SMITHSONIAN MATHEMATICAL TABLES 
 
 
 
 HYPERBOLIC FUNCTIONS 
 
 
 PREPARED BY 
 
 GEORGE F. BECKER AND C. E. VAN ORSTRAND 
 
 CITY OF WASHINGTON 
 PUBLISHED BY THE SMITHSONIAN INSTITUTION 
 
 1909 
 
ASTRONOMY/ 
 LIBRARY 
 
ADVERTISEMENT. 
 
 Among the early publications of the Smithsonian Institution was a very 
 important volume of meteorological tables by Dr. Arnold Guyot. They were 
 so widely used by geographers and physicists as well as by meteorologists 
 that when the fourth edition was exhausted it was decided to recast the 
 entire work and publish three separate volumes, Meteorological Tables, 
 Geographical Tables, and Physical Tables, each of which has now passed 
 through several editions. 
 
 In the application of the data of these volumes to the study of natural 
 phenomena certain mathematical tables beside those included in ordinary 
 tables of logarithms are urgently needed in order to save recurrent computa- 
 tion on the part of observers and investigators. It was therefore decided 
 to publish the present volume of Mathematical Tables, on Hyperbolic Func- 
 tions. 
 
 Hyperbolic Functions are extremely useful in every branch of pure physics 
 and in the applications of physics whether to observational and experimental 
 sciences or to technology. Thus whenever an entity (such as light, velocity, 
 electricity, or radioactivity) is subject to gradual extinction or absorption, 
 the decay is represented by some form of Hyperbolic Functions. Mercator's 
 projection is likewise computed by Hyperbolic Functions. Whenever me- 
 chanical strains are regarded as great enough to be measured they are most 
 simply expressed in terms of Hyperbolic Functions. Hence geological de- 
 formations invariably lead to such expression, and it is for that reason that 
 Messrs. Becker and Van Orstrand, who are in charge of the physical work 
 of the United States Geological Survey, have been led to prepare this volume. 
 
 CHARLES D/WALCOTT, Secretary. 
 WASHINGTON, D. C., April, 1909. 
 
 In this first reprint of the Hyperbolic Functions a few misprints of trifling import- 
 ance have been corrected and four values of the exponential have been changed by a 
 unit in the eighth significant place. 
 
 April, 1911. C. D. W. 
 
 iii 
 
 340201 
 
CONTENTS. 
 
 INTRODUCTION : PA o B 
 
 Definitions and formulas vii 
 
 Geometrical illustrations xxviii 
 
 Methods of interpolation xxxiv 
 
 Description of tables , xliii 
 
 Historical note xlviii 
 
 TABLE I : 
 
 Five place values of log sinh u, log cosh u, log tanh u, and log 
 
 coth u i 
 
 TABLE II : 
 
 Five place values of sinh u, cosh u, tanh u, and coth u . . . 87 
 
 TABLE III : 
 
 Five place values of sin u, cos u, log sin u, and log cos u, u being 
 
 expressed in radians and their angular equivalents . .' . . 173 
 
 TABLE IV : 
 
 The ascending and descending exponential to seven significant 
 
 figures with Iog 10 e u to seven places 225 
 
 Nine place values of the same with ten place logarithms from 
 
 u= i to u 100 259 
 
 Auxiliary table of multiples of log ]0 e for interpolation of Iog 10 e u . 261 
 
 TABLE V : 
 
 Five place values of natural logarithms 263 
 
 Interpolation coefficients for derivative formula 273 
 
 TABLE VI : 
 
 The gudermannian of u to seven places in radians and to the same 
 
 order of accuracy in degrees, minutes, and seconds .... 275 
 
 TABLE VII : 
 
 The anti-gudermannian to hundredths of a minute in terms of 
 the gudermannian expressed in degrees and minutes from o o' 
 to 89 59'. (This table is otherwise known as a table of me- 
 ridional parts for a spherical globe) 309 
 
 TABLE VIII : 
 
 Table for conversion of radians into angular measure and vice 
 
 versa 320 
 
 Numerical constants 321 
 
DEFINITIONS AND FORMULAS. 
 
 The hyperbolic functions are named the hyperbolic sine, cosine, tangent, 
 cotangent, secant, and cosecant from their close analogy to the circular func- 
 tions, the tangent being the ratio of the hyperbolic sine to the cosine and 
 the other three functions being reciprocals of these, as in circular trigonom- 
 etry. They are usually denoted by adding h to the symbols of the circular 
 functions, as cosh u for the hyperbolic cosine of u, sinh u for the hyperbolic 
 sine of u, etc. 1 
 
 Historically speaking, the hyperbolic functions were evolved from studies 
 of the hyperbola. They might have been developed from the geometry of 
 the ellipse or the catenary or that of other curves. These functions, how- 
 ever, may be considered independently of any geometrical interpretation and 
 can be derived from very fundamental functional theorems. 
 
 At least two methods have been devised of defining circular and hyper- 
 bolic functions analytically. One of these is due to Mr. Yvon Villarceau, 2 
 and is so extremely brief that it can be given here in a somewhat modified 
 form. 
 
 It has long been known that 
 
 \- ; "> 
 g'zmiir - j . gu -f zmitr __ gu . p(u + 2tnir)t . _ . aiu 
 
 The second of these equations has a single imaginary period, 2 zV, and the 
 third a single real period, 2 TT. Hence every exponential e u in which u is real 
 has a single imaginary period, 2 zV, and every exponential with the same base, 
 but with an imaginary exponent, has a real period, 2 v. Now, all real purely 
 circular functions may be expressed in terms of constants and exponentials 
 with purely imaginary exponents, and all real hyperbolic functions may 
 be expressed in terms of constants and exponentials with exclusively real 
 exponents. 
 
 Hence hyperbolic functions may be defined as the singly periodic expo- 
 nential functions with real exponents. The circular functions are then the 
 singly periodic exponential functions with imaginary exponents. 
 
 It remains to be considered how, from this point of view, the hyperbolic 
 functions of complex variables are to be regarded. The question almost 
 answers itself ; for 
 
 1 More compendious and convenient, but less usual, is the notation employed by B. de 
 Saint-Venant, sib. u, cob , tab u. 
 "Coinptes Rendus, Paris, vol. 83, 1876, p. 594. 
 
 vii 
 
Vlll DEFINITIONS AND FORMULAS. 
 
 which is evidently the product of two functions one circular, the other 
 hyperbolic. Such functions have a real period and an imaginary one, but 
 since they are single-valued they are not elliptic functions. 
 
 The circular and hyperbolic functions being defined as above, it is merely 
 as a matter of convenience that a few of the simpler combinations of expo- 
 nentials receive special names, as sine, cosine, etc. 
 
 The other analytical method of generalizing the two classes of functions 
 is due to Edward Lucas, 1 and is too long to be given here in full, but the 
 method may be indicated. If a and b are the two roots of the equation 
 
 where P and Q are positive or negative whole numbers, then two functions 
 may be defined as follows: 
 
 U n = -"; V n = a 
 a o 
 
 and these functions are related by the equation 
 
 Lucas develops and studies these functions, limiting n at first to whole posi- 
 tive numbers. He finds that all the theorems resulting from this study are 
 converted into those of ordinary trigonometry when U is replaced by 2 sin n 
 and Fby 2 cos n. He infers that between the limits i and minus i, n may 
 be replaced by any real value, and shows that the theorems dealing with U 
 and V when translated into trigonometric formulas on this assumption can 
 be verified. By substituting for n an imaginary argument, the hyperbolic 
 functions also are found to be comprehended in the general functions U 
 and V. 
 
 Both the circular and hyperbolic functions may further be regarded as 
 integrals of the equation 
 
 d , d l y a 
 
 If c = a\ this gives 
 
 4J 
 
 - Be, 
 
 where A and B are arbitrary constants ; so that the integral expression in 
 cludes sinh x, cosh a:, and the sum or difference of these functions. 
 If c ^-b\ 
 
 y 
 
 ~ b A l cos x -f /?, sin x. 
 1 Am. Jour, of Math., vol. i, 1878, p. 184. 
 
DEFINITIONS AND FORMULAS. XI 
 
 and PC, may be drawn from a point P to a line AB ; the sum of the angles 
 of a triangle is less than two right angles, and the angle of parallelism // (/) 
 is dependent upon the perpendicular distance p of the point P from the line 
 AB. If now any line passing through A, such as AE, is extended until the 
 perpendicular erected at its middle point is parallel to AB, the locus of the 
 points E is a boundary curve, and the revolution of this curve about AB or 
 one of its parallels develops a boundary surface. It is upon this surface of 
 constant negative curvature that L,obachevsky imagines a triangle of sides 
 a,b,c and angles A, B, C to be drawn. He establishes as fundamental rela- 
 tions between the sides and angles of this triangle l 
 
 sin A tan 77 (a) = sin B tan 77 () = sin C tan 77 (c) , 
 
 sin 77 () sin 77 (c) = sin 77 (a) cos 77 () cos 77 (r) sin 77 (a} cos A, 
 
 sin 77 () cos A cos B cos C sin 77 ( ) -f- sin B sin C, 
 
 and also proves that 
 
 sin 77 (#) = (cos in) ~ l = (cosh u} ~\ 
 tan 77 (w) = i (sin z&) -1 = (sinh #) -1 , 
 cos 77 () = / tan iu = tanh #. 
 
 Hence the preceding equations may be written 
 
 sin A sin B sin C 
 
 sinh sinh b ~ sinh ' 
 
 cosh a = cosh cosh ^ sinh sinh c cos ^4 , 
 
 cos A = cos B cos C + sin B sin C cosh a. 
 
 These formulas are, in fact, precisely those of spherical trigonometry, in 
 which the real sides a, b, c have been replaced by the imaginaries ia, ib, ic. 
 If the triangle on the boundary surface is infinitesimal, the above equations 
 reduce to the well-known relations between the sides and angles of a triangle 
 on the Euclidean plane. The theorems of non- Euclidean geometry may not 
 therefore be inconsistent with experience, for .the largest triangle which we 
 can measure is infinitesimal in comparison with a triangle on the boundary 
 surface. L,obachevsky pointed out that a triangle on a boundary surface 
 would correspond to a triangle connecting three stars in distant parts of the 
 universe, and that the postulates of his geometry, involving as they do the 
 question of the curvature of space, would be capable of experimental proof 
 if the parallaxes of distant stars could be measured with sufficient accuracy. 
 Lastly, there is an important relation between the numerical values of the 
 circular and hyperbolic functions. If the argument u assumes successive 
 values between o and + co , sinh u assumes successive values between o and 
 + co just as tan a does when a varies from o to 90; cosh u assumes values 
 between i and + co like sec /?, and tanh u assumes values between o and i 
 
 X H. P. Manning's Non-Euclidean Geometry, p. 60. 
 
Xll 
 
 DEFINITIONS AND FORMULAS. 
 
 in the same way as sin y. The variation of the hyperbolic functions through- 
 out the entire plane and their similarity to the circular functions between the 
 
 limits o and 180 is shown 
 in the diagram. Since each 
 of the functions is singly 
 periodic, there must be a 
 single value of a, (3, y cor- 
 responding to a particular 
 value of u, such that 
 
 sinh u = tan a, 
 cosh u = sec /?, 
 tanh u = sin y. 
 
 It will be found by sub- 
 stituting in the trigonomet- 
 ric formulae that a = ft = y 
 = <, and the required rela- 
 tions are therefore 
 
 cosh u = sec <, 
 sinh u = tan <, 
 tanh u = sin <. 
 
 The angle < which renders 
 it possible to evaluate the 
 hyperbolic functions by 
 means of the circular func- 
 tions is of great importance 
 in pure and applied mathe- 
 matics. Some of its prop- 
 rties and applications will 
 e considered in the section 
 on geometrical illustra- 
 tions. It is called guder- 
 mannian u and is written 
 
 <f> = gd u. 
 
 The following list of form- 
 ulae involving the hyper- 
 bolic functions might be 
 greatly extended, but it 
 includes the most useful 
 relations. 1 
 
 D 
 FIG. 3. 
 
 'Taken with additions from Prof. B. O. Peirce s Short Table of Integrals, and : 
 McMahon's Hyperbolic Functions. 
 
DEFINITIONS AND FORMULAS. xiii 
 
 A. RELATIONS BETWEEN HYPERBOLIC AND CIRCULAR FUNCTIONS. 
 
 i . sinh u = i sin iu = tan gd u. 
 
 2. cosh u cos iu = sec gd u. 
 
 3. tanh u = i tan iu = sin gd u. 
 
 4. tanh \ u tan \ gd u. 
 
 5. <? w = ( i + sin %d u) -r- cos gd u, 
 
 = [ i cos ( J TT H- tf u) ] -*- sin (i TT -f ^ ), 
 = tan(*ir + \gdu). 
 
 6. sinh z = z sin &. 
 
 7. cosh iu = cos &. 
 
 8. tanh iu = i tan u. 
 
 9. sinh ( iv) = / sin (z> =H 0, 
 
 = sinh # cos v i cosh w sin z>. 
 
 10. cosh (?^ zV) = cos (z; =F /), 
 
 = cosh cos v / sinh & sin z>. 
 
 11. cosh (miir) = cos ?^ TT. (w is an integer.) 
 
 12. sinh (2 w + i) J zV = z sin (2 ra -{- i) J TT. (w is an integer.) 
 
 B. RELATIONS AMONG THE HYPERBOLIC FUNCTIONS. 
 
 13. sinh u= \(e u <?~ M ) = sinh (a) =(csch w),- 1 
 
 = 2 tanh J w -^ ( i tanh 2 \ u} = tanh u -r- (i tanh 2 w) 
 
 14. coshw= J (e u -\-e -") = cosh ( w) == (sech a)- 1 , 
 
 (i tanh*iw)= i H-(I 
 
 15. tanhu=(e u e- u )~-(e u -^-e- u ) = tanh ( w), 
 
 = (coth )~ x = sinh ^ -=-cosh u (i sech 2 
 1 6. sech w = sech ( u) = (i tanh 2 &)%. 
 17. csch u csch ( w) = (coth 2 w i)^. 
 1 8. coth = coth ( w) = (csch 2 u -f i)^. 
 
 19. cosh 2 sinh 2 a := i. 
 
 20. sinh \ u = \/\ (cosh u i). 
 
 21. cosh i w = ]/ |(cosh u + i). 
 
 22. tanh ^ u (cosh w i) -f- sinh w, 
 
 = sinh w -T- (i + cosh wj = i/(cosh i) -^- (cosh -f i) 
 23 sinh 271 = 2 sinh w cosh w = 2 tanh u -=- (i tanh 2 u}. 
 
 24. cosh 2 = cosh 2 u + sinh 2 u 2 cosh 2 w i, 
 
 = 1+2 sinh 2 = (i + tanh 2 w) -r- (i tanh 2 w). 
 
 25. tanh 2w = 2 tanh -r- (i + tanh 2 #). 
 
 26. sinh 3 = 3 sinh u -f 4 sinh 3 w. 
 
 27. cosh 3 = 4 cosh 3 3 cosh w. 
 
 28. tanh 3& = (3 tanh u -f tanh 3 K) ~ (i -f 3 tanh 2 u). 
 
XIV DEFINITIONS AND FORMULAS. 
 
 29. sinh nu = 
 
 n cosh" 1 u sinh u -\ -~ cosh n ~* u sinlr 
 
 o 
 
 30. cosh nu = cosh" u 4 - - cosh n ~ 2 u sinh 2 u + . . . . 
 
 3 1 . sinh u 4 sinh z> = 2 sinh (w + v) cosh * (w v) . 
 
 32. sinh u sinh v = 2 cosh J (w + v) sinh J ( v). 
 
 33. cosh 2* 4- cosh v = 2 cosh i (2* 4 z>) cosh J (w v). 
 
 34. cosh u cosh v = 2 sinh J (w + v) sinh J (2* v) . 
 
 35. sinh u -j- cosh?* = (i + tanh \ u) ~- (i tanh J #) 
 
 36. (sinh u 4- cosh u) n = cosh w 4 sinh w. 
 
 37. tanh w 4- tanh v = sinh (u-\-v)-r- cosh 2^ cosh z>. 
 
 38. tanh u tanh v = sinh ( v) -f- cosh ?^ cosh v. 
 
 39. coth z/ -f- coth v sinh (w + v) -r- sinh w sinh v. 
 
 40. coth ?^ coth v = sinh (u v) ~- sinh u sinh v. 
 
 41. sinh (2* it z>) = sinh cosh v cosh sinh v. 
 
 42. cosh (7^ : z) = cosh cosh v sinh 2^ sinh z;. 
 
 43. tanh O v) = (tanh u tanh z>) -r- (i it tanh u tanh z;). 
 
 44. coth (u v} = (coth u coth z; i) -5- (coth z; coth w). 
 
 45. sinh (7^ + f) -h sinh (u v) = 2 sinh u cosh z>. 
 
 46. sinh (u + v) sinh (7^ v) = 2 cosh w sinh v. 
 
 47. cosh (a + z;) + cosh (a z;) = 2 cosh u cosh z>. 
 
 48. cosh (u -\- v) cosh (it v) = 2 sinh w sinh z;. 
 
 49. tanh \ (u + v) = (sinh 7/ + sinh v) -r- (cosh w + cosh v). 
 
 50. tanh i (u v) = (sinh u sinh z;) -f- (cosh u +cosh v). 
 
 51. coth i (# -f- z;) = (sinh 7^ sinh v) -f- (cosh u cosh v). 
 
 52. coth \ (u v) = (sinh u -f- sinh f) -5- (cosh w cosh v). 
 tanh w + tanh v sinh (2*5 -f v) 
 
 ^ tanh w tanh v ~~ sinh (u v}' 
 
 coth w + coth z> _ sinh (u + ) 
 ^ coth w coth v ~ sinh (2^ z;)* 
 
 55. sinh (w + v) + cosh (w + v) = (cosh w-f sinh u} (cosh z/ -f sinh v), 
 
 56. sinh (w 4- ^) sinh (2^ z;) = sinh 2 u sinh 2 v, 
 
 = cosh 2 7* cosh 2 v. 
 
 57. cosh (w -f cosh (w v) = cosh 2 ?^ + sinh 2 z;, 
 
 = sinh 2 ?/ + cosh 2 z/. 
 
 58. sinh (mi ii) = o. (w is an integer). 
 
 59. cosh (mi IT) ( i) m . 
 
 60. tanh (mi IT) = o. 
 
 61 . sinh (u -f mite) = ( i) m sinh u. 
 
 62. cosh (u 4 mitt) ( i) m cosh u. 
 
 63. sinh (2 m + i) i iv= i. 
 
DEFINITIONS AND FORMULAS. XV 
 
 64. COsh (2 7# + I ) |- Z TT = O. 
 
 65. sinh (~ uj = i cosh u. 
 
 66. cosh f u\ i sinh u. 
 
 67. tanh (u -f- zV) = tanh u. 
 
 C. INVERSE HYPERBOLIC FUNCTIONS. 
 
 68. sinh- 1 = log(+ j/*+ x ^cosh' 1 1/V 4- T =' 
 
 t -. 
 69. cosh- 1 * = log (w + i/V i) = sinh - 1 ^^ZTY 
 
 ( i)x 
 
 . du 
 u) Hog(i 
 
 i u 
 
 71. coth" 1 u = Hog (i -\-u) Hog (u j)==j- F = tanh l 
 
 / i u 
 
 72. sech-^^logf f\/^T : ) = 1~^ 2^v == cosh" 1 
 
 *\u * u* J J u(i u*)* u 
 
 73. csch" 1 w log ( +\/ r+ J ) I / 2 _! NV ^sinh" 1 
 
 'Vw ^ z^ 2 / J ?/(?^ 2 + ij/4 w 
 
 74. sin" 1 ^ = i sinh" 1 iu = i log (&"# + V i w' 2 ) . 
 
 75. cos" x w = i cosh" 1 u = i log (u + i V i u 2 ). 
 
 76. tan" 1 = i tanh" 1 ^ = .log (i + iu) : log (i iu). 
 
 77. cot" 1 u=.i coth" 1 iu = . log (iu i) . log (iu + i). 
 
 78. sin" 1 iu = i sinh - 1 = i log (z<* + V i -f- & 2 ) . 
 
 79. cos" 1 z"& = i cosh" 1 iu - z* log (u -f- l/ i -f- z/ 2 ). 
 
 80. tan" 1 / = z tanh x w = log ( i + u) log ( i u). 
 
 i i 
 
 81. cot" 1 iu = z* coth" 1 u = log (u -f i) H log ( i). 
 
 82. cosh" 1 | ( + ) = sinh" 1 i [u j^tanh" 1 ^ 9 *> 
 
 V K / \ W/ 2 -f-I 
 
 = 2 tanh" 1 = log #. 
 
 z^ + i 
 
 83. tann" 1 tan z* = \gd 2. u. = : 
 
 84. tan" 1 tanh w = gd~ l 2u. 
 
 85. cosh- 1 esc 2 u = sinh- 1 cot 2 u = tanh- 1 cos 2 u = log tan u. 
 
XVI DEFINITIONS AND FORMULAS. 
 
 86. tanh- 1 tan 2 (Jir -f -J-w) = T log esc it. 
 
 87. tanh" 1 tan 2 \ u = % log sec u. 
 
 88. cosh" 1 u cosh" 1 v = cosh" 1 [uv db i/ (u* i) (v* i)] 
 
 u i . i / u i \ , i ( u i \ i 
 . log u = - + _(_ _)4-_f_ __[.,_ 
 
 u 2 V u J 3 V z; / 
 
 Fw i i / u i\ 3 , i / u i \ 5 ~1 
 
 . log U= 2 - ---f ( -- - +_ -- . - +.'... 
 
 Lw-fi V -f I / V w -h I / J 
 
 3 
 
 w 2 + ?/ -- if -\- 
 234 
 
 89. sinh" 1 u sinh" 1 v = sinh" 1 [u V i+i/ l vV'i+tt 
 
 D. SERIES. 
 
 91. log = O i) ~(u 2 + y ( i) 3 
 
 U I . T / U T \ 2 . 
 
 92 
 
 93 
 
 94. log 
 
 95- log 
 
 97 
 
 98. 
 
 99. tanh = - 
 
 O 
 
 100. coth=i + 
 
 101. 
 
 ,02. 
 
 -- ' h '" - ... ("large.) 
 
 245 
 
DEFINITIONS AND FORMULAS. XV11 
 
 104. u=gd- l <j> = <i> + - <p 3 -f <p 5 -f - <p 7 -|- . . . (<?<) 
 
 6 24 5040 V 2 / 
 
 24 
 
 i u* i 3 u b 135 d 
 
 105. sinh u = u - + . . . (u 2 < i.) 
 
 23 245 2467 
 
 _L_3_J_ + J _3_JLJ (^ 2 >i) 
 
 2 4 4 & 4 24 66 w 6 
 
 106. cosh" 1 u = log 2 u -^-j ---^4 -~|T e (^' 2 >O 
 
 22 U 2 4 4 4 2 4 6 6 # 
 
 107. tanh" 1 u = u -j z^ 3 H 2^ 5 + w 7 + . . . (# 8 <i.) 
 
 O 3 l 
 
 III I I 
 
 108. coth - 1 u = tanh" = 1 r -\- ^H r+ (X>i-) 
 
 u 11 $u 5 7 u 
 
 , i 2 i w 2 i 3 w 4 i 3 5 ^ 6 
 
 IOQ. seen" 1 & = cosh" = log ... 
 
 u u 22 244 2466 (& 2 <i) 
 
 .,,1 i ii 131 J35 1 
 
 1 10. each" 1 u = sinh" 1 
 
 u 2 $u* 2 4 5& 5 2 4 6 yw 7 
 
 -f . . . (*>!.) 
 
 22 244 2 
 
 H. DERIVATIVES. 
 
 - -fa =uU ^ -Hog**)- 
 
 ? sinh 
 
 d cosh w 
 
 i io. - = = sinh u. 
 du 
 
 d tanh 2^ 
 
 117. - - =sech 2 u. 
 
 du 
 
 d coth u 
 
 118. - - = csch 2 a. 
 
 o'w 
 
 ^<f sech u 
 119. - -= sech u. tanh u. 
 du 
 
 d csch u 
 120. - - = csch u. coth . 
 
 121. - 
 
 du Vu* -f 
 
XV111 DEFINITIONS AND FORMULAS. 
 
 d cosh l u i 
 
 122. 
 
 123. 
 124- 
 125- 
 126. 
 127. 
 
 du I'V i 
 d tanh ~ l u i 
 
 du i zt 2 ' 
 d coth 1 u i 
 
 du i 
 
 d sech T u 
 
 du u |/ ! w 2 
 
 d csch l u i 
 
 du ~ u i/V -f i 
 d^u 
 
 I28 _s^ = secw . ** 
 du 
 
 F. INTEGRATE. (INTEGRATION CONSTANTS ARE OMITTED.) 
 
 129. J sinh u du = cosh u. 
 
 130. J cosh u du = sinh . 
 
 131. j tanh udu = log cosh w. 
 
 132. j coth u du = log sinh u. 
 
 133. j sech u du 2 tan ~~ 1 M = gd u. 
 
 r ft 
 
 134. I csch u du= log tanh 
 
 135. J sinh n udu = sinh" 1 u. cosh ft -J pinh" 2 dfoN 
 
 = sinh n + 1 u cosh w I sinh " + * u du. 
 
 n + i w -f- i */ 
 
 1-16. ( cosh"z^ ^ = sinh w. cosh"- 1 ?^ H I cosh" ~ 2 7^ du, x 
 
 / w w *^ 
 
 = sinh u cosh" + l u -\ I cosh" + - u du. 
 
 n + i n + \J 
 
 137. \ u sinh 21 du = u cosh ?/ sinh ft. 
 
 138. J u cosh w afo = u sinh ^ cosh u. 
 
 139. J //' sinh u du = (u z +2} cosh u 2 u sinh u. 
 
 140. J //" sinh u du = u n cosh u ?t?fn-i .sinh u 
 
 -f w (rc i)J u n ~ 2 sinh 7^. 
 
DEFINITIONS AND FORMULAS. XIX 
 
 149. 
 
 141. J sinh 2 u du =% (sinh u cosh u u). 
 
 142. j sinh u. cosh u du = \ cosh (2 u). 
 
 143. J cosh 2 udu=\ (sinh w cosh w + w). 
 
 144. J tanh 2 udu = u tanh &. 
 
 145. j coth 2 u du = u coth w. 
 
 146. j sech 2 u du= tanh &. 
 
 147. j sech 3 u du = \ sech u tanh w 4- |- gd u. 
 
 148. J csch 2 u du = coth u. 
 
 . jsinh" 1 u du = u sinh- 1 u (i -f u 2 )^. 
 
 150. j cosh" 1 u du = u cosh" 1 u (u z i)%. 
 
 151. j tanh" 1 u du = tanh- 1 w + i log (i w 2 ). 
 
 152. J 7* sinh- 1 aflfo = J | (2 w 2 -f- i) sinh- 1 w w (i 4- * 
 J 53- J a cosh~ l udu =-J (2 w 2 i) cosh 1 u u (2** i)% . 
 
 154. J (cosh a -f cosh w) l du = 2 csch . tanh ~ l (tanh -j- w. tanh J ), 
 
 = csch log cosh \ (u + a) log cosh ( a) 
 
 J 55- J ( cos a + cos ^ u}~ 1 du = 2 esc <z. tan -1 (tanh -J- w. tan |- ). 
 
 156. J (i -f cos a. cosh ) x du = 2 esc <z. tanh~ l (tanh ^ ?/. tan %a}. 
 
 157. J sinh u cos & afo = \ (cosh w. cos w -f- sinh z^. sin w). 
 
 158. J cosh w. cos udu = ^ (sinh z*. cos + cosh u. sin ). 
 
 159. J sinh w. sin udu -|- (cosh ;/. sin u sinh 74. cos u). 
 
 i6o. J cosh u. sin u du = \ (sinh w. sin 7^ cosh 7/. cos u). 
 f 
 161. J sinh (mu) sinh (w) ^ v vn 
 
 = ^ 2 ^ 2 I l sinh (ww) cosh (mu) n cosh (ww) sinh (mu)\ 
 
XX DEFINITIONS AND FORMULAS. 
 
 162. J cosh (mu) sinh (nu) dn 
 
 = 2 _ 2 m sinh (nu) sinh (mu} n cosh (nu) cosh (mu) I 
 
 163. 1 cosh (mu} cosh (#) afo 
 
 = z _ 2 w sinh (mu} cosh (#&) n sinh (;*) cosh (ww) 
 1 64. J sinh u tanh & </ = sinh u gd u. 
 
 /u 
 cosh u coth udu = cosh 4~ log tanh 
 
 166. J sec & du = gd~ x w. 
 
 167. J sec 3 <</< = J (i + tan 2 <)^aftan < = | sec < tan <j> + \ gd - 1 <^>, 
 
 = \ tan < (i -J- tan 2 <#>)^ + ^ sinh" 1 (tan <#> ). Here <j>=gdu. 
 
 C du . u C du u 
 
 168 I , , =smh~ . I J -- 2Tlz =sin- 
 
 / ( 2 + a 2 )^ J (a 2 u*y* a' 
 
 C du . u C du u 
 
 I ^ > 9- ~~7~2 -- in/" =cosh~ . ^-J7=cos~ 
 
 / (u 2 a 2 )^ a ^ (a 2 u 2 ) X a' 
 
 /du i . u C du i . u 
 
 - = tanh" 1 . -tan" 1 - 
 
 O 2 0< ^ J a 2 -\- u* a a' 
 
 du i ^ u C du i ,11 
 7-2^ - =- coth" 1 . = = cot~ 
 
 (u 2 a 2 ) u>a a a J a 2 + u* a a' 
 
 du i u C du i u 
 
 ^r/ = sech" 1 . ^/ = sec" . 
 
 u(a 2 2 )^ a a J u (u- a 2 )% a a 
 
 du l v, - 1 u C du _L -i u 
 u (a 2 + u 2 ) 1 /* - ~^ C ~^' J n(u' a*) ~~~'~^ C ~^' 
 
 /du i au + b 
 
 7 rr T~ r~^? = /= sinh- ^ a positive, ac >b'\ 
 
 (au 2 +2bu+c)* |/ a (ac &y* 
 
 i au-\- b 
 
 = v= (.-&> 
 
 i au 4- b 
 
 = = cos- 1 -^ ' a negative. 
 
 !/_# {tracy* 
 
 /du i aw -f b 
 
 u* u == - * ^^^' 
 
 aw 4- b ac<b\ 
 
 (f-acj* au + b <(& acY*. 
 
 i aw 4- b ac<b\ 
 
 coth 
 
 _ t au 4- b ac<b\ 
 
/du 
 (a u)(u 
 
 DEFINITIONS AND FORMULAS. 
 2 
 
 XXI 
 
 or - tan 
 
 llT 
 
 \ 
 
 \ h _ 
 
 tanh- 1 
 
 ^=T' 
 
 b a 
 
 or 
 
 coth- 1 \\ u - (The real form is to be taken.) 
 a b 
 
 
 / 
 (a - 
 
 du 
 
 or - coth 
 
 (baf/* * b a 
 
 -W-r^- 
 
 ^ h n 
 
 \ & u 
 
 or 
 
 tan 
 
 " 1 
 
 
 ( a 
 w __ ^^ w = w 2 a*)*- i 2 cosh- 1 -- 
 
 real form is to be taken -) 
 
 179. 
 180. 
 181 
 182. 
 
 JV-* 2 -*^ = *(- 
 
 ^2 _J_ ^2^ ^ __ ^ u ^ U 2 _j_ 
 
 /_ <1U 
 ~a" 
 
 c - e<lu 
 
 sn- 
 
 2 sinh- 1 . 
 
 
 ; 
 w 
 
 w /* 
 
 I n m ~ l 
 a J 
 
 du. 
 
 du 
 
 e au 
 
 r * ^ 
 
 i8s. I a a u = - : 
 
 J Moga 
 
 /" w n TZ" w n - ] n (n i) M u* * . 
 u n a u du = - T H- - y 
 
 log a (log ) 2 (log ) 8 
 
 n (n i) (w 2) . . 21 u 
 (log^)^ 1 
 
 Ca u du a u F i log a (log a) 2 
 
 lo^. I r ^^: I n _ i T 7 o 7 r~r r ,; 
 
 Qogg) n ~ T f ^ U ^ "1 
 
 " (- 2)(^- 3 ) . . . 2.1 J // J' 
 
 Ca u du (7^1oga) 2 , ( 
 
 jgg. I- -=\QVU-\-U^ ' 
 
 J n 
 
XXli DEFINITIONS AND FORMULAS. 
 
 /du i r ~\ 
 
 -^+6^ == isa l mu ~ log (a + ^" } J 
 
 / 
 
 du 
 
 I9i 
 
 /du i 
 
 (a 4- fe mu )^ = m '~\_ * 0g ^ V ~*~ ^"' M ~~ ' ^ 
 
 - log (l/a + ^ wu + I/a)! - 
 
 I93 ' J ( i + / == i f u 
 
 /e au loer u i r e au du 
 e uu log u du = - . 
 
 a a J u 
 
 195. J log u du = u log u ?<. 
 
 196. ftf" 
 
 197. J (log w) n du = u (log ?0 n n J ( lo g ") n ~ l <#* 
 
 Jw m + 1 Clog; ?0 n n r 
 
 tc (log )- du = - j- + i m + l j 
 
 r (log )</< (logM)"^ 1 
 
 J 99- J - "IT ' nI 
 
 J^ , i r du 
 
 (log w) n = " ( i)(log/^) n - 1 w i J (log?^)"" 1 
 
 /?^ m du u m + l m-\- i f* n m du 
 
 (logw) w " (w i) (logw)"- 1 " w i J (Iog70 n ~ l 
 
 <"* 
 log 
 
 /?<"* rfw r e~y 
 
 - dy, where JF = (m 4- log . 
 lo ?^ ^ 
 
 C_du_ __ i 
 
 2 5 ' J u (log w " (n i ) (log ) n - l 
 
 206. J ( 4- ^?0 m lg w ^ M = 
 
 l 
 
 f ( + ^/) BI ! //// -i 
 J -S- 
 
DEFINITIONS AND FORMULAS. XX111 
 
 207. j u m log (a 4- bu) du 
 
 1 \~ m+i i f A Cu m + l du~\ 
 
 0* 4- i L J a + w J* 
 
 C loer (# 4 ^^) du 
 
 208. I s - i 
 
 J w 
 
 bu i ( bu\* i / bu 
 log a .log + --- ? ( ) +-( - 
 
 /log ^^ ^ _ i F_ log u C _ du _ -i 
 
 (a + bu) m ~ : b(mi) L (a + tu) m - l+ J n (a + t>u) m ~ l J. 
 
 /log u du i i /* log O + ^ w ) 
 
 ^__ = _i og . log(a + te) ___j_ i__ i rfw . 
 
 21 1. f( + M) log <fo = ^^ log - 
 
 \s 20 
 
 /log u du 
 
 212 
 
 2) V (a + bu) 4- l/alog (\/ a + bu 
 
 - J# log (l/4-^~ l/), if >o, 
 
 = y [(log 2) I/ (a + bu) 4- 2 iX-^tan- 1 ^^^^f a <o. 
 
 213- f ^~ a2 " 2 rf = * * = r a). 
 
 */0 2 2 a V2 ' 
 
 214. 
 
 . f 
 
 Jo 
 
 216. 
 
 . f ?-"" l/HIdu =^ J * 
 
 Jo 2 A ~~ ' 
 
 X-JQ ^ ^nw ) 
 
 . I -=-du = JJL- 
 
 Jo |/ K \ w 
 
 2l8 ' ' '- m 'V r o. 
 
 az 9 . JV * 
 
 /0 Sll 
 
 sinh (nu) 2, w 
 
 220. r u 
 
 Jo sin 
 
 sinh (?^) " " 4 2 ' 
 
DEFINITIONS AND FORMULAS. 
 
 /* "" / 7T 
 
 221. J Q sinh (mu) . sinh () du = J o cosh (wz*) . cosh (nu) du 
 
 = o, if m is different from n. 
 
 222. I ''cosh 2 (mu) du = P* sinh 2 (ww) afo = 1^1. 
 
 /O o/O 2 
 
 X+ilT 
 sinh (mu) du = o. 
 i* 
 
 /i JT 
 
 224. cosh (raw) afo = o. 
 
 i/O 
 
 XtTT 
 sinh (ftttt) cosh (MM) ^ =o. 
 -i 
 
 J7T 
 sinh (OTK) cosh (mu) du = o. 
 _ . 
 
 r l logu 7T 2 
 
 227. I - du = -- . 
 
 /o i w 6 
 
 r 1 log u 7T 2 
 
 228. I - du = -- . 
 
 JQ i + u 12 
 
 r 1 iog 7T 2 
 
 220. -du = -- . 
 
 Jo i u 1 8 
 
 C l , ( I + U\ du 7T 2 
 
 230. I log I - - ) - = 
 a jo '\i u ) u 4 
 
 X 1 log M du 7t 
 
 (l - u >)% = -T log2 ' 
 
 * ' rfa A + 
 
 233- r oog *)" ^ = c !)" 
 
 /0 
 
 235 
 
 .36 
 237- 
 
DEFINITIONS AND FORMULAS. XXV 
 
 G. FORMULAS FOR THE SOLUTION OF PSEUDO- SPHERICAL TRIANGLES. 
 
 a. Right Triangles. 
 cot U (a) sinh a 
 
 sin A = 
 cos A = 
 
 cot 11 () sinh c 
 
 cos 77 (b) _ tanh b 
 cos // () tanh c 
 
 sin Z? t. 
 
 cos ^4 = ; .. , N = sm B cosh 
 sin 11 (a) 
 
 cot77() sinh 
 
 cot ^4 = 
 
 cos = 
 
 cos 77 (a) tanh 
 cosll(a tanh a 
 
 cos 77 (V) tanh 
 
 _, sin A , . 
 
 cos B = . ... = sin A cosh 
 sin u (o) 
 
 cot 77 (b) sinh 
 sin B= 
 
 cot >5 = 
 
 cot^ (V) sinh 
 cot/7 () sinh 
 
 cos /y ^ tanh b 
 
 tan J. tan B = sin 77 (V) = sin 77 (a) sin 77 (). 
 = sech <: = sech a sech 3. 
 
 b. Oblique Triangles. 
 The general relations are : 
 
 cosh a = cosh b cosh sinh sinh c cos ^4. 
 sin ^4 sinh b = sin .Z? sinh a. 
 coth a sinh b cosh cos C + sin C cot A . 
 
 cos ^4 = cos B cos C -4- sin Z? sin C cosh a. 
 
 Forti solves the six typical cases in the following manner: 
 CASE i. Given a, b, c. Put zp = a -f b + c. Then, 
 
 tan I A = J sinh (I ).sinh(/> g) . 
 ' sinh /> sinh (/ a) 
 
 The conditions are a < b + c; b <ia + c; and < <z + b. 
 
 CASE 2. Given a, b, A. Draw the geodetic line CD perpendicular to AB. 
 
 Then a>CD; A < i ; cot i C> o ; and tanh ^ ^ > o- 
 
XXVI DEFINITIONS AND FORMULAS. 
 
 sinh b sin A 
 
 sin B = 
 
 l ^_ 
 
 sinh a 
 an ^ (A B) sinh ^ (a 4- b} 
 
 sinh 
 
 ! _ _ 
 
 CASK 3. Given a, b, C. 2 & = * (A + #-f C). 
 
 i / xf r>\ i 
 
 tan A + B = cot 
 
 sinh (0-Hh 
 
 sin A sin (A -f- C) 
 sin (A -f A) sin (A -f B) 
 
 CASE 4. Given ^, B,c. A + B <* and DBC <DBG. The angle 
 is the angle between the geodetic DB drawn perpendicular to AC and the 
 geodetic BG drawn parallel to AC. 
 
 i r ^/sinh (/> a) sinh (p b} 
 
 tan *- \ - ; 7 ; , , r 
 
 sinh/ sinh (p c) 
 
 CASE 5. Given A, B, a. a > CZ? and ^4 + B < TT. 
 Solve the two right triangles formed by the geodetic line CD drawn per- 
 pendicular to A B. 
 
 CASE 6. Given A, B, C. A+ B+ C<~. 
 
 sin A sin (A -)- A) 
 sin (A + B) sin (A + C) ' 
 
 H. FORMULAS FOR THE SOLUTION OF THE Cusic 1 . 
 
 If a cubic equation is given in the form 
 
 -f- 0,2* -f- bz -\- c = o, 
 
 it can be reduced by the substitution z = x - - to the simpler form 
 
 v5 
 **+/*+ f = O, 
 
 'Taken from 1% Ingenieurs Taschenbuch der Htitte, Berlin, i8th edition. 
 
DEFINITIONS AND FORMULAS. XXV11 
 
 CASE i . When x z -\- px q = o; p and q positive. Compute the auxiliary 
 variable u from sinh u = ^ ^f ^; then the roots are 
 
 Xl = =t= 2 v"~\p sinh \ u. 
 
 x^ = V \p sinh \u-\-i V~p cosh | u. 
 
 x 3 = I/ \p sinh -I u i V p cosh \ u. 
 CASE 2. When x* px $ = o; p and q positive, (i/) 3 < (\ qf. Com- 
 
 pute from cosh u = 2 ' T ^M/> tnen tlie roots are 
 
 '/ 2 
 
 = =F 2 l^ -|-/> cosh 
 
 x^ = I/ \p cosh \u -\r i V p sinh \ u. 
 x z = V \P cosh J * t/ ^ sinh ^ w. 
 
 CASE 3. When # 3 /j; q =o-, p and ^ positive. (^-/) 3 >(-J- ^) 2 . Com- 
 pute the angle u from cos u = ^-^7\~^\y'> then tlie roots are 
 
 x^ = =F 2 I/ 7 |/> cos ^ w. 
 
 ^T 2 = =h 2 I/ |/> COS (i + 120). 
 
 x 9 = =i= 2 I/ -^/> cos (^ w + 240). 
 CASE 4. When x* pxq = o; / and ^ positive. (-J- ff = 
 
 For applications of hyperbolic and circular functions to the solution of the 
 cubic whose coefficients are general (i. e., real or complex), see a brief paper 
 by Mr. W. D. Lambert in American Mathematical Monthly for April, 1906. 
 
GEOMETRICAL ILLUSTRATIONS OF HYPERBOLIC 
 
 FUNCTIONS.. 
 
 The algebraic relationship of the hyperbolic functions to the circular func- 
 tions has been discussed in the section on definitions and formulas. A close 
 relationship also exists between the elliptic functions and the hyperbolic 
 functions. Thus it may be shown that the elliptic integral of the first kind, 
 
 V i 
 
 sn 
 
 in which k is the modulus and < the amplitude, reduces to = gd~ l < when 
 k = i . The elliptic functions thus degenerate into the hyperbolic functions 
 when the modulus is equal to unity. A case in point is the elastica, the 
 equation of which takes the form of an elliptic integral, excepting when the 
 modulus is unity. It then reduces to the two equations 
 
 X 1/2 
 
 = K 2 tanh u; - = , 
 a a cosh u 
 
 which is a syntractrix described by the free end of a rod whose middle point 
 traces out the tractory. 1 
 
 Ligowski gives the following easy geometrical method of demonstrating 
 the relations between the hyperbolic and circular functions. Let the equation 
 of the circle of unit radius be 
 
 and call 
 
 y 
 
 u c the arc of this circle from the positive x axis to the point x c y c 
 Then, of course, the circle may be repre- 
 sented by the two equations 
 
 x c = cos u c ; y c = sin u c . 
 Now, the area of the circular sector, whose 
 
 O 77 T 
 
 chord is 2y c , is - - u c , so that x c and 
 
 y c may be regarded as the cosine and sine of 
 a sector u c . The ellipse may be derived 
 from the unit circle by multiplying the or- 
 dinates y c by b. Hence, in the ellipse, the 
 area of the sector subtended by the chord 
 2 y e is, say, n e and u e = bn c . 
 
 1 If in these equations m is substituted for 2 they represent any syntractrix. The two 
 equations, with this substitution, can be combined to the following : 
 
 (au 
 
 ' 
 
 showing that the curve is traced by a point on a circle of radius am whose center is in 
 motion. It is noteworthy that if in this equation the hyperbolic sector u is replaced by 
 a circular sector </>, the new equation represents a prolate or a curtate cycloid, or In tier 
 the syncycloid. Thus the syntractrix may be considered as a syncycloid with an infinite 
 
 period. 
 
 acxviii 
 
GEOMETRICAL ILLUSTRATIONS. xxix 
 
 Thus 
 
 Uf, 
 
 x c cos u c = cos -r- 
 
 so that for the ellipse, 
 
 . 
 
 y c = sin w c = y = sin 
 
 ^2 , ^ _ . 
 
 * e ~ 72 ~ - 1 
 
 , 
 
 x e =x e = cos ; y e = b sin -7-- 
 
 
 
 The equation 
 
 jt 2 y = i 
 
 represents an equilateral hyperbola, and if u is the area of the hyperbolic 
 sector whose chord is 2_y, then there can be no objection to writing 
 
 x = cosh u ; y = sinh u, 
 
 where cosh and sinh are functions whose nature is still to be determined. 
 The most evident relation is 
 
 cosh 2 u sinh 2 u = i . 
 
 Now if i = V i, the hyperbola may be written 
 
 which is an ellipse whose major axis is unity and whose minor axis is i. 
 Comparing this with the ellipse discussed above, it appears at once that 
 
 x = cosh u = cos -> 
 i 
 
 -.. . . . u 
 
 y = sinh u = i sin r> 
 
 or, in an equivalent form, 
 
 cosh u = cos iu ; sinh u = i sin iu, 
 cosh iu = cos u ; sinh iu = i sin u. 
 
 The investigation of cosh u and sinh u can be completed in various ways ; 
 for example, by writing out the series for cos iu and i sin iu and showing 
 that their sum or difference is e M . 
 
 The geometrical properties of the hyperbolic functions themselves are com- 
 monly discussed in reference to the equilateral hyperbola. They could also 
 be derived from the geometry of the ellipse without reference to the hyper- 
 bola ; but a more perspicuous method seems to be to study the relations of 
 these functions to both curves at the same time. 1 
 
 In any ellipse, 
 
 J See Bull. Geol. Soc. Am., vol. 2, 1891, p. 49, and Am. Jour. Sci., vol. 46, 1893, p. 337. 
 
XXX 
 
 GEOMETRICAL ILLUSTRATIONS. 
 
 the area a (3 may be chosen as the unit area, so that the equation of the 
 
 curve becomes 
 
 
 By varying the value of a in this equation a family of ellipses is obtained 
 each of area TT, all with the same center and all with axes lying in the axes 
 of coordinates. The envelope of this system of curves is the hyperbola 
 xy = ^-, and this may be conceived as generated by the motion of a single 
 point. The coordinates of the point P lt at which the hyperbola is tangent 
 to the ellipse, are 
 
 Via \ 2 
 
 and the coordinates of the point c at which the hyperbola is tangent to the 
 unit circle, are 
 
 i 
 
 = 7T 
 
 <~*d 
 
 4: 
 
 
 
 J X-t * ' 
 
 * i 
 
 
 n 
 
 f ;*tt*s 
 
 ~tv(jL ^'"- ' 
 
 FIG. 5. 
 
 If the hyperbola is conceived as generated by the point c in moving from 
 its original position to P l (or as a " line of flow "), its radius vector sweeps 
 over an hyperbolic sector ocP r If this area is called , then by a well- 
 known formula, dtl = x dy - y dx, 
 
GEOMETRICAL ILLUSTRATIONS. XXXI 
 
 and because xy = %, 
 
 dy dx\ 
 
 du = i I - - ) . 
 
 J \ y x ) 
 
 Since no integration constant is required, 
 
 u =. \ log = \ log a 2 or a = e w . 
 x l 
 
 The area u is the sector oP l cP^ where the coordinates of P t are x 2 =y iy 
 and y 2 = x r It is noteworthy that two other areas, AP l cP z B and CD P l 
 cP 2 , have this same value, for evidently 
 
 X% /*.Va 
 
 y dx = I X dy = log a = U. 
 J 2/i 
 
 The length of the chord /> /> 8 is 
 
 and half of this, or /> a, is the hyperbolic sine which may evidently be put 
 in the form 
 
 e u_ e -u 
 
 smh u = . 
 
 2 
 
 Since the curve P l cP 2 is an hyperbola, 
 
 and therefore 
 
 + *- 
 
 oa= |/ 1 sinh 2 u = - - = cosh u. 
 
 The diameters connecting the points of intersection of the unit circle and 
 the ellipse whose axes are a and a 1 , may be called the isocyclic diameters 
 of the ellipse, because the circle and the ellipse have the same area. These 
 diameters are not conjugate. If the ellipse is conceived as the section on 
 the greatest and least axes ot an ellipsoid of unit volume, the isocyclic 
 diameters are the traces of the circular sections of the ellipsoid. The coordi- 
 nates of one of the points of intersection, say E, are 
 
 x = 
 
 l/a 2 -hl 
 
 and therefore the angle v, which the vector oE makes with the major axis of 
 the ellipse, is given by the relation 
 
 tan v a 1 =e 
 and it follows that 
 
 I tan f 2v\ = -J- (cot v tan v) = sinh u. 
 is angle ( 2v\ is gd u, or the gudermannian of u, so that in any 
 
XXX11 GEOMETRICAL ILLUSTRATIONS- 
 
 ellipse whatever the angle made by any line parallel to one isocyclic diameter 
 with a perpendicular on the other isocyclic diameter is the gudermannian of the 
 natural logarithm of the semi-major axis, this being expressed in terms of the 
 isocyclic radius, which in the general case is the square root of the prod- 
 uct of the semiaxes. 1 In the diagram the gudermannian bob^ is shown as 
 bisected by the axis of the hyperbola, and it is worth remarking that if the 
 ellipse were to be distorted into a circle by compressing the major axis and 
 elongating the minor axis, the line ob would be brought into coincidence 
 with ob^ so that gd u can be defined as the angle through which an isocyclic 
 diameter has swept when the ellipse has been derived from a circle by irro- 
 tational plane strain. 
 
 The angle 45 -f f which occurs in the formula for meridional parts 
 
 is the angle made by either isocyclic diameter of the ellipse with the minor 
 axis, and the tangent of this angle is the semi-major axis a. 
 
 The twofold relations of the hyperbolic functions to the hyperbola and 
 the ellipse are illustrated in a somewhat different manner in figure 6. 
 
 Here the curve p l c p z is an arc of an hyperbola jy 2 x 1 = i. If the area 
 of the sector o p l c p^ is called u, a /> 1 = sinh u and oa = cosh u. Make 
 bc=p l a and draw the associated ellipse shown in the diagram. Then the 
 angle boc=gdu / bo = cosh u and 
 
 tan gd u = sinh u 
 sec gd u = cosh u 
 sin gdu = tanh u. 
 
 The ellipse has corresponding properties. Since the gudermannian is the 
 angle between either isocyclic diameter and a line perpendicular to the other, 
 the line ob may be regarded as coinciding with one isocyclic diameter and the 
 axis of abscissas with the other. The major axis of the ellipse then bisects 
 
 L The isocyclic diameter used in this illustration of hyperbolic functions lies in the 
 circular section of a shear ellipsoid, or an ellipsoid in which the mean axis is a mean 
 proportional between the greatest and least axes. The position of the circular section 
 of the general ellipsoid is also readily expressed in terms of hyperbolic functions. Let 
 the equation of the ellipsoid be 
 
 *- 2 v ? 9.2 
 
 + IT + !*>> 
 
 If = cosh u lt and -j- = cosh w 2 , 
 the angle v which the circular section makes with the greatest axis is given by 
 
 i b a - * tanh w, 
 
 tan = T tanh = c -._ b -* = ..nhl^' 
 
 If Ul = w, and -?- = a this expression reduces to tan v = a -\ or to the case of the 
 shear ellipsoid. 
 
GEOMETRICAL ILLUSTRATIONS. XXX111 
 
 the angle 90 gdu, its magnitude is 2 e u , and the equation of the ellipse is 
 
 4 xy tan gd u 
 
 tan 2 
 
 -+- i) = i. 
 
 ' By varying the value of tan gd u (or sinh u) a system of ellipses is obtained 
 whose envelopes are y i , so that if any one of the ellipses is supposed 
 to be derived from the circle by distortion, the process is that generally 
 known as "shearing motion or scission." 
 
 If the points in the circle are sought which correspond to the points on the 
 
 FIG. 6. 
 
 major axis of the ellipsoid, it will be found that the angle between the two 
 positions (the angle of rotation) is equal to the gudermannian. 1 
 
 If instead of the horizontal, the vertical line in figure 6 had been taken as 
 coinciding with the isocyclic diameter of the ellipse, the result would have 
 been the discovery of a system of ellipses whose envelopes are x d= i, 
 similar in all respects excepting orientation to that discussed. 
 
 1 Love's Treatise on the Theory of Elasticity, vol. i, p. 43. 
 
METHODS OF INTERPOLATION. 
 
 It is not easy to describe the use of the tables which follow without some 
 notes on the methods of interpolation with reference to which they are 
 arranged. In all of them the argument advances by equal increments, each 
 equal, say, to o>. It is required to find a value of the function F interme- 
 diate between two tabulated values, F Q and F lt corresponding to a fractional 
 value of the argument or to wo>, where n is always less than unity, and 
 preferably less than one-half. 
 
 Let F n be the value of the function to be determined ; let Fi and /*!. 2 be 
 tabulated values of F immediately preceding F ot and let F lt F^ be values 
 immediately following F . Denote F l F by a ly other first differences (A') 
 being similarly represented. If also a a a l = b^ b l b Q = c lt etc. , the whole 
 system of functions and differences is shown in the following schedule : l 
 
 F 
 
 A' 
 
 A" 
 
 A'" 
 
 A 
 
 J 
 
 * 
 
 >-, 
 
 
 b" 
 
 
 d" 
 
 
 r 
 
 
 a" 
 
 
 c" 
 
 
 ^' 
 
 
 ^-i 
 
 
 b' 
 
 
 d' 
 
 
 f 
 
 
 a 
 
 
 c 
 
 
 e 
 
 
 ^0 
 
 
 t>o 
 
 
 d * 
 
 
 /. 
 
 F, 
 
 a \ 
 
 * 
 
 c i 
 
 4 
 
 *\ 
 
 /, 
 
 
 
 *, 
 
 
 < 
 
 
 / 
 
 The most familiar formula of interpolation is due to Newton, and in the 
 above notation it may be written thus: 
 
 F n F = na^ 
 
 n ftt i) Q -2) 
 
 2\ 
 
 , 
 
 n (n i) (n 2) ( 3) , 
 - a, 
 
 J The notation and general outline of treatment here presented closely follow Mr. 
 Herbert L. Rice's treatise, Theory and Practice of Interpolation, 1899. The Nichols 
 Press, Lynn, Massachusetts. 
 
 xxxiv 
 
METHODS OF INTERPOLATION. XXXV 
 
 The coefficients are those of the binomial theorem. This formula is appli- 
 cable to the first intervals of a series, which is not the case with any other 
 mode of interpolation. It may also be adapted to the last intervals by sub- 
 stituting n for n and a, b' ', c", d" ', . . . for^, b iy c^ d^ . . . . In systematic 
 interpolation, such as is involved in the construction of tables, it is usual to 
 employ the more rapidly converging formulas of Stirling or Bessel; but when 
 a computing machine and a table of products are available it is sometimes 
 less laborious to compute an extra term of Newton's formula than to calcu- 
 late and apply the mean differences called for by the other methods. Both 
 Stirling's and Bessel' s formulas can be derived from Newton's by known 
 relations between the several differences. 
 
 In Stirling's formula the mean of the first differences next preceding and 
 following F Q is made use of instead of only the latter, as in Newton's formula. 
 The third differences are similarly treated, so that # , c , etc., being new 
 quantities, are defined by 
 
 These mean values are used in conjunction with the even differences on the 
 same horizontal line with F Q in the schedule, and Stirling's formula is 
 
 n* n (n 2 i) ri l (n 2 i) 
 
 F n Ft = nat+-^b, + - ^i- r + - ^T" 
 
 (' i)Q 2 4) . 
 
 5! *"" 
 
 To interpolate backward it is only needful to substitute n for n. 
 
 In Bessel's formula use is made of mean differences of the even orders, and 
 if b\ d, etc. , are these means they are defined in terms of the scheduled differ- 
 ences, thus : 
 
 They are used in conjunction with the simple odd differences a r c ly etc., and 
 
 the formula is 
 
 p p_ n i n ( n T ) fl-L. n ( n *)(** i) t(n-\-i)n(n i (n 2) . 
 
 2 ! 3 ! 4 ! 
 
 ; + !)( i) (n 2) ( 
 
 5 
 
 When n = ^, or for interpolation to the middle of an interval, the co- 
 efficient of ^ vanishes and F n F is independent of third differences, which 
 is clearly a great advantage. In general this method is very advantageous 
 .when n approaches one-half, while Stirling's formula is preferred for small 
 values of n. 
 
 V7*_ - i.) n\n- -i; ^ ^; ^n -%) 
 
 f \ l ~T . 
 
XXXVI METHODS OF INTERPOLATION. 
 
 When Bessel's formula is used for backward interpolation, it may be 
 written 
 
 *__/?= - na > + i^H (A*L) -."'"--H"-*)^ ..... > 
 
 being taken as positive. 
 
 A distinct method of interpolation is founded directly upon Taylor's 
 theorem. If F ' F ", etc., are the successive derivatives of F , and w is the 
 constant increment of the argument, this fundamental theorem may be 
 written 
 
 zr Z7 V , * w2 V . " S ' ^o'" * * ^o" 
 
 /^ ^ = o,^ + -J-0 ___^ T^ ...... 
 
 and this becomes an interpolation formula when the derivatives are ex- 
 pressed in terms of the differences. This is readily accomplished to any 
 degree of exactness whenever the differences become rigorously or sensibly 
 constant at some particular order and the tabular interval is small relatively 
 to the period of the function. To find the numerical values of the deriva- 
 tives it is not necessary that the analytical expression of the function should 
 be known ; for, rearranging the terms of the formula of Bessel and Stirling 
 according to ascending powers of n and comparing coefficients, 
 
 (Bessel.) (Stirling.) 
 
 -.. .^-Ifo.-K + 
 
 f." = (*-*',-T<r <* + *.+ ) = (*.-**,+ 
 
 Hence, to compute the first derivative, say from Stirling's formula, when 
 the 6th differences and -fa of the mean of the corresponding third differences 
 are negligible, it is only needful to take the mean of the first differences pre- 
 ceding and following the tabular value of the function, subtract from it one- 
 sixth () of the mean of the corresponding third differences, and divide the 
 result by o>. 
 
 Newton's formula gives for arguments near the beginning of the series of 
 tabular values : 
 
METHODS OF INTERPOLATION. XXXV11 
 
 and for arguments near the end of the series of tabular values, 
 F; = (' + * *' + i c" + i d" + \ e'" + . . . 
 F>' = 4 (<*' + c" + H d" + f *'" + . . .) 
 
 The differences of the derivatives may of course be found and discussed 
 in the same manner as those of any other function, and the higher deriva- 
 tives, F n " ', Fn" t ..... can be expressed in terms of the differences of Fn . 
 To distinguish the differences of F' from those of F t they may be denoted 
 by Greek letters, and the notation is exhibited in the following scheme : 
 
 a y a^ -\- a = 2 a Q 
 
 F; ft s 
 
 a i 7i 7i + y = 2 7o 
 
 FS A 
 
 s 
 
 ^ 
 
 Using Stirling's formulae, page xxxvi, the successive derivatives inclusive 
 of fifth differences are now 
 
 and the interpolation formula may be written 
 
 or, neglecting fifth differences, 
 
 and for backward interpolation 
 
 / n \ n * a n ( n 2 \ ~| 
 
 ;' --a o +- ^ o - _ (- -- :) yo j. 
 
XXXV111 METHODS OF INTERPOLATION. 
 
 In the tables which follow, the first derivatives multiplied by <o are tabu- 
 lated in units of the last decimal place of the tabulated function (except 
 Table VII), and the remaining quantities required in the computation can 
 be found by mere inspection. The higher order of differences will be needed 
 only for a very few arguments at the beginning or end of those tabular 
 values whose numerical magnitudes approach o or oo. For the remaining 
 arguments it will be found that the -$ part of the second difference of to F n f 
 is not great enough to influence the result, and it is therefore sufficient to use 
 
 2 
 
 wa o being the mean first difference of w F' corresponding to F . This formula 
 is rigorous when third differences are zero. In most cases can be found 
 
 mentally, and since o> f Fj -\- oj is here to be regarded as an interpolated 
 
 value of w F ', no confusion can arise as to the sign of the correction. It thus 
 becomes almost as easy to include ^ a o in the computation as to omit it. A 
 convenient rule is : Find by linear interpolation the value ^ F' for one-half 
 
 the interval f J ; multiply this interpolated value by the entire interval (?i) 
 
 and apply the product to the tabular value of the function, either positively 
 or negatively, according as the function is increasing or decreasing. To 
 illustrate the application of this rule, find Iog 10 sinh 0.00304. In this case 
 n = 0.4 and the table gives 
 
 ^0 = 7-4771 2; >F ' = 1447.7; *> = -48,3, 
 
 the last two quantities being expressed in units of the fifth decimal place. 
 Interpolating a> F' linearly for one-half the interval, 
 
 H 
 
 u) F n = to (F f -\ s) J 4477 0.2 x 48,3 = 1438,0 ; 
 
 ~ 
 
 multiplying this value by n and adding the result to the tabular value of the 
 function, there results 
 
 /;= 1438,0 X 0.4 + 7. 47712 -=7.48287. 
 The corresponding difference formula (Bessel's) is 
 
 The derivative formula () with two terms has the advantage of being much 
 more convenient than the difference formula, while the accuracy of the two 
 is the same (five-eighths of a unit) when the derivatives are tabulated to the 
 
METHODS OF INTERPOLATION. XXXIX 
 
 same order of decimal as the function. In the case of linear interpolation, 
 however, it is in general more accurate to use the differences, the maximum 
 error of the difference formula being one -half of a unit and that of the de- 
 rivative formula three-fourths of a unit in the next succeeding decimal place. 
 The accuracy of the two formulas is the same when the next succeeding 
 decimal of the derivative is tabulated. The error of the derivative formula 
 is then simply the error of the tabular value, while the error of the difference 
 formula may be =, > or < than that of the tabular value, but is never greater 
 than one-half of a unit. 
 
 Interpolation formulas which are applicable only to a single function are 
 rarely advantageous, because as much time is often consumed in looking them 
 up as is saved by employing them ; but some formulas applicable to hyper- 
 bolic functions are so simple that when once suggested they can hardly be 
 forgotten. Thus, Taylor's theorem gives at once 
 
 n 2 o> 2 n 3 co 3 
 cosh (u -j- n o>) cosh u = n o> sinh u -| cosh u -j j sinh u -f . . . , 
 
 and the form for the sine is of course similar. Again, when, as here, the 
 cosine is tabulated with an argument in terms of radians, 
 
 cos (u + n co) cos u = no) sin u cos u -j j sin u -f- . . . . , 
 
 the series for the sine being similar. 
 So, too, 
 
 log c (u + n w) log,, u = log e ( J + -^ 
 n ot . n* u? . n* > 3 
 
 Simplest of all is the exponential, 
 
 e u + n_ e u ^ e u e n<*_ l=e 
 
 = e u (-\- o. 01 n + o.ooo, 05 rc 2 -f 0.000,000,167 n 3 + . . .), (> o.oi) 
 = "(+ o. ooi n -f- o.ooo, 000,5 n 2 -f- . . .). (</>= o .ooi) 
 
 The series in ni may be replaced by 7z, and this may have any finite value. 
 Especially when a computing machine is available, this formula is easily ap- 
 plied and is, of course, rigorous. 
 
 From time to time inverse interpolation by a method more accurate than 
 first differences is called for ; indeed, whenever interpolation of a function 
 by higher differences is needful, it is equally needful that the argument cor- 
 responding to a given function should be ascertained by a like process. The 
 method ordinarily pursued in such cases is to estimate two values of the argu- 
 ment, one a little greater and the other a little less than that of the required 
 argument, interpolate corresponding values of the function, and finally inter- 
 polate linearly over the reduced interval for a final value of the argument. 
 
xl METHODS OF INTERPOLATION. 
 
 Another method consists in interpolating values of the function and its deriv- 
 atives for an approximate value of the required interval and then computing 
 a correction to this approximate value by means of a reversed Taylor's series. 1 
 If second differences only are to be taken into account, the usual method 
 of procedure is to estimate an approximate value of w, say ri ', and with this 
 estimated value we interpolate linearly as before and find the value of & /v 
 
 ~T 
 
 corresponding to one-half of the estimated interval ( J . Then the required 
 
 interval () is equal to the difference between the given value and the nearest 
 tabular of the function divided by w F n > . This method is in fact simply the 
 
 reverse of the one for direct interpolation. A recomputation is of course 
 necessary if the values of n and n' are not practically the same. As an illus- 
 tration, find u when Iog 10 sinh 11 7.48287. We first compute 
 
 , 7.48287 7.47712 
 1448,0 
 
 then the value of w /v in terms of the last tabular unit is found as before 
 
 2 
 
 by linear interpolation to be 1438,0. Hence 
 
 7.48287 7.47712 
 n = - - ^ - = 0.40 and u = 0.00304. 
 
 Since the estimated and computed values of the interval agree, there is no 
 need of a recomputation. 
 
 The methods which are based upon an estimated value of the argument 
 are unsystematic and clumsy. It is much better to use a formula which 
 gives the required result by a direct and rigorous method. To find such a 
 formula, divide Taylor's series (eq. a) by w /?', and put 
 
 F n F S F' f atFJ" ^ F " 5 /o' . 
 
 then the interpolation formula may be written 
 
 Reversing this series in accordance with the relation, 2 
 
 x = 2- + ^ ( - ,) + 4 ( , + 2 a?) 
 
 i ^ 5 i 
 
 2 ^ 2 1 
 
 1 Rice's Theory and Practice of Interpolation, section 83. 
 
 2 Prof. James McMahon : " On the General Term in the Reversion of Series." Hull. 
 Am. Math. Soc., April, 1894. 
 
METHODS OF INTERPOLATION. xli 
 
 which is the reversed series of 
 
 and rearranging the terms, 1 
 
 n = n l -}-n l [ ^/ 2 + 2 (^/ 2 ) 2 5 ( n if^ + 1 4 ( n i/ 2 Y + ] 
 + "? [,/, (-1+5 (!/,) - 21 (^/ 2 ) 2 + . . )] 
 + v* \_nJi (1+6 !/,) + 3 (i/ 8 ) 2 +...] 
 + / [-i/.+ ] , W- 
 
 In the actual computation it is convenient to put 
 
 r= n ' ; 
 
 2 u> /*" ' 
 
 then, when successive values of Fn are tabulated in units of the last decimal 
 place, and Stirling's coefficients are used, 
 
 n if* = rt ( a o : k 7o) ^1/3 = i r w (A T2 S o) 
 
 i /4 = T2 r <o y Wi/5 <rV ^ 8 - 
 
 The formula is rigorous inclusive of fifth differences, and does not require 
 the computation of an approximate value of n. It is applicable to any func- 
 tion or series of tabulated values whose successive derivatives become evanes- 
 cent. It is particularly convenient when differences higher than the second 
 are neglected. The formula then becomes 
 
 n = n l + ! [ r w a -\- 2 (ra> a ) 2 5 (r a> a ) 3 + 14 (ro) a ) 4 ] . 
 
 Since r a a is a very small quantity, the higher powers are seldom needed, and, 
 should they be required, are easily taken into account. As an example, let 
 it be required to find u when Iog 10 sinh u = 7.48287. We compute 
 
 .= 7.48287 - 7 .477i 2 =04Q 
 
 ! 0.40 
 
 r=- - 1 7- = - - - = 0.0001; 
 
 20* F 9 2 x i447>7 
 and 
 
 n l rioa Q = 0.40 x o.oooi X ( 48,3) = o.oo. 
 
 Hence n = n^ = 0.40 and w = 0.00304, the same as obtained by the other 
 method. 
 
 When F n = e u , it is easily shown, either by means of series (d) or by inde- 
 pendent methods, that 
 
 n= + n l 0.005 n \ + 0.000,033 ?/j 3 + . . . , (a = o.oi ) 
 
 n=-\-n l 0.0005 V + ..... O = o.ooi) 
 
 These formulae afford an easy means of finding the natural logarithm of a 
 
 1 See, also, " Inverse Interpolation by Means of a Reversed Series," Phil. Mag., May, 1908. 
 
xlii 
 
 METHODS OP INTERPOLATION. 
 
 number from the tabular values of e u . Thus, to find the natural logarithm 
 of 0.9642102, we compute 
 
 0.9646403 0.9642102 
 
 n i 7- 7 ~ ==r '44587' 
 
 0.0009646403 
 
 Substituting in the last of the above equations 
 
 n = 0.44587 0.0005 x (o.45) 2 = 0.44577, 
 hence nat log of 0.9642102 = 0.0364458. 
 
 One of the most important applications of differences is the detection of 
 errors in values tabulated at equal intervals of the argument. It may be 
 shown by substitution in the schedule of differences (page xxxiv) that an 
 error, + e, in F Q produces errors in the successive differences of any order 
 which are multiples of e, the law of distribution of the multiples being that 
 of the corresponding coefficients of the binomial theorem, and the signs of 
 the errors being alternately positive and negative. Since some order of dif- 
 ferences of every continuous function must vanish, the presence of an error 
 in a tabular value must ultimately result in producing successive differences 
 of a certain order which alternate in sign. A comparison of these differences 
 with the corresponding binomial coefficients enables one to estimate the mag- 
 nitude of the error. Thus in the series which follows : 
 
 X 
 
 X 3 
 
 A' 
 
 A" 
 
 A"' 
 
 Aiv 
 
 13 
 
 2197 
 
 
 
 
 
 
 
 547 
 
 
 
 
 14 
 
 2744 
 
 
 84 
 
 
 
 
 
 631 
 
 
 6 
 
 
 15 
 
 3375 
 
 
 90 
 
 
 + 2 
 
 
 
 721 
 
 
 8 
 
 
 16 
 
 4096 
 
 
 98 
 
 
 - 8 
 
 
 
 819 
 
 
 
 
 
 17 
 
 4915 
 
 
 98 
 
 
 + 12 
 
 
 
 917 
 
 
 12 
 
 
 18 
 
 5832 
 
 
 110 
 
 
 - 8 
 
 
 
 1027 
 
 
 4 
 
 
 19 
 
 6859 
 
 
 114 
 
 
 + 2 
 
 
 
 1141 
 
 
 6 
 
 
 20 
 
 8000 
 
 
 120 
 
 
 
 
 
 1261 
 
 
 
 
 21 
 
 9261 
 
 
 
 
 
 the alternation in sign occurs in the fourth-order differences, and the numer- 
 ical values are twice the coefficients of (a + ) 4 . Hence there is an error of 
 4- 2 units in the value 4915. The corrections 2, +8, 12, -f 8, 2 ap- 
 plied to the fourth differences causes them to vanish, and the corrections 2, 
 4-6, 6, 4-2 applied to the third differences reduces them to a constant 
 
 This method is particularly useful in detecting large accidental errors in a 
 series of .observed values and in estimating their magnitudes. 
 
DESCRIPTION OF TABLES. 
 
 Table I is devoted to 5-place values of the logarithmic hyperbolic sine, 
 cosine, tangent, and cotangent of u expressed in radians. The argument 
 u advances by ten-thousandths from o to o.i, by thousandths from o.i to 
 3.0, and by hundredths from 3.0 to 6.0 In this as in all the tables (except 
 Table VII), instead of the first differences, the first derivatives of the func- 
 tions multiplied by the tabular interval (w) are tabulated in units of the last 
 decimal place, under the heading w/^'. As noted above, this agrees with 
 much of the most authoritative modern practice and facilitates interpolation. 
 It did not appear worth while to extend the tabulation of the table beyond 
 six radians, because higher values are seldom needed ; but in Table IV a few 
 very high values of e - u are given, from which in case of need the hyper- 
 bolic functions can be found. 
 
 In Table II the natural values of the hyperbolic functions are tabulated 
 for the same arguments as in Table I. In some instances the values are 
 given to one or to two places of decimals more than would be obtained by 
 taking the inverse logarithms of the preceding table. 
 
 Table III gives sin u = i sinh iu and cos u = cosh in with their loga- 
 rithms to 5 decimal places, the argument u being expressed in radians. 
 The tabulation extends from u = o.oooo to o. 1000, and from u = o. 100 to 
 
 i. 600, because 90 = 1.570 7963 radians; so that, this value of -- being 
 
 borne in mind, the table affords the means of finding the sine or cosine of any 
 arc expressed in radians. 
 
 Independently of hyperbolic functions, this table is often convenient. It 
 also facilitates the computation of the principal hyperbolic functions of 
 complex variables. Thus 
 
 sinh (ft iv) = sinh u cos vi cosh u sin v, 
 cosh (u iv) = cosh u cos v == / sinh u sin v, 
 
 and to compute either of these functions it is only needful to take out two 
 tabulated logarithms from Table III, two from Table I, make two additions, 
 and look out two antilogarithms. It is of course conceivable that all the 
 four quantities involved should be tabulated once for all ; but even if u and 
 v advanced only by hundredths, such a table would occupy 200 pages. To 
 find from it functions corresponding to u and v expressed in thousandths 
 would require three interpolations a process quite as laborious as the use 
 of the tables here given. 
 
 Space which would otherwise be vacant is utilized to give the angular 
 values of the radian arguments, or a table of conversion of radians from 
 
 xliii 
 
xliv DESCRIPTION OF TABLES, 
 
 o.oooo to o. 1000 and from o. 100 to 1.600 into degrees, minutes, seconds, 
 and hundredths of a second. 
 
 Table IV gives the values of Iog 10 e u , e u and e ~ u to 7 decimal places from 
 u = o.ooo to 3.000 and from 3.00 to 6.00. The values of e u and e~ " enter 
 into a vast number of equations representing natural phenomena, especially 
 those (as Cournot remarked) which can be classed under the generic denom- 
 ination of phenomena of absorption or gradual extinction. The ascending 
 and descending exponentials may be regarded at will either as hyperbolic 
 functions or as independent components of hyperbolic functions, since 
 
 e " = cosh u sinh u 
 while, on the other hand, 
 
 e u e~ u e u -f e~ u 
 sinh 21 = ; cosh u = ; 
 
 e u e~ u TT 
 
 tanh u = - - ; gd u == 2 tan ~ l e u -- . 
 
 6 ~T~ 6 2 
 
 It is further evident that a table of e " is a table of natural antilogarithms. 
 Formula e on page xli affords an easy means of obtaining the natural loga- 
 rithm of a number from the tabular values of c u . It is of course unneces- 
 sary to give the derivative of e u , since this is e u , while the derivative e~ u is 
 e ~ M . In general the interpolation or extrapolation of the function is 
 very easy. (See formula c, page xxxix). The logarithm of e ~ " is not given 
 because, being merely the arithmetical complement of the Iog 10 e u , it can 
 be read off as fast as'it can be written down. 
 
 In any table of Iog 10 e u where the interval of u is % the difference of 
 successive logarithms is constant and equal to ^ Iog 10 <? or 0.4342 9448*0. 
 If the logarithm of e u + n<a is required, this will be 
 
 (u + not} Iog 10 e = Iog 10 e u + nu Iog 10 e. 
 
 Hence it is practicable to prepare an extended table of proportional parts or 
 a table of n Iog 10 e which is applicable to any table of Iog 10 e u when the tab- 
 ulated values are multiplied by </>. Such an auxiliary table is given at the 
 
 close of Table IV, in which the argument varies from o.ooo to 0.500. If 
 
 ID is unity, this is merely a 5-place table of Iogi e u . If, on the other hand, 
 ia is o.ooi, as in the earlier part of Table IV, the auxiliary table gives the 
 increments corresponding to n to 8 places of decimals. Thus, if log, & - 088245 
 is required, Table IV gives log, <?- 088 = 0.0382179, the auxiliary table gives 
 
 for = 0.245, n log,,, e = 0.10640; and since & = o.ooi, <u n Iog 10 c = 
 at 
 
 0.00010640, which added to log, - 088 , gives log, <?- 088245 == 0.0383243. In 
 
 the latter portion of Table IV & is only o.oi; so that, if the Iog 10 e*-- 
 wanted, the main table gives log ^= 1.3028834, and ^ times n log c is 
 o 0010640; so that the required number is i 3039474. 
 
DESCRIPTION OF TABLES. 
 
 When Iog 10 e u is required for u > 6.00 the auxiliary table is insufficient to 
 give 7-place values. Then the main table, IV, may be used as an auxiliary 
 table. Thus 
 
 I g ^11.088245 = I g e \\ _f_ I g ^0.088245 
 
 = 4.777 2 393 +0.0383243 = 4.8155636. 
 
 In the second part of Table IV values of e - u and the logarithms of e u are 
 given, u varying from i to 100. The logarithms are given to 10 decimals ; 
 the other functions to 9 significant figures. Such high values are seldom 
 needed, but are included here lest these tables might some times fail the 
 computer. 
 
 Table V gives the natural logarithms of numbers from i to 1000, with 
 their derivatives to 5 places of decimals. These derivatives are merely the 
 
 reciprocals of the arguments, and since log e (-) = log e >', the logarithms 
 
 of the derivatives are the tabulated logarithms taken negatively. The 
 table thus gives, in addition to the logarithms of 1000 whole numbers, the 
 logarithms of 1000 proper fractions lying between o.ooi and unity. 
 
 THe interpolation of natural logarithms is much less simple than is that 
 of common logarithms, and this is the main reason why the latter are pre- 
 ferred for computation. A few simple rules, however, facilitate the needful 
 calculations. When the natural logarithm of a vulgar fraction is required 
 it is best to look out the logarithm of both numerator and denominator and 
 subtract. If the natural logarithm is required of a fractional number stated 
 decimally and less than 21.000, no attempt should be made to interpolate it 
 directly, because the third differences of the table cannot be neglected for 
 numbers so near the beginning of the table. If the number lies between 
 10.000 and 21.000, as, for example, 12.345, it should be written 123.45 / 10 > 
 and the required logarithm will be nat log 123.45 nat log 10. It is safe to 
 interpolate the first of these between nat log 123 and nat log 124, using the 
 formula for second differences. If the number whose logarithm is to be 
 found lies between i and 10, as, for example, 8.2468, it should be written 
 824.68 / 100, so that the required quantity is nat log 824.68 nat log 100. 
 The first of these logarithms can be found by using only the mean first 
 differences or the tabulated derivatives between the logarithms of 824 and 
 825. For values of the argument between 21 and 158 interpolation requires 
 the use of second differences, while above 158 average first differences or 
 the first derivative is sufficiently accurate, inasmuch as the error involved is 
 less than half a unit in the fifth decimal place. 
 
 It would be possible to interpolate the negative logarithms of the smaller 
 fractions given by the derivatives that is, from the reciprocal of 159 on to 
 the end of the table, or for numbers between 0.00628 and o.ooioo but this 
 would not be expedient, because these reciprocals are themselves rounded 
 values. If the natural logarithm of 0.0068352 is wanted as accurately as 
 
DESCRIPTION OF TABLES. 
 
 the tables will give it, it is best to find the logarithm of 683.52 and to sub- 
 tract from it the logarithm of 100,000. (See also formula e, page xli.) 
 
 The use of second differences may be avoided altogether if the computer 
 chooses, for any number not lying between 158 and 1,000 may be multiplied 
 and divided by another number which will bring the numerator within 
 these limits. Thus, if, as before, nat log 12.345 is required, this number 
 may be written 246.90 / 20, and the natural logarithm of the numerator found 
 by help of the derivative, less nat log 20, is the required value. 
 
 The awkwardness of a table of natural logarithms is inherent and cannot 
 be overcome by any device. It depends on the fact that e and the base of 
 numeration, the number 10, are incommensurable quantities. If our numer- 
 ation were duodecimal, as it might have been had six fingers to a hand been 
 the rule instead of the exception, 12 would also have been the most convenient 
 base for a table of logarithms. A great table of natural logarithms, such as 
 Barlow's 8-place table of all numbers from i to 10,000, is only a little more 
 convenient than that here offered, and with it, too, it is expedient to multiply 
 any small number by a factor such that the product approaches 10,000. 
 
 Table VI gives the values of the gudermannian of u to 7 places from 
 u = o.ooo to u = 3.000 and from u = 3.00 to u = 6.00. In this table u is 
 expressed in radians, and %d u both in radians and in angular measure. For 
 theoretical work the gudermannian in radians is usually the more convenient, 
 but for use in finding hyperbolic functions it must be reduced to an angle. 
 
 The gudermannian, gd #, is connected with the hyperbolic functions by 
 the following well-known relations : 
 
 sinh u = tan gd u / cosh u = sec gd u ; tanh u = sin gd u 
 tanh -- = tan \ gd u ; u = log e tan ( - - 4- 
 
 Thus Table VI, with the help of a y-place table of logarithms of the cir- 
 cular functions, gives y-place values of the hyperbolic functions. 
 
 The derivative of gd u is sech u, and can be used independently of the 
 gudermannian. 
 
 Table VII is substantially a reversion of Table VI, and gives the anti- 
 gudermannian in terms of the gudermannian, both, however, being expressed 
 in minutes and decimals of a minute. If m is the antigudermannian ex- 
 pressed in minutes and u the same function expressed in radians, 
 
 = 3437-7468 u = 3437.7468 loge tan ( - 
 
 Table VII is a table of m, and if m is multiplied by o.ooo 2908 8821 the 
 product is u in radians. This table is known to navigators as a table of 
 Meridional Parts for a Spherical Globe. It is frequently of use in the dis- 
 cussion of physical questions and is the very foundation of navigation with 
 Mercator charts. In the more modern works on navigation, however, the 
 
DESCRIPTION OF TABLES. xlvii 
 
 ellipticity of the meridian is allowed for in computing tables of meridional 
 parts, and consequently this table will probably never be reproduced in a 
 navigator. For this reason it is here preserved for computers who are not 
 engaged in navigation. 
 
 To test this table, which is borrowed from Inman, 200 of the values, or 
 one in every 27 entries, were compared with Gudermann's y-decimal place 
 table of the antigudermannian in radian measure. In nearly all cases Inman's 
 last figure was confirmed, but in a few instances the last figure is incorrect 
 by a unit. Inquiry into these cases showed that the maximum error detected 
 was less than o 006 of a minute. Thus the last figure is not absolutely trust- 
 worthy, but is near enough to enable the computer to interpolate accurately 
 to 5 places. If 7 places of the antigudermannian are required, they can be 
 found by inverse interpolation in Table VI. 
 
 The earlier part of Table VII may be interpolated by first differences with- 
 out considerable error. At about 843O / one-eighth of the second difference 
 becomes approximately half a unit in the last tabulated place, and beyond 
 this point second differences should be taken into account. 
 
 Table VIII is a table for converting radians into angular measure and 
 vice versa. A few numerical constants are appended. 
 
HISTORICAL NOTE. 
 
 The first and most important application of the functions now known 33 
 hyperbolic was made by Gerhard Mercator (Kremer) when he issued his 
 map on " Mercator 's projection," in 1569, or, as some say, in 1550, while 
 Bowditch gives the date as 1566. To this day substantially all of the deep- 
 sea navigation of the world is carried on by the help of this projection, 
 which has been modified only to the extent of correcting the "meridional 
 parts" for the ellipticity of the meridian. Mercator' s problem was to find 
 a projection on which the loxodrome should be a straight line. The solu- 
 tion is unique, and for a spherical globe is \gd where A is the latitude, 
 
 m the "meridional part," or the ordinate on the projection of a point in 
 latitude A., and a is the radius of the sphere. Of course, this relation gives 
 
 m 
 
 = loge tai 
 
 a 
 
 and this Mercator must have tabulated. He published his map without 
 explanation, however, and it was left to Edward Wright in 1599 to state 
 the formula for m. 
 
 "The actual inventor of the hyperbolic trigonometry," says Professor 
 McMahon, "was Vincenzo Riccati, S. J. (Opuscula ad res Phys. et Math, 
 pertinens, Bonpniae, 1757). He adopted the notation Sh. <j>, C/i. <#>, for the 
 hyperbolic functions and Sc. <, Cc. <f> for the circular ones. He proved the 
 addition theorem geometically, and derived a construction for the solution 
 of a cubic equation. Soon after Daviet de Foncenex showed how to inter- 
 change circular and hyperbolic functions by the use of |/ - i , and gave 
 the analogue of de Moivre's theorem, the work resting more on analogy, 
 however, than on clear definition (Reflex, sur les quant, imag., Miscel. 
 Turin Soc., Tom. i). Johann Heinrich Lambert systematized fhe subject 
 and gave the serial developments and the exponential expressions. He 
 adopted the notation sinh , etc., and introduced the transcendent angle, 
 now called the gudermannian, using it in computation and in the construc- 
 tion of tables 1 ." 
 
 C. Gudermann published an important memoir on Potential or Cyclic- 
 hyperbolic functions in 1830*, followed by extended tables. In recogni- 
 
 1 James McMahon, Hyperbolic Functions, p. 71. 
 
 7 Crelle's Journal, vols. 6, 7, 8, and 9. These memoirs were afterwards reprinted in a 
 separate volume. xlviii 
 
HISTORICAL NOTE. xlix 
 
 tion of his contributions to the subject, Cay ley, in I862, 1 proposed the 
 name gudermannian 2 for the angle which Lambert called transcendent, 
 and which had been variously designated by others. Among other more 
 recent works on hyperbolic functions are Siegmund Giinther's Lehre 
 von den Hyperbelfunctionen, 1881, and Mr. James McMahon's Hyper- 
 bolic Functions, 4th edition, 1906. 
 
 The first large table of hyperbolic functions we have met with is Legen- 
 
 dre's table of log tan ( + ) to 12 decimals. The argument advances 
 \ 4 2 / 
 
 by increments of 30 minutes, but five differences are tabulated to facilitate 
 interpolation. 3 Gudermann in 1831 published a table of the same func- 
 tion, using centesimal degrees and advancing by hundredths of a degree 
 (oo'32".4) from o to an entire quadrant, the function being given to seven 
 decimal places. This was later supplemented by a table advancing by hun- 
 dredths of a degree from 88 to 100, the function being given to eleven 
 decimal places. Gudermann also gave a 9-place table of log cosh u, log 
 sinh u, and log tanh u, from u = 2.000 to u = 5.000, and a lo-place 
 table of the same functions from u = 5.00 to u = 12.00. 
 
 In 1862 Z. F. W. Gronau 4 published a 5-place table of hyperbolic func- 
 tions, the argument being the gudermannian gd u in sexagesimal degrees 
 and minutes. He tabulated to this argument log cosh &, log sinh u y and the 
 
 Briggs logarithm of f -f J instead of the natural logarithms of this 
 
 function, following therein a suggestion of Lambert. 
 
 A In 1890 W. Ligowski issued his Tafeln der Hyperbelfunctionen und der 
 Kreisfunctionen, which is admirably accurate and much the most useful 
 collection of tables of the hyperbolic functions hitherto printed. He filled 
 the gap left by Gudermann by computing log sinh , log cosh u, and log 
 tanh u from u =0.000 to 2.000. These he gives to only 5 places, but in 
 addition he tabulates gd u in degrees, minutes, seconds, and decimals of a 
 second. These values are in all cases sufficiently accurate to enable the com- 
 puter to take out from an ordinary table of logarithms 7 -place values of the 
 logarithms of cosh &, sinh , and tanh u. The argument ranges from o.ooo 
 to 2.000 and from 2.00 to 6.00 for gd u, while log cosh u and log sinh u are 
 carried up to u = 9.00. Ligowski also gives the natural functions cosh u, 
 sinh u, cos u, and sin u to 6 decimals for values of u in radians from o.oo to 
 2 oo, the cosh u and sinh u being continued to u = 8.00. The only fault 
 we can find with Ligowski 's tables is that the increments of the argument 
 are sometimes inconveniently large. 
 
 1 Phil. Mag., vol. 24, p. 19. 
 
 2 Thus spelled in Cayley's paper. 
 
 3 Exercises de Cal. Int., vol. 2, 1816. 
 
 *Neueste Schriften der Naturforscher-Gesellschaft in Danzig, vol. 6, 1862. 
 
1 HISTORICAL NOTE. 
 
 In 1883 F. W. Newman published a 12 place table 1 of the descending ex- 
 ponential from it = o.ooo to u = 15.349, and a i4-place table of the same func- 
 tion advancing by two- thousandths from 15.350 to 17.298 and by five-thou- 
 sandths from 17.298 to 27.635. In the same volume appeared Mr. J. W. L. 
 Glaisher's tables of the ascending and descending exponential to nine sig- 
 nificant figures, with lo-place logarithms. The argument advances by one- 
 thousandth to o.i ; by one-hundredth to 2.00; by one-tenth to 10, and by a 
 single unit to 500. 
 
 Mr. A. Forti's Nuove Tavole delle Funzioni Iperboliche were pub- 
 lished in 1892. The hyperbolic sines, cosines, and tangents, together 
 with their logarithms, are given to six decimals from o.oooo to 0.2000, 
 from 0.200 to 2.000, and from 2.00 to 8.00. Frequent errors, however, of 
 one, two, and three units in the last decimal place practically limit these 
 tables to five places. The gudermannian is tabulated in degrees, minutes, 
 seconds, and tenths of a second, and the logarithms of the arguments are 
 given to seven places. 
 
 In the volume here presented the first thousand values of log sinh u, log 
 cosh u, and log tanh u have been computed; the remaining values have been 
 taken from the tables of Gudermann or Ligowski. The values of the nat- 
 ural hyperbolic sines and cosines for values of the argument < o. i and of 
 the tangents for arguments > 2.0 have been computed; the remaining values 
 have been taken from the tables of Forti and Ligowski. A recomputation 
 of a great number of the borrowed values was made in order to obtain the 
 required accuracy. The values of coth u and log coth u have been computed. 
 In Table III the sines and cosines were obtained by interpolation from 
 the 7-place values of natural sines and cosines given in Hiilsse's Vega, 
 where the argument is expressed in angle. The logarithms of the sines and 
 cosines and the angular equivalents of the arguments have been computed. 
 In Table IV the values of c ~ u are all taken from Newman's great 
 table. Those of c + u from o.ooo to o. 100 and from i to 100 are from 
 Glaisher's table. The remainder we computed, checking the results by 
 Glaisher's table or by reciprocating. It should be noted that the 7 place 
 table of e n given in Hiilsse's edition of Vega is inaccurate and really 
 amounts to no more than a 5 place table. The logarithms of e n were com- 
 puted independently of the values of e u . 
 Tables V and VIII are borrowed. 
 
 The values of gd u in Table VI in terms of angle are taken from Ligow- 
 ski, excepting the thousand values between u = 2.000 and 3.000. These 
 were interpolated from Ligowski's values (2.00 to 3.00) with due checks on 
 his accuracy. In preparing the table of gdu in radians it was necessary for 
 us to make an independent computation of this function from u = 0.300 to 
 u = 3.000 in order to secure accuracy in the seventh significant figure. 
 The remaining values were derived from Ligowski by converting angles 
 
 1 Cambridge Phil. Soc., Trans., vol. 13, 1883. 
 
HISTORICAL NOTE. li 
 
 into radians. A considerable number of his values, however, were tested 
 by independent computation. 
 
 Table VII is borrowed from the Nautical tables of James Inman, revised 
 by James W. Inman, London, 1867, with a few small corrections. 
 
 Finally, it may be remarked that the derivatives as given in these tables 
 have been computed for them. They are not derived from the diSerences 
 of the values as printed, but from more extended values, or are computed 
 independently, and the error of the derivatives as well as of the functions is 
 less than one-half of a unit in the next succeeding decimal place. 
 
 These tables were prepared in connection with the geophysical work of 
 the United States Geological Survey, and are published with the permission 
 of the Director. 
 
 GEORGE F. BECKER. 
 C. E. VAN ORSTRAND. 
 
 WASHINGTON, D. C., January, 1908. 
 
TABLE I 
 
 LOGARITHMS OF HYPERBOLIC FUNCTIONS 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 loq shh M 
 
 * Fo' 
 
 log cosh u 
 
 F O ' 
 
 log tanh u 
 
 - Fo' 
 
 log coth u 
 
 o.oooo 
 
 CO 
 
 CO 
 
 o.ooooo 
 
 0,0 
 
 oo 
 
 =F co 
 
 oo 
 
 .0001 
 
 6.0OOOO 
 
 43429,4 
 
 .00000 
 
 
 6.00000 
 
 43429,4 
 
 4.OOOOO 
 
 .0002 
 
 .30103 
 
 21714,7 
 
 .00000 
 
 
 .30103 
 
 21714,7 
 
 3.69897 
 
 .0003 
 
 .47712 
 
 14476,5 
 
 .00000 
 
 
 .47712 
 
 14476,5 
 
 .52288 
 
 .0004 
 
 .60206 
 
 10857,4 
 
 .00000 
 
 
 .60206 
 
 10857,4 
 
 39794 
 
 0.0005 
 
 6.69897 
 
 8685,9 
 
 o.ooooo 
 
 0,0 
 
 6.69897 
 
 8685,9 
 
 3-30103 
 
 .0006 
 
 .77815 
 
 7238,2 
 
 .00000 
 
 
 .77815 
 
 7238,2 
 
 .22185 
 
 .0007 
 
 .84510 
 
 6204,2 
 
 .00000 
 
 
 .84510 
 
 6204,2 
 
 15490 
 
 .0008 
 
 .90309 
 
 5428,7 
 
 .00000 
 
 
 .90309 
 
 5428,7 
 
 .09691 
 
 .0009 
 
 .95424 
 
 4825,5 
 
 .00000 
 
 
 .95424 
 
 4825,5 
 
 .04576 
 
 O.OOIO 
 
 7.00000 
 
 4342,9 
 
 o.ooooo 
 
 0,0 
 
 7.00000 
 
 4342,9 
 
 3.OOOOO 
 
 .OOII 
 
 04139 
 
 3948,1 
 
 .00000 
 
 
 .04139 
 
 3948,1 
 
 2.95861 
 
 .0012 
 
 .07918 
 
 3619,1 
 
 .00000 
 
 
 .07918 
 
 3619,1 
 
 .92082 
 
 .0013 
 
 II394 
 
 3340,7 
 
 .00000 
 
 
 .11394 
 
 3340,7 
 
 .88606 
 
 .0014 
 
 . 14613 
 
 3102,1 
 
 .00000 
 
 
 . 14613 
 
 3102,1 
 
 .85387 
 
 0.0015 
 
 7.17609 
 
 2895,3 
 
 o.ooooo 
 
 0,0 
 
 7.17609 
 
 2895,3 
 
 2.82391 
 
 .0016 
 
 .20412 
 
 2714,3 
 
 .00000 
 
 
 .20412 
 
 2714,3 
 
 .79588 
 
 .0017 
 
 .23045 
 
 2554,7 
 
 .00000 
 
 
 .23045 
 
 2554,7 
 
 76955 
 
 .0018 
 
 25527 
 
 2412,7 
 
 .00000 
 
 
 .25527 
 
 2412,7 
 
 74473 
 
 .0019 
 
 .27875 
 
 2285,8 
 
 .00000 
 
 
 .27875 
 
 2285,8 
 
 .72125 
 
 O.OO2O 
 
 7-30103 
 
 2171,5 
 
 o.ooooo 
 
 0,0 
 
 7.30103 
 
 2171,5 
 
 2.69897 
 
 .0021 
 
 .32222 
 
 2068,1 
 
 .00000 
 
 
 . 32222 
 
 2068, 1 
 
 .67778 
 
 .OO22 
 
 .34242 
 
 1974,1 
 
 .00000 
 
 
 .34242 
 
 1974,1 
 
 .65758 
 
 .OO23 
 
 .36173 
 
 1888,2 
 
 .00000 
 
 
 .36173 
 
 1888,2 
 
 .63827 
 
 .OO24 
 
 .38021 
 
 1809,6 
 
 .00000 
 
 
 .38021 
 
 1809,6 
 
 .61979 
 
 0.0025 
 
 7-39794 
 
 1737,2 
 
 o.ooooo 
 
 0,0 
 
 7.39794 
 
 1737,2 
 
 2.60206 
 
 .0026 
 
 .41497 
 
 1670,4 
 
 .00000 
 
 
 .41497 
 
 1670,4 
 
 .58503 
 
 .OO27 
 
 .43136 
 
 1608,5 
 
 .00000 
 
 
 .43136 
 
 1608,5 
 
 .56864 
 
 .0028 
 
 .44716 
 
 I55IJ 
 
 .00000 
 
 
 .44716 
 
 1551,0 
 
 .55284 
 
 .0029 
 
 .46240 
 
 1497,6 
 
 .00000 
 
 
 .46240 
 
 1497,6 
 
 .53760 
 
 O.OO30 
 
 7.47712 
 
 1447,7 
 
 o.ooooo 
 
 0,0 
 
 7.47712 
 
 1447,6 
 
 2.52288 
 
 .0031 
 
 .49136 
 
 1401,0 
 
 .00000 
 
 
 .49136 
 
 1400,9 
 
 .50864 
 
 .0032 
 
 .50515 
 
 1357,2 
 
 .00000 
 
 
 .50515 
 
 1357,2 
 
 .49485 
 
 .0033 
 
 .51851 
 
 1316,0 
 
 .00000 
 
 
 .51851 
 
 1316,0 
 
 .48149 
 
 .0034 
 
 .53148 
 
 1277,3 
 
 .00000 
 
 
 .53148 
 
 1277,3 
 
 .46852 
 
 0.0035 
 
 7.54407 
 
 1240,8 
 
 o.ooooo 
 
 0,0 
 
 7.54407 
 
 1240,8 
 
 2.45593 
 
 .0036 
 
 .55630 
 
 1206,4 
 
 .00000 
 
 
 .55630 
 
 1 206,4 
 
 44370 
 
 .0037 
 
 .56820 
 
 ii73,8 
 
 .00000 
 
 
 .56820 
 
 1173,8 
 
 .43180 
 
 .0038 
 
 .57978 
 
 1142,9 
 
 .00000 
 
 
 .57978 
 
 1142,9 
 
 .42022 
 
 .0039 
 
 59107 
 
 1113,6 
 
 .00000 
 
 
 .59106 
 
 1113.6 
 
 .40894 
 
 0.0040 
 
 7.60206 
 
 1085,7 
 
 o.ooooo 
 
 0,0 
 
 7.60206 
 
 1085,7 
 
 2.39794 
 
 .0041 
 
 .61279 
 
 1059,3 
 
 .00000 
 
 
 .61278 
 
 1059,2 
 
 .38722 
 
 .0042 
 
 .62325 
 
 1034,0 
 
 .00000 
 
 
 .62325 
 
 1034,0 
 
 .37675 
 
 .0043 
 
 .63347 
 
 IOIO,O 
 
 .00000 
 
 
 .63347 
 
 IOIO,O 
 
 .36653 
 
 .0044 
 
 .64345 
 
 987,0 
 
 .00000 
 
 
 .64345 
 
 987,0 
 
 .35655 
 
 0.0045 
 
 7.65321 
 
 065,1 
 
 o.ooooo 
 
 0,0 
 
 7.65321 
 
 965,1 
 
 2.34679 
 
 .0046 
 
 .66276 
 
 944.1 
 
 .00000 
 
 
 .66275 
 
 944,1 
 
 .33725 
 
 .0047 
 
 .67210 
 
 924,0 
 
 .00000 
 
 
 .67209 
 
 924,0 
 
 .32791 
 
 .0048 
 
 .68124 
 
 904,8 
 
 .00001 
 
 
 .68124 
 
 004,8 
 
 .31876 
 
 .0049 
 
 .69020 
 
 886,3 
 
 .00001 
 
 
 .69019 
 
 886,3 
 
 .30981 
 
 0.0050 
 
 7.69807 
 
 868,6 
 
 0.00001 
 
 0,0 
 
 7.69807 
 
 868,6 
 
 2.30103 
 
 u 
 
 log tan ad u 
 
 F ' 
 
 log sec gd u 
 
 -Fo' 
 
 log sin gd u 
 
 -Fo' 
 
 log esc gd u 
 
 SMITHSONIAN TABLES 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 o> Fo' 
 
 log cosh u 
 
 -FO' 
 
 log tanh u 
 
 Fo' 
 
 log coth u 
 
 0.0050 
 
 7.69897 
 
 868,6 
 
 O.OOOOI 
 
 0,0 
 
 7.69897 
 
 868,6 
 
 2.30103 
 
 .0051 
 
 .70757 
 
 851,6 
 
 .00001 
 
 
 .70757 
 
 851,5 
 
 .29243 
 
 .0052 
 
 .71601 
 
 835,2 
 
 .00001 
 
 
 .71600 
 
 835,2 
 
 .28400 
 
 .0053 
 
 .72428 
 
 819,4 
 
 .00001 
 
 
 .72427 
 
 819,4 
 
 .27573 
 
 .0054 
 
 .73240 
 
 804,3 
 
 .00001 
 
 
 .73239 
 
 804,2 
 
 .26761 
 
 0.0055 
 
 7.74036 
 
 789,6 
 
 O.OOOOI 
 
 0,0 
 
 7.74036 
 
 789,6 
 
 2.25964 
 
 .0056 
 
 .74819 
 
 775,5 
 
 .00001 
 
 
 .74818 
 
 775,5 
 
 .25182 
 
 .0057 
 
 .75588 
 
 761,9 
 
 .00001 
 
 
 .75587 
 
 761,9 
 
 .24413 
 
 .0058 
 
 .76343 
 
 748,8 
 
 .00001 
 
 
 .76342 
 
 748,8 
 
 .23658 
 
 .0059 
 
 .77085 
 
 736,i 
 
 .00001 
 
 
 .77085 
 
 736,1 
 
 .22915 
 
 0.0060 
 
 7.77815 
 
 723,8 
 
 O.OOOOI 
 
 0,0 
 
 7.77815 
 
 723,8 
 
 2.22185 
 
 .0061 
 
 .78533 
 
 712,0 
 
 .00001 
 
 
 .78532 
 
 711,9 
 
 .21468 
 
 .0062 
 
 .79239 
 
 700,5 
 
 .00001 
 
 
 79239 
 
 700,5 
 
 .20761 
 
 .0063 
 
 79934 
 
 689,4 
 
 .00001 
 
 
 .79933 
 
 689,3 
 
 .20067 
 
 .0064 
 
 .80618 
 
 678,6 
 
 .00001 
 
 
 .80617 
 
 678,6 
 
 . 19383 
 
 0.0065 
 
 7.81292 
 
 668,1 
 
 O.OOOOI 
 
 0,0 
 
 7.81291 
 
 668,1 
 
 2.18709 
 
 .0066 
 
 .81955 
 
 658,0 
 
 .00001 
 
 
 .81954 
 
 658,0 
 
 .18046 
 
 .0067 
 
 .82608 
 
 648,2 
 
 .00001 
 
 
 .82607 
 
 648,2 
 
 . 17393 
 
 .0068 
 
 .83251 
 
 638,7 
 
 .00001 
 
 
 .83250 
 
 638,6 
 
 . 16750 
 
 .0069 
 
 .83885 
 
 629,4 
 
 .00001 
 
 
 .83884 
 
 629,4 
 
 .16116 
 
 0.0070 
 
 7.84510 
 
 620,4 
 
 O.OOOOI 
 
 0,0 
 
 7.84509 
 
 620,4 
 
 2.15491 
 
 .0071 
 
 .85126 
 
 6n,7 
 
 .00001 
 
 
 .85125 
 
 611,7 
 
 .14875 
 
 .0072 
 
 .85734 
 
 603,2 
 
 .00001 
 
 
 .85732 
 
 603,2 
 
 .14268 
 
 .0073 
 
 .86333 
 
 594,9 
 
 .00001 
 
 
 .86332 
 
 594,9 
 
 .13668 
 
 .0074 
 
 .86924 
 
 586,9 
 
 .00001 
 
 
 .86922 
 
 586,9 
 
 . 13078 
 
 0.0075 
 
 7.87507 
 
 579,1 
 
 O.OOOOI 
 
 0,0 
 
 7.87505 
 
 579,0 
 
 2.12495 
 
 .0076 
 
 .88082 
 
 57i,4 
 
 .00001 
 
 
 .88081 
 
 57i,4 
 
 .11919 
 
 .0077 
 
 .88649 
 
 564,0 
 
 .00001 
 
 
 .88648 
 
 564,0 
 
 .11352 
 
 .0078 
 
 .89210 
 
 556,8 
 
 .00001 
 
 
 .80209 
 
 556,8 
 
 . 10791 
 
 .0079 
 
 .89763 
 
 549,7 
 
 .00001 
 
 
 .89762 
 
 549,7 
 
 . 10238 
 
 0.0080 
 
 7.90309 
 
 542,9 
 
 O.OOOOI 
 
 0,0 
 
 7.90308 
 
 542,8 
 
 2.09692 
 
 .0081 
 
 .90849 
 
 536,2 
 
 .00001 
 
 
 .90848 
 
 536,i 
 
 .09152 
 
 .0082 
 
 .91382 
 
 529,6 
 
 .00001 
 
 
 .91380 
 
 529,6 
 
 .08620 
 
 .0083 
 
 .91908 
 
 523,2 
 
 .00001 
 
 
 .91907 
 
 523,2 
 
 .08093 
 
 .0084 
 
 .92428 
 
 517,0 
 
 .00002 
 
 
 .92427 
 
 5i7,o 
 
 .07573 
 
 0.0085 
 
 7.92942 
 
 510,9 
 
 0.00002 
 
 0,0 
 
 7.92941 
 
 5io,9 
 
 2.07059 
 
 .0086 
 
 93450 
 
 505,0 
 
 .00002 
 
 
 93449 
 
 505,o 
 
 .06551 
 
 .0087 
 
 .93952 
 
 499,2 
 
 .00002 
 
 
 .93951 
 
 499,2 
 
 .06049 
 
 .0088 
 
 .94449 
 
 493,5 
 
 .00002 
 
 
 .04447 
 
 493,5 
 
 05553 
 
 .0089 
 
 .94940 
 
 488,0 
 
 .00002 
 
 
 .94938 
 
 487,9 
 
 .05062 
 
 0.0090 
 
 7.95425 
 
 482,6 
 
 O.OOO02 
 
 0,0 
 
 7.95423 
 
 482,5 
 
 2.04577 
 
 .0091 
 
 .95905 
 
 477,3 
 
 .00002 
 
 
 .95903 
 
 477,2 
 
 .04097 
 
 .0092 
 
 .96379 
 
 472,1 
 
 .00002 
 
 
 .96378 
 
 472,0 
 
 .03622 
 
 .0093 
 
 .96849 
 
 467,0 
 
 .00002 
 
 
 .96847 
 
 467,0 
 
 .03153 
 
 .0094 
 
 .97313 
 
 462,0 
 
 .00002 
 
 
 .97312 
 
 462,0 
 
 .02688 
 
 0.0095 
 
 7.97773 
 
 457,2 
 
 O.OOOO2 
 
 0,0 
 
 7.97771 
 
 457,i 
 
 2.02229 
 
 .0096 
 
 .98228 
 
 452,4 
 
 .00002 
 
 
 .98226 
 
 452,4 
 
 .01774 
 
 .0097 
 
 .98678 
 
 447,7 
 
 .00002 
 
 
 .98676 
 
 447,7 
 
 .01324 
 
 .0098 
 
 .99123 
 
 443,2 
 
 .00002 
 
 
 .99121 
 
 443,1 
 
 .00879 
 
 .0099 
 
 .99564 
 
 438,7 
 
 .00002 
 
 
 .99562 
 
 438,7 
 
 .00438 
 
 O.OIOO 
 
 8.00001 
 
 434,3 
 
 O.OOOO2 
 
 0,0 
 
 7.09999 
 
 434,3 
 
 2.OOOOI 
 
 u 
 
 log tan gd u 
 
 <> FQ' 
 
 log sec gd u 
 
 -Fo' 
 
 log sin gd u 
 
 W Fo' 
 
 log esc gd u 
 
 SMITHSONIAN TABLES 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 Fo' 
 
 log cosh u 
 
 
 
 log tanh u 
 
 Fo' 
 
 log coth u 
 
 O.OIOO 
 
 8.OOOOI 
 
 434,3 
 
 O.OOOO2 
 
 O,O 
 
 7.99999 
 
 434,3 
 
 2.OOOOI 
 
 .OIOI 
 
 00433 
 
 430,0 
 
 .00002 
 
 
 8.00431 
 
 430,0 
 
 1.99569 
 
 .0102 
 
 .00861 
 
 425,8 
 
 .OOO02 
 
 
 .00859 
 
 425,7 
 
 .99141 
 
 .0103 
 
 .01284 
 
 421,7 
 
 .OOOO2 
 
 
 .OI282 
 
 421,6 
 
 .98718 
 
 .0104 
 
 .01704 
 
 417,6 
 
 .OOOO2 
 
 
 .OI7O2 
 
 417,6 
 
 .98298 
 
 0.0105 
 
 8.O2I20 
 
 413,6 
 
 O.OOOO2 
 
 0,0 
 
 8.02II7 
 
 413,6 
 
 1.97883 
 
 .0106 
 
 .02531 
 
 409,7 
 
 .00002 
 
 
 .02529 
 
 409,7 
 
 97471 
 
 .0107 
 
 .02939 
 
 405,9 
 
 .OOOO2 
 
 
 .02937 
 
 405,9 
 
 .97063 
 
 .0108 
 
 03343 
 
 402,1 
 
 .00003 
 
 
 .03341 
 
 402,1 
 
 .96659 
 
 .0109 
 
 .03744 
 
 398,5 
 
 .00003 
 
 
 .03741 
 
 398,4 
 
 .96259 
 
 O.OIIO 
 
 8.04140 
 
 394,8 
 
 O.OOOO3 
 
 0,0 
 
 8.04138 
 
 394,8 
 
 1.95862 
 
 .OIII 
 
 .04533 
 
 39i,3 
 
 .00003 
 
 
 .04531 
 
 391,2 
 
 .95409 
 
 .OII2 
 
 .04923 
 
 387,8 
 
 .00003 
 
 
 .O492O 
 
 387,7 
 
 
 .0113 
 
 .05309 
 
 384,4 
 
 .00003 
 
 
 .05306 
 
 384,3 
 
 .04694 
 
 .0114 
 
 .05691 
 
 381,0 
 
 .00003 
 
 
 .05689 
 
 380,9 
 
 943II 
 
 0.0115 
 
 8.06071 
 
 377,7 
 
 0.00003 
 
 0,0 
 
 8.06068 
 
 377,6 
 
 1.93932 
 
 .0116 
 
 06447 
 
 374,4 
 
 .00003 
 
 0,1 
 
 .06444 
 
 374,4 
 
 .93556 
 
 .0117 
 
 .06820 
 
 371,2 
 
 .00003 
 
 
 .06817 
 
 37i,2 
 
 .93183 
 
 .0118 
 
 .07189 
 
 368,1 
 
 .00003 
 
 
 .07186 
 
 368,0 
 
 .92814 
 
 .0119 
 
 .07556 
 
 365,0 
 
 .00003 
 
 
 .07553 
 
 364,9 
 
 .92447 
 
 O.OI2O 
 
 8.07919 
 
 36i,9 
 
 0.00003 
 
 0,1 
 
 8.07916 
 
 36i,9 
 
 1.92084 
 
 .OI2I 
 
 .08280 
 
 358,9 
 
 .00003 
 
 
 .08276 
 
 
 .91724 
 
 .OI22 
 
 .08637 
 
 356,0 
 
 .00003 
 
 
 .08634 
 
 355,9 
 
 .91366 
 
 .OI23 
 
 .08992 
 
 353,i 
 
 .00003 
 
 
 .08988 
 
 353,0 
 
 .91012 
 
 .OI24 
 
 09343 
 
 350,3 
 
 .00003 
 
 
 .09340 
 
 350,2 
 
 .90660 
 
 0.0125 
 
 8.00692 
 
 347,5 
 
 0.00003 
 
 0,1 
 
 8.09689 
 
 347,4 
 
 I.903II 
 
 .OI26 
 
 .10038 
 
 344,7 
 
 .00003 
 
 
 .10035 
 
 344,6 
 
 .89965 
 
 .0127 
 
 . 10382 
 
 342,0 
 
 .00004 
 
 
 . 10378 
 
 341,9 
 
 .89622 
 
 .0128 
 
 . 10722 
 
 339,3 
 
 .00004 
 
 
 .10719 
 
 339,3 
 
 .89281 
 
 .OI29 
 
 .11060 
 
 336,7 
 
 .00004 
 
 
 .11057 
 
 336,6 
 
 .88943 
 
 0.0130 
 
 8.11396 
 
 334,1 
 
 0.00004 
 
 0,1 
 
 8.11392 
 
 334,0 
 
 I.8860S 
 
 .0131 
 
 .11728 
 
 331,5 
 
 .00004 
 
 
 .11725 
 
 331,5 
 
 .88275 
 
 .0132 
 
 . 12059 
 
 329,0 
 
 .00004 
 
 
 . 12055 
 
 329,0 
 
 .87945 
 
 .0133 
 
 .12386 
 
 326,6 
 
 .00004 
 
 
 .12383 
 
 326,5 
 
 .87617 
 
 .0134 
 
 .12712 
 
 324,1 
 
 .00004 
 
 
 .12708 
 
 324,1 
 
 .87292 
 
 0.0135 
 
 8.13035 
 
 321,7 
 
 0.00004 
 
 0,1 
 
 8.13031 
 
 33L7 
 
 1.86969 
 
 .0136 
 
 . 13355 
 
 319,4 
 
 .00004 
 
 
 .13351 
 
 319,3 
 
 .86649 
 
 0137 
 
 . 13673 
 
 317,0 
 
 .00004 
 
 
 .13669 
 
 3i7,o 
 
 .86331 
 
 .0138 
 
 .13989 
 
 
 .00004 
 
 
 .13985 
 
 
 .86015 
 
 .0139 
 
 .14303 
 
 312,5 
 
 .00004 
 
 
 .14299 
 
 312,4 
 
 .85701 
 
 0.0140 
 
 8. 14614 
 
 310,2 
 
 0.00004 
 
 0,1 
 
 8.14610 
 
 310,2 
 
 1.85390 
 
 .OI4I 
 
 . 14923 
 
 308,0 
 
 .00004 
 
 
 . 14919 
 
 308,0 
 
 .8508l 
 
 .0142 
 
 .15230 
 
 305,9 
 
 .00004 
 
 
 .15226 
 
 305,8 
 
 .84774 
 
 .0143 
 .0144 
 
 .15535 
 .15838 
 
 303,7 
 301,6 
 
 .00004 
 .00005 
 
 
 .15531 
 .15833 
 
 303,7 
 301,6 
 
 .84469 
 .84167 
 
 0.0145 
 
 8.16138 
 
 299,5 
 
 0.00005 
 
 0,1 
 
 8.16134 
 
 299,5 
 
 1.83866 
 
 .0146 
 
 . 16437 
 
 297,5 
 
 .00005 
 
 
 . 16432 
 
 297,4 
 
 .83568 
 
 .0147 
 
 . 16733 
 
 295,5 
 
 .00005 
 
 
 .16729 
 
 295,4 
 
 .83271 
 
 .0148 
 
 .17028 
 
 293,5 
 
 .00005 
 
 
 .17023 
 
 293,4 
 
 .82977 
 
 .0149 
 
 .17320 
 
 291,5 
 
 .00005 
 
 
 .17315 
 
 291,4 
 
 .82685 
 
 0.0150 
 
 8.17611 
 
 289,6 
 
 0.00005 
 
 0,1 
 
 8.17606 
 
 289,5 
 
 1.82394 
 
 U 
 
 log tan gd u 
 
 *F ' 
 
 log sec gd u 
 
 Fo' 
 
 log sin gd u 
 
 F ' 
 
 log esc gd u 
 
 SMITHSONIAN TABLES 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 Fo' 
 
 log cosh u 
 
 FO' 
 
 log tanh u 
 
 w Fo' 
 
 log coth u 
 
 0.0150 
 
 8.17611 
 
 289,6 
 
 0.00005 
 
 0,1 
 
 8.17606 
 
 289,5 
 
 1.82394 
 
 .0151 
 
 .17899 
 
 287,6 
 
 .O0005 
 
 
 .17894 
 
 287,6 
 
 .82106 
 
 .0152 
 
 .18186 
 
 285,7 
 
 .00005 
 
 
 .18181 
 
 285,7 
 
 .81819 
 
 .0153 
 
 .18471 
 
 283,9 
 
 .00005 
 
 
 .18466 
 
 283,8 
 
 .81534 
 
 .0154 
 
 .18754 
 
 282,0 
 
 .00005 
 
 
 18749 
 
 282,0 
 
 .81251 
 
 0.0155 
 
 8.19035 
 
 280,2 
 
 0.00005 
 
 0,1 
 
 8.19030 
 
 280,1 
 
 1.80970 
 
 .0156 
 
 .19314 
 
 278,4 
 
 .00005 
 
 
 .19309 
 
 278,3 
 
 .80691 
 
 .0157 
 
 .19592 
 
 276,6 
 
 .00005 
 
 
 .19586 
 
 276,6 
 
 .80414 
 
 .0158 
 
 .19868 
 
 274,9 
 
 .00005 
 
 
 .19862 
 
 274,8 
 
 .80138 
 
 .0159 
 
 .20142 
 
 273,2 
 
 .00005 
 
 
 .20136 
 
 273,1 
 
 .79864 
 
 0.0160 
 
 8.20414 
 
 271,5 
 
 0.00006 
 
 0,1 
 
 8.20408 
 
 271,4 
 
 1.79592 
 
 .0161 
 
 .20684 
 
 269,8 
 
 .00006 
 
 
 .20679 
 
 269,7 
 
 .79321 
 
 .0162 
 
 .20953 
 
 268,1 
 
 .00006 
 
 
 .20948 
 
 268,0 
 
 .79052 
 
 .0163 
 
 .21221 
 
 266,5 
 
 .00006 
 
 
 .21215 
 
 266,4 
 
 .78785 
 
 .0164 
 
 .21486 
 
 264,8 
 
 .00006 
 
 
 .21480 
 
 264,8 
 
 .78520 
 
 0.0165 
 
 8.21750 
 
 263,2 
 
 o.oooo5 
 
 0,1 
 
 8.21744 
 
 263,2 
 
 1.78256 
 
 .0166 
 
 .22OI3 
 
 26l,6 
 
 .00006 
 
 
 .22007 
 
 261,6 
 
 .77993 
 
 .0167 
 
 .22274 
 
 200,1 
 
 .00006 
 
 
 .22268 
 
 260,0 
 
 77732 
 
 .0168 
 
 .22533 
 
 258,5 
 
 .00006 
 
 
 .22527 
 
 258,5 
 
 .77473 
 
 .0169 
 
 .22791 
 
 257,0 
 
 .00006 
 
 
 .22785 
 
 256,9 
 
 .77215 
 
 0.0170 
 
 8.23047 
 
 255,5 
 
 0.00006 
 
 0,1 
 
 8.23041 
 
 255,4 
 
 1.76959 
 
 .0171 
 
 .23302 
 
 254,o 
 
 .00006 
 
 
 .23295 
 
 253,9 
 
 .76705 
 
 .0172 
 
 .23555 
 
 252,5 
 
 .00006 
 
 
 .23549 
 
 252,4 
 
 76451 
 
 .0173 
 
 .23807 
 
 251,1 
 
 .00006 
 
 
 .23800 
 
 251,0 
 
 .76200 
 
 .0174 
 
 .24057 
 
 249,6 
 
 .00007 
 
 
 .24051 
 
 249,5 
 
 75949 
 
 0.0175 
 
 8.24306 
 
 248,2 
 
 0.00007 
 
 0,1 
 
 8.24299 
 
 248,1 
 
 i. 75701 
 
 .0176 
 
 24554 
 
 246,8 
 
 .00007 
 
 
 24547 
 
 246,7 
 
 75453 
 
 .0177 
 
 .24800 
 
 245,4 
 
 .00007 
 
 
 .24793 
 
 245,3 
 
 .75207 
 
 .0178 
 
 .25044 
 
 244,0 
 
 .00007 
 
 
 25037 
 
 243,9 
 
 .74963 
 
 .0179 
 
 .25288 
 
 242,6 
 
 .60007 
 
 
 .25281 
 
 242,6 
 
 .74719 
 
 0.0180 
 
 8.25530 
 
 241,3 
 
 0.00007 
 
 0,1 
 
 8.25523 
 
 241,2 
 
 1.74477 
 
 .0181 
 
 .25770 
 
 240,0 
 
 .00007 
 
 
 .25763 
 
 239,9 
 
 .74237 
 
 .0182 
 
 .26010 
 
 238,6 
 
 .00007 
 
 
 .26002 
 
 238,6 
 
 .73998 
 
 .0183 
 
 .26248 
 
 237,3 
 
 .00007 
 
 
 .26240 
 
 237,3 
 
 .73760 
 
 .0184 
 
 .26484 
 
 236,1 
 
 .00007 
 
 
 .26477 
 
 236,0 
 
 .73523 
 
 0.0185 
 
 8.26720 
 
 234,8 
 
 0.00007 
 
 0,1 
 
 8.26712 
 
 234,7 
 
 1.73288 
 
 .0186 
 
 .26954 
 
 233,5 
 
 .00008 
 
 
 .26946 
 
 233,4 
 
 .73054 
 
 .0187 
 
 .27187 
 
 232,3 
 
 .00008 
 
 
 .27179 
 
 232,2 
 
 .72821 
 
 .0188 
 
 .27418 
 
 231,0 
 
 .00008 
 
 
 .27411 
 
 231,0 
 
 .72589 
 
 .0189 
 
 .27649 
 
 229,8 
 
 .00008 
 
 
 .27641 
 
 229,7 
 
 .72359 
 
 0.0190 
 
 8.27878 
 
 228,6 
 
 0.00008 
 
 0,1 
 
 8.27870 
 
 228,5 
 
 1.72130 
 
 .0191 
 
 .28106 
 
 227,4 
 
 .00008 
 
 
 .28098 
 
 227,3 
 
 .71902 
 
 .0192 
 
 .28333 
 
 226,2 
 
 .00008 
 
 
 .28325 
 
 226,1 
 
 .71675 
 
 .0193 
 
 .28558 
 
 225,1 
 
 .00008 
 
 
 .28550 
 
 225,0 
 
 .71450 
 
 .0194 
 
 .28783 
 
 223,9 
 
 .00008 
 
 
 .28775 
 
 223,8 
 
 .71225 
 
 0.0195 
 
 8.20006 
 
 222,7 
 
 o.ooooS 
 
 0,1 
 
 8.28998 
 
 222,7 
 
 1.71002 
 
 .0196 
 
 .29228 
 
 221,6 
 
 .00008 
 
 
 .29220 
 
 221,5 
 
 .70780 
 
 .0197 
 
 .29449 
 
 220,5 
 
 .00008 
 
 
 .29441 
 
 220,4 
 
 .70559 
 
 .0198 
 
 .29669 
 
 219,4 
 
 .00009 
 
 
 .29661 
 
 219,3 
 
 .70339 
 
 .0199 
 
 .29888 
 
 218,3 
 
 .00009 
 
 
 .29880 
 
 2l8,2 
 
 .70120 
 
 O.O2OO 
 
 8.30106 
 
 217,2 
 
 0.00009 
 
 0,1 
 
 8.30097 
 
 217,1 
 
 1.69903 
 
 U 
 
 log tan gd u 
 
 Fo' 
 
 log sec gd u 
 
 Fo' 
 
 log sin gd u 
 
 o Fo' 
 
 log esc gd u 
 
 SMITHSONIAN TABLES 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 <o Fo' 
 
 log cosh u 
 
 -Fo' 
 
 log tanh u 
 
 co Fo' 
 
 log coth u 
 
 0.02OO 
 
 8.30106 
 
 217,2 
 
 O.OOO09 
 
 0,1 
 
 8.30097 
 
 217,1 
 
 1.69903 
 
 .O2OI 
 
 .30323 
 
 216,1 
 
 .OOOOQ 
 
 
 .30314 
 
 2 1 6,0 
 
 .69686 
 
 .C2O2 
 
 .30538 
 
 215,0 
 
 .00009 
 
 
 .30529 
 
 214,9 
 
 .69471 
 
 .0203 
 
 30753 
 
 214,0 
 
 .00009 
 
 
 .30744 
 
 213,9 
 
 .69256 
 
 .O204 
 
 .30966 
 
 212,9 
 
 .00009 
 
 
 .30957 
 
 212,8 
 
 .69043 
 
 0.0205 
 
 8.3H78 
 
 211,9 
 
 0.00009 
 
 0,1 
 
 8.31169 
 
 211,8 
 
 1.68831 
 
 .0206 
 
 .31390 
 
 210,9 
 
 .00009 
 
 
 .31381 
 
 210,8 
 
 .68619 
 
 .0207 
 
 .31600 
 
 209,8 
 
 .00009 
 
 
 .31591 
 
 209,7 
 
 .68409 
 
 .0208 
 
 .31809 
 
 208,8 
 
 .00009 
 
 
 .31800 
 
 208,7 
 
 .68200 
 
 .0209 
 
 .32018 
 
 207,8 
 
 .00009 
 
 
 .32008 
 
 207,7 
 
 .67992 
 
 O.02IO 
 
 8.32225 
 
 206,8 
 
 O.OOOIO 
 
 0,1 
 
 8.32216 
 
 206,7 
 
 1.67784 
 
 .O2II 
 
 .32431 
 
 205,9 
 
 .00010 
 
 
 .32422 
 
 205,8 
 
 .67578 
 
 .O2I2 
 
 .32637 
 
 204,9 
 
 .00010 
 
 
 .32627 
 
 204,8 
 
 .67373 
 
 .O2I3 
 
 .32841 
 
 203,9 
 
 .00010 
 
 
 .32831 
 
 203,8 
 
 .67169 
 
 .0214 
 
 .33045 
 
 203,0 
 
 .00010 
 
 
 .33035 
 
 202,9 
 
 .66965 
 
 0.0215 
 
 8.33247 
 
 202,0 
 
 O.OOOIO 
 
 0,1 
 
 8.33237 
 
 20 1, 9 
 
 1.66763 
 
 .0216 
 
 33449 
 
 2OI,I 
 
 .00010 
 
 
 .33439 
 
 201,0 
 
 .66561 
 
 .0217 
 
 .33649 
 
 2OO,2 
 
 .00010 
 
 
 .33639 
 
 200,1 
 
 .66361 
 
 .0218 
 
 .33849 
 
 199,2 
 
 .00010 
 
 
 .33839 
 
 199,2 
 
 .66161 
 
 .O2I9 
 
 .34048 
 
 198,3 
 
 .00010 
 
 
 .34037 
 
 198,2 
 
 .65963 
 
 0.0220 
 
 8.34246 
 
 197,4 
 
 O.OOOII 
 
 0,1 
 
 8.34235 
 
 197,3 
 
 1.65765 
 
 .0221 
 
 .34443 
 
 196,5 
 
 .OOOII 
 
 
 .34432 
 
 196,4 
 
 .65568 
 
 .O222 
 
 .34639 
 
 195,7 
 
 .OOOII 
 
 
 .34628 
 
 195,6 
 
 .65372 
 
 .0223 
 
 .34834 
 
 194,8 
 
 .OOOII 
 
 
 .34823 
 
 194,7 
 
 .65177 
 
 .0224 
 
 .35028 
 
 193,9 
 
 .OOOII 
 
 
 .35018 
 
 193,8 
 
 .64982 
 
 0.0225 
 
 8.35222 
 
 I93,i 
 
 O.OOOII 
 
 0,1 
 
 8.35211 
 
 193,0 
 
 1.64789 
 
 .0226 
 
 .35415 
 
 192,2 
 
 .OOOII 
 
 
 .35403 
 
 192,1 
 
 .64597 
 
 .0227 
 
 .356o6 
 
 191,4 
 
 .OOOII 
 
 
 35595 
 
 191,3 
 
 .64405 
 
 .0228 
 
 35797 
 
 190,5 
 
 .OOOII 
 
 
 .35786 
 
 190,4 
 
 .64214 
 
 .O229 
 
 .35987 
 
 189,7 
 
 .OOOII 
 
 
 .35976 
 
 189,6 
 
 .64024 
 
 O.O230 
 
 8.36177 
 
 188,9 
 
 O.OOOII 
 
 0,1 
 
 8.36165 
 
 188,8 
 
 1.63835 
 
 .O23I 
 
 .36365 
 
 188,0 
 
 .00012 
 
 
 .36353 
 
 187,9 
 
 .63647 
 
 .0232 
 
 .36553 
 
 187,2 
 
 .00012 
 
 
 .36541 
 
 187,1 
 
 .63459 
 
 .0233 
 
 .36740 
 
 186,4 
 
 .00012 
 
 
 .36728 
 
 186,3 
 
 .63272 
 
 .0234 
 
 .36926 
 
 185,6 
 
 .00012 
 
 
 .36914 
 
 185,5 
 
 .63086 
 
 0.0235 
 
 8.37IH 
 
 184,8 
 
 O.OOOI2 
 
 0,1 
 
 8.37099 
 
 184,7 
 
 1.62901 
 
 .0236 
 
 .37295 
 
 184,1 
 
 .00012 
 
 
 .37283 
 
 184,0 
 
 .62717 
 
 .0237 
 
 .37479 
 
 183,3 
 
 .00012 
 
 
 .37467 
 
 183,2 
 
 .62533 
 
 .0238 
 
 .37662 
 
 182,5 
 
 .00012 
 
 
 .37649 
 
 182,4 
 
 .62351 
 
 .0239 
 
 .37844 
 
 181,7 
 
 .00012 
 
 
 .37832 
 
 181,6 
 
 .62168 
 
 0.0240 
 
 8.38025 
 
 181,0 
 
 0.00013 
 
 O,I 
 
 8.38013 
 
 180,9 
 
 1.61987 
 
 .O24I 
 
 .38206 
 
 180,2 
 
 .00013 
 
 
 .38193 
 
 180,1 
 
 .61807 
 
 .O242 
 
 .38386 
 
 179,5 
 
 .00013 
 
 
 .38373 
 
 179,4 
 
 .61627 
 
 .0243 
 
 .38565 
 
 178,8 
 
 .00013 
 
 
 .38552 
 
 178,7 
 
 .61448 
 
 .0244 
 
 .38743 
 
 178,0 
 
 .00013 
 
 
 .38730 
 
 177,9 
 
 .61270 
 
 0.0245 
 
 8.38921 
 
 177,3 
 
 0.00013 
 
 0,1 
 
 8.38908 
 
 177,2 
 
 1.61092 
 
 .0246 
 
 .39098 
 
 176,6 
 
 .00013 
 
 
 .30085 
 
 176,5 
 
 .60915 
 
 .0247 
 
 .39274 
 
 175,9 
 
 .00013 
 
 
 .39261 
 
 175,8 
 
 .00739 
 
 .0248 
 
 39450 
 
 175,2 
 
 .00013 
 
 
 .30436 
 
 T75,o 
 
 .60564 
 
 .0249 
 
 .39624 
 
 174,5 
 
 .00013 
 
 
 .39611 
 
 174,3 
 
 .60389 
 
 0.0250 
 
 8.39799 
 
 173,8 
 
 0.00014 
 
 0,1 
 
 8,39785 
 
 173,6 
 
 1.60215 
 
 u 
 
 log tan gd u 
 
 Fo' 
 
 log sec gd u 
 
 F ' 
 
 log sin gd u 
 
 F,/ 
 
 log esc gd u 
 
 SMITHSONIAN TABLE* 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 <-Fo' 
 
 log cosh u 
 
 F O ' 
 
 log tanh u 
 
 Fo' 
 
 loo coth u 
 
 0.0250 
 
 8.39799 
 
 173,8 
 
 0.00014 
 
 0,1 
 
 8.39785 
 
 173,6 
 
 1.60215 
 
 .0251 
 
 .39972 
 
 173,1 
 
 .00014 
 
 
 .39958 
 
 173,0 
 
 .60042 
 
 .0252 
 
 .40145 
 
 172,4 
 
 .00014 
 
 
 .40131 
 
 172,3 
 
 .59869 
 
 .0253 
 
 40317 
 
 171,7 
 
 .00014 
 
 
 40303 
 
 171,6 
 
 .59697 
 
 .0254 
 
 .40488 
 
 171,0 
 
 .00014 
 
 
 .40474 
 
 170,9 
 
 .59526 
 
 0.0255 
 
 8.40659 
 
 170,3 
 
 0.00014 
 
 0,1 
 
 8.40645 
 
 170,2 
 
 1.59355 
 
 .0256 
 
 .40829 
 
 i69,7 
 
 .00014 
 
 
 .40815 
 
 169,6 
 
 .59185 
 
 .0257 
 
 .40998 
 
 169,0 
 
 .00014 
 
 
 .40984 
 
 168,9 
 
 .59016 
 
 .0258 
 
 .41167 
 
 168,4 
 
 .00014 
 
 
 .4H52 
 
 168,3 
 
 .58848 
 
 .0259 
 
 .41335 
 
 167,7 
 
 .00015 
 
 
 .41320 
 
 167,6 
 
 .58680 
 
 0.0260 
 
 8.41502 
 
 167,1 
 
 0.00015 
 
 0,1 
 
 8.41488 
 
 167,0 
 
 1.58512 
 
 .0261 
 
 .41669 
 
 166,4 
 
 .00015 
 
 
 .41654 
 
 166,3 
 
 .58346 
 
 .0262 
 
 .41835 
 
 165,8 
 
 .00015 
 
 
 .41820 
 
 l65,7 
 
 .58180 
 
 .0263 
 
 .412001 
 
 165,2 
 
 .00015 
 
 
 .41986 
 
 165,1 
 
 .58014 
 
 .0264 
 
 .42165 
 
 164,5 
 
 .00015 
 
 
 .42150 
 
 164,4 
 
 .57850 
 
 0.0265 
 
 8.42330 
 
 163,9 
 
 0.00015 
 
 0,1 
 
 8.42314 
 
 163,8 
 
 1.57686 
 
 .0266 
 
 .42493 
 
 163,3 
 
 .00015 
 
 
 .42478 
 
 163,2 
 
 .57522 
 
 .0267 
 
 .42656 
 
 162,7 
 
 .00015 
 
 
 .42641 
 
 162,6 
 
 57359 
 
 .0268 
 
 .42819 
 
 162,1 
 
 .00016 
 
 
 .42803 
 
 162,0 
 
 57197 
 
 .0269 
 
 .42980 
 
 161,5 
 
 .00016 
 
 
 .42965 
 
 161,4 
 
 57035 
 
 0.0270 
 
 8.43142 
 
 160,9 
 
 O.OOOi6 
 
 0,1 
 
 8.43126 
 
 160,8 
 
 1.56874 
 
 .0271 
 
 43302 
 
 160,3 
 
 .00016 
 
 
 .43286 
 
 160,2 
 
 .56714 
 
 .0272 
 
 .43462 
 
 159,7 
 
 .00016 
 
 
 .43446 
 
 159,6 
 
 .56554 
 
 .0273 
 
 .43622 
 
 I59,i 
 
 .00016 
 
 
 .43605 
 
 i59,o 
 
 .56395 
 
 .0274 
 
 .43780 
 
 158,5 
 
 .00016 
 
 
 .43764 
 
 158,4 
 
 56236 
 
 0.0275 
 
 8.43939 
 
 158,0 
 
 O.OOOI6 
 
 0,1 
 
 8.43922 
 
 157,8 
 
 1.56078 
 
 .0276 
 
 .44096 
 
 157,4 
 
 .00017 
 
 
 .44080 
 
 157,3 
 
 55920 
 
 .0277 
 
 .44254 
 
 156,8 
 
 .00017 
 
 
 .44237 
 
 156,7 
 
 .55763 
 
 .0278 
 
 .44410 
 
 156,3 
 
 .00017 
 
 
 44393 
 
 156,1 
 
 .55607 
 
 .0279 
 
 .44566 
 
 155,7 
 
 .00017 
 
 
 .44549 
 
 155,6 
 
 55451 
 
 0.0280 
 
 8.44721 
 
 I55,i 
 
 0.00017 
 
 0,1 
 
 8.44704 
 
 i55,o 
 
 1.55206 
 
 .0281 
 
 .44876 
 
 154,6 
 
 .00017 
 
 
 .44859 
 
 154,5 
 
 .55141 
 
 .0282 
 
 .45031 
 
 154,0 
 
 .00017 
 
 
 45013 
 
 153,9 
 
 .54987 
 
 .0283 
 
 .45184 
 
 153,5 
 
 .00017 
 
 
 45i67 
 
 153,4 
 
 .54833 
 
 .0284 
 
 .45338 
 
 153,0 
 
 .00018 
 
 
 45320 
 
 152,8 
 
 .54680 
 
 0.0285 
 
 8.45490 
 
 152,4 
 
 O.OOOlS 
 
 0,1 
 
 8-45473 
 
 152,3 
 
 1.54527 
 
 .0286 
 
 45643 
 
 I5i,9 
 
 .00018 
 
 
 .45625 
 
 151,8 
 
 54375 
 
 .0287 
 
 .45794 
 
 I5i,4 
 
 .00018 
 
 
 45776 
 
 151,2 
 
 .54224 
 
 .0288 
 
 .45945 
 
 150,8 
 
 .00018 
 
 
 45927 
 
 150,7 
 
 54073 
 
 .0289 
 
 .46096 
 
 150,3 
 
 .00018 
 
 
 .46078 
 
 150,2 
 
 53922 
 
 0.0290 
 
 8.46246 
 
 149,8 
 
 0.00018 
 
 0,1 
 
 8.46228 
 
 149,7 
 
 1-53772 
 
 .0291 
 
 .46395 
 
 149,3 
 
 .00018 
 
 
 .46377 
 
 149,2 
 
 53623 
 
 .0292 
 
 .46544 
 
 148,8 
 
 .00019 
 
 
 .46526 
 
 148,6 
 
 53474 
 
 .0293 
 
 .46693 
 
 148,3 
 
 .00019 
 
 
 .46674 
 
 148,1 
 
 53326 
 
 .0294 
 
 .46841 
 
 147,8 
 
 .00019 
 
 
 .46822 
 
 147,6 
 
 .53178 
 
 0.0295 
 
 8.46989 
 
 147,3 
 
 0.00019 
 
 0,1 
 
 8.46970 
 
 147,1 
 
 I 53030 
 
 .0296 
 
 .47136 
 
 146,8 
 
 .00019 
 
 
 .47116 
 
 146,6 
 
 .52884 
 
 .0297 
 
 .47282 
 
 146,3 
 
 .00019 
 
 
 .47263 
 
 146,1 
 
 .52737 
 
 .0298 
 
 .47428 
 
 145,8 
 
 .00019 
 
 
 .47409 
 
 145,7 
 
 .52591 
 
 .0299 
 
 .47574 
 
 145,3 
 
 .00019 
 
 
 47554 
 
 145,2 
 
 .52446 
 
 0.0300 
 
 8.47719 
 
 144,8 
 
 O.OOO20 
 
 0,1 
 
 8.47699 
 
 144,7 
 
 1.52301 
 
 u 
 
 log tan gd u 
 
 Fo' 
 
 log sec gd u 
 
 Fo' 
 
 log sin gd u 
 
 w Fo' 
 
 log esc gd u 
 
 SMITHSONIAN TABLES 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 Fo' 
 
 log cosh u 
 
 -FO' 
 
 log tanh u 
 
 Fo' 
 
 log coth u 
 
 0.0300 
 
 8.47719 
 
 144,8 
 
 O.OO02O 
 
 0,1 
 
 8.47699 
 
 144,7 
 
 I.5230I 
 
 .0301 
 
 .47863 
 
 144,3 
 
 .00020 
 
 
 .47844 
 
 14-1,2 
 
 .52156 
 
 .0302 
 
 .48007 
 
 143,8 
 
 .00020 
 
 
 .47987 
 
 143,7 
 
 .52013 
 
 .0303 
 
 .48151 
 
 143,4 
 
 .00020 
 
 
 .48131 
 
 143,2 
 
 .51869 
 
 .0304 
 
 .48294 
 
 142,9 
 
 .00020 
 
 
 .48274 
 
 142,8 
 
 .51726 
 
 0.0305 
 
 8.48437 
 
 142,4 
 
 O.OOO20 
 
 O,I 
 
 8.48417 
 
 142,3 
 
 I.5I583 
 
 .0306 
 
 .48579 
 
 142,0 
 
 .OO020 
 
 
 .48559 
 
 141,8 
 
 .51441 
 
 .0307 
 
 .48721 
 
 I4i,5 
 
 .0002O 
 
 
 .48700 
 
 141,4 
 
 .51300 
 
 .0308 
 
 .48862 
 
 141,0 
 
 .00021 
 
 
 .48841 
 
 140,9 
 
 .5H59 
 
 .0309 
 
 .49003 
 
 140,6 
 
 .OOO2I 
 
 
 .48982 
 
 140,5 
 
 .51018 
 
 0.0310 
 
 8.49143 
 
 140,1 
 
 O.OOO2I 
 
 0,1 
 
 8.49122 
 
 140,0 
 
 1.50878 
 
 .0311 
 
 .49283 
 
 139,7 
 
 .O002I 
 
 
 .49262 
 
 139,6 
 
 .50738 
 
 .0312 
 
 .49423 
 
 139,2 
 
 .O002I 
 
 
 .49401 
 
 139,1 
 
 .50599 
 
 .0313 
 
 .49562 
 
 138,8 
 
 .00021 
 
 
 49540 
 
 138,7 
 
 .50460 
 
 .0314 
 
 .49700 
 
 138,4 
 
 .OOO2I 
 
 
 .49679 
 
 138,2 
 
 .50321 
 
 0.03'is 
 
 8.40838 
 
 137,9 
 
 O.OOO22 
 
 0,1 
 
 8.49817 
 
 137,8 
 
 1.50183 
 
 .0316 
 
 .49976 
 
 137,5 
 
 .OOO22 
 
 
 49954 
 
 137,3 
 
 .50046 
 
 .0317 
 
 .50113 
 
 I37,o 
 
 .OO022 
 
 
 .50091 
 
 136,9 
 
 .49909 
 
 .0318 
 
 .50250 
 
 136,6 
 
 .OO022 
 
 
 .50228 
 
 136,5 
 
 .49772 
 
 .0319 
 
 .50386 
 
 136,2 
 
 .OOO22 
 
 
 .50364 
 
 136,1 
 
 .49636 
 
 0.0320 
 
 8.50522 
 
 135,8 
 
 O.OOO22 
 
 0,1 
 
 8.50500 
 
 135,6 
 
 1.49500 
 
 .0321 
 
 .50658 
 
 135,3 
 
 .OO022 
 
 
 .50636 
 
 135,2 
 
 .49364 
 
 .0322 
 
 .50793 
 
 134,9 
 
 .00023 
 
 
 
 .50771 
 
 134,8 
 
 .49229 
 
 .0323 
 
 .50928 
 
 134,5 
 
 .00023 
 
 
 .50905 
 
 134,4 
 
 .49095 
 
 .0324 
 
 .51062 
 
 134,1 
 
 .00023 
 
 
 .51039 
 
 133,9 
 
 .48961 
 
 0.0325 
 
 8.51196 
 
 133,7 
 
 O.OO023 
 
 0,1 
 
 8.5H73 
 
 133,5 
 
 1.48827 
 
 .0326 
 
 .51329 
 
 133,3 
 
 .00023 
 
 
 .51306 
 
 I33,i 
 
 .48694 
 
 .0327 
 
 .51463 
 
 132,9 
 
 .00023 
 
 
 .51439 
 
 132,7 
 
 .48561 
 
 .0328 
 
 .51595 
 
 132,5 
 
 .00023 
 
 
 .51572 
 
 132,3 
 
 .48428 
 
 .0329 
 
 .51727 
 
 132,1 
 
 .00023 
 
 
 .51704 
 
 I3i,9 
 
 .48296 
 
 0.0330 
 
 8.51859 
 
 I3i,7 
 
 O.O0024 
 
 0,1 
 
 8.51836 
 
 I3i,5 
 
 1.48164 
 
 0331 
 
 .51991 
 
 I3i,3 
 
 .00024 
 
 
 51967 
 
 131,1 
 
 .48033 
 
 -0332 
 
 .52122 
 
 130,9 
 
 .00024 
 
 
 .52098 
 
 130,7 
 
 .47902 
 
 0333 
 
 .52252 
 
 130,5 
 
 .00024 
 
 
 .52228 
 
 130,3 
 
 .47772 
 
 0334 . 
 
 .52383 
 
 130,1 
 
 .OO024 
 
 
 .52358 
 
 129,9 
 
 .47642 
 
 0.0335 
 .0336 
 
 8.52513 
 .52642 
 
 129,7 
 129,3 
 
 o 00024 
 .00025 
 
 0,1 
 
 8.52488 
 .52618 
 
 129,5 
 
 129,2 
 
 I.475I2 
 .47382 
 
 0337 
 
 .52771 
 
 128,9 
 
 .00025 
 
 
 .52747 
 
 128,8 
 
 .47253 
 
 .0338 
 
 .52900 
 
 128,5 
 
 .00025 
 
 
 .52875 
 
 128,4 
 
 .47125 
 
 0339 
 
 .53028 
 
 128,2 
 
 .00025 
 
 
 .53003 
 
 128,0 
 
 .46997 
 
 0.0340 
 
 8.53156 
 
 127,8 
 
 0.00025 
 
 0,1 
 
 8.53I3I 
 
 127,6 
 
 1.46869 
 
 .0341 
 
 .53284 
 
 127,4 
 
 .00025 
 
 
 .53259 
 
 127,3 
 
 .46741 
 
 .0342 
 
 534II 
 
 127,0 
 
 .00025 
 
 
 .53386 
 
 126,9 
 
 .46614 
 
 0343 
 
 .53538 
 
 126,7 
 
 .00026 
 
 
 53512 
 
 126,5 
 
 .46488 1 
 
 0344 
 
 ^^ 
 
 .53664 
 
 126,3 
 
 .00026 
 
 
 .53639 
 
 126,1 
 
 .46361 
 
 0.0345 
 
 8.53791 
 
 125,9 
 
 0.00026 
 
 0,1 
 
 8.53765 
 
 125,8 
 
 1.46235 
 
 .0346 
 
 .53916 
 
 125,6 
 
 .00026 
 
 0,2 
 
 .53890 
 
 125,4 
 
 .46110 
 
 0347 
 
 .54042 
 
 125,2 
 
 .00026 
 
 
 .54016 
 
 125,1 
 
 4S9&4 
 
 .0348 
 
 .54167 
 
 124,8 
 
 .00026 
 
 
 .54140 
 
 124,7 
 
 .45860 
 
 .0349 
 
 .54291 
 
 124,5 
 
 .00026 
 
 
 .54265 
 
 124,3 
 
 .45735 
 
 0.0350 
 
 8.S44I6 
 
 124,1 
 
 0.00027 
 
 0,2 
 
 8.54389 
 
 124,0 
 
 1.45611 
 
 u 
 
 log tan gd u 
 
 Fo' 
 
 log sec gd u 
 
 F ' 
 
 log sin gd u 
 
 F ' 
 
 log esc gd u 
 
 
 SMITHSONIAN TABLE* 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 w Fo' 
 
 log cosh u 
 
 F ' 
 
 log tanh u 
 
 w Fo' 
 
 log coth u 
 
 0.0350 
 
 8.54416 
 
 124,1 
 
 0.00027 
 
 0,2 
 
 8.54389 
 
 124,0 
 
 I.456II 
 
 .0351 
 
 .54540 
 
 123,8 
 
 .00027 
 
 
 .54513 
 
 123,6 
 
 .45487 
 
 .0352 
 
 .54663 
 
 123,4 
 
 .00027 
 
 
 .54636 
 
 123,3 
 
 .45364 
 
 .0353 
 
 .54786 
 
 123,1 
 
 .00027 
 
 
 54759 
 
 122,9 
 
 .45241 
 
 .0354 
 
 .54909 
 
 122,7 
 
 .00027 
 
 
 .54882 
 
 122,6 
 
 .45n8 
 
 0.0355 
 
 8.55032 
 
 122,4 
 
 0.00027 
 
 0,2 
 
 8.55005 
 
 122,2 
 
 1-44995 
 
 0356 
 
 .55154 
 
 I22,O 
 
 .00028 
 
 
 .55127 
 
 121,9 
 
 .44873 
 
 .0357 
 
 .55276 
 
 121,7 
 
 .00028 
 
 
 .55248 
 
 121,5 
 
 44752 
 
 .0358 
 
 .55398 
 
 121,4 
 
 .00028 
 
 
 55370 
 
 121,2 
 
 .44630 
 
 0359 
 
 .55519 
 
 I2I,O 
 
 .00028 
 
 
 55491 
 
 120,9 
 
 .44509 
 
 0.0360 
 
 8.55640 
 
 120,7 
 
 0.00028 
 
 0,2 
 
 8.55611 
 
 120,5 
 
 1.44389 
 
 .0361 
 
 .55700 
 
 120,4 
 
 .00028 
 
 
 .55732 
 
 1 2O,2 
 
 .44268 
 
 .0362 
 
 .55880 
 
 I20.O 
 
 .00028 
 
 
 .55852 
 
 119,9 
 
 .44148 
 
 .0363 
 
 .56000 
 
 H9,7 
 
 .00029 
 
 
 .55972 
 
 H9,5 
 
 .44028 
 
 .0364 
 
 .56120 
 
 119,4 
 
 .00029 
 
 
 .56091 
 
 119,2 
 
 .43909 
 
 0.0365 
 
 8.56239 
 
 119,0 
 
 0.00029 
 
 0,2 
 
 8.56210 
 
 118,9 
 
 1.43790 
 
 .0366 
 
 .56358 
 
 118,7 
 
 .00029 
 
 
 .56329 
 
 118,6 
 
 .43671 
 
 .0367 
 
 .56476 
 
 118,4 
 
 .00029 
 
 
 .56447 
 
 1 1 8,2 
 
 43553 
 
 .0368 
 
 .56595 
 
 118,1 
 
 .00029 
 
 
 .56565 
 
 H7,9 
 
 43435 
 
 .0369 
 
 .56712 
 
 117,7 
 
 .00030 
 
 
 .56683 
 
 117,6 
 
 .43317 
 
 0.0370 
 
 8.56830 
 
 117,4 
 
 0.00030 
 
 0,2 
 
 8.56800 
 
 H7,3 
 
 1.43200 
 
 .0371 
 
 .50947 
 
 ii7,i 
 
 .00030 
 
 
 .56917 
 
 117,0 
 
 .43083 
 
 .0372 
 
 .57064 
 
 116,8 
 
 .00030 
 
 
 .57034 
 
 116,6 
 
 .42966 
 
 0373 
 
 .57i8i 
 
 116,5 
 
 .00030 
 
 
 .57151 
 
 116,3 
 
 .42849 
 
 .0374 
 
 .57297 
 
 116,2 
 
 .00030 
 
 
 .57267 
 
 116,0. 
 
 .42733 
 
 0.0375 
 
 8.57413 
 
 H5,9 
 
 0.00031 
 
 0,2 
 
 8.57383 
 
 H5,7 
 
 1.42617 
 
 .0376 
 
 57529 
 
 115,6 
 
 .00031 
 
 
 .57498 
 
 H5,4 
 
 .42502 
 
 .0377 
 
 .57644 
 
 H5,3 
 
 .00031 
 
 
 .57614 
 
 115,1 
 
 .42386 
 
 .0378 
 
 .57760 
 
 114,9 
 
 .00031 
 
 
 .57729 
 
 114,8 
 
 .42271 
 
 .0379 
 
 .57874 
 
 114,6 
 
 .00031 
 
 
 .57843 
 
 114,5. 
 
 .42157 
 
 0.0380 
 
 8.57989 
 
 114,3 
 
 0.00031 
 
 0,2 
 
 &.S7957 
 
 114,2 
 
 1.42043 
 
 .0381 
 
 .58103' 
 
 114,0 
 
 .00032 
 
 
 .58071 
 
 113,9 
 
 .41929 
 
 .0382 
 
 .58217 
 
 113,7 
 
 .00032 
 
 
 .58185 
 
 113,6 
 
 .41815 
 
 .0383 
 
 .58330 
 
 H3,4 
 
 .00032 
 
 
 .58299 
 
 H3,3 
 
 .41701 
 
 .0384 
 
 58444 
 
 113,2 
 
 .00032 
 
 
 .58412 
 
 113,0 
 
 .41588 
 
 0.0385 
 
 8.58557 
 
 112,9 
 
 0.00032 
 
 0,2 
 
 8.58525 
 
 112,7 
 
 I.4I475 
 
 .0386 
 
 .58670 
 
 112,6 
 
 .00032 
 
 
 .58637 
 
 112,4 
 
 .41363 
 
 .0387 
 
 .58782 
 
 112,3 
 
 .00033 
 
 
 .58749 
 
 112,1 
 
 .41251 
 
 .0388 
 
 .58894 
 
 II2,O 
 
 .00033 
 
 
 .58861 
 
 111,8 
 
 .41139 
 
 .0389 
 
 .59006 
 
 111,7 
 
 .00033 
 
 
 .58973 
 
 in,5. 
 
 .41027 
 
 0.0390 
 
 8.59H7 
 
 111,4 
 
 0.00033 
 
 0,2 
 
 8.59084 
 
 111,2 
 
 1.40916 
 
 .0391 
 
 .59229 
 
 iii.i 
 
 .00033 
 
 
 .59196 
 
 111,0 
 
 .40804 
 
 .0392 
 
 .59340 
 
 110,8 
 
 .00033 
 
 
 .59306 
 
 110,7 
 
 .40694 
 
 .0393 
 
 59450 
 
 110,6 
 
 .00034 
 
 
 .59417 
 
 110,4 
 
 .40583 
 
 .0394 
 
 59561 
 
 110,3 
 
 .00034 
 
 
 .59527 
 
 110,1 
 
 40473 
 
 0.0395 
 
 8.59671 
 
 110,0 
 
 0.00034 
 
 0,2 
 
 8.59637 
 
 109,8 
 
 1.40363 
 
 .0396 
 
 .59781 
 
 109,7 
 
 .00034 
 
 
 .59747 
 
 109,6 
 
 .40253 
 
 0397 
 
 .59890 
 
 109,5 
 
 .00034 
 
 
 .59856 
 
 109,3 
 
 .40144 
 
 .0398 
 
 .60000 
 
 109,2 
 
 .00034 
 
 
 .59965 
 
 109,0 
 
 .40035 
 
 0399 
 
 .60109 
 
 108,9 
 
 .00035 
 
 
 .60074 
 
 108,7 
 
 .39926 
 
 0.0400 
 
 8.60218 
 
 108,6 
 
 0.00035 
 
 0,2 
 
 8.60183 
 
 io8,5 
 
 1.39817 
 
 u 
 
 log tan gd u 
 
 <- Fo' 
 
 log sec gd u 
 
 Fo' 
 
 log sin gd u 
 
 F ' 
 
 log esc gd u 
 
 SMITHSONIAN TABLES 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 F ' 
 
 log cosh u 
 
 F ' 
 
 log tanh u 
 
 Fo' 
 
 log coth u 
 
 0.0400 
 
 8.60218 
 
 108,6 
 
 0.00035 
 
 0,2 
 
 8.60183 
 
 108,5 
 
 I.398I7 
 
 .0401 
 
 .60326 
 
 108,4 
 
 .00035 
 
 
 .60291 
 
 108,2 
 
 .39709 
 
 .0402 
 
 .60434 
 
 108,1 
 
 .00035 
 
 
 .60399 
 
 107,9 
 
 .39601 
 
 .0403 
 
 .60542 
 
 107,8 
 
 .00035 
 
 
 .60507 
 
 107,6 
 
 39493 
 
 .0404 
 
 .60650 
 
 107,6 
 
 .00035 
 
 
 .60615 
 
 107,4 
 
 .39385 
 
 0.0405 
 
 8.60757 
 
 107,3 
 
 0.00036 
 
 0,2 
 
 8.60722 
 
 107,1 
 
 I .39278 
 
 .0406 
 
 .60865 
 
 IO7,O 
 
 .00036 
 
 
 .60829 
 
 106,9 
 
 .39171 
 
 .0407 
 
 .60971 
 
 106,8 
 
 .00036 
 
 
 .60935 
 
 106,6 
 
 .39065 
 
 .0408 
 
 .61078 
 
 106,5 
 
 .00036 
 
 
 .61042 
 
 106,3 
 
 .38958 
 
 .0409 
 
 .6~n84 
 
 100,2 
 
 .00036 
 
 
 .61148 
 
 106,1 
 
 .38852 
 
 0.0410 
 
 8.61291 
 
 106,0 
 
 0.00036 
 
 0,2 
 
 8.61254 
 
 105,8 
 
 1.38746 
 
 .0411 
 
 .61396 
 
 105,7 
 
 .00037 
 
 
 .61360 
 
 105,5 
 
 .38640 
 
 .0412 
 
 .61502 
 
 105,5 
 
 .00037 
 
 
 .61465 
 
 105,3 
 
 .38535 
 
 .0413 
 
 .61607 
 
 105,2 
 
 .00037 
 
 
 .61570 
 
 105,0 
 
 .38430 
 
 .0414 
 
 .61712 
 
 105,0 
 
 .00037 
 
 
 .61675 
 
 104,8 
 
 .38325 
 
 0.0415 
 
 8.61817 
 
 104,7 
 
 0.00037 
 
 0,2 
 
 8.61780 
 
 104,5 
 
 1.38220 
 
 .0416 
 
 .61922 
 
 104,5 
 
 .00038 
 
 
 .61884 
 
 104,3 
 
 .38116 
 
 .0417 
 
 .62026 
 
 104,2 
 
 .00038 
 
 
 .61988 
 
 104,0 
 
 .38012 
 
 .0418 
 
 .62130 
 
 104,0 
 
 .00038 
 
 
 .62092 
 
 103,8 
 
 .37908 
 
 .0419 
 
 .62234 
 
 103,7 
 
 .00038 
 
 
 .62196 
 
 103,5 
 
 .37804 
 
 0.0420 
 
 8.62338 
 
 103,5 
 
 0.00038 
 
 0,2 
 
 8.62299 
 
 103,3 
 
 I.3770I 
 
 .0421 
 
 .62441 
 
 103,2 
 
 .00038 
 
 
 .62403 
 
 103,0 
 
 .37597 
 
 .0422 
 
 .62544 
 
 103,0 
 
 .00039 
 
 
 .62505 
 
 102,8 
 
 37495 
 
 .0423 
 
 .62647 
 
 102,7 
 
 .00039 
 
 
 .62608 
 
 102,5 
 
 .37392 
 
 .0424 
 
 .62750 
 
 102,5 
 
 .00039 
 
 
 .62711 
 
 102,3 
 
 .37289 
 
 0.0425 
 
 8.62852 
 
 102,2 
 
 0.00039 
 
 0,2 
 
 8.62813 
 
 102,1 
 
 1.37187 
 
 .0426 
 
 .62954 
 
 IO2,O 
 
 .00039 
 
 
 .62915 
 
 101,8 
 
 .37085 
 
 .0427 
 
 .63056 
 
 101,8 
 
 .00040 
 
 
 .63016 
 
 101,6 
 
 .36984 
 
 .0428 
 
 .63158 
 
 101,5 
 
 .00040 
 
 
 .63118 
 
 101,3 
 
 .36882 
 
 .0429 
 
 .63259 
 
 101,3 
 
 .00040 
 
 
 .63219 
 
 101,1 
 
 .36781 
 
 0.0430 
 
 8.63360 
 
 101,1 
 
 0.00040 
 
 0,2 
 
 '8.63320 
 
 100,9 
 
 1.36680 
 
 .0431 
 
 .63461 
 
 100,8 
 
 .00040 
 
 
 .63421 
 
 100,6 
 
 .36579 
 
 .0432 
 
 .63562 
 
 100,6 
 
 .00041 
 
 
 .63521 
 
 100,4 
 
 .36479 
 
 0433 
 
 .63662 
 
 100,4 
 
 .00041 
 
 
 .63622 
 
 100,2 
 
 .36378 
 
 0434 
 
 .63763 
 
 IOO,I 
 
 .00041 
 
 
 .63722 
 
 99,9 
 
 .36278 
 
 0.0435 
 
 8.63863 
 
 99,9 
 
 0.00041 
 
 0,2 
 
 8.63822 
 
 99,7 
 
 1.36178 
 
 .0436 
 
 .63962 
 
 99,7 
 
 .00041 
 
 
 .63921 
 
 99,5 
 
 
 .0437 
 
 .64062 
 
 99,4 
 
 .00041 
 
 
 .64020 
 
 99,3 
 
 .35980 
 
 .0438 
 
 .64161 
 
 99,2 
 
 .00042 
 
 
 .64120 
 
 99,0 
 
 .35880 
 
 .0439 
 
 .64260 
 
 99,0 
 
 .00042 
 
 
 .64219 
 
 98,8 
 
 .35781 
 
 0.0440 
 
 8.64359 
 
 98,8 
 
 0.00042 
 
 0,2 
 
 8.64317 
 
 98,6 
 
 1.35683 
 
 .0441 
 
 .64458 
 
 98,5 
 
 .00042 
 
 
 .64416 
 
 98,4 
 
 .35584 
 
 .0442 
 
 .64556 
 
 98,3 
 
 .00042 
 
 
 .64514 
 
 98,1 
 
 .35486 
 
 0443 
 
 .64655 
 
 98,1 
 
 .00043 
 
 
 .64612 
 
 97,9 
 
 .35388 
 
 .0444 
 
 .64753 
 
 97,9 
 
 .00043 
 
 
 .64710 
 
 97,7 
 
 .35290 
 
 0.0445 
 
 8.64850 
 
 97,7 
 
 0.00043 
 
 0,2 
 
 8.64807 
 
 97,5 
 
 I.35I93 
 
 .0446 
 
 .64948 
 
 97,4 
 
 .00043 
 
 
 .64905 
 
 97,2 
 
 .35095 
 
 .0447 
 
 .65045 
 
 97,2 
 
 .00043 
 
 
 .65002 
 
 97,0 
 
 .34998 
 
 .0448 
 
 .65142 
 
 97,o 
 
 .00044 
 
 
 .65009 
 
 96,8 
 
 34901 
 
 .0449 
 
 .65239 
 
 96,8 
 
 .00044 
 
 
 .65195 
 
 96,6 
 
 .34805 
 
 0.0450 
 
 8.65336 
 
 96,6 
 
 0.00044 
 
 0,2 
 
 8.65292 
 
 96,4 
 
 1.34708 
 
 u 
 
 log tan od u 
 
 Fo' 
 
 log tec gd u 
 
 Fo' 
 
 log tin gd u 
 
 Fo' 
 
 log esc gd u 
 
 SMITHSONIAN TABLCS 
 
 10 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 F ' 
 
 log cosh u 
 
 F O ' 
 
 log tanh u 
 
 Fo' 
 
 log coth u 
 
 0.0450 
 
 8.65336 
 
 96,6 
 
 0.00044 
 
 0,2 
 
 8.65292 
 
 96,4 
 
 1.34708 
 
 .0451 
 
 .65432 
 
 96,4 
 
 .00044 
 
 
 .65388 
 
 96,2 
 
 .34612 
 
 .0452 
 
 .65529 
 
 96,1 
 
 .00044 
 
 
 .65484 
 
 96,0 
 
 .34516 
 
 .0453 
 
 .65625 
 
 95,9 
 
 .00045 
 
 
 .65580 
 
 95,7 
 
 .34420 
 
 .0454 
 
 .65721 
 
 95,7 
 
 .00045 
 
 
 .65676 
 
 95,5 
 
 .34324 
 
 0.0455 
 
 8.65816 
 
 95,5 
 
 0.00045 
 
 0,2 
 
 8.65771 
 
 95,3 
 
 1.34229 
 
 .0456 
 
 .65912 
 
 95,3 
 
 .00045 
 
 
 .65866 
 
 95,1 
 
 .34134 
 
 0457 
 
 .66007 
 
 95,1 
 
 .00045 
 
 
 .65961 
 
 949 
 
 .34039 
 
 .0458 
 
 .66102 
 
 94,9 
 
 .00046 
 
 
 .66056 
 
 94,7 
 
 33944 
 
 .0459 
 
 .66197 
 
 94,7 
 
 .00046 
 
 
 .66151 
 
 94,5 
 
 .33849 
 
 0.0460 
 
 8.66291 
 
 94,5 
 
 0.00046 
 
 0,2 
 
 8.66245 
 
 943 
 
 1.33755 
 
 .0461 
 
 .66385 
 
 94,3 
 
 .00046 
 
 
 .66339 
 
 94,1 
 
 .33661 
 
 .0462 
 
 .66480 
 
 94,1 
 
 .00046 
 
 
 .66433 
 
 93,9 
 
 .33567 
 
 .0463 
 
 .66574 
 
 93,9 
 
 .00047 
 
 
 .66527 
 
 93,7 
 
 33473 
 
 .0464 
 
 .66667 
 
 93,7 
 
 .00047 
 
 
 .66621 
 
 93,5 
 
 .33379 
 
 0.0465 
 
 8.66761 
 
 93,5 
 
 0.00047 
 
 0,2 
 
 8.66714 
 
 93,3 
 
 1.33286 
 
 .0466 
 
 .66854 
 
 93,3 
 
 .00047 
 
 
 .66807 
 
 93,1 
 
 .33193 
 
 .0467 
 
 .66947 
 
 93,1 
 
 .00047 
 
 
 .66900 
 
 92,9 
 
 .33100 
 
 .0468 
 
 .67040 
 
 92,9 
 
 .00048 
 
 
 .66993 
 
 92,7 
 
 .33007 
 
 .0469 
 
 .67133 
 
 92,7 
 
 .00048 
 
 
 .67085 
 
 92,5 
 
 .32915 
 
 0.0470 
 
 8.67226 
 
 92,5 
 
 0.00048 
 
 0,2 
 
 8.67178 
 
 92,3 
 
 1.52822 
 
 .0471 
 
 .67318 
 
 92,3 
 
 .00048 
 
 
 .67270 
 
 92,1 
 
 .32730 
 
 .0472 
 
 .67410 
 
 92,1 
 
 .00048 
 
 
 .67362 
 
 91,9 
 
 .32638 
 
 0473 
 
 .67502 
 
 91,9 
 
 .00049 
 
 
 .67454 
 
 91,7 
 
 .32546 
 
 .0474 
 
 .67594 
 
 91,7 
 
 .00049 
 
 
 .67545 
 
 91,5 
 
 .32455 
 
 0.0475 
 
 8.67686 
 
 91,5 
 
 0.00049 
 
 0,2 
 
 8.67637 
 
 91,3 
 
 1.32363 
 
 .0476 
 
 .67777 
 
 91,3 
 
 .00049 
 
 
 .67728 
 
 91,1 
 
 .32272 
 
 .0477 
 
 .67868 
 
 9i,i 
 
 .00049 
 
 
 .67819 
 
 90,9 
 
 .32181 
 
 .0478 
 
 .67959 
 
 90,9 
 
 .00050 
 
 
 .67910 
 
 90,7 
 
 .32090 
 
 .0479 
 
 .68050 
 
 90,7 
 
 .00050 
 
 
 .68000 
 
 90,5 
 
 .32000 
 
 0.0480 
 
 8.68141 
 
 90,5 
 
 0.00050 
 
 0,2 
 
 8.68091 
 
 90,3 
 
 I.3I9Q9 
 
 .0481 
 
 .68231 
 
 90,4 
 
 .00050 
 
 
 .68181 
 
 90,2 
 
 .31819 
 
 .0482 
 
 .68322 
 
 00,2 
 
 .00050 
 
 
 .68271 
 
 90,0 
 
 .31729 
 
 .0483 
 
 .68412 
 
 90,0 
 
 .00051 
 
 
 .68361 
 
 89,8 
 
 .31639 
 
 .0484 
 
 .68501 
 
 89,8 
 
 .00051 
 
 
 .68451 
 
 89,6 
 
 .31549 
 
 0.0485 
 
 8.68591 
 
 89,6 
 
 0.00051 
 
 0,2 
 
 8.68540 
 
 80,4 
 
 1.31460 
 
 .0486 
 
 .68681 
 
 89,4 
 
 .00051 
 
 
 .68629 
 
 89,2 
 
 .31371 
 
 .0487 
 
 .68770 
 
 89,2 
 
 .00051 
 
 
 .68719 
 
 89,0 
 
 .31281 
 
 .0488 
 
 .68859 
 
 89,1 
 
 .00052 
 
 
 .68808 
 
 88,9 
 
 .31192 
 
 .0489 
 
 .68948 
 
 88,9 
 
 .00052 
 
 
 .68896 
 
 88,7 
 
 .31104 
 
 0.0490 
 
 8.69037 
 
 88,7 
 
 0.00052 
 
 0,2 
 
 8.68985 
 
 88,5 
 
 I.3IOI5 
 
 .0491 
 
 .69126 
 
 88,5 
 
 .00052 
 
 
 .69073 
 
 88,3 
 
 .30927 
 
 .0492 
 
 .69214 
 
 88,3 
 
 .00053 
 
 
 .69161 
 
 88,1 
 
 .30839 
 
 0493 
 
 .69302 
 
 88,2 
 
 .00053 
 
 
 .69250 
 
 87,9 
 
 .30750 
 
 .0494 
 
 .69390 
 
 88,0 
 
 .00053 
 
 
 .69337 
 
 87,8 
 
 .30663 
 
 0.0495 
 
 8.69478 
 
 87,8 
 
 0.00053 
 
 0,2 
 
 8.69425 
 
 87,6 
 
 1.30575 
 
 .0496 
 
 .69566 
 
 87,6 
 
 .00053 
 
 
 69513 
 
 87,4 
 
 .30487 
 
 .0497 
 
 .69654 
 
 87,5 
 
 .00054 
 
 
 .69600 
 
 87,2 
 
 .30400 
 
 .0498 
 
 .69741 
 
 87,3 
 
 .00054 
 
 
 .69687 
 
 87,1 
 
 .30313 
 
 .0499 
 
 .69828 
 
 87,1 
 
 .00054 
 
 
 .69774 
 
 86,9 
 
 .30226 
 
 0.0500 
 
 8.69915 
 
 86,9 
 
 0.00054 
 
 0,2 
 
 8.69861 
 
 86,7 
 
 I.30I39 
 
 u 
 
 log tan gd u 
 
 W Fo' 
 
 log sec gd u 
 
 Fo' 
 
 log sin gd u 
 
 F O ' 
 
 logcscgdu 
 
 SMITHSONIAN TABLES 
 
 II 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 a, Fo' 
 
 log cosh u 
 
 F</ 
 
 log tanh u 
 
 Fo' 
 
 log coth u 
 
 0.0500 
 
 8.69915 
 
 86,9 
 
 O.OOO54 
 
 0,2 
 
 8.69861 
 
 86,7 
 
 I.30I39 
 
 .0501 
 
 .70002 
 
 86,8 
 
 .00054 
 
 
 .69947 
 
 86,5 
 
 .30053 
 
 .0502 
 
 .70089 
 
 86,6 
 
 .00055 
 
 
 .70034 
 
 86,4 
 
 .29966 
 
 .0503 
 
 .70175 
 
 86,4 
 
 .00055 
 
 
 .70120 
 
 86,2 
 
 .29880 
 
 .0504 
 
 .70261 
 
 86,2 
 
 .00055 
 
 
 .70206 
 
 86,0 
 
 .29794 
 
 0.0505 
 
 8.70348 
 
 86,1 
 
 0.00055 
 
 0,2 
 
 8.70292 
 
 85,9 
 
 1.29708 
 
 .0506 
 
 70434 
 
 85,9 
 
 .00056 
 
 
 .70378 
 
 85,7 
 
 .29622 
 
 .0507 
 
 .70519 
 
 85,7 
 
 .00056 
 
 
 .70464 
 
 85,5 
 
 .29536 
 
 .0508 
 
 .70605 
 
 85,6 
 
 .00056 
 
 
 .70549 
 
 85,3 
 
 .29451 
 
 .0509 
 
 .70691 
 
 85,4 
 
 .00056 
 
 
 .70634 
 
 85,2 
 
 .29366 
 
 0.0510 
 
 8.70776 
 
 85,2 
 
 0.00056 
 
 0,2 
 
 8.70719 
 
 85,0 
 
 1.29281 
 
 .0511 
 
 .70861 
 
 85,1 
 
 .00057 
 
 
 .70804 
 
 84,8 
 
 .29196 
 
 .0512 
 
 .70946 
 
 84,9 
 
 .00057 
 
 
 .70889 
 
 8-U7 
 
 .29111 
 
 .0513 
 
 .71031 
 
 84,7 
 
 .00057 
 
 
 .70974 
 
 84,5 
 
 .20026 
 
 .0514 
 
 7III5 
 
 84,6 
 
 .00057 
 
 
 .71058 
 
 84,3 
 
 .28942 
 
 0.0515 
 
 8.7I2OO 
 
 84,4 
 
 0.00058 
 
 0,2 
 
 8.7II42 
 
 84,2 
 
 1.28858 
 
 .0516 
 
 .71284 
 
 84,2 
 
 .00058 
 
 
 .71226 
 
 84,0 
 
 .28774 
 
 .0517 
 
 .71368 
 
 84,1 
 
 .00058 
 
 
 .71310 
 
 83,9 
 
 .28690 
 
 .0518 
 
 .71452 
 
 83,9 
 
 .00058 
 
 
 71394 
 
 83,7 
 
 .28606 
 
 .0519 
 
 .71536 
 
 83,8 
 
 .00058 
 
 
 .71478 
 
 83,5 
 
 .28522 
 
 0.0520 
 
 8.71620 
 
 83,6 
 
 0.00059 
 
 0,2 
 
 8.71561 
 
 83,4 
 
 1.28439 
 
 .0521 
 
 .71703 
 
 83,4 
 
 .00059 
 
 
 .71644 
 
 83,2 
 
 .28356 
 
 .0522 
 
 .71787 
 
 83,3 
 
 .00059 
 
 
 .71728 
 
 83,0 
 
 .28272 
 
 .0523 
 
 .71870 
 
 83,1 
 
 .00059 
 
 
 .71811 
 
 82,9 
 
 .28189 
 
 .0524 
 
 .71953 
 
 83,0 
 
 .00000 
 
 
 .71893 
 
 82,7 
 
 .28107 
 
 0.0525 
 
 8.72036 
 
 82,8 
 
 0.00060 
 
 0,2 
 
 8.71976 
 
 82,6 
 
 1.28024 
 
 .0526 
 
 .72119 
 
 82,6 
 
 .00060 
 
 
 .72059 
 
 82,4 
 
 .27941 
 
 .0527 
 
 .722OI 
 
 82,5 
 
 .00060 
 
 
 .72141 
 
 82,3 
 
 .27859 
 
 .0528 
 
 .72284 
 
 82,3 
 
 .00061 
 
 
 .72223 
 
 82,1 
 
 .27777 
 
 .0529 
 
 .72366 
 
 82,2 
 
 .00061 
 
 
 .72305 
 
 81,9 
 
 .27695 
 
 0.0530 
 
 8.72448 
 
 82,0 
 
 0.00061 
 
 0,2 
 
 8.72387 
 
 81,8 
 
 1.27613 
 
 .0531 
 
 .72530 
 
 81,9 
 
 .00061 
 
 
 .72469 
 
 81,6 
 
 .27531 
 
 .0532 
 
 .72612 
 
 81,7 
 
 .00061 
 
 
 .72550 
 
 81,5 
 
 .27450 
 
 0533 
 
 .72693 
 
 81,6 
 
 .00062 
 
 
 .72632 
 
 81,3 
 
 .27368 
 
 .0534 
 
 .72775 
 
 81,4 
 
 .00062 
 
 
 .72713 
 
 81,2 
 
 .27287 
 
 0.0535 
 
 8.72856 
 
 81,3 
 
 0.00062 
 
 0,2 
 
 8.72794 
 
 81,0 
 
 1.27206 
 
 .0536 
 
 .72937 
 
 81,1 
 
 .00062 
 
 
 .72875 
 
 80,9 
 
 .27125 
 
 0537 
 
 .73018 
 
 81,0 
 
 .00063 
 
 
 .72956 
 
 80,7 
 
 .27044 
 
 .0538 
 
 .73099 
 
 80,8 
 
 .00063 
 
 
 .73036 
 
 80,6 
 
 .26964 
 
 .0539 
 
 .73180 
 
 80,7 
 
 .00063 
 
 
 .73H7 
 
 80,4 
 
 .26883 
 
 0.0540 
 
 8.73260 
 
 80,5 
 
 0.00063 
 
 0,2 
 
 8.73197 
 
 80,3 
 
 1.26803 
 
 .0541 
 
 73341 
 
 80,4 
 
 .00064 
 
 
 .73277 
 
 80, i 
 
 .26723 
 
 .0542 
 
 73421 
 
 80,2 
 
 .00064 
 
 
 .73357 
 
 80,0 
 
 .26643 
 
 .0543 
 
 73501 
 
 80,1 
 
 .00064 
 
 
 .73436 
 
 79,8 
 
 .26564 
 
 .0544 
 
 .73581 
 
 79,9 
 
 .00064 
 
 
 .73517 
 
 79,7 
 
 .26483 
 
 0.0545 
 
 8.73661 
 
 79,8 
 
 0.00064 
 
 0,2 
 
 8.73597 
 
 79,5 
 
 1.26403 
 
 .0546 
 
 73741 
 
 79,6 
 
 .00065 
 
 
 .73676 
 
 79,4 
 
 .26324 
 
 .0547 
 
 .73820 
 
 79,5 
 
 .00065 
 
 
 73755 
 
 79,2 
 
 .26245 
 
 .0548 
 
 .73900 
 
 79,3 
 
 .00065 
 
 
 .73835 
 
 79,1 
 
 .26165 
 
 .0549 
 
 73979 
 
 79,2 
 
 .00065 
 
 
 .739M 
 
 78,9 
 
 .26086 
 
 0.0550 
 
 8.74058 
 
 79,0 
 
 0.00066 
 
 0,2 
 
 8.73993 
 
 78,8 
 
 I.2OOO7 
 
 u 
 
 log tan gd u 
 
 -FO' 
 
 log sec gd u 
 
 F ' 
 
 log sin gd u 
 
 -Fo' 
 
 logcscgdu 
 
 SMITHSONIAN TABLES 
 
 12 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 Fo' 
 
 log cosh u 
 
 Fo' 
 
 log tanh u 
 
 Fo' 
 
 log coth u 
 
 0.0550 
 
 8.74058 
 
 79,0 
 
 O.OOO66 
 
 0,2 
 
 8-73993 
 
 78,8 
 
 1.26007 
 
 .0551 
 
 .74137 
 
 78,9 
 
 .00066 
 
 
 .74071 
 
 78,7 
 
 .25929 
 
 .0552 
 
 .74216 
 
 78,8 
 
 .00066 
 
 
 .74150 
 
 78,5 
 
 .25850 
 
 0553 
 
 74295 
 
 78,6 
 
 .00066 
 
 
 .74228 
 
 78,4 
 
 .25772 
 
 .0554 
 
 74373 
 
 78,5 
 
 .00067 
 
 
 74307 
 
 78,2 
 
 .25693 
 
 0.0555 
 
 8.74452 
 
 78,3 
 
 0.00067 
 
 0,2 
 
 8.74385 
 
 78,i 
 
 1.25615 
 
 .0556 
 
 .74530 
 
 78,2 
 
 .00067 
 
 
 .74463 
 
 77,9 
 
 25537 
 
 0557 
 
 .74608 
 
 78,0 
 
 .00067 
 
 
 .74541 
 
 77,8 
 
 .25459 
 
 .0558 
 
 .74686 
 
 77,9 
 
 .00068 
 
 
 .74618 
 
 77,7 
 
 .25382 
 
 .0559 
 
 .74704 
 
 77,8 
 
 .00068 
 
 
 .74696 
 
 77,5 
 
 .25304 
 
 0.0560 
 
 8.74841 
 
 77,6 
 
 0.00068 
 
 0,2 
 
 8.74773 
 
 77,4 
 
 1.25227 
 
 .0561 
 
 .74919 
 
 77,5 
 
 .00068 
 
 
 .74851 
 
 77,3 
 
 .25149 
 
 .0562 
 
 .74996 
 
 77,4 
 
 .00069 
 
 
 .74928 
 
 77,i 
 
 .25072 
 
 0563 
 
 75074 
 
 77,2 
 
 .00069 
 
 
 75005 
 
 77,o 
 
 .24995 
 
 .0564 
 
 .75151 
 
 77,1 
 
 .00069 
 
 
 .75082 
 
 76,8 
 
 .24918 
 
 0.0565 
 
 8.75228 
 
 76,9 
 
 0.00069 
 
 0,2 
 
 8.75159 
 
 76,7 
 
 1.24841 
 
 .0566 
 
 .75305 
 
 76,8 
 
 .00070 
 
 
 .75235 
 
 76,6 
 
 .24765 
 
 .0567 
 
 .75382 
 
 76,7 
 
 .00070 
 
 
 .75312 
 
 76,4 
 
 .24688 
 
 .0568 
 
 75458 
 
 76,5 
 
 .00070 
 
 
 .75388 
 
 76,3 
 
 .24612 
 
 .0569 
 
 .75535 
 
 76,4 
 
 .00070 
 
 
 .75464 
 
 76,2 
 
 .24536 
 
 0.0570 
 
 8.75611 
 
 76,3 
 
 O.OOO7I 
 
 0,2 
 
 8.75540 
 
 76,0 
 
 1.24460 
 
 .0571 
 
 .75687 
 
 76,1 
 
 .00071 
 
 
 .75616 
 
 75,9 
 
 .24384 
 
 .0572 
 
 .75763 
 
 76,0 
 
 .OOO7I 
 
 
 .75692 
 
 75,8 
 
 .24308 
 
 .0573 
 
 .75839 
 
 75,9 
 
 .00071 
 
 
 .75768 
 
 75,6 
 
 .24232 
 
 .0574 
 
 .75915 
 
 75,7 
 
 .00072 
 
 
 .75844 
 
 75,5 
 
 .24156 
 
 0.0575 
 
 8.75991 
 
 75,6 
 
 0.00072 
 
 0,2 
 
 8.75919 
 
 75,4 
 
 1.24081 
 
 .0576 
 
 .76066 
 
 75,5 
 
 .00072 
 
 0,2 
 
 75994 
 
 75,2 
 
 .24006 
 
 .0577 
 
 .76142 
 
 75,4 
 
 .00072 
 
 o,3 
 
 .76069 
 
 75,1 
 
 .23931 
 
 .0578 
 
 .76217 
 
 75,2 
 
 .00073 
 
 
 .76144 
 
 75,o 
 
 .23856 
 
 .0579 
 
 .76292 
 
 75,i 
 
 .00073 
 
 
 .76219 
 
 74,8 
 
 .23781 
 
 0.0580 
 
 8.76367 
 
 75,o 
 
 0.00073 
 
 o,3 
 
 8.76294 
 
 74,7 
 
 1.23706 
 
 .0581 
 
 .76442 
 
 74,8 
 
 .00073 
 
 
 .76369 
 
 74,6 
 
 .23631 
 
 .0582 
 
 .76517 
 
 74,7 
 
 .00074 
 
 
 .76443 
 
 74,5 
 
 .23557 
 
 .0583 
 
 .76591 
 
 74,6 
 
 .00074 
 
 
 .76518 
 
 74,3 
 
 .23482 
 
 0584 
 
 .76666 
 
 74,5 
 
 .00074 
 
 
 .76592 
 
 74,2 
 
 .23408 
 
 0.0585 
 
 8.76740 
 
 74,3 
 
 0.00074 
 
 0,3 
 
 8.76666 
 
 74,1 
 
 1.23334 
 
 .0586 
 
 .76815 
 
 74,2 
 
 .00075 
 
 
 .76740 
 
 73,9 
 
 .23260 
 
 .0587 
 
 .76889 
 
 74,1 
 
 .00075 
 
 
 .76814 
 
 73,8 
 
 .23186 
 
 .0588 
 
 .76963 
 
 73,9 
 
 .00075 
 
 
 .76888 
 
 73,7 
 
 .23112 
 
 .0589 
 
 .77037 
 
 73,8 
 
 .00075 
 
 
 .76961 
 
 73,6 
 
 .23039 
 
 0.0590 
 
 8.77110 
 
 73,7 
 
 0.00076 
 
 0,3 
 
 8.77035 
 
 73,4 
 
 1.22965 
 
 .0591 
 
 .77184 
 
 73,6 
 
 .00076 
 
 
 .77108 
 
 73,3 
 
 .22892 
 
 .0592 
 
 .77258 
 
 73,4 
 
 .00076 
 
 
 .77181 
 
 73,2 
 
 .22819 
 
 .0593 
 
 77331 
 
 73,3 
 
 .00076 
 
 
 .77255 
 
 73,1 
 
 .22745 
 
 .0594 
 
 .77404 
 
 73,2 
 
 .00077 
 
 
 .77328 
 
 72,9 
 
 .22672 
 
 0.0595 
 
 8.77477 
 
 73,i 
 
 0.00077 
 
 0,3 
 
 8.77400 
 
 72,8 
 
 1.22600 
 
 .0596 
 
 .77550 
 
 73,o 
 
 .00077 
 
 
 .77473 
 
 72,7 
 
 .22527 
 
 .0597 
 
 .77623 
 
 72,8 
 
 .00077 
 
 
 .77546 
 
 72,6 
 
 .22454 
 
 .0598 
 
 .776o6 
 
 72,7 
 
 .00078 
 
 
 .77618 
 
 72,5 
 
 .22382 
 
 .0599 
 
 .77769 
 
 72,6 
 
 .00078 
 
 
 .77691 
 
 72,3 
 
 .22309 
 
 0.0600 
 
 8.77841 
 
 72,5 
 
 0.00078 
 
 o,3 
 
 8.77763 
 
 72,2 
 
 1.22237 
 
 u 
 
 og tan gd u 
 
 Fo' 
 
 log sec gd u 
 
 Fo' 
 
 log sin gd u 
 
 Fo' 
 
 log esc gd u 
 
 SMITHSONIAN TABLES 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 - Fo' 
 
 log cosh u 
 
 F ' 
 
 log tanh u 
 
 F ' 
 
 log coth u 
 
 0.0600 
 
 8.77841 
 
 72,5 
 
 0.00078 
 
 0,3 
 
 8.77763 
 
 72,2 
 
 1.22237 
 
 .0601 
 
 .77914 
 
 72,3 
 
 .00078 
 
 
 .77835 
 
 72,1 
 
 .22165 
 
 .0602 
 
 .77986 
 
 72,2 
 
 .00079 
 
 
 .77907 
 
 72,0 
 
 .22093 
 
 .0603 
 
 .78058 
 
 72,1 
 
 .00079 
 
 
 77979 
 
 7i,8 
 
 .22021 
 
 .0604 
 
 .78130 
 
 72,0 
 
 .00079 
 
 
 .78051 
 
 71,7 
 
 .21949 
 
 0.0605 
 
 8.78202 
 
 71,9 
 
 0.00079 
 
 o,3 
 
 8.78123 
 
 71,6 
 
 I.2I877 
 
 .0606 
 
 .78274 
 
 7i,8 
 
 .00080 
 
 
 .78194 
 
 7i,5 
 
 .21806 
 
 .0607 
 
 .78346 
 
 7i,6 
 
 .00080 
 
 
 .78266 
 
 7i,4 
 
 21734 
 
 .0608 
 
 .78417 
 
 7i,5 
 
 .00080 
 
 
 .78337 
 
 7i,3 
 
 .21663 
 
 .0609 
 
 .78489 
 
 71,4 
 
 .00086 
 
 
 .78408 
 
 7i,i 
 
 .21592 
 
 0.0610 
 
 8.78560 
 
 71,3 
 
 0.00081 
 
 o,3 
 
 8.78479 
 
 71,0 
 
 I.2I52I 
 
 .0611 
 
 .78631 
 
 71,2 
 
 .00081 
 
 
 .78550 
 
 70,9 
 
 .2-1450 
 
 .0612 
 
 .78702 
 
 7i,i 
 
 .00081 
 
 
 .78621 
 
 70,8 
 
 .21379 
 
 .0613 
 .0614 
 
 .78773 
 .78844 
 
 70,9 
 70,8 
 
 .00082 
 .00082 
 
 
 .78692 
 .78762 
 
 70,7 
 70,6 
 
 .21308 
 .21238 
 
 0.0615 
 
 8.78915 
 
 70,7 
 
 0.00082 
 
 o,3 
 
 8.78833 
 
 70,4 
 
 I.2II67 
 
 .0616 
 
 .78986 
 
 70,6 
 
 .00082 
 
 
 .78903 
 
 70,3 
 
 .21097 
 
 .0617 
 
 .79056 
 
 70,5 
 
 .00083 
 
 
 .78973 
 
 70,2 
 
 .21027 
 
 .0618 
 
 .79127 
 
 70,4 
 
 .00083 
 
 
 .79044 
 
 70,i 
 
 .20956 
 
 .0619 
 
 .79197 
 
 70,3 
 
 .00083 
 
 
 .79114 
 
 70,0 
 
 .20886 
 
 0.0620 
 
 8.79267 
 
 70,1 
 
 0.00083 
 
 o,3 
 
 8.79184 
 
 69,9 
 
 1.20816 
 
 .0621 
 
 .79337 
 
 70,0 
 
 .00084 
 
 
 79253 
 
 69,8 
 
 .20747 
 
 .0622 
 
 .79407 
 
 69,9 
 
 .00084 
 
 
 .79323 
 
 69,6 
 
 .20677 
 
 .0623 
 
 79477 
 
 69,8 
 
 .OOO&l 
 
 
 79393 
 
 69,5 
 
 .20607 
 
 .0624 
 
 79547 
 
 69,7 
 
 .00084 
 
 
 .79462 
 
 69,4 
 
 .20538 
 
 0.0625 
 
 8.79616 
 
 69,6 
 
 0.00085 
 
 o,3 
 
 8-79532 
 
 69,3 
 
 1.20468 
 
 .0626 
 
 .79686 
 
 69,5 
 
 .00085 
 
 
 .79601 
 
 69,2 
 
 .20399 
 
 .0627 
 
 .79755 
 
 69,4 
 
 .00085 
 
 
 .79670 
 
 69,1 
 
 .20330 
 
 .0628 
 
 .79825 
 
 69,2 
 
 .00086 
 
 
 79739 
 
 69,0 
 
 .20261 
 
 .0629 
 
 .79894 
 
 69,1 
 
 .00086 
 
 
 .79808 
 
 68,9 
 
 .20192 
 
 0.0630 
 
 8.79963 
 
 69,0 
 
 0.00086 
 
 0,3 
 
 8.79877 
 
 68,8 
 
 1.20123 
 
 .0631 
 
 .80032 
 
 68,9 
 
 .00086 
 
 
 .79945 
 
 68,6 
 
 .20055 
 
 .0632 
 
 .80101 
 
 68,8 
 
 .00087 
 
 
 .80014 
 
 68,5 
 
 .19986 
 
 .0633 
 
 .80169 
 
 68,7 
 
 .00087 
 
 
 .80082 
 
 68,4 
 
 .19918 
 
 .0634 
 
 .80238 
 
 68,6 
 
 .00087 
 
 
 .80151 
 
 68,3 
 
 .19849 
 
 0.0635 
 
 8.80307 
 
 68,5 
 
 0.00088 
 
 o,3 
 
 8.80219 
 
 68,2 
 
 1.19781 
 
 .0636 
 
 .80375 
 
 68,4 
 
 .00088 
 
 
 .80287 
 
 68,1 
 
 .19713 
 
 .0637 
 
 .80443 
 
 68,3 
 
 .00088 
 
 
 .80355 
 
 68,0 
 
 .19645 
 
 .0638 
 
 .80512 
 
 68,2 
 
 .00088 
 
 
 .80423 
 
 67,9 
 
 . 19577 
 
 .0639 
 
 .80580 
 
 68,1 
 
 .00089 
 
 
 .80491 
 
 67,8 
 
 .19509 
 
 0.0640 
 
 8.80648 
 
 68,0 
 
 0.00089 
 
 0,3 
 
 8.80559 
 
 6>,7 
 
 I.I944T 
 
 .0641 
 
 .80716 
 
 67,8 
 
 .00089 
 
 
 .80626 
 
 67,6 
 
 . 19374 
 
 .0642 
 
 .80783 
 
 67,7 
 
 .00089 
 
 
 .80694 
 
 67,5 
 
 .19306 
 
 .0643 
 
 .80851 
 
 67,6 
 
 .00000 
 
 
 .80761 
 
 67,4 
 
 . 19239 
 
 .0644 
 
 .80919 
 
 67,5 
 
 .00090 
 
 
 .80829 
 
 6>,3 
 
 .19171 
 
 0.0645 
 
 8.80986 
 
 6>,4 
 
 o.ooooo 
 
 o,3 
 
 8.80896 
 
 67,1 
 
 I . 19104 
 
 .0646 
 
 .81053 
 
 67,3 
 
 .00091 
 
 
 .80963 
 
 67,0 
 
 .10037 
 
 .0647 
 
 .81121 
 
 67,2 
 
 .00091 
 
 
 .81030 
 
 66,9 
 
 .18970 
 
 .0648 
 
 .81188 
 
 67,1 
 
 .00091 
 
 
 .81007 
 
 66,8 
 
 .18003 
 
 .0649 
 
 .81255 
 
 67,0 
 
 .00091 
 
 
 .81164 
 
 66,7 
 
 .18836 
 
 0.0650 
 
 8.81322 
 
 66,9 
 
 0.00092 
 
 0,3 
 
 8.81230 
 
 66,6 
 
 I . 187/0 
 
 u 
 
 log tan gd u 
 
 F O ' 
 
 log sec gd u 
 
 -Fo' 
 
 log sin gd u 
 
 F ' 
 
 log esc gd u 
 
 SMITHSONIAN TABLES 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 lOQ sinh u 
 
 Fo' 
 
 log cosh u 
 
 F ' 
 
 log tanh u 
 
 F ' 
 
 log coth u 
 
 0.0650 
 
 8.81322 
 
 66,9 
 
 0.00092 
 
 0,3 
 
 8.81230 
 
 66,6 
 
 I . 18770 
 
 .0651 
 
 .81389 
 
 66,8 
 
 .00092 
 
 
 .81297 
 
 66,5 
 
 . 18703 
 
 .0652 
 
 .81456 
 
 66,7 
 
 .00092 
 
 
 .81363 
 
 66,4 
 
 .18637 
 
 .0653 
 
 .81522 
 
 66,6 
 
 .00093 
 
 
 .81430 
 
 66,3 
 
 . 18570 
 
 .0654 
 
 .81589 
 
 66,5 
 
 .00093 
 
 
 .81496 
 
 66,2 
 
 .18504 
 
 0.0655 
 
 8.8l65'5 
 
 66,4 
 
 0.00093 
 
 0,3 
 
 8.81562- 
 
 66,1 
 
 1.18438 
 
 .0656 
 
 .81722 
 
 66,3 
 
 .00093 
 
 
 .81628 
 
 66,0 
 
 .18372 
 
 .0657 
 
 .81788 
 
 66,2 
 
 .00094 
 
 
 .81694 
 
 65,9 
 
 .18306 
 
 .0658 
 
 .81854 
 
 66,1 
 
 .00094 
 
 
 .81760 
 
 65,8 
 
 .18240 
 
 .0659 
 
 .81920 
 
 66,0 
 
 .00094 
 
 
 .81826 
 
 65,7 
 
 . 18174 
 
 0.0660 
 
 8.81986 
 
 65,9 
 
 0.00095 
 
 0,3 
 
 8.81891 
 
 65,6 
 
 1 . 18109 
 
 .0661 
 
 .82052 
 
 65,8 
 
 .00095 
 
 
 .81957 
 
 65,5 
 
 .18043 
 
 .0662 
 
 .82118 
 
 65,7 
 
 .00095 
 
 
 .82022 
 
 65,4 
 
 .17978 
 
 .0663 
 
 .82183 
 
 65,6 
 
 .00095 
 
 
 .82088 
 
 65,3 
 
 .17912 
 
 .0664 
 
 .82249 
 
 65,5 
 
 .00096 
 
 
 .82153 
 
 65,2 
 
 .17847 
 
 0.0665 
 
 8.82314 
 
 65,4 
 
 0.00096 
 
 0,3 
 
 8.82218 
 
 65,1 
 
 I.I7782 
 
 .0666 
 
 .82380 
 
 65>3 
 
 .00096 
 
 
 .82283 
 
 65,0 
 
 .17717 
 
 .0667 
 
 .82445 
 
 65,2 
 
 .00097 
 
 
 .82348 
 
 64,9 
 
 .17652 
 
 .0668 
 
 .82510 
 
 65,1 
 
 .00097 
 
 
 .82413 
 
 64,8 
 
 .17587 
 
 .0669 
 
 .82575 
 
 65,0 
 
 .00097 
 
 
 .82478 
 
 64,7 
 
 .17522 
 
 0.0670 
 
 8.82640 
 
 64,9 
 
 0.00097 
 
 0,3 
 
 8.82543 
 
 64,6 
 
 I. 17457 
 
 .0671 
 
 .82705 
 
 64,8 
 
 .00098 
 
 
 .82607 
 
 64,5 
 
 .17393 
 
 .0672 
 
 .82770 
 
 64,7 
 
 .00098 
 
 
 .82672 
 
 64,4 
 
 .17328 
 
 .0673 
 
 .82834 
 
 64,6 
 
 .00098 
 
 
 .82736 
 
 64,3 
 
 .17264 
 
 .0674 
 
 .82899 
 
 64,5 
 
 .00099 
 
 
 .82800 
 
 64,2 
 
 .17200 
 
 0.0675 
 
 8.82963 
 
 64,4 
 
 0.00099 
 
 . 0,3 
 
 8.82864 
 
 64,1 
 
 1.17136 
 
 .0676 
 
 .83028 
 
 6^3 
 
 .00099 
 
 
 .82929 
 
 64,1 
 
 . 17071 
 
 .0677 
 
 .83092 
 
 64,2 
 
 .00099 
 
 
 .82994 
 
 64,0 
 
 .17006 
 
 .0678 
 
 .83156 
 
 64,2 
 
 .00100 
 
 
 .83056 
 
 63.9 
 
 .16944 
 
 .0679 
 
 .83220 
 
 64,1 
 
 .00100 
 
 
 .83120 
 
 63,8 
 
 .16880 
 
 0.0680 
 
 8.83284 
 
 64,0 
 
 O.OOIOO 
 
 0,3 
 
 8.83184 
 
 63,7 
 
 1. 16816 
 
 .0681 
 
 .83348 
 
 63,9 
 
 .OOIOI 
 
 
 .83248 
 
 63,6 
 
 .16752 
 
 .0682 
 
 .83412 
 
 63,8 
 
 .OOIOI 
 
 
 .833H 
 
 63,5 
 
 .16689 
 
 .0683 
 
 .83476 
 
 63,7 
 
 .OOIOI 
 
 
 .83375 
 
 63,4 
 
 .16625 
 
 .0684 
 
 .83539 
 
 63,6 
 
 .00102 
 
 
 .83438 
 
 63,3 
 
 . 16562 
 
 0.0685 
 
 8.83603 
 
 63,5 
 
 0.00102 
 
 0,3 
 
 8.83501 
 
 63,2 
 
 1.16499 
 
 .0686 
 
 .83666 
 
 63,4 
 
 .00102 
 
 
 .83564 
 
 63,1 
 
 .16436 
 
 .0687 
 
 .83730 
 
 63,3 
 
 .00102 
 
 
 .83627 
 
 63,0 
 
 . 16373 
 
 .0688 
 
 .83793 
 
 63,2 
 
 .00103 
 
 
 .83690 
 
 62,9 
 
 . 16310 
 
 .0689 
 
 .83856 
 
 63,1 
 
 .00103 
 
 
 .83753 
 
 62,8 
 
 . 16247 
 
 0.0690 
 
 8.83919 
 
 63,0 
 
 0.00103 
 
 0,3 
 
 8.83816 
 
 62,7 
 
 1.16184 
 
 .0691 
 
 .83982 
 
 63,0 
 
 .00104 
 
 
 .83879 
 
 62,7 
 
 .16121 
 
 .0692 
 
 .84045 
 
 62,9 
 
 .00104 
 
 
 .83941 
 
 62,6 
 
 .16059 
 
 .0693 
 
 .84108 
 
 62,8 
 
 .00104 
 
 
 .84004 
 
 62,5 
 
 .15996 
 
 .0694 
 
 .84171 
 
 62,7 
 
 .00105 
 
 
 .84066 
 
 62,4 
 
 . 15934 
 
 0.0695 
 
 8.84233 
 
 62,6 
 
 0.00105 
 
 0,3 
 
 8.84129 
 
 62,3 
 
 1.15871 
 
 .0696 
 
 .84296 
 
 62,5 
 
 .00105 
 
 
 .84191 
 
 62,2 
 
 .15809 
 
 .0697 
 
 .84358 
 
 62,4 
 
 .00105 
 
 
 .84253 
 
 62,1 
 
 . 15747 
 
 .0698 
 
 .84421 
 
 62,3 
 
 .00106 
 
 
 .84315 
 
 62,0 
 
 .15685 
 
 .0699 
 
 .84483 
 
 62,2 
 
 .00106 
 
 
 .84377 
 
 61,9 
 
 . 15623 
 
 0.0700 
 
 8.84545 
 
 62,1 
 
 0.00106 
 
 0,3 
 
 8.84439 
 
 61,8 
 
 1.15561 
 
 u 
 
 loo tan od u 
 
 Fo' 
 
 log sec gd u 
 
 F/ 
 
 log sin gd u 
 
 F ' 
 
 log esc gd u 
 
 SMITHSONIAN TABLES 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 u. Fo' 
 
 log cosh u 
 
 F O ' 
 
 log tanh u 
 
 Fo' 
 
 log coth u 
 
 0.0700 
 
 8.8 4 545 
 
 62,1 
 
 0.00106 
 
 0,3 
 
 8.84439 
 
 6!,8 
 
 I.ISS^I 
 
 .0701 
 
 .84607 
 
 62,1 
 
 .00107 
 
 
 .84501 
 
 61,8 
 
 15499 
 
 .0702 
 
 .84669 
 
 62,0 
 
 .00107 
 
 
 .84562 
 
 61,7 
 
 .15438 
 
 .0703 
 
 .84731 
 
 61,9 
 
 .00107 
 
 
 .84624 
 
 61,6 
 
 .15376 
 
 .0704 
 
 .84793 
 
 61,8 
 
 .00108 
 
 
 .84686 
 
 6i,5 
 
 .15314 
 
 0.0705 
 
 8.84855 
 
 6i,7 
 
 0.00108 
 
 0,3 
 
 8.84747 
 
 61,4 
 
 I.I5253 
 
 .0706 
 
 .84917 
 
 61,6 
 
 .00108 
 
 
 .84808 
 
 61,3 
 
 .15192 
 
 .0707 
 
 .84978 
 
 61,5 
 
 .00108 
 
 
 .84870 
 
 61,2 
 
 15130 
 
 .0708 
 
 .85040 
 
 6M 
 
 .00109 
 
 
 .84931 
 
 61,1 
 
 .15069 
 
 .0709 
 
 .85101 
 
 61,4 
 
 .00109 
 
 
 .84992 
 
 61,0 
 
 .15008 
 
 0.0710 
 
 8.85162 
 
 61,3 
 
 O.OOI09 
 
 0,3 
 
 8.85053 
 
 61,0 
 
 I . 14947 
 
 .0711 
 
 .85224 
 
 61,2 
 
 .OOIIO 
 
 
 .85114 
 
 60,9 
 
 .14886 
 
 .0712 
 
 .85285 
 
 61,1 
 
 .00110 
 
 
 .85175 
 
 60,8 
 
 . 14825 
 
 .0713 
 
 .85346 
 
 61,0 
 
 .OOIIO 
 
 
 .85235 
 
 60,7 
 
 . 14765 
 
 .0714 
 
 .85407 
 
 60,9 
 
 .00111 
 
 
 .85296 
 
 60,6 
 
 . 14704 
 
 0.0715 
 
 8.85468 
 
 60,8 
 
 O.OOIII 
 
 0,3 
 
 8.85357 
 
 6o,5 
 
 I.I4643 
 
 .0716 
 
 .85528 
 
 60,8 
 
 .OOIII 
 
 
 .85417 
 
 60,4 
 
 .14583 
 
 .0717 
 
 .85589 
 
 60,7 
 
 .OOII2 
 
 
 .85478 
 
 60,4 
 
 . 14522 
 
 .0718 
 
 .85650 
 
 60,6 
 
 .OOII2 
 
 
 .85538 
 
 60,3 
 
 .14462 
 
 .0719 
 
 .85710 
 
 60,5 
 
 .OOII2 
 
 
 .85598 
 
 60,2 
 
 .14402 
 
 0.0720 
 
 8.85771 
 
 60,4 
 
 O.OOII2 
 
 0,3 
 
 8.85658 
 
 60,1 
 
 I . 14342 
 
 .0721 
 
 .85831 
 
 60,3 
 
 .00113 
 
 
 .85718 
 
 60,0 
 
 .14282 
 
 .0722 
 
 .85891 
 
 60,3 
 
 .00113 
 
 
 .85778 
 
 59,9 
 
 .14222 
 
 .0723 
 
 .85952 
 
 60,2 
 
 .00113 
 
 
 .85838 
 
 59,9 
 
 .14162 
 
 .0724 
 
 .86012 
 
 60,1 
 
 .OOII4 
 
 
 .85898 
 
 
 .14102 
 
 0.0725 
 
 8.86072 
 
 60,0 
 
 O.OOII4 . 
 
 0,3 
 
 8.85958 
 
 59,7 
 
 I . 14042 
 
 .0726 
 
 .86132 
 
 59,9 
 
 .OOII4 
 
 
 .86017 
 
 59,6 
 
 .13983 
 
 .0727 
 
 .86192 
 
 59,8 
 
 .00115 
 
 
 .86077 
 
 59,5 
 
 .13923 
 
 .0728 
 
 .86251 
 
 59,8 
 
 .00115 
 
 
 .86137 
 
 59,5 
 
 13863 
 
 .0729 
 
 .86311 
 
 59,7 
 
 .OOII5 
 
 
 .86196 
 
 59,4 
 
 .13804 
 
 0.0730 
 
 8.86371 
 
 59,6 
 
 O.OOII6 
 
 0,3 
 
 8.86255 
 
 59,3 
 
 I . 13745 
 
 .0731 
 
 .86430 
 
 59,5 
 
 .00116 
 
 
 .86314 
 
 59,2 
 
 .13686 
 
 .0732 
 
 .86400 
 
 59,4 
 
 .OOIl6 
 
 
 .86374 
 
 59,1 
 
 .13626 
 
 .0733 
 
 .86549 
 
 59,4 
 
 .OOII7 
 
 
 .86433 
 
 59,0 
 
 .13507 
 
 .0734 
 
 .86609 
 
 59,3 
 
 .00117 
 
 
 .86492 
 
 59,0 
 
 .13508 
 
 0.0735 
 
 8.86668 
 
 59,2 
 
 O.OOII7 
 
 o,3 
 
 8.86551 
 
 58,9 
 
 I. 13449 
 
 .0736 
 
 .86727 
 
 59,1 
 
 .OOIlS 
 
 
 .86609 
 
 58,8 
 
 .13391 
 
 0737 
 
 .86786 
 
 59,o 
 
 .OOIlS 
 
 
 .86668 
 
 58,7 
 
 .13332 
 
 .0738 
 
 .86845 
 
 59,0 
 
 .OOIlS 
 
 
 .86727 
 
 58,6 
 
 . 13273 
 
 .0739 
 
 .86904 
 
 58,9 
 
 .OOIlS 
 
 
 .86785 
 
 58,6 
 
 .13215 
 
 0.0740 
 
 8.86963 
 
 58,8 
 
 O.OOII9 
 
 0,3 
 
 8.86844 
 
 58,5 
 
 I.I3I56 
 
 .0741 
 
 .87022 
 
 58,7 
 
 .OOII9 
 
 
 .86902 
 
 58,4 
 
 .13098 
 
 .0742 
 
 .87080 
 
 58,6 
 
 .OOII9 
 
 
 .86961 
 
 58,3 
 
 . 13039 
 
 .0743 
 
 87139 
 
 58,6 
 
 .OOI2O 
 
 
 .87019 
 
 58,2 
 
 .12981 
 
 .0744 
 
 .87197 
 
 58,5 
 
 .OOI20 
 
 
 .87077 
 
 58,2 
 
 .12923 
 
 0.0745 
 
 8.87256 
 
 584 
 
 O.OOI2O 
 
 0,3 
 
 8.87135 
 
 58,1 
 
 1.12865 
 
 .0746 
 
 .87314 
 
 58,3 
 
 .OOI2I 
 
 
 .87193 
 
 58,0 
 
 .13807 
 
 .0747 
 
 .87372 
 
 58,2 
 
 .00121 
 
 
 .87251 
 
 57,9 
 
 . 12749 
 
 .0748 
 
 .87431 
 
 58,2 
 
 .00121 
 
 
 .87309 
 
 57,8 
 
 .12691 
 
 .0749 
 
 .87489 
 
 58,1 
 
 .00122 
 
 
 .87367 
 
 57,8 
 
 .12633 
 
 0.0750 
 
 8.87547 
 
 58,0 
 
 O.OOI22 
 
 0,3 
 
 8.87425 
 
 57,7 
 
 I. I 2575 
 
 u 
 
 log tan <jd u 
 
 Fo' 
 
 log sec gd u 
 
 Fo' 
 
 log sin gd u 
 
 -Fo' 
 
 log esc gd u 
 
 SMITHSONIAN TABLES 
 
 16 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 - Fo' 
 
 log cosh u 
 
 F O ' 
 
 log tanh u 
 
 Fo' 
 
 log coth u 
 
 0.0750 
 
 8.87547 
 
 58,0 
 
 O.OOI22 
 
 0,3 
 
 8.87425 
 
 57,7 
 
 I.I2575 
 
 .0751 
 
 .87605 
 
 57,9 
 
 .OOI22 
 
 
 .87482 
 
 57,6 
 
 .12518 
 
 .0752 
 
 .87663 
 
 57,9 
 
 .00123 
 
 
 .87540 
 
 57,5 
 
 .12460 
 
 0753 
 
 .87721 
 
 57,8 
 
 .00123 
 
 
 .87508 
 
 57,5 
 
 . 12402 
 
 .0754 
 
 .87778 
 
 57,7 
 
 .00123 
 
 
 .87655 
 
 57,4 
 
 12345 
 
 0.0755 
 
 8.87836 
 
 57,6 
 
 O.OOI24 
 
 0,3 
 
 8.87712 
 
 57,3 
 
 I.I2288 
 
 .0756 
 
 .87894 
 
 57,6 
 
 .OOI24 
 
 
 .87770 
 
 57,2 
 
 . 12230 
 
 .0757 
 
 .8795*1 
 
 57,5 
 
 .OOI24 
 
 
 .87827 
 
 57,2 
 
 .12173 
 
 .0758 
 
 .88009 
 
 57,4 
 
 .00125 
 
 
 .87884 
 
 57,i 
 
 .12116 
 
 .0759 
 
 .88066 
 
 57,3 
 
 .00125 
 
 
 .87941 
 
 57,o 
 
 .12059 
 
 0.0760 
 
 8.88123 
 
 57,3 
 
 O.OOI25 
 
 0,3 
 
 8.87098 
 
 56,9 
 
 I . 12002 
 
 .0761 
 
 .88180 
 
 57,2 
 
 .OOI26 
 
 
 .88055 
 
 56,8 
 
 .11945 
 
 .0762 
 
 .88238 
 
 57,1 
 
 .OOI26 
 
 
 .88112 
 
 56,8 
 
 .11888 
 
 .0763 
 
 .88295 
 
 57,o 
 
 .OOI26 
 
 
 .88168 
 
 56,7 
 
 .11832 
 
 .0764 
 
 .88352 
 
 57,o 
 
 .00127 
 
 
 .88225 
 
 56,6 
 
 .H775 
 
 0.0765 
 
 8.88408 
 
 56,9 
 
 O.OOI27 
 
 0,3 
 
 8.88282 
 
 56,5 
 
 1.11718 
 
 .0766 
 
 .88465 
 
 56,8 
 
 .OOI27 
 
 
 .88338 
 
 56,5 
 
 .11662 
 
 .0767 
 
 .88522 
 
 56,7 
 
 .OOI28 
 
 
 .88394 
 
 56,4 
 
 .11606 
 
 .0768 
 
 .88579 
 
 56,7 
 
 .00128 
 
 
 .88451 
 
 56,3 
 
 .H549 
 
 .0769 
 
 .88635 
 
 56,6 
 
 .OOI28 
 
 
 .88507 
 
 56,3 
 
 .H493 
 
 0.0770 
 
 8.88692 
 
 56,5 
 
 0.00129 
 
 0,3 
 
 8.88563 
 
 56,2 
 
 i. H437 
 
 .0771 
 
 .88748 
 
 56,4 
 
 .OOI29 
 
 
 .88620 
 
 56,i 
 
 .11380 
 
 .0772 
 
 .88805 
 
 56,4 
 
 .OOI29 
 
 
 .88676 
 
 56,0 
 
 .11324 
 
 .0773- 
 
 .88861 
 
 56,3 
 
 .OOI3O 
 
 
 .88732 
 
 56,0 
 
 .11268 
 
 .0774 
 
 .88917 
 
 56,2 
 
 .00130 
 
 
 .88787 
 
 55,9 
 
 .11213 
 
 0.0775 
 
 8.88974 
 
 56,2 
 
 O.OOI3O 
 
 0,3 
 
 8.88843 
 
 55,8 
 
 1.11157 
 
 .0776 
 
 .89030 
 
 56,1 
 
 .00131 
 
 
 .88899 
 
 55,7 
 
 .IIIOI 
 
 .0777 
 
 .89086 
 
 56,o 
 
 .00131 
 
 
 .88955 
 
 55,7 
 
 .11045 
 
 .0778 
 
 .89142 
 
 55,9 
 
 .00131 
 
 
 .89010 
 
 55,6 
 
 .10990 
 
 0779 
 
 .89198 
 
 55,9 
 
 .00132 
 
 
 .89066 
 
 55,5 
 
 .10934 
 
 0.0780 
 
 8.89253 
 
 55,8 
 
 0.00132 
 
 0,3 
 
 8.89122 
 
 55.5 
 
 i . 10878 
 
 .0781 
 
 .89309 
 
 55,7 
 
 .00132 
 
 
 .89177 
 
 55,4 
 
 .10823 
 
 .0782 
 
 .89365 
 
 55,6 
 
 .00133 
 
 
 .89232 
 
 55,3 
 
 .10768 
 
 .0783 
 
 .89421 
 
 55,6 
 
 .00133 
 
 
 .89288 
 
 55,2 
 
 . 10712 
 
 .0784 
 
 .89476 
 
 55,5 
 
 .00133 
 
 
 .89343 
 
 55,2 
 
 .10657 
 
 0.0785 
 
 8.89532 
 
 55,4 
 
 O.OOI34 
 
 0,3 
 
 8.89398 
 
 55,1 
 
 1.10602 
 
 .0786 
 
 .89587 
 
 55,4 
 
 .00134 
 
 
 .89453' 
 
 55,0 
 
 .10547 
 
 .0787 
 
 .89642 
 
 55,3 
 
 .00134 
 
 
 .89508 
 
 55,o 
 
 .10492 
 
 .0788 
 
 .89698 
 
 55,2 
 
 .00135 
 
 
 .89563 
 
 54,9 
 
 . 10437 
 
 .0789 
 
 .89753 
 
 55,2 
 
 .00135 
 
 
 .89618 
 
 54,8 
 
 . 10382 
 
 0.0790 
 
 8.89808 
 
 55,i 
 
 . 0.00135 
 
 0,3 
 
 8.89672 
 
 54,7 
 
 i . 10328 
 
 .0791 
 
 .89863 
 
 55,o 
 
 .00136 
 
 
 .89727 
 
 54,7 
 
 . 10273 
 
 .0792 
 
 .89918 
 
 54,9 
 
 .00136 
 
 
 .89782 
 
 54,6 
 
 .10218 
 
 .0793 
 
 .89973 
 
 54,9 
 
 .00136 
 
 
 .89836 
 
 54,5 
 
 . 10164 
 
 .0794 
 
 .90028 
 
 54,8 
 
 .00137 
 
 
 .89891 
 
 54,5 
 
 .10109 
 
 0.0795 
 
 8.90082 
 
 54,7 
 
 0.00137 . 
 
 0,3 
 
 8.89945 
 
 54,4 
 
 I . 10055 
 
 .0796 
 
 .00137 
 
 54,7 
 
 .00137 
 
 
 .90000 
 
 54,3 
 
 .10000 
 
 .0797 
 
 .90192 
 
 54,6 
 
 .00138 
 
 
 .90054 
 
 54,3 
 
 .09946 
 
 .0798 
 
 .90246 
 
 54,5 
 
 .00138 
 
 
 .90108 
 
 54,2 
 
 .09892 
 
 0799 
 
 .90301 
 
 54,5 
 
 .00138 
 
 
 .90162 
 
 54,1 
 
 .09838 
 
 0.0800 
 
 8.90355 
 
 54,4 
 
 0.00139 
 
 0,3 
 
 8.90216 
 
 54,1 
 
 1.09784 
 
 u 
 
 log tan gd u 
 
 Fo' 
 
 log sec gd u 
 
 Fo' 
 
 log sin gd u 
 
 Fo' 
 
 log esc gd u 
 
 SMITHSONIAN TABLES 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 Fo' 
 
 log cosh u 
 
 F ' 
 
 log tanh u 
 
 Fo' 
 
 log coth u 
 
 0.0800 
 
 8.00355 
 
 54,4 
 
 0.00139 
 
 0,3 
 
 8.90216 
 
 54,1 
 
 1.09784 
 
 .0801 
 
 .90410 
 
 54,3 
 
 .00139 
 
 
 .90271 
 
 54,0 
 
 .09729 
 
 .0802 
 
 .90464 
 
 54,3 
 
 .00140 
 
 
 .00324 
 
 53,9 
 
 .09676 
 
 .0803 
 
 .90518 
 
 54,2 
 
 .00140 
 
 
 .90380 
 
 53,9 
 
 .09620 
 
 .0804 
 
 .90572 
 
 54,1 
 
 .00140 
 
 
 .90432 
 
 53,8 
 
 .09568 
 
 0.0805 
 
 8.90626 
 
 54,1 
 
 0.00141 
 
 o,3 
 
 8.90486 
 
 53,7 
 
 I.095I4 
 
 .0806 
 
 .90681 
 
 54,0 
 
 .00141 
 
 o,3 
 
 .90540 
 
 53,6 
 
 .09460 
 
 .0807 
 
 90734 
 
 53,9 
 
 .00141 
 
 o,3 
 
 90593 
 
 ' 53,6 
 
 .00407 
 
 .0808 
 
 .00788 
 
 53,9 
 
 .00142 
 
 0,4 
 
 .90647 
 
 53,5 
 
 .09353 
 
 .0809 
 
 .00842 
 
 53,8 
 
 .00142 
 
 0,4 
 
 .90700 
 
 53,4 
 
 .09300 
 
 0.0810 
 
 8.00896 
 
 53,7 
 
 O.OOI42 
 
 0,4 
 
 8.90754 
 
 53,4 
 
 1.09246 
 
 .0811 
 
 .90950 
 
 53,7 
 
 .00143 
 
 
 .90807 
 
 53,3 
 
 .09193 
 
 .0812 
 
 .91003 
 
 53,6 
 
 .00143 
 
 
 .90860 
 
 53,3 
 
 .09140 
 
 .0813 
 
 .91057 
 
 53,5 
 
 .00143 
 
 
 .90914 
 
 53,2 
 
 .09086 
 
 .0814 
 
 .91110 
 
 53,5 
 
 .00144 
 
 
 .90967 
 
 53,1 
 
 .09033 
 
 0.0815 
 
 8.91164 
 
 53,4 
 
 0.00144 
 
 0,4 
 
 8.9IO2O 
 
 53,1 
 
 1.08980 
 
 .0816 
 
 .91217 
 
 53,3 
 
 .00144 
 
 
 .91073 
 
 53,0 
 
 .08927 
 
 .0817 
 
 .91271 
 
 53,3 
 
 .00145 
 
 
 .91126 
 
 52,9 
 
 .08874 
 
 .0818 
 
 .91324 
 
 53,2 
 
 .00145 
 
 
 .91179 
 
 52,9 
 
 .08821 
 
 .0819 
 
 .91377 
 
 53,1 
 
 .00145 
 
 
 .91231 
 
 52,8 
 
 .08769 
 
 0.0820 
 
 8.91430 
 
 53,1 
 
 0.00146 
 
 0,4 
 
 8.91284 
 
 52,7 
 
 1.08716 
 
 .0821 
 
 .91483 
 
 53,0 
 
 .00146 
 
 
 .91337 
 
 52,7 
 
 .08663 
 
 .0822 
 
 .91536 
 
 53,o 
 
 .00147 
 
 
 .91390 
 
 52,6 
 
 .08610 
 
 .0823 
 
 .91589 
 
 52,9 
 
 .00147 
 
 
 .91442 
 
 52,5 
 
 .08558 
 
 .0824 
 
 .91642 
 
 52,8 
 
 .00147 
 
 
 .91495 
 
 52,5 
 
 .08505 
 
 0.0825 
 
 8.91695 
 
 52,8 
 
 0.00148 
 
 0,4 
 
 8.91547 
 
 52,4 
 
 1.08453 
 
 .0826 
 
 .91747 
 
 52,7 
 
 .00148 
 
 
 .91599 
 
 52,3 
 
 .08401 
 
 .0827 
 
 .91800 
 
 52,6 
 
 .00148 
 
 
 .91652 
 
 52,3 
 
 .08348 
 
 .0828 
 
 .91853 
 
 52,6 
 
 .00149 
 
 
 .91704 
 
 52,2 
 
 .08296 
 
 .0829 
 
 .91905 
 
 52,5 
 
 .00149 
 
 
 .91756 
 
 52,1 
 
 .08244 
 
 0.0830 
 
 8.91958 
 
 52,4 
 
 0.00149 
 
 0,4 
 
 8.91808 
 
 52,1 
 
 1.08192 
 
 .0831 
 
 .92010 
 
 52,4 
 
 .00150 
 
 
 .91860 
 
 52,0 
 
 .08140 
 
 .0832 
 
 .92062 
 
 52,3 
 
 .00150 
 
 
 .91912 
 
 52,0 
 
 .08088 
 
 .0833 
 
 .92115 
 
 52,3 
 
 .00151 
 
 
 .91964 
 
 51,9 
 
 .08036 
 
 .0834 
 
 .92167 
 
 52,2 
 
 .00151 
 
 
 .92016 
 
 51,8 
 
 .07984 
 
 0.0835 
 
 8.92219 
 
 52,1 
 
 0.00151 
 
 0,4 
 
 8.92068 
 
 5i,8 
 
 1.07932 
 
 .0836 
 
 .92271 
 
 52,1 
 
 .00152 
 
 
 .92120 
 
 5i,7 
 
 .07880 
 
 .0837 
 
 .92323 
 
 52,0 
 
 .00152 
 
 
 .92171 
 
 5i,6 
 
 .07829 
 
 .0838 
 
 .92375 
 
 5i,9 
 
 .00152 
 
 
 .92223 
 
 5i,6 
 
 .07777 
 
 .0839 
 
 .92427 
 
 5i,9 
 
 .00153 
 
 
 .92274 
 
 5i,5 
 
 .07726 
 
 0.0840 
 
 8.02479 
 
 51,8 
 
 0.00153 
 
 0,4 
 
 8.92326 
 
 51,5 
 
 1.07674 
 
 .0841 
 
 .92531 
 
 5i,8 
 
 .00153 
 
 
 .92377 
 
 51,4 
 
 .07623 
 
 .0842 
 
 .92583 
 
 5i,7 
 
 .00154 
 
 
 .92429 
 
 51,3 
 
 07571 
 
 .0843 
 
 .92634 
 
 5i,6 
 
 .00154 
 
 
 .92480 
 
 51,3 
 
 .07520 
 
 .0844 
 
 .92686 
 
 51,6 
 
 .00154 
 
 
 .92531 
 
 51,2 
 
 .07469 
 
 0.0845 
 
 8.92737 
 
 51,5 
 
 0.00155 
 
 0,4 
 
 8.92582 
 
 51,2 
 
 1.07418 
 
 .0846 
 
 .92789 
 
 5i,5 
 
 .00155 
 
 
 .92634 
 
 5i,i 
 
 .07366 
 
 .0847 
 
 .92840 
 
 5M 
 
 .00156 
 
 
 .92685 
 
 51,0 
 
 .07315 
 
 .0848 
 
 .92892 
 
 51,3 
 
 .00156 
 
 
 .92736 
 
 5i,o 
 
 .07264 
 
 .0849 
 
 .92943 
 
 51,3 
 
 .00156 
 
 
 .92787 
 
 50,9 
 
 .07213 
 
 0.0850 
 
 8.92994 
 
 51,2 
 
 0.00157 
 
 0,4 
 
 8.92837 
 
 50,8 
 
 1.07163 
 
 u 
 
 log tin fld u 
 
 - Fo' 
 
 log tec gd u 
 
 - Fo' 
 
 log sin gd u 
 
 -FO' 
 
 log esc gd u 
 
 SMITHSONIAN TABLES 
 
 18 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 Fo' 
 
 log cosh u 
 
 F ' 
 
 log tanh u 
 
 F ' 
 
 log coth u 
 
 0.0850 
 
 8.92994 
 
 51,2 
 
 0.00157 
 
 0,4 
 
 8.92837 
 
 50,8 
 
 1.07163 
 
 .0851 
 
 .93045 
 
 51,2 
 
 .00157 
 
 
 .92888 
 
 50,8 
 
 .07112 
 
 .0852 
 
 .93096 
 
 51,1 
 
 .00157 
 
 
 .92939 
 
 50,7 
 
 .07061 
 
 .0853 
 
 .93148 
 
 51,0 
 
 .00158 
 
 
 .92990 
 
 50,7 
 
 .O7OIO 
 
 .0854 
 
 .93199 
 
 51,0 
 
 .00158 
 
 
 .93040 
 
 50,6 
 
 .06960 
 
 0.0855 
 
 8.93250 
 
 50,9 
 
 0.00159 
 
 0,4 
 
 8.93091 
 
 50,5 
 
 1.06909 
 
 .0856 
 
 .93300 
 
 50,9 
 
 .00159 
 
 
 .93141 
 
 50,5 
 
 .06859 
 
 .0857 
 
 .93351 
 
 50,8 
 
 .00159 
 
 
 .93192 
 
 50,4 
 
 .06808 
 
 .08^8 
 
 .93402 
 
 50,7 
 
 .00160 
 
 
 .93242 
 
 50,4 
 
 .06758 
 
 .0859 
 
 93453 
 
 50,7 
 
 .00160 
 
 
 .93293 
 
 50,3 
 
 .06707 
 
 0.0860 
 
 8.93503 
 
 50,6 
 
 0.00160 
 
 0,4 
 
 8.93343 
 
 50,3 
 
 1.06657 
 
 .0861 
 
 93554 
 
 50,6 
 
 .00161 
 
 
 93393 
 
 50,2 
 
 .06607 
 
 .0862 
 
 .93604 
 
 50,5 
 
 .00161 
 
 
 .93443 
 
 50,1 
 
 06557 
 
 .0863 
 
 .93655 
 
 50,4 
 
 .00162 
 
 
 93493 
 
 50,i 
 
 .06507 
 
 .0864 
 
 .93705 
 
 50,4 
 
 .00162 
 
 
 .93543 
 
 50,o 
 
 .06457 
 
 0.0865 
 
 8.93756 
 
 50,3 
 
 0.00162 
 
 0,4 
 
 8.93593 
 
 50,o 
 
 1.06407 
 
 .0866 
 
 .938o6 
 
 50,3 
 
 .00163 
 
 
 .93643 
 
 49,9 
 
 .06357 
 
 .0867 
 
 .93856 
 
 50,2 
 
 .00163 
 
 
 .93693 
 
 49,8 
 
 .06307 
 
 .0868 
 
 93907 
 
 50,2 
 
 .00163 
 
 
 93743 
 
 49,8 
 
 .06257 
 
 .0869 
 
 93957 
 
 50,i 
 
 .00164 
 
 
 93793 
 
 49,7 
 
 .06207 
 
 0.0870 
 
 8.94007 
 
 50,o 
 
 0.00164 
 
 0,4 
 
 8.93843 
 
 49,7 
 
 I.06I57 
 
 .0871 
 
 .94057 
 
 50,0 
 
 .00165 
 
 
 .93892 
 
 49,6 
 
 .06108 
 
 .0872 
 
 .94107 
 
 49,9 
 
 .00165 
 
 
 93942 
 
 49,6 
 
 .0605? 
 
 .0873 
 
 .94157 
 
 49,9 
 
 .00165 
 
 
 .93991 
 
 49,5 
 
 .06009 
 
 .0874 
 
 .94206 
 
 49,8 
 
 .00166 
 
 
 .04041 
 
 49,4 
 
 .05959 
 
 0.0875 
 
 8.94256 
 
 49,8 
 
 0.00166 
 
 0,4 
 
 8.94090 
 
 49,4 
 
 1.05910 
 
 .0876 
 
 .94306 
 
 49,7 
 
 .00166 
 
 
 .94140 
 
 49,3 
 
 .05860 
 
 .0877 
 
 .94356 
 
 49,6 
 
 .00167 
 
 
 .04189 
 
 49,3 
 
 .05811 
 
 .0878 
 
 .94405 
 
 49,6 
 
 .00167 
 
 
 .94238 
 
 49,2 
 
 .05762 
 
 .0879 
 
 .94455 
 
 49,5 
 
 .00168 
 
 
 .94287 
 
 49,2 
 
 .05713 
 
 0.0880 
 
 8.94504 
 
 49,5 
 
 0.00168 
 
 0,4 
 
 8.94336 
 
 49,1 
 
 1.05664 
 
 .0881 
 
 .94554 
 
 49,4 
 
 .00168 
 
 
 94385 
 
 49,0 
 
 .05615 
 
 .0882 
 
 .94603 
 
 49,4 
 
 .00169 
 
 
 94434 
 
 49,0 
 
 .05566 
 
 .0883 
 
 .94652 
 
 49,3 
 
 .00169 
 
 
 .94483 
 
 48,9 
 
 .05517 
 
 .0884 
 
 .94702 
 
 49,3 
 
 .00169 
 
 
 94532 
 
 48,9 
 
 .05468 
 
 0.0885 
 
 8.94751 
 
 49,2 
 
 0.00170 
 
 0,4 
 
 8.94581 
 
 48,8 
 
 1.05419 
 
 .0886 
 
 .94800 
 
 49,1 
 
 .06170 
 
 
 .94630 
 
 48,8 
 
 .05370 
 
 .0887 
 
 .94849 
 
 49,1 
 
 .00171 
 
 
 94679 
 
 48,7 
 
 .05321 
 
 .0888 
 
 .94898 
 
 49,0 
 
 .00171 
 
 
 .94727 
 
 48,7 
 
 .05273 
 
 .0889 
 
 .94947 
 
 49,0 
 
 .00171 
 
 
 .94776 
 
 48,6 
 
 .05224 
 
 0.0890 
 
 8.94996 
 
 48,9 
 
 0.00172 
 
 0,4 
 
 8.94825 
 
 48,5 
 
 I.05I75 
 
 .0891 
 
 .95045 
 
 48,9 
 
 .00172 
 
 
 .94873 
 
 48,5 
 
 .05127 
 
 .0892 
 
 .95094 
 
 48,8 
 
 .00173 
 
 
 .94922 
 
 48,4 
 
 .05078 
 
 .0893 
 
 .95143 
 
 48,8 
 
 .00173 
 
 
 .94970 
 
 48,4 
 
 .05030 
 
 .0894 
 
 .95192 
 
 48,7 
 
 .00173 
 
 
 .95018 
 
 48,3 
 
 .04982 
 
 0.0895 
 
 8.95240 
 
 48,7 
 
 0.00174 
 
 0,4 
 
 8.95067 
 
 48,3 
 
 1.04933 
 
 .0896 
 
 .95289 
 
 48,6 
 
 .00174 
 
 
 .95H5 
 
 48,2 
 
 .04885 
 
 .0897 
 
 95337 
 
 48,5 
 
 .00174 
 
 
 .95163 
 
 48,2 
 
 .04837 
 
 .0898 
 
 .95386 
 
 48,5 
 
 .00175 
 
 
 .95211 
 
 48,1 
 
 .04789 
 
 .0899 
 
 95434 
 
 48,4 
 
 .00175 
 
 
 .95259 
 
 48,0 
 
 .04741 
 
 0.0900 
 
 8.95483 
 
 48,4 
 
 0.00176 
 
 0,4 
 
 8.95307 
 
 48,0 
 
 1.04693 
 
 u 
 
 log tan gd u 
 
 Fo' 
 
 log sec gd u 
 
 F ' 
 
 log sin gd u 
 
 Fo' 
 
 log esc gd u 
 
 SMITHSONIAN TABLES 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 Fo' 
 
 log cosh u 
 
 F</ 
 
 log tanh u 
 
 Fo' 
 
 log coth u 
 
 0.0900 
 
 8.95483 
 
 48,4 
 
 0.00176 
 
 0,4 
 
 8.95307 
 
 48,0 
 
 1.04693 
 
 .0901 
 
 95531 
 
 48,3 
 
 .00176 
 
 
 95355 
 
 47,9 
 
 .04645 
 
 .0902 
 
 .95580 
 
 48,3 
 
 .00176 
 
 
 .95403 
 
 47,9 
 
 04597 
 
 .0903 
 
 .95628 
 
 48,2 
 
 .00177 
 
 
 95451 
 
 47,8 
 
 .04549 
 
 .0904 
 
 .95676 
 
 48>2 
 
 .00177 
 
 
 95499 
 
 47,8 
 
 .04501 
 
 0.0905 
 
 8.95724 
 
 48,1 
 
 0.00178 
 
 0,4 
 
 8-95547 
 
 47,7 
 
 1.04453 
 
 .0906 
 
 957/2 
 
 48,1 
 
 .00178 
 
 
 95594 
 
 47,7 
 
 .04406 
 
 .0907 
 
 .95820 
 
 48,0 
 
 .00178 
 
 
 95642 
 
 47,6 
 
 04358 
 
 .0908 
 
 .95868 
 
 48,0 
 
 .00179 
 
 
 .95689 
 
 47,6 
 
 .04311 
 
 .0909 
 
 .95916 
 
 47,9 
 
 .00179 
 
 
 95737 
 
 47,5 
 
 .04263 
 
 0.0910 
 
 8.95964 
 
 47,9 
 
 0.00180 
 
 0,4 
 
 8.95784 
 
 47,5 
 
 1.04216 
 
 .0911 
 
 .96012 
 
 47,8 
 
 .00180 
 
 
 .95832 
 
 47,4 
 
 .04168 
 
 .0912 
 
 .96060 
 
 47,8 
 
 .00180 
 
 
 .95879 
 
 47,4 
 
 .04121 
 
 .0913 
 
 .96107 
 
 47,7 
 
 .00181 
 
 
 .95927 
 
 47,3 
 
 .04073 
 
 .0914 
 
 .96155 
 
 47,6 
 
 .00181 
 
 
 95974 
 
 47,3 
 
 .04026 
 
 0.0915 
 
 8.96203 
 
 47,6 
 
 0.00182 
 
 0,4 
 
 8.96021 
 
 47,2 
 
 1.03979 
 
 .0910 
 
 .96250 
 
 47,5 
 
 .00182 
 
 
 .96068 
 
 47,1 
 
 .03932 
 
 .0917 
 
 .96298 
 
 47,5 
 
 .00182 
 
 
 96115 
 
 47,1 
 
 .03885 
 
 .0918 
 
 .96345 
 
 47,4 
 
 .00183 
 
 
 96163 
 
 47,0 
 
 03837 
 
 .0919 
 
 .96393 
 
 47,4 
 
 .00183 
 
 
 .96210 
 
 47,0 
 
 .03790 
 
 0.0920 
 
 8.96440 
 
 47,3 
 
 0.00184 
 
 0,4 
 
 8.96256 
 
 46,9 
 
 1.03744 
 
 .0921 
 
 .96487 
 
 47,3 
 
 .00184 
 
 
 96303 
 
 46,9 
 
 .03697 
 
 .0922 
 
 .96535 
 
 47,2 
 
 .00184 
 
 
 .96350 
 
 46,8 
 
 .03650 
 
 .0923 
 
 .96582 
 
 47,2 
 
 .00185 
 
 
 .96397 
 
 46,8 
 
 .03603 
 
 .0924 
 
 .96629 
 
 47,1 
 
 .00185 
 
 
 .96444 
 
 46,7 
 
 .03556 
 
 0.0925 
 
 8.96676 
 
 47,1 
 
 0.00186 
 
 0,4 
 
 8.96491 
 
 46,7 
 
 1.03509 
 
 .0926 
 
 .96723 
 
 47,0 
 
 .00186 
 
 
 96537 
 
 46,6 
 
 03463 
 
 .0927 
 
 .96770 
 
 47,0 
 
 .00186 
 
 
 .96584 
 
 46,6 
 
 .03416 
 
 .0928 
 
 .96817 
 
 46,9 
 
 .00187 
 
 
 .96630 
 
 46,5 
 
 03370 
 
 .0929 
 
 .96864 
 
 46,9 
 
 .00187 
 
 
 .96677 
 
 46,5 
 
 .03323 
 
 0.0930 
 
 8.96911 
 
 46,8 
 
 0.00188 
 
 0,4 
 
 8.96723 
 
 46,4 
 
 1.03277 
 
 .0931 
 
 .96958 
 
 46,8 
 
 .00188 
 
 
 .96770 
 
 46,4 
 
 .03230 
 
 .0932 
 
 .97004 
 
 46,7 
 
 .00188 
 
 
 .96816 
 
 46,3 
 
 .03184 
 
 0933 
 
 .97051 
 
 46,7 
 
 .00189 
 
 
 .96862 
 
 46,3 
 
 .03138 
 
 0934 
 
 .97098 
 
 46,6 
 
 .00189 
 
 
 .96909 
 
 46,2 
 
 .03091 
 
 0.0935 
 
 8.97144 
 
 46,6 
 
 0.00190 
 
 0,4 
 
 8.96955 
 
 46,2 
 
 1.03045 
 
 .0936 
 
 .97191 
 
 46,5 
 
 .00190 
 
 
 .97001 
 
 ,46,1 
 
 .02999 
 
 0937 
 
 .97237 
 
 46,5 
 
 .00190 
 
 
 .97047 
 
 46,1 
 
 .02953 
 
 .0938 
 
 .97284 
 
 46,4 
 
 .00191 
 
 
 97093 
 
 46,0 
 
 .02007 
 
 0939 
 
 97330 
 
 46,4 
 
 .00191 
 
 
 .97139 
 
 46,0 
 
 .02861 
 
 0.0040 
 
 8.97377 
 
 46,3 
 
 0.00192 
 
 0,4 
 
 8.97185 
 
 45,9 
 
 1.02815 
 
 .0941 
 
 .97423 
 
 46,3 
 
 .00102 
 
 
 .97231 
 
 45,9 
 
 .02769 
 
 .0942 
 
 .97469 
 
 46,2 
 
 .OOI92 
 
 
 .97277 
 
 45,8 
 
 .02723 
 
 .0943 
 
 .97516 
 
 46,2 
 
 .00193 
 
 
 97323 
 
 45,8 
 
 .02677 
 
 .0944 
 
 .97562 
 
 46,1 
 
 .00193 
 
 
 .97368 
 
 45,7 
 
 .02632 
 
 0.0945 
 
 8.97608 
 
 46,1 
 
 O.OOT94 
 
 0,4 
 
 8.974M 
 
 45,7 
 
 1.02586 
 
 .0946 
 
 .97654 
 
 46,0 
 
 .00194 
 
 
 .97460 
 
 45,6 
 
 .02540 
 
 .0947 
 
 97700 
 
 46,0 
 
 .00194 
 
 
 .97505 
 
 45,6 
 
 .02495 
 
 .0948 
 
 .97746 
 
 45,9 
 
 .00195 
 
 
 97551 
 
 45,5 
 
 .02449 
 
 .0949 
 
 97792 
 
 45,9 
 
 .00195 
 
 
 .97597 
 
 45,5 
 
 .02403 
 
 0.0950 
 
 8.97838 
 
 45,9 
 
 0.00106 
 
 OA 
 
 8.9764-' 
 
 45,4 
 
 1.02358 
 
 u 
 
 loo tan gd u 
 
 -Fo' 
 
 loo sec gd u 
 
 Fo' 
 
 log sin gd u 
 
 Fo' 
 
 log esc gd u 
 
 SMITHSONIAN TABLES 
 
 20 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 Fo' 
 
 log cosh u 
 
 F ' 
 
 log tanh u 
 
 Fo' 
 
 log coth u 
 
 0.0950 
 
 8.97838 
 
 45,9 
 
 0.00196 
 
 0,4 
 
 8.97642 
 
 45,4 
 
 1.02358 
 
 .0951 
 
 .97883 
 
 45,8 
 
 .00196 
 
 
 .97687 
 
 45,4 
 
 .02313 
 
 .0952 
 
 .97929 
 
 45,8 
 
 .00197 
 
 
 97733 
 
 45,3 
 
 .02267 
 
 .0953 
 
 .97975 
 
 45,7 
 
 .00197 
 
 
 .97778 
 
 45,3 
 
 .02222 
 
 .0954 
 
 .98021 
 
 45,7 
 
 .00197 
 
 
 .97823 
 
 45,2 
 
 .02177 
 
 0.0955 
 
 8.98066 
 
 45,6 
 
 0.00198 
 
 0,4 
 
 8.97869 
 
 45,2 
 
 1.02131 
 
 .0956 
 
 .98112 
 
 45,6 
 
 .00198 
 
 
 .979H 
 
 45,2 
 
 .02086 
 
 .0957 
 
 .98157 
 
 45,5 
 
 .00199 
 
 
 .97959 
 
 45,i 
 
 .02041 
 
 .0958 
 
 .98203 
 
 45,5 
 
 .00199 
 
 
 .98004 
 
 45,1 
 
 .01996 
 
 .0959 
 
 .98248 
 
 45*4 
 
 .00199 
 
 
 .98049 
 
 45,0 
 
 .01951 
 
 0.0960 
 
 8.98294 
 
 45,4 
 
 0<O02po 
 
 0,4 
 
 8.98094 
 
 45,0 
 
 1.01906 
 
 .0961 
 
 .98339 
 
 45,3 
 
 .00200 
 
 
 .98139 
 
 44,9 
 
 .01861 
 
 .0962 
 
 .98384 
 
 45,3 
 
 .OO2OI 
 
 
 .98184 
 
 44,9 
 
 .01816 
 
 .0963 
 
 .98430 
 
 45,2 
 
 .00201 
 
 
 .98229 
 
 44,& 
 
 .01771 
 
 .0964 
 
 .98475 
 
 45,2 
 
 .00201 
 
 
 98273 
 
 44,8 
 
 .01727 
 
 0.0965 
 
 8.98520 
 
 45,1 
 
 0.00202 
 
 0,4 
 
 8.98318 
 
 44,7 
 
 1.01682 
 
 .0966 
 
 .98565 
 
 45,1 
 
 .OO202 
 
 
 .98363 
 
 44,7 
 
 .01637 
 
 .0967 
 
 .98610 
 
 45,1 
 
 .00203 
 
 
 .98408 
 
 44,6 
 
 .01592 
 
 .0968 
 
 .98655 
 
 45,o 
 
 , .00203 
 
 
 .98452 
 
 44,6 
 
 .01548 
 
 .0969 
 
 .98700 
 
 45,o 
 
 .OO2O4 
 
 
 .98497 
 
 44,5 
 
 .01503 
 
 0.0970 
 
 8.98745 
 
 44,9 
 
 O.O02O4 
 
 0,4 
 
 8.98541 
 
 44,5 
 
 1. 01459 
 
 .0971 
 
 .98790 
 
 44,9 
 
 .OO2O4 
 
 
 .98586 
 
 44,5 
 
 .01414 
 
 .0972 
 
 .08835 
 
 44,8 
 
 .OO2O5 
 
 
 .98630 
 
 44,4 
 
 .01370 
 
 .0973 
 
 .08880 
 
 44,8 
 
 .OO2O5 
 
 
 .98675 
 
 44,4 
 
 .01325 
 
 .0974 
 
 .98925 
 
 44,7 
 
 .00206 
 
 
 .98719 
 
 44,3 
 
 .01281 
 
 0.0975 
 
 8.98969 
 
 44,7 
 
 O.O0206 
 
 0,4 
 
 8.98763 
 
 44,3 
 
 1.01237 
 
 .0976 
 
 .90014 
 
 44,6 
 
 .00207 
 
 
 .98807 
 
 44,2 
 
 .01193 
 
 .0977 
 
 .99059 
 
 44,6 
 
 .O02O7 
 
 
 .98852 
 
 44,2 
 
 .01148 
 
 .0978 
 
 .99103 
 
 44,5 
 
 .OO2O7 
 
 
 .98896 
 
 44,1, 
 
 .01104 
 
 .0979 
 
 .99148 
 
 44,5 
 
 .O0208 
 
 
 .98940 
 
 44,1 
 
 .01060 
 
 0.0980 
 
 8.99192 
 
 44,5 
 
 O.OO2O8 
 
 0,4 
 
 8.98984 
 
 44,0 
 
 I. 01016 
 
 .0981 
 
 .99237 
 
 44,4 
 
 .00209 
 
 
 .99028 
 
 44,0 
 
 .00972 
 
 .0982 
 
 .99281 
 
 44,4 
 
 .OO2O9 
 
 
 .99072 
 
 43,9 
 
 .00928 
 
 .0983 
 
 99325 
 
 44,3 
 
 .O02O9 
 
 
 .99116 
 
 43,9 
 
 .00884 
 
 .0984 
 
 99370 
 
 44,3 
 
 .00210 
 
 
 .99160 
 
 43,9 
 
 .00840 
 
 0.0985 
 
 8.99414 
 
 44,2 
 
 0.00210 
 
 0,4 
 
 8.09203 
 
 43,8 
 
 1.00797 
 
 .0986 
 
 .99458 
 
 44,2 
 
 .OO2II 
 
 
 .99247 
 
 43,8 
 
 .00753 
 
 .0987 
 
 .99502 
 
 44,2 
 
 .002 I I 
 
 
 .99291 
 
 43,7 
 
 .00709 
 
 .0988 
 
 .99546 
 
 44,1 
 
 .00212 
 
 
 .99335 
 
 43,7 
 
 .0066,5 
 
 .0989 
 
 .99590 
 
 44,1- 
 
 .OO2I2 
 
 
 .99378 
 
 43,6 
 
 .006*22 
 
 0.0090 
 
 8.99634 
 
 44,0 
 
 O.OO2I2 
 
 0,4 
 
 8.99422 
 
 43,6 
 
 1.00578 
 
 .0991 
 
 .99678 
 
 44,0 
 
 .00213 
 
 
 .99466 
 
 43,5 
 
 .00534 
 
 .0992 
 
 .99722 
 
 43,9 
 
 .00213 
 
 
 .99509 
 
 43,5 
 
 .00491 
 
 .0993 
 
 .99766 
 
 43,9 
 
 .OO2I4 
 
 
 99553 
 
 43,4 
 
 .00447 
 
 .0994 
 
 .99810 
 
 43,8 
 
 .00214 
 
 
 .99596 
 
 43,4 
 
 .00404 
 
 0.0095 
 
 8.99854 
 
 43,8 
 
 0.00215 
 
 0,4 
 
 8.99639 
 
 43,4 
 
 1.00361 
 
 .0096 
 
 .99898 
 
 43,7 
 
 .00215 
 
 
 .99683 
 
 43,3 
 
 .00317 
 
 .0997 
 
 .99941 
 
 43,7 
 
 .00215 
 
 
 .99726 
 
 43,2 
 
 .00274 
 
 .0098 
 
 .99985 
 
 43,7 
 
 .002X6 
 
 
 .99769 
 
 43,2- 
 
 .00231 
 
 .0999 
 
 9.00029 
 
 43,6 
 
 .00216 
 
 
 .99812 
 
 43,2. 
 
 .00188 
 
 O.IOOO 
 
 9.00072 
 
 43,6 
 
 0.00217 
 
 0,4 
 
 8.99856 
 
 43,1 
 
 1.00144 
 
 u 
 
 log tan gd u 
 
 Fn' 
 
 log sec gd u 
 
 F ' 
 
 log sin gd u 
 
 Fo' 
 
 log esc gd u 
 
 SMITHSONIAN TABLES 
 
 21 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 Fo' 
 
 log cosh u 
 
 F O ' 
 
 log tanh u 
 
 Fo' 
 
 log coth u 
 
 O.IOO 
 
 9.00072 
 
 435,7 
 
 O.OO2I7 
 
 4,3 
 
 8.99856 
 
 431,4 
 
 1.00144 
 
 .IOI 
 
 .00506 
 
 431,5 
 
 .OO22I 
 
 4,4 
 
 9.00285 
 
 427,1 
 
 0.99715 
 
 .102 
 
 00935 
 
 427,3 
 
 .00226 
 
 4,4 
 
 .00710 
 
 422,8 
 
 .99290 
 
 .103 
 
 .01360 
 
 423,1 
 
 .00230 
 
 4,5 
 
 .01131 
 
 418,7 
 
 .98869 
 
 .104 
 
 .01782 
 
 419,1 
 
 .00234 
 
 4,5 
 
 .01547 
 
 414,6 
 
 98453 
 
 0.105 
 
 9.02199 
 
 415,1 
 
 0.00239 
 
 4,5 
 
 9.01960 
 
 410,6 
 
 0.98040 
 
 .106 
 
 .02612 
 
 411,2 
 
 .00244 
 
 4,6 
 
 .02368 
 
 406,7 
 
 .97632 
 
 .107 
 
 .03021 
 
 407,4 
 
 .00248 
 
 4,6 
 
 .02773 
 
 402,8 
 
 .97227 
 
 .108 
 
 .03427 
 
 403,7 
 
 .00253 
 
 4,7 
 
 .03174 
 
 399,o 
 
 .96826 
 
 .109 
 
 .03829 
 
 400,0 
 
 .00257 
 
 4,7 
 
 .03571 
 
 395,3 
 
 .96429 
 
 O.IIO 
 
 9.04227 
 
 396,4 
 
 0.00262 
 
 4,8 
 
 9.03965 
 
 391,6 
 
 0.96035 
 
 .III 
 
 .04621 
 
 392,9 
 
 .00267 
 
 4,8 
 
 -04354 
 
 388,1 
 
 .95646 
 
 .112 
 
 .05013 
 
 389,4 
 
 .00272 
 
 4,8 
 
 .04741 
 
 384,5 
 
 .95259 
 
 113 
 
 .05400 
 
 386,0 
 
 .00277 
 
 4,9 
 
 .05124 
 
 381,1 
 
 .94876 
 
 .114 
 
 05785 
 
 382,6 
 
 .00282 
 
 4,9 
 
 .05503 
 
 377,7 
 
 .94497 
 
 O.IIS 
 
 9.06165 
 
 379,3 
 
 O.O0287 
 
 5,0 
 
 9.05879 
 
 374,3 
 
 0.94121 
 
 .116 
 
 .06543 
 
 376,1 
 
 .OO292 
 
 5,0 
 
 .06252 
 
 37i,i 
 
 .93748 
 
 .117 
 
 .06918 
 
 372,9 
 
 .00297 
 
 5,i 
 
 .06621 
 
 367,8 
 
 .93379 
 
 .118 
 
 .07289 
 
 309,8 
 
 .00302 
 
 5,1 
 
 .06987 
 
 364,7 
 
 .93013 
 
 .119 
 
 .07657 
 
 366,7 
 
 .00307 
 
 5,i 
 
 .07350 
 
 36i,5 
 
 .92650 
 
 O.I2O 
 
 9.08022 
 
 363,6 
 
 0.00312 
 
 5,2 
 
 9.07710 
 
 358,5 
 
 0.92290 
 
 .121 
 
 .08384 
 
 360,7 
 
 .00317 
 
 5,2 
 
 .08067 
 
 355,4 
 
 .91933 
 
 .122 
 
 .08744 
 
 357,7 
 
 .00322 
 
 5,3 
 
 .08421 
 
 352,5 
 
 .91579 
 
 .123 
 
 .09100 
 
 354,9 
 
 .00328 
 
 5,3 
 
 .08772 
 
 349,5 
 
 .91228 
 
 .124 
 
 .09453 
 
 352,0 
 
 .00333 
 
 5,4 
 
 .09120 
 
 346,7 
 
 .90880 
 
 O.I25 
 
 9.09804 
 
 349,2 
 
 0.00338 
 
 5,4 
 
 9.09466 
 
 343,8 
 
 0.90534 
 
 .126 
 
 .10152 
 
 346,5 
 
 .00344 
 
 5,4 
 
 .09808 
 
 34i,i 
 
 .00192 
 
 .127 
 
 . 10497 
 
 343,8 
 
 .00349 
 
 5,5 
 
 . 10148 
 
 338,3 
 
 .89852 
 
 .128 
 
 .10840 
 
 34M 
 
 .00355 
 
 5,5 
 
 . 10485 
 
 335,6 
 
 .89515 
 
 .129 
 
 .11179 
 
 338,5 
 
 .00360 
 
 5,6 
 
 .10819 
 
 333,0 
 
 .89181 
 
 0.130 
 
 9.H5I7 
 
 336,0 
 
 0.00366 
 
 5,6 
 
 9.IH5I 
 
 330,3 
 
 0.88849 
 
 .131 
 
 .11851 
 
 333,4 
 
 .00372 
 
 5,7 
 
 .11480 
 
 327,8 
 
 .88520 
 
 .132 
 
 .12183 
 
 330,9 
 
 .00377 
 
 5,7 
 
 .11806 
 
 325,2 
 
 .88194 
 
 .133 
 
 .12513 
 
 328,5 
 
 .00383 
 
 5,7 
 
 .12130 
 
 322,7 
 
 .87870 
 
 .134 
 
 .12840 
 
 326,0 
 
 .00389 
 
 5,8 
 
 .12452 
 
 320,3 
 
 .87548 
 
 0.135 
 
 9.I3I65 
 
 323,7 
 
 0.00395 
 
 5,8 
 
 9.I277I 
 
 317,8 
 
 0.87229 
 
 .136 
 
 .13488 
 
 321,3 
 
 .00400 
 
 5,9 
 
 .13087 
 
 315,4 
 
 .86913 
 
 .137 
 
 .13808 
 
 319,0 
 
 .00406 
 
 5,9 
 
 . 13402 
 
 3i3,i 
 
 .86598 
 
 .138 
 
 .14126 
 
 3i6,7 
 
 .00412 
 
 6,0 
 
 .13713 
 
 3io,7 
 
 .86287 
 
 .139 
 
 .14441 
 
 314,5 
 
 .00418 
 
 6,0 
 
 . 14023 
 
 308,5 
 
 .85977 
 
 0.140 
 
 9- 14755 
 
 312,2 
 
 0.00424 
 
 6,0 
 
 9.14330 
 
 306,2 
 
 0.85670 
 
 .141 
 
 .15066 
 
 310,0 
 
 .00430 
 
 6,1 
 
 .14635 
 
 304,0 
 
 .85365 
 
 .142 
 
 .15375 
 
 307,9 
 
 .00436 
 
 6,1 
 
 .14938 
 
 301,8 
 
 .85062 
 
 143 
 
 .15682 
 
 305,8 
 
 .00443 
 
 6,2 
 
 .15239 
 
 299,6 
 
 .84761 
 
 .144 
 
 .15986 
 
 303,7 
 
 .00449 
 
 6,2 
 
 .15538 
 
 297,5 
 
 .84462 
 
 0.145 
 
 9.16289 
 
 301,6 
 
 0.00455 
 
 6,3 
 
 9.15834 
 
 295,4 
 
 0.84166 
 
 .146 
 
 .16589 
 
 299,6 
 
 .00461 
 
 6,3 
 
 .16128 
 
 293,3 
 
 .83872 
 
 .147 
 
 .16888 
 
 297,6 
 
 .00468 
 
 6,3 
 
 .16420 
 
 291,2 
 
 .83580 
 
 .148 
 
 .17185 
 
 295,6 
 
 .00474 
 
 6,4 
 
 .16711 
 
 289,2 
 
 .83289 
 
 .149 
 
 17479 
 
 293,6 
 
 .00480 
 
 6,4 
 
 .16999 
 
 287,2 
 
 .83001 
 
 0.150 
 
 9.17772 
 
 291,7 
 
 0.00487 
 
 6,5 
 
 9-17285 
 
 285,2 
 
 0.82715 
 
 u 
 
 log tan ad u 
 
 Fo' 
 
 log sec gd u 
 
 -Fo' 
 
 log sin gd u 
 
 Fo' 
 
 log esc gd u 
 
 SMITHSONIAN TABLES 
 
 22 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 Fo' 
 
 log cosh u 
 
 F<>' 
 
 log tanh u 
 
 Fo' 
 
 log coth u 
 
 0.150 
 
 9- 17772 
 
 291,7 
 
 0.00487 
 
 6,5 
 
 9.17285 
 
 285,2 
 
 0.82715 
 
 .151 
 
 .18063 
 
 289,8 
 
 .00493 
 
 6,5 
 
 .17569 
 
 283,3 
 
 .82431 
 
 .152 
 
 .18351 
 
 287,9 
 
 .00500 
 
 6,6 
 
 .17852 
 
 281,4 
 
 .82148 
 
 .153 
 
 .18638 
 
 286,1 
 
 .00506 
 
 6,6 
 
 . 18132 
 
 279,5 
 
 .81868 
 
 .154 
 
 .18924 
 
 284,2 
 
 .00513 
 
 6,6 
 
 .18411 
 
 277,6 
 
 .81589 
 
 0.155 
 
 9.19207 
 
 282,4 
 
 0.00520 
 
 6,7 
 
 9.18687 
 
 275,8 
 
 0.81313 
 
 .156 
 
 .19488 
 
 280,6 
 
 .00526 
 
 6,7 
 
 .18962 
 
 273,9 
 
 .81038 
 
 .157 
 
 .19768 
 
 278,9 
 
 .00533 
 
 6,8 
 
 . 19235 
 
 272,1 
 
 .80765 
 
 .158 
 
 .20046 
 
 277,1 
 
 .00540 
 
 6,8 
 
 .19506 
 
 270,3 
 
 .80494 
 
 .159 
 
 .20323 
 
 275,4 
 
 .00547 
 
 6,8 
 
 . 19776 
 
 268,6 
 
 .80224 
 
 0.160 
 
 9.20597 
 
 273,7 
 
 0.00554 
 
 6,9 
 
 9.20044 
 
 266,9 
 
 0.79956 
 
 .161 
 
 .20870 
 
 272,1 
 
 .00560 
 
 6,9 
 
 .20310 
 
 265,1 
 
 .79690 
 
 .162 
 
 .21141 
 
 270,4 
 
 .00567 
 
 7,o 
 
 .20574 
 
 263,4 
 
 .79426 
 
 .163 
 
 .21411 
 
 268,8 
 
 .00574 
 
 7,o 
 
 .20837 
 
 261,8 
 
 .79163 
 
 .164 
 
 .21679 
 
 267,2 
 
 .00581 
 
 7,i 
 
 .21097 
 
 260,1 
 
 .78903 
 
 0.165 
 
 9.21945 
 
 265,6 
 
 0.00589 
 
 7,i 
 
 9.21357 
 
 258,5 
 
 0.78643 
 
 .166 
 
 .22210 
 
 264,0 
 
 .00506 
 
 7,1 
 
 .21614 
 
 256,9 
 
 .78386 
 
 .167 
 
 .22473 
 
 262,5 
 
 .00603 
 
 7,2 
 
 .21871 
 
 255,3 
 
 .78129 
 
 .168 
 
 .22735 
 
 260,9 
 
 .00610 
 
 7,2 
 
 .22125 
 
 253,7 
 
 .77875 
 
 .169 
 
 .22995 
 
 259,4 
 
 .00617 
 
 7,3 
 
 .22378 
 
 252,2 
 
 .77622 
 
 0.170 
 
 9.23254 
 
 257,9 
 
 0.00625 
 
 7,3 
 
 9.22629 
 
 250,6 
 
 0.77371 
 
 .171 
 
 .23511 
 
 256,4 
 
 .00632 
 
 7,4 
 
 .22879 
 
 249,1 
 
 .77121 
 
 .172 
 
 .23767 
 
 255,0 
 
 .00639 
 
 7,4 
 
 .23128 
 
 247,6 
 
 .76872 
 
 .173 
 
 .24021 
 
 253,5 
 
 .00647 
 
 7,4 
 
 .23374 
 
 246,1 
 
 .76626 
 
 .174 
 
 .24274 
 
 252,1 
 
 .00654 
 
 7,5 
 
 .23620 
 
 244,6 
 
 .76380 
 
 0.175 
 
 9.24525 
 
 250,7 
 
 0.00662 
 
 7,5 
 
 9.23864 
 
 243,2 
 
 0.76136 
 
 .176 
 
 .24775 
 
 249,3 
 
 .00669 
 
 7,6 
 
 .24106 
 
 241,7 
 
 .75894 
 
 .177 
 
 .25024. 
 
