LIBRARY OF THE UNIVERSITY OF CALIFORNIA. Deceived V JAN 11 1 393 ..... 189 ^Accessions No. 4-QQ5"3 . Class No, JOHN WILEY & SONS, 53 E. Tenth Street, New York, PUBLISH : THE RAILROAD SPIRAL. The Theory of the Compound Transition Curve reduced to Practical Formulas and Rules for Application in Field Work, with Complete Tables of Deflections and Ordinates for five hundred Spirals. By Wm. H. Searles, C.E., author of "Field Engineering," Member of Am. Soc. of C. E. Pocket-book form $1 50 " It should have a place in the library of every Civil Engineer in the world." Rnil wan -*(/? FIELD ENGINEERING. A HAND-BOOK of the Theory and Practice of RAIL- WAY SURVEYING, LOCATION and CONSTRUCTION, de- signed for CLASS-ROOM, FIELD, and OFFICE USE, and containing a large number of Useful Tables, Original and Selected. By Wm. H. Searles, C.E., late Prof, of Geodesy at Rensselasr Polytechnic Inst., Troy. This vol- ume contains many short and unique methods of Laying Out, Locating, and Constructing Compound Curves, Side Tracks, and Railroad Lines generally. It is also intended as a text-book for Scientific Schools. Pocket-book form. Ninth edition, 1890 12mo, morocco, 3 00 "The book is admirable. The internal arrangements and ap- pearance are excellent. It is an easy work to refer to, and is plain and clear. There is no useless lumber in it. Every sen- tence belongs there." PROF. DAVIS, University of Michigan. l-tlE CIVIL ENGINEER'S FIELD-BOOK. Designed for the use of the LOCATING ENGINEER. Containing Tables of Actual Tangents and Arcs, ex- pressed in chords of 600 feet for every minute of inter- section, from to 90, from a 1 curve to a 10 curve in- clusive. Also, Tables of Formulae applicable to Railroad Curves and the location of Frogs, together with Radii, Long Chords, Grades, Tangents, Natural Sines, Natural Versed Sines, Natural External Secants, etc. With Ex- planatory Problems. By Edward Butts, C.E. 12mo, morocco flaps, 2 50 " The work is a monument of patience on the part of the au- thor, and should prove a labor saving investment to the pur- chaser. It is a ' Henck ' elaborated, and this is quite recommend- ation enough to the practising engineer." Engineering News. TREATISE ON LEVELLING BY VERTICAL AN- GLES, And the Method of Measuring Distances by Telescope and Rod. With Tables of Heights for all angles, from zero to 22i^ degrees (in minutes), for any distance re- quired. By August Faul, C.E. . . . 8vo, limp cloth, 1 00 TABLES FOR CALCULATING THE CUBIC CON- TENTS OF EXCAVATIONS AND EMBANK- MENTS BY AN IMPROVED METHOD OF DIAGONALS AND SIDE TRIANGLES. By J. R. Hudson. New edition, with additional tables, 8vo, cloth, 1 00 "Hudson's Tables for Computing Earthwork are well known to Engineers, and by many are considered indispensable." Railway Age. CIVIL ENGINEER'S POCKET-BOOK Of Mensuration, Trigonometry, Surveying, Hydraulics, Hydrostatics, Instruments and their adjustments, Strength of Materials, Masonry, Principles of Wooden and Iron Roof and Bridge Trusses, Stone Bridges and Culverts, Trestles, Pillars, Suspension Bridges, Dams, Railroads, Turnouts, Turning Platforms, Water Stations, Cost of Earthwork, Foundations, Retaining Walls, etc. In addition to which the elucidation of certain important Principles of Construction is made in a more simple man- ner than heretofore. By J. C. Trautwine, C.E. 12mo, morocco flaps, gilt edges. 32d thousand, revised and enlarged, with new illustrations, by J. C. Trautwine, Jr., C. E. 1889 $5 00 "It is the best Civil Engineer's Pocket book in existence." American Engineer. A METHOD OF CALCULATING THE CUBIC CON- TENTS OF EXCAVATIONS AND EMBANK- MENTS BY THE AID OF DIAGRAMS, Together with Directions for Estimating the Cost of Earthwork. By John C. Trautwine, C.E. Ninth edition, revised and enlarged by J. C. Trautwine, Jr. 8vo, cloth, 2 00 THE FIELD PKACTICE OF LAYING OUT CIR- CULAR CURVES FOR RAILROADS. By J. C. Trautwine, Civil Engineer. 12th edition, re- vised by J. C. Trautwine, Jr. . . 12mo, limp morocco, 2 50 " Probably the most complete and perfect treatise on the single subject of Railroad Curves that is published in the English language." Engineering News. THE ECONOMIC THEORY OF THE LOCATION OF RAILWAYS. An Analysis of the Conditions controlling the laying out of Railways to effect the most judicious expenditure of capital. By Arthur M. Wellington, Chief Engineer of the Vera Cruz and Mexico Railway, etc. New and improved edition 8vo, 5 00 "Mr. Wellington has done great service to the Railroad pro- fession; more particularly to Engineers, Managers, and Superin- ' tendents, by bringing together in a single volume such a mass of valuable matter. It should be in every Railway Library." Railway Age. A TREATISE UPON CABLE OR ROPE TRACTION. As applied to the working of STREET and other RAIL- WAYS. (Revised and enlarged from Engineering.) By J. Bucknall Smith, C.E. With illustrations and folding plates . 4to, cloth, 250 "The publication of this book seems to us to be most timely. The subject is ably handled by an experienced Engineer." American Machinist. A TREATISE ON CIVIL ENGINEERING. By O. H. Mahan. Revised and edited, with additions and new plates, by Prof. De Volson Wood. With an Appendix and complete Index. New edition, with chap- ter on River Improvements by F. A. Mahan. 8vo, cloth, 5 00 "This is the standard text-book on this subject." RAILROAD ENGINEERS' FIELD-BOOK AND EX- PLORERS' GUIDE. Especially adapted to the use of Railroad Engineers, on LOCATION and CONSTRUCTION, and to the Needs of the Explorer in making EXPLORATORY SUR- VEYS. By H. C. Goodwin 12mo, morocco flap, 2 50 THE CIVIL ENGINEER'S FIELD-BOOK: DESIGNED FOR THE USE OP THE LOCATING ENGINEER. CONTAINING TABLES OF ACTUAL TANGENTS, AND ARCS EXPRESSED IN CHORDS OF 100 FEET FOR EVERY MINUTE OF INTER- SECTION, FROM TO 90, FROM A 1 CURVE TO A 10 CURVE, INCLUSIVE; ALSO TABLES OF FORMULAE APPLICABLE TO RAILROAD CURVES AND THE LOCATION OF FROGS; TOGETHER WITH RADII, LONG CHORDS, GRADES, NATURAL TANGENTS, NATURAL SINES, NATURAL VERSED SINES, NATURAL EXTERNAL SECANTS, ETC. BY EDWAED BUTTS, CIVIL ENGINEER. SECOND AND REVISED EDITION. NEW YORK: WILEY AND SONS, TENTH STREET .oor west of Broadway. Copyright, 1886, By JOHN WILEY & SONS. PREFACE. IN preparing this book it lias been the author's design to present a volume based on the most economic principles of field engineering. Many good books of the kind are in print, yet none of them, it is believed, have presented the subject to the full extent of a labor-saving medium. Considerable time is spent in making mathematical field- calculations, thereby delaying the party and increasing the expense of the survey. To eliminate many of the errors that occur in, these calculations, and advance the progress of field- operations, extensive, hitherto unpublished, tables have been added to this work, and others previously published have been enlarged to prevent the field-work extending beyond their bounds. The formulae are comparatively arranged in a more systematic manner. The work of computing the tables has been thoroughly done, and it is believed will be found strictly reliable. An effort has been made to make the problems general, and therefore applicable to any case that may arise in a long practice. Throughout the work each problem is arranged with reference to the last preceding figure. Should this volume prove itself an assistant to the field- engineer, and fill the space for which it is designed, the author's wish will be fully realized. E. B. KANSAS CITY, Mo., August, 1885. TJHIVBBSITY CIVIL ENGINEER'S FIELD-BOOK. CURVE FORMULAE AND PROBLEMS. \ ABBREVIATIONS. T = Tangent, BA or BO. R = Radius, AD or CD. J Intersection, angle FBCor EBA. D = Deflection, angle for 100 ft. chords, BAa or BCe. d = Sub-deflection, angle for any chord less than 100 ft., B Af or BCg. E = External Secant, Be. M= Middle Ordinate, Jc>. C Chord, or Long Chord, any chord of 100 ft. or more, Aa or A G. c Sub-chord, any chord less than 100 ft., AforgC. A = Arc, the length of the curve in chords of 100 ft., AabcdeC. CIVIL ENGINEER'S FIELD-BOOK. TABLE I. TO FIND THE TANGENT. GIVEN. FORMULA. GIVEN. FORMULA. R, I T T T R tan A7 (7,7 BJ, AD, AJ T T T C 50 tan |7 2 cos \I ,, tan II sin D = E cot II vers 7 BJX AD AJ TABLE II. TO FIND THE RADIUS. GIVEN. FORMULA. GIVEN. FORMULA. T,I D R R R T cot 7 C, 7 J7, 7 AJ, AB, BJ R R R C 50 2 sin 7 M sin D E vers ^7 A J X AB exsec 7 BJ TABLE III. TO FIND THE DEFLECTION. GIVEN. FORMULA. GIVEN. FORMULA. GIVEN. FORMULA. R *">=*! r, / 50 tan */ A, I \I sin D y A TABLE IV. TO FIND THE EXTERNAL SECANT. GIVEN. FORMULA. GIVEN. FORMULAE. R I E R exsec -^-7 C I ^_ ^exsecU T I E T tan 1 7 7^ Sln U ^ jz M cos ^ 7 E ^^ ' cos 7 ' CUKYE FORMULA AND PROBLEMS. TABLE V. TO FIND THE MIDDLE ORDINATE. GIVEN. FORMULA. GIVEN. FORMULAE. *,/ M - R vers J J 0,7 M = iC tan J7 T,7 MJF nna 1 7" XV, 7 7? 77* M= R -(Rcos^I) Hf KE E,I M R + E TABLE VI. TO FIND THE CHORD. GIVEN. FORMULA. GIVEN. FORMULA. x?, 7 O = 2R sin J7 jftj = 2^coti7 T I sin ^7 ' cosi ' ^"^exsec |7 TABLE VII. TO FIND THE INTERSECTION. GIVEN. FORMULAE. GIVEN. FORMULA. DA M A ^ ^ = Too M, R vers 7 = xt T T, f2 tani/=^ E,R exsec \I = o X?, C C,T cos i/ = -^ TO FIND THE ARC. Problem 1. Given the 1, FBC = 41, and the D, BAa = 2, to find the -4, AabcdeC. Formula. Example. ^IAA i^= 20 30' = 1230' : -j) 100 D = 2 = T20 7 " = 10 ' 5 Result, yl = 1025.00 4 CIVIL ENGINEER'S FIELD-BOOK. TO FIND THE SUB-DEFLECTIOK Problem 2. Given the c, Af 75 ft., and the D y BAa = 4 18', to find the d, BAf. Formula. Example. _ DC D = 4 18' = 258' "100 c = 75 1290 1806 Result, 100. I 19350. I 193.50 - 3 13' 30" = d. Problem 3. Many sub-deflections may be calculated quickly by the fol- lowing method: Multiply the degree of the given curve by 0.3, and multiply the product thus obtained by the length of the given sub-chord, and then reduce the second product one denomination; the result will be the required sub-deflection. Given the c, gC 30 ft., and the degree of curve aDb = 2, to find the d, BCg. Example. Degree of curve = 2 .3 .6 c = 30. Second product 18 Reduced one denomination 18'0 = d. EXPLANATION. When it is required to run a curve very accurately the above formulae, although generally used, are not correct. This will be readily understood by considering that the shorter the chords the nearer the approach to the circumference of the circle, and the longer the chords the nearer the approach to the diameter of the circle. The base of most field-work and calculations is one hundred feet. Therefore when a chord is shorter than this base it should be proportionally longer than would be indicated in a deflection calculated by the above method, and vice versa when a chord is longer than this base. The deflection must first be calculated as indicated by Prob- lem 2 or 3, after which correct the sub chord by the following. CURVE FORMULAE AND PROBLEMS. 5 Problem 4. Given the d, BAf 6, and the R, AD = 359.265, to find the c, Af. Formula. Example. c = 2Rsmd. 2R= 718.53 d = 6 sin 0.10453 215559 359265 287412 71853 Products = 75.1079409 v lv C- "d 7 / Problem 5. Given the 1, FBC = 45, and the 11, AD = 637.275, to lay out a curve by ordinates when the curve begins 60 ft. beyond a station and ends 60 ft. back of a station. By Table I. the T, BA and BC = R tan \I = 263.97 By Table III. sin D = -^ = 4 30'. By Problem 1, A = ^100 = 500. Denote BAa' by d. " BAV " D'Ec. " Aa' " c. " AV " CEc. " aa " o. Denote a'Aa by x. " VAb " x'Ec. " Aa " y. f< Ab " y'Ec. " bb' " o'. CIVIL ENGINEER S FIELD-BOOK. r By Problem 2, d = =^ = 148', and D' = d + D = 1 48' luu + 4 30' = 6 18'. Then x = \I - d = 22 30' - 148' = 20 42', and x' = \I - D' = 22 30' - 6 18' = 16 12'. By Problem 4, c 2R sin d 40.03, and C 139.86/&. To find yEc. Formula. Example. y = ccosx. # = 20 42' cos 0.93544 c= 4003 280632 374176 Product y - 37.4456632 To find oEc. Formula. Example. o = c sin x. x 20 42' sin 0.35347 c 40.03 Product o = 106041 141388 14.1494041 Problem 6. Given the /, FBC = 45, and the n t AD = 637.275, to lay out a curve from points on the tangents AB and CB when the CURVE FORMULA AND PROBLEMS. 7 curve begins 60 ft. beyond a station and ends 60 ft. back of a station. By Table I. the I\ BA and BC = R tan \I = 263.96 By Table III. sin D = ~ = 4 30'. By Problem 1, A = 100 = 500. Denote BAa by d. Denote Aa by c. " BAb " D'. "- Ab " G. " BAc " D". " Ac " C'. " Aa' " #. " #' " y. " AV " x r . " w " y. " ^4c' <4 x". " cc' " y". By Problem 2, c? = ^ = 1 48', and D' = d + D = 1 48' + 4 30' = 6 18', and D" = d + 2D = 1 48' + 9 = 10 48'. By Problem 4, c = 2R sin d = 40.03, and G = 139.86, and C' = 238.83 To find x. Formula. Example. x = ccosd. d = r8' cos 0.99951 e= 40.03 299853 399804 Product x = 40.0103853 Use the same method to find x' and x". To find y. Formula. Example, y c sin d. d = 1 48' sin 0.03141 c ~ 40.03 9423 12564 Product y = 1.2573423 Use the same method to find y' and y". Then, for locating the other half of the curve, begin at C and run towards B, using the same formulae as given above. CIVIL ENGINEER'S FIELD-BOOK. Problem 7. Given the R, AD = 1432.69 of a located curve AabcC, it is desired to run another curve A'a'b'c'C' parallel to it at a given distance of A A' = 75 ft. The chords A a, ah EC are 100 ft. long. Denote the chords A a', a'b'Kc, by x. Denote AD by R , then R = AD - AA = 1432.69 - 75 = 1357.69 By Table III. sin D = ~ = 2. To find x. Formula. Example. a = 272' sin U. 2 R' = 2715.38 D = 2 sin 0.03490 24438420 1086152 814614 Product x= 94.7667620 If it is desired to run the curve A"a"b"c"C", add the distance AA" to the R, AD, and use the above method. CURVE FORMULAE AND PROBLEMS. Problem 8. Given the R, AD 2864.93, to locate a curve when the point of intersection B is inaccessible. Make the offset AN 12 ft. = a, and run NR parallel to AG intersecting the tangent BU at P, and turn the angle RPH = OB 14 = 14 = I. By Table I. the T, BA and BG = R tan 1 = 351.76 Denote PO by x, and PB by z. Determine the unknown sides of the triangle BPO by the following formulae: To find x. Formula. Example. x = a cot /. / = 14 cot 4.01078 a = 12. 802156 401078 Product x = 48.12936 To find z. Formula. Example. a I 14~1 a = ["Quotient z = z = sin J sin 0.24192 J 12.0000 [_49.60 96768 232320 217728 145920 NO - AB = 351.76, and NP(= NO + 0P' = 351.76 + 48.13) 399.89 from P, a point 12 ft. at right angles to the point of curve A. 10 CIVIL ENGINEER'S FIELD-BOOK. The point of tangent C (= BO BP = 351.76 - 49.60) 302. 16 from P. By Table III. sin D = ~ = 1. { K By Problem 1, A = 100 = 700. Problem 9. Given the R, AD = 287.939, and the distance around the curve, AC = 200 ft., to locate the point C from a point on the tangent A G. The R, AD being that of a 20 curve, the angle FBC 40 = /, and by Table VI. the chord AC = 2R sin |7 = 196.962 = C. Make the distance AG = AC. Then invariably the angle AGGnudAGG = i/ = 10. Calculate the distance GC = x by the following: Formula. Example. L 20= 393.924 7 = 10 cos 0.98481 393924 3151392 1575696 3151392 3545316 Product x = 387.94029444 CURVE FORMULAE AND PROBLEMS. 11 Problem 1O. Given the 7?, AD = 1632.40, to locate the beginning and end of a curve when the point of intersection B is inaccessible. Continue the tangent EA to JV, also the tangent HCto P. Measure the distance JVP = 359.20 = a, and turn the angle FPN = 33 43' = b, and the angle GNP = 28 35' = c; then the angle GBP = b + c = 33 43' + 28 35' = 62 18' = 7. By Table I. the I\ BA and BC = R tan 1 = 986.67 Denote BN by x, and BP by z. Determine the unknown sides of the triangle NBP by the following formulae: To find x. Formula. Example. asmb b 33 43' sin 0.55509 : sin/ = 359.20 1110180 499581 277545 / = 62 18'"] 166527 _ ["Result x = sin 0. 88539 J 199. 3883280 L225. 19 177078 223103 ' 177078 460252 442695 175578 88539 870390 12 CIVIL ENGINEER'S FIELD-BOOK. To find z, Formula, Example. _ a sin e c = 28 35' sin 0.47844 ~-~s^T *= 359.20 956880 430596 J = 62 18'~ 143532 PResult 2 = '~| sin 0. 88539 171. 8556480 l94. 10 88539 833166 796851 363154 354156 88539 14490 NA = T - x = 986.67 - 225.19 = 761.48, the distance from N to the point of curve A. PC = T - z = 986.67 - 194,10 = 792.57, the distance from P to the point of tangent (7. Problem 1 1 . Given the /, FBO = 58, to locate a curve through a given point 1L Find the point Q on the tangent J3A where the angle BGH = K = 29. Measure the distance Oil = 40 ft. = a, also the distance BO = 500 ft. = b. Denote OK by x, and HK\-y y, and QA by z. CURVE FORMULAE AND PROBLEMS. 13 Calculate x and z by the following formula?: To find x. Formula. Example, x = 2b cos \T. \I 29 cos 0.87462 2b = 1000. Product x = 874.62000 Then y = x - a = 874.62 - 40. = 834.62 To find z. Formula. z = Example. y = 834.62 a = 40. 33384.80 Result z 182.71 28 I 233 224 362 I 984 724 3647 I 26080 25529 36541 I 55100 36541 The tangent BA and BC = b + z = 500. + 182.71 = 682.71 By Table II. the 11, AD = Tcot i/= 1231.64 Problem 12. Given the /, FBG = 41 36', and the distance CJ= 8.62 a, to determine how far toward G, A' must be from A to start the curve A'C', which is similar to AC, to have it run into the tangent C'K parallel to Oil at the given distance a. 14 CIVIL ENGINEER'S FIELD-BOOK. Denote the distance A A' by x and calculate it by the following: Formula. Example. a I 41 36'~1 a ("Quotient x = ~ sin 7 sin 0.66393 J 8.6200|_12.98 66393 198070 132786 652840 597537 553030 Problem 13. Given the R, AD = 1432.69, and the /, FBO = 62 30', of a located curve AC to find the R\ AD' of another curve to start from the same point A and end in the tangent C'K parallel to OH at a given distance CC' = 42.60 = a. Denote the distance DD' by x and calculate it by the fol- lowing. Formula. Example. \a \I 31 15'"] \a = ["Quotient x = ~ sin i/ gin o,51877j21.3000L41.05 207508 54920 51877 304300 Then R = R + x = 1432.69 + 41.05 = 1473.74 CURVE FORMULAE AND PROBLEMS. 15 Problem 14. Given the R, AD = 1910.03, and the /, FBC = 31 30' of a located curve AC, to find the H' ; AD' of another curve to start from the same point A, and end in the tangent C'K, par- allel to GH&i a given distance, GO' = 14 ft. = a. Denote the distance DD' by x, and calculate it by the fol- lowing: Formula. Example. a I = 31 30'~| a = ["Quotient x = vers /' vers 0.14736J14.0000L90.00 133624 73760 73680 x = 8000 Then R' = R + x = 1910.08 4- 95.00 == 2005.08 COMPOUND CURVES. Problem 15. Having run the curve A C with the R, AD = 955.366 and the I, FBC 54 30', it is desired to flatten the curve at each end, a distance of A G and CH = 150 ft. with a radius of AD' and CD' = 1910.08 = R'. 16 CIVIL ENGINEER'S FIELD-BOOK. Required the radius GD" and IID" = r, to join the two curves A O and Gil at G and //. The R', AD', and CD' being that of a 3 curve, the angle AD'G = 4 30', also CD' II = 4 30'. The angle GD'U =1- (AD'G + CD' 11) = 54 30' - 9 = 45 30' = /'. Denote R 1 - R by a; then a = 1910.08-955.366 = 954.714. Denote the distance D"D' by x, and calculate it by the fol- lowing: Formula. Example. as'mil a = 954.714 * = "sin 1' I* = 27 15' sin 45787 6682998 7637712 6682998 4773570 iP = 22 45' ~| 3818856 TResult x = sin 0.38671J437.13489918LH30.39 38671 50424 38671 117538 116013 152599 116013 365861 Then r = E' x = 1910.08 - 1130.39 ~ 779.6 CURVE FORMULAE AND PROBLEMS. 17 Problem 1 6. Given the chord AC' = 600 ft. = O, and the angle BAG' = 45, and the angle BO' A 67 36', to find the radii CD and CD' to lay out the compound curve AGO'. The angle GAG' = %BAC = -22 30' = a, and the' angle CO A = $BC'A = 33 48' = b. The angle A GC 1 = 180 - (22 30' + 33 48') = 123 42' = e. Denote the chord A G by x, and the chord CO' by y, and cal- culate the two sides, x and y t of the triangle AGG' by the fol- lowing formulae : To find x. Formula. C sin b x = sm e Example. b = 33 48' sin 0.55630 C= 600. e = 12342H 333.78000 FResult X = 8in0.83195> 378 [401.80 100000 83195 ?.68050 18 CIVIL ENGINEER'S FIELD-BOOK. To find y. Formula. Example. ff sin a a = 22 30' sin 0.38268 ~^T7~ = 600. e = 123 42 r sin 0.83195 229.60800 166390 "Result y = 275.98 632180 582365 498150 415975 821750 748755 729950 The angle GAG' = %'BB' C |/to the curve AC, and sim- ilarly the angle GO A = %GB '0' = $1 to the curve CO'. Having thus found the chords A C, and CC' the R, CD, by Table II. = --^- r = 524.20, and the R, CD = 248.05 2 sm |/ Problem 1 7. Given the angle FBC' = 112 36', and the distance ^4J5 = 600.870 = a, and the distance C*-B = 459.557 = 5, to find the radii CD and CD to lay out the compound curve A CC' . Denote the angle BAG' by x, and the angle BC' A by y, and the distance AC' by g. The angle ABC' = 180 - 112 36' = 67 24' = c, and + # = 112 36' , Calculate a?, y, and 2, by the following formulae: To find half the difference between x and y. tan $(y x) = Formula, (a b) tan $(x + y) CURVE FORMULA AND PROBLEMS. 19 Example. a b= 141.313 + y)= 56 18' tan 1.49944 565253 565252 1271817 1271817 565252 a + b =q 141313 ["Result tan tfy-a?) = 1060. 427J 211.89036472 L-19982 = 11 18' 3060427 10584766 9543843 10409234 9543843 8653917 8483416 1705012 Then x = *( + y) - l(y -x)= 56 18' - 11 18' = 45 and y = \(x + y) + \(y - x) = 56 18' + 11 18' = 67 36'. To find s. Formula. a z = sin c. sm y Example. y = 67 86'"] a = I" a = sin y -649.90 I . sin 0.92455J 600.870 [j 554730 461400 c = 67 24' sin 92321 369820 915800 129980 194970 129980 584910 Result z = 599.9941790 Then by Problem 16, the chord AC = 401.20 and the chord CO = 275.98 By Table II. the R t CD = .*\r= 524.20, and the J?, OD' = 248.05. CIVIL EKGIKEEK'S FIELD-BOOK. REVERSED CURVES. Problem 1 8. Given the angle C r AF = 20 = a, and the distance AC' = 400 ft. = C, to find the R, CD and CD' to join the* two paral- lel lines AF and EG' with the reversed curve ACG'. Formula. R= _$c_ sin a Example. a = 20~| i(7 = ["Quotient. sin 0.34202J 100.000 [_292. 380 68404 315960 307818 81420 68404 130160 102606 275540 Problem 19. Given the angle C'AF= 3 31' = a, and the distance AE 14 ft. = d, to find the R, CD and CD' to join the two par- allel lines ,4^ and EG' with the reversed curve ACG' . Calculate the distance AC' = C by the following: CURVE FORMULAE AND PROBLEMS. Formula. Example. _ d_^ a 3 31H d ("Quotient. C = ~ siu a sin 0. 06134 J 1 4.000 [_228. 236 12268 17320 12268 50520 49072 14480 12268 22120 18402 37180 Then by Problem 18, the R, CD and CD' = ~- = 930.208 Problem 2O. Given the distance AF 196.11 = b, and the distance AE = 14 ft. = d y to find the R, CD and CD' to join the two par- allel lines J.^ 7 and EC' with the reversed curve AGO'. Calculate the angle C' AF = a by the following: Formula. Example. d b =~\ d = ("Quotient, tan a = tan a = r 196. 11 J 14.0000 L-07139 = 4 05' 137277 27230 19611 76190 58833 173570 Then by Problem 19 the distance AC' = ~ 196.605 sin a And by Problem 18 the R, CD and CD = 4-^~ = 690.230 bin a CIVIL ENGINEER'S FIELD-BOOK. Problem 21. Given the R, CD and CD = 819.02 and the angle C'AF = 3 15' = a, to find the distance AF =. b. Formula. Example. b = 2R sin 2a. 2R = 1638.04 2a = 6 30' sin 0.11320 3276080 491412 163804 163804 Product b = 185.4261280 Ei Problem 22. Given the angle C'AF= 3 45' = |J, and the R', CD = 941.60, and the distance AE = 14 ft. = d, to find the R, CD' of the curve CC' to join the tangent JC r , which is parallel to AF at the given distance, and complete the reversed curve ACC'. Denote AC by (7, and AC' by C", and CC' by C. Calculate C' and C" by the following formulae: To find C'. Formula. Example. C' = 2R' sin !/. 2R = 1883.20 i/ = 3 45' sin 0.06540 7532800 941600 1129920 Product C' = 123.1612800 CURVE FORMULA AND PROBLEMS. To find C". Formula. c" = -J-, , sin Example. i/= 3 45' I d = ["Quotient. C" = sin 0.06540J 14.000 [_214.067 13080 9200 6540 26GOO 26160 44000 39240 47600 Then C = C" - C 1 = 214.067 - 123.161 = 90.906 Having Urns found C by Table II. R = sin .= 695.0 Problem 23. Given the /, OBF = 14 32', and tlie distance BB' = 548.5 rr a , and 7', GB'JI = 10 30, to find the ^, CT) and CD' to join the two lines EB and I?'// with the reversed curve ACC'. 24 CIVIL EITGINEEU'S FIELD-BOOK. Formula, a tan i/ + tan Example. 7 21' tan 0.12899 5 15' tan 0.09189 tan 1 a = fResult. 8 548.50 taniT = .22088 548.50 2483.24 J 441 76 L 106740 88352 183880 176704 66264 54960 44L76 107840 Problem 24. Given the R, AD = 1661.0 and the R', AD' = 941.6 and the R", CD" = 235 4, and the distance Aa and eC' = 20 ft. = d, to join the two parallel curves Ae and aG' with the re- versed curve AGG'. Required the /', ADD", and the /", D'D'G', to determine the length of the curve AG, and the length of the curve GG'. Find all the sides of the triangle DD'D" by the following method: The distance D'D" = R' + R" = 941.6 + 235.4 = 1177.0 = a, and D'D = R + d - R" = 1661.0 + 20. - 235.4 = 1445.6 = b, and DD' = R + R = 1661.0 + 941.6 = 2602.6 = c. Ma _i_ b _|_ C ) = 2612.6 = s. CURVE FORMULA AND PROBLEMS. Then calculate /' and /" by the following formulae: To find /'. Formula. sin 1' ($ a) (s c) n(s a} (s c) = 14356.0000 ac 306326.02J 122530408 Example. Quotient = .0046865101 6] 36 r- |_ i- sin |_ = Result, r/' = .06846 3 55' 30" 210295920 183795612 128 1086 1024 265003080 245060816 1364 6251 5456 /' = 7 51' 199422640 183795612 13686 1 79501 To find /". .Formula. . _ sin I'c 156270280 153163010__ 31072700" 30632602 44009SOO Example. T = 7 51' sin 0.13658 c = 2602.6 81948 27316 81948 27316 b "1355.4631 08 ["Result, sin I" = 1445.6 [28912 [^24589= 66343 57824 85191 72280 129110 115648 134628 CIVIL ENGINEER'S FIELD-BOOK. FROG PROBLEMS. ABBREVIATIONS. N = Frog number. D = Degree of curve. C = Chord, AC. F = Frog angle, HEG. L = Distance, JE. S = Length of switch-rail. R = Radius, AD. T Tangent, BA. I = Intersection, FBG. G = Gauge of track, JK. Problem 25. Given the frog measurements EN = 8.55 = a, and IIG 0.95 = b t to find the frog number N. Formula. Example. _a b ="| a ("Quotient. N ~ *" 0.95J8.55L9. 8.55 Problem 26. Given the frog measurements EN = 8.55 = a, and IIG 0.95 = &, to find the F, II KG. Formula. Example. F-- a =~H& = FQuotient, tan \F = ~ a 8. 55 JO. 4750 L. 05555 = 3 10' 47" 4275 4750 CURVE FORMULA AND PROBLEMS. 27 Problem 27. Given the frog number N, 9, to find Hie F t IIEG. Formula. Example. 0.50 N =~] ["Quotient, tan %F = N 9 J 0. 50 L 05555 = 3 10' 47" 45 50 Problem 28. Given the It, AD = 150.656, and the G, JK = 4.708, and the L, JE = 37.664, to find the F, IIEG. Formula. L tan F = Example. R \G =~| Z = ["Quotient, tan ^ = 148. 302 J 37.6640 L. 25397 = 14 15' 296604 800360 741510 588500 444906_ 1435940 1334718 1012220 28 CIVIL ENGINEER'S FIELD-BOOK. Problem 29. Given the R, AD = 150.656, and the F, HEG = 14 15', to find the C, AC. 'Formula. C = 211 sin $F. Example. 2R = 301.312 $F= 7 07' 30" sin 0.124035 1506560 903936 1205248 602624 301312 Product C = 37.373233920 Problem SO. Given the F, HKQ- = 14 15', and the It, AD = 150.656, and the G, JK = 4.708 to find the L, JE. Formula. L = (ll- i#) tan F. Example. E - |# = 148.302 F = 14 15' tan 0.25397 1038114 1334718 444906 741510 296604 Product L = 37.66425894 Problem 31 . Given the G, JK 4.708, and the frog number N~ = 4, to find the L, JE. Formula. Example. L = 2GN. 2G = 9.416 N= 4 Product L = 37.664 CURVE FORMULAE AND PROBLEMS. Problem 32. Given the L, JE = 37.664 to find the length of the switch- rail 8. Formula. Example. _ L ~~| L = ["Quotient. 8 = ~ 3 - 36 3.36J37.664L11.209 336 406 336 704 672 3200 The above formula is for a gauge of 4.708; for a three-foot gauge. S = - TO FIND THE TANGENT Oil RADIUS. To find the T, BA or BC, or the R, AD. The F, BEG = .FJW7 = 7. Then by Table I. T = R tan \I, and by Table II. R- TcotiL Problem 33. Given the R, AD = 762.696, and the G, JK - 4.708, to find the F, Q-K11 of the middle frog in a three-throw switch. Formula. vers F = 30 CIVIL ENGINEER'S FIELD-BOOK. Example. IQ) =-| G = ("Quotient, vers +F = 1530. 1J 4.7080 1_. 003076 = 4 29' 45" 45903 117700 107107 105930 Problem 34. Given the R, AD = 762.696, and the F, IIEG = 8 59' 30", to find the distance AE = I. Formula. I = It tan \F. Example. B = 762.696 $F = 4 29' 45" tan 0.078628 6101568 1525392 4576176 6101568 5338872 Product I = 59.9(5926 L088 Problem 35. To find the frog angle when the main track is curving in the same direction as the proposed turnout. Given the curve of the main track, AF = 5, and the curve of the turnout AL = 9 30'. Subtracting the lesser curve from CURVE FORMULA AND PROBLEMS. 31 the greater, we have a departure of 4 30', with a relative radius of 1273.57 = R '. Then given R 1 = 1273.57, and the G, JK = 4.708, to find the F, IIEG. Formula. Example. R' + Q =n G = ["Quotient, vers F = 1275. 924 J 4.708000 L 00368 = 4 55' 3827772 8802280 7655544 11467360 Problem 36. Given the R, AD' = 603.805, and the R'< AD = 1146.28, and the F t IIEG = 4 55', and the G, JK = 4.708, to find the chord AC= C. By the following method solve the required parts of the triangle EDD': The distance DD' = R - R = 1146.28 - 603.805 = 542.475 = a. The distance D'/S = 7? + \G = 603.805 + 2.354 = 606.159 = b. To find the angle EDD = I'. Formula. . T , b sin F b Example. = 606.159 = 4 55' sin 0.08571 a F 606159 4243113 3030795 4849272 a - 51.95388789 Result, sin /' = 542.475 j 4883275 |_.09577 = 529'44" 3131137 2712375 4187628 3797325 3903039 32 CIVIL ENGINEER S FIELD-BOOK. Then the angle AD' C = I' + F = 5 29' 44" + 4 55' = 10 24' 44" = /. By Table VI. C = 2It siii I/ = 109.58. Problem 37. To locate a frog when the main track is curving in a direc- tion opposite to that of the proposed turnout. Given the curve of the main track AF = 3, and the curve of the proposed turnout AL 9, and the G, JK = 4.708 Adding the lesser curve to the greater, we have a' departure of 12 with a relative radius of 478.339 = R'. To find the F t HEG. Formula. Example. $Q = n G = Pvers. F = 480.693 J 4.708000 L 00979 = 8 01' 30" 4326237 3817630 3364851 4527790 4326237 2015530 Then relatively the angle CD' A = 6 01' 08" = /. Then, given the R, AD' = 637.275, and the /, ADC = 6 01' 08", to find the chord A C = C. By Table VI. C = 2E sin \I = 66.91 CURVE FORMULAE AND PROBLEMS. M o W o . CO I! N Is ^- ^j 00 ^ QC OS c? ? ' 05 CIVIL ENGINEER'S FIELD-BOOK. TABLE IX. RIGHT TRIANGLES. TO FIND A. GIVEN. FORMULAE. GIVEN. FORMULAE. 5 6, c tan A - c, b cot A - c b 6, a S inA=l c, a cos A = - a TO FIND B. 6,c 6, a cot B - - cos J5 = - a c, 6 c, a tan B b sin B =.- a TO FIND a. A,b A,c 6 .B, 6 b ~ sin A ~ cos ^[ cos 1? c ~sin B TO FIND b. A,c A, a b = c tan ^4 6 = a sin ^l 5, a B, c b a cos J5 5 = c cot TO FIND c. A, a c = a cos .4 c = b cot ^4 B,a c = a sin 5 c = b tan 5 CURVE FORMULAE AND PROBLEMS. 35 TABLE X. OBLIQUE TRIANGLES. TO FIND a, ft, c. TO FIND A, B, C. GIVEN. FORMULAE. GIVEN. FORMULAE. A, ft, C A,B,c A,B,b a ft c ft sin C a, ft, C A, 6, c -4, a, ft sin^L sm sin C ft sin C sin A c sin A a c sin .4 sinB ft sin B ft a sin .4 sin .4 ft TO FIND A,B,C. GIVEN. FORMULA. a, c, s a, ft, s ft, c, s /(s - a) (s - c) an ^ |/ ac i p A* a ) ( s k) ^/ aft - in , c _ . As-b)(s- c) Y be 36 CIVIL ENGINEER'S FIELD-BOOK. TABLE XI. LONG CHORDS, DEFLECTIONS, AND ORDINATES. CURVE. LONG CHORDS. DEFLEC- TIONS. ORDI- NATES. 200 ft. 300 ft. 4OO ft. 500 ft. GOO ft. 599.733 700 ft. |j H go Chord. 25. 50. 1 199.992 299.970 399.924 499.848 699.574 .873 1.745 .164 .218 2 199.970 299.878 399.695 499.391 598.934 698.295 1.745 3.490 .327 .436 3 199.931 299.726 399.315 498.630 597.604 696.168 2.618 5.235 .491 .655 4 199.878 299.513 398.782 497.566 595 744 693.196 3.490 6.980 .655 .873 5 199.810 299.239 398.099 496.201 593.358 689.386 4.362 8.724 ,818 1.091 6 199.726 298.904 397.264 494.534 590.449 684.745 5.234 10.467 .982 1.309 7 199.627 298.509 396.278 492.568 587.021 679.285 6.105 12.210 1.146 1.528 8 199.513 298.054 395.142 490.306 583.081 673.015 6.976 13.951 1.310 1.746 9 199.383 297.538 393.857 487.749 578.633 665.950 7.846 15.692 1.474 1.965 10 199.239 296.962 392.424 484.900 573 686 658.105 8.716 17.431 1.638 2.183 11* 199.079 296.325 390.843 481.762 568.245 649.496 9.585 19.169 1.802 2.402 13 198.904 295.629 389.116 478.338 562.321 640.142 10.453 20.906 1.967 2.620 13 198.714 294.874 387.243 474.633 555.921 630.062 11.320 22.641 2.131 2.839 14 198.509 294.059 385.225 470.649 549.056 619 278 12.187 24.374 2.296 3.058 15 198.289 293.185 383.065 466.390 541.736 607.812 13.053 26.105 2.461 3.277 16 198054 292.252 380.763 461.862 533 972 595.688 13.917 27.835 2.625 3.496 17 197.803 291.261 37'8.320 457.069 525.776 582.933 14.781 29.562 2.791 3.716 18 197.538 290.211 375.739 452.015 517.160 569.571 15.643 31.287 2.956 3.935 19 197.256 289.104 373.021 446.706 508.139 555.634 16.505 33.010 3.121 4.155 30 196.962 287.939 370.167 441.147 498.724 541.147 17.365 34.730 3.287 4.374 CURVE FORMULA AND PROBLEMS. TABLE XII. RADII. 37 M Curve. 1 3 1 3 | 4 Curve. Curve. Curve. Curve. 5 Curve. 6 Curve. 7 Curve. 8 Curve, 9 Curve. O 5729.65 2864.93 1910.08 1432.69 1146.28 955.366 819.020 716.779 637.275 1 343775. 5635.72 2841.26 1899.53 1426. 74; 1142. 47 952.722 817.077 715.291 636.099 3 171887. 5544 83 2817.97 1889.09 1420.85 1138.69 950.093 815.144 713.810 634.928 3 114592. 5456.82 2795.06 1878.77 1415.01 1134.94 947.478 813.238 712.335 633.761 4 85943.7 5371.56 2772 53 1868.56 1409 21 1131.21 944.877 811.303 710.865 632.599 5 68754.9 5288.92 2750.35 1858.47 1403.46 1127.50 942.291 809.397 709.402 631.440 6 57295.8 5208 . 79 2728 . 52 1 848 . 48 1 397 . 76 1123.82 939 719 807.499 707.945 630.286 7 49110.7 5131.05 2707.04 1838.59 1392.10 1120.16 937.161 805.611 706.493 629.136 8 -12971.8 5055.59 2685.89 1828.82 1386.49 1116.52 934.616 803.731 705.048 627.991 9 38197.2 4982.332665.08^819.141380.92 1112.91 932.086 801.860 703.609 626.849 1O 34377.5 4911. is'2644. 58 1809.57 1375.40 1109.33 929.569 799.997 702.175 625.712 11 31252.3 4841.98 2624.39 1800.10 1369.92 1105.76 927.066 798.144 700.748 624.579 13 28647.8 4774.74 2604.51 1790.73 1364.49 1102.22 924.576 796.299 699.326 623.450 13 26444.2 4709 . 33 2584 . 93 1 781 . 45 1359 . 1 1098.70 922.100 794 462 697.910 622.325 14 24555.4 4645.69 2565.65 1772.27 1353.75 1095.20 J19.637 792.634 696.499 621.203 15 22918.3 4583.75 2546.64 1763.18 1348.45 1091.73 917.187 790.814 695.095 620.087 16 21485.9 4523.44 2527.92 1754.19 1343.15 1088.28 914.750 789.003 693.696 618.974 17 20222.1 4464.70 2509.47 1745 26 1337.65 1084.85 912.326 787.210 692.302 617.865 18 19098.6 4407.46 2491.29 1736.48 1332.77 1081.44 909.915 785.405 690.914 616.760 19 18093.4 4351.67 2473. 371727. 75 j 1327. 63 1078.05 907.517 783.618 689.532 615.660 30 17188.8 4297 . 28 2455 . 70 1 719 . 1.2 1322 . 53 1074.68 905.131 781.840 688.156 P.14.563 31 16370.2 4244.23 2438.29 1710.56 1317.46 1071.34 902.758 780.069 686.785 613.470 33 15626.1 4192.47 2421.12 1702.10 1312. 4311068.01 900.397 778.307 685.419 612.380 33 14946.7 4141.96 2404.19 1693.72 1307.45 1064.71 898.048 776.552 684.059 611.295 34 14323.6 4092.66 2387.50 1685.42 1302.50 1061.43 895.712 774.806 682.704 610.214 35 13751.04044.51 2371.04 1677.201297.58 1058.16 893.388 773.067 681.354 609.136 36 13222.113997.49 2354.80 1669.06 1292.71 1054.92 891.076 771.336 680.010 608.062 37 12732.4 3951.54 2338.78 1661.00 1287.87 1051.70 H88.776 769.613 678.671 606.992 38 12277.7 3906.54 2322.98 1653.01 1283.07 1048.48 886.488 767.897 677.338 605.926 39 11854.3 3862.74 2307.39 1645.11 1278.30 1045.31 884.211 766.190 676.008 604.864 3O 11459.2 3819.83 2292.01 1637.28 1273.57 1042.14 881 946 764.489 674.686 603.805 31 11089.6 3777.85 2276.84 1629.52 1268.87 1039.00 879.693 762.797 673.369 602.750 33 10743.0 3736.79 2261.86 1621.84 1264.21 1035.87 877.451 761.112 672 056 601.698 33 10417.5 3696.61 2247.08 1614.22 1259.58 1032.76 875.221 759.434 670.748 600.651 34 101 Il.li3o57. 29 '2232. 49 1606.68 1254.98 1029.67 873 002 757.764 669.446 599.607 35 9822 18 3618.802218.09 1599.21 1250.42 1026.60 S70.795 756.101 668.148 598.567 36 9549.34 3581 .10 2203.87 1591.81 1245.89 1023.55 868.598 754.445 666.856 597.530 37 9291.293544.19 2189.84 .1584.48 1241.40 1020.51 866.412 752.796 665.568 596.497 38 9046.75 3508.02 2175.98 1577.21 1236.94 1017.49 864 238 751.155 664.286 595.467 39 8814.78 3472.592162.30 1570.01 1232. 51 11014.50 8G2.0V5 749.521 663.008 594.441 j 40 8594.41 3437 . 87 2148 . 79 1562 . 88 1 228 . 1 1 ' 101 1 . 51 S59.922 747.894 661.736 593.419 41 8384.80 3403.83 2135 44 1555.81 1223.74 1008.55 857.780 746.274 660.468 592.400 43 8185.16 3370.46 2122.26 1548.80 1219.40 1005.60 855.648 744.661 659.20:. 591.384 43 7994.81:3337.74 2109.24 1541.86 1215.30 1002.67 853.527 743.055 657.947 590.372 44 78 1 3 . 1 1 3305 . 65 2096 39 1 534 . 98 1 2 10 . 82 999 . 762 851.417 741.456 656 694 589.364 45 7639 . 49 3274 . 1 7 2083 . 68 1 528 . 16 1 206 . 57 996 . 867 849.317 739.864 655.446 588 359 46 7473.42 3243.29 -,'071. 13 1521.40 1202.36 993.988 847.228 738.279 654.202 587.357 47 7314.41 3212.982058.73 1514.70 1198.17991.126 845.148 736.701 652.963 586.359 48 7162.03 3183.23 2046.48 1508.06 1194. 01 '988. 280 843.080 735.129651.729 585.364 49 7015.87 3154. 03!2034. 37 1501.48 1189.88 985.451 841.021 733.564 650.499 584.373 50 6875.55 3125.36 2022. 41 '1494.95 1185.78 982.638 838.972 732.005 649.274 583.385 51 6740.74 3097.20 2010.59 1488.481181.71 979.840 836.933 730.454648.054 582.400 53 66 1 1 . 12 3069 55 1 998 . 90 1482 . 07 1 1 77 . 66 977 . 060 834.904 728.909646.838 581.419 53 6486.38 3042.39 1987.35 1475.71 1173.65 974.294 832.885 727. 370 '645. 627 580.441 54 6366.263015.71 1915.93 1469. 41 '1169. 66 971.544 830.876 725 838644.420 579.466 55 6250.51 2989.48 1964.64 1463.16 1165.70 968.810 828.876 724 312643.218 578.494 56 6138.90 2963. 7 1 1953. 48 1456.96 1161.76 966.091 826.886 722.79*642.021 577.526 57 61 >31 . 20 2938 39 1 942 . 4 4 1450 . 8 1 1 1 57 . 85 903 . 387 824.905 721.280640.828 576.561 58 ! 5927. 2-2 2013.49 1931 .53 1444.72 1153.97 960.698 822.934 719.774639.639 575.599 59 58-.'G . 76 2889 . 01 | 1920 . 75, 1438 .68 1150. 1 1 958. 025 820.973 718.273638.455 574.641 CIVIL ENGINEER'S FIELD-BOOK. TABLE XII. RADII -Continued. M 10 Curve. 11 Curve. Curve 13 Curve. 14 Curve. 15 Curve. Curve. 17 Curve. 18 Curve. 19 Curve. o~ 573.686 521.671 478.339441.684 410.275 383 065 1359. 265 338. 273 319.623 302.943 1 572.734 520.885 477.678441.120 409 790 382 . 64 \ 358 . 893 337 . 945 319.330 302.680 2 571.784 520.100 477.018440.559 409. 306 382. 220 ! 358. 523 337.616 319.037 302.417 3 570.839 219.318 476 361 439.999 408.823 381. 799 1358.153 337 289 318.745 302.155 4 569.896 518.539 475.705 439.440 408.341 381.380357.784336.962 318.453 301.893 5 568.957 517.761 475.052 438.882 407.860 380.961 357.415 336.636 318.162 301.632 6 568.020 516.986 474.400 438.326 407.380 380.543357.048336.310 317.871 301.371 7 567.087 516.214 473.750 437.772 406.902 380.125356.681 335.985 317.581 301.111 8 566.156 515.443 473.102 437.219 406.424 379 . 709 356 . 31 5 335 . 660 317. 292 300.851 9 565.229 514.675 472.455 436.667 405.948 379.294355.950 335.337 317.003 300.592 10 564.305 513.909 471.810 436.117 405.473 378.880355.585 335.013 316.715 300.333 11 563.384 513.146 471.167 435 568 404.998 378.466355.222 334. 691 1316. 427 300.074 12 13 562.466 561.551 512.385 511.626 470.526 469 887 435.020 434.474 404.526 404.055 378 . 054 ; 354 . 859 334 . 369 1 3 1 6 . 1 39 377.642 351 496 334.048 315.853 299.816 299.559 14 560.638 510.869 469.249 433 929 403.583 377.231 354.135 333.727 315.566 299.302 15 559.729 510.115 4G8.613 433.385 403.114 376.821 353.774333.407 315.281 299.045 16 558.823 509 363 467.978 432.844 402.645 376.412 8:8.414 333.088 314.993 298.789 17 557.920 508.613 467.346 432.300 402.178 376.004 353. 054 1332. 769 314.711 298.533 18 557.019 507.865 466 715 431.764 401.712 375.597 352.696 332.451 314 426 298 278 19 556.122 507.120 466.086 431.226 401.246 375.191 352.338 332.133 314.143 298.023 20 555.227 506.376 465.459 430.690 400.782 374.786351.981 331.816313.860 297.768 21 554.336 505.635 464.833:430.154 400.319 374.381 351, 625 331 . 500 313.577 297.514 22 553.447 504.896464.209429.620 399 857 373.977351.269 331.184313.295 297.260 23 552.561 504.159463.586429.088 399.396 373 575350.914 330.869313.013 297.007 24 551.678 503.425 462.966428.557 398 . 937 373 . 1 73 350 . 560 330 . 555 31 2 . 732 296.755 25 550.800 502 692 462.347428.026 398.4781372.772 350.207 330.241 312.452 296.502 26 549.920 501.962461.729427.498 398.020372.372 349.854 329.928 312.172 296.250 27 549.046 501.233461.114426.971 397.564 371.972 349. 502:329. 615 311. 892 295.999 28 548.174 500.507 460.500426.445 397.108 371.574 349.150329.303 311.613 295.748 29 547.305 499.783 459.887425.920 396.653 371.176 348.800 328.991 311.335 295.497 30 546.438 499.061 459.276 425 396 396.200 370.780 348.450 328.689 311 056 295.247 31 545.575 498.342 458.667424.874 395.747 370.384 348.101 328.370 310.779 294 998 32 544.714 497.624 458.060424.354 395.296 369.989 347.752328.061 310.502 294.748 33 543.856 496 908 457.454423.834 394.841 369.595 347.405327.751 310.225 294.500 34 543 001 496.195 456.850423.316 394.396 369.202 347.057 327.443309.949 294 251 35 542.148 495.483 4. r ;6.247422.799 393.948 368.809 346. 71 li 327. 135 309 614 294.003 36 541 298 494.774 455.646422 283 393.501 368.418 346 365 326.828 309.399 293 756 37 540.451 494.066 455.047421.769 393.054 368 027 346.021 326.521 309.124 293.509 38 539.606 493.361 454.449421.256 392.609 367.637 845,676 326.215 308.850 293.262 39 538.764 492.657 453.853420.743392.165 367.248 345.333 325.909 308.577 293.015 40 537.924 49! .956 453.259420.233:391.722 366.859 344.990325.604 303 303 292.770 41 537.088 491.257 452.664 419.723 391.280 366.472:344.647 325 530308.031 292.524 43 536.253 490.559 452.073:419.215 390.838 366.0851344.306 324.996:307.759 292.279 43 44 535.422 534.593 489.864 489.171 451.482418.708 450.894 418 203 390.398 389.959 365 . 691 343 . 965 324 . 692 307 . 487 365 .315343. 625 324 . 390 307 .216 292.034 291.790 45 533.767 488.479 450.307417.698 389.521 364.931 343.285 324.088306.945 291.546 46 532.943 487.790 449.722417.195 389.084 364 547 342.947 323.786306.675 291.303 47 532.120 487.103 449.138416.693 388.647 364.165 342.609 323.485306.405 291.060 48 531.303 486.417 448.556416.192 388.212363.783 342.271 323.184 306.136 290.818 49 530.487 485.733 447.975415.692 387.778363.402 341.934 322.885305.868 290.575 50 529.673 485.051 447.395j415.194 387.34.' 3G3.022 341.598 322.585 305 599 290.334 51 528.862 484.372 446 818414.697 386.912 362.643341.263 322.237 305.332 290.092 5*3 528.053 483.694 446.241 414.201 386.481 362.264 340.928 821.989:305.064 289.851 53 527.247 483.018 445.666 413.706386.050 361.887 340 594 321. 691 1304 797 289.611 54 526.443 482.344 445.093 413.212385 621 361.510 340. 2GO 321.394304.531 289.371 55 525.642 481.671 444.521 412.720385.193 361.134 339.928 321.097:304.265 289.131 56 524.843 481.001 443.951 412.229384.765 360.758339.595 320.801 304.000 288.892 57 524.046 480.333 443.382 411.739384.339 360. 384! 339 265 320.506303.735 288.653 58 523.252 479.666 442 814 411.250383.913 360.010338.933 320.211 303.470 288.414 59 522.461 479.001 442.248 410.762383.488 359.637338.603 319.916 303.206 288.176 CURVE FORMULAE AND PROBLEMS. 39 TABLE XIII. GRADES. Grade per 100 ft. Rise per Mile. Grade per 100 ft. Rise per Mile. Grade per 100 ft. Rise Mite. Grade per 100 ft. Rise per Mile. .05 2.640 .59 31.152 1.13 59 664 1.67 88.176 .06 8.168 .60 31.680 1.14 60.192 1.68 88.704 .07 3.696 .61 32.208 1.15 60.720 1.69 89.232 .08 4.224 .62 32.736 1.16 61.248 1.70 89.760 .09 4.752 .63 33.264 17 61.776 1.71 90.288 .10 5.280 i .64 33 792 .18 62.304 1.72 90.816 .11 5.808 .65 34.320 .19 62.832 1.73 91.344 .12 6.336 .66 34.848 .20 63.360 1.74 91.872 ,w 6.864 .67 35 376 .21 63 888 1.75 92.400 .14 7.392 .68 35.904 .22 64.416 1.76 92.928 .15 7.920 ! .69 36.432 .23 64.944 1.77 93.456 .16 8.448 | .70 36.960 24 65.472 1 78 93.984 .17 8.976 j .71 37.488 .25 6G.OOO 1.79 94.512 .18 9.504 .72 38.016 .26 66.528 1.80 95.040 .19 10.032 .73 38.544 .27 67.056 1.81 95.568 .20 10 560 74 39 072 .28 67.584 1.82 96 096 .21 11.088 .75 39.600 .29 68.112 1.83 96 624 .22 11.616 .70 40.128 .30 68.640 1.84 97.152 !23 12.144 .77 40.656 31 69 168 1 85 97.680 .24 12.672 .78 41.184 32 69.696 1.86 98.208 .25 13 200 .79 41.712 33 70.224 1.87 98.736 .26 13.728 .80 42.240 .31 70.752 1.88 99.264 .27 14 256 .81 42.768 35 71.280 1.89 99.792 .28 14.784 .8-3 43.296 .36 71.803 1.90 100.320 .29 15.312 .83 43.824 .37 72.333 1.91 100.848 .30 15.840 ! .81 44.352 38 72.864 1.92 101.376 .31 16.368 1 .85 44.880 .39 73.392 1.93 101.904 .32 16 896 .86 45.408 .40 73.92) 1.94 102.432 .33 17.421 .87 45.936 .41 74.448 1.95 102.960 .34 17.952 .88 46.464 .42 74.976 1.96 103.488 .35 18.480 .89 46.992 .43 75.504 1.97 104.016 .36 19.008 .90 47.520 1 .44 76.032 1 98 104.514 .37 19.536 .91 48.048 .45 76.560 1.99 105.072 .38 20.064 .92 48.576 .46 77.088 2 oa 105.600 .39 20.592 .93 49.104 .47 77.616 2.10 110.880 .40 21.120 .94 49.632 .48 78.144 2.20 116.160 .41 21.648 .95 50.160 .49 78.672 2.30 121.440 .42 22 176 .96 50.688 .50 79 200 2.40 126.720 .43 22.704 .97 51.216 .51 79.728 2.50 132 000 .44 23.232 .98 51.744 .52 80.256 2.60 137.280 .45 23.760 .99 52.272 .53 80 784 2.70 142.560 .46 24.288 .00 52.800 .54 81.312 2.80 147.840 .47 24.816 .01 53.328 .55 81.840 2.90 153 120 .48 25.344 .02 53.856 .56 82.3(38 3.00 158.400 .49 25 872 .03 54.384 .57 82.896 3.10 163.6SO .50 26.400 .04 54.912 .58 83.424 3.20 168.960 .51 26.928 .05 55.440 59 83.952 3.30 174.240 .52 27.456 .06 55.968 .60 84.480 3.40 179.520 .53 27.984 .07 56.496 .61 85.008 3.50 184.800 .54 28.512 .08 57.024 .62 85.536 3.60 190.0SO .55 29.040 .09 57.552 63 86 064 3.70 195.360 .56 29.568 .10 58.080 .64 86 592 3.80 200.640 .57 30.096 1 11 58.608 .65 87.120 3.90 205.920 .58 30.624 1.12 59.136 .66 87.648 4.00 211.200 40 CIVIL ENGINEER'S FIELD-BOOK. EXPLANATION OF TABLE XIV. MINUTES EXPRESSED IN DECIMALS. In the third column, under the heading of " 1 Curve, Arc," will be found the minutes given in the first column under **0," expressed in decimals of a degree, by simply putting the decimal point two places to the left. For example: 6' = .10 and 54' = .90 Proof: 6' + 54' = 1, and .10 + .90 = 1.00 - 1. In like manner all arcs to a one degree curve are expressions of their intersections decimally. TO FIND THE TANGENT. Given the /, FBC 42 38', and the degree of curve AC = 5, to find the T, BA and BC. Find the number corresponding to the number of whole degrees in the given /, at the top of the left or right hand column, after which descend the column until the correspond- ing minutes in the given I is reached, then on the same line to the right or left under the heading " 5 Curve, Tan.," will be found the required T = 447.301 Problem 38. Given the /, FBC = 24 50', and the degree of curve AC ~ 4 12', to find the l\ BA and BC. Select the tan. to the given / from the curve column corre- CURVE FORMULAE AND PROBLEMS. 41 spending to the number of whole degrees in the given curve. Multiply this by the number of whole degrees in the given curve, and divide the product by the given curve expressed decimally. Example. 1= 24 50'. 4 Curve, Tan. = 315.435 Number of whole degrees = 4 Given curve = 4 12' = 4.20 1261.740 1260 ^Result, T 1740 1680 600 TO FIND THE ARC. Given the /, FBO = 56 40', and the degree of curve AC = 9, to find the A, AfabcC. Find the number corresponding to the number of whole de- grees in the given /at the top of the left or right hand column, after which descend the column until the corresponding minutes in the given 1 is reached, then on the same line to the right or left under the heading " 9 Curve, Arc" will be found the required A = 629.630 Problem 39. Given the /, FBG = 96 18', and the degree of curve AC = 2 15', to find the A, AfabcC. To the number of whole degrees in the given J affix the fractional part expressed decimally; also to the number of whole degrees in the given curve affix the fractional part ex- pressed decimally, and divide the former by the latter. The quotient will be the required A. Example. Given curve =~] J = 96 18' ("Quotient, A = en curve =~"| 3 15' = 2.25J 2 15' = 2.25 J 96.30 [J2.SQ = 4280 ft. 900 630 450 1800 42 CIVIL ENGINEERS FIELD-BOOK. TO FIND THE SUB-DEFLECTION. Given the c, Af = 90 ft., and the degree of curve AC = 5, to find the d, BAf. Take half the given c 45, and find the number correspond- ing to it in the column headed " 5 Curve, Arc." Then in the upper right or left hand corner of the table will be found the degrees, beneath which on a line with the corresponding num- ber will be found the minutes of the required d. Thus the d, BAf = 2 15'. Problem 4O. Given the C, Af = 60 ft., and the degree of curve AC = 4 30', to find the d, BAf. Multiply the degree of the given curve expressed decimally by half the given c, and find the number corresponding to it in the column headed "1 Curve, Arc." Then in the top right or left hand corner of the table will be found the degrees beneath which on a line with the corresponding number will be found the minutes of the required d. Example. Given curve 4 30' = 4.5 |c = 30 Product 135.0 = l21' = d. TO FIND THE INTERSECTION. GIVEN THE CURVE AND ARC. Given the degree of the curve AC 10, and the A, AfabcG = 485.000, to find the /, FBG. Find the number corresponding to the given A in the column headed "10 Curve, Arc." Then in the upper right or left hand corner of the table will be found the degrees, be- neath which on a line with the corresponding number will be found the minutes of the required / = 48 30', CURVE FORMULAE AK I) PROBLEMS. 43 GIVEN THE CURVE AND TANGENT. Given the degree of the curve AC = 7, and the T, BA and BC 171.601, to find the 7, FBG. Find the number corresponding to the given Tin the column headed "7 Curve, Tan." Then in the upper right or left hand corner of the table will be found the degrees, beneath which on a line witL the corresponding number will be found the minutes of the required I = 23 40'. TO FIND THE DEGREE OF CURVE. GtVEN THE INTERSECTION AND TANGENT. Given the /, FBC= 37 33', and the T, BA and BG= 195.02, to find the degree of the curve AC. Find .the number corresponding to the number of whole degrees in the given / at the top of the left or right hand column, after which descend the column until the correspond- ing minutes in the given / is reached; then on the same -line to the right or left seek a number under the heading ''Tan." corresponding to the given T\ at the top of the column in which the corresponding number is found will be found the required degree of curve = 10. GIVEN THE INTERSECTION AND ARC. Given the /, FBC 42 18', and the A, AfabcC= 528.750, to find the degree of the curve AC. Find the number corresponding to the number of whole degrees in the given /at the top of the left or right hand col- umn, after which descend the column until the corresponding minutes in the given /is reached; then on the same line to the right or left seek a number under the heading " Arc" corre- sponding to the given A ; at the top of the column in which the corresponding number is found will be found the required degree of curve = 8. TABLE XIV. ACTUAL TANGENTS, AND ARCS EXPRESSED IN CHORDS OF 100 FEET FOR EVERY MINUTE OF INTERSECTION, FROM TO 90, FROM A 1 CURVE TO A 10 CURVE, INCLUSIVE. TABLE XIV. ACTUAL TANGENTS, ETC. M. 1 Curve. 3 Curve. 3 Curve. 4 Curve. 5 Curve. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. 1 .830799 1.66667 .415415 .833333 .276962 .555556 .207740 .416667 .166211 .333333 2 1.66160 3.33333 . 830830 1.6666? .553923 1.11111 .415480 .833333 .332421 .600007 3 2.49240 5.00000 1.24624 2.50000 .830885 1.66667 .623220 1.25000 .498032 1.00000 4 3.32320 6.66667 1.66166 3.33333 1.10785 2.22222 .830960 1.66607 .664842 1.33:J33 5 4.15400 8.33333 2.07707 4.16667 1.38481 2.777781.0:3870 2.08333 .83105:3 1 . 60007 6 4.98480 10.0000 2.49249 5.00000 1.66177 3 333331.24644 2.50000 . 997264 2.00000 7 5.81559 11.6667 2.90790 5.83:333 1.93873 3.888891.45418 2.91667 1.16347 2.33:333 8 6.64639 13.3333 3.32332 6.66667 2.21569 4.44444 1.60192 3.33333 1.32968 2.60007 9 7.47719 15.000(3 3.73873 7.50000 2.49265 5.00000 1.80900 3.75000 1.49590 3.00000 10 18.30799 16.6667 4.15415 8.33333 2.7G962 5.55556 2 07740 4.16667 1.66211 3.33333 11 9.16744 18.. 3333 4.58389 9.16667 3.05613 6.11111 2.29230 4.58333 1.83405 3.66667 13 10.0269 20.0000 5.01363 10.0000 3.34264 6.66667 2.50721 5.00000 2.00599 4.00000 13 10.8577 21.6667 5.42904 10.&333 3.61960 7.222222.71495 5.41667 2.17220 4.33:333 14 11.6885 23.3333 5.84446 11.6667 3.89656 7.777782.92269 5.83333 2.3:3841 4.66607 15 12 5193 25.0000 6.25987 12.5000 4.17352 8.333333.13043 6.25000 2.50462 5.00000 16 is.asoi 26.6667 6.67529 13.33J33 4.45049 8. 88889 '3. 3381 7 6.66067 2.67083 5.333:33 17 14 '.1809 28.3:333 7.09070 14.1667 4 72745 9.44444 3.54591 7.083:33 2.83704 5 C0667 18 15.0117 30.0000 7.50612 15.0000 5.00441 10.00003 75365 7.50000 3.00325 6.00000 19 15.8425 31.6667 7.92153 15.8333 5.28137 10.55563.96139 7.91667 3.16946 6.33333 2O 16.6733 a3. 3333 8.33695 16.6667 5.55833 11.11114.16913 8.33a33 3.33567 6.66667 21 17.5041 35.0000 8.75236 17.5000 5.83529 11.6667 4.37687 8.75000 3.50189 7.00000 22 18.a349 36.6667 9.16778 18.3333 6.11226 12.22224.58461 9.16667 3.66810 7.33333 23 19.1657 38.333:3 9.58319 19.1667 6.38922 12.77784.79235 9.58333 3.83431 7.66067 24 19.9965 40.0000 9.99861 20.0000 6.66618 13.33335.00009 10.0000 4.00052 8.00000 25 20.8273 41.6667 10.4140 20.8333 6.94314 13.88895.20783 10.4167 4.16673 8.33333 26 21.6581 43.33-13 10.8294 21.6667 7.22010 14.44445.41557 10.8333 4.33294 8.66607 27 22.4889 45.0000 11.2449 22.5000 7.49706 15.00005.62331 11.2500 4.49915 9.00000 28 23.3197 46.6667 11.6603 23.a333 7.77403 15.5556 5.83105 11.6667 4 66536 9.33333 29 24.1505 48.3333 12.0757 24.1667 8.05099 16.1111 6.0:3879 12.0833 4.83157 9.66667 30 24.9813 50.0000 12.4911 25.0000 8.32795 16.6667 6.24653 12.5000 4.99778 10.0000 31 25.8121 51.6667 12.9065 25.8333 8.60491 17.2222 6.45427 12.9167 5.16399 10.3333 33 26 6429 53.3333 13.3219 26.6667 8.88187 17.7778 6 66201 13.3333 5.3:3020 10.6667 33 27.5023 55.0000 13.7517 27.5HOO 9.16S38 18.33-336.87691 13.7500 5.50214 11.0000 34 28.3618 56.6667 14.1814 28.3333 J. 45 490 18.88897.09182 14.1667 5.67409 11.3333 35 29.1926 58.3333 14.5968 29.1667 9.73186 19.4444 7.29956 14 5833 5.84030 11.6667 36 30.0234 60.0000 15.0122 30.0000 10.0088 20.0000 7.50730 15.0000 6.00651 12 0000 37 30.8542 61.6667 15.4276 30.8333 10.2858 20.55567.71504 15.4167 6.17272 12.3333 38 39 31.6850 32.5158 63.3333 65.0000 15.8431 16.2585 31.6667 32.5000 10 5627 10.8397 21.1111 7.92278 21.66678.13052 15.8333 16.2500 6 33893 6.50514 12.6667 13.0000 4O 33.3466 66.6667 16.6739 33.3333 11.1167 22.22228.33826 16.6667 6.67135 13.3:333 41 34.1774 68.3333 17.0893 34.1667 11.3936 22.7778 8.54600 17.0833 6.83756 13.6667 43 35.0082 70.0000 17.5047 a5.oooo 11.6706 23.33338.75374 17.5000 7.00377 14.0000 43 35.8390 71.6667 17.9201 35.8333 11 9476 23.88898.96148 17.9167 7.16998 14.3333 44 36.6698 73 33:33 18.3356 36.6667 12.2245 24.44449.16922 18.3333 7.33619 14.6667 45 37.5006 75.0000 18.7510 37.5000 12.5015 25.0000,9.37096 18.7500 7.50240 15.0000 46 38.3314 76.6667 19.1664 38 3333 12.7784 25.55569.58470 19.1667 7.66861 15.3333 47 39.1622 78.3333 19.5818 39.1667 13.0554 26.1111 9.79244 19.5833 7.83482 15.6607 48 139.9930 80.0000 19.9972 40.0000 13 3324 26.6667110.0002 20.0000 8.00103 16.0000 49 40.8238 81.6667 20 4126 40.8333 13 6093 27.222210.2079 20.4167 8.16725 16.3333 5O 41.6546 83.3333 20.8280 41.6667 13.8863 27.777810.4157 20.8333 8.33346 16.6667 51 42 4&54 85.0000 21.2435 42.5000 14.1632 28.3333 10.6234 21.2500 8.49967 17.0000 53 43.3162 86.6667 21.6589 43.3333 14.4402 28. 8889! 10. 8311 21.6667 8.66588 17.3333 53 144.1470 88.3:333 22.0743 44 1667 14.717229 4444) 11. 0389 22.0833 8.83209 17 6667 54 ! 44 9778 90.0000 22.4897 45 0000 14. 9941 ! 30. 0000 11. 2466 22.5000 8.99830 18.0000 55 45.837291.6667 22.9194 45.8333 15.280630.555611.4615 22.9167 9.17024 18.3:333 56 46.696693.3338 23.3492 46.6667 15.5672 31.1111 11 6764 23.3333 9.34218 18.6007 57 : 47. 5274 ! 95. 0000 23.7646 47.5000 15.8441 31 6667 11. 8842 123.7500 9.50839 19.0000 58 48.3582,96.6667 24.180048.3333 16. 1211 132. 2222 12.0919 24.1667 9.07400 19.33:33 59 49.1890,98.3333 24.5954 49.1667 16. 3980,32.77781 12. 2996 24.58:33 9.84081119.6667 46 TABLE XIV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 Curve. 1O Curve. O M. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. .138529 .277778 .118758 .238095 .103933 208333 .092404 .185185 .083185 .166667 1 .27705? .555556 .237516 .476190 .207866 .416667 .184808 .370370 .166370 .333333 2 .415580 .833333 .356274 .714285 .311799 .625000 .277212 .555556 .249555 .500000 3 .554115 1.11111 .475032 .952380 .415732 .833333 369617 .740741 .332740 .666667 4 .692643 1.38889 .593789 1.19048 .519666 .04167 .462021 .925926 .415925 .833333 5 .831172 1.66667 .712547 1 .42856 .623599 .25000 .554425 1.11111 .499110 1.00000 6 ,969701 1.94444 .831305 1.66667 .727532 .45833 .646829 1.29630 .582295 1.16667 7 1.10823 2.22222 .950063 1.90476 .831465 .66667 .739233 1.48148 .665480 1.33333 8 1.24676 2.500001.06882 2.14286 .935398 .87500 .831637 1.66667 .748665 1.50000 9 1.38529 2.77778 1.18758 2.38095 1.03933 2.08333 .924041 1.85185 .831851 1.66667 10 1.52859 3.05556 1.31043 2.61905 1.14685 2.29167 1.01963 2.03704 .917904 1.83333 11 1.67190 3. 33333 1 1.43329 2.85714 1.2543? 2.50000 1.11522 2.22222 1.00396 2.00000 12 1.81043 3.61111 1.55204 3.09524 1.35830 2.70833 1.20763 2.40741 1.08714 2.16667 13 1.94895 3.88889 1.67080 3.33333 1.46223 2.91667 1.30003 2.59259 1.17033 2.33333 14 2.08748 4.16667 1.78956 3. 57143 1.56616 3.12500 1.39243 2.77778 1.25351 2.50000 15 2.22601 4.44444 1.90832 3.80952 1.67010 3.33333 1.48484 2.96296 1.33670 2.6666? 16 2.36454 4.72222 2.02707 4.04762 1.77403 3.54167 1.57724 3.14815 1.41988 2.83333 17 2.50307 5.00000 2.14583 4.28556 1 .87796 3.75000 1.66905 3.33333 1.50307 3.00000 18 2.64160 5.27778 2.26459 4.52381 1.981903.95833 1.76205 3.51&52 1 .58625 3.16667 19 2.78013 S. 55556 2.38335 4.70190 2.08583 4.16667 1.85446 3.70370 1.66944 3.33333 20 2.91866 5.83333 2.50211 5.00000 2.18976 4.37500 1.94686 3.88889 1.75262 3.50000 21 305718 6.11111 2.62086 5.23810 2 293704.58333 2.03920 4.07407 1.83581 3.66667 22 3.19571 6.38889 2.73962 5.47619 2.39763 4.79167 g. 13167 4.25926 1.91899 3.83333 23 3.33424 6.6666? 2.85838 5.71429 2.50156 5.00000 2.2240? 4.44444 2.00218 4.00000 24 3.47277 6.94444 2.97714 5.95238 2.60550|5 20833 2.31648 4.62963 2.08536 4.1666? 25 3.61130 7.22222 3.09590 6.19048 2.709435.416(7 2.40888 4.81481 2.16855 4.33333 26 3.74983 7.50000 3.21465 6.42856 2.81336 5.62500 2.50128 5.00000 2.25173 4.50000 27 3.88836 7.77778 3.33341 6.6666? 2.917295.83333 2.59369 5.18518 2.33492 4.66667 28 4.02688 8.05556 3.45217 6.90476 3.021236.04167 2.68609 5.37037 2.41810 4.83333 29 4.16541 8.33333 3.57093 7.14286 3. 12516 6.25000 2.77850 5.55556 2.50129 5.00000 3O 4.30394 8.61111 3.68969 7.38095 3.22909 6.45833 2.87090 5.74074 2.58447 5.16667 31 4.44247 8.88889 3.80844 7.61905 3.33303 6.66667 2.96331 5.92593 2.66766 5.33333 32 4.58578 9.16667 3.93130 7.85714 3.44054 6.87500 3.05890 6.11111 2.75371 5.50000 33 4.72908 9.44444 4.05415 8.09524 3,54806 7.08333 3.15449 6.29630 2.83977 5.6666? 34 4.86761 9.72222 4.17291 8.33333 3.65199 7.29167 3.24689 6.48148 2.92295 5.83333 35 5.00614 10.0000 4.29166 8.57143 3.75593 7.50000 3.33929 6.66667 3.00614 6.00000 36 5.14467 10.2778 4.41042 8.80952 3.85986 7.70833 3.43170 6.&5185 3.08932 6.16667 37 5.28320 10.5556 4.52918 9.04762 3.96379 7.91667 3.52410 7.03704 3.17251 6.33333 38 5.42172 10.8333 4.64794 9.28556 4.0677'3 8.12500 3.61651 7.22222 3.25569 6.50000 39 5.56025 11.1111 4.76670 9.52381 4.17166 8.33333 3.70891 7.40741 3.33888 6.66667 4O 5.69878 11.3889 4.88545 9.76190 4.27559 8.54167 3.80132 7.59259 3.42206 6.83333 41 5.83731 11.6667 5.00421 10.0000 4.37953 8.75000 3.89372 7.77778 3.50525 7.00000 42 5.97584 11.9444 5.12297 10.2381 4.48346 8.95833 3.98612 7.96296 3.58843 7.16667 43 6.11437 12.2222 5.24173 10.4762 4.58739 9.1666? 4.07853 8.14815 3.67162 7.33333 44 6.25290 12.5000 5.36049 10.7143 4.69133 9.37500 4.17093 8.3&S33 3.75480 7.50000 45 6.39143 12.7778 5.47924 10.9524 4.79526 9.58333 4.26334 8.51852 3.83799 7.6666? 46 6.52995 13.05565.59800 11.1905 4.8991919.79167 4.35574 8 70370 3.92117 7.83333 47 6.66848 13. 3333 ! 5. 716 ,"6 11.4286 5.00312 10.0000 4.44814 8.88889 4.00436 8.00000 48 6.80701 13.6111 5.83552 11.6667 5.10706 10.2083 4.54055 9.07407 4.08754 8.16667 49 6.94554 13.8889 5.95428 11.9048 5.21099 10.4167 4.63295 9.25926 4.17073 8.33333 5O 7.08407 14.1667 6.07303 12.1429 5.31492 10.6250 4.72536 9.44444 4.25391 8.50000 51 7.22260 14.44446.19179 12.3810 5.41886 10.8333 4.81776 9.62963 4.33710 8.60667 52 7.36113 14.72226.31055 12.6191 5.52279 11.0417 4.91017 9.81481 4.42028 8.83333 53 7.49965 15.00006.42931 12.8571 5.62672 11.2500 5.00257 10.0000 4.5034? 9.00000 54 7.64296 15.27786.55216 13.0952 5.73424 11.4583 5.09816 10.1852 4.58952 9.1066? 55 7.78627 15.55566.67501 13.3333 5.S417'611.666? 5.19375 10.3704 4. 67557 9.33333 56 7.92479 15. 8333 '6. 79377 13.5714 5.9456911.8750 5.28615 10.5556 4.75876 9.50000 57 8. 06&321 16. 1111:6. 91253 13.8095 6.04962 12.0833 5.37856 10.7407 4.84194 9.66067 58 8.20185 16.3889:7.03129 14.0476 6.15356 12. 291715. 47096 10.9259 4.92513 9.83333, 59 TABLE XIV. ACTUAL TANGEKTS, ETC. 1 1 Curve. 2 Curve. 3 Curve. 4 Curve. 5 Curve. M. Tan. Arc. Tan. Arc. 50.0000 Tan. Arc. Tan. Arc. 25.0000 Tan. Arc. O 50.0198 100.00025.0108 16.6750 33.3333 12.5074 10.0070 20.0000 1 50.8500 101.667 25.4263 50.8333 16.9520! 33. 8889 12.7151 25.4167 10.173220.3333 2 51.6814 103.333 25.8417 51.6667 17.2289134.4444 12.9229 2.'). 8333 10. 3394 20.6667 3 52.5122105.000'26.2571 52.5000 17.5059:35.0000 13.1306 26.2500 10.5057 21.0000 4 53.3130 106.667 26.6725 53.3333 17.782835.5556 13.3383 26.666710.6719 21.3333 5 54.1738 108.333 27.0879 54.1667 18.059836.1111 13.5461 27.0833 10.83S1 21.6667 6 55.0046illO.000 27.50:33 55.0000 18.3368 36.6667 13.7538 27.5000 11.0013 22.0000 7 55.8354111.667 27.9187 55.8333 18.613737.2222 13.9616 27.9167 11.1705 22.3333 8 56.6662 113.333 28.3342 56.6667 18.8907 37.7778 14.1693 28.3333 11.3367 22.6667 9 57.4970 115.000 28.7496 57.5000 19.1677 38.3333 14.3770 28.7500 11.5029 23.0000 10 58.3278 116.667 29.1650 58.3333 19.4446 38.8889 14.584829.1667 11.6691 23 3333 11 59.1586 118.333 29.5804 59.1667 19.7216 39.4444 14.792529.5S33 11.835323.6667 18 59 . 9894 i 1 20 . 000 29 . 9958 60.0000 19.9985 40.0000 15.000330.0000 12.0016! 24. 0000 13 60.8202 121.667 30.4112 60.8333 20.2755 40.5556 15.2080 80.4167 12.167824.3333 14 61.6510 123.33330.8266 61.6667 20.5525 41.1111 15.4157 30.8333 12.3340 24.6667 15 62.4818 125.000 31.2421 62.5000 20.8294 41.6667 15.6235 31.2500 12.5002 25.0000 16 63.3126 1 26. 667 ! 31. 6575 63.3333 21.1064 42.2222 15.8312 31.6667 12.6664 25.3333 17 64.1721 128.333 32.0872 64.1667 21.3929 42.7778 16.0461 32.0833 12.8383 25.6667 18 65.0315 130.000 32.5170 65.00JO 21.6794 43.3333 16.2610 32.5000 13.0103 26.0000 19 65.8623 131.667 32.9324 65.8333 21.9564 43.8889 16.4688 32.9167 13.1765 26.3333 30 66.6931 133.333 33.3478 66.6667 22.2333 44.4444 16.6765 33.3333 13.3427 26.6667 21 67.5239 135.000 33.7632 67.5000 22.5103 45.0000 16.884--J 33.7500 13.5089 27.0000 22 68.3547 136. 667134.1786 68.3333 22.7873 45.5556 17.0920 34.1667 13.6751 27.3333 23 69.1855 138. 333 '34. 59 10 69.1667 23.0642 46.1111 17.2997 34.5833 13.8413 27.6667 24 70.0163 140.00035.0094 70.0000 23.3412 46.6667 17.5075 35.0000 14.0075 28.0000 25 70.8471 141'. 667 3.-). 4249 70.8333 23.6181 47.2222 17.7152 35.4167 14.1738 8. 3333 36 71.6779 143.33335.8403 71.6667 23.8951 47.7778 17.9230 35.8333 14.3400 28.6667 21 72.5087 145.00036.2557 72.5000 24.1721 48.3333 18.1307 36.2500 14.5062 29.00CO 28 73.3395 146.667 36.6711 73.3333 24.4490 48.8889 18.3384 36.6667 14.6724 29.3333 29 74.1703 148.333 37.0865 74.1667 24.7260 49.4144 18.5462 37.0833 14.8386 29.6667 30 75.0011 150.000 37.5019 75.0000 25.0029 50.0000 18.7539 37.5000 15.0048 30.0000 31 75.8319 151. 667 3 r. 91 73 75.8333 25.2799 50.5556 18.961737.9167 15.171030.8333 32 76.6627 1 53. 333 ; 33. 3328 76.6667 25.5569 51.1111 19.1694 38.3333 15.3372 30.6667 33 77.4935 155.00038.7482 77.5000 25.8338 51.6667 19.3771 38.7500 15.5034 31.0000 34 78.3243 156.667 39.1636 78.3333 26.1108 52.2222 19.5849 39 1667 15.6696 31.3333 35 36 79.1551 79.9859 158.33339.5790 160.00039.9944 79.1667 80.0000 26.3878 26.6647 52.7778 53.3333 19.7926 20.0004 39.583315.8359 40.000016.0021 31.6667 32.0000 37 80.8167 161.66740.4098 80.8333 26.9417 53.8889 20.2081 40.416716.1683 32.3333 38 81.6475 163.333 40.8253 81.6667 27.2186 54.4444 20.4158 40.8333 16.3345 32.6667 39 82.5070 165.000 41.2550 82.5000 27.5052 55.0000 20.6307 41.2500 16.5064 33.0000 4O 83.3664 166.667 41.6847 83.3333 27.7917 55.5556 20.8456 41.6667 16.6784 33.3333 41 84.1972 168.33342.1001 84.1667 28.0686 56.1111 21.0534 42.0833 16.8446 33.6667 4 a 85.0280 170.000 42.5156 85.0000 28.3456 56.6667 21.2611 42.5000 17.0108 34.0000 43 85.8588 171.667 42.9310 85.8333 28.6225 57.2222 21.4689 42.9167 17.1770 34.3333 44 86 6896 173.333 43.3464 86.6667 28.8995 57.7778 21.6766 43.3333 17.3432 34.0667 45 87.5204 175.000 43.761887.5000 29.1765 58.3333 21.8843 43.7500 17.5094 35.0000 46 88.3512 176.667 44.1772 88.3333 29.4534 58.8889 22.0921 44.1667 17.6756 35.3333 47 89.1820 178.33344.592689.1667 29.7304 59.4444 22.2998 44.5833 17.8418 35.C667 48 90.0128 180.000 45. 0081 190.0000 30.0074 60.0000 22.5076 45.0000 18.0081 36.0000 49 90.8436 181.667 45.4235:90.8333 30.2843 60.5556 22.7153 45.4167 18.174336.3333 50 91.6744 183.333 45.838991.6667 30.5613 61.1111 22.9230 45.8333 18.340536.6667 51 92.5052 185.000 46.2543 92.5000 30.8382 61.6667 23.1308 46.2500 18.506737.0000 52 93.3360 186.667 46.669793.3333 31.1152 62.2222 23.3385 46.6667 18. 6729 '37. 3333 53 94.1668 188,333 47.0851 94.1667 31.3922 62.7778 23.5463 47.0833 18.8391; 37. 6667 54 94.9976 190.000 47.5005 95.0000 31.6691 63.3333 23.754047.5000 1 9. 0053 : 38. 0000 55 95.8284 191.667 47.916095.8333 31.9461 63.8889 23.9617 47.9167 19.171538.3333 56 96.6592 193.333 48.331496.6667 32.2230 64.4444 24.1695 48.3333 19.337738.6667 57 97.4900 1 95 . 000 48 . 7468 ' 97 . 5000 32. 5000 j 65. 0000 24 . 3772 48 . 7500: 1 9 . 5040 39 . 0000 58 98.3208 196.667 49.162298.3333 33.7770 65.5556 24 . 5850 49 . 1 667 i 1 9 . 6702 39 . 33S3 59 99.1802 198.33349.591999.1667 33.0635 66.1111 24.7999 49.5833 19.8421 39.6667 48 TABLE XIV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 Curve. 1O Curve. 1 Tan. Arc. Tan. 7715004 Arc. 14.2856 Tan. 6.25749 Arc. 12.5000 Tan. Arc. Tan. Arc. M. 8.34038 16.6667 5.56337 11.1111 5.00831 10.0000 8.47891 16.9444 7.26880 14.5238 6.36142 12.7083 5.65577 11.2963 5.0915010.1667 1 8.61744 17.2222 7.387'56 14.7619 6.46536 12.9167 5.74818 11.4815 5.17468 10.3333 8.75597 17.5000 7.50632 15.0000 6.56929 13.1250 5.84058 11.6667 5.25787 10.5000 3 8.89449 17.7778 7.62508 15.2381 6.67322 13.3333 5.93298 11.8519 5.3410510.6667 4 9.03302 18.0556 7.743*3 15.4762 6.77715 13.5417 6.02539 12.0370 5.42424 10.8333 5 9.17155 18.3333 7.86259 15.7143 6.88109 13.7500 6.11779 12.2222 5.5074211.0000 6 9.31008 18.6111 7.98135 15.9524 6.98502 13.9583 6.21020 12.4074 5.59061 11.1667 7 9.44861 18.8889 8.10011 16.1905 7.08895 14.1667 6.30260 12.5926 5.6737911.3333 8 9.58714 19.1667 8.21887 16.4286 7.19289 14.3750 6.39500 12.7778 5.75698 11.5000 9 9.72567 19.4444 8.33762 16.6667 7.29682 14.5833 6.48741 12.9630 5.8401611.6667 1O 9.86420 19.7222 8.45638 16.9048 7.40075 14.7917 6.57981 13.1482 5.92335 11.8333 11 10.0027 20.0000 8.57514 17.1429 7.50469 15.0000 6.67222 13.3333 6.00653 12.0000 13 10.141320.2778 8.69390 17.3810 7.60862 15.2083 6.76462 13.5185 6.08972 12.1667 13 10. 2798 120.5556 8.81266 17.6191 7.71255 15.4167 6.85703 13.7037 6.17290 12.3333 14 10.4183120.8333 8.93141 17.8571 7.81649 15.6250 6.94943 13.8889 6.25609 12.5000 15 10.5568 21.1111 9.05017118.0952 7.92042 15.8333 7.04183 14.0741 6.33927 12.6667 16 10.7001 21.3889 9.1730218.3333 8.02794 16.0417 7.13742 14.2593 6.42533 12.8333 17 10.8434 21.6667 9.29588J18.5714 8.13545 16.2500 7.23301 14.4444 6.51138 13.0000 18 10.9820 21.9444 9.41463 18.8095 8.23939 16.4583 7.32542 14.6296 6.59457 13.1667 19 11.1205 22.2222 9.53339 19.0476 8.34332 16.6667 7.41782 14.8148 6.67775 13.3S33 2O 11.2590 22.5000 9.65215 19.2856 8.44725 16.8750 7.51023 15.0000 6.76094 13.5000 21 11.3976 22.7778 9.77091119.5238 8.55119 17.0833 7.60263 15.1852 6.84412 13.6667 22 11.5361 23.0556 9.88967119.7619 8.65512 17.2917 7.69504 15.3704 6.92731 13.8333 23 11.6746 23.3833 10.008420.0000 8.75905 17.5000 7.78744 15.5556 7.01049 14.0000 24 11.8132 23.6111 10.1272 20.2381 8.86298 17.7083 7.87984 15.7407 7.09368 14.1667 25 11.9517 23.8889 10.2459 20.4762 8.96692 17.9167 7.97225 15.9259 7.17686 14.3333 26 12.0902 24.1667 10.3647 20.7143 9.07X185 18.1250 8.06465 16.1111 7.26005 14.5000 27 12.2287 24.4444 10.4835 20.9524 9.17478 18.3333 8.15706 16.2963 7.34323 14.6667 28 12.3673 24.7222 10.6022 21.1905 9.27872 18.5417 8.24946 16.4815 7.42642 14.8333 29 12.5058 25.0000 10.7210 21.4286 9.38265 18.7500 8.34186 16.6667 7.50960 15.0000 30 12.6443 25.2778 10.8397 21.6667 9.48658 18.9583 8.43427 16.8519 7.59279 15.1667 31 12.7829 25.5556 10.9585 21.9048 9.59052 19.1667 8.52667 17.0370 7.67597 15.3333 32 12.9214 25.8383 11.0772 22.1429 9.69445 19.3750 8.61908 17.2222 7.75916 15.5000 33 13.0599 26.1111 11.1960 22.3810 9.79838 19.5833 8.71148 17.4074 7.84234 15.6667 34 13.1984 26.3889 11.3148 22.6191 9.90232 19.7917 8.80389 17.5926 7.92553 15.8333 35 13.3370 26.6667 11.4335 22.8571 10.0062 20.0000 8.89629 17.7778 8.00871 16.0000 36 13.4755 26.9444 11.552323.0952 10.1102 20.2083 8.98869 17.9630 8.09190 16.1667 37 13.6140 27.2222 11.671023.3383 10.2141 20.4167 9.08110 IS. 1482 8.17508 16.3333 38 13.7573 27.5000 11.793923.5714 10.3216 20.6250 9.17669 18.3338 8.26114 16.5000 39 13.9006 27.7778 11.916723.8095 10.4291 20.8333 9.27228 18.5185 8.34719 16.6667 4O 14.0392 28.0556 12.035524.0476 10.5331 21.0417 9.36468 18.7037 8.43037 16.8333 41 14.1777 28.3333 12.154324.2856 10.6370 21.2500 9.45709 18.8889 8.51356 17.0000 42 14.3162 28.6111 12. 2730 124.5238 10.7409 21.4583 9.54949 19.0741 8.59674 17.1667 43 14.4547 28.8889 12.391824.7619 10.8449 21.6667 9.64190 19.2593 8.67993 17.3333 44 14.5983 29.1667 12.510525.000<> 10.9488 21.8750 9.73430 19.4444 8.76311 17.5000 45 14.7318 29.4444 12.629325.2381 11.0527 22.0833 9.82670 19.6296 8.84630 17.6667 46 14. 8703:29.7222 12.748025.4762 11.1567 22.2917 9.91911 19.8148 8.92948 17.8333 47 15.008930.0000 12.866825.7143 11.2606 22.5000 10.0115 20.0000 9.01267 18.0000 48 15.1474j30.2778 12.985625.9524 11.3645 22.7083 10.1039 20.1852 9.09585 18.1667 49 15. 2859 '30. 5556 13.104326.1905 11.4685 22.9167 10.1963 20.3704 9.17904 18.3333 5O 15.4244130.8333 13.2231 26.4286 11.5724 23.1250 10.2887 20.5556 9.26223 18.5000 51 15.563031.1111 13.341826.6667 11.676323.3333 10.3811 20.7407 9.34541 18.6667 52 15.701531.3889 13.460626.9048 11.780323.5417 10.4735 20.9259 9.42860 18.8333 53 15.840031.6667 13.579427.1429 11.8842s23.7'500 10.5659 21.1111 9.51178 19.0000 54 15.978631.9444 13.6981 27.3810 11.9881123.9583 10.6583 21.2963 9.59497 19.1667 55 16.1171 32. 2222J13. 81 69 27. 6191 12.0921 24.1667 10.7507 21.4815 9.67815 19.3333 56 16. 2556 ! 32. 5000 13.935627.8571 12.196024.3750 10.8431 21.6667 9.76134 19.5000 57 16.3941 32.7778 14.0544 28.0952 12.299924.5833 10.9356 21.8519 9.84452 19 6667 58 16.537533.0556 14.177228.3333 12.407524.7917 11.0311 22.0370 9.93057 19.8333 59 49 TABLE XIV. ACTUAL TANGENTS, ETC. 2 1 Curve. 2 Curve. 3 Curve. 4 Curve. 5 Curve. M. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. ~1F l6o~7040 200.000 50.0217 100.000 33.350066.6667 25.014850.0000 20.0140 40.0000 i 100.870 201 . 667 50.4371 100.833 33 627067.2222 25.222550.4167 20.1803 40.3333 3 101.701 203.333 50.8525 101.667 33.903967.7778 25.430250.8333 20.3405 40.0067 3 103.53-2 205.000 51.2679 102.500 34. 180968.3333 25.638051.2500 20.5127 41.0000 4 103.363 206.667 51.6833 103.333 34.457808.8889 25.8457 51.6667 20.6789 41.3333 5 101.194 208.333 52.0988 104.107 34.734869.4444 26.0535 52.0833 20.8451 41.6667 6 105.021 210.000 52.5142 105.000 35.0118:70.0000 20.2012 52.5000 21.0113 42.0000 7 105.855 211.667 52.9296 105.833 35. 2887 70. 5556 26.4089 52.9107 21.1775 42.3333 8 100. G8G 213.333 53.8450 106.G-.i7 r>. 5657 71.1 111 20.6767 53.3333 21.3437 42.6667 9 107.517 215.000 53.7604 107.500 35.8427 71.6667 20.8844 53.75UU 21.5099 43.0000 1O 108.348 216.667 54.1758 108.333 36.119672.2222 27.0922 54.1667 21.6762 43.3333 11 109.178 218.333 54.5912 109.167 3(3.3960 72.7778 tf.aMKJ 54.5833 21.842443.0007 12 110 009 220.000 )5.0067 110.000 36.07:35 73.3333 27.5070 55.0000 22.0080 44.0000 13 110.810 221.667 55.4221 110.833 36.9505 7.3.8889 27.7154 55.4167 22.1748 44.3333 14 111.671 223.333 >5.8'375 111.667 37.2275 7'4.4444 27.9231 55.8333 22.341044.6667 15 112.502 225.000 56.2529 112.500 37.50H 75.0000 28.1309 56.2500 22.5072 45.0000 16 113.332 226.667 56.6633 113.333 37.7814 75.5550 28.3380 56.6007 22.673445.3333 17 114.163 228.333 57.0837 114. 107 38.0583 76.1111 28.5403 57.0833 22.8396 45.0007 18 114.994 230.000 57.4991 115.000 33.3353 76.GOG7 28.7'541 57.5-000 38.006846.0UOO 19 115.825 231.667 57.9146 115.833 38.6123 7? 222'; 28.9018 57.9167 23.1721 40.3333 20 116.656 233 333 58.3300 116.887 38.8892 77.7778 29.1696 58.3333 23.3383 46.6667 31 117.515 235.000 58 . 7597 117.500 39.1757 78.3333 29.3345 53.7 500 23.5102 47.0000 22 118.375 236 667 59.1895 118.333 39.4623 78.8839 29.5994 59.1667 23. G821 47.3333 23 119.205 238.333 59.6049 119.167 39.7392 79.4414 29.8071 59.5833 23.8484 47.0667 24 120.036 240.000 60.0203 120.000 40.0102 80.0000 30.0119 60.0000 24.014048.0000 25 120.867 241.667 60.4357 120.833 40.2931 80.5556 30.2226 60.4167 24.1808 48.3333 26 121.698 243.333 60.8511 121.667 40.5701 81.1111 30.4303 60.8333 24.347048.0007 27 122.529 245.000 61.2665 122.500 40 8471 81.6667 30.6381 61.2500 24.5132 49.0000 28 123.359 246.667 61.6819 123.333 41.1240 82. 22, '2 30.8158 61.6667 24.0794 49.3333 39 124.190 248.333 62.0974 124.167 41.4010 82.7778 31.0536 62.0833 24.8456 49.6067 30 125.021 250.000 62.5128 125.000 41.6779 83.3333 31.2613 62.5000 25 0118 50.0000 31 125.852 251.667 62.9282 125.833 41.9549 83.8889 31.4690 62.9107 25.1780 50.3333 32 126.683 253.333 63.3436 126.667 42.2319 84.4444 '31.6768 63.3333 25.3443 50.6607 33 127.513 255.000 63.7590 127.500 42.5088 85.0000 31.8845 63.7500 25.510551.0000 34 1 28.344 256.667 64.1744 128.&33 42.7858 85.5556 32.0923 64.1667 25.G7'67 51.3333 35 129.175 258.333 64.5898 129.167 43.0628 86.1111 32.3000 64.5833 25.8429 51 . 6667 36 130.006 260.000 65.0053 130.000 43.3397 86.6607 32.5077 65.0000 20.0091 52.0000 37 130.837 261.667 65.4207 130.833 43.6167 87.2222 32.7155 65.4107 20.1753 52.3333 38 131.667 263.333 65.8361 131.667 43.8936 87.7778 32.9232 65.8333 26.3415 52.0(567 39 132.527 265.000 66.2658 132.500 44.1802 88.3333 33.1381 66.2500 26.5135 53.0000 40 133.386 266.667 66.6956 133.333 44.466788.8889 33.3530 06.6667 26.6854 53.3333 41 134.217 268.333 67.1110 131.167 44.7436:89.4444 33.5608 67.08:33 26.8516 53. (5007 42 135.048 270.000 67.5264 135.000 45.020G 90.0000 33.7085 67.5000 27.0178 54.0000 43 135.879 271.667 67.9418 135.833 45.29:590.5550 33.9702 67.9167 27.184054.3333 44 136.709 273.333 68.3572 13 ; >. 667 45.574591.1111 34.1840 68.3333 27.3502 54 . 6(567 45 137.510 275.000 68.7726 137.500 45.851591.6607 34.3917 68.7500 27.5165 55 0000 46 138.371 276.667 69.1881 138.333 46.128492.2222 34.5995 09.1667 '27.082755.3333 47 139.202 278.333 69.6035 139.167 16.4054 92.7778 34.8072 69.5833 27.8489 55.0067 48 140.033 280.000 70.0189 140.000 46.082493.3333 35-0149 70.0000 28.0151 56.0000 49 140.863 281.667 70.4313 140.833 16 959393.H889 35.2227 70.4167 28.1813 56.3333 5O 141.694283.333 70.8497141.007 17.2363 94.4444 35.4304 70.8333 28.3475 56.6667 51 142.525285.000 71.2651 142.500 47.5132 95.0000 85.638-2 71.250028.5187 57 0000 52 143.356286.667 71.6805 143.333 47.7902 95.5556 35.8459 71.66K7 28. (5799 57. 3333 53 144.18728S.333 72.0960 144.167 48.0672 96.1111 36.0536 72.0833 28.8461 57.6667 54 145.017290.000 72.5114 145.000 4H.3441 96.6667 36.2614 72.5000 29. 01 23 ! 58. 0000 55 145. 84 8 201.007 72. 9268 H 5. 833 48.6211 07.2222 36.4691 72.916729.1780 58.3333 56 146.679293.333 73.3422 146.067 48.8980 97.7778 36.6709 73.3333 29.3448 58.6607 57 147. 510 S95. 000 73.7576 147.500 49.1750 98 3333 36.8846 73.750029.5110 59.0000 58 148.341 296.6'V? 74.1730 148.383 49 . 4520 ! 98 . 8889 37 . 0923 74 . 1 667 29 . 6772 59.3383 59 149.200298.333 74.6028 149.167 49. 73^5 199.4444 137. 3072 > 74. 5833 29.8491 59.6667 50 TABLE XIV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 Curve. 1O Curve. 2 Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. M. 16.080888.3333 14.3001 28.5714 12.5150 25.0000 11.1207 22.2222 10.0100 20.0000 (f 16.81 93 33 .6111 14.416838. 8095 1:3.0189 25.2083 11.2191 22.4074 10. QMS 20.1607 i It). 95: 8 33.8889 14.5370 29.0470 12.7228 #3.4107 11.3115 22.5926 10.1830 20.8333 1 7 . 0963 34 . 1 607 j 14 . 0504 ^9 . 2850 12.8208 25.0250 11.4039 22.7778 10.2002 20.5000 3 17. 8349.34. 44441 14. 7T51 89.5:338 12.9307 25.8333 11.4904 88.9030 10.3494 20.6607 4 17.373484.7222 14.893929.7019 13.0340 20.041*; 11.5888 23.1482 10.4326 20.8333 5 17.511935.0000 15.012030.0000 13.1380 20.2500 11.0812 23.8333 10.5157 21.0000 G 17.65U5;85.8778 15.131430.2381 13.2425 20.4583 11.7736 23.5185 10.5989 21.16G7 7 17.789035.5550 15.XJ50230.4702 13.3404 20.0607 11.8600 23.7037 10.6821 21.3333 17.9275 35.8333 15.308930.7143 13.4504 20.8750 11.9584 23.8889 10.7653 21.5000 i) 18.0600 36.1111 15.487730.9524 13.5543 27.0833 12.0508 24.0741 10.8485 21.6667 10 18.SJ046l36.S889 15.600431.1905 13.6582 27.2917 12.1432 24.2593 10.9317 21.83:33 11 18.3431 30.0007 15.725231.4280 13.7622 27.5000 12.2356 24.4444 11.0148 22.0CCO 12 18.481030.9444 15.843931.6067 13.8061 27.7083 12.328024.6290 11.0980 22.1607 13 18.020237.2222 15.902731.9048 13.9700 27.9167 12.4204 24.8148 11.1812 22.3333 14 18.7587 37.5000 10.081532.1429 14.0740 28.1250 12.5128 25.0000 11.2644 22 5000 15 18.8972 37 . 7778 16.200232.3810 14.177'9 28.3333 12.6052 25.1852 11.3470 22.6667 16 19.035738.0550 10.319032.6190 14.2818 28.5417 12.6976 25.37'04 11.4308 22.8333 17 19.174338.3333 16.437732.8571 14.3858 28.7500 12.7900 25.5556 11.5140 23.00CO 18 19.3128 38.6111 16.556533.0952 14.4897 28.9583 12.8824 25.7407 11.5971 23.1067 19 19.4513 38.8889 16.675233.3333 14.5930 29.1667 12.9748 25.9259 11.6803 23.3333 20 19.5940 39.1607 16.7981 33.5714 14.7012 29.3750 13.0704 26.1111 11.7004 23.5000 21 19.7379 39.4444 16.921033.8095 14.8087 29.5833 13.1660 26.2963 11.8524 23.6667 22 19.8705 39.7222 17.039734.0470 14.9126 29.7917 13.2584 26.4815 11.9356 23.8333 23 20.0150 40.0000 17.158534.2856 15.0165 30.0000 13.3508 20.6667 12.0188 24.0000 24 20.1535 40.2778 17.277234.5238 15.1205;30.2083 13.4432 26.8519 12.1020 24.1667 25 20.2921 40.5550 17.396034.7619 15. 2244130. 4167 13.5356 27.0370 12.1852 24.3333 26 20.4300 40.8333 17.514735.0000 15. 3283 130.6250 13.6280 27.222-; 12.2684 84.5000 27 20.5091 41.1111 17.033535.2381 15.4323 30.8333 13.7204 27.4074 12.3515 24.6667 28 20.7070 41.3889 17.752335.4762 15.5362 31.0417 13.8128 27.5926 12.4347 24.8333 29 20.8-162 41.6667 17.871035.7143 15.6401 31.2500 13.9052 27 . 7778 12.5179 25.0000 80 20.98-17 41.9444 17.989835.9524 15.7441 31.4583 13.9976 27.9030 12.0011 J5.1GG7 31 21.1232 42.2222 18.108536.1905 15.8480 31.6667 14.0900 28.1482 12.6843 85.8333 32 21.2618 42.5000 18.227330.4280 15.9519 31.8750 14.1824 28.3333 12.7675 25.5000 33 21.4003 42.7778 18.346036.6667 16.0559 32.0833 14.2748 28.5185 12.8507 25.6667 34 21.5388 43.0556 18.464836.9048 16.1598 32.2917 14.3673 28.7C37 12.9338 25.8333 35 21.6773 43.3333 18.583637.1429 16.2037 32.5000 14.4597 28.8880 18.0170 26.0000 36 21.8159 43.6111 18.702337.3810 16.3077 3-'. 7083 14.5521 89.0741 13.1002 26.1667 37 21.9544 43.8889 18.8211 37.6190 16.4710 32.9167 14.6445 29.2593 13.1F34 26.3333 88 22.0977 44.1667 18.943937.8C71 16.5791 33.1250 14.7401 29.4444 13.2694 26.5000 39 22.2410 44.4444 19.0668 38.' 0952 16.0866 33.3333 14.8356 29.6296 13.3555 26.6G67 40 22. 3795| 44. 7222 19.185538.3333 16.7906 33.5417 14.9280 29. 814 e; 13.4387 26.8333 41 22.5181:45.0000 19.304338.5714 16.8945 33.7500 15.0205 30.0000 13.5219 27.0000 42 22.6566:45.2778 19.4231 38.8095 16.9984 33.9583 15.1129 30.1S52 13.6051 27.1G67 43 22.7951 45.5556 19.541839.0476 17.1024 34.1667 15.2053 30.8704 13.6882 27.3333 44 22 933745.8333 19.660639.2856 17.2063 34.3750 15.2977 30.5556 13.7714 27.5000 45 23.072246.1111 19.779339.5228 7.3102 31.5833 15.3901 30.7407 13.8546 27.6G67 46 23.210746.3880 19.8981 39.7619 7.4142 31.7917 15.4825 30.9259 13.937'8 27.F333 47 23.319246.0067 20.016840.0000 7.5181 35.0000 15.5749 31.1111 14.0210 28.0000 48 23.487840.9444 20.135640.2381 7.6220 35.2083 15.6673 31.2963 14.1042 28.1C67 49 23.6263 47.2222 20.254440.4762 7.72f>0 35.4167 15.7597 31.4815 14.? 874 88.3333 50 28.764$ 47.5000 20.3731 40.7143 7.8299 35.6250 15.8521 31.C667 14.2705 28.5000 51 23.9031 47.7778 20.491940.9524 7.9338 35.8333 15.9445 31.8519 14.3537 28.6667 52 24.0419 -18.0556 20.610641.1005 18.0378 36.0417 16.036932.0370 14.4369 28.8333 53 24. ISO-! 48.3333 20.729441.4286 IS. 1417 36 2500 16.1293 32 2222 14.5201 29.0000 54 24. 31 SO 48.6111 20.848241.0667 18.2456 36.4583 16.2217 32 .'4074 14.6033 29.1G67 55 24.4575 48.8889 20.966941.9048 18.3406 30.6067 16.3141 32.5926 14.6865 29.3333 56 24.5900 49.1667 21.085742.1429 18.4535 36.8750 16.4065 32.7778 14.7696 29.5000 57 24.7315 49.444-1 21.204442.3810 18.5574 37.0833 16.4989 32.9630 14.8598 29.6667 58 24.8778 49.7222 21.327342.6190 18.0650 37.2917 16.5945 33.1482 14.9389 29.8333 59 51 TABLE XIV. ACTUAL TANGENTS, ETC. 3 1 Curve. 2 Curve. 3 Curve. 4 Curve. 5 Curve. M. Tan. Arc. Tan. Arc. Tail. I Arc. Tan. Arc. Tan. Arc. O 50.060 oo.uoo 75.0325 150.000 0.0250 100. 000 ,37. 5222; 75. 0000 30.0211 60.0000 1 50.890 01.667 75.4479 150.8:33 0.3020 1UO. 556; 37. 7299 75.4167 30.187:-) 60.3333 2 51.721 03.33375.8633 151.667 0.5789 10 1 . 1 1 1 37 . 9376 ; 7 o . 833:3 30 . 8535 60.6667 3 52.552 05.000 6.2788 52.500 0.8559 101.667 38.1454 76.2500 30.5197 61.0000 4 53.383 06.667 6.6942 153.333 1.1328 102.22238 3531 76.666730.6859 61.3333 5 51.214 08.333 7.1090 154.167 ol.4098 102.778 38.5609 77.083330.8521 61 6607 6 55.044 10.000 7.5250 155.000 ol.6868 103.333 38.7686 77.500031.0183 62.0000 i 55.875 11.667 "7.9404 155.833 ol.9637 103.889 38.9763 77.916731.1845 62.3332 8 56.706 13.333 "8.3558 156.667 o2.2407 104.444 39.1841 78.3:33331.3508 62.6667 9 57.537 315.000 "8.7713 157.500 o2.5176 105.000 39.3918 78.750031.5170 63.0000 1O 58.368 316.667 79.1867 158.333 52.7946 105.556 39.5996 79.166731.6832 63.3333 11 59.198 318.333 "9.6021 159.167 53.0716 106.111 39.8073 79. 5833 '31. 8494 03.6667 12 60.029 320.000 80.0175 160.000 53.3485 106.667 40.0150 80.000032.0156 04.0000 13 60.860 321.667 80.4329 160.833 >3.6255 107.222 40.2228 80.410732.1818 64.3333 14 161.691 323.333 80.8483 161.667 53.9025 107.778 40.4305 80.8333:32.3480 64.6667 15 162.522 325.000 81.2637 162.500 54.1794 108.333 40.6383 81.250083.5142 65.0000 16 163.352 326.667 81.6792 163.333 54.4564 108.889 40.846081.666732.6804 65.3333 17 164.212 328.333 82.1089 164.167 54.7429 109.444 41.0609 82. 0833 ^2.8524 65.6667 18 165.071 330.000 82.5386 165.000 55.0294 110.000 41.2758 82.500033.0243 06.0000 19 165.902 331.667 82.9540 165.833 55.3064 110.556 41.4835 82.9167 33.1905 66.3333 2O 166.733 333.333 83.3695 166.667 55.5833 111.111 41.6913 83.3333 33.3567 66.6667 21 167.564 335.000 83.7849 167.500 55.8603 111.667 41.8990 83.7500 33.5230 67.0000 22 168.394 336.667 84.2003 168.333 56.1373 112.222 42.1068 84.1667 33.6892 67.3333 23 169.225 338.333 84.6157 169.167 56.4142 112.778 42.3145 84.5833 33.8554 67.6667 24 170.056 340.000 85.0311 170.000 56.6912 113.333 42.5222 85.0000 34.0216 68.0000 25 170.887 341.667 85.4465 170.833 56.9681 113.889 42.7300 85.4167 34.1878 68.3333 26 27 171.718 172.548 343.333 345.000 85.8620 86.2774 171.667 172.500 57.2451 57.5221 114.444 115.000 42.9377 43.1455 85.833334.354068.6667 86.250034.520269.0000 28 173.379 346.667 86.6928 173.333 57.7990 115.556 43.3532 86.6667 34.6864 69.3333 29 174.210 348.333 87.1082 174.167 58.0760 116.111 43.5609 87.0833 34.8526 69.6667 3O 175.041 350.000 87.5236 175.000 58.3529 116.667 43.7687 87.500035.0189 70.0000 31 175.872 351.667 87.9-390 175.833 58.6299 117.222 43.9764 87. 9 167 ,35.1851 j 70. 3333 32 176.702 353.333 88.3544 176.667 58. 9069! 117. 778 44.1842 88.333335.351370.6667 33 177.562 355.000 88.7842 177.500 59.1934 118.333 44.3991 88 . 7500 35 . 5232 71 . 0000 34 178.421 356.667 89.2139 178.333 59.4799 118.889 44.6140 89.166735.6952 71.33:33 35 179.252 358.333 89. 6293 1179.1 67 59.7569 119.444 44.8217 89.583335.8614 71 . 6667 36 180.083 360.000 90.0447 180.000 60.0338120.000 45.0294 90.000036.0276 72.0000 37 180.914 361.667 90.4602 180.833 60.3108 120.556 45.2372 90.416736.1938 72.3333 38 181.744 363.333 90.8756 181.66" 60.5877 121 .111 45.4449 90.833336.3600 72.6667 39 182.575 365.000 91.2910 182.500 60.8647 121.667 45.6527 91 . 2500 36.5262 73.0000 4O 183.406 366.667 91.7064 183.3a3 61.1417 122.222 45.8604 91 . 6667 36.6924 73.3333 41 184.23" 368.333 92 1218 184.16" 61.4186 122.778 46.0681 92.0833 36.8588 73.6667 42 185.068 370.000 92.5372 185.000 61.6956 123.333 46.2759 92.5000 37.0248 74.0000 43 185.898 371.667 92.9527 185.83.' 61.9725 123.889 46.4836 92.9167 37.1911 74.3333 44 186.729 373.333 93.3681 186.66~ 62.2495 124.444 46.691493.3333 37.3573 74.6667 45 187.560 375.000 93.7835 187.500 62.5265 125.000 46.8991 93.7500 37.5235 75.0000 46 188.39 376.667 94.1989 188.333 62.8034 125.556 47.106894.1667 37.6897 75.3333 47 189.222 378. as: 94.6143 189.16" 63.0804 126.111 47.3146 94.5833 37.8559 75.6667 48 190.05'. 380.000 95.0297 190.00 63.3574 126.667 47.5223 95.0000 38.0221 76.0000 49 190.883 831. .66? 95. 4451 | 190. 833 63.63431127.222 47.7301 95.4167 38.1883 76.3333 50 191.714 383.333 95.8606 191. 66 r 63.9113 127.77? 47.937895.833338.3545 76 .6667 51 192.574 38=). 000 96.2903 192.50C 64.1978 128.333 18.152796.250038.5265 77.0000 52 193.43: 386.66" 96.7200 193.33' 64.484:-] 128.88S 48 . 3676 96 . 6667 38 . 698 4 77.3333 53 194.264 388.333 97.1355 194.16~ 64.7613 129.444 48.575497.083338.8646 77.6667 54 195.095 390.000 97.5509195.000 65.0382 130.000 48.7831 97.5000,39.0308 78.0000 55 185.935 391.667 97.96^3 195.83: 65.3152 130.556 48.990897.9167 39.1970 78.3333 56 196.756 393.333 98.3817 196.66" 65.5921 131.111 4 9 . 1 986 98 . 3333 39 . 3(533 78 . 6667 rj * 197.587 395.000 98.7971 197.500 65.8691 131.667 49 . 4063 98 . 7500 39 . 5295 1 79 . 0000 5 198.418 396 667 99.2125 198.333 66.1461 132.222 49 . 61 41 i 99 . 1 667 39 . 6957 79 . 3333 59 199.249 398.333 99.6279,199.16' 6(5.4230 132.778 49.8218 99.5833 39.8619|79.6667 TABLE XIV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 Curve, 1O Curve. 3 Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. M. 25.0211,50.0000 21.4501 42.8571 18.7725:37.5000 16.0901 33.3333 15.0249 W.Ot'OO O 25.159750.2778 21.568943.0952 18.876437.7083 16.7825 33.5185 15.1081 30.1667 1 25.298250.5556 21.087043.3333 18'. 9803 37 9107 16.8749 33.7037 15.1913 30.3333 2 25.4367,50.8333 -21.800443.5714 19.084338.1250 16.9673 33.8889 15.2745 30.5000 3 25 575351.1111 -21.925243.8095 19.188238.3333 17.0597 34.0741 15.3577 30.6667 4 25.713851.3889 22.043944.0170 19. 2921! 38. 5417 17.1521 34.2593 15.4409 30.8333 5 25.852351.6667 22.162744.2850 19.396138.7500 17.2445 34.4444 15.5241 31.0000 6 25.990851.9444 22.2814 44.5238 19.500038.9583 17.3369 34.6296 15.0072 31.1007 7 26.129452.2222 22.4002 44.7619 19.603939 1667 17.4293 34.8148 15.6904 31.3333 8 26.2679 52 5000 22.5190 45.0000 19.7079 39.3750 17.5217 35.0000 15.7736 31.5000 9 26.4064 52.7778 22.6377 45.2381 19.8118 39.5833 17.6141 35.1852 15.8568 31.6667 1O 26.5450 53.0556 22.7565 45.4762 19.915739.7917 17.7065 35.3704 15.9400 31.8333 11 26.6835 53.3333 22.8752 45.7143 20. 0197 140.0000 17.7990 35.5550 16.0232 32.0000 12 26.8220 53.6111 2-2.9940 45.9524 20.123640.2083 17.8914 35.7407 16.1063 32.1007 13 26.9605 53.8889 23.1127 46.1905 20.2275 40.4107 17.9838 35.9259 16.1895 32.3333 14 27.0991 54.1667 23.2315 46.4286 20.3315 40.0250 18.0762 36.1111 16.27'27 32.5000 15 27 237'6 54.4444 23.3503 46.6607 20.4354 40.8333 18.1080 36.2963 16.3559 32.0007 16 27^3809 54.7222 23.4731 46.9048 20.5429 41.0417 18.2642 30.4815 16.4420 32.8333 17 27.5242 55.0000 23.5960 47.1429 20.6504 41.25CO 18.3597 36.6667 10.5280 33.0000 18 27.6627 55.277* 23.7147 47.3810 20.7544 41.4583 18.4522 36.8519 16.6112 33.1667 19 27.8013 55.5556 23.8335 47.6190 20.8583 41.6667 18.5446 37.0370 16.6944 33.3333 2O 27.9398 55.8333 23.9522 47.8571 20.9622 41.8750 18.6370 37.2222 16.777'6 33.5000 21 28.0783 56.1111 24.0710 48.0952 21.0662 42.0833 18.7294 37.4074 10.8007 83.0007 22 28.2169 56.3889 24.1898 48.3323 21.1701 42.2917 18.8218 37.5926 16.9439 33>33 23 28.3554 56.0667 24.3085 48.5714 21.2740 42.5000 18.9142 37.7778 ".0271 34.0000 24 28.4939 56.9444 24.4273 48.8095 21.3780 42.7083 19.0066 37.9630 1".1103 34.1007 25 28.6324 57.2222 24 5460 49.0476 21.4819 42.9167 19.0990 38.1482 17.1935 34.3333 26 28.7710 57.5000 24.0648 49.2850 21.5858 43.1250 19.1914 38.3333 " 2707 34.5000 27 28.9095 57.7778 24.7835 49.5238 21.6898 43.3333 19.2838 38.5185 "^3599 34.G6C7 28 29.0480 58.0556 24.9023 49.7619 21.7937 43.5417 19.3762 38.7037 17.4430 34.8333 29 29.1866 58.3333 25.0211 50.0COO 21.8976 43.7500 19.4686 38.8889 ".5262 35.0000 30 29.3-251 58.0111 25.1398 50.2381 22.0016 43.9583 19.5610 39.0741 ".6094 35.1667 31 29.4630 58.8889 25.2586 50.47'62 22.1055 44.1667 19.6534 39.2593 ".6920 35.3333 32 29.0069 59.1667 25.3814 50.7143 22.2130 44.3750 19.7490 39.4444 ".7787 35.5000 33 29.7502 59.4444 25:5043 50.9524 22.3205 44.5833 19.8446 39.6296 ".8047 35.6607 34 29.8888 59.7222 25.6230 51.1905 22.4245 44.7917 19.9370 39.8148 ".9479 35.8333 35 30.0273 00.0000 25.7418 51.4286 22.5?84 45.0000 20.0294 40.0000 18.0311 30.0000 36 30.1658 60.2778 25.8006 51.6667 22.6323 45.2083 20.1218 40.1852 18.1143 30.1007 37 30.3043 60.5556 25.9793 51.9048 22.7363 45.4167 20.2142 40.3704 18.1974 30.3333 38 30.4429 60.8333 26.0981 52.1429 22.8402 45.6250 20.3066 40.5556 18.2806 36.5000 39 30.5814 61.1111 26.2168 5-2.3810 22.9441 45.8333 20.3990 40.7407 18.3638 36.6667 40 30.7199 61.3889 26.3356 52.6190 23.0481 46.0417 20.4914 40.9259 18.4470 36.8333 41 30.8585 61.6667 26.4543 52.8571 23.1520 46.2500 20.5838 41.1111 18.5302 37.0000 42 30.9970 61.9444 26.5731 53.0952 23.2559 46.4583 20.6762 41.2963 18.6134 37.1007 43 31.1355 62.2222 26.6919 53.3333 23.3599 46.6667 20.7686 41.4815 18.6966 37.3333 44 31.2740 62.5000 26.8106 53.5714 23.4638 46.8750 20.8610 41.6667 18.7797 37.5000 45 31.4126 62.7778 26.9294 53.8095 23.5677 47.0833 20.9534 41.8519 18.8629 37.0007 46 31.5511 03.0556 27.0481 54.0476 23.6717 47.2917 21.0458 42.0370 18.9461 37.8333 47 31.6896 63.3333 27.1669 54.2856 23.7756 47.5000 21.1382 42.2222 19.0293 38.0000 48 31.8282 63.6111 27.2857 54.5238 23.8795 47.7083 21.2307 42.4074 19.1125 38.1067 49 31.9667 63.8889 27.4044 54.7619 23.9835 47.9167 21.3231 42.5926 19.1957 38.3333 50 32.1100 64.1667 27.527'3 55.0000 24.0910 48.1-250 21.4186 42.7778 19.2817 38.5000 51 32.253304.4444 27.6501 55.2381 24.1985 48.3333 21.5142 42.9630 19.3678 38.6607 52 32.3018 04.7222 27.7089 55.4762 24.3024 48.5417 21.6066 43.1482 19.4510 38.8S33 53 32.530305.0000 27.8870 55.7143 24.4064 48.7500 21.6990 43.3333 19.5341 39.0000 54 32.00S9G5.2778 28.0004 55.9524 24.5103 48.95H3 21.7914 43.5185 19.0173 39.1607 55 3-3. 8074,65. 555fi 28.1251 50.1905 24.6142 49.1667 21.8839 43.7037 19.7005 39.333* 56 3-2.9)59 05.8333 28.2-139 56.4280 24.7182 49.3750 21.9763 43.8889 19.7837 39.5000 57 38.0845l66.llll 28.36-27 50.00(57 24.8221 49.5833 22.0087 44.0741 19.8069 39.0007 58 33.223066.3889 28.4814 56.9048 24.9260 49.7917 22.1611 44.2593 19.9501 39.8333, 59 53 TABLE XIV. ACTUAL TANGENTS, ETC. 40 1 Curve. 3 Curve. 3 Curve. 4 Curve. 5 Curve. M. Tan. Arc. Tan. Are. Tan. Arc. Tan. Arc. Tan. Arc. 200.079400.000 100.043200.000 66.7000 133.3:33 50.0295 100.00040.0281 80.0000 1 200.910401.667 100.459200.833 66.9770 133.889 50.2373 100.41740.1943 80.3333 3 201. 741' 403. 333 100.874 201.667 67.2539 134.444 50.4450 100. 833! 40. 3605 80.0007 3 302.572405.000 101.290 202.500 67 . 5309 1 35 . 000 50 . 6528 101.25040.5207 81.0000 4 203.403406.667 101 .705 203.333 67 8078 135.556 50.8605 101 .667140.6929 81.3333 5 204.233408.333 102.120 204.167 08.0848 136. 11 1)51. 0682 102.083 40.8592 81.6667 G 205.064410.000 102.536 205.000 68.3618 136 667:51.2760102.500 41.025482.0000 7 205.924411.667 102.966 205.833 08.6483 137.222 ! 51.4909 102 917 41.1073 82.3333 8 206 783413 333 103 395 206.667 68 9348 137. 778! 51. 7 058 103.333 41.3692 82.0007 9 207.614 415.000 1U3.811 207.500 69.2117 138.333 51.9135 103.750 41.535583.0000 1O 208.445 416.667 104.226 208.333 69.4887 138.889 52.1213 104.167 41.7017 83 3333 11 209.275418 333 104.612 209.167 69.1657 139.444 52.3290 104.583 41.8679 83 6667 13 210.106420.000 105.057 210.000 70.0426 140000 52.5307 105.000 42.0341 84 0000 13 210.937 421.667 105 472 210.833 70.3196 140.556 52.7445 105 417 42.2003 84.3333 14 211.768423.333 105.888 211.667 70.5960 141.111 53.9522 105.833 42.36455 84.0007 15 212.599425.000 1 00.303 212.500 70 8735 141.667 53. 1600! 106. 250 42.532785.0000 16 213. 4291426. 667 106.719 213 333 71.1505 142.222 53 3077 106.667 42.698985.3333 17 214.260428.333 107.134 214.167 71.4274 142 778 53.5754 107.083 42.8051 85.0007 18 10 215.091 430.000 215.922431.667 107.549 107.965 215.000 215.833 71.7044 71.9814 143.333 143.889 53.7832 53.9909 107.500 107.917 43.0314 43.1976 86.0000 86.3333 30 216 753 433.333 108.380 216.667 72.2583 144.444 54.1987 108.333 43.3038 86.6607 31 217.583435.000 108.796 217.500 72.5353 145.000 54.4064 108.750 43.5300 87.0000 33 218. 4141430.6*57 109.211 218.333 72.8122 145.556 54.6141 109.107 43.690287.3333 33 219.274 438.333 109.641 219.167 73.09SS 140 111 54. 82901 109. 583 43 8681 87.0007 34 220.133 440.000 110.071 220.000 73.3853 146.667 55.0439 110.000 44.0401 88 00(50 35 36 220.1)64 221.795 441.667 443. 333 110.486 110.901 220. 833 221.667 73.6022 73.9392 147.222 147.778 55.2517 110.417 55.4594 110.833 44.2003 44.3725 88.3333 83.6667 37 222.626 445.000 111.317 222.500 74.2162 148.333 55.6672,111.250 44.5387 89.0000 38 223.456 446.067 111.732 223.313 74.4931 148.889 55.8749 111.667 44.7019 89.3333 39 224.287 448.3-13 112.148 224.167 74.7701 149.444 56.0827 112.083 44.8711 89.0007 30 225.118 450.000 112.563 225.000 75.0470 150 000 56.2904 112.500 45.0373 90.0000 31 225.949 451.667 112.979 225.883 75.3240 150.556 56.4981 112 917 45.2036 90.3333 33 226.780 453.333 113 394 226.667 75.6010 151.111 56.7059 113.333 45.3698 90.0007 33 227.610 455.000 113.809 227.500 75.8779 151.667 56.9136 113.750 45.5360 91.0000 34 228.441 456.667 114.225 228.333 76.1549 152.222 57.1214 114.167 45.7022 91.3333 35 2-29.272 458.333 114.640 229.167 76.4319 152.778 57.3291 114.583 45. 8684 1 91. 660 / 36 230.103 4GO.OOO 115.056 230.000 76.7088 153.333 57.5308 115.000 46 0346 92.0000 37 230.962461.667 115.485 230.833 76 9953 153.889 57.7517 115.417 46.2065 92.3333 38 23 1.822 '463. 333 115.915 231.667 77.2818 154.444 57.9006 115.833 46.3785 92.6067 39 232.652 465.000 116.330 232.500 77.5588 155.000 58.1744 116.250 46.5447 93.0000 4O 233.483 466.667 116.746 233.333 77.8358 155.556 58.3821 116.667 46.7109 93.3333 41 234.314468.333 117.161 234.167 78.1127 156.111 58.5899 117.083 46.8771 93.6007 43 43 235.145470.000 235.976| 471. 667 117.577 117.992 235.000 2a5. 833 78.3897 78.6666 156.667 157.222 58.7976117.500 59. 0053! 117. 917 47.043394.0000 47.2095194.3333 44 236.806473.333 118.408 236.667 78.9436 157.778 59.2131 118.333 47.3758 94.0007 45 237. 637 i 475. 000 118.823 237.500 79.2206 158.333 59. 4208| 118. 750 47.5420:95.0000 46 238.468476.667 119.233 238.333 79 4975 158.889 59.6286 119.167 47.7082 95.3333 47 239.299478.333 119.654 239.167 79.7745 159.444 59.8363119.583 47. 8744 195.6607 48 240.130480.000 120.069 240.000 80.0515 160.000 60.0440 120.000 48.0406 96.0000 49 240. 960 481. C67 120.485 240. 833 80.3284 100.556 60.2518 120.417 48.2068j96.3333 50 241.791 483.333 120.900 241.667 80 6054 161.111 60.4595 120.833 48.3730 96 6007 51 242.651 485.000 121.330 242.500 80.8019 101.6(37 60. 6744 1121.250 48.545097.0000 53 343.510 486.667 121.760 243.333 81.1784 102.222 60.8893 121.667 48.7109 1)7.3333 53 .'44.341 488.333 122.175 244.107 HI. 4651 162.778 61 .0971 122.083 48.8831 [97.6667 54 215.172 490.000 122.590 245.000 81.7323 163.333 61.3048 122.500 49.045)398.0000 55 246.003 491 .667 123.006 215.833 S2.00U3 163.889 61.5125 122.917 49.2155 98.3333 r^/r 346.833 493.333 123.421 246.607 82.2802 164.444 61.7203128.333 49.3817 98.6007 57 217.664 495.000 123.837 247.500 82.5632 165.00061.9280 128.750 49.5480 99.0000 58 218.495 496.667 124.252 248.333 82.8402 lG5.55602.ia58 124.167 49 7142 99.3333 59 249.326 498.333 124.607 249.107 83.1171 166.111 62.3435)124.583 49.8804 99.6067 54 TABLE XIV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 Curve. 1O Curve. 4 Tan. Arc. Tan. Arc. Tan. 25 0300 Arc. 50.0000 Tan. 2272535 Arc. 44.4444 Tan. 2070332 Arc. M. 33.3615 66.6667 28.6002 57.1429 40.0000 O 33.5000 66.9444 28.7189 57.3810 25.1339 50.2083 22.3459 44.6296 20.1164 40.1667 1 88.6386 67.2222 28.8377 57.6190 ^5 2378 M).4167 .'2.4383 44.8148 20.1996 40.3333 2 33.7771 67.5000 28.9564 57.8571 25.3418 50.6250 22.5307 45.0000 20.2828 40.5000 3 33.9156 67.7778 29.0752 58.0952 25.4457 50.8333 22.6231 45.1852 20.3660 40.6667 4 34.0542 68.0556 29.1940 58.3333 25.5496 51.0417 22.7155 45.3704 20.4492 40.8333 5 34.1927 68.3883 29.3127 58.5714 26 6536 51.2500 22.8079 45.5556 20.5324 41.0000 6 34.3360 68.6111 29.4356 58.8095 25.7611 51.4583 22.9035 45.7407 20.6184 41.1667 7 31.4793 68.8889 29.5584 59.0476 25.8686 51 . 6667 22.9991 45.9259 20.7045 41.3333 8 34.6178 69.1667 29.6772 59.2856 25.9725 51.8750 23.0915 46.1111 20.7877 41.5000 9 34.7564 69.4444 29.7959 59.5238 26.0765 52.0833 23.1&39 46.2963 20.8708 41.6667 10 34.8049 69.7222 29.914759.7619 26.1804 52.2917 23.276346.4815 20.954041.8333 11 35.0334 70.0000 30.0335 60.0000 26.2843 52.5000 23.368746.6667 21.037242.0000 12 35.1719 70.277830.1522 60.2381 26.3883 52.7083 23.4611 46.8519 21.120442.1667 13 35.3105 70.555630.2710 60.4762 26.4922 52.9167 23. 5535! 47. 0370 21.2036 42.3333 14 35.4490 70.83:53:30.3897 60.7143 26.5961 53.1250 23.6459I47 2222 21.2868;42.5000 15 35.5875 71.1111 30. 5085| 60. 9524 26.7000 53.3333 23.7383 47.4074 21.369942.6667 16 35.7261 71.3889 30. 6272! 61. 1905 26.8040 53.5417 23.8307 47 5926 21. 4531 J42. 8333 17 35.8646 71.6667 30.7460 61.4286 26.9079 53.7500 23.9231 47.7778 21. 5363 '43.0000 18 30.0031 71.9444 30.8648 61.6667 27.0118 53.9583 24.0155 47.9630 21.6195 43.1667 19 36.1416 72.2222 30.9835 61.9048 27.1158 54.1667 24.1079 48.1482 21.7027 43.3333 20 36.2802 72.5000 31.1023 62.1429 27.2197 54.3750 24.2003 48.3333 21.7859 43...000 21 86.4187 72.7778 31.2210 62.3810 27.3236 54.5833 24.2927 48.5185 21.8691 43.6667 22 36.5620 73.0556 31.3439 62.6190 27 4312 54.7917 24.38^3 48.7037 21.9551 43.8333 23 36.7053 73.3333 31.4667 62.8571 27.5387 55.0000 24.4839 48.8889 22.0412 44.0000 24 36.8438 73.6111 31.5855 63 095:. 27.6426 55.2083 24.5763 49.0741 22.1243 44.1667 25 36.982-1 73.8889 31.7043 63 3333 27.7465 55.4167 24.6687 49.2593 22.2075 44.3333 26 37.1209 74.1667 31.8230 63.5714 27.8505 55.6250 24.7611 49.4444 22.2907 44.5000 27 37.2594 74 4444 31.9418 63.8095 27.9544 55.8333 24.8535 49.6296 22.3739 44.6667 28 37.3380 74.7222 32.0605 64.0470 28.0583 56.0417 24.9459 49.8148 22.4571 44.8333 29 37.5365 75.0000 32.1793 64.2R5T 28.1623 56.2500 25.0383 50.0000 22.5403 45 0000 30 37.675C 75 2778 32.2980 64.5238 28.2662 56.4583 25 1307 50.1852 22.6235 45.1667 31 37 8135 75.5556 32.4168 64.7619 28.3701 56.6667 25.2231 50.3704 22.7066 45.3333 32 37.9521 75.8333 32 5356 65.0000 28.4741 56.8750 25.3155 50.5556 22.7898 45.5000 33 38.0906 76.1111 32.6543 65.2381 28.5780 57.0833 25.4079 50.7407 22.8730 45.6667 34 38.2291 70.3889 32.7731 65.4762 28 68T9 57.2917 25.5004 50.9259 22.9562 45.8833 35 3S 367? 76 6667 32.8918 65.7143 28.7859 57.5000 25 5928 51.1111 23.0394 46.0000 36 38.5110 76 9444 33.0147 65 9524 28.8934 57.7083 25.6883 51.2963 23.1254 46.1667 37 38.6513 77.2222 88.1875 66.1905 29.0009 57.9167 25.7839 51 4815 23.2115 46.3333 38 38.7928 77.5000 33 2563 66.4286 29.1048 58.1250 25.8763 51.6667 23.2947 46.500U 39 38.9313 77.7778 33.3751 66.6667 29.2088 58.3333 25.9687 51.8519 ?3.3779 46.6667 40 39.0699 78.0556 33.4938 66.9048 29.3127 58 5417 26.0612 52.0370 23.4610 46.83^3 41 39.2084 78.8388 33 6126,67.1429 29.4166 58.7500 26.1536 52.2222 23.5442 47.0000 42 39.3469 78.6111 88.781367.8810 29.5206 58.9583 26.2460152.4074 23.6274 47.1667 43 39.4854 78.8889 33. 8501 j 67. 61 90 29.6245 59.1667 26.338452.5926 23.7106 47.3333 44 39.6240 79.1667 33. 9088 7. 8571 29.7284 59.3750 26. 4308! 52. 7778 23.7938 47.5000 45 39 7625 79.4444 34.087668.0952 29.8324 59.5838 26. 5232 ! 52. 9630 23. 877047.66C7 4G 39.9010 79.7222 34 2064 68.8333 29.9363 59.7917 26.6156J 53. 1482 23 960247.83:i3 47 40.0396 80.0000 34.3251 68.5714 30.0402 60.0000 26.7080 3.8383 24.043348.0000 48 40 1781 80 2778 34.4439 68.8095 30.1442 60.2083 26.8004.53.5185 24.1265 48.1667 49 40.3166 80.5556 34.5626 69.0476 30.2481 60.4167 26.892853.7037 24.2097 48.3333 5O 40.4580 80.833331.685569.2856 80.3556 60.62.M) 26.988453.8889 24.2958 48 5000 51 40 6032 85.1111 34.808369.5238 30.4631 60.8333 27.084054 0741 24.381848.6667 52 40.7418 81.3889 31.9271 69.7619 30.5671 61.0417 27.176454.2593 24.465048.8333 53 40.8803 81. 6667! 35 045970.0000 30 6710 61.2500 27.2688 54.4444 24.548249.0000 54 41.0188 81. 9444 35. 1646 70. 23S1 30.7749 61.4583 27. 361 2 54.629* 24.6314 49 1667 55 41.1573 82. 2222 35. 2834 70. 47(5-. 30.8789 61 .66(57 27.4536 54.8148 24.714649.3333 50 41.2959 82.500035.4021 70. 7H3 30.9828 61.8750 27.546055.0000 24.797749.5000 57 41.4344 82 7778 35.5209 70.9524 31.0867 62 0833 27.638455.1852 24.880949.6667 58 4 1 . 5? 57 49.793999.4444 49.932499.7222 42.687385.2381 42.8061 85.4762 37.358674.5833 37.4625l74.791" 33.214566.296 33. 3069 166.481 29.900759.666 r 29.983959.833^ ' 58 \ 59 57 TAT5LE XIV. ACTUAL TANGENTS, ETC 6 1 Curve. 3 Curve. 3 Curve. 4 Curve. 5 Curve. M. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. ~~O~ 300.291 600 . 000 1 50 . 1 5 1 300 . 000 100.107 200.000 75.0873 150.000 00.0705 120.000 1 301.122 601.667 150.56(5 300.883 100.3S4 200.556 75 2950 150.417 60.2427 120.3:>3 3 301.953 (303.333 lf>0. 982 30 1.607 100 661 201.111 75.5028 150.833 60 4090 120.007 3 302.783 605 . 000 151 . 397 302 . 500 100.938201.667 75.7105 151.250 60.5752 121 000 4 303.614 606. 6671151.813 303. 333 101.215 202.222 75.9182 151.667 60 7414 121 333 5 304.445 608. 333 ! 152. 228 j 304. 167 101.492 202.778 76.1260 152.083 60.9070 121.007 6 305.276 610.000 152. 643 '305. 000 101.769 203.333 76.3337 152 500 01.0738 122 000 7 306.107 611.667 153.059305.833 102.046 203.889 76.5415 152.917 01.2400 122 333 8 306.937 613.333 153. 474 1306.667 102.323 204.444 76.7492 153.333 61.4062 122.007 9 307.797 615.000 153.904 307.500 102.609 205.000 76.9641 153.750 61.5782 123.000 10 308.656 616.667 154.334 308.333 102.896 205.556 77.1790 154.167 61.7501 123.333 11 309 487 618.333 154. 749 ! 309. 167 103.173 206.111 77.3808 154.583 01.9163 123.007 13 310.318 620.000 155. 1651310. 000 103.450 206.667 77.5945 155.000 02.0825 124.000 13 311.149 621.667 155.580310.833 103.727 207.222 77.8022 155.417 02.2487 124.333 14 311.979 623.333 155.995311.667 104.004 207.77878.0100 155.833 02.4149 124 007 15 312.810 625 000 156.411 312.500 104.281 2J8.333 78.2177 156 250 02 5812 125 000 16 313.641 626.667 156.826 313 333 104.558 208.889 78.4255 150.007 02.7474 125.333 17 314.472 628.333 157.242 314.167 104.835 209.444 78.6332 157.083 02.9136 125.007 18 315.303 630.000 157.657 315.000 105.112 210.000 78.8409 157.500 63.0798 126.000 19 316.162 631.667 158.087 315.833 105.398 210.556 79.0558 157.917 63.2517 120.333 30 317.022 633 333 158.517 316.667 105.685 211.111 79.2707 158.333 63.4237 126.607 31 317.852 635.000 158.932 317.500 105.962 211.667 79.4785 15S.750 03.5899 127.000 33 318 683 636 667 159.347 318 333 106.239 212.222 79.0862 159.107 63.7501 127.333 33 319.514 638.333 159 763 319.167 106.516 212 778 79 8940 159 583 03.9223 127.667 34 320.345 640.000 160.178 320.000 106.793 213.333 80.1017 160.000 04.0885 128.000 35 321.176 641.667 160.594 320 833 107.070 213.889 80 3094 160.417 64 2547 128.333 36 322.006 643.333 161.009 321.667 107.341'. 214.414 80.5172 160.833 64.4209 128.007 37 322.837 645.000 161.424 322.500 107.623 215.000 80.7249 161.250 64.5871 129.000 38 323.668 646.667 161.840 323.333 107.900 215.556 80.9327 161.667 04.7534 129.333 39 324.499 648.333 162.255 324.167 108.177 216.111 81.1401 162.083 64.9196 129.607 30 325.330 650.000 162.671 325.000 108 454 216.607 81.3181 162 500 65.0858 130.000 31 326 189651.667 163.100 325.833 108.741 217.222 81.5630 102.917 05.2577 130.333 33 327.048 653. 333 163. 530 326.667 109.027 217.778 81.7779 103.333 65.4297 130.607 33 327.879 655.000 163.946 327.500 109.304 218.333 81.9857 103 750 65.5959 131.000 34 328.710 656.667164.361 328.333 109 581 218.889 82.1934 164.167 65.7621 131.333 35 329.541 658.333 164.776 329.167 109 858 219.444 82.4012 164.583 65.9283 131.667 36 330.372 660.000165.192 330.000 110.135 220.000 82.0089 165.000 66 0945 132 000 37 331 202 66 1 . 667 1 65 . 607 1 330 . 833 110.412 220.556 82.8166 165.417 66.2607 132.383 38 39 332.033 332.864 663.333 665.000 166.023 166.438 331.667 332.500 110.689 110.966 221.111 221.667 83.0244 83.2321 105.833 166.250 66.4269 66.5931 132.607 133.000 40 333.695 666.667 166.854 333.333 111.243 222.222 83.4399 166.667 66.7593 133.333 41 334.554 668.333 167.283334.167 111.530222 778 83.0548 167.083 66.9313 133.607 43 335.414 670.000 167.713335.000 111.816223.333 83.8697 167.500 67.1032 134.000 43 336.245 671.667 168.128 335.833 112.093223.889 84.0774 167.917 67.2694 131.333 44 337.075 673.333 168.544 336.667 112.370 224.444 84.2852 168.333 67.4357 134.667 45 337.906 67o.OOO 168.959 337.500 112.647 225.000 84 4929 168.750 67.6019 135.000 46 338 737 676.667 169.3751338.3:53 112.924225.556 84.7006 169.167 67.7081 135.333 47 339.568 678.333 169.7901339.167 113.201 226. 11 1184.9084 169.583 07. 9343 1 135. 607 48 340.399 680.000 170.205 340.000 113.478 226.667 85.1161 170.000 68.1005 130.000 49 341.229 681.667 170.621 340.833 113.755 227.222 85.3239 170.417 68.2667 136.333 50 342.060 683.333 171.036 341.667 114.032 227.778 85.5316 170.833 08.4329 136.607 51 342.891 685.000 171.452342.500 114.309 228.333 85.7393 171.250 08.5991 137.000 53 343.722 686.667 171.867J343.333 114.586 228.889 85.9471 171.667 68.7(553 137.383 53 344.581 688.333 172.297 344.167 114.872 229.444 86.1620 172.083 08.9373 137 0(i7 54 345.441 690.000 172.727 345.000 115.159 230.000 86.3709 172.500 09.1092 13H.OOO 55 346.271 691.667 173.142345.833 115.436 230.556 86.5846 172.917 09.2754 138.383 56 347.102 693.333 173.557346.667 115.713 231.111 HO. 792 4 173.333 09.4410 188.007 57 347.033I695.000I178.973J347.500 115.990 231.667 87.0001 173.750 09.0079 139.0'H) 58 1 348. 704 696.667 174.388 318.333 116.267 232.222 87.207'8 174.107 09 7741 139 383 59 349.595 698.333; 174. 804 349.167 116.544 232.778 87.4156 174.58309.9403 139.007 58 TABLE XIV. ACTUAL TANGENTS, ETC. G Curve. 7 Curve. 8 Curve. 9 Curve. 10 Curve. G Tan. Arc. Tan Arc. Tan. [ Arc. Tan. Arc. Tan. Arc. M. f,0. 0709! 100 00042 924885.7143 37. 5664! 75 0000 33.3093 66.6667 30.0671 60.0000 o 50. 2095 (100.278 43 0480 85.9524 37. 6704 175.2083 33.4917 66.8519 30.1503 60.1067 1 50.3480 100.556J43.HB8 86 1905 37.774375 4167 33.5841 07.037( 30.2335 60.3333 2 50 4865 100.833,43.2811 86.42.S6 37 8782175.6250 33 6765 67.2222 30.3166 60.5000 3 50.0251 101.111 43.3999 86.6667 37 9822 75.8333 33.7689 67.4074 30.399? 60.6667 4 50.7636 101.389 43.5186 86.9048 38.0801 76 0417 33.8013 67.5926 30.4830 60.8333 5 50.9021 101.66743.6374 87.1429 38 1900 76.2500 33.9537 67.7778 30.5662 61.000( 6 51.0406 101.94443.7561 87.3810 38.2940 76.4583 34.0461 67.9630 30.6494 61.1667 7 51.1792 102.222 43.8749 87.6190 38.3070 70.6(167 34.1385 68.1482 30.7326 61.3333 8 51.8225 102.500 43.9977 87.8571 38.5054 76.8750 34.2341 68.3333 30.8186 01.5000 9 51.4658 102.778 44.1206 88.0952 38.6129 77.0833 34.3297 68.5185 30.9047 61.6667 10 5 1.6043 11 03. 056 44. 2394 88.33:33 38.710977.2917 34.4221 68.7037 30.987961.8333 11 51.7428 103.333 44.3581 88.5714 38.820877.5000 34.5145 68.8889 31.071062.0000 12 51 8814 103.611 44.4769 88.8095 38.924777.7083 34.6069 69.0741 31.154262.1667 13 52. 01 991 103. 88 44.5956 89.0476 39.028777.9167 34.6993 69.2593 31.2374 62.3333 14 52 15841104.167 44-7144 89 2856 39 1326 78.1250 34.7917 69 4444 31.3206 62.5000 15 52.2009 104.444 52. 4 355; 104. 722 44.8331 44.9519 89.5238 89.7619 39.2365 78.3333 39.340578.5417 34.8842 34.9766 69.6296 69.8148 31.4038 31 4870 62.6667 62.83:33 16 17 52.5740 105.000 45.0707 90.0000 30.4444 78.7500 35.0690 70.0000 31.5702 63.0000 18 52.7173 105.278 45.1935 90.2381 39.5519 78.9583 35.1640 70.1852 31.6562 63.1667 19 52.8606 105.556 45.3164 90.4762 39.6594 79.1667 35.2601 70.3704 31.7423 63.3333 2O 52.9991 105.833 45.4351 00.7143 39. 7634 179.3750 35.3525 70.5556 31.8254 63.5000 21 53.1377 106 111 45.5539 90.9524 30 8673 79.5833 35.4450 70.7407 31.9080 63.6007 22 53.2762 1 06.389 45.0726 91.1905 30.9712 79.7917 35.5374 70.9250 31.9918 63.8333 23 53.414? 106.667 45 7914 91.4286 40.0752 80.0000 35.6298 71.1111 32.0750 64.0000 24 53.5533 106.944 45.9102 91.6667 40. 1791 180. 2083 35.7222 71.2963 32.1582 64.1667 25 53.6918 107.222 46.0289 91.9048 40.2830180.4107 35.8146 71.4815 32.2414 64.3333 26 53.8303 107.500 46.1477 92.1429 40.3870 80.6250 35.9070 71.6667 32.3246 04.5000 27 53.9688 107.778 46.2664 92.3810 40.4909 80.8333 35.9994 71.8519 32.4077 64.6667 28 54.1074 108.056 46.3852 02.6190 40.5948 81.0417 36.0918 72.0370 32.4909 04.8333 29 54.2459 108.333 46.5030 92.8571 40.6988 81.2500 36.1842 72.2222 32.5741 05.0000 30 54.3892 108.611 46.6268 93.0952 40.8063 81 .4583 36.2798 72.4074 32.6602 05.1667 31 54.5325 108.889 46.7497 93.3333 40.9138 81.6667 36.3754 72.5926 32.7462 65.3333 '32 54.6710 109.16? 46.8684 93.5714 41 0177 81.8750 36.4678 72.7778 32.8294 65.5000 33 54.8096 109.444 46.9872 93 8095 41.1217 82.0833 36.5602 72.9630 32.9126 65.6667 34 54.9481 109.722 47.1059 U.0476 41.2256 82.2917 36.6526 73.1482 32.9958 05.8333 35 55.0866 110.000 47.2247 94.2856 41.3205 82.5000 36.7450 73.3333 33.0790 66.0000 3G 55.2252 110.278 47.3434 94.5238 41.4335 82.7083 36.8374 73.5185 33.1621 66.1667 37 55.3637 110.55647.4622 94.7019 41.5374 82.9167 30.9298 73.7037 33 2453 66.3333 38 55.5022 110. 833|47. 5810 95.0000 41.6413 83.1250 37.0222 73.8889 33.3285 66.5000 39 55.6407 111.111147.6997 95.2381 41.7453 83.3333 37.1146 74.0741 33.4117 66.6667 4O 55.7840 111.3S947.8226 95.4762 41.8528 83.5417 37.2102 74.2593 33.4978 66.8333 41 55.9274 111. (567 4 7. 9454 95.7143 41.9603 83.7500 37.3058 74.4444 33.5838 67.0000 42 56.0659 111.94448.0642 95.9524 42.0642 83.9583 37.3982 74.6296 33.667067.1667 43 56 2044 112 222:48 1829 96.1905 42.1682 84.1667 37.490G 74.8148 33.7502 67.3333 44 56.3429 112.50048.3017 96.4286 42.2721 84.3750 37.5830 75.0000 33.8S34 67.5000 45 56.4815 112.778 48.4205 96.6667 42.37GO 84.5833 37.6754 75.1852 33.9165 67.6667 46 56.6200 113.05648.5392 96.9048 42.4800 84.7917 37.7678 75.3704 33.9997 67.8333 47 56.7585 113.333 48.6580 97.1429 42.583985.0000 37.8602 75.5556 34.0829 08.0000 48 56.8971 113.611:48.7767 97.3810 42.6878 85.2083 37.9526 75.7407 34.1661 68.1667 49 57.0356 113. 880 ! 48. 8955 97.6190 42.7918 85.4167 38.0450 75.9259 34.2493 68.3333 no 57.1741 114.16749.0142 97.8571 42.8957 85. 6250 138. 1374 76.1111 34.3325 68 50CO 61 57.3126 114.44449.1330 08.0952 42.9996 85.8333 38.2298 76.2963 34.4157 68.6667 52 57.4559 114.72249.2559 98.3333 43.1071 86.0417 38.3254 76.4815 34.5017 08.8333 53 57.5993 115.000:49.8787 98.5714 43.2147 86.2500 38.4210 76.6667 34.587869.0000 54 57.7378 115.27849.4975 98.8095 43. 31 86 86. 4583 38.5134 76.8519 34.670969.1667 55 57.8763 115.55649.6162 99.0476 48.4225 86.6667 38.6058 77.0370 34.7541 09.3333 56 58.0148 115.83349.7350 99.2856 3 . 5265 i 86 . 8750 1 38 . 6982 77.2222 34.8373 69.5000 57 58.1534 116.111 49.8537 09.5238 43.6304 87.0833 38.7906 77.4074 34.9205 69.6067 58 58.2919 116.38949.9725 99.7619 3. 7343 87. 2917 38. 8830 77.5920 35.003769.8333 59 59 TABLE XIV. ACTUAL TANGENTS, ETC. 7 1 Curve. 3 Curve. 3 Curve. 4 Curve. 5 Curve. M. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. 3.-)0.425 700.000 175.219 350.000 1 1 6 . 820 233 . 333 87 . 6233 175.000 70.1065 140.000 1 351.25(5 701.667 175.635 350.833 117.097233.88987.8311 175.417 7D.2727 140.333 3 352.087 703.333 1 76.050J351 667 1 1 7 . 374 23 4 . 444 88 . 0388 1 75 . 833 70.4389 140.667 3 352.946 705.000 176.480352.500 117.661 235.00088.2537 176.250 70. 6108:141. 000 4 353.806 706 667 176.909 353.333 117.947 235 . 556 88 . 4686 1 76 . 667 70.7828 141.333 5 354.637 708.333 177.325354.167 118 224 ! 236. 111188. 6763 177.083 70.9490141.0(57 6 355.467 710.000 177.740355 000 118.501236.66788.8841 177.500 71. 1152! 142. 000 7 356.298 711.667 178.156 355.833 118.778237.222:89.0918 177.917 71.2814 142.333 8 357.129 713.333 178 571 356.667 119.055237.77889.2996 178.333 71.4476 142.667 9 357.960 715.000 178.987 357.500 119. 332 238. 333,89. 5073 178.750 71.6138 143.000 1O 358.791 716.667 179.402 358.333 119.609 238.889 89.7150 179.167 71.7801 143.333 11 359.621 718.333 179. 8171359. 167 119.886 239.444 89.9228 179.583 71.9463 143.667 13 360.452 720.000 180.233360.000 120.163240.00090.1305 180.000 72.1125 144.000 13 361.312 721.667 180.662360.833 120.450240.556:90.3454 180.417 72.2844 144.333 14 362.171 723.333 181.092361.667 120.736241.111 90.5603 180.833 72.4564 144.667 15 363.002 725.000 181.508362.500 121.013241.66790.7681 181.250 72.6226 145.000 16 363.833 726.667 181.923,363.333 121.290 242.22290.9758 181.667 72.7888 145.333 17 364.664 728.333 182.338364.167 121.567 242.77891.1836 182.083 72.9550 145.667 18 365.494 730.000 182. 754 ;365.000 121.844 243.33391.3913 182.500 73.1212 146.000 19 366.325 731.667 183.169365.833 122.121 243.889 91.5990 182.917 13.2874 146.333 30 367.156 733.333183.585366.667 122.398 244.444 91.8068 183.333 73.4536 146.667 31 367.987 735.000184.000367.500 122.675245.00092.0145 183.750 73.6198 147.000 33 368.818 736.667 184.4163(58.333 122.952 245.556 92.2223 184.167 73.7860 147.333 33 369.677 738.333184.845 369.167 123.238 246.111 92.4372 184.583 73.9580 147.6(57 34 370.536 740.000 185.275 370.000 123.525 246.66792.6521 185.000 74.1299 148.000 35 371.367 741.667185.6901370.833 123.802 247.22292.8598185.417 74.2961 148.333 35.000 206.619 412.500 137.755 275.000 103.326206.250 82.6697 165.000 16 414.082 826.667 207.048 413.3:33 138.041 275.556 103.541 206.667 82.8417 165.333 17 414.913 828.333 207.464 414.167 138.318 276.111 103.748i20r.083 83.0079 165.667 18 415.743 830.000 207.879 415.000 138.595 276.667 103.956207.500 83.1741 166.000 19 416.574 831.667 208.295 415.833 138.872 277.222 104.164 207.917 83.3403 166.333 20 417.405 833.333 208.710 416.667 139.149 277.778 104.371 208.333 83.5065 166.667 21 418.236 835.000 209.126 417.500 139.426 278.333 104.5791208.750 83.6727 167.000 22 419.067 836.667 209.541 418.333 139.703 278.889 104. 787|209. 167 83.8389 167.333 23 419.926 838.333 209.971 419.167 139.990 279.444 105. 002! 209. 583 84.0109 167.667 24 420.785 840.000 210.400 420.000 140.276 280.000 105.217 210.000 84.1828 168.000 25 421.616 841.667 210.816 420.833 140.553 280.556 105.424 210.417 84.3490 168.333 2(> 422.417 843.333 211.231 421.667 140.830 281.111 105.632 210.833 84.5152 168 667 27 423.278 845.000 211.647 422.500 141.107 281.667 105.840 211.25084.6814 169.000 28 424.109 846.667 212.062 423.333 141.384 282.222 106.048 211.66784.8476 169.333 29 424.939 848.3:33 212.478 424.167 141.661 282.778 106.255 212.083 85.0139 169.667 3O 425.770 850.000 212. 8Q3 425.000 141.938 283.333 106.463 212.500 85.1801 170.000 31 426.630 85 1.667 213.323 425.833 142.225 283.889 106.678 212. 9! 7185. 8520 170.333 32 427.489 853.333 213.752 426.667 142.511 284.444 106.893 213.33385.5240 170.667 33 428.320 855.000 214.168 427.500 142.788 285.000 107.101 2 13. 750 '85. 6902 171.000 34 429 151 856.667 214.583 428.333 143.065 285.556 107.308 214.167,85.8564 171.333 35 429.982858.333 214.999 429.167 143.342 286.111 107.516 214.58386.0226 171.667 36 430. 812 ! 860. 000 215.414 430.000 143.619 286.667 107.724 215. 000|86. 1888 172. 000 37 431.643 861.667 215.830 430.833 143.896 287.222 107.932 21 5 . 41 7 i 86 . 3550 1 72 . 333 38 432.474863.333 216.245 431.667 144.173 287.778 108.139 215. 633 86. 3121172.667 39 433.333 865.000 216.675 432.500 144.459 288.833 108.354 216.250 86.6932 173.000 4O 434.193 866.667 217.104 133.333 144.746 288.889 108.569 216.667 86.8651 173.333 41 435.024 868.333 217.520 434.167 145.023 289.444 108.777 217.083 87.0313 173.667 42 435.854 870.000 217.935 435.000 145.300 290.000 108.985 217.50087.1975 174.000 43 436.685 871.667 218.351 43>. 833 145.577 290.556 109.192 217.91787.3637174.333 44 437.516 873.333 218.766 136.667 145.854 291.111 109.400 218.33387.5299174.667 45 43 S. 3 47 875.000 219.181 437.500 146.131 291.867 109.608 218.750 87.6962 175.000 46 439.178 876.667 219.597 438.333 146.408 292.222 109.816 219.16787.8624 175.333 47 440.037 878.333 2-20.027 439.167 146.694 292.778 110.031 219. 583 ' 88 . 0343 1 75 . 667 48 49 410.897 441.727 880.000 881.667 220.456 220.872 440.000 440.833 146.981 147.258 293.333 293.889 110.245 110.453 220.000 220.417 88.2062 176.000 88.3725,176.333 50 412.558 883.333 221.287 441.667 147.535 294.444 110.661 220.833 88. 538?! 176. 667 51 443.389 885.000 221.703 442.500 147.812 295.000 110.869 221 . 250 88 . 7049 1 1 77. 0(10 52 444.220 886.667 222.118 443.333 148.089 295.556 111.076 221. 667 88. 8711 j 177.333 53 415.051 888.333 222.533 444.167 148.365 296.111 111.284 22 .' . 083 89 . 0373 1 77 . 667 54 445.881 890.000 222.949 445.000 148.642 296.667 111.492 222 . 500 89 . 2035 1 1 78 . 000 55 116.741 891.667 223.379 445.833 148.929 297.222 111.707 222 . 91 7 89 . 3755, 178 . 333 5(1 447.600 893.333 223.808 446.667 149.215 297.778 111.922 223 . 333 89 . 5474 1 178 . 667 57 148.431 895.000 224.224 447.500 149.492 298.333 112.129 223.75089.7136 179.000 58 449.262 896.667 224.639 448.333 149.769 298.889 112.337 224.16789.8798 17'9.333 59 450.093 898.333 225.055 449.167 150.046 299.444 112.545 224.58390.0460179.667 TABLE XIV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 Curve. 1O Curve. 8 Tan. | Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. M. 66.8090 133.333 57.2741 114.286 50.1244 100.000 44.5643 88.8889 40.1181 80.0000 ~O 66.9475 133.611 57.3928 114.524 50.228-1 100.208 44 . 6567 89.0741 40.2013 80.1667 1 67.0861 133.889 57.5116 114.762 50.3323 100.417 44.7491 89.2593 40.2845 80.3333 2 67.2246 134.167 57.6303 115.000 50.4362 100.625 44.8415 89.4444 40.367780.5000 3 67.3631 134.444 57.7491 115.238 50.5402 100.833 44.9339 89.6296 40.4509 80.6667 4 67.5017 134.722 57.8679 115.476 50.6441 101.042 45.0263 89.8148 40.5341 80.8333 5 67.6402 135.000 57.9866 115.714 50.7480 101.250 45.1187 90.0000 40.6172 81.0000 6 87.7835 ia5.278 58.1095 115.952 50.8555 101.458 45.2143 90.1852 40.7033 81.1667 7 67.9268 135.556 58.2323 116.190 50.9631 101.667 45.3099 90.3704 40.7894 81.3333 8 68.0653 135.8:33 58 3511 116.429 51.0670 101.875 45.4023 90.5556 40.8725 81.5000 9 68.2039 136.111 58.4698 116.667 51.1709 102.083 45.4947 90.7407 40.9557 81.6667 1O 68.3424 136.389 58.5886 116.905 51.2749 102.292 45.5871 90 9259 41.0389 81.8333 11 68.4809 136.667 58.7073 117.143 51.3788 102.500 45.6795 91.1111 41.1221 82.0000 13 68.6194 136.944 58.8261 117.381 51.4827 102.708 45.7719 91.2963 41.2053 82.1667 13 68.7580 137.222 58.9449 117.619 51.5867 102.917 45.8643 91.4815 41.2885 82.3333 14 68.9013 137.500 59.0677 117.857 51.6942 103.125 45.9599 91.6667 41.3745 82.5000 15 69.0446 137.778 59.1906 118.095 51.8017 103.333 46.0555 91.8519 41.4606 82 6667 16 69.1831 138.050 59.3093 118.333 51.9056 103.542 46.1479 92.0370 41.5438 82.8333 17 69.3216 138.333 59.4281 118.571 52.0096 103.750 46.2403 92.2222 41.6269 83.0000 18 69.4602 138.631 59.5468 118.810 52.1135 103.958 46.3327 92.4074 41.7101 83.1667 19 69.5987 138.889 59.6656 119.048 52.2174 104.167 46.4251 92.5926 41.7933 83.3333 20 69.7372 139.167 59.7844 119.286 52.3214 104.375 46.5175 92.7778 41.8765 83.5000 21 69.8758 139.444 59.9031 119.524 52.4253 104.583 46.6099 92.9630 41.9597 83.6667 22 70.0191 139.722 60.0260 119.762 52.5328 104.792 46.7055 93.1482 42.0457 83.8333 23 70.1624 140.000 60.1488 120.000 52.6403 105.000 46.8011 93.3333 42.1318 84.0000 24 70.3009 140,278 60.2676 120.238 52.7443 105.208 46.8935 93.5185 42.2150 84.1667 25 70.4394 140.556 00.3863 120.476 52.8482 105.417 46.9859 93.7037 42.2982 84.3333 26 70.5780 140.833 60.5051 120.714 52.9521 105.625 47.0783 93.8889 42.3813 84.5000 27 70.7165 141.111 60.6239 120.952 53.0560 105.833 47.1707 94.0741 42.4645 84.6667 28 70.8550 141.389 60.7426 121.190 53.1600 106.042 47.2631 94.2593 42.5477 84.8333 29 70.9935 141.667 60.8614 121.429 53.2639 106.250 47.3555 94.4444 42.6309 85.0000 30 71.1368 141.944 60.9842 121.667 53.3714 106.458 47.4511 94.6296 42.7170 85.1667 31 71.2801 142.222 61.1071 121.905 53.4790 106.667 47.5467 94.8148 42.8030 85.3333 32 71.4187 142.500 61.2258 122.143 53.5829 106.875 47.6391 95.0000 42.8862 85.5000 33 71.5572 142.778 61.3446 122.381 53.6868 107.083 47.7315 95.ia52 42.9694 85.6667 34 71 . 6957 143.056 61.4634 122.619 53.7908 107.292 47.8239 95.3704 43.0526 85.8333 35 71.8343 143.333 61.5821 122.857 53.8947 107.500 47.9163 95.5556 43.1357 86.0000 36 71.9728 143.611 61.7009 123.095 53.9986 107.708 48.0087 95.740? 43.2189 86.1667 37 72.1113 143.889 61.8196 123.333 54.1025 107.917 48.1011 95.9259 43.3021 86.3333 38 72.2546 144. 1G7 61.9425 123.571 54.2101 108.125 48.1967 96.1111 43.3882 86.5000 39 72.3979 144.444 62.0653 123.810 54.3176 108.333 48.2923 96.2963 43.4742 86.6667 4O 72.5365 144.72-' 62.1841 124.048 54.4215 108.542 48.3847 96.4815 43.5574 86.8333 41 72.6750 145.000 62.3028 124.286 54.5254 108.750 48.4771 96.6667 43.6406 87.0000 42 72.8185 145.278 62.4216 124.524 54.6294 108.958 48.5695 96.8519 43.7238 87.1667 43 72.9520 145.55G 62.5404124.762 54.7333 109.167 48.6619 97.0370 43.8070 87.3333 44 73.0906 145.833 62.a591|125.000 54.8372 109.375 48.7543 97.2222 43.8901 87.5000 45 73.2291 146.111 62.7779125.238 54.9412 109.583 48.8467 97.4074 43.9733 87.6667 46 73.3721 146.389 62.9007125.476 55.0487 109.792 48.9423 97.5926 44.0594 87.8333 47 73.5157 146.667 63.0236125.714 55.1562 110.000 49.0379 97.7778 44.1454 88.0000 48 73.6542 146.944 63.1423125.952 55.2601 110 208 49.1303 97.9630 44.2286 88.1667 49 | 73.7928 147.222 63.2611 126.190 55.3641 110.417 49.2227 98.1482 44.3118 F8.3333 50 73.9313 147.500 63.3799 126.429 55.4680 110.625 49.3151 98.3333 44 . 3950 88.5000 51 74.0698 147.778 63.4986 126.667 55.5719 110.833 49.4075 98.5185 44.4782 88.6667 52 74.2084 148.056 63.6174 126.905 55.6759 111.042 49.4999 98.7037 44.5614 88.8333 53 74.3469 148.333 63.7361 127.143 55.7798 111.250 49.5923 98.8889 44.6446 89.0000 54 74.4902 148.611 63.a590 127.381 55.8873 111.458 49.6879 99.0741 44.7306 89.1667 55 74.6335 148.889 63.9818 127.619 55.9948 111.667 49.7835 99.2593 44.8167 89. 3383 56 74.7720 149.167 64.1006 127.857 56.0988 111.875 49.8759 99.4444 44.8998 89.5000 57 74.9106 149.444 64.2194 128.095 56.2027 112. 083 49.9683 99.6296 44.9830 89.6667 58 75.0491 149.722 64.3381 128.333 56.3066 112.292 50.0607 99.8148 45.0662 89.8333 59 63 TABLE XIV. ACTUAL TANGENTS, ETC. 9 1 Curve. 2 Curve. 3 Curve. 4 Curve. 5 Curve. M. Tan. Arc. Tan. Arc. Tan. 150.323 Arc. Tan. Arc. Tan. Arc. 450.9:>3 900.000 225.47'0 450.000 300. 000 112.753 225.000 90.2122 180.000 1 451.754 901.667 225.885 450.833 150.600 300.556 112.960 225.417 90.3784 180.333 2 452.585 903.333 226.301 451.667 150.877 301.111 113.168 225.833 90.5447 180.667 3 453.445 905.000 226.731 452.500 151.164 301.667 113.383 226.250 90.7l6b 181.000 4 454.304 906.667 227.160 453.333 151.450 302.222 113.598 226.667 90.8885 181.333 5 455.135 908.333 227.576 454.167 151.727 302.778 113.806 227.083 91.0548 181.667 6 455.966 910.000 227.991 455.000 152.004 303.333 114.013 227.500 91.2210 182.000 7 456.796 911.667 228.407 455.833 152.281 303.889 114.221 227.917 91.3872 182.333 8 457.627 913.333 228.822 456.667 152.558 304.444 114.429 228.333 91.5534 182.667 9 458.487 915.000 229.252 457.500 152.845 305.000 114.644 228.750 91.7253 183.000 10 459.340 916.667 229.681 458.333 153.131 305.556 114 859 229.167 91.8973 183.333 11 460.17J 918.333 230.097 459.167 153.408 306.111 115.066 229.583 Q2.0635 183.667 13 461.008 920.000 230.512 460.000 153.685 306.667 115.274 230.000 92.2297 184.000 13 461.838 921.667 230.928 460.833 153.962 307.222 115.482 230.417 92.3959 184.333 14 462.669 923.333 231.343 461.667 154.239 307.778 115.690 230.833 92.5621 184.667 15 463.500 925.000 231.759 462.500 154.516 308.333 115.897 231.250 92.7283 185.000 16 464.331 926.667 232.174 463.333 154.793 308.889 116.105 231.667 92.8945 185.333 17 465.190 928.333 232.604 464.167 155.079 309.444 116.320 232.083 93.0665 185.667 18 466.050 930.000 233.033 465.000 155.366 310.000 116.535 232.500 93.2384 186.000 19 466.881 931.667 233.449 465.833 155.643 310.556 116.743 232.917 93.4046 186.333 20 467.711 933.333 233.864 466.667 155.920 311.111 116.950 233.333 93.5708 186.667 21 468.542 935.000 234.280 467.500 156.197 311.667 117.158 233.750 93.7370 187.000 22 469.373 936.667 234.695 468.333 156.474 312.222 117.366 234.167 93.9033 187.333 23 470.204 938.333 235.110 469.167 156.751 312.778 117.574 234.583 94.0695 187.667 24 471.035 940.000 235.526 470.000 157.028 313.333 117.781 235.000 94.2357 188.000 25 471.894 941.667 235.956 470.833 157.314 313.889 117.996 235.417 94.4076 188.3:33 26 472.753 943.333 236.385 471.667 157.601 314.444 118.211 235.833 94.5796 188.667 27 473.584 945.000 236.801 472.500 157.878 315.000 118.419 236.250 94.7458 189.000 28 474.415 946.667 237.216 473.333 158.155 315.556 118.627 236.667 94.9120 189.333 29 475.246 948.333 237.632 474.167 158.432 316.111 118.834 237.083 95.0782 189.667 30 476.077 950.000 238.047 475.000 158.709 316.667 119.042 237.500 95.2444 190.000 31 476.936 951.667 38.477 475.833 158.995 317.222 119.257 237.917 95.4163 190.333 32 477.796 953.333 238.907 476.667 159.282 317.778 119.472 238.333 95.5883 190.667 33 478.627 955.000 i39.322 477.500 159.559 318.333 119.680 238.750 95.7545 191.000 34 479.457 956.667 239.737 478.333 159.835 318.889 119.887 239.167 95.9207 191.333 35 480.289 958.333 240.153 479.167 160.112 319.444 120.095 239.583 96.0869 191.667 36 481.119 960,000 240.568 480.000 160.389 320.000 120.303 240.000 96.2531 192.000 37 481.978 961.667 240.998 480.833 160.676 320.556 120.518 240.417 96.4251 192.333 38 482.838 963.333 241.428 481.667 160.962 321.111 120.733 240.833 96.5970 192.667 39 483.668 965.000 241.843 482.500 161.239 321.667 120.941 241.250 96.7632 193.000 4O 484.499 966.667 242.258 483.333 161.516 322.222 121.148 241.667 96.9294 193.333 41 485.330 968.333 242.674 484.167 161.793 322.778 121.356 242.083 07.0956 193.667 42 486.161 970.000 243.089 485.000 162.070 323.333 121.564 242.500 97.2619 194.000 43 486.992 971.667 243.505 485.833 162.347 323.889 121.771 242.917 97.4281 194.333 44 487.822 973.333 243.920 486.667 162.624 324.444 121.979 243.3:33 J7.5943 194.667 45 488.682 975.000 244.350 487.500 162.911 325.000 122.194 2-13.750 97.7662 195.000 46 189.541 976.667 244.780 488.333 163.197 325.556 122.409 244.167 97.9382 195.333 47 490.372 978.333 245.195 489.167 163.474 326.111 122.617 244.583 98.1044 195.667 48 491.203 980.000 245.610 490.000 163.751 326.667 122.825 245.000 98.2706 196.000 49 492.034 981.667 246.026 490.833 164.028 327.222 123.032 245.417 98.4368 196.333 50 492.864 983.333 246.441 491.667 164.305 327.778 123.240 245.833 98.6030 196.667 51 493.724 985.000 246.871 492.500 164.592 328.333 123.455 246.250 98.7749 97.000 52 494.583 986.667 247.301 493.333 164.878 328.889 123.670 246.667 98.9469 197.333 53 495.414 988.333 247.716 494.167 65.155 329.444 123.878 247.083 99.1131 197.667 54 496.245 990.000 248.132 495.000 165.432 330.000 24.085 247.500 99.2793 198.000 55 497.076991.667 248.547 495.833 65.709 330.556 124.293 247.917 99.4455 198.333 56 497.907 993.333 248.962 496.667 65.986 331.111 124.501 248.333 99.6117 198.667 57 498.766 995.000 249.392 497.500 66.272 331.667 124.716 248.750 99.7837 199.000 58 499.625996.667 249.822 498. 333 166.559 332.222 124.931 249.167 99.9556 99.333 59 500.456:998.333 250.2371499.167 166.836 332.778 125.138 249.583 00.122 99.667 64 TABLE XIV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 Curve. 1O Curve. 