8 
 
 2303-5 
 
 89 
 
 2' 
 
 5633-7 
 
 8034.2 
 
 2305-8 
 
 2' 
 
 4' 
 
 5636.9 
 
 8036.6 
 
 2308. i ^a4 
 
 4' 
 
 6' 
 
 5640.2 ; 
 
 8038.9 
 
 2310.4 
 
 6' 
 
 8' 
 
 5643-5 < 
 
 8041 .3 
 
 2312. 7^ : : 
 
 8' 
 
 10' 
 
 5646.8 
 
 8043.6 
 
 2315- o| : : 
 
 10' 
 
 12' 
 
 5650.1 
 
 8046 .0 
 
 2317-3 & 
 
 12' 
 
 14' 
 
 5653-4 
 
 8048.3 
 
 23I9-6 : : 
 
 14' 
 
 16' 
 
 5656-7 
 
 8050.7 
 
 2321.9" MOO 
 
 16' 
 
 18' 
 
 5660 .0 
 
 8053.1 
 
 2323.2 ->0cj 
 
 i8 r 
 
 2O' 
 
 5663.3 
 
 8055-5 
 
 2326.6 3 : : 
 
 20' 
 
 22' 
 
 5666.6 
 
 8057.8 
 
 2328.9 < 
 
 22' 
 
 24' 
 
 5669.9 
 
 8060. 2 
 
 2331.2 
 
 24' 
 
 26' 
 
 5673-2 
 
 8062 .5 
 
 2333-5 
 
 26' 
 
 28' 
 
 5676-5 
 
 8064. 9 
 
 2335-8 
 
 28' 
 
 104 
 
IX. FUNCTIONS OF A ONE-DEGREE CURVE. 
 
 Whole 
 Angle. 
 
 Tangent 
 Distance. 
 
 Long 
 Chord. 
 
 External 
 Secant. 
 
 Whole 
 Angle. 
 
 89 30' 
 
 5679.8 
 
 8067.3 
 
 2338.2 
 
 89 30' 
 
 32' 
 
 5683.1 
 
 8069.6 
 
 2340.5 
 
 32' 
 
 34' 
 
 5686.4 ^4 
 
 8072 .0 
 
 2342.8 
 
 34' 
 
 36' 
 
 5689.8 
 
 8074.4 
 
 2345.1 . 
 
 36' 
 
 38' 
 
 5693. I ^ = 
 
 8076.8 
 
 2347-4"; - 
 
 38' 
 
 40' 
 
 5696.4'^ ^ 
 
 8079 . 2 
 
 2349-8^- = 
 
 40' 
 
 42' 
 
 5699.8 '5r : 
 
 8081.6 
 
 2352.1^ 
 
 42' 
 
 44' 
 
 5703 - 1 fi 
 
 8083.9 
 
 2354. 4 -a- - 
 
 44' 
 
 46' 
 
 576. 4 ^" " N 
 
 8086.3 
 
 2356.8^ 
 
 46' 
 
 48' 
 
 5709-7 io 
 
 8088.7 
 
 2359. i ^ : : 
 
 48' 
 
 50' 
 
 5713-0^^ 
 
 8091 .0 
 
 vO w c. 
 2361.5 chocs' 
 
 50' 
 
 52' 
 
 5716.45- = 
 
 8093.4 
 
 2363-8,3 
 
 52' 
 
 54' 
 
 57I9-7 
 
 8095-7 
 
 2366 . 2 ^ : : 
 
 54' 
 
 56' 
 
 5723- 
 
 8098.1 
 
 2368.5 
 
 56' 
 
 58' 
 
 5726.3 
 
 8100 . 5 
 
 2370.9 
 
 58' 
 
 9O 
 
 5729.6 
 
 8102 .9 
 
 2373-3 
 
 9O 
 
 2' 
 
 5732.9 
 
 8105.2 
 
 2375-7 
 
 2' 
 
 4' 
 
 5736.3 ^ 
 
 8107 .6 
 
 2378.1 
 
 4' 
 
 v 
 
 5739-6 
 
 8109 . 9 
 
 2380.4 4 
 
 6' 
 
 8' 
 
 5743-o | 
 
 8112.3 
 
 2382.8 - 
 
 8 7 
 
 10' 
 
 5746.3 * 
 
 8114.6 
 
 2385.1 ! 
 
 10' 
 
 12' 
 
 5749-7 ;g 
 
 8117 .0 
 
 2387-5 
 
 12' 
 
 14' 
 
 5753-0 ^ 
 
 8119.3 
 
 2389-8 a 
 
 14' 
 
 16' 
 
 5756.4 
 
 8121 .7 
 
 2392-2 ^ 
 
 16' 
 
 18' 
 
 5759-7 ^ 
 
 8124.0 
 
 2394.6 - 
 
 18' 
 
 20' 
 
 5763 .0 Ji< ^^ 
 
 8126.4 
 
 2397-0 ^o? 
 
 20' 
 
 22' 
 
 5766. 4;g= | 
 
 8128.7 
 
 2399-4,6, 5 
 
 22' 
 
 24' 
 
 5769 . 7 *3 " 
 
 8131.1 
 
 2401.8^5 < 
 
 24' 
 
 26' 
 
 5773-0-^ 
 
 8i33-4 
 
 2404.1 g_ 
 
 26' 
 
 28' 
 
 5776.4^ 
 
 8i35-8 
 
 2406 . 5 " 
 
 28' 
 
 30' 
 
 5779-8f H 
 
 8138.1 
 
 2408 .9 ,0: 
 
 30' 
 
 32' 
 
 5783-1 Jt4 
 
 8140.5 
 
 2411.3^0 e, ^ 
 
 32' 
 
 34' 
 
 5786.5 + 6 
 
 8142 .8 
 
 2413.7 ^- H 
 
 34' 
 
 36' 
 
 5789.8? : * 
 
 8145.2 
 
 2416. i 5- 
 
 36' 
 
 38' 
 
 5793.2^ -g 
 
 8i47-5 
 
 2418. 5 <" 5 
 
 38' 
 
 40' 
 
 5796.6 
 
 8149.8 
 
 2420.9 -^ 
 
 40' 
 
 42' 
 
 5800.0 
 
 8152.2 
 
 2423-3 " 
 
 42' 
 
 44' 
 
 5803.3 S 
 
 8154-5 
 
 2425-7 
 
 44' 
 
 46' 
 
 5806.7 
 
 8156.9 
 
 2428.1 
 
 46' 
 
 48' 
 
 58IO.I 
 
 8159.2 
 
 2430.5 | 
 
 48' 
 
 5' 
 
 5813.5 ^ 
 
 8161.6 
 
 2432.9 5 
 
 50' 
 
 52' 
 
 
 8163.9 
 
 2435-3 
 
 52' 
 
 54'. 
 
 5820.3 
 
 8166.2 
 
 2437-7 
 
 54' 
 
 56' 
 
 5823.7 
 
 8168. 6 
 
 2440 . i 
 
 56' 
 
 58' 
 
 5827.0 
 
 8170.9 
 
 2442.5 
 
 58' 
 
 105 
 
IX. FUNCTIONS OF A ONE-DEGREE CURVE. 
 
 Whole 
 Angle. 
 
 Tangent 
 Distance. 
 
 Long 
 Chord. 
 
 External 
 Secant. 
 
 Whole 
 Angle. 
 
 91 
 
 5830.4 
 
 8173.3 
 
 2445.0 
 
 91 
 
 2' 
 
 5833.8 
 
 8175.6 
 
 2447.4 
 
 2' 
 
 4' 
 
 5837.2 
 
 8178.0 
 
 2449.8 
 
 4; 
 
 6' 
 
 5840 .6 
 
 8180.3 
 
 2452.3 
 
 
 8' 
 
 5844.0 
 
 8182.6 
 
 2454.7 + 
 
 8' 
 
 10' 
 
 5847-4 
 
 8184.9 
 
 2457-1 
 
 ro' 
 
 Mi' 
 
 5850.8 
 
 8187.2 
 
 2459-5 ^ 
 
 12' 
 
 14' 
 
 5854-2 
 
 8189.6 
 
 2462.0 E 
 
 14' 
 
 16' 
 
 5857.6 
 
 8191 .9 
 
 2464.4 
 
 16' 
 
 18' 
 
 5861.0 
 
 8194.3 
 
 2466.8 
 
 18' 
 
 ao' 
 
 5864.5 *c>4 
 
 8196.6 
 
 2469.3 
 
 20' 
 
 22' 
 
 5867.9 - 
 
 8199 .0 
 
 2471.7 ^o 
 
 22 7 
 
 24' 
 
 5871 -3 : ~ 
 
 8201 .3 
 
 2474-2 ,: 5 
 
 24' 
 
 26' 
 
 5874.8-3 
 
 8203.6 
 
 2476 . 6 ^ < 
 
 26' 
 
 28' 
 
 5878. 2 |T = 
 
 8205 .9 
 
 2479.1 | : 
 
 28' 
 
 3 0/ 
 
 58Si. 6 * :: 
 
 8208.2 
 
 2481.5^ 
 
 30' 
 
 32' 
 
 5885 . O MOO 
 
 8210.6 
 
 2484. o- 
 
 32' 
 
 34' 
 
 5888.5 jjrtj 
 
 8212 .9 
 
 2486 . 4 ^ "? 
 