 247,9 
 
 .00677 
 
 7,6 
 
 .24347 
 
 240,3 
 
 .75653 
 
 .178 
 
 .25271 
 
 246,5 
 
 .00684 
 
 7,6 
 
 .24587 
 
 238,9 
 
 .75413 
 
 .179 
 
 .25517 
 
 245,2 
 
 .00692 
 
 7,7 
 
 .24825 
 
 237,5 
 
 .75175 
 
 0.180 
 
 9-25762 
 
 243,9 
 
 0.00700 
 
 7,7 
 
 9.25062 
 
 236,1 
 
 0.74938 
 
 .181 
 
 .26005 
 
 242,5 
 
 .00708 
 
 7,8 
 
 .25297 
 
 234,8 
 
 .74703 
 
 .182 
 
 .26247 
 
 241,3 
 
 .00715 
 
 7,8 
 
 .25531 
 
 233,4 
 
 .74469 
 
 .183 
 
 .26487 
 
 240,0 
 
 .00723 
 
 7,9 
 
 .25764 
 
 232,1 
 
 .74236 
 
 .184 
 
 .26727 
 
 238,7 
 
 .00731 
 
 7,9 
 
 .25996 
 
 230,8 
 
 .74004 
 
 0.185 
 
 9-26965 
 
 237,4 
 
 0.00739 
 
 7,9 
 
 9.26226 
 
 229,5 
 
 0.73774 
 
 .186 
 
 .27201 
 
 236,2 
 
 .00747 
 
 8,0 
 
 .26454 
 
 228,2 
 
 .73546 
 
 .187 
 
 .27437 
 
 234,9 
 
 .00755 
 
 8,0 
 
 .26682 
 
 226,9 
 
 .73318 
 
 .188 
 
 .27671 
 
 233,7 
 
 .00763 
 
 8,1 
 
 .26908 
 
 225,7 
 
 .73092 
 
 .189 
 
 .27904 
 
 232,5 
 
 .00771 
 
 8,1 
 
 .27133 
 
 224,4 
 
 .72867 
 
 O.IOO 
 
 9.28136 
 
 231,3 
 
 0.00779 
 
 8,2 
 
 9.27357 
 
 223,2 
 
 0.72643 
 
 .191 
 
 .28367 
 
 230,1 
 
 .00787 
 
 8,2 
 
 .27580 
 
 221,9 
 
 .72420 
 
 .192 
 
 .28597 
 
 229,0 
 
 .00796 
 
 8,2 
 
 .27801 
 
 220,7 
 
 .72109 
 
 .193 
 
 .28825 
 
 227,8 
 
 .00804 
 
 8,3 
 
 .28021 
 
 219,5 
 
 .71979 
 
 .194 
 
 .20052 
 
 226,7 
 
 .00812 
 
 8,3 
 
 .28240 
 
 218,3 
 
 .71760 
 
 0.195 
 
 9.29278 
 
 225,5 
 
 0.00821 
 
 8,4 
 
 9.28458 
 
 217,2 
 
 0.71542 
 
 .196 
 
 .29503 
 
 224,4 
 
 .00829 
 
 8,4 
 
 .28674 
 
 216,0 
 
 .71326 
 
 .197 
 
 .29727 
 
 223,3 
 
 .00837 
 
 8,4 
 
 .28890 
 
 214,9 
 
 .71110 
 
 .198 
 
 .20950 
 
 222,2 
 
 .00846 
 
 8,5 
 
 .29104 
 
 213,7 
 
 .70896 
 
 .199 
 
 .30172 
 
 221,1 
 
 .00854 
 
 8,5 
 
 .29317 
 
 212,6 
 
 .70683 
 
 O.2OO 
 
 9.30392 
 
 22O,O 
 
 0.00863 
 
 8,6 
 
 9.29529 
 
 211,5 
 
 0.70471 
 
 U 
 
 log tan gd u 
 
 Fo' 
 
 log sec gd u 
 
 F ' 
 
 log sin gd u 
 
 F ' 
 
 log esc gd u 
 
 SMITHSONIAN TABLES 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 Fo' 
 
 log cosh u 
 
 Fo' 
 
 log tanh u 
 
 Fo' 
 
 log coth u 
 
 O.200 
 
 9.30392 
 
 22O,0 
 
 0.00863 
 
 8,6 
 
 9.29529 
 
 211,5 
 
 0.70471 
 
 .201 
 
 .30612 
 
 219,0 
 
 .00871 
 
 8,6 
 
 .29740 
 
 210,4 
 
 .70200 
 
 .202 
 
 .30830 
 
 217,9 
 
 .00880 
 
 8,7 
 
 .29950 
 
 209,3 
 
 .70050 
 
 .203 
 
 .31047 
 
 2 1 6,9 
 
 .00889 
 
 8,7 
 
 .30159 
 
 208,2 
 
 .69841 
 
 .204 
 
 .31264 
 
 215,8 
 
 .00897 
 
 8,7 
 
 .30366 
 
 207,1 
 
 .69634 
 
 O.205 
 
 9.31479 
 
 214,8 
 
 0.00906 
 
 8,8 
 
 9.30573 
 
 206,0 
 
 0.69427 
 
 .206 
 
 .31693 
 
 213,8 
 
 .00915 
 
 8,8 
 
 .30778 
 
 205,0 
 
 .69222 
 
 .207 
 
 .31907 
 
 212,8 
 
 .00924 
 
 8,9 
 
 .30983 
 
 203,9 
 
 .69017 
 
 .208 
 
 .32119 
 
 211,8 
 
 .00933 
 
 8,9 
 
 .31186 
 
 202,9 
 
 .68814 
 
 .209 
 
 .32330 
 
 210,8 
 
 .00942 
 
 8,9 
 
 .31389 
 
 20 1, 9 
 
 .68611 
 
 0.2IO 
 
 9.32541 
 
 209,8 
 
 0.00951 
 
 9,0 
 
 9.31590 
 
 200,8 
 
 0.68410 
 
 .211 
 
 .32750 
 
 208,9 
 
 .00960 
 
 9,0 
 
 .31790 
 
 199,8 
 
 .68210 
 
 .212 
 
 .32958 
 
 207,9 
 
 .00969 
 
 9,i 
 
 .31000 
 
 198,8 
 
 .68010 
 
 .213 
 
 .33166 
 
 207,0 
 
 .00978 
 
 9,1 
 
 .32188 
 
 197,9 
 
 .67812 
 
 .214 
 
 33372 
 
 206,0 
 
 .00987 
 
 9,2 
 
 .32385 
 
 196,9 
 
 .67615 
 
 O.2I5 
 
 9.33578 
 
 205,1 
 
 0.00996 
 
 9,2 
 
 9.32582 
 
 195,9 
 
 0.67418 
 
 .216 
 
 .33783 
 
 204,2 
 
 .01005 
 
 9,2 
 
 .32777 
 
 194,9 
 
 .67223 
 
 .217 
 
 .33986 
 
 203,3 
 
 .OIOI5 
 
 9,3 
 
 .32972 
 
 194,0 
 
 .67028 
 
 .218 
 
 .34189 
 
 202,4 
 
 .01024 
 
 9,3 
 
 .33165 
 
 I93,o 
 
 .66835 
 
 .219 
 
 34391 
 
 201,5 
 
 .01033 
 
 9,4 
 
 .33358 
 
 192,1 
 
 .66642 
 
 O.220 
 
 9-34592 
 
 200,6 
 
 0.01043 
 
 9,4 
 
 9-33549 
 
 191,2 
 
 0.66451 
 
 .221 
 
 34792 
 
 199,7 
 
 .01052 
 
 9,4 
 
 33740 
 
 190,3 
 
 .66260 
 
 .222 
 
 .34991 
 
 198,8 
 
 .01062 
 
 9,5 
 
 33930 
 
 189,3 
 
 .66070 
 
 .223 
 
 .35190 
 
 198,0 
 
 .01071 
 
 9,5 
 
 .34119 
 
 188,4 
 
 .65881 
 
 .224 
 
 .35387 
 
 197,1 
 
 .01081 
 
 9,6 
 
 34307 
 
 187,5 
 
 .65693 
 
 O.225 
 
 9.35584 
 
 196,3 
 
 O.OIOOO 
 
 9,6 
 
 9-34494 
 
 186,7 
 
 0.65506 
 
 .226 
 
 .35780 
 
 195,4 
 
 .OIIOO 
 
 9,7 
 
 .34680 
 
 185,8 
 
 .65320 
 
 .227 
 
 35975 
 
 194,6 
 
 .01109 
 
 9,7 
 
 .34865 
 
 184,9 
 
 .65135 
 
 .228 
 
 .36169 
 
 193,8 
 
 .01119 
 
 9,7 
 
 .35050 
 
 184,0 
 
 .64950 
 
 .229 
 
 .36362 
 
 193,0 
 
 .OII2Q 
 
 9,8 
 
 .35234 
 
 183,2 
 
 .64766 
 
 0.23O 
 
 9.36555 
 
 192,1 
 
 O.OII39 
 
 9,8 
 
 9.35416 
 
 182,3 
 
 0.64584 
 
 .231 
 
 .36747 
 
 I9i,3 
 
 .OII49 
 
 9,9 
 
 .35598 
 
 181,5 
 
 .64402 
 
 .232 
 
 .36938 
 
 190,5 
 
 .OII58 
 
 9,9 
 
 35779 
 
 180,6 
 
 .64221 
 
 233 
 
 .37128 
 
 189,8 
 
 .01168 
 
 9,9 
 
 35959 
 
 179,8 
 
 .64047 
 
 234 
 
 .37317 
 
 189,0 
 
 .01178 
 
 IO,O 
 
 .36139 
 
 179,0 
 
 .63861 
 
 0.235 
 
 9.37506 
 
 188,2 
 
 O.OII88 
 
 IO,O 
 
 9-36317 
 
 178,2 
 
 0.63683 
 
 .236 
 
 .37694 
 
 187,4 
 
 .01198 
 
 10,1 
 
 .36495 
 
 177,4 
 
 .63505 
 
 237 
 
 .37881 
 
 186,7 
 
 .OI208 
 
 10,1 
 
 .36672 
 
 176,6 
 
 .63328 
 
 .238 
 
 .38067 
 
 185,9 
 
 .OI2I9 
 
 10,1 
 
 .36848 
 
 175,8 
 
 .63152 
 
 239 
 
 .38252 
 
 185,2 
 
 .01229 
 
 IO,2 
 
 .37024 
 
 175,0 
 
 .62976 
 
 0.240 
 
 9.38437 
 
 184,4 
 
 0.01239 
 
 10,2 
 
 9.37198 
 
 174,2 
 
 0.62802 
 
 .241 
 
 .38621 
 
 183,7 
 
 .01249 
 
 10,3 
 
 .37372 
 
 173,4 
 
 .62628 
 
 .242 
 
 .38805 
 
 183,0 
 
 .01259 
 
 10,3 
 
 .37545 
 
 172,6 
 
 .62455 
 
 243 
 
 .38987 
 
 182,2 
 
 .01270 
 
 10,4 
 
 .37717 
 
 I7L9 
 
 .62283 
 
 .244 
 
 .39169 
 
 181,5 
 
 .01280 
 
 10,4 
 
 .37889 
 
 171,1 
 
 .62111 
 
 0.245 
 
 9.39350 
 
 180,8 
 
 0.01291 
 
 10,4 
 
 9.38060 
 
 170,4 
 
 0.61940 
 
 .246 
 
 .39531 
 
 180,1 
 
 .01301 
 
 10,5 
 
 .38230 
 
 169,6 
 
 .61770 
 
 .247 
 
 .39710 
 
 179,4 
 
 .01312 
 
 10,5 
 
 .38309 
 
 168,9 
 
 .61601 
 
 .248 
 
 .30889 
 
 178,7 
 
 .01322 
 
 10,6 
 
 .38567 
 
 168,1 
 
 .61433 
 
 .249 
 
 .40068 
 
 178,0 
 
 .01333 
 
 10,6 
 
 .38735 
 
 167,4 
 
 .61265 
 
 0.250 
 
 9.40245 
 
 177,3 
 
 0.01343 
 
 10,6 
 
 9.38002 
 
 166,7 
 
 0.61098 
 
 u 
 
 log tan od u 
 
 Fo' 
 
 log sec gd u 
 
 -Fo' 
 
 log sin gd u 
 
 -Fo' 
 
 log esc gd u 
 
 SMITHSONIAN TABLES 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 *> Fo' 
 
 log cosh u 
 
 Fo' 
 
 log tanh u 
 
 Fo' 
 
 log coth u 
 
 0.250 
 
 9.40245 
 
 177,3 
 
 0.01343 
 
 10,6 
 
 9.38902 
 
 166,7 
 
 0.61098 
 
 .251 
 
 .40422 
 
 170,0 
 
 .01354 
 
 10,7 
 
 .39069 
 
 166,0 
 
 .60931 
 
 .252 
 
 .40599 
 
 176,0 
 
 .01365 
 
 10,7 
 
 .39234 
 
 165,3 
 
 .60766 
 
 .253 
 
 .40774 
 
 175,3 
 
 .01375 
 
 10,8 
 
 39399 
 
 164,5 
 
 .60601 
 
 254 
 
 .40949 
 
 174,6 
 
 .01386 
 
 10,8 
 
 .39563 
 
 163,8 
 
 .60437 
 
 0.255 
 
 9.4H24 
 
 174,0 
 
 0.01397 
 
 10,8 
 
 9.39727 
 
 163,1 
 
 0.60273 
 
 .256 
 
 .41297 
 
 173,3 
 
 .01408 
 
 10,9 
 
 .39890 
 
 162,5 
 
 .60110 
 
 .257 
 
 .41470 
 
 172,7 
 
 .01419 
 
 10,9 
 
 .40052 
 
 161,8 
 
 .59948 
 
 .258 
 
 .41043 
 
 172,0 
 
 .01430 
 
 II,O 
 
 .40213 
 
 161,1 
 
 .59787 
 
 .259 
 
 .41814 
 
 I7i,4 
 
 .01441 
 
 II,O 
 
 40374 
 
 160,4 
 
 .59626 
 
 0.260 
 
 9.41086 
 
 170,8 
 
 0.01452 
 
 II,O 
 
 9.40534 
 
 159,7 
 
 0.59466 
 
 .261 
 
 .42156 
 
 170,2 
 
 .01463 
 
 n, i 
 
 .40693 
 
 I59,i 
 
 .59307 
 
 .262 
 
 .42326 
 
 169,5 
 
 .01474 
 
 n, i 
 
 .40852 
 
 158,4 
 
 .59148 
 
 .263 
 
 .42495 
 
 168,9 
 
 .01485 
 
 11,2 
 
 .41010 
 
 157,8 
 
 
 .264 
 
 .42664 
 
 168,3 
 
 .01496 
 
 11,2 
 
 .41168 
 
 I57,i 
 
 .58832 
 
 0.265 
 
 9.42832 
 
 167,7 
 
 0.01507 
 
 11,2 
 
 9.41324 
 
 156,5 
 
 0.58676 
 
 .266 
 
 .42999 
 
 167,1 
 
 .01519 
 
 n,3 
 
 .41480 
 
 155,8 
 
 .58520 
 
 .267 
 
 .43166 
 
 166,5 
 
 .01530 
 
 n,3 
 
 .41636 
 
 155,2 
 
 .58364 
 
 .268 
 
 43332 
 
 165,9 
 
 .01541 
 
 11,4 
 
 .41791 
 
 154,5 
 
 .58209 
 
 .269 
 
 .43498 
 
 165,3 
 
 .01553 
 
 11,4 
 
 .41945 
 
 153,9 
 
 .58055 
 
 0.270 
 
 9.43663 
 
 164,7 
 
 0.01564 
 
 11,4 
 
 9.42099 
 
 153,3 
 
 0.57901 
 
 .271 
 
 .43827 
 
 164,2 
 
 .01576 
 
 n,5 
 
 .42252 
 
 152,7 
 
 .57748 
 
 .272 
 
 43991 
 
 163,6 
 
 .01587 
 
 n,5 
 
 .42404 
 
 152,1 
 
 .57596 
 
 .273 
 
 .44154 
 
 163,0 
 
 .01599 
 
 11,6 
 
 .42556 
 
 151,4 
 
 57444 
 
 .274 
 
 .44317 
 
 162,4 
 
 .01610 
 
 11,6 
 
 .42707 
 
 150,8 
 
 .57293 
 
 0.275 
 
 9.44479 
 
 161,9 
 
 0.01622 
 
 n,7 
 
 9.42857 
 
 150,2 
 
 0.57143 
 
 .276 
 
 .44641 
 
 161,3 
 
 .01634 
 
 n,7 
 
 .43007 
 
 149,6 
 
 .56993 
 
 .277 
 
 .44802 
 
 160,8 
 
 .01645 
 
 n,7 
 
 .43157 
 
 149,0 
 
 .56843 
 
 .278 
 
 .44962 
 
 160,2 
 
 .01657 
 
 11,8 
 
 .43305 
 
 148,5 
 
 .56695 
 
 .279 
 
 .45122 
 
 159,7 
 
 .01669 
 
 11,8 
 
 .43454 
 
 147,9 
 
 .56546 
 
 0.280 
 
 9.45282 
 
 I59,i 
 
 o. 01681 
 
 11,9 
 
 9.43601 
 
 147,3 
 
 0.56399 
 
 .281 
 
 .45441 
 
 158,6 
 
 .01693 
 
 11,9 
 
 .43748 
 
 146,7 
 
 .56252 
 
 .282 
 
 45599 
 
 158,1 
 
 .01704 
 
 11,9 
 
 .43895 
 
 146,1 
 
 .56105 
 
 .283 
 
 .45757 
 
 157,5 
 
 .01716 
 
 1 2,0 
 
 .44040 
 
 145,6 
 
 .55960 
 
 .284 
 
 .45914 
 
 I57,o 
 
 .01728 
 
 12,0 
 
 .44186 
 
 145,0 
 
 .55814 
 
 0.285 
 
 9.46071 
 
 156,5 
 
 0.01740 
 
 12,1 
 
 9.44330 
 
 144,4 
 
 0.55670 
 
 .286 
 
 .46227 
 
 156,0 
 
 .01752 
 
 12,1 
 
 44475 . 
 
 143,9 
 
 .55525 
 
 .287 
 
 .46383 
 
 155,5 
 
 .01765 
 
 12,1 
 
 .44618 
 
 143,3 
 
 .55382 
 
 .288 
 
 .46538 
 
 154,9 
 
 .01777 
 
 12,2 
 
 .44761 
 
 142,8 
 
 .55239 
 
 .289 
 
 .46693 
 
 154,4 
 
 .01789 
 
 12,2 
 
 .44904 
 
 142,2 
 
 .55096 
 
 0.290 
 
 9.46847 
 
 153,9 
 
 0.01801 
 
 12,3 
 
 9.45046 
 
 141,7 
 
 0.54954 
 
 .291 
 
 .47001 
 
 153,4 
 
 .01813 
 
 12,3 
 
 .45187 
 
 141,1 
 
 .54813 
 
 .292 
 
 .47154 
 
 152,9 
 
 .01826 
 
 12,3 
 
 .45328 
 
 140,6 
 
 .54672 
 
 .293 
 
 .47306 
 
 152,4 
 
 .01838 
 
 12,4 
 
 .45468 
 
 140,1 
 
 .54532 
 
 .294 
 
 .47459 
 
 152,0 
 
 .01851 
 
 12,4 
 
 .45608 
 
 139,5 
 
 54392 
 
 0.295 
 
 9.47610 
 
 I5i,5 
 
 0.01863 
 
 12,5 
 
 9-45747 
 
 139,0 
 
 0.54253 
 
 .296 
 
 .47762 
 
 151,0 
 
 .01875 
 
 12,5 
 
 .45886 
 
 138,5 
 
 .54H4 
 
 .297 
 
 .47912 
 
 150,5 
 
 .01888 
 
 12,5 
 
 .46024 
 
 138,0 
 
 .53976 
 
 .298 
 
 .48063 
 
 150,0 
 
 .01900 
 
 12,6 
 
 .46162 
 
 137,5 
 
 .53838 
 
 .299 
 
 .48212 
 
 149,6 
 
 .01913 
 
 12,6 
 
 .46299 
 
 136,9 
 
 .53701 
 
 0.300 
 
 9.48362 
 
 149,1 
 
 0.01926 
 
 12,7 
 
 9.46436 
 
 136,4 
 
 0.53564 
 
 u 
 
 log tan gd u 
 
 F O ' 
 
 log sec gd u 
 
 F</ 
 
 log sin gd u 
 
 F O ' 
 
 logcscgdu 
 
 SMITHSONIAN TABLES 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 Fo' 
 
 log cosh u 
 
 F ' 
 
 log tanh u 
 
 - Fo' 
 
 log coth u 
 
 0.300 
 
 9.48352 
 
 149,1 
 
 0.01926 
 
 12,7 
 
 9.40436 
 
 136,4 
 
 0.53564 
 
 .301 
 
 .48510 
 
 148,6 
 
 .01938 
 
 12,7 
 
 .46572 
 
 135,9 
 
 .53428 
 
 .302 
 
 .48J59 
 
 148,2 
 
 .01951 
 
 12,7 
 
 .46708 
 
 135,4 
 
 .53292 
 
 .303 
 
 .48807 
 
 U7,7 
 
 .01964 
 
 12,8 
 
 46843 
 
 134,9 
 
 .53157 
 
 .304 
 
 .48954 
 
 147,2 
 
 .01977 
 
 12,8 
 
 .46978 
 
 134,4 
 
 53022 
 
 0.305 
 
 9.49IOI 
 
 146,8 
 
 0.01989 
 
 12,8 
 
 9.47112 
 
 133,9 
 
 0.52888 
 
 .306 
 
 .49248 
 
 146,3 
 
 .02002 
 
 12,9 
 
 .47245 
 
 133,4 
 
 .52755 
 
 .307 
 
 49394 
 
 U5,9 
 
 .02015 
 
 12,9 
 
 47379 
 
 133,0 
 
 .52621 
 
 .308 
 
 49540 
 
 145,4 
 
 .02028 
 
 13,0 
 
 475II 
 
 132,5 
 
 .52489 
 
 .309 
 
 .49685 
 
 145,0 
 
 .02041 
 
 13,0 
 
 .47644 
 
 132,0 
 
 .52356 
 
 0.310 
 
 9.49830 
 
 144,6 
 
 0.02054 
 
 13,0 
 
 9-47775 
 
 I3L5 
 
 0.52225 
 
 .311 
 
 49974 
 
 I44,i 
 
 .02067 
 
 13,1 
 
 .47007 
 
 131,0 
 
 .52093 
 
 .312 
 
 .50118 
 
 H3,7 
 
 .02080 
 
 13,1 
 
 .48037 
 
 130,6 
 
 .51963 
 
 .313 
 
 .50261 
 
 143,3 
 
 .02094 
 
 13,2 
 
 .48168 
 
 130,1 
 
 51832 
 
 .314 
 
 .50404 
 
 142,8 
 
 .02107 
 
 13,2 
 
 .48298 
 
 129,6 
 
 .51702 
 
 0.315 
 
 9.50547 
 
 142,4 
 
 O.02I2O 
 
 13,2 
 
 9.48427 
 
 129,2 
 
 0.51573 
 
 .316 
 
 .50689 
 
 142,0 
 
 .02133 
 
 13,3 
 
 .48556 
 
 128,7 
 
 .51444 
 
 .317 
 
 .50831 
 
 141,6 
 
 .O2I4J 
 
 13,3 
 
 .48684 
 
 128,2 
 
 .51316 
 
 .318 
 
 .50972 
 
 141,1 
 
 .02l6o 
 
 13,4 
 
 .48812 
 
 127,8 
 
 .51188 
 
 .319 
 
 .51113 
 
 140,7 
 
 .02173 
 
 13,4 
 
 .48940 
 
 127,3 
 
 .51060 
 
 0.320 
 
 9.51254 
 
 140,3 
 
 O.O2I87 
 
 13,4 
 
 9.49067 
 
 126,9 
 
 0.50933 
 
 .321 
 
 .51394 
 
 139,9 
 
 .02200 
 
 13,5 
 
 .49194 
 
 126,4 
 
 .50806 
 
 .322 
 
 .51534 
 
 139,5 
 
 .O22I4 
 
 13,5 
 
 .49320 
 
 126,0 
 
 .50680 
 
 .323 
 
 .51673 
 
 I39,i 
 
 .O2227 
 
 13,6 
 
 .49446 
 
 125,5 
 
 .50554 
 
 .324 
 
 .51812 
 
 138,7 
 
 .02241 
 
 13,6 
 
 49571 
 
 125,1 
 
 .50429 
 
 0.325 
 
 9.51950 
 
 138,3 
 
 O.O2254 
 
 13,6 
 
 9.49696 
 
 124,7 
 
 0.50304 
 
 .326 
 
 .52088 
 
 137,9 
 
 .02268 
 
 13,7 
 
 .49820 
 
 124,2 
 
 .50180 
 
 .327 
 
 . 52226 
 
 137,5 
 
 .O2282 
 
 13,7 
 
 .49944 
 
 123,8 
 
 .50056 
 
 .328 
 
 .52363 
 
 I37,i 
 
 .02295 
 
 13,8 
 
 .50068 
 
 123,4 
 
 49932 
 
 .329 
 
 .52500 
 
 136,7 
 
 .02309 
 
 13,8 
 
 .50191 
 
 122,9 
 
 .49809 
 
 0.330 
 
 9-52637 
 
 136,3 
 
 O.02323 
 
 13,8 
 
 9.503U 
 
 122,5 
 
 0.49686 
 
 .331 
 
 .52773 
 
 136,0 
 
 .02337 
 
 13,9 
 
 .50436 
 
 122,1 
 
 .49564 
 
 .332 
 
 .52909 
 
 135,6 
 
 .02351 
 
 13,9 
 
 .50558 
 
 121,7 
 
 49442 
 
 333 
 
 53044 
 
 135,2 
 
 .02365 
 
 14,0 
 
 .50679 
 
 121,3 
 
 49321 
 
 334 
 
 .53179 
 
 134,8 
 
 .02379 
 
 14,0 
 
 .50800 
 
 120,8 
 
 .49200 
 
 0.335 
 
 9.53314 
 
 134,5 
 
 0.02393 
 
 14,0 
 
 9.50921 
 
 120,4 
 
 0.40079 
 
 336 
 
 .53448 
 
 - I34,i 
 
 .02407 
 
 14,1 
 
 .51041 
 
 1 2O,O 
 
 .48959 
 
 337 
 
 .53582 
 
 133,7 
 
 .02421 
 
 14,1 
 
 .51161 
 
 119,6 
 
 .48839 
 
 .338 
 
 .53715 
 
 133,3 
 
 02435 
 
 14,1 
 
 .51281 
 
 119,2 
 
 .48719 
 
 339 
 
 .53849 
 
 I33,o 
 
 .02449 
 
 14,2 
 
 .51400 
 
 118,8 
 
 .48600 
 
 0.340 
 
 9.53981 
 
 132,6 
 
 0.02463 
 
 14,2 
 
 9.5I5I8 
 
 1 1 8,4 
 
 0.48482 
 
 341 
 
 .54114 
 
 132,3 
 
 .02478 
 
 14,3 
 
 .51636 
 
 1 1 8,0 
 
 .48364 
 
 342 
 
 .54246 
 
 I3i,9 
 
 .02492 
 
 14,3 
 
 .51754 
 
 117,6 
 
 .48246 
 
 343 
 
 .54378 
 
 I3i,5 
 
 .025O6 
 
 14,3 
 
 .51872 
 
 117,2 
 
 .48128 
 
 344 
 
 .54509 
 
 131,2 
 
 .02520 
 
 14,4 
 
 .51989 
 
 116,8 
 
 .48011 
 
 0.345 
 
 9.54640 
 
 130,8 
 
 0.02535 
 
 14,4 
 
 9.52105 
 
 116,4 
 
 0.47895 
 
 .346 
 
 .54771 
 
 130,5 
 
 .02549 
 
 14,5 
 
 .52221 
 
 116,0 
 
 47779 
 
 347 
 
 .54901 
 
 130,1 
 
 .02564 
 
 14,5 
 
 .52337 
 
 H5,7 
 
 47 ' 3 
 
 .348 
 
 .55031 
 
 129,8 
 
 .02578 
 
 i-l,5 
 
 .52453 
 
 "5,3 
 
 47547 
 
 349 
 
 .55l6l 
 
 129,5 
 
 02593 
 
 14,6 
 
 .52568 
 
 114,9 
 
 47432 
 
 0.350 
 
 9.55200 
 
 129,1 
 
 0.02607 
 
 14,6 
 
 9.52682 
 
 "4,5 
 
 0.47318 
 
 u 
 
 log tan gd u 
 
 Fo' 
 
 log tec gd u 
 
 -Fo' 
 
 log sin gd u 
 
 Fo' 
 
 log esc gd u 
 
 SMITHSONIAN TABLES 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 Fo' 
 
 log cosh u 
 
 Fo' 
 
 log tanh u 
 
 Fo' 
 
 log coth u 
 
 0.350 
 
 9.55290 
 
 129,1 
 
 0.02607 
 
 14,6 
 
 9.52682 
 
 114,5 
 
 0.47318 
 
 .351 
 
 .55419 
 
 128,8 
 
 .02622 
 
 14,6 
 
 .52797 
 
 114,1 
 
 .47203 
 
 .352 
 
 .55547 
 
 128,4 
 
 .02637 
 
 14,7 
 
 .52911 
 
 H3,7 
 
 .47089 
 
 .353 
 
 .55676 
 
 128,1 
 
 .02651 
 
 14,7 
 
 .53024 
 
 H3,4 
 
 .46976 
 
 .354 
 
 .55804 
 
 127,8 
 
 .02666 
 
 14,8 
 
 .53137 
 
 H3,O 
 
 .46863 
 
 0.355 
 
 F*rw 
 
 9-55931 
 
 127,4 
 
 0.02681 
 
 14,8 
 
 9.53250 
 
 112,6 
 
 0.46750 
 
 .356 
 
 .56059 
 
 127,1 
 
 .02696 
 
 14,8 
 
 .53363 
 
 112,3 
 
 .46637 
 
 357 
 
 .56185 
 
 . 126,8 
 
 .02711 
 
 14,9 
 
 .53475 
 
 111,9 
 
 . .46525 
 
 358 
 
 .56312 
 
 126,5 
 
 .02726 
 
 14,9 
 
 53586 
 
 m,5 
 
 .46414 
 
 .359 
 
 .56438 
 
 126,1 
 
 .02740 
 
 I5,o 
 
 .53698 
 
 111,2 
 
 .46302 
 
 0.360 
 
 9-56564 
 
 125,8 
 
 0.02755 
 
 I5,o 
 
 9.53809 
 
 no,8 
 
 0.46191 
 
 .361 
 
 .56690 
 
 125,5 
 
 .02770 
 
 I5,o 
 
 .53919 
 
 110,5 
 
 .46081 
 
 .362 
 
 .56815 
 
 125,2 
 
 .02786 
 
 15,1 
 
 .54030 
 
 no, i 
 
 45970 
 
 .363 
 
 .56940 
 
 124,8 
 
 .02801 
 
 15,1 
 
 .54140 
 
 109,7 
 
 .45860 
 
 .364 
 
 .57065 
 
 124,5 
 
 .02816 
 
 15,1 
 
 .54249 
 
 109,4 
 
 45751 
 
 0.365 
 
 9.57189 
 
 124,2 
 
 0.02831 
 
 15,2 
 
 9.54358 
 
 109,0 
 
 0.45642 
 
 .366 
 
 .57313 
 
 123,9 
 
 .02846 
 
 15,2 
 
 .54467 
 
 108,7 
 
 45533 
 
 .367 
 
 57437 
 
 123,6 
 
 .02861 
 
 15,3 
 
 .54576 
 
 108,3 
 
 .45424 
 
 .368 
 
 .5756i 
 
 123,3 
 
 .02877 
 
 15,3 
 
 .54684 
 
 108,0 
 
 .45316 
 
 .369 
 
 .57684 
 
 123,0 
 
 .02892 
 
 15,3 
 
 54792 
 
 107,7 
 
 .45208 
 
 0.370 
 
 9.57807 
 
 122,7 
 
 0.02907 
 
 15,4 
 
 9.54899 
 
 107,3 
 
 0.45101 
 
 371 
 
 .57929 
 
 122,4 
 
 .02923 
 
 15,4 
 
 .55006 
 
 107,0 
 
 .44994 
 
 372 
 
 .58051 
 
 122,1 
 
 .02938 
 
 15,4 
 
 .55H3 
 
 106,6 
 
 .44887 
 
 373 
 
 .58173 
 
 121,8 
 
 02954 
 
 15,5 
 
 .55220 
 
 106,3 
 
 .44780 
 
 374 
 
 .58295 
 
 121,5 
 
 .02969 
 
 15,5 
 
 .55326 
 
 106,0 
 
 .44674 
 
 0.375 
 
 9.58416 
 
 121,2 
 
 0.02985 
 
 15,6 
 
 9-55432 
 
 105,6 
 
 0.44568 
 
 .376 
 
 .58537 
 
 120,9 
 
 .03000 
 
 15,6 
 
 55537 
 
 105,3 
 
 .44463 
 
 377 
 
 .58658 
 
 120,6 
 
 .03016 
 
 15,6 
 
 .55642 
 
 105,0 
 
 .44358 
 
 .378 
 
 .58779 
 
 120,3 
 
 .03031 
 
 15,7 
 
 .55747 
 
 104,6 
 
 .44253 
 
 .379 
 
 .58899 
 
 1 20,0 
 
 .03047 
 
 15,7 
 
 .55852 
 
 104,3 
 
 .44148 
 
 0.380 
 
 9.59019 
 
 119,7 
 
 0.03063 
 
 15,8 
 
 9.55956 
 
 104,0 
 
 0.44044 
 
 .381 
 
 .59138 
 
 119,5 
 
 .03079 
 
 15,8 
 
 .56059 
 
 103,7 
 
 .43941 
 
 .382 
 
 .59257 
 
 110,2 
 
 .03095 
 
 15,8 
 
 .56163 
 
 103,3 
 
 .43837 
 
 .383 
 
 .59377 
 
 118,9 
 
 .03110 
 
 15,9 
 
 .56266 
 
 103,0 
 
 .43734 
 
 .384 
 
 .59495 
 
 118,6 
 
 .03126 
 
 15,9 
 
 56369 
 
 102,7 
 
 .43631 
 
 0.385 
 
 9.59614 
 
 118,3 
 
 0.03142 
 
 15,9 
 
 9-56472 
 
 102,4 
 
 0.43528 
 
 .386 
 
 59732 
 
 118,0 
 
 .03158 
 
 16,0 
 
 .56574 
 
 IO2,I 
 
 .43426 
 
 .387 
 
 .59850 
 
 117,8 
 
 .03174 
 
 16,0 
 
 .56676 
 
 101,8 
 
 .43324 
 
 .388 
 
 .50967 
 
 ii7,5 
 
 .03190 
 
 16,1 
 
 .56777 
 
 101,4 
 
 .43223 
 
 .389 
 
 .60085 
 
 117,2 
 
 .03206 
 
 16,1 
 
 .56879 
 
 101,1 
 
 .43121 
 
 0.390 
 
 9.60202 
 
 116,9 
 
 0.03222 
 
 16,1 
 
 9-56980 
 
 100,8 
 
 0.43020 
 
 391 
 
 .60319 
 
 116,7 
 
 .03238 
 
 16,2 
 
 .57080 
 
 100,5 
 
 .42920 
 
 392 
 
 .60435 
 
 116,4 
 
 .03255 
 
 16,2 
 
 .57i8i 
 
 100,2 
 
 .42819 
 
 393 
 
 .60551 
 
 116,1 
 
 .03271 
 
 16,2 
 
 .57281 
 
 99,9 
 
 .42719 
 
 394 
 
 .60668 
 
 H5,9 
 
 .03287 
 
 16,3 
 
 .57380 
 
 99,6 
 
 .42620 
 
 0.395 
 
 9.60783 
 
 H5,6 
 
 0.03303 
 
 16,3 
 
 9.5748o 
 
 99,3 
 
 0.42520 
 
 .396 
 
 .60899 
 
 H5,3 
 
 .03320 
 
 16,4 
 
 57579 
 
 99,0 
 
 .42421 
 
 397 
 
 .61014 
 
 115,1 
 
 .03336 
 
 16,4 
 
 .57678 
 
 98,7 
 
 .42322 
 
 398 
 
 .61129 
 
 114,8 
 
 .03353 
 
 16,4 
 
 57776 
 
 98,4 
 
 .42224 
 
 399 
 
 .61244 
 
 114,6 
 
 .03369 
 
 16,5 
 
 .57875 
 
 98,1 
 
 .42125 
 
 0.400 
 
 9.61358 
 
 H4,3 
 
 0.03385 
 
 16,5 
 
 9-57973 
 
 97,8 
 
 0.42027 
 
 u 
 
 log tan gd u 
 
 Fo' 
 
 log sec gd u 
 
 w Fo' 
 
 log sin gd u 
 
 Fo' 
 
 log esc gdu 
 
 SMITHSONIAN TABLES 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 Fo' 
 
 log cosh u 
 
 F ' 
 
 log tanh u 
 
 Fo' 
 
 log coth u 
 
 0.400 
 
 9.6I358 
 
 114,3 
 
 0.03385 
 
 16,5 
 
 9-57973 
 
 97,8 
 
 0.42027 
 
 .401 
 
 .61472 
 
 114,0 
 
 .03402 
 
 16,5 
 
 .58070 
 
 97,5 
 
 .41930 
 
 .402 
 
 .61586 
 
 113,8 
 
 .03419 
 
 16,6 
 
 .58168 
 
 97,2 
 
 .41832 
 
 .403 
 
 .61700 
 
 H3,5 
 
 03435 
 
 16,6 
 
 .58265 
 
 96,9 
 
 .41735 
 
 .404 
 
 .61813 
 
 H3,3 
 
 .03452 
 
 16,6 
 
 .58361 
 
 96,6 
 
 .41639 
 
 0.405 
 
 9.61926 
 
 H3,o 
 
 0.03468 
 
 16,7 
 
 9.58458 
 
 96,3 
 
 0.41542 
 
 .406 
 
 .62039 
 
 112,8 
 
 .03485 
 
 16,7 
 
 .58554 
 
 96,i 
 
 .41446 
 
 .407 
 
 .62152 
 
 112,5 
 
 .03502 
 
 16,8 
 
 .58650 
 
 95,8 
 
 .41350 
 
 .408 
 
 .62264 
 
 112,3 
 
 .03519 
 
 16,8 
 
 .58746 
 
 95,5 
 
 .41254 
 
 .409 
 
 .62376 
 
 112,0 
 
 03535 
 
 16,8 
 
 .58841 
 
 95,2 
 
 .4H59 
 
 0.410 
 
 9.62488 
 
 in,8 
 
 0.03552 
 
 16,9 
 
 9.58936 
 
 94,9 
 
 0.41064 
 
 .411 
 
 .62600 
 
 111,6 
 
 .03569 
 
 16,9 
 
 .50031 
 
 94,6 
 
 .40069 
 
 .412 
 
 .62711 
 
 in,3 
 
 .03586 
 
 16,9 
 
 .59125 
 
 94,4 
 
 .40875 
 
 .413 
 
 .62823 
 
 in, i 
 
 .03603 
 
 17,0 
 
 .59220 
 
 94,1 
 
 .40780 
 
 .414 
 
 .62934 
 
 110,8 
 
 .03620 
 
 17,0 
 
 .593U 
 
 93,8 
 
 .40686 
 
 0.415 
 
 9.63044 
 
 110,6 
 
 0.03637 
 
 I7,i 
 
 9.59407 
 
 93,5 
 
 0.40593 
 
 .416 
 
 .63155 
 
 110,4 
 
 .03654 
 
 I7,i 
 
 59501 
 
 93,3 
 
 .40499 
 
 .417 
 
 .63265 
 
 no, i 
 
 .03671 
 
 I7,i 
 
 59594 
 
 93,0 
 
 .40406 
 
 .418 
 
 .63375 
 
 109,9 
 
 .03688 
 
 17,2 
 
 .59687 
 
 92,7 
 
 .40313 
 
 .419 
 
 .63485 
 
 109,6 
 
 .03706 
 
 17,2 
 
 .59779 
 
 92,4 
 
 .40221 
 
 0.420 
 
 9.63594 
 
 109,4 
 
 0.03723 
 
 17,2 
 
 9.59871 
 
 92,2 
 
 0.40129 
 
 .421 
 
 .63704 
 
 109,2 
 
 .03740 
 
 17,3 
 
 .59963 
 
 91,9 
 
 .40037 
 
 .422 
 
 .63813 
 
 109,0 
 
 .03757 
 
 17,3 
 
 .60055 
 
 91,6 
 
 39945 
 
 .423 
 
 .63922 
 
 108,7 
 
 .03775 
 
 17,3 
 
 .60147 
 
 91,4 
 
 .39853 
 
 .424 
 
 .64030 
 
 108,5 
 
 .03792 
 
 17,4 
 
 .60238 
 
 91,1 
 
 .39762 
 
 0.425 
 
 9.64139 
 
 108,3 
 
 0.03810 
 
 17,4 
 
 9.60329 
 
 90,8 
 
 0.30671 
 
 .426 
 
 .64247 
 
 108,0 
 
 .03827 
 
 17,5 
 
 .60420 
 
 00,6 
 
 .39580 
 
 .427 
 
 .64355 
 
 107,8 
 
 .03844 
 
 17,5 
 
 .60510 
 
 90,3 
 
 .39490 
 
 .428 
 
 .64462 
 
 107,6 
 
 .03862 
 
 17,5 
 
 .60600 
 
 90,1 
 
 39400 
 
 .429 
 
 .64570 
 
 107,4 
 
 .03880 
 
 17,6 
 
 .60690 
 
 89,8 
 
 .39310 
 
 0.430 
 
 9.64677 
 
 107,1 
 
 0.03897 
 
 17,6 
 
 9.60780 
 
 89,6 
 
 0.39220 
 
 .431 
 
 .64784 
 
 106,9 
 
 .03915 
 
 17,6 
 
 .60869 
 
 89,3 
 
 .39131 
 
 .432 
 
 .64891 
 
 106,7 
 
 .03932 
 
 17,7 
 
 .60959 
 
 89,0 
 
 .39041 
 
 433 
 
 .64997 
 
 106,5 
 
 .03950 
 
 17,7 
 
 .61047 
 
 88,8 
 
 .38953 
 
 434 
 
 .65104 
 
 106,3 
 
 .03968 
 
 17,7 
 
 .61136 
 
 88,5 
 
 .38864 
 
 0.435 
 
 9.65210 
 
 106,0 
 
 0.03086 
 
 17,8 
 
 9.61224 
 
 88,3 
 
 0.38776 
 
 .436 
 
 .65316 
 
 105,8 
 
 .04003 
 
 17,8 
 
 .61313 
 
 88,0 
 
 .38687 
 
 437 
 
 .65422 
 
 105,6 
 
 .04021 
 
 17,9 
 
 .61401 
 
 87,8 
 
 .38599 
 
 .438 
 
 .65527 
 
 105,4 
 
 .04039 
 
 17,9 
 
 .61488 
 
 87,5 
 
 .38512 
 
 439 
 
 .65633 
 
 105,2 
 
 .04057 
 
 17,9 
 
 .61576 
 
 87,3 
 
 .38424 
 
 0.440 
 
 9.65738 
 
 105,0 
 
 0.04075 
 
 18,0 
 
 9.61663 
 
 87,0 
 
 0.38337 
 
 .441 
 
 .65843 
 
 104,8 
 
 .04093 
 
 18,0 
 
 .61750 
 
 86,8 
 
 .38250 
 
 .442 
 
 .65947 
 
 104,6 
 
 .04111 
 
 18,0 
 
 .61836 
 
 86,5 
 
 .38164 
 
 443 
 
 .66052 
 
 104,4 
 
 .04129 
 
 18,1 
 
 .61923 
 
 86,3 
 
 .38077 
 
 .444 
 
 .66156 
 
 104,2 
 
 .04147 
 
 18,1 
 
 .62009 
 
 86,1 
 
 .37091 
 
 0.445 
 
 9.66260 
 
 104,0 
 
 0.04165 
 
 18,1 
 
 9.62095 
 
 85,8 
 
 0.37005 
 
 .446 
 
 .66364 
 
 103,7 
 
 .04183 
 
 18,2 
 
 .62180 
 
 85,6 
 
 .37820 
 
 447 
 
 .66468 
 
 103,5 
 
 .04202 
 
 18,2 
 
 .62266 
 
 85,3 
 
 37734 
 
 .448 
 
 .66571 
 
 103,3 
 
 .04220 
 
 18,3 
 
 .62351 
 
 85,1 
 
 .37649 
 
 .449 
 
 .66674 
 
 103,1 
 
 .04238 
 
 18,3 
 
 .62436 
 
 84,9 
 
 37564 
 
 0.450 
 
 9.66777 
 
 102,9 
 
 0.04256 
 
 18,3 
 
 9.62521 
 
 84,6 
 
 0.37479 
 
 u 
 
 log tan gd u 
 
 Fo' 
 
 log sec gd u 
 
 <- F,,' 
 
 log sin gd u 
 
 Fo' 
 
 log esc gd u 
 
 SMITHSONIAN TABLCS 
 
 28 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 <- Fo' 
 
 log cosh u 
 
 F ' 
 
 log tanh u 
 
 Fo' 
 
 log coth u 
 
 0.450 
 
 9.66777 
 
 102,9 
 
 0.04256 
 
 18,3 
 
 9.62521 
 
 84,6 
 
 0.37479 
 
 .451 
 
 .66880 
 
 102,7 
 
 .04275 
 
 18,4 
 
 .62605 
 
 84,4 
 
 .37395 
 
 .452 
 
 .66983 
 
 102,5 
 
 .04293 
 
 18,4 
 
 .62690 
 
 8 4 ,I 
 
 37310 
 
 453 
 
 .67085 
 
 102,3 
 
 .04312 
 
 18,4 
 
 .62774 
 
 83,9 
 
 .37226 
 
 454 
 
 .67187 
 
 102,1 
 
 .04330 
 
 18,5 
 
 .62857 
 
 83,7 
 
 .37143 
 
 0.455 
 
 9.67289 
 
 101,9 
 
 0.04348 
 
 18,5 
 
 9.62941 
 
 83,4 
 
 0.37059 
 
 .456 
 
 .67391 
 
 101,8 
 
 .04367 
 
 18,5 
 
 .63024 
 
 83,2 
 
 .36976 
 
 457 
 
 .67493 
 
 101,6 
 
 .04386 
 
 18,6 
 
 .63107 
 
 83,0 
 
 .36893 
 
 458 
 
 .67594 
 
 101,4 
 
 .04404 
 
 18,6 
 
 .63190 
 
 82,8 
 
 .36810 
 
 459 
 
 .67696 
 
 101,2 
 
 .04423 
 
 18,6 
 
 .63273 
 
 82,5 
 
 .36727 
 
 0.460 
 
 9.67797 
 
 101,0 
 
 0.04441 
 
 18,7 
 
 9.63355 
 
 82,3 
 
 0.36645 
 
 .461 
 
 .67898 
 
 100,8 
 
 .04460 
 
 18,7 
 
 .63438 
 
 82,1 
 
 .36562 
 
 .462 
 
 .67998 
 
 100,6 
 
 .04479 
 
 18,7 
 
 .63519 
 
 81,8 
 
 .36481 
 
 463 
 
 .68099 
 
 100,4 
 
 .04498 
 
 18,8 
 
 .63601 
 
 81,6 
 
 .36399 
 
 .464 
 
 .68199 
 
 100,2 
 
 .04516 
 
 18,8 
 
 .63683 
 
 81,4 
 
 .36317 
 
 0.465 
 
 9.68299 
 
 100,0 
 
 0.04535 
 
 18,9 
 
 9.63764 
 
 81,2 
 
 0.36236 
 
 .466 
 
 .68399 
 
 99,8 
 
 .04554 
 
 18,9 
 
 .63845 
 
 81,0 
 
 .36155 
 
 467 
 
 .68499 
 
 99,7 
 
 .04573 
 
 18,9 
 
 .63926 
 
 80,7 
 
 .36074 
 
 .468 
 
 .68599 
 
 99,5 
 
 .04592 
 
 19,0 
 
 .64007 
 
 80,5 
 
 .35993 
 
 .469 
 
 .68698 
 
 99,3 
 
 .04611 
 
 19,0 
 
 .64087 
 
 80,3 
 
 .35913 
 
 0.470 
 
 9.68797 
 
 99,i 
 
 0.04630 
 
 19,0 
 
 9.64167 
 
 80,1 
 
 0.35833 
 
 .471 
 
 .68896 
 
 98,9 
 
 .04649 
 
 19,1 
 
 .64247 
 
 79,9 
 
 35753 
 
 .472 
 
 .68995 
 
 98,7 
 
 .04668 
 
 19,1 
 
 .64327 
 
 79,6 
 
 .35673 
 
 473 
 
 .69094 
 
 98,6 
 
 .04687 
 
 19,1 
 
 .64406 
 
 79,4 
 
 35594 
 
 474 
 
 .69192 
 
 98,4 
 
 .04706 
 
 19,2 
 
 .64486 
 
 79,2 
 
 .35514 
 
 0.475 
 
 9.69290 
 
 98,2 
 
 0.04726 
 
 19,2 
 
 9.64565 
 
 79,0 
 
 0.35435 
 
 .476 
 
 .69388 
 
 98,0 
 
 .04745 
 
 19,2 
 
 .64644 
 
 78,8 
 
 .35356 
 
 477 
 
 .69486 
 
 97,8 
 
 .04764 
 
 19,3 
 
 .64722 
 
 78,6 
 
 .35278 
 
 .478 
 
 .69584 
 
 97,7 
 
 .04783 
 
 19,3 
 
 .64801 
 
 78,4 
 
 35109 
 
 479 
 
 .69682 
 
 97,5 
 
 .04803 
 
 19,3 
 
 .64879 
 
 78,2 
 
 35I2I 
 
 0.480 
 
 9.69779 
 
 97,3 
 
 0.04822 
 
 19,4 
 
 9.64957 
 
 77,9 
 
 0.35043 
 
 .481 
 
 .69876 
 
 97,i 
 
 .04841 
 
 19,4 
 
 .65035 
 
 77,7 
 
 .34965 
 
 .482 
 
 .69973 
 
 97,o 
 
 .04861 
 
 19,4 
 
 .65H3 
 
 77,5 
 
 .34887 
 
 .483 
 
 .70070 
 
 96,8 
 
 .04880 
 
 19,5 
 
 .65190 
 
 77,3 
 
 .34810 
 
 .484 
 
 .70167 
 
 96,6 
 
 .04900 
 
 19,5 
 
 .65267 
 
 77,i 
 
 34733 
 
 0.485 
 
 9.70264 
 
 65,5 
 
 0.04919 
 
 19,6 
 
 9.65344 
 
 76,9 
 
 0.34656 
 
 .486 
 
 .70360 
 
 96,3 
 
 .04939 
 
 19,6 
 
 .65421 
 
 76,7 
 
 34579 
 
 .487 
 
 .70456 
 
 96,1 
 
 .04959 
 
 19,6 
 
 .65498 
 
 76,5 
 
 34502 
 
 .488 
 
 .70552 
 
 95,9 
 
 .04978 
 
 19,7 
 
 .65574 
 
 76,3 
 
 .34426 
 
 .489 
 
 .70648 
 
 95,8 
 
 .04998 
 
 19,7 
 
 .65650 
 
 76,1 
 
 34350 
 
 0.490 
 
 9.70744 
 
 95,6 
 
 0.05018 
 
 19,7 
 
 9.65726 
 
 75,9 
 
 0.34274 
 
 491 
 
 .70839 
 
 95,4 
 
 .05037 
 
 19,8 
 
 .65802 
 
 75,7 
 
 .34198 
 
 .492 
 
 70935 
 
 95,3 
 
 .05057 
 
 19,8 
 
 .65878 
 
 75,5 
 
 .34122 
 
 493 
 
 .71030 
 
 95,i 
 
 .05077 
 
 19,8 
 
 .65953 
 
 75,3 
 
 34047 
 
 .494 
 
 .71125 
 
 95,o 
 
 .05097 
 
 19,9 
 
 .66028 
 
 75,1 
 
 .33972 
 
 0.495 
 
 9.71220 
 
 94,8 
 
 0.05117 
 
 19,9 
 
 9.66103 
 
 74,9 
 
 0.33897 
 
 .496 
 
 .71315 
 
 94,6 
 
 .05137 
 
 19,9 
 
 .66178 
 
 74,7 
 
 .33822 
 
 497 
 
 .71409 
 
 94,5 
 
 .05156 
 
 20,0 
 
 .66253 
 
 74,5 
 
 .33747 
 
 .498 
 
 .71503 
 
 94,3 
 
 .05176 
 
 20,0 
 
 .66327 
 
 74,3 
 
 .33673 
 
 .499 
 
 .71598 
 
 94,1 
 
 .05196 
 
 20,0 
 
 .66401 
 
 74,i 
 
 33599 
 
 0.500 
 
 9.71692 
 
 94,0 
 
 0.05217 
 
 20,1 
 
 9.66475 
 
 73,9 
 
 0.33525 
 
 u 
 
 log tan gd u 
 
 - Fo' 
 
 log sec gd u 
 
 Fo' 
 
 log sin gd u 
 
 Fo' 
 
 logcscgdu 
 
 SMITHSONIAN TABLES 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 Fo' 
 
 log cosh u 
 
 IV 
 
 log tanh u 
 
 - Fo' 
 
 log coth u 
 
 0.500 
 
 9.71692 
 
 94,0 
 
 0.05217 
 
 20,1 
 
 9.66475 
 
 73,9 
 
 0.33525 
 
 .501 
 
 .71786 
 
 93,8 
 
 .05237 
 
 20,1 
 
 .66549 
 
 73,7 
 
 33451 
 
 .502 
 
 .71879 
 
 93,7 
 
 .05257 
 
 20,1 
 
 .66623 
 
 73,5 
 
 .33377 ; 
 
 .503 
 
 .71973 
 
 93,5 
 
 .05277 
 
 2O,2 
 
 .66696 
 
 73,3 
 
 .33304 
 
 .504 
 
 .72066 
 
 93,3 
 
 .05297 
 
 20,2 
 
 .66769 
 
 73,1 
 
 .33231 
 
 0.505 
 
 9.72160 
 
 93,2 
 
 0.05317 
 
 2O,2 
 
 9.66842 
 
 72,9 
 
 0.33158 
 
 .506 
 
 .72253 
 
 93,0 
 
 .05338 
 
 20,3 
 
 .66915 
 
 72,8 
 
 .33085 
 
 .507 
 
 .72346 
 
 92,9 
 
 .05358 
 
 20,3 
 
 .66988 
 
 72,6 
 
 .33012 
 
 .508 
 
 .72438 
 
 92,7 
 
 .05378 
 
 20,3 
 
 .67060 
 
 72,4 
 
 .32940 
 
 .509 
 
 .72531 
 
 92,6 
 
 .05399 
 
 20,4 
 
 .67133 
 
 72,2 
 
 .32867 
 
 0.510 
 
 9.72624 
 
 92,4 
 
 0.05419 
 
 20,4 
 
 9.67205 
 
 72,0 
 
 0.32795 
 
 .511 
 
 .72716 
 
 92,3 
 
 .05439 
 
 20,4 
 
 .67277 
 
 7i,8 
 
 32723 
 
 .512 
 
 .72808 
 
 92,1 
 
 .05460 
 
 20,5 
 
 .67348 
 
 7i,6 
 
 .32652 , 
 
 .513 
 
 .72900 
 
 92,0 
 
 .05480 
 
 20,5 
 
 .67420 
 
 7i,5 
 
 .32580 ; 
 
 .514 
 
 .72992 
 
 91,8 
 
 .05501 
 
 20,5 
 
 .67491 
 
 71,3 
 
 .32509 
 
 0.515 
 
 9.73084 
 
 91,7 
 
 0.05521 
 
 20,6 
 
 9-67562 
 
 7i,i 
 
 0.32438 ; 
 
 .516 
 
 .73175 
 
 9i,5 
 
 .05542 
 
 20,6 
 
 .67633 
 
 70,9 
 
 .32367 
 
 .517 
 
 .73267 
 
 91,4 
 
 .05563 
 
 20,6 
 
 .67704 
 
 70,7 
 
 .32296 
 
 .518 
 
 .73358 
 
 91,2 
 
 .05583 
 
 20,7 
 
 .6/775 
 
 70,5 
 
 .32225 
 
 .519 
 
 73449 
 
 9i,i 
 
 .05604 
 
 20,7 
 
 .67845 
 
 70,3 
 
 .32155 
 
 0.520 
 
 9-73540 
 
 90,9 
 
 0.05625 
 
 20,7 
 
 9.67916 
 
 70,2 
 
 0.32084 
 
 .521 
 
 .73631 
 
 90,8 
 
 .05645 
 
 20,8 
 
 .67986 
 
 70,0 
 
 .32014 
 
 .522 
 
 .73722 
 
 90,6 
 
 .05666 
 
 20,8 
 
 .68056 
 
 69,8 
 
 .31944 
 
 .523 
 
 .73812 
 
 90,5 
 
 .05687 
 
 20,8 
 
 .68125 
 
 69,6 
 
 .31875 ; 
 
 .524 
 
 .73903 
 
 90,3 
 
 .05708 
 
 20,9 
 
 .68195 
 
 69,5 
 
 .31805 
 
 0.525 
 
 9-73993 
 
 90,2 
 
 0.05729 
 
 20,9 
 
 9.68264 
 
 69,3 
 
 0.31736 
 
 .526 
 
 .74083 
 
 90,o 
 
 05750 
 
 20,9 
 
 .68333 
 
 69,1 
 
 .31667 
 
 .527 
 
 .74173 
 
 89,9 
 
 .05771 
 
 21,0 
 
 .68402 
 
 68,9 
 
 .31598 
 
 .528 
 
 .74263 
 
 89,8 
 
 .05792 
 
 2I,O 
 
 .68471 
 
 68,7 
 
 .31529 
 
 .529 
 
 74353 
 
 89,6 
 
 .05813 
 
 2I,O 
 
 .68540 
 
 68,6 
 
 .31460 
 
 0.530 
 
 9.74442 
 
 89,5 
 
 0.05834 
 
 21,1 
 
 9.68608 
 
 68,4 
 
 0.31392 
 
 .531 
 
 74532 
 
 89,3 
 
 .05855 
 
 21,1 
 
 .68677 
 
 68,2 
 
 .31323 
 
 .532 
 
 .74621 
 
 89,2 
 
 .05876 
 
 21,1 
 
 .68745 
 
 68,0 
 
 .31255 
 
 533 
 
 74710 
 
 89,1 
 
 .05897 
 
 21,2 
 
 .68813 
 
 67,9 
 
 .31187 
 
 534 
 
 74799 
 
 88,9 
 
 .05918 
 
 21,2 
 
 .68880 
 
 67,7 
 
 .31120 
 
 0.535 
 
 9.74888 
 
 88,8 
 
 0.05940 
 
 21,2 
 
 9.68948 
 
 67,5 
 
 0.31052 
 
 .536 
 
 .74976 
 
 88,6 
 
 .05961 
 
 21,3 
 
 .69016 
 
 67,4 
 
 .30984 
 
 537 
 
 .75065 
 
 88,5 
 
 .05982 
 
 21,3 
 
 .69083 
 
 67,2 
 
 
 538 
 
 .75153 
 
 88,4 
 
 .06004 
 
 21,3 
 
 .69150 
 
 67,0 
 
 .30850 
 
 539 
 
 .75242 
 
 88,2 
 
 .06025 
 
 21,4 
 
 .69217 
 
 66,9 
 
 .30783 
 
 0.540 
 
 9-75330 
 
 88,1 
 
 0.06046 
 
 21,4 
 
 9.69284 
 
 66,7 
 
 0.30716 
 
 541 
 
 .75418 
 
 88,0 
 
 .06068 
 
 21,4 
 
 .69350 
 
 66,5 
 
 .30650 
 
 .542 
 
 .75506 
 
 87,8 
 
 .06089 
 
 21,5 
 
 .69417 
 
 66,3 
 
 .30583 
 
 .543 
 
 75594 
 
 87,7 
 
 .06111 
 
 21,5 
 
 ,69483 
 
 66,2 
 
 .30517 
 
 544 
 
 .75681 
 
 87,6 
 
 .06132 
 
 21,5 
 
 .69549 
 
 66,0 
 
 .30451 
 
 0.545 
 
 9.75769 
 
 87,4 
 
 0.06154 
 
 21,6 
 
 9.69615 
 
 65,9 
 
 0.30385 
 
 .546 
 
 .75856 
 
 87,3 
 
 .06175 
 
 21,6 
 
 .69681 
 
 65,7 
 
 .30319 
 
 547 
 
 75943 
 
 87,2 
 
 .06197 
 
 21,6 
 
 .69746 
 
 65,5 
 
 .30254 
 
 .548 
 
 .76030 
 
 87,0 
 
 .06219 
 
 21,7 
 
 .69812 
 
 65,4 
 
 .30188 
 
 549 
 
 .76117 
 
 86,9 
 
 .06240 
 
 21,7 
 
 .69877 
 
 65,2 
 
 .30123 
 
 0.550 
 
 9.76204 
 
 86,8 
 
 0.06262 
 
 21,7 
 
 9.69942 
 
 65,0 
 
 0.30058 
 
 u 
 
 log tan gd u 
 
 -Fo' 
 
 log sec gd u 
 
 Fo' 
 
 log sin gd u 
 
 Fo' 
 
 log esc gd u 
 
 SMITHSONIAN TABLES 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 Fo' 
 
 log cosh u 
 
 Fo' 
 
 log tanh u 
 
 Fo' 
 
 log coth u 
 
 0.550 
 
 9.76204 
 
 86,8 
 
 0.06262 
 
 21,7 
 
 9.69942 
 
 65,0 
 
 0.30058 
 
 .551 
 
 .76291 
 
 86,6 
 
 .06284 
 
 21,8 
 
 .70007 
 
 64,9 
 
 .29993 
 
 .552 
 
 .76377 
 
 86,5 
 
 .06306 
 
 21,8 
 
 .70072 
 
 64,7 
 
 .29928 
 
 553 
 
 .76464 
 
 86,4 
 
 .06327 
 
 21,8 
 
 .70137 
 
 64,5 
 
 .29863 
 
 .554 
 
 .76550 
 
 86,3 
 
 .06349 
 
 21,9 
 
 . 7O2OI 
 
 64,4 
 
 .29799 
 
 0.555 
 
 9.76636 
 
 86,1 
 
 0.06371 
 
 21,9 
 
 9.70265 
 
 64,2 
 
 0.29735 
 
 .556 
 
 .76722 
 
 86,0 
 
 .06393 
 
 21,9 
 
 .70329 
 
 64,1 
 
 .29671 
 
 557 
 
 .76808 
 
 85,9 
 
 .06415 
 
 22,0 
 
 .70393 
 
 63,9 
 
 .29607 
 
 .558 
 
 .76894 
 
 85,7 
 
 .06437 
 
 22,0 
 
 .70457 
 
 63,7 
 
 29543 
 
 559 
 
 .76980 
 
 85,6 
 
 .06459 
 
 22,0 
 
 .70521 
 
 63,6 
 
 .29479 
 
 0.560 
 
 9.77065 
 
 85,5 
 
 0.06481 
 
 22,1 
 
 9.70584 
 
 63,4 
 
 0.29416 
 
 .561 
 
 .77151 
 
 85,4 
 
 . .06503 
 
 22,1 
 
 .70648 
 
 63,3 
 
 .29352 
 
 .562 
 
 .77236 
 
 85,2 
 
 .06525 
 
 22,1 
 
 .70711 
 
 63,1 
 
 .29289 
 
 563 
 
 .77321 
 
 85,1 
 
 .06547 
 
 22,2 
 
 .70774 
 
 63,0 
 
 .29226 
 
 564 
 
 .77406 
 
 85,0 
 
 .06570 
 
 22,2 
 
 .70837 
 
 62,8 
 
 .29163 
 
 0.565 
 
 9-77491 
 
 84,9 
 
 0.06592 
 
 22,2 
 
 9.70900 
 
 62,7 
 
 .29100 
 
 .566 
 
 .77576 
 
 84,8 
 
 .06614 
 
 22,3 
 
 .70962 
 
 62,5 
 
 .29038 
 
 .567 
 
 .77661 
 
 84,6 
 
 .06636 
 
 22,3 
 
 .71025 
 
 62,3 
 
 .28975 
 
 .568 
 
 77745 
 
 84,5 
 
 .06659 
 
 22,3 
 
 .71087 
 
 62,2 
 
 .28913 
 
 .569 
 
 .77830 
 
 84,4 
 
 .06681 
 
 22,3 
 
 .71149 
 
 62,0 
 
 .28851 
 
 0.570 
 
 9.77914 
 
 84,3 
 
 0.06703 
 
 22,4 
 
 9.7I2II 
 
 61,9 
 
 0.28789 
 
 571 
 
 .77998 
 
 84,2 
 
 .06726 
 
 22,4 
 
 .71273 
 
 6i,7 
 
 .28727 
 
 572 
 
 .78083 
 
 84,0 
 
 .06748 
 
 22,4 
 
 .71334 
 
 61,6 
 
 .28666 
 
 573 
 
 .78167 
 
 83,9 
 
 .06771 
 
 22,5 
 
 .71396 
 
 61,4 
 
 .28604 
 
 574 
 
 .78250 
 
 83,8 
 
 .06793 
 
 22,5 
 
 .71457 
 
 61,3 
 
 .28543 
 
 0.575 
 
 9.78334 
 
 83,7 
 
 O.o68l6 
 
 22,5 
 
 9.7I5I9 
 
 61,1 
 
 0.28481 
 
 576 
 
 .78418 
 
 83,6 
 
 .06838 
 
 22,6 
 
 .71580 
 
 61,0 
 
 .28420 
 
 577 
 
 .78501 
 
 83,4 
 
 .06861 
 
 22,6 
 
 .71641 
 
 60,8 
 
 .28359 
 
 578 
 
 .78585 
 
 83,3 
 
 .06883 
 
 22,6 
 
 .71701 
 
 60,7 
 
 .28299 
 
 579 
 
 .78668 
 
 83,2 
 
 .06906 
 
 22,7 
 
 .71762 
 
 60,5 
 
 .28238 
 
 0.580 
 
 9.78751 
 
 83,1 
 
 0.06329 
 
 22,7 
 
 9.71822 
 
 60,4 
 
 0.28178 
 
 .581 
 
 .78834 
 
 83,0 
 
 .06951 
 
 22,7 
 
 .71883 
 
 60,2 
 
 .28117 
 
 .582 
 
 .78917 
 
 82,9 
 
 .06974 
 
 22,8 
 
 .71943 
 
 60, i 
 
 .28057 
 
 .583 
 
 .79000 
 
 82,7 
 
 .06097 
 
 22,8 
 
 .72003 
 
 60,0 
 
 .27997 
 
 .584 
 
 .79082 
 
 82,6 
 
 .07020 
 
 22,8 
 
 .72063 
 
 59,8 
 
 .27937 
 
 0.585 
 
 9.79165 
 
 82,5 
 
 0.07043 
 
 22,9 
 
 9.72123 
 
 59,7 
 
 0.27877 
 
 .586 
 
 .79247 
 
 82,4 
 
 .07065 
 
 22,9 
 
 .72182 
 
 59,5 
 
 .27818 
 
 .587 
 
 79330 
 
 82,3 
 
 .07088 
 
 22,9 
 
 .72242 
 
 59,4 
 
 .27758 
 
 .588 
 
 .79412 
 
 82,2 
 
 .O7III 
 
 23,0 
 
 .72301 
 
 59,2 
 
 .27699 
 
 .589 
 
 .79494 
 
 82,1 
 
 .07134 
 
 23,0 
 
 .72360 
 
 59,1 
 
 .27640 
 
 0.500 
 
 9.79576 
 
 82,0 
 
 0.07157 
 
 23,0 
 
 9.72419 
 
 58,9 
 
 0.27581 
 
 591 
 
 .79658 
 
 81,8 
 
 .07180 
 
 23,0 
 
 .72478 
 
 58,8 
 
 .27522 
 
 592 
 
 79740 
 
 8i,7 
 
 .07203 
 
 23,1 
 
 .72537 
 
 58,7 
 
 .27463 
 
 593 
 
 .79822 
 
 81,6 
 
 .07226 
 
 23,1 
 
 .72595 
 
 58,5 
 
 .27405 
 
 594 
 
 .79903 
 
 8i,5 
 
 .07249 
 
 23,1 
 
 .72654 
 
 58,4 
 
 .27346 
 
 0.595 
 
 9.79985 
 
 81,4 
 
 0.07273 
 
 23,2 
 
 9.72712 
 
 58,2 
 
 0.27288 
 
 .596 
 
 .80066 
 
 81,3 
 
 .07296 
 
 23,2 
 
 .72770 
 
 58,1 
 
 .27230 
 
 597 
 
 .80147 
 
 81,2 
 
 .07319 
 
 23,2 
 
 .72828 
 
 58,0 
 
 .27172 
 
 .598 
 
 .80228 
 
 81,1 
 
 
 23,3 
 
 .72886 
 
 57,8 
 
 .27114 
 
 .599 
 
 .80309 
 
 81,0 
 
 .07366 
 
 23,3 
 
 72944 
 
 57,7 
 
 .27056 
 
 0.600 
 
 9.80390 
 
 80,9 
 
 0.07389 
 
 23,3 
 
 9.73001 
 
 57,5 
 
 0.26099 
 
 u 
 
 log tan gd u 
 
 Fo' 
 
 log sec gd u 
 
 a. Fo' 
 
 log sin gd u 
 
 Fo' 
 
 log esc gd u 
 
 SMITHSONIAN TABLES 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 Fo' 
 
 log cosh u 
 
 -IV 
 
 log tanh u 
 
 Fo' 
 
 log coth u 
 
 0.600 
 
 9.80300 
 
 80,9 
 
 0.07389 
 
 23,3 
 
 9-73001 
 
 57,5 
 
 0.26999 
 
 .601 
 
 .80471 
 
 80,8 
 
 .07412 
 
 23,4 
 
 .73059 
 
 57,4 
 
 .26941 
 
 .602 
 
 .80552 
 
 80,7 
 
 .07436 
 
 23,4 
 
 .73116 
 
 57,3 
 
 .26884 
 
 .603 
 
 .80632 
 
 80,5 
 
 .07459 
 
 23,4 
 
 .73173 
 
 57,1 
 
 .26827 
 
 .604 
 
 .80713 
 
 80,4 
 
 .07482 
 
 23,4 
 
 .73231 
 
 57,o 
 
 .26769 
 
 0.605 
 
 9.80793 
 
 80,3 
 
 0.07506 
 
 23,5 
 
 9.73287 
 
 56,9 
 
 0.26713 
 
 .606 
 
 .80$74 
 
 8o,2 
 
 .07529 
 
 23,5 
 
 .73344 
 
 56,7 
 
 .26656 
 
 .607 
 
 .80954 
 
 80, 1 
 
 07553 
 
 23,5 
 
 73401 
 
 56,6 
 
 .26599 
 
 .608 
 
 .81034 
 
 8o,0 
 
 .07576 
 
 23,6 
 
 73457 
 
 56,5 
 
 .26543 
 
 .609 
 
 .81114 
 
 79,9 
 
 .07600 
 
 23,6 
 
 73514 
 
 56,3 
 
 .26486 
 
 0.610 
 
 9.8II94 
 
 79,8 
 
 0.07624 
 
 23,6 
 
 9-73570 
 
 56,2 
 
 0.26430 
 
 .611 
 
 .81273 
 
 79,7 
 
 .07647 
 
 23,7 
 
 . .73626 
 
 56,0 
 
 .26374 
 
 .612 
 
 .81353 
 
 79,6 
 
 .07671 
 
 23,7 
 
 .73682 
 
 55,9 
 
 .26318 
 
 .613 
 
 .81433 
 
 79,5 
 
 .07695 
 
 23,7 
 
 .73738 
 
 55,8 
 
 .26262 
 
 .614 
 
 .81512 
 
 79,4 
 
 .07718 
 
 23,8 
 
 73794 
 
 55,7 
 
 .26206 
 
 0.615 
 
 9.8I59I 
 
 79,3 
 
 0.07742 
 
 23,8 
 
 9.73849 
 
 55,5 
 
 0.26151 
 
 .616 
 
 .81671 
 
 79,2 
 
 .07766 
 
 23,8 
 
 .73905 
 
 55,4 
 
 .26095 
 
 .617 
 
 .81750 
 
 79,1 
 
 .07790 
 
 23,8 
 
 .73960 
 
 55,3 
 
 .26040 
 
 .618 
 
 .81829 
 
 79,0 
 
 .07814 
 
 23,9 
 
 .74015 
 
 55,1 
 
 .25985 
 
 .619 
 
 .81908 
 
 78,9 
 
 .07838 
 
 23,9 
 
 .74070 
 
 55,o 
 
 .25930 
 
 0.620 
 
 9.81987 
 
 78,8 
 
 0.07861 
 
 23,9 
 
 9.74125 
 
 54,9 
 
 0.25875 
 
 .621 
 
 .82065 
 
 78,7 
 
 .07885 
 
 24,0 
 
 .74180 
 
 54,7 
 
 .25820 
 
 .622 
 
 .82144 
 
 78,6 
 
 .07909 
 
 24,0 
 
 74235 
 
 54,6 
 
 .25765 
 
 .623 
 
 .82223 
 
 78,5 
 
 .07933 
 
 24,0 
 
 .74289 
 
 54,5 
 
 .257H 
 
 .624 
 
 .82301 
 
 78,4 
 
 .07957 
 
 24,1 
 
 74344 
 
 54,3 
 
 .25656 
 
 0.625 
 
 9.82380 
 
 78,3 
 
 0.07982 
 
 24,1 
 
 9.74398 
 
 54,2 
 
 0.25602 
 
 .626 
 
 .82458 
 
 78,2 
 
 .08006 
 
 24,1 
 
 .74452 
 
 54,i 
 
 .25548 
 
 .627 
 
 .82536 
 
 78,1 
 
 .08030 
 
 24,1 
 
 .74506 
 
 54,0 
 
 .25494 
 
 .628 
 
 .82614 
 
 78,0 
 
 .08054 
 
 24,2 
 
 .74560 
 
 53,8 
 
 .25440 
 
 .629 
 
 .82692 
 
 77,9 
 
 .08078 
 
 24,2 
 
 .74614 
 
 53,7 
 
 .25386 
 
 0.630 
 
 9.82770 
 
 77,8 
 
 0.08162 
 
 24,2 
 
 9.74667 
 
 53,6 
 
 0.25333 
 
 .631 
 
 .82848 
 
 77,7 
 
 .08126 
 
 24,3 
 
 .74721 
 
 53,5 
 
 .25279 
 
 .632 
 
 .82925 
 
 77,6 
 
 .08151 
 
 24,3 
 
 
 53,3 
 
 .25226 
 
 .633 
 
 .83003 
 
 77,5 
 
 .08175 
 
 24,3 
 
 . 74828 
 
 53,2 
 
 .25172 
 
 .634 
 
 .83080 
 
 77,4 
 
 .08200 
 
 24,4 
 
 .74881 
 
 53,1 
 
 .25119 
 
 0.635 
 
 9.83158 
 
 77,3 
 
 0.08224 
 
 24,4 
 
 9-74934 
 
 53,0 
 
 0.25066 
 
 .636 
 
 .83235 
 
 77,3 
 
 .08248 
 
 24,4 
 
 .74987 
 
 52,8 
 
 .25013 
 
 637 
 
 .83312 
 
 77,2 
 
 .08273 
 
 24,4 
 
 .75040 
 
 52,7 
 
 .24060 
 
 .638 
 
 .83389 
 
 77,i 
 
 .08297 
 
 24,5 
 
 .75092 
 
 52,6 
 
 .24008 
 
 .639 
 
 .83466 
 
 77,o 
 
 .08322 
 
 24,5 
 
 -75I45 
 
 52,5 
 
 .24855 
 
 0.640 
 
 9.83543 
 
 76,9 
 
 0.08346 
 
 24,5 
 
 9.75197 
 
 52,3 
 
 0.24803 
 
 .641 
 
 .83620 
 
 76,8 
 
 .08371 
 
 24,6 
 
 .75249 
 
 52,2 
 
 .24751 
 
 .642 
 
 .83697 
 
 76,7 
 
 .08395 
 
 24,6 
 
 75302 
 
 52,1 
 
 .24698 
 
 .643 
 
 .83774 
 
 76,6 
 
 .08420 
 
 24,6 
 
 75354 
 
 52,o 
 
 .24646 
 
 .644 
 
 .83850 
 
 76,5 
 
 .08445 
 
 24,7 
 
 .75406 
 
 51,9 
 
 .24594 
 
 0.645 
 
 9.83927 
 
 76,4 
 
 0.08469 
 
 24,7 
 
 9-75457 
 
 51,7 
 
 0.24543 
 
 .646 
 
 .84003 
 
 76,3 
 
 .08494 
 
 24,7 
 
 .75509 
 
 
 .24491 
 
 .647 
 
 .84079 
 
 76,2 
 
 .08519 
 
 24,7 
 
 .75561 
 
 51,'s 
 
 .24439 
 
 .648 
 
 .84155 
 
 76,1 
 
 .08543 
 
 24,8 
 
 .75612 
 
 5i,4 
 
 .24388 
 
 .649 
 
 .84232 
 
 76,1 
 
 .08568 
 
 24,8 
 
 .75663 
 
 51,3 
 
 .24337 
 
 0.650 
 
 9.84308 
 
 76,0 
 
 0.08593 
 
 24,8 
 
 9.75715 
 
 Si.i 
 
 0.24285 
 
 u 
 
 log tan gd u 
 
 FO' 
 
 log sec gd u 
 
 Fo' 
 
 log sin gd u 
 
 Fo' 
 
 log esc gd u 
 
 SMITHSCNIAN TABLES 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 F ' 
 
 log cosh u 
 
 F ' 
 
 log tanh u 
 
 Fo' 
 
 log coth u 
 
 0.650 
 
 9.84308 
 
 76,0 
 
 0.08593 
 
 24,8 
 
 9.75715 
 
 51,1 
 
 0.24285 
 
 .651 
 
 .84383 
 
 75,9 
 
 .08618 
 
 24,9 
 
 .75766 
 
 51,0 
 
 .24234 
 
 .652 
 
 .84459 
 
 75,8 
 
 .08643 
 
 24,9 
 
 75817 
 
 50,9 
 
 .24183 
 
 .653 
 
 .84535 
 
 75,7 
 
 .08668 
 
 24,9 
 
 .75867 
 
 50,8 
 
 .24133 
 
 .654 
 
 .84611 
 
 75,6 
 
 .08693 
 
 24,9 
 
 .75918 
 
 50,7 
 
 .24082 
 
 0.655 
 
 9.84686 
 
 75,5 
 
 0.08718 
 
 25,0 
 
 9.75969 
 
 50,6 
 
 0.24031 
 
 .656 
 
 .84762 
 
 75,4 
 
 .08742 
 
 25,0 
 
 .76019 
 
 50,4 
 
 .23981 
 
 .657 
 
 .84837 
 
 75,4 
 
 .08768 
 
 25,0 
 
 .76070 
 
 50,3 
 
 .23930 
 
 .658 
 
 .84912 
 
 75,3 
 
 .08793 
 
 25,1 
 
 .76120 
 
 50,2 
 
 .23880 
 
 .659 
 
 .84988 
 
 75,2 
 
 .08818 
 
 25,1 
 
 .76170 
 
 50,i 
 
 .23830 
 
 0.660 
 
 9.85063 
 
 75,i 
 
 0.08843 
 
 25,1 
 
 9.76220 
 
 50,o 
 
 0.23780 
 
 .661 
 
 .85138 
 
 75,o 
 
 .08868 
 
 25,1 
 
 .76270 
 
 49,9 
 
 .23730 
 
 .662 
 
 .85213 
 
 74,9 
 
 .08893 
 
 25,2 
 
 .76320 
 
 49,7 
 
 .23680 
 
 .663 
 
 .85288 
 
 74,8 
 
 .08918 
 
 25,2 
 
 .76369 
 
 49,6 
 
 .23631 
 
 .664 
 
 .85362 
 
 74,7 
 
 .08943 
 
 25,2 
 
 .76419 
 
 49,5 
 
 .23581 
 
 o 665 
 
 9.85437 
 
 74,7 
 
 0.08969 
 
 25,3 
 
 9.76469 
 
 49,4 
 
 0.23531 
 
 !666 
 
 .85512 
 
 74,6 
 
 .08994 
 
 25,3 
 
 .76518 
 
 49,3 
 
 .23482 
 
 .667 
 
 .85586 
 
 74,5 
 
 .09019 
 
 25,3 
 
 .76567 
 
 49,2 
 
 23433 
 
 .668 
 
 .85661 
 
 74,4 
 
 .09045 
 
 25,3 
 
 .76616 
 
 49,1 
 
 .23384 
 
 .669 
 
 85735 
 
 74,3 
 
 .09070 
 
 25,4 
 
 .76665 
 
 48,9 
 
 23335 
 
 0.670 
 
 9.85809 
 
 74,2 
 
 0.09095 
 
 25,4 
 
 9.76714 
 
 48,8 
 
 0.23286 
 
 .671 
 
 .85884 
 
 74,2 
 
 .09121 
 
 25,4 
 
 .76763 
 
 48,7 
 
 .23237 
 
 .672 
 
 .85958 
 
 74,1 
 
 .09146 
 
 25,5 
 
 .76812 
 
 48,6 
 
 .23188 
 
 .673 
 
 .86032 
 
 74,o 
 
 .09172 
 
 25,5 
 
 .76860 
 
 48,5 
 
 .23140 
 
 .674 
 
 .86106 
 
 73,9 
 
 .09197 
 
 25,5 
 
 .76909 
 
 48,4 
 
 .23091 
 
 0.675 
 
 9.86180 
 
 73,8 
 
 0.09223 
 
 25,5 
 
 9.76957 
 
 48,3 
 
 0.23043 
 
 .676 
 
 .86253 
 
 73,7 
 
 .09248 
 
 25,6 
 
 77005 
 
 48,2 
 
 .22995 
 
 .677 
 
 .86327 
 
 73,7 
 
 .09274 
 
 25,6 
 
 .77053 
 
 48,1 
 
 .22947 
 
 .678 
 
 .86401 
 
 73,6 
 
 .09300 
 
 25,6 
 
 .77101 
 
 47,9 
 
 .22899 
 
 .679 
 
 .86474 
 
 73,5 
 
 .09325 
 
 25,7 
 
 .77149 
 
 47,8 
 
 .22851 
 
 0.680 
 
 9.86548 
 
 73,4 
 
 0.09351 
 
 25,7 
 
 9.77197 
 
 47,7 
 
 0.22803 
 
 .681 
 .682 
 
 .86621 
 .86694 
 
 73,3 
 73,3 
 
 .09377 
 .09402 
 
 25,7 
 25,7 
 
 .77245 
 .77292 
 
 47,6 
 
 47,5 
 
 .22755 
 22708 
 
 .683 
 
 .86768 
 
 73,2 
 
 .09428 
 
 25,8 
 
 .77340 
 
 47,4 
 
 22660 
 
 .684 
 
 .86841 
 
 73,i 
 
 .09454 
 
 25,8 
 
 .77387 
 
 47,3 
 
 .22613 
 
 0.685 
 
 9.86914 
 
 73,0 
 
 0.09480 
 
 25,8 
 
 9-77434 
 
 47,2 
 
 0.22566 
 
 .686 
 
 .86987 
 
 72,9 
 
 .09505 
 
 25,9 
 
 .77481 
 
 47,i 
 
 .22519 
 
 .687 
 
 .87060 
 
 72,9 
 
 .09531 
 
 25,9 
 
 .77528 
 
 47,o 
 
 .22472 
 
 .688 
 
 .87133 
 
 72,8 
 
 .09557 
 
 25,9 
 
 .77575 
 
 46,9 
 
 .22425 
 
 .689 
 
 .87205 
 
 72,7 
 
 .09583 
 
 25,9 
 
 .77622 
 
 46,8 
 
 .22378 
 
 0.690 
 
 9.87278 
 
 72,6 
 
 0.09609 
 
 26,0 
 
 9.77669 
 
 46,7 
 
 0.22331 
 
 .691 
 
 .87351 
 
 72,5 
 
 .09635 
 
 26,0 
 
 .77715 
 
 46,6 
 
 .22285 
 
 .692 
 
 .87423 
 
 72,5 
 
 .09661 
 
 26,0 
 
 .77762 
 
 46,4 
 
 .22238 
 
 .693 
 
 .87495 
 
 72,4 
 
 .09687 
 
 26,1 
 
 .77808 
 
 46,3 
 
 .22192 
 
 .694 
 
 .87568 
 
 72,3 
 
 .09713 
 
 26,1 
 
 .77855 
 
 46,2 
 
 .22145 
 
 0.695 
 
 9.87640 
 
 72,2 
 
 0.09739 
 
 26,1 
 
 9.77901 
 
 46,1 
 
 O.22O99 
 
 .696 
 
 .87712 
 
 72,2 
 
 .09765 
 
 26,1 
 
 .77947 
 
 46,0 
 
 .22053 
 
 .697 
 
 .87784 
 
 72,1 
 
 .09792 
 
 26,2 
 
 .77993 
 
 45,9 
 
 .22OO7 
 
 .698 
 
 .87856 
 
 72,0 
 
 .09818 
 
 26,2 
 
 78039 
 
 45,8 
 
 .21961 
 
 .699 
 
 .87928 
 
 71,9 
 
 .09844 
 
 26,2 
 
 .78084 
 
 45,7 
 
 .21916 
 
 0.700 
 
 9.88000 
 
 7i,9 
 
 0.09870 
 
 26,2 
 
 9.78130 
 
 45,6 
 
 0.21870 
 
 u 
 
 log tan gd u 
 
 Fo' 
 
 log sec gd u 
 
 Fo' 
 
 log sin gd u 
 
 F O ' 
 
 log esc gd u 
 
 SMITHSONIAN TABLES 
 
 33 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 <- Fo' 
 
 log cosh u 
 
 Fo' 
 
 log tanh u 
 
 Fo' 
 
 log coth u 
 
 0.700 
 
 9.88000 
 
 71,9 
 
 0.09870 
 
 26,2 
 
 9.78130 
 
 45,6 
 
 0.21870 
 
 .701 
 
 .88072 
 
 7i,8 
 
 .09895 
 
 26,3 
 
 .78176 
 
 45,5 
 
 .21824 
 
 .702 
 
 .88144 
 
 7i,7 
 
 .09923 
 
 26,3 
 
 .78221 
 
 45,4 
 
 .21779 
 
 703 
 
 .88216 
 
 7i,6 
 
 .09949 
 
 26,3 
 
 .78266 
 
 45,3 
 
 .21734 
 
 .704 
 
 .88287 
 
 7i,6 
 
 .09975 
 
 26,4 
 
 .78312 
 
 45,2 
 
 .21688 
 
 0.705 
 
 9.88359 
 
 7i,5 
 
 O.IOO02 
 
 26,4 
 
 9.78357 
 
 45,i 
 
 0.21643 
 
 .706 
 
 .88430 
 
 7i,4 
 
 .10028 
 
 26,4 
 
 .78402 
 
 45,0 
 
 .21598 
 
 .707 
 
 .88502 
 
 7i,3 
 
 .10055 
 
 26,4 
 
 .78447 
 
 44,9 
 
 21553 
 
 .708 
 
 .88573 
 
 7i,3 
 
 .10081 
 
 26,5 
 
 .78492 
 
 44,8 
 
 .21508 
 
 .709 
 
 .88644 
 
 71,2 
 
 .10108 
 
 26,5 
 
 .78536 
 
 447 
 
 .21464 
 
 0.710 
 
 9.88715 
 
 7i,i 
 
 0.10134 
 
 26,5 
 
 9.78581 
 
 44,6 
 
 0.21419 
 
 .711 
 
 .88786 
 
 71,0 
 
 .10161 
 
 26,5 
 
 .78626 
 
 44,5 
 
 .21374 
 
 .712 
 
 .88857 
 
 71,0 
 
 .10187 
 
 26,6 
 
 .78670 
 
 44,4 
 
 .21330 
 
 .713 
 
 .88928 
 
 70,9 
 
 .10214 
 
 26,6 
 
 .78714 
 
 44,3 
 
 .21286 
 
 .714 
 
 .88999 
 
 70,8 
 
 . 10240 
 
 26,6 
 
 .78759 
 
 44,2 
 
 .21241 
 
 0.715 
 
 9.89070 
 
 70,8 
 
 0.10267 
 
 26,7 
 
 9.78803 
 
 44,1 
 
 0.21197 
 
 .716 
 
 .89141 
 
 70,7 
 
 .10294 
 
 26,7 
 
 .78847 
 
 44,0 
 
 2II53 
 
 .717 
 
 .89211 
 
 70,6 
 
 . 10320 
 
 26,7 
 
 .78891 
 
 43,9 
 
 .21109 
 
 .718 
 
 .89282 
 
 70,5 
 
 . 10347 
 
 26,7 
 
 .78935 
 
 43,8 
 
 .21065 
 
 .719 
 
 .89352 
 
 70,5 
 
 . 10374 
 
 26,8 
 
 .78978 
 
 43,7 
 
 .21022 
 
 0.720 
 
 9.89423 
 
 70,4 
 
 O.I04QI 
 
 26,8 
 
 9-79022 
 
 43,6 
 
 0.20978 
 
 .721 
 
 .89493 
 
 70,3 
 
 .10427 
 
 26,8 
 
 .79066 
 
 43,5 
 
 .20934 
 
 .722 
 
 .89563 
 
 70,3 
 
 . 10454 
 
 26,8 
 
 .79109 
 
 43,4 
 
 .20891 
 
 .723 
 
 .89634 
 
 70,2 
 
 .10481 
 
 26,9 
 
 .79153 
 
 43,3 
 
 .20847 
 
 .724 
 
 .89704 
 
 70,i 
 
 .10508 
 
 26,9 
 
 .79196 
 
 43,2 
 
 .20804 
 
 0.725 
 
 9.89774 
 
 70,0 
 
 0.10535 
 
 26,9 
 
 9.79239 
 
 43,1 
 
 O.2O76I 
 
 .726 
 
 .89844 
 
 70,o 
 
 . 10562 
 
 27,0 
 
 .79282 
 
 43,0 
 
 .20718 
 
 .727 
 
 .89914 
 
 69,9 
 
 .10589 
 
 x 27,0 
 
 .79325 
 
 42,9 
 
 .20675 
 
 .728 
 
 .89984 
 
 69,8 
 
 . 10616 
 
 27,0 
 
 .79368 
 
 42,8 
 
 .20632 
 
 .729 
 
 .90054 
 
 69,8 
 
 .10643 
 
 27,0 
 
 .79411 
 
 42,7 
 
 .20589 
 
 0.730 
 
 9.90123 
 
 69,7 
 
 0.10670 
 
 27,1 
 
 9.79453 
 
 42,6 
 
 0.20547 
 
 .731 
 
 .90193 
 
 69,6 
 
 .id&97 
 
 27,1 
 
 .79496 
 
 42,5 
 
 .20504 
 
 .732 
 
 .90263 
 
 69,6 
 
 . 10724 
 
 27,1 
 
 .79538 
 
 42,5 
 
 .20462 
 
 733 
 
 .90332 
 
 69,5 
 
 .10751 
 
 27,1 
 
 .79581 
 
 42,4 
 
 .204^9 
 
 .734 
 
 .90402 
 
 69,4 
 
 . 10778 
 
 27,2 
 
 .79623 
 
 42,3 
 
 .20377 
 
 0.735 
 
 9.90471 
 
 69,4 
 
 o.io8o5 
 
 27,2 
 
 9.79665 
 
 42,2 
 
 0.20335 
 
 .736 
 
 .90540 
 
 69,3 
 
 .10833 
 
 27,2 
 
 .79708 
 
 42,1 
 
 .20292 
 
 737 
 
 .00610 
 
 69,2 
 
 .10860 
 
 27,2 
 
 79750 
 
 42,0 
 
 .20250 
 
 .738 
 
 .00679 
 
 69,2 
 
 .10887 
 
 27,3 
 
 .79791 
 
 41,9 
 
 .20209 
 
 739 
 
 .90748 
 
 69,1 
 
 .10915 
 
 27,3 
 
 .79833 
 
 41,8 
 
 .20167 
 
 0.740 
 
 9.90817 
 
 69,0 
 
 0.10942 
 
 27,3 
 
 9.79875 
 
 4L7 
 
 0.20125 
 
 .741 
 
 .90886 
 
 69,0 
 
 .10969 
 
 27,3 
 
 .79917 
 
 41,6 
 
 .20083 
 
 .742 
 
 .90955 
 
 68,9 
 
 .10997 
 
 27,4 
 
 .79958 
 
 41,5 
 
 .20042 
 
 743 
 
 .91024 
 
 68,8 
 
 . i 1024 
 
 27,4 
 
 .80000 
 
 41,4 
 
 .20000 
 
 744 
 
 .91092 
 
 68,8 
 
 .11051 
 
 27,4 
 
 .80041 
 
 41,3 
 
 .19959 
 
 0.745 
 
 9.9Il6l 
 
 68,7 
 
 0.11079 
 
 27,5 
 
 9.80082 
 
 41,2 
 
 O.I99l8 
 
 .746 
 
 .91230 
 
 68,6 
 
 .11106 
 
 27,5 
 
 .80124 
 
 41,2 
 
 .19876 
 
 747 
 
 .91298 
 
 68,6 
 
 11134 
 
 27,5 
 
 .80165 
 
 41,1 
 
 .19835 
 
 .748 
 
 .91367 
 
 68,5 
 
 .11161 
 
 27,5 
 
 .80206 
 
 41,0 
 
 .19794 
 
 749 
 
 .91436 
 
 r*s, 4 
 
 .11189 
 
 27,6 
 
 .80247 
 
 40,9 
 
 . 19753 
 
 0.750 
 
 9.91504 
 
 68,4 
 
 o. 11216 
 
 27,6 
 
 9.80288 
 
 40,8 
 
 0.19712 
 
 u 
 
 log tan od u 
 
 Fo' 
 
 log sec gd u 
 
 Fo' 
 
 log sin gd u 
 
 - Fo' 
 
 log esc gd u 
 
 SMITHSONIAN TABLE* 
 
 34 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 <- Fo' 
 
 log cosh u 
 
 F O ' 
 
 log tanh u 
 
 F ' 
 
 log coth u 
 
 0.750 
 
 9.91504 
 
 68,4 
 
 o. 11216 
 
 27,6 
 
 9.80288 
 
 40,8 
 
 0.19712 
 
 .751 
 
 .91572 
 
 68,3 
 
 .11244 
 
 27,6 
 
 .80328 
 
 40,7 
 
 .19672 
 
 .752 
 
 .91641 
 
 68,2 
 
 .11272 
 
 27,6 
 
 .80369 
 
 40,6 
 
 .19631 
 
 753 
 
 .91709 
 
 68,2 
 
 .11299 
 
 27,7 
 
 .80410 
 
 40,5 
 
 .19590 
 
 754 
 
 .91777 
 
 68,1 
 
 .11327 
 
 27,7 
 
 .80450 
 
 40,4 
 
 . 19550 
 
 0.755 
 
 9.91845 
 
 68,1 
 
 O.H355 
 
 27,7 
 
 9.80490 
 
 40,3 
 
 0.19510 
 
 .756 
 
 .91913 
 
 68,0 
 
 . 1.1382 
 
 27,7 
 
 .80531 
 
 40,3 
 
 .19469 
 
 757 
 
 .91981 
 
 67,9 
 
 .11410 
 
 27,8 
 
 .80571 
 
 40,2 
 
 . 19429 . 
 
 758 
 
 .92049 
 
 67,9 
 
 .11438 
 
 27,8 
 
 .80611 
 
 40,1 
 
 .19389 
 
 759 
 
 .92117 
 
 67,8 
 
 .11466 
 
 27,8 
 
 .80651 
 
 40,0 
 
 .19349 
 
 0.760 
 
 9.92185 
 
 67,7 
 
 O.H493 
 
 27,8 
 
 9.80691 
 
 39,9 
 
 0.19309 
 
 .761 
 
 .92252 
 
 67,7 
 
 .11521 
 
 27,9 
 
 .80731 
 
 39,8 
 
 .19269 
 
 .762 
 
 .92320 
 
 67,6 
 
 .11549 
 
 27,9 
 
 .80771 
 
 39,7 
 
 .19229 
 
 .763 
 
 .92387 
 
 67,6 
 
 .11577 
 
 27,9 
 
 .80810 
 
 39,6 
 
 .19100 
 
 .764 
 
 .92455 
 
 67,5 
 
 .11605 
 
 27,9 
 
 .80850 
 
 39,6 
 
 .19150 
 
 0.765 
 
 9.92522 
 
 67,4 
 
 0.11633 
 
 28,0 
 
 9.80889 
 
 39,5 
 
 0.19111 
 
 .766 
 
 .92590 
 
 67,4 
 
 .11661 
 
 28,0 
 
 .80929 
 
 39,4 
 
 .19071 
 
 
 .92657 
 
 67,3 
 
 .11689 
 
 28,0 
 
 .80968 
 
 39,3 
 
 .19032 
 
 768 
 
 .92724 
 
 67,3 
 
 .11717 
 
 28,0 
 
 .81007 
 
 39,2 
 
 .18993 
 
 .769 
 
 .92792 
 
 67,2 
 
 .11745 
 
 28,1 
 
 .81047 
 
 39,1 
 
 .18953 
 
 0.770 
 
 9.92859 
 
 67,1 
 
 O.H773 
 
 28,1 
 
 9.81086 
 
 39,0 
 
 0.18914 
 
 .771 
 
 .92926 
 
 67,1 
 
 .11801 
 
 28,1 
 
 .81125 
 
 39,o 
 
 .18875 
 
 .772 
 
 .92993 
 
 67,0 
 
 . i 1829 
 
 28,1 
 
 .81164 
 
 38,9 
 
 .18836 
 
 773 
 
 .93000 
 
 67,0 
 
 .11858 
 
 28,2 
 
 .81202 
 
 38,8 
 
 .18798 
 
 774 
 
 .93127 
 
 66,9 
 
 .11886 
 
 28,2 
 
 .81241 
 
 38,7 
 
 . 18759 
 
 0.775 
 
 9.93194 
 
 66,8 
 
 0.119)14 
 
 28,2 
 
 9.81280 
 
 38,6 
 
 o. 18720 
 
 776 
 
 .93261 
 
 66,8 
 
 .11942 
 
 28,2 
 
 .81318 
 
 38,5 
 
 .18682 
 
 777 
 
 .93327 
 
 66,7 
 
 .11970 
 
 28,3 
 
 .81357 
 
 38,4 
 
 .18643 
 
 778 
 
 93394 
 
 66,7 
 
 .H999 
 
 28,3 
 
 .81395 
 
 38,4 
 
 .18605 
 
 779 
 
 .93461 
 
 66,6 
 
 . 12027 
 
 28,3 
 
 .81434 
 
 38,3 
 
 .18566 
 
 0.780 
 
 9.93527 
 
 66,5 
 
 0.12055 
 
 28,3 
 
 9.81472 
 
 38,2 
 
 0.18528 
 
 .781 
 
 93594 
 
 66,5 
 
 .12084 
 
 28,4 
 
 .81510 
 
 38,1 
 
 .18490 
 
 .782 
 
 .93660 
 
 66,4 
 
 .12112 
 
 28,4 
 
 .81548 
 
 38,0 
 
 . 18452 
 
 .783 
 
 .93727 
 
 66,4 
 
 .12141 
 
 28,4 
 
 .81586 
 
 37,9 
 
 .18414 
 
 .784 
 
 93793 
 
 66,3 
 
 .I2IO9 
 
 28,4 
 
 .81624 
 
 37,9 
 
 .18376 
 
 0.785 
 
 9.93859 
 
 66,2 
 
 O.I2I97 
 
 28,5 
 
 9.81662 
 
 37,8 
 
 0.18338 
 
 .786 
 
 .93925 
 
 66,2 
 
 .12226 
 
 28,5 
 
 .81699 
 
 37,7 
 
 . 18301 
 
 .787 
 
 .93992 
 
 66,1 
 
 . 12254 
 
 28,5 
 
 .81737 
 
 37,6 
 
 .18263 
 
 .788 
 
 .94058 
 
 66,1 
 
 .12283 
 
 28,5 
 
 .81775 
 
 37,5 
 
 . 18225 
 
 .789 
 
 .94124 
 
 66,0 
 
 .12312 
 
 28,6 
 
 .81812 
 
 37,4 
 
 .18188 
 
 0.790 
 
 9.94190 
 
 66,0 
 
 0.12340 
 
 28,6 
 
 9.81850 
 
 37,4 
 
 0.18150 
 
 .791 
 
 .94256 
 
 65,9 
 
 .12369 
 
 28,6 
 
 .81887 
 
 37,3 
 
 .18113 
 
 .792 
 
 .94321 
 
 65,8 
 
 .12397 
 
 28,6 
 
 .81924 
 
 37,2 
 
 .18076 
 
 793 
 
 .94387 
 
 65,8 
 
 . 12426 
 
 28,7 
 
 .81961 
 
 37,i 
 
 .18039 
 
 794 
 
 94453 
 
 65,7 
 
 .12455 
 
 28,7 
 
 .81998 
 
 37,0 
 
 .18002 
 
 0.795 
 
 9.94519 
 
 65,7 
 
 o. 12483 
 
 28,7 
 
 9-82035 
 
 37,0 
 
 0.17965 
 
 796 
 
 .94584 
 
 65,6 
 
 .12512 
 
 28,7 
 
 .82072 
 
 36,9 
 
 . 17928 
 
 797 
 
 .94650 
 
 65,6 
 
 .12541 
 
 28,8 
 
 .82109 
 
 36,8 
 
 .17891 
 
 798 
 
 .94716 
 
 65,5 
 
 .12570 
 
 28,8 
 
 .82146 
 
 36,7 
 
 . 17854 
 
 799 
 
 .94781 
 
 65,5 
 
 .12598 
 
 28,8 
 
 .82183 
 
 36,6 
 
 .17817 
 
 0.800 
 
 9.94846 
 
 65,4 
 
 o. 12627 
 
 28,8 
 
 9.82219 
 
 36,6 
 
 0.17781 
 
 u 
 
 tog tan gd u 
 
 a, Fo' 
 
 log sec gd u 
 
 F ' 
 
 log sin gd u 
 
 Fo' 
 
 log esc gd u 
 
 SMITHSONIAN TABLES 
 
 35 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 Fu' 
 
 log cosh u 
 
 F ' 
 
 log tanh u 
 
 Fo' 
 
 log coth u 
 
 0.800 
 
 9.94846 
 
 65,4 
 
 0.12627 
 
 28,8 
 
 9.82219 
 
 36,6 
 
 0.17781 
 
 .801 
 
 .94912 
 
 65,3 
 
 .12656 
 
 28,9 
 
 .82256 
 
 36,5 
 
 17744 
 
 .802 
 
 94977 
 
 65,3 
 
 .12685 
 
 28,9 
 
 .82292 
 
 36,4 
 
 .17708 
 
 .803 
 
 .95042 
 
 65,2 
 
 . 12714 
 
 28,9 
 
 .82329 
 
 36,3 
 
 . 17671 
 
 .804 
 
 .95io8 
 
 65,2 
 
 . 12743 
 
 28,9 
 
 .82365 
 
 36,2 
 
 17635 
 
 0.805 
 
 9-95173 
 
 65,1 
 
 0.12772 
 
 29,0 
 
 9.82401 
 
 36,2 
 
 o. 17599 
 
 .806 
 
 .95238 
 
 65,1 
 
 .12801 
 
 29,0 
 
 .82437 
 
 36,1 
 
 . 17563 
 
 . .807 
 
 95303 
 
 65,0 
 
 . 12830 
 
 29,0 
 
 .82473 
 
 36,0 
 
 . 17527 
 
 .808 
 
 .95368 
 
 65,O 
 
 .12859 
 
 29,0 
 
 .82509 
 
 35,9 
 
 .17491 
 
 .809 
 
 95433 
 
 64,9 
 
 .12888 
 
 29,1 
 
 .82545 
 
 35,9 
 
 17455 
 
 0.810 
 
 9.95498 
 
 04,9 
 
 0.12917 
 
 29,1 
 
 9.82581 
 
 35,8 
 
 0.17419 
 
 .811 
 
 .95563 
 
 64,8 
 
 . 12946 
 
 29,1 
 
 .82617 
 
 35,7 
 
 .17383 
 
 .812 
 
 .95627 
 
 64,8 
 
 . 12975 
 
 29,1 
 
 .82652 
 
 35,6 
 
 .17348 
 
 .813 
 
 .95692 
 
 64,7 
 
 .13004 
 
 29,2 
 
 .82688 
 
 35,5 
 
 .17312 
 
 .814 
 
 95757 
 
 64,6 
 
 . 13033 
 
 29,2 
 
 .82723 
 
 35,5 
 
 .17277 
 
 0.815 
 
 9.95821 
 
 64,6 
 
 0.13063 
 
 29,2 
 
 9.82759 
 
 35,4 
 
 0.17241 
 
 .816 
 
 .95886 
 
 64,5 
 
 .13092 
 
 29,2 
 
 .82794 
 
 35,3 
 
 .17206 
 
 .817 
 
 95950 
 
 64,5 
 
 .13121 
 
 29,2 
 
 .82829 
 
 35,2 
 
 .17171 
 
 .818 
 
 .96015 
 
 64,4 
 
 .13150 
 
 29,3 
 
 .82865 
 
 35,2 
 
 .17135 
 
 .819 
 
 .96079 
 
 64,4 
 
 .13180 
 
 29,3 
 
 .82900 
 
 35,1 
 
 .17100 
 
 0.820 
 
 9.96144 
 
 64,3 
 
 o. 13209 
 
 29,3 
 
 9.82935 
 
 35,0 
 
 0.17065 
 
 .821 
 
 .96208 
 
 64,3 
 
 .13238 
 
 29,3 
 
 .82970 
 
 34,9 
 
 . 17030 
 
 .822 
 
 .96272 
 
 64,2 
 
 .13268 
 
 29,4 
 
 .83005 
 
 34,9 
 
 .16995 
 
 .823 
 
 .96336 
 
 64,2 
 
 . 13297 
 
 29,4 
 
 . 83040 
 
 34,8 
 
 .16960 
 
 .824 
 
 .96401 
 
 64,1 
 
 . 13326 
 
 29,4 
 
 .83074 
 
 34,7 
 
 .16926 
 
 0.825 
 
 9.96465 
 
 64,1 
 
 0.13356 
 
 29,4 
 
 9.83109 
 
 34,6 
 
 0.16891 
 
 .826 
 
 .96529 
 
 64,0 
 
 .13385 
 
 29,5 
 
 .83144 
 
 34,6 
 
 .16856 
 
 .827 
 
 .96593 
 
 64,0 
 
 .13415 
 
 29,5 
 
 .83178 
 
 34,5 
 
 .16822 
 
 .828 
 
 .96657 
 
 63,9 
 
 .13444 
 
 29,5 
 
 .83213 
 
 34,4 
 
 . 16787 
 
 .829 
 
 .96721 
 
 63,9 
 
 .13474 
 
 29,5 
 
 .83247 
 
 34,3 
 
 .16753 
 
 0.830 
 
 9.96784 
 
 63,8 
 
 0.13503 
 
 29,6 
 
 9.83281 
 
 34,3 
 
 0.16719 
 
 .831 
 
 .96848 
 
 63,8 
 
 .13533 
 
 29,6 
 
 .83316 
 
 34,2 
 
 .16684 
 
 .832 
 
 .96912 
 
 63,7 
 
 .13562 
 
 29,6 
 
 .83350 
 
 34J 
 
 .16650 
 
 .833 
 
 .96976 
 
 63,7 
 
 .13592 
 
 29,6 
 
 .83384 
 
 34,o 
 
 .16616 
 
 .834 
 
 .97039 
 
 63,6 
 
 . 13622 
 
 29,6 
 
 .83418 
 
 34,0 
 
 . 16582 
 
 0.835 
 
 9.97103 
 
 63,6 
 
 0.13651 
 
 29,7 
 
 9.83452 
 
 33,9 
 
 0.16548 
 
 .836 
 
 .97167 
 
 63,5 
 
 .13681 
 
 29,7 
 
 .83486 
 
 33,8 
 
 .16514 
 
 .837 
 
 .97230 
 
 63,5 
 
 .13711 
 
 29,7 
 
 .83519 
 
 33,8 
 
 . 16481 
 
 .838 
 .839 
 
 .97293 
 97357 
 
 63,4 
 63,4 
 
 . 13740 
 . 13770 
 
 29,7 
 
 .83553 
 .83587 
 
 33,7 
 33,6 
 
 . 16447 
 .16413 
 
 0.840 
 
 9.97420 
 
 63,3 
 
 0.13800 
 
 29,8 
 
 9.83620 
 
 33,5 
 
 o. 16380 
 
 .841 
 
 .97484 
 
 63,3 
 
 . 13830 
 
 29,8 
 
 83654 
 
 33,5 
 
 . 16346 
 
 .842 
 
 .97547 
 
 63,2 
 
 .13860 
 
 29,8 
 
 .83687 
 
 33,4 
 
 .16313 
 
 .843 
 
 .97610 
 
 63,2 
 
 .13889 
 
 29,9 
 
 .83721 
 
 33,3 
 
 . 16279 
 
 .844 
 
 .97673 
 
 6 3 ,I 
 
 .13919 
 
 29,9 
 
 .83754 
 
 33,3 
 
 . 16246 
 
 0.845 
 
 9.97736 
 
 63,1 
 
 0.13949 
 
 29,9 
 
 9.83787 
 
 33,2 
 
 o. 16213 
 
 .846 
 
 .97799 
 
 63,0 
 
 13979 
 
 29,9 
 
 .83820 
 
 33,1 
 
 .16180 
 
 .847 
 
 .97862 
 
 63,0 
 
 .14009 
 
 29,9 
 
 83853 
 
 33,0 
 
 .16147 
 
 .848 
 
 .97925 
 
 62,9 
 
 . T4039 
 
 30,0 
 
 .83886 
 
 33,o 
 
 .16114 
 
 .849 
 
 .97988 
 
 62,9 
 
 .14069 
 
 30,0 
 
 .83919 
 
 32,9 
 
 .16081 
 
 0.850 
 
 9.98051 
 
 62,8 
 
 0.14009 
 
 30,0 
 
 9.83952 
 
 32,8 
 
 o. 16048 
 
 u 
 
 loo tan gd u 
 
 Fo' 
 
 log tec gd u 
 
 F' 
 
 log sin gd u 
 
 -Fo' 
 
 log etc gd u 
 
 SMITHSONIAN TABLES 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 Fo' 
 
 log cosh u 
 
 F ' 
 
 log tanh u 
 
 Fo' 
 
 log coth u 
 
 0.850 
 
 9.98051 
 
 62,8 
 
 0.14099 
 
 30,0 
 
 9.83952 
 
 32,8 
 
 0.16048 
 
 .851 
 
 .98114 
 
 62,8 
 
 . 14129 
 
 30,0 
 
 83985 
 
 32,8 
 
 .16015 
 
 .852 
 
 .98177 
 
 62,7 
 
 .14159 
 
 30,1 
 
 .84018 
 
 32,7 
 
 . 15982 
 
 .853 
 
 .98239 
 
 62,7 
 
 .14189 
 
 30,1 
 
 .84050 
 
 32,6 
 
 .15950 
 
 .854 
 
 .98302 
 
 62,7 
 
 .14219 
 
 30,1 
 
 .84083 
 
 32,6 
 
 .15917 
 
 0.855 
 
 9-98365 
 
 62,6 
 
 0.14249 
 
 30,1 
 
 9-84115 
 
 32,5 
 
 0.15885 
 
 .856 
 
 .98427 
 
 62,6 
 
 . 14279 
 
 30,1 
 
 .84148 
 
 32,4 
 
 .15852 
 
 .857 
 
 .98490 
 
 62,5 
 
 .14310 
 
 30,2 
 
 .84180 
 
 32,3 
 
 .15820 
 
 .858 
 
 .08552 
 
 62,5 
 
 . 14340 
 
 30,2 
 
 .84213 
 
 32,3 
 
 .15787 
 
 .859 
 
 .98615 
 
 62, 4 
 
 .14370 
 
 30,2 
 
 .84245 
 
 32,2 
 
 .15755 
 
 0.860 
 
 9.98677 
 
 62,4 
 
 0.14400 
 
 30,2 
 
 9.84277 
 
 32,1 
 
 0.15723 
 
 .861 
 
 .98739 
 
 62,3 
 
 .14430 
 
 30,3 
 
 .84309 
 
 32,1 
 
 .15691 
 
 .862 
 
 .98802 
 
 62,3 
 
 .14461 
 
 30,3 
 
 .84341 
 
 32,0 
 
 .15659 
 
 .863 
 
 .98864 
 
 62,2 
 
 .14491 
 
 30,3 
 
 .84373 
 
 31,9 
 
 . 15627 
 
 .864 
 
 .98926 
 
 62,2 
 
 . I452I 
 
 30,3 
 
 .84405 
 
 31,9 
 
 .15595 
 
 0.865 
 
 9.98988 
 
 62,1 
 
 0.14552 
 
 30,3 
 
 9.84437 
 
 31,8 
 
 o. 15563 
 
 .866 
 
 99051 
 
 62,1 
 
 .14582 
 
 30,4 
 
 .84469 
 
 31,7 
 
 .15531 
 
 .867 
 
 .99113 
 
 62,1 
 
 .14612 
 
 30,4 
 
 .84500 
 
 31,7 
 
 .15500 
 
 .868 
 
 .99175 
 
 62,0 
 
 . 14643 
 
 30,4 
 
 .84532 
 
 31,6 
 
 .15468 
 
 .69 
 
 .99237 
 
 62,0 
 
 .14673 
 
 30,4 
 
 .84563 
 
 31,5 
 
 .15437 
 
 0.870 
 
 9.99299 
 
 61,9 
 
 0.14704 
 
 30,5 
 
 9.84595 
 
 31,5 
 
 0.15405 
 
 .871 
 
 .99361 
 
 61,9 
 
 . 14734 
 
 30,5 
 
 .84626 
 
 31,4 
 
 .15374 
 
 .872 
 
 .99422 
 
 61,8 
 
 . 14765 
 
 30,5 
 
 .84658 
 
 31,3 
 
 .15342 
 
 .873 
 
 .99484 
 
 61,8 
 
 .14795 
 
 30,5 
 
 .84689 
 
 31,3 
 
 I53II 
 
 .874 
 
 .99546 
 
 6i,7 
 
 . 14826 
 
 30,5 
 
 .84720 
 
 31,2 
 
 .15280 
 
 0.875 
 
 9.99608 
 
 61,7 
 
 o. 14856 
 
 30,6 
 
 9.84751 
 
 3i,i 
 
 0. 15249 
 
 .876 
 
 .99669 
 
 6i,7 
 
 .14887 
 
 30,6 
 
 .84783 
 
 3IJ 
 
 .15217 
 
 .877 
 
 .99731 
 
 61,6 
 
 . I49I7 
 
 30,6 
 
 .84814 
 
 31,0 
 
 .15186 
 
 .878 
 
 99793 
 
 61,6 
 
 . 14948 
 
 30,6 
 
 84845 
 
 30,9 
 
 .15155 
 
 .879 
 
 .99854 
 
 61,5 
 
 .14979 
 
 30,7 
 
 .84875 
 
 30,9 
 
 .15125 
 
 0.880 
 
 9.99916 
 
 6i,5 
 
 0.15009 
 
 30,7 
 
 9.84006 
 
 30,8 
 
 0.15094 
 
 .881 
 
 .99977 
 
 61,4 
 
 .15040 
 
 30,7 
 
 .84937 
 
 30,7 
 
 .15063 
 
 .882 
 
 0.00038 
 
 61,4 
 
 .15071 
 
 30,7 
 
 .84968 
 
 30,7 
 
 . 15032 
 
 .883 
 
 .00100 
 
 61,3 
 
 .15101 
 
 30,7 
 
 .84998 
 
 30,6 
 
 .15002 
 
 .884 
 
 .00161 
 
 61,3 
 
 .15132 
 
 30,8 
 
 .85029 
 
 30,5 
 
 . I497I 
 
 0.885 
 
 O.OO222 
 
 61,3 
 
 0.15163 
 
 30,8 
 
 9.85059 
 
 30,5 
 
 0.14941 
 
 .886 
 
 .00284 
 
 61,2 
 
 .15194 
 
 30,8 
 
 .85090 
 
 30,4 
 
 . 14910 
 
 .887 
 
 .00345 
 
 61,2 
 
 .15225 
 
 30,8 
 
 .85120 
 
 30,3 
 
 .14880 
 
 .888 
 
 .00406 
 
 61,1 
 
 .15255 
 
 30,9 
 
 .85151 
 
 30,3 
 
 . 14849 
 
 .889 
 
 .00467 
 
 61,1 
 
 .15286 
 
 30,9 
 
 .85181 
 
 30,2 
 
 . 14819 
 
 0.890 
 
 O.O0528 
 
 61,0 
 
 O.I53I7 
 
 30,9 
 
 9.85211 
 
 30,2 
 
 0.14789 
 
 .891 
 
 .00589 
 
 61,0 
 
 .15348 
 
 30,9 
 
 .85241 
 
 30,1 
 
 .14759 
 
 .892 
 
 .00650 
 
 61,0 
 
 .15379 
 
 30,9 
 
 .85271 
 
 30,0 
 
 . 14729 
 
 .893 
 
 .00711 
 
 60,9 
 
 .15410 
 
 3i,o 
 
 .85301 
 
 30,0 
 
 .14699 
 
 .894 
 
 .00772 
 
 60,9 
 
 .15441 
 
 3i,o 
 
 .85331 
 
 29,9 
 
 .14669 
 
 0.895 
 
 0.00833 
 
 60,8 
 
 0.15472 
 
 3i,o 
 
 9.85361 
 
 29,8 
 
 0.14639 
 
 .896 
 
 .00894 
 
 60,8 
 
 . 15503 
 
 3i,o 
 
 .85391 
 
 29,8 
 
 .14609 
 
 .897 
 
 .00955 
 
 60,8 
 
 .15534 
 
 3i,o 
 
 .85421 
 
 29,7 
 
 . 14579 
 
 .898 
 
 .01015 
 
 60,7 
 
 .15565 
 
 3i,i 
 
 .85450 
 
 29,6 
 
 . 14550 
 
 .899 
 
 .01076 
 
 60,7 
 
 .15596 
 
 3i,i 
 
 .85480 
 
 29,6 
 
 .14520 
 
 o.eoo 
 
 0.01137 
 
 60,6 
 
 o. 15627 
 
 3i,i 
 
 9.85509 
 
 29,5 
 
 o. 14491 
 
 u 
 
 log tan gd u 
 
 w Fo' 
 
 log sec gd u 
 
 Fo' 
 
 log sin gd u 
 
 *> Fo' 
 
 log esc gd u 
 
 SMITHSONIAN TABLES 
 
 37 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 Fo' 
 
 log cosh u 
 
 F O ' 
 
 log tanh u 
 
 F O ' 
 
 log coth u 
 
 0.900 
 
 O.OII37 
 
 60,6 
 
 0.15627 
 
 31,1 
 
 9.85509 
 
 29,5 
 
 O.I449I 
 
 .901 
 
 .01197 
 
 60,6 
 
 .15658 
 
 31,1 
 
 .85539 
 
 29,5 
 
 .14461 
 
 .902 
 
 .01258 
 
 60,5 
 
 .15689 
 
 31,2 
 
 .85568 
 
 29,4 
 
 .1443-' 
 
 .903 
 
 .01318 
 
 60,5 
 
 .15721 
 
 31,2 
 
 .85598 
 
 29,3 
 
 .14402 
 
 .904 
 
 .01379 
 
 60,5 
 
 15752 
 
 31,2 
 
 .85627 
 
 29,3 
 
 14373 
 
 0.905 
 
 0.01439 
 
 60,4 
 
 0.15783 
 
 31,2 
 
 9.85656 
 
 29,2 
 
 0.14344 
 
 .906 
 
 .01500 
 
 60,4 
 
 .15814 
 
 31,2 
 
 .85685 
 
 29,2 
 
 .14315 
 
 .907 
 
 .01560 
 
 60, 3 
 
 .15846 
 
 31,3 
 
 .85715 
 
 29,1 
 
 .14285 
 
 .908 
 
 .01620 
 
 60,3 
 
 .15877 
 
 31,3 
 
 85744 
 
 29,0 
 
 . 14256 
 
 .909 
 
 .01681 
 
 60,3 
 
 .15908 
 
 31,3 
 
 85773 
 
 29,0 
 
 . 14227 
 
 0.910 
 
 O.OI74I 
 
 60,2 
 
 0.15939 
 
 31,3 
 
 9.85801 
 
 28,9 
 
 O.I4I99 
 
 .911 
 
 .OlSoi 
 
 60,2 
 
 .15971 
 
 31,3 
 
 .85830 
 
 28,8 
 
 .14170 
 
 .912 
 
 .01861 
 
 60,1 
 
 .16002 
 
 3M 
 
 .85859 
 
 28,8 
 
 . 14141 
 
 .913 
 
 .01921 
 
 60,1 
 
 .16033 
 
 31,4 
 
 .85888 
 
 28,7 
 
 .14112 
 
 .914 
 
 .01981 
 
 60,1 
 
 .16065 
 
 31,4 
 
 .85917 
 
 28,7 
 
 .14083 
 
 0.915 
 
 0.02041 
 
 60,0 
 
 0.16096 
 
 31,4 
 
 9.85945 
 
 28,6 
 
 0.14055 
 
 .916 
 
 .02101 
 
 60,0 
 
 .16128 
 
 31,4 
 
 85974 
 
 28,5 
 
 . 14026 
 
 .917 
 
 .02l6l 
 
 59,9 
 
 .16159 
 
 31,5 
 
 .86002 
 
 28,5 
 
 .13998 
 
 .918 
 
 .O222I 
 
 59,9 
 
 .16191 
 
 31,5 
 
 .86031 
 
 28,4 
 
 .13969 
 
 .919 
 
 .02281 
 
 59,9 
 
 . 16222 
 
 31,5 
 
 .85059 
 
 28,4 
 
 .13941 
 
 0.920 
 
 0.02341 
 
 59,8 
 
 0.16254 
 
 31,5 
 
 9.86088 
 
 28,3 
 
 0.13912 
 
 .921 
 
 .O240I 
 
 59,8 
 
 . 16285 
 
 31,5 
 
 .86116 
 
 28,2 
 
 .13884 
 
 .922 
 
 .02461 
 
 59,8 
 
 .16317 
 
 31,6 
 
 .86144 
 
 28,2 
 
 .13856 
 
 .923 
 
 .02520 
 
 59,7 
 
 .16348 
 
 31,6 
 
 .86172 
 
 28,1 
 
 . 13828 
 
 .924 
 
 .02580 
 
 59,7 
 
 .16380 
 
 31,6 
 
 .86200 
 
 28,1 
 
 .13800 
 
 0.925 
 
 O.O2640 
 
 59,6 
 
 0.16411 
 
 3i,6 
 
 9.86228 
 
 28,0 
 
 o. 13772 
 
 .926 
 
 .02699 
 
 59,6 
 
 .16443 
 
 3i,6 
 
 .86256 
 
 27,9 
 
 .13744 
 
 .927 
 
 .02759 
 
 59,6 
 
 .16475 
 
 3i,7 
 
 .86284 
 
 27,9 
 
 .13716 
 
 .928 
 
 .02819 
 
 59,5 
 
 .16506 
 
 3i,7 
 
 .86312 
 
 27,8 
 
 .13688 
 
 .929 
 
 .02878 
 
 59,5 
 
 .16538 
 
 3i,7 
 
 .86340 
 
 27,8 
 
 .13660 
 
 0.930 
 
 0.02937 
 
 59,4 
 
 0.16570 
 
 31,7 
 
 9.86368 
 
 27,7 
 
 0.13632 
 
 .931 
 
 .02997 
 
 59,4 
 
 .16602 
 
 3i,7 
 
 .86395 
 
 27,7 
 
 .13605 
 
 .932 
 
 .03056 
 
 59,4 
 
 .16633 
 
 3i,8 
 
 .86423 
 
 27,6 
 
 . 13577 
 
 933 
 
 .03116 
 
 59,3 
 
 .16665 
 
 3i,8 
 
 .86450 
 
 27,5 
 
 . 13550 
 
 934 
 
 .03175 
 
 59,3 
 
 .16697 
 
 31,8 
 
 .86478 
 
 27,5 
 
 . 13522 
 
 0.935 
 
 0.03234 
 
 59,3 
 
 0.16729 
 
 3i,8 
 
 9-86505 
 
 27,4 
 
 0.13495 
 
 .936 
 
 .03293 
 
 59,2 
 
 . 16761 
 
 3i,9 
 
 .86533 
 
 27,4 
 
 .13467 
 
 937 
 
 .03353 
 
 59,2 
 
 .16792 
 
 3i,9 
 
 .86560 
 
 27,3 
 
 .13440 
 
 .938 
 
 .03412 
 
 59,1 
 
 .16824 
 
 3i,9 
 
 .86587 
 
 27,3 
 
 .13413 
 
 939 
 
 .03471 
 
 59,1 
 
 .16856 
 
 3i,9 
 
 .86615 
 
 27,2 
 
 .13385 
 
 0.940 
 
 0.03530 
 
 59,1 
 
 0.16888 
 
 3i,9 
 
 9.86642 
 
 27,1 
 
 o. 13358 
 
 .941 
 
 .03589 
 
 59,0 
 
 .16920 
 
 32,0 
 
 .86669 
 
 27,1 
 
 .13331 
 
 942 
 
 .03648 
 
 59,0 
 
 .16952 
 
 32,0 
 
 .86696 
 
 27,0 
 
 . 13304 
 
 943 
 
 .03707 
 
 59,0 
 
 .16984 
 
 32,0 
 
 .86723 
 
 27,0 
 
 . 13277 
 
 .944 
 
 .03766 
 
 58,9 
 
 .17016 
 
 32,0 
 
 .86750 
 
 26,9 
 
 . 13250 
 
 0.945 
 
 0.03825 
 
 58,9 
 
 o. 17048 
 
 32,0 
 
 9.86777 
 
 26,9 
 
 0.13223 
 
 .946 
 
 .03884 
 
 58,9 
 
 .17080 
 
 32,0 
 
 .86804 
 
 26,8 
 
 .13196 
 
 947 
 
 .03943 
 
 58,8 
 
 .17112 
 
 32,1 
 
 .86830 
 
 26,7 
 
 .13170 
 
 .948 
 
 .04001 
 
 58,8 
 
 .17144 
 
 32,1 
 
 .86857 
 
 26,7 
 
 .13143 
 
 .949 
 
 .04060 
 
 58,7 
 
 .17176 
 
 32,1 
 
 .86884 
 
 26,6 
 
 .13116 
 
 0.950 
 
 0.04119 
 
 58,7 
 
 0.17208 
 
 32,1 
 
 9.86910 
 
 26,6 
 
 0.13090 
 
 u 
 
 log tan gd u 
 
 -Fo' 
 
 log sec gd u 
 
 -Fo' 
 
 log sin gd u 
 
 * Fo' 
 
 log esc gd u 
 
 SMITHSONIAN TABLCS 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 loo sinh u 
 
 Fo' 
 
 log cosh u 
 
 Fo' 
 
 log tanh u 
 
 Fo' 
 
 log coth u 
 
 0.950 
 
 0.04119 
 
 58,7 
 
 0.17208 
 
 32,1 
 
 9.86910 
 
 26,6 
 
 0.13090 
 
 .951 
 
 .04178 
 
 58,7 
 
 . I724I 
 
 32,1 
 
 .86937 
 
 26,5 
 
 .13063 
 
 .952 
 
 .04236 
 
 58,6 
 
 17273 
 
 32,2 
 
 .86963 
 
 26,5 
 
 .13037 
 
 953 
 
 .04295 
 
 58,6 
 
 .17305 
 
 32,2 
 
 .86990 
 
 26,4 
 
 .13010 
 
 954 
 
 .04353 
 
 58,6 
 
 . 17337 
 
 32,2 
 
 .87016 
 
 26 >4 
 
 .12984 
 
 0.955 
 
 0.04412 
 
 58,5 
 
 0.17369 
 
 32,2 
 
 9.87043 
 
 26,3 
 
 0.12957 
 
 .956 
 
 .04470 
 
 58,5 
 
 .17402 
 
 32,2 
 
 .87069 
 
 26,2 
 
 .12931 
 
 957 
 
 .04529 
 
 58,5 
 
 .17434 
 
 32,3 
 
 .87095 
 
 26,2 
 
 .12905 
 
 .958 
 
 .04587 
 
 58,4 
 
 .17466 
 
 32,3 
 
 .87121 
 
 26,1 
 
 . 12879 
 
 959 
 
 .04646 
 
 58,4 
 
 .17498 
 
 32,3 
 
 .87147 
 
 26,1 
 
 .12853 
 
 0.960 
 
 0.04704 
 
 58,4 
 
 O.I753I 
 
 32,3 
 
 9.87173 
 
 26,0 
 
 o. 12827 
 
 .961 
 
 .04763 
 
 58,3 
 
 . 17563 
 
 32,3 
 
 .87199 
 
 26,0 
 
 .12801 
 
 .962 
 
 .04821 
 
 58,3 
 
 .17595 
 
 32,4 
 
 .87225 
 
 25,9 
 
 .12775 
 
 .963 
 
 .04879 
 
 58,2 
 
 . 17628 
 
 32,4 
 
 .87251 
 
 25,9 
 
 . 12749 
 
 .964 
 
 .04937 
 
 58,2 
 
 .17660. 
 
 32,4 
 
 .87277 
 
 25,8 
 
 . 12723 
 
 0.965 
 
 0.04996 
 
 58,2 
 
 0.17693 
 
 32,4 
 
 9.87303 
 
 25,8 
 
 0.12697 
 
 .966 
 
 .05054 
 
 58,1 
 
 . 17725 
 
 32,4 
 
 .87329 
 
 25,7 
 
 .12671 
 
 .967 
 
 .05112 
 
 58,1 
 
 17757 
 
 32,5 
 
 .87354 
 
 25,7 
 
 .12646 
 
 .968 
 
 .05170 
 
 58,1 
 
 .17790 
 
 32,5 
 
 .87380 
 
 25,6 
 
 .12620 
 
 .969 
 
 .05228 
 
 58,0 
 
 . 17822 
 
 32,5 
 
 .87406 
 
 25,5 
 
 .12594 
 
 0.970 
 
 0.05286 
 
 58,0 
 
 0.17855 
 
 32,5 
 
 9.87431 
 
 25,5 
 
 0.12569 
 
 .971 
 
 .05344 
 
 58,0 
 
 .17887 
 
 32,5 
 
 .87456 
 
 25,4 
 
 .12544 
 
 972 
 
 .05402 
 
 57,9 
 
 . 17920 
 
 32,6 
 
 .87482 
 
 25A 
 
 .12518 
 
 973 
 
 .05460 
 
 57,9 
 
 . 17953 
 
 32,6 
 
 .87507 
 
 25,3 
 
 . 12493 
 
 974 
 
 .05518 
 
 57,9 
 
 .17985 
 
 32,6 
 
 87533 
 
 25,3 
 
 . 12467 
 
 0.975 
 
 0.05576 
 
 57,8 
 
 o. 18018 
 
 32,6 
 
 9.87558 
 
 25,2 
 
 0.12442 
 
 .976 
 
 .05633 
 
 57,8 
 
 .18050 
 
 32,6 
 
 .87583 
 
 25,2 
 
 .12417 
 
 977 
 
 .05691 
 
 57,8 
 
 .18083 
 
 32,6 
 
 .87608 
 
 25,1 
 
 . 12392 
 
 .978 
 
 .05749 
 
 57,7 
 
 .18116 
 
 32,7 
 
 .87633 
 
 25,1 
 
 . 12367 
 
 979 
 
 .05807 
 
 57,7 
 
 . 18148 
 
 32,7 
 
 .87658 
 
 25,0 
 
 .12342 
 
 0.980 
 
 0.05864 
 
 57,7 
 
 0.18181 
 
 32,7 
 
 9.87683 
 
 25,0 
 
 0.12317 
 
 .981 
 
 .05922 
 
 57,6 
 
 .18214 
 
 32,7 
 
 .87708 
 
 24,9 
 
 . 12292 
 
 .982 
 
 .05980 
 
 57,6 
 
 . 18246 
 
 32,7 
 
 87733 
 
 24,9 
 
 .12267 
 
 .983 
 
 .06037 
 
 57,6 
 
 .18279 
 
 32,8 
 
 .87758 
 
 24,8 
 
 . 12242 
 
 .984 
 
 .06095 
 
 57,5 
 
 .18312 
 
 32,8 
 
 .87783 
 
 24,8 
 
 .12217 
 
 0.985 
 
 0.06152 
 
 57,5 
 
 0.18345 
 
 32,8 
 
 9.87807 
 
 24,7 
 
 0.12193 
 
 .986 
 
 .06210 
 
 57,5 
 
 .18378 
 
 32,8 
 
 .87832 
 
 24,7 
 
 .12168 
 
 .987 
 
 .06267 
 
 57,4 
 
 . 18410 
 
 32,8 
 
 .87857 
 
 24,6 
 
 . 12143 
 
 .988 
 
 .06325 
 
 57,4 
 
 .18443 
 
 32,9 
 
 .87881 
 
 24,6 
 
 .12119 
 
 .989 
 
 .06382 
 
 57,4 
 
 .18476 
 
 32,9 
 
 .87906 
 
 24,5 
 
 .12094 
 
 0.990 
 
 0.06439 
 
 57,3 
 
 0.18509 
 
 32,9 
 
 9.87930 
 
 24,5 
 
 0.12070 
 
 .991 
 
 .06497 
 
 57,3 
 
 .18542 
 
 32,9 
 
 .87955 
 
 24,4 
 
 .12045 
 
 .992 
 
 .06554 
 
 57,3 
 
 .18575 
 
 32,9 
 
 .87979 
 
 24,3 
 
 .I2O2I 
 
 993 
 
 .06611 
 
 57,2 
 
 .18608 
 
 32,9 
 
 .88003 
 
 24,3 
 
 .11997 
 
 .994 
 
 .06669 
 
 57,2 
 
 .18641 
 
 33,0 
 
 .88028 
 
 24,2 
 
 .11972 
 
 0.995 
 
 0.06726 
 
 57,2 
 
 o. 18674 
 
 33,0 
 
 9.88052 
 
 24,2 
 
 O.II948 
 
 .996 
 
 .06783 
 
 57,2 
 
 . 18707 
 
 33,o 
 
 .88076 
 
 24,1 
 
 .11924 
 
 997 
 
 .06840 
 
 57,i 
 
 . 18740 
 
 33,0 
 
 .88100 
 
 24,1 
 
 .II90O 
 
 .998 
 
 .06897 
 
 57,i 
 
 .18773 
 
 33,0 
 
 .88124 
 
 24,0 
 
 .11876 
 
 .999 
 
 .06954 
 
 57,i 
 
 .18806 
 
 33,1 
 
 .88148 
 
 24,0 
 
 .11852 
 
 I.OOO 
 
 0.07011 
 
 57,o 
 
 0.18839 
 
 33,1 
 
 9.88172 
 
 23,9 
 
 O.II828 
 
 u 
 
 log tan gd u 
 
 - Fo' 
 
 log sec gd u 
 
 Fo' 
 
 log sin gd u 
 
 co Fo' 
 
 log esc gd u 
 
 SMITHSONIAN TABLES 
 
 39 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 Fo' 
 
 log cosh u 
 
 F ' 
 
 log tanh u 
 
 Fo' 
 
 log coth u 
 
 1. 000 
 
 O.07OII 
 
 57,o 
 
 0.18839 
 
 33,1 
 
 9.88172 
 
 23,9 
 
 0.11828 
 
 .001 
 
 .07068 
 
 57,o 
 
 .18872 
 
 33,1 
 
 .88196 
 
 23,9 
 
 .11804 
 
 .002 
 
 .07125 
 
 57,o 
 
 .18905 
 
 33,1 
 
 .88220 
 
 23,8 
 
 .11780 
 
 .003 
 
 .07182 
 
 56,9 
 
 .18938 
 
 33,1 
 
 .88244 
 
 23,8 
 
 .11756 
 
 .004 
 
 .07239 
 
 56,9 
 
 .18971 
 
 33,1 
 
 .88268 
 
 23,8 
 
 .11732 
 
 1.005 
 
 0.07296 
 
 56,9 
 
 0.19004 
 
 33,2 
 
 9.88291 
 
 23,7 
 
 0.11709 
 
 .006 
 
 07353 
 
 56,8 
 
 .19038 
 
 33,2 
 
 .88315 
 
 23,7 
 
 .11685 
 
 .007 
 
 .07410 
 
 56,8 
 
 .19071 
 
 33,2 
 
 .88339 
 
 23,6 
 
 .11661 
 
 .008 
 
 .07466 
 
 56,8 
 
 . 19104 
 
 33,2 
 
 .88362 
 
 23,6 
 
 .11638 
 
 .009 
 
 .07523 
 
 56,7 
 
 .18137 
 
 33,2 
 
 .88386 
 
 23,5 
 
 .11614 
 
 1. 010 
 
 0.07580 
 
 56,7 
 
 0.19171 
 
 33,3 
 
 9.88409 
 
 23,5 
 
 0.11591 
 
 .Oil 
 
 .07637 
 
 56,7 
 
 . 19204 
 
 33,3 
 
 .88433 
 
 23,4 
 
 .11567 
 
 .012 
 
 .07693 
 
 56,7 
 
 .19237 
 
 33,3 
 
 .88456 
 
 23,4 
 
 II544 
 
 .013 
 
 .07750 
 
 56,6 
 
 . 19270 
 
 33,3 
 
 .88480 
 
 23,3 
 
 .11520 
 
 .014 
 
 .07807 
 
 56,6 
 
 . 19304 
 
 33,3 
 
 .88503 
 
 23,3 
 
 .11497 
 
 1. 015 
 
 0.07863 
 
 56,6 
 
 0.19337 
 
 33,3 
 
 9.88526 
 
 23,2 
 
 O.H474 
 
 .016 
 
 .07920 
 
 56,5 
 
 . 19370 
 
 33,4 
 
 .88549 
 
 23,2 
 
 .11451 
 
 .017 
 
 .07976 
 
 56,5 
 
 .19404 
 
 33,4 
 
 .88572 
 
 23,1 
 
 . I 1428 
 
 .018 
 
 .08033 
 
 56,5 
 
 19437 
 
 33,4 
 
 .88595 
 
 23,1 
 
 .11405 
 
 .019 
 
 .08089 
 
 56,4 
 
 . I947I 
 
 33,4 
 
 .88619 
 
 23,0 
 
 .11381 
 
 I.O2O 
 
 0.08146 
 
 56,4 
 
 0.19504 
 
 33,4 
 
 9.88642 
 
 23,0 
 
 0.11358 
 
 .021 
 
 .08202 
 
 56,4 
 
 . 19537 
 
 33,5 
 
 .88664 
 
 22,9 
 
 .11336 
 
 .022 
 
 .08258 
 
 56,4 
 
 .19571 
 
 33,5 
 
 .88687 
 
 22,9 
 
 .11313 
 
 .023 
 
 .08315 
 
 56,3 
 
 .19604 
 
 33,5 
 
 .88710 
 
 22,8 
 
 .11290 
 
 .024 
 
 .08371 
 
 56,3 
 
 .19638 
 
 33,5 
 
 .88733 
 
 22,8 
 
 .11267 
 
 I.O25 
 
 0.08427 
 
 56,3 
 
 0.19671 
 
 33,5 
 
 9.88756 
 
 22,7 
 
 0.11244 
 
 .026 
 
 .08483 
 
 56,2 
 
 . 1970S 
 
 33,5 
 
 .88779 
 
 22,7 
 
 .11221 
 
 .027 
 
 .08540 
 
 56,2 
 
 . 19738 
 
 33,6 
 
 .88801 
 
 22,6 
 
 .11109 
 
 .028 
 
 .08596 
 
 56,2 
 
 . 19772 
 
 33,6 
 
 .88824 
 
 22,6 
 
 .11176 
 
 .029 
 
 .08652 
 
 56,i 
 
 .19806 
 
 33,6 
 
 .88846 
 
 22,6 
 
 .11154 
 
 1.030 
 
 0.08708 
 
 56,i 
 
 0.19839 
 
 33,6 
 
 9.88869 
 
 22,5 
 
 0.11131 
 
 .031 
 
 .08764 
 
 56,i 
 
 .19873 
 
 33,6 
 
 .88891 
 
 22,5 
 
 .11109 
 
 .032 
 
 .08820 
 
 56,i 
 
 .19006 
 
 33,6 
 
 .88914 
 
 22,4 
 
 .11086 
 
 .033 
 
 .08876 
 
 56,0 
 
 .19940 
 
 33,7 
 
 .88936 
 
 22,4 
 
 .11064 
 
 .034 
 
 .08932 
 
 56,0 
 
 .19974 
 
 33,7 
 
 .88959 
 
 22,3 
 
 .11041 
 
 1.035 
 
 0.08988 
 
 56,0 
 
 0.20007 
 
 33,7 
 
 9.88981 
 
 22,3 
 
 0.11019 
 
 .036 
 
 .09044 
 
 55,9 
 
 .20041 
 
 33,7 
 
 .89003 
 
 22,2 
 
 .10997 
 
 037 
 
 .09100 
 
 55,9 
 
 .20075 
 
 33,7 
 
 .89025 
 
 22,2 
 
 .10975 
 
 .038 
 
 .09156 
 
 55,9 
 
 .20109 
 
 33,7 
 
 .89048 
 
 22,1 
 
 .10952 
 
 .039 
 
 .09212 
 
 55,9 
 
 .20142 
 
 33,8 
 
 .80070 
 
 22,1 
 
 .10930 
 
 1.040 
 
 0.09268 
 
 55,8 
 
 0.20176 
 
 33,8 
 
 9.89092 
 
 22,0 
 
 0.10008 
 
 .041 
 
 .09324 
 
 55,8 
 
 .20210 
 
 33,8 
 
 .89114 
 
 22,0 
 
 . 10886 
 
 .042 
 
 .09379 
 
 55,8 
 
 .20244 
 
 33,8 
 
 .89136 
 
 22,0 
 
 .10864 
 
 .043 
 
 .09435 
 
 55,7 
 
 .20278 
 
 33,8 
 
 .89158 
 
 21,9 
 
 .10842 
 
 .044 
 
 .09491 
 
 55,7 
 
 .20311 
 
 33,9 
 
 .89180 
 
 21,9 
 
 .10820 
 
 1.045 
 
 0.09547 
 
 55,7 
 
 0.20345 
 
 33,9 
 
 9.89201 
 
 21,8 
 
 0. 10799 
 
 .046 
 
 .09602 
 
 55,7 
 
 .20379 
 
 33,9 
 
 .89223 
 
 21,8 
 
 10777 
 
 .047 
 
 .09658 
 
 55,6 
 
 .20413 
 
 33,9 
 
 .89245 
 
 21,7 
 
 . 10755 
 
 .048 
 
 .097H 
 
 55,6 
 
 .20447 
 
 33,9 
 
 .89267 
 
 21,7 
 
 10733 
 
 .049 
 
 .09769 
 
 55,6 
 
 .20481 
 
 33,9 
 
 .89288 
 
 21,6 
 
 .10712 
 
 1.050 
 
 0.09825 
 
 55,6 
 
 0.20515 
 
 34,0 
 
 9.89310 
 
 21,6 
 
 0.10690 
 
 u 
 
 log tan gd u 
 
 - Fo' 
 
 log sec gd u 
 
 Fo' 
 
 log sin gd u 
 
 Fflf 
 
 log esc gd u 
 
 SMITHSONIAN TABLES 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 Fo' 
 
 log cosh u 
 
 Fo' 
 
 log tanh u 
 
 Fo' 
 
 log coth u 
 
 1.050 
 
 0.09825 
 
 55,6 
 
 0.20515 
 
 34,0 
 
 9.89310 
 
 21,6 
 
 0.10690 
 
 .051 
 
 .09880 
 
 55,5 
 
 .20549 
 
 34,0 
 
 .89331 
 
 21,6 
 
 .10669 
 
 .052 
 
 .09936 
 
 55,5 
 
 .20583 
 
 34,0 
 
 .89353 
 
 21,5 
 
 .10647 
 
 .053 
 
 .09991 
 
 55,5 
 
 .20617 
 
 34,0 
 
 .89375 
 
 21,5 
 
 .10625 
 
 054 
 
 .10047 
 
 55,4 
 
 .20651 
 
 34,0 
 
 .89396 
 
 21,4 
 
 .10604 
 
 1.055 
 
 0. IOI02 
 
 55,4 
 
 0.20685 
 
 34,0 
 
 9.89417 
 
 21,4 
 
 0.10583 
 
 .056 
 
 . 10158 
 
 55,4 
 
 .20719 
 
 34,1 
 
 .89439 
 
 21,3 
 
 . 10561 
 
 .057 
 
 .10213 
 
 55,4 
 
 .20753 
 
 34,1 
 
 .89460 
 
 21,3 
 
 . 10540 
 
 .058 
 
 .10268 
 
 55,3 
 
 .20787 
 
 34,1 
 
 .89481 
 
 21,2 
 
 .10519 
 
 059 
 
 . 10324 
 
 55,3 
 
 .20821 
 
 34,1 
 
 .89502 
 
 21,2 
 
 .10498 
 
 i. 060 
 
 0.10379 
 
 55,3 
 
 0.20855 
 
 34,1 
 
 9.89524 
 
 21,2 
 
 0.10476 
 
 .061 
 
 . 10434 
 
 55,3 
 
 .20889 
 
 34J 
 
 .89545 
 
 21,1 
 
 .10455 
 
 .062 
 
 .10489 
 
 55,2 
 
 .20924 
 
 34,2 
 
 .89566 
 
 21,1 
 
 .10434 
 
 .063 
 
 . 10545 
 
 55,2 
 
 .20958 
 
 34,2 
 
 .89587 
 
 21,0 
 
 .10413 
 
 .064 
 
 .10600 
 
 55,2 
 
 .20992 
 
 34,2 
 
 .89608 
 
 21,0 
 
 . 10392 
 
 1.065 
 
 0.10655 
 
 55,1 
 
 0.21026 
 
 34,2 
 
 9.89629 
 
 20,9 
 
 0.10371 
 
 .066 
 
 . 10710 
 
 55,i 
 
 .21060 
 
 34,2 
 
 .89650 
 
 20,9 
 
 . 10350 
 
 .067 
 
 .10765 
 
 55,i 
 
 .21094 
 
 34,2 
 
 .89671 
 
 20,9 
 
 .10329 
 
 .068 
 
 .10820 
 
 55,1 
 
 .21129 
 
 34,3 
 
 .89692 
 
 20,8 
 
 .10308 
 
 .069 
 
 .10875 
 
 55,0 
 
 .21163 
 
 34,3 
 
 .89712 
 
 20,8 
 
 .10288 
 
 1.070 
 
 o. 10930 
 
 55,0 
 
 0.21197 
 
 34,3 
 
 9.89733 
 
 20,7 
 
 0.10267 
 
 .071 
 
 .10985 
 
 55,o 
 
 .21232 
 
 34,3 
 
 .89754 
 
 20,7 
 
 .10246 
 
 .072 
 
 . i 1040 
 
 '55,o 
 
 .21266 
 
 34,3 
 
 .89774 
 
 2O,6 
 
 .10226 
 
 .073 
 
 .11095 
 
 54,9 
 
 .21300 
 
 34,3 
 
 .89795 
 
 2O,6 
 
 .10205 
 
 .074 
 
 .11150 
 
 54,9 
 
 21335 
 
 34,4 
 
 .89816 
 
 20,6 
 
 .10184 
 
 1.075 
 
 0.11205 
 
 54,9 
 
 0.21369 
 
 34,4 
 
 9.89836 
 
 20,5 
 
 0.10164 
 
 .076 
 
 .11260 
 
 54,9 
 
 .21403 
 
 34,4 
 
 .89857 
 
 20,5 
 
 .10143 
 
 .077 
 
 .11315 
 
 54,8 
 
 .21438 
 
 34,4 
 
 .89877 
 
 20,4 
 
 .10123 
 
 .078 
 
 .11370 
 
 54,8 
 
 .21472 
 
 34,4 
 
 .89898 
 
 20,4 
 
 . IOI02 
 
 .079 
 
 .11424 
 
 54,8 
 
 .21507 
 
 34,4 
 
 .89918 
 
 20,3 
 
 .10082 
 
 1.080 
 
 0.11479 
 
 54,8 
 
 0.21541 
 
 34,4 
 
 9.89938 
 
 20,3 
 
 0.10062 
 
 .081 
 
 .11534 
 
 54,7 
 
 .21575 
 
 34,5 
 
 .89959 
 
 20,3 
 
 .IOO4I 
 
 .082 
 
 .11589 
 
 54,7 
 
 .21610 
 
 34,5 
 
 .89979 
 
 20,2 
 
 .IOO2I 
 
 .083 
 
 .11643 
 
 54,7 
 
 .21644 
 
 34,5 
 
 .89999 
 
 20,2 
 
 .IOOOI 
 
 .084 
 
 .11698 
 
 54,7 
 
 .21679 
 
 34,5 
 
 .90019 
 
 20,1 
 
 .09981 
 
 1.085 
 
 o.i 1753 
 
 54,6 
 
 0.21713 
 
 34,5 
 
 9.90039 
 
 20,1 
 
 0.09961 
 
 .086 
 
 .11807 
 
 54,6 
 
 .21748 
 
 34,5 
 
 .00059 
 
 20,1 
 
 .09941 
 
 .087 
 
 .11862 
 
 54,6 
 
 .21782 
 
 34,6 
 
 .90079 
 
 20,0 
 
 .09921 
 
 .088 
 
 .11916 
 
 54,5 
 
 .21817 
 
 34,6 
 
 .90099 
 
 2O,O 
 
 .09901 
 
 .089 
 
 .11971 
 
 54,5 
 
 .21852 
 
 34,6 
 
 .00119 
 
 19,9 
 
 .09881 
 
 1. 000 
 
 o. 12025 
 
 54,5 
 
 0.21886 
 
 34,6 
 
 9.00139 
 
 19,9 
 
 0.09861 
 
 .091 
 
 .12080 
 
 54,5 
 
 .21921 
 
 34,6 
 
 .90159 
 
 19,9 
 
 .09841 
 
 .092 
 
 .12134 
 
 54,4 
 
 .21955 
 
 34,6 
 
 .90179 
 
 19,8 
 
 .09821 
 
 .093 
 
 .12189 
 
 54,4 
 
 .21990 
 
 34,7 
 
 .90199 
 
 19,8 
 
 .09801 
 
 .094 
 
 . 12243 
 
 54,4 
 
 .22025 
 
 34,7 
 
 .90218 
 
 19,7 
 
 .09782 
 
 1.095 
 
 0.12298 
 
 54,4 
 
 0.22059 
 
 34,7 
 
 9.90238 
 
 19,7 
 
 0.09702 
 
 .096 
 
 . 12352 
 
 54,4 
 
 .22094 
 
 34,7 
 
 .90258 
 
 19,6 
 
 .09742 
 
 .097 
 
 .12406 
 
 54,3 
 
 .22129 
 
 34,7 
 
 .90277 
 
 19,6 
 
 .09723 
 
 .098 
 
 . 12461 
 
 54,3 
 
 .22164 
 
 34,7 
 
 .90297 
 
 19,6 
 
 .09703 
 
 .099 
 
 .12515 
 
 54,3 
 
 .22198 
 
 34,7 
 
 .90317 
 
 19,5 
 
 .09683 
 
 1. 100 
 
 0.12569 
 
 54,3 
 
 0.22233 
 
 34,8 
 
 9.90336 
 
 19,5 
 
 0.09664 
 
 u 
 
 log tan gd u 
 
 Fo' 
 
 log sec gd u 
 
 Fo' 
 
 log sin gd u 
 
 Fo' 
 
 log esc gd u 
 
 SMITHSONIAN TABLES 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 F ' 
 
 log cosh u 
 
 F O ' 
 
 log tanh u 
 
 F ' 
 
 log coth u 
 
 I.IOO 
 
 0.12569 
 
 54,3 
 
 0.22233 
 
 34,8 
 
 9.90336 
 
 19,5 
 
 0.09664 
 
 .101 
 
 .12623 
 
 54,2 
 
 .22268 
 
 34,8 
 
 90356 
 
 19,4 
 
 .09644 
 
 .102 
 
 ..12678 
 
 54,2 
 
 .22303 
 
 34,8 
 
 .90375 
 
 19,4 
 
 .09625 
 
 .103 
 
 .12732 
 
 54,2 
 
 .22337 
 
 34,8 
 
 .90394 
 
 19,4 
 
 .09606 
 
 .104 
 
 .12786 
 
 54,2 
 
 .22372 
 
 34,8 
 
 .90414 
 
 19,3 
 
 .09586 
 
 I.IO5 
 
 0.12840 
 
 54,1 
 
 0.22407 
 
 34,8 
 
 9.90433 
 
 19,3 
 
 0.09567 
 
 .106 
 
 .12894 
 
 54,1 
 
 .22442 
 
 34,9 
 
 .90452 
 
 19,2 
 
 .09548 
 
 .107 
 
 .12948 
 
 54,1 
 
 .22477 
 
 34,9 
 
 .90472 
 
 19,2 
 
 .09528 
 
 .108 
 
 .13002 
 
 54,1 
 
 .22512 
 
 34,9 
 
 .90491 
 
 19,2 
 
 .09509 
 
 .109 
 
 .13056 
 
 54,0 
 
 .22547 
 
 34,9 
 
 .00510 
 
 19,1 
 
 .09490 
 
 I. IIC 
 
 O.I3III 
 
 54,0 
 
 0.22582 
 
 34,9 
 
 9.90529 
 
 19,1 
 
 0.09471 
 
 .in 
 
 .13165 
 
 54,0 
 
 .22616 
 
 34,9 
 
 .90548 
 
 19,1 
 
 .09452 
 
 .112 
 
 .13218 
 
 54,0 
 
 .22651 
 
 35,0 
 
 .90567 
 
 19,0 
 
 .09433 
 
 .113 
 
 . 13272 
 
 53,9 
 
 .22686 
 
 35,0 
 
 .90586 
 
 19,0 
 
 .09414 
 
 .114 
 
 .13326 
 
 53,9 
 
 .22721 
 
 35,0 
 
 .90605 
 
 18,9 
 
 09395 
 
 1. 115 
 
 0.13380 
 
 53,9 
 
 0.22756 
 
 35,0 
 
 9.90624 
 
 18,9 
 
 0.09376 
 
 .116 
 
 .13434 
 
 53,9 
 
 .22791 
 
 35,0 
 
 .90643 
 
 18,9 
 
 .09357 
 
 .117 
 
 .13488 
 
 53,8 
 
 .22826 
 
 35,o 
 
 .90662 
 
 18,8 
 
 .09338 
 
 .118 
 
 13542 
 
 53,8 
 
 .22861 
 
 35,o 
 
 .90680 
 
 18,8 
 
 .09320 
 
 .119 
 
 .13596 
 
 53,8 
 
 .22896 
 
 35,1 
 
 .90609 
 
 18,7 
 
 .09301 
 
 1. 120 
 
 0.13649 
 
 53,8 
 
 0.22931 
 
 35,i 
 
 9.90718 
 
 18,7 
 
 0.09282 
 
 .121 
 
 13703 
 
 53,8 
 
 .22967 
 
 35,i 
 
 .90737 
 
 18,7 
 
 .09263 
 
 .122 
 
 . 13757 
 
 53,7 
 
 .23002 
 
 35,1 
 
 .90755 
 
 18,6 
 
 .09245 
 
 .123 
 
 .I38u 
 
 53,7 
 
 .23037 
 
 35,1 
 
 90774 
 
 18,6 
 
 .09226 
 
 .124 
 
 .13864 
 
 53,7 
 
 .23072 
 
 35,1 
 
 .90792 
 
 18,6 
 
 .09208 
 
 1. 125 
 
 0.13918 
 
 53,7 
 
 0.23107 
 
 35,1 
 
 9.90811 
 
 i8,5 
 
 0.09189 
 
 .126 
 
 . 13972 
 
 53,6 
 
 .23142 
 
 35,2 
 
 .90830 
 
 18,5 
 
 .09170 
 
 .127 
 
 .14025 
 
 53,6 
 
 .23177 
 
 35,2 
 
 .90848 
 
 18,4 
 
 .09152 
 
 .128 
 
 . 14079 
 
 53,6 
 
 .23213 
 
 35,2 
 
 .90866 
 
 18,4 
 
 .09134 
 
 .129 
 
 .14133 
 
 53,6 
 
 .23248 
 
 35,2 
 
 .90885 
 
 18,4 
 
 .09115 
 
 1.130 
 
 0.14186 
 
 53,5 
 
 0.23283 
 
 35,2 
 
 9.90903 
 
 18,3 
 
 0.09097 
 
 .131 
 
 .14240 
 
 53,5 
 
 .23318 
 
 35,2 
 
 .90921 
 
 18,3 
 
 .00079 
 
 .132 
 
 .14293 
 
 53,5 
 
 .23353 
 
 35,3 
 
 .90040 
 
 18,3 
 
 .09060 
 
 .133 
 
 14347 
 
 53,5 
 
 23389 
 
 35,3 
 
 .90958 
 
 18,2 
 
 .09042 
 
 .134 
 
 .14400 
 
 53,5 
 
 .23424 
 
 35,3 
 
 .90976 
 
 18,2 
 
 .09024 
 
 1. 135 
 
 0.14454 
 
 53,4 
 
 0.23459 
 
 35,3 
 
 9.90004 
 
 18,1 
 
 0.09006 
 
 .136 
 
 . 14507 
 
 53,4 
 
 .23495 
 
 35,3 
 
 .91012 
 
 18,1 
 
 .08988 
 
 .137 
 
 .14560 
 
 53,4 
 
 .23530 
 
 35,3 
 
 .91030 
 
 18,1 
 
 .08970 
 
 .138 
 
 . 14614 
 
 53,4 
 
 .23565 
 
 35,3 
 
 .91049 
 
 18,0 
 
 .08951 
 
 .139 
 
 . 14667 
 
 53,3 
 
 .23601 
 
 35,4 
 
 .91067 . 
 
 18,0 
 
 .08933 
 
 1.140 
 
 0.14720 
 
 53,3 
 
 0.23636 
 
 35,4 
 
 9.91085 
 
 18,0 
 
 0.08915 
 
 .141 
 
 14774 
 
 53,3 
 
 .23671 
 
 35,4 
 
 .91102 
 
 17,9 
 
 .08898 
 
 .142 
 
 . 14827 
 
 53,3 
 
 .23707 
 
 35,4 
 
 .91120 
 
 17,9 
 
 .08880 
 
 .143 
 
 .14880 
 
 53,3 
 
 .23742 
 
 35,4 
 
 .9H38 
 
 17,8 
 
 .08862 
 
 .144 
 
 M934 
 
 53,2 
 
 .23778 
 
 35,4 
 
 .9H56 
 
 17,8 
 
 .08844 
 
 1. 145 
 
 o. 14987 
 
 53,2 
 
 0.23813 
 
 35,4 
 
 9.91174 
 
 17,8 
 
 0.08826 
 
 .146 
 
 .15040 
 
 53,2 
 
 .23848 
 
 35,5 
 
 .91192 
 
 17,7 
 
 .08808 
 
 .147 
 
 .15093 
 
 53,2 
 
 .23884 
 
 35,5 
 
 .91209 
 
 17,7 
 
 .08791 
 
 .148 
 
 .15146 
 
 53,2 
 
 .23919 
 
 35,5 
 
 .91227 
 
 17,7 
 
 .08773 
 
 .149 
 
 .15200 
 
 53,1 
 
 .23955 
 
 35,5 
 
 .91245 
 
 17,6 
 
 .08755 
 
 1.150 
 
 0.15253 
 
 53,1 
 
 0.23900 
 
 35,5 
 
 9.91262 
 
 17,6 
 
 0.08738 
 
 u 
 
 log tan ad u 
 
 F ' 
 
 log sec gd u 
 
 Fo' 
 
 log sin gd u 
 
 -Fo' 
 
 logcscgdu 
 
 SMITHSONIAN TABLE* 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 F ' 
 
 log cosh u 
 
 F ' 
 
 log tanh u 
 
 Fo' 
 
 log coth u 
 
 1.150 
 
 0.15253 
 
 53,i 
 
 0.23990 
 
 35,5 
 
 9.91262 
 
 17,6 
 
 0.08738 
 
 .151 
 
 .15306 
 
 53,i 
 
 .24026 
 
 35,5 
 
 .91280 
 
 17,6 
 
 .08720 
 
 .152 
 
 15359 
 
 53,1 
 
 .24061 
 
 35,5 
 
 .91297 
 
 17,5 
 
 .08703 
 
 .153 
 
 .15412 
 
 53,o 
 
 .24097 
 
 35,6 
 
 .91315 
 
 17,5 
 
 .08685 
 
 154 
 
 15465 
 
 53,o 
 
 .24133 
 
 35,6 
 
 .91332 
 
 17,5 
 
 .08668 
 
 I.I55 
 
 0.15518 
 
 53,0 
 
 0.24168 
 
 35,6 
 
 9.91350 
 
 17,4 
 
 0.08650 
 
 .156 
 
 .15571 
 
 53,o 
 
 .24204 
 
 35,6 
 
 .91367 
 
 17,4 
 
 .08633 
 
 157 
 
 . 15624 
 
 53,o 
 
 .24239 
 
 35,6 
 
 .91385 
 
 17,3 
 
 .08615 
 
 .158 
 
 15677 
 
 52,9 
 
 .24275 
 
 35,6 
 
 .91402 
 
 17,3 
 
 .08598 
 
 .159 
 
 .15730 
 
 52,9 
 
 .24311 
 
 36,6 
 
 .91419 
 
 17,3 
 
 .08581 
 
 1.160 
 
 0.15783 
 
 52,9 
 
 0.24346 
 
 35,7 
 
 9.91436 
 
 17,2 
 
 0.08564 
 
 .161 
 
 .15836 
 
 52,9 
 
 .24382 
 
 35,7 
 
 .91454 
 
 17,2 
 
 .08546 
 
 .162 
 
 .15888 
 
 52,9 
 
 .24418 
 
 35,7 
 
 .91471 
 
 17,2 
 
 .08529 
 
 .163 
 
 I594I 
 
 52,8 
 
 .24453 
 
 35,7 
 
 .91488 
 
 I7,i 
 
 .08512 
 
 .164 
 
 .15994 
 
 52,8 
 
 .24489 
 
 35,7 
 
 .91505 
 
 17,1 
 
 .08495 
 
 1.165 
 
 0.16047 
 
 52,8 
 
 0.24525 
 
 35,7 
 
 9.91522 
 
 I7,i 
 
 0.08478 
 
 .166 
 
 .16100 
 
 52,8 
 
 .24560 
 
 35,7 
 
 .91539 
 
 17,0 
 
 .08461 
 
 .167 
 
 .16152 
 
 52,7 
 
 .24596 
 
 35,8 
 
 .91556 
 
 17,0 
 
 .08444 
 
 .168 
 
 . 16205 
 
 52,7 
 
 .24632 
 
 35,8 
 
 .91573 
 
 17,0 
 
 .08427 
 
 .169 
 
 .16258 
 
 52,7 
 
 .24668 
 
 35,8 
 
 .91590 
 
 16,9 
 
 .08410 
 
 1.170 
 
 0.16311 
 
 52,7 
 
 0.24703 
 
 35,8 
 
 9.91607 
 
 16,9 
 
 0.08393 
 
 .171 
 
 . 16363 
 
 52,7 
 
 .24739 
 
 35,8 
 
 .91624 
 
 16,9 
 
 .08376 
 
 .172 
 
 . 16416 
 
 52,6 
 
 .24775 
 
 35,8 
 
 .91641 
 
 16,8 
 
 08359 
 
 .173 
 
 .16469 
 
 52,6 
 
 .24811 
 
 35,8 
 
 .91658 
 
 16,8 
 
 .08342 
 
 .174 
 
 .16521 
 
 52,6 
 
 .24847 
 
 35,9 
 
 .91674 
 
 16,8 
 
 .08326 
 
 1. 175 
 
 0.16574 
 
 52,6 
 
 0.24883 
 
 35,9 
 
 9.91691 
 
 16,7 
 
 0.08309 
 
 .176 
 
 .16626 
 
 52,6 
 
 .24919 
 
 35,9 
 
 .91708 
 
 16,7 
 
 .08292 
 
 .177 
 
 .16679 
 
 52,5 
 
 .24954 
 
 35,9 
 
 .91724 
 
 16,7 
 
 .08276 
 
 .178 
 
 .16731 
 
 52,5 
 
 .24990 
 
 35,9 
 
 .91741 
 
 16,6 
 
 .08259 
 
 .179 
 
 . 16784 
 
 52,5 
 
 .25026 
 
 35,9 
 
 .91758 
 
 16,6 
 
 .08242 
 
 1.180 
 
 0.16836 
 
 52,5 
 
 0.25062 
 
 35,9 
 
 9.91774 
 
 16,6 
 
 0.08226 
 
 .181 
 
 .16889 
 
 52,5 
 
 .25098 
 
 35,9 
 
 .91791 
 
 16,5 
 
 .08209 
 
 .182 
 
 .16941 
 
 52,4 
 
 .25134 
 
 36,0 
 
 .91807 
 
 16,5 
 
 .08193 
 
 .183 
 
 .16994 
 
 52,4 
 
 .25170 
 
 36,0 
 
 .91824 
 
 16,4 
 
 .08176 
 
 .184 
 
 . 17046 
 
 52,4 
 
 .25206 
 
 36,0 
 
 .91840 
 
 16,4 
 
 .08160 
 
 1.185 
 
 0.17009 
 
 52,4 
 
 0.25242 
 
 36,0 
 
 9.91857 
 
 16,4 
 
 0.08143 
 
 .186 
 
 .17151 
 
 52,4 
 
 .25278 
 
 36,0 
 
 .91873 
 
 16,3 
 
 .08127 
 
 .187 
 
 . 17203 
 
 52,3 
 
 .253U 
 
 36,0 
 
 .91889 
 
 16,3 
 
 .oSlII 
 
 .188 
 
 . 17256 
 
 52,3 
 
 .25350 
 
 36,0 
 
 .91906 
 
 16,3 
 
 .08094 
 
 .189 
 
 .17308 
 
 52,3 
 
 .25386 
 
 36,1 
 
 .91922 
 
 16,2 
 
 .08078 
 
 1.190 
 
 0.17360 
 
 52,3 
 
 0.25422 
 
 36,1 
 
 9.91938 
 
 16,2 
 
 0.08062 
 
 .191 
 
 .17413 
 
 52,3 
 
 .25458 
 
 36,1 
 
 .91954 
 
 16,2 
 
 .08046 
 
 .192 
 
 .17465 
 
 52,2 
 
 .25494 
 
 36,1 
 
 .91970 
 
 16,2 
 
 .08030 
 
 .193 
 
 .17517 
 
 52,2 
 
 .25530 
 
 36,1 
 
 .91987 
 
 16,1 
 
 .08013 
 
 .194 
 
 .17569 
 
 52,2 
 
 .25567 
 
 36,1 
 
 .92003 
 
 16,1 
 
 .07997 
 
 1. 195 
 
 0.17621 
 
 52,2 
 
 0.25603 
 
 36,1 
 
 9.92019 
 
 16,1 
 
 0.07981 
 
 .196 
 
 . 17674 
 
 52,2 
 
 .25639 
 
 36,2 
 
 .92035 
 
 16,0 
 
 .07965 
 
 .197 
 
 . 17726 
 
 52,2 
 
 .25675 
 
 36,2 
 
 .92051 
 
 16,0 
 
 .07949 
 
 .198 
 
 .17778 
 
 52,1 
 
 .257H 
 
 36,2 
 
 .92067 
 
 16,0 
 
 07933 
 
 .199 
 
 .17830 
 
 52,1 
 
 .25747 
 
 36,2 
 
 .92083 
 
 15,9 
 
 .07917 
 
 1. 200 
 
 0.17882 
 
 52,1 
 
 0.25784 
 
 36,2 
 
 9.92009 
 
 15,9 
 
 0.07901 
 
 u 
 
 log tan gd u 
 
 Fo' 
 
 log sec gd u 
 
 w Fo' 
 
 log sin gd u 
 
 F O ' 
 
 log esc gd u 
 
 SMITHSONIAN TABLES 
 
 43 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 Fo' 
 
 log cosh u 
 
 IV 
 
 log tanh u 
 
 Fo' 
 
 log coth u 
 
 I.2OO 
 
 0.17882 
 
 52,1 
 
 0.25784 
 
 36,2 
 
 9.92099 
 
 15,9 
 
 0.07901 
 
 .2OI 
 
 17934 
 
 52,1 
 
 .25820 
 
 36,2 
 
 .92114 
 
 15,9 
 
 .07886 
 
 .202 
 
 .17986 
 
 52,1 
 
 .25856 
 
 36,2 
 
 .92130 
 
 15,8 
 
 .07870 
 
 .203 
 
 .18038 
 
 52,0 
 
 .25892 
 
 36,2 
 
 .92146 
 
 15,8 
 
 .07854 
 
 .204 
 
 .18090 
 
 52,0 
 
 .25929 
 
 36,3 
 
 .92162 
 
 15,8 
 
 .07838 
 
 1.205 
 
 0.18142 
 
 52,0 
 
 0.25965 
 
 36,3 
 
 9.92178 
 
 15,7 
 
 0.07822 
 
 .206 
 
 .18194 
 
 52,0 
 
 .26001 
 
 36,3 
 
 .92193 
 
 15,7 
 
 .07807 
 
 .207 
 
 . 18246 
 
 52,0 
 
 .26037 
 
 36,3 
 
 .92209 
 
 15,7 
 
 .07791 
 
 .208 
 
 .18298 
 
 5i,9 
 
 .26074 
 
 36,3 
 
 .92225 
 
 15,6 
 
 .07775 
 
 .209 
 
 .18350 
 
 5i,9 
 
 .26110 
 
 36,3 
 
 .92240 
 
 15,6 
 
 .07760 
 
 I.2IO 
 
 0.18402 
 
 51,9 
 
 0.26146 
 
 36,3 
 
 9.92256 
 
 15,6 
 
 0.07744 
 
 .211 
 
 . 18454 
 
 51,9 
 
 .26183 
 
 36,3 
 
 .92271 
 
 15,5 
 
 .07729 
 
 .212 
 
 .18506 
 
 5L9 
 
 .26219 
 
 36,4 
 
 .92287 
 
 15,5 
 
 .07713 
 
 .213 
 
 .18558 
 
 5i,9 
 
 .26255 
 
 36,4 
 
 .92302 
 
 15,5 
 
 .07698 
 
 .214 
 
 .18610 
 
 5i,8 
 
 .26292 
 
 36,4 
 
 .92318 
 
 15,4 
 
 .07682 
 
 1. 215 
 
 0.18662 
 
 5i,8 
 
 0.26328 
 
 36,4 
 
 9.92333 
 
 15,4 
 
 0.07667 
 
 .216 
 
 .18713 
 
 5i,8 
 
 .26365 
 
 36,4 
 
 .92349 
 
 15,4 
 
 .07651 
 
 .217 
 
 . 18765 
 
 5i,8 
 
 .26401 
 
 36,4 
 
 .92364 
 
 15,4 
 
 .07636 
 
 .218 
 
 .18817 
 
 5i,8 
 
 .26437 
 
 36,4 
 
 .92379 
 
 15,3 
 
 .07621 
 
 .219 
 
 .18869 
 
 51,7 
 
 .26474 
 
 36,5 
 
 .92395 
 
 15,3 
 
 .07605 
 
 1.220 
 
 0.18920 
 
 51,7 
 
 0.26510 
 
 36,5 
 
 9.92410 
 
 15,3 
 
 0.07500 
 
 .221 
 
 .18972 
 
 5i,7 
 
 .26547 
 
 36,5 
 
 .92425 
 
 15,2 
 
 .07575 
 
 .222 
 
 .19024 
 
 51,7 
 
 .26583 
 
 36,5 
 
 .92440 
 
 15,2 
 
 .07560 
 
 .223 
 
 .19075 
 
 51,7 
 
 .26620 
 
 36,5 
 
 .92456 
 
 15,2 
 
 .07544 
 
 .224 
 
 .19127 
 
 51,7 
 
 .26656 
 
 36,5 
 
 .92471 
 
 15,1 
 
 .07529 
 
 I.22S 
 
 O.I9I79 
 
 5i,6 
 
 0.26693 
 
 36,5 
 
 9.92486 
 
 I5,i 
 
 0.07514 
 
 .226 
 
 .19230 
 
 5i,6 
 
 .26729 
 
 36,5 
 
 .92501 
 
 I5,i 
 
 .07499 
 
 .227 
 
 . 19282 
 
 5i,6 
 
 .26766 
 
 36,6 
 
 .92516 
 
 I5,o 
 
 .07484 
 
 .228 
 
 .19334 
 
 5i,6 
 
 .26802 
 
 36,6 
 
 .92531 
 
 I5,o 
 
 .07469 
 
 .229 
 
 .19385 
 
 5i,6 
 
 .26839 
 
 36,6 
 
 .92546 
 
 I5,o 
 
 .07454 
 
 1.230 
 
 0.19437 
 
 5i,5 
 
 0.26876 
 
 36,6 
 
 9.92561 
 
 I5,o 
 
 0.07439 
 
 .231 
 
 .19488 
 
 5i,5 
 
 .26912 
 
 36,6 
 
 .92576 
 
 14,9 
 
 .07424 
 
 .232 
 
 . 19540 
 
 5i,5 
 
 .20949 
 
 36,6 
 
 .92591 
 
 H,9 
 
 .07409 
 
 233 
 
 . I959I 
 
 51,5 
 
 .26985 
 
 36,6 
 
 .92606 
 
 14,9 
 
 .07394 
 
 .234 
 
 .19643 
 
 51,5 
 
 .27022 
 
 36,6 
 
 .92621 
 
 14,8 
 
 .07379 
 
 1.235 
 
 0.19694 
 
 51,5 
 
 0.27059 
 
 36,7 
 
 9.92635 
 
 14,8 
 
 0.07365 
 
 .236 
 
 . 19746 
 
 51,4 
 
 .27095 
 
 36,7 
 
 .92650 
 
 14,8 
 
 .07350 
 
 .237 
 
 . 19797 
 
 51,4 
 
 .27132 
 
 36,7 
 
 .92665 
 
 14,7 
 
 .07335 
 
 .238 
 
 .19848 
 
 51,4 
 
 .27169 
 
 36,7 
 
 .92680 
 
 14,7 
 
 .07320 
 
 239 
 
 .19900 
 
 51,4 
 
 .27205 
 
 36,7 
 
 .92694 
 
 14,7 
 
 .07306 
 
 1.240 
 
 O.I995I 
 
 51,4 
 
 0.27242 
 
 36,7 
 
 9.92709 
 
 14,7 
 
 0.07291 
 
 .241 
 
 .20003 
 
 5i,4 
 
 .27279 
 
 36,7 
 
 .92724 
 
 14,6 
 
 .07276 
 
 .242 
 
 .20054 
 
 5i,3 
 
 .27316 
 
 36,7 
 
 .92738 
 
 14,6 
 
 .07262 
 
 .243 
 
 .20105 
 
 51,3 
 
 .27352 
 
 36,8 
 
 .92753 
 
 14,6 
 
 .07247 
 
 .244 
 
 .20157 
 
 51,3 
 
 .27389 
 
 36,8 
 
 .92767 
 
 14,5 
 
 .07233 
 
 1.245 
 
 0.20208 
 
 51,3 
 
 0.27426 
 
 36,8 
 
 9.92782 
 
 14,5 
 
 0.07218 
 
 .246 
 
 .20259 
 
 51,3 
 
 .27463 
 
 36,8 
 
 .92796 
 
 14,5 
 
 .07204 
 
 .247 
 
 .20310 
 
 51,2 
 
 .27499 
 
 36,8 
 
 .92811 
 
 14,4 
 
 .07189 
 
 .248 
 
 .20362 
 
 51,2 
 
 .27536 
 
 36,8 
 
 .92825 
 
 14,4 
 
 .07175 
 
 .249 
 
 .20413 
 
 51,2 
 
 27573 
 
 36,8 
 
 .92840 
 
 14,4 
 
 .07160 
 
 1.250 
 
 0.20464 
 
 51,2 
 
 0.27610 
 
 36,8 
 
 9.92854 
 
 14,4 
 
 0.07146 
 
 u 
 
 log tan gd u 
 
 -Fo' 
 
 log sec gd u 
 
 -Fo' 
 
 log sin gd u 
 
 - Fo' 
 
 log esc gd u 
 
 SMITHSONIAN TABLES 
 
 44 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 Fo' 
 
 log cosh u 
 
 F ' 
 
 log tanh u 
 
 F ' 
 
 log coth u 
 
 1.250 
 
 0.20464 
 
 51,2 
 
 0.27610 
 
 36,8 
 
 9.92854 
 
 14,4 
 
 0.07146 
 
 .251 
 
 .20515 
 
 51,2 
 
 .27647 
 
 36,9 
 
 .92868 
 
 14,3 
 
 .07132 
 
 .252 
 
 .20566 
 
 51,2 
 
 .27684 
 
 36,9 
 
 .92883 
 
 14,3 
 
 .07117 
 
 .253 
 
 .20618 
 
 51, 
 
 .27721 
 
 36,9 
 
 .92897 
 
 14,3 
 
 .07103 
 
 .254 
 
 .20669 
 
 51, 
 
 27757 
 
 36,9 
 
 .92911 
 
 14,2 
 
 .07089 
 
 1.255 
 
 0.20720 
 
 Si, 
 
 0.27794 
 
 36,9 
 
 9.92926 
 
 14,2 
 
 0.07074 
 
 .256 
 
 .20771 
 
 51, 
 
 .27831 
 
 36,9 
 
 .92940 
 
 14,2 
 
 .07060 
 
 .257 
 
 .20822 
 
 5i, 
 
 .27868 
 
 36,9 
 
 .92954 
 
 14,2 
 
 .07046 
 
 .258 
 
 .20873 
 
 51, 
 
 .27905 
 
 36,9 
 
 .92968 
 
 14,1 
 
 .07032 
 
 .259 
 
 .20924 
 
 5i,o 
 
 .27942 
 
 36,9 
 
 .92982 
 
 14,1 
 
 .07018 
 
 1.260 
 
 0.20975 
 
 5i,o 
 
 0.27979 
 
 37,o 
 
 9.92996 
 
 14,1 
 
 0.07004 
 
 .261 
 
 .21026 
 
 5i,o 
 
 .28016 
 
 37,o 
 
 .93010 
 
 14,0 
 
 .06990 
 
 .262 
 
 .21077 
 
 5i,o 
 
 .28053 
 
 37,o 
 
 .93024 
 
 14,0 
 
 .06976 
 
 .263 
 
 .21128 
 
 5i,o 
 
 .28090 
 
 37,o 
 
 .93038 
 
 14,0 
 
 .06962 
 
 .264 
 
 .21179 
 
 5i,o 
 
 .28127 
 
 37,o 
 
 .93052 
 
 14,0 
 
 .06948 
 
 1.265 
 
 0.21230 
 
 50,9 
 
 0.28164 
 
 37,0 
 
 9.93066 
 
 13,9 
 
 0.06934 
 
 .266 
 
 .21281 
 
 50,9 
 
 .28201 
 
 37,0 
 
 .93080 
 
 13,9 
 
 .06920 
 
 .267 
 
 .21332 
 
 50,9 
 
 .28238 
 
 37,o 
 
 .93094 
 
 13,9 
 
 .06906 
 
 .268 
 
 .21383 
 
 50,9 
 
 .28275 
 
 37,1 
 
 .93108 
 
 13,8 
 
 .06892 
 
 .269 
 
 .21434 
 
 50,9 
 
 .28312 
 
 37,1 
 
 .93122 
 
 13,8 
 
 .06878 
 
 1.270 
 
 0.21485 
 
 50,9 
 
 0.28349 
 
 37,1 
 
 9.93135 
 
 13,8 
 
 0.06865 
 
 .271 
 
 .21536 
 
 50,9 
 
 .28386 
 
 37,i 
 
 .93149 
 
 13,8 
 
 .06851 
 
 .272 
 
 .21586 
 
 50,8 
 
 .28423 
 
 37,1 
 
 .93163 
 
 13,7 
 
 .06837 
 
 273 
 
 .21637 
 
 50,8 
 
 .28460 
 
 37,1 
 
 .93177 
 
 13,7 
 
 .06823 
 
 .274 
 
 .21688 
 
 50,8 
 
 .28498 
 
 37,1 
 
 .93190 
 
 13,7 
 
 .06810 
 
 1.275 
 
 0.21739 
 
 50,8 
 
 0.28535 
 
 37,1 
 
 9.93204 
 
 13,6 
 
 0.06796 
 
 .276 
 
 .21790 
 
 50,8 
 
 .28572 
 
 37,2 
 
 .93218 
 
 13,6 
 
 .06782 
 
 .277 
 
 .21840 
 
 50,8 
 
 .28609 
 
 37,2 
 
 .93231 
 
 13,6 
 
 .06769 
 
 .278 
 
 .21891 
 
 50,7 
 
 .28646 
 
 37,2 
 
 .93245 
 
 13,6 
 
 06755 
 
 .279 
 
 .21942 
 
 50,7 
 
 .28683 
 
 37,2 
 
 .93258 
 
 13,5 
 
 .06742 
 
 1.280 
 
 0.21993 
 
 50,7 
 
 0.28721 
 
 37,2 
 
 9.93272 
 
 13,5 
 
 0.06728 
 
 .281 
 
 .22043 
 
 50,7 
 
 .28758 
 
 37,2 
 
 .93285 
 
 13,5 
 
 .06715 
 
 .282 
 
 .22094 
 
 50,7 
 
 .28795 
 
 37,2 
 
 .93299 
 
 13,5 
 
 .06701 
 
 .283 
 
 .22145 
 
 50,7 
 
 .28832 
 
 37,2 
 
 .93312 
 
 13,4 
 
 .06688 
 
 .284 
 
 .22195 
 
 50,6 
 
 .28869 
 
 37,2 
 
 .93326 
 
 13,4 
 
 .06674 
 
 1.285 
 
 0.22246 
 
 50,6 
 
 0.28907 
 
 37,3 
 
 9-93339 
 
 13,4 
 
 O.o666l 
 
 .286 
 
 .22296 
 
 50,6 
 
 .28944 
 
 37,3 
 
 93353 
 
 13,3 
 
 .06647 
 
 .287 
 
 .22347 
 
 50,6 
 
 .28981 
 
 37,3 
 
 .93366 
 
 13,3 
 
 .06634 
 
 .288 
 
 .22398 
 
 50,6 
 
 .29018 
 
 37,3 
 
 93379 
 
 13,3 
 
 .06621 
 
 .289 
 
 .22448 
 
 50,6 
 
 .29056 
 
 37,3 
 
 93392 
 
 13,3 
 
 .06608 
 
 1.200 
 
 0.22499 
 
 50,6 
 
 0.29093 
 
 37,3 
 
 9.93406 
 
 13,2 
 
 0.06594 
 
 .291 
 
 .22549 
 
 50,5 
 
 .29130 
 
 37,3 
 
 .93419 
 
 13,2 
 
 .06581 
 
 .292 
 
 .22600 
 
 50,5 
 
 .29168 
 
 37,3 
 
 .93432 
 
 13,2 
 
 .06568 
 
 .293 
 
 .22650 
 
 50,5 
 
 .29205 
 
 37,3 
 
 93445 
 
 13,2 
 
 .06555 
 
 .294 
 
 .22701 
 
 50,5 
 
 .29242 
 
 37,4 
 
 .93458 
 
 I3,i 
 
 .06542 
 
 1.295 
 
 0.22751 
 
 50,5 
 
 0.29280 
 
 37,4 
 
 9.93472 
 
 I3,i 
 
 0.06528 
 
 .296 
 
 .22802 
 
 50,5 
 
 .29317 
 
 37,4 
 
 .93485 
 
 13,1 
 
 .06515 
 
 .297 
 
 .22852 
 
 50,4 
 
 .29355 
 
 37,4 
 
 .93498 
 
 I3,i 
 
 .06502 
 
 .298 
 
 .22003 
 
 50,4 
 
 .29392 
 
 37,4 
 
 935II 
 
 13,0 
 
 .06489 
 
 .299 
 
 .22953 
 
 50,4 
 
 .29429 
 
 37,4 
 
 .93524 
 
 I3,o 
 
 .06476 
 
 1.300 
 
 0.23004 
 
 50,4 
 
 0.29467 
 
 37,4 
 
 9-93537 
 
 I3,o 
 
 0.06463 
 
 u 
 
 log tan gd u 
 
 Fo' 
 
 log sec gd u 
 
 ' Fo' 
 
 log sin gd u 
 
 Fo' 
 
 log esc gd u 
 
 SMITHSONIAN TABLES 
 
 45 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 <o Fo' 
 
 log cosh u 
 
 F ' 
 
 log tanh u 
 
 Fo' 
 
 log coth u 
 
 1.300 
 
 0.23004 
 
 50,4 
 
 0.29467 
 
 37,4 
 
 9-93537 
 
 13,0 
 
 0.06463 
 
 .301 
 
 23054 
 
 50,4 
 
 .29504 
 
 37,4 
 
 93550 
 
 12,9 
 
 .06450 
 
 .302 
 
 .23104 
 
 50,4 
 
 .29542 
 
 37,4 
 
 .93563 
 
 12,9 
 
 .06437 
 
 .303 
 
 .23155 
 
 50,4 
 
 .29579 
 
 37,5 
 
 .93576 
 
 12,9 
 
 .06424 
 
 .304 
 
 .23205 
 
 50,3 
 
 .29617 
 
 37,5 
 
 .93588 
 
 12,9 
 
 .06412 
 
 1.305 
 
 0.23255 
 
 50,3 
 
 0.29654 
 
 37,5 
 
 9.93601 
 
 12,8 
 
 0.06399 
 
 .306 
 
 .23306 
 
 50,3 
 
 .29692 
 
 37,5 
 
 .93614 
 
 12,8 
 
 .06386 
 
 .307 
 
 .23356 
 
 50,3 
 
 .29729 
 
 37,5 
 
 .93627 
 
 12,8 
 
 .06373 
 
 .308 
 
 .23406 
 
 50,3 
 
 .29767 
 
 37,5 
 
 .93640 
 
 12,8 
 
 .06360 
 
 .309 
 
 .23457 
 
 50,3 
 
 .29804 
 
 37,5 
 
 .93652 
 
 12,7 
 
 .06348 
 
 1.310 
 
 0.23507 
 
 50,2 
 
 0.29842 
 
 37,5 
 
 9.93665 
 
 12,7 
 
 0.06335 
 
 .311 
 
 .23557 
 
 50,2 
 
 29879 
 
 37,5 
 
 .93678 
 
 12,7 
 
 .06322 
 
 .312 
 
 .23607 
 
 50,2 
 
 .29917 
 
 37,6 
 
 .93691 
 
 12,7 
 
 .06309 
 
 .313 
 
 23657 
 
 50,2 
 
 .29954 
 
 37,6 
 
 .93703 
 
 12,6 
 
 .06297 
 
 .314 
 
 .23708 
 
 50,2 
 
 .29992 
 
 37,6 
 
 .93716 
 
 12,6 
 
 .06284 
 
 1.315 
 
 0.23758 
 
 50,2 
 
 0.30029 
 
 3>,6 
 
 9.93728 
 
 12,6 
 
 0.06272 
 
 .316 
 
 .23808 
 
 50,2 
 
 .30067 
 
 37,6 
 
 93741 
 
 12,6 
 
 .06259 
 
 .317 
 
 .23858 
 
 50,1 
 
 .30105 
 
 37,6 
 
 93754 
 
 12,5 
 
 .06246 
 
 .318 
 
 .23008 
 
 50,1 
 
 .30142 
 
 37,6 
 
 .93766 
 
 12,5 
 
 .06234 
 
 .319 
 
 .23958 
 
 50,i 
 
 .30180 
 
 37,6 
 
 93779 
 
 12,5 
 
 .06221 
 
 1.320 
 
 0.24009 
 
 50,1 
 
 0.30217 
 
 37,6 
 
 9.93791 
 
 12,5 
 
 0.06209 
 
 .321 
 
 .24059 
 
 50,1 
 
 30255 
 
 37,7 
 
 .93804 
 
 12,4 
 
 .06196 
 
 .322 
 
 .24109 
 
 50,1 
 
 .30293 
 
 37,7 
 
 .93816 
 
 12,4 
 
 .06184 
 
 .323 
 
 .24159 
 
 50,1 
 
 .30330 
 
 37,7 
 
 .93828 
 
 12,4 
 
 .06172 
 
 .324 
 
 .24209 
 
 5o,o 
 
 .30368 
 
 37,7 
 
 .93841 
 
 12,4 
 
 .06159 
 
 1.325 
 
 0.24259 
 
 50,o 
 
 0.30406 
 
 37,7 
 
 9.93853 
 
 12,3 
 
 0.06147 
 
 .326 
 
 .24309 
 
 5o,o 
 
 .30444 
 
 37,7 
 
 .93865 
 
 12,3 
 
 .06135 
 
 .327 
 
 .24359 
 
 50,o 
 
 .30481 
 
 37,7 
 
 .93878 
 
 12,3 
 
 .06122 
 
 .328 
 
 .24409 
 
 50,0 
 
 .30519 
 
 37,7 
 
 .93890 
 
 12,3 
 
 .06110 
 
 .329 
 
 .24459 
 
 50,0 
 
 30557 
 
 37,7 
 
 .93902 
 
 12,2 
 
 .06098 
 
 1.330 
 
 0.24509 
 
 50,o 
 
 0-30594 
 
 37,8 
 
 9.93914 
 
 12,2 
 
 0.06086 
 
 .331 
 
 .24559 
 
 49,9 
 
 .30632 
 
 37,8 
 
 .93927 
 
 12,2 
 
 .00073 
 
 .332 
 
 .24609 
 
 49,9 
 
 .30670 
 
 37,8 
 
 93939 
 
 12,2 
 
 .06061 
 
 .333 
 
 .24659 
 
 49,9 
 
 .30708 
 
 37,8 
 
 .93951 
 
 12,1 
 
 .06049 
 
 334 
 
 .24709 
 
 49,9 
 
 .30746 
 
 37,8 
 
 .93963 
 
 12,1 
 
 .06037 
 
 1.335 
 
 0.24759 
 
 49,9 
 
 0.30783 
 
 37,8 
 
 9-93975 
 
 12,1 
 
 0.06025 
 
 .336 
 
 .24808 
 
 49,9 
 
 .30821 
 
 37,8 
 
 .93987 
 
 12,1 
 
 .06013 
 
 337 
 
 .24858 
 
 49,9 
 
 .30859 
 
 37,8 
 
 93999 
 
 1 2,O 
 
 .06001 
 
 .338 
 
 .24908 
 
 49,9 
 
 .30897 
 
 37,8 
 
 .94011 
 
 1 2,O 
 
 .05989 
 
 339 
 
 .24958 
 
 49,8 
 
 .30935 
 
 37,8 
 
 .04023 
 
 12,0 
 
 05977 
 
 1.340 
 
 0.25008 
 
 49,8 
 
 0.30972 
 
 37,9 
 
 9.94035 
 
 12,0 
 
 0.05965 
 
 341 
 
 .25058 
 
 49,8 
 
 .31010 
 
 37,9 
 
 .94047 
 
 11,9 
 
 .05953 
 
 .342 
 
 .25107 
 
 49,8 
 
 .31048 
 
 37,9 
 
 .94059 
 
 n,9 
 
 .05941 
 
 343 
 
 .25157 
 
 49,8 
 
 .31086 
 
 37,9 
 
 .94071 
 
 11,9 
 
 .05929 
 
 344 
 
 .25207 
 
 49,8 
 
 .31124 
 
 37,9 
 
 94083 
 
 11,9 
 
 .05917 
 
 1-345 
 
 0.25257 
 
 49,8 
 
 0.31162 
 
 37,9 
 
 9.94095 
 
 11,8 
 
 0.05905 
 
 .346 
 
 .25306 
 
 49,7 
 
 .31200 
 
 37,9 
 
 .94107 
 
 11,8 
 
 .05893 
 
 347 
 
 .25356 
 
 49,7 
 
 .31238 
 
 37,9 
 
 .94119 
 
 n,8 
 
 .05881 
 
 .348 
 
 .25406 
 
 49,7 
 
 .31276 
 
 37,9 
 
 94130 
 
 n,8 
 
 .05870 
 
 349 
 
 .25456 
 
 49,7 
 
 .3I3U 
 
 37,9 
 
 .94142 
 
 n,8 
 
 .05858 
 
 1.350 
 
 0.25505 
 
 49,7 
 
 0.31352 
 
 38,0 
 
 9.04154 
 
 ii,7 
 
 0.05846 
 
 u 
 
 loo tin gd u 
 
 Fo' 
 
 log tec gd u 
 
 Fo' 
 
 log sin gd u 
 
 *.F ' 
 
 log esc gd u 
 
 SMITHSONIAN TABLES 
 
 4 6 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 Fo' 
 
 log cosh u 
 
 F ' 
 
 log tanh u 
 
 Fo' 
 
 log coth u 
 
 1.350 
 
 0.25505 
 
 49,7 
 
 0.31352 
 
 38,0 
 
 9.94154 
 
 n,7 
 
 0.05846 
 
 .351 
 
 .25555 
 
 49,7 
 
 .31390 
 
 38,0 
 
 .94166 
 
 u,7 
 
 .05834 
 
 .352 
 
 .25605 
 
 49,7 
 
 .31428 
 
 38,0 
 
 .94177 
 
 n,7 
 
 .05823 
 
 353 
 
 .25654 
 
 49,6 
 
 .31465 
 
 38,0 
 
 .94189 
 
 n,7 
 
 .05811 
 
 354 
 
 .25704 
 
 49,6 
 
 .31503 
 
 38,0 
 
 .94201 
 
 n,6 
 
 .05799 
 
 1-355 
 
 0.25754 
 
 49,6 
 
 0.3I54I 
 
 38,0 
 
 9.94212 
 
 11,6 
 
 0.05788 
 
 356 
 
 .25803 
 
 49,6 
 
 .31580 
 
 38,0 
 
 .94224 
 
 11,6 
 
 .05776 
 
 357 
 
 .25853 
 
 49,6 
 
 .31618 
 
 38,0 
 
 .94235 
 
 11,6 
 
 .05765 
 
 .358 
 
 .25902 
 
 49,6 
 
 .31656 
 
 38,0 
 
 .94247 
 
 n,5 
 
 .05753 
 
 359 
 
 .25952 
 
 49,6 
 
 .31694 
 
 38,1 
 
 .94258 
 
 n,5 
 
 .05742 
 
 1.360 
 
 0.26002 
 
 49,6 
 
 0.31732 
 
 38,1 
 
 9.94270 
 
 n,5 
 
 0.05730 
 
 .361 
 
 .26051 
 
 49,5 
 
 .31770 
 
 38,1 
 
 .94281 
 
 n,5 
 
 .05719 
 
 .362 
 
 .26101 
 
 49,5 
 
 .31808 
 
 38,1 
 
 .94293 
 
 11,4 
 
 .05707 
 
 .363 
 
 .26150 
 
 49,5 
 
 .31846 
 
 38,1 
 
 .94304 
 
 11,4 
 
 .05696 
 
 .364 
 
 .26200 
 
 49,5 
 
 .31884 
 
 38,1 
 
 .94316 
 
 11,4 
 
 .05684 
 
 1.365 
 
 0.26249 
 
 49,5 
 
 0.31922 
 
 38,1 
 
 9.94327 
 
 ii,4 
 
 0.0567^3 
 
 .366 
 
 .26299 
 
 49,5 
 
 .31960 
 
 38,1 
 
 .94338 
 
 11,4 
 
 .05662 
 
 .367 
 
 .26348 
 
 49,5 
 
 .31998 
 
 38,1 
 
 94350 
 
 u,3 
 
 .05650 
 
 .368 
 
 .26398 
 
 49,5 
 
 .32036 
 
 38,1 
 
 .94361 
 
 n,3 
 
 .05639 
 
 .369 
 
 .26447 
 
 49,4 
 
 .32075 
 
 38,2 
 
 94372 
 
 n,3 
 
 .05628 
 
 1.370 
 
 0.26496 
 
 49,4 
 
 0.32113 
 
 38,2 
 
 9.94384 
 
 n,3 
 
 0.05616 
 
 371 
 
 .26546 
 
 49,4 
 
 .32151 
 
 38,2 
 
 94395 
 
 11,2 
 
 .05605 
 
 372 
 
 .26595 
 
 49,4 
 
 .32189 
 
 38,2 
 
 .94406 
 
 11,2 
 
 05594 
 
 373 
 
 .26645 
 
 49,4 
 
 .32227 
 
 38,2 
 
 .94417 
 
 11,2 
 
 .05583 
 
 374 
 
 .26694 
 
 49,4 
 
 .32266 
 
 38,2 
 
 .94429 
 
 11,2 
 
 .05571 
 
 1-375 
 
 0.26743 
 
 49,4 
 
 0.32304 
 
 38,2 
 
 9.94440 
 
 11,2 
 
 0,05560 
 
 376 
 
 .26793 
 
 49,3 
 
 .32342 
 
 38,2 
 
 94451 
 
 1 1,1 
 
 05549 
 
 377 
 
 .26842 
 
 49,3 
 
 .32380 
 
 38,2 
 
 .94462 
 
 11,1 
 
 .05538 
 
 .378 
 
 .26891 
 
 49,3 
 
 .32418 
 
 38,2 
 
 94473 
 
 11,1 
 
 .05527 
 
 379 
 
 .26941 
 
 49,3 
 
 .32457 
 
 38,2 
 
 .94484 
 
 11,1 
 
 .05516 
 
 1.380 
 
 0.26990 
 
 49,3 
 
 0.32495 
 
 38,3 
 
 9-94495 
 
 11,0 
 
 0.05505 
 
 .381 
 
 .27039 
 
 49,3 
 
 .32533 
 
 38,3 
 
 .94506 
 
 11,0 
 
 .05494 
 
 .382 
 
 .27089 
 
 49,3 
 
 .32571 
 
 38,3 
 
 .94517 
 
 11,0 
 
 .05483 
 
 .383 
 
 .27138 
 
 49,3 
 
 .32610 
 
 38,3 
 
 .94528 
 
 11,0 
 
 .05472 
 
 .384 
 
 .27187 
 
 49,2 
 
 .32648 
 
 38,3 
 
 94539 
 
 11,0 
 
 .05461 
 
 1.385 
 
 0.27236 
 
 49,2 
 
 0.32686 
 
 38,3 
 
 9-94550 
 
 10,9 
 
 0.05450 
 
 .386 
 
 .27286 
 
 49,2 
 
 .32725 
 
 38,3 
 
 .94561 
 
 10,9 
 
 .05439 
 
 .387 
 
 .27335 
 
 49,2 
 
 .32763 
 
 38,3 
 
 .94572 
 
 10,9 
 
 .05428 
 
 .388 
 
 .27384 
 
 49,2 
 
 .32801 
 
 38,3 
 
 .94583 
 
 10,9 
 
 .05417 
 
 .389 
 
 .27433 
 
 49,2 
 
 .32840 
 
 38,3 
 
 94594 
 
 10,8 
 
 .05406 
 
 1.390 
 
 0.27482 
 
 49,2 
 
 0.32878 
 
 38,4 
 
 9.94604 
 
 10,8 
 
 0.05396 
 
 391 
 
 .27532 
 
 49,2 
 
 .32916 
 
 38,4 
 
 .94615 
 
 10,8 
 
 .05385 
 
 .392 
 
 .27581 
 
 49,2 
 
 .32955 
 
 38,4 
 
 .94626 
 
 10,8 
 
 .05374 
 
 393 
 
 .27630 
 
 49,1 
 
 .32993 
 
 38,4 
 
 .94637 
 
 10,8 
 
 .05363 
 
 394 
 
 .27679 
 
 49,i 
 
 .33031 
 
 38,4 
 
 .94648 
 
 10,7 
 
 .05352 
 
 1-395 
 
 0.27728 
 
 49,1 
 
 0.33070 
 
 38,4 
 
 9.94658 
 
 10,7 
 
 0.05342 
 
 .396 
 
 .27777 
 
 49,1 
 
 .33108 
 
 38,4 
 
 .94669 
 
 10,7 
 
 .05331 
 
 397 
 
 .27826 
 
 49,1 
 
 .33147 
 
 38,4 
 
 .94680 
 
 10,7 
 
 .05320 
 
 .398 
 
 .27875 
 
 49,1 
 
 .33185 
 
 38,4 
 
 .94690 
 
 10,6 
 
 .05310 
 
 399 
 
 .27925 
 
 49,1 
 
 .33224 
 
 38,4 
 
 .94701 
 
 10,6 
 
 .05299 
 
 1.400 
 
 0.27974 
 
 49,1 
 
 o . 33262 
 
 38,5 
 
 9.94712 
 
 10,6 
 
 0.05288 
 
 u | log tan gd u 
 
 F ' 
 
 log sec gd u 
 
 Fo' 
 
 log sin gd u 
 
 F O ' 
 
 logcscgdu 
 
 SMITHSONIAN TABLES 
 
 47 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 - Fo' 
 
 log cosh u 
 
 -Fo' 
 
 log tanh u 
 
 Fo' 
 
 log coth u 
 
 1.400 
 
 0.27974 
 
 49,1 
 
 0.33262 
 
 38,5 
 
 9.94712 
 
 10,6 
 
 0.05288 
 
 .401 
 
 .28023 
 
 49,0 
 
 33300 
 
 38,5 
 
 .94722 
 
 10,6 
 
 .05278 
 
 .402 
 
 .28072 
 
 49,0 
 
 33339 
 
 38,5 
 
 94733 
 
 10,6 
 
 .05267 
 
 .403 
 
 .28121 
 
 49,0 
 
 .33377 
 
 38,5 
 
 .94743 
 
 io,5 
 
 .05257 
 
 .404 
 
 .28170 
 
 49,0 
 
 .33416 
 
 38,5 
 
 94754 
 
 10,5 
 
 .05246 
 
 1.405 
 
 0.28219 
 
 49,0 
 
 0.33454 
 
 38,5 
 
 9.94764 
 
 10,5 
 
 0.05236 
 
 .406 
 
 .28268 
 
 49,0 
 
 33493 
 
 38,5 
 
 94775 
 
 10,5 
 
 .05225 
 
 .407 
 
 .28317 
 
 49,0 
 
 33531 
 
 38,5 
 
 .94785 
 
 10,5 
 
 .05215 
 
 .408 
 
 .28366 
 
 49,0 
 
 .33570 
 
 38,5 
 
 .94796 
 
 10,4 
 
 .05204 
 
 .409 
 
 .28 4 I5 
 
 48,9 
 
 .33608 
 
 38,5 
 
 .94806 
 
 10,4 
 
 .05194 
 
 1.410 
 
 0.28464 
 
 48,9 
 
 0.33647 
 
 38,5 
 
 9.94817 
 
 10,4 
 
 0.05183 
 
 .411 
 
 .28512 
 
 48,9 
 
 .33686 
 
 38,6 
 
 94827 
 
 10,4 
 
 .05173 
 
 .412 
 
 .28561 
 
 48,9 
 
 .33724 
 
 38,6 
 
 .94837 
 
 10,3 
 
 .05163 
 
 .413 
 
 .28610 
 
 48,9 
 
 .33763 
 
 38,6 
 
 .94848 
 
 10,3 
 
 .05152 
 
 .414 
 
 .28659 
 
 48,9 
 
 .33801 
 
 38,6 
 
 .94858 
 
 10,3 
 
 .05142 
 
 1.415 
 
 0.28708 
 
 48,9 
 
 0.33840 
 
 38,6 
 
 9.94868 
 
 10,3 
 
 0.05132 
 
 .416 
 
 .28757 
 
 48,9 
 
 .33878 
 
 38,6 
 
 .94879 
 
 10,3 
 
 .05121 
 
 .417 
 
 .28806 
 
 48,9 
 
 .33917 
 
 38,6 
 
 .94889 
 
 10,2 
 
 .05111 
 
 .418 
 
 .28855 
 
 48,8 
 
 33956 
 
 38,6 
 
 .94899 
 
 10,2 
 
 .05101 
 
 .419 
 
 .28903 
 
 48,8 
 
 33994 
 
 38,6 
 
 .94909 
 
 10,2 
 
 .05091 
 
 1.420 
 
 0.28952 
 
 48,8 
 
 0.34033 
 
 38,6 
 
 9.94919 
 
 10,2 
 
 0.05081 
 
 .421 
 
 .20001 
 
 48,8 
 
 .34071 
 
 38,6 
 
 .94930 
 
 10,2 
 
 .05070 
 
 .422 
 
 .29050 
 
 48,8 
 
 .34110 
 
 38,7 
 
 .94940 
 
 IO,I 
 
 .05060 
 
 .423 
 
 .29099 
 
 48,8 
 
 .34U9 
 
 38,7 
 
 .94950 
 
 IO,I 
 
 .05050 
 
 .424 
 
 .29147 
 
 48,8 
 
 .34187 
 
 38,7 
 
 .94960 
 
 IO,I 
 
 .05040 
 
 1.425 
 
 0.29196 
 
 48,8 
 
 0.34226 
 
 38,7 
 
 9.94970 
 
 IO,I 
 
 0.05030 
 
 .426 
 
 .29245 
 
 48,8 
 
 .34265 
 
 38,7 
 
 .94980 
 
 10,1 
 
 .05020 
 
 .427 
 
 .29294 
 
 48,7 
 
 .34304 
 
 38,7 
 
 .94990 
 
 IQ,O 
 
 .05010 
 
 .428 
 
 .29342 
 
 48,7 
 
 34342 
 
 38,7 
 
 .95000 
 
 IO,O 
 
 .O5OOO 
 
 .429 
 
 .29391 
 
 48,7 
 
 .34381 
 
 38,7 
 
 .95010 
 
 10,0 
 
 .04990 
 
 1.430 
 
 0.29440 
 
 48,7 
 
 0.34420 
 
 38,7 
 
 9.95020 
 
 IO,O 
 
 0.04980 
 
 .431 
 
 .29489 
 
 48,7 
 
 .34458 
 
 38,7 
 
 .95030 
 
 10,0 
 
 .04970 
 
 .432 
 
 .29537 
 
 48,7 
 
 .34497 
 
 38,7 
 
 .95040 
 
 9,9 
 
 .04060 
 
 .433 
 
 .29586 
 
 48,7 
 
 34536 
 
 38,8 
 
 .95050 
 
 9,9 
 
 .04950 
 
 434 
 
 .29635 
 
 48,7 
 
 .34575 
 
 38,8 
 
 .95060 
 
 9,9 
 
 .04940 
 
 1.435 
 
 0.29683 
 
 48,7 
 
 0.34613 
 
 38,8 
 
 9.95070 
 
 9,9 
 
 0.04930 
 
 .436 
 
 .29732 
 
 48,6 
 
 34652 
 
 38,8 
 
 .95080 
 
 9,9 
 
 .04920 
 
 .437 
 
 .29781 
 
 48,6 
 
 .34691 
 
 38,8 
 
 .95090 
 
 9,8 
 
 .04910 
 
 .438 
 
 .29829 
 
 48,6 
 
 34730 
 
 38,8 
 
 .95009 
 
 9,8 
 
 .04901 
 
 .439 
 
 .29878 
 
 48,6 
 
 .34769 
 
 38,8 
 
 .95109 
 
 9,8 
 
 .04891 
 
 1.440 
 
 O.29926 
 
 48,6 
 
 0.34807 
 
 38,8 
 
 9.95119 
 
 9,8 
 
 0.04881 
 
 .441 
 
 .29975 
 
 48,6 
 
 .34846 
 
 38,8 
 
 .95129 
 
 9,8 
 
 .04871 
 
 442 
 
 .30024 
 
 48,6 
 
 .34885 
 
 38,8 
 
 .95139 
 
 9,7 
 
 .04861 
 
 443 
 
 .30072 
 
 48,6 
 
 .34924 
 
 38,8 
 
 .95148 
 
 9,7 
 
 .04852 
 
 444 
 
 .30121 
 
 48,6 
 
 .34963 
 
 38,8 
 
 .95158 
 
 9,7 
 
 .04842 
 
 1.445 
 
 0.30169 
 
 48,5 
 
 0.35002 
 
 38,9 
 
 9.95168 
 
 9,7 
 
 0.04832 
 
 .446 
 
 .30218 
 
 48,5 
 
 .35040 
 
 38,9 
 
 .95177 
 
 9,7 
 
 .04823 
 
 .447 
 
 .30266 
 
 48,5 
 
 .35079 
 
 38,9 
 
 .95187 
 
 9,6 
 
 .04813 
 
 .448 
 
 .30315 
 
 48,5 
 
 .35118 
 
 38,9 
 
 .95197 
 
 9,6 
 
 .04803 
 
 .449 
 
 .30363 
 
 48,5 
 
 .35157 
 
 38,9 
 
 .95206 
 
 9,6 
 
 .04794 
 
 1.450 
 
 O.3O4I2 
 
 48,5 
 
 0.35196 
 
 38,9 
 
 9.95216 
 
 9,6 
 
 0.04784 
 
 u 
 
 log tan ad u 
 
 Fo' 
 
 log iec gd u 
 
 Fo' 
 
 log tin gd u 
 
 Fo' 
 
 log esc gd u 
 
 SMITHSONIAN TABLES 
 
 4 8 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 F ' . 
 
 log cosh u 
 
 F ' 
 
 log tanh u 
 
 Fo' 
 
 log coth u 
 
 1.450 
 
 0.30412 
 
 48,5 
 
 0.35196 
 
 38,9 
 
 9.95216 
 
 9,6 
 
 0.04784 
 
 .451 
 
 .30460 
 
 48,5 
 
 .35235 
 
 38,9 
 
 .95225 
 
 9,6 
 
 .04775 
 
 .452 
 
 .30509 
 
 48,5 
 
 .35274 
 
 38,9 
 
 .95235 
 
 9,5 
 
 .04765 
 
 453 
 
 .30557 
 
 48,5 
 
 .35313 
 
 38,9 
 
 .95245 
 
 9,5 
 
 .04755 
 
 454 
 
 .30606 
 
 48,4 
 
 35352 
 
 38,9 
 
 .95254 
 
 9,5 
 
 .04746 
 
 1. 455 
 
 0.30654 
 
 48,4 
 
 0.35391 
 
 38,9 
 
 9.95264 
 
 9,5 
 
 0.04736 
 
 .456 
 
 .30703 
 
 48,4 
 
 .35429 
 
 39,o 
 
 .95273 
 
 9,5 
 
 .04727 
 
 457 
 
 .30751 
 
 48,4 
 
 .35468 
 
 39,0 
 
 .95283 
 
 9,5 
 
 .04717 
 
 .458 
 
 30799 
 
 48,4 
 
 .35507 
 
 39,o 
 
 .95292 
 
 9,4 
 
 .04708 
 
 459 
 
 .30848 
 
 48,4 
 
 .35546 
 
 39,0 
 
 .95301 
 
 9,4 
 
 .04699 
 
 1.460 
 
 0.30896 
 
 48,4 
 
 0.35585 
 
 39,0 
 
 9.953H 
 
 9,4 
 
 0.04689 
 
 .461 
 
 .30945 
 
 48,4 
 
 .35624 
 
 39,0 
 
 95320 
 
 9,4 
 
 .04680 
 
 .462 
 
 .30993 
 
 48,4 
 
 .35663 
 
 39,0 
 
 95330 
 
 9,4 
 
 .04670 
 
 .463 
 
 .31041 
 
 48,3 
 
 .35702 
 
 39,0 
 
 .95339 
 
 9,3 
 
 .04661 
 
 .464 
 
 .31090 
 
 48,3 
 
 35741 
 
 39,0 
 
 .95348 
 
 9,3 
 
 .04652 
 
 1.465 
 
 0.31138 
 
 48,3 
 
 0.35780 
 
 39,0 
 
 9.95358 
 
 9,3 
 
 0.04642 
 
 .466 
 
 .31186 
 
 48,3 
 
 .35819 
 
 39,0 
 
 .95367 
 
 9,3 
 
 .04633 
 
 .467 
 
 .31235 
 
 48,3 
 
 .35858 
 
 39,0 
 
 .95376 
 
 9,3 
 
 .04624 
 
 .468 
 
 .31283 
 
 48,3 
 
 .35897 
 
 39,1 
 
 .95385 
 
 9,2 
 
 .04615 
 
 469 
 
 .31331 
 
 48,3 
 
 .35937 
 
 39,1 
 
 .95395 
 
 9,2 
 
 .04605 
 
 1.470 
 
 0.31379 
 
 48,3 
 
 0.35976 
 
 39,1 
 
 9.95404 
 
 9,2 
 
 0.04506 
 
 .471 
 
 .31428 
 
 48,3 
 
 .36015 
 
 39,1 
 
 .95413 
 
 9,2 
 
 04587 
 
 .472 
 
 .31476 
 
 48,3 
 
 .36054 
 
 39,1 
 
 95422 
 
 9,2 
 
 .04578 
 
 473 
 
 .31524 
 
 48,2 
 
 .36093 
 
 39,i 
 
 95431 
 
 9,2 
 
 .04569 
 
 474 
 
 .31572 
 
 48,2 
 
 .36132 
 
 39,1 
 
 95441 
 
 9,i 
 
 .04559 
 
 1. 475 
 
 0.31621 
 
 48,2 
 
 0.36171 
 
 39,1 
 
 9-95450 
 
 9,i 
 
 0.04550 
 
 .476 
 
 .31669 
 
 48,2 
 
 .36210 
 
 39,1 
 
 95459 
 
 9,i 
 
 .04541 
 
 477 
 
 .31717 
 
 48,2 
 
 .36249 
 
 39,i 
 
 .95468 
 
 9,i 
 
 .04532 
 
 .478 
 
 31765 
 
 48,2 
 
 .36288 
 
 39,i 
 
 95477 
 
 9,i 
 
 .04523 
 
 479 
 
 .31814 
 
 48,2 
 
 .36328 
 
 39,1 
 
 .95486 
 
 9,o 
 
 .04514 
 
 1.480 
 
 0.31862 
 
 48,2 
 
 0.36367 
 
 39,2 
 
 9-95495 
 
 9,o 
 
 0.04505 
 
 .481 
 
 .31910 
 
 48,2 
 
 .36406 
 
 39,2 
 
 .95504 
 
 9,o 
 
 .04496 
 
 .482 
 
 .31958 
 
 48,2 
 
 .36445 
 
 39,2 
 
 .95513 
 
 9,o 
 
 .04487 
 
 .483 
 
 .32006 
 
 48,1 
 
 .36484 
 
 39,2 
 
 .95522 
 
 9,o 
 
 .04478 
 
 .484 
 
 .32054 
 
 48,1 
 
 .36523 
 
 39,2 
 
 95531 
 
 9,0 
 
 .04469 
 
 1.485 
 
 0.32102 
 
 48,1 
 
 0.36563 
 
 39,2 
 
 95540 
 
 8,9 
 
 .04460 
 
 .486 
 
 .32151 
 
 48,1 
 
 .36602 
 
 39,2 
 
 95549 
 
 8,9 
 
 .04451 
 
 .487 
 
 .32199 
 
 48,1 
 
 .36641 
 
 39,2 
 
 .95558 
 
 8,9 
 
 .04442 
 
 .488 
 
 .32247 
 
 48,1 
 
 .36680 
 
 39,2 
 
 .95567 
 
 8,9 
 
 .04433 
 
 .489 
 
 .32295 
 
 48,1 
 
 .36719 
 
 39,2 
 
 .95576 
 
 8,9 
 
 .04424 
 
 1.490 
 
 0.32343 
 
 48,1 
 
 0.36759 
 
 39,2 
 
 9.95584 
 
 8,8 
 
 0.04416 
 
 .491 
 
 .32391 
 
 48,1 
 
 .36798 
 
 39,2 
 
 .95593 
 
 8,8 
 
 .04407 
 
 .492 
 
 .32439 
 
 48,1 
 
 .36837 
 
 39,2 
 
 .95602 
 
 8,8 
 
 .04398 
 
 .493 
 
 .32487 
 
 48,0 
 
 .36876 
 
 39,3 
 
 .956n 
 
 8,8 
 
 .04389 
 
 494 
 
 .32535 
 
 48,0 
 
 .36916 
 
 39,3 
 
 .95620 
 
 8,8 
 
 .04380 
 
 1.495 
 
 0.32583 
 
 48,0 
 
 0.36955 
 
 39,3 
 
 9-95628 
 
 8,8 
 
 0.04372 
 
 .496 
 
 .32631 
 
 48,0 
 
 .36994 
 
 39,3 
 
 .95637 
 
 8,7 
 
 .04363 
 
 497 
 
 .32679 
 
 48,0 
 
 .37033 
 
 39,3 
 
 .95646 
 
 8,7 
 
 .04354 
 
 .498 
 
 .32727 
 
 48,0 
 
 .37073 
 
 39,3 
 
 .95655 
 
 8,7 
 
 .04345 
 
 .499 
 
 .32775 
 
 48,0 
 
 .37H2 
 
 39,3 
 
 95663 
 
 8,7 
 
 .04337 
 
 1.500 
 
 0.32823 
 
 48,0 
 
 0.37I5I 
 
 39,3 
 
 9.95672 
 
 8,7 
 
 0.04328 
 
 u 
 
 loo tan gd u 
 
 Fo' 
 
 log sec gd u 
 
 Fo' 
 
 log sin gd u 
 
 Fo' 
 
 1 og esc gd u 
 
 SMITHSONIAN TABLES 
 
 49 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 Fo' 
 
 log cosh u 
 
 F ' 
 
 log tanh u 
 
 Fo' 
 
 log coth u 
 
 1.500 
 
 0.32823 
 
 48,0 
 
 0.37I5I 
 
 39,3 
 
 9.95672 
 
 8,7 
 
 0.04328 
 
 .501 
 
 .32871 
 
 48,0 
 
 .37191 
 
 39,3 
 
 .95681 
 
 8,7 
 
 .04319 
 
 .502 
 
 .32919 
 
 48,0 
 
 .37230 
 
 39,3 
 
 .95689 
 
 8,6 
 
 .04311 
 
 .503 
 
 .32967 
 
 48,0 
 
 .37269 
 
 39,3 
 
 .95698 
 
 8,6 
 
 .04302 
 
 .504 
 
 .33015 
 
 47,9 
 
 .37309 
 
 39,3 
 
 -95707 
 
 8,6 
 
 .04293 
 
 1.505 
 
 0.33063 
 
 47,9 
 
 0.37348 
 
 39,3 
 
 9.95715 
 
 8,6 
 
 0.04285 
 
 .506 
 
 33III 
 
 47,9 
 
 .37387 
 
 39,4 
 
 .95724 
 
 8,6 
 
 .04276 
 
 .507 
 
 .33159 
 
 47,9 
 
 37427 
 
 39,4 
 
 95732 
 
 8,5 
 
 .04268 
 
 .508 
 
 .33207 
 
 47,9 
 
 .37466 
 
 39,4 
 
 .95741 
 
 8,5 
 
 .04259 
 
 .509 
 
 .33255 
 
 47,9 
 
 .37505 
 
 39,4 
 
 95749 
 
 8,5 
 
 .04251 
 
 1.510 
 
 0.33303 
 
 47,9 
 
 0.37545 
 
 39,4 
 
 9.95758 
 
 8,5 
 
 0.04242 
 
 .511 
 
 33350 
 
 47,9 
 
 .37584 
 
 39,4 
 
 .95766 
 
 8,5 
 
 .04234 
 
 .512 
 
 .33398 
 
 47,9 
 
 .37624 
 
 39,4 
 
 95775 
 
 8,5 
 
 .04225 
 
 .513 
 
 .33446 
 
 47,9 
 
 .37663 
 
 39,4 
 
 .95783 
 
 8,4 
 
 .04217 
 
 .514 
 
 33494 
 
 47,8 
 
 .37702 
 
 39,4 
 
 95792 
 
 8,4 
 
 .04208 
 
 1.515 
 
 0.33542 
 
 47,8 
 
 0-37742 
 
 39,4 
 
 9.958oo 
 
 8,4 
 
 0.04200 
 
 .516 
 
 33590 
 
 47,8 
 
 .37781 
 
 39,4 
 
 .95808 
 
 8,4 
 
 .04192 
 
 .517 
 
 .33638 
 
 47,8 
 
 .37821 
 
 39,4 
 
 .95817 
 
 8,4 
 
 .04183 
 
 .518 
 
 .33685 
 
 47,8 
 
 .37860 
 
 39,4 
 
 .95825 
 
 8,4 
 
 .04175 
 
 .519 
 
 33733 
 
 47,8 
 
 .37900 
 
 39,5 
 
 .95834 
 
 8,3 
 
 .04166 
 
 1.520 
 
 0.33781 
 
 47,8 
 
 0.37939 
 
 39,5 
 
 9.95842 
 
 8,3 
 
 0.04158 
 
 .521 
 
 .33829 
 
 47,8 
 
 37979 
 
 39,5 
 
 .95850 
 
 8,3 
 
 .04150 
 
 .522 
 
 .33877 
 
 47,8 
 
 .38018 
 
 39,5 
 
 .95859 
 
 8,3 
 
 .04141 
 
 .523 
 
 .33924 
 
 47,8 
 
 .38057 
 
 39,5 
 
 .95867 
 
 8,3 
 
 .04133 
 
 .524 
 
 33972 
 
 47,8 
 
 .38097 
 
 39,5 
 
 .95875 
 
 8,3 
 
 .04125 
 
 1.525 
 
 0.34020 
 
 47,7 
 
 0.38136 
 
 39,5 
 
 9.95883 
 
 8,2 
 
 0.04117 
 
 .526 
 
 .34068 
 
 47,7 
 
 .38176 
 
 39,5 
 
 .95892 
 
 8,2 
 
 .04108 
 
 .527 
 
 .34H5 
 
 47,7 
 
 .38215 
 
 39,5 
 
 95900 
 
 8,2 
 
 .04100 
 
 .528 
 
 .34163 
 
 47,7 
 
 .38255 
 
 39,5 
 
 .95908 
 
 8,2 
 
 .04092 
 
 .529 
 
 .34211 
 
 47,7 
 
 .38295 
 
 39,5 
 
 .95916 
 
 8,2 
 
 .04084 
 
 1.530 
 
 0.34258 
 
 47,7 
 
 0.38334 
 
 39,5 
 
 9.95924 
 
 8,2 
 
 0.04076 
 
 .531 
 
 .34306 
 
 47,7 
 
 .38374 
 
 39,5 
 
 95933 
 
 8,1 
 
 .04067 
 
 .532 
 
 34354 
 
 47,7 
 
 .38413 
 
 39,6 
 
 95941 
 
 8,1 
 
 .04059 
 
 533 
 
 .34402 
 
 47,7 
 
 .38453 
 
 39,6 
 
 95949 
 
 8,1 
 
 .04051 
 
 534 
 
 34449 
 
 47,7 
 
 .38492 
 
 39,6 
 
 .95957 
 
 8,1 
 
 .04043 
 
 1.535 
 
 0.34497 
 
 47,7 
 
 0.38532 
 
 39,6 
 
 9.95965 
 
 8,1 
 
 0.04035 
 
 .536 
 
 .34545 
 
 47,6 
 
 .38571 
 
 39,6 
 
 .95973 
 
 8,1 
 
 .04027 
 
 537 
 
 .34592 
 
 47,6 
 
 .38611 
 
 39,6 
 
 .95981 
 
 8,0 
 
 .04019 
 
 .538 
 
 .34640 
 
 47,6 
 
 .38651 
 
 39,6 
 
 .95989 
 
 8,0 
 
 .04011 
 
 539 
 
 .34687 
 
 47,6 
 
 .38690 
 
 39,6 
 
 95997 
 
 8,0 
 
 .04003 
 
 1.540 
 
 0.34735 
 
 47,6 
 
 0.38730 
 
 39,6 
 
 9.06005 
 
 8,0 
 
 0.03995 
 
 541 
 
 .34783 
 
 47,6 
 
 .38769 
 
 39,6 
 
 .96013 
 
 8,0 
 
 .03987 
 
 542 
 
 34830 
 
 47,6 
 
 .38809 
 
 39,6 
 
 .96021 
 
 8,0 
 
 .03979 
 
 .543 
 
 .34878 
 
 47,6 
 
 .38849 
 
 39,6 
 
 .96029 
 
 8,0 
 
 .03971 
 
 .544 
 
 .34925 
 
 47,6 
 
 .38888 
 
 39,6 
 
 .96037 
 
 7,9 
 
 .03963 
 
 1.545 
 
 0.34973 
 
 47,6 
 
 0.38928 
 
 39,6 
 
 9.96045 
 
 7,9 
 
 0.03955 
 
 .546 
 
 35021 
 
 47,6 
 
 .38968 
 
 39,7 
 
 .96053 
 
 7,9 
 
 .03947 
 
 .547 
 
 .35068 
 
 47,6 
 
 .30007 
 
 39,7 
 
 .96061 
 
 7,9 
 
 .03939 
 
 .548 
 
 .35n6 
 
 47,5 
 
 .39047 
 
 39,7 
 
 .96069 
 
 7,9 
 
 .03931 
 
 549 
 
 .35163 
 
 47,5 
 
 .39087 
 
 39,7 
 
 .96077 
 
 7,9 
 
 .03923 
 
 1.550 
 
 0.35211 
 
 47,5 
 
 0.39126 
 
 39,7 
 
 9.96084 
 
 7,8 
 
 0.03916 
 
 u 
 
 log tan gd u 
 
 F ' 
 
 log sec gd u 
 
 stfV 
 
 log sin gd u 
 
 -V 
 
 log esc gd u 
 
 SMITHSONIAN TABLES 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 Fo' 
 
 log cosh u 
 
 F ' 
 
 log tanh u 
 
 -Fo' 
 
 log coth u 
 
 1.550 
 
 0.352II 
 
 47,5 
 
 0.39126 
 
 39,7 
 
 9.96084 
 
 7,8 
 
 0.03916 
 
 .551 
 
 .35258 
 
 47,5 
 
 .39166 
 
 39,7 
 
 .96092 
 
 7,8 
 
 .03908 
 
 .552 
 
 .35306 
 
 47,5 
 
 .39206 
 
 39,7 
 
 .96100 
 
 7,8 
 
 .03900 
 
 553 
 
 35353 
 
 47,5 
 
 .39245 
 
 39,7 
 
 .96108 
 
 7,8 
 
 .03892 
 
 554 
 
 35401 
 
 47,5 
 
 .39285 
 
 39,7 
 
 .96116 
 
 7,8 
 
 .03884 
 
 1.555 
 
 0.35448 
 
 47,5 
 
 0.39325 
 
 39,7 
 
 9.96123 
 
 7,8 
 
 0.03877 
 
 .556 
 
 .35496 
 
 47,5 
 
 .39365 
 
 39,7 
 
 .96131 
 
 7,7 
 
 .03869 
 
 557 
 
 35543 
 
 47,5 
 
 .39404 
 
 39,7 
 
 ' .96139 
 
 7,7 
 
 .03861 
 
 .558 
 559 
 
 35591 
 .35638 
 
 47,5 
 47,5 
 
 .39444 
 .39484 
 
 39,7 
 39,7 
 
 .96147 
 .96154 
 
 7,7 
 7,7 
 
 .03853 
 .03846 
 
 1.560 
 
 0.35686 
 
 47,4 
 
 0.39524 
 
 39,8 
 
 9.96162 
 
 7,7 
 
 0.03838 
 
 .561 
 
 .35733 
 
 47,4 
 
 .39563 
 
 39,8 
 
 .06170 
 
 7,7 
 
 .03830 
 
 .562 
 
 35780 
 
 47,4 
 
 .39603 
 
 39,8 
 
 .96177 
 
 7,7 
 
 .03823 
 
 .563 
 
 35828 
 
 47,4 
 
 .30643 
 
 39,8 
 
 .96185 
 
 7,6 
 
 .03815 
 
 564 
 
 .35875 
 
 47,4 
 
 .39683 
 
 39,8 
 
 .96193 
 
 7,6 
 
 .05807 
 
 1.565 
 
 0.35923 
 
 47,4 
 
 0.39722 
 
 39,8 
 
 9.96200 
 
 7,6 
 
 0.03800 
 
 .566 
 
 35970 
 
 %J+J^r* 
 
 47,4 
 
 .39762 
 
 39,8 
 
 .96208 
 
 7,6 
 
 .03792 
 
 .567 
 
 .36017 
 
 47,4 
 
 .39802 
 
 39,8 
 
 .96215 
 
 7,6 
 
 .03785 
 
 .568 
 
 .36065 
 
 47,4 
 
 .39842 
 
 39,8 
 
 .96223 
 
 7,6 
 
 .03777 
 
 .569 
 
 .36112 
 
 47,4 
 
 .39882 
 
 39,8 
 
 .06231 
 
 7,5 
 
 .03769 
 
 1-570 
 
 0.36160 
 
 47,4 
 
 0.39921 
 
 39,8 
 
 9-96238 
 
 7,5 
 
 0.03762 
 
 571 
 
 .36207 
 
 47,4 
 
 .39961 
 
 39,8 
 
 .96246 
 
 7,5 
 
 03754 
 
 572 
 
 .36254 
 
 47,3 
 
 .40001 
 
 39,8 
 
 96253 
 
 7,5 
 
 .03747 
 
 573 
 
 .36302 
 
 47,3 
 
 .40041 
 
 39,8 
 
 .96261 
 
 7,5 
 
 .03739 
 
 574 
 
 .36349 
 
 47,3 
 
 .40081 
 
 39,9 
 
 .96268 
 
 7,5 
 
 .03732 
 
 1-575 
 
 0.36396 
 
 47,3 
 
 0.40121 
 
 39,9 
 
 9.96276 
 
 7,5 
 
 0.03724 
 
 .576 
 
 .36444 
 
 47,3 
 
 .40161 
 
 39,9 
 
 .96283 
 
 7,4 
 
 .03717 
 
 577 
 
 .36491 
 
 47,3 
 
 '.40200 
 
 39,9 
 
 .96291 
 
 7,4 
 
 .03709 
 
 .578 
 
 .36538 
 
 47,3 
 
 .40240 
 
 39,9 
 
 .96298 
 
 7,4 
 
 .03702 
 
 5.79 
 
 .36585 
 
 47,3 
 
 .40280 
 
 39,9 
 
 .96305 
 
 7,4 
 
 .03695 
 
 1.580 
 
 0.36633 
 
 47,3 
 
 0.40320 
 
 39,9 
 
 9.96313 
 
 7,4 
 
 0.03687 
 
 .581 
 
 .36680 
 
 47,3 
 
 .40360 
 
 39,9 
 
 .96320 
 
 7,4 
 
 .03680 
 
 .582 
 
 .36727 
 
 47,3 
 
 .40400 
 
 39,9 
 
 .96327 
 
 7,4 
 
 .03673 
 
 .583 
 
 .36775 
 
 47,3 
 
 .40440 
 
 39,9 
 
 .96335 
 
 7,3 
 
 .03665 
 
 .584 
 
 .36822 
 
 47,2 
 
 .40480 
 
 39,9 
 
 .96342 
 
 7,3 
 
 .03658 
 
 1.585 
 
 0.36869 
 
 47,2 
 
 0.40520 
 
 39,9 
 
 9.96349 
 
 7,3 
 
 0.03651 
 
 .586 
 
 .36916 
 
 47,2 
 
 .40560 
 
 39,9 
 
 .96357 
 
 7,3 
 
 .03643 
 
 .587 
 
 .36964 
 
 47,2 
 
 .40599 
 
 39,9 
 
 .96364 
 
 7,3 
 
 .03636 
 
 .588 
 
 370II 
 
 47,2 
 
 .40639 
 
 39,9 
 
 .96371 
 
 7,3 
 
 .03629 
 
 .589 
 
 .37058 
 
 47,2 
 
 .40679 
 
 40,0 
 
 .96379 
 
 7,3 
 
 .03621 
 
 1.590 
 
 0.37105 
 
 47,2 
 
 0.40719 
 
 40,0 
 
 9.96386 
 
 7,2 
 
 0.03614 
 
 591 
 
 .37152 
 
 47,2 
 
 .40759 
 
 40,0 
 
 .96393 
 
 7,2 
 
 .03607 
 
 592 
 
 .37200 
 
 47,2 
 
 .40799 
 
 40,0 
 
 .96400 
 
 7,2 
 
 .03600 
 
 593 
 
 .37247 
 
 47,2 
 
 .40839 
 
 40,0 
 
 .96407 
 
 7,2 
 
 .03593 
 
 .594 
 
 .37294 
 
 47,2 
 
 .40879 
 
 40,0 
 
 .96415 
 
 7,2 
 
 .03585 
 
 1-595 
 
 0.37341 
 
 47,2 
 
 0.40919 
 
 40,0 
 
 9.06422 
 
 7,2 
 
 0.03578 
 
 .596 
 
 .37388 
 
 47,2 
 
 .40959 
 
 40,0 
 
 .96429 
 
 7,2 
 
 .03571 
 
 597 
 
 37435 
 
 47,1 
 
 .40099 
 
 40,0 
 
 .96436 
 
 7,i 
 
 03564 
 
 .598 
 
 .37482 
 
 47,1 
 
 .41039 
 
 40,0 
 
 .96443 
 
 7,1 
 
 .03557 
 
 .599 
 
 37530 
 
 47,1 
 
 .41079 
 
 40,0 
 
 .96450 
 
 7,i 
 
 .03550 
 
 T. 600 
 
 0.37577 
 
 47,1 
 
 0.41119 
 
 40,o 
 
 9.96457 
 
 7,1 
 
 0.03543 
 
 u 
 
 log tan gd u 
 
 F ' 
 
 log sec gd u 
 
 F ' 
 
 log sin gd u 
 
 Fo' 
 
 log esc gd u 
 
 SMITHSONIAN TABLES 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 F ' 
 
 log cosh u 
 
 IV 
 
 log tanh u 
 
 Fo' 
 
 log coth u 
 
 1. 600 
 
 0-37577 
 
 47,1 
 
 0.41119 
 
 40,0 
 
 9.96457 
 
 7,i 
 
 0.03543 
 
 .601 
 
 .37624 
 
 
 .4H59 
 
 
 .96465 
 
 
 03535 
 
 .602 
 
 .37671 
 
 
 .41199 
 
 
 .96472 
 
 
 .03528 
 
 .603 
 
 .37718 
 
 
 .41239 
 
 
 .96479 
 
 
 .03521 
 
 .604 
 
 .37765 
 
 
 .41279 
 
 40,1 
 
 .96486 
 
 7,o 
 
 .03514 
 
 1.605 
 
 0.37812 
 
 47,1 
 
 0.4I3I9 
 
 40,1 
 
 9.96493 
 
 7,0 
 
 0.03507 
 
 .606 
 
 .37859 
 
 
 .41360 
 
 
 .96500 
 
 
 .03500 
 
 .607 
 
 .37906 
 
 
 .41400 
 
 
 .96507 
 
 
 .03493 
 
 .608 
 
 37953 
 
 
 .41440 
 
 
 .96514 
 
 
 .03486 
 
 .609 
 
 .38001 
 
 
 .41480 
 
 
 .96521 
 
 
 .03479 
 
 1.610 
 
 0.38048 
 
 47,0 
 
 0.41520 
 
 40,1 
 
 9.96528 
 
 7,o 
 
 0.03472 
 
 .611 
 
 .38095 
 
 
 .41560 
 
 
 .06535 
 
 6,9 
 
 03465 
 
 .612 
 
 .38142 
 
 
 .41600 
 
 
 .96542 
 
 
 .03458 
 
 .613 
 
 .38189 
 
 
 .41640 
 
 
 .96548 
 
 
 .03452 
 
 .614 
 
 .38236 
 
 
 .41680 
 
 
 .96555 
 
 
 .03445 
 
 1.615 
 
 0.38283 
 
 47,0 
 
 0.41720 
 
 40,1 
 
 9-96562 
 
 6,9 
 
 0.03438 
 
 .616 
 
 .38330 
 
 
 .41761 
 
 
 .96569 
 
 
 .03431 
 
 .617 
 
 .38377 
 
 
 .418^1 
 
 
 .96576 
 
 
 .03424 
 
 .618 
 
 38424 
 
 
 .41841 
 
 
 96583 
 
 6,8 
 
 .03417 
 
 .619 
 
 .38471 
 
 
 .41881 
 
 
 .96590 
 
 
 .03410 
 
 1.620 
 
 0.38518 
 
 47,0 
 
 0.41921 
 
 40,2 
 
 9.96597 
 
 6,8 
 
 0.03403 
 
 .621 
 
 .38565 
 
 
 .41961 
 
 
 .96603 
 
 
 .03397 
 
 .622 
 
 .38612 
 
 
 .42001 
 
 
 .96610 
 
 
 .03390 
 
 .623 
 
 .38659 
 
 46,9 
 
 .42042 
 
 
 .96617 
 
 
 03383 
 
 .624 
 
 .38705 
 
 
 .42082 
 
 
 .96624 
 
 
 .03376 
 
 1.625 
 
 0.38752 
 
 46,9 
 
 0.42122 
 
 40,2 
 
 9.96630 
 
 6,7 
 
 0.03370 
 
 .626 
 
 .38799 
 
 
 .42162 
 
 
 .96637 
 
 
 .03363 
 
 .627 
 
 .38846 
 
 
 .42202 
 
 
 .96644 
 
 
 .03356 
 
 .628 
 
 .38893 
 
 
 .42243 
 
 
 .96651 
 
 
 .03349 
 
 .629 
 
 .38940 
 
 
 .42283 
 
 
 .96657 
 
 
 .03343 
 
 1.630 
 
 0.38987 
 
 46,9 
 
 0.42323 
 
 40,2 
 
 9.96664 
 
 6,7 
 
 0.03336 
 
 .631 
 
 39034 
 
 
 42363 
 
 
 .96671 
 
 
 .03329 
 
 .632 
 
 .39081 
 
 
 .42403 
 
 
 .96677 
 
 
 .03323 
 
 .633 
 
 .39128 
 
 
 .42444 
 
 
 .96684 
 
 6,6 
 
 .03316 
 
 .634 
 
 .39175 
 
 
 .42484 
 
 
 .96691 
 
 
 .03309 
 
 1.635 
 
 0.39221 
 
 46,9 
 
 0.42524 
 
 40,2 
 
 9.96697 
 
 6,6 
 
 0.03303 
 
 .636 
 
 .39268 
 
 
 .42564 
 
 40,3 
 
 .96704 
 
 
 .03296 
 
 .637 
 
 .39315 
 
 46,8 
 
 .42605 
 
 
 .96710 
 
 
 .03290 
 
 .638 
 
 .39362 
 
 
 .42645 
 
 
 .96717 
 
 
 .03283 
 
 639 
 
 .39409 
 
 
 .42685 
 
 
 .96724 
 
 
 .03276 
 
 1.640 
 
 0.39456 
 
 46,8 
 
 0.42725 
 
 40,3 
 
 9.96730 
 
 6,5 
 
 0.03270 
 
 .641 
 
 39502 
 
 
 .42766 
 
 
 .96737 
 
 
 .03263 
 
 .642 
 
 39549 
 
 
 .42806 
 
 
 .96743 
 
 
 .03257 
 
 .643 
 
 .39596 
 
 
 .42846 
 
 
 .06750 
 
 
 .03250 
 
 .644 
 
 .39643 
 
 
 .42887 
 
 
 96756 
 
 
 .03244 
 
 1.645 
 
 0.39690 
 
 46,8 
 
 0.42927 
 
 40,3 
 
 9.96763 
 
 6,5 
 
 0.03237 
 
 .646 
 
 .39736 
 
 
 .42967 
 
 
 .96769 
 
 
 .03231 
 
 .647 
 
 .39783 
 
 
 .43008 
 
 
 .96776 
 
 
 .03224 
 
 .648 
 
 .39830 
 
 
 .43048 
 
 
 .96782 
 
 6,4 
 
 .03218 
 
 .649 
 
 .39877 
 
 
 .43088 
 
 
 .96788 
 
 
 .03212 
 
 1.650 
 
 0.39923 
 
 46,8 
 
 0.43129 
 
 40.3 
 
 9.96795 
 
 6,4 
 
 0.03205 
 
 u 
 
 log tan gd u 
 
 Fo' 
 
 log sec gd u 
 
 * Fo' 
 
 \OQ sin gd u 
 
 Fo' 
 
 log esc gd u 
 
 SMITHSONIAN TABLES 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 F ' 
 
 log cosh u 
 
 F ' 
 
 log tanh u 
 
 Fo' 
 
 log coth u 
 
 1.650 
 
 0.39923 
 
 46,8 
 
 0.43129 
 
 40,3 
 
 9.06795 
 
 6,4 
 
 0.03205 
 
 .651 
 
 .39970 
 
 46,7 
 
 .43169 
 
 
 .96801 
 
 
 .03199 
 
 .652 
 
 .40017 
 
 
 .43209 
 
 40,4 
 
 .96808 
 
 
 .03192 
 
 .653 
 
 .40064 
 
 
 .43250 
 
 
 .96814 
 
 
 .03186 
 
 .654 
 
 .40110 
 
 
 .43200 
 
 
 .96820 
 
 
 .03180 
 
 1.655 
 
 0.40157 
 
 46,7 
 
 0.43330 
 
 40,4 
 
 9.06827 
 
 6,4 
 
 0.03173 
 
 .656 
 
 .40204 
 
 
 43371 
 
 
 .96833 
 
 6,3 
 
 .03167 
 
 .657 
 
 .40251 
 
 
 434II 
 
 
 .96840 
 
 
 .03160 
 
 .658 
 
 .40297 
 
 
 .43451 
 
 
 .96846 
 
 
 .03154 
 
 .659 
 
 .40344 
 
 
 43492 
 
 
 .96852 
 
 
 .03148 
 
 1.660 
 
 0.40391 
 
 46,7 
 
 0.43532 
 
 40,4 
 
 9.96858 
 
 6,3 
 
 0.03142 
 
 .661 
 
 40437 
 
 
 43573 
 
 
 .96865 
 
 
 .03135 
 
 .662 
 
 .40484 
 
 
 .43613 
 
 
 .96871 
 
 
 .03129 
 
 .663 
 
 .40531 
 
 
 .43653 
 
 
 .96877 
 
 
 .03123 
 
 .664 
 
 40577 
 
 
 .43694 
 
 
 .96883 
 
 6,2 
 
 .03117 
 
 1.665 
 
 0.40624 
 
 46,7 
 
 0.43734 
 
 40,4 
 
 9.96890 
 
 6,2 
 
 0.03110 
 
 .666 
 
 .40671 
 
 46,6 
 
 43775 
 
 
 .96896 
 
 
 .03104 
 
 .667 
 
 .40717 
 
 
 .43815 
 
 
 .96902 
 
 
 .03098 
 
 .668 
 
 .40764 
 
 
 .43856 
 
 
 .96908 
 
 
 .03092 
 
 .669 
 
 .40811 
 
 
 .43896 
 
 40,5 
 
 .96915 
 
 
 .03085 
 
 1.670 
 
 0.40857 
 
 46,6 
 
 0.43937 
 
 40,5 
 
 9.96921 
 
 6,2 
 
 0.03079 
 
 .671 
 
 .40004 
 
 
 .43977 
 
 
 .96927 
 
 
 .03073 
 
 .672 
 
 .40950 
 
 
 .44017 
 
 
 .90933 
 
 6,1 
 
 .03067 
 
 .673 
 
 .40097 
 
 
 .44058 
 
 
 .96939 
 
 
 .03061 
 
 .674 
 
 .41044 
 
 
 .44098 
 
 
 .96945 
 
 
 .03055 
 
 1.675 
 
 0.41090 
 
 46,6 
 
 0.44139 
 
 40,5 
 
 9.96951 
 
 6,1 
 
 0.03049 
 
 .676 
 
 .4H37 
 
 
 .44179 
 
 
 .96957 
 
 
 .03043 
 
 677 
 
 .41183 
 
 
 .44220 
 
 
 .96964 
 
 
 .03036 
 
 .678 
 
 . .41230 
 
 
 .44260 
 
 
 .96970 
 
 
 .03030 
 
 .679 
 
 .41277 
 
 
 .44301 
 
 
 .06976 
 
 
 .03024 
 
 i. 680 
 
 0.41323 
 
 46,6 
 
 0.44341 
 
 40,5 
 
 9.06982 
 
 6,0 
 
 0.03018 
 
 .681 
 
 .41370 
 
 46,5 
 
 .44382 
 
 
 .96988 
 
 
 .03012 
 
 .682 
 
 .41416 
 
 
 .44422 
 
 
 .96994 
 
 
 .03006 
 
 .683 
 
 .41463 
 
 
 .44463 
 
 
 .97000 
 
 
 .03000 
 
 .684 
 
 .41509 
 
 
 .44503 
 
 
 .97006 
 
 
 .02994 
 
 1.685 
 
 0.41556 
 
 46,5 
 
 0.44544 
 
 40,5 
 
 9.97012 
 
 6,0 
 
 0.02988 
 
 .686 
 
 .41602 
 
 
 .44585 
 
 
 .97018 
 
 
 .02982 
 
 .687 
 
 .41649 
 
 
 .44625 
 
 40,6 
 
 .97024 
 
 
 .02976" 
 
 .688 
 
 .41695 
 
 
 .44666 
 
 
 .97030 
 
 5,9 
 
 .02970 
 
 .689 
 
 .41742 
 
 
 .44706 
 
 
 .97036 
 
 
 .02964 
 
 1.690 
 
 0.41788 
 
 46,5 
 
 0.44747 
 
 40,6 
 
 9.97042 
 
 5,9 
 
 0.02958 
 
 .691 
 
 .41835 
 
 
 .44787 
 
 
 .97047 
 
 
 .02953 
 
 .692 
 
 .41881 
 
 
 .44828 
 
 
 .97053 
 
 
 .02947 
 
 .693 
 
 .41928 
 
 
 .44869 
 
 
 97059 
 
 
 .02941 
 
 694 
 
 .41974 
 
 
 .44909 
 
 
 .97065 
 
 
 02935 
 
 1.695 
 
 0.42021 
 
 46,5 
 
 0.44950 
 
 40,6 
 
 9.97071 
 
 5,9 
 
 0.02929 
 
 .696 
 
 .42067 
 
 
 .44990 
 
 
 .97077 
 
 
 .02923 
 
 .697 
 
 .42114 
 
 46,4 
 
 .45031 
 
 
 .97083 
 
 5,8 
 
 .02917 
 
 .608 
 
 .42160 
 
 
 .45072 
 
 
 .97089 
 
 
 .02911 
 
 .699 
 
 .42207 
 
 
 45II2 
 
 
 .97094 
 
 
 .02906 
 
 1.700 
 
 0.42253 
 
 46,4 
 
 0.45153 
 
 40,6 
 
 9.97100 
 
 5,8 
 
 0.02000 
 
 u 
 
 log tan gd u 
 
 o Fo' 
 
 log sec gd u 
 
 F ' 
 
 log sin gd u 
 
 Fo' 
 
 log esc gd u 
 
 SMITHSONIAN TABLES 
 
 53 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 Fo' 
 
 log cosh u 
 
 Fo' 
 
 log tanh u 
 
 Fo' 
 
 log coth u 
 
 1.700 
 
 0.42253 
 
 46,4 
 
 0.45153 
 
 4O,6 
 
 9-97100 
 
 5,8 
 
 0.02QOO 
 
 .701 
 
 .42299 
 
 
 .45193 
 
 
 .97106 
 
 
 .02894 
 
 .702 
 
 .42346 
 
 
 .45234 
 
 
 .97112 
 
 
 .02888 
 
 .703 
 
 .42392 
 
 
 .45275 
 
 
 .97118 
 
 
 .02882 
 
 .704 
 
 .42439 
 
 
 .45315 
 
 
 .97123 
 
 
 .02877 
 
 1.705 
 
 0.42485 
 
 46,4 
 
 0.45356 
 
 40,7 
 
 9.97129 
 
 5,7 
 
 0.02871 
 
 .706 
 
 .42531 
 
 
 45397 
 
 
 .97135 
 
 
 .02865 
 
 .707 
 
 .42578 
 
 
 45437 
 
 
 .97141 
 
 
 .02859 
 
 .708 
 
 .42624 
 
 
 45478 
 
 
 .97146 
 
 
 .02854 
 
 .709 
 
 .42671 
 
 
 .45519 
 
 
 .97152 
 
 
 .02848 
 
 1.710 
 
 0.42717 
 
 46,4 
 
 0.45559 
 
 40,7 
 
 9.97158 
 
 5,7 
 
 0.02842 
 
 .711 
 
 .42763 
 
 
 .45600 
 
 
 .97163 
 
 
 .02837 
 
 .712 
 
 .42810 
 
 
 .45641 
 
 
 .97169 
 
 
 .02831 
 
 .713 
 
 .42856 
 
 46,3 
 
 .45681 
 
 
 97175 
 
 
 .02825 
 
 .714 
 
 .42002 
 
 
 45722 
 
 
 .97180 
 
 5,6 
 
 .02820 
 
 1.715 
 
 0.42949 
 
 46,3 
 
 0.45763 
 
 40,7 
 
 9.97186 
 
 5,6 
 
 0.02814 
 
 .716 
 
 .42995 
 
 
 .45803 
 
 
 .97192 
 
 
 .02808 
 
 .717 
 
 .43041 
 
 
 .45844 
 
 
 .97197 
 
 
 .02803 
 
 .718 
 
 .43088 
 
 
 45885 
 
 
 97203 
 
 
 .02797 
 
 .719 
 
 43134 
 
 
 .45926 
 
 
 .97208 
 
 
 .02792 
 
 1.720 
 
 0.43180 
 
 46,3 
 
 0.45966 
 
 40,7 
 
 9.97214 
 
 5,6 
 
 0.02786 
 
 .721 
 
 .43227 
 
 
 .46007 
 
 
 .97220 
 
 
 .02780 
 
 .722 
 
 .43273 
 
 
 .46048 
 
 
 .97225 
 
 
 02775 
 
 .723 
 
 .43319 
 
 
 .46089 
 
 
 .97231 
 
 5,5 
 
 .02769 
 
 .724 
 
 .43365 
 
 
 .46129 
 
 40,8 
 
 .97236 
 
 
 .02764 
 
 1.725 
 
 0.43412 
 
 46,3 
 
 0.46170 
 
 40,8 
 
 9.97242 
 
 5,5 
 
 0.02758 
 
 .726 
 
 .43458 
 
 
 .46211 
 
 
 97247 
 
 
 02753 
 
 .727 
 
 -43504 
 
 
 .46252 
 
 
 97253 
 
 
 .02747 
 
 .728 
 
 43551 
 
 
 .46292 
 
 
 .97258 
 
 
 .02742 
 
 .729 
 
 43597 
 
 
 .46333 
 
 
 .97264 
 
 
 .02736 
 
 1.730 
 
 0.43643 
 
 46,2 
 
 0.46374 
 
 40,8 
 
 9.97269 
 
 5,5 
 
 0.02731 
 
 .731 
 
 .43689 
 
 
 .46415 
 
 
 97275 
 
 
 .02725 
 
 .732 
 
 .43736 
 
 
 .46455 
 
 
 .97280 
 
 5,4 
 
 .02720 
 
 .733 
 
 .43782 
 
 
 .46496 
 
 
 .97285 
 
 
 .02715 
 
 734 
 
 .43828 
 
 
 .46537 
 
 
 .97291 
 
 
 .02709 
 
 1.735 
 
 0.43874 
 
 46,2 
 
 0.46578 
 
 40,8 
 
 9.97206 
 
 5,4 
 
 0.02704 
 
 .736 
 
 .43920 
 
 
 .46619 
 
 
 97302 
 
 
 .02698 
 
 737 
 
 .43967 
 
 
 .46660 
 
 
 .97307 
 
 
 .02693 
 
 .738 
 
 .44013 
 
 
 .46700 
 
 
 .97313 
 
 
 .02687 
 
 739 
 
 .44059 
 
 
 .46741 
 
 
 .97318 
 
 
 .02682 
 
 1.740 
 
 0.44105 
 
 46,2 
 
 0.46782 
 
 40,8 
 
 9.97323 
 
 5,4 
 
 0.02677 
 
 .741 
 
 .44151 
 
 
 .46823 
 
 
 .97329 
 
 5,3 
 
 .02671 
 
 .742 
 
 .44198 
 
 
 .46864 
 
 
 97334 
 
 
 .02666 
 
 743 
 
 .44244 
 
 
 46905 
 
 
 97339 
 
 
 .02661 
 
 .744 
 
 .44290 
 
 
 .46945 
 
 40,9 
 
 .97345 
 
 
 .02^55 
 
 1.745 
 
 0.44336 
 
 46,2 
 
 0.46986 
 
 40,9 
 
 9-97350 
 
 5,3 
 
 0.02650 
 
 .746 
 
 .44382 
 
 
 .47027 
 
 
 97355 
 
 
 .02645 
 
 747 
 
 .44428 
 
 
 .47068 
 
 
 .97360 
 
 
 .02640 
 
 748 
 
 44475 
 
 46,1 
 
 .47109 
 
 
 .97366 
 
 
 .02634 
 
 749 
 
 44521 
 
 
 .47150 
 
 
 97371 
 
 
 .02629 
 
 1.750 
 
 0.44567 
 
 46,1 
 
 0.47191 
 
 40,9 
 
 9.97376 
 
 5,3 
 
 0.02624 
 
 u 
 
 log tan gd u 
 
 Fo' 
 
 log tec gd u 
 
 Fo' 
 
 log tin gd u 
 
 Fo' 
 
 log esc gd u 
 
 SMITMONIA* 
 
 54 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 Fo' 
 
 log cosh u 
 
 F ' 
 
 log tanh u 
 
 -Fo' 
 
 log coth u 
 
 1.750 
 
 0.44567 
 
 46,1 
 
 0.47I9I 
 
 40,9 
 
 9.97376 
 
 5,3 
 
 0.02624 
 
 .751 
 
 .44613 
 
 
 .47231 
 
 
 97382 
 
 5,2 
 
 .02618 
 
 .752 
 
 .44659 
 
 
 .47272 
 
 
 .97387 
 
 
 .02613 
 
 753 
 
 44705 
 
 
 .47313 
 
 
 97392 
 
 
 .02608 
 
 754 
 
 .44751 
 
 
 47354 
 
 
 97397 
 
 
 .02603 
 
 1.755 
 
 0.44797 
 
 46,1 
 
 0.47395 
 
 40,9 
 
 9-97402 
 
 5,3 
 
 0.02598 
 
 756 
 
 .44844 
 
 
 .47436 
 
 
 .97408 
 
 
 .02592 
 
 .757 
 
 .44890 
 
 
 .47477 
 
 
 97413 
 
 
 .02587 
 
 758 
 
 .44936 
 
 
 .47518 
 
 
 .97418 
 
 
 .02582 
 
 759 
 
 .44982 
 
 
 47559 
 
 
 .97423 
 
 
 .02577 
 
 1.760 
 
 0.45028 
 
 46,1 
 
 0.47600 
 
 40,9 
 
 9.97428 
 
 5,1 
 
 0.02572 
 
 .761 
 
 45074 
 
 
 .47641 
 
 
 97433 
 
 
 .02567 
 
 .762 
 
 .45120 
 
 
 .47682 
 
 
 97439 
 
 
 .02561 
 
 .763 
 
 .45166 
 
 
 47722 
 
 
 97444 
 
 
 .02556 
 
 .764 
 
 .45212 
 
 
 .47763 
 
 41,0 
 
 97449 
 
 
 .02551 
 
 1.765 
 
 0.45258 
 
 46,1 
 
 0.47804 
 
 41,0 
 
 9-97454 
 
 5,1 
 
 0.02546 
 
 .766 
 
 .45304 
 
 46,0 
 
 .47845 
 
 
 97459 
 
 
 .02541 
 
 .767 
 
 45350 
 
 
 .47886 
 
 
 .97464 
 
 
 .02536 
 
 .768 
 
 .45396 
 
 
 .47927 
 
 
 .97469 
 
 
 .02531 
 
 .769 
 
 .45442 
 
 
 .47968 
 
 
 97474 
 
 
 .02526 
 
 1.770 
 
 0.45488 
 
 46,0 
 
 0.48009 
 
 41,0 
 
 9-97479 
 
 5,0 
 
 0.02521 
 
 771 
 
 45534 
 
 
 .48050 
 
 
 .97484 
 
 
 .02516 
 
 772 
 
 .45580 
 
 
 .48091 
 
 
 .97489 
 
 
 .02511 
 
 773 
 
 .45627 
 
 
 .48132 
 
 
 .97494 
 
 
 .02506 
 
 774 
 
 .45673 
 
 
 .48173 
 
 
 .97499 
 
 
 .02501 
 
 1.775 
 
 0.45719 
 
 46,0 
 
 0.48214 
 
 41*0 
 
 9.97504 
 
 5,0 
 
 0.02496 
 
 776 
 
 .45765 
 
 
 .48255 
 
 
 .97509 
 
 
 .02491 
 
 777 
 
 .45810 
 
 
 .48296 
 
 
 .97514 
 
 
 .02486 
 
 .778 
 
 .45856 
 
 
 .48337 
 
 
 .97519 
 
 
 .02481 
 
 779 
 
 45902 
 
 
 .48378 
 
 
 .97524 
 
 
 .02476 
 
 1.780 
 
 0.45948 
 
 46,0 
 
 0.48419 
 
 41,0 
 
 9.97529 
 
 40 
 
 0.02471 
 
 .781 
 
 45994 
 
 
 .48460 
 
 
 97534 
 
 
 .02466 
 
 .782 
 
 .46040 
 
 
 .48501 
 
 
 . -97539 
 
 
 .02461 
 
 .783 
 
 .46086 
 
 
 .48542 
 
 
 .97544 
 
 
 .02456 
 
 784 
 
 .46132 
 
 
 .48583 
 
 
 .97549 
 
 
 .02451 
 
 1.785 
 
 0.46178 
 
 45,9 
 
 0.48624 
 
 4U 
 
 9-97554 
 
 4,9 
 
 0.02446 
 
 .786 
 
 .46224 
 
 
 .48666 
 
 
 97559 
 
 
 .02441 
 
 .787 
 
 .46270 
 
 
 .48707 
 
 
 .97564 
 
 
 .02436 
 
 .788 
 
 .46316 
 
 
 .48748 
 
 
 .97568 
 
 
 .02432 
 
 .789 
 
 .46362 
 
 
 .48789 
 
 
 ..97573 
 
 
 .02427 
 
 1.790 
 
 0.46408 
 
 45,9 
 
 0.48830 
 
 41,1 
 
 9.97578 
 
 48 
 
 0.02422 
 
 .791 
 
 .46454 
 
 
 .48871 
 
 
 .97583 
 
 
 .02417 
 
 .792 
 
 .46500 
 
 
 .48912 
 
 
 .97588 
 
 
 .02412 
 
 .793 
 
 .46546 
 
 
 .48953 
 
 
 97593 
 
 
 .02407 
 
 794 
 
 .46592 
 
 
 .48994 
 
 
 97597 
 
 
 .02403 
 
 1.795 
 
 0.46637 
 
 45,9 
 
 0.49035 
 
 41,1 
 
 9.97602 
 
 4,8 
 
 0.02398 
 
 .796 
 
 .46683 
 
 
 .49076 
 
 
 .97607 
 
 
 .02393 
 
 797 
 
 .46729 
 
 
 .49H7 
 
 
 .97612 
 
 
 .02388 
 
 .798 
 
 .46775 
 
 
 .49159 
 
 
 .97617 
 
 
 .02383 
 
 799 
 
 .46821 
 
 
 .49200 
 
 
 .97621 
 
 
 .02379 
 
 1.800 
 
 0.46867 
 
 45,9 
 
 0.49241 
 
 4LI 
 
 9.97626 
 
 4,8 
 
 0.02374 
 
 u 
 
 log tan gd u 
 
 F ' 
 
 log sec gd u 
 
 Fo' 
 
 log sin gd u 
 
 F O ' 
 
 logcscgdu 
 
 SMITHSONIAN TABLES 
 
 55 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 Fo' 
 
 log cosh u 
 
 -Fo' 
 
 log tanh u 
 
 F ' 
 
 log coth u 
 
 1.800 
 
 0.46867 
 
 45,9 
 
 0.49241 
 
 41,1 
 
 9.97626 
 
 4,8 
 
 0.02374 
 
 .801 
 
 .46913 
 
 
 .49282 
 
 
 .97631 
 
 4,7 
 
 .02369 
 
 .802 
 
 .46959 
 
 
 .49323 
 
 
 .97636 
 
 
 .02364 
 
 .803 
 
 .47004 
 
 
 .49364 
 
 
 .97640 
 
 
 .02360 
 
 .804 
 
 .47050 
 
 45,8 
 
 .49405 
 
 
 .97645 
 
 
 02355 
 
 1.805 
 
 0.47096 
 
 45,8 
 
 0.49446 
 
 41,1 
 
 9.97650 
 
 4,7 
 
 0.02350 
 
 .806 
 
 .47142 
 
 
 .49488 
 
 
 .97654 
 
 
 .02346 
 
 .807 
 
 .47188 
 
 
 .49529 
 
 41,2 
 
 .97659 
 
 
 .02341 
 
 .808 
 
 .47234 
 
 
 49570 
 
 
 .97664 
 
 
 .02336 
 
 .809 
 
 .47279 
 
 
 .49611 
 
 
 .97668 
 
 
 .02332 
 
 1.810 
 
 0.47325 
 
 45,8 
 
 0.49652 
 
 41,2 
 
 9.97673 
 
 4,7 
 
 0.02327 
 
 .811 
 
 47371 
 
 
 .49693 
 
 
 .97678 
 
 4,6 
 
 .02322 
 
 .812 
 
 .47417 
 
 
 49734 
 
 
 .97682 
 
 
 .02318 
 
 .813 
 
 .47463 
 
 
 .49776 
 
 
 .97687 
 
 
 .02313 
 
 .814 
 
 47509 
 
 
 .49817 
 
 
 .97692 
 
 
 .02308 
 
 1.815 
 
 0.47554 
 
 45,8 
 
 0.49858 
 
 41,2 
 
 9.97696 
 
 4,6 
 
 0.02304 
 
 .816 
 
 .47600 
 
 
 .49899 
 
 
 97701 
 
 
 .02299 
 
 .817 
 
 .47646 
 
 
 .49940 
 
 
 97705 
 
 
 .02295 
 
 .818 
 
 .47692 
 
 
 .40982 
 
 
 .97710 
 
 
 .02200 
 
 .819 
 
 47737 
 
 
 .50023 
 
 
 .97715 
 
 
 .02285 
 
 1.820 
 
 0.47783 
 
 45,8 
 
 0.50064 
 
 41,2 
 
 9.97719 
 
 4,6 
 
 0.02281 
 
 .821 
 
 .47829 
 
 
 .50105 
 
 
 .97724 
 
 
 .02276 
 
 .822 
 
 .47875 
 
 
 .50146 
 
 
 .97728 
 
 4,5 
 
 .02272 
 
 .823 
 
 .47921 
 
 
 .50188 
 
 
 97733 
 
 
 .02267 
 
 .824 
 
 .47966 
 
 
 .50229 
 
 
 97737 
 
 
 .02263 
 
 1.825 
 
 0.48012 
 
 45,7 
 
 0.50270 
 
 41,2 
 
 9-97742 
 
 4,5 
 
 0.02258 
 
 .826 
 
 .48058 
 
 
 .50311 
 
 
 .97746 
 
 
 .02254 
 
 .827 
 
 .48104 
 
 
 .50353 
 
 
 97751 
 
 
 .02249 
 
 .828 
 
 .48149 
 
 
 .50394 
 
 
 97755 
 
 
 .02245 
 
 .829 
 
 .48195 
 
 
 50435 
 
 
 .97760 
 
 
 .02240 
 
 1.830 
 
 0.48241 
 
 45,7 
 
 0.50476 
 
 41,3 
 
 9.97764 
 
 4,5 
 
 0.02236 
 
 .831 
 
 .48286 
 
 
 .50518 
 
 
 .97769 
 
 
 .02231 
 
 .832 
 
 .48332 
 
 
 . .50559 
 
 
 97773 
 
 
 .02227 
 
 .833 
 
 .48378 
 
 
 .50600 
 
 
 .97778 
 
 4,4 
 
 .02222 
 
 .834 
 
 .48424 
 
 
 .50641 
 
 
 .97782 
 
 
 .02218 
 
 1.835 
 
 0.48469 
 
 45,7 
 
 0.50683 
 
 41,3 
 
 9.97787 
 
 4,4 
 
 0.02213 
 
 .836 
 
 .48515 
 
 
 .50724 
 
 
 97791 
 
 
 .02209 
 
 .837 
 
 .48561 
 
 
 .50765 
 
 
 .97796 
 
 
 .02204 
 
 .838 
 
 .48606 
 
 
 .50806 
 
 
 .97800 
 
 
 .02200 
 
 .839 
 
 .48652 
 
 
 .50848 
 
 
 .97804 
 
 
 .02196 
 
 1.840 
 
 0.48698 
 
 45,7 
 
 0.50889 
 
 41,3 
 
 9.97809 
 
 4,4 
 
 0.02191 
 
 .841 
 
 .48743 
 
 
 .50930 
 
 
 .97813 
 
 
 .02187 
 
 .842 
 
 .48789 
 
 
 .50972 
 
 
 .97817 
 
 
 .02183 
 
 .843 
 
 .48835 
 
 
 .51013 
 
 
 .97822 
 
 
 .02178 
 
 .844 
 
 .48880 
 
 
 .51054 
 
 
 .97826 
 
 4,3 
 
 .02174 
 
 1.845 
 
 0.48926 
 
 45,7 
 
 0.51096 
 
 41,3 
 
 9.97831 
 
 4,3 
 
 0.02169 
 
 .846 
 
 .48972 
 
 45,6 
 
 .5H37 
 
 
 .97835 
 
 
 .02165 
 
 .847 
 
 .49017 
 
 
 .5H78 
 
 
 .97839 
 
 
 .02161 
 
 .848 
 
 .40063 
 
 
 .51219 
 
 
 .97843 
 
 
 .02157 
 
 .849 
 
 .49109 
 
 
 .51261 
 
 
 .97848 
 
 
 .02152 
 
 1.850 
 
 0.49154 
 
 45,6 
 
 0.51302 
 
 41,3 
 
 9.97852 
 
 4,3 
 
 0.02148 
 
 u 
 
 log tan gd u 
 
 Fo' 
 
 log tec gd u 
 
 -Fo' 
 
 log tin gd u 
 
 - Fo' 
 
 log esc gd u 
 
 iMITHSONIAN 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 Fo' 
 
 log cosh u 
 
 F ' 
 
 log tanh u 
 
 F ' 
 
 log coth u 
 
 1.850 
 
 0.49IS4 
 
 45,6 
 
 0.51302 
 
 41,3 
 
 9.97852 
 
 4,3 
 
 0.02148 
 
 .851 
 
 .49200 
 
 
 .51343 
 
 
 .97856 
 
 
 .02144 
 
 .852 
 
 .49246 
 
 
 .51385 
 
 
 .97861 
 
 
 .02139 
 
 .853 
 
 .49291 
 
 
 .51426 
 
 
 .97865 
 
 
 .02135 
 
 .854 
 
 49337 
 
 
 .51468 
 
 4M 
 
 .97869 
 
 
 .02131 
 
 1.855 
 
 0.49382 
 
 45,6 
 
 0.51509 
 
 4M 
 
 9.97873 
 
 4*3 
 
 0.02127 
 
 .856 
 
 .49428 
 
 
 .51550 
 
 
 .97878 
 
 4,2 
 
 .O2I22 
 
 .857 
 
 .49474 
 
 
 .51592 
 
 
 .97882 
 
 
 .02118 
 
 .858 
 
 .49519 
 
 
 .51633 
 
 
 .97886 
 
 
 .02114 
 
 .859 
 
 .49565 
 
 
 .51674 
 
 
 .97890 
 
 
 .02110 
 
 1.860 
 
 0.49610 
 
 45,6 
 
 0.51716 
 
 41,4 
 
 9.97895 
 
 4,2 
 
 0.02105 
 
 .861 
 
 .49656 
 
 
 .51757 
 
 
 .97899 
 
 
 .02101 
 
 .862 
 
 .49702 
 
 
 .51708 
 
 
 .97903 
 
 
 .02097 
 
 .863 
 
 49747 
 
 
 .51840 
 
 
 .97907 
 
 
 02093 
 
 .864 
 
 49793 
 
 
 .51881 
 
 
 979II 
 
 
 .02089 
 
 1.865 
 
 0.49838 
 
 45,6 
 
 0.51923 
 
 41,4 
 
 9.97916 
 
 4,2 
 
 0.02084 
 
 .866 
 
 .49884 
 
 
 .51964 
 
 
 .97920 
 
 
 .02080 
 
 .867 
 
 .49929 
 
 
 .52005 
 
 
 .97924 
 
 
 .02076 
 
 .868 
 
 H9975 
 
 
 .52047 
 
 
 .97928 
 
 4*1 
 
 .O2072 
 
 .869 
 
 .50020 
 
 45,5 
 
 .52088 
 
 
 97932 
 
 
 .02068 
 
 1.870 
 
 0.50066 
 
 45,5 
 
 0.52130 
 
 41,4 
 
 9.97936 
 
 4,1 
 
 O.O2O64 
 
 .871 
 
 .50112 
 
 
 .52171 
 
 
 .97940 
 
 
 .02060 
 
 .872 
 
 50157 
 
 
 .52212 
 
 
 97945 
 
 
 .02055 
 
 .873 
 
 .50203 
 
 
 .52254 
 
 
 97949 
 
 
 .02051 
 
 .874 
 
 .50248 
 
 
 .52295 
 
 
 97953 
 
 
 .02047 
 
 1.875 
 
 0.50294 
 
 45,5 
 
 0.52337 
 
 41,4 
 
 9-97957 
 
 4,1 
 
 0.02043 
 
 .876 
 
 .50339 
 
 
 .52378 
 
 
 .97961 
 
 
 .02039 
 
 .877 
 
 .50385 
 
 
 .52420 
 
 
 .97965 
 
 
 .02035 
 
 .878 
 
 .50430 
 
 
 .52461 
 
 
 .97969 
 
 
 .02031 
 
 .879 
 
 .50476 
 
 
 .52503 
 
 
 .97973 
 
 
 .02027 
 
 i. 880 
 
 0.50521 
 
 45,5 
 
 0.52544 
 
 41,5 
 
 9.97977 
 
 4,0 
 
 0.02023 
 
 .881 
 
 .50567 
 
 
 .52585 
 
 
 .9798i 
 
 
 .02019 
 
 .882 
 
 .50612 
 
 
 .52627 
 
 
 .97985 
 
 
 .02015 
 
 .883 
 
 .50658 
 
 
 .52668 
 
 
 .97989 
 
 
 .0201 i 
 
 .884 
 
 .50703 
 
 
 .52710 
 
 
 97993 
 
 
 .02007 
 
 1.885 
 
 0.50749 
 
 45,5 
 
 0.52751 
 
 41,5 
 
 9-97997 
 
 4,0 
 
 0.02003 
 
 .886 
 
 .50704 
 
 
 .52793 
 
 
 .98001 
 
 
 .01099 
 
 .887 
 
 .50840 
 
 
 .52834 
 
 
 .98005 
 
 
 .01995 
 
 .888 
 
 .50885 
 
 
 .52876 
 
 
 .98009 
 
 
 .01991 
 
 .889 
 
 .50931 
 
 
 .52917 
 
 
 .98013 
 
 
 .01987 
 
 1.890 
 
 0.50976 
 
 45,5 
 
 0.52959 
 
 41,5 
 
 9.98017 
 
 4,0 
 
 0.01983 
 
 .891 
 
 .51021 
 
 
 .53000 
 
 
 .98021 
 
 
 .01979 
 
 .892 
 
 .51067 
 
 45,4 
 
 .53042 
 
 
 .98025 
 
 
 .01975 
 
 .893 
 
 .51112 
 
 
 .53083 
 
 
 .98029 
 
 3,9 
 
 .01971 
 
 .894 
 
 .51158 
 
 
 .53125 
 
 
 98033 
 
 
 .01967 
 
 1.895 
 
 0.51203 
 
 45,4 
 
 0.53166 
 
 4i,5 
 
 9-98037 
 
 3,9 
 
 0.01963 
 
 .896 
 
 .51249 
 
 
 .53208 
 
 
 .98041 
 
 
 .01959 
 
 .897 
 
 .51294 
 
 
 .53249 
 
 
 .98045 
 
 
 .01955 
 
 .898 
 
 .51340 
 
 
 .53291 
 
 
 .98049 
 
 
 .01951 
 
 .899 
 
 .51385 
 
 
 .53332 
 
 
 .98053 
 
 
 .01947 
 
 1.900 
 
 0.51430 
 
 45,4 
 
 0.53374 
 
 4i,5 
 
 9.98057 
 
 3,9 
 
 0.01943 
 
 u 
 
 log tan gd u 
 
 F ' 
 
 log sec gd u 
 
 Fo' 
 
 log sin gd u 
 
 W 
 
 log esc gd u 
 
 SMITHSONIAN TABLES 
 
 57 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 Fo' 
 
 log cosh u 
 
 -Fo' 
 
 log tanh u 
 
 Fo' 
 
 log eoth u 
 
 1.900 
 
 0.51430 
 
 45,4 
 
 0.53374 
 
 41,5 
 
 9.98057 
 
 3,9 
 
 0.01943 
 
 .901 
 
 .51476 
 
 
 .53415 
 
 
 .98060 
 
 
 .01940 
 
 .902 
 
 .51521 
 
 
 .53457 
 
 
 .98064 
 
 
 .01936 
 
 .903 
 
 .51567 
 
 
 .53498 
 
 
 .98068 
 
 
 .01932 
 
 . .904 
 
 .51612 
 
 
 53540 
 
 
 .98072 
 
 
 .01928 
 
 1.905 
 
 0.51657 
 
 45,4 
 
 0.53581 
 
 41,5 
 
 9.98076 
 
 3,8 
 
 0.01924 
 
 .906 
 
 .51703 
 
 
 .53623 
 
 41,6 
 
 .98080 
 
 
 .01920 
 
 .907 
 
 .51748 
 
 
 .53665 
 
 
 .98084 
 
 
 .01916 
 
 .908 
 
 .51794 
 
 
 .53706 
 
 
 .98087 
 
 
 .01913 
 
 .909 
 
 .51839 
 
 
 .53748 
 
 
 .98091 
 
 
 .01909 
 
 1.910 
 
 0.51884 
 
 45,4 
 
 0.53789 
 
 41,6 
 
 9.98095 
 
 3,8 
 
 0.01905 
 
 .911 
 
 .51930 
 
 
 .53831 
 
 
 .98099 
 
 
 .OIOOI 
 
 .912 
 
 .51975 
 
 . 
 