9 Tan. Arc. Tan. Arc. Tan. Arc. 112.500 Tan. 50.1531 Arc. Tan. 45.14~94 Arc. 90.0000 M. 75.1876 150.000 64.4569 128.571 56.4106 100.000 75.3261 150.278 64.5756 128.810 56.5145 112.70850.2455 100.185 45.2326 90.1667 1 75.4647 150.556 64.6944 129.048 56.6184 112.91750.3380 100.370 45.3158 90.3333 2 75.6080 150.833 64.8172 129.286 56.7260 113.12550.4335 100.556 45.4018 90.5000 3 75.7513 151.111 64.9401 129.524 56.8335 113.33350.5291 100.741 45.4879 90.6667 4 75.8898 151.389 65.0588 129.762 56.9374 113.542(50.6215 100.926 45.5711 90.8333 5 76.0283 151.667 65 1776 130.000 57.0413 113.750 50.7139 101.111 45.6542 91.0000 6 76.1669 151.944 65.2964 130.238 57.1453 113.958 50.8063 101.296 45.7374 91.1667 7 76.3054 152.222 65.4151 130.476 57 2492 114.167 50.8987 101.481 45.8206 91.3333 8 76.4487 152.500 65.5380 130.714 57.3567 114.375 50.9943 101.667 45.9067 91.5000 9 76.5920 152.778 65.6608 130.952 57.4642 114.583 51.0899 101.852 45.9927 91.6667 10 76.7305 153.056 65.7796 131.190 57.5682 114.792 51.1823 102.037 46.0759 91.8333 11 76.8691 153.333 65.8983 131.429 57.6721 115.000 51.2747 102.222 46.1591 92.0000 12 77.0076 153.611 66 0171 131.667 57.7760 115.208 51.3671 102.407 46.2423 92.1667 13 77.1461 153.889 66.1359 131.905 57.8800 115.417 51.4595 102.593 46.3255 92.3333 14 77.2847 154.167 66.2546 132.143 57.9839 115.625 51.5520 102.778 46.4086 92.5000 15 77.4232 154.444 66.3734 132.381 58.0878 115.833 51.6444 102.963 46. 4918 192.6667 16 77.5665 154.722 66.4962 132.619 58.1954 116.042 51.7399 103.148 46.5779 92.a333 17 77.7098 155.000 66.6191 132.857 58.3029 116.250 51.8355 103.333 46.6639 93.0000 18 77.8483 155.278 66.7378 133.095 58.4068 116.458 51.9279 103.519 46.7471 93.1667 19 77.9868 155.556 66.8566 133.333 58.5107 116.667 52.0203 103.704 46.8303 93.3a33 20 78.1254 155. 833 66.9754 133.571 58.6147 116.875 52.1127 103.889 46.9135 93.5000 21 78.2639 156.111 67.0941 133.810 58.7186 117.083 52.2052 104.074 46.9967 93.6667 22 78.4024 156.389 67.2129 134.048 58.8225 117.292 52.2976 104.259 47.0799 93.8333 23 78.5410 156.667 67.3316 134.286 58.9265 117.500 52.3900 104.444 47.1630 94.0000 24 78.6843 156.944 67.4545 134.524 59.0340 117.708 52.4856 104.630 47.2491 94.1667 25 78.8276 157.222 67.5773 134.762 59.1415 117.917 52.5811 104.815 47.3352 94.3333 26 78.9661 157.500 f 7. 6961 135.000 59.2454 118.125 52.6735 105.000 47.4183 94.5000 27 79.1046 157.778 67.8149 135.238 59.3494 118.333 52.7660 105.185 47.5015 94.6667 28 79.2432 158.056 67.9336 135.476 59.4533 118.542 52.8584 105.370 47.5847 94.8333 29 79.3817 158.333 68.0524 135.714 59.5572 118.750 52.9508 105.556 47.6679 95.0000 SO 79.5250 158.611 68.1752 135.952 59.6648 118.958 53.0463 105.741 47.7540 95.1667 31 79.6683 158.889 68.2981 136.190 59.7723 119.167 53.1419 105.926 47.8400 95.3333 32 79.8068 159.167 68.4168 136.429 59.8762 119.375 53.2343 106.111 47.9232 95.5000 33 79.9454 159.444 68.5356 136.667 59.9801 119.583 53.3267 106.296 48.0064 95.6667 34 80.0839 159.722 68.6543 136.905 60.0841 119.792 53.4192 106.481 48.0896 95.8333 35 80.2224 160.000 68.7731 137.143 60.1880 120.000 53.5116 106.667 48.1727 96.0000 36 80.3657 160.278 68.8960 137.381 60.2955 120.208 53.6071 106.852 48.2588 96.1667 37 80.5090 160.556 69.0188 137.619 60.4030 120.417 53.7027 107.037 48.3449 96.3333 38 80.6476 160.833 69.1376 137.857 60.5070 120.625 53.7951 107.222 48.4280 96.5000 39 80.7861 161.111 69.2563 138.095 60.6109 120.833 53.8875 107.407 48.5112 96.6667 40 80.9246 161.389 69.3751 138.333 60.7148 121.042 53.9799 107.593 48.5944 96.8333 41 81.0631 161.667 69.4938 138.571 60.8188 121.250 54.0724 107.778 48.6776 97.0000 42 81.2017 161.944 69.6126 138.810 60.9227 121.458 54.1648 107.963 48.7608 97.1667 43 81.3402 162.222 69.7314 139.048 61.0266 121.667 54.2572 108.148 48.8440 97.3333 44 81.4835 162.500 69.8542 139.286 61.1342 121.875 54.3528 108.333 48.9300 97.5000 45 81.6268 162.778 69.9771 139.524 61.2417 122.083 54.4483 108.519 49.0161 97.6667 46 81.7053 IGS.Oofi 70.0958 139.762 61.3456 122.292 54.5407 108.7'04 49.0993 97.8333 47 81.9039 103.333 70.2146 140.000 61.4495 122.500 54.6332 108.889 49.1824 98.0000 48 82.0424 163.611 70.3333 140.238 61.5535 122.708 54.7256 109.074 49.2656 98.1667 49 82.1809 163.889 70.4521 140.476 61.6574 122.917 54.8180 109.259 49.3488 98.3333 50 82.3242 164.167 70.5749 140.714 61.7649 123.125 54.9136 109.444 49.4349 98.5000 51 82.4675 164.444 70.6978 140.952 61.8724 123.333 55.0091 109.630 49.5209 98.6667 52 82.6061 164.722 70.8166 141.190 61.9764 123.542 55.1015 109.815 49.6041 98.8333 53 82.7446 165.000 70.9353 141.429 62.0803 123.750 55.1939 110.000 49.6873 99.0000 54 82.8831 165.278 71.054lil41.667 62.1842 123.958 55.2864 110.185 49.7705 99.1667 55 83.0216 165.556 71. 1728' 141. 905 62.2882 124.167 55.3788 110.37049.8537 99.3333 56 83.1650 165.833 71.2957 142.143 62.3957 124.37'5 55.4743 110.55649.9397 99.5000 57 83.3083 166.111 71.4185 142.381 62.5032 124.583 55.5699 110.741 50.0258 99.6667 58 83.4468 166.389 71.5373 142.619 62.6071 124.792 55.6623 110.92650.1089199.8333 59 65 TABLE XIV, ACTUAL TANGENTS, ETC. 10 1 Curve. 3 Curve. 3 Curve. 4 Curve. 5 Curve. M. ~~O Tan. 501.287 Arc. Tan. Arc. Tan. Arc. Tan. 125.346 Arc. Tan. Arc. 1000.00 250.653500.000 167.113 333.333 250.000 100.288200.000 1 502.118 1001.67 251.068500.833 167.390 333.889 1 25. 554 i 250. 41 7 100.454 200.333 2 50:3.949 1003.33 251.484501.667 167.667 384.444 125.762 250.833 100.620200.607 3 503.77'.) 1005.00 251.899502.500 167.944 335.000 125.969 251.250 100.787201.000 4 504.610 1006.67 252.314503.333 168.221 335.556 126.177 251.667 100.953201.333 5 505.470 1008.33 252.744 504.167 168.507 336.111 126.392 252.083 101.125201.607 6 500.329 1010.00 253.174 505.000 168.794 336.667 126.607 252.500 101.297202.000 7 507.160 1011.67 253.589505.833 169.071 337.222 126.815 252.917 101.403202.333 8 507.991 1013.33 254.005j506. 667 169.348 337.778 127.022 253.333 101.629202.667 9 508.822 1015.00 254.420 507.500 169.625 338.333 127.230 253.750 101.795 203.000 1O 509.652 1016.67 254.836 508.333 169.902 338.889 127.438 254.167 101.962 203.333 11 5lO.5l2i10l8.33 255.265509.167 170.188 339.444 127.653 254.583 102.134 203.667 13 511.371 1020.00 255.695510.000 170.475 340.000 127.808 255.000 102.305 204.000 13 512.a02l021.67 256.110510.83-3 170.752 340.556 128.075 255.417 102.472 204.333 14 513.0331023.33 256. 526 ! 51 1.667 171.029 341.111 128.283 255.833 102.638 204.667 15 513.8641025.00 856.941512.500 171.306 341.667 128.491 256.250 102.804 205.000 16 514. 094:1026. 67 257.357513.333 171.582 342.222 128.699 256.667 102.970 205.333 17 515.554 1028.33 257.786 ! 514.167 171.869 342.778 128.913 257.083 103.142 205.667 18 516.41311030.00 258. 216 : 515. 000 172.156 343.333 129.128 257.500 103.314 206.000 19 517.244 1031.67 258.632 515.833 172.432 343.889 129.336 257.917 103.480 206.333 2O 518.075 1033.33 259.047 516.667 172.709 344.444 129.544 258.333 103.647 206.667 21 51 8. 906! 1035. 00 259 462 '51 7. 500 172.986 345.000 129. 752(258.750 103.813 207.000 33 519.737 1036.67 259. 878 1518.333 173.263 345 . 556 129.959 259.167 103.979 207.333 33 520.596 1038.33 260.308519.167 173.550 346 111 130.174 259.583 104.151 207.667 34 521.455 1040.00 260.737520.000 173.83C. 346.667 130.389 260. OUO 104.323 208.000 35 522.286 1041.67 26 1.1 53 1520. 833 174.113 347.222 130.597 260.417 104.489 208.333 36 523.117 1043.33 261.568521.667 174 390 347.778 130.805 260.833 104.655 208.667 3 7 523.948 1045.00 261.9841522.500 174.607 348.333 131.012 261.250 104.822 209.000 38 524.779)1046.67 262.399 523.333 174.944 348.889 131.220 2(51 . 667 104.988 209.333 39 525.638 1048.33 262.829 524.167 175.231 319:444 131.435 262.083 105.160 209.667 30 526.498 1050.00 263.258 525 000 75.517 350.000 131.650 262.500 105.332 210.000 31 527. 328! 1051. 67 263.674 525.833 75.794 350.556 131.858 262.917 105.498 210.333 528.159 1053.33 264.089 526.667 76.071 351.111 132.065 263.333 105.664 210.607 33 528.990 1055.00 264.505 527.500 76.348 351.607 132.273 263.750 105.830 211.000 34 529.821 1056.67 264.920 528.333 76.625 352.222 132.481 264.167 105.997 211.333 35 530.680 1058.33 265.350 529.167 76.912 352.778 132.696 264.583 106.168 211.667 36 531.540 1060.00 265.780 530.000 77.198 353 333 132.911 265 . OCO 106.340 212.000 37 532.370 1061 67 266.195 530.833 77.475 353.889 133.118 205.417 106.507 212.333 38 533.201 1063.33 266.610 531.667 77.752 354.444 133.326 265.833 106.673 212.607 39 534.032 1065.00 267.026 532.500 ITS. 029 355.000 133.534 266.250 106.839 213.000 4O 534.863 1066.67 267.441 533.333 178.306 355.556 133.742 266.667 107.005 213 333 41 535.722 1068.33 267.871 534.167 178.592 356.111 133.957 267.083 107.177 213 667 43 536.582 1070.00 268.301 535.000 178.879 356.667 134.171 267.500 107 349 214.000 43 537.413 1071.67 268.716 535.833 179.15(5 357.222 134.379 267". 91 7 107.515 214.383 44 538.243 1073.33 269.132 536.667 179.433 357.778 134.587 208.333 107.682 214.667 45 539.074 1075.00 269.547 537.500 179.710 358.333 134.795 268.750 107.848 215.000 46 539.905 1076.67 269.962 538.333 179.987 358.889 135.002 269.107 108. 014 1215.333 47 48 540.764 541.624 1078.33 1080.00 270.392 270.822 539.167 540.000 180.273 180.560 359.444 300.000 135.217 135.432 209.583 27'0.000 108.18fi215.007 108.358216.0(0 49 542.455 1081.67 271.237 540.833 1 80. 837 j 360. 556 135.640 270.417 108.524216.333 5O 543.285 1083.33 271.653 541.667 181.114361.111 135.848 270.833 108.690 216.067 51 544.116 1085.00 272.068 542.500 181.391 361.667 136.055271.250 108.856 217.000 53 544 947 1086.67 272.483 543.333 181.668362.222 136.263271.667 109.023 217.333 53 54 545 806 546.666 1088.33 1090.00 272.913 273.343 544.167 545.000 181.954362.778 182.241 363.333 136.478 272.083 136.693272.500 109.195 109.367 217.667 218.000 55 547.497 1091.67 273.758 545.833 182.518363.889 136.901 272.917 109. 533 1 21 8. 333 56 548.328 1093.33 274.174 546.667 182.795364.444 137.10S273.333 109 699218.667 57 549.187 1095.00 274.604 547.500 183.081 365.000 137.323273.750 109.871 219.000 58 550.046 1096 67 275.033 548.333 183. 368; 365. 556 137.5-J8274.107 110 0431219.333 59 550.87711098 33 275.449 549.167 183.645366.111 137. 74 6 2 74. 583 110.209219.667 TABLE XIV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 Curve. 1O Curve. 10. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. M. 83.5853 166.667 71.6561! 142. 857 62.7111 125.000 55.7547 111.111 50.1921 100.000 O 83.7238 166.944 71.7748143.095 (52.8150 125.208 55.8472 111.29650.2753 100.167 1 83.8624 167.222 71.8936 143.333 62.9189 125.417 55.9396 111.481 50.3585 100. ass 2 84.0009 167.500 72.0123 143.571 63.0229 125.625 56.0320 111.6G7 50.4417 100.500 3 84.1394 167.778 72.1311 143.810 63.1268 125.833 56.1244 111.852 50.5249 100.667 4 84.2827 168.056 72.2539 144.048 63.2343 126.042 56.2200 112.037 50.6109 100.833 5 84.4260 168.333 72.3768 144.286 63.3418 126.250 56.3155 112.222 50.6970 101.000 6 84.5646 168.611 72.4956 144.524 63.4458 126.458 56.4080 112.407 50.7802 101.167 7 84.7031 168.889 72.6143 144.762 63.5497 126.667 56.5004 112.593 50.8(534 101.333 8 84.8416 169.167 72.7331 145.000 63.6536 126.875 56.5928 112.778 50.9465 101.500 9 84.9802 169.444 72.8518 145.238 63.7576 127.083 56.6852 112.963 51.0297 101.667 10 85.1235 169.722 72. 9747 1 145. 476 63.8651 127.292 56.7808 113.148 51.1158 101. 833 11 85.2668 170.000 73.0975 145.714 63.9726 127.500 56.8763 113.333 51.2018 102.000 12 85.4053 170.278 73.2163 145.952 64.0765 127.708 56.9687 113.519 51.2850 102.167 13 85.5438 170.556 73.3350146.190 (54.1805 127.917 57.0612 113.704 51.3682 102.333 14 85.6824 170.833 73.4538146.429 64.2844 128.125 57.1536 113.889 51.4514 102.500 15 85.8209 171.111 73.5726 146.667 64.3883 128.333 57.2460 114.074 51.5346 102.667 16 85.9642 171.389 73.6954 146.905 64.4959 128.542 57.3415 114.259 51.6206 102.833 17 86.1075 171.667 73.8183 147.143 64. (503-1 128.750 57.4371 114.444 51.7067 103.000 18 86.2460 171.944 73.9370 147.381 64.7073 128.958 57.5295 114.630 51.7899 103.167 19 86.3845 172.222 74.0558 147.619 64.8112 129.167 57.6219 114.815 51.8730 103.333 20 86.5231 172.500 74.1745 147.857 64.9152 129.375 57.7144 115.000 51.9562 103.500 21 86.6616 172.778 74.2933 148.095 (55.0191 129.583 57.8068 115.185 52.0394 103.667 86.8049 173.056 74.4162 148.333 65.1266 129.792 57.9023 115.370 52.1255 103.833 23 86.9482 173.333 74.53901148.571 65.2341 130.000 57.9979 115.556 52.2115 104.000 24 87.0867 173.611 74.6578 148.810 65.3381 130.208 58.0903 115.741 52.2947 104.167 25 87.2253 173.889 74.7765 149.048 65.4420 130.417 58.1827 115.926 52.3779 104.333 26 87.3638 174.167 74.8953 149.286 65.5459 130.625 58.2751 116.111 52.4611 104.500 27 87.5023 174.444 75.0140 149.524 65.6499 130.833 58.3676 116.296 52.5443 104.667 28 87.6456 174.722 75.1369 149.762 65.7574 131.042 58.4631 116.481 52.6303 104.833 29 87.7889 175.000 75.2597 150.000 65.8649 131.250 58.5587 116.667 52.7164 105.000 30 87.9275 175.278 75.3785 150.238 65.9688 131.458 58.6511 116.852 52.7996 105.167 31 88.0660 175.556 75.4973 150.476 66.0728 131.667 58.7435 117.037 52.8827 105.333 32 88.2045 175.833 75.6160 150.714 66.1767 131.875 58.8359 117.222 52.9659 105.500 33 88.3431 176.111 75.7348 150.952 66.2806. 132.083 58.9284 117.407 53.0491 105.667 34 88.4864 176.389 75.8576 151.190 66.3882 132.292 59.0239 117.593 53.1352 105.833 35 88.6297 176.667 75.9805 151.429 66.4957 132.500 59.1195 117.778 53.2212 106.000 36 88.7682 176.944 76.0992 151 .667 66.5996 132.708 59.2119 117.963 53.3044 106.167 37 88.9067 177.222 76.2180 151.905 66.7035 132.917 59.3043 118.148! 53. 3876 106.333 38 89.0453 177.500 76.3368 152.143 66.8075 133.125 59.3967 118.333 53.4708 106.500 39 89.1838 177.778 76.4555 152.381 66.9114 133.333 59.4891 118.519 53.5540 106.667 4O 89.3271 178.056 76.5784 152.619 67.0189 133.542 59.5847 118.704 53.6400 106.833 41 89.4704 178.333 76.7012!l52.a57 67.1264 133.750 59.6803 118.889 53.7261 107.000 42 89.6089 89.7475 178.611 178.889 76.8200 153. 095 76.93871153.333 67.2304 67.3343 133.958 134.167 59.7727 59.8651 119.07'4 119.259 53.8092 53.8924 107.167 107.333 43 44 89.8860 179.167 77.0575 153.571 67.4382 134.375 59.9575 119.444 53.9756 107.500 45 90.0245 179.444 77.1762 153.810 67.5422 134.583 60.0499 119.630 54.0588 107.667 46 90.1678 179.722 77.2991 154.048 67.6497 134.792 60.1455 119.815 54.1449 107.833 47 90.3111 180.000 77.4220 154.286 67.7572 135. 0(K 60.2411 120.000 54.2309 108. OCX 48 90.4496 180.278 77.5407 154.524 67.8611 135.208 60.3335 120.185 64.3141 108.167 49 90.5882 180.556 77.6595 154.762 67.9651 135.417 60.4259 120.370 54.3973 108.333 50 90.7267 180.833 77. 7782 i 155. 000 68.0690 135.625 60.5183 120.556 54.4805 108.500 51 90.8652 181.111 77.8970 155. 238 68.1729 135.833 60.6107 120,741 54.5637 108.667 52 91.0085 181.389 78.0198 155.476 68.2805 136.042 60.7063 120.92654.6497 108.833 53 91.1518 181.66? 78.1427155.714 68.3880 136.250 60.8019 121.111 54.7358 109.000 54 91.2904 181.944 78 2615; 155. 952 68.4919 136.458 60.8943 121.29654.8189 109.167 55 91.4289 182.222 78.3802156.190 68.5958 136.667 60.9867 121. 481 154.9021 109.333 56 91.5722 182.500 78.5031 156.429 68.7034 136.875 61.0823 121.66754.9882 109.500 57 91.7155 182.778 7'8. 6259 156. 667 68.8109 137.083 61.1779 121 .852 55.0742 109.667 58 91.8540 183 056 78.7447156.905 68.9148 137.292 61.2703 122.037 55.1574 109.833 59 67 TABLE XIV. ACTUAL TANGENTS, ETC. 11 1 Curve. 2 Curve. 3 Curve. 4 Curve. 5 C irve. M. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. 551.708 1100.00 275.864 550.000 183.922 366.667 137.954 275.000 110.375 240.000 1 552.539 1101.67 276.280 550.833 184.199 367.242 138.161 475.417 110.542 240.333 2 553.370 1103.33 276.695 551.667 184.476 367.778 138.369 275.833 110.708 220.667 3 554.229 1105.00 277.125 552.500 184.764 368.333 138.584(276.250 110.880 241.000 4 555.088 1106.67 277.554 553.333 185.049 368.889 138.799 276.667 111.054 241.333 5 555.919 1108.33 477.97'0 554.167 185.346 369.444 139.007 477.083111.218 441.667 6 556.750 1110.00 278.385 555.000 185. 60^ 370.000 139.214 277.5001111.384 244.000 - 7 557.581 1111.67 278.801 555.833 185.879 370.556 139.424 477.917 111.550 222.333 8 558.412 1113.33 479.216 556.667 186.156 37 1 .111 139.630 478.333 111.716 222.667 9 559.271 1115.00 279.646 557.500 186.443 371.66"; 139.845 478.750 111.888 243.000 1O 560.131 1116.67 280.076 558.333 186.729 372.244 140.060 279.167 112.060 223.333 11 560.961 1118.33 280.491 559.167 187.006 372.778 140.268 279.583 112.247 423.667 12 561.792 1120.00 280.906 560.000 187.283 373.333 140.475 480.000 112.393 224.000 13 562.623 1121.67 281.322 560.833 187.560 373.889 140.683 480.417 112.559 224.333 14 563.454 1123.33 281.737 561.667 187.837 374.444 140.891 480.833 112.725 224.667 15 564.313 1125.00 282.167 562.500 188.124 375.000 141.10(3 281.250 112.897 425.000 16 565.173 1126.67 282.597 563.333 188.410 375.556 (41.321 281.667 113.069 225.333 17 566.003 1128.33 483.014 564.167 188.687 376.111 141.548 482.083 113.235 425.667 18 566.834 1130.00 283.428 565.000 188.964 376.667 141.736 484.500 113.401 446.000 19 567.694 1131.67 283.857 565.833 189.251 377.224 141.951 482.917 113.573 226.333 20 568.553 1133.33 284.287 566. 667 189.537 377.778 142.166 483.333 113.745 226.667 21 569.384 1135.00 284.702 567.500 189.814 378.333 144.381 483.750 113.912 247.000 22 570.215 1136.67 285.118 568.333 190.091 378.889 142.596 284.167 114.078 247.333 23 571.046 1138.33 385.683 569.167 190.368 379.444 144.796 284.583 114.244 247.667 24 571.876 1140.00 285.949 570.000 190.645 380.000 142.997 285.000 114.410 448.000 25 572.736 1141.67 286.378 570.833 190.932 380.556 143.212 285.417 114.582 448.333 2G 573.595 1143.33 286.808 571.667 191.218 381.111 143.447 285.833 114.754 448.667 21 574.426 1145.00 287.224 572.500 191.495 381.667 143.634 486.250 114.920 249.000 28 575.257 1146.67 287.639 573.333 191.772 382.222 143.842 286.667 115.087 249.333 29 576.088 1148.33 288.054 574.167 194.049 382.778 144.050 287.083 115.253 229.667 30 576.918 1150.00 288.470 575.000 192.326 383.333 144.258 287.500 115.419 230.000 31 577.778 1151.67 288.900 575.833 192.612 383.889 144.472 287.917 115.591 230.333 32 578.637 1153.33 289.329 576.667 192.899 384.444 144.687 288.333 115.763 230.667 33 579.468 1155.00 289.745 577.500 193. 176 385.000 144.895 488.750 115.929 231.000 34 580.299 1156.67 290.160 578.333 193.453 385.556 145.103 289.167 116.095 231.333 35 581.158 1158.33 290.590 579.167 193.739 386.111 145.318 289.583 116.267 231.667 36 582.018 1160.00 291.020 580.000 194.026 386.667 145.533 490.000 116.439 434.000 37 582.849 1161.67 291.435 580.833 194.303 387.224 145.740 290.417 116.605 232.333 38 583.679 1163.33 291.850 581.667 194.580 387.778 145.948 290.833 116.772 234.667 39 584.510 1165.00 292.266 582.500 194.857 388.333 146.156 291.250 116.938 233.000 40 585.341 1166.67 292.681 583.333 195.134 388.889 146.364 291.667 117.104 233.333 41 586.200 1168.33 293.111 584.167 195.420 389.444 146.579 294.083 117.276 233.667 42 587.060 1170.00 293.541 585.000 195.707 390.000 146.793 294.500 117.448 434.000 43 587.891 1171.67 293.956 585.833 195.984 390.556 147.001 294.917 117.614 234.333 44 588.722 1173.33 294.372 586.667 196.261 391.111 147.209 293.333 117.780 234.667 45 589.581 1175.00 294.801 587.500 196.547 391.667 147.424 493.750 117.954 235.000 46 590.440 1176.67 295.231 588.333 196.834 392.222 147.639 494.167 118.124 235.333 47 591.271 1178.33 495.646 589.167 197.111 392.778 147. 846 j 494. 583 118.290 235.667 48 592.102 1180.00 496.062 590.000 197.388 393.333 148.054 295.000 118.457 236.000 49 592.933 1181.67 296.477 590.833 197.665 393.889 148.262 295.417 118.623 236.333 50 593.764 1183.33 296.893 591.667 197.942 394.444 148.470 295.833 118.789 236.667 51 594.623 1185.00 297.322 592.500 198.228 395.000 148.685 296. 2501118. 961 437.000 52 595.483 1186.67 297.752 593.333 198 515 395.556 148 899 296.6671119 133 237.333 53 596.313 1188.33 298. 168 1594.167 198.792396.111 149.107 297.083; 119. 299 237.667 54 597.144 1190.00 498.583595.000 199. 069 1396.667 149.315 297.500 11 9. 465 1238. 000 55 598.004 1191.67 299.013595.833 199.355397.222 149.530 297.917 119. 6371238.833 56 598.863 1193.33 299.442596.667 199.642397.778 149.745 298.333 119.809i238.667 57 599.694 1195.00 299.858597.500 199.919398.333 149.952 498.750 119.975239.000 58 600.525 1196.67 300.273598.333 400.195398.889 150.160 499.167 140.144239.333 59 601.355 1198.33 300.6891599.167 400.472399.444 150.368 499.583140.308239.667 68 TABLE XIV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 Curve, 1O Curve. 11 "iST Tan. Arc. Tan. Arc. Tan. | Arc. Tan. Arc. Tan. Arc. 91.9926 183.333 78.8634 157.143 69.0187 137.500 61.3627122.222 55.2406 110.000 ~o~ 92.1311 183.611 78.9822 157.381 69.1227137.708 61.4551 122.407 55.3238 110.167 i 92.2696 183.889 79.1009 157.619 69.2266 137.917 61.5475 122.593 55.4070 110.333 2 92.4129 184.167 79.2238 157.857 69.3341 138.125 61.6431 122.778 55.4930 110.500 3 92.5562 184.444 79.3467 158.095 69.4416 138.333 61.7387 122.963 55.5791 1 10.607 4 92.6948 184.722 79 4654 158.333 69.5456 138.542 61.8311 123.148 55.6623 110 833 5 92.8333 185.000 79.5842 158.571 69.6405 13P..750 61.9235 123.333 55.7455 111.000 6 92.9718 185.278 79.7029 158.810 69.7534138.958 62.0159 123.519 55.8286 111.1(57 7 93.1104 185.556 79.8217 159.048 69.8574 139.167 62.10831123.704 55.9118 111.333 8 93.2537 185.833 79.9445 159.286 69.9649 139.375 62.2039 123.889 55.9979 111.500 9 93.3970 186.111 80.0674 159.524 70.0724 139.583 62.2995 124.074 56.0839 111 667 1O 93.5355 186.389 80.1861 159.762 70.1763 139 792 62.3919 124.259 56.1671 111.833 11 93.6740 186.667 80.3049 160.000 70.2803 140000 62.4843 124.444 56.2503 112.000 12 93.8126 186.944 80.4237 160.238 70.3842 140.208 62.5767 124.630 56.3335 112.167 13 93.9511 187.222 80.5424 160.476 70.4881 140.417 62.6691 124.815 56.4167 112.333 14 94.0944 187.500 80.6653 160.714 70.5957 140.625 62.7647 125.000 56.5027 112.500 15 94.2377 187.778 80.7881 160.952 70.7032 140.833 62.8603 125.185 56.5888 112.667 16 94.3762 188.056 80.9069 161.190 70.8071 141.042 62.9527 125.370 56.6720 112.833 17 94.5147 188.333 81.0256 161.429 70.9110 141.250 63.0451 125.556 56.7551 113.000 18 94.6581 188.611 81 . 1485 161.667 71.0186 141.458 63.1407 125.741 56.8412 113.167 19 94.8014 188.889 81.2713 161.905 71.1261 141.667 63.2363 125.926 56.9273 113.333 20 94.9399 189.167 81.3901 162.143 71.2300 141.875 63.3287 126.111 57.0104 113.500 21 95.0784 189.444 81.5089 162.381 71.3339 142.083 63.4211 126.296 57.0936 113.667 22 95.2169 189.722 81.6276 162.619 71.4879 142.292 63.5135 126.481 57.1768 113.833 23 95.3555 190.000 81.7464 162.857 71.5418 142.500 63.6059 126.667 57.2600 114.000 24 95:4988 190.278 81.8692 163.09? 71.6493 142.708 63.7015 126.852 57.3460 114.167 25 95.6421 190.556 81.9921 163.333 71.7568 142.917 63.7971 127.037 57.4321 114.333 26 95.7806 190.833 82.1108 163.571 71.8608 143.125 63.8895 127.222 57.5153 114.500 27 95.9191 191.111 82.2296 163.810 71.9647 143.333 63.9819 127.407 57.5985 114.667 28 96.0577 191.389 82.3484 164.048 72.0686 143.542 64.0743 127.593 57.6817 114.833 29 96.1962 191.667 82.4671 164.286 72.1726 143.750 64.1667 127.778 57.7648 115.000 30 96.3395 191.944 82.5900 164.524 72.2801 143.958 64.2623 127.963 57.8509 115.167 31 96.4828 192.222 82.7128 164.762 72.3876 144.167 64.3579 128.148 57.9369 115.333 32 96.6213 192.500 82.8316 165.000 72.4915 144.375 64.4503 128.333 58.0201 115.500 33 96.7599 192.778 82.9503 165.238 72.5955 144.583 64.5427 128.519 58.1033 115.667 34 96.9032 193.056 83.0732 165.476 72.7030 144.792 64.6383 128.704 58.1894 115.833 35 97.0465 193.333 83.1960 165.714 72.8105 145.000 64.7339 128.889 58.2754 116.000 36 97.1850 193.611 83.3148 165.952 72.9144 145.208 64.8263 129.074 58.3586 116.167 37 97.3235 193.889 83.4336 166.190 73.0184 145.417 64.9187 129.259 58.4418 116.333 38 97.4621 194.167 83.5523 1-66.429 73.1223 145.625 65.0111 129.444 58.5250 116.500 39 97.6006 194.444 83.6711 166.667 73.2262 145.833 65.1035 129.630 58.6082 116.66V 40 97.7439 194.722 83.7939 166.905 73.3338 146.042 65.1991 129.815 58.6942 116.833 41 97.8872 195.000 83.9168 167.143 73.4413 146.250 65.2947 130.000 58.7803 117.000 43 98.0257 195.278 84.0355 167.381 73.5452 146.458 65.3871 130.185 58.8635 117.167 43 98.1643 195.556 84.1543 167.619 73.6491 146.667 65.4795 130.370 58.9466 117.333 44 98.3076 195.833 84.2772 167.857 73.7567 146.875 65.5751 130.556 59.0327 117.500 45 98.4509 196.111 84 . 4000 168.095 73.8642 147.083 65.6707 130.741 59.1187 117.667 46 98.5894 196.389 84.5188 168.333 73.9681 147.292 65.7631 130.926 59.2019 117.833 47 98.7279 196.667 84.6375 168.571 74.0720 147.500 65.8555 131.111 59.2851 118.000 48 98.8665 196.944 84.7563 168.810 74.1760 147.708 65.9479 131.296 59.3683 118.167 49 99.0050 197.222 84.8750 169.048 74.2799 147.917 66.0403 131.481 59.4515 118.333 50 99.1483 197.500 84.9979 169.286 74.3874 148.125 66.1359 131.667 59.5375 118.500 51 99.2916 197.778 85.1207 169 524 74.4949 148.333 66.2315 131.852 59.6236 118.667 52 99.4301 198.056 S5.2395 169.762 74.5989 148.542 66.3239 132.037 59.7068 118.833 53 99.5687 198.333 85.3583 170.000 74,7028 148.750 66.4163 132.222 59.79*00 119.000 54 99.7120 198.611 85.4811 170.238 74.8103 148.958 66.5119 132.407 59.8760 119.167 55 99.8553 198.889 85.6040 170 476 74.9178 149.167 66.6075 132.593 59.9621 119.333 56 99.9938 199.167 85.7227 170.714 75.0218 149.375 66.6999 132.778 60.0453 119.500 57 100.132 199.444 85.8415 170.952 75.1257 149.583 66.7923 132.963 60.1284 119.667 58 100.271 199.722 85.9602 171.190 75.2296 149.792 66.8847 133.148 60.2116 119.833 59 69 TABLE XIV. ACTUAL TANGENTS, ETC. 12 liiT 1 Curve. 2 Curve. 3 Curve. 4 Curve. 5 C Tan. urve. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. o eoOre 1200.oO 301.104 600.000 200 749 400 . 001 150.576 300.000 120.474 240.000 i 603.046 1201 .67 301,531 600.833 201.030 400.556 150.791 300.417 120.646 240.333 2 603.90o 1203.33 301,964 601.667 201 322 401.111 151.006 300.833 120.818 240.667 3 604.788 1205.00 302.379 602.500 201.599 401 . 667 151.213 301.250 120.984 241.000 4 505.567 1206.67 302 79 J 603.333 201.876 402.222 151.421 301.667 121.150 241.333 5 600.4-26 1208.33 303.224 604.167 202.163 402.778 151.636 302.083 121.322 241 667 G 607 286 1210.00 3)3 654 o05.000 202.449 403.333 151.851 302.500 121.494 242.000 7 60S. 116 1211.67 3 J 4. 069 505.833 202. 72( 403.889 152.059 302.917 121.660 242.333 8 608.917 1213.33 304.485 606 . 667 203.003 404.444 152.266 303.333 121.827 242.667 9 60 J. 778 1215.00 304.900 607.500 203.230 405.000 152.474 303.750 121.993 243.000 10 610.609 1216.67 305.316 603.333 203 . 557 405.556 152.682 304.167 122.159 243.333 11 611.468 1218.33 3)5.745 509.167 203 . 844 406.111 152.897 304.583 122.331 243.667 13 612.328 1220.00 306.175 510.000 201.13) 4015.667 153.112 305.000 122.503 244.000 13 613.158 1221.67 306.590 610 833 204.407 407.222 153.319 305.417 122.669 244.333 14 513.989 1223.33 30r.006611.66r 201.684 407.778 153.527 305.833 122.835 244.667 15 614.849 1225.00 307 436612.500 204.971 408.333 153. 742 1306. 250 1-23.007 245.000 16 615.708 1226.67 30 7. 865 613.333 2 35 . 257 408.889 153. 957 1306.667 123.179 245.333 17 616.539 1228.33 303.281 611.167 205.534 409.444 154.165 307.083 123.345 245.667 18 617.370 1230.00 503.696 615.000 3*5.811 410.000 54.372307.500 1-23.512 246.000 19 618.229 1231.67 309.126 615.833 208. 09 > 410.556 154.587 307.917 123.684 246.333 30 619.089 1233.33 309.556 616.667 206.381 411.111 54.802 308.333 123.856 246.667 21 619.919 1235.00 309.971 617.500 206.661 411.667 55.010 308.750 124.022 247.000 22 620.750 1236.67 310.33? 618.333 206.938 412.222 55.218 309.167 124.188 217.333 23 621.581 1238.35 310.802 619.167 207.215 112.778 55.4ft 309.583 124.354 247.667 34 622.412 1240.00 311.217 620.000 207.492 413.333 55.633 310.000 124.520 248.000 35 625.271 1241.67 311.647 620.833 207.779 413.889 55.848 310.417 121.692 248.333 36 624.131 1243.33 312.077 621.667 203.065 414.444 56.003 310.833 24.864 248.607 37 521.962 1245.00 312.492 622.500 208.342 415.000 56.271 311.250 125.030 219.000 28 625.792 1246.67 312 908 623.333 208.619 415.556 56.478 311.667 125.197 249.333 39 626.652 1248.33 313.337 624.167 208.905 416.111 56.693 312.083 125.369 249.667 30 627.511 1250.00 313.767 625.000 209.192 416.667 58.908 312.500 25.541 250.000 31 628.342 1251.67 314.183 625.833 209.469 417.222 57.116 312.917 25 . 7i i7 250.333 33 629.173 1253.33 314.598 626.667 209.746 417.778 57.324 313.333 145.878 250.667 33 630.032 1255.00 315.028 627.500 210.032 418.333 57.539 313.750 126.045 251.000 34 630.892 1256.67 315.457 623.333 210.319 418.889 57.753 314.167 126.217 251.333 35 6H.723 125S.33 315.873 629.167 210.596 419.444 57.961 314.583 126.3S3 251.667 36 632.553 1260.00 316.288 630.000 210.873 420 000 58.169 315.000 126.549 252.000 37 633.413 1261.67 316.718 630.833 211.159 420.556 58.384 315.417 126.721 252.333 38 634.272 1263.33 317.148 631.667 211.446 421.111 58.59'.) 315.833 126.893 252.607 39 635.103 1265.00 317.563 632.500 211.723 421.667 158.807 316.250 127.059 253.000 4O 635.931 1266.67 317.979 633.333 212.000 422.222 159.014 316.667 127.226 253.333 41 636.765 1268.33 318 394 634.167 212.2771422.778 159.222 317.083 127.392 253.607 43 137.595 1270.0D 318.809635.000 212.554423.333 159.430 317.500 127.558 254.000 43 638.455 1271.67 319.239615.833 212.840423.889 159.645 317.917 127.730 254.333 44 639.31411273.33 319.669 636.667 213.127424.444 159.860 318.333 127.902 254.667 45 610.145 1275.00 320.08} 637.500 213.404425.000 160.067 318.750 128.068 255.000 46 610.976 1276.67 320.500638.333 213.681425.556 160.275 319.167 128.231 255.333 47 541.835 1278.33 320.929639.167 213.967426.111 160.490 319.583 128.40(5 255.667 48 612.695 1280.00 32 1.359 6 to. 000 214.251426.667 160.705 320.000 128.578 256.000 49 643.526 1281.67 321.775 610.833 214.531427.222 160.913 320.417 12H.744 256.333 1 5O 644.356 1283.33 322.190 641.667 214.808427.778 161.120 320.833 128.911 256.607 51 645.216 1285.00 322.620642.500 215.094428.333 161.335 321.250 129.033 257.000 53 646.075 1286.67 323.050:643.333 215.381 428.889 161.550 321.667 129.255 257.333 53 616 906 12,88.33 323. 465; 644. 167 215.658429.444 161.758 322.083 129.421 257.667 54 647.737 1290.00 323.880645.000 215.935430.000 161.966 322.500 129.587 258.000 55 648.596 1291.67 32 1. 310645. 833 216.221 430.556 162.181 322.917 129.759 258.333 56 649.456 1293.33 324.740646.607 216.508431.111 162.395 323.333 129.931 258.667 57 650.287 1295.00 325.155647.500 216.785431.667 162.603 323.750 130. 097 1259.000 58 651.117 1296.67 895.871648.888 217.061 432.222 162.811 324.167 130. 263 1 259. 333 59 651.977 1298.33 326. 000 1649.1 67 217.348432.778 163 026 324 583 130. 435 1 259. 667 70 TABLE XIV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 Curve. 1O Curve. 12 M. Tan. Arc. Tan. Arc. 1 Tan. Arc. Tan. Arc. Tan. Arc. 100.409 200.000 86.0790 17 1.429 175.3336 150.000 66.9771 133.333 60.2948 120. 000 ~o" 100.553 100.696 200.278 200.556 86.2019 86.3247 171. 667)75. 4411 150.208 171.90575.5486 150.417 67.0727 67.1683 133.519 133.704 60.3809 60.4669 120.167 120.333 1 2 100.834 200.833 86.4435 172.143 75.6525 150.625 67.2607 133.889 60.5501 120.500 3 100.973 201.111 86.5622 172.381 75.7565 150.833 67.3531 134.074 60.6333 120.667 4 101.116 201.389 86.6851 172.619 75.8640 151.042 67.4487 134.259 60.7193 120.833 5 101.260 201.667 86.8079 172.857 75.9715 151.250 67.5442 134.444 60.8054 121.000 G 101.398 201.944 86.9267 173.095 76.0754 151.458 67.6366 134.630 60.8886 121.167 7 101.537 202.222 87.0454 173.333 76.1794 151.667 67.7291 134.815 60.9718 121.333 8 101.675 202.500 87.1642 173.571 76.2833 151.875 67.8215 135.000 61.0550 121.500 9 101.814 202.778 87.2830 173.810 76.3872 152.083 67.9139 135.185 61.1381 121.667 1O 101.957 203.056 87.4058 174.048 76.4948 152.292 68.0094 135.370 61.2242 121.833 11 105.100 203.333 87.5287 174.286 76.6023 152.500 68.1050135.556 61.3102 122.000 1 2 102.239 203.611 87.6474 174.524 76.7062 152.708 68.1974135.741 61.3934 122.167 13 102.377 203.889 87.7662 174.762 76.8101 152.917 68.2898135.926 61.4766 122.333 14 102.521 204.167 87.8890 175.000 76.9177 153.125 68.3854136.111 61.5627 122.500 15 102.664 204.444 88.0119 175.238 77.0252 153.333 68.4810 136.296 61.6487 122.667 16 102.803 204.722 88.1306 17'5.476 77.1291 153.542 68. 5734 1136.481 61.7319 122.833 17 102.941 205.000 88.2494 175.714 77.2330153.750 68.6658136.667 61.8151 123.000 18 103.084 205.278 88.3723 175.952 77.3406 153.958 68.7614 136.852 61.9011 123.167 19 103.228 205.556 88.4951 176.190 77.4481 154.167 68.8570 137.037 61.9872 123.333 20 103.366 205.833 88.6139 176.429 77.5520 154.375 68.9494 137.222 62.0704 123.500 21 103.505 206.111 88.7326 176.667 77.6559154.583 69.0418 137.407 62.1536 123.667 22 103.643 206.384 88.8514 176.905 77.7599 154.792 69.1342 137.593 62.2368 123.833 23 103.782 206.667 88.9701 177.143 77. 8638 1155. 000 69.2266 137.778 62.3199 124.000 24 103. 925 1206.944 89.0930 177.381 77.9713J155.208 69.3222 137.963 62.4060 124.167 25 104. 068! 207. 222 89.2158 177.619 78.07881155.417 69.4178 138.148 62.4920 124.333 26 104.207 207.500 89.3346 177.857 78.1828 155.625 69.5102 138.333 62.5752 124.500 27 104.345 207.778 89.4534 178.095 78.2867 155.833 69.6026 138.519 62.6584 124.667 28 104.489 208.056 89.5762 178.333 78.3942 156.042 69.6982 138.704 62.7445 124.833 29 104.632 208.333 89.6991 178.571 78.5017 156.250 69.7938 138.889 62.8305 125.000 30 104.771 208.611 89.8178 178.810 78.6057 156.458 69.8862 139.074 62.9137 125.167 31 104.909 208.889 89.9366 179.048 78.7096 156.667 69.9786 139.259 62.9969 125.333 32 105. 052 1209.167 90.0594 179.286 78.8171 156.875 70.0742 139.444 63.0829 125.500 33 105.196:209.444 90.1823 179.524 78.9246 157.083 70.1698 139.630 63.1690 125.667 34 105. 334 1209. 722 90.3010 179.762 79.0286 157.292 70.2622 139.815 63.2522 125.833 35 105.473 210.000 90.4198 180.000 79.1325 157.500 70'. 3546 140.000 63.3354 126.000 36 105.616J210.278 90.5427 180.238 79.2400 157.708 70.4502 140.185 63.4214 126.167 37 105.759i210.556 90.6655 180.476 79.3475 157.917 70.5458 140.370 63.5075 126.333 38 105.898 210.833 90.7843 180.714 79.4515 158.125 70.6382 140.556 63.5907 126.500 39 106.036 211:111 90.9030 180.952 79.5554 158.333 70.7306 140.741 63.6738 126.667 40 106.175 211.389 91.0218 181.190 79.6593 158.542 70.8230 140.926 63.7570 126.833 41 106.314211.667 91.1405 181.429 79. 7633 '158. 750 70.9154 141.111 63.8402 127.000 42 106.459211.944 91.2634 181.667 79.8708 158.958 71.0110 141.296 63.9263127.167 43 106.600212.222 91.3862 181.905 79.9783159.167 71.1066 141.481 64.0123 127.333 44 106.739212.500 91.5050 182.143 80.0822 159.375 71.1990 141.667 64. 0955 ; 127. 500 45 106.877 212.778 91.6238 182.381 80.1862 159.583 71.2914 141.852 64.1787127.607 46 107.020 213.056 91.7466 182.619 80.2937 159.792 71.3870 142.037 64.2647127.833 47 107.164 213.333 91.8695 182.857 80.4012 160.000 71.4826 142.222 64.3508 128.000 48 107-302 213.611 91.9882 183.095 80.5051 160.208 71.5750 142.407 64.4340 128.167,49 107.441 213.889 92.1070 183.333 80.6091 160.417 71.6674 142.593 64.5172 1 28.333 50 107.584 214.167 92.209H 183.571 80.7166 160.625 71.7630 142.778 64.6032128.500 51 107.727 214.444 92.3527 183.810 80.8241 160.833 71.8586 142.96?, 64.6893 128.667: 52 107. 866 214 722 92.4714 184.048 80.9280 161.042 71.9510 143.148 64. 7725! 128. 833 53 108.005 21 o! 000 92.5902 184.286 81.0320 161.250 72.0434 143.333 64.8556 129.000 54 108.148 215.278 92.7131 184.524 SI. 1395 161.458 72.1390143.519 64.9417:129.167 55 108-291 215.556 92.8359 184.762 SI. 2470 161.667 72.2345143.704 65.0278 129.333 56 108.430 215.833 92.9547 185.000 81.3509 161.875 '2.3270143.889 65.1109 129.500 57 108.568 216.111 93.0734 185.238 81.4549 162.083 "2.4194 144.074 65.1941 129.667 58 108.712 21 6. 389 193.1 963 185. 476181. 5624 162.292 "-2.5149 144.259 65. 28021 129. 833 59 71 TABLE XIV. ACTUAL TANGENTS, ETC- 13 1 Curve. 2 Carve. 3 Curve. 4 Curve. 5 Curve. M. Tau. Are. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. 652.8:3(3 1300.00 326.430 650.000217.632 433.333 163.241 325.000 130.60? 260.000 1 653.667 1301.67 326.846 650.833217.911 433. 889 163. 448 325. 4 r 130.77:3 260.8:3:3 2 654.498 1303.3 327.261 651.667.218.188 434.444 163.656325.83: 130.940260.607 3 655.329 1305.00 327.676 652.500218.465 435.000 163.864326.250 131.106261.000 4 656.164 1308.6? 328.092 653. 333 '218. 7452 435.556 164. 072 326. 66~ 181. 27S 261.333 5 657.011 1308.33 328.522 654.167219.029 436.111 164.287327.08: 131.444 261.667 6 657.878 1310.00 328.951 655.000219.315 436.667 164.501 327.500 131.616 262.000 7 658. 70J 1311.67 329.367 655.833219.592 437.222 164.709 327.917 131.782 262.333 8 659.510 1313.33 329.782 656.6671219.869 437.778 164.917 328. 33? 131.948 262.667 9 660.399 1315.00 330.212 657.500 220.156 438.333 165.132 328.750 132.120 263.000 10 661.259 1316.67 330.642 658.333 220.442 438.889 165.347 329.167 132.292 263.333 11 662.090 1318.33 331.057 659.167220.719 439.444 165.554 329.583 132.458 263.667 13 662.921 1320.00 331.472 660.000220.996 440.000 165.762 330.000 132.625 264.00) 13 663.780 1321.67 331.902 660.833221.283 440.556 165.977 330.417 132.797 264.333 14 664.639 1323.33 332.332 661.667221.569 441.111 166.192 330.833 132.968 264.667 15 665.470 1325.00 332.747 662.500i221.846 441.66? 166.400 331.250 133.135 265.000 16 666.301 1326.67 533.163 663.333222.123 442.222 166.608 331.667 133.301 265.333 17 667.160 1328. ,33 333.592 664.167222.410 442.778 166.822 332.08:3 133.473 265.667 18 668.020 1330.00 334.022 665.OOiV222.696 443.333 167.037 332.500 133.645 266.000 19 668.851 1331.67 334.438 665.833 222.973 443.889 167.245 332.917 133.811 266.333 30 669.681 1333.33 194.858 666.667 223.250 444.444 167.453 333.333 133.977 266.667 21 670.541 1335.00 335.283 667.500 223 537 445.000 167.668 333.750 134.149 267.000 22 671.400 1336.67 335.712 668.333 223.823 445.556 167.883 334.167 134. 32 1(267. 333 23 672.231 1338.33 336.128 669.167 224.100 446.111 168.090 334.583 134.487 267.667 34 673.062 1340.00 336.543 670.000 224.377 446.667 1 68. 298 335.000 34.654 268.000 35 673.921 1341.67 336.973 670.833 224.664 447.222 168.513 335.417 34.825 268.303 36 674.781 1343.33 3:37.403 671.667 224.950 447.778 168.728 335.833 34.997 268.667 37 675.612 1345.00 337.818 672.500 225.227 448.333 168.936 336.250 35.164 269.000 38 676.442 1346.67 338.234 673.333 225.504 448.889 169.143 336 667 35.330 269.333 39 677.302 1348.33 338.663 674.167 225.791 449.444 169.358 337.083 135.502 269.667 30 678.161 1350.00 339.093 675.000 226.077 450.000 169.573 337.500 35.674 270.000 31 678.992 1351.67 339.509 675.833 226.354 450.556 169.781 337.917 35.840 270.333 33 679.823 1353.33 339.924 676.667 226.631 451.111 169.989 338.3:33 36.006 270.667 33 680.682 1355.00 340.354 677.500 226.918 451.667 170.204 338.750 36.178 271.000 34 681.542 1356.67 340.783 678.333 227.204 452.222 170.418 339.167 36.350 271.333 35 682.373 1358.33 341.199 679.167 227.481 452.778 70.626 339.583 36.516 271.667 36 683.203 1360.00 341.614 680.000 227.758 453.333 70.834 340.000 36.682 272.000 37 684.063 1361.67 342.044 680.833 228.044 453.889 171.049 340.417 36.854 272.333 38 684.922 1363.33 542.474 681.667 228.331 454.444 71 .264 340.833 37.026 272.667 39 685.753 1365.00 342.889 682.500 228.608 455.000 71.472 341.250 37.193 273.000 4O 686.584 1366.67 343.305 683.333 228.885 455.556 71.679 341.667 37,359 273.333 41 687.443 1368.33 343.734 684.167 229.171 456 111 171.894 342 083 37.531 273.667 43 688.303 1370.00 344.164 685.000 229.453 456 . 667 172.109 342.500 37.703 274.000 43 689 134 1371 67 344.579 685.833 229.735 457.222 172.317 342.917 37.869274.333 44 689.964 1373.33 344.995 686.667 230.012 457.778172.525 343.333 38.035 274 . 667 45 690.824 1375.00 345.425 687.500 230 29S 458.333 172.739 343 750 38.207 275.000 46 691.683 1376.67 345.854 688.333 230.585 458.889 172.954 344.167 38.379 275.333 47 692.514 1378.33 346.270 689.167 330.862 459.444 173.102 344.583 38.545 275.667 48 49 693.345 694.204 1380.00 1381.67 346.685 347.115 690.000 690.833 231.139 231.425 460.000 460.556 173.370 173.585 345.000 345.417 38.711 38.883 276.000 276.333 5O 695.064 1383.33 347.545 691.667 231.712 461.111 173.800 345.833 39.055 276.667 51 695.895 1385 00 347.960 692.500231.989 461. 667 1174.007 346.250 39.221 277.000 53 696.725 1386.67 348.375 693.333232.266 462.222 174.215 346.667 39.388 277.333 53 697.585 1388.33 348.805 604.167:232.552 462.778:174.430 347.083 39.560 277.667 54 698.444 390.00 349.235 695.000232.839 463.333 174. 645 i 347. 500 39.732 278.000 55 599.275 1391.67 349.650 695.833233.116 463.889 174.853347.917 39.898 278.333 56 700.106 1393.33 350.066 696.667233.393 464.444 175.060348.333 40.064 278.607 57 700.965 395.00 350.496 697.500233.679 465.000 175.275|348.750 40.236 279.000 .58 701.895 1396.67 50.925 698.333233.966 465.556 175.490:349.167 40.408 279.333 59 702.656 1398.33 51.341 699.167,234.243 466. Ill 1175.698:349. 583 40.574 279.667 TABLE XIV. ACTUAL TANGENTS, ETC 6 Curve. 7 Curve. 8 Curve. 9 Curve. 1O Curve. 13 Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan Arc. M. 103.855:216.607 93.3191 185.714 81.0699162.500 72.6105 144.444 65.3662 130.000 () 106. 993 216. 944 93.4379 185.952 81.7738162.708 72.7029 144.630 65.4494 130.167 1 109. 132 217. 22 93.5566 186.190 81.8778162.917 72 7 953 144.815 65.5326 130.333 2 109.2701217.500 93.6754 186.429 81.9817 163.125 72.8878 145.000 65.6158 130.500 3 109.409 217.778 93.7942186.667 82.0856 163.333 72.9802 145. 185 65.6990 130.667 4 109.552 218.056 93.9170 186.905 82.1932163.542 73.0757 145.370 65.7850 130.833 5 109.696 218.333 94. 0399 187. 143 82. 3007)163. 750 73.1713 145.556 65.8711 131.000 6 109.834 218.611 94.1586 187.381 82.4046:163.958 73.2637 145.741 65.9543 131.167 7 109.973 218.889 94.2774 187.619 82. 5085 1164.167 73.3561 145.926 66.0374 131.333 8 110.116 219.167 94.4002 187.857 82.6161 164.375 73.4517 146.111 66.1235 131.500 9 110.259 219.444 94.5231 188.095 82.7236 164.583 73.5473 146.296 66.2096 131.667 1O 110.398 219.722 94.6419 188.333 82.8275 164.792 73.6397 146.481 66.2927 131.833 11 110.53(3 220.000 94.7606 188.571 82.9314 165.000 73.7321 146.667 66.3759 132.000 12 110.680 220.278 94.8835 188.810 83.0390 165.208 73.8277 146.852 66.4620 132.167 13 110.823 220.556 95.0063 189.048 83.1465 165.417 73 9233 147.037 66.5480 132.333 14 110.961 220.833 95.1251 189.286 83.2504 165.625 74.0157 147.222 66.6312 132.500 15 111.100 221.111 95.2438 189.524 83.3543 165.8:33 74.1081 147.407 66.7144 132.667 16 111.243 221.389 95.3667 189.762 83.4619 166.042 74.2037 147.593 66.8005 132.833 17 111.387 221.667 95. 4895 1190.000 83.5694 166.250 74.2993 147.778 66.8865 133.000 18 111.525 221.944 95.6083 190.238 83.6733 166.458 74.3917 147.963 66.9697 133.167 19 111.664 222.222 95.7271 190.476 83.7772 166.667 74.4841 148.148 67.0529 133 333 20 111.807 222.500 95.8499 190.714 83.8848 166.875 74.5797 148.333 67.1389 133.500 21 111.950 222.778 95.9728 190.952 as. 99243 167.083 74.6753 148.519 67.2250 133.667 22 112.089 223.056 96. 0915' 191. 190 84.0962 167.292 74.7677 148.704 67.3082 133.833 23 112.227 223.338 96.2103ll91.429 84.200! 167.500 74.8601 148.889 67.3914 134.000 24 112.371 223.611 96.3331 191.667 84.3077 167.708 74.9557 149.074 67.4774 134.167 25 112.514 223.889 96.4560 191.905 84.4152 167.917 75.0513 149.259 67.5635 1:34.333 26 112.652 224.167 96.5747 192.143 84.5191 168.125 75.1437 149.444 67.6467 134.500 27 112.791 224.444 96.6935 192.381 84.623U 168.333 75.2361 149.630 67.7298 134.667 28 112.934 224.722 96.8163 192.619 84.7306 168.542 75.3317 149.815 67.8159 134.833 29 113.078 225.000 96.9392 192.857 84 8381 168.750 75.4273 150.000 67.9019 135.000 3O 113.216 225.278 97.0580 193.095 84.9450 168.958 75.5197 150.185 G7.9851 135.167 31 113.356 225.556 97.1767 193.333 85.0459 169.167 75.6121 150.370 68.0683 135.3:33 32 113.498 225.833 97.2996 193.571 85.1535 169.375 75.7077 150.556 68.1544 135.500 33 113.641 226.111 97.4224 193.810 85.2610 169.583 75.8033 150.741 68.2404 135.667 34 113.780 226.389 97.5412 194.048 85 3649 169.792 75.8957 150.926 68.3236 135 833 35 113.918 226.667 97.6599 194.2<86 85.4688 170.000 75. -9881 151.111 68.4068 136.000 36 114.062 226.944 97.7828 194.524 85.5764 170.208 76.0837 151.296 68.4928 136.167 37 114.205 227.222 97.9056 194.762 R5.6839 170.417 76.1793 151.481 68.5789 136.333 38 114.343 227.500 08.0244 195.000 85.7878 170.625 76.2717 151.667 68.6621 136.500 39 114.482 227.778 98.1432 195.238 85.8917 170.833 76.3641 151.852 68.7453 136.667 40 114.625 228.056 98.2660 195.476 85.9993 171.042 76.4596 152.037 68.8313 136.833 41 114.769 228.333 98.3889 195.714 86.1068 171.250 76.5552 152.222 68.9174 137.000 42 114.907 228.611 98.5076 195.952 86.2107 171 .458 76.6476 152.407 69.0006 137.167 43 115.046 228.889 98.6264 196.190 86.3146 171.667 76.7400 152.593 69.0837 137.333 44 115.189 229.167 98. 7492 i 196. 429 86.4222 171.875 76.8356 152.778 69.1698 137.500 45 115.332 229.444 98.8721 196 667 86.5297 172.083 76.9312 152.963 69.2559 137.607 46 115.471 229.722 98.9908196.905 86.6336 172.292 77.0236 153.148 69.3390 137.833 47 115.609 230. (00 99.1096 197.143 86.7375 172.500 77.1160 153.333 69.4222 138.000 48 115.7'53 230.278 99.2325 197.381 86.8451 172.708 77.2116 153.519 69.5083 138.167 49 115.896 230 556 09.3553 197.619 86.9526 172.917 77.3072 153.704 69.5943 138.3:33 5O 116.034 230.833 99.4741 197.857 87.0565 173.125 77.3996 153.889 69.6775 138.500 51 116.173231.111 99.5928198.095 87.1604 173 333 77.4920 154.074 69.7607 138.667 52 116.316 231.389 99.7157 198.333 87.2680 173.542 77.5876 154.25969.8468 1:38.833 53 116.460 231.667 99 8385 198.571 87.3755 173.750 77.6832 154 44469.9328139000 54 116 5981281.944 99 9573 198.810 87.4794 173.958 77.7756 154.630170 0160 139.167 55 116.737232 222 100.07'6 199 048 87.5833 174 167 77 8680 154. 81 5 ; 70. 0992 139.333 56 116.880232.500 100.199 199.286 87.6909 174.375 77.9636 155.00070.1852 139.500 57 117.023232.778 100.322 199 524 87.7984 174.583 78.0592 155.1&5J70.2713 139.667 58 117.162233.056 100.440 199.762 87.9023 174.792 78.1516 155.370170.3545 139.833 59 73 TABLE XIV. ACTUAL, TANGENTS, ETC. 140 1 Curve. 2 Curve. 3 Curve. 4 Curve. 5 Curve. IviT Tan. Arc. Tan. Arc. Tan. 2347520 Arc. Tan. Arc. Tan. Arc. o 703.480 1400.00 851.756 7UO.OOO 406.667 175.906 350.000 140. 740 280. 000 i 04 346 1401.67 S53.186 700.833 J34.806 467.222 176.121 350.417 140.912 280.3*3 2 705. 205 403.33 352.616 701.667 235.093 467.778 176.335 350.833 141.084 V80.007 3 "06.065 405.00 353.045 702.500 235.379 468.333 176.550 '351.250 141.2561281.000 4 "06.924 406.67 353.475 703.333 .>35.606 408.889 176.765 351.607 141.428 281.333 5 "07.755 408.133 353.890 704.107 235.943 469.444 176.973 352.083 141.594 281 607 708.586 410.00 354.306 705.000 236.220 470.000 177.181 352.500 141.760 282.000 7 "09.445 411.67 354.736 705.833 236.506 470.556 177.396 352.917 141.932 282.333 8 "10 305 1413.33 355.165 706.667 236.793 471.111 177.611 353.3:33 142.104 282.607 9 "11.136 1415.00 355.581 707.500 237.070 471.667 177.818 353.750 142.271 283.000 10 "11.966 1416.67 355.996 708.333 237.347 472.222 178.026 354.167 142.437 283. a33 11 "12.826 1418.33 356.426709.167 237.633 472 7i'8 178.241 354.583 142.609 283.667 12 713.685 1420.00 356.856 710.000 237.920 473 '.333 178.456355.000 142.781 284.000 13 714.516 1421.67 357.271 710.833 238.197 473.889 178. 664 a55. 41 7 142.947 284.333 14 715.347 1423.33 357.687711.667 238.473 474.444 178.871 355.833 143.113 284.667 15 716.206 1425.00 358.116 712.500 238.760 475.000 179.086,356.250 143.285 285.000 10 717.066 1426.67 358.546 713.333 239.047 475.556 179.301 356.667 143.457 285.333 17 717.896 1428.33 358.961 714.167 239.323 476.111 179.509 357.083 143.623 285.667 18 718.727 1430.00 359.377 715.000 239.600 476.667 179.717 357.500 143.789 286.000 19 719.587 1431.67 359.807 715.833 239.887 477 . 222 179.932 357.917 143.961 286.333 2O 720.446 1433.33 360.236 716.667 240.173 477.778 180.146 358.333 144.133 286.667 21 721.277 14&5.00 360.652 717.500 240.45: 478.333 180.354 358.750 144.299 287.000 22 722.108 1436.67 361.067 718.333 240.727 478.889 180.502 359.167 144.466 287.333 23 722.967 1438.33 301.497 719.167 241.014 479.444 180.777 359.583 144.638 287.007 24 723.827 1440.00 361.927 720.000 241. 300 480.000 180.992 300.000 144. 810 1288.000 25 724.657 1441.67 362.342 720.833 241.577 480.556 181.199 360.417 144.976 288.333 26 725.488 1443.33 362.757 721.667 241.854 481.111 181.407 360.8313 145.142288.607 27 726.348 1445.00 363.187 722.500 242.141 481.667 181.622 361.250 145.314 289.000 28 727.207 1446.67 363.617 723,333 242.427 4S2.222 181.837 361.607 145.486289.333 29 728.067 1448.33 364.047 724,167 242.714 482.778 182.052 362.083 145.658289 607 SO 728.926 1450.00 364.476 725.000 243.000 483.333 182.267 362.500 145.8:30290.000 31 729.757 1451.67 364.892 725.833 243.277 483.889 182.475 362.917 145.996290.333 32 730.588 1453.33 365.307 726.667 243.554 484.444 182.682 363.333 146.162 290.607 33 731 .447 1455.00 365.737 727.500 243.841 485.000 182.897 303.750 146. 334 291. 000 34 732.307 1456.67 366.167 728.333 244.127 485.556 183.112 304.167 146.506 291.333 35 733.137 1458.33 366.582 729.167 244.404 486.111 183.320 364.583 146.672 201.607 36 733.968 1460.00 366.998 730.000 244.681 486.667 183.528 365.000 146. 838 : 292. 000 37 734.828 1461.67 367.427 7:30.833 244.968 487.222 183.742 365.417 147.010 292.333 38 735.687 1463.33 367.857 731.667 245.254 487.778 183.957 305.83: 147. 182 292. Of 7 39 736.518 1465.00 368.272 732.500 245.531 488.333 i 84. 165 306.250 147.349 293.000 4O 737.349 1466.67 368.688 7:33.333 245.808 488.889 184.373 366.66" 147.515 293.333 41 738.208 1468.33 369,118 734.167 216.095 489.444 184.588 307.083 147.687 293.667 42 739.068 1470.00 369.547 735. 000 246.381 490.000 184.803 307.500 147.859 294.000 43 739.927 1471.67 369.977 735.833 246.668 490.556 185.018 307.91" 148.031'294.333 44 740.786 1473.33 370.407 736.667 246.954 491.111 185.232 308. ass 148.203 294.007 45 741.617 1475.00 370.822 737.500 247.231 491.66" 185.440 368.750 148.369295.000 46 742.448 1476.67 371.233 738.333 247.508 492.22'. 185.648 369.16" 148.535 295.333 47 743.307 1478.33 371.667 739.167 247.795 492.778 185.803 369.583 148.7W 205.007 48 744.167 1480.00 372.097 740. (XX 248.081 403.33: 186.078 370.000 148.879 296.000 49 744.998 1481.67 372.513 740.833 248.358 493.889 186.286 370.417 149.045,296.333 1 50 745.829 1483. a 372.928 741.667 248.635494.444 186.493 370 83: 149.211 206.667 51 7'46.688 1485.00 373.358 742.500 248.922495.000 186.708 371.250 149.383297.000 52 747.547 1486 67 373.787 743.333 249.208495 5U 186.923 371.60" 149.555 297.333 53 748.378 1488.33 374.203 744.167 249 4&5406.111 187.131 372.08: 149.721 27.f>07 54 749.209 1490.00 374.618 745.000 249.762496.66" 187.339 372.500 149. 888 298. Of 55 750.068 1491.6" 375.048 745.833 250. 049 497. 22x 187.553372.91" 150.060 208.333 56 750.928 1493.3: 375.478 746.66" 250.335497.778 187.768373.33: 150.231 208.007 57 751.787 1495.00 375.907 747.500 250.622498.333 187.983373.750 150.403 209.000 58 752. 647 1496.6" 376.337 748.33: 250.908498.881) 188.198374.16* 150.575 200.333 59 753.47811498.3: 376.753 749.16" 251.185499.444 188.406 374.58: 1 50. 742 299. Of, 7 74 TABLE XIV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 Curve. 1O Curve. 14 Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. M. 117.300 233.333 100.559 200.000 88.0062 175.000 78.2440 155.556 70.4377 140.000 117.444 233.611 100.682 200.238 88.1138 175.208 78.3396 155.741 70.5237 140.167 1 117.587 233.889 100.805 200.476 88.2213 175.417 78.4352 155.926 70.6098 140.333 2 117.730 234.167 100.928 200.714 88.3288 175.625 78.5308 156.111 70.6958 140.500 3 117.874 234.444 101.051 200.952 88.4363 175.833 78.6264 156.296 70.7819 140.667 4 118.012 234 722 101.169201.190 88.5402 176.042 78.7188 156.481 70.8651 140.833 5 118.151 235.000 101.288201.429 88.6442 176.250 78.8112 156 667 70.9482 141.000 6 118.294 118.437 235.278 '35.556 101.411 201.667 101. 534 1201. 905 88.7517 88.8592 176.458 176.667 78.9068 79.0024 156.852 157.037 71.0343 71.1203 141.167 141.333 7 8 118.576 235.833 101.653 202.143 88.9631 176.875 79.0948 157.222 71.2035 141.500 9 118.714 236.111 101.771 202.381 89.0671 177.083 79.1872 157.407 71.2867 141.667 10 118.858 236.389 101.894 202.619 89.1746 177.292 79.2828 157 593 71.3728 141.833 11 119.001 ,36 667 102.017202.857 89.2821 177.500 79.3783 157.778 71.4588 142.000 12 119.139J236.944 102.130203.095 89.3860 177.708 79.4708 157.963 71.5420 142.167 13 119.278237.222 102.255203.333 89.4900 177.917 79.5632158.148 71.6252 142.333 14 119.421i237.500 102.377203.571 89.5975 178.125 79.6587 158.333 71.7112 142.500 15 119 565237.778 102.500203.810 89.7050 178.333 79.7543158.519 71.7973 142.667 16 119.703238.056 102.619204.048 89.8089 178.542 79.8467 158.704 71.8805142.833 17 H9. 842 238.383 102.738204.286 89.9129 178.750 79 9391 158.889 71 9637 143.000 18 119.985 238.611 102.861 204.524 90.0204 178 958 80.0347 159.074 72.0497 143.167 19 120.128 238.889 102.984 204.762 90.1279 179.167 80.1303 159.259 72.1358 143.333 20 120.267 239.167 103.102 205.000 90.2318 179 375 80.2227 159.444 72.2190 143.500 21 120.405 239.444 103.221 205.238 90.3358 179.583 80.3151 159 630 72.3021 143.667 22 12.). 549 239.722 103.344 205.476 90.4433 179.792 80.4107 159.815 72.3882 143.833 23 120.692 240.000 103.467 205.714 90.5508 180.000 80.5063 160.000 72.4743 144.000 24: 120.830 240.278 103.585 205.952 90.6547 180.208 80.5987 160.185 72.5574 144.167 2r> 120.969 240.556 103.704 206 190 90.7587 180.417 80.69ll i l(.;0.370 72.6106 144.333 26 121.112 240.833 103.827 206.429 90 8662 180.625 80.7867 160.550 72 . 7267 144.500 27 121.256 241.111 103.950 206.667 90.9737 180.833 80.8823 160.741 72.8127 144.667 28 121.399 241.3-9 104.073 206.905 91.0812 181.042 80.9779 160. 92 72.8988 144.833 29 121.542 241.667 104.196 207.143 91.1887 181.250 81.0735 161.111 72.9848 145.000 30 121.681 241.944 104.314 207.381 91.2927 181.458 8l.1659il61.296 73.0680 145.167 31 121.819 242.222 104.433 207.619 91.3966 181.667 81.2583 161.481 73.1512 145.333 32 121.962 242.500 104.556 207.857 91. 5041 '181. 875 81.3539161.667 73.2373 145.500 33 122.106 242.778 104.679 208.095 91.61161182 083 81.4486 161.852 73.3233 145.667 34 122.244 243.056 104.798 208.333 91.7156 182.292 81.5419 162.037 73.4065 145.838 35 122.383 243 333 104.916 208.571 91.8195 182.500 81.6343 162.222 73.4897 146.000 36 122.526 243.611 105.039 208.810 91.9270 182.708 81.7299162.407 73 . 5757 146.167 37 122.669 243.889 105.162 209.048 92.0345 182.917 81.8255 162.593 7'3. 66 18 146.333 38 122.808 244.167 105.281 209.286 92.1385 183.125 81.9179 162.778 73.7450il46.50u 39 122.947 244.444 105.400 209.524 92.2424 183.333 82.0103 162.963 73.8282 146. 6G7 40 123.090 244.722 105.522 209.762 92.3499 183.542 82.1059 163.148 73 9142 146.833 41 123.233 245.000 105.645 210.000 92.4574 183.750 82.2015 163.333 74.0003 147.000 42 123.376 245.278 105.768 210.23S 92.5650 183.958 82.2970 163.519 74.0863 147.167 43 123.520 245.556 105.891 210.476 92.6725 184.167 82 3926 163.704 74.1724 147.333 44 123.658 245.833 106.010 210.714 92.7764 184.375 82.4850 163.889 74.2556 147.500 45 123.797 246.111 106.129 210.952 92.8S03 184.583 82 5774 164.074 74.3387 147.667 46 123.940 246.389 106.251 211.190 92. 9879 1 184. 792 82.6730 164.259 74.4248 147.833 47 124.083 246.667 106. 374 1211. 429 93.0954 185.000 82.7686164.444 74.5109 148.000 48 124.222 246.944 106.493 211.667 93.1993 185.208 82.8610 164.630 74.5940 148.167 49 124.360 247.22? 106.612211.905 93.3032 185.417 82.9534 164.815 74.6772 148.333 5O 124.504 247.500 106.735212.143 93.4108 185.625 83.0490165.000 74.7633148.500 51 124.647 247.778 106.857212.381 93.5183 185.833 83.1446 1 (5.185 74. 84 93 1148. 667 52 124.786 848.036 106.976212.619 93.6222 186. 042 83. 23701 65. 37'0 74.9325148.833 53 124.924 248.333 107.095212.857 93.721.1 186. 250 I 83. 3294 165.556 75.0157 149.000 54 125.067 248.611 107.218213.095 93.8337 1 86 . 4 58 1 S3 . 4250 1 65 . 741 75.1018 149.167 55 125.211 248.889 107.341 213.333 93.9412 186. 667 183.5206 165.926 75.1878 149.333 5fi 125.354 249.167 107.464 213.571 94.0487 186. 875; 83. 61 62 166.111 75.2739 149 500 57 125.497 249.444 107.586 213.810 94.1562 187.083 83.7118 166.296 75.3599 149.667 58 125. 6361249. 7221107. 705 214.048 94.2601 187.292 83.8042 166.481 75.4431 149.833 59 75 TABLE XIV. ACTUAL TANGENTS, ETC. 15 1 Curve. 2 Curve. 3 Curve. 4 Curve. 5 Curve. M. Tan. Arc. Tan. 377.168 Arc. Tan. Arc. Tan. Arc. Tan. 150.908 Arc. 754.3081500.00 750.000 251.402 500.000 188.614 375.000 300.000 1 755.1681501.07 377.598 750.833 251 . 740 500.550 188.828 375.417 151.080300.333 2 756.027 1503.33 378.028 751.607 252.035 501.111 180.043 375.833 151.252300.007 3 756.8581505.00 378.443 752.500 252.312 501.007 180.251 376.250 151.418301.000 4 757.689 1506.67 378.858 753.333252.589 502.222 189.459 370.607 151.584,301.333 5 758.5481508.33 379.288 754.167i252.875 502.778 189.674 377 . 083 151.756301.607 6 759.408 1510.00 379.718 755.000253.162 503.333 189.889 377.500 151. 928 1302. 000 7 700.2671511.67 380.148 755.833253.449 503.880 190.104377.917 152.100302.333 8 761. 1271513. 33 380.577 756.667 253.735 504.444 100.319378.333 152.272 302.607 9 761.9581515.00 380.993 757.500 254.012 505.000 190. 526] 378. 750 152.438 303.000 1 10 762 788 1516.67 381.408 758.333 254.289 505.556 190.734379.167 152.604 303.333 11 703.648 1518.33 381.838 759.167 254.575 506.111 190.949379.583 152.776 303.007 12 764.5071520.00 382.268 760.000 254.862 506.607 101.1041380.000 152.948 304.000 13 765.338 1521.67 382.683 760.833 255.139 507.222 191.372380.417 153.114 304.333 14 706.169 1523.33 383.098 761.667 255.416 507.778 191.579380.833 153.281 304.607 15 767.0281525.00 383.528 762.500 255.702 508.333 191.794 381.250 153.453 305.000 16 767.888 1526.67 383.958 763.333 255.989 508.889 192.009 381.667 153.624 305.333 17 768.7471528.33 384.388 764.167 256.275 509.444 192.224 382.083 153. 796! 305. 607 18 769.6071530.00 384.817 705.000 256.562 510.000 192.439 382.500 153.968306.000 19 770.437 1531.67 385.233 765.833 256.839 510.556 192.647 382.917 154.135300.333 20 771.268 1533.33 385.648 766.667 257.116 511.111 192.854 383.333 154.301 306.667 21 772.1281535.00 380.078 767.500 257.402 511.607 193.009 383.750 154.473307.000 22 772. 987 i 1536. 67 386.508 768.333 257.680 512.222 193.284 384.107 154.645307.333 23 773.8471538.33 386.937 769.167 257 . 975 512 778 193.499 384.583 154.817 307.007 24 774.706 1540.00 387.367 770.000 258.202 513.333 103.714 385.000 154.089:308.000 25 775.5371541.67 387.783 770.833 258.539 513.880 103.922 385.417 155.155 308.333 26 776.368 1543.33 3<88.198 771.607 258.810 514.444 104.120 385.833 155.321 308.607 27 777.227J 1545. 00 388.628 772. 500 259.1 02 515.000 194.344 380.250 155.403300.000 28 778.086 1546.07 389.057 773.333259.389 515.550 194.550 386.067 155.605 309.333 29 778.917 1548.33 389.473 774.167 059.666 516.111 104.767 387.083 155.831 300.007 30 779.748 1550.00 389.888 775.000 259.943 516.667 194.975 387.500 155.997 310.000 31 780.6081551.67 390.318 775.833 260.229 517.222 195.100 387.917 156.169,810.383 32 781. 467 i 1553. 33 300.748 776.667 260.510 517.778 195.405 388.333 156. 341 1310.667 33 782.326 1555 00 301.178 777.500 200.802 518.333 195.619 388.750 156.513311.000 34 783.186 1556.07 301.607 778.333 261.080 518.889 195.834 389.167 156.685 311.333 35 784.017 1558.33 392.023 779.167 261.366 519.444 196.042 389.583 156.851 311.667 36 784. 84711560. 00 392.438 780.000 261.643 520.000 196.250 300.000 157.017 312.000 37 38 785.707 786.566 1561.67 1563.33 302.868 303.298 780.833 781.667 261.929520.556 202.216521.111 196.465 196.680 300.417 390.833 157.189 312.333 157 3611312.667 39 787.426 1565.00 393.727 782.500 262.502521.667 196.895 301.250 157.533313.000 40 788.285 1566.67 394.157 783.333 262.789 522.222 197.109 391.667 157.705 313.333 41 789.116 1568.33 394.572 784.167 203.066 522.778 157.317 302.083 157.871 313.667 42 789.947 1570.00 394.988 785.000 203.343 523.333 197.525 302.500 158.038 314.000 43 790.806 1571.67 395.418 785.833 263.029 523.889 107.740 392.917 158. 210; 31 4. 333 44 791.666 1573.33 395.847 786.007 263.910 524.444 107.055303.333 158.382314.667 45 792.497 1575.00 396.263 787.500 264.193 525.000 198. 103 1 303. 750 158. 548! 315. 000 46 793.327 1576.67 396.078 188.333264.470 525.556 198.370304.107 158.714315.333 47 794.187 1578.33 397.108 789.167 204.750 526.111 198,585894.583 158.886 315.667 48 795.046 1580.00 397.538 700.000205.043 526.607 108.800 ! 305.000 159 058316.000 49 795.906 1581.67 397.967 790.833 205.329 527.222 199.015 395.417 159.230316.333 50 796.765 1583.33 308.397 791.667 205.610 527.778 199.230 305.833 159. 402 '310 007 51 797.596 1585.00 308.813 792.500 205.893 528.333 100.438306.250 159.568317.000 52 798.427 1586.67 399 . 228 703 . 333 ' 206 . 1 70 1 528 . 880 109.645306.667 159.734317.333 53 799.286 1588.33 399 . 658 794 . 1 07 j 266 . 450 520 . 444 1 99 . 860 307 . 083 150.006 317.607 54 800.146 1590.00 400.087 705.000 200.743 530.000 200.075 307.500 100.078 318.000 55 801.005 1591.67 400.517 705.833 207.020 53 >.556 200.200 307.017 100.250 318.333 56 801.865 1593.33 400 . 947 706 . 007 207 . 31(5 j 53 1 . 1 1 1 ' 200 . 505 308 . 333 160.42-2 318.667 57 802.605 1595.00 401 . 302 707 . 500 i 207 . 503 53 1 . 607 200 .713 308 . 750 100.588 310.000 58 803.526 1596.67 401 . 778 i 708 . 333 207 . 870 53-2 . 22:2 200 . 920 300 . 1 67 100.754 310.333 59 804.386 1598.33 402.208 799.167 208.156 532.77.8 1201 .135 399,583 160.926 319.607 TABLE XIV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 Curve. 1O Curve. 15 Tail. Arc. Tan. Arc. Tan. Arc. Tan. Arc. i Tan. Arc. M. 1*5.774 250.000 107.824 214.286 94.3641 187.50083.8966 166.06775.5*63 150.000 125.918 250.278 107.947 214.524 94.4716 187.708 83.9922 166.85275.6123 150.167 1 126.061 250.556 108.070 214.762 94.5791 187.91784.0878 167.03775.6984 150.333 2 126.200 250.833 108.188 215.000 94.6830 188.12584.180^ 1U7. 222 75. 7816 150.500 3 126.338 251.111 108.307 215.238 94.7870 188.33384.2726 167.40775.8648 150.667 4 126.481 251.389 108.430 215.476 94.8945 188.54284.3682 167.59375.9508 150.833 5 126.625 251.667 108.553 215.714 95.U02U 188.75084.4638 167. 778 7'6. 0369 151.000 6 126.768 251.944 108.67'6 215.952 95.1095 188.95884.5594 167. 9C3 76.1229 151.167 7 126.911 252.222 108.799 216.190 95.2171 189.167:84.6549 108. 148 '76. 2090 151.333 8 127.050 252.500 108.917 216.429 95.3210 189. 37584. 747 3 168.33376.2922 151.500 9 127.188 252.778 109.036 216.667 95.4249 189.58384.8398 168.51976.3753 151.667 1O 127.332 253.056 109.159 216.905 95.5324 189.79284.9353 168.70476.46i4 151.833 11 127.475 253.333 109.282 217.143 95.6400 190.000 85.0309 168.8897'(i.5i75 152.000 12 127.613 253.611 109.401 217.381 95.7439 190.20885.12:33 169.07470.6300 152.167 13 127.752 253.889 109.519 217.619 95.8478 190.41785.2157 169.25976.7138 152.333 14 127.895 254. 1G7 109.642 217.857 95.9553 190.62585.3113 169.44476.7999 152.500 15 128.039 254.444 109.765 218.095 96.0629 190.88885.4069 169.63076.8859 152.667 16 128.182 254.722 109.888 218.333 96.1104 191. 042 '85. 5025 169.815 76.9720 152.833 17 128.325 255.000 110.011 218.571 96 2779 191. 250185.5981 170.00077.0580 153.000 18 128.464 255.278 110.129 218.810 96.3818 191 ,458'85. 6905 170.18577.1412 153.167 19 128.602 255.556 110.248 219.048 96.4858 191.667 85.7829 170.37077.2244 153.333 2O 128.746 255.833 110.371 219.286 96.5933 191. 875 185. 87 85 170.556 77.3105 153.500 21 128.889 256.111 110.494 219.524 96.7008 192.083 85.9741 17 0.741; 77. 3965 153.667 22 129.032 256.389 110.617 219.762 96.8063 192. 292 '86. 0697 17'0.92677.4826 153.833 23 129.176 256.667 110.740 220.000 96.9158 192. 500 '86.1653 171.111 77.5686 154.000 24 129.314 256.944 110.856 220.238 97.0198 192.70886.2577 171.29677.6518 154.167 25 129.453 257.222 110.977 220. 47 (J 97.1237 192.917 86.3501 171.481 77.7'350 154.333 26 129.596 257.500 111.100 220.714 97.2312 I U3. 125 86. 4457 171. 667I77. 8210 154.500 27 129.739 257.778 111.223 220.952 97.3387 193.333 # i. 5413 171.85277.9071 154.667 28 129.878 258. C56 111.342 .'21.190 97.4427 1 93. 542 : 86. 6337 172. 037 i 7 7. 9903 154.833 29 130.016 258.333 111.460 221.429 97'. 5466 193.750 86.7261 172.222 78.07'35 155.000 3O 130.160 258.611 111.583 221.667 97.6541 193.95886.8217 172.4077'8.1595 155.167 31 130.303 258.889 111.706 221.905 97.7616 194.167 86.9173 172.59378.2456 155.333 32 130.446 259.167 111.829 222.143 97.8691 194.375 87.0128 172. 77'8 : 7'8. 3316 155.500 33 130.589 259.444 111.952 222.381 97.9767 194.58387.1084 172.96378.4177 155.667 34 130.728 259.722 112.071 222.619 98.0806 194.79287.2008 173.14878.5009 155.833 35 130.867 260.000 112.189 222.857 98.1845 195.000! 87. 2932 173.33378.5841 156.000 36 131.010 260.278 112.312 223.095 98.2920 195.20887.3888 173.51978.6701 156.167 37 131.153 260.556 112.435 223.333 98.3996 195.41787.4844 173.704 7'8.75<32 156.333 38 131.296 260.833 112.558 2^3.571 98.5071 195.625 87.5800 173. 889 7'8. 8422 156.500 39 131.440 261.111 112.681 223.810 98.6146 195.833 87.6756 17'4.07478.9283 156.667 4O 131.578261.389 112.799 224.048 98.7185 196.042 87.7680 174.25979.0115 156.833 41 131.717261.667 112.918 224.286 98.8225 196.250 87.8604 174.44479.0946 157.000 42 131. 860J261.944 113.041 224.524 98.9300 196.458 87.9560 174.63079.1807 157.107 43 132.003262.222 113.164 224.762 99.0375 196.667 88.0516 174.81579.2667 157.3S3 44 132. 142 1262.500 113.283 225.000 99.1414 196.87588.1440 175.00079.3499 157.500 45 132.280J262.778 113.401 225.238 99.2454 197.083 88.2364 175.18579.4331 157.667 46 132.424263.056 113.524 225.476 99.3529 197. 292 188.3320 175.37079.5192 157.833 47 132.567263.333 113.647 225.714 99.4604 197.500 88.4276 175.55679.6052 158.000 48 132.710 263.611 113.770 225.952 99.5679 197.708 88.5232 175.741 79.6913 158. 167' 49 132.854 263.889 113.893 226.190 99.6754 197.917 88.6188 175.92679.7773 158.3-33 50 132.992264.167 114.012 226.429 99.7794 198.125 88.7112 176.111 79.8605 158.500 51 133.131 264.444 114.130 226.667 99.8833 198.333 88.8036 176.29679.9437 158.607 52 133.274264.722 114.253 226 905 99.9908 198.542 88.8992 176.481 80.0298 158.833 53 133.417265.000 114.376 227.143 100.098 198.750 88.9948 176.66780.1158 159.000 54 133.561 265.278 114.499 227.381 100.206 198.958 89.0903 176.85280.2019 159.167 55 133.704 Of -5. 550 114.622 227.619 100.313 199.167 89.1859 177.03780.2879 159.333 56 133.H43-2fi5.83:-! 114 741 227.857 100.417 199.375 89.2783 177.22280.3711 159.500 57 133.981 266.111 114.859228.095 100.521 199.583 89.3707 177.40780.4543 159.667 58 134.124 266.389 1 t4.882J228.333jlOO.629 199.792 89.4663 177.59380.5403 159.833 59 77 TABLE XIV. ACTUAL TAKGENTS, ETC. 16 1 Curve. 2 Curve. 3 Curve. 4 Curve. 5 Curve. M. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. A re. ~~O~ 805.245 1600.00 402.1537 800.000 268.443 533.333ia01.350 400.000 161.098 320.000 1 806.104 1601.67 403.067 800.833 268.729 533. 889i201.565 400.417 101.270 320.333 3 806.964 1603.33 403.497 80 1.607'! 269. 01 6 534.444201.780 400.833 161.442 320.667 3 807.795 1605.00 403.912 802. 500)269. 293 535 .000! 201. 988 401.250 161.608 321.000 4 808.626 1606.6? 404.328 803. 33-1209. 570 535.556 202.190 401.667 161.774 321.333 5 809.485 1608.33 404.757 bO 4. 107 269 856 536.111 202.410 402.083 161.946 321 . 667 6 810.344 1610.00 405.187 805.000270.143 536.667 202.625 402.500 162. 118 322. 000 7 811.204 1611.67 405.617 805 833270.429 537.222 202.840 402.917 162.290322 333 8 812.063 1613. 33 406.047 306. 667|270. 716 537.778 203. 055 403. 333 162.462322.007 9 812.894 1615.00 406.462 807.500 270.993 538.333 203.263 403.750 162.628323.000 10 813.725 1616.67 406 877 808.333 271.270 538.889 203.471 404.167 162.795323.333 11 814.584 1618. as 407.307 809.167 271 .556 539.444 203.686404.583 162.967|323.067 12 815.444 1620.00 407.737 810.000 271.843 540.000 203.900405.000 163. 131) '324 000 13 816.303 1621.67 408.167 810.833 272.129 540.556 204.115405.417 163.311 o24.3:%3 14 817.163 1623. 33 408.596 811.667 272.416 541.111 d04.SJ040o.833 163.482324.667 15 817 993 1625.00 409.012 812.500 272.693 541.667 204. 538! 406. 250 103.649,325 000 16 818.824 1626.67 409.4-37 813.333 272.970 542.222 204 746 406.667 103.8151325.333 17 819.684 1628.33 409.857 814.16. 273.256 542.778 204.961 407.083 163.987325.667 18 820.543 1630.00 410.287 815.000 273.543 543.333 205.176 407.500 164.159326.000 19 821.403 1631.67 410.716 815.833 273.829 543.889 205.390 407.917 104.331 320.333 2O 822.262 1633 33 411. 14G 816.667 274.116 544.414 205 605 408.333 164.503 326 667 31 823.122 1035 00 411.576 817.500 274.402 545.000 205.820 40S.750 164. 675| 327 000 23 823.981 1636 67 412.00(5 818333 274.639 545.556 206.035 409.16; 164 847 327 333 23 824.812 1638.33 412.421 819.167 274.966 546.111 206.243 40!) 583 165.013 327 667 24 825.643 1640.00 412.836 820.000 275.243 516.667' 206.451 410.000 105.179 328.000 25 826.502 1641.67 413.260 820.8-33 275.529 547.222 -.'06.606 410 417 165.351 328.333 26 827.361 1643.33 413.696 821.667 275.816 547.778 206.880 410.833 165.523 328.607 27 828.221 1645.00 414.126 822.500 276.102 548.333 207.095 411.250 165.695 329.000 28 829.080 1616.67 414.555 823.333 278.898 548.889 207.310 411.667 165.867 329.333 29 829.911 1648. 33 414.971 824.167 276.666 549.444 207.518 412.063 166.033 329.667 30 830.742 1650.00 415.386 825.000 276.912 550.000 207.726 412 500 166.199 330.000 31 831.601 1651 . 67 415 816 825.833 277.229 550.556 207.941 412.917 166.371 330,333 32 832 461 1653 33 416.246 826.667 277 516 551.111 208.156 413.333 166.543 330.667 33 833.320 1655.00 410.675 827.500 277.802 5M.667 208.370 413.750 166 715 331.000 34 834.180 1656.67 417.105 828.333 278.089 552.222 208. 5S5 414.167 166.887 331.333 35 835.011 1658.33 417.521 829.167 278.366 5 ? >2 778 208.793 414.583 107.053 331.667 36 835.841 1660.00 417.936 830.000 278.642 553.333 309.001 415.000 167.219 332 000 37 836.701 1661.67 418.366 830.833 278.929 553.889 209.216 415.417 167.391 332.833 38 837.560 1663.33 418.795 831.667 279.215 554.444 209.421 415.833 167.563 332.667 39 838.420 1665.00 419.225 832.500 279.502 555.000 209.646 416.250 167.735 333.000 40 839.279 1666.67 419.655 833.333 279.789 555.556 209.860 416.667 167.907 333.333 41 840.139 1668.33 420.085 834.167 280.075 556.111 210.075 417.083 168 079 333.667 42 840.998 1670.00 420.514 835 000 280.362 556.667 210.290 417.500 168.251 334.000 43 841.829 1671.67 420.930 835.833 280.639 557.222 210.498 417.917 168.417 334.333 44 842.660 1673.33 421.345 836 667 280.915 557.778 310.706 418.333 168. 583! 334. 667 45 843.519 1675.00 421.775 837.500 281.202 5.58.333 210 921 418.750 168 755335.000 46 844.379 1676.67 422.205 838.333 281. 48S 558.889 211.136 416.167 168.927 335. ,333 47 845.238 1678.33 422.634 839.167 281.775 V>9.444 211.350 419.583 169.099335.667 48 846.097 1680.00 423. 06 4 840.000 282 062 560.000 211.565 420.000 169.271 336.000 49 846.928 1681.67 423 480 840.833 282.338 500.556 211.773, 420. 417 169.437 336.333 50 847.759 1683.33 423.895 841.667 282.615 561. 111 211.981 420.833 169.604 336.667 51 848.618 1685.00 424.325 842.500 2S2.902 )(>]. 607 21 2. 19(5; 42 1.250 169.776337.000 53 849.478 1686.67 424.755 843.333 283.188 562.222 212.411 421.667 169.947 337.333 53 850.337 1688.33 125.184 844.167 2S3 . 475 "62 . 778 i 2 1 2 . 626 4 22 . 083 170.119:337.007 54 851.197 1690.00 425.614 845.000 283 . 7 u i 5< J:J . 330 ! 21 2 . 840 422 . 500 1 1 70 . 291 i 338 . 000 55 852.056 1691.67 426.044 845. 83:5 28LOJ8 5(i:] SS^ .'!:-. 055 422.0171170.463 338.3*3' 56 852.916 1693 33 426.473 846.667 284.335 ;754 444 213.270 423. 333' 170. 635 .348. 667 57 853.746 1695.00 426.889 847.500 284.011 <5 5.0:M> 213.478 423. 750,170.8111 339.000 58 854.577 1696.67 427 . 304 818. 333 , 284 . 888 ! 5< 15 f,r,6 2 ! 3 . 686 424 . 1 (57 1 70 . 968 389 . 333 59 855.437 1698.33 427.734 849.167 285.175i566.lHhJ13.90I 424. 583 J 7 1.1 40 3:39.067 TABLE XIV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 C Tan. iirve. Arc. 9 Curve. 1O Curve. 16 M. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. 1 34.208 266.667 115.105 228.571 100.736 200.00089.5619 177.778 80.6264 160.000 o 134.411 266.944 115.228 228.810100.844 200.20889.6575 177.963 80.7124 160.167 1 134.554 267.222 115 351 229.048100.951 200.41789.7531 17B.148 80.7985 160.333 2 134.693 267.500 115.469 229.286101.055 200.62589.8455 178.333 80.8817 160.500 3 134.831 267.778 115.588 229.524 101.159 200.83389.9379 178.519 80.9649 160.667 4 184.975 268.056 115.711 229.762101.267 201.04290.0335 178.704 81.0509 160.833 5 135.118 268 333 115.834 230.000! 101. 374 201.250:90.1291 178.889 81.1370 161.000 6 135.261 268.611 115.957 230.238 101 482 201. 458 ! 90. 2247 179.074 81.2230 161.167 7 1,35.405 268.889 116.080 230.476 101.589 201.667 90.3203 179 259 81.3091 161.333 8 135.543 269.167 116.198 230.714 101.693 201.875 90.4127 179.444 81.3923 161.500 9 135.682 269.444 116.317 230.952 101 . 7 97 202.083 90.5051 179.630 81.4754 161.667 10 135.825 269.722 116 4401231.190 101.905 202. 292 190.6007 179.815 81.5615 161.833 11 135.968! 270. 000 11 6. 563^ 231. 429 102.012 202.500 90.6903 180.000 81.6476 162.000 12 136.112 270.278 116.686J231.667 102.120 202.708 90.7919 180.185 81.7336 162.167 13 136.255 270.556 116 809231.905 102.227 202.917 90.8874 180.370 81.8197 162.333 14 136.393 270.833 116.927 232.143 102.331 203.125 90 9798 180.556 81.9028 162.500 15 136.532 271.111 117.046 232 381 102.435 203 333 91.07'*3 180.741 81.9860 162.667 16 136.675 271.389 117.169 232.619 102.542 203.542 91.1078 180.936 82.0721 162.833 17 136.818 271.667 117.292 232.857 102.650 203.750 91.2634 181.11] 82.1581 163.000 18 136.902 271.944 117.415 233.095 102.758 203.958 91.3590 181.290 82.2442 163.167 19 137.105 272.222 117.538 233.333 102 865 204.167 91 .4546 181.481 82.3302 163.333 2O 137.248 272.500 117.600 233.571 102.973 204.375 91.5502 181.667 82.4163 163.500 21 137.302 272.778 117.783 233.810 103.080 204.583 91.64.-8 181.852 82.50^4 163.667 22 137.530 273.056 117.902 234.048 103.184 204.792 91.7382 182.037 82. sans 163.833 23 137.669 273.333 118.021 234.286 103 288 205.000 91.8300 182.222 82.6087 164.00U 24 137.812 273.011 118.144 234.524 103.395 205.208 91.9262 182.407 82.7548 104.167 25 137.955 273.889 118.266 234.762 103.503 205.417 92.0218 182.593 82.8408 164.333 26 138.099 274.167 118.389 235.000 103.610 205.625 92.1174 182.778 82.9269 1(54.500 27 138.242 274.444 118.512 235.238 103.718 205.833 92.2130 182.963 83.0120 164.667 28 138.381 274.722 118.631 235.476 103.822 206.042 92.3054 183.148 83.0961 164.833 29 138 519 275-. 000 118.750 235.714 103.926 206.250 92.3978 183.333 S3 1793 165.000 30 138.662 275.278 118.873 235.952 104.033 206.458 92.4934 183.519 b3 2(554 105.167 31 188.800 275.556 118.995 236.190 104.141 206.667 92.5890 183.704 83.3514 165.333 32 183.949 275.833 119.118 236.429 104.248 206 875 92.6845 183.889 83.4375 105.500 33 139.092 276.111 119.241 236.667 104.356 207.083 92.7801 184.074 83.5285 165.607 34 139.231 276.389 119.360 236.905 104.460 207 292 92. ( S725 184.259 83.6007 105.833 35 139.309 276.667 119.479 237.143 104.564 207.500 92.9649 184.444 83.0809 106.000 36 139 513 276.944 119.601 237.381 104.671 207.708 93.0605 184.630 83.7750 166.107 37 139 656 277 222 119.724 237.619 104.779 207.917 D3.1561 184.815 83.8620 106.333 38 139.799 277! 500 119 847 237.857 104.886 208.125 93.2517 185.000 83.9481 166.500 39 139.943 277.778 119.970 238 095 104.994 208.333 93.3473 185.185 84.0341 166.C67 4O 140.086 278.050 120.093 238. S33 105.101 208.542 93.4429 185.370 84.1202 166.833 41 140.229 278.333 120.216 238.571 105 209 208.750 93.5385 185.556 84.2062 167.000 42 140.308 278.611 120.334 238.810 105.313 208.958 93.6309 185.741 84.2804 167.107 43 140.500 278.889 120.453 239.048 105.417 209.167 93.7233 185.926 84.3726 167.334 44 140.050 279 107 120.576 239.286 105.524 209.375 93.H189 186.111 84.4586 167.500 45 140.793 2T9.444 120.699 239.524 105.632 209.583 03.9145 186.296 84.5447 167.667 46 140.930 279.722 120.822 239.762 105.739 209.792 94.0101 186.481 84.6307 167 833 47 141.079 280.000 120.945 240.000 105.847 210. OM 194. 1057 186.667 84.7168 168.000 48 141.218 280.278 121.063 240 238 105.951 210.208 94.1981 18G.852 84.8000 168.167 49 141.356 280.550 121.182 240.476 10fi.0'.5 210.417 04.2905 187.C37 84.8832 168.333 50 141.500280 833 121.305240.714 106.162 210.625 94.3861 187.222 84.9692 168.500 51 141. 6431281. 111 121. 4281240. 952 106 270 210.833 94.4810 187.407 85.05*8 168.667 52 141 . 786 281 . 38!) j 1 21 . 55 1 1 241 . 1 90i 1 00 . 3T7 211.042 94.5772 187.503 85.1413 168.833 53 141.930! 281. 667 121.074 241.429 100.485 211.25094.6728 187.778 85.2274 169.000 54 142.073:281.944 121.796 241.067(106.592 211.458 94.7684 1S7.903 85.3134 169.167 55 142.216 282.222 121.919!241.905100.700 211.167 94. 80401 18-'. 148 85.3905 169.333 56 142.355 282.500 1 22 . 038 242 . 1 43 1 06 . 804 211.87594 9504: 188.3: ;H 85.4827 169.500 57 142.493 282.778 122.157242.381 106.908 212. C83 95.0488J188.519 85.5050 109 007 58 142 6371283.056 122.280 242.619 107.015 212.292 96. 1444} 188. 704 85.6519 109.833 59 79 TABLE XIV. ACTUAL TANGENTS, ETC. 17 1S7 1 Curve. 2 Curve. 3 Curve. 4 Curve. 5 Curve. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. ~~o" 850.296 1700.00 428.164 85'). 000 285.461 5H6.667 214.116 425.000 171.312 340.000 1 857.156 1701.67 428.594 850.833 285.748 567.222 214.330 425.417 171.483 340.333 2 858.015 1703.33 429.023 851.667 286.034 567.778 214.545 425.833 171.655 340.667 3 858.875 1705.00 429.453 852.500 286.321 568.333 214.760 426.250 171.827 341.00(3 4 859.734 1706 67- 429.883 853.333 286.608 568.889 214.975 426.667 171.999 341.333 5 860.565 1708.33 430.298 854.167 286.884 569.444 215.183 427.083 172.166 341.667 6 861.396 1710.00 430.714 855.000 5287.161 570.000 215.391 427.500 172.332 342.000 7 86-2.255 1711.67 431.143 855.833 287.448 570.556 215.606 427.917 172.504 342.3:53 8 863.114 1713.33 431.573 856.667 287.734 571.111 215.820 428.333 172.676 342.667 9 863.974 1715.00 432.003 857.500 288.021 571.667 216.035 428.750 172.848 343.000 10 864 833 1716.67 432.433 858.333 288.307 572.222 216.250 429.167 173.020 343.333 11 865.693 1718.33 432.862 859.167 288.594 572.778 216.465 429.583 178.191 343.667 12 866.552 1720.00 433.292 860.000 288.880 573.888 216.680 430.000 173.363 344.000 13 867.383 1721.67 433.707 860.833 289.157 573.889 210.888 430.417 173.530 344.333 14 868.214 1723.33 434 123 861.667 289.434 574.444 217.096 430.833 173.696 344.667 15 869.073 1725.00 434.553 862. 5 r O 289 721 575.000 217.310 431.250 173.868 345.000 16 869.933 1726.67 434.982 863.333 290.007 575.556 217.5-tf 431.667 174.040 345.333 17 870.792 1728.33 435.412 864.167 290.294 576.111 217.740 432.083 174.212 345.667 18 871.652 1730.00 435.842 865.000 290.580 576.607 217.955 432.500 174.384 346.000 19 872.511 1731.67 436.272 865.833 290.867 577.222 218 170 432.917 174.556 346.333 20 873.371 1733.33 436.701 866.667 291.153 577.778 218 385 433.333 174.727 346.667 21 874.201 1735.00 437.117 867.500 291.430 578.333 218 593 433.750 174.894 347.000 22 875.032 1736.67 437.532 868.333 291.707 578. S89 218.800 434.167 175.060 347.333 23 875.892 1738.33 437.962 869.167 291.994 579.444 219.015 434.583 175.232 347.667 24= 876.751 1740.00 438.392 870.000 292.280 580.000 219.230 435.000 175.404 348.000 25 877.610 1741.67 438.821 870.833 292.567 580.556 219 445 435.417 175.576 348.333 26 878.470 1743.33 439.251 871.667 202.853 581.111 219.660 43'.833 175.748 348.667 27 879.329 1745.00 439.681 872.500 293.140 581.667 219.875 436.250 175.920 349.000 28 880.189 1746.67 440.111 873.333 293.426 582.222 220.090 436.667 176.092 349.333 29 881.020 1748.33 440.526 874.167 293.703 582.778 220.298 437.083 176.258 349.667 30 881.850 1750.00 440.941 875.000 -?93.980 583 333 220.505 437. 5HO 176.424 350.000 31 882.710 1751.67 441.371 875.833 294.267 583.889 220.720 437.917 176.596 350.333 32 883.569 1753.33 441.801 876.667 294.553 584.445 220.935 438.333 176.768 350.667 33 884.429 1755.00 442.231 877.500 294.840 585.000 221.150 438.750 176.940 351.000 34 885.288 1756.67 442.660 878.333 295.126 585.556 221.365 439.167 177.112 351.333 35 886.148 1758.33 443.090 879.167 295.413 586.111 221.580 439.583 177.284 351.667 36 887.007 1760.00 443.520 880.000 295.699 586.667 221.795 440.000 177.450 352.000 37 887.867 1761.67 443.950 880.833 295.986 587.222 222.010 440.417 177.628 352.333 38 888.726 1763.33 444.379 881.667 296.273 587.778 222.225 440.833 177.799 352.607 39 889.557 1765.00 444.795 882.500 296.549 588.333 222.432 441.250 177.966 353.000 40 890.388 1766.67 445.210 883.333 296 826 588.889 222.640 441.667 178.132 353.333 41 891.247 1768.33 445.640 884.167 297.113 589.444 222.855 442.083 178 304 353.667 42 892.107 1770.00 446.070 885.000 297.399 590.000 223.070 442.500 178.476 354.000 43 892.966 1771.67 446.499 885.833 297 686 590.556 223. 2S5 442.917 178.648 354.333 44 893.825 1773.33 446.929 886.667 297.972 591.111 223.500 443.333 178.820 354.667 45 894.685 1775.00 447.359 887.500 298.259 591.667 223.715 443.750 178.992 355.000 46 895.544 1776.67 447.789 888.333 298.546 592.222 223.929444.167 179.164 355.333 47 896.404 1778.33 448.218 889.167 298.832 592.778 224.144444.583 179.336 355.667 48 897.263 1780.00 448.648 890.000 299.119 593.333 224. 359 ! 4 45. 000 179.507 356.000 49 898.094 1781.67 449.063 890.833 299.395 593.889 224.567 445.417 179.674 356.333 50 898.925 1783.33 449.479 891.667 299.672 594.444 -.'24.775 445.833 179.840 356.067 51 899.784 1785.00 449.909 892.500 299.959 595 000 224.W044ti.250 180.012357.000 53 900.644 1786.67 450 338 893.333 300.245 595 556 225 . 2( )5 416 . f U57 ! 1 80 1 84 357 . 333 53 901.503 1788.33 450.7(58 894.167 300.532 596 1 1 1 1 225 . 4 1 9 4 4 7 . 083 1 80 . 3M5 357 . 667 54 902.363 1790.00 451.198 895.000 300.818 596. 667 J225.63 4 4-17.500 180.528 358. 000 55 903 222 1791.67 451 628 895.833 301.105 597 . 222 225 849 447 . 9 1 7 1 80 . 700 358 . 333 56 904.081 1793.33 452.057 896.667 301.302 597 . 778 i 226 . 064 448 . 333 1 1 80 872 35S . 6H7 57 904.941 1795.00 452.487 897.500 301.67S 598.333 226.279 448.750 1 SI .043 359.000 58 905.800 1796.67 452.917 898.333 301.965 598. 889 1 226. 494 449.167 181 .215 359.333 59 906.631 1798 ..33 453.332 899.1671302 242 599. 444 1226.702 449. 583 11 81. 382 359.007 TABLE XIV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 Curve. 1O Curve. 17 Tan. Arc. 2837333 Tan. 122.402 Arc. Tan. Arc. 212.500 Tan. Arc. Tan. Arc. M. 142.780 242.857 107.123 95.2400 188.889 85.7380 170.000 142.923 283.611 122.525 243.095 107.230 212.708 % 3356 1 89. 074 j 85. 8240 170.107 1 143.007 283.889 122.648 243.333 107.338 212.917 95.4312 189.259 85.9101 170.333 2 143.210 284.167 122.771 243.571 107.445 213.125 95.5268 189.444 85.9961 170.500 3 143.353 284.444 122.894 243.810 107.553 213.333 95.6224 189.630 86.0822 170.667 4 143.492 284.722 123.013 244.048 107.657 213.542 95.7148 189.815 86.1654 170.833 5 143.630 285.000 123.131 244.286 107.761 213.750 95.8072 190.000 86.2486 171.000 6 143.774 285.278 123.254 244.524 107.868 213.958 95.9028 190.185 86.3346 171.167 7 143.917 285.556 123.377 244.762 107.976 214.167 95 9983 190.370 86.4207 171.333 8 144.060 285.833 123.500 245.000 108.083 214.375 96.0939 190.556 86.5067 171.500 9 144.203 286.111 123.623 245.238 108.191 214.583 96.1895 190.741 86.5928 171.667 10 144.347 286.389 123.746245.476 108.298 214.792 96.2851! 190. 926 86.6788 171.833 11 144.490 286.667 123.869i245.7l4 108.406 215 000 96. 3807J191.111 86.7649 172.000 13 144.629 286.944 123.987245.952 108 510 215.208 96.4731 191.296 86.8481 172.167 13 144.767 287.222 124. 106! 246. 190 108.614 215.417 96.5655 191.481 86.9312 172.333 14 144.910 287.500 124. 229 1246. 429 108.721 215 625 96.6611 191.667 87.0173 172.500 15 145.054 287.778 124.352246.667 108.829 215.833 96.7567 191.852 87.1033 172.667 16 145.197 288.056 124.4751246.905 108.936 216 042 96.8523 192.037 87.1894 172.833 17 145.340 288.333 124.5971247.143 109.044 216.250 96.9479 192.222 87.2755 173.000 18 145.484 288.611 124.720 247.381 109.151 216.458 97.0435 192.407 87.3615 173.167 19 145.627 288.889 124.843 247.619 109.259 216.667 97.1391 192.593 87.4476 173.333 3O 145.766 289.167 124.9621247.857 109.363 216.875 97.2315 192.778 87.5307 173.500 31 145.904 146.047 289.444 289.722 125.081 125 204 248.095 248.333 109.467 109.574 217.083 217.292 97.3239 97.4195 192.963 193.148 87.6139 87.7000 173.667 173.833 33 146.191 290.000 125.326 248.571 109.682 217.500 97.5151 193.333 87.7860 174.000 34 146.334 290.278 125.449 248.810 109.789 217.708 97.6106 193.519 87.8721 174.167 35 146.477 290.556 125.572 249.048 109.897 217.917 97.7062 193.704 87.9581 174.333 36 146.621 290.833 125.695 249.286 110.004 218.125 97.8018 193.889 88.0442 174.500 37 146.764 291.111 125 818 249.524 110.112 218.333 97.8974 194.074 88.1303 174.667 38 146.902 291.389 125.937 249.762 110.216 218.542 97.9898 194.259 88.2134 174.833 39 147.041 291.667 126.055 250.000 110.320 218.750 98.0822 194.444 88.2966 175.000 30 147.184 291.944 126.178 250.238 110.427 218.958 98.1778 194.630 88.3827 175.167 31 147.328 292.222 126.301 250.476 110.535 219.167 98.2734 194.815 88.4687 175.333 33 147.471 292.500 126.424 250.714 110.642 219.375 98.3690 195.000 88.5548 175.500 33 147.614 292.778 126.547 250.952 110.750 219.583 98.4646 1P5.185 88.6408 175.667 34 147.757 293.056 126.670 251.190 110.857 219.792 98.5602 195.370 88.7269 175.833 35 147.901 293.333 126.792 251.429 110.965 220.000 98.6558 195.556 88.8129 176.000 36 148.044 293.611 126.915 251.667 111.072 220.208 98.7514 195.741 88.8990 176.167 37 148.187 293.889 127.038 251.905 111.180 220.417 98.8469 195.926 88.9850 176.333 38 148.326 294.167 127.157 252.143 111.284 220.625 98.9393 196.111 89.0682 176.500 39 148.464 294.444 127.276 252.381 111.388 220.833 99.0318 196.296 89.1514 176.667 4O 148.608 294 722 127.399 252.619 111.495 221.042 99.1273 196.481 89.2375 176.833 41 148.751 295.000 127.521 252.857 111.603 221.250 99.2229 196.667 89.3235 177.000 43 148.894 295.278 127.644 253.095 111.710 221.458 99.3185 196.852 89.4096 177.167 43 149.038 295.556 127.767 253.333 111.818 221.667 99.4141 197.037 89.4956 177.333 44 149.181 295.833 127.890 253.571 111.925 221.875 99.5097 197.222 89.5817 177.500 45 149.324 296.111 128.013 253.810 112.033 222.083 99.6053 197.407 89.6677 177.667 46 149.468 296.389 128.136254.048 112.140 222.292 99.7009 197.593 89.7538 177.833 47 149.611 296.667 128.258 254.286 112.248 222.500 99.7965 197.778 89.8398 178.000 48 149.749 296.944 128.377 254.524 112.352 222.708 99.8889 197.963 89.9230 178.167 49 149.888 297.222 128.496 254.762 112.456 222.917 99.9813 198.148 90.0062 178.333 5O 150.031 297 500 128.619 255.000 112.563223.125 100.077 198.333 90.0923 178.500 51 150.175 297.778 128.742 255.238 112.671 223.333 100.172 198.519 90.1783 178.607 53 150. 31 81298.056 128.865 255.476 112.778223.542 100.208 198.704 90.2644 178.833 53 150. 461 J298.333 128. 9871255. 714 112.886223.750 100.364 198.889 90.3504 179.000 54 150.604 298.611 129.110:255.952 112.993223.958 100. 459:199. 074 90.4365 179.107 55 150. 748i 298. 889 129.233256.190 113.101 224.167 100.555199.259 90.5225 179.33:' 56 150.891 299.167 129.356256.429 113.208224.375 100.650199.444 90.6086 179.500 57 1 5 1. 03 4 ' 299. 444 129.479256.667 113.316224.583 100.746 199.630 90.6946 179.007 58 151. 173 1299.722 1 29 . 598 ; 256 . 905 1 1 13 . 420 224 . 792 100.838^99^ aO.TTTb 179.833 59 81 TABLE XIV. ACTUAL TANGENTS, ETC. 18 1 Curve. 3 Curve. 3 Curve. 4 Curve. 5 Curve. M. Tan. Arc. Tan. Arc. Tan. 1 Arc. Tan. Arc. Tan. Arc. O 907^462 1800.00 453 748 900.000 302 51S 600. 000 226.909 450.000 181.548 360.000 1 908. 321 1801.67 454.177 900.K33 302.805600.556 227.124 450.417 181.720 360.333 2 909.181 1803.33 454.60? 901.6157 303. 091 '601. Ill 227.339 450.833 181.892 360.007 3 910.040 1805.00 455.037 902.500 303.378601.667 227 554 451.250 188.064 361.000 4 910.900 1806.67 455.467 903.333 303. 665 1 602. 222 227.709 451 . 667 182.236 361.333 5 911.759 1808.33 455.896 904.167 303. 951 1602.778 227.984 452.083 182.408 361 . 007 6 912.619 1810.00 456.326 905.000 304. 238 1603.333 228.199 452.500 182.579 302.000 7 913.478 1811.67 456.756 905.833 304.524 603.889 228.414 452.917 182.751 362.333 8 914.338 1813.33 457.186 906.667 304.811 604.444 228.629 453.333 182.923 362.007 9 915.197 1815.00 157.615 907.500 305.097 605.000 228.844 453.750 183.095 363.000 10 916.056 1816.67 15S.045 908.333 305.384 605.556 229.058 454.167 183.267 363 333 11 91(5.887 1818.35 458.4HO <)< 19.167 305.661 606.111 229.206 454.583 183.433 303 007 13 917.718 1820.00 458.876 910.000 305.938 606.667 229.474 455.000 183.600 304.000 13 918.577 1821.67 459.806 910.833 306.224 607.222 229.689 455.417 183.772 304.333 14 919.437 1823 33 459.73o 911.667 306.511 607.778 229.904 455.833 183.944 364.667 15 920.296 1825.00 460.165 912.500 306.797 (508.333 230.119 456.250 184.115 305.000 16 921.156 1826.67 460.595 013.333 307.084 608.889 230 334 456.607 184.287 365.333 17 922.015 1828.33 461.025 914.167 307.370 609.444 230.548 457.083 184.459 365.667 18 922.875 1830.00 461.454 915 000 307.657 610.000 230.763 457.500 184.631 366.000 19 923.734 1831.67 461.884 915.833 307.943 610.550 230.978 457.917 184.803 366.333 20 924.594 1833.33 462.314 916.667 308.230 611.111 231.193 458.333 184.975 366.667 21 925.453 1835.00 462.743 917.500 308.516 611.067 231.408 458.750 185.147 367.000 22 926.313 1836.67 463.173 918.333 308 803 612 222 231 . 623 459.167 185.319 367.333 23 927.143 1838.33 463.589 919.167 309.080 612 778 231.831 459.583 185.485 367.607 34 927.974 1840.00 464.004 920.000 309.357 613.333 232.038 460.000 185.652 368.000 25 928.834 1841 67 464.434 920 833 309.643 613.889 232.253 460.417 185.823 368.333 26 929.693 1843 33 464.864 921.667 309.930 614.444 232.408 460 833 185.995 368.067 21 930.552 1845.00 465.293 922.500 310.216 615.000 232.683 461 250 186.167 369.000 28 931.412 1846.67 465.723 923.333 310.503 015. 550 232.898 461.067 186.339 369.333 29 932.271 1848.33 460.153 924.167 310.789 616.111 233.113 462.083 186.511 369. G67 3O 933.131 1850.00 466.582 925.000 311.076 616.667 233.328 462.500 186.683 370.000 31 933.990 1851.67 467.012 925.833 311.362 6! 7. 222 233.543 462.917 186.855 370.333 33 934.850 1853.33 4157.442 926.667 311.049 617.778 233.758 463.3-33 187.027 370. G67 33 935.709 1855.00 467.872 927.500 311.93o 018.333 233.973 463.750 187.199 371.000 34 936.569 1856.67 468 301 928.333 312.222 618.889 234. 1S8 464.167 187.371 371.333 35 937.428 1858.33 468.731 929.167 312.508 619.444 234.402 464.583 187.543 171.607 36 938.287 1860.00 469.161 930.000 312.795 620.000 234.617 465.000 187.715 372.000 37 939.118 1861.67 469.576 930.833 313.072 020.550 234.825 465.417 187.881 372.333 38 939.949 1863.33 469.992 981.667 313.319 621.111 235.033 465.833 188.047 372.667 39 940.809 1865.00 470.422 932.500 313.635 621.667 235.248 466.250 188.219 373.000 4O 941.668 1866.67 470.851 933.333 313.922 622.222 235.463 466.667 188.391 373.333 41 942.527 1868.33 471.281 934.167 314.208 622.778 235.678 167.083 188.563 373.667 43 943.387 1870.00 471.711 935.000 314.495 023.333 235.892 467.500 188.735 374.000 43 944.246 1871.67 472.140 935.833 314.781 623.889 236.107 467.917 188.907 374.333 44 945.106 1873.33 472.570 936.667 315.008 624.444 236.322 468.333 189.079 374.067 45 945.965 1875.00 473.000937.500 315.354 625.000 236.537 468.750 189.251 375.000 46 946.825 1876.67 473.430938.333 31^.641 625.556 236.752469.167 189.423 375.383 47 947.684 1878.33 473.859939.167 315.927 626.111 236. 967 1 469. 583 189.595 375.607 48 948.544 1880.00 474.289940.000 316.214 626.667 237.182:470.000 189.767 376.000 49 949.403 1881.67 474.719 940.833 316.500 627.222 237.397 470.417 189.939 376.333 50 950.262 1883.33 475.149 941.667 316.787627.778 237.612 470.833 190.111 376.607 51 951.122 1885.00 475.578:942.500 317.073628.333 237.827 471.250 190.282 377.000 53 951.981 1886.67 476.008:943.333 317.360628.889 238.041 471.667 190.454 377.333 53 952.841 1888.33 476. 438 1 944. 167 317.646629.444 238.256 472.083 190.626 377.667 54 953.700 1890.00 476.868945.000 317.933630.000 238.471 472.500 190.798 378.000 55 954.531 1891.67 477.283945.833 318.210 6:30.556 238.679 472.917 190.965 378.333 56 955.362 1893.33 477.698946.607 318.487631.111 238.887 473.333 191.131 378.667 57 956.321 1895.00 478.128947.500 31 8. 773 631. 667 239.102 478.750 191.303379.000 58 957.081 1896.67 478.558948.333 319.060632.222239.317 474.167 191.475379.333 59 957.940 1898.33 478.988949.167 319.346632.778:239.531 474.583 1 91.6471379. 667 TABLE XIV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 C Curve. 1O Curve, 18 Tan. Arc. Tan. Arc. Tan. Arc, Tan. Arc. Tan. Arc. " M. 151.311 300 000 129.716257.143 113.524 225.000 100.931 200.000 90.8610 180.000 o 151.455 151.598 300.278 300.556 129.839257.381H13.631 129.962257.619 113 739 225 208 225.417 101.026 101.122 200.185 200.370 90.9471 91.0331 180.167 180.333 1 2 151.741 300.833 130.085j257.857 113.846 2-,'5.625 101.218 200.556 91.1192 180.500 3 151.885 301.111 130.208258.095 113.954 225.833 101.313 J00.741 91.2052 180.667 4 158.088 301.389 130.331 258.333 114.061 226.042 101.409 200.926 91.2913 180.833 5 152.171 301.667 130.4531258.571 114.169 226.250 101.504 201.111 91.3773 181.000 6 15*. 315 301.944 130.576 258.810 114.276 226.458 101.600 201.296 91 .4634 181.167 7 152.458 30 .5. 222 130.699 259.048 114.384 226.667 101.695 201.481 91.5494 181.333 8 152.601 302.500 130.822 259.286 114.491 226.875 101.791 201.667 91.6355 181.500 9 152.745 302.778 130.945 259.524 114.599 227.083 101.887 201.852 91.7216 181 667 1O 158.888 303.056 131.064 259.762 114.703 227.292 101.979 202.037 91 8047 181.833 11 153.022 303.333 131.182 260.000 114.807 227.500 102.071 202.222 91.8879 182.000 13 153.165 303.611 131.305 260.238 114.914 227.708 102.167 202.407 91.9740 182.167 13 153.308 303.889 131.428 260.476 115.022 227.917 102.263 202.593 92.0600 182.333 14 153.451 304.167 131.551 260.714 115.129 228.125 102.358 202.778 92.1461 182.500 15 153.595 304.444 131.674 260.952 115.237 228.333 102.454 202.963 92.2321 182 667 16 153.738 304.722 131.797 261.190 115.344 228.542 102.549 203.148 92.3182 182.833 17 153.881 305.000 131.920 261.429 115.452 228.750 102.645 203.333 92.4042 183.000 18 154.025 305.27'8 132.042 261.667 115.559 228.958 102.741 203.519 92.4903 183.167 19 154.168 305.556 132.165 261.905 115 667 229.167 102.836 203.704 92.5764 183.333 20 154.311 305.833 132 288 262.143 115.774 229.375 102.932 203.889 92.6624 183.500 21 154.455 306.111 132.411 262.381 115.882 229.583 103.027 204.074 92.7485 183.667 22 154.593 306.389 132.530 262.619 115.986 229.792 103.120 204.259 92.8316 183.833 23 154.732 306.667 132.648 268.857 116.090 230.000 103.212 204.444 92.9148 184.000 34 154.875 306.944 132.771 263.095 116.197 230.208 103.308 204.630 93.0009 184.167 25 155.018 307.222 132.894 263 333 116 305 230.417 103.403 204.815 93.0869 184.333 26 155.162 307.500 133.017 263.571 116.412 230.625 103.499 205.000 93.1730 184.500 21 155.30n 307.778 133.140 263.810 116.520 230.833 103.595 205.185 93.2590 184.667 28 155.448 308.056 133.263 264.048 116.627 231.042 103.690 205.370 93.3451 184.833 29 155.592 308.333 1 as. 386 264.286 116.735 231.250 103.786 205.556 93.4311 185.000 3O 155.735 308.611 133.508 264.524 116.842 231 458 103.881 205.741 93.5172 185.167 31 155.878 308.889 133.631 264.762 116.950 231.667 103.977 205.926 93.6033 185.333 32 156.021 309.167 133.754 265.000 117.057 231.875 104.073 06.111 93.6893 185.500 33 156.165 309.444 133.877 265.238 117.165 232.083 104.168 206.296 93.7754 185.667 34 156.308 309.722 134.000 265.476 117.272 232.292 104.264 206.481 93.8614 185.833 35 156.451 310.000 134.123 *'65.714 117.380 232.500 104.359 206.667 93.9475 186.000 36 156.590 310.278 134.241 265.952 117.484 232.708 104.452 206.852 94.0307 186.167 37 156.728 310.556 134.360 266.190 117.588 232.917 104.544 207.037 94.1138 186.333 38 156.872 310.833 134.483 206.429 117.695 233.125 104.640 207.222 94.1999 186.500 39 157.015 311.111 134.606 266.667 117.803 233.333 104.735 207.407 94.2859 186.667 40 157.158 311.389 134.729 266.905 117.910 233.542 104.831 207.593 94.3720 186.833 41 157.302 311.677 134.852 267.143 118.018 233.750 104.926 207.778 94.4581 187.000 43 157.445 311.944 134.974 267.381 118.125 233 958 105.022 207.963 94.5441 187.167 43 157.588 312.222 135.097 267.619 118.233 234.167 105.118 208.148 94.6302 187.333 44 157.732 312.500 135.220 267.857 118.340 234.375 105.213 208.333 94.7162 187.500 45 157.875 312.778 135.343 268.095 118.448 234.583 105.309 208.519 94.8023 187.667 46 158.018 313.056 135.466 268.333 118.555 234 792 105.404 208.704 94.8883 187.833 47 158.1(51 313.333 135.589 268.571 118.663 235.000 105.500 208.889 94.9744 188.000 48 158.305 313.611 135.712 268.810 118.770 235.208 105.596 209.074 95.0604 188.167 49 158.448 313.889 135.834 269.048 118.878 235.417 105.691 209.259 95.1465 188.333 5O 158.591 314.167 135.957 269.286'll8.985 235.625 105 787 209.444 95.2325 188.500 51 158.735 314.444 136 080 1 269. 524 119.093 235.833 105.882 209.630 95.3186 188.667 53 158.878 314.722 136.203269.762 119.200 236.042 105.978 209.815 95.4046 188.833 53 159.021 315.000 136.326 270.000119.308 236.250 106.074 210.000 95.4907 189 000 54 159.160 315.278 136.445 270.238119.412 236.458 106.166 210.185 95.5739 189.167 55 159.298 315.556 136.563 270.476119.516 236.667 106.258 210.370 95.6571 189.333 5<> 159.442 315.833 136.686 270.714 119.623 236.875 106.354 210.556 95.7431 189.500 57 159.585 316.111 136.809 270.952 119.731 237.083 106.450 210.741 95.8292 189.667 58 159.728316.389 136.932 271.190119.838 237.292 106. 5451210. 926 95.9152 189.833 59 83 TABLE XTV. ACTUAL TANGENTS, ETC. 10= 1 Curve. 2 Curve. 3 Curve. 4 Curve. 5 Curve. M. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. O 958.800 1900.00 479.417 950.000 319.633 (533.333 239.746,475.000 191.818 380.000 1 959.659 1901.67 479.847 950.833 319.9196:33.889 239.961 475.417 191.990 380.333 2 960. 19 1903.33 480.277 951.667 320.206 634.444 240.176 475.833 192.162 380.607 3 961.378 1905.00 480.707 952.500 320.49-2.635.000 240.391 476.250 192.334 381.000 4 962.237 1906.67 481.136 953.3-33 320.779 035. 556 240.606 476.667 192.506 381.333 r> 968.097 1908. as 481.566 954.167 321.065636.111 240.821 477.083 192.678 381.667 G 903.956 1910.00 481.996 955.000 321.352 636.667 241.036 477.500 192.850 382.000 7 964.816 1911.67 482.426 955.833 321.638 637.222 241.251 477.917 193.022 382.333 8 905.675 1913.33 482.855 956.667 321.925 637.778 241.466 478.333 193.194 382.667 9 966.535 1915.00 483.285 957.500 322.211 638.333 241.680 478.750 193.366 383.000 1O 967.394 1916.67 483.715 958.333 322.498 638.889 241.895 479.167 193.538 383.333 11 968.254 1918.33 484.145 959.167 322.784 639.444 242.110 479.583 193.710 383.667 12 969.113 1920.00 484.574 960.000 323.071 640.000 242.325 480.000 193.882 384.000 13 969.972 1921.67 485.004 960.833 323.357 640.556 242.540480.417 194.054 384.333 14 970.832 1923.33 485.434 961.667 323.644 641.111 242.755 ; 480.833 194.228 384.667 15 971.691 1925.00 485.863 962.500 323.930 641.667 242. 970 '481. 250 194.398 385.000 16 972.551 1926.67 486.293 963.333 324.217 642.222 243.1851481.667 194.570 385.333 17 973.410 1928.33 486.723 964.167 324.503 642.778 243.400 482.083 194.742 385.667 18 974.270 1930.00 487.153 965. Ottii 324.790 643.333 243.615 482.500 194.913 386.000 19 975,100 1931.67 487.568 965.833 325.067 643.889 243.822 482.917 195.080 386.333 20 975.931 1933.33 487.984 966.667 325.344 644.444 244.030 483.333 195.246 386.667 21 976.791 1935.00 488.413 967.500 325.630 645.000 244.245 483.750 195.418 387.000 22 977.650 1936.67 488.843 968.333 325.917 645.556 244.460 484.167 195.590 387.333 23 978.510 19:38.33 489.273 969.167 326.203 646.111 244.675 484.583 195.762 387.667 24 979.369 1940.00 489.702 970.000 326.490 646.667 244.890 485.000 195.934 388.000 25 980.229 1941.67 490.132 970.833 326.776 647.222 245.105 485.417 196.106 388.333 26 981.088 1943.33 490.562 971.667 327.063 647.778 245.320 485.833 196.278 388.667 27 981.947 1945.00 490.992 972.500 327.350 648. 3m 245.534 486.250 196.449 389.000 28 982.807 1946.67 491.421 973.333 327.636 648.889 245.749 486.007 196.621 389.333 29 983.666 1948.33 491.851 974.167 327.923 649.444 245.964 487.083 196.793 389.667 30 984.526 1950.00 492.281 975.000 328.209 650.000 246.119 487.500 196.965 390.000 31 985.385 1951.67 492.711 975.833 328.496 050.556 246.394 487.917 197.137 390.333 32 986.245 1953.33 493.140 976.667 328.782 651.111 246.609 488.333 197.309 390.667 33 987.104 1955.00 493.570 977.500 329.069 651.667 246.824 488.750 197.481 391.000 34 987.964 1956.67 494.000 978.333 329.355 652.222 247.039 489.167 197.653 391.333 35 988.823 1958.33 494.430 979.167 329.642 652.778 247.254 489.583 197.825 391.667 36 989.682 1960.00 494.859 980.000 329.928 653.3:33 247.469 490.000 197.997 392.000 37 990.542 1961.67 495.289 980.833 330.215 653.889 247.683 490.417 198.169 392.3133 38 991.401 1963.33 495.719 981.607 330.501 654.444 247.898 490.833 198.341 392.667 39 992.261 1965.00 496.149 982.500 330.788 655.000 248.113 491.250 198.513 393.000 40 993.120 1966.67 496.578 983.333 331.074 655.556 248.328 491.667 198.685 393.333 41 993.980 1968.33 497.008 984.167 331.361 656.111 248.543 492.083 198.857393.667 42 994.839 1970.00 497.438 985.000 331.647 656.667 248.758 492.500 199.029 394.000 43 995.699 1971.6? 497.868 985.833 331.934 657.222 248.973 492.917 199.201 394.333 44 996.558 1973.33 498.297 986.667 332.220 657.778 249.. 188 493.333 199.372394.667 45 997.417 1975.00 498.727 987.500 332.507 658.333 249.403 493.750 199.544395.000 46 998.277 1976.67 499.157 988.333 32.793 658.889 249.618 494.167 199.716395.333 47 999.136 1978.33 499.586 989.167 333.080 659.444 249.832 494.583 199.888395.067 48 999.996 1980.00 500.016 990.000 333.366 660.000 250.047 495.000 200.060:396.000 49 1000.86 1981.67 500.446 990.833 333.653 600.556 250.262 495.417 200.232 396.333 50 1001.71 1983.33 500.876 991.667 333.939 661.111 250.477 495.8:33 200.404 396.667 51 1002.57 1985.00 501.305 992.500 334.226 661.667 250.692 496.250 200. 576 ! 397. 000 52 1003.43 1986.67 501.735 993.333 334.512 662.222 250.907 496.667 200.748397.333 53 1004.29 1988.33 502.165 994.167 334.799 66 2. 778 1251. 122 497.083 200.920397.667 54 1005.15 1990.00 502.595 995.000 335.085 663 . 333 251 . 337 497 . 500 201.092398.000 55 1006.01 1991.67 503.024 995.833 335.372 003. 889 251. 552 '497. 91 7 2dl.264398.333 56 1006.87 1993.33 503.454 996.667 335.658 664.444251.767498.333 201.436398.667 57 1007.73 1995.00 503.884 997.500 335.945 665.000,251.982498.750 201.608399.000 58 1008.59 1996.67 504.314 998.333 336.231 665 . 556 252 . 1 96 '499 . 1 67 201.780 399.333 59 1009.45 1998.33 504.743 999.167 336.518 666.111:252.411499.583 201.952 399.667 84 TABLE XIV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 Curve. 1O Curve. 19 Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. M. 159. 8721310. OUT 137.055 271 .429 119.946 237.500 106. 641)211. Ill 96.0013 190.000 ~~O~ 160.015 316.944 137.178271.667 120.053 237.708 106.736211.296 96.0873 190.16? 1 160.158 317.222 137.300271.905 120.161 237.917 106.8*2 211.481 96.1734 190.333 o 160. 301 1317.500 137.423272.143 120.268 238.125 106.927 211.667 96.2594 190.500 3 160.445317.778 137.546272.381 120.376 238.333 107.023 211.852 96.3455 190.667 4 160.588318.056 137. 669; 272. 619 120.484 538.542 107.119 212.037 96.4315 190.833 5 160.731 318.333 187. 7921272. 857 120.591 238.750 107.214 212.222 96.5176 191.000 6 160.875 318.611 137.915;273.095 120.699 238.958 107.310 212.407 96.6037 191.167 7 161.018 318.889 138.038273.333 120.806 239.16? 107.405 212.593 96.6897 191.333 8 161.161 319.167 138.160 273.571 120.914 239.375 107.501 212.778 96.7758 191.500 9 161.305 319.444 138.283 273.810 121.021 239.583 107.597 212.963 96.8618 191.66? 10 161.448 319.722 138.406 274.048 121.129 239.792 107.692 213.148 96.9479 191.833 11 161.591 320.000 138.529 274.286 121.236 240.000 107.788 213.333 97.0339 192.000 12 161.735 320.278 138.652 274.524 121.344 240.208 107.883 213.519 97.1200 192.167 13 161.878 320.556 1:38.775 274.762 121.451 240.41? 107.979 213.704 97.2060 192.333 14 162.021 320.833 138.898 275.000 121.559 240.625 108.075 213.889 97.2921 192.500 15 162.164 321.111 139.020 275.238 121.666 240.833 108.170 214 074 97.3781 192.667 16 162.308 321.389 139.143 275.476 121.774 241.042 108.266 214.259 97.4642 192.833 17 162.451 321.667 139.266 275.714 121.881 241.250 108.361 214.444 97.5502 193.000 18 162.590 321.944 139.385 275.952 121.985 241.458 108.454 214.630 97.6334 193.167 19 162.728 322.222 139.504 276.190 122.089 241.667 108.546 214.815 97.7166 193.333 20 162.871 322.500 139.626 276.429 122.197 241.875 108.642 215.000 97.802? 193.500 21 163.015 322.778 139.749 276.667 122.304 242.083 108.737 215.185 97.8887 193.66? 22 163.158 323.056 139.872 276.905 122.412 242.292 108.833 215.370 97.9748 193.833 23 163.301 323.333 139.995 277.143 122.519 242.500 108.929 215.556 98.0608 194.000 24 163.445 323.611 140.118 277.381 122.627 242.708 109.024 215.741 98.1469 194.167 25 163.588 323.889 140.241 277.619 122.734 242.91? 109.120 215.926 98.2329 194.333 20 163.731 324.167 140.364 277.857 122.842 243.125 109.215 216.111 98.3190 194.500 27 163.875 324.444 140.486 278.095 122.949 243.333 109.311 216.296 98.4050 194.667 28 164.018 324.722 140.609 278.333 123.057 243.542 109.406 216.481 98.4911 194.833 29 164.161 325.000 140.732 278.571 123.164 243.750 109.502 216.667 98.5771 195.000 30 164.304 325.278 140.855 27'8.810 123.272 243.958 109.598 216.852 98.6632 195.16? 31 164.448 325.556 140.978 279.048 123.379 244.16? 109.693 217.037 98.7493 195.333 32 164.591 325.833 141.101 279.286 123.487 244.375 109.789 217.222 98.8353 195.500 33 164.734 326.111 141.224 279.524 123.594 244.583 109.884 217.407 98.9214 195.667 34 164.878 326.389 141.346 279.762 123. 702 244.792 109.980 217.593 99.0074 195.833 35 165.021 326.667 141.469 280.000 123.809 245.000 110.076 217.778 99.0935 196.000 30 165.164 326.944 141.592 280.238 123.917 245.208 110.171 217.963 09.1795 196.167 37 165.308 327.222 141.715 280.476 124.024 245". 417 110.267 218.148 99.2656 196.333 38 165.451 327.500 141.838 280.714 124.132 245. G25 110.362 218.333 99.3516 196.500 39 165.594 327.778 141.961 280.952 124.239 245.833 110.458 218.519 99.4377 196.667 4O 165.738 328.056 142.084 281.190 124.347 246.042 110.554 218.704 99.5287 196.833 41 165.881 328.3:33 142.206 281 .429 124.454 246.250 110.649 218.889 99.6098 197.000 42 166.024 328.611 142.329 281.667 124.562 246.458 110.745 219.074 99.6958 197.167 43 166.167 328.889 142.452 281.905 124.669 246.667 110.840 219.259 99.7819 197.333 44 166.311 329.167 142.575 282.143 124.777 246.875 110.936 219.444 99.8680 197.500 45 166.454 329.444 142.698 282.381 124.885 247.083 111.032 219.630 99.9540 197.667 46 166.597 329.722 142.821 282.619 124.992 247.292 111.12? 219.815 100.040 197.833 47 166.741 330.000 142.944 282 857 125.100 247.500 111.223 220.000 100.126 198.000 48 166.884 330.278 143.066 283.095 125.207 247.708 111.318 220.185 100.212 198.167 49 167.027 330.556 143.189 2a3.333 125.315 247.917 111.414 220.370 100.298 198.333 50 167.171 330.833 143.312 283.571 125.422 248.125 111.509 220.556 100.384 198.500 51 167.314 331.111 143.435 283.810 125.530 248.333 111.605 220.741 100.470 198.667 52 167.457 331.389 143.558 284.048 125.637 248.542 111.701 220.926 100.556 198.833 53 167.601 331.667 143.681 284.286 125.745 248.750 111.796 221.111 100.642 199.000 54 107.744 331.944 143.803 284.524 125.852 248.958 111.892 221.296 100.728 199.167 55 167. 887 1332,222 143.9261284.762 125.960 249.167 111.987 221.481 100.814 199.333 56 168.030332.500 144.049:285.000 126.067 249.375 112.083 221.667 100.901 199.500 57 168.174 332.778 144.172 285.238 126.175 249.583 112.179 221.852 100.987 199.667 58 168.317 333.056 144.295 285.476 126.282249.792 112.274 222.03? 101.073199.833 59 85 TABLE XTV. ACTUAL TANGENTS, ETC. 20 1 Curve. 2 Curve. 3 Curve. 4 Curve. 5 Curve. M. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. O 1010.31 2000.01 505. 173! 1000. (X 336.804 666.667 252.626500.000 202.124 400.000 1 1011.10 2001.67 505. 603 i 1000. 83 337.091 667.222 252 841:500.417 202.295 400.333 2 1012.03 2003.33 506.033 1001.67 337.377 667.778 253.056 500.833 202.467 400.667 3 1012.89 2005.00 506.462 1002. 5( 337.664 668.333 253.271 501.250 202.639 401.000 4 1013.75 2006.67 506.892 1003.33 337.950 668.889 253.486 501 . 667 202.811 401 . 333 5 1014.61 2008.33 507 322 1004.17 338.237 669.444 253.701 502.083 202.983 401.667 1015.47 2010.00 507.752 1005. OU 338.523 670.000 253.9l6i502.500 203.155402.000 7 1016.33 2011.67 508.181 1005.83 338.810 670.556 254.131 502.917 203.327 402.333 8 1017.18 2013.33 508.611 1006.67 339.097 671.111 254.345503.333 203.499 402.667 9 1018.04 2015.00 509.041 1007.5C 339.383 671.667 254.560 503.750 203.671 403.000 1O 1018.90 2016.67 509.471 1008.33 339.670 672 222 254.775 504.167 203.843 403.333 11 1019.76 2018.33 509.900 1009.17 389'. 956 672.778 254.990504.583 204.015 403.667 13 1030.65 2020.00 510.3301010.00 340.243 673.333 255.205 505.000 204.187 404.000 13 1021.48 2021.67 510.760 1010.83 340.529 673.889 255. 420 i 505. 41 7 204.359 404.333 14 1022.34 2023.33 511.1891011.67 340.816 674.444 255.635 505.833 204.531 404.667 15 1023.20 2025.00 511.61911012.50 341.102 675.000 255.850 506.250 204.703 405.000 16 1024.06 2026.67 512.049 1013.33 341.389 675.556 256.065 506.667 204.875 405.333 17 1024.92 2028.33 512.479 1014.17 o41.675 676.111 256.280 507.083 205.047 405.667 18 1025.78 2030.00 512.908:1015.00 341.962 676.667 256.494 507.500 205.219 406.000 19 1026.6-1 2031.67 513.338 1015.83 342.248 677.222 256.709 507.917 205.390 406.333 20 1027.50 2033.33 513.768 1016.67 342.535 677.778 256.924 508.333 205.562 406.667 31 1028.36 2035.00 514.198 1017.50 342.821 678.333 257.139 508.750 205.734 407.000 22 10-29.22 2036.67 514.627 1018.33 343.108 678.889 257.354 509.167 205.906 407.333 23 1030.08 2038.33 515.057 1019.17 343.394 679.444 257.569 509.583 206.078 407.667 24 1030.94 2040.00 515.48711020.00 313.681 680.000 257.784 510.000 206.250 408.000 25 1031.80 2041.67 515.91711020.83 343.967 680.556 257.999 510.417 206.422 408.333 26 1032.65 2043.33 516 346 1021.67 344.254 681.111 258.214 510.833 206.594 408 667 37 1033.51 2045.00 516.7761022.50 344.510 681.667 258.429 511.250 206.766 409.000 38 1034.37 2046.67 517.206 1023.33 344 827 682.222 258.644 511.667 206.938 409.333 39 1035.23 2048.33 517.63(5 1024.17 345.113 682.778 258.858 512.083 207.110 409.667 3O 1036.09 2050.00 518.065 1025.00 345.400 683.333 259.073 512.500 207.282 410.000 31 1036.95 2051.67 518.495 1025.83 345 686 683.889 259.288 512.917 207.454 410.333 33 1037.81 2053.33 518.925 1026.67 345.973 684.444 259.503 513.333 207.626 410.667 33 1038.67 2055.00 519.355 1027.50 346.259 685.000 259.718 513.750 207.798 411.000 34 1039.53 2056.67 519.784 1028.33 346.546 685.556 259.933 514.167 207.970 411.333 35 1040.39 2058.33 >20.214 1029.17 346.832 686.111 260.148 514.583 208.142 411.667 36 1041.25 2060.00 520.644 1030.00 347.119 686.667 260.363 515.000 208.313 412.000 37 1042.11 2061.67 521.073 1030.83 347.405 687.222 260.578 515.417 208.485 412.333 38 1042.97 2063.33 521 . 503 1031.67 347.692 687.778 260.793 515.833 208.657 412.667 39 1043.83 2065.00 521.933 1032.50 347.978 688.333 261.007 516.250 208.829 413.000 40 1044.69 2066.67 522.363 1033.33 348.265 688.889 261.222 516.667 209.001 413.333 41 1045.55 2068.33 522.792 1034.17 348.551 689.444 261.437517.083 209.173 413.667 43 046.41 2070.00 523.222 1035.00 548.388 690.000 261. 652 1517.500 209.345 414.000 43 047.27 2071.67 523.652 1035.83 349.124 690.556 261.867517.917 209.517 414.333 44 048.12 2073.33 524.082 1036.67 349.411 691.111 262.082518.333 209.689 414.667 45 1048.98 2075.00 524.511 1037.50 349.697 691.867 262.297518.750 209.861 415.000 46 049.84 2076.67 524.941 1038.33 349.984 692.222 262.512519.167 210.033 415.333 47 050.70 2078.33 525.371 1039.17 350.270 692.778 262.727519.583 210.205 415.667 48 051.56 2080.00 525.801 1040.00 350.557 693.333 262.942520.000 210.377 416.000 49 052.45 2081.67 526.245 1040.83 350.853 693.889 263.164520.417 210.554 416.333 | 5O 053.34 2083.33 526.689 1041.67 351.149694.444 263.386 520.833 210.732 416.667 51 054.20 2085.00 327.118 1042.50 351.436695.000 263.601 521.250 210.904 417.000 53 055.06 2086.67 -27.548 1043.33 351.722695.556 263.816521.667 211.076417.333 53 055.92 2088.33 527.978 1044.17 152 i )09 696 . 1 1 1 ! 264 . 030 52'.' . 083 211.248417.667 54 056.78 2090.00 528 . 408 i 1 045 . 00 352 . 295 696 . 667 264 . 245 522 . 500 211.420418.000 55 057.64 2091.67 528 . 837 1 1 045 . S3 352 . 582 697 . 222 264 . 460 522 .917 21 1. 592 1 41 8. 333 56 058.502093.33 529.267 1046.67 352.868 697.778 264.675523.333 211.764 418.667 57 059. &5 2095.00 529 . 697 1 047 . 50 353 . 1 55 698 . 333 264 . H90 523 . 750 211.936419.000 58 060.21 2096.67 530 . 1 27 1 048 . 33 353 .441 698 . 889 265 . 1 05 524 . 1 67 212.108 419.3:33 59 1061.07 2098.33 >30. 556J 1049. 17 353.728 699.444 265.320 524.583 212.280 419.667 TABLE XIV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 Curve. 10 Curve. 20 Tan. Arc. 333.333 Tan. Arc. Tan. Arc. Tan. 112.370 Arc. Tan. Arc. 200.000 M. 168.460 144.418 285.714 126.390 250.000 222.222 101.159 168.604 333.611 144.541 285.952 126.497 250.208 112.465 222.407 101.245 200.167 1 168.747 333.889 144.663 286.190 126.605 250.417 112.561 222.593 101.331 200.333 2 168. 890(334. 167 169.034 334.444 144.786 144.909 286 429 286.667 126.712 126.820 250.625 250 833 112.657 112.752 222.778 222.963 101.417 101.503 200.500 200.667 3 4 169.177 334.722 145.032 286.905 126.927 251.042 112.848 223.148 101.589 200.833 5 169.320 335.000 145.155 287.143 127.035 251.250 112.943 223.333 101.675 201.000 6 169.463 335.278 145.278 287.381 127.142 251.458 113.039 223.519 101.761 201.167 7 169.607 335.556 145.401 287.619 127.250 251.667 113.134 223.704 101.847 201.333 8 169.750 335.833 145.523 287.857 127.357 251.875 113.230 223.889 101.933 201.500 9 169.893 336.111 145.646 288.095 127.465 252.083 113.326 224.074 102.019 201.667 10 170.037 336.389 145. 7691288. 333 127.572 252.292 113.421 224.259 102.105 201.833 11 170.180 336.667 145.892 288.571 127.680 252.500 113.517 224.444 102. 191 1202. 000 12 170.323 336.944 146.015 288.810 127.787 252.708 113.612 224.630 102.277202.167 13 170.467 337.222 146.138 289.048 127.895 252.917 113.708224.815 102.363202.333 14 170.610 337.500 146.261 289.286 128.003 253.125 113.804 225.000 102.450202.500 15 170.753 337.778 146.383 289.524 128.110 253.333 113.899 225.185 102.5361202 667 16 170.897 338.056 146.506 289.762 128.218 253.542 113.995 225.370 102.622202.833 17 171.040 338.333 146.629 290.000 128.325 253.750 114.090 225.556 102.708203.000 18 171.183 338.611 146.752 290.238 128.433 253.958 114.186 225.741 102.794 203.167 19 171.326 338.889 146.875 290.476 128.540 254.167 114.282 225.926 102.880 203. 3S3 20 171.470 339.167 146.998 290.714 128.648 254.375 114.377 226.111 102.966203.500 21 171.613 339.444 147.121 290.952 128.755 254.583 114.473 226.296 103.052203.667 22 171.756 339.722 147.243 291.190 128.863 254.792 114.568 226.481 103.138 203.833 23 171.900 340.000 147.366 291.429 128.970 255.000 114.664 226.667 103.224 204.000 24 172.043 340.278 147.489 291.661 129.078 255.208 114.760 226.852 103.310 204.107 25 172.186 340. 55G 147.612 291.905 129.185 255.417 114.855 227.037 103.396 204.333 26 172.330 340.833 147.786 292.143 129.293 255.625 114.951 227.222 103.482 204.500 27 172.473 341.111 147.858 292.381 129.400 255.833 115.046 227.407 103.568 204.667 28 172.616 341.389 147.980 292.619 129.508 256.042 115.142 227.593 103.654 204.833 29 172.760 341.667 148.103 292.857 129/615 256.250 115.237 227.778 103.740 205.000 30 172.903 341.944 148.226 293.095 129.723 256.458 115.333 227.963 103.826 205.167 31 173.046 342.222 148.349 293.333 129.830 256.667 115.429 228.148 103.912 205.333 32 173.189 342.500 148 472 293.571 129.938 256.875 115.524 228.333 103.998 205.500 33 173.333 342.778 148.595 293.810 130.045 257.083 115.620228.519 104.085 205.667 34 173.476 343.056 148.718 294.048 130.153 257.292 115.715228.704 104.171 205.833 35 173.619 343.333 148.840 294.286 130.260 257.500 115.811'i228.889 104.257 206.000 36 173.763 343.611 148.963 294.524 130.368 257.708 115.907229.074 104.343i206.167 37 173.906 343.889 149.086 294.762 130.475 257.917 116.002229.259 104.429206.333 38 174.049 344.167 149.209 295.000 130.583 258.125 116.098 229.444 104.515 206.500 39 174.193 344.444 149.332 295.238 130.690 258.333 116 193 229.630 104.601 206.667 40 174.336 344.722 149.455 295.476 130.798 258.542 116.289229.815 104.6871206 833 41 174.479 345.000 149.578 295.714 130.905 258.750 116.385230.000 104 773J207.000 42 174.622 345.278 149.700 295.952 131.013 258 958 116.480230.185 104.859 207.167 43 174.766 345.556 149.823 296.190 131.121 259.167 116.576230.370 104.945 207.333 44 174.909 345.833 149.946 296.429 131.228 259.375 116.671 230 556 105.031 207.500 45 175.052 346.111 150.069 296.667 131.336 259.583 116.767230.741 105.117207.667 46 175.196 346.389 150.192 296.905 131.443 259.792 116.863230.926 105.203207.833 47 175.339 346.667 150.315 297.143 131.551 260.000 116.958231.111 105.289208.000 48 175.487 346.944 150.442 297.381 131.662 260.208 117.057 231.296 105.378 208.167 49 175.635 347.222 150.569 297.619 131.773 260.417 117.156 231.481 105.467 208.333 50 175.778 347.500 150.691 297.857 131.880 260.625 117.251 231.667 105.553208.500 51 175.922 347.778 150.814298.095 131.988 260.833 117.347231.852 105.639208 667 52 176.065 348.056 150.937298.333 132.095 261.042 117.442232.037 105. 725; 208. 833 53 176.208 348.333 151.060298.571 132.203 261.250 117.538232.222 105.811i209.000 54 176.352348.611 151.183298.810 132.310 261.458 117.634232.407 105.897209.167 55 176.495348.889 151.306299.048 132 418 261.667 117.729232.593 105.983209.333 56 176.638J349.167 151.429299.286 132.525 261.875 117.825232.778 106.069209.500 57 176.782349.444 151.551 299.524 132.633 262.083 117.920232.963 106.156209.667 58 176.925349.722 151.674299.762 132.740 262.292 118.016233.148 106.242209.833 59 87 TABLE XIV. ACTUAL TANGENTS, ETC/ 81 1 Curve. 2 Curve. 3 Curve. 4 Curve. 5 Curve. M. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. ~o" 1061.93 2100.00 530.986 1050.00 354.014 ? 00. 000 265.535 525.000 212.452 420.000 1 IOCS. 79 2101.67 531.416 1050.83 354.301 700.556 265.750 525.417 212.623 420.333 2 1063.65 2103.33 531.846 1051.67 354.587 701.111 265.965 525.833 212.795 420. 6G7 3 1064.51 2105.00 532.275 1052.50 354.874 701.66? 266.179 526.250 212.967 421. COO 4 1065.37 2106.67 532.705 3053.33 355.1 GO 702.222 266.39-1 526.66? 213.139 421.333 5 106.23 2108.33 533.135 1054.17 355.447 702.778 266.609 527.083 213.311 421.067 6 1067.09 2110.00 533.565 1055.00 355.733 703.333 266.824 527.500 213.483 422.000 7 1067.95 2111.6? 533.994 1055.83 356.020 703.889 267.039 527.917 213.655 422.333 8 1068.81 2113.33 534.424 1056.67 356. SOU 704.444 267.254 528.333 213.827 422.667 9 1069.67 2115.00 534.854 1057.50 356.593 705.000 267.469 528.750 213.999 423.000 10 1070.53 2116.67 535.284 1058.33 356.879 705.556 267.684 529.167 214.171 423. a33 11 1071.39 2118.33 535.713 1059.17 357.1(56 706.111 267.899 529.583 214.343 423.667 12 1072.25 2120.00 536.143 1060.00 357.452 706.667 268.114 530.000 214.515 424.000 13 1073.13 2121.67 536.587 1060.83 357.748 707.222 268.336 530.417 214.693 424.333 14 1074.02 2123.33 537.031 1061.67 358.044 707.778 268.558 530.833 214.870 424.667 15 1074.88 2125.00 537.461 1062.50 358.331 708.333 268.773 531.250 215.042 425.000 10 1075.74 2126.67 537.891 1063.33 358.618 708.889 268.988 531.667 215.214 425.333 17 1076.60 2128.33 538.320 1064.17 358.904 709.444 269.202 532.083 215.386 425.667 18 1077.46 2130.00 538.750 1065.00 359.191 710.000 269.417 532.500 215.558 426.000 19 1078.32 2131.67 539.180 1065.83 359.477 710.556 269.632 532.917 215.730 426.333 20 1079.18 2133.33 539.610 1066.67 359.764 711.111 269.847 533.333 215.902 426.667 21 1080.04 2135.00 540.039 1067.50 360.050 711.667 270.062 533.? 50 216.074 427.000 22 1080.90 2136.67 540.469 1068.33 360.337 712.222 270.277 534.167 216.246 427.333 23 1081.76 2138.33 540.899 1069.17 360.623 712.778 270.492 534.583 216.418 427.667 24 1082.6-3 2140.00 541.329 1070.00 360.910 713.333 270.707 535.000 216.590 428.000 25 1083.48 2141.67 541.758 1070.83 361.196 713.889 270.922 535.417 216.762 428.333 26 1084.34 2143.33 542.188 1071.67 361.483 714.444 271.137 535.833 216.933 428.667 27 1085.20 2145.00 542.618 1072.50 361.769 715.000 271.351 536.250 217.105 429.000 28 1086.06 2146.67 543 047 1073.33 362.056 715.556 271.566 536.667 217.277 429.333 29 1086.94 2148.33 543.492 1074.17 362.352 716.111 271.788 537.083 217.455 429.667 30 1087.83 2150.00 543.930 1075.00 362.648 716.667 2?'2.011 537.500 217.633 430.000 31 1088.69 2151.67 544.365 1075.83 362.934 717.222 272.225 537.917 217.805 430.333 32 1089.55 2153.33 544.795 1076.67 363.221 717.778 2? 2. 440 538.333 217.977 430.667 33 1090.41 2155.00 545.225 1077.50 363.507 718.333 272.655 538.750 218.149 431.000 34 1091.27 2156.67 545.655 1078.33 363.794 718.889 272.870 539.167 218.320 431.333 35 1092.13 2158.33 546.084 1079.17 364.080 719.444 273.085 539.583 218.492 431.667 30 1092.99 2160.00 546.514 1080.00 364.367 720.000 273.300 540.000 218.664 432.000 37 1093.85 2161.67 546.944 1080.83 364.653 720.556 273.515 540.417 218.836 432.333 38 1094.71 2163.33 547.374 1081.67 364.910 721.111 273.730 510.833 219.008 432.667 39 1095.57 2165.00 547.803 1082.50 365.226 721.667 273.945 541.250 219.180 433.000 40 1096.43 2166.67 548.233 1083.33 365.513 722.222 274.160 541.667 219.352 433.333 41 1097.29 2168.33 548.663 1084.17 365.799 722.778 274.374 542.083 219.524 433.667 42 1098.14 2170.00 549.092 1085.00 366.086 723.333 274.589 542.500 219.696 434.000 43 1099.03 2171.67 549.537 1085.83 366.382 723.889 274.811 542.917 219.874 434.333 44 1099.92 2173.33 549.981 1086.67 366.678 724.444 275.033 543.333 220.051 434.607 45 1100.78 2175.00 550.410 1087.50 366.965 725.000 2?5.248 543.750 220.2-23 435.000 46 1101.64 2176.6? 550.840 1088.33 367.251 725.556 275.463 544.167 220.395 435.333 47 1102.50 2178.33 551.270 1089.17 367.538 726.111 275.678 5I4.5S3 220.567 435.667 48 1103.36 2180.00 551.7001090.00 367.824 726.667 275.803545.000 220.739 436.000 49 1104.22 2181.67 552.129 1090.83 368.111 727.222 276.108 545.417 220.911 436.333 50 1105.08 2183.33 552.559 1091.67 368.397 727.778 276.323 545.833 221.083 436.667 51 1105.94 8185.00 552. 9S9 1092. 50' 308.68 1 728.333 276 53S 546.250 221.255 437.000 52 1106.80 2186.67 553.419 1093.33 3H8.9TO 728. 8S9 276.753 546.667 221.427 437.333 53 1107.66 2188.33 553.848 1004.17369.257 729.444 276.968 547.083 221.599 437.667 54 1108.52 2190.00 554.278 1095.00369.543 730.000 277.183 547.500 221.771 438.000 55 56 1109.402191.67 1110.292193.33 554.722 555.166 1095.83369.839 1096.67370.135 730.556 731.111 277.405 277.627 547.917 548.333 221.948 222.126 438.333 438.667 57 1111.152195.00 555.596 1097.50 370.422 731.667 277.842 548.750 222.298 439.000 58 1112.01 2196.67 556.026 1098.33370.708 732.222 278.056 549.167 222.470439.333 59 1112.87 2198.33 556.455 1099.17370.995 732.778 278.271 549.583 222.642 439.667 88 TABLE XIV. ACTUAL TANGENTS, ETC. V 6 Curve. 7 Curve. 8 Curve. 9 Curve. 10 Curve. 31 Tan. Arc. Tan. Arc. Tan. Arc. Tan. | Arc. Tan. Arc. M. 177.008 350.000151.797 300.000 132.848 *!G2.500 118.112^33.333 1UG.3~28 ZioTcoo ~O" 177.212 350.278 151.920 300.238 132.955 262.708 118.207 233.519 100.414 .'10.167 1 177.355 350.556 152.043|300.476 133.063 262.917 118.303 233.704 106.500 210.333 2 177.498 350.833 152. 106 300.714 133.171 263.125 118.398 233.889 106.586 210.500 3 177.641 351.111 152.289 300.952 133.278 263.333 118.494 234.074 106.672 ,210. CG7 4 177.785 351.389 152.411 301.190 133.386 263.542 118.590 234.259 106.758 210.833 5 177.928 351.667 152.534 301.429 133.493 263.750 118.685 234.444 106.844 211.000 6 178.071 351.944 152.657 301.667 133.601 263.958 118.781 234.630 106.930 211.167 7 178.215 352.222 152.780 301.905 133.708 264.167 118.876 234.815 107.016 211.333 8 178.358 352.500 152.903 302.143 133.816 264.375 118.972 235.000 107.102 211.500 9 178.501352.778 153.026 302.381 133.923 264.583 119.067 235.185 107.188 211 667 10 178.645 353. 05G 153.148 302.619 134.031 264 792 119.163 235.370 107.274 211.833 11 178.788858.333 153.271 302.857 134.138 265.000 119.259 235.556 107.360 212.000 13 178.936353.611 153.398 303. 09? 134.249 265.208 119.357 235.741 107.449 212.167 13 179.084:353.889 153.525,303.333 134.360 265.417 119.456 235.926 107.538 212.333 14 179.227354.167 153.648 303.571 134.468 265.625 119.552 236.111 107.624 212.500 15 179.371 354.444 153.771 303.810 134.575 265.833 119.647 236.296 107.710 212.667 16 179.514 354.722 153.894:304.048 134.683 266.042 119.743 236.481 107.796 212.833 17 179.657 355.000 154.017 304.280 134.790 266.250 119.839 236.667 107.882 213.000 18 179.801 355.278 154.140 304.524 134.898 266.458 119.934 236.852 107.968 213.167 19 179.944 355.556 154.262 304.762 135.005 266.667 120.030 237.037 108.054 213.333 20 180.087 355.833 154. 385! 305. 000 135.113 266.875 120.125 IL'37.222 108.141 213.500 31 180.231 356.111 154.508 305.238 135.220 267.083 120.221 237.407 108.227 213.667 22 180.374 356.389 154.631 305.476 135.328 267.292 120.317 237.593 108.313 213.833 23 180.517 356.067 154.754 305.714 135.436 267.500 120.412 237.778 108.399 214.000 24 180.660 356.944 154.877 ! 305.952 135.548 267.708 120.508 237.963 108.485 214.167 25 180.804 357.222 154.999 306.190 185.651 267.917 120.603 238.148 108.571 214.333 26 180.947 357.500 155.122306.429 135.758 268.125 120.699 538.333 108.657 214.500 37 181.090 357.778 155.245 306.667 135.866 268.333 120.794 238.519 108.743 214.667 38 181.238 358.056 155/372 306.905 135.977 268.542 120.893 238.704 108.832 214.833 39 181.386 358.333 155.499 307.143 136.088 268.750 120.992 238.889 108.921 215.000 30 181.530 358.611 155.622 307.381 136.195 2G8.958 121.088 239.074 109.007 215.167 31 181.673 358.889 155.745j307.619 136.303 269.167 121.183 239.259 109.093 215.333 33 181.816 359.167 155.868 307.857 136.410 269.375 121.279 239.444 109.179 215.500 33 181.960 359.444 155.990308.095 136.518 269.583 121.374 239.630 109.265 215.667 34 182.103 359.722 156.113 308.333 136.625 269.792 121.470 239.815 109.351 215.833 35 182.246 360.000 156.236 308.571 136.733 270.000 121.566 240.000 109.437 216.000 36 182.390 360.278 156.359^308.810 136.840 270.208 121.661 240.185 109.523 216.167 37 182.533 360.556 156.482:309.048 136.948 270.417 121.757 240.370 109.609 216.333 38 182.676 360.833 156.605 309.286 137.055 270.625 121.852 240.556 109.695 216.500 39 182.820 361.111 156.728 309.524 137.163 270.833 121.948 240.741 109.781 216.667 40 182 963 361.389 156.850 309.762 137.270 271.042 122.044 240.926 109.867 216.833 41 183.106 361.667 156.973310.000 137.378 271.250 122.139 241.111 109.953 217.000 43 183.254 361.944 157.100 310.238 137.489 271.458 122.238 241.296 110.042 217.107 43 183.402 362.222 157. 227 i 310. 476 137.600 271.667 122.337 241.481 110.131 217.333 44 183.546 362.500 157.350 310.714 137.708 271.875 122.432 241.667 110.217 217.500 45 183.689 362.778 I57.473l310.952 137.815 272.083 122.528 241.852 110.303 217.667 46 1 S3. 832 363.056 157.596 311.190 137.923 272.292 122.623 242.037 110.389 217.833 47 183.976 363.333 157.719 311.429 138.030 272.500 122.719 242.222 110.475 218.000 48 184.119 363.611 157.841 311.667 138.138 272.708 122.815 242.407 110.561 218.167 49 184.262 363.889 157.964311.905 138.245 272.917 122.910 242.593 110.648 218.333 50 184.405 364.167 158.087312.143 1 38. 353 i 273. 125 123.006 242.778 110.734 218.500 51 184 549364.444 158.210312.381 138. 4 60 J273.333 123.101 242.963 110.820 218.607 53 184. 692 ; 364. 722 158.333 312.619 138.568J273.542 123.197 243.148 110.906 218.833 53 184. 835 1365.000 158.456 312.857 138.675i273.750 123.293 243.333 110.992 219.000 54 184.983365.278 158.583313.095 188.786273.958 123.391 243.519 111.081 219.167 55 185.132365.556 158.710 313.333 188.898274.167 123.490 243.704 111.170 219.333 56 185 275365.833 158.832 813. f. 71 139.005274.375 123.586 243 889 111.256 219.500 57 185.418366.111 158.955 313.810139.113274.583 123.681 244.074 111.342 219.667 58 185.561 366.389 1 59 . C78 3 1 4 . 048 i 1 31) . 220 274 . 792 123.777 244.259 111.428 219.833 59 89 TABLE XIV. ACTUAL TANGENTS, ETC. 83 1 Curve. 2 Curve. 3 Curve. 4 Curve. 5 Curve. MT Tan. Arc. Tan. Arc. Tan. Arc. 733.333 Tan. Arc. Tan. Arc. O 1113.73 2200.00 556.885 1100.00 371.281 278.486 550.000 222.814 440.000 1 1114.59 2:201.67 557.315 1100.83 371.568 733.889 278 . 658 550 .417 222 . 986 440 . 333 3 1115.45 2203.33 557.745 1101.67 371.854 734.444 278.916 550.833 223.158 440.667 3 111(5.31 2205.00 558.174 1102.50 372.141 735.000 279.088551.250223.330441.000 4 1117.17 2206.67 558.604 1103.33 372.427 735.556 279. 346 55t 667 223.502441.333 5 1118.06 2208.33 559.048 1104.17 372.723 736.111 279.568552.083 223.079441.667 6 1118.94 2210.00 559.492 1105.00 373.020 736.667 279.790552.500 223.857 442.000 7 1119.80 2211.67 559.922 1105.83 373.306 737.222 280.005552.917 224.029 442.333 S 1120.66 2213.33 560.352 1106.67 373.593 737.778 280. 