 34' 
 
 36' 
 
 5892 .O N "*- 
 
 8215.2 
 
 2488.9 "^ - 
 
 36' 
 
 38' 
 
 5895-4|: : 
 
 8217.5 
 
 2491.3?: , 
 
 38' 
 
 40' 
 
 5898.8 
 
 8219.8 
 
 2493-8 g 
 
 40' 
 
 42' 
 
 5902.3 
 
 8222 . i 
 
 2496 . 2 'a 
 
 42' 
 
 44' 
 
 5905-7 
 
 8224.5 
 
 2498.7 ^ 
 
 44' 
 
 46' 
 
 5909.2 
 
 8226.8 
 
 2501.1 
 
 46' 
 
 48' 
 
 5912 .6 
 
 8229 . i 
 
 2503-6 ^ 
 
 48' 
 
 So' 
 
 5916.0 
 
 8231.4 
 
 2506.1 ^ 
 
 5o; 
 
 52' 
 
 59*9-5 
 
 8233.8 
 
 2508.6 ^ 
 
 
 54' 
 
 5922.9 
 
 8236.1 
 
 2511 . o 
 
 54' 
 
 56' 
 
 5926.4 
 
 8238.4 
 
 2513 . 5 
 
 56' 
 
 58' 
 
 5929.8 
 
 8240.7 
 
 2516 .0 
 
 58' 
 
 92 
 
 5933-2 
 
 8243.0 
 
 2518.5 
 
 92 
 
 2' 
 
 5936.7 ^4 
 
 8245.3 
 
 2521 . o 
 
 2' 
 
 4' 
 
 5940.1 . 
 
 8247.7 
 
 2523-5 "^ 
 
 4' 
 
 6' 
 
 5943. 6 ,g: : 
 
 8250.0 
 
 2526 .06,- 
 
 6' 
 
 8' 
 
 5947 -o-g 
 
 8252.3 
 
 2528.5^ " 
 
 8' 
 
 10' 
 
 5950-5 | : : 
 
 8254.6 
 
 2531. o|: : 
 
 10' 
 
 12' 
 
 5954-0 _ . 
 
 8256.9 
 
 2533-5^ 
 
 12' 
 
 14' 
 
 5957- 4 xVo 
 
 8259.2 
 
 2536.0^: = 
 
 14' 
 
 16' 
 
 5960 . 9 oi t^vd 
 
 8261.5 
 
 2538.5 gtt 
 
 16' 
 
 18' 
 
 5964.3 $ 
 
 8263.8 
 
 2541.0 4 
 
 18' 
 
 20' 
 
 5967. 8 |= = 
 
 8266.1 
 
 2543- 5 5 : : 
 
 20 X 
 
 22' 
 
 5971-3 
 
 8268.4 
 
 2546 .0 
 
 22' 
 
 24' 
 
 5974-8 
 
 8270.8 
 
 2548.5 
 
 24' 
 
 26' 
 
 5978.2 
 
 8273.1 
 
 255 1 - 1 
 
 26' 
 
 28' 
 
 598i.7 
 
 8275.4 
 
 2553 -6 
 
 28' 
 
 106 
 
IX. FUNCTIONS OF A ONE-DEGREE CURVE. 
 
 i Whole 
 f Angle. 
 
 Tangent 
 Distance. 
 
 Long 
 Chord. 
 
 External 
 Secant. 
 
 Whole 
 Angle. 
 
 92 30' 
 
 5985-2 
 
 8277.7 
 
 2556.1 
 
 92 30' 
 
 3*' 
 
 5988.7 
 
 8280.0 
 
 2558.6 
 
 32' 
 
 34' 
 
 5992.2 
 
 8282.3 
 
 2561 . I 
 
 34' 
 
 36' 
 
 5995-7 ^* + 
 
 8284.6 
 
 2563.7 
 
 36' 
 
 38' 
 
 5999-1 *e ^ 
 
 8286.9 
 
 2566.2 
 
 38' 
 
 40' 
 
 6002 .6 5" 
 
 8289.2 
 
 2568.7 
 
 40' 
 
 42' 
 
 6006. i 15. 
 
 8291.5 
 
 2571.2 
 
 42' 
 
 44' 
 
 6009. 6 " ' 
 
 8293.8 
 
 2573-8 
 
 44' 
 
 46' 
 
 6013.1 g. . 
 
 8296. I 
 
 2576.3 
 
 46' 
 
 48' 
 
 6oi6.6^ H 
 
 8298.4 
 
 2578.9 
 
 48' 
 
 5o' 
 
 6020.1 SjS'S 
 
 8300. 7 
 
 2581.4 
 
 5; 
 
 5*' 
 
 6023.6^" 
 
 8303.0 
 
 2584.0 4 
 
 52 
 
 54' 
 
 6027. i j : : 
 
 8305-3- 
 
 2586.5 6 
 
 54 
 
 56' 
 
 6030.6 
 
 8307.6 
 
 2589.1 X 
 
 56' 
 
 58' 
 
 6034.1 
 
 8309.9 
 
 2591.6 "g 
 
 58' 
 
 93 
 
 6037.7 
 
 8312.2 
 
 2594.1 to 
 
 93 
 
 2' 
 
 6041 .2 
 
 8314-5 
 
 2596.7 % 
 
 2' 
 
 4' 
 
 6044.7 
 
 8316.8 
 
 2599.2 vo 
 
 4' 
 
 6' 
 
 6048.3 
 
 8319.1 
 
 2601.8 ^% 
 
 6' 
 
 8' 
 
 6051.8 
 
 8321.4 
 
 2604.4^0- ;g 
 
 8' 
 
 10' 
 
 6055.3 
 
 8323-7 
 
 2606. 9? < 
 
 10' 
 
 12' 
 
 6058.9 
 
 8326.0 
 
 2609. 5. : 
 
 12' 
 
 14' 
 
 6052 .4 
 
 8328.3 
 
 26l2 .0 CO 
 
 14' 
 
 16' 
 
 6056.0 
 
 8330.6 
 
 2614.6 ,: 
 
 16' 
 
 18' 
 
 6059.5 
 
 8332.9 
 
 2617 .2 ?? . 
 
 1 8' 
 
 
 . . <$ 
 
 
 CO O ^ 
 
 
 20' 
 
 6073.0 ^c-" 
 
 8335.1 
 
 2619.8^ w : 
 
 20' 
 
 22' 
 
 6076.65: : 
 
 8337-4 
 
 2622 .4^- S5 
 
 22' 
 
 2 4' 
 
 6080. I *-< 
 
 8339-7 
 
 2625.0 -g 
 
 24' 
 
 26' 
 
 6083.7-*= = 
 
 8342.0 
 
 2627.5 -a 
 
 26' 
 
 28' 
 
 6087.2 co 
 
 8344.2 
 
 2630.1 < 
 
 28' 
 
 30' 
 
 6090. 7 : ' 
 
 8346.5 
 
 2632.7 ^ 
 
 30' 
 
 32' 
 
 6094.3 ": 
 
 8348.8 
 
 2635.3 y 
 
 32' 
 
 34' 
 
 6097.8 3 
 
 8351-1 
 
 2637.9 ^ 
 
 34' 
 
 36' 
 
 6ioi.4^ : , 
 
 8353-3 
 
 2640.4 3j 
 
 36' 
 
 38' 
 
 6104.9 ^ 
 
 8355.6 
 
 2643.0 
 
 38' 
 
 4o' 
 
 6108.5 
 
 8357-9 
 
 2645 -6 
 
 40' 
 
 42' 
 
 6112 .0 
 
 8360.2 
 
 2648.2 
 
 42' 
 
 44' 
 
 6115 .6 
 
 8362.4 
 
 2650.8 
 
 44' 
 
 46' 
 
 6119.2 
 
 8364.7 
 
 2653.4 
 
 46' 
 
 48' 
 
 6122 . 7 
 
 8367.0 
 
 2656.0 
 
 48' 
 
 50' 
 
 6126 . 3 
 
 8369-3 
 
 2658.6 
 
 50' 
 
 52' 
 
 6129.9 
 
 8371.6 
 
 266l . 2 
 
 52' 
 
 54'- 
 
 6i33-4 
 
 8373-8 
 
 2663.8 
 
 54' 
 
 56' 
 
 6137.0 
 
 8376.1 
 
 2666.4 
 
 56' 
 
 58' 
 
 6140 . 6 
 
 8378.4 
 
 266Q .O 
 
 58' 
 
 107 
 
IX. FUNCTIONS OF A ONE-DEGREE CURVE. 
 
 Whole 
 Angle. 
 
 Tangent 
 Distance. 
 
 Long 
 Chord . 
 
 External 
 Secant. 
 