 .53872 
 
 
 .98103 
 
 
 .01897 
 
 .913 
 
 .52020 
 
 
 .53914 
 
 
 .08106 
 
 
 .01804 
 
 .914 
 
 .52066 
 
 
 .53956 
 
 
 .98110 
 
 
 .01890 
 
 1.915 
 
 0.52III 
 
 45,4 
 
 0.53997 
 
 41,6 
 
 9.98114 
 
 3,8 
 
 0.01886 
 
 .916 
 
 .52157 
 
 
 54039 
 
 
 .98118 
 
 
 .01882 
 
 .917 
 
 . 52202 
 
 45,3 
 
 .54080 
 
 
 .98122 
 
 
 .01878 
 
 .918 
 
 52247 
 
 
 .54122 
 
 
 .98125 
 
 
 .01875 
 
 .919 
 
 .52293 
 
 
 .54164 
 
 
 .98129 
 
 3,7 
 
 .01871 
 
 1.920 
 
 0.52338 
 
 45,3 
 
 0.54205 
 
 41,6 
 
 9.98133 
 
 3,7 
 
 0.01867 
 
 .921 
 
 .52383 
 
 
 .54247 
 
 
 .98137 
 
 
 .01863 
 
 .922 
 
 .52429 
 
 
 .54288 
 
 
 .98140 
 
 
 .01860 
 
 .923 
 
 .52474 
 
 
 .54330 
 
 
 .98144 
 
 
 .01856 
 
 .924 
 
 .52519 
 
 
 .54372 
 
 
 .98148 
 
 
 .01852 
 
 1.925 
 
 0.52565 
 
 45,3 
 
 0.54413 
 
 41,6 
 
 9.98I5I 
 
 3,7 
 
 0.01849 
 
 .926 
 
 .52610 
 
 
 .54455 
 
 
 .98155 
 
 
 .01845 
 
 .927 
 
 52655 
 
 
 .54496 
 
 
 08159 
 
 
 .01841 
 
 .928 
 
 .52700 
 
 
 .54538 
 
 
 .98162 
 
 
 .01838 
 
 .929 
 
 .52746 
 
 
 .5458o 
 
 
 .98166 
 
 
 .01834 
 
 1.930 
 
 0.52791 
 
 45,3 
 
 0.54621 
 
 41,6 
 
 9.98170 
 
 3,7 
 
 0.01830 
 
 .931 
 
 .52836 
 
 
 .54663 
 
 
 .98173 
 
 
 .01827 
 
 .932 
 
 .52882 
 
 
 .54705 
 
 
 .98177 
 
 3,6 
 
 .01823 
 
 933 
 
 .52927 
 
 
 .54746 
 
 
 .98181 
 
 
 .01819 
 
 .934 
 
 .52972 
 
 
 .54788 
 
 41,7 
 
 .98184 
 
 
 .01816 
 
 1.935 
 
 0.53018 
 
 45,3 
 
 0.54830 
 
 41,7 
 
 9.98188 
 
 3,6 
 
 o. 01812 
 
 .936 
 
 .53063 
 
 
 .54871 
 
 
 .98192 
 
 
 .01808 
 
 937 
 
 .53108 
 
 
 .54913 
 
 
 .98195 
 
 
 .01805 
 
 .938 
 
 .53153 
 
 
 54955 
 
 
 .98199 
 
 
 .01801 
 
 939 
 
 53199 
 
 
 .54996 
 
 
 .98202 
 
 
 .01798 
 
 1.940 
 
 0.53244 
 
 45,3 
 
 0.55038 
 
 41,7 
 
 9.98206 
 
 3,6 
 
 0.01794 
 
 .941 
 
 .53289 
 
 
 .55080 
 
 
 .98210 
 
 
 .01700 
 
 942 
 
 53334 
 
 
 .55121 
 
 
 .98213 
 
 
 .01787 
 
 943 
 
 .5338o 
 
 45,2 
 
 .55163 
 
 
 .98217 
 
 
 .01783 
 
 944 
 
 .53425 
 
 
 .55205 
 
 
 .98220 
 
 
 .01780 
 
 1-945 
 
 0.53470 
 
 45,2 
 
 0.55246 
 
 41,7 
 
 9.98224 
 
 3,6 
 
 0.01776 
 
 .946 
 
 .53515 
 
 
 .55288 
 
 
 .98227 
 
 3,5 
 
 QI773 
 
 .947 
 
 .53561 
 
 
 .55330 
 
 
 .98231 
 
 
 .01769 
 
 .948 
 
 .53606 
 
 
 .55371 
 
 
 .98235 
 
 
 .01765 
 
 949 
 
 .53651 
 
 
 .55413 
 
 
 .98238 
 
 
 .01762 
 
 1.950 
 
 0.53696 
 
 45,2 
 
 0.55455 
 
 41,7 
 
 9.98242 
 
 3,5 
 
 0.01758 
 
 u 
 
 log tan ad u 
 
 * Fo' 
 
 log sec gd u 
 
 Fo' 
 
 log sin gd u 
 
 Fo' 
 
 log esc gd u 
 
 SMITHSONIAN TABLES 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 Fo' 
 
 log cosh u 
 
 F ' 
 
 log tanh u 
 
 Fo' 
 
 log coth u 
 
 1.950 
 
 0.53696 
 
 45,2 
 
 0.55455 
 
 41,7 
 
 9.98242 
 
 3,5 
 
 0.01758 
 
 .951 
 
 .53742 
 
 
 .55496 
 
 
 .98245 
 
 
 .01755 
 
 .952 
 
 .53787 
 
 
 .55538 
 
 
 .98249 
 
 
 .01751 
 
 953 
 
 .53832 
 
 
 .55580 
 
 
 .98252 
 
 
 .01748 
 
 954 
 
 .53877 
 
 
 .55622 
 
 
 .98256 
 
 
 .01744 
 
 1-955 
 
 0.53922 
 
 45,2 
 
 0.55663 
 
 41,7 
 
 9.98259 
 
 3,5 
 
 0.01741 
 
 .956 
 
 .53968 
 
 
 55705 
 
 
 .98263 
 
 
 .01737 
 
 957 
 
 .54013 
 
 
 55747 
 
 
 .98266 
 
 
 .01734 
 
 .958 
 
 .54058 
 
 
 .55788 
 
 
 .98269 
 
 
 .01731 
 
 959 
 
 .54103 
 
 
 .55830 
 
 
 .08273 
 
 
 .01727 
 
 1.960 
 
 o'. 54148 
 
 45,2 
 
 0.55872 
 
 41,7 
 
 9.98276 
 
 3,4 
 
 0.01724 
 
 .961 
 
 .54194 
 
 
 .55914 
 
 
 .98280 
 
 
 .01720 
 
 .962 
 
 .54239 
 
 
 .55955 
 
 
 .08283 
 
 
 .01717 
 
 .963 
 
 . 54284 
 
 
 55997 
 
 
 .98287 
 
 
 .01713 
 
 .964 
 
 .54329 
 
 
 56039 
 
 41,8 
 
 .98290 
 
 
 .01710 
 
 1.965 
 
 0.54374 
 
 45,2 
 
 0.56081 
 
 41,8 
 
 9.98294 
 
 3,4 
 
 0.01706 
 
 .966 
 
 .54419 
 
 
 .56122 
 
 
 .98297 
 
 
 .01703 
 
 .967 
 
 .54465 
 
 
 .56164 
 
 
 .98300 
 
 
 .01700 
 
 .968 
 
 .54510 
 
 
 .56206 
 
 
 .98304 
 
 
 .01696 
 
 .969 
 
 54555 
 
 
 .56248 
 
 
 .98307 
 
 
 .01693 
 
 1.970 
 
 0.54600 
 
 45,2 
 
 0.56290 
 
 41,8 
 
 9.983II 
 
 3,4 
 
 0.01689 
 
 .971 
 
 .54645 
 
 45,1 
 
 .56331 
 
 
 .98314 
 
 
 .01686 
 
 .972 
 
 .54690 
 
 
 .56373 
 
 
 .98317 
 
 
 .01683 
 
 973 
 
 .54736 
 
 
 56415 
 
 
 .98321 
 
 
 .01679 
 
 974 
 
 .54781 
 
 
 .56457 
 
 
 .98324 
 
 
 .01676 
 
 1.975 
 
 0.54826 
 
 45,1 
 
 0.56498 
 
 41,8 
 
 9.98327 
 
 3,3 
 
 0.01673 
 
 .976 
 
 .54871 
 
 
 .56540 
 
 
 .98331 
 
 
 .01669 
 
 .977 
 
 .54916 
 
 
 .'56582 
 
 
 .98334 
 
 
 .01666 
 
 .978 
 
 .54961 
 
 
 
 
 .98337 
 
 
 .01663 
 
 979 
 
 .55006 
 
 
 .56666 
 
 
 98341 
 
 
 .01659 
 
 1.080 
 
 0.55051 
 
 45,1 
 
 0.56707 
 
 41,8 
 
 9.98344 
 
 3,3 
 
 0.01656 
 
 .981 
 
 .55097 
 
 
 .56749 
 
 
 .98347 
 
 
 .01653 
 
 .082 
 
 .55142 
 
 
 .56791 
 
 
 .98351 
 
 
 .01649 
 
 .983 
 
 .55187 
 
 
 .56833 
 
 
 .98354 
 
 
 .01646 
 
 .984 
 
 .55232 
 
 
 .56875 
 
 
 .98357 
 
 
 .01643 
 
 1.985 
 
 0.55277 
 
 45,1 
 
 0.56916 
 
 41,8 
 
 9.98360 
 
 3,3 
 
 0.01640 
 
 .986 
 
 .55322 
 
 
 .56958 
 
 
 .08364 
 
 
 .01636 
 
 .987 
 
 .55367 
 
 
 57000 
 
 
 .98367 
 
 
 .01633 
 
 .988 
 
 .55412 
 
 
 .57042 
 
 
 .98370 
 
 
 .01630 
 
 .989 
 
 55457 
 
 
 .57084 
 
 
 .98374 
 
 
 .01626 
 
 1.900 
 
 0.55502 
 
 45,1 
 
 0.57126 
 
 41,8 
 
 9.98377 
 
 3,2 
 
 0.01623 
 
 991 
 
 55547 
 
 
 .57167 
 
 
 .98380 
 
 
 .01620 
 
 .992 
 
 .55593 
 
 
 .57209 
 
 
 98383 
 
 
 .01617 
 
 993 
 
 .55638 
 
 
 .57251 
 
 
 98387 
 
 
 .01613 
 
 .994 
 
 .55683 
 
 
 57293 
 
 
 .98390 
 
 
 .01610 
 
 1.995 
 
 0.55728 
 
 45,1 
 
 0.57335 
 
 4i,9 
 
 9.98393 
 
 3,2 
 
 0.01607 
 
 .996 
 
 .55773 
 
 
 57377 
 
 
 .98396 
 
 
 .01604 
 
 .997 
 
 .55818 
 
 
 57419 
 
 
 .08399 
 
 
 .01601 
 
 .998 
 
 .55863 
 
 
 .57460 
 
 
 .08403 
 
 
 .01597 
 
 .999 
 
 .55908 
 
 
 57502 
 
 
 .98406 
 
 
 .01594 
 
 2.000 
 
 0.55953 
 
 45,o 
 
 0.57544 
 
 41,9 
 
 9.98409 
 
 3,2 
 
 0.01591 
 
 u 
 
 log tan gd u 
 
 Fo' 
 
 log sec gd u 
 
 Fo' 
 
 log sin gd u 
 
 Fo' 
 
 log esc gd u 
 
 SMITHSONIAN TABLES 
 
 59 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 F ' 
 
 log cosh u 
 
 F</ 
 
 log tanh u 
 
 Fo' 
 
 log coth u 
 
 2.0OO 
 
 0.55953 
 
 45,o 
 
 0.57544 
 
 41,9 
 
 9.98409 
 
 3,2 
 
 0.01591 
 
 .OOI 
 
 .55998 
 
 
 .57586 
 
 
 .98412 
 
 
 .01588 
 
 .002 
 
 
 
 .57628 
 
 
 .98415 
 
 
 .01585 
 
 .003 
 
 .56088 
 
 
 .57670 
 
 
 .98418 
 
 
 .01582 
 
 .004 
 
 .56133 
 
 
 57712 
 
 
 .98422 
 
 
 .01578 
 
 2.OO5 
 
 0.56178 
 
 45,o 
 
 0.57754 
 
 41,9 
 
 9.98425 
 
 3,2 
 
 0.01575 
 
 .006 
 
 .56223 
 
 
 57795 
 
 
 .98428 
 
 3.1 
 
 .01572 
 
 .007 
 
 .56268 
 
 
 .57837 
 
 
 .98431 
 
 
 .01569 
 
 .008 
 
 .56313 
 
 
 .57879 
 
 
 .98434 
 
 
 .01566 
 
 .009 
 
 .56358 
 
 
 57921 
 
 
 .98437 
 
 
 .01563 
 
 2.0IO 
 
 0.56403 
 
 45,o 
 
 0.57963 
 
 41,9 
 
 9.98440 
 
 3,1 
 
 0.01560 
 
 .Oil 
 
 .56448 
 
 
 .58005 
 
 
 .98444 
 
 
 .01556 
 
 .012 
 
 .56493 
 
 
 .58047 
 
 
 .98447 
 
 
 .01553 
 
 .013 
 
 .56538 
 
 
 .58089 
 
 
 -98450 
 
 
 .01550 
 
 .OI4 
 
 .56583 
 
 
 .58131 
 
 
 .98453 
 
 
 .01547 
 
 2.OIS 
 
 0.56628 
 
 45,0 
 
 0.58172 
 
 41,9 
 
 9.98456 
 
 3,1 
 
 0.01544 
 
 .Ol6 
 
 .56673 
 
 
 .58214 
 
 
 .98459 
 
 
 .01541 
 
 .017 
 
 .56718 
 
 
 .58256 
 
 
 .98462 
 
 
 .01538 
 
 .018 
 
 56723 
 
 
 .58298 
 
 
 .98465 
 
 
 .01535 
 
 .OIQ 
 
 .56808 
 
 
 .58340 
 
 
 .98468 
 
 
 .01532 
 
 2.020 
 
 0.56853 
 
 45,0 
 
 0.58382 
 
 41,9 
 
 9.98471 
 
 3,1 
 
 0.01529 
 
 .021 
 
 .56898 
 
 
 .58424 
 
 
 .98474 
 
 
 .01526 
 
 .022 
 
 
 
 .58466 
 
 
 98477 
 
 3,0 
 
 .01523 
 
 .023 
 
 .56988 
 
 
 .58508 
 
 
 .98480 
 
 
 .01520 
 
 .024 
 
 .57033 
 
 
 .58550 
 
 
 .98484 
 
 
 .01516 
 
 2.O25 
 
 0.57078 
 
 45,0 
 
 0.58592 
 
 41,9 
 
 9.98487 
 
 3,0 
 
 0.01513 
 
 .026 
 
 .57123 
 
 
 .58634 
 
 
 .98490 
 
 
 .01510 
 
 .027 
 
 .57168 
 
 
 .58676 
 
 
 .98493 
 
 
 .01507 
 
 .028 
 
 .57213 
 
 
 .58718 
 
 42,0 
 
 .98496 
 
 
 .01504 
 
 .029 
 
 .57258 
 
 
 .58760 
 
 
 98499 
 
 
 .01501 
 
 2.030 
 .031 
 
 0.57303 
 .57348 
 
 45,0 
 
 0.58802 
 
 .58843 
 
 42,0 
 
 9.98502 
 .98505 
 
 3,o 
 
 0.01498 
 .01495 
 
 .032 
 
 .57393 
 
 44,9 
 
 .58885 
 
 
 .98508 
 
 
 .01492 
 
 033 
 
 .57438 
 
 
 .58927 
 
 
 .98511 
 
 
 .01489 
 
 .034 
 
 .57483 
 
 
 .58969 
 
 
 .98514 
 
 
 .01486 
 
 2.035 
 
 0.57528 
 
 44,9 
 
 0.59011 
 
 42,0 
 
 9.98517 
 
 3,0 
 
 0.01483 
 
 .036 
 
 57573 
 
 
 .59053 
 
 
 .98519 
 
 
 .01481 
 
 037 
 
 .57618 
 
 
 .59095 
 
 
 .98522 
 
 
 .01478 
 
 .038 
 
 .57663 
 
 
 .59137 
 
 
 .98525 
 
 2,9 
 
 .01475 
 
 .039 
 
 .57708 
 
 
 .59179 
 
 
 .98528 
 
 
 .01472 
 
 2.040 
 
 0.57753 
 
 44,9 
 
 0.59221 
 
 42,0 
 
 9.98531 
 
 2,9 
 
 0.01469 
 
 .041 
 
 .57797 
 
 
 .59263 
 
 
 .98534 
 
 
 .01466 
 
 .042 
 
 .57842 
 
 
 .59305 
 
 
 .98537 
 
 
 .01463 
 
 .043 
 
 .57887 
 
 
 .59347 
 
 
 .98540 
 
 
 .01460 
 
 044 
 
 57932 
 
 
 .59389 
 
 
 .98543 
 
 
 .01457 
 
 2.045 
 
 0.57977 
 
 44,9 
 
 0.59431 
 
 42,0 
 
 9.98546 
 
 2,9 
 
 0.01454 
 
 .046 
 
 .58022 
 
 
 .59473 
 
 
 .98549 
 
 
 .01451 
 
 .047 
 
 .58067 
 
 
 .59515 
 
 
 .98552 
 
 
 .01448 
 
 .048 
 
 .58112 
 
 
 .59557 
 
 
 .98555 
 
 
 .01445 
 
 .049 
 
 .58157 
 
 
 59599 
 
 
 .98558 
 
 
 .01442 
 
 2.050 
 
 0.58202 
 
 44,9 
 
 0.50641 
 
 42,0 
 
 9.98560 
 
 2,9 
 
 0.01440 
 
 u log tin gd u 
 
 -Fo' 
 
 log sec gd u 
 
 tv 
 
 log sin gd u 
 
 -Fo' 
 
 log esc gd u 
 
 
 SMITHSONIAN TABLE* 
 
 60 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 Fo' 
 
 log cosh u 
 
 F ' 
 
 log tanh u 
 
 Fo' 
 
 log eoth u 
 
 2.050 
 
 0.58202 
 
 44,9 
 
 0.59641 
 
 42,0 
 
 9-98560 
 
 2,9 
 
 0.01440 
 
 .051 
 
 .58246 
 
 
 .59683 
 
 
 .98563 
 
 
 .01437 
 
 .052 
 
 .58291 
 
 
 59725 
 
 
 .98566 
 
 
 .01434 
 
 .053 
 
 .58336 
 
 
 .59767 
 
 
 .98569 
 
 
 .01431 
 
 .054 
 
 .58381 
 
 
 .59809 
 
 
 .98572 
 
 
 .01428 
 
 2.055 
 
 0.58426 
 
 44,9 
 
 0.59851 
 
 42,0 
 
 9.98575 
 
 2,9 
 
 0.01425 
 
 .056 
 
 .58471 
 
 
 .59893 
 
 
 .98578 
 
 2,8 
 
 .01422 
 
 057 
 
 .58516 
 
 
 .59935 
 
 
 .98580 
 
 
 .01420 
 
 .058 
 
 .58561 
 
 
 59977 
 
 
 .98583 
 
 
 .01417 
 
 .059 
 
 .58606 
 
 
 .60019 
 
 
 .98586 
 
 
 .01414 
 
 2.060 
 
 0.58650 
 
 44,9 
 
 0.60061 
 
 42,0 
 
 9.98589 
 
 2,8 
 
 0.01411 
 
 .061 
 
 .58695 
 
 
 .60104 
 
 
 .98592 
 
 
 .01408 
 
 .062 
 
 .58740 
 
 
 .60146 
 
 
 .08595 
 
 
 .01405 
 
 .063 
 
 .58785 
 
 
 .60188 
 
 
 .98597 
 
 
 .01403 
 
 .064 
 
 .58830 
 
 
 .60230 
 
 42,1 
 
 .98600 
 
 
 .01400 
 
 2.065 
 
 0.58875 
 
 44,8 
 
 0.60272 
 
 42,1 
 
 9.98603 
 
 2,8 
 
 0.01397 
 
 .066 
 
 .58920 
 
 
 .60314 
 
 
 .98606 
 
 
 .01394 
 
 .067 
 
 .58964 
 
 
 .60356 
 
 
 .98609 
 
 
 .01391 
 
 .068 
 
 .59009 
 
 
 .60398 
 
 
 .98611 
 
 
 .01389 
 
 .069 
 
 59054 
 
 
 .60440 
 
 
 .98614 
 
 
 .01386 
 
 2.070 
 
 0.59009 
 
 44,8 
 
 0.60482 
 
 42,1 
 
 9.98617 
 
 2,8 
 
 0.01383 
 
 .071 
 
 .59144 
 
 
 .60524 
 
 
 .98620 
 
 
 .01380 
 
 .072 
 
 .59189 
 
 
 .60566 
 
 
 .98622 
 
 
 .01378 
 
 .073 
 
 .59233 
 
 
 .60608 
 
 
 .98625 
 
 
 .01375 
 
 .074 
 
 .59278 
 
 
 .60650 
 
 
 .98628 
 
 2,7 
 
 .01372 
 
 2.075 
 
 0.59323 
 
 44,8 
 
 0.60692 
 
 42,1 
 
 9-98631 
 
 2,7 
 
 0.01369 
 
 .076 
 
 .59368 
 
 
 .60734 
 
 
 .98633 
 
 
 .01367 
 
 077 
 
 .59413 
 
 
 .60777 
 
 
 .98636 
 
 
 .01364 
 
 .078 
 
 59457 
 
 
 .60819 
 
 
 .98639 
 
 
 .01361 
 
 .079 
 
 .59502 
 
 
 .60861 
 
 
 .98642 
 
 
 .01358 
 
 2.080 
 
 0.59547 
 
 44,8 
 
 0.60903 
 
 42,1 
 
 9.98644 
 
 2,7 
 
 0.01356 
 
 .081 
 
 59592 
 
 
 .60945 
 
 
 .98647 
 
 
 .01353 
 
 .082 
 
 .59637 
 
 
 .60987 
 
 
 .98650 
 
 
 .01350 
 
 .083 
 
 .59681 
 
 
 .61029 
 
 
 .98652 
 
 
 .01348 
 
 .084 
 
 .59726 
 
 
 .61071 
 
 
 .98655 
 
 
 .01345 
 
 2.085 
 
 0.59771 
 
 44,8 
 
 0.61113 
 
 42,1 
 
 9-98658 
 
 2,7 
 
 0.01342 
 
 .086 
 
 .59816 
 
 
 .61155 
 
 
 .98660 
 
 
 .01340 
 
 .087 
 
 .59861 
 
 
 .61198 
 
 
 .98663 
 
 
 .01337 
 
 .088 
 
 .59905 
 
 
 .61240 
 
 
 .98666 
 
 
 .01334 
 
 .089 
 
 .59950 
 
 
 .61282 
 
 
 .98668 
 
 
 .01332 
 
 2.000 
 
 0.59995 
 
 44,8 
 
 0.61324 
 
 42,1 
 
 9.98671 
 
 2,7 
 
 0.01329 
 
 .091 
 
 .60040 
 
 
 .61366 
 
 
 .98674 
 
 
 .01326 
 
 .092 
 
 .60085 
 
 
 .61408 
 
 
 .98676 
 
 2,6 
 
 .01324 
 
 .093 
 
 .60129 
 
 
 .61450 
 
 
 .98679 
 
 
 .01321 
 
 .094 
 
 .60174 
 
 
 .61492 
 
 
 .98682 
 
 
 .01318 
 
 2.095 
 
 0.60219 
 
 44,8 
 
 0.61535 
 
 42,1 
 
 9.98684 
 
 2,6 
 
 0.01316 
 
 .096 
 
 .60264 
 
 
 .61577 
 
 
 .98687 
 
 
 .01313 
 
 .097 
 
 .60308 
 
 
 .61619 
 
 
 .98690 
 
 
 .01310 
 
 .098 
 
 .60353 
 
 
 .61661 
 
 
 .98692 
 
 
 .01308 
 
 099 
 
 .60398 
 
 
 .61703 
 
 
 .98695 
 
 
 .01305 
 
 2. TOO 
 
 0.60443 
 
 44,8 
 
 o.6i745 
 
 42,1 
 
 9.98697 
 
 2,6 
 
 0.01303 
 
 U 
 
 log tan gd u 
 
 *> Fo' 
 
 log sec gd u 
 
 w Fo' 
 
 log sin gd u 
 
 F O ' 
 
 log esc gd u 
 
 SMITHSONIAN TABLES 
 
 61 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 Fo' 
 
 log cosh u 
 
 F ' 
 
 log tanh u 
 
 Fo' 
 
 log coth u 
 
 2.IOO 
 
 0.60443 
 
 44,8 
 
 0.61745 
 
 42,1 
 
 9.98697 
 
 2,6 
 
 0.01303 
 
 .101 
 
 .60487 
 
 44,7 
 
 .61787 
 
 
 .98700 
 
 
 .01300 
 
 .102 
 
 .60532 
 
 
 .61830 
 
 42,2 
 
 .98703 
 
 
 .01297 
 
 .103 
 
 .00577 
 
 
 .61872 
 
 
 .08705 
 
 
 .01295 
 
 .104 
 
 .60622 
 
 
 .61914 
 
 
 .98708 
 
 
 .01292 
 
 2.105 
 
 0.6o666 
 
 447 
 
 0.61956 
 
 42,2 
 
 9.98710 
 
 2,6 
 
 0.01290 
 
 .106 
 
 .60711 
 
 
 .61998 
 
 
 .98713 
 
 
 .01287 
 
 .107 
 
 .60756 
 
 
 .62040 
 
 
 .98716 
 
 
 .01284 
 
 .108 
 
 .60801 
 
 
 .62083 
 
 
 .98718 
 
 
 .01282 
 
 .109 
 
 .60845 
 
 
 .62125 
 
 
 .98721 
 
 
 .01279 
 
 2. no 
 
 0.6o8oo 
 
 44,7 
 
 0.62167 
 
 42,2 
 
 9.98723 
 
 2,6 
 
 0.01277 
 
 .in 
 
 .60935 
 
 
 .62209 
 
 
 .98726 
 
 2,5 
 
 .01274 
 
 .112 
 
 .60979 
 
 
 .62251 
 
 
 .98728 
 
 
 .01272 
 
 .113 
 
 .61024 
 
 
 .62293 
 
 
 .98731 
 
 
 .01269 
 
 .114 
 
 .61069 
 
 
 .62336 
 
 
 98733 
 
 
 .01267 
 
 2.II5 
 
 0.61114 
 
 447 
 
 0.62378 
 
 42,2 
 
 9.98736 
 
 2,5 
 
 0.01264 
 
 .116 
 
 .61158 
 
 
 .62420 
 
 
 .98738 
 
 
 .01262 
 
 .117 
 
 .61203 
 
 
 .62462 
 
 
 .98741 
 
 
 .01259 
 
 .118 
 
 .61248 
 
 
 .62504 
 
 
 .98743 
 
 
 .01257 
 
 .Up 
 
 .61292 
 
 
 .62546 
 
 
 .98746 
 
 
 .01254 
 
 2.I2O 
 
 0.61337 
 
 447 
 
 0.62589 
 
 42,2 
 
 9.98748 
 
 2,5 
 
 0.01252 
 
 .121 
 
 .61382 
 
 
 .62631 
 
 
 .98751 
 
 
 .01249 
 
 .122 
 
 .61427 
 
 
 .62673 
 
 
 .98753 
 
 
 .01247 
 
 .123 
 
 .61471 
 
 
 .62715 
 
 
 .98756 
 
 
 .01244 
 
 .124 
 
 .61516 
 
 
 .62757 
 
 
 .98758 
 
 
 .01242 
 
 2.125 
 
 0.61561 
 
 447 
 
 0.62800 
 
 42,2 
 
 9.98761 
 
 2,5 
 
 0.01239 
 
 .126 
 
 .61605 
 
 
 .62842 
 
 
 .98763 
 
 
 .01237 
 
 .127 
 
 .61650 
 
 
 .62884 
 
 
 .98766 
 
 
 .01234 
 
 .128 
 
 .61695 
 
 
 .62926 
 
 
 .98768 
 
 
 .01232 
 
 .I2Q 
 
 .61739 
 
 
 .62969 
 
 
 .98771 
 
 
 .01229 
 
 2.130 
 
 0.61784 
 
 447 
 
 0.63011 
 
 42,2 
 
 9.98773 
 
 2,5 
 
 0.01227 
 
 .131 
 
 .61829 
 
 
 .63053 
 
 
 .98776 
 
 2,4 
 
 .01224 
 
 .132 
 
 .61873 
 
 
 .63095 
 
 
 .98778 
 
 
 .01222 
 
 133 
 
 .61918 
 
 
 .63137 
 
 
 .98781 
 
 
 .01219 
 
 .134 
 
 .61963 
 
 
 .63180 
 
 
 .98783 
 
 
 .01217 
 
 2.I3S 
 
 0.62007 
 
 447 
 
 0.63222 
 
 42,2 
 
 9.98785 
 
 2,4 
 
 0.01215 
 
 .136 
 
 .62052 
 
 
 .63264 
 
 
 .98788 
 
 
 .01212 
 
 .137 
 
 .62097 
 
 
 .63306 
 
 
 .98790 
 
 
 .OI2IO 
 
 .138 
 
 .62141 
 
 
 .63349 
 
 
 .98793 
 
 
 .01207 
 
 .139 
 
 .62186 
 
 
 .63391 
 
 
 .98795 
 
 
 .01205 
 
 2.140 
 
 0.62231 
 
 446 
 
 0.63433 
 
 42,2 
 
 9.98798 
 
 2,4 
 
 O.OI2O2 
 
 .141 
 
 .62275 
 
 
 .63475 
 
 
 .98800 
 
 
 .OI2OO 
 
 .142 
 
 .62320 
 
 
 .63518 
 
 
 .98802 
 
 
 .OIIOjS 
 
 143 
 
 .62365 
 
 
 .63560 
 
 42,3 
 
 .98805 
 
 
 .01195 
 
 .144 
 
 .62409 
 
 
 .63602 
 
 
 .98807 
 
 
 .01193 
 
 2.145 
 
 0.62454 
 
 44,6 
 
 0.63644 
 
 4?,3 
 
 9.98810 
 
 2,4 
 
 0.01190 
 
 .146 
 
 .62498 
 
 
 .63687 
 
 
 .08812 
 
 
 .01188 
 
 .147 
 
 .62543 
 
 
 .63729 
 
 
 .98814 
 
 
 .01186 
 
 .148 
 
 .62588 
 
 
 .63771 
 
 
 .98817 
 
 
 .01183 
 
 .149 
 
 .62632 
 
 
 .63813 
 
 
 .98819 
 
 
 .01181 
 
 2.150 
 
 0.62677 
 
 446 
 
 0.63856 
 
 42,3 
 
 9.98821 
 
 24 
 
 0.01179 
 
 u 
 
 loo tan gd u 
 
 -FO' 
 
 log sec gd u 
 
 Fo' 
 
 log sin gd u 
 
 -Fo' 
 
 log esc gd u 
 
 SMITHSONIAN TABLE* 
 
 62 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 <- Fo' 
 
 log cosh u 
 
 F ' 
 
 log tanh u 
 
 Fo' 
 
 log coth u 
 
 2.150 
 
 0.62677 
 
 44,6 
 
 0.63856 
 
 42,3 
 
 9.98821 
 
 2,4 
 
 O.OII79 
 
 .151 
 
 .62722 
 
 
 .63898 
 
 
 .98824 
 
 
 .01176 
 
 .152 
 
 .62766 
 
 
 .63940 
 
 
 .98826 
 
 2,3 
 
 .01174 
 
 .153 
 
 .62811 
 
 
 .63982 
 
 
 .98828 
 
 
 .01172 
 
 .154 
 
 .62855 
 
 
 .64025 
 
 
 .98831 
 
 
 .01169 
 
 2.155 
 
 0.62900 
 
 44,6 
 
 0.64067 
 
 42,3 
 
 9.98833 
 
 2,3 
 
 0.01167 
 
 .156 
 
 .62945 
 
 
 .64109 
 
 
 .98835 
 
 
 .01165 
 
 .157 
 
 .62989 
 
 
 .64152 
 
 
 .98838 
 
 
 .01162 
 
 .158 
 
 63034 
 
 
 .64194 
 
 
 .98840 
 
 
 .01100 
 
 .159 
 
 .63079 
 
 
 .64236 
 
 
 .98842 
 
 
 .01158 
 
 2.160 
 
 0.63123 
 
 44,6 
 
 0.64278 
 
 42,3 
 
 9.98845 
 
 2,3 
 
 O.OII55 
 
 .161 
 
 .63168 
 
 
 .64321 
 
 
 .98847 
 
 
 .01153 
 
 .162 
 
 .63212 
 
 
 .64363 
 
 
 .98849 
 
 
 .01151 
 
 .163 
 
 .63257 
 
 
 .64405 
 
 
 .98852 
 
 
 .01148 
 
 .164 
 
 .63302 
 
 
 .64448 
 
 
 .98854 
 
 
 .01146 
 
 2.165 
 
 0.63346 
 
 44,6 
 
 0.64490 
 
 42,3 
 
 9.98856 
 
 2,3 
 
 0.01144 
 
 .166 
 
 .63391 
 
 
 .64532 
 
 
 .98859 
 
 
 .01141 
 
 .167 
 
 .63435 
 
 
 .64574 
 
 
 .98861 
 
 
 .01139 
 
 .168 
 
 .63480 
 
 
 .64617 
 
 
 .98863 
 
 
 .01137 
 
 .169 
 
 .63524 
 
 
 .64659 
 
 
 .98865 
 
 
 .01135 
 
 2.170 
 
 0.63569 
 
 44,6 
 
 0.64701 
 
 42,3 
 
 9.98868 
 
 2,3 
 
 0.01132 
 
 .171 
 
 
 
 .64744 
 
 
 .98870 
 
 
 .01130 
 
 .172 
 
 .63658 
 
 
 .64786 
 
 
 .98872 
 
 
 .01128 
 
 .173 
 
 .63703 
 
 
 .64828 
 
 
 .98874 
 
 
 .01126 
 
 .174 
 
 .63747 
 
 
 .64871 
 
 
 .98877 
 
 2,2 
 
 .01123 
 
 2.175 
 
 0.63792 
 
 44,6 
 
 0.64913 
 
 42,3 
 
 9.98879 
 
 2,2 
 
 O.OII2I 
 
 .176 
 
 .63836 
 
 
 .64955 
 
 
 .98881 
 
 
 .OIII9 
 
 .177 
 
 .63881 
 
 
 .64998 
 
 
 .98883 
 
 
 .OIII7 
 
 .178 
 
 .63926 
 
 
 .65040 
 
 
 .98886 
 
 
 .01114 
 
 .179 
 
 .63970 
 
 
 .65082 
 
 
 .98888 
 
 
 .01112 
 
 2.180 
 
 0.64015 
 
 44,6 
 
 0.65125 
 
 42,3 
 
 9.98890 
 
 2,2 
 
 O.OIIIO 
 
 .181 
 
 .64059 
 
 
 .65167 
 
 
 .98892 
 
 
 .OIIOS 
 
 .182 
 
 .64104 
 
 44,5 
 
 .65209 
 
 
 .98894 
 
 
 .01106 
 
 .183 
 
 .64148 
 
 
 .65252 
 
 
 .98897 
 
 
 .OII03 
 
 .184 
 
 .64193 
 
 
 .65294 
 
 
 .98899 
 
 
 .01101 
 
 2.185 
 
 0.64237 
 
 44,5 
 
 0.65336 
 
 42,3 
 
 9.98901 
 
 2,2 
 
 0.01099 
 
 .186 
 
 .64282 
 
 
 .65379 
 
 
 .98903 
 
 
 .01097 
 
 .187 
 
 .64326 
 
 
 .65421 
 
 42,4 
 
 .98905 
 
 
 .01095 
 
 .188 
 
 .64371 
 
 
 .65463 
 
 
 .98908 
 
 
 .01092 
 
 .189 
 
 .64416 
 
 
 .65506 
 
 
 .98910 
 
 
 .01090 
 
 2.190 
 
 0.64460 
 
 44,5 
 
 0.65548 
 
 42,4 
 
 9.98912 
 
 2,2 
 
 0.01088 
 
 .191 
 
 .64505 
 
 
 .65590 
 
 
 .98914 
 
 
 .01086 
 
 .192 
 
 .64549 
 
 
 .65633 
 
 
 .98916 
 
 
 .01084 
 
 .193 
 
 .64594 
 
 
 .65675 
 
 
 .98919 
 
 
 .01081 
 
 .194 
 
 .64638 
 
 
 .65718 
 
 
 .98921 
 
 
 .01079 
 
 2.195 
 
 0.64683 
 
 44,5 
 
 0.65760 
 
 42,4 
 
 9.98923 
 
 2,2 
 
 0.01077 
 
 .196 
 
 .64727 
 
 
 .65802 
 
 
 .98925 
 
 
 .01075 
 
 .197 
 
 .64772 
 
 
 65845 
 
 
 .98927 
 
 2,1 
 
 .01073 
 
 .198 
 
 .64816 
 
 
 .65887 
 
 
 .98929 
 
 
 .01071 
 
 .199 
 
 .64861 
 
 
 .65929 
 
 
 .98931 
 
 
 .01069 
 
 2. 2OO 
 
 0.64005 
 
 44,5 
 
 0.65972 
 
 42,4 
 
 9.98934 
 
 2,1 
 
 0.01066 
 
 U 
 
 log tan gd u 
 
 Fo' 
 
 log sec gd u 
 
 Fo' 
 
 log sin gd u 
 
 Fo' 
 
 log esc gd u 
 
 SMITHSONIAN TABLES 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 F ' 
 
 log cosh u 
 
 FV 
 
 log tanh u 
 
 F O ' 
 
 log coth u 
 
 2.2OO 
 
 0.64905 
 
 44,5 
 
 0.65972 
 
 42,4 
 
 9.98934 
 
 2,1 
 
 0.01066 
 
 .2OI 
 
 .64950 
 
 
 .66014 
 
 
 .98936 
 
 
 .01064 
 
 .202 
 
 .64994 
 
 
 .66056 
 
 
 .98938 
 
 
 .01062 
 
 .203 
 
 .65039 
 
 
 .66099 
 
 
 .98940 
 
 
 .01060 
 
 .204 
 
 .65083 
 
 
 .66141 
 
 
 .98942 
 
 
 .01058 
 
 2.2O5 
 
 0.65128 
 
 44.5 
 
 0.66184 
 
 42,4 
 
 9.98944 
 
 2,1 
 
 O.OIO56 
 
 .206 
 
 .65172 
 
 
 .66226 
 
 
 .98946 
 
 
 .01054 
 
 .207 
 
 .65217 
 
 
 .66268 
 
 
 .98948 
 
 
 .01052 
 
 .208 
 
 .65261 
 
 
 .66311 
 
 
 .98950 
 
 
 .01050 
 
 .209 
 
 .65306 
 
 
 .66353 
 
 
 .98953 
 
 
 .01047 
 
 2.210 
 
 0.65350 
 
 445 
 
 0.66396 
 
 42,4 
 
 9.98955 
 
 2,1 
 
 0.01045 
 
 .211 
 
 .65395 
 
 
 .66438 
 
 
 .98957 
 
 
 .01043 
 
 .212 
 
 .65439 
 
 
 .66480 
 
 
 .98959 
 
 
 .01041 
 
 .213 
 
 .65484 
 
 
 .66523 
 
 
 .98961 
 
 
 .01039 
 
 .214 
 
 .65528 
 
 
 .66565 
 
 
 .98963 
 
 
 .01037 
 
 2.215 
 
 0.65573 
 
 44,5 
 
 0.666o8 
 
 42,4 
 
 9.98965 
 
 2,1 
 
 0.01035 
 
 .216 
 
 .65617 
 
 
 .66650 
 
 
 .98967 
 
 
 .01033 
 
 .217 
 
 .65662 
 
 
 .66692 
 
 
 .98969 
 
 
 .01031 
 
 .218 
 
 .65706 
 
 
 .66735 
 
 
 .98971 
 
 
 .01029 
 
 .219 
 
 .65751 
 
 
 .66777 
 
 
 .98973 
 
 
 .01027 
 
 2.22O 
 
 0.65795 
 
 44,5 
 
 0.66820 
 
 42,4 
 
 9.98975 
 
 2,0 
 
 0.01025 
 
 .221 
 
 .65840 
 
 
 .66862 
 
 
 .98977 
 
 
 .01023 
 
 .222 
 
 .65884 
 
 
 .66905 
 
 
 .98979 
 
 
 .0102 I 
 
 .223 
 
 .65928 
 
 
 .66947 
 
 
 .98982 
 
 
 .01018 
 
 .224 
 
 .65973 
 
 
 .66989 
 
 
 .98084 
 
 
 .01016 
 
 2.225 
 
 O.66OI7 
 
 44,5 
 
 0.67032 
 
 42,4 
 
 9.98986 
 
 2,0 
 
 0.01014 
 
 .225 
 
 .66062 
 
 
 .67074 
 
 
 .98988 
 
 
 .OIOI2 
 
 .227 
 
 .66106 
 
 
 .67117 
 
 
 .98990 
 
 
 .OIOIO 
 
 .223 
 
 .66151 
 
 44A 
 
 .67159 
 
 
 .98992 
 
 
 .01008 
 
 .229 
 
 .66195 
 
 
 .67202 
 
 
 .98994 
 
 
 .01006 
 
 2.230 
 
 0.66240 
 
 444 
 
 0.67244 
 
 42,4 
 
 9.98996 
 
 2,0 
 
 O.OIO04 
 
 .231 
 
 .66284 
 
 
 .67286 
 
 
 .98998 
 
 
 .01002 
 
 .232 
 
 .66328 
 
 
 .67329 
 
 
 .99000 
 
 
 .01000 
 
 .233 
 
 .66373 
 
 
 .67371 
 
 
 .09002 
 
 
 .00998 
 
 234 
 
 .66417 
 
 
 .674U 
 
 
 .99004 
 
 
 .00996 
 
 2.235 
 
 0.66462 
 
 444 
 
 0.67456 
 
 42,4 
 
 9.99006 
 
 2,0 
 
 0.00994 
 
 .236 
 
 .66506 
 
 
 .67499 
 
 
 .99008 
 
 
 .00992 
 
 237 
 
 .66551 
 
 
 .67541 
 
 42,5 
 
 .99010 
 
 
 .00990 
 
 .238 
 
 .66595 
 
 
 .67583 
 
 
 .99012 
 
 
 .00988 
 
 .239 
 
 .66640 
 
 
 .67626 
 
 
 .99014 
 
 
 .00986 
 
 2.240 
 
 0.66684 
 
 444 
 
 0.67668 
 
 42,5 
 
 9.99016 
 
 2,0 
 
 0.00984 
 
 .241 
 
 .66728 
 
 
 .67711 
 
 
 .99018 
 
 
 .00982 
 
 .242 
 
 .66773 
 
 
 .67753 
 
 
 .90019 
 
 
 .00981 
 
 .243 
 
 .66817 
 
 
 .67796 
 
 
 .99021 
 
 
 .00979 
 
 .244 
 
 .66862 
 
 
 .67838 
 
 
 .99023 
 
 
 .00977 
 
 2.245 
 
 0.66906 
 
 44,4 
 
 0.67881 
 
 42,5 
 
 9.90025 
 
 1,9 
 
 0.00975 
 
 .246 
 
 .66950 
 
 
 .67923 
 
 
 .99027 
 
 
 .00973 
 
 .247 
 
 .66995 
 
 
 .67966 
 
 
 .99029 
 
 
 .00971 
 
 .248 
 
 .67039 
 
 
 .68008 
 
 
 .99031 
 
 
 .00969 
 
 .249 
 
 .67084. 
 
 
 .68051 
 
 
 .99033 
 
 
 .00967 
 
 2.250 
 
 0.67128 
 
 444 
 
 0.68093 
 
 42,5 
 
 9.00035 
 
 1,9 
 
 0.00965 
 
 u 
 
 log tan gd u 
 
 Fo' 
 
 log sec gd u 
 
 F ' 
 
 log sin gd u 
 
 -Fo' 
 
 log esc gd u 
 
 SMITHSONIAN TABLES 
 
 6 4 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 Fo' 
 
 log cosh u 
 
 Fo' 
 
 log tanh u 
 
 Fo' 
 
 log eoth u 
 
 2.250 
 
 0.67128 
 
 MA 
 
 0.68093 
 
 42,5 
 
 9.99035 
 
 1,9 
 
 0.00965 
 
 .251 
 
 .67173 
 
 
 .68136 
 
 
 .09037 
 
 
 .00963 
 
 .252 
 
 .67217 
 
 
 .68178 
 
 
 .99039 
 
 
 .00961 
 
 .253 
 
 .67261 
 
 
 .68220 
 
 
 .99041 
 
 
 .00959 
 
 .254 
 
 .67306 
 
 
 .68263 
 
 
 .99043 
 
 
 .00957 
 
 2.255 
 
 0.67350 
 
 44*4 
 
 0.68305 
 
 42,5 
 
 9.99045 
 
 1,9 
 
 0.00955 
 
 .256 
 
 .67394 
 
 
 .68348 
 
 
 .99047 
 
 
 .00953 
 
 .257 
 
 .67439 
 
 
 .68390 
 
 
 .09048 
 
 
 .00952 
 
 .258 
 
 .67483 
 
 
 .68433 
 
 
 .99050 
 
 
 .00950 
 
 .259 
 
 .67528 
 
 
 .68475 
 
 
 .99052 
 
 
 .00948 
 
 2.260 
 
 0.67572 
 
 44,4 
 
 0.68518 
 
 42,5 
 
 9.99054 
 
 1,9 
 
 0.00946 
 
 .261 
 
 .67616 
 
 
 .68560 
 
 
 .99056 
 
 
 .00944 
 
 .262 
 
 .67661 
 
 
 .68603 
 
 
 .09058 
 
 
 .00942 
 
 .263 
 
 .67705 
 
 
 .68645 
 
 
 ;99o6o 
 
 
 .00940 
 
 .264 
 
 .67750 
 
 
 .68688 
 
 
 .09062 
 
 
 .00938 
 
 2.265 
 
 0.67794 
 
 44,4 
 
 0.68730 
 
 42,5 
 
 9.09064 
 
 1,9 
 
 0.00936 
 
 .266 
 
 .67838 
 
 
 .68773 
 
 
 .99065 
 
 
 .00935 
 
 .267 
 
 .67883 
 
 
 .68815 
 
 
 .99067 
 
 
 .00933 
 
 .268 
 
 .67927 
 
 
 .68858 
 
 
 .99069 
 
 
 .00931 
 
 .269 
 
 .67971 
 
 
 .68900 
 
 
 .99071 
 
 
 .00929 
 
 2.270 
 
 0.68016 
 
 MA 
 
 0.68943 
 
 42,5 
 
 9.99073 
 
 1,9 
 
 0.00927 
 
 .271 
 .272 
 
 .68060 
 .68105 
 
 
 .68985 
 .69028 
 
 
 .99075 
 .99077 
 
 1,8 
 
 .00925 
 .00923 
 
 273 
 
 .68149 
 
 
 .69070 
 
 
 .09078 
 
 
 .00922 
 
 .274 
 
 .68193 
 
 
 .69113 
 
 
 .99080 
 
 
 .00920 
 
 2.275 
 
 0.68238 
 
 MA 
 
 0.69156 
 
 42,5 
 
 9.99082 
 
 1,8 
 
 0.00918 
 
 .276 
 
 .68282 
 
 
 .69198 
 
 
 .99084 
 
 
 .00916 
 
 .277 
 
 .68326 
 
 
 .69241 
 
 
 .99086 
 
 
 .00914 
 
 .278 
 
 .68371 
 
 
 .69283 
 
 
 .99088 
 
 
 .00912 
 
 .279 
 
 .68415 
 
 44,3 
 
 .69326 
 
 
 .99089 
 
 
 .00911 
 
 2.280 
 
 0.68459 
 
 44,3 
 
 0.69368 
 
 42,5 
 
 9.99091 
 
 1,8 
 
 0.00909 
 
 .281 
 
 .68504 
 
 
 .69411 
 
 
 .99093 
 
 
 .00907 
 
 .282 
 
 .68548 
 
 
 .69453 
 
 
 .99095 
 
 
 .00905 
 
 .283 
 
 .68592 
 
 
 .69496 
 
 
 .99097 
 
 
 .00903 
 
 .284 
 
 .68637 
 
 
 .69538 
 
 
 .99098 
 
 
 .00902 
 
 2.285 
 
 0.68681 
 
 44,3 
 
 .0.69581 
 
 42,5 
 
 9.99100 
 
 1,8 
 
 0.00900 
 
 .286 
 
 .68725 
 
 
 .69623 
 
 
 .99102 
 
 
 .00898 
 
 .287 
 
 .68770 
 
 
 .69666 
 
 
 .99104 
 
 
 .00896 
 
 .288 
 
 .68814 
 
 
 .69708 
 
 
 .09106 
 
 
 .00894 
 
 .289 
 
 .68858 
 
 
 .69751 
 
 
 .99107 
 
 
 .00893 
 
 2. 20O 
 
 0.68903 
 
 44,3 
 
 0.69794 
 
 42,5 
 
 9.09109 
 
 1,8 
 
 0.00891 
 
 .291 
 
 .68947 
 
 
 .69836 
 
 
 .99111 
 
 
 .00889 
 
 .292 
 
 .68991 
 
 
 .69879 
 
 42,6 
 
 .99H3 
 
 
 .00887 
 
 293 
 
 .60036 
 
 
 .69921 
 
 
 .99H5 
 
 
 .00885 
 
 .294 
 
 .69080 
 
 
 .69964 
 
 
 .99116 
 
 
 .00884 
 
 2.295 
 
 0.69124 
 
 44,3 
 
 0.70006 
 
 42,6 
 
 9.99118 
 
 1,8 
 
 0.00882 
 
 .296 
 
 .69169 
 
 
 .70049 
 
 
 .99120 
 
 
 .00880 
 
 .297 
 
 .69213 
 
 
 .70091 
 
 
 .99122 
 
 
 .00878 
 
 .298 
 
 .69257 
 
 
 .70134 
 
 
 .99123 
 
 
 .00877 
 
 .299 
 
 .69302 
 
 
 .70177 
 
 
 .99125 
 
 i,7 
 
 .00875 
 
 2.3OO 
 
 0.69346 
 
 44,3 
 
 0.70219 
 
 42,6 
 
 9.99127 
 
 i,7 
 
 0.00873 
 
 U 
 
 log tan gd u 
 
 Fo' 
 
 log sec gd u 
 
 Fo' 
 
 log sin gd u 
 
 Fo' 
 
 log esc gd u 
 
 SMITHSONIAN TABLES 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 Fo' 
 
 log cosh u 
 
 F ' 
 
 log tanh u 
 
 Fo' 
 
 log coth u 
 
 2.300 
 
 0.69346 
 
 44,3 
 
 0.70219 
 
 42,6 
 
 9.99127 
 
 1,7 
 
 0.00873 
 
 .301 
 
 .69390 
 
 
 .70262 
 
 
 .99129 
 
 
 .00871 
 
 .302 
 
 .69435 
 
 
 .70304 
 
 
 99130 
 
 
 .00870 
 
 .303 
 
 .69479 
 
 
 .70347 
 
 
 .99132 
 
 
 .00868 
 
 .304 
 
 .69523 
 
 
 70389 
 
 
 .99134 
 
 
 .00866 
 
 2.305 
 
 0.69568 
 
 44,3 
 
 0.70432 
 
 42,6 
 
 9.99136 
 
 1,7 
 
 0.00864 
 
 .306 
 
 .69612 
 
 
 70475 
 
 
 .99137 
 
 
 .00863 
 
 .307 
 
 .69656 
 
 
 .70517 
 
 
 99139 
 
 
 .00861 
 
 .308 
 
 .69700 
 
 
 .70560 
 
 
 .99141 
 
 
 .00859 
 
 .309 
 
 .69745 
 
 
 .70602 
 
 
 .99142 
 
 
 .00858 
 
 2.310 
 
 0.69789 
 
 443 
 
 0.70645 
 
 42,6 
 
 9.99144 
 
 1,7 
 
 0.00856 
 
 .311 
 
 .69833 
 
 
 .70687 
 
 
 .99146 
 
 
 .00854 
 
 .312 
 
 .69878 
 
 
 .70730 
 
 
 .99148 
 
 
 .00852 
 
 .313 
 
 .69922 
 
 
 .70773 
 
 
 .99149 
 
 
 .00851 
 
 .314 
 
 .69966 
 
 
 .70815 
 
 
 .99151 
 
 
 .00849 
 
 2.315 
 
 O.7OOIO 
 
 443 
 
 0.70858 
 
 42,6 
 
 9.99153 
 
 1,7 
 
 0.00847 
 
 .316 
 
 .70055 
 
 
 .70900 
 
 
 .99154 
 
 
 .00846 
 
 .317 
 
 .70099 
 
 
 .70943 
 
 
 .99156 
 
 
 .00844 
 
 .318 
 
 .70143 
 
 
 .70986 
 
 
 .99158 
 
 
 .00842 
 
 .319 
 
 .70188 
 
 
 .71028 
 
 
 99159 
 
 
 .00841 
 
 2.320 
 
 0.70232 
 
 44,3 
 
 0.71071 
 
 42,6 
 
 9.99l6l 
 
 1,7 
 
 0.00839 
 
 .321 
 
 .70276 
 
 
 .7IH3 
 
 
 .99163 
 
 
 .00837 
 
 .322 
 
 .70320 
 
 
 .71156 
 
 
 .99164 
 
 
 .00836 
 
 .323 
 
 .70365 
 
 
 .71199 
 
 
 .99166 
 
 
 .00834 
 
 .324 
 
 .70409 
 
 
 .71241 
 
 
 .99168 
 
 
 .00832 
 
 2.325 
 
 0.70453 
 
 44,3 
 
 0.71284 
 
 42,6 
 
 9.99169 
 
 1,7 
 
 0.00831 
 
 .326 
 
 70497 
 
 
 .71326 
 
 
 .99171 
 
 
 .00829 
 
 .327 
 
 .70542 
 
 
 .71369 
 
 
 .99173 
 
 
 .00827 
 
 .328 
 
 .70586 
 
 
 .71412 
 
 
 .99174 
 
 
 .00826 
 
 .329 
 
 .70630 
 
 
 -.71454 
 
 
 .99176 
 
 1,6 
 
 .00824 
 
 2.330 
 
 0.70675 
 
 443 
 
 0.7U97 
 
 42,6 
 
 9.99178 
 
 1,6 
 
 0.00822 
 
 .331 
 
 .70719 
 
 
 .71539 
 
 
 .99179 
 
 
 .00821 
 
 .332 
 
 .70763 
 
 
 .71582 
 
 
 .99181 
 
 
 .00819 
 
 .333 
 
 .70807 
 
 
 .71625 
 
 
 .99183 
 
 
 .00817 
 
 334 
 
 .70852 
 
 
 .71667 
 
 
 99184 
 
 
 .00816 
 
 2.335 
 
 0.70896 
 
 443 
 
 0.7I7IO 
 
 42,6 
 
 9.99186 
 
 1,6 
 
 0.00814 
 
 .336 
 
 .70940 
 
 442 
 
 .71753 
 
 
 .99188 
 
 
 .008'I2 
 
 337 
 
 .70984 
 
 
 .71795 
 
 
 .99189 
 
 
 .00811 
 
 .338 
 
 .71029 
 
 
 .71838 
 
 
 .99191 
 
 
 .00809 
 
 339 
 
 .71073 
 
 
 .71880 
 
 
 .99192 
 
 
 .00808 
 
 2.340 
 
 0.7IH7 
 
 44,2 
 
 0.71923 
 
 42,6 
 
 9.99194 
 
 1,6 
 
 0.00806 
 
 .341 
 
 .71161 
 
 
 .71966 
 
 
 .99196 
 
 
 .00804 
 
 342 
 
 .71206 
 
 
 .72008 
 
 
 .99197 
 
 
 .00803 
 
 343 
 
 .71250 
 
 
 .72051 
 
 
 .99199 
 
 
 .00801 
 
 344 
 
 .71294 
 
 
 .72094 
 
 
 .99200 
 
 
 .00800 
 
 2-345 
 
 O.7I338 
 
 44,2 
 
 0.72136 
 
 42,6 
 
 9.99202 
 
 1,6 
 
 0.00798 
 
 346 
 
 .71382 
 
 
 .72179 
 
 
 .99204 
 
 
 .00706 
 
 347 
 
 .71427 
 
 
 .72221 
 
 
 .09205 
 
 
 .00795 
 
 .348 
 
 .71471 
 
 
 .72264 
 
 
 .99207 
 
 \ 
 
 .00793 
 
 349 
 
 .71515 
 
 
 .72307 
 
 
 .99208 
 
 
 .00792 
 
 2.350 
 
 0.71559 
 
 44,2 
 
 0.72349 
 
 42,6 
 
 9.99210 
 
 1,6 
 
 0.00790 
 
 u 
 
 log tin ad u 
 
 Fo' 
 
 log fee gd u 
 
 Fo' 
 
 log sin gd u 
 
 F</ 
 
 log esc gd u 
 
 SMITHSONIAN TABLCS 
 
 66 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 u, Fo' 
 
 log cosh u 
 
 F ' 
 
 log tanh u 
 
 Fo' 
 
 log coth u 
 
 2.350 
 
 0.71559 
 
 44,2 
 
 0.72349 
 
 42,6 
 
 9.99210 
 
 1,6 
 
 0.00790 
 
 .351 
 
 .71604 
 
 
 .72392 
 
 
 .99212 
 
 
 .00788 
 
 .352 
 
 .71648 
 
 
 .72435 
 
 
 .99213 
 
 
 .00787 
 
 .353 
 354 
 
 .71692 
 .71736 
 
 
 .72477 
 .72520 
 
 42,7 
 
 .99215 
 .99216 
 
 
 .00785 
 .00784 
 
 2.355 
 .356 
 
 0.71781 
 .71825 
 
 44,2 
 
 0.72563 
 .72605 
 
 42,7 
 
 9.99218 
 .99219 
 
 1,6 
 
 0.00782 
 .00781 
 
 357 
 
 .71869 
 
 
 .72648 
 
 
 .99221 
 
 
 .00779 
 
 358 
 
 .71913 
 
 
 .72691 
 
 
 .99223 
 
 
 .00777 
 
 359 
 
 .71957 
 
 
 .72733 
 
 
 .99224 
 
 
 .00776 
 
 2.360 
 
 O.720O2 
 
 44,2 
 
 0.72776 
 
 42,7 
 
 9.99226 
 
 1,5 
 
 0.00774 
 
 .361 
 
 .72046 
 
 
 .72819 
 
 
 .99227 
 
 
 .00773 
 
 .362 
 
 .72000 
 
 
 .72861 
 
 
 .99229 
 
 
 .00771 
 
 .363 
 
 .72134 
 
 
 .72904 
 
 
 .99230 
 
 
 .00770 
 
 ST\ 
 
 .364 
 
 .72178 
 
 
 .72947 
 
 
 .99232 
 
 
 .00768 
 
 2.365 
 
 0.72223 
 
 44,2 
 
 0.72989 
 
 42,7 
 
 9.99233 
 
 1,5 
 
 O.O0767 
 
 .366 
 
 .72267 
 
 
 .73032 
 
 
 .99235 
 
 
 .00765 
 
 .367 
 
 .723H 
 
 
 .73075 
 
 
 .99236 
 
 
 .00764 
 
 .368 
 
 .72355 
 
 
 .73H7 
 
 
 .99238 
 
 
 .OO762 
 
 .369 
 
 .72399 
 
 
 .73160 
 
 
 .99239 
 
 
 .00761 
 
 2.370 
 
 0.72444 
 
 44,2 
 
 0.73203 
 
 42,7 
 
 9.99241 
 
 1,5 
 
 0.00759 
 
 371 
 
 372 
 
 .72488 
 .72532 
 
 
 .73245 
 .73288 
 
 
 .99242 
 .99244 
 
 
 .00758 
 .00756 
 
 373 
 
 .72576 
 
 
 73331 
 
 
 .99245 
 
 
 .00755 
 
 374 
 
 .72620 
 
 
 73373 
 
 
 .99247 
 
 
 .00753 
 
 2.375 
 
 0.72665 
 
 44,2 
 
 0.73416 
 
 42,7 
 
 9.99249 
 
 1,5 
 
 0.00751 
 
 .376 
 
 .72709 
 
 
 73459 
 
 
 .99250 
 
 
 .00750 
 
 377 
 
 .72753 
 
 
 .73501 
 
 
 .99252 
 
 
 .00748 
 
 378 
 
 .72797 
 
 
 .73544 
 
 
 .99253 
 
 
 .00747 
 
 .379 
 
 .72841 
 
 
 .73587 
 
 
 .99254 
 
 
 .00746 
 
 2.380 
 
 0.72885 
 
 44,2 
 
 0.73630 
 
 42,7 
 
 9.99256 
 
 i,5 
 
 0.00744 
 
 .381 
 
 .72930 
 
 
 .73672 
 
 
 .99257 
 
 
 .00743 
 
 .382 
 
 .72974 
 
 
 .73715 
 
 
 .99259 
 
 
 .00741 
 
 .383 
 
 .73018 
 
 
 .73758 
 
 
 .99260 
 
 
 .00740 
 
 .384 
 
 .73062 
 
 
 .73800 
 
 
 .99262 
 
 
 .00738 
 
 2.385 
 
 0.73106 
 
 44,2 
 
 0.73843 
 
 42,7 
 
 9.99263 
 
 1,5 
 
 0.00737 
 
 .386 
 
 .73151 
 
 
 .73886 
 
 
 .99265 
 
 
 .00735 
 
 .387 
 
 .73195 
 
 
 .73928 
 
 
 .99266 
 
 
 .00734 
 
 .388 
 
 .73239 
 
 
 .73971 
 
 
 .99268 
 
 
 .00732 
 
 .389 
 
 .73283 
 
 
 .74014 
 
 
 .99269 
 
 
 .00731 
 
 2.390 
 
 0.73327 
 
 44,2 
 
 0.74056 
 
 42,7 
 
 9.99271 
 
 i,5 
 
 0.00729 
 
 .391 
 
 73371 
 
 
 .74099 
 
 
 .99272 
 
 
 .00728 
 
 392 
 
 .73416 
 
 
 .74142 
 
 
 .99274 
 
 
 .00726 
 
 .393 
 
 .73460 
 
 
 .74185 
 
 
 .99275 
 
 1,4 
 
 .00725 
 
 394 
 
 .73504 
 
 
 .74227 
 
 
 .99277 
 
 
 .00723 
 
 2.395 
 
 0.73548 
 
 44,2 
 
 0.74270 
 
 42,7 
 
 9.99278 
 
 1,4 
 
 0.00722 
 
 .396 
 
 73592 
 
 
 .74313 
 
 
 .99279 
 
 
 .00721 
 
 397 
 
 .73636 
 
 
 .74355 
 
 
 .99281 
 
 
 .00719 
 
 .398 
 
 .73680 
 
 
 .74398 
 
 
 .99282 
 
 
 .00718 
 
 399 
 
 .73725 
 
 
 .74441 
 
 
 .99284 
 
 
 .00716 
 
 2.400 
 
 0.73769 
 
 44,2 
 
 0.74484 
 
 42,7 
 
 9.99285 
 
 1,4 
 
 0.00715 
 
 u 
 
 log tan grf u 
 
 Fo' 
 
 log sec gd u 
 
 F ' 
 
 log sin gd u 
 
 Fo' 
 
 log esc gd u 
 
 SMITHSONIAN TABLES 
 
 67 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 loo sinh u 
 
 jy 
 
 log cosh u 
 
 -FO' 
 
 log tanh u 
 
 Fo' 
 
 log coth u 
 
 2.400 
 
 0.73709 
 
 44,2 
 
 0.74484 
 
 42,7 
 
 9.99285 
 
 1,4 
 
 0.00715 
 
 .401 
 
 .73813 
 
 44,1 
 
 .74526 
 
 
 .99287 
 
 
 .00713 
 
 .402 
 
 .73857 
 
 
 .74569 
 
 
 .99288 
 
 
 .00712 
 
 .403 
 
 73901 
 
 
 .74612 
 
 
 .99289 
 
 
 .00711 
 
 .404 
 
 73945 
 
 
 .74655 
 
 
 .99291 
 
 
 .00709 
 
 2.405 
 
 0.73990 
 
 44,1 
 
 0.74697 
 
 42,7 
 
 9.99292 
 
 1,4 
 
 0.00708 
 
 .406 
 
 .74934 
 
 
 74740 
 
 
 .99294 
 
 
 .00706 
 
 .407 
 
 .74078 
 
 
 .74783 
 
 
 .99295 
 
 
 .00705 
 
 .408 
 
 .74122 
 
 
 .74825 
 
 
 .99297 
 
 
 .00703 
 
 .409 
 
 .74166 
 
 
 .74868 
 
 
 .99298 
 
 
 .00702 
 
 2.410 
 
 0.74210 
 
 441 
 
 0.749H 
 
 42,7 
 
 9.99299 
 
 1,4 
 
 0.00701 
 
 .411 
 
 .74254 
 
 
 .74954 
 
 
 99301 
 
 
 .00699 
 
 .412 
 
 74298 
 
 
 .74996 
 
 
 .99302 
 
 
 .00698 
 
 .413 
 
 .74343 
 
 
 .75039 
 
 
 .09304 
 
 
 .00696 
 
 .414 
 
 .74387 
 
 
 .75082 
 
 
 .99305 
 
 
 .00695 
 
 2.415 
 
 0.74431 
 
 44,1 
 
 0.75125 
 
 42,7 
 
 9.99306 
 
 1,4 
 
 0.00694 
 
 .416 
 
 74475 
 
 
 .75167 
 
 
 .99308 
 
 
 .00692 
 
 .417 
 
 .74519 
 
 
 .75210 
 
 
 .99309 
 
 
 .00691 
 
 .418 
 
 .74563 
 
 
 .75253 
 
 
 .99310 
 
 
 .00690 
 
 .419 
 
 .74607 
 
 
 .75296 
 
 
 .99312 
 
 
 .00688 
 
 2.420 
 
 0.74652 
 
 44,1 
 
 0.75338 
 
 42,7 
 
 9.99313 
 
 1,4 
 
 0.00687 
 
 .421 
 
 .74696 
 
 
 .75381 
 
 
 .99315 
 
 
 .00685 
 
 .422 
 
 .74740 
 
 
 .75424 
 
 42,8 
 
 .99316 
 
 
 .00684 
 
 .423 
 
 .74784 
 
 
 .75467 
 
 
 .99317 
 
 
 .00683 
 
 .424 
 
 .74828 
 
 
 .75509 
 
 
 .99319 
 
 
 .00681 
 
 2.425 
 
 0.74872 
 
 44,1 
 
 0.75552 
 
 42,8 
 
 9.99320 
 
 1,4 
 
 0.0068o 
 
 .426 
 
 .74916 
 
 
 .75595 
 
 
 99321 
 
 
 .00679 
 
 .427 
 
 .74960 
 
 
 .75638 
 
 
 .99323 
 
 
 .00677 
 
 .428 
 
 .75004 
 
 
 .75680 
 
 
 99324 
 
 
 .00676 
 
 .429 
 
 .75049 
 
 
 .75723 
 
 
 .99325 
 
 1,3 
 
 .00675 
 
 2.430 
 
 0.75093 
 
 44,1 
 
 0.75766 
 
 42,8 
 
 9.99327 
 
 1,3 
 
 0.00673 
 
 .431 
 
 .75137 
 
 
 .75809 
 
 
 .99328 
 
 
 .00672 
 
 .432 
 
 .75i8i 
 
 
 .75851 
 
 
 .99329 
 
 
 .00671 
 
 433 
 
 .75225 
 
 
 .75894 
 
 
 99331 
 
 
 .00669 
 
 434 
 
 .75269 
 
 
 .75937 
 
 
 .99332 
 
 
 .00668 
 
 2.435 
 
 0.75313 
 
 44,1 
 
 0.75980 
 
 42,8 
 
 9-99333 
 
 1,3 
 
 0.00667 
 
 .436 
 
 .75357 
 
 
 .76022 
 
 
 .99335 
 
 
 .00665 
 
 437 
 
 .75401 
 
 
 .76065 
 
 
 .99336 
 
 
 .00664 
 
 -438 
 
 .75445 
 
 
 .76108 
 
 
 99337 
 
 
 .00663 
 
 439 
 
 75490 
 
 
 .76151 
 
 
 99339 
 
 
 .00661 
 
 2.440 
 
 0.75534 
 
 44,1 
 
 0.76104 
 
 42,8 
 
 9.99340 
 
 1,3 
 
 0.00660 
 
 .441 
 
 .75578 
 
 
 .76236 
 
 
 99341 
 
 
 .00659 
 
 .442 
 
 .75622 
 
 
 .76279 
 
 
 99343 
 
 
 .00657 
 
 443 
 
 .75666 
 
 
 .76322 
 
 
 99344 
 
 
 .00656 
 
 .444 
 
 75710 
 
 
 .76365 
 
 
 .99345 
 
 
 .00655 
 
 2.445 
 
 0.75754 
 
 44,1 
 
 0.76407 
 
 42,8 
 
 9-99347 
 
 1,3 
 
 0.00653 
 
 .446 
 
 .75798 
 
 
 .76450 
 
 
 .99348 
 
 
 .00652 
 
 447 
 
 .75842 
 
 
 .76493 
 
 
 99349 
 
 
 .00651 
 
 .448 
 
 .75886 
 
 
 .76536 
 
 
 .99351 
 
 
 .00649 
 
 .449 
 
 75930 
 
 
 .76579 
 
 
 .99352 
 
 
 .00648 
 
 2.450 
 
 0.75975 
 
 44,1 
 
 0.76621 
 
 42,8 
 
 9-99353 
 
 1,3 
 
 o.oo6Li7 
 
 u 
 
 log tan gd u 
 
 Fo' 
 
 log sec gd u 
 
 Fo' 
 
 log sin gd u 
 
 4V 
 
 log esc gd u 
 
 SMITHSJONIMN TABLES 
 
 68 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 loo sinh u 
 
 Fo' 
 
 log cosh u 
 
 -Fo' 
 
 log tanh u 
 
 F ' 
 
 log coth u 
 
 2.450 
 
 0.75975 
 
 44,1 
 
 0.76621 
 
 42,8 
 
 9-99353 
 
 1,3 
 
 0.00647 
 
 .451 
 
 .76019 
 
 
 .76664 
 
 
 99354 
 
 
 .00646 
 
 .452 
 
 .76063 
 
 
 .76707 
 
 
 .99356 
 
 
 .00644 
 
 453 
 
 .76107 
 
 
 .76750 
 
 
 99357 
 
 
 .00643 
 
 454 
 
 .76151 
 
 
 .76793 
 
 
 99358 
 
 
 .00642 
 
 2.455 
 
 0.76195 
 
 44,1 
 
 0.76835 
 
 42,8 
 
 9.99360 
 
 1,3 
 
 0.00640 
 
 456 
 
 .76239 
 
 
 .76878 
 
 
 .09361 
 
 
 .00639 
 
 457 
 
 .76283 
 
 
 .76921 
 
 
 .99362 
 
 
 .00638 
 
 .458 
 
 .76327 
 
 
 .76964 
 
 
 99363 
 
 
 .00637 
 
 459 
 
 .76371 
 
 
 .77006 
 
 
 .99365 
 
 
 .00635 
 
 2.460 
 
 0.76415 
 
 44,1 
 
 0.77049 
 
 42,8 
 
 9.99366 
 
 1,3 
 
 0.00634 
 
 .461 
 
 .76459 
 
 
 77092 
 
 
 99367 
 
 
 .00633 
 
 .462 
 
 .76503 
 
 
 .77135 
 
 
 .99369 
 
 
 .00631 
 
 463 
 
 .76547 
 
 
 .77178 
 
 
 .99370 
 
 
 .00630 
 
 .464 
 
 .76592 
 
 
 .77220 
 
 
 99371 
 
 
 .00629 
 
 2.465 
 
 0.76636 
 
 44,1 
 
 0.77263 
 
 42,8 
 
 9.99372 
 
 1,3 
 
 0.00628 
 
 .466 
 
 .76680 
 
 
 .77306 
 
 
 99374 
 
 
 .00626 
 
 .467 
 
 .76724 
 
 
 77349 
 
 
 .99375 
 
 
 .00625 
 
 .468 
 
 .76768 
 
 
 77392 
 
 
 .99376 
 
 1,2 
 
 .00624 
 
 .469 
 
 .76812 
 
 
 77435 
 
 
 99377 
 
 
 .00623 
 
 2.470 
 
 0.76856 
 
 44.1 
 
 0.77477 
 
 42,8 
 
 9-99379 
 
 1,2 
 
 0.00621 
 
 .471 
 
 .76900 
 
 
 77520 
 
 
 .99380 
 
 
 .00620 
 
 .472 
 
 .76944 
 
 
 .77563 
 
 
 .9938i 
 
 
 .00619 
 
 473 
 
 .76988 
 
 
 .77606 
 
 
 .99382 
 
 
 .00618 
 
 474 
 
 .77032 
 
 
 .77649 
 
 
 .99384 
 
 
 .00616 
 
 2.475 
 
 0.77076 
 
 44*0 
 
 0.77691 
 
 42,8 
 
 9.99385 
 
 1,2 
 
 0.00615 
 
 .476 
 
 .77120 
 
 
 77734 
 
 
 .99386 
 
 
 .00614 
 
 477 
 
 .77164 
 
 
 77777 
 
 
 .99387 
 
 
 .00613 
 
 .478 
 
 .77208 
 
 
 .77820 
 
 
 .99388 
 
 
 .00612 
 
 479 
 
 .77252 
 
 
 .77863 
 
 
 .99390 
 
 
 .00610 
 
 2.480 
 
 0.77296 
 
 44,0 
 
 0.77906 
 
 42,8 
 
 9.99391 
 
 1,2 
 
 0.00609 
 
 .481 
 
 .77340 
 
 
 .77948 
 
 
 99392 
 
 
 .00608 
 
 .482 
 
 .77384 
 
 
 .77991 
 
 
 .99393 
 
 
 .00607 
 
 483 
 
 .77429 
 
 
 .78034 
 
 
 
 
 .00606 
 
 .484 
 
 77473 
 
 
 .78077 
 
 
 .99396 
 
 
 .00604 
 
 2.485 
 
 0.77517 
 
 44,0 
 
 0.78120 
 
 42,8 
 
 9-99397 
 
 1,2 
 
 0.00603 
 
 .486 
 
 .77561 
 
 
 .78163 
 
 
 .99398 
 
 
 .00602 
 
 .487 
 
 .77605 
 
 
 .78205 
 
 
 99399 
 
 
 .00601 
 
 .488 
 
 .77649 
 
 
 .78248 
 
 
 .09401 
 
 
 00599 
 
 .489 
 
 .77693 
 
 
 .78292 
 
 
 .99402 
 
 
 .00598 
 
 2.490 
 
 0.77737 
 
 44,0 
 
 0.78334 
 
 42,8 
 
 9.99403 
 
 1,2 
 
 0.00597 
 
 .491 
 
 .77781 
 
 
 .78377 
 
 
 .99404 
 
 
 .00596 
 
 .492 
 
 .77825 
 
 
 .78420 
 
 
 .99405 
 
 
 00595 
 
 .493 
 
 .77869 
 
 
 .78462 
 
 
 .99406 
 
 
 .00594 
 
 .494 
 
 .77913 
 
 
 .78505 
 
 
 .99408 
 
 
 .00592 
 
 2.495 
 
 0.77957 
 
 44,0 
 
 0.78548 
 
 42,8 
 
 9.99409 
 
 1,2 
 
 0.00591 
 
 .496 
 
 .78001 
 
 
 .78591 
 
 
 .09410 
 
 
 .00590 
 
 497 
 
 .78045 
 
 
 .78634 
 
 
 .99411 
 
 
 .00589 
 
 .498 
 
 .78089 
 
 
 .78677 
 
 
 .99412 
 
 
 .00588 
 
 .499 
 
 .78133 
 
 
 .78719 
 
 
 .99414 
 
 
 .00586 
 
 2.500 
 
 < 0.78177 
 
 44,0 
 
 0.78762 
 
 42,8 
 
 9.99415 
 
 1,2 
 
 0.00585 
 
 u 
 
 log tan gd u 
 
 Fo' 
 
 log sec gd u 
 
 Fo' 
 
 log sin gd u 
 
 F O ' 
 
 log esc gd u 
 
 SMITHSONIAN TABLES 
 
 69 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 loo sinh u 
 
 Fo' 
 
 log cosh u 
 
 F ' 
 
 log tanh u 
 
 Fo' 
 
 log coth u 
 
 2.500 
 
 0.78177 
 
 44,0 
 
 0.78762 
 
 42,8 
 
 9.99415 
 
 1,2 
 
 0.00585 
 
 .501 
 
 .78221 
 
 
 .78805 
 
 
 .99416 
 
 
 .00584 
 
 .502 
 
 .78265 
 
 
 .78848 
 
 42,9 
 
 99417 
 
 
 .00583 
 
 .503 
 
 .78309 
 
 
 .78891 
 
 
 .99418 
 
 
 .00582 
 
 .504 
 
 .78353 
 
 
 .78934 
 
 
 .99419 
 
 
 .00581 
 
 2.505 
 
 0.78397 
 
 44,0 
 
 0.78977 
 
 42,9 
 
 9.99421 
 
 1,2 
 
 0.00579 
 
 .506 
 
 .78441 
 
 
 .79019 
 
 
 .99422 
 
 
 .00578 
 
 .507 
 
 .78485 
 
 
 .79062 
 
 
 .99423 
 
 
 00577 
 
 .508 
 
 .78529 
 
 
 79105 
 
 
 .99424 
 
 
 .00576 
 
 .509 
 
 .78573 
 
 
 .79148 
 
 
 99425 
 
 1,1 
 
 .00575 
 
 2.510 
 
 0.78617 
 
 44,0 
 
 0.79I9I 
 
 42,9 
 
 9.99426 
 
 1,1 
 
 0.00574 
 
 .511 
 
 .78661 
 
 
 .79234 
 
 
 99427 
 
 
 .00573 
 
 .512 
 
 .78705 
 
 
 .79277 
 
 
 .99429 
 
 
 .00571 
 
 .513 
 
 .78749 
 
 
 .79319 
 
 
 .99430 
 
 
 .00570 
 
 .514 
 
 .78793 
 
 
 .79362 
 
 
 .99431 
 
 
 .00569 
 
 2.515 
 
 0.78837 
 
 44,0 
 
 0.79405 
 
 42,9 
 
 9-99432 
 
 1,1 
 
 0.00568 
 
 .516 
 
 .78881 
 
 
 .79448 
 
 
 99433 
 
 
 .00567 
 
 .517 
 
 .78925 
 
 
 79491 
 
 
 99434 
 
 
 .00566 
 
 .518 
 
 .78969 
 
 
 .79534 
 
 
 99435 
 
 
 .00565 
 
 .519 
 
 .79013 
 
 
 .79577 
 
 
 99437 
 
 
 .00563 
 
 2.520 
 
 0.79057 
 
 44,0 
 
 0.79619 
 
 42,9 
 
 9.99438 
 
 1,1 
 
 0.00562 
 
 .521 
 
 .79101 
 
 
 .79662 
 
 
 99439 
 
 
 .00561 
 
 .522 
 
 .79145 
 
 
 79705 
 
 
 .99440 
 
 
 .00560 
 
 .523 
 
 .79189 
 
 
 .79748 
 
 
 99441 
 
 
 .00559 
 
 .524 
 
 .79233 
 
 
 .79791 
 
 
 .99442 
 
 
 .00558 
 
 2.525 
 
 0.79277 
 
 44,0 
 
 0.79834 
 
 42,9 
 
 9-99443 
 
 1,1 
 
 0.00557 
 
 .526 
 
 79321 
 
 
 .79877 
 
 
 99444 
 
 
 .00556 
 
 .527 
 
 .79365 
 
 
 .79920 
 
 
 .99446 
 
 
 .00554 
 
 .528 
 
 .79409 
 
 
 .79962 
 
 
 99447 
 
 
 00553 
 
 .529 
 
 79453 
 
 
 .80005 
 
 
 .99448 
 
 
 00552 
 
 2.530 
 
 0.79497 
 
 44,0 
 
 0.80048 
 
 42,9 
 
 9.09449 
 
 1,1 
 
 0.00551 
 
 .531 
 
 79541 
 
 
 .80091 
 
 
 99450 
 
 
 .00550 
 
 .532 
 
 .79585 
 
 
 .80134 
 
 
 99451 
 
 
 .00549 
 
 533 
 
 .79629 
 
 
 .80177 
 
 
 .99452 
 
 
 .00548 
 
 534 
 
 .79673 
 
 
 .80220 
 
 
 .99453 
 
 
 .00547 
 
 2.535 
 
 0.79717 
 
 44,0 
 
 0.80263 
 
 42,9 
 
 9-99454 
 
 1,1 
 
 0.00546 
 
 .536 
 
 .79761 
 
 
 .80306 
 
 
 99455 
 
 
 .00545 
 
 537 
 
 .79805 
 
 
 .80348 
 
 
 99456 
 
 
 .00544 
 
 .538 
 
 .70849 
 
 
 .80391 
 
 
 .99458 
 
 
 .00542 
 
 539 
 
 .79893 
 
 
 .80434 
 
 
 99459 
 
 
 .00541 
 
 2.540 
 
 0.79937 
 
 44,0 
 
 0.80477 
 
 42,9 
 
 9.99460 
 
 1,1 
 
 0.00540 
 
 541 
 
 .79981 
 
 
 .80520 
 
 
 .99461 
 
 
 .00539 
 
 542 
 
 .80025 
 
 
 .80563 
 
 
 .99462 
 
 
 .00538 
 
 543 
 
 .80069 
 
 
 .80606 
 
 
 .99463 
 
 
 .00537 
 
 544 
 
 .80113 
 
 
 .80649 
 
 
 .99464 
 
 
 .00536 
 
 2.545 
 
 0.80157 
 
 44,0 
 
 0.80692 
 
 42,9 
 
 9.99465 
 
 1,1 
 
 0.00535 
 
 546 
 
 .80201 
 
 
 .80734 
 
 
 .99466 
 
 
 00534 
 
 .547 
 
 .80245 
 
 
 .80777 
 
 
 .99467 
 
 
 00533 
 
 .548 
 
 .80289 
 
 
 .80820 
 
 
 .99468 
 
 
 .00532 
 
 549 
 
 .80333 
 
 
 .80863 
 
 
 .99469 
 
 
 .00531 
 
 2.550 
 
 0.80377 
 
 44,0 
 
 0.80906 
 
 42,9 
 
 9.99470 
 
 1,1 
 
 0.00530 
 
 u 
 
 log tan <jd u 
 
 F ' 
 
 log sec gd u 
 
 F ' 
 
 log sin gd u 
 
 Fo' 
 
 log esc gd u 
 
 SMITHSONIAN TABLES 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 Fo' 
 
 log cosh u 
 
 F O ' 
 
 log tanh u 
 
 F ' 
 
 log coth u 
 
 2.550 
 
 0.80377 
 
 44,0 
 
 0.80906 
 
 42,9 
 
 9-99470 
 
 1,1 
 
 0.00530 
 
 .551 
 
 .80420 
 
 
 .80949 
 
 
 .99471 
 
 
 .00529 
 
 552 
 
 .80464 
 
 
 :8o992 
 
 
 99473 
 
 
 .00527 
 
 553 
 
 .80508 
 
 
 .81035 
 
 
 99474 
 
 
 .00526 
 
 554 
 
 .80552 
 
 
 .81078 
 
 
 99475 
 
 
 .00525 
 
 2.555 
 
 0.80596 
 
 44,0 
 
 o. 81121 
 
 42,9 
 
 9.99476 
 
 1,0 
 
 0.00524 
 
 .556 
 
 .80640 
 
 
 .81164 
 
 
 99477 
 
 
 .00523 
 
 557 
 
 .80684 
 
 
 ..81206 
 
 
 .99478 
 
 
 .00522 
 
 .558 
 
 .80728 
 
 
 .81249 
 
 
 99479 
 
 
 .00521 
 
 559 
 
 .80772 
 
 
 .81292 
 
 
 .99480 
 
 
 .00520 
 
 2.560 
 
 0.8o8l6 
 
 44,0 
 
 0.81335 
 
 42,9 
 
 9.99481 
 
 1,0 
 
 0.00519 
 
 .561 
 
 .80860 
 
 
 .81378 
 
 
 .99482 
 
 
 .00518 
 
 .562 
 
 .80904 
 
 43,9 
 
 .81421 
 
 
 .99483 
 
 
 .00517 
 
 .563 
 
 .80948 
 
 
 .81464 
 
 
 .99484 
 
 
 .00516 
 
 .564 
 
 .80992 
 
 
 .81507 
 
 
 .99485 
 
 
 .00515 
 
 2.565 
 
 0.81036 
 
 43,9 
 
 0.81550 
 
 42,9 
 
 9.99486 
 
 I,O 
 
 0.00514 
 
 .566 
 
 .81080 
 
 
 .81593 
 
 
 .99487 
 
 
 .00513 
 
 .567 
 
 .81124 
 
 
 .81636 
 
 
 .99488 
 
 
 .00512 
 
 .568 
 
 .81168 
 
 
 .81678 
 
 
 .99489 
 
 
 .00511 
 
 .569 
 
 .81212 
 
 
 .81721 
 
 
 99490 
 
 
 .00510 
 
 2.570 
 
 0.81256 
 
 43,9 
 
 0.81764 
 
 42,9 
 
 9.99491 
 
 1,0 
 
 0.00509 
 
 571 
 
 .81299 
 
 
 .81807 
 
 
 99492 
 
 
 .00508 
 
 572 
 
 .81343 
 
 
 .81850 
 
 
 99493 
 
 
 .00507 
 
 573 
 
 .81387 
 
 
 .81893 
 
 
 .99494 
 
 
 .00506 
 
 574 
 
 .81431 
 
 
 .81936 
 
 
 99495 
 
 
 .00505 
 
 2.575 
 
 0.81475 
 
 43,9 
 
 0.81979 
 
 42,9 
 
 9.99496 
 
 1,0 
 
 0.00504 
 
 .576 
 
 .81519 
 
 
 .82022 
 
 
 99497 
 
 
 .00503 
 
 577 
 
 .81563 
 
 
 .82065 
 
 
 .99498 
 
 
 .00502 
 
 578 
 
 .81607 
 
 
 .82108 
 
 
 99499 
 
 
 .00501 
 
 579 
 
 .81651 
 
 
 .82151 
 
 
 99500 
 
 
 .00500 
 
 2.580 
 
 0.81695 
 
 43,9 
 
 0.82194 
 
 42,9 
 
 9.99501 
 
 1,0 
 
 0.00499 
 
 .581 
 
 .81739 
 
 
 .82237 
 
 
 .99502 
 
 
 .00498 
 
 .582 
 
 .81783 
 
 
 .82279 
 
 
 99503 
 
 
 .00497 
 
 .583 
 
 .81827 
 
 
 .82322 
 
 
 .99504 
 
 
 .00496 
 
 .584 
 
 .81871 
 
 
 .82365 
 
 
 .99505 
 
 
 .00495 
 
 2.585 
 
 0.81915 
 
 43,9 
 
 0.82408 
 
 42,9 
 
 9.99506 
 
 1,0 
 
 0.00494 
 
 .586 
 
 .81958 
 
 
 .82451 
 
 
 99507 
 
 
 .00493 
 
 .587 
 
 .82002 
 
 
 .82494 
 
 
 .99508 
 
 
 .00492 
 
 .588 
 
 .82046 
 
 
 .82537 
 
 
 .99509 
 
 
 .00491 
 
 .589 
 
 .82090 
 
 
 .82580 
 
 
 99510 
 
 
 .00490 
 
 2.590 
 .591 
 
 0.82134 
 .82178 
 
 43,9 
 
 0.82623 
 
 .82666 
 
 42,9 
 
 9.995II 
 99512 
 
 1,0 
 
 0.00489 
 
 .00488 
 
 592 
 
 .82222 
 
 
 .82709 
 
 
 .99513 
 
 
 .00487 
 
 593 
 
 .82266 
 
 
 .82752 
 
 
 .99514 
 
 
 .00486 
 
 594 
 
 .82310 
 
 
 .82795 
 
 
 .99515 
 
 
 .00485 
 
 2.595 
 .596 
 
 0.82354 
 .82398 
 
 43,9 
 
 0.82838 
 .82881 
 
 42,9 
 
 9.99516 
 .99517 
 
 1,0 
 
 0.00484 
 .00483 
 
 .597 
 .598 
 
 .82442 
 .82485 
 
 
 .82924 
 .82967 
 
 43,0 
 
 .99518 
 .99519 
 
 
 .00482 
 .00481 
 
 599 
 
 .82529 
 
 
 .83010 
 
 
 .99520 
 
 
 .00480 
 
 2.600 
 
 0.82573 
 
 43,9 
 
 0.83052 
 
 43,o 
 
 9.99521 
 
 1,0 
 
 0.00479 
 
 u 
 
 log tan gd u 
 
 w Fo' 
 
 log sec gd u 
 
 F ' 
 
 log sin gd u 
 
 Fo' 
 
 log esc gd u 
 
 SMITHSONIAN TABLES 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 fV 
 
 log cosh u 
 
 Fo' 
 
 log tanh u 
 
 F ' 
 
 log coth u 
 
 2.600 
 
 0.82573 
 
 43,9 
 
 0.83052 
 
 43,0 
 
 9.99521 
 
 1,0 
 
 0.00479 
 
 .601 
 
 .82617 
 
 
 .83095 
 
 
 .99522 
 
 
 .00478 
 
 .602 
 
 .82661 
 
 
 .83138 
 
 
 .99523 
 
 
 .00477 
 
 .603 
 
 .82705 
 
 
 .83181 
 
 
 .99524 
 
 
 .00476 
 
 .604 
 
 .82749 
 
 
 .83224 
 
 
 .99525 
 
 
 .00475 
 
 2.605 
 
 0.82793 
 
 43,9 
 
 0.83267 
 
 43,0 
 
 9.99526 
 
 o,9 
 
 0.00474 
 
 .606 
 
 .82837 
 
 
 .83310 
 
 
 .99527 
 
 
 .00473 
 
 .607 
 
 .82881 
 
 
 .83353 
 
 
 
 99527 
 
 
 .00473 
 
 .608 
 
 .82925 
 
 
 .83396 
 
 
 .99528 
 
 
 .00472 
 
 .609 
 
 .82968 
 
 
 .83439 
 
 
 .99529 
 
 
 .00471 
 
 2.610 
 
 0.83012 
 
 43,9 
 
 0.83482 
 
 43,0 
 
 9.99530 
 
 0,9 
 
 0.00470 
 
 .611 
 
 .83056 
 
 
 .83525 
 
 
 .99531 
 
 
 .00469 
 
 .612 
 
 .83100 
 
 
 .83568 
 
 
 99532 
 
 
 .00468 
 
 .613 
 
 .83144 
 
 
 .83611 
 
 
 99533 
 
 
 .00467 
 
 .614 
 
 .83188 
 
 
 .83654 
 
 
 99534 
 
 
 .00466 
 
 2.615 
 
 0.83232 
 
 43,9 
 
 0.83697 
 
 43,0 
 
 9-99535 
 
 0,9 
 
 0.00465 
 
 .6l6 
 
 .83276 
 
 
 .83740 
 
 
 .99536 
 
 
 .00464 
 
 .617 
 
 .83320 
 
 
 .83783 
 
 
 .99537 
 
 
 .00463 
 
 .6l8 
 
 .83364 
 
 
 .83826 
 
 
 .99538 
 
 
 .00462 
 
 .619 
 
 .83407 
 
 
 .83869 
 
 
 99539 
 
 
 .00461 
 
 2.620 
 
 0.83451 
 
 43,9 
 
 0.83912 
 
 43,0 
 
 9.99540 
 
 0,9 
 
 0.00460 
 
 .621 
 
 .83495 
 
 
 .83955 
 
 
 .99541 
 
 
 .00459 
 
 .622 
 
 .83539 
 
 
 .83998 
 
 
 .99541 
 
 
 .00459 
 
 .623 
 
 .83583 
 
 
 .84041 
 
 
 .99542 
 
 
 .00458 
 
 .624 
 
 .83627 
 
 
 .84084 
 
 
 99543 
 
 
 .00457 
 
 2.625 
 
 0.83671 
 
 43,9 
 
 0.84127 
 
 43,0 
 
 9-99544 
 
 0,9 
 
 0.00456 
 
 .626 
 
 .83715 
 
 
 .84170 
 
 
 .99545 
 
 
 .00455 
 
 .62 7 
 
 .83759 
 
 
 .84213 
 
 
 .99546 
 
 
 .00454 
 
 .628 
 
 .83802 
 
 
 .84256 
 
 
 99547 
 
 
 .00453 
 
 .629 
 
 .83846 
 
 
 .84299 
 
 
 .99548 
 
 
 .00452 
 
 2.630 
 
 0.83800 
 
 43,9 
 
 0.84341 
 
 43,o 
 
 9.99549 
 
 0,9 
 
 0.00451 
 
 .631 
 
 .83934 
 
 
 .84384 
 
 
 99550 
 
 
 .00450 
 
 .632 
 
 .83978 
 
 
 .84427 
 
 
 .99551 
 
 
 .00449 
 
 .633 
 
 .84022 
 
 
 .84470 
 
 
 99551 
 
 
 .00449 
 
 .634 
 
 .84066 
 
 
 .84513 
 
 
 .99552 
 
 
 .00448 
 
 2.635 
 
 0.84110 
 
 43,9 
 
 0.84556 
 
 43,0 
 
 9-99553 
 
 0,9 
 
 0.00447 
 
 .636 
 
 .84154 
 
 
 .84599 
 
 
 .99554 
 
 
 .00446 
 
 .637 
 
 .84197 
 
 
 
 
 .99555 
 
 
 .00445 
 
 .638 
 
 .84241 
 
 
 ^84685 
 
 
 .99556 
 
 
 .00444 
 
 .639 
 
 .84285 
 
 
 .84728 
 
 
 99557 
 
 
 .00443 
 
 2.640 
 
 0.84329 
 
 43,9 
 
 0.84771 
 
 43,0 
 
 9.99558 
 
 0,9 
 
 0.00442 
 
 .641 
 
 .84373 
 
 
 .84814 
 
 
 99559 
 
 
 .00441 
 
 .6 4 2 
 
 .84417 
 
 
 .84857 
 
 
 99559 
 
 
 .00441 
 
 .643 
 
 .84461 
 
 
 .84900 
 
 
 .99560 
 
 
 .00440 
 
 .644 
 
 .84505 
 
 
 .84943 
 
 
 .99561 
 
 
 .00439 
 
 2.645 
 
 0.84548 
 
 43,9 
 
 0.84086 
 
 43,0 
 
 9.99562 
 
 0,9 
 
 0.00438 
 
 .646 
 
 .84592 
 
 
 .85029 
 
 
 .99563 
 
 
 .00437 
 
 .647 
 
 .84636 
 
 
 .85072 
 
 
 .99504 
 
 
 .00436 
 
 .648 
 
 .84680 
 
 
 .85115 
 
 
 .99565 
 
 
 .00435 
 
 .649 
 
 .84724 
 
 
 .85158 
 
 
 .99566 
 
 
 .00434 
 
 2.650 
 
 0.84768 
 
 43,9 
 
 0.85201 
 
 43,0 
 
 9.99566 
 
 0,9 
 
 0.00434 
 
 u 
 
 log tan gd u 
 
 -Fo' 
 
 log sec gd u 
 
 -Fo' 
 
 log sin gd u 
 
 -Fo' 
 
 log esc gd u 
 
 SMITHSONIAN TABLES 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 Fo' 
 
 log cosh u 
 
 F ' 
 
 log tanh u 
 
 Fo' 
 
 log coth u 
 
 2.650 
 
 0.84768 
 
 43,9 
 
 0.85201 
 
 43,0 
 
 9.99566 
 
 0,9 
 
 0.00434 
 
 .651 
 
 .84812 
 
 
 .85244 
 
 
 .99567 
 
 
 00433 
 
 .652 
 
 .84855 
 
 
 .85287 
 
 
 .99568 
 
 
 .00432 
 
 653 
 
 .84899 
 
 
 .85330 
 
 
 .99509 
 
 
 .00431 
 
 .654 
 
 .84943 
 
 
 .85373 
 
 
 99570 
 
 
 .00430 
 
 2.655 
 
 0.84987 
 
 43,9 
 
 0.85416 
 
 43,0 
 
 9.99571 
 
 0,9 
 
 0.00429 
 
 .656 
 
 .85031 
 
 
 .85459 
 
 
 99572 
 
 
 .00428 
 
 .657 
 
 .85075 
 
 
 .85502 
 
 
 99572 
 
 
 .00428 
 
 .658 
 
 .85119 
 
 
 .85545 
 
 
 .99573 
 
 
 .00427 
 
 .659 
 
 .85162 
 
 
 .85588 
 
 
 99574 
 
 
 .00426 
 
 2.660 
 
 0.85206 
 
 43,9 
 
 0.85631 
 
 43,0 
 
 9-99575 
 
 0,8 
 
 0.00425 
 
 .661 
 
 .85250 
 
 
 .85674 
 
 
 .99576 
 
 
 .00424 
 
 .662 
 
 .85294 
 
 
 .85717 
 
 
 .99577 
 
 
 .00423 
 
 .663 
 
 .85338 
 
 
 .85760 
 
 
 .99578 
 
 
 .00422 
 
 .664 
 
 .85382 
 
 
 .85803 
 
 
 .99578 
 
 
 .00422 
 
 2.665 
 
 0.85426 
 
 43,9 
 
 ; o. 85846 
 
 43,0 
 
 9-99579 
 
 0,8 
 
 0.00421 
 
 .666 
 
 .85469 
 
 
 .85889 
 
 
 .9958o 
 
 
 .00420 
 
 .667 
 
 .85513 
 
 
 .85932 
 
 
 .99581 
 
 
 .00419 
 
 .668 
 
 .85557 
 
 43,8 
 
 .85975 
 
 
 .99582 
 
 
 .00418 
 
 .669 
 
 .85601 
 
 
 .86018 
 
 
 .99583 
 
 
 .00417 
 
 2.670 
 
 0.85645 
 
 43,8 
 
 0.86061 
 
 43,0 
 
 9.99583 
 
 0,8 
 
 0.00417 
 
 .671 
 
 .85689 
 
 
 .86104 
 
 
 .99584 
 
 
 .00416 
 
 .672 
 
 .85733 
 
 
 .86147 
 
 
 .99585 
 
 
 .00415 
 
 .673 
 
 .85776 
 
 
 .86190 
 
 
 .99586 
 
 
 .00414 
 
 .674 
 
 .85820 
 
 
 .86233 
 
 
 .99587 
 
 
 .00413 
 
 2.675 
 
 0.85864 
 
 43,8 
 
 0.86276 
 
 43,0 
 
 9.99588 
 
 0,8 
 
 0.00412 
 
 .676 
 
 .85908 
 
 
 .86320 
 
 
 .99588 
 
 
 .00412 
 
 .677 
 
 .85952 
 
 
 .86363 
 
 
 .99589 
 
 
 .00411 
 
 .678 
 
 .85996 
 
 
 .86406 
 
 
 .99590 
 
 
 .00410 
 
 .679 
 
 .86039 
 
 
 .86449 
 
 
 99591 
 
 
 .00409 
 
 2.680 
 
 0.86083 
 
 43,8 
 
 0.86492 
 
 43,0 
 
 9.99592 
 
 0,8 
 
 0.00408 
 
 .681 
 
 .86127 
 
 
 .86535 
 
 
 99592 
 
 
 .00408 
 
 .682 
 
 .86171 
 
 
 .86578 
 
 
 99593 
 
 
 .00407 
 
 .683 
 
 .86215 
 
 
 .86621 
 
 
 99594 
 
 
 .00406 
 
 .684 
 
 .86259 
 
 
 .83664 
 
 
 99595 
 
 
 .00405 
 
 2.685 
 
 0.86302 
 
 43,8 
 
 0.86707 
 
 43,0 
 
 9.99596 
 
 0,8 
 
 0.00404 
 
 .686 
 
 .86346 
 
 
 .86750 
 
 
 .99597 
 
 
 .00403 
 
 .687 
 
 .86300 
 
 
 .86793 
 
 
 99597 
 
 
 .00403 
 
 .688 
 
 .86434 
 
 
 .86836 
 
 
 .99598 
 
 
 .00402 
 
 .689 
 
 .86478 
 
 
 .86879 
 
 
 99599 
 
 
 .00401 
 
 2.690 
 
 0.86522 
 
 43,8 
 
 0.86922 
 
 43,0 
 
 9.99600 
 
 0,8 
 
 0.00400 
 
 .691 
 
 .86565 
 
 
 .86955 
 
 
 .99601 
 
 
 .00399 
 
 .692 
 
 .86609 
 
 
 .87008 
 
 
 .99601 
 
 
 .00399 
 
 .693 
 
 .86653 
 
 
 .87051 
 
 
 .99602 
 
 
 .00398 
 
 .694 
 
 .86697 
 
 
 .87094 
 
 
 .99603 
 
 
 .00397 
 
 2.695 
 
 0.86741 
 
 43,8 
 
 0.87137 
 
 43,o 
 
 9.99604 
 
 0,8 
 
 0.00396 
 
 .696 
 
 .86785 
 
 
 .87180 
 
 
 .99605 
 
 
 .00395 
 
 .697 
 
 .86828 
 
 
 .87223 
 
 
 .99605 
 
 
 00395 
 
 .698 
 
 .86872 
 
 
 .87266 
 
 
 .99606 
 
 
 .00394 
 
 .699 
 
 .86916 
 
 
 .87309 
 
 
 .99607 
 
 
 .00393 
 
 2.700 
 
 0.86960 
 
 43,8 
 
 0.87352 
 
 43,o 
 
 9.99608 
 
 0,8 
 
 0.00392 
 
 u 
 
 log tan gd u 
 
 Fo' 
 
 log sec gd u 
 
 w Fo' 
 
 log sin gd u 
 
 Fo' 
 
 log esc gd u 
 
 SMITHSONIAN TABLES 
 
 73 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 -W 
 
 log cosh u 
 
 Fo' 
 
 log tanh u 
 
 Fo' 
 
 log coth u 
 
 2.700 
 
 0.86960 
 
 43,8 
 
 0.87352 
 
 43,0 
 
 9.99608 
 
 0,8 
 
 0.00392 
 
 .701 
 
 .87004 
 
 
 .87395 
 
 
 .99608 
 
 
 .00392 
 
 .702 
 
 .87048 
 
 
 .87438 
 
 
 .99609 
 
 
 .00391 
 
 .703 
 
 .87091 
 
 
 .87481 
 
 
 .99610 
 
 
 .00390 
 
 .704 
 
 .87135 
 
 
 .8/524 
 
 
 .99611 
 
 
 .00389 
 
 2.705 
 
 0.87179 
 
 43,8 
 
 0.87567 
 
 43,0 
 
 9.99612 
 
 0,8 
 
 0.00388 
 
 .706 
 
 .87223 
 
 
 .87610 
 
 
 .99612 
 
 
 .00388 
 
 .707 
 
 .87267 
 
 
 .87654 
 
 
 .99613 
 
 
 .00387 
 
 .708 
 
 .87310 
 
 
 .87697 
 
 
 .99614 
 
 
 .00386 
 
 .709 
 
 .87354 
 
 
 .87740 
 
 
 .99615 
 
 
 .00385 
 
 2.710 
 
 0.87398 
 
 43,8 
 
 0.87783 
 
 43,o 
 
 9.99615 
 
 0,8 
 
 0.00385 
 
 .711 
 
 .87442 
 
 
 .8782(1 
 
 
 .99616 
 
 
 .00384 
 
 .712 
 
 .87486 
 
 
 .87869 
 
 
 .99617 
 
 
 .00383 
 
 .713 
 
 .87530 
 
 
 .87912 
 
 
 .99618 
 
 
 .00382 
 
 .714 
 
 .87573 
 
 
 .87955 
 
 
 .90619 
 
 
 .00381 
 
 2.715 
 
 0.87617 
 
 43,8 
 
 0.87998 
 
 43,1 
 
 9.99619 
 
 0,8 
 
 0.00381 
 
 .716 
 
 .87661 
 
 
 .88041 
 
 
 .99620 
 
 
 .00380 
 
 .717 
 
 .87705 
 
 
 .88084 
 
 
 .99621 
 
 
 .00379 
 
 .718 
 
 .87749 
 
 
 .88127 
 
 
 .99622 
 
 
 .00378 
 
 .719 
 
 .87792 
 
 
 .881/0 
 
 
 .99622 
 
 
 .00378 
 
 2.720 
 
 0.87836 
 
 43,8 
 
 0.88213 
 
 43,1 
 
 9.99623 
 
 0,8 
 
 0.00377 
 
 .721 
 
 .87880 
 
 
 .88256 
 
 
 .99624 
 
 
 .00376 
 
 .722 
 
 .87924 
 
 
 .88299 
 
 
 .99625 
 
 
 .00375 
 
 .723 
 
 .87968 
 
 
 .88342 
 
 
 .99625 
 
 o,7 
 
 .00375 
 
 .724 
 
 .88011 
 
 
 .88385 
 
 
 .99626 
 
 
 .00374 
 
 2.725 
 
 0.88055 
 
 43,8 
 
 0.88428 
 
 43,1 
 
 9.99627 
 
 o,7 
 
 0.00373 
 
 .726 
 
 .88099 
 
 
 .88471 
 
 
 .99628 
 
 
 .00372 
 
 
 .88143 
 
 
 .88515 
 
 
 .99628 
 
 
 .00372 
 
 .728 
 
 .88187 
 
 
 .88558 
 
 
 .99629 
 
 
 .00371 
 
 .729 
 
 .88230 
 
 
 .88601 
 
 
 .99630 
 
 
 .00370 
 
 2.730 
 
 0.88274 
 
 43,8 
 
 0.88644 
 
 43,1 
 
 9.99631 
 
 o,7 
 
 0.00369 
 
 .731 
 
 .88318 
 
 
 .88687 
 
 
 .99631 
 
 
 .00369 
 
 .732 
 
 .88362 
 
 
 .88730 
 
 
 .99632 
 
 
 .00368 
 
 733 
 
 .88406 
 
 
 .88773 
 
 
 .99633 
 
 
 .00367 
 
 734 
 
 .88449 
 
 
 .88816 
 
 
 .99633 
 
 
 .00367 
 
 2.735 
 
 o. 88493 
 
 43,8 
 
 0.88859 
 
 43,1 
 
 9.99634 
 
 o,7 
 
 0.00366 
 
 .736 
 
 .88537 
 
 
 .88002 
 
 
 .99635 
 
 
 .00365 
 
 737 
 
 .88581 
 
 
 .88945 
 
 
 .99636 
 
 
 .00364 
 
 .738 
 
 .88625 
 
 
 .88988 
 
 
 .99636 
 
 
 .00364 
 
 739 
 
 .88668 
 
 
 .89031 
 
 
 .99637 
 
 
 .00363 
 
 2.740 
 
 0.88712 
 
 43,8 
 
 0.89074 
 
 43,1 
 
 9.99638 
 
 o,7 
 
 0.00362 
 
 .741 
 
 .88756 
 
 
 .89117 
 
 
 09639 
 
 
 .00361 
 
 .742 
 
 .88800 
 
 
 .89161 
 
 
 .99639 
 
 
 .00361 
 
 .743 
 
 .888*4 
 
 
 .89204 
 
 
 .99640 
 
 
 .00360 
 
 744 
 
 .88887 
 
 
 .89247 
 
 
 .99641 
 
 
 .00359 
 
 2.745 
 
 0.88931 
 
 43,8 
 
 0.89290 
 
 43,1 
 
 9.99641 
 
 o,7 
 
 0.00359 
 
 .746 
 
 .88975 
 
 
 .89333 
 
 
 .99642 
 
 
 .00358 
 
 
 .89019 
 
 
 .89376 
 
 
 .99643 
 
 
 .00357 
 
 .748 
 
 .89063 
 
 
 .89419 
 
 
 .99644 
 
 
 .00356 
 
 .749 
 
 .89106 
 
 
 .89462 
 
 
 .99644 
 
 
 .00356 
 
 2.750 
 
 0.89150 
 
 43,8 
 
 0.89505 
 
 43J 
 
 9.99645 
 
 0,7 
 
 0.00355 
 
 u 
 
 log tan od u 
 
 -Fo' 
 
 log sec gd u 
 
 * Fo' 
 
 log sin gd u 
 
 ,w 
 
 log esc gd u 
 
 SMITHSONIAN TABLE* 
 
 74 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 F ' 
 
 log cosh u 
 
 -Fo' 
 
 log tanh u 
 
 Fo' 
 
 log coth u 
 
 2.750 
 
 0.89150 
 
 43,8 
 
 0.89505 
 
 43,1 
 
 9.99645 
 
 o,7 
 
 0.00355 
 
 .751 
 
 .89194 
 
 
 .89548 
 
 
 .99646 
 
 
 .00354 
 
 .752 
 
 .89238 
 
 
 .89591 
 
 
 .99646 
 
 
 .00354 
 
 .753 
 
 .89281 
 
 
 .89634 
 
 
 .99647 
 
 
 .00353 
 
 754 
 
 .89325 
 
 
 .89677 
 
 
 .99648 
 
 
 .00352 
 
 2.755 
 
 0.89369 
 
 43,8 
 
 0.89720 
 
 43,1 
 
 9.99649 
 
 o,7 
 
 0.00351 
 
 .756 
 
 .89413 
 
 
 .89764 
 
 
 .99649 
 
 
 .00351 
 
 757 
 
 .89457 
 
 
 .89807 
 
 
 .99650 
 
 
 .00350 
 
 758, 
 
 j 
 
 .89500 
 
 
 .89850 
 
 
 99651 
 
 
 .00349 
 
 759 
 
 .89544 
 
 
 .89893 
 
 
 .99651 
 
 
 .00349 
 
 2.760 
 
 0.89588 
 
 43,8 
 
 0.89936 
 
 43,1 
 
 9.99652 
 
 o,7 
 
 0.00348 
 
 .761 
 
 .89632 
 
 
 .89979 
 
 
 .99653 
 
 
 .00347 
 
 .762 
 
 .89676 
 
 
 .90022 
 
 
 .99653 
 
 
 .00347 
 
 .763 
 
 .89719 
 
 
 .90065 
 
 
 .99654 
 
 
 .00346 
 
 .764 
 
 .89763 
 
 
 .90108 
 
 
 .99655 
 
 
 .00345 
 
 2.765 
 
 0.89807 
 
 43,8 
 
 0.90151 
 
 43,1 
 
 9.99656 
 
 o,7 
 
 0.00344 
 
 .766 
 
 .89851 
 
 
 .90194 
 
 
 .99656 
 
 
 .00344 
 
 .767 
 
 .89894 
 
 
 .90237 
 
 
 .99657 
 
 
 .00343 
 
 .768 
 
 .89938 
 
 
 .90281 
 
 
 .99658 
 
 
 .00342 
 
 .769 
 
 .89982 
 
 
 .90324 
 
 
 .99658 
 
 
 .00342 
 
 2.770 
 
 0.90026 
 
 43,8 
 
 0.90367 
 
 43,1 
 
 9.99659 
 
 o,7 
 
 0.00341 
 
 .771 
 
 .90069 
 
 
 .90410 
 
 
 .99660 
 
 
 .00340 
 
 .772 
 
 .90113 
 
 
 .90453 
 
 
 .99660 
 
 
 .00340 
 
 773 
 
 .90157 
 
 
 .90496 
 
 
 .99661 
 
 
 .00339 
 
 774 
 
 .90201 
 
 
 .90539 
 
 
 .99662 
 
 
 .00338 
 
 2-775 
 
 0.90245 
 
 43,8 
 
 0.90582 
 
 43,1 
 
 9.99662 
 
 o,7 
 
 0.00338 
 
 .776 
 
 .90288 
 
 
 .90625 
 
 
 .99663 
 
 
 .00337 
 
 777 
 
 .90332 
 
 
 .90668 
 
 
 .99664 
 
 
 .00336 
 
 .778 
 
 .90376 
 
 
 .90712 
 
 
 .99664 
 
 
 .00336 
 
 779 
 
 .90420 
 
 
 .90755 
 
 
 .99665 
 
 
 .00335 
 
 2.780 
 
 0.90463 
 
 43,8 
 
 0.90798 
 
 43,1 
 
 9.99666 
 
 o,7 
 
 0.00334 
 
 .781 
 
 .90507 
 
 
 .90841 
 
 
 .99666 
 
 
 .00334 
 
 .782 
 
 .90551 
 
 
 .90884 
 
 
 .99667 
 
 
 .00333 
 
 .783 
 
 .90595 
 
 
 .90927 
 
 
 .99668 
 
 
 .00332 
 
 .784 
 
 .90638 
 
 
 .90970 
 
 
 .99668 
 
 
 .00332 
 
 2.785 
 
 0.90682 
 
 43,8 
 
 0.91013 
 
 43,1 
 
 9.99669 
 
 o,7 
 
 0.00331 
 
 .786 
 
 .00726 
 
 
 .91056 
 
 
 .99670 
 
 
 .00330 
 
 .787 
 
 .90770 
 
 
 .91099 
 
 
 .99670 
 
 
 .00330 
 
 .788 
 
 .90813 
 
 
 .91142 
 
 
 .99671 
 
 
 .00329 
 
 .789 
 
 .90857 
 
 
 .91186 
 
 
 .99672 
 
 
 .00328 
 
 2.790 
 
 0.90901 
 
 43>8 
 
 0.91229 
 
 43,1 
 
 9.99672 
 
 o,7 
 
 0.00328 
 
 .791 
 
 .90945 
 
 
 .91272 
 
 
 .99673 
 
 
 .00327 
 
 .792 
 
 .90989 
 
 
 .91315 
 
 
 .99674 
 
 
 .00326 
 
 .793 
 
 .91032 
 
 
 .91358 
 
 
 .99674 
 
 
 .00326 
 
 794 
 
 .91076 
 
 
 .91401 
 
 
 .99675 
 
 
 .00325 
 
 2-795 
 
 O.9II2O 
 
 43,8 
 
 0.91444 
 
 43,1 
 
 9.99676 
 
 0,6 
 
 0.00324 
 
 .796 
 
 .91164 
 
 
 .91487 
 
 
 .99676 
 
 
 .00324 
 
 .797 
 
 .91207 
 
 
 .91530 
 
 
 .99677 
 
 
 .00323 
 
 .798 
 
 .91251 
 
 
 .91574 
 
 
 .99678 
 
 
 .00322 
 
 .799 
 
 .91295 
 
 
 .91617 
 
 
 .99678 
 
 
 .00322 
 
 2.800 
 
 0.91339 
 
 43,8 
 
 0.91660 
 
 43.1 
 
 9.99679 
 
 0,6 
 
 0.00321 
 
 u 
 
 log tan gd u 
 
 Fo' 
 
 log sec gd u 
 
 Fo' 
 
 log sin gd u 
 
 w Fo' 
 
 log esc gd u 
 
 SMITHSONIAN TABLES 
 
 75 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 Fo' 
 
 log cosh u 
 
 -Fo' 
 
 log tanh u 
 
 Fo' 
 
 log coth u 
 
 2.800 
 
 0.91339 
 
 43,8 
 
 0.91660 
 
 43,1 
 
 9.99679 
 
 0,6 
 
 0.00321 
 
 .801 
 
 .91382 
 
 
 .91703 
 
 
 .99679 
 
 
 .00321 
 
 .802 
 
 .91426 
 
 
 .91746 
 
 
 .99680 
 
 
 .00320 
 
 .803 
 
 .91470 
 
 43,7 
 
 .91789 
 
 
 .99681 
 
 
 .00319 
 
 .804 
 
 .91514 
 
 
 .91832 
 
 
 .99681 
 
 
 .00319 
 
 2.805 
 
 0.91557 
 
 43,7 
 
 0.91875 
 
 43,1 
 
 9.99682 
 
 0,6 
 
 0.00318 
 
 .806 
 
 .91601 
 
 
 .91918 
 
 
 .99683 
 
 
 .00317 
 
 .807 
 
 .91645 
 
 
 .91962 
 
 
 .99683 
 
 
 .00317 
 
 .808 
 
 .91689 
 
 
 .92005 
 
 
 .99684 
 
 
 .00316 
 
 .809 
 
 .91732 
 
 
 .92048 
 
 
 .99685 
 
 
 * .00315 
 
 2.810 
 
 0.91776 
 
 43,7 
 
 0.92091 
 
 43,1 
 
 9.99685 
 
 0,6 
 
 0.00315 
 
 .811 
 
 .91820 
 
 
 .92134 
 
 
 .99686 
 
 
 .00314 
 
 .812 
 
 .91864 
 
 
 .92177 
 
 
 .99686 
 
 
 .00314 
 
 .813 
 
 .91907 
 
 
 .92220 
 
 
 .99687 
 
 
 .00313 
 
 .814 
 
 .91951 
 
 
 .92263 
 
 
 .99688 
 
 
 .00312 
 
 2.815 
 
 0.91995 
 
 43,7 
 
 0.92306 
 
 43,1 
 
 9.99688 
 
 0,6 
 
 O.OO3I2 
 
 .816 
 
 .92039 
 
 
 .92350 
 
 
 .99689 
 
 
 .00311 
 
 .817 
 
 .92082 
 
 
 .92393 
 
 
 .90690 
 
 
 .00310 
 
 .818 
 
 .92126 
 
 
 .92436 
 
 
 .99690 
 
 
 .00310 
 
 .819 
 
 .92170 
 
 
 .92479 
 
 
 .99691 
 
 
 .00309 
 
 2.820 
 
 0.92213 
 
 43,7 
 
 0.92522 
 
 43,1 
 
 9.99691 
 
 0,6 
 
 0.00309 
 
 .821 
 
 .92257 
 
 
 .92565 
 
 
 .09692 
 
 
 .00308 
 
 .822 
 
 .92301 
 
 
 .92608 
 
 
 .99693 
 
 
 .00307 
 
 .823 
 
 .92345 
 
 
 .92651 
 
 
 .99693 
 
 
 .00307 
 
 .824 
 
 .92388 
 
 
 .92695 
 
 
 .99694 
 
 
 .00306 
 
 2.825 
 
 0.92432 
 
 43,7 
 
 0.92738 
 
 43,1 
 
 9.99694 
 
 0,6 
 
 0.00306 
 
 .826 
 
 92476 
 
 
 .92781 
 
 
 .99695 
 
 
 .00305 
 
 .827 
 
 .92520 
 
 
 .92824 
 
 
 .99696 
 
 
 .00304 
 
 .828 
 
 .92563 
 
 
 .92867 
 
 
 .99606 
 
 
 .00304 
 
 .829 
 
 .92607 
 
 
 .92910 
 
 
 .99697 
 
 
 .00303 
 
 2.830 
 
 0.92651 
 
 43,7 
 
 0.92953 
 
 43,1 
 
 9.99698 
 
 0,6 
 
 0.00302 
 
 .831 
 
 .92695 
 
 
 .92996 
 
 
 .99698 
 
 
 .00302 
 
 .832 
 
 .92738 
 
 
 .93040 
 
 
 99609 
 
 
 .00301 
 
 .833 
 
 .92782 
 
 
 .93083 
 
 
 .99699 
 
 
 .00301 
 
 .834 
 
 .92826 
 
 
 .93126 
 
 
 .99700 
 
 
 .00300 
 
 2.835 
 
 0.92869 
 
 43,7 
 
 0.93169 
 
 43,1 
 
 9.99701 
 
 0,6 
 
 O.OO2O9 
 
 .836 
 
 .92913 
 
 
 .93212 
 
 
 .99701 
 
 
 .00299 
 
 .837 
 
 .92957 
 
 
 .93255 
 
 
 .99702 
 
 
 .00298 
 
 .838 
 
 93001 
 
 
 .93298 
 
 
 .99702 
 
 
 .00298 
 
 .839 
 
 .93044 
 
 
 93341 
 
 
 .09703 
 
 
 .00297 
 
 2.840 
 
 0.93088 
 
 43,7 
 
 0.93385 
 
 43,1 
 
 9.99704 
 
 0,6 
 
 0.00296 
 
 .841 
 
 .93132 
 
 
 .93428 
 
 
 .09704 
 
 
 .00296 
 
 .842 
 
 .93176 
 
 
 93471 
 
 
 .99705 
 
 
 .00295 
 
 .843 
 
 .93219 
 
 
 .93514 
 
 
 99705 
 
 
 .00295 
 
 .844 
 
 .93263 
 
 
 93557 
 
 
 .99706 
 
 
 .00294 
 
 2.845 
 
 0.93307 
 
 43,7 
 
 0.93600 
 
 43J 
 
 9.99706 
 
 0,6 
 
 0.00204 
 
 .846 
 
 93350 
 
 
 .93643 
 
 
 .99707 
 
 
 .00293 
 
 .847 
 
 93394 
 
 
 .93687 
 
 
 .99708 
 
 
 .00202 
 
 .848 
 
 .93438 
 
 
 .93730 
 
 
 .09708 
 
 
 .00292 
 
 .849 
 
 .93482 
 
 
 .93773 
 
 
 .99709 
 
 
 .OO29I 
 
 2.850 
 
 0.93525 
 
 43,7 
 
 0.93816 
 
 43J 
 
 9.09709 
 
 0,6 
 
 0.00291 
 
 u 
 
 log tan od u 
 
 F ' 
 
 log sec gd u 
 
 Fo' 
 
 log sin gd u 
 
 -Fo' 
 
 log esc gd u 
 
 SMITHSONIAN TABLCS 
 
 -r, 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 Fo' 
 
 log cosh u 
 
 F ' 
 
 log tanh u 
 
 Fo' 
 
 log coth u 
 
 2.850 
 
 0.93525 
 
 43,7 
 
 0.93816 
 
 43,1 
 
 9.99709 
 
 0,6 
 
 O.OO29I 
 
 .851 
 
 .93569 
 
 
 .93859 
 
 
 .99710 
 
 
 .00200 
 
 .852 
 
 .93613 
 
 
 .93902 
 
 
 997II 
 
 
 .00289 
 
 .853 
 
 .93657 
 
 
 93945 
 
 
 .997H 
 
 
 .00289 
 
 .854 
 
 .93700 
 
 
 .93989 
 
 
 .99712 
 
 
 .00288 
 
 2.855 
 
 0.93744 
 
 43,7 
 
 0.94032 
 
 43,1 
 
 9.99712 
 
 0,6 
 
 0.00288 
 
 .856 
 
 .93788 
 
 
 .94075 
 
 
 .99713 
 
 
 .00287 
 
 .857 
 
 .93831 
 
 
 .94118 
 
 
 .99713 
 
 
 .00287 
 
 .858 
 
 .93875 
 
 
 .94161 
 
 
 .99714 
 
 
 .00286 
 
 .859 
 
 .93919 
 
 
 .94204 
 
 
 .99715 
 
 
 .00285 
 
 2.860 
 
 0.93963 
 
 43,7 
 
 0.94247 
 
 43,1 
 
 9.99715 
 
 0,6 
 
 0.00285 
 
 .861 
 
 .94006 
 
 
 .94291 
 
 
 .99716 
 
 
 .00284 
 
 .862 
 
 .94050 
 
 
 94334 
 
 
 .99716 
 
 
 .00284 
 
 .863 
 
 .94094 
 
 
 94377 
 
 
 .99717 
 
 
 .00283 
 
 .864 
 
 .94137 
 
 
 .94420 
 
 
 .99717 
 
 
 .00283 
 
 2.865 
 
 0.94181 
 
 43,7 
 
 0.94463 
 
 43,1 
 
 9.99718 
 
 0,6 
 
 0.00282 
 
 .866 
 
 .94225 
 
 
 .94506 
 
 
 .99719 
 
 
 .00281 
 
 .867 
 
 .94269 
 
 
 94549 
 
 
 .99719 
 
 
 .00281 
 
 .868 
 
 .94312 
 
 
 94593 
 
 
 .99720 
 
 
 .00280 
 
 .869 
 
 .94356 
 
 
 94636 
 
 43,2 
 
 .99720 
 
 
 .00280 
 
 2.870 
 
 0.94400 
 
 43,7 
 
 0.94679 
 
 43,2 
 
 9-99721 
 
 0,6 
 
 0.00279 
 
 .871 
 
 .94443 
 
 
 .94722 
 
 
 .99721 
 
 
 .00279 
 
 .872 
 
 .94487 
 
 
 94765 
 
 
 .99722 
 
 
 .00278 
 
 .873 
 
 94531 
 
 
 .94808 
 
 
 .99722 
 
 
 .00278 
 
 .874 
 
 94575 
 
 
 .94852 
 
 
 99723 
 
 
 .00277 
 
 2.875 
 
 0.94618 
 
 43,7 
 
 0.94895 
 
 43,2 
 
 9.99724 
 
 0,6 
 
 0.00276 
 
 .876 
 
 .94662 
 
 
 .94938 
 
 
 .99724 
 
 
 .00276 
 
 .877 
 
 .94706 
 
 
 .94981 
 
 
 99725 
 
 
 .00275 
 
 O-O 
 
 .94749 
 
 
 .95024 
 
 
 99725 
 
 o,5 
 
 00275 
 
 ^879 
 
 94793 
 
 
 .95067 
 
 
 .99726 
 
 
 .00274 
 
 2.880 
 
 0.94837 
 
 43,7 
 
 0.95110 
 
 43,2 
 
 9.99726 
 
 o,5 
 
 0.00274 
 
 .881 
 
 .94880 
 
 
 .95154 
 
 
 .99727 
 
 
 .00273 
 
 .882 
 
 .94924 
 
 
 .95197 
 
 
 .99727 
 
 
 .00273 
 
 .883 
 
 .94968 
 
 
 .95240 
 
 
 .99728 
 
 
 .00272 
 
 .884 
 
 .95012 
 
 
 95283 
 
 
 .99728 
 
 
 .00272 
 
 2.885 
 
 0.95055 
 
 43,7 
 
 0.95326 
 
 43,2 
 
 9.99729 
 
 o,5 
 
 0.00271 
 
 .886 
 
 95099 
 
 
 .95369 
 
 
 .99730 
 
 
 .00270 
 
 .887 
 
 .95143 
 
 
 .95413 
 
 
 .99730 
 
 
 .00270 
 
 .888 
 
 .95186 
 
 
 .95456 
 
 
 .99731 
 
 
 .00269 
 
 .889 
 
 .95230 
 
 
 95499 
 
 
 .99731 
 
 
 .00269 
 
 2.890 
 
 0.95274 
 
 43,7 
 
 0.95542 
 
 43,2 
 
 9-99732 
 
 o,5 
 
 0.00268 
 
 .891 
 
 .95317 
 
 
 .95585 
 
 
 99732 
 
 
 .00268 
 
 .892 
 
 .95361 
 
 
 .95628 
 
 
 99733 
 
 
 .00267 
 
 893 
 
 .95405 
 
 
 .95672 
 
 
 99733 
 
 
 .00267 
 
 .894 
 
 95449 
 
 
 .95715 
 
 
 99734 
 
 
 .00266 
 
 2.895 
 
 0.95492 
 
 43,7 
 
 0.95758 
 
 43,2 
 
 9.99734 
 
 0,5 
 
 0.00266 
 
 .896 
 
 .95536 
 
 
 .95801 
 
 
 99735 
 
 
 .00265 
 
 .897 
 
 .95580 
 
 
 .95844 
 
 
 99735 
 
 
 .00265 
 
 .898 
 
 .95623 
 
 
 .95887 
 
 
 .99736 
 
 
 .00264 
 
 .899 
 
 .95667 
 
 
 95931 
 
 
 99737 
 
 
 .00263 
 
 2.900 
 
 0.957H 
 
 43,7 
 
 0.95974 
 
 43,2 
 
 9-99737 
 
 0,5 
 
 0.00263 
 
 u 
 
 log tan gd u 
 
 F O ' 
 
 log sec gd u 
 
 Fo' 
 
 log sin gd u 
 
 Fo' 
 
 logcscgdu 
 
 SMITHSONIAN TABLES 
 
 77 
 
Logarithms of Hyperbolic Functions. 
 
 , u 
 
 log sinh u 
 
 Fo' 
 
 log cosh u 
 
 F O ' 
 
 log tanh u 
 
 Fo' 
 
 log coth u 
 
 2.900 
 
 0.957H 
 
 43,7 
 
 0.95974 
 
 43,2 
 
 9.99737 
 
 0,5 
 
 0.00263 
 
 .901 
 
 95754 
 
 
 .96017 
 
 
 .99738 
 
 
 .00262 
 
 .902 
 
 .95798 
 
 
 .96060 
 
 
 .99738 
 
 
 .00262 
 
 .903 
 
 .95842 
 
 
 .96103 
 
 
 99739 
 
 
 .00261 
 
 .904 
 
 .95885 
 
 
 .96146 
 
 
 99739 
 
 
 .00261 
 
 2.905 
 
 0.95929 
 
 43,7 
 
 0.96190 
 
 43,2 
 
 9.99740 
 
 o,5 
 
 O.OO2OO 
 
 .906 
 
 .95973 
 
 
 .96233 
 
 
 99740 
 
 
 .O02OO 
 
 .907 
 
 .96017 
 
 
 .96276 
 
 
 .99741 
 
 
 .00259 
 
 .908 
 
 .96060 
 
 
 .96319 
 
 
 .99741 
 
 
 .00259 
 
 .909 
 
 .96104 
 
 
 .96362 
 
 
 .99742 
 
 
 .00258 
 
 2.910 
 
 0.96148 
 
 43,7 
 
 0.96405 
 
 43,2 
 
 9.99742 
 
 o,5 
 
 0.00258 
 
 .911 
 
 .96191 
 
 
 .96449 
 
 
 .99743 
 
 
 (00257 
 
 .912 
 
 .96235 
 
 
 .96492 
 
 
 .99743 
 
 
 .00257 
 
 .913 
 
 .96279 
 
 
 .96535 
 
 
 .99744 
 
 
 .00256 
 
 .914 
 
 .96322 
 
 
 .96578 
 
 
 .99744 
 
 
 .00256 
 
 2.915 
 
 0.96366 
 
 43,7 
 
 0.96621 
 
 43,2 
 
 9-99745 
 
 o,5 
 
 0.00255 
 
 .916 
 
 .96410 
 
 
 .96664 
 
 
 .99745 
 
 
 .00255 
 
 .917 
 
 .96453 
 
 
 .96708 
 
 
 .99746 
 
 
 .00254 
 
 .918 
 
 .96497 
 
 
 .96751 
 
 
 99746 
 
 
 .00254 
 
 .919 
 
 .96541 
 
 
 .96794 
 
 
 99747 
 
 
 .00253 
 
 2.920 
 
 0.96584 
 
 43,7 
 
 0.96837 
 
 43,2 
 
 9-99747 
 
 o,5 
 
 0.00253 
 
 .921 
 
 .96628 
 
 
 .96880 
 
 
 .99748 
 
 
 .00252 
 
 .922 
 
 .96672 
 
 
 .96923 
 
 
 .99748 
 
 
 .00252 
 
 .923 
 
 .96716 
 
 
 .96967 
 
 
 99749 
 
 
 .00251 
 
 .924 
 
 .96759 
 
 
 .97010 
 
 
 .99749 
 
 
 .00251 
 
 2.925 
 
 0.96803 
 
 43,7 
 
 0.97053 
 
 43,2 
 
 9.99750 
 
 o,5 
 
 0.00250 
 
 .926 
 
 .96847 
 
 
 .97096 
 
 
 99750 
 
 
 .00250 
 
 .927 
 
 .96890 
 
 
 97139 
 
 
 .99751 
 
 
 .00249 
 
 .928 
 
 .96934 
 
 
 .97183 
 
 
 99751 
 
 
 .00249 
 
 .929 
 
 .96978 
 
 
 .97226 
 
 
 .99752 
 
 
 .00248 
 
 2.930 
 
 0.97021 
 
 43,7 
 
 0.97269 
 
 43,2 
 
 9.99752 
 
 o,5 
 
 0.00248 
 
 .931 
 
 .97065 
 
 
 .97312 
 
 
 .99753 
 
 
 .00247 
 
 .932 
 
 .97109 
 
 
 .97355 
 
 
 99753 
 
 
 .00247 
 
 933 
 
 .97152 
 
 
 .97398 
 
 
 99754 
 
 
 .00246 
 
 934 
 
 .97196 
 
 
 .97442 
 
 
 99754 
 
 
 .00246 
 
 2.935 
 
 0.97240 
 
 43,7 
 
 0.97485 
 
 43,2 
 
 9-99755 
 
 o,5 
 
 0.00245 
 
 .936 
 
 .97283 
 
 
 .97528 
 
 
 .99755 
 
 
 .00245 
 
 937 
 
 .97327 
 
 
 97571 
 
 
 .99756 
 
 
 .00244 
 
 .938 
 
 97371 
 
 
 .97614 
 
 
 .99756 
 
 
 .00244 
 
 939 
 
 .97414 
 
 
 .97658 
 
 
 99757 
 
 
 .00243 
 
 2.940 
 
 0.97458 
 
 43,7 
 
 0.97701 
 
 43,2 
 
 9-99757 
 
 o,5 
 
 0.00243 
 
 .941 
 
 97502 
 
 
 97744 
 
 
 .99758 
 
 
 .00242 
 
 .942 
 
 97545 
 
 
 .97787 
 
 
 99758 
 
 
 .00242 
 
 943 
 
 .97589 
 
 
 .97830 
 
 
 .99759 
 
 
 .00241 
 
 944 
 
 .97633 
 
 
 .97874 
 
 
 .99759 
 
 
 .00241 
 
 2.945 
 
 0.97676 
 
 43,7 
 
 0.97917 
 
 43,2 
 
 9.99760 
 
 o,5 
 
 0.00240 
 
 .946 
 
 .97720 
 
 
 .97960 
 
 
 .99760 
 
 
 .00240 
 
 947 
 
 .97764 
 
 
 .98003 
 
 
 .99761 
 
 . 
 
 .00239 
 
 .948 
 .949 
 
 .97807 
 .97851 
 
 
 .98046 
 .98089 
 
 
 .9976i 
 .99762 
 
 
 .00239 
 .00238 
 
 2.950 
 
 0.97895 
 
 43,7 
 
 0.98133 
 
 43,2 
 
 9.99762 
 
 o,5 
 
 0.00238 
 
 u 
 
 loo tan gd u 
 
 F ' 
 
 log tec gd u 
 
 F ' 
 
 log sin gd u 
 
 Fo' 
 
 logcscgdu 
 
 SMITHSONIAN TABLES 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 Fo' 
 
 log cosh u 
 
 F<>' 
 
 log tanh u 
 
 Fo' 
 
 log coth u 
 
 2.950 
 
 0.97895 
 
 43,7 
 
 0.98133 
 
 43,2 
 
 9.99762 
 
 o,5 
 
 0.00238 
 
 .951 
 
 .97938 
 
 
 .98176 
 
 
 .99763 
 
 
 .00237 
 
 .952 
 
 .97982 
 
 
 .98219 
 
 
 .99763 
 
 
 .00237 
 
 953 
 
 .98026 
 
 
 .98262 
 
 
 .99763 
 
 
 .00237 
 
 954 
 
 .98069 
 
 
 .98305 
 
 
 .99764 
 
 
 .00236 
 
 2.955 
 
 0.98II3 
 
 43,7 
 
 0.98349 
 
 43,2 
 
 9-99764 
 
 o,5 
 
 0.00236 
 
 .956 
 
 .98157 
 
 
 .98392 
 
 
 .99765 
 
 
 .00235 
 
 957 
 
 .98200 
 
 
 .98435 
 
 
 .99765 
 
 
 00235 
 
 .958 
 
 .98244 
 
 
 .98478 
 
 
 .99766 
 
 
 .00234 
 
 959 
 
 .98288 
 
 
 .98521 
 
 
 .99766 
 
 
 .00234 
 
 2.960 
 
 0.98331 
 
 43,7 
 
 0.98565 
 
 43,2 
 
 9.99767 
 
 o,5 
 
 0.00233 
 
 .961 
 
 .98375 
 
 
 .98608 
 
 
 
 
 .00233 
 
 .962 
 
 .98419 
 
 
 .08651 
 
 
 .99768 
 
 
 .00232 
 
 963 
 
 .98462 
 
 
 .98694 
 
 
 .99768 
 
 
 .00232 
 
 .964 
 
 .98506 
 
 
 .98737 
 
 
 .99769 
 
 
 .00231 
 
 2.965 
 
 0.98550 
 
 43,7 
 
 0.98781 
 
 43,2 
 
 9.99769 
 
 o,5 
 
 0.00231 
 
 .966 
 
 .98593 
 
 
 .98824 
 
 
 .99770 
 
 
 .00230 
 
 .967 
 
 .98637 
 
 
 .98867 
 
 
 .99770 
 
 
 .00230 
 
 .968 
 
 .98681 
 
 
 .98910 
 
 
 99770 
 
 
 .00230 
 
 .969 
 
 .98724 
 
 
 98953 
 
 
 .99771 
 
 
 .00229 
 
 2.970 
 
 0.98768 
 
 43,7 
 
 0.98997 
 
 43,2 
 
 9.99771 
 
 0,5 
 
 0.00229 
 
 .971 
 
 .98812 
 
 
 .99040 
 
 
 99772 
 
 
 .00228 
 
 .972 
 
 .08855 
 
 
 .99083 
 
 
 .99772 
 
 
 .00228 
 
 973 
 
 .98899 
 
 
 .99126 
 
 
 .99773 
 
 
 .00227 
 
 974 
 
 .98943 
 
 
 .99169 
 
 
 99773 
 
 
 .00227 
 
 2.975 
 
 0.98986 
 
 43,7 
 
 0.99213 
 
 43,2 
 
 9-99774 
 
 o,5 
 
 0.00226 
 
 .976 
 
 .99030 
 
 
 .99256 
 
 
 99774 
 
 
 .00226 
 
 977 
 
 .99074 
 
 
 .99299 
 
 
 99775 
 
 
 .00225 
 
 978 
 
 .99H7 
 
 
 99342 
 
 
 .99775 
 
 0,4 
 
 .00225 
 
 979 
 
 .99161 
 
 
 .99385 
 
 
 99775 
 
 
 .00225 
 
 2.980 
 
 0.99205 
 
 43,7 
 
 0.99429 
 
 43,2 
 
 9.99776 
 
 0,4 
 
 0.00224 
 
 .981 
 
 .99248 
 
 
 .99472 
 
 
 .99776 
 
 
 .00224 
 
 .982 
 
 .99292 
 
 
 .99515 
 
 
 99777 
 
 
 .00223 
 
 .983 
 
 .99336 
 
 
 .99558 
 
 
 .99777 
 
 
 .00223 
 
 .984 
 
 99379 
 
 
 .99601 
 
 
 .99778 
 
 
 .00222 
 
 2.985 
 
 0.99423 
 
 43,7 
 
 0.99645 
 
 43,2 
 
 9.99778 
 
 0,4 
 
 O.OO222 
 
 .986 
 
 .99466 
 
 
 .99688 
 
 
 .99779 
 
 
 .OO22I 
 
 .987 
 
 .99510 
 
 
 .99731 
 
 
 99779 
 
 
 .OO22I 
 
 .988 
 
 99554 
 
 
 99774 
 
 
 99779 
 
 
 .00221 
 
 .989 
 
 99597 
 
 
 .99818 
 
 
 .99780 
 
 
 .00220 
 
 2.990 
 
 0.99641 
 
 43,6 
 
 0.99861 
 
 43,2 
 
 9.99780 
 
 0,4 
 
 0.00220 
 
 .991 
 
 .99685 
 
 
 .99904 
 
 
 .99781 
 
 
 .00219 
 
 .992 
 
 .99728 
 
 
 .99947 
 
 
 .99781 
 
 
 .OO2I9 
 
 993 
 
 .99772 
 
 
 .99990 
 
 
 .99782 
 
 
 .OO2l8 
 
 .994 
 
 .99816 
 
 
 1.00034 
 
 
 .99782 
 
 
 .00218 
 
 2.995 
 
 0.99859 
 
 43,6 
 
 1.00077 
 
 43,2 
 
 9.99783 
 
 0,4 
 
 0.00217 
 
 .996 
 
 .99903 
 
 
 .00120 
 
 
 .99783 
 
 
 .00217 
 
 997 
 
 99947 
 
 
 .00163 
 
 
 .99783 
 
 
 .00217 
 
 .998 
 
 .99990 
 
 
 .00206 
 
 
 .99784 
 
 
 .00216 
 
 .999 
 
 1.00034 
 
 
 .00250 
 
 
 .99784 
 
 
 .00216 
 
 3.000 
 
 1.00078 
 
 43,6 
 
 1.00293 
 
 43,2 
 
 9.99785 
 
 0,4 
 
 0.00215 
 
 u 
 
 log tan gd u 
 
 F ' 
 
 log sec gd u 
 
 Fo' 
 
 log sin gd u 
 
 Fo' 
 
 log esc gd u 
 
 SMITHSONIAN TABLES 
 
 79 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 F ' 
 
 log cosh u 
 
 -Fo' 
 
 log tanh u 
 
 Fo' 
 
 log coth u 
 
 3.00 
 
 1.00078 
 
 436,5 
 
 1.00293 
 
 432,1 
 
 9.99785 
 
 4,3 
 
 O.OO2I5 
 
 .01 
 
 .00514 
 
 436,4 
 
 .00725 
 
 432,2 
 
 .99789 
 
 4,2 
 
 .00211 
 
 .02 
 
 .00950 
 
 436,4 
 
 .01157 
 
 432,2 
 
 99793 
 
 4,1 
 
 .OO2O7 
 
 .03 
 
 .01387 
 
 436,3 
 
 .01589 
 
 432,3 
 
 99797 
 
 4,1 
 
 .00203 
 
 .04 
 
 .01823 
 
 436,3 
 
 .02022 
 
 432,3 
 
 .90801 
 
 4,0 
 
 .00199 
 
 3.05 
 
 1.02259 
 
 436,2 
 
 1.02454 
 
 432,4 
 
 9.90805 
 
 3,9 
 
 0.00195 
 
 .06 
 
 .02696 
 
 43^2 
 
 .02886 
 
 432,4 
 
 99809 
 
 3,8 
 
 .OOI9I 
 
 .07 
 
 .03132 
 
 436,2 
 
 .03319 
 
 432,4 
 
 .99813 
 
 3,7 
 
 .00187 
 
 .08 
 
 .03568 
 
 436,1 
 
 .03751 
 
 432,5 
 
 .99817 
 
 3,7 
 
 .00183 
 
 .09 
 
 .04004 
 
 436,1 
 
 .04184 
 
 432,5 
 
 .99820 
 
 3,6 
 
 .OOlSo 
 
 3.10 
 
 I .04440 
 
 436,1 
 
 1.04616 
 
 432,5 
 
 9.99824 
 
 3,5 
 
 0.00176 
 
 .11 
 
 .04876 
 
 436,0 
 
 .05049 
 
 432,6 
 
 .99827 
 
 3,4 
 
 .00173 
 
 .12 
 
 .05312 
 
 436,0 
 
 .05481 
 
 432,6 
 
 99831 
 
 3,4 
 
 .00169 
 
 13 
 
 .05748 
 
 436,0 
 
 .059H 
 
 432,6 
 
 99834 
 
 3,3 
 
 .00l66 
 
 .14 
 
 .06184 
 
 435,9 
 
 .06347 
 
 432,7 
 
 .99837 
 
 3,3 
 
 .OOl63 
 
 3-15 
 
 1.06620 
 
 435,9 
 
 1.06779 
 
 432,7 
 
 9.99841 
 
 3,2 
 
 0.00159 
 
 .16 
 
 .07056 
 
 435,9 
 
 .07212 
 
 432,7 
 
 .99844 
 
 3,1 
 
 .OOI56 
 
 .17 
 
 .07492 
 
 435,8 
 
 .07645 
 
 432,8 
 
 .99847 
 
 3,1 
 
 .00153 
 
 .18 
 
 .07927 
 
 435,8 
 
 .08078 
 
 432,8 
 
 .99850 
 
 3,0 
 
 .00150 
 
 .19 
 
 .08363 
 
 435,8 
 
 .08510 
 
 432,8 
 
 .99853 
 
 2,9 
 
 .00147 
 
 3.20 
 
 1.08799 
 
 435,7 
 
 1.08943 
 
 432,9 
 
 9.99856 
 
 2,9 
 
 O.OOI44 
 
 .21 
 
 .09235 
 
 435,7 
 
 .09376 
 
 432,9 
 
 .99859 
 
 2,8 
 
 .OOI4I 
 
 .22 
 
 .09670 
 
 435,7 
 
 .09809 
 
 432,9 
 
 .99861 
 
 2,8 
 
 .00139 
 
 23 
 
 .IOIO6 
 
 435,7 
 
 . 10242 
 
 432,9 
 
 .99864 
 
 2,7 
 
 .OOI36 
 
 .24 
 
 .10542 
 
 435,6 
 
 .10675 
 
 433,0 
 
 .99867 
 
 2,7 
 
 .00133 
 
 3-25 
 
 i. 10977 
 
 435,6 
 
 I. 11108 
 
 433,0 
 
 9.99869 
 
 2,6 
 
 O.OOI3I 
 
 .26 
 
 .11413 
 
 435,6 
 
 .11541 
 
 433,0 
 
 .99872 
 
 2,6 
 
 .00128 
 
 .27 
 
 .11849 
 
 435,6 
 
 .11974 
 
 433,0 
 
 .99875 
 
 2,5 
 
 .00125 
 
 .28 
 
 .12284 
 
 435,5 
 
 . 12407 
 
 433,1 
 
 .99877 
 
 2,5 
 
 .00123 
 
 .29 
 
 . 12720 
 
 435,5 
 
 .12840 
 
 433,1 
 
 .99879 
 
 2,4 
 
 .00121 
 
 3-30 
 
 I.I3I5S 
 
 435,5 
 
 I.I3273 
 
 433,1 
 
 9.99882 
 
 2,4 
 
 O.OOIlS 
 
 31 
 
 .13591 
 
 435,5 
 
 .13706 
 
 433J 
 
 .99884 
 
 2,3 
 
 .OOIl6 
 
 32 
 
 .14026 
 
 435,4 
 
 .14139 
 
 433,2 
 
 .99886 
 
 2,3 
 
 .00114 
 
 33 
 
 .14461 
 
 435,4 
 
 14573 
 
 433,2 
 
 .99889 
 
 2,2 
 
 .OOIII 
 
 34 
 
 .14897 
 
 435,4 
 
 .15006 
 
 433,2 
 
 .99891 
 
 2,2 
 
 .OOIO9 
 
 3-35 
 
 i 15332 
 
 435-,4 
 
 I. 15439 
 
 433,2 
 
 9.99893 
 
 2,1 
 
 0.00107 
 
 .36 
 
 .15768 
 
 435,3 
 
 .15872 
 
 433,2 
 
 .99895 
 
 2,1 
 
 .00105 
 
 37 
 
 .16203 
 
 435,3 
 
 .16306 
 
 433,3 
 
 .99897 
 
 2,1 
 
 .00103 
 
 38 
 
 .16638 
 
 435,3 
 
 . 16739 
 
 433,3 
 
 .99899 
 
 2,0 
 
 .OOIOI 
 
 39 
 
 . 17073 
 
 435,3 
 
 . 17172 
 
 433,3 
 
 99901 
 
 2,0 
 
 .00099 
 
 3.40 
 
 i . 17509 
 
 435,3 
 
 1.17605 
 
 433,3 
 
 9.99903 
 
 1,9 
 
 0.00097 
 
 .41 
 
 .17944 
 
 435,2 
 
 .18039 
 
 433,3 
 
 .99905 
 
 1,9 
 
 .00095 
 
 .42 
 
 . 18379 
 
 435,2 
 
 . 18472 
 
 433,4 
 
 .99907 
 
 1,9 
 
 .00093 
 
 43 
 
 .18814 
 
 435,2 
 
 .18906 
 
 433,4 
 
 .99909 
 
 1,8 
 
 .00091 
 
 .44 
 
 .19250 
 
 435,2 
 
 .19339 
 
 433,4 
 
 .99911 
 
 1,8 
 
 .00089 
 
 3-45 
 
 1.10685 
 
 435,2 
 
 I . 19772 
 
 433,4 
 
 9.99912 
 
 1,8 
 
 0.00088 
 
 .46 
 
 .20120 
 
 435,2 
 
 .20206 
 
 433,4 
 
 .99914 
 
 i,7 
 
 .00086 
 
 47 
 
 .20555 
 
 435,1 
 
 .20639 
 
 433,5 
 
 .90916 
 
 i,7 
 
 .00084 
 
 .48 
 
 .20900 
 
 435,1 
 
 .21073 
 
 433,5 
 
 .99918 
 
 1,6 
 
 .00082 
 
 .49 
 
 .21425 
 
 435,1 
 
 .21506 
 
 433,5 
 
 .99919 
 
 1,6 
 
 .00081 
 
 3-50 
 
 1.21860 
 
 435,1 
 
 1.21940 
 
 433,5 
 
 9.99921 
 
 i/) 
 
 0.00079 
 
 u 
 
 loo tan od u 
 
 F ' 
 
 log sec gd u 
 
 F ' 
 
 log sin gd u 
 
 Fo' 
 
 log esc gd u 
 
 SMITHSONIAN TABLES 
 
 80 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 Fo' 
 
 log cosh u 
 
 wF ' 
 
 log tanh u 
 
 F ' 
 
 log coth u 
 
 3.50 
 
 I. 21860 
 
 435,1 
 
 1.21940 
 
 433,5 
 
 9.99921 
 
 1,6 
 
 O.OOO79 
 
 .51 
 
 .22296 
 
 
 .22373 
 
 
 .99922 
 
 
 .00078 
 
 .52 
 
 .22731 
 
 
 .22807 
 
 
 .99924 
 
 1,5 
 
 .00076 
 
 .53 
 
 .23166 
 
 435,0 
 
 .23240 
 
 
 .99925 
 
 
 .00075 
 
 .54 
 
 .23601 
 
 
 .23674 
 
 433,6 
 
 .99927 
 
 
 .00073 
 
 3.55 
 
 1.24036 
 
 435,0 
 
 1.24107 
 
 433,6 
 
 9.99928 
 
 1,4 
 
 0.00072 
 
 .56 
 
 .24471 
 
 
 .24541 
 
 
 99930 
 
 
 .00070 
 
 57 
 
 .24906 
 
 
 .24975 
 
 
 .99931 
 
 
 .00069 
 
 .58 
 
 .25341 
 
 
 .25408 
 
 
 99933 
 
 1,3 
 
 .00067 
 
 59 
 
 .25776 
 
 
 .25842 
 
 
 99934 
 
 
 .00066 
 
 3.60 
 
 I.262II 
 
 434,9 
 
 1.26275 
 
 433,6 
 
 9-99935 
 
 1,3 
 
 0.00065 
 
 .61 
 
 .26646 
 
 
 .26709 
 
 433,7 
 
 .99936 
 
 
 .00064 
 
 .62 
 
 .27080 
 
 
 .27143 
 
 
 .99938 
 
 1,2 
 
 .00062 
 
 .63 
 
 .27515 
 
 
 .27576 
 
 
 99939 
 
 
 .00061 
 
 .64 
 
 .27950 
 
 
 .28010 
 
 
 .99940 
 
 
 .00060 
 
 3.65 
 
 1.28385 
 
 434,9 
 
 1.28444 
 
 433,7 
 
 9.99941 
 
 1,2 
 
 0.00059 
 
 .66 
 
 .28820 
 
 
 .28878 
 
 
 .99942 
 
 
 .00058 
 
 .67 
 
 .29255 
 
 
 .29311 
 
 
 99944 
 
 i,i 
 
 .00056 
 
 .68 
 
 .29690 
 
 434,8 
 
 .29745 
 
 
 99945 
 
 
 .00055 
 
 .69 
 
 .30125 
 
 
 .30179 
 
 433,8 
 
 .99946 
 
 
 .00054 
 
 3-70 
 
 1.30559 
 
 434,8 
 
 1.30612 
 
 433,8 
 
 9.99947 
 
 1,1 
 
 0.00053 
 
 
 .30994 
 
 
 .31046 
 
 
 .99948 
 
 1,0 
 
 .00052 
 
 72 
 
 .31429 
 
 
 .31480 
 
 
 .99949 
 
 
 .00051 
 
 73 
 
 .31864 
 
 
 .31914 
 
 
 .99950 
 
 
 .00050 
 
 74 
 
 .32299 
 
 
 .32348 
 
 
 99951 
 
 
 .00049 
 
 3-75 
 
 1.32733 
 
 434,8 
 
 1.32781 
 
 433,8 
 
 9.99952 
 
 1,0 
 
 0.00048 
 
 76 
 
 .33'l68 
 
 
 .33215 
 
 
 99953 
 
 0,9 
 
 .00047 
 
 77 
 
 .33603 
 
 
 .33649 
 
 
 99954 
 
 
 .00046 
 
 .78 
 
 .34038 
 
 434,7 
 
 .34083 
 
 
 99955 
 
 
 .00045 
 
 79 
 
 34472 
 
 
 .34517 
 
 433,9 
 
 .99956 
 
 
 .00044 
 
 3.8o 
 
 1.34007 
 
 434,7 
 
 I-3495I 
 
 433,9 
 
 9-99957 
 
 0,9 
 
 0.00043 
 
 .81 
 
 35342 
 
 
 .35384 
 
 
 .99957 
 
 
 .00043 
 
 .82 
 
 .35777 
 
 
 .35818 
 
 
 .99958 
 
 0,8 
 
 .00042 
 
 .83 
 
 .36211 
 
 
 .36252 
 
 
 99959 
 
 
 .00041 
 
 84 
 
 .36646 
 
 
 .36686 
 
 
 .99960 
 
 
 .00040 
 
 3.85 
 
 i.37o8i 
 
 434,7 
 
 1.37120 
 
 433,9 
 
 9.99961 
 
 0,8 
 
 0.00039 
 
 .86 
 
 .37515 
 
 
 .37554 
 
 
 .99961 
 
 
 .00039 
 
 .87 
 
 .37950 
 
 
 .37988 
 
 
 .99962 
 
 
 .00038 
 
 .88 
 
 .38385 
 
 
 .38422 
 
 
 .99963 
 
 o,7 
 
 .00037 
 
 .89 
 
 .38819 
 
 
 .38856 
 
 
 .99964 
 
 
 .00036 
 
 3.90 
 
 1.39254 
 
 434,7 
 
 1.39290 
 
 433,9 
 
 9.99964 
 
 o,7 
 
 0.00036 
 
 .91 
 
 .39689 
 
 434,6 
 
 .39724 
 
 
 99965 
 
 
 .00035 
 
 .92 
 
 .40123 
 
 
 .40158 
 
 434,0 
 
 .99966 
 
 
 .00034 
 
 93 
 
 .40558 
 
 
 .40591 
 
 
 .99966 
 
 
 .00034 
 
 .94 
 
 .40993 
 
 
 .41025 
 
 
 .99967 
 
 
 .00033 
 
 3-95 
 
 1.41427 
 
 434,6 
 
 I.4I459 
 
 434,0 
 
 9.99968 
 
 0,6 
 
 0.00032 
 
 .96 
 
 .41862 
 
 
 .41893 
 
 
 .99968 
 
 
 .00032 
 
 .97 
 
 .42296 
 
 
 .42327 
 
 
 .99969 
 
 
 .00031 
 
 .98 
 
 .42731 
 
 
 .42761 
 
 
 .99970 
 
 
 .00030 
 
 99 
 
 .43166 
 
 
 .43195 
 
 
 .99970 
 
 
 .00030 
 
 4.00 
 
 1.43600 
 
 434,6 
 
 1.43629 
 
 434,0 
 
 9.99971 
 
 0,6 
 
 0.00029 
 
 u 
 
 log tan gd u 
 
 Fo' 
 
 log sec gd u 
 
 F ' 
 
 log sin gd u 
 
 w Fo' 
 
 log esc gd u 
 
 SMITHSONIAN TABLES 
 
 81 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 F ' 
 
 log cosh u 
 
 Fo' 
 
 log tanh u 
 
 Fo' 
 
 log coth u 
 
 4.00 
 
 1.43600 
 
 434,6 
 
 1.43629 
 
 434,0 
 
 9-99971 
 
 0,6 
 
 O.OOO29 
 
 .01 
 
 .44035 
 
 
 .44063 
 
 
 99971 
 
 
 .00029 
 
 .02 
 
 .44409 
 
 
 44497 
 
 
 99972 
 
 
 .OO028 
 
 .03 
 
 .44904 
 
 
 .44931 
 
 
 99973 
 
 0,5 
 
 .OO027 
 
 .04 
 
 45339 
 
 
 .45365 
 
 
 99973 
 
 
 .OO027 
 
 4-05 
 
 1.45773 
 
 434,6 
 
 1.45799 
 
 434,0 
 
 9-99974 
 
 o,5 
 
 0.00026 
 
 .06 
 
 .46208 
 
 
 .46233 
 
 
 99974 
 
 
 .00026 
 
 .07 
 
 .46642 
 
 434,5 
 
 .46668 
 
 
 99975 
 
 
 .00025 
 
 .08 
 
 .47077 
 
 
 .47102 
 
 
 99975 
 
 
 .O0025 
 
 .09 
 
 475II 
 
 
 .47536 
 
 434,1 
 
 .99976 
 
 
 .00024 
 
 4.10 
 
 1.47946 
 
 434,5 
 
 1.47970 
 
 434,1 
 
 9.99976 
 
 o,5 
 
 0.00024 
 
 .11 
 
 .48380 
 
 
 .48404 
 
 
 99977 
 
 
 .00023 
 
 .12 
 
 .48815 
 
 
 .48838 
 
 
 99977 
 
 
 .00023 
 
 13 
 
 .49249 
 
 
 .49272 
 
 
 .99978 
 
 0,4 
 
 .00022 
 
 .14 
 
 .49684 
 
 
 .49706 
 
 
 .99978 
 
 
 .OO022 
 
 4-15 
 
 i . 501 18 
 
 434,5 
 
 1.50140 
 
 434,1 
 
 9.99978 
 
 0,4 
 
 O.OOO22 
 
 .16 
 
 .50553 
 
 
 50574 
 
 
 99979 
 
 
 .00021 
 
 17 
 
 .50987 
 
 
 .51008 
 
 
 99979 
 
 
 .00021 
 
 .18 
 
 .51422 
 
 
 .51442 
 
 
 .99980 
 
 
 .00020 
 
 .19 
 
 .51856 
 
 
 .51876 
 
 
 .99980 
 
 
 .00020 
 
 4.2O 
 
 1.52291 
 
 434,5 
 
 I.523IO 
 
 434,1 
 
 9.99980 
 
 0,4 
 
 O.OOO2O 
 
 .21 
 
 .52725 
 
 
 .52745 
 
 
 .99981 
 
 
 .OOOI9 
 
 .22 
 
 .53160 
 
 
 .53179 
 
 
 .99981 
 
 
 .OOOI9 
 
 23 
 
 53594 
 
 
 .53613 
 
 
 .99982 
 
 
 .00018 
 
 .24 
 
 .54029 
 
 
 .54047 
 
 
 .99982 
 
 
 .00018 
 
 4-25 
 
 1.54463 
 
 434,5 
 
 I.5448I 
 
 434,1 
 
 9.99982 
 
 0,4 
 
 O.OOOlS 
 
 .26 
 
 .54898 
 
 
 .54915 
 
 
 .99983 
 
 0,3 
 
 .OOOI7 
 
 .27 
 
 55332 
 
 
 .55349 
 
 
 .99983 
 
 
 .00017 
 
 .28 
 
 .55767 
 
 
 .55783 
 
 
 .99983 
 
 
 .OOOI7 
 
 .29 
 
 .56201 
 
 
 .56217 
 
 
 .99984 
 
 
 .OOOl6 
 
 4-30 
 
 1.56636 
 
 434,5 
 
 1.56652 
 
 434,1 
 
 9.99984 
 
 0,3 
 
 O.OOOI6 
 
 31 
 
 .57070 
 
 
 .57086 
 
 
 99984 
 
 
 .00016 
 
 32 
 
 .57505 
 
 434,4 
 
 .57520 
 
 
 .99985 
 
 
 .00015 
 
 33 
 
 57939 
 
 
 57954 
 
 
 .99985 
 
 
 .OOOI5 
 
 34 
 
 .58373 
 
 
 .58388 
 
 
 .99985 
 
 
 .00015 
 
 4-35 
 
 1.58808 
 
 434,4 
 
 1.58822 
 
 434,1 
 
 9.99986 
 
 0,3 
 
 O.OOOI4 
 
 .36 
 
 .59242 
 
 
 .59256 
 
 434,2 
 
 .99986 
 
 
 .OOOI4 
 
 37 
 
 .59677 
 
 
 .59691 
 
 
 .99986 
 
 
 .00014 
 
 38 
 
 .60111 
 
 
 .60125 
 
 
 .99086 
 
 
 .00014 
 
 39 
 
 .60546 
 
 
 .60559 
 
 
 .99987 
 
 
 .00013 
 
 4.40 
 
 1.60080 
 
 434,4 
 
 1.60993 
 
 434,2 
 
 9.99987 
 
 0,3 
 
 O.OOOI3 
 
 .41 
 
 .61414 
 
 
 .61427 
 
 
 .99987 
 
 
 .OOOI3 
 
 .42 
 
 .61849 
 
 
 .61861 
 
 
 .99987 
 
 
 .OOOI3 
 
 43 
 
 .62283 
 
 
 .62296 
 
 
 .99988 
 
 0,2 
 
 .OOOI2 
 
 .44 
 
 .62718 
 
 
 .62730 
 
 
 .99988 
 
 
 .OOOI2 
 
 4-45 
 
 1.63152 
 
 434A 
 
 1.63164 
 
 434,2 
 
 9.99988 
 
 0,2 
 
 O.OOOI2 
 
 .46 
 
 .63587 
 
 
 .63598 
 
 
 99988 
 
 
 .OOOI2 
 
 47 
 
 .64021 
 
 
 .64032 
 
 
 .99989 
 
 
 .00011 
 
 .48 
 
 .64455 
 
 
 .64467 
 
 
 .99989 
 
 
 .00011 
 
 49 
 
 .64890 
 
 
 .64901 
 
 
 .99989 
 
 
 .0001 1 
 
 4-50 
 
 1.65324 
 
 434A 
 
 1.65335 
 
 434,2 
 
 9.99989 
 
 0,2 
 
 O.OOOII 
 
 u 
 
 loo tan ad u 
 
 - Fo' 
 
 log tec gd u 
 
 Fo' 
 
 logsingdu 
 
 F O ' 
 
 log csc gd u 
 
 SMITHSONIAN TABLES 
 
 82 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 Fo' 
 
 log cosh u 
 
 F ' 
 
 log tanh u 
 
 F</ 
 
 log coth u 
 
 4.50 
 
 1.65324 
 
 434,4 
 
 1.65335 
 
 434,2 
 
 9.99989 
 
 0,2 
 
 O.OOOII 
 
 .51 
 
 .65759 
 
 
 .65769 
 
 
 .99989 
 
 
 .00011 
 
 .52 
 
 .66193 
 
 
 .66203 
 
 
 99990 
 
 
 .00010 
 
 53 
 
 .66627 
 
 
 .66637 
 
 
 .99990 
 
 
 .000 10 
 
 54 
 
 .67062 
 
 
 .67072 
 
 
 .99990 
 
 
 .00010 
 
 4-55 
 
 1.67496 
 
 434,4 
 
 1.67506 
 
 434,2 
 
 9-99990 
 
 0,2 
 
 O.OOOIO 
 
 .56 
 
 .67931 
 
 
 .67940 
 
 
 .99990 
 
 
 .00010 
 
 57 
 
 .68365 
 
 
 .68374 
 
 
 .99991 
 
 
 .00009 
 
 .58 
 
 .68799 
 
 
 .68808 
 
 
 .99991 
 
 
 .00009 
 
 59 
 
 .69234 
 
 
 .69243 
 
 
 .99991 
 
 
 .00009 
 
 4.60 
 
 1.69668 
 
 434,4 
 
 1.69677 
 
 434,2 
 
 9.99991 
 
 0,2 
 
 0.00009 
 
 .61 
 
 .70102 
 
 
 .70111 
 
 
 .99991 
 
 
 .00009 
 
 .62 
 
 .70537 
 
 
 .70545 
 
 
 99992 
 
 
 .00008 
 
 .63 
 
 .70971 
 
 
 .70979 
 
 
 99992 
 
 
 .00008 
 
 .64 
 
 .71406 
 
 
 .71414 
 
 
 .99992 
 
 
 .00008 
 
 4.65 
 
 1.71840 
 
 434,4 
 
 1.71848 
 
 434,2 
 
 9.99992 
 
 0,2 
 
 0.00008 
 
 .66 
 
 . 72274 
 
 
 .72282 
 
 
 .99992 
 
 
 .00008 
 
 .67 
 
 .72709 
 
 
 .72716 
 
 
 .99992 
 
 
 .00008 
 
 .68 
 
 .73143 
 
 
 .73151 
 
 
 99993 
 
 0,1 
 
 .00007 
 
 .69 
 
 .73577 
 
 
 .73585 
 
 
 99993 
 
 
 .00007 
 
 4.70 
 
 1.74012 
 
 434,4 
 
 I.740I9 
 
 434,2 
 
 9-99993 
 
 0,1 
 
 0.00007 
 
 71 
 
 .74446 
 
 
 74453 
 
 
 .99993 
 
 
 .00007 
 
 .72 
 
 .74881 
 
 
 .74887 
 
 
 99993 
 
 
 .00007 
 
 73 
 
 .75315 
 
 
 75322 
 
 
 99993 
 
 
 .00007 
 
 .74 
 
 .75749 
 
 
 .75756 
 
 
 99993 
 
 
 .00007 
 
 4-75 
 
 1.76184 
 
 434,4 
 
 1.76190 
 
 434,2 
 
 9-99993 
 
 0,1 
 
 0.00007 
 
 .76 
 
 .76618 
 
 
 .76624 
 
 
 .99994 
 
 
 .00006 
 
 77 
 
 .77052 
 
 
 .77059 
 
 
 .99994 
 
 
 .00006 
 
 .78 
 
 .77487 
 
 
 77493 
 
 
 .99994 
 
 
 .00006 
 
 79 
 
 .77921 
 
 
 .77927 
 
 
 99994 
 
 
 .00006 
 
 4.80 
 
 1.78355 
 
 434,4 
 
 1.78361 
 
 434,2 
 
 9-99994 
 
 0,1 
 
 0.00006 
 
 .81 
 
 .78790 
 
 
 .78796 
 
 
 .99994 
 
 
 .00006 
 
 .82 
 
 .79224 
 
 
 .79230 
 
 
 .99994 
 
 
 .00006 
 
 .83 
 
 .79658 
 
 434,3 
 
 .79664 
 
 
 99994 
 
 
 .00006 
 
 .84 
 
 .80093 
 
 
 .80098 
 
 
 99995 
 
 
 .00005 
 
 4.85 
 
 1.80527 
 
 434,3 
 
 1.80532 
 
 434,2 
 
 9-99995 
 
 0,1 
 
 0.00005 
 
 .86 
 
 .80962 
 
 
 .80967 
 
 
 99995 
 
 
 .00005 
 
 .87 
 
 .81396 
 
 
 -.81401 
 
 
 .99995 
 
 
 .00005 
 
 .88 
 
 .81830 
 
 
 .81835 
 
 
 .99995 
 
 
 .00005 
 
 .89 
 
 .82265 
 
 
 .82269 
 
 
 99995 
 
 
 .00005 
 
 4.90 
 
 1.82699 
 
 434,3 
 
 1.82704 
 
 434,2 
 
 9-99995 
 
 0,1 
 
 0.00005 
 
 .91 
 
 .83133 
 
 
 .83138 
 
 
 .99995 
 
 
 .00005 
 
 .92 
 
 .83568 
 
 
 .83572 
 
 
 .99995 
 
 ' 
 
 .00005 
 
 93 
 
 .84002 
 
 
 .84006 
 
 
 .99995 
 
 
 .00005 
 
 .94 
 
 .84436 
 
 
 .84441 
 
 434,3 
 
 .99996 
 
 
 .00004 
 
 4-95 
 
 1.84871 
 
 434,3 
 
 1.84875 
 
 434,3 
 
 9.99996 
 
 0,1 
 
 0.00004 
 
 .96 
 
 .85305 
 
 
 .85309 
 
 
 .99996 
 
 
 .00004 
 
 97 
 
 .85739 
 
 
 .85743 
 
 
 .99996 
 
 
 .00004 
 
 .98 
 
 .86174 
 
 
 .86178 
 
 
 .99996 
 
 
 .00004 
 
 99 
 
 .86608 
 
 
 .86612 
 
 
 99996 
 
 
 .00004 
 
 5-00 
 
 1.87042 
 
 434,3 
 
 1.87046 
 
 434,3 
 
 9.99996 
 
 0,1 
 
 0.00004 
 
 u 
 
 log tan gd u 
 
 Fo' 
 
 log sec gd u 
 
 Fo' 
 
 log sin gd u 
 
 Fo' 
 
 logcscgdu 
 
 SMITHSONIAN TABLES 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 
 
 log cosh u 
 
 IV 
 
 log tanh u 
 
 Fo' 
 
 log eoth u 
 
 5.00 
 
 1.87042 
 
 434,3 
 
 1.87046 
 
 434,3 
 
 9.99996 
 
 0,1 
 
 0.00004 
 
 .01 
 
 .87477 
 
 
 .87480 
 
 
 .99996 
 
 
 .00004 
 
 .02 
 
 .879H 
 
 
 .87915 
 
 
 .99996 
 
 
 .00004 
 
 03 
 
 .88345 
 
 
 .88349 
 
 
 .99996 
 
 
 .00004 
 
 .04 
 
 .88780 
 
 
 .88783 
 
 
 .99996 
 
 
 .00004 
 
 5-05 
 
 1.89214 
 
 434,3 
 
 1.89217 
 
 434,3 
 
 9.99906 
 
 0,1 
 
 0.00004 
 
 .06 
 
 .89648 
 
 
 .89652 
 
 
 .99997 
 
 
 .00003 
 
 .07 
 
 .90083 
 
 
 .90086 
 
 
 .99997 
 
 
 .00003 
 
 .08 
 
 00517 
 
 
 .90520 
 
 
 99997 
 
 
 .00003 
 
 .09 
 
 .00951 
 
 
 .90955 
 
 
 .99997 
 
 
 .00003 
 
 5. 10 
 
 I.9I386 
 
 434,3 
 
 I.9I389 
 
 434,3 
 
 9-99997 
 
 0,1 
 
 0.00003 
 
 .11 
 
 .91820 
 
 
 .91823 
 
 
 .99997 
 
 
 .00003 
 
 .12 
 
 .92254 
 
 
 .92257 
 
 
 .90997 
 
 
 .00003 
 
 13 
 
 .92689 
 
 
 .92692 
 
 
 .99997 
 
 
 .00003 
 
 .14 
 
 .93123 
 
 
 .93126 
 
 
 .99997 
 
 
 .00003 
 
 5-15 
 
 1.93557 
 
 434,3 
 
 1.93560 
 
 434,3' 
 
 9.99997 
 
 0,1 
 
 0.00003 
 
 .16 
 
 93992 
 
 
 93994 
 
 
 .99997 
 
 
 .00003 
 
 .17 
 
 .94426 
 
 
 .94429 
 
 
 99997 
 
 
 .00003 
 
 .18 
 
 .94860 
 
 
 .94863 
 
 
 99997 
 
 
 .00003 
 
 .19 
 
 .95294 
 
 
 .95297 
 
 
 99997 
 
 
 .00003 
 
 5-20 
 
 1.95729 
 
 434,3 
 
 I.9573I 
 
 434,3 
 
 9-99997 
 
 0,1 
 
 0.00003 
 
 .21 
 
 .96163 
 
 
 .96166 
 
 
 .99997 
 
 
 .00003 
 
 .22 
 
 .96597 
 
 
 .96600 
 
 
 99997 
 
 
 .00003 
 
 23 
 
 .97032 
 
 
 .97034 
 
 
 .99998 
 
 0,0 
 
 .00002 
 
 .24 
 
 .97466 
 
 
 .97409 
 
 
 .99998 
 
 
 .00002 
 
 5.25 
 
 1.97900 
 
 434,3 
 
 1.97903 
 
 434,3 
 
 9.99998 
 
 0,0 
 
 O.OOOO2 
 
 .26 
 
 .98335 
 
 
 .08337 
 
 
 .99998 
 
 
 .00002 
 
 .27 
 
 .98769 
 
 
 58771 
 
 
 99998 
 
 
 .00002 
 
 .28 
 
 .99203 
 
 
 .99206 
 
 
 .99998 
 
 
 .00002 
 
 .29 
 
 .99638 
 
 
 .99640 
 
 
 .99998 
 
 
 .00002 
 
 5.30 
 
 2.00072 
 
 434,3 
 
 2.00074 
 
 434,3 
 
 9.99998 
 
 0,0 
 
 O.OOO02 
 
 .31 
 
 .00506 
 
 
 .00508 
 
 
 .99998 
 
 
 .OOOO2 
 
 .32 
 
 .00941 
 
 
 .00943 
 
 
 99998 
 
 
 .OOOO2 
 
 .33 
 
 01375 
 
 
 .01377 
 
 
 .99998 
 
 
 .OOOO2 
 
 .34 
 
 .01809 
 
 
 .01811 
 
 
 .99998 
 
 
 .00002 
 
 5.35 
 
 2.02244 
 
 434,3 
 
 2.02246 
 
 434,3 
 
 9.99998 
 
 0,0 
 
 O.OOOO2 
 
 .36 
 
 .02678 
 
 
 .02680 
 
 
 .90998 
 
 
 .OOO02 
 
 .37 
 
 .03112 
 
 
 .03114 
 
 
 .99998 
 
 
 .OOOO2 
 
 38 
 
 03547 
 
 
 .03548 
 
 
 .99008 
 
 
 .OOOO2 
 
 39 
 
 .03981 
 
 
 .03983 
 
 
 .09998 
 
 
 .OOOO2 
 
 5.40 
 
 2.04415 
 
 434,3 
 
 2.04417 
 
 434,3 
 
 9.99998 
 
 0,0 
 
 O.OOO02 
 
 .41 
 
 .04849 
 
 
 .04851 
 
 
 .99998 
 
 
 .OO002 
 
 .42 
 
 .05284 
 
 
 .05285 
 
 
 .99998 
 
 
 .OOOO2 
 
 43 
 
 .05718 
 
 
 .05720 
 
 
 .99998 
 
 
 .O0002 
 
 44 
 
 .06152 
 
 
 .06154 
 
 
 .99998 
 
 
 .00002 
 
 5-45 
 
 2.06587 
 
 434,3 
 
 2.06588 
 
 434,3 
 
 9.99998 
 
 0,0 
 
 O.OOOO2 
 
 .46 
 
 .07021 
 
 
 .07023 
 
 
 .90998 
 
 
 .OOOO2 
 
 .47 
 
 07455 
 
 
 .07457 
 
 
 .99998 
 
 
 .OOOO2 
 
 .48 
 
 .07890 
 
 
 .07891 
 
 
 .99998 
 
 
 .OOOO2 
 
 .49 
 
 .08324 
 
 
 .08325 
 
 
 99999 
 
 
 .OOOOI 
 
 5-50 
 
 2.08758 
 
 434,3 
 
 2.08760 
 
 434,3 
 
 9.90009 
 
 0,0 
 
 0.00001 
 
 u 
 
 log tan gd u 
 
 -Fo' 
 
 log sec gd u 
 
 Fo' 
 
 log sin gd u 
 
 Fo' 
 
 log esc gd u 
 
 SMITHSONIAN TABLES 
 
Logarithms of Hyperbolic Functions. 
 
 u 
 
 log sinh u 
 
 F ' 
 
 log cosh u 
 
 Fo' 
 
 log tanh u 
 
 Fo' 
 
 log coth u 
 
 5.50 
 
 2.08758 
 
 434,3 
 
 2.08760 
 
 434,3 
 
 9.99999 
 
 0,0 
 
 O.OOOOI 
 
 .51 
 
 .09193 
 
 
 .09194 
 
 
 .99999 
 
 
 .00001 
 
 52 
 
 .09627 
 
 
 .09628 
 
 
 .99999 
 
 
 .00001 
 
 -53 
 
 .10061 
 
 
 .10063 
 
 
 99999 
 
 
 .00001 
 
 54 
 
 .10495 
 
 
 . 10497 
 
 
 .99999 
 
 
 .00001 
 
 5-55 
 
 2.10930 
 
 434,3 
 
 2.10931 
 
 434,3 
 
 9-99999 
 
 0,0 
 
 O.OOOOI 
 
 .56 
 
 .11364 
 
 
 .11365 
 
 
 .99999 
 
 
 .00001 
 
 .57 
 
 .11798 
 
 
 .11800 
 
 
 .99999 
 
 
 .00001 
 
 .58 
 
 . 12233 
 
 
 . 12234 
 
 
 .99999 
 
 
 .00001 
 
 59 
 
 .12667 
 
 
 .12668 
 
 
 .99999 
 
 
 .00001 
 
 5.6o 
 
 2.13101 
 
 434,3 
 
 2.13103 
 
 434,3 
 
 9-99999 
 
 0,0 
 
 O.OOOOI 
 
 .61 
 
 . 13536 
 
 
 . 13537 
 
 
 99999 
 
 
 .00001 
 
 .62 
 
 . 13970 
 
 
 . I397I 
 
 
 99999 
 
 
 .00001 
 
 .63 
 
 .14404 
 
 
 .14405 
 
 
 99999 
 
 
 .00001 
 
 .64 
 
 . 14839 
 
 
 . 14840 
 
 
 99999 
 
 
 .00001 
 
 5.65 
 
 2.15273 
 
 434,3 
 
 2.15274 
 
 434,3 
 
 9-99999 
 
 0,0 
 
 O.OOOOI 
 
 .66 
 
 . 15707 
 
 
 .15708 
 
 
 99999 
 
 
 .00001 
 
 .67 
 
 .16141 
 
 
 .16142 
 
 
 99999 
 
 
 .00001 
 
 .68 
 
 . 16576 
 
 
 . 16577 
 
 
 .99999 
 
 
 .00001 
 
 .69 
 
 . 17010 
 
 
 .17011 
 
 
 .99999 
 
 
 .00001 
 
 5-70 
 
 2.17444 
 
 434,3 
 
 2.17445 
 
 434,3 
 
 9-99999 
 
 0,0 
 
 O.OOOOI 
 
 7i 
 
 . 17879 
 
 
 .17880 
 
 
 99999 
 
 
 .00001 
 
 72 
 
 .18313 
 
 
 .18314 
 
 
 .99999 
 
 
 .00001 
 
 73 
 
 . 18747 
 
 
 . 18748 
 
 
 99999 
 
 
 .00001 
 
 74 
 
 . 19182 
 
 
 . 19182 
 
 
 99999 
 
 
 .00001 
 
 5-75 
 
 2.19616 
 
 434,3 
 
 2.19617 
 
 434,3 
 
 9-99999 
 
 0,0 
 
 O.OOOOI 
 
 76 
 
 .20050 
 
 
 .20051 
 
 
 99999 
 
 
 .00001 
 
 77 
 
 . 20484 
 
 
 .20485 
 
 
 .99999 
 
 
 .00001 
 
 .78 
 
 .20919 
 
 
 .20920 
 
 
 .99999 
 
 
 .00001 
 
 79 
 
 .21353 
 
 
 .21354 
 
 
 99999 
 
 
 .00001 
 
 5.8o 
 
 2.21787 
 
 434,3 
 
 2.21788 
 
 434,3 
 
 9-99999 
 
 0,0 
 
 O.OOOOI 
 
 .81 
 
 . 22222 
 
 
 .22222 
 
 
 99999 
 
 
 .00001 
 
 .82 
 
 .22656 
 
 
 .22657 
 
 
 99999 
 
 
 .00001 
 
 .83 
 
 .23090 
 
 
 .23091 
 
 
 99999 
 
 
 .00001 
 
 .84 
 
 .23525 
 
 
 .23525 
 
 
 99999 
 
 
 .00001 
 
 5.85 
 
 2.23959 
 
 434,3 
 
 2.23960 
 
 434,3 
 
 9-99999 
 
 0,0 
 
 O.OOOOI 
 
 .86 
 
 
 
 .24394 
 
 
 99999 
 
 
 .00001 
 
 .87 
 
 .24828 
 
 
 .24828 
 
 
 99999 
 
 
 .00001 
 
 .88 
 
 .25262 
 
 
 .25262 
 
 
 99999 
 
 
 .00001 
 
 .89 
 
 .25696 
 
 
 .25697 
 
 
 99999 
 
 
 .00001 
 
 5.90 
 
 2.26130 
 
 434,3 
 
 2.26I3I 
 
 434,3 
 
 9-99999 
 
 0,0 
 
 O.OOOOI 
 
 .91 
 
 .26565 
 
 
 .26565 
 
 
 99999 
 
 
 .00001 
 
 .92 
 
 .26999 
 
 
 .27000 
 
 
 99999 
 
 
 .00001 
 
 93 
 
 27433 
 
 
 .27434 
 
 
 99999 
 
 
 .00001 
 
 .94 
 
 .27868 
 
 
 .27868 
 
 
 99999 
 
 
 .00001 
 
 5-95 
 
 2.28302 
 
 434,3 
 
 2.28303 
 
 434,3 
 
 9-99999 
 
 0,0 
 
 O.OOOOI 
 
 .96 
 
 .28736 
 
 
 .28737 
 
 
 99999 
 
 
 .00001 
 
 97 
 
 .29171 
 
 
 .29171 
 
 
 .99999 
 
 
 .00001 
 
 .98 
 
 .29605 
 
 
 .29605 
 
 
 -99999 
 
 
 .OOOOI 
 
 .99 
 
 .30039 
 
 
 .30040 
 
 
 .99999 
 
 
 .00001 
 
 6.00 
 
 2.30473 
 
 434,3 
 
 2.30474 
 
 434,3 
 
 9-99999 
 
 0,0 
 
 O.OOOOI 
 
 u 
 
 log tan gd u 
 
 <- Fo' 
 
 log sec gd u 
 
 w Fo' 
 
 log sin gd u 
 
 Fo' 
 
 log csc gd u 
 
 SMITHSONIAN TABLES 
 
TABLE II 
 
 NATURAL HYPERBOLIC FUNCTIONS 
 
 87 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinh u 
 
 F ' 
 
 cosh u 
 
 Fo' 
 
 tanh u 
 
 Fo' 
 
 coth u 
 
 - Fo' 
 
 o.oooo 
 
 O.OOOOO 
 
 10,0 
 
 I. 00000 
 
 0,0 
 
 O.OOOOO 
 
 10,0 
 
 00 
 
 <x 
 
 .0001 
 
 .OOOIO 
 
 
 .00000 
 
 
 .OOOIO 
 
 
 IOOOO.OO 
 
 1000000,0 
 
 .0002 
 
 .0002O 
 
 
 .00000 
 
 
 .00020 
 
 
 5000.00 
 
 250000,0 
 
 .0003 
 
 .O0030 
 
 
 .00000 
 
 
 .00030 
 
 
 3333.33 
 
 mm, i 
 
 .0004 
 
 .00040 
 
 
 .00000 
 
 
 .00040 
 
 
 2500.00 
 
 62500,0 
 
 0.0005 
 
 O.OOO5O 
 
 IO,O 
 
 I.OOOOO 
 
 0,0 
 
 0.00050 
 
 10,0 
 
 2000.00 
 
 40000,0 
 
 .OO06 
 
 .00060 
 
 
 .00000 
 
 
 .00060 
 
 
 1666.67 
 
 27777,8 
 
 .OO07 
 
 .O0070 
 
 
 .00000 
 
 
 .00070 
 
 
 1428.57 
 
 20408,2 
 
 .0008 
 
 .OOOSO 
 
 
 .00000 
 
 
 .00080 
 
 
 1250.00 
 
 15625,0 
 
 .0009 
 
 .00090 
 
 
 .00000 
 
 
 .00090 
 
 
 IIII. II 
 
 12345,7 
 
 O.OOIO 
 
 O.OOIOO 
 
 IO,O 
 
 I.OOOOO 
 
 0,0 
 
 O.OOIOO 
 
 10,0 
 
 1000.00 
 
 10000,0 
 
 .OOII 
 
 .OOIIO 
 
 
 .00000 
 
 
 .OOIIO 
 
 
 909.09 
 
 8264,5 
 
 .0012 
 
 .00120 
 
 
 .00000 
 
 
 .00120 
 
 
 833.33 
 
 6944,4 
 
 .0013 
 
 .00130 
 
 
 .00000 
 
 
 .00130 
 
 
 769.23 
 
 5917,2 
 
 .0014 
 
 .00140 
 
 
 .00000 
 
 
 .00140 
 
 
 714.29 
 
 5102,0 
 
 0.0015 
 
 0.00150 
 
 IO,O 
 
 I.OOOOO 
 
 0,0 
 
 0.00150 
 
 10,0 
 
 666.67 
 
 4444,4 
 
 .0016 
 
 .00160 
 
 
 .00000 
 
 
 .00160 
 
 
 625.00 
 
 3906,2 
 
 .0017 
 
 .00170 
 
 
 .00000 
 
 
 .00170 
 
 
 588.24 
 
 3460,2 
 
 .0018 
 
 .00180 
 
 
 .00000 
 
 
 .00180 
 
 
 555.56 
 
 3086,4 
 
 .0019 
 
 .00190 
 
 
 .00000 
 
 
 .00190 
 
 
 526.32 
 
 2770,1 
 
 O.OO2O 
 
 O.OO2OO 
 
 10,0 
 
 I.OOOOO 
 
 0,0 
 
 0.00200 
 
 10,0 
 
 500.00 
 
 2500,0 
 
 .0021 
 
 .OO2IO 
 
 
 .00000 
 
 
 .00210 
 
 
 476. 19 
 
 2267,6 
 
 .OO22 
 
 .00220 
 
 
 .00000 
 
 
 .00220 
 
 
 454.55 
 
 2066, 1 
 
 .OO23 
 
 .OO23O 
 
 
 .00000 
 
 
 .00230 
 
 
 434.78 
 
 1800,4 
 
 .O024 
 
 .00240 
 
 
 .00000 
 
 
 .00240 
 
 
 416.67 
 
 1736,1 
 
 O.O025 
 
 0.00250 
 
 IO S O 
 
 I.OOOOO 
 
 0,0 
 
 0.00250 
 
 10,0 
 
 400.00 
 
 1600,0 
 
 .0026 
 
 .00260 
 
 
 .00000 
 
 
 .00260 
 
 
 384.62 
 
 1479,3 
 
 .0027 
 
 .O027O 
 
 
 .00000 
 
 
 .00270 
 
 
 370.37 
 
 1371,7 
 
 .0028 
 
 .O028O 
 
 
 .00000 
 
 
 .00280 
 
 
 357.14 
 
 1275,5 
 
 .0029 
 
 .00290 
 
 
 .00000 
 
 
 .00290 
 
 
 344.83 
 
 1189,1 
 
 O.O03O 
 
 0.00300 
 
 10,0 
 
 I.OOOOO 
 
 0,0 
 
 0.00300 
 
 IO,O 
 
 333.33 
 
 IIII, I 
 
 .0031 
 
 .OO3IO 
 
 
 .00000 
 
 
 .00310 
 
 
 322.58 
 
 1040,6 
 
 .0032 
 
 .O032O 
 
 
 .00001 
 
 
 .00320 
 
 
 312.50 
 
 976,6 
 
 .0033 
 
 .00330 
 
 
 .00001 
 
 
 .00330 
 
 
 303.03 
 
 918,3 
 
 .0034 
 
 .00340 
 
 
 .00001 
 
 
 .00340 
 
 
 294.12 
 
 865,1 
 
 0.0035 
 
 0.00350 
 
 IO,O 
 
 I.OOOOI 
 
 0,0 
 
 0.00350 
 
 10,0 
 
 285.72 
 
 816,3 
 
 .0036 
 
 .00360 
 
 
 .00001 
 
 
 .00360 
 
 
 277.78 
 
 771,6 
 
 .0037 
 
 .00370 
 
 
 .00001 
 
 
 .00370 
 
 
 270.27 
 
 730,5 
 
 .0038 
 
 .00380 
 
 
 .00001 
 
 
 .00380 
 
 
 263.16 
 
 692,5 
 
 .0039 
 
 .00390 
 
 
 .00001 
 
 
 .00300 
 
 
 256.41 
 
 657,5 
 
 0.0040 
 
 O.OO4OO 
 
 10,0 
 
 I.OOOOI 
 
 0,0 
 
 0.00400 
 
 10,0 
 
 250.00 
 
 625,0 
 
 .0041 
 
 .004IO 
 
 
 .00001 
 
 
 .00410 
 
 
 243.90 
 
 594,9 
 
 .0042 
 
 .OO42O 
 
 
 .00001 
 
 
 .00420 
 
 
 238.10 
 
 566,9 
 
 .0043 
 
 .00430 
 
 
 .00001 
 
 
 .00430 
 
 
 232.56 
 
 540,8 
 
 .0044 
 
 .00440 
 
 
 .00001 
 
 
 .00440 
 
 
 227.27 
 
 516,5 
 
 0.0045 
 
 0.00450 
 
 10,0 
 
 I.OOOOI 
 
 0,0 
 
 0.00450 
 
 10,0 
 
 222.22 
 
 493,8 
 
 .0046 
 
 .00460 
 
 
 .00001 
 
 
 .00460 
 
 
 217.39 
 
 472,6 
 
 .0047 
 
 .00470 
 
 
 .00001 
 
 
 .00470 
 
 
 212.77 
 
 452,7 
 
 .0048 
 .0049 
 
 .00480 
 .00400 
 
 
 .00001 
 
 .00001 
 
 
 .00480 
 
 .00490 
 
 
 208.33 
 
 204.08 
 
 434,0 
 
 416,5 
 
 0.0050 
 
 0.00500 
 
 10,0 
 
 I.OOOOI 
 
 0,1 
 
 0.00500 
 
 IO,O 
 
 200.00 
 
 400,0 
 
 u 
 
 tan gd u 
 
 Fo' 
 
 sec gd u 
 
 - Fo' 
 
 sin gd u 
 
 Fo' 
 
 csc gd u 
 
 - Fo' 
 
 SMITHSONIAN TABLCS 
 
 88 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinh u 
 
 <-FO' 
 
 cosh u 
 
 Fo' 
 
 tanh u 
 
 Fo' 
 
 coth u 
 
 Fo' 
 
 0.0050 
 
 0.00500 
 
 IO,O 
 
 I.OOOOI 
 
 0,1 
 
 0.00500 
 
 IO,O 
 
 200.00 
 
 400,0 
 
 .0051 
 
 .005IO 
 
 
 .00001 
 
 
 .00510 
 
 
 196.08 
 
 384,5 
 
 .0052 
 
 .O0520 
 
 
 .00001 
 
 
 .00520 
 
 
 192.31 
 
 369,8 
 
 .0053 
 
 .00530 
 
 
 .00001 
 
 
 .00530 
 
 
 188.68 
 
 356,0 
 
 .0054 
 
 .00540 
 
 
 .00001 
 
 
 .00540 
 
 
 185.19 
 
 342,9 
 
 0.0055 
 
 0.00550 
 
 IO,O 
 
 I.O0002 
 
 0,1 
 
 0.00550 
 
 IO,O 
 
 181.82 
 
 330,6 
 
 .0056 
 
 .00560 
 
 
 .00002 
 
 
 .00560 
 
 
 178.57 
 
 3i8,9 
 
 .0057 
 
 .00570 
 
 
 .00002 
 
 
 .00570 
 
 
 175.44 
 
 307,8 
 
 .0058 
 
 .00580 
 
 
 .00002 
 
 
 .00580 
 
 
 172.42 
 
 297,3 
 
 .0059 
 
 .00590 
 
 
 .00002 
 
 
 .00590 
 
 
 169.49 
 
 287,3 
 
 0.0060 
 
 0.00600 
 
 IO,O 
 
 I.OOO02 
 
 0,1 
 
 0.00600 
 
 IO,O 
 
 166.67 
 
 277,8 
 
 .0061 
 
 .00610 
 
 
 .OO002 
 
 
 .00610 
 
 
 163.94 
 
 268,7 
 
 .0062 
 
 .00620 
 
 
 .OOOO2 
 
 
 .00620 
 
 
 161.29 
 
 260,1 
 
 .0063 
 
 .00630 
 
 
 .O0002 
 
 
 .00630 
 
 
 158.73 
 
 251,9 
 
 .0064 
 
 .00640 
 
 
 .OOOO2 
 
 
 .00640 
 
 
 156.25 
 
 244,1 
 
 0.0065 
 
 0.00650 
 
 10,0 
 
 I.OOOO2 
 
 0,1 
 
 0.00650 
 
 10,0 
 
 153.85 
 
 236,7 
 
 .0066 
 
 .00660 
 
 
 .OOO02 
 
 
 .00660 
 
 
 151.52 
 
 229,6 
 
 .0067 
 
 .00670 
 
 
 .00002 
 
 
 .00670 
 
 
 149.26 
 
 222,8 
 
 .0068 
 
 .00680 
 
 
 .OOO02 
 
 
 .00680 
 
 
 147.06 
 
 216,3 
 
 .0069 
 
 .00690 
 
 
 .OOOO2 
 
 
 .00690 
 
 
 144.93 
 
 210,0 
 
 0.0070 
 
 0.00700 
 
 10,0 
 
 I.OOOO2 
 
 0,1 
 
 0.00700 
 
 10,0 
 
 142.86 
 
 204,1 
 
 .0071 
 
 .00710 
 
 
 .00003 
 
 
 .00710 
 
 
 140.85 
 
 I08,4 
 
 .0072 
 
 .O072O 
 
 
 .00003 
 
 
 .00720 
 
 
 138.89 
 
 192,9 
 
 .0073 
 
 .00730 
 
 
 .00003 
 
 
 .00730 
 
 
 136.99 
 
 187,6 
 
 .0074 
 
 .00740 
 
 
 .OOOO3 
 
 
 '.00740 
 
 
 135.14 
 
 182,6 
 
 0.0075 
 
 0.00750 
 
 IO,O 
 
 I.OOOO3 
 
 0,1 
 
 0.00750 
 
 IO,O 
 
 133.34 
 
 177,8 
 
 .0076 
 
 .00760 
 
 
 .OOOO3 
 
 
 .00760 
 
 
 131.58 
 
 173,1 
 
 .0077 
 
 .00770 
 
 
 .00003 
 
 
 .00770 
 
 
 129.87 
 
 168,7 
 
 .0078 
 
 .00780 
 
 
 .00003 
 
 
 .00780 
 
 
 128.21 
 
 164,4 
 
 .0079 
 
 .00790 
 
 
 .OOOO3 
 
 
 .00790 
 
 
 126.58 
 
 160,2 
 
 0.0080 
 
 O.OOSOO 
 
 10,0 
 
 I.OOOO3 
 
 01, 
 
 0.00800 
 
 IO,O 
 
 125.00 
 
 156,2 
 
 .0081 
 
 .OoSlO 
 
 
 .00003 
 
 
 .00810 
 
 
 123.46 
 
 152,4 
 
 .0082 
 
 .00820 
 
 
 .00003 
 
 
 .00820 
 
 
 121.95 
 
 148,7 
 
 .0083 
 
 .00830 
 
 
 .00003 
 
 
 .00830 
 
 
 120.48 
 
 145,2 
 
 .0084 
 
 .00840 
 
 
 .OOOO4 
 
 
 .00840 
 
 
 119.05 
 
 141,7 
 
 0.0085 
 
 0.00850 
 
 10,0 
 
 I.OOOO4 
 
 0,1 
 
 0.00850 
 
 IO,O 
 
 117.65 
 
 138,4 
 
 .0086 
 
 .00860 
 
 
 .OOOO4 
 
 
 .00860 
 
 
 116.28 
 
 135,2 
 
 .0087 
 
 .00870 
 
 
 .00004 
 
 
 .00870 
 
 
 114.95 
 
 132,1 
 
 .0088 
 
 .00880 
 
 
 .00004 
 
 
 .00880 
 
 
 113.64 
 
 129,1 
 
 .0089 
 
 .00890 
 
 
 .00004 
 
 
 .00890 
 
 
 112.36 
 
 126,2 
 
 0.0090 
 
 o.ooooo 
 
 10,0 
 
 1.00004 
 
 0,1 
 
 0.00900 
 
 10,0 
 
 III. II 
 
 123,5 
 
 .0091 
 
 .00910 
 
 
 .00004 
 
 
 .00910 
 
 
 109.89 
 
 120,8 
 
 .0092 
 
 .00920 
 
 
 .00004 
 
 
 .00920 
 
 
 108.70 
 
 118,1 
 
 .0093 
 
 .00930 
 
 
 .00004 
 
 
 .00930 
 
 
 107.53 
 
 115,6 
 
 .0094 
 
 .00940 
 
 
 .00004 
 
 
 .00940 
 
 
 106.39 
 
 113,2 
 
 0.0095 
 
 0.00950 
 
 10,0 
 
 1.00005 
 
 0,1 
 
 0.00950 
 
 10,0 
 
 105.27 
 
 110,8 
 
 .0096 
 
 .00960 
 
 
 .00005 
 
 
 .00960 
 
 
 104.17 
 
 108,5 
 
 .0097 
 
 .00970 
 
 
 .00005 
 
 
 .00970 
 
 
 103.10 
 
 106,3 
 
 .0008 
 
 .00980 
 
 
 .00005 
 
 
 .00980 
 
 
 102.04 
 
 104,1 
 
 .0099 
 
 .00090 
 
 
 .00005 
 
 
 .00990 
 
 
 101.01 
 
 102,0 
 
 O.OIOO 
 
 0.01000 
 
 IO,O 
 
 I.OOOO5 
 
 0,1 
 
 O.OIOOO 
 
 10,0 
 
 IOO.OO 
 
 100,0 
 
 u 
 
 tan gd u 
 
 F ' 
 
 sec gd u 
 
 - Fo' 
 
 sin gd u 
 
 Fo' 
 
 csc gd u 
 
 F ' 
 
 SMITHSONIAN TABLES 
 
 89 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinh u 
 
 F O ' 
 
 cosh u 
 
 Fo' 
 
 tanh u 
 
 Fo' 
 
 coth u 
 
 - Fo' 
 
 O.OIOO 
 
 O.OIOOO 
 
 10,0 
 
 1.00005 
 
 0,1 
 
 O.OIOOO 
 
 IO,O 
 
 100.003 
 
 1000,0 
 
 .OIOI 
 
 .OIOIO 
 
 
 .00005 
 
 
 .OIOIO 
 
 
 99.013 
 
 980,3 
 
 .0102 
 
 .01020 
 
 
 .00005 
 
 
 .01020 
 
 
 98.043 
 
 961,1 
 
 .0103 
 
 .01030 
 
 
 .00005 
 
 
 .01030 
 
 
 97.091 
 
 942,6 
 
 .0104 
 
 .01040 
 
 
 .00005 
 
 
 .01040 
 
 
 '96.157 
 
 924,5 
 
 0.0105 
 
 0.01050 
 
 10,0 
 
 1.00006 
 
 0,1 
 
 0.01050 
 
 IO,O 
 
 95.242 
 
 907,0 
 
 .0106 
 
 .01060 
 
 
 .00006 
 
 
 .01060 
 
 
 94.343 
 
 890,0 
 
 .0107 
 
 .01070 
 
 
 .00006 
 
 
 .01070 
 
 
 93.462 
 
 873,4 
 
 .0108 
 
 .01080 
 
 
 .00006 
 
 
 .01080 
 
 
 92.595 
 
 857,3 
 
 .0109 
 
 .01090 
 
 
 .00006 
 
 
 .01090 
 
 
 91.747 
 
 841,6 
 
 O.OIIO 
 
 O.OIIOO 
 
 10,0 
 
 1.00006 
 
 0,1 
 
 O.OIIOO 
 
 IO,O 
 
 90.913 
 
 826,4 
 
 .OIII 
 
 .OHIO 
 
 
 .00006 
 
 
 .01110 
 
 
 90.094 
 
 811,6 
 
 .OII2 
 
 .OII2O 
 
 
 .00006 
 
 
 .OII20 
 
 
 89.289 
 
 797,2 
 
 .0113 
 
 .01130 
 
 
 .00006 
 
 
 .01130 
 
 
 88.499 
 
 783,1 
 
 .0114 
 
 .01140 
 
 
 .00006 
 
 
 .01140 
 
 
 87.723 
 
 769,4 
 
 0.0115 
 
 0.01150 
 
 IO,O 
 
 1.00007 
 
 0,1 
 
 0.01150 
 
 IO,0 
 
 86.960 
 
 756,1 
 
 .0116 
 
 .01100 
 
 
 .00007 
 
 
 .01160 
 
 
 86.211 
 
 743,1 
 
 .0117 
 
 .01170 
 
 
 .00007 
 
 
 .01170 
 
 
 85.474 
 
 730,5 
 
 .0118 
 
 .01180 
 
 
 .00007 
 
 
 .01180 
 
 
 84.750 
 
 718,2 
 
 .0119 
 
 .01190 
 
 
 .00007 
 
 
 .01190 
 
 
 84.038 
 
 706,1 
 
 O.OI2O 
 
 O.OI2OO 
 
 10,0 
 
 1.00007 
 
 0,1 
 
 O.OI2OO 
 
 10,0 
 
 83.337 
 
 694,4 
 
 .OI2I 
 
 .OI2IO 
 
 
 .00007 
 
 
 .OI2IO 
 
 
 82.649 
 
 683,0 
 
 .0122 
 
 .OI220 
 
 
 .00007 
 
 
 .01220 
 
 
 81.971 
 
 671,8 
 
 .OI23 
 
 .01230 
 
 
 .00008 
 
 
 .01230 
 
 
 81.305 
 
 660,9 
 
 .0124 
 
 .01240 
 
 
 .00008 
 
 
 .01240 
 
 
 80.649 
 
 650,3 
 
 0.0125 
 
 O.OI25O 
 
 IO,O 
 
 1.00008 
 
 0,1 
 
 0.01250 
 
 IO,O 
 
 80.004 
 
 640,0 
 
 .OI26 
 
 .OI26O 
 
 
 .00008 
 
 
 .01260 
 
 
 79.369 
 
 629,8 
 
 .OI27 
 
 .OI270 
 
 
 .00008 
 
 
 .01270 
 
 
 78.744 
 
 620,0 
 
 .0128 
 
 .OI28O 
 
 
 .00008 
 
 
 .01280 
 
 
 78.129 
 
 6 10,3 
 
 .OI29 
 
 .OI20O 
 
 
 .00008 
 
 
 .01290 
 
 
 77.524 
 
 600,9 
 
 O.OI3O 
 
 O.OI3OO 
 
 IO,O 
 
 1.00008 
 
 O,I 
 
 0.01300 
 
 10,0 
 
 76.927 
 
 591,7 
 
 .0131 
 
 .01310 
 
 
 .00009 
 
 
 .01310 
 
 
 76.340 
 
 582,7 
 
 .0132 
 
 .OI32O 
 
 
 .00009 
 
 
 .01320 
 
 
 75.762 
 
 573,9 
 
 0133 
 
 .01330 
 
 
 .00009 
 
 
 .01330 
 
 
 75.192 
 
 565,3 
 
 .0134 
 
 .01340 
 
 
 .00009 
 
 
 .01340 
 
 
 74.631 
 
 556,9 
 
 0.0135 
 
 0.01350 
 
 10,0 
 
 1.00009 
 
 0,1 
 
 0.01350 
 
 IO,O 
 
 74.079 
 
 548,7 
 
 .0136 
 
 .01360 
 
 
 .00009 
 
 
 .01360 
 
 
 73.534 
 
 540,6 
 
 .0137 
 
 .01370 
 
 
 .00009 
 
 
 .01370 
 
 
 72.997 
 
 532,8 
 
 .0138 
 
 .01380 
 
 
 .00010 
 
 
 .01380 
 
 
 72.468 
 
 525,1 
 
 .0139 
 
 .01390 
 
 
 .00010 
 
 
 .01390 
 
 
 71.947 
 
 517,5 
 
 O.OI4O 
 
 O.OI4OO 
 
 IO,O 
 
 I.OOOIO 
 
 0,1 
 
 0.01400 
 
 IO,O 
 
 71.433 
 
 510,2 
 
 .0141 
 
 .OI4IO 
 
 
 .00010 
 
 
 .01410 
 
 
 70.927 
 
 503,0 
 
 .OI42 
 
 .OI42O 
 
 
 .00010 
 
 
 .01420 
 
 
 70.427 
 
 495,9 
 
 .0143 
 
 .01430 
 
 
 .00010 
 
 
 .01430 
 
 
 69.935 
 
 489,0 
 
 .0144 
 
 .01440 
 
 
 .00010 
 
 
 .01440 
 
 
 69.449 
 
 482,2 
 
 0.0145 
 
 O.OI45O 
 
 10,0 
 
 I.OOOII 
 
 0,1 
 
 0.01450 
 
 IO,0 
 
 68.970 
 
 475,6 
 
 .0146 
 
 .01460 
 
 
 .OOOII 
 
 
 .01460 
 
 
 68.498 
 
 469,1 
 
 .0147 
 
 .01470 
 
 
 .OOOII 
 
 
 .01470 
 
 
 68.032 
 
 462,7 
 
 .0148 
 
 .01480 
 
 
 .OOOII 
 
 
 .01480 
 
 
 67.573 
 
 456,5 
 
 .0149 
 
 .01400 
 
 
 .OOOII 
 
 
 .01490 
 
 
 67.119 
 
 450,4 
 
 0.0150 
 
 O.OI5OO 
 
 10,0 
 
 I.OOOII 
 
 0,2 
 
 0.01500 
 
 IO,0 
 
 66.672 
 
 444,4 
 
 U 
 
 tan gd u 
 
 Fo' 
 
 sec gd u 
 
 Fo' 
 
 sin gd u 
 
 Fo' 
 
 csc gd u 
 
 - Fo' 
 
 SMITHSONIAN TABLES 
 
 90 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinh u 
 
 u>F ' 
 
 COSh u 
 
 Fo' 
 
 tanh u 
 
 - Fo' 
 
 coth u 
 
 Fo' 
 
 0.0150 
 
 .CISCO 
 
 IO,O 
 
 I.OOOII 
 
 0,2 
 
 0.01500 
 
 10,0 
 
 66.672 
 
 4444 
 
 .0151 
 
 .01510 
 
 
 .OOOII 
 
 
 .01510 
 
 
 66.230 
 
 438,5 
 
 .0152 
 
 .OI52O 
 
 
 .00012 
 
 
 .01520 
 
 
 65.795 
 
 432,8 
 
 .0153 
 
 .01530 
 
 
 .00012 
 
 
 .01530 
 
 
 65.365 
 
 427,2 
 
 .0154 
 
 .01540 
 
 
 .00012 
 
 
 .01540 
 
 
 64.940 
 
 421,6 
 
 0.0155 
 
 0.01550 
 
 IO,0 
 
 I.OOOI2 
 
 0,2 
 
 O.OI55O 
 
 10,0 
 
 .64.521 
 
 416,2 
 
 .0156 
 
 .01560 
 
 
 .00012 
 
 
 .01560 
 
 
 64.108 
 
 410,9 
 
 0157 
 
 .01570 
 
 
 .OOOI2 
 
 
 .01570 
 
 
 63.699 
 
 405,7 
 
 .0158 
 
 .01580 
 
 
 .OOOI2 
 
 
 .01580 
 
 
 63.296 
 
 400,5 
 
 .0159 
 
 .01590 
 
 
 .00013 
 
 
 .01590 
 
 
 62.898 
 
 395,5 
 
 0.0160 
 
 O.OI60O 
 
 IO,O 
 
 I.OOOI3 
 
 0,2 
 
 0,01000 
 
 10,0 
 
 62.505 
 
 390,6 
 
 .0161 
 
 .Ol6lO 
 
 
 .OOOI3 
 
 
 .Ol6lO 
 
 
 62.117 
 
 385,8 
 
 .0162 
 
 .01620 
 
 
 .00013 
 
 
 .01620 
 
 
 61.734 
 
 381,0 
 
 0163 
 
 .01630 
 
 
 .00013 
 
 
 .01630 
 
 
 61.355 
 
 376,3 
 
 .0164 
 
 .01640 
 
 
 .00013 
 
 
 .01640 
 
 
 60.981 
 
 37i3 
 
 0.0165 
 
 0.01650 
 
 IO,0 
 
 I.OOOI4 
 
 0,2 
 
 0.01650 
 
 10,0 
 
 60.612 
 
 367,3 
 
 .0166 
 
 .Ol66o 
 
 
 .00014 
 
 
 .01660 
 
 
 60.247 
 
 362,9 
 
 .0167 
 
 .01670 
 
 
 .OOOI4 
 
 
 .01670 
 
 
 59-886 
 
 358,5 
 
 .0168 
 
 .01680 
 
 
 .OOOI4 
 
 
 .01680 
 
 
 59-529 
 
 354,3 
 
 .0169 
 
 .01690 
 
 
 .00014 
 
 
 .01690 
 
 
 59-177 
 
 350,1 
 
 0.0170 
 
 O.OI70O 
 
 10,0 
 
 I.OOOI4 
 
 0,2 
 
 O.OI7OO 
 
 IO,O 
 
 58.829 
 
 346,0 
 
 .0171 
 
 .OI7IO 
 
 
 .00015 
 
 
 .01710 
 
 
 58.485 
 
 342,0 
 
 .0172 
 
 .OI72O 
 
 
 .00015 
 
 
 .01720 
 
 
 58.145 
 
 338,0 
 
 0173. 
 
 .01730 
 
 
 .00015 
 
 
 .01730 
 
 
 57.809 
 
 334,1 
 
 .0174 
 
 .OI74O 
 
 
 .00015 
 
 
 .01740 
 
 
 57.477 
 
 330,3 
 
 0.0175 
 
 O.OI75O 
 
 10,0 
 
 I.OOOI5 
 
 0,2 
 
 0.01750 
 
 IO,O 
 
 57.149 
 
 326,5 
 
 .0176 
 
 .01760 
 
 
 .00015 
 
 
 .01760 
 
 
 56.824 
 
 322,8 
 
 .0177 
 
 .01770 
 
 
 .00016 
 
 
 .01770 
 
 
 56.503 
 
 319,2 
 
 .0178 
 
 .01780 
 
 
 .00016 
 
 
 .01780 
 
 
 56.186 
 
 315,6 
 
 .0179 
 
 .01790 
 
 
 .OOOl6 
 
 
 .01790 
 
 
 55.872 
 
 312,1 
 
 0.0180 
 
 O.OlSoO 
 
 IO,O 
 
 I. OOOl6 
 
 0,2 
 
 O.OlSoo 
 
 IO,O 
 
 55 562 
 
 308,6 
 
 .0181 
 
 .OlSlO 
 
 
 .000l6 
 
 
 .OlSlO 
 
 
 55.255 
 
 305,2 
 
 .0182 
 
 .Ol82O 
 
 
 .00017 
 
 
 .01820 
 
 
 54.951 
 
 301,9 
 
 .0183 
 
 .01830 
 
 
 .00017 
 
 
 .01830 
 
 
 54-651 
 
 298,6 
 
 .0184 
 
 .01840 
 
 
 .00017 
 
 
 .01840 
 
 
 54-354 
 
 295,3 
 
 0.0185 
 
 O.OI85O 
 
 IO,O 
 
 I.OOOI7 
 
 O,2 
 
 0.01850 
 
 10,0 
 
 54.060 
 
 292,2 
 
 .0186 
 
 .01860 
 
 
 .00017 
 
 
 .01860 
 
 
 53.770 
 
 289,0 
 
 .0187 
 
 .01870 
 
 
 .OOOI7 
 
 
 .01870 
 
 
 53.482 
 
 285,9 
 
 .0188 
 
 .01880 
 
 
 .OOOlS 
 
 
 .01880 
 
 
 53.198 
 
 282,9 
 
 .0189 
 
 .01800 
 
 
 .00018 
 
 
 .01890 
 
 
 52.916 
 
 279,9 
 
 0.0190 
 
 0.01900 
 
 IO,O 
 
 I.OOOlS 
 
 0,2 
 
 0.01900 
 
 10,0 
 
 52.638 
 
 277,0 
 
 .0191 
 
 .OI9IO 
 
 
 .OOOlS 
 
 
 .01910 
 
 
 52.362 
 
 274,1 
 
 .0192 
 
 .OI92O 
 
 
 .OOOlS 
 
 
 .01920 
 
 
 52.090 
 
 271,2 
 
 .0193 
 
 .01930 
 
 
 .OOOI9 
 
 
 .01930 
 
 
 51.820 
 
 268,4 
 
 .0194 
 
 .OI94O 
 
 
 .00019 
 
 
 .01940 
 
 
 5L553 
 
 265,7 
 
 0.0195 
 
 O.OI95O 
 
 IO,0 
 
 I.OOOI9 
 
 0,2 
 
 0.01950 
 
 10,0 
 
 51.289 
 
 263,0 
 
 .0196 
 
 .01960 
 
 
 .00019 
 
 
 .01960 
 
 
 51.027 
 
 260,3 
 
 .0197 
 
 .OI97O 
 
 
 .00019 
 
 
 .01970 
 
 
 50.768 
 
 257,6 
 
 .0198 
 
 .01980 
 
 
 .OO02O 
 
 
 .01980 
 
 
 50.512 
 
 255,0 
 
 .0109 
 
 .01990 
 
 
 .OOO20 
 
 
 .01990 
 
 
 50.258 
 
 252,5 
 
 O.O2OO 
 
 O.O2OOO 
 
 IO,O 
 
 I.OOO2O 
 
 0,2 
 
 O.020OO 
 
 IO,O 
 
 50.007 
 
 250,0 
 
 U 
 
 tan gd u 
 
 Fo' 
 
 sec gd u 
 
 Fo' 
 
 sin gd u 
 
 Fo' 
 
 esc gd u 
 
 Fo' 
 
 SMITHSONIAN TABLES 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinh u 
 
 F ' 
 
 cosh u 
 
 oFo' 
 
 tanh u 
 
 Fo' 
 
 coth u 
 
 Fo' 
 
 O.O2OO 
 
 O.O20OO 
 
 IO,O 
 
 I.O0020 
 
 O,2 
 
 O.O20OO 
 
 IO,O 
 
 50.007 
 
 250,0 
 
 .0201 
 
 .02010 
 
 
 .00020 
 
 
 .O2OIO 
 
 
 49.758 
 
 247,5 
 
 .0202 
 
 .O2O2O 
 
 
 .OOO2O 
 
 
 .O2O2O 
 
 
 49.512 
 
 245,o 
 
 .0203 
 
 .0203O 
 
 
 .00021 
 
 
 .O2O3O 
 
 
 49.268 
 
 242,6 
 
 .02O4 
 
 .02040 
 
 
 .O002I 
 
 
 .02O40 
 
 
 49.026 
 
 240,3 
 
 O.O205 
 
 O.O2O50 
 
 IO,O 
 
 I.O002I 
 
 0,2 
 
 0.02O5O 
 
 IO,O 
 
 48.787 
 
 237,9 
 
 .0206 
 
 .02O6O 
 
 
 .O002I 
 
 
 .02000 
 
 
 48.551 
 
 235,6 
 
 .O207 
 
 .02O70 
 
 
 .00021 
 
 
 .02070 
 
 
 48.316 
 
 233,3 
 
 .0208 
 
 .O2O8O 
 
 
 .00022 
 
 
 .02080 
 
 
 48.084 
 
 231,1 
 
 .0209 
 
 .02000 
 
 
 .00022 
 
 
 .O2OOO 
 
 
 47.854 
 
 228,9 
 
 O.O2IO 
 
 O.O2IOO 
 
 IO,O 
 
 I.OOO22 
 
 0,2 
 
 O.O2IOO 
 
 10,0 
 
 47.626 
 
 226,7 
 
 .O2I I 
 
 .021 10 
 
 
 .OOO22 
 
 I 
 
 .021 10 
 
 
 47.400 
 
 224,6 
 
 .O2I2 
 
 .O2I2O 
 
 
 .OOO22 
 
 
 .02I2O 
 
 
 47.177 
 
 222,5 
 
 .0213 
 
 .02I3O 
 
 
 .00023 
 
 
 .02130 
 
 
 46.955 
 
 220,4 
 
 .O2I4 
 
 .O2I4O 
 
 
 .OOO23 
 
 
 .02I4O 
 
 
 46.736 
 
 218,3 
 
 0.0215 
 
 0.02150 
 
 10,0 
 
 I.O0023 
 
 0,2 
 
 0.02150 
 
 IO,O 
 
 46.519 
 
 216,3 
 
 .0216 
 
 .02100 
 
 
 .00023 
 
 
 .02100 
 
 
 46.303 
 
 214,3 
 
 .O2I7 
 
 .02170 
 
 
 .00024 
 
 
 .02170 
 
 
 46.090 
 
 212,3 
 
 .0218 
 
 .02180 
 
 
 .00024 
 
 
 .O2l8o 
 
 
 45.879 
 
 210,4 
 
 .O2I9 
 
 .02190 
 
 
 .OOO24 
 
 
 .O2IOX) 
 
 
 45-669 
 
 208,5 
 
 O.O22O 
 
 O.O22OO 
 
 IO,O 
 
 I.OOO24 
 
 0,2 
 
 O.O22OO 
 
 IO,O 
 
 45.462 
 
 206,6 
 
 .O22I 
 
 .022IO 
 
 
 .OOO24 
 
 
 .02210 
 
 
 45.256 
 
 204,7 
 
 .O222 
 
 .O222O 
 
 
 .OOO25 
 
 
 .O222O 
 
 
 45.052 
 
 202,9 
 
 .O223 
 
 .0223O 
 
 
 .00025 
 
 
 .0223O 
 
 
 44.850 
 
 2OI,I 
 
 .O224 
 
 .O224O 
 
 
 .00025 
 
 
 .O224O 
 
 
 44.650 
 
 199,3 
 
 0.0225 
 
 0.02250 
 
 10,0 
 
 I.OOO25 
 
 0,2 
 
 O.O225O 
 
 10,0 
 
 44.452 
 
 197,5 
 
 .O226 
 
 .O226O 
 
 
 .OOO26 
 
 
 .O226O 
 
 
 44.255 
 
 195,7 
 
 .O227 
 
 .O227O 
 
 
 .00026 
 
 
 .02270 
 
 
 44.060 
 
 194,0 
 
 .0228 
 
 .O228O 
 
 
 .OOO26 
 
 
 .02280 
 
 
 43.867 
 
 192,3 
 
 .O229 
 
 .02290 
 
 
 .OOO26 
 
 
 .02290 
 
 
 43.676 
 
 190,7 
 
 O.O23O 
 
 0.02300 
 
 10,0 
 
 1.00026 
 
 0,2 
 
 O.O23OO 
 
 IO,O 
 
 43.486 
 
 189,0 
 
 .O23I 
 
 .O23IO 
 
 
 .00027 
 
 
 .O23IO 
 
 
 43.298 
 
 187,4 
 
 .O232 
 
 .O232O 
 
 
 .OOO27 
 
 
 .0232O 
 
 
 43.111 
 
 185,8 
 
 .0233 
 
 .02330 
 
 
 .OOO27 
 
 
 .02330 
 
 
 42.926 
 
 184,2 
 
 .0234 
 
 .02340 
 
 
 .00027 
 
 
 .02340 
 
 
 42.743 
 
 182,6 
 
 0.0235 
 
 0.02350 
 
 IO,O 
 
 I.OO028 
 
 0,2 
 
 0.02350 
 
 10,0 
 
 42.561 
 
 181,1 
 
 .0236 
 
 .02360 
 
 
 .OOO28 
 
 
 .02360 
 
 
 42.381 
 
 179,5 
 
 .0237 
 
 .02370 
 
 
 .OO028 
 
 
 .02370 
 
 
 42.202 
 
 178,0 
 
 .0238 
 
 .02380 
 
 
 .00028 
 
 
 .02380 
 
 
 42.025 
 
 176,5 
 
 .0239 
 
 .023yO 
 
 
 .00029 
 
 
 .02300 
 
 
 41.849 
 
 175,0 
 
 O.O24O 
 
 0.02400 
 
 10,0 
 
 I.OOO29 
 
 0,2 
 
 0.02400 
 
 10,0 
 
 41.675 
 
 173,6 
 
 .0241 
 
 .O24IO 
 
 
 .OOO29 
 
 
 .O24IO 
 
 
 41.502 
 
 172,1 
 
 .O242 
 
 .O2420 
 
 
 .00029 
 
 
 .02420 
 
 
 41.330 
 
 170,7 
 
 .0243 
 
 .02430 
 
 
 .00030 
 
 
 .02430 
 
 
 41.160 
 
 169,3 
 
 .0244 
 
 .02440 
 
 
 .OOO3O 
 
 
 .02440 
 
 
 40.992 
 
 167,9 
 
 0.0245 
 
 O.O245O 
 
 10,0 
 
 1.00030 
 
 0,2 
 
 O.O2450 
 
 IO,O 
 
 40.824 
 
 166,6 
 
 .0246 
 
 .02460 
 
 
 .00030 
 
 
 .02400 
 
 
 40.659 
 
 165,2 
 
 .0247 
 
 .02470 
 
 
 .00031 
 
 
 .02469 
 
 
 40.494 
 
 163,9 
 
 .0248 
 
 .02480 
 
 
 .00031 
 
 
 .02479 
 
 
 40.331 
 
 162,6 
 
 .0249 
 
 .02400 
 
 
 .OOO3I 
 
 
 .02489 
 
 
 40.169 
 
 161,3 
 
 0.0250 
 
 O.O25OO 
 
 IO,O 
 
 I.0003I 
 
 0,3 
 
 O.02499 
 
 10,0 
 
 40.008 
 
 160,0 
 
 u 
 
 tin gd u 
 
 - Fo' 
 
 sec gd u 
 
 Fo' 
 
 sin gd u ... F ' 
 
 csc gd u 
 
 - Fo' 
 
 SMITHSONIAN TABLE* 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinh u 
 
 F O ' 
 
 cosh u 
 
 F ' 
 
 tanh u 
 
 Fo' 
 
 coin u 
 
 Fo' 
 
 0.0250 
 
 O.O25OO 
 
 IO,O 
 
 I.OOO3I 
 
 0,3 
 
 0.02499 
 
 10,0 
 
 40.008 
 
 160,0 
 
 .0251 
 
 .02510 
 
 
 .OOO32 
 
 
 .02509 
 
 
 39.849 
 
 158,7 
 
 .0252 
 
 .02520 
 
 
 .OOO32 
 
 
 .02519 
 
 
 39.691 
 
 157,4 
 
 .0253 
 
 .02530 
 
 
 .O0032 
 
 
 .02529 
 
 
 39.534 
 
 156,2 
 
 .0254 
 
 .02540 
 
 
 .OOO32 
 
 
 02539 
 
 
 39.379 
 
 155,0 
 
 0.0255 
 
 O.O255O 
 
 10,0 
 
 1.00033 
 
 0,3 
 
 0.02549 
 
 IO,O 
 
 39.224 
 
 153,8 
 
 .0256 
 
 .02560 
 
 
 .00033 
 
 
 .02559 
 
 
 39.071 
 
 152,6 
 
 .0257 
 
 .02570 
 
 
 .00033 
 
 
 .02569 
 
 
 38.919 
 
 i5i,4 
 
 .0258 
 
 .02580 
 
 
 .00033 
 
 
 .02579 
 
 
 38.768 
 
 . 150,2 
 
 .0259 
 
 .02590 
 
 
 .00034 
 
 
 .02589 
 
 
 38.619 
 
 149,0 
 
 0.0260 
 
 0.02600 
 
 10,0 
 
 1.00034 
 
 0,3 
 
 0.02599 
 
 10,0 
 
 38.470 
 
 147,9 
 
 .0261 
 
 .026lO 
 
 
 .00034 
 
 
 .02609 
 
 
 38.323 
 
 146,8 
 
 .0262 
 
 .O262O 
 
 
 .00034 
 
 
 .02619 
 
 
 38.177 
 
 145,7 
 
 .0263 
 
 .02630 
 
 
 .00035 
 
 
 .02629 
 
 
 38.032 
 
 144,5 
 
 .0264 
 
 .02640 
 
 
 .00035 
 
 
 .02639 
 
 
 37-888 
 
 143,4 
 
 0.0265 
 
 0.02650 
 
 IO,O 
 
 1.00035 
 
 0,3 
 
 0.02649 
 
 IO,O 
 
 37.745 
 
 142,4 
 
 .0266 
 
 .02660 
 
 
 .00035 
 
 
 .02659 
 
 
 37.603 
 
 I4i,3 
 
 .0267 
 
 .02670 
 
 
 .00036 
 
 
 .02669 
 
 
 37.462 
 
 140,2 
 
 .0268 
 
 .02680 
 
 
 .00036 
 
 
 .02679 
 
 
 37.322 
 
 139,2 
 
 .0269 
 
 .02690 
 
 
 .00036 
 
 
 .02689 
 
 
 37.184 
 
 138,2 
 
 0.0270 
 
 O.O27OO 
 
 IO,O 
 
 1.00036 
 
 0,3 
 
 0.02699 
 
 IO,O 
 
 37.046 
 
 137,1 
 
 .0271 
 
 .O27IO 
 
 
 .00037 
 
 
 .02709 
 
 
 36.909 
 
 136,1 
 
 .0272 
 
 .02720 
 
 
 .00037 
 
 
 .02719 
 
 
 36.774 
 
 135,1 
 
 .0273 
 
 .02730 
 
 
 .00037 
 
 
 .02729 
 
 
 36.639 
 
 134,1 
 
 .0274 
 
 .02740 
 
 
 .00038 
 
 
 .02739 
 
 
 36.505 
 
 133,2 
 
 0.0275 
 
 0.02750 
 
 IO,O 
 
 1.00038 
 
 0,3 
 
 0.02749 
 
 10,0 
 
 36.373 
 
 132,2 
 
 .0276 
 
 .02760 
 
 
 .00038 
 
 
 .02759 
 
 
 36.241 
 
 131,2 
 
 .0277 
 
 .02770 
 
 
 .00038 
 
 
 .02769 
 
 
 36.110 
 
 130,3 
 
 .0278 
 
 .02780 
 
 
 .00039 
 
 
 .02779 
 
 
 35.980 
 
 129,4 
 
 .0279 
 
 .02790 
 
 
 .00039 
 
 
 .02789 
 
 
 35.852 
 
 128,4 
 
 0.0280 
 
 O.O28OO 
 
 IO,O 
 
 1.00039 
 
 0,3 
 
 0.02799 
 
 10,0 
 
 35.724 
 
 127,5 
 
 .0281 
 
 .O28lO 
 
 
 .00039 
 
 
 .02809 
 
 
 35.597 
 
 126,6 
 
 .0282 
 
 .O282O 
 
 
 .00040 
 
 
 .02819 
 
 
 35.470 
 
 125,7 
 
 .0283 
 
 .02830 
 
 
 .00040 
 
 
 .02829 
 
 
 35.345 
 
 124,8 
 
 .0284 
 
 .02840 
 
 
 .00040 
 
 
 .02839 
 
 
 35.221 
 
 124,0 
 
 0.0285 
 
 O.O285O 
 
 IO,O 
 
 1.00041 
 
 0,3 
 
 0.02849 
 
 10,0 
 
 35.097 
 
 123,2 
 
 .0286 
 
 .02860 
 
 
 .00041 
 
 
 .02859 
 
 
 34.975 
 
 122,2 
 
 .0287 
 
 .02870 
 
 
 .00041 
 
 
 .02869 
 
 
 34.853 
 
 121,4 
 
 .0288 
 
 .02880 
 
 
 .00041 
 
 
 .02879 
 
 
 34.732 
 
 120,5 
 
 .0289 
 
 .02890 
 
 
 .00042 
 
 
 .02889 
 
 
 34.612 
 
 H9,7 
 
 0.0290 
 
 O.O2OOO 
 
 IO,O 
 
 1.00042 
 
 0,3 
 
 0.02899 
 
 10,0 
 
 34.492 
 
 118,9 
 
 .0291 
 
 .O29IO 
 
 
 .00042 
 
 
 .02909 
 
 
 34.374 
 
 118,1 
 
 .0292 
 
 .0292O 
 
 
 .00043 
 
 
 .02919 
 
 
 34.256 
 
 117,2 
 
 .0293 
 
 .O293O 
 
 
 .00043 
 
 
 .02929 
 
 
 34.139 
 
 116,4 
 
 .0294 
 
 .02940 
 
 
 .00043 
 
 
 .02939 
 
 
 34.023 
 
 115,7 
 
 0.0295 
 
 0.02950 
 
 10,0 
 
 1.00044 
 
 0,3 
 
 0.02949 
 
 10,0 
 
 33.908 
 
 114,9 
 
 .0296 
 
 .02960 
 
 
 .00044 
 
 
 .02959 
 
 
 33.794 
 
 114,1 
 
 .0297 
 
 .O297O 
 
 
 .00044 
 
 
 .02969 
 
 
 33.680 
 
 H3,3 
 
 .0298 
 
 .02980 
 
 
 .00044 
 
 
 .02979 
 
 
 33.567 
 
 112,6 
 
 .0299 
 
 .02990 
 
 
 .00045 
 
 
 .02989 
 
 
 33.455 
 
 111,8 
 
 0.0300 
 
 0.03000 
 
 10,0 
 
 1.00045 
 
 0,3 
 
 0.02999 
 
 IO,O 
 
 33.343 
 
 in, i 
 
 u 
 
 tan gd u 
 
 <- Fo' 
 
 sec gd u 
 
 Fo' 
 
 sin gd u 
 
 Fo' 
 
 csc gd u 
 
 Fo' 
 
 SMITHSONIAN TABLES 
 
 93 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinh u 
 
 F</ 
 
 cosh u 
 
 Fo' 
 
 tanh u 
 
 Fo' 
 
 coth u 
 
 *> Fo' 
 
 0.0300 
 
 0.03000 
 
 10,0 
 
 1.00045 
 
 0,3 
 
 0.02999 
 
 10,0 
 
 33.343 
 
 III,I 
 
 .0301 
 
 .O30IO 
 
 
 .00045 
 
 
 .03009 
 
 
 33.233 
 
 1 10,3 
 
 .0302 
 
 .03020 
 
 
 .00046 
 
 
 .03019 
 
 
 33.123 
 
 109,6 
 
 .0303 
 
 .03030 
 
 
 .00046 
 
 
 .03029 
 
 
 33.013 
 
 108,9 
 
 .0304 
 
 .03040 
 
 
 .00046 
 
 
 .03039 
 
 
 32.905 
 
 108,2 
 
 0.0305 
 
 O.03O5O 
 
 IO,O 
 
 1.00047 
 
 0,3 
 
 0.03049 
 
 10,0 
 
 32.797 
 
 107,5 
 
 .0306 
 
 .03060 
 
 
 .00047 
 
 
 .03059 
 
 
 
 106,8 
 
 .0307 
 
 .03070 
 
 
 .00047 
 
 
 .03069 
 
 
 32 . 584 
 
 106,1 
 
 .0308 
 
 .03080 
 
 
 .00047 
 
 
 .03079 
 
 
 32.478 
 
 105,4 
 
 .0309 
 
 .03000 
 
 
 .00048 
 
 
 .03089 
 
 
 32.373 
 
 104,7 
 
 0.0310 
 
 0.03IOO 
 
 IO,O 
 
 1.00048 
 
 0,3 
 
 0.03099 
 
 IO,O 
 
 32.268 
 
 104,0 
 
 .0311 
 
 .O3III 
 
 
 .00048 
 
 
 .03109 
 
 
 32.165 
 
 103,4 
 
 .0312 
 
 .O3I2I 
 
 
 .00049 
 
 
 .03119 
 
 
 32.062 
 
 102,7 
 
 .0313 
 
 .03131 
 
 
 .00049 
 
 
 .03129 
 
 
 31.959 
 
 102,0 
 
 .0314 
 
 .03141 
 
 
 .00049 
 
 
 .03139 
 
 
 31.858 
 
 101,4 
 
 0.0315 
 
 0.03I5I 
 
 IO,O 
 
 1.00050 
 
 0,3 
 
 0.03149 
 
 10,0 
 
 31.757 
 
 100,7 
 
 .0316 
 
 .03161 
 
 
 .00050 
 
 
 .03159 
 
 
 31.656 
 
 IOO,I 
 
 .0317 
 
 .03171 
 
 
 .00050 
 
 
 .03169 
 
 
 31.556 
 
 99,5 
 
 .0318 
 
 .03181 
 
 
 .00051 
 
 
 .03179 
 
 
 31.457 
 
 98,9 
 
 .0319 
 
 .03191 
 
 
 .00051 
 
 
 .03189 
 
 
 31.359 
 
 98,2 
 
 0.0320 
 
 0.03201 
 
 10,0 
 
 1.00051 
 
 0,3 
 
 0.03199 
 
 IO,O 
 
 31.261 
 
 97,6 
 
 .0321 
 
 .03211 
 
 
 .00052 
 
 
 .03209 
 
 
 31.163 
 
 97,o 
 
 .0322 
 
 .03221 
 
 
 .00052 
 
 
 .03219 
 
 
 31.067 
 
 96,4 
 
 .0323 
 
 .03231 
 
 
 .00052 
 
 
 .03229 
 
 
 30.971 
 
 95,8 
 
 .0324 
 
 .03241 
 
 
 .00052 
 
 
 .03239 
 
 
 30.875 
 
 95,2 
 
 0.0325 
 
 O.O325I 
 
 IO,O 
 
 1.00053 
 
 0,3 
 
 0.03249 
 
 IO,O 
 
 30.780 
 
 94,6 
 
 .0326 
 
 .03261 
 
 
 .00053 
 
 
 .03259 
 
 
 30.686 
 
 94,1 
 
 .0327 
 
 .03271 
 
 
 .00053 
 
 
 .03269 
 
 
 30.592 
 
 93,5 
 
 .0328 
 
 .03281 
 
 
 .00054 
 
 
 .03279 
 
 
 30.499 
 
 92,9 
 
 .0329 
 
 .03291 
 
 
 .00054 
 
 
 .03289 
 
 
 30.406 
 
 92,4 
 
 0.0330 
 
 0.03301 
 
 IO,O 
 
 1.00054 
 
 0,3 
 
 0.03299 
 
 10,0 
 
 30.314 
 
 9i,8 
 
 .0331 
 
 .03311 
 
 
 .00055 
 
 
 .03309 
 
 
 30.223 
 
 91,2 
 
 .0332 
 
 .03321 
 
 
 .00055 
 
 
 .03319 
 
 
 30.132 
 
 90,7 
 
 .0333 
 
 .03331 
 
 
 .00055 
 
 
 .03329 
 
 
 30.041 
 
 90,1 
 
 0334 
 
 .03341 
 
 
 .00056 
 
 
 03339 
 
 
 29.951 
 
 89,6 
 
 0.0335 
 
 0.03351 
 
 IO,O 
 
 1.00056 
 
 0,3 
 
 0.03349 
 
 IO,O 
 
 29.862 
 
 89,1 
 
 .0336 
 
 .03361 
 
 
 .00056 
 
 
 03359 
 
 
 29.773 
 
 88,5 
 
 0337 
 
 03371 
 
 
 .00057 
 
 
 .03369 
 
 
 29.685 
 
 88,0 
 
 .0338 
 
 03381 
 
 
 .00057 
 
 
 03379 
 
 
 29.597 
 
 87,5 
 
 .0339 
 
 .03391 
 
 
 .00057 
 
 
 .03389 
 
 
 29.510 
 
 87,0 
 
 0.0340 
 
 O.O34OI 
 
 IO,O 
 
 1.00058 
 
 0,3 
 
 0.03399 
 
 IO,O 
 
 29.423 
 
 86,6 
 
 .0341 
 
 .034H 
 
 
 .00058 
 
 
 .03409 
 
 
 29.337 
 
 86,0 
 
 .0342 
 
 .03421 
 
 
 .00058 
 
 
 03419 
 
 
 29.251 
 
 85,5 
 
 .0343 
 
 03431 
 
 
 .00059 
 
 
 .03429 
 
 
 29.166 
 
 85,0 
 
 0344 
 
 .03441 
 
 
 .00059 
 
 
 03439 
 
 
 29.081 
 
 84,5 
 
 0.0345 
 
 0.03451 
 
 10,0 
 
 1.00060 
 
 0,3 
 
 0.03449 
 
 IO,O 
 
 28.997 
 
 84,0 
 
 .0346 
 
 .03461 
 
 
 .00060 
 
 
 .03459 
 
 
 28.913 
 
 83,5 
 
 0347 
 
 .03471 
 
 
 .00060 
 
 
 .03469 
 
 
 28.830 
 
 83,0 
 
 .0348 
 
 .03481 
 
 
 .00061 
 
 
 .03479 
 
 
 28.747 
 
 82.5 
 
 .0349 
 
 .03491 
 
 
 .00061 
 
 
 .03489 
 
 
 28.665 
 
 82,1 
 
 0.0350 
 
 O.O35OI 
 
 10,0 
 
 i. 00061 
 
 0,4 
 
 0.03499 
 
 1 0,0 
 
 28.583 
 
 81,6 
 
 u 
 
 tan gd u 
 
 Fo' 
 
 sec gd u 
 
 Fo' 
 
 sin gd u 
 
 Fo' 
 
 csc gd u 
 
 - Fo' 
 
 SMITHSONIAN TABLES 
 
 94 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinh u 
 
 Fo' 
 
 cosh u 
 
 "Fo' 
 
 tanh u 
 
 Fo' 
 
 colh u 
 
 Fo' 
 
 0.0350 
 
 0.03501 
 
 IO,O 
 
 I. 00061 
 
 0,4 
 
 0.03499 
 
 IO,O 
 
 28.583 
 
 81,6 
 
 0351 
 
 .03511 
 
 
 .00062 
 
 
 .03509 
 
 
 28.502 
 
 81,1 
 
 0352 
 
 .03521 
 
 
 .00062 
 
 
 .03519 
 
 
 28.421 
 
 80,7 
 
 .0353 
 
 .03531 
 
 
 .00062 
 
 
 .03529 
 
 
 28.340 
 
 80,2 
 
 .0354 
 
 .03541 
 
 
 .00063 
 
 
 03539 
 
 
 28.260 
 
 79,8 
 
 0.0355 
 
 \J+J*J 
 
 0.03551 
 
 10,0 
 
 1.00063 
 
 0,4 
 
 0.03549 
 
 IO,O 
 
 28.181 
 
 79,3 
 
 .0356 
 
 .03561 
 
 
 .00063 
 
 
 .03558 
 
 
 28.102 
 
 78,9 
 
 .0357 
 
 .03571 
 
 
 .00064 
 
 
 .03568 
 
 
 28.023 
 
 78,4 
 
 .0358 
 
 .03581 
 
 
 .00064 
 
 
 .03578 
 
 
 27.945 
 
 78,o 
 
 .0359 
 
 .03591 
 
 
 .00064 
 
 
 .03588 
 
 
 27.867 
 
 77,6 
 
 0.0360 
 
 0.03601 
 
 10,0 
 
 1.00065 
 
 0,4 
 
 0.03598 
 
 IO,O 
 
 27.790 
 
 77,i 
 
 .0361 
 
 .03611 
 
 
 .00065 
 
 
 .03608 
 
 
 27.713 
 
 76,7 
 
 .0362 
 
 .03621 
 
 
 .00066 
 
 
 .03618 
 
 
 27.636 
 
 76,3 
 
 .0363 
 
 .03631 
 
 
 .00066 
 
 
 .03628 
 
 
 27.560 
 
 75,9 
 
 .0364 
 
 .03641 
 
 
 .00066 
 
 
 .03638 
 
 
 27.485 
 
 75,4 
 
 0.0365 
 
 0.03651 
 
 10,0 
 
 1.00067 
 
 0,4 
 
 0.03648 
 
 10,0 
 
 27.409 
 
 75,0 
 
 .0366 
 
 .03661 
 
 
 .00067 
 
 
 .03658 
 
 
 27.335 
 
 74,6 
 
 .0367 
 
 .03671 
 
 
 .00067 
 
 
 .03668 
 
 
 27.260 
 
 74,2 
 
 .0368 
 
 .03681 
 
 
 .00068 
 
 
 .03678 
 
 
 27.186 
 
 73,8 
 
 .0369 
 
 .03691 
 
 
 .00068 
 
 
 .03688 
 
 
 27.113 
 
 73,4 
 
 0.0370 
 
 0.03701 
 
 10,0 
 
 1.00068 
 
 0,4 
 
 0.03698 
 
 IO,O 
 
 27.039 
 
 73,0 
 
 .0371 
 
 .03711 
 
 
 .00069 
 
 
 .03708 
 
 
 26.067 
 
 72,6 
 
 .0372 
 
 .03721 
 
 
 .00069 
 
 
 .03718 
 
 
 26.894 
 
 72,2 
 
 .0373 
 
 .03731 
 
 
 .00070 
 
 
 .03728 
 
 
 26.822 
 
 7i,8 
 
 0374 
 
 .03741 
 
 
 .00070 
 
 
 .03738 
 
 
 26.750 
 
 7i,5 
 
 0.0375 
 
 0.03751 
 
 10,0 
 
 1.00070 
 
 0,4 
 
 0.03748 
 
 IO,O 
 
 26.679 
 
 7i,i 
 
 .0376 
 
 .03761 
 
 
 .00071 
 
 
 .03758 
 
 
 26.608 
 
 70,7 
 
 .03/7 
 
 03771 
 
 
 .00071 
 
 
 .03768 
 
 
 26.538 
 
 70,3 
 
 .0378 
 
 .03781 
 
 
 .00071 
 
 
 .03778 
 
 
 26.468 
 
 70,0 
 
 0379 
 
 .03791 
 
 
 .00072 
 
 
 .03788 
 
 
 26.398 
 
 69,6 
 
 0.0380 
 
 0.03801 
 
 IO,O 
 
 1.00072 
 
 0,4 
 
 0.03798 
 
 10,0 
 
 26.328 
 
 69,2 
 
 .0381 
 
 .03811 
 
 
 .00073 
 
 
 .03808 
 
 
 26.259 
 
 68,9 
 
 .0382 
 
 .03821 
 
 
 .00073 
 
 
 .03818 
 
 
 26.191 
 
 68,5 
 
 .0383 
 
 .03831 
 
 
 .00073 
 
 
 .03828 
 
 
 26.122 
 
 68,1 
 
 .0384 
 
 .03841 
 
 
 .00074 
 
 
 .03838 
 
 
 26.054 
 
 67,8 
 
 0.0385 
 
 0.03851 
 
 10,0 
 
 1.00074 
 
 0,4 
 
 0.03848 
 
 10,0 
 
 25.987 
 
 67,4 
 
 .0386 
 
 .03861 
 
 
 .00075 
 
 
 .03858 
 
 
 25.920 
 
 67,1 
 
 .0387 
 
 .03871 
 
 
 .00075 
 
 
 .03868 
 
 
 25.853 
 
 66,7 
 
 .0388 
 
 .03881 
 
 
 .00075 
 
 
 .03878 
 
 
 25.786 
 
 66,4 
 
 .0389 
 
 .03891 
 
 
 .00076 
 
 
 .03888 
 
 
 25.720 
 
 66,1 
 
 0.0300 
 
 O.0390I 
 
 10,0 
 
 1.00076 
 
 0,4 
 
 0.03898 
 
 10,0 
 
 25.654 
 
 65,7 
 
 .0391 
 
 .039H 
 
 
 .00076 
 
 
 .03908 
 
 
 25.588 
 
 65,4 
 
 .0392 
 
 .03921 
 
 
 .00077 
 
 
 .03918 
 
 
 25.523 
 
 64,0 
 
 0393 
 
 .03931 
 
 
 .00077 
 
 
 .03928 
 
 
 25.458 
 
 64,7 
 
 0394 
 
 .03941 
 
 
 .00078 
 
 
 .03938 
 
 
 25.394 
 
 64,4 
 
 0.0395 
 
 0.03951 
 
 IO,0 
 
 1.00078 
 
 0,4 
 
 0.03948 
 
 10,0 
 
 25.330 
 
 64,1 
 
 .0306 
 
 .03061 
 
 
 .00078 
 
 
 .03958 
 
 
 25.266 
 
 63,7 
 
 .0397 
 
 .03971 
 
 
 .00079 
 
 
 .03968 
 
 
 25.202 
 
 63,4 
 
 .0398 
 
 .03981 
 
 
 .00079 
 
 
 .03978 
 
 
 25 . 139 
 
 63,1 
 
 0399 
 
 .03991 
 
 
 .00080 
 
 
 .03988 
 
 
 25.076 
 
 62,8 
 
 0.0400 
 
 O.O4OOI 
 
 IO,0 
 
 1.00080 
 
 0,4 
 
 0.03998 
 
 10,0 
 
 25.013 
 
 62,5 
 
 u tan gd u 
 
 F O ' 
 
 sec gd u 
 
 Fo' 
 
 sin gd u 
 
 Fo' 
 
 csc gd u 
 
 - Fo' 
 
 I 
 
 
 
 
 
 
 
 SMITHSONIAN TABLES 
 
 95 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinh u 
 
 Fo' 
 
 COSh u 
 
 wF ' 
 
 tanh u 
 
 - Fo' 
 
 coth u 
 
 Fo' 
 
 0.0400 
 
 O.O4OOI 
 
 10,0 
 
 1.00080 
 
 0,4 
 
 0.03998 
 
 10,0 
 
 25.013 
 
 62,5 
 
 .0401 
 
 .04011 
 
 
 .00080 
 
 
 .04008 
 
 
 24.951 
 
 62,2 
 
 .0402 
 
 .04021 
 
 
 .00081 
 
 
 .04018 
 
 
 24.889 
 
 61,8 
 
 .0403 
 
 .04031 
 
 
 .OOoSi 
 
 
 .04028 
 
 
 24.827 
 
 61,5 
 
 .0404 
 
 .04041 
 
 
 .00082 
 
 
 .04038 
 
 
 24.766 
 
 61,2 
 
 0.0405 
 
 0.04051 
 
 IO,O 
 
 I.OOO82 
 
 0,4 
 
 0.04048 
 
 IO,O 
 
 24.705 
 
 60,8 
 
 .0406 
 
 .04061 
 
 
 .00082 
 
 
 .04058 
 
 
 24.644 
 
 60,6 
 
 .0407 
 
 .04071 
 
 
 .00083 
 
 
 .04068 
 
 
 24.584 
 
 60,3 
 
 .0408 
 
 .04081 
 
 
 .00083 
 
 
 .04078 
 
 
 24.523 
 
 60,0 
 
 .0409 
 
 .04091 
 
 
 .00084 
 
 
 .04088 
 
 
 24.464 
 
 59,7 
 
 0.0410 
 
 O.O4IOI 
 
 IO,O 
 
 1.00084 
 
 0,4 
 
 0.04098 
 
 IO,O 
 
 24.404 
 
 59,5 
 
 .0411 
 
 .04111 
 
 
 .00084 
 
 
 .04108 
 
 
 24.345 
 
 59,2 
 
 .0412 
 
 .04121 
 
 
 .00085 
 
 
 .04118 
 
 
 24.286 
 
 58,9 
 
 .0413 
 
 .04131 
 
 
 .00085 
 
 
 .04128 
 
 
 24.227 
 
 58,7 
 
 .0414 
 
 .04141 
 
 
 .00086 
 
 
 .04138 
 
 
 24.168 
 
 58,3 
 
 0.0415 
 
 0.04151 
 
 IO,O 
 
 1.00086 
 
 0,4 
 
 0.04148 
 
 10,0 
 
 24.IIO 
 
 58,0 
 
 .0416 
 
 .04161 
 
 
 .00087 
 
 
 .04158 
 
 
 24.052 
 
 57,8 
 
 .0417 
 
 .04171 
 
 
 .00087 
 
 
 .04168 
 
 
 23.995 
 
 57,5 
 
 .0418 
 
 .04181 
 
 
 .00087 
 
 
 .04178 
 
 
 23.937 
 
 57,2 
 
 .0419 
 
 .04191 
 
 
 .00088 
 
 
 .04188 
 
 
 23.880 
 
 56,9 
 
 0.0420 
 
 0.04201 
 
 10,0- 
 
 1.00088 
 
 0,4 
 
 0.04198 
 
 IO,O 
 
 23.824 
 
 56,7 
 
 .0421 
 
 .04211 
 
 
 .00089 
 
 
 .04208 
 
 
 23.767 
 
 56,4 
 
 .0422 
 
 .04221 
 
 
 .00089 
 
 
 .04217 
 
 
 23.7H 
 
 56,i 
 
 .0423 
 
 .04231 
 
 
 .00089 
 
 
 .04227 
 
 
 23.655 
 
 55,9 
 
 .0424 
 
 .04241 
 
 
 .00090 
 
 
 .04237 
 
 
 23.599 
 
 55,6 
 
 0.0425 
 
 0.04251 
 
 IO,O 
 
 I.OOOOO 
 
 0,4 
 
 0.04247 
 
 IO,O 
 
 23.544 
 
 55,3 
 
 .0426 
 
 .04261 
 
 
 .00091 
 
 
 .04257 
 
 
 23-488 
 
 55,1 
 
 .0427 
 
 .04271 
 
 
 .00091 
 
 
 .04267 
 
 
 23-433 
 
 54,8 
 
 .0428 
 
 .04281 
 
 
 .00092 
 
 
 .04277 
 
 
 23.379 
 
 54,6 
 
 .0429 
 
 .04291 
 
 
 .00092 
 
 
 .04287 
 
 
 23.324 
 
 54,3 
 
 0.0430 
 
 0.04301 
 
 10,0 
 
 1.00092 
 
 0,4 
 
 0.04297 
 
 10,0 
 
 23.270 
 
 54,0 
 
 .0431 
 
 .043H 
 
 
 .00093 
 
 
 .04307 
 
 
 23.216 
 
 53,8 
 
 .0432 
 
 .04321 
 
 
 .00093 
 
 
 .04317 
 
 
 23-163 
 
 53,6 
 
 .0433 
 
 .04331 
 
 
 .00094 
 
 
 .04327 
 
 
 23.109 
 
 53,3 
 
 .0434 
 
 .04341 
 
 
 .00094 
 
 
 04337 
 
 
 23.056 
 
 53,1 
 
 0.0435 
 
 0.04351 
 
 IO,O 
 
 1.00095 
 
 0,4 
 
 0.04347 
 
 10,0 . 
 