220 1553.333 224.201 442.667 9 1131.62 2215.00 560.781 1107.50 373.879 738.333 280.435 553.750 224.373 443.000 10 1123.38 2216.67 561.211 1108.33 374.166 738.889 280.650 554.167 224.545 443.333 11 1123.24 2218.33 561.641 1109.17 374.452 739.444 280.865 554.583 224.717 443.667 12 ii2i.io 2220.00 562.071 1110.00 374.739 740.000 281.079 555.000 224.889444.000 13 1124.96 2221.67 562.500 1110.83 375.025 740.556 281.294 555.417 225. 061 1444.333 14 1125.82 2223.33 562.930 1111.67 375.312 741.111 281.509 555.833 225.233444.667 15 1126.71 2225.00 563.374 1112.50 375.608 741.667 281.731 556.250 2-,'5.410445.000 16 1127.60 2226.67 563.818 1113.33 375.904 742.222 281.953 556.667 22.5. 588 '445. 333 17 1128.45 2228.33 564.248 1114.17 376.190 742.778 282.168557.083 225.760l445.667 18 1129.31 2230.00 564.678 1115.00 376 . 477 743., 333 282.383 557.500 225.932 446.000 19 1130.17 2231.67 565.107 1115.83 376.763 743.889 282.598 557.917 226.104 446.333 20 1131.03 2233.33 565.537 1116.67 377.050 744.444 282.813 558.333 226.276 446.667 21 1131.89 2235.00 565.967 1117.50 377.336 745.000 283.028558.750 226.448 447.000 22 1132.75 2236.67 566.397 1118.33 377.623 745.556 283. 243 '559. 167 226.620 447.333 23 1133.64 2238.33 566.841 1119.17 377.919 746.111 283.465 559. 5S3 226.797 447.667 24 1134.53 2240.00 567.285 1120.00 378.215 746.667 283.687 560.000 226.975 448.000 35 1135.39 2241.67 567.715 1120.83 578.501 747.222 283.902 560.417 227.147 448.333 20 1136.25 2243.33 568.144 1121.67 378.788 747.778 284.117 560.833 227.319 448.667 27 1137.11 2245.00 5(58.574 112 2326.67 589.832 1163.33 393.247 775.556 294.962 581.667 235.996 465.333 17 1180.48 2328.33 590.262 1164.17 393.534 7:6.111 ,395.177 582.083 236.168 465. 6G7 18 1181.31 2330.00 590.691 1165.00 393.820 776. 66 1' 295.392 582.500 226.340 466.000 19 1182.20 ,'331.67 591.121 1165.83 394.107 777.222 295.607 582.917 236.512 466.333 20 1183.06 2333.33 591 . 551 1166.67 394.393 777.778 295.822 583.333 236.684 466.667 21 1183.95 2335.00 591.995 1167.50 394.689 778.333 2UG.044 583.750 336.862 467.000 22 1184.83 2336.67 592.439 1168.33 394.985 778.889 296.266 584.167 337.039 467.333 23 118.5.69 2338.33 592.869 1169.17 395.272 779.444 296.481 584.583 237.211 467.667 34 1186.55 2340.00 593.298 1170.00 395.558 780.000 ,'96.696 585.000 237. 3S3 168.000 25 1187.41 2341.67 593.728 1170.83 395.845 780.556 296.911 585.417 '337 555 468.3.33 36 1188.27 2343.33 594.158 1171.67 396.131 781.111 297.126 585.833 337 727 468.667 37 1189.10 3345.00 594.602 1172.50 396.428 781.667 297.348 586.250 337.905 469.000 38 1190.05 234<>.G7 595 046 1173.33 396.724 782.222 297.570 586 667 338.082 469.333 39 1190.91 2348.33 595 476 1174.17 397.010 782.778 297.785 587.083 238.254 469.667 3O 1191.77 2350.00 595.905 1175.00 397.297 783.333 ?38.000 587.500 238.426 470.000 31 1192.63 2351.67 596 335 1175.83 397.583 783.889 298.214 587.917 238 598 470.333 33 1193.49 #53.33 598.765 1176.67 397.870 784.444 298.429 588.333 238.770 470.667 33 1194.37 2355.00 597.209 1177.50 398.166 785.000 298.651 588.750 238.948 471.000 34 1195.26 2356.67 597.653 1178.33 39S.462 785.556 298.873 589.167 239.125 471.333 35 1196.12 2358.33 598.083 1179.17 398.748 786.111 299.088 589.583 339.297 471.667 36 1196.98 2360.00 598.513 1180.00 399.035 786.667 299.303 590.000 239.469 472.000 37 1197.84 3351.67 598.942 1180.83 399.321 787.222 299.518 590.417 339.641 472.333 38 1198.70 2363.33 599.37-3 1181.67 399.603 787.778 299.733 590.833 339.813 472.667 39 1199.59 3365.00 599.816 1182.50 399.904 788.333 299.955 591.250 239.991 473.000 4O 1200.48 2366.67 600.260 1183.33 (00.200 788.889 300 177 591.667 240.169 473.333 41 1201.34 2368.33 6)0.690 1184.17 100.486 789. 44 < 300. 38 592.083 240.341 473.667 43 1202.20 2370.00 601.120 1185.00 +00.773 790 000 300.607 592.500 240.512 474.000 43 1203.08 2371 67 601.561 1185.83 401.069 790.556 300.829 592.917 240.690 474.333 44 1203.97 2373.33 602.008 1186.67 401.365 791.111 301.051 593 333 340.868 474.667 45 1204.83 2375.00 602.437 1187.50 101.652 791.667 301.266 593.750 241.010 475.000 46 1205.69 2376.67602.867 1188.33 401.938 792.222 301.481 594.167 241.212 475.333 47 1206.55 2378.33603.297 1189.17 402.225 792. 77S 301.696 594.583 241.384 475.667 48 1207.41 2380.00 603.727 1190.00 402.511 793.333 301.911 595.000 241.556 476.000 49 1208.30 2381.67 604.171 1190.83 402.807 793.889 302.133 595.417 241.733 476.333 5O 1209 19 2383.33 604.615 1191.67 403.103 794.444 302.355 595.833 241.911 476.667 51 1210.04 2385 00 605.045 1192.50 403.390 795.000 302.570 596.250 242.083 477.000 53 1210.90 2386.67 605.474 1193.33 403.676 795.556 302.785 596.667 242.255 477.333 53 1211.76 2388.33 605.904 1194.1: 403.963 796.111 303.000 597.083 342.427 477.667 54 1212.62 2390.00 606.3341195.00 404.249 796.667 303.215 597 500 342.599 478.000 55 1213.51 2391.67 606.778 1195.83 404.545 797.223 303.437 597.917 342.776 478.3:33 56 1214.40 2393.33 607.222 1196.67 404.841 797.778 303.659 598.333 242. 954 1 478. 667 57 1215.26 2395.00 607.6521197.50 405.128 798.333 303.874 598.750 243.126479.000 58 1216.12 2396.67 608.081 1198.33 405.414 798.889 304.088 599.167 243.298479.333 59 1217.01 2398.33608.525:1199 17 405.7111799.444 304.311 599.583 243. 476 J479.667 92 TABLE XIV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve, 9 Curve, 1O Curve. 23 M? Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. 194.370383.333 166.630 328.571 145.829 287.500 129.653 255.556 116.717230.000 O 194.518383.011 166.757 328.810 145.940 287.708 129.751 255.741 116.806230.167 1 194.660383.889 166.883 329.048 146.051 287.917 129.850 255.926 116.895230.333 2 194.809384.107 167.000 329.280 146.159 288.125 129.946 256.111 116.981 230.500 3 194. 953; 384. 444 167.129 329.524 146.206 288.3:33 130.041 256.296 117.067230.667 4 195.096,384.722 167.252 329.762 146.374 288.542 130.137 256.481 117.153230.833 5 195. 239 385. 000 167.375 330.000 140.4cSl 288.750 130.232 256.667 117.239231.000 6 195.383385.278 167.498 330.238 146.589 288.958 130.328 256.852 117.325231.167 7 195.526385.556 167.621 330.476 146.696 289.167 130.424 257.037 117.41li231.333 8 195.674 385.833 167.748 330.714 146.807 289.375 130.522 257.222 117.500 231.500 9 195.822 386.111 167.874 330.952 146.918 289.583 130.621 257.407 117.589 231 .667 10 195.965386.389 107.997 331.190 147.026 289.792 130.717 257.593 117.675 231.833 11 196.109386.667 168.120331.429 147.138 290.000 130.812 257.778 117.761 232.000 13 196.252380.944 168.243331.667 147.241 290.208 130.908 257.963 117. 847j232.167 13 196.395:387.222 108.366 331.905 147.348 290.417 131.004 258.148 117.933232.333 14 196. 543 '387. 500 168.493 332.143 147.460 290.625 131.102 258.333 118. 022 ' 232. 500 15 196.692 387.778 168.620 332.381 147.571 290.833 131.201 258.519 118. Ill 1232.667 16 196.835 388.056 168.743 332.619 147.678 291.042 131.297 258.704 118.197 232.833 17 196.978 388.333 168.866 332.857 147.780 291.250 131.392 258.889 118.283 233.000 18 197.121 388.611 168.988 333.095 147.893 291.458 131.488 259.074 118.369 233.167 19 197.265 388.889 169.111 333.333 148.001 291.667 131.583 259.259 118.455 233.333 30 197.413 389.167 169.238 333.571 148.112 291.875 131.682 259.444 118.544 233.500 31 197.561 389.444 169.365 333.810 148.223 292.083 131.781 259.630 118.633 233.667 33 197.704 389.722 169.488 334.048 148.330 292.292 131.877I259.815 118.719 233.833 33 197.848 390.000 169.611 334.286 148.438 292.500 131.97'2!260.000 118.805 234.000 24 197.991 390.278 169.734 334.524 148.545 292.708 132.068 200.185 118.891 234.167 25 198.134 390.556 169.857 334.76-> 148.653 292.917 132.163 260.370 118.978 234. a33 36 198.282 390.833 169.983 335.000 148.7'64 293.125 132.262 260.556 119.066 234.500 37 198.430 391.111 170.110 335.238 148.875 293.333 132.361 260.741 119.155 234.667 28 198.574 391.389 170.233 335.476 148.983 293.542 132.457 260.926 119.241 234.833 29 198.717 391.667 170.356 335.714 149.090 293.750 132.552 261.111 119.327 235.000 30 198.860 391.944 170.479 335.952 149.198 293.958 132.648 261.296 119.414 235.167 31 199.004 392.222 170.602 336.190 149.305 294.167 132.743 261.481 119.500 235.333 32 199.152 392.500 170.729 336.429 149.416 294.375 132.842 261.667 119.589 235.500 33 199.300 392.778 170.856 336.667 149.527 294.583 132.941 261 .852 119.677 235.667 34 199.443 393.056 170.979 336.905 149.635 294.792 133.036 262,037 119.763 235. a33 35 199.586 393.333 171.101 337.143 149.742 295.000 133.132 262.222 119.850 236.000 36 199.730 393.611 171.224 337.381 149.850 295.208 133.228 262.407 119.936 236.167 37 199.873 393.889 171.347 337.619 149.957 295.417 133.323 262.593 120.022 236.333 38 200.021 394.167 171.474 337.857 150.069 295.625 133.422 262.778 120.111 236.500 39 200.169 394.444 171.601 338.095 150.180 295.833 i as. 521 262.963 120.199 236.667 4O 200.312 394. 782 171.724 338.333 150.287 296.042 133.616 263.148 120.286 236.833 41 ; 200.456 395.000 171.847 338.571 150.395 296.250 133.712 263.333 120.372 237.000 43 200. 604 1 395. 278 171.974 S38.810 150.506 296.458 133.811 263519 120.461 237.167 43 200.752 395.556 172.101 339.048 150.617 296.667 133.909 263.704 120.549 237.333 44 200.895 895.833 172.223 339.286 150.724 296.875 134.005 263.889 120.636 237.500 45 201.038396.111 172.346 339.524 150.832 297.083 134.101 264.074 120.722 237.667 46 201.182396.389 172.469 339.762 150.939 297.292 134.196 264.259 120.808 237.833 47 201.325396.667 172.592 340.000 151.047 297.500 134.292 264.444 120.894 238.000 48 201.473 396.944 172.719 340.238 151.158 297.708 134.391 264.630 120.983 238.167 49 201.621 397.222 172.846 340.476 151.269 297.917 134.489 264.815 121.071 238.333 50 201.765 397.500 172.969 340.714 151.377 298.125 134.585 265.000 121.158 238.500 51 201.908397.778 173.092 MO. 952 151.484 298.333 134.681 265.185 121.244 238.667 53 202.051 398.056 173.2141341. 190 151.592 298.542 134.776 265.37'0 121.330 238.833 53 202.194398.333 173.337 341.429 151.699 298.750 134.872 265.556 121.416 239.000 54 202.343398.611 173.461 341.667 151.810 298.958 134.971 265.741 121.505 239.167 55 202.491 398.889 173.591 341 .905 151.921 299.167135.069 265.926 121.594 239.3:33 56 202.634399.167 173.714342.143 152.029 299.375135.165266.111 121.680 239.500 57 202.777399.444 173. 837 342. 381 152.137 299.583 135.261 266.296 121.766 239.667 58 202.925399.722 173.964 342.619 152.248 299.7921135.359266.481 121.855 239.833 59 TABLE XIV. ACTUAL TANGENTS, ETC. 24 1 Curve. 2 Curve. 3 Curve. 4 Curve. 5* Curve. M. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. 1217.89 2400.00 608. 97011200. 00'406. 007 800.000 304.533 600.000 243.053 480.000 1 1218.75 2401.67 609 . 399 1200 . 83 : 406 . 293 800.556 304.747 600.417 243.825 480.333 2 1219.61 2403 33 609 . 829 i 1201 . 67 406 . 580 HO 1 . 1 1 1 304.9(8 600.833 243 5)97 480.007 3 1220.4V 2405.00 310.259 1202.50406.866 801.66? 305 . 1 77 601.250 244.109 481.000 4 1221.33 2406.67 610.688 1203.33 407.153 802.222 305.31)2 601 . 607 244.341 481.333 5 1222.22 2408.33 611.133 1204.17 407.449 802. 7, "8 -505.614 002 . 083 244 519 481.007 6 1223.11 2410.00 611.577 1205.00 407.745 803.333 DU5.M38 002.500 244.690 482.KX) 7 12-23.97 2411.67 612.0061205.83 408.031 803.88!) 306.051 00-2.917 244.868 482.333 8 1224.83 2413 33 612.436 1206.67 408.318 804.444 306.260 t)03.333 245.040 482.007 9 1225.72 2415.00 612.880 1207 50 408.614 805.000 306.488 003.750 245.218 483.000 1O 1226.60 2416.67 613.324 1208.33 408.910 805.556 306.710 604.167 245.396 483.333 11 I227.4G 2418.33 613.754 1209.17 409.196 806.111 "306.925 604.583 245.508 483.067 12 1228.32 2420.00 614.184 1210.00 409.483 806.667 307.140 605.000 245.740 484.000 13 1229.21 2421.67 614.628 1210.83 409.779 807.222 307.363 605.417 245.917 484.333 14 1230.10 2423.33 615.072 1211.67 410.075 807.778 307.584 605.833 246.095 484.667 15 1230.96 2425.00 615.502 1212.50 410.365 808.333 '307.799 606.250 246.267 485.000 16 1231.82 2426.67 615.931 1213.33 410.618 808.889 308.014 606.667 246.439 485.333 17 1232.68 2428.33 616.361 1214.17410.935 809.444 308.229 607.083 246.611 485.667 18 1233.54 2430.00 616.791 1215.00 411.221 810.000 308.444 607.500 246.783 480.000 19 1234.42 2431.67 617.235 1215.83 411.517 810.550 308.666 607.917 246.960 486.333 2O 1235.31 2433.33 617.679 1216.67 411.813 811.111 308.888 608.333 247.138 486.667 21 1236.17 2435.00 618.109 1217.50 412.100 811.667 109.108 608.750 247.310 487.000 22 1237.03 24:}6.67 618.538 1218.33 412.386 812.222 309.318 009.167 247.482 487. 333 23 1237.92 2438.33 618.982 1219.17 412.682 812.778 '309.540 609.583 247.660 487.667 24 1238.81 2440.00 619.427 12-20.00 412.978 813.333 309.762 610.000 247.837 488.000 25 1259.67 2441.67 619.856 1220.85 413.265 813.889 309.977 610.417 248.009 488.333 26 1240.53 2443.33 620.286 1221.67 413.551 814.444 310.192 610.833 248.181 488.667 27 1241.41 2445.00 620.730 1322.50 413.847 815.000 310.414 611.250 248.359 489.000 28 1242.30 2446.67 621.174 1223.33 414.144 815.556 310.636 611.667 248.536 489.333 29 1243.16 2448.33 621.604 1224.17 414.430 816.111 310.851 612.083 248.708 489.667 30 1244.02 2450.00 622.034 1225.00 414.717 816.667 311.066 612.500 248.880 490.000 31 1244.91 2451.67 022.478 1225.83 415.013 817.222 311.288 612.917 249.058 490.333 32 1245.80 2453.33 622.922 1226.67 415.309 817.778 311.510 613.333 249.236 490.667 33 1246.66 2455.00 623.351 1227.50 415.595 818.333 311.725 613.750 249.408 491.000 34 1247.52 2456.67 623.781 12-28.33 415.882 818.889 311.940 614.167 249.580 491.333 35 1248.40 2458.33 624.225 1229.17 416.178 819.444 312.162 614.583 249.757 491.667 36 1249.29 2460.00 624.669 1230.00 416.474 820.000 312.384 615.000 249.935 492.000 37 1250.15 2461.67 625.099 1230.83 416.760 820.556 312.599 615.417 250.107 492.333 38 1251.01 2463.33 625.529 1231.67 417.047 821.111 312.814 615.833 250.279 492.667 39 1251.87 2465.00 625.959 1232.50 417.333 821.667 313.028 616.250 250.451 493.000 40 1252.73 2466.67 626.388 1233.33 417.620 822 222 313.243 616.667 250.623 493.333 41 1253.622468.33 626.832 1234.17 417.916 822 '.178 313.465 617.083 250.800 493.607 42 1-J54. 51 2470.00 627.276 1235.00 418.212 823.333 313.687 617.50T 250.978 494.000 43 1255.3712471.67 627.706| 1235. 83 418.499 823.889 313.902 617.917 251.150 494.333 44 1256. 23 '24? 3. 33 628.136 1236.67 418.785 824.444 314.117 618.333 251.322 494.007 45 1257.11 2175.00 628.580 1237.50 419.081 825.000 314.339 618.7 - 50 251.500 495.000 46 1258.002476.67 629.021 1238.33 419.377 825 . 5oC 314.561 019.167 251.677 495. S33 47 1258.86 2478. as 629.454 1239.17 419.664)826. Ill 314.776 619.583 251.849 495.607 48 1259. 72 '2480. 00 629.884 1240.00 419.950l826.667 314.991 620.000 252.021 496.000 49 1260.61:2481.67 630.328 1240.83 420. 246 j 827. 222 315.213 620.417 252.199 496.333 50 1261.502483.33 630.772 1241 67 420.542 827.778 315.435 620.833 252.376 496.667 51 1262.362185.00 631.201 1242.50 420.829 828.333 315.650 621.250 252.548 497.000 52 1263.222486.67 631.631 1243.33 421.115 828.889 315. R65 621.667 252.720 497.333 53 1264.102488.33 632.075 1244.17 421.411 829.444 316.087 622.083 252.898 497.667 54 1204. 99 2490. 00 632.519 1245.00 421.707 830.000 316.309 622.500 253.076 498.000 55 1265. 85 12491. 67 632.949 1245.83 421.994 830.556 316.524 622.917 253.248 498.333 56 1266.71 2493.33 633.379 1246.67 422.280 831.111 316.739 623.333 253.420 498.667 57 1267.602495.00 633.823 1247.50 422.577 831.667 316.961 023.750 253.597 499 000 58 1268.492496.67 634.267 1248.33 422.873 832.222 317.183 624.167 253.775 499.333 59 1269. 35 2 198. 33 634.697 1249.17 423.159 832.778 317.398 624.583 253.947 499.667 94 TABLE XIV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 Curve. 1O Curve. 24 Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. M. 203.073 00. 000 174. OK I 34'-'. 857 52.359 300.000 35.458)266.667 21.943 240.000 "~o~ 80S. 21 7 00.278 174.214343.095 52.466 300.208 35.554 266.852 22.030 240.167 i 203.360 00.556 174.337 343.333 52.574 300.417 35.649 267.037 22.116 240.333 2 203.503 00.833 174.459343.571 52.681 300.625 35.745 -267.222 22.202 240.500 3 203.647 01.111 174. 5S2 43.810 52.789 300.833 35.840 267.407 122.288 240.667 4 203.795 01.389 174.709 44.048 52.900 301.042 35.939 267.593 122.377 240.8:33 5 203.943 401.667 174.836 344.286 53.011 301.250 36.038 267.77'8 122.466 241.000 6 204.086 401.944 174.959 344.524 53.118 301.458 36.134 267.963 122.552 241.167 7 204.229 402.222 175.082 344.762 53.226 301.667 36.229 268.148 122.638 241. 333 8 204.377 02.500 175.209 345.000 53.337 301.875 36.328 ,268.333 122.727 241.500 9 204.526 402.778 175.336 345.238 53.448 302.083 36.427 268.519 122.816 241.667 10 204.669 403. 056 175.459 345.476 53.55(5 302.29s! 36.522 268.704 122.902 241.833 11 204.81:2 03.333 175.581 345.714 53.663 302.500 136.618 268.889 122.988 242.000 12 204.960 03.611 175.708 345.952 53.774 302.708 36.717 269.074 123.077 242.167 13 205.108 403.889 175.835 346.190 53.885 302.917 36.815 269.259 123.165 242.333 14 205.252 404.167 175.958 346.429 153.993 303.125 136.911 269.444 123.252 242.500 15 205.395 404.444 176.081 346.667 154.100 303.333 137.007 269.630 123.338 24-2.667 16 205. 538 404.722 176.204 346.905 154.208 303.542 137. 102 269.815 123.424 242.833 17 205.682 405.000 176.327 347.143 54.316 303.750 137.198 270.000 123.510 243.000 18 205.830 405.278 176.454 347.381 154.427 303.958 137.297 270.185 123.599 243.167 19 205.978 405.556 176.581 347.619 154.538 304.167 137.395 270.370 123.688 243.333 20 206.121 405.833 176.704 347.857 154.645 304.375 137.491 270.556 123.774 243.500 21 206.264 406.111 176.826 348.095 154.753 304.583 137.587 270.741 123.860 243.667 22 206.412 406.389 176.953 348.333 154.864 304.79:2 137.685 270.926 1*23.949 243.833 23 206.561 406.667 177.080 348.571 154.975 305.000 137.784 271.111 124.037 244.000 24 206 704 406.944 177.203 348.810 155.082 305.208 187.880 271,296 124.124 244.167 25 206 .347 407.222 177.326 349.048 155.190 305.417 137 975 271.481 124.210 244.333 26 206.995 407.500 177.453 349.280 155.301 305.625 138.074 271.667 124.298 244.500 27 207.143 407.778 177.580 349.524 155.412 305.833 138.173 271.852 124.387 244.667 28 207.287 408.056 177.703 349. 70S 155.520 306.042 138.268 272.037 124.473 244.833 29 207.430 408. 333 177.826 a50.00f 155.627 306.250 138.364 272.222 124.560 245.000 30 207.578 408.611 177.953 350.238 155.738 306.458 138.463 272.407 124.648 245.167 31 207.726 408.889 178.079 350.476 155.849 306.667 138.502 272.593 124.737 245.333 32 207.869 409.167 178.202 &50.714 155.957 306.875 138.657 272.778 124.823 245.500 33 208.013 409.444 178.325 350.952 156.064 307 083 138.753 272.963 124.909 245.667 34 208.161 409.722 178.452 351.190 156.176 307.292 138. a52 273.148 124.998 245.833 35 208.309 410.000 178 579 351 .429 156.287 307.500 138.950 273.333 125.087 246.000 36 208.452 410.278 178.702 351.667 156.394 307.708 139.046 273.519 125.173 246.167 37 208.595 410.556 178.825 351.905 156.502 307.91" 139.141 273.704 125.259 246.333 38 208.739 410.833 178.948 352.143 156.609 308.125 139.237 273.889 125.345 246.500 39 208.882 411.111 179.070 352.381 156.717 308.333 139.333 274.074 125.432 246.667 40 209.030 411.389 179.197 352.619 156.828 308.542 139.431 274.259 125.520 246.833 41 209.178 411.667 179.324 352.85" 156.939 308.750 139.530 274.444 125.609 247.000 42 209. 32!^ 411.944 179.447 353. 095 157.046 308.958 139.626 274.630 125.695 247.16" 43 209.465 412.22V 179.570 353.333 157.154 309.16" 139.721 274.81F 125.781 247.333 44 209.613 412.500 179.697 353.57 157.265 309.375 139.820 275.000 125.870 247.500 45 209.761 412.778 179.824 353.810 157.376 309.583 139.919 275.18. 125.959 247.66" 46 209.904 413.056 179.947 354.048 157.484 309.792 140.015 275. 37C 126.045 247.833 47 210.048 413.333 180.070 354. 28C 157.59 310.000 140.110 275.55 126.13 248.000 48 210.196 413.611 180.197 354.524 157.702 310.208 140.209 275.74 126.220 248.16" 49 210.344 413.889 180.324 354.762 157.813 310.41" 140.308 275.926 126.309 248.333 50 210.48" 414.167 180.446 355.000 157.921 310.62. 140.403 276.11 126.395 248.500 51 210.630 414.444 180.569 355.238 158. 02F 310. as, 140.499 276.296 126.48 248.66' 52 210.77 414.722 180 69f 355.47 158.140 311.042 140.598 276.48 126.570 248.833 53 210.92 415.000 180.82: ,355.714 158.25 311.250 140.696 276.66 126.65S 249.00(1 54 211.070 415.27* 180. 94< 355.952 158.35 311.45 140.792 276. &5 126.745 249 16" 55 211.21 415.556 ISl.Oflfl 356.19 158.466 311.66 140.888 277.03 126.83 249.333 56 211.36 415.833 181.106 356.42<1 158.5r 311 .87. 140.986 277.22* 126. 9& 249.500 57 211.50 416.111 181.323 356.66 158. 68? 312.08. 141.085 277.40 127.009 249.66" 58 811.663 416.889 181.446 356.90 158.79 312.29 141.181 277. 5& 127.095 249.833 59 95 TABLE XIV. ACTUAL TANGENTS, ETC. 25 1 Curve. 2 Curve. 3 Curve. 4 Curve. 5 Curve. BiT ~~o~ Tan. 1270.21 Arc. Tan. Arc. Tan. Arc. 83^333 Tun. 317.613 Arc. G25.000 Tan. Arc. 2500.00 635.126 1250.00 423.446 254.119 500.000 i 1271.09 2501.67 635.570 1250.83 423.742 833.889 sir. 835 (525.417 254.296 500.333 2 1271.98 2503.33 636.014 1251.67 424.038 834.444 318.057 625.833 254.474 500.667 3 1272.87 2505.00 636.459 1252.50 424. a34 835.000 318.279 626.250 254.652 501.000 4 1273.76 2506.67 636.903 1253.33 424.630 835.556 318.501 626.667 254.830 501.333 5 1274.62 2508.33 637.332 1254.17 424.916 836.111 318.716 627.083 255.001 501 . 6(57 6 1275.48 2510.00 637.762 1255.00 425.203 836.667 318.931 627.500 255.173 502.000 7 1276.37 2511.67 638.206 1255.83 425.499 837.222 319.153 627.917 255.351 502.333 8 1277.25 2513.33 638.650 1256.67 425.795 837.778 319.375 628.333 255.529 502.667 9 1278.11 .2515.00 639.080 1257.50 426.082 838.333 319.590 628.750 255.701 503.000 10 1278.97 2516.67 639.510 1258.33 426.368 838.889 319.805 629.167 255.873 503.333 11 1279.86 2518.33 639.954 1259.17 426.664 839.444 320.027 629.583 256.050 503.667 12 1280.75 2520.00 640.398 1260.00 426.960 840.000 320.249 630.000 256.228 504.000 13 1281.61 2521.67 640.828 1260.83 427.247 840.556 320.464 630.417 256.400 504.333 14 1282.47 2533.33 641.257 1261.67 427.533 841.111 320.679 630.833 256.572 504.667 15 1283.86 2525.00 641.701 1262.50 427.829 841.667 320.901 631.250 256.750 505.000 16 1284.24 2526.67 642.145 1263 33 428.125 842.222 321.123 631.667 256.927 505.333 17 1285.10 2528.33 642.575 1264.17 428.412 842.778 321.338 632.083 257.099 505.667 18 1285.96 2530.00 643.005 1265.00 428.698 843.333 321.553 632.500 257.271 506.000 19 1286.85 2531.6? 643.449 1265.83 428.994 843.889 321.775 632.917 257.449 506.333 2O 1287.74 2533.33 643.893 1266.67 429.290 844.444 321.997 633.333 257.626 506.667 21 1288.60 2535.00 644.323 1267.50 429.577 845.000 322.212 633.750 257.798 507.000 22 1289.46 2533.67 644.752 1268.33 429.864 845.556 322.427 634.167 257.970 507.333 23 1290.35 2538.33 645.197 1269.17 430.160 846.111 32-2.040 634.583 258.148 507.667 24 1291.23 2540.00 645.641 1270.00 430.456 846.667 322.871 635.000 258.326 508.000 25 1292.12 2541.67 646.085 1270.83 430.752 847.222 323.093 635.417 258.503 508.333 26 1293.01 2543.33 646.529 1271.67 431.048 847.778 323.315 635.833 258.681 508.667 27 1293.87 2545.00 646.958 1272.50 431 .334 848.333 323.530 636.250 258.853 509.000 28 1294.73 2546.67 647.388 1273.33 431.621 848.889 323.745 636.667 259.025 509.333 29 1295.62 2548.33 647.832 1274.17 431.917 849.444 323.967 637.083 259.203 509.667 3O 1296.51 2550.00 648.276 1275.00 432.213 850.000 324.189 637.500 259.380 510.000 31 1297.36 2551.67 648.706 1275.83 432.499 850.556 324.404 637.917 259.552 510.333 32 1298.22 2553.33 649.136 1276.67 432.786 851.111 324.619 638.333 259.724 510.667 33 1299.11 2555.00 649.580 1277.50 433.082 851.667 324.841 638.750 259.902 511.000 34 1300.00 2556.67 650.024 1278.33 433.378 852.222 325.063 639.167 260.079 511.333 35 1300.86 2558.33 650.454 1279.17 433.665 852.778 325.278 639.583 260.251 511.667 36 1301.72 2560.00 650.883 1280 00 433.951 853.333 325.493 640.000 260.423 512.000 37 1302.61 2561.67 651.328 1280. 83 434.247 853.889 325.715 640.417 260.601 512.333 38 1303.50 2563.33 651.772 1281.67 434 543 a54.444 325 937 640.833 260.779 512.667 39 1304.38 2565.00 652.216 1282.50 434.839 855.000 326.159 641.250 260.956 513.000 40 1305.27 2566.67 652.660 1283.33 435.135 855.556 326 381 641.667 261.134 513.333 41 1300.13 2568 33 653.089 1284.17 435.422 856.111 326.596 642.083 261.306 513.667 42 1306.99 2570.00 653.519 1285.00 435.708 856 667 326.811 642.500 261.478 514.000 43 1307.88 2571.67 053.963 1285.83 436.004 857.222 327.033 642.917 261.656 514.333 44 1308.77 2573.33 654.407 1286.67 436.300 857.778 327.255 643.333 261.833 514.667 45 1309.63 2575.00 654.837 1287.50 436.587 &78.3S3 327.470 643.750 262.005 515.000 46 1310.49 2576.67 655.267 1288.33 436.873 858.889 327.685 644.167 262.177 515.383 47 1311.37 2578.33 655.711 1289.17 437.170 859.444 327.907 644.583 202.355 515.667 48 1312.26 2580.00 656.155 1290.00 437.466 S60.000 328.129 645.000 262.533 516.000 49 1313.15 2581.67 656.599 1290.83 437.762 860.556 328.351 645.417 262.710 516.333 5O 1314.04 2583.33 657.043 1291.67 438.058 8(51.111 328.573 645.833 262.888 516 667 51 1314.90 2585.00 657.473 1292.50 438.344 ^61.007 328.788 646.250 263.060 517.000 52 1315.76 2586.67 657.903 1293.33 438.631 862.222 329.003 646.667 203.232 517.333 53 1316.64 2588.33 658.347 1294.17 438.927 802.778 329.225 647.083 263.409 517.607 54 1317.53 2590.00 658.791 1295.00 439.223 863.333 329.447 647.500 263.587 518.000 55 1318.4-2 2591.67 659.235 1295.83 439.519 863.889 329.669 647.917 263.765 518.383 56 1319.31 2593.33 659.679 1296.67 439.815 864.444 3-29.891 648.833 263.942 518.007 57 1320.17 2595.00 660.1 OS 1297 50 440.102 865.000 380.106 648.750 204.114 519.000 58 1321.03 2596.67 660.538 1298.33 440.388 865.556 330.321 649.167 264.286 519.333 59 1321.92 2598.33 660.982 1299.17 440.684 866.111 33). 543 649.583 264.464 519. 667 - 96 TABLE XIV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9* Curve. 1O Curve. 25 Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. M. 211.796 416.667 181.568 357.143 158.903 312.500 141.27(3 277.778 127.181 250.000 O 211.944 416.944 181.695 357.381 159.014 312.708 141.375 277.903 127.270 250.167 1 212.092 417.222 181.822 357.619159.125 312.917 141.474 278.148 127.359 250.333 2 212.240 417.500 181.949 357.857 159.236 313.125 141.573 278.333 127.448 250.500 3 212.388 417.778 182.076 358.095 159.347 313.333 141.671 278.519 127.537 250.667 4 212.532 418.056 182.199 358.333 159.455 313.542 141 767 278.704 127.623 250.833 5 212.675 418.333 182.322 358.571 159.562 313.750 141.863 278.889 127 709 251.000 6 212.823 418.611 182.449 358.810 159.673 313.958 141.961 279.074 127.798 251.167 7 212.971 418.889 182.576 359.048 159.785 314.167 142.060 279.259 127.887 251.333 8 213.114 419.167 182.699 359.286 159.892 314.375 142.156 279.444 127.973 251.500 9 213.258 419.444 182.822 359.524 160.000 314.583 142.251 279.630 128.059 251.667 1O 213.40(5 419.722 182.949359.762 160.111 314.792 142.350 279.815 128.148 251.833 11 213.554 420.000 183.075360.000 160.222 315.000 142.449 280.000 128.237 252.000 12 213.697 420.278 183.198360.238 160.329 315.208 142.545 280.185 128.323 252.167 13 213.840 420.556 183.321 360.476 160.437 315.417 142.640 280.370 128.409 252.333 14 213.988 420.833 183.448360.714 160.548 315.625 142.739 280.556 128.498 252.500 15 214.137 421.111 183.575360.952 160.659 315.833 142.838 280.741 128.587 252.667 16 214.280 421.389 183.698361.190 160.767 316.042 142.933 280.926 128.673 252.833 17 214.423 421.667 183. 821 '361. 429 160.874 316.250 143.029 281.111 128.759 253.000 18 214.571 421.944 183.948 361.667 160.985 316.458 143.128 281.296 128.848 253.167 19 214.719 422.222 184.075 361.905 161.096 316.667 143.226 281.481 128.937 253.333 20 214.863 422.500 184.198362.143 161.204 316.875 143.322 281.667 129.023 253.500 21 215.006 4522.778 184.320362.381 161.311 317.083 143.418 281.852 129.109 253.667 22 215.154 423.056 184.4471 362. 619 161.422 317.292 143.516 282.037 129.198 253.833 23 215.302 423.333 184.574362.857 161.533 317.500 143.615 282.222 129.287 254.000 24 215.450 423.611 184.701363.095 161.645 317.708 143.714 282.407 129.376 254.167 25 215.598 423.889 184. 828 1363.333 161.756 317.917 143.813 282.593 129.465 254.333 26 215.742 424.167 184.951 363.571 161.863 318.125 143.908 282.778 129.551 254.500 27 215.885 424.444 185.074 363.810 161.971 318.333 144.004 282.963 129.637 254.667 28 216.033 424.722 185.201 364.048 162.082 318.542 144.103 283.148 129.726 254.833 29 216.181 425.000 185.328 364.286 162.193 318.750 144.201 283.333 129.815 255.000 30 216.324 425.278 185.451 364.524 162.300 318.958 144.297 283.519 129.901 255.167 31 216.468 425.556 185.574 364.762 162.408 319.167 144.393 283.704 129.987 255.333 32 216.616 425.833 185.700 365.000 162.519 319.375 144.491 283.889 130.076 255.500 33 216.764 426.111 185.827 365.238 162.630 319.583 144.590 284.074 130.164 255.667 34 216.907 426.389 185.950 365.470 162.738 319.792 144.686 284.259 130.251 255.833 35 217.050 426.667 186.073 365.714 162.845 320.000 144.781 284.444 130.337 256.000 36 217.199 426.944 186 200 365.952 162.956 320.208 144.880 284.630 130.426 256.167 37 217.347 427.222 186.327 366.190 163 067 320.417 144.979 284.815 130.514 256.333 38 217.495 427.500 186.454 366.429 163.179 320.625 145.078 285.000 130.603 256.500 39 217.643 427.778 186.581 366.667 163.290 320.833 145.176 285.185 130.692 256.667 4O 217.786 428.056 186.704 366 905 163.397 321.042 145.272 285.370 130.778 256.833 41 217.929 428.333 186.827 367.143 163.505 321.250 145.368 285.556 130.864 257.000 42 218.077 428.611 186.954 367.381 163.616 321.458 145.466 285.741 130.953 257.167 43 218.226 428.889 187.080 367.619 163 727 321.667 145.565 285.926 131.042 257.333 44 218.369 429.167 187.203 367.857 163.834 321.875 145.661 286.111 131.128 257.500! 45 218.512 429.444 187.326 368.095 163.942 322.083 145.756 286.296 131.214 257. 667 ' 46 218.660l429.72:> 187.4531368.333 164.053 322.292 145.855 286.481 131.303 257.833 47 218.808430.000 187.580368.571 164.164 322.500 145.954 286.667 131.392 258.000 48 218.956 430.278 187.707 368.810 164.275 322.708 146.053 286.852 131.481 258. 1G7 49 219.105 430.556 187.834 369.048 164.386 322.917 146.151 287.037 131.570 258.3.3 50 219.248 430.833 187.957309.286 1 64. 494 ! 323. 125 146.247 287.222 131.656 258.500 51 219.391 431.111 188.080369.524 164. 601 1323. 333 146.343 287.407 131.742 258.6(57 52 219.539 431.389 188.2078fi9.762 164.712323.542 146.441 287.593 131.831 258.833 53 219.687 431.667 188.33* 370.000 164.824323.750 146.540 287.778 131.920 259.000 54 219.835 431.944 188.4(Jl 370.238 164.935323.958 146.639 287.963 132.009 259.167 55 219.983 482.222 1S8.5K7-370.476 165.046324.167 146.738 288.148 132.098 259.333 56 220.127 432.500 188. 710:370. 714 165.153324.375 146.833 288.333 132.184 259.500 57 220.270 432.778 188. 8153 370. 952 165.261 324 583 146.929 288.519 132.270 259.667 58 220.418 433.056 188.9601371.190 165.372324.792ll47.028 288.704 132.359 259.833 59 97 TABLE XIV. ACTUAL TANGENTS, ETC. 26 1 Carve. 2 Curve. 3 Curve. 4 Curve. 5 Curve. M. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. ~~0~ 1322.802600.00 661.426 1300.00 440.980 866.667 330.765 650.000 264.642 520.000 1 1 323. 66 ( 2601. 67 661.856 1300.83 441.267 867.222 330. 9SO| 650. 41 7 2(54.814 520.333 2 1324.522603.33 662.286 1301.67 441.553 867.778 33 1.1 95650. 833 264.986 520.667 3 1325.41 2605.00 662.7:30 1302.50 441.849 868.333 331.417 651.250 265 163 521.000 4 1326.30J2606.6? 663.174 1303.33 442.145 868.889 881.889 651.667 265.341 521.333 5 1327.19 2608.33 663.618 1304.17 442.441 869.444 331.861 652.083 265.519 521.66? 6 1328.08 2610.00 (564.062 1305.00 442.737 870.000 332.083 652.500 2(55.696 522.000 7 1328.94 2611.67 664.492 1305.83 443.024 870.556 332.298 652.917 265.868 522 333 8 1329.79 2613.33 664.922 1306.67 443.310 871.111 332.513 653.333 266.040 522.667 9 1330.68 2615.00 665.366 1307.50 443.607 871.66? 332.735 653.750 266.218 523.000 10 1331.57 2616.67 665.810 1308.33 443.903 872.222 332.957 654.16? 266.395 523.333 11 1332.46 2618.33 666.254 1309.17 444.199 872.778 333.179 654.583 266.573 523.667 12 1333.352620.00 666.698 1310.00 444.495 873.333 333.401 655.000 2(56.751 524.000 13 1334.21 2621.67 667.128 1310.83 444.781 873.889 333.616I655. 417 266.923 524.3:33 14 1335.07 2623.33 667.557 1311.67 445.068 874.444 333.831 655.833 267.095 524.667 15 1335.95 2625 00 668.001 1312.50 445.364 875.000 334.053656.250 267.272 525 000 16 1336.84 2626.67 668.445 1313. as 445.660 875.556 334.2751656.667 267.450 525.333 17 1337.73 2628.33 568.890 1314.17 445.956 876.111 334.497 657.083 267.628 525.667 18 1338.62 2630.00 (569.334 1315.00 446.252 876.667 334.719 657.500 267.805 526.000 19 1339.48 2631.67 669.763 1315.83 446.539 877.222 334.934 657.917 267.977 526.333 20 1340.34 2633 33 670.193 1316.67 446.825 877.778 335.149 658.333 268.149 526.667 21 1341.23 2635.00 670.637 1317.50 447.121 878.333 335.371 658.750 268.32? 527.000 22 1342.11 2636 67 671.081 1318 33 447.417 878.889 335.593 659.167 268.505 527.333 23 1343.00 2638.33 671.525 1319.17 447.713 879.444 335.815 659.583 268.682 527.667 24 1343.89 2640.00 671.969 1320.00 448.009 880.000 336.037 660.000 268.860 528.000 25 1344.75 2641.67 672.399 1320.83 448.296 880.556 336.252 660.417 269.032 528.333 26 1345.61 2643.33 672.829 1321.67 448.582 881.111 336.467 660.833 269.204 528.667 27 1346.50 2645.00 673.273 1322.50 448.878 881.667 336.689 661.250 269.382 529.000 28 1347.38 2646.67 673.717 1323.33 449.174 882.222 336.911 661.66? 269.559 529.333 29 1348.27 2648.33 674.161 1324.17 449.47'0 882.778 337.133 662.083 269.73? 529.667 30 1349.16 2650.00 674.605 1325.00 449.767 ^83.333 337.356 662.500 269.915 530.000 31 1350.05 2651.67 675.049 1325. a3 450.063 ^83.889 337 578 662.917 270.092 530.333 32 1350.94 2653.33 675.493 1326.67 450.359 884.444 337.800 663.333 270.270 530.667 33 1351.80 2655.00 675.923 1327.50 450.645 885.000 338.015 663.750 270.442 531.000 34 1352.66 2656.67 676.353 1328.33 450.932 885.556 338.229 664.167 270.614 531.333 35 1353.54 2658.33 676 797 1329.17 451 . 228 886.111 338.452 664.583 270.791 531.667 36 1354.43 2660.00 677.241 1330.00 451.524 886.667 338.674 665.000 270.969 532000 37 1355.32 2661.67 677.685 1330.83 451.820 887.222 338.896 665.417 271.147 532.333 38 1356.21 9688.81 678.189 1331.67 452.116 887.778 339.118 665.833 271.324 532.667 39 1357.07 2665.00 678.559 1332.50 452.402 888.333 339.3:33 666.250 271.496 533.000 4O 1357.93 2666.67 678.988 1333.33 452.689 888.889 339.548 666.667 271.668 533.333 41 1358.82 2668.33 679.432 1334.17 452.985 S89.444 339.770 667.083 271.846 533.667 42 1359.70 2670.00 679.877 1335 00 453.281 S90.000 339.992 667.500 272.024 534.000 43 1360.59 2671.67 080.321 1335.83 453.577 ^90.556 340.214 667.917 272.201 534.333 44 1361.48 2673.33 680.765 1336 67 453.873 891.111 340.436 668.333 272.379 534.667 45 1362.37 2675.00 681.209 ia37.50 454.169 891.66? 340.658 668.750 272.557 535.000 46 1363.26 2676.67 681.653 1338.33 454.465 892.222 340.880 660.167 272.734 535.333 ;47 1364.12 2678.33 682.083 1339.17 454 752 892.778 341.095 669.583 272.906:535.667 48 1364.97 2680.00 682.512 1340.00 455.038 893.333 341.310 670.000 273.078536.000 49 1365.86 2681.67 682.956 1340.83 455.334 893.889 341 532 670.417 273.256 536.333 50 1366.75 2683.33 683.400 1341.67 455.630 804.444 341.754 670.833 273.434 536.667 51 1367.64 2685.00 683.844 1342.50 455.927 895.000 341.976 671.250 273.611 537.000 52 1368.53 2686.67 684.289 1343.33 456.223 H95 556 342.198 671.667 273.789537.333 53 1369.41 2688 33 684.733 1314.17 456.519 896.111 3 42. 420 672. OR3 273.967537.667 54 1370.30 2690.00 685.1771345.00 456.815 896.667 342.642672.500 274.144538.000 55 1371.16 2691.67 685.6061345.83 457.101 897.222 34-2. 857 072. 91 7 274.316538.333 56 1372.02 2693 . 33; 686 . 03fi 1 346 . 67 457.388 897.778 343. 072! 673. &33 274.488588.667 57 1372 91 2695 . 00 . 686 . 480 1 347 . 50 457.6,84 ^98.333 243.294673.750 274.666539.000 58 1373.80 2696. 67 686. 924 11348. 33 457.980 898.889 343.516674.167 274.844539.333 59 1374.69 2698. 33: 687. 368 '1349. 17 458.276 899.444 343.738674.583 275.021 539.667 TABLE XIV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 Curve. 1O Curve. 36 Tan. 220.5(56 Arc. 433 333 Tan. 18-J.087 Arc. 371.429 Tan. Arc. Tail. Arc. Tan. 132T448 Arc. 260.000 M7 O 165.483 325.000 147.126 288.889 &J0.710 433.611 189.210371.667 165.590325.208 147.222 289.074 132.534 260.167 1 220.853 433.889 189.333371.905 165.698 325.417 147.318 289 259 132.620 260.333 3 221.001 434.167 189.460,372.143 165.809 325. 62 147.416 289 444 132.709 260.500 3 221. 149 431.444 189.587 372.381 1*55.920 325.833 147.515 289.630 132.798 260.667 4 221.297 434.722 189.714 372.619 166.031 326.042 14-7.614 289.815 132.887 260.833 5 221.445 435.000 189.841 372.857 166.142 326.250 147.713 290.000 132.976 261.000 6 221.588 435.278 189.963 373.095 166.250 326.458 147.808 290.185 133.062 261.167 7 221.732 435.556 190 086 373.333 166.357 326.667 147.904 290.370 133.148 261.333 8 221.880 4:35.833 190.213 373.571 166.469 326.875 148.003 290.556 133.237 261.500 9 222.028 436.111 190.340 373.810 166.580 327.083 148.101 290.741 133.326 261.667 10 222.170 436.389 190.467 374.048 166.691 327.292 148.200 290.926 133.414 261.833 ] 1 222.324 436.667 190.594 374.286 166.802 327. 500 148.299 291.111 133.503 262.000 12 222.467 436.944 190.717 374.524 166.909 327.708 148.395 291.296 133. 5S9 262.167 13 222.611 437.222 190.840 374.762 167.017 327.917 148.490 291 .481 133.675 262.333 14 222.759 437.500 190.967 375.000 167.128 328.125 148.589 291.667 133.764 262.500 15 222.907 437.778 191.094 375.238 167.239 328 333 148.688 291.852 133.853 262.667 16 223.055 438.056 191.221 375.476 167.350 328.542 148.787 292.037 133.942 262.833 17 223.203 4:38.333 191.348 375.714 167.461 328.750 148.8R5 292.222 134.031 263.000 18 223.340 438. Gil 191.470 375.952 167.569 328.958 148.981 292.407 134.117 263.167 19 223.490 438.889 191.593 376.190 167 676 329.167 149.077 292.593 134.203 263.33:3 2O 223.6:38 439.167 191.720 376.429 167.787 329.375 149.175 292.778 134.292 263.500 21 223.786 439.444 191.847 376.667 167.898 329.583 149.274 292.963 K34.381 263.667 22 223.934 439.722 191.974 376.905 168.010 329.792 149.373 293.148 134.470 263.833 23 224.082 440.000 192.101 377.143 168.121 330.000 149.472 293.3:33 134.559 264.000 24 224.225 440.27'8 192 224 377.381 168.228 330.208 149.567 293.519 134.645 264.167 25 224.369 440.556 19.5.347 377.619 168.336 330.417 149.603 293.704 134 731 264.333 26 224.517 440.833 192.474 377.857 168.447 330.625 149.762 293.889 134.820 264.500 21 224.665 441.111 192.601 378.095 168.558 330.833 149.8(50 294.074 134.909 264.667 28 224.813 441.389 192.728 378.333 168.669 331.042 149.959 294.259 134.998 264.833 29 224.961 441.667 192.855 378.571 168.780 331.250 150.058 294.444 135.087 265.000 30 225.109 441.944 192.982 378.810 168 891 1331.458 150.157 294.630 135.176 265.167 31 225.257 442.222 193.108 379.048 169.002 33 1.667 150.255 294.815 135 265 265.333 32 225.400 442.500 193.231 379.286 169.110 331.875 150.351 295.000 135.351 265.500 33 225.544 442.778 193.354 379.524 169.217 332.083 150.447 295.185 135.437 265.667 34 225.692 443.056 193.481 379.762 169.328 332 292 150.545 295.370 1,35.526 265.833 35 225.840 443.333 193.608 380.000 169.440 332.500 150.644 295.556 135.615 266.000 36 225.988 443.611 193.735 380 238 169.551 332.708 150.743 295.741 ia5.703 066.167 37 226.136 443.889 193.862 380.476 169.662 332.917 150.842 295.926 1:35.790 266. 3a3 38 226.279 444.167 193.985 380.714 169.769 333.125 150.937 296.111 135.878 266.500 39 226.423 444.444 194.108 380.952 169.877 333.338 151.033 296.296 135.964 266.667 40 226.571 444.722 194.235 381.190 169.988 333.542 151.132 296.481 136.053 266.833 41 226.719 445.000 194 362 381.429 170.099 333.750 151.230 296.667 136.142 267.000 4=2 226.867 445.278 194.489 381.667 170.210 333.958 151.329 296.852 136.231 267.167 43 227.015 445.556 194.615 381.905 170.321 334.167 151 428 297.037 136.320 267.333 44 227.163 445. 833 194.742 382.143 170.432 334.375 151 .527 297.222 136.409 267.500 45 227 311 446.111 194.869j382.38l 170.543 334.583 151.626 297.407 136.498 067.667 46 227.454 446.389 194.992382.619 170.651 3:34.792 151.721 297.593 136.584 267 833 47 227.598 446.667 195.115382.857 170.758 335.000 151.817 297.778 136.670 268.000 48 227.746 446.944 195.242 383.095 170.870 335.208 151.916 297.963 136.759 268.167 49 227.894 417.222 195.3M 383.333 170.981 335.417 152.014 29^.148 136.848 268.333 50 228.042 447.500 195. 49(1383. 571 171.092 335.625 152.113 298.333 136.9-37 268.500 51 228.190 447.778 195.623383.810 171 203 335.833 152.212 298.519 137 026 268.667 52 228.338 418.056 195.7f)03K4.048 171 314 33(5.042 152.311 298.704 137.115 068 833 53 228.486 448. 333 195. 87 7 3S4. 280 171.42:. 336.250 152.405) 298.889 137.204 269.000 54 208. (>:>,<) 228 77 3 4 J 8. 611 196.000384.524 4 18. 889' 196. 122 38 4. 762 171.533 171.640 336.458 336. f ,67 152.505 152.601 299.074 299.259 137.290 137.376 269.167 269.333 55 56 228.901 449.167)196.249 3S5.000 171.751 336.875 152.699 099.444 137.465 269.500 57 229 069 449.444 19(5.376 3S5.238 171 862 337.083 152.798 299.630 137.554 069 667 r>8 229.2l7i4l9 722 190.503 385.476 171.973 337.292 152.897 299.815 137.643 269. 833 59 99 TABLE XIV. ACTUAL TANGENTS, ETC. 37 M. 1 Curve. 2 Curve. 3 Curve. 4 Curve. 5 Curve. Tail. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. ~~cT 1375.57 2700.00 687.812 1:350.00 458.572 900.000 3437960 (3?5.000 275.199 540.000 1 1376.46 2701.67 688.256 1350.83 458. H6H 900.556 344.182 675.417 275.377 540. ai3 2 1377.35 2703.33 688.701 1351 67 459.161 901.111 344.404 675.833 275.5M 540.607 3 1378.21 2705.00 689.130 1352.50 459.451 U01.0G7 344.619 676.250 275.726 541.000 4 1379.0? 2706 67 689.560 1353.33 459.737 9U2.222 344.834 370 . 667 275.898 541.333 5 1379.96 2708.33 690.004 1354.17 460.033 U02.778 345.050 077.083 276.070 541.607 6 1380.85 2710.00 690.448 1355.00 460.329 903. sas 345.278 677.500 276.253 542.000 7 1381.73 2711.67 690.892 1:355.83 4(50.625 903.889 345.500 677.91? 276.431 542.333 8 1382.62 2713.33 691.336 1356.67 460.921 904.444 345.722 078.33:3 352.786 691.667 282.260 553.333 41 1411.76 2768.33 705.904 1384.17 470.634 922.778 353.008 092.083 282.438 553.667 42 1412.65 2770.00 706.348 1385.00 470.930 923.3:33 353.230 692.500 282.615 554.000 43 1413.53 2771.67 706.793 1385.83 471.226 923.889 353.452 692.917 282.793 554.333 44 1414.42 2773. as 707.237 1386.67 471.522 924.444 353.674 693.333 282.971 554.667 45 1415.31 2775.00 707.681 1387.50 471.818 925.000 353.896 693.750 283.148 555.000 46 1416.20 2776.67 708.125 1388.33 472.114 925.556 354.118 694.16? 283.326 555. a33 47 1417.06 2778.33 708.554 1389.17 472.401 926.111 354. .333 694.583 283.498 555.667 48 1417.92 2780.00 708.984 1390.00 472.687 9*6.667 354.548 695.000 283.670 556.000 49 1418.80 2781.67 709.428 1390.83 472.984 927.222 354.770 695.417 283.848 556.333 50 1419.69 2783.33 709 872 1391.67 473.280 927.778 354.992 695.833 284.025 556.667 51 1120.58 2785.00 710.316 1392.50 473.576 928.333 355.214 096.250 284.2(3 557.000 52 1121.47 2786.67 710.760 1393.33 473.872 928.889 355.436 696.607 284.381 557.33;3 53 1422.36 2788.33 711.205 1394.17 474.168 929.444 355.658 697.083 284.558 557.667 54 1423.25 2790.00 711.649 1395.00 474.464 930.000 355.880 697.500 284.730 558.000 55 1424 13 2791.67 712.093 1395.83 474.760 930.556 356.102 097.917 284.914 558.333 56 1425.02 2793.33 712.537 1396.67 475. 050 931.111 356.324 698. 333 285.091 558.667 57 1425.91 2795.00 712.981 1397.50 475.352 931.667 356.546 098.750 285.269 559.000 58 1426.80 2796.67 713.425 1398. as 475.648 932.222 356.768 699.167 285.44? 559.333 59 1427.69 2798.33 713.869 1399.17 475.914 932. 7781356. 9'J1 099.583 2a5.624 559.667 100 TABLE XIV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 Curve. 1O Curve. 27 Tan. Arc. Tan. Arc. Tan. Arc. 337 500 Tan. Arc. 300.000 Tan. 137.731 Arc. M. &J9.365 450.000 196.630 385.714 172.084 152.996 270.000 a 229.513 450.278 196.757 385.952 172.196 337.708 153.095 300.185 137.820270.167 i 229.661 450.556 196.884 386.190 172.307 337.917 153.193 300.370 137.909 ^70.333 2 229.805 450.833 197.007 386.429 172.414 338.125 153.289 300.556 137.995270.500 3 229.948 451.111 197.130 386.667 172.522 338.333 153.384 300.741 138.081 270.607 4 230.096 451.389 197.257 386.905 172.633 338.542 153.483 300.926 138.170 27'0.833 5 230.244 -151.667 197.384 387.143 172.744 338.750 153.582 301.111 138.259271.000 G 230.392 451.944 197.511 387.381 172.855 338.958 153.681 301.296 138.348 271.167 7 230.540 452.222 197.638 387.619 172.966 339.167 153.780 301.481 138.437 271.333 8 230.688 452.500 197.765 387.857 173.077 339.375 153.878 301.667 138.526 271.500 9 230.836 452.778 197.892 388.095 173.188 339.583 153.977 301.852 138.615 271.667 10 230.985 453.056 198 019 388.333 173.299 339.792 154.076 302.037 138.704 271 833 11 231.133 453.333 198.145 388.571 173.411 340.000 154.175 302.222 138.793 272.000 12 231.276 453.611 198.268 888.810 173.518 340.208 154.270 302.407 138.879 272 167 13 231.419 453.889 198.391 389.048 173.626 340.417 154.366 302.593 138.965 272.3:33 14 231.567 454.167 198.518 389.286 173.737 340 625 154.465 302.778 139.054 272.500 15 231.715 454.444 198.645 389.524 173.848 340.833 154.563 302.963 139.143 272 667 16 231.863 454.722 198.772 389.762 173.959 341.042 154.662 303.148 139.232 272.833 17 232.012 455.000 198.899 390.000 174.070 341.250 154.761 303.333 139.321 273.000 18 232.160 455.278 199.026 390.238 174.181 341.458 154.860 303.519 139.409 273.167 19 232.308 455.556 199.153 390.476 174.292 341.667 154.959 303.704 139.498 273.333 20 232.456 455.833 199.280 390.714 174.403 341.875 155.057 303.889 139.587 273.500 21 232.004 456.111 199.407 390.952 174.514 342.083 155.156 304.074 139.676 273.667 22 232.747 456,389 199.530 391.190 174.622 342.292 155.252 304.259 139.762 273.833 23 232. b90 456.667 199.652 391.429 174.729 342.500 155 347 304.444 139.848 274.000 24 233.039 456.944 199.779 391.667 174.841 342.708 155.446 304.630 139.937 274.167 25 233.197 457.222 199.906 391.905 174.952 342 917 155.545 304.815 140.026 274.333 26 233.335 457.500 200.033 392.143 175.063 343.125 155.644 305.000 140.115 274.500 27 233.483 457.778 200.160 392.381 175.174 343.333 155.742 305.185 140.204 274.667 28 233.631 458.056 200.287 392.619 175.285 343.542 155.841 305.370 140.293 274.833 29 233.779 458.333 200.414 392.857 175.396 343.750 155.940 305.556 140.382 275.000 30 233.927 458.611 200.541 393.095 175.507 343.958 156.039 305.741 140.471 275.167 31 234.075 458.889 200. 668 j 393. 333 175.618 344.167 156.137 305.926 140.560 275.333 32 234.223 459.167 200.795 393.571 175.729 344.375 156.236306.111 140.649 275.500 33 234.371 459.444 200.922393.810 175.840 344.583 156.335306.296 140.738 275.667 34 894.515 459.722 201.045:394.048 175.948 344.792 156.431 306.481 140 824 275.833 35 384.658 460.000 201.168394.286 176.055 345.000 156.526306.667 140.910 276.000 36 234. 806 '400. 27 8 201.295394.524 176.167 345.208 156.6251306.852 140.999 276.167 37 234. 954 1460. 556 201.422394.762 176.278 345.417 156.724 307.037 141.088 276.333 38 235.102J460.833 201.548395.000 1 176.389 345.625 156.823 307.222 141.176 276.500 39 235.250461.111 201.675395.238 176.500 345.833 156.921 307.407 HI. 265 276.667 40 235.398461.389 201.802395.476 176.611 346.04? 157.020 307.593 141.354 276. 8S3 41 235.546461.667 201.929395.714 176.722 346.250 157.119307.778 141.443 277.000 42 235.695461.944 202.056395.952 176.833 346.458 157.2181307.963 141.532 277.167 43 235 843462.222 202.183396/190 176.944 346.667 157. 316*308. 148 141.621 277.333 44 235.991 462.500 202.310396.429 17 .055 346.875 157.415308.333 141.710 277.500 45 23(5.139 462.778 202.437396.667 17 .166 347.083 157.514308.519 141.799 277.007 46 236.282 463.056 202.560396.905 17 .274 347.292 157.610 308.704 141.885 277.833 47 236.425 463.333 202.683397.143 17 .381 347.500 157.705 308.889 141.971 278.000 48 236.573 463.611 202.810 397.381 177.493 347.708 157.804 309.074 142.060 278.167 49 236.722 463.889 202.937 397.619 17~.604 347.917 157.903 309.259 142.149 278.333 50 230.870 464.167 203.064397.857 17^.715 348.125 158.001 309.444 142.23F 278.500 51 237.018 464.444 203.191 398.095 17 .826 348.333 158.100 309.630 142.3-.7278.667 52 237.166 464.722 203.3183D8.333 177.937 348.542 158.199 309.815 142.410 278.833 53 237.314 465.000 203.445 398 571 178.048 348.750 158.298 310.000 142.505 27'9.000 54 237.462 465.278 203.571 398.810 178.159 348.958 158.397 310.185 142.593279.167 55 237.610 4R5.556 203.698 399.048 178.270 349.167 158.495 310.370 142.682:279.333 56 237.758 465.833 203.825 399.286 178.381 149.375 158.594 310.556 142.771,27'9.500 57 237.906 166.111 203.952 399.524 178.493 349.583 158.693 310.741 142. 860 1279. 607 58 238.054 466.389 204.079 399.762 178.604 349.792 158.792 310.926 142. 949 |279. 833 59 101 TABLE XIV. ACTUAL TANGENTS, ETC. 28 1 Curve. 2 Curve. 3 Curve. 4 Curve. 5 Curve. M. Tau. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. 1428.57 2800.00 714.313 1400.00 476.240933.333 357.213 700.000 285.802 560.000 1 14-29.46 2801.67 714.757 1400.83 476.536933.889 357.435 700.417 285.980 500.333 2 1430.35 2803.33715.201 1401.67 476.832934.444 357.057 700.833 286.157 560.607 3 1431.24 2805.00 715.645 1402.50 477.128935.000 357.879 701.250 286 335 5(11.000 4 1432.13 2806.67 716.089 1403.33 477.424 935.556 358.101 701.607 286.513 561.333 5 1433.01 2808.33 716.533 1404.17 477.721 936.111 358.323 702.083 286.690 501.667 6 1433.90 2810.00 716.977 1405.00 478.017936.667 358.545 702.500 286.868 562.000 7 1434.76 2811.67 717 407 1405.83 478.303937.222 358.760 702.917 287.040 562.333 8 1435.62 2813.33 717.837 1406.67 478.590937.778 358.975 703.333 287.212 562.667 9 1436.51 2815.00 718.281 1407.50 478.886938.333 359.197 703.750 287.390 563.000 10 1437.40 2816.67 713.725 1408.33 479 182938.889 359.419 704.167 287.567 563 333 11 1438.29 2818.33,719.169 1409.17 479.478939.444 359.641 704.583 287.745 563 667 13 1439,17 2820.00 719 613 1410.00 479.774940.000 359.863 705.000 287.923 564.000 13 1440.06 5821.67 720.057 1410.83 480.070940.556 360.085 705.417 288.100 564.333 14 1410.05 2823 33 720.501 1411.67 480 366 941.1 11 360.307 705.833 288.278 564.667 15 1441.84 2825.00 720.94') 1412.50 480 662941.667 360.529 706.250 288.456 565.000 16. 144-2. 73 2826.67 721.389 1413.33 480.958942.222 360.751 706.667 288.633 565.333 17 1443.61 2828,33 721.833 1414.17 481.254942.778 360.973 707.083 288.811 565.667 18 1444.50 2830.00 722.278 1415.00 481.550943.333 361.195 707.500 288.989 566 000 19 1445.39 2831.67 722.722 1415.83 481.846:943.889 361.418 707.917 289.160 566.333 20 1446.28 2833.33 723.166 1416.67 482.142944.444 361.640 708.333 289.344 566.667 21 1447.17 2835.00 723.610 1417.50 482.438945.000 361.802 708.750 289.522 567.000 22 1448.05 2836.67 724.054 1418 33 482.735945.556 362.084 709.167 289.699 567.333 23 1448.94 2838.33 724.498 1419.17 483.031 946.111 362.306 709.583 289.877 567.667 24: 1449.83 2840.00 724.942 14-20.00 483.327946.667 36-2.528 710.000 290.055 508.00!) 25 1450.72 2841 67 725.186 1420 83 483. 6. >:{ 947. 222 362.750 710.41? 290.232 568.333 26 1451.61 3843 .33 725.830 14-21.67 483.919947.778 362.972 710.833 290.410 568.667 27 1452 49 2845.00 726.274 1422.50 484.215948.333 363.194 711 250 290.588 5(59.000 28 1453.38 2846.67 726.718 1423.33 484.511 948.889 363.416 711.667 290.765 569.333 29 1454.2? 2848.33 727.162 1424.17 484,807949.444 363.638 712.083 290.943 569. C67 30 1455, 16 2850.00 727.606 1425.00 485.103950.000 363.860 712.500 291.121 570.000 31 1456.05 2851 ,67 728 050 1425.83 485.399950.556 364.082 712.917 291.298 570.333 32 1456.94 2853.33 728.494 14-26.67 485. 695951. Ill 304.304 713.333 291.470 570.667 33 1457.82 2855.00 728.938 1427.50 485.991:951.667 364.526 713.750 291 654 571.000 34 1458.71 2856.67 729.383 1428.33 486.287952.222 364 749 714.167 291.831 571.333 35 1459.60 2858.33 729 827 1429.17 486. 583 952. 77H 364.971 714.583 292.009 571.667 36 1460.49 2860.00 730.271 1430.00 486.879953.333 365.193 715.000 292.187 572.000 37 1461.38 2861.67 730.715 1430.83 487.175-953.889 365.415 715.417 292.364 572.333 38 1462.26 2803.33 731.159 14-51.67 487.472i'954.444 305.637 715.838 292.542 572.667 39 1463. 15 2865.00 731.603 1432.50 487.768955.000 365.859 716.250 292.720 573.000 40 1464,04 2866.67 732.017 1433.33 488.064:955.556 366.081 716.667 292 897 573.333 41 14(54.93 2868,33 732.491 1434.17 488.360556.111 366.303 717.083 293.075 573.667 42 1465. 8:> 2870,00 732.9% 1435.00 488.656956.667 366.525 717.500 293.253 574.000 43 1466.70 2871.67 733.379 1435.83 488 952-957.222 366'. 747 717.917 293.430 574.333 44 1467.59 2873.33 733.8231436.67 489.248957.778 366.969 718.333 293.608 574.667 45 1468.48 2875.00 734. 2(37(1437.50 489.544 958.333 367.191 718.750 295.786 575.000 46 1469.57 2876.67 734.71111438.33 489.840958.889 367.413 719.167 293.964 575.333 47 1470.26 2878.33 735.155J1439.17 490.136959.444 367.635 719.583 294.141 575.667 48 1471,14 2880.00 735. 599! 1440. 00 190. 432 '960. 000 367.857 720.000 294.319 576.000 49 1472.03 2881.67 736.043 1440.83 490.728.960.556 368.080 720.417 294.497 576.333 50 1472.92 2883.33 736. 4H8 1441.67 491.624961.111 368.302 720.833 294.674 576.667 51 1473.81 2385.00 736.932 1442.50 491. 320% 1.66? 368.524 721.250 294.852 577.000 52 1474.70 2886.67 737.376 1443.33 491 .-61 6 962. 222 368.746 721.667 295.030 577.333 53 1475.59 2888.33 737.820 1444.17 491J912962.778 308.968 722.083 295.207 577.607 54 1476.47 2890.00 738.264 H45.00 492 .209 -963.333 309.190 722.500 295.385 578.000 35 1477.36 2891. .67 788.708 1445.83 492.505963.889 369.412 722.917 295 563 578.333 56 1478.25 2893.33 739.152 1446.67 492. flOl 964,444 369.634 723.333 295.740 578.667 57 1479..14 2895.00 739.596 1447.50 493.097965.000 369.856 723.750 295.918 579.000 58 1480.03 2896.07 740.040 1418.33 4 03. 393 965.550 370 078 724.167 290.096 579.333 59 1480.91 2898.33 740.484 1449.17 4D3.6S9 906.1 11 370.300 724. 5831 296. 273 579.667 102 TABLE XIV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 Curve. 10 Curve. 28 Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. M. 288.202 466.667 204.206 400.000 178.715 350.000 158.890 311.111 143.038 280.000 O 238.350 466.944 204.333 400.238 178.826:350 208 158.989 311.296 143.127 280.167 1 238.499 467.222 204.460 400.476 178.937 350.417 159.088 311.481 143.216 280.333 2 238. 64T 467.500 204.587 400.714 179.048 350.625 159 187 311.667 143.305 280.500 3 238.795 467.778 204.714 400.952 179.159 350.833 159.286 311.852 143.394 280.667 4 238.943 468.056 204.841 401.190 179.270 351.042 159.384 312.037 143.483 280.833 5 239.091 4(58. 333 204.968 401.429 179.381 351.250 159.483 312.222 143.572 281.000 6 239.234 468.611 205.091 401.667 179.489 351.458 159.579 312.407 143.658 281.167 7 239.377 468.889 205.214 401.905 179.596 351.667 159.674 312.593 143.744 281.333 8 239.526 469.167 205.341 402.143 179.707 351.875 159.773 312.778 143.833 281.500 9 239.674 469.444 205.467 402.381 179.819 352.083 159.872 312.963 143.922 281.667 1O 239.822 469.722 205.594 402.619 179.930 352.292 159.971 313.148 144.010 281.833 11 239.970 470.000 205.721 402.857 180.041 352.500 160.069 313.333 144.099 282.000 12 240.118 470.278 205.848 403.095 180.152 353.708 160.168 313.519 144.188 282 167 13 240.266 470.556 205.975 403 333 180.263 352.917 160.267 313.704 144.277 282.333 14 240.414 470.833 206.102 403.571 180.374 353.125 160.366 313.889 144.366 282.500 15 240.562 471.111 206.229 403.810 180.485 353.333 160.465 314.074 144.455 282.667 16 240.710 471.389 206.356 404.048 180.596 353.542 160.563 314.259 144.544 282.833 17 240.858 471.667 206.483 404.286 180.707 353.750 160.662 314.444 144.633 283.000 18 241.006 471.944 206.610 404.524 180.818 353.958 160.761 314.630 144.722 283.167 19 241.154 472.222 206.737 404.762 180.930 354.167 160.860 314.815 144.811 283.333 2O 241.303 472.500 206.864 405.000 181.041 354.375 160.958 315.000 144.900 283.500 21 241.451 472.778 206.991 405.238 181.152 354.583 161.057 315.185 144.989 283.667 22 241.59:> 473.056 207.118 405.476 181.263 354.792 161.156 315.370 145.078 283.833 23 241.747 473.333 207.245 405.714 181.374 355.000 161.255 315.556 145.166 284.000 24 241.895 473.611 207.372 405.952 181.485 355.208 161.354 315.741 145.255 284.167 25 242.043 473.889 207.499 406.190 181.596 355.417 161.45-2 315.926 145.344 284.333 26 242.191 474.167 207.626 406.429 181.707 355.625 161.551 316.111 145.433 284.500 27 242.339 474.444 207.753 406.667 181.818 355.833 161.650 316.296 145.522 284.667 28 242.487 474.722 207.880 400.905 181.929 356.042 161.749 316.481 145.611 284.883 29 242.635 475.000 208.006 407.143 182.041 356.250 161.847 316 667 145.700 285.000 30 242.783 475.278 208.133 407.381 182.152 356 458 161.946 31 G. 852 145.789 285.167 31 242.931 475.556 208.260 407.619 182.263 356.667 162.045 317.037 145.878 285.333 32 243.080 475.833 208.387 407.857 182.374 356.875 162.144 317.222 145.967 285.500 33 243.228 476.111 208.514 408.095 182.485 357.083 162.243 317.407 146.056 285.667 34 243.376 476.389 208.641 408.333 182.596 357.292 162.341 317.593 146.145 285.833 35 243.524 476.667 208.768 408.571 182.707 357.500 162.440 317.778 146.234 286.000 36 243.672 476.944 208.895 408.810 182.818 357.708 162.539 317.963 146.322 286.167 37 243.820 477.222 209.022 409.048 182.929 357.917 162.638 318.148 146.411 286.333 38 243.968 477.500 209.149 409.286 183.040 358.125 162.736 318.333 146.500 286.500 39 244.116 477.778 209.276 409.524 183.152 358.333 162.835 318.519 146.589 286.667 40 244.264 478.056 209.403 409.762 183.263 358.542 162.934 318.704 146.678 286.833 41 244.412 478.333 209.530 410.000 183.374 358.750 163.033 318.889 146.767 287.000 42 244.560 478.611 209.657 410.238183.485 358 958 163.132 319.074 146.856 287.167 43 244.708 478.889 209.784 410.476 183.596 359.167 163.'230 319.259 146.945 287.333 44 244.857 479.167 209.911 410.714183.707 359.375 163.329 319.444 147.034 287.500 45 245.005 479.444 210.038 410.952 183.818 a^9.583 163.428 319.630 147.123 287.667 46 245.153 479.722 210.165 411.190183.929 359.792 163.527 319.815 147.212 287.833 47 245.301 480.000 210.292 411. 429 j 184. 040 360.000 163.625 320.000 147.301 288.000 48 245.449 480.278 210.418 411.667 184.151 360.208 163.724 320.185 147.390 288.167 49 245.597 480.556 210.545 411.905 184.263 360 417 163.823 320.370 147.478 288.333 50 245 . 745 480.833 210.672 412.143 184.374 360.625 163.92-2 320.556 147.567 288.500 51 245.893 481.111 210.799 412.381 184 4a5 360.833 164.0-21 320.741 147 656 288 667 52 246.041 481.389 210.926 412.619184.596 8(51.042 164.119 320.926 147.745 288.833 53 246.189 481.667 211.053 412.857184.707 361.250 164.218 321 111 147.834 289.000 54 246.337 481.944 211.180 413.095184.818 361.458 164.317321.296 147.9-23 289.107 55 246.485 482.222 211.307 4 13. 333 184. 929 '361.667 164 416321 481 148.012 289.333 56 246.633 482.500 211.434 413.571 185. 040i361.875 164.514 321.667 148.101 289.500 57 246.782 482.778 211.561 413.810185.151 362.083 164.613 321.852 148.190 289.667 58 246.930 483.056 211.688 414.048 185.262 362.292 164.71-2 3-22.037 148.279 289.833 59 103 TABLE XIV. ACTUAL TANGENTS, ETC. 3<> ~M^ 1 Curve. 3 Curve. 3 Curve. 4 Curve. 5 Curve. Tan. Arc. Tan. Arc. Tan. Are. Tan. Arc. Tan. Arc. 1481.80 2900 . 00 740. 92b 1450.00 493.985 966.667 370.522 725.000 296.451 580.000 i 1482 69 2901.67 741.372 1450.8) 494.281 967.222 370.744 725.417 296.629 580. 3. 2 1483.58 2903.33 741.816 1451.67 494.577 967.778 370.966 725.833 296.806 580.007 3 1484.47 2905.00 742.260 1452.50 494.873 968.333 371.188 726.250 296.984 581.000 4 1485.35 2906.67 742.704 1453.33 495.169 968.889 371.411 726.667 297.162 581.3:33 5 1486.24 2008.33 743.149 1454.17 495.465 969.444 371.633 727.083 297.339 581.667 6 1487.13 2910.00 743.593 1455.00 495.761 970.000 371.855 727.500 297.517 582.000 7 1488. OJ 2911.67 744.037 1455.83 496.057 970.556 372.077 727.917 S97.695 582.3:33 8 1488.91 2913.33 744.481 1456.67 496.353 971.111 372.299 728.333 297.872 582.667 9 1489.79 2915.00 744.925 1457.50 496.649 971.667 372.521 728.750 298.050 583.000 10 1490.68 2916 67 745.369 1458.33 496.946 972.222 372.743 729.167 298.228 583.333 11 1491.57 2918.33 745.813 1459.17 497.242 972.778 372.965 729.583 298.405 583.667 13 1492.46 2920.00 746.257 1460.00 497.538 973.333 373.187 730.000 298.583 584.000 13 1493.35 2921.67 746.701 1460.83 497.834 973.889 373.409 730.417 298.761 584.333 14 1494.24 2923.33 747.145 1461.67 498.130 974.444 373.631 730.8313 298.938 584.667 15 1495.12 2925.00 747.589 1462.50 498.426 975.000 373.853 731.250 299.116 585.000 16 1496.01 2926.67 748.033 1463.33 498.722 975.556 374.075 731.667 299.294 585.333 17 1496.90 2928.33 748.477 1464.17 499.018 976.111 374.297 732.083 299. 471 1 585. 667 18 1497.79 2930.00 748.921 1465.00 199.314 976.667 374. 51 9 ^32. 500 299.649 586.000 19 1498.68 2931.67 749.305 1465.83 499.610 977.222 374.742 732.917 299.827 586,333 20 1499.56 2933.33 749.809 1466.67 499.906 977.778 374.964 733.333 300.004 586.667 31 1500.45 2935.00 750.254 1467.50 500.202 978.333 375.186 733.750 300.182 587.000 22 1501.34 2936.67 750.698 1468.33 500.498 978.889 375.408 734.167 300.360 587.333 23 1502.26 2938.33 751.156 1469.17 500.801 979.444 375 . 637 734.583 300.543 587.667 34 1503.17 2940.00 751.614 1470.00 501.109 980.000 375.866 735.000 300.727 588.000 35 1504.06 2941.67 752.058 1470.83 501.406 980.556 376.088 735.417 300.904 588.333 36 1504.95 2913.33 752.503 1471.67 501.702 981.111 376.310 735.833 301.082 588.667 37 1505.84 2945.00 752.947 1472.50 501.998 981.667 376.532 736.250 301.260 589.000 38 1506.73 2946.67 753.391 1473.33 502.294 982.222 376.754 730.667 301.437 589.333 39 1507.61 2948.33 753.835 1474.17 502.590 982.778 376.977 737.083 301.615 589.667 30 1508.50 2950.00 754.279 1475.00 502.886 983.333 377.199 737.500 301 793 590.000 31 1509.39 2951.67 754.723 1475.83 503.182 983.889 377.421 737.917 301.970 590.333 33 1510.28 2953.33 755.167 1476.67 503.478 984.444 377.643 738.333 302.148 590.667 33 1511.17 2955.00 755.611 1477.50 503.774 985.000 377.865 738.750 302.326 591.000 34 1512.05 2956.67 756.055 1478.33 504.070 985.556 378.087 739.167 302.503 591.333 35 1512.94 2958.33 756.499 1479.17 504.366 986.111 378.309 739.583 302.681 591 . 6(57 36 1513. as 2960.00 756.943 1480.00 504.662 986.667 378.531 740.000 302.859 592.000 37 1514.72 2961.67 757.387 1480.83 504.958 987.222 378.753 740.417 303.036 592.333 38 1515.61 2963.33 757.831 1481.67 505.254 987.778 378.975 740.8:33 303.214 592.667 39 1516.50 2965.00 758.275 1482.50 505.550 988.333 379.197 741.250 303.392 593 000 40 1517.38 2966.67 758.719 1483.33 505.846 988.889 379 419 741.667 303.569 593.333 41 1518.30 2968.33 759.178 1484.17 506.152 989.444 379.649 742.083 303.753 593.607 43 1519.22 2970.00 759.636 1485.00 506.458 990.000 379.878 742.500 303.930 594.000 43 1520.10 2971.67 760.080 1485.83 506.754 990.556 380.100 742.917 304.114 594.333 44 1520.99 2973.33 760.524 1486.67 507.050 991.111 380.322 743.333 304.291 594.607 45 1521.88 2975.00 760.968 1487.50 507.346 991.667 380.544 743.750 304.469 595.000 46 1522.77 2976.67 761.412 1488.33 507.642 992.222 380 766 744.167 304.647 595.333 47 1523.66 2978.33 761.857 1489.17 507.938 992.778 380.988 744.583 304.825 595.667 48 1524.55 2980.00 762.301 1490.00 508.234 993. a33 381.210 745.000 305.002 596.000 49 1525.43 2981.67 762.745 1490.83 508.530 993.889 381.432 745.417 305.180 596.333 50 1526.32 2983.33 763.189 1491.67 508.826 994.444 381.054 745.833 305.358 596.667 51 1527.21 2985.00 763.633 1492.50 509 122 995.000 381.876 746.250 305.535 507.000 53 1528.10 2986.67 764.077 1493.33 509.418 995.556 382.098 746.667 305.713 597.33:3 53 1528.99 2988.33 764.521 1494.17 509.714 996.111 382.320 747.083 305.891 59r.6'i7 54 1529.87 2990.00 764.965 1495.00 510.010 996.667 382. 543 ! 747. 500 306.068 598.000 55 1530.79 2991 . 67 765.4231495.83 510.316 997.222 382.772 747.917 806.253 598.333 50 1531.71 2993.33 765.882 1496.67 510.622 997.778 388.001 748.333 306.43559S.Gf,7 57 1532.60 2995.00 766.326 1497.50 510.918 998.333 383.223 748.750 306.613509.000 58 1533.48 2996.67 766.77'0 1498.33 511 214 998.889 383.445 749.167 306 790 590 . 333 59 153 4. 371-2998. 33 767. 21411499. 17 511.510 999.444 383.667749.583 306.968599.007 104 TABLE XTV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 Curve. 1O Curve. 29 Tan. 2477078 Arc. 483.333 Tan. Arc. Tan. Arc. Tan. 161.811 Arc. 322.222 Tan. 1487368 Arc. M7 211.815 414.286 185.374 302.500 390.00(i o 247.226 483.611 211.942 414.524 185.485 362. 70S 164.909 322.407 148.457 290.107 1 247.374 483.889 212.069 414.762 185.596 362.917 165.008 322.593 148.546 390.333 2 247.522 484.167 212.196 415.000 185.707 303.125 165.107 322.778 148.634 390.500 3 247.670 484.444 212.323 415.238 185.818 363.333 165.206 322.963 148.723 290.607 4 247.818 484.722 212.450 415.476 185.929 363 542 165.305 323.148 148.812 -390.833 5 247.966 485.000 212.577 415.714 186.040 363.750 165.403 323.333 148.901 291.000 6 248.114 485.278 212.704 415.952 186.151 363.958 165.502 3-33.519 148.990 291.167 7 248.262 485.556 212.830 416.190 186.202 364.167 165.601 323.704 149.079 291.333 8 248.410 485.833 212.957 416.429 186.374 364.375 165.700 323.889 149.168 291.500 9 248.559 486.111 213.084 416.667 186.485 364.583 165.798 324 074 149.257 291.667 10 248.707 486.389 213.211 416.905 186.590 364.792 165.897 324.259 149.346 291.833 11 248.855 486.667 213.338 417.143 186.707 365.000 165.996 324.444 149.435 292.000 13 249.003 486.944 213.465 417.381 186.818 365.208 166.095 3-34.630 149.524 292.167 13 249.151 487.222 213.592 417.619 186.929 365.417 166.194 824.815 149.613 292.333 14 249.299 487.500 313.719 417.857 187.040 365.625 166.292 325.000 149.701 292.500 15 249.447 487.778 213.846 418.095 187.151 365.833 166.391 325.185 149.790 292.667 16 249.595 488.056 213.973 418.333 187.262 366.042 166.490 325.370 149.879 292.833 17 249.743 488.333 214.100 418.571 187.373 306.250 166.589 325.556 149.968 293.000 18 249.891 488.611 314.227 418.810 187.485 366.458 166.687 325.741 150.057 293.167 19 250.030 488.889 214.354 419.048 187.596 366.667 166.780 325.926 150.146 293 333 20 250.187 489.167 214.481 419.286 187.707 366 875 166.885 326.111 150.235 293.500 21 1350.336 489.444 214.608 419.524 187.818 367.083 166.984 326.296 150.324 293.667 22' 250.488 489.722 214.739 419.762 187.93-3 367.292 167.086 3-36.481 150.416 293.833 23 250.641 490.000 214.870 420.000 188.047 367.500 167.188 326.667 150.508 294.000 24 250.789 490. 27S 214.997 420.238 188.158 367.708 167.287 3-36.852 150.596 294.167 25 20.937 490.556 215.124 420.476 188.269 307.917 167.385 327.037 150.685 294.333 26 251. C80 490.833 215.251 420.714 188.380 368.125 167.484 327.222 150.774 294.500 27 251.2J34 491.111 215.378 420.952 188.492 368.333 167.583 327.407 150.863 294.667 28 251.382 491.389 215.505 421.190 188.603 368.542 167.682 327.593 150.952 294.633 29 251.530 491.667 215.63-3 421.429 188.714 368.750 167.780 327.778 151.041 295.000 3O 251.678 491.944 215.758 421.667 188.825 368.958 167.879 327.963 151.130 295.167 31 251.826 492.222 215.885 421.905 188.936 369.167 167.978 328.148 151.219 295.333 33 251.974 492.500 216.012 422.143 189.047 369.375 168.077 328.333 151.308 295.500 33 252.1-32 492.778 216.139 422.381 189.158 369.583 168.176 3-38.519 151.397 295.667 34 252.270 493.056 216.266 422.619 189.269 369.792 168.274 328.704 151.486 295 >33 35 252.418 493.333 216.393 422 857 189.380 370.000 168.373 328.889 151.575 296.000 36 252.506 493.611 216.520 423.095 189.491 370.208 168.472 329.074 151.664 296.167 37 25-3.714 493.889 216.647 423.333 189.603 370.417 168.571 329.259 151.752 296.333 38 252.863 494.167 216.774 423.571 189.714 370.625 168.609 329.444 151.841 296.500 39 253.011 494.444 216.901 423.810 189.825 370.833 168.768 329.630 151.930 296.667 40 253.163 494.722 217.032 424.048 189.939 371.042 168.870 329.815 152.022 296.833 41 253.316 495.000 217.163 424.286 190.054 371.250 168.972 330.000 152.114 297. COO 42 253.464 495.278 217.290 424.524 190.165 371.458 169.071 330.185 152.203 297.167 43 253.612 495.556 217.417 424.762 190.276 371.667 169.170 330.370 152.292 297.333 44 253.761 495.833 217.544 425.000 190.387 371.875 169.268 330.556 152.381 297.500 45 253.909 496.111 217.671 425.238 190.499 372.083 169.367 330.741 152.470 297.667 46 254.057 496.389 217.798 425.476 190.610 372.292 169.466 330.926 152.558 297.833 47 254.205 490 607 217.925 425.714 190.721 372.500 169.565 331.111 152.647 298.000 48 254.353 496.944 318.052 425.952 190.832 372.708 169.664 331.296 152.736 298.167 49 254.501 497.22-3 218.179 426.190 190.943372.917 169.76-3 331.481 152.825 298.333 50 254.649 497.500 218.306 426.429 191.054373.125 169.861 331.667 152.914 298.500 51 254.797 497.778 218.433 426.667 191.165373.333 169.960 331.852 153.003 298.667 52 254.945 498.056 218.560 426.905 191.276373.542 170.059 332.037 153.092 298.833 53 255.093 498.333 218.686 427.143 191.387373.750 170.157 332.222 153.181 299.000 54 255.246 498.611 218.818 427.381 191.502373.958 170.259 33-3.407 153.273 299.167 55 255.399 498.889 218.949 427.619 191.617374.167 170.361 332.593 153.364 299.333 5(5 255.547 499.167 219.076 427.857 191.728374.375 170.460 332 778 153.453 299.500 57 255.695 499.444 219.202 428.095 191.839374.583 170. 559 1332. 963 153.542 299.607 58 255.843 499.722 219.3-39 428.333 191.950374.79-3 170.6581333.148 153. 631 1299.833| 59 105 TABLE XIV. ACTUAL TANGENTS, ETC. 30 1 Curve. 2 Curve. Tan. | Arc. 3 Curve. 4 Curve. 5 Curve. M. Tan. Are Tan. Arc. Tan. Arc. Tan. Arc. O 1535.26 3000.00 767.658 1500.00 511.806 1000.00 383.889 750. 000 307. 146 (500. 000 1 1586.15 3001.67 768 . 102 1500.83 512.102 1000.5(5 884. HI 750.417:307.323000.333 2 1537.04 3003.33 7(58.546 1501.67 512.3*$ 1001.11 >:8 1.333 750.833307.501 600.667 3 1587.92 3005.00 768.990 1502.50 512.091 10(11.07 384.. 555 751.250307.679601.000 4 1538.81 3006.67 769.434 1503.33 512.99(1 1 002.2, ! 384.778 751.667 307.856601.333 5 1539.70 3008.33 769.878 1504.17 513.280 1002.78 385.000 752.083 308.034601.607 6 1540.59 3010.00 770.322 1505.00 513.582 1003.33 385.222 752.500 308.212602.000 7 1541 51 3011.67 770.781 1505.83 513.888 1003.89 385.451 752.917 308.395602.333 8 1542.42 3013. M 771.239 1506.67 514.194 1004.44 385 680 753.333 308.579602.067 9 1543.31 3015.00 771.683 1507.50 514.490 1005.00 385.902 753.750 308.756 603.000 | 10 1544.20 3016.67 772.127 1508.33 514.786 1005.56 386.124 754.167 308.934603.333 11 1545.09 3018.33 772.571 1509.17 515.082 1006.11 386.346 754.583 309.112603.667 12 1545.97 3020.00 773.015 1510.00 515.378 1006.67 886.568 755.000 309.289,604.000 13 1546.8(5 3021.67 773.459 1510. as 515.674 1007.22 386.790 755.417 309.467604.333 14 1547.75 3023.33 773 904 1511.67 515.970 1007.78 387.013 755.8.33 309.645604.667 15 1548.64 3025.00 774.348 1512.50 516.266 1008.33 387.235 756.250 309.822605.000 16 1549.53 3026.67 774.792 1513.33 516.562 1008.89 387.457 756.007 310.000:605.333 17 1550.44 -J028.33 775.250 1514.17 516.868 1009.44 387.686 757.083 310.183 605.667 18 1551.3(5 3030.00 775.708 1515.00 517.173 1010.00 387.915 757.500 310.307 606.000 19 1552.25 3031.67 776.153 1515.83 517.469 1010.56 388.137 757.917 310.544 606.333 20 1553.14 3033.33 776.597 1516.67 517.765 1011.11 388.359 758.333 310.722 606.667 21 1554.02 3035.00 777.041 1517.50 518.061 1011.67 388.581 758.750 310.900 607.000 22 1554.91 3036.6; 777.485 1518.33 518.358 1012.22 388.803 759.167 311.077 607.333 23 1555.80 3038.33 777.929 1519.17 518.654 1012.78 389.025 7'59.583 311.255 607.667 24 1556.69 3040.00 778.37'3 1520.00 518.950 1013 33 389.248 760.000 311.488 008.000 25 1557.61 3041. (57 778.831 1520.83 519.255 1013.89 389.477 760.417 311.616 608.333 26 1558.52 W43.33 779.290 1521.67 519.561 1014.44 389.706 760.833 311.800 608 667 27 1559.41 3045.00 779.734 1522.50 519.857 1015.00 389.928 761.250 311.977 609.000 28 1560.30 3046.67 780.178 1523.33 520.153 1015.56 390.150 761.067 312.155 609.333 29 1561.19 3048.33 780.622 1524.17 520.449 1016.11 390.372 762.083 312.333 609.607 30 1562.07 3050.00 781.066 1525.00 520.745 1016.67 390.594 762.500 312.510 010.000 31 1562.96 3051.67 781.510 1525.83 521.041 1017.22 390.816 762.917 312.688 610.333 32 1563.85 3053.33 781.954 1526.67 521.337 1017.78 391.038 763. aS3 312.866 610.667 33 1564.77 3055.00 782.412 1527.50 521.643 1018.33 391.268 763.750 313.049 611.000 34 1565.68 3056.67 782.871 1528. as 521.948 1018.89 391.497 764.167 313.232 611.333 35 1566.57 3058.33 783.315 1529.17 522.245 1019.44 391.719 764.583 313.410 611.667 36 1567.46 3060.00 783.759 1530.00 522.541 1020.00 391.941 765.000 313.588 612.000 37 1568.35 3061.67 784.203 1530.83 522.837 1020.56 392.163 765.417 313.765 612.333 38 1569.24 3063.33 784.647 1531.67 523.1 as 1021.11 392.385 765.833 313.943 612.667 39 1570.12 3065.00 785.091 1532.50 523.429 1021.87 392.607 766.250 314.121 613.000 40 1571.01 3066.67 785.535 1533.33 523.725 1022.22 392.829 766.667 314.299 613.333 41 1571.93 3068.33 785.994 1534.17 o24.030 1022.78 393.059 767.083 314.482 613.667 42 1572.85 3070.00 786.452 1535.00 524.336 1023.33 393.288 767.500 314.665 614.000 43 1573.73 3071.67 786.896 1535.83 524.632 1023.89 393.510 767.917 3M.843 614.333 44 1574.62 3073.33 787.340 1536.67 524 928 1024.44 393.73* 768.383 315.021 614.007 45 1575.51 3075.00 7'87.784 1537.50 525.224 1025.00 393.954 768.750 315.198 615.000 46 1576.40 3076.67 788.228 1538.33 525.520 1025.56 394.176 769.167 315.376,615.333 47 1577.32 3078.33 788.687 1539.17 525.826 1026.11 304.405 769.583 315.. 559: 6 15. 007 48 1578.23 3080.00 789.145 1540.00 5-26.132 1026.67 394.634 770.000 315.743 010.000 49 1579.12 3081.67 789.589 1540.83 526.428 1027.22 394.857 770.417 315.920 616.333 50 1580.01 3083.33 790.033 1541.67 526.724 1027.78 395.079 770.833 :<1 0.008 010 007 51 1580.90 3085.00 790.477 1542.50 527.020 1028.33 395.301 771.250 3H> 276 (517 000 52 1581.78 3086.67 790.921 15-13.33 527.316 1028.89 395.523 771.607 3; 6. 454 017.333 53 1582.67 30S8.33 791.365 1544.17 527.012 1029 44 305.745 77.. 083 3 Hi. 031 017.007 54 55 1583.56 1584.48 3090.00 3091.67 791.809 792.268 1545.00 1545.83 527.908 528.214 1030.00 1030.56 395.967772.500 390.196772.917 316.800 310 002 518 000 51 K. 333 56 15S5.39 3093. 33 792.726 154(5.67 528.519 J031.11 300 425 7 73. 333 ! 3 1 7J7<; sis. 007 57 1586.28 3095.00 793.170 1547.50 528.815 1031.67 39(U)47 77 3. 7'.5() 3 17. 3:.:! 519.000 58 1587.17 3096.67 793.614 1548.33 529.111 1032.22 390.869 774.1(17 317.531 >19.3:-:3 59 1588.06 3098.33 794.058 1549.17 529 407 1032.78 397.092774.583 317.709 019.067 106 TABLE XIV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 Curve. 10 Curve. 3O Tan. Arc. Tan. Arc. Tan. 1 92.061 Arc. 375.000 Tan. 170.756 Arc. 333.333 Tan. 153.720 Arc. M. 255.991 500.000 219.456 428.571 300.000 O 250.139 500.278 219.583 428.810 192.172 375.208 170.855 3:33.519 153.809 300.167 1 250.288 500.556 219.710 429.048 192.283 375.417 170.954 333.704 153.898 300.333 2 256.436 500.833 219.837 429.286 192.394 375.625 171.053 333.889 153.987 300.500 3 256.584 501.111 219.964 429.524 192.506 375.833 171.152 334.074 154.076 300.667 4 256.732 501.389 220.091 429.762 192.617 376.042 171.250 334.259 154.165 300.833 5 256.880 501.667 220.218 430.000 192.728 376.250 171.349 334.444 154.254 301.000 6 857.083 501.944 220.349 430.2138 192.842 376.458 171.451 334.630 154.346 301.167 7 257.186 502.222 220.480 430.476 192.957 376.667 171.553 334.815 154.437 301.333 8 257.334 502.500 220 ..607 430.714 193.068 376.875 171.652 335.000 154.526 301.500 9 257.482 502.778 220.734 430.952 193.179 377.083 171.751 335.185 154.615 301.667 1O 257.630 503.056 220.861 431.190 193.290 377.292 171.849 335.370 154.704 301.833 11 257.778 503.333 220.988 431.429 193.402 377.500 171.948 335.556 154.793 302.000 12 257.926 503.611 221.115 431.667 193.513 377.708 172.047 335.741 154.882 302.167 13 258.074 503.889 221.242 431 . 905 193.624 377.917 172.146 335.926 154.971 302.333 14 258.222 504.167 221.369 432.143 193.735 378.125 172.244 336.111 155.060 302.500 15 258.370 504.444 221.496 432.381 193.846 378.333 172.343 336.296 155.149 302.667 16 258.523 504.72^ 221.627 432.619 193.961 378.542 172.445 336.481 155.240 302.833 17 258.676 505.000 221.758 432.857 194.075 378.750 172.547 336.667 155.332 303.000 18 258.824 505.278 221.885 433.095 194.186 378.958 172.646 336.852 155.421 303.167 19 258.972 505.556 222.012 433.333 194.298 379.167 172.745 337.037 155.510 303.333 20 259.120 505.833 222.139 433.571 194.409 379.375 172.844 337 222 155.599 -303.500 21 259.268 506.111 222.266 433.810 194.520 379.583 172.942 33?! 407 155.688 303.667 22 259.416 506.389 222 393 434.048 194.631 379.792 173.041 337.593 155.777 303.833 23 259 564 506.667 222.519 434.286 194. 742 380.000 173.140 337.778 155.866 304.000 24 259.717 506.944 222.651 434.524 194.857 380.208 173.242 337.963 155.958 304.167 25 259.870 507.222 222.782 434.762 194.971 380.417 173.344 338.148 156.049 304.333 26 260.018 507.500 222.909 435.000 195.082 380.625 173.443 338.333 156.138 304.500 27 260.166 507.778 223.035 435.238 195.193 380.833 173.541 338.519 156.227 304.667 28 260.314 508.056 223.162 435.476 195.305 381.042 173.640 338.704 156.316 304.833 29 260.462 508.333 223 289 435.714 195.416 381.250 173.739 338.889 156.405 305.000 30 260.611 508.611 223.416 435.952 195.527 381.458 173.838 339.074 156.494 305.167 31 260.759 508.889 223.543 436.190 195.638 381.667 173.936 339.259 156.583 305.333 32 260.911 509.167 223.674 436.429 195.753 381.875 174.038 339.444 156.675 305.500 33 261.064 509.444 223.805 436.667 195.867 382.083 174.140 339.630 156.766 305.667 34 261.212 509.722 223.932 436.905 195.978 382.292 174.239 339.815 156 855 305.833 35 261.361 510.000 224.059 437.143 196.089 382.500 174.338 340.000 156.944 306.000 36 261.509 510.278 224.186 437.381 196.201 382.708 174.437 340.185 157.033 306.167 37 261.657 510.556 224.313 437.619 1% 312 382.917 174.535 340.370 157.122 306.333 28 261.805 510.833 224.440 437.857 196.423 383.125 174.634 340.556 157.211 3C6.500 39 261.953 511.111 224 567 438.095 196.534 383.333 174.733 340.741 157.300 306.667 40 262.106 511.389 224.698 438. 333 196.649 383.542 174.835 340.926 157.392 306 833 41 262.259 511.667 224.829 438.571 196.763 383.750 174.937 341.111 157.484 307.000 42 262.407 511.944 224.956 438.810 196.874 383 958 175.036 341.296 157.573 307.167 43 262.5.55 512.222 225.083 439.048 196.985 384.167 175.134 341.481 157.661 307.333 44 262.703 512.500 225.210 439.286 197.097 384.375 175.233 341.667 157.750 307.500 45 262.851 512.778 225.337 439.524 197.208 384.583 175.332 341.852 157.839 307.667 46 263.004 513.056 225.468 439.762 197.322 384.792 175.434 342.037 157.931 307.833 47 263.157 513.333 225.599 440.000 197.437 385.000 175.536 342 222 158.023 308.000 48 263.305 513.611 225.726 440.238 197.548 385.208 175.635 342.407 158.112 308.167 49 263.453 513.889 225. 853 440.476 197.659 385.417 175.734 342.593 158.201 308.333 50 263.601 514.167 2:25.980 440 714 197.770 385.625 175.832 342.778 158.290 308.500 51 263.749 514.444 226.107 440.952 197.881 385.833 175.931 342.963 158.379 308.667 52 263 897 514.722 226.234 441.190 197.993 386.042 176.030 343.148 158.467 '308.833 53 264.045 515.000 226.361 441.429 198.104 386.250 176.129 343.333 158.556 309.000 54 264.198 515.278 226.492 441.667 198.218386.458 176.231 343.519 158.648 309.167 55 264.351 515.556 226.623 441.905 198. 333 1386. 667 176 333 343.704 158.740 309.333 56 264.499 515.833 226.750 442.143 198.444336.875 176.431 343.889 158.829 309.500 57 264.647 516.111 226.877 442.381 198.555387.083 176.530 344.074 158.918 309.667 58 264.795 516.389 227.004 442.619 198.666387.292 176.629 344.259 159.007 309.833 59 107 TABLE XIV. ACTUAL TANGENTS, ETC. 31 1 Curve. 2 Curve. 3 Curve. 4 Curve. 5 Curve. M. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. O 1588.95 3100.00 794.502 1550.00 529.103 1033.33 397.314 715.000 317.8S6 6^U.OOO 1 1 589. 8(5 3101.67 794.961 1550.83 530.009 1033.89 397.543 775.417 318.070 020.333 2 1590.78 3103.33 795.419 1551.67 530.315 1034.44 397.772 775.833 318.253 620.667 3 1591.07 3105.00 795.863 1552.50 530.611 1035.00 397.994 776.250 318.431 621.000 4 1593.56 3106.67 796.307 1553.33 530.907 1035.56 398.216 776.667 318.609 621.333 5 1593.44 3108.33 796 751 1554.17 531.203 1036.11 398.438 777.083 318.786 021.667 6 1594.33 3110.00 797^195 1555.00 531.499 1036.67 398.600 777.500 318.964 G--22.000 7 1595.25 3111.67 797.654 1555.83 531 . 804 1037.22 398.890 777.917 319.147 622.333 8 1596.17 3113.33 798.112 1556.67 532.110 1037.78 399.119 778.333 319.331 622.607 9 1597.05 3115.00 798.556 1557.50 532.406 1038.33 399.341 778.750 319.508 623.000 1O 1597.94 3116.67 799.000 1558.33 532.702 1038.89 399.563 779.167 319.686 623.333 11 1598.86 3118.33 799.459 1559.17 533 COS 1039.41 399.792 779.583 319.869 623.667 12 1599.78 3120.00 799.91? 1560.00 533.313 1040.00 400.021 780.000 3-20.053 624.000 13 1600.66 3121.67 800.3(51 1560.83 533.609 1040.56 400.243 780.417 320.231 624.333 14 1601.55 3123.33 800.805 1561.67 533.906 1041.11 400.406 780.833 320.408 624.667 15 1602.44 3125.00 801.249 1562.50 53 1. 202 1011.67 400.688 781.250 320.586 625.000 16 1603.33 3126.67 801.693 1563.33 534.498 1012.22 400.910 781 . 667 320.764 625.333 17 1604.24 3128.33 802.152 1564.17 534.803 1042.78 401 . 139 782.083 320.947 625.667 18 1605.16 3130.00 802.610 1565.00 535.109 1043.33 401 . 368 782.500 321.130 626.000 19 1606.05 3131.67 803.054 1565.83 535.405 1013.89 401.590 ; 82. 917 321.308 626.333 20 1606.91 3133.33 803.498 1566.67 535.701 1044.41 401.812 783.333 321.486 626.667 21 1607.83 3135.00 803 942 1567.50 535.997 1015.00 403.031 783.750 321.663 627.000 22 1608.71 3136.67 804.386 1568.33 536.293 1045.56 402 250 1-84.161 321.841 627.333 23 1609.63 3138.33 804.845 1569.17 536.599 1046.11 402.486 784.583 322.024 627.667 34 1610.55 3140.00 805.303 1570.00 536. 90 J 1040.07 402.715 785.000 322.208 628.000 25 1611.44 3141.67 805.747 1570.83 387.300 1047.22 402.937 785.417 322.386 628.333 26 1612.32 3143.33 806.191 1571.67 537.497 1047.78 403.159 785.833 322.563 628.667 21 1613.24 3145.00 806.650 1572.50 537.802 1048.33 103.388 786.250 322.747 629.000 28 1614.16 3146.67 807.108 1573.33 538.108 1048.89 403.617 786.667 322.930 629.333 29 1615.05 3148.33 807.552 1574.17 538.404 1049.44 403.839 787.083 323.108 629.667 3O 1615.93 3150.00 807.996 1575.00 538.700 1050.00 404.06-2 787.500 323.285 630.000 31 1616.82 3151.67 808.440 1575.83 533.996 1050.56 404.284 787.917 323 463 630.333 32 1617.71 3153.33 808.884 1576.67 539.292 1051.11 404.506 788.333 323.641 630.667 33 1618.63 3155.00 809.343 1577.50 539.598 1051.67 404.735 788.750 323.824 631.000 34 1619.54 3156.67 809.801 1578.33 539.903 1052.22 404.964 789.107 324.008 631.333 35 1620.43 3158.33 810.245 1579.17 540.199 1052.7H 405.186 789.583 324.185 631.667 36 1621.32 3160.00 810.689 1580.00 540.495 1053.33 405.408 790 000 324.363 632.000 37 1622.24 3161.67 811.148 1580.83 540.801 1053.89 405.638 790.41? 3-24.546 032.333 38 1623.15 3163.33 811.606 1581.67 541.10"7 1054.44 405.867 790.832 324.730 632.667 39 1624.04 3165.00 812.050 1582.50 541.403 1055.00 \ 06. 089 791.250 324.907 033.000 40 1624.93 3166.67 812.491 15S3.P.3 541.699 1055.56 406.311 791.667 325.085 033.333 41 1625.82 3168.33 81 2. 93 s 1584.17 541.995 1056.11 406.533 792.083 3-25.263 033.667 43 1626.70 3170.00 813.382 1585.00 542.291 1056.67 406.755792.500 325.440 034.000 43 1627.62 3171.67 813.841 1585.83 542.596 1057.22 406. 984 '792. 91 7 325.624 034.333 44 1628.54 3173.33 814.299 1586.67 542.902 1057.78 407.213:793.333 325.807 034.607 45 1629.43 3175.00 814.743 1587.50 543.198 1058.33 407.436,793.750 325.985 035.000 46 1630.31 3176.67 815.187 1588.33 543.494 1058.89 407. 058i 794. 167 326.108 035.333 47 1631.23 3178.33 815.646 1589.17 543.800 1059.44 407. 887! 794. 583 326.346 035.007 48 1632.15 3180.00 816.104 1590.00 544.105 1060.00 408. 1 16 ' 795. 000 326.529 036.000 49 1633.04 3181.67 816.548 1590.83 544.401 1060.56 408. 338:795. 417 326.707 636.333 50 1633.92 3183.33 816.992 1591.67 544.698 1061.11 408.560795.833 326.885 636.667 51 1634.84 3185.00 817.450 1592.50 545.003 1061.67 408.789 79G.250 327.068 037.000 52 1635.76 3186.67 817. 909 11593. 33 545.309 1062.22 409.019 796.607 327.251 037.333 53 1636.65 3188.33 818.35311594.17 545.605 1062.78 409.241 797.083 327.429 037.007 54 1637.53 3190.00 S18.797' 1595.00 545.901 1063.33 409. 463 5 797. 500 227.607 038.000 55 1638.45 3191.67 319.255 1595.83 546.20(5 1063.89 409.692:797.917 327.790 038.333 56 1639.37 3193.33 819.714 1596.67 546.512 1064.44 409 92 1 798 . 333 327 . 974 038.607 57 1640.26 3195.00 820.15811597.50 546.808 1065.00 410.143 T98. 750 328. 151 039.000 58 1641.14 3196.67 820.602 1598.33 547.104 1005.56 410.305 799.167 328.329039.333 59 1642.06 3198.33 821.060 1599.17 547.410 1066.11 410.595,799.583 328. 512 1039. 607 108 TABLE XIV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 Curve. 1O Curve. 31 Tan. 204.943 Arc. 516.667 Tan. 227.131 Arc. Tan. Are. Tan. Arc. Tan. 15970~96 Arc. 310.000 M. ~o 442.857 198.777 387.500 176.758 344.444 265.096 516.944 227.262 443.095 198.892 387.708 176.830 344.630 159.187 310.167 i 265.249 517.222 227.393 443.333 199.007 387.917 176.932 344.815 159.279 310.333 2 265.397 517.500 227.520 443.571 199.118 388.125 177.030 345.000 159.368 310.500 3 265.545 517.778 227.647 443.810 199.229 388.333 177.129 345.185 159'. 457 310.667 4 265.693 518.056 227.774 444.048 199.340 388.542 177.228 345.370 159 546 310 833 5 965.841 518.333 227.900 444.286 199.451 388.750 177.327 345.556 159.635 311.000 6 265.994 518.611 228.031 444.524 199.566 388.958 177.429 345.741 159.727 311.167 7 266.147 518.889 228.163 444.762 199.681 389.167 177.531 345.926 159.819 311.333 8 266.295 519.167 228.289 445.000 199.792 389.375 177.629 346.111 159.907 311.500 9 266.443 266.596 519.441 519.722 228.416 228.547 445.238 445.476 199.903 200.017 389.583 389.792 177.728 177.830 346.296 346.481 159.996 160.088 311 667 311.833 10 11 266.749 520.000 228.679 445.714 200.132 390.000 177.932 346.667 160.180i312.000 12 266.89? 52 J. 278 228.805 445.952 200.243 390.208 178.031 346.852 160.269 312.167 13 267.045 520.556 228.932 446.190 200.354 390.417 178.130 347.037 160.358 312.333 14 267.193 520.833 229.059 446.429 200.465 390.625 178.228 347.222 160.447 312.500 15 267.341 521.111 229.186 446.667 200. 57( 390.833 178.327 347.407 160.536 312.667 16 267.494 521.389 229. 31 7! 446. 905 200.691 391.042 178.429 347.593 160.627 312.833 17 267.647 521.667 2^9.448 447.143 200.806 391.250 178.531 347.778 160.719 313.000 18 267.795 521.944 229.575 447.381 200.917 391.458 178.630 347.963 160.808 313.167 19 267.943 522.222 229.702 447.619 201.028 391.667 178.729 348.148 160.897 313.333 20 268.091 522.500 229.829 447.857 201.139 391.875 178.827 348.333 160.986 313.500 21 268.239 522.77'8 229.956 448.095 201.250 392.083 178.926 348.519 161.075 313.667 22 268.392 523.056 230.087 448.333 201.365 392.292 179.028 348.704 161.167 313.833 23 268.545 523.333 2:30.218 448.571 201 .480 392.500 179.130 348.889 161.258 314.000 24 268.693 523.611 230.345 448.810 201.591 392.708 179.229 349.074 161.347 314.167 25 268.841 523.889 230.472 449.048 201.702 392.917 179.328 349.259 161.436 314.333 26 268.994 524.167 230.603 449.286 201.817 393.125 179.430 349.444 161.528 314.500 27 269.147 524.444 J30.734 449 524 201.931 393.333 179.532 349.630 161.620 314.667 28 269.295 524 722 230.861 449.762 202.042 393.542 179.630 349.815 161.709 314.833 29 269.443 525.000 230.988 450. OCO 202.153 393.750 179.729 350.000 161.798 315.000 30 269.591 525.278 231.115 450.238 202.265 393.958 179.828 350.185 161.887 315.167 31 269.739 525.556 231.242 450.476 202.376 394.167 179.927 350.370 161.976 315.333 32 269.892 525.833 231.373 450.714 202.490 394.375 180.029 350.556 162.067 315.500 33 270.045 526.111 231.504 450.952 202.605 394.583 180.131 350.741 162.159 315.667 34 270.193 526.389 881.681 451.190 202.716 394.792 180.229 350.926 162.248 315.833 35 270.341 526.667 231.758 451.429 202.827 395.000 180.328 351.111 162.337 316.000 36 270.494 526.944 231.889 451.667 202.942 395.208 180.430 351.296 162.429 316.167 37 270.647 527.222 232.020 451.905 203.057 395.417 180.532 351.481 162.521 316.333 38 270.795 527.500 232.147 452.143 203.168 395.625 180.631 351.667 162.610 316.500 39 270.943 527.778 232.274 452.381 203.279 395.833 180.730 351.852 162.698 316.667 40 271.091 528.056 332.401 452.619 203.390 396.042 180.828 352.037 162.787 316.833 41 271.239 528.333 232.5-<8 452.857 203.501 396.250 180.927 352.222 162.876 317.000 42 271.392 528.611 232.659 453.095 203.616 396.458 181.029 352.407 162.968 317.167 43 271.545 528.889 .232.790 453.333 203.730 396.667 181.131 352.593 163 060 317.333 44 271.693 529.167 232.917 453.571 203.841 396.875 181.230 352.778 163.149 317.500 45 271.841 529.444 233.044 453.810 203.953 397.083 181.329 352.963 163.238 317.667 40 271.994 529.722 233.175 454.048 204.067 397.292 181.431 353.148 163.329 317.833 47 272.147 530.000 <233.306 454.286 204.182 397.500 181.533 353.333 163.421 318.000 48 272.295 530.278 233.433 454.524 204 293 397.708 181.631 353.519 163.510 318.167 49 272 443 ^30.556 233.560 454.762 204.404 397.917 181.730 353.704 163.599 318.333 5O 272 ! 696 530.833 233.691 455.000 204.519 398.125 181.832 353 889 163.691 318.500 51 272.749 531.111 233.822 455.238 204.633 398.333 181.934 354.074 163.783 318.667 52 272.897531.389 233.949 455.476 204.745 398.542 182.033 354,259 163.872 318.833 53 273.045531.667 234.076 455.714 204.856 398.750 182.132 354.444 163.9(1 319.000 54 273.1981531.944 234.207455.952 204.970 398.958 182 234 354 630 164.052 '319.167 55 273. 350 1532.222 234.338450.190 205.085 399.167 182.336 354.815 164.144 319.333 5C> 273.498532.500 234. 465'456. 429 205.196 399.375 182.434 355.000 164.233 319.500 57 273.6471532.778 234.592456.667 205.307 399.583 182.533 355. 1R5 164.322 319.667 58 273. 7 99 1533.056 234.723456.905 205.422 399.792 182.635 355.370 164.414 319.833 59 109 TABLE XIV. ACTUAL TANGENTS, ETC. 32 1 Curve. 3 Curve. 3 Curve. 4 Curve. 5 Curve. M. ~~O" Tun. T642.98 Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. 3200. 00 821.519 1600.00 547.715 1066.67 410.824 800.000 328.696 640.000 1 1643.87 3. '01. 67 821.963 1600.83 548.012 1067.22 411.046 800.417 328.873 640.333 3 1644.75 3203.33 822.407 1601.67 548.308 1067.78411.208 800.833 329.051 640.667 3 1645.67 3205.00 822.865 1602.50 548.613 1068.33 411.497 801.250 329.235 641.000 4 1646.59 3206.67 823.324 1603. 33 548.919 1068.89 411.726 801.667 329.418 641.333 5 1647 47 3208.33 823.768 1604.17 549.215 1069.44 411.919 802.083 329.590 641.667 6 1648.315 3210.00 824.212 1605.00 549.511 1070.00 412.171 802.500 329.773 642.000 7 1649.25 3211.67 824.656 1605.83 549.807 1070.56 412.393 802.917 329.951 642.333 8 1650.1-1 3213.33 825.100 1606.67 550.103 1071.11 412.615 803.333 330.129 642.667 9 1651.06 3215.00 825.558 1607.50 550.409 1071.67 412.844 803.750 330.312 643.000 10 1651.97 3216.67 826.017 1608.33 550.714 1072.22 413.073 804.167 330.495 643.333 11 1652.89 3218.33 826.475 1609.17 551.020 1072.78 413.302 804.583 330.679 643.607 13 1653.81 3220.00 820.933 1610.00 551.325 1073.33 413.532 805.000 330.862 644.000 13 1654.69 3221.67 827.377 1610.83 551.622 1073.89 413.754 805.417 331.040 644.333 14 1655.58 3223.33 827.822 1611.67 551.918 1074.44 413.976 805.833 331.218 644.667 15 1656.50 3225.00 828.280 1612.50 552.223 1075.00 414.205 806.250 331.401 645.000 10 1657.42 3226.67 828.738 1613.33 552.529 1075.56 414.434 806.667 331.584 645.333 17 1658.30 3228.33 829.182 1614.17 552.825 1076.11 414.656 807.083 331.762 645.667 18 1659.19 3230.00 829.626 1615.00 553.121 1076.67 414.878 807.500 331.940 646.000 19 1660.11 3231.67 830.085 1615.83 553.427 1077.22 415.108 807.917 332.123 646.333 30 1661.03 3233.33 830.543 1616.67 553.732 1077.78 415.337 808.333 332.307 646.667 21 1661.91 3235.00 830.987 1617.50 554.028 1078.33 415.559 808.750 332.484 647.000 22 1662.80 3236.67 881.481 1618. as 554.324 1078.89 415.781 809.167 332.662 647.333 23 1663.72 3238.33 831.890 1619.17 554.630 1079.44 416.010 809.583 332.845 647.667 24 1664.64 3240.00 832.348 1620.00 554.936 1080.00 416.239 810.000 333.029 648.000 25 1665.52 3241.67 832.792 1620.83 555.232 1080.56 416.461 810.417 333.206 648.333 26 1666.41 3243.33 833.236 1621.67 555.528 1081.11 416.081 810.833 333.881 648.667 37 1667.33 3245.00 833.695 1622.50 555.833 1081.67 416.913 811.250 388.667 649.000 28 1668.24 3246.67 834.153 1623.33 556.139 1082.22 417.142 811.667 333.751 649.333 29 1669.13 3248.33 834.597 1624.17 556.435 1082.78 417.364 812.083 333.929 649.667 30 1670.02 3250.00 835.041 1625.00 556.731 1083.33 417.586 812.500 334.106 650.000 31 1670.94 3251.67 835.500 1625.83 557.037 1083.89 417.815 812.917 334.290 650.333 32 1671.85 3253.33 835.958 1626.67 557.342 1084.44 418.045 813.333 334.473 650.667 33 1672.74 3255.00 836.402 1627.50 557.638 1085.00 418.267 813.750 334.651 651.000 34 1673.63 3256.67 836.846 1628.33 557.934 1085.56 418.489 814.167 334.828 651.333 35 1674.55 3258.33 837.304 1629.17 558.240 1086.11 418.718 814.583 135.012 651.667 36 1675.46 3260.00 837.763 1630.00 558.546 1086.67 418.947 815.000 335.195 652.000 37 1676.38 3261.67 838.221 1630.83 558.851 1087.22 419.176 815.417 335.379 652.333 38 1677.30 3263.33 838.680 1631.67 559.157 1087.78 419.406 815.833 835.563 652.667 39 1678.19 3265.00 839.124 1632.50 559.453 1088. 33 419.628 816.250 335.740 653.000 4O 1679.07 3266.67 839.568 1633.33 559.749 1088.89 419.850 816.667 335.917 653.333 41 1679.99 3268.33 840.026 1634.17 560.055 1089.44 420.079 817.083 336.101 653.667 43 1680.91 3270.00 840.485 1635.00 560.360 1090.00 420.308 817.500 336.284 054.000 43 1681.80 3271.67 840.929 1635.83 560.656 1090.50 420.530 817.917 336.462 654. 333 44 1682.68 3273.33 841.373 1636.67 560.952 1091.11 420.752 818.333 336.640 654.667 45 1683.60 3275.00 841. as i 1637.50 561.258 1091.67 420.982 818.750 336.823 655.000 46 1684.52 3276.67 842.289 1638.33 561.564 1092.22 421.211 819.167 337.006 655.833 47 1685.43 3278.33 842.748 1639.17 561.869 1092.78421.440 '819.583 337.190 655.667 48 1686.35 3280.00 843.206 1610.00 562.175 1093.33421.669 820.000 337.373 656.000 49 1687.24 3281.67 843.650 1640.83 562.471 1093.89 421.891 820.417 337.551 656.333 5O 1688.13 3283.33 844.094 1641.67 562.767 1094.44 422.113 820.833 337.728 656.607 51 1689 04 3285.00 844.553 1642.50 563.072 1095.00422.343 821.250 337.912 657.000 53 1689.96 3286.67 845.011 1643.33 563.378 1095.56422.572 821.667 338.095 657.333 53 1690.85 3288.33 845.455 1644.17563.674 1096.lli422.794 822.083 338.273 657.667 54 1691.74 3290.00 845.899 1645.00 563.970 1096.67:423.016 822.500 338.451 658.000 55 1692 65 3291.67 846.358 1645.83 564.276 1097.22 423.245 822.917 338.634 658.333 56 1693.57 3293.33 846.816 1 646 . 67 564 . 58 1 1 1 097 . 78 423 . 475 823.333 338.817 658.667 57 1694.49 3295.00 847.274 1647.50 564.887 1098.33 423.704 823.750 339.001 659.000 58 1695.40 3296.67 847.733 1648.33 565. 193 1 1098. 89 423.933 824.167 339.184 659.333 59 1696.29 3298.33 848.177 1649.17 565.48911099.44 424.155 824 583 339.362 659.667 110 TABLE XIV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 Curve. 1O Curve. 32 M. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. | Arc. 273.952 533.333 234.854 457.143 205.537 400.000 182.737 355.556 10 4. 506 320.0i() ~o~ 274.100 533.611 234.981 457.381 205.648 400.208 182.836 355.741 164.594320.167 1 274.218 533.889 235.108 457.619 205.759 400.417 182.935 355.926 164.683320.333 2 274.401 534.167 235.239 457.857 205.874 400.625 183.037 356.111 164.775320.500 3 274.554 534.444 235.3701458.095 205.988 400.833 183.139 356.296 164.867 320.067 4 274.702 534.722 235.497 458.333 206.099 401.042 183.237 356.481 164.956 320.833 5 274.850 535.001) 235.624 458.571 206.210 401.250 183.336 356.667 165.045 321.000 6 274.998 535.278 235.751 458.810 206.321 401.458 183.435 356.852 165.134 321 . 107 7 275.147 535.55(5 235.878 459.048 206.433 401.667 183.534 357.037 105.223 321.333 8 275.299 535.833 236.009 459.286 206.547 401.875 183.636 357.222 165.314 321.500 9 275.452 536.111 236.140 459.524 206.662 402. 083 183.738 357.407 165.406 321.667 10 275.605 536.389 236.271 459.762 206.777 402.292 183.840 357.593 165.498 321.833 11 275.758 536.667 236 402 460.000 206.891 402.500 183.942 357.778 165.590 322.000 12 275.906 536.944 236.529 460.238 207.002 402.708 184.040 357.963 165.679 322.167 13 276.054 5*7.222 236.656 460.476 207.114 402.917 184.139 358.148 165.768 322.333 14 276.207 537.500 236.787 460.714 207.228 403.125 184.241 358.333 165.859 322.500 15 276.360 537.778 236.918 460.952 207.343 403.333 184.343 358.519 165.951 322.667 16 276.508 538.056 237.045 461.190 207.454 403.542 184.442 358.704 166.040 322.833 17 276.656 538.333 237.172 461.429 207.565 403.750 184.541 358.889 166.129 323.000 18 276.809 538.611 237.303 461.667 207.680 403.958 184.643 359.074 166.221 323.167 19 276.962 538.889 237.434 461.905 207.794 404.167 184.745 359.259 166.313 323.333 2O 277.110 539.167 237.561 462.143 207.906 404.375 184.843 359.444 166.402 323.500 21 277 258 539.444 237.688 462.381 208.017 404.583 184.942 359.630 166.491 323.667 22 277.411 539.722 237.819 41)2.01!) 208.131 404.792 185.044 359.815 166.582 323.833 23 277.564 540.000 237.950 462.857 208.246 405 .DOO 185.146 360.000 166.674 324.000 24 277.712 540.278 238.077 463.095 208.357 405.208 185.245 360.185 166.763 321.167 25 277.860 540.556 238.204 463.333 208.468 405.417 185.344 300.370 166.852 324.333 26 27'8.013 540. 833 238.335 463.571 208.583 405.625 185.446 360.556 166.944 324.500 27 278.165 541.111 238.466 463.810 208.698 405.833 185.547 360.741 167.036 324.667 28 278.314 541.389 238.593 464.048 208.809 406.042 185.646 360.926 167.124 324.833 29 278.462 541.667 238 720 464.286 208.920 406.250 185.745 361.111 167.213 325.000 30 278.615 541.944 238.851 464.524 209.025 406.458 185.847 361.296 167.305 325.167 31 278.767 542.222 238.98^ 464.762 209.149 406.667 185 949 361.481 167.397 325.333 32 278.915 542.500 239.109 465.000 209.260 406.875 186.048 361.667 167.486 325.500 33 279.064 542.778 239.236 465.238 209.371 407.083 186.147 361.852 167.575 325.667 34 279.216 543.056 239.367 465.476 209.486 407.292 186.248 362.037 167.667 325.833 35 279.369 543.333 239.498 465.714 209.601 407.500 186.350 362.222 167.758 326.000 36 279.522 543.611 239 629 465.952 209.715 407.708 186. 4521362. 407 167.850 326.167 37 27'9.675 543.889 239.760 466.190 209.830 407.917 186.554 362.593 167.942 326.333 38 279.823 544.167 239.887 466.429 209.941 408.125 186.653 362.778 168.031 326.500 39 279.971 544.444 240.014 466.667 210.052 408.333 186.752 362.963 168.120 326.667 4O 2H0.124 544.722 240.145 466.905 210.167 408.542 186.854 363.148 168.212 326.833 41 280,277 545.000 240.276 467.143 210.282 408.750 186.956 363.333 168.303 327.000 42 280. 425 '545. 278 240.403 467.381 210.39: J , 408.958 187.055 363.519 168.392 327.167 43 280. 57 3 '545. 550 240.530 467.619 210.504 409.167 187.153 363.704 168.481 327.333 44 280.726515.8*3 240.661 467.857 210.619 409.375 187.255 363.889 168.573 327.500 45 280.879 546.111 240.792 468.095 210.733 409.583 187.&57 364.074 168.665 327.667 46 281.032 546.389 240.923 468.333 210.848 409.792 187.459 364.259 168.757 327.833 47 281.184 546.66; 241.054 4(58.571 210 063 410.000 187.561 364.444 168.848 328.000 48 281.333 546.944 241.181 468.810 211 074 410.20,^ 187.660 364.630 168.937 328.167 49 281.481 547.222 241.308 469 048 211.185 410.417 187.759 364.815 169.026 328.333 5O 281.633 547.500 241.430 4U9.286 211.300 410.625 187.861 365.000 169.118 328.500 51 281.786 547.778 241.570 469.524 211.414 410.833 187.963 365.185 169.210 328.667 52 281.934 548.056 241.697 469.762 211.525 411.042 188.062365.370 169.299 328.833 53 282.082 548.333 241.824 470.000 211.636 411.250 188.160 365.556 169.388 329.000 54 282.235 548.611 241.955 47'0.238 211.751 411.458 188.262 365.741 169.479 329.167 55 82.388 548.889 242.086470.476 211.806 411.667 188.364 365.926 169.571 329.333 56 282.541 549.167 242.217470.714 211.980 411.875 188.466 366.111 169.663 329.500 57 282.694 549.444 242.348470.952 212.095 412.083 188.568 366.296 169.755 329.667 58 282.842 549.722 242.475471.190 212.206 412.292 188.667 366.481 169.844 329.833 59 111 TABLE XIV. ACTUAL TANGENTS, ETC. 33 1 Curve. 2 Curve. 3 Curve. 4 Curve. 5 Curve. M. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. ~~O~ 1697.16 3300.00 848.62 1650. OC 565.785 1100.00 424.377 825.00< 339.540 660.000 1 1698.10 3301.67 849.079 1650.82 566.090 1100.56 424.606 825.417 339.723 660.333 2 1699.01 3303.33 849.538 1651.6? 566.396 1101.11 424.836 825.833 339.906 660.667 3 1699.93 3305.00 849.996 1652.50 566.702 1101.67 425.065 826.250 340.090 661.00D 4 1700.85 3306.67 850.454 1653.33 567.007 1102.22 425.294 826.667 340.273 661.333 5 1701.73 3308.33 850.899 1654.17 567.303 1102.78 425.516 827.08? 340.451 661.667 6 1702.62 3310.00 851.343 1655.00 567.599 1103.33 425.738 827.500 340.629 662.000 7 1703.54 3311.67 851.801 1655.83 567.905 1103.89 425.967 827.917 340.812 662.333 8 1704.46 3313.33 852.259 1656.67 568.211 1104.44 426.197 828.333 340.995 662.067 9 1705.37 3315.00 852.718 1657.50 568.516 1105.00 426.426 828.750 341.179 663.000 10 1706.29 3316.67 853.176 1658.33 568.822 1105.56 426.655 829.167 341.362 663.333 11 1707.18 3318.33 853 620 1659.17 569.118 1106.11 426.877 829.583 341.540 663.667 12 1708.0? 3320.00 854.064 1660.00 569.414 1106.67 427.099 830.000 341.718664.000 13 1708.98 3321.67 854.523 1660.83 569.720 1107.22 427.328 830.417 341.901 664.333 14 1709.90 3323.33 854.981 1661.67 570 025 1107.78 427.558 830.833 342.084664.667 15 1710.82 3325.00 855.439 1662.50 570.331 1108.33 427 787 831.250 342.268 665.000 1(> 1711.73 3326.67 855.898 1663.33 570.636 1108.89 428.' 01 6 831.667 342. 451 '665. 333 17 1712.62 3328.33 856.342 1664.17 570.932 1109.44 428.238 832.083 342.629'665.667 18 19 1713.51 1714.43 3330.00 3331.67 856.786 857.244 1665.00 1665.83 571.229 571.534 1110.00 1110.56 428.460 428.690 832.500 832.917 342.806 342.990 666.000 666.333 30 1715.34 3333.33 857.703 1666.67 571.840 1111.11 428.919 833.333 343.173 666.667 31 1716.26 3335.00 858.161 1667.50 572.145 1111.67 429.148 833.750 343 357667.000 22 1717.18 3336.67 858.620 1668.33 572.451 1112.22 429.377 834.167 343.540667.333 23 24 1718.06 1718.95 3338.33 3340.00 859.064 859.508 1669.17 1670.00 572.747 573.043 1112.78 1113.33 429.599 429.821 834.583 835.000 343.718607.667 343.895668.000 25 1719.87 3341.67 859.966 1670.83 573.349 1113.89 430.051 835.417 344.079668.333 3(> 1720.79 3343. 33 860.424 1671.67 573.654 1114.44 430.280 835.833 344.262 668.667 27 721.70 3345.00 860.883 1672.50 573.960 1115.00 430.509 836.250 344.446 669.000 38 722.62 3346.67 861.341 1673.33 574.266 1115.56 430.788 836 667 314.629 669.333 29 723.54 3348.33 861.800 1674.17 574.571 1116.11 430.967 837.083 344.812 669.667 30 724.45 3350.00 862.258 1675.00 574.877 1116.67 431.197 837.500 344.996 670.000 31 725.34 3351.67 862.702 1675.83 575.173 1117.22 431.419 837.917 345.174 670.333 32 726.23 3353.33 863.146 1676.67 575.469 1117.78 431.641 838.333 345.351 67'0.667 33 7*7.15 3355.00 863.604 1677.50 575.775 1118.33 431.870 838.750 345.535 671.000 34 728.06 3356.67 364.063 678.33 576.080 1118.89 432.099 839.167 345.718 671.333 35 728.98 3358.33 864.521 679.17 576.386 1119.44 432.329 839.583 345.901 671.667 36 729.90 3360.00 864.980 1680.00 576.691 1120.00 432.558 840.000 346.085 672.000 37 730.81 3331.67 865.438 680.83 576.997 1120.56 432.787 840.417 346.268 672.333 38 731.73 3i)3.33 865.896 1681.67 577.303 .121.11 433.016 810.833 34(5.452 072.667 39 732.62 365.00 866.341 1682.50 577.599 1121.67 433.238 841.250 346.629 673.000 4O 733.51 366.67 66.785 683.33 577.895 1122.22 433.460 841.667 340.807 673.333 41 731.42 368.331867.243 1684.17 578.200 1122.78 33.090 S42.083 346.990 673.667 43 735.34 370.00867.701 1685.00 578.506 1123.33 433.919 842.500 347.174 674.000 43 736. 26 371 67868.160 685.83578.812 1123.89 34.148 812.917 347.357 074.333 44 737.17 3373.33 363.618 686.67 579.117 1124.44 34.377 843.333 347.541 674.667 45 733.09 3375.00 869.077 687.50 579.423 1125.00 434.607 843.750 347.724 075.000 4 a 739.01 3376.67 809.535 688.33 579.728 1125.56 34.83(5 844.167 347.907 675.333 47 739.89 3378.33 869.979 689.17 580.024 126.11 435.058 844.583 348.085 075.607 48 740.78 3380.00 870.423 690.00 580.321 1126.67 35.280 845.000 348.2(53 676.000 49 741.70 3331.67 870.881 690.83 580.626 1127.22 435.509 845.417 343.446 676.333 50 7'42.62 33S3.33 871.340 691.67 580.932 1127.78 35.738 845.833 348.630 676.667 51 743.53 3385 00 87 1.798 692.50581.2371128.33 35.968 846.250 348.813 677.000 53 7'4 4. 45 3386. 67 872.257 693.33581.543 1128.89 36.197 846.667 348.996 677.333 53 745. 37| 3388. 33 872.715 694.17 581.8491129.44 36.426 847.083 349.180 677.607 54 740.23 3390.00 873.173 1695.00 582.1541130.00 36.655 847 500 349.3(53 078.000 55 747 . 1 7 3301 . 67 : 873 .617 1695 . 83 582 . 450 1 130 . 56 36.877 847.917 349.541 678.333 5(J 748 . 06 3393 . 33 874 . 06 1 1 696 . 67 582 . 746 11 31 . 1 1 37.099 818.333 349.719 678.607 57 748 . 98 3395 . 00 874 . 520 1 697 . 50 583 . 052 1 1 3 1 . 67 37 329 848.750 319.902 679.000 58 749.8!) 3390.67 874.978 1698.33 583.358 1132.22 37.55S 849.167 350.085 679.333 59 750.81 3398.33 875.437 1699.17 583.663 1132.78 37.787 849.583 350.269679.667 112 TABLE XIV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 Curve. 1O Curve. looo Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. M. 282.990 550.000 242.602 471.429 212.317 412.500 188.766 366.667 169.933 330.000 o 283.143 550.278 242.733 471.667 212.432 412.708 188.868 366.852 170.024 330.167 1 283.296 550.556 242.861 471.905 212.547 412.917 188.970 367.037 170.116 330.333 2 283.449 550.833 242.995 472.143 212.661 413.125 189.072 367.222 170.208 330.500 3 283.602 551.111 243.126 472.381 212.776 413.333 189.174 367.407 170.300 330.667 4 283.750 551.389 243.253 472.619 212.887 413.542 189.272 367.593 170.389 330.833 5 283.898 551.667 243.380 472.857 212.998 413.750 189.371 367.778 170.478 331.000 6 284.051 551.944 243.511 473.095 213.113 413.958 189.473 367.963 170.569 331.167 7 284.203 552.222 243.642 473.333 213.228 414.167 189.575 368.148 170. 661 1331.333 8 284.356 553 r 500 243.773 473.571 213.342 414.375 189.677 368.333 170.753 331.500 9 284.509 552.778 243.904 473.810 213.457 414.583 189.779 368.519 170.845 331.667 10 284.657 553.056 244.031 474.048 213.568 414.792 189.878 368.704 170.934 331.833 11 284.805 553.333 244.158 474.286 213.679 415.000 189.977 368.889 171.023 332.000 12 284.958 553.611 244.289 474.524 213.794 415.208 190.078 369.074 171.114 332.167 13 285.111 553.889 244.420 474.762 213.909 415.417 190.180 369.259 171.206 332.333 14 285.264 554.167 244.551 475.000 214.023 415.625 190.282 369.444 171.298 332.500 15 285.417 554.444 244.682 475.238 214.138 415.833 190.384 369.630 171.390 332.667 16 285.565 554.722 244.809 475.476 214.249 416.042 190.483 369.815 171.479 332.833 17 285.713 555.000 244.936 475.714 214.360 416.250 190.582 370.000 171.568 333.000 18 285.866 555.278 245.067 475.952 214.475 416.458 190.684 370.185 171.659 333.167 19 286.019 555.556 245.198 476.190 214.590 416.667 190.786 370.370 171.751 333.333 2O 286.171 555.833 245.329 476.429 214.704 416.875 190.888 370.556 171.843 333.500 21 286.324 556.111 245.460 476.667 214.819 417.083 190.990 370.741 171.935 333.667 22 286.472556.389 245.587 476.905 214.930 417.292 191.089 370.926 172.024 333.833 23 286.621 556.667 245.714 477.143 215.041 417.500 191.187 371.111 172.113 334.000 24 286.773556.944 245.845 477.381 215.156 417.708 191.289 371.296 172.204 334.167 25 286. 92(5 i 557. 222 245.976 477. 61 !) 215.270 417.917 191.391 371.481 172.296 334.333 26 287.079 557.500 246.107 477.857 215.385 418.125 191.493 371.667 172.388 334.500 27 287.232 557.778 246.238 478.095 215.500 418.333 191.595 371.852 172.480 334.667 28 287.385 558.056 246.369 478.333 215.615 418.542 191. C97 372.037 172.572 334.833 29 287.538 558.333 246.500 478.571 215.729 418.750 91.799 372.222 172.663 335.000 30 287.686 558.611 246.627 478.810 215.840 418.958 191.898 372.407 172.752 335.167 31 287.834 558.889 246.754 479.048 215.951 419.167 191.997 372.593 172.841 335.333 32 287.987 559.167 246.885 479.286 216.066 419.375 192.099 372.778 172.933 335.500 33 288.140 559.444 247.016 479 524 216.181 419.583 192.201 372.963 173.025 335 667 34 288.292 559.722 247.147 479.762 216.295 419.792 192.303 373.148 173.117 335 833 35 288.445 560.000 247.278 480.000 216.410 420.000 192.405 373-. 333 173.208 836.000 36 288.598 560.278 247.410 480.238 216.525 420.208 192.506 373 51!) 173.300 336.167 37 288.751 560 556 247.541 480.476 216.640 420.417 192.608 373.704 173.392 336.333 38 288.899 560.833 247.668 480.714 216.751 420.625 192.707 373.889 173.481 336.500 39 289.047 561.111 247.794 480.952 216.862 420.833 192.806 374.074 173.570 336.667 4O 289.200 561.389 247.925 481.190 216.976 421.042 192.908 374.259 173.662 336 . 833 41 289.353 561.667 248.057 481.429 217. C91 421.250 193.010 374.444 173.753 337.000 42 289.506 561.944 248.188 481.667 217.206 421.458 193.112 374.630 173.845 337.167 43 289.659 562.222 248.319 481.905 217.320 421.667 193.214 374.815 173.937 337.333 44 289.811 562.500 248.450 482.143 217.435 421.875 193.316 375.000 174.029 337.500 45 289.964 562.778 248.581 482.381 217.550 422.083 193.418 375.185 174.121 337.667 46 290.1121563.056 248.708 482.619 217.661 422.292 193.517 375.370 174.210 337.833 47 290.260563.333 248.835 482.857 217.772 422.500 193.615 375.556 174.298 338.000 48 290.413 563.611 248.966 483.095 217.887 422.708 193.717 375.741 174.390 338.167 49 290.566 563.889 249.097 4a^.333 218.001 422.917 193.819 375.926 174.482 338.333 5O 290.719 564.167 249.228 483.571 218.116 423.125 193.921 376.111 174.574 338.500 51 290.872 564.444 249.359 483.810 218.231 423. 3a3 194.023 376.296 174.666 338.667 52 291.025 564.722 249.490 484.048 218.345 423.542 194.125 376.481 : 74 . 757 338.833 53 291.178 565.000 249.621 484.286 218.460 423.750 194.227 376.667 174.849 339 000 54 291.326 565.278 249.748 484.524 218.571 423.958 194.326 376.852 174.938 339.167 55 291.474 565.556 249.875 484.762 218.682 424.167 194.425 377.037 175.027 339.333 50 291.627 565.833 250.006 485.000 218.797 424.375 194.527377.222 175.119 339.500 57 291.780 566.111 250.137 485.238 218. P12 424.583 194.629377.407 175.211 339.667 58 291.932 566.389250.268 485.476 219.026424.792 194.7311377.593 175.302 339. B33 59 113 TABLE XIV. ACTUAL TANGENTS, ETC. 34 1 Curve. 3 Curve. 3 Curve. 4 Curve. 5 Curve. M. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. 1751.73 3400.00 875.895 1700.00 583.909 1133.33 488.016 850.000 350.452 080.000 1 1752.64 3401.67 876 353 1700.83 584.274 1138.80 43S.246 850.417 350.636 680.333 2 1753.56 3403 33 876.812 1701.67 584.58d 1134.44 438.475 850.833 350.819 080.607 3 1754.48 3405.00 877.270 1702.50 584.886 1135.00 438.704 851.250 351.002 681.000 4 1755.39 3406.67 877.729 1703.33 585.191 1135.56 438.933 851.667 351.186 681.333 5 1756.31 3408.33 878.187 1704.17 585.497 1136.11 439.102 852.083 351.369 081.007 6 1757.23 3410.00 878.645 1705.00 585.802 1136.67 439.392 852.500 351.553 682.000 7 1758.11 3411.67 879.089 1705.83 586.093 1137.22 439.014 852.917 351.730 682.333 8 1759.00 3413.33 879.534 1706.67 5SO . 805 1137.78 489.830 853.333 351.908 082 007 9 1759.92 3415.00 879.992 1707 50 586.700 1138.33 440.005 853.750 352.091 683.000 10 1760.84 3416 67 880.450 1708.33 587.006 1138.89 440.294 854.167 352.275 683.333 11 1761.75 3418.33 880.909 1709.17 587.311 1139.44 440.524 854.583 352.458 683.667 12 1762.67 3420.00 881.367 1710.00 587.617 1140.00 440.753855.000 352.642 684.000 13 1763.59 3421.67 881.825 1710.83 587.923 1140.56 440 982 855.417 352.825 684. 333 14 1764.50 3423.33 882.284 1711.67 588.228 1141.11 441.211 855.833 353.008 684.667 15 1765.42 3425.00 882.742 1712.50 588.534 1141.67 441.440 856.250 353.192 685.000 16 1766.34 3426.67 883. 20l! 1713. 33 588.839 1142.22 441.670856.667 353.375 685. 333 17 1767.25 3428.33 883.659J1714.17 589.145 1142.78 441.899857.086 353 559 685.667 18 1768.17 3430.00 884.117 1715 00 589.451 1143.33 442.1-8 857.500 353.742 686.000 19 1769.06 3431.67 884.561 1715.83 589.747 1143.89 442.350 857.917 353.920 686.333 30 1769.95 3433.33 885.006 1716.67 590.043 1144.44 442.572 858.333 354.097 686.667 31 1770.86 3435.00 885.464 1717.50 590.348 1145.00 442.801 858.750 854.281 687.000 22 1771.78 3436.67 885.922 1718.33 590.654 1145.56 443.03! 859.167 354.464 687.333 23 1772.70 3438.33 886.381 1719.17 590.960 1146.11 443.260 859.583 354.648 687.667 34 1773.61 3440.00 886.839 1720.00 591.265 1146.67 443.489860.000 354.831 688.000 35 1774.53 3441.67 887.297 1720.88 591 571 1147.22 443.718 860.417 355.014 688.333 36 1775.45 3443.33 887.756 1721.67 591.870 1147.78 443.948860.833 355.198 688.667 37 1776.36 3445.00 888.214 1722.50 592.182 1148.33 444.177 861 250 355.381 689.000 38 1777.28 3446.67 888.673 1723.83 592.488 1148.89 444.406 861.607 355. 565 1689.383 39 1778.20 3448.33 889.131 1724.17 592.793 1149.44 444.635 862.083 355.748 689.667 30 1779.11 3450.00 889.589 1725.00 593.099 1150.00 444.865 862.500 355.931 690.000 31 1780.03 3451.67 890.048 1725.83 593.405 1150.56 445.094 862.917 350.115690.333 33 1780.95 3453.33 890 500 1726.67 593.710 1151.11 445.323 803.333 356.298 690.667 33 1781.86 3455.00 890.965 1727.50 594.016 1151.67 445.552 803.750 356.482691.000 34 1782.78 3456.67 891.423 1728.33 594.321 1152.22 445.781 804.167 356.605091.333 35 1783.70 3458.33 891.881 1729.17 594.627 1152.78 446.011 864.583 356.848601.667 36 1784.61 3460.00 892.340 1730.00 594.933 1153.33 446.240865.000 357.032692.000 37 1785.50 3461.67 892.784 1730.83 595.220 1153.89 416.462 865.417 357.210092.333 38 1786.39 3463.33 893.228 1731.67 595.525 1154.44 446.684 865.833 357.387692.667 39 1787.31 3465.00 893.686 1732.50 595.830 1155.00 446.913866.250 357.571 693.000 40 1788.22 3466.67 894.145 1733.33 596.136 1155.56 447.143866.667 357.754003.333 41 1789.14 3468.33 894.603 1734.17 596.442 1156.11 447.372867.083 357.937693.667 43 1790.06 3470.00 895.061 1735.00 596.747 1156.67 447.601 867.500 35S.121 694.000 43 1790.97 3471.67 895.520 1735.83 597.053 1157.22 447.830807.917 358 304 004.333 44 1791.89 3473.33 895.978 1736.67 597.358 1157.78 448.059 80S. 333 358.488694.607 45 1792.81 3475.00 896.437 1737.50 597.664 1158.33 448.289 808.750 358.071 095.000 46 1793.72 3476.67 896.895 1738.33 597.970 1158.89 448.518809.167 358.854095.333 47 1794.64 3478.33 897.353 1739.17 598.275 1159.44 448.747 809.583 350.038 695.607 48 1795.56 3480.00 897.812 1740.00 598.581 1160.00 448.976870.000 350.2211696.000 49 1796.47 3481.67 898.270 1740.83 598.880 1160.56 449.206870.417 359.405696.333 5O 1797.39 3483.33 898.729 1741 67 599.192 1161.11 449.435 870.833 359. 5F8 696. 667 51 1798.31 3485.00 899.187 1742.50 599.498 1101.07 449.664 871.250 359.771 697 000 53 1799.22 3486 67 899.645 1743.33 599.803 1102.22 449.893871.667 359.955 097.383 53 1800.14 3488.33 900.104 1744.17 600.109 1102.78 450.123 872.083 360.138697.067 54 1801.06 3490.00 900.562 1745.00 600.415 1103.33 450.352 872.500 360.322698.000 55 1801.97 3491.67 901.0201745.83 000.720 1163.89 450.581 872.917 360. 505 1 698. 333 56 1802.89 3493. 33 1901. 479 1746.67 601.026 1164.44 450.810 873.333 360.688698.667 57 1803.81 3495.00 901 .937 1747.50 601 .331 1165.00 451.039873.750 360. 872| 009 000 58 1804.73 3496.67 902. 396 1748. 33! 00 1.637 1165.56 451.269 874.167 361.055609.333 59 1805.61 3498.33 902. 854 ; 1749. 17 1601.943 1166.11 451 . 498 874 . 583 36 1 . 239 \ 699 . 607 114 TABLE XIV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 Curve. 10 Curve. 34 Tan. Arc. 566^667 Tan. 250.399 Arc. 485.714 Tan. Arc. Tan. Arc. Tan. Arc. M. ~7T 292.085 219.141425.000 194.833 377.778 175.394 340.000 292.238 566.944 250.530 485.952 219.256425.208 194.934 377.963 175.486 340.167 i 292.391 567.222 250.661 486 190 219.370 425.417 195.036 378.148 175.578 340.333 2 292.544 567.500 250.792 486.429 219.485 425.625 195.138 378.333 175.670 340.500 3 292.697 567.778 250.923 486.667 219.600 425.833 195.240 378.519 175.761 340.667 4 292.850 568.056 251.054 486.905 219.715 426.042 195.342 378.704 175.853 340 833 5 293.002 568.333 251.185 487.143 2 19. 829 1426.250 195.444 378.889 175.945 341.000 6 293.150 568.611 251.312 487.381 219.940 426.458 195.543 379.074 176.034 341.167 7 293.299 568.889 251.439 487.619 >20.051 426.667 195.642 379.259 176.123 341.333 8 293.451 569.167 251.570 487.857 220.166 426.875 195.744 379.444 176.215 341.500 9 293.604 569.444 251.701 488.095 220.281 427.083 195.846 379 630 176.306 341.667 10 293 . 757 569.722 251.832488.333 220.395 427.292 195.948 379.815 176 398 341.833 11 293 910! 570. 000 251.9(53488.571 220 510 427.500 196.050 380.000 176.490 342.000 12 294.063570.278 252.094488.810 220.625 427.708 196.152 380 185 176.582 342.167 13 294.216 570.556 252.225489.048 220.740 427.917 196.254 380 370 176.674 342.333 14 294.369 570.833 252.356489.286 220.854 428 125 196 356 380.556 17'6.765 342.500 15 294.521 571.111 252.487489.524 220 969 428.333 196.458 380.741 176 857 34-.'. 667 16 294.674 571.3*9 252.618:489.762 221.084 428.542 196.560 380.926 176.949 342.833 17 294.827 571.667 252.7501490.000 221.198 428.750 196.661 381.111 177.041 343.000 18 294.975 571.944 252.876 490.238 221.309 428 958 196.760 381.296 177.130 343.167 19 295.123 572.222 253.003 490.476 221.4-20 429.167 196.859 381.481 177.219 343.333 2O 295.276 572.500 253.134 490.714 221.535 429 375 196.961 3S1 667 177.310 343.500 21 295.429 572.778 253 268 490.952 221.650 429.583 197.063 381.852 177.402 343.667 22 295.582 573.056 253.397 491.190 221.765 429.792 197.165 382.037 177.494 343.833 23 295.735 573 333 253.528 491 .429 221.879 430.000 197 267 382.222 177.586 344.000 24: 295 888 573.611 253.659 491.667 221.994 430.208 197.369 382.407 177.677 344.167 25 296.040 573.889 253.790 491.905 222.109 430.417 197.471 382.593 177.769 344.333 26 296.193 574.167 253.921 492.143 222.223 430.625 197.573 382.778 177.861 344.500 21 296.346 574.444 254.052 492.381 222.338 430.833 197.675 382.963 177.953 344.667 28 296.499 574.722 254.183 492.619 222.453 431.042 197.777 383.148 178 045 344.833 29 296.652 575.000 254.314 492.857 222.567 431.250 197.879 383.333 178.136 345 000 30 296.805 575.278 254.445 493.095 2-22.682 431.458 197.981 383.519 178.228 345.167 31 296.958 575.556 254.576 493.333 222.797 431.667 198 083 383.704 178.320 345.333 32 297.110 575.833 254.707 493.571 222.911 431.875 198.185 383.889 178.412 345.500 33 297.263 576.111 254.838 493.810 223.026 432 083 198.287 384.074 178.504 345.667 34 297.416 576.389 254.969 494.048 223.141 432.292 198.388 3S4.259 178.595 345.833 35 297.569 576.667 255.100 494.280 223.255 432.500 198.490 384 . 444 178.687 346.000 36 297.717 576.944 255.227 494.524 223.367 432.7'08 198.589 384.630 178.776 346.167 37 297.865 577.22v 255.354 494.762 223.478 432.917 198.688 384.815 178.865 346.333 38 298.018 577.500 255.485 495.000 223.592 433.125 198.790 385.000 178.957 346.500 39 298.171 577.778 255.616 495.238 223.707 433.333 198.892 385.185 179.049 346.667 40 298.324 578.0.56 255.747 495.476 223.822 433.542 198.994 385.370 179.140 346.833 41 298.477 578.333 255.878 495.714 223 936 433.750 199.096 385.556 179.232 347.000 4:2 298.630 578.611 256.009 495.952 224.051 433 958 199.198 385.741 179.324 347.167 43 2U8. 7S2 578.889 256.140 496.190 224.166 434.167 199.300 385.926 179.416 347.333 44 298.935 579.167 256.271 496.429 224.280434.375 199.402 386.111 179.508 347.500 45 299 088 579.444 256.402 496 667 224.395434.583 199.504 386.296 179.599 347.667 46 299 241 579.722 256.533 496.905 224.510434.792 199.606 386.481 179.691 347.833 47 299 394 580.000 256.664 497.143 224.624:435.000 199.7'08 386.667 179.783 348.000 48 299.547 580.278 256 . 795 497.381 224.739435.208 199.810 386.852 179.875 348.167 49 299.700 580.556 256.927 497.619 224.854 435.417 199.912 387.037 179.967 348.333 5O 299.852580.833 257.058 497.857 '224.969 435.625 200.014 387.222 180.058 348 500 51 300 005 581.111 257.189 498.095 225.083 435.833 200.115 387.407 180.150348.667 52 300.158 581.389 257.320 498.333 225. 198 1436. 042 200.217 387.593 180.242348.833 53 300.311 581.667 257.451 498.571 225 313436.250 200.319 387.778 180.334349.000 54 300. 464 1581.944 257.582 498.810 225.427436.458 200.421 387.963 180.425 349 167 55 300.617 582.222 257.713 499.048 225.542436.667 200.523 388.148 180.517349.333 56 300.770 582.500 257.844 499.286 225.657436.875 200.625 388.333 180.609349.500 57 300.922582.778 257.975 499.524 225.771437.083 200.727 388.519 180.701 349.667 58 301. 075 1583.056 258.106 499.762 225.886437.292 200.829 388.704 180.793349.833 59 115 TABLE XIV. ACTUAL TANGENTS, ETC. 35 1 Curve. 2 Curve. 3 Curve. 4 Curve. 5 Curve. M. Tan. Arc. 3500.00 Tan. 903.312 Arc. 1750.00 Tan. 602 248 Arc. 1166. 67 Tan. Arc. Tan. Arc. 1806.56 451.727 875.000 861.422 700.000 1 1807.48 3501.67 903.771 1750.83 602.554 1167.22 451.956 875.417 361.605 700.333 2 1808.3'.) 3503.33 904.229 1751.67 602.859 1167.78 452.186 875.833 361.789 700.607 3 1809.31 3505.00 904.688 1752.50 603.165 1108.3:3 452 415 876.250 361.972 701.000 4 1810.23 3506.67 905.146 1753.33 003.471 1168.89 452.644 876.667 362.156 701.333 5 1811.14 3508.33 905.604 1754.17 603.776 1169 44 452.873 877.083 362.339 701.007 6 1812.06 '3510.00 906.063 1755.00 604.082 1170.00 453.103 877.500 362.523 702.000 7 1810.98 3511.67 906.521 1755.83 604.388 1170.56 453.332 877.917 302.700 702.333 8 1813.89 8513.88 906.980 1756.67 604.693 1171.11 453.561 878.333 302.889 702. G07 9 1814.81 3515.00 907.438 1757.50 604.999 1171.67 453.790 8?'8.750 363.073 703.000 1O 1815.7:5 3516.67 907.896 1758.33 605 304 1172.22 454 019 879.167 363 250 703 333 11 1816.64 3518 33 908.355 1759.17 605.610 1172 78 454 249 879. 583 1363. 440 703 667 13 1817.56 3520.00 908.813 1760.00 605.916 1173.33 454.478 880. 000i363. 623 704.000 13 1818.48 3521.67 909.271 1760.83 606.221 1173.81) 454.707 880.417363.806 704.333 14 1819.39 :3523.33 909.730 1761.67 606 527 1174.44 454 936 880. 833 i 363. 990 704.667 15 1820.31 3525.00 910.188 1762.50 606.832 1175.00 455.100 881.250364.173 705.000 16 1821.23 3526.67 910.647 1763.33 607.138 1175.56455.395 881.667 364.357 705.333 17 1822.14 3528.33 911.105 1764.17 607.444 1176.11 455.624 882 083 364.540 705.667 18 19 1823.06 1823.98 3530.00 3531.6? 911.563 912 022 1765.00 1765.83 607.749 608.055 1176 67 1177.22 455.853 456.083 H82.500 882.917 364.723 364.907 706.000 706.333 20 1821.89 3533 33 912.480 1766.67 608.360 1177.78 456.312 883.333 365 090 706.667 21 1825.81 3535.00 912.939 1767.50 008. 606 1178.33 456.541 883.750 365.274 707.000 22 1826.73 3536.6? 913.397 1768.33 608.972 1178.89 456.7?'0 884.167 365.457 707.333 23 1827.64 3538.33 913.855 1769.17 609.277 1179.44 456.999 884.583 305.640 707.667 34 1828.56 3540.00 914.314 1770.00 609.583 1180.00 457.229 885.000365.824 708.000 25 1829.48 3541.67 914.772 1770.83 009.889 1180.56 457.458 885.417366.007 708.333 26 1830.39 3543.33 915.231 1771.67 610.194 1181.11 457.687 885.833300.191 708.007 21 1831.31 3545.00 915.689 1772.50 610.500 1181.67 457.916 886.250306.374 709.000 28 1832.23 3546.67 916.147 1773.33 610.805 1182.22 458.146 886.00? 306.557 709.333 39 1833.14 3548.33 916.606 1774.17 611.111 1182.78 458.375 887.083300.741 709.667 30 1834.06 3550.00 917.064 1775.00 611.417 1183.33 458.604 887.500366.924 710.000 31 183 L 98 3551.67 917.522 1775.83 611.722 1183.89 458.833 887.917307.108 710.333 32 1835.89 3553.33 917.981 1776.67 612.028 1184.44 459.063 888.333367.291 710.667 33 1836.81 3555.00 918.439 1777.50 612.333 1185.00 459.292 888.750367.4?'4 711.000 34 1837.73 .'5556.67 918 898 1778.33 012.639 1185.56 459.521 889. 167 1367.658 711.333 35 1838.64 3558.33 919.356 1779.17 612.945 1186.11 459.750 889.583 367.841 711.667 36 1839.56 3560.00 919.814 1780.00 613.250 1186 67 459.979 890. 000 '308. 025 712.000 37 18-10.51 3561.67 920.287 1780.83 613.565 1187.22 460.216 890.417308.214 712.333 38 1841.45 3563.33 920.760 1781.67 013.881 1187.78 460.452 890.833 308.403 712.667 39 1842.37 3565.00 921.218 1782.50 014.180 1188.33 400.681 891.250368.586 713.000 4O 1843.29 3566.67 921.677 1783.33 614.492 1188.89 460.911 891.667308.770 713.333 41 1844.20 3568 33 1)22.135 1784.17 614.797 1189.44 401.140 892.083308.953 713.607 43 1845.12 3570.00 922.593 1785.00 615.103 1190.00 461.369 892.500369.137 714.000 43 1846.04 3571.67 1)23.052 1785.83 015.409 1190.56 461.598 892.917309.320 714.333 44 1846.95 3573.33 9-23.510 i?'86.67 615.711 1191.11 401.828 893.333309.503 714.607 45 1847.8?' 3575.00 923 969 1787.50 616.020 1191.67 462.057 893.750309.087 715.000 46 1848.79 3576.67 924.427 1788 33 616.326 1193.22 462.280 894.107309.870 7l5.3:-;3 47 1849.70 3578.33 924.885 1789.17 610.631 1192.78 402.515 894.583370.054 715.607. 48 1850.62 3580.00 925.344 1790.00 016.93? 1193.33 402.745 895.000370.237 716.000 49 1851.54 3581 . 07 925.802 1?90.S3 617.242 1193.89 462.974 895.417370.420 716.333 50 1852.45 3583.33 926.261 1701.67 017 548 1194.44 463.203 895.833370.604 716 607 51 1853.37 3585.00 926.719 1792.50 617.854 1195.00 403.432 896.250370.787 717.000 53 1854.29 3586.67 927 1? 7 1793.3:3 018.159 1195.56 463.601 896.667370.971 717.333 53 1855.23 3588.33 927.650 1?94 17 618.474 1196.11 463.898 897. 083 3? 1.1 60 717.607 54 1856.18 3590.00 928.123 1795.00618.790 1196 67464.134 897 500371.349 718.000 55 1857.09 3591.67 928.581 1795.83619.095 1197.22464.303 897.917371.532 718.333 56 1858.01 3593.33 9J !9. 040 1796 67 019.401 1197.78464.593 80S. 333 371. 71 6 718.007 57 1858.93 3595.00929.498 1797 50 619 706 1198.334(54.822 898.750371.899:719.000 58 1859.84 3596.67929.956 1798.33620.012 1198.89405.051 899.167372.082:719.333 59 1860.76 3598. 33! 930. 415 1799.17 620.318 1199.44 465.280 899.583 372.266 ?19.6G7 11(3 TABLE XTV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 Curve. 1O Curve. 35 Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. M. 301.228 583.333258.237 500.000 226.001 437.500 200.931 388.889 180.884 350.000 o 301.381 583.6111258.368 500.238 226.115437.708 201.033 389.074 180.976 350.167 1 301.534 583.880258.499 500.476 226.2301437.917 201.135 389.259 181.068 350.333 2 301.687 584.1671258.630 500.714 226.345438.125 201.237 389.444 181.160 350.500 3 301.840 584.444! 258 761 500.952 226.459438.333 201.339 389.630 181.252 350.667 4 301.992 584.722258.892 501.190 226.574 438.542 201.441 389.815 181.343 350.833 5 802.145 585.000259.023 501.429 226.689438.750 201.543 390.000 181.435 351.000 6 302.298 585.278259.154 501.667 226. 803 '438. 958 201.645 390.185 181.527 351.167 7 302.451 585.556259.285 501.905 226.918439.167 201.747 390.370 181.619 351 . 333 8 302.604 585. 833-259.416 502.143 227. 033 439.375 201.849 390.556 181,711 351.500 9 302.757 586.111 259.547 502.381 227.148 439.583 201.951 390.741 181.802 351.667 1O 302.910 586.389259.678 502.619 227.262 439.792 202.053 390.926 181.894 351.833 11 303.062 586.667 259.809 502.857 227.377 440.000 202.155 391.111 181.986 352.000 303.215 586.944 259.941 503.095 227.492 440.208 202.257 391.296 182.078 352.167 13 303.368 587.222260.072 503.333 227.606 440.417 202.359 391.481 182.169 352.333 14 303.521 587. 500 1260. 203 503.571 227.721 440.625 202.461 391.667 182.261 352.500 15 303.674 587.778260.334 503.810 227.836 440.833 202.563 391.852 182.353 352.667 16 303.827 588.056:260.465 504.048 227.950 441.042 202.665 392.037 182.445 352.833 17 303.980 588.333260.596 504.286 228.065 441.250 202.767 392.222 182.537 353.000 18 304.132 588.611 260.727 504.524 228.180 441.458 202.868 392.407 182.628 353.167 19 304.285 588.889260.858 504.762 228.294 441.667 202.970 392.593 182.720 353.333 20 304 . 438 589.167260.989 505.000 228.409 441.875 203.072 392.778 182.812 353.500 21 304.591 589.444 261.120 505.238 228.524 442.083 203.174 392.963 182.904 353.667 22 304.744 589.722261.251 505.476 228.638 442.292 203.276 393.148 182.996 353.833 23 304.897 590.000261.382 505.714 228.753 442.500 203.378 393.333 183.087 354.000 24 305.050 590.278261.513 505.952 228 868 442.708 203.480 393.519 183.179 354.167 25 305.202 590. 556 [261.644 506.190 228.982 442.917 203.582 393.704 183.271 354.3133 26 305.355 590. 833; 261. 775 506.429 229.097 443.125 203.684 393.889 183.363 354.500 27 305.508 591.111 261.906 506.667 229.212 443.333 203.786 394.074 183.455 354.667 28 305.661 591.389 262.037 506.905 229.327 443.542 203.888 394.259 183.546 354.833 29 305.814 591.667 262.168 507.143 229.441 443.750 203.990 394.444 183.638 355.000 30 305.967 591.944 262.299 507.381 229.556 443.958 204.092 394.630 i as. 730 355.167 31 306.120 592.222 262.430 507.619 229.671 444.167 204.194 394.815 183.822 355.333 32 306.272 592.500 262.561 507.857 229.785 444.375 204.296 395.000 183.913 355.500 33 306.425 592.778 262.692 508.095 229.900 444.583 204.398 395.185 184.005 355.667 34 306.578 593.056 262.823 508.333 230.015 444.792 204.500 395.370 184.097 355. a33 35 306.731 593.333 262.955 508.571 230.129445.000 204.602 395.556 184.189 356.000 36 306.889 593.611 263.090 508.810 230. 248 ! 445. 