 Whole 
 Angle. 
 
 94 
 
 6144. 2 
 
 8380.7 
 
 2671 .6 
 
 94 
 
 2' 
 
 6147.8 
 
 8383-0 
 
 2674.2 
 
 2' 
 
 4' 
 
 6151 .4 
 
 8385.2 
 
 2676.8 
 
 4' 
 
 6' 
 
 6I55-0 
 
 8387.5 
 
 2679.5 
 
 6' 
 
 8' 
 
 6158.6 
 
 8389.8 
 
 2682.1 4 
 
 8' 
 
 10' 
 
 6162 . I 
 
 8392.1 
 
 2684.7 6 
 
 10' 
 
 12' 
 
 6165.7 
 
 8394.3 
 
 2687.3 ^ 
 
 12' 
 
 14' 
 
 6169.3 
 
 8396.6 
 
 2690.0 
 
 14' 
 
 16' 
 
 6172 .9 ... 
 
 8398.9 
 
 2692.6 (g 
 
 16' 
 
 18' 
 
 6176.5 ^:r 
 
 8401 . I 
 
 2695.3 js 
 
 18' 
 
 20' 
 
 6180. i : = 
 
 8403.4 
 
 2697.9 ^ 
 
 20' 
 
 22' 
 
 6183.8-3 
 
 8405 . 7 
 
 2700 .6 *> <> 
 
 22' 
 
 24' 
 
 6187. 4 'E : = 
 
 8408.0 
 
 2703. 2|: 
 
 24' 
 
 26' 
 
 6191 .0 ^ 
 
 8410. 2 
 
 2705-9-3 < 
 
 26' 
 
 28' 
 
 6194.6 : = 
 
 8412.5 
 
 2708.5 .- 
 
 28' 
 
 30' 
 
 6198. 2 w rLvcJ 
 
 8414-7 
 
 2711 . 2 ^ 
 
 3 0/ 
 
 32' 
 
 6201 .9 ^ 
 
 8417 .0 
 
 2713. 9-^ : 
 
 32' 
 
 34' 
 
 6205.5^ : 
 
 8419.3 
 
 2716.5^ 
 
 34' 
 
 36' 
 
 6209. I < 
 
 8421.5 
 
 2719. 2^^"". 
 
 36' 
 
 38' 
 
 6212 . 7 
 
 8423.8 
 
 2721 .8 ?: . 
 
 38' 
 
 40' 
 
 6216.3 
 
 8426 . o 
 
 2724.5 *g 
 
 40' 
 
 42' 
 
 6220.0 
 
 8428.3 
 
 2727.2 j?- 
 
 42' 
 
 44' 
 
 6223.6 4 
 
 8430.5 
 
 2729.8 " 
 
 44' 
 
 46' 
 
 6227.3 
 
 8432.8 
 
 2732.5 ^ 
 
 46' 
 
 48' 
 
 6230.9 
 
 8435-0 
 
 2735.2 4 
 
 48' 
 
 5o' 
 
 6234.5 I? 
 
 8437-3 
 
 2737-9 ^ 
 
 5o; 
 
 52' 
 
 6238.2 'a 
 
 8439-5 
 
 2740.6 < 
 
 
 54' 
 
 6241.8 ^ 
 
 8441.8 
 
 2743-3 
 
 54' 
 
 56' 
 
 6245-5 6-^ 
 
 8444. o 
 
 2746.0 
 
 56' 
 
 58' 
 
 6249. i " ^ 
 
 8446.3 
 
 2748.6 ^ 
 
 58' 
 
 95 
 
 6252-7!: 
 
 8448.6 
 
 2 75 J -3 ^ 
 
 95 
 
 2' 
 
 6256. 4 ^ 
 
 8450.9 
 
 2754-0 . .;*: 
 
 2' 
 
 4' 
 
 6260 .0 . 
 
 8453-1 
 
 2756-7 "' a ^ 
 
 4' 
 
 6' 
 
 6263.7^4 
 
 8455-4 
 
 2 759.4^: 'a 
 
 6' 
 
 8' 
 
 6267.3 ~ 
 
 8457-6 
 
 2762. i^ " 
 
 8' 
 
 10' 
 
 6271.0^ 
 
 8459-8 
 
 2764.8.?: 2 
 
 10' 
 
 12' 
 
 6274.7^ -3 
 
 8462 . 1 
 
 2767-5^ j 
 
 I2 7 
 
 14' 
 
 6278.3 a 
 
 8464.3 
 
 277. 2 ' -c 
 
 14' 
 
 16' 
 
 6282.0 
 
 8466.6 
 
 2772.9^-5 
 
 16' 
 
 18' 
 
 6285.7 
 
 8468.8 
 
 2775.6 M 
 
 18' 
 
 
 
 
 id 
 
 
 20' 
 
 6289.4 *; 
 
 8471.1 
 
 
 20' 
 
 22' 
 
 6293.1 
 
 8473-3 
 
 2781.0 
 
 22' 
 
 24' 
 
 6296.7 
 
 8475-6 
 
 2783-7 
 
 24' 
 
 36' 
 
 6300.4 
 
 8477-8 
 
 2786.5 
 
 26' 
 
 28' ' 6304.1 
 
 8480. I 
 
 2789.2 
 
 28' 
 
 108 
 
IX. FUNCTIONS OF A ONE-DEGREE CURVE. 
 
 Whole 
 Angle. 
 
 Tangent 
 Distance. 
 
 Long 
 Chord. 
 
 External 
 Secant. 
 
 Whole 
 Angle. 
 
 95 3*>' 
 
 6307.8 
 
 8482.3 
 
 2791.9 
 
 95 30' 
 
 32' 
 
 63II-5 
 
 8484.6 
 
 2794.6 
 
 32' 
 
 34' 
 
 6315.2 
 
 8486.8 
 
 2797.4 
 
 34' 
 
 36' 
 
 6318.9 ^ds4 
 
 8489.1 
 
 2800.1 . . . 
 
 36' 
 
 38' 
 
 6322 .6 6 
 
 8491.3 
 
 28O2 .9 * ^M 
 
 38' 
 
 40' 
 
 6326.3 2" 
 
 8493-5 
 
 2805. 6= = 
 
 40' 
 
 42' 
 
 6330.0 - - 
 
 8495-8 
 
 2808.3-3 
 
 42' 
 
 44' 
 
 6333- 7 ' ' 
 
 8498.0 
 
 2811.1-5,= = 
 
 44' 
 
 46' 
 
 6337.4 fc : : 
 
 8500. 2 
 
 2813.9^ 
 
 46' 
 
 48' 
 
 634L I 00 
 
 8502 .4 
 
 2816.6^- : 
 
 48' 
 
 5' 
 
 6344-8 B 
 
 8504.6 
 
 CO t- 
 28l9 .4 rOO 4 
 
 50' 
 
 52' 
 
 6348.5-0 
 
 8506.8 
 
 2822 . 2 ^ M 
 
 52' 
 
 54' 
 
 6352. 2 5= =, 
 
 8509 .0 
 
 2825. ojp = 
 
 
 56' 
 
 6356.0 
 
 85II.3 
 
 2827.7 
 
 56' 
 
 58' 
 
 6359.7 
 
 8513.5 
 
 2830.5 
 
 58' 
 
 96 
 
 6363.4 
 
 8515-8 
 
 2833.2 
 
 96 
 
 2' 
 
 6367.1 
 
 8518.0 
 
 2836.0 
 
 2' 
 
 4' 
 
 6370.8 64 
 
 8520.3 
 
 2838.7 
 
 4' 
 
 6' 
 
 6374-6 . - 
 
 8522.5 
 
 2841.5 
 
 6' 
 
 8' 
 
 6378.3 I* ; 
 
 8524.8 
 
 2844.3 
 
 8' 
 
 10' 
 
 6382.0 -5 
 
 8527.0 
 
 2847.1 
 
 10' 
 
 12' 
 
 6385-7 & 
 
 
 2849.9 
 
 12' 
 
 14' 
 
 6389-5 ^ 
 
 853I-5 
 
 2852.7 
 
 14' 
 
 16' 
 
 6393-2 
 
 8533-7 
 
 2855.4 
 
 16' . 
 
 18' 
 
 6397-0 ^2 
 
 8535-9 
 
 2858.2 
 
 18' 
 
 20' 
 
 6400.7 ?; 
 
 8538.1 
 
 2861 .0 ""** 
 
 20' 
 
 22' 
 
 6404- 5 | | 
 
 8540.3 
 
 2863.8 6, . 
 
 22' 
 
 24' 
 
 6408.3^ < 
 
 8542.5 
 
 2866.6^ " 
 
 24' 
 
 26' 
 
 6412 .0 % 
 
 8544.8 
 
 2869.4| : . 
 
 26' 
 
 28' 
 
 6415.8^ 
 
 8547-0 
 
 2872.2'^" 
 
 28' 
 
 30' 
 
 6419-5! 
 