 23.003 
 
 52,8 
 
 .0436 
 
 .04361 
 
 
 .00095 
 
 
 .04357 
 
 
 22.95O 
 
 52,6 
 
 .0437 
 
 .04371 
 
 
 .00095 
 
 
 .04367 
 
 
 22.898 
 
 52,3 
 
 .0438 
 
 .04381 
 
 
 .00096 
 
 
 04377 
 
 
 22.846 
 
 52,i 
 
 .0439 
 
 .04391 
 
 
 .00096 
 
 
 .04387 
 
 
 22.794 
 
 5i,9 
 
 0.0440 
 
 0.04401 
 
 IO,0 
 
 1.00097 
 
 0,4 
 
 0.04397 
 
 IO,O 
 
 22.742 
 
 5i,6 
 
 .0441 
 
 .04411 
 
 
 .00097 
 
 
 .04407 
 
 
 22.690 
 
 51,4 
 
 .0442 
 
 .04421 
 
 
 .00098 
 
 
 .04417 
 
 
 22.639 
 
 51,2 
 
 0443 
 
 .04431 
 
 
 .00008 
 
 
 .04427 
 
 
 22.588 
 
 50,9 
 
 .0444 
 
 .04441 
 
 
 .00099 
 
 
 .04437 
 
 
 22.537 
 
 50,7 
 
 0.0445 
 
 0.04451 
 
 10,0 
 
 1.00099 
 
 0,4 
 
 0.04447 
 
 IO,O 
 
 22.487 
 
 50,5 
 
 .0446 
 
 .04461 
 
 
 .00099 
 
 
 04457 
 
 
 22.436 
 
 50,2 
 
 .0447 
 
 .04471 
 
 
 .00100 
 
 
 .04467 
 
 
 22.386 
 
 50,0 
 
 .0448 
 
 .04481 
 
 
 .00100 
 
 
 .04477 
 
 
 22.336 
 
 49,8 
 
 .0449 
 
 .04492 
 
 
 .OOIOI 
 
 
 .04487 
 
 
 22.287 
 
 49,6 
 
 0.0450 
 
 O.O4502 
 
 IO,O 
 
 I.OOIOI 
 
 0,5 
 
 0.04497 
 
 1 0,0 
 
 22.237 
 
 49,3 
 
 u 
 
 tan gd u 
 
 - Fo' 
 
 sec gd u 
 
 Fo' 
 
 sin gd u 
 
 Fo' 
 
 esc gd u - Fo' 
 
 SMITHSONIAN TABLES 
 
 96 
 
Natural Hyperbolic Functions. 
 
 u 
 
 tinh u 
 
 F ' 
 
 cosh u 
 
 F ' 
 
 tanh u 
 
 Fo' 
 
 COth u 
 
 Fo' 
 
 0.0450 
 
 O.O45O2 
 
 10,0 
 
 I.OOIOI 
 
 0,5 
 
 0.04497 
 
 10,0 
 
 22.237 
 
 49,3 
 
 .0451 
 
 .04512 
 
 
 .00102 
 
 
 .04507 
 
 
 22.188 
 
 49,1 
 
 .0452 
 
 .04522 
 
 
 .00102 
 
 
 .04517 
 
 
 22.139 
 
 48,9 
 
 .0453 
 
 .04532 
 
 
 .00103 
 
 
 .04527 
 
 
 22.OOO 
 
 48,7 
 
 .0454 
 
 .04542 
 
 
 .00103 
 
 
 .04537 
 
 
 22.042 
 
 48,5 
 
 0.0455 
 
 0.04552 
 
 10,0 
 
 1.00104 
 
 o,5 
 
 0.04547 
 
 10,0 
 
 21.993 
 
 48,3 
 
 .0456 
 
 .04562 
 
 
 .00104 
 
 
 .04557 
 
 
 21-945 
 
 48,1 
 
 .0457 
 
 .04572 
 
 
 .00104 
 
 
 .04567 
 
 
 21.897 
 
 47,8 
 
 .0458 
 
 .04582 
 
 
 .00105 
 
 
 04577 
 
 
 21.849 
 
 47,6 
 
 .0459 
 
 .04592 
 
 
 .00105 
 
 
 .04587 
 
 
 21.802 
 
 47,4 
 
 0.0460 
 
 0.04602 
 
 10,0 
 
 1.00106 
 
 o,5 
 
 0.04597 
 
 10,0 
 
 21.754 
 
 47,2 
 
 .0461 
 
 .04612 
 
 
 .00106 
 
 
 .04607 
 
 
 21.707 
 
 47,o 
 
 .0462 
 
 .04622 
 
 
 .00107 
 
 
 .04617 
 
 
 21.660 
 
 46,8 
 
 .0463 
 
 .04632 
 
 
 .00107 
 
 
 .04627 
 
 
 21.614 
 
 46,6 
 
 .0464 
 
 .04642 
 
 
 .00108 
 
 
 .04637 
 
 
 21.567 
 
 46,4 
 
 0.0465 
 
 0.04652 
 
 . 10,0 
 
 1.00108 
 
 o,5 
 
 0.04647 
 
 10,0 
 
 21.521 
 
 46,2 
 
 .0466 
 
 .04662 
 
 
 .00109 
 
 
 .04657 
 
 
 21.475 
 
 46,0 
 
 .0467 
 
 .04672 
 
 
 .00109 
 
 
 .04667 
 
 
 21.429 
 
 45,8 
 
 .0468 
 
 .04682 
 
 
 .OOIIO 
 
 
 .04677 
 
 
 21.383 
 
 45,6 
 
 .0469 
 
 .04692 
 
 
 .OOIIO 
 
 
 .04687 
 
 
 21.338 
 
 45,4 
 
 0.0470 
 
 0.04702 
 
 IO,0 
 
 I. OOIIO 
 
 o,5 
 
 0.04697 
 
 IO,O 
 
 21.292 
 
 45,2 
 
 .0471 
 
 .04712 
 
 
 .OOIII 
 
 
 .04707 
 
 
 21.247 
 
 45,o 
 
 .0472 
 
 .04722 
 
 
 .OOIII 
 
 
 .04716 
 
 
 21. 2O2 
 
 44,9 
 
 0473 
 
 .04732 
 
 
 .OOII2 
 
 
 .04726 
 
 
 21.157 
 
 44,7 
 
 .0474 
 
 .04742 
 
 
 .OOII2 
 
 
 .04736 
 
 
 21.113 
 
 44,5 
 
 0.0475 
 
 0.04752 
 
 10,0 
 
 1.00113 
 
 o,5 
 
 0.04746 
 
 IO,O 
 
 21.068 
 
 44,3 
 
 .0476 
 
 .04762 
 
 
 .00113 
 
 
 .04756 
 
 
 2I.O24 
 
 44,1 
 
 .0477 
 
 .04772 
 
 
 .00114 
 
 
 .04766 
 
 
 2O.O80 
 
 43,9 
 
 .0478 
 
 .04782 
 
 
 .00114 
 
 
 .04776 
 
 
 20.936 
 
 43,7 
 
 .0479 
 
 .04792 
 
 
 .00115 
 
 
 .04786 
 
 
 20.893 
 
 43,6 
 
 0.0480 
 
 0.04802 
 
 10,0 
 
 1.00115 
 
 o,5 
 
 0.04796 
 
 IO,O 
 
 20.849 
 
 43,4 
 
 .0481 
 
 .04812 
 
 
 .00116 
 
 
 .04806 
 
 
 20.806 
 
 43,2 
 
 .0482 
 
 .04822 
 
 
 .00116 
 
 
 .04816 
 
 
 20.763 
 
 43,0 
 
 .0483 
 
 .04832 
 
 
 .00117 
 
 
 .04826 
 
 
 20.720 
 
 42,8 
 
 .0484 
 
 .04842 
 
 
 .00117 
 
 
 .04836 
 
 
 20.677 
 
 42,7 
 
 0.0485 
 
 0.04852 
 
 10,0 
 
 I. 00118 
 
 o,5 
 
 0.04846 
 
 10,0 
 
 20.635 
 
 42,5 
 
 .0486 
 
 .04862 
 
 
 .00118 
 
 
 .04856 
 
 
 20.592 
 
 42,3 
 
 .0487 
 
 .04872 
 
 
 .00119 
 
 
 .04866 
 
 
 20.550 
 
 42,1 
 
 .0488 
 
 .04882 
 
 
 .00119 
 
 
 .04876 
 
 
 20.508 
 
 42,0 
 
 .0489 
 
 .04892 
 
 
 .00120 
 
 
 .04886 
 
 
 20.466 
 
 41,8 
 
 0.0490 
 
 0.04902 
 
 10,0 
 
 I. 00120 
 
 o,5 
 
 0.04896 
 
 10,0 
 
 2O.424 
 
 41,6 
 
 .0491 
 
 .04912 
 
 
 .00121 
 
 
 .04006 
 
 
 20.383 
 
 41,4 
 
 .0492 
 
 .04922 
 
 
 .00121 
 
 
 .04916 
 
 
 20.342 
 
 4i,3 
 
 .0493 
 
 .04932 
 
 
 .00122 
 
 
 .04926 
 
 
 20.300 
 
 41,1 
 
 .0494 
 
 .04942 
 
 
 .00122 
 
 
 .04936 
 
 
 20.259 
 
 40,9 
 
 0.0495 
 
 0.04952 
 
 10,0 
 
 I.OOI23 
 
 o,5 
 
 0.04946 
 
 10,0 
 
 2O.2I9 
 
 40,8 
 
 .0496 
 
 .04962 
 
 
 .00123 
 
 
 .04956 
 
 
 2O.I78 
 
 40,6 
 
 .0497 
 
 .04972 
 
 
 .00124 
 
 
 .04966 
 
 
 20.137 
 
 40,5 
 
 .0498 
 
 .04982 
 
 
 .00124 
 
 
 .04976 
 
 
 20.097 
 
 40,3 
 
 .0499 
 
 .04992 
 
 
 .00125 
 
 
 .04986 
 
 
 20.057 
 
 40,1 
 
 0.0500 
 
 O.O5OO2 
 
 IO,O 
 
 I.OOI25 
 
 o,5 
 
 0.04996 
 
 10,0 
 
 20.017 
 
 40,0 
 
 u 
 
 tan gd u 
 
 F ' 
 
 sec gd u 
 
 Fo' 
 
 sin gd u 
 
 Fo' 
 
 esc gd u 
 
 - Fo' 
 
 SMITHSONIAN TABLES 
 
 97 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinh u 
 
 Fo' 
 
 cosh u 
 
 F ' 
 
 tanh u 
 
 Fo' 
 
 coth u 
 
 Fo' 
 
 0.0500 
 
 O.O5OO2 
 
 IO,O 
 
 1.00125 
 
 0,5 
 
 0.04996 
 
 IO,O 
 
 20.017 
 
 4O,O 
 
 .0501 
 
 .O50I2 
 
 
 .00126 
 
 
 .05006 
 
 
 19-977 
 
 39,8 
 
 .0502 
 
 .O5O22 
 
 
 .00126 
 
 
 .05016 
 
 
 19-937 
 
 39,6 
 
 .0503 
 
 .05032 
 
 
 .00127 
 
 
 .05026 
 
 
 19.897 
 
 39,5 
 
 .0504 
 
 .05042 
 
 
 .00127 
 
 
 .05036 
 
 
 19.858 
 
 39,3 
 
 0.0505 
 
 0.05052 
 
 IO,O 
 
 1.00128 
 
 0,5 
 
 0.05046 
 
 IO,O 
 
 I9.8I9 
 
 39,2 
 
 .0506 
 
 .05062 
 
 
 .00128 
 
 
 .05056 
 
 
 19.780 
 
 39,0 
 
 .0507 
 
 .05072 
 
 
 .00129 
 
 
 .05066 
 
 
 19.741 
 
 38,9 
 
 .0508 
 
 .05082 
 
 
 .00129 
 
 
 .05076 
 
 
 19.702 
 
 38,7 
 
 .0509 
 
 .05092 
 
 
 .00130 
 
 
 .05086 
 
 
 19.663 
 
 38,6 
 
 0.0510 
 
 0.05102 
 
 IO,O 
 
 1.00130 
 
 0,5 
 
 0.05096 
 
 10,0 
 
 19.625 
 
 38,4 
 
 .0511 
 
 .05112 
 
 
 .00131 
 
 
 .05106 
 
 
 I9o87 
 
 38,3 
 
 .0512 
 
 .05122 
 
 
 .02131 
 
 
 .05116 
 
 
 19.548 
 
 38,1 
 
 .0513 
 
 .05132 
 
 
 .00132 
 
 
 .05126 
 
 
 I9.5IO 
 
 38,0 
 
 .0514 
 
 .05142 
 
 
 .00132 
 
 
 .05135 
 
 
 19.472 
 
 37,8 
 
 0.0515 
 
 O.O5I52 
 
 10,0 
 
 1.00133 
 
 0,5 
 
 0.05145 
 
 10,0 
 
 19.435 
 
 37,7 
 
 .0516 
 
 .05162 
 
 
 .00133 
 
 
 .05155 
 
 
 19-397 
 
 37,5 
 
 .0517 
 
 .05172 
 
 
 .00134 
 
 
 .05165 
 
 
 19.360 
 
 37,4 
 
 .0518 
 
 .05182 
 
 
 .00134 
 
 
 .05175 
 
 
 19.322 
 
 37,2 
 
 .0519 
 
 .05192 
 
 
 .00135 
 
 
 .05185 
 
 
 19.285 
 
 37,1 
 
 0.0520 
 
 0.05202 
 
 IO,O 
 
 1.00135 
 
 0,5 
 
 0.05195 
 
 IO,O 
 
 19.248 
 
 36,9 
 
 .0521 
 
 .05212 
 
 
 .00136 
 
 
 .05205 
 
 
 19.211 
 
 36,8 
 
 .0522 
 .0523 
 
 .05222 
 .05232 
 
 
 .00136 
 
 .00137 
 
 
 .05215 
 .05225 
 
 
 19.174 
 19.138 
 
 36,7 
 36,5 
 
 .0524 
 
 .05242 
 
 
 .00137 
 
 
 .05235 
 
 
 19.101 
 
 36,4 
 
 0.0525 
 
 0.05252 
 
 10,0 
 
 1.00138 
 
 0,5 
 
 0.05245 
 
 IO,O 
 
 19.065 
 
 36,2 
 
 .0526 
 
 .05262 
 
 
 .00138 
 
 
 .05255 
 
 
 I9.O29 
 
 36,1 
 
 .0527 
 
 .05272 
 
 
 .00139 
 
 
 .05265 
 
 
 18.093 
 
 36,0 
 
 .0528 
 
 .05282 
 
 
 .00139 
 
 
 .05275 
 
 
 18.957 
 
 35,8 
 
 .0529 
 
 .05292 
 
 
 .00140 
 
 
 .05285 
 
 
 I8.92I 
 
 35,7 
 
 0.0530 
 
 0.05302 
 
 IO,O 
 
 1.00140 
 
 0,5 
 
 0.05295 
 
 1 0,0 
 
 18.886 
 
 35,6 
 
 .0531 
 
 .05312 
 
 
 .00141 
 
 
 .05305 
 
 
 18.850 
 
 35,4 
 
 .0532 
 
 .05323 
 
 
 .00142 
 
 
 .05315 
 
 
 18.815 
 
 35,3 
 
 .0533 
 
 .05333 
 
 
 .00142 
 
 
 .05325 
 
 
 18.779 
 
 35,2 
 
 0534 
 
 .05343 
 
 
 .00143 
 
 
 .05335 
 
 
 18.744 
 
 350 
 
 0.0535 
 
 0.05353 
 
 IO,O 
 
 I. 00143 
 
 o,5 
 
 0.05345 
 
 10,0 
 
 18.709 
 
 34,9 
 
 .0536 
 
 .05363 
 
 
 .00144 
 
 
 05355 
 
 
 18.675 
 
 34,8 
 
 .0537 
 
 .05373 
 
 
 .00144 
 
 
 .05365 
 
 
 18.640 
 
 34,6 
 
 .0538 
 
 .05383 
 
 
 .00145 
 
 
 .05375 
 
 
 18.605 
 
 34,5 
 
 0539 
 
 .05393 
 
 
 .00145 
 
 
 .05385 
 
 
 18.571 
 
 34,4 
 
 0.0540 
 
 0.05403 
 
 IO,O 
 
 1.00146 
 
 o,5 
 
 0.05395 
 
 IO,O 
 
 18.537 
 
 34,3 
 
 .0541 
 
 .05413 
 
 
 .00146 
 
 
 .05405 
 
 
 I8.5O2 
 
 34,1 
 
 .0542 
 
 .05423 
 
 
 .00147 
 
 
 .05415 
 
 
 18.468 
 
 34.0 
 
 .0543 
 .0544 
 
 .05433 
 .05443 
 
 
 .00147 
 .00148 
 
 
 05425 
 .05435 
 
 
 18.434 
 18.400 
 
 33,9 
 33,8 
 
 0.0545 
 
 0.05453 
 
 10,0 
 
 1.00149 
 
 o,5 
 
 0.05445 
 
 1 0,0 
 
 18.367 
 
 33,6 
 
 .0546 
 
 .05463 
 
 
 .00149 
 
 
 .05455 
 
 
 18.333 
 
 33,5 
 
 .0547 
 
 .05473 
 
 
 .00150 
 
 
 .05465 
 
 
 I8.3OO 
 
 33,4 
 
 .0548 
 
 .05483 
 
 
 .00150 
 
 
 05475 
 
 
 18.266 
 
 33,3 
 
 .0549 
 
 .05493 
 
 
 .00151 
 
 
 .05484 
 
 
 18.233 
 
 33,1 
 
 0.0550 
 
 0.05503 
 
 10,0 
 
 1.00151 
 
 0,6 
 
 0.05494 
 
 1 0,0 
 
 18.200 
 
 33,0 
 
 u 
 
 tan gd u 
 
 Fo' 
 
 sec gd u 
 
 Fo' 
 
 tin gd u 
 
 - F u ' 
 
 esc gd u 
 
 Fo' 
 
 SMITHSONIAN TABLES 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinh u 
 
 F ' 
 
 cosh u 
 
 Fo' 
 
 tanh u 
 
 FO' 
 
 coth u 
 
 F ' 
 
 0.0550 
 
 0.05503 
 
 10,0 
 
 1.00151 
 
 0,6 
 
 0.05494 
 
 10,0 
 
 18.200 
 
 33,0 
 
 .0551 
 
 .05513 
 
 
 .00152 
 
 
 .05504 
 
 
 18.167 
 
 32,9 
 
 .0552 
 
 .0552J-. 
 
 
 .00152 
 
 
 .05514 
 
 
 18.134 
 
 32,8 
 
 .0553 
 
 .05533 
 
 
 .00153 
 
 
 .05524 
 
 
 18.102 
 
 32,7 
 
 .0554 
 
 .05543 
 
 
 .00153 
 
 
 .05534 
 
 
 18.069 
 
 32,5 
 
 0.0555 
 
 0.05553 
 
 10,0 
 
 1.00154 
 
 0,6 
 
 0.05544 
 
 10,0 
 
 18.037 
 
 32,4 
 
 0556 
 
 .05563 
 
 
 .00155 
 
 
 .05554 
 
 
 l8.004 
 
 32,3 
 
 .0557 
 
 .05573 
 
 
 .00155 
 
 
 .05564 
 
 
 17.972 
 
 32,2 
 
 .0558 
 
 .05583 
 
 
 .00156 
 
 
 .05574 
 
 
 17.940 
 
 32,1 
 
 .0559 
 
 .05593 
 
 
 .00156 
 
 
 .05584 
 
 
 17.908 
 
 32,0 
 
 0.0560 
 
 0.05603 
 
 IO,O 
 
 I. 00157 
 
 0,6 
 
 2.05594 
 
 10,0 
 
 17.876 
 
 31,9 
 
 .0561 
 
 .05613 
 
 
 .00157 
 
 
 .05604 
 
 
 17.844 
 
 3i,7 
 
 .0562 
 
 .05623 
 
 
 .00158 
 
 
 .05614 
 
 
 I7.8I2 
 
 31,6 
 
 0563 
 
 05633 
 
 
 .00159 
 
 
 .05624 
 
 
 I7.78I 
 
 31,5 
 
 .0564 
 
 .05643 
 
 
 .00159 
 
 
 .05634 
 
 
 17.749 
 
 31,4 
 
 0.0565 
 
 0.05653 
 
 10,0 
 
 I. 00160 
 
 0,6 
 
 0.05644 
 
 IO,O 
 
 17.718 
 
 31,3 
 
 .0566 
 
 .05663 
 
 
 .00160 
 
 
 05654 
 
 
 17.687 
 
 3i,2 
 
 .0567 
 
 .05673 
 
 
 .00161 
 
 
 .05664 
 
 
 17.656 
 
 3i,i 
 
 .0568 
 
 .05683 
 
 
 .00161 
 
 
 .05674 
 
 
 17.625 
 
 3i,o 
 
 .0569 
 
 .05693 
 
 
 .00162 
 
 
 .05684 
 
 
 17.594 
 
 30,9 
 
 0.0570 
 
 0.05703 
 
 10,0 
 
 1.00162 
 
 0,6 
 
 0.05604 
 
 IO,O 
 
 17.563 
 
 30,7 
 
 0571 
 
 .05713 
 
 
 .00163 
 
 
 .05704 
 
 
 17.532 
 
 30,6 
 
 .0572 
 
 .05723 
 
 
 .00164 
 
 
 05714 
 
 
 17.502 
 
 30,5 
 
 .0573 
 
 05733 
 
 
 .00164 
 
 
 .05724 
 
 
 17.471 
 
 30,4 
 
 0574 
 
 .05743 
 
 
 .00165 
 
 
 .05734 
 
 
 17.441 
 
 30,3 
 
 0.0575 
 
 0.05753 
 
 10,0 
 
 1.00165 
 
 0,6 
 
 0.05744 
 
 10,0 
 
 17.410 
 
 30,2 
 
 .0576 
 
 .05763 
 
 
 .00166 
 
 
 .05754 
 
 
 17.380 
 
 30,1 
 
 .0577 
 
 .05773 
 
 
 .00167 
 
 
 .05764 
 
 
 17.350 
 
 30,0 
 
 .0578 
 
 .05783 
 
 
 .00167 
 
 
 .05774 
 
 
 17.320 
 
 29,9 
 
 .0579 
 
 .05793 
 
 
 .00168 
 
 
 .05784 
 
 
 17.290 
 
 . 29,8 
 
 0.0580 
 
 0.05803 
 
 10,0 
 
 1.00168 
 
 0,6 
 
 0.05794 
 
 10,0 
 
 I7.26l 
 
 29,7 
 
 .0581 
 
 .05813 
 
 
 .00169 
 
 
 .05803 
 
 
 17.231 
 
 29,6 
 
 .0582 
 
 .05823 
 
 
 .00169 
 
 
 .05813 
 
 
 17.202 
 
 29,5 
 
 .0583 
 
 .05833 
 
 
 .00170 
 
 
 .05823 
 
 
 17.172 
 
 29,4 
 
 .0584 
 
 .05843 
 
 
 .00171 
 
 
 05833 
 
 
 17.143 
 
 29,3 
 
 0.0585 
 
 0.05853 
 
 10,0 
 
 1.00171 
 
 0,6 
 
 0.05843 
 
 10,0 
 
 17.114 
 
 29,2 
 
 .0586 
 
 .05863 
 
 
 .00172 
 
 
 .05853 
 
 
 17.084 
 
 29,1 
 
 .0587 
 
 .05873 
 
 
 .00172 
 
 
 .05863 
 
 
 17.055 
 
 29,0 
 
 .0588 
 
 .05883 
 
 
 .00173 
 
 
 .05873 
 
 
 17.026 
 
 28,9 
 
 .0589 
 
 .05893 
 
 
 .00174 
 
 
 .05883 
 
 
 16.998 
 
 28,8 
 
 0.0500 
 
 0.05903 
 
 IO,0 
 
 I. 00174 
 
 0,6 
 
 0.05893 
 
 IO,0 
 
 16.069 
 
 28,7 
 
 .0591 
 
 .05913 
 
 
 .00175 
 
 
 05003 
 
 
 16.940 
 
 28,6 
 
 .0592 
 
 .05923 
 
 
 .00175 
 
 
 .05913 
 
 
 16.912 
 
 28,5 
 
 .0593 
 
 05933 
 
 
 .00176 
 
 
 .05923 
 
 
 16.883 
 
 28,4 
 
 .0594 
 
 05943 
 
 
 .00176 
 
 
 .05933 
 
 
 16.855 
 
 28,3 
 
 0.0595 
 
 0.05954 
 
 IO,O 
 
 1.00177 
 
 0,6 
 
 0.05943 
 
 IO,O 
 
 16.827 
 
 28,2 
 
 .0596 
 
 .05964 
 
 
 .00178 
 
 
 05953 
 
 
 16.798 
 
 28,1 
 
 .0597 
 
 .05974 
 
 
 .00178 
 
 
 .05063 
 
 
 16.770 
 
 28,0 
 
 .0598 
 
 .05984 
 
 
 .00179 
 
 
 .05973 
 
 
 16.742 
 
 27,9 
 
 .0599 
 
 .05994 
 
 
 .00179 
 
 
 05083 
 
 
 16.714 
 
 27,8 
 
 0.0600 
 
 0.06004 
 
 10,0 
 
 1.00180 
 
 0,6 
 
 0.05093 
 
 10,0 
 
 16.687 
 
 27,7 
 
 u 
 
 tan gd u 
 
 Fo' 
 
 sec gd u 
 
 Fo' 
 
 sin gd u 
 
 Fo' 
 
 csc gd u 
 
 Fo' 
 
 SMITHSONIAN TABLES. 
 
 99 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinh u 
 
 Fo' 
 
 cosh u 
 
 -Fo' 
 
 tanh u 
 
 Fo' 
 
 coth u 
 
 Fo' 
 
 0.0600 
 
 0.06004 
 
 IO,O 
 
 I.OOlSo 
 
 0,6 
 
 0.05993 
 
 IO,O 
 
 16.687 
 
 27,7 
 
 .0601 
 
 .06014 
 
 
 .OOlSl 
 
 
 .06003 
 
 
 16.659 
 
 27,7 
 
 .0602 
 
 .06024 
 
 
 .OOlSl 
 
 
 .06013 
 
 
 16.631 
 
 27,6 
 
 .0603 
 
 .06034 
 
 
 .00182 
 
 
 .06023 
 
 
 16.604 
 
 27,5 
 
 .0604 
 
 .00044 
 
 
 .00182 
 
 
 .06033 
 
 
 16.576 
 
 27,4 
 
 0.0605 
 
 0.06054 
 
 IO,O 
 
 1.00183 
 
 0,6 
 
 0.06043 
 
 IO,O 
 
 16.549 
 
 27,3 
 
 .0606 
 
 .06064 
 
 
 .00184 
 
 
 .06053 
 
 
 16.522 
 
 27,2 
 
 .0607 
 
 .06074 
 
 
 .00184 
 
 
 .06063 
 
 
 16.495 
 
 27,1 
 
 .0608 
 
 .06084 
 
 
 .00185 
 
 
 .06073 
 
 
 16.468 
 
 27.0 
 
 .0609 
 
 .06094 
 
 
 .00185 
 
 
 .06082 
 
 
 16.441 
 
 26,9 
 
 0.0610 
 
 0.06104 
 
 IO,O 
 
 I.OOI86 
 
 0,6 
 
 0.06092 
 
 IO,O 
 
 16.414 
 
 26,8 
 
 .0611 
 
 .06114 
 
 
 .00187 
 
 
 .06102 
 
 
 16.387 
 
 26,8 
 
 .0612 
 
 .06124 
 
 
 .00187 
 
 
 .06112 
 
 
 16.360 
 
 26,7 
 
 .0613 
 
 .06134 
 
 
 .00188 
 
 
 .06122 
 
 
 16.334 
 
 26,6 
 
 .0614 
 
 .06144 
 
 
 .00189 
 
 
 .06132 
 
 
 16.307 
 
 26,5 
 
 0.0615 
 
 0.06154 
 
 IO,O 
 
 1.00189 
 
 0,6 
 
 0.06142 
 
 10,0 
 
 16.281 
 
 26,4 
 
 .0616 
 
 .06164 
 
 
 .OOIOO 
 
 
 .06152 
 
 
 16.254 
 
 26,3 
 
 .0617 
 
 .06174 
 
 
 .00100 
 
 
 .06162 
 
 
 16.228 
 
 26,2 
 
 .0618 
 
 .06184 
 
 
 .00191 
 
 
 .06172 
 
 
 16.202 
 
 26,1 
 
 .0619 
 
 .06194 
 
 
 .00192 
 
 
 .06182 
 
 
 16.176 
 
 26,1 
 
 0.0620 
 
 0.06204 
 
 10,0 
 
 I.OOI92 
 
 0,6 
 
 0.06192 
 
 10,0 
 
 16.150 
 
 26,0 
 
 .0621 
 
 .06214 
 
 
 .00193 
 
 
 .06202 
 
 
 16.124 
 
 25,9 
 
 .0622 
 
 .06224 
 
 
 .00194 
 
 
 .06212 
 
 
 16.098 
 
 25,8 
 
 .0623 
 
 .06234 
 
 
 .00194 
 
 
 .06222 
 
 
 16.072 
 
 25,7 
 
 .0624 
 
 .06244 
 
 
 .00195 
 
 
 .06232 
 
 
 16.046 
 
 25,6 
 
 0.0625 
 
 0.06254 
 
 IO,O 
 
 I.OOI95 
 
 0,6 
 
 0.06242 
 
 IO,O 
 
 16.021 
 
 25,6 
 
 .0626 
 
 .06264 
 
 
 .00196 
 
 
 .06252 
 
 
 15.995 
 
 25,5 
 
 .0627 
 
 .06274 
 
 
 .00197 
 
 
 .06262 
 
 
 15.970 
 
 25,4 I 
 
 .0628 
 
 .06284 
 
 
 .00197 
 
 
 .06272 
 
 
 15.944 
 
 25,3 
 
 .0629 
 
 .06294 
 
 
 .00198 
 
 
 .06282 
 
 
 15.919 
 
 25,2 
 
 0.0630 
 
 0.06304 
 
 10,0 
 
 I.OOI99 
 
 0,6 
 
 0.06292 
 
 IO,O 
 
 15.894 
 
 25,2 
 
 .0631 
 
 .06314 
 
 
 .00199 
 
 
 .06302 
 
 
 15.869 
 
 25,1 
 
 .0632 
 
 .06324 
 
 
 .OO2OO 
 
 
 .06312 
 
 
 15.844 
 
 25,0 
 
 .0633 
 
 .06334 
 
 
 .OO2OO 
 
 
 .06322 
 
 
 15.819 
 
 24,9 
 
 .0634 
 
 .06344 
 
 
 .OO2OI 
 
 
 .06332 
 
 
 15.794 
 
 24,8 
 
 0.0635 
 
 0.06354 
 
 IO,0 
 
 I.OO2O2 
 
 0,6 
 
 0.06342 
 
 10,0 
 
 15.769 
 
 24,8 
 
 .0636 
 
 .06364 
 
 
 .00202 
 
 
 .06351 
 
 
 15.744 
 
 24,7 
 
 .0637 
 
 .06374 
 
 
 .OO2O3 
 
 
 .06361 
 
 
 15.720 
 
 24,6 
 
 .0638 
 
 .06384 
 
 
 .OO2O4 
 
 
 .06371 
 
 
 15.695 
 
 24,5 
 
 .0639 
 
 .06394 
 
 
 .00204 
 
 
 .06381 
 
 
 15.671 
 
 24,5 
 
 0.0640 
 
 0.06404 
 
 10,0 
 
 I.OO205 
 
 0,6 
 
 0.06391 
 
 10,0 
 
 15.646 
 
 24,4 
 
 .0641 
 
 .06414 
 
 
 .OO2O6 
 
 
 .06401 
 
 
 15.622 
 
 24,3 
 
 .0642 
 
 .06424 
 
 
 .00206 
 
 
 .06411 
 
 
 15.598 
 
 24,2 
 
 .0643 
 
 .06434 
 
 
 .OO2O7 
 
 
 .06421 
 
 
 15.574 
 
 24,2 
 
 .0644 
 
 .06444 
 
 
 .OO2O7 
 
 
 .06431 
 
 
 15.549 
 
 24,1 
 
 0.0645 
 
 0.06454 
 
 10,0 
 
 I.OO2O8 
 
 0,6 
 
 0.06441 
 
 IO,O 
 
 15.525 
 
 24,0 
 
 .0646 
 
 .06464 
 
 
 .00209 
 
 
 .06451 
 
 
 15.501 
 
 23,9 
 
 .0647 
 
 .06475 
 
 
 .00209 
 
 
 .06461 
 
 
 15.478 
 
 23,9 
 
 .0648 
 
 .06485 
 
 
 .00210 
 
 
 .06471 
 
 
 15.454 
 
 23,8 
 
 .0649 
 
 .06495 
 
 
 .00211 
 
 
 .06481 
 
 
 15.430 
 
 23,7 
 
 0.0650 
 
 0.06505 
 
 10,0 
 
 I.OO2II 
 
 o,7 
 
 0.06491 
 
 IO,O 
 
 15.406 
 
 23,6 
 
 u 
 
 tan gd u 
 
 Fo' 
 
 sec gd u 
 
 Fo' 
 
 sin gd u 
 
 - Fo' 
 
 csc gd u 
 
 Fo' 
 
 SMITHSONIAN TABLCS 
 
 IOO 
 
Natural Hyperbolic Function^ 
 
 u 
 
 sinh u 
 
 -Fo' 
 
 cosh u 
 
 F ' 
 
 tanh i- 
 
 Fo'" 
 
 coiK tf '. 
 
 *F ' 
 
 0.0650 
 
 0.06505 
 
 IO,O 
 
 I.002II 
 
 o,7 
 
 0.06491 
 
 10,0 
 
 15.406 
 
 23,6 
 
 .0651 
 
 .05515 
 
 
 .00212 
 
 
 .06501 
 
 
 15.383 
 
 23,6 
 
 .0652 
 
 .06525 
 
 
 .00213 
 
 
 .06511 
 
 
 15-359 
 
 23,5 
 
 .0653 
 
 .06535 
 
 
 .00213 
 
 
 .06521 
 
 
 15.336 
 
 23,4 
 
 .0654 
 
 .06545 
 
 
 .OO2I4 
 
 
 .06531 
 
 
 15-312 
 
 23,3 
 
 0.0655 
 
 0.06555 
 
 IO,O 
 
 I.OO2I5 
 
 o,7 
 
 0.06541 
 
 10,0 
 
 15.289 
 
 23,3 
 
 .0656 
 
 .06565 
 
 
 .OO2I5 
 
 
 .06551 
 
 
 15.266 
 
 23,2 
 
 .0657 
 
 .06575 
 
 
 .OO2l6 
 
 
 .06561 
 
 
 15.243 
 
 23,1 
 
 .0658 
 
 .06585 
 
 
 .00217 
 
 
 .06571 
 
 
 15.219 
 
 23,1 
 
 .0659 
 
 .06595 
 
 
 .OO2I7 
 
 
 .06580 
 
 
 15.196 
 
 23,0 
 
 0.0660 
 
 O.O66O5 
 
 IO,O 
 
 I.OO2I8 
 
 o,7 
 
 0.06590 
 
 IO,O 
 
 15.174 
 
 22,9 
 
 .0661 
 
 .06615 
 
 
 .O02I9 
 
 
 .06600 
 
 
 15.151 
 
 22,9 
 
 .0662 
 
 .06625 
 
 
 .00219 
 
 
 .06610 
 
 
 15.128 
 
 22,8 
 
 .0663 
 
 .06635 
 
 
 .OO220 
 
 
 .06620 
 
 
 15.105 
 
 22,7 
 
 .0664 
 
 .06645 
 
 
 .OO22I 
 
 
 .06630 
 
 
 15.082 
 
 22,6 
 
 0.0665 
 
 0.06655 
 
 IO,O 
 
 I.OO22I 
 
 o,7 
 
 0.06640 
 
 IO,O 
 
 15.060 
 
 22,6 
 
 .0666 
 
 .06665 
 
 
 .00222 
 
 
 .06650 
 
 
 15.037 
 
 22,5 
 
 .0667 
 
 .06675 
 
 
 .00223 
 
 
 .06660 
 
 
 15.015 
 
 22,4 
 
 .0668 
 
 .06685 
 
 
 .00223 
 
 
 .06670 
 
 
 14.992 
 
 22,4 
 
 .0669 
 
 .06695 
 
 
 .00224 
 
 
 .06680 
 
 
 14.970 
 
 22,3 
 
 0.0670 
 
 0.06705 
 
 IO,O 
 
 1.00225 
 
 o,7 
 
 0.06690 
 
 IO,O 
 
 14.948 
 
 22,2 
 
 .0671 
 
 .06715 
 
 
 .00225 
 
 
 .06700 
 
 
 14.925 
 
 22,2 
 
 .0672 
 
 .06725 
 
 
 .OO226 
 
 
 .06710 
 
 
 14.903 
 
 22,1 
 
 .0673 
 
 .06735 
 
 
 .OO227 
 
 
 .06720 
 
 
 14.881 
 
 22,O 
 
 .0674 
 
 .06745 
 
 
 .00227 
 
 
 .06730 
 
 
 14.859 
 
 22,O 
 
 0.0675 
 
 0.06755 
 
 IO,O 
 
 1.00228 
 
 o,7 
 
 0.06740 
 
 10,0 
 
 14-837 
 
 21,9 
 
 .0676 
 
 .06765 
 
 
 .OO229 
 
 
 .06750 
 
 
 14-815 
 
 21,8 
 
 .0677 
 
 .06775 
 
 
 .O0229 
 
 
 .06760 
 
 
 14-794 
 
 21,8 
 
 .0678 
 
 .06785 
 
 
 .00230 
 
 
 .06770 
 
 
 14.772 
 
 21,7 
 
 .xtf79 
 
 .06795 
 
 
 .00231 
 
 
 .06780 
 
 
 14.750 
 
 21,7 
 
 0.0680 
 
 0.06805 
 
 10,0 
 
 I.OO23I 
 
 o,7 
 
 0.06790 
 
 IO,O 
 
 14.729 
 
 ' 21,6 
 
 .0681 
 
 .06815 
 
 
 .00232 
 
 
 .06799 
 
 
 14.707 
 
 21,5 
 
 .0682 
 
 .06825 
 
 
 .00233 
 
 
 .06809 
 
 
 14.685 
 
 21,5 
 
 .0683 
 
 .06835 
 
 
 .00233 
 
 
 .06819 
 
 
 14.664 
 
 21,4 
 
 .0684 
 
 .06845 
 
 
 .00234 
 
 
 .06829 
 
 
 14.643 
 
 21,3 
 
 0.0685 
 
 0.06855 
 
 10,0 
 
 1.00235 
 
 o,7 
 
 0.06839 
 
 IO,O 
 
 14.621 
 
 21,3 
 
 .0686 
 
 .06865 
 
 
 .00235 
 
 
 .06849 
 
 
 14.600 
 
 21,2 
 
 .0687 
 
 .06875 
 
 
 .00236 
 
 
 .06859 
 
 
 14.579 
 
 21,2 
 
 .0688 
 
 .06885 
 
 
 .00237 
 
 
 .06869 
 
 
 14.558 
 
 21,1 
 
 .0689 
 
 .06895 
 
 
 .00237 
 
 
 .06879 
 
 
 H-537 
 
 21,0 
 
 0.0690 
 
 0.06005 
 
 IO,O 
 
 1.00238 
 
 o,7 
 
 0.06889 
 
 IO,O 
 
 I4.5I6 
 
 21,0 
 
 .0691 
 
 .06916 
 
 
 .00239 
 
 
 .06899 
 
 
 14-495 
 
 20,9 
 
 .0692 
 
 .06926 
 
 
 .00240 
 
 
 .06909 
 
 
 14.474 
 
 20,8 
 
 .0693 
 
 .06936 
 
 
 .00240 
 
 
 .06919 
 
 
 14-453 
 
 20,8 
 
 .0694 
 
 .06946 
 
 
 .00241 
 
 
 .06929 
 
 
 14.432 
 
 20,7 
 
 0.0695 
 
 0.06956 
 
 IO,O 
 
 1.00242 
 
 o,7 
 
 0.06939 
 
 IO,O 
 
 14.412 
 
 20,7 
 
 .0696 
 
 .06966 
 
 
 .00242 
 
 
 .06949 
 
 
 14.391 
 
 20,6 
 
 .0697 
 
 .06976 
 
 
 .00243 
 
 
 .06959 
 
 
 14.370 
 
 20,6 
 
 .0698 
 
 .06986 
 
 
 .00244 
 
 
 .06969 
 
 
 14.350 
 
 20,5 
 
 .0699 
 
 .06996 
 
 
 .00244 
 
 
 .06979 
 
 
 14.329 
 
 20,4 
 
 0.0700 
 
 0.07006 
 
 10,0 
 
 1.00245 
 
 0,7 
 
 0.06989 
 
 IO,O 
 
 14.309 
 
 20,4 
 
 u 
 
 tan gd u 
 
 Fo' 
 
 sec gd u 
 
 Fo' 
 
 sin gd u 
 
 Fo' 
 
 esc gd u 
 
 F O ' 
 
 SMITHSONIAN TABLES 
 
 101 
 
'Natural Hyperbolic Functions. 
 
 u 
 
 .*mhu .F ' 
 
 cosh iv 
 
 Fo* 
 
 tanh u 
 
 Fo' 
 
 coth u 
 
 * Fo' 
 
 0.0700 
 
 0.07006 
 
 10,0 
 
 1.00245 
 
 0,7 
 
 0.06989 
 
 IO,O 
 
 14.309 
 
 20,4 
 
 .0701 
 
 .07016 
 
 
 .00246 
 
 
 .06999 
 
 
 14.289 
 
 20,3 
 
 .0702 
 
 .07026 
 
 
 .00247 
 
 
 .07008 
 
 
 14.268 
 
 20,3 
 
 .0703 
 
 .07036 
 
 
 .00247 
 
 4 
 
 .07018 
 
 
 14.248 
 
 20,2 
 
 .0704 
 
 .07046 
 
 
 .00248 
 
 
 .07028 
 
 
 14.228 
 
 2O, I 
 
 0.0705 
 
 0.07056 
 
 10,0 
 
 1.00249 
 
 o,7 
 
 0.07038 
 
 10,0 
 
 14.208 
 
 20,1 
 
 .0706 
 
 .07066 
 
 
 .00249 
 
 
 .0/048 
 
 
 14.188 
 
 20,0 
 
 .0707 
 
 .07076 
 
 
 .00250 
 
 
 .07058 
 
 
 14.168 
 
 20,0 
 
 .0708 
 
 .07086 
 
 
 .00251 
 
 
 .07068 
 
 
 14.148 
 
 19,9 
 
 .0709 
 
 .07006 
 
 
 .00251 
 
 
 .07078 
 
 9,9 
 
 14.128 
 
 19,9 
 
 0.0710 
 
 0.07106 
 
 IO,0 
 
 1.00252 
 
 o,7 
 
 0.07088 
 
 9,9 
 
 14.108 
 
 19,8 
 
 .0711 
 
 .07116 
 
 
 .00253 
 
 
 .07098 
 
 
 14.088 
 
 19,7 
 
 .0712 
 
 .07126 
 
 
 .00254 
 
 
 .07108 
 
 
 14.069 
 
 19,7 
 
 .0713 
 
 .07136 
 
 
 .00254 
 
 
 .07118 
 
 
 14.049 
 
 19,6 
 
 .0714 
 
 .07146 
 
 
 .00255 
 
 
 .07128 
 
 
 14.029 
 
 19,6 
 
 0.0715 
 
 0.07156 
 
 IO,O 
 
 1.00256 
 
 o,7 
 
 0.07138 
 
 9,9 
 
 14.010 
 
 19,5 
 
 .0716 
 
 .07166 
 
 
 .00256 
 
 
 .07148 
 
 
 13.990 
 
 19,5 
 
 - .0717 
 
 .07176 
 
 
 .00257 
 
 
 .07158 
 
 
 13.971 
 
 19,4 
 
 .0718 
 
 .07186 
 
 
 .00258 
 
 
 .07168 
 
 
 13.952 
 
 19,4 
 
 .0719 
 
 .07196 
 
 
 .00259 
 
 
 .07178 
 
 
 13.932 
 
 19,3 
 
 0.0720 
 
 0.07206 
 
 10,0 
 
 1.00259 
 
 o,7 
 
 0.07188 
 
 9,9 
 
 13.913 
 
 19,3 
 
 .0721 
 
 .07216 
 
 
 .00200 
 
 
 .07108 
 
 
 13.894 
 
 19,2 
 
 .0722 
 
 .07226 
 
 
 .00261 
 
 
 .07207 
 
 
 13.874 
 
 19,2 
 
 .0723 
 
 .07236 
 
 
 .00261 
 
 
 .07217 
 
 
 13.855 
 
 19,1 
 
 .0724 
 
 .07246 
 
 
 .00262 
 
 
 .07227 
 
 
 13.836 
 
 19,0 
 
 0.0725 
 
 0.07256 
 
 IO,O 
 
 1.00263 
 
 o,7 
 
 0.07237 
 
 9,9 
 
 13.817 
 
 I9,o 
 
 .0726 
 
 .07266 
 
 
 .00264 
 
 
 .07247 
 
 
 13.798 
 
 18,9 
 
 .0727 
 
 .07276 
 
 
 .00264 
 
 
 .07257 
 
 
 13.779 
 
 18,9 
 
 .0728 
 
 .07286 
 
 
 .00265 
 
 
 .07267 
 
 
 I3.76I 
 
 18,8 
 
 .0729 
 
 .07296 
 
 
 .00266 
 
 
 .07277 
 
 
 13.742 
 
 1-8,8 
 
 0.0730 
 
 0.07306 
 
 10,0 
 
 1.00267 
 
 o,7 
 
 0.07287 
 
 9,9 
 
 13.723 
 
 18,7 
 
 .0731 
 
 .07317 
 
 
 .00267 
 
 
 .07297 
 
 
 13.704 
 
 18,7 
 
 .0732 
 
 .07327 
 
 
 .00268 
 
 
 .07307 
 
 
 13.686 
 
 18,6 
 
 .0733 
 
 07337 
 
 
 .00269 
 
 
 .07317 
 
 
 13.667 
 
 18,6 
 
 .0734 
 
 .07347 
 
 
 .00269 
 
 
 .07327 
 
 
 13.648 
 
 18,5 
 
 0.0735 
 
 0.07357 
 
 IO,O 
 
 1.00270 
 
 o,7 
 
 0.07337 
 
 9,9 
 
 13.630 
 
 18,5 
 
 .0736 
 
 .07367 
 
 
 .00271 
 
 
 .07347 
 
 
 I3.6il 
 
 1*4 
 
 .0737 
 
 .07377 
 
 
 .00272 
 
 
 .07357 
 
 
 13.593 
 
 18,4 
 
 .0738 
 
 .07387 
 
 
 .00272 
 
 
 .07367 
 
 
 13-575 
 
 18,3 
 
 0739 
 
 .07397 
 
 
 .00273 
 
 
 07377 
 
 
 13.556 
 
 18,3 
 
 0.0740 
 
 0.07407 
 
 10,0 
 
 1.00274 
 
 o,7 
 
 0.07387 
 
 9,9 
 
 13.538 
 
 18,2 
 
 .0741 
 
 .07417 
 
 
 .00275 
 
 
 .07306 
 
 
 13.520 
 
 18,2 
 
 .0742 
 
 .07427 
 
 
 .00275 
 
 
 .07406 
 
 
 13.502 
 
 18,1 
 
 0743 
 
 .07437 
 
 
 .00276 
 
 
 .07416 
 
 
 13.484 
 
 18,1 
 
 .0744 
 
 .07447 
 
 
 .00277 
 
 
 .07426 
 
 
 13.466 
 
 18,0 
 
 0.0745 
 
 0.07457 
 
 10^0 
 
 1.00278 
 
 o,7 
 
 0.07436 
 
 9,9 
 
 13.448 
 
 1 8,0 
 
 .0746 
 
 .07467 
 
 
 .00278 
 
 
 .07446 
 
 
 13.430 
 
 17,9 
 
 .0747 
 
 07477 
 
 
 .00279 
 
 
 .07456 
 
 
 13.412 
 
 17.> ! 
 
 .0748 
 
 .07487 
 
 
 .00280 
 
 
 .07466 
 
 
 13-394 
 
 I?J 
 
 .0/49 
 
 .07497 
 
 
 .00281 
 
 
 .07476 
 
 
 13.376 
 
 17,8 
 
 0.0750 
 
 0.07507 
 
 10,0 
 
 1.00281 
 
 0,8 
 
 0.07486 
 
 9,9 
 
 13.358 
 
 17,7 
 
 u tan ad u * f ,' 
 
 sec gd u 
 
 -Fo' 
 
 in 0.1 u 
 
 - Fo' 
 
 esc gd u 
 
 - Fo' 
 
 SMITHSONIAN TABLES 
 
 102 
 
Natural Hyperbolic Functions. 
 
 u 
 
 inhu 
 
 F ' 
 
 COSh u 
 
 F ' 
 
 tanh u 
 
 - Fo' 
 
 coth u 
 
 Fo' 
 
 0.0750 
 
 0.07507 
 
 10,0 
 
 I.OO28I 
 
 0,8 
 
 0.07486 
 
 9,9 
 
 13.358 
 
 17,7 
 
 .0751 
 
 .07517 
 
 
 .OO282 
 
 
 .07496 
 
 
 13.341 
 
 17,7 
 
 .0752 
 
 .07527 
 
 
 .00283 
 
 
 .07506 
 
 
 13.323 
 
 17,7 
 
 .0753 
 
 .07537 
 
 
 .00284 
 
 
 .07516 
 
 
 13.305 
 
 17,6 
 
 .0754 
 
 07547 
 
 
 .00284 
 
 
 .07526 
 
 
 13.288 
 
 17,6 
 
 0.0755 
 
 0.07557 
 
 IO,O 
 
 I.OO285 
 
 0,8 
 
 0.07536 
 
 9,9 
 
 13.270 
 
 17,5 
 
 * *^*^ 
 
 .0756 
 
 .07567 
 
 
 .00286 
 
 
 .07546 
 
 
 13.253 
 
 17,5 
 
 .0757 
 
 .07577 
 
 
 .00287 
 
 
 .07556 
 
 
 13.235 
 
 17,4 
 
 .0758 
 
 .07587 
 
 
 .00287 
 
 
 .07566 
 
 
 13.218 
 
 17,4 
 
 .0759 
 
 .07597 
 
 
 .00288 
 
 
 .07575 
 
 
 13.201 
 
 17,3 
 
 0.0760 
 
 0.07607 
 
 IO,0 
 
 1.00289 
 
 0,8 
 
 0.07585 
 
 9,9 
 
 13.183 
 
 17,3 
 
 .0761 
 
 .07617 
 
 
 .OO290 
 
 
 .07595 
 
 
 13.166 
 
 17,2 
 
 .0762 
 
 .07627 
 
 
 .OO29O 
 
 
 .07605 
 
 
 13.149 
 
 17,2 
 
 .0763 
 
 .07637 
 
 
 .OO29I 
 
 
 .07615 
 
 
 13.132 
 
 I7,i 
 
 .0764 
 
 .07647 
 
 
 .OO292 
 
 
 .07625 
 
 
 13.114 
 
 I7,i 
 
 0.0765 
 
 0.07657 
 
 IO,O 
 
 1.00293 
 
 0,8 
 
 0.07635 
 
 9,9 
 
 13.097 
 
 I7J 
 
 .0766 
 
 .07667 
 
 
 .00294 
 
 
 .07645 
 
 
 13.080 
 
 17,0 
 
 .0767 
 
 .07678 
 
 
 .00294 
 
 
 .07655 
 
 
 13.063 
 
 I7,o 
 
 .0768 
 
 .07688 
 
 
 .00295 
 
 
 .07665 
 
 
 13-046 
 
 16,9 
 
 .0769 
 
 .07698 
 
 
 .00296 
 
 
 .07675 
 
 
 13.030 
 
 16,9 
 
 0.0770 
 
 0.07708 
 
 IO,O 
 
 1.00297 
 
 0,8 
 
 0.07685 
 
 9,9 
 
 13.013 
 
 16,8 
 
 .0771 
 
 .07718 
 
 
 .00297 
 
 
 .07695 
 
 
 12.996 
 
 16,8- 
 
 .0772 
 
 .07728 
 
 
 .00298 
 
 
 .07705 
 
 
 12.979 
 
 16,7 
 
 0773 
 
 .07738 
 
 
 .00299 
 
 
 .07715 
 
 
 12.962 
 
 16,7 
 
 .0774 
 
 .07748 
 
 
 .00300 
 
 
 .07725 
 
 
 12.946 
 
 16,7 
 
 0.0775 
 
 0.07758 
 
 IO,O 
 
 1.00300 
 
 0,8 
 
 0.07735 
 
 9,9 
 
 12.929 
 
 16,6 
 
 .0776 
 
 .07768 
 
 
 .00301 
 
 
 .07744 
 
 
 12.912 
 
 16,6 
 
 .0777 
 
 .07778 
 
 
 .00302 
 
 
 .07754 
 
 
 12.896 
 
 16,5 
 
 .0778 
 
 .07788 
 
 
 .00303 
 
 
 .07764 
 
 
 12.879 
 
 16,5 
 
 .0779 
 
 .07798 
 
 
 .00304 
 
 
 .07774 
 
 
 12.863 
 
 16,5 
 
 0.0780 
 
 0.07808 
 
 10,0 
 
 1.00304 
 
 0,8 
 
 0.07784 
 
 9,9 
 
 12.847 
 
 16,4 
 
 .0781 
 
 .07818 
 
 
 .00305 
 
 
 .07794 
 
 
 12.830 
 
 16,4 
 
 .0782 
 
 .07828 
 
 
 .00306 
 
 
 .07804 
 
 
 12.814 
 
 16,3 
 
 .0783 
 
 .07838 
 
 
 .00307 
 
 
 .07814 
 
 
 12.797 
 
 16,3 
 
 .0784 
 
 .07848 
 
 
 .00307 
 
 
 .07824 
 
 
 12.781 
 
 16,2 
 
 0.0785 
 
 0.07858 
 
 IO,O 
 
 1.00308 
 
 0,8 
 
 0.07834 
 
 9,9 
 
 12.765 
 
 16,2 
 
 .0786 
 
 .07868 
 
 
 .00309 
 
 
 .07844 
 
 
 12.749 
 
 16,2 
 
 .0787 
 
 .07878 
 
 
 .00310 
 
 
 .07854 
 
 
 12.733 
 
 16,1 
 
 .0788 
 
 .07888 
 
 
 .00311 
 
 
 .07864 
 
 
 12.717 
 
 16,1 
 
 .0789 
 
 .07898 
 
 
 .00311 
 
 
 .07874 
 
 
 12.701 
 
 16,0 
 
 0.0790 
 
 0.07908 
 
 IO,O 
 
 1.00312 
 
 0,8 
 
 0.07884 
 
 9,9 
 
 12.685 
 
 16,0 
 
 .0791 
 
 .07918 
 
 
 .00313 
 
 
 .07894 
 
 
 12.669 
 
 15,9 
 
 .0792 
 
 .07928 
 
 
 .00314 
 
 
 .07903 
 
 
 12.653 
 
 15,9 
 
 .0793 
 
 .07938 
 
 
 .00315 
 
 
 .0791*3 
 
 
 12.637 
 
 15,9 
 
 .0794 
 
 .07948 
 
 
 .00315 
 
 
 .07923 
 
 
 12.621 
 
 15,8 
 
 0.0795 
 
 0.07958 
 
 IO,O 
 
 1.00316 
 
 0,8 
 
 0.07933 
 
 9,9 
 
 12.605 
 
 15,8 
 
 .0796 
 
 .07968 
 
 
 .00317 
 
 
 07943 
 
 
 12.589 
 
 15,7 
 
 .0797 
 
 .07978 
 
 
 .00318 
 
 
 .07953 
 
 
 12-574 
 
 15,7 
 
 .0798 
 
 .07988 
 
 
 .00319 
 
 
 .07963 
 
 
 12.558 
 
 15,7 
 
 .0799 
 
 .07999 
 
 
 .00319 
 
 
 .07973 
 
 
 12.542 
 
 15,6 
 
 0.0800 
 
 0.08009 
 
 10,0 
 
 1.00320 
 
 0,8 
 
 0.07983 
 
 9,9 
 
 12.527 
 
 15,6 
 
 u 
 
 tan gd u 
 
 w Fo' 
 
 sec gd u 
 
 Fo' 
 
 sin gd u 
 
 Fo' 
 
 esc gd u 
 
 F O ' 
 
 SMITHSONIAN TABLES 
 
 103 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinh u 
 
 Fo' 
 
 cosh u 
 
 Fo' 
 
 tanh u 
 
 Fo' 
 
 coth u 
 
 Fo' 
 
 0.0800 
 
 0.08009 
 
 IO,O 
 
 1.00320 
 
 0,8 
 
 0.07983 
 
 9,9 
 
 12.527 
 
 15,6 
 
 .0801 
 
 .08019 
 
 
 .00321 
 
 
 .07993 
 
 
 12.511 
 
 15,6 
 
 .0802 
 
 .08029 
 
 
 .00322 
 
 
 .08003 
 
 
 12.496 
 
 15,5 
 
 .0803 
 
 .08039 
 
 
 .00323 
 
 
 .08013 
 
 
 12.480 
 
 15,5 
 
 .0804 
 
 .08049 
 
 
 .00323 
 
 
 .08023 
 
 
 12.465 
 
 15,4 
 
 0.0805 
 
 O.O8O59 
 
 IO,O 
 
 1.00324 
 
 0,8 
 
 0.08033 
 
 9,9 
 
 12.449 
 
 15,4 
 
 .0806 
 
 .08069 
 
 
 .00325 
 
 
 .08043 
 
 
 12.434 
 
 15,4 
 
 .0807 
 
 .08079 
 
 
 .00326 
 
 
 .08053 
 
 
 12.418 
 
 15,3 
 
 .0808 
 
 .08089 
 
 
 .00327 
 
 
 .08062 
 
 
 12.403 
 
 15,3 
 
 .0809 
 
 .08099 
 
 
 .00327 
 
 
 .08072 
 
 
 12.388 
 
 15,2 
 
 0.0810 
 
 O.o8l09 
 
 10,0 
 
 1.00328 
 
 0,8 
 
 0.08082 
 
 9,9 
 
 12.373 
 
 15,2 
 
 .0811 
 
 .08119 
 
 
 .00329 
 
 
 .08092 
 
 
 12.357 
 
 15,2 
 
 .0812 
 
 .08129 
 
 
 .00330 
 
 
 .08102 
 
 
 12.342 
 
 I5,i 
 
 .0813 
 
 .08139 
 
 
 .00331 
 
 
 .08112 
 
 
 12.327 
 
 I5,i 
 
 .0814 
 
 .O8l49 
 
 
 .00331 
 
 
 .08122 
 
 
 12.312 
 
 I5,i 
 
 0.0815 
 
 O.o8l59 
 
 IO,O 
 
 1.00332 
 
 0,8 
 
 0.08132 
 
 9,9 
 
 12.297 
 
 15,0 
 
 .0816 
 
 .08169 
 
 
 .00333 
 
 
 .08142 
 
 
 12.282 
 
 I5,o 
 
 .0817 
 
 .08179 
 
 
 .00334 
 
 
 .08152 
 
 
 12.267 
 
 14,9 
 
 .0818 
 
 .08189 
 
 
 .00335 
 
 
 .08162 
 
 
 12.252 
 
 14,9 
 
 .0819 
 
 .08199 
 
 
 .00336 
 
 
 .08172 
 
 
 12.237 
 
 14,9 
 
 0.0820 
 
 0.08209 
 
 10,0 
 
 1.00336 
 
 0,8 
 
 0.08182 
 
 9,9 
 
 12.222 
 
 14,8 
 
 .0821 
 
 .08219 
 
 
 .00337 
 
 
 .08192 
 
 
 12.208 
 
 14,8 
 
 .0822 
 
 .08229 
 
 
 .00338 
 
 
 .08202 
 
 
 12.193 
 
 14,8 
 
 .0823 
 
 .08239 
 
 
 .00339 
 
 
 .08211 
 
 
 12.178 
 
 14,7 
 
 .0824 
 
 .08249 
 
 
 .00340 
 
 
 .08221 
 
 
 I2.I63 
 
 14,7 
 
 0.0825 
 
 0.08259 
 
 IO,O 
 
 1.00341 
 
 0,8 
 
 0.08231 
 
 9,9 
 
 12.149 
 
 14,7 
 
 .0826 
 
 .08269 
 
 
 .00341 
 
 
 .08241 
 
 
 12.134 
 
 14,6 
 
 .0827 
 
 .08279 
 
 
 .00342 
 
 
 .08251 
 
 
 12.119 
 
 14,6 
 
 .0828 
 
 .08289 
 
 
 .00343 
 
 
 .08261 
 
 
 12.105 
 
 14,6 
 
 .0829 
 
 .08299 
 
 
 .00344 
 
 
 .08271 
 
 
 12.000 
 
 14,5 
 
 0.0830 
 
 0.08310 
 
 IO,O 
 
 1.00345 
 
 0,8 
 
 0.08281 
 
 9,9 
 
 I2.O76 
 
 14,5 
 
 .0831 
 
 .08320 
 
 
 00345 
 
 
 .08291 
 
 
 12.061 
 
 14,4 
 
 .0832 
 
 .08330 
 
 
 .00346 
 
 
 .08301 
 
 
 12.047 
 
 14,4 
 
 .0833 
 
 .08340 
 
 
 .00347 
 
 
 .08311 
 
 
 12.033 
 
 U,4 
 
 .0834 
 
 .08350 
 
 
 .00348 
 
 
 .08321 
 
 
 12.018 
 
 14,3 
 
 0.0835 
 
 0.08360 
 
 IO,O 
 
 1.00349 
 
 0,8 
 
 0.08331 
 
 9,9 
 
 12.004 
 
 14,3 
 
 .0836 
 
 .08370 
 
 
 .00350 
 
 
 .08341 
 
 
 11.990 
 
 14,3 
 
 .0837 
 
 .08380 
 
 
 .00350 
 
 
 .08351 
 
 
 11-975 
 
 14,2 
 
 .0838 
 
 .08390 
 
 
 .00351 
 
 
 .08360 
 
 
 11.961 
 
 14,2 
 
 .0839 
 
 .08400 
 
 
 .00352 
 
 
 .08370 
 
 
 11.947 
 
 14,2 
 
 0.0840 
 
 0.08410 
 
 1 0,0 
 
 1.00353 
 
 0,8 
 
 0.08380 
 
 9,9 
 
 H.933 
 
 14 J 
 
 .0841 
 
 .08420 
 
 
 00354 
 
 
 .08390 
 
 
 11.919 
 
 14,1 
 
 .0842 
 
 .08430 
 
 
 .00355 
 
 
 .08400 
 
 
 11.905 
 
 14.1 
 
 .0843 
 
 .08440 
 
 
 .00356 
 
 
 .08410 
 
 
 11.890 
 
 14,0 
 
 .0844 
 
 .08450 
 
 
 .00356 
 
 
 .08420 
 
 
 11.876 
 
 M,o 
 
 0.0845 
 
 0.08460 
 
 10,0 
 
 1.00357 
 
 0,8 
 
 0.08430 
 
 9,9 
 
 11.862 
 
 14,0 
 
 .0846 
 
 .08470 
 
 
 .00358 
 
 
 .08440 
 
 
 11.849 
 
 13,9 
 
 .0847 
 
 .08480 
 
 
 00359 
 
 
 .08450 
 
 
 11.835 
 
 13,9 
 
 .0848 
 
 .08400 
 
 
 .00360 
 
 
 .08460 
 
 
 11.821 
 
 13,9 
 
 .0849 
 
 .08500 
 
 
 .00361 
 
 0,9 
 
 .08470 
 
 
 11.807 
 
 13,8 
 
 0.0850 
 
 O.O85IO 
 
 IO,O 
 
 1.00361 
 
 0,9 
 
 0.08480 
 
 9,9 
 
 ".793 
 
 13,8 
 
 u 
 
 tan gd U 
 
 Fo' 
 
 sec gd u 
 
 Fo' 
 
 sin gd u 
 
 - Fo' 
 
 esc gd u 
 
 F ' 
 
 SMITHSONIAN TABLES 
 
 104 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinh u 
 
 F ' 
 
 cosh u 
 
 Fu' 
 
 tanh u 
 
 - Fo' 
 
 coth u 
 
 Fo' 
 
 0.0850 
 
 O.OSSIO 
 
 10,0 
 
 I.OO36l 
 
 0,9 
 
 0.08480 
 
 9,9 
 
 11-793 
 
 13,8 
 
 .0851 
 
 .08520 
 
 
 .00362 
 
 
 .08490 
 
 
 11.779 
 
 13,8 
 
 .0852 
 
 .08530 
 
 
 .00363 
 
 
 .08499 
 
 
 11.765 
 
 13,7 
 
 .0853 
 
 .08540 
 
 
 .00364 
 
 
 .08509 
 
 
 11.752 
 
 13,7 
 
 .0854 
 
 .08550 
 
 
 .00365 
 
 
 .08519 
 
 
 n.738 
 
 13,7 
 
 0.0855 
 
 0.08560 
 
 IO,O 
 
 I.OO366 
 
 0,9 
 
 0.08529 
 
 9,9 
 
 11.724 
 
 13,6 
 
 .0856 
 
 .08570 
 
 
 .00367 
 
 
 .08539 
 
 
 11.711 
 
 13,6 
 
 .0857 
 
 .08580 
 
 
 .00367 
 
 
 .08549 
 
 
 11.697 
 
 13,6 
 
 .0858 
 
 .08591 
 
 
 .00368 
 
 
 .08559 
 
 
 11.684 
 
 13,6 
 
 .0859 
 
 .08601 
 
 
 .00369 
 
 
 .08569 
 
 
 11.670 
 
 13,5 
 
 0.0860 
 
 o. 08611 
 
 IO,O 
 
 1.00370 
 
 0,9 
 
 0.08579 
 
 9,9 
 
 11.657 
 
 13,5 
 
 .0861 
 
 .08621 
 
 
 .00371 
 
 
 .08589 
 
 
 11.643 
 
 13,5 
 
 .0862 
 
 .08631 
 
 
 .00372 
 
 
 .08599 
 
 
 11.630 
 
 13,4 
 
 .0863 
 
 .08641 
 
 
 .00373 
 
 
 .08609 
 
 
 11.616 
 
 13,4 
 
 .0864 
 
 .08651 
 
 
 .00373 
 
 
 .08619 
 
 
 11.603 
 
 13,4 
 
 0.0865 
 
 0.08661 
 
 IO,O 
 
 1.00374 
 
 0,9 
 
 0.08628 
 
 9,9 
 
 11.590 
 
 13,3 
 
 .0866 
 
 .08671 
 
 . 
 
 .00375 
 
 
 .08638 
 
 
 11.576 
 
 13,3 
 
 .0867 
 
 .O868l 
 
 
 .00376 
 
 
 .08648 
 
 
 11.563 
 
 13,3 
 
 .0868 
 
 .08691 
 
 
 .00377 
 
 
 .08658 
 
 
 11.550 
 
 13,2 
 
 .0869 
 
 .08701 
 
 
 .00378 
 
 
 .08668 
 
 
 n.536 
 
 13,2 
 
 0.0870 
 
 0.08711 
 
 IO,O 
 
 1.00379 
 
 o,9 
 
 0.08678 
 
 9,9 
 
 11.523 
 
 13,2 
 
 .0871 
 
 .08721 
 
 
 .00380 
 
 
 .08688 
 
 
 11.510 
 
 I3,i 
 
 .0872 
 
 .08/31 
 
 
 .00380 
 
 
 .08608 
 
 
 11.497 
 
 I3,i 
 
 .0873 
 
 .08741 
 
 
 .00381 
 
 
 .08708 
 
 
 11.484 
 
 13,1 
 
 .0874 
 
 .08751 
 
 
 .00382 
 
 
 .08718 
 
 
 11.471 
 
 13,1 
 
 0.0875 
 
 O.o876l 
 
 10,0 
 
 1.00383 
 
 0,9 
 
 0.08728 
 
 9,9 
 
 11.458 
 
 I3,o 
 
 .0876 
 
 .08771 
 
 
 .00384 
 
 
 .08738 
 
 
 11-445 
 
 I3,o 
 
 .0877 
 
 .08781 
 
 
 .00385 
 
 
 .08748 
 
 
 11.432 
 
 13,0 
 
 .0878 
 
 .08791 
 
 
 .00386 
 
 
 .08758 
 
 
 11.419 
 
 12,9 
 
 .0879 
 
 .0880I 
 
 
 .00387 
 
 
 .08767 
 
 
 11.406 
 
 12,9 
 
 0.0880 
 
 0.08811 
 
 10,0 
 
 1.00387 
 
 0,9 
 
 0.08777 
 
 9,9 
 
 n.393 
 
 12,9 
 
 .0881 
 
 .08821 
 
 
 .00388 
 
 
 .08787 
 
 
 11.380 
 
 12,8 
 
 .0882 
 
 .08831 
 
 
 .00389 
 
 
 .08797 
 
 
 11.367 
 
 12,8 
 
 .0883 
 
 .08841 
 
 
 .00390 
 
 
 .08807 
 
 
 H-354 
 
 12,8 
 
 .0884 
 
 .08852 
 
 
 .00391 
 
 
 .08817 
 
 
 11.342 
 
 12,8 
 
 0.0885 
 
 0.08862 
 
 10,0 
 
 1.00392 
 
 0,9 
 
 0.08827 
 
 9,9 
 
 11-329 
 
 12,7 
 
 .0886 
 
 .08872 
 
 
 .00393 
 
 
 .08837 
 
 
 11.316 
 
 12,7 
 
 .0887 
 
 .08882 
 
 
 .00394 
 
 
 .08847 
 
 
 11.304 
 
 12,7 
 
 .0888 
 
 .08892 
 
 
 .00395 
 
 
 .08857 
 
 
 11.291 
 
 12,6 
 
 .0889 
 
 .08902 
 
 
 .00395 
 
 
 .08867 
 
 
 11.278 
 
 12,6 
 
 0.0890 
 
 0.08912 
 
 10,0 
 
 1.00396 
 
 0,9 
 
 0.08877 
 
 0,9 
 
 11.266 
 
 12,6 
 
 .0891 
 
 .08922 
 
 
 .00397 
 
 
 .08886 
 
 
 H.253 
 
 12,6 
 
 .0892 
 
 .08932 
 
 
 .00398 
 
 
 .08896 
 
 
 i i . 240 
 
 12,5 
 
 .0893 
 
 .08942 
 
 
 .00309 
 
 
 .08906 
 
 
 11.228 
 
 12,5 
 
 .0894 
 
 .08952 
 
 
 .00400 
 
 
 .08916 
 
 
 11.215 
 
 12,5 
 
 0.0895 
 
 0.08962 
 
 IO,O 
 
 1.00401 
 
 0,9 
 
 0.08926 
 
 9,9 
 
 11.203 
 
 12,5 
 
 .0896 
 
 .08972 
 
 
 .00402 
 
 
 .08936 
 
 
 11.191 
 
 12,4 
 
 .0897 
 
 .08982 
 
 
 .00403 
 
 
 .08946 
 
 
 11.178 
 
 12,4 
 
 .0898 
 
 .08992 
 
 
 .00403 
 
 
 .08956 
 
 
 11.166 
 
 12,4 
 
 .0899 
 
 .09002 
 
 
 .00404 
 
 
 .08966 
 
 
 ii. 153 
 
 12,3 
 
 0.0900 
 
 0.00012 
 
 10,0 
 
 1.00405 
 
 0,9 
 
 0.08976 
 
 9,9 
 
 11.141 
 
 12,3 
 
 u 
 
 tan gd u 
 
 Fo' 
 
 sec gd u 
 
 Fo' 
 
 sin gd u 
 
 Fo' 
 
 esc gd u 
 
 Fo' 
 
 SMITHSONIAN TABLES 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinh u 
 
 Fo' 
 
 cosh u 
 
 FO' 
 
 tanh u 
 
 Fo' 
 
 coth u 
 
 <> Fo' 
 
 0.0900 
 
 0.09012 
 
 IO,O 
 
 1.00405 
 
 0,9 
 
 0.08976 
 
 9,9 
 
 11.141 
 
 12,3 
 
 .0901 
 
 .09022 
 
 
 .00406 
 
 
 .08986 
 
 
 11.129 
 
 12,3 
 
 .0902 
 
 .09032 
 
 
 .00407 
 
 
 .08996 
 
 
 II.II7 
 
 12,3 
 
 .0903 
 
 .09042 
 
 
 .00408 
 
 
 .09006 
 
 
 I I . 104 
 
 12,2 
 
 .0904 
 
 .09052 
 
 
 .00409 
 
 
 .09015 
 
 
 11.092 
 
 12,2 
 
 0.0905 
 
 0.09062 
 
 IO,O 
 
 1.00410 
 
 0,9 
 
 0.09025 
 
 9,9 
 
 11.080 
 
 12,2 
 
 .0906 
 
 .09072 
 
 
 .00411 
 
 
 .09035 
 
 
 11.068 
 
 12,1 
 
 .0907 
 
 .09082 
 
 
 .00412 
 
 
 .09045 
 
 
 11.056 
 
 12,1 
 
 .0008 
 
 .00092 
 
 
 .00413 
 
 
 .09055 
 
 
 11.043 
 
 12,1 
 
 .0909 
 
 .09103 
 
 
 .00413 
 
 
 .09065 
 
 
 11.031 
 
 12,1 
 
 0.0910 
 
 0.09113 
 
 10,0 
 
 1.00414 
 
 0,9 
 
 0.00075 
 
 9,9 
 
 11.019 
 
 12,0 
 
 .0911 
 
 .09123 
 
 
 .00415 
 
 
 .09085 
 
 
 11.007 
 
 1 2,O 
 
 .0912 
 
 .09133 
 
 
 .00416 
 
 
 .09095 
 
 
 10.995 
 
 1 2,O 
 
 .0913 
 
 .09143 
 
 
 .00417 
 
 
 .09105 
 
 
 10.983 
 
 1 2,O 
 
 .0914 
 
 .09153 
 
 
 .00418 
 
 
 .09115 
 
 
 10.971 
 
 11,9 
 
 0.0915 
 
 0.09163 
 
 IO,O 
 
 1.00419 
 
 o,9 
 
 O.O9I25 
 
 9,9 
 
 10.959 
 
 11,9 
 
 .0916 
 
 .09173 
 
 
 .00420 
 
 
 .09134 
 
 
 10.948 
 
 11,9 
 
 .0917 
 
 .09183 
 
 
 .00421 
 
 
 .09144 
 
 
 10.936 
 
 11,9 
 
 .0918 
 
 .09193 
 
 
 .00422 
 
 
 .09154 
 
 
 10.924 
 
 n,8 
 
 .0919 
 
 .09203 
 
 
 .00423 
 
 
 .09164 
 
 
 10.912 
 
 n,8 
 
 0.0920 
 
 0.09213 
 
 10,0 
 
 1.00423 
 
 0,9 
 
 0.09174 
 
 9,9 
 
 10.900 
 
 11,8 
 
 .0921 
 
 .09223 
 
 
 .00424 
 
 
 .09184 
 
 
 10.888 
 
 11,8 
 
 .0922 
 
 .09233 
 
 
 .00425 
 
 
 .09194 
 
 
 10.877 
 
 ",7 
 
 .0923 
 
 .09243 
 
 
 .00426 
 
 
 .O9204 
 
 
 10.865 
 
 n,7 
 
 .0924 
 
 .09253 
 
 
 .00427 
 
 
 .09214 
 
 
 10.853 
 
 n,7 
 
 0.0925 
 
 0.09263 
 
 IO,O 
 
 1.00428 
 
 0,9 
 
 O.09224 
 
 9,9 
 
 10.842 
 
 n,7 
 
 .0926 
 
 .09273 
 
 
 .00429 
 
 
 .09234 
 
 
 10.830 
 
 11,6 
 
 .0927 
 
 .09283 
 
 
 .00430 
 
 
 .09244 
 
 
 10.818 
 
 n,6 
 
 .0928 
 
 .09293 
 
 
 .00431 
 
 
 .09253 
 
 
 10.807 
 
 n,6 
 
 .0929 
 
 .09303 
 
 
 .00432 
 
 
 .09263 
 
 
 10.795 
 
 11,6 
 
 0.0930 
 
 0.09313 
 
 IO,O 
 
 1.00433 
 
 0,9 
 
 0.09273 
 
 9,9 
 
 10.784 
 
 n,5 
 
 .0931 
 
 .09323 
 
 
 .00434 
 
 
 .09283 
 
 
 10.772 
 
 n,5 
 
 .0932 
 
 .09333 
 
 
 .00435 
 
 
 .09293 
 
 
 10.761 
 
 ii,5 
 
 .0933 
 
 .09344 
 
 
 .00436 
 
 
 .09303 
 
 
 10.749 
 
 n,5 
 
 .0934 
 
 .09354 
 
 
 .00436 
 
 
 .09313 
 
 
 10.738 
 
 H,4 i 
 
 0.0935 
 
 0.09364 
 
 10,0 
 
 1.00437 
 
 o,9 
 
 0.09323 
 
 9,9 
 
 10.726 
 
 11,4 
 
 .0936 
 
 .09374 
 
 
 .00438 
 
 
 .09333 
 
 
 10.715 
 
 11,4 
 
 0937 
 
 .09384 
 
 
 .00439 
 
 
 09343 
 
 
 10.704 
 
 11,4 
 
 .0938 
 
 .09394 
 
 
 .00440 
 
 
 09353 
 
 
 10.692 
 
 n,3 
 
 .0939 
 
 .09404 
 
 
 .00441 
 
 
 .09362 
 
 
 10.681 
 
 ii,3 
 
 0.0940 
 
 0.094U 
 
 IO,O 
 
 1.00442 
 
 0,9 
 
 0.09372 
 
 9,9 
 
 10.670 
 
 ii,3 
 
 .0941 
 
 .09424 
 
 
 .00443 
 
 
 .09382 
 
 
 10.658 
 
 H,3 
 
 .0942 
 
 .09434 
 
 
 .00444 
 
 
 .09392 
 
 
 10.647 
 
 11,2 
 
 0943 
 
 .09444 
 
 
 .00445 
 
 
 .00402 
 
 
 10.636 
 
 11,2 
 
 .0944 
 
 09454 
 
 
 .00446 
 
 
 .09412 
 
 
 10.625 
 
 11,2 
 
 0.0945 
 
 0.09464 
 
 IO,O 
 
 1.00447 
 
 0,9 
 
 0.09422 
 
 9,9 
 
 10.613 
 
 II,-' 
 
 .0946 
 
 .09474 
 
 
 .00448 
 
 
 .09432 
 
 
 10.602 
 
 II, I 
 
 .0947 
 
 .09484 
 
 
 .00449 
 
 
 .09442 
 
 
 10.591 
 
 II, I 
 
 .0948 
 
 .09494 
 
 
 .00450 
 
 0,9 
 
 09452 
 
 
 10.580 
 
 II, I 
 
 .0949 
 
 .09504 
 
 
 .00451 
 
 1,0 
 
 .09462 
 
 
 10.569 
 
 II, I 
 
 0.0950 
 
 0.09514 
 
 IO,O 
 
 1.00452 
 
 1,0 
 
 0.00472 
 
 9,9 
 
 10.558 
 
 11,0 
 
 u 
 
 tin gd u 
 
 -Fo' 
 
 sec gd u 
 
 - Fo' 
 
 sin gd u 
 
 Fo' 
 
 esc gd u 
 
 - Fo' 
 
 SMITHSONIAN TABLES 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinh u 
 
 F ' 
 
 cosh u 
 
 F ' 
 
 tanh u 
 
 Fo' 
 
 coth u 
 
 Fo' 
 
 0.0950 
 
 0.09514 
 
 10,0 
 
 1.00452 
 
 1,0 
 
 0.09472 
 
 9,9 
 
 10.558 
 
 11,0 
 
 .0951 
 
 .09524 
 
 
 .00453 
 
 
 .09481 
 
 
 10.547 
 
 11,0 
 
 .0952 
 
 09534 
 
 
 .00453 
 
 
 .09491 
 
 
 10.536 
 
 11,0 
 
 .0953 
 
 .09544 
 
 
 .00454 
 
 
 .09501 
 
 
 10.525 
 
 11,0 
 
 0954 
 
 .09554 
 
 
 .00455 
 
 
 .095H 
 
 
 10.514 
 
 11,0 
 
 0.0955 
 
 0.09565 
 
 10,0 
 
 1.00456 
 
 1,0 
 
 0.09521 
 
 9,9 
 
 10.503 
 
 10,9 
 
 .0956 
 
 .09575 
 
 
 .00457 
 
 
 .09531 
 
 
 10.492 
 
 10,9 
 
 .0957 
 
 .09585 
 
 
 .00458 
 
 
 .09541 
 
 
 10.481 
 
 10,9 
 
 .0958 
 
 .09595 
 
 
 .00459 
 
 
 .09551 
 
 
 10.470 
 
 10,9 
 
 .0959 
 
 .09605 
 
 
 .00460 
 
 
 .09561 
 
 
 10.459 
 
 10,8 
 
 0.0960 
 
 0.09615 
 
 10,0 
 
 1.00461 
 
 1,0 
 
 0.09571 
 
 9,9 
 
 10.449 
 
 10,8 
 
 .0961 
 
 .09625 
 
 
 .00462 
 
 
 .09581 
 
 
 10.438 
 
 10,8 
 
 .0962 
 
 .09635 
 
 
 .00463 
 
 
 .09590 
 
 
 10.427 
 
 10,8 
 
 .0963 
 
 .09645 
 
 
 .00464 
 
 
 .09600 
 
 
 10.416 
 
 10,7 
 
 .0964 
 
 .09655 
 
 
 .00465 
 
 
 .09610 
 
 
 10.406 
 
 10,7 
 
 0.0965 
 
 0.09665 
 
 10,0 
 
 1.00466 
 
 I,O 
 
 0.09620 
 
 9,9 
 
 10.395 
 
 10,7 
 
 .0966 
 
 .09675 
 
 
 .00467 
 
 
 .09630 
 
 
 10.384 
 
 10,7 
 
 .0967 
 
 .09685 
 
 
 .00468 
 
 
 .09640 
 
 
 10.373 
 
 10,7 
 
 .0968 
 
 .09695 
 
 
 .00469 
 
 
 .09650 
 
 
 10.363 
 
 10,6 
 
 .0969 
 
 .09705 
 
 
 .00470 
 
 
 .09660 
 
 
 10.352 
 
 10,6 
 
 0.0970 
 
 0.097IS 
 
 IO,O 
 
 1.00471 
 
 1,0 
 
 0.09670 
 
 9,9 
 
 10.342 
 
 10,6 
 
 .0971 
 
 .09725 
 
 
 .00472 
 
 
 .09680 
 
 
 10.331 
 
 10,6 
 
 .0972 
 
 .09735 
 
 
 .00473 
 
 
 .09689 
 
 
 10.320 
 
 10,6 
 
 0973 
 
 09745 
 
 
 .00474 
 
 
 .09699 
 
 
 10.310 
 
 io,5 
 
 .0974 
 
 .09755 
 
 
 .00475 
 
 
 .09709 
 
 
 10.299 
 
 10,5 
 
 0.0975 
 
 0.09765 
 
 IO,O 
 
 1.00476 
 
 1,0 
 
 0.09719 
 
 9,9 
 
 10.289 
 
 10,5 
 
 .0976 
 
 .09776 
 
 
 .00477 
 
 
 .09729 
 
 
 10.278 
 
 10,5 
 
 .0977 
 
 .09786 
 
 
 .00478 
 
 
 .09739 
 
 
 10.268 
 
 10,4 
 
 .0978 
 
 .09796 
 
 
 .00479 
 
 
 .09749 
 
 
 10.258 
 
 10,4 
 
 .0979 
 
 .09806 
 
 
 .00480 
 
 
 .09759 
 
 
 10.247 
 
 10,4 
 
 0.0980 
 
 0.09816 
 
 IO,O 
 
 1.00481 
 
 1,0 
 
 0.09769 
 
 9,9 
 
 10.237 
 
 10,4 
 
 .0981 
 
 .09826 
 
 
 .00482 
 
 
 .09779 
 
 
 10.226 
 
 10,4 
 
 .0982 
 
 .09836 
 
 
 .00483 
 
 
 .09788 
 
 
 10.216 
 
 10,3 
 
 .0983 
 
 .09846 
 
 
 .00484 
 
 
 .09798 
 
 
 10.206 
 
 10,3 
 
 .0984 
 
 .09856 
 
 
 .00485 
 
 
 .09808 
 
 
 10.195 
 
 10,3 
 
 0.0985 
 
 0.09866 
 
 IO,O 
 
 1.00486 
 
 1,0 
 
 0.09818 
 
 9,9 
 
 10.185 
 
 10,3 
 
 .0986 
 
 .09876 
 
 
 .00486 
 
 
 .09828 
 
 
 10. 175 
 
 10,3 
 
 .0987 
 
 .09886 
 
 
 .00487 
 
 
 .09838 
 
 
 10.165 
 
 10,2 
 
 .0988 
 
 .09896 
 
 
 .00488 
 
 
 .09848 
 
 
 10.154 
 
 10,2 
 
 .0989 
 
 .09906 
 
 
 .00489 
 
 
 .09858 
 
 
 10.144 
 
 10,2 
 
 0.0900 
 
 0.00916 
 
 IO,O 
 
 1.00490 
 
 1,0 
 
 0.09868 
 
 9,9 
 
 10.134 
 
 10,2 
 
 .0991 
 
 .09926 
 
 
 .00491 
 
 
 .09878 
 
 
 10.124 
 
 10,1 
 
 .0992 
 
 .09936 
 
 
 .00492 
 
 
 .09888 
 
 
 10.114 
 
 10,1 
 
 .0993 
 
 .09946 
 
 
 .00493 
 
 
 .09897 
 
 
 10. 104 
 
 10,1 
 
 .0994 
 
 .09956 
 
 
 .00494 
 
 
 .09907 
 
 
 10.093 
 
 10,1 
 
 0.0995 
 
 0.09966 
 
 IO,O 
 
 1.00495 
 
 1,0 
 
 0.09917 
 
 9,9 
 
 10.083 
 
 10,1 
 
 .0996 
 
 .00976 
 
 
 .00496 
 
 
 .09927 
 
 
 10.073 
 
 10,0 
 
 .0997 
 
 .09987 
 
 
 .00497 
 
 
 .09937 
 
 
 10.063 
 
 10,0 
 
 .0098 
 
 .09997 
 
 
 .00498 
 
 
 .09947 
 
 
 10.053 
 
 10,0 
 
 .0999 
 
 .10007 
 
 
 .00499 
 
 
 .09957 
 
 
 10.043 
 
 10,0 
 
 O.IOOO 
 
 0.10017 
 
 10,1 
 
 1.00500 
 
 1,0 
 
 0.00967 
 
 9,9 
 
 10.033 
 
 10,0 
 
 u 
 
 tan gd u 
 
 F O ' 
 
 sec gd u 
 
 F ' 
 
 sin gd u 
 
 <> Fo' 
 
 esc gd u 
 
 O,FO' 
 
 SMITHSONIAN TABLES 
 
 107 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinh u 
 
 Fo' 
 
 cosh u 
 
 O.FO' 
 
 tanh u 
 
 Fo' 
 
 coth u 
 
 Fo' 
 
 0;IOO 
 
 O.IOOI7 
 
 100,5 
 
 1.00500 
 
 10,0 
 
 0,09967 
 
 99,0 
 
 10.0333 
 
 996,7 
 
 .101 
 
 .10117 
 
 100,5 
 
 .00510 
 
 10,1 
 
 .10066 
 
 99,0 
 
 9.9346 
 
 977,o 
 
 .IO2 
 
 .IO2l8 
 
 100,5 
 
 .00521 
 
 10,2 
 
 . IOI65 
 
 99,0 
 
 .8379 
 
 957,9 
 
 .103 
 
 .10318 
 
 100,5 
 
 .00531 
 
 10,3 
 
 .10264 
 
 98,9 
 
 7430 
 
 939,3 
 
 .104 
 
 .10419 
 
 100,5 
 
 .00541 
 
 10,4 
 
 .10363 
 
 98,9 
 
 .6500 
 
 921,2 
 
 0.105 
 
 0.10519 
 
 100,6 
 
 1.00552 
 
 10,5 
 
 o. 10462 
 
 98,9 
 
 9.5588 
 
 903,7 
 
 .106 
 
 .10620 
 
 100,6 
 
 .00562 
 
 10,6 
 
 .10560 
 
 98,9 
 
 .4693 
 
 886,7 
 
 .107 
 
 .IO72O 
 
 100,6 
 
 .00573 
 
 10,7 
 
 .10659 
 
 98,9 
 
 .3814 
 
 870,1 
 
 .108 
 
 .10821 
 
 1 00,6 
 
 .00584 
 
 10,8 
 
 .10758 
 
 98,8 
 
 .2952 
 
 854,0 
 
 .109 
 
 .10922 
 
 100,6 
 
 .00595 
 
 10,9 
 
 .10857 
 
 98,8 
 
 .2106 
 
 838,4 
 
 O.IIO 
 
 O.IIO22 
 
 100,6 
 
 1.00606 
 
 11,0 
 
 o. 10956 
 
 98,8 
 
 9- 1275 
 
 823,1 
 
 .in 
 
 .11123 
 
 100,6 
 
 .00617 
 
 n, i 
 
 .11055 
 
 98,8 
 
 .0460 
 
 808,3 
 
 .112 
 
 . I 1223 
 
 100,6 
 
 .00628 
 
 11,2 
 
 .HI53 
 
 98,8 
 
 8.9659 
 
 793,9 
 
 .113 
 
 .11324 
 
 100,6 
 
 .00639 
 
 n,3 
 
 .11252 
 
 98,7 
 
 .8872 
 
 779,8 
 
 .114 
 
 .11425 
 
 100,7 
 
 .00651 
 
 n,4 
 
 .11351 
 
 98,7 
 
 .8099 
 
 766,1 
 
 O.II5 
 
 O.II525 
 
 100,7 
 
 1.00662 
 
 n,5 
 
 0.11450 
 
 98,7 
 
 8.7340 
 
 752,8 
 
 .116 
 
 .11626 
 
 100,7 
 
 .00674 
 
 11,6 
 
 .11548 
 
 98,7 
 
 .6593 
 
 739,8 
 
 .117 
 
 .11727 
 
 100,7 
 
 .00685 
 
 n,7 
 
 .11647 
 
 98,6 
 
 .5860 
 
 727,2 
 
 .118 
 
 .11827 
 
 100,7 
 
 .00697 
 
 11,8 
 
 .11746 
 
 98,6 
 
 .5139 
 
 714,9 
 
 .119 
 
 .11928 
 
 100,7 
 
 .00709 
 
 11,9 
 
 .11844 
 
 98,6 
 
 4430 
 
 702,8 
 
 0.120 
 
 0.12029 
 
 100,7 
 
 1.00721 
 
 1 2,0 
 
 0.11943 
 
 98,6 
 
 8-3733 
 
 691,1 
 
 .121 
 
 .12130 
 
 100,7 
 
 .00733 
 
 12,1 
 
 .12041 
 
 98,6 
 
 .3048 
 
 679,7 
 
 .122 
 
 . 12230 
 
 100,7 
 
 .00745 
 
 12,2 
 
 .12140 
 
 98,5 
 
 .2373 
 
 668,5 
 
 .123 
 
 .12331 
 
 100,8 
 
 .00757 
 
 12,3 
 
 . 12238 
 
 98,5 
 
 .1710 
 
 657,7 
 
 .124 
 
 .12432 
 
 100,8 
 
 .00770 
 
 12,4 
 
 12337 
 
 98,5 
 
 .1058 
 
 647,0 
 
 O.I25 
 
 o. 12533 
 
 100,8 
 
 1.00782 
 
 12,5 
 
 0.12435 
 
 98,5 
 
 8.0416 
 
 636,7 
 
 .126 
 
 . 12633 
 
 100,8 
 
 .00795 
 
 12,6 
 
 . 12534 
 
 98,4 
 
 7.9785 
 
 626,6 
 
 .127 
 
 12734 
 
 100,8 
 
 .00808 
 
 12,7 
 
 .12632 
 
 98,4 
 
 .9163 
 
 616,7 
 
 .128 
 
 .12835 
 
 1 00,8 
 
 .00820 
 
 12,8 
 
 .12731 
 
 98,4 
 
 .8551 
 
 607,0 
 
 .129 
 
 .12936 
 
 100,8 
 
 .00833 
 
 12,9 
 
 .12829 
 
 98,4 
 
 7949 
 
 597,6 
 
 0.130 
 
 0.13037 
 
 100,8 
 
 1.00846 
 
 13,0 
 
 o. 12927 
 
 98,3 
 
 7.7356 
 
 588, 4 
 
 .131 
 
 .13138 
 
 100,9 
 
 .00859 
 
 13,1 
 
 . 13026 
 
 98,3 
 
 .6772 
 
 579,4 
 
 .132 
 
 .13238 
 
 100,9 
 
 .00872 
 
 13,2 
 
 .13124 
 
 98,3 
 
 6197 
 
 570,6 
 
 133 
 
 . U339 
 
 100,9 
 
 .00886 
 
 13,3 
 
 . 13222 
 
 98,3 
 
 .5631 
 
 562,0 
 
 134 
 
 .13440 
 
 100,9 
 
 .00899 
 
 13,4 
 
 .13320 
 
 98,2 
 
 .5073 
 
 553,6 
 
 0.135 
 
 o. 13541 
 
 100,9 
 
 1.00913 
 
 13,5 
 
 0.13419 
 
 98,2 
 
 7.4524 
 
 545,4 
 
 .136 
 
 .13642 
 
 100,9 
 
 .00926 
 
 13,6 
 
 .13517 
 
 98,2 
 
 .3982 
 
 537,3 
 
 .137 
 
 . 13743 
 
 100,9 
 
 .00940 
 
 13,7 
 
 .13615 
 
 98,1 
 
 .3449 
 
 529,5 
 
 .138 
 
 .13844 
 
 IOI,O 
 
 .00954 
 
 13,8 
 
 13713 
 
 98,1 
 
 .2923 
 
 521,8 
 
 139 
 
 . 13945 
 
 IOI,0 
 
 .00968 
 
 13,9 
 
 .13811 
 
 98,1 
 
 .2405 
 
 514,3 
 
 O.I4O 
 
 0.14046 
 
 IOI,O 
 
 1.00982 
 
 14,0 
 
 0.13909 
 
 98,1 
 
 7.1895 
 
 506,9 
 
 .141 
 
 . 14147 
 
 101,0 
 
 .00096 
 
 14,1 
 
 .14007 
 
 98,0 
 
 .1391 
 
 499,7 
 
 .142 
 
 . 14248 
 
 IOI,O 
 
 .01010 
 
 14,2 
 
 . 14105 
 
 98,0 
 
 .0895 
 
 492,6 
 
 143 
 
 . 14349 
 
 101,0 
 
 .01024 
 
 14,3 
 
 . 14203 
 
 98,0 
 
 .0406 
 
 485,7 
 
 .144 
 
 .14450 
 
 101,0 
 
 .01039 
 
 14,4 
 
 .14301 
 
 98,0 
 
 6.9924 
 
 478,9 
 
 0.145 
 
 0.14551 
 
 IOI, 
 
 1.01053 
 
 14,6 
 
 0. 14399 
 
 97,9 
 
 6.9448 
 
 472,3 
 
 .146 
 
 . 14652 
 
 101, 
 
 .01068 
 
 14,7 
 
 . 14497 
 
 97,9 
 
 .8979 
 
 465,8 
 
 .147 
 
 . 14753 
 
 IOI, 
 
 .01082 
 
 14,8 
 
 14595 
 
 97,9 
 
 .8517 
 
 459,5 
 
 .148 
 
 .14854 
 
 IOI, 
 
 .01097 
 
 14,9 
 
 .14693 
 
 97,8 
 
 .8060 
 
 453,2 
 
 .149 
 
 - 14955 
 
 IOI, 
 
 .01112 
 
 i5,o 
 
 . I479I 
 
 97,8 
 
 .7610 
 
 447,1 
 
 0.150 
 
 0.15056 
 
 101,1 
 
 1.01127 
 
 I5,i 
 
 0.14889 
 
 97,8 
 
 6.7166 
 
 441,1 
 
 U 
 
 tan gd u 
 
 Fo' 
 
 sec gd u 
 
 Fo' 
 
 in gd u 
 
 Fo' 
 
 esc gd u 
 
 FV 
 
 SMITHSONIAN TABLES 
 
 108 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinh u 
 
 F ' 
 
 cosh u 
 
 c-Fo' 
 
 tanh u 
 
 *Fo' 
 
 coth u 
 
 C Fo' 
 
 0.150 
 
 0.15056 
 
 101,1 
 
 I. 01127 
 
 I5,i 
 
 0.14889 
 
 97,8 
 
 6.7166 
 
 441,1 
 
 .151 
 
 .15157 
 
 IOI,I 
 
 .01142 
 
 I&2 
 
 .14986 
 
 97,8 
 
 .6728 
 
 435,3 
 
 .152 
 
 . 15259 
 
 101,2 
 
 .01157 
 
 15,3 
 
 .15084 
 
 97,7 
 
 .6295 
 
 429,5 
 
 .153 
 
 .15360 
 
 101,2 
 
 .01173 
 
 15,4 
 
 .15182 
 
 97,7 
 
 .5869 
 
 423,9 
 
 .154 
 
 .15461 
 
 101,2 
 
 .01188 
 
 15,5 
 
 15279 
 
 97,7 
 
 .5448 
 
 418,3 
 
 0.155 
 
 0.15562 
 
 101,2 
 
 I. 01204 
 
 15,6 
 
 0.15377 
 
 97,6 
 
 6.5032 
 
 412,9 
 
 .156 
 
 .15663 
 
 101,2 
 
 .01219 
 
 15,7 
 
 .15475 
 
 97,6 
 
 .4622 
 
 407,6 
 
 .157 
 
 15765 
 
 101,2 
 
 .01235 
 
 15,8 
 
 . 15572 
 
 97,6 
 
 .4217 
 
 402,4 
 
 .158 
 
 .15866 
 
 101,3 
 
 .01251 
 
 15,9 
 
 . 15670 
 
 97,5 
 
 .3817 
 
 397,3 
 
 .159 
 
 . 15967 
 
 101,3 
 
 .01267 
 
 16,0 
 
 . 15767 
 
 97,5 
 
 .3422 
 
 392,2 
 
 0.160 
 
 O.l6o68 
 
 101,3 
 
 1.01283 
 
 16,1 
 
 0.15865 
 
 97,5 
 
 6.3032 
 
 387,3 
 
 .161 
 
 . 16170 
 
 101,3 
 
 .01299 
 
 16,2 
 
 .15962 
 
 97,5 
 
 .2648 
 
 382,5 
 
 .162 
 
 . 16271 
 
 101,3 
 
 .01315 
 
 16,3 
 
 .16060 
 
 97,4 
 
 .2267 
 
 377,7 
 
 .163 
 
 . 16372 
 
 101,3 
 
 .01331 
 
 16,4 
 
 .16157 
 
 97,4 
 
 .1892 
 
 
 .164 
 
 16474 
 
 101,3 
 
 .01348 
 
 16,5 
 
 . 16254 
 
 97,4 
 
 .1521 
 
 368,5 
 
 0.165 
 
 0.16575 
 
 101,4 
 
 1.01364 
 
 16,6 
 
 0.16352 
 
 97,3 
 
 6.H55 
 
 364,0 
 
 .166 
 
 .16676 
 
 101,4 
 
 .01381 
 
 16,7 
 
 .16449 
 
 97,3 
 
 .0793 
 
 359,6 
 
 .167 
 
 .16778 
 
 101,4 
 
 .01398 
 
 16,8 
 
 . 16546 
 
 97,3 
 
 .0436 
 
 355,2 
 
 .168 
 
 .16879 
 
 101,4 
 
 .01415 
 
 16,9 
 
 .16644 
 
 97,2 
 
 .0083 
 
 35i,o 
 
 .169 
 
 .16981 
 
 101,4 
 
 .01431 
 
 17,0 
 
 .16741 
 
 97,2 
 
 5-9734 
 
 346,8 
 
 0.170 
 
 o. 17082 
 
 101,4 
 
 1.01448 
 
 I7,i 
 
 o. 16838 
 
 97,2 
 
 5.9389 
 
 342,7 
 
 .171 
 
 .17183 
 
 ioi,5 
 
 .01466 
 
 17^2 
 
 .16935 
 
 97,i 
 
 .9048 
 
 338,7 
 
 .172 
 
 .17285 
 
 ioi,5 
 
 .01483 
 
 17,3 
 
 . 17032 
 
 97,1 
 
 .8712 
 
 334,7 
 
 .173 
 
 .17386 
 
 101,5 
 
 .01500 
 
 17,4 
 
 .17129 
 
 97,1 
 
 .8379 
 
 330,8 
 
 .174 
 
 .17488 
 
 101,5 
 
 .01518 
 
 17,5 
 
 .17226 
 
 97,o 
 
 .8050 
 
 327,0 
 
 0.175 
 
 0.17589 
 
 ioi,5 
 
 I. 01535 
 
 17,6 
 
 o. 17324 
 
 97,0 
 
 5.7725 
 
 323,2 
 
 .176 
 
 .17691 
 
 101,6 
 
 .01553 
 
 17,7 
 
 . 17420 
 
 97,o 
 
 .7404 
 
 319,5 
 
 .177 
 
 .17793 
 
 101,6 
 
 .01571 
 
 17,8 
 
 .17517 
 
 96,9 
 
 .7086 
 
 315,9 
 
 .178 
 
 .17894 
 
 101,6 
 
 .01588 
 
 17,9 
 
 .17614 
 
 96,9 
 
 .6772 
 
 312,3 
 
 .179 
 
 .17996 
 
 101,6 
 
 .01606 
 
 18,0 
 
 .17711 
 
 96,9 
 
 .6461 
 
 308,8 
 
 0.180 
 
 0.18097 
 
 101,6 
 
 1.01624 
 
 18,1 
 
 0.17808 
 
 96.8 
 
 5.6154 
 
 305,3 
 
 .181 
 
 .18199 
 
 101,6 
 
 .01643 
 
 18,2 
 
 . 17905 
 
 96,8 
 
 .5851 
 
 301,9 
 
 .182 
 
 . 18301 
 
 101,7 
 
 .01661 
 
 18,3 
 
 .18002 
 
 96,8 
 
 5550 
 
 298,6 
 
 .183 
 
 . 18402 
 
 101,7 
 
 .01679 
 
 18,4 
 
 .18098 
 
 96,7 
 
 .5253 
 
 295,3 
 
 .184 
 
 .18504 
 
 101,7 
 
 .01698 
 
 18,5 
 
 . 18195 
 
 96,7 
 
 .4060 
 
 292,1 
 
 0.185 
 
 0.18606 
 
 101,7 
 
 1.01716 
 
 18,6 
 
 o. 18292 
 
 96,7 
 
 5.4669 
 
 288,9 
 
 .186 
 
 . 18707 
 
 101,7 
 
 .01735 
 
 18,7 
 
 .18388 
 
 96,6 
 
 .4382 
 
 285,8 
 
 .187 
 
 .18809 
 
 101,8 
 
 .01754 
 
 18,8 
 
 .18485 
 
 96,6 
 
 .4098 
 
 282,7 
 
 .188 
 
 .18911 
 
 101,8 
 
 .01772 
 
 18,9 
 
 . 18582 
 
 96,5 
 
 .3817 
 
 279,6 
 
 .189 
 
 .19013 
 
 101,8 
 
 .01791 
 
 19,0 
 
 .18678 
 
 96,5 
 
 .3539 
 
 276,6 
 
 0.190 
 
 0.19115 
 
 101,8 
 
 I. 01810 
 
 19,1 
 
 0.18775 
 
 96,5 
 
 5.3263 
 
 273,7 
 
 .191 
 
 .19216 
 
 101,8 
 
 .01830 
 
 19,2 
 
 .18871 
 
 96,4 
 
 .2991 
 
 270,8 
 
 .192 
 
 .19318 
 
 101,8 
 
 .01849 
 
 19,3 
 
 .18967 
 
 96,4 
 
 .2722 
 
 268,0 
 
 193 
 
 . 19420 
 
 101,9 
 
 .01868 
 
 19,4 
 
 .19064 
 
 96,4 
 
 .2455 
 
 265,2 
 
 .194 
 
 . 19522 
 
 101,9 
 
 .01888 
 
 19,5 
 
 .19160 
 
 96,3 
 
 .2191 
 
 262,4 
 
 0.195 
 
 0.19624 
 
 101,9 
 
 1.01907 
 
 19,6 
 
 0.19257 
 
 96,3 
 
 5.1930 
 
 259,7 
 
 .196 
 
 . 19726 
 
 101,9 
 
 .01927 
 
 19,7 
 
 .19353 
 
 96,3 
 
 .1672 
 
 257,0 
 
 .197 
 
 .19828 
 
 101,9 
 
 .01947 
 
 19,8 
 
 .19449 
 
 96,2 
 
 .1416 
 
 254,4 
 
 .198 
 
 .19930 
 
 102,0 
 
 .01967 
 
 19,9 
 
 . 19545 
 
 96,2 
 
 .1163 
 
 251,8 
 
 -.199 
 
 .20032 
 
 102,0 
 
 .01987 
 
 20,0 
 
 .19641 
 
 96,1 
 
 .0913 
 
 249,2 
 
 0.200 
 
 0.20134 
 
 IO2,O 
 
 1.02007 
 
 20,1 
 
 0.19738 
 
 06,1 
 
 5.0665 
 
 246,7 
 
 U 
 
 tan gd u 
 
 F ' 
 
 sec gd u 
 
 a. Fo' 
 
 sin gd u 
 
 Fo' 
 
 esc gd u 
 
 <- Fo' 
 
 SMITHSONIAN TABLES 
 
 109 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinhu 
 
 <-Fo' 
 
 cosh u 
 
 FO' 
 
 tanh u 
 
 UFO' 
 
 coth u 
 
 Fo' 
 
 O.20O 
 
 0.20134 
 
 IO2.O 
 
 1.02007 
 
 20,1 
 
 0.19738 
 
 96,1 
 
 5.0665 
 
 246,7 
 
 .2OI 
 
 .20236 
 
 IO2,O 
 
 .02027 
 
 20,2 
 
 .19834 
 
 96,1 
 
 .0419 
 
 244,2 
 
 .202 
 
 .20338 
 
 IO2,0 
 
 .02047 
 
 20,3 
 
 .19930 
 
 96,0 
 
 .0176 
 
 241,8 
 
 .203 
 
 .20440 
 
 IO2,I 
 
 .02068 
 
 20,4 
 
 .20026 
 
 96,0 
 
 4.9936 
 
 239,4 
 
 .204 
 
 .20542 
 
 IO2,I 
 
 .02088 
 
 20,5 
 
 .20122 
 
 96,0 
 
 9698 
 
 237,0 
 
 O.205 
 
 0.20644 
 
 IO2,I 
 
 1.02109 
 
 20,6 
 
 O.2O2I8 
 
 95,9 
 
 4.9462 
 
 234,6 
 
 .206 
 
 .20746 
 
 102,1 
 
 .02129 
 
 20,7 
 
 .20313 
 
 95,9 
 
 .9228 
 
 232,3 
 
 .207 
 
 .20848 
 
 102,2 
 
 .02150 
 
 20,8 
 
 .20409 
 
 95,8 
 
 .8997 
 
 230,1 
 
 .208 
 
 .20950 
 
 102,2 
 
 .02171 
 
 2I,O 
 
 .20505 
 
 95,8 
 
 .8768 
 
 227,8 
 
 .209 
 
 .21052 
 
 IO2,2 
 
 .02192 
 
 21,1 
 
 .20601 
 
 95,8 
 
 .8542 
 
 225,6 
 
 O.2IO 
 
 0.21155 
 
 IO2,2 
 
 1.02213 
 
 21,2 
 
 0.20697 
 
 95,7 
 
 4.8317 
 
 223,5 
 
 .211 
 
 .21257 
 
 IO2,2 
 
 .02234 
 
 21,3 
 
 .20792 
 
 95,7 
 
 .8095 
 
 221,3 
 
 .212 
 
 .21359 
 
 102,3 
 
 .02256 
 
 21,4 
 
 .20888 
 
 95,6 
 
 .7874 
 
 219,2 
 
 .213 
 
 .21461 
 
 102,3 
 
 .02277 
 
 21,5 
 
 .20984 
 
 95,6 
 
 .7656 
 
 217,1 
 
 .214 
 
 .21564 
 
 102,3 
 
 .02299 
 
 21,6 
 
 .21079 
 
 95,6 
 
 .7440 
 
 215,1 
 
 0.215 
 
 0.21666 
 
 102,3 
 
 1.02320 
 
 21,7 
 
 0.21175 
 
 95,5 
 
 4.7226 
 
 213,0 
 
 .2l6 
 
 .21768 
 
 102,3 
 
 .02342 
 
 21,8 
 
 .21270 
 
 95,5 
 
 .7014 
 
 211,0 
 
 .217 
 
 .21871 
 
 102,4 
 
 .02364 
 
 21,9 
 
 .21366 
 
 95,4 
 
 .6804 
 
 209,1 
 
 .218 
 
 .21973 
 
 102,4 
 
 .02386 
 
 22,0 
 
 .21461 
 
 95,4 
 
 .6596 
 
 2O7.I 
 
 .219 
 
 .22075 
 
 102,4 
 
 .02408 
 
 22,1 
 
 .21556 
 
 95,4 
 
 .6390 
 
 205,2 
 
 O.22O 
 
 0.22178 
 
 102,4 
 
 1.02430 
 
 22,2 
 
 0.21652 
 
 95,3 
 
 4.6186 
 
 203,3 
 
 .221 
 
 .22280 
 
 102,5 
 
 .02452 
 
 22,3 
 
 .21747 
 
 95,3 
 
 .5983 
 
 201,4 
 
 .222 
 
 .22383 
 
 102,5 
 
 .02474 
 
 22,4 
 
 .21842 
 
 95,2 
 
 .5/83 
 
 199,6 
 
 .223 
 
 .22485 
 
 102,5 
 
 .02497 
 
 22,5 
 
 .21938 
 
 95,2 
 
 .5584 
 
 197,8 
 
 .224 
 
 .22588 
 
 102,5 
 
 .02519 
 
 22,6 
 
 .22033 
 
 95,1 
 
 .5387 
 
 196,0 
 
 O.225 
 
 0.22690 
 
 102,5 
 
 1.02542 
 
 22,7 
 
 0.22128 
 
 95,1 
 
 4.5192 
 
 194,2 
 
 .226 
 
 .22793 
 
 102,6 
 
 .02565 
 
 22,8 
 
 .22223 
 
 95,1 
 
 .4999 
 
 192,5 
 
 .227 
 
 .22895 
 
 102,6 
 
 .02588 
 
 22,9 
 
 .22318 
 
 95,o 
 
 .4807 
 
 190,8 
 
 .228 
 
 .22998 
 
 102,6 
 
 .02610 
 
 23,0 
 
 .22413 
 
 95,o 
 
 .4617 
 
 189,1 
 
 .229 
 
 .23101 
 
 102,6 
 
 .02634 
 
 23,1 
 
 .22508 
 
 94,9 
 
 .4429 
 
 187,4 
 
 O.23O 
 
 0.23203 
 
 102,7 
 
 1.02657 
 
 23,2 
 
 0.22603 
 
 94.0 
 
 4.4242 
 
 i85,7 
 
 .231 
 
 .23306 
 
 102,7 
 
 .02680 
 
 23,3 
 
 .22698 
 
 94,8 
 
 .4057 
 
 184,1 
 
 .232 
 
 .23409 
 
 102,7 
 
 .02703 
 
 23,4 
 
 .22793 
 
 94,8 
 
 .3874 
 
 182,5 
 
 233 
 
 .23511 
 
 102,7 
 
 .02727 
 
 23,5 
 
 .22887 
 
 94,8 
 
 .3692 
 
 180,9 
 
 234 
 
 .23614 
 
 102,8 
 
 .02750 
 
 23,6 
 
 .22982 
 
 94,7 
 
 3512 
 
 179,3 
 
 0.235 
 
 0.23717 
 
 102,8 
 
 I .02774 
 
 23,7 
 
 0.23077 
 
 94,7 
 
 4.3334 
 
 177,8 
 
 .236 
 
 .23820 
 
 102,8 
 
 .02798 
 
 23,8 
 
 .23171 
 
 94,6 
 
 .3157 
 
 176,2 
 
 .237 
 
 .23922 
 
 102,8 
 
 .02822 
 
 23,9 
 
 .23266 
 
 94,6 
 
 .2981 
 
 174,7 
 
 .238 
 
 .24025 
 
 102,8 
 
 .02846 
 
 24,0 
 
 .23361 
 
 94,5 
 
 .2807 
 
 173,2 
 
 239 
 
 .24128 
 
 102,9 
 
 .02870 
 
 24,1 
 
 .23455 
 
 94,5 
 
 2635 
 
 171,8 
 
 0.240 
 
 0.24231 
 
 102,9 
 
 1.02894 
 
 24,2 
 
 0.23550 
 
 94,5 
 
 4.2464 
 
 170,3 
 
 .241 
 
 .24334 
 
 102,9 
 
 .02918 
 
 24,3 
 
 .23644 
 
 94,4 
 
 .2294 
 
 168,9 
 
 .242 
 
 .24437 
 
 102,9 
 
 .02043 
 
 24,4 
 
 .23738 
 
 94,4 
 
 .2126 
 
 l6>,5 
 
 .243 
 
 .24540 
 
 103,0 
 
 .02967 
 
 24,5 
 
 .23833 
 
 94,3 
 
 .1959 
 
 166,1 
 
 .244 
 
 .24643 
 
 103,0 
 
 .02992 
 
 24,6 
 
 .23927 
 
 94,3 
 
 .1794 
 
 164,7 
 
 0.245 
 
 0.24746 
 
 103,0 
 
 1.03016 
 
 24,7 
 
 0.24021 
 
 94,2 
 
 4.1630 
 
 163,3 
 
 .246 
 
 .24849 
 
 103,0 
 
 .03041 
 
 24,8 
 
 .24115 
 
 94,2 
 
 .1467 
 
 162,0 
 
 .247 
 
 .24952 
 
 103,1 
 
 .03066 
 
 25,0 
 
 .24210 
 
 94,1 
 
 .1306 
 
 160,6 
 
 .248 
 
 .25055 
 
 103,1 
 
 .03091 
 
 25,1 
 
 .24304 
 
 94,1 
 
 .1146 
 
 159,3 
 
 .249 
 
 .25158 
 
 103,1 
 
 .03116 
 
 25,2 
 
 24398 
 
 94,0 
 
 .0987 
 
 158,0 
 
 0.250 
 
 0.25261 
 
 103,1 
 
 1.03141 
 
 25,3 
 
 0.24402 
 
 94,0 
 
 4.0830 
 
 156,7 
 
 u tan gd u 
 
 F ' 
 
 sec od u 
 
 Fo' 
 
 sin od u 
 
 Fo' 
 
 esc gd u 
 
 a, Fo' 
 
 SMITHSONIAN TABLES 
 
 110 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinh u 
 
 F ' 
 
 cosh u 
 
 wF ' 
 
 tanh u 
 
 Fo' 
 
 coth u 
 
 Fo' 
 
 0.250 
 
 O.2526I 
 
 103,1 
 
 1.03141 
 
 25,3 
 
 0.24492 
 
 94,0 
 
 4.0830 
 
 156,7 
 
 .251 
 
 .25364 
 
 103,2 
 
 .03167 
 
 25,4 
 
 .24586 
 
 94,0 
 
 .0674 
 
 155,4 
 
 .252 
 
 .25468 
 
 103,2 
 
 .03192 
 
 25,5 
 
 .24680 
 
 93,9 
 
 .0519 
 
 154,2 
 
 .253 
 
 .25571 
 
 103,2 
 
 .03218 
 
 25,6 
 
 24774 
 
 93,9 
 
 .0365 
 
 152,9 
 
 .254 
 
 .25674 
 
 103,2 
 
 .03243 
 
 25,7 
 
 .24867 
 
 93,8 
 
 .O2I3 
 
 151,7 
 
 0.255 
 
 0.25777 
 
 103,3 
 
 1.03269 
 
 25,8 
 
 0.24961 
 
 93,8 
 
 4.0062 
 
 150,5 
 
 .256 
 
 .25881 
 
 103,3 
 
 .03295 
 
 25,9 
 
 .25055 
 
 93,7 
 
 3.9912 
 
 149,3 
 
 .257 
 
 .25984 
 
 103,3 
 
 .03321 
 
 26,0 
 
 .25149 
 
 93,7 
 
 .9763 
 
 148.1 
 
 .258 
 
 .26087 
 
 103,3 
 
 .03347 
 
 26,1 
 
 .25242 
 
 93,6 
 
 .9616 
 
 146,9 
 
 .259 
 
 .26191 
 
 103,4 
 
 .03373 
 
 26,2 
 
 .25336 
 
 93,6 
 
 9470 
 
 145,8 
 
 0.260 
 
 0.26294 
 
 103,4 
 
 1.03399 
 
 26,3 
 
 0.25430 
 
 93,5 
 
 3.9324 
 
 144,6 
 
 .261 
 
 .26397 
 
 103,4 
 
 .03425 
 
 26,4 
 
 .25523 
 
 93,5 
 
 .9180 
 
 143,5 
 
 .262 
 
 .26501 
 
 103,5 
 
 .03452 
 
 26,5 
 
 .25617 
 
 93,4 
 
 .9037 
 
 142,4 
 
 .263 
 
 .26604 
 
 103,5 
 
 .03478 
 
 26,6 
 
 .25710 
 
 93,4 
 
 .8895 
 
 141,3 
 
 .264 
 
 .26708 
 
 103,5 
 
 .03505 
 
 26,7 
 
 .25803 
 
 93,3 
 
 .8755 
 
 140,2 
 
 0.265 
 
 0.26811 
 
 103,5 
 
 1.03532 
 
 26,8 
 
 0.25897 
 
 93,3 
 
 3.8615 
 
 139,1 
 
 .266 
 
 .26915 
 
 103,6 
 
 .03559 
 
 26,9 
 
 .25990 
 
 93,2 
 
 .8476 
 
 138,0 
 
 .267 
 
 .27018 
 
 103,6 
 
 .03586 
 
 27,0 
 
 .26083 
 
 93,2 
 
 .8339 
 
 137,0 
 
 .268 
 
 .27122 
 
 103,6 
 
 .03613 
 
 27,1 
 
 .26176 
 
 93,1 
 
 .8203 
 
 135,9 
 
 .269 
 
 .27226 
 
 103,6 
 
 .03640 
 
 27,2 
 
 .26269 
 
 93,1 
 
 .8067 
 
 134,9 
 
 0.270 
 
 0.27329 
 
 103,7 
 
 1.03667 
 
 27,3 
 
 0.26362 
 
 93,1 
 
 3-7933 
 
 133,9 
 
 .271 
 
 .27433 
 
 103,7 
 
 .03695 
 
 27,4 
 
 .26456 
 
 93,0 
 
 7799 
 
 132,9 
 
 .272 
 
 .27537 
 
 103,7 
 
 .03722 
 
 27,5 
 
 .26548 
 
 93,0 
 
 .7667 
 
 I3L9 
 
 .273 
 
 .27640 
 
 103,7 
 
 .03750 
 
 27,6 
 
 .26641 
 
 92,9 
 
 .7536 
 
 130,9 
 
 .274 
 
 .27744 
 
 103,8 
 
 .03777 
 
 27,7 
 
 .26734 
 
 92,9 
 
 .7405 
 
 129,9 
 
 0.275 
 
 0.27848 
 
 103,8 
 
 1.03805 
 
 27,8 
 
 0.26827 
 
 92,8 
 
 3.7276 
 
 128,9 
 
 .276 
 
 .27952 
 
 103,8 
 
 .03833 
 
 28,0 
 
 .26920 
 
 92,8 
 
 .7147 
 
 128,0 
 
 - .277 
 
 .28056 
 
 103,9 
 
 .03861 
 
 28,1 
 
 .27013 
 
 92,7 
 
 .7020 
 
 127,0 
 
 .278 
 
 .28159 
 
 103,9 
 
 .03889 
 
 28,2 
 
 .27105 
 
 92,7 
 
 .6893 
 
 126,1 
 
 .279 
 
 .28263 
 
 103,9 
 
 03917 
 
 28,3 
 
 .27198 
 
 92,6 
 
 .6768 
 
 125,2 
 
 0.280 
 
 0.28367 
 
 J03,9 
 
 1.03946 
 
 28,4 
 
 0.27291 
 
 92,6 
 
 3-6643 
 
 124,3 
 
 .281 
 
 .28471 
 
 104,0 
 
 03974 
 
 28,5 
 
 .27383 
 
 92,5 
 
 .6519 
 
 123,4 
 
 .282 
 
 .28575 
 
 104,0 
 
 .04003 
 
 28,6 
 
 .27476 
 
 92,5 
 
 .6396 
 
 122,5 
 
 .283 
 
 .28679 
 
 104,0 
 
 .04031 
 
 28,7 
 
 .27568 
 
 92,4 
 
 .6274 
 
 121,6 
 
 .284 
 
 .28783 
 
 104,1 
 
 .04060 
 
 28,8 
 
 .27660 
 
 92,4 
 
 .6153 
 
 120,7 
 
 0.285 
 
 0.28887 
 
 104,1 
 
 1.04089 
 
 28,9 
 
 0.27753 
 
 92,3 
 
 3-6033 
 
 119,8 
 
 .286 
 
 .28991 
 
 104,1 
 
 .04118 
 
 29,0 
 
 .27845 
 
 92,2 
 
 .5913 
 
 119,0 
 
 .287 
 
 .29006 
 
 104,1 
 
 .04147 
 
 29,1 
 
 .27937 
 
 92,2 
 
 5795 
 
 118,1 
 
 .288 
 
 .29200 
 
 104,2 
 
 .04176 
 
 29,2 
 
 .28029 
 
 92,1 
 
 .5677 
 
 H7,3 
 
 .289 
 
 .29304 
 
 104,2 
 
 .04205 
 
 29,3 
 
 .28121 
 
 92,i 
 
 .5560 
 
 116,5 
 
 O.2OO 
 
 0.29408 
 
 104,2 
 
 1.04235 
 
 29,4 
 
 0.28213 
 
 92,0 
 
 3.5444 
 
 115,6 
 
 .291 
 
 .29512 
 
 104,3 
 
 .04264 
 
 29,5 
 
 .28305 
 
 92,0 
 
 .5329 
 
 114,8 
 
 .292 
 
 .29617 
 
 104,3 
 
 .04294 
 
 29,6 
 
 .28397 
 
 9i,9 
 
 .5214 
 
 114,0 
 
 .293 
 
 .29721 
 
 104,3 
 
 .04323 
 
 29,7 
 
 .28489 
 
 9i,9 
 
 .5101 
 
 113,2 
 
 .294 
 
 .29825 
 
 104,4 
 
 .04353 
 
 29,8 
 
 .28581 
 
 9i,8 
 
 .4988 
 
 112,4 
 
 0.295 
 
 0.29930 
 
 104,4 
 
 1.04383 
 
 29,9 
 
 0.28673 
 
 91,8 
 
 3.4876 
 
 111,6 
 
 .296 
 
 .30034 
 
 104,4 
 
 .04413 
 
 30,0 
 
 .28765 
 
 9i,7 
 
 .4765 
 
 110,9 
 
 .297 
 
 .30139 
 
 104,4 
 
 .04443 
 
 30,1 
 
 .28856 
 
 9i,7 
 
 .4654 
 
 no, i 
 
 .298 
 
 .30243 
 
 104,5 
 
 04473 
 
 30,2 
 
 .28948 
 
 91,6 
 
 4545 
 
 109,3 
 
 .299 
 
 .30348 
 
 104,5 
 
 .04503 
 
 30,3 
 
 .29040 
 
 91,6 
 
 .4436 
 
 108,6 
 
 0.300 
 
 0.30452 
 
 104,5 
 
 1.04534 
 
 30,5 
 
 0.29131 
 
 9i,5 
 
 3.4327 
 
 107,8 
 
 u tan gd u 
 
 *> Fo' 
 
 sec gd u 
 
 - Fo' 
 
 sin gd u 
 
 w Fo' 
 
 esc gd u 
 
 Fo' 
 
 SMITHSONIAN TABLES 
 
 III 
 
Natural Hyperbolic Functions. 
 
 u 
 
 tinh u 
 
 -FV 
 
 cosh u 
 
 wF ' 
 
 tanh u 
 
 Fo' 
 
 coth u 
 
 Fo' 
 
 0.300 
 
 0.30452 
 
 1045 
 
 1.04534 
 
 30,5 
 
 0.29131 
 
 91,5 
 
 3.4327 
 
 107,8 
 
 .301 
 
 30557 
 
 104,6 
 
 .04564 
 
 30,6 
 
 .29223 
 
 91,5 
 
 .4220 
 
 107,1 
 
 .302 
 
 .30661 
 
 104,6 
 
 .04595 
 
 30,7 
 
 .293M 
 
 91,4 
 
 .4113 
 
 106,4 
 
 .303 
 
 .30766 
 
 104,6 
 
 .04626 
 
 30,8 
 
 .29406 
 
 91,4 
 
 .4007 
 
 105,6 
 
 .304 
 
 .30870 
 
 104,7 
 
 .04656 
 
 30,9 
 
 .29497 
 
 91,3 
 
 3902 
 
 104,9 
 
 0.305 
 
 0.30975 
 
 104,7 
 
 1.04687 
 
 3i,o 
 
 0.29588 
 
 91,2 
 
 3.3797 
 
 104,2 
 
 .306 
 
 .31080 
 
 104,7 
 
 .04718 
 
 3i,i 
 
 .29679 
 
 91,2 
 
 .3693 
 
 103,5 
 
 .307 
 
 .3H85 
 
 104,7 
 
 .04750 
 
 31,2 
 
 .29771 
 
 91,1 
 
 .3590 
 
 102,8 
 
 .308 
 
 .31289 
 
 104,8 
 
 .04781 
 
 3i,3 
 
 .29862 
 
 91,1 
 
 .3488 
 
 102,1 
 
 .309 
 
 .31394 
 
 104,8 
 
 .04812 
 
 3i,4 
 
 29953 
 
 91,0 
 
 .3386 
 
 101,5 
 
 0.310 
 
 0.31499 
 
 104,8 
 
 1.04844 
 
 3i,5 
 
 0.30044 
 
 91,0 
 
 3.3285 
 
 100,8 
 
 .311 
 
 .31004 
 
 104,9 
 
 .04875 
 
 3i,6 
 
 .30135 
 
 90,9 
 
 .3184 
 
 100,1 
 
 .312 
 
 .31709 
 
 104,9 
 
 .04007 
 
 3i,7 
 
 .30226 
 
 90,9 
 
 .3085 
 
 99,5 
 
 .313 
 
 .3l8l4 
 
 104,9 
 
 .04939 
 
 3i,8 
 
 .30316 
 
 90,8 
 
 .2985 
 
 98,8 
 
 .314 
 
 .31919 
 
 105,0 
 
 .04970 
 
 3i,9 
 
 .30407 
 
 90,8 
 
 .2887 
 
 98,2 
 
 0.315 
 
 0.32024 
 
 105,0 
 
 I .05002 
 
 32,0 
 
 0.30408 
 
 90,7 
 
 3.2789 
 
 97,5 
 
 .316 
 
 .32129 
 
 105,0 
 
 .05034 
 
 32,1 
 
 .30589 
 
 90,6 
 
 .2692 
 
 96,9 
 
 .317 
 
 .32234 
 
 105,1 
 
 .05067 
 
 32,2 
 
 .30679 
 
 90,6 
 
 .2595 
 
 96,2 
 
 .318 
 
 .32339 
 
 105,1 
 
 .05009 
 
 32,3 
 
 .30770 
 
 90,5 
 
 .2499 
 
 95,6 
 
 .319 
 
 .32444 
 
 105,1 
 
 .05131 
 
 32,4 
 
 .30860 
 
 90,5 
 
 .2404 
 
 95,o 
 
 0.320 
 
 0.32549 
 
 105,2 
 
 1.05164 
 
 32,5 
 
 0.30951 
 
 90,4 
 
 3-2309 
 
 94,4 
 
 .321 
 
 .32654 
 
 105,2 
 
 .05196 
 
 32,7 
 
 .31041 
 
 90,4 
 
 .2215 
 
 93,8 
 
 .322 
 
 .32759 
 
 105,2 
 
 .05229 
 
 32,8 
 
 .3H3I 
 
 90,3 
 
 .2122 
 
 93,2 
 
 .323 
 
 .32865 
 
 105,3 
 
 .05262 
 
 32,9 
 
 .31222 
 
 90,3 
 
 .2O29 
 
 92,6 
 
 .324 
 
 .32970 
 
 105,3 
 
 .05295 
 
 33,0 
 
 .31312 
 
 90,2 
 
 1937 
 
 92,0 
 
 0.325 
 
 0.33075 
 
 105,3 
 
 1.05328 
 
 33,1 
 
 0.31402 
 
 90,1 
 
 3-1845 
 
 91,4 
 
 .326 
 
 .33181 
 
 105,4 
 
 .05361 
 
 33,2 
 
 .31492 
 
 90,1 
 
 .1754 
 
 90,8 
 
 .327 
 
 .33286 
 
 105,4 
 
 05394 
 
 33,3 
 
 .31582 
 
 90,0 
 
 .1663 
 
 90,3 
 
 .328 
 
 .33391 
 
 105,4 
 
 .05428 
 
 33,4 
 
 .31672 
 
 90,0 
 
 .1573 
 
 89,7 
 
 .329 
 
 33497 
 
 105,5 
 
 .05461 
 
 33,5 
 
 .31762 
 
 89,9 
 
 .1484 
 
 89,1 
 
 0.330 
 
 0.33602 
 
 105,5 
 
 1.05495 
 
 33,6 
 
 0.31852 
 
 89,9 
 
 3.1395 
 
 88,6 
 
 .331 
 
 .33708 
 
 105,5 
 
 .05528 
 
 33,7 
 
 .31942 
 
 89,8 
 
 .1307 
 
 88,0 
 
 .332 
 
 .33813 
 
 105,6 
 
 .05562 
 
 33,8 
 
 .32032 
 
 89,7 
 
 .1219 
 
 87,5 
 
 333 
 
 .33919 
 
 105,6 
 
 .05506 
 
 33,9 
 
 .32121 
 
 89,7 
 
 .1132 
 
 86,9 
 
 334 
 
 .34024 
 
 105,6 
 
 .05630 
 
 34,0 
 
 .32211 
 
 89,6 
 
 .1045 
 
 86,4 
 
 '0.335 
 
 0.34130 
 
 105,7 
 
 1.05664 
 
 34,1 
 
 0.32301 
 
 89,6 
 
 3.0959 
 
 85,8 
 
 .336 
 
 .34236 
 
 105,7 
 
 .05608 
 
 34,2 
 
 .32300 
 
 89,5 
 
 .0874 
 
 85.3 
 
 337 
 
 34342 
 
 105,7 
 
 05732 
 
 34,3 
 
 .32480 
 
 89,5 
 
 .0789 
 
 84,8 
 
 .338 
 
 34447 
 
 105,8 
 
 .05767 
 
 34,4 
 
 .32569 
 
 89,4 
 
 .0704 
 
 84,3 
 
 339 
 
 34553 
 
 105,8 
 
 .05801 
 
 34,6 
 
 .32658 
 
 89,3 
 
 .0620 
 
 83,8 
 
 0.340 
 
 0.34659 
 
 105,8 
 
 1.05836 
 
 34,7 
 
 0.32748 
 
 89,3 
 
 3.0536 
 
 83,2 
 
 341 
 
 .34765 
 
 105,9 
 
 .05871 
 
 34,8 
 
 .32837 
 
 89,2 
 
 0453 
 
 82,7 
 
 .342 
 
 .34871 
 
 105,9 
 
 .05905 
 
 34,9 
 
 .32926 
 
 89,2 
 
 .0371 
 
 82,2 
 
 343 
 
 34977 
 
 105,9 
 
 .05940 
 
 35,0 
 
 .33015 
 
 89,1 
 
 .0289 
 
 8i,7 
 
 344 
 
 .35082 
 
 106,0 
 
 05975 
 
 35,i 
 
 .33104 
 
 89,0 
 
 .0207 
 
 81,2 
 
 0.345 
 
 0.35188 
 
 106,0 
 
 i. 06011 
 
 35,2 
 
 0.33193 
 
 89,0 
 
 3.0126 
 
 80,8 
 
 .346 
 
 .35295 
 
 1 06,0 
 
 .06046 
 
 35,3 
 
 .33282 
 
 88,9 
 
 .0046 
 
 80,3 
 
 347 
 
 35401 
 
 106,1 
 
 .06081 
 
 35,4 
 
 33371 
 
 88,9 
 
 2.9966 
 
 79,8 
 
 .348 
 
 .35507 
 
 106,1 
 
 .06117 
 
 35,5 
 
 -334<60 
 
 88,8 
 
 .9886 
 
 79,3 
 
 349 
 
 35613 
 
 106,2 
 
 .06152 
 
 35,6 
 
 33549 
 
 88,7 
 
 .9807 
 
 7,8 
 
 0.350 
 
 0.35719 
 
 106,2 
 
 i. 06188 
 
 35,7 
 
 0.33638 
 
 88,7 
 
 2.9729 
 
 78,4 
 
 u 
 
 tan gd u 
 
 Fo' 
 
 sec gd u 
 
 Fo' 
 
 sin gd u 
 
 Fo' 
 
 esc gd u 
 
 Fo' 
 
 SMITHSONIAN TABLES 
 
 112 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinh u 
 
 F ' 
 
 cosh tt 
 
 Fo' 
 
 tanh u 
 
 Fo' ' 
 
 coth u 
 
 -Fo' 
 
 0.350 
 
 0.35719 
 
 106,2 
 
 I. 06188 
 
 35,7 
 
 0.33638 
 
 88,7 
 
 2.9729 
 
 78,4 
 
 .351 
 
 .35825 
 
 106,2 
 
 .06224 
 
 35,8 
 
 .33726 
 
 88,6 
 
 .9651 
 
 77,9 
 
 .352 
 
 35931 
 
 106,3 
 
 .06259 
 
 35,9 
 
 .33815 
 
 88,6 
 
 .9573 
 
 77,5 
 
 353 
 
 .36038 
 
 106,3 
 
 .06295 
 
 36,0 
 
 33903 
 
 88,5 
 
 .9496 
 
 77,o 
 
 354 
 
 .36144 
 
 106,3 
 
 .06332 
 
 36,1 
 
 33992 
 
 88,4 
 
 9419 
 
 76,5 
 
 0.355 
 
 0.36250 
 
 106,4 
 
 1.06368 
 
 36,3 
 
 0.34080 
 
 88,4 
 
 2.9343 
 
 76,1 
 
 .356 
 
 .36357 
 
 106,4 
 
 .06404 
 
 36,4 
 
 .34169 
 
 88,3 
 
 .9267 
 
 75,7 
 
 357 
 
 36463 
 
 106,4 
 
 .06440 
 
 36,5 
 
 .34257 
 
 88,3 
 
 .9191 
 
 75,2 
 
 358 
 
 .36570 
 
 106,5 
 
 .06477 
 
 36,6 
 
 34345 
 
 88,2 
 
 .9116 
 
 74,8 
 
 359 
 
 .36676 
 
 106,5 
 
 .06514 
 
 36,7 
 
 34433 
 
 88,1 
 
 .9042 
 
 74,3 
 
 0.360 
 
 0.36783 
 
 106,6 
 
 1.06550 
 
 36,8 
 
 0.34521 
 
 88,1 
 
 2.8968 
 
 73,9 
 
 .361 
 
 .36889 
 
 106,6 
 
 .06587 
 
 36,9 
 
 .34609 
 
 88,0 
 
 .8894 
 
 73,5 
 
 .362 
 
 .36996 
 
 106,6 
 
 .06624 
 
 37,o 
 
 .34697 
 
 88,0 
 
 .8821 
 
 73,i 
 
 363 
 
 37102 
 
 106,7 
 
 .06661 
 
 37,1 
 
 .34785 
 
 87,9 
 
 .8748 
 
 72,6 
 
 .364 
 
 .37209 
 
 106,7 
 
 .06698 
 
 37,2 
 
 .34873 
 
 87,8 
 
 .8675 
 
 72,2 
 
 0.365 
 
 0.37316 
 
 106,7 
 
 1.06736 
 
 37,3 
 
 0.34961 
 
 87,8 
 
 2.8603 
 
 71,8 
 
 .366 
 
 .37423 
 
 106,8 
 
 .06773 
 
 37,4 
 
 .35049 
 
 87,7 
 
 .8532 
 
 71,4 
 
 .367 
 
 .37529 
 
 106,8 
 
 .06810 
 
 37,5 
 
 .35136 
 
 87,7 
 
 .8460 
 
 71,0 
 
 .368 
 
 .37636 
 
 106,8 
 
 .06848 
 
 37,6 
 
 .35224 
 
 87,6 
 
 .8390 
 
 70,6 
 
 .369 
 
 37743 
 
 106,9 
 
 .06886 
 
 37,7 
 
 .35312 
 
 87,5 
 
 .8319 
 
 70,2 
 
 0.370 
 
 0.37850 
 
 106,9 
 
 1.06923 
 
 37,9 
 
 0.35399 
 
 87,5 
 
 2.8249 
 
 69,8 
 
 371 
 
 .37957 
 
 107,0 
 
 .06061 
 
 38,0 
 
 .35487 
 
 87,4 
 
 .8180 
 
 69,4 
 
 372 
 
 .38064 
 
 107,0 
 
 .06999 
 
 38,i 
 
 35574 
 
 87,3 
 
 .8110 
 
 69,0 
 
 373 
 
 .38171 
 
 107,0 
 
 .07037 
 
 38,2 
 
 .35661 
 
 87,3 
 
 .8042 
 
 68,6 
 
 .374 
 
 .38278 
 
 107,1 
 
 .07076 
 
 38,3 
 
 35749 
 
 87,2 
 
 7973 
 
 68,2 
 
 0.375 
 
 0.38385 
 
 107,1 
 
 1.07114 
 
 38,4 
 
 0.35836 
 
 87,2 
 
 2.7905 
 
 67,9 
 
 .376 
 
 .38492 
 
 107,2 
 
 .07152 
 
 38,5 
 
 .35923 
 
 87,1 
 
 .7837 
 
 67,5 
 
 377 
 
 .38599 
 
 107,2 
 
 .07191 
 
 38,6 
 
 .36010 
 
 87,0 
 
 7770 
 
 67,1 
 
 378 
 
 38707 
 
 107,2 
 
 .07230 
 
 38,7 
 
 .36097 
 
 87,0 
 
 .7703 
 
 66,7 
 
 379 
 
 .38814 
 
 107,3 
 
 .07268 
 
 38,8 
 
 .36184 
 
 86,9 
 
 .7637 
 
 66,4 
 
 0.380 
 
 0.38921 
 
 107,3 
 
 1.07307 
 
 3&9 
 
 0.36271 
 
 86,8 
 
 2.7570 
 
 66,0 
 
 .381 
 
 .39028 
 
 107,3 
 
 .07346 
 
 39,0 
 
 .36358 
 
 86,8 
 
 7505 
 
 65,7 
 
 .382 
 
 .39136 
 
 107,4 
 
 .07385 
 
 39,i 
 
 .36444 
 
 86,7 
 
 7439 
 
 65,3 
 
 .383 
 
 .39243 
 
 107,4 
 
 . .07425 
 
 39,2 
 
 36531 
 
 86,7 
 
 .7374 
 
 64,9 
 
 .384 
 
 39351 
 
 107,5 
 
 .07464 
 
 39,4 
 
 .36618 
 
 86,6 
 
 .7309 
 
 64,6 
 
 0.385 
 
 0.39458 
 
 107,5 
 
 1.07503 
 
 39,3 
 
 0.36704 
 
 86,5 
 
 2.7245 
 
 64,2 
 
 .386 
 
 .39566 
 
 107,5 
 
 .07543 
 
 39,6 
 
 .36791 
 
 86,5 
 
 .7181 
 
 63,9 
 
 .387 
 
 .39673 
 
 107,6 
 
 .07582 
 
 39,7 
 
 .36877 
 
 86,4 
 
 .7117 
 
 63,5 
 
 .388 
 
 .3978i 
 
 107,6 
 
 .07622 
 
 39,8 
 
 .36063 
 
 86,3 
 
 7054 
 
 63,2 
 
 .389 
 
 .39889 
 
 107,7 
 
 .07662 
 
 39,9 
 
 .37050 
 
 86,3 
 
 .6991 
 
 62,8 
 
 0.390 
 
 0.39996 
 
 107,7 
 
 1.07702 
 
 40,0 
 
 0.37136 
 
 86,2 
 
 2.6928 
 
 62,5 
 
 391 
 
 .40104 
 
 107,7 
 
 .07742 
 
 40,1 
 
 .37222 
 
 86,1 
 
 .6866 
 
 62,2 
 
 392 
 
 .40212 
 
 107,8 
 
 .07782 
 
 40,2 
 
 .37308 
 
 86,1 
 
 .6804 
 
 61,8 
 
 393 
 
 .40319 
 
 107,8 
 
 .07822 
 
 40,3 
 
 
 86,0 
 
 .6742 
 
 6i,5 
 
 394 
 
 .40427 
 
 107,9 
 
 .07863 
 
 40,4 
 
 .3748o 
 
 86,0 
 
 .6681 
 
 61,2 
 
 0.395 
 
 0.40535 
 
 107,9 
 
 1.07903 
 
 40,5 
 
 0.37566 
 
 85,9 
 
 2.6620 
 
 60,9 
 
 .396 
 
 .40643 
 
 107,9 
 
 .07944 
 
 40,6 
 
 .37652 
 
 85,8 
 
 .6559 
 
 60,5 
 
 397 
 
 .40751 
 
 108,0 
 
 .07984 
 
 40,8 
 
 .37738 
 
 85,8 
 
 .6499 
 
 60,2 
 
 .398 
 
 .40859 
 
 108,0 
 
 .08025 
 
 40,9 
 
 .37824 
 
 85,7 
 
 .6438 
 
 59,9 
 
 .399 
 
 .40967 
 
 108,1 
 
 .08066 
 
 41,0 
 
 .37909 
 
 85,6 
 
 .6379 
 
 59,6 
 
 0.400 
 
 0.41075 
 
 108,1 
 
 1.08107 
 
 41,1 
 
 0.37995 
 
 85,6 
 
 2.6319 
 
 59,3 
 
 u 
 
 tan gd u 
 
 F ' 
 
 sec gd u 
 
 w Fo' 
 
 sin gd u 
 
 Fo' 
 
 esc gd u 
 
 F ' 
 
 SMITHSONIAN TABLES. 
 
Natural Hyperbolic Functions. 
 
 a 
 
 sinh u 
 
 F ' 
 
 cosh u 
 
 coFo' 
 
 tanh u 
 
 Fo' 
 
 coth u 
 
 - F ' 
 
 0.400 
 
 0.41075 
 
 108,1 
 
 1.08107 
 
 41,1 
 
 0.37995 
 
 85,6 
 
 2.6319 
 
 59,3 
 
 .401 
 
 .41183 
 
 108,1 
 
 .08148 
 
 41,2 
 
 .38080 
 
 85,5 
 
 .6260 
 
 59,0 
 
 .402 
 
 .41292 
 
 108,2 
 
 .08190 
 
 41,3 
 
 .38166 
 
 85,4 
 
 .6201 
 
 58,7 
 
 403 
 
 .41400 
 
 108,2 
 
 .08231 
 
 41,4 
 
 .38251 
 
 85,4 
 
 .6i43 
 
 58,3 
 
 .404 
 
 .41508 
 
 108,3 
 
 .08272 
 
 41,5 
 
 .38337 
 
 85,3 
 
 .6085 
 
 58,0 
 
 0.405 
 
 0.41616 
 
 108,3 
 
 1.08314 
 
 41,6 
 
 0.38422 
 
 85,2 
 
 2.6027 
 
 57,7 
 
 .406 
 
 .41725 
 
 108,4 
 
 .08356 
 
 41,7 
 
 38507 
 
 85,2 
 
 5969 
 
 57,4 
 
 .407 
 
 .41833 
 
 108,4 
 
 .08397 
 
 41,8 
 
 .38592 
 
 85,1 
 
 .5912 
 
 57,i 
 
 .408 
 
 .41941 
 
 108,4 
 
 .08439 
 
 4i,9 
 
 .38677 
 
 85,0 
 
 .5855 
 
 56,8 
 
 .409 
 
 .42050 
 
 108,5 
 
 .08481 
 
 42,0 
 
 .38762 
 
 85,0 
 
 .5798 
 
 56,6 
 
 0.410 
 
 0.42158 
 
 108,5 
 
 1.08523 
 
 42,2 
 
 0.38847 
 
 84,9 
 
 2.5742 
 
 56,3 
 
 .411 
 
 .42267 
 
 108,6 
 
 .08566 
 
 42,3 
 
 .38932 
 
 84,8 
 
 .5686 
 
 56,0 
 
 .412 
 
 .42376 
 
 108,6 
 
 .08608 
 
 42,4 
 
 .39017 
 
 84,8 
 
 .5630 
 
 55,7 
 
 413 
 
 .42484 
 
 108,7 
 
 .08650 
 
 42,5 
 
 .39102 
 
 84,7 
 
 5574 
 
 55,4 
 
 .414 
 
 .42593 
 
 108,7 
 
 .08693 
 
 42,6 
 
 .39186 
 
 84,6 
 
 .5519 
 
 55,i 
 
 0.415 
 
 0.42702 
 
 108,7 
 
 1.08736 
 
 42,7 
 
 0.39271 
 
 84,6 
 
 2.5464 
 
 54,8 
 
 .416 
 
 .42810 
 
 108,8 
 
 .08778 
 
 42,8 
 
 .39356 
 
 84,5 
 
 .5409 
 
 54,6 
 
 .417 
 
 .42919 
 
 108,8 
 
 .08821 
 
 42,9 
 
 .39440 
 
 84,4 
 
 5355 
 
 54,3 
 
 .418 
 
 .43028 
 
 108,9 
 
 .08864 
 
 43,0 
 
 .39524 
 
 84,4 
 
 .5301 
 
 54,0 
 
 .419 
 
 .43137 
 
 108,9 
 
 .08907 
 
 43,1 
 
 .39609 
 
 84,3 
 
 .5247 
 
 53,7 
 
 0.420 
 
 0.43246 
 
 109,0 
 
 1.08950 
 
 43,2 
 
 0.39693 
 
 84,2 
 
 2.5193 
 
 53,5 
 
 .421 
 
 .43355 
 
 109,0 
 
 .08994 
 
 43,4 
 
 39777 
 
 84,2 
 
 .5140 
 
 53,2 
 
 .422 
 
 .43464 
 
 109,0 
 
 .09037 
 
 43,5 
 
 .39861 
 
 84,1 
 
 .5087 
 
 52,9 
 
 .423 
 
 43573 
 
 109,1 
 
 .09081 
 
 43,6 
 
 39945 
 
 84,0 .5034 
 
 52,7 
 
 .424 
 
 .43682 
 
 109,1 
 
 .09124 
 
 43,7 
 
 .40029 
 
 84,0 
 
 .4982 
 
 52,4 
 
 0.425 
 
 0.43791 
 
 109,2 
 
 1.09168 
 
 43,8 
 
 0.40113 
 
 83,9 
 
 2.4929 
 
 52,2 
 
 .426 
 
 -43900 
 
 109,2 
 
 .09212 
 
 43,9 
 
 .40197 
 
 83,8 
 
 .4877 
 
 5i,9 
 
 .427 
 
 .44009 
 
 109,3 
 
 .09256 
 
 44,0 
 
 .40281 
 
 83,8 
 
 .4826 
 
 5i,6 
 
 .428 
 
 .44119 
 
 109,3 
 
 .09300 
 
 44,1 
 
 .40365 
 
 83,7 
 
 4774 
 
 5i,4 
 
 .429 
 
 .44228 
 
 109,3 
 
 09344 
 
 44,2 
 
 .40449 
 
 83,6 
 
 .4723 
 
 5i,i 
 
 0.430 
 
 0.44337 
 
 109,4 
 
 1.09388 
 
 44,3 
 
 0.40532 
 
 83,6 
 
 2.4672 
 
 50,9 
 
 431 
 
 .44447 
 
 109,4 
 
 .09433 
 
 44,4 
 
 .40616 
 
 83,5 
 
 .4621 
 
 50,6 
 
 432 
 
 .44556 
 
 109,5 
 
 .09477 
 
 44,6 
 
 .40609 
 
 83,4 
 
 .4571 
 
 50,4 
 
 433 
 
 .44666 
 
 109,5 
 
 .09522 
 
 44,7 
 
 .40783 
 
 83,4 
 
 4520 
 
 50,1 
 
 434 
 
 44775 
 
 109,6 
 
 .09567 
 
 44,8 
 
 .40866 
 
 83,3 
 
 4470 
 
 49,9 
 
 0.435 
 
 0.44885 
 
 109,6 
 
 1.09611 
 
 44,9 
 
 0.40949 
 
 83,2 
 
 2.4421 
 
 49,6 
 
 .436 
 
 44995 
 
 109,7 
 
 .09656 
 
 45,o 
 
 .41032 
 
 83,2 
 
 .4371 
 
 49,4 
 
 437 
 
 .45104 
 
 109,7 
 
 .09701 
 
 45,1 
 
 .41115 
 
 83,1 
 
 4322 
 
 49,2 
 
 .438 
 
 45214 
 
 109,7 
 
 .09747 
 
 45,2 
 
 .41199 
 
 83,0 
 
 .4273 
 
 48,9 
 
 439 
 
 45324 
 
 109,8 
 
 .09792 
 
 45,3 
 
 .41282 
 
 83,0 
 
 .4224 
 
 48,7 
 
 0.440 
 
 0.45434 
 
 109,8 
 
 1.09837 
 
 45,4 
 
 0.41364 
 
 82,9 
 
 2.4175 
 
 48,4 
 
 .441 
 
 45543 
 
 109,9 
 
 .09883 
 
 45,5 
 
 .41447 
 
 82,8 
 
 .4127 
 
 48,2 
 
 .442 
 
 .45653 
 
 109,9 
 
 .09928 
 
 45,7 
 
 .41530 
 
 82,8 
 
 .4079 
 
 48,0 
 
 443 
 
 .45763 
 
 IIO,O 
 
 .09974 
 
 45,8 
 
 .41613 
 
 82,7 
 
 .4031 
 
 47,7 
 
 .444 
 
 .45873 
 
 110,0 
 
 .J0020 
 
 45,9 
 
 .41695 
 
 82,6 
 
 .3983 
 
 47,5 
 
 0.445 
 
 0.45083 
 
 no, i 
 
 I. IO066 
 
 46,0 
 
 0.41778 
 
 82,5 
 
 2.3936 
 
 47,3 
 
 .446 
 
 .46093 
 
 no, i 
 
 .IOII2 
 
 46,1 
 
 .41861 
 
 82,5 
 
 .3889 
 
 47,1 
 
 447 
 
 .46204 
 
 IIO,2 
 
 . IOI58 
 
 46,2 
 
 41943 
 
 82,4 
 
 .3842 
 
 46,8 
 
 .448 
 
 .46314 
 
 IIO,2 
 
 .I02O4 
 
 46,3 
 
 .42025 
 
 82,3 
 
 3795 
 
 46,6 
 
 449 
 
 .46424 
 
 110,3 
 
 .10251 
 
 46,4 
 
 .42108 
 
 82,3 
 
 3749 
 
 46,4 
 
 0.450 
 
 0.46534 
 
 110,3 
 
 I.I0297 
 
 46,5 
 
 0.42190 
 
 82,2 
 
 2.3702 
 
 46,2 
 
 u 
 
 tan gd u 
 
 Fo' 
 
 tec gd u 
 
 - Fo' 
 
 in od u 
 
 -Fo' 
 
 esc gd u 
 
 -Fo' 
 
 SMITHSONIAN TABLC3 
 
 114 
 
Natural Hyperbolic Functions. 
 
 
 
 sinh u 
 
 F ' 
 
 cosh u 
 
 <oFo' 
 
 tanh u 
 
 Fo' 
 
 coth u 
 
 -Fo' 
 
 0.450 
 
 0.46534 
 
 H0,3 
 
 I . 10297 
 
 46,5 
 
 0.42190 
 
 82,2 
 
 2.3702 
 
 46,2 
 
 .451 
 
 .46645 
 
 no,3 
 
 .10344 
 
 46,6 
 
 .42272 
 
 82,1 
 
 .3656 
 
 46,0 
 
 .452 
 
 .46755 
 
 110,4 
 
 . 10300 
 
 46,8 
 
 .42354 
 
 82,1 
 
 .3610 
 
 45,7 
 
 453 
 
 .46865 
 
 110,4 
 
 . 10437 
 
 46,9 
 
 .42436 
 
 82,0 
 
 .3565 
 
 45,5 
 
 454 
 
 .46976 
 
 no,5 
 
 . 10484 
 
 47,0 
 
 .42518 
 
 81,9 
 
 3519 
 
 45,3 
 
 0.455 
 
 0.47086 
 
 110,5 
 
 i. 10531 s 
 
 47,1 
 
 0.42600 
 
 8i,9 
 
 2.3474 
 
 45,1 
 
 456 
 
 .47197 
 
 110,6 
 
 . 10578 
 
 47,2 
 
 .42682 
 
 81,8 
 
 3429 
 
 44,9 
 
 -457 
 
 .47307 
 
 110,6 
 
 .10625 
 
 47,3 
 
 .42764 
 
 8i,7 
 
 .3384 
 
 44,7 
 
 .458 
 
 .47418 
 
 110,7 
 
 .10673 
 
 47,4 
 
 .42845 
 
 81,6 
 
 3340 
 
 44,5 
 
 459 
 
 .47529 
 
 110,7 
 
 . 10720 
 
 47,5 
 
 .42927 
 
 81,6 
 
 3295 
 
 44,3 
 
 0.460 
 
 0.47640 
 
 110,8 
 
 i . 10768 
 
 47,6 
 
 0.43008 
 
 8i,5 
 
 2.3251 
 
 44,1 
 
 .461 
 
 47750 
 
 110,8 
 
 .10816 
 
 47,8 
 
 .43000 
 
 81,4 
 
 3207 
 
 43,9 
 
 .462 
 
 .47861 
 
 110,9 
 
 .10863 
 
 47,9 
 
 .43171 
 
 81,4 
 
 .3164 
 
 43,7 
 
 463 
 
 .47972 
 
 110,9 
 
 .10911 
 
 48,0 
 
 43253 
 
 &i,3 
 
 .3120 
 
 43,5 
 
 .464 
 
 .48083 
 
 III,O 
 
 .10959 
 
 48,1 
 
 43334 
 
 81,2 
 
 3077 
 
 43,3 
 
 0.465 
 
 0.48194 
 
 III,O 
 
 i. 11007 
 
 48,2 
 
 0.43415 
 
 81,2 
 
 2.3033 
 
 43,1 
 
 .466 
 
 .48305 
 
 in, i 
 
 . i 1056 
 
 48,3 
 
 .43496 
 
 81,1 
 
 .2991 
 
 42,9 
 
 .467 
 
 .48416 
 
 iii.i 
 
 . i i 104 
 
 48,4 
 
 43577 
 
 8 1,0 
 
 .2948 
 
 42,7 
 
 .468 
 
 .48527 
 
 111,2 
 
 .IH53 
 
 48,5 
 
 .43658 
 
 80,9 
 
 .2905 
 
 42,5 
 
 .469 
 
 .48638 
 
 111,2 
 
 .11201 
 
 48,6 
 
 43739 
 
 80,9 
 
 .2863 
 
 42,3 
 
 0.470 
 
 0.48750 
 
 111,2 
 
 1.11250 
 
 48,7 
 
 0.43820 
 
 80,8 
 
 2.2821 
 
 42,1 
 
 .471 
 
 .48861 
 
 in,3 
 
 . 11299 
 
 48,9 
 
 .43901 
 
 80,7 
 
 .2779 
 
 4i,9 
 
 .472 
 
 .48972 
 
 in,3 
 
 .11348 
 
 49,0 
 
 .43981 
 
 80,7 
 
 .2737 
 
 41,7 
 
 .473 
 
 .49084 
 
 111,4 
 
 .11397 
 
 49,1 
 
 .44062 
 
 80,6 
 
 .2695 
 
 41,5 
 
 474 
 
 .49195 
 
 111,4 
 
 .11446 
 
 49,2 
 
 .44M3 
 
 80,5 
 
 .2654 
 
 41,3 
 
 0.475 
 
 0.49306 
 
 ni,5 
 
 I. I 1495 
 
 49,3 
 
 0.44223 
 
 80,4 
 
 2.2613 
 
 41,1 
 
 .476 
 
 .49418 
 
 in,5 
 
 .11544 
 
 49,4 
 
 .44303 
 
 80,4 
 
 .2572 
 
 40,9 
 
 477 
 
 49530 
 
 111,6 
 
 .11594 
 
 49,5 
 
 .44384 
 
 80,3 
 
 .2531 
 
 40,8 
 
 .478 
 
 .40641 
 
 ni,6 
 
 .11643 
 
 49,6 
 
 44464 
 
 80,2 
 
 .2490 
 
 40,6 
 
 479 
 
 49753 
 
 111,7 
 
 .11693 
 
 49,8 
 
 44544 
 
 80,2 
 
 .2450 
 
 40,4 
 
 0.480 
 
 0.49865 
 
 ni,7 
 
 1.11743 
 
 49,9 
 
 0.44624 
 
 80, i 
 
 2.2409 
 
 40,2 
 
 .481 
 
 .49976 
 
 111,8 
 
 .11793 
 
 5o,o 
 
 .44704 
 
 80,0 
 
 .2369 
 
 40,0 
 
 .482 
 
 .50088 
 
 111,8 
 
 .11843 
 
 5o,i 
 
 .44784 
 
 79,9 
 
 .2329 
 
 39,9 
 
 .483 
 
 . 50200 
 
 111,9 
 
 .11893 
 
 50,2 
 
 .44864 
 
 79,9 
 
 .2289 
 
 39,7 
 
 .484 
 
 .50312 
 
 111,9 
 
 .11943 
 
 50,3 
 
 44944 
 
 79,8 
 
 .2250 
 
 39,5 
 
 0.485 
 
 0.50424 
 
 1 1 2,0 
 
 I.II994 
 
 50,4 
 
 0.45024 
 
 79,7 
 
 2.2210 
 
 39,3 
 
 .486 
 
 .50536 
 
 II2,O 
 
 .12044 
 
 50,5 
 
 45104 
 
 79,7 
 
 .2171 
 
 39,2 
 
 .487 
 
 .50648 
 
 112,1 
 
 .12095 
 
 50,6 
 
 .45183 
 
 79,6 
 
 .2132 
 
 39,0 
 
 .488 
 
 .50760 
 
 112,1 
 
 .12145 
 
 50,8 
 
 45263 
 
 79,5 
 
 .2093 
 
 38,8 
 
 .489 
 
 .50872 
 
 112,2 
 
 .12196 
 
 50,9 
 
 .45342 
 
 79,4 
 
 .2054 
 
 38,6 
 
 0.400 
 
 0.50084 
 
 112,2 
 
 i . 12247 
 
 5i,o 
 
 0.45422 
 
 79,4 
 
 2. 2Ol6 
 
 38,5 
 
 .491 
 
 51097 
 
 112,3 
 
 .12298 
 
 5i,i 
 
 45501 
 
 79,3 
 
 .1978 
 
 38,3 
 
 .492 
 
 .51209 
 
 112,3 
 
 . 12349 
 
 51,2 
 
 .45580 
 
 79,2 
 
 1939 
 
 38,1 
 
 493 
 
 .51321 
 
 112,4 
 
 . 12401 
 
 5i,3 
 
 .45659 
 
 79,2 
 
 .I9OI 
 
 38,0 
 
 494 
 
 .51434 
 
 112,5 
 
 . 12452 
 
 5i,4 
 
 45739 
 
 79,1 
 
 .1863 
 
 37,8 
 
 0.495 
 
 0.51546 
 
 112,5 
 
 1.12503 
 
 5i,5 
 
 0.45818 
 
 79,0 
 
 2.1826 
 
 37,6 
 
 .495 
 
 .51659 
 
 112,6 
 
 . 12555 
 
 5i,7 
 
 .45897 
 
 78,9 
 
 .1788 
 
 37,5 
 
 497 
 
 .51771 
 
 112,6 
 
 .12607 
 
 5i,8 
 
 45975 
 
 78,9 
 
 .17,51 
 
 37,3 
 
 .498 
 
 .51884 
 
 112,7 
 
 . 12659 
 
 5i,9 
 
 .46054 
 
 78,8 
 
 .1714 
 
 37,1 
 
 .499 
 
 .51997 
 
 112,7 
 
 .12711 
 
 52,0 
 
 .46133 
 
 78,7 
 
 .1676 
 
 37,0 
 
 0.500 
 
 0.52110 
 
 112,8 
 
 1.12763 
 
 52,1 
 
 0.46212 
 
 78,6 
 
 2.1640 
 
 36,8 
 
 
 tan gd u 
 
 u, Fo' 
 
 sec gd u 
 
 Fo' 
 
 sin gd u 
 
 Fo' 
 
 csc gd u 
 
 *> Fo' 
 
 SMITHSONIAN TABLES 
 
Natural Hyperbolic Functions. 
 
 a 
 
 sinh u 
 
 *>F ' 
 
 cosh u 
 
 F ' 
 
 tanh u 
 
 Fo' 
 
 coth u 
 
 - Fo' 
 
 0.500 
 
 0.52IIO 
 
 112,8 
 
 1.12763 
 
 52,1 
 
 0.46212 
 
 78,6 
 
 2.1640 
 
 36,8 
 
 .501 
 
 . 52222 
 
 112,8 
 
 .12815 
 
 52,2 
 
 .46290 
 
 78,6 
 
 .1603 
 
 36,7 
 
 .502 
 
 .52335 
 
 112,9 
 
 .12867 
 
 52,3 
 
 .46369 
 
 78,5 
 
 .1566 
 
 36,5 
 
 \J J*J 
 
 .503 
 
 .52448 
 
 112,9 
 
 .12919 
 
 52,4 
 
 .46447 
 
 78,4 
 
 .1530 
 
 36,4 
 
 504 
 
 .52561 
 
 113,0 
 
 .12972 
 
 52,6 
 
 .46526 
 
 78,4 
 
 1493 
 
 ^ 
 
 36,2 
 
 0.505 
 
 0.52674 
 
 H3,0 
 
 1 . 13025 
 
 52,7 
 
 0.46604 
 
 78,3 
 
 2.1457 
 
 3^,O 
 
 .506 
 
 .52787 
 
 113,1 
 
 13077 
 
 52,8 
 
 .46682 
 
 78,2 
 
 .1421 
 
 35,9 
 
 507 
 
 .52900 
 
 H3,I 
 
 .13130 
 
 52,9 
 
 .46760 
 
 78,1 
 
 .1386 
 
 35,7 
 
 -''*/ 
 
 .508 
 
 .53013 
 
 113,2 
 
 .13183 
 
 53,o 
 
 .46839 
 
 78,1 
 
 .1350 
 
 35,6 
 
 .509 
 
 .53127 
 
 113,2 
 
 .13236 
 
 53,1 
 
 .46917 
 
 78,0 
 
 .1314 
 
 35,4 
 
 0.510 
 
 0.53240 
 
 H3,3 
 
 I . 13289 
 
 53,2 
 
 0.46995 
 
 77,9 
 
 2.1279 
 
 35,3 
 
 .511 
 
 53353 
 
 H3,3 
 
 13343 
 
 53,4 
 
 .47072 
 
 77,9 
 
 .1244 
 
 35,i 
 
 .512 
 
 .53466 
 
 H3,4 
 
 .13396 
 
 53,5 
 
 .47150 
 
 77,8 
 
 .1209 
 
 35,o 
 
 513 
 
 .53580 
 
 H3,4 
 
 . 13450 
 
 53,6 
 
 .47228 
 
 77,7 
 
 .1174 
 
 34,8 
 
 .5H 
 
 .53693 
 
 113,5 
 
 13503 
 
 53,7 
 
 .47306 
 
 77,6 
 
 1139 
 
 34,7 
 
 0.515 
 
 0.53807 
 
 H3,6 
 
 I.I3557 
 
 53,8 
 
 0.47383 
 
 77,5 
 
 2. 1105 
 
 34,5 
 
 .516 
 
 53920 
 
 H3,6 
 
 .13611 
 
 53,9 
 
 .47461 
 
 77,5 
 
 .I07O 
 
 34,4 
 
 Si? 
 
 .54034 
 
 H3,7 
 
 .13665 
 
 54,0 
 
 .47538 
 
 77,4 
 
 .1036 
 
 34,3 
 
 .518 
 
 .54U8 
 
 H3,7 
 
 .13719 
 
 54,1 
 
 .47615 
 
 77,3 
 
 .1002 
 
 34,1 
 
 .519 
 
 .54262 
 
 H3,8 
 
 13773 
 
 54,3 
 
 .47693 
 
 77,3 
 
 .0968 
 
 34,0 
 
 0.520 
 
 0-54375 
 
 H3,8 
 
 1.13827 
 
 54,4 
 
 0.47770 
 
 77,2 
 
 2.0934 
 
 33,8 
 
 .521 
 
 .54489 
 
 H3,9 
 
 .13882 
 
 54,5 
 
 .47847 
 
 77,i 
 
 .0000 
 
 33,7 
 
 .522 
 
 .54603 
 
 H3,9 
 
 .13936 
 
 54,6 
 
 .47924 
 
 77,o 
 
 .0866 
 
 33,5 
 
 523 
 .524 
 
 .54717 
 .54831 
 
 114,0 
 114,0 
 
 .13991 
 . 14046 
 
 54,7 
 54,8 
 
 .48001 
 .48078 
 
 77,o 
 76,9 
 
 .0833 
 
 .0799 
 
 33,4 
 33,3 
 
 0.525 
 
 0.54945 
 
 114,1 
 
 I.I4IOI 
 
 54,9 
 
 0.48155 
 
 76,8 
 
 2.0766 
 
 33,1 
 
 .526 
 
 .55059 
 
 114,2 
 
 .14156 
 
 55,1 
 
 .48232 
 
 76,7 
 
 .0733 
 
 33,0 
 
 527 
 
 .55173 
 
 114,2 
 
 .14211 
 
 55,2 
 
 .48308 
 
 76,7 
 
 .0700 
 
 32,9 
 
 .528 
 
 .55288 
 
 H4,3 
 
 .14266 
 
 55,3 
 
 48385 
 
 76,6 
 
 .0668 
 
 32,7 
 
 .529 
 
 55402 
 
 H4,3 
 
 .14321 
 
 55,4 
 
 .48462 
 
 76,5 
 
 .0635 
 
 32,6 
 
 0.530 
 
 0.55516 
 
 114,4 
 
 I 14377 
 
 55,5 
 
 0.48538 
 
 76,4 
 
 2.0602 
 
 32,4 
 
 531 
 
 .55631 
 
 114,4 
 
 .14432 
 
 55,6 
 
 48615 
 
 76,4 
 
 .0570 
 
 32,3 
 
 532 
 
 .55745 
 
 H4,5 
 
 .14488 
 
 55,7 
 
 .48691 
 
 76,3 
 
 .0538 
 
 32,2 
 
 533 
 
 .55860 
 
 H4,5 
 
 14544 
 
 55,9 
 
 48767 
 
 76,2 
 
 .0506 
 
 32,0 
 
 534 
 
 .55974 
 
 114,6 
 
 .14600 
 
 56,0 
 
 .48843 
 
 76,i 
 
 .0474 
 
 3i,9 
 
 0-535 
 
 0.56089 
 
 "4,7 
 
 I . 14656 
 
 56,1 
 
 0.48919 
 
 76,i 
 
 2.0442 
 
 3i,8 
 
 .536 
 
 . 56204 
 
 H4,7 
 
 .14712 
 
 56,2 
 
 .48995 
 
 76,0 
 
 .0410 
 
 3i,7 
 
 537 
 
 .56318 
 
 114,8 
 
 .14768 
 
 56,3 
 
 .49071 
 
 75,9 
 
 .0378 
 
 3i,5 
 
 .538 
 
 . 56433 
 
 114,8 
 
 .14825 
 
 56,4 
 
 .49147 
 
 75,8 
 
 .0347 
 
 3i,4 
 
 539 
 
 .56548 
 
 114,9 
 
 .14881 
 
 56,5 
 
 .49223 
 
 75,8 
 
 .0316 
 
 3i,3 
 
 0.540 
 
 0.56663 
 
 114,9 
 
 I . 14938 
 
 56,7 
 
 0.49299 
 
 75,7 
 
 2.0284 
 
 3iJ 
 
 541 
 
 .56778 
 
 H5,o 
 
 .14994 
 
 56,8 
 
 49374 
 
 75,6 
 
 .0253 
 
 3i,o 
 
 .542 
 
 .56893 
 
 U5,i 
 
 .15051 
 
 56,9 
 
 49450 
 
 75,5 
 
 .0222 
 
 30,9 
 
 543 
 
 .57008 
 
 H5,i 
 
 .15108 
 
 57,o 
 
 .49526 
 
 75,5 
 
 .OI92 
 
 30,8 
 
 544 
 
 .57123 
 
 115,2 
 
 .15165 
 
 57,1 
 
 .49601 
 
 75,4 
 
 .Ol6l 
 
 30,6 
 
 0.545 
 
 0.57238 
 
 H5,2 
 
 I.I5223 
 
 57,2 
 
 0.49676 
 
 75,3 
 
 2.OI3O 
 
 30,5 
 
 .546 
 
 57354 
 
 H5,3 
 
 .15280 
 
 57,4 
 
 .49752 
 
 75,2 
 
 .OIOO 
 
 30,4 
 
 547 
 
 .57469 
 
 H5,3 
 
 .15337 
 
 57,5 
 
 .49827 
 
 75,2 
 
 .007O 
 
 30,3 
 
 548 
 
 .57584 
 
 H5,4 
 
 .15395 
 
 57,6 
 
 .49902 
 
 75,i 
 
 .0039 
 
 30,2 
 
 549 
 
 57700 
 
 H5,5 
 
 .15452 
 
 57,7 
 
 .49977 
 
 75,0 
 
 .0009 
 
 30,0 
 
 0.550 
 
 0.57815 
 
 H5,5 
 
 I.I55IO 
 
 57,8 
 
 0.50052 
 
 749 
 
 1.9979 
 
 29,9 
 
 1 
 
 tan gd u 
 
 Fo' 
 
 sec gd u 
 
 - Fo' 
 
 sin gd u 
 
 Fo' 
 
 esc od u 
 
 -Fo' 
 
 SMITHSONIAN TABLES 
 
 116 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinh u 
 
 F ' 
 
 cosh u 
 
 F ' 
 
 tanh u 
 
 Fo' 
 
 coth u 
 
 Fo' 
 
 0.550 
 
 0.57815 
 
 H5,5 
 
 I.I55IO 
 
 57,8 
 
 0.50052 
 
 74,9 
 
 1.9979 
 
 29,9 
 
 .551 
 
 .57931 
 
 115,6 
 
 .15568 
 
 57,9 
 
 .50127 
 
 74,9 
 
 .9949 
 
 29,8 
 
 .552 
 
 .58046 
 
 115,6 
 
 .15626 
 
 58,0 
 
 . 50202 
 
 74,8 
 
 .9920 
 
 29,7 
 
 553 
 
 .58162 
 
 H5,7 
 
 .15684 
 
 58,2 
 
 .50277 
 
 74,7 
 
 .9890 
 
 29,6 
 
 554 
 
 .58278 
 
 H5,7 
 
 .15742 
 
 58,3 
 
 .50351 
 
 74,6 
 
 .9860 
 
 29,4 
 
 0.555 
 
 0.58393 
 
 H5,8 
 
 1.15801 
 
 58,4 
 
 0.50426 
 
 74,6 
 
 1.9831 
 
 29,3 
 
 .556 
 
 .58509 
 
 H5,9 
 
 .15859 
 
 58,5 
 
 .50500 
 
 74,5 
 
 .9802 
 
 29,2 
 
 557 
 
 .58625 
 
 H5,9 
 
 .15918 
 
 58,6 
 
 .50575 
 
 74,4 
 
 .9773 
 
 29,1 
 
 558 
 
 .58741 
 
 116,0 
 
 .15976 
 
 58,7 
 
 .50649 
 
 74,3 
 
 9744 
 
 29,0 
 
 559 
 
 .58857 
 
 116,0 
 
 .16035 
 
 58,9 
 
 .50724 
 
 74,3 
 
 .9715 
 
 28,9 
 
 0.560 
 
 0.58973 
 
 116,1 
 
 1.16094 
 
 59,o 
 
 0.50798 
 
 74,2 
 
 1.9686 
 
 28,8 
 
 .561 
 
 .59089 
 
 116,2 
 
 .16153 
 
 59,i 
 
 .50872 
 
 74,1 
 
 .9657 
 
 28,6 
 
 .562 
 
 .59205 
 
 116,2 
 
 .id? 12 
 
 59,2 
 
 .50946 
 
 74,0 
 
 .9629 
 
 28,5 
 
 .563 
 
 59322 
 
 116,3 
 
 . 16272 
 
 59,3 
 
 .51020 
 
 74,o 
 
 .9600 
 
 28,4 
 
 .564 
 
 .59438 
 
 "6,3 
 
 .16331 
 
 59,4 
 
 .51094 
 
 73,9 
 
 .9572 
 
 28,3 
 
 0.565 
 
 0.59554 
 
 116,4 
 
 i . 16390 
 
 59,6 
 
 0.51168 
 
 73,8 
 
 1.9544 
 
 28,2 
 
 .566 
 
 .59671 
 
 116,5 
 
 . 16450 
 
 59,7 
 
 .51242 
 
 73,7 
 
 .9515 
 
 28,1 
 
 .567 
 
 .59787 
 
 116,5 
 
 .16510 
 
 59,8 
 
 .51315 
 
 73,7 
 
 .9487 
 
 28,0 
 
 .568 
 
 .59904 
 
 116,6 
 
 . 16570 
 
 59,9 
 
 .51389 
 
 73,6 
 
 .9459 
 
 27,9 
 
 .569 
 
 .60020 
 
 116,6 
 
 .16630 
 
 00,0 
 
 .51462 
 
 73,5 
 
 .9432 
 
 27,8 
 
 0.570 
 
 0.60137 
 
 116,7 
 
 1.16690 
 
 60,1 
 
 0.51536 
 
 73,4 
 
 1.9404 
 
 27,7 
 
 .571 
 
 .60254 
 
 116,7 
 
 . 16750 
 
 60,3 
 
 .51609 
 
 73,4 
 
 .9376 
 
 27,5 
 
 572 
 
 .60371 
 
 116,8 
 
 .16810 
 
 60,4 
 
 .51683 
 
 73,3 
 
 .9349 
 
 27,4 
 
 .573 
 
 .60487 
 
 116,9 
 
 .16871 
 
 60,5 
 
 .51756 
 
 73,2 
 
 9321 
 
 27,3 
 
 574 
 
 .60604 
 
 116,9 
 
 .16931 
 
 60,6 
 
 .51829 
 
 73,1 
 
 .9294 
 
 27,2 
 
 0.575 
 
 0.60721 
 
 117,0 
 
 1.16992 
 
 60,7 
 
 0.51902 
 
 73,i 
 
 1.9267 
 
 27,1 
 
 .576. 
 
 .60838 
 
 117,1 
 
 . 17053 
 
 60,8 
 
 .51975 
 
 73,0 
 
 .9240 
 
 27,0 
 
 577 
 
 60955 
 
 117,1 
 
 .17113 
 
 61,0 
 
 .52048 
 
 72,9 
 
 .9213 
 
 26,9 
 
 .578 
 
 .61073 
 
 117,2 
 
 .17174 
 
 61,1 
 
 .52121 
 
 72,8 
 
 .9186 
 
 26,8 
 
 .579 
 
 .61190 
 
 117,2 
 
 .17236 
 
 61,2 
 
 .52194 
 
 72,8 
 
 .9159 
 
 26,7 
 
 0.580 
 
 0.61307 
 
 H7,3 
 
 I . 17297 
 
 61,3 
 
 0.52267 
 
 72,7 
 
 I.9I33 
 
 26,6 
 
 .581 
 
 .61424 
 
 ii7,4 
 
 .17358 
 
 61,4 
 
 .52339 
 
 72,6 
 
 .9106 
 
 26,5 
 
 .582 
 
 .61542 
 
 H7,4 
 
 .17420 
 
 6i,5 
 
 .52412 
 
 72,5 
 
 .9080 
 
 26,4 
 
 .583 
 
 .61659 
 
 H7,5 
 
 .17481 
 
 6i,7 
 
 .52484 
 
 72,5 
 
 9053 
 
 26,3 
 
 .584 
 
 .61777 
 
 117,5 
 
 .17543 
 
 61,8 
 
 .52557 
 
 72,4 
 
 .9027 
 
 26,2 
 
 0.585 
 
 0.61894 
 
 117,6 
 
 1.17605. 
 
 61,9 
 
 0.52629 
 
 72,3 
 
 1.9001 
 
 26,1 
 
 .586 
 
 .62012 
 
 H7,7 
 
 .17667 
 
 62,0 
 
 .52701 
 
 72,2 
 
 .8975 
 
 26,0 
 
 .587 
 
 .62130 
 
 117,7 
 
 . 17729 
 
 62,1 
 
 .52773 
 
 72,2 
 
 .8949 
 
 25,9 
 
 .588 
 
 .62247 
 
 117,8 
 
 .17791 
 
 62,2 
 
 .52846 
 
 72,1 
 
 .8923 
 
 25,8 
 
 .589 
 
 .62365 
 
 H7,9 
 
 .17853 
 
 62,4 
 
 .52918 
 
 72,o 
 
 .8897 
 
 25,7 
 
 0.590 
 
 0.62483 
 
 H7,9 
 
 i . 17916 
 
 62,5 
 
 0.52990 
 
 7i,9 
 
 1.8872 
 
 25,6 
 
 591 
 
 .62601 
 
 118,0 
 
 . 17978 
 
 62,6 
 
 .53061 
 
 7i,8 
 
 .8846 
 
 25,5 
 
 .592. 
 
 -" . 62719 
 
 118,0 
 
 .18041 
 
 62,7 
 
 .53133 
 
 7i,8 
 
 .8821 
 
 25,4 
 
 593 
 
 .62837 
 
 118,1 
 
 . 18104 
 
 62,8 
 
 . 53205 
 
 7i,7 
 
 .8795 
 
 25,3 
 
 594 
 
 .62955 
 
 118,2 
 
 . 18167 
 
 63,0 
 
 .53277 
 
 7i,6 
 
 .8770 
 
 25,2 
 
 0.595 
 
 0.63073 
 
 118,2 
 
 i . 18230 
 
 63,1 
 
 0.53348 
 
 7i,5 
 
 1.8745 
 
 25,1 
 
 .596 
 
 .63192 
 
 "8,3 
 
 . 18293 
 
 63,2 
 
 53420 
 
 7i,5 
 
 .8720 
 
 25,0 
 
 .597 
 
 .63310 
 
 118,4 
 
 .18356 
 
 63,3 
 
 53491 
 
 7i,4 
 
 .8695 
 
 24,9 
 
 .598 
 
 .63428 
 
 "8,4 
 
 . 18419 
 
 63,4 
 
 .53562 
 
 7i,3 
 
 .8670 
 
 24,9 
 
 599 
 
 .63547 
 
 "8,5 
 
 .18483 
 
 63,5 
 
 .53634 
 
 71,2 
 
 .8645 
 
 24,8 
 
 0.600 
 
 0.63665 
 
 "8,5 
 
 i . 18547 
 
 63,7 
 
 0.53705 
 
 71,2 
 
 1.8620 
 
 247 
 
 u 
 
 tan gd u 
 
 *> Fo' 
 
 sec gd u 
 
 F ' 
 
 sin gd u 
 
 Fo' 
 
 esc gd u 
 
 Fo' 
 
 SMITHS >NIAN TABLES 
 
 117 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinh u 
 
 F ' 
 
 cosh u 
 
 "Fo' 
 
 tanh u 
 
 Fo' 
 
 coth u 
 
 * Fo' 
 
 0.600 
 
 0.63665 
 
 "8,5 
 
 1.18547 
 
 63,7 
 
 0.53705 
 
 71,2 
 
 1.8620 
 
 24,7 
 
 .601 
 
 63784 
 
 118,6 
 
 .18610 
 
 63,8 
 
 .53776 
 
 7IJ 
 
 .8596 
 
 24,6 
 
 .002 
 
 .63903 
 
 118,7 
 
 .18674 
 
 63,9 
 
 .53847 
 
 71,0 
 
 .8571 
 
 24,5 
 
 .603 
 
 .64021 
 
 "8,7 
 
 .18738 
 
 64,0 
 
 .53918 
 
 70,9 
 
 .8547 
 
 24,4 
 
 .604 
 
 .64140 
 
 11818 
 
 .18802 
 
 64,1 
 
 .53989 
 
 70,9 
 
 .8522 
 
 24,^ 
 
 0.605 
 
 0.64259 
 
 "8,9 
 
 1.18866 
 
 64,3 
 
 0.54060 
 
 70,8 
 
 1.8498 
 
 24,2 
 
 .606 
 
 ,64378 
 
 "8,9 
 
 .18931 
 
 64,4 
 
 .54131 
 
 70,7 
 
 .8474 
 
 24,1 
 
 .607 
 
 .64497 
 
 119,0 
 
 .18995 
 
 04,5 
 
 .54201 
 
 70,6 
 
 .8450 
 
 24,0 
 
 .608 
 
 .64616 
 
 119,1 
 
 .19060 
 
 64,6 
 
 .54272 
 
 70,5 
 
 .8426 
 
 24,0 
 
 .609 
 
 .64735 
 
 119,1 
 
 . 19124 
 
 64,7 
 
 54342 
 
 70,5 
 
 .8402 
 
 23,9 
 
 0.610 
 
 0.64854 
 
 "9,2 
 
 I . 19189 
 
 64,9 
 
 0.54413 
 
 70,4 
 
 1.8378 
 
 23,8 
 
 .611 
 
 .64973 
 
 "9,3 
 
 . 19254 
 
 65,O 
 
 .54483 
 
 70,3 
 
 .8354 
 
 23,7 
 
 .612 
 
 .65093 
 
 "9,3 
 
 .19319 
 
 65,i 
 
 .54553 
 
 70,2 
 
 .8331 
 
 23,6 
 
 .613 
 
 .65212 
 
 "9,4 
 
 . 19384 
 
 65,2 
 
 .54624 
 
 70,2 
 
 .8307 
 
 23,5 
 
 .614 
 
 .65331 
 
 119,4 
 
 .19449 
 
 65,3 
 
 .54694 
 
 7o,i 
 
 .8284 
 
 23,4 
 
 0.615 
 
 0.65451 
 
 "9,5 
 
 1.19515 
 
 65,5 
 
 0.54764 
 
 70,0 
 
 1.8260 
 
 23,3 
 
 .616 
 
 .65570 
 
 "9,6 
 
 .19580 
 
 65,6 
 
 .54834 
 
 69,9 
 
 .8237 
 
 23,3 
 
 .617 
 
 .65690 
 
 119,6 
 
 .19646 
 
 65,7 
 
 .54904 
 
 69,9 
 
 .8214 
 
 23,2 
 
 .618 
 
 .65810 
 
 "9,7 
 
 . 19712 
 
 65,8 
 
 .54973 
 
 69,8 
 
 .8191 
 
 23,1 
 
 .619 
 
 .65929 
 
 "9,8 
 
 . 19778 
 
 65,9 
 
 .55043 
 
 69,7 
 
 .8168 
 
 23,0 
 
 0.620 
 
 0.66049 
 
 "9,8 
 
 1.19844 
 
 66,0 
 
 0.55"3 
 
 69,6 
 
 I.8I45 
 
 22,9 
 
 .621 
 
 .66169 
 
 119,9 
 
 .19910 
 
 66,2 
 
 .55182 
 
 69,5 
 
 .8122 
 
 22,8 
 
 .622 
 
 .66289 
 
 120,0 
 
 .19976 
 
 66,3 
 
 .55252 
 
 69,5 
 
 .8099 
 
 22,8 
 
 .623 
 
 .66409 
 
 120,0 
 
 .20042 
 
 66,4 
 
 55321 
 
 69,4 
 
 .8076 
 
 22,7 
 
 .624 
 
 .66529 
 
 I2O,I 
 
 .20109 
 
 66,5 
 
 .55391 
 
 69,3 
 
 .8054 
 
 22,6 
 
 0.625 
 
 0.66649 
 
 1 2O,2 
 
 1.20175 
 
 66,6 
 
 0.55400 
 
 69,2 
 
 1.8031 
 
 22,5 
 
 .626 
 
 .66769 
 
 120,2 
 
 .20242 
 
 66,8 
 
 .55529 
 
 69,2 
 
 .8009 
 
 22,4 
 
 .627 
 
 .66890 
 
 120,3 
 
 .20309 
 
 66,9 
 
 .55598 
 
 69,1 
 
 .7986 
 
 22,4 
 
 .628 
 
 .67010 
 
 120,4 
 
 .20376 
 
 67,0 
 
 .55667 
 
 69,0 
 
 .7964 
 
 22,3 
 
 .629 
 
 .67130 
 
 120,4 
 
 .20443 
 
 67,1 
 
 55736" 
 
 68,9 
 
 .7942 
 
 22,2 
 
 0.630 
 
 0.67251 
 
 120,5 
 
 1.20510 
 
 67,3 
 
 0.55805 
 
 68,9 
 
 I.79I9 
 
 22,1 
 
 .631 
 
 .67371 
 
 I2O,6 
 
 .20577 
 
 67,4 
 
 .55874 
 
 68,8 
 
 .7897 
 
 22,0 
 
 .632 
 
 .67492 
 
 1 2O,6 
 
 .20645 
 
 67,5 
 
 .55943 
 
 68,7 
 
 .7875 
 
 22,0 
 
 .633 
 
 .67613 
 
 120,7 
 
 .20712 
 
 67,6 
 
 .56011 
 
 68,6 
 
 .7853 
 
 21,9 
 
 634 
 
 .67734 
 
 120,8 
 
 .20780 
 
 67,7 
 
 .56080 
 
 68,6 
 
 .7832 
 
 21,8 
 
 0.635 
 
 0.67854 
 
 120,8 
 
 1.20848 
 
 67,9 
 
 0.56149 
 
 68,5 
 
 1.7810 
 
 21,7 
 
 .636 
 
 .67975 
 
 120,9 
 
 .20916 
 
 68,0 
 
 .56217 
 
 68,4 
 
 .7788 
 
 21,6 
 
 .637 
 
 .68096 
 
 I2I,O 
 
 .20084 
 
 68,1 
 
 .56285 
 
 68,3 
 
 .7767 
 
 21,6 
 
 .638 
 
 .68217 
 
 121,1 
 
 .21052 
 
 68,2 
 
 .56354 
 
 68,2 
 
 7745 
 
 21,5 
 
 639 
 
 .68338 
 
 121,1 
 
 .2II2O 
 
 68,3 
 
 .56422 
 
 68,2 
 
 .7724 
 
 21,4 
 
 0.640 
 
 0.68459 
 
 121,2 
 
 I.2II89 
 
 68,5 
 
 0.56490 
 
 68,1 
 
 1.7702 
 
 21,3 
 
 .641 
 
 .68581 
 
 121,3 
 
 .21257 
 
 68,6 
 
 .56558 
 
 68,0 
 
 .7681 
 
 21,3 
 
 .642 
 
 .68702 
 
 121,3 
 
 .21326 
 
 68,7 
 
 .56626 
 
 67,9 
 
 .7660 
 
 21,2 
 
 .643 
 
 .68823 
 
 121,4 
 
 .21395 
 
 68,8 
 
 .56694 
 
 67,9 
 
 .7639 
 
 21,1 
 
 .644 
 
 .68945 
 
 121,5 
 
 .21463 
 
 68,9 
 
 .56762 
 
 67,8 
 
 .7618 
 
 21,0 
 
 0.645 
 
 0.69066 
 
 121,5 
 
 I.2I532 
 
 69,1 
 
 0.56829 
 
 67,7 
 
 1-7597 
 
 21,0 
 
 .646 
 
 .69188 
 
 121,6 
 
 .21602 
 
 69,2 
 
 .56897 
 
 67,6 
 
 .7576 
 
 2O,9 
 
 .647 
 
 .69309 
 
 121,7 
 
 .21671 
 
 69,3 
 
 .56965 
 
 67,6 
 
 7555 
 
 20,8 
 
 .648 
 
 .69431 
 
 121,7 
 
 .21740 
 
 69,4 
 
 .57032 
 
 67,5 
 
 7534 
 
 20,7 
 
 649 
 
 .69553 
 
 121,8 
 
 .2l8lO 
 
 09,6 
 
 .57100 
 
 67,4 
 
 .7513 
 
 20,7 
 
 0.650 
 
 0.69675 
 
 121,9 
 
 I.2I879 
 
 69,7 
 
 0.57167 
 
 67,3 
 
 1.7493 
 
 2O.6 
 
 u 
 
 tan od u 
 
 F</ 
 
 sec gd u 
 
 -Fo' 
 
 sin gd u 
 
 Fo' 
 
 esc gd u 
 
 Fo' 
 
 SMITHSONIAN TABLES 
 
 118 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinh u 
 
 O.FO' 
 
 cosh u 
 
 <oF ' 
 
 tanh u 
 
 Fo' 
 
 coth u 
 
 F ' 
 
 0.650 
 
 0.69675 
 
 121,9 
 
 1.21879 
 
 69,7 
 
 0.57167 
 
 67,3 
 
 1.7493 
 
 20,6 
 
 .651 
 
 .69797 
 
 121,9 
 
 .21949 
 
 69,8 
 
 .57234 
 
 67,2 
 
 .7472 
 
 20,5 
 
 .652 
 
 .69919 
 
 1 22,0 
 
 .22019 
 
 69,9 
 
 57301 
 
 67,2 
 
 .7452 
 
 20,5 
 
 .653 
 
 .70041 
 
 122,1 
 
 .22089 
 
 7o,o 
 
 .57369 
 
 67,1 
 
 7431 
 
 20,4 
 
 .654 
 
 .70163 
 
 122,2 
 
 .22159 
 
 70,2 
 
 .57436 
 
 67,0 
 
 .74H 
 
 20,3 
 
 0.655 
 
 0.70285 
 
 122,2 
 
 1.22229 
 
 70,3 
 
 0.57503 
 
 66,9 
 
 I.739I 
 
 20,2 
 
 .656 
 
 .70407 
 
 122,3 
 
 .22300 
 
 70,4 
 
 57570 
 
 66,9 
 
 7370 
 
 2O,2 
 
 .657 
 
 .70530 
 
 122,4 
 
 .22370 
 
 70,5 
 
 .57636 
 
 66,8 
 
 .7350 
 
 20,1 
 
 .658 
 
 .70652 
 
 122,4 
 
 .22441 
 
 70,7 
 
 57703 
 
 66,7 
 
 .7330 
 
 20,O 
 
 .659 
 
 70775 
 
 122,5 
 
 .22511 
 
 70,8 
 
 57770 
 
 66,6 
 
 .7310 
 
 2O,0 
 
 0.660 
 
 0.70897 
 
 122,6 
 
 1.22582 
 
 70,9 
 
 0.57836 
 
 66,5 
 
 1.7290 
 
 19,9 
 
 .661 
 
 .7I02O 
 
 122,7 
 
 .22653 
 
 71,0 
 
 57903 
 
 66,5 
 
 .7270 
 
 19,8 
 
 .662 
 
 .71142 
 
 122,7 
 
 .22724 
 
 7i,i 
 
 .57969 
 
 66,4 
 
 .7251 
 
 19,8 
 
 .663 
 
 .71265 
 
 122,8 
 
 .22795 
 
 71,3 
 
 .58036 
 
 66,3 
 
 .7231 
 
 19,7 
 
 .664 
 
 .71388 
 
 122,9 
 
 .22867 
 
 71,4 
 
 . 58102 
 
 66,2 
 
 .7211 
 
 19,6 
 
 0.665 
 
 0.7I5H 
 
 122,9 
 
 1.22938 
 
 71,5 
 
 0.58168 
 
 66,2 
 
 I.7I92 
 
 19,6 
 
 .666 
 
 .71634 
 
 123,0 
 
 .23010 
 
 7i,6 
 
 .58234 
 
 66,1 
 
 .7172 
 
 19,5 
 
 .667 
 
 .71757 
 
 123,1 
 
 .23081 
 
 7i,8 
 
 .58300 
 
 66,0 
 
 7153 
 
 19,4 
 
 .668 
 
 .71880 
 
 123,2 
 
 .23153 
 
 7i,9 
 
 .58366 
 
 65,9 
 
 .7133 
 
 19,4 
 
 .669 
 
 .72003 
 
 123,2 
 
 .23225 
 
 72,0 
 
 .58432 
 
 65,9 
 
 .7114 
 
 19,3 
 
 0.670 
 
 0.72126 
 
 123,3 
 
 1.23297 
 
 72,1 
 
 0.58498 
 
 65,8 
 
 1.7095 
 
 19,2 
 
 .671 
 
 .72250 
 
 123,4 
 
 .23369 
 
 72,2 
 
 58564 
 
 65,7 
 
 .7075 
 
 19,2 
 
 .672 
 
 .72373 
 
 123,4 
 
 .23442 
 
 72,4 
 
 .58629 
 
 65,6 
 
 .7056 
 
 19,1 
 
 .673 
 
 .72497 
 
 123,5 
 
 .23514 
 
 72,5 
 
 .58695 
 
 65,5 
 
 .7037 
 
 19,0 
 
 .674 
 
 .72620 
 
 123,6 
 
 .23587 
 
 72,6 
 
 .58760 
 
 65,5 
 
 .7018 
 
 19,0 
 
 0.675 
 
 0.72744 
 
 123,7 
 
 1.23659 
 
 72,7 
 
 0.58826 
 
 65,4 
 
 1.6999 
 
 18,9 
 
 .676 
 
 .72868 
 
 123,7 
 
 .23732 
 
 72,9 
 
 .58891 
 
 65,3 
 
 .6980 
 
 18,8 
 
 .677 
 
 .72091 
 
 123,8 
 
 .23805 
 
 73,o 
 
 .58957 
 
 65,2 
 
 .6962 
 
 18,8 
 
 .678 
 
 .73H5 
 
 123,9 
 
 .23878 
 
 73,i 
 
 .59022 
 
 65,2 
 
 .6943 
 
 18,7 
 
 .679 
 
 .73239 
 
 124,0 
 
 .23951 
 
 73,2 
 
 .59087 
 
 65,1 
 
 .6924 
 
 18,6 
 
 0.680- 
 
 -0.73363 
 
 124,0 
 
 1.24025 
 
 73,4 
 
 0.59152 
 
 65,0 
 
 1.6906 
 
 18,6 
 
 .681 
 
 .73487 
 
 124,1 
 
 .24098 
 
 73,5 
 
 59217 
 
 64,9 
 
 .6887 
 
 18,5 
 
 .682 
 
 .73611 
 
 124,2 
 
 .24172 
 
 73,6 
 
 .59282 
 
 64,9 
 
 .6869 
 
 18,5 
 
 .683 
 
 .73735 
 
 124,2 
 
 .24245 
 
 73,7 
 
 59347 
 
 64,8 
 
 .6850 
 
 18,4 
 
 .684 
 
 .73860 
 
 124,3 
 
 .24319 
 
 73,9 
 
 594II 
 
 64,7 
 
 .6832 
 
 18,3 
 
 0.685 
 
 0.73984 
 
 124,4 
 
 1.24393 
 
 74,0 
 
 0.59476 
 
 64,6 
 
 1.6813 
 
 18,3 
 
 .686 
 
 .74109 
 
 124,5 
 
 .24467 
 
 74,1 
 
 59541 
 
 64,5 
 
 .6795 
 
 18,2 
 
 .687 
 
 .74233 
 
 124,5 
 
 .24541 
 
 74,2 
 
 .59605 
 
 64,5 
 
 .6777 
 
 18,1 
 
 .688 
 
 74358 
 
 124,6 
 
 .24616 
 
 74,4 
 
 .59670 
 
 64,4 
 
 .6759 
 
 18,1 
 
 .689 
 
 .74482 
 
 124,7 
 
 .24690 
 
 74,5 
 
 59734 
 
 64,3 
 
 .6741 
 
 18,0 
 
 0.690 
 
 0.74607 
 
 124,8 
 
 1.24765 
 
 74,6 
 
 0.59798 
 
 64,2 
 
 1.6723 
 
 18,0 
 
 .691 
 
 74732 
 
 124,8 
 
 .24839 
 
 74,7 
 
 .59862 
 
 64,2 
 
 .6705 
 
 17,9 
 
 .692 
 
 .74857 
 
 124,9 
 
 .24914 
 
 74,9 
 
 50927 
 
 64,1 
 
 .6687 
 
 17,8 
 
 .693 
 
 .74982 
 
 125,0 
 
 .24989 
 
 75,o 
 
 .59991 
 
 64,0 
 
 .6669 
 
 17,8 
 
 .694 
 
 .75107 
 
 125,1 
 
 .25064 
 
 75,i 
 
 .60055 
 
 63,9 
 
 .6652 
 
 17,7 
 
 0.695 
 
 0.75232 
 
 125,1 
 
 I.25I39 
 
 75,2 
 
 o. 60118 
 
 63,9 
 
 1.6634 
 
 17,7 
 
 .696 
 
 .75357 
 
 125,2 
 
 .25214 
 
 75,4 
 
 .60182 
 
 63,8 
 
 .6616 
 
 17,6 
 
 .697 
 
 .75482 
 
 125,3 
 
 .25290 
 
 75,5 
 
 .60246 
 
 63,7 
 
 .6599 
 
 17,6 
 
 .698 
 
 .75607 
 
 125,4 
 
 .25365 
 
 75,6 
 
 .60310 
 
 63,6 
 
 .6581 
 
 17,5 
 
 .699 
 
 75733 
 
 125,4 
 
 .25441 
 
 75,7 
 
 .60373 
 
 63,6 
 
 .6564 
 
 17,4 
 
 0.700 
 
 0.75858 
 
 125,5 
 
 I.255I7 
 
 75,9 
 
 0.60437 
 
 63,5 
 
 1.6546 
 
 17,4 
 
 u 
 
 tan gd u 
 
 F ' 
 
 sec gd u 
 
 Fo' 
 
 sin gd u 
 
 Fo' 
 
 esc gd u 
 
 F ' 
 
 SMITHSONIAN TABLES 
 
 IIQ 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinh u 
 
 F O ' 
 
 cosh u 
 
 F ' 
 
 tanh u 
 
 Fo' 
 
 coth u 
 
 Fo' 
 
 0.700 
 
 0.75858 
 
 125,5 
 
 I.255I7 
 
 75,9 
 
 0.60437 
 
 63,5 
 
 1.6546 
 
 17,4 
 
 .701 
 
 .75984 
 
 125,6 
 
 25593 
 
 76,0 
 
 .60500 
 
 63,4 
 
 .6529 
 
 17,3 
 
 .702 
 
 .76110 
 
 125,7 
 
 .25669 
 
 76,1 
 
 .60564 
 
 63,3 
 
 .6512 
 
 17,3 
 
 .703 
 
 .76235 
 
 125,7 
 
 .25745 
 
 76,2 
 
 .60627 
 
 63,2 
 
 .6494 
 
 17,2 
 
 .704 
 
 .76361 
 
 125,8 
 
 .25821 
 
 76,4 
 
 .60690 
 
 63,2 
 
 .6477 
 
 17,1 
 
 0.705 
 
 0.76487 
 
 125,9 
 
 1.25898 
 
 76,5 
 
 0.60753 
 
 63,1 
 
 1.6460 
 
 17,1 
 
 .706 
 
 .76613 
 
 126,0 
 
 .25974 
 
 76,6 
 
 .60816 
 
 63,0 
 
 6443 
 
 17,0 
 
 .707 
 
 .76739 
 
 126,1 
 
 .26051 
 
 76,7 
 
 .60879 
 
 62,9 
 
 .6426 
 
 17,0 
 
 .708 
 
 .76865 
 
 126,1 
 
 .26128 
 
 76,9 
 
 .60942 
 
 62,9 
 
 .6409 
 
 16,9 
 
 .709 
 
 .76991 
 
 126,2 
 
 .26205 
 
 77,o 
 
 .61005 
 
 62,8 
 
 .6392 
 
 16,9 
 
 0.710 
 
 0.77H7 
 
 126,3 
 
 1.26282 
 
 77,1 
 
 0.61068 
 
 62,7 
 
 1.6375 
 
 16,8 
 
 .711 
 
 .77244 
 
 126,4 
 
 .26359 
 
 77,2 
 
 .61130 
 
 62,6 
 
 .6358 
 
 16,8 
 
 .712 
 
 .77370 
 
 126,4 
 
 .26436 
 
 77,4 
 
 .61193 
 
 62,6 
 
 .6342 
 
 16,7 
 
 .713 
 
 77497 
 
 126,5 
 
 .26514 
 
 77,5 
 
 .61255 
 
 62,5 
 
 
 16,7 
 
 .714 
 
 .77623 
 
 126,6 
 
 .26591 
 
 77,6 
 
 .61318 
 
 62,4 
 
 .6308 
 
 16,6 
 
 0.715 
 
 0.77750 
 
 126,7 
 
 1.26669 
 
 77,7 
 
 0.61380 
 
 62,3 
 
 1.6292 
 
 16,5 
 
 .716 
 
 .77876 
 
 126,7 
 
 .26747 
 
 77,9 
 
 .61443 
 
 62,2 
 
 .6275 
 
 16,5 
 
 .717 
 
 .78003 
 
 126,8 
 
 .26825 
 
 78,0 
 
 .61505 
 
 62,2 
 
 .6259 
 
 16,4 
 
 .718 
 
 .78130 
 
 126,9 
 
 .26903 
 
 78,i 
 
 .61567 
 
 62,1 
 
 .6242 
 
 16,4- 
 
 .719 
 
 .78257 
 
 127,0 
 
 .26981 
 
 78,3 
 
 .61629 
 
 62,O 
 
 .6226 
 
 16,3 
 
 0.720 
 
 0.78384 
 
 127,1 
 
 1.27059 
 
 78,4 
 
 0.61691 
 
 61,9 
 
 1.6210 
 
 16,3 
 
 .721 
 
 .785H 
 
 127,1 
 
 .27138 
 
 78,5 
 
 .61753 
 
 61,9 
 
 .6194 
 
 16,2 
 
 .722 
 
 .78538 
 
 127,2 
 
 .27216 
 
 78,6 
 
 .61815 
 
 61,8 
 
 .6177 
 
 16,2 
 
 .723 
 
 .78766 
 
 127,3 
 
 .27295 
 
 78,8 
 
 .61876 
 
 61,7 
 
 .6161 
 
 16,1 
 
 .724 
 
 .78893 
 
 127,4 
 
 .27374 
 
 78,9 
 
 .61938 
 
 61,6 
 
 .6145 
 
 16,1 
 
 0.725 
 
 0.7902O 
 
 127,5 
 
 1.27453 
 
 79,o 
 
 0.62000 
 
 61,6 
 
 1.6129 
 
 16,0 
 
 .726 
 
 .79M8 
 
 127,5 
 
 .27532 
 
 79,i 
 
 .62061 
 
 61,5 
 
 .6113 
 
 16,0 
 
 .727 
 
 .79275 
 
 127,6 
 
 .27611 
 
 79,3 
 
 .62123 
 
 61,4 
 
 .6097 
 
 15,9 
 
 .728 
 
 .79403 
 
 127,7 
 
 .27690 
 
 79,4 
 
 .62184 
 
 61,3 
 
 .6081 
 
 15,9 
 
 .729 
 
 79531 
 
 127,8 
 
 .27770 
 
 79,5 
 
 .62245 
 
 61,3 
 
 .6065 
 
 15,8 
 
 0.730 
 
 0.79659 
 
 127,8 
 
 1.27849 
 
 79,7 
 
 0.62307 
 
 61,2 
 
 1.6050 
 
 15,8 
 
 .731 
 
 .79786 
 
 127,9 
 
 .27929 
 
 79,8 
 
 .62368 
 
 61,1 
 
 .6034 
 
 15,7 
 
 .732 
 
 .79914 
 
 128,0 
 
 .28009 
 
 79,9 
 
 .62429 
 
 61,0 
 
 .6018 
 
 15,7 
 
 .733 
 
 .80042 
 
 128,1 
 
 .28089 
 
 80,0 
 
 .62490 
 
 61,0 
 
 .6003 
 
 15,6 
 
 734 
 
 .80171 
 
 128,2 
 
 .28169 
 
 80,2 
 
 .62551 
 
 60,9 
 
 5087 
 
 15,6 
 
 0.735 
 
 0.80299 
 
 128,2 
 
 1.28249 
 
 80,3 
 
 0.62611 
 
 60,8 
 
 1.5972 
 
 15,5 
 
 .736 
 
 .80427 
 
 128,3 
 
 .28330 
 
 80,4 
 
 .62672 
 
 60,7 
 
 .5956 
 
 15,5 
 
 737 
 
 .80555 
 
 128,4 
 
 .28410 
 
 80,6 
 
 .62733 
 
 60,6 
 
 .5941 
 
 15,4 
 
 .738 
 
 .80684 
 
 128,5 
 
 .28491 
 
 80,7 
 
 .62794 
 
 60,6 
 
 .5925 
 
 15,4 
 
 .739 
 
 .80812 
 
 128,6 
 
 .28572 
 
 80,8 
 
 .62854 
 
 60,5 
 
 .5910 
 
 15,3 
 
 0.740 
 
 0.80941 
 
 128,7 
 
 1.28652 
 
 80,9 
 
 0.62915 
 
 60,4 
 
 1.5895 
 
 15,3 
 
 .741 
 
 .81070 
 
 128,7 
 
 .28733 
 
 81,1 
 
 .62975 
 
 60,3 
 
 .5879 
 
 15,2 
 
 .742 
 
 .81109 
 
 128,8 
 
 .28815 
 
 81,2 
 
 .63035 
 
 60,3 
 
 5864 
 
 15,2 
 
 743 
 
 .81327 
 
 128,9 
 
 .28896 
 
 81,3 
 
 .63095 
 
 60,2 
 
 .5849 
 
 
 744 
 
 .81456 
 
 129,0 
 
 .28977 
 
 81,5 
 
 .63156 
 
 60, i 
 
 .5834 
 
 I5J 
 
 0.745 
 
 0.81585 
 
 129,1 
 
 1.29059 
 
 81,6 
 
 0.63216 
 
 60,0 
 
 I.58I9 
 
 15,0 
 
 .746 
 
 .81714 
 
 129,1 
 
 .29140 
 
 81,7 
 
 .63276 
 
 60,0 
 
 0804 
 
 I5,o 
 
 747 
 
 .81844 
 
 129,2 
 
 .29222 
 
 81,8 
 
 .63336 
 
 59,9 
 
 .5780 
 
 14,9 
 
 .748 
 
 .81973 
 
 129,3 
 
 .29304 
 
 82,0 
 
 .63395 
 
 59,8 
 
 5774 
 
 14,9 
 
 749 
 
 .82102 
 
 129,4 
 
 .29386 
 
 82,1 
 
 .63455 
 
 59,7 
 
 .5759 
 
 14,8 
 
 0.750 
 
 0.82232 
 
 129,5 
 
 1.29468 
 
 82.2 
 
 0.63515 
 
 59,7 
 
 1.5744 
 
 14,8 
 
 u 
 
 tan gd u 
 
 .F.< 
 
 sec gd u 
 
 -Fo' 
 
 in gd u 
 
 <- Fo' 
 
 esc gd u 
 
 - Fo' 
 
 SMITHSONIAN TABLES 
 
 120 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinh u 
 
 F ' 
 
 cosh u 
 
 Fo' 
 
 tanh u 
 
 F O ' 
 
 coth u 
 
 Fo' 
 
 0.750 
 
 0.82232 
 
 129,5 
 
 1.29468 
 
 82,2 
 
 0.63515 
 
 59,7 
 
 1-5744 
 
 14,8 
 
 .751 
 
 .82361 
 
 129,6 
 
 .29551 
 
 82,4 
 
 .63575 
 
 59,6 
 
 5730 
 
 14,7 
 
 .752 
 
 .82491 
 
 129,6 
 
 .29633 
 
 82,5 
 
 .63634 
 
 59,5 
 
 .5715 
 
 14,7 
 
 .753 
 
 .82620 
 
 129,7 
 
 .29716 
 
 82,6 
 
 .63694 
 
 59,4 
 
 .5700 
 
 14,6 
 
 754 
 
 .82750 
 
 129,8 
 
 .29798 
 
 82,8 
 
 63753 
 
 59,4 
 
 .5686 
 
 14,6 
 
 0.755 
 
 0.82880 
 
 129,9 
 
 1.29881 
 
 82,9 
 
 0.63812 
 
 59,3 
 
 1.5671 
 
 14,6 
 
 .756 
 
 .83010 
 
 130,0 
 
 .29964 
 
 83,0 
 
 .63871 
 
 59,2 
 
 .5656 
 
 14,5 
 
 757 
 
 .83140 
 
 130,0 
 
 .30047 
 
 83,1 
 
 .63931 
 
 59,i 
 
 .5642 
 
 14,5 
 
 758 
 
 .83270 
 
 130,1 
 
 .30130 
 
 83,3 
 
 .63990 
 
 59,1 
 
 .5628 
 
 14,4 
 
 759 
 
 .83400 
 
 130,2 
 
 .30214 
 
 83,4 
 
 .64049 
 
 59,0 
 
 5613 
 
 14,4 
 
 0.760 
 
 0.83530 
 
 130,3 
 
 1.30297 
 
 83,5 
 
 0.64108 
 
 58,9 
 
 1.5599 
 
 14,3 
 
 .761 
 
 .83661 
 
 130,4 
 
 .30381 
 
 83,7 
 
 .64167 
 
 58,8 
 
 .5584 
 
 14,3 
 
 .762 
 
 .83791 
 
 130,5 
 
 .30464 
 
 83,8 
 
 .64225 
 
 58,8 
 
 .5570 
 
 14,2 
 
 .7^3 
 
 .83922 
 
 130,5 
 
 .30548 
 
 83,9 
 
 .64284 
 
 58,7 
 
 .5556 
 
 14,2 
 
 .764 
 
 . 84052 
 
 130,6 
 
 .30632 
 
 84,1 
 
 .64343 
 
 58,6 
 
 5542 
 
 14,2 
 
 0.765 
 
 0.84183 
 
 130,7 
 
 1.30716 
 
 84,2 
 
 0.64401 
 
 58,5 
 
 1.5528 
 
 14,1 
 
 .766 
 
 .84314 
 
 130,8 
 
 .30801 
 
 84,3 
 
 .64460 
 
 58,4 
 
 .5514 
 
 14,1 
 
 .767 
 
 .84445 
 
 130,9 
 
 .30885 
 
 84,4 
 
 .64518 
 
 58,4 
 
 .5500 
 
 14,0 
 
 .768 
 
 .84576 
 
 131,0 
 
 .30970 
 
 84,6 
 
 .64576 
 
 58,3 
 
 .5486 
 
 14,0 
 
 .769 
 
 .84707 
 
 131,1 
 
 .31054 
 
 84,7 
 
 .64635 
 
 58,2 
 
 5472 
 
 13,9 
 
 0.770 
 
 0.84838 
 
 131,1 
 
 I.3H39 
 
 84,8 
 
 0.64693 
 
 58,i 
 
 1.5458 
 
 13,9 
 
 .771 
 
 .84969 
 
 131,2 
 
 .31224 
 
 85,0 
 
 .64751 
 
 58,i 
 
 .5444 
 
 13,9 
 
 .772 
 
 .85100 
 
 I3i,3 
 
 .31309 
 
 85,1 
 
 .64809 
 
 58,0 
 
 .5430 
 
 13,8 
 
 773 
 
 .85231 
 
 131,4 
 
 .31394 
 
 85,2 
 
 .64867 
 
 57,9 
 
 .5416 
 
 13,8 
 
 774 
 
 .85363 
 
 131,5 
 
 .31479 
 
 85,4 
 
 .64925 
 
 57,8 
 
 .5402 
 
 13,7 
 
 0.775 
 
 0.85494 
 
 131,6 
 
 I.3I565 
 
 85,5 
 
 0.64983 
 
 57,8 
 
 1.5389 
 
 13,7 
 
 .776 
 
 .85626 
 
 I3i,7 
 
 .31650 
 
 85,6 
 
 .65040 
 
 57,7 
 
 5375 
 
 13,6 
 
 777 
 
 .85758 
 
 I3i,7 
 
 .31736 
 
 85,8 
 
 .65098 
 
 57,6 
 
 .536i 
 
 13,6 
 
 .778 
 
 .85889 
 
 131,8 
 
 .31822 
 
 85,9 
 
 .65156 
 
 57,5 
 
 .5348 
 
 13,6 
 
 779 
 
 .86021 
 
 131,9 
 
 .31908 
 
 86,0 
 
 .65213 
 
 57,5 
 
 5334 
 
 13,5 
 
 0.780 
 
 0.86153 
 
 132,0 
 
 1.31994 
 
 86,2 
 
 0.65271 
 
 57,4 
 
 I.532I 
 
 13,5 
 
 .781 
 
 .86285 
 
 132,1 
 
 .32080 
 
 86,3 
 
 .65328 
 
 57,3 
 
 .5307 
 
 13,4 
 
 .782 
 
 .86417 
 
 132,2 
 
 .32166 
 
 86,4 
 
 .65385 
 
 57,2 
 
 .5294 
 
 13,4 
 
 .783 
 
 .86550 
 
 132,3 
 
 .32253 
 
 86,5 
 
 .65443 
 
 57,2 
 
 .5281 
 
 13,3 
 
 .784 
 
 .86682 
 
 132,3 
 
 .32340 
 
 86,7 
 
 .65500 
 
 57,1 
 
 .5267 
 
 13,3 
 
 0.785 
 
 0.86814 
 
 132,4 
 
 1.32426 
 
 86,8 
 
 0.65557 
 
 57,0 
 
 1.5254 
 
 13,3 
 
 .786 
 
 .86947 
 
 132,5 
 
 .32513 
 
 86,9 
 
 .65614 
 
 56,9 
 
 .5241 
 
 13,2 
 
 -787- 
 
 .87079 
 
 132,6 
 
 .32600 
 
 87,1 
 
 .65671 
 
 56,9 
 
 .5228 
 
 13,2 
 
 .788 
 
 .7212 
 
 132,7 
 
 .32687 
 
 87,2 
 
 .65727 
 
 56,8 
 
 .5214 
 
 I3,i 
 
 .789 
 
 .87345 
 
 132,8 
 
 .32775 
 
 87,3 
 
 .65784 
 
 56,7 
 
 .5201 
 
 I3,i 
 
 0.790 
 
 0.87478 
 
 132,9 
 
 1.32862 
 
 87,5 
 
 0.65841 
 
 56,6 
 
 1.5188 
 
 I3J 
 
 .791 
 
 .87610 
 
 132,9 
 
 .32950 
 
 87,6 
 
 .65898 
 
 56,6 
 
 .5175 
 
 13,0 
 
 792 
 
 .87743 
 
 I33,o 
 
 .33037 
 
 87,7 
 
 65954 
 
 56,5 
 
 .5162 
 
 13,0 
 
 793 
 
 .87877 
 
 I33,i 
 
 .33125 
 
 87,9 
 
 .66011 
 
 56,4 
 
 .5149 
 
 12,9 
 
 794 
 
 .88010 
 
 133,2 
 
 .33213 
 
 88,0 
 
 .66067 
 
 56,4 
 
 5136 
 
 12,9 
 
 0.795 
 
 0.88143 
 
 133,3 
 
 I.3330I 
 
 88,1 
 
 0.66123 
 
 56,3 
 
 1.5123 
 
 12,9 
 
 .796 
 
 .88276 
 
 133,4 
 
 .33389 
 
 88,3 
 
 .66179 
 
 56,2 
 
 .5110 
 
 12,8 
 
 .797 
 
 .88410 
 
 133,5 
 
 .33478 
 
 88,4 
 
 .66236 
 
 56,i 
 
 .5098 
 
 12,8 
 
 .798 
 
 .88543 
 
 133,6 
 
 .33566 
 
 88,5 
 
 .66292 
 
 56,i 
 
 .5085 
 
 12,8 
 
 799 
 
 .88677 
 
 133,7 
 
 .33655 
 
 88,7 
 
 .66348 
 
 56,o 
 
 .5072 
 
 12,7 
 
 0.800 
 
 0.88811 
 
 133,7 
 
 1-33743 
 
 88,8 
 
 0.66404 
 
 55,9 
 
 1.5059 
 
 12,7 
 
 u 
 
 tan gd u 
 
 Fo' 
 
 sec gd u 
 
 Fo' 
 
 sin gd u 
 
 - Fo' 
 
 esc gd u 
 
 F ' 
 
 SMITHSONIAN TABLES 
 
 121 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinh u 
 
 F ' 
 
 cosh u 
 
 coFo' 
 
 tanh u 
 
 W Fo' 
 
 coth u 
 
 Fo' 
 
 0.800 
 
 0.888II 
 
 133,7 
 
 1-33743 
 
 88,8 
 
 0.66404 
 
 55,9 
 
 1.5059 
 
 12,7 
 
 .801 
 
 .88944 
 
 133,8 
 
 .33832 
 
 88,9 
 
 .66460 
 
 55,8 
 
 5047 
 
 12,6 
 
 .802 
 
 .80078 
 
 133,9 
 
 33921 
 
 89,1 
 
 .66515 
 
 55,8 
 
 5034 
 
 12,6 
 
 .803 
 
 .89212 
 
 134,0 
 
 .34011 
 
 89,2 
 
 .66571 
 
 55,7 
 
 .5022 
 
 12,6 
 
 .804 
 
 .89346 
 
 134,1 
 
 .34100 
 
 89,3 
 
 .66627 
 
 55,6 
 
 .5009 
 
 12,5 
 
 0.805 
 
 0.89480 
 
 134,2 
 
 1.34189 
 
 89,5 
 
 0.66682 
 
 55,5 
 
 1.4996 
 
 12,5 
 
 .806 
 
 .89615 
 
 134,3 
 
 .34279 
 
 89,6 
 
 .66738 
 
 55,5 
 
 .4984 
 
 12,5 
 
 .807 
 
 .89749 
 
 134,4 
 
 34368 
 
 89,7 
 
 .56793 
 
 55,4 
 
 4972 
 
 12,4 
 
 .808 
 
 .89883 
 
 134,5 
 
 34458 
 
 89,9 
 
 .60849 
 
 55,3 
 
 4959 
 
 12,4 
 
 .809 
 
 .90018 
 
 1345 
 
 .34548 
 
 90,o 
 
 .66904 
 
 55,2 
 
 4947 
 
 12,3 
 
 0.810 
 
 0.90152 
 
 134,6 
 
 1.34638 
 
 00,2 
 
 0.66959 
 
 55,2 
 
 1.4935 
 
 12,3 
 
 .811 
 
 .90287 
 
 134,7 
 
 .34729 
 
 90,3 
 
 .67014 
 
 55,i 
 
 .4922 
 
 12,3 
 
 .812 
 
 .90422 
 
 134,8 
 
 .34819 
 
 90,4 
 
 .67069 
 
 55,o 
 
 .4910 
 
 12,2 
 
 .813 
 
 .90557 
 
 134,9 
 
 .34909 
 
 90,6 
 
 .67124 
 
 54,9 
 
 .4898 
 
 12,2 
 
 .814 
 
 .90692 
 
 135,0 
 
 .35000 
 
 90,7 
 
 .67179 
 
 54,9 
 
 .4886 
 
 12,2 
 
 0.815 
 .816 
 
 0.90827 
 .90962 
 
 I35,i 
 135,2 
 
 I.3509I 
 .35182 
 
 90,8 
 91,0 
 
 0.67234 
 .67289 
 
 54,8 
 
 54,7 
 
 1.4873 
 .4861 
 
 12,1 
 12,1 
 
 .817 
 
 .91097 
 
 135,3 
 
 .35273 
 
 91,1 
 
 .67343 
 
 54,6 
 
 .4849 
 
 12,0 
 
 .818 
 
 .91232 
 
 135,4 
 
 .35364 
 
 91,2 
 
 .67398 
 
 54,6 
 
 .4837 
 
 I2,O 
 
 .819 
 
 .91368 
 
 135,5 
 
 35455 
 
 91,4 
 
 67453 
 
 54,5 
 
 .4825 
 
 12,0 
 
 0.820 
 
 0.91503 
 
 135,5 
 
 1.35547 
 
 9i,5 
 
 0.67507 
 
 54,4 
 
 1.4813 
 
 11,9 
 
 .821 
 
 .91639 
 
 135,6 
 
 .35638 
 
 91,6 
 
 .67561 
 
 54,4 
 
 .4801 
 
 11,9 
 
 .822 
 
 91775 
 
 135,7 
 
 35730 
 
 9i,8 
 
 .67616 
 
 54,3 
 
 .4789 
 
 11,9 
 
 .823 
 
 .91910 
 
 135,8 
 
 .35822 
 
 91,9 
 
 .67670 
 
 54,2 
 
 4778 
 
 11,8 
 
 .824 
 
 .92046 
 
 135,9 
 
 .35914 
 
 92,0 
 
 .67724 
 
 54,1 
 
 .4766 
 
 11,8 
 
 0.825 
 
 0.92182 
 
 136,0 
 
 1.36006 
 
 92,2 
 
 0.67778 
 
 54,1 
 
 1.4754 
 
 11,8 
 
 .826 
 
 .92318 
 
 136,1 
 
 .36098 
 
 92,3 
 
 .67832 
 
 54,0 
 
 4742 
 
 n,7 
 
 .827 
 
 92454 
 
 136,2 
 
 36190 
 
 92,5 
 
 .67886 
 
 53,9 
 
 4731 
 
 u,7 
 
 .828 
 
 .92591 
 
 136,3 
 
 .36283 
 
 92,6 
 
 .67940 
 
 53,8 
 
 .4719 
 
 n,7 
 
 .829 
 
 .92727 
 
 136,4 
 
 .36376 
 
 92,7 
 
 .67994 
 
 53,8 
 
 4707 
 
 n,6 
 
 0.830 
 
 0.92863 
 
 136,5 
 
 1.36468 
 
 92,9 
 
 0.68048 
 
 53,7 
 
 1.4696 
 
 11,6 
 
 .831 
 
 .93000 
 
 136,6 
 
 .36561 
 
 93,o 
 
 .68101 
 
 53,6 
 
 .4684 
 
 11,6 
 
 .832 
 
 .93137 
 
 136,7 
 
 .36654 
 
 93,i 
 
 .68155 
 
 53,5 
 
 .4672 
 
 n,5 
 
 .833 
 
 .93273 
 
 136,7 
 
 .36748 
 
 93,3 
 
 .68208 
 
 53,5 
 
 .4661 
 
 n,5 
 
 .834 
 
 93410 
 
 136,8 
 
 .36841 
 
 93,4 
 
 .68262 
 
 534 
 
 .4649 
 
 n,5 
 
 0.835 
 
 0.93547 
 
 136,9 
 
 1.36934 
 
 93,5 
 
 0.68315 
 
 53,3 
 
 1.4638 
 
 11,4 
 
 .836 
 
 .93684 
 
 i37,o 
 
 370*8 
 
 93,7 
 
 .68368 
 
 53,3 
 
 .4627 
 
 11,4 
 
 .837 
 
 .93821 
 
 i37,i 
 
 37122 
 
 93,8 
 
 .68422 
 
 53,2 
 
 .4615 
 
 11,4 
 
 .838 
 
 .93958 
 
 137,2 
 
 .37216 
 
 94,o 
 
 .68475 
 
 53,i 
 
 .4604 
 
 ii,3 
 
 .839 
 
 94095 
 
 137,3 
 
 37310 
 
 94,1 
 
 .68528 
 
 53,0 
 
 4593 
 
 ii,3 
 
 0.840 
 
 0.94233 
 
 137,4 
 
 1.37404 
 
 94,2 
 
 0.68581 
 
 53,0 
 
 i.458i 
 
 ii,3 
 
 .841 
 
 94370 
 
 137,5 .37498 
 
 94,4 
 
 .68634 
 
 52,9 
 
 45/0 
 
 11,2 
 
 .842 
 
 .94508 
 
 137,6 .37593 
 
 94,5 
 
 .68687 
 
 52,8 
 
 4559 
 
 11,2 
 
 .843 
 
 .94645 
 
 137,7 ! .37687 
 
 94,6 
 
 .68739 
 
 52,7 
 
 .4548 
 
 11,2 
 
 .844 
 
 .94783 
 
 137,8 
 
 .37782 
 
 94,8 
 
 .68792 
 
 52,7 
 
 4537 
 
 11,1 
 
 0.845 
 
 O.9492I 
 
 137,9 
 
 1.37877 
 
 94,9 
 
 0.68845 
 
 52,6 
 
 1.4525 
 
 11,1 
 
 .846 
 
 95059 
 
 138,0 
 
 37972 
 
 95,1 
 
 .68807 
 
 52,5 
 
 .4514 
 
 II,! 
 
 .847 
 
 .95197 
 
 138,1 
 
 .38067 
 
 95,2 
 
 .68950 
 
 52,5 
 
 .4503 
 
 11,0 
 
 .848 
 
 95335 
 
 138,2 
 
 .38162 
 
 95,3 
 
 .6000.2 
 
 52,4 
 
 .4492 
 
 11,0 
 
 .949 
 
 95473 
 
 138,3 
 
 .38258 
 
 95,5 
 
 .69055 
 
 52,3 
 
 .4481 
 
 11,0 
 
 0.850 
 
 0.95612 
 
 138,4 
 
 1.38353 
 
 95,6 
 
 0.69107 
 
 52,2 
 
 1.4470 
 
 10,9 
 
 
 
 tan gd u 
 
 F O ' 
 
 sec gd u 
 
 Fo' 
 
 sin gd u 
 
 F ' 
 
 esc gd u 
 
 Fo' 
 
 SMITHSONIAN TABLES 
 
 122 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinh u 
 
 F ' 
 
 cosh u 
 
 F O ' 
 
 tanhu 
 
 F ' 
 
 coth u 
 
 <-F O ' 
 
 0.850 
 
 0.95612 
 
 138,4 
 
 1.38353 
 
 95,6 
 
 0.69107 
 
 52,2 
 
 1.4470 
 
 10,9 
 
 .851 
 
 95750 
 
 138,4 
 
 .38449 
 
 95,7 
 
 .69159 
 
 52,2 
 
 4459 
 
 10,9 
 
 .852 
 
 .95888 
 
 138,5 
 
 .38545 
 
 95,9 
 
 .69211 
 
 52,1 
 
 4449 
 
 10,9 
 
 .853 
 
 .96027 
 
 138,6 
 
 .38641 
 
 96,0 
 
 .69263 
 
 52,0 
 
 4438 
 
 10,8 
 
 .854 
 
 .96166 
 
 138,7 
 
 .38737 
 
 96,2 
 
 69315 
 
 52,0 
 
 .4427 
 
 10,8 
 
 0.855 
 
 0.96305 
 
 138,8 
 
 1.38833 
 
 96,3 
 
 0.69367 
 
 51,9 
 
 1.4416 
 
 10,8 
 
 .856 
 
 .96443 
 
 138,9 
 
 .38929 
 
 96,4 
 
 .69419 
 
 5i,8 
 
 .4405 
 
 10,8 
 
 .857 
 
 .96582 
 
 139,0 
 
 .39026 
 
 96,6 
 
 69471 
 
 5i,7 
 
 4395 
 
 10,7 
 
 .858 
 
 .96721 
 
 139,1 
 
 39122 
 
 96,7 
 
 .69523 
 
 5i,7 
 
 .4384 
 
 10,7 
 
 .859 
 
 .96861 
 
 139,2 
 
 .39219 
 
 96,9 
 
 .69574 
 
 5i,6 
 
 4373 
 
 10,7 
 
 0.860 
 
 O.97OOO 
 
 139,3 
 
 I.393I6 
 
 97,0 
 
 0.69626 
 
 5i,5 
 
 1.4362 
 
 10,6 
 
 .861 
 
 .97139 
 
 139,4 
 
 .39413 
 
 97,1 
 
 .69677 
 
 5i,5 
 
 4352 
 
 10,6 
 
 .862 
 
 .97279 
 
 139,5 
 
 .39510 
 
 97,3 
 
 .69729 
 
 5i,4 
 
 -4341 
 
 10,6 
 
 .863 
 
 .97418 
 
 139,6 
 
 .39608 
 
 97,4 
 
 .69780 
 
 5i,3 
 
 .4331 
 
 10,5 
 
 .864 
 
 .97558 
 
 139,7 
 
 39705 
 
 97,6 
 
 .69831 
 
 51,2 
 
 .4320 
 
 io,5 
 
 0.865 
 
 0.97698 
 
 139,8 
 
 1.39803 
 
 97,7 
 
 0.69882 
 
 51,2 
 
 I.43IO 
 
 io,5 
 
 .866 
 
 .97838 
 
 139,9 
 
 .39901 
 
 97,8 
 
 .69934 
 
 5i,i 
 
 .4299 
 
 10,4 
 
 * .867 
 
 .97978 
 
 140,0 
 
 39999 
 
 98,0 
 
 .69985 
 
 5i,o 
 
 .4289 
 
 10,4 
 
 .868 
 
 .98118 
 
 140,1 
 
 .40097 
 
 98,1 
 
 .70036 
 
 5i,o 
 
 .4278 
 
 10,4 
 
 .869 
 
 .98258 
 
 140,2 
 
 .40195 
 
 98,3 
 
 .70087 
 
 50,9 
 
 .4268 
 
 10,4 
 
 0.870 
 
 0.98398 
 
 140,3 
 
 1.40293 
 
 98,4 
 
 0.70137 
 
 50,8 
 
 1.4258 
 
 10,3 
 
 " .871 
 
 .98538 
 
 140,4 
 
 .40392 
 
 98,5 
 
 .70188 
 
 50,7 
 
 .4247 
 
 10,3 
 
 .872 
 
 .98679 
 
 140,5 
 
 .40490 
 
 98,7 
 
 .70239 
 
 50,7 
 
 4237 
 
 10,3 
 
 .873 
 
 .98819 
 
 140,6 
 
 .40589 
 
 98,8 
 
 .70290 
 
 50,6 
 
 .4227 
 
 10,2 
 
 .874 
 
 .98960 
 
 140,7 
 
 .40688 
 
 99,o 
 
 .70340 
 
 50,5 
 
 4217 
 
 10,2 
 
 0.875 
 
 O.99IOI 
 
 140,8 
 
 1.40787 
 
 99,1 
 
 0.70391 
 
 50,5 
 
 1.4206 
 
 10,2 
 
 .876 
 
 .99241 
 
 140,9 
 
 .40886 
 
 99,2 
 
 .70441 
 
 50,4 
 
 .4196 
 
 10,2 
 
 .877 
 
 .99382 
 
 141,0 
 
 .40985 
 
 99,4 
 
 .70491 
 
 50,3 
 
 .4186 
 
 10,1 
 
 .878 
 
 .99523 
 
 141,1 
 
 .41085 
 
 99,5 
 
 .70542 
 
 50,2 
 
 .4176 
 
 10,1 
 
 .879 
 
 .99665 
 
 141,2 
 
 .41184 
 
 99,7 
 
 .70592 
 
 50,2 
 
 .4166 
 
 10,1 
 
 0.880 
 
 0.99806 
 
 I4i,3 
 
 1.41284 
 
 99,8 
 
 0.70642 
 
 50,1 
 
 1.4156 
 
 10,0 
 
 .881 
 
 99947 
 
 141,4 
 
 .41384 
 
 99,9 
 
 .70692 
 
 5o,o 
 
 .4146 
 
 10,0 
 
 .882 
 
 1.00089 
 
 i4i,5 
 
 .41484 
 
 100,1 
 
 .70742 
 
 50,0 
 
 .4136 
 
 10,0 
 
 .883 
 
 .00230 
 
 141,6 
 
 .41584 
 
 100,2 
 
 .70792 
 
 49,9 
 
 .4126 
 
 IO,O 
 
 .884 
 
 .00372 
 
 I4i,7 
 
 .41684 
 
 100,4 
 
 .70842 
 
 49,8 
 
 .4116 
 
 9,9 
 
 0.885 
 
 1.00514 
 
 141,8 
 
 1.41785 
 
 100,5 
 
 0.70892 
 
 49,7 
 
 1.4106 
 
 9,9 
 
 .886 
 
 .00655 
 
 141,9 
 
 .41886 
 
 100,7 
 
 .70941 
 
 49,7 
 
 .4096 
 
 9,9 
 
 .887 
 
 .00797 
 
 142,0 
 
 .41986 
 
 100,8 
 
 .70991 
 
 49,6 
 
 .4086 
 
 9,8 
 
 .888 
 
 .00939 
 
 142,1 
 
 .42087 
 
 100,9 
 
 .71040 
 
 49,5 
 
 .4076 
 
 9,8 
 
 .889 
 
 .01081 
 
 142,2 
 
 .42188 
 
 IOI,I 
 
 .71090 
 
 49,5 
 
 .4067 
 
 9,8 
 
 0.890 
 
 1.01224 
 
 142,3 
 
 1.42289 
 
 IOI,2 
 
 0.7H39 
 
 49,4 
 
 1.4057 
 
 9,8 
 
 .891 
 
 .01366 
 
 142,4 
 
 .42391 
 
 101,4 
 
 .71189 
 
 49,3 
 
 .4047 
 
 9,7 
 
 .892 
 
 .01508 
 
 142,5 
 
 .42492 
 
 ioi,5 
 
 .71238 
 
 49,3 
 
 .4037 
 
 9,7 
 
 .893 
 
 .01651 
 
 142,6 
 
 .42594 
 
 101,7 
 
 .71287 
 
 49,2 
 
 .4028 
 
 9,7 
 
 .894 
 
 .01794 
 
 142,7 
 
 .42695 
 
 101,8 
 
 .71336 
 
 49,1 
 
 .4018 
 
 9,7 
 
 0.895 
 
 1.01936 
 
 142,8 
 
 1.42797 
 
 101,9 
 
 0.71385 
 
 49,0 
 
 1.4008 
 
 9,6 
 
 .896 
 
 .02079 
 
 142,9 
 
 .42899 
 
 102,1 
 
 .71434 
 
 49,0 
 
 3999 
 
 9,6 
 
 .897 
 
 .02222 
 
 I43,o 
 
 .43001 
 
 102,2 
 
 .71483 
 
 48,9 
 
 3989 
 
 9,6 
 
 .898 
 
 .02365 
 
 I43,i 
 
 .43104 
 
 102,4 
 
 .71532 
 
 48,8 
 
 .3980 
 
 9,5 
 
 .899 
 
 .O25O8 
 
 143,2 
 
 .43206 
 
 102,5 
 
 .71581 
 
 48,8 
 
 3970 
 
 9,5 
 
 0.900 
 
 I.O2652 
 
 143,3 
 
 1.43309 
 
 102,7 
 
 0.71630 
 
 48,7 
 
 I.396I 
 
 9,5 
 
 u 
 
 tan gd u 
 
 Fo' 
 
 sec gd u 
 
 -FO' 
 
 sin gd u 
 
 <-F ' 
 
 esc gd u 
 
 O.FO' 
 
 SMITHSONIAN TABLES 
 
 I2 3 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinh u 
 
 IV 
 
 cosh u 
 
 15 
 
 tanh u 
 
 
 
 cothu 
 
 Fo' 
 
 0.900 
 
 1.02652 
 
 143 
 
 1.43309 
 
 103 
 
 0.71630 
 
 48,7 
 
 I.396I 
 
 9,5 
 
 .901 
 
 .02795 
 
 143 
 
 434II 
 
 103 
 
 .71678 
 
 48,6 
 
 .3951 
 
 9,5 
 
 .902 
 
 .02938 
 
 144 
 
 .43514 
 
 103 
 
 .71727 
 
 48,6 
 
 3942 
 
 9,4 
 
 .903 
 
 .03082 
 
 144 
 
 
 103 
 
 .71776 
 
 48,5 
 
 .3932 
 
 9,4 
 
 .904 
 
 .03226 
 
 144 
 
 .43720 
 
 103 
 
 .71824 
 
 48,4 
 
 .3923 
 
 9,4 
 
 0.905 
 
 1.03370 
 
 144 
 
 1.43824 
 
 103 
 
 0.71872 
 
 48,3 
 
 I.39I4 
 
 9,4 
 
 .906 
 
 .03513 
 
 144 
 
 43927 
 
 104 
 
 .71921 
 
 48,3 
 
 .3904 
 
 9,3 
 
 .907 
 
 .03657 
 
 144 
 
 .44031 
 
 104 
 
 .71969 
 
 48,2 
 
 .3895 
 
 9,3 
 
 .908 
 
 .03801 
 
 144 
 
 .44134 
 
 104 
 
 .72017 
 
 48,1 
 
 .3886 
 
 9,3 
 
 .909 
 
 .03946 
 
 144 
 
 .44238 
 
 104 
 
 .72065 
 
 48,1 
 
 .3876 
 
 9,3 
 
 0.910 
 
 1.04090 
 
 144 
 
 1-44342 
 
 104 
 
 0.72113 
 
 48,0 
 
 1.3867 
 
 9,2 
 
 .911 
 
 .04234 
 
 144 
 
 .44446 
 
 104* 
 
 .72161 
 
 47,9 
 
 .3858 
 
 9,2 
 
 .912 
 
 .04379 
 
 145 
 
 .44551 
 
 104 
 
 .72209 
 
 47,9 
 
 .3849 
 
 9,2 
 
 .913 
 
 .04523 
 
 145 
 
 .44655 
 
 105 
 
 .72257 
 
 47,8 
 
 .3840 
 
 9,2 
 
 .914 
 
 .04668 
 
 145 
 
 .44760 
 
 105 
 
 .72305 
 
 47,7 
 
 .3830 
 
 9,1 
 
 0.915 
 
 1.04813 
 
 145 
 
 1.44865 
 
 105 
 
 0.72352 
 
 47,7 
 
 1.3821 
 
 9,1 
 
 .916 
 
 .04958 
 
 145 
 
 .44969 
 
 105 
 
 .72400 
 
 47,6 
 
 .3812 
 
 9,1 
 
 .917 
 
 .05103 
 
 145 
 
 45075 
 
 105 
 
 .72448 
 
 47,5 
 
 3803 
 
 9J 
 
 .918 
 
 .05248 
 
 145 
 
 .45180 
 
 105 
 
 .72495 
 
 47,4 
 
 .3794 
 
 9,0 
 
 .919 
 
 .05393 
 
 145 
 
 .45285 
 
 105 
 
 .72542 
 
 47,4 
 
 .3785 
 
 9,0 
 
 0.920 
 
 1.05539 
 
 145 
 
 1.45390 
 
 106 
 
 0.72590 
 
 47,3 
 
 1.3776 
 
 9,0 
 
 .921 
 
 .05684 
 
 145 
 
 .45496 
 
 106 
 
 .72637 
 
 47,2 
 
 .3767 
 
 9,0 
 
 .922 
 
 .05830 
 
 146 
 
 .45602 
 
 106 
 
 .72684 
 
 47,2 
 
 .3758 
 
 8,9 
 
 .923 
 
 05975 
 
 146 
 
 .45708 
 
 106 
 
 .72731 
 
 47,1 
 
 3749 
 
 8,9 
 
 .924 
 
 .06121 
 
 146 
 
 .45814 
 
 106 
 
 .72778 
 
 47,0 
 
 3740 
 
 8,9 
 
 0.925 
 
 1.06267 
 
 146 
 
 1.45920 
 
 106 
 
 0.72825 
 
 47,0 
 
 I-373I 
 
 8,9 
 
 .926 
 
 .06413 
 
 146 
 
 .46026 
 
 106 
 
 .72872 
 
 46,9 
 
 .3723 
 
 8,8 
 
 .927 
 
 .06559 
 
 146 
 
 .46133 
 
 107 
 
 .72919 
 
 46,8 
 
 
 8,8 
 
 .928 
 
 .06705 
 
 146 
 
 .46239 
 
 107 
 
 .72966 
 
 46,8 
 
 3705 
 
 8,8 
 
 .929 
 
 .06851 
 
 146 
 
 .46346 
 
 107 
 
 .73013 
 
 46,7 
 
 .3696 
 
 8,8 
 
 0.930 
 
 1.06998 
 
 146 
 
 1.46453 
 
 107 
 
 0.73059 
 
 46,6 
 
 1.3687 
 
 8,7 
 
 .931 
 
 .07144 
 
 147 
 
 .46560 
 
 107 
 
 .73106 
 
 46,6 
 
 .3679 
 
 8,7 
 
 .932 
 
 .07291 
 
 147 
 
 .46667 
 
 107 
 
 .73153 
 
 46,5 
 
 .3670 
 
 8,7 
 
 .933 
 
 .07438 
 
 147 
 
 .46775 
 
 107 
 
 .73199 
 
 46,4 
 
 .3661 
 
 8,7 
 
 934 
 
 .07584 
 
 147 
 
 .46882 
 
 108 
 
 73245 
 
 46,4 
 
 .3653 
 
 8,6 
 
 0.935 
 
 ^tj^j 
 
 1.07731 
 
 147 
 
 1.46900 
 
 108 
 
 0.73292 
 
 46,3 
 
 1.3644 
 
 8,6 
 
 .936 
 
 .07878 
 
 147 
 
 .47098 
 
 108 
 
 .73338 
 
 46,2 
 
 .3636 
 
 8,6 
 
 937 
 
 .08026 
 
 147 
 
 .47206 
 
 icS 
 
 .73384 
 
 46,1 
 
 .3627 
 
 8,6 
 
 .938 
 
 .08173 
 
 147 
 
 .47314 
 
 108 
 
 73430 
 
 46,1 
 
 .3618 
 
 8,5 
 
 939 
 
 .08320 
 
 147 
 
 .47422 
 
 108 
 
 73476 
 
 46,0 
 
 .3610 
 
 8,5 
 
 0.940 
 
 1.08468 
 
 148 
 
 1-47530 
 
 T08 
 
 0.73522 
 
 45,9 
 
 1.3601 
 
 8,5 
 
 .941 
 
 .08615 
 
 148 
 
 .47639 
 
 109 
 
 73568 
 
 45,9 
 
 3593 
 
 8,5 
 
 .942 
 
 .08763 
 
 148 
 
 .47748 
 
 109 
 
 .73614 
 
 45,8 
 
 .3584 
 
 8,5 
 
 943 
 
 .08911 
 
 148 
 
 .47857 
 
 109 
 
 .73660 
 
 45,7 
 
 .3576 
 
 8,4 
 
 944 
 
 .00059 
 
 148 
 
 .47966 
 
 109 
 
 73705 
 
 45,7 
 
 3568 
 
 8,4 
 
 0.945 
 
 1.09207 
 
 148 
 
 1.48075 
 
 109 
 
 0.73751 
 
 45,6 
 
 1.3559 
 
 . 8,4 
 
 .946 
 
 .09355 
 
 148 
 
 .48184 
 
 109 
 
 .73797 
 
 45,5 
 
 3551 
 
 8,4 
 
 .947 
 
 09503 
 
 148 
 
 .48293 
 
 IIO 
 
 .73842 
 
 45,5 
 
 3542 
 
 8,3 
 
 .948 
 
 .09651 
 
 148 
 
 .48403 
 
 1 10 
 
 .73888 
 
 45.4 
 
 .3534 
 
 8,3 
 
 .049 
 
 .09800 
 
 149 
 
 .48513 
 
 IIO 
 
 73933 
 
 45,3 
 
 .3526 
 
 8,3 
 
 0.950 
 
 1.09948 
 
 149 
 
 1.48623 
 
 IIO 
 
 0.73978 
 
 4*3 
 
 I.35I7 
 
 8,3 
 
 u 
 
 tan gd u 
 
 Fo' 
 
 sec gd u 
 
 .w 
 
 sin gd u 
 
 -P.' 
 
 esc gd u 
 
 jjW 
 
 SMITHSONIAN TABLES 
 
 124 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinh u 
 
 Fo' 
 
 cosh u 
 
 Fb' 
 
 tanh u 
 
 F O ' 
 
 coth u 
 
 U.FO' 
 
 0.950 
 
 1.09948 
 
 149 
 
 1.48623 
 
 no 
 
 0.73978 
 
 45,3 
 
 I.35I7 
 
 8,3 
 
 .951 
 
 .10097 
 
 149 
 
 .48733 
 
 no 
 
 .74024 
 
 45,2 
 
 .3509 
 
 8,2 
 
 .952 
 
 . 10246 
 
 149 
 
 .48843 
 
 no 
 
 .74069 
 
 45,1 
 
 3501 
 
 8,2 
 
 953 
 954 
 
 . 10395 
 .10544 
 
 149 
 149 
 
 .48953 
 .49064 
 
 no 
 in 
 
 .74114 
 .74159 
 
 45,1 
 45,0 
 
 .3493 
 .3485 
 
 8,2 
 8,2 
 
 0.955 
 
 1.10693 
 
 149 
 
 I.49I74 
 
 in 
 
 0.74204 
 
 44,9 
 
 1.3476 
 
 8,2 
 
 .956 
 
 .10842 
 
 149 
 
 .49285 
 
 in 
 
 .74249 
 
 44,9 
 
 .3468 
 
 8,1 
 
 957 
 
 .10991 
 
 149 
 
 .49396 
 
 in 
 
 .74294 
 
 44,8 
 
 .3400 
 
 8,1 
 
 958 
 
 .11141 
 
 ISO 
 
 49507 
 
 in 
 
 .74338 
 
 44,7 
 
 .3452 
 
 8,1 
 
 959 
 
 .11291 
 
 150 
 
 .49618 
 
 in 
 
 .74383 
 
 44,7 
 
 3444 
 
 8,1 
 
 0.960 
 
 I . I 1440 
 
 150 
 
 1.49729 
 
 in 
 
 0.74428 
 
 44,6 
 
 1.3436 
 
 8,1 
 
 .961 
 
 .11590 
 
 150 
 
 .49841 
 
 112 
 
 74472 
 
 44,5 
 
 .3428 
 
 8,0 
 
 .962 
 
 .11740 
 
 ISO 
 
 .49953 
 
 112 
 
 .74517 
 
 44,5 
 
 .3420 
 
 8,0 
 
 .963 
 
 .11890 
 
 150 
 
 .50064 
 
 112 
 
 .74561 
 
 44,4 
 
 .3412 
 
 8,0 
 
 964 
 
 . 12040 
 
 150 
 
 .50176 
 
 112 
 
 .74606 
 
 44,3 
 
 .3404 
 
 8,0 
 
 0.965 
 
 1.12190 
 
 150 
 
 I . 50289 
 
 112 
 
 0.74650 
 
 44,3 
 
 1.3396 
 
 7,9 
 
 .966 
 
 .12341 
 
 ISO 
 
 .50401 
 
 112 
 
 .74694 
 
 44,2 
 
 .3388 
 
 7,9 
 
 .967 
 
 .12491 
 
 151 
 
 .50513 
 
 112 
 
 .74738 
 
 44,1 
 
 .3380 
 
 7,9 
 
 .968 
 
 . 12642 
 
 151 
 
 .50626 
 
 113 
 
 .74782 
 
 44,1 
 
 3372 
 
 7.9 
 
 .969 
 
 . 12792 
 
 151 
 
 50739 
 
 H3 
 
 .74826 
 
 44,0 
 
 .3364 
 
 7,9 
 
 0.970 
 
 I . 12943 
 
 151 
 
 1.50851 
 
 H3 
 
 0.74870 
 
 43,9 
 
 1.3356 
 
 7,8 
 
 .971 
 
 .13094 
 
 151 
 
 .50964 
 
 H3 
 
 .74914 
 
 43,9 
 
 3349 
 
 7,8 
 
 .972 
 
 .13245 
 
 151 
 
 .51078 
 
 H3 
 
 .74958 
 
 43,8 
 
 3341 
 
 7,8 
 
 973 
 
 .13396 
 
 I5i 
 
 .51191 
 
 H3 
 
 -75002 
 
 43,7 
 
 3333 
 
 7,8 
 
 974 
 
 . 13547 
 
 151 
 
 .51304 
 
 114 
 
 .75046 
 
 43,7 
 
 .3325 
 
 7,8 
 
 0.975 
 
 I.I3699 
 
 151 
 
 1.51418 
 
 114 
 
 0.75089 
 
 43,6 
 
 I.33I7 
 
 7,7 
 
 .976 
 
 . 13850 
 
 152 
 
 .51532 
 
 114 
 
 .75133 
 
 43,6 
 
 .3310 
 
 7,7 
 
 .977 
 
 .14002 
 
 152 
 
 .51646 
 
 114 
 
 .75176 
 
 43,5 
 
 3302 
 
 7,7 
 
 .978 
 
 .14154 
 
 152 
 
 .51760 
 
 114 
 
 .75220 
 
 43,4 
 
 .3294 
 
 7,7 
 
 .979 
 
 . 14305 
 
 152 
 
 .51874 
 
 114 
 
 .75263 
 
 43,4 
 
 .3287 
 
 7,7 
 
 0.980 
 
 I . 14457 
 
 152 
 
 1.51988 
 
 144 
 
 0.75307 
 
 43,3 
 
 1.3279 
 
 7,6 
 
 .981 
 
 .14609 
 
 152 
 
 .52103 
 
 H5 
 
 .75350 
 
 43,2 
 
 .3271 
 
 7,6 
 
 .982 
 
 .14761 
 
 152 
 
 .52218 
 
 H5 
 
 75393 
 
 43,2 
 
 .3264 
 
 7,6 
 
 .983 
 
 .14914 
 
 152 
 
 .52332 
 
 115 
 
 .75436 
 
 43,1 
 
 .3256 
 
 7,6 
 
 .984 
 
 .15066 
 
 152 
 
 .52447 
 
 H5 
 
 75479 
 
 43,0 
 
 .3249 
 
 7,6 
 
 0.985 
 
 1.15219 
 
 153 
 
 1.52563 
 
 US 
 
 0.75522 
 
 43,0 
 
 1.3241 
 
 7,5 
 
 .986 
 
 I537I 
 
 153 
 
 .52678 
 
 H5 
 
 .75565 
 
 42,9 
 
 .3234 
 
 7,5 
 
 .987 
 
 .15524 
 
 153 
 
 .52793 
 
 116 
 
 .756o8 
 
 42,8 
 
 .3226 
 
 7,5 
 
 .988 
 
 .15677 
 
 153 
 
 .52909 
 
 116 
 
 .75651 
 
 42,8 
 
 .3219 
 
 7,5 
 
 .989 
 
 . 15830 
 
 153 
 
 .53025 
 
 116 
 
 .75694 
 
 42,7 
 
 .3211 
 
 7,5 
 
 0.990 
 
 I.I5983 
 
 153 
 
 I.53I4I 
 
 116 
 
 0.75736 
 
 42,6 
 
 1.3204 
 
 7,4 
 
 991 
 
 . 16136 
 
 153 
 
 .53257 
 
 116 
 
 75779 
 
 42,6 
 
 .3196 
 
 7,4 
 
 .992 
 
 .16289 
 
 153 
 
 53373 
 
 116 
 
 .75821 
 
 42,5 
 
 .3189 
 
 7,4 
 
 993 
 
 .16443 
 
 153 
 
 .53489 
 
 116 
 
 .75864 
 
 42,4 
 
 .3182 
 
 7,4 
 
 .994 
 
 .16596 
 
 154 
 
 .53606 
 
 117 
 
 .75906 
 
 42,4 
 
 .3174 
 
 7,4 
 
 0.995 
 
 I . 16750 
 
 154 
 
 1.53722 
 
 117 
 
 0.75949 
 
 42,3 
 
 1.3167 
 
 7,3 
 
 .996 
 
 .16904 
 
 154 
 
 .53839 
 
 117 
 
 75991 
 
 42,3 
 
 .3159 
 
 7,3 
 
 997 
 
 .17058 
 
 154 
 
 .53956 
 
 117 
 
 .76033 
 
 42,2 
 
 3152 
 
 7,3 
 
 .998 
 
 .17212 
 
 154 
 
 .54073 
 
 117 
 
 .76075 
 
 42,1 
 
 .3145 
 
 7,3 
 
 .999 
 
 .17366 
 
 154 
 
 .54191 
 
 117 
 
 .76117 
 
 42,1 
 
 .3138 
 
 7,3 
 
 I.OOO 
 
 I.I7520 
 
 154 
 
 1.54308 
 
 118 
 
 0.76159 
 
 42,0 
 
 I.3I30 
 
 7,2 
 
 u 
 
 tan gd u 
 
 Fo' 
 
 sec gd u 
 
 wF ' 
 
 sin gd u 
 
 F ' 
 
 esc gd u 
 
 F ' 
 
 SMITHSONIAN TABLES 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinhu 
 
 Fo' 
 
 cosh u 
 
 F ' 
 
 tanh u 
 
 FO' 
 
 cothu 
 
 Fo' 
 
 1. 000 
 
 I.I7520 
 
 154 
 
 1.54308 
 
 118 
 
 0.76159 
 
 42,0 
 
 I.3I30 
 
 7,2 
 
 .001 
 
 . 17674 
 
 154 
 
 .54426 
 
 118 
 
 .76201 
 
 41,9 
 
 .3123 
 
 7,2 
 
 .002 
 
 . 17829 
 
 155 
 
 54543 
 
 118, 
 
 .76243 
 
 41,9 
 
 
 7,2 ' 
 
 .003 
 
 .17984 
 
 155 
 
 .54661 
 
 118 
 
 .76285 
 
 41,8 
 
 .3109 
 
 7,2 
 
 .004 
 
 .18138 
 
 155 
 
 54779 
 
 118 
 
 .76327 
 
 41,7 
 
 .3102 
 
 7,2 
 
 1.005 
 
 1.18293 
 
 155 
 
 1.54898 
 
 118 
 
 0.76369 
 
 41,7 
 
 1.3094 
 
 7,1 
 
 .006 
 
 . 18448 
 
 155 
 
 .55016 
 
 118 
 
 .76410 
 
 41,6 
 
 .3087 
 
 
 .007 
 
 .18603 
 
 155 
 
 .55134 
 
 119 
 
 .76452 
 
 41,6 
 
 .3080 
 
 7! i 
 
 .008 
 
 .18758 
 
 155 
 
 .55253 
 
 119 
 
 .76493 
 
 41,5 
 
 3073 
 
 7,1 
 
 .009 
 
 .18914 
 
 155 
 
 55372 
 
 119 
 
 76535 
 
 41,4 
 
 .3066 
 
 
 I.OIO 
 
 1.19069 
 
 155 
 
 I-5549I 
 
 119 
 
 0.76576 
 
 41,4 
 
 1.3059 
 
 7,1 
 
 .on 
 
 .19225 
 
 156 
 
 .55610 
 
 119 
 
 .76618 
 
 41,3 
 
 .3052 
 
 7,o 
 
 .012 
 .013 
 
 .19380 
 . 19536 
 
 156 
 156 
 
 55729 
 .55849 
 
 119 
 
 120 
 
 76659 
 .76700 
 
 41,2 
 41,2 
 
 .3045 
 .3038 
 
 7,o 
 7,o 
 
 .014 
 
 .19692 
 
 156 
 
 .55969 
 
 120 
 
 .76741 
 
 41,1 
 
 .3031 
 
 7,o 
 
 1.015 
 
 1.19848 
 
 156 
 
 1.56088 
 
 I2O 
 
 0.76782 
 
 41,0 
 
 1.3024 
 
 7,o 
 
 .016 
 
 .20004 
 
 156 
 
 .56208 
 
 I2O 
 
 .76823 
 
 41,0 
 
 .3017 
 
 6,9 
 
 .017 
 
 .20l6o 
 
 156 
 
 .56328 
 
 I2O 
 
 .76864 
 
 40,9 
 
 .3010 
 
 6,9 
 
 .018 
 
 .20317 
 
 156 
 
 .56449 
 
 I2O 
 
 .76905 
 
 40,9 
 
 .3003 
 
 6,9 
 
 .019 
 
 .20473 
 
 157 
 
 56569 
 
 I2O 
 
 .76946 
 
 40,8 
 
 .2996 
 
 6,9 
 
 i. 020 
 
 1.20630 
 
 157 
 
 1.56689 
 
 121 
 
 0.76987 
 
 40,7 
 
 1.2989 
 
 6,9 
 
 .021 
 
 .20787 
 
 157 
 
 .56810 
 
 121 
 
 .77027 
 
 40,7 
 
 .2982 
 
 6,91 
 
 .022 
 
 .20944 
 
 157 
 
 -56931 
 
 121 
 
 .77068 
 
 40,6 
 
 .2976 
 
 6,8 
 
 .023 
 
 .2IIOI 
 
 157 
 
 .57052 
 
 121 
 
 .77109 
 
 40,5 
 
 .2969 
 
 6,8! 
 