208 204.707 395.741 184.284 356.167 37 307.046 593.889 263.225 509.048 230.366445.417 204.812 395.926 184.378 356.333 38 307.199 594.167 263.356 509.286 230.481 445.625 204.914 396.111 184.470 356.500 39 307.352 594.444 263 487 509.524 230.595 445.833 205.016 396.296 184.562 356.667 4O 307.505 594.722263.618 509.762 230.710446.042 205.118 396.481 184.654 356.833 41 307.658 595.000263.749 510.000 230.825446.250 205.220 396.667 184.745 357.000 42 307.811 595.278263.880 510.238 230.939446.458 205.322 396.852 184.837 357.167 43 307.963 595.556264.011 510.476 231.054446.667 205.424 397.037 184.929 357.3^33 44 308.116 595.833264.142 514,714 231.169446.875 205.526 397.222 185.021 357.500 45 308.269 596.111 264.273 510.952 231.283447.083 205.628 397.407 185.113 357.667 46 308.422 596.389 264.404 511.190 231.398447.292 205.730 397.593 185.204 357.833 47 308.575 596 667264.535 511.429 231.513447.500 205.832397.778 185.296 358.000 48 308.728 596.944 264.666 511.667 231.627447.708 205.934 ^397.963 185.388 358.167 49 308.881 597.222264.797 511.905 231.742447.917 206.036 308.148 185.480 358.333 50 309.033 597.500264.928 512.143 231.857448.125 206.138 398.333 185.571 358.500 51 309.186 597.778265.059 512.381231.971 448.333 206.240 398.519 185.663 358.667 52 309.344 598 056 265.195 512.619 232.090 448.542 206.345 398.704 ia5 758 358.8:33 53 309.502 598.333265.330512.857 232.208448.750 206.450 398.889 185.853 359.000 54 309.654 598.611 265.461 513.095 232.323 448. 958 206 552 399.074 185.944 359.167 55 309.807 598.889265.59i 513. .333 232 . 437 449 . 1 67 206 654 399.259 186.036 359.333 56 309.960 599.167265.723513.571 232.552449.375 206.756 399.444 186.128 359.500 57 310.113 310.266 599.444 265.854 513.810 232.667 449 583 599.722 265.985 5 14. 048 1232. 781 449.792 206.858399.630 206.960l399.815 186.220 186.312 359.667 359.833 58 59 117 TABLE XIV. ACTUAL TANGENTS, ETC. 36 1 Curve. 2 Curve. 3 Curve. 4 Curve. 5 Curve. M. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. 1861.68 3600.00 930.873 1800.00 620.623 1200.00 465.510900.000 372 449 720.000 1 1862.59 3601.67 931.331 1800.83 620.929 1200.56 465 739 900.417 372.633 720.333 2 1863.51 3603.33 931.790 1801.67 621.234 1201.11 465. 968! 900. 833 372.810 720.667 3 1864.43 3605.00 932.248 1802.50 621.540 1201.67 466. 197 1901. 250 373.000 721.000 4 1865.34 3606.67 9:32.707 1803.33 621.846 1202.22 466.427,901.667 373.183 721.333 5 1866.26 3608.33 933.165 1804.17 622.151 1202.78 466.656902.083 373.366 721.067 6 1867.18 3610.00 933.623 1805.00 622.457 1203.33 466.885902.500 373 550 722.000 7 1868.12 3611.67 934.096 1805.83 622.772 1203.89 467.121 902.917 373.739 722. 333 8 1869.07 3613.33 934.569 1806.67 623.087 K'04.44 467.358|'J03.333 373. 928 1722. 607 9 1869.99 3615.00 935.027 1807.50 623.393 1205.00 467.587 903.750 374.111 723.000 10 1870.90 3616.67 935.486 1808.33 623.698 1205.56 467.816 904.167 374.295 723.333 11 1871.82 3618.33 935.944 1809.17 624.004 1206.11 468.045 904.583 374.478 723.667 12 1872.74 3620.00 936.402 1810.00 624.310 1206.67 408.275 905.000 374 662 724.000 13 1873.65 3621.67 936.861 1810.83 624.615 1207.22 468.504 905.417 374.845 724.3:33 14 1874.57 3623.33 937.319 1811.67 624.921 1207.78 468.733 905.833 375.028 724.667 15 1875 49 3625.00 937.778 1812.50 625.226 1208.33 408.962 906.250 375.212 725 000 16 1876.40 3626.67 938.236 1813.33 625.532 1208.89 469 192 906.667 375.395 725.383 17 1877.35 3628.33 938.709 1814.17 625.847 1209.44 469.428 907.083 875.584 725.667 18 1878.29 3630.00 939.181 1815.00 626.162 1210.00 469.604 907.500 375.774 726.000 19 1879.21 3631.67 939.640 1815.83 626.468 1210.56 469.894 907.917 375.957 726.333 20 1880.13 3633.33 940.098 1816.67 626.774 1211.11 470.123 908.333 376.140 726.667 21 1881.04 3635.00 940.557 1817.50 627.079 1211.67 470.352 908.750 376.324 727.000 22 1881.96 3636 67 941.015 1818,33 627.385 1212.22 470.581 909.167 376.507 727.333 23 1882.88 3638.33 941.473 1819.17 027.690 1212.78 470 811 909 583 376.691 727.667 24: 1883.79 3640.00 941.932 1820.00 627.996 1213.33 471.040 910.000 376.874 728.000 25 1884.74 3(541 . 67 942.404 1820.83 028.311 1213.89 471.270 910.41? 377.063 728.333 2G 1885.69 3643.33 942.877 1821.67 628.626 1214.44 471.513 910.833 377.252 728.607 21 1886 60 3645.00 943.336 1822.50 628.932 1215.00 471.742 911.250 877.486 729.000 28 1887.52 3646.67 943.794 1823.33 629.238 1215.56 471.971 911.667 377.619 729.333 29 1888.44 3648.33 944.252 1824.17 629.543 1216.11 472.200 912.083 377.802 729.007 30 1889.35 3650.00 944.711 1825.00 629.849 1216.67 472.430 912.500 377.986 730.000 31 1890.27 3651.67 945.169 1825.83 630.154 1217.22 472.659 912.917 378.169 730.333 32 1891.19 3653.33 945.627 1826.67 630.460 1217.78 472.888 913.333 378 353 730.607 33 1892.13 3655.00 946.100 1827.50 630.775 1218.33 473.124 913.750 378.542 731.000 34 1893.08 3656.67 946.573 1828.33 631.090 1218.89 473.361 914.16? 378.731 731.333 35 1893.99 3658.33 947.031 18<59.17 531.396 1219.44 473.590 914.583 378. 914 731.667 36 1894.91 3660.00 947.490 1830.00 631.702 1220.00 473.819 915.000 379.098 732 000 37 1895.83 3661.67 947.948 1830.83 632.007 1220.56 474.048 915.417 379.281 732.333 38 1896.74 3663.33 948.406 1831.67 632.313 1221.11 474.278 915.833 379.465 732.607 39 1897.66 3665.00 948.865 1832.50 632.618 1221.67 474.507 916.250 :379.648 733.000 4O 1898.58 3666.67 949.323 1833.33 632.924 1222.22 474.736 916.667 379.831 733.333 41 1899.52 3668.33 949.796 1834.17 633.239 1222.78 474.973 917.083 '380.020 733.667 42 1900.47 3670.00 950.269 1835.00 C33.554 1223.33 475.209 917.500 380.210 734.000 43 1901.38 3671.67 950.727 1835.83 633.860 1223.89 475.438 917.917 380.393 734.333 44 1902.30 3673.33 951.185 1836.67 634.166 1224.44 475.667 918.333 380.576 7:34.667 45 1903.22 3675.00 951.644 1837.50 634.471 1225.00 475.897 918.750 380.760 735.000 46 1904.13 3676.67 952.102 1838.33 634.777 1225.56 476.126 919.167 380.943 735.333 47 1905.08 3678.33 952.575 1839.17 635.092 1226.11 476.362 919.583 381.132 735.667 48 1906.03 3680.00 953.048 1840.00 635.407 1226.67 476.599 920.000 481.888 736.000 49 1906.94 3681.67 953.506 1840.83 635.713 1227.22 476.828 920.41? 381.505 736.333 50 1907.86 3683.33 953.964 1841.67 636.018 1227.78 477.057 920.833 381.688 736.667 51 1908.78 3685.00 954.423 1842.50 636.324 1228.33 477.286 921.250 381.872 ? 37. 000 52 1909.69 3686.67 954.881 1843.33 636.630 1228.89 477.516 921.667 382.055 737.333 53 1910.64 3688.33 955.354 1844.17 636.945 1229.44 477.752 922.083 382.2441737.607 54 1911.58 3690.00 955.827 1845.00 637.260 1230.00 477.988 922.500 382.433:738.000 55 1912.50 3691.67 956.285 1845.83 637.566 1230.56 478.218 922.91? $82. 61 7 788. 3*3 56 1913.42 3693 3:3 956.743 1846.67 637.871 1231.11 478.447 923.333 382. 800 : 7*8. 667 57 1914.83 3695.00 957.202 1847. 5( 038.177 1231.67 478.676 :3 ?:>( 382. 984 i 739.0(0 58 1915.25 3096.67 957.660 1848.33 638.482 1232.22 478.905924.16? 383.107 739.3:;:) 59 1916.20 3698.33 958.133 1849.1? 638.798 1232.78 479. 142 1924. 583 383.356 739.007 118 TABLE XIV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 Curve. 1O Curve. 36 Tan. 310.419 Arc. eooTooo Tan. 2667lil> Arc. 5147286 Tan. 2327896 Arc. 450TOOO Tan. 2077062 Arc. 4007000 Tan. I Arc. 18^740313607000 M. ~O~ 310. 572 GOO. 278 266.247 514.524 233.011 450.208 207.164 400.185 186.495 360.167 1 310.724 600.556 266.378 514.762 233.125 450.417 207.266 400.370 186.587 360.3:33 2 310.8771600.833 266.509 515.000 2:33.240 450.625 207.368 400.556 186.679 360.500 3 811.080601.111 266.640 515.238 233.355 450.833 207.470 400.741 186.770 360.667 4 311.183 601.389 266.771 515.476 233.470 451.042 207.572 400.926 186.862 360.833 5 311.336 601.667 266.902 515.714 233.584 451.250 207.673 401.111 186.954 361.000 6 311.494 601.944 267.037 515.952 233.702 451.458 207.779 401.296 187.049 361.167 7 311.651 602.222 267.172 516.190 233.821 451.667 207.884 401.481 187.143 361.333 8 311.804 602.500 267.304 516.429 233.935 451.875 207.986 401.667 187.235 361.500 9 311.957 602.778 267.435 M6.667 234.050 452.083 208.088 401.852 187.327 361.667 1O 312.110 603.056 267.566 :>16.905 234.165 452.292 208.190 402.037 187.419 361.833 11 312.263 603.3:33 267.697 517.143 234.279 452.500 208.292 402.222 187.511 362.000 12 312.415 603.611 267.828 517.381 234.394 452.708 208.394 402.407 187.602 362.167 13 312.568 603.889 267.959 517.619 234.509 452.917 208.496 402.593 187.694 362.333 14 312.721 604.167 268.090 517.857 234.624 453.125 208.598 402.778 187.786 362.500 15 312.874 604.444 268.221 518.095 234.738 453333 208.700 402.963 187.878 362.667 16 313.032 604.722 268.356 518.333 234.857 453.542 208.805 403.148 187.972 362.833 17 313.189 605.000 268.491 518.571 234.975 453.750 208.910 403.333 188.067 363.000 18 313.342 605.278 268.622 518.810 235.089 453.958 209.012 403.519 188.159 363.167 19 313.495 605.556 268 753 519.048 235.204 454.167 209.114 403.704 188.251 363.333 2O 313.648 605.833 268.884 519.286 235.319 454.375 209.216 403.889 188.342 363.500 21 313.801 606.111 269.015 519.524 235.434 454.583 209.318 404.074 188.434 363.667 22 313.954 606.389 269.146 519.762 235.548 454.792 209.420 404.259 188.526 363.833 23 314.106 606.667 269.277 520.000 235.663 455.000 209.522 404.444 188.618 364.000 24 314.264 606.944 269.412 520 238 235.781 455.208 209.627 404.630 188.712 364.167 25 314.422 607.222 269.548 520.476 235.899 455.417 209.732 404.815 188.807 364.333 26 314.575 007.500 269.679 520.714 236.014 455.625 209.834 405.000 188.899 364.500 27 314.727 607.778 269.810 520.952 -'36.129 455.833 209.930 405.185 188 991 364.667 28 314.880 608.056 269.941 521.190 236.243 456.042 210.038 405.370 189.082 364.833 29 315.033 608.333 270.072 521.429 236.358 456.250 210.140 405.556 189.174 365.000 30 315.186 608.611 270.203 521.667 236.473 456.458 210.242 405.741 189.266 365.167 31 315.339 608.889 270.334 521.905 236.588 456.667 210.344 405.926 189.358 365.333 32 315.497 609.167 270.469 522.143 236.706 456 875 210.441) 406.111 189.452 365.500 33 315.654 609.444 270.601 522.381 236.824 457.083 210.554 406.296 189.547 365.667 34 315.807 609.722 270.735 522.619 236.939 457.292 210.656 406.481 189.639 365.833 35 315.960 610.000 270.866 522.857 237.053 457.500 210.758 406.667 189.731 366.000 36 316.113 610.278 270.997 523.095 237.168 457.708 210.860 406.852 189.822 366.167 37 316.266 610.556 271.128 523.333 237.283 457.917 210.962 407.037 189.914 366.333 38 316.418 610.833 271.259 523.571 237.397 458.125 211.064 407.222 190.006 366.500 39 316.571 611.111 271.390 523.810 237.512 458.333 211.166 407.407 190.098 366.667 4O 316.729 611.389 271.526 524.048 237.630 458.542 211.271 407.593 190.193 366.833 41 316.887 611.667 271 661 524.286 237.749 458.750 211.376 407.778 190.287 367.000 42 317.039 611.944 271.792 524.524 237.863 458.958 211.478 407.963 190.379 367.167 43 317.192 612.222 271.923 524.762 237.978 459.167 211.580 40S.148 190.471 367.33-3 44 317.345 612.500 272.054 525.000 238.093 459.375 211.682 408.333 190.563 367.500 45 317.498 612.778 272.185 525.238 238.207 459.583 211.784 408.519 190.654 367.667 46 317.656 613.056 272.320 525.476 238.326 459.792 211.889 408.704 190.749 367.833 47 317.813 613.333 272.455 525.714 238.444 460.000 211.994 408.889 190.844 368.000 48 317.966 613.611 272.586 525.952 238.559 460.208 212.096 409.074 190.935 368.167 49 318.119 613.889 272.717 526.190 238.673 460.417 212.198 409.259 191.027 368.333 5O 318.272 614.167 272.848 526.429 238.788 460.625 212.300 409.444 191.119 368.500 51 318.425 614.444 272.979 526.667 238.903 460.833 212.402 409.630 191.211 368.667 52 318.582 614.722 273.114 526.905 239.021 461.042 212.507 409.815 191.305 368 833 53 318.740 615.000 273.250 527.143 239.139 461.250 212 612 410.000 191.400 369.000 54 318.893615.278 273. 3*1 1527. 381 239.254461.458 212.714 410. 185 191 .492 369.167 55 319.046 615.556 273.512527.619 239.369461.C-67 212.816 410 370 191.584 369.333 56 319.1!)9615.833 273.643527.857 239.483461.875 212.918 410 556 191.676 369.500 57 319.35li6l6.ni 273.774528.095 239.598462.083 213.020 410.741 191.767 369.667 58 319.509616.389 273.909528.333 239.716'462.292213.125 410.926 191.862 369.833 59 119 TABLE XIV. ACTUAL TANGENTS, ETC. 37 Ivi7 1 Curve. 2 Curve. 3 Curve. 4 Curve. 5 Curve. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. 1917.14 3700.00 95H.OOO 1KW.OO 639.113 1233.33 479.378 925.000 383.545 740.000 1 1918.008701.07959 0(54 1850.83 639.418 1233.89 479.607 925.417 383.729 740 333 2 1918.973703.33 959.522 1851.67 639.724 1234.44 479.837 925.833 383.912 740.607 3 1919.893705.00 959.981 1852.50 640.030 1235.00 480.000 926.250 384.090 741.000 4 1920.81:3706 67 960.439 1853.33 640.335 1235.56 480.295 920.607 384.279 741.:J33 5 1921.758708.38 960.912 1854.17 640.650 1236.11 480.531 1(27.083 384.408 741.607 6 19*22.703710.00 961.385 1855.00 640.966 1236.67 480.768 927.500 384.657 742.000 7 1923.62 3711.67 961.843 1855.83 641.271 1237.22 480.997 927.917 384.841 742.333 8 1924.53 3713.33 962.301 1856.67 041.577 1237.78 481.226 928.333 385.024 742.007 9 1925.45 3715.00 962.760 1857.50 041.882 1238.33 481.455 928.750 385.207 743.000 10 1926.373716.67 963.218 1858.33 642.188 1238.S9 481.685 929.167 385.391 743.333 11 1927.31 3718.33 963.691 1859.17 642.503 1239.44 481.921 929.583 385.580 743.007 13 1928.263720.00 964.164 1860.00 642.818 1240.00 482.157 930.000 385.769 744.000 13 1929. 17 13721. 67 964.622 1860.83 643.124 1240.56 482.387 930.417 385.952 744.333 14 1930.093723.33 965.080 1861.67 643.430 1241.11 482.616 930.833 386.136 744.607 15 1931.013725.00 965.539 1862.50 643.735 1241.67 482.845 931.250 386.319 745.000 16 1931. 92 1 3726. 67 965.997 1863.33 644.041 1242.22 483. 074 931.667 386.503 745.333 17 1932.873728.33 966.470 1864.17 044.356 1242.78 483.311 932.083 386.692 745.607 18 1933.81 3730.00 966.943 1865.00 044.671 1243.33 483.547 932.500 386.881 746.000 19 1934.73 3731.67 967.401 1865.83 644.977 1243.89 483.776 932.917 387.064 746.333 20 1935.65 3733.33 967.859 1866.67 645.282 1244.44 484.006 933.333 387.248 746 . 667 21 1936.59 3735.00 908.332 1867.50 645.597 1245.00 484.242 933.750 387.437 747.000 22 1937.54 3736.67 968.805 1868.33 645.913 1245.50 484.478 934.107 387.020 747.333 23 1938.46 3738.33 969.263 1869.17 646.218 1240.11 484.708 934.583 387.809 747.607 34 1939.37 8740.00 909.722 1870.00 646.524 1246.67 484.937 935.000 387.993 748.000 25 1940.32 3741.67 970.194 1870.83 646.839 1247.22 485.173 935.417 388.182 748.333 2G 1941.26 3743.33 970.667 1871.67 647.154 1247.78 485.410 935.833 388.371 748.667 27 1942.18 3745.00 971.125 1872 .'50 647.460 1248.33 485.639 936.250 388.555 749.000 28 1943 10 3746.67 971.584 1873.33 647.765 1248.89 485.868 936.607 388.738 749.333 29 1944.01 3748.33 972.042 1874.17 648.071 1249.44 486.097 937.083 388.921 749.667 30 1944.93 3750.00 972.500 1875.00 648.377 1250.00 486.327 937.500 389.105 750.000 31 1945.88 3751.67 972.973 1875.83 648.692 1250.56 486.503 937.917 389.294 750.333 32 1946.82 3753. 33 973.446 1876.67 649.007 1251.11 486.799 938.333 389.483 750.607 33 1947.74 3755.00 973.904 1877.50 649.313 1251.07 487.029 938.750 389.006 751.000 34 1948.65 3756.67 974.363 1878.33 049.618 1252.22 487.258 939.167 389.850 751.333 35 1949.60 3758.33 974.835 1879.17 649.933 1252.78 487.494 939.583 390.039 751.667 36 1950.54 3760.00 975.308 1880.00 650.249 1253.33 487.731 940.000 390.228 752.000 37 1951.46 3761.67 975.767 1880.83 650.554 1253.89 487.960 940.417 390.412 752.333 38 1952 38 3763.33 976.225 1881.07 050.860 1254.44 488.189 940.833 390.595 752.667 39 1953.32 3705.00 976.698 1882.50 651.175 1255.00 488.426 941.250 390.784 753.000 40 1954.27 3766.67 977.170 1883.33 651.490 1255.56 488.662 941.667 390.973 753.333 41 1955.19 3768.33 977.629 1884.17 651.796 1256.11 488.891 942.083 391.157 753.667 42 1956.10 3770.00 978.087 1885.00 652.101 1256.67 489.120 942.500 391.340 754.000 43 1957.05 3771.67 978.560 1885.83 052.416 1257.22 489.357 942.917 391.529 754.333 44 1957.99 3773.33 979.033 1886.67 652.732 1257.78 489.593 943.333 391.718 754.607 45 1958.91 3775.00 979.491 1887.50 653.037 1258.33 489.822 943.750 391.902 755.000 46 1959.83 3776.67 979.949 1888.33 653.343 1258.89 490.052 944.167 392.085 755.333 47 1960 77 3778.33 980.422 1889.17 653.658 1259.44 490.288 944.583 392.274 755.607 48 1961.72 3780.00 980.895 1890.00 653.973 1260.00 490.524 945 000 392.463 756.000 49 1962.63 3781.67 981.353 1890.83 G54.279 1260.56 490.754 945.417 392.647 756.333 5O 1963.55 3783.33 981.812 1891.67 654.584 1261.11 490.983 945.833 392.830 756.667 51 1964.50 3785.00 982.284 1892.50 654.900 1261.67 491.219946.250 393 019 757.000 53 1965.44 3786.67 982.757 1893.33 655.215 1262.22 491.456,946.667 393.208 757.333 53 1966.30 3788.33 983.215 1S94.17 655 5:20 1262.78 491.685947.083 393.392 757.607 54 1967.28 3790.00 983.674 1895.00 655.826 1263.33 491.914:947.500 393.575 758.000 55 1968.22 3791.67 984.14611895.83 656.141 1263.89 492.15l'947.917 393.764 758.333 56 1969.17 3793.33 984.6191896.67 656.456 1264.44 492.387 948.333 393.954 758.607 57 1970.08 3795.00 985.0781897.50 656.762 1265.00 49.2.616948.750 394. 137 1759.000 58 1971.00 3796.67 985.5361898.33 657.008 1205.56 492.845949.167 394.320759.333 59 1971.94 3798.33 9^6.009 1899.17 657.383 1266.11 493.082949.583 394. 509 1759.007 120 'TABLE XIV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 Curve. 1O Curve. 37" Tan. 319.667 Arc. 616.667 Tan. 274.044 Arc. Tan. Arc. Tan. Arc. 411.111 Tan. 191.957 Arc. 370.000 M. 528.571 239.835 462 500 213.230 O 3 19.8:20 616.944 274.175528.810239.949 462.708 213.332 411.296 192.048 370.167 1 319.972 617.222 274.306 529.048 240 064 462.917 213.434 411.481 192.140 370.333 2 320.125 617.500 274.437 529.286 240.179 463.125 213.536 411.667 192.232 370.500 3 320.278 617.778 274.568 529.524 240.293 463.333 213.638 411.852 192.324 370.667 4 320.436 618.056 274.703 529.762 240.412 463.542 213.743 412.037 192.418 370.833 5 320.593 618.333 274.838 530.000 240.530 463.750 213.849 412.222 192.513 371.000 6 320.746 618.611 274.970 530.238 240.644 463.958 213.951 412.407 192.605 371.167 7 320.899 618.889 275.101 530.476 240.759 464.167 214.053 412.593 192.697 371.333 8 321.052 619.167 275.232 530.714 240.874 464.375 214.155 412.778 192.788 371.500 9 321.205 619.444 275.363 530.952 240.989 464.583 214.256 412.963 192.880 371.667 10 321.363 619.722 275.498 531 . 190 241.107 464.792 214.362 413.148 192.975 371.833 11 321.520 620.000 275.633 531.429 241.225 465.000 214.467 413.333 193.070 372.000 12 321.673 620.278 275.764 531.667 241.340465.208 214.569 413.519 193.161 372.167 13 321.826 620.556 275.895 531.905 241.454 465.417 214.671 413.704 193.253 372.333 14 321.979 620.833 276.026 532.143 241.569 465 625 214.773 413.889 193.345 372.500 15 322.132 621.111 276.157 532.381 241.684 465.833 214.875 414.074 193.437 372.667 16 322.289 621.389 276.292 532.619 241.802 466.042 214.980 414.259 193.531 372.8.33 17 322.447 621.667 276.42, 532.857 241.920 466.250 215.085 414.444 193.626 373.000 18 322.600 621.944 276.558 533.095 242.035 466.458 215.187 414.630 193.718 373.167 19 322.753 622.222 276.689 533.333 242.150 466.667 215.289 414.815 193.810 373.333 20 322.910 622.500 276.825 333.571 242.268 466.875 215.394 415.000 193.904 373.500 21 323.068 622.778 276.960 533.810 242.386 467.083 215.499 415.185 193.999 373.667 22 323.221 623.056 277.091 534.048 242.501 467.292 215.601 415.370 194.091 373.833 23 323.374 623.333 277.222 534.286 242.616 467.500 215.703 415.556 194.183 37'4.000 24 323.531 623.611 277.357 534.524 242.734 467.708 215.808 415.741 194.277 374.167 25 323.689 623.889 277.492 534.762 242.852 467 917 215.913 415.926 194.372 374.333 26 323.842 624.167 277.623 535.000 242.967 468.125 216.015 416.111 194.464 374.500 27 323.995 624.444 277.754 535.238 243.082 468.333 216.117 416.296 194.555 374.667 28 324.147 624.722 277.885 535.476 243.196 468.542 216.219 416.481 194.647 374.833 29 324.300 625.000 278.016 535.714 243.311 468.750 216.321 416.667 194.739 375.000 30 324.458 625.278 278.151 535.952 243.429 468.958 216.426 416.852 194.834 375.167 31 324.616 625.556 278.287 536.190 243.547 469.167 216.532 417.037 194.928 375.3133 32 324.768 625.833 278.418 586.429 243.662 469.375 216.634 417.222 195.020 375.500 33 324.921 626.111 278.549 536.667 243.777 469.583 216.735 417.407 195.112 375.667 34 325.079 626.389 278.684 536.905 243.895 469.792 216.841 417.593 195.207 375.833 35 325.237 626.667 278.819 537.143 244.013 470.000 216.946 417.778 195.301 376.000 36 325.389 626.944 278.950 537.381 244.128 470.208 217.048 417.963 195.393 376.167 37 325.542 627.222 279.081 537.619 244.243 470.417 217.150 418.148 195.485 376.333 38 325.700 627.500 279.216 537.857 244.361 470.625 217.255 418.333 195.579 376.500 39 325.858 627.778 279.351 538.095 244.479 470. 833 217.360 418.519 195.674 376.667 40 326.010 628.056 279.482 538.333 244.594 471.042 217.462 418.704 195.766 376.833 41 326.163 628.333 279.613 538 571 244.709 471.250 217.564 418.889 195.858 377.000 42 326.321 628.611 279.749 538.810 244.827 471.458 217.669 419.074 195.952 377.167 43 326.479 628.889 279.884 539.048 244.945 471.667 217.774 419.259 196.047 377.333 44 326.631 629.167 280.015 539.286 245.060 471.875 217.876 419.444 196.139 377.500 45 326.781 629.444 280.146 539.524 245.175 472.083 217.978 419.630 196.231 377.667 46 326.942 629.722 280.281 539.762 245.293 472.292 218.083 419.815 196.325 377.833 47 327.100 630.000 280.416 540.000 245.411 472.500 218.188 420.000 196.420 378.000 48 327.252 630.278 280.547 540.238 245.526 472.708 218.290 420.185 196.512 378.167 49 327.405 630.556 280.678 540.476 245.640 472.917 218.392 420.370 196.604 378.333 50 327.563 630.833 280.813 540.714 245.759 473.125 218.498 420.556 196.698 378.500 51 327.721 631.111 280.348 540.952 245.877 473.333 218.603 420.741 196.793 378.667 52 327.873 631.389 281.079 541.190 245.992 473.542 218.705 420.926 196.885 378.833 53 328.026 631.667 281.210 541.429 246.106 473.750 218.807 421.111 196.976 379.000 54 328.184 631.944 281.346 541.667 246.225 473.958 218.912 421.296 197.071 379.167 55 328.342 632. 22 -2 281.481 541.905 246.343 474.167 219.017 421.481 197.166 379.333 56 328.494 632.500 281.612 542.143 246.458 474.375 219.119 421.667 197.258 379.500 57 328.647 632.778 281.743 542.381 246.572 474.583 219.221 421.852 197.349 379.667 58 328.805 633.056 281.878 542.619 246.691 474.792 219.326 422.037 197.444 379.833 59 131 TABLE XIV. ACTUAL TANGENTS, ETC. 38 M7 1 Curve. 2 Curve. 3 Curve. 4 Curve. 5 Curve. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. I Arc. ~0~ 1972.89 3800.00 9S6.481 1900.00 657.698 1266.67 493.318 950.000394.699760.000 1 1973.81 3801.67 986.9401900.83 658.003 1267.22 493.547 950.417394 882 760.333 2 1974.72 3803.33 987. 398 1 1901. 67 658.309 1267.78 493.777 950.833395.065 760.667 3 1975.67 3805.00 987.871 1902.50 658.624 1268.33 494.013 951.250395.255 761.000 4 1976.61 3806.67 988.344 1903.33 658.939 1268.89 494.249 951.667395.444 761.333 5 1977. 53 1 3808. 33 988.802:1904.17 659.245 1269.44 494.479 952.083395.627 761.667 6 1978.45 3810.00 989. 260 ! 1905. 00 659.551 1270.00 494.708 952.500395.810 762.000 7 1979.3!) 3811.67 989.733 1905.83 659.866 1270.56 494.944 952.9J7i396.000 762.333 8 1980.34 3813.33 990.206 1906.67 660.181 1271.11 495.181 953.333396.189 762.667 9 1981.28 3815.00 990.678 1907.50 660.496 1271.67 495.417 953.750 396.378 763.000 10 1982.23 3816.67 991.151 1908.33 660.811 1272.22 495.653 954.167 396.567 763.333 11 1983.15 3818.33 991.610 1909.17 661.117 1272.78 495.883 954.583:396.750 763 667 12 13 1934.06 1985.01 3820.00 3821.67 992.068 992.541 1910.00 1910.83 661.423 661.738 1273.33 1273.89 496.112 496.348 955.000J 396. 934 955.417397.123 764.000 764.333 14 1985.95 3823 33 993. 013 [191 1.67 662.053 1274.44 496.585 955.833:397.312 764.667 15 1986.87 3825.00 993. 472 ! 191 2. 50 662.358 1275.00 496.814 956. 250; 397.495 765.000 16 1987.79 3826.67 993.930il913.33 662.664 1275.56 497.043 956. 667 j 397. 679 765.333 17 1988.73 3828.33 994.403 1914.17 662.979 1276.11 497.280 957.083397.868 765 . 667 18 1989.68 3830.00 994.876 1915.00 663.294 1276.6? 497.516 957.500 398.057 766.000 19 1990.60 3831.67 995.334 1915.83 663.600 1277.22 497.745 957.917 398.241 766.333 20 1991.51 3833.33 995.792 1916.67 663 906 1277.78 497.974 958.333 398.424 766.667 21 1992.46 3835.00 996.265 1917.50 664.221 1278.33 498.211 958.750398.613 767.000 22 1993.40 3836.67 996.738 1918.33 664.536 1278.89 498.447 959.167 398.802 767.333 23 1994.35 3838.33 997.211 1919.17 664.851 1279.44 498.684 959.583 398.991 767.667 24 1995.29 3840.00 997.683 1920.00 665.166 1280.00 498.920 960.000 399.181 768.000 25 1996.21 3841 67 998.142 1920 83 665.472 1280.56 499.149 960.417 399.364 768.333 26 1997.13 3843 33 998.600 1921.67 665.777 1281.11 499.378 960.833 399.547 768.667 27 1998.07 3845.00 999.073 1922.50 666.093 1281.67 499.615 961 250 399.730 769.000 28 1999.02 3846.67 999.545 1923.33 666.408 1282.22 499.851 961 . 667 399.926 769.333 29 1999.96 3848.33 1000.02 1924.17 666.723 1282.78 500.088 962.083 400.115 769.667 30 2000.91 3850.00 1000.49 1925.00 667.038 1283.33 500.324 962.500 400.304 770.000 31 2001.83 3&51.67 1000.95 1925.83 667.344 1283.89 500.553 962.917 400.48? 770.333 32 2002.74 3853.33 1001.41 1926.67 667.649 1284.44 500.782 963.333 400.671 770.667 33 2003.69 3855.00 1001.88 1927.50 667.965 1285.00 501.019 963.750 400. 86( 771.000 34 2004.63 3856.67 1002.35 1928.33 668.280 1285.56 501.255 964.167 401.049 771.333 35 2005.58 3858.33 1002.83 1929.17 668.595 1286.11 501.492 964.583 401.238 771.667 36 2006.52 3860.00 1003.30 1930.00 668.910 1286.67 501.728 965.000 401.427 772.000 37 2007.44 3861.67 1003.76 1930.83 669.216 1287.22 501.957 965.417 401.611 772.333 38 2008.36 3863.33 1004.22 1931.67 669.521 1287.78 502.186965.833 401.794 772.667 39 2009.30 3865.00 1004.79 1932.50 669.836 1288.33 502.423 966.250 401.983 773.000 4O 2010.25 3866.67 1005.16 1933. as 670.152 1288.89 502.659 966.667 402.172 773.333 41 2011.19 3868.33 1005.73 1934.17 670.467 1289.44 502.896967.083 402.361 773.667 42 2012.14 3870.00 1006.11 1935.00 670.782 1290.00 503 132 967.500 402.551 774.000 43 2013.06 3871.67 1006.56 1935.83 671.088 1290.56 503.361 967.917 402.734 774.333 44 2013.97 3873.33 1007.02 1936.67 671.393 1291.11 503.591 968.333 402.917 774.667 45 2014.92 3875.00 1007.50 1937.50 671. 708 J1291. 67 503.827l96S.750 403.107 775.000 46 2015.86 3876.67 1007.97 1938.33 672. 023 '1292. 22 504.063969.167 403.296 775.333 47 2016.81 3878.33 1008.44 1939.17 672.339! 1292. 78 504.300969.583 403.485 775.667 48 2017.75 3880.00 1008.91 1940.00 672.65411293.33 504.536:970.000 403.674 776.000 49 2018.67 3881.67 1009.37 1940.83 672.959 1293.89 504.765,970.417 403.857 776.333 50 2019.59 3883.33 1009.83 1941.67 673.265 1294.44 504.995970.833 404.041 776.667 51 2020.53 3885.00 1010.30 1942.50 673.580 1295.00 505 231 971.2501404.230 777.000 52 2021.48 3886.67 1010.78 1943.33 673.895 1295.56 505.467971*667404.419 777.333 53 2022.42 3888.33 1011.25 1944.17 674.210 1296.11 505.704 972.083404.608 777.667 54 2023.37 3890.00 1011.72 1945.00 674.526 1296.67 505.940972.500:404.797 778.000 55 2024.293891.67 1012.18 1945.83 674.831 1297.22 506.169972.917404.981 778.333 56 2025. 20 3893. 33! 101 2. 64 19-16.67 673.187 1297.78 506 . 399 973 . 333 405 . 1 64 778.667 57 2026.153895.00 1013.11 1947.50 575.452 1298.33 506 . 635 973 . 750 '4 05 . 353 779.000 58 2027. 09 13896.67 1013.58 1948.33 675.767 1298.88 506.871 974.167405.542 779.333 59 2028. 0413898. 33 1014. 06 1949.1? 676.082 1299.44 507.108974.583i405.732 779.667 TABLE XIV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 Curve. 1O Curve. 38 Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. M. 328.963 633.333 282.013542.857 246.809 475.000 219.431 422.222 197.539 380.000 O 329.115633.611 282.144543.095 246.923 475.208 219.533 422.407 197.630 380.167 ' 1 329. 268 1633.889 329.426634.167 282.2751543 333 282.410543.571 247.038 247.156 475.417 475.625 219. 635 219.740 422.593 422.778 197.722 197.817 380.333 380.500 2 3 329.583 634.444 282.545:543.810 247.275 475.833 219.845 422.963 197.912 380.667 4 329.736 634.722 282.677 544.048 247.389 476.042 219.947 423.148 198.003 380.833 5 329.881) 635.000 282.808 544.286 247.504 476.250 220.049 423.333 198.095 381.000 6 330.047 635.278 282.943 544.524 247.622 476.458 220.154 423.519 198.190 381.167 7 330.204 635.556 283.078 544.762 247.741 476.667 220.260 423.704 198.284 381 .333 8 330.362 635.833 283.213 545.000 247.859 476.875 220.365 423.889 198.379 381.500 9 330.520 636.111 283.348 545.238 247.977 47". 083 220.470 424.074 198.474 381 667 10 330.673 636.389 283.479 545.476 248.092 47". 292 220.572 424.259 198.566 381.833 11 330 825 636.667 283.610 545.714 248.207 47". 500 220.674 424.444 198.657 382.000 12 330.983 636.944 883,746 545.952 248.325 47". 708 220.779 424.630 198.752 382 167 13 331.141 637.222 283.880 546.190 24.443 47". 917 220.884 424.815 198.847 382.333 14 331.294 637.500 284.012 546.429 248.558 478.125 220.986 425.000 198.938 382.:.00 15 881.446 637.778 284.143 546.667 248.672 478.333 221.088 425.185 199.030 382 667 16 331.604 638.056 284.278 546.905 248.791 478.542 221.193 425.370 199.125 382.833 17 331.762 638.333 284.413 547.143 248.909 478.750 221.298 425.556 199.220 383.000 18 331.915 638.611 284.544 547.381 249.024 478.958 221.400 425.741 199.311 383.167 19 332.067 638.889 284.675 547.619 249.138 479.167 221.502 425.926 199.403 383.333 2O 332.225 639.167 284.810 547.857 249.257 479.375 221.607 426.111 199.498 383.500 21 332.383 6:39.444 284.945 548.095 249.375 479.583 221.713 426.296 199.592 383. C67 2 2 332.540 639.722 285.080 548.333 249.493 479.792 221.818 426.481 199.687 383.833 23 332. 60S 640.000 285.215 548.571 249.611 480.000 221.923 426.667 199.782 384.000 24 332.851 640.278 285.347 548.810 249.726 480.208 222.025 426.852 199.874 384 107 25 383.004 640.556 285.478 549.048 249.841 480.417 222.127 427.037 199.965 384.333 26 333.161 640.833 285.613 549.286 249.959 480.625 222.232 427.222 209.060 384.500 27 333.319 641.111 285.748 549.524 250.077 480.833 222.337 427.407 200.155 384.667 28 333.477 641.389 285.883 549.762 250.196 481.042 222.442 427.593 200.249 384.833 29 333.634 641.667 286.018 550.000 250.314 481.250 222.547 427.778 200.344 385.000 30 3:33.787 641.944 289 149 550.238 250.429 481 458 222.649 427.963 200.436 385.167 31 333.940 642. 22* 286.280 550.476 250 543 481.667 222.751 428.148 200.528 385.333 32 834.098 642.500 286.415 550.714 250.661 481.875 222.856 428.333 200.622 385.500 33 334.255 642.778 286.550 550.952 250.780 482.083 222.962 428.519 200.717 385.667 34 334.413 643.056 286.686 551.190 250.898 482.292 223.067 428.704 200.812 385.833 35 334.571 643.333 286.821 551.429 251.016 482.500 223.172 428.889 200.906 386.000 36 334.723 643.611 286.952 551.667 251.131 482.708 223.274 429.074 200.998 386.167 37 3:34.876 643.889 287.083 551.905 251.246 482.917 223.376 429.259 201.090 386.333 38 335.034 644.167 287.218 552.143 251.364 483.125 223.481 429.444 201.184 386.500 39 335.192 644.444 287.353 552.381 251.482 483.333 223.586 429.630 201.279 386.667 4O 335.349 644.722 287.488 552.619 251.600 483.542 223.691 429.815 201.374 386.833 41 335.507 645.000 287.623 552.857 251.719 483.750 223.796 430.000 201.468 387.000 42 335.660 645.278 287.754 553.095 251.833 483 958 223.898 430.185 201.560 387.167 43 3:35.813 645.556 287.885 553.333 251.948 484.167 224.000 430.370 .201.652 387.3:33 44 335.970 645.833 288.021 553.571 252.066 484.375 224.106 430.556 201.747 387.500 45 336.128 646.111 288.156 553.810 252.185 484.583 224.211 430.741 201.841 387.607 46 336.285 646.389 288.291 554.048252.303 484.792 224.316 430.926 201.936 387.833 47 336 443 646.667 288.426 554.286 252.421 485.000 224.421 431.111 208.031 388.000 48 336.596 646.944 288.557554.524 252.536 485.208 224 523 431.296 202.122 388.167 49 336.749 647.222 288.688554.762 252.651 485.417 224.625 431.481 202.214 388.333 5O 336 906 647.500 288.823555.000252 769 485.625 224.730 431.667 202.309 388. 00 51 3:37.064 647 . 77'8 288 . 958 555 . 23S 252 . 887 485.833 224.835 431.852 202.404 388. 007 52 337.222 648.056 280.094 555.476 253.005 486.042 224.940 432.037 202.498 388. K33 53 337.370 64S 3331289 . 220 555 . 714 253 .124 486.250 225.045 432.222 202.59.3 389.000 54 337.532 648.611 289.30D 555.952 2ft3 238 48(5.458 225.147 432.407 202.685 389.167 55 337 . OH5 64H . 889 289 . 491 556 . 1 90 253 . 353 486.667 225.249 432.593 202.776 389.333 56 337.843 6-19. 107 289. (26 556.429 253.471 486.875 225.355 432.778 202.871 389.500 57 338.000 649.444 289 761 556.667 253.590 487.083 225.460 432.963 202.966 389.607 58 338 . 158^ 649 . 702 289 . 896 556 . 905 253 . 708 487.292 225.565 433.148 203.060 389.833 59 TABLE XIV. ACTUAL TANGENTS, ETC. 39 1 Curve. 3 Curve. 3 Curve, 4 Curve. 5 Curve. M. Tan. 2028798 Arc. Tan. A re. Tan. Arc. Tan. Arc. 975.000 Tan. Arc. 780. UOO O 3900.00 1014.53 1950.00 676.398 1300.00 507.344 405.921 1 2029.93 3901.67 1015.00 1950.83 676.713 1300.56 507.581 975.417 406.110 780. 333 2 2030.87 3903.33 1015.47 1951.67 677.028 1301.11 507.817 975.833 406.299 780.607 3 2031.79 3905.00 1015.93 1952.50 077.333 1301.67 508.046 976.250 406.482 781.000 4 2032.71 3906.67 1016.39 1953.33 077 . G3 ( J 1302.22 508.275 976.667 406.660 781.333 5 2033 65 3908.33 1016.86 1954.17 077. 95^ 1302.78 508.512 977.083 406.855 781.667 6 203 t. GO 3910.00 1017.34 1955.00 078.269 1303.33 508.748 977.500 407.044 182.000 7 2035.54 3911.67 1017.81 1955.83 078.585 1303.89 508.985 977.917 407.233 782.333 8 2033.49 3913.33 1018.28 1956.67 678.900 1304.44 509.221 978.333 407.422 782.607 9 2037.43 3915.00 1018.75 1957.50 679.215 1305.00 509.457 978.750 407.611 783.000 1O 2038.38 3916.67 1019.23 1958.33 679.530 1305.56 509.694 979.167 407.801 ; 83. 333 11 2039.30 3918.33 1019.69 1959.17 679.836 1306.11 509.923 979.583 407.984 783. G07 12 2040.21 3920.00 1020.14 1960.00 680.141 1306.07 510.152 980.000 408.107 784.000 13 2041.16 3921.67 1020.62 1960.83 680.456 1307.22 510.389 9S0.417 408.357 784.333 14 2042.10 3923.33 1021.09 1961.67 680.772 1307.78 510.625 980.833 408.546 784.067 15 2043.05 3925.00 1021.56 1962.50 681.087 1308.33 510.861 981.250 408.735 785.000 16 2044.00 3926.67 1022.04 1963.33 681.402 1308.89 511.098 981.667 408.924 785.333 17 2044.94 3928.33 1022.51 1904.17 681.717 1309.44 511.334 982.083 409.113 785.607 18 2045.89 3930.00 1022.98 1965.01 68.2.03.' 1310.00 511.571 982.500 409.302 786.000 19 2046.83 3931.67 1023.45 1965.83 682.347 1310.56 511.807 982.917 409.491 786.333 20 2047.78 3933.33 1023.93 1966.67 682.663 1311.11 512.043 983.333 409.680 786.667 21 2048.69 3935.00 1024.38 1967.50 682.968 1311.67 512.273 983.750 409.804 787.000 22 2049.61 3936.67 1024.84 1968.33 683.274 1312.22 512.502 984.167 410.047 787.333 23 2050.56 3938.33 1025.32 1909.17 683.589 1312.78 512.738 984.583 410.236 787.007 34 2051.50 39 JO. 00 1025.79 1970.00 683.904 1313.33 512.975 985.000 410.426 788.000 35 2052.45 3941.67 1026.26 1970.83 684.219 1313.89 513.211 985.417 410.615 788.333 36 2053 39 3913.33 1026.73 1971.67 084.534 1314.44 513.447 985.833 410.804 788.607 37 2054.34 3945.00 1027.21 1972.50 684.850 1315. CO 513.084 986.250 410.993 789.000 38 2055.28 3946.67 1027.68 HI73.33 685.165 1315.50 513.920 986.667 411.182 789.333 39 2056.23 3948.33 1028. 15 1974.17 085.480 1316.11 514.157 987.083 411.371 789.007 30 2057.17 3950.00 1028 62 1975.00 685.795 1316.67 514.393 987.500 411.560 790.000 31 2058.12 3951.67 1029.10 1975.83 086.110 1317.22 514.629 987.917 411.750 790.333 33 2059.06 3953.33 1029.57 1976.67 086.425 1317.78 514.800 988.333 411.939 790.067 33 2059.98 3955.00 1030 03 1977.50 686.731 1318.33 515.095 888.750 412.122 791.000 34 2060.90 3956.67 1030.49 1978.33 087.037 1318.89 515.324 989.167 412.305 791.333 35 2061.84 3958.33 1030.96 1979.17 687.352 1319.44 515.561 989.583 412.495 791. G07 36 2062.79 3960.00 1031.43 1980.00 687.667 1320.00 515.797 990.000 412.684 792.000 37 ^063.73 3961.67 1' :31.90 1980.83 687.982 1320.56 516.033 990.417 412.873 792.333 38 2064.68 3963.33 1032.38 1981.67 688.297 1321.11 516.270 990.833 413.062 792.007 39 2065.62 3965.00 1032.85 1982.50 688.612 1321.67 516.506 991.250 413.251 793 000 40 2066.57 3966.67 1033.32 1983.33 688.928 1322.22 516.743 991.667 413.440 793.333 41 2067.52 3968.33 1033.80 1984.17 689.243 1322.78 516.979 992.083 413.629 793.667 43 2068.46 3970.00 1031.27 19a5.00 089.558 1323.33 517.215 992.500 413.819 794.000 43 2069.41 3971.67 1034.74 1985.83 689.873 1323.89 517.452 992.917 414 008 794.333 44 2070.35 3973.33 1035.21 1986.67 690.188 1324.44 517.088 993.3,'33 414.197 794.607 45 2071.30 3975.00 1035.69 1987.50 690.503 1325.00 517.925 993.750 414.386 795.000 46 .W2.243976.67 1036.16 1988.33 690.819 1325.56 518.161 994.167 414.575 795.333 47 2073.163978.33 1036.62 1989.17 691.124 1320.11 518.390 994.583 414.758 795. G67 48 2074.083980.00 1037.08 1990.00 691.430 1&6.67 5l8.19i995.000 414.942 796.000 49 2075.023981.67 1037.55 1990.83 091.745 1327.22 518.856 995.417 415.131 796.333 50 2075.973983.33 1038.02 1991.67 692.060 1327.78 519.C9.; 995.833 415.320 796.667 51 2076.91 3985.00 1038.49 1992.50 692.375 1328.33 519.3-29 996.250 41 5. 509 j 797. 000 53 2077. 80 3986. 67 1038.97 1993.33 692.691 1328.89:519.505 996.667 415 G98 797.333 53 2078. 80 13988. 33 1039.44 1994.17 093.006 1329. 44!519. 801 997.083 415.888 797.007 54 2079. 75 13990. 00 11039. 91 1995.00 693.321 1330.00520.038 997.500 416.077 798.000 55 2080.603991.671040.39 1995.83 693 636 1330.50520.274 997.917 416.260 798.333 56 2081.643993.831048.86 1996.67 093.951 1331.11 520.511 998.833 416.455 798.667 57 2082.583995.001041.33 1997.50 694.266 1331.67520.747 998.750 416.644 799.000 58 J083. 53 3996. 07 104 1.80 1998.33 694.581 1332.22520.983 999.167 416.833 799.333 59 12081. 4813998. 33; 1045. 28 1999.17694.897 1332.78521.220 999.583 417.022 799.667 124 TABLE XIV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 Curve. 10 Curve. 30 Tan. Arc. Tan. Arc. Tan. 253.826 Arc. Tan. Arc. Tan. Arc. 390".000 M. O 338.310 650. OUO 290.031 557.143 487.500 225.670 433.333 203.155 838.473 050.278 2 2138.42 4093.33 1069.252040.67 712.880 1304.44 534.709 1023.33427.815 818.607 57 2139.37 4095.00 1069.722047.50 713 195 1305.00 534.945 1023.754-38.004 819.000 58 2140.31 4096.67 1070.19,2048.33 713.510 1305.56 535.181 1024.174-38.193 819.333 59 2141.26 4098.33 1070. 67 j 2049. 17 713.8261366.11 535.418 1024.58.428.382 819.667 126 TABLE XIV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 Curve. 10 Curve. 4O 3l7 Tan. Arc. Tan. Arc. Tan. | Arc. Tan. Arc. Tan. Arc. 347.726 666.667298.099 571.429 260 . 886 500 . 000 '231 . 947 444 . 444 208 - 806 400 . 000 o 347.884 666. 944 298. 234s 57 1.667 261.005 500. 208 '232. 052 444.630120* 901|400.167 1 348.041 667.222 298.869 571. 905 261.123500.417232.157 444. 815! 20^ 995400.333 2 348.199 667. 500 298. 504 1 572. 143 261.241 500.625232.263 445.000 20 .090 400.500 3 348.357 667.778298.639 572.381 261.359500 833:232.368 445.185j20lM85400.667 4 348.514 668.056298.774 572.619 261.478 501.042 232.473 445 . 370 20S . 279 400 . 833 5 348.672 668.333298.909 572.857 261.596501.250 232.578 445.556 209.374401.000 6 348.829 668.611:299.045 573.095 261.714501.458 232.683 445.741 209. 4691401. 167 7 348.987 668.889299.180573.333 261.833501.667 232.788 445.926 209.563 401.333 8 349.145 669.167 299.315 573.571 261.951 501.875 232.893 446.111 209.658 401.500 9 349.302 669.444 299.450 573.810 262.069 502.083 232.999 446.296 209.752 401.667 10 349.460 669. 722 299. 5&5 574.048 262.187502.292 233.104 446. 481 1209. 847 401.833 11 349.618 670.000299.720 574 286 262.306 502.500 233.209 446.667 209.942 402.000 13 349.775 670. 278 i 299. 855 574.524 262.424 502.708 233. 31 4 1446.852 210.036 402.167 13 349.933 670.556299.991 574.762 262 542 502.917 233.419 447.037 210.131 402.333 14 350.091 670. 833 1 300. 126 575.000 262.660503.125 233.524 447.222 210.226 402.500 15 350.248 671.1 Hi 300. 261 575.238 262.779:503.333 233.630 447.407 210.320 402.667 16 350.406 671.389300.396 575.476 262. 897 |503.542 233.735 447.593 210.415 402.833 17 350.563 671.667300.531 575.714 263.015 503.750 233.840 447.778 210.510 403.000 18 350.721 671.944 300.666 575.952 263.133 503.958 233.945 447.963 210.604 403.167 19 350.879 672.222 300.801 576.190 263.252 504.167 234.050 448.148 210.699 403.333 2O 351.036 672.500 300.937 576.429 263.3;OJ504.375 234.155 448.333 210.794 403.500 31 351.194 672.778 301.072 576.667 263.488 504.583 234.260 448.519 210.888 403.667 22 351.. 352 673.056 301.207 576.905 263.607 504.792 234.366 448.704 210.983 403.833 23 351. 509 673.333 301.342 577.143 263.725 505.000 234.471 448.889 211.078 404.000 24 351.667 673.611 301.477 577.381 263.843 '505.208 234.57'6 449.074 211.172 404.167 25 351.825 673.889 301.612 577.619 263.961 505.417 234.681 449.259 211.267 404.333 26 351.982 674.167 301.747 577.857 264.080 505.625 234.786 449.444 211.362 404.500 21 352.140 674.444 301.883 578.095 264.198 505.833 234.891 449.630 211.456 404.667 28 352.297 674.722 302.018 578.333 264.316 506.042 234.996 449.815 211.551 404.833 29 352.455 675.000 302.153 578.571 264.434 506.250 235.102 450.000 211.646 405.000 3O 862.613 675.278 302.288 578.810 264.553 506.458 2a5.207 450.185 211.740 405.167 31 352.770 675.556 302.423 579.048 264.671 506.667 235.312 450.370 211.835 405.333 32 852.928 675.833 302.558 579.286 264.789 506.875 235.417 450.556 211.930 405.500 33 b53.086 676.111 302.693 579.524 264.908 507.083 235.522 450.741 212.024 405.667 34 353.243 676.389 302.828 579.762 265.026 507.292 235.627 450.926 212.119 405.833 35 353.401 676.667 302 964 580.000 265.144 507.500 235.732 451.111 212.214 406.000 36 863.559 676.944 303.099 580.238 265.262 507.708 235.838 451.296 212.308 406.167 37 353.716 677.222 303.234 580.476 265.381 507.917 235.943 451.481 212.403 406.333 38 353.874 677.500 303.369 580.714 265.499 508.125 236.048 451.667 212.498 406.500 39 354.031 677.778 303 504 580.952 265.617 508.333 236.153 451.852 212.592 406.667 40 354.189(678.056 303.639 581.190 265.735 508.542 236.258 452.037 212.687 406.833 41 354.347 678.333 303.774 581.429 265.854 508.750 236.363 452 222 212.782 407.000 42 354.504 678.611 303.910 581.667 265.972 508.958 236.469 452.407 212.876 407.167 43 354.662678.889 304 045 581.905 266.090 509.167 236.574 452.593 212.971 407.333 44 354.824679.167304.184 582.143 266.212 509.375 236.682 452.778 213.068 407.500 45 354.987679.444304 323 582.381 266.334 509. 5&3 236.790 452.963 213.168 407.667 46 355. 144 ! 679. 722 304. 458 582 619 266.452509.792 236.896 453.148 213.261 407.833 47 355 . 302 680 . 000 304 . 593 582.857 266. 570 !510. 000 237.001 453.333 213.355 408.000 48 355.460 680.278 304.729 583.095 266.689 510.208 237.106 453.519 213.450 408.167 49 355.617 680.556 304.864 583.333 266.807 510.417 237.211 453.704 213.545 408.333 50 355 . 775 680 . 833 304 . 909 583.571 266.925510.625 237.316 453.889 213.639408.500 51 355.933681.111 805.134:583.810 267.044510.883 237.421 454.074 21 3. 734 '408. 667 52 356.090681.389305.269 584.048 267.162 511.042 237.526 454.259 213.829408.833 53 356. 248 681. 6671305. 404 584.286 267.280 511.250 237.632 454.444 213 923409.000 54 356.406681.944305.53!) 584.524 267.398 511.458 -'37.737 454.630 214.018 409.167 55 356 . 563 682 . 222 305 . (>75 584.762 267.517 511.667 237.842 454.815 214.113409.333 56 356.721 682. 500 305. H 10 585.000 267.635 511.875 237.947 155.000 214.207409.500 57 356 . 878 682 . 778 305 . 945 5S5.238 267.753 512.083 238.052 455.185 214.302409.667 58 357.036:683.056306.080 585.476 267.871 512.292 238.157 455.370 214.397409.833 59 127 TABLE XIV. ACTUAL TANGENTS, ETC. 41 1ST 1 Curve. 2 Carve. 3 Curve. 4 Curve. 5 Curve. Tan. Arc. Tan. Arc Tan. Arc. Tan. Arc. Tan. Arc. O [2142.20 4100.00 10n. 14 2050.00; 714. 141 1366.67 535.654 1025.00 428.571 820.000 1 12143.18 4101.671071.632050.83 714.465 1367. 22 535 . 898 i 1 025 . 42 428 . 766 820.333 2 2144.15 4103.331072.11 2051.67 714.790 1367.78 536.141 1025.83 428.961 820.667 3 2145.10 4105.00 1072.59 -,'052.50 715.105 1368.33 536.378 1026.25 429.150 821.000 4 2146.04 4106.67 1073.06 2053.33 715.420 1368.89 536.614 1026.67 429.339 821.333 5 2146.99 4108.33 10?3.53 2054.1? 715.736 1369.44 536.850 1027.08 429.528 821.6(57 6 2147.93 4110.00 1074.00 2055.00 716.051 1370.00 537.087 1027.50 429.71? 8-J2.000 7 2148.88 4111.6? 1074.48 2055.83 716.366 1370.56 537.323 1027.92 429.907 822.333 8 2149.82 4113.33 1074.95 2056.67 716.681 1371.11 537.560 1028.33 430.0% 822.667 9 2150.7? 4115.00 1075.42 2057.50 716.996 1371.6? 537.796 1028. 7'5 430.285 823.000 10 2151.71 1116.6? 1075.90 2058.33 717.311 1372.22 538.032 1029.17 430.474 823.333 11 2152.69 4118.33 1076.38 2059.17 717.636 1372.78 538.276 1029.58 130.669 823.667 13 2153 66 4120.00 1076.87 -'060.00 717.961 1373.33 538.520 1030.00 4:10.864 824 000 13 2154.61 4121.67 1077.34 2060.83 718.276 1373.89 538.756 1030.4:3 331.053 824.333 14 2155.55 4123.33 1077.8-' 2061. 6 r 718.591 1374.41 538.992 1030.83 431.242 824.667 15 2156.50 4125.00 1078.29 2062.50 718.906 1375.00 539.22!) 1031.25 431.431 825.000 16 2157.44 412(5.67 1078.76 2063.33 719.222 1375.56 539.465 1031.6? 431.620 825.333 17 2158.3',) 4128.33 1079.23 2064.1? 719.53? 1376.11 539.701 1032.08 431.809 825.667 18 2159.33 4130.00 1079.71 2065.00 719.852 1376.67 539 938 1032.50 431.999 826.000 19 2160.28 1131.67 1080.18 ^065.83 720.167 1377.22 540.17'4 1032.92 432.188 826.333 20 2161.22 4133.33 1080.65 2066.67 720.482 1377.78 540.411 1033.33 432.37? 826.667 81 2162.20 4135.00 1081.14 2067.50 720.80? 1378 33 510.654 1033.75 432.572 8-,'7.000 22 2163.17 4136.6? 1081.63 2068.33 721.132 1378.89 540. 80S 1034.1? 432.767 827. 333 23 2164.12 4138.33 1082.10 2069.1? 721.44? 1379.44 541.134 1031.58 432.956 827.667 24 2165.06 4140.00 1082.5? 2070.00 721.762 1380.00 541.371 1035.00 433.145 828.000 25 2166.01 4141.67 1083.04 2070.83 722.077 1380.56 541.607 1035.42 433.334 828.333 26 2166.95 4143.33 1083.52 2071.67 722.392 1381.11 541.843 1035.83 433.523 828.667 2V 2167.90 4145.00 1083.99 2072.50 722.707 1381.6? 542.080 1036.25 433.712 829.000 28 2168.84 4146.6? 1084.46 2073.33 723.0:>3 1382.22 542.316 1036.6? 433.901 829.333 29 2169.82 4148.33 1084.95 2074.17 723.347 1382.78 542.560 1037.08 434.096 829.667 30 2170.79 4150.00 1085.44 2075.00 723 672 1383.33 542.803 1037.50 434.291 830.000 31 2171.74 4151.67 1085.91 2075.83 723.987 1383.89 543 010 1037.92 434.480 830.333 32 12172.68 4153.33 1086.38 2076.67 724.302 1384.44 543.276 1038.33 434.669 830.667 33 2173.63 4155.00 1086 85 2077.50 724.617 1385.00 543.512 1038.75 434.859 831.000 34 2174.57 4156.67 IU87.33 2078.33 724.933 1385.56 543.749 1039.17 435.048 831.333 35 2175.52 4158.33 1087.80 2079.17 725.248 1386.11 543.985 1039.58 435.237 831 . 667 36 2176.46 4160.00 1088.27 2080.00 725.563 1386.67 544.222 1040.00 435.426 832.000 37 2177.44 4161.67 1088.76 2080.83 725.888 1387.22 544.465 1040.42 435.621 832.333 38 2178.41 4163.33 1089.25 2081.6? 726.212 1387.78 544.709 1040.83 435.816 832.667 39 2179.36 4165.00 1089.72 2082.50 726.528 1388.33 544.945 1041.25 436.005 833.000 40 2180.30 4166.67 1090.19 2083.33 726.843 1388.89 545.182 104L67 436.194 833.333 41 2181.25 4168.33 1090.66 2084.17 727.158 1389.44 545.418 1042.08 436.383 833.667 43 2182.19 4170.00 1091.14 2085.00 727.473 1390.00 545.654 1042.50 436.572 834.000 43 2183.17 4171.67 1091.62 2085.83 727.798 1390.56 545.898 1042.92 436 767 834.333 44 2184.14 4173.33 1092.11 2086.67 728.122 1391.11 546.141 1043.33 436.962 834.667 45 2185.09 4175.00 1092.58 2087.50 728.438 1391.6? 546.378 1043.75 437.151 835.000 46 2186.03 4176.67 1093.062088.33 728.753 1392.22 546.614 1044.17 437.340 835.333 47 2186.98 4178.33 1093.53 2089.17 729.068 1392.78 546.851 1044.58 437.529 835.667 48 2187.92 4180.00 1094.00 2090.00729.383 1393.33 547.08? 1045.00 437.718 836.000 49 2188.90 4181.67 1094.49 2090.83 729.708 1393.89 547.331 1045.42 437.913 836.333 50 2189.87 4183.33 1094.98 2091.67 730.033 1394.44 547.574 1045.83 438.108 836.667 51 2190.82 4185.00 1095.45 2092.50730.348 1395.00 547.811 1046.25438.297 837.000 52 2191.76 4186.67 1095.92 2093.33730.663 1395.56 548.047 1046. 6?! 438. 486 837.333 53 2192.71 4188.33 1096.39 2094.17730.978 1396.11 548 283 1047.081438.676 837.667 54 2193.65 4190.00 1096.87 2095.00731.293 1396.67 548.520 1047.50438.865 838.000 55 2194.63 4191.67 1097.35 2095.83731.618 1397.22 548.763 1047. 921439. 060 a38.333 56 2195.60 4193.33 1097.84 2096.67731.943 1397.78 549 00711048.33 439.254 838.667 57 2196.55 4195.00 1098.31 2097.50732.258 1398.33 549 . 243 1 048 . 75 439 . 444 839.000 58 59 2197.49 2198.44 4196.67 4198.33 1098.79 1099.26 2098.33 732.573 2099.17732.888 1398.89 1399.44 549. 480 1049. 17|439. 633 549. 71 6l 1049. 58! 439. 822 839. 333 839.667 128 TABLE XIV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 Curve. 10 Curve. 41 Tan. Arc. Tail. Arc. Tan. Arc. Tan. Arc. Tan. Arc. M. 357.194 6837338 306.215 585.714 267. 990 1512.500 238^262 455.556 214.491 410.000 357.356 683.611 306.354 585.952 268.112 512.708 238.371 455.741 214.589 410.167 1 357.519 683.889 306.494 586.190 268.233 512.917 238.479 455.926 214.686 410.333 2 357.676 684.167 306.629 586.429 268.352 513.125 238.584 456.111 214.781 410.500 3 357.834 684.444 306.764 586.667 268 470 513.333 238.689 456.296 214.876 410.667 4 357.991 684.722 306.899 586.905 268.588 513.542 238.795 456.481 214.970 410.833 5 358.149 685.000 307.034 587.143 268.706 518:750 238.900 456.667 215.065 411.000 6 358.307 685.278 307.169 587.381 268.825 513.958 239.005 456.852 215.160 411.167 7 358.464 685.556 307.304 587.619 268.943 514.167 239.110 457.037 215.254 411.333 8 358.622 685.833 307.440 587.857 269.061 514.375 239.215 457.222 215.349 411.500 9 358.780 686.111 307.575 588.095 269.180 514.583 239.320 457.407 215.443 411.667 10 358.942 686.389 307.714 588.338 269.301 514.7'J2 239.429 457.593 215.541 411.833 11 359.104 686.667 307.853 588.571 269.423 515 000 239.537 457.778 215.639 412.000 12 359.262 686.944 307.988 588.810 269.541 515.208 239.642 457.963 215.733 412.167 13 359.420 687.222 308.123 589.048 269.660 515.417 239.747 458.148 215.828 412.333 14 359.577 687.500 308.259 589.286 269.778 515.625 239.852 458.333 215.923 412.500 15 359.735 687.778 308.394 589 524 269.89(5 515.833 239.958 458.519 216.017 412.667 16 359.893 688.056 308.529 589.762 270.015 516.042 240.063 458.704 216.112 412.833 17 360.050 688.333 308.664 590.000 270.133 516.250 240.168 45*. 889 216.207 413.000 18 360.208 688.611 308.799 590.238 270.251 516.458 240.273 459.074 216.301 413.167 19 360. 36G 688.889 308.934 590.476 270.369 516.667 240.378 459.259 216.396 413.338 2O 360.528 689.167 309.074 590.714 270.491 516.875 240.487 459.444 216.493 413.500 21 360.690 689.444 309.213 590.95* 270.613 517.083 240.595 459.630 216.591 413.667 22 360.848 689.722 309.348 591.190 270.731 517.292 240.700 459.815 216.686 413.838 23 361.006 690.000 309.483 591.429 270.850 517.5HO 240.805 460.000 216.780 414.000 24 361.163 690.278 309.618 591.667 270.968 517.708 240.910 460.185 216.875 414.167 25 361.321 690.556 309.753 591.905 271.086 517.917 241.015 460.370 216.970 414.333 2G 361.479 690.833 309-888 592.143 271.204 518.125 241.121 460.556 217.064 414.500 27 361.636 691.111 310.024 592.381 271 323 518.333 241.226 460.741 217.159 414.667 28 361.799 691.389 310.163 592.619 271.445 518.542 241.334 460.926 217.256 414 833 29 361.961 691.667 310.302 592.857 271.566 518.750 241.442 461.111 217.354 415.000 3O 362.119 691.944 310.437 593.095 271.685 518.958 241.548 461.296 217.449 415.167 31 362.276 692.222 310.572 593.338 271.803 519.167 241.653 461.481 217.543 415.333 32 362.434 692.500 310.707 593..'. 71 271.921 519.375 241.758 461.667 217.638 415.500 33 362.592 692.778 310 843 593.810 272.039 519.583 241.863 461.852 217.733 415.667 34 362.749 693.056 310.978 594.048 272.158 519.792 241.968 462.037 217.827 415.833 35 362.907 693.333 311.113 594.286 272.276 520.000 242.073 402.222 217.922 416.000 36 363.069 693.611 311.252 594.524 272.398 520.208 242.182 462.407 218.019 416.167 37 363.232 693.889 311.391 594.762 272.520 520.417 242.290 462.593 218.117 416.383 38 363.389 694.167 311.526 595.000 272.638 520.625 242.395 462.778 218.212 416.500 39 363.547 694.444 311.662 595.238 272.756 520.833 242.500 462.963 218.306 416.667 40 363.705 694.722 311.797 595.476 272.876 521.042 242.605 463.148 218.401 416.833 41 363.862 695.000 311.932 595.714 272.993 521.250 24-2.711 463.333 218.496 417.000 42 364.025 695.278 312.071 595.952 273.115 521.458 242.819 463.519 218.593 417.167 43 364.187 695.556 312.210 596.190 273.236 5-21.667 242 927 463.704 218.691 417.338 44 364.345 695.833 312.346 596.429 273.355 521.875 243.032 463 889 218.785 417.500 45 364.502 696.111 312.481 596.667 5*78.473 522.083 243.138 464.074 218 880 417.667 46 364.660 696.389 312.616 596.905 273.591 522. V92 243 243 464.259 218.975 4 17. 880 47 364 818 696.667 312.751 597.148 273.710 52-2.500 243.348 464.444 219.069 418.000 48 364.980 696.944 312.890 597.381 273.831 522.708 243.456 464.630 219.167 418.167 49 365.142 697.222 313.029 597.619 273.953 522.917 243.565 464.815 219.264 418.333 50 365.300 (597.500 813.165 597.857 274.072 5-23.125 243.670 465.000 219.359 418.500 51 365.458 697.778 313.300 508.09? 274.190 523.333 243.775 4(55.185 219.454 418.667 52 365.615 698.05(5 313.435 598.333 274.308 523.542 243.880 465.370 219.548 418.838 53 365.778 698.333 313.570 598.571 274.426 523.750 243.985 465.556 219.643 419.000 54 365.935 698.611 813.709 598.810 374.548 523.958 244.093 465.741 219.740 419.167 55 866.098 698.889 313. 84K 599.048 274.670 524 . 1 67 244.202 465.926 219.888 419.338 56 366.255 699.167 318.984 599.286 274.788 524.375 244.307 466.111 219.933 419.500 57 366.413 699.444 314.119 599.524 274.907 524.583 244 412 466.296 220.027 419.667 58 366.571 699.722 314.254 599.762 275.025 524 792244.517 466.481 220.122 419.833 59 '139 TABLE XIV. ACTUAL TANGENTS, ETC. 43 1 Curve. 3 Curve. 3 Curve. 4 Curve. 5 Curve. M. Tan. Arc. Tan. Arc. Tail. Arc. Tan. Arc. Tan. Arc. ~0~ 2199.38 4200.1.0 1099.73 2100.00 733.203 1400.00 549 952 10:0.00 440.011 840.000 1 2200.36 4-201.67 1100.2-2 2100.83 733.528 1400.50 550.196 1050.4-2 440.200 840.333 3 2201.33 4203.33 1100.71 V101.67 733.8f,3 1401.11 550.439 1050.83 440.401 840.607 3 2-202.28 4205.00 1101.18 2102.50 734.108 1401.07 550.670 1051.25 440.590 841.000 4 2203.22 4206.67 1101.65 2103.33 734.483 1402.22 550.912 1051.67 440.779 841.333 5 2-204.20 4208.33 1102.14 2104.1? 734.808 1402. 7b 551.150 1052.08 440.974 841.667 6 2205.1? 4210.00 1102.63 2105.00 735.132 1403.33 551.399 1052.50 441.169 842.000 7 2206.12 4211.67 1103.10 2105.83 735.448 1403.89 551.630 1052.92 441. 3E8 842.333 8 2207.06 4213.33 1103.57 2106.67 535.763 14'4.44 551.872 1053.33 441.547 842.667 9 2208.01 4215.00 1104.04 2107.50 736.078 1405.00 552.109 1053.75 441.736 843.000 1O 2208.95 4216.67 1104.52 2108.33 736.393 1405.56 552.345 1054.1? 441.925 843.333 11 2209.93 4218.33 1105.00 2109.1? 730.7181406.11 552.589 1054.58 442.120 843.667 13 2210.90 4220.00 1105.49 2110.00 737.0431406.67 552.832 1055.00 442.315 844.000 13 2211.85 4221.6? 1105.96 2110.83 i 37.3581407. 22 553.068 1055.42 442.504 844.333 14 2212.79 4223.33 1106.44 2111.67 737.6731407.78 553.305 1055.83 442.693 844.607 15 2213.76 4225.00 1106.92 2112.50 737.998 1408.33 553.548 1056.25 142.888 845.000 16 2214.74 4226.67 1107.41 2113.33 738.322:1408.89 553.792 1056.67 4 43. (.83 845.333 17 2215.68 4228.33 1107.88 2114.17 738.03? 1409.44 554.028 1057.08 443.272 845.607 18 2216.63 4230.00 1108.36 2115.00 733 9531410.00 554.205 1057.50 443.461 846.000 19 2217.60 4231.67 1108.84 2115.83 739.277 1410.50 554.508 1057.92 443.656 846.333 20 2218.58 4233.33 1109.33 2116.6? 739 602 1411.11 554.752 1058.33 443.851 846.667 21 2219.52 4235.00 1109.80 2117.50 739.9171411.6? 554.988 1058.75 444.040 847.000 22 2220.47 4236.67 1110.27 2118.33 740.2321412.22 555.225 1059.1? 444.229 847.333 23 2221.41 4238.33 1110.75 2119.17 740.548 1412.78 555.461 1059.58 444.418 847.667 24 2222.36 4240.00 1111.22 2120.00 740.803 1413.33 555.697 1060.00 444.608 848.000 25 2223.33 4241.6? 1111.71 2120.83 741.187 1413.89 555.941 1000.42 444.802 848.333 36 2224 31 4243.33 1112.19 2121.67 741.512 1414.44 556.185 1060.83 444.997 848.667 37 2225.25 4245.00 1112.6? 2122.50 741.827 1415.00 556.421 1061.25 445.186 849.000 38 2226.20 4246.6? 1113.14 2123.33 742.142 1415.56 556.657 1061.67 445.376 849.333 39 2227.1? 4248.33 1113.63 2124.17 742.467 1416.11 556.901 1062.08 445.570 849.667 30 2228.15 4250.00 1114.11 2125.00 742.792 1416.67 557.144 1062.50 445.765 850.000 31 2229.09 4251.6? 1114.59 2125.83 743.107 1417.22 557.381 1062.92 445.955 850.333 33 2230.04 4253.33 1115.06 2126.6? 7'43.422 1417.78 557.617 1063.33 446.144 850.667 33 2231.01 4255.00 1115.55 2127.50 743.747 1418.33 557.861 1063.75 446.339 851.000 34 2231.99 4256.67 1116. as 2128.33 744.072 1418.89 558.104 1064.17 446 533 851.333 35 2232.93 4258.33 1116.51 2129.17 744 387 1419.44 558.341 1064.58 446.723 851.667 36 2233.88 4200.00 1116.98 2130.00 744.702 1420.00 558.577 1065.00 446.912 852.000 37 2234.85 4261.6? 1117.4? 2130.83 745.027 1420.56 558.821 1065.4-2 447.107 852.333 38 2235.82 4263.33 1117.95 2131.6? 745.351 1421.11 559.064 1065.83 447.301 852.667 39 2236.7? 4265.00 1118.43 213-2.50 745.667 1421.67 559.301 1066.25 447.491 853.000 40 2237.71 4266.67 1118.90 2133.33 745.982 1422.22 559.537 1066.67 447.680 853.333 41 2-238.69 4268.33 1119.39 2134.17 746.306 1422.78 559.781 1067.08 447.875 853.667 43 2239.66 4270.00 1119.87 2135.00 746.631 1423. 33 500.024 1067.50 448.069 854.000 43 2240.61 4271.67 1120.35 2135.83 746.946 1423.89 560.261 1067.92 448.259 854.333 44 -2241.55 4273.33 1120.82 2136.67 747.261 1424.44 560.49? 1068.33 448.448 854.667 45 2242.53 4-275.00 1121.30 2137.50 747.586 1425.00 560.741 1068.75 448.643 855.000 46 2243.50 4276. G7 1121.79 2138.33 747.911 1425.56 560.984 1069.17 448.837 855.333 47 2244 48 4278.33 1122 28 2139.17 748.236 1426.11 561.228 1069.58 449.032 855.667 48 2-245. 4 r > 4280.00 1122 77 2140.00 748.560 1426.6? 561.471 1070.00 449.227 856.000 49 2246.40 4281.67 1123^24 2140.83 748.876 1427.22 561.708 1070.42 449.416 856.333 5O 2247.34 4283.33 1123.71 2141.67 749.191 1427.78 561.944 1070.83 449.605 856.667 51 2248.31 4285.00 11-24.20 2142.50 749.515 1428.33 562.188 1071.25 449.800 857.000 53 2249.2* 4286.07 1124.69 2143.33 749.840 1428.89 562.431 1071.67 449.995 857.333 53 .2250.23 4288.33 1125.1(1 2144.17 750.155 14-29.44 562 OOS 1072.08 450.184 857.667 54 ' -2-251. 18 4290.00 1125.63 2145.00 750.470 1430.00 50-2.904 107-2.50 450.373 58.000 55 ; y25:2.i5 4291.67 1126.12 2145.83 750.795 1430.50 503.1 47 107-2.92 450 51 '8 858.333 56 2. '53. 13 4293.33 1126.61 2146.67 751.120 1431.11 503.391 1073.33 450.7H3 858.667 57 2-254.07 4295.00 1127.08 2147.50 7 5 1.435 '143 1.0? 5C3.0-2? 1073.75 450.95-2 859.00) 58 2 .'55. 0:2 4296:67 1127.55 2148.33 751.7501432.22 503.801 1074.1? 451.141 859.333 59 2-255.99 4298.33 1128.04 2149.1? 752. 075 11432. 78 564. It--? 1074 58 451.336 859.007 130 TABLE XIV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 Curve. 1O Curve. 42 Tail. Arc. Tan. Arc. Tan. Arc. Tan . Arc. Tan. Arc. M. 366.728700.000 614 . 389 600 . 000 275 . 143 525 . 000 244. 622 j 466. 667 220.217 420.000 366.891 700.27'H 31 4 528 600 . 238 275 . 265 : 525 . 208 244.731 466.852 220.314 420.167 1 367.053 700.556 314.667600.476275.387 525.417 244.839 467.037 220.412 420.333 2 367. an 700.833 314. 8031600. 714 275. 505 525.625 244.944 467.222 220.506 420.500 3 367.368 701.111 314.938 600.952275.623 525.833 245.049 467.407 220.601 420.667 4 367.531 701.389 315.077 601.190275.745 526.042 245.158 467.593 220.698 420.833 5 367.693 701.667 315.216 601.429275.867 526.250 245.266 467.778 220.796 421.000 6 367.851 701.944 315.351 601.667! 275. 985 526.458 245.371 467.963 220.891 421.167 7 368.008 702.222 315.486 601.905 276.104 526.667 245.476 468.148 220.985 421.333 8 368.166 7'02.500 315.622 602.143 276.222 526.875 245.582 468.333 221.080 421.500 9 368.324 702.778 315.757 602.381 276.340 527.083 245.687 468.519 221.175 421.667 10 368.486 703.056 315.896 602.619 276.462 527.292 245.795 468.704 221.272 421.833 11 368.649 703.333 316.035 602.857 276.584 527.500 245.903 468.889 221 .370 422.000 12 368.806 703.611 316.170 603.095 276.702 527.708 246.008 469.074 221.464 422.167 13 368.964 703.889 316.305 603.333 276.820 527.917 246.114 469.259 221.559 422. 333 14 369.126 704.167 316.445 603.571 276.942 528.125 246.222 469.444 221.657 422.500 15 369.289 704.444 316.584 603.810 277.064 528.333 246.330 469.630 221.754 422.667 16 369.446 704.722 316.719 604.048 277.182 528.542 246.435 469.815 221.849 422.833 17 369.604 705.000 316.854 604.286 277.301 528.750 246.541 470.000 221.943 423.000 18 369.766 705.278 316.993 604.524 277.422 528.958 246.649 470.185 222.041 423.167 19 369.929 705.556 317.133 604.762 277.544 529.167 246.757 470.370 222.138 423.333 2O 370.086 705.833 317.268 605.000 277.663 529.375 246.862 470.556 222.233 423.500 21 370.244 706.111 317.403 605.238 277.781 529.583 246.968 470.741 222.328 423.667 22 370.402 706.389 317.538 605.476 277.899 529.792 247.073 470.926 222.422 423.833 23 370.559 706.667 317.673 605.714 278.017 530.000 247.178 471.111 222.517 424.000 24 370.722 7'06.944 317.812 605.952 278.139 530.208 247.286 471.296 222.615 421.167 25 370.884 707.222 317.952 606.190 278.261 530.417 247.395 471.481 222.712 424.333 26 371.042 707.500 318.087 606.429 278.379 530.625 247.500 471.667 222.807 424.500 27 871.199 707.778 318.222 606.667 278.498 530.833 247.605 471.852 222.901 424.667 28 371.362 708.056 318.361 606.905 278.620 531.042 247.713 472.037 222.999 424.833 29 371.524 708.333 318.500 607.143 278.741 531.250 247.822 472.222 223.097 425.000 3O 371.682 708.611 318.636 607.381 278.860 531.458 247.927 4V2.407 223.191 425.167 31 371.840 708.889 318.771 607.619 278.978 531.667 248.032 472.593 223.286 425.333 32 372.002 709.167 318.910 607.857 279.100 531.875 248.140 472.778 223.383 425.500 33 372.164 709.444 319.049 608.095 279.222 532.083 248.248 472.963 223.481 425.667 34 372.322 709.722 319.184 608.333 279.340 532.292 248.354 473.148 223.576 425.833 35 372.480 710.000 319.319 608.571 279.458 532.500 248.459 473.333 223.670 426.000 36 372.642 710.278 319.459 608.810 279.580 532.708 248.567 473.519 223.768 426.167 37 372.804 710.556 3 i 9. 598 609 048 279.702 532.917 248.675 473.7'04 223.865 426.333 38 372.962 710.833 319.733 609.286 279.820 533.125 248.781 473.889 223.960 426.500 39 373.120 711.111 319.868 609.524 279.938 533.333 248 886 474.074 224.055 426.667 40 373.282 711.389 320.007 609.762 280.060 533.542 248.994 474.259 2-.M.152 426. 833 41 373.445 711.66; 320.147 610.000 280.182 533.750 249.102 474.444 224.250 427.000 42 373.602 711.944 320.282 610.238 280.300 533.958 249.208 474.630 224.344 427.167 43 373.760 712.222 320.417 610.476 280.419 534.167 249.313 474.815 224. 43S 427.333 44 373.922 712.500 320.556 610.714 280.540 534,375 249.421 475.000 224.536 427.500 45 374.085 712.778 320.695 610.952 280.662 534.583 249.529 475.185 224.634 427.667 46 374.247 713.056 320.835 611.190280.784 534.792 249.638 475.370 224.732 427.833 47 374.409 713.333 320.974 611.429280.906 535.000 249.746 475.556 224.829 428.000 48 374.567 713.611 321.109 611.667 281.024 535.208 249.851 475.741 224.924 428.167 49 374.725 713.889 321.244 611.905 281.143 535.417 249.956 475.926 225.018 428.333 50 374.887 714.167 321.383612.143281.264 535.625 250.065 476.111 225.116 428.500 51 375.050 714.444 321.523 612.38li281.386 535.833 250.173 476.296 225.213 428.667 52 o75.207 714.722 321.658 612.619281.505 536.042 250.278 476.481 225.308 428.833 53 375.365 715.0 321.793 612.857281.623 536.250 250.383 476.667 225.403 429.000 54 375.527715.278 321 932 613.095281.745 536.458 250.492 476.852 225.500 429.167 55 375. 090 715. ?56 322.071 613.333281.867 536.667 250.600 477.037 225.598 429.333 56 375.847 715.833 322.207 613.571 281.985 536.875 250.705 477.222 225.692 429.500 57 376.005 716.111 322.342 613.810282.103 537.083 250.810 477.407 225.787 429.667 58 376.167 716.389 322.481 614.048282.225 537.292 250.919 477.593 225.885 429. K33: . r ;l> 131 TABLE XIV. ACTUAL TANGENTS, ETC. 43 1 Curve. 3 Curve. 3 Curve. 4 Curve. f 5 Curve. M. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. O 2256.97 4300.00 1128.52 2150.00 "52.400 1433.33 364.351 1075.00 451.531 860.000 1 2257.94 4301.67 129.0! 2150.K3 "52.724 1433.89 564.594 1075.42 451.726 860.333 3 2258.91 4303.33 129 50 2151.67 753.049 1434.44 564.838 1075.83 451.921 860.667 3 2259.80 4305.00 129.97 2152.50 "53.364 1435.00 565.074 1076.25 452.110 861.000 4 2260.81 4306.67 130.44 2153.33 '53.679 1435.56 565.311 076.67 452.299 861.333 5 2261.78 4308.33 130.93 2154.17 754.004 1436.11 565.554 1077.08 452.494 861.667 6 22(52.75 4310.00 131.42 2155.00 "54.329 1436.67 565.798 1077.50 452.689 862.000 7 2263.73 4311.67 131.91 2155.83 "54.654 1437.22 566.041 1077.92 452.884 862.333 $ 2264.70 4313.33 132.39 2156.67 "54.9781437.78 566.285 1078. &3 453.079 862.667 9 2265.65 4315.00 1132.86 2157.50 755.293 1438.33 566.521 1078.75 453.268 863.000 10 2266.59 4316.67 1133.34 2158.33 "55.609 1438.89 566.758 1079.17 453.457 863.333 11 2267.57 4318.33 1133.82 2159.17 "55.933 1439.44 567.001 1079.58 453.652 863.667 12 2268.54 1320.00 134.31 2160.00 56.258 1440.00 567.245 1080.00 453.847 864.000 13 2269.49 4321.67 1134.78 2160.83 756.573 1440.56 567.481 1080.42 454.036 864.333 14 2270.43 4323.33 135.26 2161.67 "56.8881441.11 567.718 1080.83 454.225 864.667 15 2271.4! 4325.00 1135.74 2162.50 "57.213 1441.67 367.965 1081.25 454.420 865.000 16 2272.38 4326.67 1136.23 21 63. ;33 57.538 1442.22 568.205 1081.67 454.615 865.333 17 2273.35 4328.33 1136.72 2164.17 "57.862 1442.78 368.448 1082.08 454.810 865.667 18 2274.33 4330.00 1137.21 2165.00 "58.187 1443.33 568.692 1082. 50 J455.004! 866. 000 19 2275.27 4331.67 1137.68 2165.83 '58.502 1443.89 568.928 1082.92 455.194 866.333 2O 2276.22 4333.33 138.15 2166.67 "58.817 1444.44 569.165 1083.33 455.383 866.667 31 2277.19 4335.00 1138.64 2167.50 "59.142 1445.00 569.408 1083.75 455.578 867.000 83 2278.17 4336.67 1139.12 2168.33 "59.46711445.56 569.652 1084.17 455.772 867.333 83 2279.14 4338.33 1139.61 2169.17 "59.792 1446 11 569.895 1084.58 455.967 867.667 34 2280.11 4310.00 1140.10 2170.00 760.116 1446.67 570.139 1085.00 456.162 868.000 35 2281.09 4341.67 1140.59 2170.83 "60.441 1447 22 570.383 1085.42 456.357 868.333 36 2282.06 4343.33 1141.07 2171.67 760.766 1447.78 570.626 1085.83 456.552 868.667 37 2283.01 4345.00 1141.55 2172.50 761.081 1448.33 570.862 1086.25 456.741 869.000 38 2283.95 4346.67 1142.02 2173.33 761.3961448.89 571.099 1086 67 456.930 869.333 39 2284.93 4348.33 1142.51 2174.17 761.721 1449.44 371.342 1087.08 457.125 869.667 30 2285.90 4350.00 1142.99 2175.00 762.046 1450 00 571.586 1087.50 457.320 870 000 31 2286.88 4351.67 1143.48 2175.83 762.370 1450.56 571.830 1087.92 457.515 870.333 33 2287.85 4353.33 1143.97 2176.67 762.695 1451.11 572.073 1088.33 457.710 870.667 33 2288.79 4355.00 1144.44 2177.50 763.010 1451.67 572.310 1088.75 457.899 871.000 34 2289 74 4356.67 1144.91 2178.33 763.325 1452.22 572.546 1089.17 458.088871.333 35 2290.71 4358.33 1145.40 2179.17 763.650 1452.78 572.789 1089.58 458.283 871.667 36 2291.69 4360.00 1145.89 2180.00 703.975 1453.33 573.033 1090.00 458.478 87'2.000 37 2292.66 4361.67 1146.37 2180.83 764.299 1453.89 573.277 1090.42 458 672 872.333 38 2293.64 4363.33 1146.86 2181.67 764.624 1454.44 573.520 1090.83 458.867 872.667 39 2294.61 4365.00 1147.35 2182.50 764.949 1455.00 573.764 1091.25 459.062 873.000 4O 2295.58 4366.67 1147.83 2183.33 765.274 1455.56 574.007 1091.67 459.257 873.333 41 2296.53 4368.33 1148.31 2184.17 765.589 1456.11 .374.244 1092. 08] 459. 446 873.667 48 2297.48 4370.00 1148.78 2185.00 765.904 1456.67 574.481 1092.50 459.635 874.000 43 2298.45 4371 67 1149.27 ^185.83 766.229 1457.22 574.724 1092.92 459.830 87'4.333 44 2299.42 4373.33 1149.75 2186.67 766.553 1457.78 574.967 1093.33 460 025 874.667 45 2300.40 4375.00 1150.24 2187.50 766.878 1458.33 575 211 1093.75 460.220 875.000 46 2301.37 4376.67 1150.73 2188.33 767.203 1458.89 575.454 1094.17 460.415 875.333 47 2302.35 4378.33 1151.21 2189.17 767.527 1459.44 575.698 1094.58 460.610 875.667 48 2303.32 4380.00 1151.70 2190.00 767. &52 11460.00 575.941 1095.00 460.805 876.000 49 2304.29 4381.67 1152.19 2190.83 768.177 1460.56 576.185 1095.42 460.999 876.333 5O 2305.27 4383.33 1152.68 2191.67 768.502 1461.11 576.428 1095.83 461.194 876.667 51 2306.21 4385 00 1153.15 2192.50 768.817 1461.67 576.665 1096.25 461.383 877.000 2307.16 4386.67 1153.62 2193.33 769.132 1462.22 576.901 1096.67 461.573 877.333 53 2308.134388.3*3 1154.11 2194.17 769.457 1462.78 577.145 1097.08 461.767 877.667 54 2309.11 4390.00 1154.60 2195.00 769.781 1463.33 577.388 1097 50 461.962 878.000 55 231J.084391.67 1155.08 2195.83 770.106 1463.89 577.632 1097.92 462.157 878.333 56 2311.054393.33 1155.57 2196.67 770.431 1464.44 577.876 1098.?3 462.352 878.667 57 2312.034395.00 1156.06 2197.50 770.755 1465.00 57'8.119 1098.75 462.547 879.000 58 2313.004396.67 1156.54 2198.33 771.080 1465.56 578.363 1099.17 462.742 879.333 59 2313.984398.3; 1157.03 2199.17 771.4051 1466. 11 1578. 606 1099.58 462.937 879.667 132 TATVLE XIV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 Curve. 1O Curve. 43 Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. M. 870.330716.667 322.620614.286 282. 347 i 537. 500 251.027 477.778 225.982 430.000 376.492716.944 W2. 759 614. 524 282. 469 i 537. 708 251.135 477.963 226.080 430.167 1 376.655 717.222 322.899614.762 282.51)0537.917 251.244 478.148 226.177 430.333 2 376.812 717.500 J23.034 615.000 282. 709 1538.1 25 251.349 478.333 226.272 430.500 3 376.970 717.778 323. 169 61 5. 238 282.8271538.3:33 251.454 478.519 226.367 430.667 4 377.132 718.056 323.308 615.476 282.949538.542 251.562 478.704 226.464 430. sas 5 377.295 718.333 323.447 615.714 283.071 538.750 251.671 478.889 226.562 431.000 6 377.457 718.611 323.587 615.952 283.193 538.958 251.77'9 479.074 226.659 431.167 7 377.619 718.889 323.726 616.190 283 314 539.167 251.887 479.259 226.757 431.333 8 377.777 719.167 323.861 616.429 283.433 539.375 251.992 479.444 226.851 431.500 9 377.935 719.444 323.996 616.667 283.551 539.583 252.098 479.630 226.946 431.667 10 378.097 719.722 324.135 616.905 283.673 539.792 252.206 479.815 227.044 431.833 11 378.260 720.000 324.275 617.143 283.795 540.000 252 314 480.000 227.141 432.000 12 378.417 720.278 324.410 617.381 283. 91 3 540.208 252.419 480.185 227.236 432.167 13 378.575 720.556 S24.545 617.619 284.031 540.417 252.525 480.370 227.330 432.333 14 378.737 720.833 324.684 617.857 284.153 540.625 252.633 480.556 227.428 432.500 15 378.900 721.111 324.823 618.095 284.275 540.833 252.741 480.741 227.525 432.667 16 379.062 721 . 389 '324.963 618.333 284.397 541.042 252.850 480.926 227.623 432.833 17 379.225 721.667 325.102 618.571 284.519 541.250 252.958 481.111 227.720 433.000 18 379.382 721.944 325.237 618.810 284.637 541.458 253.063 481.296 227.815 433.167 19 379.540 722 222 325.372 619.048 284.755 541.667 253.168 481.481 227.910 433.333 20 379.702 722 .'500 325.511 619.286 284.877 541.875 253.277 481.667 228.007 433.500 21 379.865 722.778 325.650 619 524 284.999 542.083 253.385 481.852 228.105 433.667 22 380.027 723.056 325.790 619.762 285.121 5.42.292 253.493 482.037 228.202 433.833 23 380.189 723.333 325.929 620.000 285.243 542.500 253.602 482.222 228.300 434.000 24 380.352 723.611 326.068 620.238 285.364 542.708 253.710 482.407 228.397 434.167 25 380.514 723.889 326.207 620.476 285.486 542.017 253.818 482.593 228.495 434.333 2G 380.672 724.167 326.343 620.714 285.605 543.125 253.923 482.778 228.590 434.500 27 380.830 724.444 326.478 620.952 285.723 543.333 254.029 482.963 228.684 434.667 28 380.992 724.722 326.617 621.190 285.845 543.542 254.137 483.148 228.782 434.833 29 381.154 725.000 326.756 621.429 285.966 543.750 254.245 483.333 228.879 435.000 30 381.317 725.278 326.895 621.667 286. Oh8 543.958 254.354 483 519 228.977 435.167 31 381.479 725 556 327.035 621.905 286.210 544.167 254.462 483.704 229.074 435.333 32 381.637 725.833 327.170 622.143 286.328 544.375 254.567 483.889 229.169 435.500 33 381.794 726.111 327.305 622.381 286.447 544.583 254.672 484.074 229.264 435.667 34 381.957 726.389 327.444 622.619 286.569 544.792 254.780 484.259 229.361 435.833 35 883.119 726.667 327.583 622.857 286.690 545.000 254.889 484.444 229 459 436.000 36 382.282 726.944 327.723 623.095 286.812 545.208 254.997 484.630 229.556 436.167 37 382.444 727.222 327.862 623.333 286.9:34 545.417 255.106 484.815 229.654 436.333 38 382.607 727.500 328.001 623.571 287.056 545.625 255.214 485.000 229.751 436.500 39 382.769 727.778 328.140 623.810 287.178 545.833 255.322 485.185 229.849 436.667 4O 382.927 728.056 328.275 624.048 287.296 546.042 255.427 485.370 229.944 436.833 41 383.084 728.333 328.411 624.286 287.414 546.250 255.532 485.556 230.038 437.000 42 383.247 728.611 328.550 624.524 287.536 546.458 255.641 485.741 230.136 437.167 43 383.409 728.889 328 689 624.762 287.658 546.667 255.749 485.926 230.233 437.333 44 383.571 729.167 328.828 625.000 287.780 546.875 255.857 486.111 230.331 437.500 45 383.734 729.444 328.968 625.238 287.902 547.083 255.966 486.296 230.428 437.667 46 383.896 729.72v> 329.107 625.476 288.024 547.292 256.074 486.481 230. P26 437.833 47 384.059 730.000 329.246 625.714 288.146 547.500 256.182 486.667 230.623 438.000 48 384.221 730.278 329.385 625.952 288.267 547.708 256.291 486.852 230.721 438.167 49 384.384 730.556 329.524 626.190 288. 3S9 547.917 256.399 487.037 230.818 438.333 5O 384. 541 1730. 833 329.660 626.429 288.507 548.125 256.504 487.222 230.913 438.500 51 384.699731.111 329.795 626.667 288.626 548 333 256.609 487.407 231 .008 438.667 52 384.861 731.389 329.934 626.905 288.748 548.542 256.718 487.593 231.105 438.833 53 385.001 731.667 330.073 627.143 288.869 548.750 256.826 487.778 231.203 439.000 54 385.186 731.944 330.212 627.381 288.991 548.958 256.934 487.963 231.300 439.167 55 385.848 732.222 330.352 627.619 289.113 549.167 257.043 488.148 231.398 439.383 56 385.511 732.500 330.491 627.857 289.235 549.375 257.151 488.333 231.495 439.500 57 385.673 732.778 330.630 628.095 289.357549.583 257.259 488.519 231.593 439.667 58 385.836 733.056 330.769 628.333 289.479549.792 257.368 488.704 231.690 439.833 59 133 TABLE XIV. ACTUAL TANGENTS, ETC. 440 1 Curve. 2 Curve. 3 Curve. 4 Curve. 5 Curve- M. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. <) 2314.95 4400.00 1157.52 2200.00771.730 1466.67 578.850 1100.00463.132880.000 1 >315.90 4401.67 1157.992200.83772.045 1467.22 579.086 1100.42463.321 880.333 2 2316.84 4403.33 1158.46 2201. 671772. 360 1467.78 579.323 1100.63463.510880.667 3 2317.82 4405.00 1158.95 2202.50772.685 1468. 33 579.566 1101.25463.705881.000 4 2318.79 4406.67 1159.44 2203.33 773.009 1468.89 579.810 1101. 67 ; 463. 900 881.333 5 2319.76 4408.33 1159.92 2204.17 773.334 1469.44580.053 1102.08:464.094 881.667 2320.74 4410.00 1160.41 2205.00 773.659 1470.00,580.297 1102. 50|464. 289 882.000 7 2321.71 4411.67 1160.90 2205.83 773.984 1470.56 580.540 1102.92,464.484 882.333 8 2322.60 4413.33 1161.39 2206. 67J 774. 308 1471.11 580.784 1103.33 464.679 882.667 9 2323.66 4415.00 1161.87 2207.50 774.633 1471.67 581.027 1103.75 464.874 883.000 10 2324.63 4416.67 1162.36 2208.33 774.958 1472.22 581.271 1104.17 465.069 883.333 11 2325.61 4418.33 1162.85 2209.17 775.282 1472.78 581.515 1104.58 465.264 883.667 12 2326.58 4420.00 1163.33 2210.00 775.607 1473.33 581.758 1105.00 465.458 884.000 13 2327.56 4421.67 1163.82 2210.83 775.932 1473.89 582.002 1105.42 465.653 884.3:53 14 2328.53 4423.33 1164.31 2211.67 776.257 1474.44 582.245 1105.83465.848 884.667 15 2329.50 4425.00 1164.79 2212.50 776.581 1475.00 582.489 1106.25 466.043 885.000 16 2330.48 4426.67 1165.28 2213.33 776.906 1475.56 582.732 1106.67 466.238 885.333 17 3331.42 4428.33 1165.75 2214.17 777.221 1476.11 582.969 1107.08 466.427 885.667 18 2332.37 4430.00 1166.23 2215.00 777.536 1476.67 583.205 1107.50 466.616 886.000 19 2333.34 4431.67 1166.71 2215.83 777.861 1477.22 583.449 1107.92 466.811 886.333 20 2334.32 4433.33 1167.20 2216.67 778.186 1477.78 583.692 1108.33 467.006 886.667 21 2:335.29 4435.00 1167.69 2217.50 778.510 1478.33 583.936 1108.75 467.201 887.000 22 2336.26 4436.67 1168.18 2218.33 778.835 1478.89 584.179 1109.17 467.396 887.333 23 2337.24 4438.33 1168.66 2219.17 779.160 1479.44 584.423 1109.58 467.591 887.667 24 23:38.21 4440.00 1169.15 2220.00 779.485 1480.00 584.666 1110.00 467.785 888.000 25 2339.19 4441.67 1169.64 2220.83 779.809 1480.56 584.910 1110.42 467.980 888.333 26 2340.16 4443.33 1170.12 2221.67 780.134 1481.11 585.154 1110.83 468,175 888.667 27 2341.13 4445.00 1170.61 2222.50 780.459 1481.67 585.397 1111 25 468.370 889.000 28 2342.11 4446.67 1171.10 2223.33 780.783 1482.22 585.641 1111.67 468.565 889.333 29 2343.08 4448.33 1171.58 2224.17 781.108 1482.78 585.884 1112.08 468.760 889.667 3O 2344.06 4450.00 1172.07 2225.00 781.433 1483.33 586.128 1112.50 468.955 890.000 31 2345.03 4451.67 1172.56 2225.83 781.758 1483.89 586.371 1112.92 469.149 890.333 32 2346.01 4453.33 1173.05 2226.67 782.082 1484.44 586.615 1113.33 469.344 890.667 33 2346.98 4455.00 1173.53 2227.50 782.407 1485.00 586.858 1113.75 469.539 891.000 34 2347.95 4456.67 1174.02 2228.33 782.732 1485.56 587.102 1114.17 469.734 891.333 35 2348.93 4458.33 1174.51 2229.17 783.056 1486.11 587.346 1114.58 469.929 891.667 36 2319.90 4460.00 1174.99 2230.00 783.381 1486.67 587.589 1115.00 470.124 892.000 37 2350.88 4461.67 1175.48 2230.83 783.706 1487.22 587 833 1115.42 470.319 892.333 38 2351.85 4463.33 1175.97 2231.67 784.031 1487.78 588.076 1115.83 470.514 892.667 39 2352.82 4465.00 1176.45 2232.50 784.355 1488.33 588.320 1116.25 470.708 893.000 40 2353.80 4466.67 1176.94 2233.33 784.680 1488.89 588.563 1116.67 470.903 893.333 41 23o4.77 4468.33 1177.43 2234.17 785.005 1489.44 588.807 1117.08 471.098 893.667 42 2355.75 4470.00 1177.92 2235.00 785.329 1490.00 589.050 1117.50 471.293 894.000 43 2856.78 4471.67 1178.40 2235.83 785.654 1490.56 589.294 1117.92 471.488 894.333 44 2357.69 4473.33 1178.89 2236.67 785.979 1491.11 589.538 1118. as 471.683 894.667 45 2358.67 4475.00 1179.38 2237.50 786.304 1491.67 589.781 1118.75 471.878 895.000 46 2359.64 4476.67 1179.86 2238.35 786.628 1492.22 590.025 1119.17 472.072 895.333 47 2360.62 4478.33 1180.35 2239.17 786.953 1492.78 590.268 1119.58 472.267 895.667 48 23>>1.59 4480.00 1180.84 2240.00 787.278 1493.33 590.512 1120.00 472.462 896.000 49 2362.56 4481.67 1181.33 2240.83 787.602 1493.89 590.755 1120.42 472.657 896.333 50 2363.54 4483.33 1181.81 2241.67 787.927 1494.44 590.999 1120.83 472.852 896.667 51 2364.51 4485.00 1182.30 2242.50 788.252 1495.00 591.243 1121.25 473.047 897.000 52 2365.49 4486 67 1182.79 2243.33 788.577 1495.56 591.486 1121.67 473.242 897.333 53 2366.46 4488. 33 nas. 27 2244.17 788.901 1496.11 591.730 1122.08 473.437 897.667 54 2367.43 4490.00 1183.76 2245.00 789.226 1496.67 591.973 1122.50 473.631 898.000 55 2368.41 4491.67 1184.25 2245.83 789.551 1497.22 592.217 1122.92 473.826 898.333 56 2369.38 4493.33 1184.73 2246.67 789.875 1497.78 592.460 1123.33 474.021 S98.667 57 2370.36 4495.00 11&5.22 2247.50 790.200 1498.33 592.704 1123.75 474.216 899.000 58 2371.33 4496.67 1185.71 2248.33 790.525 1498.89 592.947 1124.17 474.411 899. aS3 59 2372.30 4498. a3 1186.20 2249.17 790.850 1499.44 593.191 1124.58 474.606 899.667 131 TABLE XIV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 Curve. 1O Curve. 440 Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. M. 385.998 733.838 330.909 628.571 289.601 550.000 257.476 488.889 231.788 440.000 ~o" 386.156 733. 611 1331.044 628.810 289.719550.208 257.581 s 489. 074 281.888 440.10? i 386.313 783.889 331.179 629.048 289.837 550.417 257. 686 1 489. 259 231.97? 440.338 02.982 947.667 24 2515.14 4740.00 1257.62 2370.00 838. 46S 1580.00 628.908 1185.00 503.183 948.000 25 2516.15 4741.67 1258.12 2370.83 838.802 1580.56 629.159 1185.42 503.383 948.333 26 2517.15 4743.33 1258.62 2371.67 839.136 1581.11 629.409 1185.83 503.584 948.667 27 2518.12 4745.00 1259.11 2372.50 839.461 1581.67 629.653 1186.25 503.779 949.000 28 2519.10 4746.67 1259.60 2373.33 839.78(5 1582.2:3 629.896 1186.67 503.973 949.333 29 2520.10 4748.33 1260.10 2374.17 840.120 1582.78 630.147 1187.08 504.174 949.667 30 2521.10 4750.00 1260.60 2375.00 840.454 1583.33 630.398 1187.50 504.375 950.000 31 2522.11 4751.67 1261.10 2375.83 840.789 1583.89 (530.649 1187.92 504.575 950.333 32 3523.11 4753.33 1261.60 2376.67 841.123 1584.44 630.899 1188.33 504.776 950.667 33 2524.11 4755.00 1262.10 2377.50 841.457 1585.00 631.150 1188.75 504.97(5 951.000 34 2525.11 4756.67 1262.60 2378.33 841.791 1585.56 631.401 1189.17 505.177 951.333 35 2526.09 4758.33 1263.09 2379.17 842.116 1586.11 631.644 1189.58 505.372 951.667 36 2527.06 4760.00 1263.58 2380.00 842.441 1586.67 631.888 1190.00 505.567 952.000 37 2528.06 4761.67 1264.08 2380.83 842.775 1587.22 632.139 1190.42 505.707 952.333 38 2529.07 4763.33 1264.58 2381.67 843.109 1587.78 632.389 1190.83 505.9(58 952.667 39 2530.07 4765.00 1265.08 2382.50 843.444 1588.33 632.640 1191.25 506.160 953.000 4O 2531.07 4766.67 1265.58 2383.33 843.778 1588.89 632.891 1191.67 506.369 953.333 41 2532.08 4768.33 1-256.08 2384.17 844.112 1589.44 633.142 1192.08 506.570 1)53.667 42 2533.08 4770.00J12G6 59 2385.00 844.446 1590.00 033.392 1192.50 506.770 954.000 43 2534.05 4771.67 1267.07 2385.83 844.771 1590.56 633.636 1192.92 506.965 954.333 44 2535.03 4773.33 1267.56 2386.67 845.096 1591.11 633.879 1193.33 507.160 954.0(57 45 2536.03 4775.00 1268.06 2387.50 845.430 1591.67 634.130 1193.75 507.361 955.000 46 &37.08 4776.67|1268.56 2388.33 845.764 1592.22 634. 881 11 194.1? 507.561 955.333 47 4538.03 4778.33H269.06 2389.17 846.099 1592.78 634.6321194.58 507.762 055.6(57 48 2539.04 4780.00 1269.57 2-390.00 846.433 1593.33 634.882 1195.00 507.963 956.000 49 2540.04 4781.67 1270.07 2390.83 846.767 1593.89 635.133 1195.42 508.163 J56.333 5O 2541.04 4783.33 1270.57 2391.67 847.101 1594.44 635.384 1195.83 508.364 956.667 51 2542.05 4785.00 1271.07 2392.50 847.436 1595.00 635.6341196.25 508 564 957.000 52 2543 . 05 4786 . 67 i 1 271 . 57 2393 . 33 847.770 1595.56 635.885 1196.67 508.765 )57.333 53 2544.02 4788.33 1272.06 2394.17 848. 095)1596. 11 036.129 1197.08 508. 9CO 957.667 54 sJ545.004790.00 1272.542395.00 848 419 '1596. 67 636.3721197.50 509.155 958.000 55 2546 . 00 ' 4791 . 67 1 273 . 05 2395 . 83 848.754 1597.22 636.6231197.92 509.355 958.333 56 53547.004793.33 1273.55 2396.67 849.0881597.78 636.8741198.33 509.556 958.667 57 ! 2548. 00 4795. 00 '1274 052397.50 849.422 1598.33 637.124 1198.75 509.756 K59.000 58 25 4 9 . 1 4796 . 67 1 274 . 55 2398 33 84 9. 75(5 1598.89 537.375 1199.17 509.957 959.333 59 2550. 01 14:98.33 1275.05 2399.17 850.091 1599.44 637.626 1199.58 510.158 J59.607 140 TABLE XIV. ACTUAL TANGENTS, ETC. G Curve. 7 Curve. 8 Curve. 9 Curve. 10 Curve. 47" Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. 470.000 M. ~O~ 415.404 783.333 356.118671.429 311.663 587.500 277.091 522.222 249.446 415.572 783.611 356.261 671.667 311.788 587.708 277.203 522.407 249.546 470.167 1 415.739 783.889 356.405671.905 311.914 587.917 277.314 522.593 249.647 470.333 2 415.901 784.167 356.544 672.143 312.036 588.125 277.423 522.778 249.744 470.500 3 416.004 784.444 356.683672.381 312.158 588.333 277.531 522.963 249.842 470.607 4 416.2-31 784.722 356.826672.619 312.283 588.542 277.643 523.148 249.942 470.833 5 416.398 785.000 356.970 672.857 312.409 588.750 277.754 523.333 250.043 471.000 416.565 785.278 357.113673.095 312.534 588.958 277.866 523.519 250.143 471.167 7 416.732 785.556 357.256 673.333 312.659 589.167 277.977 523.704 250.244 471.333 8 416.895 785.833 357.396 673.571 312.781 589.375 278.085 523.889 250.341 471.500 9 417.057 786.111 357.535 673.810 312.903 589.583 278.194 524.074 250.439 471 . 667 1O 417.224 786.389 357.678:674.048 313.029589.792 5578.306 524.259 250.539 471.833 11 417.392 786.667 357.822 674. 286 313.154590.000 278.417 524.444 250.639 472.000 1 2 417.559 786.944 357.965674.524 313.279590.208 278.528 524.630 250.740 472.167 13 417.726 787.222 358.108674.762 313.405590.417 278.640 524.815 250.840 472.333 14 417 888 787.500 358.247 675.000 3 1 3. 527 i 590 625 278.748 525.000 250.938 472.500 15 418.051 787.778 358.387 675.238 313.649590.833 278.857 525.185 251.035 472.667 10 418.218 788.056 358.5301675.476 313.774591.042 278.968 525.370 251.136 472.833 17 418.385 788.333 358.673 675.714 313.899591.250 279.080 525.556 251.230 473.000 18 418.552 788.611 358.817 675.952 314.025 591.458 279.191 525.741 251.336 473.167 19 418.720 788.889 358.960 676.190 314.150 591.667 279.303 525.926 251.437 473.333 2O 418.882 789.107 359 099 076.429 314.272 591.875 279.411 526.111 251.534 473.500 21 419.044 789.444 359.239 676.667 314.394 592.083 279.519 526.290 251.632 473.667 22 419.212 789 722 359.382 676.905 314.519 592.292 279.631 526.481 251.732 473.833 23 419.379 ;9o ! ooo 359.525 677.143 314.645 592.500 279.742 526.667 251.833 474.000 24 419.546 790.278 359.668 677.381 314.770 592.708 27D.854 526.852 251.933 474.167 25 419.713 790.556 359.812 677.619 314.896i592 917 279.965 527.037 252.033 474.333 26 419.87(5 790.833 359.951 677.857 315.018 593.125 280.074 527.222 252.131 474.500 37 420.038 791.111 300.090 678.095 315.139 593.333 280.182 527.40; 252.228 474.667 28 420.205 791.389 360.234 678.333 315.265 593.542 280.294 527.593 252.329 474.833 29 420.372 791.667 360.377 678 571 315.390 593.750 280.405 527.778 252.429 475.000 30 420.539 791.944 360.520 678.810 315.516 593.958 280.517 527.963 252.530 475.167 31 420.707 792.222 360.664 679.048 315.641 594.167 280.628 528.148 252.630 475.333 32 420.874 792.500 360.807 679.286 315.767 594.375 280.740 528.333 252.730 475.500 33 421.011 792.778 360.950 679.524 315.892 594.583 280.851 528.519 252.831 475.667 34 421.203 793.056 361.089 679.762 316.014 594.792 280.960 528.704 252.928 475.833 35 421.300 793.333 361.229 680.000 316.136 595.000 281.068 528.889 253.020 476.000 36 421 . 533 793.611 361.372 680.238 316.261 595.208 281.179 529.074 253.126 476.167 37 421 . 700 793.889 361.515 680.476 316.387 595.417 281.291 529.259 253.227 476.333 38 421.867 794.167 361.659 680.714 316.512 595.625 281.402 529.444 253.327 476.500 39 422.035 794.444 361.802 680.952 316.638 595.833 281.514 529. 63P 253.428 476. 6G7 40 422.202 794.722 361.945 681.190 316.763 596.042 281.625 529.815 253.528 476.833 41 432.369 795.000 302.089 681.429 316.888 596.250 281.737 530.000 253.628 477.000 48 422.531 795.278 362.228 681.667 317.010 596.458 281.845 530.185 253.726 477.167 43 422.091 795.556 362.367 681.905 317.132 596.667 281.954 530.370 253.823 477.333 44 422.8611795.833 362.510 682.143 317.258 596.875 282.065 530.556 253.924 477.500 45 423.028 1 796. Ill 362.654 682.381 317.383 597.083 282.177 530.741 254.024 477.667 46 423. 195 796. 3S9 362.797 682.619 317.508597.292 282.288 530.926 254.125 477.833 47 423.363796.667 362.940 682 857 317.634597.500 282.400 531 111 254.225 478.000 48 423.530 796.944 363.084 683.095 317.759 597.708 282.511 531.296 254.325 478.167 49 423.097 797.222 363.227 683.333 317.885 597.917 282.623 531.481 254.426 478.333 50 423.861 797.500 363. 370 6K3. 571 318.010598.125 282.734 531.667 254.526 478.500 51 424.031 797.778363.514 683.810 318.136598.333 282.846 531.852254.627 478.667 53 424.194 798.050303.653684.048 318.257598.542 282.954 532.037 254.724 478.833 53 424.350 798 333363.7921684.286 318 379598.750 283.063 532.222 254.822 479.000 54 424.523 798 .611 363 936 684 . 524 318.505598.958 283.174 532.407 254.922 479.167 55 424.691 798. 889 364. 07 9 084. 7'02 318.630599.167 283.286 532.593 255.022 479.333 56 434.858 799.167364.222685.000 318.756599.375 283.397 532.778 255.123 479.500 57 425.025 799 444364.366685.238 318.881 599.588288.609 532.963 255.223 479.667 58 425.192 799.722364.509685.476 3 1 9 . 006 599 . 792 1 283 . 620 533.148 255.324 479.833' 59 141 TABLE XIV. ACTUAL TANGENTS, ETC. 48 1 Curve. 3 Curve. 3 Curve. 4 Curve. 5 Curve. M. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. o y.V>l Ul' 4800. 00 1275.55 2400.00 850 425 1600. 00 637. 877 ; 1200. 00 510.358 960.000 1 &53.01 4801.67 1276 05 2400.83 850.759 1600.50638.1271200.42 510.559 960.333 53 2553 02 4803.33 1276.56 2401.67 851.093 1001.11 038 378 1200.83 510.759 960.607 3 2554.02 4805.00 1277.06 2402.50 851.428 1001.67 638.029 1201.25 510.960 961.000 4 2555.02 4806.67 1277.56 2403.33 851.762 1002.22 038.879 1201.67 511.161 961.333 5 2556.00 4808.33 1278.05 2404.17 852.087 1602.78639.123 1202.08 511.356 961.607 (> 3556.97 4810.00 1278.53 2405.00 852.411 1003.33 03'J.367 1202.50 511.550 962.000 7 2557.97 4811.67 1279.03 2405.83 fe52.740 16H3.89 639.617 1202.92 511.751 962.333 8 2558.98 4813.33 1279.54 2406.67 853.080 1604.44 639.868 1203.33 511.952 962.607 9 2559.98 4815.00 1280.04 2407.50 853.414 1605.00 640.119 1203.75 512.152 963.000 10 2560.98 4816.67 1280.54 2408.33 853.748 1605.56 640.369 1204.17 512.353 963.333 11 2561 98 4818.33 1281.04 2409.17 854.083 1600 11 640.620 1204.58 512.553 963 007 13 3562.99 4820.00 1281.54 2410.00 854.417 1606.67 640.871 1205.00 512.754 904.000 13 3563.99 4821.67 1282.04 2410.83 854.751 1007.22 641 . 122 1205.42 512.955 964.333 14 2564.99 4823 33 1282.54 2411.67 855.086 1607.78 641.372 1205.83 513.155 964.607 15 2566.00 4825.00 1283.04 2412.50 855.420 1008.33641.623 1206.25 513.356 965.000 1.6 2567.00 4826.67 1283.55 2413.33 855.754 1008.89 641.874 1206.67 513.556 965.333 17 2568.00 4828.33 1284.05 2414.17 856.088 1609. 441642. 124 1207.08 513.757 905.067 18 2569.00 4830 00 1284.55 2415 00 856.423 1610.00 642.375 1207.50 513.958 906 000 19 2570.01 4831.67 1285.05 2415.83 856.757 1610.50 642.620 1207.92 514.158 966.333 30 2571.01 4833.33 1285.55 2416.67 857.091 1611.11 642.877 1208.33 514.359 966.667 21 2572.01 4835.00 1286.05 2417.50 857.425 1611.67 643.127 1208.75 514.559 967.000 33 2573.01 4836.67 1286.55 2418 33 857.760 1612.22643.378 1209.17 514.760 967.333 33 2574.02 4838.33 1287.06 2419.17 858.094 1612.78 643.629 1-209.58 514.961 907.0(57 34 2575.02 4840.00 1287.56 2420.00 858.428 1613.33 643.880 1210.00 515.101 968.000 35 2576.02 4841 67 1288.06 2420 83 858.762 1613.89 644.130 1210.42 515.302 908.333 36 2577.02 4843.33 1288.56 2421.67 859.097 1614.44!044.381 1210.83 515.562 968.667 37 5278.03 4845.00 1289.06 2422.50 859.431 1615.00 044.632 1211.25 515.763 909.000 38 2579.03 4846.67 1289.56 2423.33 859.765 1615. 561044. 882il211. 67 515.904 969.333 39 2580.03 4848.33 1290.06 2424.17 860.099 1616.11 645.133 1212.08 516.164 969.667 30 2581.04 4850.00 1290.57 2425.00 860.434 1616.67 645.384 1212.50 516.365 970.000 31 2582.04 4851.67 1291.07 2425.83 860.768 1617.22 645.635 1212.92 516.565 970.333 33 2583.04 4853.33 1291.57 2426.67 861.102 1617. 78 : 645. 885 1213.33 516.766 970.667 33 2584.04 4855.00 1292.07 2427.50 8517437 1618.33 646.130 1213.75 516.967 971.000 34 2585.05 4856.67 1292.57 2428.33 861.771 1618.89646.387 1214.17 517.167 971.333 35 2586.05 4858.33 1293.07 2429.17 862.105 1619.44 646.637 1214.58 517.368 971.667 36 2587.05 4860.00 1293.57 2430.00 862.439 1620.00646.888 1215.00 517.568 972.000 37 2588.05 4861.67 1294.07 2430.83 862 774 1620.56 647.139 1215.42 517.709 972.333 38 2589.06 4863.33 1294.58 2431.67 863.108 1621.11 647.390 1215.83 517.970 972.667 39 2590.06 4865.00 1295.08 2432.50 863.442 1621.67 647.640 1216.25 518.170 973.000 4O 2591.06 4866.67 1295.58 2433.33 863 . 776 1622.22 647.891 1216.67 518.371 973.333 41 2592.07 4868.33 1296.08 2434.17 864.111 1622.78648.142 1217.08 518.571 973.667 43 2593.07 4870.00 1296.58 2435.00 864.445 1623.33 648.393 1217.50 518.772 974.000 43 2594.07 4871.67 1297.08 2435.83 864.779 1623.89 648.643 1217.92 518.973 974.333 44 2595.07 4873.33 1297.58 2436.67 865.113 1624.44 648.894 1218.33 519.173 974.667 45 2596.08 4875.00 1298.09 2437.50 865.448 1625.00649.145 1218.75 519.374 975.000 46 2597.08 4876.67 1298.59 2438. 33 865.782 1625.56 649.395 1219.17 519.574 975.333 47 2598.08 4878. 33 1299.09 2439.17 866.116 1626.11 649.646 1219.58 519.775 975.607 48 2599.08 4880.00 1299.59 2440.00 866.450 1626.67 649.897 1220.00 519.970 976.000. 49 2600.09 4881.67 1300.09 2440.83 866.785 1627.22,650.148 1220.42 520.176 976.333 5O 2601.09 4883.33 1300.59 2441.67 867.119 16-27.78650.398 1220.83 520.377 976.667 51 2602.09 4885.00 1301.09 2442.50 867.458 1628.33 050.049 1221.25 520.577 977.000 53 2603.09 4886.67 1301.59 2443.33 867.788 1628.89650.900 1221.07 520.778 977.333 53 2004.10 4888.33 1302.10 2444.17 868.122 1629.44 651.150 1222.08 520.979 977.607 54 2605.10 4890.00 1302.60 2445.00 868.456 1030.00 651.401 1222.50 521.179 978.000 55 2606.10 4891.67 1303.10 ?445.83 868.790 1630.56651.652 1222.92 521.380 978.333 56 2607.11 4893.33 1303.60 2446.67 869.125 1631.11 651. 90S 12-23.33 521.580 978.667 57 2608.14 4895.00 1304.12 2447.50 869.468 1631.67 652.160 1223.75 521.787 979.000 58 2609.17 4896.67 1304.63 2448.33 S69.812 1632.22 652.4181224.17 521 . 993 979.333 59 2610.17 4898.33 1305.13 2449.K 870.146 1632.78 652. 66911224. 58 522.194 979.667 TABLE XIV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 Curve. 1O Curve. 48 Tan. Arc. Tan. | Arc. Tan. Arc. Tan. Arc. Tan . Arc. M. 425.859800.000 364.652685.714 319.132 600.000283.732 533.333 255.424480.000 O 425.527j800.278 364. 796 6S5. 952 319.257 600. 208 '283. 843 533.519 255.524 480.167 1 425. 694*800. 566 364.939686.190 319.383 600.417283.955 533.704 255.625 480.333 2 425.b6l|800.S83 365.082686.429 319.508 600.625284.066 533.889 255.725 480.500 3 426.028801.111 365.226686.667 319.634 600.833 284.178 534.074 255.826 480.667 4 4-26.191 801.389 365.365 686.905 319.756601.042 284.286534.259 255.923 480.833 5 426.353 801.667 365.504 687.143 319.877:601.250 284.394 534.444 256.021 481.000 6 426.520 801.944 365.647 687.381 320.003601.458 284.506534.630 256.121 481.167 7 426.687 802.222 365.791 687.619 320.128601.667 284.617534.815 256. 2S1 481 .333 8 426 854 802.500 365.934 687.857 320.254 601.875 284.729 535.000 256.322 481.500 427.022 802.778 366.077 688.095 320.379 602 083 284.841 535.185 256.422 481.667 10 427.181)803.056 366.221 688.333 320.505 602.292 284.952 535.370 256.523 481.833 11 427 356 803.333 366.364 688.571 320.630 602.500 285.064 535.556 256.623 482.000 12 427.523803.611 366.507 688.810 320.755 602.708 285.175 535.741 256.723 482.167 13 427.690803.889 366.651 689.048 320.881 602.917 285.287 535.926 256.824 482.333 14 427.858804.167 366.794 689.286 321.006 603.125 285.398 536.111 256.924 482.500 15 428.025804.444 366.937 689.524 321 132 603.333 285.510 536.296 257.025 482.667 1(J 428. 192 ;804. 722 367.081 689.762 321.257 603.542 285.621 536.481 257.125 482.833 17 428. 359 1805.000 367.224 690.000 321.383 603.750 285.733 536.667 257.225 483.000 18 428.526 805.278 367.367 690.238 321.508 603.958 285.844 536.852 257.326 483.167 19 428.694 805.556 367.511 690.476 321.633 604.167 285.956 537.037 257.426 483.333 2O 428.861 805.833 367.654 690.714 321.759 604.375 286.067 537.222 257.527 483.500 21 429.028806.111 367.797 690.952 321.884 604.583 286.179 537.407 257.627 483.667 22 429.195806.389 367 941 691.190 322.010 604.792 286.290 537.593 257.727 483.833 23 429.362800.667 368.084 691.429 322.135 605.000 286.402 537.778 257.828 484.000 24 429.530806.944 368.227 691.667 322.261 605.208 286.513 537.963 257.928 484.167 25 429.697 807. 22< 368.371 691.905 322.386 605.417 286.625 538.148 258.029 484.333 26 429.864 807. 500 368.514 692.143 322.512 605.625 286.736 538.333 258.129 484.500 27 430.031 807.778 368.657 692.381 322 637 605.833 286.848 538.519 258.229 484.667 28 430.198 808.056 368.801 692.619 322.762 606.042 286.959 538.704 258.330 484.833 29 430.365 808.333 368.944 692.857 322 888 606.250 287.071 538.889 258.430 485.000 3O 430.533808.611 369.087 693.095 323.013 606.458 287.182 539.074 258.530 485.167 31 430.700808.889 369.231 693.333 323.139 606.667 287.294 539.259 258.631 485.333 32 430.867809.167 369.374 693.571 323.264 606.875 287.406 539.444 258.731 485.500 33 431.034 809.444 369.517 693.810 323.390 607.083 287.517 539.630 258.832 485.667 34 431.201 809.722 369.661 694.048 323.515 607.292 287.629 539.815 258.932 485.833 35 431.369810.000 369.804 694.286 323.640 607.500 287.740 540.000 259.032 486.000 3G 431.536 810.278 369.947 694.524 323.766 607.708 287.852 540.185 259.133 486.167 37 431.703 810.556 370.091 694.762 323.891 607.917 287.963 540.370 259.233 486.333 38 431.870 810.833 370.234 695.000 324.017 608.125 288.075 540.556 259.334 486.500 39 432.037 811.111 370.377 695.238 324.142 608.333 288.186 540.741 259.434 486.667 4O 432.205 811.389 370.521 695.476 324.268 608.542 288.298 540.920 259.534 486.833 41 432.372 811.667 370.664 695.714 324.393 608.750 288 409 541.111 259.635 487.000 42 432.539 811.944 370 807 695.952 324.519 608 958 288.521 541.296 259.735 487.167 43 432.706 812.222 370.950 696.190 324.644 609.167 288.632 541.481 259.83(i J 87. 333 44 432.873 812.500 371.094 696.429 324.769 609.375 288.744 541.667 259 936 487.500 45 433.041 812.778 371.237 696.667 324.895 609.583 288.855 541.852 260 036 487.667 4G 433.208 813.056 371.380 696.905 325.020 609.792 288.967 542.037 260.137 487.833 47 433.375 813.333 371.524 697.143 325.146 610.000 289.078 542.222 260.237 488.000 48 433.542 813.611 371.667 697.381 325.271 610.208 289.190 542.407 260.338 488.167 49 433.709 813.889 371.810 697. fil 9 325.397 610.417 289.301 542.593 260.438 488.333 50 433.876 814.167 371.954 697.857 325.522 610.625 289. 41 3 1542.778 260.538 488.500 51 434.041 814.444 372.097 698.095 325.647 610.833 289.524:542.96? 260 639 488.667 52 434.211 814. 722J372.240 698.333 325.773 611.042 289.636543.148 260.739 488.833 53 434.378 81 5.000' 372. 3841 698. 571 325.898 611.250 289.747543.333 260.840 489.000; 54 434.545 81 5. 278 372. 5271 698. 810 326.024 611.458 289. 859 543. 51 < 260.940 489.167; 55 434.712 815.556 372.670 699.048 326.149 611.667 289.971 543.704 261.040 489.333 r>(> 484.884 815.833372.818699.286 326.278 611.875 290.085543.889 261.144 489.500j 57 435.056 816.111 372.965 699.524 435 . 224 ! 8 1 6 . 389 373 . 1 09 ' 699 . 762 326.407 326.533 612.083 612.292 290.200544.074 290.311:544 259 261.247 261.347 489.667 58 489.833 59 143 TABLE XIV. ACTUAL TANGENTS, ETC. 49 1 Curve. 2 Curve. 3 Curve. 4 Curve. 5 Curve. M. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. 2611.17 4900.00 1305.632450.00 870.481 1633.33 652.920 1225.00 522.394 980.000 1 2612.18 4901.67 1306.14 2450.83 870.815 1633.89 653.171 1225.42 522.595 980.333 2 2613.18 4903.33 1306.64 2451.67 871.149 1634.44 653.421 1225.83 52-2.795 980.667 3 2614.18 4905.00 1307.14 2452.50 871.484 16:35.00 653.672 1226.25 522.996 981.000 4 2615.18 4906.67 1307.64 2453.33 871.818 1635.56 653. 923 11'226. 67 523.197 981.333 5 2616.19 4908.33 1308.14 2454.17 872.152 1636.11 654.173 1227.08 523.397981.667 6 2617.19 4910.00 1308.64 2455.00 872.486 1636.67 654.424 1227.50 523.598982.000 7 2618.19 4911.67 1309.14 2455.83 872.821 1637.22 654.675 1227.92 523.798982.333 8 2619.19 4913.33 1309.65 2456.67 873.1551637.78 654.926 1228.33 523.999982.667 9 2620.20 4915.00 1310.15 2457.50 873.489,1638.33 655.176 1228.75 524.200983.000 10 2621.20 4916.67 1310.65 2458.33 873.8231638.89 655.427 1229.17 524.400983.333 11 2622.23 4918.33 1311.16 2459.17 874.167 1639.44 655.685 1229.58 524.607983.667 12 2623.26 4920.00 1311.68 2460.00 874.511 1640.00 655.943 1230.00 524.813984.000 13 2624.27 4921.67 1312.18 2460.83 874.845 1640.56 656.194 1230.42 525.013984.333 14 2625.27 4923.33 1312.68 2461.67 875.180 1641.11 656.444 1230.83 525.214984.667 15 2626.27 4925.00 1313.18 2462.50 875.514 1641.67 656.695 1231.25 525.415985.000 16 2627.27 4926.67 1313.69 2463.33 875.848 1642.22 656.946 1231.67 525.615985.333 17 2628.28 4928.33 1314.19 2464.17 876.182 1642.78 657.196 1232.08 525.816985.667 18 2629.28 4930.00 1314.69 2465. OJ 876.517 1643.33 657.447 1232.50 526. 01 6 : 986. 000 19 2630.28 4931.67 1315.19 2465.83 876.851 1643.89 657.698 1232.92 526.217 986.333 20 2631.28 4933.33 1315.69 2466.67 877.185 1644.44 657.949 1233.33 526.418 986.667 21 2632.32 4935.00 1316.21 2467.50 877.529 1645.00 658.206 1233.75 526. 624 1987. 000 22 2633.35 4936.67 1316.72 2468.33 877.873 1645.56 658.464 1234.17 526. 830 i 987. 3:33 23 2634.35 4938.33 1317.22 2469.17 878.207 1646.11 658.715 1234.58 527.031 987.667 24 2635.35 4940.00 1317.72 2470.00 878.541 1646.67 658.966 1235.00 527 2311988.000 25 2636.36 4941.67 1318.23 2470.83 878.876 1647.22 659.216 1235.42 527.432988.333 26 2637.36 4913.33 1318.73 2471.67 879.210 1647.78 659.467 1235.83 527.633988.667 27 2638.36 4945.00 1319.23 2472.50 879.544 1648.33 659.718 1236.25 527.8331989.000 28 2639.36 4946.67 1319.73 2473.33 879.878 1648.89 659.969 1236.67 528.034 989.333 29 2640.39 4948.33 1320.25 2474.17 880.222 1649.44 660.227 1237.08 528.240 989.667 30 2641.43 4950.00 1320.76 2475.00 880.566 1650.00 660.484 1237.50 528.447 990.000 31 2642.43 4951.67 1321.26 2475.83 880.900 1650.56 660.735 1237.92 528.647 990.333 32 2643.43 4953.33 1321.76 2476.67 881.235 1651.11 660.986 1238.33 528.848 990.607 33 2644.43 4955.00 1332.27 2477.50 881.569 1651.67 661.237 1-238.75 5-29.048 991.000 34 2645.44 4956.67 1322.77 2478.33 881.903 1652.22 661.487 1239.17 529.249 991.333 35 2646.44 4958.33 1323 27 2479.17 882.237 1652.78 661,738 1239.58 5-29.450 991.667 36 2647.44 4960.00 1323.77 2480.00 882.572 1653.33 661.989 1240.00 529.650 992.000 37 2648.47 4961.67 1324.29 2480.83 882.915 1653.89 062.247 1240.42 529.856 992.333 38 2649.50 4963.33 1324.80 2481.67 883.259 1654.44 662.505 1240.83 530.063 992.607 39 2650.51 4965.00 1345.30 2482.50 883.593 1655.00 662.755 1241.25 530.203 993.000 4O 2651.51 4966.67 1335 80 2483.33 883.928 1655.56 663.006 1241.67 530.464 993.333 41 2652.51 4968.33 1326.31 2484.17 884.262 1656.11 663.257 1242.08 530.665 993.607 42 2653.52 497'0.00 1326.81 2485.00 884.596 1656.67 063.507 1242.50 530.865 994.000 43 2654.55 4971.67 1327.32 2485.83 884.940 1657.22 063.765 1242.9-2 531.072 994.333 44 2655.58 4973.33 1327.84 2486.67 885.284 1657.78 664.023 1243.33 531.278 994.607 45 2656.58 4975.00 1328.34 2487.50 8S5.618 1658.33 664.274 1243.75 531.478 995.000 46 2657.58 4976.67 13-28 84 2488.33 8S5.952 1658.89 664.525 1244.17 531.679 995.333 47 2658.59 4978.33 1329.34 2489.17 886.287 1659.44 664.775 1244.58 531.880 995.067 48 2659.59 4980.00 1329.84 2490.00 886.621 1660.00 065.026 1245.00 532.080 996.000 49 2(360.62 4981.67 1330.36 2490.83 886.905 1660.56 665.284 1245.42 532.287 996.333 5O 2661.65 4983.33 1330.87 2491.67 887.309 1601.11 665.542 1245.83 53-2.493 996.607 51 2662.65 4985.00 1331.38 241)2.50 887.643 1661.67 665.793 1246.25 582.694997.000 52 2603.664986.67 1331.88 2493.33 887.977 1662.22 666.043 1246.67 532.894 997.333 53 2664.694988.33 1332.39 2494.17 S88.321 1662.78 666.301 1247.08 533.100997.607 54 2665.724990.00 1332.91 2495.00 888.665 1663.33 666.559 1247.50 533.307998.000 55 2666.724991.67 1333.41 2495.83 888.999 1603.89 606.810 1247.92 533.507998.333 56 2667.734993.33 1333.91 2496.67 889.3331664.44 667.060 1248.33 533.708998.667 57 2668.7:14995.00 1334.41 2107.50 889.66816(55.00 667.311 1248.75 533.909 999.000 58 2669.734996.67 1334.91 2498.33 890.002 1665.56 667.562 1249.17 534.109999.333 59 2670.764998.33 1335.432499.17 890.346 1666.11 667.820 1249.58 534.315999.667 144 TABLE XIV. ACTUAL TANGENTS, ETC. G Curve. 7 Curve. 8 Curve. 9 Curve. 1O Curve. 49 Tan. Arc. Tan. Arc. Tan. Arc. Tan. A re. 544.444 Tan. Arc. M. 435.391 816.667 373.252 700.000 326.658 612.500 290.423 261.448 490.000 435.558 816.944 373.395 700.238 326.784 612.708 290.535 544.630 261.548 490.167 1 435.725 817.222 373.539 700.476 326.909 612.917 290.646 544.815 261.648 490.333 2 435.892 817.500 373.682 700.714 327.034 613.125 290.758 545.000 261.749 490.500 3 436.059 817.778 373.825 700.952 327.160 613.333 290.869 545.185 261.849 490.667 4 436.227 818.056 373.969 701.190 327.285 613 542 290.981 545.370 261.950 490.833 5 436.394 818.333 374.112 701.429 327.411 613.750 291.092 545.556 262.050 491.000 436.561 818.611 374.255 701.667 327.536 613.958 291.204 545.741 262.150 491.167 7 436.728 818.889 37'4.399 701.905 327.662 614.167 291.315 545.926 262.251 491.333 8 436.895 819.167 374.542 702.143 327.787 614.375 291.427 546.111 262.351 491.500 9 437.063 819.444 374.685 702.381 327.912 614.583 291.538 546.296 262.452 491.667 10 437.235 819.722 374.833 702.619 328.041 614.792 291.653 546.481 262.555 491.833 11 437.407 820.000 374.980 702 857 328.171 615.000 291.768 546.667 262.658 44)2.000 12 437. 57 i 820.278 375.123 703.095 328.296 615.208 291.879 546.852 262.759 492.167 13 437.741 820.556 375.267 703.333 328.421 615.417 291.991 547.037 262.859 492.333 14 437.908 820.833 375.410 703.571 328.547 615.625 292.102 547.222 262.959 492.500 15 438.075 821.111 375.553 703.810 328.672 615.833 292.214 547.407 263.060 492.667 16 438.242 821.389 375.697 704. 048 328.798 616.042 292.325 547.593 263.160 492.833 17 438.410 821.667 375.840 704.286 328.923 616.250 292.437 547.778 263.261 493.000 18 438.577 821.944 375.983 704.524 329.049 616.458 292.548 547.963 263.361 493.167 19 438.744 822.222 376.127 704.762 329.174 616.667 292.660 548.148 263.461 493.333 2O 438.916 822.500 376.274 705.000 329.303 616.875 292.775 548.333 263.565 493.500 21 439.088 822.778 376.422 705.238 329.432 617.083 292.889 548.519 263.668 493.667 22 439.255 823.05*. 376.565 705.47T, 329.557 617.292 293.001 548.704 263.768 493.833 23 439.42',' 823.333 376.708 705.714 329.683 617. 500 293.112 548.889 263.869 494.000 24 439. 590 823.611 376.852 705.952 329.808 617.708 293.224 549.074 263.969 494.167 25 439.757 823.889 376.995 706.190 3-J9.934 617.917 293.335 549.251) 264.069 494.333 2G 439.924 824.16? 377. 138 706.429 330 059 618.125 293.447 549.444 264.170 494.500 27 440.091 S>4.444 477.282 706.667 330.185 618.333 293.558 549.630 264.270 494.667 28 440.263 824.722 377.429 706.905 330.314 618.542 293.673 549.815 264.374 494.833 29 440.435 825.000 377.576 707.143 330.443 618.750 293.788 550.000 264.477 495.000 30 440.602 825.278 377 720 707.381 330.568 618.958 293.899 550.185 264 . 577 495.167 31 440.769 825.556 377.863 707.619 330.694 619.167 294.011 550.370 264.678 495.333 32 440.937 825.833 378.006 707. 857 330.819 619.37'5 294.122 550.556 264.778 495.500 33 441.104 826.111 378.150 708.095 330.944 619.583 294.234 550.741 264.878 495.667 34 441.271 826.389 378.293 708. 333 331.070 619.792 294.345 550.926 264.979 495.833 35 441.438 826.667 37'8.436 708.571 331.195 620.000 294.457 551.111 265.079 496.000 36 441.610 826.944 378.584 708.810 331.324 620.208 294.572 551.296 265.182 496.167 37 441.782 827.222 378 731 709.048 331.453 620.417 294.680 551.481 265.286 496.333 38 441.949 827.500 378.875 709.286 331.579 620.625 294.798 551.667 265.386 496.500 39 442.117 827.778 379.018 709.524 331.704 620.833 294.909 551.852 265.486 496.667 40 442.284 828.056 379.161 709.762 331.830 621.042 295.021 552.037 265.587 496.833 41 442.451 828.333 379.304 710.000 331.955 621.250 295.132 552.222 265.687 497.000 42 442.623 828.611 379.452 710.238 332.084 621.458 295.247 552.407 265.791 497.167 43 442.795 828.889 379.599 710.476 332.213 621.667 295.362 552.593 265.894 497.333 44 442.962 829.167 379.743 710.714 a3 2. 339 621.875 295.473 552.778 265.994 497.500 45 443.129 829.444 379.886 710.952 332.464 622.083 295.585 552.963 266.095 497.667 46 443.296 829.722 380.029 711.190 332. 5S9 622.292 295.696 553.148 266.195 497.838 47 443 464 830.000 380.173 711.429 332.715 622.500 295.808 553.333 266.295 498.000 48 443.636 830.278 380.320 711.667 332.844 622.708 295.923 553.519 266.399 498.167 49 443.808 830.556 380.468 711.905 332.973 622.917 296.037 553.704 266.502 498.333 50 443.975 830.833 380.611 712.143 333.098 623.125 296.149 553.889 266.602 498.500 51 444.142 831.111 380.754 712.381 333.224 623.3.33 296.260 554.074 266.703 498.667 52 444.314 831.38!) 380.902 712.619 333 353 623.542 296.375 554.259,266.806 498.833 53 444.486 831.667 381.049 712.857 333.482 623.7'50 296.490 554.444266.909 499.000 54 444.653 831.944 381.192 713.095 333.607 623.958 2J6.601 554.630267.010 499.167 55 444.8201832.222 381.336 713.333 333.S 33 624.167 2156.713 554.815267.110 499.333 56 444.987 832.500 381.479 713.571 333.858 621.375 296.824 555.000267.210 499.500 57 445.155 832.778 381.622 713.810 333.984 624.583 296.936 555.185267.311 499.667 58 445.327833.056 381.770 714.048 334.113 624.792 297.051 555.370 267.414 499.833 59 145 TABLE XIV. ACTUAL TANGENTS, ETC. 5O 1 Curve. 2 Curve. 3 Curve. 4 Curve. 5 Curve. M. Tan. Arc. 5000.00 Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. 2671.79 13^5.95 2500.00 890.689 1666.07 068.078 1250.00 5:34.522 1000.00 1 3672.80 5001.67 1336.45 2500.83 891 024 1667.22 668.328 1250.42 534.722 1000.33 3 2(573.80 5003.33 1336.95 2501.67 891.358 1667.78 668.579 1250.83 534.923 1000.67 3 2074.83 5005.00 1337.46 2502.50 891.702 1668.33 668.837 1251.25 535.129 1001.00 4 2675.86 501)6.67 1337.98 2503.33 892.046 1668.89 669.095 1251.67 535.336 1001. 33 5 2676.86 5008.33 1338.48 2504.17 892.380 1669.44 669.346 1252.08 535.536 1001.67 6 2677.87 5010.00 13:38.98 2505.00 892.714 1670.00 669.596 1252.50 535.737 1002.00 7 2678.87 5011.67 1339.48 2505.83 893.048 1670.56 669.847 1252.92 535.937 1002.33 8 2679.87 5013.33 1339.99 2506.67 893.383 1671.11 670.098 1253.33 536.138 1002.67 9 2680.90 5015.00 1340.50 2507.50 893.726 1671.67 670.356 1253.75 536.344 1003.00 10 2681.93 5016.67 1341.02 2508. as 894.070 1672.22 670.614 1254.17 536.551 1003. as 11 2682.94 5018.33 1341.52 2509.17 894. 405' 1672. 78 670.864 1254.58 536.751 1003.67 13 2683.94 5020.00 1342.02 2510.00 894.739 1673 33 671.115 1255.00 536,952 1004.00 13 2684.97 5021.67 1342.53 2510.83 895.083:1673.89 671.373 1255.42 537.158 1004. as 14 2686.00 5023.33 1343.05 2511.67 895. 426; 1674. 44 671.631 1255.83 537.365 1004.67 15 2687.01 5025.00 1343.55 2512.50 895.761 1675.00 671.881 1256.25 537.565 1005.00 16 2688.01 5026.67 1344.05 2513.33 896.095 1675.56 672.132 1256.67 537.766 1005.33 17 2689.04 5028.33 1344.57 2514.17 896.439 1676.11 672.390 1257.08 537.972 1005.67 18 2690.07 5030.00 1345.08 2515.00 896.783 1676.67 672.648 1257.50 538.178 1006.00 19 2691.07 5031.67 1345.59 2515.83 897.117 1677.22 672.899 1257.92 538.379 1006.33 20 2692.08 soas.as 1346.09 2516.67 897.451 1677.78 673.149 1258.33 538.580 1006.67 21 2693.11 5035.00 1346.60 2517.50 897.795 1678. as 673.407 1258.75 538.786 1007.00 22 2694.14 5036.67 1347.12 2518.33 898.139 1678.89 673.665 1259.17 538.992 1007.33 23 2695.14 5038. as 1347.62 2519.17 898.473 1679.44 673.916 1259.58 539.193 1007.67 24 2696.14 5040.00 1348.12 2520.00 898.807 1680.00 674.167 1260.00 539.394 1008.00 25 2697.18 5041.67 1348.64 2520.83 899.151 1680.56 674 424 1260.42 539.600 1008.33 26 2698.21 5043.33 1349.15 2521.67 899.495 1681.11 074.682 1260.83 539.806 1008.67 27 2699.24 5045.00 1349.67 2522.50 899.839 1681.87 674.940 1261.25 540.013 1009.00 28 2700.27 5046.67 1350.18 2523.33 900.183 1682.22 675.198 1261.67 540.219 1009.33 29 2701 .27 5048.33 1350.69 2524.17 900.517 1682.78 675.449 1262.08 540.419 1009.67 30 2702.27 5050.00 1351.19 2525.00 900.851 1683.33 675.700 1262.50 540.620 1010.00 31 2703.31 5051.67 ia51.70 2525.83 901.195 1683.89 075.957 1262.92 540.826 1010.33 32 2704.34 5053. as 1352.22 2526.67 901.539 1684.44 676.215 1263.33 541.033 1010.67 33 2705.34 5055.00 ia52.72 2527.50 901.873 1685.00 676.466 1263.75 541.2:33 1011.00 34 2706.34 5056.67 1353.22 2528. 33 902.207 1685.56 676.717 1264.17 541.434 1011.33 35 2707.37 5058. as 1353.74 2529.17 902.551 1686.11 676.975 1264.58 541.640 1011.67 36 2708.41 5060.00 1354.25 2530.00 902 895 1686.67 677.233 1265.00 541.847 1012.00 37 2709.41 5061.67 1354.75 2530.83 903.229 1687.22 677.483 1265.42 542.047 1012.33 38 2710.41 5063. as 1355.26 2531.67 903.563 1687.78 077.734 1265.83 542.248 1012.67 39 2711.44 5065.00 1355.77 2532.50 903.907 1688.3S 677.992 1266.25 542.454 1013.00 4O 2712.47 5066.67 1356.29 2533.33 904.251 1688.89 678.250 1266.67 542.660 1013.33 41 2713.50 5068.33 1:356 80 2534.17 904.595 1689.44 078.508 1267.08 542.867 1013.67 42 2714.54 5070.00 1357.32 2535.00 904.939 1690.00 678.766 1267.50 543.073 1014.00 43 44 2715.54 2716.54 5071.67 5073.33 1357.82 ia58.32 2535.83 2536.67 905.2731690.56 905.6071091.11 679.016 679.267 1267.92 1268.33 543.274 543.474 1014.33 1014.67 45 2717.57 5075.00 1358.84 2537.50 905.951 1691.67 079.525 1268.75 543.681 1015.00 46 2718.60 5076.67 1359. a5 2538.33 906.295 1692.22 679.783 1269.17 543.887 1015. as 47 2719.61 5078.33 1359.85 2539.17 906.629 1692.78 680.033 1269.58 544.088 1015.67 48 2720.61 5080.00 1360.35 2540.00 906.963 1693.33 680.284 1270.00 544.288 1016.00 49 2721.64 5081.67 1360.87 2540.83 907.307 1693.89 680.542 1270.42 544.494 1016.33 5O 2722.67 5083.33 1361,39 2541.67 907.651 1694.44 680.800 1270.83 544.701 1016.67 51 2723.70 5085.00 1361.90 2542.50 907.995 1695.00 681.058 1271.25 544.907 1017.00 52 2724.74 5086.67 1362.42 2543. as 908.339 1695.56 681.316 1271.67 545.113 1017.33 53 2725.74 5088. a3 1362.92 2544.17 908.6731696.11 681.566 1272.08 545.314 1017.67 54 2726.74 5090.00 1363.42 2545.00 909.00711696.67 681.817 1272.50 545.515 1018.00 55 2727.77 5091.67 1:363.94 2545.83 909. 351 ! 1697. 22 082.075 1-J72.92 545.721)1018.33 56 2728.80 5093. as 1364.45 2546. #? 909.6951697.78 682.3:33 1273. as 545. 927 [101 8. 67 57 2729.83 5095.00 1364.97 2547.50 910.039 1698. as 082.591 1273.75 540.1:34 1019. 00 58 2730.87 5096.67 1365.48 2548.33 910.382 1698.89 682.849 1274.17 M6.340J1019.33 59 2731.90 5098.33 1366.00 2549.17 910.726 1699.44 683.107 1274.58 516.546il019.67 146 TABLE XIV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 Curve. 10 Curve. 5O Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. M. 445.499 833.333 381.917 714 286 334 242625.000 297.165555.556267.517 500.000 445.666 833.6111382.060 714.524 334.367625.208 297. 27? 1555. 741 267.618 500.16? 1 445.883 833.8891382 204 714.762 334.493625.417 297. 388 555. 920267.71 8 500.333 2 446.005 S34.167 382.351 715.000 334.622625.625 297.503556.111 207.821 500.500 3 446.17? 834.444 382.499 715.238 334.751 625 833 297.618 556.296267.925 500.66? 4 446.344 446 511 834.722 835.000 382.642 382.785 715.476 715.714 334.876 626.042 335.001 626 250 297.729 297.841 556.481 556.667 208.025 268.125 500.833 501.000 5 6 446.678 835.278 382.929 715.952 335.127 626.458 297.952 556.852 268.226 501.167 7 446.846 835.556 383.072 716.190 335.252 626.667 298.064 557.037 268.326 501.333 8 447.018 835.833 383.219 716.429 335.381 626-875 298.179 557.222 268.430 501.500 9 447.190 836.111 383.367 716.667 335. 510 |627.083 298.293 557.407 268.533 501 . 667 10 447.35? 836.359 383.510 716.905 335.636627.292 298.405 557.593 268.633 501.833 11 447.524 447.696 836.667 836.944 383.653 383.801 717.143 717.381 335. 761 S627.500 335.890627.708 298.516 298.631 557.778 557.963 268.734 502.000 268.837502.167 12 13 447.868 837.222 383.948 717.619 986.019 627.917 298.746 558.118 268.940502.333 14 448.035 837.500 384.092 717.85? 336.145 628.125 298.857 558.333 209.040502.500 15 448.202 837.778 384.235 718.095 336.270 628.333 298.969 558.519 269.141 502 667 16 448.374 838.056 384.382 718.333 886.899 628.542 299 084 558.704 269.244 502.833 17 448.546 838.333 384.530 718.571 336.528 628.750 299.198 558.889 269.347 503.000 18 448.713 838.611 384.673 718.810 336.654 628.958 299.310 559.074 269.448 503.167 19 448.881 838.889 384.816 719.048 336.779 629.167 299.421 559.259 269.548 503.333 2O 449.053 839.167 284.964 719.286 336.908629.375 299.536 559.444 269.651 503.500 21 449.224 839.444 385.111 719.524 337. 037 1629.583 299.651 559.630 269.755 503.667 22 449.392 839.722 385.255 719.762 337.1631629.792 299.762 559.815 269.855 5Q3.833 23 449.559 840.000 385.398 720.000 337. 288; 630. 000 299.874 560.000 269.956 504.000 24 449.731 840.278 385.545 720.238 337.417630.208 299.988 560.185 270.059 504.167 25 449.903 840.556 385.693 720.476 337.546 630.417 300.103 560.370 270.162 504.333 26 450.075 840.833 385.840 720.714 337.675630.625 300.218 560.556 270.265 504.500 27 450.247 841.111 385.988 720.952 337.804 630 833 300.333 560.741 270.369 504.667 28 450.414 841.389 386.131 721.190 337.929631.042 300.444 560.926 270.469 504.833 29 450.581 841.667 386.274 721.429 338.055 631.250 300.556 561.111 270.569 505.000 30 450.753 841.944 386.422 721.667 338.184631.458 800.670 561.290 270.673 505.167 31 450.925 842.222 386.569 721.905 338.313631.667 300.785 561.481 270.776 505.333 32 451.092 842.500 386.713 722.143 338.438631.875 300 897 561 667 270.876 505.500 33 451.259 842.778 386.856 722.381 338.564 632.083 301.008 561.852 270 977 505.667 34 451.431 843.056 387.003 722 619 338.693632.292 301.123 562.037 271.080 505.833 35 451.603 843.333 387.151 722.857 338.822 632.500 301.237 562 222 271.183 506.000 36 451.771 P43.611 3S7.294 723.095 338.947 632 708 301.349 562.407 271.284 506.167 37 451.938 843.889 387.437 723.033 339.073632.91? 301.461 562.593 271 384 506.333 38 452.110 844.167 387.585 723.571 339.202 633.125 301.575 562.778 271.487 5C6.500 39 452.282 844.444 387.732 723.810 339.331 633.333 301.690 562.963 271.591 506.667 40 452.454 844.722 387.880 724.048 339. 460:633. 542 301.805 563.148 271.694 506.833 41 452.626 452.793 845.000 845.278 388.027 388.170 724.286 724.524 339.589033.750 339.714 633 958 301.919503.333271.797 302. 031 1 563. 51 9 271. 897 507.000 507.167 42 43 452.960 845.556 388.314 724.762 339.840634.167 302.142563.704 271.998 507.333 44 453.132 845.833 388.461 725.000 339.969 634 375 302.257563.889272.101 507.500 45 453,304 846.111 388.609 725.238 340.098 634.583 302 . 372 564 074 272 . 204 507.667 46 453.471 846.389 388.752 725.476 340.223 634.792 302.483564.259272 305 507.838 47 453.638 846.66? 388.895 725.714 340.349 635.000 302 . 595 j 564 . 444 272 . 405 508.000 48 453.810 846.944 389.043 725.952 340.478 635.208 302. 710 564. 630 1 272. 518 508.167 49 453.982 847.222 389.190 726.190 340 607 635.417 302.8.24564.815 272.612 508.333 50 454.154 847.500 389.337 726.429 340.73(> 635.625 302 . 939 505 . 000 272 .715 508.500 51 454.326 847.778 389.485 726.667 340.865 035.833 303 . 054 565 . 1 85 27 2 . S 18 508 . 667 52 454.498848.056 389.628 726.905 340.990636.042 303 . 1 65 565 . 370 272 . 9 1 9 508 . 833 53 454.661848.888 389.772 727.143 341.116036.250 303 . 277 565 . 556 273 .019 509 . 000 54 454.832848.611 389.919 727.381 341.245636.458 3,'3 . 391 565 . 741 273 . 1 22 50!) . 1 67 55 455.004848.889 390.066 727. (i 19 341.374636.607 303.506 505.926 273.226 509.333 56 455.176849.167 390.214 727.85? 341.503636.875 303.1.21 566.111 273.329 509.500 57 455.348849.444 390.361 728.095 341. 632 1637. 083 303.736 566.296 273.432 509.067 r>8 455.520849.722 390.509 728.333 341 . 761 i 637 . 292 303 . 850 566 . 481 273 . 535 509 . K-J3 59 147 TABLE XIV. ACTUAL TANGENTS, ETC. 51 1 Curve. 3 Curve. 3 Curve. 4 Curve. 5 Curve. M. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. ~~0 273:2.93 5100. 00 11366. 51 2550.00 911.070 1700.00 683.364 1275.00 546.753 1020.00 1 2733.93 5101.67 1367.02 2550.83 911.404 1700.56 683.615 1275.42 546.9531020.33 3 2734.93 5103.33 1367.52 2551.67 1)11.738 1701.11 683.866 1275.8:1 547.154 1020.6;' 3 2735.97 5105.00 1368.03 2552.50 912.08-3 1701.67 684.124 1276.25 547. 300 10-21.03 4 2737.00 5106.67 1368.55 2553.33 912.426 1702.22 684.382 1-376.6: 547.566 1021.33 5 2738.03 5108.33 1369.06 2554.17 912.770 1702.78 684.640 1277.08 547.773 1021.67 6 2739.06 5110.00 1369.58,2555.00 913.114 1703.33 684.897 1277.50 547.979 1022.0J 7 2740.06 5111.67 1370.08 2555.83 913.448 1703.89 685.148 1277.9-3 548.180 1022.33 8 2741.06 5113.33 1370.58 2556.67 913.782 1704.44 685.399 1278.33 548.380 1022.67 9 2742.10 5115.00 1371.10 2557.50 914.126 1705.00 685.657 1278.75 548.587 1023.00 10 2743.13 5116.67 1371.61 2558.33 914.470 1705.56 685.915 1279.17 548.793 1023.33 11 2744.16 5118.33 1372.13 2559.17 914.814 1706.11 686.173 1279.58 518.999 1023.67 13 2745.19 5120.00 1372.65 2560.00 915.158 1706.67 686.430 1280.00 549.2061024.00 13 2746.22 5121.67 1373.16 2560.83 915.501 1707.22 686.688 1280.42 549.412 1024.33 14 2747.25 5123.33 1373.68 2561.67 915.845 1707.78 686.946 1280.83 549.018 1024.67 15 2748.28 5125.00 1374.19 2562.50 916.189 1708.33 687.204 1281.25 549.825 1025.00 16 2749.32 5126.67 1374.71 2563.33 916.533 1708.89 687.462 1281.67 550.031 1025.33 17 2750.32 5128.33 1375.21 2564.17 916 867 1709.44 687.713 1282.08 550.232 1025.67 18 2751.32 5130.00 1375.71 2565.00 917.201 1710.00 687.963 1282.50 550.432 1026.00 19 2752.35 5131.67 1376.23 2565.83 917.545 1710.56 688.221 1282.92 550.639 1026.33 20 2753.38 5133.33 1376.74 2566.67 917.889 1711.11 688.479 1283.33 550.845 1026.67 21 2754.41 5135.00 1377.26 2567.50 918.233 1711.67 688.737 1283.75 551.051 10-37.00 *8 2755.45 5136.67 1377.77 25158.33 91 S. 577 1712.22 688 99:> 1284.17 551.258 1027.33 33 2756-. 48 5138.33 1378.29 2569.17 918 920 1712.78 689.253 1284.58 551.4641027.67 34 2757.51 5140.00 1378.80 2570.00 919.264 1713.33 t>89.51' 1285.00 551.6701028.00 35 2758.54 5141.67 1379.32 2570.83 919.608 1713.89 689.769 1285.42 55 1.877 [10-38. 33 36 2759.57 5143.33 1379.84 2571.67 919.952 1714.44 690.026 1285.83 552.0831028.67 37 2760.57 5145.00 1380.34 2572.50 920.286 1715.00 690.277 1286.25 552.283:1029.00 38 2761.58 5146.67 138 J. 84 2573.33 920.620 1715.56 690.528 1286.67 552.484! 1029. 33 39 2762.61 5148.33 1381.35 2574.17 920.964 1716.11 690.786 1287.08 552.690 1029.67 30 2763.64 5150.00 1381.87 2575.00 9-21.308 1716.67 691.044 1287.50 552.897 1030.00 31 2764.67 5151.67 138-3.39 2575.83 931.652 1717.22 691.302 1287.92 553.103 1030.33 33 2765.70 5153.33 1382.90 2576.67 921.996 1717.78 691.559 1288.33 553.309 1030.67 33 2766.73 5155.00 1383 42 2577.50 93-3. 339 1718.33 691.817 1288.75 553.516 1031.00 34 2767.76 5156.67 1383.93 2578.33 922.683 1718.89 (592.075 1289.17 553.722 1031.33 35 2768.80 5158.33 1384.45 2579.17 923.027 1719.44 692.333 1289.58 553.928 1031.67 36 2769 83 5160.00 1384.96 2580.00 923.371 1720.00 692.591 1290.00 554.135 1032.00 37 2770.86 5161.67 1385.48 2580.83 933.715 1720.56 692.849 1290.42 554.341 1032.33 38 2771.89 5163.33 1386.00 2581.67 924.059 1721.11 693.107 1290.83 554.547 1032.67 39 2772.92 511J5.00 1385.51 2582.50 924.402 1721.67 693.365 1291.25 554.754 1033.00 40 2773.95 5166.67 1387.03 2583.33 924.746 1722.22 693.623 1291.67 554.960 1033.33 41 2774.98 5168.33 1387.54 2584.17 925.090 1722.78 693.880 1292.08 555.166 1033.67 43 2776.02 5170.00 1388.06 2585.00 935.434 1723.33 694.138 1292.50 555.373 1034.00 43 27J7.05 5171.67 1388.57 2585.83 925.778 1723.89 694.396 1292.92 555.579 1034.33 44 2778.08 5173.33 1389.09 2586.67 926.121 1724.44 694.654 1293.33 555.785 1034.67 45 2779.08 5175.00 1389.59 2587.50 926.456 1725.00 694.905 1293.75 555.986 1035 00 46 2780.08 5176.67 1390.09 2588.33 926.790 1725.56 695.156 1294.17 556.187 1035.33 47 2781.11 5178.33 1390 61 2589.17 927.134 1726.11 695.413 1294.58 556.393 1035.67 48 2782.15 5180.00 1391.12 2590.00 927.478 1726.67 695.671 1295.00 556.599 1036.00 49 2783.18 5181.67 1391.64 2590.83 927.821 1727.22 695.929 1295.42 556.806 1036.33 50 2784.21 5183.33 1392.16 2591.67 928.165 1727.78 696.187 1295.83 557.012 10-36.67 51 2785.24 5185.00 1392.67 2592.50 928.509 1728.33 696.445 1296.25 557.218 1037.00 53 278(5.27 5186.67 1393.19 2593.33 928.853 1728.89 696.703 1296.67 557.425 1037.33 53 2787.30 5188.33 1393.702594.17 929.197 1729.44 696.961 1297. 08 1 557. 631 1037.67 54 55 2788.33 2789. 37 5190.00 5191.67 1394.222595.00 1394. 73 12595. 83 929 . 540 929.881 1730.01* 1730.56 697.219 697.476 1297.50 1297.92 557.837 558.043 1038.00 1038.33 56 57 2790.40 2791.43 5193.33 5195.00 1395. 25 j 2596. 67 1395.772597.50 930.228 930.57-3 1731.11 1731.67 697 734 697.992 1298.33558.250 1298.75558.456 1038.67 1039.00 58 2792.46 5196.67 1396.282598.33 930.916 1732.22 698.2501299.17558.662 1039.33 59 2793.49 5198.33 1396.8012599.17 931.260 173-3.78 698. . r ;08l 1299. 58:558. 8(39 1039.67 148 TABLE XIV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 Curve. 1O Curve. 51 Tan. Arc. Tan. Arc. Tail. Arc. Tan. Arc. Tan. Arc. M. 455.69:; tso.coo 390.656 728.571 341.890 637.500 303.965 566.6671273.639 510.000 O 455. 860 850.278 390.799 728.810 342.015 637.708 304.077566.852 273.739 510.167 1 456.02? 850.556 390.913 729.048 342.141 637.917 304.188 567.037 273.839 510.333 2 456.199 850.833 391.090 729.286 342.270 638.125 304.303 567.222 273.943 510.500 3 456.371 8r>i.ni 391.238 729.524 3 1 2. 399 G38.333 304.417 567.407 274.046 .110.667 4 456.543 851.389 391.385 729.762 342.528 638.542 304.532 567.593 274.149 510.833 5 456.715 851.667 391.532 730.000 342.657 638.750 304.647 567.778 274.252 511.000 6 456.882 851.944 391.676 730.238 S42.782 638.958 304.758 567.963 274.353 511.167 7 457. 049 852.222 391.819 730.476 342.908 639.167 304.870 568.148 274.453 511.333 8 457.221 S52.500 391.967 730 714 343.037 639.375 304.985 568.333 274.557 511.500 9 457.393 852.77'S 392.114 730.952 343.166 639.583 305.099 568.519 274.660 511 667 1O 457.565 853.056 '392.261 731 . 190 343 295 639.792 305.214 568.704 274.763 511.833 11 457.737 853.333 392.409 731.429 343.424 640 000 305.329 56*. 889 274.866 512.000 12 457.909 853.611 392.556 731.667 343.553 640.208 305.443 569.074 274.970 512.167 13 458.081 853.889 392.704 731.905 343.682 640.417 305.558 569.259 275.073 512.333 14 458.253 854.167 392 851 732.143 343.811 640.625 305.673 569.444 275.176 512.500 15 458.425 854.444 392.999 732.381 343.940 640.833 305.788 569.630 275.279 512.667 16 458.592 854.722 393.142 732.619 314.065 641.042 305.899 569.815 275.380|512.833 17 458.759 855.000 393.285 732.857 344.191 641.250 306.011 570.000 275.480513.000 18 458.931 855.278 393.433 733.095 344.320 641.458 306.125 570.185 275.583 513.167 19 459.103 855.556 393.580 73-3.333 344.449 641.667 306.240 570.370 275.687 513.333 20 459.275 855.833 393.727 733.571 344.578 641.875 306.355 570.556 275.790513.500 21 459.447 856.111 393.875 733.810 344.707 642. 083 306.469 570.741 275.893 513.667 22 459.619 56.389 394. (22 734.048 344.836 642.292 306.584 570.926 275.996 513.833 23 459.791 856.667 394.170 734.286 344.965 642. 5ul 306.699 571.111 276. 100 514.00C 24 459.963 856.944 394.317 734.524 345.094 642.708 306.814 571.296 276.203 514.167 25 460.135 857.222 394.465 734. 76L 345.223 642.917 306.928 571.481 276.3d6 514.333 26 460.302 857.500 394.608 735.000 345.348 643.125 307.040 571.667 276.407 514.500 21 460.469 857.778 394.751 735. 23b 345.474 643.333 307.151 571.852 276.507 514.667 28 460. 641 858.056 394.899 735.476 345.603 643.542 307.266 572.037 276.610 514.833 29 460.813 858.333 395.046 735.714 345.732 643.750 307.381 572.222 276.714 515.000 3O 460.985 858.611 395.193 735.952 345.861 643.958 307.495 572.407 276.817 515.167 31 461.157 858.889 395.341 736.190 345.990 644.167 307.610 572.593 276.920 515.333 32 461.329 859.167 395.488 736.429 346.119 644. 37f 307.725 572.778277.023 515.500 33 461.501 859.444 395.636 736.6(57 346.248 644. 583 307.840 572.963 277.127 515.667 34 461.673 859.722 395.783 736.905 346.377 644.792 307.954 573.148 277.230 515.833 35 461.845 860.000 395.931 737.143 346.506 645.000 308.069 573.333 277.333 516.000 36 462.017 860.278 396.078 737.381 346.635 645.208 308.184 573.519 277.436 516.167 37 462.189 860.556 396.225 737.619 340.764 645.417 308.298 573.704 277.540 516,333 38 462.361 860.833 396.373 737.857 346.893 645.625 308.413 573.889 277.643 516.500 39 462.533 861.111 396.520 738.09? 347.022 645.833 308 528 574.074 277.746 516.667 40 462.705 861.389 396.668 738.333 347.151 646.042 308.643 574.259 277.849 516.833 41 462.877 861.667 396.815 738.571 347.280 646.250 308.757 574.444 277.953 517.000 42 463.049 861.944 396.963 738.810 347.409 646.458 308.872 574.630 278.056 517.167 43 463.221 862.222 397.110 739.048 347.538 646.667 308.987 574.815 278.159 517.333 44 463.388 862.500 397.253 739.286 347.663 646.875 309.098 575.000 278.260 517.5CK 45 463.555 862.778 397.397 7'39.524 347.789 647.083 309.210 575. 185 278.360 517.667 46 463.727 863.056 397.544 739.762 347.918 647.292 309.324 575.370 278.463 517.833 47 463.899 863.333 397.691 740. (XX 348.047 647.500 309.439 575.556 278.567 518.000 48 464.071 863.61J 397.839 740.238 348.170 647.708 309.554 575.741 278.670 518.167 49 464.243 863.889 397.986 740.476 348.305 647.917 309.669 575.926 278.773 518.333 50 464.415 864.16; 398.134 740.714 348.434 648.125 309.783 576.111i278. 876 518.500 51 464.587 864.444 398 281 740.952 348.563 648.333 309.898 576. 296 '278. 980 518.667 52 464.759 864.722 398.429 741.190 348.692 648.542 310.013 576. 481 i279.083 518.833 53 464 931 865. 00! i 398.576 741.429 348.821 648.750 310.127 576.667279.186 519,000 54 465.103 865.278 398.723 741.667 348.950 648.958 310.242 576.852279.289 519.167 55 465.275 865.556 398.871 741.905 349.079 649.167 310.357 577.037279.393 519.333 56 465.447 865.833 399.018 742.143 349.208 649.375 310.472 577.222279.490 519.500 57 465.619 866.111 399.166 742.381 349.837 649.583 310.586 577.407279.599 519.667 58 465. 791 1866.389 399.313 742.619 349.466 649.792 310.701 577.593279.703 519.833 59 149 TABLE XIV. ACTUAL TANGENTS, ETC. 53 1 Curve. 3 Curve. 3 Curve. 4 Curve. 5 Curve. M. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. ~~O~ ,2794. 