 8549.2 
 
 2875.0^: s 
 
 3' 
 
 32' 
 
 6423-3 - 
 
 8551 .4 
 
 2877 .8 coco ro 
 
 32' 
 
 34' 
 
 6427. o 2 
 
 8553-6 
 
 2880.6 "23 
 
 34' 
 
 36' 
 
 6430.8^ 6 
 
 8555-9 
 
 2883.4?- . 
 
 36' 
 
 38' 
 
 6434. 6 < <>2 
 
 8558.1 
 
 2886. 2 <J" " 
 
 38' 
 
 40' 
 
 6438.3 &! 
 
 8560.3 
 
 2889.0 
 
 40' 
 
 42' 
 
 6442 . i 13^ 
 
 8562.5 
 
 2891.8 
 
 42' 
 
 44' 
 
 6445-8 ftg 
 
 8564.7 
 
 2894.6 
 
 44' 
 
 46' 
 
 6449 .6 /; "? 
 
 8567.0 
 
 2897.4 
 
 46' 
 
 48' 
 
 6453-4 ^H 
 
 8569.2 
 
 2900. 2 
 
 48' 
 
 5' 
 
 6457-2 ^3 
 
 8571 .4 
 
 2903.1 
 
 5' 
 
 5 2 ' 
 
 6461 .0 "*<! 
 
 8573.6 
 
 2905.9 
 
 52' 
 
 54' 
 
 6464.8 ? 
 
 8575-8 
 
 2908 . 7 
 
 54' 
 
 56' 
 
 6468.6 < 
 
 8578.0 
 
 2911 .6 
 
 56' 
 
 58' 
 
 6472.4 
 
 8580.2 
 
 2914.4 
 
 58' 
 
 109 
 
IX. FUNCTIONS OF A ONE-DEGREE CURVE. 
 
 Whole 
 Angle. 
 
 Tangent 
 Distance. 
 
 Long 
 Chord. 
 
 External 
 Secant. 
 
 Whole 
 Angle. 
 
 97 
 
 6476. I 
 
 8582 .4 
 
 2917.3 
 
 97 
 
 2' 
 
 6479.9 
 
 8584.6 
 
 292O . 2 
 
 2' 
 
 4' 
 
 6483.7 
 
 8586.8 
 
 2923.0 
 
 4' 
 
 6' 
 
 6487.5 4 
 
 8589.0 
 
 2925.9 
 
 6' 
 
 8' 
 
 6491.3 * 
 
 8591.2 
 
 2928.7 4 
 
 8' 
 
 10' 
 
 6495.1 fc 
 
 8593 5 
 
 2931 .6 
 
 10' 
 
 12' 
 
 6498.9 fi 
 
 8595.7 
 
 2934.5 * 
 
 12' 
 
 14' 
 
 6502.7 
 
 8597-9 
 
 2937-3 8 
 
 14' 
 
 16' 
 
 
 8600 . i 
 
 2940.2 
 
 16' 
 
 18' 
 
 6510.4 ^ 
 
 8602.3 
 
 2943-0 
 
 18' 
 
 20' 
 
 6514.2 . . r: 
 
 8604.5 
 
 2945-9 ^ 
 
 20' 
 
 22' 
 
 6518.0 * 
 
 8606.7 
 
 2948.8 ^<>? 
 
 22' 
 
 24' 
 
 6521 .9 r 5; 
 
 8608.9 
 
 2951 . 7 o- ;g 
 
 24' 
 
 26' 
 
 6525-7^ 
 
 8611.1 
 
 '2954.5-3 < 
 
 26' 
 
 28' 
 
 6529. 5 = 
 
 8613.3 
 
 2957. 4. g: 
 
 28' 
 
 30' 
 
 6533.3 fc. 
 
 8615.5 
 
 2960.3 ^ 
 
 3 O/ 
 
 32 
 
 6537-2*^ . 
 
 8617.7 
 
 2963.2 = 
 
 32' 
 
 34 
 
 6541 .0 woo ? 
 
 8619 . 9 
 
 2966. 1 ^^4 
 
 34' 
 
 36' 
 
 6544.8 "So 
 
 8622.1 
 
 2968.9 ^' M 
 
 36; 
 
 38' 
 
 6548.7?: 5 
 
 8624.3 
 
 2971. 8|; | 
 
 
 40' 
 
 ^2 
 
 6552.5 -g 
 
 8626.5 
 
 < ^ 
 
 2974.7 g 
 
 40' 
 
 42' 
 
 6556-4 < 
 
 8628.7 
 
 2977.6 -ft 
 
 42' 
 
 44' 
 
 6560.2 
 
 8630.8 
 
 2980.5 r 
 
 44' 
 
 46' 
 
 6564.0 
 
 8633.0 
 
 2983.4 -2 
 
 46' 
 
 48' 
 
 6567.9 M 
 
 8635-2 
 
 2986.3 ^ 
 
 48' 
 
 50' 
 
 6571.8 5 
 
 8637.4 
 
 2989.2 -d 
 
 5' 
 
 52' 
 
 6575.7 < 
 
 8639.6 
 
 2992.1 ^ 
 
 $2 f 
 
 54' 
 
 6579.5 
 
 8641 .8 
 
 2995.0 
 
 54' 
 
 56 
 
 6583.4 
 
 8644.0 
 
 2997.9 
 
 56' 
 
 58' 
 
 6587.2 
 
 8646.2 
 
 3000 . 8 
 
 58' 
 
 98 
 
 6591.1 
 
 8648.4 
 
 3003.8 
 
 98 
 
 2' 
 
 6595.0 ^4 
 
 8650.6 
 
 3006.7 . 
 
 2' 
 
 4' 
 
 6598.8 . - 
 
 8652.8 
 
 3009 . 6 ^<*-* 
 
 4' 
 
 6' 
 
 6602 . 7 : = 
 
 8655.0 
 
 3012.5 ^6, . 
 
 6' 
 
 8' 
 
 6606.6-3 
 
 8657.2 
 
 
 8' 
 
 10' 
 
 6610.5 c| : ^ 
 
 8659.3 
 
 30i8. 4 |: : 
 
 10' 
 
 12' 
 
 6614.4 ^ 
 
 8661.5 
 
 3021.3^ 
 
 12' 
 
 14' 
 
 6618.3 *-" 
 
 8663.7 
 
 3024.2 ,0: : 
 
 14' 
 
 16' 
 
 6622.2 N^cS 
 
 8665.8 
 
 3027.2 9 ^ 
 
 16' 
 
 18' 
 
 6626.1 
 
 8668.0 
 
 3030.1 ^M Jf 
 
 18' 
 
 20' 
 
 6630.05: : 
 
 8670.2 
 
 TJ 
 3033. I ^ , 
 
 20' 
 
 22' 
 
 6633.9^ 
 
 8672.4 
 
 3036.0 
 
 22' 
 
 24' 
 
 6637.8 
 
 8674.5 
 
 3039.0 
 
 24' 
 
 26' 
 
 6641 . 7 
 
 8676.7 
 
 3042.0 
 
 26' 
 
 28' 
 
 6645.6 
 
 8678.9 
 
 3044.9 
 
 28' 
 
 110 
 
IX. FUNCTIONS OF A ONE-DEGREE CURVE. 
 
 i Whole 
 Angle. 
 
 Tangent 
 Distance. 
 
 Long 
 Chord. 
 
 External 
 Secant. 
 
 Whole 
 Angle. 
 
 98 30' 
 
 6649.5 
 
 868I.I 
 
 3047.9 
 
 98 30' 
 
 32' 
 
 6653-5 
 
 8683.3 
 
 3050.9 
 
 32' 
 
 34' 
 
 6657.4 
 
 8685.5 
 
 3053.9 
 
 34' 
 
 36' 
 
 6661.3 u^4 
 
 8687.6 
 
 3056.8 . . . 
 
 36' 
 
 38' 
 
 666s . 2 . H 
 
 ^P: : 
 
 8689.8 
 
 3059.8^? 
 
 38' 
 
 40' 
 
 6669. I g" 
 
 86,92 .0 
 
 3062 .8 ^ : : 
 
 40' 
 
 42' 
 
 6673 . i 2. 
 
 8694 . 2 
 
 3065.8-3 
 
 42' 
 
 44' 
 
 6677. og : : 
 
 8696.3 
 
 3068.8-^ = 
 
 44' 
 
 46' 
 
 6681.0 g. . 
 