 .024 
 
 .21258 
 
 157 
 
 .57173 
 
 121 
 
 .77U9 
 
 40,5 
 
 .2962 
 
 6,8 
 
 1.025 
 
 I.2I4I5 
 
 157 
 
 1.57295 
 
 121 
 
 0.77190 
 
 40,4 
 
 1.2955 
 
 6,8 
 
 .026 
 
 .21572 
 
 157 
 
 .57416 
 
 122 
 
 .77230 
 
 40,4 
 
 .2948 
 
 6,8 1 
 
 .027 
 
 .21730 
 
 158 
 
 .57538 
 
 122 
 
 .77270 
 
 40,3 
 
 .2942 
 
 6,7 
 
 .028 
 
 .21887 
 
 158 
 
 .57660 
 
 122 
 
 .77310 
 
 40,2 
 
 .2935 
 
 6,7' 
 
 .029 
 
 .22045 
 
 158 
 
 .57782 
 
 122 
 
 77351 
 
 40,2 
 
 .2928 
 
 6,7: 
 
 1.030 
 
 I . 222O3 
 
 158 
 
 1.57904 
 
 122 
 
 0-77391 
 
 40,1 
 
 1.2921 
 
 6,7 
 
 .031 
 
 .22361 
 
 158 
 
 .58026 
 
 122 
 
 .77431 
 
 40,0 
 
 .2915 
 
 6,7! 
 
 .032 
 
 .22519 
 
 158 
 
 .58148 
 
 123 
 
 77471 
 
 40,0 
 
 .2908 
 
 6,7 
 
 033 
 
 .22677 
 
 158 
 
 .58271 
 
 123 
 
 775" 
 
 39,9 
 
 .2901 
 
 6,6 ; 
 
 .034 
 
 .22836 
 
 158 
 
 .58394 
 
 123 
 
 77551 
 
 39,9 
 
 .2895 
 
 6,6 
 
 1.035 
 
 1.22994 
 
 159 
 
 1.58517 
 
 123 
 
 0-77591 
 
 39,8 
 
 1.2888 
 
 6,6 
 
 .036 
 
 .23153 
 
 159 
 
 .58640 
 
 123 
 
 .77630 
 
 39,7 
 
 .2882 
 
 6,6 
 
 .037 
 
 .233H 
 
 159 
 
 .58763 
 
 123 
 
 .77670 
 
 39,7 
 
 .2875 
 
 6,6 
 
 .038 
 
 .23470 
 
 159 
 
 .58886 
 
 123 
 
 77710 
 
 39,6 
 
 .2868 
 
 6,6 
 
 039 
 
 .23629 
 
 159 
 
 .59010 
 
 124 
 
 77749 
 
 39,6 
 
 .2862 
 
 6,5 
 
 1.040 
 
 1.23788 
 
 159 
 
 I.59I34 
 
 124 
 
 0.77789 
 
 39,5 
 
 1.2855 
 
 6,5 
 
 .041 
 
 23947 
 
 159 
 
 .59257 
 
 124 
 
 .77828 
 
 39,4 
 
 2849 
 
 6,5 
 
 .042 
 
 .24107 
 
 159 
 
 .59381 
 
 124 
 
 .77868 
 
 39,4 
 
 .2842 
 
 6,5 
 
 .043 
 
 .24266 
 
 160 
 
 .59506 
 
 124. 
 
 .77907 
 
 39,3 
 
 .2836 
 
 6,5 
 
 .044 
 
 .24426 
 
 160 
 
 59630 
 
 124 
 
 .77946 
 
 39,2 
 
 .2829 
 
 6,5 
 
 1.045 
 
 1.24585 
 
 160 
 
 1-59755 
 
 125 
 
 0.77985 
 
 39,2 
 
 1.2823 
 
 6,4 
 
 .046 
 
 24745 
 
 160 
 
 .50879 
 
 125 
 
 .78025 
 
 39,1 
 
 .2816 
 
 6,4 
 
 .047 
 
 .24905 
 
 160 
 
 .60004 
 
 125 
 
 .78064 
 
 39,1 
 
 .2810 
 
 6,4 
 
 .048 
 
 .25065 
 
 160 
 
 .60129 
 
 125 
 
 .78103 
 
 39,0 
 
 .2804 
 
 6,4 
 
 .049 
 
 .25225 
 
 160 
 
 .60254 
 
 125 
 
 .78142 
 
 38,9 
 
 .2797 
 
 6,4 
 
 1.050 
 
 1.25386 
 
 160 
 
 1.60379 
 
 125 
 
 0.78181 
 
 38,9 
 
 I.279I 
 
 6,4 
 
 u 
 
 tan gd u 
 
 -Fo' 
 
 sec gd u 
 
 -Fo' 
 
 tin gd u 
 
 IV 
 
 esc gd u 
 
 -Fo' 
 
 SMITHSONIAN TABLES 
 
 126 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinh u 
 
 Fo' 
 
 cosh u 
 
 F ' 
 
 tanh u 
 
 FO' 
 
 coth u 
 
 O.FO' 
 
 1.050 
 
 1.25386 
 
 160 
 
 1.60379 
 
 125 
 
 0.78181 
 
 38,9 
 
 I.279I 
 
 6,4 
 
 .051 
 
 .25546 
 
 161 
 
 .60505 
 
 126 
 
 .78219 
 
 38,8 
 
 .2785 
 
 6,3 
 
 .052 
 
 .25707 
 
 161 
 
 .60631 
 
 126 
 
 .78258 
 
 38,8 
 
 .2778 
 
 6,3 
 
 053 
 
 .25867 
 
 161 
 
 .60756 
 
 126 
 
 .78297 
 
 38,7 
 
 .2772 
 
 6,3 
 
 054 
 
 .26028 
 
 161 
 
 .60882 
 
 126 
 
 .78336 
 
 38,6 
 
 .2766 
 
 6,3 
 
 1.055 
 
 1.26189 
 
 161 
 
 I. 61008 
 
 126 
 
 0.78374 
 
 38,6 
 
 1.2759 
 
 6,3 
 
 .056 
 
 .26350 
 
 161 
 
 .61135 
 
 126 
 
 .78413 
 
 38,5 
 
 .2753 
 
 6,3 
 
 .057 
 
 .26511 
 
 161 
 
 .61261 
 
 127 
 
 .78451 
 
 38,4 
 
 .2747 
 
 6,2 
 
 .058 
 
 .26673 
 
 161 
 
 .61388 
 
 127 
 
 .78400 
 
 38,4 
 
 .2741 
 
 6,2 
 
 .059 
 
 .26834 
 
 162 
 
 .61514 
 
 127 
 
 .78528 
 
 38,3 
 
 2734 
 
 6,2 
 
 i. 060 
 
 1.26996 
 
 162 
 
 1.61641 
 
 127 
 
 0.78566 
 
 38,3 
 
 1.2728 
 
 6,2 
 
 .061 
 
 .27157 
 
 162 
 
 .61768 
 
 127 
 
 .78605 
 
 38,2 
 
 .2722 
 
 6,2 
 
 .062 
 
 .27319 
 
 162 
 
 .61896 
 
 127 
 
 .78643 
 
 38,2 
 
 .2716 
 
 6,2 
 
 .063 
 
 .27481 
 
 162 
 
 .62023 
 
 127 
 
 .78681 
 
 38,1 
 
 .27IO 
 
 6,2 
 
 .064 
 
 .27643 
 
 162 
 
 .62151 
 
 128 
 
 .78719 
 
 38,0 
 
 .2703 
 
 6,1 
 
 1.065 
 
 1.27806 
 
 162 
 
 1.62278 
 
 128 
 
 0.78757 
 
 38,0 
 
 1.2697 
 
 6,1 
 
 .o(j3 
 
 .27968 
 
 162 
 
 .62406 
 
 128 
 
 . 78795 
 
 37,9 
 
 .2691 
 
 6,1 
 
 .067 
 
 .28130 
 
 163 
 
 .62534 
 
 128 
 
 78833 
 
 37,9 
 
 .2685 
 
 6,1 
 
 .068 
 
 .28293 
 
 163 
 
 .62662 
 
 128 
 
 .78871 
 
 37,8 
 
 .2679 
 
 6,1 
 
 .069 
 
 .28456 
 
 163 
 
 .62791 
 
 128 
 
 .78508 
 
 37,7 
 
 .2673 
 
 6,1 
 
 1.070 
 
 1.28619 
 
 163 
 
 1.62919 
 
 129 
 
 0.78946 
 
 37,7 
 
 1.2667 
 
 6,0 
 
 .071 
 
 .28782 
 
 163 
 
 .63048 
 
 129 
 
 .78984 
 
 37,6 
 
 .2661 
 
 6,0 
 
 .072 
 
 .28945 
 
 163 
 
 .63177 
 
 129 
 
 .79021 
 
 37,6 
 
 .2655 
 
 6,0 
 
 073 
 
 .29108 
 
 163 
 
 .63306 
 
 129 
 
 .79059 
 
 37,5 
 
 .2649 
 
 6,0 
 
 .074 
 
 .29271 
 
 163 
 
 .63435 
 
 129 
 
 .79096 
 
 37,4 
 
 .2043 
 
 6,0 
 
 1.075 
 
 1.29435 
 
 164 
 
 1.63565 
 
 129 
 
 0.79134 
 
 37,4 
 
 1.2637 
 
 6,0 
 
 .076 
 
 .29598 
 
 164 
 
 .63694 
 
 130 
 
 .79171 
 
 37,3 
 
 .2631 
 
 6,0 
 
 .077 
 
 .29762 
 
 164 
 
 .63824 
 
 130 
 
 . 79208 
 
 37,3 
 
 .2625 
 
 5,9 
 
 .078 
 
 .29926 
 
 164 
 
 .63954 
 
 130 
 
 .79246 
 
 37,2 
 
 .2619 
 
 5,9 
 
 079 
 
 .30090 
 
 164 
 
 .64084 
 
 130 
 
 .79283 
 
 37,1 
 
 .2613 
 
 5,9 
 
 1.080 
 
 1.30254 
 
 164 
 
 1.64214 
 
 130 
 
 0.79320 
 
 37,1 
 
 1.2607 
 
 5,9 
 
 .081 
 
 .30418 
 
 164 
 
 .64344 
 
 130 
 
 79357 
 
 37,o 
 
 .2601 
 
 5,9 
 
 ' .082 
 
 .30583 
 
 164 
 
 .64475 
 
 131 
 
 79394 
 
 37,o 
 
 .2595 
 
 5,9 
 
 .083 
 
 .30747 
 
 165 
 
 .64605 
 
 131 
 
 79431 
 
 36,9 
 
 .2590 
 
 5,8 
 
 .084 
 
 .30912 
 
 165 
 
 .64736 
 
 131 
 
 .79468 
 
 36,8 
 
 .2584 
 
 5,8 
 
 1.085 
 
 I.3I077 
 
 165 
 
 1.64867 
 
 131 
 
 0.79505 
 
 36,8 
 
 1.2578 
 
 5,8 
 
 .086 
 
 .31242 
 
 165 
 
 .64098 
 
 131 
 
 79541 
 
 36,7 
 
 .2572 
 
 5,8 
 
 .087 
 
 .31407 
 
 165 
 
 .65130 
 
 131 
 
 79578 
 
 36,7 
 
 .2566 
 
 5,8 
 
 .088 
 
 .31572 
 
 165 
 
 .65261 
 
 132 
 
 .79615 
 
 36,6 
 
 .2560 
 
 5,8 
 
 .089 
 
 .31737 
 
 165 
 
 .65393 
 
 132 
 
 .79651 
 
 36,6 
 
 .2555 
 
 5,8 
 
 1.090 
 
 I.3I903 
 
 166 
 
 1.65525 
 
 132 
 
 0.79688 
 
 36,5 
 
 1.2549 
 
 5,7 
 
 .091 
 
 .32068 
 
 166 
 
 .65657 
 
 132 
 
 .79724 
 
 36,4 
 
 .2543 
 
 5,7 
 
 .092 
 
 .32234 
 
 166 
 
 .65789 
 
 132 
 
 .79761 
 
 36,4 
 
 .2538 
 
 5,7 ' 
 
 .093 
 
 .32400 
 
 166 
 
 .65921 
 
 132 
 
 .79797 
 
 36,3 
 
 .2532 
 
 5,7 
 
 .094 
 
 .32566 
 
 166 
 
 .66053 
 
 133 
 
 -79833 
 
 36,3 
 
 .2526 
 
 5,7 
 
 1.095 
 
 1.32732 
 
 166 
 
 I. 66186 
 
 133 
 
 0.79870 
 
 36,2 
 
 1.2520 
 
 5,7 
 
 .096 
 
 .32808 
 
 166 
 
 .66319 
 
 133 
 
 .79906 
 
 36,2 
 
 .2515 
 
 5,7 
 
 .097 
 
 .33065 
 
 166 
 
 .66452 
 
 133 
 
 .79942 
 
 36,1 
 
 .2509 
 
 5,6 
 
 .098 
 
 .33231 
 
 167 
 
 .66585 
 
 133 
 
 .79978 
 
 36,0 
 
 .2503 
 
 5,6 
 
 .099 
 
 .33398 
 
 167 
 
 .66718 
 
 133 
 
 .80014 
 
 36,0 
 
 .2498- 
 
 5,6 
 
 I. 100 
 
 1.33565 
 
 167 
 
 1.66852 
 
 134 
 
 0.80050 
 
 35,9 
 
 1.2492 
 
 5,6 
 
 u 
 
 tan gd u 
 
 wF ' 
 
 sec gd u 
 
 F O ' 
 
 sin gd u 
 
 Fo' 
 
 esc gd u 
 
 Fo' 
 
 SMITHSONIAN TABLES 
 
 127 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinh u 
 
 <oF ' 
 
 cosh u 
 
 Fo' 
 
 tanh u 
 
 F ' 
 
 cothu 
 
 <-F ' 
 
 I.IOO 
 
 1.33565 
 
 167 
 
 1.66852 
 
 134 
 
 0.80050 
 
 35,9 
 
 1.2492 
 
 5,6 
 
 .101 
 
 33732 
 
 167 
 
 .66986 
 
 134 
 
 .80086 
 
 35,9 
 
 .2487 
 
 5,6 
 
 .102 
 
 .33899 
 
 167 
 
 .67119 
 
 134 
 
 .80122 
 
 35,8 
 
 .2481 
 
 5,6 
 
 .103 
 
 .34066 
 
 167 
 
 .67253 
 
 134 
 
 .80157 
 
 35,7 
 
 2475 
 
 5,6 
 
 .104 
 
 .34233 
 
 167 
 
 .67387 
 
 134 
 
 .80193 
 
 35,7 
 
 .2470 
 
 5,5 
 
 1. 105 
 
 I.3440I 
 
 168 
 
 1.67522 
 
 134 
 
 0.80229 
 
 35,6 
 
 1.2464 
 
 5,5 
 
 .106 
 
 .34568 
 
 168 
 
 .67656 
 
 135 
 
 .80264 
 
 35,6 
 
 2459 
 
 5,5 
 
 .107 
 
 34/36 
 
 168 
 
 .67791 
 
 135 
 
 .80300 
 
 35,5 
 
 2453 
 
 5,5 
 
 .108 
 
 34904 
 
 168 
 
 .67926 
 
 135 
 
 80335 
 
 35,5 
 
 .2448 
 
 5,5 
 
 .109 
 
 .35072 
 
 168 
 
 .68061 
 
 135 
 
 .80371 
 
 35,4 
 
 .2442 
 
 5,5 
 
 I. IIO 
 
 1.35240 
 
 168 
 
 1.68196 
 
 135 
 
 0.80406 
 
 35,3 
 
 1.2437 
 
 5,5 
 
 .in 
 
 .35408 
 
 168 
 
 .68331 
 
 135 
 
 .80442 
 
 35,3 
 
 .2431 
 
 5,5 
 
 .112 
 
 .35577 
 
 168 
 
 .68467 
 
 136 
 
 80477 
 
 35,2 
 
 .2426 
 
 5,4 
 
 .113 
 
 35745 
 
 169 
 
 .68602 
 
 136 
 
 .80512 
 
 35,2 
 
 .2421 
 
 5,4 
 
 .114 
 
 .35914 
 
 169 
 
 .68738 
 
 136 
 
 .80547 
 
 35,1 
 
 .2415 
 
 5,4 
 
 I.H5 
 
 1.36083 
 
 169 
 
 1.68874 
 
 136 
 
 0.80582 
 
 35,1 
 
 1.2410 
 
 5,4 
 
 .116 
 
 .36252 
 
 169 
 
 .69010 
 
 136 
 
 .80617 
 
 35,o 
 
 .2404 
 
 5,4 
 
 .117 
 
 .36421 
 
 169 
 
 .69147 
 
 136 
 
 .80652 
 
 35,0 
 
 2399 
 
 5,4 
 
 .118 
 
 .36590 
 
 169 
 
 .69283 
 
 137 
 
 .80687 
 
 34,9 
 
 
 5,4 
 
 .119 
 
 .36759 
 
 169 
 
 .69420 
 
 137 
 
 .80722 
 
 34,8 
 
 .2388 
 
 5,3 
 
 T.I2O 
 
 1.36929 
 
 170 
 
 1.69557 
 
 137 
 
 0.80757 
 
 34,8 
 
 1.2383 
 
 5,3 
 
 ."?! 
 
 .37098 
 
 170 
 
 .69694 
 
 137 
 
 .80792 
 
 34,7 
 
 .2378 
 
 5,3 
 
 .122 
 
 .37268 
 
 170 
 
 .69831 
 
 137 
 
 .80826 
 
 34,7 
 
 .2372 
 
 5,3 
 
 .123 
 
 .37438 
 
 170 
 
 .69968 
 
 137 
 
 .80861 
 
 34,6 
 
 .2367 
 
 5,3 
 
 .124 
 
 .37608 
 
 170 
 
 .70106 
 
 138 
 
 .80896 
 
 34*6 
 
 .2362 
 
 5,3 
 
 1. 125 
 
 1.37778 
 
 170 
 
 1.70243 
 
 138 
 
 0.80930 
 
 34,5 
 
 1.2356 
 
 5,3 
 
 .125 
 
 37949 
 
 170 
 
 .70381 
 
 138 
 
 .80965 
 
 34,4 
 
 .2351 
 
 5,3 
 
 .127 
 
 .38119 
 
 171 
 
 .70519 
 
 138 
 
 .80909 
 
 34,4 
 
 .2346 
 
 5,2 
 
 .128 
 
 .38290 
 
 171 
 
 .70658 
 
 138 
 
 .81033 
 
 34,3 
 
 .2341 
 
 5,2 
 
 .129 
 
 .38460 
 
 171 
 
 .70706 
 
 138 
 
 .81068 
 
 34,3 
 
 2335 
 
 5,2 
 
 I.I30 
 
 1.38631 
 
 171 
 
 1.70934 
 
 139 
 
 O.8IIO2 
 
 34,2 
 
 1.2330 
 
 5,2 
 
 .131 
 
 .38802 
 
 171 
 
 .71073 
 
 139 
 
 .81136 
 
 34,2 
 
 .2325 
 
 5,2 
 
 .132 
 
 .38973 
 
 171 
 
 .71212 
 
 139 
 
 .81170 
 
 34,1 
 
 .2320 
 
 5,2 
 
 133 
 
 .39145 
 
 171 
 
 .71351 
 
 139 
 
 .81204 
 
 34,1 
 
 .2315 
 
 5,2 
 
 134 
 
 .39316 
 
 171 
 
 .71490 
 
 139 
 
 .81238 
 
 34,0 
 
 .2309 
 
 5,2 
 
 1. 135 
 
 1.39488 
 
 172 
 
 1.71630 
 
 139 
 
 0.81272 
 
 33,9 
 
 1.2304 
 
 5,1 
 
 .136 
 
 39^59 
 
 172 
 
 .71769 
 
 140 
 
 .81306 
 
 33,9 
 
 .2209 
 
 5,1 
 
 .137 
 
 .39831 
 
 172 
 
 .71909 
 
 140 
 
 .81340 
 
 33,8 
 
 
 5,i 
 
 .138 
 
 .40003 
 
 172 
 
 72049 
 
 140 
 
 .81374 
 
 33,8 
 
 .2289 
 
 5,1 
 
 .139 
 
 .40175 
 
 172 
 
 .72189 
 
 140 
 
 .81408 
 
 33,7 
 
 .2284 
 
 5,1 
 
 1.140 
 
 1.40347 
 
 172 
 
 1.72329 
 
 140 
 
 0.81441 
 
 33,7 
 
 1.2279 
 
 5,1 
 
 .141 
 
 .40520 
 
 172 
 
 .72470 
 
 141 
 
 .81475 
 
 33,6 
 
 .2274 
 
 5,1 
 
 .142 
 
 .40692 
 
 173 
 
 .72610 
 
 141 
 
 .81509 
 
 33,6 
 
 .2269 
 
 5,1 
 
 .143 
 
 .40865 
 
 173 
 
 .72751 
 
 141 
 
 .81542 
 
 33,5 
 
 .2264 
 
 5,o 
 
 .144 
 
 .41038 
 
 173 
 
 .72892 
 
 141 
 
 .81576 
 
 33,5 
 
 .2259 
 
 5,o 
 
 1. 145 
 
 1.41211 
 
 173 
 
 1.73033 
 
 141 
 
 0.81609 
 
 33,4 
 
 1.2254 
 
 5,o 
 
 .146 
 
 .41384 
 
 173 
 
 .73175 
 
 141 
 
 .81642 
 
 33,3 
 
 .2249 
 
 5,o 
 
 .147 
 
 .41557 
 
 173 
 
 .73316 
 
 142 
 
 .81676 
 
 33,3 
 
 .2244 
 
 5,o 
 
 .148 
 
 .41731 
 
 173 
 
 .73458 
 
 142 
 
 .81709 
 
 33,2 
 
 .2239 
 
 5,o 
 
 .149 
 
 .41904 
 
 174 
 
 73599 
 
 142 
 
 .81742 
 
 33,2 
 
 . 233 \ 
 
 5,o 
 
 1.150 
 
 1.42078 
 
 174 
 
 I-7374I 
 
 142 
 
 0.81775 
 
 33,1 
 
 1.2229 
 
 5,0 
 
 u 
 
 tan gd u 
 
 -Fo' 
 
 sec gd u 
 
 F ' 
 
 singdu 
 
 F ' 
 
 csc gd u 
 
 wF ' 
 
 SMITHSONIAN TABLE* 
 
 128 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinhu 
 
 F ' 
 
 cosh u 
 
 <-Fo' 
 
 tanhu 
 
 F O - 
 
 coth u 
 
 -IV 
 
 1.150 
 
 1.42078 
 
 174 
 
 I-7374I 
 
 142 
 
 o. -81775 
 
 33,1 
 
 1.2229 
 
 5,0 
 
 .151 
 
 .42252 
 
 174 
 
 .73884 
 
 142 
 
 .81809 
 
 33,1 
 
 .2224 
 
 4,9 
 
 .152 
 
 .42426 
 
 174 
 
 .74026 
 
 142 
 
 .81842 
 
 33,0 
 
 .2219 
 
 4,9 
 
 .153 
 
 .42600 
 
 174 
 
 .74168 
 
 143 
 
 .81875 
 
 33,0 
 
 .2214 
 
 4,9 
 
 .154 
 
 .42774 
 
 174 
 
 .743H 
 
 143 
 
 .81907 
 
 32,9 
 
 .2209 
 
 4,9 
 
 1. 155 
 
 1.42948 
 
 174 
 
 1.74454 
 
 143 
 
 0.81940 
 
 32,9 
 
 1.2204 
 
 4,9 
 
 .156 
 
 .43123 
 
 175 
 
 .74597 
 
 143 
 
 .81973 
 
 32,8 
 
 .2199 
 
 4,9 
 
 .157 
 
 .43297 
 
 175 
 
 .74740 
 
 143 
 
 .82006 
 
 32,8 
 
 .2194 
 
 4,9 
 
 .158 
 
 .43472 
 
 175 
 
 .7488 4 
 
 143 
 
 .82039 
 
 32,7 
 
 .2189 
 
 4,9 
 
 .159 
 
 .43647 
 
 175 
 
 .75027 
 
 144 
 
 .82071 
 
 32,6 
 
 .2185 
 
 4,8 
 
 1.160 
 
 1.43822 
 
 175 
 
 I.75I7I 
 
 144 
 
 0.82104 
 
 32,6 
 
 I. 2180 
 
 4,8 
 
 .161 
 
 .43998 
 
 175 
 
 .75315 
 
 144 
 
 .82137 
 
 32,5 
 
 2175 
 
 4,8 
 
 .162 
 
 .44173 
 
 175 
 
 .75459 
 
 144 
 
 .82169 
 
 32,5 
 
 .2170 
 
 4,8 
 
 .163 
 
 44349 
 
 176 
 
 .75603 
 
 144 
 
 .82202 
 
 32,4 
 
 .2165 
 
 4,8 
 
 .164 
 
 .44524 
 
 176 
 
 .75748 
 
 145 
 
 .82234 
 
 32,4 
 
 .2160 
 
 4,8 
 
 1.165 
 
 1.44700 
 
 176 
 
 1.75892 
 
 145 
 
 0.82266 
 
 32,3 
 
 1.2156 
 
 4,8 
 
 .166 
 
 .44876 
 
 176 
 
 .76037 
 
 145 
 
 .82299 
 
 32,3 
 
 .2151 
 
 4,8 
 
 .167 
 
 .45052 
 
 176 
 
 .76182 
 
 145 
 
 .82331 
 
 32,2 
 
 .2146 
 
 4,8 
 
 1 68 
 
 .45228 
 
 176 
 
 .76327 
 
 145 
 
 .82363 
 
 32,2 
 
 .2141 
 
 4,7 
 
 [169 
 
 .45405 
 
 176 
 
 .76472 
 
 145 
 
 .82395 
 
 32,1 
 
 .2137 
 
 4,7 
 
 1.170 
 
 I.4558I 
 
 177 
 
 1.76618 
 
 146 
 
 0.82427 
 
 32,1 
 
 1.2132 
 
 4,7 
 
 -171 
 
 .45758 
 
 177 
 
 .76764 
 
 146 
 
 .82459 
 
 32,0 
 
 .2127 
 
 4,7 
 
 .172 
 
 .45935 
 
 177 
 
 .76009 
 
 146 
 
 .82491 
 
 32,0 
 
 .2123 
 
 4,7 
 
 173 
 
 .46112 
 
 177 
 
 .77056 
 
 146 
 
 .82523 
 
 3i,9 
 
 .2118 
 
 4,7 
 
 .174 
 
 .46289 
 
 177 
 
 .77202 
 
 146 
 
 .82555 
 
 3i,8 
 
 .2113 
 
 4,7 
 
 1. 175 
 
 1.46466 
 
 177 
 
 1.77348 
 
 146 
 
 0.82587. 
 
 3i,8 
 
 1.2108 
 
 4,7 
 
 .176 
 
 .46644 
 
 177 
 
 77495 
 
 147 
 
 .82619 
 
 3i,7 
 
 .2104 
 
 4,7 
 
 .177 
 
 .46821 
 
 178 
 
 .77641 
 
 147 
 
 .82650 
 
 3i,7 
 
 .2009 
 
 4,6 
 
 .178 
 
 .46999 
 
 178 
 
 .77788 
 
 147 
 
 .82682 
 
 3i,6 
 
 .2095 
 
 4,6 
 
 .179 
 
 .47177 
 
 178 
 
 77935 
 
 147 
 
 .82714 
 
 3i,6 
 
 .2090 
 
 4,6 
 
 1.180 
 
 1.47355 
 
 178 
 
 1.78083 
 
 147 
 
 0.82745 
 
 31,5 
 
 1.2085 
 
 4,6 
 
 .181 
 
 47533 
 
 178 
 
 .78230 
 
 148 
 
 .82777 
 
 3i,5 
 
 .2081 
 
 4,6 
 
 .182 
 
 .47711 
 
 178 
 
 78378 
 
 148 
 
 .82808 
 
 3i,4 
 
 .2076 
 
 4,6 
 
 .183 
 
 .47890 
 
 179 
 
 .78526 
 
 148 
 
 .82840 
 
 3i,4 
 
 .2072 
 
 4,6 
 
 .184 
 
 .48068 
 
 179 
 
 .78673 
 
 148 
 
 .82871 
 
 3i,3 
 
 .2067 
 
 4,6 
 
 1.185 
 
 1.48247 
 
 179 
 
 1.78822 
 
 148 
 
 0.82902 
 
 3i,3 
 
 1.2062 
 
 4,6 
 
 .186 
 
 .48426 
 
 179 
 
 .78970 
 
 148 
 
 .82933 
 
 31,2 
 
 .2058 
 
 4,5 
 
 .187 
 
 .48605 
 
 179 
 
 .79H9 
 
 149 
 
 .82965 
 
 31,2 
 
 .2053 
 
 4,5 
 
 .188 
 
 .48784 
 
 179 
 
 .79267 
 
 149 
 
 .82996 
 
 3M 
 
 .2049 
 
 4,5 
 
 .189 
 
 .48964 
 
 179 
 
 .79416 
 
 149 
 
 .83027 
 
 3i,i 
 
 .2044 
 
 4,5 
 
 1.190 
 
 I.49I43 
 
 180 
 
 1.79565 
 
 149 
 
 0.83058 
 
 31,0 
 
 1.2040 
 
 4,5 
 
 .191 
 
 .49323 
 
 180 
 
 797H 
 
 149 
 
 .83089 
 
 31,0 
 
 .2035 
 
 4,5 
 
 .192 
 
 .49502 
 
 180 
 
 79864 
 
 150 
 
 .83120 
 
 30,9 
 
 .2031 
 
 4,5 
 
 193 
 
 .40682 
 
 180 
 
 .80013 
 
 150 
 
 .83151 
 
 30,9 
 
 .2026 
 
 4>5 
 
 .194 
 
 .49862 
 
 180 
 
 .80163 
 
 150 
 
 .83182 
 
 30,8 
 
 .2022 
 
 4,5 
 
 I.I95 
 
 1.50043 
 
 180 
 
 1.80313 
 
 ISO 
 
 0.83212 
 
 30,8 
 
 1.2017 
 
 4,4 
 
 .196 
 
 .50223 
 
 180 
 
 .80463 
 
 ISO 
 
 .83243 
 
 30,7 
 
 .2013 
 
 4,4 
 
 .197 
 
 .50404 
 
 181 
 
 .80614 
 
 ISO 
 
 .83274 
 
 30,7 
 
 .2009 
 
 4,4 
 
 .198 
 
 .50584 
 
 181 
 
 .80764 
 
 151 
 
 83304 
 
 30,6 
 
 .2004 
 
 4,4 
 
 .199 
 
 .50765 
 
 '181 
 
 .80915 
 
 I5i 
 
 .83335 
 
 30,6 
 
 .2000 
 
 4,4 
 
 i. 200 
 
 1.50946 
 
 181 
 
 i. 81066 
 
 151 
 
 0.83365 
 
 30,5 
 
 i. 1995 
 
 4,4 
 
 u 
 
 tan gd u 
 
 O>F O ' 
 
 sec gd u 
 
 F O ' 
 
 sin gd u 
 
 <oF ' 
 
 esc gd u 
 
 wF ' 
 
 SMITHSONIAN TABLES 
 
 129 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinh u 
 
 IV 
 
 cosh u 
 
 F O ' 
 
 tanh u 
 
 *FO' 
 
 coth u 
 
 F ' 
 
 1.200 
 
 1.50946 
 
 181 
 
 I. 81066 
 
 151 
 
 0.83365 
 
 30,5 
 
 I.I995 
 
 4,4 
 
 .201 
 
 .51127 
 
 181 
 
 .81217 
 
 151 
 
 .83396 
 
 30,5 
 
 .1991 
 
 4,4 
 
 .202 
 
 .51309 
 
 181 
 
 .81368 
 
 151 
 
 .83426 
 
 30,4 
 
 .1987 
 
 4,4 
 
 .203 
 
 .51490 
 
 182 
 
 .81519 
 
 151 
 
 .83457 
 
 30,3 
 
 .1982 
 
 4,4 
 
 .204 
 
 .51672 
 
 182 
 
 .81671 
 
 152 
 
 .83487 
 
 30,3 
 
 .1978 
 
 4,3 
 
 1.205 
 
 I.5I853 
 
 182 
 
 1.81823 
 
 152 
 
 0.83517 
 
 30,2 
 
 I . 1974 
 
 4,3 
 
 .206 
 
 .52035 
 
 182 
 
 .81974 
 
 152 
 
 .83548 
 
 30,2 
 
 .1969 
 
 4,3 
 
 .207 
 
 .52217 
 
 182 
 
 .82127 
 
 . 152 
 
 .83578 
 
 30,1 
 
 .1965 
 
 4,3 
 
 .208 
 
 .52400 
 
 182 
 
 .82279 
 
 152 
 
 .83608 
 
 30,1 
 
 .1961 
 
 4,3 
 
 .209 
 
 .52582 
 
 182 
 
 .82431 
 
 153 
 
 .83638 
 
 30,0 
 
 .1956 
 
 4,3 
 
 I.2IO 
 
 1.52764 
 
 183 
 
 1.82584 
 
 153 
 
 0.83668 
 
 30,0 
 
 I . 1952 
 
 4,3 
 
 .211 
 
 .52947 
 
 183 
 
 .82737 
 
 153 
 
 .83698 
 
 29,9 
 
 .1948 
 
 4,3 
 
 .212 
 
 .53130 
 
 183 
 
 .82890 
 
 153 
 
 .83728 
 
 29,9 
 
 1943 
 
 4,3 
 
 213 
 
 .53313 
 
 183 
 
 83043 
 
 153 
 
 .83758 
 
 29,8 
 
 .1939 
 
 4,3 
 
 .214 
 
 .53496 
 
 183 
 
 .83197 
 
 153 
 
 .83788 
 
 29,8 
 
 .1935 
 
 4,2 
 
 i. 215 
 
 1.53679 
 
 183 
 
 1.83350 
 
 154 
 
 0.83817 
 
 29,7 
 
 I.I93I 
 
 4,2 
 
 .216 
 
 .53863 
 
 184 
 
 .83504 
 
 154 
 
 .83847 
 
 29,7 
 
 .1926 
 
 4,2 
 
 .217 
 
 .54046 
 
 184 
 
 .83658 
 
 154 
 
 .83877 
 
 29,6 
 
 .1922 
 
 4,2 
 
 .218 
 
 .54230 
 
 184 
 
 .83812 
 
 154 
 
 .83506 
 
 29,6 
 
 .1918 
 
 4,2 
 
 .219 
 
 .54414 
 
 184 
 
 .83966 
 
 154 
 
 .83936 
 
 29,5 
 
 .1914 
 
 4,2 
 
 I.22O 
 
 1.54598 
 
 184 
 
 1.84121 
 
 155 
 
 0.83965 
 
 29,5 
 
 1.1910 
 
 4,2 
 
 .221 
 
 .54782 
 
 184 
 
 .84276 
 
 155 
 
 .83995 
 
 29,4 
 
 .1905 
 
 .4,2 
 
 .222 
 
 .54966 
 
 184 
 
 .84430 
 
 155 
 
 .84024 
 
 29,4 
 
 .1901 
 
 4,2 
 
 .223 
 
 .55151 
 
 185 
 
 .84586 
 
 155 
 
 .84054 
 
 29,3 
 
 .1897 
 
 4,2 
 
 .224 
 
 .55336 
 
 185 
 
 .84741 
 
 155 
 
 .84083 
 
 29,3 
 
 .1893 
 
 4,1 
 
 1.225 
 
 1-55520 
 
 185 
 
 1.84896 
 
 156 
 
 0.84112 
 
 29,3 
 
 1.1889 
 
 4,1 
 
 .226 
 
 55705 
 
 185 
 
 .85052 
 
 156 
 
 .84142 
 
 29,2 
 
 .1885 
 
 4,1 
 
 .227 
 
 .55891 
 
 185 
 
 .85208 
 
 156 
 
 .84171 
 
 29,2 
 
 .1881 
 
 4,1 
 
 .228 
 
 06076 
 
 185 
 
 .85364 
 
 156 
 
 .84200 
 
 29,1 
 
 .1877 
 
 4,1 
 
 .229 
 
 .56261 
 
 186 
 
 .85520 
 
 156 
 
 .84229 
 
 29,1 
 
 .1872 
 
 4,1 
 
 1.230 
 
 1.56447 
 
 186 
 
 1.85676 
 
 156 
 
 0.84258 
 
 29,0 
 
 i.i858 
 
 4,1 
 
 .231 
 
 .56633 
 
 186 
 
 .85833 
 
 157 
 
 .84287 
 
 29,0 
 
 .1864 
 
 4,1 
 
 .232 
 
 .56819 
 
 186 
 
 .85989 
 
 157 
 
 .84316 
 
 28,9 
 
 .1860 
 
 4,1 
 
 233 
 
 57005 
 
 186 
 
 .86146 
 
 157 
 
 .84345 
 
 28,9 
 
 .1856 
 
 4,1 
 
 234 
 
 .57191 
 
 186 
 
 .86303 
 
 157 
 
 .84374 
 
 28,8 
 
 .1852 
 
 4,1 
 
 1.235 
 
 i 57377 
 
 186 
 
 1.86461 
 
 157 
 
 0.84402 
 
 28,8 
 
 i . 1848 
 
 4,0 
 
 .236 
 
 .57564 
 
 187 
 
 .86618 
 
 158 
 
 .84431 
 
 28,7 
 
 1844 
 
 4,0 
 
 .237 
 
 57750 
 
 187 
 
 .86/76 
 
 158 
 
 .84460 
 
 28,7 
 
 .1840 
 
 4,o 
 
 .238 
 
 . 57937 
 
 187 
 
 .86934 
 
 158 
 
 .84488 
 
 28,6 j . 1836 
 
 4,0 
 
 .239 
 
 .58124 
 
 187 
 
 .87092 
 
 158 
 
 .84517 
 
 28,6 
 
 .1832 
 
 4,0 
 
 1.240 
 
 1.58311 
 
 187 
 
 1.87250 
 
 158 
 
 0.84546 
 
 28,5 
 
 i . 1828 
 
 4,0 
 
 .241 
 
 .58499 
 
 187 
 
 .87408 
 
 158 
 
 .84574 
 
 28,5 
 
 .1824 
 
 4,0 
 
 .242 
 
 .58686 
 
 188 
 
 .87567 
 
 159 
 
 .84602 
 
 28,4 
 
 .1820 
 
 4,0 
 
 .243 
 
 .58874 
 
 188 
 
 .87726 
 
 159 
 
 .84631 
 
 28,4 
 
 .1816 
 
 4,0 
 
 .244 
 
 .59062 
 
 188 
 
 .87885 
 
 159 
 
 .84659 
 
 28,3 
 
 .1812 
 
 4,0 
 
 1.245 
 
 1.59250 
 
 188 
 
 1.88044 
 
 159 
 
 0.84688 
 
 28,3 
 
 i. 1808 
 
 3,9 
 
 .246 
 
 
 188 
 
 .88203 
 
 159 
 
 .84716 
 
 28,2 
 
 .1804 
 
 3,9 
 
 .247 
 
 .59626 
 
 188 
 
 .88363 
 
 160 
 
 .84744 
 
 28,2 
 
 .1800 
 
 3,9 
 
 .248 
 
 ^59815 
 
 */^ */ 
 
 189 
 
 .88522 
 
 160 
 
 .84772 
 
 28,1 
 
 .1796 
 
 3,9 
 
 .249 
 
 .60003 
 
 189 
 
 .88682 
 
 160 
 
 .84800 
 
 28,1 
 
 .1792 
 
 3,9 
 
 1.250 
 
 1.60192 
 
 189 
 
 1.88842 
 
 160 
 
 0.84828 
 
 28,0 
 
 1.1789 
 
 3,9 
 
 u 
 
 tan od u 
 
 F ' 
 
 sec gd u 
 
 Fo' 
 
 sin gd u 
 
 -FO' 
 
 esc gd u 
 
 -Fo' 
 
 SMITHSONIAN TABLES 
 
 130 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinhu 
 
 F ' 
 
 cosh u 
 
 Fo' 
 
 tanhu 
 
 *>Fo' 
 
 coth u 
 
 Fo' 
 
 1.250 
 
 1.60192 
 
 189 
 
 1.88842 
 
 160 
 
 0.84828 
 
 28,0 
 
 1.1789 
 
 3,9 
 
 .251 
 
 .60381 
 
 189 
 
 .89003 
 
 160 
 
 .84856 
 
 28,0 
 
 .1785 
 
 3,9 
 
 .252 
 
 .60570 
 
 189 
 
 .89163 
 
 161 
 
 .84884 
 
 27,9 
 
 .1781 
 
 3,9 
 
 .253 
 
 .00759 
 
 189 
 
 .89324 
 
 161 
 
 .84912 
 
 27,9 
 
 .1777 
 
 3,9 
 
 .254 
 
 .60949 
 
 189 
 
 .89485 
 
 161 
 
 .84940 
 
 27,9 
 
 .1773 
 
 3,9 
 
 1.255 
 
 1.61138 
 
 190 
 
 1.89646 
 
 161 
 
 0.84968 
 
 27,8 
 
 1.1769 
 
 3,9 
 
 .256 
 
 .61328 
 
 190 
 
 .89807 
 
 161 
 
 .84996 
 
 27,8 
 
 .1765 
 
 3,8 
 
 -257 
 
 .61518 
 
 190 
 
 .89968 
 
 162 
 
 .85023 
 
 27,7 
 
 .1761 
 
 3,8 
 
 .258 
 
 .61708 
 
 190 
 
 .90130 
 
 162 
 
 .85051 
 
 27,7 
 
 .1758 
 
 3,8 
 
 .259 
 
 .61898 
 
 190 
 
 .90292 
 
 162 
 
 .85079 
 
 27,6 
 
 .1754 
 
 3,8 
 
 1.260 
 
 1.62088 
 
 190 
 
 1.90454 
 
 162 
 
 0.85106 
 
 27,6 
 
 1.1750 
 
 3,8 
 
 .261 
 
 .62279 
 
 IQI 
 
 .90616 
 
 162 
 
 .85134 
 
 27,5 
 
 .1746 
 
 3,8 
 
 .262 
 
 .62470 
 
 191 
 
 .90778 
 
 162 
 
 .85161 
 
 27,5 
 
 .1742 
 
 3,8 
 
 .263 
 
 .62661 
 
 I 9 I 
 
 .90941 
 
 163 
 
 .85189 
 
 27,4 
 
 1739 
 
 3,8 
 
 .264 
 
 .62851 
 
 .191 
 
 .9H04 
 
 163 
 
 .85216 
 
 27,4 
 
 .1735 
 
 3,8 
 
 1.265 
 
 1.63043 
 
 191 
 
 1.91267 
 
 163 
 
 0.85244 
 
 27,3 
 
 1.1731 
 
 3,8 
 
 .266 
 
 .63234 
 
 191 
 
 .91430 
 
 163 
 
 .85271 
 
 27,3 
 
 .1727 
 
 3,8 
 
 .267 
 
 .63426 
 
 192 
 
 .91593 
 
 163 
 
 .85298 
 
 27,2 
 
 .1724 
 
 3,7 
 
 .268 
 
 .63617 
 
 192 
 
 .91757 
 
 164 
 
 .85325 
 
 27,2 
 
 .1720 
 
 3,7 
 
 .269 
 
 .63809 
 
 192 
 
 .91920 
 
 164 
 
 .85353 
 
 27,1 
 
 .1716 
 
 3,7 
 
 1.270 
 
 1.64001 
 
 192 
 
 1.92084 
 
 164 
 
 0.85380 
 
 27,1 
 
 1.1712 
 
 3,7 
 
 .271 
 
 .64193 
 
 192 
 
 .92248 
 
 164 
 
 .85407 
 
 27,1 
 
 .1709 
 
 3,7 
 
 .272 
 
 .64386 
 
 192 
 
 .92413 
 
 164 
 
 85434 
 
 27,0 
 
 .1705 
 
 3,7 
 
 273 
 
 .64578 
 
 193 
 
 .92577 
 
 165 
 
 .85461 
 
 27,0 
 
 .1701 
 
 3,7 
 
 .274 
 
 .64771 
 
 193 
 
 .92742 
 
 165 
 
 .85488 
 
 26,9 
 
 .1698 
 
 3,7 
 
 1.275 
 
 1.64964 
 
 193 
 
 1.92907 
 
 165 
 
 0.85515 
 
 26,9 
 
 1.1694 
 
 3,7 
 
 .276 
 
 .65157 
 
 193 
 
 .93072 
 
 165 
 
 .85542 
 
 26,8 
 
 .1690 
 
 3,7 
 
 277 
 
 .65350 
 
 193 
 
 .93237 
 
 165 
 
 .85568 
 
 26,8 
 
 .1687 
 
 3,7 
 
 .278 
 
 .65543 
 
 193 
 
 93402 
 
 166 
 
 .85595 
 
 26,7 
 
 .1683 
 
 3,6 
 
 .279 
 
 .65736 
 
 194 
 
 .93568 
 
 166 
 
 .85622 
 
 26,7 
 
 .1679 
 
 3,6 
 
 1.280 
 
 1.65930 
 
 194 
 
 1.93734 
 
 166 
 
 0.85648 
 
 26,6 
 
 I . 1676 
 
 3,6 
 
 .281 
 
 .66124 
 
 194 
 
 .93900 
 
 166 
 
 .85675 
 
 26,6 
 
 .1672 
 
 3,6 
 
 .282 
 
 .66318 
 
 194 
 
 .94066 
 
 166 
 
 .85702 
 
 26,6 
 
 .1668 
 
 3,6 
 
 .283 
 
 .66512 
 
 194 
 
 .94233 
 
 167 
 
 .85728 
 
 26,5 
 
 .1665 
 
 3,6 
 
 .284 
 
 .66706 
 
 194 
 
 94399 
 
 167 
 
 .85755 
 
 26,5 
 
 .1661 
 
 3,6 
 
 1.285 
 
 1.66901 
 
 195 
 
 1.94566 
 
 167 
 
 0.85781 
 
 26,4 
 
 I . 1658 
 
 3,6 
 
 .286 
 
 .67096 
 
 195 
 
 94733 
 
 167 
 
 .85808 
 
 26,4 
 
 .1654 
 
 3,6 
 
 .287 
 
 .67200 
 
 195 
 
 .94900 
 
 167 
 
 .85834 
 
 26,3 
 
 .1650 
 
 3,6 
 
 .288 
 
 .67485 
 
 195 
 
 .95068 
 
 167 
 
 .85860 
 
 26,3 
 
 .1647 
 
 3,6 
 
 .289 
 
 .67680 
 
 195 
 
 95235 
 
 168 
 
 .85886 
 
 26,2 
 
 .1643 
 
 3,6 
 
 1.290 
 
 1.67876 
 
 195 
 
 1.95403 
 
 168 
 
 0.85913 
 
 26,2 
 
 I . 1640 
 
 . 3,5 
 
 .291 
 
 .68071 
 
 196 
 
 95571 
 
 168 
 
 .85939 
 
 26,1 
 
 .1636 
 
 3,5 
 
 .292 
 
 .68267 
 
 196 
 
 95739 
 
 168 
 
 .85965 
 
 26,1 
 
 .1633 
 
 3,5 
 
 293 
 
 .68463 
 
 196 
 
 .95907 
 
 168 
 
 .85991 
 
 26,1 
 
 .1629 
 
 3,5 
 
 .294 
 
 .68659 
 
 196 
 
 .96076 
 
 169 
 
 .86017 
 
 26,0 
 
 .1626 
 
 3,5 
 
 1.295 
 
 1.68855 
 
 196. 
 
 1.96245 
 
 169 
 
 0.86043 
 
 26,0 
 
 I . 1622 
 
 3,5 
 
 .296 
 
 .60051 
 
 196 
 
 .96414 
 
 169 
 
 .86069 
 
 25,9 
 
 .1619 
 
 3,5 
 
 .297 
 
 .69248 
 
 197 
 
 .96583 
 
 169 
 
 .86095 
 
 25,9 
 
 .1615 
 
 3,5 
 
 .298 
 
 .69444 
 
 197 
 
 .96752 
 
 169 
 
 .86121 
 
 25,8 
 
 .1612 
 
 3,5 
 
 299 
 
 .69641 
 
 197 
 
 .96922 
 
 170 
 
 .86147 
 
 25,8 
 
 .1608 
 
 3,5 
 
 1.300 
 
 1.69838 
 
 197 
 
 1.97091 
 
 170 
 
 0.86172 
 
 25,7 
 
 1.1005 
 
 3,5 
 
 u 
 
 tan gd u 
 
 F O ' 
 
 sec Qd u 
 
 FO' 
 
 sin gd u 
 
 w FO' 
 
 esc gd u 
 
 F ' 
 
 SMITHSONIAN TABLES 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinhu 
 
 F ' 
 
 cosh u 
 
 F ' 
 
 tanhu 
 
 coFo' 
 
 cothu 
 
 -FO' 
 
 1.300 
 
 1.69838 
 
 197 
 
 I.9709I 
 
 170 
 
 0.86172 
 
 25,7 
 
 I . 1605 
 
 3,5 
 
 .301 
 
 .70035 
 
 197 
 
 .97261 
 
 170 
 
 .86198 
 
 25,7 
 
 . 1601 
 
 3,5 
 
 .302 
 
 .70233 
 
 197 
 
 .97431 
 
 170 
 
 .86224 
 
 25,7 
 
 .1598 
 
 3,5 
 
 .303 
 
 .70430 
 
 198 
 
 .97602 
 
 170 
 
 .86249 
 
 25,6 
 
 1594 
 
 3,4 
 
 .304 
 
 .70628 
 
 198 
 
 .97772 
 
 171 
 
 .86275 
 
 25,6 
 
 I59I 
 
 3,4 
 
 1.305 
 
 1.70826 
 
 198 
 
 1-97943 
 
 171 
 
 0.86300 
 
 25,5 
 
 1.1587 
 
 3,4 
 
 .306 
 
 .71024 
 
 198 
 
 .98114 
 
 171 
 
 .86326 
 
 25,5 
 
 1584 
 
 3,4 
 
 .307 
 
 .71222 
 
 198 
 
 .98285 
 
 171 
 
 .86351 
 
 25,4 
 
 .1581 
 
 3,4 
 
 .308 
 
 .71420 
 
 198 
 
 .98456 
 
 i/i 
 
 .86377 
 
 25,4 
 
 .1577 
 
 3,4 
 
 .309 
 
 .71619 
 
 199 
 
 .98628 
 
 172 
 
 .86402 
 
 25,3 
 
 1574 
 
 3,4 
 
 1.310 
 
 I.7l8l8 
 
 199 
 
 1.98800 
 
 172 
 
 0.86428 
 
 25,3 
 
 1.1570 
 
 3,4 
 
 .311 
 
 .72017 
 
 199 
 
 .98972 
 
 172 
 
 .86453 
 
 25,3 
 
 .1567 
 
 3,4 
 
 .312 
 
 .72216 
 
 199 
 
 .99M4 
 
 172 
 
 .86478 
 
 25,2 
 
 1564 
 
 3,4 
 
 313 
 
 .72415 
 
 199 
 
 .99316 
 
 172 
 
 .86503 
 
 25,2 
 
 .1560 
 
 3,4 
 
 .314 
 
 .72614 
 
 199 
 
 .99489 
 
 173 
 
 .86528 
 
 25,1 
 
 .1557 
 
 3,4 
 
 1.315 
 
 1.72814 
 
 200 
 
 1.99661 
 
 173 
 
 0.86554 
 
 25,1 
 
 I. 1554 
 
 3,3 
 
 .316 
 
 .73014 
 
 200 
 
 .99834 
 
 173 
 
 .86579 
 
 25,0 
 
 .1550 
 
 3,3 
 
 .317 
 
 .73214 
 
 2OO 
 
 2.00007 
 
 173 
 
 .86604 
 
 25,0 
 
 .1547 
 
 3,3 
 
 .318 
 
 -73414 
 
 2OO 
 
 .00181 
 
 173 
 
 .86629 
 
 25,0 
 
 .1544 
 
 3,3 
 
 .319 
 
 .73614 
 
 200 
 
 00354 
 
 174 
 
 .86653 
 
 24,9 
 
 .1540 
 
 3,3 
 
 1.320 
 
 I.738I4 
 
 2OI 
 
 2.00528 
 
 174 
 
 0.86678 
 
 24,9 
 
 i -1537 
 
 3,3 
 
 .321 
 
 .74015 
 
 2OI 
 
 .00702 
 
 174 
 
 . 81.703 
 
 24,8 
 
 1534 
 
 3,3 
 
 .322 
 
 .74216 
 
 2O I 
 
 .00876 
 
 174 
 
 .86728 
 
 24,8 
 
 .1530 
 
 3,3 
 
 323 
 
 .74417 
 
 201 
 
 .01050 
 
 174 
 
 .86753 
 
 24,7 
 
 .1527 
 
 3,3 
 
 .324 
 
 .74618 
 
 201 
 
 .01225 
 
 175 
 
 .86778 
 
 24,7 
 
 .1524 
 
 3,3 
 
 1.325 
 
 I.748I9 
 
 2OI 
 
 2.01309 
 
 i75 
 
 0.85802 
 
 24,7 
 
 1.1520 
 
 3,3 
 
 .326 
 
 .75021 
 
 2O2 
 
 .01574 
 
 175 
 
 .86827 
 
 24,6 
 
 .1517 
 
 3,3 
 
 .327 
 
 .75222 
 
 202 
 
 .01749 
 
 175 
 
 .86851 
 
 24,6 
 
 .1514 
 
 3,3 
 
 .328 
 
 75424 
 
 2O2 
 
 .01925 
 
 175 
 
 .86876 
 
 24,5 
 
 .1511 
 
 3,2 
 
 .329 
 
 .75626 
 
 2O2 
 
 .02100 
 
 176 
 
 .86900 
 
 24,5 
 
 .1507 
 
 3,2 
 
 1.330 
 
 1.75828 
 
 2O2 
 
 2.02276 
 
 176 
 
 0.86925 
 
 24,4 
 
 I . 1504 
 
 3,2 
 
 .331 
 
 .76031 
 
 202 
 
 .02452 
 
 176 
 
 .86949 
 
 24,4 
 
 .1501 
 
 3,2 
 
 .332 
 
 . 76233 
 
 203 
 
 .02628 
 
 i 7 5 
 
 .86974 
 
 24,4 
 
 .1408 
 
 3,2 
 
 .333 
 
 .76436 
 
 203 
 
 .02804 
 
 176 
 
 .86998 
 
 24,3 
 
 .1495 
 
 3,2 
 
 .334 
 
 .76639 
 
 203 
 
 .02981 
 
 177 
 
 .87022 
 
 24,3 
 
 .1491 
 
 3,2 
 
 1.335 
 
 1.76842 
 
 203 
 
 2.03158 
 
 177 
 
 0.87047 
 
 24,2 
 
 1.1488 
 
 3,2 
 
 .336 
 
 .77045 
 
 203 
 
 03335 
 
 177 
 
 .87071 
 
 24,2 
 
 .1485 
 
 3,2 
 
 337 
 
 77249 
 
 2O4 
 
 .03512 
 
 177 
 
 87095 
 
 24,1 
 
 .1482 
 
 3,2 
 
 .338 
 
 77452 
 
 204 
 
 .03689 
 
 177 
 
 .87119 
 
 24,1 
 
 .1479 
 
 3,2 
 
 .339 
 
 .77656 
 
 2O4 
 
 .03867 
 
 178 
 
 .87143 
 
 24,1 
 
 1475 
 
 3,2 
 
 1-340 
 
 1.77860 
 
 204 
 
 2.04044 
 
 178 
 
 0.87167 
 
 24,0 
 
 I.I472 
 
 3,2 
 
 341 
 
 .78064 
 
 204 
 
 .04222 
 
 178 
 
 .87191 
 
 24,0 
 
 .1469 
 
 3,2 
 
 .342 
 
 .78268 
 
 204 
 
 .04401 
 
 178 
 
 .87215 
 
 23,9 
 
 .1466 
 
 3,1 
 
 343 
 
 .78473 
 
 205 
 
 .04579 
 
 178 
 
 .87239 
 
 23,9 
 
 . 1463 
 
 3,1 
 
 344 
 
 .78677 
 
 205 
 
 .04758 
 
 179 
 
 .87263 
 
 23,9 
 
 .1460 
 
 3,1 
 
 1-345 
 
 1.78882 
 
 205 
 
 2.04936 
 
 179 
 
 0.87287 
 
 23,8 
 
 I.I456 
 
 3,1 
 
 .346 
 
 .79087 
 
 205 
 
 .05115 
 
 179 
 
 .87311 
 
 23,8 
 
 .1453 
 
 3J 
 
 347 
 
 .79293 
 
 205 
 
 05294 
 
 179 
 
 .87334 
 
 23,7 
 
 . M50 
 
 3,1 
 
 .348 
 
 .79498 
 
 205 
 
 .05474 
 
 179 
 
 .87358 
 
 23,7 
 
 .1447 
 
 3.1 
 
 349 
 
 .79704 
 
 206 
 
 .05653 
 
 180 
 
 .87382 
 
 23,6 
 
 .1444 
 
 3,i 
 
 T.350 
 
 1.79909 
 
 206 
 
 2.05833 
 
 180 
 
 0.87405 
 
 23,6 
 
 I . 1441 
 
 3.1 
 
 u 
 
 tan ad u 
 
 - F,,' 
 
 sec gd u 
 
 Fo' 
 
 sin gd u 
 
 F,/ 
 
 esc gd u 
 
 -Fo' 
 
 SMITHSONIAN TABLES 
 
 132 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinh u | w Fo' cosh u 
 
 u>Fo' 
 
 tanh u 
 
 O>F O ' 
 
 cothu 
 
 F ' 
 
 1.350 
 
 1.79909 
 
 206 2.05833 
 
 180 
 
 0.87405 
 
 23,6 
 
 1.1441 
 
 3,1 
 
 .351 
 
 .80115 
 
 206 .06013 
 
 180 
 
 .87429 
 
 23,6 
 
 .1438 
 
 3,1 
 
 .352 
 
 .80321 
 
 206 
 
 .06194 
 
 180 
 
 .87452 
 
 23,5 
 
 .1435 
 
 3,1 
 
 353 
 
 ' .80528 
 
 206 
 
 .06374 
 
 181 
 
 .87476 
 
 23,5 
 
 .1432 
 
 3,1 
 
 354 
 
 .80734 
 
 207 
 
 .06555 
 
 181 
 
 .87499 
 
 23,4 
 
 .1429 
 
 3,1 
 
 1.355 
 
 1.80041 
 
 207 
 
 2.06735 
 
 181 
 
 0.87523 
 
 23,4 
 
 1.1426 
 
 3,1 
 
 356 
 
 .81148 
 
 207 
 
 .06916 
 
 181 
 
 .87546 
 
 23,4 
 
 .1423 
 
 3,0 
 
 .357 
 
 .81355 
 
 207 
 
 .07098 
 
 181 
 
 .87570 
 
 23,3 
 
 .1419 
 
 3,o 
 
 .358 
 
 .81562 
 
 207 
 
 .07279 
 
 182 
 
 .87593 
 
 23,3 
 
 .1416 
 
 3,0 
 
 359 
 
 .81769 
 
 207 
 
 .07461 
 
 182 
 
 .87616 
 
 23,2 
 
 .1413 
 
 3,0 
 
 1.360 
 
 I.8I977 
 
 208 
 
 2.07643 
 
 182 
 
 0.87639 
 
 23,2 
 
 1.1410 
 
 3,o 
 
 .361 
 
 .82184 
 
 208 
 
 .07825 
 
 182 
 
 .87662 
 
 23,2 
 
 .1407 
 
 3,0 
 
 .362 
 
 .82392 
 
 208 
 
 .08007 
 
 182 
 
 .87686 
 
 23,1 
 
 .1404 
 
 3,0 
 
 .363 
 
 .82600 
 
 208 
 
 .08190 
 
 183 
 
 .87709 
 
 23,1 
 
 .1401 
 
 3,0 
 
 364 
 
 .82809 
 
 208 
 
 .08372 
 
 . 183 
 
 .87732 
 
 23,0 
 
 .1398 
 
 3,0 
 
 1.365 
 
 1.83017 
 
 209 
 
 2.08555 
 
 183 
 
 0.87755 
 
 23,0 
 
 I . 1395 
 
 3,0 
 
 .366 
 
 .83226 
 
 209 
 
 .08738 
 
 183 
 
 .87778 
 
 23,0 
 
 
 3,o 
 
 .367 
 
 .83435 
 
 209 
 
 .08922 
 
 183 
 
 .87801 
 
 22,9 
 
 .1389 
 
 3,0 
 
 .368 
 
 .83644 
 
 209 
 
 .09105 
 
 184 
 
 .87824 
 
 22,9 
 
 .1386 
 
 3,0 
 
 .369 
 
 83853 
 
 209 
 
 .09289 
 
 184 
 
 .87846 
 
 22,8 
 
 .1384 
 
 3,0 
 
 1.370 
 
 1.84062 
 
 209 
 
 2.09473 
 
 184 
 
 0.87869 
 
 22,8 
 
 1.1381 
 
 3,0 
 
 371 
 
 .84272 
 
 2IO 
 
 ,09657 
 
 184 
 
 .87892 
 
 22,7 
 
 .1378 
 
 2,9 
 
 372 
 
 .84482 
 
 2IO 
 
 .09841 
 
 184 
 
 .87915 
 
 22,7 
 
 .1375 
 
 2,9 
 
 373 
 
 .84691 
 
 2IO 
 
 .10026 
 
 185 
 
 .87937 
 
 22,7 
 
 .1372 
 
 2,9 
 
 374 
 
 .84902 
 
 2IO 
 
 .1021 I 
 
 185 
 
 .87960 
 
 22,6 
 
 .1369 
 
 2,0 
 
 1.375 
 
 I.85II2 
 
 210 
 
 2.10306 
 
 185 
 
 0.87983 
 
 22,6 
 
 1.1366 
 
 2,9 
 
 .376 
 
 .85322 
 
 211 
 
 .10581 
 
 185 
 
 .88005 
 
 22,6 
 
 .1363 
 
 2,9 
 
 377 
 
 85533 
 
 211 
 
 .10766 
 
 186 
 
 .88028 
 
 22,5 
 
 .1360 
 
 2,9 
 
 .378 
 
 .85744 
 
 211 
 
 .10952 
 
 186 
 
 .88050 
 
 22,5 
 
 .1357 
 
 2,9 
 
 379 
 
 .85955 
 
 211 
 
 .11138 
 
 186 
 
 .88073 
 
 22,4 
 
 .1354 
 
 2,9 
 
 1.380 
 
 I.86I66 
 
 211 
 
 2.11324 
 
 186 
 
 0.88095 
 
 22,4 
 
 1.1351 
 
 2,9 
 
 .381 
 
 .86378 
 
 212 
 
 .11510 
 
 186 
 
 .88117 
 
 22,4 
 
 .1348 
 
 2,9 
 
 .382 
 
 .86589 
 
 212 
 
 .11697 
 
 187 
 
 .88140 
 
 22,3 
 
 .1346 
 
 2,9 
 
 .383 
 
 .86801 
 
 212 
 
 .11883 
 
 187 
 
 .88162 
 
 22,3 
 
 . 1343 
 
 2,9 
 
 .384 
 
 .87013 
 
 212 
 
 .12070 
 
 187 
 
 .88184 
 
 22,2 
 
 .1340 
 
 2,9 
 
 1.385 
 
 1.87225 
 
 212 
 
 2.12257 
 
 187 
 
 0.88207 
 
 22,2 
 
 1 . 1337 
 
 2,9 
 
 .386 
 
 .87437 
 
 212 
 
 .12445 
 
 187 
 
 .88229 
 
 22,2 
 
 .1334 
 
 2,8 
 
 .387 
 
 .87650 
 
 213 
 
 .12632 
 
 188 
 
 .88251 
 
 22,1 
 
 .1331 
 
 2,8 
 
 .388 
 
 .87863 
 
 213 
 
 .12820 
 
 188 
 
 .88273 
 
 22,1 
 
 .1328 
 
 2,8 
 
 .389 
 
 .88076 
 
 213 
 
 .13008 
 
 188 
 
 .88295 
 
 22,O 
 
 .1326 
 
 2,8 
 
 1.390 
 
 1.88289 
 
 213 
 
 2.13196 
 
 188 
 
 0.88317 
 
 22,0 
 
 1.1323 
 
 2,8 
 
 .391 
 
 .88502 
 
 213 
 
 .13385 
 
 189 
 
 .88339 
 
 22,O 
 
 .1320 
 
 2,8 
 
 .392 
 
 .88716 
 
 214 
 
 13573 
 
 189 
 
 .88361 
 
 21,9 
 
 .1317 
 
 2,8 
 
 393 
 
 .88929 
 
 214 
 
 .13762 
 
 189 
 
 .88383 
 
 21,9 
 
 .1314 
 
 2,8 
 
 394 
 
 .89143 
 
 214 
 
 .13951 
 
 189 
 
 .88405 
 
 21,8 
 
 .1312 
 
 2,8 
 
 1.395 
 
 1.89357 
 
 214 
 
 2.141-40 
 
 189 
 
 0.88427 
 
 21,8 
 
 1.1309 
 
 2,8 
 
 396 
 
 .89571 
 
 214 
 
 . 14330 
 
 190 
 
 .88448 
 
 21,8 
 
 .1306 
 
 2,8 
 
 397 
 
 .89786 
 
 215 
 
 . 14520 
 
 190 
 
 .88470 
 
 21,7 
 
 .1303 
 
 2,8 
 
 .398 
 
 .90000 
 
 215 
 
 .14709 
 
 190 
 
 .88492 
 
 21,7 
 
 .1300 
 
 2,8 
 
 399 
 
 .90215 
 
 215 
 
 .14900 
 
 190 
 
 .88513 
 
 21,7 
 
 .1298 
 
 2,8 
 
 1.400 
 
 1.00430 
 
 215 
 
 2.15090 
 
 190 
 
 0.88535 
 
 21,6 
 
 i. 1295 
 
 2,8 
 
 u 
 
 tan gd u 
 
 F O ' 
 
 sec gd u 
 
 -FO' 
 
 sin gd u 
 
 F ' 
 
 csc gd u 
 
 F O ' 
 
 SMITHSONIAN TABLES 
 
 133 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinh u 
 
 F ' 
 
 cosh u 
 
 Fo' 
 
 tanh u 
 
 Fo' 
 
 coth u 
 
 Fo' 
 
 1.400 
 
 1.90430 
 
 215 
 
 2.15000 
 
 190 
 
 0.88535 
 
 21,6 
 
 1.1295 
 
 2,8 
 
 .401 
 
 .90645 
 
 215 
 
 .15280 
 
 191 
 
 88557 
 
 21,6 
 
 .1292 
 
 2,8 
 
 .402 
 
 .90861 
 
 215 
 
 I547I 
 
 191 
 
 .88578 
 
 21,5 
 
 .1289 
 
 2,7 
 
 .403 
 
 .91076 
 
 216 
 
 .15662 
 
 191 
 
 .88600 
 
 21,5 
 
 .1287 
 
 2,7 
 
 .404 
 
 .91292 
 
 216 
 
 .15853 
 
 191 
 
 .88621 
 
 21,5 
 
 .1284 
 
 2,7 
 
 1.405 
 
 1.91508 
 
 216 
 
 2.16045 
 
 192 
 
 0.88643 
 
 21,4 
 
 1.1281 
 
 2,7 
 
 .406 
 
 .91724 
 
 216 
 
 . 16236 
 
 192 
 
 .88664 
 
 21,4 
 
 .1279 
 
 2,7 
 
 .407 
 
 .91940 
 
 216 
 
 .16428 
 
 192 
 
 .88686 
 
 21,3 
 
 .1276 
 
 2,7 
 
 .408 
 
 -92I57 
 
 217 
 
 .16620 
 
 192 
 
 .88707 
 
 21,3 
 
 .1273 
 
 2,7 
 
 .409 
 
 .92374 
 
 217 
 
 .16812 
 
 192 
 
 .88728 
 
 21,3 
 
 .1270 
 
 2,7 
 
 1.410 
 
 I.9259I 
 
 217 
 
 2.17005 
 
 193 
 
 0.88749 
 
 21,2 
 
 1.1268 
 
 2,7 
 
 .411 
 
 .92808 
 
 217 
 
 .17198 
 
 193 
 
 .88771 
 
 21,2 
 
 .1265 
 
 2,7 
 
 .412 
 
 .93025 
 
 217 
 
 .17391 
 
 193 
 
 .88792 
 
 21,2 
 
 .1262 
 
 2,7 
 
 .413 
 
 .93242 
 
 218 
 
 .17584 
 
 193 
 
 .88813 
 
 21,1 
 
 .1260 
 
 2,7 
 
 .414 
 
 .93460 
 
 218 
 
 . 17777 
 
 193 
 
 .88834 
 
 21,1 
 
 1257 
 
 2,7 
 
 1.415 
 
 1.93678 
 
 218 
 
 2.17971 
 
 194 
 
 0.88855 
 
 21,0 
 
 i . 1254 
 
 2,7 
 
 .416 
 
 .93896 
 
 218 
 
 . 18164 
 
 194 
 
 .88876 
 
 21,0 
 
 .1252 
 
 2,7 
 
 .417 
 
 .94114 
 
 218 
 
 . 18358 
 
 194 
 
 .88897 
 
 21,0 
 
 .1249 
 
 2,7 
 
 .418 
 
 .94333 
 
 219 
 
 .18553 
 
 194 
 
 .88918 
 
 20,9 
 
 .1246 
 
 2,6 
 
 .419 
 
 .94551 
 
 219 
 
 18747 
 
 195 
 
 .88939 
 
 20,9 
 
 .1244 
 
 2,6 
 
 1.420 
 
 1.94770 
 
 219 
 
 2.18942 
 
 195 
 
 0.88960 
 
 20,9 
 
 1.1241 
 
 2,6 
 
 .421 
 
 .94989 
 
 219 
 
 .19137 
 
 195 
 
 .88081 
 
 20,8 
 
 .1238 
 
 2,6 
 
 .422 
 
 .95209 
 
 219 
 
 . 19332 
 
 195 
 
 .89002 
 
 20,8 
 
 .1236 
 
 2,6 
 
 423 
 
 .95428 
 
 22O 
 
 .19527 
 
 195 
 
 .89022 
 
 20,8 
 
 1233 
 
 2,6 
 
 .424 
 
 .95648 
 
 22O 
 
 .19723 
 
 196 
 
 .89043 
 
 20,7 
 
 .1231 
 
 2,6 
 
 1.425 
 
 1.95867 
 
 22O 
 
 2.19918 
 
 196 
 
 0.89064 
 
 20,7 
 
 i . 1228 
 
 2,6 
 
 .426 
 
 .96087 
 
 22O 
 
 .20114 
 
 196 
 
 .89084 
 
 20,6 
 
 .1225 
 
 2,6 
 
 .427 
 
 .96308 
 
 220 
 
 .20310 
 
 196 
 
 .89105 
 
 20,6 
 
 .1223 
 
 2,6 
 
 .428 
 
 .96528 
 
 221 
 
 .20507 
 
 197 
 
 .89126 
 
 20,6 
 
 .1220 
 
 2,6 
 
 .429 
 
 .96749 
 
 221 
 
 .20704 
 
 197 
 
 .89146 
 
 20,5 
 
 .1218 
 
 2,6 
 
 1.430 
 
 1.96970 
 
 221 
 
 2.20900 
 
 197 
 
 0.89167 
 
 20,5 
 
 1.1215 
 
 2,6 
 
 .431 
 
 .97191 
 
 221 
 
 .21097 
 
 197 
 
 .89187 
 
 20,5 
 
 .1212 
 
 2,6 
 
 .432 
 
 .97412 
 
 221 
 
 .21295 
 
 197 
 
 .89208 
 
 20,4 
 
 .1210 
 
 2,6 
 
 433 
 
 .97633 
 
 221 
 
 .21492 
 
 198 
 
 .89228 
 
 20,4 
 
 .I2O7 
 
 2,6 
 
 434 
 
 .97855 
 
 222 
 
 .21690 
 
 198 
 
 .89248 
 
 20,3 
 
 .1205 
 
 2,6 
 
 1-435 
 
 1.98076 
 
 222 
 
 2.21888 
 
 198 
 
 0.89269 
 
 20,3 
 
 I.I2O2 
 
 2,5 
 
 .436 
 
 .08298 
 
 , 222 
 
 .22086 
 
 198 
 
 .89289 
 
 20,3 
 
 .I2OO 
 
 2,5 
 
 437 
 
 .98521 
 
 222 
 
 .22285 
 
 199 
 
 .89309 
 
 20,2 
 
 .1197 
 
 2,5 
 
 .438 
 
 .98743 
 
 222 
 
 .22483 
 
 199 
 
 .89329 
 
 20,2 
 
 1195 
 
 2,5 
 
 439 
 
 .98966 
 
 223 
 
 .22682 
 
 199 
 
 .89350 
 
 20,2 
 
 .1192 
 
 2,5 
 
 1.440 
 
 1.99188 
 
 223 
 
 2.22881 
 
 199 
 
 0.89370 
 
 2O, I 
 
 I.II89 
 
 2,5 
 
 .441 
 
 .99411 
 
 223 
 
 .23080 
 
 199 
 
 .89390 
 
 2O, I 
 
 .1187 
 
 2,5 
 
 .442 
 
 .99635 
 
 223 
 
 .23280 
 
 200 
 
 .89410 
 
 2O, I 
 
 .1184 
 
 2,5 
 
 443 
 
 .99858 
 
 223 
 
 .23480 
 
 200 
 
 .89430 
 
 2O,O 
 
 .1182 
 
 2,5 
 
 444 
 
 2.00082 
 
 224 
 
 .23680 
 
 200 
 
 .89450 
 
 20,O 
 
 .1179 
 
 2,5 
 
 1-445 
 
 2.00305 
 
 224 
 
 2.23880 
 
 200 
 
 0.89470 
 
 2O,O 
 
 1.1177 
 
 2,5 
 
 .446 
 
 .00529 
 
 224 
 
 .24080 
 
 201 
 
 .89490 
 
 19,9 
 
 .1174 
 
 2,5 
 
 447 
 
 .00753 
 
 224 
 
 .24281 
 
 2OI 
 
 .89510 
 
 19,9 
 
 .1172 
 
 2,5 
 
 .448 
 
 .00978 
 
 224 
 
 .24482 
 
 201 
 
 .89530 
 
 19,8 
 
 .1109 
 
 2,5 
 
 449 
 
 .01202 
 
 225 
 
 .24683 
 
 2OI 
 
 .89550 
 
 19,8 
 
 .1167 
 
 2,5 
 
 1.450 
 
 2.01427 
 
 225 
 
 2.24884 
 
 201 
 
 0.89569 
 
 19,8 
 
 I.II65 
 
 2,5 
 
 u 
 
 tan gd u 
 
 F ' 
 
 sec gd u 
 
 F.' 
 
 tin gd u 
 
 IV 
 
 csc gd u 
 
 Fo' 
 
 SMITHSONIAN TABLCD 
 
 134 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinhu 
 
 F ' 
 
 cosh u 
 
 Fo' 
 
 tanh u 
 
 F ' 
 
 coth u 
 
 Fo' 
 
 1.450 
 
 2.01427 
 
 225 
 
 2.24884 
 
 201 
 
 0.89569 
 
 19,8 
 
 I . I 165 
 
 2,5 
 
 .451 
 
 .01652 
 
 225 
 
 .25086 
 
 202 
 
 .89589 
 
 19,7 
 
 .1162 
 
 2,5 
 
 .452 
 
 .01877 
 
 225 
 
 .25288 
 
 202 
 
 .89609 
 
 19,7 
 
 .nob 
 
 2,5 
 
 453 
 
 .02103 
 
 225 
 
 .25490 
 
 202 
 
 .89628 
 
 19,7 
 
 .1157 
 
 2,4 
 
 454 
 
 .02328 
 
 226 
 
 .25692 
 
 202 
 
 .89648 
 
 19,6 
 
 .1155 
 
 2,4 
 
 1. 455 
 
 2.02554 
 
 226 
 
 2.25894 
 
 203 
 
 0.89668 
 
 19,6 
 
 1.1152 
 
 2,4 
 
 .456 
 
 .02780 
 
 226 
 
 .26097 
 
 203 
 
 .89687 
 
 19,6 
 
 .1150 
 
 2,4 
 
 457 
 
 .03006 
 
 226 
 
 .26300 
 
 203 
 
 .89707 
 
 19,5 
 
 .1147 
 
 2,4 
 
 .458 
 
 .03233 
 
 227 
 
 .26503 
 
 203 
 
 .89726 
 
 19,5 
 
 1145 
 
 2,4 
 
 459 
 
 03459 
 
 227 
 
 .26706 
 
 203 
 
 .89746 
 
 19,5 
 
 1143 
 
 2,4 
 
 1.460 
 
 2.03686 
 
 227 
 
 2.26910 
 
 2O4 
 
 0.89765 
 
 19,4 
 
 i . i 140 
 
 2,4 
 
 .461 
 
 .03913 
 
 227 
 
 .27114 
 
 2O4 
 
 .89785 
 
 19,4 
 
 .1138 
 
 2,4 
 
 .462 
 
 .04140 
 
 227 
 
 .27318 
 
 2O4 
 
 .89804 
 
 19,4 
 
 .1135 
 
 2,4 
 
 .463 
 
 .04368 
 
 228 
 
 .27522 
 
 204 
 
 .89823 
 
 19,3 
 
 .ii33 
 
 2,4 
 
 .464 
 
 .04595 
 
 228 
 
 .27726 
 
 205 
 
 .89843 
 
 19,3 
 
 .1131 
 
 2,4 
 
 1.465 
 
 2.04823 
 
 228 
 
 2.27931 
 
 205 
 
 0.89862 
 
 19,2 
 
 i . i 128 
 
 2,4 
 
 .466 
 
 .05051 
 
 228 
 
 .28136 
 
 205 
 
 .89881 
 
 19,2 
 
 .1126 
 
 2,4 
 
 .467 
 
 .05280 
 
 228 
 
 .28341 
 
 205 
 
 .89900 
 
 19,2 
 
 .1123 
 
 2,4 
 
 .468 
 
 .05508 
 
 229 
 
 .28547 
 
 206 
 
 .89920 
 
 19,1 
 
 .1121 
 
 2,4 
 
 .469 
 
 .05737 
 
 229 
 
 .28752 
 
 206 
 
 .89939 
 
 19,1 
 
 .1119 
 
 2,4 
 
 1.470 
 
 2.05965 
 
 229 
 
 2.28958 
 
 206 
 
 0.89958 
 
 19,1 
 
 I.III6 
 
 2,4 
 
 .471 
 
 .06195 
 
 229 
 
 .29164 
 
 206 
 
 .89977 
 
 19,0 
 
 .1114 
 
 2,4 
 
 .472 
 
 .06424 
 
 229 
 
 .29370 
 
 206 
 
 .89996 
 
 19,0 
 
 .1112 
 
 2,3 
 
 .473 
 
 .06653 
 
 230 
 
 .29577 
 
 207 
 
 .90015 
 
 19,0 
 
 .IIO9 
 
 2,3 
 
 .474 
 
 .06883 
 
 230 
 
 .29784 
 
 207 
 
 .90034 
 
 18,9 
 
 .1107 
 
 2,3 
 
 1.475 
 
 2.07113 
 
 23O 
 
 2.29991 
 
 207 
 
 0.90053 
 
 18,9 
 
 1. 1105 
 
 2,3 
 
 .476 
 
 .07343 
 
 230 
 
 .30198 
 
 207 
 
 .90072 
 
 18,9 
 
 .IIO2 
 
 2,3 
 
 .477 
 
 .07573 
 
 230 
 
 .30405 
 
 208 
 
 .90090 
 
 18,8 
 
 .IIOO 
 
 2,3 
 
 .478 
 
 .07804 
 
 231 
 
 .30613 
 
 208 
 
 .90109 
 
 18,8 
 
 .1008 
 
 2,3 
 
 479 
 
 .08034 
 
 231 
 
 .30821 
 
 208 
 
 .90128 
 
 18,8* 
 
 .1095 
 
 2,3 
 
 1.480 
 
 2.08265 
 
 231 
 
 2.31029 
 
 208 
 
 0.00147 
 
 18,7 
 
 I. 1093 
 
 2,3 
 
 .481 
 
 08497 
 
 231 
 
 .31238 
 
 208 
 
 .90166 
 
 18,7 
 
 .1091 
 
 2,3 
 
 .482 
 
 .08728 
 
 231 
 
 .31446 
 
 209 
 
 .90184 
 
 18,7 
 
 .1088 
 
 2,3 
 
 .483 
 
 .08959 
 
 232 
 
 .31655 
 
 209 
 
 .90203 
 
 18,6 
 
 .1086 
 
 2,3 
 
 .484 
 
 .09191 
 
 232 
 
 , .31864 
 
 209 
 
 .90221 
 
 18,6 
 
 .1084 
 
 2,3 
 
 1.485 
 
 2.09423 
 
 232 
 
 2.32073 
 
 209 
 
 0.90240 
 
 18,6 
 
 1.1082 
 
 2,3 
 
 .486 
 
 .09655 
 
 232 
 
 .32283 
 
 210 
 
 .90259 
 
 18,5 
 
 .1079 
 
 2,3 
 
 .487 
 
 .09888 
 
 232 
 
 .32493 
 
 2IO 
 
 .90277 
 
 18,5 
 
 .1077 
 
 2,3 
 
 .488 
 
 . IOI2O 
 
 233 
 
 .32703 
 
 2IO 
 
 .90296 
 
 18,5 
 
 .1075 
 
 2,3 
 
 .489 
 
 .10353 
 
 233 
 
 .32913 
 
 210 
 
 .90314 
 
 18,4 
 
 .1072 
 
 2,3 
 
 1.490 
 
 2.10586 
 
 233 
 
 2.33123 
 
 211 
 
 0.90332 
 
 18,4 
 
 i . 1070 
 
 2,3 
 
 .491 
 
 .10819 
 
 233 
 
 33334 
 
 211 
 
 .90351 
 
 18,4 
 
 .1068 
 
 2,2 
 
 .492 
 
 .11053 
 
 234 
 
 .33545 
 
 211 
 
 .90369 
 
 18,3 
 
 .1066 
 
 2,2 
 
 493 
 
 .11286 
 
 234 
 
 .33756 
 
 211 
 
 .90388 
 
 18,3 
 
 .1063 
 
 2,2 
 
 494 
 
 .11520 
 
 234 
 
 .33968 
 
 212 
 
 .00406 
 
 18,3 
 
 .1061 
 
 2,2 
 
 1.495 
 
 2.11754 
 
 234 
 
 2.34179 
 
 212 
 
 0.90424 
 
 18,2 
 
 i . 1059 
 
 2,2 
 
 .496 
 
 .11089 
 
 234 
 
 34391 
 
 212 
 
 .00442 
 
 18,2 
 
 .1057 
 
 2,2 
 
 497 
 
 . 12223 
 
 235 
 
 .34603 
 
 212 
 
 .90460 
 
 18,2 
 
 .1055 
 
 2,2 
 
 .498 
 
 . 12458 
 
 235 
 
 .34816 
 
 212 
 
 .90479 
 
 18,1 
 
 .1052 
 
 2,2 
 
 .499 
 
 .12693 
 
 235 
 
 .35028 
 
 213 
 
 90497 
 
 18,1 
 
 .1050 
 
 2,2 
 
 1.500 
 
 2.12928 
 
 235 
 
 2.35241 
 
 213 
 
 0.90515 
 
 18,1 
 
 i . 1048 
 
 2,2 
 
 u 
 
 tan gd u 
 
 wF ' 
 
 sec gd u 
 
 F ' 
 
 sin gd u 
 
 O.FO' 
 
 esc gd u 
 
 F O ' 
 
 SMITHSONIAN TABLES 
 
 135 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinhu 
 
 F/ 
 
 cosh u 
 
 F O ' 
 
 tanhu 
 
 F ' 
 
 coth u 
 
 F ' 
 
 1.500 
 
 2.12928 
 
 235 
 
 2.35241 
 
 213 
 
 0.90515 
 
 18,1 
 
 I . 1048 
 
 2,2 
 
 .501 
 
 .13163 
 
 235 
 
 .35454 
 
 213 
 
 .90533 
 
 18,0 
 
 .1046 
 
 2,2 
 
 .502 
 
 13399 
 
 2 3 6 
 
 .35667 
 
 213 
 
 00551 
 
 18,0 
 
 .1044 
 
 2,2 
 
 .503 
 
 . 13635 
 
 2 3 6 
 
 .35881 
 
 214 
 
 .90569 
 
 18,0 
 
 .1041 
 
 2,2 
 
 .504 
 
 .13871 
 
 2 3 6 
 
 .36095 
 
 214 
 
 .90587 
 
 17,9 
 
 .1039 
 
 2,2 
 
 1.505 
 
 2.14107 
 
 2 3 6 
 
 2.36309 
 
 214 
 
 0.90605 
 
 17,9 
 
 1. 1037 
 
 2,2 
 
 .506 
 
 14343 
 
 237 
 
 .36523 
 
 214 
 
 .90623 
 
 17,9 
 
 .1035 
 
 2,2 
 
 .507 
 
 .14580 
 
 237 
 
 .36737 
 
 215 
 
 .90641 
 
 17,8 
 
 .1033 
 
 2,2 
 
 .508 
 
 .14817 
 
 237 
 
 .36952 
 
 215 
 
 .90658 
 
 17,8 
 
 .1030 
 
 2,2 
 
 .509 
 
 .15054 
 
 237 
 
 .37167 
 
 215 
 
 .90676 
 
 17,8 
 
 .1028 
 
 2,2 
 
 1.510 
 
 2.15291 
 
 237 
 
 2.37382 
 
 215 
 
 0.90694 
 
 17,7 
 
 I . 1026 
 
 2,2 
 
 .511 
 
 15529 
 
 238 
 
 37597 
 
 216 
 
 .90712 
 
 17,7 
 
 .1024 
 
 2,2 
 
 .512 
 
 .15766 
 
 238 
 
 .37813 
 
 216 
 
 .90729 
 
 17,7 
 
 .1022 
 
 2,1 
 
 .513 
 
 .16004 
 
 238 
 
 .38029 
 
 216 
 
 .90747 
 
 17,6 
 
 .1020 
 
 2,1 
 
 .514 
 
 . 16242 
 
 238 
 
 .38245 
 
 216 
 
 .90765 
 
 17,6 
 
 .1018 
 
 2,1 
 
 1.515 
 
 2.16481 
 
 238 
 
 2.38461 
 
 216 
 
 0.90782 
 
 17,6 
 
 I.IOI5 
 
 2,1 
 
 .516 
 
 .16719 
 
 239 
 
 .38678 
 
 217 
 
 .90800 
 
 17,6 
 
 .1013 
 
 2,1 
 
 .517 
 
 .16958 
 
 239 
 
 .38895 
 
 217 
 
 .90817 
 
 17,5 
 
 .IOII 
 
 2,1 
 
 .518 
 
 .17197 
 
 239 
 
 -39II2 
 
 217 
 
 .90835 
 
 17,5 
 
 .1009 
 
 2,1 
 
 .519 
 
 . 17436 
 
 239 
 
 .39329 
 
 217 
 
 .90852 
 
 17,5 
 
 .1007 
 
 2,1 
 
 1.520 
 
 2.17676 
 
 240 
 
 2-39547 
 
 218 
 
 0.90870 
 
 17,4 
 
 I. 1005 
 
 2,1 
 
 .521 
 
 .17915 
 
 240 
 
 .39765 
 
 218 
 
 .90887 
 
 17,4 
 
 .1003 
 
 2,1 
 
 .522 
 
 .18155 
 
 240 
 
 .39983 
 
 218 
 
 .90905 
 
 17,4 
 
 .1001 
 
 2,1 
 
 .523 
 
 . 18395 
 
 240 
 
 .40201 
 
 218 
 
 .90922 
 
 17,3 
 
 .0998 
 
 2,1 
 
 .524 
 
 .18636 
 
 240 
 
 .40419 
 
 219 
 
 .90939 
 
 17,3 
 
 .0996 
 
 2,1 
 
 1.525 
 
 2.18876 
 
 241 
 
 2.40638 
 
 219 
 
 0.90957 
 
 17,3 
 
 1.0094 
 
 2,1 
 
 .526 
 
 .19117 
 
 241 
 
 .40857 
 
 219 
 
 90974 
 
 17,2 
 
 .0992 
 
 2,1 
 
 .527 
 
 .19358 
 
 241 
 
 .41076 
 
 219 
 
 .90991 
 
 17,2 
 
 .0000 
 
 2,1 
 
 .528 
 
 .19599 
 
 241 
 
 .41296 
 
 220 
 
 .91008 
 
 17,2 
 
 .0988 
 
 2,1 
 
 .529 
 
 .19840 
 
 . 242 
 
 .41516 
 
 220 
 
 .91025 
 
 I7,i 
 
 .0986 
 
 2,1 
 
 1.530 
 
 2.20082 
 
 242 
 
 2.41736 
 
 220 
 
 0.91042 
 
 I7,i 
 
 1.0984 
 
 2,1 
 
 .531 
 
 .20324 
 
 242 
 
 .41956 
 
 220 
 
 .91060 
 
 I7,i 
 
 .0082 
 
 2,1 
 
 .532 
 
 .20566 
 
 242 
 
 .42176 
 
 221 
 
 .91077 
 
 I7,i 
 
 .0080 
 
 2,1 
 
 533 
 
 .20808 
 
 242 
 
 42397 
 
 221 
 
 .91094 
 
 I7,o 
 
 .0978 
 
 2,1 
 
 534 
 
 .21051 
 
 243 
 
 .42618 
 
 221 
 
 .91111 
 
 I7,o 
 
 .0976 
 
 2,0 
 
 1.535 
 
 2.21293 
 
 243 
 
 2.42839 
 
 221 
 
 0.91128 
 
 I7,o 
 
 1.0974 
 
 2,0 
 
 .536 
 
 .21536 
 
 243 
 
 .43060 
 
 222 
 
 9II45 
 
 16,9 
 
 .0972 
 
 2,O 
 
 .537 
 
 .21780 
 
 243 
 
 .43282 
 
 222 
 
 .91161 
 
 16,9 
 
 .0970 
 
 2,0 
 
 .538 
 
 .22023 
 
 244 
 
 .43504 
 
 222 
 
 .9H78 
 
 16,9 
 
 .0968 
 
 2,0 
 
 539 
 
 .22267 
 
 244 
 
 .43726 
 
 222 
 
 .91195 
 
 16,8 
 
 .0965 
 
 2,0 
 
 1.540 
 
 2.22510 
 
 244 
 
 2.43949 
 
 223 
 
 O.9I2I2 
 
 16,8 
 
 1.0063 
 
 2,O 
 
 541 
 
 .22755 
 
 244 
 
 .44171 
 
 223 
 
 .91229 
 
 16,8 
 
 .0961 
 
 2,O 
 
 542 
 
 .22099 
 
 244 
 
 44394 
 
 223 
 
 .91246 
 
 16,7 
 
 .0959 
 
 2,0 
 
 .543 
 544 
 
 1 23488 
 
 245 
 245 
 
 .44617 
 .44841 
 
 223 
 223 
 
 .91262 
 .91279 
 
 16,7 
 16,7 
 
 0957 
 .0955 
 
 2,O 
 2,0 
 
 1-545 
 
 2.23733 
 
 245 
 
 2.45064 
 
 224 
 
 0.91296 
 
 16,7 
 
 1.0953 
 
 2,0 
 
 .546 
 
 .23978 
 
 245 
 
 .45288 
 
 224 
 
 .91312 
 
 16,6 
 
 .0951 
 
 2,0 
 
 547 
 
 .24224 
 
 246 
 
 45512 
 
 224 
 
 .91329 
 
 16,6 
 
 0949 
 
 2,0 
 
 .548 
 
 .24469 
 
 246 
 
 .45736 
 
 224 
 
 .91345 
 
 16,6 
 
 0947 
 
 2,0 
 
 549 
 
 .24715 
 
 246 
 
 .45961 
 
 225 
 
 .91362 
 
 16,5 
 
 .0945 
 
 2,0 
 
 1.550 
 
 2.24961 
 
 246 
 
 2.46186 
 
 225 
 
 0.91379 
 
 16,5 
 
 1.0943 
 
 2,0 
 
 u 
 
 tan gd u 
 
 F</ 
 
 sec gd u 
 
 F ' 
 
 sin gd u 
 
 F ' 
 
 esc gd u 
 
 F O ' 
 
 SMITHSONIAN TABLES 
 
 136 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinh u 
 
 F ' 
 
 cosh u 
 
 F ' 
 
 tanh u 
 
 F O ' 
 
 cothu 
 
 F ' 
 
 1.550 
 
 2.24961 
 
 2 4 6 
 
 2.46186 
 
 225 
 
 0.91379 
 
 16,5 
 
 1.0943 
 
 2,0 
 
 .551 
 
 .25207 
 
 246 
 
 .46411 
 
 225 
 
 .91395 
 
 16,5 
 
 .0942 
 
 2,0 
 
 .552 
 
 .25454 
 
 247 
 
 .46636 
 
 225 
 
 .91411 
 
 16,4 
 
 .0940 
 
 2,0 
 
 .553 
 
 .25701 
 
 247 
 
 .46862 
 
 226 
 
 .91428 
 
 16,4 
 
 .0938 
 
 2,0 
 
 554 
 
 .25948 
 
 247 
 
 .47088 
 
 226 
 
 91444 
 
 16,4 
 
 .0936 
 
 2,0 
 
 1-555 
 
 2.26195 
 
 247 
 
 2.47314 
 
 226 
 
 0.91461 
 
 16,3 
 
 1.0934 
 
 2,0 
 
 .556 
 
 .26442 
 
 248 
 
 .47540 
 
 226 
 
 .91477 
 
 16,3 
 
 .0932 
 
 2,0 
 
 557 
 
 .26690 
 
 248 
 
 .47767 
 
 227 
 
 .9U93 
 
 16,3 
 
 .0930 
 
 1,9 
 
 .558 
 
 .26938 
 
 248 
 
 .47993 
 
 227 
 
 .91510 
 
 16,3 
 
 .0928 
 
 1,9 
 
 .559 
 
 .27186 
 
 248 
 
 .48221 
 
 227 
 
 .91526 
 
 16,2 
 
 .0926 
 
 1,9 
 
 1.560 
 
 2.27434 
 
 248 
 
 2.48448 
 
 227 
 
 0.91542 
 
 16,2 
 
 1.0924 
 
 1,9 
 
 .561 
 
 .27683 
 
 249 
 
 .48675 
 
 228 
 
 .91558 
 
 16,2 
 
 .0922 
 
 1,9 
 
 .562 
 
 .27932 
 
 249 
 
 .48903 
 
 228 
 
 .91574 
 
 16,1 
 
 .0920 
 
 1,9 
 
 .563 
 
 .28181 
 
 249 
 
 .49131 
 
 228 
 
 .91591 
 
 16,1 
 
 .0918 
 
 i,9 
 
 .564 
 
 .28430 
 
 249 
 
 .49360 
 
 228 
 
 .91607 
 
 16,1 
 
 .0916 
 
 1,9 
 
 1.565 
 
 2.28679 
 
 250 
 
 12.49588 
 
 229 
 
 0.91623 
 
 16,1 
 
 I.09I4 
 
 1,9 
 
 .566 
 
 .28929 
 
 250 
 
 .49817 
 
 229 
 
 .91639 
 
 16,0 
 
 .0912 
 
 1,9 
 
 .567 
 
 .29179 
 
 250 
 
 .50046 
 
 229 
 
 .91655 
 
 16,0 
 
 .0911 
 
 1,9 
 
 .568 
 
 .29429 
 
 250 
 
 .50275 
 
 220 
 
 .91671 
 
 16,0 
 
 .0909 
 
 1,9 
 
 .569 
 
 .29680 
 
 251 
 
 .50505 
 
 230 
 
 .91687 
 
 15,9 
 
 .0907 
 
 1,9 
 
 1.570 
 
 2.29930 
 
 251 
 
 2.50735 
 
 230 
 
 0.91703 
 
 15,9 
 
 1.0905 
 
 1,9 
 
 571 
 
 .30181 
 
 251 
 
 .50965 
 
 230 
 
 .91718 
 
 15,9 
 
 .0903 
 
 1,9 
 
 572 
 
 .30432 
 
 251 
 
 .5H95 
 
 230 
 
 .91734 
 
 15,8 
 
 .0901 
 
 1,9 
 
 573 
 
 .30683 
 
 251 
 
 .51426 
 
 231 
 
 .91750 
 
 15,8 
 
 .0899 
 
 1,9 
 
 574 
 
 30935 
 
 252 
 
 .51656 
 
 231 
 
 .91766 
 
 15,8 
 
 .0897 
 
 1,9 
 
 1.575 
 
 2.31187 
 
 252 
 
 2.51887 
 
 231 
 
 0.91782 
 
 15,8 
 
 1.0895 
 
 1,9 
 
 .576 
 
 .31439 
 
 252 
 
 .52119 
 
 231 
 
 .91797 
 
 15,7 
 
 .0894 
 
 1,9 
 
 577 
 
 .31691 
 
 252 
 
 .52350 
 
 232 
 
 .91813 
 
 15,7 
 
 .0892 
 
 1,9 
 
 .578 
 
 31943 
 
 253 
 
 .52582 
 
 232 
 
 .91829 
 
 15,7 
 
 .0890 
 
 1,9 
 
 .579 
 
 .32196 
 
 253 
 
 .52814 
 
 232 
 
 .91845 
 
 15,6 
 
 .0888 
 
 1,9 
 
 1.580 
 
 2.32449 
 
 253 
 
 2.53047 
 
 232 
 
 0.91860 
 
 15,6 
 
 1.0886 
 
 1,9 
 
 .581 
 
 .32702 
 
 253 
 
 .53279 
 
 233 
 
 .91876 
 
 15,6 
 
 .0884 
 
 1,8 
 
 .582 
 
 .32956 
 
 254 
 
 .53512 
 
 233 
 
 .91891 
 
 15,6 
 
 .0882 
 
 1,8 
 
 .583 
 
 .33209 
 
 254 
 
 .53745 
 
 233 
 
 .91907 
 
 15,5 
 
 .0881 
 
 1,8 
 
 .584 
 
 .33463 
 
 254 
 
 53978 
 
 233 
 
 .91922 
 
 15,5 
 
 .0879 
 
 1,8 
 
 1.585 
 
 2.33717 
 
 254 
 
 2.54212 
 
 234 
 
 0.91938 
 
 15,5 
 
 1.0877 
 
 1,8 
 
 .586 
 
 .33972 
 
 254 
 
 .54446 
 
 234 
 
 .91953 
 
 15,4 
 
 0875 
 
 1,8 
 
 .587 
 
 .34226 
 
 255 
 
 .54680 
 
 234 
 
 .91969 
 
 15,4 
 
 0873 
 
 1,8 
 
 .588 
 
 .34481 
 
 255 
 
 .54914 
 
 234 
 
 91984 
 
 15,4 
 
 .0871 
 
 1,8 
 
 .589 
 
 .34736 
 
 255 
 
 .55149 
 
 235 
 
 .92000 
 
 15,4 
 
 .0870 
 
 1,8 
 
 1.500 
 
 2.34991 
 
 255 
 
 2.55384 
 
 235 
 
 0.92015 
 
 15,3 
 
 1.0868 
 
 1,8 
 
 591 
 
 .35247 
 
 256 
 
 55619 
 
 235 
 
 .92030 
 
 15,3 
 
 .0866 
 
 1,8 
 
 .592 
 
 35502 
 
 256 
 
 .55854 
 
 236 
 
 .92046 
 
 15,3 
 
 .0864 
 
 1,8 
 
 593 
 
 .35758 
 
 256 
 
 .56090 
 
 236 
 
 .92061 
 
 15,2 
 
 .0862 
 
 1,8 
 
 594 
 
 .36015 
 
 256 
 
 .56326 
 
 236 
 
 .92076 
 
 15,2 
 
 .0861 
 
 1,8 
 
 1.595 
 
 2.36271 
 
 257 
 
 2.56562 
 
 236 
 
 0.92091 
 
 15,2 
 
 1.0859 
 
 1,8 
 
 .596 
 
 .36528 
 
 257 
 
 .56798 
 
 237 
 
 .92106 
 
 15,2 
 
 .0857 
 
 1,8 
 
 597 
 
 .36785 
 
 257 
 
 .57035 
 
 237 
 
 .92122 
 
 15,1 
 
 .0855 
 
 1,8 
 
 .598 
 
 .37042 
 
 257 
 
 .57272 
 
 237 
 
 .92137 
 
 I5,i 
 
 0853 
 
 1,8 
 
 .599 
 
 37299 
 
 258 
 
 .57509 
 
 237 
 
 .92152 
 
 I5,i 
 
 .0852 
 
 1,8 
 
 1. 600 
 
 2.37557 
 
 258 
 
 2.57746 
 
 238 
 
 0.92167 
 
 I5,i 
 
 1.0850 
 
 1,8 
 
 u 
 
 tan gd u 
 
 F O ' 
 
 sec gd u 
 
 F O ' 
 
 sin gd u 
 
 wF ' 
 
 esc gd u 
 
 > Fo' 
 
 SMITHSONIAN TABLES 
 
 137 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinh u 
 
 O.FO' 
 
 cosh u 
 
 Fo' 
 
 tanhu 
 
 O.FO' 
 
 coth u 
 
 O.FO' 
 
 1. 600 
 
 2.37557 
 
 258 
 
 2.57746 
 
 2 3 8 
 
 0.92167 
 
 15,1 
 
 1.0850 
 
 1,8 
 
 .601 
 
 .3/815 
 
 258 
 
 .57984 
 
 238 
 
 .92182 
 
 15,0 
 
 .0848 
 
 1,8 
 
 .602 
 
 .38073 
 
 258 
 
 .58222 
 
 238 
 
 .92197 
 
 15,0 
 
 .0846 
 
 i3 
 
 .603 
 
 .38331 
 
 258 
 
 .58460 
 
 2 3 8 
 
 .92212 
 
 15,0 
 
 .0845 
 
 1,8 
 
 .604 
 
 .38590 
 
 259 
 
 .58699 
 
 239 
 
 .92227 
 
 14,9 
 
 .0843 
 
 1,8 
 
 1.605 
 
 2.38849 
 
 259 
 
 2.58937 
 
 239 
 
 0.92242 
 
 14,9 
 
 1.0841 
 
 1,8 
 
 .606 
 
 .39108 
 
 259 
 
 .59176 
 
 239 
 
 .92257 
 
 14,9 
 
 .0839 
 
 1,7 
 
 .607 
 
 .39367 
 
 259 
 
 .59416 
 
 239 
 
 .92272 
 
 14,9 
 
 .0838 
 
 ,7 
 
 .608 
 
 .39626 
 
 260 
 
 .59655 
 
 240 
 
 .92286 
 
 14,8 
 
 .0836 
 
 ,7 
 
 .609 
 
 ' .39886 
 
 260 
 
 .59895 
 
 240 
 
 .92301 
 
 14,8 
 
 .0834 
 
 ,7 
 
 1.610 
 
 2.40146 
 
 260 
 
 2.60135 
 
 240 
 
 0.92316 
 
 14,8 
 
 1.0832 
 
 ,7 
 
 .611 
 
 .40406 
 
 260 
 
 .60375 
 
 240 
 
 .92331 
 
 14,8 
 
 .0831 
 
 ,7 
 
 .612 
 
 .40667 
 
 261 
 
 .60616 
 
 241 
 
 .92346 
 
 H,7 
 
 .0829 
 
 ,7 
 
 .613 
 
 .40928 
 
 261 
 
 .60857 
 
 241 
 
 .92360 
 
 14,7 
 
 .0827 
 
 ,7 
 
 .614 
 
 .41189 
 
 261 
 
 .61098 
 
 241 
 
 .92375 
 
 14,7 
 
 .0825 
 
 ,7 
 
 1.615 
 
 2.41450 
 
 261 
 
 2.61339 
 
 241 
 
 0.92390 
 
 14,6 
 
 1.0824 
 
 1,7 
 
 .616 
 
 .41711 
 
 262 
 
 .61581 
 
 242 
 
 .92404 
 
 14,6 
 
 .0822 
 
 1,7 
 
 .617 
 
 .41973 
 
 262 
 
 .61822 
 
 242 
 
 .92419 
 
 14,6 
 
 .0820 
 
 1,7 
 
 .618 
 
 .42235 
 
 262 
 
 .62064 
 
 242 
 
 .92433 
 
 14,6 
 
 .0819 
 
 1,7 
 
 .619 
 
 .42497 
 
 262 
 
 .62307 
 
 242 
 
 .92448 
 
 14,5 
 
 .0817 
 
 1,7 
 
 1.620 
 
 2.42760 
 
 263 
 
 2.62549 
 
 243 
 
 0.92462 
 
 14,5 
 
 1.0815 
 
 1,7 
 
 .621 
 
 .43022 
 
 263 
 
 .62792 
 
 243 
 
 .92477 
 
 14,5 
 
 .0814 
 
 1,7 
 
 .622 
 
 .43285 
 
 263 
 
 .63035 
 
 243 
 
 .92491 
 
 14,5 
 
 .0812 
 
 1,7 
 
 .623 
 
 .43548 
 
 263 
 
 .63279 
 
 244 
 
 .92506 
 
 14,4 
 
 .0810 
 
 1,7 
 
 .624 
 
 .43812 
 
 264 
 
 .63522 
 
 244 
 
 .92520 
 
 14,4 
 
 .0808 
 
 1,7 
 
 1.625 
 
 2.44075 
 
 264 
 
 2.63767 
 
 244 
 
 0.92535 
 
 14,4 
 
 1.0807 
 
 1,7 
 
 .626 
 
 44339 
 
 264 
 
 .64011 
 
 244 
 
 .92549 
 
 14,3 
 
 .0805 
 
 1,7 
 
 .627 
 
 .44603 
 
 264 
 
 .64255 
 
 245 
 
 .92563 
 
 14,3 
 
 .0803 
 
 1,7 
 
 .628 
 
 .44868 
 
 264 
 
 .64500 
 
 245 
 
 .92578 
 
 14,3 
 
 .0802 
 
 1,7 
 
 .629 
 
 .45132 
 
 265 
 
 .64745 
 
 245 
 
 .92592 
 
 14,3 
 
 .0800 
 
 1,7 
 
 1.630 
 
 2.45397 
 
 265 
 
 2.64900 
 
 245 
 
 0.92606 
 
 14,2 
 
 1.0708 
 
 1,7 
 
 .631 
 
 .45662 
 
 265 
 
 .65236 
 
 246 
 
 .92620 
 
 14,2 
 
 .0797 
 
 1,7 
 
 .632 
 
 .45928 
 
 265 
 
 .65482 
 
 246 
 
 92635 
 
 14,2 
 
 .0795 
 
 1,7 
 
 .633 
 
 .46193 
 
 266 
 
 ' .65728 
 
 246 
 
 .92649 
 
 14,2 
 
 .0793 
 
 1,6 
 
 .634 
 
 .46459 
 
 266 
 
 .65974 
 
 246 
 
 .92663 
 
 I4,i 
 
 .0792 
 
 1,6 
 
 1.635 
 
 2.46725 
 
 266 
 
 2.66221 
 
 247 
 
 0.92677 
 
 I4,i 
 
 1.0790 
 
 1,6 
 
 .636 
 
 .46992 
 
 266 
 
 .66467 
 
 247 
 
 .92691 
 
 14,1 
 
 .0789 
 
 1,6 
 
 .637 
 
 .47258 
 
 267 
 
 .66715 
 
 247 
 
 .92705 
 
 14,1 
 
 .0787 
 
 1,6 
 
 .638 
 
 .47525 
 
 267 
 
 .66962 
 
 248 
 
 .92/19 
 
 14,0 
 
 .0785 
 
 1,6 
 
 639 
 
 47792 
 
 267 
 
 .67210 
 
 248 
 
 .92733 
 
 14,0 
 
 .0784 
 
 1,6 
 
 1.640 
 
 2.48059 
 
 267 
 
 2.67457 
 
 248 
 
 0.92747 
 
 14,0 
 
 1.0782 
 
 1,6 
 
 .641 
 
 .48327 
 
 268 
 
 .67706 
 
 248 
 
 .92761 
 
 14,0 
 
 .0780 
 
 1,6 
 
 .642 
 
 .48595 
 
 268 
 
 .67954 
 
 249 
 
 .92775 
 
 13,9 
 
 0779 
 
 1,6 
 
 .643 
 
 .48863 
 
 268 
 
 .68203 
 
 249 
 
 .92789 
 
 12,9 
 
 .0777 
 
 1,6 
 
 .644 
 
 .49131 
 
 268 
 
 .68452 
 
 249 
 
 .92803 
 
 13,9 
 
 .0776 
 
 1,6 
 
 1.645 
 
 2.40400 
 
 269 
 
 2.68701 
 
 249 
 
 0.92817 
 
 13,9 
 
 1.0774 
 
 1,6 
 
 .646 
 
 .40669 
 
 269 
 
 .68951 
 
 250 
 
 .92831 
 
 13,8 
 
 0772 
 
 1,6 
 
 .647 
 
 .49938 
 
 269 
 
 .69200 
 
 250 
 
 .92844 
 
 13,8 
 
 .0771 
 
 1,6 
 
 .648 
 
 .50207 
 
 269 
 
 .6945] 
 
 250 
 
 .92858 
 
 13,8 
 
 .0769 
 
 1,6 
 
 .649 
 
 .50477 
 
 270 
 
 .69701 
 
 250 
 
 .92872 
 
 13,7 
 
 .0768 
 
 1,6 
 
 1.650 
 
 2.50746 
 
 270 
 
 2.69951 
 
 251 
 
 0.92886 
 
 13,7 
 
 1.0766 
 
 1,6 
 
 u 
 
 tan gd u 
 
 Fo' 
 
 sec gd u 
 
 -FO' 
 
 sin gd u 
 
 Fo' 
 
 esc gd u 
 
 -FO' 
 
 SMITHSONIAN TABLE* 
 
 J38 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinhu 
 
 w Fo' 
 
 cosh u 
 
 -Fo' 
 
 tanh u 
 
 Fo' 
 
 coth u 
 
 F ' 
 
 1.650 
 
 2.50746 
 
 270 
 
 2.69951 
 
 251 
 
 0.92886 
 
 13,7 
 
 1.0766 
 
 1,6 
 
 .651 
 
 .51017 
 
 270 
 
 .70202 
 
 251 
 
 .92899 
 
 13,7 
 
 .0764 
 
 1,6 
 
 .652 
 
 .51287 
 
 270 
 
 .70454 
 
 251 
 
 .92913 
 
 13,7 
 
 .0763 
 
 1,6 
 
 .653 
 
 .51557 
 
 271 
 
 .70705 
 
 252 
 
 .92927 
 
 13,6 
 
 .0761 
 
 1,6 
 
 .654 
 
 .51828 
 
 271 
 
 .70957 
 
 252 
 
 .92940 
 
 13,6 
 
 .0760 
 
 1,6 
 
 1.655 
 
 2.52099 
 
 271 
 
 2.71209 
 
 252 
 
 0.92954 
 
 13,6 
 
 1.0758 
 
 1,6 
 
 .656 
 
 .52371 
 
 271 
 
 .71461 
 
 252 
 
 .92968 
 
 13,6 
 
 .0756 
 
 1,6 
 
 .657 
 
 .52642 
 
 272 
 
 .71713 
 
 253 
 
 .92981 
 
 13,5 
 
 0755 
 
 1,6 
 
 .658 
 
 .52914 
 
 272 
 
 .71966 
 
 253 
 
 .92995 
 
 13,5 
 
 .0753 
 
 1,6 
 
 .659 
 
 .53186 
 
 272 
 
 .72219 
 
 253 
 
 .93008 
 
 13,5 
 
 .0752 
 
 1,6 
 
 1.660 
 
 2.53459 
 
 272 
 
 2.72472 
 
 253 
 
 O.93O22 
 
 13,5 
 
 1.0750 
 
 1,6 
 
 .661 
 
 53731 
 
 273 
 
 .72726 
 
 254 
 
 93035 
 
 13,4 
 
 0749 
 
 1,6 
 
 .662 
 
 .54004 
 
 273 
 
 .72980 
 
 254 
 
 .93049 
 
 13,4 
 
 0747 
 
 i,5 
 
 .663 
 
 .54277 
 
 273 
 
 .73234 
 
 254 
 
 .93062 
 
 13,4 
 
 .0746 
 
 i,5 
 
 .664 
 
 54551 
 
 273 
 
 .73489 
 
 255 
 
 93075 
 
 13,4 
 
 0744 
 
 1,5 
 
 1.665 
 
 2.54824 
 
 274 
 
 2.73743 
 
 255 
 
 0.93089 
 
 13,3 
 
 1.0742 
 
 1,5 
 
 .666 
 
 .55098 
 
 274 
 
 .73998 
 
 255 
 
 .93102 
 
 13,3 
 
 .0741 
 
 i,5 
 
 .667 
 
 .55372 
 
 274 
 
 .74253 
 
 255 
 
 .93115 
 
 13,3 
 
 0739 
 
 1,5 
 
 .668 
 
 .55647 
 
 275 
 
 .74509 
 
 256 
 
 .93129 
 
 13,3 
 
 .0738 
 
 i,5 
 
 .669 
 
 55921 
 
 275 
 
 .74765 
 
 256 
 
 .93142 
 
 13,2 
 
 .0736 
 
 i,5 
 
 1.670 
 
 2.56196 
 
 275 . 
 
 2.75021 
 
 256 
 
 0.93155 
 
 13,2 
 
 1.0735 
 
 1,5 
 
 .671 
 
 .56471 
 
 275 .75277 
 
 256 
 
 .93168 
 
 13,2 
 
 0733 
 
 i,5 
 
 .672 
 
 .56747 
 
 276 .75534 
 
 257 
 
 .93182 
 
 13,2 
 
 .0732 
 
 i,5 
 
 .673 
 
 .57022 
 
 276 
 
 .75791 
 
 257 
 
 .93195 
 
 13,1 
 
 .0730 
 
 i,5 
 
 .674 
 
 .57298 
 
 276 
 
 .76048 
 
 257 
 
 .93208 
 
 13,1 
 
 .0729 
 
 1,5 
 
 1.675 
 
 2.57574 
 
 276 
 
 2.76305 
 
 258 
 
 0.93221 
 
 I3J 
 
 1.0727 
 
 1,5 
 
 .676 
 
 .57851 
 
 277 
 
 .76563 
 
 258 
 
 .93234 
 
 13,1 
 
 .0726 
 
 i,5 
 
 .677 
 
 .58127 
 
 277 
 
 .76821 
 
 258 
 
 .93247 
 
 I3,o 
 
 .0724 
 
 1,5 
 
 .678 
 
 .58404 
 
 277 
 
 .77079 
 
 258 
 
 .93260 
 
 I3,o 
 
 .0723 
 
 i,5 
 
 .679 
 
 .58682 
 
 277 
 
 .77338 
 
 259 
 
 .93273 
 
 I3,o 
 
 .0721 
 
 i,5 
 
 i. 680 
 
 2.58959 
 
 278 
 
 2.77596 
 
 259 
 
 0.93286 
 
 I3,o 
 
 1.0720 
 
 1,5 
 
 .681 
 
 .59237 
 
 278 
 
 .77856 
 
 259 
 
 .93299 
 
 I3,o 
 
 .0718 
 
 1,5 
 
 .682 
 
 .59515 
 
 278 
 
 .78115 
 
 260 
 
 -933I2 
 
 12,9 
 
 .0717 
 
 1,5 
 
 .683 
 
 59793 
 
 278 
 
 .78375 
 
 260 
 
 .93325 
 
 12,9 
 
 .0715 
 
 1,5 
 
 .684 
 
 .60072 
 
 279 
 
 .78635 
 
 260 
 
 .93338 
 
 12,9 
 
 .0714 
 
 1,5 
 
 1.685 
 
 2.60350 
 
 279 
 
 2.78895 
 
 260 
 
 0-93351 
 
 12,9 
 
 1.0712 
 
 1,5 
 
 .686 
 
 .60629 
 
 279 
 
 .79155 
 
 261 
 
 .93364 
 
 12,8 
 
 .0711 
 
 1,5 
 
 .687 
 
 .60909 
 
 279 
 
 .79416 
 
 25 1 
 
 .93376 
 
 12,8 
 
 .0709 
 
 1,5 
 
 .688 
 
 .61188 
 
 280 
 
 .79677 
 
 261 
 
 .93389 
 
 12,8 
 
 .0708 
 
 i,5 
 
 .689 
 
 .61468 
 
 280 
 
 .79938 
 
 261 
 
 93402 
 
 12,8 
 
 .0706 
 
 1,5 
 
 i. 600 
 
 2.61748 
 
 280 
 
 2.80200 
 
 262 
 
 0.934IS 
 
 12,7 
 
 1.0705 
 
 1,5 
 
 .691 
 
 .62028 
 
 280 
 
 .80462 
 
 262 
 
 93427 
 
 12,7 
 
 .0703 
 
 1,5 
 
 .692 
 
 .62309 
 
 281 
 
 .80724 
 
 262 
 
 93440 
 
 12,7 
 
 .0702 
 
 1,5 
 
 .693 
 
 .62590 
 
 281 
 
 .80087 
 
 263 
 
 93453 
 
 12,7 
 
 .0701 
 
 1,5 
 
 .694 
 
 .62871 
 
 281 
 
 .81249 
 
 263 
 
 .93465 
 
 12,6 
 
 .0699 
 
 1,4 
 
 1.695 
 
 2.63152 
 
 282 
 
 2.81512 
 
 263 
 
 0.93478 
 
 12,6 
 
 1.0698 
 
 1,4 
 
 .696 
 
 .63434 
 
 282 
 
 .81776 
 
 263 
 
 .93491 
 
 12,6 
 
 .0696 
 
 1,4 
 
 .697 
 
 .63716 
 
 282 
 
 .82039 
 
 264 
 
 93503 
 
 12,6 
 
 .0695 
 
 1,4 
 
 .698 
 
 .63998 
 
 282 
 
 .82303 
 
 264 
 
 .93516 
 
 12,5 
 
 .0693 
 
 i,4 
 
 699 
 
 .64280 
 
 283 
 
 .82567 
 
 264 
 
 .93528 
 
 12,5 
 
 .0692 
 
 1,4 
 
 1.700 
 
 2.64563 
 
 283 
 
 2.82832 
 
 265 
 
 0.93S4I 
 
 12,5 
 
 1.0691 
 
 1,4 
 
 u 
 
 tan gd u 
 
 *> FO' sec Qd u 
 
 wF ' 
 
 sin gd u 
 
 coFo' 
 
 esc gd u 
 
 *>FO' 
 
 SMITHSONIAN TABLES 
 
 139 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinh u 
 
 F ' 
 
 cosh u 
 
 F ' 
 
 tanh u 
 
 -FO* 
 
 coth u 
 
 -FO' 
 
 1.700 
 
 2.64563 
 
 283 
 
 2.82832 
 
 265 
 
 0.93541 
 
 12,5 
 
 1.0691 
 
 1,4 
 
 .701 
 
 .64846 
 
 28 3 
 
 .83096 
 
 265- 
 
 93553 
 
 12,5 
 
 .0689 
 
 1,4 
 
 .702 
 
 .65129 
 
 28 3 
 
 .83361 
 
 265 
 
 .93566 
 
 12,5 
 
 .0688 
 
 1,4 
 
 .703 
 
 .65413 
 
 284 
 
 .83627 
 
 265 
 
 935/8 
 
 12,4 
 
 .0686 
 
 1,4 
 
 .704 
 
 65697 
 
 384 
 
 .83892 
 
 266 
 
 93591 
 
 12,4 
 
 .0685 
 
 1,4 
 
 1.705 
 
 2.65981 
 
 284 
 
 2.84158 
 
 266 
 
 0.93603 
 
 12,4 
 
 1.0683 
 
 1,4 
 
 .706 
 
 .66265 
 
 284 
 
 .84424 
 
 266 
 
 .93615 
 
 12,4 
 
 .0682 
 
 1,4 
 
 .707 
 
 .66550 
 
 285 
 
 .84690 
 
 267 
 
 .93628 
 
 12,3 
 
 .O68l 
 
 1,4 
 
 .708 
 
 .66834 
 
 285 
 
 .84957 
 
 267 
 
 .93640 
 
 12,3 
 
 .0679 
 
 1,4 
 
 .709 
 
 .67119 
 
 285 
 
 .85224 
 
 267 
 
 .93652 
 
 12,3 
 
 .0678 
 
 1,4 
 
 r.7io 
 
 2.67405 
 
 285 
 
 2.85491 
 
 267 
 
 0.93665 
 
 12,3 
 
 1.0676 
 
 1,4 
 
 .711 
 
 .67690 
 
 286 
 
 .85759 
 
 268 
 
 .93677 
 
 12,2 
 
 .0675 
 
 1,4 
 
 .712 
 
 .67976 
 
 286 
 
 .86027 
 
 268 
 
 .93689 
 
 12,2 
 
 .0674 
 
 1,4 
 
 .713 
 
 .68262 
 
 286 
 
 .86295 
 
 268 
 
 .93701 
 
 12,2 
 
 .0672 
 
 1,4 
 
 .714 
 
 .68549 
 
 287 
 
 * 
 
 .86563 
 
 269 
 
 .93714 
 
 12,2 
 
 .0671 
 
 1,4 
 
 1.715 
 
 2.68836 
 
 287 
 
 2.86832 
 
 269 
 
 0.93726 
 
 12,2 
 
 1.0669 
 
 1,4 
 
 .716 
 
 .69123 
 
 287 
 
 .87101 
 
 269 
 
 .93738 
 
 12,1 
 
 .0668 
 
 1,4 
 
 .717 
 
 .69410 
 
 287 
 
 .87370 
 
 269 
 
 93750 
 
 12,1 
 
 .0667 
 
 1,4 
 
 .718 
 
 .69697 
 
 288 
 
 .87640 
 
 270 
 
 .93762 
 
 12,1 
 
 .0665 
 
 1,4 
 
 .719 
 
 .69985 
 
 288 
 
 .87910 
 
 270 
 
 .93774 
 
 12,1 
 
 .0664 
 
 1,4 
 
 1.720 
 
 2.70273 
 
 288 
 
 2.88180 
 
 270 
 
 0.93786 
 
 12,0 
 
 1.0663 
 
 1,4 
 
 .721 
 
 .70561 
 
 288 
 
 .88450 
 
 271 
 
 .93798 
 
 12,0 
 
 .0661 
 
 1,4 
 
 .722 
 
 .70850 
 
 289 
 
 .88721 
 
 271 
 
 .93810 
 
 12,0 
 
 .0660 
 
 1,4 
 
 .723 
 
 .7H39 
 
 289 
 
 .88992 
 
 271 
 
 .93822 
 
 1 2,O 
 
 .0658 
 
 1,4 
 
 .724 
 
 .71428 
 
 289 
 
 .89263 
 
 271 
 
 .93834 
 
 12,0 
 
 .0657 
 
 1,4 
 
 1.725 
 
 2.7I7I7 
 
 290 
 
 2.89535 
 
 272 
 
 0.93846 
 
 11,9 
 
 1.0656 
 
 1,4 
 
 .726 
 
 .72007 
 
 290 
 
 .89807 
 
 272 
 
 .93858 
 
 11,9 
 
 .0654 
 
 1,4 
 
 .727 
 
 .72297 
 
 290 
 
 .90079 
 
 272 
 
 .93870 
 
 11,9 
 
 .0653 
 
 1,3 
 
 .728 
 
 .72587 
 
 290 
 
 .90351 
 
 273 
 
 .93882 
 
 11,9 
 
 .0652 
 
 1,3 
 
 .729 
 
 .72878 
 
 291 
 
 .90624 
 
 273 
 
 .93894 
 
 11,8 
 
 .0650 
 
 1,3 
 
 1.730 
 
 2.73168 
 
 291 
 
 2.90897 
 
 273 
 
 0.93906 
 
 11,8 
 
 1.0649 
 
 1,3 
 
 .731 
 
 .73460 
 
 291 
 
 .91170 
 
 273 
 
 .93917 
 
 11,8 
 
 .0648 
 
 1,3 
 
 732 
 
 73751 
 
 291 
 
 .91444 
 
 274 
 
 .93929 
 
 11,8 
 
 .0646 
 
 1,3 
 
 733 
 
 .74042 
 
 292 
 
 .91718 
 
 274 
 
 .93941 
 
 11,8 
 
 .0645 
 
 1,3 
 
 734 
 
 74334 
 
 292 
 
 .91992 
 
 274 
 
 93953 
 
 n,7 
 
 .0644 
 
 1,3 
 
 1-735 
 
 2.74626 
 
 292 
 
 2.92266 
 
 275 
 
 0.93964 
 
 n,7 
 
 1.0642 
 
 1,3 
 
 .736 
 
 .74919 
 
 293 
 
 .92541 
 
 275 
 
 .93976 
 
 n,7 
 
 .0641 
 
 1,3 
 
 737 
 
 .75211 
 
 293 
 
 .92816 
 
 275 
 
 .93988 
 
 n,7 
 
 .0640 
 
 1,3 
 
 .738 
 
 75504 
 
 293 
 
 .93092 
 
 276 
 
 93999 
 
 11,6 
 
 .0638 
 
 ,3 
 
 739 
 
 .75708 
 
 293 
 
 .93367 
 
 276 
 
 .94011 
 
 n,6 
 
 .0637 
 
 ,3 
 
 1.740 
 
 2.7^091 
 
 294 
 
 2.93643 
 
 276 
 
 0.94023 
 
 11,6 
 
 1.0636 
 
 ,3 
 
 .741 
 
 .76385 
 
 294 
 
 .93919 
 
 276 
 
 .94034 
 
 11,6 
 
 0634 
 
 ,3 
 
 742 
 
 .76679 
 
 294 
 
 .94196 
 
 277 
 
 .94046 
 
 11,6 
 
 .0633 
 
 ,3 
 
 .743 
 
 76973 
 
 294 
 
 94473 
 
 277 
 
 94057 
 
 n,5 
 
 .0632 
 
 ,3 
 
 744 
 
 .77268 
 
 295 
 
 94750 
 
 277 
 
 .94069 
 
 ii,5 
 
 .0631 
 
 ,3 
 
 1.745 
 
 2.77563 
 
 295 
 
 2.95027 
 
 278 
 
 0.94080 
 
 n,5 
 
 1.0629 
 
 ,3 
 
 .746 
 
 
 295 
 
 .95305 
 
 278 
 
 .94092 
 
 n,5 
 
 .0628 
 
 ,3 
 
 747 
 
 '78153 
 
 296 
 
 .95583 
 
 278 
 
 .94103 
 
 11,4 
 
 .0627 
 
 ,3 
 
 .748 
 
 .78449 
 
 396 
 
 .95861 
 
 278 
 
 .94H5 
 
 TI.4 
 
 .0625 
 
 ,3 
 
 749 
 
 .78745 
 
 296 
 
 .96140 
 
 279 
 
 .94126 
 
 11,4 
 
 .0624 
 
 ,3 
 
 1-750 
 
 2.79041 
 
 296 
 
 2.96419 
 
 279 
 
 0.94138 
 
 11,4 
 
 1.0623 
 
 1,3 
 
 u 
 
 tan od u 
 
 F ' 
 
 tec gd u 
 
 -FO' 
 
 tin od u 
 
 r; 
 
 csc od u 
 
 F,/ 
 
 SMITHSONIAN TABLES 
 
 I 4 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinhu 
 
 F ' 
 
 cosh u 
 
 F ' 
 
 tanhu 
 
 F ' 
 
 cothu 
 
 F ' 
 
 1.750 
 
 2.79041 
 
 296 
 
 2.96419 
 
 279 
 
 0.94138 
 
 11,4 
 
 1.0623 
 
 1,3 
 
 .751 
 
 .79338 
 
 297 
 
 .96698 
 
 279 
 
 .94149 
 
 11,4 
 
 .0621 
 
 1.3 
 
 .752 
 
 .79635 
 
 297 
 
 .96978 
 
 280 
 
 .94160 
 
 ii,3 
 
 .0620 
 
 1,3 
 
 753 
 
 .79932 
 
 297 
 
 .97257 
 
 280 
 
 .94172 
 
 n,3 
 
 .0619 
 
 1,3 
 
 754 
 
 .80229 
 
 298 
 
 97537 
 
 280 
 
 .94183 
 
 ii,3 
 
 .0618 
 
 1,3 
 
 1.755 
 
 '2.80527 
 
 298 
 
 2.97818 
 
 281 
 
 0.94194 
 
 n,3 
 
 I. 0616 
 
 1,3 
 
 .756 
 
 .80825 
 
 298 
 
 .98098 
 
 281 
 
 .94205 
 
 ii,3 
 
 .0615 
 
 1,3 
 
 757 
 
 .81123 
 
 298 
 
 .98379 
 
 281 
 
 .94217 
 
 11,2 
 
 .0614 
 
 1,3 
 
 758 
 
 .81422 
 
 299 
 
 .98661 
 
 281 
 
 .94228 
 
 11,2 
 
 .0613 
 
 1,3 
 
 .759 
 
 .81721 
 
 299 
 
 .98942 
 
 282 
 
 94239 
 
 11,2 
 
 .0611 
 
 1,3 
 
 1.760 
 
 2.82020 
 
 299 
 
 2.99224 
 
 282 
 
 0.94250 
 
 11,2 
 
 I. 0610 
 
 1,3 
 
 .761 
 
 .82319 
 
 300 
 
 .99506 
 
 282 
 
 .94261 
 
 1 1,1 
 
 .0669 
 
 1,3 
 
 .762 
 
 .82619 
 
 300 
 
 .99789 
 
 283 
 
 .94273 
 
 11,1 
 
 .0608 
 
 1,3 
 
 .763 
 
 .82919 
 
 300 
 
 3.00072 
 
 283 
 
 .94284 
 
 11,1 
 
 .0606 
 
 1,2 
 
 .764 
 
 .83219 
 
 300 
 
 .00355 
 
 283 
 
 .94295 
 
 11,1 
 
 .0605 
 
 1,2 
 
 1.765 
 .766 
 
 2.83519 
 .83820 
 
 301 
 301 
 
 3.00638 
 .00922 
 
 284 
 284 
 
 0.94306 
 
 .94317 
 
 11,1 
 
 II,O 
 
 1.0604 
 .0603 
 
 1,2 
 1,2 
 
 .767 
 
 .84121 
 
 301 
 
 .01206 
 
 284 
 
 .94328 
 
 11,0 
 
 .0601 
 
 1,2 
 
 .768 
 
 .84422 
 
 301 
 
 .01490 
 
 284 
 
 94339 
 
 11,0 
 
 .0600 
 
 1,2 
 
 .769 
 
 .84724 
 
 302 
 
 .01774 
 
 285 
 
 94350 
 
 11,0 
 
 .0599 
 
 1,2 
 
 1.770 
 
 2.85026 
 
 302 
 
 3.02059 
 
 285 
 
 0.94361 
 
 11,0 
 
 1.0598 
 
 1,2 
 
 771 
 
 .85328 
 
 302 
 
 .02344 
 
 285 
 
 .94372 
 
 10,9 
 
 .0596 
 
 1,2 
 
 772 
 
 .85631 
 
 303 
 
 .02630 
 
 286 
 
 .94383 
 
 10,9 
 
 .0595 
 
 1,2 
 
 773 
 
 .85933 
 
 303 
 
 .02916 
 
 286 
 
 .94394 
 
 10,9 
 
 .0594 
 
 1,2 
 
 774 
 
 .86237 
 
 303 
 
 .03202 
 
 286 
 
 .94405 
 
 10,9 
 
 .0593 
 
 1,2 
 
 1.775 
 
 2.86540 
 
 303 
 
 3.03488 
 
 287 
 
 0.04416 
 
 10,9 
 
 1.0591 
 
 1,2 
 
 .776 
 
 .86844 
 
 304 
 
 .03775 
 
 287 
 
 .94426 
 
 10,8 
 
 .0590 
 
 1,2 
 
 777 
 
 .87147 
 
 304 
 
 .04062 
 
 287 
 
 94437 
 
 10,8 
 
 .0589 
 
 1,2 
 
 .778 
 
 .87452 
 
 304 
 
 .04349 
 
 287 
 
 .94448 
 
 10,8 
 
 .0588 
 
 1,2 
 
 .779 
 
 .87756 
 
 305 
 
 .04637 
 
 288 
 
 .94459 
 
 10,8 
 
 .0587 
 
 1,2 
 
 1.780 
 
 2.88o6l 
 
 305 
 
 3.04925 
 
 288 
 
 0.04470 
 
 10,8 
 
 1.0585 
 
 1,2 
 
 .781 
 
 .88366 
 
 305 
 
 .05213 
 
 288 
 
 .94480 
 
 10,7 
 
 .0584 
 
 1,2 
 
 .782 
 
 .88671 
 
 306 
 
 .05501 
 
 289 
 
 .94491 
 
 10,7 
 
 .0583 
 
 1,2 
 
 .783 
 
 .88977 
 
 306 
 
 .05790 
 
 289 
 
 .94502 
 
 10,7 
 
 .0582 
 
 1,2 
 
 .784 
 
 .89283 
 
 306 
 
 .06079 
 
 289 
 
 .94513 
 
 10,7 
 
 .0581 
 
 1,2 
 
 1.785 
 
 2.89589 
 
 306 
 
 3-06369 
 
 290 
 
 0.94523 
 
 10,7 
 
 1.0579 
 
 1,2 
 
 .786 
 
 .89896 
 
 307 
 
 .06659 
 
 290 
 
 94534 
 
 10,6 
 
 .0578 
 
 1,2 
 
 .787 
 
 .90202 
 
 307 
 
 .06949 
 
 290 
 
 .94544 
 
 10,6 
 
 .0577 
 
 1,2 
 
 .788 
 
 .90510 
 
 307 
 
 .07239 
 
 291 
 
 .94555 
 
 10,6 
 
 .0576 
 
 1,2 
 
 .789 
 
 .90817 
 
 308 
 
 .07530 
 
 291 
 
 .94565 
 
 10,6 
 
 0575 
 
 1,2 
 
 1.790 
 
 2.91125 
 
 308 
 
 3.07821 
 
 291 
 
 0.94576 
 
 10,6 
 
 1.0574 
 
 1,2 
 
 791 
 
 .91433 
 
 308 
 
 .08112 
 
 291 
 
 .94587 
 
 10,5 
 
 .0572 
 
 1,2 
 
 .792 
 
 .91741 
 
 308 
 
 .08403 
 
 292 
 
 94597 
 
 io,5 
 
 .0571 
 
 1,2 
 
 793 
 
 .92049 
 
 309 
 
 .08695 
 
 292 
 
 .94608 
 
 io,5 
 
 .0570 
 
 1,2 
 
 .794 
 
 .92358 
 
 309 
 
 .08988 
 
 292 
 
 .94618 
 
 io,5 
 
 .0569 
 
 1,2 
 
 1.795 
 
 2.92667 
 
 309 
 
 3.09280 
 
 293 
 
 0.94629 
 
 10,5 
 
 1.0568 
 
 1,2 
 
 .796 
 
 .92977 
 
 310 
 
 .09573 
 
 293 
 
 .94639 
 
 10,4 
 
 .0566 
 
 1,2 
 
 797 
 
 .93287 
 
 310 
 
 .09866 
 
 293 
 
 .94649 
 
 10,4 
 
 .0565 
 
 1,2 
 
 .798 
 
 93597 
 
 3io 
 
 .10160 
 
 294 
 
 .94660 
 
 10,4 
 
 .0564 
 
 1,2 
 
 799 
 
 .93907 
 
 3io 
 
 .10453 
 
 294 
 
 .94670 
 
 10,4 
 
 .0563 
 
 1,2 
 
 1.800 
 
 2.94217 
 
 3ii 
 
 3.10747 
 
 294 
 
 0.94681 
 
 10,4 
 
 1.0562 
 
 1,2 
 
 u 
 
 tan gd u 
 
 F O ' 
 
 sec gd u 
 
 F ' 
 
 sin gd u 
 
 <oF ' 
 
 esc gd u 
 
 F O ' 
 
 SMITHSONIAN TABLES 
 
 141 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinh u 
 
 F ' 
 
 cosh u 
 
 F ' 
 
 tanh u 
 
 Fr 
 
 coth u 
 
 F0' 
 
 1.800 
 
 2.94217 
 
 311 
 
 3-10747 
 
 294 
 
 0.94681 
 
 10,4 
 
 I.O5O2 
 
 1,2 
 
 .801 
 
 .94528 
 
 311 
 
 .11042 
 
 295 
 
 .94691 
 
 10,3 
 
 .0561 
 
 1,2 
 
 .802 
 
 .94840 
 
 311 
 
 .11336 
 
 295 
 
 .94701 
 
 10,3 
 
 .0560 
 
 1,2 
 
 .803 
 
 .95151 
 
 312 
 
 .11631 
 
 295 
 
 .94712 
 
 10,3 
 
 .0558 
 
 1*1 
 
 .804 
 
 .95463 
 
 312 
 
 .11927 
 
 295 
 
 .94722 
 
 10,3 
 
 .0557 
 
 1,1 
 
 1.805 
 
 2.95775 
 
 312 
 
 3.12222 
 
 296 
 
 0.94732 
 
 10,3 
 
 1.0556 
 
 1,1 
 
 .806 
 
 .96087 
 
 313 
 
 .12518 
 
 296 
 
 .94742 
 
 10,2 
 
 .0555 
 
 1,1 
 
 .807 
 
 .96400 
 
 313 
 
 . 12814 
 
 296 
 
 .94753 
 
 10,2 
 
 .0554 
 
 1,1 
 
 .808 
 
 .96713 
 
 313 
 
 .13111 
 
 297 
 
 .94763 
 
 10,2 
 
 .0553 
 
 1,1 
 
 .809 
 
 .97026 
 
 313 
 
 .13408 
 
 297 
 
 94773 
 
 10,2 
 
 .0552 
 
 1,1 
 
 1.810 
 
 2.97340 
 
 314 
 
 3.13705 
 
 297 
 
 0.94783 
 
 10,2 
 
 1.0550 
 
 1,1 
 
 .811 
 
 .97654 
 
 314 
 
 .14003 
 
 298 
 
 94793 
 
 10,1 
 
 .0549 
 
 1,1 
 
 .812 
 
 .97968 
 
 314 
 
 .14300 
 
 298 
 
 .94803 
 
 10,1 
 
 .0548 
 
 1,1 
 
 .813 
 
 .98282 
 
 315 
 
 .14599 
 
 298 
 
 .94814 
 
 10,1 
 
 0547 
 
 1,1 
 
 .814 
 
 .98597 
 
 315 
 
 .14897 
 
 299 
 
 .94824 
 
 10,1 
 
 .0546 
 
 1,1 
 
 1.815 
 
 2.98912 
 
 315 
 
 3.I5I96 
 
 299 
 
 0.94834 
 
 10,1 
 
 1.0545 
 
 1,1 
 
 .816 
 
 .99227 
 
 315 
 
 .15495 
 
 299 
 
 .94844 
 
 IO,O 
 
 .0544 
 
 1,1 
 
 .817 
 
 99543 
 
 316 
 
 . 15794 
 
 300 
 
 .94854 
 
 IO,O 
 
 0543 
 
 1,1 
 
 .818 
 
 99859 
 
 316 
 
 .16094 
 
 300 
 
 .94864 
 
 IO,O 
 
 .0541 
 
 1,1 
 
 .819 
 
 3.00175 
 
 316 
 
 . 16394 
 
 300 
 
 .94874 
 
 10,0 
 
 .0540 
 
 1,1 
 
 1.820 
 
 3-00492 
 
 317 
 
 3.16694 
 
 300 
 
 0.94884 
 
 10,0 
 
 1.0539 
 
 1,1 
 
 .821 
 
 .00808 
 
 317 
 
 .16995 
 
 301 
 
 .94894 
 
 IO,0 
 
 .0538 
 
 1,1 
 
 .822 
 
 .01126 
 
 317 
 
 .17296 
 
 301 
 
 .94904 
 
 9,9 
 
 .0537 
 
 1,1 
 
 .823 
 
 .01443 
 
 318 
 
 . 17597 
 
 301 
 
 .94914 
 
 9,9 
 
 .0536 
 
 1,1 
 
 .824 
 
 .01761 
 
 318 
 
 .17899 
 
 302 
 
 .94924 
 
 9,9 
 
 .0535 
 
 1,1 
 
 1.825 
 
 3.02079 
 
 318 
 
 3.18201 
 
 302 
 
 0.94933 
 
 9,9 
 
 1.0534 
 
 1,1 
 
 .826 
 
 .02397 
 
 319 
 
 . 18503 
 
 302 
 
 94943 
 
 9,9 
 
 .0533 
 
 1,1 
 
 .827 
 
 .02716 
 
 319 
 
 .18805 
 
 303 
 
 94953 
 
 9,8 
 
 .0532 
 
 1,1 
 
 .828 
 
 .03035 
 
 319 
 
 .19108 
 
 303 
 
 .94963 
 
 9,8 
 
 0530 
 
 1,1 
 
 .829 
 
 03354 
 
 319 
 
 .19411 
 
 303 
 
 .94973 
 
 9,8 
 
 .0529 
 
 1,1 
 
 1.830 
 
 3-03674 
 
 320 
 
 3.I97I5 
 
 304 
 
 0.94983 
 
 9,8 
 
 1.0528 
 
 1,1 
 
 .831 
 
 .03994 
 
 320 
 
 .20019 
 
 304 
 
 .94092 
 
 9,8 
 
 .0527 
 
 1,1 
 
 .832 
 
 .04314 
 
 320 
 
 .20323 
 
 304 
 
 .95002 
 
 9,7 
 
 .0526 
 
 1,1 
 
 .833 
 
 .04634 
 
 321 
 
 .20627 
 
 305 
 
 95012 
 
 9,7 
 
 .0525 
 
 1,1 
 
 .834 
 
 .04955 
 
 321 
 
 .20932 
 
 305 
 
 .95022 
 
 9,7 
 
 .0524 
 
 1,1 
 
 1.835 
 
 3.05276 
 
 321 
 
 3-21237 
 
 305 
 
 0.95031 
 
 9,7 
 
 1.0523 
 
 1,1 
 
 .836 
 
 .05597 
 
 322 
 
 
 306 
 
 .95041 
 
 9,7 
 
 .0522 
 
 1,1 
 
 .837 
 
 .05919 
 
 322 
 
 .21849 
 
 306 
 
 .95051 
 
 9,7 
 
 .0521 
 
 1,1 
 
 .838 
 
 .06241 
 
 322 
 
 .22155 
 
 306 
 
 .95060 
 
 9,6 
 
 .0520 
 
 1,1 
 
 .839 
 
 .06563 
 
 322 
 
 .22461 
 
 307 
 
 .95070 
 
 9,6 
 
 .0519 
 
 1,1 
 
 1.840 
 
 3.06886 
 
 323 
 
 3.22768 
 
 307 
 
 0.95080 
 
 9,6 
 
 1.0518 
 
 1,1 
 
 .841 
 
 .07209 
 
 323 
 
 .23075 
 
 307 
 
 .95089 
 
 9,6 
 
 .0516 
 
 1,1 
 
 .842 
 
 .07532 
 
 323 
 
 .23382 
 
 308 
 
 .95009 
 
 9,6 
 
 0515 
 
 1,1 
 
 .843 
 
 .07856 
 
 324 
 
 .23600 
 
 308 
 
 .95108 
 
 9,5 
 
 .0514 
 
 1,1 
 
 .844 
 
 .08180 
 
 324 
 
 .23998 
 
 308 
 
 .95n8 
 
 9,5 
 
 .0513 
 
 1,1 
 
 1.845 
 
 3.08504 
 
 324 
 
 3.24306 
 
 309 
 
 0.95127 
 
 9,5 
 
 1.0512 
 
 1,1 
 
 . .846 
 
 .08828 
 
 325 
 
 .24615 
 
 309 
 
 .95137 
 
 9,5 
 
 .0511 
 
 I,O 
 
 .847 
 
 .09153 
 
 325 
 
 .24924 
 
 309 
 
 .95146 
 
 9,5 
 
 .0510 
 
 1,0 
 
 .848 
 
 .09478 
 
 325 
 
 .25233 
 
 309 
 
 .95156 
 
 9,5 
 
 .0500 
 
 1,0 
 
 .849 
 
 .09803 
 
 326 
 
 .25543 
 
 310 
 
 .95165 
 
 9,4 
 
 .0508 
 
 I,O 
 
 1.850 
 
 3.10129 
 
 326 
 
 3.25853 
 
 310 
 
 0.95175 
 
 94 
 
 1.0507 
 
 I,O 
 
 u 
 
 tan gd u 
 
 F ' 
 
 sec gd u 
 
 F ' 
 
 sin gd u 
 
 F ' 
 
 esc gd u 
 
 FY 
 
 SMITHSONIAN TABLES 
 
 142 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinh u 
 
 O.FO' 
 
 cosh u 
 
 Fo' 
 
 tanhu 
 
 Fo* 
 
 coth u 
 
 <> FO' 
 
 1.850 
 
 3.IOI29 
 
 326 
 
 3.25853 
 
 310 
 
 0.95175 
 
 9,4 
 
 1.0507 
 
 1,0 
 
 .851 
 
 . 10455 
 
 326 
 
 .26163 
 
 310 
 
 .95184 
 
 9,4 
 
 .0506 
 
 1,0 
 
 .852 
 
 .10781 
 
 326 
 
 .26474 
 
 311 
 
 .95193 
 
 9,4 
 
 .0505 
 
 1,0 
 
 .853 
 
 .11108 
 
 327 
 
 .26785 
 
 311 
 
 .95203 
 
 9,4 
 
 .0504 
 
 1,0 
 
 .854 
 
 .11435 
 
 327 
 
 .27096 
 
 311 
 
 .95212 
 
 9,3 
 
 .0503 
 
 1,0 
 
 1.855 
 
 3.11762 
 
 327 
 
 3.27408 
 
 312 
 
 0.95221 
 
 9,3 
 
 1.0502 
 
 1,0 
 
 .856 
 
 .12090 
 
 328 
 
 .27719 
 
 312 
 
 .95231 
 
 9,3 
 
 .0501 
 
 1,0 
 
 .857 
 
 .12418 
 
 328 
 
 .28032 
 
 312 
 
 .95240 
 
 9,3 
 
 .0500 
 
 1,0 
 
 .858 
 
 . 12746 
 
 328 
 
 .28344 
 
 313 
 
 .95249 
 
 9,3 
 
 .0409 
 
 I,O 
 
 .859 
 
 . 13074 
 
 329 
 
 .28657 
 
 313 
 
 .95259 
 
 9,3 
 
 .0498 
 
 1,0 
 
 1.860 
 
 3.13403 
 
 329 
 
 3.28970 
 
 313 
 
 0.95268 
 
 9,2 
 
 1.0497 
 
 1,0 
 
 .861 
 
 13732 
 
 329 
 
 .29284 
 
 314 
 
 95277 
 
 9,2 
 
 .0496 
 
 I,O 
 
 .862 
 
 .14062 
 
 330 
 
 .29598 
 
 314 
 
 .95286 
 
 9,2 
 
 .0495 
 
 1,0 
 
 .863 
 
 . 14392 
 
 330 
 
 .29912 
 
 314 
 
 .95296 
 
 9,2 
 
 0494 
 
 1,0 
 
 .864 
 
 .14722 
 
 330 
 
 .30227 
 
 315 
 
 .95305 
 
 9,2 
 
 .0493 
 
 1,0 
 
 1.865 
 
 3.15052 
 
 331 
 
 3.30542 
 
 315 
 
 0.95314 
 
 9,2 
 
 1.0492 
 
 1,0 
 
 .866 
 
 .15383 
 
 331 
 
 .30857 
 
 315 
 
 95323 
 
 9,1 
 
 .0491 
 
 ,0 
 
 .867 
 
 .15714 
 
 331 
 
 .3H72 
 
 316 
 
 95332 
 
 9,1 
 
 .0490 
 
 ,o 
 
 .868 
 
 .16045 
 
 331 
 
 .31488 
 
 316 
 
 95341 
 
 9,1 
 
 .0489 
 
 ,o 
 
 .869 
 
 .16377 
 
 332 
 
 .31804 
 
 316 
 
 95350 
 
 9,1 
 
 .0488 
 
 1,0 
 
 1.870 
 
 3.16709 
 
 332 
 
 3.32I2I 
 
 317 
 
 0.95359 
 
 9,1 
 
 1.0487 
 
 1,0 
 
 .871 
 
 . 17041 
 
 332 
 
 .32438 
 
 317 
 
 .95368 
 
 9,0 
 
 .0486 
 
 ,0 
 
 .872 
 
 . 17374 
 
 333 
 
 .32755 
 
 317 
 
 .95378 
 
 9,o 
 
 .0485 
 
 1,0 
 
 .873 
 
 .17706 
 
 333 
 
 .33073 
 
 318 
 
 .95387 
 
 9,0 
 
 .0484 
 
 1,0 
 
 .874 
 
 .18040 
 
 333 
 
 .33390 
 
 318 
 
 .95396 
 
 9,0 
 
 .0483 
 
 1,0 
 
 1.875 
 
 3.18373 
 
 344 
 
 3.33709 
 
 318 
 
 0.95405 
 
 9,0 
 
 1.0482 
 
 1,0 
 
 .876 
 
 . 18707 
 
 334 
 
 .34027 
 
 319 
 
 .95414 
 
 9,o 
 
 .0481 
 
 1,0 
 
 .877 
 
 .19041 
 
 334 
 
 .34346 
 
 319 
 
 95422 
 
 8,9 
 
 .0480 
 
 I,O 
 
 .878 
 
 . 19376 
 
 335 
 
 .34665 
 
 319 
 
 95431 
 
 8,9 
 
 .0479 
 
 I,O 
 
 879 
 
 .19711 
 
 335 
 
 .34985 
 
 320 
 
 95440 
 
 8,9 
 
 .0478 
 
 1,0 
 
 i. 880 
 
 3.20046 
 
 335 
 
 3.35305 
 
 320 
 
 0.95449 
 
 8,9 
 
 1.0477 
 
 ,o 
 
 .881 
 
 .20381 
 
 336 
 
 .35625 
 
 320 
 
 .95458 
 
 8,9 
 
 .0476 
 
 ,o 
 
 .882 
 
 .20717 
 
 336 
 
 .35946 
 
 321 
 
 .95467 
 
 8,9 
 
 .0475 
 
 1,0 
 
 .883 
 
 .21053 
 
 336 
 
 .36266 
 
 321 
 
 .95476 
 
 8,8 
 
 .0474 
 
 ,o 
 
 .884 
 
 .21390 
 
 337 
 
 .36588 
 
 321 
 
 .95485 
 
 8,8 
 
 .0473 
 
 I,O 
 
 1.885 
 
 3.21726 
 
 337 
 
 3.36909 
 
 322 
 
 0.95493 
 
 8,8 
 
 1.0472 
 
 1,0 
 
 .886 
 
 .22063 
 
 337 
 
 .37231 
 
 322 
 
 .95502 
 
 8,8 
 
 .0471 
 
 1,0 
 
 .887 
 
 .22401 
 
 338 
 
 37553 
 
 322 
 
 955II 
 
 8,8 
 
 .0470 
 
 1,0 
 
 .888 
 
 .22738 
 
 338 
 
 .37876 
 
 323 
 
 95520 
 
 8,8 
 
 .0469 
 
 I,O 
 
 .889 
 
 .23076 
 
 338 
 
 .38199 
 
 323 
 
 .95529 
 
 8,7 
 
 .0468 
 
 1,0 
 
 1.890 
 
 3.234IS 
 
 339 
 
 3.38522 
 
 323 
 
 0.95537 
 
 8,7 
 
 1.0467 
 
 1,0 
 
 .891 
 
 .23753 
 
 339 
 
 .38846 
 
 324 
 
 .95546 
 
 8,7 
 
 .0466 
 
 1,0 
 
 .892 
 
 .24093 
 
 339 
 
 .39170 
 
 324 
 
 95555 
 
 8,7 
 
 .0465 
 
 1,0 
 
 .893 
 
 24432 
 
 339 
 
 39494 
 
 324 
 
 .95563 
 
 8,7 
 
 .0464 
 
 1,0 
 
 .894 
 
 .24772 
 
 340 
 
 .39818 
 
 325 
 
 95572 
 
 8,7 
 
 .0463 
 
 0,9 
 
 1.895 
 
 3.25112 
 
 340 
 
 3.40143 
 
 325 
 
 o.9558i 
 
 8,6 
 
 1.0462 
 
 0,9 
 
 .896 
 
 .25452 
 
 340 
 
 .40469 
 
 325 
 
 .95589 
 
 8,6 
 
 .0461 
 
 0,9 
 
 .897 
 
 .25792 
 
 341 
 
 .40794 
 
 326 
 
 .95598 
 
 8,6 
 
 .0460 
 
 0,9 
 
 .898 
 
 .26133 
 
 341 
 
 .41120 
 
 326 
 
 .95607 
 
 8,6 
 
 .0460 
 
 0,9 
 
 .899 
 
 .26475 
 
 341 
 
 .41447 
 
 326 
 
 .95615 
 
 8,6 
 
 .0459 
 
 0,9 
 
 1.900 
 
 3.26816 
 
 342 
 
 3.41773 
 
 327 
 
 0.95624 
 
 8,6 
 
 1.0458 
 
 0,9 
 
 u 
 
 tan gd u 
 
 F ' 
 
 sec gd u 
 
 F/ 
 
 sin gd u 
 
 F ' 
 
 esc gd u 
 
 FO' 
 
 SMITHSONIAN TABLES 
 
 143 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinh u 
 
 wF ' 
 
 cosh u 
 
 F O ' 
 
 tanh u 
 
 F O ' 
 
 cothu 
 
 F,' 
 
 1.900 
 
 3.26816 
 
 342 
 
 3.41773 
 
 327 
 
 0.95624 
 
 8,6 
 
 1.0458 
 
 0,9 
 
 .001 
 
 .27158 
 
 342 
 
 .42100 
 
 327 
 
 .95632 
 
 8,5 
 
 0457 
 
 0,9 
 
 .902 
 
 .27500 
 
 342 
 
 .42427 
 
 328 
 
 .95641 
 
 8,5 
 
 .0456 
 
 0,9 
 
 .903 
 
 .27843 
 
 343 
 
 .42755 
 
 328 
 
 .95649 
 
 8,5 
 
 .0455 
 
 0,9 
 
 .904 
 
 .28186 
 
 343 
 
 .43083 
 
 328 
 
 .95658 
 
 8,5 
 
 .0454 
 
 0,9 
 
 1.905 
 
 3.28529 
 
 343 
 
 3.43412 
 
 329 
 
 0.95666 
 
 8,5 
 
 1.0453 
 
 0,9 
 
 .906 
 
 .28873 
 
 344 
 
 43740 
 
 329 
 
 .95675 
 
 8,5 
 
 0452 
 
 0,9 
 
 .907 
 
 .29217 
 
 344 
 
 .44069 
 
 329 
 
 .95683 
 
 8,4 
 
 .0451 
 
 0,9 
 
 .908 
 
 .29561 
 
 344 
 
 .44399 
 
 330 
 
 .95692 
 
 8,4 
 
 .0450 
 
 o,9 
 
 .909 
 
 .29906 
 
 345 
 
 .44728 
 
 330 
 
 95700 
 
 8,4 
 
 .0449 
 
 0,9 
 
 1.910 
 
 3.30250 
 
 345 
 
 3.45058 
 
 330 
 
 0.95709 
 
 8,4 
 
 i .0448 
 
 o,9 
 
 .911 
 
 .30596 
 
 345 
 
 
 331 
 
 .95717 
 
 8,4 
 
 .0447 
 
 0,9 
 
 .912 
 
 .30941 
 
 346 
 
 .45720 
 
 331 
 
 .95725 
 
 8,4 
 
 0447 
 
 o,9 
 
 .913 
 
 .31287 
 
 346 
 
 .46051 
 
 331 
 
 .95734 
 
 8,4 
 
 .0446 
 
 0,9 
 
 .914 
 
 .31633 
 
 346 
 
 .46382 
 
 332 
 
 .95742 
 
 8,3 
 
 0445 
 
 0,9 
 
 1.915 
 
 3-31980 
 
 347 
 
 3.46714 
 
 332 
 
 0.95750 
 
 8,3 
 
 1.0444 
 
 0,9 
 
 .916 
 
 .32327 
 
 347 
 
 47046 
 
 332 
 
 95759 
 
 8,3 
 
 .0443 
 
 0,9 
 
 .917 
 
 .32674 
 
 347 
 
 47379 
 
 333 
 
 .95767 
 
 8,3 
 
 .0442 
 
 0,9 
 
 .918 
 
 .33021 
 
 348 
 
 .47712 
 
 333 
 
 95775 
 
 8,3 
 
 .0441 
 
 0,9 
 
 .919 
 
 .33369 
 
 348 
 
 48045 
 
 333 
 
 .95783 
 
 8,3 
 
 .0440 
 
 0,9 
 
 1.920 
 
 3.33718 
 
 348 
 
 3.48378 
 
 334 
 
 0.95792 
 
 8,2 
 
 '1.0439 
 
 0,9 
 
 .921 
 
 .34066 
 
 349 
 
 .48712 
 
 334 
 
 .95800 
 
 8,2 
 
 .0438 
 
 0,9 
 
 .922 
 
 34415 
 
 349 
 
 .40046 
 
 334 
 
 .95808 
 
 8,2 
 
 .0438 
 
 0,9 
 
 .923 
 
 .34764 
 
 349 
 
 .49381 
 
 335 
 
 .95816 
 
 8,2 
 
 .0437 
 
 0,9 
 
 .924 
 
 .35H4 
 
 350 
 
 .49716 
 
 335 
 
 .95825 
 
 8,2 
 
 .0436 
 
 0,9 
 
 1.925 
 
 3.35464 
 
 350 
 
 3.50051 
 
 335 
 
 0.95833 
 
 8,2 
 
 1.0435 
 
 0,9 
 
 .926 
 
 .35814 
 
 350 
 
 50387 
 
 336 
 
 .95841 
 
 8,1 
 
 .0434 
 
 0,9 
 
 .927 
 
 .36164 
 
 351 
 
 .50723 
 
 336 
 
 .95849 
 
 8,1 
 
 .0433 
 
 0,9 
 
 .928 
 
 .36515 
 
 351 
 
 .51059 
 
 337 
 
 .95857 
 
 8,1 
 
 .0432 
 
 0,9 
 
 .929 
 
 .36867 
 
 351 
 
 .51396 
 
 337 
 
 .95865 
 
 8,1 
 
 .0431 
 
 0,9 
 
 1.930 
 
 3.37218 
 
 352 
 
 3.51733 
 
 337 
 
 0.95873 
 
 8,1 
 
 1.0430 
 
 0,9 
 
 .931 
 
 .37570 
 
 352 
 
 .52070 
 
 
 .95881 
 
 8,1 
 
 .0430 
 
 0,9 
 
 .932 
 
 .37922 
 
 352 
 
 .52408 
 
 338 
 
 .95890 
 
 8,1 
 
 .0429 
 
 0,9 
 
 933 
 
 .38275 
 
 353 
 
 .52746 
 
 338 
 
 .95898 
 
 8,0 
 
 .0428 
 
 0,9 
 
 934 
 
 .38628 
 
 353 
 
 .53085 
 
 339 
 
 .95906 
 
 8,0 
 
 .0427 
 
 0,9 
 
 1-935 
 
 3.38981 
 
 353 
 
 3.53423 
 
 339 
 
 0.959U 
 
 8,0 
 
 1.0426 
 
 0,9 
 
 .936 
 
 39335 
 
 354 
 
 .53763 
 
 339 
 
 .95922 
 
 8,0 
 
 0425 
 
 0,9 
 
 937 
 
 .39689 
 
 354 
 
 .54102 
 
 .340 
 
 95930 
 
 8,0 
 
 .0424 
 
 0,9 
 
 .938 
 
 .40043 
 
 354 
 
 .54442 
 
 340 
 
 .95938 
 
 8,0 
 
 0423 
 
 0,9 
 
 939 
 
 .40397 
 
 355 
 
 .54782 
 
 340 
 
 95945 
 
 7,9 
 
 0423 
 
 0,9 
 
 1.940 
 
 3.40752 
 
 355 
 
 3.55123 
 
 341 
 
 0.95953 
 
 7,9 
 
 1.0422 
 
 o,9 
 
 .941 
 
 .41108 
 
 355 
 
 .55464 
 
 341 
 
 .95961 
 
 7,9 
 
 .0421 
 
 0,9 
 
 942 
 
 .41463 
 
 356 
 
 .55805 
 
 341 
 
 .95969 
 
 7,9 
 
 .0420 
 
 0,9 
 
 943 
 
 .41819 
 
 356 
 
 .56147 
 
 342 
 
 95977 
 
 7,9 
 
 .0419 
 
 0,9 
 
 .944 
 
 .42176 
 
 356 
 
 .56489 
 
 342 
 
 .95985 
 
 7,9 
 
 .0418 
 
 o,9 
 
 1.945 
 
 3.42532 
 
 357 
 
 3.56831 
 
 343 
 
 0.95993 
 
 7,9 
 
 1.0417 
 
 0,9 
 
 .946 
 
 .947 
 
 .42889 
 .43247 
 
 a 
 
 .57174 
 .57517 
 
 343 
 343 
 
 .96001 
 .96009 
 
 7,8 
 7,8 
 
 .0417 
 .0416 
 
 0,9 
 0,9 
 
 .948 
 
 .43604 
 
 358 
 
 .57860 
 
 344 
 
 .96016 
 
 7,8 
 
 .0415 
 
 0,9 
 
 .949 
 
 .43962 
 
 358 
 
 .58204 
 
 344 
 
 .96024 
 
 7,8 
 
 .0414 
 
 0,9 
 
 1.950 
 
 3.44321 
 
 359 
 
 3.58548 
 
 344 
 
 0.96032 
 
 7,8 
 
 1.0413 
 
 0,8 
 
 u 
 
 tan gd u 
 
 Fo' 
 
 sec gd u 
 
 FO' 
 
 sin gd u 
 
 Fo' 
 
 esc gd u 
 
 FO' 
 
 SMITHSONIAN TABLC 
 
 144 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinh u 
 
 Fc' 
 
 cosh u 
 
 FO' 
 
 tanhu 
 
 F ' 
 
 cothu 
 
 -IV 
 
 1.950 
 
 3.44321 
 
 359 
 
 3.58548 
 
 344 
 
 0.96032 
 
 7,8 
 
 1.0413 
 
 0,8 
 
 .951 
 
 .44679 
 
 359 
 
 .58893 
 
 345 
 
 .96040 
 
 7,8 
 
 .0412 
 
 
 .952 
 
 .45038 
 
 359 
 
 .59237 
 
 345 
 
 .96047 
 
 7,7 
 
 .0412 
 
 
 953 
 
 .45398 
 
 360 
 
 .59583 
 
 345 
 
 .96055 
 
 7,7 
 
 .0411 
 
 
 954 
 
 .45758 
 
 360 
 
 .59928 
 
 346 
 
 .96063 
 
 7,7 
 
 .0410 
 
 
 1-955 
 
 3.46118 
 
 360 
 
 3.60274 
 
 346 
 
 0.96071 
 
 7,7 
 
 1.0409 
 
 0,8 
 
 .956 
 
 .46478 
 
 361 
 
 .60620 
 
 346 
 
 .96078 
 
 7,7 
 
 .0408 
 
 
 957 
 
 .46839 
 
 261 
 
 .60967 
 
 347 
 
 .96086 
 
 7,7 
 
 .0407 
 
 
 958 
 
 .47200 
 
 361 
 
 .61314 
 
 347 
 
 .96094 
 
 7,7 
 
 .0407 
 
 
 959 
 
 .47562 
 
 362 
 
 .61662 
 
 348 
 
 .96101 
 
 7,6 
 
 .0406 
 
 
 1.960 
 
 3.47923 
 
 362 
 
 3.62009 
 
 348 
 
 0.96109 
 
 7,6 
 
 1.0405 
 
 0,8 
 
 .961 
 
 .48286 
 
 362 
 
 .62357 
 
 348 
 
 .96117 
 
 7,6 
 
 .0404 
 
 
 .962 
 
 .48648 
 
 363 
 
 .62706 
 
 349 
 
 .96124 
 
 7,6 
 
 .0403 
 
 
 .963 
 
 .49011 
 
 363 
 
 .63055 
 
 349 
 
 .96132 
 
 7,6 
 
 .0402 
 
 
 .964 
 
 .49374 
 
 363 
 
 .63404 
 
 349 
 
 .96139 
 
 7,6 
 
 .0402 
 
 
 1.965 
 
 3.49738 
 
 364 
 
 3.63753 
 
 350 
 
 0.96147 
 
 7,6 
 
 1.0401 
 
 0,8 
 
 .966 
 
 .50102 
 
 364 
 
 .64103 
 
 350 
 
 .96155 
 
 7,5 
 
 .0400 
 
 
 .967 
 
 .50466 
 
 364 
 
 .64454 
 
 350 
 
 .96162 
 
 7,5 
 
 .0399 
 
 
 .968 
 
 .50831 
 
 365 
 
 .64804 
 
 351 
 
 .96170 
 
 7,5 
 
 .0398 
 
 
 .969 
 
 .51196 
 
 365 
 
 .65155 
 
 35i 
 
 .96177 
 
 7,5 
 
 .0397 
 
 
 1.970 
 
 3.5I56I 
 
 366 
 
 3.65507 
 
 352 
 
 0.96185 
 
 7,5 
 
 1.0397 
 
 0,8- 
 
 .971 
 
 .51927 
 
 366 
 
 .65858 
 
 352 
 
 .96192 
 
 7,5 
 
 .0306 
 
 
 972 
 
 .52293 
 
 366 
 
 .66211 
 
 352 
 
 .96199 
 
 7,5 
 
 -0395 
 
 
 .973 
 
 .52659 
 
 367 
 
 .66563 
 
 353 
 
 .96207 
 
 7,4 
 
 .0394 
 
 
 .974 
 
 .53026 
 
 367 
 
 '.66916 
 
 353 
 
 .96214 
 
 7,4 
 
 .0393 
 
 
 1-975 
 
 3-53393 
 
 367 
 
 3.67269 
 
 353 
 
 0.96222 
 
 7,4 
 
 1.0393 
 
 0,8 
 
 .976 
 
 .53760 
 
 368 
 
 .67623 
 
 354 
 
 .96229 
 
 7,4 
 
 .0392 
 
 
 977 
 
 .54128 
 
 368 
 
 .67977 
 
 354 
 
 .96237 
 
 7,4 
 
 .0391 
 
 
 .978 
 
 .54496 
 
 368 
 
 .68331 
 
 354 
 
 .96244 
 
 7,4 
 
 .0390 
 
 
 .979 
 
 54855 
 
 369 
 
 .68686 
 
 355 
 
 .9^251 
 
 7,4 
 
 .0389 
 
 
 1.980 
 
 3.55234- 
 
 369 
 
 3.69041 
 
 355 
 
 0.96259 
 
 7,3 
 
 1.0389 
 
 0,8 
 
 .981 
 
 .55603 
 
 369 
 
 .69396 
 
 356 
 
 .962^66 
 
 7,3 
 
 .0388 
 
 
 .982 
 
 55972 
 
 370 
 
 .69752 
 
 356 
 
 .96273 
 
 7,3 
 
 .0387 
 
 
 .983 
 
 .56342 
 
 370 
 
 .70108 
 
 356 
 
 .96281 
 
 7,3 
 
 .0386 
 
 
 .984 
 
 .56713 
 
 370 
 
 .70465 
 
 357 
 
 .96288 
 
 7,3 
 
 .0386 
 
 
 1.985 
 
 3.57083 
 
 37i 
 
 3.70821 
 
 357 
 
 0.96295 
 
 7,3 
 
 1.0385 
 
 0,8 
 
 .986 
 
 .57454 
 
 37i 
 
 .71179 
 
 357 
 
 .06302 
 
 7,3 
 
 .0384 
 
 
 .987 
 
 .57826 
 
 372 
 
 .71536 
 
 358 
 
 .96310 
 
 7,2 
 
 .0383 
 
 
 .988 
 
 .58197 
 
 372 
 
 .71894 
 
 358 
 
 .96317 
 
 7,2 
 
 .0382 
 
 
 .989 
 
 .58569 
 
 372 
 
 72253 
 
 359 
 
 .96324 
 
 7,2 
 
 .0382 
 
 
 1.990 
 
 3.58042 
 
 373 
 
 3.72611 
 
 359 
 
 0.96331 
 
 7,2 
 
 1.0381 
 
 0,8 
 
 .991 
 
 59315 
 
 373 
 
 .72971 
 
 359 
 
 .96339 
 
 7,2 
 
 .0380 
 
 
 .992 
 
 .59588 
 
 373 
 
 .73330 
 
 360 
 
 .96346 
 
 7,2 
 
 .0379 
 
 
 993 
 
 .60061 
 
 374 
 
 .73690 
 
 360 
 
 .96353 
 
 7,2 
 
 .0379 
 
 
 .994 
 
 60435 
 
 374 
 
 .74050 
 
 360 
 
 .96360 
 
 7,1 
 
 .0378 
 
 
 1.995 
 
 3.60809 
 
 374 
 
 3-744II 
 
 361 
 
 0.96367 
 
 7,1 
 
 1.0377 
 
 0,8 
 
 .996 
 
 .61184 
 
 375 
 
 74772 
 
 361 
 
 .96374 
 
 7,i 
 
 .0376 
 
 
 997 
 
 .61559 
 
 375 
 
 .75133 
 
 362 
 
 .96382 
 
 7,i 
 
 .0375 
 
 
 .998 
 
 .61934 
 
 375 
 
 75495 
 
 362 
 
 .96389 
 
 7,i 
 
 .0375 
 
 
 999 
 
 .62310 
 
 376 
 
 .75857 
 
 362 
 
 .96396 
 
 7,i 
 
 .0374 
 
 
 2.OOO 
 
 3.62686 
 
 376 
 
 3.76220 
 
 363 
 
 0.96403 
 
 7,i 
 
 1.0373 
 
 0,8 
 
 U 
 
 tan gd u 
 
 Fo' 
 
 sec gd u 
 
 F ' 
 
 sin gd u 
 
 Fo' 
 
 esc gd u 
 
 F O ' 
 
 SMITHSONIAN TABLES 
 
 145 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinh u 
 
 F ' 
 
 cosh u 
 
 -FO' 
 
 tanh u 
 
 Fo 
 
 coth u 
 
 F' 
 
 2.0OO 
 
 3.62686 
 
 376 
 
 3 . 76220 
 
 363 
 
 0.96403 
 
 7,i 
 
 1-0373 
 
 r 0,8 
 
 .OOI 
 
 .63062 
 
 377 
 
 .76582 
 
 363 
 
 .96410 
 
 7ti 
 
 .0372 
 
 
 .002 
 
 .63439 
 
 377 
 
 .76940 
 
 363 
 
 .96417 
 
 7,o 
 
 .0372 
 
 
 .003 
 
 .63816 
 
 
 .77309 
 
 364 
 
 .96424 
 
 7,o 
 
 .0371 
 
 
 .004 
 
 .64194 
 
 378 
 
 .77673 
 
 364 
 
 .96431 
 
 7,o 
 
 .0370 
 
 
 2.005 
 
 3.64572 
 
 378 
 
 3./8038 
 
 365 
 
 0.96438 
 
 7,o 
 
 1.0369 
 
 0,8 
 
 .006 
 
 .64950 
 
 378 
 
 .78402 
 
 365 
 
 .96445 
 
 7,o 
 
 .0369 
 
 0,8 
 
 .007 
 
 .65328 
 
 379 
 
 .78768 
 
 365 
 
 .96452 
 
 7,o 
 
 .0368 
 
 o,7 
 
 .008 
 
 .65707 
 
 379 
 
 .79133 
 
 366 
 
 .96459 
 
 7,o 
 
 .0367 
 
 
 .009 
 
 .66087 
 
 379 
 
 79499 
 
 366 
 
 .96466 
 
 6,9 
 
 .0366 
 
 
 2.0IO 
 
 3.66466 
 
 380 
 
 3.79865 
 
 366 
 
 0.96473 
 
 6,9 
 
 1.0366 
 
 0,7 
 
 .Oil 
 
 .66846 
 
 380 
 
 .80232 
 
 367 
 
 .96480 
 
 6,9 
 
 .0365 
 
 
 .012 
 
 .67227 
 
 38i 
 
 .80599 
 
 367 
 
 .96487 
 
 6,9 
 
 .0364 
 
 
 .013 
 
 .67608 
 
 38i 
 
 .80966 
 
 368 
 
 .96493 
 
 6,9 
 
 .0363 
 
 
 .014 
 
 .67989 
 
 38i 
 
 .81334 
 
 368 
 
 .06500 
 
 6,9 
 
 .0363 
 
 
 2.015 
 
 3.68370 
 
 382 
 
 3.81702 
 
 368 
 
 0.96507 
 
 6,9 
 
 1.0362 
 
 o,7 
 
 .016 
 
 .68752 
 
 382 
 
 .82071 
 
 369 
 
 .96514 
 
 6,9 
 
 .0361 
 
 
 .017 
 
 .69134 
 
 382 
 
 .82440 
 
 369 
 
 .96521 
 
 6,8 
 
 .0360 
 
 
 .018 
 
 .69517 
 
 383 
 
 .82809 
 
 370 
 
 .96528 
 
 6,8 
 
 .0360 
 
 
 .019 
 
 .69900 
 
 383 
 
 .83179 
 
 370 
 
 .96535 
 
 6,8 
 
 .0359 
 
 
 2.O2O 
 
 3.70283 
 
 384 
 
 3.83549 
 
 370 
 
 0.96541 
 
 6,8 
 
 1.0358 
 
 o,7 
 
 .021 
 
 .70667 
 
 384 
 
 .83919 
 
 371 
 
 .96548 
 
 6,8 
 
 .0358 
 
 
 .022 
 
 .71051 
 
 384 
 
 .84290 
 
 371 
 
 .96555 
 
 6,8 
 
 0357 
 
 
 .023 
 
 .71436 
 
 385 
 
 .84662 
 
 371 
 
 .96562 
 
 6,8 
 
 .0356 
 
 
 .024 
 
 .71821 
 
 385 
 
 .85033 
 
 372 
 
 .96568 
 
 6,7 
 
 .0355 
 
 
 2.025 
 
 3.72206 
 
 385 
 
 3.85405 
 
 372 
 
 0.96575 
 
 6,7 
 
 1.0355 
 
 o,7 
 
 .026 
 
 .72591 
 
 386 
 
 .85778 
 
 373 
 
 .96582 
 
 6,7 
 
 .0354 
 
 
 .027 
 
 .72977 
 
 386 
 
 .86150 
 
 373 
 
 .96589 
 
 6,7 
 
 .0353 
 
 
 .028 
 
 .73364 
 
 387 
 
 .86524 
 
 373 
 
 .96595 
 
 6,7 
 
 .0352 
 
 
 .029 
 
 .73750 
 
 387 
 
 .86897 
 
 374 
 
 .96602 
 
 6,7 
 
 .0352 
 
 
 2.030 
 
 3.74138 
 
 387 
 
 3.87271 
 
 374 
 
 0.96609 
 
 6,7 
 
 1.0351 
 
 o,7 
 
 .031 
 
 .74525 
 
 388 
 
 .87645 
 
 375 
 
 .96615 
 
 6,7 
 
 0350 
 
 
 .032 
 
 74913 
 
 388 
 
 .88020 
 
 375 
 
 .96622 
 
 6,6 
 
 0350 
 
 
 .033 
 
 75301 
 
 388 
 
 .88395 
 
 375 
 
 .96629 
 
 6,6 
 
 0349 
 
 
 .034 
 
 .75090 
 
 389 
 
 .88771 
 
 376 
 
 .96635 
 
 6,6 
 
 0348 
 
 
 2.035 
 
 3.76079 
 
 389 
 
 3.89147 
 
 376 
 
 0.96642 
 
 6,6 
 
 1-0347 
 
 o,7 
 
 .036 
 
 .76468 
 
 390 
 
 .89523 
 
 376 
 
 .96648 
 
 6,6 
 
 0347 
 
 
 037 
 
 .76858 
 
 390 
 
 .89900 
 
 377 
 
 .96655 
 
 6,6 
 
 0346 
 
 
 .038 
 
 .77248 
 
 390 
 
 .90277 
 
 377 
 
 .96662 
 
 6,6 
 
 0345 
 
 
 039 
 
 .77638 
 
 391 
 
 .90654 
 
 378 
 
 .96668 
 
 6,6 
 
 0345 
 
 
 2.040 
 
 3.78029 
 
 391 
 
 3.91032 
 
 378 
 
 0.96675 
 
 6,5 
 
 1-0344 
 
 o,7 
 
 .041 
 
 .78420 
 
 391 
 
 .91410 
 
 378 
 
 .96681 
 
 6,5 
 
 .0343 
 
 
 .042 
 
 .78812 
 
 392 
 
 .91789 
 
 379 
 
 .96688 
 
 6,5 
 
 0343 
 
 
 043 
 
 .79204 
 
 392 
 
 .92168 
 
 379 
 
 .96694 
 
 6,5 
 
 .034-' 
 
 
 044 
 
 .79596 
 
 393 
 
 .92547 
 
 380 
 
 .96701 
 
 6,5 
 
 .0341 
 
 
 2.045 
 
 3.79989 
 
 393 
 
 3.92927 
 
 380 
 
 0.96707 
 
 6,5 
 
 1.0340 
 
 o,7 
 
 .046 
 
 .80382 
 
 393 
 
 .93307 
 
 380 
 
 .96714 
 
 6,5 
 
 0340 
 
 
 .047 
 
 .80776 
 
 394 
 
 .93688 
 
 38r 
 
 .96720 
 
 6,5 
 
 0339 
 
 
 .048 
 
 .81169 
 
 394 
 
 .94069 
 
 38i 
 
 .96727 
 
 6,4 
 
 .0338 
 
 
 .049 
 
 .81564 
 
 394 
 
 .94450 
 
 382 
 
 .06733 
 
 6,4 
 
 .0338 
 
 
 2.050 
 
 3.81958 
 
 395 
 
 3-94832 
 
 382 
 
 0.96740 
 
 6,4 
 
 1.0337 
 
 o,7 
 
 u 
 
 tan gd u 
 
 F ' 
 
 sec gd u 
 
 F O ' 
 
 tin gd u 
 
 Fo* 
 
 esc gd u 
 
 FV 
 
 SMITHSONIAN TABLES 
 
 146 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinhu 
 
 Fo' 
 
 cosh u 
 
 <-FO' 
 
 tanh u 
 
 F ' 
 
 coth u 
 
 F ' 
 
 2.050 
 
 3.81958 
 
 395 
 
 3.94832 
 
 382 
 
 0.96740 
 
 6,4 
 
 1.0337 
 
 o,7 
 
 .051 
 
 .82353 
 
 395 
 
 .95214 
 
 382 
 
 .96746 
 
 6,4 
 
 .0336 
 
 
 .052 
 
 .82749 
 
 396 
 
 95597 
 
 383 
 
 .96752 
 
 6,4 
 
 .0336 
 
 
 / -053 
 
 .83145 
 
 396 
 
 95979 
 
 383 
 
 .96759 
 
 6,4 
 
 .0335 
 
 
 054 
 
 .83541 
 
 396 
 
 .96363 
 
 384 
 
 .96765 
 
 6,4 
 
 0334 
 
 
 2.055 
 
 3.83937 
 
 397 
 
 3.96747 
 
 384 
 
 0.96771 
 
 .6,4 
 
 1.0334 
 
 o,7 
 
 .056 
 
 .84334 
 
 397 
 
 .97131 
 
 34 
 
 .96778 
 
 6,3 
 
 0333 
 
 
 .057 
 
 .84732 
 
 398 
 
 97515 
 
 385 
 
 .96784 
 
 6,3 
 
 .0332 
 
 
 .058 
 
 .85129 
 
 398 
 
 .97900 
 
 385 
 
 .96790 
 
 6,3 
 
 .0332 
 
 
 059 
 
 .85527 
 
 398 
 
 .98285 
 
 386 
 
 .96797 
 
 6,3 
 
 .0331 
 
 
 2.060 
 
 3.85926 
 
 399 
 
 3.98671 
 
 386 
 
 0.96803 
 
 6,3 
 
 1.0330 
 
 o,7 
 
 .061 
 
 .86325 
 
 399 
 
 .99057 
 
 386 
 
 .96809 
 
 6,3 
 
 .0330 
 
 
 .062 
 
 .86724 
 
 399 
 
 99444 
 
 387 
 
 .96816 
 
 6,3 
 
 .0329 
 
 
 .063 
 
 .87124 
 
 400 
 
 .99831 
 
 387 
 
 .96822 
 
 6,3 
 
 .0328 
 
 
 .064 
 
 .87524 
 
 400 
 
 4.00218 
 
 388 
 
 .96828 
 
 6,2 
 
 .0328 
 
 
 2.065 
 
 3.87924 
 
 401 
 
 4.00606 
 
 388 
 
 0.06834 
 
 6,2 
 
 1.0327 
 
 o,7 
 
 .066 
 
 .88325 
 
 401 
 
 .00994 
 
 388 
 
 .96841 
 
 6,2 
 
 .0326 
 
 
 .067 
 
 .88726 
 
 401 
 
 .01382 
 
 389 
 
 .96847 
 
 6,2 
 
 .0326 
 
 
 .068 
 
 .89128 
 
 402 
 
 .01771 
 
 389 
 
 .96853 
 
 6,2 
 
 .0325 
 
 
 .069 
 
 .89530 
 
 402 
 
 .02161 
 
 390 
 
 .96859 
 
 6,2 
 
 .0324 
 
 
 2.070 
 
 3.89932 
 
 403 
 
 4.02550 
 
 390 
 
 0.96865 
 
 6,2. 
 
 1.0324 
 
 o,7 
 
 .071 
 
 .90335 
 
 403 
 
 .02941 
 
 390 
 
 .96872 
 
 6,2 
 
 .0323 
 
 
 .072 
 
 .90738 
 
 403 
 
 .03331 
 
 391 
 
 .96878 
 
 6,1 
 
 .0322 
 
 
 .073 
 
 .91141 
 
 404 
 
 .03722 
 
 391 
 
 .96884 
 
 6,1 
 
 .0322 
 
 
 .074 
 
 .91545 
 
 404 
 
 .04113 
 
 392 
 
 .96890 
 
 6,1 
 
 .0321 
 
 
 2.075 
 
 3.91950 
 
 405 
 
 4.04505 
 
 392 
 
 0.96896 
 
 6,1 
 
 1.0320 
 
 o,7 
 
 .076 
 
 .92354 
 
 405 
 
 .04897 
 
 392 
 
 .96902 
 
 6,1 
 
 .0320 
 
 0,6 
 
 .077 
 
 .92759 
 
 405 
 
 .05290 
 
 393 
 
 .96908 
 
 6,1 
 
 .0319 
 
 
 .078 
 
 .93165 
 
 406 
 
 .05683 
 
 393 
 
 .06914 
 
 6,1 
 
 .0318 
 
 
 .079 
 
 93571 
 
 406 
 
 .06076 
 
 394 
 
 .96920 
 
 6,1 
 
 .0318 
 
 
 2.080 
 
 3-93977 
 
 406 
 
 4.06470 
 
 394 
 
 0.06926 
 
 ' 6,1 
 
 1.0317 
 
 0,6 
 
 .081 
 
 .94384 
 
 407 
 
 .06864 
 
 394 
 
 .96933 
 
 6,0 
 
 .0316 
 
 
 .082 
 
 .94791 
 
 407 
 
 .07259 
 
 395 
 
 .96939 
 
 6,0 
 
 .0316 
 
 
 .083 
 
 .95198 
 
 408 
 
 .07654 
 
 395 
 
 .96945 
 
 6,0 
 
 .0315 
 
 
 .084 
 
 .95606 
 
 408 
 
 .08049 
 
 396 
 
 .96951 
 
 6,0 
 
 .0315 
 
 
 2.085 
 
 3.96014 
 
 408 
 
 4.08445 
 
 396 
 
 0.96957 
 
 6,0 
 
 1.0314 
 
 0,6 
 
 .086 
 
 .96423 
 
 409 
 
 .08841 
 
 396 
 
 .96963 
 
 6,0 
 
 .0313 
 
 
 .087 
 
 .96832 
 
 409 
 
 .09238 
 
 397 
 
 .96969 
 
 6,0 
 
 .0313 
 
 
 .088 
 
 .97241 
 
 410 
 
 .00635 
 
 397 
 
 .96975 
 
 6,0 
 
 .0312 
 
 
 .089 
 
 .97651 
 
 410 
 
 .10032 
 
 398 
 
 .96980 
 
 5,9 
 
 .0311 
 
 
 2.000 
 
 3.08061 
 
 410 
 
 4-10430 
 
 398 
 
 0.96986 
 
 5,9 
 
 1.0311 
 
 0,6 
 
 .091 
 
 .98472 
 
 411 
 
 .10828 
 
 398 
 
 .95992 
 
 5,9 
 
 .0310 
 
 
 .092 
 
 .98883 
 
 411 
 
 .11227 
 
 399 
 
 .96998 
 
 5,9 
 
 .0309 
 
 
 093 
 
 .99294 
 
 412 
 
 .11626 
 
 399 
 
 .97004 
 
 5,9 
 
 .0309 
 
 
 .094 
 
 .99706 
 
 412 
 
 . 12026 
 
 400 
 
 .97010 
 
 5,9 
 
 .0308 
 
 
 2.095 
 
 4.OOII9 
 
 412 
 
 4.12426 
 
 400 
 
 0.97016 
 
 5,9 
 
 1.0308 
 
 0,6 
 
 .006 
 
 .00531 
 
 413 
 
 .12826 
 
 401 
 
 .97022 
 
 5,9 
 
 .0307 
 
 
 .097 
 
 .00944 
 
 413 
 
 .13227 
 
 401 
 
 .97028 
 
 5,9 
 
 .0306 
 
 
 .098 
 
 .01358 
 
 414 
 
 . 13628 
 
 401 
 
 .97034 
 
 5,8 
 
 .0306 
 
 
 .099 
 
 .01771 
 
 414 
 
 .14029 
 
 402 
 
 .97039 
 
 5,8 
 
 .0305 
 
 
 2.100 
 
 4.02186 
 
 414 
 
 4.I443I 
 
 402 
 
 0.97045 
 
 5,8 
 
 1.0304 
 
 0,6 
 
 u 
 
 tan gd u 
 
 F O ' 
 
 sec gd u 
 
 F O ' 
 
 sin gd u 
 
 F ' 
 
 esc gd u 
 
 F O ' 
 
 SMITHSONIAN TABLES 
 
 147 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinh u 
 
 F ' 
 
 cosh u 
 
 F O ' 
 
 tanh u 
 
 Fo' 
 
 coth u 
 
 ~ Fo' 
 
 2.IOO 
 
 4.02186 
 
 414 
 
 4.I443I 
 
 402 
 
 0.97045 
 
 5,8 
 
 1.0304 
 
 0,6 
 
 .IOI 
 
 .02600 
 
 415 
 
 .14834 
 
 403 
 
 .97051 
 
 5,8 
 
 .0304 
 
 
 .102 
 
 .03015 
 
 415 
 
 . 15237 
 
 403 
 
 .97057 
 
 5,8 
 
 .0303 
 
 
 .103 
 
 .03431 
 
 416 
 
 .15640 
 
 403 
 
 .97063 
 
 5,8 
 
 0303 
 
 
 .104 
 
 03847 
 
 416 
 
 .16043 
 
 404 
 
 .97068 
 
 5,8 
 
 .0302 
 
 
 2.105 
 
 4.04263 
 
 416 
 
 4.16447 
 
 404 
 
 0.97074 
 
 5,8 
 
 I.030I 
 
 0,6 
 
 .106 
 
 .04680 
 
 417 
 
 .16852 
 
 405 
 
 .97080 
 
 5,8 
 
 .0301 
 
 
 .107 
 
 .05097 
 
 417 
 
 .17257 
 
 405 
 
 .97086 
 
 5,7 
 
 .0300 
 
 
 .108 
 
 .05514 
 
 4 l8 
 
 .17662 
 
 406 
 
 .97091 
 
 5,7 
 
 .0300 
 
 
 .109 
 
 .05932 
 
 418 
 
 .18068 
 
 406 
 
 .97097 
 
 5,7 
 
 .0299 
 
 
 2.IIO 
 
 4.06350 
 
 418 
 
 4. 18474 
 
 406 
 
 0.97103 
 
 5,7 
 
 1.0298 
 
 0,6 
 
 .III 
 
 .06769 
 
 419 
 
 . 18881 
 
 407 
 
 .97109 
 
 5,7 
 
 .0298 
 
 
 .112 
 
 .07188 
 
 419 
 
 .19288 
 
 407 
 
 .97H4 
 
 5,7 
 
 .0297 
 
 
 113 
 
 .07607 
 
 420 
 
 .19695 
 
 408 
 
 .97120 
 
 5,7 
 
 .0297 
 
 
 .114 
 
 .08027 
 
 42O 
 
 .20103 
 
 408 
 
 .97126 
 
 5,7 
 
 .0296 
 
 
 2. 115 
 
 4.08448 
 
 421 
 
 4.20511 
 
 408 
 
 0.97I3I 
 
 5,7 
 
 1.0295 
 
 0,6 
 
 .116 
 
 .08868 
 
 421 
 
 .20920 
 
 409 
 
 .97137 
 
 5,6 
 
 .0295 
 
 
 .117 
 
 .09289 
 
 421 
 
 .21329 
 
 409 
 
 .97143 
 
 5,6 
 
 .0294 
 
 
 .118 
 
 .097H 
 
 422 
 
 .21738 
 
 410 
 
 .97148 
 
 5,6 
 
 .0294 
 
 
 .119 
 
 . 10133 
 
 422 
 
 .22148 
 
 410 
 
 .97154 
 
 5,6 
 
 .0293 
 
 
 2.120 
 
 4.I05S5 
 
 423 
 
 4.22558 
 
 411 
 
 0.97159 
 
 5,6 
 
 1.0292 
 
 0,6 
 
 .121 
 
 .10978 
 
 423 
 
 .22969 
 
 411 
 
 .97165 
 
 5,6 
 
 .0292 
 
 
 .122 
 
 .11401 
 
 423 
 
 .23380 
 
 411 
 
 .97171 
 
 5,6 
 
 .0291 
 
 
 .123 
 
 .11825 
 
 424 
 
 .23792 
 
 412 
 
 .97176 
 
 5,6 
 
 .0291 
 
 
 .124 
 
 . 12249 
 
 424 
 
 .24204 
 
 412 
 
 .97182 
 
 5,6 
 
 .0290 
 
 
 2.I2S 
 
 4.12673 
 
 425 
 
 4.24617 
 
 413 
 
 0.97187 
 
 5,5 
 
 1.0289 
 
 0,6 
 
 .126 
 
 .13098 
 
 425 
 
 .25029 
 
 413 
 
 .97193 
 
 5,5 
 
 .0289 
 
 
 .127 
 
 . 13523 
 
 425 
 
 .25443 
 
 414 
 
 .97198 
 
 5,5 
 
 .0288 
 
 
 .128 
 
 13949 
 
 426 
 
 .25856 
 
 414 
 
 .97204 
 
 5,5 
 
 .0288 
 
 
 .129 
 
 . 14375 
 
 426 
 
 .26271 
 
 414 
 
 .97209 
 
 5,5 
 
 .0287 
 
 
 2.130 
 
 4.14801 
 
 427 
 
 4.26685 
 
 415 
 
 0.97215 
 
 5,5 
 
 1.0286 
 
 0,6 
 
 .131 
 
 .15228 
 
 427 
 
 .27100 
 
 415 
 
 .97220 
 
 5,5 
 
 .0286 
 
 
 .132 
 
 .15656 
 
 428 
 
 .27516 
 
 416 
 
 .97226 
 
 5,5 
 
 .0285 
 
 
 .133 
 
 .16083 
 
 428 
 
 .27932 
 
 416 
 
 .97231 
 
 5,5 
 
 .0285 
 
 
 .134 
 
 .16512 
 
 428 
 
 .28348 
 
 417 
 
 .97237 
 
 5,4 
 
 .0284 
 
 
 2.135 
 
 4.16940 
 
 429 
 
 4-28765 
 
 417 
 
 0.97242 
 
 5,4 
 
 1.0284 
 
 0,6 
 
 .136 
 
 .17369 
 
 429 
 
 .29182 
 
 417 
 
 .97248 
 
 5,4 
 
 .0283 
 
 
 .137 
 
 .17798 
 
 430 
 
 .29599 
 
 418 
 
 .97253 
 
 5,4 
 
 .0282 
 
 
 .138 
 
 . 18228 
 
 430 
 
 .30017 
 
 418 
 
 .97258 
 
 5,4 
 
 .0282 
 
 
 .139 
 
 .18658 
 
 430 
 
 .30436 
 
 419 
 
 .97264 
 
 5,4 
 
 .0281 
 
 
 2.140 
 
 4.19089 
 
 431 
 
 4.30855 
 
 419 
 
 0.97269 
 
 5,4 
 
 1.0281 
 
 0,6 
 
 .141 
 
 .19520 
 
 431 
 
 .31274 
 
 420 
 
 .97275 
 
 5,4 
 
 .0280 
 
 
 .142 
 
 .10952 
 
 432 
 
 .31694- 
 
 420 
 
 .97280 
 
 5,4 
 
 .0280 
 
 
 .143 
 
 .20384 
 
 432 
 
 .32114 
 
 420 
 
 .97285 
 
 5,4 
 
 .0279 
 
 
 .144 
 
 .20816 
 
 433 
 
 .32534 
 
 421 
 
 .97291 
 
 5,3 
 
 .0278 
 
 
 2.145 
 
 4.21249 
 
 433 
 
 4.32955 
 
 421 
 
 0.97296 
 
 5,3 
 
 1.0278 
 
 0,6 
 
 .146 
 
 .21682 
 
 433 
 
 .33377 
 
 422 
 
 .97301 
 
 5,3 
 
 .0277 
 
 
 .147 
 
 .22115 
 
 434 
 
 33799 
 
 422 
 
 .97307 
 
 5,3 
 
 .0277 
 
 
 .148 
 
 .22549 
 
 434 
 
 .34221 
 
 423 
 
 .97312 
 
 5,3 
 
 .0276 
 
 
 .149 
 
 .22084 
 
 435 
 
 .34644 
 
 423 
 
 .97317 
 
 5,3 
 
 .0276 
 
 
 2.150 
 
 4.23419 
 
 435 
 
 4.35067 
 
 423 
 
 0.97323 
 
 5,3 
 
 1.0275 
 
 0,6 
 
 u 
 
 tan od u 
 
 Fo' 
 
 sec od u 
 
 Fo' 
 
 sin gd u 
 
 tv 
 
 esc 0d u 
 
 F' 
 
 SMITHSONIAN TABLES 
 
 148 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinh u 
 
 -Fa' 
 
 cosh u 
 
 Fo" 
 
 tanh u 
 
 F 
 
 coin u 
 
 Fo' 
 
 2.150 
 
 4.23419 
 
 435 
 
 4.35067 
 
 423 
 
 0.97323 
 
 5,3 
 
 1.0275 
 
 0,6 
 
 .151 
 
 .23854 
 
 435 
 
 35491 
 
 424 
 
 .97328 
 
 5,3 
 
 .0275 
 
 
 .152 
 
 .24290 
 
 436 
 
 .35915 
 
 424 
 
 97333 
 
 5,3 
 
 .0274 
 
 
 .153 
 
 .24726 
 
 436 
 
 .36339 
 
 425 
 
 .97338 
 
 5,3 
 
 .0273 
 
 
 154 
 
 .25162 
 
 437 
 
 .36764 
 
 425 
 
 97344 
 
 5,2 
 
 .0273 
 
 
 2.155 
 
 4.25599 
 
 437 
 
 4.37190 
 
 426 
 
 0.97349 
 
 5,2 
 
 1.0272 
 
 0,6 
 
 .156 
 
 .26037 
 
 438 
 
 .37615 
 
 426 
 
 97354 
 
 5,2 
 
 .0272 
 
 0,6 
 
 157 
 
 .26475 
 
 438 
 
 .38042 
 
 426 
 
 .97359 
 
 5,2 
 
 .0271 
 
 o,5 
 
 .158 
 
 .26913 
 
 438 
 
 .38468 
 
 427 
 
 .97365 
 
 5,2 
 
 .0271 
 
 o,5 
 
 .159 
 
 .27352 
 
 439 
 
 .38896 
 
 427 
 
 97370 
 
 5,2 
 
 .0270 
 
 o,5 
 
 2.160 
 
 4.27791 
 
 439 
 
 4.39323 
 
 428 
 
 0.97375 
 
 5,2 
 
 I.027O 
 
 o,5 
 
 .161 
 
 .28230 
 
 440 
 
 .39751 
 
 428 
 
 .97380 
 
 5,2 
 
 .0269 
 
 
 .162 
 
 .28670 
 
 440 
 
 .40180 
 
 429 
 
 97385 
 
 5,2 
 
 .0268 
 
 
 .163 
 
 .29111 
 
 441 
 
 .40608 
 
 429 
 
 97390 
 
 5,2 
 
 .0268 
 
 
 .164 
 
 -29551 
 
 441 
 
 .41038 
 
 430 
 
 .97396 
 
 5,1 
 
 .0267 
 
 
 2.165 
 
 4.29993 
 
 441 
 
 4.41468 
 
 430 
 
 0.97401 
 
 5,1 
 
 1.0267 
 
 0,5 
 
 .166 
 
 .30434 
 
 442 
 
 .41898 
 
 430 
 
 .97406 
 
 5,1 
 
 .0266 
 
 
 .167 
 
 .30876 
 
 442 
 
 .42328 
 
 431 
 
 974II 
 
 5,1 
 
 .0266 
 
 
 .168 
 
 .31319 
 
 443 
 
 .42760 
 
 431 
 
 .97416 
 
 5,1 
 
 .0265 
 
 
 .169 
 
 .31762 
 
 443 
 
 .43191 
 
 432 
 
 .97421 
 
 5,1 
 
 .0265 
 
 
 2.170 
 
 4.32205 
 
 444 
 
 4.43623 
 
 432 
 
 0.97426 
 
 5,1 
 
 1.0264 
 
 o,S 
 
 .171 .32649 
 
 444 
 
 .44056 
 
 433 
 
 97431 
 
 5,1 
 
 .0264 
 
 
 .172 
 
 .33093 
 
 444 
 
 .44488 
 
 433 
 
 97436 
 
 5,i 
 
 .0263 
 
 
 .173 
 
 .33538 
 
 445 
 
 .44922 
 
 434 
 
 .97441 
 
 5,i 
 
 .0263 
 
 
 .174 
 
 .33983 
 
 445 
 
 45355 
 
 434 
 
 .97446 
 
 5,o 
 
 .0262 
 
 
 2.175 
 
 4.34429 
 
 446 
 
 4.45790 
 
 434 
 
 0.97452 
 
 5,o 
 
 1.0262 
 
 o,5 
 
 .176 
 
 .34875 
 
 446 
 
 .46224 
 
 435 
 
 97457 
 
 5,o 
 
 .0261 
 
 
 .177 
 
 35321 
 
 447 
 
 .46659 
 
 435 
 
 .97462 
 
 5,o 
 
 .0260 
 
 
 .178 
 
 .35768 
 
 447 
 
 .47095 
 
 436 
 
 .97467 
 
 5,o 
 
 .0260 
 
 
 .179 
 
 .36215 
 
 448 
 
 .47531 
 
 436" 
 
 .97472 
 
 5,o 
 
 .0259 
 
 
 2.180 
 
 4.36663 
 
 448 
 
 4.47967 
 
 437 
 
 0.97477 
 
 5,o 
 
 1.0259 
 
 o,5 
 
 .181 
 
 37III 
 
 448 
 
 .48404 
 
 437 
 
 .97482 
 
 5,o 
 
 .0258 
 
 
 .182 
 
 37560 
 
 449 
 
 .48842 
 
 438 
 
 .97487 
 
 5,o 
 
 .0258 
 
 
 .183 
 
 .38009 
 
 449 
 
 .49279 
 
 438 
 
 .97491 
 
 5,o 
 
 .0257 
 
 
 .184 
 
 .38459 
 
 450 
 
 .49718 
 
 438 
 
 .97496 
 
 4,9 
 
 .0257 
 
 
 2.185 
 
 4.38909 
 
 450 
 
 4.50156 
 
 439 
 
 0.97501 
 
 4,9 
 
 1.0256 
 
 o,5 
 
 .186 
 
 39359 
 
 451 
 
 .50595 
 
 439 
 
 .97506 
 
 4,9 
 
 .0256 
 
 
 .187 
 
 .39810 
 
 451 
 
 .51035 
 
 440 
 
 975II 
 
 4,9 
 
 .0255 
 
 
 .188 
 
 .40261 
 
 451 
 
 .51475 
 
 440 
 
 .97516 
 
 4,9 
 
 0255 
 
 
 .189 
 
 .40713 
 
 452 
 
 .51916 
 
 441 
 
 97521 
 
 4,9 
 
 .0254 
 
 
 2.190 
 
 4.4H65 
 
 452 
 
 4.52356 
 
 441 
 
 0.97526 
 
 4,9 
 
 1.0254 
 
 0,5 
 
 .191 
 
 .41617 
 
 453 
 
 .52798 
 
 442 
 
 .97531 
 
 4,9 
 
 0253 
 
 
 .192 
 
 .42070 
 
 453 
 
 .53240 
 
 442 
 
 .97536 
 
 4,9 
 
 .0253 
 
 
 .193 
 
 .42524 
 
 454 
 
 .53682 
 
 443 
 
 97541 
 
 4,9 
 
 .0252 
 
 
 .194 
 
 .42978 
 
 454 
 
 .54125 
 
 443 
 
 97545 
 
 4,8 
 
 .0252 
 
 
 2.195 
 
 4.43432 
 
 455 
 
 4.54568 
 
 443 
 
 0.97550 
 
 4,8 
 
 1.0251 
 
 0,5 
 
 .196 
 
 .43887 
 
 455 
 
 55012 
 
 444 
 
 .97555 
 
 4,8 
 
 .0251 
 
 
 .197 
 
 .44342 
 
 455 
 
 .55456 
 
 444 
 
 .97560 
 
 4,8 
 
 .0250 
 
 
 .198 
 
 44798 
 
 456 
 
 55900 
 
 445 
 
 .97565 
 
 4,8 
 
 .0250 
 
 
 .199 
 
 .45254 
 
 456 
 
 .56345 
 
 445 
 
 .97570 
 
 4,8 
 
 .0249 
 
 
 2.200 
 
 4.457H 
 
 457 
 
 4.56791 
 
 446 
 
 0.97574 
 
 4,8 
 
 1.0249 
 
 o,5 
 
 U 
 
 tan gd u 
 
 F O ' 
 
 sec gd u 
 
 FO' 
 
 sin gd u 
 
 coFo' 
 
 esc gd u 
 
 F ' 
 
 SMITHSONIAN TABLES 
 
 149 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinh u 
 
 F.' 
 
 cosh u 
 
 -F ' 
 
 tanhu 
 
 Fo' 
 
 coth u 
 
 -Fo' 
 
 2.2OO 
 
 4-457II 
 
 457 
 
 4.56791 
 
 446 
 
 0.97574 
 
 4,8 
 
 1.0249 
 
 o,5 
 
 .2OI 
 
 .46168 
 
 457 
 
 57237 
 
 446 
 
 97579 
 
 4,8 
 
 .0248 
 
 
 .202 
 
 .46625 
 
 458 
 
 .57683 
 
 447 
 
 .97584 
 
 4,8 
 
 .0248 
 
 
 .203 
 
 .4/083 
 
 458 
 
 .58130 
 
 447 
 
 .97589 
 
 4,8 
 
 .0247 
 
 
 .204 
 
 47541 
 
 459 
 
 .58577 
 
 448 
 
 97593 
 
 4,8 
 
 .0247 
 
 
 2.2O5 
 
 4.48000 
 
 459 
 
 4.59025 
 
 448 
 
 0.97598 
 
 4,7 
 
 1.0246 
 
 o,5 
 
 .206 
 .207 
 
 .48459 
 .48919 
 
 459 
 460 
 
 59473 
 59922 
 
 448 
 449 
 
 .97603 
 .97608 
 
 4,7 
 
 4,7 
 
 .0246 
 .0245 
 
 
 .208 
 
 49379 
 
 460 
 
 .60371 
 
 449 
 
 .97612 
 
 4,7 
 
 .0245 
 
 
 .209 
 
 .49840 
 
 461 
 
 .60821 
 
 450 
 
 .97617 
 
 4,7 
 
 .0244 
 
 
 2.2IO 
 
 4.50301 
 
 461 
 
 4.61271 
 
 450 
 
 0.97622 
 
 4,7 
 
 1.0244 
 
 o,5 
 
 .211 
 
 .50762 
 
 462 
 
 .61721 
 
 451 
 
 .97626 
 
 4,7 
 
 .0243 
 
 
 .212 
 
 .51224 
 
 462 
 
 .62172 
 
 451 
 
 97631 
 
 4,7 
 
 .0243 
 
 
 .213 
 
 .51687 
 
 463 
 
 .62624 
 
 452 
 
 .97636 
 
 4,7 
 
 .0242 
 
 
 .214 
 
 52149 
 
 463 
 
 .63076 
 
 452 
 
 .97640 
 
 4,7 
 
 .0242 
 
 
 2.2IS 
 
 4.52613 
 
 464 
 
 4-63528 
 
 453 
 
 0.97645 
 
 4,7 
 
 1.0241 
 
 o,5 
 
 .216 
 
 53077 
 
 464 
 
 .63981 
 
 453 
 
 .97650 
 
 4,6 
 
 .0241 
 
 
 .217 
 
 53541 
 
 464 
 
 .64434 
 
 454 
 
 .97654 
 
 4,6 
 
 .0240 
 
 
 .218 
 
 54005 
 
 465 
 
 .64888 
 
 454 
 
 .97659 
 
 4,6 
 
 .0240 
 
 
 .219 
 
 54471 
 
 465 
 
 .65342 
 
 454 
 
 .97664 
 
 4,6 
 
 . .0239 
 
 
 2.22O 
 
 4.54936 
 
 466 
 
 4.65797 
 
 455 
 
 0.97668 
 
 4,6 
 
 1.0239 
 
 0,5 
 
 .221 
 
 55402 
 
 466 
 
 .66252 
 
 455 
 
 .97673 
 
 4,6 
 
 .0238 
 
 
 .222 
 
 .55869 
 
 467 
 
 .66708 
 
 456 
 
 .97678 
 
 4,6 
 
 .0238 
 
 
 .223 
 
 .56336 
 
 467 
 
 .67164 
 
 456 
 
 .97682 
 
 4,6 
 
 .0237 
 
 
 .224 
 
 .56803 
 
 468 
 
 .67620 
 
 457 
 
 .97687 
 
 4,6 
 
 .0237 
 
 
 2.225 
 
 4.57271 
 
 468 
 
 4.68078 
 
 457 
 
 0.97691 
 
 4,6 
 
 1.0236 
 
 0,5 
 
 .226 
 
 57739 
 
 469 
 
 .68535 
 
 458 
 
 .97606 
 
 4,6 
 
 .0236 
 
 
 .227 
 
 .58208 
 
 469 
 
 .68993 
 
 458 
 
 .97700 
 
 4,5 
 
 0235 
 
 
 .228 
 
 .58677 
 
 469 
 
 .69451 
 
 459 
 
 .97705 
 
 4,5 
 
 .0235 
 
 
 .229 
 
 .59147 
 
 470 
 
 .69910 
 
 459 
 
 .97709 
 
 4,5 
 
 .0234 
 
 
 2.230 
 
 4.59617 
 
 470 
 
 4.70370 
 
 460 
 
 0.97714 
 
 4,5 
 
 1.0234 
 
 o,5 
 
 .231 
 
 .60087 
 
 471 
 
 .70830 
 
 460 
 
 .97718 
 
 4,5 
 
 .0233 
 
 
 .232 
 
 60559 
 
 471 
 
 .71290 
 
 461 
 
 .97723 
 
 4,5 
 
 .0233 
 
 
 .233 
 
 .61030 
 
 472 
 
 .71751 
 
 461 
 
 97727 
 
 4,5 
 
 .0233 
 
 
 .234 
 
 .61502 
 
 472 
 
 .72212 
 
 462 
 
 97732 
 
 4,5 
 
 .0232 
 
 
 2.235 
 
 4.61974 
 
 473 
 
 4.72674 
 
 462 
 
 0.97736 
 
 4,5 
 
 1.0232 
 
 o,5 
 
 .236 
 
 .62447 
 
 473 
 
 .73136 
 
 462 
 
 .97741 
 
 4,5 
 
 .0231 
 
 
 237 
 
 .62921 
 
 474 
 
 73599 
 
 463 
 
 97745 
 
 4,5 
 
 .0231 
 
 
 .238 
 
 .63395 
 
 474 
 
 .74062 
 
 463 
 
 97750 
 
 4,4 
 
 .0230 
 
 
 .239 
 
 .63869 
 
 475 
 
 .74525 
 
 464 
 
 97754 
 
 4,4 
 
 .0230 
 
 
 2.240 
 
 4-64344 
 
 475 
 
 4.74989 
 
 464 
 
 0-97759 
 
 4,4 
 
 1.0229 
 
 o,5 
 
 .241 
 
 .64819 
 
 475 
 
 .75454 
 
 465 
 
 .97763 
 
 4,4 
 
 .0229 
 
 
 .242 
 
 .65295 
 
 476 
 
 .75919 
 
 465 
 
 97768 
 
 4,4 
 
 .0228 
 
 
 .243 
 
 .65771 
 
 476 
 
 .76385 
 
 466 
 
 97772 
 
 4,4 
 
 .0228 
 
 
 .244 
 
 .66247 
 
 477 
 
 .76851 
 
 466 
 
 .97776 
 
 4,4 
 
 .0227 
 
 
 2.245 
 
 4.66724 
 
 477 
 
 4.77317 
 
 467 
 
 0.97781 
 
 4,4 
 
 1.0227 
 
 o,5 
 
 .246 
 
 .67202 
 
 478 
 
 .77784 
 
 467 
 
 .97785 
 
 4,4 
 
 .0227 
 
 
 .247 
 
 .67680 
 
 478 
 
 .78252 
 
 468 
 
 97790 
 
 4,4 
 
 .0226 
 
 
 .248 
 
 .68158 
 
 479 
 
 .78719 
 
 468 
 
 97794 
 
 4,4 
 
 .0226 
 
 
 .249 
 
 .68637 
 
 479 
 
 .79188 
 
 469 
 
 .97798 
 
 4,4 
 
 .0225 
 
 
 2.250 
 
 4.69117 
 
 480 
 
 4.79657 
 
 469 
 
 0.97803 
 
 4,3 
 
 1.0225 
 
 o,5 
 
 u 
 
 tan gd u 
 
 Fo' 
 
 tec gd u 
 
 Fo' 
 
 sin ad u 
 
 Fo' 
 
 esc ad u 
 
 F ' 
 
 SMITHSONIAN T*ai.r 
 
 150 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinh u 
 
 F ' 
 
 cosh u 
 
 F ' 
 
 tanh u 
 
 F " 
 
 coth u 
 
 Fo' 
 
 2.250 
 
 4.69117 
 
 480 
 
 4.79657 
 
 469 
 
 0.97803 
 
 4,3 
 
 I.O225 
 
 o,5 
 
 .251 
 
 69597 
 
 480 
 
 .80126 
 
 470 
 
 .97807 
 
 4,3 
 
 .O224 
 
 
 .252 
 
 .70077 
 
 481 
 
 .80596 
 
 470 
 
 .97811 
 
 4,3 
 
 .O224 
 
 
 .253 
 
 .70558 
 
 4 8l 
 
 .81066 
 
 471 
 
 .978l6 
 
 4,3 
 
 .O223 
 
 
 - .254 
 
 .71039 
 
 482 
 
 .81537 
 
 471 
 
 .97820 
 
 4,3 
 
 .0223 
 
 o,5 
 
 2.255 
 
 4.71521 
 
 482 
 
 4.82008 
 
 472 
 
 0.97824 
 
 4,3 
 
 I.O222 
 
 0,4 
 
 .256 
 
 .72003 
 
 482 
 
 .82480 
 
 472 
 
 .97829 
 
 4,3 
 
 .O222 
 
 
 .257 
 
 .72486 
 
 483 
 
 .82952 
 
 472 
 
 .97833 
 
 4,3 
 
 .O222 
 
 
 .258 
 
 .72069 
 
 483 
 
 .83425 
 
 473 
 
 .97837 
 
 4,3 
 
 .O22I 
 
 
 259 
 
 .73453 
 
 484 
 
 .83898 
 
 473 
 
 .97841 
 
 4,3 
 
 .0221 
 
 
 2.260 
 
 4-73937 
 
 484 
 
 4.84372 
 
 474 
 
 0.97846 
 
 4,3 
 
 I.O22O 
 
 OA 
 
 .261 
 
 .74422 
 
 485 
 
 .84846 
 
 474 
 
 .97850 
 
 4,3 
 
 .O22O 
 
 
 .262 
 
 .74907 
 
 485 
 
 .85321 
 
 475 
 
 .97854 
 
 4,2 
 
 .O2I9 
 
 
 .263 
 
 75392 
 
 486 
 
 .85796 
 
 475 
 
 .97858 
 
 4,2 
 
 .O2I9 
 
 
 .264 
 
 .75878 
 
 486 
 
 .86272 
 
 476 
 
 .97863 
 
 4,2 
 
 .0218 
 
 
 2.265 
 
 4.76365 
 
 487 
 
 4.86748 
 
 476 
 
 0.97867 
 
 4,2 
 
 I. 02l8 
 
 0,4 
 
 .266 
 
 .76852 
 
 487 
 
 .87224 
 
 477 
 
 .97871 
 
 4,2 
 
 .0218 
 
 
 .267 
 
 77339 
 
 488 
 
 .87701 
 
 477 
 
 .97875 
 
 4,2 
 
 .0217 
 
 
 .268 
 
 .77827 
 
 488 
 
 .88179 
 
 478 
 
 .97879 
 
 4,2 
 
 .O2I7 
 
 
 .269 
 
 .78316 
 
 489 
 
 .88657 
 
 478 
 
 .97884 
 
 4,2 
 
 .0216 
 
 
 2.270 
 
 4.78804 
 
 489 
 
 4.89136 
 
 479 
 
 0.97888 
 
 4,2 
 
 I. 02l6 
 
 0,4 
 
 .271 
 
 .79294 
 
 490 
 
 .89615 
 
 479 
 
 .97892 
 
 4,2 
 
 .O2I5 
 
 
 .272 
 
 .79784 
 
 490 
 
 .90094 
 
 480 
 
 .97896 
 
 4,2 
 
 .O2I5 
 
 
 .273 
 
 .80274 
 
 491 
 
 .90574 
 
 480 
 
 .97900 
 
 4,2 
 
 .0214 
 
 
 274 
 
 .80765 
 
 491 
 
 91055 
 
 481 
 
 .97905 
 
 4,1 
 
 .O2I4 
 
 
 2.275 
 
 4.81256 
 
 492 
 
 4.91536 
 
 481 
 
 0.97909 
 
 4,1 
 
 I.O2I4 
 
 0,4 
 
 .276 
 
 .81748 
 
 492 
 
 .92017 
 
 482 
 
 .97913 
 
 4,1 
 
 .0213 
 
 
 .277 
 
 .82240 
 
 492 
 
 .92499 
 
 482 
 
 .97917 
 
 4,1 
 
 .0213 
 
 
 .278 
 
 .82733 
 
 493 
 
 .92982 
 
 483 
 
 .97921 
 
 4,1 
 
 .O2I2 
 
 
 .279 
 
 .83226 
 
 493 
 
 .93465 
 
 483 
 
 .97925 
 
 4,1 
 
 .O2I2 
 
 
 2.280 
 
 4.83720 
 
 494 
 
 4.93948 
 
 484 
 
 0.97929 
 
 4,1 
 
 I. 021 I 
 
 0,4 
 
 .281 
 
 .84214 
 
 494 
 
 .94432 
 
 484 
 
 97933 
 
 4,1 
 
 .O2II 
 
 
 .282 
 
 .84709 
 
 495 
 
 .94917 
 
 485 
 
 97937 
 
 4,1 
 
 .O2I I 
 
 
 .283 
 
 .85204 
 
 495 
 
 .95402 
 
 485 
 
 97942 
 
 4,1 
 
 .O2IO 
 
 
 .284 
 
 .85699 
 
 496 
 
 .95887 
 
 486 
 
 .97946 
 
 4,1 
 
 .O2IO 
 
 
 2.285 
 
 4.86196 
 
 496 
 
 4.96373 
 
 486 
 
 0.97950 
 
 4,1 
 
 I.O2O9 
 
 0,4 
 
 .286 
 
 .86692 
 
 497 
 
 .96859 
 
 487 
 
 97954 
 
 4,1 
 
 .O2O9 
 
 
 .287 
 
 .87189 
 
 497 
 
 .97346 
 
 487 
 
 .97958 
 
 4,o 
 
 .0208 
 
 
 .288 
 
 .87687 
 
 498 
 
 .97834 
 
 488 
 
 .97962 
 
 4,0 
 
 .0208 
 
 
 .289 
 
 .88185 
 
 498 
 
 .98322 
 
 488 
 
 .97966 
 
 4,0 
 
 .0208 
 
 
 2.290 
 
 4.88684 
 
 499 
 
 4.98810 
 
 489 
 
 0.97970 
 
 4,0 
 
 I.O2O7 
 
 0,4 
 
 .291 
 
 .89183 
 
 499 
 
 .99299 
 
 489 
 
 .97974 
 
 4,0 
 
 .O2O7 
 
 
 .292 
 
 .89682 
 
 500 
 
 .99789 
 
 490 
 
 .97978 
 
 4,0 
 
 .0206 
 
 
 293 
 
 .90182 
 
 500 
 
 5.00279 
 
 490 
 
 .97982 
 
 40 
 
 .02O6 
 
 
 .294 
 
 .90683 
 
 501 
 
 .00769 
 
 491 
 
 .97986 
 
 4,0 
 
 .O2O6 
 
 
 2.295 
 
 4.91184 
 
 5oi 
 
 5.01260 
 
 491 
 
 0.97990 
 
 4,o 
 
 I.O2O5 
 
 0,4 
 
 .296 
 
 .91685 
 
 502 
 
 .01751 
 
 492 
 
 .97994 
 
 4,0 
 
 .O2O5 
 
 
 .297 
 
 .92187 
 
 502 
 
 .02243 
 
 492 
 
 .97998 
 
 4,0 
 
 .O2O4 
 
 
 .298 
 
 .92690 
 
 503 
 
 .02736 
 
 493 
 
 .98002 
 
 4,0 
 
 .02O4 
 
 
 .299 
 
 .93193 
 
 503 
 
 .03229 
 
 493 
 
 .98006 
 
 3,9 
 
 .0203 
 
 
 2.300 
 
 4.93696 
 
 504 
 
 5.03722 
 
 494 
 
 0.98010 
 
 3,9 
 
 1.0203 
 
 0,4 
 
 u 
 
 tan gd u 
 
 Fo' 
 
 sec gd u 
 
 Fo' 
 
 sin gd u 
 
 F ' 
 
 csc gd u 
 
 F ' 
 
 SMITHSONIAN TABLES 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinh u 
 
 F ' 
 
 cosh u 
 
 <-FO' 
 
 tanh u 
 
 F* 
 
 cothu 
 
 F O ' 
 
 2.300 
 
 4.93096 
 
 504 
 
 5.03722 
 
 494 
 
 0.98010 
 
 3,9 
 
 1.0203 
 
 0,4 
 
 .301 
 
 .94200 
 
 504 
 
 .04216 
 
 494 
 
 .98014 
 
 3,9 
 
 .0203 
 
 
 .302 
 
 94705 
 
 505 
 
 .04710 
 
 495 
 
 .98018 
 
 3,9 
 
 .0202 
 
 
 .303 
 
 .95210 
 
 505 
 
 .05205 
 
 495 
 
 .98021 
 
 3,9 
 
 .O2O2 
 
 
 .304 
 
 .95715 
 
 506 
 
 .05701 
 
 496 
 
 .98025 
 
 3,9 
 
 .O2OI 
 
 
 2.305 
 
 4.96221 
 
 506 
 
 5.06197 
 
 496 
 
 0.08029 
 
 3,9 
 
 I. 0201 
 
 04 
 
 .306 
 
 .96727 
 
 507 
 
 .06693 
 
 497 
 
 .98033 
 
 3,9 
 
 .02OI 
 
 
 .307 
 
 97234 
 
 507 
 
 .07100 
 
 497 
 
 .98037 
 
 3,9 
 
 .O2OO 
 
 
 .308 
 
 97742 
 
 508 
 
 .07688 
 
 498 
 
 .98041 
 
 3,9 
 
 .02OO 
 
 
 .309 
 
 .98250 
 
 508 
 
 .08186 
 
 498 
 
 98045 
 
 3,9 
 
 .0199 
 
 
 2.310 
 
 4.98758 
 
 509 
 
 5.08684 
 
 499 
 
 0.98049 
 
 3,9 
 
 I.OI99 
 
 0,4 
 
 .311 
 
 .99267 
 
 509 
 
 .09183 
 
 499 
 
 .98053 
 
 3,9 
 
 .0109 
 
 
 .312 
 
 .99777 
 
 5io 
 
 .09683 
 
 500 
 
 .08056 
 
 3,8 
 
 .0108 
 
 
 .313 
 
 5.00286 
 
 5io 
 
 . 10183 
 
 500 
 
 .08060 
 
 3,8 
 
 .0198 
 
 
 .314 
 
 .00797 
 
 5ii 
 
 .10683 
 
 501 
 
 .98064 
 
 3,8 
 
 .0197 
 
 
 2.315 
 
 5.01308 
 
 5ii 
 
 5 ii 184 
 
 50i 
 
 0.98068 
 
 3,8 
 
 1. 0197 
 
 0,4 
 
 .316 
 
 .01819 
 
 512 
 
 .11686 
 
 502 
 
 .98072 
 
 3,8 
 
 .0197 
 
 
 .317 
 
 .02331 
 
 512 
 
 .12188 
 
 502 
 
 .98076 
 
 3,8 
 
 .0196 
 
 
 .318 
 
 .02844 
 
 513 
 
 .12691 
 
 503 
 
 .98079 
 
 3,8 
 
 .0196 
 
 
 .319 
 
 03357 
 
 513 
 
 .13194 
 
 503 
 
 .98083 
 
 3,8 
 
 .0195 
 
 
 2.320 
 
 5.03870 
 
 514 
 
 5.13697 
 
 504 
 
 0.98087 
 
 3,8 
 
 I. 0195 
 
 0,4 
 
 .321 
 
 .04384 
 
 5H 
 
 . 14202 
 
 504 
 
 .98091 
 
 3,8 
 
 .0195 
 
 
 .322 
 
 .04898 
 
 515 
 
 .14706 
 
 505 
 
 .98095 
 
 3,8 
 
 .0194 
 
 
 .323 
 
 .05413 
 
 5i5 
 
 .15211 
 
 505 
 
 .98098 
 
 3,8 
 
 .0194 
 
 
 .324 
 
 .05929 
 
 5i6 
 
 .15717 
 
 506 
 
 .98102 
 
 3,8 
 
 .0193 
 
 
 2.325 
 
 5-06445 
 
 5i6 
 
 5.16223 
 
 506 
 
 0.98106 
 
 3,8 
 
 1.0193 
 
 0,4 
 
 .326 
 
 .06961 
 
 517 
 
 . 16730 
 
 507 
 
 .98110 
 
 3,7 
 
 .0193 
 
 
 .327 
 
 .07478 
 
 517 
 
 . 17237 
 
 507 
 
 .08113 
 
 3,7 
 
 .0192 
 
 
 .328 
 
 .07996 
 
 5i8 
 
 .17745 
 
 508 
 
 .98117 
 
 3,7 
 
 .0192 
 
 
 .329 
 
 .08514 
 
 5i8 
 
 .18253 
 
 509 
 
 .98121 
 
 3,7 
 
 .0192 
 
 
 2.330 
 
 5.09032 
 
 519 
 
 5.18762 
 
 509 
 
 0.98124 
 
 3,7 
 
 1.0191 
 
 0,4 
 
 .331 
 
 .09551 
 
 519 
 
 . 19271 
 
 5io 
 
 .98128 
 
 3,7 
 
 .0191 
 
 
 .332 
 
 .10071 
 
 520 
 
 .19781 
 
 5io 
 
 .98132 
 
 3,7 
 
 .0190 
 
 
 333 
 
 .10591 
 
 520 
 
 .20291 
 
 5H 
 
 .98136 
 
 3,7 
 
 .0190 
 
 
 .334 
 
 .mil 
 
 521 
 
 .20802 
 
 5ii 
 
 98139 
 
 3,7 
 
 .0190 
 
 
 2-335 
 
 5-11632 
 
 521 
 
 5.21314 
 
 512 
 
 0.98143 
 
 3,7 
 
 1.0189 
 
 0,4 
 
 .336 
 
 .12154 
 
 522 
 
 .21825 
 
 512 
 
 .98147 
 
 3,7 
 
 .0189 
 
 
 337 
 
 . 12676 
 
 522 
 
 .22338 
 
 5T3 
 
 .98150 
 
 3,7 
 
 .0188 
 
 
 .338 
 
 .13199 
 
 523 
 
 .22851 
 
 513 
 
 .08154 
 
 3,7 
 
 .0188 
 
 
 339 
 
 . 13722 
 
 523 
 
 .23364 
 
 514 
 
 .98158 
 
 3,7 
 
 .0188 
 
 
 2.340 
 
 5.14245 
 
 524 
 
 5.23878 
 
 514 
 
 0.98161 
 
 3,6 
 
 1.0187 
 
 0,4 
 
 341 
 
 . M770 
 
 524 
 
 .24393 
 
 515 
 
 .98165 
 
 3,6 
 
 .0187 
 
 
 342 
 
 .15294 
 
 525 
 
 .24908 
 
 515 
 
 .98169 
 
 3,6 
 
 .0187 
 
 
 343 
 
 .15819 
 
 525 
 
 .25423 
 
 5i6 
 
 .98172 
 
 3,6 
 
 .0186 
 
 
 344 
 
 16345 
 
 526 
 
 .25939 
 
 5i6 
 
 .98176 
 
 3,6 
 
 .0186 
 
 
 2.345 
 
 5.16871 
 
 526 
 
 5.26456 
 
 517 
 
 0.98179 
 
 3,6 
 
 1.0185 
 
 0,4 
 
 .346 
 
 .17398 
 
 527 
 
 .26973 
 
 517 
 
 .98183 
 
 3,6 
 
 .0185 
 
 
 347 
 
 . 17925 
 
 527 
 
 .27491 
 
 5i8 
 
 .98187 
 
 3,6 
 
 .0185 
 
 
 .348 
 
 .18453 
 
 528 
 
 .28009 
 
 5i8 
 
 .98190 
 
 3,6 
 
 .0184 
 
 
 349 
 
 .18981 
 
 529 
 
 .28528 
 
 519 
 
 98194 
 
 3,6 
 
 .0184 
 
 
 2.350 
 
 5.I95IO 
 
 529 
 
 5.20047 
 
 520 
 
 O.o8l97 
 
 3,6 
 
 I. 0184 
 
 0,4 
 
 u 
 
 tan gd u 
 
 Fo' 
 
 sec od u 
 
 Fo' 
 
 sin gd u 
 
 Ft* 
 
 esc ad u 
 
 Fo' 
 
 SMITHSONIAN TABLCS 
 
 152 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinh u 
 
 Fu' 
 
 cosh u 
 
 <-Fo' 
 
 tanhu 
 
 F ' 
 
 coth u 
 
 <" Fo' 
 
 2.350 
 
 5.I95IO 
 
 529 
 
 5.20047 
 
 520 
 
 0.98197 
 
 3,6 
 
 1.0184 
 
 0,4 
 
 .351 
 
 .20039 
 
 530 
 
 .29567 
 
 520 
 
 .98201 
 
 3,6 
 
 .0183 
 
 
 .352 
 
 .20569 
 
 530 
 
 .30087 
 
 521 
 
 .98204 
 
 3,6 
 
 .0183 
 
 
 353 
 
 .2IIOO 
 
 531 
 
 .30608 
 
 521 
 
 .98208 
 
 3,6 
 
 .0182 
 
 
 .^54 
 
 .21630 
 
 531 
 
 .3H29 
 
 522 
 
 .98212 
 
 3,5 
 
 .0182 
 
 
 2.355 
 
 5.22162 
 
 532 
 
 5.3I65I 
 
 522 
 
 0.98215 
 
 3,5 
 
 1.0182 
 
 0,4 
 
 .356 
 
 .22694 
 
 532 
 
 .32174 
 
 523 
 
 .98219 
 
 3,5 
 
 .Oi8l 
 
 
 .357 
 
 .23226 
 
 533 
 
 .32697 
 
 523 
 
 .08222 
 
 3,5 
 
 .Ol8l 
 
 
 358 
 
 .23759 
 
 533 
 
 33220 
 
 524 
 
 .98226 
 
 3,5 
 
 .Ol8l 
 
 
 359 
 
 .24293 
 
 534 
 
 33744 
 
 524 
 
 .98229 
 
 3,5 
 
 .0180 
 
 
 2.360 
 
 5.24827 
 
 534 
 
 5.34209 
 
 525 
 
 0.98233 
 
 3,5 
 
 1.0180 
 
 0,4 
 
 .361 
 
 .25361 
 
 535 
 
 34794 
 
 525 
 
 .98236 
 
 3,5 
 
 .0180 
 
 
 .362 
 
 .25896 
 
 535 
 
 .35319 
 
 526 
 
 .98240 
 
 3,5 
 
 .0179 
 
 
 .363 
 
 .26432 
 
 536 
 
 .35845 
 
 526 
 
 .98243 
 
 3,5 
 
 .0179 
 
 
 .364 
 
 .26968 
 
 536 
 
 .36372 
 
 527 
 
 .98247 
 
 3,5 
 
 .0178 
 
 
 2.365 
 
 5.27504 
 
 537 
 
 5.36899 
 
 528 
 
 0.98250 
 
 3,5 
 
 1.0178 
 
 0,4 
 
 .366 
 
 .28042 
 
 537 
 
 .37427 : 528 
 
 .98254 
 
 3,5 
 
 .0178 
 
 
 .367 
 
 .28579 
 
 538 
 
 .37955 529 
 
 .98257 
 
 3,5 
 
 .0177 
 
 
 .368 
 
 .29118 
 
 538 
 
 .38484 1 529 
 
 .98261 
 
 3,4 
 
 .0177 
 
 
 .369 
 
 .29656 
 
 539 
 
 .39014 
 
 530 
 
 .98264 
 
 3,4 
 
 .0177 
 
 
 2.370 
 
 5.30196 
 
 540 
 
 5.39544 
 
 530 
 
 0.98267 
 
 3,4 
 
 1.0176 
 
 0,4 
 
 371 
 
 30735 
 
 540 
 
 .40074 ! 531 
 
 .98271 
 
 3,4 
 
 .0176 
 
 
 372 
 
 .31276 
 
 541 
 
 .40605 531 
 
 .98274 
 
 3,4 
 
 .0176 
 
 
 373 
 
 .31817 
 
 541 
 
 .4H37 I 532 
 
 .98278 
 
 3,4 
 
 0175 
 
 
 374 
 
 .32358 
 
 542 
 
 .41669 
 
 532 
 
 .98281 
 
 3,4 
 
 0175 
 
 
 2.375 
 
 5.32900 
 
 542 
 
 5.42201 
 
 533 
 
 0.98285 
 
 3,4 
 
 1.0175 
 
 0,4 
 
 .376 
 
 33442 
 
 543 
 
 .42735 533 
 
 .98288 
 
 3,4 
 
 .0174 
 
 0,4 
 
 377 
 
 .33985 
 
 543 
 
 .43268 534 
 
 .98291 
 
 3,4 
 
 .0174 
 
 0,4 
 
 .378 
 
 .34529 
 
 544 
 
 .43803 535 
 
 .98295 
 
 3,4 
 
 .0173 
 
 o,3 
 
 379 
 
 .35073 
 
 544 
 
 .44337 
 
 535 
 
 .98298 
 
 3,4 
 
 .0173 
 
 0,3 
 
 2.380 
 
 5.35618 
 
 545 
 
 5.44873 
 
 536 
 
 0.98301 
 
 3,4 
 
 1.0173 
 
 0,3 
 
 .381 
 
 .36163 
 
 545 
 
 .45409 
 
 536 
 
 98305 
 
 3,4 
 
 .0172 
 
 
 .382 
 
 .36708 
 
 546 
 
 45945 
 
 537 
 
 .98308 
 
 3,4 
 
 .0172 
 
 
 383 
 
 .37255 
 
 546 
 
 .46482 
 
 537 
 
 .98311 
 
 3,3 
 
 .0172 
 
 
 .384 
 
 .37801 
 
 547 
 
 .47020 
 
 538 
 
 .98315 
 
 3,3 
 
 .0171 
 
 
 2.385 
 
 5.38349 
 
 548 
 
 5.47558 
 
 538 
 
 0.98318 
 
 3,3 
 
 1.0171 
 
 . 0,3 
 
 .386 
 
 .38897 
 
 548 
 
 .48096 
 
 539 
 
 .98322 
 
 3,3 
 
 .0171 
 
 
 .387 
 
 39445 
 
 549 
 
 48635 
 
 539 
 
 98325 
 
 3,3 
 
 .0170 
 
 
 .388 
 
 39994 
 
 549 
 
 .49175 
 
 540 
 
 .98328 
 
 3,3 
 
 .0170 
 
 
 .389 
 
 40543 
 
 550 
 
 .49715 
 
 541 
 
 .98331 
 
 3,3 
 
 .6170 
 
 
 2.390 
 
 5.41093 
 
 550 
 
 5.50256 
 
 541 
 
 0.08335 
 
 3,3 
 
 1.0169 
 
 o,3 
 
 391 
 
 .41644 
 
 551 
 
 .50798 542 
 
 .98338 
 
 3,3 
 
 .0169 
 
 
 392 
 
 .42195 
 
 551 
 
 .51339 ! 542 
 
 .98341 
 
 3,3 
 
 .0169 
 
 
 393 
 
 .42746 
 
 552 
 
 .51882 : 543 
 
 .98345 
 
 3,3 
 
 .0168 
 
 
 394 
 
 .43299 
 
 552 
 
 .52425 543 
 
 .98348 
 
 3,3 
 
 .0168 
 
 
 2.395 
 
 5.43851 
 
 553 
 
 5.52969 544 
 
 0.98351 
 
 3,3 
 
 1.0168 
 
 o,3 
 
 .396 
 
 .44405 
 
 554 
 
 .53513 1 544 
 
 .98354 
 
 3,3 
 
 .0167 
 
 
 .397 
 
 .44958 
 
 554 
 
 .54057 ' 545 
 
 .98358 
 
 3,3 
 
 .0167 
 
 
 .398 
 
 .45513 
 
 555 
 
 .54603 546 
 
 .98361 
 
 3,3 
 
 .0167 
 
 
 399 
 
 .46068 
 
 555 
 
 .55148 
 
 546 
 
 98364 
 
 3,2 
 
 .0166 
 
 
 2.400 
 
 5.46623 
 
 556 
 
 5.55095 
 
 547 
 
 0.98367 
 
 3,2 
 
 i. 0166 
 
 o,3 
 
 u 
 
 tan gd u 
 
 -Fo' 
 
 sec gd u < F</ 
 
 sin ad u 
 
 Fo' 
 
 esc gd u 
 
 F ' 
 
 SMITHSONIAN TABLES 
 
 153 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinh u 
 
 F ' 
 
 cosh u 
 
 -FO' 
 
 tanhu 
 
 F f 
 
 coth u 
 
 F ' 
 
 2.400 
 
 5.46623 
 
 556 
 
 5.55695 
 
 547 
 
 0.98367 
 
 3,2 
 
 I. Ol66 
 
 0,3 
 
 .401 
 
 .47179 
 
 556 
 
 .56242 
 
 547 
 
 .98371 
 
 3,2 
 
 .0166 
 
 
 .402 
 
 47735 
 
 557 
 
 .56789 
 
 548 
 
 .98374 
 
 3,2 
 
 .0165 
 
 
 .403 
 
 .48292 
 
 557 
 
 57337 
 
 548 
 
 .98377 
 
 3,2 
 
 .0165 
 
 
 .404 
 
 .48850 
 
 558 
 
 .57886 
 
 549 
 
 .98380 
 
 3,2 
 
 .0165 
 
 
 2.405 
 
 5.49408 
 
 558 
 
 5.58435 
 
 549 
 
 0.98384 
 
 3,2 
 
 1.0164 
 
 o,3 
 
 .406 
 
 .49967 
 
 559 
 
 58984 
 
 550 
 
 .98387 
 
 3,2 
 
 .0164 
 
 
 .407 
 
 .50526 
 
 560 
 
 .59535 
 
 551 
 
 98390 
 
 3,2 
 
 . .0164 
 
 
 .408 
 
 .51086 
 
 560 
 
 .60086 
 
 551 
 
 .98393 
 
 3,2 
 
 .0163 
 
 
 .409 
 
 .51646 
 
 56i 
 
 .60637 
 
 552 
 
 .98396 
 
 3,2 
 
 .0163 
 
 
 2.410 
 
 5.52207 
 
 56i 
 
 5.61189 
 
 552 
 
 0.98400 
 
 3,2 
 
 I.OI63 
 
 0,3 
 
 .411 
 
 .52769 
 
 562 
 
 .61741 
 
 553 
 
 .98403 
 
 3,2 
 
 .Ol62 
 
 
 .412 
 
 
 562 
 
 .62294 
 
 553 
 
 .98406 
 
 3,2 
 
 .Ol62 
 
 
 .413 
 
 .53893 
 
 563 
 
 .62848 
 
 554 
 
 .98409 
 
 3,2 
 
 .0162 
 
 
 .414 
 
 544-56 
 
 563 
 
 .63402 
 
 554 
 
 .98412 
 
 3,2 
 
 .Ol6l 
 
 
 2.415 
 
 5-55020 
 
 564 
 
 5.63957 
 
 555 
 
 0.98415 
 
 3J 
 
 1.0161 
 
 o,3 
 
 .416 
 
 .55584 
 
 565 
 
 .64512 
 
 556 
 
 .98418 
 
 3,1 
 
 .0161 
 
 
 .417 
 
 .56149 
 
 565 
 
 .65068 
 
 556 
 
 .98422 
 
 3,1 
 
 .0160 
 
 
 .418 
 
 .56715 
 
 566 
 
 .65624 
 
 557 
 
 .98425 
 
 3,1 
 
 .0160 
 
 
 .419 
 
 .57280 
 
 566 
 
 .66181 
 
 557 
 
 .98428 
 
 3,1 
 
 .0160 
 
 
 2.420 
 
 5.57847 
 
 567 
 
 5.66739 
 
 558 
 
 0.98431 
 
 3,1 
 
 1.0159 
 
 o,3 
 
 .421 
 
 .58414 
 
 567 
 
 .67297 
 
 558 
 
 .98434 
 
 3,1 
 
 .0159 
 
 
 .422 
 
 .58981 
 
 568 
 
 .67856 
 
 559 
 
 98437 
 
 3J 
 
 .0159 
 
 
 .423 
 
 59550 
 
 568 
 
 .68415 
 
 5 6o 
 
 98440 
 
 3,1 
 
 .0158 
 
 
 .424 
 
 .60118 
 
 569 
 
 .68975 
 
 560 
 
 .98443 
 
 3,1 
 
 .0158 
 
 
 2.425 
 
 5.60688 
 
 570 
 
 5.69535 
 
 56i 
 
 0.98446 
 
 3,1 
 
 1.0158 
 
 o,3 
 
 .426 
 
 .61257 
 
 570 
 
 .70096 
 
 56i 
 
 .98450 
 
 3,1 
 
 0157 
 
 
 .427 
 
 .61828 
 
 571 
 
 .70658 
 
 562 
 
 .98453 
 
 3,1 
 
 0157 
 
 
 .428 
 
 .62399 
 
 57i 
 
 .71220 
 
 562 
 
 .98456 
 
 3,1 
 
 0157 
 
 
 .429 
 
 .62970 
 
 572 
 
 .71783 
 
 563 
 
 .98459 
 
 3,1 
 
 0157 
 
 
 2.430 
 
 5.63542 
 
 572 
 
 5.72346 
 
 564 
 
 0.98462 
 
 3J 
 
 1.0156 
 
 0,3 
 
 .431 
 
 .64115 
 
 573 
 
 .72910 
 
 564 
 
 98465 
 
 3,0 
 
 .0156 
 
 
 .432 
 
 .64688 
 
 573 
 
 73474 
 
 565 
 
 .98468 
 
 3,0 
 
 .0156 
 
 
 433 
 
 .65262 
 
 574 
 
 74039 
 
 565 
 
 08471 
 
 3,o 
 
 0155 
 
 
 434 
 
 .65836 
 
 575 
 
 74605 
 
 566 
 
 .98474 
 
 3,0 
 
 0155 
 
 
 2.435 
 
 5.66411 
 
 575 
 
 5.75I7I 
 
 566 
 
 0.98477 
 
 3,o 
 
 1.0155 
 
 o,3 
 
 .436 ! .66986 
 
 576 
 
 .75738 
 
 567 
 
 .08480 
 
 3,o 
 
 0154 
 
 
 437 
 
 67563 
 
 576 
 
 76305 
 
 568 
 
 .08483 
 
 3,o 
 
 .0154 
 
 
 .438 
 
 .68139 
 
 577 
 
 76873 
 
 568 
 
 .98485 
 
 3,0 
 
 .0154 
 
 
 439 
 
 .68716 
 
 577 
 
 77441 
 
 569 
 
 .98489 
 
 3,0 
 
 .0153 
 
 
 2.440 
 
 5.69294 
 
 578 
 
 5.78010 
 
 569 
 
 0.98492 
 
 3,0 
 
 i. 0153 
 
 o,3 
 
 .441 
 
 .69872 
 
 579 
 
 .78580 
 
 570 
 
 .98495 
 
 3,o 
 
 0153 
 
 
 .442 
 
 .70451 
 
 579 
 
 .79150 
 
 570 
 
 .98498 
 
 3,o 
 
 .0152 
 
 
 443 
 
 .71031 
 
 580 
 
 79721 
 
 571 
 
 .98501 
 
 3,o 
 
 .0152 
 
 
 .444 
 
 .71611 
 
 58o 
 
 .80292 
 
 572 
 
 .98504 
 
 3,0 
 
 .0152 
 
 
 2.445 
 
 5.72I9I 
 
 58i 
 
 5.80864 
 
 572 
 
 0.98507 
 
 3,0 
 
 1.0152 
 
 0,3 
 
 .446 
 
 .72772 
 
 58i 
 
 .81436 
 
 573 
 
 .98510 
 
 3,0 
 
 .0151 
 
 
 447 
 
 73354 
 
 582 
 
 .82009 
 
 573 
 
 .98513 
 
 3,0 
 
 .0151 
 
 
 .448 
 
 .73936 
 
 583 
 
 .82583 
 
 574 
 
 .98516 
 
 2,9 
 
 .0151 
 
 
 .449 
 
 .74519 
 
 583 
 
 .83157 
 
 575 
 
 .98519 
 
 2,9 
 
 .0150 
 
 
 2.450 
 
 5.75103 
 
 584 
 
 5.83732 
 
 575 
 
 0.98522 
 
 2,9 
 
 1.0150 
 
 0,3 
 
 u 
 
 tan gd u 
 
 <- F,,' 
 
 sec gd u 
 
 -Fo' 
 
 sin gd u 
 
 F ' 
 
 esc gd u 
 
 FO' 
 
 SMITHSONIAN TABLCS 
 
 154 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinhu 
 
 Fo' 
 
 cosh u 
 
 F ' 
 
 tanhu 
 
 -FO' 
 
 cothu 
 
 F O ' 
 
 2.450 
 
 5.75103 
 
 584 
 
 5.83732 
 
 575 
 
 0.98522 
 
 2,9 
 
 1.0150 
 
 0,3 
 
 .451 
 
 .75687 
 
 584 
 
 
 576 
 
 .98525 
 
 2,9 
 
 .0150 
 
 
 .452 
 
 .76271 
 
 585 
 
 .84883 
 
 576 
 
 .98528 
 
 2,9 
 
 .0149 
 
 
 / .453 
 
 .76856 
 
 585 
 
 .85460 
 
 577 
 
 .98530 
 
 2,9 
 
 .0149 
 
 
 454 
 
 77442 
 
 586 
 
 .86037 
 
 577 
 
 .98533 
 
 2,9 
 
 .0149 
 
 
 2.455 
 
 5.78029 
 
 587 
 
 5.86615 
 
 578 
 
 0.98536 
 
 2,9 
 
 1.0149 
 
 0,3 
 
 .456 
 
 .78615 ' 
 
 587 
 
 .87193 
 
 579 
 
 .98539 
 
 2,9 
 
 .0148 
 
 
 457 
 
 .79203 
 
 588 
 
 .87772 
 
 579 
 
 '.98542 
 
 2,9 
 
 .0148 
 
 
 .458 
 
 .79791 
 
 588 
 
 .88352 
 
 580 
 
 .98545 
 
 2,9 
 
 .0148 
 
 
 459 
 
 .80380 
 
 589 
 
 .88932 
 
 580 
 
 .98548 
 
 2,9 
 
 .0147 
 
 
 2.460 
 
 5.80969 
 
 590 
 
 5.89512 
 
 58i 
 
 0.98551 
 
 2,9 
 
 I. 0147 
 
 0,3 
 
 .461 
 
 .81559 
 
 590 
 
 .90094 
 
 582 
 
 .98554 
 
 2,9 
 
 .0147 
 
 
 .462 
 
 .82149 
 
 59i 
 
 .90675 
 
 582 
 
 .98556 
 
 2,9 
 
 .0146 
 
 
 .463 
 
 .82740 
 
 59i 
 
 .91258 
 
 583 
 
 .98559 
 
 2,9 
 
 .0146 
 
 
 .464 
 
 .83332 
 
 592 
 
 .91841 
 
 583 
 
 .98562 
 
 2,9 
 
 ^ .0146 
 
 
 2.465 
 
 5.83924 
 
 592 
 
 5.92425 
 
 584 
 
 0.98565 
 
 2,8 
 
 1.0146 
 
 0,3 
 
 .466 
 
 .84516 
 
 593 
 
 .93009 
 
 585 
 
 .98568 
 
 2,8 
 
 .0145 
 
 
 .467 
 
 .85110 
 
 594 
 
 .93594 
 
 585 
 
 .98571 
 
 2,8 
 
 .0145 
 
 
 .468 
 
 .85704 
 
 594 
 
 .94179 
 
 586 
 
 .98574 
 
 2,8 
 
 .0145 
 
 
 .469 
 
 .86298 
 
 595 
 
 .94765 
 
 586 
 
 .98576 
 
 2,8 
 
 .0144 
 
 
 2.470 
 
 5.86893 
 
 595 
 
 5-95352 
 
 .587 
 
 O.Q8579 
 
 2,8 
 
 1.0144 
 
 0,3 
 
 .471 
 .472 
 
 .87489 
 .88085 
 
 596 
 
 597 
 
 95939 
 .96527 
 
 ft 
 
 .98582 
 .98585- 
 
 2,8 
 2,8 
 
 .0144 
 
 .0144 
 
 
 473 
 
 .88682 
 
 597 
 
 .97H5 
 
 589 
 
 .98588 
 
 2,8 
 
 .0143 
 
 
 474 
 
 .89279 
 
 498 
 
 .97704 
 
 589 
 
 .98590 
 
 2,8 
 
 .0143 
 
 
 2.475 
 
 S.89877 
 
 598 
 
 5.98294 
 
 590 
 
 0.98593 
 
 2,8 
 
 I. 0143 
 
 0,3 
 
 .476 
 
 .90476 
 
 599 
 
 .98884 
 
 59i 
 
 .98596 
 
 2,8 
 
 .0142 
 
 
 477 
 
 91075 
 
 599 
 
 .99474 
 
 59i 
 
 .98599 
 
 2,8 
 
 .0142 
 
 
 .478 
 
 .91675 
 
 600 
 
 6.00066 
 
 592 
 
 .98602 
 
 2,8 
 
 .0142 
 
 
 479 
 
 .92275 
 
 601 
 
 .00658 
 
 592 
 
 .98604 
 
 2,8 
 
 .0142 
 
 
 2.480 
 
 5.92876 
 
 601 
 
 6 .01250 
 
 593 
 
 0.98607 
 
 2,8 
 
 1.0141 
 
 0,3 
 
 .481 
 
 .93478 
 
 602 
 
 .01844 
 
 593 
 
 .98610 
 
 2,8 
 
 .0141 
 
 
 .482 
 
 .94080 
 
 602 
 
 .02437 
 
 594 
 
 .98613 
 
 2,8 
 
 .0141 
 
 
 .483 
 
 .94682 
 
 603 
 
 .03032 
 
 595 
 
 .98615 
 
 2,7 
 
 .0140 
 
 
 .484 
 
 .95286 
 
 604 
 
 .03627 
 
 595 
 
 .98618 
 
 2,7 
 
 .0140 
 
 
 2.485. 
 