52 5200.00 1397.31 .'000.00,931.603 1733.33 698.706 1300.00 5.59.075 1040.00 1 2795.55 5-201.67 1397.83 2600.83 931.947 1733.89 699.024 1300.4-2 559.281 1040.33 2 2796.58 5203.33 1398.34 '601.67 932.291 1734.44 699.282 1300.83 559 488 1040.67 3 2797.62 5205.00 1398.86 2602.50 932.635 1785.00699.540 1301.25 559.694 1041.00 4 2798.65 5206.67 1399.158 2603.33 932.971) 1735.56699.797 1301.67 559.900 1041.33 5 2799.68 5208.33 1399.89 26i)4.17 933.322 1736.lli700.055 1302.08 560.107 1041.67 6 2800.71 5210.00 1400.41 2605.00 933.666 1736. 67(700. 31 3 1302.50 560.313 1042.00 7 2801.74 5211.67 1400.92 2605.83 934.010 1737. 22 ! 700. 571 1302.92 500.519 1042.33 8 2802.77 5213.33 1401.44 2606.67 9-34.354 1737.78 700 829 1303. 33 560.726 1042.67 9 2803.80 5215.00 1401.95 2607.50 934.698 1738.33 701.087 1303.75 560.932 1043.00 1O 2804.84 5216.67 1402.47 2608.33 9a5.041 1738.89 701.345 1304.17 561.138 1043.33 11 2805.87 5218.33 1402.98 2609.17 935.385 1739.44 701.603 1304.58 561.345 1043.67 13 2806.90 5220.00 1403.50 2610.00 935.729 1740.00 701.861 1305.00 561.551 1044.00 13 2807.96 5221.67 1404.03 2610.83 936.082 1740.56 702.126 1305.42 561.763 1044. as 14 2809.02 5223.33 1404.56 2611.67 936.436 1741.11 702.391 1305.83 501.1)75 1044.67 15 2810.05 5225.00 1405.08 2612.50 936.780 1741.67 702.648 1306.25 502.182 1045.00 16 2811.08 5226.67 1405.59 2613.33 937.123 1742.22 702.906 1306.67 562.388 1045.33 17 2812.11 5228.33 1406.11 2614.17 937.467 1742.78 703.164 1307.08 562.594 1045.07 18 2813.14 5230.00 140(5.62 2615.00 937.811 1743.33 703.422 1307.50 562. 81 1 1046.00 19 2814.1? 5231.67 1407.14 2615.83 938.155 1743.89 703.680 1307.92 563.007 1046.33 20 2815.21 5233.33 1407.65 2616.67 938.499 1744.44 703.9.38 1308. as 563.213 1046.67 21 2816.24 5235.00 1408.17 2617.50 938.843 1745.00 704.196 1308.75 563.420 1047.00 22 2817.2? 5236.67 1408.69 2618.33 9-59.186 1745.56 704.454 1301). 17 563.620 1047.33 23 2818.30 5238.33 1409.20 2619.17 939.530 1746.11 704.712 1309.58 503.832 1047.67 34 2819.33 5240.00 1409.72 2620.00 939.874 1746.67 704.969 1310.00 564.039 1048.00 35 2820.36 5241.67 1410.23 2620.83 940.218 1747.22 705.227 1310.42 564.245 1048.33 36 28-21.39 5243.33 1410.75 2621.67 940.562 1747.78 705.485 1310.83 564 451 1048.67 37 2822.43 5245.00 1411.26 262-2.50 910.905 1748.33 705.743 1311.25 564.658 1049.00 28 2823.46 5246.67 1411.78 2623.3'} 941.249 1718.89 700.001 1311.67 564.864 10-19. 33 39 2824.52 5248.33 141.2.31 2024. i; U41.603 1749.44 70t5.260 1312.08 50.5. 071 1049.67 30 2825.58 5250.00 1412.84 2625.00 941.056 1750.00 706.531 1312.50 565.288 1050.00 31 2826.61 5251 . 67 1413 36 2625.83 942.300 1750.50 700.789 1312.92 50.5.494 1050.33 33 2827.64 5253.33 1413.87 2626.67 942.644 1751.11 707.047 1313.33 56c.701 1050.67 33 2828.67 5255.00 1414.39 2627.50 942.987 1751.67 707.305 1313.75 565.907 1051.00 34 2829.70 5256.67 1414.90 2628.33 943.331 1752.22 707. 563 1314.17 566.113 1051.33 35 2830.73 5258.33 1415.42 403.748 749.762 353.347 656.042314.152 583.148 282.809 524.833 29 471.141 875.000 403.900 750.000 353.480 056.250 314.270 583.333 282.915 525.000 3O 471.313 875.278 404.047 750.238 353.609 H56.458 314.384 583.519 283.018 525.167 31 471.485 875.550 404.195 750.476 353.738 656.667314.499 583.704 ^3.U'2 525.333 32 471.657 875.833 404.342 750.714 353.867 666.875814.614 583.889 283.225 525. 5CO 33 471.829 876.111 404.489 750.952 353.996 657. 083! 31 4. 728 584.074 283.328 525.667 34 472.000 876.389 404 637 751.190 354.125 657.2921314.843 584.259 283.431 525.833 35 472.172 876.667 404.784 751.429 354.254 657.500314.958 584.444 283.535 526.000 36 472.344 876.944 404 932 751.667 854.888 657.708 315.073 584.630 283.638 526.167 37 472.516 877.222 405.079 751.905 354.512 657.917 315.187 584. 815 283.741 526.333 38 472.688 877.500 405.226 752.143 354.641 658.125 315.302 585.000 283.845 526.500 39 472.860 877.778 405.374 752.381 354.770 658.333315.417 585.185 283.948 526.667 40 473.037 878.056 405.525 752.619 354.903 658. 5421815. 535 585.370 284.054 526.833 41 473 214 878.333 405.677 752.857 355.035 658.750315.653 585.556 284.160 527.000 42 473.386 878.611 405.824 753.095 355.164 658.958 315.767 585.741 284.263 527.167 43 473.558 87'8.8S9 405.972 753.333 355.293 659.167 315.882 585.926 284 367 527.333 44 473.730 879.167 406.119 753.571 355.422 659.375 315.997 586.111 284.470 527.500 45 473.902 879.444 406.267 753.810 955.652 659.583 316.111 586.296 284.573 527.667 46 474.074 879.722 406 414 754.048 355.681 659.792 316.226 586.481 284.676 527.833 47 474.246 880. OTO 406.561 754.286 355.810 660.000 316.341 586.667 284.780 528.000 48 474.422 880.278 406.713 754.524 355.942 660.208 316.459 586.852 284.886 528.167 49 474 599 880. r 56 406.865 754.762 356.075 660.417 316.577 587.037 284.992 528.333 50 474.771 880.833 407.012 755.000 356.204 6(50.625 316.691 587.222 285.095 528.500 51 474.943 881.111 407.159 755.238 356.383 660.833 316.806 587.407 285.198 528.667 52 475.115 881.389 407.307 755.476 3515.462 661.042 316.921 587.593285.302 528.833 53 475.287 881.667 407.454 755.714 356.591 661.250 317.035 587.778*85.405 52!). 000 54 475.464 8S 1.1)44 407.606 755.902856 723 (561.458 317.153 587. 9b3 285. 5 11 5-/9.167 55 475. 640 1 882. 222 407.757 756.190356.856 661.667 317.271 588.148285.617 529.333 56 475.812882.500 407.905 756.429 356.985 661.875 317.386 588.333285.721 529 . f>00 57 475.984 8H2.778 408.052 756.667 357.114 662.083 317.501 588.519285.824 529.6(57 58 476.156883.056 408.200 756.905 357.243 662.292317.615 588.704 285.927 529.833 59 151 TABLE XIV. ACTUAL TANGENTS, ETC. 53 1 Curve. 2 Curve. 3 Curve. 4 Curve. 5 Curve. M. Tan. Arc. 5300.00 Tan. Arc. Tau. 952.328 Arc. Tan. Arc. Tan. Arc. 2856.69 1428.40 2650.00 176H.07 714.311 1325.00 571.512 1000.00 1 2857.72 5301.07 1428.91 2050.83 1)52.672 1707.22 714.568 1325.42 571.719 1000.33 3 2858.75 5303.33 1429.43 2051.07 953.015 1707.78 714.820 1325.83 571.925 1060.67 3 | 2859.81 5305.00 1429.96 2652.50 953.309 1768.33 715.091 1326.25 572.137 1001.00 4 2800.87 5308.67 1430.49 2653.33 953.722 1708.89 715.350 1326.67 572.349 1001.33 5 2801.90 5308. 33 1431.00 2054.17 954.006 1709.44 715.014 1327.08 572.555 1061.07 G 2802.93 5310.00 1431.52 2655.00 9.54.410 1770.00 715.872 1327.50 572.702 1062.00 7 2803.99 5311.67 1432.05 2655.83 954.703 1770.56 710.137 1327.92 572.974 1002.33 8 2805.05 5313.33 1432.58 2056.07 955.110 1771.11 710.402 1328.33 573.180 1002.07 9 2800.09 5315.00 1433.10 2657.50 955.400 1771.67 710.660 1328.75 573.392 1003.00 1O 2867.12 5316.67 14-33.61 2658.33 955.804 1772.22 716.918 1329.17 573.599 1003.33 11 2868.15 5318.33 1434.13 2659.17 956.148 1772.78 717.176 1329.58 573.805 1003.07 12 2809.18 5320.00 1434.64 2660.00 956.492 1773.33 717.434 1330700 574.011 1004.00 13 2870.24 5321.07 1435.17 2600.83 956.845 1773.89 717.699 1330.42 574.2231004.33 14 2871.30 5323.33 1435.70 2661.67 957.198 1774.44 717.964 1330.83 574.435 1004.67 15 2872.33 5325.00 1436.22 2662.50 957.542 1775.00 718.222 1331.25 574.6421065.00 16 2873.30 5320.07 1436.73 2663.33 957.886 1775.56 718.480 1331.67 574.848 1065.33 17 2874.39 5328.33 1437.25 2604.17 958.230 1776.11 718.738 1332.08 575.0541065.67 18 2875.42 5330.00 1437.77 2665.00 958.574 1776.67 718.995 1332.50 575.201 1006.00 19 2876.48 5331.67 1438.30 2665.83 958.927 1777.22 719.261 1332.92 575.473 1066.33 20 2877.54 5333.33 1438.83 2666.67 959.280 1777.78 719.526 1333.33 575.085 1066.67 21 2878.58 5335.00 1439 34 2667.50 959.024 1778.33 719.783 1 333.75 575.891 1007.00 22 2879.61 5336.67 1439.86 2668.33 959.908 1778.89 720.041 1334.17 .170.097(1007.33 23 2880.07 5338.33 1440.39 2669.17 900.321 1779.44 72^.306 1334.58 576.309 1067.67 21 2881.73 5340.00 1440.92 2670.00 900.675 1780.00 720.571 1335.00 576.522 1068.00 25 2882.70 5341.67 1441.43 2670.83 961.019 1780.56 720.829 1335.42 576.7281068.33 2G 2883.79 5343.33 1441.95 2671.67 1)61.888 1781.11 721.087 1335.83 576.934 1068.67 21 2884.85 5345.00 1442.48 2072.50 961.710 1781.67 721.352 1336.25 577.140 1069.00 2$ 2885.91 5346.67 1443.01 2673.33 903.069 1782.22 721.017 1336 07 577.358 1009.33 29 288(5.94 5348.33 1443.52 2674.17 962.413 1782.78 721.875 1337.08 577.565 1069.67 30 2887.97 5350.00 1444.04 2675.00 962.757 1783.33 722.133 1337.50 577.771 1070.00 31 2889.03 5351.67 1444.57 2075.83 903.110 1783.89 722.398 1337.92 577.983 1070.33 32 2890.09 5353.33 1445.10 2076.67 963.463 1784.44 722.063 1338.33 578.195 1070.07 33 2891.12 5355.00 1445.62 2677.50 963.807 1785.00 722.921 1338.75 578.401 1071.00 34 2892.10 5356.67 1446.13 2078.33 964.151 1785.56 723.179 1339.17 578.608 1071.33 35 2893.22 5358.33 1446.66 2679.17 964.504 1786.11 723.444 1339.58 578.814 1071.67 36 2894. 2S 5360.00 1447.19 2680.00 964.858 1786.07 723.709 1340.00 579.020 1072.00 37 2895.31 5361.67 1447.71 2080.83 965.202 1787.22 723.967 1340.42 579.23211072.33 38 2896.34 5363.33 1448.22 2681.67 965.545 '787.78 724.225 1340.83 579.415 1072.67 39 2897.40 5365.00 1448.75 2682.50 905.899 788.33 724.490 1341.25 579.657 1073.00 40 2898.46 5366.67 1449.28 2683.33 963.252 788.89 724.755 1341.67 579.809 1073.33 41 2899.49 5368.33 1449.80 2084.17 906.596 789.44 725.013 1342.08 580.075 1073.07 42 29:>0.52 5370.00 1450.31 2085.00 960.940 790.00 725.271 1342.50 580.281 1074.00 43 2901.58 5371.67 1450.84 2085.83 9(57.293 1790.56 725.530 1342.92 580.493 1074.33 44 2902.64 5373.33 1451.37 2086.67 967.617 1791.11 725.801 1313 33 580. 705 '1074. 07 45 2903.07 5375.00 1451.89 2687.50 967.990 1791.67 726.059 1343 75 580.9121075.00 46 2904.70 5376.67 1452.40 2688.33 968.334 1792.22 726.317 1344.17 581. 11 8! 1075. 33 47 [2905.76 5378.33 1452.93 2689.17 968.088 1792.78 726.582 1344.58 581. 330; 1075. 07 48 '2006.82 5380.00 1453.46 2690.00 969.041 1793.33 726.847 1345.00 581.542 1076.00 49 2907.85 5381.67 1453.98 2690.83 969.385 1793.89 727.105 1345.42 581.749 1076.33 50 2908.89 5383.33 1454.50 2691.67 969.729 1794.44 727.362 1345.83 581.955 1076.67 51 2909.95 5385.00 1455.03 2692.50 970.082 1795.00 727.627 1316.25 58 J.I 07; 1077. 00 52 2911.01 5386.67 1455.56 2693.33 970.435 1795.56 727.892 1346.07 582.379 1077.33 53 2912.07 5388.33 1456.09 2694.17 970.789 1790.11 728. 15S 1347.08 582.591 1077.07 54 2913.13 5390.00 1456.62 2695.00 971.1421796.07 728 423 1317 50 582. S03 1078.00 55 2914.16 5391.67 1457.13 2095.83 971.486 1797.22 728.080 1347.92 583.009 1078.33 56 2915.19 5393.33 1457.65 2096.67 971.8301797.78 728.938 13l8.: J ,3i583.216 1078.07 57 2916.25 5395.00 1458.18 2097.50 972.183 1798.33 729 . 203 1 3 48 . 75 53 . 428 1 079 . 00 58 2917.31 5396.67 1458.71 2698.33 972.530 1798.89 729 . 408 1 3 10.1 7 583 .(3401 01 9 . 33 59 2918.37 5398.33 1459.24 2099 17 972.890 1799.44 729.733 1319.58!583.852 1079.07 152 TABLE XIV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 Curve. 10 Curve. 53- Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. M. 476.328 8837333 408.347 757.143 357.372 662.500 317.730588.889 286.030 530.000 O 476.500 883.611 408.494 757.381 357.501 662.7081317.845589.074 286.134 530.167 1 476.672 883.889 408.642 757.619 357.630 662.917 317.959589.259 286.247 530.333 2 476.849 884.167 408.793 757.857 357.763 663.125 318.077 589.444 286.343 530.500 3 477.026 884.444 408.945 758.095 357.895 663.333 318.195 589.630 286.449 530.667 4 477.198 884.722 409.092 758.333 358.024 663.542 318.310 589.815 286.552 530.833 5 477.370 885.000 409.240 758.571 358.153 663.750 318.425 590.000 286.656 531.000 6 477.546 885.278 409.391 758.810 358.286 063.958 318.543 590.185 286.762 531.167 7 477.723 885.556 409.543 759.048 358.419 664.167 318.660 590.370 286.868 531.333 3 477.895 885.833 409.690 759.286 358.548 664.375 318.775 590.556 286.971 531.500 9 478.067 886.111 409.838 759.524 358.677 664.583 318.890 590.741 287.074 531.667 10 478.239 886.389 409.985 759.762 358.806664.792 319.005 590.926 287.178 531.833 11 478.411 886.667 410.132 760.000 358.935665.000 319.119 591.111 287.281 532.000 12 478.588 886.944 410.284 760.238 359.0671665.208 319.237 591.296 287.387 532.167 13 478.765 887.222 410.435 760.476 359. 200 1665.417 319.355 591.481 287.493 532.333 14 478.936 887.500 410.583 760.714 359.329:665.625 319.470 591.667 287.596 532. f,00 15 479.1 Ob 887.778 410.730 760.952 359. 458 1665.833 319.584 591.852 287.700 532.667 16 479.280 888.056 410.878 761.190 359.587 666.042 319.699 592.037 287.803 532.833 17 479.452 888.333 411.025 761.429 359.716 666.250 319.814 592.222 287.906 533. OOC 18 479.629 888.611 411.177 761.667 359.849 666.458 319.932 592.407 288.012 533.167 19 479.806 888.889 411.328 761.905 359.981 666.667 320.050 592.593 288.119 533.333 20 479.978 889.167 411.476 762.143 360.110 666.875 320.164 592.778 288.222 533.500 21 480.150 889.444 411.623 762.381 360.239 667.083 320.279 592.963 288.325 533.667 22 480.327 889.722 411.775 762.619 360.372 667.292 320.397 593.148 288.431 533.833 23 480.503 890. ('00 411.926 762.857 360.504 667.500 320.515 593.333 288.537 534.001 24 480.675 890.278 412.073 763.095 360.633 667.708 320.630 593 519 288.641 534.167 25 480.847 890.556 412.221 763.333 360.762 667.917 320.744 593.704 288.744 534.333 26 481.024 890.833 412.372 763.571 360.895 668.125 320.862 593.889 288.850 534. 50( 27 481.201 891.111 412.524 763.810 361.028 668.333 320.980 594.074 288.956 534.667 28 481.373 891.389 412.671 764.048 361.157 668.542 321.095 594.259 289.059 534.833 29 481.545 891.667 412.819 764.286 361.286 668.750 321.210 594.444 289.163 535. 00( 30 481.721 891.944 412.970 764.524 361.418 668.958 321.327 594.630 289.269 535.167 31 481.898 892.222 413.122 764.762 361.551 669.167 321.445 594.815 289.375 535.333 32 482.070 892.500 413.269 765. 0()( 361.680 669.375 321.560 595.000 289.478 535.500 33 482.242 892.778 413.417 765.238 361.809 669.583 321.675 595.185 289.581 535.667 34 482.419 893.056 413.568 765.476 361.942 669.792 321.793 595.370 289.688 535.833 35 482.596 893.333 413.720 765.714 362.074 670.000 321.911 595.556 289.794 536.000 36 482.768 893.611 413.867 765.952 362.203 670.208 322.025 595.741 289.897 536.167 37 482.939 893.889 414.015 766.190 362.332 670.417 322.140 595.926 290.000 536.333 38 483.116 894.167 414.166 766.429 362.465 670.625 322.258 596.111 290.106 536.500 39 483.293 894.444 414.318 766.667 362.597 670.833 322.376 596.296 290.213 536.667 40 4&3.46S 894.722 414.465 766.905 362.726 671.042 322.490 596.481 290.316 536.833 41 483.637 895.000 414.612 767.143 362.855 671.250 322.605 596.667 290.419 537.000 42 483.814 895.278 414.764 767.381 362.988 671.458 322.723 596.852 290.525 537.167 43 483.990 895.556 414.915 767.619 363.121 671.667 322.841 597.037 290.631 537.333 44 484 162 895.833 415.063 767.857 363.250 671.875 322.956 597.222 290.735 537.500 45 484.334 896.111 415.210 768.095 363.379 672.083 323.070 597.407 290.838 537.667 46 484.511 896.389 415.362 768.333 363.511 672.292 323.188 597.593 290.944 537.833 47 484.688 896.667415.513 768.571 363.644 672.500 323.306 597.778 291.050 538.000 48 484.860 896.944 415.661 768.810 363.773 672.708 323.421 597.963 291.153 538.167 49 485.032 897.222 415.808 769.048 363.902 672.91? 323.536 598.148 291.257 538.333 50 485.208 897.500 415.960 769.286 364.035 673.125 323.653 598.333 291.363 538.500 51 485.385 897.778 416.111 769.524 364.167 673.333 323.771 598.519 291.469 538.667 52 485.562 898.056 416.263 769.762 364.300 673.542 323.889 598.704 291.575 538.833 53 485.739 898.333 416.414 770.000 364.432 673.750 324.007 598.889 291.681 539.000 54 485.911 486.083 898.611 898.889 416.562 416.709 770.238 770.476 364.561 673.958 364.690674.167 324.122 324.237 599.074 599.259 291.784 291.888 539.167 539.333 55 56 486.2591899.167 416.861 770.714 364.823 674.375 324.354 599.444 291.994 539.500 57 486.436899.444 417.012 770.952 364.956674.583 324.472 599.630 292.100 539.667 58 486.613i899.722417.164 771 . 190 365.088674.792 324.590 599.815 292.206 539.833 59 153 TABLE XIV. ACTUAL TANGENTS, ETC. 54 1 Curve. 3 Curve. 3 Curve. 4 Curve. 5 Curve. M[7 ~o~ Tan. 2919743 Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. 584.004 Arc. 5400.00 1459.77 2 -00.00 973.243 1SOO.OO 729.999 1350.00 1080.00 1 2920.46 5401.6? 14 i ;0.2,s 2? 00. &i 913.587 IKK). 50 730.250 1350.42 584.270 1080.33 3 2921.49 5403 33 1400.80 2?01.6: 9 Hi. 931 1801.11 730.514 1350.83 584.477 1080.07 3 2922.55 5405 . 00 1461.33 2702.50 J74.384 1801.67. 730.779 1351.25 584.089 1081.00 4 2923.61 5406.6? 1461.86 2703.33 J74.G37 1802.22 731.044 1351.67 584.901 1081.33 5 2924.67 5408.33 1462 39 2704.1? 974.991 1802.78 731.309 1352.08 585.113 1(81.67 6 2925.73 5410.00 1462.92 2705.0.1 975.344 1803.33 731.574 1352.50 585.325 1082.00 7 2926.76 5411.6? 1463.43 2705.83 975.688 1803.89 731.832 1352.92 585.531 1083.33 8 2927.79 5413.33 1463.95 2706.67 976.032 1804.44 732.090 1353.33 585.738 1082 67 9 2928.85 5415.00 1464.48 2707.50 976.385 1805.00 732.355 1353.75 585.950 1083.00 1O 2929.91 5416.67 1465.01 2708.33 i)76.739 1805.56 732.620 1354.17 586.162 1083.33 11 2930.97 5418.33 1465.54 2709.1? 977.092 1806.11 732.885 1354.58 586.374 1083.67 12 2932.03 5420.00 1466.07 2710.00 977.445 1806.67 733.150 1355.00 586.580:1084.00 13 2933.07 5421.6? 1466.5'J 2710.83 977.789 1807.22 733.408 1355.42 580.792 1084.33 14 2934.10 5423.33 1467 10 2711.6? 978.133 1807.78 733.666 1355.83 580.999 1084.67 15 2935.16 5425.00 1467.63 2712.50 978.486 1808.33 733.931 1356.25 587.211 1085.00 16 2936.22 5426.67 1468.16 2713.83 978.840 1808.89 734.190 1356.6? 587.4231085.33 17 2937.28 5428 33 1468.69 2714.17 979.193 1809.44 734.461 1357.08 587.635 1085.67 18 2938 34 3 430. 00 1469.22 2715.00 979.546 1810.00 734.726 1357.50 587.847 1086.00 19 2939.37 5431.6? 1469.74 2715.83 979.890 1810.56 734.984 1357.92 588.053 1086.33 30 2940.40 5433.33 1470.25 2716.67 980.234 1811.11 735.242 1358.33 588.259 1086.67 31 2941.46 5435.00 1470.78 2717.50 980.587 1811.67 735.50? 1358.75 588. 4? 1(1087.00 33 2942.52 5436.67 1471.31 2718.33 980.941 1812.22 735.772 1359.17 588.684J1087.33 33 2943.58 54138.33 1471.84 2719.1? 981.294 1812.78 736.037 1359.58 588.896 1087.67 34 2944.64 5440.00 1472.37 2720.00 981.647 1813.33 736.302 1360.00 589.108 1088.00 35 2945.70 5441.6? 1472.90 2720.83 982.001 1813.89 736.567 1360.42 589.320 1088.33 36 2946.76 5443.33 1473.43 2721.67 982.354 1814.44 736.832 1360.83 589.532 1088.67 37 2947.82 5445.00 1473.96 2722.50 982.708 1815.00 737.098 1361 25 589.744 1089.00 38 2948.88 5446.6? 1474.49 2723.33 983.061 1815.56 737.303 1301.67 589.950 1089.33 39 2949.91 5448.33 1475.01 2724.1? 983.405 1816.11 737.620 1362.08 590.162 1089.67 30 2950.94 5450.00 1475.52 2725.00 983.749 1816.67 737.878 1362.50 590.309 1090.00 31 2952.00 5451.6? 1476.05 2725.83 984.102 1817.22 738.143 1362.92 590.581 1090.33 33 2953.06 5453.33 1476.58 2726.67 984.455 1817.78 738.408 1363.33 590.793 1090.67 33 2954.12 5455.00 1477.11 2727.50 984.809 1818.33 738.673 1363.75 591.005 1091.00 34 2955.18 5456.67 1477.64 2728.33 1)85.162 1818.89 738.939 1364.17 591.217 1091.33 35 2956.24 5458.33 1478.17 2729.17 985.516 1819.44 739.204 1364.58 591.429 1091.67 36 2957.30 5460.00 1478.70 2730.00 985.869 1820.00 739 469 1365.00 591.641 1092.00 37 2958.36 5461.6? 1479.23 2730.83 986.222 1820.56 739.734 1365.42 591.853! 1092. 33 38 2959.42 5463.33 1479.76 2131.6? 986.575 1821.11 739.999 1365.83 592.065 1092.67 39 2960.48 5465.00 1480.30 2732.50 986.929 1821.67 740.264 1366.25 592.277 1093.00 40 2961.54 5466.67 1480.83 2733.33 987.282 1822.22 740.529 1366.6? 592.489 1093.33 41 2962.57 5468.33 1481.34 2734.17 987.626 1822.78 740.78? 1367.08 592.696 1093.67 43 2963.60 5470.00 1481.86 2735.00 987.970 1823.33 741.045 1367.50 592.902 1094.00 43 2964.66 5471.67 1482.39 2735.83 988.323 1823.89741.310 1367.92 593.114 1 094.3 S 44 2965.72 5473.33 1482.92 2736.67 988.677 1824.441741.575 1368.331593.320 1094.67 45 2966.78 5475.00 1483.45 2737.50 989.030 1825.00:741.840 1368. 75 1 593. 538 1095.00 46 2967.84 5476.67 1483.98 2738.33 989.383 1825.56 742.105 1369.17 593.750 1095.33 47 2968.90 5478.33 1484.51 2739.17 989.737 1826.11 742.370 1369.58 593.962 1095.07 48 2969.96 5480.00 1485 04 2740.00 990.090 1826.6? 742.635 1370. 00 594.1741 1096. 00 49 2971.02 5481.67 1485.57 2740.83 990.443 1827.22 742.900 1370.42 594.386 1096.33 5O 2972.08 5483.33 1486.10 2741.67 990.797 1827.78 743.165 1370.83 594.598 1096.67 51 2973.14 5485.00 1486.63 2742.50 991.150 1828.33743.430 1371.25:594.810 1097.00 53 2974.20 5486 67 1487.16 2743.33 991.503 1828.89743.695 1371.67595.022 1097.33 53 2975.26 5488.33 1487.69 2744.17 991.857 1829.44743.960 1372.08595.235 1097.07 54 2976.32 5490.00 1488.22 2745.00 992.210 1830.00744.225 1 372. 50 : 595. 447 1098.00 55 2977.385491.67 1488.752745.83 992.564 1830.56 744.490 1372.92 595. 659! 1098. 33 5612978.445493.33 1489. 28 [2746. 67 992.917 1 83 1 . 1 1 744 . 755 ! 1 373 . 33 595 . 871 1 098 . 67 57 3979.505495.00 1489.81 2747.50 993 . 270 1 83 1 . 67 74 1 . 020 1 1 373 . 75 596 . 083 1 099 00 58 2980.565496.67 1490.34 2748.33 993 . 624 1832 . 22 745 . 285 j 1374 . 1 ? 5. -6 . 295 1 099 . 33 5912981.625498.33 1490.8? 2749 1 7 993 . 9771 1 832 . 78 745 . 550! 1374 . 58 59(1 . 507 1 099 . 67 154 TABLE XIV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 Curve. 1O Curve. 54 Tan. Arc. Tan. 417.315 Arc. 771 .429 Tau. 365.221 Arc. Tan. Arc. Tan. Arc. 540.000 M7 ~o" 486.790 JOO.OOO 675.000 324.708 600.000 292.312 486.962 900. 27S 417.463 771.667 365.350 675.208:324.823 600.185 292.415 540.167 i 487.134 900.550 417.610 771.905 365.479 675. 41 7 j 324. 938 600.370 292.519 540.333 2 487.310 900.833 417.762 772.143 365 612 675.625325.055 600.556 292.625 540.500 3 487.487 901.111 417.913 772.381 365.744 675.833 325.173 600.741 292.731 540.667 4 487.664 901.3=9 418.065 772.619 365.877 676.042 325.291 600. 926' 292. 837 540.833 5 487.841 901.667 418.216 772.857 366.009 676.250 325.409 601.111 292.943 541.000 6 488. 012 901.944 418.364 773.095 366.138 676.458 325.524 601.296 293.047 541.167 7 488.184 902.222 418.511 773.333 366.267 676.667 325.639 601.481 293.150 541.333 8 488.361 902.500 418.662 773.571 366.400 676.875 325.756 601.667 293.256 541.500 9 488.538 902.778 418.814 773.810 366.533 677.083 325.874 601.852 293.362 541.667 1O 488.715903.056 418.966 774.048 366.665 677.292 325.992 602.037 293.468 541.833 11 488.891 903.333 419.117 774.280 366.798 677.500 326.110 602.222 293.574 542.000 12 489.063903.611 419.264 774.524 366.927 677.708 326.225 602.407 293.678 542.167 13 489.235903.889 419 412 774.762 367.056 677.917 326.340 602.593 293.781 542.333 14 489.412904.167 419.563 775.000 367.188 678.125 326.45? 602.778 293.887 542.500 15 489.589 J04.444 419.715 775.238 367.321 678.333 326.575 602.963 293.993 542.667 16 489.766 904.722 419.866 775.476 367.454 678.542 326.693 603.148 294.099 542.833 17 489.942 905.000 420.018 775.714 367.586 678.750 326.811 603.333 294.205 543.000 18 490.114 905.278 420.165 775.952 367.715 678.958 326.926 603.519 294.309 543.167 19 490.286 905.556 420.313 776.190 367.844 679.167 327.041 603.704 294.412 543.333 20 490.463 905.833 420.464 776.429 367.977 679 375 327 158 603.889 294.518 543.500 21 490.640 906.111 420.616 776.667 368.109 679.583 327.276 604.074 294.624 543.667 22 490.817 906.389 420.767 776.905 368.242 679.792 327.394 604.259 294.730 543.833 23 490.993 906.667 420.919 777.143 368.375 680.000 327.512 604.444 294.836 544.000 24 491.170 906.944 421.070 777.381 368.507 680.208 327.630 604.630 294.943 544.167 25 491.347 907.22V 421.222 777.619 368.640 680.417 327.748 604.815 295.049 544.333 26 491.523 907.500 421.373 777.857 368.773 680.625 327.866 605.000 295.155 544.500 27 491.700 907.778 421.525 778.095 368.905 (580.833 327.984 605.185 295.261 544.667 28 491.872 908.056 421.672 778.333 369.034 681.042 328.098 605.370 295.364 544.833 29 492.044 908.333 421.820 778.571 369.103 681.250 328.213 605.556 295.468 545.000 30 492.221 908.611 421.971 778.810 369.296 681. 45b 328.331 605.741 295.574 545.167 31 492.398 908.889 422.123 779.048 369.428 681.667 328.449 605.926 295.680 545.333 32 492.574 909.167 422.274 779.286 369.561 681.875 328.507 606.111 295.786 545.500 33 492.751 909.444 422.426 779.524 369.694 682 083 328.685 606.296 295.892 545.667 34 492.928 909.722 422.577 779.762 369.826 682.292 328.803 606.481 295.998 545.833 35 493.105 910.000 422.729 780.000 369.959 682.500 328.920 606.667 296.104 546.000 36 493.281 910.278 422.880 780.238 370.091 682.708 329.038 606.852 296.210 546. 16 r 37 493.458 1)10.556 423.032 780.476 370.224 682.917 329.156 607.037 296.317 546.333 38 493.635 910.833 423.183 780.714 370.357 683.125 329.274 607.222 296.423 546.500 39 493.812 911.111 423.335 780.952 370.489 683.333 329.392 607.407 296.529 546.66" 40 493.984 911.389 423.482 781.190 370.618 683.542 329.507 607.593 296.632 546.833 41 494.156 911.667 423.630 781.429 370.747 683.750 329.621 607.778 296.735 547.000 42 494.332 911.944 423.781 781.667 370 880 683.958 329.739 607.963 296.841 547. 16 r 43 494.509 912.222 423.933 781.905 371.012 684.167 329.857 608.148 296.948 547.333 44 494.686 912.500 424.084 782.143 371.145 684.375 329.975 608.333 297.054 547.500 45 494.863 912.778 424.236 782.381 371.278 684.583 330.093 608.519 297.160 547. 66 r 46 495.039 913.056 424.387 782.619 371.410 684.792 330.211 608 704 297.266 547.833 47 495.216 913.333 424.539 782.857 371.543 685.000 330.329 608.889 297.372 548.000 48 495.393 913.611 424.690 783.095 371.675 685.208 330.447 609.074 297.478 548.16^ 49 495.569 913.889 424.842 783.333 371.808 685.417 330.565 609.259 297.584 548.333 50 495.746 914.167 424.994 783.571 371.941 685.625 330.683 609.444 297.691 548.500 51 495.923 914.444 425.145 783.810 372.073 685.833330.800 609.630 297.797 548. 66' 52 496.100 496.276 914.722 915.000 425.297 425.448 784.048 784.286 372.206 372. 338 686.042330.918 686.250331.036 609.815 610.000 297.903 298.009 548.833 549.001. 53 54 496.453915.278 425.600 784.524 372.47 686.458331.154 610.185 298.115 549 167 55 496.630915.556 425.751 784.765, 372.604 686.667 331 .272 610.370 298.221 549.333 56 496.807 915.833 425.903 785.000 372.736 686.875331.390610.556 298.327 549.500 57 496.983 916.111 426.054 785 238 372.869 687 . 083 i 331 . 508 610 . 741 298.433 549.667 58 497.1601916.389 426.206 785.476 373.002 687. 292 331. 6261610. 926 298.540 549.833 59 155 TABLE XIV. ACTUAL TANGENTS, ETC. 55 1 Curve. 2 Curve. 3 Curve. 4 Curve. 5 Curve. M. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. 59t) .719 Arc. O 2982 68 5500.00 1491.40 2750.00 994.330 1 8-13.33 745.815 1375.00 1 2983 '.74 5501.67 1491.93 2750.83 994.684 1833.81) 746.080 1375.42 596.931 1100.33 2 2984.80 5503.33 1492.46 2751.67 995.037 1834.44 746.346 1375.83 597.143 1100.6? 3 2985. 8(3 5505.00 1492.99 2752.50 995.390 1835.00 746.611 1376.25 597. 355 ! 1101. 00 4 2986.92 5506.67 1493.52 2753.33 995.744 18:45.56 746.876 1376.67 597. 567) 1101. 33 5 2987.98 5508.33 1494.05 2754.17 996.097 1836.11 747.141 1377.08 597.779 1101.6? 6 2989.04 5510.00 1494.58 2755.00 996.451 1836.67 747.406 1377.50 597.991 1102.00 7 2990.10 5511.67 1495.11 2755.83 996.804 1837.22 747.671 1377.92 598.203 1102.3:] 8 2991.16 5513.33 1495.64 2756.67 997.157 1837.78 747.936 1378.33 598.415 1102.6? 9 2992.22 5515.00 1496.17 2757.50 997.511 1838.33 748.201 1378.75 598.628 1103.00 10 2993.28 5516.67 1496.70 2758.33 997.864 1838.89 748.466 1379.17 598.840 1103 33 11 2994.34 5518.33 1497.23 2759.17 998.217 1839.44 748.731 1379.58 599.052 1103.6? 12 2995.40 5520.00 1497.76 2760.00 998.571 1840.00 748.996 1380.00 599.264 1104.00 13 2996.46 5521.67 1498 29 2760.83 998.924 1840.56 749.261 1380.42 599.476 1104.33 14 2997.52 5523.33 1498.82 2761.67 999.277 1841.11 749.526 1380.83 599.688 1104.67 15 2998.58 5525.00 1499.35 2762.50 999.631 1841.67 749.791 1381.25 599.900 1105.00 16 2999.64 5526.67 1499.8^ 2763.33 999.984 1842.22 750.056 1381.67 600.112 1105.33 17 3000.70 5528. 3 3 1500.41 2764.17 1000.34 1842.78 750.321 1382.08 600.324 1105.6? 18 3001.76 5530.00 1500.94 2765.00 1000.69 1843.33 750.586 1382.50 600.536 1106.00 19 3002.82 5531.6? 1501.47 2765.83 1001.04 1843.89 750.851 1382.92 600.748 1106.33 2O 3003.88 5533.33 1502.00 2766.67 1001.40 1844.44 751.116 1383.33 600.960 1106.6? 21 3004.94 5535.00 1502.53 2767.50 1001.75 1845.00 751.381 1383.75 601.172 1107.00 22 3006.00 5536.6? 1503.06 2768.33 1002.10 1845.56 751.646 1384.17 601.384 1107.33 23 3007.06 5538.33 1503.59 2769.17 1002.46 1846.11 751.912 1384.58 601.596 1107.6? 24 3008.12 5540.00 1504.12 2770.00 1002.81 1846.67 752.177 1385.00 601.808 1108.00 25 3009.18 5541.67 1504.66 2770.83 1003.16 1847.22 752.442 1385.42 602.021 1108.33 26 3010.24 5543.33 1505.18 2771.67 1003.5-2 1847.78 7'52.707 1385.83 602.233 1108.67 27 3011.30 5545.00 1505.71 2772.50 1003.87 1848.33 752.972 1386.25 602.445 1109.00 28 3012.36 5546.67 1506.24 2773.33 1004.22 1848.89 753.237 1386.67 602.657 1109.33 29 3013.45 5548.33 1506.78 2774.17 1004.59 1849.44 753 509 1387.08 602.875 1109.67 30 3014.54 5550.00 1507.33 2775.00 1004.95 1850.00 753.781 1387.50 603.092 1110.00 31 3015.60 5551.67 1507.86 2775 . 83 1005.30 1850.56 754.046 1387.92 603.304 1110.33 32 3016.66 5553.33 1508.39 2776.67 1005.66 1851.11 754.311 1388.38 603.516 1110.67 33 3017.72 5555.00 1508.92 2777.50 1006.01 1851.67 754.576 1388.75 603.728 1111.00 34 3018.78 5556.67 1509.45 2778.33 1006.36 1852.22 754.841 1389.17 603.941 1111.33 35 3019.84 5558.33 1509.98 2779.17 1006.72 1852.78 755.106 1389.58 604.153 1111.67 36 3020.90 5560.00 1510.51 2780.00 1007.07 1853.33 755.371 139J.OO 604.365 1112.00 37 3021.96 5561.67 1511.04 2780.83 1007.42 1853.89 755.637 1390.42 604.57? 1112.33 38 3023.02 5563.33 1511.57 2781.67 1007.78 1854,44 755.902 1390.83 604.789 1112.67 39 3024.08 5565.00 1512.10 2782.50 1008.13 1855.00 756.167 1391.25 605.001 1133.00 4O 3025.14 5568.67 1512.63 2783.33 1008.48 1855.56 756.432 1391.67 605.213 1113.33 41 3026.23 5568.33 1513.17 2784.17 1008.851856.11 756.704 1392.08 605.431 1113.67 42 3027.32 5570.00 1513.71 2785.00 1009.21 1856.67 756.976 1392.50 605.649 1114.00 43 44 3028.38 30-29.44 5571.67 5573.33 1514.24 1514.77 2785.83 2786.67 1009. 56 [ 1857. 22 1009.92 1857.78 757.241 757.506 1392.92 1393.33 605.861 606.073 1114.33 1114.67 45 3030.50 5575.00 1515.30 2787.50 1010.27 1858.33 757.771 1393.75 606.285 1115.00 46 3031.56 5576 . 67 1515.83 2788.33 1010. 62! 1858. 89 758.036 1394.17 606.497 1115.33 47 3032.62 5578.33 1516.36 2789.17 1010.98 1859.44 758.301 1394.58 606.709 1115.67 48 3033.68 5580.00 1516.89 2790.00 1011.331860.00 758.566 1395.00 606.921 1116.00 49 3034.77 5581.67 1517.44 2790.83 1011.69 1860.56 758.839 1395.42 607.139 1116.33 50 3035.86 5583.33 1517.98 2791.67 1012.06 1861.11 759.111 1395.83 607.356 1116.67 51 3036.92 5585.00 1518.51 2792.50 1012.4l|l861.67 759.376 1396.25 607.569 1117.00 52 3037.98 5586.67 1519.04 2793.33 1012.761862.22 759.641 1396.67 607.781 1117.33 53 3J39.04 5588.33 1519.57 2794.17 1013.12 1862.78 759.9061397.08 607.993 1117.67 54 3040.09 5590.00 15-20.10 2795.00 1013. 47 1 1868. 33 760.171! 1397. 50 608.205 1118.00 55 3041.15 5591. 67 11520. 63 2795.83 1013.82 1863 89 760.4361397.92 608.417 1118.33 50 3042.21 5593.331521.16 2796.67 1014.181864.44 760.701 1398.33 608.629 1118.67 57 3043.30 5595.00 1521.71 2797.50 1014.54 1865.00 760.973 1398.75 608.847 1119.00 58 3044.39 5596.67 1522.25 2798.33 1014.90 1865.56 761.2461399.17 609.064 1119.33 59 (3045.45 5598.331522.78 2799.17 1015.261866.11 761.511 1399. 58 609. 276 1119.67 .156 TABLE XIV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 Curve. 10 Curve. 55 Tan. 497^337 Arc. 916.667 Tan. Arc. Tan. Arc. 687.500 Tan. Arc. Tan. Arc. 31. 426.357 785.714 373.134 331.744 611.111 298.646 550.000 497.514 916.944 426.509 785.952 313.267687.708 331.861 611.296 298.752550.16? 1 497.690 917.222 426.660 786.190 373.399 687.917 331.979 611.481 298.858 550.333 497.867 917.500 426.812 786.429 373.532 688.125 332.097 611.667 298.964 550.500 3 498.044 917.778 426.963 786.66? 373.665 688.333 332.215 611.852;299.070 550.667 4 498.221 918.056 427.115 786 905 373.797 688.542 332.333 612.037 299.176 550.833 5 498.39? 918.3:33 427.266 787.143 373.930 688.750 332.451 612.222 299.283 551.000 6 498.574 918.611 427.418 787.381 374.062688.958 332.569 612.407 299.389 551.167 7 498.751 918.889 427.569 787.619 374.195689.167 332.68? 612.593 299.495 551.333 8 498.928 919.167 427.721 787.857 374.328 689.375 332.805 612.778 299.601 551.500 9 499.104 919.444 427.872 788.095 374.460 689.583 332.923 612.963 299.707 551.667 1O 499.281 919.722 428.02! 7S8.333 374.593 689.79;: 333.040 613.148 299.813 551.833 11 499.458 920.000 428.175 788.571 374.725 690. COO 333.158 613.333 299.919 552.000 12 499.635 920.278 428.327 78S.810 374.858 690.208 333.276 613.519 300.025 552 . 1 67 13 499.811 920.556 428.478 789.048 374.991 690.417 333.394 613.701 300.132 552.333 14 499.988 920.833 428.630 789.286 375.123 690.625 333.512 613.889 300.238 552.500 15 500.165 921.111 428.781 789.524 375.25S 690 833 333.630 614.074 300.344 552.667 16 500.342 921.389 423.933 789.762 375.388 691.042 333.748 614.259 300.450 552.833 17 500.518 921.667 429.085 790. 000 375.521 691.250 333.866 614.444 300.556 553.000 18 500.695 921.944 429.236 790.238 375.654 691.458 333.984 614.630 300.662 553.167 19 500.872 922.222 429.388 790.476 375.786 691.667 334.101 614.815 300.768 553.333 20 501.049 922.500 429.539 ?'90.714 375.919 691.875 334.219 615.000 300.875 553.500 21 501.225 922.778 429.691 790.952 376.051 692.083 334.337 615.185 300.981 553.66? 22 501.402 923.056 429.842 791.190 376.184 692.292 334.455 615.370 301.087 553.833 23 501.579 923.333 429.994 791.429 376.317 692.500 334.573 615.556 301.193 554.000 24 501.755 923.611 430.145 791.667 376.449 692.708 334.691 615.741 301.299 554.167 25 501.932 923.889 430.297 791.905 376.582 692.917 334.809 615.926 301.405 554.333 26 502.109 924.167 430.448 792.143 376.714 693.125 334.927 616.111 301.511 554.500 27 502.286 924.444 430.600 792.381 376.847 693.333 335.045 616.296 301.617 554.667 28 502.46? 924.722 430.755 792.619 376.983 693.542 335.166 616.481 301.726 554.833 29 502.649 9*5.000 430.911 792.857 377.119 693.750 335.287 616.667 301.835 555.000 30 502.826 925.278 431.062 793.095 377.252 693.958 335.405 616.852 301.942 555.167 31 503.002 925.556 431.214 793.333 377.385 694.16? 335.523 617.037 302.048 555.333 32 503.179 J25.833 431.365 793.571 377.517 694.375 335.640 617.222 302.154 555.500 33 503.356 J26.111 431.517 793.810 377.650 694.583 335.758 617.407 302.260 555.667 34 503.532 926.389 431.669 794.048 377.782 694.792 335.876 617.5U3 302.366 555.833 35 503.709 J26.667 431.820 794.286 377.915 695.000 335.994 617.778 302.472 556.000 36 503.886 926.944 431.972 794.524 378.048 695.208 336.112 617.963 302.578 556.16? 37 504.063 927.222 432.123 794.762 378.180 695.417 336.230 618.148 302.685 556.333 38 504.239 927.500 432.275 795.000 378.313 695.625 336.348 618.333 302.791 556.500 39 504.416 927.778 432.426 795.238 378.445 695.833 336.466 618.519 302.897 556.667 4O 504.598 928.056 432.582 795.476 378.582 696.042 336.58? 618.704 303.006 556.833 41 504.779 928.333 432.737 795 714 378.718 696.250 336.708 618.889 303.115 557.000 42 504.956 928.611 432.88:' 333 452.124 825.714 395.084 722.500 351.792 642.222 316.694 578.000 48 527.574 903.611 452.279 825.952 395.820 722.708 351.913 642.407 316.803 578.16? 49 527.750 903.889 452.435 826.190 395.950 722.917 352.034 642.593 316.912 578.333 50 527.937 904.167 452.590 820.420 3%. 093 723.125 352.155 642.778 317.021 578.500 51 528.119 !tf54 444 452.746 826.667 396.229 723.333 352.276 642.963 317.130 578.607 52 528.300 1)04.722 452.902 826.905 390 305 723.542 352.398 643.148 317.239 578.833 53 528.482 965.000 453.057 827.143 396 501 723.750 352.519 643.333 317.348 579.000 54 528.663 965.278 453.213 827.381 396.637 723.958 352.640 643 519 317.457 579.167 55 528.845 965.556 453.368 827.619 396.774 724.167 352.761 643.704 317.566 579.333 56 529.027 965.833 453.524 827.857 396.910 724.375 352.882 643.889 317.675 579.500 57 529.208 966.111 453.680 828.095 397.046 724.583 353.003 644.074 317.784 579.667 58 529.390 966.389 453.835 828.333 397.182 724.792 353.124 644.259 317.893 579.833 59 161 TABLE XIV. ACTUAL TANGENTS, ETC. 58 M7 1 Curve. 2 Curve. 3 Curve. 4 Curve. 5 Curve. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. o 3176.00 5800.00 1588.06 2900.00 1058.78 1933.33 794.154 1450.00 635.394:1160.00 1 3177.09 5801.67 1588.60 2900.83 1059.14 1933.89 794.427 1450.42 635.012 1160.33 2 3178.18 5803.33 1589.15 2901.67 1059.50 1934.44 794.699 1450.83 635.8301160.67 3 3179.27 5805.00 1589.69 2902.50 1059.87 1935.00 794.971 1451.25 636.0481161.00 4 3180.36 5806.67 1590.24 2903.33 1060.23 1935.56 795.243 1451.07 636.266 1161.33 5 3181.45 5808.33 1590.78 2904.17 1060.59 1936.11 795.515 1452.08 636.48311161.67 3182.53 5810.00 1591.33 2905.00 1060.95 1936.67 795.788 1452.50 636.701 1162.00 7 3183.62 5811.67 1591.87 2905.83 1061.32 1937.22 796.060 1452.92 636.919 1162.33 8 3184.71 5813.33 1592.41 2906.67 1061.68 1937.78 796.332 1453.33 637.137 1162.67 9 3185.80 5815.00 1592.96 2907.50 1062.04 1938.33 796.604 1453.75 637.355 1163.00 1O 3186.89 5816.67 1593.50 2908.33 1062.41 1938.89 796.877 1454.17 637.572 1163.33 11 3187.98 5818.33 1594.05 2909.17 1062.771939.44 797.149 1454.58 037.790! 1163. 67 12 3189.07 5820.00 1594.59 2910.00 1063.131940.00 797.421 1455.00 638.008 1164.00 13 3190.15 5821.67 1595.14 2910.83 1063.491940.56 797.693 1455.42 638.226 1164.33 14 3191.24 5823 33 1595.68 2911.67 1063.86 1941.11 797.965 1455.83 638.444 1164.67 15 3192.36 5825.00 1596.24 2912.50 1064.23:1941.67 798.245 1456.25 6:38.667 1165.00 16 3193.48 5826.67 1596.80 2913.33 1064.60 1942.22 798.524 1456.67 638.891 1165.33 17 3194.57 5828.33 1597.34 2914.17 1064.97 1942.78 798.796 1457.08 639.1081165.67 18 3195.65 5830.00 1597.89 2915.00 1065.33 1943.33 799.069 1457.50 639.3261166.00 19 3196.74 5831.67 1598.43 2915.83 1065.69 1943.89 799.341 1457.92 639.544 1166.33 20 3197.83 5833.33 1598.97 2916.67 1066.05 1944.44 799.613 1458.33 639.762 1166.67 21 3198.92 5835.00 1599.52 2917.50 1066.42 1945.00 799.885 1458.75 639. 980| 1167. 00 22 3200.01 5836.67 1600.06 2918.33 1066.78 1945.56 800.157 1459.17 640.197 1167.33 23 3201.10 5838.33 1600.61 2919.17 1067.14 1946.11 800.430 1459.58 640.415 1167.67 24= 3202.19 5840.00 1601.15 2920.00 1067.51 1946.67 800.702 1460.00 640.633 1168.00 25 3203.28 5841 67 1601.70 2920 83 1067.87 1947.22 800.974 1460.42 640.851 1108.33 26 3204.36 5843.33 1602.24 2921.67 1068.23 1947.78 801.246 1460.83 641. 069! 1188. 67 37 3205.45 5845.00 1602.79 2922.50 1068.59 1948. as 801.518 1461.25 641.2861169.00 28 3206.54 5846.67 1603.33 2923.33 1068.96 1948.89 801.791 1461.67 641.504lll69.33 29 3207.66 5848.33 1603.89 2924.17 1069.33 1949.44 802.070 1462.08 641.728 1169.67 30 3208.78 5850.00 1604.45 2925.00 1069.70 1950.00 802.349 1462.50 641.951 1170.00 31 3209.86 5851.67 1604.99 2925.83 1070.07 1950.56 802.622 1462.92 642.1691170.33 32 3210.95 5853.33 1605.54 2926.67 1070.43 1951.11 802.894 1403.33 642.387J1170.67 33 3212.04 5855.00 1606.08 2927.50 1070.79 1951.67 803.166 1463.75 642.605| 1171. 00 34 35 3213.13 3214.22 5856.67 5858.33 1606.62 1607.17 2928.33 2929.17 1071.15 1071.52 1952.22 1952.78 803.438 803.710 1464.17 1464.58 642. 822 i 1171. 33 643.040 1171.67 36 3215.31 5860.00 1607.71 2930.00 1071 88 1953.33 803.983 1465.00 643.258 1172.00 37 3216.42 5861.67 1608.27 2930.83 1072.25 1953.89 804.262 1465.42 643.48111172.33 38 3217.54 5863.33 1608.83 2931.67 1072.62 1954.44 804.541 1405.83 643.705:1172.67 39 3218.63 5865.00 1609.37 2932.50 1072.99 1955.00 804.814 1466.25 643.923 1173.00 40 3219.72 5866.67 1609.92 2933.33 1073.35 1955.56 805.086 1406.67 644.141 1173.33 41 3280.81 5868.33 1610.40 20:34.17 1073.71 1956.11 805.358 1467.08 644.358 1173.67 4:2 3221.90 -)870.00 1611.01 2935.00 1074.08 1956.67 805.630 1407.50 644.576 1174.00 43 3222.99 5871 . 67 1611.55 2935.83 1074.44 1957.22 805.902 1407.92 044.794 1174.33 44 3224.07 5873.38 1612.10 2936.67 1074.80 1957.78 806.175 1408.33 645.012 1174.67 45 3225.19 5S75.00 1612.65 2937.50 1075.17 1958.33 806.454 1408.75 645.235 1175.00 6 3226.31 5876.67 1613.21 2938.33 1075.55 1958.89 806.733 1409.17 045.459 1175.33 --7 3227.40 5878.33 1613.76 2939.17 1075.91 1959.44 807.006 1469.58 645.677 1175.67 48 3228.49 5880.00 1614.30 2940.00 1076.27 1960.00 807.278 1470.00 645.894 1176.00 49 3229.57 5881.67 1614.85 2940.83 1076.64 1960.56 807.550 1470.42 646.112 1176.33 5O 3230.66 5883.33 1615.39 2941.67 1077.00 1961.11 807.822 1470.83 643.330 1176.67 51 53 8281.78 3232.90 5885.00 5886.67 1615.95 1616 51 2942.50 2943.33 1077.37 1077.74 1961.67 1962.22 808.102 808.381 1471.25 1471.67 640.554 1177.00 040. 77711177. 33 53 3233.99 5888.33 1617.05 2944.17 1078.11 1962.78 808.653 1472.08 646.9951177.67 54 3235.07 5890.00 1617.60 2945.00 1078.47 IJ'03.33 808.925 1472.50 647.2131178.00 55 838.19 5891.67 1618.16 2945.83 1078.84 19(53.89 809.205 1472.92 647.436 1178.33 56 3237.31 5893.33 1618.71 2946.67 1079.21 1964.44 S09.484 1473.33 047.6001178.67 57 3238.40 5895.00 1619.26 2947.50 1079.58 1905. 00 809.756 1473.75 647.877 1179.00 58 3239:49 5896.67 1619.80 2948.33 1079.94 1965.56 810.029 1474.17 648.095 1179.33 59 3240. 581 5898. 33 1620.352949.17 1080.301906.11 810.301 1474.58 048.3131179.67 162 TABLE XIV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 Curve. 1O Curve. 58 Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Ivii7 529.571 966.667 453.991 828.571 397.318 725.000 353.245 644.444 318.002 580.000 ~~0~ 529.753 966.944 454.147 828.810 397.454 725.208 353.366 644.630 318.111 580.167 1 529.934 967.222 454.302 829.048 397.591 725.417 353.487 644.815 318.220 580.333 2 530.116 967.500 454.458 829.286 397.727 725.625 353.608 645.000 318.329 580.500 3 530.297 967.778 454.613 829.524 397.863 725.833 353.729 645.185 318.438 580.667 4 530.479 968.056 454.769 829.762 397.999 726.042 353.850 645.370 318.547 580.833 5 530.800 968.333 454.925 830.000 398.135 726.250 353.972 645.550 318.656 581.000 6 530.842 968.611 455.08,' 630.238 31(8.272 726.458 354.093 645.741 318.765 581.167 7 531.023 968.889 455.236 830.476 398.408 726.667 354.214 645.926 318.874 581 .333 8 531.205 969.167 455.391 830.714 398.544 726.875 354.335 646.111 318.983 581.500 9 531.386 969.444 455.547 830.952 398.680 727 083 354.456 646.296 319.092 581 667 10 531.5681969.722 455.703 831.190 398.816 727.292 354.577 646.481 319.201 581.833 11 531.749970.000 455. 85b 831.429 398.953 727.500 354.698 646.667 319.310 582.000 12 531.931 970.278 456.014 831.667 .99.089 727.708 354.819 646.852 319.419 582 167 13 532.112970.556 456.170 831.905 399.225 727.917 354.940 647.037 319.528 582.333 14 532.299970.833 456.329 832.143 399.365 728.125 355.064 647.222 319.640 582.500 15 532.485 971.111 456.489 832.381 399.504 728.333 355.189 647.407 319.752 582 667 16 532.666 971.389 456.645 832.619 399.641 7'28.542 355.310 647.593 319.861 582.833 17 532.848 971.667 456.800 832.857 399.777 7'28.750 355.431 647.778 319.970 583.000 18 533.030 971.944 456.956 833.095 399.913 728.958 355.552 647.963 320.079 583.167 19 533.211 972.222 457.111 833.333 400.049 729.167 355.673 648.148 320.188 583.333 2O 533.393 533.574 972.500 972.778 457.267 457.423 833.571 833.810 400.185 400.322 729.375 729.583 355.794 355.915 648. 333 ! 320. 297 648.519320.406 583.500 583.667 21 22 633.756 973.056 457.573 834.048 400.458 729.792 356.036 648.704 320.515 583.833 23 533.937 973.333 457.734 834.286 400.594 730.000 356.157 648.889 320.624 584.000 24 534.119 973.611 457.889 834 . 524 400.730 730.208 356.278 649.074 320.733 584.167 25 534.300973.889 534. 482 974.167 458.045 458.201 834.762 835.000 400 866 401.003 730.417 730.625 356.400 356.521 649 259 649.444 320.842 320.951 584.333 584.500 26 27 534.663 974.444 458.356 835.238 401.139 730.833 356.642 649.630 821.060 584.667 28 534.850 974.722 458.516 835.476 401.278 731.042 356.766 649.815 321.172 584.833 29 535.036 975.000 458.676 835.714 401.418 731.250 356.890 650.000 321.284 585.000 30 535.217 975.278 458.831 835.952 401.554 731.458 357.011 650.185 321.393 585.167 31 535.399 975.556 458.987 836.190 401.691 731.667 357.132 650.370 321.502 585.333 32 535.580 975.833459.143 836.429 401.827 731.875 357.254 650.550 321.611 585.500 33 535.762 976.111459.298 836.667 401.963 732.083 357.375 650.741 321.720 585.667 34 535.943 976.389 459.454 &36.905 402.099 732.292 357.496 650.920 321.829 585.833 35 536.125 976.667 459.609 837.143 402.235 732.500 357.617 651.111 321.938 586.000 36 536.311 976.944 459.769 837.38! 402.375 732.708 357.741 651.296 322.049 586.167 37 536.498 977.222459.929 837.619 402.515 732.917 357.865 651 481 322.161 586.333 38 536.679 977.500 460.084 83Z.857 402.651 733.125 357.986 651.667 322.270 586.500 39 536.861 977.778 460.240 838.095 402.787 733.333 358 107 651.852 322.379 586.667 40 537.042 978.056460.396 838 333 402.923 733.542 358.229 052.037 322.488 586.833 41 537.224 978.333460.551 838.571 403.060 733.750 358 350 52 222 322.597 587.000 42 537.405 978.611460.707 838.810 403.196 733 958 ,358.471 652.407 322.700 587.167 43 537.587 97S. 889 460. 863 839.048 403.332 734.167 358-. 592 652.593 322.815 587.333 44 537.773 979.167:461.022 839.280 403.472 734.375 358.716 052.778 322.927 587.500 45 537.959 979.444'461.182 839.524 403.612 734. sas 358.840 652.963 323.031) 587.607 46 538.141 979.722461.338 839.762 403.748 734.792 358.961 653.148 323.148 587.833 47 538.322 980.000461.493 840.000 403.884 735.000 359.082 653.333 323.257 588.000 48 538.504 980.278 461.649 840.238 404.020 735.208 359.204 653.519 323.300 588.167 49 538.685 980.556 461.804 840.470 404.150 735.417 &59.325 053.704 323.475 588.333 5O 538.872 980.833461.964 840.714 404.296 735.625 359.449 053.889 323.587 588.500 51 5:59.058 981.111 462 124 840.952 404.430 735.833 &59.573 054.074 323.099 588.667 52 539.239 981. 389; 462. 2? 9 841.190 404.572 736.042 359.694 654 259 323. 8C8 588.833 53 539.421 981.667402.435 841.429 404.708 736.250 359.815 654.444 323.917 589.000 54 539.607 981. 94 4 ! 462. 595 841.667 404.848 736.458 359.940 054.630 324.029 589.167 55 539.794 982.222462.754 841.905 404.988 736.667 360.064 654.815 324.141 589.333 56 539.975 982.500,462.910 842.143 405.124 736.875 300.185 655.000 324.250 589.500 57 540.157 982.778463.066 842.381 405.260 737.083 360.306 655.185 324.359 589.667 58 540.338 983.056463.221 842.619 405.396 737.292 300.427 055.370 324.468 589.833 59 163 TABLE XIV. ACTUAL TANGENTS, ETC. 59 1 Curve. 2 Curve. 3 Curve. 4 Curve. 5 Curve. M. Tan. *Wl.fl6 Arc. Tan. Arc. 2950.00 Tan. 1080.67 Arc. Tan. Arc. Tan. Arc. 5900.0011620.89 1966.67 810.573 1475.00648.531 1180.00 1 3242.78 5901.67 1621.45 2950.83 1081.04 1967.22 810.852 1475.42648.754!ll80.33 9 3243. 9 J 5903.33 1622.01 2951 . 67 1081.41 1967.78 811.132 1475.83648.978 1180.67 3 3244.99 5905.00 1622.55 2952.50 1081.77 11)68.33 811.404 1476.25649.196 1181.00 4 1246.08 5906.67 1623.10 2953.33 1082.14 1968.89 81 1 . 67 6 1476.67.649.4131181.33 5 3247.19 5008.83 1623.66 2954.17 1082.51 1969.44 811.956 1477.08649.637 ; 1181.S7 6 3248.31 5910.00 1624.21 2955.00 1082.88 1970.00 812.235 1477. 50 649. 861 '1182.00 7 3249.40 5911.67 1624.76 2955.83 1083.24 1970.56 812.507 1477.92650.078 1182.33 8 3250.49 5913.33 1625.30 2956.67 1083.61 1971.11 812.779 1478.33 650.296 1182.67 9 3251.58 5915. OU 1625.85 2957.50 1083.97 1971.67 813.052 1478.75 650.514 1183.00 10 3253.67 5916 67 1626.39 2958. ^3 1084.33 1972.22 813 324 1479.17 650.732 1183.33 11 325:3.78 5918.33 1626 95 2959.1; 1084.71 1972.78 813.603 1479.58650.955 ! 1183.67 12 325 4. 9U 5920.00 1627.51 2960.00 1085.08 1973.133 813.883 1480. 00^51. 179 1184.00 13 3*65.99 5921.67 1628.05 2960.8:} 1085.44 1973.89 814.155 1480.42651.397 1184.33 14 3257.08 5923.33 1628 60 2961.67 1085.80 1974.44 814.427 1480.83651.614 1184.67 15 1*58.19 5925. OU 1629.16 2962.50 1086.18 1975.00 814.706 1481.25651.838 1185.00 16 3259.31 5926.67 1629.72 29G3.3-3 1086.55 1975.56 814.986 1481.67 652.061 1185.33 17 32(50.40 5928.33 1630.26 2964.17 1086 91 1976.11 815.258 1482.08652.279 1185.67 18 3261.49 5930.00 1630.80 2965. OJ 1087.27 1976.67 815.530 1482.50652.497 1186.00 19 3262.61 .3931.67 1631.3(5 2965. 83 1087.65 1977.22 815.810 1482.92 652.720 1186.33 20 3203.72 ->933.33 1631 92 2966.67 1088.02 1977.78 816.089 1483.33 652.944 1186.67 21 3264.81 5935.00 163.1.47 2967.50 1088.38 1978.33 816.361 1483.75653.16-2 1187.00 22 3265.90 5936.67 1633.01 2968.33 1088.75 1978.89 816.633 1484.17 653.380 1187.33 23 3267 02 5938.33 1633.57 2969.17 1089.12 1979.44 816.913 1484.58653 603 1187.67 24 3268 14 940.00 1634 13 2970.00 1089.49 1980.00 817.192 1485.00653.82; 1188.00 25 3269.2.') 5941.67 1634.69 2970.83 1089.86 1980.56 817.471 1485.42 654.050 1188.33 26 3*70.81 5913.33 1635.24 2971.67 1090.24 1981.11 817.751 1485.83654.274 1188.67 27 3271.46 5945.00 1635.79 2972.50 1090.60 1981.67 818.02:3 1486.25 654.491 1189.00 28 3272.55 5946.67 1636.33 2973.33 1090.96 1982.22 818.295 1486.67 654.7'09 1189.33 29 3273.66 5948.33 1636.89 2974.17 1091.33 1984.78 818.575 1187.08 654.933 1189.67 30 3274.78 5950.00 1637.45 2975.00 1091.71 1983.33 818.854 1487.50 655.156 1190.00 31 3275.87 5951.67 1638.00 2975.83 1092 07 1983.89 819.126 1487.92655 374 1190.33 32 3276.96 5953.33 1638.54 2976.67 1092.43 1984.44 819.398 1488.33655.59-2 1190.67 33 3278.08 5955.00 1639.10 2977.50 1092.80 1985.00 819 678 1488.75655.815 1191.00 34 3279.19 5956. 67 '1639. 66 2978.33 1093.18 1985.56 819.957 1489.17 656.039 1191.33 35 3280.31 5958.33:1640.22 2979.17 1093.55 1986.11 820.237 1489.58 656.262 1191.67 36 3281.43 5960.00; 1640. 77 2980.00 1093.92 1936.67 820.516 1490.00 656.486 1192.00 37 3282.52 5961. 67! 16 41. 32 2980.83 1094.28 1987.22 820.788 1490.42 656.704 1192.33 38 3283.61 5963.33 1641 86 2981.67 1094.65 1987.78 821.060 1490.83 656.922 1192.67 39 3284.72 5965.00 1642.42 2982.50 1095.02 1988.33 821.340 1491.25 657.145 1193.00 4O 3285.84 5966.67 1642.98 2983.33 1095.39 1988.89 821.619 1491.67 657.369 1193.33 41 3286.93 5968.331643.52 2984.17 1095.76 1989.44 821.891 1492.08 657.586 1193.67 42 3288.02 5970.00 1644.07 2985.00 1095: 12 1990.00 822.163 1492.50 657 . 804 1194.00 43 3289.13 5971.67 1644.63 2985.83 1096.49 1990.56 822.443 1492.92 658.028 111)4.33 44 3290.25 5913.33 1615.19 2986.67 1096 86 1991.11 822.722 1493.33 658.251 1194.67 45 3291.37 5975.001645.74 2987.50 1097.24 1991.67 823.002 1493.75 658.475 1195.00 46 3292. 49| 5979: v3. 33 1648.51 2991.67 1099.08 1994.44 824.384 1495.83 659.581 1196.67 51 3298.02 5985.00 1649.07 2992.50 1099 45 1 995. 00 j 824 664 1496.25 659.804 1197.00 52 3299.13 5986.67 1649.63 2993.33 1099.82 1995.56824.943 1496.67 660.028 1197.33. 53 3:300.2.-) 5988.33 1650.19 2994.17 1100.20 1996.11 ! 825.222 1497.08 660.252 1197.67 54 3301.37 5990.00 1650.74 2995.00 1100.57 1 996 . 67 i 825 . 502 1 497 . 50 660 . 475 1198.00 55 3302.46 5991.671651.29 2995.83 1100.93 1997.22825.774 1497.92660.693 1198.33 56 3303.51 .-)993.3i 1651.83 2996.67 1101.29 1997.7882(5.046 1498.33660.911 1198.67 57 3304. (Hi 51195.00 1652 39 2997.50 1101 67 1 998 . 33 8-26 . 325 1 498 . 75 66 1 . 1 34 1199.00 58 3305. 78 5996.67 1652.95 2998. 33 1102.04 1998. 89 820. (105 1499. 17 661. 35S 1199.33 59 3306. IX) 5998.33 1653.51 2999.17 1102.41 1999.44 826.884'14G9.58 6(51 .581 1199.67 164 TABLE XIV. ACTUAL TANGENTS, ETC. Curve. 7 Curve. 8 Curve. 9 Curve. 1O Curve. 59 Tan. Arc. Tan. Arc. Tan. 405.533 Arc. Tan. Arc. Tan. Arc. 590.000 M7 540.520983.333 463.377 842 857 737.500 360.548 655.556324.577 o 540.706983.611 463.537 843.095 405.672737.7'08 360.672 655.741 324. 688 590.167 1 540.89-2 983.889 463.696843.333 405.812737.917 360.797 655.920324.800 590.333 2 541.074984.167 463.852 843.571 405.948 738.12.-) 360.918 050.111 324.909 590.500 3 541.255 984.444 464.008 843.810 406.084 738.333 361.039 056.290325.018 590.667 4 541.442984.722 464.167 8 44.048 406.224 738.542 361.163 656.481 325.130 590.833 5 541.628 986.000 464.327 844.286 406.364 138.750 301 287 656.667 325.242591.000 6 541.809985.278 464.483 844.524 406. SOU 738.958 361.409656.852 325.351 591.167 7 541.991 985.556 464.638 844.762 406.636 739.167 361.530 657.037 325.460 591.333 8 542.172 985.833 464.794 845.000 406.773739.375 361.651 657.222 325.569 591.500 9 542.354 986.111 464.949 845.238 406.909739.583 361.772 657.407 325.678 591.667 1O 542.540 986.389 405. 109 845. 47G 407.049739.792 361.896 657.593 325.790 591.833 11 542.727 986.667 465.269 845.714 407.188740.000 362.020 657.778 325.902 592.000 12 542.908 986.944 465.424 845.952 407.325740.208 362.141 657.963 326.011 592.167 13 543.090987.222 465.580 846.190 407.461 740.417 362.262 658.148 326.120 592.333 14 543.276 987.500 465.740 846.429 407.600740.625 362.387 658.333 326.232 592.500 15 543.4621987.778 465.899 846.667 407.740740.833 362 511 658.519 326.344 592.667 16 543.644 988. 05C 466.055 846.905 407.876741.042 362.632 658.704 326.453 592.833 17 543. 825 i 988.3:33 466.211 847.143 408.013741.250 362.753 658.889 326.562 593.000 18 544.012988.611 466.370 847.381 408.152 741.458 362.877 659.074 326.673 593.167 19 544.198988.889 466.530 847.619 408.292741.667 363.002 659.259 326.785 593.333 30 544.379989.167 466.686 847.857 408. 428 1741. 875 363.123 659.444 326.894 593.500 21 544.561 989.444 466.841 848.095 408.565742.083 363.244 659.630 327.003 593.667 22 544.747 989.722 467.001 848.333 408.704 742.292 303.368 659.815 327.115 593.833 23 544.933 990.000 467.161 848.571 408.844 742.500 363.492 660.000 327.227 594.000 24 545.120 990.27'8 467.320 848.810 408.984 742. 70S 363.617 660.185 327.3:39 594.167 25 545. 306 1990. 55(3 467.480 849. 04b 409.124 742.917 363.741 060.370 327.451 594. 333 26 545.488 990.833 467 636 849.286 409. 260 743.125 363.862 660.556 327.560 594.500 27 545.669 991.111 467.791 849.524 409.396 743.333 363.983 660.741 327.669 594.667 28 545.855 991.389 467.951 849.762 409.536 743.542 364.107 660.926 327,781 594.833 29 546.042 991.667 468.111 850.000 409.676 743.750 364.232 661.111 327.892 595.000 30 546.223 991.944 468.266 850. 2S8 409.812 743.958 364.353 661.296 328.001 595.167 31 546.405 992.222 468.422 850.476 409.948 744.167 364.474 661.481 328.110 595.333 32 546.591 992.500 468 582 850.714 410.088 744.375 364.598 661.667 328.222 595.500 33 546.777 992.778 468.741 850.952 410.227 744.583 364.722 661.852 328.334 595.667 34 546.964 993.056 468.901 851.190 410 367 744.792 364.847 662.037 328.446 595.833 35 547. 150 993. 333 547.331 993.611 469 061 469.217 851.429 851.667 410.507 745.000 410.643J745.208 364.971 365.092 662.222 662.407 328.558 328.667 596.000 596.167 36 37 547.513 993.889 469.372 851.905 410 779 745.417 365.213 662.593 328.776 596.333 38 547.699 994.167 469.532 852.143 410.919 745.625 365.337 662.778 328.888 596.500 39 547.886 994.444 469.692 852.381 411.059 745.88? 865.462 662.963 329.000 596.667 40 548.067 994.722 469.847 852.619 411.195 746.04^ 365.583 663.148 329.109 596.833 41 548.249 995.000 470.003 852.857 411.331 746.250 365.704 663.333 329.218 597.000 42 548.435 995.278 470.162 853.095 411.471S746.458 365.828 663.519329.330 597.167 43 548. 62 i| 995. 556 470.322 853.333 411.611 746.667 365.952 663. 7'04 1329.441 597.333 44 5 48. 807 1995. 833 470.482853.571 411.751 7'46.875 366.077 663.889 329.553 597.500 45 548.994 996.111 470.642853.810 411.890747.088 366.201 664.074 329.665 597.667 46 549.180 996.389 470.801 854.048 412.030 747.292 366.325 664.259 329.777 597.833 47 549.366 996.667 470.961 854.286 412.170 747.500 366.449 664.444 329.889 598.000 48 549.548 996.944 471.117 854.524 412.306 747.708 366.570 664.630 329.998 598. 167 49 549.729997.222 471.272 854.762 412.442 747.917 366.691 664.815 330.107 598.333 50 549.916 997.500 471.432 855.000 412.582 748.125 366.816 665.000 330.219 598.500 51 550.102 997.778 471.592 855.238 412.722 748.333 366.940 665.185330.331 598.607 52 550.288998.056 471.751 855.476 412.862 748.542 367.064 605. 370 1 330. 443 598.833 53 550.475998.333 471.911 855.714 413.001 748.750 367,189 665.556330.554 599.000 54 550.656 998.611 472.067 855.958 41 3. 138! 748. 958 367.310 665. 741 1330. 663 599.167 55 550.838 998.889 472.222 806. 190 413.274 749.167 367.431 665. 926330. 772 599.33:3 56 551.024999.167 472. 382 1856.429 413.414 749.375 367.555 6C6.111 330.884 599.500 57 551.210 999.444 472. 542: 856. (JO 7 413.553 749.583 367.679666.296330.996 599.607 58 551.39? 999. 75k 472.701:85G.90f 413.693749.792 367.804 666. 481 J331. 108 599. 833 59 165 TABLE XIV. ACTUAL TANGENTS, ETC. 60 "SET 1 Curve. 2 Curve. 3 Curve. 4 Curve. 5 Curve. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. ~~o" 3308.01 6000.00 1654.07 3000.00 1102.78 2000.00 827.164 1500.00 661.805 1200.00 i 3309.13 6001.67 1654.63 3000.83 1103.16 2000.56 827.443 1500.42 662.028 1200.33 2 3310.25 6003.33 1655.18 3001.67 1103.53 20U1.11 827.723 1500.83 662.252 1200.67 3 3311.37 6005.00 1655.74 3002.50 1103.90 2001.67 828.002 1501.25 662.475 1201.00 4 3312.48 6006.67 1656.30 3003.33 1104.27 2002.22 828.281 1501.67 662 . 699 1201.33 5 3313.57 6008.33 1656.85 3004.17 1104.64 2002.78 828.5531502.08 662.917 1201.67 6 3314.66 6010.00 1657.39 3005.00 1105.00 2003 33 828.8*5 1502.50 663.134 1202.00 7 3315.7816011.67 1657.95 3005.83 1105 37 2003.81) -S29.105 1502.92 663.358 1202.33 8 331 6. 89! G013. 33 1658.51 3006.67 1105.7:; 2004.44 829.384 1503.33 663.581 1202.67 9 3318.01 6015.00 1659.07 3007.50 1106.12 2005.00 829.664 15U3.75 663.805 1203.00 10 3319.13 6016.67 1659.63 3008.33 1*>6.49 2005.56 829.943 1504.17 664.029 1203.33 11 3320.25 6018.33 1660.18 3009.17 1106.86 2006.11 S30.222 1504.58 664.252 1003.67 12 3321.36 6020.00 1660.74 3010.00 1107.24 2006.67 830.502 1505.00 664.476 1204.00 13 3322.48 6021.67 1661.30 3010.83 1107.61 2007.22 830.781 1505.42 664.699 1204.33 14 3223.60 6023.33 1661.86 3011.67 1107.98 2007.78 831.060 1505.83 664.923 1204.67 15 8324.72 6025.00 1662.42 3012.50 1108.35 2008.33 831.340 1506.25 665.146 1205.00 16 3325.83 6026.67 1662.98 3013.33 1108.73 2008.89 831.619 1506.67 665.370 1205.33 17 3326.95 6028.33 1663.54 3014.17 1109.10 2009.44 831.899 1507. OS 665.593 1205.67 18 3328.07 6030.00 1664.09 3015.00 1109.47 2010.00 832.178 1507.50 665.817 1206.00 19 3329.18 (5031.67 1664.65 3015.83 1109. M 2010.56 832.457 1507.92 606.040 1206.33 2O 3330.30 6033.33 1665.21 3016.67 1110.21 2011.11 832.737 1508.33 666.264 1206.67 21 3331.39 6035.00 1605. 70 3017.50 1110 58 2011.67 833.009 1508.75 666.482 1207.00 22 3332.48 6036.67 1666.30 3018.33 1110.94 2012.22 833.281 1509.17 666.699 1207.33 23 3333.60 6038.33 1666.86 3019.17 1111.31 2012.78 838.561 1509.58 666.923 1207.67 24 3334.71 6040.00 1667.42 3020.00 1111.69 2013.33 833.840 1510.00 667.146 1208.00 25 3335.83 6041.67 1667.98 3020.83 1112.06 2013.89 834.119 1510.42 667.370 1208.33 26 3336.95 6043. 33 1668.54 3021.67 1112.43 2014.44 834.399 1510.83 667.593 1208.67 27 3338.07 6045.00 1669.09 3022.50 1112.80 2015.00 834.678 1511.25 607.817 1209.00 28 3339.18 6016.67 1669.65 3023.33 1113.18 2015.56 834.957 1511.67 668.041 1209.33 29 3340.30 6048.33 1670.21 3024.17 1113.55 2016.11 835.237 1512.08 668.264 1209.67 30 3341.42 6050.00 1670.77 3025.00 1113.92 2016.67 835.516 1512.50 668.488 1210.00 31 3342.53 6051.67 1671.33 3025.83 1114.29 2017.22 835.796 1512.92 668.711 1210.33 32 3343 65 6053.33 1671.89 3026.67 1114.67 2017.78 836.075 1513.33 668.935 1210.67 33 3344.77 6055.00 1672.45 3027.50 1115.04 2018.33 836.354 1513.75 669.158 1211.00 34 3345.89 6056.6? 1673.00 3028.33 1115.41 2018.89 836.634 1514.17 669.382 1211.33 35 3347.00 6058.33 1673.56 3029.17 1115.78 2019.44 836.913 1514.58 669.605 1211.67 36 3348.12 6060.00 1674.12 3030.00 1116.16 2020.00 837.192 1515.00 669.829 1212.00 37 3349 24 6061.67 1674.68 3030.83 1116.53 2020.56 837.472 1515.42 670.052 1212.33 38 3350.36 6063.33 1675.24 3031.67 1116.90 2021.11 837.751 1515.83 670.276 1212.67 39 3351.47 6065.00 1675.80 3032.50 1117.27 2021.67 838.031 1516.25 670.499 1213.00 40 3352.59 6066.67 1676.36 3033.33 1117.65 2022.22 838.310 1516.67 670.723 1213.33 41 3353.71 6068.33 1676.92 3034.17 1118.0212022. 78 838.589 1517.08 670.946 1213.67 42 3354.82 6070.00 1677.47 3035.00 1118 39:2023.33 838.869 1517.50 671.1701214.00 43 3355.94 6071.67 1678.03 3035.83 1118.76 ! 2023.89 839.148 1517.92 671.393 1214.33 44 3357.06 0073.33 1678.59 3036.67 1119.132024.44 839.427 1518.33 671.617 1214.67 45 3358.21 6075.00 1679.16 3037.50 1119.522025.00 839.714 1518.75 671.846 1215.00 46 3359.35 6076.67 1679.74 3038.33 1119 902025.56 840.000 1519.17 672.075 1215.33 47 3300.47 6078.33 1680.30 3039.17 1120.272026.11 840.280 1519.58 672.299 1215.67 48 3361.59 6080.00 1680.85 3040.00 1120.64 2026.67 840.559 1520.00 072.522 1216.00 49 3362.70 6081.67 1681.41 3040.83 1121.02 2027.22 840.839 1520.42 672.746 1216.33 50 3363.82 6083.33 1681.97 3041.67 1121.39 2027.78 841.118 1520.83 672.970 1216.67 51 3364.94 6085.00 1682.53 3042.50 1121.76 2028.33 841.397 1521.25 073 .103 1217.00 52 3366.05 6086.67 1683.09 30-13.33 1122.13 2028.89 841.677 1521.67 673.417 1217.33 53 3367.17 6088.33 1683.65 3044.17 1122.51 2029.44 841.956 152, '.08 673.640 2 1 7 . 67 54 13368.29 6090.00 1684.21 3045.00 1122.882030.00 842.235 1522.50 673.864 1218.00 55 3369.41 6091.67 1684.77 3045.83 1123.252030.56 842.515 1522.92 074.087 1318.33 56 3370.52 6093. 33 1685.32 3046.67 1123.622031.11 842.794 1523.33 674.311 1218.67 57 13371.64 6095.00 1685.88 3047.50 1124.002031.67 843.074 1523.75 674.584 1219.00 58 3372.76 6096.67 1686.44 3048.33 1124.372032.22 813.353 1524.17 674.758 1219.33 59 3373.90 6098.33 1687.01 3049.17 1124.75 2032.78 843 640 1524.58 074.987 1219.67 166 TABLE XIV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 Curve. 10 Curve. 6O , Ta n . Arc. Tan. | Arc. Tan. Arc. Tan. Arc. Tan. Arc. M. 55 1 . 58:5 1 000 . 00 4 72 . 80 1 857 .143 413.833 750.000 367.928 666.667 331.220 600.000 ~O~ 55 1 . 760 1 000 . 28 473 . 021 i 857 . 381 413.973 750.208i368.052 666.852 331.332 600.167 1 551.955 100J. 50 473.181 857.619 414.112 750. 41 7 1368.1 76 667.037 331.444 600.333 3 552.142! 1000. 83 473.340 857.857 414.252 750. 625 ! 368. 301 667.222 331.555 600.500 3 552.328 1001.11 473.500 858.095 414.392 750.833368.425 667.407 331.667 600.667 4 552.510 1001.39 473. 6GO 858.333 414.528 751.042 368.546 667.593 331.776 600.833 5 55-3.09] 1001.67 473.819 858.571 414.664 751.250 368.667 667.778 331.885 601.000 6 552.877 1001.94 473.975 858.810 414.804 751.458 368.791 667.963 331.997 601.167 7 553.064 1002.22 474.131 859.048 414.944 751.667 368.916 668.148 332.109 601.333 8 553.250 1002.50 474.290 859.286 415.084 751.875 369.040 668.333 332.221 601.500 9 553.436 1002.78 474.450 859.524 415.223 752.083 369.164 668.519 332. a33 601.667 1O 553.623 1003.06 474.610 859.762 415.363 752.292 369.288 668.704 332.445 601.833 11 553.809 553.995 1003.33474.769 1003.61 474.929 860.000 860.238 415.503 415.643 752.500 752.708 369.413 369.537 668.889 669.074 332.557 332.668 602.000 602.167 13 13 554.181 1003.89 475.089 860.476 415.783 752.917)369.661 669.259 333.780 602.333 14 554. 3U8 1004.17 475.249 860.714 415.922 753.125 369.785 669.444 332.892 602.500 15 554.554 1004.44 475.408 860.952 416.062 753.833 369.910 669.630 333.004 602.667 16 564.740 1004.72 475.568 861.190 416.202 753.542370.034 669.815 333 116 602.833 17 554.927 1005.00 475.728 861.429 416.342 753.750370.158 670.000 333.228 603.000 18 555.113 1005.28 475.887 861.667 416.481 753.958 370.282 670.185 333.340 603.167 19 555.299 1005.56 476.047 861.905 416.621 754.167 370.407 670.370 333.452 603.333 20 555.481 1005.83 476.203 862.343 416.757 754.375370.528 670.556 333.561 603.500 31 555.662 1006.11 476.358 862.381 416 894 754.583370.649 670.741 333.670 603.667 33 555.849 1006.39 476.518 862 619 417.033 754.792370.773 670.926 333.781 603.833 33 556.035 1(106.67 476.678 862.857 417.173 755.000370.897 671.111 333.893 604.000 34 556.22! 1006.94 476.837 863.095 417.313 755.208 371.022 671.296 334.005 604.167 35 556.407 1007.22 47-6.097 863.333 417.453 755.417 371.146 671.481 334.117 604.333 36 556.594 1007.50 477.157 803.571 417.592 755.625 371.270 671 CG7 334.229 604.500 37 556.780 1007.78 477.317 863.810 417.732 755.833371.395 671.852 334.341 604.667 38 556.966 1008.06 477.476 864.048 417.872 756.042 371.519 672.037 334.453 604.833 39 557.153 1008.33 477.636 864.286 418.012 756.250 371 .643 672 222 334.564 605.000 30 557.339 1008.61 477.796 864.524 418.151 758.4581371 767 672.407 334.676 605.167 31 557.525 1008.89 477.955 864.762 418.291 756.667 371.892 672.593 334.788 605.333 33 557.712 1009.17 478.115 865.000 418.431 756.875 372.016 672.778 334.900 605.500 33 557.898 1009.44 478.275 865.238 418.571 757.083 372. 140 67'2.963 335.012 605.667 34 558.084 1009.72 478.435 865.476 418.711 757.292 372.264 673.148 335.124 605.833 35 558.270 1010.00 478.594 865.714 418.850 757.500372.389 673.333 335.236 606.000 36 558 457 1010.28 478.754 865.952 418.990 757.708 372.513 673.519 335.348 606.167 37 558.643 1010.56 478.914 866.190 419.130 757.917 372.637 673.704 335.459 606.333 38 558.829 1010.83 479.073 866.429 419.270 758.125 372.761 673.889 335.571 606.500 39 559.016 1011.11 479.233 866.667 419.409 758.333 372.886 674.074 335.683 G06.667 4O 559.202 1011.39 479.393 866.905 419.549 758.542 373.010 674.259 1335.795 606 833 41 559.388 1011.67 479.553 867.143 419.689 758.750 373.134 674.444 335 907 607.000 43 559.574 1011.94 479.712 867.381 419.829 758 958 373.259 674.630 336 019 607.167 43 559.761 1012.22 479.872 867.619 419.969 759.167 373.383 674.815 336.131 607.333 44 559.952 1012.50 480 036 867.857 420.112 759.375 373.510 675.000 336.245 607.500 45 560.143 1012.78 480.200 868.095 420.255 759.583 373.638 675.185 336.360 607.667 46 560.329 1013.06 480.359 868.333 420 395 759.792 373.762 675.370 336.472 607.833 47 560.516 1013.33 480.519 868.571 420.535 760.000 373.886 675.556 336.584 608.000 48 560.702 1013.61 480.679 868.810 420.675 760.208 374.011 675.741 336. 69f 608.167 49 560.888 1013.89 480.838 869.048 420.814 7G0.417 37'4.135 675.926 336.808 608.333 50 561.074 1014.17 480.998 809 286 420.954 760.625 374.259 676.111 336.919 608.500 51 561.261 1014.44 481.158 869.524 421.094 760. 833 374.383 676.296 337.031 608.667 53 561.447 1014.72 481.318 869.762 421.234 761.042 374.508 676.481 337.143 608.833 53 561.633 1015.00 481.477 870.000 421.373 761.250(374.632 676.667 337.255 609.000 54 561.820 1015.28 181.637 870. 23S 421.513 761.458374.756 676.852 337.367 609.167 55 563.006 1015.56 481 . 797 870.476 421.653 761.6671374.880 677.037 337.479 609.333 56 562.192 1015.83 481.956 870.714 421.793 761.875375.005 677.222 337.591 609.500 57 562.379 1016.11 482.116 870.952 421.932 762. 083 : 37 5. 129 677.407 337.703 609.667 58 502. 570 11016.39 -183.280 871.190 422.076 7'62. 292 1375.256 677.593 337.817 609.833 59 167 TABLE XIV. ACTUAL TANGENTS, ETC. 61" 1 Curve. 2 Curve. 3 Curve. 4 Curve. 5 Curve. M. Tun. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. 3375.05 0100.00 1087.59 3050.00 1125.1320.-J3.33 S tt . '.)->6 1525.00 675.210 1220.00 1 3376. 176101. 67 1088.15 3050.83 1125.51 2033.89 844.205 1525.42 675.440 1220.33 2 3377.2816103.83 1088.70 3051 . 07 1125.88 2034.4} 844.485 1525.88 675.663 1220.67 3 3378.406105.00 1689.26 3052.50 1126.25 2035.00 844 764 1526.25 675.887 1221.00 4 3379.55 6106.07 1689.82 3053.33 1120.02 2035.50 845 . 14 1520.07 076.110 1221.33 5 3380.64 6108.33 1690.38 3054.17 1120.99 2030.11 845.323 1527.08 676.334 1221.07 6 3381.75 6110.00 16J0.94 3055.00 1127.37 2030.07 845.002 1527.50 676.557 1222.00 7 3382.87 6111.67 1691.50 3055.83 1127.7*4 2037.22 845.882 1527.92 676.781 1222.33 8 3383.99 6113.33 1092.06 3050.67 1128.11 2037.78 846.161 1528.33 677.004 1222.67 9 3385.13 6115.00 1692.63 3057.50 1128.49 2038.33 846.448 1528.75 677.234 1223.00 10 3386.28 6116.67 1693.20 3058.33 1128.88 2038.89 846.734 1529.17 677.463 1223. as 11 3387.40 0118.33 1093.76 3059.17 1129.25 2039.44 847.013 1529.58 677.686 1223.67 12 3388. M 0120.00 1694.32 3060.00 1129.02 2040.00 847.293 1530.00 677.910 122400 13 3389.63 6121.67 1694.88 3060.83 1129.99 2040.50 S47.572 1530.42 678.134 1224.33 14 3390.75 6123.33 1695.44 3001.67 1130.37 2041.11 847.852 1530.83 678.357 1224.67 15 3391.87 6125.00 1696.00 3062.50 1130.74 2041.07 848.131 1531.25 678.581 1225.00 16 3392.98 6126.67 1690.55 3003.33 1131.11 2042.22 848.410 1531.67 078.804 1225.33 17 3394.13 0128.33 1697.13 3064.17 1131.49 2042.78 848.697 1532.08 679.033 1225.67 18 3395.28 6130. OU 16^7.70 3065.00 1131.88 2043.33 848.983 1532.50 679.263 1226.00 19 339o.39 6131.67 1698.26 3065.83 1132.25 2043.89 849.263 1532.92 679. 4SO 1226.33 30 3397.51 6133.33 1698.82 3066.67 1132.62 2044.44 849.542 1533.33 679.710 1226.67 21 3398.03 6135.0U 1099.38 3067.50 1132.99 2045.00 849.822 1533.75 679.933 1227.00 33 3339. 15 6136.0; 1099.93 3068.33 1133.37 2045.50 850.101 1534.17 080.157 1227.33 23 3400.89 6138.33 1700.51 3069.17 1133.75 2040.11 850.387 1534.58 080 380 1227.67 24 3402.04 6140.00 1701.08 3070.00 1134.13 2046.07 850.674 1535.00 080.015 1228.00 25 3403.15 0141.67 1701.04 3070.83 1134.50 2047.22 850.953 1535.42 080.839 1228.33 20 3404.27 6143.33 1702.20 3071.67 1134.87 2047.78 851.233 1535.83 681.062 1228.67 27 .'3405.39 6145.00 1702.70 3072.50 11 3o. 25 2048.33 851.512 1536.25 681.286 1229.00 28 3406 51 6146.67 1703.32 3073.33 1135.62 2048.89 851.792 1536 67 081.509 1229.33 29 3407.05 6148.33 1703.89 3074.17 1136.00 2049.44 852.078 1537.08 081. 7'39 1229.67 30 3408.80 6150.00 1704.46 3075.00 1136.38 2050.00 852.365 1537.50 081.968 1230.00 31 3409.92 6151.67 1705.02 3075.83 1130.76 2050.56 852.044 1537.92 082.191 1230.33 32 3 41 1.03 6153.33 1705.58 3076.67 1137.13 2051.11 852.923 1538.33 682.415 1230.67 33 3412.16 0155.00 1706.15 3077.50 1137.51 2051.67 853.210 1538.7'5 682.644 1231.00 34 3413.32 6156.67 1706.72 3078.33 1137.89 2052.22 853.490 1539.17 682 873 1231.33 35 3414.44 6158.33 1707.28 3079.17 1138.20 2052.78 858.77* 1539.58 683.097 1231.67 30 3415.56 6160.00 1707.84 3080.00 1138.64 2053.33 854.055 1540.00 683.320 1232.00 37 3416.08 6161.67 1708.40 3080.83 1139.01 2053.89 854.335 1540.42 683.544 1232.33 38 8 417.79 6103.33 1708.96 3081.67 1139.38 2054.44 854.614 1540.83 6N3 767 1232.67 39 3118.94 0105.00 1709.53 3082.50 1139.70 2055.00 854.900 1541.25 083.997 1233.00 40 3420.09 6166.67 1710.11 3083.33 1140.15 2055. 56 855.187 1541.67 684.236 1233.33 41 3421.20 6168.33 1710.60 3084.17 1140.52 2056.11 855.460 1542.08 684.450 1233.67 42 3422.32 6170.00 1711.22 3085.00 1140.892050.67 855 746 1542.50 684.673 1234.00 43 3423.47 6171.07 1711.80 3085.83 1141.272057.22 856.032 1542.92 684.902 1234.33 44 3424.01 6173.33 1712.373080.07 1141.652057.78 850.818 1543.33 685.132 1234.07 45 3425.73 0175.00 1712.933087.50 1142.032058.33 856.598 1543.75 685.355 1235 00 46 47 3426.85 3427 99 0176.67 617'8.33 1713.493088.33 1714.0G ! 3089.17 1142.402058.89 1142.782059.44 856.878 857.164 1514.17 1544.58 685.579 685 808 1235.33 1235.67 48 3129.14 0180.00 1714. 6313090. 00 1143.162060.0' 857 451 1515.00 686 037 1236.00 49 343 J. 26 6181.67 1715.19 3090.83 1143.542060.56 857.730 1545.42 686.261 1236.33 50 3431.37 6183.33 1715.75 3091.67 1143.91 2001.11 858 009 1545.83 686.484 1236.67 51 3132 52 6185.00 716.32 3092.50 1144.29 2001.67 858.296 1546.25 686.713 1237.00 52 3433.66 6186.67 716.90 3093.33 1144.07 2062.22 858.582 1546.67 686.943 1237.33 53 3434 78 6188.33 717.45 3094.17 1145.05 2002.78 858.862 1517.08 687.160 1237.07 54 3435.90 6190.00 718.01 3095.00 1145.42 2003.33 859.111 1547.50 687.390 1238.00 55 3437.05 0191.67 718.59 3095.83 1145.80 2003.89 859.428 1547.92 687.019 1238.33 56 3138.19 6193.33 719.16 3096.07 1146.18 2004.44 859.714 1548.33 687.848 1238.67 57 3439.31 6195.00 719.72 3097.50 1140.55 2005.00 859.994 1548.75 688.072 1239.00 58 3440.43 6196.07 1720 28 3098.33 1146 93 2065.56860.273 1549.17 688.295 1239.33 59 3441.57 0198.33 1720.85 3099.17 1147.31 2066. 11 i860. 560 1549.581688.525 1239.67 168 TABLE XIV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 Curve. 1O Curve. 61 1ST Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. 562.761 1016.67 482.444871.429422.219 762.500 375.384 677.778 337.932 610.000 562.947 1016.94 482. 003 871. 667 422. 3f>9 762.708 37 5 . 508 677.963 338.044 610.167 i 663.138 1017.22 482.763 871.905422.499 762.917 375.632 678.148 338.156 610. 333 3 563.320 1017.50 482.923 872.143 422.639 703.125 375.757 678.333 338.268 610.500 3 563.506 1017.78 483.083 872.381 422.778 763.333 375.881 678.519 338,380 610.667 4 563.692 1018.06 483.242 872.619 422.918 763.542 376.005 678.704 338.491 610.833 5 563.878 1018.33 483.402 872.857 423.058 763.7'50 376.129 67S.889 338.603 611.000 6 564.065 1018.61 483.562 873.095 423.198 763.958 376.254 679.074 338 715 611.167 7 564.251 1018.89 483.721 873.333 423.337 764.167 376.378 679.259 338.827 611.333 8 564.442 1019.17 483.885 873.571 423.481 764.375 376.505 679.444 338.942 611.500 9 564.633 1019.44 484.049 873.810 423.624 764.583 376.633 679.630 339.056 611 667 10 564.819 1019.72 484.209 874.048 423.764 764.792 376.757 679.815 339.168 611.833 11 565.006 1020.00 484.368 874.286 423 904 765 000 376.881 680.000 339.280 612.000 12 565.192 1020.28 484.528 874.524 424.043 765.208 377.006 680.185 339.392 612.167 13 565.378 1020.56 484.688 874.762 424.183 765.417 377.130 680.370 339.504 612.333 14 565.565 1020.83 484.847 875.000 424.323 765.625 377.254 680.556 339.616 612.500 15 565.751 1021.11 485.007 875.238 424.463 765.833 377.378 680.741 339.728 612.007 16 565.942 1021.39 485.171 875.476 424.606 766.042 377.506 680.926 339.842 612.833 17 566.133 1021.67 485. 335 875.714 424.749 766.250 377.633 681.111 339.957 613.000 18 566.319 1021.94 485.495 875.952 424.889 766.458 377.758 681.296 340.069 613.167 19 566.506 1022.22 485.654 876.190 425.029 766.667 377.882 681.481 340.181 613.333 20 566.692 1022.50 485.814 876.429 425.169 766.875 378.006 681.667 340.293 613.500 31 566.878 1022.78 485.974 876.667 425.309 767.083 378.130 681.852 340.405 613.607 22 567.069 1023.06 486.137 876.905 425,452 767.292 378 258 682.037 340.519 613.833 23 567.200 1023.33 486.301 877.143 425.595 767.500 318.385 682.222 340.634 614.000 24 567.447 1023.61 486.461 877.381 425.735 767.708 378.510 682.407 340.746 614.167 25 567.633 1023.89 486.621 877.619 425.875 767.917 378.634 682.593 340.858 614.333 26 507 819 1024.17 486.780 877.857 426.015 768.125 378.758 682.778 340.970 614.500 21 568.006 1024.44 486.940 878.095 426.154 768.333 378.882 682.963 341.082 614.667 2% 568.197 1021.72 487.104 878.333 426.298 768.542 379.010 683.148 341.196 614.833 2 1029.72 490.011 882.619 428. H42 772.292 381. 272 1 686. 481 343.233 617.833 47 57 .779 1030.00 490.175 882.857 428.986 772.500 381 .400 686.667 343.348 618.000 48 57 .966 1030.28 490.335 883.095 429.125 772.708 381.524 686.852 343.460 618.167 49 572.152 1030.56 490.495 883.333 429.2f>5 772.917 381.648 687.037 343.571 618.333 5O 572.343 1030.83 490.658 883.571 429.409 773.125 381.776 687.222 343.686 618.500 51 572.534 1031.11 490.822 883.810 429.552 773.333 381.903 687.407 343.801 618.667 53 572.720 1031.39 490.982 884.048 429.692 773.542 382.027 687.593 343.913 618.833 53 572.907 1031.67 491.142 884.286429.831 773.750 382.152 687.778 344.025 619.000 54 573.098 1031.9-1 491.305 884.524429.975 773.95S 382.279 687.963 344.139 019.167 55 573.289 1032.22 491.469 884.762430.118 774.167 382.407 688.148 344.254 619.333 56 573.475 1032.50 491.629 885.000430.258 774.375 382 531 688. 333 344.366 519.500 57 573.661 1032.78 41)1. 7 89 885. 238 430. 398 774.583 382.655 688.519 344.478 619.667 58 573.852 1033. C6 491.953885.476430.541 774.792 382.783 688.704 344.593 619.833 59 169 TABLE XIV. ACTUAL TANGENTS, ETC. 62 1 Curve. 2 Curve. 3 Curve. 4 Curve. 5 Curve. M. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc ~~~O~ 3442.72 6200. i;0 1721.42 3100.00 1147.69 8066. ($7 860 846 1550.00 688.754 1240.00 1 H43.86 6 JO 1.67 1721. 99 3100.83 1148.07 2067.22 861.133 1550.4- 688.988 1240.33 2 -544"). 0! 6203.33 1722.57 3101.67 1148.45 2067.78 861.419 1550.83 689.212 1240.67 3 3146.13 6205.00 1723.13 3102.50 1148.83 2068.33 861.699 1551.25 689.436 1241.00 4 3147.24 6206.67 1723.69 3103.33 1149.20 2068.89 861.978 1551.67 689.659 1241.33 5 3148.39 6.208. :J3 1724.26 3104.17 1149.58 2069.44 862.264 1552.08 689.889 1241 67 6 3149.54 6210.00 1724.83 3105.00 1149.96 2070.00 862.551 1552.50 690.118 1242.00 7 3150.68 6211.67 1725.40 3105.83 1150.35 2070.56 862.838 1552.92 690.347 1242.33 8 MM. 88 6213.33 1725.98 3106.67 1150.73 2071.11 863.124 1553.33 690.576 1242.67 9 3453.94 6215.00 1726.54 3107.50 1151.10 2071.67 863.403 1553.75 690.800 1243.00 10 3454.08 6216.67 1727.09 3108.33 1151.47 2072.22 863.683 1554.17 691.023 1243.33 11 3455.21 6. '18. 33 1727.68 3109.17 1151.85 2072.78 863.969 1554.58 691.253 1243.67 13 3(56.35 62-30.00 1728.24 3110.00 1152.24 3073.88 864.256 1555.00 691.482 1244.00 13 3457.50 6221.67 172S.81 3110.83 1152.62 2073.89 864.542 1555.42 691.711 1244.33 14 3158.65 6223.33 1729.39 3111.67 1153.00 2074.44 864.829 1555.83 691.940 1244.67 15 3459.76 6225.00 1729.95 3112.50 1153.37 2075.00 865.108 1556.25 692.164 1245.00 10 3460.88 6226.67 1730.50 3113.33 1153.75 2075.56 865.388 1556.67 692. 38S 1245.33 17 3462.03 6228.33 1731.08 3114.17 1154.13 2076.11 865.674 1557.08 692.617 1245.67 18 3463.17 6230.00 1731.65 3115.00 1154.51 2076.67 865 961 1557.50 692.846 1246.00 19 3464.32 6231.67 1733.22 3115.83 1154.89 2077.22 866.247 1557.92 693 075 1246. 33 20 3465.46 6233.33 1732.80 3116.67 1155.27 2077.78 866.534 1558.33 693.305 1246.67 21 8466.68 6235.00 1733.35 3117.50 1155.65 2078.33 866.803 1558.75 693.528 1247.00 22 3467.70 6236.67 1788.91 3118.83 1156.02 2078.89 867.093 1559.17 693.752 1247.33 23 3468.84 623S.33 734.49 3119.17 1156.40 2079.44 867.369 1559.58 693.981 1247.67 24 3469.99 6240.00 735.06 3120.00 1156.78 2080.00 867.666 1560.00 694.210 1248.00 25 3471.14 6241.67 735.63 3120.83 1157.16 2080.56 867 952 1560.42 694.431) 1248.33 26 3472.28 6243.33 736.20 3121.67 1157.55 2081.11 868.239 1560.83 694.669 1248.67 27 3473.43 6245.00 736.78 3122.50 1157.93 2081.6? 868.535 1561.25 694.898 1249.00 28 3474.57 6246.67 737.35 3123.33 1158.31 2082.22 868.812 1561.67 695.127 1249.33 29 3475.69 6248.33 737.91 3124.17 1158.68 2082.78 869.091 1562.08 695.351 1249.67 30 3476.81 6250.00 738.47 3125.00 1159.06 2083.33 860.371 1562.50 695.574 1250.00 31 3477.95 6251.67 739.04 3125.83 1159.44 2083.89 869.657 1562.92 695.803 1250.33 32 3479.10 6253.33 739.61 3126.67 1159.82 2084.44 869.944 1563.33 696.033 1250.67 33 3480.25 6255.00 740.19 3127.50 1160.20 2085.00 870.230 1563.75 696.262 1251.00 34 3181.39 6256.67 740.76 3128.33 1160.58 2085.56 870.517 1564.17 696.491 1-351.33 35 36 34S3.54 3483.68 6258.33 6260.00 741.33 741.91 3129.17 1160.97 3130. OO 1 11 61. 35 2086.11 2086.67 870.803 871.090 1564.58 1565.00 696.720 696.950 1251.67 1252.00 37 3184.83 6261.67 742.48 3130.83 1161.73 2087.23 871.376 1565.4.' 697.179 1252.33 38 3485.03 6263.33 743.0J 3131.67 1162.11 2087.78 8? 1.6(53 1565.83 607.408 1252.67 39 3437.12 6265.00 743.63 3133.501162.49 2088.33 871.919 1566.25 697.637 1253.00 40 348S.27 6266.67 744.20 3133.33 1162.88 2088.89 872.236 1566.67 697.867 1253.33 41 3489.41 6368.33 744.77 3134.17 1163.26 2089.44 872 523 1567.06 698.096 1253.67 42 3490.56 6270.00 745.34 3135.00 1163.64 2090.00 872.809 1567.50 698.325 1254.00 43 3491.68 6371.67 745.90 3135.83 1164.01 2090.56 873.088 1567.92 698.549 1254.33 44 3192.79 6373.33 746.46 3136.67 1164.38 2091.11 873.368 1568.33 698.772 1254.67 45 3493.94 6J75.00 747.033137.50 1164.77 3091.67 873.654 1568.75 699.003 1255.00 46 3495.01) 6276.67 1747. 6113138. 33 ! 1165. 15 2092.22 873.941 1569.17 699.231 1255.33 47 3496.23 6278.33 748.183139.17 1165.53 2092.78 874.227 1569.58 699.460 1255.67 48 49 3497.38 3498.52 6280.00 6281.67 748 75 3140.00 1749.333140.83 1165.91 1166.29 2093.33 2093.89 874.514 874.801 1570.00 1570.42 699.689 1256.00 699.9191256.33 50 3499.67 6283.33 1749.90 3141.67 1166.68 2094.44 875. 087 ' 1570. 83 700.1481256.67 51 3500.82 6285.00 1750.47 3142.50 1167.06 2095.00 875 374 1571.25 700.377 1257.00 52 3501.96 6286.67 1751.05 3143.33 1167.44 2095.56 875.6601571.67 700.606 1257.33 53 3503.1! 6288.331751.63 3144.171167.82 2096.11 875.947 1572.08 700. 836 11257. 67 54 3504.25 6290.00 1752.19 3145.00 1168.20 2096.67 876 283 1572.50 701.065 1258.00 55 3505.40 6291.67 1752.76 3145.83 1168.59 2097.22 876.520 1572.92 7'0 1.294 1258. 33 56 3506.55 6293.33 1753.34 3146.671168.97 2097.78 876.806 1573.33 701.523 1258.67 57 3507.6!) 6295.00 1753.91 3147.50 1169.35 2098.33 877.093 1573.75 701.7531259.00 58 3508.84 6296.67 1754.48 3148.331169.73 2098.89 877.379 1574.17 701.982 1259.33 59 3509.98 6298.33 1755.06 3149.17 1170.12 2099.44877.6661574 58 70-3.211 1259.67 170 TABLE XIV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 Curve. 10 Curve. 63 Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. M. 574.044 1033.33 492.116885.714 430.684 775.000 382.910 688.889 344.707 620.000 574.235 1033.01 492. 280 '885. 952 430.828 775.208 383.037689.074 314.822 620.167 I 574.420 1033.89 492.444886.190 430.971 775.417 383.165689.259 344.937 620.333 2 574 012 1034.17 492.604886.429 431.111 775.625 383. 28S 689.444 345.049 620.500 3 674.798 1034.44 492.703886.667 431.251 775.833 383.413 089.630 345.161 620.667 4 574.989 1034.72 492.927 880.905 431.394 776.042 383.541 689.815 315.275 620.833 5 575.180 1035.00 493.091 887.143 431.537 776.250 383.608 690.000 345.390 621.000 6 575.372 1035.28 493.255 887.381 431.681 776.458 3S3.79G 690.185 345.505 621.167 7 575.503 1035.50 493.419 887.619 431.824 776.607 3S3.923 690.370 345.619 621.333 8 575.749 1035.83 493.578 887.857 431.964 776.875 384.048 090.556 345.731 621.500 9 575.935 1036.11 493.738 888.095 432.104 77". 083 384.172 690.741 345.843 621.667 10 570.120 1030.39 493 902 888.333 482.247 77". 292 384.299 090.926 345.958 621.833 11 570.317 1030.67 494.060 888.571 432.390 77". 500 384.427 691 .111 346.073 622.000 13 570.508 1036.94 494.229 888.810 432.534 77". 708 384.664 691.290 346.187 622.167 13 570.699 1037.22 494.393 889 048 432 677 77". 917 334.082 691.481 346.302 622.333 14 570.880 1037.50 494.553 889.280 432 817 778.125 384.800 691.067 340.414 622.500 15 577.072 1037.78 494.713 889.524 432.957 778.333 384.930 091.852 346.526 622.667 16 577.203 1038.06 494.870 889.702 433.100 778.542 385.058i 092. 037 346.641 622.833 17 577.454 1038.33 495.040 890.000 433 243 778.750 385.185 692.222 346.755 623.000 18 577.645 1038.61 495.204 890.238 433.387 778.958 385.313 692.407 346.870 623.167 19 577.836 1038.89 495.368 890.470 433.530 779.167 385.440 692.593 346.985 623.333 20 578.023 1039.17 495.528 890.714 433.670 779.375 385.504 692.778 347.097 623.500 21 578.209 1039.44 495.087 890.952 433 810 779.583 385.088 092.903 347.209 623. 667 22 578.400 1039.72 495.851 891.190 433.953 779.792 385. 8161693. 148 347.323 6243. 833 23 578.591 1040.00 490.015 891.429 434.090 780.000 385.943 093.333 347.438 624.000 24 578.782 1040.28 490.179 891.667 434.240 780.208 386.071 093.519 347.553 624.167 25 578.973 1040.50 490.342 891.905 434.383 780.417 386.198 093.704 347.668 624.333 26 579.104 1040.83 490.500 892.143 434.526 780.625 386.326 693.88!) 347.782 624.500 27 579.355 1041.11 490. 6iO 892.381 484.6ft) 780.833 386.453 694.074 347.897 624.667 28 579.542 1041.39 490.830 892.019 434.809 781.042 386.577 694.259 348.009 624.833 29 579.728 1041.67 496.989 892.857 434.949 781.250 386.702 694.444 348.121 625.000 30 579.919 1041.94 497.153 893.095 435.093 781.458 386.829 094.630 248.236 625.167 31 580.110 1042.22 497.317 893.333 435.236 781.007 386.957 694.815 348.350 625.333 32 580.301 1042.50 497.481 893.571 435.379 781.875 387.084 695.000 348.465 625.500 33 580 492 1012.78 497.045 893.810 435.523 782.083 387.212 095.185 348.580 625.667 34 580 083 1043.06 497.808 894.048 435.000 782.292 387.339 095.370 348.694 625.833 35 580.874 1043.33 497.972 894.286 435.809 782.500 387.466 095.556 348.809 626.000 36 581.000 1043.01 498.130 894.524 435.953 782.708 387.594095.741 348.924 626.167 37 581.257 1043.89 498.300 894.762 430.090 788.917 387.721 695.926 349.039 626. 333 38 581.448 1044.17 498.464 895.000 436.239 783.125 387.849 096.111 349.153 020.500 39 581.639 1044.44 498.628 895.238 436.383 783.333 387.976 696.296 349.268 626.667 40 581.830 1044.72 498.791 895.476 430.520 783.542 388.104 696.481 349.3*3 626.833 41 582.021 1045.00 498.955 895.714 436.669 783.750 388.231 696. (567 349.498 627.000 42 582.207 1045.28 499.115895.952 436.809 783.958 388.355 096.852 349.610 627.167 43 582.394 1045.50 499.275896.190 436.949 784.107 388.480 697.037 349.721 627.333 44 582.585 1045.83 499.438896.429 437.092 784.375 388.607 697.222 349.836 627.500 45 582.776 1046.11 499.602896.607 437.236 784.583 388.735 697.407 349.951 627.007 46 582.907 1046.39 499.706890.905 437.379 784.792 388.862 697.593 350.006627.833 47 583.158 1046.07 199.930 897. 143 437.522 785.000 388.990 697.778 350.180628.000 48 583.349 1040.94 500.094897.381 437.666 785.208 389.117 697.963 350.295 028.107 49 583.540 1047.22 500.257897.619 437.809 785.417 389.244 698.148 350.410 628.333 50 583.731 1047.50 500.421 897.857 437.953 785.625 389.372698.333 350.525628.500 51 583.922 1047.78 500.585 89S.095 438.090 785.833 389.499 698.519 350.639628.667 52 584.113 1048.00 500.7491898.333 438.239 786.042389.627 698.704 350.754 028.833 53 584.304 1048.33 5D0.913898.571 438 383 786.250389.754 698.889 350 809 629.000 54 584.495 1048.01 501. 070 S9S. 810 438.520 786.458389.882 699.074 350.983 0->9.167 55 584 . 080 1048.89 501.-J40 8SW.048 438.669 780.007390.009 699.259 351.098 029.333 56 584.877 1049,17 501.404 899.280 438.813 780.875390.137 699.444 351.213 029.500 57 685.061) 1049 44 501. 508; 899. 524 438.950787.083390.264 699.630 351.328 029.007 58 585.200 1049.72 501.732] 899. 702 439.099 787.292 390. 392 1 699. 815 351.442029.833 59 171 TABLE XIV. ACTUAL TANGENTS, ETC. 63 1 Curve. 2 Curve. 3 Curve. 4 Curve. 5 Curve. M. ~O~ Tan. 3511.13 Arc. Tan. Arc. Tan. Arc. 2100.00 Tan. 877.952 Arc. Tan. Arc. 1260.00 16300.00 1755.633150.00 1170.50 1575.00 702.440 1 35 1 2 . 28 630 1 . 07 1 756 . 20 31 50 . 83 1170.8Sl2100.5ti 878. 23U 1575.42 702. (570 1260.33 > 3513.42 6303.33 1756.783151.67 1 1 71 . 20 2 1 ( ) 1 . 1 1 ; 8 , 8 . 520 1 575 . s:j 702 . 899 1260.67 3 3514.57 6305 . 00 1 757 . 35 i 3 1 52 . 50 1171.64:2101.07 878.812 157(5.25 703.128 1261.00 4 3515.71 6308 . 67 1 757 . 92 \ 31 53 . 33 1172.03 2102.22 819. 09ti 1576.07703.357 1261.33 5 3510.86 6308.33 1758.4913154. 1? 1172.41 2102.78 879.385 1577.08 7'03.587 1261.07 6 3518.01 6310.00 1759.07,3155.00 1172.79 2103.33 879.672 1577. 50:703. 816 1262.00 7 3519.15 6311.67 1759.64 3155.83 1173.17 2103.89 879.958 1577. 92 1704. 045 1262.33 8 3520.30 6313.33 1760.21 3156.67 1173.55 2104.44 880.245 1578.33704.274 1262.07 9 3521.44 6315.00 1760.79 3157.50 1173.94 2105.00 880.531 1578.75 704.504 1263.00 10 3522.59 6316.67 1761.36 3158.33 1174.32 2105.50 880.818 1579.17 704.733 1263.33 11 3523 73 6318.33 1761.93 3159.17 1174.70 2106 11 881.104 1579.58704.902 1263.67 12 3584.88 6320.00 1762.50 3160.00 1175.08 2106.67 881.391 1580.00705.191 1264.00 13 3526.06 6321.67 1763.09 3160.83 1175.47 2107.22 881.685 1580.42705.426 1264.33 14 3527.23 6323.33 1763.68 3161.67 1175.86J2107.78 881.978 1580.831705.661 1264.07 15 3528.38 6325.00 1764.25 3162.50 1176. 2512108. 33 882.205 1581. 25 7'05. 891 1205.00 16 3529.52 63-36.67 1761 83 3163.33 1176.632108.89 882.551 1581.07 700.120 1205.33 17 3530. G7 6328.33 1765.40 31(54.17 1177.01 2109.44 882 . 838 1 582 . ( >8 , 7 00 . 349 1205.07 18 3531.81 6330.00 1765.97 3165.00 1177.39 2110 00 883 .12411 582 . 50 7'00 . 578 1200.00 19 3532.96 6331.67 1766.54 3165.83 1177.77 2110.56 883.41111582.92700.808 1266.33 20 3534 11 6333.33 1767.12 3166.67 1178.16 2111.11 883.008 1583.33 707.037 1266.67 21 3535.25 6335.00 1767.69 3167.50 1178.54 2111.67 883.984 1583.75707.260 1207.00 22 3536.40 6336.67 1768.26 3168.33 1178.92 2112.22 884. 271 j 1 581. 17: 7t '7. 4 95 1207.33 23 3537.54 633S.33 1768.84 3169.17 1179.30 2112.78 884.557 1584.58 707.725 1207.07 24 3538.69 6310.00 1769.41 3170.00 1179.68 2113.33 884.814 1585. 00 707. 954 1268.00 25 3539.84 6341.67 1769.98 3170.83 1180.07 2113.89 885.130 1585.42708.183 1268.33 26 3540.98 6343.33 1770.56 3171.67 118J.45 2114.44 885.417 1585. 83 1708.41 3 1268.67 27 3542.16 6345.00 1771.14 3172.50 1180.81 2115.00 885.710 158(5. 25 17 OS. 04 7 1269.00 28 3543.33 6346.67 1771.73 3173.33 1181.23 2115.5(5 880.001 1586 67708.882 1269.33 29 3544.48 6348.33 1772.30 3174.17 1181.61 2116.11 880.291 1587.08 709.112 1269.67 30 3545.62 6350.00 1772.88 3175.00 1182.00 2110.67 883 . 577 1587.50 7'09.341 1270.00 31 3546.77 6351.67 1773.45 3175.83 1182.38 2117.22 880 804 1587.92 709.570 1270.33 32 3547.91 6353.33 1774.0:3 3176.67 1182.76 2117.78 887.150 1588.33 7'09.800 1270.07 33 8649.06 6355.00 1774.59 3177.50 1183.14 2118.33 887.437 1588.75 710.029 1271.00 34 3550.21 6356.67 1775.17 3178.33 1183.52 2118.8!) 887.723 1589.17 710.258 1271.33 35 3551.38 6358.33 1775.76 3179.17 1183.92 2119.44 888.017 158!). 58 710.493 1271.67 36 3552.55 6360.00 1776.34 3180.00 1184.31 2120. OU 888.311 1590.00 710.728 1272.00 37 3553.70 6361.67 1776.92 3180.83 1184.69 2120.56 888.597 1590.42 710.957 1272.33 38 3554.85 6363.33 1777.49 3181.67 1185.07 2121.11 888.884 1590.83 711.187 1272.07 39 3555.99 6365.00 1778.06 3182.50 1185.45 2121.67 889.170 1591.25 711.410 1273.00 40 3557.14 6366.67 1778.63 3183.33 1185.83 2122.22 889.457 1591.67 711.645 1273.33 41 3558.31 6368.33 1779.22 3184.17 1186 23 2122.78 889.751 1592.08 711.880 1273.07 42 3559.49 6370.00 1779.81 3185.00 1186.02 2123.33 890.044 1592.50 712.115 1274.00 43 3560.63 6371.67 1780.38 3185.83 1187.00 2123.89 890.331 1592.92 712.344 1274.33 44 3561.78 6373.33 1780.96 3186.67 1187.38 2124.44 <90.G17 1593 33 712.573 1274.07 45 3562.93 6375.00 1781.53 3187.50 1187.76 2125.00 890.904 1593.75 712.803 1275.00 46 3564.07 6376.67 1782.10 3188.33 1188.15 2125.56 891.190 1594. 17; 71 3. 032 1275.33 47 3565.25 6378.33 1782.69 3189.17 1188.54 2126.11 891.484 1594.58713.267 1275.67 48 3566.42 6380.00 1783.28 3190.00 1188.93 2126.C.7 891.778 1595.00 713.502 1276.00 49 3567.57 6381.67 1783.85 3190.83 118J.31 2127.22 892.064 1595. 42! 713. 731 1276.33 50 3568.71 6383.33 1784.42 3191.67 1189.69 2127 78 892.351 1595.83 713.960 1270.07 51 3569.86 6385.00 1781.99 3192.50 1190 08 2128.33 892.638 1596.25 714.190 1277.00 52 3571.00 6386.67 1785.57 3193.33 1190.46 2128.89 892.924 1596.67:714.419 1277.33 53 3572.18 6388.33 1786.15 3194.17 .190.85 2129.41 893.218 1597.08714.654 1277.07 54 3573.35 6390.00 1786.74 3195.00 1191.24 2130.00 893.511 597.50 714.889 1278.00 55 3574.50 6391.67 1787.32 3195.83 1191.62 2130.56 893.798 1597.92715.118 1278.33 56 8575.65 8393.88 1787.893196.67 1192.00 2131.11 894 085 1598.33715.347 1278.07 57 3576.79 6395.00 1788.46 3197.50 1192.39 2131.67 8!)4 371 1598.75:715.577 1279.00 58 3577.94 6396.67 1789 03 3198.33 1192.77 2132 22 894.658 1599. 17! 715. 806 1279.33 59 3579.11 6398.33 1789.62 3199.17 1193.16 2132! 78 894.951 1599. 58 171 6. 041 1279.67 TABLE XIV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 Curve. 1O Curve. 63 M. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. | Arc. 585.451 1050.001501.895 900.000 439.243,787.500 390 .519 700 . 000 351 . 557 630 . 000 O 585.642 1050. 28 1502. 059 900.238 439.386 787.708 390 646 700 . 1 85 351 . 672 630 . 1 67 1 585.832 1050.56 502.223 900.470 439.529 787.917 390 . 7 74 700 . 370 35 1 . 787 630 333 586.024 1050.83 502.387 900.71- 439.673 788.125 390.901 700.556351.901 630.500 3 586.215 1051 . 1 1 502.551 439.816 788.333 391.029 700. 741; 352. 01 6 630. 667 4 586.406 1051.39 502.7I4'901.190 439.960 788.542 391.150 700.926352.131 630.833 5 586.597 1051.67 502.878 901.429 440.103 788.750 391.284 701.111 352.246 631.000 6 586.7881051.94 503 042 901. 667 440.246 788.958 391.411 701.296352.360631.167 7 586.979 1052.22 503.206901.905 440.390 789.167 391.539 701. 481 1&52. 475 631. 333 8 587.170 1052.50 503.370 902.143 440.5:33789.375 391.660 701.667 352.590 631.500 9 587.361 1052.78 503.533 902.381 440.676789.583 391.794 701.852 352.705 631.667 1O 587.553:1053 06 503.697902.619 440.820789.792 391.921 702.037 352.819631.833 11 587.744 1053.33 503.861 902.857 440.963790.000 392 048 702.222 352.934632.000 13 587.939 1053:61 504.029 903.095 441.110790.208 392.179 702.407353.052 632.167 13 588.135 1053.S9 504.197 903.333 441.257 790.417 392.310 702.593353 169632.333 14 588.326 1054.17 504.361 903.571 441.400 790:625 392.437 702.778 353.284 632.f,00 15 588.517 1054.44 504.524 903.810 441.544 790.833 392.565 702.963 353.399632.667 16 588.7081054.72 504.688 904.048 441.687 791.042 392.692 703.148 353.513632.833 17 588.900 I055.ni 504.852 904. 28( 441.830 791.250 392.820 703.333 353.628633.000 18 589.091 1055.28 505.016 904.524 411.974 791.458 392.947 703 519 353.743 633.167 19 589.282 1055.56 505.180 904.762 442.117 791.667 393.074 703.704 353.858 633 333 2O 589.473 1055.83 505.343 905.000 442.260 791.875 393 202 703.889 353.972 633 500 21 589.664 1056 . 1 1 505.507 905.238 442.404 792.083 393.329 704 074 354.087 633.667 589.855 1056.39 505.671 905.476 442.547 792.292 393.457 704.259 354.202 633.833 23 590.046 1056.67 505.8:35 905.714 442. 69( 792.500 393.584 704 444 354.317 634.000 24 590.237 1056.94 505.999 905.952 442.834 792.708 393.712 704.630 354.431 634.167 25 590.428 1057 22 506.163 906.190 442.977 792.917 393.839 704.815 354.546 6:34.333 26 590.624 1057.50 506.330 906.429 443.124 793.125 393.970 705.000 351. (164 634.500 27 590.820 1057.78 506.498 906.667 443.271 793.333 394.100 705.185 354.781 634.667 28 591.011 1058.06 506.662 906.905 443.414 793.542 394.228 705.370 354.896 634.833 29 591.202 1058.33 5C6.826 907.143 443.558 793.750 394.355 705.556 355.011 635.000 30 591.393 1058.61 506.990 907.381 443.701 793.958 394.483 705.741 355.126 635.167 31 591.584 1058.89 507.15-i 907.619 443.844 794.167 394.610 705.926 355 240 635.333 32 591.775 1059.17 507.317 907.857 443.988 794.375 394.738 706.111 355.355 635.500 33 591 . 966 1059.44 507.481 908.095 444.131 794.583 394.865 706.296 355.470 635.667 34 592.162 1059.72 507.649 908.333 444.278 794.792 394.996 706.481 355.587 635 833 35 592.358 1060.00 507.817 908.571 444.425 795.000 395.126 706.667 355.705 636.000 36 592.549 1060.28 507. 9S1 908.810 444.568 795.208 395.254 706.852 355.820 636.167 37 592.740 1060.50 508.145 909. (-48 444.712 795.417 395.381 707.037 355.9:34 636.333 38 592.931 1060.83 508.308 909.286 444.855 795.625 395.509 707.222 356.049 636.500 39 593.122 1061.11 508.472 909.524 444.998 795.833 395.636 707.407 356.164 636.667 40 5U8.318 1061.39 508.640 909.76-.' 445 145 796.042 395.767 707.593 356.282 636.833 41 593.514 1061.67 508.808 910.000 445.292 796.250 395.898 707.778 356.399 637.000 42 593.705 1061.94 508.972 910.238 445.436 796.458 396.025 707.963 356.514 637.167 43 593.896 1062.22 509.136 910.476 445.579 796.667 396.152 708.148 356.629 637.833 44 594.087 106:2.50 509.299 910.714 445.722 796.875 396.280 "08.333 356.743 637.500 45 594.278 1062.78 509.463 910.952 445.866 797.083 396.407 "08.519 356 858 637.667 46 594.474 1063.06 509.631 911.190 446.013 797.292 396.538 "08.704 356.976 637.833 47 594.670 1063.33 509.799 911.429 446.160 797.500 396.669 "08.S89 357.093 638.000 48 594.861 1063.61 509.963 911.887 446.303 797.708 396.796 "09.074 357.Ji08 638.167 49 595.052 1063.89 510.127 911.905 416.446 797.917 396.924 '09.259 357.323 638.333 5O 595.243 1064.17 510.290 912.143 446.590 798.125 397.051 "09.444 357.438 638.500 51 595 434 1064.44 510.454 912.381 446.733 798.333 397.178 "09.630 357. flf* i38.G67 52 595.630 1084.72 510.622 912.619 446.880 798.542 397.309 "09.815 357.670638.833 53 595.826 1065.00 510.790 912.857 447.027 798. 7'50 397.440 "10.000 357. 7>7 639 000 54 596.017 1065.28 510.954 913.095 447.170 798.958 397.567 "10.185 357.902639.167 55 596.208 1065.56 511.118 913.333 447.314 799.167 397.695 "10.370 358.017639.333 56 596 399 1065.83 511.281 913.571 447.457 799.375 307.822 "10.556 358.132639.500 57 596.590 1066.11 511.445 913.810 4(7.600 799.583 397.950 -"10.741 358.246639 667 58 596.786 1066.39 511.613 914.048 447.747 1*99 792 398.080 "10.926 358.364639.833 59 173 TABLE XIV. ACTUAL TANGENTS, ETC. 64 1 Curve. 3 Curve. 3 Curve. 4 Curve. 5 Curve. ^7 Tan. Arc. Tan. Arc. Tan. 1193.55 Arc. 2133733 Tan. Arc. Tan. Arc. o 3580.29 6400.00 1790.21 3200.00 895.245 1600.00 716.276 1280.00 i 8581.43 6401.67 1790.78 3200.83 1193.93 2133.8'J8J)5.532 1600.42 716.505 1280.33 3 3582.58 6403 33 1791.35 3201.67 1194.32 2134.44895.818 1600.83 716.734 1280. (57 3 3583.75 6405.00 1791.94 3202.50 1194.71 2135.00896.112 1601.25 716.969 1281.00 4 3584.93 6406.67 1792.53 3203.33 1195.10 2135.56896.405 1601.67 717.204 1281.33 5 3586. OT 6408.33 1793.10 3204.17 1195.48 2136.11 896.692 1602.08 717.434 1281.67 6 3587.22 6410.00 1793.6!^ 3205.0D 1195.86 2136.67 896.979 1602.50 717.663 1282.00 7 3588.39 6411.67 1794.26 3205.83 1196 25 2137.22 897.272 1602.92 717.898 1282.33 8 3589.5? 6413.33 1794.85 3206.67 1196.65 2137.78897.566 16d3.33 718.133 1*82.67 9 3590.71 6415.00 1795.4-2 3207 50 1197.03 2138.33 897.852 1603.75 718.362 1283.00 1O 11 3591.86 3593.03 6416.67 6418.33 1796.00 1796.58 3208.33 3209.17 1197.41 1197.80 213S.89 2139.44 898.139 898.433 1604.17 1604.58 718.591 7 IS. 82(5 1283.33 1283.67 13 3594.21 6420.00 1797.17 3210.00 1198.19 2140.00 898.726 1605.00 7 19.. 061 1284.00 13 3595.36 6421.67 1797.74 3210.83 1198.58 2140.56 899.013 1605.42 719.291 1284.33 14 3596.50 6423.33 1798.32 3211.67 119S.96 2141.11 899.300 1605.83 719.520 1284.67 15 3597.68 6425.00 179S.90 3212.50 1199.35 2141.67 899.593 1606.25 719.755 1285.00 16 3598.85 6426.67 1799.49 3213.33 1199.74 2142.22 899.887 1606.67 719.990 1285 33 17 3600.03 6428 33 1800.08 3214.17 1200.13 2142.78 900.181 1607.08 720.225 1285.67 18 3601.20 6430.00 1800.67 3215.00 1200.52 2143.33 900.474 1607.50 720.460 1286.00 19 3602.35 6431.67 1801.24 3215.83 1200.91 2143.89 900.761 1607.92 720.689 1286.33 2O 3603.49 6433.33 1801.81 3216.67 1201.29 2144.44 901.047 1608.33 720.918 1286.67 31 3604.07 6435.00 1802.40 3217.50 1201.68 2145.00 901.341 1608.75 721.153 1287.00 22 3(505.84 6436.67 1802.99 3218.33 1202.07 2145 53 901.635 1609.17 721 .388 1287.33 23 3606.99 6438.33 1803.56 3219.17 1202.45 2146.11 901.921 1609.5S 721.618 1287.67 24 3608.13 6440.00 1804.13 3220. OJ 1202.83 2146.67 902.208 1610.00 721.847 1288.00 25 3609.31 6441 . 67 1801.72 3220.85 1203.23 2147.22 9">2.502 1H10.42 722.082 1288.33 26 3610.48 6443.33 1805.31 3221.67 1203.62 2147.78 902.795 1610.83 722.31? 1288.67 21 3611.66 6445.00 1805.89 3222.50 1204.01 2148.33 903.089 1611 25 722.552 1289.00 28 3612.83 6446.67 1806.48 3223.33 1204.40 2148.89 903.383 1611.67 722.78? 1289.33 29 3613.98 6448.33 1807.05 3224.17 1204.78 2149.44 903.669 1612.08 723.016 1289.67 30 3615.12 6450.00 1807.63 3225.00 1205.16 2150.00 903.956 1612.50 723.245 1290.00 31 3616.30 6451.67 1808.2! 3225.83 1205 56 2150.56 904.249 1612.92 723.480 1290.33 32 3617.47 6453.33 1808.80 3226.67 1205.95 2151.11 904 543 1613.33 723.715 1290.67 33 3618.65 6455.00 1809.39 3227.50 1206.34 2151.67 904.837 1613.75 723.950 1291.00 34 3619.82 (5456.67 1809.9S 3228.33 1206.73 2152.22 905.131 1614.17 724.185 1291.33 35 36-20.97 6458.33 1810.55 3229.17 1207.11 2152.78 905.417 1614.58 724.415 1291.67 36 3622.11 6460.00 1811.12 3230.00 1207.50 2153.33 905.704 1615.00 724.644 1292.00 37 3623 29 6461.67 1811.71 3230.83 1207.89 2153.89 905.997 1615.42 724.879 1292.33 38 3621.46 6463.33 1812.30 3231.67 1208.28 2154.44 906.291 1615.83 725.114 1292.67 39 3625.64 6465.00 1812.88 3232.50 1208.6? 2155.00 90,3.585 1616.25 725.349 1293.00 4O 3626.81 6466.67 1813.47 3233.33 1209.06 2155.56 906.878 1616.67 725.584 1293.33 41 3627.99 6468.33 1814.06 3234.17 1209.45 2156.11 907.172 1617.08 725.819 1293.67 43 3629.16 6470.00 1814.65 3235.00 1209.84 2156.67 907.466 1617.50 726.054 1294.00 43 3630.31 6471.67 1815,22 3235.83 1210.23 2157.22 907.752 1617.92 726.283 1294.33 44 3631.45 6473.33 1815.79 3236.67 1210.61 2157.78 908.039 1618.33 726.512 1294.67 45 3632.63 6475.00 1816.38 3237.50 1211.00 2158.33 908.333 1618.75 726.747 1295.00 46 3633.80 6476.67 1816.97 3238.33 1211.39 2158.89 908.626 1619.17 726.982 1295.33 47 3634.98 6478.33 1817.55 3. '39. 17 1211.78 2159.44 908.920 1619.58 727.217 1295.67 48 3636.15 6480.00 1818.14 3240.00 '212 17 2160.00 909.214 1620.00 727.452 1296.00 49 3637.33 6481.67 1818.73 3240.83 1212.57 2160.56 909.507 1620.42 727.687 1296. 33 50 3638.50 6483 33 1819.32 3241 67 1212.96 8ttl.11 909.801 1620.83 727.922 1296.67 51 3639.67 6485.00 1819.90 3242.50 1213.35 2161.67 910.095 1621.25 728.157 1297.00 53 3640.85 6486 67 1820.49 3243.33 1213.71 2162.22 910. 3S9 1621.67 728.392 1297.33 53 3641.99 6488.33 1821.06 3244.17 1214.12 2162.78 910.675 1622.08 728.621 1297.67 54 3643.14 6490.00 1821.64 3245.00 1214.51 21 a<*. 83 910.962 1622.50 728.851 1298.00 55 3644.32 6491.67 1822.22 3245.83 1214.90 2163.89911.255 1622.92 729.086 1298.33 56 3645.49 6493 33 1822.81 3246.67 1215 29 2164.44 911.549 1623.33 729.321 1298.67 57 3646.66 6495.00 1823.40 3247.50 1215.68 21 65.00! 91 1.843 1623.75 729.556 1299 00 58 3647.84 6496.67 1823.99 3248.33 1216.07 2165.56912.136 1624.1? 729 791 1299.33 59 3649. Olj 6498. 33 1824.57 3249.1? 1216. 4612166. 11 : 912. 430 1624.58 730.026 1299.67 174 TABLE XIV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 Cnrve. 1O Curve. 64 Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. M. 596.982 1066.67 511.781 9H.28C) 447.894 800.000398.211 711.111 358.482 640.000 597.173 1066.94 511.945914.524 448.038 800.208398.338 711.296 358.596 640.167 1 597.364 1067.22 512.109914.762 448.181 800.417398.466 711.481 358.711 640.333 3 597.560 1067.50 512.276915.000 448.328 800. 625 '398 596 711.667 358.829 640.500 3 597.756 1067.78 512.444 915. 23H 448.475 800. 833 '398. 727 711.852 358.946 640.667 4 597.94; 1068.06 512.608 915.476 448.618 801.042 398.854 712.037 359.061 640.833 5 598.138 1068 .33 512.772 915.714 448.762 801.250 39S.982 712.222 359.176 641.000 6 598.334 1068.61 512.940 915 952 448.909 801.458 399.113 712.407 359.293 641.167 7 598.530 1068.89 513.108 916.190 449.055 801.667 399 . 243 712.593 359.411 641.333 8 598.721 1069.17 513.272 916.429 449.199 801.875 399.371 712.778 359.526 641.500 9 598.912 1069.44 513.435 916.667 449.342 802.083 399.498712.963 359.640 641.667 1O 599.108 1069.72 513.603 916.905 449.489802.292 399.629713.148 359.758 641.833 11 599.304 1070.00 513.771 917.143 449 636802.500 399.759713.333 359 876 642.000 13 599.495 1070.28 513.935 917.381 449.779802.708 399.887713.519 359.990 642.167 13 599.686 1070.56 514.099 917.619 449.923802.917 400.014713.704 300.105 642.333 14 599.882 1070. as 514.267 917.85? 450. 07 0803." 125 400.145713.889 360.223 642.500 15 000.077 1071.11 514.435 918.095 450.217803.333 400.27'6714.074 360.340 642.667 16 600.273 1071.39 514.603 918.333 450.364803.542 400.406714.259 360.458 642.833 17 600.469 1071.67 514.770 918.571 450.511 803.750 400.537714.444 360.576 643.000 18 600.660 1071.94 514.934 918.810 450.654 803.958 400.664 714.630 360.690 643.167 19 600.851 1072.2v 515.098 919.048 450 797 804.167 400.792 714.815 360.805 643.333 30 601.047 1072.50 515.266 919.286 450.944 804.375 400.922 715.000 360 923 643.500 31 601.243 1072.78 515 434 919.524 451.091 804.583 401.053 715.185 361.040 643.667 33 601.434 1073.06 515.598 919.762 451.234 804.792 401.181 715.370 361.155 643.833 33 601.625 1073.33 515.761 920.000 451 378 805.000 401.308 715.556 361.270 644.000 34 601.821 1073.61 515.929 920.238 451.525 805 208 401.439 715.741 361.387 644.167 35 602.017 1073.89 516.097 920.476 451.672 805.417 401.569 715.926 361.505 644.333 36 602.213 1074.17 516.265 920.714 451.819 805.625 401.700 716.111 361.623 644.500 37 602.408 1074.44 516.433 920.952 451.966 805.833 401.831 716.296 361.740 644.667 38 602.600 1074.72 516.597 921 190 452.109 806.042 401.958 716.481 361.855 644.833 39 602.791 1075.00 516.761 921.429 452.252 806.250 402.085 716.667 361.970 645.000 3O 602.987 1075.28 516.929 921.607 452.399 806.458 402.216 716.852 362.087 645.167 31 603.182 1075.56 517.096 921 905 452.546 806.667 402.347 71 \037 362.205 645.333 33 603.378 1075.83 517.264 922.143 452.693 806.875 402.477 7r.222 362.322 645.500 33 603.574 1076.11 517.43V 1 922.381 452.840 807.083 402. 60H 7r.407 362.440 645.067 34 603.765 1076.39 517.596 922.619 452.983 807.292 402.735 7r.593 362.555 645.833 35 603.956 1076.67 517.700 922.857 453.127 807.500 402.863 717.778 362.670 646.000 36 604.152 1076.94 517.928 923.095 453.274 807.708 402.994 717.963 362.787 646.167 37 604.348 1077.22 518.096 923.333 453.421 807.917 403.124 718.148 362.905 646.333 38 604.544 1077.50 518.264 923.571 453.568 808.125 4U3.255 718.333 363.022 646.500 39 604.740 1077.78 518.431 923.810 453.715 808 333 403.385 718.519 363.140 646.667 4O 604.935 1078.06 518.599 924.048 453.861 808.542 403.516 718 704 363.258 646.833 41 605.131 1078.33 518.767 924.280 454.008 808.750 403.647 718.889 363.375 647.000 43 605.322 1078.61 518.931 924.524 454.152 808.958 403.774 719.074 363.490 647.167 43 605.513 1078 89 519.095 924.762 454.295 809.167 403.902 719.259 363.605 647.333 44 605.709 1079.17 519.263 925.000 454.442 809 375 404.032 719.444 363.722 647.500 45 605.905 1079.44 519.431 925.238 454.589 809.583 404.163 719.630 363.840 647.667 46 606.101 1079.72 519 599 925.476 454.736 809.792 404.294 719.815 3G3.957 647.833 47 606.297 1080.00 519.766 925.714 454.883 810.000 404.424 720.000 364.075 648.000 48 606.493 1080.28 519.934 925.952 455.030 810.208 404.555 720.185 364.193 648.167 49 | 606.689 1080.56 520.102926.190 455.177 810 417 404.686 720.370 -564.310 648.333 5O 606.884 1080.83 520.270926.429 455.324 810.625 404.816 720.556 364.428 648 500 51 607.080 1081.11 520.438926.667 455.471 810.833 404.947 720 741 364.546 648.607 53 607.271 1081.39 520. 602 '926. 905 455.614 811.042 405.074 720.926 364.660 648.833 53 607.462 1081.67 520.766 927.143 455.757 811.250 405.202 721.111 364.775 649.00( 54 607.658 1081.9) 520.934 927.381 455.904 811.458 405.332 721.296 364.893 649 107 55 607.854 1082.2-,' 521.101 927.619 456.05! 811.007 405.463 721.481 305.010 049.333 56 608.050 1082.50 521.269 927.857 456.198 811.875 405.594 721.667 365.128 649 500 57 608.246 1082.78 521.437 928.095 456.345 812.083 405.724 721.852 365.245 649.667 58 608.442 1083.06 521.605 928.333 456.492 812.29.' 405.855 722. 037 365.363 649.833 59 175 TABLE XIV. ACTUAL TANGENTS, ETC. 65 1 Carve. 2 Curve. 3 Curve. 4 Curve. 5 Curve. IST ~~o Tittt. 3~050~l9 Arc. Tan. A re. Tan. Arc. Tan. Arc. Tan. Arc. 6500.03 1825.163250.00 1216.85 2160.67 912.724 1625.00 730.261 1300.00 i 8051.8(3 0501 . 67 18^5.75'3250.H3 1217.25 2307.22 913.018:1025.42 730.496 1300.33 2 805:3.54 05U3 . 33 1826. 34 '325 1.07 1217.64 2107.78 913.311 1025.83 730. 731 i 1300. 67 3 305:3.71 0505.00 1826.923252 50 1218.03 2168.33 913.005 1020.25 730.966 1301.00 4 3054.89 6500 07 1827.51 3253.33 1218.42 2168.89 913.899 1020.07 731.201 1301.33 5 3056.06 6508.33 1828.10 3254.17 1218.81 2169.44 914.192 1027.08 731.436 1301.67 6 3057.24 6510.00 1828.68 3255.00 1219.20 2170.00 914.480 1027.50 731.671 1302.00 7 3058.41 6511.67 1829.27 3255.83 1219.00 2 70.56 914.780 1027.92 731.906 1302.33 8 3059.58 6513 33 1829.86 3256.67 1219.99 2 71.11 915.073 1028.33 732.140 1302.67 9 3060.76 6515.00 1830.45 3257.50 1220.38 2 71.67 915.307 1628.75 732.375 1303.0J 1O 3661.93 6516.67 1831.03 3258.33 1220.77 2 72.22 915.661 1629.17 732.010 1303 33 11 3603.11 6518.33 1831.62 3259.17 1221.16 2 72.78 915.955 1629.58 7'32.845 1303 07 12 3664.28 6520.00 1832.21 3200.00 1221.55 2 73.33 916.248 1030.00 733.080 130400 13 3605.40 6521.67 1832.80 3260.83 1221.95 2 73.89 916.542 1030.42 733.315 1304.33 14 3000.63 6523.33 1833.38 3261.67 1222.31 2 74.44 916.830 1030.83 733.530 1304.67 15 3007.81 6525.00 1833.97 3262.50 1222.73 2 75.00 917.129 1031.25 7'33.785 1305.00 16 3668.98 6526.67 1834.50 3263.33 1223.12 2 75.56 917. 423| 1031. 07 734.020 1305.33 17 3670.16 6528.33 1835.15 3264.17 1223.51 2176.11 817.717 1032 08 734.255 1305.6? 18 3671.33 6530.00 1835.73 3265.00 1223.90 2176.67 918.010 1632.50 734.490 1306.00 19 3672.51 6531.67 1830.32 3265.83 1224.29 2177.22 918.304 1632.92 734.725 1306.33 20 3673.68 6533.33 1836.91 3268.67 1224.69 2177.78 918.598 1033.33 734.960 1306.67 21 3674.85 6535.00 18:57.49 3267.50 1225.08 2178.33 918.892 1033.75 735.195 1307.00 22 3676.03 6530.6; 1838.08 3268.33 1225.47 2178.89 919.185 1034. n 735.430 1307.33 23 3677.20 6538.33 1838/07 3209.17 12-25.80 2179.44 919.479 1034.58 735.005 1307.67 24 3678.38 0540.00 1839 20 327'0.00 1220.25 2180.00 919.773 1035.00 735.900 1308 00 25 3679.55 6541.67 1839.84 3270.83 1220 64 2180.56 920.000 1035.42 730.135 1308.33 26 1880.73 0543.33 1840.43 3271.07 1227.01 2181.11 920.360 1035.83 730.370 1308.67 27 3081.90 6545.00 1841.02 3272.50 1227.43 2181.07 920 654 1030.25 730 005 1309.00 28 3683.08 6546.67 1841.61 3273.33 1227.82 21M2.22 920.947 1630.07 730.840 1309.33 29 3081.25 6548.33 1842.19 3274.17 1228.21 2182.78 921.241 1037.08 737.075 1309.67 3O 3685.43 6550.00 1842.78 3275.00 1228.60 2183.33 921.535 1037.50 737.310 1310.00 31 36,%.0'J 0551 . 67 18J3.37 3275.83 1228.9'.) 21S3.S9 921.829 1037 92 737.545 1310.33 3 2 3087.77 6553.33 1843.95 3276.67 1229.3S 2184.44 922.122 1038.33 737.780 1310.67 33 3088.95 0555.00 1844.54 3-277.50 1229.78 2185.00 922.410 1038.75 738.015 1311.00 34 3090.12 0550.67 1845.13 3278.33 1230.17 2 1 85 . 56 922.710 1639.17 738.250 1311.33 35 3091.3'} 6558.33 1845.73 3-279.17 1230.57 2180.11 923.011 1639.58 738.491 1311.67 36 9602.58 0560.00 1846.33 328J 00 1230.01 2180.07 923.311 1040.00 738.732 1312.00 37 3693.70 6561.67 1846.92 3280.83 1231.36 2187.22 923.005 1640.42 738.907 1312.33 38 3094.88 6503.33 1847.51 3281.67 1231.75 2187.78 923.899 1640.83 739.202 1312.67 39 3696.05 0565.00 1848.09 3282.50 1232.14 2188.33 924.193 1641.25 739.437 1313.00 40 3697.23 6566.67 1848.68 3283.33 1232.54 2188.89 924.486 1641.67 739.672 1313.33 41 3688.40 6508.33 1849.27 3284.17 1232.93 2189.44 924 . 780 1642.08 739.907 1313.67 42 3699.58 6570.00 1849.86 3285.00 1233.32 2190 00 925.074 1642 50 740.142 1314.00 43 3700.75 6571.67 1850.44 3285.83 1233.71 2190.56 925.307 1642.92 740.377 1314.33 44 3701 93 6573.33 1851.03 3286.07 1234.10 2191.11 925.661 1643.33 740.012 1314.67 45 3703.13 6575.00 1851.63 3287.50 1234.50 2191.67 925.962 1643.75 740.852 1315.00 46 3704.33 0570.67 1852.23 3288 33 1234 90 2 192.2 J 926.263 1644.17 741.093 1315.33 47 3705.51 6578.3:; 1852.823289.17 1235.30 2192 78 926.556 1644.58 741.328 1315.67 48 8706.68 6580.00 1853.41 3290.00 1235.69 2193.33 926.850 1645.00 741.563 1316.00 49 3707.80 6581.07 1854.00 3290.83 1236.08 2193 89 927.144 1645.42 741.798 1316.33 5O 3709.03 6583.33 1854.58 3291.67 1236.47 2194.44 927.438 1645.83 742.033 1316 67 51 3710.21 6585.00 1855.17 3292.50 1230.80 2195.00 927.731 1646.25 742. 208 11317. 00 52 3711.38 6586.67 1855.76 3293.33 1237.25 2195.56 928.025 1646.07 742. 503 '13 17. 33 53 3712.58 6588.33 1856.36 3294 17 1237.66 2196.11 928.320:1047.08 742.744 1317.07 54 3713 79 6590.00 1856.96 3295.00 1238.00 2196.67 928. 027 i 1047. 50 742.984 1318.00 55 3714.96 6591.67 1857.55 3295.83 1238.45 2197.22 928. 920 '104 7. 92 743.219 1318.33 56 3716.14 6593.33 1858.14 3296. 67 ! 1238. 84 3197.78 929.214 1648.33 743.4.=v4 1318.07 57 3717.31 6595.00 1858.72 3297. 50 11239. 23 21 98. 33 929.508 1048''. 75 7 43.089 1319.00 58 3718.49 6596.67 1859.31 3298.33 12:i9.622l98.8J) 929.80111049.17 743.924 1319.33 59 3719.69 6598.33 1859.91 3299.17 1240. 0212199.44 9:>,0. 102 1049.58 744.105 1319.07 176 TABLE XTV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 Curve. 10 C Tan. urve. 65 Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Arc. M. 608. 638; 1083. 33 521.773 928.571 456 639 812.500 405.986722.222365.481 650.000 ~O~ 608.833 1083.61 521.941 928.810456.786812.708 406. 116 722. 40? J365. 598 050.167 1 609.059 1083.89 522.109 929.048456.933 812.917 406.247722.593365.716 050.333 2 609.225 1084.1? 522.277 929.286457.080 813.125 406.377 722.778 365.833 650.500 3 609.421 1084.44 522.445 929.524457.227 813.333 406.508 722.963 365.951 650.667 4 609.617 1084.72 522.613 929.762457.374 813.542 406.639723.148 366.069 650.833 5 609.813 1085.00 522.780 930.000457.521 813.750 406.769 7*43.838 366.186 651.000 6 610.008 1085.28 522.948 930.238 457.668 813.958 406.900 723.519 366.304 651 . 167 610.204 1085.56 .123.116 930.476 457.815 814.167 407.031 723.704 366.421 651.333 8 610.400 1085.83 523.284 930.714 457.961 814.375 407.161 723.889 366.539 651.500 9 610.596 1086.11 523.452 930.952 458.108 814.588 407.292 724.074 366.65? 651.66? 10 610.792 1086.39 523. 620 931.190 458.255 814.792 407.423 724.259 366.774 651.833 11 610.988 1086.67 523.788 931.429 458.402 815.000 407.553 724.444 366.892 652.000 12 611.184 1086.94 523.956 931.66? 458.549 815.208 407.684 724.630 367.010 652.16? 13 611.379 1087.22 524.124 931.905 458.696 815.417 407.815 724.815 367.127 652.333 14 611.575 1087.50 524.292 932.143 458.843 815.625 407.945 725.000 367.245 652.500 15 811. 771 11087. 78 524.459 932.381 458.990 815.833 408 076 725.185 367.362 652.667 16 611.96? 1088.06 524.627 932.619 459.13? 816.042 408.206 725.370 367.480 652.833 17 612.16oild88.33 524.795 932.857 459.284 816.250 408.337 725.556 367.598 653.000 18 612.359 1088.61 524 . 963 933.095 459.431 816.458 408.468 725.741 367.715 653.167 19 612.555 1088.89 525.131 933.333 459.578 816.66? 408.598 725.926 367.833 653.333 2O 612.750 1089.17 525.299 933.571 459.725 816.875 408.729 726.111 367.950 653.500 21 612.940 1089.44 525.46? 933.810 459.872 817.083 408.860 726.296 368.068 653.667 22 613. 142 1089.72 525.635 934.048 460 019 817.292 408 990 726.481 368.186 653.833 23 613.338 1090.00 525.803 934.286 460.166 817.500 409.121 7*6.667 368.303 654.000 24 613.534 1090.28 525.970 934.524 460.312 817.7'08 409.252 726.852 368.421 654.167 25 613.730 1090.50 526. 138 1)34.762 460.459 817.917 409.382 727.037 368.538 654.333 2G 613.925 1090.83 526. 300 935.000 460.606 818.125 409.513 727.222 368.656 654.500 27 614.121 1091.11 526.474 935.238 460.753 818.333 409.643 727.407 368.77'4 654 . 66? 28 614.317 1091.39 526.642 935.476 460.900 818.542 409.774 727.593 368.891 654.833 29 614.513 1091 67 526.810 935.714 461.047 818.750 109.905 727.778 369.009 655.000 30 614.709 1091.94 526.978 935.952 461.194 818.958 410.035 727.963 369.126 655.16? 31 614.905 1092.22 527.140 1)30.190 461.341 819.167 410.160 728.148 369.244 655.333 32 615.101 1092.50 527.314 936.429 461.488 819.375 410.297 728.333 369 362 655.500 33 615.290 1092.78 527.482 936.667 461.635 819.583 410.42? 728.519 369.479 655.667 34 (515.497 1093 06 527.654 936.905 461.785 819.792 410.561 728.704 369.600 655.833 35 015.0'.)HH>93.33 527.826 1)37.143 461.936 820.000 410.695 728.889 369.720 656.000 36 015 6. 392 1 1686. 25 765.199 1349.00 38 3826.03 6746.67 1913.09 3373.33 1275 48 2248.89 956.6931686.67 765.440 1349.33 39 3827.23 6748.33 1913.69 3374.17 1275.88 2249.44 956.994 1687.08 765.681 1349.67 30 3S28.4J 6750.00 1914.29 3375.00 1276.28 2250.00 957.295 1687.50 765.921 1350.00 31 3829.64 6751.67 1914.89 3375.83 1276.68 2250.56 957.596 1687.92 766.162 1350.33 33 3830.84 6753.33 1915.49 3376.67 1277.08 2251 . 1 1 957.897 1688.33 766.403 1350.67 33 3832.05 6755.00 1916.09 3377.50 1277.48 2251.67 958.197 1688.75 766.644 1351.00 34 3833.25 6756.67 1916.70 3378.33 1277.88 2252.22 958.498 1689.17 766.884 1351.33 35 3834.45 6758.33 1917.30 3379.17 1278.28 2252.78 958.799 1689.58 767.125 1351.67 36 3835.66 6760.00 1917.90 3380.00 1278.68 2253.33 959.100 1690.00 767.366 1352.00 37 38 3836.80 3838.06 6761.67 6763.33 1918.50 1919.10 3380.83 3381.67 1279.09 1279.49 2253.89 2254.44 959. 401 j 161)0. 42 959.702 1690.83 767.606 767.847 1352.33 1352.67 39 3839.27 6765.00 1919.70 3332.50 1279.89 2253.0' 1)60.003 1691.25 768.088 1353.00 40 3840.47 6766.67 1920.31 3383.33 1280.29 2255.56 960.303 1691.67 768.329 1353.33 41 3841.70 6768.33 1920.92 3384.17 1280.70 2256.11 960.61111692.08 768.575 1353.67 43 3842.93 6710.00 1921 54 3385.00 1281.11 2256.67 960.920 1692.50 768.821 1354.00 43 3844.14 6771.67 1922.14 3385.83 1281.51 2257.22 901 . 220 1692.92 7(59.062 1354.33 44 3845.34 6773.33 1922.74 3336.67 1281.91 2257.78 961.521 1693.33 769.303 1354.67 45 3846 54 6775.00 1923 34 33S7.5P 1282.31 2258. .33 961.822 1693.75 769.544 1355.00 46 3847.75 6776.67 1923.94 3388.33 1282 71 2258.89 962.123 1694.1? 769.784 1355.33 47 3848.95 6778.33 1924.55 3389.17 1283.12 2259.44 962.424 1694.58 770.025 1355.67 48 3850.15 6780.00 1925.15 3390.00 1283.52 2260.00 962.725 1695.00 770.266 1356.00 49 3851.36 6781.67 1925.75 3390.83 1283.92 2260.56 963.026 1695.42 770.506 1356.33 50 3852.56 6783.33 1926.35 3391.67 1284.32 226 1.11 968.898 1695.83 770.747 1356.67 51 53 3853.79 3855.02 6785.00 6786.67 1926.97 1927.58 3392.50 3393.33 1284.73 1285.14 2261.67 2262.22 963.634 963.942 1696.25 1696.67 770.994 771.240 1357.00 1357.33 53 3856.23 6788.33 1928.18 3394.17 1285.54 2262.78 9(14.243 1697.08 771.481 1357.67 54 3857.43 6790.00 1928 79 3395.00 1285.94 2263.33 964.544 1697.50 771.722 1358.00 55 3858.63 6791.67 1929.39 3395.83 1286.34 2263.89 964.845 1697.92 ? 71. 962 1358.33 56i3859.84 6793.33 57 380 1.07 1 6795. 00 1929.99 1930.60 3396.67 3397.50 1280.74 1287.16 2264.44 2265.00 965.146 965.454 1698.33 1698.75 772.203 1358.67 772.4491359.00 58 3863.30 6796.67 1931.22 3398.33 1287.57 2265.56 965.7621699.17 772.696 1359.33 59 3863.50,6798.33 1931.82 3399.17 1287.97 2266.11 96ft. 063! 1699.58 772.937il359.67 180 TABLE XIV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 Curve. 1O Curve. 67 Tan. Arc. Tan. I Arc. Tan. Arc. 837.500 Tan. 4217803 Arc. Tan. Arc. M. 632. 350; 11 16. 67 542.101 957.143 474.429 744.444 379.720 670.000 O 632.546 1116.94 542.209957.381 474.576 837.708421.9:33 744.630 379.83? 670.167 1 632 . 742 ! 1 1 1 7 . 22 542 . 437 957 . 619 474.723 837.917422.064 744.815 379.955 670.333 2 632.942 1117.50 542.609957.857 474.874 838.125 422.198 745.000 380.075 670.500 3 633.143 1117.78542.781 958.095 475.024 838.333 422.332 745.185 380.196 670.607 4 633.343 1118.06 542.953 958.333 475.175 838.542 422.465 745.370 380.316 670.833 5 633.544 1118.33543.125 958 571 475.325 838.750 422.599 745.556 380.43? 671.000 6 633.745 1118.61 543.297 958.810 475.476 838.958 422.733 745.741 380.55? 671.16? 7 633.945 1118.89 543.469 959.048 475.626 839.167 422.867 745.926 380.678 671.333 8 6:34 . 146 1119.17 5 43. 641 959.286 475.77? 839.375 423.001 746.111 380.798 671.500 9 634.347 1119. 44'543. 813 959.524 475.928 839.583 423.134 746.296 380.919 671.66? 1O 634.547 1119.72 543. 985 1959.762 476.078 839.792 423.268 746.481 381.039 671.833 11 6:34.748 1120.00 544.157 960.000 476.229 840.000 423.402 746.66? 381.160 672.000 13 634.948 1120.28544.329 960.238 476.379 840.208 423.536 746. 852 381.280 672.16? 13 635.149 1120.56 544.501 960.476 476.530840.417J423.670 747.03? 381 401 672.333 14 635. 3501 11 20. 83:54 4. 673 960.714 476.680 840 .625 '423. 804 747.222 381.521 672.500 15 635.550 1121.11 544.845 960.952 476.831 840.833423.937 747.407 381.641 672.66? 16 635.751 1121.39545.017 .mi. 190 476.981 841.042 424.071 747.593 381.762672.833 17 635.953 1121.67 545.189 J6 1.429 477.132 841.250 424.205 747.778 381.882 673.000 18 636.152 1121.94 545.361 961.667 477.282 841.458 424.339 747.963 382.003 673.16? 19 636.353 1122.22 545.533 961.905 477.433 841.66? 424.473 748.148 382.123 673.333 30 636.553 1122.50 545.705 962.143 477.583 841.875 424 607 748.1333 382 244 673.500 31 636.754 1122.781545.877 962.381 477.734 842.083 424.740 748.519 382.364 673.667 636.955 1123.06546.049 962.619 477.884 842.292 424.874 748.704 382 485 673.833 33 637.155 1123.33 546.221 962 857 478.035 842.500 425.008 748.889 382.605 674.000 24 637.356 1123.61 546.393 963.095 478.185 842.708 425.142 749.074 382.726 674.16? 25 637.557 1123.89 546.565 903.333 478.336 842 917 425.276 749.259 382.846 674.333 26 637.757 1124. 17|546. 737 963.571 478.486 843.125 425.410 749.444 382.967 674.500 27 637.958 1124.44 546.909 963.810 478.637 843 . 333 425.543 749.630 383.087 674.66? 28 638.158 1124.72 547.081 964.048 478.787 843.542 425.677 749.815 383.208 674.833 39 638.359 1125.00 547.253 964.286 478.938 843.750 425 811 750.000 383.328 675.000 30 638.560 1125.28547.425 964.524 479.089 843.958 425.945 750.185 383.449 675.16? 31 638.760 1125.56 547.597 964.762 479.239 844.16? 426.079 750.370 383.569 075.333 33 638.961 1125.83:547.769 965.000 479.390 844.375 426.212 750.556 383.690 675.500 33 639.162 1126.11 547.941 965.238 479.540 844.583 426.346 750.741 383.810 075.667 34 639.362 1126.39 548.113 965.476 479.691 844.792 426.480 750.926 383.931 675.833 35 639.563 1126.67 548.285 965.714 479.841 845.000 426.614 751.111 384.051 676.000 36 639.763 1126.94 548.457 965.952 479.992 845.208 426 . 748 751.296 384.171 676.167 37 639.964 1127.2.' 548.629 966.190 480.142 845.417 426.882 751.481 384.292 676.333 38 640 165 1127.50 548.801 966.429 480.293 &4S.625 427.015 751.667 384.412 676.500 39 610.365 1127.78 548.973 966.66? 480.443 845.8:33 427.149 751.852 384.533 676.667 4O 640.571 1128.06 549.149966.905 480 597 846.042 427.286 7*2.08? 384.050 076.833 41 640.770 1128.33 549.325967.143 480.751 846. 250! 427. 423 752.222 384.780 677.000 43 640.977 112-'. 61 !549. 497 907. 381 480.902 846.458427.55? 752.407 884.9011 077.16? 43 641.177 1128.89 549.609 967.619 481.053 846.667 427.691 5*2.598 385.021 077.333 44 641.378 1129.17i549.841 967.85? 481.203 846.875427.825 752.778 385.141 077.500 45 641.579 1129.44 550.013 908.095 481. 354 847.083427.959 752.963 385.201 677.667 46 641.7791129.72 550 185 968.333 481.504 847.292428.092 753.148 385.382 677.833 47 641.980J1130.00 550.35? 908.571 481.655 847.500428.226 753.333 385.502 678.000 48 642.181 1130.28 550.529 968.810 481.805 847.708428.360 753 519 385.623 678.16? 49 612.381 1130.56 550.701 969.048 481.956 847.917 428.494 753.704 385.743 678.333 5O 642.587 1130.83 550.877 969.286 482.110 848.125 428.631 753.889 385.86? 678.500 51 642.792 1131.11 551.053 969.524 482.264 848.333428.768 754.074 385.990 678.66? 53 642.993 1131.39551.225 909.762 482.414 848.542428.902 754.259 386.111 678.833 53 643.193 1131.67551.397 643.394sll31.94551.569 970 000 970.2:38 482.565 482.715 848.750429.036 848.958'429.169 754.444 754.630 386.231 380.351 679.000 679.16? 54 55 643.595 1132.22 551.741 970.476 482.866 849.167429.303 754.815386.472 679.333 56 643.8001132.50.551.917 970.714 483.020 849.375429.440 755.000 386.595 679.500 57 644.005 1132.78 552.093 970.952 483.174 849.583429.577 755.185 386.719 679.667 58 644.206 1133.06 552.265 971.190 483.325 849.792429.711 755.370 386.839 679.833 59 181 TABLE XIV. ACTUAL TANGENTS, ETC. 68 1 Curve, 2 Curve. 3 Curve. 4 Curve. 5 Curve. M. Tan. Arc. Tan. Arc. Tan . Arc. Tan. Arc. Tan. Arc. o 3861.71 6800.00 1932.42 3400.00 1288.37 J266.07960.364 1700.00 773.177 1300.00 1 3865.91 0801.07 1933.03 3400.83 1288.77 2207.22900.005 1700.42 773.418 1300.33 9 3867.11 6803.33 1933.63 3401.67 1289.17 22(57.78966.965 1700.83 773.659 1360.67 3 3808.34 6805.00 1934.24 3402.50 1289.58 2268.33907.273 1701.25 773.905 1301.00 4 3869.58 0806.67 1934.86 3403.33 1289.99 .'208.89907.582 1701.67 774.152 1361.33 5 387-1.78 6808.33 1935.40 3404.17 1290.39 2269.44967.882 1702.08 774.392 1361.07 6 3871.98 6810.00 1936.06 3405.00 1290.79 2270.00908.183 1702.50 774.633 1362.00 7 3873.19 6811.67 1936.66 3405.83 1291.19 2270.50968.484 1702.92 774.874 1362.33 8 3874.39 6813.33 1937.27 3406.67 1291.60 2271.11 968.785 1703.33 775.115 1362.67 9 3875.62 6815.00 1937.88 3407.50 1292.01 2271.67 969.093 1703.75 775.361 1363.00 1O 3876.85 0816.67 1938.50 3408.33 1292.42 2272.22 969.401 1704.17 775.607 1363.33 11 3878.06 6818.33 1939.10 3409.17 1292.82 2272.78969.702 1704.58 775.848 1363.67 12 3879.26 6820.00 1939.70 3410.00 1293.22 2273.33970.003 1705.00 776.089 1364.00 13 3880.49 6821.67 1940.32 3410.83 1293.63 2273.89970.311 1705.42 776.335 1364.33 14 3881.72 6823 33 1940.93 3411.67 1294.04 2274.44 970.619 1705.83 776.582 1364.07 15 3882.93 6825.00 1941.53 3412.50 1294.44 2275.00970.920 1706.25 776.822 1365.00 10 3884.13 6826.67 1942.14 3413.33 1294.84 2275.56971.221 1706.67 777.003 1365.33 17 3885.33 6828.33 1912.74 3414.17 1295.24 2276.11 971.521 1707.08 777.304 1365.07 18 3886.54 6830.00 1943.34 3415 00 1295.65 2276.67971.822 1707.50 777.545 1366 00 19 3887.77 6831.67 1943.96 3415.83 1296.06 2277.22 972.130 1707.92 777.791 1366.33 20 3889.00 6833.33 1944.57 3416.67 1296.47 2277.78 972.438 1708.33 778.038 1366.67 21 3890.20 6835.00 1945.17 3417.50 1296.87 2278.33972.739 1708.75 778.278 1367.00 22 3891 41 6836.67 1945.77 3418.33 1297.27 2278.89973.040 1709.17 778.519 1367.33 23 3892.64 6838.33 1946.39 3419.17 1297.68 2279. 44 ! 973. 348 1709.58 778.765 1367.67 24 3893 87 6840.00 1947.01 3420.00 1298.09 2280.00973.656 1710.00 779.012 1368.00 25 3895.07 6841 67 1947.61 3420 83 1298.49 2280.56973.957 1710.42 779.253 1368.33 26. 3896.28 6843 33 1948.21 3421.67 1298.89 2281.11 974.258 1710.83 779.493 1308.67 27 3897.51 6845.00 1948.83 3422.50 1299.30 2281.67 974.566 1711.25 779.740 1309.00 28 3898.74 6846.67 1949.44 3423.33 1299.71 2282. 22 1 974. 874 1711.67 779.980 1309.33 29 3899.97 6848.33 1950.06 3424.17 1300.12 2282.78 975.182 1712.08 780.233 1369.67 30 3901.20 6850.00 1950 67 3425.00 1300.54 2283.33 975.490 1712.50 780.479 1370.00 31 390-2.41 6851.67 1951.28 3425.83 1300.94 J283.89i975.791 1712.92 780.720 1370.33 32 3903.61 6853.33 1951.88 3426.67 1301.34 2284.44 976.092 1713.33 780.961 1370.67 33 3904.84 6855.00 1952.49 3427.50 1301.75 2285.00 976.400 1713.75 781.207 1371.00 34 3906.07 6856.67 1953.11 3428.33 1302.16 2285.56 976.708 1714.17 781.453 1371.33 35 3907.28 6858.33 1953.71 3429.17 1302.56 J286.ll 977.009 1714.58 781.694 1371.67 36 3908.48 6860.00 1954.31 J430.00 1302.96 2286.67 977.309 1715.00 781.935 1372.00 37 3909.71 6861.67 1954.93 3430.83 1303.37 2287.22 9:7.618 1715.42 782.181 1372.33 38 3910.94 6863.33 1955.54 3431.67 1303.78 J287.78 977.926 1715.83 782.428 1372.67 39 3912.18 6865.00 1956.16 3432.50 1304.19 2288.33 978.234 1716.25 782.674 1373.00 40 3013.41 6866.67 1956.78 3433.33 1304.60 2288.89 978.542 1716.67 782.921 1373.33 41 3914.61 6868.33 1957.38 3434.17 1305.00 2289.44 978.842 1717.08 783.161 1373.67 42 3915.81 6870.00 1957.98 3435.00 1305.41 J290.00 979.143 1717.50 783.402 1374.00 43 3917.05 6871.67 1958.60 3435.83 1305.8-,' 2290.56 979.451 1717.92 783.649 1374.33 44 3918.28 6873.33 1959.21 3436.67 1306.23 2291.11 979.759 1718.33 783.895 1374.07 45 3919.51 6875.00 1959.83 3437.50 1306.64 2291.67 980.067 1718.75 784.141 1375.00 46 39 .'0.74 0876.67 1960.44 3438.33 1307.05 2292 22 980.375 1719.17 784.388 1375.33 47 3921.95 6878.33 1961.04 3439.17 1307.45 2292! 78 980.676 1719.58 784.629 1375.67 48 3923.15 6880.00 1961.65 3440.00 1307.85 2293 . 33 980.977 17'20.00 784.869 1376.00 49 3924.38 6881.67 1962.26 3440.83 1308.26 2293.89 981.285 1720.42 785.116 1376.33 50 3925.61 6883.33 1962.88 3441.67 1308.67 2294.44 981.593 1720.83 785.302 1376.67 51 3926.84 6885.00 1963.49 3442.50 1309.08 2295.00 981.901 1721.25 785.609 1377.00 52 3928.08 6886.67 1964.11 3443.33 1309.49 2295.56 982.209 1721.67 785.855 1377.33 53 31)29.31 0888.33 1964.73 3444.17 1309.90 2296.11 982.517 1722.08 7'86.102 1377.07 54 3930.54 6890.00 1965.34 3445.00 1310.31 2296.67 982.825 1722.50 786.348 1378.00 55 3931.74 0891.67 1965.94 3445.83 1310.72 2297.22 983.126 1722.92 786.589 1378.33 56 3932.95 0893. 33 1966.55 3446.67 1311.12 2297.78 983.427 1723.33 786.830 1378.67 57 3934.18 6895.00 1967.16 3447.50 1311.53 2298.33 983.735 1723.75 787.070 1379.00 58 3935.41 0896.67 1967.78 3448.33 1311.94 2298.89 984.043 1724.17 787.3-22 1379.33 59 3936.64 6898.33 1968.39 3449.17 1312.35 2299.44 984.. 351 1724.58 787.509 1379.07 182 TABLE XIV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 Curve. 10 Curve. 68 Tan. Arc. Tan. Arc. Tan. 483.475 Arc. Tan. Arc. Tan . Arc. M. 644.407 1133.33 552.437 971.429 850.000 429.845 755.556 386.960680.000 644.607 1133.61 552.609 971.667 483.626^850.208 429.979 755.741 387.080680.167 1 644.808 1133.89 552.781 971.905 483.776850.417 430.113 755.926 387.201 680.333 2 645.013 1134.17 552.957 972.143 483.930850.625 430.250 756.111 387. 324 680.1 f -00 3 645.219 1134.44 553.133 972.381 484. 084 850. 833 430.387 756.296 387.447 680.067 4 645.419 1134.72 553.305 97'2.619 484.235851.042 430.520 756.481 387. f 68 680. 833 5 645.620 1135.00 553 477 972.857 484. 386 '851. 250 430.654 756 667 387.688681.000 (> 645.821 1135.28 553.649 973.095 484.536851.458 430.788 756. 85',' 387.809681 167 7 646.021 1135.56 553.821 973.333 484.687 851.667 430.922 757.037 387.929681.333 8 646.22? 1135.83 553.997 973.571 484.841 851.875 431.059 757.222 388.052 681.500 9 646.432 1136.11 554.173 973.810 484.995 852 083 431.196 757.407 388.176 681.667 1O 646.633 1136.39 554.345 974.048 485. 145 1852. 292 431. 330 1 757. 593 388.296:681.833 11 646.833 1136.67 554.517 974.286 485.296 852.500 431. 464 1 757. 778 388.417682.000 12 647.039 1136.94 554.691 974.524 485.450 852.708 431.601 757.963 388.540 682 167 13 647.244 1137.22 554.870 974.762 485.604 852.917 431 738 758.148 388.663 682.333 14 647.445 1137.50 555 042 975.000 485.755 853.125 431.871 758.333 388.784 682. 