 8698.5 
 
 3071. 8<2 
 
 46' 
 
 48' 
 
 6684 . 9 * V"w 
 
 8700. 7 
 
 3074.7.0: 5 
 
 48' 
 
 50' 
 
 6688.8 S'S'S 
 
 8702 .9 
 
 Ov O 00 
 
 3077.7 n4 
 
 50' 
 
 52' 
 
 6692.8,5* 
 
 8705 .0 
 
 3080.7 ^ H 
 
 52' 
 
 54' 
 
 6696.7^ = 
 
 8707 . 2 
 
 3083.75= = 
 
 54' 
 
 56' 
 
 6700 .6 
 
 8709.3 
 
 3086.7 
 
 56' 
 
 58' 
 
 6704 . 6 
 
 87H.5 
 
 3089.7 
 
 58' 
 
 99 
 
 6708.5 
 
 8713.7 
 
 3092.7 
 
 99 
 
 2' 
 
 6712.5 
 
 8715.9 
 
 3095.7 
 
 2' 
 
 4' 
 
 6716.5 
 
 8718.0 
 
 3098.7 
 
 4' 
 
 6' 
 
 6720 .4 
 
 8720 .2 
 
 3IOI.7 ^ 
 
 6' 
 
 8' 
 
 6724.4 
 
 8722.3 
 
 3104.8 
 
 8' 
 
 10' 
 
 6728.3 -g 
 
 8724.5 
 
 3107.8 
 
 10' 
 
 12' 
 
 6732.3 -a 
 
 8726.6 
 
 3110.8 *g 
 
 12' 
 
 I 4 / 
 
 6736.3 < 
 
 8728.8 
 
 3113-8 '2, 
 
 14' 
 
 16' 
 
 6740.2 S 
 
 8730.9 
 
 3H6.9 ^ 
 
 16' 
 
 18' 
 
 6744-2 ^ 
 
 8733.1 
 
 3119.9 
 
 1 8' 
 
 20' 
 
 6748. I "'><> 
 
 8735.3 
 
 3122.9 + 
 
 20' 
 
 22' 
 
 6752. l|: | 
 
 8737.4 
 
 3126 .0 o, c 
 
 22' 
 
 24' 
 
 6756.1-3 * 
 
 8739.6 
 
 3129.0^" ^ 
 
 24' 
 
 26' 
 
 
 8741.7 
 
 3132.0 ^ 
 
 26' 
 
 28' 
 
 6764.0 w 
 
 8743.9 
 
 3 I 35 I '$" 
 
 28' 
 
 30' 
 
 6768. o| r 
 
 8746.0 
 
 3138.1^: 
 
 3' 
 
 32' 
 
 6772 .0 3>< 4 
 
 8748.2 
 
 3141 .1 OvK . 
 
 32' 
 
 34' 
 
 6776.0 3 M 
 
 8750.3 
 
 3144.2 ^^ M 
 
 34' 
 
 36' 
 
 6780.0 5. 
 
 8752.5 
 
 3147.25. 6 
 
 36' 
 
 38' 
 
 6784. o<T -g 
 
 8754.7 
 
 3150. 3<~ 2 
 
 38' 
 
 40' 
 
 6788.0 
 
 8756.8 
 
 3153.4 . 
 
 40' 
 
 42' 
 
 6792.0 
 
 8759.0 
 
 3156.4 2 
 
 42' 
 
 44' 
 
 6796.1 ^ 
 
 8761.1 
 
 3I59-5 <2 
 
 44' 
 
 46' 
 
 68OO . I oc 
 
 8763.3 
 
 3162.6 -: 
 
 46' 
 
 48' 
 
 6804.1 
 
 8765.4 
 
 3165.6 ^ 
 
 48' 
 
 50' 
 
 6808. I | 
 
 8767.5 
 
 3168.7 | 
 
 50' 
 
 52' 
 
 68l2. I 
 
 8769.7 
 
 3171.8 
 
 52' 
 
 54' 
 
 68l6. I 
 
 8771.8 
 
 3174.8 
 
 54' 
 
 56' 
 
 6820.2 
 
 8774.0 
 
 3 J 77-9 
 
 56' 
 
 58' 
 
 6824.2 
 
 8776.1 
 
 3181 .0 
 
 58' 
 
 111 
 
IX. FUNCTIONS OF A ONE-DEGREE CURVE. 
 
 Whole 
 Angle. 
 
 Tangent 
 Distance. 
 
 Long 
 Chord. 
 
 External 
 Secant. 
 
 Whole 
 Angle. 
 
 1OO 
 
 6828.2 
 
 8778.2 
 
 3184.1 
 
 1OO 
 
 2' 
 
 6832.2 
 
 8780.3 
 
 3187.2 
 
 2' 
 
 4' 
 
 6836.3 
 
 8782.5 
 
 3190.3 
 
 4' 
 
 6' 
 
 6840.3 
 
 8784.6 
 
 3193.4 
 
 6' 
 
 8' 
 
 6844 .4 
 
 8786.8 
 
 3196.5 ? 
 
 8' 
 
 10' 
 
 6848.4 
 
 8789.0 
 
 3199.6 | 
 
 io r 
 
 12' 
 
 6852.5 
 
 8791.1 
 
 3202.7 -3 
 
 I2 7 
 
 14' 
 
 6856.5 
 
 8793.3 
 
 3205.8 -g 
 
 14' 
 
 16' 
 
 6860.6 "& + 
 
 8795.4 
 
 3208.9 w 
 
 16' 
 
 18' 
 
 6864. 7 6 6- 
 
 8797.6 
 
 3212.0 
 
 18' 
 
 to] 
 
 6868. 7 H 
 
 8799.7 
 
 3215.1 % 
 
 20' 
 
 22' 
 
 
 8801.8 
 
 3218.2 ^ 
 
 * 22' 
 
 24' 
 
 6876. 9 
 
 8803.9 
 
 3221.3 jig 
 
 24' 
 
 26' 
 
 6881. o||= 
 
 8806. I 
 
 3224.5 -3 
 
 26' 
 
 28' 
 
 6885.0 o ^ 
 
 J roc/300 
 
 88o8.2 
 
 3227.6 . 
 
 28' 
 
 3o' 
 
 6889.1 $ 
 
 8810.3 
 
 3230.8 < 
 
 30' 
 
 32' 
 
 6893.2?, - 
 
 8812.4 
 
 3233.9 2 
 
 32' 
 
 34' 
 
 6897. 3 <f 
 
 8814.6 
 
 3237. 1 ^ . 
 
 34' 
 
 36' 
 
 6901.3 
 
 8816.7 
 
 3240.2 ,^ ? 
 
 36' 
 
 38' 
 
 6905.4 
 
 8818. 8 
 
 3243.4^|| 
 
 38' 
 
 40' 
 
 6909.5 
 
 8821.0 
 
 3246.5^ i 
 
 40' 
 
 42' 
 
 6913.6 4 
 
 8823.1 
 
 3249.6-^ -^ 
 
 42' 
 
 44' 
 
 6917.7 
 
 8825 .2 
 
 3252 .80: & 
 
 44' 
 
 46' 
 
 6921.8 j| 
 
 8827.4 
 
 3255.9.0 ^ 
 
 46' 
 
 48 
 
 6925.9 ^ 
 
 8829.5 
 
 3259.1 o t 
 
 48' 
 
 50' 
 
 6930.0 |, 
 
 8831.6 
 
 3262.3^^ 
 
 50' 
 
 52' 
 
 6934.1 < 
 
 8833.7 
 
 
 52' 
 
 54' 
 
 6938.2 . ;2 
 
 8835-8 
 
 3268,'6^-g^ 
 
 54' 
 
 56' 
 
 6942.3 !?4<2 
 
 8838.0 
 
 3271-7 ', 
 
 56' 
 
 58' 
 
 6946.4^: 
 
 8840.1 
 
 3274-9 g 
 
 58' 
 
 101 
 
 /; /: ^ ^ 
 6950.6 g^ *d 
 
 8842.2 
 
 3278.1 X 
 
 
 2' 
 
 6954.8$- r 
 
 8844-3 
 
 3281.2 M 
 
 2' 
 
 4' 
 
 6958.9 - 
 
 8846.4 
 
 3284.4 -c? 
 
 4' 
 
 6' 
 
 6963-0^ . 
 
 88^8.6 
 
 3287.6 ?6 
 
 6' 
 
 8' 
 
 6967.1 ^06H 
 
 88^0.7 
 
 3290.8 
 
 8' 
 
 10' 
 
 6 97 I - 2 ^.*5 
 
 8852.8 
 
 3294.0 -^ 
 
 io r 
 
 12' 
 
 6975 .4 2~ *e3 
 
 8854.9 
 
 3297.2 n 
 
 12' 
 
 14' 
 
 6979.5 ', 
 
 8857.0 
 
 3300.4 ^ 
 
 14' 
 
 16' 
 
 6983.7 ^ 
 
 8859.2 
 
 3303.6 ^ 
 
 16' 
 
 18' 
 
 6987.8 ^ 
 
 8861.3 
 
 3306.8 
 
 18' 
 
 20' 
 
 6991.9 | 
 
 8863.4 
 
 3310.1 % 
 
 20' 
 
 22' 
 
 6996 . I *- 
 
 8865.5 
 
 3313 .3 
 
 22' 
 
 24' 
 
 7OOO.2 3 
 
 8867.6 
 
 3316.6 
 
 24' 
 
 26' 
 
 7004.4 
 
 8869.7 
 
 33I9.8 
 
 26' 
 
 28' 
 
 7008.5 
 
 8871.8 
 
 3323-0 
 
 28' 
 
 110 
 
IX. FUNCTIONS OP A ONE-DEGREE CURVE. 
 
 Whole 
 Angle. 
 