 5.95890 
 
 604 
 
 6.04222 
 
 596 
 
 0.08621 
 
 2,7 
 
 1.0140 
 
 0,3 
 
 .486 
 
 .96494 
 
 605 
 
 .04818 
 
 596 
 
 .98624 
 
 2,7 
 
 .0140 
 
 
 487 
 
 .97099 
 
 605 
 
 05415 
 
 597 
 
 .98626 
 
 2,7 
 
 .0139 
 
 
 .488 
 
 .97705 
 
 606 
 
 .06013 
 
 598 
 
 .98629 
 
 2,7 
 
 .0139 
 
 
 .489 
 
 .08311 
 
 607 
 
 .06611 
 
 598 
 
 .98632 
 
 2,7 
 
 .0139 
 
 
 2.490 
 
 5.98918 
 
 607 
 
 6.07209 
 
 599 
 
 0.98635 
 
 2,7 
 
 1.0138 
 
 0,3 
 
 .491 
 
 .99526 
 
 608 
 
 .07809 
 
 000 
 
 .9S637 
 
 2,7 
 
 .0138 
 
 
 .492 
 
 6.00134 
 
 608 
 
 .08408 
 
 600 
 
 .98640 
 
 2,7 
 
 .0138 
 
 
 493 
 
 .00743 
 
 609 
 
 .00009 
 
 601 
 
 .98643 
 
 2,7 
 
 .0138 
 
 
 494 
 
 .01352 
 
 610 
 
 .09610 
 
 601 
 
 .98645 
 
 2,7 
 
 .0137 
 
 
 2.495 
 
 6.01962 
 
 610 
 
 6.IO2II 
 
 602 
 
 0.98648 
 
 2,7 
 
 I. 0137 
 
 0,3 
 
 .496 
 
 .02572 
 
 611 
 
 . 10814 
 
 603 
 
 .98651 
 
 2,7 
 
 .0137 
 
 
 497 
 
 .03183 
 
 611 
 
 .11417 
 
 603 
 
 .98653 
 
 2,7 
 
 .0136 
 
 
 .498 
 
 03795 
 
 612 
 
 . 12020 
 
 604 
 
 .98656 
 
 2,7 
 
 .0136 
 
 
 .499 
 
 .04408 
 
 613 
 
 . 12624 
 
 604 
 
 .98659 
 
 2,7 
 
 .0136 
 
 
 2.500 
 
 6.05020 
 
 613 
 
 6.13229 
 
 605 
 
 0.98661 
 
 2,7 
 
 1.0136 
 
 Q,3 
 
 u 
 
 tan gd u 
 
 F O ' 
 
 sec gd u 
 
 -PC' 
 
 sin gd u 
 
 Fo' 
 
 csc gd u 
 
 F ' 
 
 SMITHSONIAN TABLES 
 
 155 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinh u 
 
 F ' 
 
 cosh u 
 
 IV 
 
 tanh u 
 
 W Fo' 
 
 coth u 
 
 ~ Fo' 
 
 2.500 
 
 6.05020 
 
 6l 3 
 
 6. 13229 
 
 605 
 
 0.98661 
 
 2,7 
 
 1.0136 
 
 0,3 
 
 .501 
 
 .05634 
 
 614 
 
 .13834 
 
 606 
 
 .98664 
 
 2,7 
 
 .0135 
 
 
 .502 
 
 .06248 
 
 614 
 
 .14440 
 
 606 
 
 .98667 
 
 2,6 
 
 .0135 
 
 
 .503 
 
 .06863 
 
 615 
 
 .15047 
 
 607 
 
 .98669 
 
 2,6 
 
 .0135 
 
 
 .504 
 
 .07478 
 
 616 
 
 .15654 
 
 607 
 
 .98672 
 
 2,6 
 
 .0135 
 
 
 2.505 
 
 6.08004 
 
 616 
 
 6.16262 
 
 608 
 
 0.98675 
 
 2,6 
 
 I. 0134 
 
 0,3 
 
 .506 
 
 .08711 
 
 617 
 
 .16870 
 
 609 
 
 .98677 
 
 2,6 
 
 .0134 
 
 
 .507 
 
 .09328 
 
 617 
 
 .17479 
 
 609 
 
 .98680 
 
 2,6 
 
 .0134 
 
 
 .508 
 
 .09946 
 
 618 
 
 .18089 
 
 610 
 
 .98683 
 
 2,6 
 
 .0134 
 
 
 .509 
 
 . 10564 
 
 619 
 
 .18699 
 
 611 
 
 .98685 
 
 2,6 
 
 .0133 
 
 
 2.510 
 
 6.IH83 
 
 619 
 
 6.19310 
 
 611 
 
 0.98688 
 
 2,6 
 
 1.0133 
 
 0,3 
 
 .511 
 
 . 1 1803 
 
 620 
 
 .19921 
 
 612 
 
 .98690 
 
 2,6 
 
 .0133 
 
 
 .512 
 
 . 12423 
 
 621 
 
 20534 
 
 612 
 
 .98693 
 
 2,6 
 
 .0132 
 
 
 .513 
 
 .13044 
 
 621 
 
 .21146 
 
 613 
 
 .98696 
 
 2,6 
 
 .0132 
 
 
 .514 
 
 .13665 
 
 622 
 
 .21760 
 
 614 
 
 .98698 
 
 2,6 
 
 .0132 
 
 
 2.515 
 
 6.14287 
 
 622 
 
 6.22374 
 
 614 
 
 0.98701 
 
 2,6 
 
 1.0132 
 
 0,3 
 
 .516 
 
 . 14910 
 
 623 
 
 .22988 
 
 615 
 
 .98703 
 
 2,6 
 
 .0131 
 
 
 .517 
 
 15533 
 
 624 
 
 .23603 
 
 616 
 
 .98706 
 
 2,6 
 
 .0131 
 
 
 .518 
 
 .16157 
 
 624 
 
 .24219 ! 616 
 
 .08708 
 
 2,6 
 
 .0131 
 
 
 .519 
 
 . 16782 
 
 625 
 
 .24836 
 
 617 
 
 .98711 
 
 2,6 
 
 .0131 
 
 
 2.520 
 
 6.17407 
 
 625 
 
 6.25453 
 
 617 
 
 0.98714 
 
 2,6 
 
 1.0130 
 
 0,3 
 
 .521 
 
 .18033 
 
 626 
 
 .26071 
 
 618 
 
 .08716 
 
 2,6 
 
 .0130 
 
 
 .522 
 
 .18659 
 
 627 
 
 .26689 
 
 619 
 
 .98719 
 
 2,5 
 
 .0130 
 
 
 .523 
 
 .19286 
 
 627 
 
 .27308 
 
 619 
 
 .98721 
 
 2,5 
 
 .0130 
 
 
 .524 
 
 .19914 
 
 628 
 
 .27927 
 
 620 
 
 .98724 
 
 2,5 
 
 .0129 
 
 
 2.525 
 
 6.20542 
 
 629 
 
 6.28548 
 
 621 
 
 0.98726 
 
 2,5 
 
 1.0129 
 
 0,3 
 
 .526 
 
 .21171 
 
 629 
 
 .29169 
 
 621 
 
 .98729 
 
 2,5 
 
 .0129 
 
 
 .527 
 
 .21800 
 
 630 
 
 .29750 
 
 622 
 
 .98/31 
 
 2,5 
 
 .0128 
 
 
 .528 
 
 .22430 
 
 630 
 
 .30412 
 
 622 
 
 .98734 
 
 2,5 
 
 .0128 
 
 
 .529 
 
 .23061 
 
 631 
 
 .31035 
 
 623 
 
 .98736 
 
 2,5 
 
 .0128 
 
 
 2.530 
 
 6.23692 
 
 632 
 
 6.31658 
 
 624 
 
 0.98739 
 
 2,5 
 
 1.0128 
 
 0,3 
 
 .531 
 
 .24324 
 
 632 
 
 . 32282 
 
 624 
 
 .98741 
 
 2,5 
 
 .0127 
 
 
 .532 
 
 .24957 
 
 633 
 
 .32907 
 
 625 
 
 .98744 
 
 2,5 
 
 .0127 
 
 
 533 
 
 .25590 
 
 634 
 
 .33532 
 
 626 
 
 .98746 
 
 2,5 
 
 .0127 
 
 
 534 
 
 .26224 
 
 634 
 
 .34158 
 
 626 
 
 .08749 
 
 2,5 
 
 .0127 
 
 
 2.535 
 
 6.26858 
 
 635 
 
 6.34785 
 
 627 
 
 0.98751 
 
 2,5 
 
 1.0126 
 
 0,3 
 
 .536 
 
 27494 
 
 635 
 
 .35412 
 
 627 
 
 .98754 
 
 2,5 
 
 .0126 
 
 
 537 
 
 .28129 
 
 636 
 
 .30040 
 
 628 
 
 .98756 
 
 2,5 
 
 .0126 
 
 
 .538 
 
 .28766 
 
 637 
 
 .36668 
 
 629 
 
 .98759 
 
 2,5 
 
 .0126 
 
 
 .539 
 
 .29403 
 
 637 
 
 .37297 
 
 629 
 
 .98761 
 
 2,5 
 
 .0125 
 
 
 2.540 
 
 6.30040 
 
 638 
 
 6.37927 
 
 630 
 
 0.98764 
 
 2,5 
 
 I. 0125 
 
 0,3 
 
 541 
 
 .30678 
 
 639 
 
 .38557 
 
 631 
 
 .98766 
 
 2,5 
 
 .0125 
 
 0,3 
 
 542 
 
 .31317 
 
 639 
 
 .39188 
 
 631 
 
 .98769 
 
 2,4 
 
 .0125 
 
 0,3 
 
 543 
 
 .31957 
 
 640 
 
 .39820 
 
 632 
 
 .98771 
 
 2,4 
 
 .0124 
 
 o,3 
 
 544 
 
 .32597 
 
 640 
 
 .40452 
 
 633 
 
 .98773 
 
 2,4 
 
 .0124 
 
 0,2 
 
 2.545 
 
 6.33238 
 
 641 
 
 6.41085 
 
 633 
 
 0.98776 
 
 2,4 
 
 1.0124 
 
 0,2 
 
 .546 
 
 .33879 
 
 642 
 
 .41719 
 
 634 
 
 .98778 
 
 2,4 
 
 .0124 
 
 
 is 
 
 .34521 
 .35164 
 
 642 
 643 
 
 .42353 
 .42088 
 
 635 
 635 
 
 .98781 
 .98783 
 
 A4 
 
 2,4 
 
 .0123 
 .0123 
 
 
 .549 
 
 .35807 
 
 644 
 
 .43623 
 
 636 
 
 .98786 
 
 24 
 
 .0123 
 
 
 2.550 
 
 6.30451 
 
 644 
 
 6.44259 
 
 636 
 
 0.98788 
 
 2,4 
 
 1.0123 
 
 CX2 
 
 u 
 
 tan gd u 
 
 F O ' 
 
 sec gd u 
 
 F O ' 
 
 tin gd u 
 
 F ' 
 
 csc gd u 
 
 Fo' 
 
 SMITHSONIAN TABLE* 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinh u 
 
 w p y > 
 
 cosh u 
 
 O.FO' 
 
 tanh u 
 
 F ' 
 
 coth u 
 
 F ' 
 
 2.550 
 
 6.36451 
 
 644 
 
 6.44259 
 
 636 
 
 0.98788 
 
 2,4 
 
 I.OI23 
 
 0,2 
 
 .551 
 
 .37096 
 
 645 
 
 .44896 
 
 637 
 
 .98790 
 
 2,4 
 
 .OI22 
 
 
 \-552 
 
 .37741 
 
 646 
 
 .45533 
 
 638 
 
 98793 
 
 2,4 
 
 .0122 
 
 
 553 
 
 .38387 
 
 646 
 
 .46172 
 
 638 
 
 .98795 
 
 2,4 
 
 .OI22 
 
 
 554 
 
 .39033 
 
 647 
 
 .46810 
 
 639 
 
 .98798 
 
 2,4 
 
 .OI22 
 
 
 2.555 
 
 6.39680 
 
 647 
 
 6.47450 
 
 640 
 
 0.98800 
 
 2,4 
 
 I.OI2I 
 
 0,2 
 
 .556 
 
 .40328 
 
 648 
 
 .48090 
 
 640 
 
 .98802 
 
 2,4 
 
 .OI2I 
 
 
 557 
 
 .40977 
 
 649 
 
 .48730 
 
 641 
 
 .98805 
 
 2,4 
 
 .OI2I 
 
 
 .558 
 
 .41626 
 
 649 
 
 49372 
 
 642 
 
 .98807 
 
 2,4 
 
 .OI2I 
 
 
 559 
 
 .42275 
 
 650 
 
 .50014 
 
 642 
 
 .98810 
 
 2,4 
 
 .OI2O 
 
 
 2.560 
 
 6.42926 
 
 651 
 
 6.50656 
 
 643 
 
 0.98812 
 
 2,4 
 
 I.OI2O 
 
 0,2 
 
 .561 
 
 43577 
 
 651 
 
 .51299 
 
 644 
 
 .98814 
 
 2,4 
 
 .OI2O 
 
 
 .562 
 
 .44228 
 
 6 5 2 
 
 .51943 
 
 644 
 
 .98817 
 
 2,4 
 
 .OI2O 
 
 
 .563 
 
 .44880 
 
 653 
 
 .52588 
 
 645 
 
 .98819 
 
 2,3 
 
 .OI2O 
 
 
 .564 
 
 .45533 
 
 653 
 
 .53233 
 
 646 
 
 .98821 
 
 2,3 
 
 .0119 
 
 
 2.565 
 
 6.46187 
 
 654 
 
 6.53879 
 
 646 
 
 0.98824 
 
 2,3 
 
 I.OII9 
 
 0,2 
 
 .566 
 
 .46841 
 
 655 
 
 .54525 
 
 647 
 
 .98826 
 
 2,3 
 
 .OI 19 
 
 
 .567 
 
 .47496 
 
 655 
 
 .55173 
 
 647 
 
 .98828 
 
 2,3 
 
 .OII9 
 
 
 .568 
 
 .48152 
 
 656 
 
 .55820 
 
 648 
 
 .98831 
 
 2,3 
 
 .0118 
 
 
 .569 
 
 .48808 
 
 656 
 
 .56469 
 
 649 
 
 .98833 
 
 2,3 
 
 .0118 
 
 
 2.570 
 
 6.49464 
 
 657 
 
 6.57118 
 
 649 
 
 0.98835 
 
 2,3 
 
 I.OIlS 
 
 0,2 
 
 571 
 
 .50122 
 
 658 
 
 .57768 
 
 650 
 
 .98838 
 
 2,3 
 
 .0118 
 
 
 572 
 
 .50780 
 
 658 
 
 .58418 
 
 651 
 
 .98840 
 
 2,3 
 
 .OII7 
 
 
 573 
 
 .51439 
 
 659 
 
 .59069 
 
 651 
 
 .98842 
 
 2,3 
 
 .OII7 
 
 
 .574 
 
 .52098 
 
 660 
 
 59721 
 
 652 
 
 98845 
 
 2,3 
 
 .OII7 
 
 
 2.575 
 
 6.52758 
 
 660 
 
 6.60374 
 
 653 
 
 0.98847 
 
 2,3 
 
 I.OII7 
 
 0,2 
 
 .576 
 
 .53419 
 
 661 
 
 .61027 
 
 653 
 
 .98849 
 
 2,3 
 
 .OIl6 
 
 
 577 
 
 .54080 
 
 662 
 
 .61680 
 
 654 
 
 .98851 
 
 2,3 
 
 .OIl6 
 
 
 .578 
 
 54742 
 
 662 
 
 .62335 
 
 655 
 
 .98854 
 
 2,3 
 
 .OIl6 
 
 
 .579 
 
 .55405 
 
 663 
 
 .62990 
 
 655 
 
 .98856 
 
 2,3 
 
 .OIl6 
 
 
 2.580 
 
 6.56068 
 
 664 
 
 6.63646 
 
 656 
 
 0.98858 
 
 2,3 
 
 I. 0115 
 
 0,2 
 
 .581 
 
 .56732 
 
 664 
 
 .64302 
 
 657 
 
 .98860 
 
 2,3 
 
 .0115 
 
 
 .582 
 
 57397 
 
 665 
 
 .64959 
 
 657 
 
 .98863 
 
 2,3 
 
 :oii5 
 
 
 .583 
 
 .58062 
 
 666 
 
 -.65617 
 
 658 
 
 .98865 
 
 2,3 
 
 .0115 
 
 
 .584 
 
 .58728 
 
 666 
 
 .66275 
 
 659 
 
 .98867 
 
 2,3 
 
 .0115 
 
 
 2.585 
 
 6.59395 
 
 667 
 
 6.66934 
 
 659 
 
 0.98870 
 
 2,2 
 
 1.0114 
 
 0,2 
 
 .586 
 
 .60062 
 
 668 .67594 
 
 660 
 
 .98872 
 
 2,2 
 
 .0114 
 
 
 .587 
 
 .60730 
 
 668 .68254 
 
 661 
 
 98874 
 
 2,2 
 
 .0114 
 
 
 .588 
 
 .61398 
 
 669 
 
 .68915 
 
 661 
 
 .98876 
 
 2,2 
 
 .0114 
 
 
 .589 
 
 .62068 
 
 670 
 
 .69577 
 
 662 
 
 .98878 
 
 2,2 
 
 .0113 
 
 
 2.590 
 
 6.62738 
 
 670 
 
 6.70240 
 
 663 
 
 0.98881 
 
 2,2 
 
 1.0113 
 
 0,2 
 
 .591 
 
 .63408 
 
 671 
 
 .70903 
 
 663 
 
 .98883 
 
 2,2 
 
 .0113 
 
 
 .592 
 
 64079 
 
 672 
 
 .71566 
 
 664 
 
 .98885 
 
 2,2 
 
 .0113 
 
 
 593 
 
 .64751 
 
 672 
 
 .72231 
 
 665 
 
 .98887 
 
 2,2 
 
 .0113 
 
 
 594 
 
 .65424 
 
 673 
 
 .72876 
 
 665 
 
 .98890 
 
 2,2 
 
 .0112 
 
 
 2.595 
 
 6.66097 
 
 674 
 
 6.73562 
 
 666 
 
 0.98892 
 
 2,2 
 
 I.OII2 
 
 0,2 
 
 .596 
 
 .66771 
 
 674 
 
 .74228 
 
 667 
 
 .98894 
 
 2,2 
 
 .OII2 
 
 
 597 
 
 .67446 
 
 675 
 
 .74895 
 
 667 
 
 .98896 
 
 2,2 
 
 .0112 
 
 
 598 
 
 .68121 
 
 676 
 
 .75563 
 
 668 
 
 .98898 
 
 2,2 
 
 .0111 
 
 
 599 
 
 .68797 
 
 676 
 
 .76231 
 
 669 
 
 .98901 
 
 2,2 
 
 .OI 1 1 
 
 
 2.600 
 
 6.69473 
 
 677 
 
 6.76901 
 
 669 
 
 0.98903 
 
 2,2 
 
 I.OIII 
 
 0,2 
 
 u 
 
 tan gd u 
 
 F O ' 
 
 sec gd u 
 
 wF ' 
 
 sin gd u 
 
 wF</ 
 
 csc gd u 
 
 F O ' 
 
 SMITHSONIAN TABLES 
 
 157 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinh u 
 
 < Fi/ 
 
 cosh u 
 
 wF ' 
 
 tanhu 
 
 <-F ' 
 
 coth u 
 
 Fo' 
 
 2.600 
 
 6.69473 
 
 677 
 
 6.76901 
 
 669 
 
 0.98903 
 
 2,2 
 
 I.OIII 
 
 0,2 
 
 .601 
 
 .70150 
 
 678 
 
 77570 
 
 670 
 
 .98905 
 
 2,2 
 
 .0111 
 
 
 .602 
 
 .70828 
 
 678 
 
 .78241 
 
 671 
 
 98907 
 
 2,2 
 
 .OIIO 
 
 
 .603 
 
 .71507 
 
 679 
 
 .78912 
 
 67* 
 
 .98909 
 
 2,2 
 
 .OIIO 
 
 
 .604 
 
 .72186 
 
 680 
 
 .79584 
 
 6 7 2 
 
 .98911 
 
 2,2 
 
 .OIIO 
 
 
 2.605 
 
 6.72866 
 
 680 
 
 6.80256 
 
 673 
 
 0.98914 
 
 2,2 
 
 I. OIIO 
 
 0,2 
 
 .606 
 
 73547 
 
 681 
 
 .80930 
 
 674 
 
 .98916 
 
 2,2 
 
 .OIIO 
 
 
 .607 
 
 .74228 
 
 682 
 
 .81604 
 
 674 
 
 .98918 
 
 2,2 
 
 .0109 
 
 
 .608 
 
 .74910 
 
 682 
 
 .82278 
 
 675 
 
 .98920 
 
 2,1 
 
 .0109 
 
 
 .609 
 
 75593 
 
 683 
 
 .82953 
 
 676 
 
 .98922 
 
 2,1 
 
 .0109 
 
 
 2.610 
 
 6.76276 
 
 684 
 
 6.83629 
 
 676 
 
 0.98924 
 
 2,1 
 
 1.0109 
 
 0,2 
 
 .611 
 
 .76960 
 
 684 
 
 .84306 
 
 677 
 
 .98926 
 
 2,1 
 
 .0109 
 
 
 .612 
 
 .77644 
 
 685 
 
 .84983 
 
 678 
 
 .98929 
 
 2,1 
 
 .0108 
 
 
 .613 
 
 78330 
 
 686 
 
 .85661 
 
 678 
 
 9^931 
 
 2,1 
 
 .0108 
 
 
 .614 
 
 .79016 
 
 686 
 
 .86340 
 
 679 
 
 98933 
 
 2,1 
 
 .0108 
 
 
 2.615 
 
 6.79702 
 
 687 
 
 6.87019 
 
 680 
 
 0.98935 
 
 2,1 
 
 1.0108 
 
 0,2 
 
 .616 
 
 .80300 
 
 688 
 
 .87699 
 
 680 
 
 Q8937 
 
 2,1 
 
 .0107 
 
 
 .617 
 
 .81078 
 
 688 
 
 .88380 
 
 681 
 
 .98939 
 
 2,1 
 
 .0107 
 
 
 .618 
 
 .81767 
 
 689 
 
 .89061 
 
 682 
 
 .98941 
 
 2,1 
 
 .0107 
 
 
 .619 
 
 .82456 
 
 690 
 
 .89744 
 
 682 
 
 .98943 
 
 2,1 
 
 .0107 
 
 
 2.620 
 
 6.83146 
 
 690 
 
 6.90426 
 
 683 
 
 0.98946 
 
 2,1 
 
 1.0107 
 
 0,2 
 
 .621 
 
 .83837 
 
 691 
 
 .91110 
 
 684 
 
 .98948 
 
 2,1 
 
 .0106 
 
 
 .622 
 
 .84528 
 
 692 
 
 .91794 
 
 685 
 
 .98950 
 
 2,1 
 
 .0106 
 
 
 .623 
 
 .85220 
 
 692 
 
 .92479 
 
 685 
 
 .98952 
 
 2,1 
 
 .0106 
 
 
 .624 
 
 .85913 
 
 693 
 
 .93164 
 
 686 
 
 .98954 
 
 2,1 
 
 .0106 
 
 
 2.625 
 
 6.86607 
 
 694 
 
 6.93851 
 
 687 
 
 0.98956 
 
 2,1 
 
 1.0106 
 
 0,2 
 
 .626 
 
 .87301 
 
 695 
 
 .94538 
 
 687 
 
 .98958 
 
 2,1 
 
 .0105 
 
 
 .627 
 
 .87996 
 
 695 
 
 .95225 
 
 688 
 
 .98960 
 
 2,1 
 
 .0105 
 
 
 .628 
 
 .88691 
 
 696 
 
 .95914 
 
 689 
 
 .98962 
 
 2,1 
 
 .0105 
 
 
 .629 
 
 .89388 
 
 697 
 
 .96603 
 
 689 
 
 .98964 
 
 2,1 
 
 .0105 
 
 
 2.630 
 
 6.90085 
 
 697 
 
 6.97292 
 
 690 
 
 0.98966 
 
 2,1 
 
 1. 0104 
 
 0,2 
 
 .631 
 
 .90782 
 
 698 
 
 .97983 
 
 691 
 
 .98968 
 
 2,1 
 
 .0104 
 
 
 .632 
 
 .91481 
 
 699 
 
 .98674 
 
 691 
 
 .98970 
 
 2,O 
 
 .0104 
 
 
 .633 
 
 .92180 
 
 699 
 
 .99366 
 
 692 
 
 .98972 
 
 * 2,0 
 
 .0104 
 
 
 .634 
 
 .92879 
 
 700 
 
 7.00058 
 
 693 
 
 .98974 
 
 2,0 
 
 .0104 
 
 
 2.635 
 
 6.93580 
 
 701 
 
 7.00752 
 
 694 
 
 0.98977 
 
 2,0 
 
 1.0103 
 
 0,2 
 
 .636 
 
 .94281 
 
 701 
 
 .01446 
 
 694 
 
 .98979 
 
 2,0 
 
 .0103 
 
 
 .637 
 
 .94983 
 
 702 
 
 .02140 
 
 695 
 
 .98981 
 
 2,0 
 
 .0103 
 
 
 .638 
 
 .95685 
 
 703 
 
 .02835 
 
 696 
 
 .98983 
 
 2,O 
 
 .0103 
 
 
 .639 
 
 .96388 
 
 704 
 
 .03532 
 
 696 
 
 .98985 
 
 2,0 
 
 .0103 
 
 
 2.640 
 
 6.97092 
 
 704 
 
 7.04228 
 
 697 
 
 0.98987 
 
 2,0 
 
 I.OI02 
 
 0,2 
 
 .641 
 
 97797 
 
 705 
 
 .04926 
 
 698 
 
 .98989 
 
 2,O 
 
 .0102 
 
 
 .642 
 
 .98502 
 
 706 
 
 .05624 
 
 699 
 
 .98991 
 
 2,0 
 
 .0102 
 
 
 .643 
 
 .99208 
 
 706 
 
 .06323 
 
 699 
 
 .98993 
 
 2,0 
 
 .OIO2 
 
 
 .644 
 
 .99915 
 
 707 
 
 .07022 
 
 700 
 
 .98995 
 
 2,0 
 
 .OIO2 
 
 
 2.645 
 
 7.00622 
 
 708 
 
 7.07723 
 
 701 
 
 0.98997 
 
 2,0 
 
 I.OIOI 
 
 0,2 
 
 .646 
 
 .01330 
 
 7o8 
 
 .08423 
 
 701 
 
 .98999 
 
 2,0 
 
 .OIOI 
 
 
 .647 
 
 .02039 
 
 709 
 
 .09125 
 
 702 
 
 .99001 
 
 2,0 
 
 .0101 
 
 
 .648 
 
 .02748 
 
 710 
 
 .09828 
 
 703 
 
 .99003 
 
 2,0 
 
 .OIOI 
 
 
 .649 
 
 .03458 
 
 711 
 
 .10531 
 
 703 
 
 .09005 
 
 2,O 
 
 .OIOI 
 
 
 2.650 
 
 7.04169 
 
 7ii 
 
 7-II234 
 
 704 
 
 0.99007 
 
 2,0 
 
 I.OIOO 
 
 0,2 
 
 u 
 
 tan gd u 
 
 Fo' 
 
 sec gd u 
 
 Fo' 
 
 ingdu 
 
 F,/ 
 
 csc gd u 
 
 FO' 
 
 SMITHSONIAN TABLES 
 
 158 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinh u 
 
 F ' 
 
 cosh u 
 
 F ' 
 
 tanh u 
 
 F O 
 
 coth u . 
 
 Fa' 
 
 2.650 
 
 7.04169 
 
 711 
 
 7.11234 
 
 704 
 
 0.99007 
 
 2,0 
 
 I.OIOO 
 
 0,2 
 
 \ .651 
 
 .04881 
 
 712 
 
 .11939 
 
 705 
 
 .99009 
 
 2,0 
 
 .0100 
 
 
 \652 
 
 05593 
 
 713 
 
 . 12544 
 
 706 
 
 .99011 
 
 2,0 
 
 .0100 
 
 
 .653 
 
 .06306 
 
 713 
 
 . 13350 
 
 706 
 
 .90013 
 
 2,0 
 
 .0100 
 
 
 .654 
 
 .07020 
 
 7U 
 
 . 14057 
 
 707 
 
 .99015 
 
 2,0 
 
 .0100 
 
 
 2.655 
 
 7-07734 
 
 715 
 
 7.14764 
 
 708 
 
 0.99016 
 
 2,O 
 
 1.0099 
 
 0,2 
 
 .656 
 
 .08449 
 
 715 
 
 . 15472 
 
 708 
 
 .99018 
 
 2,0 
 
 .0099 
 
 
 .657 
 
 .09165 
 
 7l6 
 
 .16181 
 
 709 
 
 .99020 
 
 1,9 
 
 .0099 
 
 
 .658 
 
 .09882 
 
 717 
 
 .16891 
 
 710 
 
 .99022 
 
 i,9 
 
 .0099 
 
 
 .659 
 
 .10599 
 
 718 
 
 .17601 
 
 711 
 
 .99024 
 
 1,9 
 
 .0099 
 
 
 2.660 
 
 7.11317 
 
 718 
 
 7-18312 
 
 711 
 
 0.99026 
 
 1,9 
 
 1.0098 
 
 0,2 
 
 .661 
 
 . 12036 
 
 719 
 
 .19024 
 
 712 
 
 .99028 
 
 1,9 
 
 .0098 
 
 
 .662 
 
 . 12755 
 
 720 
 
 . 19736 
 
 713 
 
 .99030 
 
 1,9 
 
 .0098 
 
 
 .663 
 
 . 13475 
 
 720 
 
 .20449 
 
 713 
 
 .09032 
 
 1,9 
 
 .0098 
 
 
 .664 
 
 .14196 
 
 721 
 
 .21163 
 
 714 
 
 .99034 
 
 1,9 
 
 .0098 
 
 
 2.665 
 
 7.14918 
 
 722 
 
 7.21877 
 
 715 
 
 0.99036 
 
 1,9 
 
 1.0097 
 
 0,2 
 
 .666 
 
 . 15640 
 
 723 
 
 .22593 
 
 7l6 
 
 .99038 
 
 i,9 
 
 .0097 
 
 
 .667 
 
 . 16363 
 
 723 
 
 .23309 
 
 7i6 
 
 .99040 
 
 1,9 
 
 .0097 
 
 
 .668 
 
 .17086 
 
 724 
 
 .24025 
 
 717 
 
 .09042 
 
 1,9 
 
 .0097 
 
 
 .669 
 
 .17811 
 
 725 
 
 .24743 
 
 7l8 
 
 .99044 
 
 1,9 
 
 .0097 
 
 
 2.670 
 
 7.18536 
 
 725 
 
 7-25461 
 
 719 
 
 0.99045 
 
 i,9 
 
 1.0096 
 
 0,2 
 
 .671 
 
 . 19262 
 
 726 
 
 .26180 
 
 719 
 
 .99047 
 
 i,9 
 
 .0096 
 
 
 .672 
 
 .19988 
 
 727 
 
 .26900 
 
 720 
 
 .99049- 
 
 1,9 
 
 .0096 
 
 
 .673 
 
 .20715 
 
 728 
 
 .27620 
 
 721 
 
 .99051 
 
 i,9 
 
 .0096 
 
 
 .674 
 
 21443 
 
 728 
 
 .28341 
 
 721 
 
 99053 
 
 1,9 
 
 .0096 
 
 
 2.675 
 
 7.22172 
 
 729 
 
 7-29063 
 
 722 
 
 0,99055 
 
 1,9 
 
 1.0095 
 
 0,2 
 
 .676 
 
 .22902 
 
 730 
 
 .29785 
 
 723 
 
 .99057 
 
 i,9 
 
 .0095 
 
 
 .677 
 
 .23632 
 
 731 
 
 .30509 
 
 724 
 
 .99059 
 
 1,9 
 
 .0095 
 
 
 .678 
 
 ,.24363 
 
 731 
 
 .31233 
 
 724 
 
 .99060 
 
 1,9 
 
 .0095 
 
 
 .679 
 
 .25094 
 
 732 
 
 .31957 
 
 725 
 
 .99062 
 
 1,9 
 
 .0095 
 
 
 2.680 
 
 7-25827 
 
 733 
 
 7.32683 
 
 726 
 
 0.09064 
 
 1,9 
 
 1.0094 
 
 0,2 
 
 .681 
 
 .26560 
 
 733 
 
 33409 
 
 727 
 
 .99066 
 
 1,9 
 
 .0094 
 
 
 .682 
 
 .27293 
 
 734 
 
 .34136 
 
 727 
 
 .Q9068 
 
 i,9 
 
 .0094 
 
 
 .683 
 
 .28028 
 
 735 
 
 .34864 
 
 728 
 
 .09070 
 
 1,9 
 
 .0094 
 
 
 .684 
 
 .28763 
 
 736 
 
 .35592 
 
 729 
 
 .99072 
 
 1,8 
 
 .0094 
 
 
 2.685 
 
 7.29499 
 
 736 
 
 7.36321 
 
 729 
 
 0.09073 
 
 1,8 
 
 1.0094 
 
 0,2 
 
 .685 
 
 .30236 
 
 737 
 
 .37051 
 
 730 
 
 99075 
 
 1,8 
 
 .0093 
 
 
 .687 
 
 .30973 
 
 738 
 
 .37782 
 
 73i 
 
 .99077 
 
 1,8 
 
 .0093 
 
 
 .688 
 
 .31711 
 
 739 
 
 .38513 
 
 732 
 
 .99079 
 
 1,8 
 
 .0093 
 
 
 .689 
 
 32450 
 
 739 
 
 .39245 
 
 732 
 
 .99081 
 
 1,8 
 
 .0093 
 
 
 2.600 
 
 7.33190 
 
 740 
 
 7.39978 
 
 733 
 
 0.99083 
 
 1,8 
 
 1.0093 
 
 0,2 
 
 .691 
 
 33930 
 
 741 
 
 .40711 
 
 734 
 
 .90084 
 
 1,8 
 
 .0092 
 
 
 .692 
 
 34671 
 
 74i 
 
 .41446 
 
 735 
 
 .99085 
 
 1,8 
 
 .0092 
 
 
 .693 
 
 .35413 
 
 742 
 
 .42181 
 
 735 
 
 .90088 
 
 1,8 
 
 .0092 
 
 
 .694 
 
 .36156 
 
 743 
 
 .42917 
 
 736 
 
 .99090 
 
 1,8 
 
 .0092 
 
 
 2.695 
 
 7.36899 
 
 744 
 
 7.43653 
 
 737 
 
 0.99092 
 
 1,8 
 
 1.0092 
 
 0,2 
 
 .696 
 
 .37643 
 
 744 
 
 .44390 
 
 738 
 
 .99094 
 
 1,8 
 
 .0091 
 
 
 .697 
 
 .38388 
 
 745 
 
 .45128 
 
 738 
 
 .00095 
 
 1,8 
 
 .0091 
 
 
 .698 
 
 .39133 
 
 746 
 
 .45867 
 
 739 
 
 .99097 
 
 1,8 
 
 .0091 
 
 
 .699* 
 
 .39879 
 
 747 
 
 .46607 
 
 740 
 
 .99099 
 
 1,8 
 
 .0091 
 
 
 2.700 
 
 7.40626 
 
 747 
 
 7-47347 
 
 741 
 
 0.99101 
 
 1,8 
 
 1.0091 
 
 0,2 
 
 u 
 
 tan gd u 
 
 F ' 
 
 sec gd u 
 
 -Fo' 
 
 sin gd u 
 
 -Fo' 
 
 esc gd u 
 
 <-F</ 
 
 SMITHSONIAN TABLES 
 
 159 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinhu 
 
 F ' 
 
 cosh u 
 
 F ' 
 
 tanh u 
 
 F O ' 
 
 cothu 
 
 W Fo' 
 
 2.700 
 
 7.40626 
 
 747 
 
 7-47347 
 
 741 
 
 0.99101 
 
 1,8 
 
 1.0091 
 
 0,2 
 
 .701 
 
 .41374 
 
 748 
 
 .48088 
 
 741 
 
 .99103 
 
 1,8 
 
 .0091 
 
 
 .702 
 
 .42122 
 
 749 
 
 .48830 
 
 742 
 
 .99104 
 
 1,8 
 
 .0090 
 
 
 .703 
 
 .42872 
 
 750 
 
 49572 
 
 743 
 
 99io5 
 
 1,8 
 
 .0090 
 
 
 .704 
 
 .43622 
 
 750 
 
 .50315 
 
 744 
 
 .99108 
 
 1,8 
 
 .0090 
 
 
 2.705 
 
 7.44372 
 
 751 
 
 7.51059 
 
 744 
 
 0.99110 
 
 1,8 
 
 I.OOOO 
 
 0,2 
 
 .706 
 
 .45124 
 
 752 
 
 .51804 
 
 745 
 
 .99IH 
 
 1,8 
 
 .0090 
 
 
 .707 
 
 .45876 
 
 753 
 
 .52550 
 
 746 
 
 99113 
 
 1,8 
 
 .0089 
 
 
 .708 
 
 .46629 
 
 753 
 
 .53206 
 
 747 
 
 99115 
 
 1,8 
 
 .0089 
 
 
 .709 
 
 .47383 
 
 754 
 
 54043 
 
 747 
 
 .99117 
 
 1,8 
 
 .0089 
 
 
 2.710 
 
 7.48I37 
 
 755 
 
 7.54791 
 
 748 
 
 0.99118 
 
 1,8 
 
 1.0089 
 
 0,2 
 
 .711 
 
 .48892 
 
 756 
 
 55539 
 
 749 
 
 .99120 
 
 1,8 
 
 .0089 
 
 
 .712 
 
 .49648 
 
 756 
 
 .56288 
 
 750 
 
 .99122 
 
 1,7 
 
 .0089 
 
 
 .713 
 
 .50405 
 
 757 
 
 .57038 
 
 750 
 
 .99124 
 
 1,7 
 
 .0088 
 
 
 .714 
 
 .51162 
 
 758 
 
 .57789 
 
 75i 
 
 .99125 
 
 i,7 
 
 .0088 
 
 
 2.715 
 
 7.51920 
 
 759 
 
 7.58541 
 
 752 
 
 0.99127 
 
 1,7 
 
 1.0088 
 
 O,2 
 
 .716 
 
 .52679 
 
 759 
 
 .59293 
 
 753 
 
 .09129 
 
 i,7 
 
 .0088 
 
 
 .717 
 
 53439 
 
 760 
 
 .60046 
 
 753 
 
 .99131 
 
 i,7 
 
 .0088 
 
 
 .718 
 
 .54199 
 
 76i 
 
 .60800 
 
 754 
 
 .99132 
 
 i,7 
 
 .0088 
 
 
 .719 
 
 .54960 
 
 762 
 
 .61555 
 
 755 
 
 .99134 
 
 i,7 
 
 .0087 
 
 
 2.720 
 
 7-55722 
 
 762 
 
 7.62310 
 
 756 
 
 0.09136 
 
 1,7 
 
 1.0087 
 
 0,2 
 
 .721 
 
 .56485 
 
 763 
 
 .63066 
 
 756 
 
 .99138 
 
 i,7 
 
 .0087 
 
 
 .722 
 
 .57249 
 
 764 
 
 .63823 
 
 757 
 
 99139 
 
 i,7 
 
 .0087 
 
 
 .723 
 
 .58013 
 
 765 
 
 .64580 
 
 758 
 
 .99MI 
 
 i,7 
 
 .0087 
 
 
 .724 
 
 .58778 
 
 765 
 
 .65339 
 
 759 
 
 99143 
 
 i,7 
 
 .0086 
 
 
 2.725 
 
 7-59543 
 
 766 
 
 7.66098 
 
 760 
 
 0.99144 
 
 i,7 
 
 1.0086 
 
 0,2 
 
 .726 
 
 .60310 
 
 767 
 
 .66858 
 
 760 
 
 .99146 
 
 i,7 
 
 .0086 
 
 
 .727 
 
 .61077 
 
 768 
 
 .67619 
 
 761 
 
 .99148 
 
 i,7 
 
 .0086 
 
 
 .728 
 
 .61845 
 
 768 
 
 .68380 
 
 762 
 
 .59150 
 
 i,7 
 
 .0086 
 
 
 .729 
 
 .62614 
 
 769 
 
 .69142 
 
 763 
 
 .09151 
 
 i,7 
 
 .0086 
 
 
 2.730 
 
 7.63383 
 
 770 
 
 7.69905 
 
 763 
 
 0.09153 
 
 1,7 
 
 1.0085 
 
 0,2 
 
 .731 
 
 .64154 
 
 771 
 
 .70669 
 
 764 
 
 99155 
 
 i,7 
 
 .0085 
 
 
 .732 
 
 .64925 
 
 77i 
 
 .7U34 
 
 765 
 
 .09156 
 
 1,7 
 
 .0085 
 
 
 733 
 
 .65697 
 
 772 
 
 .72199 
 
 766 
 
 .99158 
 
 1,7 
 
 .0085 
 
 
 734 
 
 .66469 
 
 773 
 
 .72965 
 
 766 
 
 .99160 
 
 i,7 
 
 .0085 
 
 
 2.735 
 
 7.67242 
 
 774 
 
 7-73732 
 
 767 
 
 0.99161 
 
 i,7 
 
 1.0085 
 
 0,2 
 
 .736 
 
 .68017 
 
 774 
 
 74500 
 
 768 
 
 .99163 
 
 1,7 
 
 .0084 
 
 
 .737 
 
 .68791 
 
 775 
 
 .75268 
 
 769 
 
 .59165 
 
 1,7 
 
 .0084 
 
 
 -738 
 
 .69567 
 
 776 
 
 .76037 
 
 770 
 
 .99166 
 
 i,7 
 
 .0084 
 
 
 739 
 
 70344 
 
 777 
 
 .76807 
 
 770 
 
 .99168 
 
 i,7 
 
 .0084 
 
 
 2.740 
 
 7.7II2I 
 
 778 
 
 7.77578 
 
 771 
 
 0.99170 
 
 1,7 
 
 1.0084 
 
 0,2 
 
 .741 
 
 .71899 
 
 778 
 
 .78349 
 
 772 
 
 .99171 
 
 i,7 
 
 .0084 
 
 
 .742 
 
 .72677 
 
 779 
 
 .79122 
 
 773 
 
 .99173 
 
 1,6 
 
 .0083 
 
 
 743 
 
 73457 
 
 780 
 
 .79895 
 
 773 
 
 9PI75 
 
 1,6 
 
 .0083 
 
 
 744 
 
 .74237 
 
 78i 
 
 .80668 
 
 774 
 
 .99176 
 
 1,6 
 
 .0083 
 
 
 2.745 
 
 7.75018 
 
 78i 
 
 7.81443 
 
 775 
 
 0.99178 
 
 1,6 
 
 1.0083 
 
 0,2 
 
 .746 
 
 .75800 
 
 782 
 
 .82219 
 
 776 
 
 .99179 
 
 1,6 
 
 .0083 
 
 
 747 
 
 .76583 
 
 783 
 
 .82955 
 
 777 
 
 .99181 
 
 1,6 
 
 .0083 
 
 
 .748 
 
 .77366 
 
 784 
 
 .83772 
 
 777 
 
 .09183 
 
 1,6 
 
 .0082 
 
 
 749 
 
 .78150 
 
 785 
 
 .84549 
 
 778 
 
 .99184 
 
 1,6 
 
 .0082 
 
 
 
 2.750 
 
 7.78935 
 
 785 
 
 7.85328 
 
 779 
 
 0.99186 
 
 1,6 
 
 1.0082 
 
 0,2 
 
 u 
 
 tan gd u 
 
 Fo' 
 
 ec gd u 
 
 F ' 
 
 sin gd u 
 
 F ' 
 
 csc gd u 
 
 -FO' 
 
 SMITHSONIAN TABLES 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinhu 
 
 F ' 
 
 cosh u 
 
 w F ' 
 
 tanh u 
 
 "Fo 
 
 coth u 
 
 Fo' 
 
 2.750 
 
 7.78935 
 
 785 
 
 7.85328 
 
 779 
 
 0.99186 
 
 1,6 
 
 1.0082 
 
 0,2 
 
 .751 
 
 .79721 
 
 786 
 
 .86107 
 
 780 
 
 .99188 
 
 1,6 
 
 .0082 
 
 
 \ .752 
 
 .80507 
 
 787 
 
 .86887 
 
 78i 
 
 .99189 
 
 1,6 
 
 .0082 
 
 
 753 
 
 .81295 
 
 788 
 
 .87668 
 
 78i 
 
 .99191 
 
 1,6 
 
 .0082 
 
 
 754 
 
 .82083 
 
 788 
 
 .88450 
 
 782 
 
 .99192 
 
 *6 
 
 .0081 
 
 
 2.755 
 
 7.82872 
 
 789 
 
 7.89232 
 
 783 
 
 0.99194 
 
 1,6 
 
 I.OOSI 
 
 0,2 
 
 756 
 
 .83661 
 
 790 
 
 .90016 
 
 784 
 
 .09196 
 
 1,6 
 
 .0081 
 
 
 757 
 
 .84452 
 
 791 
 
 .90800 
 
 784 
 
 99197 
 
 1,6 
 
 .Oo8l 
 
 
 .758 
 
 .85243 
 
 792 
 
 .91585 
 
 785 
 
 .99199 
 
 1,6 
 
 .0081 
 
 
 759 
 
 .85035 
 
 792 
 
 .92370 
 
 786 
 
 .99200 
 
 1,6 
 
 .008I 
 
 
 2.760 
 
 7.86828 
 
 793 
 
 7.93157 
 
 787 
 
 O.992O2 
 
 1,6 
 
 I.OoSo 
 
 0,2 
 
 .761 
 
 .87621 
 
 794 
 
 93944 
 
 788 
 
 .99204 
 
 1,6 
 
 .0080 
 
 
 .762 
 
 .88415 
 
 795 
 
 .94732 
 
 788 
 
 .99205 
 
 ,6 
 
 .0080 
 
 
 .763 
 
 .89211 
 
 796 
 
 95521 
 
 789 
 
 .99207 
 
 ,6 
 
 .0080 
 
 
 .764 
 
 .90006 
 
 796 
 
 .96310 
 
 790 
 
 .99208 
 
 ,6 
 
 .0080 
 
 
 2.765 
 
 7.90803 
 
 797 
 
 7.97IOI 
 
 791 
 
 O.992IO 
 
 ,6 
 
 I.OOSO 
 
 0,2 
 
 .766 
 
 .91601 
 
 798 
 
 .97892 
 
 792 
 
 .99212 
 
 ,6 
 
 .0079 
 
 
 .767 
 
 .92399 
 
 799 
 
 .98684 
 
 792 
 
 .99213 
 
 ,6 
 
 .0079 
 
 
 .768 
 
 .93198 
 
 799 
 
 99477 
 
 793 
 
 .99215 
 
 ,6 
 
 .0079 
 
 
 .769 
 
 .93998 
 
 800 
 
 8.00270 
 
 794 
 
 .99216 
 
 ,6 
 
 .0079 
 
 
 2.770 
 
 7-94799 
 
 801 
 
 8.01065 
 
 795 
 
 0.99218 
 
 ,6 
 
 1.0079 
 
 0,2 
 
 771 
 
 .95600 
 
 802 
 
 .01860 
 
 796 
 
 .99219 
 
 ,6 
 
 .0079 
 
 
 .772 
 
 .96402 
 
 803 
 
 .02656 
 
 756 
 
 .99221 
 
 ,6 
 
 .0079 
 
 
 773 
 
 .97205 
 
 803 
 
 .03453 
 
 797 
 
 .99222 
 
 ,5 
 
 .0078 
 
 
 774 
 
 .98009 
 
 804 
 
 .04250 
 
 798 
 
 .99224 
 
 ,5 
 
 .0078 
 
 
 2.775 
 
 7.98814 
 
 805 
 
 8.05049 
 
 799 
 
 0.99226 
 
 ,5 
 
 1.0078 
 
 0,2 
 
 .776 
 
 .99619 
 
 806 
 
 . 05848 
 
 800 
 
 .99227 
 
 ,5 
 
 .0078 
 
 
 .777 
 
 8.00426 
 
 807 
 
 .06648 
 
 800 
 
 .99229 
 
 ,5 
 
 .0078 
 
 
 .778 
 
 .01233 
 
 807 
 
 .07449 
 
 801 
 
 .99230 
 
 ,5 
 
 .0078 
 
 
 779 
 
 .O2O40 
 
 808 
 
 .08251 
 
 802 
 
 .99232 
 
 ,5 
 
 .0077 
 
 
 2.780 
 .781 
 
 8.02849 
 .03659 
 
 809 
 810 
 
 8.09053 
 .09856 
 
 803 
 
 804 
 
 0.99233 
 .99235 
 
 ,5 
 ,5 
 
 1.0077 
 .0077 
 
 O,2 
 
 .782 
 
 .04469 
 
 811 
 
 .10660 
 
 804 
 
 .99236 
 
 ,5 
 
 .0077 
 
 
 .783 
 
 .05280 
 
 811 
 
 .11465 
 
 805 
 
 .99238 
 
 ,5 
 
 .0077 
 
 
 .784 
 
 .06092 
 
 812 
 
 .12271 
 
 806 
 
 .99239 
 
 ,5 
 
 .0077 
 
 
 2.785 
 
 8.06904 
 
 813 
 
 8.13077 
 
 807 
 
 0.99241 
 
 ,5 
 
 1.0077 
 
 0,2 
 
 .786 
 
 .07718 
 
 814 
 
 .13885 
 
 808 
 
 .99242 
 
 ,5 
 
 .0076 
 
 
 .787 
 
 .08532 
 
 815 
 
 .14693 
 
 809 
 
 99244 
 
 ,5 
 
 .0076 
 
 
 .788 
 
 .09347 
 
 816 
 
 . 15502 
 
 809 
 
 .99245 
 
 ,5 
 
 .0076 
 
 
 .789 
 
 . 10163 
 
 816 
 
 .16311 
 
 810 
 
 99247 
 
 ,5 
 
 .0076 
 
 
 2.700 
 
 8.10980 
 
 817 
 
 8.17122 
 
 811 
 
 0.99248 
 
 ,5 
 
 1.0076 
 
 0,2 
 
 .791 
 
 .11797 
 
 818 
 
 . 17933 
 
 812 
 
 .09250 
 
 ,5 
 
 .0076 
 
 
 792 
 
 .12616 
 
 819 
 
 . 18746 
 
 813 
 
 .99251 
 
 ,5 
 
 .0075 
 
 
 793 
 
 .13435 
 
 820 
 
 . 19559 
 
 813 
 
 .99253 
 
 ,5 
 
 .0075 
 
 
 .794 
 
 . 14255 
 
 820 
 
 .20373 
 
 814 
 
 .99254 
 
 ,5 
 
 .0075 
 
 
 2.795 
 
 8.15076 
 
 821 
 
 8.21187 
 
 815 
 
 0.99256 
 
 ,5 
 
 1.0075 
 
 O,2 
 
 .796 
 
 .15897 
 
 822 
 
 .22003 
 
 816 
 
 .99257 
 
 ,5 
 
 .0075 
 
 0,2 
 
 797 
 
 . 16720 
 
 823 
 
 .22819 
 
 817 
 
 .09259 
 
 ,5 
 
 .0075 
 
 0,2 
 
 .798 
 
 .17543 
 
 824 
 
 .23636 
 
 818 
 
 .Q26o 
 
 ,5 
 
 .0075 
 
 0,2 
 
 .799 
 
 .18367 
 
 824 
 
 24454 
 
 818 
 
 .99262 
 
 i,5 
 
 .0074 
 
 0,1 
 
 2.800 
 
 8.19192 
 
 825 
 
 8.25273 
 
 819 
 
 0.99263 
 
 1,5 
 
 1.0074 
 
 0,1 
 
 u 
 
 tan gd u 
 
 wF ' 
 
 sec gd u 
 
 *>Fo' 
 
 sin gd u 
 
 wF ' 
 
 esc cd u 
 
 Fo' 
 
 SMITHSONIAN TABLES 
 
 161 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinhu 
 
 F ' 
 
 cosh u 
 
 F ' 
 
 tanhu 
 
 Fo' 
 
 coth u 
 
 F ' 
 
 2.800 
 
 8. 19192 
 
 825 
 
 8.25273 
 
 819 
 
 0.99263 
 
 i,5 
 
 1.0074 
 
 0,1 
 
 .801 
 
 .20018 
 
 826 
 
 .26092 
 
 820 
 
 .99265 
 
 T ,5 
 
 .0074 
 
 
 .802 
 
 .20844 
 
 827 
 
 .26913 
 
 821 
 
 .99266 
 
 i,5 
 
 .0074 
 
 
 .803 
 
 .21671 
 
 828 
 
 .27734 
 
 822 
 
 .99268 
 
 i,5 
 
 .0074 
 
 
 .804 
 
 .22499 
 
 829 
 
 .28556 
 
 822 
 
 .99269 
 
 i,5 
 
 .0074 
 
 
 2.805 
 
 8.23328 
 
 829 
 
 8.29379 
 
 823 
 
 0.09270 
 
 i,5 
 
 1.0073 
 
 0,1 
 
 .806 
 
 .24158 
 
 830 
 
 .30203 
 
 824 
 
 .99272 
 
 i,5 
 
 .0073 
 
 
 .807 
 
 .24989 
 
 831 
 
 .31027 
 
 825 
 
 .99273 
 
 i,4 
 
 .0073 
 
 
 .808 
 
 .25820 
 
 832 
 
 .31853 
 
 826 
 
 .99275 
 
 i,4 
 
 .0073 
 
 
 .809 
 
 .26653 
 
 833 
 
 .32679 
 
 827 
 
 .99276 
 
 M 
 
 .0073 
 
 
 2.810 
 
 8.27486 
 
 834 
 
 8.33506 
 
 827 
 
 0.09278 
 
 1,4 
 
 1.0073 
 
 0,1 
 
 .811 
 
 .28320 
 
 834 
 
 34334 
 
 828 
 
 .99279 
 
 1,4 
 
 .0073 
 
 
 .812 
 
 .29154 
 
 835 
 
 .35163 
 
 829 
 
 .99281 
 
 1,4 
 
 .0072 
 
 
 .813 
 
 .29990 
 
 836 
 
 .35992 
 
 830 
 
 .99282 
 
 1,4 
 
 .0072 
 
 
 .814 
 
 .30826 
 
 837 
 
 .36823 
 
 831 
 
 59283 
 
 1,4 
 
 .0072 
 
 
 2.815 
 
 8.31664 
 
 838 
 
 8.37654 
 
 8 3 2 
 
 0.99285 
 
 1,4 
 
 1.0072 
 
 0,1 
 
 .816 
 
 .32502 838 
 
 .38486 
 
 833 
 
 .99286 
 
 1,4 
 
 .0072 
 
 
 .817 
 
 33341 839 
 
 .39319 
 
 833 
 
 .99288 
 
 1,4 
 
 .0072 
 
 
 .818 
 
 .34180 840 
 
 40153 
 
 834 
 
 .99289 
 
 1,4 
 
 .0072 
 
 
 .819 
 
 .35021 
 
 8 4 I 
 
 40987 
 
 835 
 
 .99291 
 
 1,4 
 
 .0071 
 
 
 2.820 
 
 8.35862 
 
 842 
 
 8.41823 
 
 836 
 
 0.99292 
 
 1,4 
 
 1.0071 
 
 0,1 
 
 .821 
 
 .36704 843 
 
 .42659 
 
 837 
 
 99293 
 
 1,4 
 
 .0071 
 
 
 .822 
 
 .37548 843 
 
 .43496 
 
 838 
 
 .99295 
 
 1,4 
 
 .0071 
 
 
 .823 
 
 .38391 
 
 844 
 
 .44334 
 
 838 
 
 .99296 
 
 1,4 
 
 .0071 
 
 
 .824 
 
 .39236 
 
 845 
 
 .45173 
 
 839 
 
 .99298 
 
 1,4 
 
 .0071 
 
 
 2.825 
 
 8.40082 
 
 846 
 
 8.46013 
 
 840 
 
 0.99299 
 
 1,4 
 
 1.0071 
 
 0,1 
 
 .826 
 
 .40928 
 
 847 
 
 .46853 
 
 8 4 I 
 
 99300 
 
 1,4 
 
 .0070 
 
 
 .827 
 
 .41776 
 
 848 
 
 .47695 
 
 8 4 2 
 
 99302 
 
 1,4 
 
 .0070 
 
 
 .828 
 
 .42624 
 
 849 
 
 .48537 
 
 843 
 
 .99303 
 
 1,4 
 
 .0070 
 
 
 .829 
 
 43473 
 
 849 
 
 .49380 
 
 843 
 
 99305 
 
 1,4 
 
 .0070 
 
 
 2.830 
 
 8.44322 
 
 8 5 
 
 8.50224 
 
 844 
 
 0.59306 
 
 1,4 
 
 1.0070 
 
 0,1 
 
 .831 
 
 .45173 
 
 8 5 I 
 
 .51068 
 
 845 
 
 99307 
 
 1,4 
 
 .0070 
 
 
 .832 
 
 .46025 
 
 852 
 
 .51914 
 
 846 
 
 .99309 
 
 1,4 
 
 .0070 
 
 
 .833 
 
 .46877 
 
 853 
 
 .52760 
 
 847 
 
 .99310 
 
 1,4 
 
 .0069 
 
 
 .834 
 
 .47730 
 
 854 
 
 .53008 
 
 848 
 
 993II 
 
 1,4 
 
 .0069 
 
 
 2.835 
 
 8.48584 
 
 854 
 
 8.54456 
 
 849 
 
 0.99313 
 
 1,4 
 
 1.0069 
 
 0,1 
 
 .836 
 
 49439 
 
 855 
 
 .55305 
 
 849 
 
 .99314 
 
 1,4 
 
 .0069 
 
 
 .837 
 
 .50295 
 
 8 5 6 
 
 .56155 
 
 8^0 
 
 .99316 
 
 1,4 
 
 .0069 
 
 
 .838 
 
 .51151 
 
 857 
 
 .57006 
 
 851 
 
 .99317 
 
 1,4 
 
 .0069 
 
 
 .839 
 
 .52009 
 
 858 
 
 .57857 
 
 852 
 
 .99318 
 
 1,4 
 
 .0069 
 
 
 2.840 
 
 8.52867 
 
 859 
 
 8.58710 
 
 853 
 
 0.99320 
 
 1,4 
 
 1.0069 
 
 0,1 
 
 .841 
 
 .53726 
 
 860 
 
 .59563 
 
 854 
 
 99321 
 
 1,4 
 
 .0068 
 
 
 .842 
 
 .54586 
 
 860 
 
 .60417 
 
 855 
 
 .99322 
 
 1,4 
 
 .0068 
 
 
 .843 
 
 55447 
 
 861 
 
 .61272 
 
 855 
 
 .99324 
 
 1,3 
 
 .0068 
 
 
 .844 
 
 .56309 
 
 862 
 
 .62128 
 
 856 
 
 .99325 
 
 1,3 
 
 .0068 
 
 
 2.845 
 
 8.57I7I 
 
 863 
 
 8.62085 
 
 857 
 
 0.99326 
 
 1,3 
 
 1.0068 
 
 0,1 
 
 .846 
 
 .58035 
 
 864 
 
 .63842 
 
 858 
 
 .99328 
 
 1,3 
 
 .0068 
 
 
 .847 
 
 .58899 
 
 865 
 
 .64701 
 
 859 
 
 99329 
 
 i,3 
 
 .0068 
 
 
 .848 
 
 .59764 
 
 866 
 
 .65560 
 
 860 
 
 99330 
 
 i,3 
 
 .0067 
 
 
 .849 
 
 .60630 
 
 866 
 
 .66420 
 
 861 
 
 99332 
 
 1,3 
 
 .0067 
 
 
 2.850 
 
 8.61497 
 
 867 
 
 8.67281 
 
 861 
 
 0.09333 
 
 1,3 
 
 1.0067 
 
 0,1 
 
 u 
 
 tan ad u 
 
 -Fo' 
 
 tec gd u 
 
 ly 
 
 sin gd u 
 
 -Fo' 
 
 esc gd u 
 
 F ' 
 
 SMITHSONIAN TABLE* 
 
 162 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinhu 
 
 Fo' 
 
 cosh u 
 
 F ' 
 
 tanh u 
 
 * Fo' coth u 
 
 F ' 
 
 2.850 
 
 8.61497 
 
 86 7 
 
 8.67281 
 
 861 
 
 0.99333 
 
 1,3 
 
 1.0067 
 
 0,1 
 
 i .851 
 
 .62365 
 
 868 
 
 .68143 
 
 862 
 
 99334 
 
 1,3 
 
 .0067 
 
 
 \ .852 
 
 .63233 
 
 869 
 
 .69006 
 
 863 
 
 .99336 
 
 1,3 
 
 .0067 
 
 
 .853 
 
 .64103 
 
 870 
 
 .69870 
 
 864 
 
 .99337 
 
 1,3 
 
 .0067 
 
 
 .854 
 
 .64973 
 
 871 
 
 .70734 
 
 865 
 
 .09338 
 
 1,3 
 
 .0067 
 
 
 2.855 
 
 8.65844 
 
 872 
 
 8.71600 
 
 866 
 
 0.99340 
 
 1,3 
 
 1.0066 
 
 0,1 
 
 .856 
 
 .66716 
 
 872 
 
 .72466 
 
 867 
 
 .99341 
 
 1,3 
 
 .0066 
 
 
 .857 
 
 .67589 
 
 873 
 
 73333 
 
 868 
 
 .99342 
 
 1,3 
 
 .0066 
 
 
 .858 
 
 .68463 
 
 874 
 
 .74201 
 
 868 
 
 99344 
 
 1,3 
 
 .0066 
 
 
 .859 
 
 .69337 
 
 875 
 
 .75070 
 
 869 
 
 99345 
 
 1,3 
 
 .0066 
 
 
 2.860 
 
 8.70213 
 
 876 
 
 8.75940 
 
 870 
 
 0.99346 
 
 1,3 
 
 1.0066 
 
 0,1 
 
 .861 
 
 .71089 
 
 877 
 
 .76810 
 
 871 
 
 .99348 
 
 1,3 
 
 .0066 
 
 
 .862 
 
 .71967 
 
 878 
 
 .77682 
 
 872 
 
 .99349 
 
 i,3 
 
 .0066 
 
 
 .863 
 
 .72845 
 
 879 
 
 .78554 
 
 873 
 
 99350 
 
 i,3 
 
 .0065 
 
 
 .864 
 
 .73724 
 
 879 
 
 .79428 
 
 874 
 
 99351 
 
 1,3 
 
 .0065 
 
 
 2.865 
 
 8.74604 
 
 880 
 
 8.80302 
 
 875 
 
 0.99353 
 
 1,3 
 
 1.0065 
 
 0,1 
 
 .85^ 
 
 .75484 
 
 881 
 
 .81177 
 
 875 
 
 99354 
 
 1,3 
 
 .0065 
 
 
 .867 
 
 .76366 
 
 882 
 
 .82053 
 
 876 
 
 99355 
 
 i,3 
 
 .0065 
 
 
 .868 
 
 .77248 
 
 883 
 
 
 877 
 
 99357 
 
 1,3 
 
 .0065 
 
 
 .869 
 
 .78132 
 
 884 
 
 .83807 
 
 878 
 
 99358 
 
 1,3 
 
 .0065 
 
 
 2.870 
 
 8.70016 
 
 885 
 
 8.84686 
 
 879 
 
 0.99359 
 
 1,3 
 
 1.0065 
 
 0,1 
 
 .871 
 
 .79901 
 
 886 
 
 .85565 
 
 880 
 
 .99360 
 
 1,3 
 
 .0064 
 
 
 .872 
 
 .80787 
 
 886 
 
 .86446 
 
 881 
 
 .99362 
 
 1,3 
 
 .0064 
 
 
 .873 
 
 .81674 
 
 887 
 
 .87327 
 
 882 
 
 .99363 
 
 1,3 
 
 .0064 
 
 
 874 
 
 .82562 
 
 888 
 
 .88209 
 
 883 
 
 .99364 
 
 1,3 
 
 .0064 
 
 
 2.875 
 
 8.83450 
 
 889 
 
 8.89092 
 
 883 
 
 0.99365 
 
 i,3 
 
 1.0064 
 
 0,1 
 
 .876 
 
 .84340 
 
 890 
 
 .89976 
 
 884 
 
 .99367 
 
 i,3 
 
 .0064 
 
 
 .877 
 
 .85230 
 
 891 
 
 .90861 
 
 885 
 
 .99368 
 
 1,3 
 
 .0064 
 
 
 .878 
 
 .86122 
 
 892 
 
 .91746 
 
 886 
 
 .99369 
 
 1,3 
 
 .0063 
 
 
 879 
 
 .87014 
 
 893 
 
 .92633 
 
 887 
 
 99371 
 
 1,3 
 
 .0063 
 
 
 2.880 
 
 8.87907 
 
 894 
 
 8.93520 
 
 888 
 
 0.99372 
 
 1,3 
 
 1.0063 
 
 o,r 
 
 .881 
 
 .88801 
 
 894 
 
 .94409 
 
 889 
 
 99373 
 
 1,3 
 
 .0063 
 
 
 .882 
 
 .89696 
 
 895 
 
 .95298 
 
 890 
 
 99374 
 
 1,2 
 
 .0063 
 
 
 .883 
 
 .90591 
 
 896 
 
 .96188 
 
 891 
 
 99376 
 
 1,2 
 
 .0063 
 
 
 .884 
 
 .91488 
 
 897 
 
 .97079 
 
 891 
 
 99377 
 
 1,2 
 
 .0063 
 
 
 2.885 
 
 8.92386 
 
 898 
 
 8.97971 
 
 892 
 
 0.09378 
 
 1,2 
 
 1.0063 
 
 0,1 
 
 .886 
 
 .93284 
 
 899 
 
 .98864 
 
 893 
 
 99379 
 
 1,2 
 
 .0062 
 
 
 .887 
 
 .94183 
 
 900 
 
 .99758 
 
 894 
 
 .99380 
 
 1,2 
 
 .0062 
 
 
 .888 
 
 .95084 
 
 901 
 
 9.00652 
 
 895 
 
 .09382 
 
 1,2 
 
 .0062 
 
 
 .889 
 
 .95985 
 
 902 
 
 .01548 
 
 896 
 
 .09383 
 
 1,2 
 
 .0062 
 
 
 2.890 
 
 8.96887 
 
 902 
 
 9.02444 
 
 897 
 
 0.99384 
 
 1,2 
 
 1.0062 
 
 0,1 
 
 .891 
 
 97790 
 
 003 
 
 .03342 
 
 898 
 
 99385 
 
 1,2 
 
 .0062 
 
 
 .892 
 
 .98693 
 
 004 
 
 .04240 
 
 899 
 
 99387 
 
 1,2 
 
 .0062 
 
 
 .893 
 
 .99598 
 
 905 
 
 .05139 
 
 900 
 
 99388 
 
 1,2 
 
 .0062 
 
 
 .894 
 
 9.00504 
 
 906 
 
 .06039 
 
 901 
 
 .99389 
 
 1,2 
 
 .0061 
 
 
 2.895 
 
 9.01410 
 
 007 
 
 9.06940 
 
 901 
 
 0-99390 
 
 1,2 
 
 I. 0061 
 
 0,1 
 
 .896 
 
 .02318 
 
 008 
 
 .07842 
 
 002 
 
 .09391 
 
 1,2 
 
 .0061 
 
 
 .897 
 
 .03226 
 
 009 
 
 .08745 
 
 903 
 
 .99393 
 
 1,2 
 
 .0061 
 
 
 .898 
 
 .04135 
 
 910 
 
 .09648 
 
 004 
 
 99394 
 
 1,2 
 
 .0061 
 
 
 .899 
 
 .05045 
 
 911 
 
 . 10553 
 
 905 
 
 99395 
 
 1,2 
 
 .0061 
 
 
 2.900 
 
 9.05956 
 
 911 
 
 9.H458 
 
 906 
 
 0.09396 
 
 1,2 
 
 I. 0061 
 
 0,1 
 
 u 
 
 tan gd u 
 
 Fo' 
 
 sec gd u 
 
 -FO' 
 
 sin gd u 
 
 < Fo' csc gd u 
 
 F ' 
 
 SMITHSONIAN TABLES 
 
 163 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinh u 
 
 F ' 
 
 cosh u 
 
 F O ' 
 
 tanh u 
 
 Fo' 
 
 coth u 
 
 oF ' 
 
 2.900 
 
 9.05956 
 
 911 
 
 9.H458 
 
 906 
 
 0.09396 
 
 1,2 
 
 I. 0061 
 
 0,1 
 
 .001 
 
 .06868 
 
 912 
 
 . 12365 
 
 907 
 
 .99398 
 
 1,2 
 
 .0061 
 
 
 .902 
 
 .07781 
 
 9U 
 
 . 13272 
 
 908 
 
 99399 
 
 1,2 
 
 .0060 
 
 
 .903 
 
 .08695 
 
 914 
 
 .14180 
 
 009 
 
 .99400 
 
 1,2 
 
 .0060 
 
 
 .904 
 
 .09609 
 
 915 
 
 .15090 
 
 910 
 
 .99401 
 
 1,2 
 
 .0060 
 
 
 2.905 
 
 9. 10525 
 
 9l6 
 
 9.16000 
 
 911 
 
 0.90402 
 
 1,2 
 
 I. 0060 
 
 0,1 
 
 .906 
 
 .11441 
 
 917 
 
 .16911 
 
 911 
 
 .99403 
 
 1,2 
 
 .0060 
 
 
 .907 
 
 12359 
 
 9l8 
 
 .17823 
 
 912 
 
 .99405 
 
 1,2 
 
 .0060 
 
 
 .908 
 
 . 13277 
 
 919 
 
 .18735 
 
 913 
 
 .99406 
 
 1,2 
 
 .0060 
 
 
 .909 
 
 .1410 
 
 92O 
 
 .19649 
 
 914 
 
 .99407 
 
 1,2 
 
 .0060 
 
 
 2.910 
 
 9.I5II6 
 
 921 
 
 9.20564 
 
 9i5 
 
 0.90408 
 
 1,2 
 
 1. 0060 
 
 0,1 
 
 .911 
 
 .16037 
 
 921 
 
 .21479 
 
 916 
 
 .99409 
 
 1,2 
 
 .0059 
 
 
 .912 
 
 .10959 
 
 922 
 
 .22396 
 
 917 
 
 994II 
 
 1,2 
 
 .0059 
 
 
 .913 
 
 .17882 
 
 923 
 
 .23313 
 
 918 
 
 .99412 
 
 1,2 
 
 .0059 
 
 
 .914 
 
 .18806 
 
 924 
 
 .24232 
 
 919 
 
 .99413 
 
 1,2 
 
 .0059 
 
 
 2.915 
 
 9- 19730 
 
 925 
 
 9.25I5I 
 
 920 
 
 0.99414 
 
 1,2 
 
 1.0059 
 
 0,1 
 
 .916 
 
 .20656 
 
 926 
 
 .26071 
 
 921 
 
 .99415 
 
 1,2 
 
 .0059 
 
 
 .917 
 
 .21583 
 
 927 
 
 .26092 
 
 922 
 
 .99416 
 
 1,2 
 
 .0059 
 
 
 .918 
 
 .22510 
 
 928 
 
 .27914 
 
 923 
 
 .99418 
 
 1,2 
 
 .0059 
 
 
 .919 
 
 .23438 
 
 929 
 
 .28837 
 
 923 
 
 .99419 
 
 1,2 
 
 .0058 
 
 
 2.920 
 
 9.24368 
 
 930 
 
 9.29761 
 
 924 
 
 0.99420 
 
 1,2 
 
 1.0058 
 
 0,1 
 
 .921 
 
 .25298 
 
 93i 
 
 .30686 
 
 925 
 
 .99421 
 
 1,2 
 
 .0058 
 
 
 .922 
 
 .26229 
 
 932 
 
 .31612 
 
 926 
 
 .99422 
 
 1,2 
 
 .0058 
 
 
 .923 
 
 .27161 
 
 933 
 
 .32538 
 
 927 
 
 .99423 
 
 1,1 
 
 .0058 
 
 
 .924 
 
 .28094 
 
 933 
 
 .33466 
 
 928 
 
 .99425 
 
 1,1 
 
 .0058 
 
 
 2.925 
 
 9.2O028 
 
 934 
 
 9-34395 
 
 929 
 
 0.99426 
 
 I, 
 
 1.0058 
 
 0,1 
 
 .926 
 
 29963 
 
 935 
 
 .35324 
 
 930 
 
 .99427 
 
 I, 
 
 .0058 
 
 
 .927 
 
 .30809 
 
 936 
 
 .36254 
 
 931 
 
 .99428 
 
 I, 
 
 .0058 
 
 
 .928 
 
 .31835 
 
 937 
 
 .37186 
 
 932 
 
 .99429 
 
 I, 
 
 .0057 
 
 
 .929 
 
 .32773 
 
 938 
 
 .38118 
 
 933 
 
 .99430 
 
 I, 
 
 .0057 
 
 
 2.930 
 
 9-33712 
 
 939 
 
 9.39051 
 
 934 
 
 0.09531 
 
 I, 
 
 1.0057 
 
 0,1 
 
 .931 
 
 .34651 
 
 940 
 
 .39986 
 
 935 
 
 .99433 
 
 I, 
 
 .0057 
 
 
 .932 
 
 35592 
 
 941 
 
 .40921 
 
 936 
 
 .99434 
 
 I, 
 
 .0057 
 
 
 933 
 
 .36533 
 
 942 
 
 .41857 
 
 937 
 
 99435 
 
 I, 
 
 .0057 
 
 
 934 
 
 37475 
 
 943 
 
 .42794 
 
 937 
 
 .99436 
 
 I, 
 
 0057 
 
 
 2.935 
 
 9.38419 
 
 944 
 
 9.43732 
 
 938 
 
 0.09437 
 
 I, 
 
 1.0057 
 
 0,1 
 
 .936 
 
 .39363 
 
 945 
 
 .44671 
 
 939 
 
 .99438 
 
 I, 
 
 .0057 
 
 
 937 
 
 .40308 
 
 946 
 
 .45610 
 
 940 
 
 99439 
 
 I, 
 
 .0056 
 
 
 .938 
 
 .41254 
 
 947 
 
 .46551 
 
 941 
 
 .99440 
 
 I, 
 
 .0056 
 
 
 939 
 
 .42201 
 
 947 
 
 47493 
 
 942 
 
 99441 
 
 I, 
 
 .0056 
 
 
 2.940 
 
 9.43H9 
 
 948 
 
 9.48436 
 
 943 
 
 0.99443 
 
 I. 
 
 1.0056 
 
 0,1 
 
 .941 
 
 .44098 
 
 949 
 
 .49379 
 
 944 
 
 .99444 
 
 I, 
 
 .0056 
 
 
 .942 
 
 .45048 
 
 950 
 
 .50324 
 
 945 
 
 99445 
 
 I, 
 
 .0056 
 
 
 943 
 
 45999 
 
 951 
 
 .51269 
 
 946 
 
 .99446 
 
 I, 
 
 .0056 
 
 
 944 
 
 .46950 
 
 952 
 
 .52216 
 
 947 
 
 99447 
 
 I, 
 
 .0056 
 
 
 2.045 
 
 9.47903 
 
 953 
 
 9.53163 
 
 948 
 
 0.09448 
 
 I, 
 
 1.0055 
 
 0,1 
 
 .946 
 
 .48857 
 
 954 
 
 .54H2 
 
 949 
 
 .99449 
 
 I, 
 
 0055 
 
 
 947 
 
 .49811 
 
 955 
 
 .55061 
 
 950 
 
 .450 
 
 I, 
 
 .0055 
 
 
 .948 
 
 .50767 
 
 956 
 
 .56011 
 
 951 
 
 99451 
 
 I, 
 
 .0055 
 
 
 .949 
 
 .51723 
 
 957 
 
 .56962 
 
 952 
 
 99453 
 
 I, 
 
 .0055 
 
 
 2.950 
 
 9.52681 
 
 958 
 
 9.57915 
 
 953 
 
 0.99454 
 
 1,1 
 
 1.0055 
 
 0,1 
 
 u 
 
 tan ad u 
 
 Fo' 
 
 sec gd u 
 
 Fo' 
 
 sin od u 
 
 Fo' 
 
 esc od u 
 
 -Fo 1 
 
 SMITHSONIAN TABLES 
 
 164 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinh u 
 
 Fo' 
 
 cosh u 
 
 ,F ' 
 
 tanh u 
 
 F ' 
 
 coth u 
 
 F ' 
 
 2.950 
 
 9.52681 
 
 958 
 
 9.57915 
 
 953 
 
 0.99454 
 
 
 1.0055 
 
 0,1 
 
 \ .951 
 
 53639 
 
 959 
 
 .58868 
 
 954 
 
 .99455 
 
 
 0055 
 
 
 X .952 
 
 .54598 
 
 960 
 
 .55822 
 
 955 
 
 .99456 
 
 
 .0055 
 
 
 953 
 
 55559 
 
 961 
 
 .60777 
 
 956 
 
 99457 
 
 
 .0055 
 
 
 954 
 
 .56520 
 
 962 
 
 .61733 
 
 957 
 
 99458 
 
 
 .0055 
 
 
 2.955 
 .956 
 
 9.57482 
 .58445 
 
 963 
 964 
 
 9.62600 
 .63648 
 
 957 
 
 958 
 
 0-99459 
 .99460 
 
 
 1.0054 
 .0054 
 
 0,1 
 
 .957 
 
 59410 
 
 965 
 
 .64607 
 
 959 
 
 .99461 
 
 
 .0054 
 
 
 .958 
 
 .60375 
 
 966 
 
 .65567 
 
 960 
 
 .99462 
 
 
 .0054 
 
 
 959 
 
 .61341 
 
 967 
 
 .66528 
 
 961 
 
 .99463 
 
 
 .0054 
 
 
 2.960 
 
 9.62308 
 
 967 
 
 9.67490 
 
 962 
 
 0.99464 
 
 
 1.0054 
 
 0,1 
 
 .961 
 
 .63276 
 
 968 
 
 .68452 
 
 963 
 
 .99465 
 
 
 0054 
 
 
 .962 
 
 .64245 
 
 969 
 
 .69416 
 
 954 
 
 .99467 
 
 
 .0054 
 
 
 .963 
 
 65214 
 
 970 
 
 .70381 
 
 965 
 
 .99468 
 
 
 .0054 
 
 
 .964 
 
 .66185 
 
 971 
 
 .71347 
 
 966 
 
 .99469 
 
 
 .0053 
 
 
 2.965 
 
 9.67157 
 
 972 
 
 9.72313 
 
 967 
 
 0.99470 
 
 
 1.0053 
 
 0,1 
 
 .966 
 
 .68130 
 
 973 
 
 .73281 
 
 968 
 
 .99471 
 
 
 .0053 
 
 
 .967 
 
 .69104 
 
 974 
 
 .74249 
 
 969 
 
 .99472 
 
 
 .0053 
 
 
 .968 
 
 .70078 
 
 975 
 
 .75219 
 
 970 
 
 .99473 
 
 
 .0053 
 
 
 .969 
 
 .71054 
 
 976 
 
 .76190 
 
 971 
 
 99474 
 
 IO 
 
 .0053 
 
 
 2.970 
 
 9.72031 
 
 977 
 
 9.77l6l 
 
 972 
 
 0.99475 
 
 1,0 
 
 1.0053 
 
 0,1 
 
 .971 
 
 .73008 
 
 978 
 
 .78134 
 
 973 
 
 .99476 
 
 1,0 
 
 .0053 
 
 
 .972 
 
 .73987 
 
 979 
 
 .79107 
 
 974 
 
 99477 
 
 1,0 
 
 .0053 
 
 
 .973 
 
 .74967 
 
 980 
 
 .80082 
 
 975 
 
 99478 
 
 1,0 
 
 .0052 
 
 
 .974 
 
 .75947 
 
 
 .81057 
 
 976 
 
 99479 
 
 1,0 
 
 .0052 
 
 
 2.975 
 
 9.76929 
 
 982 
 
 9.82034 
 
 977 
 
 0.99480 
 
 1,0 
 
 1.0052 
 
 0,1 
 
 .976 
 
 .77911 
 
 983 
 
 .83011 
 
 978 
 
 .09481 
 
 1,0 
 
 .0052 
 
 
 977 
 
 .78895 
 
 984 
 
 .83989 
 
 979 
 
 .99482 
 
 1,0 
 
 .0052 
 
 
 .978 
 
 .79879 
 
 985 
 
 .84969 
 
 980 
 
 .99483 
 
 1,0 
 
 .0052 
 
 
 979 
 
 .80865 
 
 986 
 
 .85949 
 
 p8l 
 
 .99484 
 
 1,0 
 
 .0052 
 
 
 2.980 
 
 9.81851 
 
 987 
 
 9.86930 
 
 982 
 
 0.99485 
 
 1,0 
 
 1.0052 
 
 0,1 
 
 .981 
 
 .82839 
 
 988 
 
 .87913 
 
 983 
 
 .99486 
 
 I,O 
 
 .0052 
 
 
 .982 
 
 83827 
 
 989 
 
 .88896 
 
 984 
 
 .99487 
 
 1,0 
 
 .0052 
 
 
 .983 
 
 .84816 
 
 990 
 
 .89880 
 
 985 
 
 .99488 
 
 1,0 
 
 .0051 
 
 
 .984 
 
 85807 
 
 991 
 
 .90866 
 
 986 
 
 99489 
 
 1,0 
 
 .0051 
 
 
 2.985 
 
 9.86798 
 
 992 
 
 9.91852 
 
 987 
 
 0.99490 
 
 1,0 
 
 1.0051 
 
 0,1 
 
 .986 
 
 .87790 
 
 993 
 
 .92839 
 
 988 
 
 99491 
 
 1,0 
 
 .0051 
 
 
 .987 
 
 .88784 
 
 994 
 
 .93828 
 
 989 
 
 99492 
 
 1,0 
 
 .0051 
 
 
 .988 
 
 .89778 
 
 995 
 
 .94817 
 
 990 
 
 99493 
 
 1,0 
 
 .0051 
 
 
 .989 
 
 .90773 
 
 996 
 
 .95807 
 
 991 
 
 99495 
 
 1,0 
 
 .0051 
 
 
 2.990 
 
 9.91770 
 
 997 
 
 9.96798 
 
 992 
 
 0.99496 
 
 1,0 
 
 1.0051 
 
 0,1 
 
 .991 
 
 .92767 
 
 998 
 
 97791 
 
 993 
 
 99497 
 
 1,0 
 
 0051 
 
 
 992 
 
 .93765 
 
 999 
 
 .98784 
 
 994 
 
 .99498 
 
 I,O 
 
 0051 
 
 
 993 
 
 .94765 
 
 IOOO 
 
 .99778 
 
 995 
 
 99499 
 
 1,0 
 
 .0050 
 
 
 994 
 
 .95765 
 
 IOOI 
 
 10.00774 
 
 996 
 
 99500 
 
 1,0 
 
 .0050 
 
 
 2. 995 
 
 9.96766 
 
 IOO2 
 
 10.01770 
 
 997 
 
 0.99501 
 
 1,0 
 
 1.0050 
 
 0,1 
 
 .996 
 
 .97768 
 
 1003 
 
 .02767 
 
 9C8 
 
 .09502 
 
 1,0 
 
 .0050 
 
 
 997 
 
 .98772 
 
 1004 
 
 03765 
 
 999 
 
 99503 
 
 1,0 
 
 .0050 
 
 
 .998 
 
 .99776 
 
 1005 
 
 .04765 
 
 IOOO 
 
 .99504 
 
 1,0 
 
 .0050 
 
 
 .999 
 
 10.00781 
 
 IO06 
 
 .05765 
 
 IOOI 
 
 .99504 
 
 1,0 
 
 .0050 
 
 
 3.000 
 
 10.01787 
 
 IOO7 
 
 10.06766 
 
 IO02 
 
 0.99505 
 
 1,0 
 
 1.0050 
 
 0,1 
 
 u 
 
 tan gd u 
 
 wF ' 
 
 sec gd u 
 
 F ' 
 
 sin gd u 
 
 F ' 
 
 esc gd u 
 
 F ' 
 
 SMITHSONIAN TABLES 
 
 165 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinhu 
 
 F ' 
 
 cosh u 
 
 OFO' 
 
 tanhu 
 
 F O ' 
 
 coth u 
 
 F ' 
 
 3.00 
 
 10.0179 
 
 IO07 
 
 10.0677 
 
 IOO2 
 
 0.99505 
 
 9,9 
 
 1.0050 
 
 1,0 
 
 .01 
 
 10. 1191 
 
 IOI7 
 
 10.1683 
 
 1012 
 
 99515 
 
 9,7 
 
 .0049 
 
 1,0 
 
 .02 
 
 IO.22I2 
 
 IO27 
 
 10.2700 
 
 IO22 
 
 .99525 
 
 9,5 
 
 .0048 
 
 I,O 
 
 .03 
 
 10.3245 
 
 1037 
 
 10.3728 
 
 1032 
 
 .99534 
 
 9,3 
 
 .0047 
 
 0,9 
 
 .04 
 
 IO.4287 
 
 1048 
 
 10.4765 
 
 1043 
 
 99543 
 
 9,1 
 
 .0046 
 
 0,9 
 
 3-05 
 
 10.5340 
 
 1058 
 
 10.5814 
 
 1053 
 
 0.99552 
 
 8,9 
 
 1.0045 
 
 0,9 
 
 .06 
 
 10.6403 
 
 1069 
 
 10.6872 
 
 1064 
 
 .99561 
 
 8,8 
 
 .0044 
 
 0,9 
 
 .07 
 
 10.7477 
 
 1079 
 
 10.7942 
 
 1075 
 
 .99570 
 
 8,6 
 
 .0043 
 
 0,9 
 
 .08 
 
 10.8562 
 
 1000 
 
 10.0022 
 
 1086 
 
 .99578 
 
 8,4 
 
 .0042 
 
 0,8 
 
 .09 
 
 10.9658 
 
 IIOI 
 
 11.0113 
 
 1097 
 
 .99587 
 
 8,2 
 
 .0041 
 
 0,8 
 
 3-10 
 
 11.0765 
 
 III2 
 
 11.1215 
 
 1108 
 
 0-99595 
 
 8,1 
 
 1.0041 
 
 0,8 
 
 .11 
 
 11.1882 
 
 1123 
 
 11.2328 
 
 1119 
 
 .99603 
 
 7,9 
 
 .0040 
 
 0,8 
 
 .12 
 
 11.3011 
 
 1135 
 
 11-3453 
 
 1130 
 
 .09611 
 
 7,8 
 
 .0039 
 
 0,8 
 
 13 
 
 11.4151 
 
 1146 
 
 11.4588 
 
 1142 
 
 .99618 
 
 7,6 
 
 .0038 
 
 0,8 
 
 14 
 
 H.5303 
 
 1157 
 
 n.5736 
 
 ii53 
 
 .99626 
 
 7,5 
 
 .0038 
 
 0,8 
 
 3-15 
 
 13.6466 
 
 1169 
 
 11,6895 
 
 1165 
 
 0.99633 
 
 7,3 
 
 1.0037 
 
 o,7 
 
 .16 
 
 11.7641 
 
 1181 
 
 11.8065 
 
 1176 
 
 .99641 
 
 7,2 
 
 .0036 
 
 o,7 
 
 .17 
 
 11.8827 
 
 1192 
 
 11.9247 
 
 1188 
 
 .99648 
 
 7,o 
 
 .0035 
 
 o,7 
 
 .18 
 
 12.0025 
 
 1204 
 
 12.0442 
 
 1 200 
 
 .99655 
 
 6,9 
 
 0035 
 
 o,7 
 
 .19 
 
 I2~ 1236 
 
 1216 
 
 12.1648 
 
 1212 
 
 .99662 
 
 6,8 
 
 .0034 
 
 o,7 
 
 3-20 
 
 12.2459 
 
 1229 
 
 12.2866 
 
 1225 
 
 0.99668 
 
 6,6 
 
 1.0033 
 
 0,7 
 
 .21 
 
 12.3694 
 
 1241 
 
 12.4097 
 
 1237 
 
 99675 
 
 6,5 
 
 .0033 
 
 o,7 
 
 .22 
 
 12.4941 
 
 1253 
 
 12.5340 
 
 1249 
 
 .99681 
 
 6,4 
 
 .0032 
 
 0,6 
 
 23 
 
 I2.62OO 
 
 1266 
 
 12.6596 
 
 1262 
 
 .99688 
 
 6,2 
 
 .0031 
 
 0,6 
 
 .24 
 
 12.7473 
 
 1279 
 
 12.7864 
 
 1275 
 
 .99694 
 
 6,1 
 
 .0031 
 
 0,6 
 
 3-25 
 
 12.8758 
 
 1291 
 
 12.9146 
 
 1288 
 
 0.99700 
 
 6,0 
 
 1.0030 
 
 0,6 
 
 .26 
 
 13.0056 
 
 1304 
 
 13.0440 
 
 1301 
 
 .99706 
 
 5,9 
 
 .0030 
 
 0,6 
 
 .27 
 
 13-1367 
 
 1317 
 
 13.1747 
 
 1314 
 
 99712 
 
 5,8 
 
 .0029 
 
 0,6 
 
 .28 
 
 13.2691 
 
 I33i 
 
 13.3067 
 
 1327 
 
 .99717 
 
 5,6 
 
 .0028 
 
 0,6 
 
 .29 
 
 13.4028 
 
 1344 
 
 I3-440I 
 
 1340 
 
 .99723 
 
 5,5 
 
 .0028 
 
 0,6 
 
 3-30 
 
 13-5379 
 
 1357 
 
 13.5748 
 
 1354 
 
 0.09728 
 
 5,4 
 
 1.0027 
 
 o,5 
 
 31 
 
 13.6743 
 
 1371 
 
 13-7108 
 
 1367 
 
 99734 
 
 5,3 
 
 .0027 
 
 o,5 
 
 32 
 
 13.8121 
 
 1385 
 
 13-8483 
 
 1381 
 
 .99739 
 
 5,2 
 
 .0026 
 
 o,5 
 
 33 
 
 13.9513 
 
 1399 
 
 13.9871 
 
 1395 
 
 .99744 
 
 5,1 
 
 .0026 
 
 o,5 
 
 34 
 
 14.0918 
 
 I4U 
 
 14.1273 
 
 1409 
 
 99749 
 
 5,o 
 
 .0025 
 
 o,5 
 
 3-35 
 
 14.2338 
 
 1427 
 
 14.2689 
 
 1423 
 
 0.99754 
 
 4,9 
 
 1.0025 
 
 o,5 
 
 .36 
 
 14.3772 
 
 1441 
 
 14.4120 
 
 1438 
 
 99759 
 
 4,8 
 
 .0024 
 
 o,5 
 
 37 
 
 14-5221 
 
 1456 
 
 14.5565 
 
 1452 
 
 .99764 
 
 4,7 
 
 .0024 
 
 o,5 
 
 .38 
 
 14.6684 
 
 1470 
 
 14.7024 
 
 1467 
 
 .99768 
 
 4,6 
 
 .0023 
 
 0,5 
 
 39 
 
 14.8161 
 
 1485 
 
 14.8498 
 
 1482 
 
 99773 
 
 4,5 
 
 .0023 
 
 o,5 
 
 3-40 
 
 14.9654 
 
 1500 
 
 14.9987 
 
 1497 
 
 0.99777 
 
 4,4 
 
 I.OO22 
 
 0,4 
 
 .41 
 
 15.1161 1515 
 
 15.1491 
 
 1512 
 
 .99782 
 
 4^4 
 
 .OO22 
 
 0,4 
 
 .42 
 
 IS.2'&\ 1530 
 
 J.5.30H 
 
 1527 
 
 .99786 
 
 4,3 
 
 .0021 
 
 0,4 
 
 43 
 
 I5.422T 1545 
 
 15.4545 
 
 1542 
 
 .99790 
 
 4,2 
 
 .OO2I 
 
 0,4 
 
 .44 
 
 15." I56l 
 
 15.6095 
 
 1558 
 
 .99795 
 
 4,1 
 
 .O02I 
 
 0,4 
 
 3-45 
 
 15.734- 1577 
 
 1-5.7661 
 
 1573 
 
 0.99799 
 
 4,0 
 
 I.OO20 
 
 0,4 
 
 .46 
 
 15.8928 1592 
 
 15.9242 
 
 1589 
 
 .99803 
 
 3,9 
 
 .002O 
 
 0,4 
 
 47 
 
 I6.O528 
 
 1608 
 
 16.0839 
 
 1605 
 
 .99807 
 
 3,9 
 
 .OOI9 
 
 0,4 
 
 .48 
 
 16.2145 
 
 1625 
 
 16.2453 
 
 1621 
 
 .99810 
 
 3,8 
 
 .OOI9 
 
 0,4 
 
 .49 
 
 16.3777 
 
 1641 
 
 16.4082 
 
 1638 
 
 .99814 
 
 3,7 
 
 .OOI9 
 
 0,4 
 
 3.50 
 
 16.5426 
 
 ,1657 
 
 16.5728 
 
 1654 
 
 0.99818 
 
 3*6 
 
 I.OOI8 
 
 0,4 
 
 u 
 
 tan gd u 
 
 -Fo' 
 
 sec od u 
 
 FO' 
 
 sin gd u 
 
 H F..' 
 
 csc gd u 
 
 FV 
 
 SMITHSONIAN TABLES 
 
 166 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinh u 
 
 w Fo' 
 
 cosh u 
 
 F ' 
 
 tanh u 
 
 ft 
 
 coth u 
 
 F ' 
 
 / 3.50 
 
 16.5426 
 
 1657 
 
 16.5728 
 
 1654 
 
 0.90818 
 
 3,6 
 
 l.OOiS 
 
 0,4 
 
 .51 
 
 16.7092 
 
 1674 
 
 16.7391 
 
 1671 
 
 .99821 
 
 3,6 
 
 .0018 
 
 0,4 
 
 .52 
 
 16.8774 
 
 1691 
 
 16.9070 
 
 1688 
 
 .99825 
 
 3,5 
 
 .0018 
 
 0,4 
 
 .53 
 
 17.0473 
 
 1708 
 
 17.0766 
 
 1705 
 
 .99828 
 
 3,4 
 
 .0017 
 
 0,3 
 
 .54 
 
 17.2190 
 
 1725 
 
 17.2480 
 
 1722 
 
 .99832 
 
 3,4 
 
 .0017 
 
 0,3 
 
 3-55 
 
 17.3923 
 
 1742 
 
 17.4210 
 
 1739 
 
 0.99835 
 
 3,3 
 
 I.OOI7 
 
 0,3 
 
 .56 
 
 17.5674 
 
 I76O 
 
 17.5958 
 
 1757 
 
 .99838 
 
 3,2 
 
 .0016 
 
 o,3 
 
 57 
 
 17.7442 
 
 1777 
 
 17.7724 
 
 1774 
 
 .99842 
 
 3,2 
 
 .0016 
 
 0,3 
 
 .58 
 
 17.9228 
 
 1795 
 
 17.9507 
 
 1792 
 
 .99845 
 
 3,1 
 
 .0016 
 
 o,3 
 
 59 
 
 I8.I032 
 
 1813 
 
 18.1308 
 
 1810 
 
 .99848 
 
 3,0 
 
 .0015 
 
 o,3 
 
 3-60 
 
 18.2855 
 
 1831 
 
 18.3128 
 
 1829 
 
 0.99851 
 
 3,0 
 
 I.OOI5 
 
 o,3 
 
 .61 
 
 18.4695 
 
 1850 
 
 18.4966 
 
 1847 
 
 .99854 
 
 2,9 
 
 .0015 
 
 0,3 
 
 .62 
 
 18.6554 
 
 1868 
 
 18.6822 
 
 1866 
 
 .99857 
 
 2,9 
 
 .0014 
 
 0,3 
 
 63 
 
 18.8432 
 
 1887 
 
 18.8697 
 
 1884 
 
 .99859 
 
 2,8 
 
 .0014 
 
 o,3 
 
 .64 
 
 19.0328 
 
 1906 
 
 19.0590 
 
 1903 
 
 .99862 
 
 2,8 
 
 .0014 
 
 0,3 
 
 3.65 
 
 19.2243 
 
 1925 
 
 19.2503 
 
 1922 
 
 0.99865 
 
 2,7 
 
 I.OOI4 
 
 o,3 
 
 .66 
 
 19.4178 
 
 1944 
 
 19-4435 
 
 1942 
 
 .99868 
 
 2,6 
 
 .0013 
 
 o,3 
 
 .67 
 
 19.6132 
 
 1964 
 
 19-6387 
 
 1961 
 
 .99870 
 
 2,6 
 
 .0013 
 
 o,3 
 
 .68 
 
 19.8106 
 
 1984 
 
 19.8358 
 
 1981 
 
 .99873 
 
 2,5 
 
 .0013 
 
 o,3 
 
 .69 
 
 20.0099 
 
 2003 
 
 20.0349 
 
 200 1 
 
 .99875 
 
 2,5 
 
 .OOI2 
 
 0,2 
 
 3.70 
 
 20.2113 
 
 2024 
 
 20.2360 
 
 2021 
 
 0.99878 
 
 2,4 
 
 I.OOI2 
 
 0,2 
 
 71 
 
 20.4U7 
 
 2044 
 
 20.4391 
 
 2041 
 
 .99880 
 
 2,4 
 
 .OOI2 
 
 0,2 
 
 .72 
 
 2O.62OI 
 
 2064 
 
 20.6443 
 
 2O52 
 
 .99883 
 
 2,3 
 
 .OOI2 
 
 0,2 
 
 73 
 
 20.8276 
 
 2085 
 
 20.8516 
 
 2083 
 
 .99885 
 
 2,3 
 
 .OOI2 
 
 0,2 
 
 74 
 
 21.0371 
 
 2106 
 
 21.0609 
 
 2IO4 
 
 .99887 
 
 2,3 
 
 .OOII 
 
 0,2 
 
 3-75 
 
 21.2488 
 
 , 2127 
 
 21.2723 
 
 2125 
 
 0.99889 
 
 2,2 
 
 I.OOII 
 
 0,2 
 
 .76 
 
 21.4626 
 
 2149 
 
 21.4859 
 
 2146 
 
 .99892 
 
 2,2 
 
 .OOII 
 
 0,2 
 
 77 
 
 21.6785 
 
 2170 
 
 21.7016 
 
 2168 
 
 .99894 
 
 2,1 
 
 .0011 
 
 0,2 
 
 .78 
 
 21.8966 
 
 2192 
 
 21.9194 
 
 2190 
 
 .5^896 
 
 2,1 
 
 .0010 
 
 0,2 
 
 79 
 
 22.1169 
 
 2214 
 
 22.1395 
 
 2212 
 
 .99898 
 
 2,0 
 
 .0010 
 
 0,2 
 
 3-80 
 
 22.3394 
 
 2236 
 
 22.3618 
 
 2234 
 
 0.99900 
 
 2,0 
 
 I. 0010 
 
 0,2 
 
 .81 
 
 22.5641 
 
 2259 
 
 22.5863 
 
 2256 
 
 .99902 
 
 2,0 
 
 .0010 
 
 0,2 
 
 .82 
 
 22./9II 
 
 2281 
 
 22.8131 
 
 2279 
 
 .99004 
 
 1,9 
 
 .0010 
 
 0,2 
 
 .83 
 
 23.0204 
 
 2304 
 
 23.0421 
 
 2302 
 
 .99905 
 
 i,9 
 
 .0009 
 
 0,2 
 
 .84 
 
 23.2520 
 
 2327 
 
 23.2735 
 
 2325 
 
 .99908 
 
 1,8 
 
 .0009 
 
 0,2 
 
 3.85 
 
 23.4859 
 
 2351 
 
 23.5072 
 
 2349 
 
 0.99909 
 
 1,8 
 
 1.0009 
 
 0,2 
 
 .86 
 
 23.7221 
 
 2374 
 
 23.7432 
 
 2372 
 
 .99911 
 
 1,8 
 
 .0009 
 
 0,2 
 
 .87 
 
 23.9608 
 
 2398 
 
 23.9816 
 
 2396 
 
 .99913 
 
 i,7 
 
 .0009 
 
 0,2 
 
 .88 
 
 24.2018 
 
 2422 
 
 24.2224 
 
 24'20 
 
 99915 
 
 i,7 
 
 .0009 
 
 0,2 
 
 .89 
 
 24.4452 
 
 2447 
 
 24.4657 
 
 2445 
 
 .99916 
 
 i,7 
 
 .0008 
 
 0,2 
 
 3-90 
 
 24.6911 
 
 2471 
 
 24.7H3 
 
 2469 
 
 0.09918 
 
 1,6 
 
 1.0008 
 
 0,2 
 
 .91 
 
 24.9395 
 
 2496 
 
 24.9595 
 
 2494 
 
 .99920 
 
 1,6 
 
 .0008 
 
 O,2 
 
 .92 
 
 25.1903 
 
 2521 
 
 25.2101 
 
 2519 
 
 .99921 
 
 1,6 
 
 .0008 
 
 0,2 
 
 93 
 
 25.4437 
 
 2546 
 
 25-4633 
 
 2544 
 
 .90923 
 
 ,5 
 
 .0008 
 
 O,2 
 
 94 
 
 25.6906 
 
 2572 
 
 25.7190 
 
 2570 
 
 .99924 
 
 ,5 
 
 .0008 
 
 0,2 
 
 3.95 
 
 25.9581 
 
 2598 
 
 25-9773 
 
 2596 
 
 0.99926 
 
 ,5 
 
 1.0007 
 
 0,1 
 
 .96 
 
 26.2191 
 
 2624 
 
 26.2382 
 
 2622 
 
 .90927 
 
 ,5 
 
 .0007 
 
 0,1 
 
 .97 
 
 26.4828 
 
 2650 
 
 26.5017 
 
 2648 
 
 .99929 
 
 ,4 
 
 .0007 
 
 0,1 
 
 .98 
 
 26.7492 
 
 2677 
 
 26.7679 
 
 2675 
 
 .99930 
 
 1,4 
 
 .0007 
 
 0,1 
 
 .99 
 
 27.0182 
 
 2704 
 
 27.0367 
 
 27O2 
 
 .99932 
 
 1,4 
 
 .0007 
 
 0,1 
 
 4.00 
 
 27.2899 
 
 2731 
 
 27.3082 
 
 2729 
 
 0.99933 
 
 1,3 
 
 1.0007 
 
 0,1 
 
 u 
 
 tan gd u 
 
 F O ' 
 
 sec gd u 
 
 <-Fo' 
 
 sin gd u 
 
 wF ' 
 
 csc gd u 
 
 F O ' 
 
 SMITHSONIAN TABLES 
 
 167 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinhu 
 
 F ' 
 
 cosh u 
 
 FO' 
 
 tanh u 
 
 - Fo' 
 
 coth u 
 
 Fo' 
 
 4.00 
 
 27.2899 
 
 2731 
 
 27.3082 
 
 2729 
 
 0.99933 
 
 1-3 
 
 I.OOO7 
 
 0,1 
 
 .01 
 
 27.5644 
 
 2758 
 
 27.5825 
 
 2756 
 
 .95934 
 
 i,3 
 
 .0007 
 
 
 .02 
 
 27.8416 
 
 2786 
 
 27.8595 
 
 2784 
 
 .99936 
 
 1,3 
 
 .0006 
 
 
 03 
 
 28.1216 
 
 2814 
 
 28.1393 
 
 2812 
 
 99937 
 
 1,3 
 
 .0006 
 
 
 .04 
 
 28.4044 
 
 2842 
 
 28.4220 
 
 2840 
 
 .99938 
 
 1,2 
 
 .0006 
 
 
 4.05 
 
 28.6900 
 
 2871 
 
 28.7074 
 
 2869 
 
 0.99939 
 
 ,2 
 
 I. 0006 
 
 0,1 
 
 .06 
 
 28.9785 
 
 2900 
 
 28.9958 
 
 2898 
 
 .99941 
 
 ,2 
 
 .0006 
 
 
 .07 
 
 29.2699 
 
 2929 
 
 29.2870 
 
 2927 
 
 .95942 
 
 ,2 
 
 .0006 
 
 
 .08 
 
 
 2958 
 
 29.5812 
 
 2956 
 
 99943 
 
 f 
 
 .0006 
 
 
 .09 
 
 29.8616 
 
 2088 
 
 29.8783 
 
 2986 
 
 .99944 
 
 j 
 
 .0006 
 
 
 4.10 
 
 30.1619 
 
 3018 
 
 30.1784 
 
 3016 
 
 0.99945 
 
 I, 
 
 I.OOO5 
 
 0,1 
 
 .u 
 
 30.4652 
 
 3048 
 
 30.4816 
 
 3047 
 
 .99946 
 
 I, 
 
 .0005 
 
 
 .12 
 
 30.7715 
 
 3079 
 
 30.7877 
 
 3077 
 
 99947 
 
 I, 
 
 .0005 
 
 
 .13 
 
 31.0809 
 
 3110 
 
 31.0970 
 
 3108 
 
 .99948 
 
 1,0 
 
 .0005 
 
 
 .14 
 
 31.3934, 
 
 3141 
 
 31.4094 
 
 3i39 
 
 99949 
 
 1,0 
 
 .0005 
 
 
 4-lS 
 
 3L709I 
 
 3172 
 
 31.7249 
 
 3171 
 
 0.09950 
 
 I,O 
 
 1.0005 
 
 0,1 
 
 .16 
 
 32.0280 
 
 3204 
 
 32.0436 
 
 3203 
 
 99951 
 
 I,O 
 
 .0005 
 
 
 .17 
 
 32.3500 
 
 3237 
 
 32.3655 
 
 3235 
 
 .99952 
 
 1,0 
 
 .0005 
 
 
 .18 
 
 32.6753 
 
 3269 
 
 32.6906 
 
 3268 
 
 99953 
 
 0,9 
 
 .0005 
 
 
 .19 
 
 33.0038 
 
 3302 
 
 33.0190 
 
 3300 
 
 99954 
 
 0,9 
 
 .0005 
 
 
 4.20 
 
 33-3357 
 
 3335 
 
 33.3507 
 
 3334 
 
 0.99955 
 
 0,9 
 
 1.0004 
 
 0,1 
 
 .21 
 
 33.6708 
 
 3369 
 
 33.6857 
 
 3367 
 
 .99956 
 
 0,9 
 
 .0004 
 
 
 .22 
 
 34.0094 
 
 3402 
 
 34.0241 
 
 3401 
 
 .99957 
 
 o,9 
 
 .0004 
 
 
 23 
 
 34.3513 
 
 3437 
 
 34.3659 
 
 3435 
 
 .99958 
 
 0,8 
 
 .0004 
 
 
 .24 
 
 34.6967 
 
 3471 
 
 34.7IH 
 
 3470 
 
 .99958 
 
 0,8 
 
 .0004 
 
 
 4-25 
 
 35.0456 
 
 3506 
 
 35.0598 
 
 3505 
 
 0.99959 
 
 0,8 
 
 I.OOO4 
 
 0,1 
 
 .26 
 
 35-3979 
 
 354 1 
 
 35.4121 
 
 3540 
 
 .99060 
 
 0,8 
 
 .0004 
 
 
 .27 
 
 35.7538 
 
 3577 
 
 35.7678 
 
 3575 
 
 .99061 
 
 0,8 
 
 .0004 
 
 
 .28 
 
 36.1133 
 
 3613 
 
 36.1271 
 
 3611 
 
 .99962 
 
 0,8 
 
 .0004 
 
 
 .29 
 
 36.4764 
 
 3649 
 
 36.4901 
 
 3648 
 
 .99962 
 
 0,8 
 
 .0004 
 
 
 4-30 
 
 36.8431 
 
 3686 
 
 36.8567 
 
 3684 
 
 0.90963 
 
 o,7 
 
 1.0004 
 
 0,1 
 
 31 
 
 37.2135 
 
 3723 
 
 37.2270 
 
 3721 
 
 99964 
 
 o,7 
 
 .0004 
 
 
 32 
 
 37.5877 
 
 376o 
 
 37.6010 
 
 3759 
 
 99965 
 
 o,7 
 
 .0004 
 
 
 33 
 
 37.9656 
 
 3798 
 
 37.9787 
 
 3797 
 
 .99965 
 
 o,7 
 
 .0003 
 
 
 34 
 
 38.3473 
 
 3836 
 
 38.3603 
 
 3835 
 
 .99966 
 
 o,7 
 
 .0003 
 
 
 4-35 
 
 38.7328 
 
 3875 
 
 38.7457 
 
 3873 
 
 0.99967 
 
 o,7 
 
 1.0003 
 
 0,1 
 
 .36 
 
 39.1222 
 
 3913 
 
 39.1350 
 
 3912 
 
 .99967 
 
 o,7 
 
 .0003 
 
 
 37 
 
 39.5155 
 
 3953 
 
 39.5281 
 
 3952 
 
 .99968 
 
 0,6 
 
 .0003 
 
 
 38 
 
 39.9128 
 
 3993 
 
 39.9253 
 
 3991 
 
 .99969 
 
 0,6 
 
 .0003 
 
 
 39 
 
 40.3UO 
 
 4033 
 
 40.3264 
 
 4031 
 
 .99969 
 
 0,6 
 
 .0003 
 
 
 4.40 
 
 40.7193 
 
 4073 
 
 40.7316 
 
 4072 
 
 0.99970 
 
 0,6 
 
 1.0003 
 
 0,1 
 
 .41 
 
 41.1287 
 
 4114 
 
 41.1408 
 
 4H3 
 
 99970 
 
 0,6 
 
 .0003 
 
 
 .42 
 
 41.5421 
 
 4155 
 
 41.5542 
 
 4154 
 
 .99971 
 
 0,6 
 
 .0003 
 
 
 43 
 
 41.9598 
 
 4197 
 
 41.9717 
 
 4196 
 
 .99972 
 
 0,6 
 
 .0003 
 
 
 .44 
 
 42.3816 
 
 4239 
 
 4-'- 3934 
 
 4238 
 
 99972 
 
 0,6 
 
 .0003 
 
 
 4-45 
 
 42.8076 
 
 4282 
 
 42.8193 
 
 4281 
 
 0.99973 
 
 o,5 
 
 1.0003 
 
 0,1 
 
 .46 
 
 43-2380 
 
 432-5 
 
 43.2495 
 
 4324 
 
 99973 
 
 o,5 
 
 .0003 
 
 
 47 
 
 43.6726 
 
 4368 
 
 43-6841 
 
 4367 
 
 99974 
 
 o,5 
 
 .0003 
 
 
 .48 
 
 44.IH7 
 
 4412 
 
 44.1230 
 
 44" 
 
 99974 
 
 o,5 
 
 .0003 
 
 
 .49 
 
 44o55I 
 
 4457 
 
 44.5663 
 
 4456 
 
 .Q997S 
 
 0,5 
 
 .0003 
 
 
 4-50 
 
 45.0030 
 
 4501 
 
 4S.OI4I 
 
 4500 
 
 0.99975 
 
 0,5 
 
 I.OOO2 
 
 0,0 
 
 u 
 
 tan gd u 
 
 F ' 
 
 sec ad u 
 
 F ' 
 
 sin gd u 
 
 Fo' 
 
 csc gd u 
 
 -Fo' 
 
 SMITHSONIAN TABUS 
 
 168 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinhu 
 
 Fo' 
 
 cosh u 
 
 uiFu' 
 
 tanh u 
 
 Fo' 
 
 cothu 
 
 wF ' 
 
 ,4.50 
 
 45.0030 
 
 4501 
 
 45.0141 
 
 4500 
 
 0.99975 
 
 0,5 
 
 I.OOO2 
 
 0,0 
 
 -51 
 
 45.4554 
 
 4547 
 
 45.4664 
 
 4546 
 
 .99976 
 
 0,5 
 
 .0002 
 
 
 ' .52 
 
 45.9124 
 
 4592 
 
 45.9232 
 
 459i 
 
 .99976 
 
 o,5 
 
 .OOO2 
 
 
 53 
 
 46.3739 
 
 4638 
 
 46.3847 
 
 4637 
 
 .99977 
 
 o,5 
 
 .O002 
 
 
 54 
 
 46.8401 
 
 4685 
 
 46.8507 
 
 4684 
 
 99977 
 
 o,5 
 
 .OOO2 
 
 
 4-55 
 
 47.3109 
 
 4732 
 
 47.3215 
 
 473i 
 
 0.99978 
 
 0,4 
 
 1.0002 
 
 0,0 
 
 .56 
 
 47.7865 
 
 478o 
 
 47-7970 
 
 4779 
 
 .99978 
 
 0,4 
 
 .OOO2 
 
 
 .57 
 
 48.2669 
 
 4828 
 
 48.2772 
 
 4827 
 
 .99979 
 
 0,4 
 
 .OOO2 
 
 
 .58 
 
 48.7521 
 
 4876 
 
 48.7623 
 
 4875 
 
 .99979 
 
 0,4 
 
 .O002 
 
 
 59 
 
 49.2421 
 
 4925 
 
 49.2523 
 
 4924 
 
 .99979 
 
 0,4 
 
 .OOO2 
 
 
 4.60 
 
 49.7371 
 
 4975 
 
 49.7472 
 
 4974 
 
 0.99080 
 
 0,4 
 
 I.OOO2 
 
 0,0 
 
 .61 
 
 50.2371 
 
 5025 
 
 50.2471 
 
 5024 
 
 .99980 
 
 0,4 
 
 .OOO2 
 
 
 .62 
 
 50.7421 
 
 5075 
 
 50.7519 
 
 5074 
 
 .99981 
 
 0,4 
 
 .OOO2 
 
 
 63 
 
 51.2522 
 
 5126 
 
 51.2619 
 
 5125 
 
 .99981 
 
 0,4 
 
 .OOO2 
 
 
 .64 
 
 51.7673 
 
 5178 
 
 51.7770 
 
 5177 
 
 .99981 
 
 0,4 
 
 .OOO2 
 
 
 4.65 
 
 52.2877 
 
 5230 
 
 52.2973 
 
 5229 
 
 0.99982 
 
 0,4 
 
 I.OOO2 
 
 0,0 
 
 .66 
 
 52.8133 
 
 5282 
 
 52.8228 
 
 5281 
 
 .99982 
 
 0,4 
 
 .OOO2 
 
 
 .67 
 
 53-3442 
 
 5335 
 
 53.3536 
 
 5334 
 
 .99982 
 
 0,4 
 
 .OOO2 
 
 
 .68 
 
 53.8804 
 
 5389 
 
 53.8897 
 
 5388 
 
 .99983 
 
 o,3 
 
 .O002 
 
 
 .69 
 
 54.4220 
 
 5443 
 
 54.4312 
 
 5442 
 
 .99983 
 
 0,3 
 
 .OOO2 
 
 
 4.70 
 
 54-9690 
 
 5498 
 
 54.9781 
 
 5497 
 
 0.99983 
 
 0,3 
 
 I.OOO2 
 
 0,0 
 
 71 
 
 55.5216 
 
 5553 
 
 55-5306 
 
 5552 
 
 .99984 
 
 0,3 
 
 .OOO2 
 
 
 .72 
 
 56.0797 
 
 5609 
 
 56.0886 
 
 5608 
 
 .99984 
 
 o,3 
 
 .OOO2 
 
 
 73 
 
 56.6434 
 
 5665 
 
 56.6522 
 
 5664 
 
 .99984 
 
 o,3 
 
 .OOO2 
 
 
 74 
 
 57.2127 
 
 5722 
 
 57.2215 
 
 5721 
 
 .99985 
 
 0,3 
 
 .OOO2 
 
 
 4-75 
 
 57.7878 
 
 578o 
 
 57.7965 
 
 5779 
 
 0.99985 
 
 0,3 
 
 I.OOOI 
 
 0,0 
 
 .76 
 
 58.3687 
 
 5838 
 
 58.3772 
 
 5837 
 
 .99985 
 
 0,3 
 
 .OOOI 
 
 
 77 
 
 58.9554 
 
 5896 
 
 58.9639 
 
 5896 
 
 .99986 
 
 0,3 
 
 .OOOI 
 
 
 78 
 
 59.5480 
 
 5956 
 
 59.5564 
 
 5955 
 
 .99986 
 
 o,3 
 
 .OOOI 
 
 
 79 
 
 60. 1465 
 
 6015 
 
 60.1548 
 
 6015 
 
 .99986 
 
 0,3 
 
 .OOOI 
 
 
 4.80 
 
 60.7511 
 
 6076 
 
 60.7593 
 
 6075 
 
 0.99986 
 
 0,3 
 
 I.OOOI 
 
 0,0 
 
 .81 
 
 61.3617 
 
 6i37 
 
 61.3699 
 
 6136 
 
 .99987 
 
 0,3 
 
 .OOOI 
 
 
 .82 
 
 61.9785 
 
 6199 
 
 61.9866 
 
 6198 
 
 .99987 
 
 0,3 
 
 .OOOI 
 
 
 .83 
 
 62.6015 
 
 6261 
 
 62.6095 
 
 6260 
 
 .99987 
 
 0,3 
 
 .OOOI 
 
 
 .84 
 
 63.2307 
 
 6324 
 
 63.2386 
 
 6323 
 
 .99987 
 
 o,3 
 
 .OOOI 
 
 
 4-85 
 
 63.8663 
 
 6387 
 
 63.8741 
 
 6387 
 
 0.99988 
 
 0,2 
 
 I.OOOI 
 
 0,0 
 
 .86 
 
 64.5082 
 
 6452 
 
 64.5160 
 
 6451 
 
 .99988 
 
 0,2 
 
 .OOOI 
 
 
 .87 
 
 65.1566 
 
 6516 
 
 65.1643 
 
 6516 
 
 .99988 
 
 0,2 
 
 .OOOI 
 
 
 .88 
 
 65.8115 
 
 6582 
 
 65.8191 
 
 6581 
 
 .99988 
 
 0,2 
 
 .OOOI 
 
 
 .89 
 
 66.4730 
 
 6648 
 
 66.4805 
 
 6647 
 
 .99989 
 
 0,2 
 
 .OOOI 
 
 
 4.90 
 
 67.1412 
 
 6715 
 
 67.1486 
 
 6714 
 
 0.99989 
 
 0,2 
 
 I.OOOI 
 
 0,0 
 
 .91 
 
 67.8160 
 
 6782 
 
 67.8234 
 
 6782 
 
 .99989 
 
 0,2 
 
 .0001 
 
 
 .92 
 
 68.4977 
 
 6850 
 
 68.5050 
 
 6850 
 
 .99989 
 
 0,2 
 
 .OOOI 
 
 
 93 
 
 69.1861 
 
 6919 
 
 .69.1934 
 
 6919 
 
 99990 
 
 0,2 
 
 .OOOI 
 
 
 94 
 
 69.8815 
 
 6989 
 
 69.8887 
 
 6988 
 
 .99990 
 
 0,2 
 
 .OOOI 
 
 
 4-95 
 
 70.5839 
 
 7059 
 
 70.5910 
 
 7058 
 
 0.09090 
 
 0,2 
 
 I.OOOI 
 
 0,0 
 
 .96 
 
 71.2934 
 
 7130 
 
 7L3004 
 
 7129 
 
 .99990 
 
 0,2 
 
 .0001 
 
 
 97 
 
 72.0100 
 
 7202 
 
 72.0169 
 
 7201 
 
 .99090 
 
 0,2 
 
 .OOOI 
 
 
 .98 
 
 72.7338 
 
 7274 
 
 72.7406 
 
 7273 
 
 .99991 
 
 0,2 
 
 .OOOI 
 
 
 .99 
 
 73.4648 
 
 7347 
 
 73.4716 
 
 7346 
 
 .99991 
 
 0,2 
 
 .OOOI 
 
 
 5-00 
 
 74.2032 
 
 7421 
 
 74.2099 
 
 7420 
 
 0.99991 
 
 0,2 
 
 I.OOOI 
 
 0,0 
 
 u 
 
 tan gd u 
 
 F O ' 
 
 sec gd u 
 
 F O ' 
 
 sin gd u 
 
 <oFu' 
 
 csc gd u 
 
 F ' 
 
 SMITHSONIAN TABLES 
 
 169 
 
Natural Hyperbolic Functions. 
 
 u 
 
 sinhu 
 
 F ' 
 
 cosh u 
 
 IV 
 
 tanh u 
 
 F O ' 
 
 cothu 
 
 IV 
 
 5.00 
 
 74.2032 
 
 7421 
 
 74.2099 
 
 7420 
 
 0.99991 
 
 0,2 
 
 I. 0001 
 
 0,0 
 
 .01 
 
 74.9490 
 
 7496 
 
 74.9557 
 
 7495 
 
 .99991 
 
 0,2 
 
 .0001 
 
 
 .02 
 
 75.7023 
 
 7571 
 
 75.7000 
 
 7570 
 
 .99991 
 
 0,2 
 
 .0001 
 
 
 03 
 
 76.4632 
 
 7647 
 
 76.4698 
 
 7646 
 
 .99991 
 
 0,2 
 
 .0001 
 
 
 .04 
 
 77-.23I8 
 
 7724 
 
 77.2382 
 
 7723- 
 
 .99992 
 
 0,2 
 
 .0001 
 
 
 5-05 
 
 78.0080 
 
 7801 
 
 78.0144 
 
 7801 
 
 0.99992 
 
 0,2 
 
 I. 0001 
 
 0,0 
 
 .06 
 
 78.7921 
 
 7880 
 
 78.7984 
 
 7879 
 
 .99992 
 
 0,2 
 
 .0001 
 
 
 .07 
 
 79.5840 
 
 7959 
 
 79.5903 
 
 7958 
 
 .99992 
 
 0,2 
 
 .0001 
 
 
 .08 
 
 80.3839 
 
 8039 
 
 80.3901 
 
 8038 
 
 .99992 
 
 0,2 
 
 .0001 
 
 
 .09 
 
 81.1918 
 
 8120 
 
 81.1980 
 
 8119 
 
 .99992 
 
 0,2 
 
 .0001 
 
 
 S.io 
 
 82.0079 
 
 8201 
 
 82.0140 
 
 8201 
 
 0.99993 
 
 0,1 
 
 I.OOOI 
 
 0,0 
 
 .11 
 
 82.8322 
 
 8284 
 
 82.8382 
 
 8283 
 
 99993 
 
 0,1 
 
 .0001 
 
 
 .12 
 
 83-6647 
 
 8367 
 
 83.6707 
 
 8366 
 
 99993 
 
 0,1 
 
 .0001 
 
 
 .13 
 
 84.5056 
 
 8451 
 
 84.5115 
 
 8451 
 
 99993 
 
 0,1 
 
 .0001 
 
 
 .14 
 
 85.3550 
 
 8536 
 
 85.3608 
 
 8535 
 
 99993 
 
 0,1 
 
 .0001 
 
 
 5.15 
 
 86.2128 
 
 8622 
 
 86.2186 
 
 8621 
 
 0.99993 
 
 0,1 
 
 I.OOOI 
 
 0,0 
 
 .16 
 
 87.0794 
 
 8709 
 
 87.0851 
 
 8708 
 
 99993 
 
 0,1 
 
 .0001 
 
 
 .17 
 
 87.9546 
 
 8796 
 
 87-9603 
 
 8795 
 
 .99994 
 
 0,1 
 
 .0001 
 
 
 .18 
 
 88.8386 
 
 8884 
 
 88.8442 
 
 8884 
 
 99994 
 
 0,1 
 
 .0001 
 
 
 .19 
 
 89.7315 
 
 8974 
 
 89.7371 
 
 8973 
 
 .99994 
 
 0,1 
 
 .0001 
 
 
 5-20 
 
 90.6334 
 
 0064 
 
 90.6389 
 
 9063 
 
 0.99994 
 
 0,1 
 
 I.OOOI 
 
 0,0 
 
 .21 
 
 91.5443 
 
 9155 
 
 91.5498 
 
 9154 
 
 99994 
 
 0,1 
 
 .0001 
 
 
 .22 
 
 92.4644 
 
 9247 
 
 92.4698 
 
 9246 
 
 .99994 
 
 0,1 
 
 .0001 
 
 
 .23 
 
 93.3937 
 
 9340 
 
 93.3991 
 
 9339 
 
 .99994 
 
 0,1 
 
 .0001 
 
 
 .24 
 
 94-3324 
 
 9434 
 
 94-3377 
 
 9433 
 
 .99994 
 
 0,1 
 
 .0001 
 
 
 5-25 
 
 95.2805 
 
 9529 
 
 95.2858 
 
 9528 
 
 0.00994 
 
 0,1 
 
 I.OOOI 
 
 0,0 
 
 .26 
 
 96.2381 
 
 9624 
 
 96.2433 
 
 9624 
 
 99995 
 
 0,1 
 
 .0001 
 
 
 .27 
 
 97.2054 
 
 9721 
 
 97.2106 
 
 9721 
 
 99995 
 
 0,1 
 
 .0001 
 
 
 .28 
 
 98. 1824 
 
 9819 
 
 98.1875 
 
 9818 
 
 99995 
 
 0,1 
 
 .0001 
 
 
 .29 
 
 99.1692 
 
 9917 
 
 99.1742 
 
 9917 
 
 99995 
 
 0,1 
 
 .0001 
 
 
 5.30 
 
 100. 1659 
 
 10017 
 
 IOO.I7O9 
 
 10017 
 
 0.99995 
 
 0,1 
 
 I. 0000 
 
 0,0 
 
 -31 
 
 101.1726 
 
 10118 
 
 101 . 1776 
 
 10117 
 
 .99995 
 
 0,1 
 
 .0000 
 
 
 32 
 
 102.1895 
 
 10219 
 
 IO2.I944 
 
 10219 
 
 99995 
 
 0,1 
 
 .0000 
 
 
 .33 
 
 103.2166 
 
 10322 
 
 103.2214 
 
 10322 
 
 99995 
 
 0,1 
 
 .0000 
 
 
 34 
 
 104.2540 
 
 10426 
 
 104.2588 
 
 10425 
 
 99995 
 
 0,1 
 
 .0000 
 
 
 5-35 
 
 105.3018 
 
 I053I 
 
 105.3065 
 
 10530 
 
 0.99995 
 
 0,1 
 
 I.OOOO 
 
 0,0 
 
 .36 
 
 106.3601 
 
 10636 
 
 106.3648 
 
 10636 
 
 .99996 
 
 0,1 
 
 .0000 
 
 
 .37 
 
 107.4291 
 
 10743 
 
 107.4338 
 
 10743 
 
 .99996 
 
 0,1 
 
 .0000 
 
 
 .38 
 
 108.5088 
 
 10851 
 
 I08.5I34 
 
 10851 
 
 .99996 
 
 0,1 
 
 .0000 
 
 
 39 
 
 109.5994 
 
 10960 
 
 109.6040 
 
 10960 
 
 .99996 
 
 0,1 
 
 .0000 
 
 
 5.40 
 
 110.7009 
 
 11071 
 
 110.7055 
 
 11070 
 
 0.99906 
 
 0,1 
 
 I.OOOO 
 
 0,0 
 
 .41 
 
 111.8136 
 
 11182 
 
 III.8l8o 
 
 11181 
 
 .99996 
 
 0,1 
 
 .0000 
 
 
 .42 
 
 H2.9375 
 
 11294 
 
 112.9418 
 
 11294 
 
 .99996 
 
 0,1 
 
 .0000 
 
 
 43 
 
 114.0724 
 
 11408 
 
 114.0768 
 
 11407 
 
 .99996 
 
 0,1 
 
 .0000 
 
 
 .44 
 
 115.2189 
 
 11522 
 
 115.2233 
 
 11522 
 
 99096 
 
 0,1 
 
 .0000 
 
 
 5-45 
 
 116.3769 
 
 11638 
 
 Il6.38l2 
 
 11638 
 
 0.99996 
 
 0,1 
 
 I.OOOO 
 
 0,0 
 
 .46 
 
 117-5466 
 
 H755 
 
 117.5508 
 
 II755 
 
 .99006 
 
 0,1 
 
 .0000 
 
 
 47 
 
 118.7280 
 
 n873 
 
 118.7322 
 
 n873 
 
 .99996 
 
 0,1 
 
 .0000 
 
 
 .48 
 
 119.9213 
 
 1 1993 
 
 119.9254 
 
 11092 
 
 .99997 
 
 0,1 
 
 .0000 
 
 
 .49 
 
 121.1265 
 
 12113 
 
 I2I.I307 
 
 12113 
 
 .99997 
 
 0,1 
 
 .0000 
 
 
 5.50 
 
 122.3439 
 
 12235 
 
 122.3480 
 
 12234 
 
 0.99997 
 
 0,1 
 
 I.OOOO 
 
 0,0 
 
 u 
 
 tan gd u 
 
 Fo' 
 
 sec gd u 
 
 -Fo' 
 
 in od u 
 
 -Fo' 
 
 csc gd u 
 
 *r 
 
 SMITHSONIAN TABLES 
 
 170 
 
Natural Hyperbolic Functions. 
 
 llx- 
 
 sinh u 
 
 F ' 
 
 cosh u 
 
 F ' 
 
 tanhu 
 
 F O ' 
 
 coth u 
 
 Fo' 
 
 3.50 
 
 122.3439 
 
 12235 
 
 122.3480 
 
 12234 
 
 0.90997 
 
 0,1 
 
 I. 0000 
 
 0,0 
 
 '.51 
 
 123-5735 
 
 12358 
 
 123.5776 
 
 12357 
 
 .99997 
 
 0,1 
 
 .0000 
 
 
 .52 
 
 124.8155 
 
 12482 
 
 124.8195 
 
 12482 
 
 99997 
 
 0,1 
 
 .0000 
 
 
 .53 
 
 I26.O7OO 
 
 12007 
 
 126.0739 
 
 12607 
 
 .99997 
 
 0,1 
 
 .0000 
 
 
 54 
 
 127.3370 
 
 12734 
 
 127.3410 
 
 12734 
 
 .99997 
 
 0,1 
 
 .0000 
 
 
 S.S5 
 
 I28.6l68 
 
 12862 
 
 128.6207 
 
 12862 
 
 0.99997 
 
 0,1 
 
 I.OOOO 
 
 0,0 
 
 56 
 
 129.9095 
 
 12991 
 
 129.9133 
 
 12991 
 
 99997 
 
 0,1 
 
 .0000 
 
 
 .57 
 
 I3I.2I5I 
 
 13122 
 
 131.2190 
 
 13122 
 
 99997 
 
 0,1 
 
 .0000 
 
 
 .58 
 
 132.5339 
 
 13254 
 
 132.5377 
 
 13253 
 
 99997 
 
 0,1 
 
 .0000 
 
 
 59 
 
 133.8659 
 
 13387 
 
 133.8697 
 
 13387 
 
 99997 
 
 0,1 
 
 .0000 
 
 
 5.6o 
 
 I35.2II4 
 
 13522 
 
 135.2150 
 
 13521 
 
 0.99997 
 
 0,1 
 
 I.OOOO 
 
 0,0 
 
 .61 
 
 136.5703 
 
 13657 
 
 136.5739 
 
 13657 
 
 99997 
 
 0,1 
 
 .0000 
 
 
 .62 
 
 137.9429 
 
 13795 
 
 137.9465 
 
 13794 
 
 .99997 
 
 0,1 
 
 .0000 
 
 
 .63 
 
 139.3293 
 
 13933 
 
 I39-3329 
 
 13933 
 
 .99997 
 
 0,1 
 
 .0000 
 
 
 .64 
 
 140.7296 
 
 14073 
 
 140.7331 
 
 14073 
 
 99997 
 
 0,1 
 
 .0000 
 
 
 5.65 
 
 142.1440 
 
 14215 
 
 142.1475 
 
 14214 
 
 0.99998 
 
 0,0 
 
 I.OOOO 
 
 0,0 
 
 .66 
 
 143.5726 
 
 14358 
 
 143.5761 
 
 14357 
 
 99998 
 
 0,0 
 
 .0000 
 
 
 .67 
 
 145.0155 
 
 14502 
 
 145.0190 
 
 14502 
 
 .99998 
 
 0,0 
 
 .0000 
 
 
 .68 
 
 146.4730 
 
 14648 
 
 146.4764 
 
 14647 
 
 .99998 
 
 0,0 
 
 .0000 
 
 
 .69 
 
 147-9451 
 
 14795 
 
 147.9485 
 
 14795 
 
 .99998 
 
 0,0 
 
 .0000 
 
 
 5.70 
 
 149.4320 
 
 14944 
 
 149.4354 
 
 14943 
 
 0.99998 
 
 0,0 
 
 I.OOOO 
 
 0,0 
 
 71 
 
 150.9339 
 
 15094 
 
 150.9372 
 
 15093 
 
 .99998 
 
 0,0 
 
 .0000 
 
 
 .72 
 
 152.4508 
 
 15245 
 
 152.4541 
 
 15245 
 
 .99998 
 
 0,0 
 
 .0000 
 
 
 73 
 
 153.9830 
 
 15399 
 
 153.9863 
 
 15398 
 
 .99998 
 
 0,0 
 
 .0000 
 
 
 .74 
 
 155.5306 
 
 15553 
 
 155.5338 
 
 15553 
 
 .99998 
 
 0,0 
 
 .0000 
 
 
 5-75 
 
 157.0938 
 
 I57IO 
 
 157.0969 
 
 15709 
 
 0.99998 
 
 0,0 
 
 I.OOOO 
 
 0,0 
 
 .76 
 
 158.6726 
 
 15868 
 
 r58.6757 
 
 15867 
 
 .99998 
 
 0,0 
 
 .0000 
 
 
 77 
 
 160.2673 
 
 16027 
 
 160.2704 
 
 16027 
 
 .99998 
 
 0,0 
 
 .0000 
 
 
 78 
 
 161.8781 
 
 16188 
 
 161.881 I 
 
 16188 
 
 99998 
 
 0,0 
 
 .0000 
 
 
 79 
 
 163 . 5O5O 
 
 16351 
 
 163.5080 
 
 16350 
 
 .99998 
 
 0,0 
 
 .0000 
 
 
 5.8o 
 
 165.1483 
 
 16515 
 
 165.1513 
 
 16515 
 
 0.99998 
 
 0,0 
 
 I.OOOO 
 
 0,0 
 
 .81 
 
 166.8081 
 
 16681 
 
 166.8111 
 
 16681 
 
 .99998 
 
 0,0 
 
 .0000 
 
 
 .82 
 
 168.4845 
 
 16849 
 
 168.4875 
 
 16848 
 
 .99998 
 
 0,0 
 
 .0000 
 
 
 .83 
 
 170.1779 
 
 17018 
 
 170.1808 
 
 17018 
 
 .99998 
 
 0,0 
 
 .0000 
 
 
 .84 
 
 171.8882 
 
 17189 
 
 171.8911 
 
 17189 
 
 .99998 
 
 0,0 
 
 .0000 
 
 
 5.85 
 
 173.6158 
 
 17362 
 
 173-6186 
 
 17362 
 
 0.99998 
 
 0,0 
 
 I.OOOO 
 
 0,0 
 
 .86 
 
 175.3006 
 
 17536 
 
 175.3635 
 
 17536 
 
 .99998 
 
 0,0 
 
 .0000 
 
 
 .87 
 
 I77.I23I 
 
 I77I3 
 
 177.1259 
 
 17712 
 
 .99998 
 
 0,0 
 
 .0000 
 
 
 .88 
 
 178.9032 
 
 17891 
 
 178.9060 
 
 17890 
 
 .99998 
 
 0,0 
 
 .0000 
 
 
 .89 
 
 180.7013 
 
 18070 
 
 180 . 7040 
 
 18070 
 
 .99998 
 
 0,0 
 
 .0000 
 
 
 5-90 
 
 182.5174 
 
 18252 
 
 182.5201 
 
 18252 
 
 0.99998 
 
 0,0 
 
 I.OOOO 
 
 0,0 
 
 .91 
 
 184.3517 
 
 18435 
 
 184.3544 
 
 18435 
 
 99999 
 
 0,0 
 
 .0000 
 
 
 .92 
 
 186.2045 
 
 18621 
 
 186.2072 
 
 18620 
 
 99999 
 
 0,0 
 
 .0000 
 
 
 93 
 
 188.0759 
 
 18808 
 
 188.0786 
 
 18808 
 
 99999 
 
 0,0 
 
 .0000 
 
 
 94 
 
 189.9661 
 
 18997 
 
 189.9688 
 
 18997 
 
 99999 
 
 0,0 
 
 .0000 
 
 
 5-95 
 
 191.8754 
 
 19188 
 
 191.8780 
 
 19188 
 
 0-99999 
 
 0,0 
 
 I.OOOO 
 
 0,0 
 
 .96 
 
 193.8038 
 
 I938i 
 
 193-8064 
 
 19380 
 
 99999 
 
 0,0 
 
 .0000 
 
 
 1 .97 
 
 195.7516 
 
 19575 
 
 I95.754I 
 
 19575 
 
 99999 
 
 0,0 
 
 .0000 
 
 
 .98 
 
 197.7189 
 
 19772 
 
 197-7214 
 
 19772 
 
 .99999 
 
 0,0 
 
 .0000 
 
 
 .99 
 
 199.7061 
 
 19971 
 
 199-7086 
 
 19971 
 
 99999 
 
 0,0 
 
 .0000 
 
 
 6.00 
 
 201.7132 
 
 20172 
 
 201.7156 
 
 20171 
 
 0.99999 
 
 0,0 
 
 I.OOOO 
 
 0,0 
 
 u 
 
 tan gd u 
 
 F O ' 
 
 sec gd u 
 
 F O ' 
 
 sin gd u 
 
 F ' 
 
 csc gd u 
 
 F</ 
 
 SMITHSONIAN TABLES 
 
 171 
 
TABLE III 
 
 NATURAL AND LOGARITHMIC CIRCULAR FUNCTIONS 
 
 173 
 
Circular Functions. 
 
 u 
 
 sin u 
 
 wF ' 
 
 COS U 
 
 F ' 
 
 log sin u 
 
 F ' 
 
 log cos u 
 
 F ' 
 
 u 
 
 o.oooo 
 
 O.OOOOO 
 
 10,0 
 
 I.OOOOO 
 
 0,0 
 
 CO 
 
 -foo 
 
 0.00000 
 
 0,0 
 
 4 tl 
 
 O 00 OO.OO 
 
 .0001 
 
 .OOOIO 
 
 
 .00000 
 
 
 6.00000 
 
 43429,4 
 
 .00000 
 
 
 o oo 20.63 
 
 .0002 
 
 .00020 
 
 
 .00000 
 
 
 .30103 
 
 21714,7 
 
 .00000 
 
 
 o oo 41.25 
 
 .0003 
 
 .00030 
 
 
 .00000 
 
 
 .47712 
 
 14476,5 
 
 .00000 
 
 
 o 01 01.88 
 
 .0004 
 
 .00040 
 
 
 .00000 
 
 
 .60206 
 
 10857,4 
 
 .00000 
 
 
 o 01 22.51 
 
 0.0005 
 
 0.00050 
 
 IO,O 
 
 I.OOOOO 
 
 0,0 
 
 6.69897 
 
 8685,9 
 
 O.OOOOO 
 
 0,0 
 
 01 43-13 
 
 .0006 
 
 .00060 
 
 
 .00000 
 
 
 .77815 
 
 7238,2 
 
 .00000 
 
 
 o 02 03.76 
 
 .0007 
 
 .00070 
 
 
 .00000 
 
 
 .84510 
 
 6204,2 
 
 .00000 
 
 
 02 24.39 
 
 .0008 
 
 .00080 
 
 
 .00000 
 
 
 .90309 
 
 5428,7 
 
 .00000 
 
 
 02 45.01 
 
 .0009 
 
 .00090 
 
 
 .00000 
 
 
 .95424 
 
 4825,5 
 
 .00000 
 
 
 o 03 05.64 
 
 0.0010 
 
 O.OOIOO 
 
 10,0 
 
 I.OOOOO 
 
 0,0 
 
 7.00000 
 
 4342,9 
 
 O.OOOOO 
 
 0,0 
 
 o 03 26.26 
 
 .OOII 
 
 .OOIIO 
 
 
 .00000 
 
 
 .04139 
 
 3948,1 
 
 .00000 
 
 
 o 03 46.89 
 
 .0012 
 
 .00120 
 
 
 .00000 
 
 
 .07918 
 
 3619,1 
 
 .00000 
 
 
 o 04 07.52 
 
 .0013 
 
 .00130 
 
 
 .00000 
 
 
 .11304 
 
 3340,7 
 
 .00000 
 
 
 o 04 28.14 
 
 .0014 
 
 .00140 
 
 
 .00000 
 
 
 . 14613 
 
 3102,1 
 
 .00000 
 
 
 04 48.77 
 
 0.0015 
 
 0.00150 
 
 IO,O 
 
 I.OOOOO 
 
 0,0 
 
 7.17609 
 
 2895,3 
 
 O.OOOOO 
 
 0,0 
 
 o 05 09.40 
 
 .0016 
 
 .00160 
 
 
 .00000 
 
 
 .20412 
 
 2714,3 
 
 .00000 
 
 
 o 05 30.02 
 
 .0017 
 
 .00170 
 
 
 .00000 
 
 
 .23045 
 
 2554,7 
 
 .00000 
 
 
 o 05 50.65 
 
 .0018 
 
 .00180 
 
 
 .00000 
 
 
 .25527 
 
 2412,7 
 
 .00000 
 
 
 o 06 11.28 
 
 .0019 
 
 .00190 
 
 
 .00000 
 
 
 .27875 
 
 2285,8 
 
 .00000 
 
 
 o 06 31.90 
 
 O.OO2O 
 
 0.00200 
 
 IO,O 
 
 I.OOOOO 
 
 0,0 
 
 7.30103 
 
 2171,5 
 
 O.OOOOO 
 
 0,0 
 
 o 06 52.53 
 
 .0021 
 
 .00210 
 
 
 .00000 
 
 
 .32222 
 
 2068,1 
 
 .00000 
 
 
 o 07 13.16 
 
 .0022 
 
 .00220 
 
 
 .00000 
 
 
 .34242 
 
 1974,1 
 
 .00000 
 
 
 o 07 33-78 
 
 .0023 
 
 .00230 
 
 
 .00000 
 
 
 .36173 
 
 1888,2 
 
 .00000 
 
 
 o 07 54.41 
 
 .0024 
 
 .00240 
 
 
 .00000 
 
 
 .38021 
 
 1809,6 
 
 .00000 
 
 
 o 08 15.04 
 
 0.0025 
 
 0.00250 
 
 IO,O 
 
 I.OOOOO 
 
 0,0 
 
 7-39794 
 
 1737,2 
 
 O.OOOOO 
 
 0,0 
 
 o 08 35.66 
 
 .0026 
 
 .00260 
 
 
 .00000 
 
 
 .41497 
 
 1670,4 
 
 .00000 
 
 
 o 08 56.29 
 
 .0027 
 
 .O027O 
 
 
 .00000 
 
 
 .43136 
 
 1608,5 
 
 .00000 
 
 
 o 09 16.91 
 
 .0028 
 
 .O0280 
 
 
 .00000 
 
 
 .44716 
 
 I55i,o 
 
 .00000 
 
 
 o 09 37-54 
 
 .0029 
 
 .O02OO 
 
 
 .00000 
 
 
 .46240 
 
 1497,6 
 
 .00000 
 
 
 o 09 58.17 
 
 0.0030 
 
 0.00300 
 
 IO,O 
 
 I.OOOOO 
 
 0,0 
 
 7.47712 
 
 1447,6 
 
 0.00000 
 
 0,0 
 
 o 10 18.79 
 
 .0031 
 
 .00310 
 
 
 .00000 
 
 
 .49136 
 
 1400,9 
 
 .00000 
 
 
 o 10 39.42 
 
 .0032 
 
 .00320 
 
 
 0.99999 
 
 
 .50515 
 
 1357,2 
 
 .00000 
 
 
 II 00.05 
 
 .0033 
 
 .00330 
 
 
 .99999 
 
 
 .51851 
 
 1316,0 
 
 .00000 
 
 
 on 20.67 
 
 .0034 
 
 .00340 
 
 
 99999 
 
 
 .53148 
 
 1277,3 
 
 .00000 
 
 
 o ii 41.30 
 
 0.0035 
 
 0.00350 
 
 10,0 
 
 0.99999 
 
 0,0 
 
 7.54407 
 
 1240,8 
 
 0.00000 
 
 0,0 
 
 O 12 01.93 
 
 .0036 
 
 .00360 
 
 
 .99999 
 
 
 .55630 
 
 1206,4 
 
 .00000 
 
 
 O 12 22.55 
 
 .0037 .00370 
 
 
 99999 
 
 
 .56820 
 
 ii73,8 
 
 .00000 
 
 
 12 43.18 
 
 .0038 
 
 .00380 
 
 
 99999 
 
 
 .57978 
 
 1142,9 
 
 .00000 
 
 
 o 13 03.81 
 
 .0039 
 
 .00390 
 
 
 99999 
 
 
 .59106 
 
 1113,6 
 
 .00000 
 
 
 o 13 24.43 
 
 0.0040 
 
 O.OO4OO 
 
 10,0 
 
 0.99999 
 
 0,0 
 
 7.60206 
 
 1085,7 
 
 O.OOOOO 
 
 0,0 
 
 o 13 45-06 
 
 .0041 
 
 .OO4IO 
 
 
 99999 
 
 
 .61278 
 
 1059,2 
 
 .00000 
 
 
 14 05.69 
 
 .0042 
 
 .OO42O 
 
 
 .99999 
 
 
 .62325 
 
 1034,0 
 
 .00000 
 
 
 o 14 26.31 
 
 .0043 
 
 .00430 
 
 
 .99999 
 
 
 .63347 
 
 1010,0 
 
 .00000 
 
 
 o 14 46.94 
 
 .0044 
 
 .00440 
 
 
 .99999 
 
 
 .64345 
 
 087,0 
 
 .00000 
 
 
 o 15 07.57 
 
 0.0045 
 
 O.O045O 
 
 10,0 
 
 0.99999 
 
 0,0 
 
 7.65321 
 
 965,1 
 
 O.OOOOO 
 
 0,0 
 
 o 15 28.19 
 
 .0046 
 
 .OO40O 
 
 
 .99999 
 
 
 .66276 
 
 944,1 
 
 .00000 
 
 
 o 15 48.82 
 
 .0047 
 
 .00470 
 
 
 .99999 
 
 
 .67210 
 
 9^4,0 
 
 .00000 
 
 
 o 16 09.44 
 
 .0048 
 
 .00480 
 
 
 99999 
 
 
 .68124 
 
 904,8 
 
 .00000 
 
 
 o 16 30.07 
 
 .0049 
 
 .00490 
 
 
 99999 
 
 
 .69019 
 
 886,3 
 
 9.99999 
 
 
 o 16 50.70 
 
 0.0050 
 
 0.00500 
 
 10,0 
 
 0.99999 
 
 0,0 
 
 7.69897 
 
 868,6 
 
 9.99999 
 
 0,0 
 
 o 17 11.32 
 
 u 
 
 isinhiu 
 
 -FO' 
 
 cosh iu 
 
 -FO' 
 
 i,' inh iu 
 
 F O ' 
 
 log cosh iu 
 
 F ' 
 
 u 
 
 log . 
 
 SMITHSONIAN TABLES 
 
Circular Functions. 
 
 u 
 
 sin u 
 
 F ' 
 
 COS U 
 
 F ' 
 
 log sin u 
 
 Fo' 
 
 log cos u 
 
 F ' 
 
 u 
 
 0.0056 
 
 0.00500 
 
 IO,0 
 
 0.99999 
 
 0,0 
 
 7.09897 
 
 868,6 
 
 9.99999 
 
 0,0 
 
 / // 
 
 o 17 11.32 
 
 .0051 
 
 .00510 
 
 
 .99999 
 
 0,1 
 
 .70757 
 
 851,6 
 
 .99999 
 
 
 o 17 31.95 
 
 .0052 
 
 .OO52O 
 
 
 .99999 
 
 
 .71600 
 
 835,2 
 
 .99999 
 
 
 o 17 52.58 
 
 0053 
 
 .00530 
 
 
 99999 
 
 
 .72427 
 
 819,4 
 
 99999 
 
 
 o 18 13.20 
 
 .0054 
 
 .00540 
 
 
 .99999 
 
 
 .73239 
 
 804,2 
 
 .99999 
 
 
 o 18 33.83 
 
 0.0055 
 
 0.00550 
 
 10,0 
 
 0.09998 
 
 0,1 
 
 7.74036 
 
 789,6 
 
 9.99999 
 
 0,0 
 
 o 18 54.46 
 
 .0056 
 
 .00560 
 
 
 .99998 
 
 
 .74819 
 
 775,5 
 
 99999 
 
 
 o 19 15.08 
 
 .0057 
 
 .00570 
 
 
 .99998 
 
 
 .75587 
 
 76i,9 
 
 99999 
 
 
 o 19 35-71 
 
 .0058 
 
 .00580 
 
 
 .99998 
 
 
 .76343 
 
 748,8 
 
 99999 
 
 
 o 19 56.34 
 
 .0059 
 
 .00590 
 
 
 .99998 
 
 
 77085 
 
 736,1 
 
 99999 
 
 
 o 20 16.96 
 
 0.0060 
 
 0.00600 
 
 IO,0 
 
 0.99998 
 
 0,1 
 
 7.77815 
 
 723,8 
 
 9.99999 
 
 0,0 
 
 20 37-59 
 
 .0061 
 
 .00610 
 
 
 .99998 
 
 
 78533 
 
 7ii,9 
 
 .99999 
 
 
 20 58.22 
 
 .0062 
 
 .00620 
 
 
 .99998 
 
 
 79239 
 
 7oo,5 
 
 99999 
 
 
 21 18.84 
 
 .0063 
 
 .00630 
 
 
 .99998 
 
 
 
 689,3 
 
 .99999 
 
 
 21 39.47 
 
 .0064 
 
 .00640 
 
 
 .99998 
 
 
 .80618 
 
 678,6 
 
 99999 
 
 
 O 22 OO.O9 
 
 0.0065 
 
 0.00650 
 
 10,0 
 
 0.09998 
 
 0,1 
 
 7.81291 
 
 668,1 
 
 9.99999 
 
 0,0 
 
 O 22 2O.72 
 
 .0066 
 
 .00660 
 
 
 .99998 
 
 
 .81954 
 
 658,0 
 
 .99999 
 
 
 22 41.35 
 
 .0067 
 
 .00670 
 
 
 .99998 
 
 
 .82607 
 
 6148,2 
 
 99999 
 
 
 o 23 01.97 
 
 .0068 
 
 .00680 
 
 
 .09998 
 
 
 .83251 
 
 638,7 
 
 99999 
 
 
 o 23 22.60 
 
 .0069 
 
 .00690 
 
 
 .99998 
 
 
 .83885 
 
 629,4 
 
 99999 
 
 
 o 23 43-23 
 
 0.0070 
 
 0.00700 
 
 10,0 
 
 0.09998 
 
 0,1 
 
 7.84509 
 
 620,4 
 
 9.99999 
 
 0,0 
 
 o 24 03.85 
 
 .0071 
 
 .00710 
 
 
 .99997 
 
 
 .85125 
 
 611,7 
 
 .99999 
 
 
 o 24 24.48 
 
 .0072 
 
 .00720 
 
 
 .99997 
 
 
 85733 
 
 603,2 
 
 99999 
 
 
 o 24 45 . i i 
 
 .0073 
 
 .00730 
 
 
 .99997 
 
 
 .86332 
 
 594,9 
 
 .99909 
 
 
 o 25 05.73 
 
 .0074 
 
 .00740 
 
 
 .99997 
 
 
 .86923 
 
 586,9 
 
 99999 
 
 
 o 25 26.36 
 
 0.0075 
 
 0.00750 
 
 10,0 
 
 0.99997 
 
 0,1 
 
 7.87506 
 
 579,0 
 
 9.99909 
 
 0,0 
 
 o 25 46.99 
 
 .0076 
 
 .00760 
 
 
 .99997 
 
 
 .88081 
 
 571,4 
 
 .99999 
 
 
 o 26 07.61 
 
 .0077 
 
 .00770 
 
 
 .99997 
 
 
 .88649 
 
 564,0 
 
 99999 
 
 
 o 26 28.24 
 
 .0078 
 
 .00780 
 
 
 .99997 
 
 
 .89209 
 
 556,8 
 
 .99999 
 
 
 o 26 48.87 
 
 .0079 
 
 .00790 
 
 
 .99997 
 
 
 .89762 
 
 549,7 
 
 99999 
 
 
 o 27 09-49 
 
 0.0080 
 
 0.00800 
 
 10,0 
 
 0.99997 
 
 0,1 
 
 7.90309 
 
 542,9 
 
 9.90999 
 
 0,0 
 
 o 27 30.12 
 
 .0081 
 
 .00810 
 
 
 .99997 
 
 
 .908148 
 
 536,2 
 
 99999 
 
 
 o 27 50.74 
 
 .0082 
 
 .00820 
 
 
 .99997 
 
 
 .91381 
 
 529,6 
 
 99999 
 
 
 o 28 11.37 
 
 .0083 
 
 .00830 
 
 
 .99997 
 
 
 .91907 
 
 523,2 
 
 99999 
 
 
 o 28 32.00 
 
 .0084 
 
 .00840 
 
 
 .09996 
 
 
 .92427 
 
 517,0 
 
 .99998 
 
 
 o 28 52.62 
 
 0.0085 
 
 0.00850 
 
 IO,O 
 
 0.99996 
 
 0,1 
 
 7.92041 
 
 510,9 
 
 9.99998 
 
 0,0 
 
 o 29 13.25 
 
 .0086 
 
 .00860 
 
 
 .99996 
 
 
 93449 
 
 505,0 
 
 .99998 
 
 
 o 29 33.88 
 
 .0087 
 
 .00870 
 
 
 .99996 
 
 
 93951 
 
 499,1 
 
 .99998 
 
 
 o 29 54-50 
 
 .0088 
 
 .00880 
 
 
 .99996 
 
 
 .94448 
 
 493,5 
 
 .99998 
 
 
 o 30 15.13 
 
 .0089 
 
 .00890 
 
 
 .99996 
 
 
 .94938 
 
 488,0 
 
 99998 
 
 
 o 30 35.76 
 
 0.0090 
 
 0.00000 
 
 10,0 
 
 0.99996 
 
 0,1 
 
 7.95424 
 
 482,5 
 
 9.99998 
 
 0,0 
 
 o 30 56.38 
 
 .0091 
 
 .00910 
 
 
 .99996 
 
 
 95904 
 
 477,2 
 
 .99998 
 
 
 o 31 17.01 
 
 .0092 
 
 .00920 
 
 
 .99996 
 
 
 .96378 
 
 472,0 
 
 .99998 
 
 
 o 31 37.64 
 
 .0093 
 
 .00930 
 
 
 .99996 
 
 
 .96848 
 
 467,0 
 
 .99998 
 
 
 o 31 58.26 
 
 .0094 
 
 .00940 
 
 
 .99996 
 
 
 .97312 
 
 462,0 
 
 .99998 
 
 
 o 32 18.89 
 
 0.0095 
 
 0.00950 
 
 10,0 
 
 0.99995 
 
 0,1 
 
 7.97772 
 
 457,1 
 
 9.99998 
 
 0,0 
 
 o 32 39-52 
 
 .0096 
 
 .00960 
 
 
 99995 
 
 
 .98226 
 
 452,4 
 
 .99998 
 
 
 o 33 00.14 
 
 .0097 
 
 .00970 
 
 
 99995 
 
 
 .98676 
 
 447,7 
 
 .99998 
 
 
 o 33 20.77 
 
 .0098 
 
 .00980 
 
 
 99995 
 
 
 .99122 
 
 443,1 
 
 .99998 
 
 
 o 33 41.40 
 
 .0099 
 
 .00990 
 
 
 99995 
 
 
 .99563 
 
 438,7 
 
 .99998 
 
 
 o 34 02.02 
 
 O.OIOO 
 
 0.01000 
 
 10,0 
 
 0.99995 
 
 0,1 
 
 7.99999 
 
 434,3 
 
 9.99998 
 
 0,0 
 
 34 22.65 
 
 u 
 
 -isinhiu 
 
 F ' 
 
 cosh iu 
 
 -FO' 
 
 ,__sinh iu 
 
 F ' 
 
 log cosh iu 
 
 F O ' 
 
 u 
 
 log . 
 
 SMITHSONIAN TABLES 
 
 175 
 
Circular Functions. 
 
 u 
 
 sin u 
 
 IV 
 
 COS U 
 
 w Fo' log sin u 
 
 Fo' 
 
 log cos u 
 
 -Fo' 
 
 U 
 
 O.OIOO 
 
 O.OIOOO 
 
 10,0 
 
 0.99995 
 
 0,1 
 
 7.99999 
 
 434,3 
 
 9.99998 
 
 0,0 
 
 o34' 22"65 
 
 .OIOI 
 
 .OIOIO 
 
 
 99995 
 
 
 8.00431 
 
 430,0 
 
 .99998 
 
 
 o 34 43-27 
 
 .0102 
 
 .OIO2O 
 
 
 .99995 
 
 
 .00859 
 
 425,8 
 
 .99998 
 
 
 o 35 03.00 
 
 .0103 
 
 .OI03O 
 
 
 .99995 
 
 
 .01283 
 
 421,6 
 
 99998 
 
 
 o 35 24.53 
 
 .0104 
 
 .OI040 
 
 
 .99995 
 
 
 .01703 
 
 417,6 
 
 .99998 
 
 
 35 45-15 
 
 0.0105 
 
 0.01050 
 
 10,0 
 
 0.99994 
 
 0,1 
 
 8.02II8 
 
 413,6 
 
 9.99998 
 
 0,0 
 
 o 36 05.78 
 
 .0106 
 
 .01000 
 
 
 .99994 
 
 
 .02530 
 
 409,7 
 
 .99998 
 
 
 o 36 26.41 
 
 .0107 
 
 .OIO/O 
 
 
 .99994 
 
 
 .02938 
 
 405,9 
 
 .99998 
 
 
 G ^6 47.03 
 
 .0108 
 
 .OIOSO 
 
 
 .99994 
 
 
 .03342 
 
 402,1 
 
 99997 
 
 
 o 37 07.66 
 
 .0109 
 
 .OIOQO 
 
 
 .99994 
 
 
 .03742 
 
 398,4 
 
 .99997 
 
 
 37 28.29 
 
 O.OIIO 
 
 O.OIIOO 
 
 10,0 
 
 0.99994 
 
 0,1 
 
 8.04138 
 
 394,8 
 
 9.99997 
 
 0,0 
 
 o 37 48.91 
 
 .OIII 
 
 .OHIO 
 
 
 99994 
 
 
 04531 
 
 39i,2 
 
 99997 
 
 
 o 38 09.54 
 
 .0112 
 
 .OI 120 
 
 
 .99994 
 
 
 .04921 
 
 387,7 
 
 .99997 
 
 
 o 38 30.17 
 
 .0113 
 
 .01130 
 
 
 .99994 
 
 
 05307 
 
 384,3 
 
 99997 
 
 
 o 38 50.79 
 
 .0114 
 
 .OII4O 
 
 
 .99994 
 
 
 .05690 
 
 380,9 
 
 99997 
 
 
 o 39 11.42 
 
 0.0115 
 
 O.OII5O 
 
 IO,O 
 
 0.99993 
 
 0,1 
 
 8.06069 
 
 377,6 
 
 9-99997 
 
 0,0 
 
 o 39 32.05 
 
 .0116 
 
 .OII60 
 
 
 99993 
 
 
 .06445 
 
 374,4 
 
 99997 
 
 0,1 
 
 o 39 52.67 
 
 .0117 
 
 .OII7O 
 
 
 99993 
 
 
 .05818 
 
 371,2 
 
 99997 
 
 
 o 40 13.30 
 
 .0118 
 
 .OIlSo 
 
 
 99993 
 
 
 .07187 
 
 368,0 
 
 .99997 
 
 
 o 40 33.92 
 
 .0119 
 
 .OIIOO 
 
 
 99993 
 
 
 .07554 
 
 364,9 
 
 ,99997 
 
 
 o 40 54-55 
 
 O.OI20 
 
 O.OI2OO 
 
 IO,0 
 
 0.99993 
 
 O,I 
 
 8.07917 
 
 36i,9 
 
 9.99997 
 
 0,1 
 
 o 41 15.18 
 
 .OI2I 
 
 .OI2IO 
 
 
 99993 
 
 
 .08277 
 
 358,9 
 
 99997 
 
 
 o 41 35.80 
 
 .0122 
 
 .OI22O 
 
 
 .99993 
 
 
 .08635 
 
 356,0 
 
 99997 
 
 
 o 41 56.43 
 
 .0123 
 
 .01230 
 
 
 .99992 
 
 
 .08989 
 
 353,1 
 
 99997 
 
 
 o 42 17.06 
 
 .OI24 
 
 .01240 
 
 
 .99992 
 
 
 .09341 
 
 350,2 
 
 99997 
 
 
 o 42 37-68 
 
 0.012-5 
 
 O.OI25O 
 
 10,0 
 
 0.99992 
 
 0,1 
 
 8.09690 
 
 347,4 
 
 9.99997 
 
 0,1 
 
 o 42 58.31 
 
 .0126 
 
 .OI2OO 
 
 
 .99992 
 
 
 .10036 
 
 344,7 
 
 99997 
 
 
 o 43 i8.94 
 
 .OI27 
 
 .OI27O 
 
 
 99992 
 
 
 10379 
 
 342,0 
 
 .9999^ 
 
 
 o 43 39.56 
 
 .0128 
 
 .OI28O 
 
 
 .99992 
 
 
 . 10720 
 
 339,3 
 
 .95996 
 
 
 o 44 00.19 
 
 .OI29 
 
 .01290 
 
 
 .99992 
 
 
 .11058 
 
 336,6 
 
 99996 
 
 
 o 44 20.82 
 
 0.0130 
 
 O.OI3OO 
 
 10,0 
 
 0.99992 
 
 0,1 
 
 8. i 1393 
 
 334,1 
 
 9-99996 
 
 0,1 
 
 o 44 41.44 
 
 .0131 
 
 .01310 
 
 
 .99991 
 
 
 .11726 
 
 331,5 
 
 .99996 
 
 
 o 45 02.07 
 
 .OI32 
 
 .OI32O 
 
 
 .99991 
 
 
 . 12056 
 
 329,0 
 
 .99996 
 
 
 45 22.70 
 
 0133 
 
 .01330 
 
 
 .99991 
 
 
 .12384 
 
 326,5 
 
 .99996 
 
 
 45 43-32 
 
 .0134 
 
 .01340 
 
 
 .99991 
 
 
 .12709 
 
 324,1 
 
 .99996 
 
 
 46 03-95 
 
 0.0135 
 
 O.OI35O 
 
 10,0 
 
 0.09991 
 
 0,1 
 
 8. 13032 
 
 321,7 
 
 9.99996 
 
 0,1 
 
 o 46 24.57 
 
 .0136 
 
 .01360 
 
 
 .99991 
 
 
 13353 
 
 319,3 
 
 .99996 
 
 
 o 46 45.20 
 
 .0137 
 
 .01370 
 
 
 99991 
 
 
 . 13671 
 
 317,0 
 
 .99996 
 
 
 47 05.83 
 
 .0138 
 
 .01380 
 
 
 99990 
 
 
 .13987 
 
 314,7 
 
 .99996 
 
 
 o 47 26.45 
 
 .0139 
 
 .01390 
 
 
 .99990 
 
 
 .14300 
 
 312,4 
 
 99996 
 
 
 47 47.08 
 
 0.0140 
 
 O.OI4OO 
 
 10,0 
 
 0.99990 
 
 0,1 
 
 8.14611 
 
 310,2 
 
 9.99996 
 
 0,1 
 
 o 48 07.71 
 
 .0141 
 
 .01410 
 
 
 99990 
 
 
 .14920 
 
 308,0 
 
 .99996 
 
 
 48 28.33 
 
 .0142 
 
 .01420 
 
 
 .99990 
 
 
 . 15227 
 
 305,8 
 
 .90996 
 
 
 48 48.96 
 
 .0143 
 
 .01430 
 
 
 .99090 
 
 
 .15532 
 
 303,7 
 
 .99096 
 
 
 49 09-59 
 
 .0144 
 
 .01440 
 
 
 .99990 
 
 
 15835 
 
 301,6 
 
 99995 
 
 
 49 30.21 
 
 0.0145 
 
 0.01450 
 
 10,0 
 
 0.99089 
 
 0,1 
 
 8.16135 
 
 299,5 
 
 9-99995 
 
 0,1 
 
 49 50.84 
 
 .0146 
 
 .01460 
 
 
 .99989 
 
 
 . 16434 
 
 297,4 
 
 99995 
 
 
 50 11-47 
 
 .0147 
 
 .01470 
 
 
 .99989 
 
 
 .16730 
 
 295,4 
 
 99995 
 
 
 o 50 32.09 
 
 .0148 
 
 .OI48O 
 
 
 .90089 
 
 
 . 17025 
 
 2934 
 
 99995 
 
 
 o 50 52.72 
 
 .0149 
 
 .01490 
 
 
 .99989 
 
 
 .17317 
 
 291,5 
 
 99995 
 
 
 51 13-35 
 
 0.0150 
 
 O.OI5OO 
 
 10,0 
 
 0.90989 
 
 0,1 
 
 8.17608 
 
 289,5 
 
 9-99995 
 
 0,1 
 
 o 51 33-97 
 
 u 
 
 -isinhiu 
 
 F ' 
 
 cosh iu 
 
 -Fo' 
 
 |og inh Iu 
 
 -Fo' 
 
 log cosh iu 
 
 -Fo' 
 
 j 
 
 SMITHSONIAN TABLES 
 
 17" 
 
Circular Functions. 
 
 u 
 
 sin u 
 
 F O ' 
 
 COS U 
 
 Fo' 
 
 log sin u 
 
 Fo' 
 
 log cos u 
 
 -FO' 
 
 u 
 
 0.0150 
 
 O.OI5OO 
 
 IO,O 
 
 0.99989 
 
 0,1 
 
 8.17608 
 
 289,5 
 
 9-99995 
 
 0,1 
 
 o5i'33"97 
 
 .0151 
 
 .OI5IO 
 
 
 
 0,2 
 
 .17896 
 
 287,6 
 
 .99995 
 
 
 o 51 54.6o 
 
 .0152 
 
 .OI52O 
 
 
 .99988 
 
 
 .18183 
 
 285,7 
 
 99995 
 
 
 o 52 15.23 
 
 .0153 
 
 .01530 
 
 
 .99988 
 
 
 .18467 
 
 283,8 
 
 .99995 
 
 
 o 52 35.85 
 
 .0154 
 
 .01540 
 
 
 .99988 
 
 
 .18750 
 
 282,0 
 
 99995 
 
 
 o 52 56.48 
 
 0.0155 
 
 0.01550 
 
 IO,O 
 
 0.99988 
 
 0,2 
 
 8.19031 
 
 280,2 
 
 9-99995 
 
 0,1 
 
 o 53 17-10 
 
 .0156 
 
 .01500 
 
 
 .99988 
 
 
 .19311 
 
 278,4 
 
 .99995 
 
 
 o 53 37.73 
 
 .0157 
 
 .01570 
 
 
 .99988 
 
 
 .19588 
 
 276,6 
 
 99995 
 
 
 o 53 58.36 
 
 .0158 
 
 .01580 
 
 
 .99988 
 
 
 .19864 
 
 274,9 
 
 99995 
 
 
 o 54 18.98 
 
 .0159 
 
 .01590 
 
 
 .99987 
 
 
 .20138 
 
 273,1 
 
 .99995 
 
 
 o 54 39.6i 
 
 0.0160 
 
 O.OIOOO 
 
 IO,O 
 
 0.99987 
 
 0,2 
 
 8.20410 
 
 271,4 
 
 9.99994 
 
 0,1 
 
 o 55 00.24 
 
 .0161 
 
 .Ol6lO 
 
 
 .99987 
 
 
 .20681 
 
 269,7 
 
 9999* 
 
 
 o 55 20.86 
 
 .0162 
 
 .Ol62O 
 
 
 .99987 
 
 
 .20950 
 
 268,1 
 
 .99994 
 
 
 o 55 41-49 
 
 .0163 
 
 .01630 
 
 
 .99987 
 
 
 .21217 
 
 266,4 
 
 99994 
 
 
 O 56 O2. 12 
 
 .0164 
 
 .01640 
 
 
 .99987 
 
 
 .21482 
 
 264,8 
 
 99994 
 
 
 o 56 22.74 
 
 0.0165 
 
 O.OI65O 
 
 IO,O 
 
 0.99985 
 
 0,2 
 
 8.21746 
 
 263,2 
 
 9.99994 
 
 0,1 
 
 o 56" 43-37 
 
 .0166 
 
 .Ol66o 
 
 
 .99986 
 
 
 .22009 
 
 261,6 
 
 .99994 
 
 
 o 57 04.00 
 
 .0167 
 
 .01670 
 
 
 .99986 
 
 
 .22270 
 
 260,0 
 
 .99994 
 
 
 o 57 24.62 
 
 .0168 
 
 .01680 
 
 
 .09986 
 
 
 .22529 
 
 258,5 
 
 99994 
 
 
 o 57 45.25 
 
 .0169 
 
 .01690 
 
 
 .99986 
 
 
 .22787 
 
 257,0 
 
 99994 
 
 
 o 58 05.88 
 
 0.0170 
 
 0.01700 
 
 10,0 
 
 0.99986 
 
 0,2 
 
 8.23043 
 
 255,4 
 
 9.99904 
 
 0,1 
 
 o 58 26.50 
 
 .0171 
 
 .OI7IO 
 
 
 .99985 
 
 
 .23298 
 
 253,9 
 
 99994 
 
 
 o 58 47.13 
 
 .0172 
 
 .OI72O 
 
 
 .95985 
 
 
 23551 
 
 252,5 
 
 99994 
 
 
 o 59 07.75 
 
 .0173 
 
 .01730 
 
 
 .99985 
 
 
 .23802 
 
 251,0 
 
 99994 
 
 
 o 59 28.38 
 
 .0174 
 
 .01740 
 
 
 .99985 
 
 
 .24053 
 
 249,6 
 
 99993 
 
 
 o 59 49.01 
 
 0.0175 
 
 0.01750 
 
 10,0 
 
 0.99985 
 
 0,2 
 
 8.24302 
 
 248,1 
 
 9-99993 
 
 0,1 
 
 oo 09.63 
 
 .0176 
 
 .01760 
 
 
 .99985 
 
 
 .24549 
 
 246,7 
 
 99993 
 
 
 oo 30.26 
 
 .0177 
 
 .01770 
 
 
 .99984 
 
 
 .24795 
 
 245,3 
 
 99993 
 
 
 oo 50.89 
 
 .0178 
 
 .01780 
 
 
 .99984 
 
 
 .25040 
 
 244,0 
 
 99993 
 
 
 01 11.51 
 
 .0179 
 
 .OI79O 
 
 
 .99984 
 
 
 .25283 
 
 242,6 
 
 99993 
 
 
 01 32.14 
 
 0.0180 
 
 O.OlSoO 
 
 IO,O 
 
 0.99984 
 
 0,2 
 
 8.25525 
 
 241,2 
 
 9-99993 
 
 0,1 
 
 oi 52.77 
 
 .0181 
 
 .OlSlO 
 
 
 .99984 
 
 
 .25766 
 
 239,9 
 
 .99993 
 
 
 02 13-39 
 
 .0182 
 
 .01820 
 
 
 .99983 
 
 
 .26005 
 
 238,6 
 
 99993 
 
 
 02 34.02 
 
 .0183 
 
 .01830 
 
 
 .99983 
 
 
 .26243 
 
 237,3 
 
 99993 
 
 
 02 54.65 
 
 .0184 
 
 .01840 
 
 
 .99983 
 
 
 .26479 
 
 236,0 
 
 99993 
 
 
 03 15-27 
 
 0.0185 
 
 O.Ol85O 
 
 IO,O 
 
 0.09983 
 
 0,2 
 
 8.26715 
 
 234,7 
 
 9-99993 
 
 0,1 
 
 03 35.00 
 
 .0186 
 
 .01860 
 
 
 .99983 
 
 
 .26949 
 
 233,5 
 
 .99992 
 
 
 03 56.53 
 
 .0187 
 
 .01870 
 
 
 .99983 
 
 
 .27182 
 
 232,2 
 
 .99992 
 
 
 04 17.15 
 
 .0188 
 
 .01880 
 
 
 .99982 
 
 
 .27413 
 
 231,0 
 
 .99992 
 
 
 04 37.78 
 
 .0189 
 
 .01890 
 
 
 .99982 
 
 
 .27644 
 
 229,8 
 
 .99992 
 
 
 04 58.40 
 
 0.0190 
 
 O.OI90O 
 
 IO,O 
 
 0.99982 
 
 0,2 
 
 8.27873 
 
 228,5 
 
 9.99992 
 
 0,1 
 
 05 19-03 
 
 .0191 
 
 .01910 
 
 
 .99982 
 
 
 .28101 
 
 227,4 
 
 .99992 
 
 
 05 39.66 
 
 .0192 
 
 .OI92O 
 
 
 .99982 
 
 
 .28327 
 
 226,2 
 
 .99992 
 
 
 06 00.28 
 
 .0193 
 
 .01930 
 
 
 .09981 
 
 
 .28553 
 
 225,0 
 
 .99992 
 
 
 06 20.91 
 
 .0194 
 
 .01940 
 
 
 .99981 
 
 
 .28777 
 
 223,8 
 
 .99992 
 
 
 06 41.54 
 
 0.0195 
 
 O.OI950 
 
 IO,O 
 
 0.99981 
 
 0,2 
 
 8.29001 
 
 222,7 
 
 9.99992 
 
 0,1 
 
 O7 Q2.l6 
 
 .0196 
 
 .01960 
 
 
 .99981 
 
 
 .29223 
 
 221,6 
 
 .99992 
 
 
 07 22.79 
 
 .0197 
 
 .OI97O 
 
 
 .99981 
 
 
 .29444 
 
 220,4 
 
 .99992 
 
 
 07 43.42 
 
 .0198 
 
 .01980 
 
 
 .99980 
 
 
 .20664 
 
 219,3 
 
 .99991 
 
 
 08 04.04 
 
 .0199 
 
 .01990 
 
 
 .99980 
 
 
 .29882 
 
 218,2 
 
 .99991 
 
 
 08 24.67 
 
 0.020O 
 
 O.O2OOO 
 
 IO,O 
 
 0.99980 
 
 0,2 
 
 8.30100 
 
 217,1 
 
 9.99991 
 
 0,1 
 
 I 08 45.30 
 
 
 . 
 i sinn iu 
 
 CO Fn' 
 
 cosh iu 
 
 ' (ll Fn' 
 
 . sinh iu 
 
 Cl> Pn' 
 
 
 01 FA' 
 
 
 
 
 " TO 
 
 
 * TO 
 
 log . 
 
 w FO 
 
 IOQ cosh iu 
 
 < TO 
 
 11 
 
 SMITHSONIAN TABLES 
 
 177 
 
Circular Functions. 
 
 u 
 
 sin u 
 
 FO' 
 
 COS U 
 
 F ' 
 
 log sin u 
 
 F O ' 
 
 loo cos u 
 
 -FO' 
 
 U 
 
 O.Q200 
 
 O.O2OOO 
 
 IO,O 
 
 0.99980 
 
 0,2 
 
 8.30100 
 
 217,1 
 
 9.99991 
 
 0,1 
 
 I 0645.30 
 
 .O2OI 
 
 .O20IO 
 
 
 .99980 
 
 
 30317 
 
 216,0 
 
 .99991 
 
 
 09 05.02 
 
 .O2O2 
 
 .O2O2O 
 
 
 .99980 
 
 
 .30532 
 
 2I'5,0 
 
 .99991 
 
 
 09 26.55 
 
 .0203 
 
 .02030 
 
 
 .99979 
 
 
 .30747 
 
 213,9 
 
 .99991 
 
 
 09 47.18 
 
 .O2O4 
 
 .02040 
 
 
 .99979 
 
 
 .30960 
 
 212,9 
 
 .99991 
 
 
 10 07.80 
 
 O.0205 
 
 O.O2O5O 
 
 IO,O 
 
 0.99979 
 
 0,2 
 
 8.31172 
 
 211,8 
 
 9.99991 
 
 0,1 
 
 10 28.43 
 
 .0206 
 
 .02060 
 
 
 .99979 
 
 
 31384 
 
 210,8 
 
 .99991 
 
 
 10 49.06 
 
 .0207 
 
 .O2O7O 
 
 
 .99979 
 
 
 31594 
 
 209,8 
 
 .99991 
 
 
 II 09.68 
 
 .0208 
 
 .02080 
 
 
 .99978 
 
 
 31803 
 
 208,8 
 
 .99991 
 
 
 II 30.31 
 
 .0209 
 
 .02090 
 
 
 99978 
 
 
 .32012 
 
 207,8 
 
 .99991 
 
 
 II 50.93 
 
 O.O2IO 
 
 0.02100 
 
 10,0 
 
 0.99978 
 
 0,2 
 
 8.32219 
 
 1206,8 
 
 9.99990 
 
 0,1 
 
 12 11.56 
 
 .O2I I 
 
 .O2IIO 
 
 
 .99978 
 
 
 .32425 
 
 205,8 
 
 .99990 
 
 
 12 32.19 
 
 .O2I2 
 
 .02120 
 
 
 .99978 
 
 
 .32630 
 
 204,8 
 
 .99990 
 
 
 12 52.8l 
 
 .0213 
 
 .02130 
 
 
 .99977 
 
 
 32835 
 
 203,9 
 
 .99990 
 
 
 13 13-44 
 
 .O2I4 
 
 .O2I4O 
 
 
 .99977 
 
 
 .33038 
 
 202,9 
 
 .99990 
 
 
 13 34.07 
 
 O.O2I5 
 
 O.O2I50 
 
 10,0 
 
 0.99977 
 
 0,2 
 
 8. 33*241 
 
 202,0 
 
 9.99990 
 
 0,1 
 
 13 54.69 
 
 .O2l6 
 
 .02IOO 
 
 
 99977 
 
 
 33442 
 
 201,0 
 
 .99990 
 
 
 H 15.32 
 
 .O2I7 
 
 .O2I7O 
 
 
 .99976 
 
 
 33643 
 
 200,1 
 
 .99990 
 
 
 14 35-95 
 
 .0218 
 
 .02l8o 
 
 
 99976 
 
 
 33842 
 
 199,2 
 
 .99990 
 
 
 H 56.57 
 
 .O2I9 
 
 .02190 
 
 
 .99976 
 
 
 .34041 
 
 198,3 
 
 .99990 
 
 
 IS 17.20 
 
 O.O22O 
 
 0.02200 
 
 10,0 
 
 0.99976 
 
 0,2 
 
 8.34239 
 
 197,4 
 
 9.99989 
 
 0,1 
 
 15 37-& 
 
 .O22I 
 
 .02210 
 
 
 .99976 
 
 
 34436 
 
 196,5 
 
 .99989 
 
 
 15 58.45 
 
 .O222 
 
 .O2220 
 
 
 -99975 
 
 
 .34632 
 
 195,6 
 
 .99989 
 
 
 16 19.08 
 
 .O223 
 
 .O223O 
 
 
 99975 
 
 
 -34827 
 
 194,7 
 
 .99989 
 
 
 16 39.71 
 
 .0224 
 
 .O224O 
 
 
 99975 
 
 
 35021 
 
 193,8 
 
 .99989 
 
 
 17 00.33 
 
 0.0225 
 
 O.O225O 
 
 IO,O 
 
 0.99975 
 
 0,2 
 
 8.35215 
 
 193,0 
 
 9.99989 
 
 0,1 
 
 17 20.96 
 
 .O226 
 
 .O2260 
 
 
 .99974 
 
 
 35407 
 
 192,1 
 
 .99989 
 
 
 17 41.58 
 
 .0227 
 
 .O2270 
 
 
 .99974 
 
 
 35599 
 
 191,3 
 
 .99989 
 
 
 18 02. 21 
 
 .0228 
 
 .02280 
 
 
 .99974 
 
 
 35790 
 
 190,4 
 
 .99989 
 
 
 18 22.84 
 
 .0229 
 
 .02200 
 
 
 .99974 
 
 
 .35980 
 
 189,6 
 
 .99989 
 
 
 18 43-46 
 
 O.023O 
 
 0.02300 
 
 10,0 
 
 0.99974 
 
 0,2 
 
 8.36169 
 
 188,8 
 
 9.99989 
 
 0,1 
 
 19 04.09 
 
 .0231 
 
 .02310 
 
 
 99973 
 
 
 .36357 
 
 188,0 
 
 .99988 
 
 
 19 24.72 
 
 .0232 
 
 .O232O 
 
 
 99973 
 
 
 36545 
 
 187,2 
 
 .99988 
 
 
 19 45-34 
 
 .0233 
 
 .02330 
 
 
 99973 
 
 
 36732 
 
 186,4 
 
 .99988 
 
 
 20 05.97 
 
 .0234 
 
 .02340 
 
 
 99973 
 
 
 36918 
 
 185,6 
 
 .99988 
 
 
 2O 26.60 
 
 0.0235 
 
 0.02350 
 
 10,0 
 
 0.99972 
 
 0,2 
 
 8.37103 
 
 184,8 
 
 9.99988 
 
 0,1 
 
 2O 47.22 
 
 .0236 
 
 .02360 
 
 
 .99972 
 
 
 37287 
 
 184,0 
 
 .99988 
 
 
 21 O7.85 
 
 .0237 
 
 .02370 
 
 
 .99972 
 
 
 37471 
 
 183,2 
 
 .99988 
 
 
 21 28.48 
 
 .0238 
 
 .O238O 
 
 
 99972 
 
 
 .37654 
 
 182,4 
 
 .99988 
 
 
 21 49.IO 
 
 .0239 
 
 .02390 
 
 
 .99971 
 
 
 .37836 
 
 181,7 
 
 .99988 
 
 
 22 09.73 
 
 0.0240 
 
 0.02400 
 
 10,0 
 
 0.99971 
 
 0,2 
 
 8.38017 
 
 180,9 
 
 9.99987 
 
 0,1 
 
 22 30.36 
 
 .0241 
 
 .O24IO 
 
 
 .99971 
 
 
 .38198 
 
 180,2 
 
 .99987 
 
 
 22 50.98 
 
 .0242 
 
 .0242O 
 
 
 .99971 
 
 
 .38377 
 
 179,4 
 
 .99987 
 
 
 23 II.6I 
 
 .0243 
 
 .02430 
 
 
 .99970 
 
 
 .3-S556 
 
 178,7 
 
 .99987 
 
 
 23 32.23 
 
 .0244 
 
 .02440 
 
 
 99970 
 
 
 .38735 
 
 178,0 
 
 .99987 
 
 
 23 52.86 
 
 0.0245 
 
 O.O245O 
 
 IO,O 
 
 0.99970 
 
 0,2 
 
 8.38912 
 
 177,2 
 
 9.99987 
 
 0,1 
 
 24 13.49 
 
 .0246 
 
 .02460 
 
 
 .99970 
 
 
 .39089 
 
 176,5 
 
 .99987 
 
 
 24 34.ii 
 
 .0247 
 
 .02470 
 
 
 .99969 
 
 
 39265 
 
 175,8 
 
 .99987 
 
 
 24 54.74 
 
 .0248 
 
 .02480 
 
 
 .99969 
 
 
 .30441 
 
 I75,i 
 
 .99987 
 
 
 25 15.37 
 
 .0249 
 
 .02490 
 
 
 .09969 
 
 
 .39615 
 
 174,4 
 
 .99987 
 
 
 25 35-99 
 
 0.0250 
 
 0.02500 
 
 10,0 
 
 0.99969 
 
 0,2 
 
 8.39789 
 
 173,7 
 
 9.99986 
 
 0,1 
 
 I 25 56.62 
 
 
 1 Ink III 
 
 fa> p ' 
 
 r>n*ti in 
 
 id f n ' 
 
 | slnh lu 
 
 Id f ' 
 
 
 u F ' 
 
 
 u 
 
 1 1 sinn lu 
 
 w TO 
 
 cosn iu 
 
 * TO 
 
 100 , 
 
 < ro 
 
 00 cosh iu 
 
 * TO 
 
 u 
 
 SMITHSONIAN TABLCS 
 
 178 
 
Circular Functions. 
 
 u 
 
 sin u 
 
 O.FO' 
 
 cos u 
 
 F ' 
 
 log sin u 
 
 Fo' 
 
 log cos u 
 
 F O ' 
 
 u 
 
 O.O25^> 
 
 O.O25OO 
 
 IO,O 
 
 0.99969 
 
 0,2 
 
 8.39780 
 
 173,7 
 
 9.99986 
 
 0,1 
 
 25 / 56' / 62 
 
 .0251 
 
 .02510 
 
 
 .99969 
 
 o,3 
 
 .39963 
 
 I73,o 
 
 .99986 
 
 
 26 17.25 
 
 .0252 
 
 .02520 
 
 
 .99968 
 
 
 .40135 
 
 172,3 
 
 .99986 
 
 
 26 37.87 
 
 .0253 
 
 .02530 
 
 
 .99968 
 
 
 .40307 
 
 171,6 
 
 .99986 
 
 
 26 58.50 
 
 .0254 
 
 .02540 
 
 
 .99968 
 
 
 .40479 
 
 170,9 
 
 .99986 
 
 
 27 19.13 
 
 0.0255 
 
 O.O2550 
 
 10,0 
 
 0.99967 
 
 0,3 
 
 8.40649 
 
 170,3 
 
 9.99986 
 
 0,1 
 
 27 39-75 
 
 .0256 
 
 .02560 
 
 
 .99967 
 
 
 .40819 
 
 169,6 
 
 .99986 
 
 
 28 00.38 
 
 .0257 
 
 .02570 
 
 
 .99967 
 
 
 .40989 
 
 168,9 
 
 .99986 
 
 
 28 21.01 
 
 .0258 
 
 .02580 
 
 
 .99967 
 
 
 .4H57 
 
 168,3 
 
 .99986 
 
 
 28 41.63 
 
 .0259 
 
 .02590 
 
 
 .99966 
 
 
 .41325 
 
 167,6 
 
 .99985 
 
 
 29 O2.26 
 
 0.0260 
 
 0.02600 
 
 IO,O 
 
 0.99966 
 
 0,3 
 
 8.41492 
 
 167,0 
 
 9.99985 
 
 0,1 
 
 29 22.88 
 
 .0261 
 
 .02610 
 
 
 .99966 
 
 
 .41659 
 
 166,4 
 
 .99985 
 
 
 29 43.51 
 
 .0262 
 
 .02620 
 
 
 .99966 
 
 
 .41825 
 
 165,7 
 
 .99985 
 
 
 30 04.14 
 
 .0263 
 
 .02630 
 
 
 .99965 
 
 
 .41991 
 
 165,1 
 
 .99985 
 
 
 30 24.76 
 
 .0264 
 
 .02640 
 
 
 .99965 
 
 
 .42155 
 
 164,5 
 
 .99985 
 
 
 30 45.39 
 
 0.0265 
 
 0.02650 
 
 IO,O 
 
 0.99965 
 
 0,3 
 
 8.42320 
 
 163,8 
 
 9.99985 
 
 0,1 
 
 31 06.02 
 
 .0266 
 
 .02660 
 
 
 .99965 
 
 
 .42483 
 
 163,2 
 
 .99985 
 
 
 31 26.64 
 
 .0267 
 
 .02670 
 
 
 99964 
 
 
 .42646 
 
 162,6 
 
 .99985 
 
 
 31 47.27 
 
 .0268 
 
 .02680 
 
 
 99964 
 
 
 .42808 
 
 162,0 
 
 99984 
 
 
 32 07-90 
 
 .0269 
 
 .02690 
 
 
 .99964 
 
 
 .42970 
 
 161,4 
 
 99984 
 
 
 32 28.52 
 
 0.0270 
 
 O.027OO 
 
 10,0 
 
 0.99964 
 
 o,3 
 
 8.43I3I 
 
 160,8 
 
 9.99984 
 
 0,1 
 
 32 49.15 
 
 .0271 
 
 .O27IO 
 
 
 .99963 
 
 
 .43292 
 
 160,2 
 
 .99984 
 
 
 33 09.78 
 
 .0272 
 
 .02720 
 
 
 .99963 
 
 
 43452 
 
 159,6 
 
 .99984 
 
 
 33 30.40 
 
 .0273 
 
 .02730 
 
 
 .99963 
 
 
 .43611 
 
 I59,o 
 
 99984 
 
 
 33 51.03 
 
 .0274 
 
 .02740 
 
 
 .99962 
 
 
 .43770 
 
 158,5 
 
 .99984 
 
 
 34 11.66 
 
 0.0275 
 
 0.02750 
 
 10,0 
 
 0.99962 
 
 0,3 
 
 8.43928 
 
 157,9 
 
 9.99984 
 
 0,1 
 
 34 32.28 
 
 .0276 
 
 .02760 
 
 
 .99962 
 
 
 .44085 
 
 157,3 
 
 .99983 
 
 
 34 52.91 
 
 .0277 
 
 .02770 
 
 
 .99962 
 
 
 .44242 
 
 156,7 
 
 .99983' 
 
 
 35 13.54 
 
 .0278 
 
 .02780 
 
 
 .99961 
 
 
 44399 
 
 156,2 
 
 99983 
 
 
 35 34.i6 
 
 .0279 
 
 .02790 
 
 
 .99961 
 
 
 44555 
 
 155,6 
 
 .99983 
 
 
 35 54-79 
 
 0.0280 
 
 0.02800 
 
 10,0 
 
 0.99961 
 
 0,3 
 
 8.44710 
 
 I55,i 
 
 9.99983 
 
 0,1 
 
 36 15.41 
 
 .0281 
 
 .02810 
 
 
 .99961 
 
 
 .44865 
 
 154,5 
 
 .99983 
 
 
 36 36.04 
 
 .0282 
 
 .02820 
 
 
 .99960 
 
 
 .45019 
 
 I54,o 
 
 .99983 
 
 
 36 56.67 
 
 .0283 
 
 .02830 
 
 
 .99960 
 
 
 .45173 
 
 153,4 
 
 .99983 
 
 
 37 17.29 
 
 .0284 
 
 .02840 
 
 
 .99960 
 
 
 .45326 
 
 152,9 
 
 .99982 
 
 
 37 37-92 
 
 0.0285 
 
 0.02850 
 
 10,0 
 
 0-99959 
 
 0,3 
 
 8.45479 
 
 152,3 
 
 9.99982 
 
 0,1 
 
 37 58.55 
 
 .0286 
 
 .02860 
 
 
 99959 
 
 
 .45631 
 
 151,8 
 
 .99982 
 
 
 38 IQ.I7 
 
 .0287 
 
 .02870 
 
 
 99959 
 
 
 .45782 
 
 I5i,3 
 
 .99982 
 
 
 38 39.8o 
 
 .0288 
 
 .02880 
 
 
 .99959 
 
 
 45933 
 
 150,8 
 
 .99982 
 
 
 39 00.43 
 
 .0289 
 
 .02890 
 
 
 .99958 
 
 
 .46084 
 
 150,2 
 
 .99982 
 
 
 39 21.05 
 
 O.O20O 
 
 0.02900 
 
 IO,O 
 
 0.99958 
 
 o,3 
 
 8.46234 
 
 149,7 
 
 9.99982 
 
 0,1 
 
 39 41.68 
 
 .O29I 
 
 .02910 
 
 
 .99958 
 
 
 .46383 
 
 149,2 
 
 .99982 
 
 
 40 02.31 
 
 .0292 
 
 .02920 
 
 
 99957 
 
 
 46532 
 
 148,7 
 
 .99981 
 
 
 40 22.93 
 
 0293 
 
 .02930 
 
 
 .99957 
 
 
 .46681 
 
 148,2 
 
 .99981 
 
 
 40 43.56 
 
 .0294 
 
 .02940 
 
 
 99957 
 
 
 .46828 
 
 147,7 
 
 .99981 
 
 
 41 04.19 
 
 0.0295 
 
 O.O295O 
 
 IO,O 
 
 0.99956 
 
 o,3 
 
 8.46976 
 
 147,2 
 
 9-99981 
 
 0,1 
 
 41 24.81 
 
 .0296 
 
 .02960 
 
 
 .99956 
 
 
 .47123 
 
 146,7 
 
 .99981 
 
 
 41 45.44 
 
 .0297 
 
 .02970 
 
 
 .99956 
 
 
 .47269 
 
 146,2 
 
 .99981 
 
 
 42 06.06 
 
 .0298 
 
 .02080 
 
 
 .99956 
 
 
 .47415 
 
 145,7 
 
 .99981 
 
 
 42 26.69 
 
 .0299 
 
 .02990 
 
 
 99955 
 
 
 .47561 
 
 H'5,2 
 
 .99981 
 
 
 42 47.32 
 
 0.0300 
 
 0.03000 
 
 10,0 
 
 0.99955 
 
 0,3 
 
 8.47706 
 
 144,7 
 
 9.09980 
 
 0,1 
 
 I 43 07.94 
 
 
 : -.: u ;,. 
 
 .) P ' 
 
 rn*h in 
 
 ii> F ' 
 
 sinh iu 
 
 P ' 
 
 . 
 
 F ' 
 
 
 U 
 
 i sinn iti 
 
 w ro 
 
 cosn lu 
 
 * ro 
 
 lOfl . 
 
 > ro 
 
 log cosh iu 
 
 *> TO 
 
 u 
 
 SMITHSONIAN TABLES 
 
 179 
 
Circular Functions. 
 
 u 
 
 sin u 
 
 O.FO' 
 
 COS U 
 
 . 
 
 log sin u 
 
 w F(j' 
 
 log cos u 
 
 -W- 
 
 u 
 
 0.0300 
 
 0.03000 
 
 10,0 
 
 0.99955 
 
 0,3 
 
 8.47706 
 
 144,7 
 
 9.90980 
 
 0,1 
 
 I 43 O7'.'o4 
 
 .0301 
 
 .03010 
 
 
 .99955 
 
 
 .47850 
 
 144,2 
 
 .99980 
 
 
 43 28.57 
 
 .0302 
 
 .03020 
 
 
 .99954 
 
 
 -47994 
 
 143.8 
 
 
 
 43 49.20 
 
 .0303 
 
 .03030 
 
 
 .99954 
 
 
 .48138 
 
 143,3 
 
 .99980 
 
 
 44 09.82 
 
 .0304 
 
 .03040 
 
 
 .99954 
 
 
 .48281 
 
 142,8 
 
 .99980 
 
 
 44 30-45 
 
 0.0305 
 
 0.03050 
 
 IO,O 
 
 0.99953 
 
 0,3 
 
 8.48423 
 
 142,3 
 
 9.99980 
 
 0,1 
 
 44 Si.oS 
 
 .0306 
 
 .03060 
 
 
 99953 
 
 
 .48565 
 
 141,9 
 
 .99980 
 
 
 45 H-70 
 
 .0307 
 
 .030/0 
 
 
 99953 
 
 
 .48707 
 
 141,4 
 
 .99980 
 
 
 45 32-33 
 
 .0308 
 
 .03080 
 
 
 .99953 
 
 
 .48848 
 
 141,0 
 
 .99979 
 
 
 45 52.06 
 
 .0309 
 
 .03090 
 
 
 .99952 
 
 
 .48989 
 
 140,5 
 
 .99979 
 
 
 46 13-58 
 
 0.0310 
 
 O.O3IOO 
 
 10,0 
 
 0.99952 
 
 o,3 
 
 8.49129 
 
 140,1 
 
 9-99979 
 
 0,1 
 
 46 34-21 
 
 .0311 
 
 .03109 
 
 
 99952 
 
 
 .49269 
 
 139,6 
 
 .99979 
 
 
 46 54-84 
 
 .0312 
 
 .03119 
 
 
 99951 
 
 
 .49408 
 
 139,2 
 
 99979 
 
 
 47 15.46 
 
 0313 
 
 .03129 
 
 
 99951 
 
 
 .49547 
 
 138,7 
 
 .99979 
 
 
 47 36.09 
 
 .0314 
 
 .03139 
 
 
 99951 
 
 
 .49686 
 
 138,3 
 
 -99979 
 
 
 47 56.71 
 
 0.0315 
 
 0.03149 
 
 10,0 
 
 0-99950 
 
 0,3 
 
 8.49824 
 
 137,8 
 
 9.99978 
 
 0,1 
 
 48 17.34 
 
 .0316 
 
 .03159 
 
 
 .99950 
 
 
 .49961 
 
 137,4 
 
 .99978 
 
 
 48 37.97 
 
 .0317 
 
 .03169 
 
 
 .99950 
 
 
 .50099 
 
 I37,o 
 
 .99978 
 
 
 48 58.59 
 
 .0318 
 
 .03179 
 
 
 99949 
 
 
 50235 
 
 136,5 
 
 .99978 
 
 
 49 19.22 
 
 .0319 
 
 .03189 
 
 
 99949 
 
 
 .50372 
 
 136,1 
 
 .99978 
 
 
 49 39.85 
 
 0.0320 
 
 0.03109 
 
 10,0 
 
 0.99949 
 
 0,3 
 
 8.50508 
 
 135,7 
 
 9.99978 
 
 0,1 
 
 50 00.47 
 
 .0321 
 
 .03209 
 
 
 .99948 
 
 
 .50643 
 
 135,2 
 
 .99978 
 
 
 50 21. 10 
 
 .0322 
 
 .03219 
 
 
 .59948 
 
 
 00778 
 
 134,8 
 
 .99977 
 
 
 50 41-73 
 
 .0323 
 
 .03229 
 
 
 .99948 
 
 
 .50913 
 
 134,4 
 
 .99977 
 
 
 5i 02.35 
 
 .0324 
 
 .03239 
 
 
 .95948 
 
 
 .51047 
 
 134,0 
 
 99977 
 
 
 51 22.98 
 
 0.0325 
 
 0.03249 
 
 10,0 
 
 0.99947 
 
 0,3 
 
 8.51181 
 
 133,6 
 
 9-99977 
 
 0,1 
 
 51 43.6i 
 
 .0326 
 
 .03259 
 
 
 .99947 
 
 
 .51314 
 
 133,2 
 
 .99977 
 
 
 52 04-23 
 
 .0327 
 
 .03269 
 
 
 .99947 
 
 
 -51447 
 
 132,8 
 
 .99977 
 
 
 52 24.86 
 
 .0328 
 
 .03279 
 
 
 .99946 
 
 
 .51580 
 
 132,4 
 
 99977 
 
 
 52 45-49 
 
 .0329 
 
 .03289 
 
 
 .99946 
 
 
 .51712 
 
 132,0 t 
 
 .99976 
 
 
 53 06. II 
 
 0.0330 
 
 0.03299 
 
 IO,0 
 
 0.99946 
 
 0,3 
 
 8.51844 
 
 131,6 
 
 9-99976 
 
 0,1 
 
 53 26.74 
 
 .0331 
 
 .03309 
 
 
 .99945 
 
 
 .51975 
 
 131,2 
 
 .99976 
 
 
 53 47-37 
 
 .0332 
 
 .03319 
 
 
 .99945 
 
 
 .52106 
 
 130,8 
 
 .99976 
 
 
 54 07-99 
 
 .0333 
 
 .03329 
 
 
 99945 
 
 
 .52236 
 
 130,4 
 
 .99976 
 
 
 54 28.62 
 
 .0334 
 
 .03339 
 
 
 99944 
 
 
 .52367 
 
 130,0 
 
 99976 
 
 
 54 49.24 
 
 0.0335 
 
 0.03349 
 
 10,0 
 
 0.99944 
 
 0,3 
 
 8.52496 
 
 129,6 
 
 9.99976 
 
 0,1 
 
 55 09.87 
 
 0336 
 
 03359 
 
 
 .99944 
 
 
 .52626 
 
 129,2 
 
 99975 
 
 
 55 30.50 
 
 0337 
 
 .03369 
 
 
 99943 
 
 
 .52755 
 
 ' 128,8 
 
 .99975 
 
 
 55 51.12 
 
 .0338 
 
 .03379 
 
 
 99943 
 
 
 .52883 
 
 128,4 
 
 .99975 
 
 
 56 n.75 
 
 0339 
 
 .03389 
 
 
 99943 
 
 
 .53012 
 
 128,1 
 
 .99975 
 
 
 56 32.38 
 
 0.0340 
 
 0.03399 
 
 IO,O 
 
 0.99942 
 
 o,3 
 
 8.53-140 
 
 127,7 
 
 9-99975 
 
 0,1 
 
 56 53-00 
 
 .0341 
 
 .03409 
 
 
 .99942 
 
 
 '53267 
 
 127,3 
 
 99975 
 
 
 57 13-63 
 
 0342 
 
 .03419 
 
 
 99942 
 
 
 .53394 
 
 126,9 
 
 99975 
 
 
 57 34-26 
 
 .0343 
 .0344 
 
 03429 
 03439 
 
 
 .99941 
 .99941 
 
 
 53521 
 .53647 
 
 126,6 
 126,2 
 
 99974 
 .99974 
 
 
 57 54-88 
 58 I5.5I 
 
 0.0345 
 
 0.03449 
 
 IO,O 
 
 0.99940 
 
 o,3 
 
 8.53773 
 
 125,8 
 
 9.99974 
 
 0,1 
 
 58 36.14 
 
 r s 
 
 .0346 
 
 .03459 
 
 
 .99940 
 
 
 .53899 
 
 125,5 
 
 99974 
 
 0,2 
 
 58 56.76 
 
 .0347 
 
 .03469 
 
 
 99940 
 
 
 .54024 
 
 125,1 
 
 99974 
 
 
 59 17-39 
 
 .0348 
 
 .03479 
 
 
 99939 
 
 
 .54149 
 
 124,7 
 
 99974 
 
 
 I 59 38.02 
 
 .0349 
 
 .03489 
 
 
 99939 
 
 
 .54274 
 
 124,4 
 
 99974 
 
 
 I 59 58-64 
 
 0.0350 
 
 0.03499 
 
 10,0 
 
 0.99939 
 
 0,3 
 
 8.54398 
 
 124,0 
 
 9-99973 
 
 0,2 
 
 2 00 19.27 
 
 
 
 r- / 
 
 
 C ' 
 
 sinh iu 
 
 Hi F ' 
 
 Inn roth iu 
 
 F ' 
 
 
 u 
 
 -isinhiu 
 
 w Fo 
 
 cosh iu 
 
 TO 
 
 
 To 
 
 toy con iu 
 
 
 
 SMITHSONIAN TABLES 
 
 180 
 
Circular Functions. 
 
 u 
 
 sin u 
 
 F ' 
 
 COS U 
 
 Fo' 
 
 log sin u 
 
 - Fo' 
 
 log cos u 
 
 <oF ' 
 
 U 
 
 v 
 
 o.0350\ 
 
 0.03499 
 
 IO,0 
 
 0.99939 
 
 0,3 
 
 8.54398 
 
 124,0 
 
 9-99973 
 
 0,2 
 
 o / // 
 2 00 19.27 
 
 .0351 
 
 .03509 
 
 
 .99938 
 
 0,4 
 
 .54522 
 
 123,7 
 
 .99973 
 
 
 2 00 39.89 
 
 .0352 
 
 .03519 
 
 
 .99938 
 
 
 .54645 
 
 123,3 
 
 99973 
 
 
 2 01 00.52 
 
 .03-53 
 
 .03-529 
 
 
 .99938 
 
 
 .54768 
 
 123,0 
 
 99973 
 
 
 2 OI 21.15 
 
 .0354 
 
 .03539 
 
 
 99937 
 
 
 .54891 
 
 122,6 
 
 99973 
 
 
 2 01 41.77 
 
 0.0355 
 
 0.03549 
 
 10,0 
 
 0.99937 
 
 0,4 
 
 8.55014 
 
 122,3 
 
 9-99973 
 
 0,2 
 
 2 O2 O2.4O 
 
 .0356 
 
 .03559 
 
 
 .99937 
 
 
 .55136 
 
 121,9 
 
 .99972 
 
 
 2 02 23.03 
 
 .0357 
 
 .03569 
 
 
 .99936 
 
 
 .552>58 
 
 121,6 
 
 .99972 
 
 
 2 02 43.65 
 
 .0358 
 
 .03579 
 
 
 .99936 
 
 
 55379 
 
 121,3 
 
 .99972 
 
 
 2 O3 04.28 
 
 0359 
 
 .03589 
 
 
 .99936 
 
 
 .55500 
 
 1 20,9 
 
 .99972 
 
 
 2 O3 24.91 
 
 0.0360 
 
 0.03'599 
 
 10,0 
 
 0.99935 
 
 0,4 
 
 8.55621 
 
 120,6 
 
 9.99972 
 
 0,2 
 
 2 03 45-53 
 
 .0361 
 
 .03609 
 
 
 .99935 
 
 
 .55741 
 
 120,3 
 
 .99972 
 
 
 2 04 06. 16 
 
 .0362 
 
 .03619 
 
 
 99934 
 
 
 .55861 
 
 119,9 
 
 .99972 
 
 
 2 04 26.79 
 
 .0363 
 
 .03629 
 
 
 99934 
 
 
 .55981 
 
 119,6 
 
 .99971 
 
 
 2 04 47.41 
 
 .0364 
 
 .03639 
 
 
 99934 
 
 
 .56101 
 
 119,3 
 
 .99971 
 
 
 2 O5 O8.O4 
 
 0.0365 
 
 0.03649 
 
 IO,O 
 
 0.99933 
 
 0,4 
 
 8.56220 
 
 118,9 
 
 9.99971 
 
 0,2 
 
 2 05 28.67 
 
 .0366 
 
 .03659 
 
 
 99933 
 
 
 .56338 
 
 118,6 
 
 .99971 
 
 
 2 05 49-29 
 
 .0367 
 
 .03669 
 
 
 .99933 
 
 
 .56457 
 
 118,3 
 
 .99971 
 
 
 2 06 09.92 
 
 .0368 
 
 .03679 
 
 
 .99932 
 
 
 .56575 
 
 118,0 
 
 .99971 
 
 
 2 O6 3O.54 
 
 .0369 
 
 .03689 
 
 
 .99932 
 
 
 06693 
 
 117,6 
 
 .99970 
 
 
 2 O6 51.17 
 
 0.0370 
 
 0.03699 
 
 10,0 
 
 0.99932 
 
 0,4 
 
 8.56810 
 
 H7,3 
 
 9.99970 
 
 0,2 
 
 2,O7 II.SO 
 
 .0371 
 
 .03709 
 
 
 .99931 
 
 
 .56927 
 
 117,0 
 
 .99970 
 
 
 2 07 32.42 
 
 .0372 
 
 .03719 
 
 
 99931 
 
 
 .57044 
 
 116,7 
 
 .99970 
 
 
 2 07 53.05 
 
 .0373 
 
 .03729 
 
 
 .99930 
 
 
 .57i6i 
 
 116,4 
 
 99970 
 
 
 2 08 13.68 
 
 .0374 
 
 .03739 
 
 
 99930 
 
 
 .57277 
 
 116,1 
 
 .99970 
 
 
 2 08 34.30 
 
 0.0375 
 
 0.03749 
 
 10,0 
 
 0.99930 
 
 0,4 
 
 8.57393 
 
 H5,8 
 
 9.99969 
 
 0,2 
 
 2 OS 54.93 
 
 .0376 
 
 .03759 
 
 
 .99929 
 
 
 .57509 
 
 H5,4 
 
 .99969 
 
 
 2 09 15.56 
 
 .0377 
 
 .03769 
 
 
 .99929 
 
 
 .57624 
 
 H5,i 
 
 .99969 
 
 
 2 O9 36.18 
 
 .0378 
 
 .03779 
 
 
 .99929 
 
 
 57739 
 
 114,8 
 
 .99969 
 
 
 2 O9 56.8l 
 
 .0379 
 
 .03789 
 
 
 .99928 
 
 
 .57854 
 
 H4,5 
 
 .99969 
 
 
 2 10 17-44 
 
 0.0380 
 
 0.03799 
 
 IO,O 
 
 0.99928 
 
 0,4 
 
 8.57968 
 
 114,2 
 
 9.99969 
 
 0,2 
 
 2 IO 38.06 
 
 .0381 
 
 .03809 
 
 
 .99927 
 
 
 .58082 
 
 H3,9 
 
 .99968 
 
 
 2 10 58.69 
 
 .0382 
 
 .03819 
 
 
 .99927 
 
 
 .58196 
 
 113,6" 
 
 .99968 
 
 
 2 II 19.32 
 
 .0383 
 
 .03829 
 
 
 .99927 
 
 
 .58309 
 
 H3,3 
 
 .90968 
 
 
 2 II 39-94 
 
 .0384 
 
 .03839 
 
 
 .99926 
 
 
 .58422 
 
 H3,o 
 
 .99968 
 
 
 2 12 OO.57 
 
 0.0385 
 
 0.03849 
 
 10,0 
 
 0.99926 
 
 0,4 
 
 8.58535 
 
 112,7 
 
 9.99968 
 
 0,2 
 
 2 12 21. 2O 
 
 .0386 
 
 .03859 
 
 
 .99926 
 
 
 .58648 
 
 112,5 
 
 .99968 
 
 
 2 12 41.82 
 
 .0387 
 
 .03869 
 
 
 .99925 
 
 
 .58760 
 
 112,2 
 
 .99967 
 
 
 2 13 02.45 
 
 .0388 
 
 .03879 
 
 
 .99925 
 
 
 .58872 
 
 111,9 
 
 .99967 
 
 
 2 13 23.07 
 
 .0389 
 
 .03889 
 
 
 .99924 
 
 
 .58984 
 
 111,6 
 
 99967 
 
 
 2 13 43.70 
 
 0.0390 
 
 0.03899 
 
 IO,O 
 
 0.99924 
 
 0,4 
 
 8.59095 
 
 in,3 
 
 9.99967 
 
 0,2 
 
 2 14 04.33 
 
 .0391 
 
 .03909 
 
 
 .99924 
 
 
 .59207 
 
 III,O 
 
 .99967 
 
 
 2 14 24.95 
 
 .0392 
 
 .03919 
 
 
 .99923 
 
 
 .59317 
 
 110,7 
 
 .99967 
 
 
 2 14 45.58 
 
 .0393 
 
 .03929 
 
 
 .99923 
 
 
 .59428 
 
 no, 5 
 
 .99966 
 
 
 2 15 06. 21 
 
 .0394 
 
 .03939 
 
 
 .99922 
 
 
 .59538 
 
 IIO,2 
 
 .99966 
 
 
 2 15 26.83 
 
 0.0395 
 
 0.03949 
 
 10,0 
 
 0.99922 
 
 0,4 
 
 8.59648 
 
 109,9 
 
 9.99966 
 
 0,2 
 
 2 15 47.46 
 
 .0396 
 
 03959 
 
 
 .99922 
 
 
 .59758 
 
 109,6 
 
 .99966 
 
 
 2 16 08.09 
 
 .0397 
 
 .03969 
 
 
 .99921 
 
 
 .59868 
 
 109,3 
 
 .99966 
 
 
 2 16 28.71 
 
 .0398 
 
 .03979 
 
 
 .99921 
 
 
 59977 
 
 109,1 
 
 .99966 
 
 
 2 l6 49-34 
 
 .0399 
 
 .03989 
 
 
 .99920 
 
 
 .60086 
 
 108,8 
 
 99965 
 
 
 2 17 09.97 
 
 0.0400 
 
 0.03999 
 
 IO,O 
 
 0.99920 
 
 0,4 
 
 8.60194 
 
 108,5 
 
 9.9996"5 
 
 0,2 
 
 2 17 30.59 
 
 u 
 
 -isinhiu 
 
 F ' 
 
 cosh iu 
 
 F ' 
 
 . sinh iu 
 
 F ' 
 
 log cosh iu 
 
 F ' 
 
 U 
 
 log . 
 
 SMITHSONIAN TABLES 
 
 181 
 
Circular Functions. 
 
 u 
 
 sin u 
 
 -FO' 
 
 COS u 
 
 - Fo' log sin u 
 
 Fo' 
 
 log cos u 
 
 -FO' 
 
 u 
 
 0.0400 
 
 0.03999 
 
 10,0 
 
 0.99920 
 
 0,4 
 
 8.60194 
 
 108,5 
 
 9.99965 
 
 0,2 
 
 2i7 / 3o'. / 59 
 
 .0401 
 
 .04009 
 
 
 .99920 
 
 
 .60303 
 
 108,2 
 
 99965 
 
 
 2 17 51.22 
 
 .0402 
 
 .04019 
 
 
 .99919 
 
 
 .60411 
 
 108,0 
 
 .99965 
 
 
 2 18 11.85 
 
 .0403 
 
 .04029 
 
 
 .99919 
 
 
 .60519 
 
 107,7 
 
 .99965 
 
 
 2 18 32.47 
 
 .0404 
 
 .04039 
 
 
 .99918 
 
 
 .60626 
 
 107,4 
 
 99965 
 
 
 2 18 53-10 
 
 0.0405 
 
 0.04049 
 
 IO,O 
 
 0.99918 
 
 0,4 
 
 8.60734 
 
 107,2 
 
 9.99964 
 
 0,2 
 
 2 19 13.72 
 
 .0406 
 
 .04059 
 
 
 .99918 
 
 
 .60841 
 
 106,9 
 
 .99964 
 
 
 2 19 34-35 
 
 .0407 
 
 .04069 
 
 
 .99917 
 
 
 .00947 
 
 106,6 
 
 99964 
 
 
 2 19 54.98 
 
 .0408 
 
 .04079 
 
 
 .99917 
 
 
 .61054 
 
 106,4 
 
 .99964 
 
 
 2 2O 15.60 
 
 .0409 
 
 .04089 
 
 
 .99916 
 
 
 .61160 
 
 106,1 
 
 .99964 
 
 
 2 20 36.23 
 
 0.0410 
 
 0.04099 
 
 10,0 
 
 0.99916 
 
 0,4 
 
 8.61266 
 
 105,9 
 
 9.99963 
 
 0,2 
 
 2 20 56.86 
 
 .0411 
 
 .04109 
 
 
 .99916 
 
 
 .61372 
 
 105,6 
 
 99963 
 
 
 2 21 17.48 
 
 .0412 
 
 .04119 
 
 
 .99915 
 
 
 .61477 
 
 105,4 
 
 99963 
 
 
 2 21 38.11 
 
 .0413 
 
 .04129 
 
 
 .99915 
 
 
 .61583 
 
 105,1 
 
 .90963 
 
 
 2 21 58.74 
 
 .0411 
 
 .04139 
 
 
 .99914 
 
 
 .61688 
 
 104,8 
 
 .99963 
 
 
 2 22 19.36 
 
 0.0415 
 
 0.04149 
 
 IO,O 
 
 0.90914 
 
 0,4 
 
 8.61792 
 
 104,6 
 
 9.99963 
 
 0,2 
 
 2 22 39.99 
 
 .0416 
 
 .04159 
 
 
 .99913 
 
 
 .61897 
 
 104,3 
 
 .99962 
 
 
 2 23 OO.62 
 
 .0417 
 
 .04169 
 
 
 .99913 
 
 
 .62OOI 
 
 104,1 
 
 .99962 
 
 
 2 23 21.24 
 
 .0418 
 
 .04179 
 
 
 .99913 
 
 
 .6210*5 
 
 103,8 
 
 .99062 
 
 
 2 23 41.87 
 
 .0419 
 
 .04189 
 
 
 .99912 
 
 
 .62209 
 
 103,6 
 
 .99962 
 
 
 2 24 O2.5O 
 
 0.0420 
 
 0.04199 
 
 IO,O 
 
 0.99912 
 
 0,4 
 
 8.62312 
 
 103,3 
 
 9.99962 
 
 0,2 
 
 2 24 23.12 
 
 .0421 
 
 .04209 
 
 
 .99911 
 
 
 .62415 
 
 103,1 
 
 .99962 
 
 
 2 24 43-75 
 
 .0422 
 
 .04219 
 
 
 .99911 
 
 
 .62518 
 
 102,9 
 
 .99961 
 
 
 2 25 04.37 
 
 .0423 
 
 .04229 
 
 
 .99911 
 
 
 .62621 
 
 102,6 
 
 .99961 
 
 
 2 25 25.0O 
 
 .0424 
 
 .04239 
 
 
 .99910 
 
 
 .62724 
 
 102,4 
 
 .99961 
 
 
 2 25 45.63 
 
 0.0425 
 
 o . 04249 
 
 IO,O 
 
 0.99910 
 
 0,4 
 
 8.62826 
 
 102,1 
 
 9.99961 
 
 0,2 
 
 2 26 06.25 
 
 .0426 
 
 .04259 
 
 
 .99909 
 
 
 .62928 
 
 101,9 
 
 .99961 
 
 
 2 26 26.88 
 
 .0427 
 
 .04269 
 
 
 .99909 
 
 
 .63030 
 
 101,6 
 
 .99960 
 
 
 2 26 47.51 
 
 .0428 
 
 .04279 
 
 
 .99908 
 
 
 .63131 
 
 101,4 
 
 .99960 
 
 
 2 27 08.I3 
 
 .0429 
 
 .04289 
 
 
 .99908 
 
 
 .63232 
 
 101,2 
 
 .99960 
 
 
 2 27 28.76 
 
 0.0430 
 
 0.04299 
 
 10,0 
 
 0.99908 
 
 0,4 
 
 8.6J333 
 
 100,9 
 
 9.99960 
 
 0,2 
 
 2 27 49-39 
 
 .0431 
 
 .04309 
 
 
 .99907 
 
 
 .63434 
 
 100,7 
 
 .99960 
 
 
 2 28 10.01 
 
 .0432 
 
 .04319 
 
 
 .99907 
 
 
 .63535 
 
 100,5 
 
 99959 
 
 
 2 28 30.64 
 
 .0433 
 
 .04329 
 
 
 .99906 
 
 
 63635 
 
 100,2 
 
 99959 
 
 
 2 28 51.27 
 
 .0434 
 
 04339 
 
 
 .99906 
 
 
 .63735 
 
 100,0 
 
 99959 
 
 
 2 29 11. 90 
 
 0.0433 
 
 0.04349 
 
 IO,O 
 
 0.99905 
 
 0,4 
 
 8.63835 
 
 99,8 
 
 9-99959 
 
 0,2 
 
 2 29 32.52 
 
 .0436 
 
 .04359 
 
 
 .99905 
 
 
 .63935 
 
 99,5 
 
 .99959 
 
 
 2 29 53-15 
 
 0437 
 
 .04369 
 
 
 .99905 
 
 
 .64034 
 
 99,3 
 
 .99959 
 
 
 2 30 13.77 
 
 .0438 
 
 .04379 
 
 
 .99904 
 
 
 .64134 
 
 99,i 
 
 .99958 
 
 
 2 30 34.40 
 
 0439 
 
 .04389 
 
 
 .99904 
 
 
 64233 
 
 98,9 
 
 .99958 
 
 
 2 30 55-02 
 
 0.0440 
 
 .0441 
 
 0.04399 
 .04409 
 
 10,0 
 
 0.09903 
 .99903 
 
 0,4 
 
 8.64331 
 .64430 
 
 98,6 
 98,4 
 
 9.99958 
 .99958 
 
 0,2 
 
 2 31 15.65 
 2 31 36.28 
 
 .0442 
 
 .04419 
 
 
 .09902 
 
 
 .64528 
 
 98,2 
 
 .99958 
 
 
 2 31 56.OO 
 
 0443 
 .0444 
 
 .04429 
 .04439 
 
 
 .09902 
 .99901 
 
 
 .64626 
 .64724 
 
 98,0 
 97,7 
 
 .99957 
 99957 
 
 
 2 32 17-53 
 
 2 32 38. 16 
 
 0.0445 
 
 0.04449 
 
 IO,O 
 
 0.99901 
 
 0,4 
 
 8.64822 
 
 97,5 
 
 9-99957 
 
 0,2 
 
 2 32 58.78 
 
 .0446 
 
 .04459 
 
 
 .99901 
 
 
 .64919 
 
 97,3 
 
 99957 
 
 
 2 33 19-41 
 
 O447 
 
 .04469 
 
 
 .99900 
 
 
 .65016 
 
 97,i 
 
 .99957 
 
 
 2 33 40.04 
 
 .0448 
 
 .04479 
 
 
 .99900 
 
 
 .65H3 
 
 06,9 
 
 .99956 
 
 
 2 34 00.66 
 
 .0449 
 
 .04488 
 
 
 .99899 
 
 
 .65210 
 
 96,7 
 
 .99956 
 
 
 2 34 21.29 
 
 0.0450 
 
 0.04498 
 
 10,0 
 
 0.99899 
 
 0,4 
 
 8.65307 
 
 96,4 
 
 9.99956 
 
 0,2 
 
 2 34 41.92 
 
 u 
 
 isinhiu 
 
 -Fo' 
 
 cosh iu 
 
 -Fo' 
 
 , 0fl inhju 
 
 -Fo' 
 
 log cosh iu 
 
 -Fo' 
 
 u 
 
 SMITHSONIAN TABLE* 
 
 182 
 
Circular Functions. 
 
 u 
 
 sin u 
 
 F ' 
 
 COS U 
 
 wFo' 
 
 log sin u 
 
 W Fo' 
 
 log cos u 
 
 wF ' 
 
 U 
 
 0.0450 
 
 o\ 04498 
 
 IO,O 
 
 0.99899 
 
 0,4 
 
 8.65307 
 
 96,4 
 
 9.99956 
 
 O,2 
 
 234 / 4i'.'92 
 
 .0451 
 
 .04508 
 
 
 .99898 
 
 o,5 
 
 .65403 
 
 96,2 
 
 .99956 
 
 
 2 35 02.54 
 
 .0452 
 
 .04518 
 
 
 .99898 
 
 
 .65499 
 
 96,0 
 
 .99956 
 
 
 2 35 23.17 
 
 .0453 
 
 .04528 
 
 
 .99897 
 
 
 .65595 
 
 95,8 
 
 99955 
 
 
 2 35 43.8o 
 
 .0454 
 
 .04538 
 
 
 .99897 
 
 
 .65691 
 
 95,6 
 
 .99955 
 
 
 2 36 04.42 
 
 0.0455 
 
 0.04548 
 
 IO,O 
 
 0.99897 
 
 o,5 
 
 8.65786 
 
 95,4 
 
 9-99955 
 
 0,2 
 
 2 36 25.05 
 
 .0456 
 
 .04558 
 
 
 .99896 
 
 
 .65881 
 
 95,2 
 
 .99955 
 
 
 2 36 45-68 
 
 0457 
 
 .04568 
 
 
 .99896 
 
 
 .65976 
 
 95,0 
 
 .99955 
 
 
 2 37 06.30 
 
 .04158 
 
 .04578 
 
 
 .99895 
 
 
 .66071 
 
 94,8 
 
 99954 
 
 
 2 37 26.93 
 
 .0459 
 
 .04588 
 
 
 .99895 
 
 
 .66166 
 
 94,6 
 
 99954 
 
 
 2 37 47.55 
 
 0.0460 
 
 0.04598 
 
 10,0 
 
 0.99894 
 
 o,5 
 
 8.66260 
 
 94,3 
 
 9-99954 
 
 0,2 
 
 2 38 08. 18 
 
 .0461 
 
 .04608 
 
 
 .99894 
 
 
 .66355 
 
 94,1 
 
 99954 
 
 
 2 38 28.81 
 
 .0462 
 
 .04618 
 
 
 .99893 
 
 
 .66449 
 
 93,9 
 
 99954 
 
 
 2 38 49-43 
 
 .0463 
 
 .04628 
 
 
 .99893 
 
 
 .66543 
 
 93,7 
 
 99953 
 
 
 2 39 10.06 
 
 .0464 
 
 .04638 
 
 
 .99892 
 
 
 .66636 
 
 93,5 
 
 99953 
 
 
 2 39 30.69 
 
 0.0465 
 
 0.04648 
 
 10,0 
 
 0.99892 
 
 o,5 
 
 8.66730 
 
 93,3 
 
 9-99953' 
 
 0,2 
 
 2 39 5I.3I 
 
 .0466 
 
 .04658 
 
 
 .99891 
 
 
 .66823 
 
 93,1 
 
 .99953 
 
 
 2 40 11.94 
 
 .0467 
 
 .04668 
 
 
 .99891 
 
 
 .66916 
 
 92,9 
 
 99953 
 
 
 2 40 32.57 
 
 .0468 
 
 .04678 
 
 
 .99891 
 
 
 .67009 
 
 92,7 
 
 99952 
 
 
 2 40 53.19 
 
 .0469 
 
 .04688 
 
 
 .99890 
 
 
 .67101 
 
 92,5 
 
 .99952 
 
 
 2 41 13.82 
 
 0.0470 
 
 0.04698 
 
 IO,O 
 
 0.99890 
 
 o,5 
 
 8.67194 
 
 92,3 
 
 9.99952 
 
 0,2 
 
 2 41 34.45 
 
 .0471 
 
 .04708 
 
 
 .99889 
 
 
 .67286 
 
 92,1 
 
 .99952 
 
 
 2 41 55-07 
 
 .0472 
 
 .04718 
 
 
 .99889 
 
 
 .67378 
 
 91,9 
 
 .99952 
 
 
 2 42 I5.70 
 
 .0473 
 
 .04728 
 
 
 .99888 
 
 
 .67470 
 
 9i,7 
 
 99951 
 
 
 2 42 36.33 
 
 .0474 
 
 .04738 
 
 
 .99888 
 
 
 .67562 
 
 91*6 
 
 99951 
 
 
 2 42 56.95 
 
 0.0475 
 
 O.O4748 
 
 IO,0 
 
 0.99887 
 
 o,5 
 
 8.67653 
 
 91,4 
 
 9-99951 
 
 0,2 
 
 2 43 17.58 
 
 .0476 
 
 .04758 
 
 
 .99887 
 
 
 .67744 
 
 91,2 
 
 .99951 
 
 
 2 43 38.20 
 
 .0477 
 
 .04768 
 
 
 .99886 
 
 
 .67835 
 
 91,0 
 
 .99951 
 
 
 2 43 58.83 
 
 .0478 
 
 .04778 
 
 
 .99886 
 
 
 .67926 
 
 90,8 
 
 .99950 
 
 
 2 44 19-46 
 
 .0479 
 
 .04788 
 
 
 .99885 
 
 
 .68017 
 
 90,6 
 
 99950 
 
 
 2 44 40.08 
 
 0.0480 
 
 0.04798 
 
 IO,O 
 
 0.99885 
 
 0,5 
 
 8.68107 
 
 90,4 
 
 9.99950 
 
 0,2 
 
 2 45 00.71 
 
 .0481 
 
 .04808 
 
 
 .99884 
 
 
 .68198 
 
 90,2 
 
 .99950 
 
 
 2 45 21.34 
 
 .0482 
 
 .04818 
 
 
 .99884 
 
 
 .68288 
 
 90,0 
 
 99950 
 
 
 2 45 41.96 
 
 .0483 
 
 .04828 
 
 
 .99883 
 
 
 .68378 
 
 89,8 
 
 99949 
 
 
 2 46 02.59 
 
 .0484 
 
 .04838 
 
 
 .99883 
 
 
 .68468 
 
 89,7 
 
 .99949 
 
 
 2 46 23.22 
 
 0.0485 
 
 0.04848 
 
 IO,O 
 
 0.99882 
 
 o,5 
 
 8.68557 
 
 89,5 
 
 9.99949 
 
 0,2 
 
 2 46 43.84 
 
 .0486 
 
 .04858 
 
 
 .99882 
 
 
 .68647 
 
 89,3 
 
 .99949 
 
 
 2 47 04.47 
 
 .0487 
 
 .04868 
 
 
 .99881 
 
 
 .68736 
 
 89,1 
 
 .99948 
 
 
 2 47 25.10 
 
 .0488 
 
 .04878 
 
 
 .99881 
 
 
 .68825 
 
 88,9 
 
 .99948 
 
 
 2 47 45.72 
 
 .0489 
 
 .04888 
 
 
 .99880 
 
 
 .68914 
 
 88,7 
 
 .99948 
 
 
 2 48 06.35 
 
 0.0490 
 
 0.04898 
 
 10,0 
 
 0.99880 
 
 o,5 
 
 8.69002 
 
 88,6 
 
 9.99948 
 
 0,2 
 
 2 48 26.98 
 
 .0491 
 
 .04908 
 
 
 .99879 
 
 
 .69091 
 
 88,4 
 
 .99948 
 
 
 2 48 47.60 
 
 . .0492 
 
 .04918 
 
 
 .99879 
 
 
 .69179 
 
 88,2 
 
 99947 
 
 
 2 49 08.23 
 
 .0493 
 
 .04928 
 
 
 .99879 
 
 
 .69267 
 
 88,0 
 
 .99947 
 
 
 2 49 28.85 
 
 .0494 
 
 .04938 
 
 
 .99878 
 
 
 .69355 
 
 87,8 
 
 .99947 
 
 
 2 49 49.48 
 
 0.0495 
 
 0.04948 
 
 10,0 
 
 0.99878 
 
 o,5 
 
 8.69443 
 
 87,7 
 
 9-99947 
 
 0,2 
 
 2 50 10. II 
 
 .0496 
 .0497 
 
 .04958 
 .04968 
 
 
 .99877 
 .99877 
 
 
 .69530 
 .69618 
 
 87,5 
 87,3 
 
 99947 
 .99946 
 
 
 2 50 30.73 
 2 50 51.36 
 
 .0498 
 
 .04978 
 
 
 .99876 
 
 
 .69705 
 
 87,1 
 
 .99946 
 
 
 2 51 11-99 
 
 .0499 
 
 .04988 
 
 
 .99876 
 
 
 .69792 
 
 87,0 
 
 .99946 
 
 
 2 51 32.6l 
 
 0.0500 
 
 0.04998 
 
 IO,O 
 
 0.99875 
 
 o,5 
 
 8.69879 
 
 86,8 
 
 9.99946 
 
 0,2 
 
 2 51 53-24 
 
 u 
 
 -isinhiu 
 
 F ' 
 
 cosh iu 
 
 F O ' 
 
 sinh iu 
 
 Fo' 
 
 ogcoshiu 
 
 F ' 
 
 U 
 
 log . 
 
 SMITHSONIAN TABLES 
 
 183 
 
Circular Functions. 
 
 I 
 
 sin u 
 
 F ' 
 
 cos u 
 
 w F log sin u 
 
 Fo' 
 
 log cos u 
 
 "Fo' 
 
 u 
 
 0.0500 
 
 0.04098 
 
 10,0 
 
 0.99875 
 
 o,5 
 
 8.69879 
 
 86,8 
 
 9.99946 
 
 0,2 
 
 2 51 53.24 
 
 .0501 
 
 .05008 
 
 
 .99875 
 
 
 .69966 
 
 86,6 
 
 99945 
 
 
 2 52 13.87 
 
 .0502 
 
 .05018 
 
 
 .99874 
 
 
 .70052 
 
 86,4 
 
 99945 
 
 
 2 52 34.49 
 
 .0503 
 
 .05028 
 
 
 .99874 
 
 
 .70138 
 
 86,3 
 
 99945 
 
 
 2 52 55.12 
 
 .0504 
 
 .05038 
 
 
 .99873 
 
 
 .70225 
 
 86,1 
 
 99945 
 
 
 2 53 15-75 
 
 0.0505 
 
 0.05048 
 
 IO,O 
 
 0.99873 
 
 o,5 
 
 8.703II 
 
 85,9 
 
 9-99945 
 
 0,2 
 
 2 53 36.37 
 
 .0506 
 
 .05058 
 
 
 .99872 
 
 
 .70397 
 
 85,8 
 
 -99944 
 
 
 2 53 57-00 
 
 .0507 
 
 .05068 
 
 
 .99872 
 
 
 .70482 
 
 85,6 
 
 .99944 
 
 
 2 54 17.63 
 
 .0508 
 
 .05078 
 
 
 .99871 
 
 
 .70568 
 
 85,4 
 
 99944 
 
 
 2 54.38.25 
 
 .0509 
 
 .05088 
 
 
 .99870 
 
 
 .70653 
 
 85,2 
 
 99944 
 
 
 2 54 58.88 
 
 0.0510 
 
 0.05098 
 
 IO,0 
 
 0.99870 
 
 o,5 
 
 8.70738 
 
 85,1 
 
 9-99943 
 
 0,2 
 
 2 55 19.51 
 
 .0511 
 
 .05108 
 
 
 .99869 
 
 
 .70823 
 
 84,9 
 
 99943 
 
 
 2 55 40.13 
 
 .0512 
 
 .05118 
 
 
 .99869 
 
 
 .70908 
 
 84,7 
 
 99943 
 
 
 2 56 00.76 
 
 .0513 
 
 .05128 
 
 
 .99868 
 
 
 .70993 
 
 84,6 
 
 99943 
 
 
 2 56 21.38 
 
 .0514 
 
 .05138 
 
 
 .99868 
 
 
 .71077 
 
 84,4 
 
 99943 
 
 
 2 56 42.01 
 
 0.0515 
 
 0.05148 
 
 10,0 
 
 0.95867 
 
 o,5 
 
 8.71162 
 
 84,3 
 
 9.99942 
 
 0,2 
 
 2 57 02.64 
 
 .0516 
 
 .05158 
 
 
 .99867 
 
 
 .71246 
 
 84,1 
 
 99942 
 
 
 2 57 23.26 
 
 .0517 
 
 .05168 
 
 
 .99866 
 
 
 .71330 
 
 83,9 
 
 .99942 
 
 
 2 57 43.89 
 
 .0518 
 
 .05178 
 
 
 .99866 
 
 
 .71414 
 
 83,8 
 
 99942 
 
 
 2 58 04.52 
 
 .0519 
 
 .05188 
 
 
 .99865 
 
 
 .71497 
 
 83,6 
 
 99941 
 
 
 2 58 25.14 
 
 0.0520 
 
 0.05198 
 
 IO,O 
 
 0.99865 
 
 o,5 
 
 8.7I58I 
 
 83,4 
 
 9.99941 
 
 O,2 
 
 2 58 45-77 
 
 .0521 
 
 .05208 
 
 
 .99864 
 
 
 .7l65 4 - 
 
 83,3 
 
 99941 
 
 
 2 59 06.40 
 
 .0522 
 
 .05218 
 
 
 .99864 
 
 
 .71747 
 
 83,1 
 
 99941 
 
 
 2 59 27.02 
 
 .0523 
 
 .05228 
 
 
 .99363 
 
 
 .71830 
 
 83,0 
 
 99941 
 
 
 2 59 47.65 
 
 -.0524 
 
 .05238 
 
 
 .99863 
 
 
 .71913 
 
 82,8 
 
 .99940 
 
 
 3 oo 08.28 
 
 0.0525 
 
 0.05248 
 
 10,0 
 
 0.99862 
 
 o,5 
 
 8.71996 
 
 82,6 
 
 9-99940 
 
 0,2 
 
 3 oo 28.90 
 
 .0526 
 
 .05258 
 
 
 .99862 
 
 
 .72079 
 
 82,5 
 
 99940 
 
 
 3 oo 49.53 
 
 .0527 
 
 .05268 
 
 
 .99861 
 
 
 .72161 
 
 82,3 
 
 99940 
 
 
 3 01 10.16 
 
 .0528 
 
 .05278 
 
 
 .99861 
 
 
 .72243 
 
 82,2 
 
 99939 
 
 
 3 01 30.78 
 
 .0529 
 
 .05288 
 
 
 .99860 
 
 
 .72325 
 
 82,0 
 
 .99939 
 
 
 3 oi 51.41 
 
 0.0530 
 
 0.05298 
 
 IO,O 
 
 0.99860 
 
 o,5 
 
 8.72407 
 
 81,9 
 
 9-99939 
 
 0,2 
 
 3 02 12.03 
 
 .0531 
 
 .05308 
 
 
 .99859 
 
 
 .72489 
 
 8i,7 
 
 99939 
 
 
 3 02 32.66 
 
 .0532 
 
 .05317 
 
 
 .99859 
 
 
 .72571 
 
 81,6 
 
 99939 
 
 
 3 02 53.29 
 
 .0533 
 
 .05327 
 
 
 .99858 
 
 
 .72652 
 
 81,4 
 
 99938 
 
 
 3 03 13.91 
 
 .0534 
 
 .05337 
 
 
 .99857 
 
 
 .72733 
 
 81,3 
 
 .99938 
 
 
 3 03 34-54 
 
 0.0535 
 
 0.05347 
 
 IO,O 
 
 0.99857 
 
 o,5 
 
 8.72815 
 
 81,1 
 
 9.99938 
 
 0,2 
 
 3 03 55-17 
 
 0536 
 
 .05357 
 
 
 .99856 
 
 
 .72896 
 
 80,9 
 
 .99938 
 
 
 3 04 15.79 
 
 0537 
 
 05367 
 
 
 .99856 
 
 
 .72977 
 
 80,8 
 
 99937 
 
 
 3 04 36.42 
 
 .0538 
 
 C5377 
 
 
 .99855 
 
 
 .73057 
 
 80,6 
 
 99937 
 
 
 3 04 57.05 
 
 0539 
 
 .05387 
 
 
 .99855 
 
 
 .73138 
 
 80,5 
 
 99937 
 
 
 3 05 17.67 
 
 0.0540 
 
 0.05397 
 
 IO,O 
 
 0.99854 
 
 o,5 
 
 8.73218 
 
 80,3 
 
 9-99937 
 
 0,2 
 
 3 05 38.30 
 
 .0541 
 
 .05407 
 
 
 .99854 
 
 
 .73299 
 
 80,2 
 
 .99936 
 
 
 3 05 58.93 
 
 .0542 
 
 .05417 
 
 
 .99853 
 
 
 73379 
 
 80,0 
 
 .99936 
 
 
 3 06 19.55 
 
 .0543 
 
 .05427 
 
 
 .99853 
 
 
 .73459 
 
 79,9 
 
 .99936 
 
 
 3 06 40. 18 
 
 0544 
 
 .05437 
 
 
 .99852 
 
 
 .73538 
 
 79,8 
 
 .99936 
 
 
 3 07 00.81 
 
 0.0545 
 
 0.05447 
 
 IO,O 
 
 0.99852 
 
 o,5 
 
 8.73618 
 
 79,6 
 
 9-99935 
 
 0,2 
 
 3 07 21.43 
 
 .0546 
 
 .05457 
 
 
 .99851 
 
 
 .73698 
 
 79,5 
 
 99935 
 
 
 3 07 42.06 
 
 0547 
 
 .05467 
 
 
 .99850 
 
 
 73777 
 
 79,3 
 
 99935 
 
 
 3 08 02.68 
 
 .0548 
 
 .05477 
 
 
 .99850 
 
 
 .73856 
 
 79,2 
 
 99935 
 
 
 3 08 23.31 
 
 0549 
 
 .05487 
 
 
 .99849 
 
 
 73935 
 
 79,0 
 
 99935 
 
 
 3 08 43-94 
 
 0.0550 
 
 0.05497 
 
 10,0 
 
 0.99849 
 
 o,5 
 
 8.74014 
 
 78,9 
 
 9-99934 
 
 0,2 
 
 3 09 04.56 
 
 2* 
 
 -isinhiu 
 
 F ' 
 
 cosh iu 
 
 -F,,' 
 
 loa $lnh lu 
 
 -Fo' 
 
 log cosh iu 
 
 wF ' 
 
 u 
 
 log . 
 
 SMITHSONIAN TABLES 
 
 184 
 
Circular Functions. 
 
 u 
 
 sinu 
 
 F O ' 
 
 COS U 
 
 F '- 
 
 log sin u 
 
 > FO' 
 
 log cos u 
 
 wF ' 
 
 u 
 
 0.0550 
 
 0.05497 
 
 IO,O 
 
 0.99849 
 
 0,5 
 
 8.74014 
 
 78,9 
 
 9-99934 
 
 0,2 
 
 309'o4.'56 
 
 .0551 
 
 .05507 
 
 
 .99848 
 
 0,6 
 
 .74093 
 
 78,7 
 
 99934 
 
 
 3 09 25.19 
 
 .0552 
 
 .05517 
 
 
 .95848 
 
 
 .74172 
 
 78,6 
 
 99934 
 
 
 3 09 45.82 
 
 .0553 
 
 .05527 
 
 
 .99847 
 
 
 .74250 
 
 78,5 
 
 99934 
 
 
 3 to 06.44 
 
 .0554 
 
 .05537 
 
 
 .99847 
 
 
 .74329 
 
 78,3 
 
 99933 
 
 
 3 10 27-07 
 
 0.0555 
 
 O.OS547 
 
 IO,O 
 
 0.99846 
 
 0,6 
 
 8.74407 
 
 78,2 
 
 9-99933 
 
 0,2 
 
 3 10 47.70 
 
 .0556 
 
 05557 
 
 
 .99845 
 
 
 .74485 
 
 78,0 
 
 99933 
 
 
 3 II 08.32 
 
 .0557 
 
 .05567 
 
 
 .99845 
 
 
 .74563 
 
 77,9 
 
 99933 
 
 
 3 II 28.95 
 
 .0558 
 
 .05577 
 
 
 .99844 
 
 
 .74641 
 
 77,7 
 
 .99932 
 
 
 3 ii 49-58 
 
 0559 
 
 .05587 
 
 
 .99844 
 
 
 74719 
 
 77,6 
 
 99932 
 
 
 3 12 10.20 
 
 0.0560 
 
 0.05597 
 
 IO,O 
 
 0.99843 
 
 0,6 
 
 8.74796 
 
 77,5 
 
 9.99932 
 
 0,2 
 
 3 12 30.83 
 
 .0561 
 
 .05607 
 
 
 .99843 
 
 
 .74873 
 
 77,3 
 
 99932 
 
 
 3 12 51.46 
 
 .0562 
 
 .05617 
 
 
 .99842 
 
 
 74951 
 
 77,2 
 
 99931 
 
 
 3 13 12.08 
 
 .0563 
 
 .05627 
 
 
 .99842 
 
 
 .75028 
 
 77,1 
 
 99931 
 
 
 3 13 32.71 
 
 .0564 
 
 .05637 
 
 
 .99841 
 
 
 .75105 
 
 76,9 
 
 99931 
 
 
 3 13 53-34 
 
 0.0565 
 
 0.05647 
 
 IO,O 
 
 0.99840 
 
 0,6 
 
 8.75182 
 
 76 
 
 9.99931 
 
 0,2 
 
 3 14 13.96 
 
 .0566 
 
 .05657 
 
 
 .99840 
 
 
 .75258 
 
 76,6 
 
 99930 
 
 
 3 14 34.59 
 
 .0567 
 
 .05667 
 
 
 .99839 
 
 
 .75335 
 
 76,5 
 
 99930 
 
 
 3 H 55-21 
 
 .0568 
 
 .05677 
 
 
 .99839 
 
 
 .754H 
 
 76,4 
 
 99930 
 
 
 3 15 15.84 
 
 .0569 
 
 .05687 
 
 
 .99838 
 
 
 .75488 
 
 76,2 
 
 99930 
 
 
 3 15 36.47 
 
 0.0570 
 
 0.05697 
 
 IO,O 
 
 0.99838 
 
 0,6 
 
 8.75564 
 
 76,1 
 
 9.99929 
 
 0,2 
 
 3 15 57.09 
 
 .0571 
 
 .05707 
 
 
 .99837 
 
 
 75640 
 
 76,0 
 
 .99929 
 
 
 3 16 17.72 
 
 .0572 
 
 .05717 
 
 
 .99836 
 
 
 .75716 
 
 75,8 
 
 .99929 
 
 
 3 16 38.35 
 
 .0573 
 
 .05727 
 
 
 .99836 
 
 
 75792 
 
 75,7 
 
 .99929 
 
 
 3 16 58.97 
 
 0574 
 
 .05737 
 
 
 .99835 
 
 
 .75867 
 
 75,6 
 
 .99928 
 
 
 3 17 19-60 
 
 0.0575 
 
 0.05747 
 
 10,0 
 
 0.99835 
 
 0,6 
 
 8.75943 
 
 75,4 
 
 9.99928 
 
 O,2 
 
 3 17 40.23 
 
 0576 
 
 .05757 
 
 
 .99834 
 
 
 .76018 
 
 75,3 
 
 .99928 
 
 0,3 
 
 3 18 00.85 
 
 .0577 
 
 .05767 
 
 
 .99834 
 
 
 .76093 
 
 75,2 
 
 .99928 
 
 
 3 18 21.48 
 
 .0578 
 
 .05777 
 
 
 .99833 
 
 
 .76169 
 
 75,1 
 
 .99927 
 
 
 3 18 42.11 
 
 .0579 
 
 .05787 
 
 
 .99832 
 
 
 .76244 
 
 74,9 
 
 99927 
 
 
 3 19 02.73 
 
 0.0580 
 
 0.05797 
 
 10,0 
 
 0.99832 
 
 0,6 
 
 8.76318 
 
 74,8 
 
 9.99927 
 
 0,3 
 
 3 19 23.36 
 
 .0581 
 
 .05807 
 
 
 .99831 
 
 
 .76393 
 
 74,7 
 
 .99927 
 
 
 3 19 43-99 
 
 .0582 
 
 .05817 
 
 
 .99831 
 
 
 .76468 
 
 74,5 
 
 .99926 
 
 
 3 20 04.61 
 
 .0583 
 
 .05827 
 
 
 .99830 
 
 
 .76542 
 
 74,4 
 
 .99926 
 
 
 3 20 25.24 
 
 .0584 
 
 .05837 
 
 
 .99830 
 
 
 .76617 
 
 74,3 
 
 .99926 
 
 
 3 20 45.86 
 
 0.0585 
 
 0.05847 
 
 10,0 
 
 0.99829 
 
 0,6 
 
 8.76691 
 
 742 
 
 9.99926 
 
 0,3 
 
 3 21 06.49 
 
 .0586 
 
 .05857 
 
 
 .99828 
 
 
 .76765 
 
 74,0 
 
 .99925 
 
 
 3 21 27.12 
 
 .0587 
 
 .05867 
 
 
 .99828 
 
 
 .76839 
 
 73,9 
 
 .99925 
 
 
 3 21 47.74 
 
 .0588 
 
 .05877 
 
 
 .99827 
 
 
 .76913 
 
 73,8 
 
 .99925 
 
 
 3 22 08.37 
 
 .0589 
 
 .05887 
 
 
 .99827 
 
 
 .76986 
 
 73,6 
 
 .99925 
 
 
 3 22 29.00 
 
 0.0590 
 
 0.05897 
 
 10,0 
 
 0.99826 
 
 0,6 
 
 8.77060 
 
 73,5 
 
 9.99924 
 
 0,3 
 
 3 22 49.62 
 
 .0591 
 
 .05907 
 
 
 .99825 
 
 
 .77133 
 
 73,4 
 
 .99924 
 
 
 3 23 10.25 
 
 .0592 
 
 .05917 
 
 
 .99825 
 
 
 .77207 
 
 73,3 
 
 .99924 
 
 
 3 23 30.88 
 
 0593 
 
 .05927 
 
 
 .99824 
 
 
 .77280 
 
 73,2 
 
 .99924 
 
 
 3 23 51.50 
 
 .0594 
 
 .05937 
 
 
 .99824 
 
 
 77353 
 
 73,0 
 
 99923 
 
 
 3 24 12.13 
 
 0.0595 
 
 0.05946 
 
 10,0 
 
 0.99823 
 
 0,6 
 
 8.77426 
 
 72,9 
 
 9.99923 
 
 0,3 
 
 3 24 32.76 
 
 .0596 
 
 .05956 
 
 
 .99822 
 
 
 77499 
 
 72,8 
 
 .99923 
 
 
 3 24 53.38 
 
 0597 
 
 .05966 
 
 
 .99822 
 
 
 77572 
 
 72,7 
 
 .99923 
 
 
 3 25 14.01 
 
 .0598 
 
 .05976 
 
 
 .99821 
 
 
 .77644 
 
 72,5 
 
 .99922 
 
 
 3 25 34.64 
 
 .0599 
 
 .05986 
 
 
 .99821 
 
 
 .77717 
 
 72,4 
 
 .99922 
 
 
 3 25 55.26 
 
 0.0600 
 
 0.05996 
 
 IO,O 
 
 0.99820 
 
 0,6 
 
 8.77789 
 
 72,3 
 
 9.99922 
 
 o,3 
 
 3 26 15.89 
 
 u 
 
 -isinhiu 
 
 wF ' 
 
 cosh iu 
 
 F O ' 
 
 sinh iu 
 
 -Fo' 
 
 ogcoshiu 
 
 F O ' 
 
 u 
 
 log 
 
 SMITHSONIAN TABLES 
 
 185 
 
Circular Functions. 
 
 u 
 
 sin u 
 
 F ' 
 
 COS U 
 
 F ' 
 
 log sin u 
 
 Fo' 
 
 log cos u 
 
 FO' 
 
 u 
 
 0.0600 
 
 0.05996 
 
 IO,O 
 
 0.99820 
 
 0,6 
 
 8.77789 
 
 72,3 
 
 9.99922 
 
 0,3 
 
 326' is'.'89 
 
 .0601 
 
 .06006 
 
 
 .99819 
 
 
 .77861 
 
 72,2 
 
 .99922 
 
 
 3 26 36.51 
 
 .0602 
 .0603 
 
 .06016 
 .06026 
 
 
 .99819 
 .99818 
 
 
 .77933 
 .78005 
 
 72,1 
 71,9 
 
 .99921 
 .99921 
 
 
 3 26 57.14 
 3 27 17.77 
 
 .0604 
 
 .06036 
 
 
 .99818 
 
 
 .78077 
 
 7i,8 
 
 .99921 
 
 
 3 27 38.39 
 
 0.0605 
 
 0.06046 
 
 IO,O 
 
 0.99817 
 
 0,6 
 
 8.78149 
 
 7i,7 
 
 9.99920 
 
 0,3 
 
 3 27 59.02 
 
 .0606 
 
 .06056 
 
 
 .99816 
 
 
 . 78221 
 
 7i,6 
 
 .99920 
 
 
 3 28 19.65 
 
 .0607 
 
 .06066 
 
 
 .99816 
 
 
 .78292 
 
 7i,5 
 
 .99920 
 
 
 3 28 40.27 
 
 .0608 
 
 .06076 
 
 
 .99815 
 
 
 .78364 
 
 7i,3 
 
 .99920 
 
 
 3 29 00.90 
 
 .0609 
 
 .06086 
 
 
 .99815 
 
 . 
 