00 15 647.645 1137.78 555.214 975.238 485.905 853:333 432.005 758.519 388 904 682 667 16 647.846 1138.06 555.386 975.476 486.056 853.542 432.139 758.704 389.025682.833 17 648.047 1138.33 555.558 975.714 486.206 853.750 432.2731758.889 389.1451683.000 18 648.252 1138.61 555.734 975.952 486.360 853.958 432.410 759.074 389.269 683.167 19 648.457 113S.89 555.910 976.190 486.514 854.167 432 547 759.259 389.392 683.333 20 648.658 1139.17 556.082 976.429 486.665 854.375 432 681 1759.444 389.513 683.500 21 648.859 1139.44 556.254 976.667 486.815 854.583 432.815 759 630 389.633 683.667 22 649.064 1139.72 556.430 976.905 486.970 854.792 432.952 759.815 389.756 683.833 23 649.269 1140.00 556.606 977.143 487 124 855.000 433.089 760.000 389 880 684.000 24 649.470 1140.28 556.778 977.381 487.274 855.208 433.222 7'60.185 390.000 684 167 25 649.671 1140.56 556.950 977.619 487.425 855.417 433.356 760.370 390.121 684.333 26 649.876 1140.83 557.126 977.857 487.579 855.625 433.493 760.556 390.244 684.500 27 650.081 1141.11 557.302 978.095 487.733 855.833 433.630 760.741 390.367 684.667 28 650.287 1141.39 557.478 978.333 487.887 856.042 433.767 760.926 390.491 684.833 29 650.492 1141.67 557.654 978.571 488.041 856 250 433.904 761.111 390.614 685.000 30 650.693 1141.94 557.826 978.810 488.192 856 458 434.038 761.296 390.734 685.167 31 650.894 1142.22 557.998 979.048 488.342 856.667 434. 172 761.481 390.855 685.333 32 651.099 1142.50 558.174 979.286 488.496 856.875 434.309 761.667 390.978 685.500 33 651.304 1142.78 558.350 979.524 488.650 857.083 434.446 761.852 391.102 685.667 34 651.505 1143.06 558.522 979.762 488.801 857.292 434.580 762.037 391.222 685.833 35 651.706 1143.33 558.694 980.000 488.951 857.500 434.714 762 222 :/.)!. 343 686.000 36 651.911 1143.61 558.871 980.238 489.106 857.708 434.851 762.407 391.466 686.167 37 652.116 1143.89 559.017 980.476 489.260 857.917 434.988 762.593 391.589 686.333 :i8 652.322 1144.17 559.223 980.714 489.414 858.125 435.125 762.778 391.713 686.500 39 652.527 1144.44 559.399 980.952 489.568 858.333 435.262 762.963 391.836 686.667 40 652. 72H 1144.72 559.571 981.190 489.718 858.542 435.396 763.148 391.956 686.833 41 652.928 1145.00 569.748 981.429 489.869 858.750 435.529 763.333 392.077 t 87. 000 42 653.134 1145.28 559.919 981.667 490.023 858 958 435.666 763.519 392.200 687.167 43 653.339 1145.56 560.095 981.905 490.177 H59.167 435 803 763.704 392.324 6S7.333 44 653.545 1145.83 560.271 982.143 490.331 859.375 435.940 763.889 392.447 687.500 45 653.750 1146.11 560.447 982. 3S1 490.485 859.583 436.077 764.074 392.570 687.667 46 653.951 1146.39 560.619 982.619 490.636 859.792 436.211 764.259 392.691 687.833 47 654 . 151 1146.67 560.791 982.857 490.786 860.000 436.345 764.444 392.811 688.000 48 654.357 1146.94 560.967 983.095 490.940 860.208 436.482 764.630 392.935 688.167 49 654.562 1147.22 561.143 983.333 491.095 860.417 436.619 764.815 393.058 688.333 50 654.788 1147.50 561.319 983.571 491.249 K60.625 436.756 765.000 393.181 688.500 51 654.973 1147.78 561 495 983.810 491.403 860.833 436.893 765.185 393.305 688.667 52 655.178 1148.06 561.672 9S4.04S 491.557 861.042 437.030 765.370 393.428 688.833 53 655.384 1148.33 561. 848 '984. 286 491.711 861.250 137.107 765.556 393.551 689.000 54 655.584 1148.61 562. 020 ' 984. 524 491.862 861. 45S 437.301 765.741 393.672 689.167 55 655.785 1148.89 562. 192 '984. 762 492.012 861.667 437.435 765.926 393.792 689.333 56 655.990 1149.17J562.368985.000 492.166 861 ,H7T. 437.572 766.111 893.916 689.500 57 05(5. 190 1149.44 562. 544 '985. 238 492.320 862.083 437.709 766.296 394.039 689.667 58 656 . 401 1 1 1 49 . 72 : 562 . 720 985 . 4 76 492.474 862.292 437.846 7G6.481 394.162 689.833 59 183 TABLE XIV. ACTUAL TANGENTS, ETC. 69" 1 Curve. 3 Curve. 3 Curve. 4 Curve. 5 Curve. M. Tan. Are. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. O 3937.8? 6900.00 1969.01 3450.00 1312.76 2300. OJ 984.6.)9 1725.00 787.815 1380.00 1 3939.11 6901.67 1969.633450.83 1313.17 2300.56 984.967 1725.42 788.062 1380.33 2 39 JO. 34 6903.33 1970.243451.67 1313.58 2301.11 985.275 1725.83 788.3081380.67 3 3941.57 6905.00 1970 86 3452.50 1313.99 2301.67 985.583 1726.25 788.5551381.00 4 3942.80 6906.67 1971.473453.33 1314.40 2302.22 985.891 1726.67 788.801 1381.33 5 3944.03 6908.33 1972.093454.17 1314.81 2302.78 986.199 1727. Oh 789.048 1381.67 6 3945.27 6910.00 1972.703155.00 1315.22 2303.33 986.507 1727.50 789.294 1382.00 7 3946.50 6911.67 1973.323455.83 1315.63 2303.89 986.815 1727.92 78^.540 1382.33 8 3947 73 6913.33 1973.943456.67 1316.05 2304.44 987.123 1728.33 789.78? 1382.67 9 3948.93 6915.00 1974.54 3457.50 1316.45 2305.00 987.424 1728.75 790.028 1383.00 10 3950.14 6916.6? 1975.14 3458.33 1316.85 2305.56 987.725 1729.1? 790.268 1383.33 11 395 1. 3 r 6918.33 1975.76 3459.17 1317.26 2306.11 988.033 1729.58 790.515 1383.67 13 3952.60 6920.00 1976.37 3460.00 1317.67 2306.67 988.341 1730.00 790.761 1384.00 13 3'.)53.83 6921.6? 1976.99 3460.83 1318.08 2307.22 988.649 1730.42 791.008 1384.33 14 3955.06 6923.33 1977.60 3461.67 1318.49 2307.78 988.95? 1730.83 791.254 1384.67 15 3956.29 6925.00 1978.22 3162.50 1318.90 230S.33 989.265 1731.25 791.501 1385.00 16 3957.53 6926.67 1978.84 3463.33 1319.31 2308.89 989.573 1731.67 791.74? 1385.33 17 3958.76 6928.33 1979.45 3464.1? 1319.72 2309.44 989.881 1732.08 791.994 1385.67 18 3959.99 6930.00 1980.0? 3465.0) 1320.13 2310.00 990.189 1732.50 792.240 1386.00 19 3961.2-.* 6931.67 1980.68 3465.83 1320.54 2310.56 990.497 1732.92 792.486 1386.33 30 396-2.45 6933.33 1981.33 3466.67 1320.95 2311.11 990.805 1733.33 792.733 1386.67 31 3963.69 6935.00 1981.92 1467.50 1321.36 2311.67 991.113 1733.75 792.979 1387.00 33 3964.92 6936.6? 1982.53 3468.33 1321.78- 2312.22 991 421 1734.1? 793.226 1387.33 33 3966.15 (5938.33 1983.15 3409.1? 1322.19 2312.78 991.730 1734.58 793.472 1387.67 34 S907.3H 6940.00 1983.76 3 470.00 1332.60 2313.33 992.038 1735.00 793.719 1388.00 35 3968.61 6941.67 1984.3813470. 83 1323 01 2313.89 992.346 1735.42 793.965 1388.33 36 396'.). 85 6913.33 1985.00 5471.6; 1323.42 2314.44 992.654 1785.88 T94.212 1388.67 37 3971.08 6945.00 1985.61 1472.50 1323.83 2315.00 992.962 1736.25 794.458 1389.00 38 3972.31 6946.67 1986. 2i 3173.33 1324.24 2315.56 993.270 1736.67 794.704 1389.33 39 3973.54 6948.33 1986.84 3174.17 13 -'4. 65 2316.11 993.578 1737.08 794.951 1389.67 3O 3974.77 (5950.00 1987.46 3475.03 1335.06 2316.6? 993.886 1737.50 795.19? 1390.00 31 3976.03 6951.67 1988.09 3475.83 1325.48 2317.2-2 994.201 1737.92 795.450 1390.33 33 3977.29 6953.33 1988.72 3476 67 1325.90 2317.78 J94.516 1738.33 795.702 1390.67 33 3978.53 6955.00 1989.31 3477.50 1326.31 2318.33 J94.824 1738.75 795.948 1391.00 34 3979. 7t> 6956.67 1989.95 3178.33 1326.72 2318.89 995.132 1739.17 796.195 1391.33 35 3980.99 6958.33 1990.57 3179.17 1327.13 2319.44 995.440 1739.58 796.441 1391.67 36 3982.22 6960.00 1991. IS 3 HO. 00 1327.54 2320.00 995.748 1740.00 796.688 1392.00 37 3983.45 6961 . 6? I W 1.80 3180.83 1327.95 2320.56 996.056 1740.42 796.934 1392.33 38 3984.69 6963.33 1992.42 3481.67 1328.37 2*21.11 996.364 1740.83 797.180 1392.67 39 3985.92 6965.00 1993.03 3182.50 1328.78 2321.67 996.672 1741.25 797,427 1393.00 4O 3987.15 6966.67 1903.65 34S3.33 1329.19 2322.22 996.980 1741.6? 797.673 1393.33 41 3988.38 6968.33 1991.26 3484.17 1329.60 232-2.78 997.288 1742.08 797.920 1393.67 43 3989.61 6970.00 1994.88 3485.00 1330.01 2323.33 997.596 1742.50 798.166 1394.00 43 3990.87 6971.6? 1995.51 3485.83 1333.43 2323.89 997.912 1742.92 793.418 1394.33 44 3992.13 6973.33 1936.14 34S6.6? 133). 85 2324.44 998.227 1713.33 798.671 1394.67 45 3993.37 6975.00 1996. 76 1 3 487. 50 1331.26 2325.00 998.535 1713.75 798.917 1395.00 46 3994.60 6976.67 1 997. 3 r 3488.33 1331.67 2325.56 998.843 1744.1? 799.163 1395.33 47 3995.83 6978.33 1997.993489.1? 1332.08 2326.11 9W.151 1744.58 799.410 1395.67 48 3997.06 6980.00 1998.60:3490.00 1332.49 2326.6? 999.459 1745.00 799.656 1396.00 49 3998.29 6981.67 1999.22 3490.83 1332.90 2327.22 999.767 1745.42 799.903 1396.33 5O 3999.52 6983.33 1999.84 3491.67 1333.31 2327.78 1000.07 1745.83 800.149 1396.67 51 4000.76 6985.00 2000.45 3492.50 1333.72 2328.33 1000.38 1746.25 800 396 1397.00 53 4001.99 6986.6? 2001.07 3493.33 1334.13 2328.89 1000 69 1746.67 800.642 1397.33 53 54 4003.25 4004.51 6988.33 6990.00 2001.70 2002.33 3491.17 3495.00 1334.55 1334.97 2329.44 1001.01 2330.00 1001.32 1747.08 1747.50 800 894 1397.67 801.1471398.00 55 4005.74 6991.67 2002.94 3495.83 1335.38 2340.56 1001.63 1747.92 801.3931398.33 58 4006.97 6993.33 2003.56 3496.67 1335.80 2331.11 1001.94 1748.33 801.63!) 1398.67 57 4008.21 6995.00 2004.18 3497.50 1336.21 2331.67 1002.25 1748.75 801.8861399.00 58 4009.44 6996.6? 2004.79 3498.33 1336.62 2332.22 1002.55 1749.17 802.132 1399.33 59 4010.70 6998.33 2005.42 3499.17 1337.04 2332.7811002.87 1749.58 802.385 1399.07 184 TABLE XIV. ACTUAL TANGENTS, ETC. o 10 Curve. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. M. 656,607 1150.00 562.890 985.7141492.629 862.500 437 983 766.607 894.286 690.000 O 650.812 1150.28 563.072 985. 952 492. 783 802.708 438.120 766.852 394.409690.167 1 05". 01 7 1150.56 563.248 986.190 492.937 802.917 438.257 767.037 394.532 690.333 2 657.223 1150.83 563.424 986.429 493.091 863.125 438.394 767.222 394.650 090.500 3 657.428 1151.11 563.600980.607 493.245 863.333 438.531 707.407 394.779 090.667 4 65". 634 1151.39 563. 776 1980.905 493.399 803.542 438.668 767.593 394.902 690.833 5 657.839 1151. 67 563.953987.143 493.553 803.750 438.805 767.778 395 026 691.000 6 658.044 1151.94 504. 129 1987. 381 493 70; 803.958 438.942 767.903 395.149 091.167 7 658.850 1152.22 564.305 987.619 493.861 804.167 439.079 768.148 395.272 691.333 8 658.451 1152.50 564.477 987.857 494.012 861.375 439.213 768.333 395.393 691.500 9 658.651 1152.78 564.649 988.095 494.162 804.583 439.347 768.519 395.513 691.667 1O 658.857 1153.00 564.825 988.333 494 317 804.792 439.484 768.704 395.037 691.833 11 659.062 1153.33 565.001 988.571 494.471 805.000 439.621 768.889 395.700 692.000 12 659.267 1153.61 505.177 988.810 494.625 865.208 439.758 769.074 395.883 692.167 13 659.473 1153.89 565.353 989.048 494.779 865.417 439.895 769.259 396.007 692.333 14 659.678 1154.17 505.529 989.280 494.933 865.625 440.032 769.444 396.130 692.500 15 659.884 1154.44 505.705 989.524 495.087 865/833 440.169 769.630 396.253 692.667 Hi 660.089 1154.72 505.881 989.762 495.241 866.042 440.306 769.815 396.377 692.833 17 660.294 1155.00 506.057 990.000 495.395 866.250 440.443 770.000 896.500 693.000 18 660.500 1155.28 566.234 990.238 495.549 806.458 440.580 770.185 390.023 093.167 19 660.705 1155.56 566.410 990.470 495.703 866.667 440.717 770.370 396.747 693 333 20 660.911 1155.83 566.586 990.714 495.858 806.875 440.854 770.556 396.870 693.500 21 661.116 1156.11 566.762 990.952 496.012 867.083 440.991 770.741 396.993 693.667 22 661.321 1156.39 566.938 991.190 496.166 867.292 441.128 770.926 397.117 693.833 23 661.527 1156.67 567.114 991.429 496.320 867.500 441.265 771.111 397.240 694.000 24 0(51.732 1156.94 567.290 991.007 496.474 807.7'08 441.402 771.290 897.MJ8 694.167 25 601.938 1157.22 567.466 991.905 496.628 867.917 441.539 771.481 397.487 094.333 2G 002.143 1157.50 567.642 992.143 496 . 782 808.125 441.070 771.667 397.610 094.500 27 662.348 1157.78 507.818 992.381 496.936 808.333 441.813 771 852 397.733 694.667 28 662.554 1158.00 567.994 992.619 497.090 808.542 441.950 772.037 397.857 694.833 29 662.759 1158.33 568.171 992.857 497.245 868.750 442.087 772 222 397.980 695.000 30 662 909 1158.61 508.351 993.095 497.402 868.958 442 227 772.407 398.106 695.167 31 663.180 1158.89 508.531 993.333 497.560 809.107 442 367 772 593 398.233 095.333 32 663.385 1159.17 568.70? 993.571 497.714 809.375 442.504 772 '.778 398 350 695.500 33 663.590 1159.44 568.883 993.810 497.868 869.583 442.641 772.963 398.479 695.667 34 063.790 1159.72 569.059 994.048 498.022 809.792 442.778 773.148 398.603 695.833 35 664.001 1160.00 569.235 991.286 498.176 870.000 442.915 773 333 398.726 696.000 36 664.207 1100.28 569.411 994.524 498.330 870.208 443.052 773.519 398.849 696.167 37 664.412 1160.56 569.587 994.762 498.485 870.417 443 J89 773.704 398.973 696.333 38 664.617 1100.83 569.763 995.000 498.639 870.025 443.320 77'3.889 399.096 696.500 39 664.823 1161.11 569.940 995.238 498.793 870.833 443.463 774.074 399 219 696.667 40 665.028 1161.39 570.116 995.470 498.947 871.042 443.600 77-4.259 399.343 696.833 41 605.234 1161.67 570.292 995.714 499.101 871.250 443.737 774.444 399 466 697.000 42 665.444lll61.94 570.472 995.952 499.259 871.458 443.878 774.630 31)9.592 697.167 43 665.654 1162.22 570.652 996.190 499.410 871.667 444.018 774.815 399.718 697.833 44 665.859 1162.50 570.828 996.429 499.571 871.875 444.155 775.000 399 842 697.500 45 666. 065 Si 162. 78 571.004990.667 499.725 872.083 444.292 775 185 399.965 697.667 46 666. 270 ; 1163. OH 571.180:996.905 499.879 872.292 444.429 775.370 400.088 697.833 47 600.476 1163.33 571.350 997.143 500.033 872.500 444.566 775.550 400.212 698.000 48 000.681 1163.01 571.533 997.381 500.187 872.708 444.703 775.741 400.335 698.167 49 666.886 1163.89 571.709 997.619 500.341 872.917 444.840 775.926 400.459 698.333 50 607.092 1164.17 571.885 997 857 500.495 873.125 444.977 776.111 400.582 698.500 51 667.297 1164.44 572.061 998.095 500.049 873.333 445.114 776.296 400.705 098.607 52 667.507 1164.72 572.241 998.333 500.807 873.542 445.254 776.481 400.831 098.833 53 667.718 1165.00 572.421 998.571 500.965 873.750 445.394 776.667 400.958 699.000 54 667.923 1165.28 572.597 998.810 501.119 873.958 445.531 776.852 401.081 699.167 55 668.128 1165.50 572.773 999. 04S 501.273 874.167 445.668 777.037 401.204 099.333 56 668.334 1165.83 572.949 999.286J501.427 874.375 445 805 777.222 401.328 699.500 57 668.539 1166.11 573.120 999.524501.581 874.583 445.942 777.407 401.451 699.667 58 668.749 1166.39 573.300 999.702501 739 874.792 440.083 777.593 401.577 699.833 59 185 TABLE XIV. ACTUAL TANGENTS, ETC. 70 1 Curve. 2 Curve. 3 Curve. 4 Curve. 5 Curve. M. Tan. Arc. 7000.00 Tan. Are. Tan. Arc. Tan. 1603.18 Arc. Tan. Arc. O 4011.96 2006.05 3500.00 1337.46 2333 33 1750.00 802.637 1400.00 1 -1013.19 7001.672006.67 3500.83 1337.87 2333.89 1003.49 1750.42 802.883 1400.33 2 4014.42 7003.332007.28 3501.67 1338.28 2334.44 1003.80 1750.83 803.130 1400.67 3 4015.65 7005. 00 12007. 90 3502.50 1338.69 2335.00 1004.11 1751.25 803.376 1401.00 4 4016.89 7006.67)2008 52 3503.33 1339.10 2335.56 1004.42 1751.67 803.623 1401.33 5 4018.15 7008.332009.15 3504.17 1339.5-2 2336.11 1004.73 1752.08 803.875 1401.67 O 4019 41 7010.002009.78 3505.00 1339.94 2336.67 1005.05 1752.50 804.127 1402.00 7 40-20.64 7011.672010.39 3505.83 1340.35 2337.22 1005 35 1752.92 804.373 1402.33 8 402 t. 87 7013. 331201 1.01 3506.67 1340.76 2337.78 1005.66 1753.33 804.620 1402.67 9 4023.13 7015.00 2011.64 3507.50 1341.18 2338.33 1005.98 1753.75 804.872 1403.00 1O 1024.39 7016.67 2012.27 3508.33 1341.60 2338.89 1006.29 1754.17 805.124 1403.33 11 4025.62 7018.33 2012.89 3509.17 1342.01 2339.44 1006.60 1754.58 805.371 1403.67 1 2 1026.86 7020.00 2013.50 3510.00 1342.42 2340.00 1 U06.91 1755.00 805.617 1404.00 13 4028.12 7021.67 2014.13 3510.83 1342.84 2340 . 56 1007.22 1755.42 805.869 1404.33 14 4029.38 7023.33 2014.76 3511.67 1343.26 2341.11 1007.54 1755.83 806.121 1404.67 15 4030.61 7025.00 2015.38 3512.50 1343.67 2341.67 1007.85 1756.25 806.368 1405.00 16 4031.84 7026.67 2015.99 3513.33 1344.09 2342.22 1008.16 1756.67 806.614 1405.33 17 4033.10 7028.33 2016.62 3514.17 1344.51 2342.78 1008.47 1757.08 806.866 1405.67 18 4034.36 7030.00 2017.25 3515.00 1344.93 2343.33 1008.79 1757.50 807.119 1406.00 19 4035.59 7031.67 2017.87 3515.83 1345.34 2343.89 1009.09 1757.92 807.365 1406.33 2O 4036.82 7033.33 2018.49 3516.67 1345.75 2344.44 1009.40 1758.33 807.612 1406.67 21 4038.09 7035.00 2019.12 3517.50 1346.17 2345.00 1009.72 758 . 75 807.864 1407.00 22 4039.35 7036.67 2019.75 3518.33 1346.59 2345.56 1010.03 759.17 808.116 1407.33 23 4040.58 7038.33 2020.36 3519.17 1347.00 2316.11 1010.34 759.58 808.362 1407.67 24: 4041.81 7040.00 2020.98 3520.00 1347.41 2346.67 1010.65 760.00 808.609 1408.00 25 4043.07 7041.67 2021.61 3520.83 1347.83 2347.22 1010.96 760.42 808.861 1408.33 26 4044.33 7043.33 2022.24 3521.67 1348.25 2347.78 1011.28 760.83 809.113 1408 67 27 4045.56 7045.00 2022.86 3522.50 1348.66 2348.33 1011 59 761.25 809.3(50 1409.00 2$ 4046.79 7046.67 2023.47 3523.33 1349.07 2348.89 1011.89 761.67 809.606 1409.33 29 4048.06 7048.33 2024.10 3524.17 1349.49 2349.44 1012.21 762.08 809.858 1409.67 30 4049.32 7050.00 2024.73 3525.00 1349.91 2350.00 1012.53 762.50 810.110 1410.00 31 4050.58 7051.67 2025.36 3525.83 1350.33 2350.56 1012 84 762.92 810.363 1410.33 32 4051.84 7053.33 2025.99 3526.67 1350.75 23')1. 11 1013.16 763.33 810.615 1410.67 33 4053.07 7055.00 2026.61 3527.50 1351.16 2351.67 1013.46 763.75 810.861 1411.00 34 4054.30 7056.67 2027.22 3528.33 1351.57 2352.22 1013.77 764.17 811.108 1411.33 35 4055.56 7058.33 2027.85 3529.17 1351.99 2352.78 1014.09 764.58 811.360 1411.67 36 4056.82 7060.00 2028.49 3530.00 1352.41 2353.33 1014.40 765.00 811.612 1412.00 37 4058.08 7061.67 2029.12 3530.83 1352.83 2353.89 1014.72 765.4-2 811.864 1412.33 38 4059.34 7063.33 20-29. 75 3531.67 1353.25 2354.41 1015.03 765.83 812.116 1412.67 39 4060.57 7065.00 2030.36 3532.50 1353.66 2355.00 1015.34 766.25 812.363 1413.00 40 4061.81 7066.67 2030.98 3533.33 1354.07 2355.56 1015 65 766.67 812 609 1413.33 41 4063.07 7068.33 2031.61 3534.17 1354.50 2356.11 1015.9(5 1767.08 812.862 1413.67 42 4064.33 7070.00 2032.24 3535.00 1354.92 2356.61 1016.28 767.50 S13.114 1414.00 43 4065.59 7071.67 2032.87 3535.83 1355.34 2357.22 1016.59 767.92 813 3(56 1414.33 44 4066.8517073.33 2033.50 3536.67 1355.76 2357.78 1016.91 768.33 813. 61H 1414.67 45 4068.11 7075.00 2034.13 3537.50 1356.18 2358.33 1017.22 7 68 . 75 813.87'0 1415.00 46 4069.37 7076.67 2034.76 3538.33 1356.60 23xS.89 1017 54 769.17 814.122 1415.33 47 4070.60 7078.33 2035.38 3539.17 1357.01 2359.44 1017.85 769.58 814.3(59 1415.67 48 4071.83 7080.00 2035.99 3540.00 1357.42 2360.00 1018.16 77'0.00 814.615 1416. (X) 49 4073.09 7081.67 2036.62 3540.83 1357.84 2360.56 1018.47 770.42 814.868 1416.33 50 4074.35 7083.33 2037.25 3511.67 1358.26 2361 . 1 1 1018.79 770.83 815.120 1416 67 51 4075.61 7085.00 2037.88 3542.50 1358.68 23(51.67 1019.10 77" 25 815.372 1417.00 52 4076.88 7086.67 2038.51 3543.33 1359.10 2362.22 1019.42 771 ! 67 815.624 1417.33 53 4078.14 7088.33 2039.14 3544.17 1359 52 2362. 78 1019.73 772.08 815.876 1417.67 54 4079. 40 [7090. 00 2039.77 3545.001359.942363.33 1020.05 772.50 816.128 1418.00 55 4 080. 6C> 7091.67 2040.40 3545.83 1360.36 2363.89 1020.36 772 . 92 816.381 1418.33 56 4081 . 92 7093 . 33 ' 204 1 . 03 ! 354(3 . 67 1 360 . 78 2364 . 44 1020.68 773.33 816. 633[1418. 67 57 4083 . 15 7095 . 00 2041 . 65 3547 . 50 1 361 1 9 23(55 . 00 1020.99 773 . 75 816.879 1419.00 58 4084 . 3S 7096 . 67 2042 . 27 3548 . 33 1 301 . 60 2365 . 56 1021.29 774.17 817.126 1419.33 59 4085 . 64 1 7098 . 33 ! 2042 . 90 1 3549 . 1 7 1362 . 02 2366.11 1021.61 1774.58 817.378ll419.67 186 TABLE XIV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 Curve. 10 Curve. 70 Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. | Arc. M. 668.960 1166.67 573.486 1000.00 501.896875.000 446.223777.778 401.703700.000 o 669.165lll66.94 573.6621000.24 502.051 875.208 446.360777.963401.827 700.167 1 669.370 1167.22 573.838 1000.48 502.205 875.417 446.497 778.148401.950 700.333 669.576 1167.50 574.014 1000.71 502.359 875.625 446.634 778.333 402.073 700.500 3 669.781 1167.78 574.190 1000.95 502.513 875.833 446.771 778.519 402.197 700.667 4 669.991 1168.06 574.370 1001.19 502.671 876.042 446.911 778.704 402.323 700.833 5 670.2021168.33 574.551 1001.43 502.828 876.250 447.051 778.889 402.449 701.000 6 670.407jll68.61 574.727 1001.67 502.982 876.458 447.188 779.074 402.573 701.167 7 670.612lll68.89 574.903 1001.91 503.137 876.667 447.325 779.259 402.696 701.333 8 670.823 1169.17 575.083 1002.14 503.294 876.875 447.465 779.444 402.822 701.500 9 671.0:331160.44 575.263 1002.38 503.452 877.083 447.606 779.630 402.948 701.667 1O 671.238)1169.72 575.439 1002.62 503.606 877.292 447. 743 1779.815 403.072 701.833 11 671.444 1170.00 575.615 1002.86 503.760 877.500 447.880780.000 403.195 702.000 12 671.654 1170.28 575.796 1003.10 503.918 877.708 448. 020 1780. 185 403.321 702.167 13 671.864 1170.56 575.976 1003.33 504.075 877.917 448.160 780.370 403.447 702.333 14 672.069 1170.83 576.152 1003.57 504.230 878.125 448.297 780.556 403.571 702.500 15 672.275 1171.11 576.328 1003.81 504.384 878.333 448.434 780.741 403.694 702.667 16 672.485 1171.39 576.508 1004.05 504.541 878.542 448.574 780.926 403.820 702.833 17 672.695 1171.67 576.688 1004.29 504.699 878.750 448.715 781.111 403.947 703.000 18 672.900 1171.94 576.864 1004.52 504.853 878.958 448.852 781.296 404.070 703.167 19 673.106 1172.22 577.040 1004.76 505.007 879.167 448.989 781.481 404.193 703.333 2O 673.316 1172.50 577.221 1005.00 505.165 879.375 449.129 781 667 404.319 703.500 21 673.526 1172.78 577.401 1005.24 505.323 879.583 449.269 781.852 404.446 703.667 22 673.732 1173.06 577.577 1005.48 505.477 879.792 449.406 782.037 404.569 703.833 23 673.937 1173.33 577.753 1005.71 505.631 880.000 449.543 782.222 404.692 704.000 24 674.147 1173.61 577.933 1005.95 505.789 880.208 449.683 782.407 404.819 704.167 25 674.357 1173.89 578.113 1006.19 505.946 880.417 449.823 782.593 404.945 704.333 26 674.563 1174.17 578.289 1006.43 506.100 880.625 449.960 782.778 405.068 704.500 27 674.768 1174.44 578.466 1006.67 506.254 880.833 450.097 782.963 405.191 704.667 28 674.978 1174.72 578.646 1006.91 506.412 881.042 450.238 783.148 405.318 704.833 29 675.189 1175.00 578.826 1007.14 506.570 881.250 450.37'8 783.333 405.444 705.000 30 675.399 1175.28 579.006 1007.38 506.728 881.458 450.518 783.519 405.570 705.167 31 67'5.609 1175.56 579.186 1007.62 506.885 881.667 450.658 783.704 405.696 705.333 32 675.814 1175.83 579.362 1007.86 507.039 881.875 450.795 783.889 405.820 705.500 33 676.020 1176.11 579.539 1008.10 507.193 882.083 450.932 784.07'4 405.943 705.667 34 676.230 1176.39 579.719 1008.33 507.351 882.292 451.072 784.259 406.069 705.833 35 676.440 1176.67 579.899 1008.57 507.509 882.500 451.213 784.444 406.195 706.000 36 676.650 1176.94 580.079 1008.81 507.667 882.708 451.353 784.630 406.322 706.167 37 676.860 1177.22 580.259 1009.05 507.824 882.917 451.493 784.815 406.448 706.333 38 677.066 1177.50 580.435 1009.29 507.978 883.125 451.630 785.000 406.571 706.500 39 677.271 1177.78 580.611 1009.52 508.132 883.333 451.767 785.185 406.695 706.667 40 677.481 1178.06 580.792 1009.76 508.290 883.542 451.907 785.370 406.821 706.833 41 677.692 1178.33 580.972 1010.00 508.448 883.750 452.047 785.556 406.947 707.000 42 677.902 1178.61 581.152 1010.24 508.606 883 958 452.188 785.741 407.073 707.167 43 678.112 1178.89 581.332 1010.48 508.7'63 884.167 452.328 785.92C 407.199 707.333 44 678.322 1179.17 581.512 1010.71 508.921 884.375 452.468 786.111 407.326 707.500 45 678.532 1179.44 581.693 1010.95 509.079 884.583 452.608 786.296 407.452 707.667 46 678.738 1179.72 581.8651 1011.19 509.233 884.792 452.745 786.481 407.575 707.8:33 47 678.943 1180.00 582.045 1011.43 509.387 885.000 452.882 786.667 407.698 708.000 48 679.153 1180.28 582.225 1011.67 509.545 885.208 453.022 786.852 407.825 708.167 49 679.364 1180.56 582.405 1011.91 509.702 885.417 453.163 787.037 407.951 708.333 5O 679.574 1180.83 582.585 1012.14 509.860 885.625 453.303 787.222 408.077 708.500 51 679.784 1181.11 582.765 1012.38 510 018 885.8:33 453.443 787.407 408.203 708.667 52 679.994 1181.39 582.946 1012.62 510.17'. 886.042 458.588 787.593 408.330 708.833 53 680.204 1181.67 583 126 1012.86 510..')33 886.250 453.723 787.778 408.456 709.000 54 680.414 1181.94 583.306 1013.10 510.491 886.458 453.864 787.963 408.582 709.167 55 680.625 1182.22 583.486 1013.33 510.648 886.667 454.004 788.148408.708 709.333 56 680.830 1182.50 583.662 1013.57 510.802 886.875 454.141 788.333408.832 709.500 57 681.035 1182.78 583.838 1013.81 510.957 887.083 454.278 788.5191408.955 709.667 58 681.2461183.06 584.019 1014.05 511.114 887.292 454.418 788. 704 1409.081 1)9.833 59 187 TABLE XIV. ACTUAL TANGENTS, ETC. 71 1 Curve. 2 Curve. 3 Curve. 4 Curve. 5 Curve. 1ST ~~02.50 1368.74 2375.00 1020.051781.25 821.413 1425.00 16 4107.07 7126.67 2053.61 3503.33 1369.16 2375 . 50 1026.971781.07 821.605 1425.33 17 4108.33 7128.33 2054.24 3564.17 1369.58 2370.11 1027.2811782.08 821.917 1425.67 18 4109.59 7130.00 2054.87 3565.00 1370.00 2370.07 1027.60:1782.50 822.109 1420.00 19 4110.85 7131.67 2055.50 3565.83 1370.43 2377.22 1027.91 1782.92 822.422 1420.33 20 4112.11 7133.33 2056.13 3566.67 1370.85 2377.78 1028.23 1783.33 822.674 1426.67 21 4113.37 7135.00 2056.76 3507.50 1371.27 2378.33 1028.54 ! 1783. 15 822.920 1427.00 22 4114.63 7136.67 2057.39 3508.33 1371.09 2378.89 1028.861784.17 823.178 1427.33 23 1115.89 7138.33 2058.02 3569.17 1372.11 4379.44 1029. 17| 1784. 58 823.430 1427.67 34 1117.15 7140.00 20.)8.65 3570.00 1372.53 23 SO. 00 10^9.49;i785.00 823.682 1428.00 25 4118.42 7141.67 2059.28 3570.83 1372.95 2380.50 1029.80 1785.42 823.935 1428.33 2G 4119.6-! 7143.33 2059.91 3571.67 1373.37 2381.11 1030.12 1785.83 824.187 1428.07 27 4120.90 7145.00 2060.56 3572.50 1373.80 2381.67 1030.44 1780.25 824.445 1429.00 28 4122.2o 7146.6? 2061.20 3573.33 1374.23 2382.22 1030.70 1786.67 824.703s 1429. 33 29 1123.51 7148.33 2061.83 3574.17 1374.6.3 2382.78 1031.08 1787.08 824.955 1429.07 30 4124.78 7150.00 2062.46 3575.00 1375.07 2383.33 1031.39 1787.50 825.207 1430.00 31 4126.04 7151.67 2063.09 3575.83 1375.49 2333.89 1031.71 1787.92 825.459 1130.33 32 4127.30 7153.33 2)63.72 3576.67 1315.91 2384.44 1032.02 1788.33 825.711 1430.07 33 4128.56 7155.00 2064.35 3577.50 1376.33 2385.00 1032.34 1788.75 825.904 1431.00 34 4129.82 7156.67 2004.98 3578.33 1376.75 2335.56 1032.05 1789.17 826.216 1431.33 35 4131 08 7158.33 2065.61 3579.17 1377 17 2386.11 1032.97 1789.58 826.468 1431.07 36 4132.34 7160.00 2066.24 3580.00 1377.59 2386.67 1033.28 1790.00 826.720 1432.00 37 4133.63 7161.67 2066.89 3580.83 1378.02 2387.22 1033.01 1790.42 826. 978 jl 432. 33 38 4134.92 7103.33 2067.53 3581.67 1378.45 2387.78 1033.93 1790.83 827.230 1432.07 39 4136.18 7105.00 2068.10 3582.50 1378.87 2388.33 1034.24 1791.25 827.488 1433.00 40 4137.44 7166.67 2068.79 3583.33 1379.29 2388.89 1034.56 1791.67 827 740 1433.33 41 4138.70 7168.33 2069.42 3584.17 1379.71 2389.44 1034.87 1792.08 827.9921433.07 42 4139.96 7170.00 2070.06 3585.00 1380.13 2390. OH 1035.19 1792.50 828.245 1434.00 43 4141.22 7171.07 2070.69 3585.83 1380.55 2390.56 1035 51 1792.92 828.497 1434.33 44 45 4142.48 4143.77 7173.33 7175.00 2071.323580.07 2071.963-87.50 1380.97 1381.40 2391.11 2391.67 1035.82 1036.14 1793.33 1793.75 828.749 1431.07 829.007 1435 00 46 4145.06 7176.6? 2072. 60 3 188. 33 1381.83 2392.22 1030.47 1794.17 829.205 1435.33 47 4146.32 7178.33 2073.243589.17 1382.25 2392.78 1030.78 1794.58 829.517J1435.07 48 4147.58 7180.03 2073.87 3590.00 1382.67 2393.33 1037.10 179x00 829.769 1436.00 49 4148.84 7181.67 2074.50 3.J90.83 1383.09 2393.89 1037.41 1795.42 830.021 1436.33 50 4150.10 7183.33 2075.13 3591.67 1383 .51 2394.44 1037.73 1795.83 830.274 1436.67 51 4151.39 7185.00 2075.773592.50 1383.94 2395.00 1038.05 1796.25 830. 531 11437. 00 52 4152.68 7186.67 2076.423593.33 1384.37 2395.56 1038.37 1796.67 830.789 1437.33 53 4153.94 7188.33 2077.053594.17 13S4.79 2396.11 1038.09 1797. OS 831.042 1437.67 54 4155.20 7190. 2077.683595.00 1385.21 2390.67 1039.00 1797.50 831.2941438.00 55 4156.46 7191.67 2078.31 3595.83 1385.03 2397.22 1039.32 1797.92 831.546 1433.33 5G 4157.72 7193.33 2078.943596.67 1386.05 2397.78 1039.031798.33 831.798 1438.07 57 4159.01 7195.00 2079.583597.50 1386.48 2398.33 1039 951798.75 83 i. 056 1439.00 58 4160.30 7190.07 2080.233598.33 1380.91 2398.89 1040.28 1799.1? 832.314 1439.33 59 4161.56 7198.33 2080.863599.17 1387.33 2399.44 1040.59 1799.58 832.5001439.67 188 TABLE XIV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 Curve. 10 Curve. 71 Tan. 681.456 Arc. 1183.33 Tan. Arc. Tan. 511.272 Arc. 887.500 Tan. Arc. Tan. Arc. 710.000 M. ~o" 584.199 1014.29 454.558 78S.889 409.207 881.666 1183.61 584.3791014.52511.430 887.708 454.698 789.074 409.334 710.167 1 681.876 1183.89 584. 559 !l014.76 511.587 887.917 454.839 789.259 409.460 710.333 2 68-3.086 1184.17 584.7391015.00511.745 888.125 454.979 789.444 409.586 710.500 3 682.297 1184.44 584.919 1015.24 511.903 888.333 455.119 789.630 409.712 710.667 4 682.507 1184.72 585.100 1015.48 512.060 888.542 455.259 789.815 409.838 710.833 5 68-2.717 1185.00 585.2801015.71 512.218 888.750 455.399 790.000 409.965 711.000 6 682.927 1185.28 585.460 1015.95 512.376 888.958 455.540 790.185 410.091 711.167 7 68,3.137 1185.56 585.640 1016.19 512.533 889.167 455.680 790.370 410.217 711.333 8 683.347 1185.83 585.820 1016.43 512.691 889.375 455.820 790.556 410.343 711.500 9 683.558 1186.11 586.001 1016.67 512.849 889.583 455.960 790.741 410.469 711 667 10 683.768 1186.39 586.181 1016.90 513.007 889.792 456.100 790.926 410.596 711.833 11 83.?8 1186.67 586. 361 11017. 14 513.164 890 000 456.241 791.111 410.722 712.000 158 684.188 1186.94 586.541 1017.38 513.322 890.208 456.381 791.296 410.848 712.167 13 684.398 1187.22 586.721 1017.62 513.480 890.417 456.521 791.481 410.974 712.333 14 684.609 1187.50 586.901 1017.86 513.637 890.625 456.661 791.667 411.100 712.500 15 684.819 1187.78 587.082 1018. 10 ! 513. 795 890.833 456.801 791.852 411.227 712.667 16 685.029 1188.06 587.262 1018.33 513.953 891.042 456.942 792.037 411.353 712.833 17 685.239 1188.33 587.442 1018.571514. 110 891.250 457.082 792.222 411.479 713.000 18 685.449 1188.61 587.622 1018.81 514.268 891.458 457.222 792.407 411.605 713.167 19 685.659 1188.89 587.802 1019.05 514.426 891.667 457.362 792.593 411.732 713.333 20 685.870 1189.17 587.983 1019.29 514.583 891.875 457.502 792.778 411.8:8 713.500 31 686.080 1189.44 588.163 1019.52514.741 892.083 457.643 792.963 411.984 713.667 22 686.290 1189.72 58S.343 1019.76514.899 S92.292 457.783 793.148 412.110 713.833 23 686.500 1190.00 588.523 1020.00 515.057 892.500 457.923 793.333 412.236 714.000 24 686.710 1190.28 5S8.703 1020.24 515.214 892.708 458.063 793.519 412.363 714.167 25 686.921 1190.56 588.884 1020.48 515.372 892.917 458.203 793.704 412.489 714.333 26 687.135 1190.83 589.068 1020.71 515.533 893.125 458.347 793 889 412.618 714.500 27 687.350 1191.11 589.252 1020.95 515.694 893.333 458.490 794.074 412.747 714.667 2S C87.561 1191.39 589.432 1021.19515.852 893.54-^ 458.630 794.259 412.873 714.833 29 687.771 1191.67 589.612 1021.43516.010 893.750 458.771 794.444 412.999 715.000 30 687.981 1191.94 589.793 1021.67 516.168 893.958 458.911 794 630 413.1-6 601 . 996 1037.62 526.848 907.917 468.406 807.037 421.674 726.333 38 702.431 1210.83 602.180 1037.86 527.009 908.125 468.550 807.222 421.803 7'26.500 39 702.646 1211.11 602.365 1038.10 527.170 908.333 468.693 807.407 421.932 726.667 4O 702.861 1211.39 602.549 1038.33 527. 331 1908.542 468 836 807.593 422.061 726.833 41 703.076 1211.67 602.733 1038.57 527.493908.750 468.980 807.778 422.190 727.000 42 703.291 1211.94 602.917 1038.81 527.654 908.958 469.123 807.963 422.319 7'27.167 43 703.506 1212.2-J 603.102 1039.05 527.815909.167 469.266 808.148 422.448 727.333 44 7r3 716 1212.50 603.282 1039.29 527.973 909.375 469.407 808.333 422.574 727.500 45 703.926 1212.78 603.462 1039.52 528.131 909.583 469.547 808.519 422.700 727.667 46 704.141 1213.06 603.646 1039.76 528.292909.792 469.690 808.704 422.830 727.833 47 704.356 1213.33 603.831 1040.00 528.453 910.000 469.834 808.889 422.959 728.000 48 7'04.571 1213.61 604.015 1040.24 528 614 910.20S 469.977 809.074 423.088 728.167 49 704.786 1213.89 604.199 1040.48 ")28. 776 910. 41 7 470.120 809.259 423.217 728.333 5O 705.001 1214.17 604.383 1040.71 528.937 910.625 470.264 809.444 423.346 728.500 51 705.216 1214.44 604.568 1040.95 529.098910.833 470.407 809.630 423.475 728.667 52 705.431 1214.72 504.752 1041.19 529.260 911.042 470 551 809.815 423.604 728.833 53 705.646 1215.00 604.936 1041.43 529.421 911.250 470.694 810.000 423.733 729.000 54 705.861 1215.28 605.121 1041.67 529.582911.458 470.837 810.185 423.862 729.167 55 706.076 1215.56 605.30511041.90 529 743 911.667 47X3.981 810.370 423.991 729.333 56 706 291 1215.83 605.4891042.14 529.905911.875 471.124 810.556 424.120 729.500 57 706.506 1216.11 605. 6731 042. 38 530. 066 912.083 471.267 810.741 424.249 729.667 58 706 721 1216.39 605.858 1042.62 530.227 912. 2921471. 411 810.926 424.379 729.833 59 191 TABLE XIV. ACTUAL TANGENTS, ETC. 73 1 Curve. 3 Curve. 3 Curve. 4 Curve. 5 Curve. M7 Tail. Arc. Tan. Are. Tan. Arc. Tau. Arc. Tun. Arc. ~~o 4239.71 7300.00 2119.93 3650.66 1413.38 2433.33 1060.13 1825.00848.201 1460.00 1 4-241.007301.67 2120.58 3650.83 1413.81 2433.89 1060.46 1825.42848.459 1460.33 3 4242.29 7303.33 2121.22 3651.67 1414.24 2434.44 1060.78 1825.83848.717 1460.67 3 4 -343.58 7305.00 2121.87 3652.50 1414.67 2435.00 1061.10 1826.25 848 975 1461.00 4 4214.87 7306.67 2122.51 3653.33 1415.10 2435.56 1061.42 1826.67 849.233 1461.33 5 4-240.16 7308.33 2123.16 3654.17 1415.53 2436.11 1061.75 1827.08849.491 1461.67 6 4247.45 7310.00 2123.80 3655.00 1415.96 2436.67 1062.07 1827.50849.749 1462.00 7 4248.74 7311.67 2124.45 3655.83 1416.39 2437.22 1062.39 1827. 92! 850. 007 1402.33 8 4250 03 7313.33 2125.09 3656.67 1416.82 2437.78 1062.71 1828.33 850.265 1462.67 9 4251.31 7315.00 2125.74 3657.50 1417.25 2438.33 1063.03 1828.75 850.523 1463.00 1O 4252.60 7316.67 2126.38 3658.33 1417.68 2438.89 1063.36 1829.17 850.780 1463.33 11 4253.92 7318.33 2127.04 3659.17 1418.12 2439.44 1063.69 1829.58 851.044 1463.67 13 4255.24 7320.00 2127.70 3660.00 1418.56 2440 00 1064.02 1830.00 851.308 1464.00 13 4256.53 7321.67 2128.34 3660.83 1418.99 2440.56 1064.34 1830.42 851.566 1464.33 14 4257.82 7323.33 2128.99 3661.67 1419.42 2441.11 1064.66 1830.83 851.824 1464.67 15 4259.11 7325.00 2129.63 3862.50 1419.85 2441.67 1064.981831.25 852.082 1465.00 1(5 4260.40 7326.67 2130.28 3663.33 1420.28 2442.22 1065. 31! 1831. 67 852.339 1465.33 17 1261.69 7328.33 2130.92 3664.17 1420.71 2442.78 1065.63 1832.08 852.597 1465.67 18 4262 . 97 7330.00 2131.57 3665.00 1421.14 2443.33 1065.95 1832.50 852.855 1466.00 19 4264.26 7331.67 2132.21 3665.83 1421.57 2443.89 1066.27 1832.92 853.113 1466.33 30 4265.55 7333.33 2132.85 3666.67 1422.00 2444.44 1066.59 1833.33 853.371 1466.67 21 4266.84 7335.00 2133.50 3667.50 1422.43 2445.00 1066.92 1833.75 853.629 1467.00 a 3 4268.13 7336.67 2134.14 3668.33 1422.86 2445.56 1067.24 1834.17 853.887 1467.33 33 4269.45 7333.33 2134.80 3669.17 1423.30 2446.11 1067.57 1834.58 854.151 1467.67 34 427'0.77 7310.00 2135.46 3670.00 1423.74 2446.67 1067.90 1835.00 854.414 1468.00 25 4272.06 7341.67 2136.11 3670.83 1424.17 2447.22 1068.22 1835.42 854.672 1468.33 36 4273.34 7343.33 2136.75 3671.67 1424.59 2447.78 1068.54 1835.83 854.930 1468.67 37 4274.63 7345.00 2137.40 3672.50 1425.02 2448.33 1068.87 1836.25 855.188 1469.00 38 4275.92 7346.67 2138.04 3673.33 1425.45 2448.89 1069.19 1836 (37 855.446 1469.33 39 4277.24 7348.33 2138.70 3674.17 1425.89 2449.44 1069.52 1837.08 855.709 1469.67 30 4278.56 7350.00 2139.36 3675.00 1426.33 2450.00 1069 85 1837.50 855.973 1470.00 31 4279.85 7351.67 2140.00 3675.83 1426.76 2450.56 1070.17 1837.92 856.231 1470.33 32 4281.14 7353.33 2140.65 3676.67 1427.19 2451.11 1070.49 1838.33 856.489 1470.67 33 4282. 4H 7355.00 2141.29 3677.50 1427.62 2451.67 1070.81 1838.75 856.747 1471.00 34 4283.72 7356.67 2141.94 3678.33 1428.05 2452.22 1071.14 1839.17 857.005 1471.33 35 4285.03 7358.33 2142.60 3679.17 1428.49 2452.78 1071.47 1839.58 857.268 1471.67 36 4286.35 7360.00 2148.25 3680.00 1428.93 2453.33 1071.801840.00 857.532 1472.00 37 4287.61 7361.67 2143.90 3680.83 1429.36 2453 . 89 1072.12 1840.42 857.790 1472.33 38 4288.93 7363.33 2144.54 3681.67 1429.79 2454.44 1072.44 1840.83 858.048 1472.67 39 4290.22 7365.00 2145.19 3682.50 1430.22 2455.00 1072.76 1841.25 858.306 1473.00 4O 4291.51 7366.67 2145.83 3683.33 1430.65 2455.56 1073.08 1841.67 858 564 1473.33 41 4292.83 7368.33 2146.49 3684.17 1431.09 2456.11 1073.41 1842.08 858.827 1473.67 43 4294.14 7370.00 2147.15 3685.00 1431.53 2456.07 1073.74 1842.50 859.091 1474.00 43 4295.43 7371.67 2147.80 3685.83 1431.96 2457.22 1074.07 1842.92 859.349 1474.33 44 4296.72 7373.33 2148.41 3686.67 1432.39 2457.78 1074.39 1843 33 859.607 1474.67 45 4298.01 7375.00 2149.10 3687.50 1432.83 2458.33 1074.72 1843 75 859.870 1475.00 46 4299. 3t> 7376.67 2149.76 3688.33 1433.27 2458.89 1075.05 1844.17 860.134 1475.33 47 4300.65 7378.33 2150.40 3689.17 1433.70 2459.44 1075.37 1844.58 860.392 1475.67 48 4301.94 7380.00 2151.05 3690 00 1434.13 2460.00 1075 69 1845.00 860.650 1476.00 49 4303.25 7381.67 2151.71 3690. 83 '1434. 57 2460.56 1076.02 1845.42 860.914 1476.33 5O 4304.57 7383.33 2152.36 3691 67 1435.00'24G1.11 1076.35 1845.83 861.177 1476.67 51 4305.86 7385.00 2153.01 3692.50 1435. 43 [246 1.67 1076.67 1846.25 861.435 1477.00 53 1307. 15 7386.67 2153.65 369 >. :-!3 1435.862462.22 1077.00 1846.67861.693 1477.33 53 4308.47 7388.33 2154.31 3694.17 1436.302462.78 1077.33 1847. 08801. 1)57 1477.67 54 55 4309.797390.00J2154.97 43H.Or 7391.672155.62 3695.00 3695.83 1436.74:2463.33 1437.172463.89 1077.66 1847.50:862.220 1077.9811847.928(12 478 1478.00 1478.33 56 4312.367393.332156.26 3696.67 1437.602464.44 1078. 30 11848.33 862. 7 36 1478.67 57 4313.68 7395.002156.92 3697.50 1438.042465.00 1078.63 1848.75 863. 000 1479.00 58 4315.007396.672157.58 3698.33 1438.482465.56 1078.96 1849.17.S63.2G3 1479.33 59 4316 29 7398.33 21 58. 22i 3699. 17 1438.91 2466.11 1079.28 1849. 58 1863. 521 1479.67 193 TABLE XIV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 Curve. 1O Curve. 73 Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. M. roe. 930 1210.07 t506.04ii 1042.86 530.388 912.500 471.554 811.111 424.508 730.000 707.150 1210.94 000.220 1043.10 530.550 912.708 471.698 811.296 424.637 730.167 1 707.305 1217.22 000.411 1043.33 530.711 912.917 471.841 811.481 424.766 730.333 2 707.680 1217.50 000 . 595 1043.57 530.872 913.125 471.984 811.667 424.895 730.500 3 707.795 1217.78 006.771) 1043.81 531.034 913.333 472.128 811.852 425.024 730.667 4 70S. 010 1218.06 606.963 1044.05 531 . 195 913.542 472.271 812.037 425.153 730.833 5 708.225 1218.33 607.1-18 1044.29 531.356 913.750 472.415 812.222 425.282 731.000 6 708.440 1218.61 607.332 1044.52 531.517 913.958 472.558 812.407 425.411 731.167 7 708.656 1218.89 007.510 1044.70 531.679 914.167 472.701 812.593 425.540 731.333 8 708.870 1219.17 607.701 1045.00 531.840 914.375 472.845 812.778 425.669 731.500 9 709.085 1219.44 607.885 1045.24 532.001 914.583 472.988 812.963 425.798 731.667 10 709 305 1219.72 008.073 1045.48 532.166 914.792 473.135 813.148 425.930 731.833 11 709.525 1220.HO 008 . 202 1045.71 532.331 915.000 473.281 813.333 426.062 732.000 12 709.740 1220.28 008.440 1045.95 532.492 915.208 473.425 813 519 426.191 732.167 13 709.955 1220.50 008.030 1046.19 532.654 915.417 47'3.568 813.704 426.320 732.333 14 710.161) 1220.83 008.814 1016.43 532.815 915.625 473.711 813.889 426.450 732.500 15 710.384 1221.11 008 999 1046.67 532.976 915.833 473.855 814.074 426.579 732.667 16 710 599 1221.39 009.183 1046.90 533.137 916.042 473.998 814.259 426.708 732.833 17 710.814 1221.07 009.30711047.14 533.299 916.250 474.142 814.444 426.837 733.000 18 711.029 1221.94 009.551 1047.38 533.460 916.458 474.285 814.630 426.966 733.167 19 711.244 1222 22 609.73611047.62 533.621 916.667 474.428 814.815 42". 095 733.333 20 711.459 1222.50 009.920 1047.86 533.782 916.875 474.572 815.000 427 227 733.500 21 711.074 1222.78610.104 1048.10 533.944 917.083 474.715 815.185 42". 359 733.667 22 711.894 1223.00010.293 1048.33 534.109 917.292 474.862 815.370 42". 488 733.833 23 712.114 1223.33 010.481 1048.57 534.273 917.500 475.008 815.556 42". 017 734.000 24 712.331 1223.01 010.005 1048.81 534 435 917.708 475.152 815.741 42". 746 734.167 25 71:2.544 1223.89 010.850 1049. (5 534.596 917.917 475.295 815.926 42". 875 734.333 26 712.759 1224.17 Oil. 034 1049.29 534. 7 o7 918.125 475.438 816.111 428 004 734.500 27 712.973 1224. 441011.218 1049.52 534. 91 U 918.333 475.582 816.290 428.133 734.667 28 713.193 1224.72 011.407 1049.76 535.083 918.542 475.728 810.481 428.265 734.833 29 713.413 1225.00 611.595 1050.00 5a5.248 918.750 475.875 816.667 428.397 735.000 30 713.028 1225.28 611.779 1050.24 535.410 918.958 476.018 816.852 428.526 735.167 31 713.843 1225.50 611.904 1050.48 535.571 919.167 476.162 817.037 428.655 735.333 32 714.058 1225.83 612.148 1050.71 535.732 919.375 470.305 817.222 428 784 735.500 33 714.273 1226 11 612.332 1050.95 535.893 919.583 470.448 817.407 428.914 735.667 34 714.493 1226.39 612.520 1051.19 536.058 919.792 470.595 817.593 429.045 735 833 35 714 712 1226.07 612.709 1051.43 536.223 920.000 476.742 817.778 429.177 736.000 36 714.927 1226.94 612.893 1051.67 536.384 920.208 476.885 817.963 429.307 736.167 37 715.142 1227.22 613.077 1051.90 536 546 920.417 477.028 818.148 429.436 736.333 38 715.357 1227.50 613.262 1052.14 536.707 920.625 477.172 818.333 429.565 736.500 39 715.572 1227.78 613 446 1052.38 536.868 920.833 477.315 818.519 429.694 736.667 40 715.792 1228.06 613.634 1052.62 537.033 921.042 477.462 818.704 429.826 736.833 41 716.012 1228.33)613.823 1052.86 537.198 921.250 477.608 818.889 429.958 737.000 42 710.227 1228.61 614.007 1053.10 537.359 921.458 477.7-52 819.074 430.087 737.167 43 716.441 1228.89614.191 1053.33 537.520 921.667 477.895 819.259 430.216 737.333 44 716.661 1229.17614.380 1053.57 53 T. 685 921.875 478.042 819.444 430.348 737.500 45 716.881 1229.44 614.568 1053.81 537.850 922.083 478.188 819.630 430.480 737.667 46 717.090 1229.72614.752 1054.05 538.011 922.292 478.332 819.815 430.609 737.833 47 717.311 1230.00614.937 1054. 29 1538.173 922.500 47'8.475 820.000 430.738 738.000 48 717.531 1230.28 615.125 1054.52 538.338 922.708 478.622 820.185 430.870 738.167 49 717.750 1230.56 615.313 1054.76 538.502 922.917 478.768 820.370 431.002 738.333 5O 717.905 1230.83 015.498 1055.00 53S.664 923.125 478.912 820.556 431.131 7'38.500 51 718.180I1231.11 015.082 1055.24538.825 923.333 479.055 820.741 431.260 738.667 52 718.400 12.11.39015.870 1055.48538.900 923.542 479.201 820.926 431.392 738.833 53 718.020,1231.07016.059 1055.71 539.155 923.750 479.348 821.111 431.524 739.000 54 718 83511231.94:616.213 1055.95 539.310 923.958 479.491 821.296 431.653 739.167 55 719.050 1232.22610.427 10:>6.19539.477 924.167 479.635 821.481 431.782 739.333 56 719.209 1232.50010.610 1056.43539.642 924.375 479.781 821.067 431.914 739.500 57 719.489 1232.78616.804 1056.67539.807 924.583 479.928 821.852 432.046 739.667 58 719.704 1233.06 616.988 1056.90 539. 968 1924. 792 480.071 822.037 432.175 739.833 59 193 TABLE XIV. ACTUAL TANGENTS, ETC. 740 1 Curve. 2 Curve. 3 Curve. 4 Curve. 5 Curve. M. Tan. 4317.58 Arc. 7400.00 Tan. Arc. 3700.00 Tan. Arc. Tan. Arc. Tan. Arc. O 2158.87 1439.34 2466.07 1 07 9 . GO 1 63 . 77'9 1480.00 1 4318.90 7401.67 2159.53 3700.83 1439.78 2467.22 1 07 9. 93 i 1850. 42 864. 043 1480.33 2 4320.21 7403 33 2160.19 3701.67 1440.22 2467.78 1080.26 1850.83864.307 1480.07 3 4821.58 7405.00 2160.84 3702.50 1440.66 2468.33 1080.59 1851. 25 864. 570 1481.00 4 4322.85 7'406.67 2161.50 3703.33 1441.10 2468.89 1080.92 1851.67864.834 1481.33 5 4324.14 7408.33 2162.15 3704.17 1441.53 2469.44 1081.24 1852.08865.092 1481.67 7 4325.43 4326 75 7410.00 7411.67 2162.79 2163.45 3705.00 3705.83 1441.96 1442.40 2470.00 2470.56 1081.57 1081.90 1852.50865.350 1852.92865.613 1482.00 1482.33 8 4328.06 7413 33 2164.11 3706.67 1442.84 2471.11 1082.23 1853. 33 1865.877 1482.67 9 4329.38 7415.00 2164.77 3707 50 1443.28 2471.67 1082.55 1853.75 866.141 1483.00 10 4330.70 7416 67 2165.43 3708.33 1443.71 2472.22 1082.88 1854.17 866.404 1483.33 11 4331.99 7418.33 3166.07 3709.17 1444.14 2472.78 1083.21 1854.58 866.6(52 1483.67 12 4333.28 7420.00 2166.72 3710.00 1444.57 2473.33 1083.53 1855.00 866.920 1484.00 13 4334 59 7421.67 2167.38 3710.83 1445.01 2473.89 1083.86 1855.42 867.184 1484.33 14 4335.91 7423.33 2168.04 3711.67 1445.45 2474.44 1084.19 1855.83867.447 1484.67 15 4337.23 7425.00 2168.69 3712.50 1445.89 2475.00 1084.52 1856.25867.711 1485.00 16 4338.55 7426.67 2169.35 3713.33 1446.33 2475 56 1084.85 1856.67 867.975 1485.33 17 4339.87 7428.33 2170.01 3714.17 1446.77 2476.11 1085.18 1857.08 868.238 1485.67 18 4341.18 7430.00 2170.67 3715 . 00 1447.21 2476.67 1085.51 1857.50 868.502 1486.00 19 4342.47 7431.67 2171.32 3715.83 1447.64 2477.22 1085.83 1857.92 868.760 1486.33 20 4343.76 7433.33 2171.96 3716.67 1448.07 2477.78 1086.15 1858.33 869.018 1486.67 21 4345.08 7435.00 2172.62 3717.50 1448.51 2478.33 1086.48 1858.75 869.281 1487.00 22 4346.40 7436.67 2173.28 3718.33 1448.95 2478.89 1086.81 1859.17 869.545 1487.33 23 4347.72 7438.33 2173.94 3719.17 1449.39 2479.44 1087.14 1859.58 869.809 1487.67 24 4349.03 7440.00 2174.60 3720.00 1449.83 2480.00 1087.47 1860.00 870.072 1488.00 25 4350.35 7441.67 2175.26 3720.81 1450.27 2480.56 1087.80 1860.42870.336 1488.33 26 4351.67 7443.33 2175.91 3721.67 1450.71 2481.11 1088.13 1860.83 870.600 1488.67 27 4352.99 7445.00 2176.57 3722.50 1451.15 2481.67 1088.46 1861 25 870.863 1489.00 28 4354.30 7446.67 2177.23 3723.33 1451.58 2482.22 1088.79 1801.67871.127 1489.33 29 4355.62 7448.33 2177 89 3724.17 1452.02 2482.78 1089.12 1862.08 871.391 1489.67 3O 4356.94 7450.00 2178.55 3725.00 1452.46 2483.33 1089.45 1862.50 871.654 1490.00 31 4358.26 7451.67 2179.21 3725.83 1452.90 2483.89 1089.78 1862. 92 ; 871. 918 1490.33 32 4359.58 7453.33 2179.87 3726.67 1453.34 2484.44 1090.11 1S63.33872.182 1490.67 33 4360.89 7455.00 2180.53 3727.50 1453.78 2485.00 1090.43 18(53.75872.445 1491.00 34 4362.21 7456.67 2181.19 3728.33 1454.22 2485.56 1090.76 1 864. 17 ! 872. 709 1491.33 35 4363.53 7458.33 2181.84 3729.17 1454.66 2486.11 1091.09 1864.58872.972 1491.67 36 4364.85 7460.00 2182.50 3730.00 1455.10 2486.67 1091.42 1865.00873.236 1492.00 37 4366.17 7461.67 2183.16 3730.83 1455.54 2487.22 1091.75 1865.42873.500 1492.33 38 4367.48 7463.33 2183.82 3731.67 1455.98 2487.78 1092.08 1865.83 873.763 1492.67 39 4368.80 7465.00 2184.48 3732.50 1456.42 2488.33 1092.41 1866.25 874.027 1493.00 40 4370.12 7466.67 2185.14 3733.33 1456.86 2488.89 1092.74 1866.67 874.291 1403.33 41 4371.44 7468.33 2185.80 3734.17 1457.30 2489.44 1093.07 1867.08874.554 1493.67 42 4372.75 7470.00 2186.45 3735.00 1457.73 2490.00 1093.40 1867. 50 874. 818 1494.00 43 4374.07 7471.67 2187.12 3735.83 1458.17 2490.56 1093.73 1867.92875.082 1494.33 44 4375.39 7473.33 2187.78 3736.67 1458.61 2491.11 1094.06 1868.33875.345 1494.67 45 4376.71 7475.00 2188.43 3737.50 1459.05 2491.67 1094.39 1868.75875.609 1495.00 46 4378.03 7476.67 2189.09 3738.33 1459.49 2492.22 1094.72 1869.17875.873 1495.33 47 4379. 34 7478.33 2189.75 3739.17 1459.93 2492.78 1095.05 1869.58876.136 1495.07 48 4380.66 7480.00 2190.41 3740.00 1460.37 2493.33 1095.38 1870.00876.400 1496.00 49 4381.98 7481.67 2191.07 3740.83 1460.81 2493.89 1095.71 1870.42876.663 1496.33 5O 4383.30 7483.33 2191.73 3741.67 1461.25 2494.44 1096 04 1870.83876.927 1496.67 51 4384.61 7485.00 2192.39 3742.50 1461.69 2495.00 i one. 37 1871.25877.191 1407.00 52 4385 93 7486.67 2193.05 3743.33 1462.13 2495.5(5 1096.70 1871.67877.454 1497.33 53 4387.25 7488.33 2193 71 3744.17 1462.57 2496.11 1097 03 1872.08877.718 1497.67 54 4388.57 7490.00 2194.36 3745.00 1463.0! 2496.67 1097.35 1872.50877.982 1498.00 55 4389.89 7491.67 2195.02 3745.83 1463.45 2497.22 1097.68 1872.92878.245 1498.83 56 4391.20 7493.33 2195.68 3746.67 1468.80 2497.78 1098.01 1873.33878.509 14 98. (57 57 4392.52 7495.00 2196.34 3747.50 1464.3-2 2498.33 1098.34 1873.75878.773 1400 00 58 59 4393.84 4395.19 7496.67 7498. 33 2197.00 2197.67 3748.33 3749.17 1464.76 1465.21 2498.89 2499.44 1098.67 1099.01 1 874. 1 7 879. 036 j 1499. 33 1874.58879.30611499.07 194 TABLE XIV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 Curve. 10 Curve. 74 M. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. 71 9. U 19 '1233. 33 617.172 1057.14 540.130 925.000480.215 822.222 432.304 740.000 O 720.139 1.233.61 617.361 1057.38 540.294 925.208480.361 822.40? 432.436 740.1(57 1 720.358 .1233. 89 617.549 1057.62 540.459 925.417480.508 822.593 432.568 740.333 2 720.578 1234.17 617. 788 1057.86 540.624 925.625480.654 822.778 488.700 740.500 3 720.798:1234.44 617.926 1058.10 540.789 925.833480.801 822.963 43 J. 832 740.667 4 721.013 1234.72 618.110 1058.33 540.950 926.042 480.944 823.148 432.961 740 833 5 721.228 1235.00 61 S. 295 1058.5? 541.112 926.250 481.088 823.333 433.090 741.000 6 7 2 1. 448 1235. 28 618.483 1058.81 541.276 926.458 481.234 823.519 433.222 741.167 7 721.667 1*35.56 618.671 1059.05 541.441 926.66? 481.381 823.704 433. 354 741.333 8 721.887 1235.83 618.860 1059.29 541.606 926.875 481.528 823.889 433.486 741.500 9 722.107 1236.11 619.048 1059.52 541.771 927.083 481.674 824.074 433.618 741.667 1O 722 3221236.39 619 232 1059.76 541 932 927.292 481.817 824.259 433.74? 741.833 11 722.5371236.67 619.417 1060.00 542.093927.500 481.961 824.444 433.876 742.000 12 722.756 1236.94 619 605 1060.24 542.258927.708 482.10? 824.630 434.008 742.167 13 722.976 1237.2V 619.793 1060.48 542. 423 927.. 91 7 482.254 824.815 434.140 742.333 14 723.196 1237.50 619.U82 1060.71 542.588928.125 482.401 825.000 434.272 742.500 15 723.416 1237.78 620.170 1060.95 542.753928.333 482.547 825.185 434.404 742,66? 16 723.635 1238.06 620.358 1061.19 542.918928.542 482.694 825.370 434.536 742.833 17 723.855 1238.33 620.547 1061.43 543.083928.750 482.840 825.556 434.668 743.000 18 724.070 1238.61 620.731 1061.67 543.244 928.958 482.984 825.741 434.79? 743.167 19 724.285 1238.89 620.915 1061.90 543.405 929.167 483.127 825.926 434.926 743.333 20 724.505 1239.1? 621.104 1062.14 543.570929.375 483.274 826.111 435.058 743.500 21 724.725 1239.44 621.292 1062.38 543.735929.583 483.420 826.296 435.190 743.66? 22 724.944 1239.72 621.481 1062.62 543.900929.792 483.56? 826.481 435.322 743 833 23 725.164 1240.00 621.669 1062.86 544.065 930.000 483.713 826.667 435.454 744.000 24 725.384 1240.28 621.857 1063.10 544.230930.208 483.860 826.852 435.586 ?44.16? 25 725.603 1240.56 622.046 1063.33 544.394 930.41? 484.007 827.03? 435.718 744 333 26 725.823 1240.83 622 234 1063.57 544.559 930.625 484.153 827.222 435. 84 ( J 744.500 21 726.043 1241.11 622.422 1063.81 544.724 930.833 484.300 827.407 435.981 744.60? 28 726.263 1241.39 622.611 1064.05 544.889 931.042 484. 44G 827.593 436.113 744.833 29 726.482 1241.67 622.799 1064.29 545.054 931.250 484.593 827 778 436.245 745 000 3O 726.702 1241.94 622.988 1064.52 545.219 931.458 484.739 827.963 436.37? 745.16? 31 726.922 1242 22 623.176 1064.76 545.384 931.66? 484.886 828.148 436.501) 745.333 32 727.142 1242.50 623.364 1065.00 545.548 931.875 485.033 828.333 436.641 745.500 33 727.361 1212.78 623 553 1065.24 545.713 932.083 485.179 828.519 436.773 745.667 34 727.581 1243.0(5 623.741 1065.48 545.878 932.292 485.326 828 704 436.905 745.833 35 727.801 1243 33 623.929 1065.71 546.043 932.500 485.472 828.889 437.037 746 000 36 728.021 1243.61 624.118 1065.95 546.208 932.708 4S5.619 829.074 437.16'J 746.16? 37 728.240 1243.89 G24.306 10(56.19 546.37'3 932 917 485.765 829.259 437.301 746.333 38 728.460 1244.17 624.495 1066.43 546.538 933.125 485.912 829.444 437.433 746.500 39 728.680 1244.44 624.683 1066.6? 546.70-2 933 333 486 059 829.630 437.565 746.667 40 728.899 1244.72 624.871 1066.90 546.86? 933.542 486.205 829.815 437.697 746.833 41 729.119 1245.00 625.060 1067.14 547.032 933.750 486 352 830.000 437.829 747.000 42 729 339 1245.28 625.248 1067.3h 547.197 933.958 486.498 830.185 437.961 7'47.167 43 729.559 1245.56 625 . 436 10(57.62 547.362 934.167 486.645 830.370 438.093 747.333 44 729 . 77H 1245.83 625.635 1067.86 547.527 934 375 486.791 830.556 438.225 747.500 45 729.998 1246.11 625.813 1068.10 547.692 934.583 486.938 830 741 438.356 747.667 4C 730.218 1246.3! 626.002 1068.33 547.856 934.792 487.085 830.926 438.488 747.833 47 730.438 124(5.6? 626.190 1068.57 548.021 935.000 487.231 831.111 438.620 748.000 48 730.657 1246.91 626.378 1068.81 548.186 935.208 487.378 831.296 438.752 748.167 49 730.877 1247.22 626.567 1069.05 548 351 935.41? 487.524 831.481 438.884 748.333 5O 731.097 1247.50 626.755 1069.29 548.516 935.625 487.671 831.66? 439.016 7'48 500 51 731.317 1247.78 626.943 1069.52 548 681 935.833 487.817 831.852 439.148 748.667 52 731.536 1248. 01 627.132 10(59.7( 548.846 936.042 487.964 832.03? 439.280 748.833 53 731.751511248.33 627.320 1070.00 549.010 93(5.250 488.111 832.222 439.412 749.000 54 73 1.97 6 j 1248. 61 627.509 1070.24 549.175 936.458 488.25? 832.407 439.544 749 167 55 732.1% 1248.89 ( '.27. (597 107'0.4S 549.340 93<>.667 488.404 832.593 489.676 749.333 56 732. 41 5i 1249.1? 6-J7.8S5 1070.71 549.505 936. 875 488.550 832.778 439.808 749 500 57 732. (535 1249.44 628.074 1070.95 549.670 937.083 488.69? 832.963 439.940 7'49.667 58 732.860 1249.7:. 628.266 1071.19 549.838937.292 488.84? 833.148 440.075 749.833 59 195 TA35LE XIY. ACTUAL TANGENTS, ETC. 75 1 Curve. 3 Curve. 3 Curve. 4 Curve. 5 Curve. M. Tan. Arc. Tan. Arc. Tau. Arc. Tan. Arc. Tan. A rc. 43'.)6.53 7500.00 2198.35 3750700 1465~66 2500.00 1099.35 1875.00 879.575 1500.00 1 4897.85 7501.67 2199.01 3750.83 1466.10 2500.56 1099.68 1875.42 879.839 1500.3:] 2 4399.17 7503.33 2199.663751.6; 1406.54 2501.11 1100.01 1875.83 880.102 1500.6; 3 4400.49 7505.00 2200 32 3752.50 1466.98 2501.67 1100.33 1876.25 880. 360 1501. Oil 4 4401.80 7506.67 2200.98 3753 . 33 14f,7.42 2502.22 1100.66 1876.67 880.030 1501.33 5 4408.12 7508.33 2201.64 3754.17 1467.86 2502.7!- 1100.99 1877.08 880.893 1501.67 6 4404.44 7510.00 2202.30 3755.00 1468.30 2503.3. 1101.32 1877.50 881.157 1502.00 7 4405.79 7511.67 2202.97 3755.83 1468.75 2503.89 1101.66 1877.92 881.426 1502.33 8 4407.13 7513 33 2203 65 3756.67 1469.20 2504.44 1102.00 1878.33 881.696 1502.67 9 4408.45 7515.00 2204.31 3757.50 1469.63 2505.00 1102.33 1878.75 881.959 1503.00 1O 4409.77 7516.67 2204.96 3758.33 1470.07 2505.56 1102.66 1879.17 882.223 1503.33 It 4411 09 7518 33 2205.62 3759.17 1470.51 2506.11 1102.99 1879.58 882.487 1503.67 12 4412.40 7520.00 2206.28 3760.00 1470.95 2506.67 1103.31 1880.00 882.750 1504.00 13 4413.75 7521.67 2206.96 3760.83 1471.40 2507. 2'.' 1103.65 1880.42 883.020 1504.33 14 4415.10 7523.33 2207.63 3761.67 1471.85 2507.78 1103 99 1880.83 883.289 1504.67 15 4416.41 7525.00 2208.29 3762.50 1472.29 2508.33 1104.32 1S81.25 883.553 1505.00 16 4417.73 7526.67 2208.95 3763 33 1472.73 2508.89 1104.65 1881.67 883.816 1505.33 17 4419.05 7528.33 2209.61 3764.17 1473.17 2509.44 1104.98 1882 08 884.080 1505.67 18 4420.37 7530.00 2210.26 3765.00 1473.61 2510.00 1105.31 1882.50 884.344 1506.00 19 4421.71 7531.67 2210.94 3765.83 1474.06 2510.56 1105.64 1882.92 884.613 1506.3:] 20 4423.06 7533 33 2211.61 3766.67 1474.51 2511.11 1105.98 1883.33 884.882 1506.67 21 4424.38 7535.00 2212.27 3767.50 1474.94 2511.67 1106 3: 1883.75 885.146 1507.00 22 4425.70 7536.6: 2212.93 3768.33 1475.38 2512.22 1106.64 1884.17 885.410 1507.33 23 4427.04 7538.33 2213.60 3769.17 1475.83 2512.78 1106.98 1884.58 885 679 1507.67 24= 4428.39 7540.00 2214.28 3770.00 1476.28 2513.33 1107.31 1885.00 885.948 1508.00 25 4429.71 7541.67 2214.93 3770.83 1476.72 2513. S9 1107.64 1885.42 886.212 1508.33 36 1431.02 7543.33 2215.59 3771.67 1477.16 2514.44 1107.97 1885.83 886.476 1508.67 37 4432.37 7545.00 2216.27 3772.50 1477.61 2515.00 1108.31 1886.25 886.745 1509.00 28 4433.72 7546.67 2216.94 3773.33 1478.06 2515.56 1108.64 1886.67 887.014 1509.33 39 4435.04 7548.33 2217.60 3774.17 1478.50 2516.11 1108.97 1887.08 887.278 1509.67 30 4436.35 7550.00 218.26 3775. CO 1478.94 2516 67 1109.30 1887.50 887.542 1510.00 31 4437.70 7551.67 2218.93 3775.83 1479.39 2517.22 1109 64 1887.92 887.811 1510.33 33 4439.05 7553.33 2219.00 3776.67 1479.83 2517.78 1109 98 1888.33 888.080 1510.67 33 4440.30 7555.00 2220.26 3777.50 1480.27 2518.33 1110.31 1888.75 888.344 1511.00 34 4441.68 7556.67 2220.92 3778.33 1480.71 2518.89 1110.64 1889.17 888.608 1511.33 35 4443 03 7558.33 2221.60 3779.17 1481.16 2519.44 1110.97 1889.58 888.877 1511.67 36 4444.37 7560.00 2222.27 3180 00 1481.61 2520 00 1111.31 1890.00 889.146 1512.00 37 4445 72 7561.67 2222.94 3780.83 1482.06 2520.56 1111.65 1890.42 889.416 1512.33 38 4447.07 7563.33 2223. 6v! 3781.67 1482.51 2521.11 1111.98 1890.83 889 . 685 1512.67 39 4448 . 39 7565.00 2221.27 3782.50 1482.95 2521.67 1112.31 1891.25 889.949 1513.00 4O 4449.70 7566.67 2224.93 3783.33 1483.39 2522. 2 J 1112.64 1891.67 890.213 1513.33 41 4451.05 7568 33 2225.61 3784.17 1483.84 2522 78 1112.98 1892.08 890.482 1513.67 43 4452 40 7570.00 2026.28 3785.00 1484 28 2523.33 1113.31 1892.50 890.751 1514.00 43 4453.71 7571.67 2226.94 3785.83 1484.72 2523 89 1113.64 1892.92 891.015 1514.33 44 4455.03 7573.33 2227.60 37'86.67 1485.16 2524.44 1113.97 1893.33 891.279 1514.67 45 4456.38 7575.00 2228.27 3787.50 1485.61 2525.00 1114.31 1893.75 891 548 1515.00 46 4457.72 7576.67 2228.91 3788 33 1486.06 2525.56 1114.65 1894.17 891.817 1515.33 47 44 r 9.07 7578.33 2229.62 37'89.17 1486.51 2526.11 1114.98 1894.58 892.087 1515.67 48 4460.42 7580.00 2230.29 3790.00 1486.96 2526.67 1115.32 1895.00 892.356 1516.00 49 4461.76 7581.67 2230.96 3790.83 1487.41 2527.22 1115.60 1895.42 892.625 1516.33 50 4463.11 7583.33 2231.64 3791.67 1487.86 2527.78 1115.99 1895.83 892.895 1516.67 51 4464.43 7585.00 2232.3013792.50 1488.302528.33 1116.32 1896.25 893.158 1517.00 53 4465 75 7586.67 2232 96 13793. 33 1488.74 2528.89 1116.65 1896.67 893.422 1517.33 53 4467.09 7588.33 2233.633794 17 1489.18 2529.44 1116.99 1897.08 893.691 1517.67 54 446S.44 7590.00 2234. 3:) 13795 00 1489.632530.00 1117.33 1897.50 893.961 1518.00 55 4469 79 7591.67 2234. 97 J3795. as 1490.082530.56 1117.66 1897.92 894 230 1518.33 56 4471 . 13 7593.33 2235.6-)] 3796 67 1490.532531.11 1118.00 1898.33 894.500 1518.67 57 4472.48 7595.00 2286.32 3797 50 1490.982531.67 1118.34 1898.75 894.769 1519.00 58 4473.83 7596.67 2236 99 3798.33 1491.432532.22 1118.67 1899.17 81)5.038 1519.33 59 4475.17 7598.33 2237.67.3799.17 1491.882532 78 1119.01 1899.58 895.308 1519.67 196 TABLE XIV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 Curve. 1O Curve. 75 Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. M. 733.084 250.00628.459 1071.43 a50.007 937.500 488.996 833.333 40.209 "50.000 O 733.304 1250.28 628.647 1071.67 a50.172 937.708 489.143 833.519 40.341 "50.167 1 733.533 250.56628.835 1071.90 050.336 937.917 489.289 833.704 40.473 50.333 2 733.743 1250.83629.024 1072.14 350.501 938.125 489.436 833.889 40.605 T>0.500 3 733.963 1251.11 629.212 1072.38 >50.000 138.333 489.583 834.074 440.737 "50.667 4 734.183 1251. 3'.) 629. 400 1072.62 350.831 W8.542 489.729 834.259 10.869 '50.833 5 734.40:3 1251.67629.589 1072.86 a50.996 J38.750 489.876 834.444 441.001 "51.000 6 734.627 1251.94629.781 1073.10 351.164 J38.958 490.026 83 1 . 630 441.136 '51.167 7 734.851 252.22 629.974 1073. 33 >5 1.333 )39.107 490.175834.815 441.271 "51.333 8 735.071 252.50 630.162 1073.57 351.498 J39.375 490.322 835.000 441.403 "51.500 9 735.291 1252.78 630.350 073.81 551 .663 939.583 490.468 835.185 441.535 "51.667 10 735.511 1253.06 630.539 074.05 351.827 >39.792 490.615 835.370 441.667 751.833 11 7:35.730 1253.33 630.727 074.29 o51.992 9IO.UH) 490.762 835.556 441.799 "52.000 12 735.955 1253.61 630.920 074.52 )52.161 J 40. 208 490.911 835. 7-M m.933 "52.167 13 736 179 1253.89 631.112 074.70 o52.329 J 40. 417 491.061 833.926 442.068 "32.333 14 736.399 1254.17 631.301 1075.0,i >52.49l ) 40. 025 491 .208 836.111 442.200 752.500 15 736.619 1254.44 631.489 075.24 552.659 JIO 833 191.354 836. 2-1)6 442.332 ~52.667 16 736.839 1254.72 631.677 1075.48 >52.824 J4 1.042 491.501 836.481 442.464 752.833 17 737.058 1255.00 631.866 075.71 552.989 J4 1.250 491.647 836.067 442 596 "53.000 18 737.283 1255.28 632.058 1075.95 553.157 941.458 491. 79 T 836.852 442.731 753.167 19 737.507 1255.56 632.251 076.19 553.325 941.667 491.947 837.037 442.866 753.333 20 737.727 1255.83 032.43d 1076.43 >53.4i)0 941.875 492.093 837.222 442.998 753.500 21 737.947 1256.11 632.627 1076.67 353 . 055 J 42. 083 492.240 837.407 443.130 753.667 22 738.171 1256.39 632.820 1076.90 053.824 J 42. 292 492.390 837.51)3 443.264 753.833 23 738.396 1256.67 633.012 1077.14 053.992 942.500 492.540 837.778 443.399 754.000 34 738.616 1256.94 633.201 1077.38 351.157 J 42. 708 492. 6S6 837.963 443.531 754.167 25 738.835 1257.22 633.3.30 1077.62 354.322 J42.917 492.833 838.148 443.663 754.333 26 739.060 1257.50 635.582 1077.80 354.490 J43.125 492 982 838.333 443.798 754.500 27 73 J. 284 1257.78 633.774 1078.10 35 1.059 J43.333 493.132 838.519 443.933 754.667 28 739.504 1258.06 633.962 1078. 3 i 354.824 943.542 193.279 833.704 444.065 754.833 29 739.724 1258.33 634.151 1078.57 554.988 ) 13. 750 493.425 838.889 444.197 755.000 30 739.918 1258.61 634.313 1078.81 555.157 J43.958 493.575 839.074 444.331 755.167 31 740.173 1258.89 634 . 536 1079.05 555.325 914.167 493.725 839.259 444.466 755.333 32 740.393 1259.17 634.724 1079.2U 555.490 944.375 493.871 839.444 444.598 755.500 33 740.612 1259.44 634.912 1079.52 555 . 655 944.583 494.018 839.630 444.730 753.667 34 740.837 1 259 . 72 635.105 1079.70 355.823 144.792 194.108 839.815 444.865 755.833 35 741.061 1260.00 035.297 1080.00 555.992 945.000 494.318 840.000 445.000 756.000 36 741.286 1260.28 63.3. 49 J 1080.24 o56.160 J45.208 494.467 840.185 445.135 756.167 37 741.510 1260.56 035.08: 1080.48 )56.329 945.417 11)4.617 840.370 445.269 756.333 38 741.730 1260.83 635.871 1080.71 356.494 945.625 494.764 840.556 445.401 756.500 39 741.951 1261.11 636.059 1080.95 556.658 945.833 494.910 840.741 445. 533 756.667 4O 742.174 1261.3;) 63<> 252 1081.19 J56.827 946.042 495.060 840. 92C 445.668 756.833 41 742.399 1261.67 636.444 1081.43 556.995 946.250 495.210 841.111 445.803 757.000 42 742.619 1261.91 636.632 1081.67 557.160 946.458 495.356 841. 29( 445.935 757.167 43 742.838 1262.22636.821 1081.90 557. 325 946.667 495.503 841.481 446.067 757.3:33 44 743.063 1262.50 637.013 1082.14 557.494 946.875 495.653 841.667 446.202 757.501 45 743.287 1262.78 637.206 1082.38 557.002 947.083 495.802 841.852 446.337 757.667 46 743.512 1263.06 037.393 1082.62 557.830 947.29v 495.95'. 842.037 446.471 757.83: 47 743.736 1263.33 037.5'.)! 1082.86 557.991 947.500 196.102 842.222 446.606 758.000 48 743.961 1263.61 637.783 1083.10 558.16; 947.708 496.252 842.407 446.741 758. I0 r 49 744.18: 1263.89 037.970 1083.33 558.336 947.917 496.401 842.593 446.876 758.3* 5O 744 40." 1264.17 038. 164 1083.57 558.501 948.125 496.548 842.778 447.008 758.500 51 741.625 1264.44 638.352 1083.81 558.665 94S.333 41)6.695 842.963 447.140 758.60" 52 744.849 1254.72 638.545 1084.0: 558.831 948.54", 496.844 843.148 447.274 758.8* 53 74:>. 074 12ii5.00638.73; 1084.21 559 00, 948 75 496.99- 843.333 447.409 759.000 54 745 . 208 1 2(35 . 28 638 . 9-Jl 1084.5;. 559.171 918.958 497.144 843.519 447.544 759.16' 55 745.523 12(55.56 039.12', 1084 7b 559.339 949.167 497.294 843.704 447.679 759.33- 56 745.747 1265. 83 639.31' 1085.00 559.508 949.375 497.443 843.889 447.814 759. 5(K 57 715.972! 1266. 11 639.507 1085.24 559.676 949 583 497.593 844.074 447.949 759.66 58 746.196 1266.39,639.700 1085.48 559.845919.792 497.743 844.259 448. 0831759. 83: 59 197 TABLE XIV. ACTUAL TANGENTS, ETC. 76 1 Curve. 2 Curve. 3 Curve. 4 Curve. 5 Curve. M. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. 4476.52.7600.00 2238.34 3800.00 149*5.33 2533.33 1119.35 1900.00895.577 1520.00 1 4477.84 7601.67 2239.00 3800.83 1492. 77 2533. 8U 1 1 1 9 . 6S 1 900. 42 895. 84 M 520. 33 2 4479.15 7603.33 2239 66 3801.67 1493.21 2534.44 1120.01 1900.83896.104 1520.67 3 4480.50 7605.00 2240.33 3802.50 1493.65 2535.00 1120.34 1901.25896.374 1521.00 4 4481.85 7606.67 2241.01 3803.33 1494.10 2535 . 5U 11 20 .-68 1901 671896.643 1521.33 5 4483.19 7608.33 2241.683804.17 1494.55 2536.11 1121.02 1902.08896.913 1521.67 6 4484.54 7610.00 2242. 35 '3805. 00 1495.00 2536.67 1121.35 1902.50 897.182 1522.00 7 4485.89 7'611.67 2243.033805.83 1495.45 2537.22 1121.69 1902.92 897.451 1522.33 8 4487.23! 76 13. 33 2243.703806.67 1495.90 2537.78 1122.03 1903.33 897.721 1522.67 9 4488.58J7615.00 2244.37 3807.50 1496.35 2538.33 1122.36 1903.75 897.990 15:23.00 1O 4489.93 7616.67 2245.05 3808.33 1496.80 2538.89 1122.70 1904.17 898.259 1523.33 11 4491.27 7618.33 2245.72 3809.17 1497.24 2539.44 1123.04 1904.58 898.529 1523.67 12 4492.62 7620.00 2246.39 3810.00 1497.69 2540.00 1123.37 1905.00 898.7981524.00 13 4493.97 7621.67 2247.06 3810.83 1498.14 2540.56 1123.71 1905.42:899.068 1524.33 14 4495.31 7623.33 2247.74J3811.67 1498.59 2541 . 1 1 1 1 24 . 05 ! 1 905 83 899 . 337 1 524 . 67 15 4496.60 7625.00 2248. 41 13812. 50 1499.04 2541.67 1124.38 1906.25 899.606 1525 00 16 4498.00 7626.67 2219.08 3813.33 1499.49 2542.22 1124.72 1906.67 899.876 1525.33 17 4499.35 7628.33 2249.76 3814.17 1499.94 2542.78 1125.06 1907.08 900.145 1525.67 18 19 4500.70 4502.04 7630.00 7631.67 2250.43 2251.10 3815.00 3815.83 1500.39 1500.84 2543.33 2543.89 1125.39 1125.73 1907.50 1907.92 900.414 900.684 1526.00 1520.33 20 4503.39 7633 33 2251.78 3816.67 1501.28 2544 44 1126 07 1908.33 900.953 1526.67 21 4504.74 7635.00 2252.45 3817.50 1501.73 2545.00 1126.40 1 90S. 75 901.223 1527 00 22 4506.08 7636 67 2253.12 3818.33 1502.18 2545.56 1126.74 1909.17 901.492 1527.33 23 4507.43 7638.33 2253.80 3819.17 1502.63 2546.11 1127.08 1909.58 901.761 1527 67 24 4508.78 7640. 00 2254.47 3820.00 1503.08 2546.67 1127.41 1910.00 902.031 1528.00 25 4510.12 7641.67 2255.14 3820.83 1503.53 2547.22 1127.75 1910.4V 902.300 1528.33 26 4511.47 7643.33 2255.82 3821.67 1503.98 2547. 7M 1128.09 1910.83 902.56'J 1528.67 27 4512.82 7645.00 2256.49 3822.50 1504.43 2548.3:3 1128.42 1911.2.') 902 839 1529.00 28 4514.16 7646.67 2257.16 3823.33 1504.88 2548.89 1128.76 1911.67 903.108 1529.33 29 4515.54 7648.33 2257.85 3824.17 1505 33 2549.44 11*9.10 1912.08 903.383 1529.67 3O 4516.91 7650.00 2258.54 3825.00 1505.79 2550.00 1129.45 1912.50 903.658 1530.00 31 4518.26 7651 . 67 2259.21 3825.83 1506.24 2550.56 1129.78 1912.92 903.928 15:30.33 32 4519.61 7653.33 .'259.89 3826.67 1506.69 2551 . 1 1 1180.1* 1913.33 904.197 1530.67 33 4520.95 7655.00 360.56 3827.50 1507.14 2551. (37 1130.46 1913.75 904.467 1531.00 34 4522.30 7656.67 >61.23 3828.33 1507.59 2552.22 1130.79 1914.17 904.736 1531.33 35 4523.64 7658.33 2:261.91 3829.17 1508.04 2552.78 1131.13 1914.58 905.005 1531.67 36 4524.99 7660.00 262.58 3830.00 1508.49 2553.33 1131.47 1915.00 905.275 1532 00 37 4526.34 7661.67 2263.25 3830.83 1508.93 2553.89 1131.80 1915.42 905.544 1532.33 38 4527.68 7663.33 263.92 3831.67 1509.38 2554.44 1132.14 1915.83 905.813 1532.67 39 4529.06 7665.00 264.61 3832.50 1509.84 2555.00 1132.48 1916.25 906.088 1533.00 40 4530.43 7666.67 2265.30 3833.33 1510.30 2555.56 1132.83 1916.67 906.364 1533.33 41 4531.78 7668.33 2265.97 3834 17 1510.75 2556.11 1133.16 1917.08 906.633 533.67 42 4533.13 7670.00 2266.65 3835.00 1511.20 2556.67 1133.50 1917.50 906.902 1534.00 43 4534.47 7671.67 2267.32 3835.83 1511 65 2557.22 1133.84 1917.92 907.172 1534.33 44 4535.82 7673.33 2267.99 3836 67 1512.10 2557.78 1134.17 1918.33 907.441 1534.67 45 4537.20 7675.00 2268.68 3837.50 1512.55 2558.33 1134.52 1918.75 907.716 1535.00 46 4538.57 7676.67 2269.37 3838.33 1513.01 558.89 1134.86 1919.17 907.991 1535.33 47 4539.92 7678.33 2270.04 3839.17 1513.46 2559.44 1135.20 1919.58 908.261 1535.67 48 4541.26 7680 00 2270.71 3840.00 1513.91 2560.00 1135.54 1920.00 908.530 1536.00 49 4542.61 7681.67 2271.39 3840.83 1514.36 2560.56 1135.87 1920.42 908.799 1536.33 50 4543.96 7683.33 2272.06 3841.67 151 4. SI 2561.11 1136.21 1920.83 909.069 1536.67 51 4545.33 7685.00 2272.75 3842.50 1515.27 2561.6! 1136.55 1921.25 909.344 1537.00 52 4546.71 7'686.67 2273.44 3843.33 1515.72 2562.22 1136.90 1921.67 909.619 1537.33 53 4548.05 7688.33 2274.11 3844.17 1516.17 2562. 7H 1137.23 1922. OS 909.888 1537.67 54 4549.40 7690.00 2274.78 3845.00 1516.62 2563. 33 1137.57 1922.50 910 15S 1538.00 55 4550.77 7691.67 2275.47 3845.83 1517.08 25(53.89 1137.91 1922.92 910.433 153S.*3 56 4552.15 7693 33 2276.16 3846.67 1517.54 2564 44 11?8.26 1923.33 910 70K 15.-S8.67 57 4553 50 7695.00 2276.83 3847.50 1517.99 2565.00 1138.59 1923.75 910.977 1539.00 58 4554.84 7696.67 2277.50 3818.33 1518.44 2565.5(5 1138.93 1924.17 911.247 1539.33 59 4556.22 7698.33 2278.19 3849.17ll5l8.90 2566.11 1139.28 1924.58 911.522 1539.67 198 TABLE XIT. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 C Lirve. Arc. 9 Curve. 1O Curve. 76 Tan. Arc. Tan. Arc. Tan. Tan. Arc. Tan. Arc. M. 746.421 1266.67639.892 1085.71 560 013 950.000 497 893 844.444 448.218 760.000 746.641 1266.94 640.080 1085.95560.178 950.208 498.039 844.630 448.350 760.167 1 746.860 1267.22640.269 1086.19 560.343 950.417 498.186 844.815 448.482 760.333 2 747.085 1267.50!640 461 1086.43 560.511 950.625 498.336 845.000 448.617 760.500 3 747.309 1267.78640.654 1086.67 560.680 950.833 498.485 845.185 448.752 760.667 4 747.534 1268.06640.846 1086.90 560.848 951.042 498.635 845.370 448.887 760.833 5 747.758 1268.33641.039 1087.14 561.016 951.250 498.785 845.556 449.021 761.000 6 747.988 1268. 61 1641.231 1087.38 561.185 951.458 498 935 845.741 449.156 761.167 7 748.208 1268.89641.424 1087.62 561.353 951.667 499.084 845.926 449.291 761.333 8 748.432 1269.17 641.616 1087.86 561.522 951.875 499.234 846.111 449.426 76 1.50C 9 748.657 1269.44 641.809 1088.10 561 . 690 952.083 499.384 846.296 449.561 761.667 10 748.881 1269.72 642.001 1088.33 561.859 952.292 499.534 846.481 449.695 761.833 11 749.106 1270.00 642.194 1088.57 562.027 952.500 499.683 846.667 449.830 762.000 12 749.330 1270.28 642.386 1088.81 562.196 952.708 499.833 846.852 449.965 762.167 13 749.555 1270.56 642.578 1089.05 562.364 952.917 499.983 847.037i450.100 762.333 14 749.779 1270 83642.771 1089.29 562.532 953.125 500 133 847.222 450.235 762.500 15 750.004 1271.11 642.963 1089.52 562.701 953 333 500.282 847.407 450.370 762.667 16 750.228 1271.39643.156 1089.76 562.869 953.542 500.432 847.593 450.504 762.833 17 750.453 1271.67 643.348 1090.00 563.038 953.750 500.582 847.778 450.639 763.000 18 750.677 1271.94 643.541 1090.24 563.206 953.958 500.73-,' 847.963 450.774 763.167 19 750.902 1272.22 643.733 1090.48 563.375 954.187 500.881 848.148 450.909 763.333 20 751.126 1272. 50 1643. 926 1090.71 563.543 954.375 501 031 848.333 451.044 763.500 21 751.351 1272.78 644.118 1090.95 563 712 954.583 501.181 848.519 451.178 763.667 22 751.575 1273.06 644.311 1091.19 563.880 954.792 501.331 848.704 451.313 763.833 23 751.800 1273.33 644.503 1091.43 564 . 048 955.000 501.48,. 848.889 451.448 764. 000 24 752.024 1273.61 644.696 1091.67 564.217 955.208 501.630 849.074 451.583 764.167 25 752.249 1273.89 644.888 1091.90 564.385 955.417 501.780 849.259 451.718 764.333 2G 752.473 1274.17 645.081 1092.14 564.554 955.625 501.930 849.444 451.853 764.500 21 752.69* 1274.44 645.273 1092.38 564.722 9.-)5.833 502.079 849.630 451.987 764.667 28 752.927 1274.72 645.470 1092.62 564.894 956.042 502.232 849 815 452.125 764.833 29 753.156 1275.00 645.666 1092.86 565.066 956.250 502.385 8'>0.000 452.263 765.000 30 753.381 127'5.28 645.859 1093 10 565.235 956.458 502.535 850.185 452.398 765.167 31 753.605 1275.56 646.051 1093.33 565.403 956.667 502.685 850 370 452132 765.333 32 753.830 1275.83 646.244 1093.57 565.572 956 875 502.835 850 556 452.667 765.5(Hi 33 754.054 1276.11 646.436 1093.81 565.740 957.083 502.984 850.741 452 >02 765.667 34 754.279 1276 39 646.621) 1094.05 565.909 957 292 503 134 850.926 452.937 765.833 35 734.508 1276 67 646.821 1094.29 566.077 957.500 503.284 851.111 453.072 7(5.6.000 30 754.728 1276.94 647.013 1094.52 566 245 957.708 503.434 851.296 453.206 766.167 37 754.952 1277.22 647.206 1094.76 566.414 957.917 503.583 851.481 453.341 766.333 38 755.182 1277.50 647.402 1095.00 566.586 958.125 503.736 851.667 453.479 766.500 39 755.411 1277.78 647.599 1095.24 566.758 958.333 503.889 851.852 453.617 766 . C67 40 755.636 1278.06 647.792 1095.48 566.926 958.542 504.039 852.037 453.751 766.833 41 755.860 1278.33 647.984 1095.71 567.095 958.750 504.189 852.222 453.886 767.000 42 756 0&5 1278.61 648.176 1095.95 567.263 958.958 504.339 852.407 454.021 767.167 43 756.309 1278.89 648.369 1096.19 567.432 959.167 504.488 852.. '.93 454.156 767.33 44 756.538 1279.17 648.566 1096.43 567.604 959.375 504.641 852.77)-' 454.294 767. 50( 45 756.768 1279.44 648.762 1096.67 567.776 959.583 504.794 852.963 454.431 767.667 40 756.992 1279.72 648.955 1096.90 567.944 959.792 504.944 853.14** 454.566 767.833 47 757.217 1280.00 649.147 1097 14 568.113 960.000 505.094 853.883 454.701 768. OCX? 48 757.441 1280.28 649.339 1097.38 568.281 960.208 505.244 853.519 454.836 768.167 49 757. 606 1280.56 649.532 1097.62 568.449 960.417 505.393 853.704 454.971 768.333 50 757.895 1280.83 649.729 1097.8(5 568 622 960.625 505 546 853.889 455.108 768.500 51 758.124 1281.11 649.925 1098.10 568.794 960.833 505.699 854.074 455.246 768.667 52 758.349 1281.39 650.118 1098.33 568.9(52 961.042 505.849 854.259 455.381 768.833 53 758.573 1281.67 650 310 1098 57 569.130 961.250 505.999 854.444 455.516 769.000 54 758.803 1281.94 650.507 1098 81 569.302 961.458 506.152 854.630 455. (553 769.167 55 759.032 1282.22 650.703 1099.05 569.474 961. C67 506.305 854.815 455.791 769.333 50 759.256 1282.50 (550.896 1099.29 569.643 961.875 506.454 855.000 455.926 769.500 57 759.481 1282.78 651.088 1099.52 569.811 962.083 506.604 855.185 456.061 769 (567 58 759.710 1283.06 651.285 1099.76 569.983 962.292 506.757 855.370 456.198 769.833 59 199 TABLE XIV. ACTUAL TANGENTS, ETC. 77 M. 1 Curve. 2 Curve. 3 C Tan. urve. Arc. 4 Curve. 5 Curve. Tan. Arc. Tan. Arc. Tan. Arc. Tan. | Arc. ~~O~ 45 7.59 7700.00 2278.88 385'i.0( 151!) 35 2566.67 1139.62 1925.00 911.797 1540.00 1 4558. W 7701.07 2279.55 3850.83 1M0.81 2567.22 11:39.90 1925.42 912 000 1540.33 g 4360.29 7703.33 2280.23 3851 67 1520 25 2507.78 1140.29 1925.83 912.330 1540.07 3 4501 60 7705.00 2280.91 3852.50 1520.71 2508. 33 1140.04 1920.25 912.611 1541.00 4 4503.04 7700 07 2281.60 3853.33 1521.17 2508.89 1140.98 1920.67 912.880 1541.33 5 4504.38 7708.33 2282.27 3854.17 1521.02 2509.44 1141.32 1927.08 913.155 1541.07 6 4505 . 7'3 7710.00 2282.95 3855.00 1522.07 2570.00 1141.65 1927.50 913.425 1542.00 7 4507.10 7711.67 2283.64 3855.83 1522 52 2570.56 1142.00 1927.92 913.700 1542.133 8 4508.48 7713.33 2284.32 3856.67 1522.98 2571.11 1142.34 1928.33 913.975 1542.67 9 4509.83 7715.00 2285.00 3857.50 1523.43 2571.67 1142.68 1928.75 914.244 1543.00 1O 4571.17 7716.67 2285.67 3858.33 1523.88 2572 22 1143.01 1929.17 914.514 1543.33 11 457:2.55 7718. as 2286.30 3859.17 1524.34 257 2. '78 1143.30 1929.58 914.789 1543.07 12 4573.9-2 7720.00 2287.04 3860.00 1524.80 2573.33 1143.7< 1930.00 915.064 1544.00 13 4575 . 30 7721.67 2287.73 3860.83 1525.26 2573.89 1144.05 1930.42 015.339 1544.33 14 4570.07 7723.33 2288.42 3801.67 1525.71 2574.44 1144.39 19:30.83 915.614 1544.07 15 4578.04 7725.00 2289.0:) 3802.50 1526.10 2575.00 1144.73 1931.25 915.883 1545.00 16 4579.37 7726.67 2289.77 3863.33 1526.61 2575 . 50 1145.00 1931.07 916.153 1545.33 17 4580.74 7728.33 2290.45 3804.17 1527.07 2570.11 1145.41 1932.08 916.428 1545.67 18 4582.1-2 7730.00 2291.14 3805.00 1527.53 2576.07 1145.75 19:32.50 916.70:3 1546.00 19 4583.49 7731.67 2291.83 3865.83 1527.99 2577.22 1140.09 1932.92 1)16.978 1546.33 20 4584.87 7733.33 2292.52 3866.67 15-28 45 2577.78 1146.44 1933.33 917.253 1546.67 21 4580.21 773o.OO 2293.19 3867.50 152S.89 2578.33 1146.78 1933.75 1)17.52:3 1547.00 22 4587.50 7736.67 2293.80 3808.33 1529.34 2578.89 1147.11 1934.17 917.792 1547.33 23 4588 93 7738.33 2294.55 3809.17 1529.80 2579.44 1147.46 1934.58 918.007 1547.67 24 4590.31 7740.00 J295.24 38 7'Q.OO 1530.20 2580.00 1147.80 19-35.00 918.342 1548.00 25 4591.08 7741.67 2295.93 3870.83 1530.72 2580.50 1148.14 1935.42 918.617 1548.33 26 4593.00 7743.33 2290.01 3871.67 1531.18 2581.11 1)48.49 1935.83 918.892 1548.07 27 4594.43 7745.00 2297.30 3872.50 1531.04 .'581.07 1148.83 1936.25 919.108 1549.00 28 4595.81 7746.67 2297.99 3873.33 1532.09 2582.22 1149.17 1936.07 1)19.443 1549.33 29 4597.10 7748.33 2298.60 3874.17 1532.54 2582.78 1149.51 1937.08 919.712 1549.67 30 4598 50 7750.00 2299.34 3875.00 1532.99 2583.33 1149.85 1937.50 919.981 1550.00 31 4599.88 7751.67 2300.02 3875.83 1533.45 2583.89 1150.19 1037.92 920.257 1550.33 32 4601.25 7753.33 2300.71 3876.67 153:3.91 2584.44 1150.54 1938.33 1)20.532 1550.67 33 4002.63 7755.00 2301.40 3877.50 1534.37 2585.0) 1150.88 1938.75 920.807 1551.00 34 4004.00 7756.67 2302.09 3878.33 1534.83 2585. 50 1151.22 19:39.17 921.082 1551.33 35 4605.38 7758.33 2302 77 3879.17 1535.28 2580.11 1151.57 1939.58 1)21.357 1551.67 30 4606.75 7760.00 J303.40 3880.00 535.74 2580.67 1151.91 1940. OJ 921.032 1552.00 37 4008.13 7761.67 2304.15 3880.83 536.20 2587.2,' 1152.20 1940.42 921.907 1552.33 38 4609.50 7763.33 2304.84 3881.07 1536.00 2587. 7S 1152.60 1940.83 922.182 1552.67 39 4010.88 7765.00 2305.52 3882.50 1537.12 2588.33 1152.94 1941.25 922.457 1553.00 40 4612.25 77'66.67 2306.21 3883.33 1537.58 2588.89 1153.29 1941.67 922.732 1553.33 41 4613.63 7768.33 2300.90 3884.17 1538.03 2589.44 1153.63 1942.08 923.008 1553.67 42 4015.00 7770.00 2307.59 3885.00 1538.49 2590.00 1153.97 1942.50 .)23.28:3 1554.00 43 4010.38 7771.67 2308,27 3885.83 1538.95 2590.50 1154.32 1942.92 923.5f,8 1554.33 44 4617.75 7773.33 2308.90 3880.67 1539.41 2591.11 1154.66 1943.33 923.833 1554. 07 45 4019.13 7775. UO 2309.05 3887.50 539.87 2591.67 1155.01 1943.75 924.108 1555.00 46 4020.50 7776.67 2310.34 3888.33 1540.33 2592.22 1155.35 1944.17 924.383 1555.33 47 4621.88 7778.33 2311.02 3889.17 1540 79 2592.78 1155.69 1944.58 924.658 1555 07 48 4023.25 7780.00 2311.71 J890.00 1541.21 3593.33 1156.04 1945.00 924.933 1550.00 49 4024.63 7781.07 2312.40 3890.83 1541.70 2593.89 1156.38 1945.42 925.208 1550.33 50 4626.00 7783.33 2313.09 3891 . 67 542.16 2594.44 1156.73 1945.83 025.48-1 1556.67 51 4627.38 7785.00 2313.77 3892.50 542.62 25D5.00 1157.07 11)40.2:, )25.759 1557.00 52 4028.70 77'86.67 2314.40 3893.33 1543. OS 2595.50 1 57.41 1940.07 120.034 1557.33 53 4630.13 7788.33 2315.15 3894.17 543.54 2596.11 1 57.70 1917.0^ J20.309 557.07 54 4631.51 7790.00 2315.84 3895.00 1543.99 2596.67 1 58.10 11)47.50 >2ii.584 ir-58.00 55 4032.88 7791.67 2316.53 3895.83 544.45 2597.22 :>8.44 1 947 . 9 -' 1)20 . 85!) j 1 .",58 . 33 56 4034.20 7793.33 2317.21 3896.67 544.91 2ot)7'.7H 1 58.79 1948.33 927. 13 ]| 1558. 07 57 1035.03 7795.00 2317.90 3897.50 545.37 25D8.33 1 59.13 11)48.75 927. 40U 1559.00 58 4037.01 7796.67 2318.59 3898.33 545.83 2598.89 159.48 1919.17 327.084 155!).:]:] 59 4638.38 7798.33 2319.28 3899.17 546.29 2599.44 1159.82 1919.58 1)27. 900 11559. 07 200 TABLE XIV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 Curve. 1O Curve. 77 Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. M. 759.939 1283.33 651.481 1100.00 570.155 962 500 506.910 855.556 456.336770.000 700.1641283.61 651.674 1100.24 570.324 9()2.708 507.000 855.741 456.471 770.167 1 760.388 1283.89 651. 8615 1100.48 570.492 962.917 507.210 855.920 456.606770.333 2 700. 01 8 1284.17 652.063 1100.71 570.664 903.125 507.362 856.111 456.743770.500 3 760.847 1284.44 652.259 1100.95 570 836 963.333 507.515 856.296 456. 88 1 770. 667 4 701.072 1284.72 652.452 1101.19 571.005963.542 507.665 856.481 457.016 770.833 5 701.290 1285.00 652.644 1101.43 571.173963.750 507.815 856.667 457.151 771.000 6 70 1. 525 ' 1285. 28 652.841 1101.67 571.345 963.958 507 968 856.852 457.288 771.167 7 70 1. 755 ! 1285. 50 653.037 1101.90 571.517 904.167 508.121 857.037 457.426 771.333 8 701.979 1285.83 653.230 1102.14 571.686 964.375 51)8.271 857.222 457.561 771.500 9 762.204 1286.11 653.422 1102.38 571.854 964.583 508.420 857.407 457.696 771.667 10 702.433 1286.39 653.619 1102.62 572.026 964.792 508 573 857.593 157.839 771.833 11 762.002 1280.07 653.815 1102 86 572.198 965 000 508.726 857.778 457.971 772.000 12 702.892 1286.94 654.012 1103.10 572.370 965.208 508.879 857.963 458.109 772.167 13 703.121 1287.22 654. 2t9 1103.33 572.542 965.417 509.032 858.148 458.246 772.333 14 703.345 1287.50 654.401 1103.57 572.711 965.625 509.182 858.333 458.381 772.500 15 703.570 1287.78 654.593 1103.81 572.879 965.833 509.332 858.519 458.516 772 . 667 10 703.799 1288.00 (554.790 1104.05 573.051 966.042 509.485 858.704 458.654 772.833 17 764.028 1288.33 654.987 1104.29 573.223 966.250 509.638 858.889 458.791 773.000 18 704.258 1288.61 655.183 1104.52 573.395 966.458 509.790 859.074 458.929 773.167 19 764.487 1288.89 655.380 1104.76 573.567 966.667 509.943 859.259 459.067 773.333 2O 704.712 1289.17 055.572 1105.00 573.736 966.875 510.093 859.444 459.202 773.500 21 764.93(5 1289.44 655.765 1105.24 573.904 967.083 510.243 859.630 459.336 773.667 22 705.165 1289. 7-; 055.961 1105.48 574.076 967.292 510.390 859.815 459.474 773.833 23 765.395 1290.00 656.158 1105.71 574.248 967.500 510.549 860.000 459 612 774.000 24 705.024 1290.28 65C.35-J 1105.95 574.420 967.708 510.702 860.185 459.749 774.167 25 705.853 1290.56 656.551 1106.19 574.592 967 917 510.855 860.370 459.887 774.333 20 706.082 1290.83 056 . 7 48 1106.43 574.764 968.125 511.0U8 860.556 460.025 774.500 27 760.812 1291.11 656.944 1106.67 574.936 968.333 511.101 860.741 460.162 774.667 28 700.536 1291.39 657.137 1106.90 575.105 968.542 511.310 860.926 460.297 774.833 29 766.761 1291.67 657.329 1107.14 575.273 968.750 511.460 861 111 460.432 775.000 30 760.990 1291.94 657 . 526 1107.38 575.445 968.958 511.613 861.290 460.570 775.167 31 707.219 1292.2, 657.722 1107.62 575.617 969.167 511.766 861.481 460.707 775.333 32 707.449 1292.50 657.919 1107 86 575.789 969.375 511.919 861.667 460.845 775.500 33 707.078 1292.78 658.115 1108.10 575.961 969.583 512.072 861.852 460.983 775.667 34 707.907 1293 0(3 658.312 1108.33 576.133 969.792 512.225 862.037 461.120 775.833 35 768.137 1293 33 658.508 1108.57 576.305 970.000 512.378 862.222 461.258 776.000 30 708.306 1293.61 658.705 1108.81 576.477 970.208 512.531 862.407 461.396776.167 37 768.595 1293.89 658.902 1109.05 576.649 970.417 512.684 862.593 461.534776.333 38 768.824 1294.17 659.098 1109.29 576.821 970.62,-) 512.837 862.778 461.671 776.500 39 769.054 1294.44 659.295 1109.52 576.994 970.833 512.990 862.963 461.809 776 . 667 4O 709.283 1294.72 659.491 1109.76 577.166 971.042 513.142 863.148 461.947)776.833 41 709.512 1295.00 659.688 1110.00 577.338 971.250 513.295 863.333 462.084 777.000 42 709.742 1295.28 659 . 884 1110.24 577.510 971.458 513.448 863 519 462.222 77". 167 43 769.971 1295.50 660.081 1110.48 577.682 9,1.667 513.601 863.704 462. 360 77'". 333 44 770.200 1295.83 660.277 1110.71 577.854 971.875 513.754 863.889 462.497 77". 500 45 770.429 1296.11 660.474 1110.95 578.026 972.083 513.907 864.074 462.635 77". 667 40 770.659 1296.3!) 660.671 1111.19 578.198 972.292 514.000 864.259 4 62. 773 '77". 833 47 770.888 1296.67 660.867 1111.43 578.370 972.500 514.213 864.444 462 910 778.000 48 771.117 1296.94 661.064 1111.67 578.542 972.708 514.366 864.630 463.048778.167 49 771.347 1297.22 661.260 1111.90 578.714 972.917 514.519 864.815 463.186'778.333 50 771.576 1297.50 661.457;ill2.14 578.886 973.125 514.672 865.000 463.323778.500 51 771. 805 '1297. 78 661.653 1112.38 579^058 973.333 514.825 865.185 463.461 778.667 52 772.034 '1298.06 0(51.850 1112.62 579.230 973.542 514.978 865.370 463.599778.833 53 772.264 1298.88 662.047 1112.86 579.402 973.750 515.131 865.556 463.737779.000 54 772.493 1298.61 662.243 1113.10 579.574 973.958 515.284 865.741 463.874779.167 55 772.72^:1298.89 662.440 1113.33 579.746 974.167 515.437 865.926 464.012779.333 50 772.9521299.17 062. 63C> 1113 57 579.918 974.375 515.590 866.111 464.150779.500 57 773.181 1299.44 662.833 1113.81 580.090 974.583 515.743 866.296 464.287779.667 58 773.4101299.72 663.029 1114.05 580.262974.792 515.890 866.481 464 425779.833 59 201 TABLE XIV. ACTUAL TANGENTS, ETC. 78 1 Cnrve. 3 Curve. 3 Curve. 4 Curve. 5 Curve. M7 Tan. Arc. Tan. Arc. Tan. Arc. 2000.00 Tan. Arc. Tan. Arc. o 4639.767800.002319.96 3900.00 1546.74 1160.16 1950.00 928.235 1500.00 1 4641.16 7801.672320 60 3900.83 1547.21 2600.50 1160.51 1950.42 928.515 1560.33 3 4012. 56 7803. 33 2321.37 3901.07 1547.68 2001.11 1100.87 1950.83 928.790 1500.07 3 4043.94 7805.00 2322.05 3902.50 1548.14 2601.67 1101.21 1951.25 929.071 1501.00 4 4645.31 7806.67 2322.74 3903.33 1548.60 2602.22 1161.55 1951.67 929.347 1501.33 5 4646.697808.33 2323.43 3904.17 1549.06 2002.78 1161.90 1952.08 929.622 1501.07 6 4648.067810.00 0324 12 3905.00 1549.51 2003.33 1162.24 1952.50 929.897 1502.00 7 4649.447811.67 2324.80 3905.83 1549.97 2603.89 1162.58 1952.92 930.172 1502.33 8 4650.81 7813.33 2325.49 3906.67 1550.43 2604.44 1162.93 1953.33 930.447 1562.67 9 4652.22 7815.00 2326.19 3907.50 1550.90 2605.00 1163.28 1953.75 930.728 1563.00 1O 4653.62 7816.67 2326.90 3908.33 1551.37 2G05.56 1163.63 1954.17 931.009 1563.33 11 4655.00 7818.33 2327.58 39U9.17 1551.83 2606.11 1163.97 1954.58 931.284 1563 67 13 4656.37 7820.00 2328.27 3910.00 1552.28 2006.07 1164.32 1955.00 931.559 1564.00 13 4657.75 7821.67 2328.96 3910.83 1552.74 2007.22 1164.66 1955.42 931 . 834 1564.33 14 4659.12 7823 33 2329.65 3911.67 1553.20 2607.78 1165.01 1955.83 932.109 1564.67 15 4660.50 7825.00 2330.33 3912.50 1553.66 2608.33 1165.35 1956.25 932.384 1565.00 16 4661.87 7826.67 2331.02 3913.33 1554.12 2608.89 1165.69 1956.07 932.0591505.33 17 4663.28 7828.33 2331.72 3914.17 1554.59 2609.44 1166.04 1957.C8 932.9401565.07 18 4004.68 7830.00 2332.43 3915 00 1555.05 2610.00 1166.40 1957.50 933.221 1500.00 19 4666.06 7831.67 2333.11 3915.83 1555.51 2610.56 1166.74 1957.92 933.496 1566.33 30 4667.43 7833.33 2333.80 3916.67 1555.97 2611.11 1167.08 1958.33 933.771 1566.67 31 4008.83 7835.00 2334.50 3917.50 1550.41 2611.67 1107.43 1 958. 75 934 05-2 1567.00 33 4070.24 7836.67 2335.20 3918.33 1550.91 2612.22 1167.79 1959.17 934.333 1507.33 33 4071.01 7838.33 2335.89 3919.17 1557.30 2612.78 1168.13 1959.58 934.008 1507.07 34 4672.99 7840.00 2330.58 3920.00 1557.82 2613.33 1168.47 11)00.00 934.883 1568.00 35 4674.30 7841 67 2337.27 3920 83 1558.28 2613.89 1168.8-2 1900.4-2 1)35.158 1508.33 36 4075.74 7843 33 2337.95 3921.67 1558.?'4 2014.41 1169.10 1900.83 935.433 1568.67 37 4077.14 7845.00 2338.00 3922.50 1559.21 2015.00 1109.51 11)01 25 935.714 1509.00 38 4078.55 7846.67 2339.30 3923.83 1559.68 2615.56 1169.86 11101.67 935 995 1569.33 39 4079.92 7848.33 2340.05 3924.17 1560.13 2016.11 1170.21 1962.08 936.270 1509.07 30 4681 30 7850.00 2340.73 3925.00 1560.59 2616.67 1170.55 1902.50 936.545 1570.00 31 4082.70 7851.67 2341.44 3925.83 1501.00 2617.22 1170.90 1902.92 936.826 1570.33 33 4684.10 7853.33 2342.14 5926.671501.53 2617.78 1171.25 1903.33 937.107 1570.07 33 4685.48 7855.00 2342 83 3927.50 1561.99 2618.33 1171.60 1903.75 937.382 1571.00 34 4086.85 7856.67 2343.51 3;)28.33 1562.45 2618.8'J 1171 94 1904.17 937.057 1571.33 35 4688.26 7858.33 2344.21 :;9.'9.17 1562.91 2619.44 1172.29 1904.58 937.938 1571.67 36 4689.60 7860.00 2344.92 ;93i).00 1563.38 2620.00 1172.64 1965.00 938.219 1572.00 37 4691.06 7861.67 2345.62 3950.83 1563.85 2020.56 1172.99 1965.42 938.500 1572.33 38 4692.47 7863.33 2346.32 3911.67 1564.32 2621.11 11T3 34 1965.83 938.780 1572.07 39 4093.84 7865.00 2347.01 3932.50 1504.78 2621.67 1173.69 1966.25 939.056 1573.00 40 4695.22 7866.67 2347.70 3933.33 1565.23 2622.22 M74 03 1966.67 939.331 1573.33 41 4696.02 7868.33 2348.40 3934.17 1565 70 20-22.78 1174.38 1967.08 939.611 1573.o7 43 4098.03 7870.00 2349.10 3935.00 1500.17 2623.33 1174.73 1967.50 939.892 1574.00 43 4699.43 7871.67 2349.80 3935.83 1566.64 2623.89 1175.09 1967.92 940.173 1574.33 44 4700.83 7873.33 2350.50 3930.67 1567.11 2624.44 1175.44 1908.33 940.454 1574.07 45 4702.21 7875.00 2351.19 3937.50 1567.56 2025.00 1175.78 1908.75 940.729 1575.00 46 4703.58 7876.67 2351.88 3938.33 1568.02 2625.56 1176.12 1969.17 941.004 1575.33 47 47'04.99 7878.33 2352.58 3939.17 1568.49 2620.11 1176.47 1969.58 941.285 1575.07 48 4700.39 7880.00 2353.28 3940.00 1568.96 2620.07 1176.83 1970.00 1)41.566 1576.00 49 4707.80 7881.67 2353.98 3940.83 1569.43 2027.22 1177.18 1970.42 941.847 1576.33 5O 47'09.20 7883.33 2354.69 3941.67 1569.89 2627 78 1177.53 1970.83 942.128 1576.07 51 53 4710.57 4711.95 7885.002355.37 7886.67.2350.06 3942.50 3943.33 1570.35 1570.81 2028.33 2628.89 1177.87 1178.22 1971.25 1971.67 942.4031577.00 942.6781577.33 53 4713.35 7888.332356.763944.17 1571.28 2629.44 1178.57 1972.08 942.959 1577.07 54 4714.70 7890.002357.463945 00 1571.75 2030.00 1178.92 1972.50 943.239 1578.00 55 4716.16 789 1.67 12358. 17 3945. 83 157-2.22 2030.50 1179.27 1972.9-2 943.520 1578.33 56 4717.56 7893.332358.873946.67 1572.68 2031 . 1 1 li;9. 62 1973.33 943.801 1578.67 57 4718.97 7895.002359.573947.50 1573.15 2031.67 1179.97 1973.75 944.082 1571). 00 58 4720.37 7'890.07,'2300.273948.33 1573.62 203-2.22 1180.32 1974.17 944.363 1579.33 59 4721.78 7898.33,2360 973949.17 1574.09 2632.78 1180.67 1974 58 944.644 1579.07 202 TABLE XIV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 Curve. 10 Curve. 78 Tan. Arc. Tan. 603.220 Arc. nir.29 Tan. 1 Arc. Tan. Arc. Tan. Arc. M. 778. wii 1300.00 580.434975.000 516.048 860 667 464.563 780.000 O 773.874 18UO. 28 6C3. 42? 1114.52 580.610 975.208 516.205 860. 852 464.703 780.167 1 74.1U8 1300.50 663.627 1114.70 580.785 975.417 516.361 867.037 464.844 780.333 2 74.337 1300.83 003.824 1115.00 580.957 975.625 516.514 867.222 464.981 780.500 3 74.50(5 1301.11 004.020 1115.2-1 581.129 975.833 516.667 867.407 465.119 780.067 4 74.795 1301.39 004.217 1115.48 581.301 976.042 516.820 867.593 465.257 780.833 5 75.025 1301.07 004.414 1115.71 581.473 976.250 516.972 867.778 465.394 781.000 6 75.254 1301.94 004.610 1115.95 581.645 976.458 517.125 807.963 405.532 781.167 7 75.483 1302.22 604.807 1116.19 581.817 976.067 517.278 868.148 405.670 781.333 8 775.717 1302.50 605.007 1116.43 581.993 976.875 517.435 808.333 465.810 781.500 9 775.951 1302.78 665.208 1116.67 582 169 977 083 517.591 868.519 465.951 781.667 10 770.181 1303.00 005.405 1116.90 582. 341 977.292 517.744 868.704 466.089 781.833 11 776.410 1303.33 005.0'Jl 1117.14 582.513 977.500 517.897 868.889 466.220 782.000 12 70.639 1303.01 065.798 1117.38 582.685 977.708 518.049 869.074 466.364 782.167 13 76.809 1303.89 005.994 1117.02 582.857 977.917 518.202 869.259 466.502 782.333 14 77.098 1304.17 000.191 1117.80 583.029 978.125 518.355 809.444 466.639 782.500 15 77.887 1304.44 600.387 1118.10 583.201 978.333 518.508 869.630 406.777 782 667 16 77.501 1304.72 600.588 1118.33 583.370 978.542 518.664 869.815 466.918 782.833 17 777.795 1305.00 006 . 789 1118.57 583.552 978.750 518.821 870.000 467.058 783.000 18 778.025 1305.28 600.985 1118.81 583.724 978.958 518.974 870.185 467.196 783.167 19 778.254 1305.56 667.182 1119.05 583.890 979.167 519.126 870.370 467.334 783.333 20 778. 48 11305. 83 067.382 1119.29 584.072 979.375 519.283 870.556 467.474 783.500 21 778.1*2 1300.11 667.583 1119.52 584.247 979.583 519.439 870.741 467.615 783.667 22 778.951 1300.39 067.780 1119.70 584.419 979.792 519.592 870.926 467.752 783.833 23 779 181 1300.07 667.970 1120.0U 584.591 980.000 519.745 871.111 467.890 784.000 24 779.410 1306.94 008.173 1120.24 584.763 980.208 519 898 871.296 468.028 784 167 25 779.039 1307.22 668.369 1120.48 584.935 980.417 520.050 871.481 468.105 784.333 26 779.873 1307.50 668 . 570 1120.71 585.111 980.625 520.207 871.607 468.300 784.500 27 780.107 1307.78 008.771 1120.95 585.287 980.83;} 520. 30S 871.852 408.447 784.667 28 780.337 1308.00 008.967 1121.19 .185.459 981.042 520.516 872.037 408.584 784.833 29 780.560 1308.33 669.164 1121.43 585.631 981.250 520.669 872.222 468.722 785.000 30 780.800 1308.61 (J69.365 1121.67 585.806 981.458 520.825 872.407 468.862 785.167 31 781.084 1308.89 609.565 1121.90 585.982 981.607 520.981 872.593 469.003 785.333 32 781.208 1309.17 009.702 1122.14 586.154 981.875 521.134 872.778 409.141 785.500 33 781.493 1309.44 009.958 1122.38 586.320 982.083 521.287 872.903 409.278 785.i>67 34 781.727 1309.72 070.159 1122.62 580.502 982.29* 521.443 873.148 409.419 785.833 35 781.961 1310.00 070.300 1122.80 586.677 982.500 521.599 873.333 409.559 786.000! 36 782.195 1310.28 070.500 1123.10 586.853 982.708 521.755 873.519 469.700 786.167 37 782.429 1310.56 070.701 1123.33 587.028 982.917 521.911 873.704 469.841 786.333 38 782. 058 j 13 10. 83 670.958 1123.57 587.200 983.125 522.064 873.889 409.978 786.500 39 782.887 1311.11 671.154 1123.81 587.372 983.333 522.217 874.074 470.116 786.667 40 783. 122' 131 1.39 671.355 1124.05 587.548 983.542 522.373 874.259 470.257 786. 833 ! 41 783.350 1311.67 671.555 1124.29 587.724 983.750 522.529 874.444 470.397 787.000 42 783.590 1311.94 671.756 1124.52 587.899 983 958 522.686 874.030 470.538 787.107:43 783.824 1312.22 671.957 1124.76 588.075 984.107 522.842 874.815 470.678 787.333' 44 784.053 1312.50 672.153 1125.00 588.247 984.375 522.995 875.000 470.810 787.500: 45 784.282 1312.78 672.350 1125.24 588.419 984.583 523.148 875.185 470.954 787.607 46 784.510 1313.00 67'2.550 1125.48 58S.595 984.792 .323.304 875.37X) 471.094 787.833 47 784.750 1313.33 672.751 1125.71 588.770 985.000 523.460 875.550 471.235 7'88.000 48 784.984 1313.61 072.952 1125.95 588.946 985.208 523.016 875.741 471.375 788.167 49 785.219 1313.89 673.152 1126.19 589.121 985.417 523.772 875.926 471.516 788.333 5O 785.448 1314.17 073.349 1126.43 589.293 985.625 523.925 876.111 471.053 788.500 51 785.077 1314.44 073.540 1126.67 589.465 985.833 524. 078! 870. 296 471.791 788.007 52 785.911 1314.72673.740 1126.90 589.641 986.042 524.234 876.481 471.9^-- 788.833 53 780.145! 1315. 00 ! 673. 947 1127.14 589.817 986.250 524.390 876.007 472.072 789.000 54 786.379 131 5. 28674.148 1127.38 589.992 980.458 524.546 876.852 472.213 789.107 55 786.613 1315. 50:674. 348 1127.62 590.168 986.067 524.703 877.037 472.353 789.333 50 786.847 1315.83:674.549 1127.80 590.344 986.875 524.859 877.222 472.494 789.500 57 787.08',' 1316. 11 '674. 750 1128.10 590.519 987.083 525.015 877.407 472.034 789.007 58 787. 31611316. 39'674. 950 1128.33590.095 987.292 525.171 877.593 472.775 789.833 59 203 TABLE XIV. ACTUAL TANGENTS, ETC. 79 1 Curve. 3 Curve. 3 Curve. 4 Curve. 5 Curve. M. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. 4723.18 7900.00 2361.683950.00 1574.56 2633.33 1181.02 1975.00 944.924 1580.00 1 4724.58 7901.67 2362.383950.83 1575.02 2633. 89 1181.37 1975.42 945.205 1580.33 3 4725.99 7903.33 2363.083951.67 1575.49 2634.44 1181 73 1975.83 945.486 1580.67 3 4727.3t 7905.00 2363.773952.51 1575.95 2635.00 11S2.01 1976.25 945.761 1581.00 4 4728.7'! 7906.67 2364.463953.33 1576.41 2635.50 1182.41 1976.67 946.036 1581.33 5 4730.14 7908.33 2365.163954.17 1576.88 2636.11 1182.76 1977.0;* 946.311 1581.67 6 4731.51 7910.00 2365.863955.00 1577.34 2636.67 1183.12 11)77.50 946.598 1582.00 7 4~.5W.tto 7911.67 2366.563955.83 1577.81 2637.22 1183.47 1977.92 946.879 1582.33 8 473 L 35 7913.33 2367.263956.67 1578.28 2637.78 1183.82 1978.33 947.161 1582.67 9 4735.76 7915.00 2367.963957.50 1578.75 2638.33 1184.17 1978.75 947.441 1583.00 10 4737.16 7916.67 2368.673958.33 1579.22 2638.89 1184.52 1979.17 947.721 1583.33 11 4738.56 7918.33 2369.373959.17 1579.68 2639.44 1184.87 1979.5S 948.002 1583.67 13 4739.97 7920.00 2370.073960.00 1580.15 2640.00 1185 22 1980.00 948.28-3 1584.00 13 4741.37 7921.67 2370.773960.83 1580.62 2640.56 1185.57 1980.42 948.564 1584.33 14 4742. ',8 7923.33 2371.473961.67 1581.09 2641.11 1185.92 1980.83 948.845 1584.67 15 4744.18 7925.00 2312.183962.50 1581.56 2641.67 1186.2: 1981.25 949.126 1585.00 16 4745.58 7926.67 2372.8831)63.33 1582.02 2642.22 1186.63 1981.67 949.400 1585.33 17 4746.99 7928.33 2373.583964.17 1582.49 2642.78 1186.9S 1982.0s 949. 6S7 1585.67 18 4748.39 7930.00 2374. 28 3965. OJ 1582.96 2643.33 1187.33 1982.50 949.968 1586.00 19 4749.79 7931.67 2374.983965.83 1583.43 2643.89 1187.68 1982.92 950.249 1586.33 20 4751.20 7933.33 2375.693966.67 1583.90 2644.44 1188.03 1983.3:^ 950.530 1586.67 31 4752.60 7935.00 2376.393967.50 1584.36 2645.00 1188.38 1983.75 1)50.811 1587.00 33 4754.01 7936.67 2377. 09 3968. 33 1584.83 2645.56 1188.73 1984.17 951.091 1587.33 33 4755.44 7938.33 2377.81 3969.17 1585.31 2646.11 1189.09 1984.58 951.378 1587.67 34 4756.87 1910.00 2378.523970.00 1585.79 2646.67 1189.45 1985.00 951.665 1588.00 35 4758.21 7941.67 2379.223970.83 1586.25 2647.22 1189.80 1985.42 951.945 1588.33 36 4759.68 i 9 43. 33 2379.933971.67 1586.72 2647.78 1190.15 19S5.83 952.226 1588.67 37 4761.08 7945.00 2380.633972.50 1587.19 2648.33 1190.50 1986.25 952.507 1589.00 38 4762 49 7946.67 2381.333973.33 1587.66 2648.89 1190.85 19S6.67 952.788 1589.33 39 4763.89 7948.33 2382.033974.17 1588.13 2649.44 1191.20 1987.08 953.069 1589.67 30 4765.29 7950.00 2382.733975.00 1588.59 2650.00 1191.55 1987.50 953.350 1590.00 31 4766.70 7951.67 2383.443975.83 1589.06 2650.56 1191.90 1987.92 953.630 1590.33 33 4768.10 7953.33 2384.143976.67 1589.53 2651.11 1192.26 1988.33 953.911 1590.67 33 4769.53 7955.00 2384.853977.50 1590.01 2651.67 1192.61 1988.75 954.198 1591.00 34 4770.96 7956.67 2385.573978.33 1590.49 2652.22 1192.97 1989.17 954.484 1591.33 35 4772.37 7958.33 2386.273979.17 1590.95 2652.78 1193.32 1989.58 954.765 1591.67 36 4773.77 7960.00 23S6.973980.00 1591.42 2653.33 1193.67 1990.00 955 046 1592.00 37 4775.18 7961.67 2387.683980.83 1591.89 2653.89 1194.03 191)0.42 955.327 1592.33 38 4776 58 7963.33 2383.383981.67 1592.36 2654.44 1194.38 1990.83 955.608 1592.67 39 4777.98 7965.00 2339. OS 3982.50 1592.83 2655.00 1194.73 1991.25 955.889 1593.00 40 4779.39 7966.67 2389.783983.33 1593.29 2655.56 1195.08 1991.67 956.169 1593.33 41 4780.82 7968.33 2390 5u 3984. 17 1593.77 2656.11 1195.44 1992.08 956.456 1593.67 43 4782.25 7970.00 2391.21 5985.00 1594.25 2656.67 1195.79 1992.50 956.743 1594.00 43 4783.66 ;9M.67 239 1.92 3 JS5. 83 1594.72 2657.22 1196.15 1992.92 957.023 1594.33 44 4785.06 7973.33 2392.623JS6.67 1595.18 2657.78 1196.50 1993.33 957.304 1594.67 45 4786.49 7975.00 2393.333987.50 1595.66:2658.33 1196.85 1993.75 957.591 1595.00 46 4787 . 92 J 976. 67 2394.053988.33 1596. 14 : 2658. 89 1197.21 1994.17 i)57 . 877 1595.33 47 4789.33 7978.33 2394.753989.17 1596.61 2659.44 1197.56 1994.58 958.158 1595.67 48 4790.73 7980.00 2395.453990.00 1597.082660.00 1197.92 1995.00 958.439 1596.00 49 4792.14 7981.67 2396.163990.83 1597.542660.56 1198.27 1995.42 958.720 1596.33 50 4793 54 7933.33 2396.863991.67 1598.01 2661.11 1198.62 1995.83 959.001 1596.67 51 4794.97 7985.00 2397.573992.50 1598.49 2661.67 1198.98 1996.25 959.287 1597.00 53 4796.40 7986.67 2398.293993.33 1598.97 2662.22 1199.33 1996.67 959.574 1597.33 53 4797.81 7988.33 2398.91)3994.17 1599.43 2662.78 1199.68 1997.08 959.855 1597.67 54 47'.i9.21 7990.00 2399.693995.00 1599.90 2663.33 1200.04 1997.50 )60.136 1598.00 55 1800.64 7991 . 67 2400.41 8995.83 1600.38 2663.89 1200.39 1997.92 %0.422 1598.33 56 4802 OS 7993. 3 i 2401.133996.67 1600.86 2664.44 1200.75 1998.33 960.709 159S.67 57 4S03.48 7995.00 2401.83391)7.50 1601.33 2(565.00 1201.10 1998.75 %0.990 1599.00 58 4804.88 7996.67 2402.533998.33 1601.79 2605.56 1201.45 1999.17 K5 1.270 1599.33 59 4806.32 7998.33 2403.25:3999.17 1602. 2712666. Ill 1201. 81 1999.58 961.557 1599.67 204 TABLE XIV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 Curve. 10 Curve. 79 Tan. Arc. Tan. 675 . 1 51 Arc. Tan. Arc. 987.500 Tan. 525.327 Arc. S77.778 Tan. Arc. 790.000 ^iT 787.550 1310.67 1128.57 590.870 472.916 o 787.784 1316.94 675.352 1128.81 591.046 987.708 525.483 877.963 473.056 790.167 i 788.018 1317.22 675.552 1129.05 591.222 987.917 525.639 878.148 473.197 790.333 2 788.24? 1317.50 675.749 1129.29 591.394 988.125 525.792 878.333 473.334 790.500 3 788.476 1317.78 675.945 1129.52 591.566 988.333 525.945 878.519 473.472 790.667 4 788.710 1318.06 676.146 1129.76 591.741 988.542 526.101 878.704 473.613 790.833 5 788.944 1318.33 676.347 1130.0J 591.917 988.750 526.258 878.889 473.753 791.000 6 789.179 1318.61 676.547 1130.24 592.092 988.958 526.414 879.074 473.894 791.167 7 789.413 1318.89 676. 74S 1130.48 592.268 989.167 526.570 879.259 474.034 791.333 8 789.647 1319.17 076.949 1130.71 592.444 989.375 526.726 879.444 474.175 791.500 9 789.881 1319.44 677.149 1130.95 592.619 989.583 526.882 879.630 474.315 791.667 1O 790.115 1319.72 677.350 1131.19 592.795 989.792 527.038 879.815 474.456 791.833 11 790.849 1320.00 677.551 1131.43 592.971 990.000 527.194 880.000 474.596 792.000 13 790.583 1320. 28 677.751 1131.67 593.146 990.208 527.350 880.185 474.7*7 792.167 13 790.817 1320.56 677.952 1131.90 593.322 990.417 527.507 880.370 474.878 792.333 14 791.051 1320.83 678.153 1132.14 593.497 990.625 527.663 880.556 475.018 792.500 15 791.285 1321.11 678.353 1132.38 593.673 990.833 527.819 880.741 475.159 792.667 16 791.519 1321.39 678.554 1132.62 593.849 991.042 527.975 880.926 475.29i> 792.833 17 791.753 1321 .67 678.755 1132.86 594.024 991.250 528.131 881.111 475.440 793.000 18 791.987 1321.94 678.955 1133.10 594.200 991.458 528.287 881.296 475.580 793.167 19 79-3.221 1322.22 679.156 1133.33 594.375 991.667 528 443 881.481 475.721 793 333 30 792.455 1322.50 679.357 1133.57 594.551 991.875 528.599 881. 6071475. 861 793.500 31 792. G90 1322.78 679.557 1133.81 594.727 992.083 528.756 881.852 476.002 793.66; 33 792.928 1323.06 679.762 1134.05 594.906 992.292 528.915 882.037 476.145 793.833 33 793.167 1323.33 679.967 1134.29 595.085 992.500 529.074 882.222 476.289 794.000 34 793.401 1323.61 680.167 1134 52 595.261 992.708 529.230 882.407 476.429 794.167 25 793.635 1323.89 680.368 1134.76 595.436 992.917 529.387 882.593 476 570 794.333 36 793.869 1324.17 680.569 1135.00 595.612 993.125 529.543 882.778 476.711 794.500 37 791.103 1324.44 680.769 1135.24 595.787 993.333 529.699 882.963 476.851 794.667 38 794.338 1324.72 680.970 1135.48 595.963 993.542 529.855 883.148 476.992 794.833 39 794.572 1325.00 681.173 1135.71 596.139 993.750 530.011 8S3.333 477.132 795.000 30 794.806 1325.28 681.371 1135.95 596.314 993.958 530.167 883.519 47". 273 795.167 31 795.040 1325.56 681.572 1136.19 596.490 994.167 530.323 883.704 47". 4 13 795.333 33 795.279 1325.83 681.777 1136.43 596.669 994.375 530.483 883.889 47". 557 795.500 33 795.517 1326.11 681.982 1136.67 596.848 994.583 530.642 884.074 47". 700 795.667 34 795.752 1326.39 682.182 1136.90 597.024 994.792 530.798 884.259 47". 841 795,833 35 795.986 1326.67 682.383 1137.14 597.200 995.000 530.954 884.444 4 7". 981 796.000 36 796.220 1326.94 682.584 1137.38 597.375 995.208 531.110 884.630 478.122 796.167 37 796.454 1327.22 682.784 1137.62 597.551 995.417 531.266 884.815 478.262 796.333 38 796.688 1327.50 682.985 1137.86 597.726 995.625 531.423 885.000 478.403 796.500 39 796 . 922 1327.78 683.185 1138.10 597.902 995.833 531.579 885.185 478.543 796.667 4O 797.161 1328.06 683.390 1138.33 598.081 996.042 531.738 885.370 478 687 796.833 41 797.400 1328.33 683.595 1138.57 598.260 996.250 531.897 885.556 478.830 797.000 43 797.634 1328.61 683.796 1138.81 598.436 996.458 532.053 885.741 478.971 797.167 43 797. 868 '1328. 89 683.996 1139.05 598.612 996.667 532.210 885.926 479.111 797.333 44 798.1 0(H329. 17 684.201 1139.29 598.791 996.875 532.369 886.111 479.255 797.500 45 798.345 1329.44 684.406 1139.52 598.970 997.083 532.528 886.296 47'9.398 ; 97. 667 46 798.57<);1329.7'2 684.606 1139.76 599.146 997.292 532.684 886.481 479.539 797.833 47 798.813 1330.00 684.8071140.00 599.321 997.500 532.841 886.667 479.679 798.000 48 799.048 1330.28 685.008 1140.24 599.497 997.708 532.997 886.852 479.820 798/167 49 799.282 1330.56 685.208 1140.48 599.672 997.917 533.153 887.037 479.960 798.333 5O 799.520 1330.83 685.413 1140 71 599.852 998.125 533.312 887.222 480.104 798.500 51 799.759 1331.11 <5S5.(>18!1140.95 600.031 998.333 533.471 887.407 480.247 79S.667 53 799.993 1331.39 (K). 819 1141.19 600.206 998.542 533.628 887. 593 480. 38S 798.833 53 800 22; 1331.6; OSti.019 1141.43 600.382 998.750 533.784 887. 77'8 1480.528 799. OCX) 54 800.466 1331.94 i.SS.224,1141.67 600.561 998.958 533.943 887. 963 480.67'2 799.167 55 800.705 1332.32 686. 129 1141.90 600.740 999.167 534.102 888.148480.815 799.333 56 800.939 1332.50 086.629 1142.14 600.916 999.375 534.258 888.333480.956 799.500 57 801.173 1332.78 (586.830 1142.38 601.092 999.583 534.415 888.519481.096 799.667 58 801.412 1333.06 687.035 1142.62 601.271 999.792 534.574 888.704481.240 799.833 59 205 TABLE XIV. ACTUAL TANGENTS, ETC. 8O 1 Curve. 2 Curve. 3 Curve. 4 Curve. 5 Curve. M. ~~O~ Tun. Arc. Tan. Arc. Tan. Arc. Tan. 1 Arc. Tan. Arc. 4807.75 8000.00 2403.96 4000.00 1602.75 2666.67 1202.17j2000.00 961.844 1600.00 1 4809.18 8001.67 2404.68 4000.83 1603.23 2667.22 1202.53:2000.42 962.130 1600.33 2 4810.61 8003.33 2405.40 4001.67 1603.70 2667.78 1202.89 2000.83 962.417 1600.67 3 4812.02 8005.00 2406.10 4002.50 1604.17 2668. 33 1203.24 2001.25 962.698 1601.00 4 4813 42 8006.67 2406.80 4003.33 1604.64 2668.89 1203.59 20U1.67 962.978 1601.33 5 4814.85 8008.33 2407.52 4004.17 1605.12 2669.44 1203.95 2002.08 963.265 1601.67 6 4816.29 8010.00 2408.23 4005.00 1605.59 2670.00 1204.30 2002.50 963.552 1602.00 7 4817.69 8011.67 2408.93 4005.83 1606.06 2670.56 1204.66 2002.92 963.832 1602.33 8 4819.09 8013.33 2409.64 4006.67 1606.53 2671.11 1205 01 2003.33 964.113 1602.6? 9 4820.53 8015.00 2410.35 4007.50 1607.01 2671.6? 1205.37 2003.75 964.400 1603.00 10 4821 96 8016.67 2411.07 4008.33 1607.49 2672.22 1205.72 2004.17 964.686 1603.33 11 4823. 3'J 8018.33 2411.78 4009.17 1607.96 2672.78 1206.08 2004.58 964.973 1603.67 13 4824.82 8^0.00 2412.50 4010.00 1608.44 2673.33 1206.44 2005.00 965.259 1604.00 13 4826.26 8021.67 2413.22 4010.83 1608.92 2673.89 1206.80 2005.42 965.546 1604.33 14 4827.69 8023.33 2413.93 4011.6? 1609.40 2674.44 1207.16 2005.83 965.833 1604.67 15 4829.09 8025.00 2414.63 4012.50 1609.86 2675.00 1207.51 2006.25 966.113 1605.00 16 4830.50 8026.67 2115 34 4013. 33 1610.33 2675.56 1207.86 2006.67 966.394 1605.33 17 4831 . 93 8028.33 2416.05 4014.17 1610.81 2676.11 1208.22 2007.08 966.681 1605.67 18 4833.36 8030.00 2416.77 4015.00 1611.29 2676.67 1208.57 2007.50 966.967 1606.00 19 4834.79 8031.67 2417.49 4015.83 1611.76 2677.22 1208.93 2007.92 967.254 1606.33 30 4836.23 8033.33 2418.20 4016.67 1612.24 2677.78 1209.29 2008.33 967.541 1606.67 21 4837.66 8035.00 2418.92 4017.50 1612 72 2678.33 1209.65 2008.75 967.827 1607.00 22 4839.09 8036.67 2419.63 4018.33 1613.20 2678.89 1210.01 2009.17 968.114 1607.33 23 1840.5 J 8038.33 2420.35 4019.17 1613.67 2679.44 1210.37 2009.58 968.400 1607.67 34 4841.96 8040.00 2421.07 4020.00 1614.15 2680.00 1210.72 2010.00 968.687 1608.00 25 4843.36 8041.67 2421.77 4020.83 1614.62 2680.56 1211.07 2010.42 968.968 1608.33 26 4844.76 8043.33 2422.47 4021.67 1615.09 2681.11 1211.43 2010.83 969.249 1608.6? 21 4846.20 8045.00 2423.19 4022.50 1615.56 2681.6? 1211.78 2011.25 969.535 1609.00 2$ 4847 63 8046.67 2423 90 4023.33 1616.04 2682.22 1212.14 2011.67 969.822 1609.33 39 4849.06 8048.33 2424.62 4024.1? 1616.52 2682.78 1212.50 2012.08 970.106 1609.67 30 4850.49 8050.00 2425.34 4025.00 1617.00 2683.33 1212.86 2012.50 970.395 1610.00 31 4851.92 8051.67 2426.05 4025.83 1617.47 2683.89 1213.22 2012.92 970.681 1610.33 33 4853.36 8053.33 2426.77 4026.67 1617.95 2684.44 1213 57 2013.38 970.968 1610.67 33 4854.79 8055.00 2427.48 4027.50 1618.43 2685.00 1213.93 2013.75 971.255 1611.00 34 4856.22 8056.6? 2428.20 4028.33 1618.91 2685.56 1214.29 2014.17 971.541 1611.33 35 4857.65 8058.33 2428.92 4029.1? 1619.38 '2686.11 1214.65 2014.58 971.828 1611.67 36 4859.09 8060.00 2429 63 4030.00 1619.86 2686.67 1215.01 2015.00 972.114 1612.00 37 4860.52 8061.67 2430.35 4030.83 1620.34 2687.22 1215.3? 2015.42 972.401 1612.33 38 4861.95 8063.33 2431.07 4031.6? 1620.82 2687.78 1215.72 2015.83 972.687 1612.67 39 4863.38 8065.00 2131.78 4032.50 1621.30 2688.33 1216.08 2016.25 972.974 1613.00 40 4864.82 8066.67 2132.50 4033.33 1621.77 2688.89 1216.44 2016.67 973.260 1613.33 41 4866.25 8068.33 2433.21 4034.1? 1622.25 2689.44 1216.80 2017.08 973.547 1613.67 43 4867.68 8070.00 2133.9:5 4035.00 1622.73 2C90.00 1217.16 2017.50 973.834 1614.00 43 4869.11 8071.67 2434.65 1035.83 1623.21 2690.56 1217.51 2017.92 974.120 1614.33 44 4870.55 8073.33 2435.36 4036.67 1623.08 2691.11 1217.87 2018.33 974.407 1614.67 45 4872.01 8075.00 2436.09 4037.50 1624.17 2691.67 1218.24 2018.75 974.699 1615.00 46 4873.47 8076.6; 2436.82 4038.33 1624.66 2692.22 1218.60 2019.17 974.991 1615.33 47 4874.90 8078.33 2437.54 4039.17 1625.13 2692.78 1218.96 2019.58 975.278 1615.67 48 4876.33 8080.00 2438.26 4040.00 1625.61 2693.33 1219.32 2020.00 975.565 1616.00 49 4877.77 8081.67 2438.9? 4040.83 1626.09 2693.89 1219.68 2020.42 975.851 1616.33 50 4879.20 8083.33 2439.69 4011.6? 1626.57 2694.44 1220.04 2020.83 976.138 1616 67 51 4880.63 8085.00 2440.40 4042.51 1627.04 2695.00 1220.39 2021.25 976.424 1617.00 53 4882.06 8086.67 2441.12 4043.3 1627.52 2695.56 1220.75 2021.6? 976.711! 161 7. 33 53 4883.50 80S8.33 2441.84 4044.1? 1628.00 2696.11 1221.11 202 .'.08 976.99? 1617.67 54 4884.93 8090.00 2442.55 4045.00 1628.48 2696.67 1221.47 -,'022.50 977.284 1018.00 55 4886.39 8091.67 2443.28 4045.83 1628.96 2697 22 1221.83 2022 .92 977.576 1618.33 56 1887.85 8093.33 2444.01 4046.67 1629.45 2697.78 1222 20 2023.33 977.869 1618.67 57 188',). 28 8095.00 2444.73 1047.50 1629.93 2698.33 1222.56 2023.75 978.155 1619.00 58 4890. 71! 8096. 67 2445.45 4048.33 1630.41 2698.89 1222.92 2024.17 978.442 1619.33 59 4892.1518098.33 2446.16 4049.1? 1630.88 2699.44 1223.272024.58 978.728 1619.67 206 TABLE XIV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 Curve. 10 Curve. 80 Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. 31. 801.651 1333733 687.240 1142.86 601.450 1000.00 534.733 888.889 481.383 800.000 ~o" 801.890 1333.61 687.444 1143.10601.6:29 1000.21 534.893 889.074 481.527 800.167 1 802.129 1333.89 687.649 1143.33601.808 1000.42 535.052 889.259 481.670 800.333 9 802 363 1334.17 687.850 1143 57 601. 98 1 1000.63 535.208 889.444 481.811 800.500 3 802.597 1334.44 688.050 1143.81 602.160 1000 83 535.364 889.630 481.951 800.667 4 802.886 1334.72 688.255 1144.05 602.339 1001.04 535.523 889.815 482.095 800.833 5 803.074 1335.00 688.460 1144.29 602.518 1001.25 535.683 890.000 482 238 801.000 6 803.308 1335.28 688.661 1144.52 602.694 1001.48 535.839 890.185 482.379 801.167 7 803.543 1335.50 688.861 1144.76 602.869 1001.67 535.995 890.370 482.519 801.333 8 803.781 1335.83 689.066 1145.00 603.048 1001.88 536.154 890.556 482 663 801.500 9 804.020 1336.11 689.271 1145.24 603.228 1002.08 536.314 890.741 482.806 801.667 1O 804.259 1336.39 689.476 1145.48 603.407 1002.29 536.473 890.926 482.949 801.833 11 804.498 1336.67 689.680 1145.71 603.586 1002.50 536.632 891.111 483.093 802.000 13 804.737 1336.94 689.885 1145.95 603.765 1002.71 536.792 891.296 483.236 802.167 13 804.976 1337.22 690.090 1146.19 603.944 1002.92 536.951 891.481 483.380 802.333 14 805.210 1337.50 690 290 1146.43 604 . 120 1003.13 537.107 891 667 483.520 802.500 15 805 444 1337.78 OW.4-J1 1146.67 604.296 1003.33 537.263 891.852 483.661 802 (567 16 805.683 1 338.06 690.696 1146.90 604 475 1003.54 537.422 892.037 483.804 802.833 17 805.9-21 1 :M . 33 690.901 1147.14 604.654 1003.75 537.582 892 222 483.948 803.000 18 806.160 1338.61 691.105 1147.38 604.833 1003.96 537.741 892.407 484.091 803.167 19 806.399 1338.89 691.310 1147.62 605.012 1004.17 537.900 892.593 484.234 803.333 20 806.638 1339.17 691.515 1147.86 60'). 192 1004.38 538.060 892.778 484.378 803.500 31 806.877 1339.44 691.720 1148.10 605.371 1004.58 538.219 892.963 484.521 803.667 33 807.116 1339.72 691.924 1148.33 605.550 1004.79 538.378 893.148 484.665 803.833 33 807.354 1340.00 692.129 1148.57 605.729 1005.00 538.538 893.333 484.808 804.000 34 807.589 1340.28 692.330 1148.81 605.905 1005.21 538.694 893.519 484.949 804.167 35 807.823 1340.56 692.531 1149.05 606.080 1005.42 538.850 893.704 485.089 804.333 36 808.061 1340.83 692.735 1149.29 606.260 1005.63 539.009 81)3.889 485.233 804.500 37 808.300 1341.11 692.940 1149.52 606.439 1005.83 539.169 894.074 485.376 804.667 38 808.539 1341.39 693.145 1149.76 606.618 1006.04 539.328 894.259 485.520 804.833 39 808.778 1341.67 693.350 1150.00 606.797 1006.25 539.487 894.444 485.663 805.000 30 809.017 1341.94 693 554 1150.24 606.976 1006.46 539.647 894.630 485.806 805.167 31 809.256 1342.22 693.759 1150.48 607.156 1006.67 539.806 894.815 485.950 805.333 33 809.495 1342.50 693.964 1150.71 607.335 1006.88 539.965 895.000 486.093 805.500 33 809.733 1342.78 694.169 1150.95 607.514 1007.08 540.125 895.185 486.237 805.667 34 809.972 1343.06 694.373 1151.19 607.693 1007.29 540.284 895.370 486.380 805.833 35 810.211 1348.88 694.578 1151.43607.872 1007.50 540.443 895.556 486.523 806.000 36 810.450 1343.61 694.783 1151.67 608.052 1007.71 540.602 895.741 486.667 806.167 37 810.689 1343.89 694. 98S 1151.90 608.231 1007.92 540.762 895.926 486 810 806.333 38 810.928 1344.17 695.192 1152.14 608.410 1008.13 540.921 896.111 486.954 806.500 39 811.166 1344.44 695.307 1152.38 608.589 1008.33 541.080 896.296 487.097 806.667 4O 811.405 1344.72 695.602 1152.62 608.768 1008.54 541.240 896.481 487.241 806.833 41 811.644 1345.00 695.807 1152.86 608.948 10C8.75 541.399 896 . 667 487.384 807.000 43 811.883 1345.28 696.011 1153.10 609.127 1008 96 541.558 896.852 487.527 807.167 43 812.122 1345.56 696.216 1 153.33 609.306 1009.17 541.718 897.037 487.671 807.333 44 812.365 1345.83 696.425 1153,57 609. 4K9 1009.38 541.880 897.222 487.817 807.500 45 812.609 1346.11 696.634 1153.81 609.672 1009.58 542.043 897.407 487.963 807.667 46 812.848 1346.39 696.839 1154.05 609.851 1009.79 542.202 897.593 488.107! 807. 833 47 813.087 1346.67 697.043 1154.29 610.030 1010.00 542.361 897.778 4H8.850 808.000 48 813.326 1346.94 697.248 1154.52 610.209 1010.21 542.521 897.963 488. 394 1 808. 167 49 813.564 1347.22 697.453 1154.76 610.388 1010.42 542.680 898.148 488.537 808.333 5O 813.808 1347.50 697.658 11 55. 00! 610. 567 1010.63 542.839 898.333 488.681 808.500 51 814.04-2 1347.78 697.86-2 1155.24 610.747 1010.83 542.999 898.519 488.824 808.067 53 814.281 1318.06 698.067 1155.48610.926 1011.04 543.158 898.704 488.967 808.833 53 814.540 1348.33 698.272 1155.71 611.105 1011.25 543 317 898.889 489.111 809.000 54 814.763 1348.61 698.481 1155.95611.288 1011.46 543.480 899.074 489.257 809.167 55 815.007 1348.89 698 690 1156.19611.471 1011.67 543.642 899.259 489 403 809.333 56 815.246 1349.17 698.894 1156.43611 650 1011.88 543.802 899.444 489.547 809.500 57 815.485 1349.44 699.099 1156.67611.8-29 1012.08 543.961 S99.630 489.690 809.667 58 815.724 1349.72699.304 1156.90012.008 1012.29544.120 899.815 489.834 809.833 59 207 TABLE XIV. ACTUAL TANGENTS, ETC. 81 1 Curve, 3 Curve. 3 Curve. 4 Curve. 5 Curve. M. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. 4893. 58; 8100. 00 2446788 4050700 [637.16 2700.00 1223.63 2025.00979.015 1620.00 1 481)5.01 8 101. (57 2447.60 -1050.83 1631.84 2700.56 1223.99 2025.42979 301 1620.33 2 4896.4-1 8103.33 2448.31 4051.67 1632.3-2 2701.11 1224.35 2025.83979.588 1620.67 3 4897.91 8105.00 2449.04 4052.50 1632.80 27'01.67 1224.71 2026.25979.880 1621.00 4 4899.37 8106.67 2449.77 4053.33 1633.29 2702.22 1225.08 2026.67980.173 1.621.33 5 4900.80 8108.33 2450.49 4054.17 1633.77 2702.78 1225.44 2027.08980.459 1021.67 6 4902.23 8110.00 2451.21 4055.00 1634.25 2703.33 1225.80 2027. 50 1980.746 1622.00 7 4903.6(3 8111 67 2451.92 4055.83 1634.72 27'03.89 1220.15 2027.92981.032 1622.33 8 4905.10 8113.33 2452.64 4056.67 1635.20 2704.44 1226.51 2028.33981.319 1622.67 9 4906.56 8115.00 2453.37 4057.50 1635 69 2705.00 1226.88 2028.75 981.611 1623.00 1O 1908.02 8116.67 2454.10 4058.33 1636.17 2705.56 1227.24 2029.17 981.903 1623.33 11 1909 45 8118.33 2 454. 82 14059. 17 1636.65 2700.11 1227.00 2029.58982.190 1623.67 12 4910.88 8120.00 2455.534060.00 1637.13 2706.67 1227.96 2030 00 982. 477 1624.00 13 4912.34 8121.67 2456.26 4060.83 1637.62 ^707.22 1228.32 2030.42982.769 1624.33 14 4913.81 8123.33 2456.99 4061.67 1638.10 2707.78 1228.69 2030.83983.061 1624.67 15 1915.24 8125.00 2457.71 4062.50 1638.58 2708.33 1229.05 2031.25983.348 1625.00 16 4916.67 8126.67 2458.43 4063.33 1639.06 2708.89 1229.41 2031.67983.634 1625.33 17 4918.13 8128.33 2459.16 4064.17 1639.55 27'09.44 1229.77 2032. 08 19813.927 1625.67 18 4919.59 8130.00 2459.89 4065.00 1640.03 2710.00 1230.14 2032 501984.219 1626.00 19 4921.02 8131.67 2460.60 4065.83 1640.51 2710.56 1230.49 2032.92 984.506 1626.33 20 4922 46 8133.33 2461.32 4066.67 1640.99 2711.11 1230.85 2033.33 984.792 1626.67 21 4923.92 8135.00 2462.05 4067.50 1641.48 2711.67 1231.22 2033.75 985.084 1627.00 22 192."). 38 8136 67 2462 . 78 4068.33 1641.96 2712.22 1231.58 2034.17 985.377 1627.33 23 4926.84 8138.33 2463.51 4069.17 1642.45 2712.78 1231 95 2034.58 985.669 1627.67 34 4928.30 8110.00 2464.24 4070.00 1642.94 2713.33 1-232.31 2035.00 985 901 1628.00 25 4929.73 8141.67 2464.96 4070.83 1643.41 2713.89 1232.07 2035.42 986.248 10-28.33 36 4931.17 8143.33 2465.67 4071 . 67 1643.89 2714.44 1233.03 2035.83 986.534 1628.67 37 4932.63 8145.00 2466.40 4072.50 1644.38 2715.00 1233.40 2030.25 986.827 1029.00 38 49:54.09 8146.67 2467.13 4073.33 1644.87 2715.56 1233.70 2'36.67 987.119 1629.33 39 4935.55 8148.33 2467.87 4074.17 1645.35 2716.11 1234.13 2037.08 987.411 1629.67 3O 1937.01 8150.00 2468 60 4075.00 1645.84 2716.67 1231.49 2037.50 987.704 1630.00 31 4938.44 8151.67 2469.31 4075.83 1646.32 2717.22 1-231.85 2037.92 987.990 1630.33 33 1939.88 8153.33 2470.03 4076.67 1646.79 2717.78 123-1 . 21 2 33.33 988.277 1630.67 33 4941.34 8155.00 2470.76 4077.50 1647.28 2718.33 1235.57 2088.75 988.509 1631.00 34 4942.80 8156.67 2471.49 4078.33 1047.77 2718.89 1 235 94 2039.17 988.861 1631.33 35 4914.26 8158.33 2472.22 4079.17 1648.26 2719.44 123t5.30 2039.58 989.154 1631.07 36 4945.72 8160.00 2472.95 4080.00 1648.74 2720.0' 1236.67 2040.00 989.446 1032.00 37 4947.15 8161.67 2473.67 4080.83 1649.22 2720.50 1237.03 2040.42 989.733 1632.33 38 4948.58 8103.33 2474.38 4081.67 1649.70 2721.11 1237.39 2040.83 990.019 1632.07 39 4950.05 81(35.00 2475.11 4082.50 1650.18 27-21.6I 1237.75 2041.25 990.311 1033.00 4O 4951.51 8166.67 2475.84 4083.33 1650.67 2722 22 1238.12 2041.67 990.604 1633.33 41 4952.97 8168.33 2476.57 4084.17 1651.16 2722^78 1-238.48 2042.08 990.890 1633.07 43 4954 . 43 8170.00 2477.30 4085.00 1651.65 2723.33 1238.85 2042.50 991.188 1034.00 43 4955.89 8171.67 2478.04 4085.83 1652.13 27553.89 1239.21 2042.92 991.481 1034.33 44 4957.35 8173.33 2478.77 4086 . 07 1652 62 2724.44 1239.58 2013.33 991.773 1634.67 45 4958.81 8175.00 2479 50 4087.50 1653.11 2725.00 1239.94 2013.75 992.065 1035.00 46 4960.27 8176.67 2480.23 4088.33 1653.59 2725.56 1240.31 2044.17 992.358 1035.33 47 49(51.73 8178.33 2480.96 4089.17 1654.08 2726.11 1240.67 2044.58 992.650 1035.67 48 49(53.19 8180.00 2481.69 4090.00 1654.57 2720.67 1241 04 204x00 992.942 1636.00 49 4964.66 8181.67 2482.42 4090.83 1655.06 2727.22 1241.40 2045.42 993.234 1030.33 5O 4966.12 8183.33 2483.15 4091.67 1655.54 2727.78 1241.77 2045.83 993.527 1036.67 51 4967.58 8185.00 2483.88 4092.50 1656.03 2728.33 1242 14 2046.25 993.819 1637.00 53 4969.04 8186.67 2484.61 4093.33 1656.52 2728.89 1242.50|2046.67 994 .111 1637.33 53 4970.50 8188.33 2485.34 4094.17 1657.00 2729.44 1242.87 2047.08 994.404 1037.07 54 4971.96 8190.00 2486.07 4095.00 1657.49 2730 00 1243.23 2047.50 994.690 1038.00 55 4973.42 8191.67 2486.80 4095.83 10.VT.98 2730.56 1243.60,2047.92 994 . 988 1638.33 56 4974.88 8193.35 2487.53 4096.07 1658.47 2731.11 1243.90 2048.33 995. 21 1038.07 57 4976.34 8195.00 2488.20 4097.50 1058.95 273 1. 67 1 1244. 33 ! 2048. 7'5 995.57'3 1039.00 58 4977.81 8196.67 2488 99 4098.33 1659.44 27 3. '.22 1244. 09 ! 2049. 17 995.865 1039.33 59 4979.27 8198.33 2489.72 4099.17 1659.93 2732 . 78 1 245 . 06 1 2049 . 58 996 . 1 57 1039.07 208 TABLE XIV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 Curve. 10 Curve. 81 ^T Tan. Arc. Tan. | Arc. Tan. Arc. Tan. Arc. Tan. Arc. 815.98-2 1350.00 699.509:1157.14 612.187 1012.50 544.280900.000 489.977810.000 o 816.301 1350.28 699.7131157.38 612.3671012.71 544.439900.185 490.121 810.167 i 816.440 1350.56 699.918 1157.62 612.540 1012.92 544.598:900.370 490.264810.333 2 816.084 1350.83 700.127 1157.86 612.729 1013.13 544. 761 1900.556 490.410810.500 3 816.927 1351.11 700.336 1158.10 612.911 1013.33 544. 923 1900.741 490.557810.067 4 817.166 1351.39 700.511 1158.33 613 0911013. 54 545.082 900.926 490.700810 833 5 817.405 1351.67 700.745 1158.57 613.270 1013. 75 545.242 901.111 490.843811.OtK) 6 817.644 1351.94 700.950 1158.81 613.4491013.9(5 545.401 901.296 490.987811.107 7 817.883 1352.24 701.155 1159.05 613.628 1014.17 545.560 901.481 491.130811.333 8 818.126,1352.50 701.364 1159.29 613.811 1014.38 545.723 901.667 491.277811.500 9 818.370-1352.78 701.572 1159.52 613.994 1014.58 545.885 901.852 491.423811 667 1O 818.609 1353.06 701.777 1159.76 614.173 1014.79 546.045 902.037 491.506811.833 11 818,8481353.33 701.982 1160.00 614.352 1015.00 546.204 902.222 491.710812.000 12 819.091 1353.61 702.191 1160.24 614.535 1015.21 546.367 902.407 491.850812.107 13 819.335 1353. 89 702.400 1160.48 614.718 1015.42 546.529 902.593 492.002812.333 14 819.574 1354.17 702.604 1160.71 614.897 1015.63 546.688 902.778 492.140812.500 15 819.813 1354.44 702.809 1160.95 615.076 1015.83 546.848 902.963 492.289812.667 16 820.0561354.72 703.018 1161.19 615.259 1016.04 547.010 903.148 492.435812.833 17 820 300 ' 1355.01' 703.227 1161.43 615.442 1016.25 547.173 903.333 492.582 813.000 18 820.539 1355.28 703.432 1161.67 615.621 1016.46 547.332 903.519 492.725 813.167 19 820.777 1355.56 703.636 1161.90 615.800 1016.67 547.491 903.704 492.869 813.333 20 821.021 1355.83 703.845 1162.14 615.983 1016.88 547 654 903 889 493.015 813.500 21 821.265 1356.11 704.054 1102.38 6J6.166 1017.08 547.810 904.074 493.161 813.667 22 821.508 1356.3C 704.263 1162.62 616.348 1017.29 547.979 904.259 493.307 813.833 23 821.752:1356.67 704.472 1162.86 616.531 101 7. 5< 548.141 904.444 493.454 814.000 24 821. 991 11356.94 704 . 677 1163.10 616.710 1017.71 548.301 904 63( 493.597 814.167 25 822.230 1357.22 704.881 1163.33 616.889 1017.92 548.460 904.815 493.741 814.333 26 822.473 1357.50 705.090 1163.57 617.072 1018.13 548.623 905.000 493.887 814.501 27 822.717 1357.78 705 299 11(53.81 617.225 1018.33 548.785 905.185 494.033 814.667 28 822.960 1358.06 705.508 1164.05 617.438 1018.54 548.948 905.370 494.179 814.833 29 823.204 1358.33 705.717 1164.29 617.621 1018.75 549.110 905.550 493.326 815.000 30 823.443 1358.61 705.9-21 1164 5'. 017.800 1018.9C 549.269 905.741 494.409 815.167 31 823.682 1358.89 706.126 1104.70 617.979 1019.17 549.429 905.926 494.613 815.333 32 823.925 1359.17 706.335 1105.00 618.102 1019.38 549.591 906.111 494.759 815.500 33 824.169 1359.44 7'06.544 1165.24 618.345 1019.58 549.754 906.296 494.905 815.667 34 824.413 1859.72 706.758 1165.48 018.527 1019.79 549 916 906.481 495.051 815.833 35 824.656 1360.(K 7'06.962 1165.71 618.710 1020.00 550.079 9 6.667 495 198 816.000 36 824.895 1360.28 707.166 1165.95 018.889 1020.21 550.238 906.852 495.341 816.167 37 825.134 1360.56 707.371 1166.19 019.009 1020.42 550.397 907.037 495.485 816.333 38 825.313 1360.83 707.580 1166.43 619.251 1020.63 550.560 907.222 495.631 816.501 39 825.621 1361.11 707.789 1166.67 619.434 1020.83 550.722 907.407 495.777 816.667 40 825.865 1361.39 707.998 1106.90 619 617 1021.04 550.885 907.593 495.923 810.833 41 82(5.1081361.67 708.207 1167.14 619.800 1021.25 551.047 907.778 496.070 817. OtX 42 826. 352 11361. 94 708.415 1107.38 619.982 1021.46 551.210 907.963 496.216 817.107 43 826.596 1362.22 708. 624 '11 67. 62 620 165 1021.67 551.372 908.148 496.362 817.333 44 826.839 1362. 5( 708.833 1 167. 86 020.348 1021.88 551.535 908.333 496.509 817.500 45 827. OS3 1362.78 709.042 1168.10 620.531 1022.08 551.697 908.519 496.655 817.667 46 827.326 1363. Cf 709.251 1168.33 620.714 1022.29 551 .860 908.704 496.801 817.833 47 827.570 1303.33 709.400 1168 57 0-20.896 1022.50 552.022 908.889 496.947 818.00< 48 827.814 1363.61 709.668 1168.81 621.079 1022.71 552.185 909.074 497.094 818.167 49 828.057 1303.89 709.8771169.05 621.20-2 1022.92 552.347 909.259 497.240 818.333 50 828.301 1364.17 710.086 1169.29621.445 1023.13 552 510 909.444 497.386 818.50< 51 828. 545 11364.4-1 710. 295 11 69. 52 62 1.627 1023.33 552.672 909.630 497.533 818.66; 52 828.788 1364.72 710.504 1169.766-21.810 .1023. 54 552. 835:909. 81 r 497.679 818.83 53 8-29. (32 1365.00 710.713 1170.00 621 .993 1023.^5 552.997910.000 497.825 819.001 54 829.275 1365.28 710.922 1170.24622.176 H'23.90 553.160910.185 497.971 819.167 55 8-9.5191365.56 711.130 1170.48022.3591024.17 553.322i910. 370 498.118 819.333 56 82!). 763 13(55.83 711.339 1170.71 622.541 1024.38 553.485 910. 6 498.264 819.500 57 830.006 13(56.11 711.548 1170.95622.724 1024.58 553.647910.741 498.410 819.667 58 830.2501366.39 711. 7571 1171. 19 622. 907 1024 79 553. 8101910. 926 498.557819.833 59 200 TABLE XIV. ACTUAL TANGENTS, ETC. $2 M. 1 Curve. 3 Curve. 3 Curve. 4 Curve. 5 Curve. Tan. Arc. Tan. Arc. Tan. Arc. Tan. | Arc. Tan. I Arc. O 4980.73 8200.00 2490.45 4100.00 1660.41:2733.33 1245.42 2050.00 996.450 1610.00 1 498*. 19 8201.67 2491.19 4100.83 1660.90! 2733. 89 1 245 . 79 2050 . 42 ] 996 . 742 J 640 . 33 3 4983.65 8203.33 2491.92 4101.67 166 1.39: 2734. 44 1246.15 2050.83 997.034 1640.67 3 4985.11 8205.00 2492.65 4102.50 1661 87 i 2735. 00 1246.522051.25997 327 1641.00 4 4986.57 8206.67 2493.38 4103.33 1662.362735.56 1246 88 2051.67 97. 619 1641.33 5 1988.03 8208.33 2494.11 4104.17 1662.85 2736.11 1247 . 25 2052 . 08 997 . 91 1 ! 1641 . 67 6 4989.49 8210.00 2494.84 4105.00 1663.34 2736.67 1247.62 2052.50 9'J8. 204 (1642.00 7 4990.95 8211.67 2495.57 4105.83 1663.82 2737.22 1247.98 2052.92 998.496 1642.33 8 4993.42 8213.33 2496.30 4106.67 1664.31 2737.78 1248.352053.331998.788 1642.67 9 4993.88 8215.00 2497.03 4107.50 1664.80 2738.33 1248.71 2053.75 999.080 1643.00 10 4995.34 8216.67 2497.76 4108.33 1665.28 2738.89 1249.08 2054.17 999.373 1643.33 11 4996.83 8218.33 2498.51 4109.17 1665.78 2739.44 1249.45 2054.58 999.671 1643.67 13 1998.33 8220.00 2499.25 4110.00 1666.28 2740.00 1249.82 2055.00999 969 1644.00 13 4999.78 8221.67 2499.98 4110.83 1666.76 2740.56 1250.19 2055.42 1000.26 1644.33 14 5001.24 8223.33 2500.71 4111.67 1667.25 2741.11 1250.55 2055.83 1000.55 1644.67 15 5002 70 8225.00 2501.44 4112.50 1667.74 2741.6; 1250.92 2056.25 1000.85 1645.00 16 5004.16 8226.67 2502.17 4113.33 1668.23 2742.22 1251.28 2056.67 1001.14 1645.33 17 5005.6-2 8228.33 2502.90 4114.17 1668.71 2742.78 1251.65 2057.08 1001.43 1645.67 18 5007.08 8230.00 2503.63 4115.00 1669.20 2743.33 12.V2.01 2057.50 1001.72 1646.00 19 5008.57 8231.67 2504.38 4115.83 1669.70 2743.89 1252.39 2057.92 1002.02 1646.33 2O 5010.06 8233.33 2505.12 4116.67 1670.19 2744.44 1252.76 2058.33 1002.32 1646.67 31 5011.52 8235.00 2505.85 4117.50 1670.68 2745.00 1253.12 2058.75 1002.61 1647.00 33 5012.99 8236.67 2506 58 4118.33 1671.17 2745.56 1253.49 2059.17 1002.90 1647.33 33 5014.45 8238.33 2507 32 4119.17 1671.65 2746.11 1253.85 2059.58 1003.20 1647.67 34 5015.91 8240.00 2508.05 4120.00 1672.14 2746.67 1254.22 2060.00 1003.49 1648.00 35 5017.40 8241.67 2508.79 4120.83 1672.64 2747 2 ' 1254.59 2060.42 1003.79 1648.33 36 5018.89 8243.33 2509.54 4121.67 1673.13 2747 .'78 (254.96 2060.83 1004.08 1648.67 37 5020 35 8245.00 2510.27 4122.50 1673.62 2748.33 1255.33 2061.25 1004.38 1649.00 38 5021.81 8246.67 2511.00 4123.33 1674.11 2748.89 1255.70 2061.67 1004.67 1649.33 39 5023.30 8248.33 2511.74 4124.17 1674.61 2749.44 1256.07 2062.08 1004.97 1649.67 30 5024.79 8250.00 2512.49 4125.00 1675.10 2750.00 1256.44 2062.50 1005.26 1650.00 31 5026.25 8251.67 2513.22 4125.83 1675.59 2750.56 1256.81 2062. 92 1005.56 1650.33 33 5027.71 8253.33 2513.95 4126.67 1676.08 2751.11 1257.17 2063. 33 ! 1005. 85 1650.67 33 5029.20 8255.00 2514.69 4127.50 1676.57 2751.67 1257.54 2063.75 1006.15 1651.00 34 5030.69 S256.67 2515.44 4128.33 1677.07 2752.22 1257.92 2064.17 1006.45 1651.33 35 5032.18 825S.33 2516.17 4129.17 1677.56 2752.78 1258.28 2064.58 1006.74 1651.67 36 5033.07 S260.00 2516.90 4130.00 1678.04 2753.33 1258.65 2065.00 1007.03 1652.00 37 5035.13 8261.67 2517.64 4130.83 1678.54 2753.89 1259.02 2065.42 1007.3311652.33 38 5H36.59 S263.33 2518.39 4131.67 1679.04 2754.41 1259.39 2065.83 1007.63 1652.67 39 5038.05 8265.00 2519.12 4132.50 1679.52 2755.00 1259.76 2066.25 1007.92 1653.00 40 5039.51 8266.67 2519.85 4133.33 1680.01 2755.56 1260.12 2066.67 1008.21 1653.33 41 43 5041.00 5012.49 8268.33 8270.00 2520.59 2521.34 4134.17 4135.00 1680.51 1681.00 2756.11 2756.67 1260.49 1260.87 2067.08 2067.50 1008.51 1653.67 1008.81 1654.00 43 5043.98 8271.67 2522.08 4135.83 1681.50 2757.22 1261.24 2067.92 1009.10 1654.33 44 5015.47 8273.33 2522.83 4136.67 1682.00 2757.78 1261.61 2068.33 1009.40 1654.67 45 5046.93 8275.00 2523.56 4137.50 1682.48 2758.33 1261.98 2068.75 1009.70 1655.00 46 47 5048.398276.67 5019.888278.33 2524.29 2525.03 4138.33 4139. 