 Tangent 
 Distance. 
 
 Long 
 Chord. 
 
 External 
 Secant. 
 
 Whole 
 Angle. 
 
 101 30' 
 
 7012.7 
 
 8873-9 
 
 3326.2 
 
 101 3 o / 
 
 3^' 
 
 7016 . 9 
 
 8876.0 
 
 3329.4 
 
 32 A 
 
 34' 
 
 7021 .0 
 
 8878.1 
 
 3332.7 
 
 34' 
 
 36' 
 
 7025.2 . . . 
 
 8880.3 
 
 3335-9 . . . 
 
 36' 
 
 38' 
 
 7029.4 "V*? 
 
 8882.4 
 
 3339-2 ^-M 
 
 38' 
 
 40' 
 
 733- 6 | : : 
 
 8884.5 
 
 3342.4^- - 
 
 40' 
 
 42' 
 
 7037-8^ 
 
 8886.6 
 
 3345. 6-g 
 
 42' 
 
 44' 
 
 7042.0-^ : 
 
 8888.7 
 
 
 44' 
 
 46' 
 
 7046 . I ^ 
 
 8890.8 
 
 3352 . i w 
 
 46' 
 
 48' 
 
 7050.3 ..3 : = 
 
 8892 .9 
 
 3355 -4 5 : : 
 
 48' 
 
 5' 
 
 7054.5 |2> 
 
 8895.0 
 
 3358.6 4--S 
 
 50' 
 
 ??.'; 
 
 7058.7 SWg. 
 
 8897.1 
 
 3361 .8 ^ 
 
 52' 
 
 54' 
 
 7062 -9 ?; : 
 
 8899.2 
 
 3365. !? : : 
 
 54' 
 
 56' 
 
 7067.!^ 
 
 8901.3 
 
 3368.3 
 
 56' 
 
 58' 
 
 7071.3 
 
 8903.4 
 
 337 1 - 6 
 
 58' 
 
 102 
 
 7075-5 
 
 8905-5 
 
 3374-9 
 
 1O2 
 
 2' 
 
 7079.8 
 
 8907 .6 
 
 3378.2 
 
 2' 
 
 4' 
 
 7084.0 
 
 8909.7 
 
 
 4' 
 
 6' 
 
 7088.2' 
 
 8911 .8 
 
 3384.7 
 
 6' 
 
 8' 
 
 7092.4 
 
 8913.9 
 
 3388.0 
 
 8' 
 
 10' 
 
 7096 .6 
 
 8916 ,o 
 
 339 J -3 
 
 TO' 
 
 12' 
 
 7100 .9 
 
 8918.1 
 
 3394-6 
 
 12' 
 
 14' 
 
 7105.1 
 
 8920.2 
 
 3397-9 
 
 14' 
 
 16' 
 
 
 8922.3 
 
 3401.2 
 
 16' 
 
 18' 
 
 7"3-5 ^^ 
 
 8924.4 
 
 3404-5 
 
 18' 
 
 20' 
 
 7117.7 ^" 
 
 8926 .4 
 
 3407.8 ^ j 
 
 20' 
 
 22' 
 
 7122 .0 ,- " 
 
 8928.5 
 
 34II- I 6. j 
 
 22' 
 
 24' 
 
 7126.2 -3 
 
 8930.6 
 
 3414.4^' 
 
 24' 
 
 26' 
 
 7130. 4 -|: : 
 
 8932.7 
 
 34I7-7 fi. - 
 
 26' 
 
 28' 
 
 7134.7 in 
 
 8934.8 
 
 342i. o|/ * 
 
 28' 
 
 30' 
 
 7138.9^ 
 
 8936,9 
 
 3424.3,0" = 
 
 30' 
 
 32' 
 
 7143.2 ^ & 
 
 8939.0 
 
 3427.6 o-.o 
 
 32 
 
 34' 
 
 7147.4 ;: 
 
 8941 . i 
 
 3431.0 ^H 1 ^ 
 
 34; 
 
 36' 
 
 7151 .72.. 
 
 8943.2 
 
 3434.3?. : 
 
 
 38' 
 
 7156. o<5" : 
 
 8945-3 
 
 3437 -6 < 
 
 38' 
 
 40' 
 
 7160.2 
 
 8947-3 
 
 3440.9 
 
 40' 
 
 42' 
 
 7 l6 4-5 
 
 8949.4 
 
 3444-2 
 
 42' 
 
 44' 
 
 7168.7 
 
 895I-5 
 
 3447-6 
 
 44' 
 
 46' 
 
 
 8953.6 
 
 3450.9 
 
 46' 
 
 48' 
 
 7177.3 
 
 8955-7 
 
 3454.2 
 
 48' 
 
 56* 
 
 7181.6 
 
 8957.7 
 
 3457-6 
 
 50' 
 
 52' 
 
 7185.9 
 
 8959.8 
 
 3460.9 
 
 5 2 
 
 54' 
 
 7190.2 
 
 8961.8 
 
 3464.3 
 
 54 ! 
 
 56' 
 
 7*94-5 
 
 8963.9 
 
 3467.6 
 
 56 
 
 58' 
 
 7198.8 
 
 8966.0 
 
 347 1 - 
 
 58' 
 
 113 
 
IX. FUNCTIONS OP A ONE-DEGREE CURVE. 
 
 Whole 
 Angle. 
 
 Tangent 
 Distance. 
 
 Long 
 
 Chord. 
 
 External 
 Secant. 
 
 Whole 
 Angle. 
 
 103 
 
 7203.1 
 
 8968.1 
 
 3474-4 
 
 IO3 
 
 2' 
 
 7207.4 
 
 8970.2 
 
 3477-8 
 
 2' 
 
 4' 
 
 7211.7 
 
 8972 . 2 
 
 348i .2 
 
 4' 
 
 6' 
 
 7216 .0 
 
 8974.3 
 
 3484.5 
 
 6' 
 
 8' 
 
 7220.3 ^~ 
 
 8976.4 
 
 3487.9 -* 
 
 a' 
 
 10' 
 
 7224.6 : 
 
 8978.4 
 
 3491-3 6 
 
 10' 
 
 12' 
 
 7229 .O . ^ 
 
 8980.5 
 
 3494-7 3 
 
 12' 
 
 14' 
 
 ?_ 
 
 8982.5 
 
 3498.1 
 
 14' 
 
 16' 
 
 7237.6 w 
 
 8984.6 
 
 3501.5 
 
 16' 
 
 1 8' 
 
 7241.9 ,0 = 
 
 8986.7 
 
 3504.9 | 
 
 i8 r 
 
 20' 
 
 7246.2 a 2 
 
 8988.7 
 
 3508.3 
 
 20'' 
 
 22' 
 
 7250.6 
 
 8990.8 
 
 3511.7 ^d N 
 
 22' 
 
 24' 
 
 7254.9 ^ : 
 
 8992 .8 
 
 3515 . I <2; ^ 
 
 24' 
 
 26' 
 
 7259.2 <f 
 
 8994.9 
 
 3518 . 5 J *3 
 
 26' 
 
 28' 
 
 7263.6 
 
 8997.0 
 
 35?* -9.fi 
 
 28' 
 
 30' 
 
 7267.9 
 
 8999 .0 
 
 3525.3^ 
 
 30' 
 
 32' 
 
 7272.3 
 
 9001 . i 
 
 3528 7 ^ : 
 
 32 
 
 34 
 
 7276.6 ^4 
 
 9003.2 
 
 3532-2 ^4 
 
 34 
 
 36' 
 
 7281 .0 
 
 9OO5 . 2 
 
 3535 - 6 TJ ~ : 
 
 36' 
 
 38' 
 
 7285-3*- - 
 
 9007.3 
 
 
 38' 
 
 40' 
 
 7289.7^ 
 
 9009.3 
 
 3542-5 
 
 t 
 
 40' 
 
 42' 
 
 7294.0 'a- - 
 
 9011 .4 
 
 3545-9 
 
 'E 
 
 42' 
 
 44' 
 
 7298.4 ^ 
 
 9013.4 
 
 3549-4 
 
 ^ 
 
 44' 
 
 46' 
 
 7302. 8 - : H ^ 
 
 9 OI 5-5 
 
 3552-8 
 
 o 
 
 46' 
 
 48' 
 
 7307.2 codd 
 
 
 3556. 3 ( 
 
 
 
 48' 
 
 5' 
 
 7311.6^- 
 
 9019 .6 
 
 3559-7' 
 
 J 
 
 5' 
 
 52' 
 
 7316. Ojj: : 
 
 9021 .6 
 
 3563-1 
 
 <^ 
 
 52/ , 
 
 54' 
 
 7320.4 
 
 9023-7 
 
 3566.6 
 
 
 54 
 
 56' 
 
 7324.8 
 
 9025.7 
 
 3570-0 
 
 
 56' 
 
 58' 
 
 7329.2 
 
 9027 .8 
 
 3573-5 
 
 
 58' 
 