 .78435 
 
 71,2 
 
 .99919 
 
 
 3 29 21.53 
 
 0.0610 
 
 0.06096 
 
 IO,O 
 
 0.99814 
 
 0,6 
 
 8.78506 
 
 7U 
 
 9.99919 
 
 o,3 
 
 3 29 42.15 
 
 .0611 
 
 .06106 
 
 
 .99813 
 
 
 .78577 
 
 7i,o 
 
 .99919 
 
 
 3 30 02.78 
 
 .0612 
 
 .06116 
 
 
 .99813 
 
 
 .78648 
 
 70,9 
 
 .99919 
 
 
 3 30 23.41 
 
 .0613 
 
 .06126 
 
 
 .99812 
 
 
 .78719 
 
 70,8 
 
 .99918 
 
 
 3 30 44-03 
 
 .0614 
 
 .06136 
 
 
 .99812 
 
 
 .78790 
 
 70,6 
 
 .99918 
 
 
 3 31 04.66 
 
 0.0615 
 
 0.06146 
 
 10,0 
 
 0.99811 
 
 0,6 
 
 8.78860 
 
 70,5 
 
 9.99918 
 
 o,3 
 
 3 31 25.29 
 
 .0616 
 
 .06156 
 
 
 .99810 
 
 
 .78931 
 
 70,4 
 
 .99918 
 
 
 3 31 45.91 
 
 .0617 
 
 .06166 
 
 
 .99810 
 
 
 .79001 
 
 70,3 
 
 .99917 
 
 
 3 32 06.54 
 
 .0618 
 
 .06176 
 
 
 .99809 
 
 
 .70071 
 
 70,2 
 
 .99917 
 
 
 3 32 27.17 
 
 .0619 
 
 .06186 
 
 
 .99808 
 
 
 .79UI 
 
 70,i 
 
 .99917 
 
 
 3 32 47-79 
 
 0.0620 
 
 0.06196 
 
 IO,O 
 
 0.99808 
 
 0,6 
 
 8.79211 
 
 70,o 
 
 9.99916 
 
 0,3 
 
 3 33 08.42 
 
 .0621 
 
 .06206 
 
 
 .99807 
 
 
 .79281 
 
 69,8 
 
 .99916 
 
 
 3 33 29.04 
 
 .0622 
 
 .06216 
 
 
 .99807 
 
 
 79351 
 
 69,7 
 
 .99916 
 
 
 3 33 49.67 
 
 .0623 
 
 .06226 
 
 
 .99806 
 
 
 .79421 
 
 69,6 
 
 .90916 
 
 
 3 34 10.30 
 
 .0624 
 
 .06236 
 
 
 .99805 
 
 
 .79490 
 
 69,5 
 
 .99915 
 
 
 3 34 30.92 
 
 0.0625 
 
 0.06246 
 
 IO,O 
 
 0.99805 
 
 0,6 
 
 8.79560 
 
 69,4 
 
 9.99915 
 
 o,3 
 
 3 34 51.55 
 
 .0626 
 
 .06256 
 
 
 .99804 
 
 
 .79629 
 
 69,3 
 
 99915 
 
 
 3 35 12. 18 
 
 .0627 
 
 .06266 
 
 
 .99804 
 
 
 .79698 
 
 69,2 
 
 .99915 
 
 
 3 35 32.8o 
 
 .0628 
 
 .06276 
 
 
 .99803 
 
 
 .79767 
 
 69,1 
 
 .99914 
 
 
 3 35 53.43 
 
 .0629 
 
 .06286 
 
 
 .99802 
 
 
 .79836 
 
 69,0 
 
 .99914 
 
 
 3 36" 14.06 
 
 0.0630 
 
 0.06296 
 
 IO,0 
 
 0.99802 
 
 0,6 
 
 8.79905 
 
 68,8 
 
 9.99914 
 
 o,3 
 
 3 36 34.68 
 
 .0631 
 
 .06306 
 
 
 .99801 
 
 
 79974 
 
 68,7 
 
 .99913 
 
 
 3 36 55-31 
 
 .0632 
 
 .06316 
 
 
 .99800 
 
 
 80043 
 
 68,6 
 
 .99913 
 
 
 3 37 15-94 
 
 .0633 
 
 .06326 
 
 
 .99800 
 
 
 .80111 
 
 68,5 
 
 .99913 
 
 
 3 37 36.56 
 
 .0634 
 
 .06336 
 
 
 .99799 
 
 
 .80180 
 
 68,4 
 
 .99913 
 
 
 3 37 57.19 
 
 0.0635 
 
 0.06346 
 
 IO,O 
 
 0.99798 
 
 0,6 
 
 8.80248 
 
 68,3 
 
 9.99912 
 
 o,3 
 
 3 38 17.82 
 
 .0636 
 
 .06356 
 
 
 .99798 
 
 
 .80316 
 
 68,2 
 
 .99912 
 
 
 3 38 38.44 
 
 .0637 
 
 .06366 
 
 
 .99797 
 
 
 80385 
 
 68,1 
 
 .99912 
 
 
 3 38 59.07 
 
 .0638 
 
 .06376 
 
 
 99797 
 
 
 .80453 
 
 68,0 
 
 .99912 
 
 
 3 39 19-69 
 
 .0639 
 
 .06386 
 
 
 .99796 
 
 
 .80521 
 
 67,9 
 
 .99911 
 
 
 3 39 40.32 
 
 0.0640 
 
 0.06396 
 
 IO,O 
 
 0.09795 
 
 0,6 
 
 8.80588 
 
 67,8 
 
 9.999H 
 
 o,3 
 
 3 40 00.95 
 
 .0641 
 
 .06406 
 
 
 .99795 
 
 
 .80656 
 
 67,7 
 
 .99911 
 
 
 3 40 21.57 
 
 .0642 
 
 .06416 
 
 
 .99794 
 
 
 .80724 
 
 67,6 
 
 .99910 
 
 
 3 40 42.20 
 
 .0643 
 
 .06426 
 
 
 .99793 
 
 
 .80791 
 
 67,4 
 
 .99910 
 
 
 3 41 02.83 
 
 .0644 
 
 .06436 
 
 
 99793 
 
 
 .80859 
 
 67,3 
 
 .99910 
 
 
 3 41 23.45 
 
 0.0645 
 
 0.06446 
 
 IO,O 
 
 0.99792 
 
 0,6 
 
 8.80926 
 
 67,2 
 
 9.99910 
 
 0,3 
 
 3 41 44-08 
 
 .0646 
 
 .06456 
 
 
 99791 
 
 
 .80993 
 
 67,1 
 
 .99909 
 
 
 3 42 04.71 
 
 .0647 
 
 .06465 
 
 
 .99791 
 
 
 .81060 
 
 67,0 
 
 .90909 
 
 
 3 42 25.33 
 
 .0648 
 
 .06475 
 
 
 .99790 
 
 
 .81127 
 
 6fo 
 
 .99909 
 
 
 3 42 45.96 
 
 .0649 
 
 .06485 
 
 
 .99789 
 
 
 .81194 
 
 66,8 
 
 .99908 
 
 
 3 43 06.59 
 
 0.0650 
 
 0.06495 
 
 1 0,0 
 
 0.99789 
 
 0,6 
 
 8.81261 
 
 65,7 
 
 9.99908 
 
 o,3 
 
 3 43 27.21 
 
 u 
 
 isinhiu 
 
 Fo' 
 
 cosh iu 
 
 -FO' 
 
 lfl Sinh iU 
 
 -FO' 
 
 log cosh iu 
 
 -FO' 
 
 u 
 
 lOfl , 
 
 SMITHSONIAN TABLES 
 
 1 86 
 
Circular Functions. 
 
 u 
 
 siriu 
 
 F ' 
 
 COS U 
 
 F ' 
 
 log sin u 
 
 Fo' 
 
 log oos u 
 
 F ' 
 
 u 
 
 0.0650 
 
 0.06495 
 
 IO,O 
 
 0.99789 
 
 O,6 
 
 8.81261 
 
 66,7 
 
 9.99908 
 
 0,3 
 
 343'27'.'2i 
 
 .0651 
 
 .06505 
 
 
 .99788 
 
 o,7 
 
 .81327 
 
 66,6 
 
 .99908 
 
 
 3 43 47.84 
 
 .0652 
 
 .06515 
 
 
 .99788 
 
 
 .81394 
 
 66,5 
 
 .99908 
 
 
 3 44 08.47 
 
 .0653 
 
 .06525 
 
 
 .99787 
 
 
 .81460 
 
 66,4 
 
 .99907 
 
 
 3 44 29.09 
 
 .0654 
 
 .06535 
 
 
 .99786 
 
 
 .81527 
 
 66,3 
 
 .99907 
 
 
 3 44 49.72 
 
 0.0655 
 
 0.06545 
 
 IO,O 
 
 0.99786 
 
 o,7 
 
 8.81593 
 
 66,2 
 
 9.99907 
 
 0,3 
 
 3 45 10.34 
 
 .0656 
 
 06555 
 
 
 .99785 
 
 
 .81659 
 
 66,1 
 
 .99906 
 
 
 3 45 30.97 
 
 .0657 
 
 .06565 
 
 
 .99784 
 
 
 .81725 
 
 66,0 
 
 .99906 
 
 
 3 45 51.60 
 
 .0658 
 
 06575 
 
 
 .99784 
 
 
 .81791 
 
 65,9 
 
 .99906 
 
 
 3 46 12.22 
 
 .0659 
 
 .06585 
 
 
 .99783 
 
 
 .81857 
 
 65,8 
 
 .99906 
 
 
 3 46 32.85 
 
 0.0660 
 
 0.06595 
 
 IO,O 
 
 0.99782 
 
 o,7 
 
 8.81923 
 
 65,7 
 
 9.99905 
 
 0,3 
 
 3 46 53.48 
 
 .0661 
 
 .06605 
 
 
 .99782 
 
 
 .81989 
 
 65,6 
 
 .99905 
 
 
 3 47 14.10 
 
 .0662 
 
 .06615 
 
 
 .99781 
 
 
 .82054 
 
 65,5 
 
 .99905 
 
 
 3 47 34.73 
 
 .0663 
 
 .06625 
 
 
 .99780 
 
 
 .82120 
 
 65,4 
 
 .99904 
 
 
 3 47 55.36 
 
 .0664 
 
 .06635 
 
 
 .99780 
 
 
 .82185 
 
 65,3 
 
 .99904 
 
 
 348 15.08 
 
 0.0665 
 
 0.06645 
 
 IO,O 
 
 0.99779 
 
 o,7 
 
 8.82250 
 
 65,2 
 
 9.99904 
 
 0,3 
 
 3 48 36.61 
 
 .0666 
 
 .06655 
 
 
 .99778 
 
 
 .82315 
 
 65,1 
 
 .99904 
 
 
 3 48 57-24 
 
 .0667 
 
 .06665 
 
 
 .99778- 
 
 
 .82380 
 
 65,0 
 
 .99903 
 
 
 3 49 17.86 
 
 .0668 
 
 .06675 
 
 
 99777 
 
 
 .82445 
 
 64,9 
 
 .99903 
 
 
 3 49 38.49 
 
 .0669 
 
 .06685 
 
 
 .99776 
 
 
 .82510 
 
 64,8 
 
 .99903 
 
 
 3 49 59-12 
 
 0.0670 
 
 0.06695 
 
 IO,O 
 
 0.99776 
 
 o,7 
 
 8.82575 
 
 64,7 
 
 9.99902 
 
 0,3 
 
 3 50 19.74 
 
 .0671 
 
 .06705 
 
 
 .99775 
 
 
 .82640 
 
 646 
 
 .99902 
 
 
 3 50 40.37 
 
 .0672 
 
 .06715 
 
 
 99774 
 
 
 .82704 
 
 64,5 
 
 .99902 
 
 
 3 51 00.09 
 
 .0673 
 
 .06725 
 
 
 99774 
 
 
 .82769 
 
 64,4 
 
 .09902 
 
 
 3 51 21.62 
 
 .0674 
 
 .06735 
 
 
 .99773 
 
 
 .82833 
 
 64,3 
 
 .99901 
 
 
 3 51 42.25 
 
 0.0675 
 
 0.06745 
 
 10,0 
 
 0.99772 
 
 o,7 
 
 8.82897 
 
 64,2 
 
 9.99001 
 
 0,3 
 
 3 52 02.87 
 
 .0676 
 
 .06755 
 
 
 .99772 
 
 
 .82962 
 
 64,1 
 
 .09901 
 
 
 3 52 23.50 
 
 .0677 
 
 .06765 
 
 
 .99771 
 
 
 .83026 
 
 64,1 
 
 .99900 
 
 
 3 52 44-13 
 
 .0678 
 
 .06775 
 
 
 .99770 
 
 
 .83090 
 
 64,0 
 
 .99900 
 
 
 3 53 04-75 
 
 .0679 
 
 .06785 
 
 
 99770 
 
 
 .83154 
 
 63,9 
 
 .99900 
 
 
 3 53 25.38 
 
 0.0680 
 
 0.06795 
 
 IO,O 
 
 0.99769 
 
 o,7 
 
 8.83217 
 
 63,8 
 
 9.99900 
 
 0,3 
 
 3 53 46.01 
 
 .0681 
 
 .06805 
 
 
 .99768 
 
 
 .83281 
 
 63,7 
 
 .99899 
 
 
 3 54 06.63 
 
 .0682 
 
 .06815 
 
 
 .99768 
 
 
 .83345 
 
 63,6 
 
 .99899 
 
 
 3 54 27.26 
 
 .0683 
 
 .06825 
 
 
 .99767 
 
 
 .83408 
 
 63,5 
 
 .90899 
 
 
 3 54 47.89 
 
 .0684 
 
 .06835 
 
 
 .99766 
 
 
 .83472 
 
 63,4 
 
 .99898 
 
 
 3 55 08.51 
 
 0.0685 
 
 0.06845 
 
 IO,O 
 
 0.99765 
 
 o,7 
 
 8.83535 
 
 63,3 
 
 9.99898 
 
 0,3 
 
 3 55 29.14 
 
 .0686 
 
 .06855 
 
 
 .99765 
 
 
 .83598 
 
 63,2 
 
 .99898 
 
 
 3 55 49.77 
 
 .0687 
 
 .06865 
 
 
 .99764 
 
 
 .83662 
 
 63,1 
 
 .99897 
 
 
 3 56 10.39 
 
 .0688 
 
 .06875 
 
 
 .99763 
 
 
 .83725 
 
 63,0 
 
 .99897 
 
 
 3 56 31.02 
 
 .0689 
 
 .06885 
 
 
 .99763 
 
 
 .83788 
 
 62,9 
 
 .99897 
 
 
 3 56 51.65 
 
 0.0600 
 
 0.06895 
 
 IO,O 
 
 0.99762 
 
 o,7 
 
 8.83850 
 
 62,8 
 
 9.99897 
 
 0,3 
 
 3 57 12.27 
 
 .0691 
 
 .06905 
 
 
 .99761 
 
 
 .83913 
 
 62,8 
 
 .99896 
 
 
 3 57 32.90 
 
 .0692 
 
 .06914 
 
 
 .99761 
 
 
 .83976 
 
 62,7 
 
 .99896 
 
 
 3 57 53.52 
 
 .0693 
 
 .06924 
 
 
 .99760 
 
 
 .84039 
 
 62,6 
 
 .99896 
 
 
 3 58 14-15 
 
 .0604 
 
 .06934 
 
 
 99759 
 
 
 .84101 
 
 62,5 
 
 .99895 
 
 
 3 58 34.78 
 
 0.0695 
 
 0.06944 
 
 IO,O 
 
 0.99759 
 
 o,7 
 
 8.84164 
 
 62,4 
 
 9.99895 
 
 0,3 
 
 3 58 55-40 
 
 .0696 
 
 .00954 
 
 
 99758 
 
 
 .84226 
 
 62,3 
 
 .99895 
 
 
 3 59 16.03 
 
 .0697 
 
 .06964 
 
 
 99757 
 
 
 .84288 
 
 62,2 
 
 .99894 
 
 
 3 59 36.66 
 
 .0698 
 
 .06974 
 
 
 .99756 
 
 
 .84350 
 
 62,1 
 
 .99894 
 
 
 3 59 57.28 
 
 .0699 
 
 .06984 
 
 
 .99756 
 
 
 .84412 
 
 62,0 
 
 .99894 
 
 
 4 oo 17.91 
 
 0.0700 
 
 0.06994 
 
 IO,0 
 
 0.99755 
 
 o,7 
 
 8.84474 
 
 6i,9 
 
 9.99894 
 
 0,3 
 
 4 oo 38.54 
 
 u 
 
 -isinhiu 
 
 wF ' 
 
 cosh iu 
 
 F ' 
 
 sinh iu 
 
 > Fo' 
 
 loo cosh iu 
 
 F O ' 
 
 u 
 
 log , 
 
 SMITHSONIAN TABLES 
 
 187 
 
Circular Functions. 
 
 u 
 
 sin u 
 
 FO' 
 
 COS U 
 
 F * 
 
 log sin u 
 
 FO' 
 
 log cos u 
 
 F ' 
 
 U 
 
 0.0700 
 
 0.06994 
 
 10,0 
 
 0.99755 
 
 o,7 
 
 8.84474 
 
 61,9 
 
 9-99894 
 
 0,3 
 
 4oo 38" 54 
 
 .0701 
 
 .07004 
 
 
 .99754 
 
 
 .84536 
 
 6i,9 
 
 .99893 
 
 
 4 oo 59.16 
 
 .0702 
 
 .07014 
 
 
 99754 
 
 
 .84598 
 
 61,8 
 
 99893 
 
 
 4 oi 19.79 
 
 .0703 
 
 .07024 
 
 
 99753 
 
 
 .84660 
 
 61,7 
 
 .99893 
 
 
 4 01 40.42 
 
 .0704 
 
 .07034 
 
 
 99752 
 
 
 .84721 
 
 61,6 
 
 .99892 
 
 
 4 02 01.04 
 
 0.0705 
 
 0.07044 
 
 10,0 
 
 0.99752 
 
 o,7 
 
 8.84783 
 
 61,5 
 
 9.99892 
 
 0,3 
 
 4 02 21.67 
 
 .0706 
 
 07054 
 
 
 .99751 
 
 
 .84844 
 
 61,4 
 
 .99892 
 
 
 4 02 42.30 
 
 .0707 
 
 .07064 
 
 
 99750 
 
 
 .84906 
 
 61,3 
 
 .99891 
 
 
 4 03 02.92 
 
 .0708 
 
 .07074 
 
 
 99749 
 
 
 .84967 
 
 61,2 
 
 .99891 
 
 
 4 03 23.55 
 
 .0709 
 
 .07084 
 
 
 .99749 
 
 
 .85028 
 
 61,2 
 
 .99891 
 
 
 4 03 44.17 
 
 0.0710 
 
 0.07094 
 
 10,0 
 
 0.99748 
 
 o,7 
 
 8.85089 
 
 61,1 
 
 9.99890 
 
 0,3 
 
 4 04 04.80 
 
 .0711 
 
 .07104 
 
 
 .99747 
 
 
 .85150 
 
 61,0 
 
 .99890 
 
 
 4 04 25.43 
 
 .0712 
 
 .07114 
 
 
 .99747 
 
 
 .85211 
 
 60,9 
 
 .99890 
 
 
 4 04 46.05 
 
 .0713 
 
 .07124 
 
 
 .99746 
 
 
 .85272 
 
 60,8 
 
 .99890 
 
 
 4 05 06.68 
 
 .0714 
 
 .07134 
 
 
 .99745 
 
 
 .85333 
 
 60,7 
 
 99889 
 
 
 4 05 27.31 
 
 0.0715 
 
 0.07144 
 
 1 0,0 
 
 0-99744 
 
 o,7 
 
 8.85394 
 
 60,6 
 
 9.99889 
 
 0,3 
 
 4 05 47.93 
 
 .0716 
 
 .07154 
 
 
 99744 
 
 
 85454 
 
 60,6 
 
 
 
 4 06 08.56 
 
 .0717 
 
 .07164 
 
 
 99743 
 
 
 .85515 
 
 60,5 
 
 99888 
 
 
 4 06 29.19 
 
 .0718 
 
 .07174 
 
 
 99742 
 
 
 85575 
 
 60,4 
 
 .99888 
 
 
 4 06 49.81 
 
 .0719 
 
 .07184 
 
 
 .99742 
 
 
 .85635 
 
 60,3 
 
 .99888 
 
 
 4 07 10.44 
 
 0.0720 
 
 0.07194 
 
 IO,0 
 
 0.99741 
 
 0,7 
 
 8.85696 
 
 60,2 
 
 9.99887 
 
 0,3 
 
 4 07 31.07 
 
 .0721 
 
 .07204 
 
 
 99740 
 
 
 .85756 
 
 00,1 
 
 .99887 
 
 
 4 07 51.69 
 
 .0722 
 
 .07214 
 
 
 99739 
 
 
 .85816 
 
 60,0 
 
 .99887 
 
 
 4 08 12.32 
 
 .0723 
 
 .07224 
 
 
 99739 
 
 
 .85876 
 
 60,0 
 
 .99886 
 
 
 4 08 32.95 
 
 .0724 
 
 .07234 
 
 
 .99738 
 
 
 .85936 
 
 59,9 
 
 .99886 
 
 
 4 08 53-57 
 
 0.0725 
 
 0.07244 
 
 IO,O 
 
 0.99737 
 
 o,7 
 
 8.85996 
 
 59,8 
 
 9.99886 
 
 0,3 
 
 4 09 14.20 
 
 .0726 
 
 .07254 
 
 
 .99737 
 
 
 .86056 
 
 59,7 
 
 .99885 
 
 
 4 09 34.82 
 
 .0727 
 
 .07264 
 
 
 .99736 
 
 
 .86115 
 
 59,6 
 
 .99885 
 
 
 4 09 55-45 
 
 .0728 
 
 .07274 
 
 ' 
 
 99735 
 
 
 86175 
 
 59,6 
 
 .99885 
 
 
 4 10 16.08 
 
 .0729 
 
 .07284 
 
 
 99734 
 
 
 .86234 
 
 59,5 
 
 99884 
 
 
 4 10 36.70 
 
 0.0730 
 
 0.07294 
 
 IO,O 
 
 0.99734 
 
 o,7 
 
 8.86294 
 
 59,4 
 
 9.99884 
 
 0.3 
 
 4 10 57-33 
 
 .0731 
 
 .07303 
 
 
 .99733 
 
 
 86353 
 
 59,3 
 
 .99884 
 
 
 4 II 17-96 
 
 .0732 
 
 .07313 
 
 
 .99732 
 
 
 .86412 
 
 59,2 
 
 .99884 
 
 
 4 u 38.58 
 
 0733 
 
 .07323 
 
 
 99731 
 
 
 .86472 
 
 59,i 
 
 .99883 
 
 
 4 u 59-21 
 
 0734 
 
 .07333 
 
 
 99731 
 
 
 86531 
 
 59,1 
 
 .99883 
 
 
 4 12 19.84 
 
 0.0735 
 
 0.07343 
 
 IO,O 
 
 0.99730 
 
 o,7 
 
 8.86590 
 
 59,0 
 
 9.99883 
 
 0,3 
 
 4 12 40.46 
 
 .0736 
 
 .07353 
 
 
 .99729 
 
 
 .86649 
 
 58,9 
 
 .99882 
 
 
 4 13 01.09 
 
 .0737 
 
 .07363 
 
 
 .99729 
 
 
 .86707 
 
 58,8 
 
 .99882 
 
 
 4 13 21.72 
 
 .0738 
 
 .07373 
 
 
 .99728 
 
 
 .86766 
 
 58,7 
 
 .99882 
 
 
 4 13 42.34 
 
 .0739 
 
 .07383 
 
 
 .99727 
 
 
 .86825 
 
 58,7 
 
 .99881 
 
 
 4 14 02.97 
 
 0.0740 
 
 0.07393 
 
 10,0 
 
 0.99726 
 
 0,7 
 
 8.86884 
 
 58,6 
 
 9-99881 
 
 0,3 
 
 4 14 23.60 
 
 .0741 
 
 .07403 
 
 
 .99726 
 
 
 .86942 
 
 58,5 
 
 .99881 
 
 
 4 M 44.22 
 
 .0742 
 
 .07413 
 
 
 .99725 
 
 
 .87001 
 
 58,4 
 
 .99880 
 
 
 4 IS 04.85 
 
 .0743 
 
 .07423 
 
 
 .99724 
 
 
 .87059 
 
 58,3 
 
 .99880 
 
 
 4 15 25.48 
 
 .0744 
 
 .07433 
 
 
 .99723 
 
 
 .87117 
 
 58,3 
 
 .99880 
 
 
 4 15 46.10 
 
 0.0745 
 
 0.07443 
 
 10,0 
 
 0.99723 
 
 0,7 
 
 8.87175 
 
 58,2 
 
 9.99879 
 
 0,3 
 
 4 16 06.73 
 
 .0746 
 
 .07453 
 
 
 .99722 
 
 
 .87234 
 
 58,1 
 
 .99879 
 
 
 4 16 27.35 
 
 .0747 
 
 .07463 
 
 
 99721 
 
 
 .87292 
 
 58,0 
 
 99879 
 
 
 4 16 47-98 
 
 .0748 
 
 .07473 
 
 
 99720 
 
 
 .87350 
 
 58,0 
 
 .99878 
 
 
 4 17 08. 61 
 
 .0749 
 
 .07483 
 
 
 .99720 
 
 
 .87408 
 
 57,9 
 
 .99878 
 
 
 4 17 29.23 
 
 0.0750 
 
 0.07493 
 
 10,0 
 
 0.99719 
 
 0,7 
 
 8.87465 
 
 57,8 
 
 9.09878 
 
 0,3 
 
 4 17 49-86 
 
 u 
 
 -isinhiu 
 
 F ' 
 
 cosh iu 
 
 F ' 
 
 | 00 $inh iu 
 
 IV 
 
 ogcoshiu 
 
 -Fo' 
 
 u 
 
 log , 
 
 SMITHSONIAN TABLES 
 
 188 
 
Circular Functions. 
 
 u 
 
 sin u 
 
 F ' 
 
 COS U 
 
 F ' 
 
 log sin u 
 
 - Fo' 
 
 log cos u 
 
 Fo' 
 
 u 
 
 
 
 
 
 
 
 
 
 
 O 4 44 
 
 0.0750 
 
 0.07493 
 
 10,0 
 
 0.99719 
 
 o,7 
 
 8.87465 
 
 57,8 
 
 9.99878 
 
 o,3 
 
 4 17 49-86 
 
 .0751 
 
 .07503 
 
 
 .99718 
 
 0,8 
 
 .87523 
 
 57,7 
 
 .99877 
 
 
 4 18 10.49 
 
 .0752 
 
 .07513 
 
 
 .99717 
 
 
 .87581 
 
 57,6 
 
 .99877 
 
 
 4 18 31.11 
 
 .0753 
 
 .07523 
 
 
 .99717 
 
 
 .87638 
 
 57,6 
 
 .99877 
 
 
 4 18 51-74 
 
 .0754 
 
 .07533 
 
 
 .99716 
 
 
 .87696 
 
 57,5 
 
 .99876 
 
 
 4 19 12.37 
 
 0.0755 
 
 0.07543 
 
 10,0 
 
 0.99715 
 
 0,8 
 
 8.87753 
 
 57,4 
 
 9.99876 
 
 0,3 
 
 4 19 32.99 
 
 .0756 
 
 .07553 
 
 
 .99714 
 
 
 .87811 
 
 57,3 
 
 .99876 
 
 
 4 19 53.62 
 
 .0757 
 
 .07563 
 
 
 .99714 
 
 
 .87868 
 
 57,3 
 
 .99875 
 
 
 4 20 14.25 
 
 .0758 
 
 .07573 
 
 
 .99713 
 
 
 .87925 
 
 57,2 
 
 .99875 
 
 
 4 20 34.87 
 
 .0759 
 
 .07583 
 
 
 .99712 
 
 
 .87982 
 
 57,1 
 
 .99875 
 
 
 4 20 55.50 
 
 0.0760 
 
 0.07593 
 
 10,0 
 
 0.99711 
 
 0,8 
 
 8.88040 
 
 57,0 
 
 9.99874 
 
 0,3 
 
 4 21 16.13 
 
 .0761 
 
 .07603 
 
 
 .99711 
 
 
 .88097 
 
 57,o 
 
 .99874 
 
 
 4 21 36.75 
 
 .0762 
 
 .07613 
 
 
 .99710 
 
 
 .88153 
 
 56,9 
 
 .99874 
 
 
 4 21 57.38 
 
 .0763 
 
 .07623 
 
 
 .99709 
 
 
 .88210 
 
 56,8 
 
 .99873 
 
 
 4 22 iS.OO 
 
 .0764 
 
 .07633' 
 
 
 .99708 
 
 
 .88267 
 
 56,7 
 
 .99873 
 
 
 4 22 38.63 
 
 0.0765 
 
 0.07643 
 
 10,0 
 
 0.99708 
 
 0,8 
 
 8.88324 
 
 56,7 
 
 9.99873 
 
 0,3 
 
 4 22 59.26 
 
 .0766 
 
 .07653 
 
 
 .99707 
 
 
 .88380 
 
 56,6 
 
 .99872 
 
 
 4 23 19.88 
 
 .0767 
 
 .07662 
 
 
 .99706 
 
 
 .88437 
 
 56,5 
 
 .99872 
 
 
 4 23 40.51 
 
 .0768 
 
 .07672 
 
 
 .99705 
 
 
 .88493 
 
 56,4 
 
 .99872 
 
 
 4 24 01.14 
 
 .0769 
 
 .07682 
 
 
 .99704 
 
 
 .88550 
 
 56,4 
 
 .99871 
 
 
 4 24 21.76 
 
 0.0770 
 
 0.07692 
 
 10,0 
 
 0.99704 
 
 0,8 
 
 8.88606 
 
 56,3 
 
 9.99871 
 
 0,3 
 
 4 24 42.39 
 
 .0771 
 
 .07702 
 
 
 .99703 
 
 
 .88562 
 
 56,2 
 
 .99871 
 
 
 4 25 03.02 
 
 .0772 
 
 .07712 
 
 
 .99702 
 
 
 .88719 
 
 56,1 
 
 .99870 
 
 
 4 25 23.64 
 
 .0773 
 
 .07722 
 
 
 .99701 
 
 
 .88775 
 
 56,1 
 
 .09870 
 
 
 4 25 44.27 
 
 .0774 
 
 .07732 
 
 
 .99701 
 
 
 .88831 
 
 56,0 
 
 .99870 
 
 
 4 26 04.90 
 
 0.0775 
 
 0.07742 
 
 10,0 
 
 0.99700 
 
 0,8 
 
 8.88887 
 
 55,9 
 
 9.99869 
 
 0,3 
 
 4 26 25.52 
 
 .0776 
 
 .07752' 
 
 
 .99699 
 
 
 .88943 
 
 55,9 
 
 .99869 
 
 
 4 26 46.15 
 
 .0777 
 
 .07762 
 
 
 .99698 
 
 
 .88998 
 
 55,8 
 
 .99869 
 
 
 4 27 06.78 
 
 .0778 
 
 .07772 
 
 
 .99698 
 
 
 ^89054 
 
 55,7 
 
 .99868 
 
 
 4 27 27.40 
 
 .0779 
 
 .07782 
 
 
 .99697 
 
 
 .89110 
 
 55,6 
 
 .99868 
 
 
 4 27 48.03 
 
 0.0780 
 
 0.07792 
 
 10,0 
 
 0.99696 
 
 0,8 
 
 8.89165 
 
 55,6 
 
 9.99868 
 
 0,3 
 
 4 28 08.65 
 
 .0781 
 
 .07802 
 
 
 .99695 
 
 
 .89221 
 
 55,5 
 
 .99867 
 
 
 4 28 29.28 
 
 .0782 
 
 .07812 
 
 
 .99694 
 
 
 .89276 
 
 55,4 
 
 .99867 
 
 
 4 28 49-91 
 
 .0783 
 
 .07822 
 
 
 .99694 
 
 
 .89332 
 
 55,4 
 
 .99867 
 
 
 4 29 10.53 
 
 .0784 
 
 .07832 
 
 
 .99693 
 
 
 .89387 
 
 55,3 
 
 .99866 
 
 
 4 29 31.16 
 
 0.0785 
 
 0.07842 
 
 10,0 
 
 0.99692 
 
 0,8 
 
 8.89442 
 
 55,2 
 
 9.99866 
 
 0,3 
 
 4 29 51.79 
 
 .0786 
 
 .07852 
 
 
 .99691 
 
 
 .89498 
 
 55,i 
 
 .99866 
 
 
 4 30 12.41 
 
 .0787 
 
 .07862 
 
 
 .99690 
 
 
 .89553 
 
 55,1 
 
 .99865 
 
 
 4 30 33.04 
 
 .0788 
 
 .07872 
 
 
 
 
 .89608 
 
 55,o 
 
 .99865 
 
 
 4 30 53-67 
 
 .0789 
 
 .07882 
 
 
 .99689 
 
 
 .89663 
 
 54,9 
 
 .99865 
 
 
 4 31 14.29 
 
 0.0700 
 
 0.07892 
 
 IO,O 
 
 0.99688 
 
 0,8 
 
 8.89718 
 
 54,9 
 
 9.99864 
 
 0,3 
 
 4 31 34-92 
 
 .0791 
 
 .07902 
 
 
 .99687 
 
 
 .89772 
 
 54,8 
 
 .99864 
 
 
 4 31 55.55 
 
 .0792 
 
 .07912 
 
 
 .99687 
 
 
 .89827 
 
 54,7 
 
 .99864 
 
 
 4 32 16.17 
 
 .0793 
 
 .07922 
 
 
 .99686 
 
 
 .89882 
 
 54,7 
 
 .99863 
 
 
 4 32 36.80 
 
 .0794 
 
 .07932 
 
 
 .99685 
 
 
 
 .89936 
 
 54,6 
 
 .99863 
 
 
 4 32 57-43 
 
 0.0795 
 
 0.07942 
 
 10,0 
 
 0,99684 
 
 0,8 
 
 8.89991 
 
 54,6 
 
 9.99863 
 
 o,3 
 
 4 33 18.05 
 
 .0706 
 
 .07952 
 
 
 .99683 
 
 
 .90045 
 
 54,4 
 
 .99862 
 
 
 4 33 38.68 
 
 .0797 
 
 .07962 
 
 
 .99683 
 
 
 .90100 
 
 54,4 
 
 .99862 
 
 
 4 33 59.31 
 
 .0798 
 
 .07972 
 
 
 .99682 
 
 
 .90154 
 
 54,3 
 
 .99862 
 
 
 
 4 34 19.93 
 
 .0799 
 
 .07982 
 
 
 .99681 
 
 
 .90208 
 
 54,2 
 
 .99861 
 
 
 4 34 40.56 
 
 0.0800 
 
 0.07991 
 
 IO,O 
 
 0.99680 
 
 0,8 
 
 8.90263 
 
 54,2 
 
 9.99861 
 
 o,3 
 
 4 35 oi . 18 
 
 u 
 
 -isinhiu 
 
 F ' 
 
 cosh iu 
 
 IV 
 
 sinh iu 
 
 O.FO' 
 
 log cosh iu 
 
 F O ' 
 
 u 
 
 log . 
 
 SMITHSONIAN TABLES 
 
 189 
 
Circular Functions. 
 
 u 
 
 sin u 
 
 F O ' 
 
 COS U 
 
 F ' 
 
 log sin u 
 
 Fo' 
 
 log cos u 
 
 F ' 
 
 u 
 
 0.0800 
 
 0.07991 
 
 10,0 
 
 0.99680 
 
 0,8 
 
 8.90263 
 
 54,2 
 
 9.99861 
 
 o,3 
 
 43s'oi'.'i8 
 
 .0801 
 
 .08001 
 
 
 .99679 
 
 
 .90317 
 
 54,1 
 
 .99861 
 
 
 4 35 21. 81 
 
 .0802 
 
 .08011 
 
 
 .99679 
 
 
 .90371 
 
 54,o 
 
 .99860 
 
 
 4 35 42.44 
 
 .0803 
 
 .08021 
 
 
 .99678 
 
 
 .90425 
 
 54,0 
 
 .99860 
 
 
 4 36 03.06 
 
 .0804 
 
 .08031 
 
 
 .99677 
 
 
 .90479 
 
 53,9 
 
 .99859 
 
 
 4 36 23.69 
 
 0.0805 
 
 0.08041 
 
 10,0 
 
 0.99676 
 
 0,8 
 
 8.90533 
 
 '53,8 
 
 9.99859 
 
 0,4 
 
 4 36 44-32 
 
 .0806 
 
 .08051 
 
 
 .99675 
 
 
 .90586 
 
 53,8 
 
 .99859 
 
 
 4 37 04.94 
 
 .0807 
 
 .08061 
 
 
 .99675 
 
 
 .90640 
 
 53,7 
 
 .99858 
 
 
 4 37 25.57 
 
 .0808 
 
 .08071 
 
 
 .99674 
 
 
 .90694 
 
 53,6 
 
 .99858 
 
 
 4 37 46.20 
 
 .0809 
 
 .08081 
 
 
 .99673 
 
 
 .90747 
 
 53,6 
 
 .99858 
 
 
 4 38 06.82 
 
 0.0810 
 
 0.08091 
 
 10,0 
 
 0.99672 
 
 0,8 
 
 8.90801 
 
 53,5 
 
 9.99857 
 
 0,4 
 
 4 38 27-45 
 
 .0811 
 
 .08101 
 
 
 .99671 
 
 
 .90854 
 
 53,4 
 
 .99857 
 
 
 4 38 48.08 
 
 .0812 
 
 .08111 
 
 
 .99671 
 
 
 .90908 
 
 53,4 
 
 .99857 
 
 
 4 39 08.70 
 
 .0813 
 
 .08121 
 
 
 .99670 
 
 
 .90961 
 
 53,3 
 
 .99856 
 
 
 4 39 29.33 
 
 .0814 
 
 .08131 
 
 
 .99669 
 
 
 .91014 
 
 53,2 
 
 .99856 
 
 
 4 39 49.96 
 
 0.0815 
 
 0.08141 
 
 10,0 
 
 0.99668 
 
 0,8 
 
 8.91068 
 
 53,2 
 
 9.99856 
 
 0,4 
 
 4 40 10.58 
 
 .0816 
 
 .08151 
 
 
 .99667 
 
 
 .91121 
 
 53>i 
 
 .99855 
 
 
 4 40 31-21 
 
 .0817 
 
 .08161 
 
 
 .99666 
 
 
 .9U74 
 
 53,o 
 
 .99855 
 
 
 4 40 51.83 
 
 .0818 
 
 .08171 
 
 
 .99666 
 
 
 .91227 
 
 53,0 
 
 .99855 
 
 
 4 41 12.46 
 
 .0819 
 
 .08181 
 
 
 .99665 
 
 
 .91280 
 
 52,9 
 
 .99854 
 
 
 4 41 33.09 
 
 0.0820 
 
 0.08191 
 
 1 0,0 
 
 0.99664 
 
 0,8 
 
 8.91333 
 
 52,8 
 
 9.99854 
 
 0,4 
 
 4 41 53.71 
 
 .0821 
 
 .08201 
 
 
 .99663 
 
 
 .91386 
 
 52,8 
 
 .99853 
 
 
 4 42 14.34 
 
 .0822 
 
 .08211 
 
 
 .99662 
 
 
 .91438 
 
 52,7 
 
 .99853 
 
 
 4 42 34.97 
 
 .0823 
 
 .08221 
 
 
 .99662 
 
 
 .91491 
 
 52,7 
 
 .99853 
 
 
 4 42 55-59 
 
 .0824 
 
 .08231 
 
 
 .99661 
 
 
 .91544 
 
 52,6 
 
 .99852 
 
 
 4 43 16.22 
 
 0.0825 
 
 0.08241 
 
 IO,O 
 
 0.99660 
 
 0,8 
 
 8.91596 
 
 52,5 
 
 9.99852 
 
 0,4 
 
 4 43 36.85 
 
 .0826 
 
 .08251 
 
 
 .99659 
 
 
 .91649 
 
 52,5 
 
 .99852 
 
 
 4 43 57-47 
 
 .0827 
 
 .08261 
 
 
 .99658 
 
 
 .91701 
 
 52,4 
 
 .99851 
 
 
 4 44 18. 10 
 
 .0828 
 
 .08271 
 
 
 .99657 
 
 
 .91753 
 
 52,3 
 
 .99851 
 
 
 4 44 38.73 
 
 .0829 
 
 .08281 
 
 
 .99657 
 
 
 .91806 
 
 52,3 
 
 .99851 
 
 
 4 44 59-35 
 
 0.0830 
 
 0.08290 
 
 IO,O 
 
 0.99656 
 
 0,8 
 
 8.91858 
 
 52,2 
 
 9.99850 
 
 0,4 
 
 4 45 19.98 
 
 '.0831 
 
 .08300 
 
 
 .99655 
 
 
 .91910 
 
 52,1 
 
 .99850 
 
 
 4 45 40.61 
 
 .0832 
 
 .08310 
 
 
 .99654 
 
 
 .91962 
 
 52,1 
 
 .99850 
 
 
 4 46 01.23 
 
 .0833 
 
 .08320 
 
 
 .99653 
 
 
 .92014 
 
 52,0 
 
 .99849 
 
 
 4 46 21.86 
 
 .0834 
 
 .08330 
 
 
 .99652 
 
 
 .92066 
 
 52,0 
 
 .99849 
 
 
 4 46 42.48 
 
 0.0835 
 
 0.08340 
 
 10,0 
 
 0.99652 
 
 0,8 
 
 8.92118 
 
 51,9 
 
 9.99848 
 
 0,4 
 
 4 47 03.11 
 
 .0836 
 
 .083-50 
 
 
 .99651 
 
 
 .92170 
 
 5i,8 
 
 .99848 
 
 
 4 47 23-74 
 
 .0837 
 
 .08360 
 
 
 .99650 
 
 
 .92222 
 
 5i,8 
 
 .99848 
 
 
 4 47 44.36 
 
 .0838 
 
 .08370 
 
 
 
 
 .92274 
 
 5i,7 
 
 .99847 
 
 
 4 48 04.99 
 
 .0839 
 
 .08380 
 
 
 .99648 
 
 
 .92325 
 
 5i,6 
 
 .99847 
 
 
 4 48 25.62 
 
 0.0840 
 
 0.08390 
 
 10,0 
 
 0.99647 
 
 0,8 
 
 8.92377 
 
 5i,6 
 
 9.99847 
 
 0,4 
 
 4 48 46.24 
 
 .0841 
 
 .08400 
 
 
 .99647 
 
 
 .92428 
 
 51,5 
 
 .99846 
 
 
 4 49 06.87 
 
 .0842 
 
 .08410 
 
 
 .99646 
 
 
 .92480 
 
 51,5 
 
 .99846 
 
 
 4 49 27.50 
 
 .0843 
 
 .08420 
 
 
 .99645 
 
 
 .92531 
 
 51,4 
 
 .99846 
 
 
 4 49 48.12 
 
 .0844 
 
 .08430 
 
 
 .99644 
 
 
 .92583 
 
 51,3 
 
 .99845 
 
 
 4 50 08.75 
 
 0.0845 
 
 0.08440 
 
 10,0 
 
 0.09643 
 
 0,8 
 
 8.92634 
 
 51,3 
 
 9.99845 
 
 0,4 
 
 4 50 29.38 
 
 .0846 
 
 .08450 
 
 
 .99642 
 
 
 .92685 
 
 51,2 
 
 .99844 
 
 
 4 50 50.00 
 
 .0847 
 
 .08460 
 
 
 .99642 
 
 
 .92736 
 
 51,2 
 
 .99844 
 
 
 4 51 10.63 
 
 .0848 
 
 .08470 
 
 
 .99641 
 
 
 .92788 
 
 5i,i 
 
 .99844 
 
 
 4 51 31-26 
 
 .0849 
 
 .08480 
 
 
 .99640 
 
 
 .92839 
 
 5i,o 
 
 .99843 
 
 
 4 51 51.88 
 
 0.0850 
 
 0.08490 
 
 10,0 
 
 0.99639 
 
 0,8 
 
 8.92890 
 
 5i,o 
 
 9.99843 
 
 0,4 
 
 4 52 12.51 
 
 u 
 
 -isinhiu 
 
 Fo' 
 
 cosh iu 
 
 F' 
 
 lno inh JU 
 
 loo p- 
 
 FV 
 
 log cosh iu 
 
 -FO' 
 
 u 
 
 SMITHSONIAN TABLES 
 
 IQO 
 
Circular Functions. 
 
 u 
 
 sin u 
 
 F ' 
 
 COS U 
 
 Fo* 
 
 log sin u 
 
 Fo' 
 
 log cos u 
 
 F O ' 
 
 u 
 
 0.0850 
 
 0.08490 
 
 10,0 
 
 0.99639 
 
 0,8 
 
 8.92890 
 
 51,0 
 
 9.99843 
 
 0,4 
 
 452 / i27si 
 
 .0851 
 
 .08500 
 
 
 .99638 
 
 0,8 
 
 .92941 
 
 50,9 
 
 .99843 
 
 
 4 52 33 -14 
 
 .0852 
 
 .08510 
 
 
 .99637 
 
 0,9 
 
 .92991 
 
 50,9 
 
 .99842 
 
 
 4 52 53.76 
 
 .0853 
 
 .08520 
 
 
 .99636 
 
 
 .93042 
 
 50,8 
 
 .99842 
 
 
 4 53 14.39 
 
 .0854 
 
 .08530 
 
 
 .99636 
 
 
 .93093 
 
 50,7 
 
 .99841 
 
 
 4 53 35-01 
 
 0.0855 
 
 0.08540 
 
 IO,O 
 
 0.99635 
 
 o,9 
 
 8.93144 
 
 50,7 
 
 9.99841 
 
 0,4 
 
 4 53 55.64 
 
 .0856 
 
 .08550 
 
 
 .99634 
 
 
 .93194 
 
 50,6 
 
 .99841 
 
 
 4 54 16.27 
 
 .0857 
 
 .08560 
 
 
 .99633 
 
 
 .93245 
 
 50,6 
 
 .99840 
 
 
 4 54 36.89 
 
 .0858 
 
 .08569 
 
 
 .99632 
 
 
 .93295 
 
 50,5 
 
 .99840 
 
 
 4 54 57.52 
 
 .0859 
 
 .08579 
 
 
 .99631 
 
 
 .93346 
 
 50,4 
 
 .99840 
 
 
 4 55 18.15 
 
 0.0860 
 
 0.08589 
 
 10,0 
 
 0.99630 
 
 o,9 
 
 8.93396 
 
 50,4 
 
 9.99839 
 
 0,4 
 
 4 55 38.77 
 
 .0861 
 
 .08599 
 
 
 .99630 
 
 
 93447 
 
 50,3 
 
 .99839 
 
 
 4 55 59.40 
 
 .0862 
 
 .08609 
 
 
 .99629 
 
 
 93497 
 
 50,3 
 
 .99838 
 
 
 4 56 20.03 
 
 .0863 
 
 .08619 
 
 
 .99628 
 
 
 .93547 
 
 50,2 
 
 .99838 
 
 
 4 56 40.65 
 
 .0864 
 
 .08629 
 
 
 .99627 
 
 
 93597 
 
 50,1 
 
 .99838 
 
 
 4 57 01.28 
 
 0.0865 
 
 0.08639 
 
 10,0 
 
 0.99626 
 
 0,9 
 
 8.93647 
 
 50,i 
 
 9.99837 
 
 0,4 
 
 4 57 21.91 
 
 .0866 
 
 .08649 
 
 
 .99625 
 
 
 .93697 
 
 50,0 
 
 99837 
 
 
 4 57 42.53 
 
 .0867 
 
 .08659 
 
 
 .99624 
 
 
 93747 
 
 50,0 
 
 .99837 
 
 
 4 58 03.16 
 
 .0868 
 
 .08669 
 
 
 .99624 
 
 
 .93797 
 
 49,9 
 
 .99836 
 
 
 4 58 23.79 
 
 .0869 
 
 .08679 
 
 
 .99623 
 
 
 .93847 
 
 49,9 
 
 .99836 
 
 
 4 58 44.41 
 
 0.0870 
 
 0.08689 
 
 10,0 
 
 0.99622 
 
 0,9 
 
 8.93897 
 
 49,8 
 
 9.99835 
 
 0,4 
 
 4 59 05.04 
 
 .0871 
 
 .08699 
 
 
 .99621 
 
 
 93947 
 
 49,7 
 
 99835 
 
 
 4 59 25.66 
 
 .0872 
 
 .08709 
 
 
 .99620 
 
 
 93997 
 
 49,7 
 
 .99835 
 
 
 4 59 46.29 
 
 .0873 
 
 .08719 
 
 
 .99619 
 
 
 .94046 
 
 49,6 
 
 .99834 
 
 
 5 oo 06.92 
 
 .0874 
 
 .08729 
 
 
 .99618 
 
 
 .94096 
 
 49,6 
 
 .99834 
 
 
 5 oo 27.54 
 
 0.0875 
 
 0.08739 
 
 10,0 
 
 0.99617 
 
 o,9 
 
 8.04145 
 
 49,5 
 
 9-99834 
 
 0,4 
 
 5 oo 48.17 
 
 .0876 
 
 .08749 
 
 
 .99617 
 
 
 .94195 
 
 49,5 
 
 .99833 
 
 
 5 01 08.80 
 
 .0877 
 
 .08759 
 
 
 .99616 
 
 
 .94244 
 
 49,4 
 
 .99833 
 
 
 5 01 29.42 
 
 .0878 
 
 .08769 
 
 
 .99615 
 
 
 .94294 
 
 49,3 
 
 99832 
 
 
 5 01 50.05 
 
 .0879 
 
 .08779 
 
 
 .99614 
 
 
 94343 
 
 49,3 
 
 .99832 
 
 
 5 02 10.68 
 
 0.0880 
 
 0.08789 
 
 IO,O 
 
 0.99613 
 
 0,9 
 
 8.94392 
 
 49,2 
 
 9.99832 
 
 0,4 
 
 5 02 31.30 
 
 .0881 
 
 .08799 
 
 
 .99612 
 
 
 .94441 
 
 49,2 
 
 .99831 
 
 
 5 02 51.93 
 
 .0882 
 
 .08809 
 
 
 .99611 
 
 
 .94491 
 
 49,1 
 
 .99831 
 
 
 5 03 12.56 
 
 .0883 
 
 .08819 
 
 
 .99610 
 
 
 .94540 
 
 49,1 
 
 .99830 
 
 
 5 03 33.i8 
 
 .0884 
 
 .08828 
 
 
 .99610 
 
 
 .94589 
 
 49,0 
 
 .99830 
 
 
 5 03 53.81 
 
 0.0885 
 
 0.08838 
 
 IO,O 
 
 0.99609 
 
 0,9 
 
 8.94638 
 
 48,9 
 
 9.99830 
 
 0,4 
 
 5 04 14.44 
 
 .0886 
 
 .08848 
 
 
 .99608 
 
 
 .94687 
 
 48,9 
 
 .99829 
 
 
 5 04 35.o6 
 
 .0887 
 
 .08858 
 
 
 .99607 
 
 
 94735 
 
 48,8 
 
 .99829 
 
 
 5 04 55.69 
 
 .0888 
 
 .08868 
 
 
 .99606 
 
 
 .94784 
 
 48,8 
 
 .90829 
 
 
 5 05 16.31 
 
 .0889 
 
 .08878 
 
 
 .99605 
 
 
 .94833 
 
 48,7 
 
 .99828 
 
 
 5 05 36.94 
 
 0.0890 
 
 0.08888 
 
 IO,O 
 
 0.99604 
 
 0,9 
 
 8.94882 
 
 48,7 
 
 9.99828 
 
 0,4 
 
 5 05 57.57 
 
 .0891 
 
 .08898 
 
 
 .99603 
 
 
 .94930 
 
 48,6 
 
 .99^27 
 
 
 5 06 18.19 
 
 .0892 
 
 .08908 
 
 
 .99602 
 
 
 .94979 
 
 48,6 
 
 .99827 
 
 
 5 06 38.82 
 
 .0893 
 
 .08918 
 
 
 .99602 
 
 
 .95027 
 
 48,5 
 
 .99827 
 
 
 5 06 59-45 
 
 .0894 
 
 .08928 
 
 
 .99601 
 
 
 .95076 
 
 48,4 
 
 .99826 
 
 
 5 07 20.07 
 
 0.0895 
 
 0.08938 
 
 10,0 
 
 0.99600 
 
 0,9 
 
 8.95124 
 
 48,4 
 
 9.99826 
 
 0,4 
 
 5 07 40.70 
 
 .0896 
 
 .08948 
 
 
 99599 
 
 
 .95173 
 
 48,3 
 
 .99825 
 
 
 5 08 01.33 
 
 .0897 
 
 .08958 
 
 
 .99598 
 
 
 .95221 
 
 48,3 
 
 .99825 
 
 
 5 08 21.95 
 
 .0858 
 
 .08968 
 
 
 99597 
 
 
 .95269 
 
 48,2 
 
 .99825 
 
 
 5 08 42.58 
 
 .0899 
 
 .08978 
 
 
 .99596 
 
 
 95317 
 
 48,2 
 
 .99824 
 
 
 5 09 03.21 
 
 0.0900 
 
 0.08988 
 
 IO,O 
 
 0.99595 
 
 0,9 
 
 8.95366 
 
 48,1 
 
 9.99824 
 
 0,4 
 
 5 09 23.83 
 
 u 
 
 isinhiu 
 
 F ' 
 
 cosh iu 
 
 F ' 
 
 sinh iu 
 
 Fo' 
 
 log cosh iu 
 
 F O ' 
 
 u 
 
 tog . 
 
 SMITHSONIAN TABLES 
 
Circular Functions. 
 
 u 
 
 sin u 
 
 F ' 
 
 COS U 
 
 Fo' log sin u 
 
 Fo' 
 
 log cos u 
 
 -FO' 
 
 u 
 
 0.0900 
 
 0.08988 
 
 IO,O 
 
 0.99595 
 
 0,9 
 
 8.95366 
 
 48,1 
 
 9.99824 
 
 0,4 
 
 509' 23'.'83 
 
 .0901 
 
 .08998 
 
 
 .99594 
 
 
 .954H 
 
 48,1 
 
 .99823 
 
 
 5 09 44.46 
 
 .0902 
 
 .00008 
 
 
 .99593 
 
 
 .95462 
 
 48,0 
 
 .99823 
 
 
 5 10 05.09 
 
 .0903 
 
 .09018 
 
 
 99593 
 
 
 95510 
 
 48,0 
 
 .99823 
 
 
 5 10 25.71 
 
 .0904 
 
 .09028 
 
 
 .99592 
 
 
 .95558 
 
 47,9 
 
 .99822 
 
 
 5 10 46.34 
 
 0.0905 
 
 0.09038 
 
 10,0 
 
 0.99591 
 
 0,9 
 
 8.95606 
 
 47,9 
 
 9.99822 
 
 0,4 
 
 5 ii 06.96 
 
 .0906 
 
 .09048 
 
 
 99590 
 
 
 .95653 
 
 47,8 
 
 .99822 
 
 
 5 ii 27.59 
 
 .0907 
 
 .00058 
 
 
 .99589 
 
 
 .95701 
 
 47,8 
 
 .99821 
 
 
 5 ii 48.22 
 
 .0908 
 
 .09068 
 
 
 .99588 
 
 
 95749 
 
 47,7 
 
 .99821 
 
 
 5 12 08.84 
 
 .0909 
 
 .09077 
 
 
 .99587 
 
 
 95797 
 
 47,6 
 
 .99820 
 
 
 5 12 29.47 
 
 0.0910 
 
 0.09087 
 
 IO,O 
 
 0.99586 
 
 0,9 
 
 8.95844 
 
 47,6 
 
 9.99820 
 
 0,4 
 
 5 12 50.10 
 
 .0911 
 
 .00097 
 
 
 .99585 
 
 
 .95892 
 
 47,5 
 
 .90820 
 
 
 5 13 10.72 
 
 .0912 
 
 .09107 
 
 
 .99584 
 
 
 95939 
 
 47,5 
 
 .90819 
 
 
 5 13 31-35 
 
 .0913 
 
 .09117 
 
 
 .99584 
 
 
 95087 
 
 47,4 
 
 .99819 
 
 
 5 13 51.98 
 
 .0914 
 
 .09127 
 
 
 .99583 
 
 
 .96034 
 
 47,4 
 
 .99818 
 
 
 5 14 12.60 
 
 0.0915 
 
 0.09137 
 
 10,0 
 
 0.99582 
 
 0,9 
 
 8.06081 
 
 47,3 
 
 9.99818 
 
 0,4 
 
 5 14 33.23 
 
 .0916 
 
 .09147 
 
 
 .99581 
 
 
 .96129 
 
 47,3 
 
 .99818 
 
 
 5 14 53-86 
 
 .0917 
 
 .09157 
 
 
 ,99580 
 
 
 .96176 
 
 47,2 
 
 .99817 
 
 
 5 15 14.48 
 
 .0918 
 
 .09167 
 
 
 ..99579 
 
 
 .96223 
 
 47,2 
 
 .99817 
 
 
 5 15 35.ii 
 
 .0919 
 
 .09177 
 
 
 .99578 
 
 
 .96270 
 
 47,1 
 
 .998l6 
 
 
 5 15 55-74 
 
 0.0920 
 
 0.09187 
 
 IO,O 
 
 0.99577 
 
 0,9 
 
 8.96317 
 
 47,1 
 
 9.998l6 
 
 0,4 
 
 5 16 16.36 
 
 .0921 
 
 .09197 
 
 
 .99576 
 
 
 .96365 
 
 47,0 
 
 .99816 
 
 
 5 16 36.99 
 
 .0922 
 
 .09207 
 
 
 99575 
 
 
 .96412 
 
 47,0 
 
 .99815 
 
 
 5 16 57.62 
 
 .0923 
 
 .09217 
 
 
 99574 
 
 
 .96458 
 
 46,9 
 
 .99815 
 
 
 5 17 18.24 
 
 .0924 
 
 .09227 
 
 
 .99573 
 
 
 .96505 
 
 46,9 
 
 .99814 
 
 
 5 17 38.87 
 
 0.0925 
 
 0.09237 
 
 10,0 
 
 0.99572 
 
 0,9 
 
 8.96552 
 
 46,8 
 
 9.09814 
 
 0,4 
 
 5 17 59-49 
 
 .0926 
 
 .09247 
 
 
 .99572 
 
 
 .96599 
 
 46,8 
 
 .09814 
 
 
 5 18 20.12 
 
 .0927 
 
 .09257 
 
 
 .99571 
 
 
 .96646 
 
 46,7 
 
 99813 
 
 
 5 18 40.75 
 
 .0928 
 
 .09267 
 
 
 .99570 
 
 
 .96692 
 
 46,7 
 
 .99813 
 
 
 5 19 01.37 
 
 .0929 
 
 .09277 
 
 
 .99569 
 
 
 .96739 
 
 46,6 
 
 .99812 
 
 
 5 19 22.00 
 
 ! 0.0930 
 
 0.09287 
 
 IO,O 
 
 0.99568 
 
 o,9 
 
 8.96786 
 
 46,6 
 
 9.99812 
 
 0,4 
 
 5 19 42.63 
 
 .0931 
 
 .09297 
 
 
 .99567 
 
 
 .96832 
 
 46,5 
 
 .99812 
 
 
 5 20 03.25 
 
 .0932 
 
 .09307 
 
 
 .99566 
 
 
 .96879 
 
 46,5 
 
 .99811 
 
 
 5 20 23.88 
 
 0933 
 
 .09316 
 
 
 .99565 
 
 
 .96925 
 
 46,4 
 
 .99811 
 
 
 5 20 44-51 
 
 0934 
 
 .09326 
 
 
 .99564 
 
 
 .96972 
 
 46,4 
 
 .99810 
 
 
 5 21 05.13! 
 
 0.0935 
 
 0.09336 
 
 10,0 
 
 0.99563 
 
 0,9 
 
 8.97018 
 
 46,3 
 
 9.09810 
 
 0,4 
 
 5 21 25.76 
 
 .0936 
 
 .09346 
 
 
 .99562 
 
 
 .97064 
 
 46,3 
 
 .99809 
 
 
 5 21 46.391 
 
 .0937 
 
 .09356 
 
 
 .99561 
 
 
 .97110 
 
 46,2 
 
 .99809 
 
 
 5 22 07.OI { 
 
 .0938 
 
 .09366 
 
 
 .99560 
 
 
 .97157 
 
 46,2 
 
 .90809 
 
 
 5 22 27.64 
 
 0939 
 
 .09376 
 
 
 99559 
 
 
 .97203 
 
 46,1 
 
 .00808 
 
 
 5 22 48.27 
 
 0.0940 
 
 0.09386 
 
 10,0 
 
 0.99559 
 
 0,9 
 
 8.97249 
 
 46,1 
 
 9.99808 
 
 0,4 
 
 5 23 08.89 
 
 .0941 
 
 .09396 
 
 
 .99558 
 
 
 .97295 
 
 46,0 
 
 .90807 
 
 
 5 23 29.52 
 
 .0942 
 
 .09406 
 
 
 99557 
 
 
 57341 
 
 46,0 
 
 .09807 
 
 
 5 23 50.14 
 
 .0943 
 
 .00416 
 
 
 .99556 
 
 
 .97387 
 
 45,9 
 
 .00807 
 
 
 5 -24 10.77 
 
 .0944 
 
 .09426 
 
 
 .99555 
 
 
 97433 
 
 45,9 
 
 .99806 
 
 
 5 24 31-40 
 
 0.0945 
 
 0.09436 
 
 10,0 
 
 0.09554 
 
 o,9 
 
 8.97479 
 
 45,8 
 
 9.99806 
 
 0,4 
 
 5 24 52.02' 
 
 .0946 
 
 .09446 
 
 
 99553 
 
 
 .97524 
 
 45,8 
 
 .99805 
 
 
 5 25 12.65; 
 
 .0947 
 
 .09456 
 
 
 .99552 
 
 
 97570 
 
 45,7 
 
 .99805 
 
 
 5 25 33.28 
 
 .0948 
 
 .09466 
 
 
 99551 
 
 
 .97616 
 
 45,7 
 
 .99805 
 
 
 5 25 53.90 
 
 .0949 
 
 .09476 
 
 
 .99550 
 
 
 .97661 
 
 45,6 
 
 .09804 
 
 
 5 26 14.53 
 
 0.0950 
 
 0.09486 
 
 10,0 
 
 0.99549 
 
 0,9 
 
 8.97707 
 
 45,6 
 
 9.09804 
 
 0,4 
 
 5 26 35-16 
 
 u 
 
 -isinhiu 
 
 -Fo' 
 
 cosh iu 
 
 -Fo' 
 
 log'-^ 
 
 -FV 
 
 log cosh iu 
 
 F ' 
 
 u 
 
 SMITHSONIAN TABLES 
 
 192 
 
Circular Functions. 
 
 u 
 
 .in u V 
 
 F ' 
 
 COS U 
 
 F ' 
 
 log sin u 
 
 Fo' 
 
 log oos u 
 
 Fo' 
 
 u 
 
 0.0950 
 
 0.09486 
 
 IO,O 
 
 0.99549 
 
 0,9 
 
 8.97707 
 
 45,6 
 
 9.99804 
 
 0,4 
 
 526'35'.'i6 
 
 .0951 
 
 .09496 
 
 
 .99548 
 
 0,9 
 
 .97753 
 
 45,5 
 
 .99803 
 
 
 5 26 55.78 
 
 .0952 
 
 .09506 
 
 
 99547 
 
 1,0 
 
 .97798 
 
 45,5 
 
 99803 
 
 
 5 27 16.41 
 
 .0953 
 
 .09516 
 
 
 .99546 
 
 
 .97844 
 
 45,4 
 
 .99802 
 
 
 S 27 37.04 
 
 .0954 
 
 .09526 
 
 
 99545 
 
 
 .97889 
 
 45,4 
 
 .99802 
 
 
 5 27 57-66 
 
 0.0955 
 
 0.09535 
 
 IO,0 
 
 0.99544 
 
 1,0 
 
 8.97934 
 
 45,3 
 
 9.99802 
 
 0,4 
 
 5 28 18.29 
 
 .0950 
 
 -09545 
 
 
 99543 
 
 
 .97980 
 
 45,3 
 
 .99801 
 
 
 5 28 38.92 
 
 .0957 
 
 .09555 
 
 
 99542 
 
 
 .98025 
 
 45,2 
 
 .99801 
 
 
 5 28 59-54 
 
 .0958 
 
 .09565 
 
 
 .99541 
 
 
 .98070 
 
 45,2 
 
 .99800 
 
 
 5 29 20.17 
 
 .0959 
 
 .09575 
 
 
 99541 
 
 
 98115 
 
 45,1 
 
 .99800 
 
 
 5 29 40.79 
 
 0.0960 
 
 0.09585 
 
 10,0 
 
 0.99540 
 
 1,0 
 
 8.98160 
 
 45,1 
 
 9.99800 
 
 0,4 
 
 5 30 01.42 
 
 .0961 
 
 .09595 
 
 
 99539 
 
 
 .98205 
 
 45,1 
 
 99799 
 
 
 5 30 22.05 
 
 .0962 
 
 .09605 
 
 
 .99538 
 
 
 .98251 
 
 45,0 
 
 99799 
 
 
 5 30 42.67 
 
 .0963 
 
 .09615 
 
 
 99537 
 
 
 .98295 
 
 45,0 
 
 .99798 
 
 
 5 3i 03.30 
 
 .0964 
 
 .09625 
 
 
 .99536 
 
 
 .98340 
 
 44,9 
 
 .99798 
 
 
 5 31 23.93 
 
 0.0965 
 
 0.09635 
 
 IO,O 
 
 0.99535 
 
 1,0 
 
 8.98385 
 
 44,9 
 
 9-99797 
 
 0,4 
 
 5 3i 44-55 
 
 .0966 
 
 .09645 
 
 
 .99534 
 
 
 .98430 
 
 44,8 
 
 .99797 
 
 
 5 32 05.18 
 
 .0967 
 
 -09655 
 
 
 .99533 
 
 
 .98475 
 
 44,8 
 
 .99797 
 
 
 5 32 25.81 
 
 .0968 
 
 .09665 
 
 
 .99532 
 
 
 .98520 
 
 44,7 
 
 .99796 
 
 
 5 32 46.43 
 
 .0969 
 
 .09675 
 
 
 99531 
 
 
 .98564 
 
 44,7 
 
 .99796 
 
 
 5 33 07.06 
 
 0.0970 
 
 0.09685 
 
 IO,O 
 
 0.99530 
 
 1,0 
 
 8.98609 
 
 44,6 
 
 9-99795 
 
 0,4 
 
 5 33 27.69 
 
 .0971 
 
 .09695 
 
 
 99529 
 
 
 .98554 
 
 44,6 
 
 99795 
 
 
 5 33 48-31 
 
 .0972 
 
 .09705 
 
 
 .99528 
 
 
 .98698 
 
 445 
 
 99795 
 
 
 5 34 08.94 
 
 .0973 
 
 .09715 
 
 
 .99527 
 
 
 .98743 
 
 44,5 
 
 99794 
 
 
 5 34 29-57 
 
 .0974 
 
 .09725 
 
 
 .99526 
 
 
 .98787 
 
 44,4 
 
 99794 
 
 
 5 34 50.19 
 
 0.0975 
 
 0.09735 
 
 IO,O 
 
 0.99525 
 
 1,0 
 
 8.98832 
 
 44,4 
 
 9-99793 
 
 0,4 
 
 5 35 10.82 
 
 .0976 
 
 .09745 
 
 
 .99524 
 
 
 .98876 
 
 44,4 
 
 99793 
 
 
 5 35 31-45 
 
 .0977 
 
 .09754 
 
 
 99523 
 
 
 .98920 
 
 44,3 
 
 99792 
 
 
 5 35 52.07 
 
 .0978 
 
 .09764 
 
 
 .99522 
 
 
 .98965 
 
 44,3 
 
 99792 
 
 
 5 36 12.70 
 
 .0979 
 
 .09774 
 
 
 99521 
 
 
 .99009 
 
 44,2 
 
 99792 
 
 
 5 36 33.32 
 
 0.0980 
 
 0.09784 
 
 IO,O 
 
 0.99520 
 
 1,0 
 
 8.99053 
 
 44,2 
 
 9.99791 
 
 0,4 
 
 5 36 53-95 
 
 .0981 
 
 .09794 
 
 
 .99519 
 
 
 .99097 
 
 44,1 
 
 .99791 
 
 
 5 37 14.58 
 
 .0982 
 
 .09804 
 
 
 .99518 
 
 
 .99141 
 
 44,1 
 
 .99790 
 
 
 5 37 35-20 
 
 .0983 
 
 .09814 
 
 
 .99517 
 
 
 .99185 
 
 44,0 
 
 .99790 
 
 
 5 37 55.83 
 
 .0984 
 
 .09824 
 
 
 .99516 
 
 
 .99229 
 
 44,0 
 
 .99789 
 
 
 5 38 16.46 
 
 0.0985 
 
 0.09834 
 
 10,0 
 
 0.99515 
 
 I,O 
 
 8.99273 
 
 43,9 
 
 9.99789 
 
 0,4 
 
 5 38 37.o8 
 
 .0986 
 
 .09844 
 
 
 .99514 
 
 
 .99317 
 
 43,9 
 
 .99789 
 
 
 5 38 57-71 
 
 .0987 
 
 .09854 
 
 
 .99513 
 
 
 .99361 
 
 43,9 
 
 .99788 
 
 
 5 39 i8.34 
 
 .0988 
 
 .09864 
 
 
 .99512 
 
 
 .90405 
 
 43,8 
 
 .99788 
 
 
 5 39 38.96 
 
 .0989 
 
 .09874 
 
 
 995II 
 
 
 99449 
 
 43,8 
 
 .99787 
 
 
 5 39 59-59 
 
 0.0990 
 
 0.09884 
 
 IO,O 
 
 0.99510 
 
 1,0 
 
 8.99493 
 
 43,7 
 
 9.99787 
 
 0,4 
 
 5 40 20.22 
 
 .0991 
 
 .09894 
 
 
 .99509 
 
 
 99536 
 
 43,7 
 
 .99786 
 
 
 5 40 40.84 
 
 .0992 
 
 .09904 
 
 
 .99508 
 
 
 .99580 
 
 43,6 
 
 .99786 
 
 
 5 4i 01.47 
 
 .0993 
 
 .09914 
 
 
 .99507 
 
 
 .99624 
 
 43,6 
 
 .99786 
 
 
 5 41 22. IO 
 
 .0994 
 
 .09924 
 
 
 .99506 
 
 
 .99667 
 
 43,5 
 
 .99785 
 
 
 5 41 42.72 
 
 0.0995 
 
 0.09934 
 
 IO,O 
 
 0.99505 
 
 I,O 
 
 8.997H 
 
 43,5 
 
 9.99785 
 
 0,4 
 
 5 42 03.35 
 
 .0996 
 
 .09944 
 
 
 99504 
 
 
 99754 
 
 43,5 
 
 .99784 
 
 
 5 42 23.97 
 
 .0997 
 
 .09953 
 
 
 .99503 
 
 
 .99798 
 
 43,4 
 
 .99784 
 
 
 5 42 44.60 
 
 .0998 
 
 .09963 
 
 
 .99502 
 
 
 .99841 
 
 43,4 
 
 .99783 
 
 
 5 43 05.23 
 
 .0999 
 
 .09973 
 
 
 99501 
 
 
 .99884 
 
 43,3 
 
 .99783 
 
 
 5 43 25.85 
 
 O.IOOO 
 
 0.09983 
 
 IO,O 
 
 0.99500 
 
 I,O 
 
 8.99928 
 
 43,3 
 
 9.99782 
 
 0,4 
 
 5 43 46.48 
 
 u 
 
 -isinhiu 
 
 F ' 
 
 cosh iu 
 
 O.FO' 
 
 sinh iu 
 
 -Fo' 
 
 log cosh iu 
 
 F O ' 
 
 u 
 
 tog . 
 
 SMITHSONIAN TABLES 
 
 193 
 
Circular Functions. 
 
 u 
 
 sin u 
 
 F ' 
 
 cos u 
 
 F * 
 
 log sin u 
 
 Fo' 
 
 log cos u 
 
 <-F ' 
 
 u 
 
 0.100 
 
 0.09983 
 
 99,5 
 
 0.99500 
 
 IO,O 
 
 8.99928 
 
 432,8 
 
 9.99782 
 
 4,4 
 
 543'46'.'48 
 
 .101 
 
 .10083 
 
 99,5 
 
 .99490 
 
 10,1 
 
 9.00358 
 
 428,5 
 
 .99778 
 
 4,4 
 
 5 47 12.75 
 
 .102 
 
 . 10182 
 
 99,5 
 
 .99480 
 
 10,2 
 
 .00785 
 
 424,3 
 
 .99774 
 
 4,4 
 
 5 50 39-01 
 
 .103 
 
 . 10282 
 
 99,5 
 
 .99470 
 
 10,3 
 
 .01207 
 
 420,2 
 
 .99769 
 
 4,5 
 
 5 54 05.28 
 
 .104 
 
 . 10381 
 
 99,5 
 
 .99460 
 
 10,4 
 
 .01625 
 
 416,1 
 
 .99765 
 
 4,5 
 
 5 57 31.54 
 
 0.105 
 
 0.10481 
 
 99,4 
 
 0.99449 
 
 io,5 
 
 9.02039 
 
 412,1 
 
 9.99760 
 
 4,6 
 
 6 oo 57.80 
 
 .106 
 
 .10580 
 
 99,4 
 
 99439 
 
 10,6 
 
 .02449 
 
 408,2 
 
 .99756 
 
 4,6 
 
 6 04 24.07 
 
 .107 
 
 .10680 
 
 99,4 
 
 .99428 
 
 10,7 
 
 .02855 
 
 404,3 
 
 99751 
 
 4,7 
 
 6 07 50.33 
 
 .108 
 
 . 10779 
 
 99,4 
 
 .99417 
 
 10,8 
 
 .03258 
 
 400,6 
 
 .99746 
 
 4,7 
 
 6 ii 16.60 
 
 .109 
 
 .10878 
 
 99,4 
 
 .99407 
 
 10,9 
 
 .03657 
 
 396,9 
 
 99741 
 
 4,8 
 
 6 14 42.86 
 
 O.IIO 
 
 0.10978 
 
 99,4 
 
 0.99396 
 
 11,0 
 
 9.04052 
 
 393,2 
 
 9-99737 
 
 4,8 
 
 6 18 09.13 
 
 .III 
 
 .11077 
 
 99,4 
 
 .99385 
 
 ii, i 
 
 .04443 
 
 389,6 
 
 99732 
 
 4,8 
 
 6 21 35.39 
 
 .112 
 
 .11177 
 
 99,4 
 
 99373 
 
 11,2 
 
 .04831 
 
 386,1 
 
 .99727 
 
 4,9 
 
 6 25 01.66 
 
 113 
 
 .11276 
 
 99,4 
 
 .99362 
 
 ii,3 
 
 .05215 
 
 382,7 
 
 .99722 
 
 4,9 
 
 6 28 27.92 
 
 .114 
 
 .11375 
 
 99,4 
 
 99351 
 
 11,4 
 
 .05596 
 
 379,3 
 
 .99717 
 
 5,o 
 
 6 31 54-19 
 
 0.115 
 
 O.I 1475 
 
 99,3 
 
 0.99339 
 
 ii,5 
 
 9.05974 
 
 376,0 
 
 9.99712 
 
 5,o 
 
 6 35 20.45 
 
 .116 
 
 -II574 
 
 99,3 
 
 .99328 
 
 11,6 
 
 .06348 
 
 372,7 
 
 99707 
 
 5,i 
 
 6 38 46.72 
 
 .117 
 
 .11673 
 
 99,3 
 
 .99316 
 
 n,7 
 
 .06719 
 
 369,5 
 
 99702 
 
 5,1 
 
 6 42 12.98 
 
 .118 
 
 II773 
 
 99,3 
 
 .99305 
 
 11,8 
 
 .07087 
 
 366,3 
 
 .99697 
 
 5,1 
 
 6 45 39.25 
 
 .119 
 
 .11872 
 
 99,3 
 
 .99293 
 
 11,9 
 
 .07452 
 
 363,2 
 
 .99692 
 
 5,2 
 
 6 49 05.51 
 
 0.120 
 
 0.11971 
 
 99,3 
 
 0.99281 
 
 12,0 
 
 9.07814 
 
 360,2 
 
 9.99687 
 
 5,2 
 
 6 52 31.78 
 
 .121 
 
 .12070 
 
 99,3 
 
 .99269 
 
 12,1 
 
 .08173 
 
 357,2 
 
 .99681 
 
 5,3 
 
 6 55 58.04 
 
 .122 
 
 .12170 
 
 99,3 
 
 .99257 
 
 12,2 
 
 .08528 
 
 354,2 
 
 .99676 
 
 5,3 
 
 6 59 24.31 
 
 .123 
 
 .12269 
 
 99,2 
 
 .99245 
 
 12,3 
 
 .08881 
 
 351,3 
 
 99671 
 
 5,4 
 
 7 02 50.57 
 
 .124 
 
 .12368 
 
 99,2 
 
 .99232 
 
 12,4 
 
 .09231 
 
 348,4 
 
 .99665 
 
 5,4 
 
 7 06 16.84 
 
 0.125 
 
 0.12467 
 
 99,2 
 
 0.99220 
 
 12,5 
 
 9.09578 
 
 345,6 
 
 9.99660 
 
 5,5 
 
 7 09 43.10 
 
 .126 
 
 . 12567 
 
 99,2 
 
 .99207 
 
 12,6 
 
 .09922 
 
 342,9 
 
 .99654 
 
 5,5 
 
 7 13 09.37 
 
 .127 
 
 .12666 
 
 99,2 
 
 .99195 
 
 12,7 
 
 .10264 
 
 340,1 
 
 .99649 
 
 5,5 
 
 7 16 35.63 
 
 .128 
 .129 
 
 . 12765 
 .12864 
 
 99,2 
 99,2 
 
 .99182 
 .99169 
 
 12,8 
 
 12,9 
 
 .10602 
 .10938 
 
 337,4 
 334,8 
 
 .99638 
 
 5,6 
 5,6 
 
 7 20 01.90 
 7 23 28.16 
 
 0.130 
 .131 
 
 0.12963 
 .13063 
 
 99,2 
 99,1 
 
 0.99156 
 .99143 
 
 13,0 
 13,1 
 
 9.11272 
 .11603 
 
 33^,2 
 329,6 
 
 9.99632 
 .99626 
 
 5,7 
 5,7 
 
 7 26 54-42 
 7 30 20.69 
 
 .132 
 
 .13162 
 
 99,1 
 
 .09130 
 
 13,2 
 
 .11931 
 
 327,1 
 
 .99621 
 
 5,8 
 
 7 33 46.95 
 
 133 
 
 .13261 
 
 99,1 
 
 .99117 
 
 13,3 
 
 . 12257 
 
 324,6 
 
 .99615 
 
 5,8 
 
 7 37 13-22 
 
 134 
 
 .13300 
 
 99,1 
 
 .99104 
 
 13,4 
 
 .12580 
 
 322,2 
 
 .99609 
 
 5,9 
 
 7 40 39.48 
 
 0.135 
 
 0. 13459 
 
 99,1 
 
 0.99090 
 
 13,5 
 
 9.12901 
 
 319,7 
 
 9.99603 
 
 5,9 
 
 7 44 05.75 
 
 .136 
 
 .13558 
 
 99,1 
 
 .99077 
 
 13,6 
 
 . 13220 
 
 317,4 
 
 99597 
 
 5,9 
 
 7 47 32.01 
 
 137 
 
 . 13657 
 
 99,1 
 
 .99063 
 
 13,7 
 
 . 13536 
 
 315,0 
 
 .99591 
 
 6,0 
 
 7 50 58.28 
 
 .138 
 
 .13756 
 
 99,0 
 
 .99049 
 
 13,8 
 
 .13850 
 
 312,7 
 
 .99585 
 
 6,0 
 
 7 54 24.54 
 
 139 
 
 .13855 
 
 99,0 
 
 .99036 
 
 13,9 
 
 .14162 
 
 310,4 
 
 .99579 
 
 6,1 
 
 7 57 5o.8i 
 
 O.I40 
 
 0.13954 
 
 99,0 
 
 0.99022 
 
 14,0 
 
 9. 14471 
 
 308,2 
 
 9-99573 
 
 6,1 
 
 8 01 17.07 
 
 .141 
 
 . 14053 
 
 99,o 
 
 .99008 
 
 14,1 
 
 . 14778 
 
 306,0 
 
 .99567 
 
 6,2 
 
 8 04 43.34 
 
 .142 
 
 .14152 
 
 99,o 
 
 .08993 
 
 14,2 
 
 .15083 
 
 303,8 
 
 .99561 
 
 6,2 
 
 8 08 09.60 
 
 143 
 
 .14251 
 
 99,0 
 
 .98979 
 
 14,3 
 
 .15385 
 
 301,6 
 
 99554 
 
 6,3 
 
 8 ii 35.87 
 
 144 
 
 . 14350 
 
 99,0 
 
 .98965 
 
 14,4 
 
 .15686 
 
 299,5 
 
 .99548 
 
 6,3 
 
 8 15 02.13 
 
 0.145 
 
 0.14449 
 
 99,0 
 
 0.08951 
 
 14,4 
 
 9.15985 
 
 297,4 
 
 9-99542 
 
 6,3 
 
 8 18 28.40 
 
 .146 
 
 .14548 
 
 98,9 
 
 .98936 
 
 14,5 
 
 .16281 
 
 295,3 
 
 99535 
 
 6,4 
 
 8 21 54-66 
 
 .147 
 
 . 14647 
 
 98,9 
 
 .98921 
 
 14,6 
 
 16575 
 
 293,3 
 
 .99529 
 
 6,4 
 
 8 25 20.93 
 
 .148 
 
 .14746 
 
 98,9 
 
 9-S007 
 
 M,7 
 
 .16868 
 
 291,3 
 
 .99523 
 
 6,5 
 
 8 28 47.19 
 
 .149 
 
 .14845 
 
 98,9 
 
 .98892 
 
 14,8 
 
 .17158 
 
 289,3 
 
 .09516 
 
 6,5 
 
 8 32 13.46 
 
 0.150 
 
 0.14944 
 
 98,9 
 
 0.98877 
 
 14,9 
 
 9. 17446 
 
 287,4 
 
 9-99510 
 
 6,6 
 
 8 35 39.72 
 
 u 
 
 -isinhiu 
 
 -Fo' 
 
 cosh iu 
 
 -FO' 
 
 loo tinh iu 
 
 t uy 
 
 F ' 
 
 log cosh iu 
 
 F O ' 
 
 u 
 
 SMITHSONIAN TABLES 
 
 (94 
 
Circular Functions. 
 
 u 
 
 sin u 
 
 F ' 
 
 cos u 
 
 Fo* 
 
 log sin u 
 
 - Fo' 
 
 log cos u 
 
 -Fo' 
 
 u 
 
 0.150 
 
 0.14944 
 
 98,9 
 
 0.98877 
 
 14,9 
 
 9.17446 
 
 287,4 
 
 9.99510 
 
 6,6 
 
 8 35' 39''72 
 
 .151 
 
 15043 
 
 98,9 
 
 .98862 
 
 I5,o 
 
 . 17733 
 
 285,4 
 
 .99503 
 
 6,6 
 
 8 39 05-99 
 
 .152 
 
 .15142 
 
 98,8 
 
 .98847 
 
 *5,i 
 
 .18017 
 
 283,5 
 
 .99496 
 
 6,7 
 
 8 42 32.25 
 
 .153 
 
 .15240 
 
 98,8 
 
 .98832 
 
 15,2 
 
 .18300 
 
 28l,6 
 
 .99490 
 
 6,7 
 
 8 45 58.52 
 
 .154 
 
 .15339 
 
 98,8 
 
 .98817 
 
 15,3 
 
 .18580 
 
 279,8 
 
 .99483 
 
 6,7 
 
 8 49 24.78 
 
 0.155 
 
 0.15438 
 
 98,8 
 
 0.98801 
 
 15,4 
 
 9.18859 
 
 277,9 
 
 9.99476 
 
 6,8 
 
 8 52 51.04 
 
 .156 
 
 15537 
 
 98,8 
 
 .98786 
 
 15,5 
 
 . 19136 
 
 276,1 
 
 .99469 
 
 6,8 
 
 8 56 17.31 
 
 157 
 
 .15636 
 
 98,8 
 
 .98770 
 
 15,6 
 
 .19411 
 
 274,3 
 
 .99463 
 
 6,9 
 
 8 59 43-57 
 
 .158 
 .159 
 
 . 15734 
 .15833 
 
 98,8 
 98,7 
 
 .98754 
 .98739 
 
 15,7 
 15,8 
 
 .19685 
 .19957 
 
 272,6 
 270,8 
 
 .99456 
 .99449 
 
 6,9 
 7,0 
 
 9 03 09.84 
 9 06 36. 10 
 
 0.160 
 
 0.15932 
 
 98,7 
 
 0.98723 
 
 15,9 
 
 9.20227 
 
 269,1 
 
 9-99442 
 
 7,o 
 
 9 10 02.37 
 
 .161 
 
 ^/-T-W 
 
 .16031 
 
 98,7 
 
 .98707 
 
 16,0 
 
 .20495 
 
 267,4 
 
 99435 
 
 7,i 
 
 9 13 28.63 
 
 .162 
 
 . 16129 
 
 98,7 
 
 .98691 
 
 16,1 
 
 .20761 
 
 265,7 
 
 .99428 
 
 7,i 
 
 9 16 54-90 
 
 .163 
 
 .16228 
 
 98,7 
 
 .98674 
 
 16,2 
 
 .21026 
 
 264,1 
 
 .99420 
 
 7,i 
 
 9 20 21. 16 
 
 .164 
 
 . 16327 
 
 98,7 
 
 .98658 
 
 16,3 
 
 .21290 
 
 202,4 
 
 99413 
 
 7,2 
 
 9 23 47-43 
 
 0.165 
 
 0.16425 
 
 98,6 
 
 0.98642 
 
 16,4 
 
 9.2I55I 
 
 200,8 
 
 9.99406 
 
 7,2 
 
 9 27 13.69 
 
 .166 
 
 . 16524 
 
 98,6 
 
 .98625 
 
 16,5 
 
 .21811 
 
 259,2 
 
 99399 
 
 7,3 
 
 9 30 39.96 
 
 .167 
 
 .16622 
 
 98,6 
 
 .98609 
 
 16,6 
 
 .22070 
 
 257,6 
 
 .99392 
 
 7,3 
 
 9 34 06.22 
 
 .168 
 
 . 16721 
 
 98,6 
 
 .98592 
 
 16,7 
 
 .22326 
 
 256,1 
 
 .99384 
 
 7,4 
 
 9 37 32.49 
 
 .169 
 
 .16820 
 
 98,6 
 
 .98575 
 
 16,8 
 
 .22582 
 
 254,5 
 
 99377 
 
 7,4 
 
 9 40 58.75 
 
 0.170 
 
 0.16918 
 
 98,6 
 
 0.98558 
 
 16,9 
 
 9.22836 
 
 253,0 
 
 9.99369 
 
 7,5 
 
 9 44 25.02 
 
 .171 
 
 .17017 
 
 98,5 
 
 .98542 
 
 17,0 
 
 .23088 
 
 251,5 
 
 .99362 
 
 7,5 
 
 9 47 51.28 
 
 .172 
 
 .17115 
 
 98,5 
 
 .98524 
 
 I7,i 
 
 .23338 
 
 250,0 
 
 99354 
 
 7,5 
 
 9 51 17-55 
 
 173 
 
 .17214 
 
 98,5 
 
 .98507 
 
 17,2 
 
 .23588 
 
 248,5 
 
 99347 
 
 7,6 
 
 9 54 43.81 
 
 .174 
 
 .17312 
 
 98,5 
 
 .98490 
 
 17,3 
 
 .23836 
 
 247,i 
 
 99339 
 
 7,6 
 
 9 58 10.08 
 
 0.175 
 
 O.I74H 
 
 98,5 
 
 0.98473 
 
 17,4 
 
 9.24082 
 
 245,6 
 
 9.99332 
 
 7,7 
 
 10 01 36.34 
 
 .176 
 
 .17509 
 
 98,5 
 
 .98455 
 
 17,5 
 
 .24327 
 
 244,2 
 
 .99324 
 
 7,7 
 
 10 05 02.61 
 
 .177 
 
 .17608 
 
 98,4 
 
 .98438 
 
 17,6 
 
 .24570 
 
 242,8 
 
 .99316 
 
 7,8 
 
 10 08 28.87 
 
 .178 
 
 .17706 
 
 98,4 
 
 .98420 
 
 17,7 
 
 .24812 
 
 241,4 
 
 .99308 
 
 7,8 
 
 10 ii 55.14 
 
 .179 
 
 .17805 
 
 98,4 
 
 .98402 
 
 17,8 
 
 .25053 
 
 240,0 
 
 .99300 
 
 7,9 
 
 10 15 21.40 
 
 0.180 
 
 0.17903 
 
 98,4 
 
 0.98384 
 
 17,9 
 
 9-25292 
 
 238,7 
 
 9.99293 
 
 7,9 
 
 10 18 47.67 
 
 .181 
 
 .18001 
 
 98,4 
 
 .98366 
 
 18,0 
 
 .25530 
 
 237,3 
 
 .99285 
 
 7,9 
 
 10 22 13.93 
 
 .182 
 
 .18100 
 
 98,3 
 
 .98348 
 
 18,1 
 
 .25767 
 
 236,0 
 
 .99277 
 
 8,0 
 
 10 25 40.19 
 
 .183 
 
 .18198 
 
 98,3 
 
 .98330 
 
 18,2 
 
 .26002 
 
 234,7 
 
 .99269 
 
 8,0 
 
 10 29 06.46 
 
 .184 
 
 .18296 
 
 98,3 
 
 .98312 
 
 18,3 
 
 .26236 
 
 233,4 
 
 .99261 
 
 8,1 
 
 10 32 32.72 
 
 .0185 
 
 0.18395 
 
 98,3 
 
 0.98294 
 
 18,4 
 
 9.26469 
 
 232,1 
 
 9.99253 
 
 8,1 
 
 10 35 58.99 
 
 .186 
 
 . 18493 
 
 98,3 
 
 .98275 
 
 18,5 
 
 .26701 
 
 230,8 
 
 .99244 
 
 8,2 
 
 10 39 25.25 
 
 .187 
 
 .18591 
 
 98,3 
 
 .98257 
 
 18,6 
 
 .26931 
 
 229,5 
 
 .99236 
 
 8,2 
 
 10 42 51.52 
 
 .188 
 
 .18689 
 
 98,2 
 
 .98238 
 
 18,7 
 
 .27160 
 
 228,3 
 
 .99228 
 
 8,3 
 
 10 46 17.78 
 
 .189 
 
 .18788 
 
 98,2 
 
 .98219 
 
 18,8 
 
 .27387 
 
 227,0 
 
 .99220 
 
 8,3 
 
 10 49 44.05 
 
 0.190 
 
 0.18886 
 
 98,2 
 
 0.98200 
 
 18,9 
 
 9.27614 
 
 225,8 
 
 9.992II 
 
 8,4 
 
 10 53 10.31 
 
 .191 
 
 .18984 
 
 98,2 
 
 .98181 
 
 19,0 
 
 .27839 
 
 224,6 
 
 .99203 
 
 8,4 
 
 10 56 36.58 
 
 .192 
 
 .10082 
 
 98,2 
 
 .98162 
 
 19,1 
 
 .28063. 
 
 223,4 
 
 .99195 
 
 8,4 
 
 ii oo 02.84 
 
 193 
 
 .19180 
 
 98,1 
 
 .98143 
 
 19,2 
 
 .28286 
 
 222,2 
 
 .99186 
 
 8,5 
 
 ii 03 29.11 
 
 .194 
 
 . 19279 
 
 98,1 
 
 .98124 
 
 19,3 
 
 .28507 
 
 221,0 
 
 .99178 
 
 8,5 
 
 ii 06 55-37 
 
 0.195 
 
 0.19377 
 
 98,1 
 
 0.98105 
 
 19,4 
 
 9.28728 
 
 219,9 
 
 9.99169 
 
 8,6 
 
 ii 10 21.64 
 
 .196 
 
 . 19475 
 
 98,1 
 
 .98085 
 
 19,5 
 
 .28947 
 
 218,7 
 
 .99160 
 
 8,6 
 
 II 13 47.90 
 
 .197 
 
 .19573 
 
 98,1 
 
 .98066 
 
 19,6 
 
 .29165 
 
 217,6 
 
 .9915-2 
 
 8,7 
 
 II 17 14.17 
 
 .198 
 
 .19671 
 
 08,0 
 
 .98046 
 
 19,7 
 
 .29382 
 
 216,5 
 
 .99143 
 
 8,7 
 
 II 20 40.43 
 
 .199 
 
 .19769 
 
 98,0 
 
 .98026 
 
 19,8 
 
 .29598 
 
 215,3 
 
 .99134 
 
 8,8 
 
 II 24 06.70 
 
 0.200 
 
 o. 1986.7 
 
 98,0 
 
 0.98007 
 
 19,9 
 
 9-29813 
 
 214,2 
 
 9.99126 
 
 8,8 
 
 II 27 32.96 
 
 U 
 
 -isinhiu 
 
 F ' 
 
 cosh iu 
 
 F O ' 
 
 sinh iu 
 
 Fo' 
 
 log cosh iu 
 
 F O ' 
 
 u 
 
 loo - 
 
 SMITHSONIAN TABLES 
 
 195 
 
Circular Functions. 
 
 u 
 
 sin u 
 
 F O ' 
 
 COS U 
 
 Fo' 
 
 log sin u 
 
 Fo' 
 
 log oos u 
 
 FO' 
 
 u 
 
 O.2OO 
 
 0.19867 
 
 98,0 
 
 0.98007 
 
 19,9 
 
 9.29813 
 
 214,2 
 
 9.99126 
 
 8,8 
 
 ii27 / 32.'o6 
 
 .2OI 
 
 .19965 
 
 98,0 
 
 .97987 
 
 20,O 
 
 .30027 
 
 213,1 
 
 .99117 
 
 8,8 
 
 ii 30 59.23 
 
 .2C2 
 
 .20063 
 
 98,0 
 
 .97967 
 
 20,1 
 
 .30239 
 
 212,1 
 
 .99108 
 
 8,9 
 
 II 34 25.49 
 
 .203 
 
 .20161 
 
 97,9 
 
 .97947 
 
 20,2 
 
 .30451 
 
 2II,O 
 
 .99099 
 
 8,9 
 
 ii 37 51.76 
 
 .204 
 
 .20259 
 
 97,9 
 
 .97926 
 
 20,3 
 
 .30661 
 
 209,9 
 
 .99090 
 
 9,o 
 
 II 41 18.02 
 
 O.205 
 
 0.20357 
 
 97,9 
 
 0.97906 
 
 20,4 
 
 9-30871 
 
 208,9 
 
 9.99081 
 
 9,0 
 
 II 44 44.29 
 
 .206 
 
 .20455 
 
 97,9 
 
 .97886 
 
 20,5 
 
 .31079 
 
 207,8 
 
 .99072 
 
 9,i 
 
 ii 48 10.55 
 
 .207 
 
 .20552 
 
 97,9 
 
 .97865 
 
 2O,6 
 
 .31286 
 
 206,8 
 
 .99063 
 
 9,i 
 
 ii 51 36.81 
 
 .208 
 
 .20650 
 
 97,8 
 
 .97845 
 
 20,7 
 
 .31493 
 
 205,8 
 
 .99054 
 
 9,2 
 
 ii 55 03.08 
 
 .209 
 
 .20748 
 
 97,8 
 
 .97824 
 
 20,7 
 
 .31698 
 
 204,8 
 
 .99044 
 
 9,2 
 
 ii 58 29.34 
 
 0.210 
 
 0.20846 
 
 97,8 
 
 0.97803 
 
 20,8 
 
 9.31902 
 
 203,8 
 
 9.99035 
 
 9,3 
 
 12 01 55-6l 
 
 .211 
 
 .20944 
 
 97,8 
 
 .97782 
 
 20,9 
 
 .32106 
 
 202,8 
 
 .99026 
 
 9,3 
 
 12 05 21.87 
 
 .212 
 
 .21042 
 
 97,8 
 
 .97761 
 
 2I,O 
 
 .32308 
 
 201,8 
 
 .99017 
 
 9,3 
 
 12 08 48.14 
 
 .213 
 
 .21139 
 
 97,7 
 
 .97740 
 
 21,1 
 
 .32509 
 
 200,8 
 
 .99007 
 
 9,4 
 
 12 12 14.40 
 
 .214 
 
 * .21237 
 
 97,7 
 
 .97719 
 
 21,2 
 
 .32709 
 
 199,8 
 
 .98998 
 
 9,4 
 
 12 15 40.67 
 
 O.2I5 
 
 0.21335 
 
 97,7 
 
 0.97698 
 
 21,3 
 
 9.32909 
 
 198,9 
 
 9.98988 
 
 9,5 
 
 12 19 O6.93 
 
 .216 
 
 .21432 
 
 97,7 
 
 .97676 
 
 21,4 
 
 .33107 
 
 197,9 
 
 .98979 
 
 9,5 
 
 12 22 33.2O 
 
 .217 
 
 .21530 
 
 97,7 
 
 .97655 
 
 21,5 
 
 .33305 
 
 197,0 
 
 .98969 
 
 9,6 
 
 12 25 59.46 
 
 .218 
 
 .21628 
 
 97,6 
 
 .97633 
 
 21,6 
 
 33501 
 
 196,0 
 
 .98960 
 
 9,6 
 
 12 29 25.73 
 
 .219 
 
 .21725 
 
 97,6 
 
 .97612 
 
 21,7 
 
 .33697 
 
 I95,i 
 
 .98950 
 
 9,7 
 
 12 32 51-99 
 
 0.220 
 
 0.21823 
 
 97,6 
 
 0.97590 
 
 21,8 
 
 9.33891 
 
 194,2 
 
 9.98940 
 
 9,7 
 
 12 36 18.26 
 
 .221 
 
 .21921 
 
 97,6 
 
 .97568 
 
 21,9 
 
 .34085 
 
 193,3 
 
 .98931 
 
 9,8 
 
 12 39 44.52 
 
 .222 
 
 .22018 
 
 97,5 
 
 .97546 
 
 22,0 
 
 .34278 
 
 192,4 
 
 .98921 
 
 9,8 
 
 12 43 10.79 
 
 .223 
 
 .22116 
 
 97,5 
 
 .97524 
 
 22,1 
 
 34470 
 
 I9i,5 
 
 .98911 
 
 9,8 
 
 12 46 37-05 
 
 .224 
 
 .22213 
 
 97,5 
 
 .97502 
 
 22,2 
 
 .34661 
 
 190,6 
 
 .98901 
 
 9,9 
 
 12 5O 03.32 
 
 0.225 
 
 0.22311 
 
 97,5 
 
 0.97479 
 
 22,3 
 
 9.34851 
 
 189,8 
 
 9.98891 
 
 9,9 
 
 12 53 29.58 
 
 .226 
 
 .22408 
 
 97,5 
 
 97457 
 
 22,4 
 
 .35041 
 
 188,9 
 
 .98881 
 
 10,0 
 
 12 56 55.85 
 
 .227 
 
 .22506 
 
 97,4 
 
 97435 
 
 22,5 
 
 .35229 
 
 188,0 
 
 .98871 
 
 10,0 
 
 13 OO 22.11 
 
 .228 
 
 .22603 
 
 97,4 
 
 .97412 
 
 22,6 
 
 .35417 
 
 187,2 
 
 .98861 
 
 10,1 
 
 13 03 48.38 
 
 .229 
 
 .22700 
 
 97,4 
 
 .97389 
 
 22,7 
 
 .35603 
 
 186,3 
 
 .08851 
 
 10,1 
 
 13 07 14-64 
 
 O.23O 
 
 0.22798 
 
 97,4 
 
 0.97367 
 
 22,8 
 
 9.35789 
 
 i85,5 
 
 9.98841 
 
 10,2 
 
 13 10 40.91 
 
 .231 
 
 .22895 
 
 97,3 
 
 97344 
 
 22,9 
 
 35974 
 
 184,7 
 
 .98831 
 
 IO,2 
 
 13 14 07.17 
 
 .232 
 
 .22992 
 
 97,3 
 
 .97321 
 
 23,0 
 
 .36158 
 
 183,8 
 
 .98821 
 
 10,3 
 
 13 17 33.44 
 
 233 
 
 .23000 
 
 97,3 
 
 .97298 
 
 23,1 
 
 .36342 
 
 183,0 
 
 .98810 
 
 10,3 
 
 13 20 59-70 
 
 234 
 
 .23187 
 
 97,3 
 
 97275 
 
 23,2 
 
 .36525 
 
 182,2 
 
 .98800 
 
 10,4 
 
 13 24 25.96 
 
 0.235 
 
 0.23284 
 
 97,3 
 
 0.97251 
 
 23,3 
 
 9-36706 
 
 181,4 
 
 9.98790 
 
 10,4 
 
 13 27 52.23 
 
 .236 
 
 .23382 
 
 97,2 
 
 .97228 
 
 23,4 
 
 .36887 
 
 180,6 
 
 .98779 
 
 10,4 
 
 13 31 18.49 
 
 .237 
 
 23479 
 
 97,2 
 
 .97205 
 
 23,5 
 
 .37068 
 
 179,8 
 
 .98769 
 
 10,5 
 
 13 34 44.76 
 
 .238 
 
 .23576 
 
 97,2 
 
 .97181 
 
 23,6 
 
 .37247 
 
 179,0 
 
 .98758 
 
 10,5 
 
 13 38 I i. 02 
 
 239 
 
 .23673 
 
 97,2 
 
 .97158 
 
 23,7 
 
 .37426 
 
 178,2 
 
 .98748 
 
 10,6 
 
 13 41 37-29 
 
 0.240 
 
 0.23770 
 
 97,1 
 
 0.97134 
 
 23,8 
 
 9.37603 
 
 177,5 
 
 9.98737 
 
 10,6 
 
 13 45 03.55 
 
 .241 
 
 .23867 
 
 97,1 
 
 .97110 
 
 23,9 
 
 .37780 
 
 176,7 
 
 .98726 
 
 10,7 
 
 13 48 29.82 
 
 .242 
 
 .23964 
 
 97,i 
 
 .97086 
 
 24,0 
 
 37957 
 
 175,9 
 
 .98716 
 
 10,7 
 
 13 51 56.08 
 
 .243 
 
 .24062 
 
 97,1 
 
 .97062 
 
 24,1 
 
 .38132 
 
 175,2 
 
 .98705 
 
 10,8 
 
 13 55 22.35 
 
 .244 
 
 .24159 
 
 97,0 
 
 .9/038 
 
 24,2 
 
 38307 
 
 174,4 
 
 .98694 
 
 10,8 
 
 13 58 48.61 
 
 0.245 
 
 0.24256 
 
 97,0 
 
 0.97014 
 
 24,3 
 
 9.38481 
 
 173,7 
 
 9.98683' 
 
 10,9 
 
 14 02 14.88 
 
 .246 
 
 24353 
 
 97,0 
 
 .96989 
 
 24,4 
 
 .38655 
 
 I73,o 
 
 .9867J 
 
 10,9 
 
 14 05 41.14, 
 
 .247 
 
 .24450 
 
 97,0 
 
 .96965 
 
 24,4 
 
 .38827 
 
 172,2 
 
 .98669 
 
 11,0 
 
 14 09 07.41 
 
 .248 
 
 24547 
 
 po0 
 
 .96941 
 
 24,5 
 
 .38999 
 
 I7i,5 
 
 .98651 
 
 11,0 
 
 14 12 33.67 
 
 .249 
 
 .24643 
 
 96,9 
 
 .96916 
 
 24,6 
 
 .39170 
 
 170,8 
 
 .98640 
 
 11,0 
 
 14 15 59-94 
 
 0.250 
 
 0.24740 
 
 96,9 
 
 0.96891 
 
 24,7 
 
 9.39341 
 
 170,1 
 
 9.08628 
 
 lit! 
 
 14 19 26.20 
 
 u 
 
 -isinhiu 
 
 F ' 
 
 cosh iu 
 
 Fo' 
 
 I 00 8inh iu 
 
 Fo' 
 
 log cosh iu 
 
 -Fo' 
 
 u 
 
 log , 
 
 SMITHSONIAN TABLES 
 
 196 
 
Circular Functions. 
 
 u 
 
 sin u 
 
 F ' 
 
 OS U 
 
 Fo' 
 
 log sin u 
 
 Fo' 
 
 log cos u 
 
 F ' 
 
 u 
 
 0.250 
 
 0.2474 
 
 96,9 
 
 0.96891 
 
 24,7 
 
 9.39341 
 
 170,1 
 
 9.98628 
 
 11,1 
 
 14 19 26.20 
 
 .251 
 
 .24837 
 
 96,9 
 
 .96866 
 
 24,8 
 
 .39510 
 
 169,4 
 
 .98617 
 
 11,1 
 
 14 22 52.47 
 
 .252 
 
 .24934 
 
 96,8 
 
 .96842 
 
 24,9 
 
 .39679 
 
 168,7 
 
 .98606 
 
 11,2 
 
 14 26 18.73 
 
 .253 
 
 .25031 
 
 96,8 
 
 .96817 
 
 25,0 
 
 .39848 
 
 168,0 
 
 .98595 
 
 11,2 
 
 14 29 45.00 
 
 .254 
 
 .25128 
 
 96,8 
 
 .96792 
 
 25,1 
 
 .40015 
 
 167,3 
 
 .98584 
 
 11,3 
 
 14 33 11.26 
 
 0.255 
 
 0.25225 
 
 96,8 
 
 0.96766 
 
 25,2 
 
 9.40182 
 
 166,6 
 
 9.98572 
 
 li,3 
 
 H 36 37-53 
 
 .256 
 
 .25321 
 
 96,7 
 
 .96741 
 
 25,3 
 
 .40349 
 
 165,9 
 
 .98561 
 
 11,4 
 
 14 40 03.79 
 
 .257 
 
 .25418 
 
 96,7 
 
 .96716 
 
 25,4 
 
 .40514 
 
 165,2 
 
 .98550 
 
 11,4 
 
 14 43 30.06 
 
 .258 
 
 .25515 
 
 96,7 
 
 .96690 
 
 25,5 
 
 .40679 
 
 164,6 
 
 .98538 
 
 n,5 
 
 14 46 56.3:2 
 
 .259 
 
 .25611 
 
 96,7 
 
 .96665 
 
 25,6 
 
 .40843 
 
 163,9 
 
 .98527 
 
 11,5 
 
 14 50 22.58 
 
 0.260 
 
 0.25708 
 
 96,6 
 
 0.96639 
 
 25,7 
 
 9.41007 
 
 163,3 
 
 9.98515 
 
 n,6 
 
 14 53 48.85 
 
 .261 
 
 .25805 
 
 96,6 
 
 .96613 
 
 25,8 
 
 .41170 
 
 162,6 
 
 .98504 
 
 11,6 
 
 14 57 iS.ii 
 
 .262 
 
 .25901 
 
 96,6 
 
 .96587 
 
 25,9 
 
 41332 
 
 162,0 
 
 .08492 
 
 11,6 
 
 15 oo 41.38 
 
 .263 
 
 .25908 
 
 96,6 
 
 .96561 
 
 26,0 
 
 .41494 
 
 161,3 
 
 .98480 
 
 n,7 
 
 15 04 07.64 
 
 .264 
 
 .26094 
 
 96,5 
 
 .96535 
 
 26,1 
 
 .41655 
 
 160,7 
 
 .98469 
 
 . I L7 
 
 15 07 33.91 
 
 0.265 
 
 0.26191 
 
 96,5 
 
 0.96509 
 
 26,2 
 
 9.4l8l5 
 
 160,0 
 
 9.98457 
 
 n,8 
 
 15 ii 00.17 
 
 .266 
 
 .26287 
 
 96,5 
 
 .96483 
 
 26,3 
 
 .41975 
 
 !594 
 
 .98445 
 
 n,8 
 
 15 14 26.44 
 
 .267 
 
 .26384 
 
 96,5 
 
 .96457 
 
 26,4 
 
 .42134 
 
 158,8 
 
 .98433 
 
 n,9 
 
 15 17 52.70 
 
 .268 
 
 .26480 
 
 96,4 
 
 .96430 
 
 26,5 
 
 .42292 
 
 158,2 
 
 .98421 
 
 n,9 
 
 15 21 l8.97 
 
 .269 
 
 .26577 
 
 96,4 
 
 .96404 
 
 26,6 
 
 .42450 
 
 157,5 
 
 .98409 
 
 12,0 
 
 15 24 45.23 
 
 
 
 
 
 
 
 
 
 
 
 0.270 
 
 0.26673 
 
 96,4 
 
 0.96377 
 
 26,7 
 
 9.42607 
 
 156,9 
 
 9.98397 
 
 12,0 
 
 15 28 11.50 
 
 .271 
 
 .26770 
 
 96,4 
 
 .96350 
 
 26,8 
 
 .42764 
 
 156,3 
 
 .98385 
 
 12,1 
 
 15 3i 37.76 
 
 .272 
 
 .26866 
 
 96,3 
 
 .96324 
 
 26,9 
 
 .42920 
 
 155,7 
 
 .98373 
 
 12,1 
 
 15 35 04.03 
 
 .273 
 
 .26962 
 
 96,3 
 
 .96297 
 
 27,0 
 
 .43075 
 
 I55,i 
 
 .98361 
 
 12,2 
 
 15 38 30.29 
 
 .274 
 
 .27058 
 
 96,3 
 
 .96270 
 
 27,1 
 
 .43230 
 
 154,5 
 
 .98349 
 
 12,2 
 
 15 41 56.56 
 
 0.275 
 
 0.27155 
 
 96,2 
 
 0.96243 
 
 27,2 
 
 9.43384 
 
 153,9 
 
 9.98337 
 
 12,3 
 
 15 45 22.82 
 
 .276 
 
 .27251 
 
 96,2 
 
 .96215 
 
 27,3 
 
 .43538 
 
 153,3 
 
 .98324 
 
 12,3 
 
 15 48 49-09 
 
 .277 
 
 .27347 
 
 96,2 
 
 .96188 
 
 27,3 
 
 .43691 
 
 ' 1:52,8 
 
 .98312 
 
 12,3 
 
 15 52 15.35 
 
 .278 
 
 .27443 
 
 96,2 
 
 .96161 
 
 27,4 
 
 43844 
 
 152,2 
 
 .08300 
 
 12,4 
 
 15 55 41.62 
 
 .279 
 
 .27539 
 
 96,1 
 
 .96133 
 
 27,5 
 
 43996 
 
 151,6 
 
 .98287 
 
 12,4 
 
 15 59 07.88 
 
 0.280 
 
 0.27636 
 
 96,1 
 
 0.96106 
 
 27,6 
 
 9.44147 
 
 151,0 
 
 9.98275 
 
 12,5 
 
 16 02 34.15 
 
 .281 
 
 .27732 
 
 96,1 
 
 .96078 
 
 27,7 
 
 .44298 
 
 150,5 
 
 .98262 
 
 12,5 
 
 16 06 00.41 
 
 .282 
 
 .27828 
 
 96,1 
 
 .96050 
 
 27,8 
 
 .44448 
 
 149,9 
 
 .98250 
 
 12,6 
 
 16 09 26.68 
 
 .283 
 
 .27924 
 
 96,0 
 
 .96022 
 
 27,9 
 
 44597 
 
 149,3 
 
 .98237 
 
 12,6 
 
 16 12 52.94 
 
 .284 
 
 .28020 
 
 96,0 
 
 .95994 
 
 28,0 
 
 .44746 
 
 148,8 
 
 .98225 
 
 12,7 
 
 16 16 19.20 
 
 0.285 
 
 0.28116 
 
 96,0 
 
 0.95966 
 
 28,1 
 
 9.44895 
 
 148,2 
 
 9.98212 
 
 12,7 
 
 16 19 45.47 
 
 .286 
 
 .28212 
 
 95,9 
 
 .95938 
 
 28,2 
 
 .45043 
 
 147,7 
 
 .98199 
 
 12,8 
 
 16 23 11.73 
 
 .287 
 
 .28308 
 
 95,9 
 
 .95910 
 
 28,3 
 
 .45190 
 
 147,1 
 
 .98186 
 
 12,8 
 
 16 26 38.00 
 
 .288 
 
 .28404 
 
 95,9 
 
 .95881 
 
 28,4 
 
 45337 
 
 146,6 
 
 .98173 
 
 12,9 
 
 16 30 04.26 
 
 .289 
 
 .28499 
 
 95,9 
 
 .95853 
 
 28,5 
 
 .45484 
 
 146,1 
 
 .98161 
 
 12,9 
 
 16 33 30.53 
 
 O.2OO 
 
 0.28595 
 
 95,8 
 
 0.95824 
 
 28,6 
 
 9.45629 
 
 145,5 
 
 9.98148 
 
 13,0 
 
 16 36 56.79 
 
 .291 
 
 .28691 
 
 95,8 
 
 .95796 
 
 28,7 
 
 45775 
 
 145,0 
 
 .98135 
 
 13,0 
 
 16 40 23.06 
 
 .292 
 
 .28787 
 
 95,8 
 
 .95767 
 
 28,8 
 
 .45919 
 
 144,5 
 
 .98122 
 
 13,1 
 
 16 43 49.32 
 
 293 
 
 .28883. 
 
 95,7 
 
 .95738 
 
 28,9 
 
 .46064 
 
 144,0 
 
 .98109 
 
 13,1 
 
 16 47 15-59 
 
 294 
 
 .28978 
 
 95,7 
 
 .95709 
 
 29,0 
 
 .46207 
 
 143,4 
 
 .98095 
 
 13,1 
 
 16 50 41.85 
 
 0.295 
 
 0.29074 
 
 95,7 
 
 0.95680 
 
 29,1 
 
 9.46350 
 
 142,9 
 
 9.98082 
 
 13,2 
 
 16 54 08.12 
 
 .296 
 
 .29170 
 
 95,7 
 
 .95651 
 
 29,2 
 
 .46493 
 
 142,4 
 
 .98069 
 
 13,2 
 
 16 57 34.38 
 
 .297 
 
 .29265 
 
 95,6 
 
 .95622 
 
 29,3 
 
 .46633 
 
 141,9 
 
 .98056 
 
 13,3 
 
 17 01 00.65 
 
 .298 
 
 .29361 
 
 95,6 
 
 95593 
 
 29,4 
 
 .46777 
 
 141,4 
 
 .980421 
 
 13,3 
 
 17 04 26.91 
 
 .299 
 
 .29456 
 
 95,6 
 
 .95563 
 
 29,5 
 
 .46918 
 
 140,9 
 
 .98029 
 
 13,4 
 
 17 07 53.i8 
 
 0.300 
 
 0.29552 
 
 95,5 
 
 0.95534 
 
 29,6 
 
 9.47059 
 
 140,4 
 
 9.98016 
 
 13,4 
 
 17 ii 19.44 
 
 u 
 
 -i sinh iu 
 
 *>Fo' 
 
 cosh iu 
 
 F ' 
 
 sinh iu 
 
 wF ' 
 
 log cosh iu 
 
 F ' 
 
 u 
 
 log . 
 
 SMITHSONIAN TABLES 
 
 197 
 
Circular Functions. 
 
 u 
 
 sin u 
 
 -Fo' 
 
 cos u 
 
 Fo' 
 
 log sin u 
 
 Fo' 
 
 log oos u 
 
 F ' 
 
 u 
 
 0.300 
 
 0.29552 
 
 95,5 
 
 0.95534 
 
 29,6 
 
 9.47059 
 
 140,4 
 
 9.98016 
 
 13,4 
 
 17 II 19 '44 
 
 .301 
 
 .29648 
 
 95,5 
 
 .95504 
 
 29,6 
 
 .47199 
 
 139,9 
 
 .08002 
 
 13,5 
 
 17 14 45.71 
 
 .302 
 
 .29743 
 
 95,5 
 
 .95474 
 
 29,7 
 
 47339 
 
 139,4 
 
 .97989 
 
 13,5 
 
 17 18 11.97 
 
 .303 
 
 .29838 
 
 95,4 
 
 95445 
 
 29,8 
 
 .47478 
 
 138,9 
 
 97975 
 
 13,6 
 
 17 21 38.24 
 
 .304 
 
 29934 
 
 95,4 
 
 .95415 
 
 29,9 
 
 .47616 
 
 138,4 
 
 .97962 
 
 13,6 
 
 17 25 04.50 
 
 0.305 
 
 0.30029 
 
 95,4 
 
 0.95385 
 
 30,0 
 
 9-47755 
 
 137,9 
 
 9.97948 
 
 i3,7 
 
 17 28 30.77 
 
 .306 
 
 .30125 
 
 95,4 
 
 95355 
 
 30,1 
 
 .47892 
 
 137,5 
 
 97934 
 
 i3,7 
 
 17 31 57.03 
 
 .307 
 
 .30220 
 
 95,3 
 
 .95324 
 
 30,2 
 
 .48029 
 
 137,0 
 
 .97920 
 
 13,8 
 
 17 35 23.30 
 
 .308 
 
 .30315 
 
 95,3 
 
 .95294 
 
 30,3 
 
 .48166 
 
 136,5 
 
 .97907 
 
 13,8 
 
 17 38 49.56 
 
 .309 
 
 .304H 
 
 95,3 
 
 .95264 
 
 30,4 
 
 .48303 
 
 136,0 
 
 .97893 
 
 13,9 
 
 17 42 15-83 
 
 0.310 
 
 0.30506 
 
 95,2 
 
 0.95233 
 
 30,5 
 
 9.48438 
 
 135,6 
 
 9.97879 
 
 13,9 
 
 17 45 42.09 
 
 .311 
 
 .30601 
 
 95,2 
 
 .95203 
 
 30,6 
 
 .48574 
 
 I35,i 
 
 .97865 
 
 14,0 
 
 17 49 08.35 
 
 .312 
 
 .30696 
 
 95,2 
 
 .95172 
 
 30,7 
 
 .48709 
 
 134,7 
 
 .97851 
 
 14,0 
 
 17 52 34.62 
 
 .313 
 
 .30791 
 
 95,1 
 
 .95141 
 
 30,8 
 
 .48843 
 
 134,2 
 
 .97837 
 
 14,1 
 
 17 56 00.88 
 
 .314 
 
 .30887 
 
 95,1 
 
 .95HI 
 
 30,9 
 
 .48977 
 
 133,7 
 
 .97823 
 
 14,1 
 
 17 59 27.15 
 
 0.315 
 
 0.30982 
 
 95,1 
 
 0.95080 
 
 31,0 
 
 9.49HO 
 
 133,3 
 
 9.97809 
 
 142 
 
 18 02 53.41 
 
 .316 
 
 .31077 
 
 95,o 
 
 .95049 
 
 3i,i 
 
 49244 
 
 132,8 
 
 97795 
 
 14,2 
 
 18 06 19.68 
 
 .317 
 
 .31172 
 
 95,0 
 
 .95017 
 
 31,2 
 
 .49376 
 
 132,4 
 
 .97780' 
 
 14,2 
 
 18 09 45.94 
 
 .318 
 
 .31267 
 
 95,0 
 
 .94986 
 
 3i,3 
 
 .49508 
 
 I3i,9 
 
 .97766 
 
 14,3 
 
 l8 13 12.21 
 
 .319 
 
 .31362 
 
 95,0 
 
 94955 
 
 31,4 
 
 .49640 
 
 131,5 
 
 97752 
 
 14,3 
 
 18 16 38.47 
 
 0.320 
 
 0.31457 
 
 94,9 
 
 0.94924 
 
 31,5 
 
 9.49771 
 
 131,1 
 
 9-97737 
 
 14,4 
 
 18 20 04.74 
 
 .321 
 
 .31552 
 
 94,9 
 
 .04892 
 
 3i,6 
 
 .49902 
 
 130,6 
 
 .97723 
 
 14,4 
 
 18 23 31.00 
 
 .322 
 
 .31646 
 
 94,9 
 
 .04860 
 
 3i,6 
 
 .50032 
 
 130,2 
 
 .97709 
 
 H,5 
 
 18 26 57.27 
 
 .323 
 
 .31741 
 
 94,8 
 
 .94829 
 
 3i,7 
 
 .50162 
 
 129,7 
 
 .97694 
 
 14,5 
 
 18 30 23.53 
 
 .324 
 
 .31836 
 
 94,8 
 
 94797 
 
 31,8 
 
 .50292 
 
 129,3 
 
 .97679 
 
 14,6 
 
 18 33 49.8o 
 
 0.325 
 
 0.3I93I 
 
 94,8 
 
 0.94765 
 
 31,9 
 
 9.50421 
 
 128,9 
 
 9.97665 
 
 14,6 
 
 18 37 16.06 
 
 .326 
 
 .32026 
 
 94,7 
 
 94733 
 
 32,0 
 
 .50550 
 
 128,5 
 
 .97650 
 
 14,7 
 
 18 40 42.33 
 
 .327 
 
 .32120 
 
 94,7 
 
 .94701 
 
 32,1 
 
 .50678 
 
 128,0 
 
 .97635 
 
 14,7 
 
 18 44 08.59 
 
 .328 
 
 .32215 
 
 94,7 
 
 .94669 
 
 32,2 
 
 .50806 
 
 127,6 
 
 .97621 
 
 14,8 
 
 18 47 34-86 
 
 .329 
 
 .32310 
 
 94,6 
 
 .94637 
 
 32,3 
 
 50933 
 
 127,2 
 
 .97606 
 
 14,8 
 
 18 51 01.12 
 
 0.330 
 
 0.32404 
 
 94,6 
 
 0.94604 
 
 32,4 
 
 9.51060 
 
 126,8 
 
 9.97591 
 
 14,9 
 
 18 54 27.39 
 
 .331 
 
 .32499 
 
 94,6 
 
 94572 
 
 32,5 
 
 .5H87 
 
 126,4 
 
 .97576 
 
 14,9 
 
 18 57 53.65 
 
 .332 
 
 3'2593 
 
 94,5 
 
 .94539 
 
 32,6 
 
 .51313 
 
 126,0 
 
 .97561 
 
 I5,o 
 
 19 01 19.92 
 
 333 
 
 .32688 
 
 94,5 
 
 .94507 
 
 32,7 
 
 .51439 
 
 125,6 
 
 .97546 
 
 I5,o 
 
 19 04 46.18 
 
 334 
 
 .32782 
 
 94,5 
 
 94474 
 
 32,8 
 
 .51564 
 
 125,2 
 
 97531 
 
 I5,i 
 
 19 08 12.45 
 
 0-335 
 
 0.32877 
 
 94,4 
 
 0.04441 
 
 32,9 
 
 9-51689 
 
 124,8 
 
 9.97516 
 
 I5,i 
 
 19 u 38.71 
 
 336 
 
 .32971 
 
 94,4 
 
 .94408 
 
 33,o 
 
 .51814 
 
 124,4 
 
 97501 
 
 15,2 
 
 19 15 04.97 
 
 337 
 
 .33066 
 
 94,4 
 
 94375 
 
 33,1 
 
 .51938 
 
 124,0 
 
 .97486 
 
 15,2 
 
 19 18 31-24 
 
 .338 
 
 .33160 
 
 94,3 
 
 94342 
 
 33,2 
 
 .52062 
 
 123,6 
 
 97470 
 
 15,3 
 
 19 21 57.50 
 
 339 
 
 .33254 
 
 94,3 
 
 .94309 
 
 33,3 
 
 .52185 
 
 123,2 
 
 97455 
 
 15,3 
 
 19 25 23.77' 
 
 0.340 
 
 0.33349 
 
 94,3 
 
 0.94275 
 
 33,3 
 
 9.52308 
 
 122,8 
 
 9-97440 
 
 15,4 
 
 19 28 50.03 
 
 341 
 
 33443 
 
 94,2 
 
 .94242 
 
 33,4 
 
 .52430 
 
 122,4 
 
 .97424 
 
 15,4 
 
 19 32 16.30! 
 
 342 
 
 .33537 
 
 94,2 
 
 .94209 
 
 33,5 
 
 .52553 
 
 1 22,O 
 
 .97409 
 
 15,5 
 
 19 35 42.56! 
 
 343 
 
 .33631 
 
 94,2 
 
 .94175 
 
 33,6 
 
 .52674 
 
 121,6 
 
 97394 
 
 15,5 
 
 19 39 08.83 
 
 344 
 
 .33726 
 
 94,1 
 
 .94141 
 
 33,7 
 
 .52796 
 
 121,2 
 
 .97378 
 
 15,6 
 
 19 42 35.09 
 
 0.345 
 
 0.33820 
 
 94,1 
 
 0.94108 
 
 33,8 
 
 9.52917 
 
 120,8 
 
 9.97362 
 
 15,6 
 
 19 46 01.36 
 
 346 
 
 .33914 
 
 94,1 
 
 .94074 
 
 ' 33,9 
 
 .53038 
 
 120,5 
 
 97347 
 
 15,7 
 
 19 49 27.62 
 
 347 
 
 .34008 
 
 94,0 
 
 .04040 
 
 34,0 
 
 .53158 
 
 120,1 
 
 .97331 
 
 15,7 
 
 19 52 53.89 
 
 .348 
 
 .34102 
 
 94,0 
 
 .04006 
 
 34,1 
 
 .53278 
 
 H9,7 
 
 .97315 
 
 15,8 
 
 19 56 20.15 
 
 349 
 
 .34196 
 
 94,0 
 
 93972 
 
 34,2 
 
 53397 
 
 119,3 
 
 97300 
 
 15,8 
 
 19 59 46.42 
 
 0.350 
 
 0.34290 
 
 93,9 
 
 0.93937 
 
 34,3 
 
 9.53516 
 
 119,0 
 
 9.97284 
 
 15,9 
 
 20 03 12.68 
 
 u 
 
 -Isinhiu 
 
 Ff 
 
 cosh iu 
 
 Fo' 
 
 . sinh iu 
 
 -Fo' 
 
 log cosh iu 
 
 F ' 
 
 u 
 
 log , 
 
 SMITHSONIAN TABLES 
 
 198 
 
Circular Functions. 
 
 u 
 
 sin u 
 
 Fo' 
 
 cos u 
 
 F ' 
 
 log sin u 
 
 Fo' 
 
 log cos u 
 
 F ' 
 
 u 
 
 0.350 
 
 0.34290 
 
 93,9 
 
 0.93937 
 
 34,3 
 
 9.53516 
 
 119,0 
 
 9.97284 
 
 15,9 
 
 20 03' 12768 
 
 .351 
 
 .34384 
 
 93,9 
 
 .93903 
 
 34,4 
 
 .53635 
 
 118,6 
 
 .97268 
 
 15,9 
 
 20 06 38.95 
 
 .352 
 
 34478 
 
 93,9 
 
 .93869 
 
 34,5 
 
 53754 
 
 118,2 
 
 .97252 
 
 16,0 
 
 20 10 05.21 
 
 353 
 
 34571 
 
 93,8 
 
 .93834 
 
 34,6 
 
 .53872 
 
 117,9 
 
 .97236 
 
 16,0 
 
 20 13 31.48 
 
 354 
 
 .34665 
 
 93,8 
 
 .93799 
 
 34,7 
 
 .53989 
 
 H7,5 
 
 .97220 
 
 16,1 
 
 20 16 57-74 
 
 0-355 
 
 0.34759 
 
 93,8 
 
 0.93765 
 
 34,8 
 
 9.54107 
 
 117,2 
 
 9.97204 
 
 16,1 
 
 2O 20 24.OI 
 
 .356 
 
 .34853 
 
 93,7 
 
 93730 
 
 34,9 
 
 .54224 
 
 116,8 
 
 .97188 
 
 16,1 
 
 20 23 50.27 
 
 357 
 
 .34946 
 
 93,7 
 
 .93695 
 
 34,9 
 
 54340 
 
 116,4 
 
 .97172 
 
 16,2 
 
 2O 27 16.54 
 
 .353 
 
 .35040 
 
 93,7 
 
 .93660 
 
 35,0 
 
 .54457 
 
 116,1 
 
 .97155 
 
 16,2 
 
 2O 3O 42.80 
 
 359 
 
 .35134 
 
 93,6 
 
 .93625 
 
 35,1 
 
 54573 
 
 115,7 
 
 .97139 
 
 16,3 
 
 20 34 09.07 
 
 0.360 
 
 0.35227 
 
 93,6 
 
 0.93590 
 
 35,2 
 
 9.54688 
 
 H5,4 
 
 9.97123 
 
 16,3 
 
 20 37 35-33 
 
 .361 
 
 .35321 
 
 93,6 
 
 .93554 
 
 35,3 
 
 .54803 
 
 H5,o 
 
 .97106 
 
 16,4 
 
 20 41 01. 60 
 
 .362 
 
 .35415 
 
 93,5 
 
 .93519 
 
 35,4 
 
 .54918 
 
 H4,7 
 
 .97000 
 
 16,4 
 
 20 44 27.86 
 
 .363 
 
 .35508 
 
 93,5 
 
 .93484 
 
 35,5 
 
 .55033 
 
 H4,3 
 
 .97074 
 
 16,5 
 
 20 47 54.12 
 
 .364 
 
 .35601 
 
 93,4 
 
 93448 
 
 35,6 
 
 .55147 
 
 114,0 
 
 97057 
 
 16,5 
 
 20 51 20.39 
 
 0.365 
 
 0.35095 
 
 93,4 
 
 0.93412 
 
 35,7 
 
 9.55261 
 
 H3,7 
 
 9.97040 
 
 16,6 
 
 20 54 46.65 
 
 .366 
 
 .35788 
 
 93,4 
 
 93377 
 
 35,8 
 
 .55374 
 
 H3,3 
 
 .97024 
 
 16,6 
 
 20 58 12.92 
 
 .367 
 
 .35882 
 
 93,3 
 
 .93341 
 
 35,9 
 
 .55487 
 
 H3,o 
 
 .97007 
 
 16,7 
 
 21 01 39.18 
 
 .368 
 
 35975 
 
 93,3 
 
 .93305 
 
 36,0 
 
 .55600 
 
 112,6 
 
 .96990 
 
 16,7 
 
 21 05 05.45 
 
 .369 
 
 .36068 
 
 93,3 
 
 .93269 
 
 36,1 
 
 .55713 
 
 112,3 
 
 .96974 
 
 16,8 
 
 21 08 3L7I 
 
 0.370 
 
 0.36162 
 
 93,2 
 
 0.93233 
 
 36,2 
 
 9.55825 
 
 1 1 2,0 
 
 9.96957 
 
 16,8 
 
 21 II 57.98 
 
 371 
 
 .36255 
 
 93,2 
 
 .93197 
 
 36,3 
 
 55937 
 
 111,6 
 
 .96940 
 
 16,9 
 
 21 15 24.24 
 
 372 
 
 .36348 
 
 93,2 
 
 .93i6o 
 
 36,3 
 
 .56048 
 
 in,3 
 
 .06923 
 
 16,9 
 
 21 18 50.51 
 
 373 
 
 .36441 
 
 93,1 
 
 .93124 
 
 36,4 
 
 .56159 
 
 III.O 
 
 .96906 
 
 17,0 
 
 21 22 16.77 
 
 374 
 
 .36534 
 
 93,1 
 
 .93087 
 
 36,5 
 
 .56270 
 
 110,7 
 
 .96889 
 
 17,0 
 
 21 25 43.04 
 
 0.375 
 
 0.36627 
 
 93,1 
 
 0.93051 
 
 36,6 
 
 9-56380 
 
 110,3 
 
 9.96872 
 
 -17,1 
 
 21 29 09.30 
 
 .376 
 
 .36720 
 
 93,0 
 
 .93014 
 
 36,7 
 
 .56491 
 
 110,0 
 
 95855 
 
 i7,i 
 
 21 32 35-57 
 
 377 
 
 .36813 
 
 93,0 
 
 .92977 
 
 36,8 
 
 .56600 
 
 109,7 
 
 .96838 
 
 17,2 
 
 21 36 01.83 
 
 .378 
 
 .36906 
 
 92,9 
 
 .92940 
 
 36,9 
 
 .56710 
 
 109,4 
 
 .96820 
 
 17,2 
 
 21 39 28.10 
 
 379 
 
 .36999 
 
 92,9 
 
 .92904 
 
 37,0 
 
 .56819 
 
 109,0 
 
 .96803 
 
 17,3 
 
 21 42 54.36 
 
 0.380 
 
 0.37092 
 
 92,9 
 
 0.92866 
 
 37,1 
 
 9.56928 
 
 108,7 
 
 9.96786 
 
 17,3 
 
 21 46 20.63 
 
 .381 
 
 .37185 
 
 92,8 
 
 .92829 
 
 37,2 
 
 .57037 
 
 108,4 
 
 .96769 
 
 17,4 
 
 21 49 46.89 
 
 .382 
 
 .37278 
 
 92,8 
 
 .92792 
 
 37,3 
 
 .57145 
 
 108,1 
 
 .96751 
 
 i7;4 
 
 21 53 13.16 
 
 .383 
 
 37370 
 
 92,8 
 
 .92755 
 
 37,4 
 
 .57253 
 
 107,8 
 
 .96734 
 
 17,5 
 
 21 56 39-42 
 
 .384 
 
 .37463 
 
 92,7 
 
 .92717 
 
 37,5 
 
 .57361 
 
 107,5 
 
 .96716 
 
 17,5 
 
 22 OO 05.69 
 
 0.385 
 
 0.37556 
 
 92,7 
 
 0.92680 
 
 37,6 
 
 9.57468 
 
 107,2 
 
 9.96699 
 
 17,6 
 
 22 03 3L95 
 
 .386 
 
 .37649 
 
 92,6 
 
 .92642 
 
 37,6 
 
 57575 
 
 106,9 
 
 .96681 
 
 17,6 
 
 22 06 58.22 
 
 .387 
 
 37741 
 
 92,6 
 
 .92605 
 
 37,7 
 
 .57682 
 
 106,6 
 
 .96663 
 
 17,7 
 
 22 IO 24.48 
 
 .388 
 
 .37834 
 
 92,6 
 
 .92567 
 
 37,8 
 
 .57788 
 
 106,3 
 
 .96646 
 
 17,8 
 
 22 13 50-74 
 
 .389 
 
 .37926 
 
 .92,5 
 
 .92529 
 
 37,9 
 
 .57894 
 
 106,0 
 
 .96628 
 
 17,8 
 
 22 17 17.01 
 
 0.390 
 
 0.38019 
 
 92,5 
 
 0.92491 
 
 38,0 
 
 9.58000 
 
 105,7 
 
 9.96610 
 
 17,9 
 
 22 20 43.27 
 
 391 
 
 .38111 
 
 92,5 
 
 .92453 
 
 38,1 
 
 .58105 
 
 105,4 
 
 .06592 
 
 17,9 
 
 22 24 09.54 
 
 392 
 
 .38204 
 
 92,4 
 
 .92415 
 
 38,2 
 
 .58211 
 
 105,1 
 
 .96574 
 
 18,0 
 
 22 27 35.80 
 
 393 
 
 .38206 
 
 92,4 
 
 .92376 
 
 38,3 
 
 .58316 
 
 104,8 
 
 .96556 
 
 18,0 
 
 22 31 02.O7 
 
 394 
 
 .38389 
 
 92,3 
 
 92338 
 
 38,4 
 
 .58420 
 
 104,5 
 
 .96538 
 
 18,1 
 
 22 34 28.33 
 
 0.395 
 
 0.38481 
 
 92,3 
 
 0.92300 
 
 38,5 
 
 9-58524 
 
 104,2 
 
 9-96520 
 
 18,1 
 
 22 37 54.60 
 
 .396 
 
 .38573 
 
 92,3 
 
 .92261 
 
 38,6 
 
 .58628 
 
 103,9 
 
 .06502 
 
 18,2 
 
 22 41 2O.86 
 
 397 
 
 .38665 
 
 92,2 
 
 .92223 
 
 38,7 
 
 .58732 
 
 103,6 
 
 .96484 
 
 18,2 
 
 22 44 47.13 
 
 -398 
 
 .38758 
 
 92,2 
 
 .92184 
 
 38,8 
 
 .58836 
 
 103,3 
 
 .96465 
 
 18,3 
 
 22 48 13.39 
 
 399 
 
 .38850 
 
 92,1 
 
 .92145 
 
 38,8 
 
 .58939 
 
 103,0 
 
 .96447 
 
 18,3 
 
 22 51 39.66 
 
 0.400 
 
 0.38942 
 
 92,1 
 
 0.92106 
 
 38,9 
 
 9.59042 
 
 102,7 
 
 9.96429 
 
 18,4 
 
 22 55 05.92 
 
 u 
 
 -isinhiu 
 
 -Fo' 
 
 cosh iu 
 
 Fo' 
 
 sinh iu 
 
 co Fo' 
 
 log cosh iu 
 
 FO' 
 
 u 
 
 loo . 
 
 SMITHSONIAN TABLES 
 
 199 
 
Circular Functions. 
 
 u 
 
 sin u 
 
 F ' 
 
 cos u 
 
 F ' 
 
 log sin u 
 
 Fo' 
 
 log cos u 
 
 "Fo' 
 
 u 
 
 0.400 
 
 0.38942 
 
 92,1 
 
 0.92106 
 
 38,9 
 
 9.59042 
 
 102,7 
 
 9.96429 
 
 18,4 
 
 2255 / 05 / . / 92 
 
 .401 
 
 .39034 
 
 92,1 
 
 .92067 
 
 39,0 
 
 .59144 
 
 102,4 
 
 .96410 
 
 18,4 
 
 22 58 32.19 
 
 .402 
 
 .39126 
 
 92,0 
 
 .92028 
 
 39,1 
 
 .59247 
 
 IO2,2 
 
 .96392 
 
 18,5 
 
 23 oi 58.45 
 
 .403 
 
 .39218 
 
 92,0 
 
 .91989 
 
 39,2 
 
 59349 
 
 101,9 
 
 .96374 
 
 18,5 
 
 23 05 24.72 
 
 .404 
 
 .39310 
 
 9i,9 
 
 .91950 
 
 39,3 
 
 .59450 
 
 101,6 
 
 .96355 
 
 18,6 
 
 23 08 50.98 
 
 0.405 
 
 0.30402 
 
 9i,9 
 
 0.91910 
 
 39,4 
 
 9.59552 
 
 101,3 
 
 9.96336 
 
 18,6 
 
 23 12 17.25 
 
 .406 
 
 .39494 
 
 9i,9 
 
 .91871 
 
 39,5 
 
 .59653 
 
 101,0 
 
 .96318 
 
 18,7 
 
 23 15 43.51 
 
 .407 
 
 39586 
 
 91,8 
 
 .91831 
 
 39,6 
 
 59754 
 
 100,7 
 
 .96299 
 
 18,7 
 
 23 19 09.78 
 
 .408 
 
 .39677 
 
 91,8 
 
 .91792 
 
 39,7 
 
 .59854 
 
 100,5 
 
 .96280 
 
 18,8 
 
 23 22 36.04 
 
 .409 
 
 .39769 
 
 91,8 
 
 .91752 
 
 39,8 
 
 55955 
 
 100,2 
 
 .96262 
 
 18,8 
 
 23 26 O2.3I 
 
 0.410 
 
 0.30861 
 
 91,7 
 
 0.91712 
 
 39,9 
 
 9.60055 
 
 99,9 
 
 9.96243 
 
 18,9 
 
 23 29 28.57 
 
 .411 
 
 39953 
 
 9i,7 
 
 .91672 
 
 40,0 
 
 .60155 
 
 99,6 
 
 .96224 
 
 18,9 
 
 23 32 54.84 
 
 .412 
 
 .40044 
 
 91,6 
 
 .91632 
 
 40,0 
 
 .60254 
 
 99,4 
 
 .96205 
 
 I9,o 
 
 23 36 21.10 
 
 .413 
 
 .40136 
 
 91,6 
 
 .91592 
 
 40,1 
 
 .60353 
 
 99,i 
 
 .96186 
 
 19,0 
 
 23 39 47.36 
 
 .414 
 
 .40227 
 
 91,6 
 
 .91552 
 
 40,2 
 
 .60452 
 
 98,8 
 
 .96167 
 
 19,1 
 
 23 43 13.63 
 
 0.415 
 
 0.40319 
 
 9i,5 
 
 0.91512 
 
 40,3 
 
 9.60551 
 
 98,6 
 
 9.96148 
 
 19,1 
 
 23 46 39.89 
 
 .416 
 
 .40410 
 
 9i,5 
 
 .91471 
 
 40,4 
 
 .60649 
 
 98,3 
 
 .96128 
 
 19,2 
 
 23 50 06. 16 
 
 .417 
 
 .40502 
 
 91,4 
 
 .91431 
 
 40,5 
 
 .60748 
 
 98,0 
 
 .96109 
 
 19,2 
 
 23 53 32.42 
 
 .418 
 
 40593 
 
 9i,4 
 
 .91390 
 
 40,6 
 
 .60845 
 
 97,8 
 
 .96090 
 
 19,3 
 
 23 56 58.69 
 
 .419 
 
 .40685 
 
 9i,3 
 
 .91350 
 
 40,7 
 
 .60943 
 
 97,5 
 
 .96071 
 
 19,3 
 
 24 oo 24-95 
 
 0.420 
 
 0.40776 
 
 9i,3 
 
 0.91309 
 
 40,8 
 
 9.61041 
 
 97,3 
 
 9.90051 
 
 19,4 
 
 24 03 51.22 
 
 .421 
 
 .40867 
 
 9i,3 
 
 .91268 
 
 40,9 
 
 .61138 
 
 97,o 
 
 .96032 
 
 19,4 
 
 24 07 17-48 
 
 .422 
 
 .40959 
 
 91,2 
 
 .91227 
 
 41,0 
 
 .61234 
 
 96,7 
 
 .96012 
 
 19,5 
 
 24 10 43-75 
 
 .423 
 
 .41050 
 
 91,2 
 
 .91186 
 
 41,0 
 
 .61331 
 
 96,5 
 
 .95993 
 
 19,6 
 
 24 14 10.01 
 
 .424 
 
 .41141 
 
 91,1 
 
 .91145 
 
 41,1 
 
 .61427 
 
 96,2 
 
 95973 
 
 19,6 
 
 24 17 36.28 
 
 0.425 
 
 0.41232 
 
 91,1 
 
 0.91104 
 
 41,2 
 
 9.61524 
 
 96,0 
 
 9.95954 
 
 19,7 
 
 24 21 02.54 
 
 .426 
 
 .41323 
 
 91,1 
 
 .91063 
 
 41,3 
 
 .61619 
 
 95,7 
 
 95934 
 
 19,7 
 
 24 24 28.8l 
 
 .427 
 
 .41414 
 
 91,0 
 
 .91021 
 
 41,4 
 
 .61715 
 
 95,5 
 
 .95914 
 
 19,8 
 
 24 27 55.07 
 
 .428 
 
 .41505 
 
 91,0 
 
 .90980 
 
 41,5 
 
 .61810 
 
 95,2 
 
 .95894 
 
 19,8 
 
 24 31 21.34 
 
 .429 
 
 41596 
 
 90,9 
 
 .90938 
 
 41,6 
 
 .61905 
 
 94,9 
 
 .95875 
 
 19,9 
 
 24 34 47.60 
 
 0.430 
 
 0.41687 
 
 90,9 
 
 0.00897 
 
 41,7 
 
 9.62000 
 
 947 
 
 9.95855 
 
 19,9 
 
 24 38 13.87 
 
 .431 
 
 .41778 
 
 90,9 
 
 .90855 
 
 41,8 
 
 .62095 
 
 94,4 
 
 .95835 
 
 20,0 
 
 24 41 40. 13 
 
 .432 
 
 .41869 
 
 90,8 
 
 .90813 
 
 4i,9 
 
 .62189 
 
 94,2 
 
 .95815 
 
 20,0 
 
 24 45 06.40 
 
 433 
 
 .41960 
 
 90,8 
 
 .00771 
 
 42,0 
 
 .62283 
 
 94,0 
 
 95795 
 
 20,1 
 
 24 48 32.66 
 
 434 
 
 .42050 
 
 90,7 
 
 .90729 
 
 42,1 
 
 .62377 
 
 93,7 
 
 95775 
 
 20,1 
 
 24 51 58.93 
 
 0.435 
 
 0.42141 
 
 90,7 
 
 0.90687 
 
 42,1 
 
 9.62471 
 
 93,5 
 
 9-95755 
 
 20,2 
 
 24 55 25.19 
 
 .436 
 
 .42232 
 
 90,6 
 
 .90645 
 
 42,2 
 
 .62564 
 
 93,2 
 
 95734 
 
 20,2 
 
 24 58 51.46 
 
 437 
 
 .42322 
 
 90,6 
 
 .00603 
 
 42,3 
 
 .62657 
 
 93,0 
 
 95714 
 
 20,3 
 
 25 02 17.72 
 
 .438 
 
 .42413 
 
 90,6 
 
 .90560 
 
 42,4 
 
 .62750 
 
 92,8 
 
 .95094 
 
 20,3 
 
 25 05 43-99 
 
 439 
 
 .42503 
 
 90,5 
 
 .90518 
 
 42,5 
 
 .62842 
 
 92,5 
 
 .95673 
 
 .20,4 
 
 25 09 10.25 
 
 0.440 
 
 0.42594 
 
 90,5 
 
 0.90475 
 
 42,6 
 
 9-62935 
 
 92,2 
 
 9.95653 
 
 20,4 
 
 25 12 36.51 
 
 .441 
 
 .42684 
 
 90,4 
 
 .90433 
 
 42,7 
 
 .63027 
 
 92,0 
 
 .95632 
 
 20,5 
 
 25 16 02.78 
 
 .442 
 
 .42775 
 
 90,4 
 
 .00390 
 
 42,8 
 
 .63119 
 
 9i,8 
 
 .95612 
 
 20,6 
 
 25 19 29.04 
 
 443 
 
 .42865 
 
 90,3 
 
 .90347 
 
 42,9 
 
 .63210 
 
 9i,5 
 
 95591 
 
 20,6 
 
 25 22 55.31 
 
 .444 
 
 .42956 
 
 90,3 
 
 .90304 
 
 43,0 
 
 .63302 
 
 9i,3 
 
 95571 
 
 20,7 
 
 25 26 21.57 
 
 0.445 
 
 0.43046 
 
 90,3 
 
 0.90261 
 
 43,0 
 
 9.63393 
 
 91,1 
 
 9.95550 
 
 20,7 
 
 25 29 47.84 
 
 .446 
 
 .43136 
 
 90,2 
 
 .90218 
 
 43,1 
 
 .63484 
 
 90,8 
 
 .95529 
 
 20,8 
 
 25 33 14.10 
 
 447 
 
 .43226 
 
 90,2 
 
 .90175 
 
 43,2 
 
 .6^575 
 
 00,6 
 
 95509 
 
 20,8 
 
 25 36 40.37 
 
 .448 
 
 .43316 
 
 00,1 
 
 .90132 
 
 43,3 
 
 .63665 
 
 90,4 
 
 .65488 
 
 20,9 
 
 25 40 06.63 
 
 .449 
 
 .43406 
 
 90,1 
 
 .90088 
 
 43,4 
 
 .63755 
 
 90,i 
 
 .95467 
 
 20,9 
 
 25 43 32.90 
 
 0.450 
 
 0.43497 
 
 90,0 
 
 0.90045 
 
 43,5' 
 
 9.63845 
 
 89,9 
 
 9.95446 
 
 21,0 
 
 25 46 59.16 
 
 u 
 
 isinhiu 
 
 F ' 
 
 cosh iu 
 
 F O ' 
 
 i on $lnh lu 
 100 , 
 
 F ' 
 
 oo cosh iu 
 
 F O ' 
 
 u 
 
 SMITHSONIAN TABLES 
 
 2OO 
 
Circular Functions. 
 
 u 
 
 sin u 
 
 F ' 
 
 cos u 
 
 Fo' 
 
 log sin u 
 
 Fo' 
 
 log cos u 
 
 F O ' 
 
 u 
 
 0.450 
 
 0.43497 
 
 00,0 
 
 0.90045 
 
 43,5 
 
 9.63845 
 
 89,9 
 
 9.95446 
 
 21,0 
 
 2546 / 59 / .'i6 
 
 .451 
 
 .43587 
 
 00,0 
 
 .90001 
 
 43,6 
 
 .63935 
 
 89,7 
 
 .95425 
 
 21,0 
 
 25 50 25.43 
 
 .452 
 
 .43677 
 
 90,0 
 
 .89958 
 
 43,7 
 
 .64025 
 
 89,4 
 
 .95404 
 
 21,1 
 
 25 53 51.69 
 
 453 
 
 .43766 
 
 89,9 
 
 
 43,8 
 
 .64114 
 
 89,2 
 
 .95383 
 
 21,1 
 
 25 57 17.96 
 
 454 
 
 .43856 
 
 89,9 
 
 .89870 
 
 43,9 
 
 .64203 
 
 89,0 
 
 .95361 
 
 21,2 
 
 26 oo 44.22 
 
 0.455 
 
 0.43946 
 
 89,8 
 
 0.89826 
 
 43,9 
 
 9.64292 
 
 88,8 
 
 9-95340 
 
 21,2 
 
 26 04 10.49 
 
 .456 
 
 .44036 
 
 89,8 
 
 .89782 
 
 44,0 
 
 .64381 
 
 88,5 
 
 .95319 
 
 21,3 
 
 26 07 36.75 
 
 457 
 
 .44126 
 
 89,7 
 
 .89738 
 
 44,1 
 
 .64469 
 
 88,3 
 
 .95298 
 
 21,4 
 
 26 ii 03.02 
 
 .458 
 
 .44216 
 
 89,7 
 
 .89694 
 
 44,2 
 
 .64557 
 
 88,1 
 
 .95276 
 
 21,4 
 
 26 14 29.28 
 
 459 
 
 .44305 
 
 89,6 
 
 .89650 
 
 44,3 
 
 .64645 
 
 87,9 
 
 .95255 
 
 21,5 
 
 26 17 55-55 
 
 0.460 
 
 0.44395 
 
 89,6 
 
 0.89605 
 
 44,4 
 
 9.64733 
 
 87,7 
 
 9.95233 
 
 21,5 
 
 26 21 21. 8l 
 
 .461 
 
 .44484 
 
 89,6 
 
 .89561 
 
 44,5 
 
 .64821 
 
 87,4 
 
 .95212 
 
 21,6 
 
 26 24 48.08 
 
 .462 
 
 44574 
 
 89,5 
 
 .89516 
 
 44,6 
 
 .64908 
 
 87,2 
 
 .95100 
 
 21,6 
 
 26 28 14.34 
 
 .463 
 
 .44663 
 
 89,5 
 
 .89472 
 
 44,7 
 
 .64995 
 
 87,0 
 
 .95169 
 
 21,7 
 
 26 31 40.6l 
 
 .464 
 
 44753 
 
 89,4 
 
 .89427 
 
 44,8 
 
 .65082 
 
 86,8 
 
 .95147 
 
 21,7 
 
 26 35 06.87 
 
 0.465 
 
 0.44842 
 
 89,4 
 
 0.89382 
 
 44,8 
 
 9.65169 
 
 86,6 
 
 9.95125 
 
 21,8 
 
 26 38 33-13 
 
 .466 
 
 .44932 
 
 89,3 
 
 .89337 
 
 44,9 
 
 .65255 
 
 86,4 
 
 .95103 
 
 21,8 
 
 26 41 59.40 
 
 .467 
 
 .45021 
 
 89,3 
 
 .89292 
 
 45,0 
 
 .65341 
 
 86,1 
 
 .95081 
 
 21,9 
 
 26 45 25.66 
 
 .468 
 
 .4$no 
 
 89,2 
 
 .89247 
 
 45,i 
 
 .65428 
 
 85,9 
 
 .95059 
 
 22,0 
 
 26 48 51.93 
 
 .469 
 
 45199 
 
 89,2 
 
 .89202 
 
 45,2 
 
 .65513 
 
 85,7 
 
 .95037 
 
 22,0 
 
 26 52 18.19 
 
 0.470 
 
 0.45289 
 
 89,2 
 
 0.89157 
 
 45,3 
 
 9.65599 
 
 85,5 
 
 9.95015 
 
 22,1 
 
 26 55 44.46 
 
 .471 
 
 45378 
 
 89,1 
 
 .89111 
 
 45,4 
 
 .65684 
 
 85,3 
 
 94993 
 
 22,1 
 
 26 59 10.72 
 
 .472 
 
 .45467 
 
 89,1 
 
 .89066 
 
 45,5 
 
 .65769 
 
 85,1 
 
 .94971 
 
 22,2 
 
 27 02 36.99 
 
 473 
 
 .45556 
 
 89,0 
 
 .80021 
 
 45,6 
 
 65854 
 
 84,9 
 
 .94949 
 
 22,2 
 
 27 06 03.25 
 
 474 
 
 .45645 
 
 89,0 
 
 .88975 
 
 45,6 
 
 .65939 
 
 84,7 
 
 .94927 
 
 22,3 
 
 27 09 29.52 
 
 0.475 
 
 0.4573'4 
 
 88,9 
 
 0.88929 
 
 45,7 
 
 9.66024 
 
 84,4 
 
 9.94904 
 
 22,3 
 
 27 12 55.78 
 
 .476 
 
 .45823 
 
 88,9 
 
 .88883 
 
 45,8 
 
 .66108 
 
 84,2 
 
 .94882 
 
 22,4 
 
 27 16 22.05 
 
 477 
 
 .45912 
 
 88,8 
 
 .88838 
 
 45,9 
 
 .66192 
 
 84,0 
 
 .94860 
 
 22,4 
 
 27 19 48.31 
 
 .478 
 
 .46000 
 
 88,8 
 
 .88792 
 
 46,0 
 
 .66276 
 
 83,8 
 
 .94837 
 
 22,5 
 
 27 23 14.58 
 
 .479 
 
 .46089 
 
 88,7 
 
 .88746 
 
 46,1 
 
 .66360 
 
 83,6 
 
 .94815 
 
 22,6 
 
 27 26 40.84 
 
 0.480 
 
 0.46178 
 
 88,7 
 
 0.88699 
 
 46,2 
 
 9-66443 
 
 83,4 
 
 9.94792 
 
 22,6 
 
 27 30 07.11 
 
 .481 
 
 .46267 
 
 88,7 
 
 .88653 
 
 46,3 
 
 .66527 
 
 83,2 
 
 .94769 
 
 22,7 
 
 27 33 33-37 
 
 .482 
 
 .46355 
 
 88,6 
 
 .88607 
 
 46,4 
 
 .66610 
 
 83,0 
 
 .94747 
 
 22,7 
 
 27 36 59.64 
 
 .483 
 
 .46444 
 
 88,6 
 
 .88561 
 
 46,4 
 
 .66693 
 
 82,8 
 
 .94724 
 
 22,8 
 
 27 40 25.90 
 
 .484 
 
 .46532 
 
 88,5 
 
 .88514 
 
 46,5 
 
 .66775 
 
 82,6 
 
 94701 
 
 22,8 
 
 27 43 52.17 
 
 0.485 
 
 0.46621 
 
 88,5 
 
 0.88467 
 
 46,6 
 
 9.66858 
 
 82,4 
 
 9.94678 
 
 22,9 
 
 27 47 18.43 
 
 .486 
 
 .46709 
 
 88,4 
 
 .88421 
 
 46,7 
 
 .66940 
 
 82,2 
 
 .94655 
 
 22,9 
 
 27 50 44-70 
 
 .487 
 
 .46798 
 
 88,4 
 
 .88374 
 
 46,8 
 
 .67022 
 
 82,0 
 
 .94633 
 
 23,0 
 
 27 54 10.96 
 
 .488 
 
 .46886 
 
 88,3 
 
 .88327 
 
 46,9 
 
 .67104 
 
 81,8 
 
 .94609 
 
 23,1 
 
 27 57 37.23 
 
 .489 
 
 .46974 
 
 88,3 
 
 .88280 
 
 47,o 
 
 .67186 
 
 81,6 
 
 .94586 
 
 23,1 
 
 28 01 03.49 
 
 0.400 
 
 0.47063 
 
 88,2 
 
 0.88233 
 
 47,1 
 
 9.67268 
 
 81,4 
 
 9.94563 
 
 23,2 
 
 28 04 29.76 
 
 .491 
 
 .47151 
 
 88,2 
 
 .88186 
 
 47,2 
 
 .67349 
 
 81,2 
 
 94540 
 
 23,2 
 
 28 07 56.02 
 
 492 
 
 .47239 
 
 88,1 
 
 .88139 
 
 47,2 
 
 .67430 
 
 81,0 
 
 .94517 
 
 23,3 
 
 28 ii 22.28 
 
 493 
 
 47327 
 
 88,1 
 
 .88092 
 
 47,3 
 
 .67511 
 
 80,8 
 
 94493 
 
 23,3 
 
 28 14 48.55 
 
 494 
 
 .47415 
 
 88,0 
 
 .88044 
 
 47,4 
 
 .67592 
 
 80,6 
 
 94470 
 
 23,4 
 
 28 18 14.81 
 
 0-495 
 
 0.47503 
 
 88,0 
 
 0.87997 
 
 47,5 
 
 9.67672 
 
 80,5 
 
 9.94447 
 
 23,4 
 
 28 21 41.08 
 
 .496 
 
 .47591 
 
 87,9 
 
 .87949 
 
 47,6 
 
 .67753 
 
 80,3 
 
 .94423 
 
 23,5 
 
 28 25 07.34 
 
 497 
 
 .47679 
 
 87,9 
 
 .87902 
 
 47,7 
 
 .67833 
 
 80, i 
 
 .94400 
 
 23,6 
 
 28 28 33.61 
 
 .498 
 
 .47767 
 
 87,9 
 
 .87854 
 
 47,8 
 
 .67913 
 
 79,9 
 
 .94376 
 
 23,6 
 
 28 31 59.87 
 
 .499 
 
 .47855 
 
 87,8 
 
 .87806 
 
 47,9 
 
 .67993 
 
 79,7 
 
 .94352 
 
 23,7 
 
 28 35 26.14 
 
 0.500 
 
 0.47943 
 
 87,8 
 
 0.87758 
 
 47,9 
 
 9.68072 
 
 79,5 
 
 9.94329 
 
 23,7 
 
 28 38 52.40 
 
 u 
 
 -isinhiu 
 
 F ' 
 
 cosh iu 
 
 F ' 
 
 , *nh " 
 
 wF ' 
 
 log cosh iu 
 
 F ' 
 
 u 
 
 loo . 
 
 SMITHSONIAN TABLES 
 
 201 
 
Circular Functions. 
 
 u 
 
 sin u 
 
 F.' 
 
 cos u 
 
 <> Fo' 
 
 log sin u 
 
 Fo' 
 
 log cos u 
 
 F f ' 
 
 n 
 
 u 
 
 
 
 
 
 
 
 
 
 
 O / 94 
 
 0.500 
 
 0.47943 
 
 87,8 
 
 0.87758 
 
 47,9 
 
 9.68072 
 
 79,5 
 
 9.94329 
 
 23,7 
 
 28 38 52.40 
 
 .501 
 
 .48030 
 
 87,7 
 
 .87710 
 
 48,0 
 
 .68152 
 
 79,3 
 
 94305 
 
 23,8 
 
 28 42 18.67 
 
 .502 
 
 .48118 
 
 87,7 
 
 .87662 
 
 48,1 
 
 .68231 
 
 79,1 
 
 .94281 
 
 23,8 
 
 28 45 44-93 
 
 .503 
 
 .48206 
 
 87,6 
 
 .87614 
 
 48,2 
 
 .68310 
 
 78,9 
 
 .94257 
 
 23,9 
 
 28 49 i i . 20 
 
 .504 
 
 .48293 
 
 87,6 
 
 .87566 
 
 48,3 
 
 .68389 
 
 78,7 
 
 .94233 
 
 24,0 
 
 28 52 37.46 
 
 0.505 
 
 0.48381 
 
 87,5 
 
 0.87517 
 
 48,4 
 
 9.68467 
 
 78,6 
 
 9.94209 
 
 24,0 
 
 28 56 03-73 
 
 .506 
 
 .48468 
 
 87,5 
 
 .87469 
 
 48,5 
 
 .68546 
 
 78,4 
 
 .94185 
 
 24,1 
 
 28 59 29.99 
 
 .507 
 
 .48556 
 
 87,4 
 
 .87421 
 
 48,6 
 
 .68624 
 
 78,2 
 
 .94161 
 
 24,1 
 
 29 02 56.26 
 
 .508 
 
 .48643 
 
 87,4 
 
 .87372 
 
 48,6 
 
 .68702 
 
 78,0 
 
 .94137 
 
 24,2 
 
 29 06 22.52 
 
 .509 
 
 .48730 
 
 87,3 
 
 .87323 
 
 48,7 
 
 .68780 
 
 77,8 
 
 .94H3 
 
 24,2 
 
 29 09 48.79 
 
 0.510 
 
 0.48818 
 
 87,3 
 
 0.87274 
 
 48,8 
 
 9.68858 
 
 77,6 
 
 9.94089 
 
 24,3 
 
 29 13 15.05 
 
 .511 
 
 .48905 
 
 87,2 
 
 .87226 
 
 48,9 
 
 .68935 
 
 77,5 
 
 .94064 
 
 24,3 
 
 29 16 41.32 
 
 .512 
 
 .48992 
 
 87,2 
 
 .87177 
 
 49,0 
 
 .69013 
 
 77,3 
 
 .94040 
 
 24,4 
 
 29 20 07.58 
 
 .513 
 
 .49079 
 
 87,1 
 
 .87128 
 
 49J 
 
 .69090 
 
 77,i 
 
 .94016 
 
 24,5 
 
 29 23 33.85 
 
 .514 
 
 .49166 
 
 87,1 
 
 .87078 
 
 49,2 
 
 .69167 
 
 76,9 
 
 .93991 
 
 24,5 
 
 29 27 oo.ii 
 
 0.515 
 
 0.49253 
 
 87,0 
 
 0.87029 
 
 49,3 
 
 9.69244 
 
 76,7 
 
 9.93967 
 
 24,6 
 
 29 30 26.38 
 
 .516 
 
 .49340 
 
 87,0 
 
 .86980 
 
 49,3 
 
 .69320 
 
 76,6 
 
 93942 
 
 24,6 
 
 29 33 52.64 
 
 .517 
 
 .49427 
 
 86,9 
 
 .86931 
 
 49,4 
 
 .69397 
 
 76,4 
 
 .93917 
 
 24,7 
 
 29 37 18.90 
 
 .518 
 
 .495H 
 
 86,9 
 
 .86881 
 
 49,5 
 
 .69473 
 
 76,2 
 
 .93893 
 
 24,8 
 
 29 40 45-17 
 
 .519 
 
 .49601 
 
 86,8 
 
 .86832 
 
 49,6 
 
 .69549 
 
 76,0 
 
 .93868 
 
 24,8 
 
 29 44 U.43 
 
 0.520 
 
 0.49688 
 
 86,8 
 
 0.86782 
 
 49,7 
 
 9.69625 
 
 75,9 
 
 9.93&43 
 
 24,9 
 
 29 47 37-70 
 
 .521 
 
 49775 
 
 86,7 
 
 .86732 
 
 49,8 
 
 .69701 
 
 75,7 
 
 .938l8 
 
 24,9 
 
 29 51 03.96 
 
 .522 
 
 .49861 
 
 86,7 
 
 .86682 
 
 49,9 
 
 .69777 
 
 75,5 
 
 93793 
 
 25,0 
 
 29 54 30.23 
 
 .523 
 
 .49948 
 
 86,6 
 
 .86632 
 
 49,9 
 
 .69852 
 
 75,3 
 
 .93768 
 
 25,0 
 
 29 57 56.49 
 
 .524 
 
 .50035 
 
 86,6 
 
 .86582 
 
 50,0 
 
 .69927 
 
 75,2 
 
 93743 
 
 25,1 
 
 30 01 22.76 
 
 0.525 
 
 0.50121 
 
 86,5 
 
 0.86532 
 
 50,1 
 
 9.70002 
 
 75,o 
 
 9.93718 
 
 25,2 
 
 30 04 49-02 
 
 .526 
 
 .50208 
 
 86,5 
 
 .86482 
 
 50,2 
 
 .70077 
 
 74,8 
 
 .93603 
 
 25,2 
 
 30 08 15.29 
 
 .527 
 
 .50294 
 
 86,4 
 
 .86432 
 
 50,3 
 
 .70152 
 
 74,6 
 
 .93667 
 
 25,3 
 
 30 n 41-55 
 
 .528 
 
 50381 
 
 86,4 
 
 .86382 
 
 50,4 
 
 .70226 
 
 74,5 
 
 .93642 
 
 25,3 
 
 30 15 07.82 
 
 .529 
 
 .50467 
 
 86,3 
 
 .86331 
 
 50,5 
 
 .70301 
 
 74,3 
 
 .93617 
 
 25,4 
 
 30 18 34.08 
 
 0.530 
 
 0.50553 
 
 86,3 
 
 0.86281 
 
 50,6 
 
 9.70375 
 
 74,1 
 
 9.93591 
 
 25,4 
 
 3O 22 OO.35 
 
 .531 
 
 .50640 
 
 86,2 
 
 .86230 
 
 50,6 
 
 .70449 
 
 74,0 
 
 .93566 
 
 25,5 
 
 30 25 26.61 
 
 .532 
 
 .50726 
 
 86,2 
 
 .86179 
 
 50,7 
 
 .70523 
 
 73,8 
 
 93540 
 
 25,6 
 
 30 28 52.88 
 
 533 
 
 .50812 
 
 86,1 
 
 .86129 
 
 50,8 
 
 .70597 
 
 73,6 
 
 .93515 
 
 25,6 
 
 30 32 19.14 
 
 .534 
 
 .50898 
 
 86,1 
 
 .86078 
 
 50,9 
 
 .70670 
 
 73,4 
 
 .93489 
 
 25,7 
 
 30 35 45-41 
 
 0.535 
 
 0.50984 
 
 86,0 
 
 0.86027 
 
 5i,o 
 
 9.70743 
 
 73,3 
 
 9.93463 
 
 25,7 
 
 30 39 11.67 
 
 -536 
 
 .51070 
 
 86,0 
 
 .85976 
 
 51,1 
 
 .70817 
 
 73,1 
 
 .93438 
 
 25,8 
 
 30 42 37-94 
 
 537 
 
 .51156 
 
 85,9 
 
 .85925 
 
 51,2 
 
 .70890 
 
 72,9 
 
 .93412 
 
 25,9 
 
 30 46 04.20 
 
 .538 
 
 .51242 
 
 85,9 
 
 .85874 
 
 51,2 
 
 .70063 
 
 72,8 
 
 .93386 
 
 25,9 
 
 30 49 30-47 
 
 .539 
 
 .5U28 
 
 85,8 
 
 .85822 
 
 51,3 
 
 .71035 
 
 72,6 
 
 .93360 
 
 26,0 
 
 30 52 56.73 
 
 0.540 
 
 O.SMH 
 
 85,8 
 
 0.85771 
 
 51,4 
 
 9.71108 
 
 72,5 
 
 9-93334 
 
 26,0 
 
 30 56 23.00 
 
 541 
 
 .51499 
 
 85,7 
 
 .85719 
 
 51,5 
 
 .71180 
 
 72,3 
 
 .93308 
 
 26,1 
 
 30 59 49.26 
 
 .542 
 
 .51585 
 
 85,7 
 
 .85668 
 
 5i,6 
 
 .71252 
 
 72,1 
 
 .93282 
 
 26,2 
 
 31 03 15.52 
 
 543 
 544 
 
 .51671 
 .51756 
 
 85,6 
 85,6 
 
 .85616 
 .85565 
 
 51,7 
 51,8 
 
 .71324 
 .71396 
 
 72,0 
 7i,8 
 
 .93256 
 .93229 
 
 26,2 
 26,3 
 
 31 06 41.79 
 31 10 08.05 
 
 0.545 
 
 0.51842 
 
 85,5 
 
 0.85513 
 
 51,8 
 
 9.7H68 
 
 7i,6 
 
 9.93203 
 
 26,3 
 
 31 13 34.32 
 
 .546 
 
 .51927 
 
 85,5 
 
 .85461 
 
 5i,9 
 
 .71540 
 
 7i,5 
 
 .93177 
 
 26,4 
 
 31 17 00.58 
 
 .547 
 
 .52013 
 
 85,4 
 
 .85409 
 
 52,0 
 
 .71611 
 
 7i,3 
 
 .93150 
 
 -><>,4 
 
 31 20 26.85 
 
 .548 
 
 .52008 
 
 85,4 
 
 .85357 
 
 52,1 
 
 .71682 
 
 71,2 
 
 .93124 
 
 26,5 
 
 31 23 53. n 
 
 549 
 
 .52183 
 
 85,3 
 
 .85305 
 
 52,2 
 
 .71753 
 
 7i,o 
 
 .93097 
 
 26,6 
 
 31 27 19-38 
 
 0.550 
 
 0.52269 
 
 85,3 
 
 0.85252 
 
 52,3 
 
 9.71824 
 
 70,8 
 
 9.93071 
 
 26^ 
 
 31 30 45.64 
 
 u 
 
 isinhiu 
 
 F,/ 
 
 cosh iu 
 
 -FO' 
 
 ._ nh iu 
 
 IV 
 
 log cosh iu 
 
 -F,,' 
 
 u 
 
 log . 
 
 SMITHSONIAN TABLES 
 
 202 
 
Circular Functions. 
 
 u 
 
 sin u 
 
 F ' 
 
 COS U 
 
 F ' 
 
 log sin u 
 
 Fo' 
 
 log oos u 
 
 Fo' 
 
 u 
 
 0.550 
 
 0.52269 
 
 85,3 
 
 0.85252 
 
 52,3 
 
 9.71824 
 
 70,8 
 
 9.93071 
 
 20\6 
 
 3i3o'4s'.'64 
 
 .551 
 
 .52354 
 
 85,2 
 
 .85200 
 
 52,4 
 
 .71895 
 
 70,7 
 
 .93044 
 
 26,7 
 
 31 34 11.91 
 
 .552 
 
 .52439 
 
 85,1 
 
 .85148 
 
 52,4 
 
 .71966 
 
 70,5 
 
 .93017 
 
 26,7 
 
 3i 37 38.17 
 
 553 
 
 .52524 
 
 85,1 
 
 .85095 
 
 52,5 
 
 .72036 
 
 70,4 
 
 .92991 
 
 26,8 
 
 31 41 04.44 
 
 554 
 
 .52609 
 
 85,0 
 
 .85043 
 
 52,6 
 
 .72106 
 
 70,2 
 
 .92964 
 
 26,9 
 
 31 44 30.70 
 
 0.555 
 
 0.52604 
 
 85,0 
 
 0.84090 
 
 52,7 
 
 9.72176 
 
 70,o 
 
 9.92937 
 
 26,9 
 
 31 47 56.97 
 
 .556 
 
 .52779 
 
 84,9 
 
 .84937 
 
 52,8 
 
 .72246 
 
 69,9 
 
 .92910 
 
 27,0 
 
 31 51 23.23 
 
 557 
 
 .52864 
 
 84,9 
 
 .84884 
 
 52,9 
 
 .72316 
 
 69,7 
 
 .92883 
 
 27,0 
 
 3-1 54 49.50 
 
 .558 
 
 .52949 
 
 84,8 
 
 .84832 
 
 52,9 
 
 .72386 
 
 69,6 
 
 .92856 
 
 27,1 
 
 31 58 15.76 
 
 559 
 
 .53034 
 
 84,8 
 
 .84779 
 
 53,o 
 
 .72455 
 
 69,4 
 
 .92829 
 
 27,2 
 
 32 01 42.03 
 
 0.560 
 
 0.53H9 
 
 84,7 
 
 0.84726 
 
 53,1 
 
 9.72525 
 
 69,3 
 
 9.92801 
 
 27,2 
 
 32 05 08.29 
 
 .561 
 
 .53203 
 
 84,7 
 
 .84672 
 
 53,2 
 
 .72594 
 
 69,1 
 
 .92774 
 
 27,3 
 
 32 08 34.56 
 
 .562 
 
 .53288 
 
 84,6 
 
 .84619 
 
 53,3 
 
 .72663 
 
 69,0 
 
 .92747 
 
 27,3 
 
 32 12 00.82 
 
 .563 
 
 .53373 
 
 84,6 
 
 .84566 
 
 53,4 
 
 .72732 
 
 68,8 
 
 .92719 
 
 27,4 
 
 32 15 27.09 
 
 .564 
 
 53457 
 
 84,5 
 
 .84512 
 
 53,5 
 
 .72801 
 
 68,7 
 
 .92692 
 
 27,5 
 
 32 18 53-35 
 
 0.565 
 
 0.53542 
 
 84,5 
 
 0.84459 
 
 53,5 
 
 9.72869 
 
 68,5 
 
 9.92665 
 
 27,5 
 
 32 22 19.62 
 
 .566 
 
 .53626 
 
 84,4 
 
 .84405 
 
 53,6 
 
 .72938 
 
 68,4 
 
 .92637 
 
 27,0 
 
 32 25 45-88 
 
 067 
 
 53710 
 
 84,4 
 
 .84352 
 
 53,7 
 
 .73006 
 
 68,2 
 
 .92609 
 
 27,7 
 
 32 29 12.15 
 
 .568 
 
 .53795 
 
 84,3 
 
 .84298 
 
 53,8 
 
 73074 
 
 68,1 
 
 .92582 
 
 27,7 
 
 32 32 38.41 
 
 .569 
 
 .53879 
 
 84,2 
 
 .84244 
 
 53,9 
 
 .73142 
 
 67,9 
 
 .92554 
 
 27,8 
 
 32 36 04.67 
 
 0.570 
 
 0.53963 
 
 84,2 
 
 0.84190 
 
 54,0 
 
 9-73210 
 
 67,8 
 
 9.92526 
 
 27,8 
 
 32 39 30.94 
 
 571 
 
 .54047 
 
 84,1 
 
 .84136 
 
 54,0 
 
 .73277 
 
 67,6 
 
 .92498 
 
 27,9 
 
 32 42 57.20 
 
 .572 
 
 .54131 
 
 84,1 
 
 .84082 
 
 54,1 
 
 .73345 
 
 67,5 
 
 .92470 
 
 28,0 
 
 32 46 23.47 
 
 573 
 
 .54216 
 
 84,0 
 
 .84028 
 
 54,2 
 
 .73412 
 
 67,3 
 
 .92442 
 
 28,0 
 
 32 49 49.73 
 
 574 
 
 54300 
 
 84,0 
 
 .83974 
 
 54,3 
 
 .73480 
 
 67,2 
 
 .92414 
 
 28,1 
 
 32 53 16.00 
 
 0.575 
 
 0.54383 
 
 83,9 
 
 0.83919 
 
 54,4 
 
 9.73547 
 
 67,0 
 
 9.92386 
 
 28,1 
 
 32 56 42.26 
 
 .576 
 
 .54467 
 
 83,9 
 
 .83865 
 
 54,5 
 
 .73614 
 
 66,9 
 
 .92358 
 
 28,2 
 
 33 oo 08.53 
 
 577 
 
 .54551 
 
 83,8 
 
 .83810 
 
 54,6 
 
 .73680 
 
 66,7 
 
 .92330 
 
 28,3 
 
 33 03 34-79 
 
 .578 
 
 .54635 
 
 83,8 
 
 .83756 
 
 54,6 
 
 .73747 
 
 66,6 
 
 .92301 
 
 28,3 
 
 33 07 01. 06 
 
 579 
 
 .54719 
 
 83,7 
 
 .83701 
 
 54,7 
 
 .73814 
 
 66,4 
 
 .92273 
 
 28,4 
 
 33 10 27.32 
 
 0.580 
 
 0.54802 
 
 83,6 
 
 0.83646 
 
 54,8 
 
 9.73880 
 
 66,3 
 
 9.92245 
 
 28,5 
 
 33 13 53-59 
 
 .581 
 
 .54886 
 
 83,6 
 
 .83591 
 
 54,9 
 
 .73946 
 
 66,2 
 
 .92216 
 
 28,5 
 
 33 17 19-85 
 
 .582 
 
 .54970 
 
 83,5 
 
 .83536 
 
 55,o 
 
 .74012 
 
 66,0 
 
 .92188 
 
 28,6 
 
 33 20 46.12 
 
 .583 
 
 .55053 
 
 83,5 
 
 .83481 
 
 55,i 
 
 .74078 
 
 65,9 
 
 .92159 
 
 28,6 
 
 33 24 12.38 
 
 .584 
 
 .55137 
 
 83,4 
 
 .83426 
 
 55,i 
 
 .74144 
 
 65,7 
 
 .92130 
 
 28,7 
 
 33 27 38.65 
 
 0.585 
 
 0.55220 
 
 83,4 
 
 0.83371 
 
 55,2 
 
 9.74210 
 
 65,6 
 
 9.92102 
 
 28,8 
 
 33 31 04.91 
 
 .586 
 
 .55303 
 
 83,3 
 
 .83316 
 
 55,3 
 
 .74275 
 
 65,4 
 
 .92073 
 
 28,8 
 
 33 34 3Li8 
 
 .587 
 
 .55387 
 
 83,3 
 
 .83261 
 
 55,4 
 
 74340 
 
 65,3 
 
 .92044 
 
 28,9 
 
 33 37 57-44 
 
 .588 
 
 55470 
 
 83,2 
 
 .83205 
 
 55,5 
 
 .74406 
 
 65,1 
 
 .92015 
 
 29,0 
 
 33 41 23.71 
 
 .589 
 
 55553 
 
 8 3 ,I 
 
 .83150 
 
 55,6 
 
 74471 
 
 65,0 
 
 .91986 
 
 29,0 
 
 33 44 49-97 
 
 0.590 
 
 0.55636 
 
 8 3 ,I 
 
 0.83094 
 
 55,6 
 
 9.74536 
 
 64,9 
 
 9.91957 
 
 29,1 
 
 33 48 16.24 
 
 -iS9i 
 
 552.13 
 
 83,0 
 
 .3038 
 
 55,7 
 
 .74600 
 
 64,7 
 
 .91928 
 
 29,1 
 
 33 51 42.50 
 
 592 
 
 .55802 
 
 83,0 
 
 .82983 
 
 55,8 
 
 .74665 
 
 64,6 
 
 .91809 
 
 29,2 
 
 33 55 08.77 
 
 593 
 
 .55885 
 
 82,9 
 
 .82927 
 
 55,9 
 
 74730 
 
 64,4 
 
 .91869 
 
 29,3 
 
 33 58 35.03 
 
 594 
 
 .55968 
 
 82,9 
 
 .82871 
 
 56,0 
 
 74794 
 
 64,3 
 
 .91840 
 
 29,3 
 
 34 02 01.29 
 
 0.595 
 
 0.56051 
 
 82,8 
 
 0.82815 
 
 56,1 
 
 9.74858 
 
 64,2 
 
 9.91811 
 
 29,4 
 
 34 05 27.56 
 
 .596 
 
 .56134 
 
 82,8 
 
 .82759 
 
 56,i 
 
 .74922 
 
 64,0 
 
 .91781 
 
 29,5 
 
 34 08 53-82 
 
 597 
 
 .56216 
 
 82,7 
 
 .82703 
 
 56,2 
 
 .74986 
 
 63,9 
 
 .91752 
 
 29,5 
 
 34 12 20.09 
 
 .598 
 
 .56299 
 
 82,6 
 
 .82646 
 
 56,3 
 
 .75050 
 
 63,8 
 
 .91722 
 
 29,6 
 
 34 15 46.35 
 
 599 
 
 .56382 
 
 82,6 
 
 .82590 
 
 56,4 
 
 .75H4 
 
 63,6 
 
 .91693 
 
 29,6 
 
 34 19 12.62 
 
 0.600 
 
 0.56464 
 
 82,5 
 
 0.82534 
 
 56,5 
 
 9.75177 
 
 63,5 
 
 9.91663 
 
 29,7 
 
 34 22 38.88 
 
 u 
 
 -i sinh iu 
 
 F ' 
 
 cosh iu 
 
 > Fo' 
 
 sinh iu 
 
 -Fo' 
 
 log cosh iu 
 
 IV 
 
 u 
 
 loo . 
 
 SMITHSONIAN TABLES 
 
 203 
 
Circular Functions. 
 
 u 
 
 sin u 
 
 U.FO' 
 
 cos u 
 
 <> Fo' log sin u 
 
 <- Fo' 
 
 log cos u 
 
 -F a ' 
 
 u 
 
 0.600 
 
 0.56464 
 
 82,5 
 
 0.82534 
 
 56,5 
 
 9.75177 
 
 63,5 
 
 9.91663 
 
 29,7 
 
 34 22' 38. '88 
 
 .001 
 
 .56547 
 
 82,5 
 
 .82477 
 
 56,5 
 
 .75241 
 
 63,3 
 
 .91633 
 
 29,8 
 
 34 26 05.15 
 
 .602 
 
 .56629 
 
 82,4 
 
 .82420 
 
 56,6 
 
 .75304 
 
 63,2 
 
 .91604 
 
 29,8 
 
 34 29 31.41 
 
 .603 
 
 .56712 
 
 82,4 
 
 .82364 
 
 56,7 
 
 75367 
 
 63,1 
 
 .91574 
 
 29,9 
 
 34 32 57-68 
 
 .604 
 
 .56794 
 
 82,3 
 
 .82307 
 
 56,8 
 
 75430 
 
 62,9 
 
 .91544 
 
 30,0 
 
 34 36 23.94 
 
 0.605 
 
 0.56876 
 
 82,3 
 
 0.82250 
 
 56,9 
 
 9-75493 
 
 62,8 
 
 9.91514 
 
 30,0 
 
 34 39 50.21 
 
 .606 
 
 .56958 
 
 82,2 
 
 .82193 
 
 57,0 
 
 .75556 
 
 62,7 
 
 .91484 
 
 30,1 
 
 34 43 16.47 
 
 .607 
 
 .57041 
 
 82,1 
 
 .82136 
 
 57,0 
 
 .75618 
 
 62,5 
 
 .91454 
 
 30,2 
 
 34 46 42.74 
 
 .608 
 
 .57123 
 
 82,1 
 
 .82079 
 
 57,1 
 
 .75681 
 
 62,4 
 
 .9H23 
 
 30,2 
 
 34 50 09.00 
 
 .609 
 
 .57205 
 
 82,0 
 
 .82022 
 
 57,2 
 
 75743 
 
 62,3 
 
 .91393 
 
 30,3. 
 
 34 53 35.27 
 
 0.610 
 
 0.57287 
 
 82,0 
 
 0.81965 
 
 57,3 
 
 9.75805 
 
 62,1 
 
 9.91363 
 
 30,4 
 
 34 57 01.53 
 
 .611 
 
 57369 
 
 81,9 
 
 .81907 
 
 57,4 
 
 .75867 
 
 62,O 
 
 .91332 
 
 30,4 
 
 35 oo 27.80 
 
 .612 
 
 .57451 
 
 81,9 
 
 .81850 
 
 57,5 
 
 .75929 
 
 61,9 
 
 .91302 
 
 30,5 
 
 35 03 54-06 
 
 .613 
 
 57532 
 
 81,8 
 
 .81793 
 
 57,5 
 
 .75991 
 
 6i,7 
 
 .91271 
 
 30,5 
 
 35 07 20.33 
 
 .614 
 
 .57614 
 
 8i,7 
 
 .81735 
 
 57,6 
 
 .76053 
 
 61,6 
 
 .91241 
 
 30,6 
 
 35 10 46.59 
 
 0.615 
 
 0.57696 
 
 8i,7 
 
 0.81677 
 
 57,7 
 
 9.76114 
 
 6i,5 
 
 9.91210 
 
 30,7 
 
 35 14 12.86 
 
 .616 
 
 .57778 
 
 81,6 
 
 .81620 
 
 57,8 
 
 .76176 
 
 61,4 
 
 .91179 
 
 30,7 
 
 35 17 39.12 
 
 .617 
 
 .57859 
 
 81,6 
 
 .81562 
 
 57,9 
 
 .76237 
 
 61,2 
 
 .91149 
 
 30,8 
 
 35 21 05.39 
 
 .618 
 
 57941 
 
 8i,5 
 
 .81504 
 
 57,9 
 
 .76298 
 
 61,1 
 
 .91118 
 
 30,9 
 
 35 24 31.65 
 
 .619 
 
 .58022 
 
 81,4 
 
 .81446 
 
 58,0 
 
 .76359 
 
 61,0 
 
 .91087 
 
 30,9 
 
 35 27 57.92 
 
 0.620 
 
 0.58104 
 
 81,4 
 
 0.81388 
 
 58,1 
 
 9.76420 
 
 60,8 
 
 9.91056 
 
 31,0 
 
 35 31 24.18 
 
 .621 
 
 .58185 
 
 81,3 
 
 .81330 
 
 58,2 
 
 .76481 
 
 60,7 
 
 .91025 
 
 3i,i 
 
 35 34 50.44 
 
 .622 
 
 .58266 
 
 81,3 
 
 .81271 
 
 58,3 
 
 .76542 
 
 60,6 
 
 .90994 
 
 3i,i 
 
 35 38 16.71 
 
 .623 
 
 .58347 
 
 81,2 
 
 .81213 
 
 58,3 
 
 .76602 
 
 60,4 
 
 .90963 
 
 31,2 
 
 35 41 42.97 
 
 .624 
 
 58429 
 
 81,2 
 
 .81155 
 
 58,4 
 
 .76663 
 
 60,3 
 
 .90931 
 
 31,3 
 
 35 45 09.24 
 
 0.625 
 
 0.58510 
 
 81,1 
 
 0.81096 
 
 58,5 
 
 9.76723 
 
 60,2 
 
 O.OOOOO 
 
 31,3 
 
 35 48 35.50 
 
 .626 
 
 .58591 
 
 81,0 
 
 .81038 
 
 58,6 
 
 .76783 
 
 60,1 
 
 .90869 
 
 3i,4 
 
 35 52 01.77 
 
 .627 
 
 .58672 
 
 81,0 
 
 .80979 
 
 58,7 
 
 .76843 
 
 59,9 
 
 .90837 
 
 31,5 
 
 35 55 28.03 
 
 .628 
 
 .58753 
 
 80,9 
 
 .80920 
 
 58,8 
 
 .76903 
 
 59,8 
 
 .90806 
 
 31,5 
 
 35 58 54.30 
 
 .629 
 
 .58834 
 
 80,9 
 
 .80862 
 
 58,8 
 
 .76963 
 
 59,7 
 
 .90774 
 
 31,6 
 
 36 02 20.56 
 
 0.630 
 
 0.58914 
 
 80,8 
 
 0.80803 
 
 58,9 
 
 9.77022 
 
 59,6 
 
 9.90743 
 
 3i,7 
 
 36 05 46.83 
 
 .631 
 
 .58995 
 
 80,7 
 
 .80744 
 
 59,o 
 
 .77082 
 
 59,4 
 
 .90711 
 
 3i,7 
 
 36 09 13.09 
 
 .632 
 
 .59076 
 
 80,7 
 
 .80685 
 
 59,1 
 
 .77141 
 
 59,3 
 
 .90679 
 
 31,8 
 
 36 12 39.36 
 
 .633 
 
 .59157 
 
 80,6 
 
 .80626 
 
 59,2 
 
 .77200 
 
 59,2 
 
 .90647 
 
 3i,9 
 
 36 16 05.62 
 
 .634 
 
 .59237 
 
 80,6 
 
 .80566 
 
 59,2 
 
 .77259 
 
 59,1 
 
 .90615 
 
 3i,9 
 
 36 19 31-89 
 
 0.635 
 
 0.59318 
 
 80,5 
 
 0.80507 
 
 59,3 
 
 9.77318 
 
 58,9 
 
 9.90583 
 
 32,0 
 
 36 22 58.15 
 
 .636 
 
 .59398 
 
 80,4 
 
 .80448 
 
 59,4 
 
 77377 
 
 58,8 
 
 .90551 
 
 32,1 
 
 36 26 24.42 
 
 .637 
 
 59479 
 
 80,4 
 
 .80388 
 
 59,5 
 
 .77436 
 
 58,7 
 
 .90519 
 
 32,1 
 
 36 29 50.68 
 
 .638 
 
 . 59559 
 
 80,3 
 
 .80329 
 
 59,6 
 
 77495 
 
 58,6 
 
 .90487 
 
 32,2 
 
 36 33 16.95 
 
 .639 
 
 .59639 
 
 80,3 
 
 .80269 
 
 59,6 
 
 .77553 
 
 58,5 
 
 .90455 
 
 32,3 
 
 36 36 43.21 
 
 0.640 
 
 0.59720 
 
 80,2 
 
 0.80210 
 
 59,7 
 
 9.77612 
 
 58,3 
 
 9.90423 
 
 32,3 
 
 36 40 09.48 
 
 .641 
 
 .50800 
 
 80, i 
 
 .80150 
 
 59,8 
 
 .77670 
 
 58,2 
 
 .90390 
 
 32,4 
 
 36 43 35-74 
 
 .642 
 
 .50880 
 
 80, i 
 
 .80090 
 
 59,9 
 
 .77728 
 
 58,i 
 
 .90358 
 
 32,5 
 
 36 47 02. 01 
 
 643 
 
 .59960 
 
 80,0 
 
 .80030 
 
 60,0 
 
 .77786 
 
 58,o 
 
 .90325 
 
 32,5 
 
 36 50 28.27 
 
 .644 
 
 .60040 
 
 80,0 
 
 .79970 
 
 60,0 
 
 .77844 
 
 57,8 
 
 .90293 
 
 32,6 
 
 36 53 54-54 
 
 0.645 
 
 0.60120 
 
 79,9 
 
 0.79910 
 
 60, i 
 
 9.77902 
 
 57,7 
 
 9.90260 
 
 32,7 
 
 36 57 20.80 
 
 .646 
 
 .60200 
 
 79,8 
 
 .79850 
 
 60,2 
 
 77959 
 
 57,6 
 
 .90227 
 
 32,7 
 
 37 oo 47-06 
 
 .647 
 
 .60280 
 
 79,8 
 
 .79790 
 
 60,3 
 
 .78017 
 
 57,5 
 
 .90195 
 
 32,8 
 
 37 04 13-33 
 
 .648 
 
 .60359 
 
 79J 
 
 .79729 
 
 60,4 
 
 .78074 
 
 57,4 
 
 .90162 
 
 32,9 
 
 37 07 39-59 
 
 .649 
 
 .60439 
 
 79,7 
 
 .79669 
 
 60,4 
 
 .78132 
 
 57.-' 
 
 .90129 
 
 32,9 
 
 37 u 05.86 
 
 0.650 
 
 0.60519 
 
 79,6 
 
 0.79608 
 
 60,5 
 
 9.78189 
 
 57,1 
 
 9.00096 
 
 33,0 
 
 37 M 32.12 
 
 u 
 
 -isinhiu 
 
 -Fo' 
 
 cosh iu 
 
 -Fo' 
 
 lofl nh iu 
 
 -Fo' 
 
 log cosh iu 
 
 -FO' 
 
 u 
 
 log , 
 
 SMITHSONIAN TABLCS 
 
 204 
 
Circular Functions. 
 
 u 
 
 sin u 
 
 F ' 
 
 cos u 
 
 Fo' 
 
 loo sin u 
 
 Fo' 
 
 log cos u 
 
 o>Fo' 
 
 u 
 
 0.650 
 
 0.60519 
 
 79,6 
 
 0.79608 
 
 60,5 
 
 9.78189 
 
 57,i 
 
 9.00096 
 
 33,0 
 
 Q 4 it 
 
 37 14 32.12 
 
 .651 
 
 .60598 
 
 79,5 
 
 .79548 
 
 60,6 
 
 .78246 
 
 57,o 
 
 .90063 
 
 33,1 
 
 37 17 58.39 
 
 .652 
 
 .60678 
 
 79,5 
 
 .79487 
 
 60,7 
 
 .78303 
 
 56,9 
 
 .90030 
 
 33,2 
 
 37 21 24.65 
 
 .653 
 
 .60757 
 
 79,4 
 
 .79426 
 
 60,8 
 
 .78360 
 
 56,8 
 
 .89997 
 
 33,2 
 
 37 24 50.92 
 
 .654 
 
 .60837 
 
 79,4 
 
 .79366 
 
 60,8 
 
 .78416 
 
 56,7 
 
 .89963 
 
 33,3 
 
 37 28 17.18 
 
 0.655 
 
 0.60916 
 
 79,3 
 
 0.79305 
 
 60,9 
 
 9.78473 
 
 56,5 
 
 9.89930 
 
 33,4 
 
 37 31 43-45 
 
 .656 
 
 .60995 
 
 79,2 
 
 .79244 
 
 61,0 
 
 .78530 
 
 56,4 
 
 .80897 
 
 33,4 
 
 37 35 09.71 
 
 .657 
 
 .61074 
 
 79,2 
 
 .79183 
 
 61,1 
 
 .78586 
 
 56,3 
 
 .89863 
 
 33,5 
 
 37 38 35.98 
 
 .658 
 
 .61154 
 
 79,1 
 
 .79122 
 
 61,2 
 
 .7864^ 
 
 56,2 
 
 .89830 
 
 33,6 
 
 37 42 02.24 
 
 .659 
 
 .61233 
 
 79,1 
 
 .79060 
 
 61,2 
 
 .78698 
 
 56,1 
 
 .89796 
 
 33,6 
 
 37 45 28,51 
 
 0.660 
 
 0.61312 
 
 79,0 
 
 0.78099 
 
 61,3 
 
 9.78754 
 
 56,o 
 
 9.89762 
 
 33,7 
 
 37 48 54-77 
 
 .661 
 
 .61391 
 
 78,9 
 
 '78938 
 
 61,4 
 
 .78810 
 
 55,8 
 
 .89729 
 
 33,8 
 
 37 52 21.04 
 
 .662 
 
 .61470 
 
 78,9 
 
 .78876 
 
 6i,5 
 
 .78866 
 
 55,7 
 
 .89695 
 
 33,8 
 
 37 55 47.30 
 
 .663 
 
 .61548 
 
 78,8 
 
 .78815 
 
 6i,5 
 
 .78922 
 
 55,6 
 
 .89661 
 
 33,9 
 
 37 59 13.57 
 
 .664 
 
 .61627 
 
 78,8 
 
 .78753 
 
 61,6 
 
 .78977 
 
 55,5 
 
 .89627 
 
 34,0 
 
 38 02 39.83 
 
 0.665 
 
 0.61706 
 
 78,7 
 
 0.78692 
 
 6i,7 
 
 9.79033 
 
 55,4 
 
 9.89593 
 
 34,1 
 
 38 06 06. 10 
 
 .666 
 
 .61785 
 
 78,6 
 
 .78630 
 
 61,8 
 
 .79088 
 
 55,3 
 
 .89559 
 
 34,1 
 
 38 09 32.36 
 
 .667 
 
 .61863 
 
 78,6 
 
 .78568 
 
 61,9 
 
 .79143 
 
 55,2 
 
 .89525 
 
 34,2 
 
 38 12 58.63 
 
 .668 
 
 .61942 
 
 78,5 
 
 .78506 
 
 61,9 
 
 .79198 
 
 55,o 
 
 .89490 
 
 34,3 
 
 38 16 24.89 
 
 .669 
 
 .62O2O 
 
 78,4 
 
 .78444 
 
 62,0 
 
 .79253 
 
 54,9 
 
 .89456 
 
 34,3 
 
 38 19 51.16 
 
 0.670 
 
 0.62099 
 
 78,4 
 
 0.78382 
 
 62,1 
 
 9.79308 
 
 54,8 
 
 9.89422 
 
 34,4 
 
 38 23 17.42 
 
 .671 
 
 .62177 
 
 78,3 
 
 .78320 
 
 62,2 
 
 .79363 
 
 54,7 
 
 .89387 
 
 34,5 
 
 38 26 43.68 
 
 .672 
 
 .62255 
 
 78,3 
 
 .78258 
 
 62,3 
 
 .79418 
 
 54,6 
 
 .89353 
 
 34,5 
 
 38 30 09.95 
 
 .673 
 
 .62333 
 
 78,2 
 
 .78196 
 
 62,3 
 
 .79472 
 
 54,5 
 
 .89318 
 
 34,6 
 
 38 33 36.21 
 
 .674 
 
 .62412 
 
 78,1 
 
 .78133 
 
 62,4 
 
 .79527 
 
 54,4 
 
 .89284 
 
 34,7 
 
 38 37 02.48 
 
 0.675 
 
 0.62400 
 
 78,1 
 
 0.78071 
 
 62,5 
 
 9.79581 
 
 54,3 
 
 9.89249 
 
 34,8 
 
 38 40 28.74 
 
 .676 
 
 .62568 
 
 78,0 
 
 .78008 
 
 62,6 
 
 .79635 
 
 54,1 
 
 .89214 
 
 34,8 
 
 38 43 55.01 
 
 .677 
 
 .62646 
 
 77,9 
 
 .77946 
 
 62,6 
 
 .79689 
 
 54,0 
 
 .89179 
 
 34,9 
 
 38 47 21.27 
 
 .678 
 
 .62724 
 
 77,9 
 
 .77883 
 
 62,7 
 
 .79743 
 
 53,9 
 
 89144 
 
 35,0 
 
 38 50 47-54 
 
 .679 
 
 .62802 
 
 77,8 
 
 .77820 
 
 62,8 
 
 79797 
 
 53,8 
 
 .89109 
 
 35,0 
 
 38 54 I3.8o 
 
 0.680 
 
 0.62879 
 
 77,8 
 
 0.77757 
 
 62,9 
 
 9.79851 
 
 53,7 
 
 9.89074 
 
 35,1 
 
 38 57 40.07 
 
 .681 
 
 .62957 
 
 77,7 
 
 .77694 
 
 63,0 
 
 .79904 
 
 53,6 
 
 .89039 
 
 35,2 
 
 39 01 06.33 
 
 .682 
 
 .63035 
 
 77,6 
 
 .77631 
 
 63,0 
 
 .79958 
 
 53,5 
 
 
 35,3 
 
 39 04 32.60 
 
 .683 
 
 .63112 
 
 77,6 
 
 .77568 
 
 63,1 
 
 .80011 
 
 53,4 
 
 .88968 
 
 35,3 
 
 39 07 58.86 
 
 .684 
 
 .63190 
 
 77,5 
 
 .77505 
 
 63,2 
 
 .80065 
 
 53,3 
 
 .88933 
 
 35,4 
 
 39 u 25.13 
 
 0.685 
 
 0.63267 
 
 77,4 
 
 0.77442 
 
 63,3 
 
 9.80118 
 
 53,2 
 
 9.88898 
 
 35,5 
 
 39 14 51.39 
 
 .686 
 
 .63345 
 
 77,4 
 
 .77379 
 
 63,3 
 
 .80171 
 
 53,1 
 
 .88862 
 
 35,6 
 
 39 18 17.66 
 
 .687 
 
 .63422 
 
 77,3 
 
 .77315 
 
 63,4 
 
 .80224 
 
 52,9 
 
 .88826 
 
 35,6 
 
 39 21 43>92 
 
 .688 
 
 .63499 
 
 77,3 
 
 .77252 
 
 63,5 
 
 .80277 
 
 52,8 
 
 .88791 
 
 35,7 
 
 39 25 10.19 
 
 .689 
 
 .63577 
 
 77,2 
 
 .77188 
 
 63,6 
 
 .80330 
 
 52,7 
 
 .88755 
 
 35,8 
 
 39 28 36.45 
 
 0.600 
 
 0.63654 
 
 77J 
 
 0.77125 
 
 63,7 
 
 9.80382 
 
 ' 52,6 
 
 9.88719 
 
 35,8 
 
 39 32 02.72 
 
 .691 
 
 .63731 
 
 77,1 
 
 .77061 
 
 63,7 
 
 .80435 
 
 52,5 
 
 .88683 
 
 35,9 
 
 39 35 28.98 
 
 .692 
 
 .63808 
 
 77,o 
 
 .76997 
 
 63,8 
 
 .80487 
 
 52,4 
 
 .88647 
 
 36,0 
 
 39 38 55.25 
 
 .693 
 
 .63885 
 
 76,9 
 
 .76933 
 
 63,9 
 
 .80540 
 
 52,3 
 
 .885ii 
 
 36,1 
 
 39 42 21.51 
 
 .694 
 
 .63962 
 
 76,9 
 
 .76869 
 
 64,0 
 
 .80592 
 
 52,2 
 
 .88575 
 
 36,1 
 
 39 45 47.78 
 
 0.695 
 
 0.64039 
 
 76,8 
 
 0.76805 
 
 64,0 
 
 9.80644 
 
 5'2,i 
 
 9.88539 
 
 36,2 
 
 39 49 14.04 
 
 .696 
 
 .64115 
 
 76,7 
 
 .76741 
 
 64,1 
 
 .80696 
 
 52,0 
 
 .88503 
 
 36,3 
 
 39 52 40.31 
 
 .697 
 
 .64192 
 
 76,7 
 
 .76677 
 
 64,2 
 
 .80748 
 
 51,9 
 
 .88467 
 
 36,4 
 
 39 56 06.57 
 
 .698 
 
 .64269 
 
 76,6 
 
 .76613 
 
 64,3 
 
 .80800 
 
 5i,8 
 
 .88430 
 
 36,4 
 
 39 59 32.83 
 
 .699 
 
 .64345 
 
 76,5 
 
 .76549 
 
 64,3 
 
 .80852 
 
 5i,7 
 
 .88394 
 
 36,5 
 
 40 02 59.10 
 
 0.700 
 
 0.64422 
 
 76,5 
 
 0.76484 
 
 64,4 
 
 9-80903 
 
 5i,6 
 
 9.88357 
 
 36,6 
 
 40 06 25.36 
 
 u 
 
 -isinhiu 
 
 IV 
 
 cosh iu 
 
 F ' 
 
 sinh iu 
 
 wF ' 
 
 log cosh iu 
 
 F O ' 
 
 u 
 
 log . 
 
 SMITHSONIAN TABLES 
 
 205 
 
Circular Functions. 
 
 1 
 
 sin u 
 
 -FO' 
 
 COS U 
 
 Fo* 
 
 log sin u 
 
 w Fo' 
 
 log cos u 
 
 -FO' 
 
 u 
 
 0.700 
 
 0.64422 
 
 76,5 
 
 0.76484 
 
 64,4 
 
 9.80903 
 
 5i,6 
 
 9.88357 
 
 36,6 
 
 40o6' 25".' 36 
 
 .701 
 
 .64498 
 
 76,4 
 
 .76420 
 
 64,5 
 
 .80955 
 
 5i,5 
 
 .88321 
 
 36,7 
 
 40 09 51.63 
 
 .702 
 
 .64575 
 
 76,4 
 
 .76355 
 
 64,6 
 
 .81006 
 
 5'i,4 
 
 .88284 
 
 36,7 
 
 40 13 17.89 
 
 .703 
 
 .64651 
 
 76,3 
 
 .76291 
 
 64,7 
 
 .81057 
 
 51,2 
 
 .88247 
 
 36,8 
 
 40 16 44.16 
 
 .704 
 
 .64727 
 
 76,2 
 
 .76226 
 
 64,7 
 
 .81109 
 
 5i,i 
 
 .88210 
 
 36,9 
 
 40 20 10.42 
 
 0.705 
 
 0.64803 
 
 76,2 
 
 0.76161 
 
 64,8 
 
 9.8ll6o 
 
 5i,o 
 
 9.88173 
 
 37,0 
 
 40 23 36.69 
 
 .706 
 
 .64880 
 
 76,1 
 
 .76096 
 
 64,9 
 
 .81211 
 
 50,9 
 
 .88136 
 
 37,o 
 
 40 27 02.95 
 
 .707 
 
 .64956 
 
 76,0 
 
 .76031 
 
 65,0 
 
 .81262 
 
 50,8 
 
 .88099 
 
 37,i 
 
 40 30 29.22 
 
 .708 
 
 .65032 
 
 76,0 
 
 .75966 
 
 65,0 
 
 .81312 
 
 50,7 
 
 .88^62 
 
 37,2 
 
 40 33 55.48 
 
 ..709 
 
 .65108 
 
 75,9 
 
 .75901 
 
 65,1 
 
 .81363 
 
 50,6 
 
 .88025 
 
 37,3 
 
 40 37 2I 75 
 
 0.710 
 
 0.65183 
 
 75,8 
 
 0.75836 
 
 65,2 
 
 9.81414 
 
 50,5 
 
 9.87588 
 
 37,3 
 
 40 40 48.01 
 
 .711 
 
 .65259 
 
 75,8 
 
 .75771 
 
 65,3 
 
 .81464 
 
 50,4 
 
 .87950 
 
 37,4 
 
 40 44 14-28 
 
 .712 
 
 .65335 
 
 75,7 
 
 .75706 
 
 65,3 
 
 .81515 
 
 50,3 
 
 .87913 
 
 37,5 
 
 40 47 40.54 
 
 .713 
 
 .65411 
 
 75,6 
 
 .75640 
 
 65,4 
 
 .81565 
 
 50,2 
 
 .87875 
 
 37,6 
 
 40 51 06. 81 
 
 .714 
 
 .65486 
 
 75,6 
 
 75575 
 
 65,5 
 
 .81615 
 
 50,1 
 
 .87838 
 
 37,6 
 
 40 54 33.07 
 
 0.715 
 
 0.65562 
 
 75,5 
 
 0.75509 
 
 65,6 
 
 9.8l665 
 
 50,0 
 
 9.87800 
 
 37,7 
 
 40 57 59-34 
 
 .716 
 
 65637 
 
 75,4 
 
 75444 
 
 65,6 
 
 .81715 
 
 49,9 
 
 .87762 
 
 37,8 
 
 41 01 25.60 
 
 .717 
 
 .65713 
 
 75,4 
 
 75378 
 
 65,7 
 
 .81765 
 
 49,8 
 
 .87724 
 
 37,9 
 
 41 04 51-87 
 
 .718 
 
 .65788 
 
 75,3 
 
 .75312 
 
 65,8 
 
 .81815 
 
 49,7 
 
 .87687 
 
 37,9 
 
 41 08 18.13 
 
 .719 
 
 .65863 
 
 75,2 
 
 .75246 
 
 65,9 
 
 .81864 
 
 49,6 
 
 .87649 
 
 38,0 
 
 41 ii 44.40 
 
 0.720 
 
 0.65938 
 
 75,2 
 
 0.75181 
 
 65,9 
 
 9.81914 
 
 49,5 
 
 9.87611 
 
 38,1 
 
 41 15 10.66 
 
 .721 
 
 .66014 
 
 75,1 
 
 75II5 
 
 66,0 
 
 .81963 
 
 49,4 
 
 .87572 
 
 38,2 
 
 41 18 36.93 
 
 .722 
 
 .66089 
 
 75,0 
 
 .75049 
 
 66,1 
 
 .82013 
 
 49,3 
 
 .87534 
 
 38,2 
 
 41 22 03.19 
 
 .723 
 
 .66164 
 
 75,o 
 
 .74982 
 
 66,2 
 
 .82062 
 
 49,2 
 
 .87496 
 
 38,3 
 
 41 25 29.45 
 
 .724 
 
 .66239 
 
 74,9 
 
 .74916 
 
 66,2 
 
 .82111 
 
 49,1 
 
 .87458 
 
 38,4 
 
 41 28 55-72 
 
 0.725 
 
 0.66314 
 
 74,8 
 
 0.74850 
 
 66,3 
 
 9.82160 
 
 49,0 
 
 9-87419 
 
 38,5 
 
 41 32 21.98 
 
 .726 
 
 .66388 
 
 74,8 
 
 .74784 
 
 66,4 
 
 .82209 
 
 48,9 
 
 .87381 
 
 38,6 
 
 41 35 48.25 
 
 .727 
 
 .66463 
 
 74,7 
 
 .74717 
 
 66,5 
 
 .82258 
 
 48,8 
 
 .87342 
 
 38,6 
 
 41 39 U.5I 
 
 .728 
 
 .66538 
 
 74,7 
 
 .74651 
 
 66,5 
 
 .82307 
 
 48,7 
 
 .87303 
 
 38,7 
 
 41 42 40.78 
 
 .729 
 
 .66612 
 
 74,6 
 
 .74584 
 
 66,6 
 
 .82356 
 
 48,6 
 
 .87265 
 
 38,8 
 
 41 46 07.04 
 
 0.730 
 
 0.66687 
 
 74,5 
 
 0.74517 
 
 66,7 
 
 9.82404 
 
 48,5 
 
 9.87226 
 
 38,9 
 
 41 49 33.31 
 
 .731 
 
 .66761 
 
 74,5 
 
 74451 
 
 66,8 
 
 .82453 
 
 48,4 
 
 .87187 
 
 38,9 
 
 41 52 59.57 
 
 .732 
 
 .66836 
 
 74,4 
 
 .74384 
 
 66,8 
 
 .82501 
 
 48,3 
 
 .87148 
 
 39,o 
 
 41 56 25.84 
 
 733 
 
 .66910 
 
 74,3 
 
 .74317 
 
 66,9 
 
 .82549 
 
 4,2 
 
 .87109 
 
 39J 
 
 41 59 52.10 
 
 .734 
 
 .66984 
 
 74,3 
 
 .74250 
 
 67,0 
 
 .82597 
 
 48,1 
 
 .87070 
 
 39,2 
 
 42 03 18.37 
 
 0.735* 
 
 0.67059 
 
 74,2 
 
 0.74183 
 
 67,1 
 
 9.82646 
 
 48,0 
 
 9-87030 
 
 39,3 
 
 42 06 44.63 
 
 .736 
 
 .67133 
 
 74,1 
 
 .74n6 
 
 67,1 
 
 .82694 
 
 47,9 
 
 .86091 
 
 39,3 
 
 42 10 10.90 
 
 .737 
 
 .67207 
 
 74,0 
 
 .74049 
 
 67,2 
 
 .82741 
 
 47,9 
 
 .86952 
 
 39,4 
 
 42 13 37.16 
 
 .738 
 
 .67281 
 
 74,0 
 
 .73982 
 
 67,3 
 
 .82789 
 
 47,8 
 
 .86912 
 
 39,5 
 
 42 17 03.43 
 
 739 
 
 .67355 
 
 73,9 
 
 .73914 
 
 67,4 
 
 .82837 
 
 47,7 
 
 .86873 
 
 39,6 
 
 4!2 2O 29.69 
 
 0.740 
 
 0.67429 
 
 73,8 
 
 0.73847 
 
 67,4 
 
 9.82885 
 
 47,6 
 
 9.86833 
 
 39,7 
 
 42 23 55.96 
 
 741 
 
 .67503 
 
 73,8 
 
 73779 
 
 67,5 
 
 .82932 
 
 47,5 
 
 .86794 
 
 39,7 
 
 42 27 22.22 
 
 .742 
 
 .67576 
 
 73,7 
 
 73712 
 
 67,6 
 
 .82979 
 
 47,4 
 
 .86754 
 
 39,8 
 
 42 30 48.49 
 
 743 
 
 .67650 
 
 73,6 
 
 .73644 
 
 67,7 
 
 .83027 
 
 47,3 
 
 .86714 
 
 39,9 
 
 42 34 14.75 
 
 744 
 
 .67724 
 
 73,6 
 
 73577 
 
 67,7 
 
 .83074 
 
 47,2 
 
 .86674 
 
 40,0 
 
 42 37 41-02 
 
 0.745 
 
 0.67797 
 
 73,5 
 
 0.73509 
 
 67,8 
 
 9.83I2I 
 
 47,1 
 
 9.86634 
 
 40,0 
 
 42 41 07.28 
 
 .746 
 
 .67871 
 
 73,4 
 
 .73441 
 
 67,9 
 
 .83168 
 
 47,0 
 
 .86594 
 
 40,1 
 
 42 44 33-55 
 
 747 
 
 .67944 
 
 73,4 
 
 73373 
 
 67,9 
 
 .83215 
 
 46,9 
 
 .86554 
 
 40,2 
 
 42 47 59-8i 
 
 .748 
 
 .68017 
 
 73,3 
 
 .73305 
 
 68,0 
 
 .83262 
 
 46,8 
 
 .86513 
 
 40,3 
 
 42 51 26.08 
 
 749 
 
 .68091 
 
 73,2 
 
 .73237 
 
 68,1 
 
 .83309 
 
 46,7 
 
 .86473 
 
 40,4 
 
 42 54 52.34 
 
 0.750 
 
 0.68164 
 
 73,2 
 
 0.73169 
 
 68,2 
 
 9.83355 
 
 46,6 
 
 9.86433 
 
 40,5 
 
 42 58 18.60 
 
 I 
 
 -itinhiu 
 
 -F" 
 
 cosh iu 
 
 -F ' 
 
 lm, slnh iu 
 
 FV 
 
 log cosh iu 
 
 Fo' 
 
 u 
 
 log , 
 
 SMITHSONIAN TABLES 
 
 2O6 
 
Circular Functions. 
 
 u 
 
 sin u 
 
 F ' 
 
 cos u 
 
 F O ' 
 
 log sin u 
 
 F O ' 
 
 log cos u 
 
 FV 
 
 u 
 
 0.750 
 
 0.68164 
 
 73,2 
 
 0.73169 
 
 68,2 
 
 9-83355 
 
 46,6 
 
 9.86433 
 
 40,5 
 
 42 58' i8'.'6o 
 
 .751 
 
 .68237 
 
 73,i 
 
 .73101 
 
 68,2 
 
 .83402 
 
 46,5 
 
 .86392 
 
 40,5 
 
 43 01 44-87 
 
 .752 
 
 .68310 
 
 73,o 
 
 .73032 
 
 68,3 
 
 .83448 
 
 46,4 
 
 .86352 
 
 40,6 
 
 43 05 11.13 
 
 753 
 
 .68383 
 
 73,o 
 
 .72964 
 
 68,4 
 
 .83495 
 
 46,3 
 
 .86311 
 
 40,7 
 
 43 08 37.40 
 
 754 
 
 .68456 
 
 72,9 
 
 .72896 
 
 68,5 
 
 .83541 
 
 46,2 
 
 .86270 
 
 40,8 
 
 43 12 03.66 
 
 0.755 
 
 0.68529 
 
 72,8 
 
 0.72827 
 
 68,5 
 
 9.83587 
 
 46,2 
 
 9.86229 
 
 40,9 
 
 43 IS 29.93 
 
 .756 
 
 .68602 
 
 72,8 
 
 .72759 
 
 68,6 
 
 83633 
 
 46,1 
 
 .86188 
 
 40,9 
 
 43 18 56.19 
 
 757 
 
 .68674 
 
 72,7 
 
 .72690 
 
 68,7 
 
 .83679 
 
 46,0 
 
 .86147 
 
 41,0 
 
 43 22 22.46 
 
 758 
 
 68747 
 
 72,6 
 
 .72621 
 
 68,7 
 
 .83725 
 
 45,9 
 
 .86106 
 
 41,1 
 
 43 25 48.72 
 
 759 
 
 .68820 
 
 72,6 
 
 .73552 
 
 68,8 
 
 .83771 
 
 45,8 
 
 .86065 
 
 41,2 
 
 43 29 14.99 
 
 0.760 
 
 0.68892 
 
 72,5 
 
 0.72484 
 
 68,9 
 
 9.83817 
 
 45,7 
 
 9.86024 
 
 41,3 
 
 43 32 41.25 
 
 .761 
 
 .68965 
 
 72,4 
 
 .72415 
 
 69,0 
 
 .83863 
 
 45,6 
 
 .85983 
 
 4i,4 
 
 43 36 07.52 
 
 .762 
 
 .69037 
 
 72,3 
 
 .72346 
 
 69,0 
 
 .83908 
 
 45,5 
 
 .85941 
 
 4i,4 
 
 43 39 33.78 
 
 .763 
 
 .69109 
 
 72,3 
 
 .72277 
 
 69,1 
 
 .83954 
 
 45,4 
 
 .85900 
 
 4i,5 
 
 43 43 00.05 
 
 .764 
 
 .69182 
 
 72,2 
 
 .72207 
 
 69,2 
 
 .83999 
 
 45,3 
 
 .85858 
 
 41,6 
 
 43 46 26.31 
 
 0.765 
 
 0.69254 
 
 72,i 
 
 0.72138 
 
 69,3 
 
 9.84044 
 
 45,2 
 
 9.85817 
 
 41,7 
 
 43 49 52.58 
 
 .766 
 
 .69326 
 
 72,1 
 
 .72069 
 
 69,3 
 
 .84089 
 
 45,1 
 
 .85775 
 
 41,8 
 
 43 53 18.84 
 
 .767 
 
 .69398 
 
 72,0 
 
 .72000 
 
 69,4 
 
 .84135 
 
 45,1 
 
 .85733 
 
 4i,9 
 
 43 56 45.ii 
 
 .768 
 
 .69470 
 
 71,9 
 
 .71930 
 
 69,5 
 
 .84180 
 
 45,0 
 
 .85691 
 
 4i,9 
 
 44 oo 11.37 
 
 .769 
 
 .69542 
 
 71,9 
 
 .71861 
 
 69,5 
 
 .84225 
 
 44,9 
 
 .85649 
 
 42,0 
 
 44 03 37.64 
 
 0.770 
 
 0.69614 
 
 7i,8 
 
 0.71791 
 
 69,6 
 
 9.84269 
 
 44,8 
 
 9-85607 
 
 42,1 
 
 44 07 03.90 
 
 .771 
 
 .69685 
 
 7i,7 
 
 .71721 
 
 69,7 
 
 .84314 
 
 44,7 
 
 .85565 
 
 42,2 
 
 44 10 30.17 
 
 .772 
 
 .09757 
 
 7i,7 
 
 .71652 
 
 69,8 
 
 .84359 
 
 44,6 
 
 .85523 
 
 42,3 
 
 44 13 56.43 
 
 773 
 
 .69829 
 
 7i,6 
 
 .71582 
 
 69,8 
 
 .84403 
 
 44,5 
 
 .85480 
 
 42,4 
 
 44 17 22.70 
 
 774 
 
 .69900 
 
 7i,5 
 
 .71512 
 
 69,9 
 
 .84448 
 
 44,4 
 
 .85438 
 
 42,5 
 
 44 20 48.96 
 
 0.775 
 
 0.69972 
 
 7i,4 
 
 0.71442 
 
 70,o 
 
 9.84492 
 
 44,3 
 
 9.85395 
 
 42,5 
 
 44 24 15.22 
 
 .776 
 
 .70043 
 
 7i,4 
 
 .71372 
 
 70,0 
 
 .84536 
 
 44,3 
 
 .85353 
 
 42,6 
 
 44 27 4L49 
 
 777 
 
 .70114 
 
 7i,3 
 
 .71302 
 
 7o,i 
 
 .84581 
 
 44,2 
 
 .85310 
 
 42,7 
 
 44 31 07.75 
 
 778 
 
 .70186 
 
 71,2 
 
 .71232 
 
 70,2 
 
 .84625 
 
 44,1 
 
 .85267 
 
 42,8 
 
 44 34 34.02 
 
 779 
 
 702S7 
 
 71,2 
 
 .71162 
 
 70,3 
 
 .84669 
 
 44,0 
 
 .85225 
 
 42,9 
 
 44 38 00.28 
 
 0.780 
 
 0.70328 
 
 7i,i 
 
 0.71091 
 
 70,3 
 
 9.84713 
 
 43,9 
 
 9.85182 
 
 43,0 
 
 44 41 26.55 
 
 .781 
 
 .70309 
 
 71,0 
 
 .71021 
 
 70,4 
 
 .84757 
 
 43,8 
 
 .85139 
 
 43,o 
 
 44 44 52.81 
 
 .782 
 
 .70470 
 
 71,0 
 
 .70951 
 
 70,5 
 
 .84800 
 
 43,7 
 
 .85096 
 
 43,1 
 
 44 48 19.08 
 
 .783 
 
 .70541 
 
 70,9 
 
 .70880 
 
 70,5 
 
 .84844 
 
 43,6 
 
 .85052 
 
 43,2 
 
 44 51 45-34 
 
 .784 
 
 .70612 
 
 70,8 
 
 .70809 
 
 70,6 
 
 .84888 
 
 43,6 
 
 .85009 
 
 43,3 
 
 44 55 II. 6l 
 
 0.785 
 
 0.70683 
 
 70,7 
 
 0.70739 
 
 70,7 
 
 9.84931 
 
 43,5 
 
 9.84966 
 
 43,4 
 
 44 58 37.87 
 
 .786 
 
 .70753 
 
 70,7 
 
 .70668 
 
 70,8 
 
 .84975 
 
 43,4 
 
 .84922 
 
 43,5 
 
 45 02 04.14 
 
 .787 
 
 .70824 
 
 70,6 
 
 .70597 
 
 70,8 
 
 .85018 
 
 43,3 
 
 .84879 
 
 43,6 
 
 45 05 30.40 
 
 .788 
 
 .70894 
 
 70,5 
 
 .70526 
 
 70,9 
 
 .85061 
 
 43,2 
 
 .84835 
 
 43,7 
 
 45 08 56.67 
 
 .789 
 
 .70965 
 
 70,5 
 
 .70456 
 
 71,0 
 
 .85104 
 
 43,1 
 
 .84792 
 
 43,7 
 
 45 12 22.93 
 
 0.790 
 
 0.71035 
 
 70,4 
 
 0.70385 
 
 71,0 
 
 9.85147 
 
 43,0 
 
 9.84748 
 
 43,8 
 
 45 15 49-20 
 
 .791 
 
 .71106 
 
 70,3 
 
 .70313 
 
 7i,i 
 
 .85190 
 
 42,9 
 
 .84704 
 
 43,9 
 
 45 19 15.46 
 
 .792 
 
 .7H76 
 
 70,2 
 
 .70242 
 
 71,2 
 
 .85233 
 
 42,9 
 
 .84660 
 
 44,0 
 
 45 22 41.73 
 
 793 
 
 .71246 
 
 70,2 
 
 .70171 
 
 71,2 
 
 .85276 
 
 42,8 
 
 .84616 
 
 44,1 
 
 45 26 07.99 
 
 .794 
 
 .71316 
 
 7o,i 
 
 .70100 
 
 7i,3 
 
 85319 
 
 42,7 
 
 .84572 
 
 44,2 
 
 45 29 34.26 
 
 0.795 
 
 0.71386 
 
 70,0 
 
 0.70028 
 
 7i,4 
 
 9.85362 
 
 42,6 
 
 9.84527 
 
 44,3 
 
 45 33 00.52 
 
 .796 
 
 .71456 
 
 70,0 
 
 .69957 
 
 7i,5 
 
 .85404 
 
 42,5 
 
 .84483 
 
 44,4 
 
 45 36 26.79 
 
 797 
 
 .71526 
 
 69,9 
 
 .69886 
 
 7i,5 
 
 .85447 
 
 42,4 
 
 .84439 
 
 44,4 
 
 45 39 53-05 
 
 .798 
 
 .71596 
 
 69,8 
 
 .69814 
 
 7i,6 
 
 .85489 
 
 42,3 
 
 .84394 
 
 44,5 
 
 45 43 19.32 
 
 799 
 
 .71666 
 
 69,7 
 
 .69742 
 
 7i,7 
 
 .85531 
 
 42,3 
 
 .84350 
 
 44,6 
 
 45 46 45.58 
 
 0.800 
 
 0.71736 
 
 69,7 
 
 0.69671 
 
 7i,7 
 
 9-85573 
 
 42,2 
 
 9.84305 
 
 44,7 
 
 45 50 11.84 
 
 u 
 
 -isinhiu 
 
 <-F ' 
 
 cosh iu 
 
 F O ' 
 
 sinh iu 
 
 F ' 
 
 log cosh iu 
 
 F ' 
 
 u 
 
 tog . 
 
 SMITHSONIAN TABLES 
 
 207 
 
Circular Functions. 
 
 u 
 
 sin u 
 
 F O ' 
 
 cos u 
 
 F ' 
 
 log sin u 
 
 - Fo' 
 
 log cos u 
 
 F O ' 
 
 u 
 
 0.800 
 
 0.71736 
 
 69,7 
 
 0.69671 
 
 71,7 
 
 9-85573 
 
 42,2 
 
 9.84305 
 
 44,7 
 
 455o'n / . / 84 
 
 .801 
 
 .71805 
 
 69,6 
 
 .69599 
 
 7i,8 
 
 .85616 
 
 42,1 
 
 .84260 
 
 44,8 
 
 45 53 38.11 
 
 .802 
 
 .71875 
 
 69,5 
 
 .69527 
 
 7i,9 
 
 .85658 
 
 42,0 
 
 .84215 
 
 44,9 
 
 45 57 04-37 
 
 .803 
 
 .71944 
 
 69,5 
 
 .69455 
 
 7i,9 
 
 .85700 
 
 41,9 
 
 .84170 
 
 45,o 
 
 46 oo 30.64 
 
 .804 
 
 .72014 
 
 69,4 
 
 .69383 
 
 72,0 
 
 .85742 
 
 41,8 
 
 .84125 
 
 45,i 
 
 46 03 56.90 
 
 0.805 
 
 0.72083 
 
 69,3 
 
 0.69311 
 
 72,1 
 
 9.85783 
 
 41,8 
 
 9.84080 
 
 45,2 
 
 46 07 23.17 
 
 .806 
 
 .72152 
 
 69,2 
 
 .69239 
 
 72,2 
 
 .85825 
 
 4i,7 
 
 .84035 
 
 45,3 
 
 46 10 49-43 
 
 .807 
 
 .72222 
 
 69,2 
 
 .69167 
 
 72,2 
 
 .85867 
 
 41,6 
 
 .83990 
 
 45,3 
 
 46 14 15.70 
 
 .808 
 
 .72291 
 
 69,1 
 
 .69095 
 
 72,3 
 
 .85908 
 
 4i,5 
 
 .83944 
 
 45,4 
 
 46 17 41.96 
 
 .809 
 
 .72360 
 
 69,0 
 
 .69022 
 
 72,4 
 
 .85950 
 
 4'i,4 
 
 .83899 
 
 45,5 
 
 46 21 08.23 
 
 0.810 
 
 0.72429 
 
 68,9 
 
 0.68950 
 
 72,4 
 
 9.85991 
 
 41,3 
 
 9.83853 
 
 45,6 
 
 46 24 34.49 
 
 .811 
 
 .72498 
 
 68,9 
 
 .68877 
 
 72,5 
 
 .86032 
 
 4i,3 
 
 .83808 
 
 45,7 
 
 46 28 00.76 
 
 .812 
 
 .72566 
 
 68,8 
 
 .68805 
 
 72,6 
 
 .86074 
 
 41,2 
 
 .83762 
 
 45,8 
 
 46 31 27.02 
 
 .813 
 
 .72635 
 
 68,7 
 
 .68732 
 
 72,6 
 
 .86115 
 
 41,1 
 
 .83716 
 
 45,9 
 
 46 34 53.29 
 
 .814 
 
 .72704 
 
 68,7 
 
 .68660 
 
 72,7 
 
 .86156 
 
 41,0 
 
 .83670 
 
 46,0 
 
 46 38 19.55 
 
 0.815 
 
 0.72773 
 
 68,6 
 
 0.68587 
 
 72,8 
 
 9.86197 
 
 40,9 
 
 9-83624 
 
 46,1 
 
 46 41 45.82 
 
 .816 
 
 .72841 
 
 68,5 
 
 .68514 
 
 72,8 
 
 .86238 
 
 40,8 
 
 .83578 
 
 46,2 
 
 46 45 12.08 
 
 .817 
 
 .72910 
 
 68,4 
 
 .68441 
 
 72,9 
 
 .86278 
 
 40,8 
 
 .83532 
 
 46,3 
 
 46 48 38.35 
 
 .818 
 
 .72978 
 
 68,4 
 
 .68368 
 
 73,0 
 
 .86319 
 
 40,7 
 
 .83485 
 
 46,4 
 
 46 52 04.61 
 
 .819 
 
 .73046 
 
 68,3 
 
 .68295 
 
 73,0 
 
 .86360 
 
 40,6 
 
 .83439 
 
 46,5 
 
 46 55 30.88 
 
 0.820 
 
 0.73i'i5< 
 
 68,2 
 
 0.68222 
 
 73,1 
 
 9.86400 
 
 40,5 
 
 9.83393 
 
 46,5 
 
 46 58 57-14 
 
 .821 
 
 .73183 
 
 68,1 
 
 .68149 
 
 73,2 
 
 .86441 
 
 40,4 
 
 .83346 
 
 46,6 
 
 47 02 23.41 
 
 .822 
 
 .73251 
 
 68,1 
 
 .68076 
 
 73,3 
 
 .86481 
 
 40,4 
 
 .83299 
 
 46,7 
 
 47 05 49.67 
 
 .823 
 
 .73319 
 
 68,0 
 
 .68002 
 
 73,3 
 
 .86522 
 
 40,3 
 
 .83252 
 
 46,8 
 
 47 09 15-94 
 
 .824 
 
 .73387 
 
 67,9 
 
 .67929 
 
 73,4 
 
 .86562 
 
 40,2 
 
 .83206 
 
 46,9 
 
 47 12 42.20 
 
 0.825 
 
 0.73455 
 
 67,9 
 
 0.67856 
 
 73,5 
 
 9.86602 
 
 40,1 
 
 9.83159 
 
 47,o 
 
 47 16 08.47 
 
 .826 
 
 .73523 
 
 67,8 
 
 .67782 
 
 73,5 
 
 .86642 
 
 40,0 
 
 .83112 
 
 47,1 
 
 47 19 34.73 
 
 .827 
 
 .73590 
 
 67,7 
 
 .67709 
 
 73,6 
 
 .86682 
 
 40,0 
 
 .83064 
 
 47,2 
 
 47 23 00.99 
 
 .828 
 
 .73658 
 
 67,6 
 
 .67635 
 
 73,7 
 
 .86722 
 
 39,9 
 
 .83017 
 
 47,3 
 
 47 26 27.26 
 
 .829 
 
 .73726 
 
 67,6 
 
 .67561 
 
 73,7 
 
 .86762 
 
 
 .82970 
 
 47,4 
 
 47 29 53.52 
 
 0.830 
 
 0.73793 
 
 67,5 
 
 0.67488 
 
 7,3,8 
 
 9.86802 
 
 39,7 
 
 9.82922 
 
 47,5 
 
 47 33 19.79 
 
 .831 
 
 .73861 
 
 67,4 
 
 .67414 
 
 73,9 
 
 .86841 
 
 39,6 
 
 .82875 
 
 47,6 
 
 47 36 46.05 
 
 .832 
 
 .73928 
 
 67,3 
 
 .67340 
 
 73,9 
 
 .86881 
 
 39,6 
 
 .82827 
 
 47,7 
 
 47 40 12.32 
 
 .833 
 
 .73995 
 
 67,3 
 
 .67266 
 
 74,0 
 
 .86920 
 
 39,5 
 
 .82779 
 
 47,8 
 
 47 43 38.58 
 
 .834 
 
 .74062 
 
 67,2 
 
 .67192 
 
 74,1 
 
 .86960 
 
 39,4 
 
 .82732 
 
 47,9 
 
 47 47 04.85 
 
 0.835 
 
 0.74130 
 
 67,1 
 
 0.67118 
 
 74,1 
 
 9.86999 
 
 39,3 
 
 9.82684 
 
 48,0 
 
 47 50 31. II 
 
 .836 
 
 .74197 
 
 67,0 
 
 .67044 
 
 74,2 
 
 .87038 
 
 39,2 
 
 .82636 
 
 48,1 
 
 47 53 57.38 
 
 .837 
 
 .74264 
 
 67,0 
 
 .66969 
 
 74,3 
 
 .87078 
 
 39,2 
 
 .82588 
 
 48,2 
 
 47 57 23.64 
 
 .838 
 
 .74331 
 
 66,9 
 
 .66895 
 
 74,3 
 
 .87H7 
 
 39,1 
 
 82539 
 
 48,3 
 
 48 oo 49.91 
 
 .839 
 
 .74398 
 
 66,8 
 
 .66821 
 
 74,4 
 
 .87156 
 
 39,0 
 
 .82491 
 
 48,4 
 
 48 04 16.17 
 
 0.840 
 
 0.74464 
 
 66,7 
 
 0.66746 
 
 74,5 
 
 9.87195 
 
 38,9 
 
 9.82443 
 
 48,5 
 
 48 07 42.44 
 
 .841 
 
 74531 
 
 66,7 
 
 .66672 
 
 74,5 
 
 .87234 
 
 38,8 
 
 .82394 
 
 48,5 
 
 48 n 08.70 
 
 .842 
 
 .74598 
 
 66,6 
 
 .66597 
 
 74,6 
 
 .87273 
 
 38,8 
 
 .82346 
 
 48,6 
 
 48 14 34-97 
 
 .843 
 
 .74664 
 
 66,5 
 
 .66523 
 
 74,7 
 
 .873" 
 
 38,7 
 
 .82297 
 
 48,7 
 
 48 18 01.23 
 
 .844 
 
 74731 
 
 66,4 
 
 .66448 
 
 74,7 
 
 .87350 
 
 38,6 
 
 .82248 
 
 48,8 
 
 48 21 27.50 
 
 0.845 
 .846 
 
 0.74797 
 .74863 
 
 66,4 
 66,3 
 
 0.66373 
 .66298 
 
 74,8 
 74,9 
 
 9.87388 
 .87427 
 
 38,5 
 38,5 
 
 9.82199 
 .82150 
 
 48,9 
 49,0 
 
 48 24 53.76 
 48 28 20.03 
 
 .847 
 
 .74930 
 
 r/,,2 
 
 .66223 
 
 74,9 
 
 .87465 
 
 38,4 
 
 .82IOI 
 
 49,1 
 
 48 31 46.29 
 
 .848 
 
 . 74906 
 
 66,1 
 
 .66148 
 
 75,0 
 
 .87504 
 
 38,4 
 
 .82052 
 
 49,2 
 
 48 35 12.56 
 
 .849 
 
 .75062 
 
 66,1 
 
 .66073 
 
 75,i 
 
 .87542 
 
 38,2 
 
 .82003 
 
 49,3 
 
 48 38 38.82 
 
 0.850 
 
 0.75128 
 
 66,0 
 
 0.65998 
 
 75,1 
 
 9.87580 
 
 38,2 
 
 9.81953 
 
 494 
 
 48 42 05.09 
 
 u 
 
 -itinhiu 
 
 F ' 
 
 cosh iu 
 
 -Fo' 
 
 ,oo'^ u 
 
 -Fo' 
 
 log cosh iu 
 
 F ' 
 
 u 
 
 SMITHSONIAN TABLKS 
 
 208 
 
Circular Functions. 
 
 u 
 
 sin u 
 
 -FO' 
 
 cos u 
 
 -Fo' 
 
 log sin u 
 
 Fo' 
 
 log cos u 
 
 F O ' 
 
 u 
 
 0.850 
 
 0.75128 
 
 66,0 
 
 0.65998 
 
 75,1 
 
 9.87580 
 
 38,2 
 
 9.81953 
 
 49,4 
 
 48 42 05.09 
 
 .851 
 
 75194 
 
 65,9 
 
 .65923 
 
 75,2 
 
 .87618 
 
 38,1 
 
 .81904 
 
 49,5 
 
 48 45 31.35 
 
 .852 
 
 .75200 
 
 65,8 
 
 .65848 
 
 75,3 
 
 .87656 
 
 38,0 
 
 .81854 
 
 49,6 
 
 48 48 57.61 
 
 .853 
 
 .75326 
 
 65,8 
 
 .65773 
 
 75,3 
 
 .87694 
 
 37,9 
 
 .81805 
 
 49,7 
 
 48 52 23.88 
 
 .854 
 
 75391 
 
 65,7 
 
 .65697 
 
 75.4 
 
 .87732 
 
 37,8 
 
 .81755 
 
 49,8 
 
 48 55 50.14 
 
 0.855 
 
 0.75457 
 
 65,6 
 
 0.65622 
 
 75,5 
 
 9.87770 
 
 37,8 
 
 9.81705 
 
 49,9 
 
 48 59 16.41 
 
 .856 
 
 .75523 
 
 65,5 
 
 .65546 
 
 75,5 
 
 .87808 
 
 37,7 
 
 .81655 
 
 5o,o 
 
 49 02 42.67 
 
 .857 
 
 75588 
 
 65,5 
 
 .65471 
 
 75,6 
 
 .87845 
 
 37,6 
 
 .81605 
 
 5o,i 
 
 49 06 08.94 
 
 .858 
 
 .75654 
 
 65,4 
 
 .65395 
 
 75,7 
 
 .87883 
 
 37,5 
 
 .81555 
 
 50,2 
 
 49 09 35.20 
 
 .859 
 
 .75719 
 
 65,3 
 
 .65320 
 
 75,7 
 
 .87920 
 
 37,5 
 
 .81504 
 
 50,3 
 
 49 13 01.47 
 
 0.860 
 
 0.75784 
 
 65,2 
 
 0.65244 
 
 75,8 
 
 9.87958 
 
 37,4 
 
 9.81454 
 
 50,4 
 
 49 16 27.73 
 
 .861 
 
 .75849 
 
 65,2 
 
 .65168 
 
 75,8 
 
 .87995 
 
 37,3 
 
 .81403 
 
 50,5 
 
 49 19 54-00 
 
 .862 
 
 .75915 
 
 65,1 
 
 .65092 
 
 75,9 
 
 .88033 
 
 37,2 
 
 .81353 
 
 50,7 
 
 49 23 20.26 
 
 .863 
 
 .75980 
 
 65,0 
 
 .65016 
 
 76,0 
 
 .88070 
 
 37,2 
 
 .81302 
 
 50,8 
 
 49 26 46.53 
 
 .864 
 
 .76045 
 
 64,9 
 
 .64940 
 
 76,0 
 
 .88107 
 
 37,1 
 
 .81251 
 
 50,9 
 
 49 30 12.79 
 
 0.865 
 
 0.76110 
 
 64,9 
 
 0.64864 
 
 76,1 
 
 9.88144 
 
 37,0 
 
 9.81200 
 
 5i,o 
 
 49 33 39.06 
 
 .866 
 
 .76174 
 
 64,8 
 
 .64788 
 
 76,2 
 
 .88181 
 
 36,9 
 
 .81149 
 
 5i,i 
 
 49 37 05.32 
 
 .867 
 
 .76239 
 
 64,7 
 
 .64712 
 
 76,2 
 
 .88218 
 
 36,9 
 
 .81098 
 
 51,2 
 
 49 40 31.59 
 
 .868 
 
 
 64,6 
 
 .64635 
 
 76,3 
 
 .88255 
 
 36,8 
 
 .81047 
 
 5i,3 
 
 49 43 57.85 
 
 .869 
 
 .76368 
 
 64,6 
 
 .64559 
 
 76,4 
 
 .88291 
 
 36,7 
 
 .80996 
 
 5i,4 
 
 49 47 24.12 
 
 0.870 
 
 0.76433 
 
 64,5 
 
 0.64483 
 
 76,4 
 
 9.88328 
 
 36,6 
 
 9.80944 
 
 5i,5 
 
 49 50 50.38 
 
 .871 
 
 .76497 
 
 64,4 
 
 .64406 
 
 76,5 
 
 .88365 
 
 36,6 
 
 .80893 
 
 51,6 
 
 49 54 16.65 
 
 .872 
 
 .76562 
 
 64,3 
 
 .64330 
 
 76,6 
 
 .88401 
 
 36,5 
 
 .80841 
 
 5i,7 
 
 49 57 42.91 
 
 .873 
 
 .76626 
 
 64,3 
 
 .64253 
 
 76,6 
 
 .88438 
 
 36,4 
 
 .80789 
 
 5i,8 
 
 50 01 09.18 
 
 .874 
 
 .76690 
 
 64,2 
 
 .64176 
 
 76,7 
 
 .88474 
 
 36,3 
 
 .80738 
 
 5i,9 
 
 50 04 35-44 
 
 0.875 
 
 0.76754 
 
 64,1 
 
 0.64100 
 
 76,8 
 
 9.88510 
 
 36,3 
 
 9.80686 
 
 52,0- 
 
 50 08 01.71 
 
 .876 
 
 .76818 
 
 64,0 
 
 .64023' 
 
 76,8 
 
 .88547 
 
 36,2 
 
 .80634 
 
 52,1 
 
 50 II 27.97 
 
 .877 
 
 .76882 
 
 63,9 
 
 .63946 
 
 76,9 
 
 .88583 
 
 36,1 
 
 .'80581 
 
 52,2 
 
 50 14 54.24 
 
 .878 
 
 .76946 
 
 63,9 
 
 .63869 
 
 76,9 
 
 .88619 
 
 36,0 
 
 .80529 
 
 52,3 
 
 50 18 20.50 
 
 .879 
 
 .77010 
 
 63,8 
 
 .63792 
 
 77,o 
 
 .88655 
 
 36,0 
 
 .80477 
 
 52,4 
 
 50 21 46.76 
 
 0.880 
 
 0.77074 
 
 63,7 
 
 0.63715 
 
 77,i 
 
 9.88691 
 
 35,9 
 
 9.80424 
 
 52,5 
 
 50 25 13.03 
 
 .881 
 
 .77138 
 
 63,6 
 
 .63638 
 
 77,i 
 
 .88727 
 
 35,8 
 
 .80372 
 
 52,6 
 
 50 28 39-29 
 
 .882 
 
 .77201 
 
 63,6 
 
 .63561 
 
 77,2 
 
 .88762 
 
 35,8 
 
 .80319 
 
 52,7 
 
 50 32 05 .56 
 
 .883 
 
 .77265 
 
 63,5 
 
 .63484 
 
 77,3 
 
 .88798 
 
 3'5,7 
 
 .80266 
 
 52,9 
 
 50 35 31-82 
 
 .884 
 
 .77328 
 
 63,4 
 
 .63406 
 
 77,3 
 
 .88834 
 
 35,6 
 
 .80213 
 
 53,0 
 
 50 38 58.09 
 
 0.885 
 
 0.77391 
 
 63,3 
 
 0.63329 
 
 77,4 
 
 9.88869 
 
 35,5 
 
 9.80160 
 
 53,i 
 
 50 42 24.35 
 
 .886 
 
 .77455 
 
 63,3 
 
 .63252 
 
 77,5 
 
 .88905 
 
 35,5 
 
 .80107 
 
 53,2 
 
 50 45 50.62 
 
 .887 
 
 .77518 
 
 63,2 
 
 .63174 
 
 77,5 
 
 .88940 
 
 35,4 
 
 .80054 
 
 53,3 
 
 50 49 16.88 
 
 .888 
 
 .77581 
 
 63,1 
 
 .63096 
 
 77,6 
 
 .88976 
 
 35,3 
 
 .80001 
 
 53,4 
 
 50 52 43.15 
 
 .889 
 
 .77644 
 
 63,0 
 
 .63019 
 
 77,6 
 
 .89011 
 
 35,2 
 
 .79947 
 
 53,5 
 
 50 56 09.41 
 
 0.800 
 
 0.77707 
 
 62,9 
 
 0.62941 
 
 77,7 
 
 9.89046 
 
 35,2 
 
 9.79894 
 
 53,6 
 
 50-59 35-68 
 
 .891 
 
 77770 
 
 62,9 
 
 .62863 
 
 77,8 
 
 .89081 
 
 35,i 
 
 79840 
 
 53,7 
 
 51 03 01.94 
 
 .892 
 
 .77833 
 
 62,8 
 
 .62786 
 
 77,8 
 
 .89116 
 
 35,o 
 
 .79786 
 
 53,8 
 
 51 06 28.21 
 
 .893 
 
 .77896 
 
 62,7 
 
 .62708 
 
 77,9 
 
 .89151 
 
 35,o 
 
 .79732 
 
 53,9 
 
 51 09 54-47 
 
 .894 
 
 .77958 
 
 62,6 
 
 .62630 
 
 78,0 
 
 .89186 
 
 34,9 
 
 .79678 
 
 54,1 
 
 51 13 20.74 
 
 0.895 
 
 0.78021 
 
 62,6 
 
 0.62552 
 
 78,o 
 
 9.89221 
 
 34,8 
 
 9.79624 
 
 54,2 
 
 51 16 47.00 
 
 .896 
 
 .78083 
 
 62,5 
 
 .62474 
 
 78,i 
 
 .89256 
 
 34,7 
 
 .79570 
 
 54,3 
 
 51 20 13.27 
 
 897 
 
 .78146 
 
 62,4 
 
 .62396 
 
 78,i 
 
 .89291 
 
 34,7 
 
 .79515 
 
 54,4 
 
 5i 23 39-53 
 
 .898 
 
 .78208 
 
 62,3 
 
 .62318 
 
 78,2 
 
 .89325 
 
 34,6 
 
 .79461 
 
 54,5 
 
 51 27 05.80 
 
 .899 
 
 .78270 
 
 62,2 
 
 .62239 
 
 78,3 
 
 .89360 
 
 34,5 
 
 .79406 
 
 54,6 
 
 51 30 32.06 
 
 0.900 
 
 0.78333' 
 
 62,2 
 
 0.62161 
 
 78,3 
 
 9.89394 
 
 34,5 
 
 9.79352 
 
 54,7 
 
 51 33 58.33 
 
 u 
 
 -isinhiu 
 
 -Fo' 
 
 cosh iu 
 
 -FO' 
 
 sinh iu 
 
 <> Fo' 
 
 log cosh iu 
 
 F O ' 
 
 u 
 
 log . 
 
 SMITHSONIAN TABLES 
 
 20Q 
 
Circular Functions. 
 
 u 
 
 sin u 
 
 F ' 
 
 COS U 
 
 Fo' 
 
 log sin u 
 
 F ' 
 
 log cos u 
 
 Fo' 
 
 u 
 
 0.900 
 
 0.78333 
 
 62,2 
 
 0.62161 
 
 78,3 
 
 9.89394 
 
 34,5 
 
 9.79352 
 
 54,7 
 
 5i33'58'.'33 
 
 .901 
 
 .78395 
 
 62,1 
 
 .62083 
 
 78,4 
 
 .89429 
 
 34,4 
 
 .79297 
 
 54,8 
 
 51 37 24.59 
 
 .902 
 
 .78457 
 
 62,0 
 
 .62004 
 
 78,5 
 
 .89463 
 
 34,3 
 
 79242 
 
 55,o 
 
 51 40 50.86 
 
 .903 
 
 .78519 
 
 6i,9 
 
 .61926 
 
 78,5 
 
 .89497 
 
 34,3 
 
 .79187 
 
 55,i 
 
 51 44 17.12 
 
 .904 
 
 .78581 
 
 61,8 
 
 .61847 
 
 78,6 
 
 .89532 
 
 34,2 
 
 .79132 
 
 55,2 
 
 51 47 43.38 
 
 0.905 
 
 0.78643 
 
 61,8 
 
 0.61769 
 
 78,6 
 
 9.89566 
 
 34,1 
 
 9-79077 
 
 55,3 
 
 51 51 09.65 
 
 .006 
 
 .78704 
 
 6i,7 
 
 .61690 
 
 7&7 
 
 .89600 
 
 34,0 
 
 .79021 
 
 55,4 
 
 51 54 35-91 
 
 .007 
 
 .78766 
 
 61,6 
 
 .61611 
 
 78,8 
 
 .89634 
 
 34,0 
 
 .78966 
 
 .55,5 
 
 51 58 02.18 
 
 .908 
 
 .78827 
 
 61,5 
 
 .61532 
 
 78,8 
 
 .89668 
 
 33,9 
 
 .78910 
 
 55,6 
 
 52 01 28.44 
 
 .909 
 
 .78889 
 
 61,5 
 
 .61453 
 
 78,9' 
 
 .89702 
 
 33,8 
 
 .78855 
 
 55,8 
 
 52 04 54-71 
 
 0.910 
 
 0.78950 
 
 61,4 
 
 0.61375 
 
 79,0 
 
 9.89735 
 
 33,8 
 
 9.78799 
 
 55,9 
 
 52 08 20.97 
 
 .911 
 
 .70012 
 
 6i,3 
 
 .61296 
 
 79,0 
 
 .89769 
 
 33,7 
 
 .78743 
 
 56,0 
 
 52 II 47.24 
 
 .912 
 
 .79073 
 
 61,2 
 
 .61217 
 
 79J 
 
 .89803 
 
 33,6 
 
 .78687 
 
 56,i 
 
 52 15 13-50 
 
 .913 
 
 .79134 
 
 61,1 
 
 .61137 
 
 79,1 
 
 .89836 
 
 33,6 
 
 .78631 
 
 56,2 
 
 52 18 39-77 
 
 .914 
 
 .79195 
 
 61,1 
 
 .61058 
 
 79,2 
 
 .89870 
 
 33,5 
 
 .78574 
 
 56,3 
 
 52 22 06.03 
 
 0.915 
 
 0.79256 
 
 61,0 
 
 0.60979 
 
 79,3 
 
 9.89903 
 
 33,4 
 
 9.78518 
 
 56,4 
 
 52 25 32.30 
 
 .916 
 
 .79317 
 
 60,9 
 
 .60900 
 
 79,3 
 
 89937 
 
 33,3 
 
 .78462 
 
 56,6 52 28 58.56 
 
 .917 
 
 .79378 
 
 60,8 
 
 .60820 
 
 79,4 
 
 .89970 
 
 33,3 
 
 .78405 
 
 56,7 
 
 52 32 24.83 
 
 .918 
 
 .79439 
 
 60,7 
 
 .60741 
 
 79,4 
 
 .00003 
 
 33,2 
 
 .78348 
 
 56,8 
 
 52 35 51-09 
 
 .919 
 
 .79500 
 
 60,7 
 
 .60662 
 
 79,5 
 
 .90036 
 
 33>i 
 
 .78291 
 
 56,9 
 
 52 39 17.36 
 
 0.920 
 
 0.79500 
 
 60,6 
 
 0.60582 
 
 79,6 
 
 9.90070 
 
 33,1 
 
 9.78234 
 
 57,0 
 
 52 42 43.62 
 
 .921 
 
 .79621 
 
 60,5 
 
 .60502 
 
 79,6 
 
 .90103 
 
 33,0 
 
 .78177 
 
 57,2 
 
 52 46 09.89 
 
 .922 
 
 .79681 
 
 60,4 
 
 .60423 
 
 79,7 
 
 .90136 
 
 32,9 
 
 .78120 
 
 57,3 
 
 52 49 36.15 
 
 923 
 
 .79742 
 
 60,3 
 
 .60343 
 
 79,7 
 
 .90168 
 
 32,9 
 
 .78063 
 
 57,4 
 
 52 53 02.42 
 
 .924 
 
 .79802 
 
 60,3 
 
 .60263 
 
 79,8 
 
 .90201 
 
 32,8 
 
 .78005 
 
 57,5 
 
 52 56 28.68 
 
 0.925 
 
 0.79862 
 
 60,2 
 
 0.60183 
 
 79,9 
 
 9.90234 
 
 32,7 
 
 9.77948 
 
 57,6 
 
 52 59 54-95 
 
 .926 
 
 .79922 
 
 60,1 
 
 .60104 
 
 79,9 
 
 .90267 
 
 32,7 
 
 77800 
 
 57,7 
 
 53 03 21.21 
 
 .927 
 
 79982 
 
 60,0 
 
 .60024 
 
 80,0 
 
 .00299 
 
 32,6 
 
 .77832 
 
 57,9 
 
 53 06 47.48 
 
 .928 
 
 .80042 
 
 59,9 
 
 59944 
 
 80,0 
 
 .90332 
 
 32,5 
 
 77774 
 
 58,0 
 
 53 10 13.74 
 
 .929 
 
 .80102 
 
 59,9 
 
 .59864 
 
 80,1 
 
 .90364 
 
 32,5 
 
 .77716 
 
 58,1 
 
 53 13 40.01 
 
 0.930 
 
 0.80162 
 
 59,8 
 
 0.59783 
 
 80,2 
 
 9.90397 
 
 32,4 
 
 9.77658 
 
 58,2 
 
 53 17 06.27 
 
 931 
 
 .80222 
 
 59,7 
 
 .59703 
 
 80,2 
 
 .90429 
 
 32,3 
 
 .77600 
 
 58,4 
 
 53 20 32.53 
 
 932 
 
 .80281 
 
 59,6 
 
 .59623 
 
 80,3 
 
 .90461 
 
 32,3 
 
 77541 
 
 58,5 
 
 53 23 58-80 
 
 933 
 
 .80341 
 
 59,5 
 
 59543 
 
 80,3 
 
 .90494 
 
 32,2 
 
 .77483 
 
 58,6 
 
 53 27 25.06 
 
 934 
 
 .80400 
 
 59,5 
 
 .59462 
 
 80,4 
 
 .90526 
 
 32,1 
 
 .77424 
 
 58,7 
 
 53 30 51-33 
 
 0.935 
 
 0.80460 
 
 59,4 
 
 0.59382 
 
 80,5 
 
 9.90558 
 
 32,1 
 
 9.77365 
 
 58,8 
 
 53 34 17-59 
 
 .936 
 
 .80519 
 
 59,3 
 
 59301 
 
 80,5 
 
 .90590 
 
 32,0 
 
 .77306 
 
 59,o 
 
 53 37 43-86 
 
 937 
 
 .80579 
 
 59,2 
 
 .59221 
 
 80,6 
 
 .90622 
 
 3L9 
 
 77247 
 
 59,1 
 
 53 41 10.12 
 
 .938 
 
 .80638 
 
 59,1 
 
 .59140 
 
 80,6 
 
 .90654 
 
 31,9 
 
 .77188 
 
 59,2 
 
 53 44 36.39 
 
 939 
 
 .80697 
 
 59,1 
 
 .59060 
 
 80,7 
 
 .90686 
 
 31,8 
 
 .77129 
 
 59,3 
 
 53 48 02.65 
 
 0.940 
 
 0.80756 
 
 59,0 
 
 0.58979 
 
 80,8 
 
 9.90717 
 
 31,7 
 
 9.77070 
 
 59,5 
 
 53 51 28.92 
 
 .941 
 
 .80815 
 
 58*9 
 
 58898 
 
 80,8 
 
 .90749 
 
 31,7 
 
 .77010 
 
 59,6 
 
 53 54 55.i8 
 
 .942 
 
 .80874 
 
 58 
 
 .58817 
 
 80,9 
 
 .90781 
 
 31,6 
 
 .76950 
 
 59,7 
 
 53 58 21.45 
 
 943 
 
 .80932 
 
 58,7 
 
 .58736 
 
 80,9 
 
 .00812 
 
 31,5 
 
 .76891 
 
 59,8 
 
 54 01 47-71 
 
 944 
 
 .80991 
 
 58,7 
 
 .58655 
 
 81,0 
 
 .90844 
 
 31,5 
 
 .76831 
 
 60,0 
 
 54 05 13.98 
 
 0.945 
 
 0.81050 
 
 58,6 
 
 0.58574 
 
 81,0 
 
 9.90875 
 
 31,4 
 
 9.76771 
 
 60,1 
 
 54 08 40.24 
 
 .946 
 
 .81108 
 
 58,5 
 
 .58493 
 
 81,1 
 
 .90906 
 
 31,3 
 
 .76711 
 
 60,2 
 
 54 12 06.51 
 
 947 
 
 .81167 
 
 58,4 
 
 .58412 
 
 81,2 
 
 .90938 
 
 31,3 
 
 .76650 
 
 60,3 
 
 54 15 32.77 
 
 .948 
 
 .81225 
 
 58,3 
 
 .58331 
 
 81,2 
 
 .90969 
 
 31,2 
 
 .76590 
 
 60,5 
 
 54 18 59.04 
 
 949 
 
 .81283 
 
 58,2 
 
 .58250 
 
 81,3 
 
 .91000 
 
 3i,i 
 
 .76529 
 
 60,6 
 
 54 22 25.30 
 
 0.950 
 
 0.81342 
 
 58,2 
 
 0.58168 
 
 81,3 
 
 9.9I03I 
 
 3U 
 
 9.76469 
 
 60,7 
 
 54 25 51-57 
 
 u 
 
 -i sinh iu 
 
 -Fo' 
 
 cosh iu 
 
 -Fo' 
 
 l ilnh lu 
 
 F U ' 
 
 log cosh iu 
 
 -Fo' 
 
 u 
 
 100 , 
 
 SMITHSONIAN TABLES 
 
 2IO 
 
Circular Functions. 
 
 u 
 
 sin u 
 
 F ' 
 
 COS U 
 
 Fo' 
 
 log sin u 
 
 Fo' 
 
 log cos u 
 
 F ' 
 
 u 
 
 
 
 
 
 
 
 
 
 
 O / 44 
 
 0.950 
 
 0.81342 
 
 58,2 
 
 0.58168 
 
 8l,3 
 
 9.9I03I 
 
 31,1 
 
 9.76469 
 
 60,7 
 
 54 25 5L57 
 
 .951 
 
 .81400 
 
 58,1 
 
 .58087 
 
 81,4 
 
 .91062 
 
 31,0 
 
 .76408 
 
 60,9 
 
 54 29 17.83 
 
 .952 
 
 .81458 
 
 58,0 
 
 .58006 
 
 8i,5 
 
 .91093 
 
 30,9 
 
 .76347 
 
 61,0 
 
 54 32 44-10 
 
 .953 
 
 .81516 
 
 57,9 
 
 . 57924 
 
 8i,5 
 
 .91124 
 
 30,9 
 
 .76286 
 
 61,1 
 
 54 36 10.36 
 
 .954 
 
 .81574 
 
 57,8 
 
 .57842 
 
 81,6 
 
 91155 
 
 30,8 
 
 .76225 
 
 61,2 
 
 54 39 36.63 
 
 0.955 
 
 0.81631 
 
 57,8 
 
 0.57761 
 
 81,6 
 
 9.91186 
 
 30,7 
 
 9.76163 
 
 61,4 
 
 54 43 02.89 
 
 .956 
 
 .81689 
 
 57,7 
 
 .57679 
 
 8i,7 
 
 .91216 
 
 30,7 
 
 .76102 
 
 6i,5 
 
 54 46 29.15 
 
 957 
 
 .81747 
 
 57,6 
 
 .57597 
 
 8i,7 
 
 .91247 
 
 30,6 
 
 .76040 
 
 61,6 
 
 54 49 55-42 
 
 .958 
 
 .81804 
 
 57,5 
 
 .57516 
 
 81,8 
 
 .91278 
 
 30,5 
 
 75979 
 
 61,8 
 
 54 53 21.68 
 
 959 
 
 .81862 
 
 57,4 
 
 57434 
 
 81,9 
 
 .91308 
 
 30,5 
 
 .75917 
 
 61,9 
 
 54 56 47-95 
 
 0.960 
 
 0.81919 
 
 57,4 
 
 0.57352 
 
 81,9 
 
 9.91339 
 
 30,4 
 
 9.75855 
 
 62,0 
 
 55 oo -14.21 
 
 .961 
 
 0.81976 
 
 57,3 
 
 .57270 
 
 82,0 
 
 .91369 
 
 30,3 
 
 75793 
 
 62,2 
 
 55 03 40.48 
 
 .962 
 
 .82034 
 
 57,2 
 
 .57188 
 
 82,0 
 
 .91399 
 
 30,3 
 
 .75731 
 
 62,3 
 
 55 07 06.74 
 
 .963 
 
 .82091 
 
 57,1 
 
 .57106 
 
 82,1 
 
 .91429 
 
 30,2 
 
 .75668 
 
 62,4 
 
 55 10 33-01 
 
 .964 
 
 .82148 
 
 57,0 
 
 .57024 
 
 82,1 
 
 .91460 
 
 30,1 
 
 .75606 
 
 62,6 
 
 55 13 59.27 
 
 0.965 
 
 0.82205 
 
 56,9 
 
 0.56942 
 
 82,2 
 
 9.91490 
 
 30,i 
 
 9-75543 
 
 62,7 
 
 55 17 25.54 
 
 .966 
 
 .82262 
 
 56,9 
 
 .56859 
 
 82,3 
 
 .91520 
 
 30,0 
 
 .75480 
 
 62,8 
 
 55 20 51.80 
 
 .967 
 
 .82319 
 
 56,8 
 
 .56777 
 
 82,3 
 
 .91550 
 
 29,9 
 
 .75417 
 
 63,0 
 
 55 24 18.07 
 
 .968 
 
 .82375 
 
 56,7 
 
 .56695 
 
 82,4 
 
 .91580 
 
 29,9 
 
 .75354 
 
 63,1 
 
 55 27 44-33 
 
 .969 
 
 .82432 
 
 56,6 
 
 .56612 
 
 82,4 
 
 .91610 
 
 29,8 
 
 .75291 
 
 63,2 
 
 55 31 10. 60 
 
 0.970 
 
 0.82489 
 
 56,5 
 
 0.56530 
 
 82,5 
 
 9.91639 
 
 29,8 
 
 9.75228 
 
 63,4 
 
 55 34 36.86 
 
 .971 
 
 82545 
 
 56,4 
 
 .56447 
 
 82,5 
 
 .91669 
 
 29,7 
 
 .75164 
 
 63,5 
 
 55 38 03.13 
 
 .972 
 
 .82601 
 
 56,4 
 
 .56365 
 
 82,6 
 
 .91699 
 
 29,6 
 
 .75101 
 
 63,6 
 
 55 41 29-39 
 
 973 
 
 .82658 
 
 56,3 
 
 .56282 
 
 82,7 
 
 .91728 
 
 29,6 
 
 .75037 
 
 63,8 
 
 55 44 55-66 
 
 974 
 
 .82714 
 
 56,2 
 
 .56200 
 
 82,7 
 
 .91758 
 
 29,5 
 
 74973 
 
 63,9 
 
 55 48 21.92 
 
 0.975 
 
 0.82770 
 
 56,i 
 
 0.56117 
 
 82,8 
 
 9.91787 
 
 29,4 
 
 9.74009 
 
 64,1 
 
 55 51 48.19 
 
 .976 
 
 .82826 
 
 56,0 
 
 .56034 
 
 82,8 
 
 .91817 
 
 29,4 
 
 .74845 
 
 64,2 
 
 55 55 14.45 
 
 977 
 
 .82882 
 
 56,0 
 
 55951 
 
 82,9 
 
 .91846 
 
 29,3 
 
 .74781 
 
 64,3 
 
 55 58 40.72 
 
 .978 
 
 .82938 
 
 55,9 
 
 .55868 
 
 82,9 
 
 91875 
 
 29,2 
 
 .74717 
 
 64,5 
 
 56 02 06.98 
 
 979 
 
 .82994 
 
 55,8 
 
 .55785 
 
 83,0 
 
 .91905 
 
 29,2 
 
 .74652 
 
 64,6 
 
 56 05 33.25 
 
 0.980 
 
 0.83050 
 
 55,7 
 
 0.55702 
 
 83,0 
 
 9.91934 
 
 29,1 
 
 9.74587 
 
 64,8 
 
 56 08 59.51 
 
 .981 
 
 .83105 
 
 55,6 
 
 .55619 
 
 83,1 
 
 .91963 
 
 29,1 
 
 74522 
 
 64,9 
 
 56 12 25-77 
 
 .982 
 
 .83161 
 
 55,5 
 
 .55536 
 
 83,2 
 
 .91992 
 
 29,0 
 
 74457 
 
 65,0 
 
 56 15 52.04 
 
 .983 
 
 .83216 
 
 55,5 
 
 55453 
 
 83,2 
 
 .92021 
 
 28,9 
 
 .74392 
 
 65,2 
 
 56 19 I8.3O 
 
 984 
 
 .83272 
 
 55,4 
 
 55370 
 
 83,3 
 
 .92050 
 
 28,9 
 
 .74327 
 
 65,3 
 
 56 22 44-57 
 
 0.985 
 
 0.83327 
 
 55,3 
 
 0.55286 
 
 83,3 
 
 9.92079 
 
 28,8 
 
 9.74262 
 
 65,5 
 
 56 26 10.83 
 
 .986 
 
 .83382 
 
 55,2 
 
 .55203 
 
 83,4 
 
 .92107 
 
 28,8 
 
 .74196 
 
 65,6 
 
 56 29 37.10 
 
 .987 
 
 .83438 
 
 55,i 
 
 .55120 
 
 83,4 
 
 .92136 
 
 28,7 
 
 .74131 
 
 65,7 
 
 56 33 03.36 
 
 .988 
 
 .83493 
 
 55,o 
 
 55036 
 
 83,5 
 
 .92165 
 
 28,6 
 
 .74065 
 
 65,9 
 
 56 36 29.63 
 
 .989 
 
 .83548 
 
 55,0 
 
 54953 
 
 83,5 
 
 .92193 
 
 28,6 
 
 .73999 
 
 66,0 
 
 56 39 55.89 
 
 0.090 
 
 0.83603 
 
 54,9 
 
 0.54869 
 
 83,6 
 
 9.92222 
 
 28,5 
 
 9.73933 
 
 66,2 
 
 56 43 22.16 
 
 .991 
 
 .83657 
 
 54,8 
 
 .54785 
 
 83,7 
 
 .92250 
 
 28,4 
 
 
 66,3 
 
 56 46 48.42 
 
 .992 
 
 .83712 
 
 54,7 
 
 .54702 
 
 83,7 
 
 .92279 
 
 28,4 
 
 1 738oo 
 
 66,5 
 
 56 50 14-69 
 
 993 
 
 .83767 
 
 54,6 
 
 .54618 
 
 83-8 
 
 .92307 
 
 28,3 
 
 .73734 
 
 66,6 
 
 56 53 40.95 
 
 .994 
 
 .83821 
 
 54,5 
 
 54534 
 
 83,8 
 
 .92335 
 
 28,3 
 
 .73667 
 
 66,8 
 
 56 57 07.22 
 
 0.995 
 
 0.83876 
 
 54,5 
 
 0.54450 
 
 83,9 
 
 9.92364 
 
 28,2 
 
 9.73600 
 
 66,9 
 
 57 oo 33-48 
 
 .996 
 
 .83930 
 
 54,4 
 
 .54366 
 
 83,9 
 
 .92392 
 
 28,1 
 
 73533 
 
 67,0 
 
 57 03 59.75 
 
 997 
 
 .83985 
 
 54,3 
 
 .54282 
 
 84,0 
 
 .92420 
 
 28,1 
 
 .73466 
 
 67,2 
 
 57 07 26.01 
 
 .998 
 
 .84039 
 
 54,2 
 
 .54198 
 
 84,0 
 
 .92448 
 
 28,0 
 
 73399 
 
 67,3 
 
 57 10 52.28 
 
 .999 
 
 .84093 
 
 54,1 
 
 54II4 
 
 84,1 
 
 .92476 
 
 27,9 
 
 73331 
 
 67,5 
 
 57 14 i8.54 
 
 I.OOO 
 
 0.84147 
 
 54,0 
 
 0.54030 
 
 84,1 
 
 9.92504 
 
 27,9 
 
 9.73264 
 
 67,6 
 
 57 17 44.8i 
 
 u 
 
 -isinhiu 
 
 F ' 
 
 cosh iu 
 
 F O ' 
 
 sinh iu 
 
 coFo' 
 
 log cosh iu 
 
 F O ' 
 
 u 
 
 tog . 
 