1 1 ; 16S2.97 16S3.47 2758.89 2759.44 1 262. 34 ! 2069. 17 1262.722069.58 1009.99 1655.33 1010.29'l655.67 48 5051.378280.00 2525.78 4110.00 16S3.96 2760.00 1263.092070.00 1010.58 1656.00 49 5052 . 86 8281 . 67 2526.52 4140.83 1684.46 2760.56 1263.46 2070.42 1010.881650.33 50 5054.35:8283.33 2527.27 4141.67 1684.96 2761.11 1263.83 2070.83 1011.18 1656.67 51 5055.81 8285.00 2528.00 4142.50 1685.45 2761.67 1264.202071.25 1011.47 1657.00 52 5057.288286.67 2528.73 4143.33 1685.93 2762.22 1264.5621)71.67 1011.76 1657.33 5:? 5058.778288.33 2529.48 4144.17 1686.43 2762. 7S 1264.91 2072.08 1012.06 1657. 07 54 5060 25 ' 8290. 00 2530.22 4145.00 16S6.93 2763.33 1 265. 3 1 2072. 50 1012.36 1658.00 55 506 1.74 '829 1.67 2530.97 4145.83 1687.42 2763.89 1265.682072.92 1012.66 1658.33 56 5063. 23 8293. 33 2531.71 4146.6? 1687.92 2764.44 1266.052073.33 1012.96 1058.67 57 5064.72i8295.00 2532.45 4147.50 1688 42 2765 . 00 1266.432073.75 1013.251659.00 58 5066.21 8296. 67 2533.20 4148.33 1688.91 2765.56 1266.802074.17 1013.55 1659.33 59 5067.678298,33 2533.94 4149.17 1689.41 2766.11 1267.17.2074 58 1013.85 : 1659.67 210 TABLE XIV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 Curve. 1O Curve. 82 Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. M. 830.494 1366.67 711.966 1171.43623.090 1025.00 553.972 911.111498.703 820.000 O 830.787 1366.94 712.175 1171.67623.272 1025.21 554.135911.296498.849 820.167 1 880.981 1367.22 712.3S4 1171 90 623.455 1025.42 554. 297 1 911. 481 49S. 996 820.333 2 831.224 1367.50 712 592 1172.14:623.638 1025.63 554.460 911.667499.142820.500 9 881.408 1367.78 712.801 1172.38623.821 1025.83 554.622 911.852499.288 820.667 4 881.712 1368.06 713.010 1172.62624.004 1026.04 554.785 912.037499.434 820.833 5 831.856 1368.33 713.219 1172.86 624 186 1026.25 554.947 912.222499.581 821.0TK) 6 832.199 1368.61 713.428 1173.10624.369 1026.46 555.110 912.407J499.72; 821 167 7 832 442 1368.89 713.637 1173.33624.552 1026.67 555.272 912.593i499.873 821.333 8 832.686 1369.17 713.845 1173.57 624.735 1026.88 555,435 912.778500 020 821.500 9 832.930 1369.44 714.054 11.73.81 624.917 1027.08 555.597 912.963500.166 821.667 10 833.178 1369.72 714.267 1174.05625.104 1027.29 555 763 913.148500.315 821.83:) 11 833.427 1370.00 714.480 1174.29625.290 1027.50 55^.929 913.333:500.464 822.00L 12 833 670 1370.28 714.689 1174.52625.473 1027.71 556.091 913.519:500.610 822.1(57 13 833.914 1370.56 714.898 1174.76625.656 1027.92 556.254 913.704 500.757 822. 3: W 14 834.157 1370.83 715 10711175.00625.838 102S.13 556.416 913.889500.903 822.500 15 831.401 1371.11 715.316 1175.24 626.021 102S.33 556.579 914.074 501 049 822.667 16 834.645 1371.39 715.524 1175.48626.204 1028.54 556.741 914.259501.196 822.833 17 834.888 1371.67 715.733 1175.71 626.387 1028.75 556.904 914.444 501.342 823.000 18 835.137 1371.94 715.946 1175.95 626.573 1028.96 557.070 914.630501.491 823.167 19 835.385 1 372 22 716.159 1176.19 626.760 1029.17 557.235 914.815501.640 823.333 2O .835.629 1372! 50 716.368 1176.43 62(5.942 1029.38 557.398 915.000501.787 823.500 21 835.872 1372.78 7 16. '577 1176.67 627.125 1029.58 557.560 9 i 5. 185 501. 933 823.667 22 836.116 1373.06 716.786 1176.90 627.308 1029.79 557.723 915.370502 079 823.833 2'3 836.360 1373.33 716.995 1177. 14^627. 491 1030.00 557.885 915.556502.225 824.000 24 836.608 1373.61 717.208 1177.38627.677 1030.21 558.051 915.741 502.375 824.167 25 836 . H56 1373.89 717.421 1177.62627.803 1030.42 558.217 915.926502.524 824.333 26 837.100 1374.17 717.629 1177.86628.046 1030.63 558.379 916.111 502.670 824.500 21 837.344 1374.44 717.83S 1178.10 628.229 1030.83 558.542 916.296502.816 824.667 28 837.592 1374.72 718.051 1178.33 628.415 1031.04 558.707 916.481^02.965 824.833 29 837.840 1375.00 718 264 1178.57 628.602 1031.25 558.873 9l6.667Wl15 825.000 30 838.084 1375.28 718.473 1178.81 628.784 1031.46 559.035 916.852503.261 825.167 31 838.328 1375.5.6 718.682 1179.05 628.967 1031.6; 559.198 917.037503.407 825.333 32 838.576 1375.83 718.895 1179.29 629.154 1031.88 559.364 917.222503.556 825 500 33 838 824 1376.11 719.108 1179.52 629.340 1032. OS 559.529 917.407503.706 825.667 34 839 068 1376.39 719.317 1179.76 629.523 1032.29 559.692 917.593503.852 825.833 35 839 312 1376.67 719.525 1180.00 629 706 1032.5(1 559.854 917.778503.998 826.000 36 839.560 1376.94 719.738 1180.24 629.892 1032.71 560.020 917.963504.147 826.167 37 839. 808 1 1377. 22 719.951 1180.48 630.078 1032.92 560.186 918.148504.296 826.333 38 840.052 1377.50 720.160 1180.71 630.261 1033.13 560.348 918.333504.443 826.500 39 840.296 1377.78 720.369 1180.95 630.444 1033.33 560.511 918.519504 589 826.667 40 8Mh544 1378.06 720.582 1181.19 630.630 1033.54 5(50 676 918.704 504.738 82(5 833 41 840.792 1378.33 720.795 1181.43 630.817 1033.75 560.842 918.889504.887 827.000 42 841.041 1378.61 721.008 1181.67 631.003 1033.SH5 5(51.008 919.074505.036 827.167 43 841.289 1378.89 721.221 1181.90 631.189 1034.17 561.17'4 919.259505.186 827.333 44 841 533 1379.17 721.430 1182.14 631.372 1034.3s 561.336 919.444505.332 827.501: 45 841 . 776 1379.44 721.638 1182.38 631.555 1034.5* 561 499 919.630505.478 827.66; 46 842.025 1379.72 721.851 1182.62 631 . 74 1 1034.79 561.664 919.815505.627 827.833 47 812.273 1380.00 722.064 1182.86 631.928 1035.00 561.830 920.000505.777 828.000 48 812.522 1380.28 722 277 1183.10 632 114 1035.21 561.996 920.185505.926 828.167 49 842 770 1380.56 722.490 1183.33 63.2.300 1035.42 562.161 920.370506.075 828.333 50 843.014:1380.83 722.699 1183.57 632.483 1035.63 562 324 920.556506.221 828.500 51 843.25711381.11 722.908 1183.81 632.666 1035.83 562.486 920.741 506.367 828.667 52 843.506 1381.3'.) 723.121 1184.05 632.852 1036.04 562.652 920.926506.517 828.833 53 843.75-1 !l3Sl.f)7 723.834 1184.29 633.039 1036.25 562.818 921.111 506.666 829.000 54 844.002 1381.94 723 547 1184.52 633.225 1036.46 562.983 921.296506.815 829.167 55 844 251 1382.2',! 723.760 1184.76 033.411 1036.67 563.149 921.481 506.964 829.333 56 844.499 1382.50 523.973 1185.00 633.598 1036.88 563.315 921.667507 113 829.500 57 844 . 748 1382.78 724 186 1185.24 633.784 1037.08 563.480 921 . 852 507 . 262 1 829 . 667 58 844.996 1383.06 724.399 1185.48 623.970 1037.29 563.646 922.037 507. 4121 829. 833 59 211 TABLE XIV. ACTUAL TANGENTS, ETC. 83 1 Curve. 2 Curve. 3 Curve. 4 Curve. 5 Curve. M. ~o~ Tan. 5069714 Arc. 8300.00 Tan. 2534.69 Arc. 4150.00 Tan. Arc. Tau. T267.54 Arc. 2075.00 Tan. Arc. 1689.91 2766.67 1014.15 1660.00 i 5070.63 8301.67 2535 42 4150.831690.39 2767.22 1267.91 2075.42 1014.44 1660.33 2 5072.12 8303.33 2536.15 4151.67 1690.88 2767.78 1268.27 2075.83 1014.73 1660.67 3 5073.61 8305.00 2536.90 4152.50 1691.38 2768.33 1268.65 2076.25 1015.03 1661.00 4 5075.09 8306.67 2537.64 4153.33!1691.87 2768.89 1269.02 2076.67 1015.33 1661.33 5 5070.58 8308.33 2538.39 4154.17:1692. 37 2769.44 1269.39 2077.08 1015.63 1661.67 6 5078 07 8310.00 2539.13 4155.00 1692.87 2770.00 1269.76 2077.50 1015.93 1662.00 7 5079.56 8311.67 2539.88 4155.83 1693.36 2770.56 1270.14 2077.92 1016.22 1662.33 8 5081.05 8313.33 2540.62 4156.67 1693.86 2771.11 1270.51 2078.33 1016.52 1662.67 5082.54 8315.00 2541.36 4157.50 1694.36 2771.67 1270.88 2078.75 1016.82 1663.00 10 5084.03 8316.67 2542.11 4158.33 1694.85 2772.22 1271.25 2079.17 1017.12 1663.33 11 5085.52 8318.33 2542.85 4159.17 1695.35 2772.78 1271.63 2079.58 1017.42 1663.67 12 5087.01 8320.00 2543.60 4160.00 1695.85 2773.33 1272.00 2080.00 1017.71 1664.00 13 5088.50 8321.67 2544.34 4160.83 1696.34 2773.89 1272.37 2080.42 1018.01 1664.33 14 5089.99 8323.33 2545.09 4161.67 1696.84 2774.44 1272.74 2080.83 1018.31 1664.67 15 5091.48 8325.00 2545.83 4162.50 1697.34 2775.00 1273.12 2081.25 1018.61 1665.00 16 501)2.97 8326.67 2546.58 4163.3311697.83 2775.56 1273.49 2081.67 1018.91 1665.33 17 5094.46 8328.33 2547.32 4164.17 1698.33 2776.11 1273.86 2082.08 1019.20 1665.67 18 5095.95 8330.00 2548.07 4165.00 1698.83 2776.67 1274.23 2082.50 1019.50 1666.00 19 5097.44 8331.67 2548.81 4165.83 1699.32 2777.22 1274.61 2082.92 1019.80 1666.33 20 5098.93 8333.33 2519.56 4166.67 1699.82 2777.78 1274.98 2083.33 1020.10 1666.67 21 5100.45 8335.00 2550.32 4167.50 700.32 2778.33 1275.36 2083.75 1020.40 1667.00 22 5101.97 8336.67 2551 08 4168.33 1700.83 2778.89 1275.74 2084.17 1020.71 1667.33 23 5103.46 8338.33 2551.82 4169.17 701.33 2779.44 1276.11 2084.58 1021.00 1667.67 24 5104.95 8340.00 2552.57 4170.00 701.82 2780.00 1276.48 2085.00 1021.30 1668.00 25 5106.44 8341 . 67 2553.31 4170.83 702.32 2780.56 1276.86 2085.42 1021.60 1668.33 26 5107.93 8343.33 2554.06 4171.67 702 82 2781. 11 1277.23 2085.83 1021.90 1668.67 27 5109:43 8345.00 2554.80 4172.50 703 31 2781.67 1277.60 2086.25 1022.20 1669.00 28 5110.91 8346.67 2555 55 4173.33 703.81 2782.22 1277.97 2086 67 1022.49 1669.33 29 5112.39 8348.33 2556.29 4174.17 1704.31 2782.78 127'8.35 2087.08 1022.79 1669.67 3O 5113.88 8350.00 2557.04 4175.00 1704.80 2783.33 1278.72 2087.50 1023.09 1670.00 31 5115 40 8351.67 2557.80 4175.83 1705.31 2783.89 1279.10 2087.92 1023.39 1670.33 32 5116.92 8353.33 2558.55 4176.67 1705.82 2784.44 1279.48 2088.33 1023.70 167'0.67 33 5118.41 8355.00 2559.30 4177.50 17'06.31 2785.00 1279.85 2088.75 1023.99 1671.00 34 5119.90 83.-)6.67 2560.04 4178.33 1706.81 2785.56 1280.22 2089.17 1024.29 1671.33 35 5121.39 8358.33 2560.79 4179.17 1707.31 2786.11 1280.60 2089.58 1024.59 1671.67 36 5122.88 8360.00 2561.53 4180. (X) 1707.80 2786.67 1280.97 2090.00 1024.89 1672.00 37 5124.40 f^GI.67 2562.29 4180.83 1708.31 2787.22 1281.35 2090.42 1025.19 1672.33 38 5125.92 K303.33 2563.05 4181.67 17'08.81 2787.78 1281.73 2090.83 1025 50 1672.67 39 5127.41 8365.00 2563.80 4182.50 1709.31 2788.33 1282.10 2091.25 1025.79 1673.00 40 5128.90 8366.67 2564.54 4183.33 1709.81 2788.89 1282.47 2091.67 1026.09 1673.33 41 5180.39 8368.33 2565.29 4184. 17[1710. 3012789. 41 1282.84 2092.08 1026.31) 1673.67 42 5131.88 8370.00 2566.03 4 1 85. OOi 1710. 80 2790. 00 1283.22 2092.50 1026.69 1674.00 43 5133.39 8371.67 2566.79 4185.83 1711.31 2790.56 1283.60 2092.92 1026.99 1674.33 44 5131.91 8373.33 2567.55 4186.671711.81 2791.11 1283.98 2093 33 1027.30 1674.67 45 5136.40 8375.00 2568.30 4187.50 1712.31 2791.67 1284.35 2093.75 1027.59 1675.00 46 5137.89 8376.67 2569.04 4188.331712.81 2792.22 1284.72 2094.17 1027.89 1675.33 47 5139.41 8378.33 2569.80 4189.17 1713.31 2792.78 1285.10 2094.58 1028.20 1675.67 48 5140.93 8380.00 2570.56 4190.001713.82 2793.33 1285.48 2095.00 1028.50 1676 00 49 5142.42 8381.67 2571.30 4190.83 1714.32 2793.89 1285.85 2095.42 1028 80 1676.33 50 5143.91 83S3.33 2572.05 4191 67 1714.81 2794.44 1286.23 2005 . 83 1029.10 1676.67 51 5145.43 8385.00 2572.81 4192.50 1715.32 2795.00 1286.61 2096.25 1029.40 1677.00 52 5146.94 8386 . 67 2573 57 1193.33 1715.82 2795.55 1286.98 2096.67 1029.70 1677.33 53 5148.46 8388.33 2574.33 4194.17 1716.33 2796.11 1287.37 2097.08 1030.01 1677.67 54 5149.98 8390.00 2575.09 4195.001716.84 i 2796.67 1287.74 2097.50 1030.31 1678.00 55 5151.47 8391.67 2575.83 4195.83 1717.33 2797.22 1288.12 2097.92 1030 61 1678.33 56 5152.96 8393.33 2576.57 4196.671717.832797.78 1288.49 2098. S3 1030.91 1678.07 57 5154.48 8335.00 2577.33 4197. 50 1718. 3412798. 33 1288.87 2098.75 1031.21 1679.00 58 5156.00 8396.67 2578.09 4198.33 1718 84:2798.89 1289.25 2099.17 1031.51 1679.33 59 5157.49 8398.33 3578.8* 4199 17 1719.34|2799 44 1289.622099.58 1031.81 1679.67 212 TABLE XIV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 Curve. 10 Curve. 83 M. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. 845.244 1383.33 724.612 1185.71 534.157 1037.50 563.812 922.222 507.561 830.000 O 845.488 1383.61 724.820 1185.95 J34.339 1037.71 563.974 922.407 507.707 830.167 1 845. 73^ 1383.89 725.029 1186.19 634.522 1037.92 564.137 922.593 507.853 830.333 2 845.980 1384.1? 725.242 1186.43 634.709 1038.13 564.303922.778 508.002 830.500 3 846.228 1384.44 725.455 1186.67 634.895 1038.33 564.468 922.963 508.152 830.66? 4 846.47? 1884.72 725.668 1186.90 635.081 1038.54 564.634 923.148 508.301 830.833 5 846.725 1385.00 725.881 1187.14 635 268 1038.75 564.800 923.333 508.450 831.000 6 84(5.974 1385.28 726.094 1187.38 635.454 1038.96 564.965 923 519 508.599 831.16? 7 847.222 1385.56 726.307 1187.62 (535.640 1039.17 565.131 923.704 508.748 831.333 8 847.470 1385.83 726.520 1187.86 635.827 1039.38 565.297 923.889 508.897 831.500 9 847.719 1386.11 726.733 1188.10 636.013 1039.58 565.462 924.074 509.047 831.667 1O 847.967 1386.39 726.946 1188.33 636.200 1039.79 565.628 924.259 509.196 831.833 11 848.216 1386.67 727.159 1188.5? 636.386 1040.00 565.794 924.444 509.345 832.000 12 848.464 1386.94 727.3721188.81 636.572 1040.21 565.959 924.630 509.494 832.167 13 848.712 1387.22 727.5851189.05 636.759 1040.42 566.125 924.815 509.643 832.333 14 848.961 1387.50 727.798 1189.29 636.945 1040.63 566.291 925.000 509.792 832.500 15 849.209 1387.78 728 0101189.52 63? . 131 1040. 83 566.457 925.185 509.942 832.667 16 849.458 1388.06 728.223 1189.76 637.318 1041.04 566.622 925.370 510.091 832.833 17 849.706 1388.33 728.4361190.00 637.504 1041.25 566.788 925.556 510.240 833.000 18 849.954 1388.61 728.649 1190.24 637.690 1041.46 566.954 925.741 510.389 833.16? 19 850.203 1388.89 728.862 1190.48 637.87? 1041.67 567.119 925.926 510.538 833.333 20 850.456 1389.17 729.079 1190.71 633.067 1041.88 567.288 926.111 510.690 833.500 21 850.709 1389.44 729. 296 ; 11 90. 95 638.257 1042.08 567.457 926.296 510.842 833.667 22 850.958 1389.72 729.509 1191. 1 851.951 1390.83 730.361 1192.14 639.189 1043.13 568.285 927.222 511.588 834.500 27 852.200 1391.11 730 574 1192.38 639.475 1043.33 568.451 927.407 511.73? 834.667 28 852.448 1391.39 730.787 1192.6L 639.561 1043.54 568.617 927.593 511.886 834.833 29 852.696 1391.6? 731.000 1192.86 C39.748 1043.75 568.783 927.778 512.035 835. 00( 3O 852.950 1391.94 731.217 1193.10 639.938 1043.96 568.951 927.963 512.188 835.167 31 853.203 1392.22 731.434 1193.33 640.12? 1044.17 569.120 928.148 512.340 835.333 32 853.451 1392.50 731.647 1193.57 640.314 1044.36 569.286 928.333 512.489 835.500 33 853.699 1392.78 731.860 1193.81 640.500 1044.58 569.452 928.519 512.638 835.667 34 853.948 1393.06 732.073 1194.05 640.687 1044.79 569.61? 928.704 512.787 835.833 35 854.196 1893.33 732.286 1191.29 640.873 1045.00 569.783 928.889 512.936 836.000 36 854.449 1393.61 732.503 1194.52 641.063 1045.21 569 . 952 929.074 513 088 836.167 37 854.703 1393.89 732.720 1194.76 641.253 1045.42 570.121 929.259 513.240 836. 33:3 38 854.951 1394.17 732.933 1195.00 641.439 1045.63 570.28? 929.444 513.389 836.500 39 855.199 1394.44 733.146 1195.24 641.626 1045.83 570.452 929.630 513.539 836.66? 4O 855.448 1394.72 733.359 1195.48 641.812 1046.04 57'0.618 929.815 513.688 836.833 41 855.696 1395.00 733.572 1195.71 641.998 1046.25 570.784 930.000 513.837 837.000 42 865.949 1395.28 733 789 1195.95 642. 18S 1046.46 570.952 930.185 513.989 837.167 43 856.203 1395.56 734.006 1196.19 642.378 1046.6? 571.121 9?0.370 514.141 837.333 44 856.451 1395.83 734.219 1196.43 642.565 1046.88 571 .287 930.556 514.290 837.500 45 856.699 1396.11 734.4321196.67 642.751 1047.08 571.453 930.741 514.439 837.667 46 856.953 1396.39 734.649 1196.90 642.941 1047.29 571.622 930.926 514.591 837.833 47 857.206 1396.67 734.8661197.14 643.131 1047.50 571.790 931.111 514.7'43 838.000 48 857.454 1396.94 735.079 1197.38 643.317 1047.71 571.956 931.296 514.892 838.167 49 857.702 1397.22 735 202 1197.62 613.501 1047.92 572.122 931.481 515.042 838.333 5O 857.956 1397.50 735.50!) 1197.86 643 . 693 1048.13 572.291 931.66? 515.1941838.500 51 858.209 1397.78 735.726 1198.10 643 8S: J , 1048 33 572.460 931.852 515.346838.667 52 858.462 1398.06 735 . 943 1 1 98 . 33 644 . 073 1043.54 572 628 932.037 515.498838.833 53 858.715 1398.33 736.1601198.57644.263 104> .75 572.79? 932.222 515. 650 839. 00( 54 858.964 1398.61 736.373 1198.81 644.450 1048 96 572.963 932.407 515.799:839.16? 55 859.212 1398.89 736.5861199.05644.636 1049.17 573.129 932.593 515.948839.333 56 859.465 1399.17 736.803 1199.29644 826 1049.38 573.298 932.778 516.100839.500 57 859.718 1399.44 737.020 1199.52645.016 1049.58 573.466 932.963 516.252839.66? 58 859 967 1399 . 72; 737 . 233 1 1 99 . 76 645 . 202 1049.79 573.632 933.148 516.401 839.833 59 213 TABLE XIV. ACTUAL TANGENTS, ETC. 84 M. 1 Curve. 2 Curve. 3 Curve. 4 Curve. 5 Curve. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. O 5158.9SS400.00 2579.58 4200.00 1719.84 2800.00 1289.99 2100.00 1032.11 680.00 1 5100.50 S401.67 2580.34 4200.83 17'20.34 2800.56 1290.37 2100.42 1032.41 1680.33 2 5162.01 8403 33 2581.10 4201.67 1720.85 2801.11 1290.75 2100.83 1032.72 080. (17 3 5108.53 S405.00 2581.86 4202.50 1721.35 2801.67 1291.13 2101.25 1033.02 1681.00 4 5165.05 8406.67 2582.62 4203.33 1721.86 2802.22 291.51 2101.67 1033.38 681.33 5 5166.57 840S.33 2583.38 4204.17 1722.37 2802.78 291.89 2102.08 1038.63 681.67 6 5168.09 8410.00 ,1584.14 4205.00 1722 87 2803.33 292.27 2102.50 1083.93 082.00 7 5169. 58 8411.67 2584.88 4205.83 1723.37 2803.89 292.64 2102.92 1034.28 1082.38 8 5171.07 8413.33 2585.63 4206.67 1723.87 ^804.44 1293.02 2103.33 1034.53 1682.67 9 5172.58 8415.00 2586.39 4207 50 1724.37 2805.00 1293.40 2103.75 1034.8:3 1683.00 1O 5174.10 8416 67 2587.15 4208.33 1724.88 2805 56 1293.78 2104.17 1035.14 16S3.33 11 5175.62 8418.33 2587.91 1209.17 1 725 . 38 2806.11 1294. 1C. 2104.58 1035.44 1683.67 13 5177.14 8420.00 2588.66 4210.00 1725.89 ,806.67 1294.54 2105.00 1035.74 1084.00 13 5178.66 8121.67 2589.42 4210.83 1726.4U 2807.22 1294.92 2105.42 1036.05 1684.33 14 5180.18 8423.33 2590.18 4211.67 1726.90 2807.78 1295.30 2105.83 1036.35 1684.67 15 5181.69 8425.00 2590.94 4212.50 1727.41 2808.33 i295.67 2106.25 1036.66 1685.00 10 5183. 21 8426.67 58301.7(1 4213.33 1727.92 2808.89 1296.05 2106.67 1036.96 1685.33 17 5184.73 8428.33 2592.46 4214.17 1728.42 2809.44 1296 43 2107.08 1037.y(i 1685.67 18 5186.25 8430.00 25U.-J.22 4215 00 1728.93 2810.00 1206. 81 2107.50 1037.57 1686.00 19 5187.77 8431.67 2593.98 4215.83 1729.43 2810.56 1297.19 2107.92 1037.87 1686.33 20 5189.29 8433.33 2594.74 4216.67 729.94 2^11.11 1297.57 2108.33 10:38.17 1686.67 21 5190.78 8485.00 2595.48 4217.50 1730 44 2811.67 1297.95 2108.75 1038.47 1687.00 22 5192.27 8436.67 598.88 4218.33 1730.93 2812.22 1298.32 2109.17 103S 77 1687.33 23 5193.78 8498.83 2596.99 4219.17 1731.44 2812.78 1298.70 2109.58 1039.07 1687.67 24 5195.30 8440.00 2597.75 4220.00 1731.95 2813.33 1299.08 2110.00! 1039. 38 1688.00 ft FJ 5196.82 8441.67 2598.51 4220. 8S 1732.45 2813.89 1299.46 21 10. 42! 1039. 68 1688. 33 3207.51 845:} . 33 2ii03.85 4226.67 1736.01 2817.78 1302.13 2113.33 1041.82 1690.67 33 5209.03 8455.00 2604.61 4227.50 1736 52 2818.33 1302.51 2113.75 1042.12 1691.00 34 >2!0.54 8456.67 2605.37 1228.33 17S7.03 2818.89 1302.89 2114.17 1042.43 1691.33 35 5212 06 8458.33 2606.13 1229.17 1737.53 2819.44 1303.27 2114.58 1042.73 1691.67 36 5213.58 8460.00 2606.89 4230.00 1738.04 2820.00 1303.65 2115.00 1043.03 1692.00 37 5215.10 8461.67 2607.64 4230.83 1738.55 2820.56 1304.03 2115.42 1043 34 1692.33 38 5216.62 8463.33 2608.40 4231.67 1739.05 2821.11 1304.41 2115.83 1043.64 1692.67 39 5218.14 8465.00 2609.16 4232.50 1739.56 2821.67 1304.79 2116.25 1043.95 1693.00 40 5219.65 8466.67 2609.92 4233.33 1740.06 2822.22 1305.17 2116.67 1044.25 1693.33 41 5221.20 8408.33 2610.70 4234.17 1740.58 2822.78 1805.55 2117.08 1044.56 1693.67 42 5222.75 8470.002511.47 4235.00 1741.10 2823.33 1305.94 2117.50 1044.87 1694.00 43 5224.27 8471.672612.23 4235.83 1741.60 2823.89 1306.32 2117.92 1045.17 1694.33 44 5225. 78 j 84; 3. 33 ! 26 12. 99 4236.67 1742.11 2824.44 1306.70 2118.33 1045.48 1694.67 45 5227.30 8475.002613.75 4237.50 1742.61 2825.00 1307.08 2118.75 1045.78 1695.00 46 5228.82 8476.672614.51 4238.33 1743.12 2825.56 1307.46 2119.17 10 46. OS 1695.33 47 5230.37 847S.332 5244.12 8493 332622 16 4246.67 1748.22 2831.11 1311. 2^ 2123.33 1049.14 1698 C.7 57 5245 6718495. 00 2622. 93 4247.50 1748.74 2831.67 1311.67 2123.75 1049.45 1699.00 58 5247.21 8496.67 26-23.70 4248. 3:j 1749.25 2832.2-. 1312.06 2124.17 1049.71* 1699.33 59 5248 . 73 1 8498 . 33 2624 . 4b 4249.17 1749. 7b 2832.78 1312.44 2124.581050.07 1699.67 214 TABLE XIV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 Curve. 1O Curve. 84 Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. M. 800.215 1400.00 737.446 1200.00 645.389 1050.00573.798:933.333 516.550 840.000 O 800.408 1400.28 737.003 1200.24 045.579 1050.21 573.907 933.519 516.702 840.167 1 800.721 1400.50 737.880 1200. 4H 045.709 1050.42574.136 J33.704 516.854 840.333 2 800. 975 1400.% 738.097 1200.71 045.959 1050. 63 (574.304 J33.889 517.007 840.500 3 801.228 1401.11 738.314 1200.95 640.148 1050.83 574.473 934.074 517.159 840.667 4 861.481 1401.39 738 531 1201 19 640.338 1051.04 574.642 934.259 517.311 840.833 5 801.734 1401.07 738.748 1201.43 046.528 1051.25 574.811 134.444 517.463 841.000 G 861.983 1401.94 738.901 1201.07 040.715 1051.46 574.977 934.630 517.612 841.167 7 802.231 1402.2;.' 739.174 1^01 90 046.901 1051.67 575.142 934.815 517.761 841.333 8 802.484 1402.50 739.391 1202.14 647.091 1051.88 575.311 J35.000 517.913 841.500 9 862.737 1402.78 739.008 1202.38 647.281 1052.08 575.480 935.185 518.065 841.667 10 862.900 1403.00 739.825 1202.62 647.471 1052.29 575.649 )35.370 518.217 841. 833 11 883.244 1403.33 740.042 1202.86 617.661 1052.50 575.818 935.556 518.369 842.000 13 803.497 1403.61 740.259 1203.10 647.851 1052.71 575.987 935.741 518.521 842.167 13 863.750 1103.89 740.476 1203.33 648.041 1052.92 576.156 935.92(5 518.673 842.333 14 864.003 1404.17 740.693 1203.57 048.231 1053.13 576.325 J36.111 518.825 842.500 15 804.256 1404.44 740.910 1203.81 048.421 1053.33 576.494 936.296 518.977 842.667 1O 804.509 1404.72 741.127 1201.05 048.611 1053.54 576.662 936.481 519.129 842.833 17 864.763 1405.00 741.344 1204.29 648.801 1053.75 576.831 936.667 519.281 843.000 18 865.010 1405.2b 741.561 1204.52 648.990 1053.96 577.000 930.852 519.433 843.167 19 865.269 1405.56 741.778 1204.76 649.180 1054.17 577. 1G9 937.037 519.585 843.333 3O 865.517 1405.83 741.991 1205.00 049.307 1054.38 577.335 937.222 519.734 843.500 31 805. 7C6 1406.11 742.204 1205.24 ti49 553 1054.58 577.500 937.407 519.884 843.667 33 800.019 1400.39 742.421 1205.48 04!) . 743 1054.7U 577.669 937.593 520.030 843.833 33 800.272 1406.07 742.638 1205.71 049.933 1055.00 577.838 937.778 520.188 844.000 34 800.525 1400.94 742.855 12-J5.95 050. 123 1055.21 578.007 937.903 520.340 844.167 35 806.778 1407.22 743.072 200.19 050.313 1055.42 578.176 938.148 520.492 844.333 36 867.036 1407.50 743.293 1206.43 050.500 1055.63 578.348 J38.333 520.047 844.500 37 807.294 1407.78 743.514 1206.67 050. 7XX) 1055.83 578.520 938.519 520.801 844.667 38 807.548 1408.00 743. 73 > 1206.90 650.890 1056.04 578.089 938.704 520.953 844.8:33 39 887.801 1408 33 743.949 1207.14 651 .080 1056.25 578.858 938.889 521.106 845.000 3O 868.054 1408 0] 744.160 1207.38 (55 1.270 1056.46 579.027 939.074 521.258 845.167 31 868.307 1408 89 744.383 1207.62 651.400 105(5.67 579.196 939.259 521.410 845.333 33 688.600 868.813 1409.17 1409.44 744. 600 j 1207. 86 744.817 1208.10 051.050 051.840 1056.88 1057.08 579.304 579.533 939.444 939.030 521.562 521.714 845.500 845.667 33 34 809.067 1409.72 745. 034 11208. 33 052.030 1057.29 579.702 939.815 521.806 845.833 35 869.320 1410.00 745.251 1208.57 052.220 1057.50 579.871 940.000 522.018 846.000 36 869.573 1410.28 745.468 1208.81 052.410 1057.71 580.040 940.185 522.170 84(5.167 37 869.826 1410.56 745. 685 |1209. 05 052.599 1057.92 580.209 940.370 522.322 846.333 38 870.079 1410.83 745.902 1209.29 052.789 1058.13 580.378 940.550 522.474 846.500 39 870.332 1411.11 746.119 1209.52 052.979 1058.33 580.547 940.741 522.626 846.667 4O 870.590 1411.39 746.340 1209.70 053.173 1058.54 580.719 940.920 522.781 846.833 41 870.848 1411.67 746.501 1210.00 653.366 1058.75 580.891 941.111 522.936 847.000 43 8 VI. 102 1411.91 746.778 1210.24 653.550 1058.96 581.060 941.296 523.088 847.167 43 871.. 355 1412.22 740.995 1210.48 653.746 1059.17 581.228 941.481 523.240 847.333 44 871.608 1412.50 747.212 1210.71 653.936 1059.38 581.397 941.667 523.392 847.500 45 871.861 1412.78 747.429 1210.95 661.1:36 1059.58 581.566 941.852 523.544 847.667 46 872.119 1413. 00 747.651 1211.19 654.320 1059.79 581.738 942.037 523.699 847.833 47 872.377 1413. 33 747.872 1211.43 054.513 1060.00 581.910 942.222 523.853 848.000 48 872.630 1413.61 748. OS9 1211.67 654.703 1060.21 582.079 942.407 524.006 848.167 49 872.883 1413.89 748. 306 1 1211. 90 654.893 1060.42 582.248942.593 524.158848.333 5O 873.130 1414.17 748.523 1212.14 655.083 1060. 63^2.417 942. 778 524.310848 500 51 873.390 1414.44 748.740 1212.38 055.273 1060. 831582. 586 942. %3 524.462848.667 53 873.048 1414.72 748.961 1212.62 055.407 106 1.04 582. 758 943.148 524.617848.838 53 873.906 1415 00 749.18", 1^12.80 055.000 106 1.25 582. 930 943. 333 524.771! 849.(KK) 54 874. 159 14T,. 28 749.391 1213.10 055. S50 10(51.46 583.099913.519 524.923 849 167 55 874.412 1415.50 749.616 1213.33 05*. 040 1001.07 583.208943.704 525.075849.333 56 874.070 1415.83 149.837 1213.57 650 234 1061.88 583.440 943.889 525. 230 849. 500 1 57 874.928 1410.11 750.058 1213.81 656 427 IOftJ.08J588.6l2 944.074 525.385849.667 58 875.181 I4l6.39750.27fa 1214.05 656.017 1062. 29:583.781(944. 259 525. 537 849.833| 59 215 TABLE XIV. ACTUAL TANGENTS, ETC. 85 1 Curve. 3* Curve. 3 Curve. 4 Curve. 5 Curve. Ivi7 Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. o 9350.25 8500.00 2625.22 4250.00 1750.2(5 2833. Jtt 1312.82 2 125. a) 1050.37 1700.00 i 5251.80 8501.67 2625.99 4250.83 1750.78 2833.89 1313.20 2125.42 1050.68 1700.33 < 5253.34 8503.33 2626.77 4251.67 1751.30 2834.44 1818.59 2125.83 1050.99 1700.0? 3 5254.86 8505.00 2627.53 4252.50 1751.80 2835.00 1313.97 2126.25 1051.29 1701.00 4 5256.38 8506.67 2628.29 4253.33 1752.31 2835.56 1314.35 2126.67 1051.60 1701.33 5 5257.93 8508.33 2629.06 4254.17 1752.82 2836.11 1314.74 2127.08 1051.91 1701.07 6 5259.47 8510.00 2629.83 4255.00 1753.34 2836 67 1315.12 2127.50 1052.22 1702.00 7 5260.99 8511.67 2630.59 4255.83 1753.85 2837.22 1315.50 2127.92 1052.52 1702.33 8 5262.51 8513.33 2631.35 4256.67 1754.3.5 2837.78 1315.88 2128.33 1052.82 1702.67 9 5264.06 8515.00 2632.13 4257.50 1754.87 2838.33 1316.27 2128.75 1053.13 1703.0J 10 5265.61 8516.67 2632.90 4258.33 1755.38 2838.89 1316.66 2129.17 1053.44 1703 33 11 5267.15 8518.33 2633.67 4259.17 1755.90 2839.44 1317.04 2129.58 1053.75 1703 67 13 5268.70 8520.00 2634.45 4260.00 1756.41 2840.00 1317.43 2130.00 1054.06 1704.00 13 5270.22 8521.67 2635.21 4260.83 1756.92 2840.56 1317.81 2130.42 1054.37 1704. 3'} 14 5271.74 8523.33 2635.96 4261.67 1757.43 2841.11 1318.19 2130.83 1054.67 1704.07 15 5273.28 8525.00 2636.74 4262.50 1757.94 2841.67 1318.58 2131.25 1054.98 1705.00 16 5274.83 8526.67 2637.51 4263 33 1758.46 2842.22 1318.96 2131.67 1055.29 1705.33 17 5276.38 8528.33 2638.29 4264.17 1758.97 2842.78 1319.35 2132 08 1055.60 1705.07 18 5277.92 8530.00 2639.06 4265.00 1759.49 2843.33 1319.74 2132.50 1055.91 1706.00 19 5279.47 8531.67 2639.83 4265.83 1760.01 2843.89 1320.12 2132.92 1056.22 1706.33 20 5281.02 8533.33 2640.61 4266.67 1760.52 2844.44 1320.51 2133.33 1056.53 1708.67 31 5282.57 85&5.00 2641.38 4267.50 1761.04 2845.00 13-30.90 2133.75 1056.84 1707.00 33 5284.11 8536.67 2642.15 4268.33 1761.55 2845.56 1321.28 2134.17 1057.15 1707.33 33 5285.63 8538.33 2642.91 4269.17 1762.06 2846.11 1321.66 2134.58 1057.45 1707.67 34 5287.15 8540.00 2643 67 4270.00 1762.56 2846.67 1322.04 2135.00 1057.75 1708.00 35 5288.70 8541.67 26-14.44 4270.83 1763.08 2847.22 1322.43 2135.42 1058.06 1708.33 36 5290.24 8543.33 2645.22 4271.67 1763.60 2847 . 78 1322.82 2135.83 1058.37 1708.67 37 5291.79 8545.00 2645.99 4272.50 1764.11 2848.33 1323.20 2136.25 1058.68 1709.00 38 5293.34 H546.67 2646.77 4273.33 1764.63 2848.89 1323.59 2136.67 1058.99 1709.33 39 5294.88 8548.33 2647.54 4274.17 1765.14 2849.44 1323.98 2137.08 1059.30 1709.67 30 5296.43 8550.00 2648.31 4275.00 1765.66 2850 00 1324.36 2137.50 1059.61 1710.00 31 5297.98 8551.67 2649. 01) 4275.83 1766.17 2850.56 1324.75 2137.92 1059.92 1710.33 33 5299.53 8553.33 2649.86 4276.67 1766.69 2851.11 1325.14 2138.33 1000.23 1710.67 33 5301.07 H555.00 2650.63 4277.50 1767.21 2851.67 1325.52 2138.75 1060.54 1711.00 34 5302.62 ci5.56.67 2651.41 4278.33 1767.72 2852.22 1325.91 2139.17 1060. 85 1711.33 35 5304.17 8558.33 2652.18 4279.17 1768.24 2852.78 1326.30 2139.58 1061.16 1711.67 36 5305.71 8560.00 2652.95 4280.00 1768.7.5 2853.33 1326.69 2140.00 1061.47 1712.00 37 5307.26 8561.67 2653.73 4280.831769.27 2853 89 1327.07 2140.42 1061.78 1712.33 38 5308.81 8563.33 3654.50 4281.67 1769.78 2854.44 1327.46 2140.83 1062 09 1712.67 39 5310.35 8565.00 3655.27 4282.50 1770.30 2855.00 1327.85 2141.25 1062.40 1713.00 4O 5311.90 8566.67 2656.05 4283.33 1770.82 2855.56 1328.23 2141.67 1062.70 1713.33 41 5313.45 8568.33 2656.82 4284.171771.33 2856.11 1328.62 2142.08 1063.01 1713.07 43 5315.00 8570.00 2657.60 4285.00 1771.85 2856.67 1329.01 2142 50 1063.32 1714.00 43 5316.54 8571.67 2658.37 4285. 83 |1772. 36 2857.22 13-29.39 2142.92 1063.63 1714.33 44 5318.09 8573.33 2659.14 4286.67 1772.88 2857. 78 ! 1329. 7 8 2143.33 1063.94 1714.67 45 5319.66 8575.00 2659.93 4287.50 1773.40 2858.331330.17 2143.75 1064.26 1715.00 46 5321.24 8576.67 2660.72 4288.33 1773.93 3858.89 1330.57 2144.17 1061.57 1715.33 47 5322.79 8578.33 2661.49 4289.17 1774.44 2859.44 1330.95 2144.58 1064.88 1715.67 48 5324.33 8580.00 2662.26 4290.00 1774.96 2860.00 1331.34 2145.00 1065.19 1716.00 49 5325.88 8581.67 3(563.04 4290.83 1775.48 2860.56 1331.73 2145.42 1065.50 1716.33 50 5327.43 8583.33 2663.81 4201.67 1775.99 2801.11 1332.122145.83 1065.81 1710 07 51 5328.98 8585.00 3664.59 4292.50 1776.51 2861.67i 1332. 50 2 146. 25 1006.12 1717.00 53 5330.52 8586.67 3665.36 4293.33 1777.02 3862.22 1332.89 2146.67 1006.43 1717.33 53 5332.07 8588.33 2666.13 4294 17 1777.54 2862 78 1333.282147.08 1000.74 1717.07 54 5333.62 8590.00 3666 91 4295.00 1778.06 2863.33 1333.60 2147.50 1067.05 1718.00 55 5335.19 8.591 . 67 2667.69 4295.83 1778.58 2803.89 1334.015 2147.92 1067.36 1718.33 56 5&36.77 8593.33 2668.48 4296 . 07 1779.11 2864.44 1334.452148.33 1067 68 1718.67 57 5338 31 8595.00 2069.26 4297 50177'9.62 2865.00 1334.842148.75 1007.99 1719.00 58 5339.86 8596.67 2070.03 4298.331780.14 2805.56 1335.222149.17 1068 30 1719.33 59 5341.44 8598.33 2670.82 4299. 17 I 1780. 6612866. 11 1335.62 2149.58 1068.01 719.07 216 TABLE XTV. ACTUAL TANGENTS, ETC 6 Curve. 7 Curve. 8 Curve. 9 Curve. 1O Curve. 85 Tan. Arc. 1416.67 Tan. Arc. Tan. Am 1062.50 Tan. Arc. Tan. Arc. M. 875.434 750.493 1214.29 656.807 583.950944.444 525.689850.000 O 875.692 1416.94 750.714 1214.52 657.000 1062.71 584.122944.630 525. 844 i 850. 167 1 875.950 1417.22 750.935 1214.76 657.194 1062.92 584.294:944.815 525.999 850.333 2 87(5.203 1417.50 751.152 1215.00 657.384 1063.13 584.463945.000 520.151 850.500 3 876.450 1417.78 751.369 1215.24 657.574 1063.33 584.631 945.185 526.303 850.667 4 876.714 1418.06 751.590 1215.48 657.767 1063.54 584.804 945.370 526.458 850.833 5 876.972 1418.33 751.811 1215.71 657.961 1063.75 584.976 945.556 526.613 851.000 6 877.225 1418.61 752.028 1215.95 658.151 1063.96 585.144 945.741 526.765 851.167 7 877.479 1418.89 752.245 1216.19 658.341 1064.17 585.313 945.926 526.917 851.333 8 877.737 1419.17 752.466 1216.43 658.534 1064. 08 585.485 946.111 527.072 851.500 9 877.995 1419.44 752.688 1216.67 658.728 1064.58 585 657 946.296 527.227 851.667 10 878.252 1419.72 752.909 1216.90 658.921 1064.79 585.830 946.481 527.382 851.833 11 878.510 1420.00 753.130 1217.14 659.115 1065.00 586.002 946.667 527.537 852.000 12 878.764 1420.28 753.347 1217.38 659.305 1005.21 586.170 946.852 527.689 852.167 13 879.017 1420.56 753.564 1217.62 659.495 1065.42 586.339 947.037 527.841 852.333 14 879.275 1420.83 753.785 1217.80 659.688 1065.03 586.511 947.222 527.996 852.500 15 879.5:33 1421.11 754.000 1218.10 659.882 1005 83 586.683 947.407 528.150 852.667 16 879.791 1421.39 754.227 1218.33 660.075 1000.04 586.856 947.593 528.305 852.833 17 880.049 1421 . 67 754.448 1218.57 600.269 1066.25 587.0^8 947.778 528.460 853.000 18 880.307 1421.94 754.670 1218.81 660.463 1066.46 587.200 947.963 528.615 853.167 19 880. 5G4 1422.22 754.891 1219.05 660.656 1066.67 587.372 948.148 528.770 853.333 2O 860.822 1422.50 755.112 1219.21 660.850 1066.88 587.544 948.333 528.925 853.500 21 881.080 1422.78 755.333 1219.52 661.043 1067.08 587.716 948.51'. 529.080 853. 67 22 881.334 1423.00 755.550 1219.76 001.233 1067.29 587.885 948.704 529.232 853.833 23 881.587 1423.33 755.767 1220.00 661.423 1067.50 588.054 948.889 529.384 854.000 24 881 '.845 1423.61 755.988 1220.24 661.617 1067.71 588.226 949.074 529.539 854.167 25 882.103 1423.89 756.209 1220.48 601.810 1067.92 588.398 949.259 529.694 854.333 26 882.301 1424.17 756.430 1220.71 602.004 1068.13 588.570 949.444 529.849 &54.500 21 882.619 1424.44 i 56. 652 1220.95 662.197 1068.33 588.742 949.630 530.003 854.667 28 882.876 1424.72 756.873 1221.19 662.391 1068.54 588.914 949.815 530.158 854.833 29 883.134 1425.00 757.094 1221.43 662.584 1068.75 589.086 950.000 530.313 855.000 30 883.392 1425.2b 757.315 1221.67 662.778 1068.96 589.258 950.185 530.468 855.167 31 883.650 1425.56 757.536 1221.90 662.971 1069.17 589.430 950.370 530.623 855.333 32 883.908 1425.83 757.757 1222.14 663.165 1009.38 589.602 950. 55t 530.77'8 855.500 33 884.160 1426.11 757.97'8 1222.38 663.358 1069.58 589.774 950.741 530.933 855.667 34 884.424 1426. 3U 758.200 1222.62 603.552 1069.79 589.946 950. 92f 531.088 855.833 35 884.682 1426.67 758.421 1222.86 663.745 1070.00 590.118 951.111 531.243 856.000 36 884.940 885.198 1426.94 1427.22 758.64-J 758.863 1223.10 1223.33 663.939 664.132 1070.21 1070.42 590.290951.291 590.462951.481 531.398 531.552 856.167 856.333 37 38 885.456 1427.50 759.084 1223.57 664.326 1070.63 590.635 951.667 531.707 856.500 39 885.714 1427.78 759.305 1223.81 664.520 1070.83 590.807 951.852 531.862 856.667 40 885.972 1428.06 759.526 1224.05 664.713 1071.04 590.979 952.037 532.017 856.833 41 886.230 1428.33 759.747 1224.29664.907 1071.25 591.151 952.222 532.172 857.000 42 886.488 1428.61 759.969 1224.52 665. 100 1 1071. 46 501.828 952.407 532.327 857.167 43 886.746 1428.89 760.190 1224 76 665.294 1071.67 591.495 952.593 532.482 S57 333 44 887.008 1429.17 760.415 1225.00665.491 1071.H8 591.670952.778 532.640 857.500 45 887.271 1429.44 700.640 1225.24 665.688 1072.08 591.845952.963 f 32. 797 857.667 46 887. 529 11429. 72 760.801 1225.48665.881 1072.29 592.017953.148 532.952 857.833 47 887.787 1430.00 761.082 1225.71 606.075 1072.50 592.189953.333 533.107 858.000 48 888.045 1430.28 761.304 1225.95 666.268 1072.71 592.362 953.519 533.262 858.167 49 888 303 1430.56 761.525 1226.19 666.462 1072.92 592.534 953.704 533.417 858.333 50 888.561 1430.83 761.746 1226.43666.656 1073.13 592.706 1953. 889 533.572 858.500 51 888.819 1431.11 761.967 1226 67660.849 1073.33 592.8781954.074 533.727 858.667 52 889.077 1431.39 762 . 1 88 1 226 . 90 667 . 043 1 0? 3 . 54 593.050954.259 533. 8S2' 858. 833 53 889.335 1431.67 702.409 1227.14 607 236 1073.75 593.222954.444 534.036859.000 54 889.598 1431.94 702 035 1227.38 667.433 1073.96 593.397 954.030 534.194859.167 55 889 860 1432.22 702.800 1227.62 067 630 1074.17 593.572954.815 534.352859.333 56 890.118 1432.50 763.081 1227.80 667.824 1074.38 593. 74 4 : 955. 000 534.507859.500 57 890.376 1432.78 763 . 302 1 228 . 1 008 . 01 7 1074 58 593 916955.185 534.662859.667 58 890.639 1433.06 703.527 1228.33 608.215 1074.79 594.092955.370 534.8201859.833 59 217 TABLE XIV. ACTUAL TANGENTS, ETC. 86 1 Curve. 2 Curve. 3 Curve. 4 Curve. 5 Curve. M. Tan. j Arc. Tan. Arc. Tan. Are. Tan. Arc. Tan. Arc. 5343.01 8600.00 2671.604300.00 1781.19 2806.67 1336.01 2150.00 1068. 93 S 720.00 1 5344. 56 8001. 07' 2672.384300.83 781.70 2867.22 1330.40 2150.421069.24 720.33 2 5340.11 8603.33 2673.154301.67 782.22 2867.78 1336.79 2150.83 1069.55! 720.07 3 5347.658605.00 2673.934302.50 782. 73 2868.33 1337.17 2151.25 1069. S6, 721.00 4 5349.208606.07 .'674.70 4303. 33 783.25 2868.89 1337.56 2151 6711070.17 721.33 5 5350.788608 33 2075.494304.17 783.78 2869.44 1337.95 2152.08 1070.48 721.67 6 5352.358610.00 2 '.76. 27 4305. 00 1784.30 2870.00 1338 35 2152.50 1070.80 722.00 7 5353.5)0 8611.67 2077 05 4305 83 1784 82 28?'0.56 1338.73 2152.92 1071.11 722 33 8 5355.45 8613.33 2677.824306.67 1785.33 2871.11 1339.12 2158.88 1071.42 1722.67 9 5857.02 8615.00 2678.61 4307.50 1785.86 2871.67 1339.52 2153.75 1071.73 1723.00 1O 5358.60 8616.67 2679 40 4308.33 1786.38 2872.22 1339.91 2154.17 1072.05 1723.33 li 5360.14 8618.33 2680.17 4309.17 1786.90 2872.78 1340 30 2154.58 1072.36 723.67 12 5361.698620.00 2680.94 4310.00 1787.41 2873.33 1340.68 2155.00 1072.67 1724 00 13 5363.2786:21.67 2681.73 4310.83 1787.942873 89 1341.08 2155.42 1072.98 1724.33 14 5364.84 8623.33 2682.52 4311.67 1788.47 ; 2874.44 1341.47 2155.83 1073.30 1724.67 15 5366.4-2 862500 2683.31 4312.50 1788.992875.00 1341.86 2156.25 1073.61 1725 00 16 5367.99 8626.67 2684.10 4313.33 1789.522875 56 1342.26 2156.67 1073.93 1725.33 17 5369.54 8628.33 2684.87 4814.1; 1790.032876.11 1342.65 2157.08 1074.24 1725.67 18 5371.09 8630.00 2685.64 4315.00 1790.552876.6? 1343 03 2157.50 1074.55 1726.00 19 5372.66 8631.67 2686.43 4315.83 1791.07 2877.22 1343.43 2157.92 1074.86 1720.33 2O 5374.24 8633 33 2687.22 4316.67 1791.602877.78 1343.82 2158.33 1075.18 1726.67 21 5375.82 8635 00 2688.01 4317.50 1792.122878.33 1344.21 2158.75 1075.49 1727.00 22 5377.39 8636 67 26^8 79 4318 33 1 792. 65 ! 287 8. 89 1344.61 2159.17 1075.81 1727.33 23 5378.91 8638.33 2689.57 4319.17 1793. 16| 2879. 44 1345.00 215!) 5S 1076.12 1727 67 34 5380.49 8640.00 2690.34 4320.00 1793.682S80.00 1345.38 2160.00 1076.43 1728.00 25 5382.06 8641.67 2691.13 4320.83 1794.202880.56 1345.78 2160 42 1076.74 1728.33 26 538 i. 64 8643.33 2691.92 4321.6? 1794.732881.11 1346.17 2160.83 1077.06 1728.67 27 5385.21 8645.00 2693.70 4322.50 1795.262881.6? 1346.56 2161.25 1077.37 1729.00 28 5386.79 8616.67 2093.49 4323.33 1795.782882.22 1346.96 2161.67 1077.69 1729.33 39 5388.36 8648.33 2094.28 4324.17 1796.31 2882.78 1347.35 2162.08 1078.00 1729.67 3O 5389.94 8650.00 2695.07 4325.00 1796.832883.33 1347.75 2162 50 1078.32 1730.00 31 5391.49 8051 or 2695.84 4325.83 1797. 35; 2883. 89 1348.13 2162.92 1078.03 7'30.33 32 5393.03 S053 33 2096.62 4326.67 1797'. 86 2884. 44 1348.52 2103.33 1078.94 1730.67 33 5394.61 8655.00 v!697.40 4327.50 1798.392885.00 1348.91 2163.75 1079.25 1731.00 34 5396.18 8656 67 2698.19 4328.33 1798.91 2885.56 1349.31 2164.17 1079.57 1 731.33 35 5397.76 8658.33 2698.98 4329.17 1799.44 2886.11 1319.70 2164.58 1079.88 1731.07 36 5399.34 8660.00 2699.77 4330.00 1799.96 2886.6? 1350.10 2165.00 1080.20 1732 00 37 5100.91 8661.67 2700.55 4330.83 1800.49 2887.22 1350.40 2165.42 1080.51 1732.33 38 5402.49 S663.33 -!701.34 4331.67 1801 01 2887.78 1350.88 2105.83 1080.83 1732.07 39 5404.06 8665.00 2702.13 4332.50 1801.54 2888.33 1351.28 2166.25 1081.14 1733.00 4O 5405.64 8666.67 2702.92 4333.33 1802 00 2888.89 1351.67 2166.67 1081.40 1733.33 41 5107.21 8668.33 2703 71 4334 17 180;. 59 2889. 44 1352.07 2167.08 1081.77 1733.67 42 5408.79 8670.00 2704.49 4335.00 1803.122890.00 1352.40 2167.50 1082.09 1734.00 43 5110.37 8671.67 2705.28 4335.83 1803.642890.56 13 -.2.85 2167.92 1082.40 1734.33 44 5411 94 8673.33 2706.07 4336 67 1804.172891.11 1353.25 2168.33 1082.72 1734.67 45 5413.52 8675.00 2706.86 4337.50 1804.692891.67 1358.04 2168.75 1083.03 1735.00 46 5415.09 8676.67 2707.65 1338.33 1805.222892.22 1354.04 2169.17 1083 35 1735.33 47 5416.67 8678.33 2708.43 4339.17 1805.74 2892.78 1354.43 2169.58 1083.66 1735.67 48 5418.24 80SO 00 2709.22 4340.00 1806.272893.33 1354.82 2170.00 1083.98 1736.00 49 5419.82 8681.67 2710.01 4310.83 1806.792893.89 1355.22 2170.42 1084.29 1736.33 5O 5421.39 8083.33 2710.80 4341.67 1807.322894 44 1355.01 2170.83 1084.61 1736.67 51 5423.00 8685.00 2711.60 4342.50 1807.85 2895. 00 1356.01 2171.25 1084.93 1737.00 52 5424.60 8686.67 2712.40 4343.33 1808.392895.56 1350.41 2171.67 1085.25 1737.33 53 5426.18 8688 33 2713.19 4344.17 1808.91 2896.11 1356.81 2172.08 1085.57 IT87.67 54 5427.75 8090.00 2713.98 4345.00 1809.442S90 67 1357.20 2172.50 1085.88 738.00 55 5429.33 8691.67 2714.71; 4345.83 1809.962S97.22 1357 60 2172.92 1086.20 738.33 56 5430.91 H693 33 2715.55 -1346.67 1810.492S97.7S 1357.99 2173.33 1086.51 7-58.67 57 5432.48 8695.00 2716.34 4347.50 1811.01 2898.33 1358.3S 2173.75 1080.83 1739.00 58 5434 06 8096.67 2717.13 4348.33 191 1.54 '2898. 89 1358.78 2174.17 1087.14 1739.33 59 5435.638698.33 2717.92 43 19. 1? 11812.06 2899 44 1359.17 2(74.58 1087.46 1739.67 218 TABLE XIV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 Curve. 1O Curve. 86 Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. M. 890.90-4 1433. 33 1763. 752 '1228.57 668 412 1075.00 594.267 955.556 534.977 860.000 O 891.160; 1433. 61 |763. 97'4|1228. 81 608.605 1075.21 594.439 955.741 535.132 800.167 1 891.41711433.89764.195 1229.05 668.799 1075. 42 594.01; 955.920 535.287 860.333 2 89i.ti75 1434.1? 764.413 l'J' H ) >>( ) 668.992 1075.63 594 . 783 956.111 535.442 800.500 3 891. 9:33; 1434.44764. 03? 1229.52 009.180 1075.83 591.955 956.290 535.597 860.607 4 892.196 1434.72764.862 1229.70 009.383 1076.04 595.130 956.481 535.755 860.833 5 892.459 1435.00 765.087 1230.00 009.580 1076.25 595,300 950.667 535.912 861.000 6 K92.717 1435.28 765.309 1230.24 669.774 1076.46 595.478 956.852 536.067 861.167 7 892.9751435.50705.530 1230.48 009.967 1076.67 595.650 957.037 536.222 861.333 8 893.237 1435.83 765.755 1230.71 070.164 1076.88 595.825 957.222 536.380 861.500 9 893.500 1436.11 765.980 1-230.95 670.361 1077.08 596.000 957.407 536.538 861.667 1O 893.758 1430.39 766 201 1231.19 670.555 1077.29 596.172 957.593 536.693 861.833 11 894.010 1436.67 766.422 1231.43 670.748 1077.50 590.344 957.778 536.848 862.000 12 894.279 1436.94 766 648 1231.67 670.945 1077.71 596.520 957.963 537.005 862.167 13 894.542 1437.22 766.873 1231.90 671.143 1077.92 596.695 958.148 537.163 862.333 14 894.804 1437.50 767.098 1232.14 671.340 1078.13 596.870 958.333 537.321 862.500 15 895.067 1437.78 767.323 1232.38 671.537 1078 33 597.045 958.519 537.479 862.667 16 895 . 325 1438.06 767 . 545 1232.02 071.730 1078.54 597.218 958.704 537.634 862.833 17 895.583 1438.33 767.706 1232.86 671 . 924 1078.75 597.390 958.889 537.788 803.000 18 895.846 1438.61 767.991 1233.10 672.121 1078.90 597.565 959.074 537.946 863.167 19 896.108 1438.89 768.216 1233.33 672.318 1079.17 597.740 959.259 538.104 863.333 20 896. 3U 1439.17 768.441 1233.57 672.515 1079.38 597.915 959.444 538.262 803.500 21 890.634 1439.44 768.667 1233.81 672.712 1079.58 598.091 959.630 538.419 863.667 22 896.892 1439.72 768.888 1234.05 672.906 1079.79 598.263 959.815 538.574 863.833 23 897.150 1440.00 769.109 1234.29 673.099 1080.00 598.435 900.000 538.729 864.000 24 897.412 1440.28 769.334 1234.52 673 296 1080.21 598.610 960.185 538.887 804.167 25 897.675 1440.56 769.559 1234.76 673.494 1080.42 598.785 960 370 539 045 864.333 26 897.938 1440.83 769.785 1235.00 673.691 1080.63 598.960 900 556 539.203 864.500 2V 898.201 1441.11 770.010 1235.24 073.888 1080.83 599.130 960.741 539.360 864.667 28 898.463 1441.39 770.235 1235.48 674.085 1081.04 599.311 960.926 539.518 864.833 29 898.726 1441 67 770.460 1235.71 674.282 1081.25 599.486 961.111 539.676 865.000 3O 898.984 1441.94 770.081 1235.95 67'4.470 1081.40 599.658 961.290 539.831 865.167 31 899.242 1442.22 770.903 1236.19 074.669 1081.67 599.830 961.481 539.986 865.333 32 899.505 1442.50 771.128 1236.43 074.800 1081.88 000.006 961.667 540.143 865.500 33 899.767 1442.78 771.353 1236.67 67'5.063 1082.08 600.181 901.852 540.301 865.667 34 900.030 1443.00 771.578 1236.90 675.260 1082.29 600.356 902.037 540.459 865.833 35 900.293 1443.33 771.803 1237.14 675.458 1082.50 000.531 962.222 540.617 806.000 36 900.556 1443.61 772.029 1237.38 675.655 1082.71 600.707 962.407 540.774 866.167 37 900.818 1443.89 772.254 1237.62 075.852 1082.92 600.88-.' 902.593 540.932 806.333 38 901.081 1444.17 772.479 1237.80 076.049 1083.13 601.057 962.778 541.090 866.500 39 901.344 1444.44 772.704 1238.10 676.246 1083.33 601.232 962.963 541.248 866.667 4O 901.607 1444. 72 1772. 930 1238.33 676.443 1083.54 601.408 963.148 541.400 866.833 41 901.809 1 445. 00 ! 773. 155 1238. 57 676.640 1083.75 601.583 963.333 541.563 867.000 43 902.132 1445.28773.380 1238.81 076.837 1083.96 001.758 963.519 541.721 867.167 43 902.395 1445.50 773.605 1239.05 677.034 1084.17 001.933 963.704 541.879 867.333 44 902.657 1445.8377'3.831 1239.29 677.232 1084.38 602.109 963.889 542 037 867.500 45 902 . 920 1446.11 774 . 050 ! 1239 . 52 677.429 1084.58 602.284 964.074 542.194 867.667 46 903. 183 11446. 39 '774. 281 1239.76 677.626 1084.79 602.459 964.259 542.352 867.833 47 903.446 1446.67774.506 1240.00 677.823 1085.00 002.634 964.444 542.510 868.000 48 903.708 1446.94,774.731 1240.24 6i 8. 020 1085.21 602.810 964.630 542.668 868.167 49 903.971 1447.22774.957 240.48 078.217 1085.42 602 985 '964. 81 5 542.825 868.333 50 904.239 1447.50775.180 2J0.71 678.418 1085.63 603. 163 1965. 000 542.986 868.500 51 904.500 1447.78775.415 240.95 078.019 1085.83 603.342965.185 543.147 868.667 52 904.709 1448. 00 775. H41 241.19078.810 1086.04 603.517905.370 543.304 808 833 53 905.032 1448.33775.800 241.43079.013 1086.25 603.692 965.556 543 402 869.000 54 90."). 294 1448.61 770.091 241.07 079.210 1086.46 603.867 965.741 543.620 869.167 55 905 . 557 1448.89770.310 1241.90 079.407 1086.07 604.043 965.926 543.778 869.333 56 905.820 1449.17770.541 1242.14 679.604 1086.88 604.218 906.111 543.936 869.500 57 906. 082 1 1449. 44 776. 7 07 906. 345 U449. 72 776. 992 1242.3S679.cS01 1242.621679.998 1087.08 1087.29 604.393 604.568 966.296 900.481 544.093 544.251 809 007 869.833 58 59 219 TABLE XIV. ACTUAL TANGENTS, ETC. 87 1 Curve. 3 Carve. 3 Curve. 4 Curve. 5 Curve. M. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. O 5437.21 8700.00 2718.70 4350.00 812.59 2900.00 1359.57 2175.001087.77 1740.00 1 5438.81 8701.67 2719.51 4350.83 1813.12 2900.50 1359.9712175.42 1088.09 1740.33 3 5440.42 8703.33 2720.31 4351.67 1813.66 2901.11 1300.37 2175.83 1088.42 1740.67 3 o441.99 8705.00 2721.10 4352.50 814.18 2901.67 1360.70 2176.25 1088.73 1741.00 4 5443.57 8706.67 2721.88 4353.33 814.71 2902.2:2 1361.16 2176.67 |1089. 05 1741.33 5 5445 14 8708.33 2722.67 4354.17 1815.23 2902.78 301.55 2177.08 1089.361741.67 5446. 7'2 8710.00 2723.46 4355*. 00 1815.76 2903.33 1361.94 2177.50 1089.08 1742.00 7 5448.32 8711.67 2724.26 4355.83 1816.30 2903.89 1362 34 2177.92 1090.00 1742.33 8 5449.93 8713.33 2725.06 4356.67 1816.83 2904.44 1362.75 2178.331090.32 1742.67 9 5451.50 8715.00 2725.85 4357.50 1817.36 2905.00 1363.14 2178.75 1090.63 1743.00 10 5153.08 8716.67 2726.64 4358.33 1817.88 2905.56 1303.53 2179.17 1090.95 1743.33 11 5454.68 8718.33 2727.44 4359.17 1818.42 2906.11 1363.94 2179.581091.27 1743.67 13 5456.29 8720.00 2728.24 4360.00 1818.952906.67 1364.84 2180.0011091 .5ft 1744.00 13 5457. 80 8721.67 ,2729.03 4360.83 1819.482907.22 1304.73 2180.42 1091.91 1744.33 14 5459.44 8723.33 2729.82 4361 . 67 1820.00 2907.78 1305.12 2180. 83! 1092. 22 1744.67 15 5461.04 8725.00 2730.62 4362.50 1820.54 2908.33 1365.53 2181.251092 54 1745.00 16 5462.65 8726.67 2731.42 4363.33 1821.07 2908.89 13:55.93 2181.67 1092.86 1745.33 17 5464.22 S7'28.33 2732.21 4364.17 1821 60 2909.44 1300.32 2182.08 1093.18 1745.67 18 5465.80 8730.00 2733.00 4365.00 1822.12 2910.00 1300.71 2182.50 1093.49 1746.00 19 5467.40 8731.67 2733.80 4365.83 1822.66 2910.56 1307.12 2182.92 1093.81 1746.33 3O 5469.01 8733.33 2734.60 4366.67 1823.19 2911.11 1367.52 2183.33 1094.14 1746.67 31 5470.58 873.5.00 2735.39 4367.50 1823.72 2911.67 1367.91 2183.75 1094.45 1747.00 33 5472.16 8736.67 2736 18 4368.33 1824.24 2912.22 1368.30 2184 17 1094.77 1747.33 33 5473.76 8738.33 2736.98 4369.17 1824.78 2912.78 1368.71 2184.58 1095.09 1747.67 34 3475.37 8740.00 2737.78 4370.00 1825. 31 |2913. 33 1369.11 2185.00 1095.41 1748.00 35 5476.97 8741.67 2738.59 4370.83 1825. 8512913. 89 1309.51 2185.42 1095.73 1748.33 36 5478.58 8743. 33 2739.39 4371.67 1826.38 2914.44 1309.91 2185.83 1096.05 1748.07 37 5480. 15 8745.00 2740.18 4372.50 1826.91 2915.01. 1370.30 2186.25 1090.37 1749.00 38 5481.73 8746.67 2740.96 4373.33 1827.43 2915.56 1370.70 2186.67 1096.68 1749.33 39 54^3.33 8748.33 2741.77 4374.17 1827.97 2916.11 1371.10 2187.08 1097.00 1749.67 3O 5484.94 8750.00 2742.57 4375.00 1828.50 2916.67 1371.50 2187.50 1097.32 1750.00 31 5486.54 8751.67 2743.37 4375.83 1829.04 2917.22 1371.90 2187.92 1097.64 1750.33 33 5488.15 8753.33 2744.17 4376.67 1829.57 2917.78 1372 30 2188. 33 1097.90 1750.67 33 5489.75 8755.00 2744 98 4377.50 1830 10 2918.33 1372.70 2188.75 1098.29 1751.00 34 5491.35 8756.67 2745.78 4378.33 1830.64 2918.89 1373.10 2189.17 1098.61 1751.33 35 5492.96 8758.33 2746.58 4379.17 1831.17 2919.44 1373.51 2189.58 1098.93 1751.67 36 5494.50 8760.00 2747.38 4380.00 1831.71 2920.00 1373.91 2190.00 1099.25 1752.00 37 5496.14 8761.67 2748.17 4380.83 1832.23 2920.5e 1374.30 2190.42 1099.56 1752.33 38 5497.71 8763.33 2748.96 4381.07 1832.76 2921.11 1374.69 2190.83 1099.88 1752.07 39 5499.32 8765.00 2749.76 4382.50 1833.29 2021.67 1375.10 2191.25 1100.20 1753.00 40 5500.92 8766.67 2750.56 4383.33 1833.83 2922.22 1375.50 2191.67 1100.52 1753.33 41 5502.53 8768.33 2751.36 4384.17 1834.36 2922.78 1375.90 2192.08 1100.84 1753.67 43 5504.13 8770.00 2752.17 4385.00 1834 90 2Q23.33 1376.30 2192.50 1101.16 1754.00 43 5505.74 8771.67 2752.97 4385.83 1835.43 2923.89 1376.70 2192.92 1101.48 1754.33 44 5507.34 8773.33 2753.77 4386.67 1835.97 2924.44 1377.10 2193.33 1101.80 1754.67 45 5508.94 8775.00 2754.57 4387.50 1836.50 21)25.00 1377.50 2193.75 1102.13 1755.00 46 5510.55 8776.67 2755.38 4388.33 1837.04 21)25.50 1377.90 2194.17 1102.45 1755.33 47 5512.15 8778.33 2756.18 4389.17 1837.57 2926.11 1378.31 2194.58 1102.77 1755.67 48 5513.76 8780.00 2756.98 4390.00 1838.11 2926.67 1378.71 2195.00 1103.09 1756.00 49 5515.36 8781.67 2757.78 4390.83 1838.64 2927.2;. 1379.11 2195.42 1103.41 1756.33 50 5516.97 8783.33 2758.58 4391.67 1839.18 29-27.78 1379.51 2195.83 1103.73 1756.67 51 53 5518.57 5520.17 8785.00 8786.67 2759.39 2760.19 4392.50 4393.33 1839.71 2928.33 1840.2529-28.89 1379.91 1380.31 2196.25 2196.67 1104.05 1104.37 1757.00 1757.33 53 5521.78 8788.33 2760.99 4394.17 1840.78 2929.44 1380.71 2197.08 1104.69 1 757 . 67 54 5523.83 8790. (X 2761.79 4395. (X 1841.32 2930. 0( 1381.11 2197.50 1105.01 1758.00 55 5525.02 8791.67 2762.61 4395.83 1841.86 2930. 5( 1881.62 2197.9-2 1105.34 1758.33 56 5526.65 8793.33 2763 43 4396.67 1842.41 2931.11 1881.98 2198.33 1105.67 1758.07 57 5528.2" 879.5. (X 2764.23 4397.51 1842.912931.67 1382.33 2198.75 1105.99 1759.00 58 5529.80 8796.6' 2765.03 4398 33 1843. 48 21)32. '2- 1382.73 2199.17 1100.31 1759.33 59 5531.40 8798.33 2765.83 4399.17 1844. 01 12932. 78 1383 13 2199.58 1100.63 1759.07 220 TABLE XIV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 Curve. 1O Curve. 87 Tan. Arc. Tan. 777.217 Arc. 1242 80 Tan. Arc. Tan. Arc. Tan. 544 409 Arc. M. 906.008 1450.00 680.1951087 50 004.744 966.667 870.000 900. 875 11450. 28 777.446 1243.10 680.396 1087.71 004.922 906. &52 544.569 870.167 1 907.143 1450.56 777.676 1243.33 680.59? 1087.9-2 005.101 967.037 544.730 870.333 2 907.406 1450.83 777.901 1243.57 680.794 1088.13 005.270 967.222 544.888 870.500 3 907.668 1451 . 1 1 778.126 1243.81 680.991 1088.33 005.451 967.407 545.046 870.667 4 907.931 1451.39 778.352 1244.05 681.188 1088.54 605.626 967.593 545.203 870.833 5 908.194 1451.67 778.577 1244.29 681.3851088.75 605.802 907.778 545.361 871.000 6 908.461 1451.94 778.806 1244.52 681.58(51088.96 605.980 967.963 545.522 871.167 7 908.729 1452.22 779.035 1244.76 681.787 1089.17 606.158 908.148 545.682 871.333 8 908.992 1452.50 779.261 1245.00 681.984 1089.38 606.334 968.333 545.840 871.500 9 909.254 1452.78 779.486 1245.24 682.181 1089.58 606.500 968.519 545.998 871.667 10 909.5ft! 1453.06 779.715 1245.48 682.3821089.79 606.687 068.704 546.159 871 .833 11 909.789 1453.33 779.945 1245.71 682.5821090.00 606.866 068.889 546.310 872.000 13 910.052 1453.61 780.170 1245.95 682.7791090.21 607.041 069.074 546.477 872.167 13 910.315 1453. 89 780.395 1246.19 682.977 1090.42 607.216 969.250 546.635 872.333 14 910.582 1454.17 780.624 1246.43 683.177 1090.63 607.395 069.444 546.795 872.500 15 910.850 1454.44 780.854 1246.67 683.378 1090.83 607.573 909.630 546 956 872.667 16 911.112 1454.72 781.079 1246.90 683.5751091.04 607.748 060.815 547.114 872.833 17 911.375 1455.00 781.304 1247.14 683. 772' 1091. 25 607.924 970.000 547.272 873.000 18 911.643 1455.28 781.533 1247.38 683.973 1091.40 008.102 070.185 547.432 873.167 19 911.910 1455.56 781.763 1247.62 684.174 1091.67 60S. 281 970.370 547.593 873.333 20 912.173 1455.83 781.988 1247.86 684.371 1091.88 608.456 970.556 547. 751 873.500 31 912.436 1456.11 782.213 1248.10 684.568 1092.08 608.031 070.741 547.908 873.667 33 912.703 1456.39 782.443 1248.33 684.769 1092.29 608.800 970.926 548.060 873.833 33 912.971 1456.67 782.672 1248.57 084.909 1092.50 608.988 971.111 548.230 874.000 34 913.238 1456.94 782.901 1248.81 685.170 1092.71 009.160 971.296 548.390 874.167 35 913.506 1457. a. 1 783.130 1249.05 685.371 1092 92 609.345 971.481 548.551 874.333 36 913.768 1457.50 783.356 1249.29 685.568 1093.13 609.520 971.667 548.700 874.500 37 914.031 1457.78 783.581 1249.52 085.765 1003.33 609.695 971.852 548.860 874.667 38 914.299 1458.06 783.810 1249.76 085.966 1003.54 609.874 072.03? 549.02? 874.833 39 914.506 1458.33 784.040 1250 00 686.166 1093.75 610.052 972.222 549.188 875.000 30 914.834 1458.61 784.269 1250.24 680.307 1003.90 610.231 072.40? 549.348 875.167 31 915.101 1458.89 784.498 1250.48 686.568 1094.17 610.409 972.593 549.500 875.333 33 915.369 1459.17 784.728 1250.71 086 . 768 1094.38 610.587 972.778 549.670 875.500 33 915.636 1459.44 784.957 1250.95 686.969 1094.58 610.766 972.963 540.830 *75.667 34 915.904 1459.72 785.180 1251.19 687.170 1094.79 010.044 973.148 549.991 875.833 35 916.171 1460.00 785 410 1251.43 087.370 1095.0(1 011.123 973.333 550.151 876.000 36 916.434 1160.28 785.641 1251.6: 687. 50S 1095.21 011.208 973 519 550.300 876.167 37 916.697 1460.56 785.8(56 1251.90 087.705 1005.42 (511.473 973.704 550.46? 876.333 38 916.964 1460.83 786.095 1252.14 087.965 1095.63 611.652 973.880 550.628 876.500 39 917.232 1461.11 786.325 1252.38 688.166 1095.83 611.830 974.074 550.788 876.66? 40 917.499 1461.3'.) 786.554 1252.62 688.367 1096.04 612.000 074.259 550.040 876.833 41 917.76? 1461.67 786.783 1252.86 688.567 1096.25 612.187 974.444 551.110 8?7.00(i 43 918.034 1461.94 787.013 1253.10 688.768 1096.46 612.365 974.630 551.270 877.167 43 918.302 1462.22 787.242 1253.33 688.969 1006.67 612.544 9 i 4. 815 551.431 877.333 44 918.569 1462.50 787.471 1253 57 689.170 1096.88 612.722 075.000 551.591 877.500 45 918.837 1462.78 787.701 1253.81 689.370 1097.08 612.901 075.185 551.752 877.667 46 919.104 1463.06 787.930 1254.05 089.571 1097.29 013.070 075.370 551 913 877.833 47 919.8721463.33 788.159 1254.20 689.772 1097.50 613 258 075.556 552.073 878.000 48 919.639 1463.61 788.389 1254.52 689.972 1007.71 613.430 075.741 552.234 878.16? 49 919.907 1463.89 788 618 1254.76 690.173 1097.92 613.614 075.926 552.395 878.333 5O 920.174 1464.17 788.84? 1255.00 090.374 1098.13 613.793 976.111 552.555 878.500 51 920.442 1464.44 789.077 1255.24 600.574 1098.33 013.971 970.296 552.716 878.667 53 920.709 1404.72 789.306 1255.48 090.775 1098.54 614.150 076.481 552.876 878.833 53 920. 977 [1465. Od 789.535 1255.71 600.076 1098.75 614.328 976.667 553.037 870.000 54 921.249 1405.28 789.709 1255.95 601.180 109". 90 614.510 976.a->2 553.201 879.167 55 921.521 1465.50 790.002 1256.19 691.384 1090.17 614.601 977.037 553.364 879.333 56 921.780 1465.83 790.231 1250.43 601.585 1090.38 614.870 977.222 553.525 879.500 57 922.056 1466.11 790.461 1256.67 691.786 1009.58 615.048 977.40? 553.685 879.607 58 922.324 1466.39 790.690 1256.90 691.987 1099.79 6 15. 227 1977.593 553 846 8?'9.833 59 221 TABLE XIV. ACTUAL TANGENTS, ETC. 88 1 Curve. 3 Curve. 3 Curve. 4 Curve. 5 Curve. M. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. O 5533.07 8800.00 2766.63 4400.00 1844.55 2933.33 13*3.53 2200.00:1106.95 1760.00 1 5534.67 8801. 67 12767. 44 4400.83 1845.08 2933.89 1383.94 2200.42 1107.27 1760.33 2 5536.27 8803.332768.24 4401.67 1845.61 21)34.44 1384.34 2200. 83 i 1107. 59 1760.67 3 5537.88 8805.00 2769.04 4402.50 1846.15 2935.00 1384.74 2201.25 1107.91 761.00 4 5539.48 8806.67 2769.84 4403.33 1846.68 2935.56 1385.14 2201.67 1108.23 761.33 5 5541.12 8808.33 2770.66 4404.17 1847.23 2936.11 1385.55 2202.08 1108.56 761.67 G 5543.75 8810.00 2771.48 4405.00 1847.77 2936.67 1385.96 2202.50 1108.89 762.00 7 5544.35 8811.67 2772.28 4405.83 1848.31 2937.22 1386.36 2202.92 1109.21 762.33 8 5545.90 8813.33 2773.08 4406.67 1848.84 2937.78 1386.76 2203.33 1109.53 762.67 9 5547.56 8815.00 2773.88 4407.50 1849.38 2938. 33 1387.16 2203.75 1109.85 1763.00 1O 5519.17 8816.67 2774.68 4408.33 1849.91 2938.89 1387.56 2204.17 1110.17 1763.33 11 5550.80 8818.33 2775.50 4409.17 1850.46 2939.44 1387.97 2204.58 1110.50 1763 67 12 5553.43 8820.00 2776.32 4410.00 1851.00 2940.00 1388.38 2205.00 1110.83 1764.00 13 5554.04 8821.67 2777.12 4410.83 1851.54 2940.56 1388.78 2205.42 1111.15 1764.33 Id- 5555.64 8823 33 2777.92 4411.67 1852.07 2941.11 1389.182205.83 1111.47 1764.67 lS 5657.2; 8825.00 2778.74 4412.50 1852.62 2941.67 1389.59 2206.25 1111.79 1765.00 16 5558.91 8826.67 2779.56 4413.83 1853.16 2942.22 1390.00 2206.67 1112.12 1765.33 17 5560.51 8828.33 2780.36 4414.17 1853.69 J942.78 1390.40 2207.08 1112.44 1765.67 18 5562 12 8830.00 2781.16 4415 .00 1854.23 2943.33 1390.80 2207.50 1112.76 17'66 00 19 5563.75 8831. 67 2781.98 4415.83 1854.77 J943.89 1391.21 2207.92 1113.09 1766.33 20 5565.38 8833.33 2782.79 4416.67 1855.32 J944.44 1391.61 2208.33 1113.42 1766.67 21 5566.99 8835.00 2783.59 4417.50 1855.85 2945.00 1392.02 2208.75 1113.74 767.00 22 5568.59 8836.67 .2784.40 4418.33 1856.39 J945.56 1392.42 $09.17 1114.06 1767.33 23 5570.22 8838.33 2785.21 4419.17 1856.93 2946.11 1392.83 2209.58 1114.3S 767.67 34 5571.86 8840.00 2786.03 4420.00 1857.48 2946.67 1393.23 2210.00 1114.71 1768.00 25 5573.46 8841 67 2786.83 4420 83 1858.01 .'947.22 1393.63 2210.4'J 1115.03 1768.33 a a 5575 . 06 8813 33 2787.63 44-J1.67 1858.55 J947.7S 1391.04 22 10. S3 1115.35 1768.67 27 5576.70 8845.00 2788.45 4422.50 IS.J9.Oi) 2948.33 1391.44 2211 25 1115.08 1769.00 28 5578.33 8846.67 2J89.27 4423.33 1859.63 ,5948.89 131)4.85 221 1 . 67 1116.01 1769.33 29 5579.96 8848.33 2790.08 4424.17 1860.18 2949.44 1395.26 2212.08 1116.33 1769.67 30 5581.60 8S50.00 2790.90 4425.00 1860.72 ;>950.00 1395.67 2212.50 1116.66 1770 00 31 5583.20 8851.67 2791.7d 4425.83 1861.26 2950.56 1396.07 2212.92 1116.98 1770.33 32 5584.80 8853.33 2792.50 4426.67 1861 79 2951.11 1396.47 2213.33 1117.30 1770.67 33 5586.44 8855.00 2793.32 4427.50 1862.34 2951.67 131)6.88 2213.75 1117.63 1771.00 34 5588.07 8856.67 2794.14 4428.33 1862.88 ,'952.22 1397.89 2214.17 1117.96 1771.33 35 5589.70 8858.33 27'94.95 4429.17 1863.43 2952.78 1397.70 2214.58 1118.28 1771.67 36 5591.34 8860.00 2795.77 4430.00 1863.97 2953.33 1398.10 2215.00 1118.61 1772.00 37 5592.97 8861.67 2796.59 4430.83 1864.52 2953.89 1398.51 2215.42 1118.94 1772.33 38 5594.60 8803.83 2797.40 4431.67 1865.06 2954.44 1398.92 2215.83 1119.26 1772.67 39 5596.24 8865.00 2798.22 4432.50 1865 60 2955.00 1399.33 2216.25 1119.59 1773.00 40 5597 87 8866.67 2799 04 4433.33 1866.15 .J955.56 1399.74 2216.67 1119.9* 1773.33 41 5599.47 8S68.33 2799.84 4434.17 1866.68 2956. 11 1400.14 2217.08 1120.24 1773.67 42 5601 08 8870. U() 2800.64 4435.00 1867.22 2956.67 1400.54 2217.50 1120.56 1774.00 43 5602.71 8871.67 2801.46 4435.83 1867.76 2957.22 1400.95 2217.92 1120.88 1774.33 44 5604.31 8873.33 2802.27 443(5.67 1868.31 2957 78 1401.36 2218.33 1121.21 1774.67 45 5605.98 8875.00 2803.01) 4437.50 1868.85 2958.33 1401.77 2218.75 1121.54 1775.00 40 5607.61 8876.67 2803 91 4438.33 1869.40 2958.89 1402.17 2-J19.17 1121.86 1775.33 47 5609.24 8878. 33 2804.72 4439.17 1809.94 2959.44 1402.58 2211). 58 1122.19 1775.67 48 5610.87 8880.00 2805.54 4140.00 1870.48 2960.00 1402.99 22-0.00 1122.52 1776.00 49 o6l2.51 8881.67 2806.36 4440.83 1871.03 2960.56 1403.40 2220.42 1122.84 1776.33 5O 5614.14 8883.33 2807.17 1441.67 1871.57 2901.11 1403.81 2220.83 1123.17 1776.67 51 5615.77 8885.002807.99 4442.5!: 1872.12 2961.67 1404.22 2221.25 1123.50 1777.00 53 06 17. 41 8886.672808.81 4443.33 1872.66 2962.22 140 4. 62 2221.67 1123.82 1777.33 53 5619.04 88SS.332809.62 4444.17 1873 21 2962.78 1405.03 2-222.08 1124.15 1777.67 54 5020.67 8890.002810.44 1445.00 1873.75 2963.33 1405.44 2222.50 1124.48 1778.00 55 5622. 31 8891.672811.26 1445.83 1874.29 2963.89 1405.85 2222.92 1124.80 177'8.33 5(> 5623.94 8893.332812.07 4446.67 1874.84 2964.44 1406.26 2223.33 1125.131778.67 57 5625.60 8895.002812.90 44*7.50 1875.392965.00 1406.67 2223.75 1125.46 1779.00 58 5627.26 8896.672813.73 4448.33 1875.952965.56 1407.0!) 2224. 17 1125.80 1779.33 59 5628.89 8898.332814.55 4449.17 1876.49,2966.11 1407.50J2224 58 1126.12 1779. C7 TABLE XIV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 Curve. 1O Curve. 88 Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. M. 922. 591 '1466. 67 790.919 1257.14 692.187 1100.00 015 . 405 977 . 778 554 . 007 880 . 000 ~O 9:22.859 14(56.94 791.149 1257.38 602.388 1100.21 015. 584; 977. 963 554. 167 880.167 1 923. 126 1467. 2* 791.378 1257.052 602.589 1100.42 615.762978.148 554.328 880.333 2 923.394 1407.50 791 . 607 1257.86 692.789 1100.63 615.041 978.333 554.489 880.500 3 923. 001 -1407.78 791.837 1258.10 692.990 1100.83 616.119978.519 554.649 880.667 4 923. 934 i 1408. 00 792.070 1258 33 603.194 1101.04 616.301 978.704 554.813 880.833 5 924.200 1468.33 792.304 1258.57 693.399 1101.25 616.482978.889 554.976 881.000 924.478 1468.61 792.533 1258.81 603.599 1101.46 616.661 979.074 555.137 881 167 7 924.741 1468.80 792.762 1259 .Of, 693.800 1101.07 616.839 979.259 555.297 881.333 8 925.008 1469.1', 702. 991 1 1259. 20 694.001 1101.88 617.018 979.444 555.458 881.500 9 925.276 1469.44 793.221 1259.52 694.201 1102 08 617.196 979.630 555.619 881 607 10 925.548 1469.7*. 793.454 1259.76 694.406 1102 29 617.378 979.815 555.782 881.833 11 925.820 1470.00 793.688 1260.00 694.610 1102.50 617.559 980.000 555.046 882.000 12 926.088 1470.28 793.917 1260.24 694.811 1102.71 017.738 980.185 556.106 882 1(57 13 926.355 1470.56 794.146 1200.48 695.011 1102.92 617.910 080.370 556.267 882.333 14 926.628 1470.83 794.380 1200.71 695.216 1103.13 018.098 980.556 556.430 882.500 15 920 900 1471.11 794.613 1200.95 695.420 1103.33 618.279 980.741 556.594 882 667 16 927.167 1 471.30 794.842 1261.10 095.021 1103.54 618.458 980.926 556.755 882.833 17 927.435 14; 1.67 795.072 1201.43 095.821 1103.75 618.636 981.111 556.915 883.000 18 927.707 1471.94 795.305 1201.67 09(5.026 1103.90 618.818 981.296 557.079 883.167 19 927.979 1472.22 795.539 1261.90 696.230 1104.17 618.999 981.481 557.242 883.333 2O 928.247 1472.51! 705.768 1262.14 600.431 1104.38 619.178 981.667 557.403 883.500 31 928.514 1472.78 795.997 1262.38 096.631 1104.58 619.350 981.852 557.564 883.667 33 928.787 1473.06 706.231 1262.62 606.836 1104.70 019.538 982.037 557.727 883.833 23 929.059 1473 3:-j 790.464 1202.80 607 040 1105.00 619.720 082.222 557.891 884.000 24 H29.327 1473.61 79. . 603 1263.10 697.241 1105.21 610.808 982.407 558.051 884 167 25 929.594 1473.89 796.923 1203.33 697.441 1105.42 620.076 982.593 558.212 884.333 36 929.866 1474.17 797.156 1263.57 697.046 1105.03 620.258 982.778 558.375 884.500 27 930.139 1474.44 ; 97. 390 1263.81 097.850 1105.83 620.440 982.963 558.539 884.667 28 930.411 1474.72 797.623 1264.05 698.054 1106.04 620.621 983.148 558.702 884.833 29 930.683 1475.00 797.856 1264.29 698.258 1106.25 620.803 983.333 558.866 885.000 30 930.951 1475. 28 798.080 1264.52 608.459 1100 40 020.981 983 5 '.$ 559.026 885.167 31 931.218 1475.56 798.315 1204.70 698.660 1100.67 621.160 983, 704 559.187 885.333 32 931.490 1475.83 798.549 1205.00 698.864 1106.88 621.341 983.889 559.351 885.500 33 931.763 1476.11 798.782 1205.24 699.068 1107.08 621.523 984.074 559.514 885.667 34 932.035 1476.39 709.015 1205.48 600.273 1107.29 621.705 984.259 559.078 885.833 35 932.307 1476.67 799.249 1265.71 699.477 1107.50 621.886 984.444 559.841 886.000 36 932.580 1476.94 799.482 1265.95 699.681 1107.71 622.068 984.630 560.005 886.167 37 932.852 1477.22 799.716 1266.19 699.885 1107.92 622.249 984.815 500.168 886.333 38 033.124 1477.50 790.949 1266.43 700.090 1108.13 622.431 985.000 500.332 886.500 39 933.396 1477.78 800.182 1266.67 700.294 1108.33 622.613 985.185 560.495 886.667 4O 933.664 1478.06 800.412 1266.90 700.495 1108.54 622.791 985.370 500.056 886.833 41 933.931 1478.33 800.041 1267.14 700.695 1108.75 622.970 985.556 500.810 887.000 42 934.204 1478.61 800.875 1267.38 7(0.900 1108 90 623.151 985.741 500.980 887.167 43 934.476 1478.89 801.108 1267.62 701.104 1109.17 623.333 985.926 501.143 887.333 44 934.748 1479.17 801.341 1267.86 701.308 1109.38 623.514 986.111 561.307 887.500 45 935.021 1479.44 801.575 1268.10 701.513 1109.58 023.696 986.290 561.470 887.007 46 935. 291 1479.72 801.808 1268.33 701.717 1109.79 623.878 986.481 561.634 887.833 47 935.565 1480.00 802.042 1268.57 701 921 1110.00 024.059 986.667 561.797 888.000 48 935.837 1480.28 802.275)1268.81 702.125 1110.21 024.241 986.852 561.961 888.167 49 936.110 1480.56 802.509 1269.05 708,880 1110 42 624.423 987.037 562.124 888.333 5O 93(5.382 1480.83 802. 742 11269. 29 702.534 1110.03 624.604 987.222 562.288 888.500 51 936 . 654 1181.11 802.975 1269 52 702.738 1110.83 624.786 987.407 562.451 888.067 52 936.927 1481.30 803.209 1269.76 702.943 1111.04 624.967 987.593 562.615 888.833 53 937.199 937.471 1481.67 1481.94 803.4421270.00 803.676 1210.24 703.147 703.351 1111.25 1111.40 625.149 625.331 087.778562.778 987.963562.942 880.000) 54 889.167 55 037.743 1482.22 803.000 1270.48 703.555 1111.67 625.512 988. 148! 563. 105 889.333 56 938.020 1482.50 804.147 1270.71 703.763 1111.88 625.697 988.888568.878 8H9.500 57 938.297 1482.78 804.3841270.95 703.971 1112.08 625.882 088.5191563.438 889.667 58 938.570 1483.06 804.617 1271.19 704.175 1112.29 026. 004 988. 704 1 503. 602 880.833 59 223 TABLE XIV. ACTUAL TANGENTS, ETC. 89 1 Curve. 2 Curve. 3 Curve. 4 Curve. 5 Curve. M. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. Tan. Arc. o 5(530.53 8900. OC 2> 15. 37! 4450. 00 1877.04 2966.67 1107.90 2225.00 1120.45 1780.ni) 1 3033.10 8901.07' 2816.184450.83 1877.58 2907.22 1408.31 2225.42 1126.78 1780.33 2 5633.71) 8903.33 28 17. CO 4451. 67 1878.12 2967.78 1408.72 2225.83 1127.10 1780.07 3 5635.43 8905. DO 2817.824452.50 1878.67 2908.33 1409.13 ^226.25 1127.43 1781.00 4 5(537. 00 8900.07 2818. 63 ! 4453. 33 1879.21 2908.89 1409.54 ^226.67 1127.76 1781.33 5 5638.69 81)08.33 2819.45 4454.17 1679.76 2969.44 1409.95 2227. Oh 1128.08 1781.67 6 5(540.32 8910.00 2820.27 4455.00 1880.30 2970.00 1410.35 2227.50 1128. 41 11782. 00 7 5641.99 8911.07 2821.10 4455.83 1880.86 2970.50 1410.77 2227.92 1128.74J1782.33 8 5643.65 8913.33 2821.93 4450.07 1881.41 2971.11 1411.19 2228.33 1129.07 1782.07 9 5645.28 891 5. OU 2822.74 4457.50 1881.952971.67 1411.59 2228.75 1129.40 1783.00 1O 5646.91 8916.67 2823.56 4458. 33 j 1882. 50 2972.22 1412.00 2229.17 1129.73 1783.33 11 5648.55 8918.33 2824.38 4459.17 1883.04 2972.78 1412.41 2229.58 1130.05 1783.07 12 5650.18 8920.00 2825.19 4400.00 1883.59 2973.33 1412.82 2230.00 1130.38 1784.00 13 5051.84 8921.6? 2826.02 4460.83 1884.14 2973.89 1413.23 2230.42 1130.71 1784.33 14 5663.60 8923.33 2826.80 4401. 67 1 1884. 70 2974.44 1413.65 2230.83 1131.05 1784.67 15 565.14 8925.00 2827.07 4402. 50! 1885. 24 2975.00 1414.00 2231.25 1131.37 1785.00 16 5056.77 8926.67 2828.49 4403.33 1885.78 2975.56 1414.47 2231.67 1131.70 1785.33 17 5658.43 8928.33 2829.32 4404.17 1886:34 2976.11 1414.88 2-232. OS 1132.03 1785.67 18 5060.09 8930.00 2830.15 4405. OJ 1886.89 2976.67 1415.30 2232.50 1132.36 1786.00 19 5661.72 8931.67 2830.97 4465.83 1887.44 2977.22 1415.71 2232.92 1132.69 1786.33 20 5663.36 8933.33 2831.78 4466.67 1887.98 2977.78 1416.11 2233.33 1133.02 1786.67 21 5665.02 8935.00 2832.61 4467.50 1888.53 2978.33 1416.53 2233.75 1133.35 1787.00 22 5606.68 8936.07 2833.44 4408.33 1889.09 2978.89 1416.94 2-234.17 1133.68 1787.33 23 5668.31 8938.33 2834.20 4409.17 1889.63 2979.44 1417.35 2234.58 1134.01 1787.67 24 5669.95 8940.00 2835.08 1470.00 1890.18 2^80.00 1417.76 2235.00 1134.34 1788.00 25 5071.61 8941.67 2835.91 4470.83 1890.73 2980.56 1418.18 2235.42 1134.67 1788.33 26 5673.27 8913.33 2836.74 4471.67 1891.28 2981.11 1418.59 2235.83 1135.00 1788.67 27 5074.90 8945.00 2837.50 4472.50 1891.83 2981.67 1419.00 2236.25 1135.33 1789.00 28 5676.54 H94G.07 2838.37 1473.33 1892.31 2982.22 1419.41 2230.67 1135.65 1789.33 29 5678.20 8948.33 2839.20 4474.17 1892.93 2982.78 1419.82 2237.08 1135.99 1789.67 30 5679.86 8950.00 2840.03 4475.00 1893.48 2983.33 1420.24 2237.50 1136.32 1790.00 31 5081.52 8951.67 2840.80 4475.83 1894 04 2983.89 1420.60 2-237.92 1136.65 1790.33 32 5683.18 8953.33 2841.70 4476.67 1894.59 2984.44 1421.07 2238.33 1136.98 1790.67 33 5084 84 8955.00 2842.53 4477.50 195.14 2985.00 1421.49 2238.75 1137.32 1791.00 34 5080.51 8956.67 2843.36 4478.33 1895.70 2985.56 1421.90 2239.17 1137.05 1791.33 35 5088.14 8958.33 2844.17 4479.17 1896.24 2986.11 1422.31 2239.58 1137.98 1791.67 36 5689.77 8960.00 2844.99 4480.00 1896.79 2986.67 1422.72 2240.00 1138.30 1792.00 37 5691.43 8961.67 2845.82 4480.83 1897.34 2987.22 1423.13 2240.42 1138.03 1792.33 38 5693.09 8963.33 2846.65 4481.67:1897.89 2987.78 1423.55 2240.83 1138.97 1792 07 39 5694.76 8965.00 2847.48 4482.50 1898.45 2988.33 1423.96 2241.25 1139.30 1793 00 40 5096.42 8966.67 2848.31 4483.33 1899.00 2988.89 1424.38 2241.67 1139.63 1793.33 41 5698.08 8908.33 2849.14 4484.17 1899.56 2989.44 1424.80 2242.08 1139.96 1793.07 42 5699.74 8970.00 2849.98 4485.001900.11 2990.00 1425.21 2242.50 1140.30 1794.00 43 5701.40 8971.67 2850.81 4485.83 1900.66 2990.56 1425.63 2242.92 1140.03 1794.33 44 5703.06 8973.33 2851.64 4486.6711901.22 2991.11 1426.04 2243.33 1140.96 1794.07 45 5704.73 8975.00 2852.47 4487.501901.77 2991.67 1426.46 2243.75 1141.29 1795.00 46 5706.39 8976.67 2853.30 4488.33 1902.33 2992.22 1426.87 2244.17 1141.63ll795.33 47 5708.05 8978.33 2854.13 4489.17,1902.88 2992.78 1427.29 2244.58 1141.96 1795.07 48 5709.71 8980.00 2854.90 4490.00 1903.43 2993.33 1427.70 2245.00 1142.29 17! '0.00 49 5711.37 8981 . 67 2855.79 4490.83 1903.99 2993.89 1428.12 2245.42 1142.62 1796.33 50 5713.03 8983.33 2856.62 4491.67 1904.54 2994.44 1428.54 2245.83 1142.96 1796.67 51 5714.70 8985.00 2857.45 4492.50 1905.09 291)5.00 1428.95 2246.25 1143.29 1797.00 52 5716.36 8986.67 2858.28 4493.331905.65 201*5.56 1429.37 2246.67 1143.62 1797.33 53 5718.02 8988.33 2859.11 4494.17 1906.20 2996.11 1429.78 2247.08 1143.95 1797.67 54 5719.68 8990.00 2859.95 4495. 001 906. 76 2990.67 1430.20 2247.50 1144.29 1798.00 55 5721 .34 8991.67 2860.78 4495.831907.31 2997.22 1430.61 2247. 92 ! 1144. 02 1798.33 56 5723.00 8993.33 2861.61 4490.67 1907.86 2997.78 1431.03 -2248.33 1144.95 1 71)8.07 57 5724.67 8995.00 2862.44 4497.501908.42 2998.33 1 431 . 44 2248 . 75 1145. 28 1 7 1)9 . 00 58 5726.33 8990.07 2803.27 4498.33 1908.97 2998.89 1431.80 2249. 1711145. 02J1799. 33 59 5727.998998.33 2804.10 4499.17 1909.53 2999.44 1432.2712249.58 1145.951 1799. 07 224 TABLE XTV. ACTUAL TANGENTS, ETC. 6 Curve. 7 Curve. 8 Curve. 9 Curve. 10 Curve. 89 Tan. Arc. Tan. Arc. Tan. A re. Tan. Arc. Tan. Arc. M. 938.8-12 1483.33 804.851 1271.43 704.380 1112.50 626.245 988.889 563 765 890.000 939.114 1483.61 805.084 1271.67 7'04.584 1112.71 626. 427 [989.074 563.929 890.167 1 939.387 1483.89 805.318 1271.90 704. 78H 1112.92 626.608 989.259 564.092 890.333 2 939.659 1484.17 805.551 1272.14 704.993 1113.13 626.790 989.444 564.256 890.500 3 939.931 1484.44 805.785 1272.38 705.197 1113.33 626.972 989.630 564.419 890.667 4 940 203 148-4.72 806.018 1272.62 7'05.401 1113.54 627.153 989.815 564.583 890.833 5 940.476 1485.00 806.251 1272.86 705.605 1113.75 627.3:-55 990.000 564.746 891.000 6 940.753 1485.28 806.489 1273.10 705.8131113.96 627.520 990.185 564.912 891.167 7 941.030 1485.56 806.726 1-J73.33 706.02111114.17 627.705990.370 565.079 891.333 8 941 . 302 1485.83 806. 96U 1273.57 706.225 1114.38 627.886 990.556 565.242 891.500 9 941.574 1486.11 807.193 1273.81 706.430 1114.58 628.068 900.741 565.406 891.667 10 941.847 1486.39 807.427 1274.05 706.634 1114.79 628.249 990.926 565.569 891.833 11 942 119 1486.67 807.660 1274.29 706.838 1115.00 628.431 991.111 565.733 892.000 13 942.396 1486.94 807.898 1274.52 707.046 1115.21 628.616 991.296 565.899 892.167 13 942.673 1487.22 808.135 1274.76 707.254 1115.42 i28.80l 991.481 566.066 892.333 14 942.945 1487.50 808.369 1275.00 707.458 1115.63 628.982 991.667 566.229 892.500 15 943.218 1487.78 S08.602 1275.24 707.663 1115.83 629.164 991 852 566 393 892.667 16 943.495 1488.06 808.840 1275.48 707 870 1116.04 629.349 992.037 566.559 892.833 17 943.772 1488.33 809.077 1275.71 708.078 1116.25 629.533 992.222 566.725 893.000 18 944.044 1488.61 809.310 1275.95 708.283 1116.46 629.715 992.407 566.889 893.167 19 944.316 1488.89 809.544 1276.19 708.487 1116.67 629.897 992.593 5G7.052 893.333 30 944.593 1489.17 809.781 1276.43 708 695 1116.88 630.082 992. 77b 567.219 893.500 31 944.870 1489.44 810.019 1276.67 708.903 nr.08 630.266 992.963 567.385 893.667 22 945.143 1489.72 810.252 1276.90 709.107 111"'. 29 630.448 993.148 567.549 893.833 23 945.415 1490.00 810.486 1277.14 709.311 iir.no 630. 030 993.333 567.712 894.000 34 945.692 1490.28 8 1 0. 723 i 1277. 38 709.519 iir.7i 630.814 993.519 567.878 894.167 35 945.969 1490.56 810.961 1277.62 709.727 iir.92 630.999 993.704 568.045 894.333 26 916.241 1490.83 811.194 1277.86 709.931 1118.13 031.181 J)93.88J 568.208 894.500 27 940.514 1491.11 811.428 1278.10 710.135 1118.33 631.362 994.074 568.372 894.667 28 946.791 1491.39 811.665 1278.33 710.343 1118.54 631.547 994.259 508.538 894.833 29 947.068 1491.67 811.903 1278.57 710.551 1118.75 031. 7S2 994.444 5C8.705 895.000 30 947.345 1491.94 M12.140 1278.81 710.759 1118.96 t31.917 994.631 508.871 895.167 31 947.622 1492.22 812.378 1279.05 710.967 1119.17 632.102 994.815 569.037 b95.333 32 947.899 1492.50 812.615 1279.29 711.175 1119.38 632.286 995.000 569.204 895.500 33 948.176 1492.78 812.853 1279.52 711.383 1119.5h ti32.47! 995 185 569.370 895.667 34 948.448 1493.00 813.086 1279.76 711.587 1119.79 632.653 995.370 569.534 895.833 35 948.721 1493.33 813.320 1280.00 711.791 1120. (X 632.835 995. 55( 569.697 896.000 36 948.998 1493.61 813.557 1280.24 7 11. 999 1120.21 633.019 995.741 569.863 896.167 37 949 275 1493.89 813.795 1280.48 712.207 1120.4^ 633.204 995.920 570.030 896.333 38 949.552 1494.17 814.032 1280.71 712.415 1120.63 633.389 996.111 570.196 S96.500 39 949.829 1494.44 814.270 1280.95 712.623 1120.83 633.574 996.290 570.303 896.667 40 950.106 1494.72 814.507 1281.19 712.830 1121.04 633.759 996.481 57'0.529 896.833 41 950.383 1495.00 814.745 1281.43 713.038 1121.25 633.943 996.667 570.695 897.000 42 950.660 1495.28 SI 4. 982 1281.67 713.246 1121.46 634.128 996.852 570.862 897.167 43 950.937 1495.56 815.220 1281.90 713.454 1121.67 r.34.313 997.037 571.028 897.333 44 951.214 1495>3 815.457 1282.14 713.662 1121. 8b 634.498 95)7.222 571 . 1 94 897.500 45 951.491 1496.11 815.695 1282.38 713.870 1122.08 634.683 997.407 571.361 897.667 46 951.768 1496.39 815.932 1282.62 714.078 1122.29 634. 86V 1 997. 593 571.527 897.833 47 952.045 1496.67 816.170 12.S2.86J 714 286 1122.50 635. 052 1997.778 571.694 898.000 48 952.322 1496.94 816.407 1283.10 714.493 1122.71 635.237 997.963 571.860 898.167 49 95-2.599 1497.22 816.645 1283.33 714.701 1122.92 635.422 998.148 572.026 898.333 50 952.876 953.153 1497.50 1497.78 816.88212?<3.57 817.120 1:281.81 714.909 1123.13 715.1171123.33 635. 607! 998. 333 635 791 998.519 572.193 572.359 898.500 898.667 51 53 953.431 1498.06 817.3571284.05 715.325 1123.54 635.976998.704 572.525 ^98.833 53 953.708 1498.33 817.595 1284.29 71?.5o3ill23.7'5 (.36.161 998.889 572.602 899. 00( 54 953.985 149S.61 817.8321284.52 715.741 1123. 9( 636.346 999.074 572.858 899.107 55 954.262 1498.89 818 070 1284. 76 : 715. 948 1124.17 636.531 999.259 573.024 899.333 56 954.531) I49,ll 818.307 12S5. 00 716. 156! 1124. oS 036.716999.444 573.191 899.500 57 954.816 1499.44 818.545 1285.24 716.364 1124.58 036.9(0999.630 573.357 HIM). (507 58 955.0931499.72 818.782 1285.48 716 572 1124.79 637.085999.815 573.524 899.833 59 225 TABLE XV. NATURAL SINES AND COSINES. 1 2 3 | 4 Sine Cosin Sine Cosin Sine j Cosin Sine Cosin 1 Sine Cosin Tooooo One. .01745 .99985 .03490 . 90039 .05234 .90803 .06976 .99750 60 1 .C0029 One. .01774 .99984 .03519 .99938 .05203 .99801; .07005 .99754 59 2 .00058 One. .01803 .99984 .03548 .99937 .05292 .99800: .07034 .99752 58 3 .00087 One. .01832 .99983 .03577 .99930 .05321 .99858 .07063 .99750 57 4 .00116: One. .01862 .90983 .03000 . 99935 .05350 .9UH57. .07092 .997481 56 5 .00145 One. .01891 .99982 .03035 .99934 .05379 .90855 .07121 .00740 55 G .00175: One. .01920 .99982 .03004 .99933 .05408 .90854 .07150 .99744! 54 7 .00204! One. .01949 .99981 .03093 .99932 .U5437 . 99852 ! .07179 .99742; 53 8 .0023.T One. .01978 .99980 .03723 .99931 .05466!. 99851' .07208 .99740 52 9 .00202 One. .02007 .99980 .03752 .99930 .05495 .99849 .07237 .99738 51 10 .00291 One. .02036 .99979 .03781 .99929 .05524 .99847 .07266 .99736 50 11 .00320 .99999 .02065 .99979 .03810 .99927 .05553 .99846 .07295 .99734 49 12 .00349 .99999 .02094 .99978 .03839 .99928 .055821.99844 .07324 .99731 48 13 .00378 .99999 .02123 .99977 .03808 .99925 .05011 .99842 .07353 .99729 47 14 .00407 .99999 .02152 .99977 .03897 .99924 .05640 .99841 .07382 .99727 46 15 .00436 .99999 .02181 .99976 .03926 .99923 .05669 .99839 .07411 .99725 45 16 .00465 .99999 .02211 .99976 .03955 .99922 .05698 .99838 .07440 .99723 44 17 .00495 .99999 .02240 .99975 .03984 .99921 .05727 .99836 .07409 .99721 43 18 .00524 .99999 .02269 .99974 .04013 .99919 .05756 .99834 .07408 .99719 42 19 .00553 .99998 .02298 .99974 .04042 .99918 .05785 .99833 .07527 .99716 41 20 .00582 .99998 .02327 .99973 .04071 .99917 .05814 .99831, .07556 .99714 40 21 .00611 .99998 .02356 .99972 .04100 .99916 .05S44 . 99829 ; .07585 .99712 39 22 .00640 .99998 .02335 .99972 .04129 .99015 .058731.99827 .07614 .99710 38 23 .00669 .99998 .02414 .99971 .04159 .99013 .05092 .99826 .(-7643 .99708 37 24 .00698 .99998 .02443 .93970 .04108 .99012 .05931 .99824 .07672 .99705 36 25 .00727 .99997 .02472 .99969 .04217 .99911 .059601.99822 .07701 .99703 35 26 .00756 .99997 .02501 .99909 .04246 .99010 .05989 .99821 .07730 .99701 34 27 .00785 .99997 .02530 .99968 .04275 .C9909 .00018 .99819 .07759 .99099 33 28 .00814 .99997 .02560 .99967 .04304 .99907 .CC047 .99817 .07788 .99696 32 29 .00844 .99996 .02589 .99906 .04333 .99006 .00076 .99815 .07817 .99694 31 30 .00873 .99996 .02618 .99966 .04302 .99905 .06105 .99813 .07846 .99692 30 31 .00902 .99998 .02647 .99965 .04391 .99904 .06134 .99812 .07875 .99689 29 32 .00931 .99998 .02670 .99904 .04420 OQOQO .06163 .99810 .079041.99687 28 33 .00960 .99995 .02705 .S99G3 .04449 ! 99901 .06192 .90808 .079331.99685 27 34 .00989 .99995 .02734 .99903 .04478 .90900 .06221 .99806 .079621.99683 26 35 .01018 .99995 .02763 .99902 .04507 .99898 .06250 .99804 .07991|.99680; 25 36 .01047 .99995 .02792 .99961 .04536 .99897 .00279 .90803 .08020: 99678 j 24 37 .01076 .99994 .02821 .99900 .04505 .99896 .00308 .99801 .080491.99676: 23 38 .01105 .99994 .02850 .99959 .04594 .99894 .06337 .99709 .080781.99673 22 39 .01134 .09994 .02379 .99959 .04623 .90893 .00366 .99797 .08107 .99671 21 40 .011641.99993 .02908 .99958 .04053 .99892 .06395 .99795 .08136 .90008 20 41 .01 193 !. 99993 .02938 .99957 .04082 .99890 .06424 .99793 .08165 .99666 19 42 .01222 .99993 .02967 .99956 .04711 .99889 .00453 .9G792 .08194 .99664 18 43 .012511.99992 .02996 .99955 .04740 .99888 .00482 .99790 .08223;. 99661 17 44 .01280 '.99992 .03025 .99954 .047C9 .99886 .00511 .99788 .08252 .00050 16 45 .01309 .99991 .03054 .99953 .04798 .90885 .00540 .99786 .08281 .99657 15 46 .01338 .99991 .03083 .99952 .04827 .99883 .00509 .90784 .08310 .99654 14 47 . 01367 j. 99991 .03112 .99952 .04856 .998821 .00598 .90782 .083391.90652! 13 48 . 01396 !. 99990 .03141 .99951 .04885 .998811 .06627 .99780 .08368 .99649: 12 49 .01425J. 99990 .03170 .99950 .04914 .99S79I .06656 .99778 .08397 .99647 11 50 .01454 .99989 .03199 .99949 .04943 .99878 j .06685 .99776 .08426 .90644 10 51 .01483 .99989 .03228 .99948 .04972 .99876 .06714 .99774 .08455 .99642 9 52 .01513L99989 .03257 .99947 .05001 .90875 .00743:. 99772 .08484 .99639 8 53 .01542 .99988 .03236 .999-16 .05030 .90873 .00773 .99770 .08513 .99037 7 54 .01571 .99988 .03316 .99945s .05059 .90872! .06802 .99708 .08543 .90635 6 55 .01600 .99987 .08345 .99944 .05088 .09870 .00831 .99706 .08571 .90632 5 56 .01 629 ;.99987 .03374 .99943 .05117 .99869 .06860 .99764 .08000 .90030 4 57 .01 658 ',99986 .03403 .99942 .05146 .99867 .00889 .99762 .08029 .90627 3 58 .016871.99986 .03432 .99941 .05175 . 90806 .00018 .99700 .08058 .90625 2 59 . 01716 L 99985 .03461 .99940 .05205 .99864 .06947 .99758 .08687 .99622 1 60 . 01745 j. 99985 .03490 .99939 .05234 .99863 .06976 .00756 .08716 .99619 / Cosin Sine Cosin Sine Cosin Sine Cosin Sine Co^in | Sine / 89 88 87 86 85 226 TABLE XV. -NATURAL SINES AND COSINES. 5 6 7 j| 8 9 ' Sine Cosin Sine Cosin Sine I Cosin Sine Cosin Sine Cosin ' o 708716 "99619 .10453 .99452 .12187 799255 713917 .99027 .15643 798769 60 1 .08745 .99617 .10482 .99449 .12216 .99251 .13946 .99023 .15672 .98764; 59 o .08774 99614 .10511 .99446 .12245 .99248 .13975 .99019 .15701 . 98760 i 58 3 .08803 99612 .10540 .99443 .12274 .99244 .14004 .99015 .15730 .98755 57 4 .08831 .99609 .10569 .99440 .12302 .99240 .14033 .99011 .15758 .98751 56 .08860 .99607 .105971.99437! .12331 .99237 .14061 .99006 .15787 .98746! 55 6 .08889 99604 .10626 j.99434 .12360 .99233 .14090 .99002 .15816 .98741! 54 7 .08918 99602 .10655 .99431 .12389 .99230! .14119 .98998 .15845 .98737 53 8 .08947 99599 . 10684 .99428 .12418 .99226 .14148 .98994 .15873 .98732 52 9 .08976 99596 .10713 .99424 .12447 .99222 .14177 .98990 .15902 .98728! 51 10 .09005 99594 .10742 .99421 .12476 .99219 .14205 .98986 .15931 .98723 50 11 .09034 99591 .10771 .99418 .12504 .99215 .14234 .98982 .15959 .98718 49 12 .09063 99588 .10800 .99415: .12533 .99211 i .14263 .98978 ; .15988 .98714 48 13 .09092 99586 .10329 .99412! .12562 . 99208 ! .14292 .98973 .16017 .98709 47 14 .09121 99583 .10858 99403 i .12591 .90204! .14320 .68969 .16046 .98704 46 15 .09150 99580 .10387 99406 .12620 .99200 .14349 .98965 .16074 .98700! 45 16 .09179 .99578 .10916 99402 j .12649 .99197; .14378 .98961 1 .16103 .98695 44 17 .09208 .99575 .10945 99399 .12678 . 99193 i .14407 .98957 .16132 .98690J 43 18 .09237 .99572 .10973 99390 .12706 .99189 .14436 .98953 i .16160 .98686 42 19 .09266 .99570 .11002 93393 .12735 .991C6 1 .14464 .98948 i .16189 .98681! 41 20 .09295 .99567 .11031 .99390 .12764 .99182! .14493 .98944 .16218 .98676 40 21 .09324 .99564 .11060 99336 .12793 .99178 .14522 .98940 ! .16246 .98671 39 22 .09353 .99562 .11039 .99333 .12822 .99175 .14551 .98936 .16275 .98667 38 23 .09382 .99559 .11118 .93330 .12851 .99171 .14580 .98931 !. 16304 .98662 37 24 .09411 .99556 .11147 .99377 .12330 .99167 .14608 .98927 .16333 .98657 36 25 .09440 .99553 .11176 .93374 .12908 .99163 .14637 .98923 .16361 .986521 35 26 .09469 .99551 .11205 .99370, .12937 .99160 .14666 .98919 .163901.98648 34 27 .09498 .99548 .11234 .99367! .12966 .99156 .14695 .98914 . 16419 .98643! 33 28 .09527 .99545 .11263 .99364 .12995 .99152 .14723 .98910 .16447 .98638 32 29 .09556 .99542 .11291 .93360 .13024 .99148 .14752 .98906 ! .16476 .98633 31 30 .09585 .99540 .11320 .99357 .13053 .99144 .14781 .98902 .16505 .98629 30 31 .09614 .99537 .11349 .99354 .13031 .99141 .14810 .98897 .16533 .98624 29 32 .09642 .99534 .11378 .99351 i .13110 .99137 .14838 .98893 .16562 .98619 28 33 .09671 .99531 .11407 .99347 .13139 .99133 .14867 .98889 i .16591 .98614! 27 34 .09700 .99528 .11436 .93344 .13163 .99129 .14896 .98884 '.16620 .98609! 26 35 .09729 .99526 .11465 .99341 .13197 .99125 .14925 .98880 .16648 .98604; 25 36 .09758 .99523 .11494 .99337 .13226 .99122 .14954 .98876 .1C677 .98600! 24 37 .09787 .99520 .11523 .99334 .13254 .99118 .14982 .98871 .16706 .98595 23 38 .09816 .99517 .11552 . 99331 j .13283 .99114: .15011 .98867 .16734 .98590! 22 39 .09845 .99514 .11580 .99327 .13312 .99110 .15040 .98863 .16763 .98585 21 40 .09874 .99511 .11609 .99324 .13341 .99106 .15069 .98858 .16792 .98580 20 41 .09903 .99508 .11638 .99320' .13370 .99102 .15097 .98854 .16820 .98575 19 42 .09932 .99506 .11667 . 93317 | .13339 .99098! .15126 .98849 .16849 .98570 18 43 .09961 .99503 .11696 . 99314 ! .13427 .99094 .15155 .98845 .16878 .98565! 17 44 .09990 .99500 .11725 .93310! .13456 .99091 .15184 .98841 .16906 .98561 16 45 .10019 .99497 .11754 99307 .13485 .99087 .15212 .98836 .16935 .98656 15 46 .10048 .99494 .11783 .99303 .13514 .99083 .15241 .98832 i .16964 .98551! 14 47 .10077 .99491 .11812 .99300! .13543 .99079 .15270 .98827 .16992 .98546 13 48 .10106 .99488 .11840 .99297! .13572 .99075 . 15299 i. 98823 |i. 17021 .98541 12 49 .10135 .99485 .11869 .99293 .13600 .99071 .15327 .98818 1 .17050 .98536 11 50 .10164 .99482 .11898 .93290 .13629 .99067 .15356 .98814 .17078 .98531 10 51 .10192 .99479 .11927 .99286 .13658 .99063 .15385 .98809 .17107 .98526 9 52 53 .10221 .10250 .99476 .99473 .11956 .11985 .99283 .99279 .13687 .13716 .99059 .99055 .15414 .15442 .98805 .98800 .171 36 j. 98521 .17164!. 98516 8 7 54 .10279 .99470 .12014 .99276 .13744 .99051 .15471 .98796 .17193 .98511 6 55 .10308 .99467 .12043 .99272 .13773 .99047 .15500 .98791 .17222 .98506 5 56 .10337 .99464 .12071 .99269 .13802 .99043 .15529 .98787 .17250 .98501 4 57 10366 .99461 .12100 .99265 .13831 .99039 .15557 .98782 .17279 .98496 3 58 .10395 .99458 .12129 .99262 .13860 .99035 .15586 .98778 .17308 .98491 2 59 .10424 .99455 .12158 .99258 .13889 .99031 .15615 .98773 .17886 .98486 1 60 .10453 .99452 .12187 .99255 .13917 .99027 .15643 .98769 .1 7365 j. 98481 f Cosin Sine Cosin Sine Cosin Sine Cosin Sine Cosin Sine t 84 83 82 81 80 227 TABLE XV. -NATURAL SINES AND COSINES. 10 11 12 13 || 14 ' Sine Cosin Sine Cosin Sine ; Cosin Sine Cosin Sine Cosin ' ~0 .17365 .98481 719081 .98163 720791 797815 722495 797437 .24192 .97030 60 1 .17393 .98476 .19109 . 98157 .208201.97809 . 22523 .97430 .24220 .97023 59 2 .17422 .98471 .19138 .98152 .20848 .97803 .22552 .97424 .24249 .97015 58 3 . 17451 .98466 .19167 .98146 .20877 .97797 .22580 .97417 .24277 .97008 57 4 . 17479 .98461 .19195 .98140 .20905 .97791 .22608 .97411 .24305 .97001 1 56 5 .17508 .98455 .19224 .98135 .20933 . 97784 ; .22637 .97404 .24333 .96994 55 6 .17537 .98450 .19252 .98129 .20962 .97778 .22665 -97398 .24362 .96987 54 7 .17565 .98445 .19281 .98124' .20990 .97772 .22693 .97391 .24390 .96980 53 8 .17594 .98440 .19309 .98118 .21019 .97766! 22722 .97384 .24418 .96973 52 9 .17623 .98435 .19338 .98112 .21047 .97760 .22750 .97378 .24446 .96966 51 10 .17651 .98430 .19306 .98107 .21076 .97754 .22778 .97371 .24474 .96959 50 11 .17680 .98425 .19395 .98101 .21104 .97748 .22807 .97365 .24503 .96952 49 12 .17708 .98420 .19423 .98096 .21132 .97742 .22835 .97358 .24531 .96945 48 13 . 17737 .98414 . 19452 .98C90 .21161 .97735 .22863 .97351 .24559 .96937! 47 14 . 17766 .98409 .19481 .98084 .21189 .97729 .228921.97345 .24587 .96930 46 15 .17794 .98404 .19509 .98079 .21218 .97723! .229201.97338 .24615 .96923 45 16 17 .17823 .17852 .98399 .98394 .19538 . 19566 .98073 .98067: .21246 .21275 .977171 .97711 ! .22948 j.97331 .22977 .97325 .24644 .24672 .96916 44 .96909 43 18 .17880 .98339 .19595 .98061 .21303 .97705 .23005 .97318 .24700 .96902 42 19 .17909 .98383 . 19623 .98056 .21331 .97698 .23033 .97311 .24728 .96894] 41 20 .17937 .98378 .19352 . 98050 .21360 .97692, .23062 .97304 .24756 .96887 40 21 .17966 .98373 .19680 .98044 .21388 .97686 .23090 .97298 .24784 .96880 39 22 .17995 .98368 .19709 .98039 .21417 .97680 .23118 .97291 .24813 .96873 38 23 .18023 .98362 .19737 .98033 .21445 .97673 .23146 .97284 .24841 .96866 37 24 .18052 .98357 .19766 . 93027 : .21474 .97667 .23175 .97278 .24869 .96858 36 25 .18081 .98352 .19794 .98021 .21502 .97661 .23203 .9?271 .24897 .96851 35 26 .181091.98347 .19833 .98016 .21530 .97655 .23231 .97264 .24925 .96844 34 27 .18138 .98341 .19851 .98010 .21559 .97348 .23280 .97057 .24954 .96837 33 28 .18166 .98336 .19880 .98004 .21587 .97342 .23283 .97251 .24982 .96829 32 29 .18195 .98331 .19908 97998 .21616 .97638 .23316 .97244 .25010 .96822 31 30 .18224 .98325 .19937 .97992 .21644 .97630 .23345 .97237 .25038 .96815 30 31 .182521.98320 .19965 .97987 .21672 .97623 .23373 .97230 .25066 .96807 29 32 .18281 .98315!! .19994 .97931 .21701 .97617: .23401 .97223 .25094 .96800 28 33 .18309 .98310 .20022 .97975 .21729 .97611 .23423 .97217 .25122 .96793 27 34 .18338 .98304 .20051 .97969 .21758 .97604 .23453 .972101 .25151 .96786 26 35 .18367 .98299 .20079 97933 .21783 .97593 .23488 .97203 .25179 .96778 25 30 .18395 .93294 .20108 97958 ! .21814 .97592 .23514 .971 96 i .25207 .96771 24 37 .18424 .98238 .20136 97952 1 .21843 .97535 .23542 .97189! .25235 .967'64 23 38 .18452 .98233 .20165 97943 .21871 .97579! .23571 .97182; .25263 .967561 22 39 .18481 .98277 .20193 97940 i .21899 .975731 .23599 .97176! .25291 .96749 21 40 .18509 .98272 .2022.2 . 97934 j .21928 .97566! .23627 .97169i .25320 .96742 20 41 .18538 .98267 .20250 97933 ' .21956 .97560 .23656 .97162 .25348 .96734 19 42 .18567 .98261 .20279 97922 21985 .97553 .23684 .97155(1 .25376 .96727 18 43 .18595 .98256 i .20307 ! 97916 .22013 .97547; .23712 .97148 .25404 .96719 17 44 .18624 .98250 .20335 97910 .22041 .97541 .23740 .971411 .25432 .98712 16 45 .18652 .98245 .20364 .97905 .22070 .975341 .23769 .97134;! .25460 .96705 15 46 .18681 .98240 .20393 .97893 .22098 .97528! .23797 .97127 ! .25488 .96697 14 47 .18710 .98234 .20421 .97893 .22126 .97521 .23825 .97120' .25516 .96690 13 48 .18738!. 98229 ij .20450 . 97887 i .22155 .97515 .23853 .97113! .25545 .96682 12 49 .18767 .98223 .20478 .97881 .22183 .97508; .23882 .97106!! .25573 .96675 11 50 .18795 .98218 .20507 .97875 .22212 .97502 .23910 .97100! .25601 .96667 10 51 .188241.98212! .20535 .97869 .22240 .97496 .23938 .97093 .25629 .96660 9 52 .18852 .98207 .20563 .978631 .22268 .97489! .23966 .97086 .25657 .96653 8 53 .18881J.98201! . 20592 i . 97857 j .22297 .97483; .23995 . 97079 ! .25685 .96645 7 54 .18910 .98196| .206201.97851 .2232o .97476 .24023 .97072 ! .25713;. 96638 6 55 .18938 .98190 . 20649 . 97845 . 22353 : . 97470 ! .24051 .97065 .25741 .96630 5 56 .18967 .98185 .20677 .97839! . 22382 . 97463 .24079 .97058 .25769 .96623 4 57 .18995 .98179 .20706 . 97833 M .22410 .97457 .241081.97051 .25798 .96615 3 58 .19024 .98174 . 20734 1. 97827 .22438 .97450 .241 36j. 97(44! .25826 .96608 2 59 .19052 .98168 .20763 .97821 .22467 .97444! .24164 . 97037 i .25854 .96600 1 60 .19081 .98163 .20791 .97815 .22495|. 97437 .24192 .97030 .25882 .96593 / Cosin Sine ! Cosin Sine Cosin 1 Sine Cosin Sine Cosin Sine - 79 II 78 77 76 75 228 TABLE XV. -NATURAL SINES AND COSINES. 15 | 16 17 18 19 ; / Sine Cosinj Sine ; Cosin Sine Cosin Sine Cosin Sine Cosin .25882 .96593 1 .27564 .96126 .29237 .95630! .30902 .95106 .32557 .94552 60 1 .25910 .96585 .27592 .9(5118 .2D265 .95622. .30929 .95097 .32584 .94542 59 2 .25938 .96578 .27620 .96110 .29293 .95613! .30957 .95088 .32612 .94533 58 3 . 25966 ! . 96570 .27648 .96102 .29321 .95605 .30985 .95079 .32639 .94523 1 57 4 .25994 .96562 .27676 .96094 .29:348 .95596 .31012 .95070 .32667 .94514 56 5 .26022 .96555 .27704 .96086 .29376 .95588 .31040 .95061 .32694 .945041 55 6 .26050 .96547 .27731 .96078 .29404 .95579 .31068 .95052 .32722 .94495 54 7 .26079 .96540 .27759! '96070 .29432 .95571 .31095 .95043 .32749 .94485 53 8 .26107 .96532 .27787 .96062 .29460 .95562 .31123 .95033 .32777 .94476 52 9 .26135 .96524 .27815 .96054 .29487 .95554 .31151 .95024 ! .32804 .94466 51 10 .26163 .96517 .27843;. 96046 .29515 .95545 .31178 .95015 .32832 .94457 50 11 .26191 .96509 .27871 .96037 .29543 .95536 .31206 .95006 ' .32859 .94447 49 12 .26219 .96502 .27899 .96029 .29571 .95528 .31233 .94997 .32887 .94438 48 13 .26247 .96494 . 27927 i. 96021 .29599 .95519 .31261 .94988 i .32914 .9H2S 47 14 .26275 .96486 .27955 .96013 .29626 .95511 .31289J.94979 1.32942!. 94418 46 15 .26303 .96479 .27983 j.96005 .29654 .95502 .31316!. 94970 .32969 .94409 45 1G .26331 .96471 .280111.95997 .29682 .95493; .31344 .94961 ! .32997 .94399 44 17 .26359 .96463 .280391.95989 .29710 .95485! .31372 .94952 i .33024 .94390 43 18 .26387 .96456 .28067 .95981 .29737 .9.5476 .31399 .94943 .33051 .94380 42 19 .26415 .96448 .28095 .95972 .29765 .85467 .31427 .94933 .33079 .94370 41 20 .26443 .96440 .28123 .95964 .29793 .95459 .31454 .94924 .33106 .94361 40 21 .26471 .96433 .28150 .95956 .29821 .95450! .31482 .94915 .33134 .94351 39 22 .26500 .96425 .28178 .95948 .29849 .95441! .31510 .94906 .33161 .94342 38 23 .26528 .96417 .28206 .95940 .29876 .95433 .31537 .94897 .33189 .94332 37 24 .26556 .96410 .28234 .95931 .29904 .95424 .31565 .94888 .33216 .94322 36 25 .26584 .96402 .28262 .95923 .29932 .95415! .31593 .94878 .33244 .94313 35 26 .26612 .96394 .28290 .95915 .29960 .95407 .31620 .94869 .33271 .94303 34 27 .26640 .96386 .28318 .95907 .29987 .95398 .31648 .94860 .33298 .94293 33 28 .26668 .96379 .28346 .95898 .30015 .95389 .31675 .94851 .33326 .94284 32. 29 .26696 .96371J .28374 .95890 .30043 .95380' .31703 .94842 .33353 .94274 31 30 .26724 .96363! .28402 .95882 .30071 .95372 .31730 .94832 .33381 .94264 30 31 .26752 .96355 .28429 .95874 .30090 .95363 .31758 .94823 .33408 .94254 29 32 .26780 .96347 .28457 .95805 .301G .95354 .81780 .94814 .33436 .94245 23 33 .26808 .96340 .28485 .95857 .30154 .95345 .31813 .94805 .33463 .94235 27 34 .26836 .96332 .23513 .95849 .30182 .95337 .31841 .94795 .33490 .94225 26 35 .26864 .96324 .28541 .95841 .30209 .95323 .31868 .94786 .33518 .94215 25 36 .26892 .96316 .28509 .95832 .30237 .95319 .31896 .94777 .33545 .94206 24 37 .26920 .96308 .28597 .95824 .30265 .95310 .31923 .94768 .33573 .94196 23 38 .26948 .96301 .28625 .95816 .30292 .95301 .31951 .94758 .33600 .94186 22 39 .26976 . 98293 .28652 .95807 .30320 .95203 .31979 .94749 .33627 .94176 21 40 .27004 .96285 .28680 .95799 .30348 .95284 .32006 .94740 .33655 .94167 20 41 .27032 .9627?' .28708 .95791 .30376 .95275 .32034 .94730 .33682 .94157 19 42 .27060 .96269 . 28736 j. 95782 .30403 .952G6 .32001 .94721 .33710 .94147 18 43 .27088 .96261 .287641.95774 .30431 .95257 .32089 .94712 .33737 .94137 17 44 .27116 .96253 .28792 .95766 .30459 .95248 .32110 .94702 .33764 .94127 16 45 .27144 .96246 .28820 .95757 .30486 .95240 .32144 .94693 .33792 .94118 15 46 .27172 .96238! .28347 .95749 .305141.952311 .32171 .94684 .33819 .94108 14 47 .27200 .96230 .28875 .95740 .30542 .95222; .32199 .94674 .33846 .94098 13 48 .272281.96222 .28903 .95732 .30570 .95213 .32227 .94665 .33874 .94088 12 49 .27256 |.96214 .28931 .95724 .30597 .95204 .32254 .94656 33901 .94078 11 50 .27284 .96206 .28959 .95715 .30625 .95195 .32282 .94640 .33929 .94068 10 51 .27312 .96198 .28987 .95707 .30653 .95186 .32309 .94637 .33956 .94058 9 52 .27340 .96190; .29015 .95698 .30680 .95177: .32337 .94627 i .33983 .94049 8 53 .27368 .96182 .29042:. 95690 .30708 .95168- .32364 .94618 |. 34011 .94039 7 54 .27396 .96174 .290701.95681 .30736 .95159 .32392 .94609 .34038 .94029 6 55 .27424 .96166 .29098 .95673 .30763 .95150 .32-119 .94599 .34065 .94019 5 56 .27452 .96158 .291261.95664 .30791 .95142 .32447 .94590 .34093 .94009 4 57 .27480 .96150 .291 54!. 95656 .30819 .95133 .32474 .93580 .341201.93999 3 58 1.27508 .96142 .291821.95647 .30846 .95124 .32502 .94571 .34147 .93989 2 59 .27536 .96134 .29209!. 95639 .30874 .95115 .32529 .94561 .34175 .93979 1 60 .27564 .96126 .29237 .95630 .80908 .95106 .32557 .94552 .34202 .93969 7 Cosin i Sine j Cosin Sine Cosin Sine Cosin Sine Cosin Sine / 74* 73 72 71 70 229 TABLE XV.-NATURAL SINES AND COSINES. 20 21 22 I 23 24 Sine Cosin Sine , Cosin Sine Cosin Sine Cosin Sine Cosin .34202 ^ 93969 . 35837 i. 93358 .37461 .92718 .39073 .92050 ".40674 .91355 60 1 .34229 .93959 .35864 .93348 .37488 .92707 .39100 .92039 .40700 .91343 59 2 .34257 .93949 .35891 .93337 .37515 .92G97 .39127 .92028 .40727 .91331 58 3 .34284 .93939 .35918 .93327 .37542 .92686 .39153 .92016 .40753 .91319 5? 4 .34311 .93929 .35945 .93316 .37569 .92675 .39180 .92005 .40780 .91307 56 5 .34339 .93919 .35973 .93306 .37595 .92664 .39207 .91994 .40806 .91295 55 6 .313661.93909 .36000 .93295 .37622 .92653 .89234 .91982 .40833 .91283 54 7 .34393 .93899 .36027 .93285 .37649 .92642 .39260 .91971 .40860 .91272 53 8 .34421 .93889 .36054 .93274 .37676 .92631 .39287 .91959] .40886 .91260 52 9 .34448 .93879 .360811.93264 .37703 .92620 .39314 .91948 .40913 .91248 51 10 .34475 .93869 .36108 .93253 .37730 .92609 .39341 .91936 .40939 .91236 50 11 .34503 .93859 .36135 .93243 . 37757 ! . 92598 .39367 .91925 .40966 .91224 49 12 .84530 . 93849 .36162 .93232 . 37784 i. 92587 .39394 .91914 .40992 .91212 48 13 .34557 .93839 .361901.93222 .37811!. 92576 .39421 .91902 .41019 .91200 47 14 .34584 .93829 .36217 .93211 .37838 .92565 .39448:. 91 891 .41045 .91188 46 15 .34612 .93819 .36244 .93201 .37865 .92554 .394741.91879 .41072 .91176 45 16 .34639 .93809 . 36271 ! . 931 90 .37892 .92543 .395011.91868 .41098 .91164 44 17 | .34666 .93799 .36298 .93180 .37919 .92532 .39528 .91856 .41125 .91152 43 18 !. 34694 .93789 .36325 .93169 .37946 .92521 .395551.91845 .41151 .91140 42 19 .34721 .93779 .36352 .93159 .37973 .92510 .39581 .91833 .41178 .91128 41 20 .34748 .93769 .36379 .93148 .37999 .92499 .39608 .91822 .41204 .91116 40 21 .34775 .93759 .36406 .93137 .38026 .92488 .39635 .91810 .41231 .91104 39 22 .34803 .93748 .36434 .93127 .38053 .92477 .39661 .91799 .41257 .91092 38 23 .34830 .93738 .36461 .93116 .38080 .92466 .39688 .91787 .41284 .91080 37 24 .34857 .93728 .36488 .93106 .38107 .92455 .39715 .91775 .41310 .91068 36 25 .34884 .93718 .36515 .93095 .38134 .92444 .39741 .91764 .41337 .91056 35 26 .34912 .93708 .36542 .93084 .38161 .92432 .39768 .91752 .41363 .91044 34 27 .34939 .93698 .36569 .93074 .381881.92421 .39795J.91741 .41390 .91032 33 28 .34966 .93688 .36596 .93063 .38215 .92410 .39822 .91729 .41416 .91020 32 29 .34993 .93677 .36623 .93052 .. C 8241 .92399 .39848 .91718 .41443 .91008 31 30 .35021 .93667 .36650 .93042 .38268 .92388 .39875 .91706 .41469 .90996 30 31 .35048 .9365? .36677 .93031 .38295 .92377 .39902 .91694 .41496 .90984 29 32 .350751.93647 . 36704 i. 93020 .38322 .S23C6 .3S92S .91683 .41522 .90972 28 33 .35102 ;.93637 .36731 .93010 .38349 .92355 .33955 .91671 .41549 .90960 27 34 .35130 .93626 .36758 .92999 .38376 .92343 .39982 .91660 .41575 .90948 26 35 .35157 .93616 .36785 .92988 .38403 .92332 .40008 .91648 .41602 .90936 25 36 .35184 .93606 .36812 .92978 .38430 .92321 .40035 .91636 .41628 .90924 24 37 .35211 .93596 .36839 '.92967 .38456 .92310 .40062 .91625 .41655 .90911 23 38 .35239 .93585 .36867 .92956 .38483 .92299 .40088 .91613 .41681 .90899 22 39 .35266 .93575 .368941.92945 .38510 .92287 .40115 .91601 .41707 .90887 21 40 .35293 .93565 .36921 .92935 .38537 .92276 .40141 .91590 .41734 .90875 20 41 .35320 '.93555 .36948 .92924 .38564 .92265 .40168 .91578 .41760 .90863 19 42 .35347 .93544 .36975 .92913 .38591 .92254 .40195 .91566 .41787 .90851 18 43 .35375 .93534 .37002 .929021 .38617 .92243 .40221 .91555 .41813 .90839 17 44 .35402 .93524 .37029 .92892' .38(344 .92231 .40248 .91543 .41840 .90826 16 45 .35429 .93514 .37056 .92881 .38671 .92220 .40275 .91531 .41866 .90814 15 46 .35456 .93503 .37083 .92870 .38698 .02209 .40301 .91519 .41892 .90802 14 47 .35484 .93493 .37110 .92859 .38725 .92198 .40328 .91508 .41919 .90790 13 48 .35511 .93483 .37137 .92849 .38752 .92186 .40355 .91496 .41945;. 90778 12 49 .35538 .93472 .37164 .92838 .38778 .92175 .40381 .91484 .41972!. 907661 11 50 .35565 .93462 .37191 .92827 .38805 .92164 .40408 .91472 . 41998 r 90753 10 51 .35592 .93452 .37218 .92816 .38832 .92152 .40434 .91461 .42024 .90741 9 52 .35619 .93441 .37245 .92805 . 38859 j. 92141 .40461!. 91449 .42051 .90729 8 53 .35647 .93431 .37272 .92794 .38886 .92130 .40488 .91437 .42077 .90717 7 54 .35674 .93420 .37299 .92784 .38912 .92119 .40514 .91425 .42104 .90704 6 55 .35701 .93410 .37326 .92773 .389391.92107 .40541 .91414 .42130 .90692 5 56 .35728 .93400 .37353 .92762 .389661.92096 .40567 .91402 .42156 .90680 4 57 .35755 .93389 .37380 .92751 .38993!. 92085 .40594 .91390 .42183 .90668 3 58 .35782 .93379 .37407 .92740 .39020 .92073' .40621 .91378 .42209 .90655 2 59 .35810 .93368 .37434 .92729 .39046 .92062 .40647 .91366 .42235 .90643 1 CO .35837 .93358 .37461 .92718 .39073 .92050 .40674 '.91355 .42262 .90631 ~ Cosin Sine Cosin Sine Cosin Sine Cosin Sine Cosin Sine 69 68 67 66 65 230 TABLE XV. NATURAL SINES AND COSINES. 25 26 27 28 29 Sine |Cosin Sine Cosin Sine Cosin Sine ' Cosin Sine Cosin o .42262 .90631 .43837 .89879 .45399 .89101 . 46947 i. 88295 .48481 .87462 60 1 .42288 .90618 .43863 .89867 .45425 .89037 . 46973 i. 88281 .48506 .87448 59 2 .42315 .90606 .43889 .89854 .45451 .89074 .46999 .88267 .48532 .87434 58 3 .42341 .90594 .43916 .89841 .45477 .89061 .47024 .88254 .48557 .87420 57 4 .42367 .90582 .43942 .89828 .45503 .89048 .47050 .88240 .485831.87406 56 5 .42394 .90569 .43968 .89816 .45529 .89035 .47076 .88226 .48608 .87391 55 6 .42420 .90557 .43994 .89803 .45554 .89021 .47101 .88213 .48634 .87377 54 7 .42446 .90545 .44020 .89790 .45580 .89008 .47127 88199 .48659 .87363 53 8 .42473 .90532 .44046 .89777 .45800 .88995 .47153 .88185 .48684 .87349 52 9 .42199 .90520 .4407'2 .89764 .45632 .88981 .47178 .88172 .48710 .87335 51 10 .42525 .90507 .44098 .89752 .45658 .88968 .47204 .88158 .48735 .87321 50 11 .42552 .90495 .44124 .89739 .45684 .88955 .47229 .88144 .48761 .87306 49 12 .42578 .90483 .44151 .89726 .45710 .88942 .47'255 .88130 .48786 .87292 48 13 .42604 .90470 .44177 .89713 .45738 .88928 .47281 .88117 .48811 .87278 47 14 .42631 .90458 .44203 .89700 .45762 .88915 .47306 .88103 .48837 .87264 46 15 .42657 .90446 .44229 .89687 .45787 .88902 .47332 .88089 .48862 .87250 45 16 .42683 .90433 .44255 .89674 .45813 .88888 .47358 .88075 .48888 .87235 44 17 .42709 .90421 .44281 .89662! .45839 .88875 .47383 .88062 .48913 .87221 43 18 .42736 .90408 .44307 .89649 .45865 .88862 .47409 .88048 .48938 .87207 42 19 .42762 .9C396 .44333 .89636 .45891 .88848 .47434 .88034 .48964 .87193 41 20 .42788 .90333 .44359 .89623 .45917 .88835 .47460 .88020 .48989 .87178 40 21 .42815 .90371 .44385 .89610 .45942 .88822 47486 .88006 .49014 .87164 39 22 .42841 .90338 .44411 .89597 .45968 .88808 .475111.87993 .49040 .87150 38 23 .42867 .90346 .44437 .89584 .45994 .83795 .47537 .87979 .49065 .87136 37 24 .42894 .903U .44461 .89571 .46020 .88782 .47562 .87965 .49090 .87121 36 23 .42920 .90321 .44490 .80558! .46046 .88768 .47588 .87951 .49116 .87107 35 26 .42946 .90309 .44516 .89545 .46072 .88755 .47614 .87937 .49141 .87093 34 27 .42972 .90206 .44542 .89532 .46097 .88741 .47639 .87923 .49166 .87079 33 28 .42999 .90284 .44568 .89519 .46123 .88728 .47665 .87909 .49192 .87064 32 29 .43025 .9^271 .44594 .80506 .46149 .88715 .47690 .87896 .49217 .87050 31 30 .43051 .90259 .44620 .89493 .46175 .88701 .47716 .87882 .49242 .87036 30 31 .43077 .90246 .44646 .89480 .46201 .88688 .47741 .87868 .49268 .87021 29 32 .43104 .90233 .44672 .83467 .46226 .88674 .47767 .87854 .49293 .87007 28 33 .43130 .90221 .44698 .89454 .46252 .88661 .47793 .87840 .49318 .86993 27 34 .43158 .90203 .44724 .89441 .46278 .88647 .47818 .87826 .49344 .86978 28 35 .43182 .90196 .44750 .89428 .46304 .88634 .47344 .87812 .49369 .86964 25 36 .43209 .90183 .44776 .89415 .46330 .88620 .47869 .87798 .49394 .86949 24 37 .43235 .90171 .44802 .89402 .46355 .88607 .47895 .87784 .49419 .86935 23 38 .43261 .90153 .44828 .89389 .46381 .88593 .47020 .87770 .49445 .86921 22 39 .43287 .90146 .44854 .80376 .46407 .88580 .47946 .87756 .49470 .86906 21 40 .43313 .90133 .44880 .89363 .46433 .88566 .47971 .87743 .49495 .86892 20 41 .43340 .90120 .44906 .89350 .46458 .88553 .47997 .87729 .49521 .86878 19 42 .43366 .90108 .44932 .80337 .46484 .88539 .48022 .87715 .49546 .86863 18 43 .43392 .90095 .44958 .80324 .46510 .88526 .48048 .87701 .49571 .86849 17 44 .43418 .90082 .44984 .89311 .46536 .88512 .48073 .87687 .49596 .86834 16 45 .43445 .90070 .45010 .89298 .46561 .88499 .48099 .87673 .49622 .86820 15 46 .43471 .90057 .45036 .89285 .46587 .88485 .48124 .87659 .49647 .86805 14 47 .43497 .90045 .45062 .89272 .46613 .88472 .48150 .87645 .49672 .86791 13 48 .43523 .90032 .45088 .89259 .46639 .88458 .48175 .87631 .49697 .86777 12 49 .43549 .90019 .45114 .89245 .46664 .88445 .48201 .87617 .49723 .86762 11 50 .43575 .90007 .45140 .89232 .46690 .88431 .48226 .87603 .49748 .86748 10 51 .43602 .89994 .45166 .89219 .46716 .88417 .48252 .87589 .49773 .86733 9 52 .43628 .89981 .45192 .89206 .46742 .88404 .48277 .87575 .49798 .86719 8 53 .43654 .89968 .45218 .89193 .46767 .88390 .48303 .87561 .49824 .86704 7 54 .43680 .89956 .45243 .89180 .46793 .88377 .4&S28 .87546 .49849 .86690 6 55 .43708 .89943 .45269 .89167 .46819 .88363 .48354 .87532 .49874 .86675 5 56 .437&S .89930 .45295 .89153 .46844 .88349 .48379 .87518 .49899 .86661 4 57 .43759 .89918 .45321 .89140 .46870 .88336 .48405 .87504 .49924 .86646 3 58 .43785 .89905 .45347 .89127 .46896 .88322 .48430 .87490 .49950 .86632 2 59 .43811 .89892 .45373 .89114 .46921 .88308 .48456 .87476 .49975 .86617 1 60 .43837 .89879 .45399 .89101 .46947 .88295 .48481 .87462 .50000 .86603 _0 / Cosin Sine Cosin Sine Cosin Sine i Cosin Sine Cosin Sine / 64 63 62 61 60 231 TABLE XV. NATURAL SINES AND COSINES. 30 31 32 | 33 34 Sine Cosin Sine Cosin Sine Cosin Sine ! Cosin Sine Cosin ~o .50000 .86603 751504 785717 752992 : .84805 754464 783867 .55919 .82904 60 l .50025 .86588 .51529 .857'02 .53017 .84789 .54488!. 83861 .55943 82887 59 2 .50050 .86573 .51554 .85687 .53041 .84774 .54513 .83835 .55968 .82871 58 3 .50076 .86559 .51579 .85672 .53066 .84759 .54537 .83819 .55992 .82855 57 4 .50101 .86544 .51604 .85657 .530911.84743 . 5450 l|. 83804 .56016 .82839 56 5 .50126 .86530 .51628 .85642 .531 15 !. 84728 .54586 .83788 .56040 .82822 55 6 .50151 .86515 .51653 .85627 .531401.84712 .54610i.83772 .56064 .82806 54 7 .50176 .86501 .51678 .85612 .53164 .84697 .546351.83756 .56088 .827'90 53 8 .50201 .86486 .51703 .85597 .53189 .84681 .54659 .83740 .56112 .82773 52 9 .50227 .86471 .51728 .85582; .53214 .84666 .54683 .83724 .56136 .82757 51 10 .50252 .86457 .51753 .85567 .53238 .84650 .54708 .837o8 .56160 .82741 50 11 .50277 .86442 .51778 .85551 .53263 .84635* .54732 .83692 .56184 .82724 49 12 .50302 .86427 .51803 .85536 .53288 .84619 .54756 .83676 .56208 .82708 48 13 .50327 .86413 .51823 .85521 .53312 .84604 .54781 .83660 .56232 .82092 47 14 .50352 .86398 .51852 .85506 .53337 .84588 .54805 .83645 .56256 .82075 46 15 .50377 .86384 .51877 .85491 .53361 .84573 .548291.83629 .50280 .82059 45 1G .50403 .86369 .51902 .85476 .53386 .84557 .54854 1.83613 .56305 .82043 44 17 .50428 .86354 .51927 .85461 .53411 .84542 .54878 .83597 ! .56329 .82020 43 18 .50453 .86340 .51952 .85446 .53435 .84526 .54902 .83581 .56353 .82610 42 19 .50478 .86325 .51977 .85431 .53460 .84511 .M927 1.83565 .56377 .82593 41 20 .50503 .86310 .52002 .85416 .53484 .84495 .54951 .83549 .56401 .82577 40 21 .50528 .86295 .52026 .85401 .53509 .84480 .54975 .83533' .56425 .82561 39 22 .50553 .86281 .52051 .85385 .53534 .84464! .54999 .83517 .56449 .82544 33 23 .50578 .86206 .52076 .85370 .53558 .84448 .55024 .83501 .56473 .82528 37 24 .50603 .86251 .52101 .85355 .53583 . 84433 : .55048 .83485 .56497 .82511 36 25 .50628 .86237 .52126 .85340 .53607 .84417 .55072 .83469 .56521 .82495 35 26 .50654 .86222 .52151 .85325 .53632 .84402 .55097 .83453 .56545 .82478 34 .50679 .86207 .52175 .85310, .53656 .84386 .55121 .83437 .56569 .82402 33 28 .50704 .86192 .52200 .85294 .53681 .84370 .55145 .83421 .56593 .82440 32 29 .50729 .86178 .52225 .85279 .53705 .84355 .55169 .83405 .50617 .82429 31 30 .50754 .86163 .52250 .85204 .53730 .84339 .55194 .83389 .56041 .82413 30 31 .50779 .86148 .52275 . 85249 ' .53754 . 84324 ! .55218 .83373 .56665 .82396 29 32 .50804 .86133 .52299 .85234 .53779 .84303 .55242 .83856 .66689 .82380 28 33 .50829 .86119 .52324 .85218 .53804 .84292 .C52G6 .83340 .50713 .82303 27 34 .50854 .86104 .52349 .85203 .53828 .84277, .55291 .83324 .56736 .82347 26 35 .50879 .86089 .52,374 .85188 .53853 .84261 1 .55315 .8:3308 .56760 .82330 25 36 .50904 .86074 .52399 .85173 .53877 .84245 .55339 .83292 .56784 .82314 24 37 .50929 .86059 .52423 .85157 .53902 .84230 .55363 .83276 .50808 .82297 23 38 .50954 .86045 .52448 .85142 .53926 .84214 .55388 .83260 .50832 .82281 1 22 39 .50979 .86030 .52473 .85127 .53951 .84198 .55412 .83244 .50856 .82264 21 40 .51004 .86015 .52498 .85112 .53975 .84182 .55436 .83228 .50880 .82248 20 41 .51029 .86000 .52522 .85090 .54000 .84167 .55460 .83212 .56904 .82231 19 42 .51054 .85985 .52547 .85081 .54024 .84151 .55484 .83195 .56928 .82214 13 43 .51079 .85970 .52572 . 85033 i .54049 .84135 .55509 .83179 .50952 .82198 17 44 .51104 .85956 .52597 .85051 1 .54073 .84120 .5o533 1.83163 .50976 .82181 16 45 .51129 .85941 .52621 .85035! .54097 .84104 .55557 .83147 .57000 .82165 15 46 .51154 .85926 .52646 .85020: .54122 .84088 .55581 .83131 .57024 .82148 14 47 .51179 .85911 .53671 .85005 .54146 .84072 .55605 .83115' .57047 ! 82 132 13 48 .51204 .85896 .52696 .84989 .54171 .84057 .55630 .R3i)9S .57071 .82115 12 49 .51229 .85881 .52?'20 .8497'4 .54195 .84041 .55654 .83082 J .57095 .82098 11 50 .51254 .85866 .52745 .84959 .54220 .84025 .55678 .83066 .57119 .82082 10 51 .51279 .85851 .52770 .84943 .54244 .84009 .55702 .&3050 .57143 .82065 9 52 .51304 .85,836 .52794 .84928 .542691.83994 .55726 .83034 .57167 .82048 8 53 .51329 .85821 .52819 .84913 .54293J.83978 .55750 .83017 .57191 .82032 7 54 .51354 .85806 .52844 .84897 .54317 .83962 .55775 .83001 .57215 .82015 6 55 .51379 .85792 .52869 .84882 .54342 .83946 .55799 .82985 .57238 .81999 5 56 .51404 .85777 .52893 .84866! .54366 .83930 .55823 .82969 .57262 .81982 4 57 .51429 .85762 .52918 .84851 | .54391 .83915 .55847 .82953 .57286 .81 965 3 58 .51454 .85747 .52943 .84836: .54415 .83899 .55871 .82936 .57310 .81949 2 59 .51479 .85732 .52967 .84820 .544401.83883 .55895 .82920 .57334 .81932 i 60 .51504 .85717 .52992 .84805 .54464 .83867H .55919 .82904; .57358 .81915! / Cosin ~Sine^ Cosin Sine" Cosin j "Sine" Cosin Sine Cosin Sii>e t 59 58 57 56 55 232 TABLE XV. NATURAL SINES AND COSINES. 35 36 37 38 39 ' Sine Cosin Sine Cosin Sine Cosin Sine Cosin Sine | Cosin ~~0 ! 757358 781915 758779 780902 ! T60182 .79864 761566 778801 762932 .77715 60 1 ! .573H1|.81899 .58802 .80885 .60205 .79846 .61589 .78783 .62955 .77690 59 2 ! .574051.81882 .58826 .80867 .60228 .79829; .61612 .78765 .62977 .77678 58 3 : .57429 .81865; .58849 .80850! .602511. 7981 li .61635 .78747 .63000 .77'660 57 4 i .57458 .81848! .58873 .80833; .60274!. 79793 i .61658 .78729 .63022 .77641 56 5 ! .57477 .81832: .58896 .80816 . 60298 L 79776 .61681 .78711 .63045 .77623 55 6 : .57501 .81815 .58920 .80799 .60321 .79758' .61704 .78694 .63068 .77605 54 7 I .57524 .81798 .58943 .80782 .60344 .797411 .61726 .78676! .63090 .77586 53 8 i .57548 .81782 .58967 .80765 .60367 .79723 .61749 .78658 .63113 .77568 52 9 .57572 .81765 .58990 .80748 .60390 .79706 .61772 .78640 .63135 .77550 51 10 j .57596 .81748 .59014 .80730 .60414 .79688 .61795 .78622 .63158 .77531 50 11 .57619 .81731 .59037 .80713 .60437 .79671 .61818 .78604 .63180 .77513 40 12 i .57643 .81714 .59061 .80696 .60460 .79653 .61841 .78586 .63203 .77494 48 13 .57667 .81698 .59084 .80679 .60483 .79635 .1864 .78568 .63225 .77476 47 14 .57691 .81681 .59108 .80662 .60506 .79618 .61887 .78550 .63248 .77458 46 15 .57715 .81664 .59131 .80644! .60529 .79600 .61909 .78532! .63271 .77439 45 16 .57738 .81647 .59154 .80627 .60553 .79583 .61932 .78514! .63293 .77421 44 17 .57762 .81631 .59178 .80610 .60576 .79565 .619551.78496! .63316 .77402 43 18 .57786 .81614 .59201 .80593 .60599 .79547 .61978 .78478! .63338 .77384 42 19 .57810 .81597 .59225 . 80576 j .60622 .79520 .62001 .7'8460; .63361 .77366 41 20 .57833 .81580 .59248 .80558 .60645 .79512 .62024 .78442 .63383 .77347 40 21 .57857 .81563 .59272 .80541 .60668 .79494 .62046 .78424 .63406 .77329 39 22 .57881 .81546 .59205 .80524: .60691 .79477 .62069 .784051 .63428 .77310 38 23 .57904 .81530 .59318 .80507 .60714 .79459 .62092 .78387! .63451 .77292 37 24 .57928 .81513 .59342 .80489 .60738 .79441 .62115 L78369J .63473 .77273 36 25 .57952 .81496 .59365 .80472 .60761 .79424 .621381.783511 .63496 .77255 35 26 .57976 .81479 .59389 .80455 .60784 .79406' .621601.78333! .63518 .77236 34 27 .57999 .81462 .59412 .80438! .60807 .79388 .62183!. 78315! .63540 .77218 33 28 .58023 .81445 .59436 .80420! .60830 .79371 .62206!. 78297 .63563 .77199 32 29 .58047 .81428 .594591.80403 60853 .79353 .622291.78279 .63585 .77181) 31 30 .58070 .81412 .59482 .80386J .60876 .79335 .62251 .78261 .63608 .77162 30 31 .58094 .81395 .59506 .80368 .60899 .79318 .62274 .78243 .63630 .77144 29 32 1 .58118 .81378 .59529 .80351 .60922 .79300 .62297 .78225 .63653 .77125 28 33 .58141 .81361 .59552 .80334 .60945 .79282 .62320 .78206 .63675 .77107 27 34 .58165 .81344: .59576 .80316! .6C968 .79264 .623421.78188 .63698 .77088 26 35 36 .58189 .81327 .58212 .81810 .59599 .59622 .80299 .80282 .0991 .61015 .79247 .79229 .62365 .78170 .62388 .78152 .63720 .63742 .77070! 25 .77051124 37 .58236J.81293 .59646 .80264 .61038 .79211 .62411 .78134! .63765!. 770331 23 38 .58260 .81276 .59669 .80247 .61061 .79193 .62433 .78116 .63787 .7701 4 l 22 39 .58283 .81259! .59693 .802301 .61084 .79176 .62456 .780981 .63810 .76996! 21 40 .58307 .81242 .59716 .80212 .61107 .791C8 .62479 . 78079 i .63832 .76977 20 41 .58330 .81225 .59739 .80195 .61130 .79140 .62502 . 78061 .63854 .76959 19 42 .58354 .81208 .59763 .80178 .61153 .79122 .62524 .78043! .63877 .76940! 18 43 .58378 .81191 .59786 .80160 .61176 .79105 .62547 .78025 .63899 .76921! 17 44 .58401 .81174 .59809 .80143 .61199 .79087 .62570 .78007 .63922 .769031 16 45 i .58425 .81157 .59832 .80125 .61222 .79069 .62592 .77988 .63944 .76884 15 46 1 .58449 .81140 .59856 .80108 .61245 .79051 .62615 .77970 .63966 .76866! 14 47 .58472 81123 .59879 .80091 .61268 .79033 .62638 .77'952! .63989 .76847 13 48 .58496 .81106 .59902 .80073 .61291 .79016 .62660 .77934 .640111.76828 12 49 .58519 .81089 .59926 .80056 .81814 .78006 .62683 .77916 .64033 .T6810 11 50 .58543 .81072 .59949 .80038 .61337 .78980 .62706 .77897 .64056 .76791 10 51 .58567 .81055 .59972 .80021 .61360 .78962 .62728 .77879 .64078 .76772 9 52 .58590 .81038 .59995 80003: .61383 .78944 .62751 .778611 .64100 .76754 8 53 .58614 .81021 .60019 .79986; .61406 .78926 .62774 .77843 .64123 .76735 ft 54 .58637 .81004 .60042 .79968 .61429 .78908 .62796 .77824 .64145 .76717 6 55 .58661 .80987 .60065 .79951; .61451 .78891 .62819 .77806 .64167 .76698 5 56 .58(584 .H(M)7'() .60089 .79934; .61474 .78873 .62842 .77788 .64190 .76679 4 57 .58708 .80953 .60112 .79916, .61497 .78855 .62864 .77769 .64212 .766611 3 58 .58731 .80936 .60135 .79899 .61520 .78837 .62887 .77751 .64234 .76642; 2 59 .58755 .80919 .601581.79881 .61543 .78819 .62909 .77733 .64256 .76623 1 60 .58779 .80902 .60182 .79864 .61566 .78801 . 62932 .77715 .64279 .76604 | Cosin Sine" Cosin Sine Cosin j Sine Cosin Sine Cosin Sine / 54 53 52 51' 50 233 TABLE XV. NATURAL SINES AND COSINES. 40 41 42 43* 44 J Sine ICosin Sine Cosin Sine 1 Cosin Sine ! Cosin Sine Cosin .64279 .76604 .65606 .75471 .00913 .74314 .68200 .73135 769466 .71934 60 1 .64301 .76586 .65628 .75452 .60935 .74295 .68221 .73116 .69487 .71914 59 2 .64323 .76567 .65650 .75433 .60956 .74276 .68242 .73090 .69508 .71894 58 3 .61316 .70548 .65672 .75414 .60978 .74256 .68204 .730?'6 . 69529 ! . 71873: 57 4 .04368 .76530j .65694 .75395 .00399 .74237 .68285 .73056 .69549 .71853 56 5 .64390 .76511 .65716 .75375 .67021 .74217 .68306 .73036 .69570 .71833 55 6 .64412 .76402 .65738 .75356 .67043 .74198 .68327 .73016 .69591 .718131 54 7 .64435 .76473 .65759 .75337 .67064 .74178 .68349 .72996 .69012 .71792 53 8 .64457 .76455 .65781 .75318 .67083 .74159 .68370 .72976 .696331.71772 52 9 .64479 .78438 .65803 . 75299 . 67107 ! . 74139 .68391 72957 . 69654 !. 71 752! 51 10 .64501 .76417 .65825 .75280 .67129 .74120 .68412 ! 72937 j .69675 .71732 50 11 .64524 .76398 .65847 .75281 .67151 .74100 .68434 .72917 .69696 .71711 49 IS .64546 .76330 .65363 .75241 .67172 .74080 .68455 .72897 .68717 .71 691 i 48 13 .64568 .76331 .65891 .75222 .67194 .74001 .68476 .72877 .69737 .71671 47 14 .64590 76342 .65913 .75203 .67215 .74041 .68497 .72857 . 69758 i. 71 650 46 15 .64612 .76323 .65935 .75184 .67237 .74022 .68518 .72837 .69779 .71630! 45 16 .64635 .76304 .65956 .75165 .67258 .74002 .68539 .72817 .69800 .716101 44 17 .64857 .76236 .65978 .75146 .67280 .73983 .68561 .72797 .69821 .71590 43 18 .646791.76207 .66000 .75128 .67301 .73963 .68582 .72777 .69842 .71569 42 19 .64701 .76248 .65022 .75107! .67323 .73944 .68603 .72757 .698621.71549 41 20 .64723 .76229 .66044 . 75088 ! .67344 .73924 .68624 .72737 .69883 .71529 40 21 .64746 .76210 .66066 . 75039 ! .67386 .73904 .68645 .72717 .69904 .71508 39 22 .64768 .7611)2 .63333 75350 .67087 .73885 .68006 .72697 .69325 .71488 38 23 .64790 .761731 .68103 75330 .67409 .7'3835 .63G88 .72677 .69946 .71468 37 24 .64812 .761541 .66131 75011 i .67430 .73848 .637'09 .7'2G57 .69968 .71447 36 25 .64834 . 78135 | .66153 74332 | .67452 .73823 .68730 .72637 .69987 .71427 35 26 .64856 1.761 16 ! .63175 74373 ! .67473 .73803 .63751 .72617! .70008 .71407 34 27 .64878 .76037! .65197 74353 .67435 .73787 .68772 .72597; .70029 .71386 33 28 .64901 .76078 .63218 74334 .67516 .73767 .68793 . 72577 ' .70049 .71306 32 29 .64923 .76059! .68240 74915 .67533 .73747 .63814 .72557 .70070 .71345 31 30 .64945 .76041! .68282 74896 .67559 .73728 .68835 .72537; .7'0091 .71325 30 31 .61967 .76022! .68284 74876 ' .67580 .73703 .68857 .72517 .70112 .71305 29 32 .64989 .76003' .66308 74857! .67632 .73383 .63878 . 72497 : 70132 .71284 28 33 .65011 .75934; .66327 74838 .67023 .73633 .63899 .72-477! .70153 .71264 27 34 .65033 .75985; .66349 74818 ! .67645 .73649 .68920 .72457 .70174 .71243 26 35 .65055|.75946 : 66371 74799 ! .67666 .73623 .68341 .72437 .70195 .71223 35 36 .65077 .75927 .66393 74780 ! .67688 .73610 .68982 .724171 .70215 .71203 24 37 .65100 .759:38 .6641 4 1. 74760 ! .67709 .73590 .68983 .72397 .70236 .71182 23 38 .651221.75889 .66438 .74741 .67730 7357'0 .69004 .72377 .70257 .71162 22 39 .65144 .75870 .68458 .74722; .67752 .73551 .69025 .72357 .70277 .71141 21 40 .65166 .75851, .66480 .74703 .67773 .73531 .69046 .72337 .70238 .71121 20 41 .65188 .75832 .66501 .74683 .67795 .73511 .69067 .72317 .70319 .71100 19 42 .65210 .75813 .68523 .74664! .67816 .73491 .63088 .72297 .70339 .71080 18 43 .65232 .75794 .68545 . 74844 .67837 .73472 .09109 .72277 .70360 .71059 17 44 .65254 .75775: .66566 .74325, .67859 .73452 .69130 . 72257 .70381 .71039 16 45 .65276 .75756 .66588 .74603 .67880 .73432 .09151 .72236 .70401 .71019 15 46 .65298 .75738: .66610 .74586 .67901 .73413 69172 722:6 .70422 .70998 14 47 .65320 .75719 .66832 .74567' .67923 .73393 .69193 .72196 .70443 .70978! 13 48 .65342 .75700 .66653 .74548 .67944 .73373 .69214 .72176 .70403 .70957! 12 49 1.65364 .75680 .66675 .74528 .67965 .73353 .69235 .72156 .70484 .70937 11 50 .65386 .75661 .66697 .74509 .67987 .73333 .69256 .72136 .70505 .70916 10 51 .65408 .75642 .66718 .74489 .68008 .73314 .69277 .72116 .70525 .70896 9 52 1.65430 .75623 .66740 .74470 .68029 .73234 .69298 .72095 .70540 .70375 8 53 .65452 .75604 .66762:.74451 .68051 .73274 .69319 .72075 .70567 1.70855 7 54 .65474 .75585: .66783 .74431 .68072 .73254 .69,340 . 72055 i .70587 .70834 6 55 .65496 '75566! .66805 .74412 .68093 .73234 .69361 .72035! .70008 .70813 5 56 .655181.75547 .66827 .74392 1 .68115 .73215 .69382 .72015 .70628 .70793 4 57 .65540 .75528 .66848 .74373 1 .68136 .73195 .69403 .71995 .70649 .70772 3 58 .65562 .75509 .668701.74358 .68157 .73175 .69424 .711,74 .70070 .70752 2 59 .65584 .75490 .66891 .74334 .68179 .73155 .69445 .71954 .70690 .70731 1 60 .65606 .75471 .00913 .74314! .68200 .73135 .69466 .71934 .70711 .70711 / Cosin Sine Cosin Sine | Cosin . Sine Cosin Sine Cosin | Sine / 49 48 il -47 46 45 234 TABLE XVI. NATURAL TANGENTS AND COTANGENTS. 1 2 3 **" Tang Cotang Tang Cotang Tang Cotang ! Tang | Cotang / .00000 In Unite. .01746 57.2900 .03492 28.6363 .05241 19.0811 |60 1 .00029 3437.75 .01775 56.3506 .03521 28.3994 .05270 18.9755 59 2 .00058 1718.87 .01804 55.4415 .03550 28.1664 .05299 18.8711 58 3 .00087 1145.92 .01833 54.5(313 .03579 27.9372 .05328 18.7678 57 4 .00116 859.436 .01862 53.7086 .03609 27.7117 .05357 18.6656 56 5 .00145 687.549 .01891 52.8821 .03638 27.4899 .05387 18.5645 55 6 .00175 572.957 .01920 52.0807 .03667 27.2715 .05416 18.4645 54 7 .00204 491.106 .01949 51.3032 .03696 27.0566 .05445 18.3655 53 8 .00233 429.718 .01978 50.5485 .03725 26.8450 .05474 18.2677 52 9 ,00262 381.971 .02007 49.8157 .03754 26.6367 .05503 18.1708 51 10 .00291 343.774 .02036 49.1039 .03783 26.4316 .05533 18.0750 50 11 .00320 312.521 .02066 48.4121 .03812 26.2296 .05562 17.9802 49 12 .00349 286.478 .02095 47.7395 .03842 26.0307 .05591 17.8863 48 13 .00378 264.441 .02124 47.0853 .03871 25.8348 .05620 17.7934 47 14 .00407 245.552 .02153 46.4489 .03900 25.6418 .05649 17.7015 46 15 .00436 229.182 .02182 45.8294 .03929 25.4517 .05678 17.6106 45 16 .00465 214.858 .02211 45.2261 .03958 25.2644 .05708 17.5205 44 17 .00495 202.219 .02240 44.6386 .03987 25.0798 .05737 17.4314 43 18 .00524 190.984 .02269 44.0661 .04016 24.8978 .05766 17.3432 42 19 .00553 180.932 .02298 43.5081 .04046 24.7185 .05795 17.2558 41 20 .00582 171.885 .02328 42.9641 .04075 24.5418 .05824 17.1693 40 21 .00611 163.700 .02357 42.4335 .04104 24.3675 .05854 17.0837 39 22 .00640 156.259 .02386 41.9158 .04133 24.1957 .05883 16.9990 38 23 .00669 149.465 .02415 41.4106 .04162 24.0263 .05912 16.9150 37 21 .00698 143.237 .02444 40.9174 .04191 23.8593 .05941 16.8319 36 25 .00727 137.507 .02473 40.4358 .04220 23.6945 .05970 16.7496 35 2(5 .00756 132.219 ,02502 39.9655 .04250 23.5321 .05999 16.6681 34 27 .00785 127.321 .02531 39.5059 .04279 23.3718 .06029 16.5874 33 28 .00815 122.774 .02560 39.0508 .04308 23.2137 .06058 16.5075 32 29 .00844 118.540 .02589 38.6177 .04337 23.0577 .06087 16.4283 31 30 .00873 114.589 .02619 38.1885 .04366 22.9038 .06116 16.3499 30 31 .00902 110.892 .02648 37.7686 .04395 22.7519 .06145 16.2722 29 32 .00931 107.426 .02677 37.3579 .04424 22.6020 .06175 16.1952 28 33 .00960 104.171 .02706 36.9560 .04454 22.4541 .06204 16.1190 27 34 .00989 101.107 .02735 36.5627 .04483 22.3081 .06233 16.0435 26 35 .01018 98.2179 .02704 3G.1776 .04512 22.1640 .06262 15.9687 25 86 .01047 95.4895 .02793 35.8006 .04541 22.0217* .06291 15.8945 24 37 .01076 92.9085 .02822 35.4313 .04570 21.8813 .06321 15.8211 23 38 .01105 90.4633 .02851 35.0695 .04599 21.7426 .06350 15.7483 22 :-;i) .01135 88.1436 .02881 34.7151 .04628 21.6056 .06379 15.6762 21 40 .01164 85.9398 .02910 34.3678 .04658 21.4704 .0&408 15.6048 20 41 .01193 83.8435 .02939 34.0273 .04687 21.3369 .06437 15.5340 19 42 .01222 81.8470 .02968 33.6935 .04716 21.2049 .06467 15.4638 18 43 .01251 79.9434 .02997 33.3662 .04745 21.0747 .06496 15.3943 17 44 .01280 78.1263 .03026 33.0452 .04774 20 9460 .06525 15.3254 16 45 .01309 76.3900 .03055 32.7303 .04803 20.8188 .06554 15.2571 15 46 .C1338 74.7292 .03084 32.4213 .04833 20.6932 .06584 15.1893 14 47 .01367 73.1390 .03114 32.1181 .04862 20.5691 .06613 15.1222 13 48 .01396 71.6151 .03143 31.8205 .04891 20.4465 .06642 15.0557 12 4') .01425 70.1533 .03172 31.5284 .04920 20.3253 .06671 14.9898 11 50 .01455 68.7501 .03201 31.2416 .04949 20.2056 .06700 14.9244 10 51 .01484 67.4019 .03230 30.9599 .04978 20.0872 .06730 14.8596 9 52 .01513 66.1055 .03259 30. 6833 .057 19.9702 .06759 14.7954 8 53 .01542 64.8580 .03288 30.4116 .05037 19.8546 .06788 14.7317 7 54 .01571 63.6567 .03317 30.1446 .05066 19.7403 .06817 14.6685 6 55 .01600 62.4992 .03346 29.8823 .05095 19.6273 .06847 14.6059 5 50 .01629 61.3829 .0:3376 29.6245 .05124 19.5156 .06876 14.5438 4 57 .01658 60.3058 .03405 29.3711 .05153 19.4051 .06905 14.4823 3 58 .01687 59.2659 .03434 29.1220 .05182 19.2959 .06934 14.4212 2 59 .01716 58.2612 .03463 28.8771 .05212 19.1879 .06963 14.3607 1 60 .01746 57.2900 .03492 28.6363 .05241 19.0811 .06993 14.3007 f Cotang Tang Cotang Tang Cotang Tang Cotang | Tang t 89 88 87 86 235 TABLE XVI. NATURAL TANGENTS AND COTANGENTS. i 1 5 ( 5 i r Tang Cotang Tang Cotang Tang Cotang Tang Cotang / .06993 14.3007 .08749 11.4301 I .10510 9.51436 .12278 8.14435 (50 1 .07022 14.2411 .08778 11.3919 .10540 9.487'81 .12308 8.12481 59 2 .07051 14.1821 .08807 11.3540 i .10569 9.46141 .12338 8.10530 68 3 .07080 14.1235 .08837 11.3163 . 10599 9.43515 .12307 8.08600 57 4 .07110 14.0655 .08866 11.2789 .10628 9.40904 .12397 8.06074 56 5 .07139 14.0079 .08895 11.2417 .10657 9.38307 .12426 8.04756 55 .07168 13.9507 .08925 11.2048 .10687 9.35724 .124E6 8.02848 54 7 .07197 13.8940 .08954 11.1681 .10716 9.33155 .12485 8.00948 53 8 .07227 13.8378 .08983 11.1316 .10746 9.30599 .12515 7.99058 52 g .07256 13.7821 .09013 11.0954 .10775 9.28058 12544 7.97176 51 10 .07'285 13.7267 .09042 11.0594 .10805 9.25530 ! 12574 7.95302 50 11 .07314 13.6719 .09071 11.0237 .10834 9.23016 .12603 7.93438 40 12 .07344 13.6174 .09101 10.9882 .10SC3 9.2C516 .1CGS3 7.91C82 4* 13 .07373 13.5634 .09130 10.9529 .10893 9.18028 .12GG2 7.89734 47 14 .07402 13.5098 .09159 10.9178 .10922 9.15554 .120C2 7.87895 40 15 .07431 13.4566 .09189 10.8829 1CG52 9.13093 .12722 7.86064 45 1C .07461 13.4039 .09218 10.8483 !lC981 9.1C646 .12751 7.84242 44 17 .07490 13.3515 .09247 10.8139 .11C11 9.08211 .12781 7.82428 43 18 .07519 13.2996 .09277 10.7797 .11010 9.05789 .12810 7.80022 42 1!) .07548 13.2480 .09306 10.7457 .11C70 9.03379 .12840 7.78825 41 20 .07578 13.1969 .09335 10.7119 .11099 9.C0983 .12869 7.77035 40 21 .07607 13.1461 .09365 10.6783 .11128 8.S8598 .12899 7 . 75254 39 22 .07636 13.0958 .09394 10.6450 .inns 8.902*7 .12929 7.7'8480 88 23 .07665 13.0458 .09423 10.6118 .11187 8. 3867 .12958 7.71715 37 24 .07695 12.9962 .09453 10.5789 .11217 8.91520 .12988 7.C9957 30 25 .07724 12.9469 .09482 10.5462 .11246 8.89165 .13017 7.68208 85 20 .07753 12.8981 .C9511 10.5136 .11276 8.868C2 .13047 7.66466 84 27 .07782 12.8496 .C9541 10.4813 .11205 8.84551 .13076 7.64732 S3 28 .07812 2.8014 .09570 10.4491 .11S35 8.82252 .13106 7.63005 29 .07841 2.7536 .09600 10.4172 .11804 8.79964 .13126 7.61287 31 30 .07870 2.7062 .09629 10.3854 .11394 8.77689 .13165 7.59575 30 31 .07899 2.6591 .09658 10.3538 .11423 8.75425 .13105 7.57872 20 32 .07929 2.6124 .09668 10.3224 .11452 8.73172 .13224 7.50176 28 33 .07958 2.5660 .09717 10.2913 .11482 8.70931 .12254 7.54487 27 34 .07987 12.5199 .09746 10.2602 .11511 8.68701 .13284 7.52806 26 35 .08017 12.4742 .09776 10.2294 .11541 8.66482 .13313 7.51132 25 36 .08046 12.4288 .09805 10.1988 .11570 8.6427'5 .13343 7.49465 24 37 .08075 12.3838 .09834 10.1683 .11600 8.62078 .13372 7.47806 23 38 .08104 12.3390 .09864 10.1381 .11629 8.59893 .13402 7.40154 22 89 .08134 12.2946 .09893 10.1C80 .11659 8.57718 .13422 7.44509 21 40 .08163 12.2505 .09923 10.0780 .11688 8.55555 .13461 7.42871 20 41 .08192 12.2067 .09952 10.0483 .11718 f 53402 .13491 7.41240 10 42 .08221 12.1032 .09981 10.0187 .11747 8.51259 .13521 7.39616 18 43 .08251 12.1201 .icon 9.98931 .11777 8.49128 .13550 7.37999 17 44 .08280 12.0772 .10040 9.96007 .11806 8.47007 . 13580 7.30389 10 45 .08309 12.0346 .10069 9.93101 .11836 8.44896 .13609 7.34786 15 46 .08339 11.9923 .10099 9.90211 .11805 8.42795 .13639 7.83190 14 47 .08368 11.9504 .10128 9.87338 .11895 8.40705 .13609 7.31600 13 48 .08397 11.9087 .10158 9.84482 .11924 8.38625 .13698 7.30018 12 49 .08427 11.8673 .10187 9.81641 .11954 8.36555 .13728 7.28442 11 50 .08456 11.8262 .10216 9.7'8817 .11983 8.34496 .13758 7.26873 10 51 J08485 11.7853 .10246 8.76009 .12013 8.32446 .13787 7.25310 9 52 .08514 11.7448 .10275 9.73217 .12042 8.30406 .13817 7.23754 8 53 .08544 11.7045 .10305 9.70441 .12072 8.28376 .13846 7.22204 f 54 .08573 11.6645 .10334 9.67680 .12101 8.26355 .13876 7.20661 55 .08602 11.6248 .10363 9.64935 .12131 8.24345 .13906 7.19125 5 56 .08632 11.5853 .10393 9.62205 .12160 8.22344 .13935 7.17594 4 57 .08661 11.5461 .10422 9.59490 .12190 8.20352 .13965 7.16071 3 58 .08690 11.5072 .10452 9.56791 .12219 8.18370 .13995 7.14553 2 59 .08720 11.4685 .10481 9.54106 .12249 8.16398 .14024 7.13042 1 60 .08749 11.4301 .10510 9.51436 .12278 8.14435 .14054 7.11537 / Cotang Tang Cotang Tang Cotang Tang Cotang Tang / 8 5 3 4 8 3 8 3 236 TABLE XVI. NATURAL TANGENTS AND COTANGENTS. 