 1O4 
 
 7333-5 
 
 9029.9 
 
 3577-0 
 
 
 1O4 
 
 2' 
 
 7337-9 a4 
 
 9031.9 
 
 3580 . 5 
 
 
 2' 
 
 4' 
 
 7342.3 M 
 
 9034.0 j 3583.9 
 
 i^ ^> 
 
 4' 
 
 6' 
 
 7346.7 : 
 
 9036 .0 
 
 3587-4 
 
 6- : 
 
 6' 
 
 8' 
 
 735 1 - 1 * g 
 
 9038,1 
 
 3590.9^ 
 
 8' 
 
 10' 
 
 7355-5 ' 
 
 9040 . 2 
 
 3594.3-^ : 
 
 10' 
 
 12' 
 
 7360.0 i-^ 
 
 9042 .2 
 
 3597-8/2 
 
 I2 X 
 
 14' 
 
 7364.4 ' H 
 
 9044.3 
 
 3601 .21,0- = 
 
 14' 
 
 1 6' 
 
 7368.8 do' 
 
 9046.3 
 
 3604. 7h^ 
 
 16' 
 
 18' 
 
 7373-2 3" 
 
 9048 .4 
 
 3608. 2 p: >j 
 
 i8 r 
 
 20' 
 
 7377-6 |- 
 
 9050.4 
 
 3611.71!' : 
 
 20' 
 
 22' 
 
 7382.1 
 
 9052.5 
 
 3615-2] 
 
 22' 
 
 24' 
 
 7386.5 
 
 9054.5 
 
 3618.7 
 
 24' 
 
 26' 
 
 7390.9 
 
 9056 .6 
 
 3622.2 
 
 26' 
 
 28' 7395-4 
 
 9058.6 3625.7 
 
 28' 
 
 114 
 
IX. FUNCTIONS OF A ONE-DEGREE CURVE. 
 
 Whole 
 Angle. 
 
 Tangent 
 Distance. 
 
 Long 
 Chord. 
 
 External 
 Secant. 
 
 Whole 
 Angle. 
 
 lO4 3 o' 
 
 7399-8 
 
 9060.6 
 
 3629.2 
 
 lO4 3 o' 
 
 32' 
 
 7404.3 
 
 9062 . 7 
 
 3632.7 
 
 32' 
 
 34' 
 36' 
 
 7408.8 
 7413-2 . . . 
 
 9064.7 
 9066.8 
 
 3636-2 . . . 
 3639.7 ">* + 
 
 34' 
 36' 
 
 38' 
 
 7417-7 "^ 
 
 9068.8 
 
 3643-3^6, = 
 
 38' 
 
 4o' 
 
 7422.1 - - 
 
 9070.8 3646.8-3 
 
 40' 
 
 42' 
 
 7426.613 
 
 9072.9 13650.3-5,; : 
 
 42' 
 
 44* 
 
 743*. O-g: = 
 
 9074.9 13653-9^ 
 
 44' 
 
 46' 
 
 7435- 5*2 
 
 9076.9 3657.4^ = 
 
 46' 
 
 48' 
 
 7440. 0<o: : 
 
 9079 .0 3661 . o i 'r. 1 ? 
 
 48' 
 
 5o; 
 
 7444.5 Sd 
 
 9081 .0 
 
 3664. 5 ^ MW 
 
 50' 
 
 
 7449-0 * 
 
 9083.0 
 
 3668.1 ^ = 
 
 52' 
 
 11' 
 
 7453-5?: : 
 
 9085 . i 
 
 3671.6 
 
 54' 
 
 56' 
 
 7458. o< 
 
 9087 . i 
 
 3675-2 
 
 56' 
 
 58' 
 
 7462.5 
 
 9089 . i 
 
 3678.8 
 
 58' 
 
 1O5 
 
 7467.0 
 
 9091 . i 
 
 3682.3 
 
 105 
 
 2' 
 
 7471-5 
 
 9093.2 3685.8 
 
 2' 
 
 4' 
 
 7476.0 
 
 9095.2 3689.4 
 
 4' 
 
 6' 
 
 7480.5 
 
 9097.2 3693-0 
 
 6' 
 
 8' 
 
 7485.0 
 
 9099.3 3696.6 
 
 . 8' 
 
 10' 
 
 7489.5 
 
 9101 . 3 3700 . 2 
 
 10' 
 
 I2 f 
 
 7494-0 
 
 9103.3 3703.8 
 
 12' 
 
 14' 
 
 7498.6 
 
 9105.3 3707-4 
 
 14' 
 
 16' 
 
 7503.1 
 
 9107.4 13711 .0 
 
 1 6' 
 
 18' 
 
 7507.6 . 
 
 9109 .4 3714 . 6 
 
 1 8' 
 
 20' 75I2.I 10C ? 
 
 9111.4 3718.2 A * j 
 
 20' 
 
 22 f 
 
 7516.7,0: i 
 
 9113.4 13721.8 d- j 
 
 22' 
 
 24' 
 26' 
 
 7521.2.3 
 
 7525- 8-:: 
 
 9H5.5 37*5-4 2 
 
 9II7-5 3729-1 .& : 
 
 24' 
 
 26' 
 
 28' 
 
 753o.3<2' 
 
 
 28' 
 
 30' 
 
 7534- 8^ :: 
 
 9121.5 
 
 3736.3 c= : 
 
 3' 
 
 3 2 ' 
 
 7539-4 JFdi? 
 
 9123.5 
 
 3739-9^^ 
 
 a; 
 
 34' 
 
 7543-9 52. 
 
 9125 .6 
 
 3743-6 *H^ 
 
 34' 
 
 36' 
 
 7548.55. . 
 
 9127 .6 
 
 3747-25. ; 
 
 36' 
 
 38' 
 
 7553-0 <T ' 
 
 9129.6 
 
 3750. 8< 
 
 38' 
 
 40' 
 
 7557-6 
 
 9131.6 
 
 3754-5 
 
 . 4' 
 
 42' 
 
 7562.1 
 
 9I33-6 
 
 3758.2 
 
 42' 
 
 44' 
 
 7566.7 
 
 9I35-6 
 
 3761.8 
 
 44' 
 
 46' 
 
 757L3 
 
 9137.6 
 
 3765-5 
 
 46' 
 
 48' 
 
 7575-9 
 
 9139.6 
 
 3769-I 
 
 48' 
 
 5' 
 
 7580.5 
 
 9141 . 6 
 
 3772.7 
 
 s; 
 
 52' 
 
 7585-1 
 
 9143.6 
 
 3776.4 
 
 
 54' 
 
 7589-7 
 
 9I45-7 
 
 3780.0 
 
 54' 
 
 56' 
 
 7594-3 
 
 9147.7 
 
 3783-7 
 
 56' 
 
 58' 
 
 7598. Q 
 
 9149.7 
 
 3787.4 
 
 58' 
 
 115 
 
IX. FUNCTIONS OF A ONE-DEGREE CURVE 
 
 Whole 
 Angle. 
 
 Tangent 
 Distance. 
 
 Long 
 Chord. 
 
 External 
 Secant. 
 
 Whole 
 Angle. 
 
 1OO 
 
 7603.5 
 
 9i5!-7 
 
 3791.0 
 
 1OO 
 
 2' 
 
 7608.1 
 
 9153.7 
 
 3794-7 
 
 2 f 
 
 4' 
 
 7612 .7 
 
 9I55-7 
 
 3798.4 
 
 4' 
 
 6' 
 
 7617.3 
 
 9I57-7 
 
 3802 .0 
 
 6' 
 
 8' 
 
 7621 .9 M 
 
 9I59-7 
 
 3805.7 
 
 8' 
 
 10' 
 
 7626.5 = 
 
 9161.7 
 
 3809.4 
 
 10' 
 
 I2 f 
 
 763LI -3 
 
 9163.7 
 
 3813-1 
 
 12' 
 
 14' 
 
 7635.7 = 
 
 9165.7 
 
 3816.8 
 
 14' 
 
 16' 
 
 7640.4 < 
 
 9167.7 
 
 3820.5 ^&* 
 
 16' 
 
 18' 
 
 7645.1 .0 = 
 
 9169.7 
 
 3824.2 ^ 
 
 18' 
 
 20' 
 
 7649.7 ,/n 
 
 9171.7 
 
 3827.9 *' ' 
 
 20.' 
 
 22' 
 
 7654.4 ^'3. 
 
 9I73-7 
 
 3831.6 "2. . 
 
 22' 
 
 24' 
 
 7659.0 ^ : 
 
 9I75-7 
 
 3835 -4 $" ' 
 
 24' 
 
 26' 
 
 7663.7 *< 
 
 9177.7 
 
 3839-1 - - 
 
 26' 
 
 28' 
 
 7668. 3 -a 
 
 9179.7 
 
 3842.8 ^" " M 
 
 28' 
 
 30' 
 
 7672.9 
 
 9181.7 
 
 3846.5 4 i^ 
 
 30' 
 
 32' 
 
 7677.6 ^ 
 
 9183.7 
 
 3850.2 ^ . 
 
 32' 
 
 34' 
 
 7682.2 ^2 
 
 9185.7 
 
 3854.0 < 
 
 34' 
 
 36' 
 
 7686.9 ^6. ' 
 
 9187.7 
 
 3857.7 
 
 36' 
 
 38' 
 
 7691 .5 %K~ 
 
 9189.7 
 
 3861.5 
 
 38' 
 
 40' 
 
 7696.2 .t: 
 
 9191.7 
 
 3865.2 
 
 40' 
 
 42' 
 
 7700.9 c& 
 
 9I93-7 
 
 3869 .0 
 
 42' 
 
 44' 
 
 7705.5 Jh 
 
 9I95-7 
 
 3872.7 
 
 44' 
 
 46' 
 
 7710.2 VC 
 
 9197.7 
 
 3876.5 
 
 46' 
 
 48' 
 
 7714.9 fg 
 
 9199.7 
 
 3880.2 
 
 48' 
 
 5 0/ 
 
 7719.6 2^' 
 
 9201 .6 
 
 3884.0 
 
 50' 
 
 5 2 ' 
 
 7724.3 SI' 
 
 9203.6 
 
 3887.8 
 
 52 ' 
 
 54' 
 
 7729.0 
 
 9205.6 
 
 3891 .6 
 
 
 56' 
 
 7733-7 
 
 9207 .6 
 
 3895 .4 ... 
 
 56' 
 
 58' 
 
 7738.4 
 
 9209 .6 
 
 3899.1 ly ; c "- 
 
 58' 
 
 1O7 
 
 7743-1 
 
 9211.5 
 
 3902.9 - : 
 
 107 
 
 2' 
 
 7747-9 - -4 
 
 92I3-5 
 
 3906.7 -g 
 
 2' 
 
 4' 
 
 7752.6 ^? C( - 
 
 9215-5 
 
 3910.5 -a- : 
 
 4' 
 
 6' 
 
 7757-3 %' - 
 
 9217.5 
 
 3914.3^ 
 
 6' 
 
 8' 
 
 7762.0 -g 
 
 9219.4 
 
 3918.1 &-^ 
 
 8' 
 
 10' 
 
 7766.7 '$." * 
 
 9221 .4 
 
 3921 .9 4ej i- 
 
 10' 
 
 12' 
 
 777J-4 g. - 
 
 9223.4 
 
 3925-7 ^ 
 
 12' 
 
 14' 
 
 7776.2 -^ 
 
 9225.4 
 
 3929.5 4- * 
 
 14' 
 
 16' 
 
 7780.9 r^^,- 
 
 9227.3 
 
 3933-3 
 
 16' 
 
 18' 
 
 7785.7 ^32. 
 
 9229-3 
 
 3937-1 
 
 18' 
 
 20' 
 
 7790.4 ^= 
 
 9231.3 
 
 3941 .0 
 
 20' 
 
 22' 
 
 7795-2 
 
 9233.3 
 
 3944-8 
 
 22' 
 
 24' 
 
 7800.0 
 
 9235-3 
 
 3948.7 
 
 24' 
 
 26' 
 
 7804.7 
 
 9237.2 
 
 3952.5 
 
 26' 
 
 28' '7809.5 
 
 9239.2 
 
 3956.4 
 
 28' 
 
 116 
 
-FUNCTIONS OF A ONE-DEGREE CURVE. 
 
 Whole 
 Angle. 
 
 Tangent 
 Distance. 
 
 Long 
 Chord . 
 
 External 
 Secant. 
 
 Whole 
 Angle. 
 
 107 30' 
 
 7814.2 
 
 9241.2 
 
 3960.2 
 
 !O7so' 
 
 3^' 
 
 7819 . o 
 
 9243.2 
 
 3964.0 
 
 32' 
 
 34' 
 
 7823.7 
 
 9245.1 
 
 3967.9 
 
 34' 
 
 36' 
 
 7828.5 
 
 9247.1 
 
 397L7 
 
 36' 
 
 38' 
 
 7833.4 
 
 9249.1 
 
 3975-6 ^- 
 
 38' 
 
 40' 
 
 7838.1 
 
 9251.0 
 
 3979-5 & ' 
 
 40' 
 
 42' 
 
 7842.9 
 
 9253.0 
 
 3983-3 "5 
 
 42' 
 
 44' 
 
 7847.7 
 
 9255.0 
 
 3987.2 .-- = 
 
 44' 
 
 46' 
 
 7852.5 . . 
 
 9256.9 
 
 3991.1 w 
 
 46' 
 
 48' 
 
 7857.3 "^ 
 
 92^8.9 
 
 3995-0 &^ 
 
 48' 
 
 5' 
 
 7862.1 s = 
 
 9260 . 8 
 
 3998.9 522 
 
 50' 
 
 5'' 
 
 7866.9^ 5 
 
 9262 .8 
 
 4002 .8 ^ 
 
 52' 
 
 54' 
 
 787L7 J ' 
 
 9264 .8 
 
 4006.7 ** = 
 
 54' 
 
 S6' 
 
 7876.5*-- 
 
 9266. 7 
 
 4010.6 
 
 56' 
 
 58' 
 
 7881.3^;; 
 
 9268.7 
 
 4014.5 
 
 58' 
 
 1O8 
 
 7886.1 zz 
 
 9270 .6 
 
 4018.3 
 
 108 
 
 2' 
 
 7890.94;*- 
 
 9272 .6 
 
 4O22 . 2 
 
 2' 
 
 4' 
 
 7895.85= 
 
 9274.5 
 
 4O26 . I 
 
 4' 
 
 6' 
 
 7900.6 
 
 9276.5 
 
 4030.0 4 
 
 6' 
 
 8' 
 
 7905.4 
 
 9278.4 
 
 4033.9 6 
 
 8' 
 
 10' 
 
 7910.2 
 
 9280 .4 
 
 4037-8 ^ 
 
 10' 
 
 12' 
 
 791 ^ .0 
 
 9282.3 
 
 4041.7 * 
 
 12' 
 
 14' 
 
 7919.9 
 
 9284.3 
 
 4045.6 03 
 
 14' 
 
 16' 
 
 7924.7 
 
 9286.3 
 
 4049.6 J3 
 
 J6' 
 
 18' 
 
 7929.6 
 
 92.88.2 
 
 4053.5 
 
 i8 x 
 
 20' 
 
 7934.5 
 
 9290 . 2 
 
 4057.4 ^cf 
 
 20' 
 
 22' 
 
 7939-3 +6 + 
 
 9292 . 2 
 
 4061 .4 6. -c 
 
 22' 
 
 24' 
 
 7944-2 . 
 
 9294. I 
 
 4065.3^ < 
 
 24' 
 
 26' 
 
 7949.1 gs = 
 
 9296 . I 
 
 4069.3 |, 
 
 26' 
 
 28' 
 
 7954.0 -g 
 
 9298.0 
 
 4073-2 " 
 
 28' 
 
 30' 
 
 7958.9 '$" = 
 
 9300 . o 
 
 4077.2 |^ 
 
 3 0/ 
 
 32' 
 
 7963-8 . . 
 
 9301 .9 
 
 4081 .2 ?*? . 
 
 32' 
 
 34' 
 
 7968.7 -Vr- 
 
 9303-Q 
 
 4085 .2 "*!; H 
 
 34 
 
 36' 
 
 7973. -6 c,~ 
 
 9305-8 
 
 4089.1 ^ : d 
 
 36' 
 
 38' 
 
 7978.5 4;**- 
 
 9307.8 
 
 4093.1 < ^ 
 
 38' 
 
 40' 
 
 7983.4 3 2 : 
 
 9309.7 
 
 4097 - 1 ', 
 
 40' 
 
 42' 
 
 7988.3 ' 
 
 93H.7 
 
 4101 .1 
 
 42' 
 
 44' 
 
 7993-2 
 
 9313.6 
 
 4105.1 
 
 44' 
 
 46' 
 
 7998.1 
 
 9315-6 
 
 4109 . o 
 
 46' 
 
 48' 
 
 8003 .0 
 
 93I7-5 
 
 4113.0 
 
 48' 
 
 50' 
 
 8007 .9 
 
 93I9-4 
 
 4117.0 ^ 
 
 5 0/ 
 
 52' 
 
 8012.8 
 
 9321 -4 
 
 4121 .0 
 
 5 2/ 
 
 54- 
 
 8017.7 
 
 9323.3 
 
 4125.0 
 
 54' 
 
 56' 
 
 8022 .6 
 
 9325.2 
 
 4129.0 
 
 56' 
 
 58' 
 
 8027.5 
 
 93 2 7 J 
 
 ^ I 33- 1 
 
 58' 
 
UNIVERSITY OF CALIFORNIA 
 LIBRARY 
 
 This is the date on which this 
 book was charged out. 
 
 APH 20 1912 
 vj\ 
 
 -? v 
 
 o^ 
 
 NOV26 t942 
 
 [30m-6,'ll] 
 
06857