8 9 10 11 Tang Cotang Tang Cotang Tang Cotang Tang Cotang ~ .14054 7.11537 .15838 6.31375 .17633 5.67128 .19438 5.14455 60 1 .14084 7.10038 .15868 6.30189 .17663 5.66165 .19468 5.13658 59 2 .14113 7.08546 .15898 6.29007 .17693 5.65205 .19498 5.12862 58 3 , 14143 7.07059 .15928 6.27829 .17723 5.64248 .19529 5.12069 57 4 .14173 7.0.5579 .15958 6.26655 .17753 5.63295 .19559 5.11279 56 5 .14202 7.04105 .15988 6.25486 .17783 5.62344 .19589 5.10490 55 81 .14232 7.02637 .16017 6.24321 .17813 5.61397 .19619 5.09704 54 7 .14262 6.91174 .16047 6.23160 .17843 5.60452 .19649 5.08921 53 8 .14291 6.99718 .16077 6.22003 .17873 5.59511 .19680 5.08139 52 9 .14321 6.98268 .16107 6.20851 .17903 5.58573 .19710 5.07360 51 10 .14351 6.96823 .16137 6.19703 .17933 5.57638 .19740 5.06584 50 11 .14381 6.95385 .161G7 6.18559 .17963 5.56706 .19770 5.05809 49 12 .14410 6.93952 .10193 6.17419 .17993 5.55777 .19801 5.05037 48 13 .14440 6.92525 .16226 6.16283 .18023 5.54851 .19831 5.04257 47 14 .14470 6.91104 .1G256 6.15151 .18053 5.53927 .19861 5.03499 46 15 .14499 6.89088 .16286 6.14023 .18033 5.53007 .19891 5.02734 45 16 .14529 6.83278 .16316 6.12399 .18113 5.52090 .19921 5.01971 44 17 .14559 6.83874 .16346 6.11779 .18143 5.51176 .19952 5.01210 43 18 .14533 6.85475 .16376 6.10364 .10173 5.50264 .19982 5.00451 42 19 .14618 6.84032 .16405 6.09552 .18203 5.49356 .20012 4.99695 41 20 .14048 6.82694 .16435 6.08444 .18233 5.48451 .20042 4.98940 40 21 .14673 6.81312 .16465 6.07340 .18263 5.47548 .20073 4.98188 39 22 .147'07 6.79036 .16495 6.03240 .10293 5.46648 .20103 4.974J38 38 23 .14737 6 . 70564 .16525 6.05143 .10323 5.457'51 .20133 4.96690 37 24 .14767 6.77199 .10555 6.04051 .18353 5.44857 .20164 4.95945 36 25 .14796 6.75838 .16535 6.02932 .18384 5.43966 .20194 4.95201 35 26 .14826 6.74483 .16615 6.01878 .18414 5.43077 .20224 4.94460 34 27 .14856 6.73133 .16645 6.00797 .10444 5.42192 .20254 4.93721 33 28 .14885 6.71789 .16674 5.99720 .10474 5.41309 .20285 4.92984 32 29 .14915 6.70450 .16704 5.93346 .10504 5.40429 .20315 4.92249 31 30 .14945 6.69116 .16734 5.97576 .18534 5.39552 .20345 4.91516 30 31 .14975 6.67787 .16764 5.96510 .18564 5.38677 .20376 4.90785 29 3;3 .15005 G. 63463 .16794 5.95448 .18594 5.37805 .20406 4.90056 28 83 .15034 6.65144 .16324 5.94390 .18624 5.36936 .20436 4.89330 27 34 .15064 6.63831 .16854 5.93335 .18654 5.3607-0 .20466 4.88605 26 35 .15094 6.62523 .16834 5.92283 .10684 5.35206 .20497 4.87882 25 36 .15124 6.61219 .16914 5.91236 .10714 5.34345 .20527 4.87162 24 37 .15153 6.59921 .16944 5.90191 .10745 5.33487 .20557 4.86444 23 38 .15183 6.58627 .16974 5.83151 .18775 5.32631 .20588 4.85727 22 39 .15213 6.5733.1 .17004 5.83114 .10805 5.31778 .20618 4.85013 21 40 .15243 6.56055 .175083 5.87080 .18835 5.30928 .20648 4.84300 20 41 .15272 6.54777 .17063 5.86051 .18865 5.30080 .20679 4.83590 19 42 .15302 6.53503 .17003 5.85024 .10895 5.29235 .207C9 4.82882 18 43 .15332 6.52234 .17123 5.84001 .10925 5.20393 .20739 4.82175 17 44 .15362 6.50970 .17153 5.82982 .10955 5.27553 .20770 4.81471 16 45 .15391 6.49710 .17183 5.81966 .10986 5.23715 .20800 4.00769 15 46 .15421 6.48456 .17213 5.80953 .19016 5.25880 .20830 4.00068 14 47 .15451 6.47206 .17243 5.79944 .19046 5.25048 .20861 4.79370 13 48 .15481 6.45931 .17273 5.73938 .1907'6 5.24213 .20391 4.7'8673 12 48 .15511 6.44720 .17303 5.77936 .19106 5.23391 .20921 4.77978 11 50 .15540 6.43484 .17333 5.76937 .19136 5.22566 .20952 4.77286 10 51 .15570 6.42253 .17363 5.75941 .19166 5.21744 .20982 4.76595 9 52 .15600 6.41026 .17393 5.74949 .19197 5.20925 .21013 4.75906 8 53 .15630 6.30804 .17423 5.73960 .19227 5.20107 .21043 4.75219 7 54 .15660 6.38587 .17453 5.72974 .19257 5.19293 .21073 4.74534 6 55 .15689 6.37374 .17483 5.71992 .19287 5.18480 .21104 4.73851 5 56 .15719 6.36165 .17513 5.71013 .19317 5.17671 .21134 4.73170 4 57 .15749 6.34961 .17543 5.70037 .19347 5.16863 .21164 4.72490 3 58 .15779 6.33761 .17573 5.69064 .19378 5.16058 .21195 4.71813 2 59 .15809 6.32566 .17603 5.68094 .19408 5.15256 .21225 4.71137 1 60 .15838 6.31375 .17633 5.67128 .19438 5.14455 .21256 4,70463 / Cotang Tang Cotang Tang Cotang Tang Cotang Tang / 81 80 1 79 78 1 237 TABLE XVI. -NATURAL TANGENTS AND COTANGENTS. 12 13 14 15 | Tang Cotang Tang Cotang Tang Cotang Tang It .21256 4.70463 .23087 4.33148 .249J33 4.01078 .26795 3.73205 60 1 .21286 4.69791 .23117 4.32573 .24964 4.00582 .26826 3.72771 59 2 .21316 4.69121 .23148 4.32001 .24995 4.00086 .26857 3.72338 58 3 .21347 4.68452 .23179 4.31430 .25026 3.99592 .26888 3.71907 57 4 .21377 4.67786 .23209 4.30860 .25056 3.99099 .26920 3.71476 56 5 .21408 4.67121 .23240 4.30291 .25087 3.98607 .26951 3.71046 55 6 .21438 4.66458 .23271 4.29724 .25118 3.98117 .26982 3.70616 54 7 .21469 4.65797 .23301 4.29159 .25149 3.97627 .27013 3.70188 53 8 .21499 4.65138 .23332 4.28595 .25180 3.97139 .27044 3.69761 52 9 .2159 4.64480 .23363 4.28032 .25211 3.96651 .27076 3.69335 51 10 .21560 4.63825 .23393 4.27471 .25242 3.96165 .27107 3.68909 50 11 .21590 4.63171 .23424 4.26911 .25273 3.95680 .27138 3.68485 49 12 .21621 4.62518 .23455 4.26352 i .25304 3.95196 .27169 3.68061 48 13 .21651 4.61868 .23485 4.25795 .25335 3.94713 .27201 3.67638 47 14 .21682 4.61219 .23516 4.25239 .25366 3.94232 .27232 3.67217 46 15 .21712 4.60572 .23547 4.24685 .25397 3.93751 .27263 3.66796 45 16 .21743 4.59927 .23578 4.24132 .25428 3.93271 .27294 3.66376 44 17 .21773 4.59283 .23608 4.23580 .25459 3.92793 .27326 3.65957 43 18 .21804 4.58641 .23639 4.23030 .25490 3.92316 .27357 3.65538 42 19 .21834 4.58001 .23670 4.22481 .25521 3.91839 .27388 3.65121 41 20 .21864 4.57363 .23700 4.21933 .25552 3.91364 .27419 3.64705 40 21 .21895 4.56726 .23731 4.21387 .25583 3.90890 .27451 3.64289 39 22 .21925 4.56091 .23702 4.20842 .25614 3.90417 .27482 3.63874 38 23 .21956 4.55458 .23793 4.20298 .25645 3.89945 .27513 3.63461 37 24 .21986 4.54826 .23823 4.19756 .25676 3.89474 .27545 3.68048 36 25 .22017 4.54196 .23854 4.19215 .25707 3.89004 .27576 3.62636 35 26 .22047 4.53568 .23885 4.18675 .25738 3.88536 .27607 3.62224 34 27 .22073 4.52941 .23916 4.18137 .25769 3.88068 .27638 3.61814 33 28 .22108 4.52316 .23946 4.17600 .25800 3.87601 .27670 3.61405 32 29 .22139 4.51693 .23977 4.17064 .25831 3.87136 .27701 3.G0996 31 30 .22169 4.51071 .24008 4.16530 .25862 3.86671 .27732 3 G0588 30 31 .22200 4.50451 .24039 4.15997 .25893 3.86208 .27764 3.60181 29 -J .22231 4.49832 .24069 4.15465 .25924 3.85745 .27795 3 . 59775 23 33 .22261 4.49215 .24100 4.14934 .25955 3.85284 i .27826 3.59370 27' 34 .22292 4.48600 .24131 4.14405 .25986 3.84824 .27858 3.58966 26 35 .22322 4.47986 .24162 4.13877 .26017 3.84364 .27889 3.58562 25 36 .22353 4.47374 .24193 4.13350 .26048 3.83906 .27921 3.58160 24 37 .22383 4.46764 .24223 4.12825 26070 3.83449 .27952 3.57758 23 33 .22414 4.46155 .24254 4.12301 .26110 3.82992 ! .27983 3.57357 22 SO .22444 4.45548 .24285 4.11778 .26141 3.82537 .28015 3.56957 ;:i 40 .22475 4-44942 .24316 4.11256 .26172 3.82083 .28046 3.56557 20 41 .22505 4.44338 .24347 4.10736 .26203 3.81630 .28077 3.56159 10 42 .22536 4.43735 .24377 4.10216 .26235 3.81177 .28109 3.557'61 18 43 .22567 4.43134 .24408 4.09699 .26266 3.80726 .28140 3.55364 17 44 .22597 4.42534 .24439 4.09182 .26297 3.80273 .28172 3.54968 16 45 .22G28 4.41936 .24470 4.08666 .26328 3.79827 .28203 3.54573 15 46 .22658 4.41340 .24501 4.08152 .26359 3.79378 .28234 8.540 14 47 .22089 4.40745 .24532 4.07639 .26390 3.78931 .28266 3.53785 13 48 .22719 4.40152 .24562 4.07127 .26421 3.784R5 .28297 3.53393 12 49 .22750 4.33560 .24593 4.06G16 .26452 3.78040 .28329 3.53001 11 50 .22781 4.38969 .24624 4.06107 .26483 3.77595 .28360 3.52609 10 51 .22811 4.38381 .24655 4.05599 .26515 3.77152 .28391 3.52219 9 52 .22842 4.37793 .24686 4.05092 .26546 3.76709 .28423 3.51829 8 53 .22872 4.37207 .24717 4.04586 .26577 3.76268 .28454 3.51441 7 54 .22903 4.36623 .24747 4.04081 .26608 3.75828 .28486 3.51053 6 55 .22934 4.36040 .24778 4.03578 .26639 S. 75388 .28517 3.50666 5 56 .22964 4.35459 .24809 4.03076 .26670 3.74950 .28549 3.50279 4 57 .22995 4.34879 .24840 4.02574 .26701 3.74512 .28580 3.49894 3 58 .23026 4.34300 .24871 4.02074 .26733 3.74075 .28612 3.49509 2 59 .23056 4.33723 .24902 4.01576 .26764 3.73640 .28643 3.49125 1 60 .23087 4.33148 .24933 4.01078 .26795 3.73205 .28075 3.48741 / Cotang Tang Cotang Tang Cotang Tang Cotang Tang / 77 76 1! 75 I 74 238 TABLE XVI. NATURAL TANGENTS AND COTANGENTS. 16 17 18 19 Tang Cotang Tang Cotang Tang Cotang Tang Cotang ' .28675 3.48741 .30573 3.27085 .J12492 3.07768 .34433 2.90421 60 1 .28706 3.48359 .30605 3.26745 .32524 3.07464 .34465 2.90147 59 2 .28738 3.47977 .30637 3.2&406 .32556 3.07160 .34498 2.89873 58 a .28769 3.47596 .30669 3.26067 .32588 3.06857 .34530 2.89600 57 4 .28800 3.47216 .30700 3.25729 .32621 3.06554 .34563 2.89327 56 5 .28832 3.46837 .30732 3.25392 .32.353 3.06252 .34596 2.89055 55 6 .288t>4 3.46458 .30764 3.25055 i .32685 3.05950 .34628 2.88783 54 7 .28895 3.46080 .30796 3.24719 .32717 3.05649 .34661 2.88511 53 S .28927 3.45703 .30828 3.24383 .32749 3.05349 .34693 2.88240 52 9 .28958 3.45327 .30860 3.24049 .327-82 3.05049 .34726 2.87970 51 10 .28990 3.44951 .30891 3.23714 .32814 3.04749 .34758 2 87700 50 11 .29021 3.44576 .30923 3.23381 .32846 3.04450 .34791 2.87430 49 12 .29053 3.44202 .30955 3.2:3048 .32878 3.04152 .34824 2.87161 48 13 .29084 3.43829 .30987 3.22715 .32911 3.03854 .34856 2.86892 47 14 .29116 3.43456 .31019 3.22384 .32943 3.03556 .34889 2.86624 46 15 .29147 3.43084 .31051 3.22053 .32975 3.03260 .34922 2.86356 45 16 .29179 3.42713 .31083 3.21722 .33007 3.02963 .34954 2.86089 44 17 .29210 3.42343 .31115 3.21392 .33040 3.02667 .34987 2.85822 43 19 .29242 3.41973 .31147 3.21063 .33072 3.02372 .85020 2.85555 42 19 .29274 3.41604 .31178 3.20734 .33104 3.02077 .35052 2.85289 41 20 .29305 3.41236 .31210 3.20406 .33136 3.01783 .35085 2.85023 40 21 .29337 3.40869 .31242 3.20079 .asie9 3.01489 .35118 2.84758 39 22 .29368 3.40502 .31274 3.19752 .3201 3.01196 .35150 2.84494 38 23 .29400 3.40136 .31306 3.19426 .332S3 3.00903 .35183 2.84229 37 24 .29432 3.39771 .31338 3.19100 .332G6 3.00611 .35216 2.83965 36 25 .29463 3.39406 .31370 3.18775 .33298 3.00319 .35248 2.83702 85 20 .29495 3.39042 .31402 3.18451 .3&330 3.00028 .35281 2.83439 34 27 .29526 3.38679 .31434 3.18127 .33363 2.99738 .35314 2.83176 83 28 .29558 3.38317 .31466 3.17804 .33395 2.99447 .35346 2.82914 82 29 .29590 3.37955 .31498 3.17481 .33427 2.99158 .35379 2.82653 31 80 .29621 3.37594 .31530 3.17159 .33460 2.98868 .35412 2.82391 30 51 .29653 3.37234 .31562 3.16838 .33492 2.98580 .35445 2.82130 29 32 .29685 3.36875 .31594 3.16517 .33524 2.98292 .35477 2.81870 28 33 .29716 3.36516 .31626 3.16197 .33557 2.98004 .35510 2.81610 27 34 .29748 3.36158 .31658 3.15877 .33589 2.97717 .35543 2.81350 28 :->5 .29780 3.35800 .31690 3.15558 .33621 2.97430 .35576 2.81091 25 36 .29811 3.35443 .31722 3.15240 .33654 2.97144 .35608 2.80833 24 37 .29843 3.3508? .31754 3.14922 .33686 2.96858 .35641 2.80574 23 38 .29875 3.34732 .31786 3.14605 .33718 2.96573 .35674 2.80316 22 39 .29906 3.34377 .31818 3.14288 .33751 2.96288 .35707 2.80059 21 40 .29938 3.34023 .31850 3.13972 .33783 2.96004 .35740 2.79802 20 41 .29970 3.33670 .31882 3.13656 .33816 2.95721 .35772 2.79545 19 42 .30001 3.33317 .31914 3.13341 .33848 2.95437 .35805 2.79289 18 43 .30033 3.32965 .31946 3.13027 .33881 2.95155 .85888 2.79033 17 44 .30065 3.32614 .31978 3.12713 .33913 2.9487'2 .85871 2.78778 10 45 .30097 3.32264 .32010 3.12400 .33945 2.94591 .35904 2.78523 15 46 .30123 3.31914 .32042 3.12087 .33978 2.94309 .35937 2.78269 14 47 .30160 3.31565 .32074 3.11775 .34010 2.94028 .35969 2.78014 13 48 .30192 3.31216 .32106 3.11464 .34043 2.93748 .36002 2.77761 12 49 .30224 3.30868 .32139 3.11153 .34075 2.93468 .36035 2.77507 11 50 .30255 3.S0521 .32171 3.10843 .34108 2.93189 .36068 2.77254 10 51 .30287 3.30174 .32203 3.10532 .34140 2.92910 .36101 2.77002 9 52 .30319 3.29829 .32235 3.10223 .34173 2.92632 .36134 2.76750 8 53 .30351 3.29483 .32267 3.09914 .34205 2.92354 .36167 2.76498 7 54 .30382 3.29139 .32299 3.09606 .34238 2.92076 .36199 2.76247 6 55 .30414 3.28795 .32331 3.09298 .34270 2.91799 .36232 2.75996 5 56 .30446 3.28452 .32363 3.08991 .34303 2.91523 .36265 2.75746 4 57 .30478 3.28109 .32396 3.08685 .34335 2.91246 .36298 2.75496 3 58 .30509 3.27767 .32428 3.08379 .34368 2.90971 .36331 2.75246 2 59 .30541 3.27426 .32460 3.08073 .34400 2.90696 .36364 2.74997 1 GO .3057-3 3.27085 .32492 3.077'08 .34433 2.90421 .36397 2.74748 _0 / Cotanr^ Tang Cotang Tang Cotang Tang Cotang Tang / 73 72 71 70 239 TABLE XVI. NATURAL TANGENTS AND COTANGENTS. 20 21 22 23 Tang Cotang Tang Cotang Tang Cotang Tang Cotang ' Oi .30397 2.74748 .88886 2.60509 .40403 2.47509 .42447 2.35585 00 1 .36430 2.74499 .38420 2.60283 .40436 2.47302 .42482 2.35395 51) c .36463 2.74251 .38453 2.60057 .40470 2,47095 .42516 2.35205 58 3 .36496 2.74004 .38487 2.59831 .40504 2.46888 .42551 2.35015 57 ^ .36529 2.73756 .38520 2.59606 .40538 2.46682 .42585 2.34825 50 5 .36562 2.73509 .38553 2.59381 .40572 2.46476 .42619 2.34636 55 G .36595 2.73263 .38587 2.59156 .40606 2.46270 .42654 2.34447 54 7 .36628 2.73017 .38620 2.58932 .40640 2.46065 .42688 2.34258 53 8 .36661 2.72771 .38654 2.58708 .40674 2.45860 4^722 2.34069 52 r .36694 2.72526 .38687 2.58484 .40707 2.45655 '.42757 2.33881 51 10 .36727 2.72281 .38721 2.58261 .40741 2.45451 .42791 2.33693 50 11 .36760 2.72036 .38754 2.58038 .40775 2.45246 .42826 2.33505 49 13 .36793 2.71792 .38787 2.57815 .40809 2.45043 .42800 2.33317 18 13 .36823 2.71548 .33821 2.57593 .40843 2.44839 .42894 2.33130 47 14 .36859 2.71305 .38854 2.57371 .40877 2.41636 .42929 2.32943 40 15 .36892 2.71062 .38888 2.57150 .40911 2.44433 .42963 2.32756 45 16 .36925 2.70819 .38921 2.56928 .40945 2.44230 .42998 2.32570 44 17 .36958 2.70577 .38955 2.56707 .40979 2.44027 .43032 2.32383 43 18 .36991 2.70335 .33983 2.56487 .41013 2.43025 .43007 2.32197 42 19 .37024 2.70094 .39022 2.56266 .41047 2.43623 .43101 2.32012 41 20 .37057 2.69853 .39055 2.56046 .41081 2.43422 .43136 2.31826 40 21 .37090 2.69612 .39089 2.55827 .41115 2.43220 .43170 2.31641 39 22 .37123 2.G9371 .33122 2.556G8 .41149 2.43019 .43205 2.31456 88 23 .37157 2.69131 .39156 2.55389 .41183 2.42319 .43233 2.31271 87 24 .37190 2.68892 .39190 2.55170 .41217 2.42618 .43274 2.31086 9Q 25 .37223 2.68653 .39223 2.54952 .41251 2.42418 .43308 2.30902 85 26 .37256 2.68414 .39257 2.54734 .41285 2.42218 .43343 2.30718 31 27 .37289 2.68175 .39290 2.54516 .41319 2.42019 .43378 2.30534 83 28 .37322 2 67937 .39324 2.54299 .41353 2.41019 .43412 2.30351 32 29 .37355 2.67700 .39357 2.54082 .41307 2. 41 020 .43447 2.30167 31 30 .37388 2.67462 .39391 2.53865 .41421 2.41421 .43481 2.29984 30 31 .37422 2.67225 .39425 2.53648 .41455 2.41223 .43516 2.29801 29 32 .37455 2.66989 .39458 2.53432 .41490 2.41025 .43550 2.29619 28 33 .37488 2.66752 .39492 2.53217 .41521 2.40827 .43585 2.29437 27 34 .37521 2.66516 .39526 2.53001 .41558 2.40629 .43620 2.29254 20 35 .37554 2.66281 .39559 2.52786 .41592 2.40432 .43654 2.29073 25 30 .37588 2.66046 .39593 2.52571 .41626 2.40235 .43689 2.28891 24 37 .37621 2.65811 .39626 2.52357 .41660 2.40038 .43724 2.28710 23 38 .37654 2.65576 .39660 2.52142 .41694 2.39841 .43758 2.28528 22 39 .37687 2.65342 .39694 2.519^9 .41728 2.39645 .43793 2.28348 21 40 .37720 2.65109 .39727 2.51715 .41763 2.39449 .43828 2:28167 20 41 .37754 2.64875 .39761 2.51502 .41797 2.39253 .43862 2.27987 19 42 .37787 2.64642 .39795 2.51289 .41831 2.3i*058 .43897 2.27806 18 43 .37820 2.64410 .39829 2.5107'6 .41865 2.38863 .43932 2.27'626 17 44 .37853 2.64177 .39862 2.50864 41899 2.38668 .43066 2.27'447 10 45 .37887 2.63945 .39896 2.50652 .41933 2.38473 .44001 2.27'267 15 46 .37920 2.63714 .39930 2.50440 .41968 2.38279 .44036 2.27'088 14 47 .37953 2.63483 .39963 2.50229 .42002 2.38084 .44071 2.20909 13 48 .37986 2.63252 .39997 2.50018 .42036 2.37891 .44105 2.26730 12 49 .38020 2.63021 .40031 2.49807 .4207'0 2.37697 .44140 2.26552 11 50 .38053 2.62791 .40065 2.49597 .42105 2.37504 .44175 2.26374 10 51 .38086 2.62561 .40098 2.49386 .42139 2.37311 .44210 2.26196 9 52 .38120 2.62332 .40132 2.49177 .42173 2.37118 .44244 2.26018 8 53 .38153 2.62103 .40166 2.48967 .42207 2.36925 .44279 2.25840 7 54 .38186 2.61874 .40200 2.487'58 .42242 2.36733 .44314 2.25663 55 .38220 2.61646 .40234 2.48549 .42276 2.36541 .44349 2.25486 5 56 .38253 2.61418 .40267 2 48340 .42310 2.36349 .44384 2.25309 4 57 .38286 2.61190 .40301 2.48132 .42345 2.36158 .44418 2.25132 3 58 .38320 2.60963 .40335 2.47924 .42379 2.35967 .44453 2.24956 2 59 38353 2.60736 .40369 2.47716 .42413 2.35776 .44488 2 24780 1 80 38386 2.60509 .40403 2.47509 .42447 2.35585 .44523 2.24604 / Cotang Tang Cotang Tang Cotang Tang Cotang Tang > 69 68 67 66 240 TABLE XVI. NATURAL TANGENTS AND COTANGENTS. 2 4 2 5 ! 2 6 2 7 Tang Cotang Tang Cotang Tang Cotang Tang Cotang .44523 2.24604 .46631 2.14451 .48773 2.05030 .50053 1.96261 60 1 .44558 2.24428 .46006 2.14288 .48809 2.04879 .50989 1.96120 59 2 .44593 2.24252 .46702 2.14125 .48845 2.04728 .51026 1.95979 58 3 .44627 2.24077 .46737 2.13963 .48881 2.04577 .51063 1.95838 57 4 .44062 2.23902 .46772 2.13801 .48917 2.04426 .51099 1.95698 56 5 .44697 2.23727 .46808 2.13639 .48953 2.04276 .51136 1.95557 55 6 .44732 2.23553 .46843 2.13477 .48989 2.04125 .51173 1.95417 54 7 .44767 2.23378 .46879 2.13316 .49026 2.03975 .51209 1.95277 53 8 .44802 2.23204 .46914 2.13154 .49062 2.03825 .51246 1.95137 5 9 .44837 2.230SO .46950 2.12993 .49098 2.03675 .51283 1.94997 51 10 .44872 2.22857 .46985 2.12832 .49134 2.03526 .51319 1.94858 50 11 .44907 2.22683 .47021 2.12671 .49170 2.03376 .51356 1.94718 49 12 .44942 2.22510 .47056 2.12511 .49206 2.0G227 .51393 1.94579 48 13 .44977 2.22337 .47'092 2.12350 .49242 2.03078 .51430 1.94440 47 11 .45012 2.22164 .47128 2.12190 .49278 2.02929 .51467 1.94301 40 15 .45047 2.21992 .47163 2.12030 .49315 2.02780 .51503 1.94162 45 10 .45082 2.21819 .47199 2.11871 .49351 2.02631 .51540 1.94023 44 17 .45117 2.21647 .47234 2.11711 .49387 2.02483 .51577 1.93885 43 18 .45152 2.21475 .47270 2.11552 .49423 2.02335 .51614 1.93746 42 10 .45187 2.21304 .47305 2.11392 .49459 2.02187 .51051 1.93608 41 20 .45222 2.21132 .47341 2.11233 .49495 2.02039 .51688 1.93470 40 21 .45257 2.20961 .47377 2.11075 .49532 2.01891 .51724 1.93332 39 22 .45292 2.20790 .47412 2.10916 .49508 2.01743 .51761 1.93195 38 23 .45327 2.20619 .47448 2.10758 .49004 2.01596 .51798 1.93057 37 84 .45362 2.20449 .47483 2.10600 .49040 2.01449 .51835 1.92920 30 25 .45397 2.20278 .47519 2.10442 .49677 2.01302 .61872 1.92782 35 20 .45432 2.20108 .47o55 2.10284 .49713 2.01155 .51909 1.92645 34 27 .45467 2.19938 .47590 2.10126 .497'49 2.01008 .51946 1.92508 33 28 .45502 2.19769 .47626 2.09909 .49786 2.00862 .51983 1.92371 32 21) .45538 2.10599 .47602 2.09811 .49822 2.00715 .52020 1.92235 31 30 .45573 2.19430 .47698 2.09654 .49858 2.00569 .52057 1.92098 30 31 .45608 2.19261 .47733 2.09498 .49894 2.00423 .52094 1.91962 29 32 .45643 2.19092 .47769 2.09341 .49931 2.00277 .52131 1.91826 28 33 .4567'8 2.18923 .47805 2.09184 .49967 2.00131 .52168 1.91690 27 34 .45713 2.18755 .47840 2.09028 .50004 1.99986 .52205 1.91554 26 35 .45748 2.18587 .47876 2.08872 .50040 1.99841 .52242 1.91418 25 30 .45784 2.18419 .47912 2.08716 .50076 1.99695 .52279 1.91282 24 37 .45819 2.18251 .47948 2.08560 .50113 1.99550 .52316 1.91147 23 38 .43854 2.18084 .47984 2.03405 .50149 1.99406 .52353 1.91012 22 39 .45889 2.17916 .48019 2.0;S250 .50185 1.99261 .52390 1.90876 21 40 .45924 2.17749 .48055 2.08094 .50222 1.99116 .52427 1.90741 20 41 .45960 2.17582 .48091 2.07939 .50258 1.98972 .52464 1.90607 19 42 .45995 2.17416 .48127 2.07785 .50295 1.98828 .52501 1.90472 18 43 .46030 2.17249 .48163 2.07630 .50331 .98684 .52538 1.90337 17 44 .46065 2.17083 .48198 2.07476 .50368 .98540 52575 1.90203 16 45 .46101 2.10917 .48234 2.07321 .50404 .98396 ! 52613 1.90069 15 46 .46136 2.16751 .48270 2.07167 .50441 .98253 .52650 1.89935 14 47 .46171 2.16585 .48306 2.07014 .50477 .98110 .52687 1.8C801 13 48 .46206 2.16420 .48342 2.06860 .50514 .97966 .52724 1.89667 12 49 .46242 2.10255 .48378 2.06706 .50550 .97823 .52761 J. 89533 11 50 .46277 2.1G090 .48414 2.06553 .50587 .97681 .52798 1.89400 10 51 .46312 2.15925 .48450 2.06400 .50623 .97538 .52836 1.89266 9 52 .46348 2.15760 .48486 2.06247 .50660 .97395 .52873 1.89133 8 53 .46383 2.15596 .48521 2.06094 .50696 .97253 .52910 1.89000 7 64 .46418 2.15432 .48557 2.05942 .50733 .97111 .52947 1.88867 6 55 .46454 2.15268 .48593 2.05790 .50769 .96969 .52985 1.88734 5 56 .46489 2.15104 .48629 2.05637 .50806 .96827 .53022 1.88602 4 57 .46525 2.14940 .48665 2.05485 .50843 .96685 .53059 1.88469 3 58 .46560 2.14777 .48701 2.05333 .50879 .96544 .53096 1.88337 2 50 .46595 2.14614 .48737 2.05182 .50916 .96402 .53134 1.88205 1 60 .46631 2.14451 .48773 2.050:30 .50953 .96261 .53171 1.88073 Cotang Tang Cotang Tang Cotang Tang Cotang Tang r 6 5 6 4 6 3 6 2 241 TABLE XVI. -NATURAL TANGENTS AND COTANGENTS. 2 8 2 9 l 1 3 3 1 Tang Cotang Tang Cotang Tang Cotang Tang Cotang .53171 1.88073 .554.91 1.80405 .57735 .73205 .60086 1.66428 60 1 .53208 1.87941 .55469 1.80281 .57774 .73089 .60126 1.66318 59 2 .53246 1.87809 .55507 1.80158 .57813 .72973 .60165 1.66209 58 3 .53283 1.87677 .55545 1.80034 .57851 .72857 .60205 1.60099 57 4 .53320 1.87546 .55583 1.79911 .57890 .72741 .60245 1.65990 56 5 .53358 1.87415 .55621 1.79788 .57929 .72625 .60284 1.65881 55 .53395 1.87283 .55659 1.79665 .57968 .72509 .60324 1.65772 54 7 .53432 1.87152 .55697 1.79542 .58007 .72393 .60364 1.65663 53 8 .53470 1.87021 .55736 1.79419 .58046 .72278 .60403 1.65554 52 9 .53507 1.86891 .55774 1.79296 .58085 .72163 .60443 1.65445 51 10 .53545 1.86760 .55812 1.79174 .58124 .72047 .60483 1.65337 50 11 .53582 1.86630 .55850 1.79051 .58162 .71932 .60522 1.65228 49 12 .53620 1.86499 .55888 1.78929 .58201 .71817 .60562 1.65120 48 18 .53657 1.86369 .55926 1.78807 .58240 .71702 .C0602 1.65011 47 14 .53694 1.86239 .55964 1.78685 .58279 .71588 .60642 1.64903 46 15 .53732 1.86109 .5G003 1.78563 .58318 .71473 .60681 1.64795 45 10 .53769 1.85979 .56041 1.78441 .58357 .71358 .60721 1.64687 44 17 .53807 1.85850 .56079 1.78319 .58396 .71244 .60761 1.64579 43 18 .53844 1.85720 .56117 1.78198 .58435 .71129 .60801 1.64471 42 19 .53882 1.85591 .50156 1.78077 i .58474 .71015 .60841 1.64363 41 20 .53920 1.85463 .56194 1.77955 .58513 .70901 .60881 1.64256 40 21 .53957 1.85333 .56232 1.77834 j .58552 .70787 .60921 1.64148 39 22 .53995 1.85204 .50270 1.77713 i .58591 .70673 .60960 1.64041 38 23 .54032 1.85075 .50309 1.77592 .58631 .70560 .61000 1.63934 37 24 .54070 1.84946 .56347 1.77471 .5867'0 .70446 .61040 1.63826 36 25 .54107 1.84818 .56385 1.77351 .58709 .70332 .61080 1.63719 35 26 .54145 1.84689 .56424 1.77230 .587'48 .70219 .61120 1.63612 34 27 .54183 1.84561 .50462 1.77110 .58787 .70106 .61160 1.63505 33 28 .54220 1.84133 .56501 1.76990 .58826 .C9992 .61200 1.63398 32 29 .54258 1.84305 .50539 1.76869 .588C5 1.69879 .61240 1.63292 31 oO .54296 1.84177 .56577 1.76749 .58905 1.69766 .61280 1.63185 30 31 .54333 1.84049 .56616 1.76629 .58944 1.69653 .61320 1.63079 29 32 .54371 1.83922 .56654 1.76510 .58983 1.69541 .61360 1.62972 28 33 .54409 1.83794 .56693 1.70390 .59022 1.69428 .61400 1.62866 27 34 .54446 1.83667 .56731 1.76271 .59061 1.69316 .61440 1.62760 26 35 .54484 1.83540 .56769 1.76151 .59101 1.69203 .61480 1.62654 25 30 .54522 1.83413 .56808 1.76032 .59140 1.69091 .61520 1.62548 24 37' .54560 1.83286 .56846 1.75913 .59179 1.68979 .61561 1.62442 23 38 .54597 1.83159 .56885 1.75794 .59218 1.68866 .61601 1.62336 22 39 .54635 1.83033 .56923 1 . 75675 .50258 1.C8754 .61641 1.62230 21 40 .54673 1.82906 .56962 1.75556 .59297 1.68643 .61681 1.62125 20 41 .54711 1.82780 .57000 1.75437 .59336 1.68531 .61721 1.62019 19 42 .547'48 1.82654 .57039 1.75319 .59376 1.68419 .61761 1.61914 18 43 .54786 1.82528 .57'078 1.75200 .59415 1.68308 .61801 1.61808 17 44 .54824 1.82402 .57116 1.75082 .59454 1.68196 .61842 1.61703 16 45 .54862 1.82276 .57155 1.74964 .59494 .68085 .61882 1.61598 15 46 .54900 1.82150 .57193 1.74846 .59533 .67974 .61922 1.61493 14 47 .54938 1.82025 .57232 1.74728 .59573 .67863 .61962 1.61388 13 48 .54975 1.81899 .57271 1.74610 .59612 .67752 .62003 1. 61283 12 49 .55013 1.81774 .57309 1.74492 .59651 .67641 .62043 1.61179 11 50 .55051 1.81649 .57348 1.74375 .59691 .67530 .62083 1.61074 10 51 .55089 1.81524 .57386 1.74257 .59730 .67419 .62124 1.60970 9 52 .55127 1.81399 .57425 1.74140 .59770 .67309 .62164 1.60865 8 53 .55165 1.81274 .57464 1.74022 .59809 .67198 .62204 1.60761 7 54 .55203 1.81150 .57503 1.73905 .59849 .67088 .62245 1.60657 6 55 .55241 1.81025 .57541 1.73788 .59888 .66978 .62285 1.60553 5 56 .55279 1.80901 .57580 1.73671 .59928 .66867 .62325 1.60449 4 57 .55317 1.80777 .57619 1.73555 .59967 1.66757 .62366 1.60345 3 58 .55355 1.80653 .57657 1.73438 .60007 1.66647 .62406 1.60241 2 59 .55393 1.80529 i .57696 1.73321 .60046 1.66538 .62446 1.60137 1 GO .55431 1.80405 1 .57735 1.73205 .60086 1.66428 .62487 1.60033 / Cotang Tang Cotang Tang Cotang Tang Cotang Tang 6 1 6 5 9 5 3 242 TABLE XVI. NATURAL TANGENTS AND COTANGENTS. 32 33 34 35 Tang Cotang Tang Cotang Tang Cotang Tang Cotang .62487 1.60033 .64941 1.53986 .67451 1.48256 J .70021 1.42815 60 1 .62527 1.59930 .64982 1.53888 .67493 1.48163 .70064 1.42726 59 2 .62568 1.59826 .65024 1.53791 .67536 1 48070 .70107 1.42638 58 3 .62608 1.59723 .65065 1.53693 .67578 1.47977 .70151 1.42550 57 4 .62649 1.59620 .65106 1.53595 .67620 1.47885 .70194 1.42462 56 5 .62689 1.59517 .65148 1.53497 .67663 1.47792 .70238 1.42374 55 6 .62730 1.59414 .65189 1.53400 .67705 1.47699 .70281 1.42286 54 7 .62770 1.59311 .65231 1.53302 .67748 1.47607 .70325 1.42198 53 8 .62811 1.59208 .65272 1.53205 .67790 1.47514 .70368 1.42110 52 9 .62852 1.59105 .65314 1.53107 .67832 1.47422 .70412 1.42022 51 10 .62892 1.59002 .65355 1.53010 .67875 1.47330 .70455 1.41934 50 11 .62933 1.58900 .65397 1.52913 .67917 1.47238 .70499 1.41847 49 12 .62973 1.58797 .65438 1.52816 .67960 1.47146 .70542 1.41759 48 13 .63014 1.58095 .65480 1.52719 .68002 1.47053 .70586 1.41672 47 14 .63055 1.58593 .65521 1.52622 .68045 1.46962 .70629 1.41584 46 15 .63095 1.58490 .65563 1.52525 .68088 1.46870 .70673 1.41497 45 16 .63130 1.58388 .65604 1.52429 .68130 1.46778 .70717 1.41409 44 7 .63177 1.58286 .65646 1.52a32 i .68173 1.46686 .70760 1.41322 43 18 .63217 1.58184 .65688 1.52235 .68215 1.46595 .70804 1.41235 42 19 .63258 1.58083 .65729 1.52139 1 .68258 1.46503 .70848 1.41148 41 20 .63299 1.57981 .65771 1.52043 j .68301 1.46411 .70891 1.41061 40 21 .63340 1.57879 .65813 1.51946 .68343 1.46320 .70935 1.40974 39 22 .63380 1.57778 .65854 1.51850 .68386 1.46229 .70979 1.40887 38 23 .63421 1.57676 .65896 1.51754 .68429 1.46137 .71023 1.40800 37 24 .63402 1.57575 .65938 1.51658 .68471 1.46046 .71066 1.40714 36 25 .63503 1.57474 .65980 1.51562 .68514 1.45955 .71110 1.40627 35 26 .63544 1.57372 .66021 1.51,466 .68557 1.45864 .71154 1.40540 *!4 27 .63584 1.57271 .00063 1.51370 .68600 1.45773 .71198 1.40454 33 28 .63625 1.57170 .66105 1.51275 .68642 1.45682 .71242 1.40367 32 29 .63666 1.57069 .C6147 1.51179 .68685 1.45592 .71285 1.40281 31 30 .63707 1.56969 .66189 1.51084 .68728 1.45501 .71329 1.40195 20 31 .63748 1.56868 .66230 1.50988 .68771 1.45410 .71373 1.40109 29 32 .63789 1.50767 .66272 1.50893 .C8814 1.45320 .71417 1.40022 28 33 .63830 1.56667 .66314 1.50797 .68857 1.45229 .714G1 1.39936 27 34 .63871 1.56566 .66356 1.50702 .68900 1.45139 .71505 1.39850 26 35 .63912 1.56466 .66398 1.50607 .68942 1.45049 .71549 1.39764 25 36 .63953 1.56366 .66440 1.50512 .08985 1.44958 .71593 1.39679 24 37 .63994 1.56205 .66482 1.50417 .69028 1.44868 .71637 1.39593 23 38 .64035 1.56165 .66524 1.50322 .69071 1.44778 .71681 1.39507 22 39 .64076 1.56065 .66506 1.50228 .69114 1.44688 .71725 1.39421 21 40 .64117 1.55966 .66608 1.50133 .69157 1.44598 .71769 1.39336 20 41 .64158 1.55866 .66650 1.50038 .69200 1.44508 .71813 1.39250 19 42 .64199 1.55766 66602 1.49944 .69243 1.44418 .7185 f 1.39165 18 43 .64240 1.55666 .66734 1.49849 .69288 1.44329 .71901 1.39079 17 44 .64281 1.55567 .66776 1.497'55 .69329 1.44239 .71946 1.38994 16 45 .64322 1.55467 .66818 1.49661 .69372 1.44149 .71990 1.38909 15 46 .64303 1.55368 .66860 1.49566 .69416 1.44060 .72034 1.38824 14 41 .64404 1.55269 .66902 1.49472 .69459 1.43970 .72078 1.38738 13 48 .64446 1.55170 .66944 1.49378 .69502 1.43881 .72122 1.38653 12 49 .64487 1.55071 .66986 1.49284 .69545 1.43792 .72167 1.385G8 11 50 .64528 1.54972 .67028 1.49190 .69588 1.43703 .72211 1.3S484 10 51 .64569 1.54873 .67071 1.49097 .69631 1.43614 .72255 1.38399 r 52 .64610 1.54774 .67113 1.49003 .09675 1.43525 .72299 1.38314 8 53 .64652 1.54675 .67155 1.48909 .69718 1.43436 .72344 1.38229 r 54 .64693 1.54576 .67197 1.48816 .69761 1.43347 ,72388 1.38145 6 5o .64734 1.54478 .67239 1.48722 .69804 1.43258 .72432 1.38060 P 5 .64775 1.54379 .67282 1.48629 .69847 1.43169 .72477 1.37976 4 5 .64817 1.54281 .67324 1.48536 .69891 1.43080 .72521 1.37891 f 5 .64858 1.54183 .67366 1.48442 .69934 1.42992 .72565 1.37807 2 5 .64899 1.54085 I .67409 1.48349 .69977 1.42903 .72610 1.37722 1 6 .64941 1.53986 j .67451 1.48256 .70021 1.42815 .72654 1.37638 Cotang | Tang Cotang | Tang Cotang Tang Cotang Tang i 57 ! 56 55 II 54 1 243 TABLE XVI. NATURAL TANGENTS AND COTANGENTS. 36 37 38 39 Tang Cotang Tang | Cotang Tang Cotang Tang 1 Cotang .72654 1.37638 .73865 1.32704 .78129 1.27994 .80978 1.23490 60 1 .72699 1.37554 .75401 1.32624 .78175 1.27917 .81027 1.23416 59 2 .72743 1.37470 .75447 1.32514 .78222 .27841 .81075 1.23343 5 ? 8 .72788 1.37386 .75492 1.32464 .78269 .27764 .81123 1.23270 57 4 .72832 1.37302 .75538 1.32384 ,.78316 .27688 .81171 1.23196 56 5 .72877 1.37218 .75584 1.32304 .78363 .27611 .81220 1.23123 55 6 .72921 1.37134 .75629 1.32224 .78410 .27535 .81268 1.23050 54 .72966 1.37050 .75675 1.32144 i .78457 1.27458 .81316 1.22977 53 B .73010 1.36967 .75721 1.32064 .78504 1.27382 .81364 1.22904 52 9 .73055 1.36883 .75767 1.31984 | .78551 1.27806 .81413 1.22831 51 10 .73100 1.36800 .75812 1.31904 .78598 1.27230 .81461 1.22758 50 11 .73144 1.36716 .75858 1.31825 .78645 1.27153 .81510 1.22685 49 I* .73189 1.36633 .75904 1.31745 .78692 1.27077 .81558 1.22612 48 13 .73234 1.36549 .75950 1.31666 .78739 1.27001 .81606 1.22539 47 14 .73278 1.36466 . 75996 1.31586 .78786 .26925 .81655 1.22467 46 15 .73323 1.36383 .76042 1.31507 .78834 .26849 .81703 1.22394 45 10 .73368 1.38300 .76088 1.31427 .78881 .26774 .81752 1.22321 44 17 .73413 1.36217 .76134 1.31348 .78928 .26698 .81800 1.22249 43 18 .73457 1.36134 .76180 1.31269 .7897'5 .26622 .81849 1.22176 42 19 .73502 1.38051 .76226 1.31190 .79022 .26546 .81898 1.22104 41 20 .73547 1.35968 .76272 1.31110 .79070 .26471 .81946 1.22031 40 21 .73592 1.35885 .76318 1.31031 .79117 1.2G395 .81995 1.21959 39 22 .73637 1.35802 ..76364 1.30952 .79164 1.26319 .82044 1.21886 38 23 .73681 1.35719 .76410 1.30873 .79212 1.2G244 .82092 1.21814 37 24 .73 72(i 1.35637 .76456 1.30795 .79259 1. 201 69 .82141 1.21742 36 25 .73771 1.35554 .76502 1.30716 .79306 1.20093 .82190 1.2167'0 35 26 .73816 1.35472 .76548 1.30637 .79354 1.2G018 .82238 1.21598 34 27 .73861 1.35389 .7'6594 1.30558 .79401 1.25943 .82287 1.21526 33 28 .73906 1.35307 .76640 1.30480 .79449 1.25867 .82336 1.21454 32 2!) .73951 1.35224 .76686 1.30401 .79496 1.25792 .82385 1.21382 31 30 .73996 1.35142 .76733 1.30323 .79544 1.25717 .82434 1.21310 30 31 .74041 1.35060 .76779 1.30244 .79591 1.25642 .82483 1.21238 29 32 .74086 1.34978 .76825 1.30166 .79639 1.25567 .82531 1.21166 28 33 .74131 1.34896 .76871 1.30087 .79686 1.25492 .82580 1.21094 27 34 .74176 1.34814 .76918 1.30009 .79734 1.25417 .82629 1.21023 26 35 .74221 1.34732 .76964 1.29931 .79781 1.25343 .82678 1.20951 25 86 .74267 1.34650 .77010 1.29853 .79829 1.25268 .82727 1.20879 24 37 .74312 1.34568 .77057 1.29775 .79877 1.25193 .82776 1.20808 23 38 .74357 1.34487 .77103 1.29696 .79924 1.25113 .82825 1.20736 22 39 .74402 1.34405 .77149 1.29618 .79972 1.25044 .82874 1.20665 21 40 .74447 1.34323 .77196 1.29541 .80020 1.24969 .82923 1.20593 20 41 .74492 1.34242 .77242 1.29463 .80067 1.24895 .82972 1.20522 19 42 .74538 1.34160 .77289 1.29385 .80115 1.24820 .83022 1.20451 18 43 .74583 1.34079 .77335 1.29307 .80163 1.24746 .83071 1.20379 17 44 .74628 1.33998 .77382 1.29229 .80211 1.24672 .83120 1.20308 16 45 .74674 1.33916 . 77428 1.29152 .80258 1.24507 .83169 1.20237 15 4(3 .74719 1.33835 .77475 1.29074 .80306 1.24523 .83218 1.20166 14 47 .74764 1.33754 .77521 1.28997 .80354 1.24449 .83268 1.20095 13 48 .74810 1.33673 .77568 1.28919 .80402 1.24375 .83317 1.20024 !12 49 .74855 1.33592 .77615 1.28842 .80450 1.24301 .a3366 1.19953 111 50 .74900 1.33511 .77661 1.28764 .80498 1.24227 .83415 1.19882 10 51 .74946 1.33430 .77708 1.28687 .80546 1.24153 .83465 1.19811 9 52 .74991 1.33349 .77754 1.28610 .80594 1.24079 .83514 1.19740 8 53 .75037 1.33268 .77801 1.28533 .80642 1.24005 .83564 1.19669 7 54 .75082 1.33187 .77848 1.28456 .80600 1.23931 .83613 1 . 19599 6 55 .75128 1.33107 .77895 1.28379 .80738 1.23858 .83662 1.19528 5 56 .75173 1.33026 .77941 1.28302 .80786 1.23784 .83712 1.19457 4 K .75219 1.32946 .77988 1.28225 .80834 1.23710 .83761 1.19387 3 58 .75264 1.32865 .78035 1.28148 .80882 1.23637 .83811 1.19316 2 5! .75310 1.32785 .78082 1.28071 .80930 1.23563 .83860 1 . 19246 1 at .75355 1.32704 .78129 1.27994 .80978 1.23490 .83910 1.19175 / Cotang Tang Cotang Tang Cotang Tang Cotang Tang f 53 52 51 50 244 TABLE XVI. NATURAL TANGENTS AND COTANGENTS. 4 4 1 4 2 4 3 Tang Cotang Tang Cotang Tang Cotang Tang Cotang .83910 . 19175 ".80929 1 . 15037 .90040 .11061 .93252 1.07237 60 1 .83960 .19105 .80980 1.14909 .90093 .10996 .93306 1.07174 59 2 .84009 .19035 .87031 1.14902 .90146 .10931 .93360 1.07112 58 3 .84059 .18904 .87082 1.14834 .90199 .10867 .93415 1.07049 57 4 .84108 .18894 .87133 1.14707 .90251 .10802 .93469 1.06987 50 5 .84158 .18824 .87184 1 . 14099 .90304 .10737 .93524 1.06925 55 6 .84208 .18754 .87'23G 1.14032 .90357 .10072 .93578 1.00802 54 7 .84258 .18684 .87287 1 . 14505 .90410 .10607 .93033 1.06800 53 8 .84307 .18014 .87:338 1.14498 .90403 .10543 .93088 1.06738 52 9 .84357 .18544 .87389 1.14430 .90516 .10478 .93742 1.06676 51 10 .84407 .18474 .87441 1.14303 .90569 .10414 .93797 1.06613 50 11 .84457 .18404 .87492 1.14290 .00021 .10349 .93852 .06551 49 12 .84507 .18334 .87543 1 . 14229 .90074 .10285 .93900 .00489 48 18 .84556 .18204 .87595 1.14102 .90727 .10220 .93901 .00427 47 14 .84006 .18194 .87046 1.14095 .90781 .10150 .94010 .00305 46 15 .84050 .18125 .87698 1.14028 .90834 .10091 .94071 .00303 45 10 .84700 .18055 .87749 .13901 .90887 .10027 .94125 .00241 44 17 .84756 .17986 .87801 .13894 .90940 .09903 .94180 .00179 43 18 .84800 .17916 .87852 .13828 .90993 .09899 .94235 .00117 42 19 .84850 .17846 .87904 .13761 .91046 .09834 .94290 .00056 41 20 .84900 1.17777 .87955 .13094 .91099 .09770 .94345 .05994 40 21 .84956 1.17708 .88007 .13027 .91153 .09706 .94400 .05932 39 23 .85000 1 . 17638 .88059 .13501 .91206 .09042 .94455 .05870 38 23 .85057 1.17509 .88110 .13494 .91259 .09578 .94510 .05809 37 24 .85107 1 . 17500 .88102 .13428 .91313 .09514 .94505 .05747 30 25 .85157 1.17430 .88214 .13301 .91366 .09450 .94620 .05685 35 x:;i .85207 1.17301 .88205 .13295 .91419 .09380 .94676 .05624 34 27 .85257 1.17292 .88317 .13223 .91473 .09322 .94731 .05562 33 28 .85308 1.17223 .88309 .13102 .91526 .09258 .94786 .05501 32 2.) .85358 1.17154 .88421 .13096 .91580 .09195 .94841 .05439 31 30 .85408 1.17085 .88473 .13029 .91633 .09131 .94896 .05378 30 31 .85458 1.17016 .88524 .12963 .91687 .09007 .94952 .05317 29 32 .85509 1.10947 .88576 .12897 .91740 .09003 .95007 .05255 28 83 .85559 1.16878 .88628 .12831 .91794 .08940 .95062 .05194 27 84 .85009 1.10809 .88680 1.12705 .91847 .08876 .95118 .05133 20 35 .85000 1.10741 .88732 1.12099 .91901 1.08813 .95173 .05072 25 3(5 .85710 1.16672 .88784 1.12033 .91955 1.08749 .95229 .05010 24 37 .85701 .16603 .88836 1.12507 .92008 1.08686 .95284 .04949 23 38 .85811 . 16535 .88888 1.12501 .92062 1.08622 .95340 .04888 22 39 .85802 .10406 .88940 1.12435 .92116 1.08559 .95395 .04827 21 40 .85912 .16398 .88992 1.12309 .92170 1.08496 .95451 .04766 20 41 .85963 .10329 .89045 1.12303 .92224 1.08432 .95506 .04705 19 12 .86014 .10201 .89097 1.12238 .92277 1.08309 .95562 .04644 18 43 .80004 .10192 .89149 1.12172 .92331 1.08306 .95618 .04583 17 44 .80115 .10124 .89201 1.12106 .92385 1.08243 .95673 .04522 18 45 .80106 .10056 .89253 1.12041 .92439 1.08179 .95729 .04461 15 40 .86216 .15987 .89306 1.11975 .92493 1.08116 .95785 .04401 14 47 .80207 .15919 .89358 1.11909 .92547 1.08053 .95841 .04340 13 48 .80318 .15851 .89410 1.11844 .92601 1 -07990 .95897 .04279 12 49 .80308 .15783 .89403 1 11778 .92655 1.07927 .95952 .04218 11 50 .80419 .15715 .89515 1.11713 .92709 1.07864 .96008 .04158 10 51 .80470 .15047 .89507 1.11648 .92763 1.07801 .96064 .04097 9 52 .80521 .15579 .89020 1.11582 .92817 .07738 .96120 .04036 8 53 .80572 .15511 .89072 .11517 .92872 .07676 .96176 .03976 7 54 .80023 .15443 .89725 .11452 .92926 .07613 .96232 .03915 55 .80074 1.15375 .89777 .11387 .92980 .07550 .96288 .03855 5 56 .80725 1.15308 .89830 .11321 .93034 .07487 .96344 1.03794 4 57 .80776 1.15240 .89883 .11256 .93088 .07425 .96400 1.03734 3 58 .80827 1.15172 .89935 1.11191 .93143 .07362 .96457 1.03674 2 59 .80878 1.15104 .89988 1.11126 .93197 .07299 .96513 1.03613 1 60 .80929 1 . 15037 .90040 1.11001 .93252 .07237 .96569 1.03553 / Cotang Tang Cotang Tang Cotang Tang Cotang Tang f 4 9 4 8 4 7 4 6 245 TABLE XVI. NATURAL TANGENTS AND COTANGENTS. t 4 t4 4 1 4 4 Tang Cotang Tang Cotang Tang Cotang .90569 1.03553 60 20 .97700 1.02355 40 40 .98843 1.01170 20 1 .90625 1.03493 59 21 .97756 1.02295 :;<> I 41 .98901 1.01112 19 2 .96681 1.0^33 58 22 .97813 1.02236 : 42 .98958 1.01053 18 3 .96738 1.03372 57 23 .97870 1.02176 37 43 .99016 1.00994 17 4 .90794 1.03312 56 24 .97927 1.02117 3<> 44 .99073 1.00935 16 5 .96850 1.03252 55 25 .97984 1.02057 35 45 .99131 1.00876 15 6 .96907 1.03192 54 26 .98041 1.01998 34 46 .99189 1.00818 14 7 .96963 1.03132 53 27 .98098 1.01939 33 47 .99247 1.00759 13 8 .97020 1.03072 52 28 .98155 1.01879 32 48 .99304 1.00701 12 9 .97076 1.03012 51 29 .98213 1.01820 31 49 .99362 1.00642 11 10 .97133 1.02952 50 30 .98270 1.01761 ao 50 .99420 1.00583 10 11 .97189 1.02892 49 31 .9&S27 1.01702 20 51 .99478 1.00525 9 12 .97246 1.02832 48 32 .98384 1.01642 28 52 .99536 1.00467 8 13 .97302 1.02772 47 33 .98441 1.01583 27 53 .99594 1.00408 7 14 .97359 1.02713 46 34 .98499 1.01524 2(5 54 .99652 1.00350 6 15 .97416 1.02653 45 35 .98556 1.01465 25 55 .99710 1.00291 5 16 .97472 1.02593 44 36 .98613 1.01406 24 50 .99768 1.00233 4 1? .97529 1.02533 43 37 .98671 1.01347 23 57 .99826 1.00175 3 18 .97586 1.02474 42 38 .98728 1.01288 22 58 .99884 1.00116 2 19 .97643 1.02414 41 39 .98786 1.01229 21 59 .99942 1.00058 1 20 .97700 1.02355 40 .40 .98813 1.01170 20 60 1.00000 1.00000 / Cotang Tang / / Cotang Tang 1 / / Cotang Tang / 4 5 4 5 4 5 246 TABLE XVII. NATURAL VERSED SINES AND EXTERNAL SECANTS. 1 2 3 o Vers. Ex. sec. Vers. Ex. sec. Vers. Ex. sec. Vers. Ex. sec. .00000 .00000 .00015 .00015 .00061 .00061 .00137 .00137 1 .00000 .00000 .00016 .00016 .00062 .00062 .00139 00139 1 2 .00000 .00000 .00016 .00016 .00063 .00063 .00140 .00140 2 3 .00000 .00000 .00017 .00017 .00064 .00064 .00142 .00142 3 4 .00000 .00000 .00017 .00017 .00065 .00065 .00143 .00143 4 5 .00000 .00000 .00018 .00018 .00066 .00066 .00145 .00145 5 6 .00000 .00000 .00018 .00018 .00067 .00067 .00146 .00147 6 7 .00000 .00000 .00019 .00019 .00068 .00068 .00148 .00148 7 8 .00000 .00000 .00020 .00020 .00069 .00069 .00150 .00150 8 9 .00000 .00000 .00020 .00020 .00070 .00070 .00151 .00151 9 10 .00000 .00000 .00021 .00021 .00071 .00072 .00153 .00153 10 11 .00001 .00001 .00021 .00021 .00073 .00073 .00154 .00155 11 12 .00001 .00001 .00022 .00022 .00074 .00074 .00156 .00156 12 13 .00001 .00001 .00023 .00023 .00075 .00075 .00158 .00158 13 14 .00001 .00001 .00023 .00023 .00076 .00076 .00159 .00159 14 15 .00001 .00001 .00024 .00024 .00077 .00077 .00161 .00161 15 16 .00001 .00001 .00024 .00024 .00078 .00078 .00162 .00163 ia 17 .00001 .00001 .00025 .00025 .00079 .00079 .00164 .00164 17 18 .00001 .00001 .00026 .00026 .00081 .00081 .00166 .00166 18 19 .00002 .00002 .00026 .00026 .00082 .00082 .00168 .00168 19 20 .00002 .00002 .00027 .00027 .00083 .00083 .00169 .00169 20 21 .00002 .00002 .00028 .00028 .00084 .00084 .00171 .00171 21 22 .0000.3 .0000.3 .00028 .00028 .00085 .00085 .00173 .00173 22 23 .00002 .00002 .00029 .00029 .00087 .00087 .00174 .00175 23 24 .00002 .00002 .00030 .00030 .00083 .00088 .00176 .00176 24 25 .00003 .00003 .00031 .00031 .00089 .00089 .00173 -.00178 25 20 .00003 .00003 .00031 .00031 .00090 .00090 .00179 .00180 26 27 .00003 .00003 .00032 .00032 .00091 .00091 .00181 .00182 27 23 .00003 .00003 .00033 .00033 .00093 .00093 .00183 .00183 28 29 .00004 .00004 .00034 .00034 .00094 .00094 .00185 .00185 29 30 .00004 .00004 .00034 .00034 .00095 .00095 .00187 .00187 30 31 .00004 .00004 .00035 .00035 .00096 .00097 .00188 .00189 31 32 .00004 .00004 .00036 .00036 .00098 .00098 .00190 .00190 32 33 .00005 .00005 .00037 .00037 .00099 .00099 .00192 .00192 33 34 .00005 .00005 .00037 .00037 .00100 .00100 .00194 .00194 34 35 .00005 .00005 .00038 .00038 .00102 .00102 .00196 .00196 35 36 .00005 .00005 .00039 .00039 .00103 .00103 .00197 .00193 33 37 .00006 .00006 .00040 .00040 .00104 .00104 .00199 .00200 37 33 .00006 .00006 .00041 .00041 .00106 .00105 .00201 .00201 38 3D .00006 .00006 .00041 .00041 .00107 .00107 .00203 .00203 39 40 .00007 .00007 .00042 .00042 .00108 .00108 .00205 .00205 40 41 .00007 .00007 .00043 .00043 .00110 .00110 .00207 .00207 41 42 .00007 .00007 .00044 .00044 .00111 .00111 .00208 .00209 42 43 .00008 .00008 .00045 .00045 .00112 .00113 .00210 .00211 43 44 .00008 .00008 .00046 .00046 .00114 .00114 .00212 .00213 41 45 .00009 .00009 .00047 .00047 .00115 .00115 .00214 .00215 45 43 .00009 .00009 .00048 .00048 .00117 .00117 .00216 .00216 46 47 .00009 .00009 .00048 .00048 .00118 .00118 .00218 .00213 47 48 .00010 .00010 .00049 .00049 .00119 .00120 .00220 .00220 48 49 .00010 .00010 .00050 .00050 .00121 .00121 .00222 .00222 49 50 .00011 .00011 .00051 .00051 .00122 .00122 .00224 .00224 50 51 .00011 .00011 .00052 .00052 .00124 .00124 .00226 .00226 51 52 .00011 .00011 .00053 .00053 .00125 .00125 .00228 .00223 52 53 .00012 .00012 .00054 .00054 .00127 .00127 .00230 .00230 53 54 .00012 .00012 .00055 .00055 .00128 .00128 .00232 .00232 54 55 .00013 .00013 .00056 .00056 .00130 .00130 .00234 .00234 55 56 .00013 .00013 .00057 .00057 .00131 .00131 .00236 .00236 56 57 ,00014 .00014 .00058 .00058 .00133 .00133 .00238 .00238 57 58 .00014 .00014 .00059 .00059 .00134 .00134 .00240 .00240 58 59 .00015 .00015 .00060 .00060 .00136 .00136 .00242 .00242 59 60 .00015 .00015 .00061 .00061 .00137 .00137 .00244 .00244 60 247 TABLE XVII. NATURAL VERSED SINES AND EXTERNAL SECANTS 4 5 6 7 Vers. Ex. sec. Vers. , Ex. sec. Vers. Ex. sec. Vers. Ex. sec. .00244 .00244 .00381 .00382 .00548 .00551 .00745 .00751 1 .00246 .00246 .00383 .00385 .00551 .00554 .00749 .00755 1 2 .00248 .00248 .00386 .00387 .00554 .00557 i .00752 .(W58 2 3 .00250 .00250 .00388 .00390 .00557 . 00500 ! .00756 .007'62 3 4 .00252 .00252 .00391 .00392 .00560 .00563 1 .00760 .00765 4 5 .00254 .00254 .00393 .00395 .00563 .00566 i .00763 .00769 5 6 .00256 .00257 .00396 .00397 .00566 .00569 .00767 .00773 6 7 .00258 .00259 .00398 .00400 .00569 .00573 .00770 .00776 7 8 .00260 .00261 .00401 .00403 .00572 .00576 .00774 .00780 8 9 .00262 .00263 .00404 .00405 .00576 .00579 .00178 .00784 9 10 .00264 .00265 .00406 .00408 .00579 .00582 .00781 .00787 10 11 .00266 .00267 .00409 .00411 .00582 .00585 .00785 .00791 11 12 .00269 .00269 .00412 .00413 .00585 .00588 .00789 .00795 12 13 .00271 .00271 .00414 .00416 .00588 .00592 .00792 .00799 13 14 .00273 .00274 .00417 .00419 .00591 .00595 .00796 .00802 14 15 .00275 .00276 .00420 .00421 .00594 ..00598 .00800 .00806 15 16 .00277 .00278 .00422 .00424 .00598 .00601 .00803 .00810 16 17 .00279 .00280 .00425 .00427 .00601 .00604 .00807 .00813 17 18 .00281 .00282 .00428 .00429 .00604 .00608 .00811 .00817 18 19 .00284 .00284 .00430 .00432 .00607 .00611 .00814 .00821 19 20 .00286 .00287 .00433 .00435 .00610 .00614 .00818 .00825 20 21 .00288 .00289 .00435 .C0438 .00614 .00617 .00822 .00828 21 22 .00290 .00291 .00438 .00440 .00617 .00621 .00825 .00832 22 23 .00293 .00293 .00441 .00443 .00620 .00624 .00829 .00836 23 24 .00295 .00296 .00444 .00440 .00623 .00627 .00833 .00840 24 25 .00297- .00298 .00-447 .00449 .00628 .00630 .00837 .00844 25 26 .00299 .00300 .00449 .00451 .00630 .C0634 .C0840 .00848 26 27 .00301 .00302 .00452 .00454 .00633 .00637 .00844 .00851 27 28 .00304 .00305 .00455 .00457 .00636 .00640 .00848 .C0855 28 29 .00306 .00307 .00458 .00460 .00640 .00644 .00852 .00859 29 80 .00308 .00309 .00460 .004G3 .00643 .C0647 .00856 .00863 30 31 .00311 .00312 .00463 .00465 .00646 .00650 .00859 .00867 31 32 .00313 .00314 .00466 .00468 .00649 .00654 .00863 .00871 32 33 .00315 .00316 .00469 .00471 .00653 .00657 i .00867 .00875 33 34 .00317 .00318 .00472 .00474 .00656 .00660 .00871 .00878 34 35 .00320 .00321 .00474 .00477 .C0659 .00664 .00875 .00882 35 36 .00322 .00323 .00477 .00480 .00663 .00667 .00878 .00886 36 37 .00324 .00326 .00480 .C0482 .00666 .00671 .00882 .00890 37 38 .00327 .00328 .00483 .00485 .00669 .00674 .00886 .00894 38 39 .00329 .00330 .00486 .00488 .00673 .00677 .00890 .00898 39 40 .00332 .00333 .00489 .00491 .00676 .00681 .00894 .00902 40 41 .oo&34 .00335 .00492 .00491 .00680 .00684 .00898 .00906 41 42 .00336 .00337 .00494 .00497 .00683 .00688 ! .C0902 .00910 42 43 .00339 .00340 .00497 .00500 .00686 .00691 .00906 .00914 43 44 .00341 .00342 .00500 .00503 .00690 .00695 ! .00909 .00918 44 45 .00343 .00345 .00503 .00506 .00693 .00698 .00913 .00922 45 46 .00346 .00347 .00506 .00509 .00697 .00701 .00917 .00926 46 47 .00348 .00350 .00509 .00512 .00700 .00705 .00921 .00930 47 48 .00351 .00352 .00512 .00515 .00703 .00708 .00925 .00934 48 49 .00353 .00354 .00515 .00518 .00707 .00712 I .00929 .00938 49 50 .00356 .00357 .00518 .00521 .00710 .00715 .00933 .00942 50 51 .00358 .00359 .00521 .00524 .00714 .00719 ! .00937 .00946 51 52 .00361 .003(52 .00524 .00527 .00717 .00722 .00941 .00950 52 53 .00363 .00364 .00527 .00530 .00721 .00726 .00945 .00954 53 54 .00365 .00367 .00530 .00533 .<0724 .00730 .00949 .00958 54 55 .00368 .00369 .00533 .00536 .00728 .00733 .00953 .00962 55 56 .00370 .00372 .00536 .00539 .00731 .007'37 .00957 .00966 56 57 .00373 .00374 .00539 .00542 .00735 .00740 .00961 .00970 57 58 .00875 .00377 .00542 .00545 .00738 .00744 .00965 .00975 58 59 .00378 . .00379 .00545 .00548 .00742 .00747 .00969 .00979 59 60 .00381 .00382 .00548 .00551 .007'45 .00751 .00973 | .00983 60 248 XVII.-NATURAL VERSED SINES AND EXTERNAL SECANTS. 8 9 10 11 / Vers. Ex. sec. Vers. Sx. sec. Vers. Ex. sec. Vers. Ex. sec. .00973 .00983 ! .01231 .01247 .01519 .01543 .01837 .01872 1 .00977 .00987 .01236 .01251 .01524 .01548 .01843 .01877 1 2 .00981 .00991 .01240 .01256 .01529 .01553 .01848 .01883 2 3 .00985 .00995 .01245 .01261 .01534 .01558 .01854 .01889 3 4 .00989 .00999 .01249 .01265 .01540 .01564 .01860 .01895 4 5 .00994 .01004 .01254 .01270 .01545 .01569 .01865 .01901 5 6 .00998 .01008 .01259 .01275 .01550 .01574 .01871 .01906 6 7 .01002 .01012 .01263 .01279 .01555 .01579 .01876 .01912 7 8 .01006 .01016 .01268 .01284 .01560 .01585 .01882 .01918 8 9 .01010 .01020 .01272 .01289 .01565 .01590 .01888 .01924 9 10 .01014 .01024 .01277 .01294 .01570 .01595 .01893 .01930 10 11 .01018 .01029 .01282 .01298 .01575 .01601 .01899 .01936 11 12 .010.22 .01033 .01286 .01303 .01580 .01606 .01904 .01941 12 13 .01027 .01037 .01291 .01308 .01586 .01611 .01910 .01947 13 14 .01031 .01041 .01296 .01313 .01591 .01616 .01916 .01953 14 15 .01035 .01046 .01300 .01318 .01596 .01622 .01921 .01959 15 16 .01039 .01050 .01305 .01323 .01601 .01627 .01927 .01965 16 17 .01043 .01054 .01310 .01327 .01606 .01633 .01933 .01971 17 18 .01047 .01059 .01314 .01332 .01612 .01638 .01939 .01977 18 19 .01052 .01063 i .01319 .01337 .01617 .01643 .01944 .01983 19 20 .01056 .01067 .01324 .01342 .01622 .01649 .01950 .01989 20 21 .01000 .01071 .01329 .01346 .01627 .01654 .01956 .01995 21 22 .01064 .01076 .01333 .01351 i .01632 .01659 .01961 .02001 22 23 .01069 .01030 .01338 .01356 .01638 .01665 .01967 .02007 23 24 .01073 .01084 .01343 .01361 .01643 .01670 .01973 .02013 24 25 .01077 .01089 .01348 .01366 .01648 .01676 .01979 .02019 25 26 .01081 .01093 .01352 .01371 .01653 .01681 .01984 .02025 26 27 .01086 .01097 .01357 .01376 .01659 .01687 .01990 .02031 27 28 .01090 .01102 .01362 .01381 .01664 .01692 .01996 .02037 28 29 .01094 .01106 .01367 .01386 .01669 .01698 .02002 .02043 29 30 .01098 .01111 .01371 .01391 .01675 .01703 .02008 .02049 30 31 .01103 .01115 .01376 .01395 .01680 .01709 .02013 .02055 31 32 .01107 .01119 .01331 .01400 .01685 .01714 .02019 .02061 32 33 .01111 .01124 .01383 .01405 .01690 .01720 .02025 .02067 as 34 .01116 .01128 .01391 .01410 .01696 .01725 .02031 .02073 34 35 .01120 .01133 .01396 .01415 .01701 .01731 .02037 .02079 35 36 .01124 .01137 .01400 .01420 .01706 .01736 ,02042 .02085 36 37 .01129 .01142 .01405 .01425 .01712 .01742 .02048 .02091 37 33 .01133 .01146 .01410 .01430 .01717 .01747 .02054 .02097 38 39 .01137 .01151 .01415 .01435 .01723 .01753 .02000 .02103 39 40 .01142 .01155 .01420 .01440 .01728 .01758 .02066 .02110 40 41 .01146 .01160 .01425 .01445 .01733 .01764 .02072 .02116 41 42 .01151 .01164 .01430 .01450 .01739 .01769 .02078 .02122 42 43 .01155 .01169 .01435 .01455 .01744 .01775 .02084 .02128 43 44 .01159 .01173 .01439 .01461 .01750 .01781 .02090 .02134 44 45 .01164 .01178 .01444 .01466 .01755 .01786 .02095 .02140 45 46 .01168 .01182 .01449 .01471 .01760 .01792 .02101 .02146 46 4? .01173 .01187 .01454 01476 .01766 .01798 .02107 .02153 47 48 .01177 .01191 .01459 .01481 .01771 .01803 .02113 .02159 48 49 .01182 .01196 .01464 .01486 .01777 .01809 .02119 .02165 49 50 .01186 .01200 .01469 .01491 .01782 .01815 .02125 .02171 50 51 .01191 .01205 .01474 .01496 .01788 .01820 .02131 .02178 51 52 .01195 .01209 .01479 .01501 .01793 .01826 .02137 .02184 52 53 .01200 .01214 .01484 .01506 .01799 .01832 .02143 .02190 53 54 .01204 .01219 .01489 .01512 .01804 .01837 .02149 .02196 54 55 .01209 .01223 .01494 .01517 .01810 .01843 .02155 .02203 55 56 .01213 .01228 .01499 .01522 .01815 .01849 .02161 .02209 56 57 .01218 .012:33 .01504 .01527 .01821 .01854 .02167 .02215 57 58 .01222 .01237 .01509 .01532 .01826 .01860 .02173 .02221 58 59 .01227 .01242 .01514 .01537 .01832 .01866 .02179 .02228 59 60 .01231 .01247 .01519 .01543 .01837 .01872 .02185 .02234 60 249 TABLE XVII. NATURAL VERSED SINES AND EXTERNAL SECANTS. / 12 13 14 15 / Vers. Ex. sec. | Vers. Ex. sec. Vers. Ex. sec. Vers. Ex. sec. .02185 .02234 .02563 .02630 .02970 .03061 .03407 .03528 1 .02191 .02240 .02570 .02637 .02977 .03009 .03415 .03530 1 2 .02197 .02247 .02576 .02644 .02985 .03076 .03422 .03541 2 3 .02203 .02253 .02583 .02651 .02992 .03084 .03430 .03552 3 4 .02210 .02259 .02589 .02658 .02999 .03091 .03438 .03560 4 5 .02216 .02266 .02596 .02665 .03006 .03099 i .03445 .03508 5 6 .02222 .02272 .02602 .02672 .03013 .03106 i .03453 .03576 6 7 .02228 .02279 .02609 .02679 .03020 .03114 .03400 .03584 7 8 .02234 .02285 .02616 .C2G86 .03027 .03121 .03408 .03592 8 9 .02240 .02291 .02622 .02693 .03034 .03129 .03476 .03601 9 10 .02246 .02298 .02629 .02700 .03041 .03137 .03483 .03009 10 11 .02252 .02304 .02635 .02707 .03048 .03144 .03491 .03017 11 12 .02258 .02311 .02042 .02714 .03055 .03152 j .03498 .03025 12 13 .02205 .02317 .02649 .02721 .03063 .03159 .03506 .03033 13 14 .02271 .02323 .02655 .02728 .03070 .03167 .0-3514 .03042 14 15 .02277 .02330 .02662 .02735 .03077 .03175 .03521 .03050 15 16 .02283 .02336 .02669 .02742 .03084 .03182 .03529 .03058 16 17 .02289 .02343 .02675 .02749 .03091 .03190 .03537 .03666 17 18 .02295 .02349 .02682 .02756 .03098 .03198 .03544 .03674 18 19 .02302 .02356 .02689 .02763 .03106 .03205 .03552 .03083 19 20 .02308 .02362 .02696 .02770 .03113 .03213 .03560 .03091 20 21 .02314 .02369 .02702 .02777 .03120 .03221 .03567 .03099 21 22 .02320 .02375 .02709 .02784 .03127 .03228 .03575 .03708 22 23 .02327 .02382 .02716 .02791 .03134 .03236 .03583 .03716 23 24 .02333 .02388 .02722 .02799 .03142 .03244 .03590 .03724 24 25 .02339 .02395 .02729 .02806 .03149 .03251 .03598 .03732 25 26 .02345 .03402 .02736 .02813 .03156 .03259 .03006 .03741 26 27 .02352 .02408 .02743 .02820 .03163 .03267 .03614 .03749 27 28 .02358 .02415 .02749 .02827 .03171 .03275 .03621 .03758 28 29 .02364 .02421 .02756 .02834 .03178 .03282 .03629 .03766 29 30 .02370 .02428 .02763 .02842 .03185 .03290 .03037 .03774 30 31 .02377 .02435 .02770 .02849 .03193 ,03298 .03645 .03783 31 32 .02383 .02441 .02777 .02856 .03200 .03306 .03053 .03791 32 33 .02389 .02448 .02783 .02803 .03207 .03313 .03000 .03799 33 34 .02396 .02454 .02790 .02870 .03214 .03321 .03008 .03808 34 S5 .02402 .02461 .02797 .02878 .03222 .03329 .03676 .03816 35 36 .02408 .02468 .02804 .02885 .03229 .03337 .03684 .03825 36 37 .02415 .02474 .02811 .02892 .03236 .03345 .03692 .03833 37 38 .02421 .02481 .02818 .02899 .03244 .03353 .03099 .03842 38 39 .02427 .02488 .02824 .02907 .03251 .03360 .03707 .08850 by 40 .02434 .02494 .02831 .02914 .03258 .03368 .03715 .03858 40 41 .02440 .02501 .02838 .02921 .03266 .03376 .03723 .03867 41 42 .02447 .02508 .02845 .02928 .03273 .03384 .03731 .03875 42 43 .02453 .02515 .02852 .02936 .03281 .03392 .03739 .03884 43 44 .02459 .02521 .02859 .02943 .03288 .03400 .03747 .03892 44 45 .02466 .02528 .02866 .02950 .03295 .03408 .03754 .03901 45 46 .02472 .02535 .02873 .02958 .03303 .03416 .03702 .03909 46 47 .02479 .02542 .02880 .02965 .03310 .03424 .03770 .03918 47 48 .02485 .02548 .02887 .02972 .03318 .03432 .03778 .03927 48 49 .02492 .02555 .02894 .02980 .03325 .03439 .03786 .03935 49 50 .02498 .02562 .02900 .02987 .03333 .03447 .03794 .03944 50 51 .02504 .02569 .02907 .02994 .03340 .03455 .03802 .03952 51 52 .02511 .02576 .02914 .03002 .03347 .03463 .03810 .03961 52 53 .02517 .02582 .02921 .03009 .03355 .03471 .03818 .03969 53 54 .02524 .02589 .02928 .03017 .03362 .03479 .03826 .03978 54 55 .02530 .02596 .02935 .03024 .03370 .03487 .03834 .03987 55 56 .02537 .02603 .02942 .03032 .03377 .03495 .03842 .03995 56 57 .02543 .02610 .02949 .03039 .03385 .03503 .03850 .04004 57 58 .02550 .02617 .02956 .03046 .03392 .03512 .03858 .04013 58 59 .02556 .02624 .02963 .03054 .03400 .03520 .03806 .04021 59 60 .02563 .02030 .02970 .03061 .03107 .03528 .03874 .04030 60 TABLE XVII. NATURAL VERSED SINES AND EXTERNAL SECANTS, 16 M 1 18 t li > Vers. ; Ex. sec. Vers. Ex. sec. Vers. Ex. sec. Vers. Ex. sec. | .03874 .04030 : .04370 .04569 .04894 .05146 .05448 .05762 1 .03882 .04039 .04378 .04578 .04903 .05156 .05458 .05773 1 2 .03890 .04047 .04387 .04588 .04912 .05166 .05467 .05783 2 3 .03898 .04056 .04395 .04597 .04921 .05176 .05477 .05794 3 4 .03906 .04065 .04404 .04600 .04930 .05186 .05486 .05805 4 5 .03914 .04073 .04412 .04616 .04939 .05196 .05496 .05815 5 6 .03922 .04082 .04421 .04625 .04948 .05206 .05505 .05826 6 7 .03930 .04091 .04429 .04635 .04957 .05216 .05515 .05836 7 8 .03938 .04100 .04438 .04644 .04907 .05226 .05524 .05847 8 9 .03946 .04108 .04446 .04653 .04976 .05S36 .05534 .05858 9 10 .03954 .04117 .04455 .04663 .04985 .05246 .05543 .05869 10 11 .03963 .04126 .04464 .04672 .04994 .05256 .05553 .05879 11 12 .03971 .04135 .04472 .04682 .05003 .05266 .05562 .05890 12 13 .03979 .04144 .04481 .04691 .05012 .05276 .05572 .05901 13 14 .03987 .04152 .04489 .047'00 .05021 .05286 .05582 .05911 14 15 .03995 .04161 .04498 .04710 .05030 .05297 .05591 .05922 15 1G .04003 .04170 .04507 .04719 .05039 .05307 .05601 .05933 16 17 .04011 .04179 .04515 .04729 .05048 .05317 .05610 .05944 17 18 .04019 .04188 .04524 .04738 .05057 .05327 .05620 .05955 18 19 .04028 .04197 .04533 .04748 .05067 .05,337 .05630 .05965 19 20 .04036 .04206 .04541 .04757 .05076 .05347 .05639 .05976 20 21 .04044 .04214 .04550 .04767 .05085 .05357 .05649 .05987 21 22 .04052 .04223 .04559 .04776 .05094 .05367 .05658 .05998 22 23 .04060 .04232 .04567 .04786 .05103 .05378 ! .05668 .06009 23 21 .04069 .04241 .04576 .04795 .05112 .05388 ! .05678 .06020 24 25 .04077 .04250 .04585 .04805 .05122 .05398 ! .05687 .06030 25 26 .04085 .04259 .04593 .04815 .05131 .05408 i .05697 .06041 26 27 .04093 .04268 .04602 .04824 .05140 .05418 i .05707 .06052 27 28 .04102 .04277 .04611 .04834 .05149 .05429 ! .C5716 .06063 28 .04110 .04286 .04620 .04843 .05158 .05439 .05726 .06074 29 30 .04118 .04295 .04628 .04853 .05168 .05449 .05736 .06085 30 31 .04126 .04304 .04637 .04863 .05177 .05460 ! .05746 .06096 31 32 .04135 .04313 .04646 .04872 .05186 .05470 ! .05755 .06107 32 33 .04143 .04322 .04655 .04882 .05195 .05480 .05765 .06118 33 34 .04151 .04331 .04663 .04891 .05205 .05490 j .05775 .06129 34 35 .04159 .04340 .04672 .04901 .05214 .05501 .05785 .06140 35 36 .04168 .04349 ! .04681 .04911 .05223 .05511 | .05794 .06151 36 37 .04176 .04358 1 .04690 .04920 .05232 .05521 .05804 .06162 37 38 .04184 .04367 .04609 .04930 .05242 .05532 .05814 .06173 38 39 .04193 .04376 : .04707 .04940 .05251 .(5542 .05824 .06184 39 40 .04201 .04385 .04716 .0495J .05260 .05552 .05833 .06195 40 41 .04209 .04394 .04725 .04959 .05270 .05563 .05843 .06206 41 42 .04218 .04403 .04734 .04969 .05279 .0557'3 ; .05853 .06217 42 43 .04226 .04413 .04743 .0497-9 .05288 .05584 .05863 .06228 43 44 .04234 .04422 .04752 .04989 .05298 .05594 .05873 .06239 44 45 .04243 .04431 .04760 .04998 .05307 .05604 .05882 .06250 45 46 .04251 .04440 .04769 .05008 .05316 .05615 .05892 .06261 46 47 .04260 .04449 .04778 .05018 .05326 .05625 .05902 .06272 47 48 .04268 .04458 .04787 .05028 .05335 .05636 j .05912 .06283 48 49 .04276 .04468 .04796 .05038 .05344 .05646 .05922 .06295 49 50 .04285 .04477 .04805 .05047 .05354 .05657 | .05932 .06306 50 51 .04293 .04486 .04814 .05057 .05363 .05667 .05942 .06317 51 52 .04302 .04495 .04823 .05067 .05373 .05678 .05951 .06328 52 53 .04310 .04504 .04832 .05077 .05382 .05688 .05961 .06339 53 54 .04319 .04514 .04841 .05087 .05391 .05699 .05971 .06350 54 55 .04327 .04523 .04850 .05097 .05401 .05709 .05981 .06362 55 56 .04336 .04532 .04858 .05107 .05410 .05720 .05991 .06373 56 57 .04344 .04541 .04867 .05116 .05420 .05730 .06001 .06384 57 58 .041353 .04551 .04876 .05126 .05429 .05741 .06011 .06895 58 59 .04361 .04560 .04885 .05136 .05439 .05751 .06021 .06407 59 60 .04370 .04569 .04894 .05146 .05448 .05762 .06031 .06418 60 251 TABLE XVII. NATURAL VERSED SINES AND EXTERNAL SECANTS, / 20 21 22 23 / Vers. Ex. sec. Vers. Ex. sec. Vers. Ex. sec. Vers. Ex. sec. .06031 .06418 .06042 .07115 .07282 .07853 .07950 .08636 1 .06041 .06429 .06652 .07126 .07293 .07866 .07961 .08649 1 2 .06051 .06440 .06663 .07138 .07303 .07879 .07972 .08663 2 3 .06061 .06452 .06673 .07150 .07314 .07892 .07984 .08676 3 4 .06071 .06463 .06684 .07162 .07325 .07904 .07995 .08090 4 5 .06081 .06474 .06694 .07174 .07336 .07917 .08006 .08703 5 6 .06091 .06486 .06705 .07186 .07347 .07930 .08018 .08717 6 7 .06101 .06497 .06715 .07199 .07358 .07943 .08029 .08730 7 8 .06111 .06508 .00726 .07211 .07369 .07955 .08041 .08744 8 9 .06121 .06520 .00736 .07-<23 .07380 .07968 .08052 .08757 9 10 .06131 .06531 .00747 .07235 .07391 .07981 .08004 .08771 10 11 .06141 .06542 .06757 .07247 .07402 .07094 .08075 .08784 11 12 .06151 .06554 .06768 .07259 .07413 .08006 .08080 .08798 12 13 .06161 .06565 .0677'8 .07271 .07424 .08019 .08098 .08811 13 14 .06171 .06577 .06789 .07283 .07435 .08032 .08109 .08825 14 15 .06181 .06588 .06799 .07295 .07446 .08045 .08121 .08839 15 16 .06191 .00600 .06810 .07307 .07457 .08058 .08132 .08852 16 17 .06201 .06611 .06820 .07320 .07468 .08071 .08144 .08866 17 18 .06211 .06622 .06831 .07332 .07479 .08084 .08155 .08880 18 19 .06221 .06634 .06841 .07344 .07490 .08097 .08167 .08893 19 20 .06231 .06645 .06852 .07356 .07501 .08109 .08178 .08907 20 21 .00241 .06657 .06863 .07368 .07512 .08122 .08190 .08921 21 22 .06252 .06668 .06873 .07380 .07523 .08135 .08201 .08934 22 23 .06262 .06680 .06884 .07393 .07534 .08148 .08213 .08948 23 24 .06272 .06691 .06894 .07405 .07545 .08161 .08225 .08962 24 25 .06282 .05703 .06905 .07417 .07556 .08174 .08236 .08975 25 26 .06292 .06715 .06916 .07429 .07568 .08187 .08248 .08989 26 27 .06302 .06726 .06926 .07442 .07579 .08200 .08259 .09003 27 28 .06312 .06738 .06937 .07454 .07590 .08213 .08271 .09017 23 29 .06323 .06749 .06948 .07466 .07601 .08226 .08282 .09030 20 80 .06333 .00761 .06958 .07479 .07612 .08239 .08294 .09044 30 31 .06343 .00773 .06969 .07491 .07623 .08252 .08306 .09058 SI 32 .06353 .06784 .06980 .07503 .07634 .08265 .08317 .09072 32 as .06363 .06796 .06990 .07516 .07645 .08278 .08329 .09086 33 34 .06374 .06807 .07001 .07528 .07657 .08291 .08340 .09099 34 35 .06384 .06819 .07012 .07540 .07668 .08305 .08352 .09113 35 36 .06394 .06831 .07022 .07553 .07679 .08318 .08364 .09127 33 37 .06404 .06843 .07033 .07565 .07690 .08331 .08375 .09141 37 38 .06415 .06854 .07044 .07578 .07701 .08344, .08387 .09155 38 39 .06425 .06866 .0?'055 .07590 .07713 .08357 .08399 .09169 39 40 .06435 .06878 .07065 .07002 .07724 .08370 .08410 .09183 40 41 .06445 .06889 .07076 .07615 .07735 .08383 .08422 .09197 41 42 .06456 .06901 .07087 .07627 .07746 .08397 .084:34 .09211 42 43 .06466 .06913 .07098 .07640 .07757 .08410 .08445 .09224 43 44 .06476 .06925 .07108 .07652 .07769 .08423 .08457 .09238 44 45 .06488 .06936 .07119 .07665 .07780 .08430 .08469 .09252 45 46 .06497 .06948 .07130 .07677 .07791 .08449 .08481 .09266 46 47 .06507 .06960 .07141 .07690 .07802 .08403 .08492 .09280 47 48 .06517 .06972 .07151 .07702 .07814 .08476 .08504 .09294 48 49 .06528 .06984 .07162 .07715 .07825 .08489 .08516 .09308 49 50 .06538 .06995 .07173 .07727 .07836 .08503 .08528 .09323 50 51 .06548 .07007 .07184 .07740 .07848 .08516 .08539 .09337 51 52 .06559 .07019 .07195 .07752 .07859 .08529 .08551 .09351 52 53 .06569 .07031 .07206 .07765 .07870 .08542 .08563 .09365 53 54 .06580 .07043 .07216 .07778 .07881 .08556 .08575 .09379 54 55 .06590 .07055 07227 .07790 .07893 .08569 .08586 .09393 .55 56 .06600 .07067 ! 07238 .07803 .07904 .08582 .08598 .09407 56 57 .06611 .07079 .07249 .07816 .07915 .08596 .08610 .09421 57 58 .06621 .07091 .07260 .07828 .07927 .08609 .08622 .09435 58 59 .06632 .07103 .07271 .07841 .07938 .08023 .08634 .09449 59 60 .06642 .07115 .07282 .07853 .0795J .08636 .08645 .09464 60 262 TABLE XVIL NATURAL VERSED SINES AND EXTERNAL SECANTS. 21 25 26 27 / Vers. Ex. sec. Vers. Ex. sec. Vers. Ex. sec. Vers. Ex. sec. .08645 .09464 .09369 .10338 .10121 .11260 .10899 .12233 1 .08657 .09478 .09382 .10353 .10133 .11276 .10913 .12249 1 2 .08669 .09492 .09394 . 10368 . 10146 .11292 .10926 .12266 2 3 .08681 .09506 .09406 .10383 .10159 .11308 .10939 .12283 3 4 .08693 .09520 .09418 .10398 .10172 .11323 .10952 .12291) 4 5 .08705 .09535 .09431 .10413 .10184 .11339 .10965 .12316 5 6 .08717 .09549 .09443 .10428 .10197 .11355 .10979 .12333 6 7 .08728 .09563 .09455 .10443 .10210 .11371 .10992 .12349 7 8 .08740 .09577 .09468 .10458 1 .10223 .11387 .11005 .12366 8 9 .08752 .09592 .09480 .10473 .10236 .11403 .11019 .12383 9 10 .08764 .09606 .09493 .10488 .10248 .11419 .11032 .12400 10 11 .08776 .09620 .09505 .10503 .10261 .11435 .11045 .12416 11 12 .0878,8 .09635 .09517 .10518 .10874 .11451 .11058 .12433 12 13 08800 .09649 .09530 .10533 .10287 .11467 .11072 .12450 13 14 ! 08812 .09663 .09542 .10549 .10300 .11483 .11085 .12467 14 15 .08824 .09678 .09554 .10564 .10313 .11499 .11098 .12484 15 16 .08836 .09692 .09567 .10579 .10326 .11515 .11112 .12501 16 17 .08848 .09707 .09579 .10594 .10338 .11531 .11125 .12518 17 18 .08860 .09721 .09592 .10609 .10351 .11547 .11138 .12534 18 19 .08872 .09735 .09604 .10625 .10304 .11563 .11152 .12551 19 20 .08884 .09750 .09617 .10640 .10377 .11579 .11165 .12568 20 21 .08896 .09764 .09629 .10655 .10390 .11595 .11178 .12585 2t 22 .08908 .09779 .09642 .10670 .10403 .11611 .11192 .12602 22 23 .08920 .09793 .09654 .10686 .10416 .11627 .11205 .12619 23 24 .08932 .09808 .09666 .10701 .10429 .11643 .11218 .12636 24 25 .08944 .09822 .09679 .10716 .10442 .11659 .11232 .12653 25 26 .08956 .09837 .09691 .10731 .10455 .11675 .11245 .12670 26 27 .08968 .09851 .09704 .10747 .10468 .11691 .11259 .12687 27 28 .08980 .09866 .09716 .10762 .10481 .11708 .11272 .12704 28 29 .08992 .09880 .09729 .10777 .10494 .11724 .11285 .12721 29 30 .09004 .09895 .09741 .10793 .10507 .11740 .11299 .12738 30 31 .09016 .09909 .09754 .10808 .10520 .11756 .11312 .12755 31 32 .09028 .09924 .09767 .10824 .10533 .11772 .11326 . 12772 32 33 .09040 .09939 .09779 .10839 .10546 .11789 .11339 .12789 33 34 .09052 .09953 .09792 .10854 .10559 .11805 .11353 .12807 34 25 .09004 .09968 .09804 .10870 .10572 .11821 .11366 .12824 35 26 .09076 .09982 .09817 .10885 .10585 .11838 .11380 .12841 36 37 .09089 .09997 .09829 .10901 .10598 .11854 .11393 .12858 37 38 .09101 .10012 .09842 .10916 .10611 .11870 .11407 .12875 38 89 .09113 .10026 .09854 .10932 .10621 .11886 .11420 .12892 39 40 .C9125 .10041 .09807 .10947 .10637 .11903 .11434 .12910 40 41 .09137 .10055 .09880 .10963 .10650 .11919 .11447 .12927 41 43 .09149 .10071 .09892 .10978 .10663 .11036 .11461 .12944 42 43 .09161 .10085 .09905 .10994 .10676 .11952 .11474 .12961 43 44 .09174 .10100 .09918 .11009 .10689 .11968 .11488 .12979 44 45 .09186 .10115 .09930 .11025 .10702 .11985 .11501 .12996 45 46 .09198 .10130 .C9943 .11041 .10715 .12001 .11515 .13013 46 47 .09210 .10144 .09955 .11056 .10723 .12018 .11528 .13031 47 48 .09222 .10159 .09968 .11072 .10741 .12034 .11542 .13048 48 49 .09234 .10174 .09981 .11087 .10755 .12051 .11555 .13065 49 50 .09247 .10189 .09993 .11103 .10708 .12067 .11569 .13083 50 51 .09259 .10204 .10006 .11119 .10781 .12084 .11583 .13100 51 53 .09271 .10218 .10019 .11134 .10794 .1*3100 .11596 .13117 52 53 .09283 .10233 .10032 .11150 .10807 .12117 .11610 .13135 53 54 .09296 .10248 .10044 .11166 .10820 .12133 .11623 .13152 54 55 .09308 .10263 .10057 .11181 .10833 .12150 .11637 .13170 55 56 .09320 .10278 . 10070 .11197 .10847 .12166 .11651 .13187 56 57 .09332 .10293 .10082 .11213 .10860 .12183 .11664 .13205 57 58 .09345 .10308 .10095 .11229 .10873 .12199 .11678 .13222 58 59 .09357 .10323 .10108 .11244 .10886 .12216 .11692 .13240 59 60 .093(59 .10338 .10121 .11260 .10899 .12233 .11705 .13257 60 253 XVII.-NATURAL VERSED SINES AND EXTERNAL SECANTS. 28 29 30 31 Vers. Ex. sec. Vers. Ex. sec. Vers. Ex. sec. Vers. Ex. sec. .11705 .13257 .12538 .14335 .13397 .15470 .14283 .16663 1 .11719 .13275 .12552 .14354 .13412 .15489 .14298 .16084 1 2 .11733 .13292 .12566 .14372 .13427 .15509 .14313 .16704 2 ft .11746 .13310 .12580 .14391 .13441 .15528 .14328 .16725 3 4 .11760 .1,3327 .12595 .14409 ' .13456 .15548 .14343 .16745 4 5 .11774 .13345 .12609 .14428 .1347'0 . 15567 .14358 .16706 5 6 .11787 .13362 .12623 .14446 .13485 .15587 .14373 .16786 6 7 .11801 .13380 .12637 .14465 .13499 .15006 .14388 .16806 7 8 .11815 .13398 .12651 .14483 .13514 .15626 .14403 .16827 8 9 .11828 .13415 .12665 .14502 .13529 .15645 .14418 .16848 9 10 .11842 .13433 .12679 .14521 .13543 .15665 .14433 .16868 10 11 .11856 .13451 .12694 .14539 .13558 .15684 .14449 .16889 11 12 .11870 .13468 .12708 .14558 .13573 .15704 .14464 .10909 12 13 .11888 .13486 .12722 .14576 .13587 .15724 .14479 .10930 13 14 .11897 .13504 .12736 .14595 .13602 .15743 .14494 .10950 14 15 .11911 .13521 .12750 .14614 .13016 .15763 .14509 .16971 15 16 .11925 .13539 .12765 .14632 .13631 .15782 .14524 .16992 16 17 .11938 .13557 .12779 .14651 .13646 . 15802 .14539 .17012 17 18 .11952 .13575 .12793 .14670 .13660 .15822 .14554 .17033 18 19 .11966 .13593 .12807 .14689 .18675 .15841 .14569 .17C54 19 20 .11980 .13610 .12822 .14707 .13690 .15801 .14584 .17075 20 21 .11994 .13628 .12836 .14726 .13705 .15881 , .14599 .17095 21 22 .12007 .13646 .12850 .14745 .13719 .15901 .14615 .17116 22 23 .12021 .13664 .12864 .14764 .13734 .15920 .14630 .17137 23 24 .12035 .13682 .12879 .14782 .13749 .15940 .14645 .17158 24 25 .12049 .13700 .12893 .14801 .13703 .15960 .14660 .17178 25 26 .12063 .13718 .12907 .14820 .13778 .15980 .14875 .17199 26 27 .12077 .13735 .12921 .14839 .13793 .16000 .14090 .17220 27 28 .12091 .13753 .12936 .14858 .13803 .10019 .14706 .17241 28 09 .12104 .13771 .12950 .14877 .13822 .10039 .14721 .17262 29 30 .12118 .13789 .12964 .14896 .13837 .10059 .14736 .17283 30 31 .12132 .13807 .12979 .14914 .13852 .10079 .14751 .17304 31 32 .12146 .13825 .12993 .14933 .13807 .10099 .14700 .17325 32 33 .12160 .13843 .13007 .14952 .13881 .10119 .14782 .17346 33 31 .12174 .13861 .13022 .14971 .13896 .10139 .14797 .17367 34 35 .12188 .13879 .13036 .14990 .13911 .10159 .14812 .17388 35 88 .12202 .13897 .13051 .15009 .13926 .10179 .14827 .17409 36 87 .12216 .13916 .13065 .15028 .13941 .10199 .14843 .17430 37 33 .12230 .13934 .13079 .15047 .13955 .10219 .14853 .17451 38 9 .12244 .13952 .13094 .15066 .13970 .10239 .14873 .17472 39 40 .12257 .13970 .13108 .15085 .13985 .10259 .14888 .17493 40 41 .12271 .13988 .13123 .15105 .14000 .10279 .14904 .17514 41 42 .12285 .14006 .13137 .15124 .14015 .10209 .14919 .17535 42 43 .12299 .14024 .13151 .15143 .14030 .10319 .14934 .17556 43 44 .12313 .14042 .13166 .15162 .14044 .10339 .14949 .17577 44 45 .12327 .14061 .13180 .15181 .14059 .16359 .14905 .17598 45 46 .12341 .14079 .13195 .15200 .14074 .16380 .14960 .17620 46 47 .12355 .14097 .13209 .15219 .14089 .10400 .14995 .17641 47 48 .12369 .14115 .13223 .15239 .14104 .10420 .15011 .17062 43 49 .12383 .14134 .13238 .15258 .14119 .10440 .15025 .17083 43 50 .12397 .14152 .13252 .15277 .14134 .16460 .15041 .17704 50 51 .12411 .14170 .13267 .15296 .14149 .16481 .15057 .17726 51 52 .12425 .14188 .13281 .15315 .14164 .16501 .15072 .17747 52 53 .12439 .14207 .13296 .15335 .14179 .16521 .15087 .17768 53 54 .12454 .14225 .13310 .15354 . .14194 .16541 .15103 .17790 54 55 .12468 .14243 .1-3325 .15373 .14208 .16562 .15118 .17811 55 56 .12482 .14262 .13339 .15393 .14223 .16582 .15134 .17832 56 57 .12496 .14280 .1.3354 .15412 .14238 .16602 .15149 .17854 57 58 .12510 .14299 .13368 .15431 .14253 .16623 .15164 .17875 58 59 .12524 .14317 .13383 .15451 .14268 . 16643 .15180 .17896 59 60 .12538 .14335 .13397 .15470 .14283 .16663 .15195 .17918 60 254 TABLE XVII. NATURAL VERSED SINES AND EXTERNAL SECANTS. 32 33 34 35 / Vers. Ex. sec Vers. Ex. sec. Vers. Ex. sec Vers. Ex. sec .15195 .17918 .16133 .19236 .17096 .20622 .18085 .22077 ~o" 1 .15211 .17939 .16149 .19259 .17113 .20645 .18101 .22102 1 2 . 15226 .17961 .16165 .19281 .17129 .20669 .18118 .22127 2 3 .15241 .17982 .16181 .19304 .17145 .20693 .18135 .22152 3 4 . 15257 .18004 .16196 .19327 .17161 .20717 .18152 .22177 4 5 .15272 .18025 .16212 .19349 .17178 .20740 .18168 .22202 5 6 . 15288 .18047 .16228 .19372 .17194 .20764 .18185 .22227 6 7 . 15303 .18068 .16244 .19394 .17210 .20788 .18202 .22252 7 8 .15319 .18090 .16260 .19417 .17227 .20812 .18218 .22277 8 9 .15334 .18111 .16276 .19440 .17243 .20836 .18235 .22302 9 10 .15350 .18133 .16292 .19463 .17259 .20859 .18252 .22327 10 11 .15365 .18155 .16308 .194a5 .17276 .20883 .18269 .22352 11 12 .15381 .18176 .16324 .19508 .17292 .20907 .18286 .22377 12 13 .15396 .18198 .16340 .19531 .17308 .20931 .18302 .22402 13 14 .15413 .18220 .16355 .19554 .17325 .20955 .18319 .22428 14 15 .15427 .18241 .16371 .19576 .17341 .20979 .18336 .22453 15 16 .15443 .18263 .16387 .19599 .17357 .21003 .18353 .2247'8 16 17 .15458 .18285 .16403 .19622 .17374 .21027 .18369 .22503 17 18 .15174 .18307 .16419 .19645 .17390 .21051 .18386 .22528 18 19 .15489 .18328 .16435 .19668 .17407 .21075 .18403 .22554 19 20 .15505 .18350 .16451 .19691 .17423 .21099 .18420 .22579 20 21 .15520 .18372 .16467 .19713 .17439 .21123 .18437 .22604 21 22 .15536 .18394 .16483 .19786 .17456 .21147 .18454 .22629 22 23 .15552 . 18416 .16499 .19759 .17472 .21171 .18470 .22655 23 24 .15567 .18437 .16515 .19782 .17489 .21195 .18487 .22680 24 25 .15583 .18459 .16531 .19805 .17505 .21220 .18504 .22706 25 26 .15598 .18481 .16547 .19828 .17522 .21244 .18521 .22731 26 27 .15614 .18503 .16563 .19851 .17533 .21268 .18538 .22756 27 28 .15630 .18525 .16579 .19874 .17554 .21292 .18555 .22782 28 29 .15645 .18547 .16595 .19897 .17571 .21316 .18572 ! .22807 29 30 .15661 .18569 .16611 .19920 .17587 .21341 .18588 .22833 30 31 .15676 .18591 .16627 .19944 .17604 .21365 .18605 .22858 31 32 .15692 .18613 .16644 .19967 .17620 .21389 .18622 .22884 32 33 .15708 .18635 .16660 .19990 .17037 .21414 .18639 .22909 33 34 .157S3 .18657 .16676 .20013 .17653 .21438 .18656 .22935 34 35 .J573U .18679 .16692 .20036 .17670 .21462 .18673 .22960 35 36 .15755 .18701 .16708 .20059 .17686 .21487 .18690 .22986 36 37 .15770 .18723 .16724 .20083 .17703 .21511 .18707 .23012 37 38 .15786 .18745 .16740 j .20106 .17719 .21535 .18724 .23037 38 39 .15802 .18767 .16756 .20129 .17736 .21560 .18741 .23003 39 40 .15818 .18790 .16772 .20152 .17752 .21584 .18758 .23089 40 41 .15833 .18812 .16788 .20176 .17709 .21609 .18775 .23114 41 42 .15849 .18834 .16805 .20193 .17736 .21033 .18792 .23140 42 43 .15865 .18856 .16821 .20222 .17802 .21658 .18809 .213166 43 44 .15880 .18878 .16837 .20246 .17819 .21682 .18826 .23192 44 45 .15898 .18901 .16853 .20269 . 17c f <35 .21707 .18843 .23217 45 46 .15912 .18923 .16869 .20292 .17852 .21731 .18860 .23243 46 47 .15923 .18945 .16885 .2C316 .17808 .21756 .18877 .23269 47 48 .15943 .18967 .16902 .20339 .17885 .21781 .18894 .23295 48 49 .15959 .18990 .16918 .20363 .17902 .21805 .18911 .23321 49 50 .15975 .19012 .16934 .20386 .17918 .21830 .18928 .23347 50 51 .15991 .19034 .16950 .20410 .17935 .21855 .18945 .23373 51 52 .16006 .19057 .16906 .20433 .17952 .21879 .18962 .23399 52 53 . 16022 .19079 .16983 .20457 .17968 .21904 .18979 .23424 53 54 .16038 .19102 .16909 .20480 .17985 .21929 .18996 .23450 54 55 .16054 .19124 .17015 .20501 .18001 .21953 .19013 .23476 55 56 .16070 .19146 .17031 .20527 .18018 .21978 .19030 .23502 56 57 .16085 .19169 .17047 .20551 .18035 .22003 .19047 .23529 57 58 .16101 .19191 .17064 .20575 .18051 .22028 .19064 .23555 58 59 .16117 .19214 .17080 .20598 .18068 .22053 .19081 .23581 59 60 .16133 .19236 .17096 .20622 .18085 .22077 .19098 .23607 60 255 TABLE XVII NATURAL VERSED SINES AND EXTERNAL SECANTS. 1 36 37 38 33 / Vers. Ex. sec. Vers. Ex. sec. Vers. Ex. sec. Vers. Ex. sec. .19098 .23607 .201S6 .25214 .21199 .20902 .22285 .28676 1 .19115 .23633 .20154 .25241 .21217 .26931 .22304 .28706 1 2 .19133 .23659 .20171 .25269 .21235 .26960 .22322 .28737 2 3 .19150 .23685 .20189 .25296 .21253 .20988 .22340 .28767 3 4 .19167 .23711 .20207 .25324 .21271 .27017 .22359 .28797 4 5 .19184 .23738 .20224 .25351 .21289 .27040 .22377 .28828 5 6 .19201 .23764 .20242 .25379 .21307 .27075 .22395 .28858 6 7 .19218 .23790 .20259 .25406 .21324 .27104 .22414 .28889 7 * 8 .19235 .23816 .20277 .25434 .21342 .27133 .22432 .28919 8 9 .19252 .23843 .20294 .25402 .21360 .27102 .22450 .28950 9 10 .19270 .23869 .20312 .25489 .21378 .27191 .22409 .28980 10 11 .19287 .23895 .20329 .25517 .21396 27221 .22487 .29011 11 12 .19304 .23922 .20347 .25545 .21414 ! 27250 .22506 .29042 12 13 .19321 .23948 .20365 .25572 .21432 .27279 .22524 .29072 13 14 .19338 .23975 .20382 .25600 .21450 .27308 .22542 .29103 14 15 .19356 .24301 .20400 .25628 .21468 .27337 .22501 .29133 15 1G .19373 .24028 .20417 .25656 .21486 .27306 .22579 .29164 16 17 .19390 .24054 .20435 .25683 .21504 .27396 .22598 .29195 17 18 .19407 .24081 .20453 .25711 21522 .27425 .22016 .29226 18 19 .19424 .24107 .20470 .25739 .'21540 .27454 .22634 .29256 19 20 .19442 .24134 .20488 .25707 .21558 .27483 .22653 .29287 20 21 .19459 .24100 .20506 .25795 .21576 .27513 .22671 .29318 21 22 .10476 .24187 .20523 .25823 .21595 .27542 .22090 .29349 22 23 .19493 .24213 .20541 .25851 .21013 .27572 .22708 .29380 23 24 .19511 .24240 .20559 .25879 .21031 .27601 .22727 .29411 24 25 .19528 .24267 .20576 .25907 .21649 .27630 .22745 .29442 25 26 .19545 .24293 .20594 .25935 .21667 .27660 .22764 .2947'3 20 27 .19562 .24320 .20612 .25963 .21685 .27689 .22782 .29504 27 28 .19580 .24347 .20029 .25991 .21703 .27719 .22801 .29535 28 29 .19597 .24373 .20647 .20019 .21721 .27748 .22819 .29506 20 30 .19614 .24400 .20665 .26047 .21739 .27778 .22838 .29597 30 31 .19632 .24427 .20082 .26075 .21757 .27807 .22856 .29628 31 32 .19649 .24454 .20700 .26104 .21775 .27837 .22875 .29059 32 33 .19666 .24481 .20718 .20132 .21794 .27'8G7 .22893 .29690 33 34 .1^684 .24508 .20736 .20100 .21812 .27896 .22912 .29721 34 35 .197'01 .24534 .20753 .26188 .21830 .27926 .22330 .29752 35 30 .19718 .24561 .20771 .26216 .21848 .27956 .22949 .29784 36 37 .19736 .24588 .20789 .26245 .21866 .27985 .22907 .29815 87 38 .19753 .24615 .20807 .26273 .21884 .28015 .22986 .29846 33 39 .19770 .21642 .20824 .26301 .21902 .28045 .23004 .29877 3!) 40 .19788 .24609 .20842 .20330 .21921 .28075 .23023 .29909 40 41 .19805 .24696 .20860 .20358 .21939 .28105 .23011 .29940 41 42 .19822 .24723 .20878 .20387 .21957 .28134 .230(50 .29971 42 43 .19840 .24750 .20895 .20415 .21975 .28164 .2307'9 .30003 43 44 .19857 .24777 .20913 .20443 .21993 .28194 .23097 .30034 44 45 .19875 .24804 .20931 .20472 .22012 .28224 .23116 .30006 45 46 .19892 .24832 .20949 .26500 .22030 .28254 .23134 .30097 46 47 .19909 .24859 .20967 .26529 .22048 .28284 .23153 .30129 47 48 .19927 .24886 .20985 .26557 .22066 .28314 .23172 .30100 48 49 .19944 .24913 .21002 .26586 .22084 .28344 .23190 .30192 49 50 .19962 .24940 .21020 .26615 .22103 .28374 .23209 .30223 50 51 .19979 .24967 .21038 .20043 .22121 .28404 .23228 .30255 51 52 .19997 .24995 .21056 .20072 .22139 .28434 .23246 .30287 52 53 .20014 .25022 .21074 .20701 .22157 .28464 .23205 .30318 53 54 .20032 .25049 .21092 .20729 .22176 .28495 .23283 .30350 54 55 .20049 .25077 .21109 .20758 .22194 .28525 .23302 .30382 55 5G .20066 .25104 .21127 .20787 .22212 .28555 .23321 .30413 56 57 .20084 .25131 .21145 .20815 ! 22231 .28585 .23339 .30445 57 58 .20101 .25159 .21163 .26844 .22249 .28615 .23358 .30477 58 59 .20119 .25186 .21181 .20873 .22267 .28646 i .23377 .30509 5'J 60 .20136 .25214 ! .21199 .20902 .22285 .28076 ! .233% .30541 60 25G TABLE XVII. NATURAL VERSED SINES AND EXTERNAL SECANTS. 40 41 42 43 Vers. Ex. sec. Vers. Ex. sec. Vers. Ex. sec. Vers. Ex. sec. .23396 .30541 .24529 .32501 .25686 .34563 .26865 .36733 1 .23414 .30573 .24548 .32535 .25705 .34599 .26884 .36770 1 2 .23433 .30605 .24567 .32508 .257-24 .34634 .20904 .36807 2 3 .23452 .30636 .24586 .32002 .25744 .34669 .26924 .36844 3 4 .23470 .30668 .24605 .32636 .25703 .34704 .26944 .36881 4 5 .23489 .30700 .24625 .32609 .25783 .34740 .20964 .36919 5 6 .23508 .30732 .24644 .32703 .25802 .34775 .26984 .36956 6 7 .23527 .30764 .24663 .32737 .25822 .34811 .27'004 .36993 7 8 .23545 .30796 .24682 .32770 .25841 .34846 .27024 .37030 8 9 .23564 .30829 .24701 .32804 .25801 .34882 .27043 .37'068 9 10 .23583 .308G1 .24720 .32838 .25880 .34917 .27003 .37105 10 11 .23602 .30893 .24739 .32872 .25900 .84053 .27083 .37143 11 12 .23620 .30925 .24759 .32905 .25920 .34988 .271C3 .37180 12 13 .23639 .30957 .2477'8 .32939 .25939 .35024 .27123 .37218 13 14 .23658 .30989 .24797 .32973 .25959 .35060 .27143 .37255 14 15 .23677 .31022 .24816 -.33007 .25978 .5095 .27103 .37293 15 16 .23696 .31054 .248S5 .33041 .25998 .35131 .27183 .37'330 16 17 .23714 .31086 .24854 .33075 .26017 .35167 .27203 .37368 17 18 .23733 .31119 .24874 .33109 .26037 .35203 .27223 .37406 18 19 .23752 .31151 .24893 .33143 .26056 .8.;2;:8 .27243 .37443 19 20 .23771 .31183 .24912 .33177 .26076 S5274 .27263 .37481 20 21 .23790 .81216 .24931 .33211 .26096 .35310 .27283 .37519 21 22 .23808 .31248 .24950 .33245 .20115 .35:346 .27303 .37556 2:2 23 .23827 .31281 .24970 .33279 .20135 .35382 .27323 .37'594 2i 24 .23846 .31313 .24989 .33314 .26154 .35418 .27343 .37'632 24 25 .23865 .31346 .25008 .33343 .26174 .35454 .273C3 .37070 25 26 .23884 .31373 .25027 .3a382 .26104 .35490 .27383 .377C8 26 27 .23903 .31411 .25047 .33416 .26213 .35526 .27403 .37746 27 28 .23922 .31443 .25066 .33451 .26233 .35502 .27423 .37784 28 29 .23941 .31476 .25085 .33485 .26253 .35598 .27443 .37822 29 30 .23959 .31509 .25104 .33519 .26272 .35634 .27403 .37860 31 .23978 .81541 .25124 .33554 .26202 .35070 .27483 .37898 31 32 .23997 .31574 .25143 .33588 .20312 .357'07 .27503 .37936 32 33 .24016 .31607 .251C3 .33622 .20381 .35743 .27523 .37'974 33 34 .24035 .31040 .25182 .33C57 .20351 .35779 .27543 .38012 34 35 .24054 .31072 .25201 .33091 .26371 .35815 .27CG3 .38051 35 36 .24073 .31705 .25220 .33726 .26300 .35852 .27583 .38089 36 37 .24092 .31733 .25240 .33700 .20410 .35888 .27603 .38127 37 38 .24111 .81771 252 r 9 .33795 .20430 .35924 .27623 .38165 33 39 .24130 .31804 * 2527 3 .33830 .26449 .35901 .27643 .38204 39 40 .24149 .31837 ! 25297 .338G4 .26469 .35997 .27063 .38242 40 41 .24168 .31870 .25317 .33899 .26489 .36034 .27683 .38280 41 42 .24187 .31903 .25333 .33934 .265C9 .30070 .277'03 .38319 42 43 .24206 .31936 .25355 .33CG8 .20528 .36107 .27723 .38357 43 44 .24225 .31969 .25375 .3-1003 .26543 .36143 .27743 .38396 44 45 .24244 .32002 .25394 .34GC3 .26508 .36180 .27764 .38434 45 46 .24262 .32035 .25414 .3407'3 I .26588 .36217 .27784 .38473 46 47 .24281 .32008 .25433 .34108 .26007 .36253 .27'804 .38512 47 48 .24300 .32101 .25452 .34142 .20627 .36290 .27'824 .38550 48 49 .24320 .32134 25472 .34177 .26647 .36327 .27844 .38589 49 50 .24339 .32168 ! 25491 .34212 .26667 .36363 .27864 ,.38628 50 51 .24358 .32201 .25511 .34247 .26686 .36400 .27884 .38666 51 52 .24377 .32234 .25530 .34282 .26706 .36437 .27905 .387'05 52 53 .24396 .32267 .25549 .34317 .26726 .36474 .27925 .38744 53 54 .24415 .32301 .25569 .34352 .26746 .36511 .27945 .38783 54 55 .24434 .32334 .25588 .34387 .26766 .36548 .27965 .38822 55 56 .24453 .32368 .25608 .34423 .20785 .36585 .27985 .38860 56 57 .24472 .32401 .25627 .34458 .26805 .36022 .28005 .38899 57 58 .24491 .32434 .25647 .34493 .26825 .36659 .28026 .33938 58 59 .24510 .32468 .25666 .34528 .38845 .30096 .28046 .38977 59 60 .24529 .32501 .25686 .34563 .26865 .36733 .28066 .39016 60 257 TABLE XVII. -NATURAL VERSED SINES AND EXTERNAL SECANTS. 44 45 46 47 1 Vers. Ex. sec. Vers. Ex. sec. Vers. Ex. sec. Vers. i Ex. sec. .28066 .39016 .29289 .41421 .30534 .43956 .31800 .46628 1 .28086 .39055 .29310 .41463 .30555 .43999 .31821 .46674 1 2 .28106 .39095 .29330 .41504 .30576 .44042 .31843 .46719 2 3 .28127 .39134 .29351 .41545 .30597 .44086 .31864 .46765 3 4 .28147 .39173 .29372 .41586 .30618 .44129 .31885 .46811 4 5 .28167 .39212 .29392 .41627 .30639 .44173 .31907 .46857 5 6 .28187 .39251 .29413 .41669 .30660 .44217 .31928 .46903 6 7 .28208 .39291 .29433 .41710 .30681 .44260 .31949 .46949 7 8 .28228 .39330 .29454 .41752 .30702 .44304 .31971 .46995 8 9 .28248 .39369 .29475 .41793 .30723 .44347 .31992 .47041 9 10 .28268 .39409 .29495 .41835 .30744 .44391 .32013 .47087 10 11 .28289 .39448 .29516 .41876 .30765 .44435 .32035 .47134 11 12 .28309 .39487 .29537 .41918 .30786 .44479 .32056 .47180 12 13 .28329 .39527 .29557 .41959 .30807 .44523 .32077 .47226 13 14 .28350 .39566 .29578 .42001 .30828 .44567 .32099 .47272 14 15 .28370 .39606 .29599 .42042 .30849 .44610 .32120 .47319 15 16 .28390 .39646 .29619 .42084 .30870 .44654 .32141 .47365 16 17 .28410 .39685 .29640 .42126 .30891 .44698 .32163 .47411 17 18 .28431 .39725 .29661 .42168 .30912 .44742 .32184 .47458 18 19 .28451 .39764 .29681 .42210 .30933 .44787 .32205 .47504 19 20 .28471 .39804 .29702 .42251 .30954 .44831 .32227 .47551 20 21 .28492 .39844 .29723 .42293 .30975 .44875 .32248 .47598 21 22 .28512 .39884 .29743 .42335 .30936 .44919 .32270 .47644 22 23 .28532 .39924 .29764 .42377 .31017 .44963 .32291 .47691 23 24 .28553 .39963 .29785 .42419 .31038 .45007 .32312 .47738 24 25 .28573 .40003 .29805 .42401 .31059 .45052 .32334 .47784 25 26 .28593 .40043 .29826 .42503 .31080 .45096 .32355 .47831 26 27 .28614 .40083 .20847 .42545 .31101 .45141 .32377 .47878 27 28 .28634 .40123 .298G8 .42587 .31122 .45185 .32398 .47925 28 29 .28655 .40163 .29888 .42630 .31143 .45229 .32420 .47972 29 80 .28675 .40203 .29909 .42672 .31105 .45274 .32441 .48019 30 31 .28695 .40243 .29930 .42714 .31186 .45319 .32462 .48066 31 32 .28716 .40283 .29951 .42756 .31207 .45363 .32484 .48113 32 33 .28736 .40324 .29971 .42799 .31228 .45408 .32505 .48160 33 34 .28757 .40364 .29902 .42841 .31249 .45452 .32527 .48207 34 35 .28777 .40404 .30013 .42883 .31270 .45497 .32548 .48254 35 36 .28797 .40444 .30034 .42926 .31291 .45542 .32570 .48301 36 37 .28818 .40485 .30054 .42968 .31312 .45587 .32591 .48349 37 38 .28838 ,40525 .30075 .43011 .31324 .45031 .32613 .48396 38 39 .28859 .40565 .30006 .43053 .318H5 .45076 .32034 .48443 39 40 .28879 .40606 .30117 .43096 .31376 .45721 .32656 .48491 40 41 .28900 .40646 .30138 .43139 .31397 .45766 .32677 .48538 41 42 .28920 .40687 .30158 .43181 .31418 .45811 .32699 .48586 42 43 .28941 .40727 .30179 .43224 .31439 .45856 .32720 .48633 43 44 .28961 .407'68 .30200 .43267 .31461 .45901 .32742 .48081 44 45 .28981 .40808 .30221 .43310 .31482 .43946 .32763 .48728 45 46 .29002 .40849 .30242 .43352 .31503 .45992 .32785 .48776 46 47 .29022 .40890 .30263 .43395 .31524 .40037 .32806 .48824 47 48 .29043 .40930 .30283 .43138 .31545 .46082 .32828 .48371 48 49 .29063 .40971 .30304 .43481 .31567 .46127 .32849 .48919 49 50 .29084 .41012 .30325 .43524 .31588 .46173 .32871 .48967 50 51 .29104 .41053 .30346 .43567 .31609 .46218 .32893 .49015 51 52 .29125 .41093 .30367 .43610 .31630 .46263 .32914 .49063 52 53 .29145 .41134 .30388 .43653 .31651 .46309 .32936 .49111 53 54 .29166 .41175 .30409 .43696 .31673 .46354 .32957 .49159 54 55 .29187 .41216 .30430 .43739 .31694 .40400 .32979 .49207 55 56 .29207 .41257 .30451 .43783 .31715 .40445 .33001 .49255 56 57 .29228 .41298 .30471 .43826 .31736 .46491 .33022 .49303 57 58 .29248 .41339 .30492 .43869 .31758 .40537 .33044 .49351 58 59 .29269 .41380 .30513 .43912 .31779 .46582 .33065 .49399 59 GO .29289 .41421 .30534 .43956 .31800 .46628 .33087 .49448 60 258 TABLE XVII. NATURAL VERSED SINES AND EXTERNAL SECANTS. ' 48 49 50* 51 / Vers. I Ex. sec. Vers. Ex. sec. Vers. Ex. sec. Vers. Ex. sec. .33087 .49448 .34394 .52425 .35721 .55572 .37068 .58902 1 .33109 .49496 .34416 .52476 .35744 .55626 .37091 .58959 1 2 .33130 .49544 .34438 .52527 .35766 .55680 .37113 .59016 2 3 .33152 .49593 .34460 .52579 .35788 .55734 .37136 .59073 3 4 .33173 .49641 .34482 .52630 .35810 .55789 .37158 .59130 4 5 .33195 .49690 .34504 .52681 .35833 .55843 .37181 .59188 5 6 .33217 .49738 .34526 .52732 .35855 .55897 .37204 .59245 6 7 .33238 .49787 .34548 .52784 .35877 .55951 .37226 .59302 7 8 .33260 .49835 .34570 .52835 .35900 .56005 .37249 .59360 8 9 .33282 .49884 .34592 .52886 .35922 .56060 .37272 .59418 9 10 .33303 .49933 .34614 .52938 .35944 .56114 .37294 .59475 10 11 .33325 .49981 .34636 .52989 .35967 .56169 .37317 .59533 11 12 .33347 .50030 .34658 .53041 .35989 .56223 .37340 .59590 12 13 .33368 .50079 .34680 .53092 .36011 .56278 .37362 .59648 13 14 .33390 .50128 .34702 .53144 .36034 .56332 .37385 .59706 14 15 .33412 .50177 .34724 .53196 .36056 .56387 .37408 .59764 15 16 .33434 .50226 .34746 .53247 .36078 .56442 .37430 .59822 16 17 .33455 .50275 .34768 .53299 .36101 .56497 .37453 .59880 17 18 .33477 .50324 .34790 .53351 .36123 .56551 .37476 .59938 18 19 .33499 .50373 .34812 .53403 .36146 .56606 .37498 .59996 19 20 .33520 .50422 .34834 .53455 .36168 .56661 .37521 .60054 20 21 .33542 .50471 .34856 .53507 .36190 .56716 .37544 .60112 21 22 .33564 .50521 .34878 .53559 .36213 .56771 .37'567 .60171 22 23 .33586 .50570 .34900 .53611 .36235 .56826 .37589 .60229 23 24 .33607 .50619 .34923 .53663 .36258 .56881 .37612 .60287 24 25 .33629 .50669 .34945 .53715 .36280 .56937 .37635 .60346 25 26 .33651 .50718 .34967 .53768 .36302 .56992 .37658 .60404 26 27 .33673 .50767 .34989 .53820 .36325 .57047 .37680 .60463 27 28 .33694 .50817 .35011 .53872 .36347 .57103 .37703 .60521 28 29 .33716 .50866 .35033 .53924 .36370 .57158 .37726 .60580 29 30 .33738 .50916 .35055 .53977 .36392 .57213 .37749 .60639 30 31 .33760 .50966 .35077 .54029 .36415 .57269 .37771 .60698 31 32 .33782 .51015 .35099 .54082 .36437 .57324 .37794 .60756 32 33 .33803 .51065 .35122 .54134 .36460 .57380 .37817 .60815 33 31 .33825 .51115 .35144 .54187 .36482 .57436 .37840 .60874 34 35 .33847 .51165 .35166 .54240 .36504 .57491 .37'862 .60933 35 36 .33809 .51215 .35188 .54292 .36527 .57547 .37885 .60992 36 37 .33891 .51265 .35210 .54345 .36549 .57603 .37908 .61051 37 38 .33912 .51314 .35232 .54398 .36572 .57659 .37931 .61111 38 39 .33934 .51364 .35254 .54451 .36594 .57715 .37954 .61170 39 40 .33956 .51415 .35277 .54504 .36617 .57771 .37976 .61229 40 41 .33978 .51465 .35299 .54557 .36639 .57827 .37999 .61288 41 42 .34000 .51515 .35321 .54610 .36662 .57883 .38022 .61348 42 43 .34022 .51565 .35343 .54663 .36684 .57939 .38045 .61407 43 44 .34044 .51615 .35365 .54716 .36707 .57995 .38068 .61467 44 45 .34065 .51665 .35388 .54769 .36729 .58051 .38091 .61526 45 46 .34087 .51716 .35410 .54822 .36752 .58108 .38113 .61586 46 47 .34109 .51766 .35432 .54876 .36775 .58164 .38136 .61646 47 48 .34131 .51817 .35454 .54929 .36797 .58221 .38159 .61705 48 49 .34153 .51867 .35476 .54982 .36820 .58277 .38182 .61765 49 50 .34175 .51918 .35499 .55036 .36842 .58333 .38205 .61825 50 51 .34197 .51968 .35521 .55089 .36865 .58390 .38228 .61885 51 52 .34219 .52019 .35543 .55143 .36887 .58447 .38251 .61945 52 53 .34241 .52069 .35565 .55196 .36910 .58503 .38274 .62005 53 54 .34262 .52120 1 .a5588 .55250 .36932 .58560 .38296 .62065 54 55 .34284 .52171 .35610 .55303 .36955 .58617 .38319 .62125 55 56 .34306 .52222 .35632 .55357 .36978 .58674 .38342 .62185 56 57 .34328 .52273 .35654 .55411 .37000 .58731 .38365 .62246 57 58 .34350 .52323 .35677 .55465 .37023 .58788 .38388 .62306 58 59 .34372 .52374 .35699 .55518 .37045 .58845 .38411 .62366 59 60 .34394 .52425 .35721 .55572 .37068 .58902 .38434 .62427 60 259 TABLE XVTT.-NATURAL VERSED SINES AND EXTERNAL SECANTS / 52 53 54 55 j Vers. Ex. sec. Vers. Ex. sec. Vers. j Ex. sec. Vers. Ex. sec. .38434 .62427 .39819 .66164 .41221 .70130 .42642 .74345 1 .38457 .62487 .39842 .66228 .41245 .70198 .42666 .74417 1 2 .38480 .62548 .39865 .66292 .41269 .70267 .42690 .74490 2 3 .38503 .62609 .39888 .66357 .41292 .70335 .42714 .74562 3 4 .38526 .62669 .39911 .66421 .41316 .70403 .42738 .74635 4 5 .38549 .62730 .39935 .66486 .41&39 .70472 .42762 .74708 5 6 .38571 .62791 .39958 .66550 .41363 .70540 .42785 .74781 6 7 .38594 .62&52 .39981 .66615 .41386 .70609 .42809 .74854 7 8 .38617 .62913 .40005 .66679 .41410 .70677 .42833 .74927 8 9 .38640 .62974 .40028 .66744 .41433 .70746 .42857 .75000 9 10 .38663 .63035 .40051 .66809 .41457 .70815 .42881 .75073 10 11 .38686 .63096 .40074 .66873 .41481 .70884 .42905 .75146 11 12 .38709 .63157 .40098 .66938 .41504 .70953 .42929 .75219 13 .38732 .63218 .40121 .67003 .41528 .71022 .42953 .75293 13 14 .38755 .63279 .40144 .67068 .41551 .71091 .42976 .75366 14 15 .38778 .63341 .40168 .67133 .41575 .71160 .43000 .75440 15 16 .38801 .63402 .40191 .67199 .41599 .71229 .43024 .75513 16 17 .38824 .63464 .40214 .67264 .41622 .71298 .43048 .75587 17 18 .38847 .63525 .40237 .67329 .41646 .71368 .43072 .75661 18 19 .38870 .6358? .40261 .67394 .41670 .71437 .43096 ,75734 19 20 .38893 .63648 .40284 .67460 .41693 .71506 .43120 .75808 20 21 .38916 .63710 .40307 .67525 .41717 .71576 .43144 .75882 21 22 .38939 .63772 .40331 .67591 .41740 .71646 .43168 .75956 22 23 .38962 .63834 .40354 .67656 .41764 .71715 .43192 .76031 23 24 .38985 .63895 .40378 .67722 .41788 .71785 .43216 .76105 24 25 .39009 .63957 .40401 .67788 .41811 .71855 .43240 .76179 25 26 .39032 .64019 .40424 .67853 .41835 .71925 .43264 .76253 26 27 .39055 .64081 .40448 .67919 .41859 .71995 .43287 .76328 27 28 .39078 .64144 .40471 .67985 .41882 .72065 .43311 .76402 28 29 .39101 .64206 .40494 .68051 .41906 .72135 .43335 .76477 29 30 .39124 .64268 .40518 .68117 .41930 .72205 .43359 .76552 30 31 .39147 .64330 .40541 .68183 .41953 .72275 .43383 .76626 31 32 .39170 .64393 .40565 .68250 .41977 .72346 .43407 .76701 32 33 .39193 .64455 .40588 .68316 .42001 .72416 .43431 .76776 33 34 .39216 .64518 .40611 .68382 .42024 .72487 .43455 .76851 34 35 .39239 .G4580 .40635 .68449 .42048 .72557 .43479 . 7^926 35 36 .39262 .64643 .40658 .68515 .42072 .72628 .43503 .77001 36 37 .39286 .64705 .40682 .G8582 .42096 .72698 .43527 .77077 37 38 .39309 .64768 .40705 .68648 .42119 .72769 .43551 .77152 38 . 39 .39332 .64831 .40728 .08715 .42143 .72840 .43575 .77227 39 40 .39355 .64894 .40752 .68782 .42167 .72911 .43599 .77303 40 41 .39378 .64957 .40775 .68848 .42191 .72982 .43623 .77378 41 42 .39401 .65020 .40799 .68915 .42214 .73053 .43647 .77454 42 43 .39424 .65083 .40822 .68982 .42238 .73124 .43671 \77530 43 44 .39447 .65146 .40846 .69049 .42262 .73195 .43695 .77606 44 45 .39471 .65209 .40869 .69116 .42285 .73267 .43720 .77681 45 46 .39494 .65272 .40893 .69183 .42309 .73338 .43744 .77757 46 47 .39517 .65336 .40916 .G9S50 .42333 .73409 .43768 .77833 47 48 .39540 .65399 .40939 .69318 .42357 .73481 .43792 .77910 48 49 .39563 .65462 .40963 .69385 .42381 .73552 .43816 .77986 49 50 .39586 .65526 .40986 .69452 .42404 .73624 .43840 .78062 50 51 .39610 .65589 .41010 .69520 .42428 .73696 .43864 .78138 51 52 .39633 .65653 .41033 .69587 .42452 .73768 .43888 .78215 62 53 .39656 .65717 .41057 .69655 .42476 .73840 .43912 .78291 53 54 .39679 .65780 .41080 .69723 .42499 .73911 .43936 .78368 54 55 .39702 .65844 .41104 .69790 .42523 .73983 .43960 .78445 55 56 .39726 .65908 .41127 .69858 .42547 74056 .43984 .78521 56 57 .39749 .65972 .41151 .69926 .42571 .74128 .44008 .78598 57 58 .39772 .66036 .41174 .69994 .42595 .74200 .44032 .78675 68 59 .39795 .66100 .41198 .70062 .42619 .74272 .44057 .78752 59 60 .39819 .66164 .41221 .70130 .42642 .74345 .44081 .78829 60 260 TABLE XVII. NATURAL VERSED SINES AND EXTERNAL SECANTO 56 57 58 59 / Vers. Ex. sec. Vers. Ex. sec. Vers. Ex. sec. Vers. ;Ex.sec. .44081 .78829 .45536 .83608 .47008 .88708 .48496 .94160 1 .44105 .78906 .45560 .83690 .47033 .88796 .48521 .94254 1 2 .44129 .78984 .45585 .83773 .47057 .88884 .48546 .94349 2 3 .44153 .79061 .45609 .83855 .47082 .88972 .48571 .94443 3 4 .44177 .79138 .45634 .83938 .47107 .89060 .48596 .94537 4 5 .44201 .79216 .45658 .84020 .47131 .89148 .48621 .94632 5 6 .44225 .79293 .45683 .84103 .47156 .89237 .48646 .94726 6 7 .44250 .79371 .45707 .84186 .47181 .89325 .48671 .94821 7 8 .44274 .79449 .45731 .84269 .47206 .89414 .48696 .94916 8 9 .44298 .79527 .45756 .84352 .47230 .89503 .48721 .95011 9 10 .44322 .79604 .45780 .84435 .47255 .89591 .48746 .95106 10 11 .44346 .79682 .45805 .84518 .47280 .89680 .48771 .95201 11 12 .44370 .79761 .45829 .84601 .47304 .89769 .48796 .95296 12 13 .44395 .79839 .45854 .84685 .47329 .89858 .48821 .95392 13 14 .44419 .79917 .45878 .84768 .47354 .89948 .48846 .95487 14 15 .44443 .79995 .45903 .84852 .47379 .90037 .48871 .95583 15 16 .44467 .80074 .45927 .84935 .47403 .90126 .48896 .95678 16 17 .44491 .80152 .45951 .85019 .47428 .90216 .48921 .95774 17 18 .44516 .80231 .45976 .85103 .47453 .90305 .48946 .95870 18 19 .44540 .80309 .46000 .85187 .47478 .90395 .48971 .95966 19 20 .44564 .80388 .46025 .85271 .47502 .90485 .48996 .96062 20 21 .44588 .80467 .46049 .85355 .47527 .90575 .49021 .96158 21 22 .44612 .80546 .46074 .85439 .47552 .90665 .49046 .96255 22 23 .44637 .80625 .46098 .85523 .47577 .90755 .49071 .96351 23 24 .44661 .80704 .46123 .85608 .47601 .90845 .49096 .96448 24 25 .44685 .80783 .46147 .85692 .47626 .90935 .49121 .96544 25 26 .44709 .80862 .46172 .85777 .47651 .91026 .49146 .96641 26 27 .44734 .80942 .46196 .85861 .47676 .91116 .49171 .967'38 27 28 .44758 .81021 .46221 .85946 .47701 .91207 .49196 .96835 28 29 .44782 .81101 .46246 .86031 .47725 .91297 .49221 .96932 29 30 .44806 .81180 .46270 .86116 .47750 .91388 .49246 .97029 30 31 .44831 .81260 .46295 .86201 .47775 .91479 .49271 .97127 31 32 .44855 .81340 .46319 .86286 .47800 .91570 .49296 .97224 32 33 .44879 .81419 .46344 .86371 .47825 .91661 .49321 .97322 33 34 .44903 .81499 .46368 .86457 .47849 .91752 .49346 .97420 34 35 .44928 .81579 .46393 .86542 .47874 .91844 .49372 .97517 35 36 .44952 .81659 .46417 .86627 .47899 .91935 .49397 .97615 36 37 .44976 .81740 .46442 .86713 .47924 .92027 .49422 .97713 37 38 .45001 .81820 .46466 .86799 .47949 .92118 .49447 .97811 38 39 .45025 .81900 .46491 .86885 .47974 .92210 .49472 .97910 39 40 .45049 .81981 .46516 .86990 .47998 .92302 .49497 .98008 40 41 .45073 .82061 .46540 .87056 .48023 .92394 ,49522 .98107 41 42 .45098 .82142 .46565 .87142 .48048 .92486 .49547 .98205 42 43 .45122 .82222 .46589 .87229 .48073 .9.2578 .49572 .98304 43 44 .45146 .82303 .46614 .87315 .48098 .92670 .49597 .98403 44 45 .45171 .82384 .46639 .87401 .48123 .92762 .49623 .98502 45 46 .45195 .82465 .46663 .87488 .48148 .92855 .49648 .98601 46 47 .45219 .82546 .46688 .87574 .48172 .92947 .49673 .98700 47 48 .45244 .82627 .46712 .87661 .48197 .93040 .49698 .98799 48 49 .45268 .82709 .46737 .87748 .48222 .93133 .49723 .98899 49 50 .45292 .82790 .46762 .87834 .48247 .93226 .49748 .98998 50 51 .45317 .82871 .46786 .87921 .48272 .93319 .49773 .99098 51 52 .45341 .82953 .46811 .88008 .48297 .93412 .49799 .99198 52 53 .45365 .83034 .46836 .88095 .48322 .93505 .49824 .99298 53 54 .45390 .83116 .46860 .88183 .48347 .93598 .49849 .99398 54 55 .45414 .83198 .46885 .88270 .48372 .93602, .49874 .99498 55 56 .45439 .a3280 .46909 .88357 .48396 .93785 .49899 .99598 56 57 .45463 .8-3362 .46934 .88445 .48421 .93879 .49924 .99698 57 58 .45487 .83444 .46959 .88532 .48446 .93973 .49950 .99799 58 59 .45512 .83526 .46983 .88620 .48471 .94066 .49975 .99899 59 60 .45536 .83608 .47008 .88708 1 .48496 .94160 .50000 .00000 60 361 TABLE XVII. -NATURAL VERSED SINES AND EXTERNAL SECANTS. 6 1 6 2 3 Vers. Ex .se Vers. Ex. sec. Vers. Ex. sec. Vers. Ex. sec. .50000 1.00000 .51519 1.06267 .53053 1.13005 .54601 1.20269 1 .50025 1.00101 .51544 1.06375 .53079 1.13122 .54627 1.20395 1 2 .50050 1.00202 .51570 1.06483 .53104 1.13239 .54653 1.20521 2 3 .50076 1.00303 .51595 1.06592 .53130 1.13356 .54679 1.20647 3 4 .50101 1.00404 .51621 1.06701 .53156 1.13473 .54705 1.20773 4 5 .50126 1.00505 .51646 1.06809 .53181 1.13590 .54731 1.20900 5 6 .50151 1.00607 .51672 1.06918 .53207 1.13707 .54757 1.21026 6 7 .50176 1.00708 .51697 1.07027 .53233 1.13825 .54782 1.21153 7 8 .50202 1.00810 .51723 1.07137 .53258 1.13942 .54808 1.21280 8 9 .50227 1.00912 .51748 1.07246 .53284 1.14060 .54834 1.21407 9 10 .50252 1.01014 .51774 1.07356 .53310 1.14178 .54860 1.21535 10 11 .50277 1.01116 .51799 1.07465 .53336 1.14296 .54886 1.21662 11 12 .50303 1.01218 .51825 1.07575 .53361 1.14414 .54912 1.21790 12 13 .50328 1.01320 .51850 1.07685 .53387 1.14533 .54938 1.21918 13 14 .50353 1.01422 .51876 1.07795 .53413 1.14651 .54964 1.22045 14 15 .50378 1.0)525 .51901 1.07905 .5:3439 1.14770 .54990 .22174 15 16 .50404 1.01628 .51927 1.08015 .53464 1.14889 .55016 .22302 16 17 .50429 1.01730 .51952 1.08126 .53490 1.15008 .55042 .22430 17 18 .50454 1.01833 .51978 1.08236 .53516 1.15127 .55068 .22559 18 19 .50479 1.01936 .52003 1.08347 .53542 1.15246 .55094 .22688 19 20 .50505 1.02039 .52029 1.08458 .53567 1.15366 .55120 .22817 20 21 .50530 1.02143 .52054 1.08569 .53593 1.15485 .55146 1.22946 21 22 .50555 1.02246 .52080 1.08680 .53619 1.15605 .55172 1.23075 22 23 .50581 1.02349 .52105 1.08791 .53645 1.15725 .55198 1.23205 23 24 .50606 1.02453 .52131 1.08903 .53670 1.15845 .55224 1.23334 24 25 .50631 1.02557 .52156 1.09014 .53096 1.15965 .55250 1.23464 25 26 .50656 1.02661 .52182 1.09126 .53722 1.16085 .55276 1.23594 26 27 .50682 1.02765 .52207 1.09238 .53748 1.16206 .55302 1.23724 27 28 .50707 1.02869 .52233 1.09350 .53774 1.16326 .55328 1.23855 28 29 .50732 1.02973 .52259 1.09462 .53799 1.16447 .55354 1.23985 29 30 .50758 1.03077 .52284 1.09574 .53825 1.16568 .55380 1.24116 30 31 .50783 1.03182 .52310 1.09686 .53851 1.16689 .55406 1.24247 31 32 .50808 1.03286 .52335 1.09799 .53877 1.16810 .55432 1.24378 32 33 .50834 1.03391 .52361 1.09911 .53903 1.16932 .55458 1.24509 33 34 .50859 1.03496 .52386 1.10024 .53928 1.17053 .55484 1.24640 34 35 .50884 1.03601 .52412 1.10137 .53954 1.17175 .55510 1.24772 35 36 .50910 1.03706 .52438 1.10250 .53980 1.17297 .55536 1.24903 36 37 .50935 1.03811 .52463 1.10363 .54006 1.17419 .55563 1.25035 37 38 .50960 1.03916 .52489 1.10477 .54032 1.17541 .55589 1 25167 38 39 .50986 1.04022 .52514 1.10590 .54058 1.17663 .55615 1.25300 39 40 .51011 1.04128 .52540 1.10704 .54083 1.17786 .55641 1.25432 40 41 .51036 1.04233 .52566 1.10817 .54109 1.17909 .55667 1.25565 41 42 .51062 1.04339 .52591 1.10931 .54135 1.18031 .55693 1.25697 42 43 .51087 1.04445 .52617 1.11045 .54161 1 . 18154 .55719 1.25830 43 44 .51113 1.04551 .52642 1.11159 .54187 1.18277 .55745 1.25963 44 45 .51138 1.04658 .52668 1.11274 .54213 1.18401 .55771 1.26097 45 46 .51163 1.04764 .52694 1.11388 .54238 1.18524 .55797 1.26230 46 47 .51189 1.04870 .52719 1.11503 .54264 1.18648 .55823 1.26364 47 48 .51214 1.04977 .52745 1.11617 .54290 1.18772 .55849 1.26498 48 49 .51239 1.05084 .52771 1.11732 .54316 1.18895 .55876 1.26632 49 50 .51265 1.05191 .52796 1.11847 .54342 1.19019 .55902 1.26766 50 51 .51290 1.05298 .52822 1.11963 .54368 1.19144 .55928 1.26900 51 52 .51316 1.05405 .52848 1.12078 .54394 1.19268 .55954 1.27035 52 53 .51341 1.05512 .52873 1.12193 .54420 1.19393 .55980 1.27169 53 54 .51366 1.05619 .52899 1.12309 .54446 1.19517 .56006 1.27304 54 55 .51392 1.05727 .52924 1.12425 .54471 1.19642 .56032 1.27439 55 56 .51417 1.05835 .52950 1.12540 .54497 1.19767 .56058 1.27574 56 57 .51443 1.05942 .52976 1.12657 .54523 1.19892 .56084 1.27710 57 58 .51468 1.06050 .53001 1.12773 .54549 1.20018 .56111 1.27845 58 59 .51494 1.06158 .53027 1.12889 .54575 1.20143 .56137 1.27981 59 60 .51519 1.06267 .53053 1.13005 .54001 1.20269 .56163 1.28117 60 262 TABLE XVII. NATURAL VERSED SINES AND EXTERNAL SECANTS. 6 40 6 5 6 6 6 7 Vers. Ex. sec. Vers. Ex. sec. Vers. Ex. sec. Vers. Ex. sec. .56163 1.28117 .57738 1.36620 ! .59326 1.45859 .60927 .55930 1 .56189 1.28253 .57765 1.36768 ; .59353 1.46020 .60954 .56106 1 2 .56215 1.28390 .57791 1.36916 .59379 1.46181 .60980 .56282 2 a .56241 1.28526 .57817 1.37064 .59406 1.46342 .61007 .56458 3 4 .56267 1.28663 .57844 1.37212 .59433 1.46504 .61034 .56634 4 5 .56294 1.28800 .57870 1.37361 .59459 1.46665 .61061 .56811 5 6 .56320 1.28937 I .57896 1.37509 i .59486 1.46827 .61088 .56988 6 7 .56346 1.29074 i .57923 1.37658 .59512 1.46989 .61114 .57165 7 8 .56372 1.29211 .57949 1.37808 .59539 1.47152 .61141 .57342 8 9 .56398 1.29349 j .57976 1.37957 .59566 1.47314 .61168 .57520 9 10 .56425 1.29487 .58002 1.3810? .59592 1. 47477 .61195 .57698 10 11 .56451 1.29625 .58028 1.38256 .59619 1.47640 .61222 .57876 11 12 .56477 1-29763 .58055 1.38406 .59645 1.47804 .61248 .58054 12 13 .56503 1.29901 .58081 1.38556 '.59672 1.47967 .61275 .58233 13 14 .56529 1.30040 .58108 1.38707 .59699 1.48131 .61302 .58412 14 15 .56555 1.30179 .58134 .38857 .59725 1.48295 .61329 .58591 15 16 .56582 1.30318 .58160 .39008 .59752 1.48459 .61356 .58771 16 17 .56608 1.30457 .58187 .39159 .59779 1.48624 .61383 .58950 17 18 .56634 1.30596 .58213 .39311 .59805 1.48789 : .61409 .59130 18 19 .56660 1.307.35 ! .58240 .39462 .59832 1.48954 .61436 .59311 19 20 .56687 1.30875 .58266 .39614 .59859 1.49119 .61463 .59491 20 21 .56713 1.31015 .58293 .39766 .59885 1.49284 .61490 .59672 21 22 .56739 1.31155 .58319 .39918 .59912 1.49450 .61517 .59853 22 23 .56765 1.31295 .58345 .40070 .59938 1.49616 .61544 .60035 23 24 .56791 1.31436 .58372 1.40222 .59965 1.49782 .61570 .60217 24 25 .56818 1.31576 .58398 1.40375 .59992 1.49948 .61597 .60399 25 2(5 .56844 1.31717 .58425 1.40528 .60018 1.50115 .61624 .60581 26 27 .56870 1.31858 .58451 1.40681 .60045 1.50282 .61651 .60763 27 28 .56896 1.31999 .58478 1.40835 .60072 1.50449 .61678 .60946 28 29 .56923 1.32140 .58504 1.40988 .60098 1.50617 .61705 .61129 29 30 .56949 1.32282 .58531 1.41142 .60125 1.50784 .61732 .61313 30 31 .56975 1.32424 .5R557 1.41296 .60152 1.50952 .61759 .61496 31 32 .57001 1.32566 .58584 1.41450 .60178 1.51120 .61785 .61680 32 33 .57028 1.32708 .58610 1.41605 .60205 1.51289 .61812 .61864 33 34 .57054 1.32850 .58637 1.41760 .60232 1.51457 .61839 .62049 34 35 .57080 1.32993 .58663 1.41914 .60259 1.51626 .61866 .62234 35 30 .57106 1. .33135 .58690 1.42070 .60285 1.51795 .61893 .62419 36 37 .571 as 1.33278 .58716 1.42225 .60312 .51965 .61920 .62604 37 38 .57159 1.33422 .58743 1.42380 .60339 .52134 .61947 .62790 38 39 .57185 1., 33565 .58769 1.42536 .60365 .52304 .61974 .62976 39 40 .57212 1.33708 .58796 1.42692 .60392 .52474 .62001 .63162 40 41 .57238 1.33852 .58822 1.42848 .60419 .52645 .62027 .63348 41 42 .57264 1.33996 .58849 1.43005 .60445 .52815 i .62054 .63535 42 43 .57291 1.34140 .58875 1.43162 .60472 .52986 .62081 .63722 43 44 .57317 1.34284 .58902 1.43318 .60499 .53157 .62108 .63909 44 45 .57343 1.34429 .58928 1.43476 .60526 .53329 .62135 .64097 45 40 .57369 1.34573 .58955 .43633 .60552 .53500 .62162 .64285 46 47 .57396 1.34718 .58981 .43790 .60579 .53672 .62189 .64473 47 48 .57422 1.34863 .59008 .43948 .60606 .53845 .62216 .64662 48 49 .57448 1.35009 .59034 .44106 .60633 .54017 .62243 .64851 49 50 . 57475 1.35154 .59061 .44264 .60659 .54190 .62270 .65040 50 51 .57501 1.35300 .59087 .44423 .60686 .54363 .62297 .65229 51 58 .57527 1., 35446 i .59114 .44582 .60713 .54536 .62324 .65419 52 53 .57554 1.35592 .59140 .44741 .60740 .54709 .62351 .65609 53 54 .57580 1.35738 .59167 .44900 .60766 .54883 .62378 .65799 54 55 .57606 1.35885 .59194 .45059 .60793 .5505? .62405 .65989 55 56 .57633 1.36031 .59220 .45219 .60820 .55231 .62431 1.66180 50 57 .57659 1.36178 .59247 .45378 .60847 .55405 .62458 1.66371 57 68 .57685 1.36325 .59273 .45539 .60873 .55580 .62485 1.66563 58 59 .57712 1.36473 .59300 .45699 .60900 .55755 .62512 1.66755 59 60 .57738 1.36620 .59326 .45859 .60927 .55930 .62539 1.66947 00 263 TABLE XVII. NATURAL VERSED SINES AND EXTERNAL SECANTS. / 68' 69 70 71 > Vers, Ex. sec Vers. Ex. sec. Vers. Ex. sec. Vers. Ex. sec 1 .62539 1.66947 .64103 1.79043 1 .65798 1.92380 .67443 2.07155 .62566 1.67139 .64190 1.79254 .65825 1.92614 .67471 2.07'415 1 ji .62593 1.67332 .64218 1.79466 .65853 1.92849 .67498 2.07675 2 J .62620 1.67525 .64245 1.79679 .65880 1.93083 .67526 2.07936 3 i .62647 1.67718 .64272 1.79891 .65907 1.93318 .67553 2.08197 i t .62674 1.67911 .64299 1.80104 .65935 1.93554 .67581 2.08459 t t .62701 1.68105 .64326 1.80318 .65962 1.93790 .67608 2.087'21 e ( .62728 1.68299 .64353 1.80531 .65989 1.94026 .67636 2.089&3 5 8 .62755 1.68494 .64381 1.80746 .66017 1.94263 .67663 2.09246 8 9 .62782 1.68689 .64408 1.80960 .66044 1.94500 .67691 2.09510 9 10 .62809 1.68884 .64435 1.81175 .66071 1.94737 .67718 2.09774 10 11 .62836 1.69079 .64462 1.81390 .66099 1.94975 .67746 2.10038 11 12 .62863 1.69275 .64489 1.81605. .66126 1.95213 .67773 2.10303 12 13 .62890 1.69471 .64517 1.81821 .66154 1.95452 .67801 2.10568 13 14 .62917 1.69667 .64544 1.82037 .66181 1.95691 .67829 2.10834 14 15 .62944 1:69864 .64571 1.82254 .66208 1.95931 .67856 2.11101 15 16 .62971 1.70061 .64598 1.82471 .66236 1.96171 .67884 2.11367 16 17 .62998 1.70258 .64625 1.82688 .GG2G3 1.96411 .67911 2.11635 17 18 .63025 1.70455 .64653 1.82906 .66290 1.96652 .67939 2.11903 18 19 .63052 1.70653 .64680 1.83124 .66318 1.96893 .G7966 2.12171 19 20 .63079 1.70851 .64707 1.83342 .66345 1.97135 .67994 2.12440 20 21 .63106 1.71050 .64734 1.83561 .66373 1.97377 .68021 2.12709 21 22 .63133 1.71249 .64761 1.83780 .(56400 1.97619 .68049 2.12979 22 23 .63161 1.71448 .64789 1.83999 .66427 1.97862 .68077 2.13249 23 24 .63188 1.71647 .64816 1.84219 .66455 1.98106 .68104 2.13520 24 25 .63215 1.71847 .64843 1.84439 .66482 1.98349 .68132 2.13791 25 26 .63242 1.72047 .64870 1.84659 .66510 1. 98594 .68159 2.14063 26 27 .63269 1.72247 .64898 1.84880 .66537 1.98838 .68187 2.14335 27 28 .63296 1.72448 .64925 1.85102 .66564 1.99083 .68214 2.14608 28 29 .63323 1.72619 .64952 1.85323 .66592 1.99329 .68242 2.14881 29 30 .63350 1.72850 .64979 1.85545 .66619 1.99574 .68270 2.15155 30 31 .63377 1.73052 .65007 1.85767 .66647 1.99821 .68297 2.15429 31 32 .63404 1.73254 .65034 1.85990 .66674 2.00067 .68325 2.15704 32 33 .63431 1.73456 .65061 1.86213 .66702 2.00315 .68352 2.15979 33 34 .63458 1.73659 .65088 1.86437 .66729 2.00562 .68380 2.16255 34 35 .63485 1.73862 .65116 1.86661 .66756 2.00810 .68408 2.16531 35 36 .63512 1.74065 .65143 1.86885 .66784 2.01059 .68435 2.16808 36 37 .63539 1.74269 .65170 1.87109 .66811 2.01308 .68463 2.17085 37 38 .63566 1.74473 .65197 1.87334 .66839 2.01557 .68490 2.17363 38 39 .63594 1.74677 .65225 1.87560 .66866 2.01807 .68518 2.17641 39 40 .63621 1.74881 .65252 1.87785 .66894 2.02057 .68546 2.17920 40 41 .63648 1.75036 .65279 1.88011 .66921 2.02308 .68573 2.18199 41 42 .63675 1.75292 .65306 1.88238 .66949 2.02559 .68601 2.18479 42 43 .63702 1.75497 .65334 1.88465 .6697'6 2.02810 .68628 2.18759 43 44 .63729 1.75703 .65361 1.88692 .67003 2.03062 .68656 2.19040 44 45 .63756 1.75909 .65388 1.88920 .67031 2.03315 .68684 2.19322 45 46 .63783 1.76116 .65416 1.89148 .67058 2.03568 .68711 2.19604 46 47 .63810 1.76323 .65443 1.89376 .67086 2.03821 .68739 2.19886 47 48 .63838 1.76530 .65470 1.89605 .67113 2.04075 .68767 2.20169 48 49 .63865 1.76737 .65497 1.89834 .67141 2.04329 .68794 2.20453 49 50 .63892 1.76945 .65525 1.90063 .67168 2.04584 .68822 2.20737 50 51 .63919 1.77154 .65552 1.90293 .67196 2.04839 .68849 2.21021 51 52 .63946 1.77362 ! .65579 1.90524 .67223 2.05094 .68877 2.21306 52 53 .63973 1.77571 ! .65607 1.90754 .67251 2.05350 .68905 2.21592 53 54 .64000 1 77780 I .65634 1.90986 .67278 2.05607 .68932 2.21878 54 55 .64027 1.77990 ! .65661 1.91217 .67306 2.05864 .68960 2.22165 55 56 .64055 1.78200 .65689 1.91449 .67333 2.06121 .68988 2.22452 56 57 .64082 1.78410 .65716 1.91681 .67361 2.06379 .69015 2.22740 57 58 .64109 1.78621 .65743 1.91914 .67388 2.06637 .69043 2.23028 58 59 .64136 1.78832 .65771 1.92147 .67416 2.06896 .69071 2.23317 59 60 .64163 1.79043 .65798 1.92380 1 .67443 2.07155 .69098 2.23607 60 264 TABLE XVII. NATURAL VERSED SINES AND EXTERNAL SECANTS. ' 72 73 74 75 Vers. Ex. sec. Vsrs. Ex. sec. Vers. Ex. sec. Vers. Ex. sec. .69098 2.23607 .70763 2.42030 .72436 2.62796 .74118 2.86370 1 .69126 2.23897 .70791 2.42356 .72404 2.63164 .74146 2.86790 1 2 .69154 2.24187 .70818 2.42683 .72492 2 63533 .74174 2.87211 2 3 .69181 2.24478 .70846 2.43010 .72520 2.63903 .74202 2.87633 3 4 .69209 2.24770 .70874 2.43337 .72548 2.64274 .74231 2.88056 4 5 .69237 2.25062 .70902 2.43666 .72576 2.64645 .74259 2.88479 5 6 69264 2.25355 .70930 2.43995 .72604 2.65018 .74287 2.88904 6 7 .69292 2.25648 .70958 2.44324 .72632 2.65391 .74315 2.89330 7 8 .69320 2.25942 .7'0985 2.44655 .72660 2.65765 .74343 2.89756 8 9 .69347 2 26237 .71013 2.44986 .72688 2.66140 .74371 2.90184 9 10 .69375 2.26531 .71041 2.45317 .72716 2.66515 .74399 2.90613 10 11 .69403 2.26827 .71069 2.45650 .72744 2.66892 .74427 2.91042 U 13 .69430 2.27123 .71097 2.45983 .72773 2.67269 .74455 2.91473 IS 13 .69458 2.27420 .71125 2.46316 .72800 2.67647 .74484 2.91904 13 14 .69486 2.27717 .71153 2.46651 .72828 2.68025 .74512 2.92337 14 15 .69514 2.28015 .71180 2.46986 .72856 2.68405 .74540 2.92770 15 10 .69541 2.28313 .71208 2.47321 .72884 2.68785 .74568 2.93204 10 17 .69569 2.28612 .71236 2.47658 .72912 2.69167 .74596 2.93640 17 18 .69597 2.28912 .71264 2.47995 .72940 2.69549 .74024 2.94076 18 19 .69624 2.29212 .71292 2.48333 .72968 2.69931 .74052 2.94514 19 20 .69652 2.29512 .71320 2.48671 .72996 2.70315 .74680 2.94952 20 21 .69680 2.298J4 .71348 2.49010 .73024 2.70700 .74709 2.95392 21 22 .69708 2.30115 .71375 2.49350 .73052 2.71085 . 74737 2.95832 22 23 .69735 2.30418 .71403 2.49691 .73080 2.71471 .74765 2.96274 23 24 .69703 2.30721 .71431 2.50032 .73108 2.71858 .74793 2.96716 24 25 .69791 2.31024 .71459 2.50374 .73136 2.72246 .74821 2.97160 25 26 .69818 2.31328 .71487 2.50716 .73164 2.72635 .74849 2.97604 20 27 .69846 2.31633 .71515 2.51000 .73192 2.73024 .74878 2.98050 27 28 .69874 2.31939 .71543 2.51404 .73220 2.73414 .74906 2.98497 28 29 .69902 2 32244 .71571 2.51748 .73248 2.73800 .74934 2.98944 29 30 .69929 2.32551 .71598 2.52094 .7'3276 2.74198 .74962 2.99393 30 31 .69957 2.32858 .71026 2.52440 .73304 2.74591 .74990 2.99843 31 32 .69985 2.33166 .71054 2.52787 .73332 2.7'4984 .75018 3.00293 32 33 .70013 2.33474 .71082 2.53134 .73360 2.75379 .75047 3.00745 33 34 .70040 2.33783 .71710 2.53482 .73388 2.75775 .75075 3.01198 34 35 .70008 2.34092 .71738 2.53831 .73416 2.76171 .75103 3.01652 35 30 .70096 2.34403 .71766 2.54181 .73444 2.76568 .75131 3.02107 30 37 .70124 2.34713 .71794 2.54531 .73472 2.76906 .75159 3.02503 37 38 .70151 2.35025 .71822 2.54883 .73500 2.77305 .75187 3.03020 38 39 .70179 2.35336 .71850 2.55235 .73529 2.77705 .75216 3.03479 39 40 .70207 2.35649 .71877 2.55587 .73557 2.78166 .75244 3.03938 40 41 .70235 2.35962 .71905 2.55940 .73585 2.78568 .75272 3.04398 41 42 .70263 2.36276 .71933 2.56294 .73613 2.78970 .75300 3.04860 42 43 .70290 2.36590 .71961 2.56649 .73641 2.79374 .75328 3.05322 43 44 .70318 2.36905 .71989 2.57005 .73009 2.79778 .75356 3.05786 44 45 .70346 2.37221 .72017 2.57361 .73097 2.80183 .75385 3.06251 45 40 .70374 2.37537 .72045 2.57718 .73725 2.80589 .75413 3.06717 40 47 .70401 2.37854 .72073 2.58076 .73753 2.80996 .75441 3.07184 47 48 .70429 2.38171 .72101 2.58434 .73781 2.81404 .75469 3.07652 48 49 .70457 2.38489 .72129 2.58794 .73809 2.81813 .75497 3.08121 49 50 .70485 2.38808 .72157 2.59154 .73837 2.82223 .75526 3.08591 50 51 .70513 2.39128 .72185 2.59514 .73865 2.82633 .75554 3.09063 51 52 .70540 2.39448 .72213 2.59876 .73893 2.83045 .75582 3.09535 52 53 .70568 2.39768 .72241 2.60238 .73921 2.83457 .75610 3.10009 53 54 .70596 2.40089 .72269 2.60601 .73950 2.83871 .75639 3.10484 54 55 .70624 2.40411 .72296 2.60965 .73978 2.84285 .75667 3.10960 55 50 .70652 2.40734 .72324 2.61330 .74006 2.84700 .75695 3.11437 50 57 .70679 2.41057 .72352 2.61695 .74034 2.85116 .75723 3.11915 57 58 .70707 2.41381 .72380 2.62061 .74062 2.85533 .75751 3.12394 58 59 .70735 2.41705 .72408 2.62428 .74090 2.85951 .75780 3.12875 59 60 .70763 2.42030 .72436 2.6279G .74118 2.86370 .75808 3.13357 60 265 XVII. NATURAL VERSED SINES AND EXTERNAL SECANTS, / 7 6 7 7 7 8 7 9 Vers. Ex. sec. Vers. Ex. sec. Vers. Ex. sec. Vers. Ex. sec. .75808 3.13357 .77505 3.44541 .79209 3.80973 .80919 4.24084 1 .75836 3.13839 .77533 3.45102 .79237 3.81633 .80948 4.24870 1 2 .75804 3.14323 .77562 3.45664 .79266 3.82294 .80976 4.25658 2 3 .75892 3.14809 .77590 3.46228 .79294 3.82956 .81005 4.26448 3 4 .75921 3.15295 .77618 3.46793 .79323 3.83621 .81033 4.27241 4 5 .75949 3.15782 .77647 3.47360 .79351 3.84288 .81062 4.28036 5 6 .75977 3.16271 .77675 3.47928 .79380 3.84956 .81090 4.28833 6 7 .76005 3.16761 .77703 3.48498 .79408 3.85627 .81119 4.29634 7 8 .76034 3.17252 .77732 3.49069 .79437 3.86299 .81148 4.30436 8 9 .76062 3.17744 .77760 3.49642 .79-165 3.86973 .81176 4.31241 9 10 .76090 3.18238 .77788 3.50216 .7'9493 3.87649 .81205 4.32049 10 11 .76118 3.187&3 .77817 3.50791 .79522 3.88327 .81233 4.32859 11 12 .76147 3.19228 .77845 3.51368 .79550 3.89007 .81262 4.33671 12 13 .76175 3.19725 .77874 3.51947 .79579 3.89689 .81290 4.34486 13 14 .76203 3.20224 .77902 3.52527 .79607 3.90373 .81319 4.35304 14 15 .76231 3.20723 .77930 3.53109 .79636 3.91058 .81348 4.36124 15 16 .76260 3.21224 .77959 3.53692 .79664 3.91746 .81376 4.36947 16 17 .76288 3.21726 .77987 3.54277 .79693 3.92436 .81405 4.37772 17 18 .76316 3.22229 .78015 3.54863 .79721 3.93128 .81433 4.38600 18 19 .76344 8.22734 .78044 3.55451 .79750 3.93821 .81462 4.39430 19 20 .76373 3.23239 .78072 3.56041 .79778 3.94517 .81491 4.40263 20 21 .76401 3.23746 .78101 3.56632 .79807 3.95215 .81519 4.41099 21 22 .76429 3.24255 .78129 3.57224 .79835 3.95914 .81548 4.41937 22 23 .76458 3.24764 .78157 3.57819 .79864 3.96616 .81576 4.42778 "' 24 .76486 3.25275 .78186 3.58414 .79892 3.97320 .81605 4.43622 24 25 .76514 3.25787 .78214 3.59012 .79921 3.98025 .81633 4.44468 25 26 .76542 3.26300 .78242 3.59611 .79949 3.98733 .81662 4.45317 26 27 .76571 3.26814 .78271 3.60211 .79978 3.99443 .81691 4.46169 27 28 .76599 3.27330 .78299 3.60813 .80006 4.00155 .81719 4.47023 28 29 .76627 3.27847 .78328 3.61417 .80035 4.00869 .81748 4.47881 29 30 .76655 3.28366 .78356 3.62023 .80063 4.01585 .81776 4.48740 30 31 .76684 3.28885 .78384 3.62630 .80092 4.02303 .81805 4.49603 31 32 .76712 3.29406 .78413 3.63238 .80120 4.03024 .81834 4.50468 82 33 .76740 3.29929 .78441 3.63849 .80149 4.03746 .81862 4.51337 33 34 .76769 3.30452 .78470 3.64461 .80177 4.04471 .81891 4.52208 34 35 .76797 3.30977 .7'8498 3.65074 .80206 4.05197 .81919 4.53081 35 36 .76825 3.31503 .78526 3.65690 .802C4 4.05926 .81948 4.53958 36 37 .76854 3.32031 .7'8555 3.66307 .80203 4.06657 .81977 4.54837 37 38 .76882 3.32560 .78583 3.66925 .80291 4.07'390 .82005 4.55720 88 39 .76910 3.33090 .78612 3.67545 .80320 4.08125 .82034 4.56605 39 40 .76938 3.33622 .78640 3.68167 .80348 4.08863 .82063 4.57493 40 41 .76967 3.34154 .78669 3.68791 .80377 4.09602 .82091 4.58383 41 42 .76995 3.34689 .78697 3.69417 .80405 4.10344 .82120 4.59277 42 43 .77023 3.35224 .787'25 8.70044 .80434 4.11088 .82148 4.60174 43 44 .77052 3.35761 .78754 3.70673 .80462 4.11835 .82177 4.81073 44 45 .77080 3.36299 .78782 3.71303 .80491 4.12583 .82206 4.61976 45 46 .77108 3.36839 .78811 3.71935 .80520 4.13334 .82234 4.62881 40 47 .77137 3.37380 .78839 3.72569 .80548 4.14087 .82263 4.63790 47 48 .77165 3.37923 .78868 3.73205 .80577 4.14842 .82292 4.64701 48 49 .77193 3.38466 .78896 3.73843 .80605 4.15599 .82320 4.65616 49 50 .77222 3.39012 .78924 3.74482 .80634 4.16359 .82349 4.66533 50 51 .77250 3.39558 .78953 3.75123 .80602 4.17121 .82377 4.67454 51 52 .77278 3.40106 .78981 3.75766 .80691 4.17886 .82406 4.68377 52 53 .77307 3.40656 .79010 3.76411 .80719 4.18652 .82435 4.6S304 58 54 .77335 3.41206 .79038 3.77057 .80748 4.19421 .82463 4.70234 54 55 .77363 3.41759 .79067 3.77705 .80776 4.20193 .82492 4.71166 55 56 ."7392 3.42312 .79095 3.78355 .80805 4.20966 .82521 4.72102 56 57 ."7420 3.42867 .79123 3.79007 .80833 4.21742 82549 4.73041 57 58 ."7448 3.43424 .79152 3.79661 .80862 4.22521 .82578 4.73983 58 59 ."7477 3.43982 .79180 3.80316 .80891 4.23301 .82607 4.74929 59 60 ."7505 3.44541 . 79209 3.80973 .80919 4.24084 .82635 4.75877 60 266 TABLE XVII. NATURAL, VERSED SINES AND EXTERNAL SECANTS. ' 80 81 82 83 / Vers. Ex. sec. Vers. Ex. sec. Vers. Ex. sec. Vers. Ex. sec. .82635 4.75877 .84357 5.39245 .86083 6.18530 .87813 7.20551 1 .82664 4.76829 .84385 5.40422 .86112 6.20020 .87842 7.22500 1 2 .82692 4.77784 .84414 5.41602 .86140 6.21517 .87871 7.24457 2 8 .82721 4.78742 .84443 5.42787 .86169 6.23019 .87900 7.26425 3 4 .82750 4.797'03 .84471 5.43977 .86198 6.24529 .87929 7.28402 4 5 .82778 4.80667 .84500 5.45171 .86227 6.26044 .87957 7.30388 5 G .82807 4.81635 .84529 5.46369 .86256 6.27566 .87986 7.32384 6 7 .82836 4.82606 .84558 5.47572 .86284 6.29095 .88015 7.34390 7 8 .82864 4. "83581 .84586 5.48779 .86313 6.30630 .88044 7.36405 8 9| .82893 4.84558 .84615 5.49991 .86342 6.32171 .88073 7.38431 9 10 .82922 4.85539 .84644 5.51208 .86371 6.33719 .88102 7.40466 10 11 .82950 4.86524 .84673 5.52429 .86400 6.35274 .88131 7.42511 11 12 .82979 4.87511 .84701 5.53655 .86428 6.36835 .88160 7.44566 12 13 .83008 4.88502 .84730 5.54886 .86457 6.38403 .88188 7.46632 13 14 .83036 4.89497 .84759 5.56121 .86486 6.39978 .88217 7.48707 14 15 .83065 4.90495 .84788 5.57361 .86515 6.41560 .88246 7.50793 15 16 .83094 4.91496 .84816 5.58606 .86544 6.43148 .88275 7.52889 16 17 .83122 4.92501 .84845 5.59855 .86573 6.44743 .88304 7.54996 17 18 .83151 4.93509 .84874 5.61110 .86601 6.46346 .88333 7.57113 18 19 .83180 4.94521 .84903 5.62369 .88630 6.47955 .88362 7.59241 19 20 .83208 4.95536 .84931 5.63633 .86659 6.49571 .88391 7.61379 20 21 .83237 4.96555 .84960 5.64902 .86688 6.51194 .88420 7.63528 21 22 .83266 4.97577 .84989 5.66176 .86717 6.52825 .88448 7.65688 22 23 .83294 4.98603 .85018 5.67454 .86746 6.54462 .88477 7.67859 23 24 .83323 4.99633 .85046 5.68738 .86774 6.56107 .88506 7.70041 24 25 .83352 5.00666 .85075 5.70027 .86803 6.57759 .88535 7.72234 25 26 .83380 5.01703 .85104 5.71321 .86832 6.59418 .88564 7.74438 26 27 .83409 5.02743 .85133 5.72620 .86861 6.61085 .88593 7.76653 27 28 .83438 5.03787 .85162 5.73924 .86890 6.62759 .88622 7.78880 28 29 .83467 5.04834 .85190 5.75233 .86919 6.64441 .88651 7.81118 29 30 .83495 5.05886 .85219 5.76547 .86947 6.66130 .88680 7.83367 30 31 .83524 5.06941 .85248 5.77866 .86976 6.67826 .88709 7.85628 31 32] .83553 5.08000 .85277 5.79191 .87005 6.69530 .88737 7.87901 32 33 .83581 5.09062 .85305 5.80521 .87034 6.71242 .88766 7.90186 33 34 .83610 5.10129 .85334 5.81856 .87063 6.72962 .88795 7.92482 34 35 .83639 5.11199 .85363 5.83196 .87092 6.74689 .88824 7.94791 35 36 .83667 5.12273 .85392 5.84542 .87120 6.76424 .88853 7.97111 36 37 .83696 5.13350 .85420 5.85893 .87149 6.78167 .88882 7.99444 37 38 .83725 5.14432 .85449 5.87250 .87178 6.79918 .88911 8.01788 38 39 .83754 5.15517 .85478 5.88612 .87207 6.81677 .88940 8.04146 39 40 .83782 5.16607 .85507 5.89979 .87236 6.83443 .88969 8.06515 40 41 i .83811 5.17700 .85536 5.91352 .87265 6.85218 .88998 8.08897 41 42 .83840 5.18797 .85564 5.92731 .87294 6.87001 .89027 8.11292 42 43 .83868 5.19898 .85593 5.94115 .87322 6.88792 .89055 8.13699 43 44 .83897 5.21004 .85622 5.95505 .87351 6.90592 .89084 8.16120 44 45 .83926 5.22113 .85651 5.96900 .87380 6.92400 .89113 8.18553 45 46 : .83954 5.23226 .85680 5.98301 .87409 6.94216 .89142 8.20999 46 47j .83983 5.24:343 .85708 5.99708 .87438 6.96040 .89171 8.23459 47 48: .84012 5.25464 .85737 6.01120 .87467 6.97873 .89200 8.25931 48 49' .84041 5.26590 .85766 6.02538 .87496 6.99714 .89229 8.28417 49 50 .84069 5.27719 .85795 6.03962 .87524 7.01565 .89258 8.30917 50 51 .84098 5.28853 .85823 6.05392 .87553 7.03423 .89287 8.&3430 51 52 .84127 5.29991 .85852 6.06828 .87582 7.05291 .89316 8.35957 52 53 .84155 5.31133 .&5881 6.08269 .87611 7.07167 .89345 8.38497 53 54 .84184 5.32279 .85910 6.09717 .87640 7.09052 .89374 8.41052 54 55 .84213 5.33429 .85939 6.11171 .87669 7.10946 .89403 8.43620 55 56 .84242 5.34584 .85967 6.12630 .87698 7.12849 .89431 8.46203 56 57 .84270 5.35743 .85996 6.14096 .87726 7.14760 .89460 8.48800 57 58 .84299 5.36906 .86025 6.15568 .87755 7.16681 .89489 8.51411 58 50 .84328 5.38073 .86054 6.17046 .87784 7.18612 .89518 8.54037 59 60 .84357 5.39245 .86083 6.18530 .87813 7.20551 .89547 8.56677 60 267 TABLE XVII. NATURAL VERSED SINES AND EXTERNAL SECANTS. / 84 85 86 / Vers. Ex. sec. Vers. Ex. sec. Vers. Ex. sec. .89547 8.50677 .91284 10.47371 .93024 13.33559 1 .89576 8.59332 .91313 10.51199 .93053 13.39547 1 2 .89605 8.62002 .91342 10.55052 .93082 13.45586 2 3 .89634 8.64687 .91371 10.58932 .93111 13.51676 3 4 .89663 8.67387 .91400 10.62837 .93140 13.57817 4 5 .89092 8.70103 .91429 10.66769 .93169 13.64011 5 6 .897*1 8.72833 .91458 10.70728 .93198 13.70258 6 7 .89750 8 . 75579 .91487 10.74714 .93227 13.76558 7 8 .89719 8.78341 .91516 10.78727 .93257 13.82913 8 9 .89808 8.81119 .91545 10.82768 .93286 13.89323 9 10 .89836 8.83912 .91574 10.86837 .93315 13.95788 10 11 .89865 8.86722 .91603 10.90934 .93344 14.02310 11 12 .89894 8.89547 .91032 10.95060 .933?'3 14.08890 12 13 .89923 8.92389 .91661 10.99214 .93402 14.15527 13 14 .89952 8.95248 .91690 11.03397 .93431 14.22223 14 15 .89981 8.98123 .91719 11.07610 .93460 14.28979 15 16 .90010 9.01015 .91748 11.11852 .93489 14.35795 16 17 .90039 9.03923 .91777 11.16125 .93518 14.42672 17 18 .90068 9.06849 .91806 11.20427 .93547 14.49611 18 19 .90097 9.09792 .91835 11.24761 .93576 14.56614 19 20 .9C126 9.12752 .91804 11.29125 .93605 14.63679 20 21 .90155 9.15730 .91893 11.33521 .93634 14.70810 21 22 .90184 9.18725 .91922 11.37948 .93663 14.78005 22 23 .90213 9.21739 .91951 11.42408 .93692 14.85208 23 24 .90242 9.24770 .91980 11.46900 .93721 14.92597 24 25 .90271 9.27819 .92009 11.51424 .93750 14.99995 25 26 .90300 9.30887 .92038 11.55982 .93779 15.07462 26 27 .90329 9.33973 .92067 11.60572 .93808 15.14999 27 28 .90358 9.37077 .92096 11.65197 .93837 15.22607 28 29 .90386 9.40201 .92125 11.69856 .93866 15.30287 29 30 .90415 9.43343 .92154 11.74550 .93895 15.38041 30 31 .90444 9.46505 .92183 11.79278 .93924 15.45869 31 32 .90473 9.49685 .92212 11.84042 .93953 15.53772 32 33 .90502 9.52886 .92241 11.88841 .93982 15.61751 33 34 .90531 9.56106 .92270 11.93677 .94011 15.69808 34 35 .90560 9.59346 .92299 11.98549 .94040 15.77944 35 36 .90589 9.62605 .92328 12.03458 .94069 15.86159 36 37 .90018 9.65885 .92357 12.08040 .94098 15.94456 37 38 .90647 9.69186 .92386 12.13388 .94127 16.02835 38 39 .90676 9.72507 .92415 12.18411 .94156 16.11297 39 40 .90705 9.75849 .92444 12.23472 .94186 16.19843 40 41 .90734 9.79212 .92473 12.28572 .94215 16.28476 41 42 .90763 9.82596 .92502 12.33712 .94244 16.37196 42 43 .90792 9.86001 .92531 12.38891 .94273 16.46005 43 44 .90821 9.89428 .92560 12.44112 .94302 16.54903 44 45 .90850 9 92877 .92539 12.49373 .94331 16.63893 45- 46 .90879 9.96348 .92618 12.54676 .94360 16.72975 46 47 .90908 9.99841 .92647 12.60021 .94389 16.82152 47 48 .90937 10.0.3356 .92676 12.65408 .94418 16.91424 48 49 .90966 10.06894 .92705 12.70838 .94447 17.00794 49 50 .90995 10.10455 .92734 12.76312 .94476 17.10262 50 51 .91024 10.14039 .92763 12.81829 .94505 17.19830 51 52 .91053 J 10.17646 .92792 12.87391 .94534 17.29501 52 53 .91082 10.21277 .92821 12.92999 .94563 17.39274 53 54 .91111 10.24932 .92850 12.98651 .94592 17.49153 54 55 .91140 10.28610 .92879 13 04350 .94621 17.59139 55 56 .91169 10.32313 .92908 13.10096 .94050 17.69233 56 57 .91197 10.36040 .92937 13.15889 .94679 17.79438 57 58 .91226 10.39792 .92966 13.21730 .94708 17.89755 58 59 .91255 10.43569 .92995 13.27620 .94737 18.00185 59 60 .91284 10.47371 .93024 13.33559 .94766 18.10732 60 268 TABLE XVII. NATURAL VERSED SINES AND EXTERNAL SECANTS. / 87 88 89 / Vers. Ex. sec. Vers. Ex. sec. Vers. Ex. sec. .94766 18.10732 .96510 27.65371 .98255 56.29869 1 .94795 18.21397 .96539 27.89440 .98284 57.26976 1 2 .94825 18.32182 .96568 28.13917 .98313 58.27431 2 3 .94854 18.43088 .96597 28.38812 .98342 59.31411 3 4 .94883 18.54119 .96636 28.64137 .9&371 60.39105 4 5 .94912 18.65275 .96655 28.89903 .98400 61.50715 5 6 .94941 18.76560 .96684 29.16120 .98429 62.66460 6 7 .94970 18.87976 .96714 29.42802 .98458 63.86572 7 8 .94999 18.99524 .96743 29.69960 .98487 65.11304 8 9 .95028 19.11208 .96772 29.97607 .98517 66.40927 9 10 .95057 19.23028 .96801 30.25758 .98546 67.75736 10 11 .95086 19.34989 .96830 30.54425 .98575 69.16047 n 12 .95115 19.47093 .968i:9 30.83623 .98604 70.62285 12 13 .95144 19.59341 .96888 31.13366 .98633 72.14583 13 14 .95173 19.71737 .96917 31.43671 .98662 73.73586 14 15 .95202 19.84283 .96946 31.74554 .98691 75.39655 15 16 .95231 19.96982 .96975 32.06030 .98720 77.13274 16 17 .95260 20.09838 .97004 32.38118 .98749 78.94968 17 18 .95289 20.22852 .97033 32.70835 .98778 80.85315 18 19 .95318 20.36027 .97062 33.04199 .98807 82.84947 19 20 .95347 20.49368 .97092 33.38232 .98836 84.94561 20 21 .95377 20.62876 .97121 33.72952 .98866 87.14924 21 2-2 .95406 20.76555 .97150 34.08380 .98895 89.46886 22 23 .95435 20.90403 .97179 34.44539 .98924 91.91387 23 2i .95464 21.04440 .97208 34.81452 .98953 94.49471 24 25 .95493 21.18653 .97237 35.19141 .98982 97.22303 25 26 .95522 21.33050 .97266 35.57633 .99011 100.1119 26 27 .95551 21.47635 .97295 35.96953 .99040 103.1757 27 28 .95580 21.62413 .97324 36.37127 .99069 106.4311 28 29 .95609 21.77386 .97353 36.78185 .99098 109.8966 29 30 .95638 21.92559 .97382 37.20155 .99127 113.5930 30 31 .95667 22.07935 .97411 37.63068 .09156 117.5444 31 32 .95696 22.23520 .97440 38.06957 .99186 121.7780 32 33 .95725 22.39316 .97470 38.51855 .99215 126.3253 33 34 .95754 22.55329 .97499 38.97797 .99244 131.2223 34 35 .95783 22.71563 .97528 39.44820 .99273 136.5111 35 36 .95812 22.88022 .97557 39.92963 .99302 142.2406 36 37 .95842 23.04712 .97586 40.42266 .99331 148.4684 37 38 .95871 23.21637 .97615 40.92772 .99360 155.2623 38 39 .95900 23.38802 .97644 41.44525 .99389 162.7033 39 40 .95929 23.56212 .97673 41.97571 .99418 170.8883 40 41 .95958 23.73873 .97702 42.51961 .99447 179.9350 41 42 .95987 23.91790 .97731 43.07746 .99476 189.9868 42 43 .96016 24.09969 .97760 43.64980 .99505 201.2212 43 44 .96045 24.28414 .97789 44.23720 .99535 213.8600 44 45 .96074 24.47134 .97819 44.84026 .99564 228.1839 45 46 .96103 24.66132 .97848 45.45963 .99593 244.5540 46 47 .96132 24.85417 .97877 46.09596 .99622 263.4427 47 48 .96161 25.04994 .97906 46.74997 .99651 285.4795 48 49 .96190 25.24869 .97935 47.42241 .99680 311.5230 49 50 .96219 25.45051 .97964 48.11406 .99709 342.7752 50 51 .96248 25.65546 .97993 48.82576 .99738 380.9723 51 52 .96277 25.86360 .98022 49 55840 .99767 428.7187 52 53 .96307 26.07503 .98051 50.31290 .99796 490.1070 53 54 .96336 26.28981 .98080 51.09027 .89825 571.9581 54 55 .96365 26.50804 .98109 51.89156 .99855 686.5496 55 56 .96394 26.72978 .98138 52.71790 .99884 858.4369 56 57 .96423 26.95513 .98168 53.57046 .99913 1144.916 57 58 .96452 27.18417 .98197 54.45053 .99942 1717.874 58 59 .96481 27.41700 .98226 55.a5946 .99971 3436.747 59 60 .96510 27.65371 .98255 56.29869 1.00000 Infinite 60 269 THIS BOOK IS DUE ON THE LAST DATE STAMPED BELOW AN INITIAL FINE OF 25 CENTS WILL BE ASSESSED FOR FAILURE TO RETURN THIS BOOK ON THE DATE DUE. THE PENALTY WILL INCREASE TO SO CENTS ON THE FOURTH DAY AND TO $1.OO ON THE SEVENTH DAY OVERDUE. fWfifii T Ifidl ijt ' '-' "'Mi ..;. it &"v :{ m ML* T P e ^ ~ S te6Q4 Q Uorf 2.% 61 REC'D UD NOV 18 b9-yAM . ; --.. ' * '"" * LD 21-100m-7,'39(402s)