 SMITHSONIAN TABLES 
 
 211 
 
Circular Functions. 
 
 u 
 
 sin u 
 
 F ' 
 
 COS U 
 
 F ' 
 
 log sin u 
 
 Fo' 
 
 log cos u 
 
 Fo' 
 
 u 
 
 I.OOO 
 
 0.84147 
 
 54,0 
 
 0.54030 
 
 84,1 
 
 9.92504 
 
 27,9 
 
 9.73204 
 
 67,6 
 
 57 I7'44"8i 
 
 .001 
 
 .84201 
 
 53,9 
 
 .53946 
 
 84,2 
 
 .92532 
 
 27,8 
 
 .73196 
 
 67,8 
 
 57 21 11.07 
 
 .002 
 
 .84255 
 
 53,9 
 
 .53862 
 
 84,3 
 
 .92560 
 
 27,8 
 
 .73128 
 
 67,9 
 
 57 24 37.34 
 
 .003 
 
 .84309 
 
 53,8 
 
 .53778 
 
 84,3 
 
 .92587 
 
 27,7 
 
 73060 
 
 68,1 
 
 57 28 03.60 
 
 .004 
 
 84363 
 
 53,7 
 
 .53693 
 
 84,4 
 
 .92615 
 
 27,6 
 
 .72992 
 
 68,2 
 
 57 31 29.87 
 
 1. 005 
 
 0.84416 
 
 53,6 
 
 0.53609 
 
 84,4 
 
 9.92643 
 
 27,6 
 
 9.72924 
 
 68,4 
 
 57 34 56.13 
 
 .006 
 
 .84470 
 
 53,5 
 
 .53524 
 
 84,5 
 
 .92670 
 
 27,5 
 
 .72855 
 
 68,5 
 
 57 38 22.40 
 
 .007 
 
 .84523 
 
 53,4 
 
 .53440 
 
 84,5 
 
 .92698 
 
 27,5 
 
 .72787 
 
 68,7 
 
 57 4i 48.66 
 
 .008 
 
 .84577 
 
 53,4 
 
 .53355 
 
 84,6 
 
 .92725 
 
 27,4 
 
 .72718 
 
 68,8 
 
 57 45 14.92 
 
 .009 
 
 .84630 
 
 53,3 
 
 .53271 
 
 84,6 
 
 .92752 
 
 27,3 
 
 .72049 
 
 69,0 
 
 57 48 41.19 
 
 1. 010 
 
 0.84683 
 
 53,2 
 
 0.53186 
 
 84,7 
 
 9.92780 
 
 27,3 
 
 9.72580 
 
 69,1 
 
 57 52 07.45 
 
 .on 
 
 .84736 
 
 53>i 
 
 53IOI 
 
 84,7 
 
 .92807 
 
 27,2 
 
 .72511 
 
 69,3 
 
 57 55 33-72 
 
 .012 
 
 .84789 
 
 53,0 
 
 .53017 
 
 84,8 
 
 .92834 
 
 27,2 
 
 .72441 
 
 69,5 
 
 57 58 59.98 
 
 .013 
 
 .84842 
 
 52,9 
 
 .52932 
 
 84,8 
 
 .9285: 
 
 27,1 
 
 .72372 
 
 69,6 
 
 58 02 26.25 
 
 .014 
 
 .84895 
 
 52,8 
 
 .52847 
 
 84,9 
 
 .92888 
 
 27,0 
 
 .72302 
 
 69,8 
 
 58 05 52.51 
 
 1. 015 
 
 0.84948 
 
 52,8 
 
 0.52762 
 
 85,0 
 
 9.92915 
 
 27,0 
 
 9.72232 
 
 69,9 
 
 58 09 18.78 
 
 .Ol6 
 
 .85001 
 
 52,7 
 
 .52677 
 
 85,0 
 
 .92942 
 
 26,9 
 
 .72162 
 
 70,1 
 
 58 12 45.04 
 
 .017 
 
 .85053 
 
 52,6 
 
 .52592 
 
 85,1 
 
 .92969 
 
 26,9 
 
 .72092 
 
 70,2 
 
 58 16 11.31 
 
 .018 
 
 .85106 
 
 52,5 
 
 .52507 
 
 85,1 
 
 .92996 
 
 26,8 
 
 .72022 
 
 70,4 
 
 58 19 37.57 
 
 .OI9 
 
 .85158 
 
 52,4 
 
 .52422 
 
 85,2 
 
 .93023 
 
 26,7 
 
 .71951 
 
 70,6 
 
 58 23 03.84 
 
 I.O2O 
 
 0.85211 
 
 52,3 
 
 0.52337 
 
 85,2 
 
 9.93049 
 
 26,7 
 
 9.71881 
 
 70,7 
 
 58 26 30.10 
 
 .O2I 
 
 .85263 
 
 52,3 
 
 .52251 
 
 85,3 
 
 .93076 
 
 26,6 
 
 .71810 
 
 70,9 
 
 58 29 56.37 
 
 .022 
 
 .85315 
 
 52,2 
 
 .52166 
 
 85,3 
 
 .93103 
 
 26,6 
 
 .71739 
 
 7i,o 
 
 58 33 22.63 
 
 .023 
 
 .85367 
 
 52,1 
 
 .52081 
 
 85,4 
 
 .93129 
 
 26,5 
 
 .71668 
 
 71,2 
 
 58 36 48.90 
 
 .024 
 
 .85419 
 
 52,0 
 
 51995 
 
 85,4 
 
 .93156 
 
 26,4 
 
 71596 
 
 71,3 
 
 58 40 15.16 
 
 1.025 
 
 0.85471 
 
 51,9 
 
 0.51910 
 
 85,5 
 
 9.93182 
 
 26,4 
 
 9.71525 
 
 7i,5 
 
 58 43 41.43 
 
 .026 
 
 .85523 
 
 51,8 
 
 .51824 
 
 85,5 
 
 .93208 
 
 26,3 
 
 .71453 
 
 7i,7 
 
 58 47 07.69 
 
 .027 
 
 .85575 
 
 5i,7 
 
 .51739 
 
 85,6 
 
 .93235 
 
 26,3 
 
 .71382 
 
 7i,8 
 
 58 50 35-96 
 
 .028 
 
 .85627 
 
 51,7 
 
 .51653 
 
 85,6 
 
 .93261 
 
 26,2 
 
 .71310 
 
 72,0 
 
 58 54 00.22 
 
 .029 
 
 .85678 
 
 5i,6 
 
 51568 
 
 85,7 
 
 .93287 
 
 26,1 
 
 .71238 
 
 72,2 
 
 58 57 26.49 
 
 1.030 
 
 0.85730 
 
 5i,5 
 
 0.51482 
 
 85,7 
 
 9.93313 
 
 26,1 
 
 9.71165 
 
 72,3 
 
 59 oo 52-75 
 
 .O3I 
 
 .85781 
 
 5i,4 
 
 .51396 
 
 85,8 
 
 93339 
 
 26,0 
 
 .71093 
 
 72,5 
 
 59 04- 19-02 
 
 .032 
 
 85833 
 
 5i,3 
 
 .51310 
 
 85,8 
 
 .93365 
 
 26,0 
 
 .71020 
 
 72,6 
 
 59 07 45.28 
 
 .033 
 
 .85884 
 
 5i,2 
 
 .51224 
 
 85,9 
 
 .93391 
 
 25,9 
 
 .70948 
 
 72,8 
 
 59 ii 11-54 
 
 .034 
 
 .85935 
 
 5i,i 
 
 .5H39 
 
 85,9 
 
 .93417 
 
 25,8 
 
 .70875 
 
 73,o 
 
 59 14 37-8i 
 
 1 .035 
 
 0.85086 
 
 5i,i 
 
 0.51053 
 
 86,0 
 
 9.93443 
 
 25.8 
 
 9.70802 
 
 73,1 
 
 59 18 04.07 
 
 .036 
 
 .86037 
 
 5i,o 
 
 .50967 
 
 86,0 
 
 .93469 
 
 25,7 
 
 .70729 
 
 73,3 
 
 59 21 30.34 
 
 .037 
 
 .86088 
 
 5O,9 
 
 .50881 
 
 86,1 
 
 93494 
 
 25,7 
 
 .70655 
 
 73,5 
 
 59 24 56.60 
 
 .038 
 
 .86139 
 
 50,8 
 
 .50794 
 
 86,1 
 
 93520 
 
 25,6 
 
 .70582 
 
 73,6 
 
 59 28 22.87 
 
 039 
 
 .86190 
 
 50,7 
 
 .50708 
 
 86,2 
 
 .93546 
 
 25,6 
 
 .70508 
 
 73,8 
 
 59 31 49.13 
 
 1.040 
 
 0.86240 
 
 50,6 
 
 0.50622 
 
 86,2 
 
 9.93571 
 
 25,5 
 
 9.70434 
 
 74,0 
 
 59 35 15.40 
 
 .041 
 
 .86291 
 
 50,5 
 
 .50536 
 
 85,3 
 
 93597 
 
 25,4 
 
 .70360 
 
 74v2 
 
 59 38 41-66 
 
 .042 
 
 .86341 
 
 50,4 
 
 .50449 
 
 85,3 
 
 .93622 
 
 25,4 
 
 .70286 
 
 74,3 
 
 59 41 07.93 
 
 .043 
 
 .86392 
 
 50,4 
 
 .50363 
 
 86,4 
 
 .93647 
 
 25,3 
 
 . 7O2I I 
 
 74,5 
 
 59 45 34-19 
 
 .044 
 
 .86442 
 
 50,3 
 
 .50277 
 
 86,4 
 
 .93673 
 
 25,3 
 
 .70137 
 
 74,7 
 
 59 49 00.46 
 
 1.045 
 
 0.86492 
 
 50,2 
 
 0.50190 
 
 86,5 
 
 9.93698 
 
 25,2 
 
 9.70062 
 
 74,8 
 
 59 52 26.72 
 
 .046 
 
 .85543 
 
 50,1 
 
 .50104 
 
 85,5 
 
 .93723 
 
 25,1 
 
 .69987 
 
 75,0 
 
 59 55 52.99 
 
 .047 
 
 .86593 
 
 50,o 
 
 .50017 
 
 86,6 
 
 .93748 
 
 25J 
 
 .69912 
 
 75,2 
 
 59 59 i<).-'5 
 
 .048 
 
 .86643 
 
 49,9 
 
 49930 
 
 86,6 
 
 93773 
 
 25,0 
 
 .<*Av 
 
 75,4 
 
 60 02 45.52 
 
 .049 
 
 .86693 
 
 49,8 
 
 .49844 
 
 86,7 
 
 .93798 
 
 25,0 
 
 .69761 
 
 75,5 
 
 6b 06 1 1 . 78 
 
 1.050 
 
 0.86742 
 
 49,8 
 
 0.49757 
 
 86,7 
 
 9.93823 
 
 24,9 
 
 <;.<*X>Hf> 
 
 75,7 
 
 60 09 38.05 
 
 u 
 
 -isinhiu 
 
 -F,/ 
 
 cosh iu 
 
 *F ' 
 
 , .sinh iu 
 
 -Fo* 
 
 log cosh iu 
 
 -F ' 
 
 u 
 
 loo . 
 
 SMITHSONIAN TABLCS 
 
 213 
 
Circular Functions. 
 
 u 
 
 sin u 
 
 F ' 
 
 cos u 
 
 F ' 
 
 log sin u 
 
 Fo' 
 
 log cos u 
 
 Fo' 
 
 u 
 
 1.050 
 
 0.86742 
 
 49,8 
 
 0.49757 
 
 86,7 
 
 9.93823 
 
 24,9 
 
 9.69686 
 
 75,7 
 
 6o09 / 38"o5 
 
 .051 
 
 .86792 
 
 49,7 
 
 .49670 
 
 86,8 
 
 .93848 
 
 24,9 
 
 .69610 
 
 75,9 
 
 60 13 04.31 
 
 .052 
 
 .86842 
 
 49,6 
 
 .49584 
 
 86,8 
 
 .93873 
 
 24,8 
 
 .69534 
 
 AI 
 
 60 16 30.58 
 
 053 
 
 .86891 
 
 49,5 
 
 .49497 
 
 86,9 
 
 .93898 
 
 24,7 
 
 .69458 
 
 76,2 
 
 60 19 56.84 
 
 .054 
 
 .86941 
 
 49,4 
 
 .49410 
 
 86,9 
 
 93922 
 
 24,7 
 
 .69381 
 
 76,4 
 
 60 23 23.11 
 
 1.055 
 
 0.86090 
 
 49,3 
 
 0.49323 
 
 87,0 
 
 9.93947 
 
 24,6 
 
 9.69305 
 
 76,6 
 
 60 26 49.37 
 
 .056 
 
 .87039 
 
 49,2 
 
 .49236 
 
 87,0 
 
 .93972 
 
 24,6 
 
 .69228 
 
 76,8 
 
 60 30 15.64 
 
 .057 
 
 .87088 
 
 49,1 
 
 .49149 
 
 87,1 
 
 .93996 
 
 24,5 
 
 .69151 
 
 77,o 
 
 60 33 4L90 
 
 .058 
 
 .87138 
 
 49,1 
 
 .49062 
 
 87,1 
 
 .94021 
 
 24,5 
 
 .69074 
 
 77,1 
 
 60 37 08.17 
 
 .059 
 
 .87187 
 
 49,0 
 
 .48974 
 
 87,2 
 
 94045 
 
 24,4 
 
 .68997 
 
 77,3 
 
 60 40 34-43 
 
 i. 060 
 
 0.87236 
 
 48,9 
 
 0.48887 
 
 87,2 
 
 9.94069 
 
 24,3 
 
 9.68920 
 
 77,5 
 
 60 44 00.69 
 
 .061 
 
 .87284 
 
 48,8 
 
 .48800 
 
 87,3 
 
 .94094 
 
 24,3 
 
 .68842 
 
 77,7 
 
 60 47 26.96 
 
 .062 
 
 .87333 
 
 48,7 
 
 .48713 
 
 87,3 
 
 .94118 
 
 24,2 
 
 .68764 
 
 77,9 
 
 60 50 53.22 
 
 .063 
 
 .87382 
 
 48,6 
 
 .48625 
 
 87,4 
 
 .94142 
 
 24,2 
 
 .68686 
 
 78,o 
 
 60 54 19.49 
 
 .064 
 
 .87430 
 
 48,5 
 
 .48538 
 
 87,4 
 
 .94166 
 
 24,1 
 
 .68608 
 
 78,2 
 
 60 57 45-75 
 
 1.065 
 
 0.87479 
 
 48,5 
 
 0.48450 
 
 87,5 
 
 9.94190 
 
 24,1 
 
 9.68530 
 
 78,4 
 
 61 01 12. 02 
 
 .066 
 
 .87527 
 
 48,4 
 
 .48363 
 
 87,5 
 
 .94214 
 
 24,0 
 
 .68451 
 
 78,6 
 
 61 04 38.28 
 
 .067 
 
 .87576 
 
 48,3 
 
 .48275 
 
 87,6 
 
 .94238 
 
 23,9 
 
 .68373 
 
 78,8 
 
 61 08 04.55 
 
 .068 
 
 .87624 
 
 48,2 
 
 .48188 
 
 87,6 
 
 .94262 
 
 23,9 
 
 .68294 
 
 79,0 
 
 61 ii 30.81 
 
 .069 
 
 .87672 
 
 48,1 
 
 .48100 
 
 87,7 
 
 .94286 
 
 23,8 
 
 .68215 
 
 79,2 
 
 61 14 57.08 
 
 . 
 1.070 
 
 0.87720 
 
 48,0 
 
 0.48012 
 
 87,7 
 
 9.94310 
 
 23,8 
 
 9.68135 
 
 79,3 
 
 61 18 23.34 
 
 .071 
 
 .87768 
 
 47,9 
 
 .47925 
 
 87,8 
 
 .94334 
 
 23,7 
 
 .68056 
 
 79,5 
 
 61 21 49.61 
 
 .072 
 
 .87816 
 
 47,8 
 
 .47837 
 
 87,8 
 
 94357 
 
 23,7 
 
 .67976 
 
 79,7 
 
 61 25 15.87 
 
 .073 
 
 .87864 
 
 47,7 
 
 47749 
 
 87,9 
 
 .94381 
 
 23,6 
 
 .67896 
 
 79,9 
 
 61 28 42.14 
 
 .074 
 
 .879H 
 
 47,7 
 
 .47661 
 
 87,9 
 
 .94405 
 
 23,6 
 
 .67816 
 
 80,1 
 
 61 32 08.40 
 
 1.075 
 
 0.87959 
 
 47,6 
 
 0.47573 
 
 88,0 
 
 9.04428 
 
 23,5 
 
 9-67736 
 
 80,3 
 
 61 35 34.67 
 
 .076 
 
 .88007 
 
 47,5 
 
 .47485 
 
 88,0 
 
 .94451 
 
 23,4 
 
 .67656 
 
 80,5 
 
 61 39 00.93 
 
 .077 
 
 .88054 
 
 47,4 
 
 47397 
 
 88,1 
 
 .94475 
 
 23,4 
 
 .67575 
 
 80,7 
 
 61 42 27.20 
 
 .078 
 
 .88101 
 
 47,3 
 
 .47309 
 
 88,1 
 
 .94498 
 
 23,3 
 
 .67494 
 
 80,9 
 
 61 45 53.46 
 
 079 
 
 .88149 
 
 47,2 
 
 .47221 
 
 88,1 
 
 .94522 
 
 23,3 
 
 .67414 
 
 81,1 
 
 61 49 19.73 
 
 1.080 
 
 0.88196 
 
 47,1 
 
 0.47133 
 
 88,2 
 
 9-94545 
 
 23,2 
 
 9.67332 
 
 81,3 
 
 61 52 45.99 
 
 .081 
 
 .88243 
 
 47,0 
 
 .47045 
 
 88,2 
 
 .94568 
 
 23,2 
 
 .67251 
 
 8i,5 
 
 61 56 12.26 
 
 .082 
 
 .88290 
 
 47,0 
 
 .46956 
 
 88,3 
 
 .94591 
 
 23,1 
 
 .67169 
 
 81,7 
 
 61 59 38.52 
 
 .083 
 
 .88337 
 
 46,9 
 
 .46868 
 
 88,3 
 
 .94614 
 
 23,0 
 
 .67088 
 
 81,9 
 
 62 03 04-79 
 
 .084 
 
 .88384 
 
 46,8 
 
 .46780 
 
 88,4 
 
 .94637 
 
 23,0 
 
 .67006 
 
 82,1 
 
 62 06 31.05 
 
 1.085 
 
 0.88430 
 
 46,7 
 
 0.46691 
 
 88,4 
 
 9.94660 
 
 22,9 
 
 9.66924 
 
 82,3 
 
 62 09 57.31 
 
 .086 
 
 .88477 
 
 46,6 
 
 .46603 
 
 88,5 
 
 .94683 
 
 22,9 
 
 .66841 
 
 82,5 
 
 62 13 23.58 
 
 .087 
 
 .88524 
 
 46,5 
 
 .46514 
 
 88,5 
 
 .94706 
 
 22,8 
 
 .66759 
 
 82,7 
 
 62 16 49.84 
 
 .088 
 
 .88570 
 
 46,4 
 
 .46426 
 
 88,6 
 
 .94729 
 
 22,8 
 
 .66676 
 
 82,9 
 
 62 20 16.11 
 
 .089 
 
 .88616 
 
 46,3 
 
 .46337 
 
 88,6 
 
 94751 
 
 22,7 
 
 .66593 
 
 83,1 
 
 62 23 42.37 
 
 1.090 
 
 0.88663 
 
 46,2 
 
 0.46249 
 
 88,7 
 
 9-94774 
 
 22,7 
 
 9.66516 
 
 83,3 
 
 62 27 08.64 
 
 .091 
 
 .88709 
 
 46,2 
 
 .46160 
 
 88,7 
 
 .94797 
 
 22,6 
 
 .66426 
 
 83,5 
 
 62 30 34.90 
 
 .092 
 
 .88755 
 
 46,1 
 
 .46071 
 
 88,8 
 
 .94819 
 
 22,5 
 
 .66343 
 
 83,7 
 
 62 34 01.17 
 
 .093 
 
 .88801 
 
 46,0 
 
 
 88,8 
 
 .94842 
 
 22,5 
 
 .66259 
 
 83,9 
 
 62 37 27.43 
 
 .094 
 
 .88847 
 
 45,9 
 
 .45894 
 
 88,8 
 
 .94864 
 
 22,4 
 
 .66175 
 
 84,1 
 
 62 40 53.70 
 
 1.095 
 
 0.88893 
 
 45,8 
 
 0.45805 
 
 88,9 
 
 9.94887 
 
 22,4 
 
 9.66091 
 
 84,3 
 
 62 44 19.96 
 
 .096 
 
 .88939 
 
 45,7 
 
 .45716 
 
 88,9 
 
 94909 
 
 22,3 
 
 .66007 
 
 84,5 
 
 62 47 46.23 
 
 .097 
 
 .88984 
 
 45,6 
 
 .45627 
 
 89,0 
 
 94931 
 
 22,3- 
 
 .65922 
 
 84,7 
 
 62 51 12.49 
 
 .098 
 
 .89030 
 
 45,5 
 
 .45538 
 
 89,0 
 
 94954 
 
 22,2 
 
 .65837 
 
 84,9 
 
 62 54 38.76 
 
 .099 
 
 .89075 
 
 45,4 
 
 .45449 
 
 89,1 
 
 .94976 
 
 22,2 
 
 .65752 
 
 85,1 
 
 62 58 05.02 
 
 I.IOO 
 
 0.89121 
 
 45,4 
 
 0.45360 
 
 89,1 
 
 9.94998 
 
 22,1 
 
 9.65667 
 
 85,3 
 
 63 01 31-29 
 
 u 
 
 -isinhiu 
 
 F ' 
 
 cosh iu 
 
 F O ' 
 
 sinh iu 
 
 F ' 
 
 log cosh iu 
 
 F O ' 
 
 u 
 
 loo . 
 
 SMITHSONIAN TABLES 
 
 213 
 
Circular Functions. 
 
 u 
 
 sin u 
 
 IV 
 
 cos u 
 
 *>Fo' 
 
 log sin u 
 
 - Fo' 
 
 log cos u 
 
 <> FO' 
 
 u 
 
 I.IOO 
 
 O.89I2I 
 
 45,4 
 
 0.45360 
 
 89,1 
 
 9.94998 
 
 22,1 
 
 9.65667 
 
 85,3 
 
 63oi'3i"29 
 
 .101 
 
 .89166 
 
 45,3 
 
 .45270 
 
 89,2 
 
 .95020 
 
 22,0 
 
 .65581 
 
 85,5 
 
 63 04 57.55 
 
 .102 
 
 .89211 
 
 45,2 
 
 .45181 
 
 89,2 
 
 .95042 
 
 22,0 
 
 .65496 
 
 85,8 
 
 63 08 23.82 
 
 .103 
 
 .89256 
 
 45,1 
 
 .45092 
 
 89,3 
 
 .95064 
 
 21,9 
 
 .65410 
 
 86,0 
 
 63 n 50.08 
 
 .104 
 
 .89301 
 
 45,0 
 
 .45003 
 
 89,3 
 
 .95086 
 
 2-1,9 
 
 65324 
 
 86,2 
 
 63 15 16.35 
 
 1.105 
 
 0.89346 
 
 44,9 
 
 0.44913 
 
 89,3 
 
 9.95108 
 
 21,8 
 
 9.65238 
 
 86,4 
 
 63 18 42.61 
 
 .106 
 
 .89391 
 
 44,8 
 
 .44824 
 
 89,4 
 
 .95130 
 
 21,8 
 
 .65151 
 
 86,6 
 
 63 22 08.88 
 
 .107 
 
 .89436 
 
 44,7 
 
 .44735 
 
 89,4 
 
 .95151 
 
 21,7 
 
 .65064 
 
 86,8 
 
 63 25 35.14 
 
 .108 
 
 .89481 
 
 44,6 
 
 .44645 
 
 89,5 
 
 .95173 
 
 21,7 
 
 .64977 
 
 87,0 
 
 63 29 OI.4I 
 
 .109 
 
 89525 
 
 44,6 
 
 .44556 
 
 89,5 
 
 95195 
 
 21,6 
 
 .64890 
 
 87,3 
 
 63 32 27.67 
 
 I. IIO 
 
 0.89570 
 
 44,5 
 
 0.44466 
 
 89,6 
 
 9.95216 
 
 21,6 
 
 9.64803* 
 
 87,5 
 
 63 35 53-93 
 
 .III 
 
 .89614 
 
 44,4 
 
 44377 
 
 89,6 
 
 .95238 
 
 21,5 
 
 .64715 
 
 87,7 
 
 63 39 20.20 
 
 .112 
 
 .89659 
 
 44,3 
 
 .44287 
 
 89,7 
 
 -95259 
 
 21,5 
 
 .64628 
 
 87,9 
 
 63 42 46.46 
 
 .113 
 
 .89703 
 
 44,2 
 
 .44197 
 
 89,7 
 
 .95281 
 
 21,4 
 
 .64540 
 
 88,1 
 
 63 46 1,2.73 
 
 .114 
 
 .89747 
 
 44,1 
 
 .44108 
 
 89,7 
 
 95302 
 
 21,3 
 
 .64451 
 
 88,4 
 
 63 49 38.99 
 
 1. 115 
 
 0.89791 
 
 44,0 
 
 0.44018 
 
 89,8 
 
 9.95323 
 
 21,3 
 
 9-64363 
 
 88,6 
 
 63 53 05.26 
 
 .116 
 
 .89835 
 
 43,9 
 
 .43928 
 
 89,8 
 
 95345 
 
 21,2 
 
 .64274 
 
 88,8 
 
 63 56 31.52 
 
 .117 
 
 .89879 
 
 43,8 
 
 .43838 
 
 89,9 
 
 .95366 
 
 21,2 
 
 .64185 
 
 89,0 
 
 63 59 5-7-79 
 
 .118 
 
 .89923 
 
 43,7 
 
 .43748 
 
 89,9 
 
 .95387 
 
 21,1 
 
 .64096 
 
 89,3 
 
 64 03 24.05 
 
 .119 
 
 .89966 
 
 43,7 
 
 .43658 
 
 90,0 
 
 .95408 
 
 21,1 
 
 .64007 
 
 89,5 
 
 64 06 50.32 
 
 I.I2O 
 
 0.90010 
 
 43,6 
 
 0.43568 
 
 90,0 
 
 9.95429 
 
 2I,O 
 
 9.63917 
 
 89,7 
 
 64 10 16.58 
 
 .121 
 
 .90054 
 
 43,5 
 
 .43478 
 
 90,i 
 
 95450 
 
 21,0 
 
 .63827 
 
 90,0 
 
 64 13 42.85 
 
 .122 
 
 .00097 
 
 43,4 
 
 .43388 
 
 90,1 
 
 .95471 
 
 20,9 
 
 .63737 
 
 90,2 
 
 64 17 09.11 
 
 .123 
 
 .90140 
 
 43,3 
 
 .43208 
 
 90,1 
 
 .95492 
 
 20,9 
 
 .63647 
 
 90,4 
 
 64 20 35.38 
 
 .124 
 
 .90184 
 
 43,2 
 
 .43208 
 
 90,2 
 
 .95513 
 
 20,8 
 
 .63556 
 
 90,6 
 
 64 24 01.64 
 
 1. 125 
 
 0.90227 
 
 43,1 
 
 0.43118 
 
 90,2 
 
 9-95534 
 
 20,8 
 
 9-63466 
 
 90,9 
 
 64 27 27.91 
 
 .126 
 
 .90270 
 
 43,0 
 
 .43027 
 
 90,3 
 
 .95554 
 
 20,7 
 
 .63375 
 
 91,1 
 
 64 30 54.17 
 
 .127 
 
 90313 
 
 42,9 
 
 .42937 
 
 90,3 
 
 95575 
 
 :20,6 
 
 .63283 
 
 9i,3 
 
 64 34 20.44 
 
 .128 
 
 .903-56 
 
 42,8 
 
 .42847 
 
 90,4 
 
 .95596 
 
 20,6 
 
 .63192 
 
 91,6 
 
 64 37 46.70 
 
 .129 
 
 90398 
 
 42,8 
 
 .42756 
 
 90,4 
 
 .95616 
 
 20,5 
 
 .63100 
 
 91,8 
 
 64 41 12-97 
 
 I.I30 
 
 0.90441 
 
 42,7 
 
 0.42666 
 
 90,4 
 
 9.95637 
 
 20,5 
 
 9.63008 
 
 92,i 
 
 64 44 39-23 
 
 .131 
 
 .00484 
 
 42,6 
 
 .42576 
 
 90,5 
 
 .95657 
 
 20,4 
 
 .62916 
 
 92,3 
 
 64 48 05.50 
 
 .132 
 
 .90526 
 
 42,5 
 
 .42485 
 
 90,5 
 
 .95678 
 
 20,4 
 
 .62824 
 
 92,5 
 
 64 51 31.76 
 
 133 
 
 .90569 
 
 42,4 
 
 .42394 
 
 90,6 
 
 .95698 
 
 20,3 
 
 .62731 
 
 92,8 
 
 64 54 58.03 
 
 134 
 
 .90611 
 
 42,3 
 
 .42304 
 
 90,6 
 
 .95718 
 
 20,3 
 
 .62638 
 
 93,0 
 
 64 58 24.29 
 
 I-I35 
 
 0.00653 
 
 42,2 
 
 0.42213 
 
 90,7 
 
 9.95738 
 
 2O,2 
 
 9-62545 
 
 93,3 
 
 65 oi 50.56 
 
 .136 
 
 .90696 
 
 42,1 
 
 .42123 
 
 90,7 
 
 95759 
 
 20,2 
 
 .62451 
 
 93,5 
 
 65 05 16.82 
 
 137 
 
 .90738 
 
 42,0 
 
 .42032 
 
 90,7 
 
 .95779 
 
 2O, I 
 
 .62358 
 
 93,8 
 
 65 08 43-08 
 
 .138 
 
 .90780 
 
 41,9 
 
 .41941 
 
 90,8 
 
 .95799 
 
 20,1 
 
 .62264 
 
 94,o 
 
 65 12 09-35 
 
 139 
 
 .90822 
 
 41,9 
 
 .41850 
 
 90,8 
 
 .95819 
 
 2O,O 
 
 .62170 
 
 94,2 
 
 65 15 35.6l 
 
 I.I40 
 
 0.90863 
 
 41,8 
 
 0.41759 
 
 90,9 
 
 9.95839 
 
 20,O 
 
 9.62075 
 
 94,5 
 
 65 19 01.88 
 
 .141 
 
 .90905 
 
 41,7 
 
 .41669 
 
 90,9 
 
 .95859 
 
 19,9 
 
 .61981 
 
 94,7 
 
 65 22 28.14 
 
 .142 
 
 90947 
 
 41,6 
 
 .41578 
 
 90,9 
 
 95879 
 
 19,9 
 
 .61886 
 
 95,0 
 
 65 25 54-41 
 
 .143 
 
 .90988 
 
 41,5 
 
 .41487 
 
 91,0 
 
 .95859 
 
 19,8 
 
 .61791 
 
 95,2 
 
 65 29 20.67 
 
 .144 
 
 .91030 
 
 41,4 
 
 .41396 
 
 91,0 
 
 .95918 
 
 19,7 
 
 .61095 
 
 95,5 
 
 65 32 46.94 
 
 1. 145 
 
 0.91071 
 
 41,3 
 
 0.41305 
 
 91,1 
 
 9.95938 
 
 19,7 
 
 9.61600 
 
 95,8 
 
 65 36 13.20 
 
 .146 
 
 .91112 
 
 41,2 
 
 .41214 
 
 91,1 
 
 .95958 
 
 19,6 
 
 .61504 
 
 96,0 
 
 65 39 39-47 
 
 .147 
 
 .91153 
 
 41,1 
 
 .41122 
 
 91,2 
 
 95977 
 
 19,6 
 
 .61408 
 
 96,3 
 
 65 43 05.73 
 
 .148 
 
 .9H95 
 
 41,0 
 
 .41031 
 
 91,2 
 
 95997 
 
 19,5 
 
 .61311 
 
 </>0 
 
 65 46 32.00 
 
 .149 
 
 .91235 
 
 40,9 
 
 .40940 
 
 9L2 
 
 .96016 
 
 19,5 
 
 .61215 
 
 96,8 
 
 65 49 58.26 
 
 i.i'SO 
 
 0.91276 
 
 40,8 
 
 0.40849 
 
 91,3 
 
 9-96036 
 
 19,4 
 
 9.6lll8 
 
 97fl 
 
 65 53 24-53 
 
 u 
 
 -isinhiu 
 
 Fo' 
 
 cosh iu 
 
 -FO' 
 
 Ion 8inh JU 
 
 -Fo' 
 
 log cosh iu 
 
 
 u 
 
 log , 
 
 SMITHSONIAN TABLES 
 
 214 
 
Circular Functions. 
 
 
 
 
 
 
 
 
 
 
 11 
 
 sin u 
 
 Fo' 
 
 cos u 
 
 F ' 
 
 log sin u 
 
 Fo' 
 
 log cos u 
 
 -PC' 
 
 u 
 
 1.150 
 
 0.91276 
 
 40,8 
 
 0.40849 
 
 91,3 
 
 9.96036 
 
 19,4 
 
 9.6lll8 
 
 97,o 
 
 6553 / 24 / . / 53 
 
 .151 
 
 .91317 
 
 40,8 
 
 .40757 
 
 91,3 
 
 96055 
 
 19,4 
 
 .6lO2I 
 
 97,3 
 
 65 56 50.79 
 
 .152 
 
 .91358 
 
 40,7 
 
 .40666 
 
 9i,4 
 
 .96075 
 
 19,3 
 
 .60923 
 
 97,6 
 
 66 oo 17.06 
 
 .153 
 
 .91399 
 
 40,6 
 
 .40575 
 
 91,4 
 
 .96094 
 
 19,3 
 
 .60826 
 
 97,8 
 
 66 03 43.32 
 
 .154 
 
 .91439 
 
 40,5 
 
 .40483 
 
 91,4 
 
 .96II3 1 
 
 19,2 
 
 .60728 
 
 98,i 
 
 66 07 09-59 
 
 1. 155 
 
 0.91479 
 
 40,4 
 
 0.40392 
 
 91,5 
 
 9.96132 
 
 19,2 
 
 9.60629 
 
 98,4 
 
 66 10 35.85 
 
 .156 
 
 .91520 
 
 40,3 
 
 .40300 
 
 91,5 
 
 .96152 
 
 19,1 
 
 .60531 
 
 98,6 
 
 66 14 02. 12 
 
 .157 
 
 .91560 
 
 40,2 
 
 .40209 
 
 91,6 
 
 .96171 
 
 19,1 
 
 .60432 
 
 98,9 
 
 66 17 28.38 
 
 .158 
 
 .91600 
 
 40,1 
 
 .40117 
 
 91,6 
 
 .96190 
 
 19,0 
 
 .60333 
 
 99,2 
 
 66 20 54.65 
 
 .159 
 
 .91640 
 
 40,0 
 
 .40026 
 
 91,6 
 
 .96209 
 
 19,0 
 
 .60234 
 
 99,4 
 
 66 24 20.91 
 
 1.160 
 
 0.91680 
 
 39,9 
 
 0.39934 
 
 9i7 
 
 9.96228 
 
 18,9 
 
 9.60134 
 
 99,7 
 
 66 27 47.18 
 
 .161 
 
 .91720 
 
 39,8 
 
 .39842 
 
 91,7 
 
 .96246 
 
 18,9 
 
 .60034 
 
 100,0 
 
 66 31 13.44 
 
 .162 
 
 .91760 
 
 39,8 
 
 .39751 
 
 91,8 
 
 .96265 
 
 18,8 
 
 59934 
 
 100,3 
 
 66 34 39.70 
 
 .163 
 
 .91800 
 
 39,7 
 
 .39659 
 
 91,8 
 
 .96284 
 
 18,8 
 
 .59834 
 
 100,5 
 
 66 38 05.97 
 
 .164 
 
 .91839 
 
 39,6 
 
 .39567 
 
 91,8 
 
 .96303 
 
 18,7 
 
 59733 
 
 100,8 
 
 66 41 32.23 
 
 1.165 
 
 0.91879 
 
 39,5 
 
 0.39475 
 
 91,9 
 
 9-96322 
 
 18,7 
 
 9.59632 
 
 IOI,I 
 
 66 44 58.50 
 
 .166 
 
 .91918 
 
 39,4 
 
 .39383 
 
 91,9 
 
 .96340 
 
 18,6 
 
 .59531 
 
 101,4 
 
 66 48 24.76 
 
 .167 
 
 .91958 
 
 39,3 
 
 .39291 
 
 92,0 
 
 96359 
 
 18,6 
 
 .59430 
 
 101,6 
 
 66 51 51.03 
 
 .168 
 
 .91997 
 
 39,2 
 
 .39199 
 
 92,0 
 
 96377 
 
 18,5 
 
 .59328 
 
 101,9 
 
 66 55 17.29 
 
 .169 
 
 .92036 
 
 39,1 
 
 .39107 
 
 92,0 
 
 .96396 
 
 18,5 
 
 .59226 
 
 102,2 
 
 66 58 43.56 
 
 1.170 
 
 0.92075 
 
 39,0 
 
 0.39015 
 
 92,1 
 
 9.96414 
 
 18,4 
 
 9.59123 
 
 102,5 
 
 67 02 09.82 
 
 .171 
 
 .92114 
 
 38,9 
 
 .38923 
 
 92,1 
 
 96433 
 
 18,4 
 
 .59021 
 
 102,8 
 
 67 05 36.09 
 
 .172 
 
 .92153 
 
 38,8 
 
 .38831 
 
 92,2 
 
 .96451 
 
 18,3 
 
 
 103,1 
 
 67 09 02.35 
 
 .173 
 
 .92192 
 
 38,7 
 
 .38739 
 
 92,2 
 
 .96469 
 
 18,2 
 
 .58815 
 
 103,4 
 
 67 12 28.62 
 
 .174 
 
 .92230 
 
 38,6 
 
 .38647 
 
 92,2 
 
 .96487 
 
 18,2 
 
 .58711 
 
 103,6 
 
 67 15 54-88 
 
 I.I75 
 
 0.92269 
 
 38,6 
 
 0.38554 
 
 92,3 
 
 9.96506 
 
 18,1 
 
 9.58607 
 
 103,9 
 
 67 19 21.15 
 
 .176 
 
 .92307 
 
 38,5 
 
 .38462 
 
 92,3 
 
 .96524 
 
 18,1 
 
 .58503 
 
 104,2 
 
 67 22 47.41 
 
 .177 
 
 .92346 
 
 38,4 
 
 .38370 
 
 92,3 
 
 .96542 
 
 18,0 
 
 .58399 
 
 104,5 
 
 67 26 13.68 
 
 .178 
 
 .92384 
 
 38,3 
 
 .38277 
 
 92,4 
 
 .96560 
 
 18,0 
 
 .58204 
 
 104,8 
 
 67 29 39-94 
 
 .179 
 
 .92422 
 
 38,2 
 
 .38185 
 
 92,4 
 
 .96578 
 
 17,9 
 
 .58189 
 
 105,1 
 
 67 33 06.21 
 
 1.180 
 
 0.92461 
 
 38,1 
 
 0.38092 
 
 92,5 
 
 9.96596 
 
 17,9 
 
 9-58084 
 
 105,4 
 
 67 36 32.47 
 
 .181 
 
 .92499 
 
 38,0 
 
 .38000 
 
 92,5 
 
 .96614 
 
 17,8 
 
 .57978 
 
 105,7 
 
 67 39 58.74 
 
 .182 
 
 .92537 
 
 37,9 
 
 .37907 
 
 92,5 
 
 .96631 
 
 17,8 
 
 .57872 
 
 106,0 
 
 67 43 25.00 
 
 .183 
 
 92574 
 
 37,8 
 
 .37815 
 
 92,6 
 
 .96649 
 
 17,7 
 
 .57766 
 
 106,3 
 
 67 46 51.27 
 
 .184 
 
 .92612 
 
 37,7 
 
 37722 
 
 92,6 
 
 .96667 
 
 17,7 
 
 .-57660 
 
 106,6 
 
 67 50 17.53 
 
 1.185 
 
 0.92650 
 
 37,6 
 
 0.37630 
 
 92,6 
 
 9.96684 
 
 17,6 
 
 9-57553 
 
 106,9 
 
 67 53 43.8o 
 
 .186 
 
 .92687 
 
 37,5 
 
 37537 
 
 92,7 
 
 .96702 
 
 17,6 
 
 57446 
 
 107,2 
 
 *>7 57 10. 06 
 
 .187 
 
 .92725 
 
 37,4 
 
 .37444 
 
 92,7 
 
 .96720 
 
 17,5 
 
 57339 
 
 107,5 
 
 68 oo 36.33 
 
 .188 
 
 .92762 
 
 37,4 
 
 37352 
 
 92,8 
 
 .96737 
 
 17,5 
 
 .57231 
 
 107,9 
 
 68 04 02.59 
 
 .189 
 
 .92800 
 
 37,3 
 
 .37259 
 
 92,8 
 
 .96755 
 
 17,4 
 
 .57123 
 
 108,2 
 
 68 07 28.85 
 
 1.190 
 
 0.92837 
 
 37,2 
 
 0.37166 
 
 92,8 
 
 9.96772 
 
 17,4 
 
 9.570I5 
 
 108,5 
 
 68 10 55.12 
 
 .191 
 
 .92874 
 
 37,1 
 
 .37073 
 
 92,9 
 
 .96789 
 
 17,3 
 
 .56906 
 
 108,8 
 
 68 14 21.38 
 
 .192 
 
 .9291-1 
 
 37,o 
 
 .36980 
 
 92,9 
 
 .96807 
 
 17,3 
 
 56797 
 
 109,1 
 
 68 17 47.65 
 
 .193 
 
 .92948 
 
 36,9 
 
 .36887 
 
 92,9 
 
 .96824 
 
 17,2 
 
 .56688 
 
 109,4 
 
 68 21 13.91 
 
 .194 
 
 .92985 
 
 36,8 
 
 .36794 
 
 93,o 
 
 .96841 
 
 17,2 
 
 .56578 
 
 109,8 
 
 68 24 40.18 
 
 1. 195 
 
 0.93022 
 
 36,7 
 
 0.36701 
 
 93,0 
 
 9-96858 
 
 I7,i 
 
 9.56468 
 
 IIO, I 
 
 68 28 06.44 
 
 .196 
 
 .93058 
 
 36,6 
 
 .36608 
 
 93,i 
 
 .96875 
 
 17,1 
 
 .56358 
 
 110,4 
 
 68 31 32.71 
 
 
 .93095 
 
 36,5 
 
 36515 
 
 93,1 
 
 .96893 
 
 17,0 
 
 .56247 
 
 110,7 
 
 68 34 58.97 
 
 .198 
 
 .93131 
 
 36,4 
 
 .36422 
 
 93,1 
 
 .06910 
 
 i7,o 
 
 .56137 
 
 III,O 
 
 68 38 25.24 
 
 .199 
 
 .93168 
 
 36,3 
 
 36329 
 
 93,2 
 
 .96927 
 
 16,9 
 
 .56025 
 
 111,4 
 
 68 41 51.50 
 
 i. 200 
 
 0.93204 
 
 36,2 
 
 0.36236 
 
 93,2 
 
 9.96943 
 
 16,9 
 
 9.55914 
 
 m,7 
 
 68 45 17.77 
 
 u 
 
 i sinh iu 
 
 F ' 
 
 cosh iu 
 
 wF ' 
 
 sinh iu 
 
 F O ' 
 
 log cosh iu 
 
 F O ' 
 
 u 
 
 loo . 
 
 SMITHSONIAN TABLES 
 
 215 
 
Circular Functions. 
 
 u 
 
 sin u 
 
 <-F ' 
 
 cos u 
 
 F * 
 
 log sin u 
 
 - Fo' 
 
 log cos u 
 
 "Fo' 
 
 u 
 
 I.2OO 
 
 0.93204 
 
 36,2 
 
 0.36236 
 
 93,2 
 
 9.96943 
 
 16,9 
 
 9.55914 
 
 111,7 
 
 684s' i 7^77 
 
 .201 
 
 .93240 
 
 36,1 
 
 .36143 
 
 93,2 
 
 .96960 
 
 16,8 
 
 .55802 
 
 112,0 
 
 68 48 44.03 
 
 .202 
 
 .932/6 
 
 36,0 
 
 .36049 
 
 93,3 
 
 .96977 
 
 16,8 
 
 .55650 
 
 1 12,4 
 
 68 52 10.30 
 
 .203 
 
 93312 
 
 36,0 
 
 .35956 
 
 93,3 
 
 .96994 
 
 16,7 
 
 55577 
 
 112,7 
 
 68 55 36.56 
 
 .204 
 
 .93348 
 
 35,9 
 
 .35863 
 
 93,3 
 
 .97011 
 
 16,7 
 
 55464 
 
 113,0 
 
 68 59 02.83 
 
 1.205 
 
 0.93384 
 
 35,8 
 
 0.35769 
 
 93,4 
 
 9.97027 
 
 16,6 
 
 9-55351 
 
 113,4 
 
 69 02 29.09 
 
 .206 
 
 93420 
 
 35,7 
 
 .35676 
 
 93,4 
 
 97044 
 
 16,6 
 
 .55237 
 
 H3,7 
 
 69 05 55.36 
 
 .207 
 
 93455 
 
 35,6 
 
 .35582 
 
 93,5 
 
 .97060 
 
 16,5 
 
 .55124 
 
 114,1 
 
 69 09 21.62 
 
 .208 
 
 93491 
 
 35,5 
 
 .35489 
 
 93,5 
 
 .97077 
 
 16,5 
 
 .55009 
 
 114,4 
 
 69 12 47.89 
 
 .209 
 
 .93526 
 
 35,4 
 
 35395 
 
 93,5 
 
 .97093 
 
 16,4 
 
 .54895 
 
 114,8 
 
 69 16 14.15 
 
 I.2IO 
 
 0.93562 
 
 35,3 
 
 0.35302 
 
 93,6 
 
 9.97IIO 
 
 16,4 
 
 9.54780 
 
 i i'5,i 
 
 69 19 40.42 
 
 .211 
 
 .93597 
 
 35,2 
 
 .35208 
 
 93,6 
 
 .97126 
 
 16,3 
 
 .54665 
 
 H5,5 
 
 69 23 06.68 
 
 .212 
 
 .93632 
 
 35,i 
 
 .35H5 
 
 93,6 
 
 .97142 
 
 16,3 
 
 54549 
 
 H5,8 
 
 69 26 32.95 
 
 .213 
 
 .93667 
 
 35,o 
 
 35021 
 
 93,7 
 
 .97159 
 
 16,2 
 
 54433 
 
 116,2 
 
 69 29 59.21 
 
 .214 
 
 93702 
 
 34,9 
 
 34927 
 
 93,7 
 
 97175 
 
 16,2 
 
 54317 
 
 "6,5 
 
 69 33 25-47 
 
 1. 215 
 
 0-93737 
 
 34,8 
 
 0.34834 
 
 93,7 
 
 9.97I9I 
 
 16,1 
 
 9-54200 
 
 116,9 
 
 69 36 51-74 
 
 .216 
 
 .93772 
 
 34,7 
 
 .34740 
 
 93,8 
 
 97207 
 
 16,1 
 
 .54083 
 
 117,2 
 
 69 40 18.00 
 
 .217 
 .218 
 
 .93806 
 .93841 
 
 34,6 
 34,6 
 
 .34646 
 .34552 
 
 93,8 
 93,8 
 
 .97223 
 .97239 
 
 16,0 
 16,0 
 
 .'53848 
 
 117,6 
 118,0 
 
 69 43 44.27 
 69 47 10. S3 1 
 
 .219 
 
 .93876 
 
 34,5 
 
 34458 
 
 93,9 
 
 .97255 
 
 15,9 
 
 .53730 
 
 "8,3 
 
 69 50 36.80 
 
 I.22O 
 
 0.93910 
 
 34,4 
 
 0.34365 
 
 93,9 
 
 9.97271 
 
 15,9 
 
 9.536n 
 
 "8,7 
 
 69 54 03.06 
 
 .221 
 
 93944 
 
 34,3 
 
 .34271 
 
 93,9 
 
 .97287 
 
 15,8 
 
 53492 
 
 119,1 
 
 69 57 29.33 
 
 .222 
 
 .93978 
 
 34,2 
 
 .34177 
 
 94,0 
 
 .97303 
 
 15,8 
 
 .53373 
 
 "9,4 
 
 70 oo 55-59 
 
 223 
 
 .94013 
 
 34,1 
 
 34083 
 
 94,0 
 
 .97319 
 
 15,7 
 
 .53253 
 
 "9,8 
 
 70 04 21.86 
 
 .224 
 
 .94047 
 
 34,0 
 
 .33989 
 
 94,0 
 
 97334 
 
 15,7 
 
 .53133 
 
 120,2 
 
 70 07 48.12 
 
 1. 225 
 
 0.94081 
 
 33,9 
 
 0.33895 
 
 94,1 
 
 9- 97350 
 
 15,6 
 
 9.53013 
 
 120,5 
 
 70 ii 14.39 
 
 .226 
 
 .94114 
 
 33,8 
 
 .33800 
 
 94,1 
 
 .97366 
 
 15,6 
 
 .52892 
 
 120,9 
 
 70 14 40.65 
 
 .227 
 
 .94148 
 
 33,7 
 
 .33706 
 
 94,1 
 
 .97381 
 
 15,5 
 
 .52771 
 
 121,3 
 
 70 18 06.92 
 
 .228 
 
 .94182 
 
 33,6 
 
 .33612 
 
 94,2 
 
 97397 
 
 15,5 
 
 .52650 
 
 121,7 
 
 70 21 33.18 
 
 .229 
 
 .94215 
 
 33,5 
 
 .33518 
 
 94,2 
 
 .97412 
 
 15,5 
 
 52528 
 
 122,1 
 
 70 24 59-44 
 
 I.23O 
 
 0.94249 
 
 33,4 
 
 0.33424 
 
 94,2 
 
 9.97428 
 
 15,4 
 
 9-52406 
 
 122,5 
 
 70 28 25.71 
 
 .231 
 
 .94282 
 
 33,3 
 
 33330 
 
 94,3 
 
 97443 
 
 15,4 
 
 .52283 
 
 122,9 
 
 70 31 51.98 
 
 .232 
 
 .94316 
 
 33,2 
 
 .33235 
 
 94,3 
 
 .97458 
 
 15,3 
 
 .52160 
 
 123,2 
 
 70 35 18.24 
 
 233 
 
 .94349 
 
 33,1 
 
 .33141 
 
 94,3 
 
 97474 
 
 15,3 
 
 .52036 
 
 123,6 
 
 70 38 44.51 
 
 234 
 
 .94382 
 
 33,0 
 
 .33047 
 
 944 
 
 .97489 
 
 15,2 
 
 .51913 
 
 124,0 
 
 70 42 10.77 
 
 1.235 
 
 0.04415 
 
 33,0 
 
 0.32952 
 
 94,4 
 
 9.97504 
 
 15,2 
 
 9.51788 
 
 124,4 
 
 70 45 37.04 
 
 .236 
 
 .94448 
 
 32,9 
 
 .32858 
 
 94,4 
 
 97519 
 
 I5,i 
 
 51664 
 
 124,8 
 
 70 49 03.30 
 
 .237 
 
 9448i 
 
 32,8 
 
 .32763 
 
 94,5 
 
 .97534 
 
 I5,i 
 
 51539 
 
 125,2 
 
 70 52 29-57 
 
 .238 
 
 .94513 
 
 32,7 
 
 .32669 
 
 94,5 
 
 97549 
 
 I5,o 
 
 .51413 
 
 125,6 
 
 70 55 55.83 
 
 239 
 
 .94546 
 
 32,6 
 
 .32574 
 
 94,5 
 
 .97564 
 
 I5,o 
 
 .51287 
 
 126,1 
 
 70 59 22.09 
 
 1.240 
 
 0.94578 
 
 32,5 
 
 0.32480 
 
 94,6 
 
 9-97579 
 
 14,9 
 
 9.5n6i 
 
 126,5 
 
 71 02 48.36 
 
 .241 
 
 .9461/1 
 
 3^,4 
 
 .32385 
 
 94,6 
 
 97594 
 
 14,9 
 
 .51034 
 
 126,9 
 
 71 06 14. <>j 
 
 .242 
 
 .94643 
 
 32,3 
 
 .32290 
 
 94,6 
 
 .97609 
 
 14,8 
 
 .50007 
 
 127,3 
 
 71 09 40.89 
 
 243 
 
 .94675 
 
 32,2 
 
 .32196 
 
 94,7 
 
 .97624 
 
 14,8 
 
 .50780 
 
 127,7 
 
 71 13 07.15 
 
 244 
 
 .94708 
 
 32,1 
 
 .32101 
 
 94,7 
 
 .97638 
 
 14,7 
 
 .50652 
 
 128,1 
 
 71 16 33.42 
 
 1.245 
 
 0.94740 
 
 32,0 
 
 0.32006 
 
 94,7 
 
 9.97653' 
 
 14,7 
 
 9.50524 
 
 128,6 
 
 71 19 59.68 
 
 .246 
 .247 
 
 .94772 
 94003 
 
 31,9 
 3i,8 
 
 .31912 
 .31817 
 
 94,8 
 94,8 
 
 .97668 
 .97682 
 
 14,6 
 14,6 
 
 50395 
 .50266 
 
 129,0 
 129,4 
 
 71 23 25.95 
 71 26 52.21 
 
 .248 
 
 
 3i,7 
 
 .31722 
 
 94,8 
 
 .97607 
 
 14,5 
 
 .50136 
 
 129,8 
 
 71 30 18.48 
 
 249 
 
 .94867 
 
 31,6 
 
 .31627 
 
 94,9 
 
 977II 
 
 14,5 
 
 .50006 
 
 130,3 
 
 71 3'3 44-74 
 
 1.250 
 
 0.94898 
 
 3i,5 
 
 0.31532 
 
 94,9 
 
 9.97726 
 
 14,4 
 
 9.49875 
 
 130,7 
 
 71 37 ".oi 
 
 u 
 
 isinhiu 
 
 F/ 
 
 cosh iu 
 
 -Fo' 
 
 i tlnh lu 
 
 FV 
 
 loo cosh iu 
 
 -FO' 
 
 u 
 
 log , 
 
 SMITHSONIAN TABLES 
 
 JI'i 
 
Circular Functions. 
 
 u 
 
 sin u 
 
 FO' 
 
 cos u 
 
 F ' 
 
 log sin u 
 
 Fo' 
 
 log cos u 
 
 *>Fo' 
 
 u 
 
 
 
 
 
 
 
 
 
 
 O / H 
 
 1.250 
 
 0.94898 
 
 3i,5 
 
 0.31532 
 
 94,9 
 
 9.97726 
 
 14,4 
 
 9.49875 
 
 130,7 
 
 71 37 11. 01 
 
 .251 
 
 .94930 
 
 31,4 
 
 .31437 
 
 94,9 
 
 .97740 
 
 14,4 
 
 .49745 
 
 131,1 
 
 71 40 37-27 
 
 .252 
 
 .94961 
 
 31,3 
 
 .31342 
 
 95,0 
 
 97755 
 
 14,3 
 
 .49613 
 
 131,6 
 
 71 44 03.54 
 
 .253 
 
 .94993 
 
 31,2 
 
 .31247 
 
 95,0 
 
 .97769 
 
 14,3 
 
 .49481 
 
 132,0 
 
 71 47 29.80 
 
 .254 
 
 .95024 
 
 31,2 
 
 .31152 
 
 95,0 
 
 .97783 
 
 14,2 
 
 49349 
 
 132,5 
 
 71 50 56.07 
 
 1.255 
 
 0.95055 
 
 31,1 
 
 0.31057 
 
 95,1 
 
 9-97797 
 
 14,2 
 
 9.40216 
 
 132,9 
 
 71 54 22.33 
 
 .256 
 
 .95086 
 
 31,0 
 
 .30962 
 
 95,i 
 
 .97812 
 
 14,1 
 
 .49083 
 
 133,4 
 
 71 57 48.60 
 
 257 
 
 .95H7 
 
 30,9 
 
 .30867 
 
 95,i 
 
 .97826 
 
 14,1 
 
 .48950 
 
 133,8 
 
 72 01 14.86 
 
 .258 
 
 .95148 
 
 30,8 
 
 .30772 
 
 95,i 
 
 .97840 
 
 14,0 
 
 .48816 
 
 134,3 
 
 72 04 41.13 
 
 .259 
 
 .95178 
 
 30,7 
 
 .30677 
 
 95,2 
 
 .97854 
 
 14,0 
 
 .48681 
 
 134,7 
 
 72 08 07.39 
 
 1.260 
 
 0.95209 
 
 30,6 
 
 0.30582 
 
 95,2 
 
 9.97868 
 
 13,9 
 
 9.48546 
 
 135,2 
 
 72 II 33.66 
 
 .261 
 
 .95240 
 
 30,5 
 
 .30486 
 
 95,2 
 
 .97882 
 
 13,9 
 
 .48411 
 
 135,7 
 
 72 14 59.92 
 
 .262 
 
 .95270 
 
 30,4 
 
 .30391 
 
 95,3 
 
 .9780 
 
 13,9 
 
 .48275 
 
 136,1 
 
 72 18 26.19 
 
 .263 
 
 95300 
 
 30,3 
 
 .30296 
 
 95,3 
 
 .97909 
 
 13,8 
 
 .48138 
 
 136,6 
 
 72 21 52.45 
 
 .264 
 
 95331 
 
 30,2 
 
 .30201 
 
 95,3 
 
 .97923 
 
 13,7 
 
 .48002 
 
 i'37,i 
 
 72 25 18.72 
 
 1.265 
 
 0.95361 
 
 30,1 
 
 0.30105 
 
 95,4 
 
 9.97937 
 
 13,7 
 
 9.47864 
 
 137,6 
 
 72 28 44-98 
 
 .266 
 
 95391 
 
 30,0 
 
 .30010 
 
 95,4 
 
 .97951 
 
 13,7 
 
 .47726 
 
 138,0 
 
 72 32 11.24 
 
 .267 
 
 95421 
 
 29,9 
 
 .29914 
 
 95,4 
 
 .97064 
 
 13,6 
 
 .47588 
 
 138,5 
 
 72 35 37-51 
 
 .268 
 
 95451 
 
 29,8 
 
 .29819 
 
 95,5 
 
 .97978 
 
 13,6 
 
 47449 
 
 I39,o 
 
 72 39 03-77 
 
 .269 
 
 .95480 
 
 29,7 
 
 .29724 
 
 95,5 
 
 .97991 
 
 13,5 
 
 47310 
 
 139,5 
 
 72 42 30.04 
 
 1.270 
 
 0.95510 
 
 29,6 
 
 0.29628 
 
 95,5 
 
 9.98005 
 
 13,5 
 
 9.47170 
 
 140,0 
 
 72 45 56.30 
 
 .271 
 
 .95540 
 
 29,5 
 
 .29533 
 
 95,5 
 
 .98018 
 
 13,4 
 
 .47030 
 
 140,5 
 
 72 49 22.57 
 
 .272 
 
 .95569 
 
 29,4 
 
 .29437 
 
 95,6 
 
 .98032 
 
 13,4 
 
 .46889 
 
 141,0 
 
 72 52 48.83 
 
 .273 
 
 95599 
 
 29,3 
 
 .29341 
 
 95,6 
 
 .98045 
 
 13,3 
 
 .46748 
 
 Hi,5 
 
 72 56 15.10 
 
 .274 
 
 .95628 
 
 29,2 
 
 .29246 
 
 95,6 
 
 .98058 
 
 13,3 
 
 .46606 
 
 142,0 
 
 72 59 41.36 
 
 1.275 
 
 0.95657 
 
 29,2 
 
 0.29150 
 
 95,7 
 
 9.98072 
 
 13,2 
 
 9.46464 
 
 142,5 
 
 73 03 07.63 
 
 .276 
 
 .95686 
 
 29,1 
 
 .29054 
 
 95,7 
 
 .98085 
 
 13,2 
 
 .46321 
 
 I43,o 
 
 73 06 33.89 
 
 .277 
 
 .95715 
 
 29,0 
 
 .28959 
 
 95,7 
 
 .98098 
 
 I3,i 
 
 .46178 
 
 143,5 
 
 73 10 oo. 16 
 
 .278 
 
 95744 
 
 28,9 
 
 .28863 
 
 95,7 
 
 .98111 
 
 I3,i 
 
 .46034 
 
 144,1 
 
 73 13 26.42 
 
 .279 
 
 .95773 
 
 28,8 
 
 .28767 
 
 95,8 
 
 .98124 
 
 13,0 
 
 .45890 
 
 144,6 
 
 73 16 52.69 
 
 1.280 
 
 0.95802 
 
 28,7 
 
 0.28672 
 
 95,8 
 
 9.98137 
 
 13,0 
 
 9-45745 
 
 I45,i 
 
 73 20 18.95 
 
 .281 
 
 .95830 
 
 28,6 
 
 .28576 
 
 95,8 
 
 .98150 
 
 I3,o 
 
 .45600 
 
 145,6 
 
 73 23 45.22 
 
 .282 
 
 .95859 
 
 28,5 
 
 .28480 
 
 95,9 
 
 .98163 
 
 12,9 
 
 45454 
 
 146,2 
 
 73 27 11.48 
 
 .283 
 
 .95887 
 
 28,4 
 
 .28384 
 
 95,9 
 
 .98176 
 
 12,9 
 
 45307 
 
 146,7 
 
 73 30 37.75 
 
 .284 
 
 .95916 
 
 28,3 
 
 .28288 
 
 95,9 
 
 .98189 
 
 12,8 
 
 45160 
 
 147,3 
 
 73 34 04.01 
 
 1.285 
 
 0.95944 
 
 28,2 
 
 0.28192 
 
 95,9 
 
 9.98202 
 
 12,8 
 
 9.45013 
 
 147,8 
 
 73 37 30.28 
 
 .286 
 
 95972 
 
 28,1 
 
 .28096 
 
 96,0 
 
 .98214 
 
 12,7 
 
 .44865 
 
 148,3 
 
 73 40 56.54 
 
 .287 
 
 .96000 
 
 28,0 
 
 .28000 
 
 06,0 
 
 .98227 
 
 12,7 
 
 .44716 
 
 148,9 
 
 73 44 22.81 
 
 .288. 
 
 .96028 
 
 27,9 
 
 .27004 
 
 96,0 
 
 .98240 
 
 12,6 
 
 .44567 
 
 149,5 
 
 73 47 49-07 
 
 .289 
 
 .96056 
 
 27,8 
 
 .27808 
 
 96,1 
 
 .98252 
 
 12,6 
 
 .44417 
 
 150,0 
 
 73 51 15.34 
 
 1.290 
 
 0.96084 
 
 27,7 
 
 0.27712 
 
 06,1 
 
 9.98265 
 
 12,5 
 
 9.44267 
 
 150,6 
 
 73 54 41.60 
 
 .291 
 
 .96111 
 
 27,6 
 
 .27616 
 
 96,i 
 
 .98277 
 
 12,5 
 
 .44116 
 
 151,1 
 
 73 58 07.86 
 
 .292 
 
 .96139 
 
 '27,5 
 
 .27520 
 
 96,1 
 
 .98290 
 
 12,4 
 
 .43965 
 
 I5i,7 
 
 74 01 34.13 
 
 .293 
 
 .96166 
 
 27,4 
 
 .27424 
 
 96,2 
 
 .08302 
 
 12,4 
 
 43813 
 
 152,3 
 
 74 05 00.39 
 
 .294 
 
 .96194 
 
 27,3 
 
 .27328 
 
 96,2 
 
 .98315 
 
 12,3 
 
 .43660 
 
 152,9 
 
 74 08 26.66 
 
 1.295 
 
 0.96221 
 
 27,2 
 
 0.27231 
 
 96,2 
 
 9.98327 
 
 12,3 
 
 9.43507 
 
 153,5 
 
 74 II 52.92 
 
 .296 
 
 .96248 
 
 27,1 
 
 .27135 
 
 96,2 
 
 .98339 
 
 12,2 
 
 43353 
 
 I54,o 
 
 74 15 19.19 
 
 297 
 
 .96275 
 
 27,0 
 
 .27039 
 
 96,3 
 
 .98351 
 
 12,2 
 
 .43199 
 
 154,6 
 
 74 18 45-45 
 
 .298 
 
 .06302 
 
 26,9 
 
 .26943 
 
 96,3 
 
 .98364 
 
 12,2 
 
 .43044 
 
 155,2 
 
 74 22 11.72 
 
 .299 
 
 .96329 
 
 26,8 
 
 .26846 
 
 96,3 
 
 .98376 
 
 12,1 
 
 .42888 
 
 155,8 
 
 74 25 37.98 
 
 1.300 
 
 0.96356 
 
 26,7 
 
 0.26750 
 
 96,4 
 
 9.98388 
 
 12,1 
 
 9.42732 
 
 156,4 
 
 74 29 04.25 
 
 u 
 
 -i sinhiu 
 
 Fo" 
 
 cosh iu 
 
 wFo' 
 
 sinh iu 
 
 F ' 
 
 log cosh iu 
 
 F O ' 
 
 u 
 
 loo . 
 
 SMITHSONIAN TABLES 
 
 217 
 
Circular Functions. 
 
 u 
 
 sin u 
 
 F ' 
 
 COS U 
 
 F ' 
 
 log sin u 
 
 Fo' 
 
 log cos u 
 
 F O ' 
 
 u 
 
 1.300 
 
 0.96356 
 
 26,7 
 
 0.26750 
 
 96,4 
 
 9.98388 
 
 12,1 
 
 9.42/32 
 
 156,4 
 
 74 29 04.25 
 
 .301 
 
 96383 
 
 26,7 
 
 .26654 
 
 96,4 
 
 .98400 
 
 12,0 
 
 .42575 
 
 i'57,o 
 
 74 32 30.51 
 
 .302 
 
 .96409 
 
 26,6 
 
 .26557 
 
 96,4 
 
 .98412 
 
 12,0 
 
 .42418 
 
 157,7 
 
 74 35 56.78 
 
 .303 
 
 .96436 
 
 26,5 
 
 .26461 
 
 96,4 
 
 .98424 
 
 11,9 
 
 .42260 
 
 158,3 
 
 74 39 23.04 
 
 .304 
 
 .96462 
 
 26,4 
 
 .26364 
 
 96,5 
 
 .98436 
 
 11,9 
 
 .42102 
 
 158,9 
 
 74 42 49.31 
 
 1.305 
 
 0.96488 
 
 26,3 
 
 0.26268 
 
 96,5 
 
 9.98447 
 
 11,8 
 
 9.41942 
 
 159,5 
 
 74 46 15.57 
 
 .306 
 
 .96515 
 
 26,2 
 
 .26171 
 
 96,5 
 
 .98459 
 
 11,8 
 
 .41782 
 
 160,2 
 
 74 49 41.84 
 
 .307 
 
 .96541 
 
 26,1 
 
 .26075 
 
 96,5 
 
 .9&47I 
 
 n,7 
 
 .41622 
 
 160,8 
 
 74 53 08.10 
 
 .308 
 
 .96567 
 
 26,0 
 
 .25978 
 
 96,6 
 
 .98483 
 
 n,7 
 
 .41461 
 
 161,4 
 
 74 56 34-37 
 
 .309 
 
 96593 
 
 25,9 
 
 .25882 
 
 96,6 
 
 .98494 
 
 11,6 
 
 .41299 
 
 162,1 
 
 75 oo 00.63 
 
 1.310 
 
 0.96618 
 
 25,8 
 
 0.25785 
 
 96,6 
 
 9.98506 
 
 11,6 
 
 9.4H37 
 
 162,7 
 
 75 03 26.90 
 
 .311 
 
 .96644 
 
 25,7 
 
 .25688 
 
 96,6 
 
 .98518 
 
 n,5 
 
 .40974 
 
 163,4 
 
 75 06 53.16 
 
 .312 
 
 .96670 
 
 25,6 
 
 .25592 
 
 96,7 
 
 .98529 
 
 n,5 
 
 .40810 
 
 164,0 
 
 75 10 19-43 
 
 .313 
 
 .96695 
 
 25,5 
 
 .25495 
 
 96,7 
 
 98541 
 
 ii,5 
 
 .40646 
 
 164,7 
 
 75 13 45.69 
 
 .314 
 
 .96721 
 
 25,4 
 
 .25398 
 
 96,7 
 
 .98552 
 
 11,4 
 
 .40481 
 
 165,4 
 
 75 17 11-0 
 
 1.315 
 
 0.06746 
 
 25,3 
 
 0.25302 
 
 96,7 
 
 9.98563 
 
 11,4 
 
 9.40315 
 
 166,1 
 
 75 20 38.22 
 
 .316 
 
 .96771 
 
 25,2 
 
 .25205 
 
 96,8 
 
 .98575 
 
 n,3 
 
 .40148 
 
 166,7 
 
 75 24 04.49 
 
 .317 
 
 .96797 
 
 25,1 
 
 .25108 
 
 96,8 
 
 .98586 
 
 n,3 
 
 39981 
 
 167,4 
 
 75 27 30.75 
 
 .318 
 
 .96822 
 
 25,0 
 
 .25011 
 
 96,8 
 
 .98597 
 
 11,2 
 
 .39814 
 
 168,1 
 
 75 30 57-01 
 
 .319 
 
 .96847 
 
 24,9 
 
 .24914 
 
 96,8 
 
 .98608 
 
 11,2 
 
 .39645 
 
 168,8 
 
 75 34 23.28 
 
 1.3-20 
 
 0.96872 
 
 24,8 
 
 0.24818 
 
 96,9 
 
 9.98620 
 
 II, I 
 
 9.39476 
 
 169,5 
 
 75 37 49.54 
 
 .321 
 
 .96896 
 
 24,7 
 
 .24721 
 
 96,9 
 
 .98631 
 
 II, I 
 
 .39306 
 
 170,2 
 
 75 41 I5.8i 
 
 .322 
 
 .96921 
 
 24,6 
 
 . 24624 
 
 96,9 
 
 .98642 
 
 11,0 
 
 .39135 
 
 170,9 
 
 75 44 42.07 
 
 .323 
 
 .96046 
 
 24,5 
 
 .24527 
 
 96,9 
 
 .98653 
 
 11,0 
 
 .38964 
 
 i7i,7 
 
 75 48 08.34 
 
 .524 
 
 .96970 
 
 24,4 
 
 .24430 
 
 97,0 
 
 .98664 
 
 10,9 
 
 .38792 
 
 172,4 
 
 75 5i 34-6o 
 
 1.325 
 
 0.06994 
 
 24,3 
 
 0.24333 
 
 97,o 
 
 9.98675 
 
 10,9 
 
 9.38619 
 
 i73,i 
 
 75 55 00.87 
 
 .326 
 
 .97019 
 
 24,2 
 
 .24236 
 
 97,o 
 
 .98686 
 
 10,8 
 
 .38446 
 
 173,9 
 
 75 58 27.13 
 
 .327 
 
 .97043 
 
 24,1 
 
 .24139 
 
 97,o 
 
 .98696 
 
 10,8 
 
 .38272 
 
 174,6 
 
 76 01 53-40 
 
 .328 
 
 .97067 
 
 24,0 
 
 .24042 
 
 97,1 
 
 .98707 
 
 10,8 
 
 38097 
 
 175,3 
 
 76 05 19.66 
 
 .329 
 
 .97091 
 
 23,9 
 
 .23945 
 
 97,1 
 
 .98718 
 
 10,7 
 
 37921 
 
 176,1 
 
 76 08 45-93 
 
 1.330 
 
 0.97H5 
 
 23,8 
 
 0.23848 
 
 97,1 
 
 9.98729 
 
 10,7 
 
 9-37744 
 
 176,9 
 
 76 12 12.19 
 
 .331 
 
 .97139 
 
 23,8 
 
 .23750 
 
 97,1 
 
 98739 
 
 10,6 
 
 .37567 
 
 177,6 
 
 76 15 38.46 
 
 .332 
 
 .97162 
 
 23,7 
 
 .23653 
 
 97,2 
 
 .98750 
 
 1 0,6 
 
 .37389 
 
 178,4 
 
 76 19 04.72 
 
 .333 
 
 .97186 
 
 23,6 
 
 .23556 
 
 97,2 
 
 .98760 
 
 10,5 
 
 37210 
 
 179,2 
 
 76 22 30.99 
 
 334 
 
 .97209 
 
 '23,5 
 
 .23459 
 
 97,2 
 
 .98771 
 
 10,5 
 
 .37031 
 
 180,0 
 
 76 25 57-25 
 
 1-335 
 
 0.97233 
 
 23,4 
 
 0.23362 
 
 97,2 
 
 9.98781 
 
 10,4 
 
 9.36851 
 
 180,8 
 
 76 29 23.52 
 
 .336 
 
 .97256 
 
 23,3 
 
 .23264 
 
 97,3 
 
 .98792 
 
 10,4 
 
 .36669 
 
 181,6 
 
 76 32 49.78 
 
 .337 
 
 .97279 
 
 23,2 
 
 .23167 
 
 97,3 
 
 .98802 
 
 10,3 
 
 .36487 
 
 182,4 
 
 76 36 l6.O5 
 
 .338 
 
 .97303 
 
 23,1 
 
 .23070 
 
 97,3 
 
 .98812 
 
 10,3 
 
 36305 
 
 183,2 
 
 76 39 42.31 
 
 339 
 
 .97326 
 
 23,0 
 
 .22973 
 
 97,3 
 
 .98823 
 
 10,3 
 
 .36121 
 
 184,0 
 
 76 43 08.58 
 
 1.340 
 
 0.97348 
 
 22,9 
 
 0.22875 
 
 97,3 
 
 9.98833 
 
 10,2 
 
 9-35937 
 
 184,8 
 
 76 46 34-84 
 
 341 
 
 .97371 
 
 22,8 
 
 .22778 
 
 97,4 
 
 .98843 
 
 10,2 
 
 .35751 
 
 185,7 
 
 76 50 oi.n 
 
 342 
 
 97394 
 
 22,7 
 
 .22681 
 
 97,4 
 
 .98853 
 
 10,1 
 
 .35565 
 
 186,5 
 
 76 53 27.37 
 
 343 
 
 .97417 
 
 22,6 
 
 .22583 
 
 97,4 
 
 .98863 
 
 10,1 
 
 .35378 
 
 187,3 
 
 76 56 53.63 
 
 344 
 
 97439 
 
 22,5 
 
 .22486 
 
 97,4 
 
 .98873 
 
 10,0 
 
 .35191 
 
 188,2 
 
 77 oo 19.90 
 
 1-345 
 
 0.97462 
 
 22,4 
 
 0.22388 
 
 97,5 
 
 9.98883 
 
 IO,O 
 
 9.35002 
 
 189,1 
 
 77 03 46.16 
 
 .346 
 
 .97484 
 
 22,3 
 
 .22291 
 
 97,5 
 
 98893 
 
 9,9 
 
 .34813 
 
 189,9 
 
 77 07 12.43 
 
 347 
 
 .97506 
 
 22,2 
 
 .22193 
 
 97,5 
 
 .98903 
 
 9,9 
 
 .34622 
 
 100,8 
 
 77 10 38.69 
 
 348 
 
 97528 
 
 22,1 
 
 .22006 
 
 97,5 
 
 .08913 
 
 9,8 
 
 .34431 
 
 i9i,7 
 
 77 14 04.96 
 
 .349 
 
 .97550 
 
 '22,0 
 
 .21998 
 
 97,6 
 
 .98023 
 
 9,8 
 
 .34239 
 
 192,6 
 
 77 17 31.22 
 
 1.350 
 
 0.97572 
 
 21,9 
 
 0.21901 
 
 97,6 
 
 9.98933 
 
 9,7 
 
 9.34046 
 
 193,5 
 
 77 20 57-49 
 
 u 
 
 -isinhiu 
 
 Fo' 
 
 cosh iu 
 
 F ' 
 
 ,00^ 
 
 F ' 
 
 ogcosh iu 
 
 F ' 
 
 u 
 
 SMITHSONIAN TABLES 
 
 218 
 
Circular Functions. 
 
 u 
 
 sin u 
 
 F ' 
 
 COS U 
 
 F ' 
 
 log sin u 
 
 Fo' 
 
 log cos u 
 
 F ' 
 
 u 
 
 1.350 
 
 0.97572 
 
 21,9 
 
 O.2I9OI 
 
 97,6 
 
 9.98933 
 
 9,7 
 
 9.34046 
 
 i93,5 
 
 772o' 57"49 
 
 .351 
 
 97594 
 
 21,8 
 
 .21803 
 
 97,6 
 
 .98942 
 
 9,7 
 
 .33852 
 
 194,4 
 
 77 24 23.75 
 
 .352 
 
 .97616 
 
 21,7 
 
 .21705 
 
 97,6 
 
 .98952 
 
 9,7 
 
 .33657 
 
 i95,3 
 
 77 27 50.02 
 
 353 
 
 .97638 
 
 21,6 
 
 .2l6o8 
 
 97,6 
 
 ,98962 
 
 9,6 
 
 .33461 
 
 196,2 
 
 77 31 16.28 
 
 354 
 
 .97659 
 
 21,5 
 
 .21510 
 
 97,7 
 
 .98971 
 
 9,6 
 
 .33264 
 
 197,2 
 
 77 34 42.55 
 
 1.355 
 
 0.97681 
 
 21,4 
 
 O.2I4I3 
 
 97,7 
 
 9.98981 
 
 9,5 
 
 9.33067 
 
 198,1 
 
 77 38 08. 81 
 
 .356 
 
 .97702 
 
 21,3 
 
 21315 
 
 97,7 
 
 .98990 
 
 9,5 
 
 .32868 
 
 199,1 
 
 77 4i 35.o8 
 
 .357 
 
 .97723 
 
 2 1, '2 
 
 .21217 
 
 97,7 
 
 .09000 
 
 9,4 
 
 .32669 
 
 200,0 
 
 77 45 01.34 
 
 .358 
 
 97744 
 
 21,1 
 
 .21119 
 
 97,7 
 
 .09009 
 
 9,4 
 
 .32468 
 
 201,0 
 
 77 48 27.61 
 
 .359 
 
 .97765 
 
 2I,O 
 
 .2IO22 
 
 97,8 
 
 .90019 
 
 9,3 
 
 .32267 
 
 202,0 
 
 77 51 53.87 
 
 . 1.360 
 
 0.97786 
 
 20,9 
 
 0.20924 
 
 97,8 
 
 9.00028 
 
 9,3 
 
 9.32064 
 
 203,0 
 
 77 55 20.14 
 
 .361 
 
 .97807 
 
 20,8 
 
 .20826 
 
 97,8 
 
 .99037 
 
 9,2 
 
 .31861 
 
 204,0 
 
 77 58 46.40 
 
 .362 
 
 .97828 
 
 20,7 
 
 .20728 
 
 97,8 
 
 .99046 
 
 9,2 
 
 .31656 
 
 205,0 
 
 78 02 12.67 
 
 .363 
 
 .97849 
 
 20,6 
 
 .20630 
 
 97,8 
 
 .99056 
 
 9,2 
 
 .31451 
 
 2O6,0 
 
 78 05 38.93 
 
 .364 
 
 .97869 
 
 20,5 
 
 .20533 
 
 97,9 
 
 .99065 
 
 9,1 
 
 .31244 
 
 207,0 
 
 78 09 05.20 
 
 1.365 
 
 0.97890 
 
 20,4 
 
 0.20435 
 
 97,9 
 
 9.99074 
 
 9,i 
 
 9.31037 
 
 2O8,O 
 
 78 12 3L46 
 
 .366 
 
 .97910 
 
 20,3 
 
 .20337 
 
 97,9 
 
 .99083 
 
 9,0 
 
 .30828 
 
 209,1 
 
 78 15 57.73 
 
 .367 
 
 .97931 
 
 20,2 
 
 .20239 
 
 97,9 
 
 .00092 
 
 9,0 
 
 .30619 
 
 210,1 
 
 78 19 23.99 
 
 .368 
 
 97951 
 
 20,1 
 
 .20141 
 
 98,0 
 
 .99101 
 
 8,9 
 
 .30408 
 
 211,2 
 
 78 22 50.25 
 
 .369 
 
 .97971 
 
 2O,O 
 
 .20043 
 
 98,0 
 
 .99110 
 
 8,9 
 
 .30106 
 
 212,3 
 
 78 26 16.52 
 
 1.370 
 
 0.97991 
 
 19,9 
 
 0.19945 
 
 98,0 
 
 9.99II9 
 
 8,8 
 
 9.29983 
 
 213,4 
 
 78 29 42.78 
 
 .371 
 
 .98011 
 
 19,8 
 
 .19847 
 
 98,0 
 
 .99127 
 
 8,8 
 
 .29769 
 
 214,5 
 
 78 33 09.05 
 
 372 
 
 .98031 
 
 19,7 
 
 19749 
 
 08.0 
 
 .99136 
 
 8,7 
 
 .29554 
 
 215,6 
 
 78 36 35-31 
 
 373 
 
 .98050 
 
 19,7 
 
 .19651 
 
 98,1 
 
 .99145 
 
 8,7 
 
 29338 
 
 216,7 
 
 78 40 01.58 
 
 374 
 
 .98070 
 
 19,6 
 
 . 19553 
 
 98,1 
 
 .09154 
 
 8,7 
 
 .29121 
 
 217,8 
 
 78 43 27.84 
 
 1.375 
 
 0.98080 
 
 19,5 
 
 0.19455 
 
 98,1 
 
 9.99162 
 
 8,6 
 
 9.28903 
 
 219,0 
 
 78 46 54.ii 
 
 .376 
 
 .98109 
 
 19,4 
 
 . 19357 
 
 08, i 
 
 .99171 
 
 8,6 
 
 .28683 
 
 220,1 
 
 78 50 20.37 
 
 377 
 
 .98128 
 
 19,3 
 
 . 19259 
 
 98,1 
 
 .99179 
 
 8,5 
 
 .28462 
 
 221,3 
 
 78 53 46.64 
 
 .378 
 
 .98147 
 
 19,2 
 
 .19160 
 
 08, t 
 
 .99188 
 
 8,5 
 
 . 28240 
 
 222,5 
 
 78 57 12.90 
 
 379 
 
 .98166 
 
 19,1 
 
 .19062 
 
 98,2 
 
 .99196 
 
 8,4 
 
 .28017 
 
 223,7 
 
 79 00 39.17 
 
 1.380 
 
 0.98185 
 
 19,0 
 
 0.18964 
 
 98,2 
 
 9.99205 
 
 8,4 
 
 9.27793 
 
 224,9 
 
 79 04 05-43 
 
 .381 
 
 .98204 
 
 18,9 
 
 .18866 
 
 98,2 
 
 .99213' 
 
 8,3 
 
 .27568 
 
 226,1 
 
 79 07 31.70 
 
 .382 
 
 .08223 
 
 18,8 
 
 .18768 
 
 98,2 
 
 .99221 
 
 8,3 
 
 .27341 
 
 227,3 
 
 79 10 57.96 
 
 .383 
 
 .98242 
 
 18,7 
 
 .18669 
 
 98,2 
 
 .99230 
 
 8,3 
 
 .27113 
 
 228,5 
 
 79 14 24.23 
 
 .384 
 
 .98260 
 
 18,6 
 
 .18571 
 
 98,3 
 
 .99238 
 
 8,2 
 
 .26884 
 
 229,8 
 
 79 17 50.49 
 
 1.385 
 
 0.98279 
 
 18,5 
 
 0.18473 
 
 98,3 
 
 9.99246 
 
 8,2 
 
 9.26654 
 
 231,1 
 
 79 21 16.76 
 
 .386 
 
 .98297 
 
 18,4 
 
 .18375 
 
 98,3 
 
 .99254 
 
 8,1 
 
 . 26422 
 
 232,3 
 
 79 24 43-02 
 
 .387 
 
 .98316 
 
 18,3 
 
 . 18276 
 
 98,3 
 
 .99262 
 
 8,1 
 
 .26189 
 
 233,6 
 
 79 28 09.29 
 
 .388 
 
 98334 
 
 18,2 
 
 .18178 
 
 98,3 
 
 .99270 
 
 8,0 
 
 25955 
 
 234,9 
 
 79 31 35-55 
 
 .389 
 
 .98352 
 
 18,1 
 
 .18080 
 
 98,4 
 
 .99278 
 
 8,0 
 
 .25719 
 
 236,3 
 
 79 35 01.82 
 
 1.390 
 
 0.08370 
 
 18,0 
 
 o. 17981 
 
 98,4 
 
 9.99286 
 
 7,9 
 
 9.25482 
 
 237,6 
 
 79 38 28.08 
 
 .391 
 
 .98388 
 
 17,9 
 
 .17883 
 
 98,4 
 
 .99294 
 
 7,9 
 
 .25244 
 
 238,9 
 
 79 41 54-35 
 
 392 
 
 .98406 
 
 17,8 
 
 .17785 
 
 98,4 
 
 .99302 
 
 7,8 
 
 .25004 
 
 240,3 
 
 79 45 20.61 
 
 393 
 
 .98424 
 
 17,7 
 
 .17686 
 
 98,4 
 
 .99310 
 
 7,8 
 
 .24763 
 
 241,7 
 
 79 48 46.88 
 
 .394 
 
 .98441 
 
 17,6 
 
 .17588 
 
 98,4 
 
 .99318 
 
 7,8 
 
 .24521 
 
 243,1 
 
 79 52 13.14 
 
 1.395 
 
 0.98459 
 
 17,5 
 
 0.17489 
 
 98,5 
 
 9.99325 
 
 7,7 
 
 9.24277 
 
 244,5 
 
 79 55 39.40 
 
 .396 
 
 .98476 
 
 17,4 
 
 . 17391 
 
 98,5 
 
 99333 
 
 7,7 
 
 .24032 
 
 245,9 
 
 79 59 05.67 
 
 397 
 
 .98494 
 
 17,3 
 
 .17292 
 
 98,5 
 
 .99341 
 
 7,6 
 
 .23785 
 
 247,4 
 
 80 02 31.93 
 
 .398 
 
 .08511 
 
 17,2 
 
 .17194 
 
 98,5 
 
 .99348 
 
 7,6 
 
 23537 
 
 248,8 
 
 80 05 58.20 
 
 399 
 
 .98528 
 
 I7,i 
 
 .17095 
 
 98,5 
 
 99356 
 
 7,5 
 
 .23288 
 
 250,3 
 
 80 09 24.46 
 
 1.400 
 
 0.98545 
 
 I7,o 
 
 0.16997 
 
 98,5 
 
 9.99363 
 
 7,5 
 
 9.23036 
 
 251,8 
 
 80 12 50.73 
 
 u 
 
 -isinhiu 
 
 <> FO' 
 
 cosh iu 
 
 F O ' 
 
 . sinh iu 
 
 c-Fo' 
 
 log cosh iu 
 
 -FO' 
 
 u 
 
 loo j 
 
 SMITHSONIAN TABLES 
 
 2IQ 
 
Circular Functions. 
 
 u 
 
 sin u 
 
 F ' 
 
 cos u 
 
 -F* 
 
 log sin u 
 
 Fo' 
 
 log cos u 
 
 F ' u 
 
 1.400 
 
 0.98545 
 
 17,0 
 
 0.16997 
 
 98,5 
 
 9.99363 
 
 7,5 
 
 9-23036 
 
 251,8 80 12 50" 73 
 
 .401 
 
 .98562 
 
 16,9 
 
 . 16898 
 
 98,6 
 
 .99371 
 
 7,4 
 
 .22784 
 
 253,3 80 16 16.99 
 
 .402 
 
 .98579 
 
 16,8 
 
 .16800 
 
 98,6 
 
 .99378 
 
 7,4 
 
 .22530 
 
 254,8 80 19 43.26 
 
 .403 
 
 .98596 
 
 16,7 
 
 . 16701 
 
 98,6 
 
 .99386 
 
 7,4 
 
 .22274 
 
 256,4 80 23 09.52 
 
 .404 
 
 .98612 
 
 16,6 
 
 .16602 
 
 98,6 
 
 99393 
 
 7,3 
 
 .22OI7 
 
 258,0 
 
 80 26 35-79 
 
 1.405 
 
 0.98629 
 
 16,5 
 
 0.16504 
 
 98,6 
 
 9.99400 
 
 7,3 
 
 9.21758 
 
 259,5 
 
 80 30 02.05 
 
 .406 
 
 .98645 
 
 16,4 
 
 .16405 
 
 98,6 
 
 .99408 
 
 7,2 
 
 .21498 
 
 261,1 
 
 80 33 28.32 
 
 .407 
 
 .98662 
 
 16,3 
 
 .16306 
 
 98,7 
 
 .99415 
 
 7,2 
 
 .21236 
 
 262,8 
 
 80 36 54.58 
 
 .408 
 
 .98678 
 
 16,2 
 
 .16208 
 
 98,7 
 
 .99422 
 
 7,1 
 
 .20972 
 
 264,4 
 
 80 40 20.85 
 
 . 409 
 
 .98694 
 
 16,1 
 
 .16109 
 
 98,7 
 
 .99429 
 
 7,i 
 
 .20707 
 
 266,1 
 
 80 43 47.ii 
 
 1.410 
 
 0.98710 
 
 16,0. 
 
 0.16010 
 
 98,7 
 
 9.99436 
 
 7,o 
 
 9.20440 
 
 267,8 
 
 80 47 13.38 
 
 .411 
 
 .98726 
 
 15,9 
 
 .15912 
 
 98,7 
 
 99443 
 
 7,o 
 
 .20172 
 
 269,5 
 
 80 50 39.64 
 
 .412 
 
 .98742 
 
 15,8 
 
 .15813 
 
 98,7 
 
 .99450 
 
 7,0 
 
 .19901 
 
 271,2 
 
 80 54 05.91 
 
 .413 
 
 .98758 
 
 15,7 
 
 .15714 
 
 98,8 
 
 99457 
 
 6,9 
 
 .19629 
 
 272,9 
 
 80 57 32.17 
 
 .414 
 
 .98773 
 
 15,6 
 
 .15615 
 
 98,8 
 
 .99464 
 
 6,9 
 
 19355 
 
 274,7 
 
 81 oo 58.44 
 
 1.415 
 
 0.98789 
 
 15,5 
 
 0.15517 
 
 98,8 
 
 9.99471 
 
 6,8 
 
 9.19080 
 
 276,5 
 
 81 04 24.70 
 
 .416 
 
 .98804 
 
 15,4 
 
 .15418 
 
 98,8 
 
 .99478 
 
 6,8 
 
 .18802 
 
 278,3 
 
 81 07 50.97 
 
 .417 
 
 .98820 
 
 15,3 
 
 .15319 
 
 98,8 
 
 .99484 
 
 6,7 
 
 .18523 
 
 280,2 
 
 81 ii 17.23 
 
 .418 
 
 .98835 
 
 15,2 
 
 . 15220 
 
 58,8 
 
 .99491 
 
 6,7 
 
 . 18242 
 
 282,0 
 
 81 14 43-50 
 
 .419 
 
 .98850 
 
 i'5,i 
 
 .15121 
 
 58,9 
 
 .99498 
 
 6,6 
 
 .17959 
 
 283,9 
 
 81 18 09.76 
 
 1.4120 
 
 0.98865 
 
 i5,o 
 
 0.15023 
 
 98,9 
 
 9-99504 
 
 6,6 
 
 9.17674 
 
 285,8 
 
 81 21 36.02 
 
 .421 
 
 .98880 
 
 14,9 
 
 . 14924 
 
 98,9 
 
 995II 
 
 6,6 
 
 .17388 
 
 287,8 
 
 81 25 02.29 
 
 .422 
 
 .98895 
 
 14,8 
 
 .14825 
 
 98,9 
 
 .99517 
 
 6,5 
 
 .17009 
 
 289,7 
 
 81 28 28.55 
 
 .423 
 
 .98910 
 
 14,7 
 
 . 14726 
 
 58,9 
 
 .99524 
 
 6,5 
 
 .16808 
 
 291,7 
 
 81 31 54.82 
 
 .424 
 
 .98924 
 
 14,6 
 
 . 14627 
 
 98,9 
 
 99530 
 
 6,4 
 
 .16515 
 
 293,7 
 
 81 35 21.08 
 
 1.425 
 
 0.98939 
 
 14,5 
 
 0.14528 
 
 98,9 
 
 9-99537 
 
 6,4 
 
 9.16221 
 
 295,8 
 
 81 38 47-35 
 
 .426 
 
 .98954 
 
 14,4 
 
 .14429 
 
 99,0 
 
 99543 
 
 6,3 
 
 .15924 
 
 297,8 
 
 81 42 13.61 
 
 .427 
 
 .98968 
 
 14,3 
 
 . 14330 
 
 99,0 
 
 99549 
 
 6,3 
 
 . 15625 
 
 209,9 
 
 81 45 39-88 
 
 .428 
 
 .98982 
 
 14,2 
 
 . 14231 
 
 99,0 
 
 .99556 
 
 6,2 
 
 . 15324 
 
 302,1 
 
 81 49 06.14 
 
 .4129 
 
 .98906 
 
 14,1 
 
 . 14132 
 
 99,0 
 
 .99562 
 
 6,2 
 
 .I5O2I 
 
 304,2 
 
 81 52 32.41 
 
 1.430 
 
 O.99OIO 
 
 14,0 
 
 o. 14033 
 
 99,0 
 
 9.99568 
 
 6,2 
 
 9.14716 
 
 306,4 
 
 81 55 58.67 
 
 .431 
 
 .99024 
 
 13,9 
 
 .13934 
 
 99,0 
 
 99574 
 
 6,1 
 
 .14408 
 
 308,6 
 
 81 59 24.94 
 
 .432 
 
 .99038 
 
 13,8 
 
 .13835 
 
 99,0 
 
 .09580 
 
 6,1 
 
 .14098 
 
 3io,9 
 
 82 02 51.20 
 
 433 
 
 .00052 
 
 13,7 
 
 . 13736 
 
 99,i 
 
 .99586 
 
 6,0 
 
 .13786 
 
 313,2 
 
 82 06 17.47 
 
 434 
 
 .99066 
 
 13,6 
 
 . 13637 
 
 99J 
 
 .99592 
 
 6,0 
 
 .13472 
 
 315,5 
 
 82 09 43-73 
 
 1-435 
 
 .99079 
 
 13,5 
 
 0.13538 
 
 99,1 
 
 9.99598 
 
 5,9 
 
 9.I3I55 
 
 317,8 
 
 82 13 10.00 
 
 .436 
 
 .99093 
 
 13,4 
 
 . 13439 
 
 99,1 
 
 .99604 
 
 5,9 
 
 .12836 
 
 320,2 
 
 82 16 36.26 
 
 437 
 
 .99106 
 
 13,3 
 
 .13340 
 
 99,1 
 
 .99610 
 
 5,8 
 
 .12515 
 
 322,7 
 
 82 20 02.53 
 
 .438 
 
 .99120 
 
 13,2 
 
 . 13241 
 
 99,1 
 
 .06616 
 
 5,8 
 
 .12191 
 
 325J 
 
 82 23 28.79 
 
 439 
 
 .99133 
 
 I3,i 
 
 .13142 
 
 99,1 
 
 .99622 
 
 5,8 
 
 .11865 
 
 327,6 
 
 82 26 55.06 
 
 1.440 
 
 0.99146 
 
 I3,o 
 
 0.13042 
 
 99,1 
 
 9.99627 
 
 5,7 
 
 9.II536 
 
 330,1 
 
 82 30 21.32 
 
 .441 
 
 .99159 
 
 12,9 
 
 .12943 
 
 99,2 
 
 .09633 
 
 5,7 
 
 .II2O4 
 
 332,7 
 
 82 33 47-59 
 
 .442 
 
 .99172 
 
 12,8 
 
 .12844 
 
 99,2 
 
 .9039 
 
 5,6 
 
 .10870 
 
 335,3 
 
 82 37 13.85 
 
 443 
 
 .09185 
 
 12,7 
 
 12745 
 
 99,2 
 
 .99644 
 
 5,6 
 
 .10534 
 
 338,0 
 
 82 40 40.12 
 
 444 
 
 .99197 
 
 12,6 
 
 .12646 
 
 99,2 
 
 .99650 
 
 5,5 
 
 .10194 
 
 340,7 
 
 82 44 06.38 
 
 1.445 
 
 0.99210 
 
 12,5 
 
 o. 12546 
 
 99,2 
 
 9.99655 
 
 5,5 
 
 9-09852 
 
 343,4 
 
 82 47 32.65 
 
 .446 
 
 .99222 
 
 12,4 
 
 .12447 
 
 99,2 
 
 .99661 
 
 5,4 
 
 .09507 
 
 346,2 
 
 82 50 58.91 
 
 447 
 
 .99235 
 
 12,3 
 
 .12348 
 
 99,2 
 
 .9</>66 
 
 5,4 
 
 .0)160 
 
 349,0 
 
 82 54 25.17 
 
 .448 
 
 .99247 
 
 12,2 
 
 .12249 
 
 99,2 
 
 .99672 
 
 5,4 
 
 .oSSog 
 
 351,9 
 
 82 57 51-44 
 
 .449 
 
 .99259 
 
 12,1 
 
 .12150 
 
 99,3 
 
 .99677 
 
 5,3 
 
 .08456 
 
 354,8 
 
 83 01 17.70 
 
 1-450 
 
 0.99271 
 
 12,1 
 
 0.12050 
 
 99,3 
 
 9.09682 
 
 5,3 
 
 9.08100 
 
 357,8 
 
 83 04 43-97 
 
 u 
 
 -isinhiu 
 
 F,,' 
 
 cosh iu 
 
 *Fo' 
 
 .0.'^ 
 
 -Fo' 
 
 log cosh iu 
 
 tt 
 
 u 
 
 SMITHSONIAN TABLCS 
 
 220 
 
Circular Functions. 
 
 
 
 
 
 
 
 
 
 I 
 
 u 
 
 sin u 
 
 -Fo' 
 
 cos u 
 
 Fo* 
 
 loo sin u 
 
 Fo' 
 
 log cos u 
 
 F O ' 
 
 u 
 
 1.450 
 
 0.09271 
 
 12,1 
 
 o. 12050 
 
 99,3 
 
 9.99682 
 
 5,3 
 
 9.08100 
 
 357,8 
 
 8304'43"97 
 
 .451 
 
 .99283 
 
 12,0 
 
 .11951 
 
 99,3 
 
 .99688 
 
 5,2 
 
 .0/740 
 
 300,8 
 
 83 08 10.23 
 
 .452 
 
 .99295 
 
 11,9 
 
 .11852 
 
 99,3 
 
 .99693 
 
 5,2 
 
 .07378 
 
 363,9 
 
 83 ii 36.50 
 
 453 
 
 .99307 
 
 11,8 
 
 .11752 
 
 99,3 
 
 .99608 
 
 5,1 
 
 .07013 
 
 367,0 
 
 83 15 02.76 
 
 454 
 
 .99319 
 
 n,7 
 
 .11653 
 
 99,3 
 
 .99703 
 
 5,1 
 
 .06644 
 
 370,i 
 
 83 18 29.03 
 
 1-455 
 
 0.99330 
 
 11,6 
 
 O.I 1554 
 
 99,3 
 
 9.99708 
 
 5,i 
 
 9.06272 
 
 373,4 
 
 83 21 55.29 
 
 .456 
 
 99342 
 
 n,5 
 
 .11454 
 
 99,3 
 
 99713 
 
 5,o 
 
 .05897 
 
 376,7 
 
 83 25 21.56 
 
 457 
 
 .99353 
 
 11,4 
 
 .11355 
 
 99,4 
 
 .99718 
 
 5,o 
 
 .05519 
 
 380,0 
 
 83 28 47.82 
 
 .458 
 
 .99365 
 
 n,3 
 
 .11256 
 
 99,4 
 
 .99723 
 
 4,9 
 
 .05137 
 
 383,4 
 
 83 32 14.09 
 
 459 
 
 .99376 
 
 11,2 
 
 .11156 
 
 99,4 
 
 .99728 
 
 4,9 
 
 .04752 
 
 386,8 
 
 83 35 40.35 
 
 1.460 
 
 0.99387 
 
 11,1 
 
 o.i 1057 
 
 99,4 
 
 9-99733 
 
 4,8 
 
 9.04364 
 
 390,4 
 
 83 39 06.62 
 
 .461 
 
 .99398 
 
 II,O 
 
 .10958 
 
 99,4 
 
 99738 
 
 4,8 
 
 .03971 
 
 394,o 
 
 83 42 32.88 
 
 .462 
 
 99409 
 
 10,9 
 
 .10858 
 
 99,4 
 
 .99742 
 
 4,7 
 
 .03576 
 
 397,6 
 
 83 45 59.15 
 
 .463 
 
 .90420 
 
 10,8 
 
 . 10759 
 
 99,4 
 
 99747 
 
 4,7 
 
 .03176 
 
 401,3 
 
 83 49 25.41 
 
 .464 
 
 .99430 
 
 10,7 
 
 .10659 
 
 99,4 
 
 .99752 
 
 4,7 
 
 .02773 
 
 405,1 
 
 83 52 51-68 
 
 1.465 
 
 0.99441 
 
 10,6 
 
 0.10560 
 
 99,4 
 
 9.99756 
 
 4,6 
 
 9.02366 
 
 409,0 
 
 83 56 17.94 
 
 .466 
 
 99451 
 
 10,5 
 
 .10460 
 
 99,5 
 
 .99761 
 
 4,6 
 
 .01955 
 
 412,9 
 
 83 59 44-21 
 
 .467 
 
 .99462 
 
 10,4 
 
 . 10361 
 
 99,5 
 
 .99766 
 
 4,5 
 
 .01540 
 
 416,9 
 
 84 03 10.47 
 
 .468 
 
 99472 
 
 10,3 
 
 . 10262 
 
 99,5 
 
 99770 
 
 4,5 
 
 .OII2I 
 
 421,0 
 
 84 06 36.74 
 
 .469 
 
 .99482 
 
 10,2 
 
 . 10162 
 
 99,5 
 
 99775 
 
 4,4 
 
 .00698 
 
 4^5,2 
 
 84 10 03.00 
 
 1.470 
 
 0.09492 
 
 IO,I 
 
 0.10063 
 
 99,5 
 
 9-99779 
 
 4,4 
 
 9.O027I 
 
 429,4 
 
 84 13 29.27 
 
 .471 
 
 .99502 
 
 IO,O 
 
 .09963 
 
 99,5 
 
 .99783 
 
 4,3 
 
 8.99839 
 
 433,7 
 
 84 16 55-53 
 
 .472 
 
 .99512 
 
 9,9 
 
 .09864 
 
 99,5 
 
 .99788 
 
 4,3 
 
 .99403 
 
 438,2 
 
 84 20 21.79 
 
 473 
 
 .99522 
 
 9,8 
 
 .09764 
 
 99,5 
 
 .99792 
 
 4,3 
 
 .98963 
 
 442,7 
 
 84 23 48.06 
 
 474 
 
 99532 
 
 9,7 
 
 .09665 
 
 99,5 
 
 .99796 
 
 4,2 
 
 .98518 
 
 447,3 
 
 84 27 14.32 
 
 1-475 
 
 0.99542 
 
 9,6 
 
 0.09565 
 
 99,5 
 
 9.99800 
 
 4,2 
 
 8.98068 
 
 452,0 
 
 84 30 40-59 
 
 .476 
 
 99551 
 
 9,5 
 
 .09465 
 
 99,6 
 
 .99805 
 
 4,1 
 
 .97614 
 
 456,8 
 
 84 34 06.85 
 
 477 
 
 .99560 
 
 9,4 
 
 .09366 
 
 99,6 
 
 .90809 
 
 4,1 
 
 97155 
 
 461,7 
 
 84 37 33-12 
 
 478 
 
 99570 
 
 9,3 
 
 .09266 
 
 99,6 
 
 .99813 
 
 4,0 
 
 .96691 
 
 466,7 
 
 84 40 59.38 
 
 479 
 
 99579 
 
 9,2 
 
 .09167 
 
 99,6 
 
 99817 
 
 4,0 
 
 .96222 
 
 471,8 
 
 84 44 25.65 
 
 1.480 
 
 0.99588 
 
 9,1 
 
 0.09067 
 
 99,6 
 
 9.99821 
 
 4,0 
 
 8.95747 
 
 477,0 
 
 84 47 5I.9I 
 
 .481 
 
 99597 
 
 9,0 
 
 .08968 
 
 99,6 
 
 .99825 
 
 3,9 
 
 .95267 
 
 482,3 
 
 84 51 18.18 
 
 .482 
 
 .99606 
 
 8,9 
 
 .08868 
 
 99,6 
 
 .99829 
 
 3,9 
 
 .94782 
 
 487,8 
 
 84 54 44-44 
 
 .483 
 
 .99615 
 
 8,8 
 
 .08768 
 
 99,6 
 
 .99832 
 
 3,8 
 
 .94292 
 
 493,4 
 
 84 58 10.71 
 
 .484 
 
 .99624 
 
 8,7 
 
 .08669 
 
 99,6 
 
 .99836 
 
 3,8 
 
 .93796 
 
 499,1 
 
 85 oi 36.97 
 
 1.485 
 
 0.99632 
 
 8,6 
 
 0.08569 
 
 99,6 
 
 9.99840 
 
 3,7 
 
 8.93294 
 
 504,9 
 
 85 05 03.24 
 
 .486 
 
 .99641 
 
 8,5 
 
 .08469 
 
 99,6 
 
 .99844 
 
 3,7 
 
 .92786 
 
 5io,9 
 
 85 08 29.50 
 
 .487 
 
 .99649 
 
 8,4 
 
 .08370 
 
 99,6 
 
 .90847 
 
 3,6 
 
 .92272 
 
 5i7,i 
 
 85 ii 55-77 
 
 .488 
 
 .99657 
 
 8,3 
 
 .08270 
 
 99,7 
 
 .99851 
 
 3,6 
 
 .91751 
 
 523,3 
 
 85 15 22.03 
 
 .489 
 
 .99666 
 
 8,2 
 
 .08171 
 
 99,7 
 
 .99855 
 
 3,6 
 
 .91225 
 
 529,8 
 
 85 18 48.30 
 
 1.490 
 
 0.09674 
 
 8,1 
 
 0.08071 
 
 99,7 
 
 9.99858 
 
 3,5 
 
 8.90692 
 
 536,3 
 
 85 22 14.56 
 
 .491 
 
 .99682 
 
 8,0 
 
 .07971 
 
 99,7 
 
 .99862 
 
 3,5 
 
 .90152 
 
 543,1 
 
 85 25 40.83! 
 
 .492 
 
 .99690 
 
 7,9 
 
 .07871 
 
 99,7 
 
 .99865 
 
 3,4 
 
 .89606 
 
 550,0 
 
 85 29 07.09 
 
 493 
 
 .99698 
 
 7,8 
 
 .07772 
 
 99,7 
 
 .09868 
 
 3,4 
 
 .89052 
 
 557,i 
 
 85 32 33.36 
 
 494 
 
 .99705 
 
 7,7 
 
 .07672 
 
 99,7 
 
 .99872 
 
 3,3 
 
 .88491 
 
 564,4 
 
 85 35 59.62 
 
 1.495 
 
 0.99713 
 
 7,6 
 
 0.07572 
 
 99,7 
 
 9.99875 
 
 3,3 
 
 8.87923 
 
 57i,9 
 
 85 39 25.89 
 
 .496 
 
 .99720 
 
 7,5 
 
 07473 
 
 99,7 
 
 .99878 
 
 3,3 
 
 .87348 
 
 579,6 
 
 85 42 52.15 
 
 497 
 
 .99728 
 
 7,4 
 
 .07373 
 
 99,7 
 
 .09882 
 
 3,2 
 
 .86764 
 
 587,4 
 
 85 46 18.41 
 
 .498 
 
 99735 
 
 7,3 
 
 .07273 
 
 99,7 
 
 .99885 
 
 3,2 
 
 .86 I7 3 
 
 595,5 
 
 85 49 44-68 
 
 .499 
 
 .99742 
 
 7,2 
 
 .07173 
 
 99,7 
 
 .99888 
 
 3,i 
 
 .85573 
 
 603,9 
 
 85 53 10.94 
 
 I.5OO 
 
 0-99749 
 
 7,i 
 
 0.07074 
 
 99,7 
 
 9.99891 
 
 3,i 
 
 8.84065 
 
 612,4 
 
 85 56 37.21 
 
 u 
 
 -isinhiu 
 
 F ' 
 
 cosh iu 
 
 F ' 
 
 sinh iu 
 
 wF ' 
 
 og cosh iii 
 
 Fo' 
 
 u 
 
 tog 
 
 SMITHSONIAN TABLES 
 
 221 
 
Circular Functions. 
 
 u 
 
 sin u 
 
 F ' 
 
 cos u 
 
 w Fo' ! log sin u 
 
 Fo' 
 
 log cos u 
 
 F O ' 
 
 u 
 
 1.500 
 
 0.99749 
 
 7,1 
 
 0.07074 
 
 99,7 
 
 9.99891 
 
 3,1 
 
 8.84965 
 
 612,4 
 
 ^5 56 37-21 
 
 .501 
 
 99757 
 
 7,0 
 
 .06974 
 
 99,8 
 
 .99894 
 
 3,1 
 
 .84348 
 
 621,2 
 
 86 oo 03.47 
 
 .502 
 
 .99763 
 
 6,9 
 
 .06874 
 
 99,8 
 
 .90897 
 
 3,0 
 
 .83722 
 
 630,3 
 
 86 03 29.74 
 
 .503 
 
 99770 
 
 6,8 
 
 .06774 
 
 99,8 
 
 .99900 
 
 2,9 
 
 .83087 
 
 639,6 
 
 86 06 56.00 
 
 .504 
 
 99777 
 
 6,7 
 
 .06675 
 
 99,8 
 
 .99903 
 
 2,9 
 
 .82443 
 
 649,2 
 
 86 10 22.27 
 
 1.505 
 
 0.99784 
 
 6,6 
 
 0.06575 
 
 99,8 
 
 9.99906 
 
 2,9 
 
 8.81789 
 
 659,1 
 
 86 13 48.53 
 
 .506 
 
 .99790 
 
 6,5 
 
 .06475 
 
 99,8 
 
 .99909 
 
 2,8 
 
 .81125 
 
 669,3 
 
 86 17 14.80 
 
 .507 
 
 99797 
 
 6,4 
 
 .06375 
 
 99,8 
 
 .99912 
 
 2,8 
 
 .80450 
 
 679,8 
 
 86 20 41.06 
 
 .508 
 
 .99803 
 
 6,3 
 
 .06276 
 
 99,8 
 
 .99914 
 
 2,7 
 
 .79765 
 
 690,7 
 
 86 24 07.33 
 
 .509 
 
 .99809 
 
 6,2 
 
 .06176 
 
 99,8 
 
 .99917 
 
 2,7 
 
 .79069 
 
 701,9 
 
 86 27 33-59 
 
 1.510 
 
 0.99815 
 
 6,1 
 
 0.06076 
 
 99,8 
 
 9.99920 
 
 2,6 
 
 8.78361 
 
 7i3,5 
 
 86 30 59-86 
 
 .511 
 
 .99821 
 
 6,0 
 
 .05976 
 
 99,8 
 
 .99922 
 
 2,6 
 
 .77642 
 
 725,4 
 
 86 34 26.12 
 
 .512 
 
 .99827 
 
 5,9 
 
 .05876 
 
 99,8 
 
 .99925 
 
 2,6 
 
 .76910 
 
 737,8 
 
 86 37 52.39 
 
 .513 
 
 .99833 
 
 5,8 
 
 .05776 
 
 99,8 
 
 .99927 
 
 2,5 
 
 .76166 
 
 750,6 
 
 86 41 18.65 
 
 .514 
 
 .99839 
 
 5,7 
 
 " .05677 
 
 99,8 
 
 .99930 
 
 2,5 
 
 .75409 
 
 763,8 
 
 86 44 44-92 
 
 1.515 
 
 0.09844 
 
 5,6 
 
 0.05577 
 
 99,8 
 
 9.99932 
 
 2,4 
 
 8.74638 
 
 777,5 
 
 86 48 11. 18 
 
 .516 
 
 .99850 
 
 5,5 
 
 .05477 
 
 99,8 
 
 99935 
 
 2,4 
 
 .73853 
 
 791,8 
 
 86 51 37-45 
 
 .517 
 
 .99855 
 
 5,4 
 
 .05377 
 
 99,9 
 
 99937 
 
 2,3 
 
 73054 
 
 806,5 
 
 86 55 03.71 
 
 .518 
 
 .99861 
 
 5,3 
 
 05277 
 
 99,9 
 
 99939 
 
 2,3 
 
 .72240 
 
 821,8 
 
 86 58 29.98 
 
 .519 
 
 .99866 
 
 5,2 
 
 .05177 
 
 99,9 
 
 .99942 
 
 2,3 
 
 .71410 
 
 837,7 
 
 87 01 56.24 
 
 1.520 
 
 0.99871 
 
 5,1 
 
 0.05077 
 
 99,9 
 
 9-99944 
 
 2,2 
 
 8.70565 
 
 854,2 
 
 87 05 22.51 
 
 .521 
 
 .99876 
 
 5,o 
 
 .04978 
 
 99,9 
 
 .99946 
 
 2,2 
 
 .69702 
 
 871,4 
 
 87 08 48.77 
 
 .522 
 
 .99881 
 
 4,9 
 
 .04878 
 
 99,9 
 
 .90948 
 
 2,1 
 
 .68821 
 
 889,3 
 
 87 12 15.04 
 
 .523 
 
 .99886 
 
 4,8 
 
 .04778 
 
 99,9 
 
 .99950 
 
 2,1 
 
 .67923 
 
 907,9 
 
 87 15 41-30 
 
 .524 
 
 .99891 
 
 4,7 
 
 .04678 
 
 99,9 
 
 99952 
 
 2,0 
 
 .67005 
 
 927,4 
 
 87 19 07.56 
 
 1.525 
 
 0.99895 
 
 4,6 
 
 0.04578 
 
 99,9 
 
 9-99954 
 
 2,0 
 
 8.66068 
 
 947,7 
 
 87 22 33.83 
 
 .526 
 
 .09900 
 
 4,5 
 
 .04478 
 
 99,9 
 
 .99956 
 
 1,9 
 
 .65110 
 
 968,8 
 
 87 26 00.09 
 
 .527 
 
 99904 
 
 4,4 
 
 .04378 
 
 99,9 
 
 .95958 
 
 i,9 
 
 .64130 
 
 99i,o 
 
 87 29 26.36 
 
 .528 
 
 .99908 
 
 4,3 
 
 .04278 
 
 99,9 
 
 .90960 
 
 i,9 
 
 .63127 
 
 1014,2 
 
 87 32 52.62 
 
 .529 
 
 99913 
 
 4,2 
 
 .04178 
 
 99,9 
 
 .99962 
 
 1,8 
 
 .62IOI 
 
 1038,5 
 
 87 36 18.89 
 
 1.530 
 
 0.99917 
 
 4,1 
 
 0.04079 
 
 99,9 
 
 9.99964 
 
 1,8 
 
 8.61050 
 
 1064,0 
 
 87 39 45-15 
 
 .531 
 
 .99921 
 
 4,0 
 
 .03979 
 
 99,9 
 
 .99966 
 
 i,7 
 
 59973 
 
 1090,7 
 
 87 43 11-42 
 
 .532 
 
 99925 
 
 3,9 
 
 .03879 
 
 99,9 
 
 .99967 
 
 i,7 
 
 .58868 
 
 1 1 18,9 
 
 87 46 37-68 
 
 533 
 
 .99929 
 
 3,8 
 
 .03779 
 
 99,9 
 
 99969 
 
 1,6 
 
 57735 
 
 1148,5 
 
 87 50 03.95 
 
 534 
 
 .99932 
 
 3,7 
 
 .03679 
 
 99,9 
 
 99971 
 
 1,6 
 
 56571 
 
 1179,7 
 
 87 53 30.21 
 
 1-535 
 
 0.99936 
 
 3,6 
 
 0.03579 
 
 99,9 
 
 9.99972 
 
 1,6 
 
 8-55375 
 
 1212,7 
 
 87 56 56.48 
 
 .536 
 
 99939 
 
 3,5 
 
 .03479 
 
 99,9 
 
 99974 
 
 i,5 
 
 .54145 
 
 1247,6 
 
 88 oo 22.74 
 
 537 
 
 99943 
 
 3,4 
 
 .03379 
 
 99,9 
 
 .99975- 
 
 i,5 
 
 .52879 
 
 1284,5 
 
 88 03 49.01 
 
 .538 
 
 .99946 
 
 3,3 
 
 .03279 
 
 99,9 
 
 99977 
 
 i,4 
 
 .51575 
 
 1323,7 
 
 88 07 15.27 
 
 539 
 
 99949 
 
 3,2 
 
 .03179 
 
 99,9 
 
 .99978 
 
 1,4 
 
 .50230 
 
 1365,4 
 
 88 10 41.54 
 
 1.540 
 
 0.99953 
 
 3,1 
 
 0.03079 
 
 IOO,O 
 
 9.99979 
 
 i,3 
 
 8.48843 
 
 1409,8 
 
 88 14 07.80 
 
 541 
 
 .99956 
 
 3,0 
 
 .02979 
 
 1 00,0 
 
 .99981 
 
 i,3 
 
 .47410 
 
 1457,1 
 
 88 17 34-07 
 
 .542 
 
 .99959 
 
 2,9 
 
 .02879 
 
 100,0 
 
 .99982 
 
 i,3 
 
 .45928 
 
 1507,7 
 
 88 21 00.33 
 
 543 
 
 .99961 
 
 2,8 
 
 .02779 
 
 100,0 
 
 99983 
 
 1,2 
 
 .44393 
 
 1562,0 
 
 88 24 26.60 
 
 544 
 
 .99964 
 
 2,7 
 
 .02679 
 
 100,0 
 
 99984 
 
 1,2 
 
 .42802 
 
 1620,3 
 
 88 27 52.86! 
 
 1.545 
 
 0.09967 
 
 2,6 
 
 0.02579 
 
 100,0 
 
 9.09986 
 
 i,i 
 
 8.41151 
 
 1683,2 
 
 88 31 I9.I3 
 
 .546 
 
 .99969 
 
 2,5 
 
 .02479 
 
 100,0 
 
 .99987 
 
 1,1 
 
 39434 
 
 I75i,i 
 
 88 34 45-39 
 
 547 
 
 .99972 
 
 2,4 
 
 .02379 
 
 100,0 
 
 .<//>S8 
 
 1,0 
 
 .37647 
 
 1824,7 
 
 88 38 11.66 
 
 .548 
 
 99974 
 
 2,3 
 
 .02279 
 
 100,0 
 
 .99089 
 
 1,0 
 
 .35783 
 
 1904,8 
 
 88 41 37-92 
 
 ..549 
 
 .99976 
 
 2,2 
 
 .02179 
 
 100,0 
 
 .99990 
 
 0,9 
 
 .33835 
 
 1992,2 
 
 88 45 04.18 
 
 1-550 
 
 0.99978 
 
 2,1 
 
 0.02079 
 
 100,0 
 
 9.99991 
 
 o,9 
 
 8.31796 
 
 2088,0 
 
 88 48 30.45 
 
 u 
 
 -isinhiu 
 
 Fo' 
 
 cosh iu 
 
 -FO' 
 
 |0 inh iu 
 
 F ' 
 
 ogcoshiu 
 
 Fo' 
 
 u 
 
 100 , 
 
 SMITHSONIAN TABLES 
 
 222 
 
Circular Functions. 
 
 u 
 
 sin u 
 
 F ' 
 
 COS U 
 
 F O ' 
 
 log sin u 
 
 wF ' 
 
 log cos u 
 
 wF ' 
 
 U 
 
 
 
 
 
 
 
 
 
 
 o / // 
 
 1.550 
 
 0.99978 
 
 2,1 
 
 +0.02079 
 
 100,0 
 
 9.99991 
 
 0,9 
 
 8.31796 
 
 2088,0 
 
 88 48 30.45 
 
 .551 
 
 .99980 
 
 2,O 
 
 .01980 
 
 
 .99991 
 
 0,9 
 
 .29656 
 
 2193,5 
 
 88 51 56.71 
 
 .552 
 
 .99982 
 
 1,9 
 
 .01880 
 
 
 .99992 
 
 0,8 
 
 .27405 
 
 2310,3 
 
 88 55 22.98 
 
 553 
 
 .99984 
 
 1,8 
 
 .01780 
 
 
 99993 
 
 0,8 
 
 25031 
 
 2440,1 
 
 88 58 49-24 
 
 554 
 
 .99986 
 
 i,7 
 
 .01680 
 
 
 .99994 
 
 o,7 
 
 .22519 
 
 2585,4 
 
 89 02 15.51 
 
 1-555 
 
 0.99988 
 
 1,6 
 
 +0.01580 
 
 100,0 
 
 9.99995 
 
 o,7 
 
 8.19854 
 
 2749,1 
 
 89 05 4L77 
 
 556 
 
 .99989 
 
 i,5 
 
 .01480 
 
 
 99995 
 
 0,6 
 
 .17014 
 
 2934,9 
 
 89 09 08.04 
 
 557 
 
 .99990 
 
 1,4 
 
 .01380 
 
 
 .99996 
 
 0,6 
 
 . 13975 
 
 3H7,7 
 
 89 12 34.30 
 
 .558 
 
 .99992 
 
 1,3 
 
 .01280 
 
 
 .99996 
 
 0,6 
 
 . 10707 
 
 3393,7 
 
 89 16 00.57 
 
 .559 
 
 99993 
 
 1,2 
 
 .01180 
 
 
 .99997 
 
 o,5 
 
 .07174 
 
 368i,4 
 
 89 19 26.83 
 
 1.560 
 
 0.99994 
 
 1,1 
 
 +0.01080 
 
 100,0 
 
 9-99997 
 
 o,5 
 
 8.03327 
 
 4022,5 
 
 89 22 53.10 
 
 .561 
 
 .99995 
 
 1,0 
 
 .00080 
 
 
 .99998 
 
 0,4 
 
 7.99106 
 
 4433,1 
 
 89 26 19.36 
 
 .562 
 
 .90996 
 
 0,9 
 
 .00880 
 
 
 .99098 
 
 0,4 
 
 94430 
 
 4937,1 
 
 89 29 45.63 
 
 .563 
 
 .99997 
 
 0,8 
 
 .00780 
 
 
 99999 
 
 o,3 
 
 .89189 
 
 5570,4 
 
 89 33 11-89 
 
 .564 
 
 .99998 
 
 o,7 
 
 .00680 
 
 
 99999 
 
 0,3 
 
 .83227 
 
 6390,0 
 
 89 36 38.16 
 
 1.565 
 
 0.90998 
 
 0,6 
 
 +0.00580 
 
 100,0 
 
 9.99999 
 
 o,3 
 
 7.76315 
 
 7492,5 
 
 89 40 04.42 
 
 .566 
 
 .99999 
 
 o,5 
 
 .00480 
 
 
 o.ooooo 
 
 0,2 
 
 .68091 
 
 9054,7 
 
 89 43 30.69 
 
 .567 
 
 .99999 
 
 0,4 
 
 .00380 
 
 
 .00000 
 
 0,2 
 
 .57936 
 
 11439,8 
 
 89 46 56.95 
 
 .568 
 
 I.OOOOO 
 
 o,3 
 
 .00280 
 
 
 .00000 
 
 0,1 
 
 .44659 
 
 15530,9 
 
 89 50 23.22 
 
 .569 
 
 I. 00000 
 
 0,2 
 
 .00180 
 
 
 .00000 
 
 0,1 
 
 .25438 
 
 24176,8 
 
 89 53 49.48 
 
 1.570 
 
 I.OOOOO 
 
 0,1 
 
 +0.00080 
 
 100,0 
 
 0.00000 
 
 0,0 
 
 6.90109 
 
 54537,4 
 
 89 57 15-75 
 
 571 . 
 
 .00000 
 
 0,0 
 
 .00020 
 
 
 .00000 
 
 0,0 
 
 6.3089471 
 
 213228,5 
 
 90 oo 42.01 
 
 .572 
 
 .00000 
 
 0,1 
 
 .00120 
 
 
 .00000 
 
 0,1 
 
 7.08051 
 
 36080,7 
 
 oo 04 08.28 
 
 573 
 
 .00000 
 
 0,2 
 
 .00220 
 
 
 .00000 
 
 0,1 
 
 .34315 
 
 19707,7 
 
 90 07 34.54 
 
 574 
 
 0.99999 
 
 0,3 
 
 .00320 
 
 
 .00000 
 
 0,1 
 
 .50565 
 
 13556,1 
 
 90 II 00.81 
 
 1.575 
 
 0.99999 
 
 0,4 
 
 0.00420 
 
 100,0 
 
 0.00000 
 
 0,2 
 
 7.6236371 
 
 10331,2 
 
 90 14 27.07 
 
 .576 
 
 .99999 
 
 o,5 
 
 .00520 
 
 
 9-99999 
 
 0,2 
 
 .71631 
 
 8345,8 
 
 90 17 53-33 
 
 .577 
 
 .99998 
 
 0,6 
 
 .00620 
 
 
 99999 
 
 0,3 
 
 .79265 
 
 7000,5 
 
 90 21 19.60 
 
 .578 
 
 .99997 
 
 o,7 
 
 .00720 
 
 
 99999 
 
 o,3 
 
 .85755 
 
 6028,6 
 
 90 24 45-86 
 
 579 
 
 99997 
 
 0,8 
 
 .00820 
 
 
 99999 
 
 0,4 
 
 .91400 
 
 5293,8 
 
 90 28 12.13 
 
 1.580 
 
 0.99996 
 
 0,9 
 
 0.00920 
 
 100,0 
 
 9.99998 
 
 0,4 
 
 7.96~396n 
 
 47i8,6 
 
 90 31 38.39 
 
 .581 
 
 99995 
 
 1,0 
 
 .01020 
 
 
 99998 
 
 0,4 
 
 8.00875 
 
 4256,1 
 
 90 35 04.66 
 
 .582 
 
 .99994 
 
 1,1 
 
 .OII2O 
 
 
 .99997 
 
 0,5 
 
 04935 
 
 3876,2 
 
 90 38 30.92 
 
 .583 
 
 -99993 
 
 1,2 
 
 .01220 
 
 
 -99997 
 
 o,5 
 
 .08648 
 
 3558,5 
 
 oo 41 57.19 
 
 .584 
 
 .99991 
 
 i,3 
 
 .01320 
 
 
 .99996 
 
 0,6 
 
 .12068 
 
 3289,0 
 
 90 45 23.45 
 
 1.585 
 
 0.09990 
 
 1,4 
 
 0.01420 
 
 100,0 
 
 9.90996 
 
 0,6 
 
 8.15239" 
 
 3057,4 
 
 oo 48 49.72 
 
 .586 
 
 .99988 
 
 i,5 
 
 .01520 
 
 
 -99995 
 
 o,7 
 
 18193 
 
 2856,3 
 
 90 52 15-98 
 
 .587 
 
 .99987 
 
 1,6 
 
 .01620 
 
 
 -99994 
 
 o,7 
 
 .20959 
 
 2680,0 
 
 go 55 42.25 
 
 .588 
 
 .99985 
 
 i,7 
 
 .01720 
 
 
 99994 
 
 0,7 
 
 .23560 
 
 2524,2 
 
 90 59 08.51 
 
 .589 
 
 .99983 
 
 1,8 
 
 .01820 
 
 
 99993 
 
 0,8 
 
 .26014 
 
 2385,5 
 
 91 02 34.78 
 
 1.590 
 
 0.99982 
 
 i,9 
 
 0.01920 
 
 100,0 
 
 9-99992 
 
 0,8 
 
 8.28336* 
 
 2261,2 
 
 91 06 01.04 
 
 .591 
 
 .99980 
 
 2,0 
 
 .02020 
 
 
 .99991 
 
 0,9 
 
 .30540 
 
 2149,3 
 
 91 09 27.31 
 
 .592 
 
 .99978 
 
 2,1 
 
 .02120 
 
 
 .99990 
 
 0,9 
 
 .32638 
 
 2047,9 
 
 91 12 53-57 
 
 .593 
 
 .99975 
 
 2,2 
 
 .02220 
 
 
 .99989 
 
 1,0 
 
 .34639 
 
 1955,6 
 
 91 16 19.84 
 
 594 
 
 99973 
 
 2,3 
 
 .02320 
 
 
 .99988 
 
 1,0 
 
 36552 
 
 1871,3 
 
 91 19 46.10 
 
 1.595 
 
 0.09971 
 
 2,4 
 
 0.02420 
 
 100,0 
 
 9.99987 
 
 i 
 
 8.383&4n 
 
 1794,0 
 
 91 23 12.37 
 
 .596 
 
 .99968 
 
 2,5 
 
 .02520 
 
 
 -99986 
 
 i 
 
 .40142 
 
 1722,8 
 
 91 26 38.63 
 
 597 
 
 .99966 
 
 2,6 
 
 .02620 
 
 
 .99985 
 
 i 
 
 -41831 
 
 1657,0 
 
 91 30 04-90 
 
 .598 
 
 .99963 
 
 2,7 
 
 .02720 
 
 
 -99984 
 
 2 
 
 43457 
 
 I596,i 
 
 91 33 31-16 
 
 .599 
 
 .99960 
 
 2,8 
 
 .02820 
 
 
 .99983 
 
 2 
 
 .45025 
 
 1539,4 
 
 91 36 57-43 
 
 1. 600 
 
 0.99957 
 
 2,9 
 
 0.02920 
 
 100,0 
 
 9.99981 
 
 1,3 
 
 8.46538, 
 
 1486,7 
 
 91 40 23-69 
 
 
 i c : n u :, 
 
 wFr/ 
 
 cosh ill 
 
 wFo' 
 
 . sinh iu 
 
 <ii P ' 
 
 . 
 
 w F,)' 
 
 ii 
 
 
 I sinn 11 
 
 w 
 
 
 
 log . 
 
 w ro 
 
 loo cosh iu 
 
 
 
 SMITHSONIAN TABLES 
 
 223 
 
TABLE IV 
 
 THE ASCENDING AND DESCENDING EXPONENTIAL AND 
 
 Log )0 (e u ) 
 
 NOTE. In Table IV, for u greater than 2.302, the tabulated values of 
 the ascending exponential may sometimes be erroneous to one unit in the 
 last place. 
 
 225 
 
The Exponential. 
 
 u 
 
 IOQio(e u ) 
 
 e u 
 
 e~ u 
 
 u 
 
 loj>io(e n ) 
 
 e n 
 
 e- 
 
 o.ooo 
 .001 
 .002 
 
 .003 
 
 .004 
 
 0.000 0000 
 .000 4343 
 .000 8686 
 .001 3029 
 
 .001 7372 
 
 I. 000 000 
 .001 OOI 
 .OO2 OO2 
 
 .003 005 
 .004 008 
 
 1. 000 0000 
 
 0.099 0005 
 
 .998 0020 
 
 .997 0045 
 .996 0080 
 
 0.050 
 .051 
 .052 
 .053 
 .054 
 
 O.O2I 7147 
 .022 I4OO 
 .022 5833 
 .023 0176 
 .023 4519 
 
 I.05I 271 
 .052 323 
 .053 376 
 .054 430 
 055 485 
 
 0.951 2294 
 950 2787 
 949 3^*9 
 .948 3800 
 947 4321 
 
 0.005 
 .006 
 .007 
 .008 
 .009 
 
 0.002 1715 
 .OO2 6058 
 .OO3 O40I 
 .003 4744 
 .003 9087 
 
 1.005 013 
 .006 018 
 .007 025 
 .008 032 
 .009 041 
 
 0.095 0125 
 .094 0180 
 .993 0244 
 .992 0319 
 .991 0404 
 
 0.055 
 .056 
 .057 
 .058 
 .059 
 
 O.O23 8862 
 .024 3205 
 .024 7548 
 .025 1891 
 .025 6234 
 
 1.056 541 
 .057 598 
 .058 656 
 059 715 
 .060 775 
 
 0.946 4851 
 
 945 5391 
 .944 5941 
 
 .943 6499 
 .942 7068 
 
 O.OIO 
 .Oil 
 
 .012 
 
 .013 
 
 .014 
 
 0.004 3429 
 .004 7772 
 .005 2115 
 .005 6458 
 .006 0801 
 
 i. oio 050 
 .on 06 1 
 
 .012 O72 
 
 .013 085 
 .014 098 
 
 0.990 0498 
 .989 0603 
 
 .988 0717 
 .087 0841 
 986 0975 
 
 0.060 
 .061 
 .062 
 063 
 .064 
 
 0.026 0577 
 .026 492O 
 .026 9263 
 .027 3606 
 .027 7948 
 
 1.061 837 
 .062 899 
 .063 062 
 .065 027 
 .066 092 
 
 0.041 7645 
 .940 8232 
 .939 8829 
 .938 9435 
 .938 0050 
 
 0.015 
 .016 
 
 .017 
 .018 
 .019 
 
 0.006 5144 
 .006 9487 
 .007 3830 
 .007 8173 
 .008 2516 
 
 1.015 113 
 .016 129 
 
 .017 145 
 
 .018 163 
 .019 182 
 
 0.085 1119 
 .984 1273 
 .983 1437 
 .982 1610 
 .981 1794 
 
 0.065 
 .066 
 .067 
 .068 
 .069 
 
 O.O28 2291 
 .028 6634 
 
 .029 0977 
 .029 5320 
 .029 9663 
 
 1.067 159 
 .068 227 
 .069 295 
 .070 365 
 .071 436 
 
 0.937 0675 
 .936 1309 
 .935 1952 
 .934 2605 
 933 3267 
 
 O.O20 
 .021 
 .022 
 
 .023 
 
 .024 
 
 0.008 6859 
 .009 I2O2 
 
 .009 5545 
 .009 9888 
 .010 4231 
 
 1.020 201 
 .021 222 
 .022 244 
 .023 267 
 .024 200 
 
 0.080 1987 
 .979 2190 
 
 .978 2402 
 .977 2625 
 .976 2857 
 
 0.070 
 .071 
 .072 
 .073 
 .074 
 
 0.030 4006 
 .030 8349 
 .031 2692 
 .031 7035 
 .032 1378 
 
 1.072 508 
 .073 58i 
 .074 655 
 .075 73i 
 .076 807 
 
 0.932 3938 
 .931 4619 
 930 5309 
 .929 6008 
 .928 6717 
 
 0.025 
 .026 
 
 .027 
 
 .028 
 .029 
 
 o.oio 8574 
 .011 2917 
 .011 7260 
 .012 1602 
 .012 5945 
 
 1.025 315 
 .026 341 
 .027 368 
 .028 306 
 .029 425 
 
 0.975 3099 
 974 3351 
 .973 3612 
 .972 3884 
 .971 4165 
 
 0.075 
 .076 
 .077 
 .078 
 .079 
 
 0.032 5721 
 .033 0064 
 .033 4407 
 033 8750 
 .034 3093 
 
 1.077 884 
 .078 063 
 .080 042 
 .081 123 
 .082 204 
 
 0.927 7435 
 .926 8162 
 .925 8899 
 .924 9644 
 .924 0399 
 
 0.030 
 .031 
 .032 
 
 .033 
 .034 
 
 0.013 0288 
 .013 4631 
 .013 8974 
 .014 3317 
 .014 7660 
 
 1.030 455 
 .031 486 
 .032 518 
 .033 551 
 034 585 
 
 0.970 4455 
 .969 4756 
 .968 5066 
 .067 5386 
 .966 5715 
 
 0.080 
 
 .081 
 .082 
 .083 
 .084 
 
 0.034 7436 
 .035 1779 
 .035 6121 
 .036 0464 
 .036 4807 
 
 1.083 287 
 .084 371 
 .085 456 
 .086 542 
 .087 629 
 
 0.923 1163 
 .922 1937 
 .921 2720 
 .920 3511 
 .919 4313 
 
 0.035 
 .036 
 .037 
 .038 
 .039 
 
 0.015 2003 
 .015 6346 
 .016 0689 
 .016 5032 
 .016 9375 
 
 1.035 620 
 .036 656 
 .037 693 
 .038 731 
 .039 770 
 
 0.065 6054 
 .064 6403 
 .063 6761 
 .962 7129 
 .961 7507 
 
 0.085 
 .086 
 .087 
 .088 
 .089 
 
 0.036 9150 
 .037 3493 
 037 7836 
 .038 2179 
 .038 6522 
 
 i. 088 717 
 .089 806 
 .000 897 
 
 .091 988 
 
 .093 081 
 
 0.918 5123 
 .917 5942 
 .916 6771 
 .915 7609 
 .914 8456 
 
 0.040 
 .041 
 .042 
 .043 
 .044 
 
 0.017 3718 
 .017 8061 
 .018 2404 
 .018 6747 
 .019 1090 
 
 1.040 811 
 .041 852 
 .042 894 
 043 938 
 .044 982 
 
 0.060 7894 
 .959 8291 
 .9588698 
 .957 9114 
 .956 9540 
 
 0.000 
 
 .091 
 .092 
 
 .093 
 .094 
 
 0.039 0865 
 .039 5208 
 .039 9551 
 .040 3894 
 .040 8237 
 
 1.094 174 
 .095 269 
 .096 365 
 .097 462 
 .098 560 
 
 0.913 9312 
 .913 0177 
 .912 1051 
 
 .911 1935 
 .910 2828 
 
 0.045 
 .046 
 
 047 
 .048 
 .049 
 
 0.019 5433 
 .019 9775 
 .020 4118 
 .020 8461 
 .021 2804 
 
 1.046 028 
 .047 074 
 
 .048 122 
 .049 171 
 .O5O 22O 
 
 0.955 9975 
 .955 0420 
 .954 0874 
 .953 1338 
 .952 1811 
 
 0.095 
 .006 
 .097 
 .098 
 .099 
 
 0.041 2580 
 .041 6923 
 .042 1266 
 .042 5609 
 .042 9952 
 
 1.009 659 
 . loo 759 
 .101 860 
 .102 063 
 .104 066 
 
 0.909 3729 
 .908 4640 
 .007 5500 
 .906 6489 
 .905 7427 
 
 0.050 
 
 0.021 7147 
 
 I.05I 271 
 
 0.951 2294 
 
 O.IOO 
 
 0.043 4294 
 
 i. 105 171 
 
 0.904 8374 
 
 log.V; 
 
 lofli,Xe u ) 
 
 e u 
 
 a'" 
 
 log t! (e u ) 
 
 ,.*-, 
 
 e u 
 
 e- 
 
 SMITHSONIAN TABLES 
 
The Exponential. 
 
 u 
 
 logio(e u ) 
 
 e u 
 
 .- 
 
 u 
 
 logio(e u ) 
 
 e u 
 
 .- 
 
 O.IOO 
 
 0.043 4294 
 
 1.105 171 
 
 0.904 8374 
 
 O.I5O 
 
 0.065 1442 
 
 1.161 834 
 
 0.860 7080 
 
 .101 
 
 .043 8637 
 
 .106 277 
 
 .903 9330 
 
 .151 
 
 .065 5785 
 
 .162 997 
 
 .859 8477 
 
 .102 
 
 .044 2980 
 
 .107 383 
 
 .903 0296 
 
 .152 
 
 .066 0128 
 
 .164 160 
 
 .858 9883 
 
 .103 
 
 .044 7323 
 
 . 108 491 
 
 .902 1270 
 
 .153 
 
 .066 4471 
 
 .165 325 
 
 .858 1297 
 
 .IO4 
 
 .045 1666 
 
 .109 600 
 
 .901 2253 
 
 .154 
 
 .0668814 
 
 .166 491 
 
 .857 2720 
 
 0.105 
 
 0.045 6009 
 
 i. no 711 
 
 0.900 3245 
 
 0.155 
 
 0.067 3156 
 
 1.167 658 
 
 0.856 4152 
 
 .105 
 
 .046 0352 
 
 .in 822 
 
 .899 4246 
 
 .156 
 
 .067 7499 
 
 .168 826 
 
 .855 5592 
 
 .107 
 
 .046 4695 
 
 .112 934 
 
 .898 5257 
 
 .157 
 
 .068 1842 
 
 .169 996 
 
 .854 7041 
 
 .108 
 
 .046 9038 
 
 .114 048 
 
 .897 6276 
 
 .158 
 
 .068 6185 
 
 .171 166 
 
 .853 8498 
 
 .109 
 
 .047 338i 
 
 .115 162 
 
 .896 7304 
 
 .159 
 
 .069 0528 
 
 .172 338 
 
 .852 9964 
 
 O.IIO 
 
 0.047 7724 
 
 1.116 278 
 
 0.895 8341 
 
 0.160 
 
 0.069 4871 
 
 i. 173 5ii 
 
 0.852 1438 
 
 .III 
 
 .048 2067 
 
 .117 395 
 
 .894 9387 
 
 .161 
 
 .069 9214 
 
 .174 685 
 
 .851 2921 
 
 .112 
 
 .048 6410 
 
 .118 513 
 
 .894 0443 
 
 .162 
 
 .070 3557 
 
 .175 860 
 
 .850 4412 
 
 .113 
 
 049 0753 
 
 .119 632 
 
 .893 1507 
 
 .163 
 
 .070 7900 
 
 '.177 037 
 
 .849 5912 
 
 .114 
 
 .049 5096 
 
 .120 752 
 
 .892 2580 
 
 .164 
 
 .071 2243 
 
 .178 214 
 
 .848 7420 
 
 1 O.H5 
 
 0.049 9439 
 
 i. 121 873 
 
 0.891 3661 
 
 0.165 
 
 0.071 6586 
 
 1. 179 393 
 
 0.847 8937 
 
 .116 
 
 .050 3782 
 
 .122 996 
 
 .890 4752 
 
 .166 
 
 .072 0929 
 
 .180 573 
 
 .847 0462 
 
 .117 
 
 .050 8125 
 
 .124 119 
 
 .889 5852 
 
 .167 
 
 .072 5272 
 
 .181 754 
 
 .846 1996 
 
 .118 
 
 .051 2467 
 
 .125 244 
 
 .8886961 
 
 .168 
 
 .072 9615 
 
 .182 937 
 
 .845 3538 
 
 .119 
 
 .051 6810 
 
 .126 370 
 
 .887 8078 
 
 .169 
 
 .073 3958 
 
 .184 120 
 
 .844 5089 
 
 0.120 
 
 0.052 1153 
 
 1.127 497 
 
 0.886 9204 
 
 0.170 
 
 0.073 8301 
 
 1.185 305 
 
 0.843 6648 
 
 .121 
 
 .052 5496 
 
 .128 625 
 
 .886 0340 
 
 .171 
 
 .074 2644' 
 
 .186 491 
 
 .842 8216 
 
 .122 
 
 .052 9839 
 
 .129 754 
 
 .885 1484 
 
 .172 
 
 .074 6987 
 
 .187 678 
 
 .841 9792 
 
 .123 
 
 .053 4182 
 
 .130 884 
 
 .884 2637 
 
 .173 
 
 .075 1329 
 
 .188866 
 
 .841 1376 
 
 .124 
 
 .053 8525 
 
 .132 016 
 
 .883 3798 
 
 .174 
 
 .075 5672 
 
 .190 056 
 
 .840 2969 
 
 0.125 
 
 0.054 2868 
 
 I.I33 148 
 
 0.882 4969 
 
 0.175 
 
 0.076 0015 
 
 1.191 246 
 
 0.839 4570 
 
 .126 
 
 .054 72ii 
 
 .134 282 
 
 .881 6148 
 
 .176 
 
 .076 4358 
 
 .192 438 
 
 .838 6180 
 
 .127 
 
 055 1554 
 
 .135 417 
 
 .880 7337 
 
 .177 
 
 .076 8701 
 
 .193 631 
 
 .837 7798 
 
 .128 
 
 .055 5897 
 
 .136 553 
 
 .879 8534 
 
 .178 
 
 .077 3044 
 
 . 194 825 
 
 .836 9424 
 
 .129 
 
 .056 0240 
 
 .137 690 
 
 .878 9740 
 
 .179 
 
 .077 7387 
 
 .196 O2I 
 
 .836 1059 
 
 0.130 
 
 0.056 4583 
 
 1.138 828 
 
 0.878 0954 
 
 0.180 
 
 0.078 1730 
 
 i. 197 217 
 
 0.835 2702 
 
 .131 
 
 .056 8926 
 
 .139968 
 
 .877 2178 
 
 .181 
 
 .078 6073 
 
 .198 415 
 
 .834 4354 
 
 .132 
 
 .057 3269 
 
 .141 108 
 
 .876 3410 
 
 .182 
 
 .079 0416 
 
 . 199 6l4 
 
 .833 6013 
 
 133 
 
 .057 7612 
 
 .142 250 
 
 .875 4651 
 
 .183 
 
 .079 4759 
 
 .2OO 8l4 
 
 .832 7682 
 
 .1.34 
 
 .058 1955 
 
 .143 393 
 
 .874 5901 
 
 .184 
 
 .079 9102 
 
 .202 016 
 
 .831 9358 
 
 0.135 
 
 0.058 6298 
 
 1.144 537 
 
 0.873 7159 
 
 0.185 
 
 0.080 3445 
 
 1.203 218 
 
 0.831 1043 
 
 .136 
 
 .059 0640 
 
 .145 682 
 
 .872 8426 
 
 .186 
 
 .080 7788 
 
 .204 422 
 
 .830 2736 
 
 .137 
 
 .059 4983 
 
 . 146 828 
 
 .871 9702 
 
 .187 
 
 .081 2131 
 
 .205 627 
 
 .829 4437 
 
 .138 
 
 .059 9326 
 
 . 147 976 
 
 .871 0987 
 
 .188 
 
 .081 6474 
 
 .206 834 
 
 .828 6147 
 
 .139 
 
 .060 3669 
 
 .149 124 
 
 .870 2280 
 
 .189 
 
 .082 0817 
 
 .208 041 
 
 .827 7865 
 
 0.140 
 
 0.060 8012 
 
 i . 150 274 
 
 0.869 3582 
 
 0.190 
 
 0.082 5160 
 
 1.209 250 
 
 0.826 9591 
 
 .141 
 
 .061 2355 
 
 .151 425 
 
 .868 4893 
 
 .191 
 
 .082 9502 
 
 .210 459 
 
 .826 1326 
 
 .142 
 
 .061 6698 
 
 .152 577 
 
 .867 6213 
 
 .192 
 
 .083 3845 
 
 .211 671 
 
 .825 3069 
 
 .143 
 
 .062 1041 
 
 .153 730 
 
 .866 7541 
 
 .193 
 
 .083 8188 
 
 .212 883 
 
 .824 4820 
 
 .144 
 
 .062 5384 
 
 .154884 
 
 .865 8877 
 
 .194 
 
 .084 2531 
 
 .214 O06 
 
 .823 6579 
 
 0.145 
 
 0.062 9727 
 
 1.156 040 
 
 0.865 0223 
 
 0.195 
 
 0.084 6874 
 
 I. 215 311 
 
 0.822 8347 
 
 .146 
 
 .063 4070 
 
 .157 196 
 
 .864 1577 
 
 .196 
 
 .085 1217 
 
 .216 527 
 
 .822 OI22 
 
 .147 
 
 .063 8413 
 
 .158 354 
 
 .863 2940 
 
 .197 
 
 .085 5560 
 
 .217 744 
 
 .821 1905 
 
 .148 
 
 .064 2756 
 
 .159 513 
 
 .862 4311 
 
 .198 
 
 .085 9903 
 
 .218 962 
 
 .820 3699 
 
 .149 
 
 .064 7099 
 
 .160 673 
 
 .861 5691 
 
 .199 
 
 .086 4246 
 
 .220 182 
 
 .819 5499 
 
 0.150 
 
 0.065 1442 
 
 1.161 834 
 
 o.86b 7080 
 
 0.200 
 
 0.086 8589 
 
 I. 22 I 403 
 
 0.818 7308 
 
 lo fle (e u ) 
 
 logio(e u ) 
 
 e u 
 
 e~ u 
 
 log e (e u ) 
 
 logio(e u ) 
 
 e" 
 
 .- 
 
 WITHSONIAN TABLES 
 
 227 
 
The Exponential. 
 
 u 
 
 looio(e u ) 
 
 e u 
 
 e- 
 
 u 
 
 logio(e n ) 
 
 e u 
 
 e~ u 
 
 O.20O 
 
 0.086 8589 
 
 I. 221 403 
 
 0.818 7308 
 
 0.250 
 
 0.108 5736' 
 
 1.284 025 
 
 0.778 8008 
 
 .201 
 
 .087 2932 
 
 .222 625 
 
 .817 9124 
 
 .251 
 
 .109 0079 
 
 .285 310 
 
 .778 0224 
 
 .202 
 
 .087 7275 
 
 .223 848 
 
 .817 0949 
 
 .252 
 
 . roo 4422 
 
 .286 596 
 
 .777 2447 
 
 .203 
 
 .088 1618 
 
 .225 072 
 
 .816 2782 
 
 .253 
 
 . 109 8765 
 
 .287 883 
 
 .776 4679 
 
 .204 
 
 .088 5961 
 
 .226 298 
 
 .815 4624 
 
 .254 
 
 .no 3108 
 
 .289 172 
 
 775 6918 
 
 O.2O5 
 
 0.089 0304 
 
 1.227 525 
 
 0.814 6473 
 
 0.255 
 
 o.i 10 7451 
 
 I. 2OO 462 
 
 0.774 9165 
 
 .206 
 
 .089 4647 
 
 .228 753 
 
 .813 8331 
 
 .256 
 
 .III 1794 
 
 .291 753 
 
 .774 1420 
 
 .207 
 
 .089 8990 
 
 .229 983 
 
 .813 0196 
 
 257 
 
 .III 6137 
 
 .293 045 
 
 773 3682 
 
 .208 
 
 .000 3333 
 
 .231 213 
 
 .812 2070 
 
 .258 
 
 .112 0480 
 
 .294 339 
 
 .772 5952- 
 
 .209 
 
 .090 7675 
 
 .232 445 
 
 .811 3952 
 
 .259 
 
 .112 4823 
 
 .295 634 
 
 .771 8230 
 
 O.2IO 
 
 0.091 2018 
 
 1.233 678 
 
 0.810 5842 
 
 0.260 
 
 O.II2 9166 
 
 1.296 930 
 
 0.771 0516 
 
 .211 
 
 .091 6361 
 
 .234 912 
 
 .809 7741 
 
 .261 
 
 113 3509 
 
 .298 228 
 
 .770 2809 
 
 .212 
 
 .092 0704 
 
 .236 148 
 
 .8089647 
 
 .262 
 
 .113 7852 
 
 .299 527 
 
 .769 5110 
 
 .213 
 
 .092 5047 
 
 237 385 
 
 .808 1561 
 
 .263 
 
 . 114 2194 
 
 .300 827 
 
 .768 7419 
 
 .214 
 
 .092 9390 
 
 .238-623 
 
 .807 3484 
 
 .264 
 
 .114 6537 
 
 .302 128 
 
 .767 9735 
 
 0.215 
 
 0.093 3733 
 
 1.239 862 
 
 0.806 5414 
 
 0.265 
 
 0.115 0880 
 
 1-303 431 
 
 0.767 2059 
 
 .216 
 
 .093 8076 
 
 .241 IO2 
 
 .805 7353 
 
 .266 
 
 .115 5-223 
 
 .304 735 
 
 .766 4391 
 
 .217 
 
 .094 2419 
 
 .242 344 
 
 .804 9300 
 
 .267 
 
 .115 9566 
 
 .306 040 
 
 .765 6731 
 
 .218 
 
 .004 6762 
 
 .243 587 
 
 .804 1254 
 
 .268 
 
 .116 3909 
 
 .307 347 
 
 .764 9078 
 
 .219 
 
 .095 1 105 
 
 .244 831 
 
 .803 3217 
 
 .269 
 
 .116 8252 
 
 .308 655 
 
 .764 1433 
 
 O.22O 
 
 0.095 5448 
 
 1.246 077 
 
 0.802 5188 
 
 0.270 
 
 0.117 2595 
 
 1.309 964 
 
 0.763 3795 
 
 .221 
 
 .095 9791 
 
 .247 323 
 
 .801 7167 
 
 .271 
 
 .117 6938 
 
 311 275 
 
 .762 6165 
 
 .222 
 
 .006 4134 
 
 .248 571 
 
 .800 9154 
 
 .272 
 
 .118 1281 
 
 .312 587 
 
 .761 8543 
 
 .223 
 
 .006 8477 
 
 .249 821 
 
 .800 1148 
 
 .273 
 
 .118 5624 
 
 .313 900 
 
 .761 0528 
 
 .224 
 
 .097 2820 
 
 .251 071 
 
 799 3i5i 
 
 .274 
 
 .118 9967 
 
 315 215 
 
 .760 3321 
 
 0.225 
 
 0.097 7163 
 
 1.252 323 
 
 0.798 5162 
 
 0.275 
 
 0.119 4310 
 
 1.316 531 
 
 0.759 5721 
 
 .226 
 
 .098 1506 
 
 .253 576 
 
 .797 7181 
 
 .276 
 
 .119 8653 
 
 .317 848 
 
 .758 8129 
 
 .227 
 
 .098 5848 
 
 .254 830 
 
 .796 9208 
 
 .277 
 
 .120 2996 
 
 .319 166 
 
 .758 0545 
 
 .228 
 
 .009 0191 
 
 .256 085 
 
 .796 1243 
 
 .278 
 
 .120 7339 
 
 .320 486 
 
 .757 2968 
 
 .229 
 
 .099 4534 
 
 .257 342 
 
 .795 5285 
 
 .279 
 
 .121 1682 
 
 .321 807 
 
 .756 5399 
 
 0.230 
 
 0.099 8877 
 
 1.258 600 
 
 0.794 '5336 
 
 0.280 
 
 O.I2I 6O25 
 
 1.323 130 
 
 0.755 7837 
 
 .231 
 
 .100 3220 
 
 .259 859 
 
 793 7395 
 
 .281 
 
 .122 0367 
 
 .324 454 
 
 755 0283 
 
 .232 
 
 .100 7563 
 
 .26l I2O 
 
 .792 9461 
 
 .282 
 
 .122 47IO 
 
 .325 779 
 
 754 2737 
 
 233 
 
 .101 1006 
 
 .262 381 
 
 .792 1536 
 
 .283 
 
 . 122 0053 
 
 .327 105 
 
 .753 5198 
 
 234 
 
 .101 6249 
 
 .263 644 
 
 .791 3618 
 
 .284 
 
 .123 3396 
 
 .328 433 
 
 .752 7666 
 
 0.235 
 
 O.IO2 O592 
 
 1.264 909 
 
 0.790 57o8 
 
 0.285 
 
 0.123 7739 
 
 1.329 762 
 
 0.752 0143 
 
 .236 
 
 . 102 4935 
 
 .266 174 
 
 .789 7807 
 
 .286 
 
 .124 2O82 
 
 331 092 
 
 .751 2626 
 
 237 
 
 .102 9278 
 
 .267 441 
 
 .788 9913 
 
 .287 
 
 . t24 6425 
 
 332 424 
 
 750 5H7 
 
 .238 
 
 .103 3621 
 
 .268 709 
 
 .788 2027 
 
 .288 
 
 .125 0768 
 
 333 757 
 
 .749 7616 
 
 .239 
 
 .103 7964 
 
 269 979 
 
 .787 4H9 
 
 .289 
 
 .125 5III 
 
 335 092 
 
 .749 0122 
 
 0.240 
 
 0.104 2307 
 
 1.271 249 
 
 0.786 6279 
 
 0.290 
 
 0.125 9454 
 
 1.336427 
 
 0.748 2636 
 
 .241 
 
 .104 6650 
 
 .272 521 
 
 .785 8416 
 
 .291 
 
 .126 3797 
 
 .337 765 
 
 .747 5'i57 
 
 .242 
 
 .105 0093 
 
 273 794 
 
 .785 0562 
 
 .292 
 
 .126 8140 
 
 .339 103 
 
 .746 7685 
 
 243 
 
 105 5336 
 
 .275 069 
 
 .784 2715 
 
 .293 
 
 .127 2483 
 
 340 443 
 
 .746 0221 
 
 .244 
 
 . 105 9679 
 
 .276 344 
 
 .783 4876 
 
 .294 
 
 .127 6826 
 
 .341 784 
 
 .745 2765 
 
 0.245 
 
 0.106 4021 
 
 1.277 621 
 
 0.782 7045 
 
 0.295 
 
 0.128 1169 
 
 1.343 126 
 
 0.744 53i6 
 
 .246 
 
 . 106 8364 
 
 .278 900 
 
 .781 9222 
 
 .296 
 
 .128 5512 
 
 .344 470 
 
 743 7874 
 
 .247 
 
 .107 2707 
 
 .280 179 
 
 .781 1407 
 
 .297 
 
 .1289855 
 
 345 815 
 
 .743 0440 
 
 .248 
 
 .107 7050 
 
 .281 460 
 
 .780 3599 
 
 .298 
 
 . 129 4198 
 
 347 162 
 
 .742 3013 
 
 .249 
 
 .108 1393 
 
 .282 742 
 
 .779 58oo 
 
 .299 
 
 .1298541 
 
 .348 510 
 
 741 5594 
 
 0.250 
 
 0.108 5736 
 
 1.284 025 
 
 0.778 8008 
 
 0.300 
 
 0.130 2883 
 
 1.349 859 
 
 0.740 8182 
 
 looe(e u ) 
 
 Iog 10 (e u ) 
 
 e u 
 
 a- 
 
 lo fl e(e u ) 
 
 log,o(e u ) 
 
 e u 
 
 6-" 
 
 SMITHSONIAN TABLES 
 
 228 
 
The Exponential. 
 
 u 
 
 logio(e u ) 
 
 e u 
 
 e~ u 
 
 u 
 
 looio(e u ) 
 
 e u 
 
 e~ u 
 
 0.300 
 
 0.130 2883 
 
 1.349 859 
 
 0.740 8182 
 
 0.350 
 
 0.152 0031 
 
 1.419 068 
 
 0.704 6881 
 
 .301 
 
 .130 7226 
 
 351 209 
 
 .740 0778 
 
 351 
 
 . 152 4374 
 
 .420 487 
 
 .703 9838 
 
 .302 
 
 .131 1569 
 
 .352 56i 
 
 .739 338i 
 
 352 
 
 .152 8717 
 
 .421 909 
 
 .703 2801 
 
 .303 
 
 .131 5912 
 
 353 914 
 
 .738 5991 
 
 353 
 
 .153 3o6o 
 
 .423 331 
 
 .702 5772 
 
 .304 
 
 .132 0255 
 
 355 269 
 
 .7378609 
 
 354 
 
 .153 7402 
 
 .424 755 
 
 .701 8750 
 
 0.305 
 
 0.132 4598 
 
 1.356 625 
 
 0.737 1234 
 
 0.355 
 
 0.154 1745 
 
 1.426 181 
 
 0.701 1734 
 
 .306 
 
 . 132 8941 
 
 357 982 
 
 .736 3866 
 
 .356 
 
 .154 6088 
 
 .427 608 
 
 .700 4726 
 
 .307 
 
 133 3284 
 
 359 341 
 
 735 6506 
 
 .357 
 
 .155 O43'i 
 
 .429 036 
 
 .699 7725 
 
 .308 
 
 .133 7627 
 
 .360 701 
 
 .734 9153 
 
 .358 
 
 .155 4774 
 
 .430 466 
 
 .699 0731 
 
 .309 
 
 .134 1970 
 
 .362 062 
 
 .734 1808 
 
 .359 
 
 155 9H7 
 
 .431 897 
 
 .6983744 
 
 0.310 
 
 0.134 6313 
 
 1.363 425 
 
 0.733 4470 
 
 0.360 
 
 0.156 3460 
 
 1.433 329 
 
 0.697 6763 
 
 .311 
 
 .135 0656 
 
 .364 789 
 
 732 7139 
 
 .361 
 
 . 156 7803 
 
 434 763 
 
 .696 9790 
 
 .312 
 
 .135 4999 
 
 .366 155 
 
 .731 98i5 
 
 .362 
 
 .157 2146 
 
 .436 199 
 
 .696 2824 
 
 .313 
 
 135 9342 
 
 .367 522 
 
 .731 2499 
 
 .363 
 
 . 157 6489 
 
 .437 636 
 
 .695 5864 
 
 314 
 
 .136 3685 
 
 .368890 
 
 730 5190 
 
 364 
 
 . 158 0832 
 
 .439 074 
 
 .694 8912 
 
 0.315 
 
 0.136 8028 
 
 1.370 259 
 
 0.729 7889 
 
 0.365 
 
 0.158 5175 
 
 1.440 514 
 
 0.694 1967 
 
 .316 
 
 .137 2371 
 
 .371 630 
 
 .729 0595 
 
 .366 
 
 .158 95i8 
 
 441 955 
 
 .693 5028 
 
 .317 
 
 .137 6714 
 
 373 003 
 
 .728 3308 
 
 .367 
 
 . 159 3861 
 
 443 398 
 
 .692 8096 
 
 .318 
 
 .138 1056 
 
 374 376 
 
 .727 6028 
 
 .368 
 
 . 159 8204 
 
 .444 843 
 
 .692 1172 
 
 .319 
 
 .138 5399 
 
 375 751 
 
 .726 8755 
 
 .369 
 
 . 160 2547 
 
 .446 288 
 
 .691 4254 
 
 0.320 
 
 0.138 9742 
 
 1.377 128 
 
 0.726 1490 
 
 0.370 
 
 0.160 6890 
 
 1.447 735 
 
 0.690 7343 
 
 .321 
 
 . 139 4085 
 
 .378 506 
 
 .725 4233 
 
 .371 
 
 .161 1233, 
 
 449 183 
 
 .690 0439 
 
 .322 
 
 . 139 8428 
 
 379 885 
 
 .724 6982 
 
 372 
 
 .161 5575 
 
 450 633 
 
 .689 3542 
 
 .323 
 
 . 140 2771 
 
 .381 265 
 
 .723 9739 
 
 373 
 
 .161 9918 
 
 .452 084 
 
 .688 6652 
 
 .324 
 
 .140 7H4 
 
 .382 647 
 
 .723 ^502 
 
 374 
 
 .162 4261 
 
 453 537 
 
 .687 9769 
 
 0.325 
 
 0.141 1457 
 
 1.384 031 
 
 0.722 5274 
 
 0.375 
 
 0.162 8604 
 
 1.454 991 
 
 0.687 2893 
 
 .326 
 
 .141 5800 
 
 .385 415 
 
 .721 8052 
 
 .376 
 
 .163 2947 
 
 .456 447 
 
 .6866023 
 
 .327 
 
 . 142 0143 
 
 .386 801 
 
 .721 0837 
 
 377 
 
 .163 7290 
 
 .457 904 
 
 .685 9161 
 
 .328 
 
 .142 4486 
 
 .388 189 
 
 .720 3630 
 
 .378 
 
 .164 1633 
 
 .459 363 
 
 .685 2305 
 
 .329 
 
 .142 8829 
 
 .389 578 
 
 .719 6430 
 
 .379 
 
 . 164 5976 
 
 .460 823 
 
 .684 5456 
 
 0.330 
 
 0.143 3172 
 
 1.390 968 
 
 0.718 9237 
 
 0.380 
 
 0.165 0319 
 
 1.462 285 
 
 0.683 8614 
 
 .331 
 
 .143 7515 
 
 .392 360 
 
 .718 2052 
 
 .381 
 
 .165 4662 
 
 .463 748 
 
 .683 1779 
 
 .332 
 
 .144 1858 
 
 .393 753 
 
 .717 4873 
 
 .382 
 
 . 165 9005 
 
 .465 212 
 
 .682 4951 
 
 333 
 
 .144 6201 
 
 395 147 
 
 .716 7702 
 
 .383' 
 
 .166 3348 
 
 .466 678 
 
 .681 8129 
 
 334 
 
 .145 0544 
 
 .396 543 
 
 .716 0538 
 
 .384 
 
 .166 7691 
 
 .468 145 
 
 .681 1314 
 
 0.335 
 
 0.145 4887 
 
 1-397 940 
 
 0.715 338i 
 
 0.385 
 
 o. 167 2034 
 
 1.469 614 
 
 0.680 4506 
 
 .336 
 
 .145 9229 
 
 .399 339 
 
 .714 6231 
 
 .386 
 
 . 167 6377 
 
 .471 085 
 
 .679 7705 
 
 337 
 
 . 146 3572 
 
 .400 739 
 
 .713 9088 
 
 .387 
 
 . 168 0720 
 
 .472 556 
 
 .679 0911 
 
 .338 
 
 .146 7915 
 
 .402 141 
 
 .713 1953 
 
 .388 
 
 .168 5063 
 
 .474 030 
 
 .678 4123 
 
 339 
 
 .147 2258 
 
 403 543 
 
 .712 4824 
 
 .389 
 
 . 168 9406 
 
 475 505 
 
 .677 7343 
 
 0.340 
 
 0.147 6601 
 
 1.404 948 
 
 0.711 7703 
 
 0.390 
 
 0.169 3748 
 
 1.476 981 
 
 0.677 0569 
 
 341 
 
 . 148 0944 
 
 .406 353 
 
 .711 0589 
 
 391 
 
 .169 8091 
 
 .478 459 
 
 .676 3802 
 
 342 
 
 .148 5287 
 
 .407 760 
 
 .710 3482 
 
 392 
 
 .170 2434 
 
 .479 938 
 
 .675 7041 
 
 343 
 
 . 148 9630 
 
 .409 169 
 
 .709 6382 
 
 393 
 
 .170 6777 
 
 .481 418 
 
 .675 0287 
 
 344 
 
 149 3973 
 
 .410 579 
 
 .708 9289 
 
 394 
 
 .171 II2O 
 
 .482 901 
 
 .674 3541 
 
 0.345 
 
 0.149 8316 
 
 1.411 990 
 
 0.708 2204 
 
 0.395 
 
 O.I7I 5463 
 
 1.484 384 
 
 0.673 6800 
 
 .346 
 
 .150 2659 
 
 .413 403 
 
 707 5125 
 
 .396 
 
 .171 9806 
 
 .485 869 
 
 .673 0067 
 
 .347 
 
 .150 7002 
 
 .414 817 
 
 .706 8053 
 
 .397 
 
 .172 4149 
 
 .487 356 
 
 .672 3340 
 
 .348 
 
 I5'i U45 
 
 .416 232 
 
 .706 0989 
 
 .398 
 
 .172 8492 
 
 .488844 
 
 .671 6620 
 
 349 
 
 .151 5688 
 
 .417 649 
 
 70S 3931 
 
 399 
 
 .173 2835 
 
 .490 334 
 
 .670 9907 
 
 0.350 
 
 0.152 0031 
 
 1.419 068 
 
 0.704 6881 
 
 0.400 
 
 0.173' 7178 
 
 1.491 825 
 
 0.670 3200 
 
 lofle(e j ) 
 
 loaio(e u ) 
 
 e u 
 
 e- tt 
 
 log e (e n ) 
 
 looio(e n ) 
 
 e u 
 
 e"* 
 
 SMITHSONIAN TABLES 
 
 229 
 
The Exponential. 
 
 u 
 
 logio(e u ) 
 
 e n 
 
 e- 
 
 u 
 
 logio(e n ) 
 
 e n 
 
 - 
 
 0.400 
 
 0.173 7178 
 
 1.491 825 
 
 0.670 3200 
 
 0.450 
 
 0.195 4325 
 
 1.568 312 
 
 0.637 6282! 
 
 .401 
 
 .174 1521 
 
 493 317 
 
 .669 6501 
 
 451 
 
 . 195 8668 
 
 .569 881 
 
 .636 ogoS 1 
 
 .402 
 
 174 5864 
 
 .494 811 
 
 .668 9807 
 
 452 
 
 .196 3011 
 
 571 452 
 
 .636 3542 
 
 .403 
 
 .175 0-207 
 
 .496 307 
 
 .668 3121 
 
 453 
 
 .196 7354 
 
 .573 024 
 
 .635 7181 
 
 .404 
 
 175 4550 
 
 497 804 
 
 .667 6441 
 
 454 
 
 .197 1697 
 
 .574 598 
 
 .635 082; 
 
 0.405 
 
 o. 175 8893 
 
 1.499 303 
 
 0.666 9768 
 
 0.455 
 
 o. 197 6040 
 
 1.576 173 
 
 0.634 448o 
 
 .406 
 
 . 176 3236 
 
 .500 803 
 
 .666 3102 
 
 .456 
 
 . 198 0383 
 
 .577 750 
 
 .633 8138 
 
 .407 
 
 . 176 7579 
 
 .502 304 
 
 .665 6442 
 
 .457 
 
 . 198 4726 
 
 .579 329 
 
 .633 1803 
 
 .408 
 
 .177 1921 
 
 503 867 
 
 .664 9789 
 
 .458 
 
 .108 0069 
 
 .580 909 
 
 .632 5475 
 
 .409 
 
 .177 6264 
 
 .505 312 
 
 .664 3142 
 
 459 
 
 .199 3412 
 
 .582 491 
 
 .631 9152 
 
 0.410 
 
 0.178 0607 
 
 1.506 818 
 
 0.663 6503 
 
 0.460 
 
 o. 199 7755 
 
 1.584 074 
 
 0.631 2836 
 
 .411 
 
 .178 4950 
 
 .508 325 
 
 .662 9869 
 
 .461 
 
 .200 2098 
 
 .585 659 
 
 .630 6527 
 
 .412 
 
 . 178 9293 
 
 .509 834 
 
 .662 3243 
 
 .462 
 
 .200 6441 
 
 .587 245 
 
 .630 0223 
 
 .413 
 
 .179 3636 
 
 511 345 
 
 .661 6623 
 
 .463 
 
 .201 0783 
 
 588 833 
 
 .629 3926 
 
 .414 
 
 .179 7979 
 
 512 857 
 
 .661 ooio 
 
 .464 
 
 .201 5126 
 
 .590 423 
 
 .628 7636 
 
 0.415 
 
 0.180 2322 
 
 I.5I4 371 
 
 0.660 3403 
 
 0.465 
 
 0.201 9469 
 
 1.592 014 
 
 0.628 1351 
 
 .416 
 
 .180 6665 
 
 .515886 
 
 .659 6803 
 
 .466 
 
 .202 38l2 
 
 593 607 
 
 .627 5073 
 
 .417 
 
 .181 1008 
 
 .517 403 
 
 .659 0209 
 
 .467 
 
 .202 8l55 
 
 .595 201 
 
 .626 8801 
 
 .4*18 
 
 .181 5351 
 
 .518 921 
 
 .658 3622 
 
 .468 
 
 .203 2408 
 
 596 797 
 
 .626 2535 
 
 .419 
 
 .181 9694 
 
 .520 440 
 
 .657 7042 
 
 .469 
 
 .203 6841 
 
 598 395 
 
 .625 6276 
 
 0.420 
 
 0.182 4037 
 
 1.521 962 
 
 0.657 0468 
 
 0.470 
 
 O.2O4 Il84 
 
 1.599 994 
 
 0.625 0023 
 
 .421 
 
 .182 8380 
 
 .523 484 
 
 .656 3901 
 
 .471 
 
 .204 5527 
 
 .601 595 
 
 .624 3776 
 
 .422 
 
 .183 2723 
 
 .525 009 
 
 .655 7340 
 
 .472 
 
 .2O4 9870 
 
 .603 197 
 
 .623 7535 
 
 .423 
 
 .183 7066 
 
 .526 534 
 
 .655 0786 
 
 473' 
 
 .205 4213 
 
 .604 801 
 
 .623 1301 
 
 .424 
 
 .184 1409 
 
 .528 062 
 
 .654 4239 
 
 474 
 
 .205 8556 
 
 .606 407 
 
 .622 5073 
 
 0.425 
 
 o. 184 5752 
 
 1.529 590 
 
 0.653 7698 
 
 0.475 
 
 0.206 2899 
 
 i. 608 014 
 
 0.621 8851 
 
 .426 
 
 .185 0094 
 
 .531 121 
 
 .653 1163 
 
 .476 
 
 .206 7242 
 
 .609 623 
 
 .621 2635 
 
 .427 
 
 .185 4437 
 
 .532 653 
 
 .652 4636 
 
 .477 
 
 .207 1585 
 
 .611 233 
 
 .620 6425 
 
 .428 
 
 .185 8780 
 
 .534 187 
 
 .651 8114 
 
 .478 
 
 .207 5928 
 
 .612 845 
 
 .620 O222 
 
 .429 
 
 .186 3123 
 
 .535 721 
 
 .651 1599 
 
 .479 
 
 .208 0271 
 
 .614 459 
 
 .619 4O25 
 
 0.430 
 
 0.186 7466 
 
 1.537 258 
 
 0.650 5091 
 
 0.480 
 
 0.208 4614 
 
 1.616 074 
 
 0.618 7834 
 
 .431 
 
 .187 1809 
 
 .538 796 
 
 .649 8589 
 
 .481 
 
 .208 8956 
 
 .617 691 
 
 .618 1649 
 
 .432 
 
 . 187 6152 
 
 .540 335 
 
 .649 2094 
 
 .482 
 
 .209 3299 
 
 .619 310 
 
 .617 547i 
 
 433 
 
 .188 0495 
 
 .541 876 
 
 .648 5605 
 
 .483 
 
 .209 7642 
 
 .620 930 
 
 .616 9298 
 
 434 
 
 . 188 4838 
 
 543 419 
 
 .647 9123 
 
 .484 
 
 .210 1985 
 
 .622 552 
 
 .616 3*32 
 
 0.435 
 
 0.188 9181 
 
 1.544 963 
 
 0.647 2647 
 
 0.485 
 
 0.210 6328 
 
 1.624 175 
 
 0.615 6972 
 
 .436 
 
 .189 3524 
 
 .546 509 
 
 .646 6177 
 
 .486 
 
 .211 0671 
 
 .625 800 
 
 .615 0818 
 
 437 
 
 .189 7867 
 
 .548 056 
 
 .645 97H 
 
 .487 
 
 .211 5014 
 
 .627 427 
 
 .614 4670 
 
 .438 
 
 .I9O 22IO 
 
 .549 605 
 
 .645 3258 
 
 .488 
 
 2ii 9357 
 
 .629 055 
 
 .613 8529 
 
 439 
 
 . 190 6553 
 
 551 155 
 
 .644 6808 
 
 .489 
 
 .212 3700 
 
 .630 685 
 
 -613 2393 
 
 0.440 
 
 O.I9I 0896 
 
 i.'552 707 
 
 0.644 0364 
 
 0.490 
 
 0.212 8043 
 
 1.632 316 
 
 0.612 6264 
 
 .441 
 
 .191 5239 
 
 .554 261 
 
 .643 3927 
 
 .491 
 
 .213 2386 
 
 .633 949 
 
 .612 0141 
 
 .442 
 
 .191 9582 
 
 555 816 
 
 .642 7496 
 
 .492 
 
 .213 6729 
 
 .635 584 
 
 .611 4024 
 
 443 
 
 .192 3925 
 
 557 372 
 
 .642 1072 
 
 .493 
 
 .214 1072 
 
 .637 221 
 
 .610 7913 
 
 .-444 
 
 .192 8267 
 
 .558 930 
 
 .641 4654 
 
 494 
 
 .214 5415 
 
 .638 859 
 
 .610 1808 
 
 O.445 
 
 O.I93 26lO 
 
 1.560 490 
 
 0.640 8243 
 
 0.495 
 
 0.214 9758 
 
 I.O4O 408 
 
 0.609 5709 
 
 -TT..J 
 .446 
 
 . 193 0953 
 
 .562 051 
 
 .640 1838 
 
 .496 
 
 .215 4101 
 
 .642 I4O 
 
 .608 0616 
 
 447 
 
 .194 1296 
 
 .563 614 
 
 .639 5439 
 
 497 
 
 215 8444 
 
 <M3 783 
 
 .608 3530 
 
 .448 
 
 .194 5639 
 
 .565 179 
 
 .638 0047 
 
 .498 
 
 .216 2787 
 
 .645 427 
 
 .607 7449 
 
 .449 
 
 .194 9982 
 
 .566 745 
 
 .638 2661 
 
 .499 
 
 .216 7129 
 
 .047 073 
 
 .607 1375 
 
 0.450 
 
 0.195 4325 
 
 1.568 312 
 
 0.637 6282 
 
 0.500 
 
 0.217 1472 
 
 1.648 721 
 
 0.6o6 5307 
 
 looe(e n ) 
 
 looio(e u ) 
 
 e n 
 
 -" 
 
 looc(e u ) looio(e n ) 
 
 e" 
 
 e~ u 
 
 SMITHSONIAN TABLES 
 
 230 
 
The Exponential. 
 
 u 
 
 looio(e u ) 
 
 e u 
 
 e~ tt 
 
 u 
 
 loaio(e u ) 
 
 e u 
 
 e~ 
 
 0.500 
 .501 
 .502 
 .503 
 .504 
 
 0.217 1472 
 .217 5815 
 .218 0158 
 .218 4501 
 .218 8844 
 
 1.648 721 
 .650 371 
 .652 O22 
 .653 675 
 .655 329 
 
 0.6o6 5307 
 .605 9244 
 .605 3188 
 .604 7138 
 .604 1094 
 
 0.550 
 .551 
 
 .552 
 553 
 .554 
 
 0.238 8620 
 .239 2963 
 .239 7306 
 .240 1648 
 .240 5991 
 
 1-733 253 
 734 987 
 .736 723 
 .738 461 
 .740 200 
 
 0.576 9498 
 .576 3731 
 .575 7971 
 .575 2216 
 .574 6466 
 
 0.505 
 
 ' .506 
 
 .507 
 
 .508 
 
 .509 
 
 0.219 3187 
 .219 7530 
 
 .220 1873 
 .220 O2l6 
 
 .221 0559 
 
 1.656 986 
 .658 643 
 .660 3O3 
 .66l 964 
 .663 627 
 
 0.603 5056 
 .602 9024 
 .602 2998 
 .601 6978 
 .601 0964 
 
 0.555 
 .556 
 557 
 .558 
 .559 
 
 0.241 0334 
 .241 4677 
 .241 9020 
 .242 3363 
 .242 7706 
 
 1.741 941 
 .743 684 
 .745 428 
 .747 175 
 .748 923 
 
 0.574 0723 
 .573 4985 
 .572 9253 
 572 3526 
 .571 7806 
 
 0.510 
 
 .511 
 .512 
 .513 
 .514 
 
 O.22I 49O2 
 .221 9245 
 .222 3588 
 .222 7931! 
 .223 2274 
 
 1.665 291 
 .666957 
 .668625 
 .670 295 
 ,671 966 
 
 O.6oo 4956 
 599 8954 
 .599 2958 
 .5986968 
 .5980984 
 
 0.560 
 .561 
 .562 
 .563 
 .564 
 
 0.243 2049 
 .243 6392 
 .244 0735 
 .244 5078 
 .244 9421 
 
 1.750 673 
 .752 424 
 .754 177 
 755 932 
 .757 689 
 
 0.571 2091 
 .570 6381 
 .570 0678 
 .569 498o 
 .568 9288 
 
 0.515 
 .516 
 .517 
 
 .518 
 .519 
 
 0.223 66l7 
 .224 0960 
 .224 5302 
 .224 9645 
 .225 3988 
 
 1.673 639 
 .675 3U 
 .676 989 
 .678 667 
 .680 346 
 
 0.597 5006 
 596 9034 
 .596 3068 
 .595 7io8 
 .595 H54 
 
 0.565 
 .566 
 .567 
 .568 
 .569 
 
 0.245 3764 
 .245 8107 
 .246 2450 
 .246 6793 
 .247 1136 
 
 1.759 448 
 .761 208 
 .762 970 
 .764 734 
 .766 500 
 
 0.568 3601 
 .567 7921 
 .567 2246 
 .566 6576 
 .566 0912 
 
 0.520 
 
 .521 
 .522 
 .523 
 .524 
 
 0.225 8331 
 .226 2674 
 .226 7OI7 
 .227 1360 
 227 5703 
 
 1.682 028 
 
 .683 711 
 .685 395 
 .687 081 
 .688 769 
 
 0.594 5205 
 .593 9263 
 593 3327 
 .592 7397 
 .592 1472 
 
 0.570 
 
 571 
 .572 
 .573 
 .574 
 
 0.247 5479 
 .247 9821 
 .248 4164 
 .248 8507 
 .249 2850 
 
 1.768 267 
 .770 036 
 771 807 
 773 58o 
 775 354 
 
 0.565 5254 
 .564 9602 
 
 .564 3955 
 .563 8314 
 .563 2679 
 
 0.525 
 
 .526 
 
 .527 
 
 .528 
 
 .529 
 
 O.228 OO46 
 .228 4389 
 .228 8732 
 .229 3075 
 .229 7418 
 
 1.690 459 
 .692 150 
 .693 843 
 .695 538 
 .697 234 
 
 0.591 5554 
 .590.9641 
 .590 3734 
 .589 7834 
 .589 1939 
 
 0.575 
 .576 
 .577 
 .578 
 579 
 
 0.249 7193 
 .250 1536 
 .250 5879 
 
 .251 O222 
 .251 4565 
 
 1.777 131 
 .778 909 
 .780 688 
 .782 470 
 784 253 
 
 0.562 7049 
 .562 1424 
 .561 5806 
 .561 0193 
 .560 4585 
 
 0.530 
 .531 
 
 .532 
 
 .533 
 534 
 
 0.230 I76l 
 .230 6lO4 
 
 .231 0447 
 .231 4790 
 .231 9133 
 
 1.698 932 
 .700 632 
 702 334 
 .704 037 
 .705 742 
 
 0.588 6050 
 .588 0167 
 .587 4289 
 .586 8418 
 .586 2553 
 
 0.580 
 .581 
 .582 
 .583 
 .584 
 
 0.251 8908 
 .252 3251 
 
 .252 7594 
 .253 1937 
 .253 6280 
 
 1.786 038 
 .787 825 
 .789 614 
 791 405 
 793 197 
 
 0.559 8984 
 559 3387 
 .558 7797 
 
 .558 2212 
 
 .557 6632 
 
 0.535 
 .536 
 537 
 .538 
 539 
 
 0.232 3475 
 .232 7818 
 .233 2161 
 .233 6504 
 .234 0847 
 
 1.707 448 
 .709 157 
 .710 867 
 .712 578 
 .714 292 
 
 0.585 6693 
 .585 0839 
 .584 4991 
 .583 9149 
 .583 3313 
 
 0.585 
 
 .586 
 .587 
 .588 
 .589 
 
 0.254 0623 
 .254 4966 
 .254 9309 
 255 3652 
 .255 7994 
 
 1.794 991 
 .796 787 
 .798 585 
 .800 384 
 .802 185 
 
 0.557 1059 
 .556 5490 
 .555 9928 
 .555 4370 
 .554 8819 
 
 0.540 
 .541 
 
 542 
 543 
 544 
 
 0.234 5190 
 .234 9533 
 .235 3876 
 .235 8219 
 .236 2562 
 
 1.716 007 
 .717 724 
 .719 442 
 .721 163 
 .722 885 
 
 0.582 7483 
 .582 1658 
 .581 5839 
 .581 0026 
 .580 4219 
 
 0.590 
 .591 
 .592 
 593 
 594 
 
 0.256 2337 
 .256 6680 
 .257 1023 
 .257 5366 
 .257 9709 
 
 1.803 988 
 .805 793 
 .807 600 
 .809 409 
 .811 219 
 
 0.554 3273 
 553 7732 
 553 2197 
 .552 6668 
 .552 1144 
 
 0.545 
 .546 
 .riff 
 
 .648 
 549 
 
 0.236 6905 
 .237 1248 
 .237 5591 
 .237 9934 
 .238 4277 
 
 1.724 608 
 .726 334 
 .728 061 
 .729 790 
 
 731 521 
 
 0.579 8418 
 .579 2622 
 .578 6833 
 .578 1049 
 .577 5270 
 
 0.595 
 .596 
 .597 
 .598 
 599 
 
 0.258 4052 
 .258 8395 
 .259 2738 
 .259 7081 
 .260 1424 
 
 1.813 031 
 .814 845 
 .816 661 
 .818 478 
 .820 298 
 
 0.551 5626 
 551 0113 
 .550 4605 
 .549 9104 
 .549 3607 
 
 0.550 
 
 0.238 8620 
 
 1.733 253 
 
 0.576 9498 
 
 0.600 
 
 0.200 5767 
 
 1.822 119 
 
 0.548 8116 
 
 log e (e a ) 
 
 looio(e u ) 
 
 e u 
 
 e- 
 
 lo fle (e u ) 
 
 lonio(e n ) 
 
 e u 
 
 e~ u 
 
 SMITHSONIAN TABLES 
 
 231 
 
The Exponential. 
 
 u 
 
 looio(e n ) 
 
 e u 
 
 e u 
 
 u 
 
 IOQio(e u ) 
 
 e 
 
 e u 
 
 0.600 
 
 0.260 5767 
 
 1.822 119 
 
 0.548 8116 
 
 0.650 
 
 0.282 2914 
 
 1.915 541 
 
 0.522 0458 
 
 .601 
 
 .261 ouo 
 
 .823 942 
 
 .548 2631 
 
 .651 
 
 .282 7257 
 
 .917 457 
 
 .521 5240 
 
 .602 
 
 .261 4453 
 
 .825 767 
 
 547 7i5i 
 
 .652 
 
 .283 1600 
 
 .919 376 
 
 .521 0027 
 
 .603 
 
 .261 8796 
 
 827 593 
 
 547 i677 
 
 -653 
 
 .283 5943 
 
 .921 296 
 
 .520 4820 
 
 .604 
 
 .262 3139 
 
 .829 422 
 
 .546 6208 
 
 .654 
 
 .284 0286 
 
 .923 218 
 
 .519 9618 
 
 0.605 
 
 0.262 7482 
 
 1.831 252 
 
 0.546 0744 
 
 0.655 
 
 0.284 4629 
 
 1.925 143 
 
 0.519 4421 
 
 .606 
 
 .263 1825 
 
 .833 084 
 
 .545 5286 
 
 .656 
 
 .284 8972 
 
 .927 069 
 
 .518 9229 
 
 .607 
 
 .263 6168 
 
 .834 918 
 
 544 9834 
 
 .657 
 
 .285 3315 
 
 .928 997 
 
 .518 4042 
 
 .608 
 
 .264 0510 
 
 .836 754 
 
 .544 4387 
 
 .658 
 
 .285 7658 
 
 .930 927 
 
 .517 8861 
 
 .609 
 
 .264 4853 
 
 .838 592 
 
 543 8945 
 
 .659 
 
 .286 2OOI 
 
 932 859 
 
 .517 3684 
 
 0.610 
 
 0.264 9196 
 
 1.840 431 
 
 0.543 3509 
 
 0.660 
 
 0.286 6344 
 
 1-934 792 
 
 0.516 8513 
 
 .611 
 
 .265 3539 
 
 .842 273 
 
 .542 8078 
 
 .661 
 
 .287 0687 
 
 .936 728 
 
 .5i6 3347 
 
 .612 
 
 .265 7882 
 
 .844 116 
 
 .542 2653 
 
 .662 
 
 .287 5O29 
 
 .938 666 
 
 515 8187 
 
 .613 
 
 .266 2225 
 
 .84*5 96i 
 
 541 7233 
 
 .663 
 
 .287 9372 
 
 .940 605 
 
 .515 3031 
 
 .614 
 
 .266 6568 
 
 .847 808 
 
 .541 1818 
 
 .664 
 
 .288 3715 
 
 942 547 
 
 .514 788i 
 
 0.615 
 
 0.267 0911 
 
 1.849 657 
 
 0.540 6409 
 
 0.665 
 
 0.288 8058 
 
 1.944 491 
 
 0.514 2735 
 
 .616 
 
 .267 5254 
 
 .851 507 
 
 .540 1005 
 
 .666 
 
 .289 2401 
 
 .946 436 
 
 .513 7595 
 
 .617 
 
 .267 9597 
 
 .853 360 
 
 .539 5607 
 
 .667 
 
 .289 6744 
 
 .948 383 
 
 .513 2460 
 
 .618 
 
 .268 3940 
 
 .855 214 
 
 .539 0214 
 
 .668 
 
 .200 IO87 
 
 950 333 
 
 .512 7330 
 
 .619 
 
 .268 8283 
 
 .857 070 
 
 .538 4827 
 
 .669 
 
 .200 5430 
 
 .952 284 
 
 .512 2205 
 
 0.620 
 
 0.269 2626 
 
 1.858 928 
 
 0.537 9444 
 
 0.670 
 
 0.290 9773 
 
 1.954 237 
 
 0.511 7086 
 
 .621 
 
 .269 6969 
 
 .860788 
 
 .537 4068 
 
 .671 
 
 .291 4116 
 
 .956 193 
 
 .511 1971 
 
 .622 
 
 .270 1312 
 
 .862 650 
 
 .5368696 
 
 .6712 
 
 .291 8459 
 
 .958 ISO 
 
 .510 6862 
 
 .623 
 
 270 5655 
 
 .864 513 
 
 .536 3330 
 
 .673 
 
 .292 2802 
 
 .960 109 
 
 .510 1758 
 
 .624 
 
 .270 9998 
 
 .866379 
 
 535 7970 
 
 .674 
 
 .292 7145 
 
 .962 070 
 
 .509 6658 
 
 0.625 
 
 0.271 434'! 
 
 1.868246 
 
 0.535 2614 
 
 0.675 
 
 0.293 1488 
 
 1.964 033 
 
 0.509 1564 
 
 .626 
 
 .271 8683 
 
 .870 115 
 
 .534 7264 
 
 .676 
 
 .293 5831 
 
 .965 998 
 
 .508 6475 
 
 .627 
 
 .272 3026 
 
 .871 986 
 
 .534 1920 
 
 .677 
 
 .294 0174 
 
 .967 965 
 
 .508 1391 
 
 .628 
 
 .272 7369 
 
 .873 859 
 
 .533 6581 
 
 .678 
 
 .294 4517 
 
 969 934 
 
 .507 6312 
 
 .629 
 
 .273 1712 
 
 .875 734 
 
 533 1247 
 
 .679 
 
 .294 8860 
 
 .971 90S 
 
 .507 1239 
 
 0.630 
 
 0.273 6055 
 
 1.877 611 
 
 0.532 59i8 
 
 0.680 
 
 0.295 3202 
 
 1-973 878 
 
 0.506 6170 
 
 .631 
 
 .274 0398 
 
 .879 489 
 
 .532 0595 
 
 .681 
 
 .295 7545 
 
 975 853 
 
 .506 1106 
 
 .632 
 
 .274 4741 
 
 .881 370 
 
 531 5277 
 
 .682 
 
 .296 1888 
 
 .977 829 
 
 .505 6048 
 
 633 
 
 .274 9084 
 
 .883 252 
 
 .530 9964 
 
 .683 
 
 .296 6231 
 
 .979 808 
 
 .505 0994 
 
 634 
 
 .275 3427 
 
 .885 136 
 
 530 4657 
 
 .684 
 
 .297 0574 
 
 .981 789 
 
 .504 5946 
 
 0.635 
 
 0.275 7770 
 
 1.887 022 
 
 0.529 9355 
 
 0.685 
 
 0.297 4917 
 
 1.983 772 
 
 0.504 0902 
 
 .636 
 
 .276 2113 
 
 .888 910 
 
 .529 4058 
 
 .686 
 
 .297 9260 
 
 .985 757 
 
 .503 5864 
 
 .637 
 
 .276 6456 
 
 .890 800 
 
 .528 8767 
 
 .687 
 
 .208 3603 
 
 .987 743 
 
 .503 0831 
 
 .638 
 
 .277 0799 
 
 .892 692 
 
 .528 3481 
 
 .688 
 
 .298 7046 
 
 .989 732 
 
 .502 5802 
 
 .639 
 
 .277 5142 
 
 .894 585 
 
 .527 8200 
 
 .689 
 
 .299 2289 
 
 .991 723 
 
 .502 0779 
 
 0.640 
 
 0.277 9485 
 
 1.896 481 
 
 0.527 2924 
 
 0.690 
 
 0.299 6632 
 
 1.993 7i6 
 
 0.501 5761 
 
 .641 
 
 .278 3828 
 
 .898 378 
 
 .526 7654 
 
 .691 
 
 .300 0975 
 
 995 7io 
 
 .501 0747 
 
 .642 
 
 .278 8171 
 
 .900 278 
 
 .526 2389 
 
 .692 
 
 .300 5318 
 
 997 707 
 
 500 5739 
 
 .643 
 
 .279 2514 
 
 .902 179 
 
 .525 7129 
 
 .693 
 
 .300 9661 
 
 .099 706 
 
 .500 0736 
 
 .644 
 
 .279 6856 
 
 .904 082 
 
 .525 i875 
 
 .694 
 
 .301 4004 
 
 2.001 706 
 
 499 5738 
 
 0.645 
 
 0.280 1199 
 
 1.905 987 
 
 0.524 6625 
 
 0.695 
 
 0.301 8347 
 
 2.003 709 
 
 0.499 0744 
 
 .646 
 
 .280 5542 
 
 .907 894 
 
 .524 1381 
 
 .696 
 
 .302 2690 
 
 .005 714 
 
 .498 5756 
 
 .647 
 
 .2800885 
 
 .909 803 
 
 .523 6143 
 
 .697 
 
 .302 7033 
 
 .007 720 
 
 .498,0773 
 
 .648 
 
 .281 4228 
 
 .911 714 
 
 .523 0909 
 
 .698 
 
 .303 1375 
 
 .009 729 
 
 497 5795 
 
 .649 
 
 .281 8571 
 
 .913 626 
 
 .522 5681 
 
 .699 
 
 .303 57i8 
 
 .011 740 
 
 .497 0821 
 
 0.650 
 
 0.282 2914 
 
 I.9IS 541 
 
 0.522 0458 
 
 0.700 
 
 0.304 0061 
 
 2.013 753 
 
 0.496 5853 
 
 looe(e) 
 
 looitXe ) 
 
 e 
 
 t 
 
 looe(e u ) 
 
 log^e") 
 
 e u 
 
 e~ 
 
 SMITHSONIAN TABLCS 
 
 232 
 
The Exponential. 
 
 u 
 
 looio(e u ) 
 
 e n 
 
 e- u 
 
 u 
 
 looio(e n ) 
 
 e u 
 
 e u 
 
 0.700 
 
 0.304 0061 
 
 2.013 753 
 
 0.496 5853 
 
 0.750 
 
 0.325 7209 
 
 2.117 ooo 
 
 0.472 366^ 
 
 .701 
 
 .304 4404 
 
 .015 767 
 
 .496 0890 
 
 751 
 
 .326 1552 
 
 .119 118 
 
 .471 894^ 
 
 .702 
 
 .304 8747 
 
 .017 784 
 
 .495 5931 
 
 .752 
 
 .326 5895 
 
 .121 238 
 
 .471 422* 
 
 .703 
 
 .305 3090 
 
 .019 803 
 
 495 0978 
 
 753 
 
 .327 0237 
 
 .123 36l 
 
 .470 95 rt 
 
 .70-4 
 
 .305 7433 
 
 .021 824 
 
 .494 6029 
 
 754 
 
 .327 458o 
 
 .125 485 
 
 .470 48oc 
 
 0.705 
 
 0.306 1776 
 
 2.023 847 
 
 0.494 1086 
 
 0.755 
 
 0.327 8923 
 
 2.127 612 
 
 0.470 oiot 
 
 .70J 
 
 .306 6119 
 
 ' .025 872 
 
 .493 6147 
 
 .756 
 
 .328 3266 
 
 .129 740 
 
 .469 540* 
 
 .707 
 
 .307 0462 
 
 .027 898 
 
 .493 1213 
 
 757 
 
 .328 7609 
 
 .131 871 
 
 .469 071 J 
 
 .708 
 
 .307 4805 
 
 .029 927 
 
 .492 6285 
 
 .758 
 
 .329 1952 
 
 .134 004 
 
 .468 602; 
 
 .709 
 
 .307 9U8 
 
 .031 958 
 
 .492 1361 
 
 759 
 
 .329 6295 
 
 .136 139 
 
 .468 134: 
 
 0.710 
 
 0.308 3491 
 
 2.033 991 
 
 0.491 6442 
 
 0.760 
 
 0.330 0638 
 
 2. 138 276 
 
 0.467 666/ 
 
 .711 
 
 .308 7834 
 
 .036 026 
 
 .491 1528 
 
 .761 
 
 330 498i 
 
 .140 416 
 
 .467 I99C 
 
 .712 
 
 .309 2177 
 
 .038 063 
 
 .490 6619 
 
 .762 
 
 330 9324 
 
 .142 557 
 
 .466 732( 
 
 .713 
 
 .309 6520 
 
 .O4O IO2 
 
 .450 1715 
 
 .763 
 
 331 3667 
 
 .144 70i 
 
 .466 265. 
 
 .714 
 
 .310 0863 
 
 .042 144 
 
 .489 6815 
 
 .764 
 
 .331 8010 
 
 . 146 846 
 
 .465 799. 
 
 0.715 
 
 0.310 5206 
 
 2.044 187 
 
 0.489 1921 
 
 0.765 
 
 0.332 2353 
 
 2.148 994 
 
 0.465 333< 
 
 .716 
 
 .310 9548 
 
 .046 23'2 
 
 .488 70312 
 
 .766 
 
 .3326696 
 
 .151 144 
 
 .464 858 
 
 .717 
 
 311 3891 
 
 .048 279 
 
 .488 2147 
 
 .767 
 
 333 1039 
 
 .153 297 
 
 .464 404^ 
 
 .718 
 
 .311 8234 
 
 .050 328 
 
 .487 7267 
 
 .768 
 
 333 5382 
 
 .155 451 
 
 .463 94CK 
 
 .719 
 
 .312 2577 
 
 .052 380 
 
 487 2393 
 
 .769 
 
 333 9725 
 
 .157 608 
 
 .463 476: 
 
 0.720 
 
 0.3-12 6920 
 
 2.054 433 
 
 0.486 7523 
 
 0.770 
 
 0.334 4068 
 
 2. 159 766 
 
 0.463 0131 
 
 .721 
 
 .313 1263 
 
 .056 489 
 
 .486 2657 
 
 771 
 
 .334 8410 
 
 .161 927 
 
 .462 550: 
 
 .722 
 
 .313 5606 
 
 .058 546 
 
 .485 7797 
 
 .772 
 
 .335 2753 
 
 .164 090 
 
 .462 o88( 
 
 .723 
 
 .313 9949 
 
 .060 606 
 
 .485 2942 
 
 .773 
 
 .335 7096 
 
 . 166 255 
 
 .461 626 
 
 .724 
 
 .314 4292 
 
 .062 667 
 
 .484 8091 
 
 774 
 
 .336 1439 
 
 .168 423 
 
 .461 164; 
 
 0.^25 
 
 0.314 8635 
 
 2.064 73*1 
 
 0.484 3246 
 
 0.775 
 
 0.336 5782 
 
 2.170 592 
 
 0.460 703$ 
 
 .726 
 
 .315 2978 
 
 .066 797 
 
 .483 8405 
 
 .776 
 
 337 0125 
 
 .172 764 
 
 .460 243. 
 
 .727 
 
 .315 7321 
 
 .068 865 
 
 .483 3569 
 
 777 
 
 .337 4468 
 
 .174 938 
 
 .459 783* 
 
 .728 
 
 .316 1664 
 
 .070 935 
 
 .482 8738 
 
 .778 
 
 .337-88ii 
 
 .177 H4 
 
 459 323; 
 
 .729 
 
 .316 6007 
 
 .073 007 
 
 .482 3911 
 
 .779 
 
 .338 3154 
 
 .179 292 
 
 .458 864< 
 
 0.730 
 
 0.317 0350 
 
 2.075 081 
 
 0.481 9090 
 
 0.780 
 
 0.338 7497 
 
 2.181 472 
 
 0.458 4o6( 
 
 731 
 
 .317 4093 
 
 077 157 
 
 .481 4273 
 
 .781 
 
 339 1840 
 
 .183 655 
 
 457 947* 
 
 732 
 
 .317 9036 
 
 .079 235 
 
 .480 9461 
 
 .782 
 
 .339 6183 
 
 .185 840 
 
 .457 490 
 
 733 
 
 .318 3379 
 
 .081 315 
 
 .480 4654 
 
 .783 
 
 .340 0526 
 
 .188 027 
 
 457 032? 
 
 .734 
 
 .318 7721 
 
 .083 398 
 
 .479 9852 
 
 .784 
 
 .340 4869 
 
 .190 216 
 
 .456 5T& 
 
 0.735 
 
 0.319 2064 
 
 2.085 482 
 
 0.479 5055 
 
 0.785 
 
 0.340 9212 
 
 2.192 407 
 
 0.456 119 
 
 .736 
 
 .319 6407 
 
 .087 569 
 
 .479 0262 
 
 .786 
 
 341 3555 
 
 .194 600 
 
 .455 66 3 < 
 
 737 
 
 .320 0750 
 
 .089 657 
 
 .478 5474 
 
 .787 
 
 .341 7898 
 
 .196 796 
 
 .455 208 
 
 .738 
 739 
 
 .320 5093 
 .320 9436 
 
 .091 748 
 .093 841 
 
 .478 0691 
 477 5913 
 
 .788 
 .789 
 
 .342 2241 
 342 6583 
 
 .198 994 
 .201 194 
 
 .454 753- 
 .454 298* 
 
 0.740 
 
 0.321 3779 
 
 2.095 936 
 
 0.477 H39 
 
 0.790 
 
 0.343 0926 
 
 2.203 396 
 
 0.453 844* 
 
 .741 
 
 .321 8122 
 
 .098 032 
 
 .476 6370 
 
 .791 
 
 .343 5269 
 
 .205 601 
 
 453 391 
 
 .742 
 
 .322 2465 
 
 .100 132 
 
 .476 1606 
 
 792 
 
 .343 9612 
 
 .207 808 
 
 .452 938- 
 
 743 
 
 .322 6808 
 
 . 102 233 
 
 .475 6847 
 
 793 
 
 344 3955 
 
 .210 017 
 
 .452 485 
 
 -744 
 
 .323 1151 
 
 .104 336 
 
 .475 2093 
 
 .794 
 
 .344 8298 
 
 .212 228 
 
 .452 033< 
 
 0.745 
 
 0.323 5494 
 
 2.106 441 
 
 0.474 7343 
 
 0.795 
 
 0.345 2641 
 
 2.214 441 
 
 0.451 58i 
 
 .746 
 
 .323 9837 
 
 .108 549 
 
 .474 2598 
 
 .796 
 
 345 6984 
 
 .216 657 
 
 .4-51 I29< 
 
 -> -747 
 
 .324 4180 
 
 .no 659 
 
 473 7858 
 
 797 
 
 .346 1327 
 
 .218 874 
 
 .450 679) 
 
 " .748 
 
 .324 8523 
 
 .112 770 
 
 .473 3122 
 
 .798 
 
 .346 5670 
 
 .221 094 
 
 .450 228 
 
 749 
 
 .325 2866 
 
 .114 884 
 
 .472 8392 
 
 799 
 
 347 0013 
 
 .223 3l6 
 
 .449 778 
 
 0.750 
 
 0.325 7209 
 
 2.117 ooo 
 
 0.472 3666 
 
 0.800 
 
 0.347 4356 
 
 2.225 541 
 
 0.449 329< 
 
 lo fle (e u ) 
 
 lo fl io(e u ) 
 
 e n 
 
 e~ u 
 
 looe(e u ) 
 
 logio(e u ) 
 
 e u 
 
 e- n 
 
 SMITHSONIAN TABLES 
 
 233 
 
The Exponential. 
 
 J 
 
 lofl W (e u ) 
 
 e u 
 
 e~ u 
 
 u 
 
 looio(e u ) 
 
 e u 
 
 e u 
 
 0.800 
 
 0.347 4356 
 
 2.225 541 
 
 0.449 3290 
 
 0.850 
 
 0.369 1503 
 
 2-339 647 
 
 0.427 4149 
 
 .801 
 
 347 8609 
 
 .227 768 
 
 .448 8799 
 
 .851 
 
 .369 5846 
 
 -341 988 
 
 .4(26 9877 
 
 .802 
 
 .348 3042 
 
 .229 096 
 
 .448 4312 
 
 .852 
 
 .370 0189 
 
 344 331 
 
 .426 5610 
 
 .803 
 
 .348 7385 
 
 .232 228 
 
 447 9830 
 
 .853 
 
 370 4532 
 
 .346 676 
 
 .426 1346 
 
 .804 
 
 .349 1728 
 
 .234 461 
 
 .447 5352 
 
 .854 
 
 370 8875 
 
 .349 024 
 
 .425 7087 
 
 0.805 
 
 0.349 6071 
 
 2.236 696 
 
 0.447 0879 
 
 0.855 
 
 0.371 3218 
 
 2.351 374 
 
 0.425 2832 
 
 .806 
 
 .350 0414 
 
 .238 934 
 
 .446 6411 
 
 .856 
 
 371 756i 
 
 353 727 
 
 .424 8581 
 
 .807 
 
 350 4756 
 
 .241 174 
 
 .446 1946 
 
 .857 
 
 .372 1904 
 
 .356 082 
 
 .424 4335 
 
 .808 
 
 350 9009 
 
 .243 417 
 
 .445 7487 
 
 .858 
 
 .372 6247 
 
 .358 439 
 
 .424 0093 
 
 .809 
 
 .351 3442 
 
 .245 66l 
 
 .445 3031 
 
 .859 
 
 373 0590 
 
 .360 799 
 
 .423 5855 
 
 0.810 
 
 0.3SI 7785 
 
 2.247 90S 
 
 0.444 8581 
 
 0.860 
 
 0-373 4933 
 
 2.363 161 
 
 0.423 1621 
 
 .811 
 
 .352 2128 
 
 .250 157 
 
 .444 4134 
 
 .861 
 
 373 9275 
 
 .365 525 
 
 .422 7391 
 
 .812 
 
 .352 6471 
 
 .252 408 
 
 443 0692 
 
 .862 
 
 .374 3618 
 
 .367 892 
 
 .422 3166 
 
 .813 
 
 .353 0814 
 
 .254 662 
 
 .443 5255 
 
 .863 
 
 374 7961 
 
 .370 261 
 
 .421 8945 
 
 .814 
 
 353 5157 
 
 .256 918 
 
 .443 0822 
 
 .864 
 
 375 2304 
 
 372 632 
 
 .421 4728 
 
 0.815 
 
 0.353 9500 
 
 2.259 176 
 
 0.4412 6393 
 
 0.865 
 
 0.375 6647 
 
 2.375 006 
 
 0.421 0516 
 
 .816 
 
 354 3843 
 
 .261 436 
 
 .442 1969 
 
 .866 
 
 .376 0990 
 
 377 382 
 
 .420 6307 
 
 .817 
 
 .354 8186 
 
 .263 699 
 
 .441 7549 
 
 .867 
 
 .376 5333 
 
 .379 76i 
 
 .420 2103 
 
 .818 
 
 355 2529 
 
 .265 963 
 
 .441 3134 
 
 .868 
 
 .376 9676 
 
 .382 142 
 
 .419 7903 
 
 .819 
 
 .355 6872 
 
 .268 230 
 
 .440 8723 
 
 .869 
 
 .377 4019 
 
 .384 525 
 
 .419 3707 
 
 0.820 
 
 0.356 1215 
 
 2.270 500 
 
 0.440 4317 
 
 0.870 
 
 0.377 8362 
 
 2.386 911 
 
 0.418 9515 
 
 .821 
 
 .356 5558 
 
 .272 771 
 
 .439 9914 
 
 .871 
 
 .378 2705 
 
 .389 299 
 
 .418 5328 
 
 .822 
 
 356 9901 
 
 .275 045 
 
 .439 5517 
 
 .872 
 
 .378 7048 
 
 .391 689 
 
 .418 1145 
 
 .823 
 
 .357 4244 
 
 .277 322 
 
 .439 1123 
 
 .873 
 
 .379 1391 
 
 .394 082 
 
 .417 6966 
 
 .824 
 
 .357 8587 
 
 .279 600 
 
 .438 6734 
 
 .874 
 
 .379 5734 
 
 .396 478 
 
 .417 2791 
 
 0.825 
 
 0.358 2929 
 
 2.281 881 
 
 0.438 2350 
 
 0.875 
 
 0.380 0077 
 
 2.398 875 
 
 0.416 8620 
 
 .826 
 
 .358 7272 
 
 .284 164 
 
 437 7970 
 
 .876 
 
 .380 4420 
 
 .401 275 
 
 .416 4454 
 
 .827 
 
 359 1615 
 
 .286 449 
 
 437 3594 
 
 .877 
 
 .380 8763 
 
 .403 678 
 
 .416 0291 
 
 .828 
 
 359 5958 
 
 .288 737 
 
 .436 9223 
 
 .878 
 
 .381 3106 
 
 .406 083 
 
 .415 6133 
 
 .829 
 
 .360 0301 
 
 .291 027 
 
 .436 4856 
 
 .879 
 
 .381 7448 
 
 .408 490 
 
 .415 1979 
 
 0.830 
 
 0.360 4644 
 
 2.293 319 
 
 0.436 0493 
 
 0.880 
 
 0.382 1791 
 
 2.410 900 
 
 0.414 7829 
 
 .831 
 
 .3608987 
 
 .295 613 
 
 435 6135 
 
 .881 
 
 .382 6134 
 
 .413 312 
 
 .414 3683 
 
 .832 
 
 .361 3330 
 
 .297 910 
 
 435 1781 
 
 .882 
 
 .383 0477 
 
 .415 726 
 
 .413 9542 
 
 .833 
 
 .834 
 
 .361 7673 
 .362 2016 
 
 .300 209 
 .302 510 
 
 434 7431 
 .434 3086 
 
 .883 
 .884 
 
 .383 4820 
 .383 9163 
 
 .418 143 
 .420 563 
 
 .413 5404 
 .413 1271 
 
 0.835 
 
 0.362 6359 
 
 2.304 814 
 
 0.433 8745 
 
 0.885 
 
 0.384 3506 
 
 2.422 984 
 
 0.412 7142 
 
 .836 
 
 .363 0702 
 
 .307 I2O 
 
 .433 4408 
 
 .886 
 
 .384 T&49 
 
 .425 409 
 
 .412 3017 
 
 .837 
 
 .363 5045 
 
 .309 428 
 
 433 0076 
 
 .887 
 
 .385 2192 
 
 427 835 
 
 .411 8896 
 
 .838 
 
 .363 9388 
 
 .311 739 
 
 .432 5748 
 
 .888 
 
 .385 653-S 
 
 .430 264 
 
 .411 4779 
 
 .839 
 
 .364 373'i 
 
 .314 052 
 
 .432 1424 
 
 .889 
 
 .3860878 
 
 .432 696 
 
 .411 0666 
 
 0.840 
 
 0.364 8074 
 
 2.316 367 
 
 0.431 7105 
 
 0.890 
 
 0.386 5'22I 
 
 2.435 130 
 
 0.410 6558 
 
 .841 
 
 .365 24-17 
 
 .318 685 
 
 .431 2790 
 
 .891 
 
 .386 9564 
 
 437 566 
 
 .410 2453 
 
 .842 
 
 .365 6760 
 
 .321 004 
 
 .430 8480 
 
 .892 
 
 .387 3907 
 
 .440 005 
 
 .409 8353 
 
 .843 
 
 .844 
 
 .366 IIO2 
 
 .366 5445 
 
 .323 327 
 .325 651 
 
 .430 4173 
 .429 9871 
 
 .893 
 .894 
 
 .387 8250 
 
 .388 2593 
 
 .442 446 
 .444 890 
 
 .409 4256 
 .409 0164 
 
 0.845 
 
 0.366 9788 
 
 2.327 978 
 
 0.429 5574 
 
 0.895 
 
 0.388 6936 
 
 2.447 336 
 
 0.408 6076 
 
 .846 
 .847 
 
 .367 4UI 
 .367 8474 
 
 330 307 
 .332 638 
 
 .429 1280 
 .428 6991 
 
 .896 
 .897 
 
 .389 1279 
 .389 5622 
 
 449 784 
 
 45-' 235 
 
 .408 1992 
 .407 7?'i2 
 
 .848 
 
 .368 2817 
 
 334 972 
 
 .428 2706 
 
 .858 
 
 .389 9964 
 
 -454 689 
 
 .407 3836 
 
 .849 
 
 .368 7160 
 
 337 308 
 
 .427 8426 
 
 .899 
 
 390 4307 
 
 457 145 
 
 .406 9764 
 
 0.850 
 
 0.369 1503 
 
 2.339 647 
 
 0.427 4149 
 
 0.900 
 
 0.390 8650 
 
 2.459 603 
 
 0.406 5697 
 
 loo-V; 
 
 loouXe") 
 
 e" 
 
 e~~ u 
 
 lo flc (e u ) 
 
 loQio(e u ) 
 
 e u 
 
 e~ u 
 
 SMITHSONIAN TABLES 
 
The Exponential. 
 
 u 
 
 looio(e u ) 
 
 e u 
 
 e- n 
 
 u 
 
 logio(e n ) 
 
 e n 
 
 e~ u 
 
 0.900 
 
 0.390 8650 
 
 2.459 603 
 
 0.406 5697 
 
 0.950 
 
 0.412 5798 
 
 2.585 710 
 
 0.386 7410 
 
 .901 
 
 .391 2993 
 
 .462 064 
 
 .406 1633 
 
 .951 
 
 .413 0141 
 
 .588 297 
 
 .386 3545 
 
 .902 
 
 391 7336 
 
 .464 527 
 
 .405 7573 
 
 .952 
 
 .413 4483 
 
 .590 886 
 
 .385 9683 
 
 903 
 
 .392 1679 
 
 .466 993 
 
 .405 35i8 
 
 953 
 
 .413 8826 
 
 593 478 
 
 .385 5825 
 
 .904 
 
 .392 6022 
 
 .469 461 
 
 .404 9466 
 
 954 
 
 .414 3l69 
 
 595 073 
 
 .385 1971 
 
 0.905 
 
 0.393 0365 
 
 2.471 932 
 
 0.404 5419 
 
 0.955 
 
 0.414 7512 
 
 2.508 671 
 
 0.384 8121 
 
 .906 
 
 393 47O8 
 
 .474 405 
 
 .404 1375 
 
 .956 
 
 .415 1855 
 
 .601 271 
 
 .384 427= 
 
 .CO7 
 
 393 905 1 
 
 .476 88 i 
 
 .403 7336 
 
 957 
 
 .415 6198 
 
 .603 873 
 
 .384 0431 
 
 y/ 
 
 .908 
 
 .909 
 
 394 3394 
 394 7737 
 
 479 359 
 .481 839 
 
 .403 3301 
 .402 9269 
 
 .958 
 959 
 
 .416 0541 
 .416 4884 
 
 .606 478 
 .609086 
 
 .383 6504 
 .383 2760 
 
 0.910 
 
 0.395 2080 
 
 2.484 323 
 
 0.402 5242 
 
 0.960 
 
 0.416 9227 
 
 2.611 696 
 
 0.382 8925 
 
 .911 
 
 .395 6423 
 
 .486 808 
 
 .402 1219 
 
 .961 
 
 .417 3570 
 
 .614 309 
 
 .382 5102 
 
 .912 
 
 .396 0766 
 
 .489 296 
 
 .401 7200 
 
 .962 
 
 .417 7913 
 
 .616 925 
 
 .382 1275 
 
 .913 
 
 .396 5109 
 
 .491 787 
 
 .401 3185 
 
 .963 
 
 .418 2256 
 
 .619 543 
 
 .381 745 
 
 .914 
 
 .396 9452 
 
 .494 280 
 
 .400 9173 
 
 .964 
 
 .418 6599 
 
 .622 164 
 
 .381 364-1 
 
 0.915 
 
 0.397 3795 
 
 2.496 775 
 
 0.400 5166 
 
 0.965 
 
 0.419 0942 
 
 2.624 788 
 
 0.380 983:2 
 
 .916 
 
 397 8137 
 
 499 273 
 
 .400 1163 
 
 .956 
 
 .419 5285 
 
 .627 414 
 
 .380 6024 
 
 .917 
 
 .398 2480 
 
 501 774 
 
 .399 7164 
 
 .967 
 
 .419 9628 
 
 .630 042 
 
 .380 222C 
 
 .918 
 
 .398 6823 
 
 .504 277 
 
 .399 3169 
 
 .968 
 
 .420 3971 
 
 .632 674 
 
 .379 &42C 
 
 .919 
 
 .399 "66 
 
 .506 782 
 
 .398 9178 
 
 .969 
 
 .420 8314 
 
 .635 308 
 
 .379 462: 
 
 0.920 
 
 0.399 5509 
 
 2.509 290 
 
 0.398 5190 
 
 0.970 
 
 0.421 2656 
 
 2.637 944 
 
 0.379 o83C 
 
 .921 
 
 399 9852 
 
 .511 801 
 
 .398 1207 
 
 971 
 
 .421 6999 
 
 .640 584 
 
 .378 7041 
 
 .922 
 
 .400 4195 
 
 .514 314 
 
 397 7228 
 
 .972 
 
 .422 1342 
 
 .643 226 
 
 .378 ysst 
 
 .923 
 
 .400 8538 
 
 .516 830 
 
 397 3253 
 
 973 
 
 .422 5685 
 
 .645 870 
 
 .377 947^ 
 
 .924 
 
 .401 2881 
 
 .519 348 
 
 .396 9281 
 
 974 
 
 .423 0028 
 
 648 517 
 
 377 569; 
 
 0.925 
 
 0.401 7224 
 
 2.521 868 
 
 0.396 53H 
 
 0.975 
 
 0.423 4371 
 
 2.651 167 
 
 0.377 192^ 
 
 .926 
 
 .402 1567 
 
 .524 39i 
 
 .396 1351 
 
 .976 
 
 .423 8714 
 
 .653 820 
 
 .376 815: 
 
 .927 
 
 .402 5910 
 
 .526 917 
 
 395 7391 
 
 .977 
 
 .424 3057 
 
 .656 475 
 
 .376 438; 
 
 .928 
 
 .403 0253 
 
 .529 445 
 
 .395 3436 
 
 .978 
 
 .424 7400 
 
 .659 133 
 
 .376 062. 
 
 .929 
 
 .403 4596 
 
 531 976 
 
 394 9485 
 
 979 
 
 .425 1743 
 
 .661 793 
 
 .375686* 
 
 0.930 
 
 0.403 8939 
 
 2.534 509 
 
 0.394 5537 
 
 0.980 
 
 0.425 6086 
 
 2.664 456 
 
 0.375 3" 
 
 931 
 
 .404 31282 
 
 537 045 
 
 394 1594 
 
 .981 
 
 .426 0429 
 
 .667 122 
 
 374 936c 
 
 .932 
 
 .404 7625 
 
 539 583 
 
 .393 7654 
 
 .982 
 
 .426 4772 
 
 .669 790 
 
 374 56i; 
 
 933 
 
 .405 1068 
 
 .542 124 
 
 .393 37i8 
 
 .983 
 
 .426 9115 
 
 .672 462 
 
 .374 i86< 
 
 934 
 
 .405 6310 
 
 .544668 
 
 .392 9786 
 
 .984 
 
 .427 3458 
 
 .675 135 
 
 .373 8i2< 
 
 0.935 
 
 0.406 0653 
 
 2.547 213 
 
 0.392 5859 
 
 0.985 
 
 0.427 7801 
 
 2.677 812 
 
 0.373 439- 
 
 .936 
 
 .406 4996 
 
 .549 762 
 
 392 1935 
 
 .986 
 
 .428 2144 
 
 .680 491 
 
 373 066 
 
 937 
 
 .406 9339 
 
 552 313 
 
 .391 8015 
 
 .987 
 
 .428 6487 
 
 .683 173 
 
 372 693 
 
 .938 
 
 .407 3682 
 
 .554 867 
 
 .391 4099 
 
 .988 
 
 .429 0829 
 
 .685 857 
 
 372 320< 
 
 939 
 
 .407 8025 
 
 .557 4*3 
 
 .391 0187 
 
 .989 
 
 .429 5172 
 
 .688545 
 
 371 948 
 
 0.94P 
 
 0.408 2368 
 
 2.559 98i 
 
 0.390 6278 
 
 0.990 
 
 0.429 9515 
 
 2.691 234 
 
 0.371 576, 
 
 .941 
 
 .408 6711 
 
 .562 543 
 
 .390 2374 
 
 .991 
 
 .430 3858 
 
 .693 927 
 
 371 205 
 
 .942 
 
 .409 1054 
 
 565 107 
 
 .3898474 
 
 .992 
 
 .430 8201 
 
 .696 622 
 
 370 834 
 
 943 
 
 .409 5397 
 
 .567 673 
 
 .389 4577 
 
 993 
 
 .431 2544 
 
 .699 320 
 
 370 463* 
 
 944 
 
 .409 9740 
 
 .570 242 
 
 .3890684 
 
 .994 
 
 431 6887 
 
 .702 021 
 
 370 093' 
 
 0.945 
 
 0.410 4083 
 
 2.572 813 
 
 0.388 6796 
 
 0.995 
 
 0.432 1230 
 
 2.704 724 
 
 0.369 723- 
 
 .946 
 
 .410 8426 
 
 575 387 
 
 .388 2911 
 
 .996 
 
 432 5573 
 
 .707 430 
 
 .369 353 
 
 947 
 
 .411 2769 
 
 577 964 
 
 .387 9030 
 
 997 
 
 .432 9916 
 
 .710 139 
 
 .368984 
 
 .948 
 
 .411 7H2 
 
 .580 543 
 
 .387 5153 
 
 .998 
 
 433 4259 
 
 .712 851 
 
 .368 615 
 
 949 
 
 .412 1455 
 
 .583 125 
 
 .387 1280 
 
 .999 
 
 .433 8602 
 
 .715 565 
 
 .368 247 
 
 0.950 
 
 0.412 5798 
 
 2.585 710 
 
 0.386 7410 
 
 1. 000 
 
 0.434 2945 
 
 2.718 282 
 
 0.367 879- 
 
 lo fle (e u ) 
 
 logio(e u ) 
 
 e u 
 
 e- n 
 
 log e (e u ) 
 
 Iog 10 (e u ) 
 
 e u 
 
 e- u 
 
 SMITHSONIAN TABLES 
 
 235 
 
The Exponential. 
 
 u 
 
 logio(e u ) 
 
 e u 
 
 .- 
 
 u 
 
 logio(e n ) 
 
 e n 
 
 e- 
 
 1. 000 
 
 0.434 2945 
 
 2.718 282 
 
 0-367 8794 
 
 1.050 
 
 0.456 0092 
 
 2.857 651 
 
 0-349 9377 
 
 .OOI 
 
 .434 7288 
 
 .721 ooi 
 
 .367 5H7 
 
 .051 
 
 .456 4435 
 
 .860 510 
 
 349 5880 
 
 .002 
 
 .435 1631 
 
 .723 724 
 
 .367 1444 
 
 .052 
 
 .456 8778 
 
 .863 372 
 
 349 2386 
 
 .003 
 
 435 5974 
 
 .726 449 
 
 366 7775 
 
 .053 
 
 457 3121 
 
 .866237 
 
 .348 8895 
 
 .004 
 
 .436 0317 
 
 .729 177 
 
 .366 4109 
 
 .054 
 
 .457 7464 
 
 .869 105 
 
 .348 5408 
 
 1.005 
 
 0.436 4660 
 
 2.731 907 
 
 0.366 0446 
 
 ^1.055 
 
 0.458 1807 
 
 2.871 975 
 
 0.348 1924 
 
 .006 
 
 .436 9002 
 
 .734 641 
 
 .365 6788 
 
 .056 
 
 .458 6150 
 
 .874 849 
 
 .347 8444 
 
 .007 
 
 437 3345 
 
 .737 377 
 
 .365 3133 
 
 057 
 
 459 0493 
 
 .877 725 
 
 347 4967 
 
 .008 
 
 .437 7688 
 
 740 115 
 
 .364 9481 
 
 .058 
 
 .459 4836 
 
 .880604 
 
 347 1494 
 
 .009 
 
 .438 2031 
 
 742 857 
 
 .364 5834 
 
 .059 
 
 459 9179 
 
 .883 486 
 
 .346 8024 
 
 1. 010 
 
 0.438 6374 
 
 2.745 601 
 
 0.364 2190 
 
 i. 060 
 
 0.460 3522 
 
 2.886 371 
 
 0.346 4558 
 
 .on 
 .012 
 
 439 0717 
 .439 5060 
 
 748 348 
 .751 098 
 
 .363 8549 
 .363 4913 
 
 .061 
 .062 
 
 .460 7864 
 .461 2207 
 
 .889 259 
 .892 150 
 
 .346 1095 
 345 7636 
 
 .013 
 
 .439 9403 
 
 753 850 
 
 .363 1280 
 
 .063 
 
 .461 6550 
 
 895 043 
 
 .345 4180 
 
 .014 
 
 .440 3746 
 
 .756 605 
 
 .362 7650 
 
 .064 
 
 .462 0893 
 
 .897 940 
 
 345 0728 
 
 1.015 
 
 0.440 8089 
 
 2.759 363 
 
 0.362 4024 
 
 1.065 
 
 0.462 5236 
 
 2.900 839 
 
 0.344 7279 
 
 .016 
 
 .441 2432 
 
 .762 124 
 
 .362 0402 
 
 .066 
 
 .462 9579 
 
 .903 741 
 
 344 3833 
 
 .0*17 
 
 .441 6775 
 
 .764 888 
 
 .361 6783 
 
 .067 
 
 .463 3922 
 
 .906 646 
 
 344 0391 
 
 .018 
 
 .442 I I 18 
 
 .767 654 
 
 .361 3169 
 
 .068 
 
 .463 8265 
 
 .909 555 
 
 343 6952 
 
 .019 
 
 .442 5461 
 
 .770 423 
 
 .360 9557 
 
 .069 
 
 .464 2608 
 
 .912 466 
 
 343 3517 
 
 i. 020 
 
 0.442 9804 
 
 2.773 195 
 
 0.360 5949 
 
 1.070 
 
 0.464 6951 
 
 2.915 379 
 
 0.343 0085 
 
 .021 
 
 .443 4147 
 
 775 969 
 
 .360 2345 
 
 .071 
 
 .465 1294 
 
 .918 296 
 
 .342 6657 
 
 .022 
 
 .443 8490 
 
 778 747 
 
 .359 8745 
 
 .072 
 
 465 5637 
 
 .921 216 
 
 .342 3232 
 
 .023 
 
 .444 2833 
 
 781 527 
 
 359 5148 
 
 .073 
 
 .465 998o 
 
 .924 139 
 
 .341 9810 
 
 .024 
 
 .444 7175 
 
 .784 3io 
 
 .359 1554 
 
 .074 
 
 .466 4323 
 
 .927 064 
 
 .341 6392 
 
 1.025 
 
 0.445 I5i8 
 
 2.787 095 
 
 0.358 7965 
 
 1.075 
 
 0.466 8666 
 
 2.929 993 
 
 0.341 2978 
 
 .026 
 
 .445 586i 
 
 .789884 
 
 358 4378 
 
 .076 
 
 .467 3009 
 
 .932 924 
 
 .340 9566 
 
 .027 
 
 .446 0204 
 
 .792 675 
 
 .358 0796 
 
 .077 
 
 467 7352 
 
 935 859 
 
 .340 6158 
 
 .028 
 
 .446 4547 
 
 795 469 
 
 357 7217 
 
 .078 
 
 .468 1695 
 
 .938 796 
 
 .340 2754 
 
 .029 
 
 .446 8890 
 
 .798 266 
 
 357 3641 
 
 .079 
 
 .468 6037 
 
 .941 736 
 
 339 9353 
 
 I.O30 
 
 0.447 3233 
 
 2.801 066 
 
 0.357 0070 
 
 1.080 
 
 0.469 0380 
 
 2.944 680 
 
 0.339 5955 
 
 .031 
 
 .447 7576 
 
 .803 868 
 
 .356 6501 
 
 .081 
 
 .469 4723 
 
 .947 626 
 
 339 2561 
 
 .032 
 
 .448 1919 
 
 .806 674 
 
 .356 2937 
 
 .082 
 
 .469 9066 
 
 950 575 
 
 .338 9170 
 
 033 
 
 .448 6262 
 
 .809 482 
 
 355 9375 
 
 .083 
 
 .470 3409 
 
 953 527 
 
 .338 5783 
 
 .034 
 
 .449 0605 
 
 .812 293 
 
 .355 58i8 
 
 .084 
 
 .470 7752 
 
 .956 482 
 
 .338 2399 
 
 1.035 
 
 0.449 4948 
 
 2.815 106 
 
 0.355 2264 
 
 1.085 
 
 0.471 2095 
 
 2.959 440 
 
 0.337 0018 
 
 .036 
 
 .449 9291 
 
 .817 923 
 
 .354 8713 
 
 .086 
 
 .471 6438 
 
 .962 401 
 
 .337 5641 
 
 .037 
 
 450 3634 
 
 .820 742 
 
 354 5i66 
 
 .087 
 
 .472 0781 
 
 .965 365 
 
 337 2267 
 
 .038 
 
 450 7977 
 
 .823 564 
 
 354 1623 ~ 
 
 .088 
 
 .472 5124 
 
 .968 331 
 
 .3368896 
 
 .039 
 
 .451 2320 
 
 .826 389 
 
 353 8083 
 
 .089 
 
 .472 9467 
 
 .971 301 
 
 .336 5529 
 
 1.040 
 
 0.451 6663 
 
 2.829 217 
 
 0-353 4547 
 
 1.090 
 
 0.473 3810 
 
 2.974 274 
 
 0.336 2165 
 
 .041 
 
 .452 1006 
 
 .832 048 
 
 .353 1014 
 
 .091 
 
 473 8153 
 
 977 250 .335 8804 
 
 .042 
 
 452 5349 
 
 .834 881 
 
 352 7485 
 
 .092 
 
 .474 2406 
 
 .980 229 .335 5447 
 
 .043 
 
 .452 9691 
 
 837 717 
 
 352 3959 
 
 .093 
 
 .474 6839 
 
 .983 210 .335 2094 
 
 .044 
 
 453 4034 
 
 .840 557 
 
 .352 0437 
 
 .094 
 
 .475 1182 
 
 .986 195 .334 8743 
 
 1.045 
 
 0.453 8377 
 
 2.843 399 
 
 0.351 6918 
 
 1.095 
 
 0.475 5525 
 
 2.989 183 0.334 5396 
 
 .046 
 
 .454 2720 
 
 .846 243 
 
 351 3403 
 
 .096 
 
 .475 9868 
 
 .992 173 
 
 334 2052 
 
 .047 
 
 .454 7063 
 
 .849 091 
 
 350 0891 
 
 .097 
 
 .476 4210 
 
 
 333 8712 
 
 .048 
 
 .455 1406 
 
 .851 942 
 
 350 6383 
 
 .098 
 
 476 8553 
 
 .998 164 
 
 333 5375 
 
 .049 
 
 455 5749 
 
 .854 795 
 
 350 2879 
 
 .099 
 
 .477 2896 
 
 3.001 163 
 
 333 2041 
 
 1.050 
 
 0.456 0092 
 
 2.857 651 
 
 0.349 9377 
 
 1. 100 
 
 0.477 7239 
 
 3.004 166 
 
 0.332 8711 
 
 log e (e) 
 
 lo fllo (e u ) 
 
 e u 
 
 e~ u 
 
 log c (e u ) 
 
 log,,,(e u ) 
 
 e n 
 
 e 
 
 SMITHSONIAN TABLES 
 
 236 
 
The Exponential. 
 
 u 
 
 looio(e u ) 
 
 e u 
 
 e- u 
 
 u 
 
 logio(e u ) 
 
 e u 
 
 e~ u 
 
 I.IOO 
 
 0.477 7239 
 
 3.004 166 
 
 0.332 8711 
 
 I.I5O 
 
 0.499 4387 
 
 3.158 193 
 
 0.316 636 
 
 .101 
 
 .478 1582 
 
 .007 172 
 
 .332 5384 
 
 .151 
 
 .499 8729 
 
 .161 353 
 
 .316 320 
 
 .102 
 
 .478 5925 
 
 .010 180 
 
 .332 2060 
 
 .152 
 
 -500 3072 
 
 .164 516 
 
 .316 004 
 
 .103 
 
 .479 0268 
 
 .013 192 
 
 .331 8740 
 
 153 
 
 .500 7415 
 
 . 167 682 
 
 .315688 
 
 .104 
 
 .479 4611 
 
 .016 207 
 
 331 5423 
 
 .154 
 
 .501 1758 
 
 .170 851 
 
 .315 372 
 
 1.105 
 
 0.479 8954 
 
 3.019 224 
 
 0.331 2109 
 
 1. 155 
 
 0.501 6101 
 
 3.174 023 
 
 0.315 057 
 
 .106 
 
 .480 3297 
 
 .022 245 
 
 330 8798 
 
 .156 
 
 .502 0444 
 
 .177 199 
 
 .314 742 
 
 .107 
 
 .480 7640 
 
 .025 269 
 
 330 5491 
 
 .157 
 
 .502 4787 
 
 . 180 378 
 
 .3U 428 
 
 .108 
 
 .481 1983 
 
 .028 296 
 
 -330 2187 
 
 .158 
 
 .502 9130 
 
 .183 560 
 
 .3H ii3 
 
 .109 
 
 .481 6326 
 
 .031 326 
 
 .329 8887 
 
 159 
 
 .503 3473 
 
 .186 745 
 
 .313 799 
 
 1. 1 10 
 
 0.482 0669 
 
 3-034 358 
 
 0.329 5590 
 
 1.160 
 
 0.503 7816 
 
 3-189 933 
 
 0.313 486 
 
 .in 
 
 .482 5012 
 
 .037 394 
 
 .329 2296 
 
 .161 
 
 .504 2159 
 
 .193 125 
 
 .313 172 
 
 .112 
 
 .482 9355 
 
 .040 433 
 
 .328 9005 
 
 .162 
 
 .504 6502 
 
 .196 320 
 
 .312 859 
 
 113 
 
 .483 3698 
 
 .043 475 
 
 .328 57i8 
 
 .163 
 
 .505 0845 
 
 .199 517 
 
 .312 547 
 
 .114 
 
 .483 8041 
 
 .046 520 
 
 .328 2434 
 
 .164 
 
 .505 5i88 
 
 ,.202 719 
 
 .312 234 
 
 I.H5 
 
 0.484 2383 
 
 3.049 568 
 
 0.327 9153 
 
 1.165 
 
 0.505 9531 
 
 3.205 923 
 
 0.311 922 
 
 .116 
 
 .484 6726 
 
 .052 619 
 
 .327 5875 
 
 .166 
 
 .506 3874 
 
 .209 130 
 
 .311 610 
 
 .117 
 
 .485 1069 
 
 .055 673 
 
 .327 2601 
 
 .!6 7 
 
 .506 8217 
 
 .212 341 
 
 .311 295 
 
 .118 
 
 .485 5412 
 
 .058 731 
 
 .326 9330 
 
 .168 
 
 .507 2560 
 
 .215 555 
 
 .310 988 
 
 .119 
 
 .485 9755 
 
 .061 791 
 
 .326 6062 
 
 .169 
 
 .507 6902 
 
 .218 772 
 
 .310 677 
 
 I.I2O 
 
 0.486 4098 
 
 3.064 854 
 
 0.326 2798 
 
 1.170 
 
 0.508 1245 
 
 3.221 993 
 
 0.310 366 
 
 .121 
 
 .486 8441 
 
 .067 921 
 
 .325 9537 
 
 .171 
 
 .508 5588 
 
 .225 216 
 
 .310 056 
 
 .122 
 
 .487 2784 
 
 .070 990 
 
 .325 6279 
 
 .172 
 
 .508 9931 
 
 .228 443 
 
 .309 746 
 
 .123 
 
 .487 7127 
 
 .074 063 
 
 .325 3024 
 
 .173 
 
 .509 4274 
 
 .231 673 
 
 .309 437 
 
 .124 
 
 .488 1470 
 
 .077 138 
 
 .324 9773 
 
 .174 
 
 .509 8617 
 
 .234 906 
 
 .309 128 
 
 1. 125 
 
 0.488 5813 
 
 3.080 217 
 
 0.324 6525 
 
 I.I75 
 
 0.510 2960 
 
 3-238 143 
 
 0.308 819 
 
 .126 
 
 .489 0156 
 
 .083 209 
 
 .324 3280 
 
 .176 
 
 510 7303 
 
 .241 383 
 
 .308 510 
 
 .127 
 
 .489 4499 
 
 .086 383 
 
 .324 0038 
 
 .177 
 
 .511 1646 
 
 .244 626 
 
 .308 202 
 
 .128 
 
 .489 8842 
 
 .089 47i 
 
 .323 6800 
 
 .178 
 
 .511 5989 
 
 .247 872 
 
 307 893 
 
 .129 
 
 .490 3185 
 
 .092 562 
 
 .323 3565 
 
 .179 
 
 .512 0332 
 
 .251 121 
 
 .307 585 
 
 I.I30 
 
 0.490 7528 
 
 3.095 657 
 
 0.323 0333 
 
 1.180 
 
 0.512 4675 
 
 3.254 374 
 
 0.307 278 
 
 .131 
 
 .491 1871 
 
 .098 754 
 
 .322 7104 
 
 .181 
 
 .512 9018 
 
 .257 630 
 
 .306 971 
 
 .132 
 
 .491 6214 
 
 .101 854 
 
 .322 3878 
 
 .182 
 
 .513 336i 
 
 .260 889 
 
 .306 664 
 
 133 
 
 .492 0556 
 
 .104 957 
 
 .322 0656 
 
 .183 
 
 .513 7704 
 
 .264 152 
 
 .306 358 
 
 134 
 
 .492 4899 
 
 .108 064 
 
 .321 7437 
 
 .184 
 
 .514 2047 
 
 .267 418 
 
 .306 052 
 
 1. 135 
 
 0.492 9242 
 
 3. i n 174 
 
 0.321 4221 
 
 1.185 
 
 0.514 6300 
 
 3.270 687 
 
 0.305 746 
 
 .136 
 
 493 3585 
 
 .114 286 
 
 .321 1009 
 
 .186 
 
 .515 0733 
 
 273 959 
 
 .305 440 
 
 137 
 
 493 7928 
 
 .117 402 
 
 .320 7799 
 
 .187 
 
 .515 5075 
 
 .277 235 
 
 .305 135 
 
 .138 
 
 .494 2271 
 
 .120 521 
 
 320 4593 
 
 .188 
 
 .515 9418 
 
 .280 514 
 
 .304 830 
 
 139 
 
 .494 6614 
 
 .123 643 
 
 .320 1390 
 
 .189 
 
 .516 3761 
 
 .283 796 
 
 .304 525 
 
 I.I40 
 
 0.495 0957 
 
 3.126 768 
 
 0.319 8190 
 
 1.190 
 
 0.516 8104 
 
 3.287 081 
 
 0.304 221 
 
 .141 
 
 495 5300 
 
 . 129 897 
 
 .319 4994 
 
 . .191 
 
 .517 2447 
 
 .290 370 
 
 .303 917 
 
 .142 
 
 .495 9643 
 
 .133 028 
 
 .319 1800 
 
 .192: 
 
 .517 6790 
 
 .293 662 
 
 .303 613. 
 
 143 
 
 .496 3986 
 
 .136 163 
 
 .318 8610 
 
 .193 
 
 .5i8 1133 
 
 .296 957 
 
 . .303 310 
 
 .144 
 
 .496 8329 
 
 .139 300 
 
 .318 5423 
 
 .194 
 
 5i8 5476 
 
 .300 256 
 
 .303 006 
 
 1. 145 
 
 0.497 2672 
 
 3.142 441 
 
 0.318 2239 
 
 1. 195 
 
 0.518 9819 
 
 3.303 558 
 
 0.302 704 
 
 .146 
 
 .497 7015 
 
 .145 585 
 
 .317 9059 
 
 .196 
 
 .519 4162 
 
 .306 863 
 
 .302 401 
 
 .147 
 
 .498 1358 
 
 148 733 
 
 .317 588i 
 
 .197 
 
 .519 8505 
 
 .310 172 
 
 .302 009 
 
 .148 
 
 .498 5701 
 
 .151 883 
 
 .317 2707 
 
 .198 
 
 .520 2848 
 
 .313 483 
 
 301 797 
 
 .149 
 
 .499 0044 
 
 .155 036 
 
 316 9536 
 
 .199 
 
 .520 7191 
 
 .316 798 
 
 .301 493 
 
 I.I5O 
 
 0.499 4387 
 
 3.158 193 
 
 0.316 6368 
 
 1.200 
 
 0.521 1534 
 
 3.320 117 
 
 0.301 194 
 
 looe(e u ) 
 
 Iofl 10 (e u ) 
 
 e u 
 
 e- u 
 
 looe(e u ) 
 
 looio(e u ) 
 
 e u 
 
 e~ u 
 
 SMITHSONIAN TABLES 
 
 237 
 
The Exponential. 
 
 u 
 
 looio(e u ) 
 
 e n 
 
 e- 
 
 u 
 
 logio(e u ) 
 
 e u 
 
 e~ u 
 
 I.2OO 
 .201 
 .202 
 .203 
 .204 
 
 0.521 1534 
 
 .521 5877 
 
 .522 0220 
 .522 4563 
 .522 8906 
 
 3.320 117 
 .323 439 
 .326 764 
 .330 092 
 333 424 
 
 0.301 1942 
 300 8932 
 .300 5924 
 .300 2920 
 .299 99i8 
 
 I.25O 
 .251 
 .252 
 .253 
 254 
 
 0.542 8681 
 543 3024 
 .543 7367 
 .544 1710 
 .544 6053 
 
 3-490 343 
 493 835 
 497 331 
 .500 830 
 504 332 
 
 0.286 5048 
 .286 2184 
 .285 9324 
 .285 6466 
 .285 3611 
 
 1.205 
 
 .206 
 
 .207 
 
 .208 
 
 .209 
 
 0.523 3249 
 .523 7591 
 524 1934 
 .524 6277 
 .525 O62O 
 
 3.336 759 
 .340 098 
 343 439 
 .346 784 
 350 133 
 
 0.299 6920 
 .299 3925 
 .299 0932 
 .298 7943 
 .298 4956 
 
 1.255 
 .256 
 
 .257 
 .258 
 .259 
 
 0.545 0396 
 
 .545 4739 
 545 9082 
 .546 3425 
 .546 7768 
 
 3.507 838 
 .5ii 348 
 .514 85i 
 .518 378 
 .521 898 
 
 0.285 0758 
 .284 7909 
 .284 5063 
 .284 2219 
 .283 9378 
 
 1. 210 
 .211 
 .212 
 .213 
 
 .214 
 
 0.525 4963 
 .525 9306 
 .526 3649 
 .526 7992 
 .527 2335 
 
 3-353 485 
 .356 840 
 .360 198 
 .363 56o 
 .366 925 
 
 0.298 1973 
 .297 8992 
 .297 6015 
 .297 3040 
 .297 0069 
 
 1.260 
 .261 
 .262 
 .263 
 .264 
 
 0.547 21 IO 
 547 6453 
 .548 0796 
 .548 5139 
 .548 9482 
 
 3.525 421 
 .528 949 
 .532 479 
 .536 014 
 .539 551 
 
 0.283 6540 
 .283 3705 
 .283 0873 
 .282 8043 
 .282 5217 
 
 1. 215 
 .216 
 .217 
 .218 
 .219 
 
 0.527 6678 
 .528 102 I 
 .528 5364 
 .528 9/07 
 .529 4050 
 
 3.370 294 
 .373 666 
 .377 041 
 .380 420 
 .383 802 
 
 0.296 7100 
 .296 4135 
 .296 1772 
 .295 8212 
 .295 5255 
 
 1.265 
 .266 
 .267 
 .268 
 .269 
 
 0.549 3825 
 
 .549 8168 
 550 2511 
 550 6854 
 551 H97 
 
 3-543 093 
 .546 638 
 .550 186 
 
 553 738 
 .557 293 
 
 0.282 2393 
 .281 9572 
 .281 6754 
 .281 3938 
 .281 1126 
 
 I.22O 
 .221 
 .222 
 .223 
 
 .224 
 
 0.529 8393 
 530 2736 
 530 7079 
 .531 1422 
 531 5764 
 
 3.387 188 
 .390 577 
 .393 969 
 397 365 
 .400 764 
 
 0.295 2302 
 294 9351 
 .294 6403 
 .294 3458 
 .294 0516 
 
 1.270 
 .271 
 .272 
 .273 
 .274 
 
 0.551 5540 
 551 9883 
 .552 4226 
 .552 8569 
 553 2912 
 
 3.56o 853 
 .564 415 
 .567 981 
 .571 55i 
 575 124 
 
 0.280 8316 
 .280 5509 
 .280 2705 
 .279 9904 
 .279 7105 
 
 1.225 
 
 .226 
 .227 
 .228 
 .229 
 
 0.532 0107 
 
 .532 4450 
 532 8793 
 533 3136 
 .533 7479 
 
 3.404 166 
 .407 572 
 .410 981 
 .414 394 
 .417 810 
 
 0.293 7577 
 .293 4641 
 .293 1708 
 .292 8777 
 .292 5850 
 
 1.275 
 .276 
 .277 
 .278 
 .279 
 
 0.553 7255 
 554 1598 
 554 5941 
 555 0283 
 555 4626 
 
 3.578 701 
 .582 282 
 .585866 
 .589 454 
 .593 045 
 
 0.279 4310 
 .279 1517 
 .278 8727 
 .2/8 5939 
 .278 3155 
 
 1.230 
 .231 
 .232 
 233 
 .234 
 
 0.534 1822 
 .534 6165 
 535 0508 
 535 4851 
 .535 9194 
 
 3.421 230 
 .424 652 
 .428 079 
 .431 509 
 .434 942 
 
 0.292 2926 
 .292 0004 
 .291 7086 
 .291 4170 
 .291 1257 
 
 1.280 
 
 [282 
 .283 
 .284 
 
 0.555 8969 
 .556 3312 
 .556 7655 
 557 1998 
 557 6341 
 
 3.596 640 
 .600 238 
 .603 840 
 .607 446 
 .611 055 
 
 0.278 0373 
 .277 7594 
 .277 4818 
 .277 2044 
 .276 9274 
 
 1.235 
 .236 
 .237 
 .238 
 .239 
 
 0.536 3537 
 .536 7880 
 .537 2223 
 537 6566 
 .538 0909 
 
 3.438 379 
 .441 819 
 .445 262 
 .448 709 
 .452 160 
 
 0.290 8348 
 .290 5441 
 .290 2537 
 .289 9636 
 .289 6737 
 
 1.285 
 .286 
 .287 
 .288 
 .289 
 
 0.558 0684 
 .558 5027 
 .558 9370 
 .559 3713 
 559 8056 
 
 3.614 668 
 .618 284 
 .621 905 
 .625 528 
 .629 156 
 
 0.276 6506 
 .276 3741 
 .276 0978 
 .275 8219 
 .275 5462 
 
 I.24O 
 .241 
 .242 
 
 .243 
 244 
 
 0.538 5252 
 .538 9595 
 539 3937 
 .539 8280 
 .540 2623 
 
 3.455 613 
 459 071 
 .462 532 
 .465 996 
 .469 464 
 
 0.289 3842 
 .289 0950 
 .288 8060 
 .288 5174 
 .288 2290 
 
 1.290 
 .291 
 292 
 293 
 .294 
 
 0.560 2399 
 .560 6742 
 .561 1085 
 .561 5428 
 .561 9771 
 
 3.632 787 
 .636 421 
 .640 059 
 .643 70i 
 .647 347 
 
 0.275 2708 
 274 9956 
 .274 7208 
 .274 4462 
 .J74 1/19 
 
 1.245 
 .246 
 .247 
 .248 
 .249 
 
 0.540 6066 
 .541 1309 
 .541 5652 
 541 9995 
 .542 4338 
 
 3.472 935 
 
 .179 888 
 .483 369 
 .486 854 
 
 0.287 9409 
 .287 6531 
 .287 3656 
 .287 0784 
 .286 79U 
 
 1.295 
 .296 
 .297 
 .298 
 .299 
 
 0.562 4114 
 .562 8456 
 .563 2709 
 .563 7142 
 .564 1485 
 
 3,650 996 
 .654 <>49 
 .658 305 
 .661 065 
 .665 629 
 
 0.273 fy/9 
 
 .273 35o6 
 ._>;:, 0774 
 .272 8045 
 
 1.250 
 
 0.542 8681 
 
 3-490 343 
 
 0.286 5048 
 
 1.300 
 
 0.564 5828 
 
 3.6Y*; 
 
 0.272 5318 
 
 ,.*(.> 
 
 looio(e u ) 
 
 e" 
 
 e- 
 
 loo,(e a ) 
 
 loo,o(e u ) 
 
 e u 
 
 e~" u 
 
 SMITHSONIAN TABLCS 
 
 238 
 
The Exponential. 
 
 u 
 
 U>Qio(e u ) 
 
 e u 
 
 e~ u 
 
 u 
 
 logio(e n ) 
 
 e u 
 
 e~ u 
 
 1.300 
 
 0.564 5828 
 
 3.669 297 
 
 0.272 53l8 
 
 1-350 
 
 0.586 2976 
 
 3.857 426 
 
 0.259 2403 
 
 .301 
 
 .565 0171 .672 9<38 
 
 .272 2594 
 
 .351 
 
 .586 73i8 
 
 .861 285 
 
 .258 9811 
 
 .302 
 
 .565 4514 
 
 .676 643 
 
 .271 9873 
 
 352 
 
 .587 1661 
 
 .865 148 
 
 .258 7223 
 
 .303 
 
 .565 8857 
 
 .680 321 
 
 .271 7154 
 
 .353 
 
 .587 6004 
 
 .869 015 
 
 .258 4637 
 
 .304 
 
 .566 3200 
 
 .684 003 
 
 .271 4438 
 
 354 
 
 .588 0347 
 
 .872 886 
 
 .258 2054 
 
 1.305 
 
 0.566 7543 
 
 3-687689 
 
 0.271 1725 
 
 1.355 
 
 0.588 4600 
 
 3.876 761 
 
 0.257 9473 
 
 .306 
 
 .567 1886 
 
 .691 379 
 
 .270 9015 
 
 356 
 
 .588 0033 
 
 .880 640 
 
 .257 6895 
 
 .307 
 
 .567 6229 
 
 .695 072 
 
 .270 6307 
 
 357 
 
 .589 3376 
 
 .884 522 
 
 .257 4319 
 
 .308 
 
 .568 0572 
 
 .698 769 
 
 .270 3602 
 
 .358 
 
 589 7719 
 
 .888409 
 
 .257 1746 
 
 .309 
 
 .568 4915 
 
 .702 469 
 
 .270 0900 
 
 .359 
 
 .590 2062 
 
 .892 299 
 
 .256 9176 
 
 1.310 
 
 0.568 9258 
 
 3.706 174 
 
 0.269 8201 
 
 1.360 
 
 0.590 6405 
 
 3-806 193 
 
 0.256 6608 
 
 .311 
 
 .569 3601 
 
 .709 882 
 
 .269 5504 
 
 .361 
 
 .591 0748 
 
 .900 091 
 
 .256 4042 
 
 .312 
 
 .569 7944 
 
 .713 593 
 
 .269 2810 
 
 .362 
 
 591 5091 
 
 .903 993 
 
 .256 1480 
 
 .313 
 
 .570 2287 
 
 .717 309 
 
 .269 0118 
 
 .363 
 
 .591 9434 
 
 .907 899 
 
 .255 8919 
 
 .314 
 
 .570 6629 
 
 .721 028 
 
 .268 7429 
 
 .364 
 
 592 3777 
 
 .911 809 
 
 .255 6362 
 
 1.315 
 
 0.571 0972 
 
 3.724 751 
 
 0.268 4743 
 
 1.365 
 
 0.592 8120 
 
 3.915 723 
 
 0.255 3807 
 
 .316 
 
 .571 5315 
 
 .728 478 
 
 .268 2060 
 
 .366 
 
 .593 2463 
 
 .919 641 
 
 .255 1254 
 
 .317 
 
 .571 9658 
 
 .732 208 
 
 .267 9379 
 
 .367 
 
 .593 6806 
 
 .923 562 
 
 .254 8704 
 
 .318 
 
 .572 4001 
 
 735 942 
 
 .267 6701 
 
 .368 
 
 .594 1149 
 
 .927 488 
 
 .254 6157 
 
 .319 
 
 .572 8344 
 
 .739 680 
 
 .267 4026 
 
 .369 
 
 594 5491 
 
 931 417 
 
 .254 3612 
 
 1.320 
 
 0.573 2687 
 
 3-743 421 
 
 0.267 1353 
 
 1.370 
 
 0.594 9834 
 
 3-935 351 
 
 0.254 1070 
 
 .321 
 
 573 7030 
 
 747 167 
 
 .266 8683 
 
 371 
 
 .595 4177 
 
 .939 288 
 
 .253 8530 
 
 .322 
 
 -574 1373 
 
 .750 916 
 
 .266 6016 
 
 372 
 
 595 8520 
 
 .943 229 
 
 .253 5993 
 
 .323 
 
 574 57i6 
 
 .754 669 
 
 .266 3351 
 
 373 
 
 .596 2863 
 
 947 174 
 
 .253 3458 
 
 .324 
 
 575 0059 
 
 .758 425 
 
 .266 0689 
 
 374 
 
 .596 7206 
 
 951 124 
 
 .253 0926 
 
 1.325 
 
 0.575 4402 
 
 3.762 185 
 
 0.265 8030 
 
 1-375 
 
 0.597 1549 
 
 3.955 077 
 
 0.252 8306 
 
 .326 
 
 .575 8745 
 
 .765 949 
 
 .265 5373 
 
 .376 
 
 597 5892 
 
 959 034 
 
 .252 5869 
 
 .327 
 
 .576 3088 
 
 .769 717 
 
 .265 2719 
 
 377 
 
 .598 0235 
 
 .062 995 
 
 .252 3344 
 
 .328 
 
 .576 7431 
 
 773 489 
 
 .265 0067 
 
 .378 
 
 .598 4578 
 
 .966 960 
 
 .252 0822 
 
 .329 
 
 577 1774 
 
 .777 264 
 
 .264 7419 
 
 379 
 
 .598 8921 
 
 .970 929 
 
 .251 8303 
 
 1.330 
 
 0.577 6117 
 
 3.781 043 
 
 0.264 4773 
 
 1.380 
 
 0.599 3264 
 
 3.974 902 
 
 0.251 5786 
 
 331 
 
 .578 0460 
 
 .784 826 
 
 .264 2129 
 
 .381 
 
 .599 7607 
 
 .978 879 
 
 .251 3271 
 
 .332 
 
 .578 4802 
 
 .788 613 
 
 .263 9488 
 
 .382 
 
 .600 1950 
 
 .982 859 
 
 .251 0759 
 
 333 
 
 .578 9M5 
 
 .792 404 
 
 .263 6850 
 
 .383 
 
 .600 6293 
 
 .986844 
 
 .250 8249 
 
 334 
 
 579 3488 
 
 .795 198 
 
 .263 4215 
 
 .384 
 
 .601 0636 
 
 .990 833 
 
 .250 5742 
 
 1-335 
 
 0-579 7831 
 
 3.799 996 
 
 0.263 1582 
 
 1.385 
 
 0.601 4979 
 
 3.994 826 
 
 0.250 3238 
 
 -336 
 
 .580 2174 
 
 .803 798 
 
 .262 8951 
 
 .386 
 
 .601 9322 
 
 .998823 
 
 .250 0736 
 
 337 
 
 .580 6517 
 
 .807 604 
 
 .262 6324 
 
 .387 
 
 .602 3664 
 
 4.002 824 
 
 .249 8237 
 
 .338 
 
 .581 0860 
 
 .811 413 
 
 .262 3699 
 
 .388 
 
 .602 8007 
 
 .006 828 
 
 .249 5740 
 
 339 
 
 .581 5203 
 
 .815 226 
 
 .262 1076 
 
 .389 
 
 .603 2350 
 
 .010 837 
 
 .249 3245 
 
 1.340 
 
 0.581 9546 
 
 3.819 044 
 
 0.261 8457 
 
 1.390 
 
 0.603 6693 
 
 4.014 850 
 
 0.249 0753 
 
 .341 
 
 .582 3889 
 
 .822 864 
 
 .261 5840 
 
 391 
 
 .604 1036 
 
 .018 867 
 
 .248 8264 
 
 342 
 
 .582 8232 
 
 .826 689 
 
 .261 3225 
 
 392 
 
 .604 5379 
 
 .022 888 
 
 .248 5777 
 
 343 
 
 583 2575 
 
 .830 518 
 
 .261 0613 
 
 393 
 
 .604 9722 
 
 .026 913 
 
 .248 3292 
 
 344 
 
 .583 6918 
 
 .834 350 
 
 .260 8004 
 
 .394 
 
 .605 4065 
 
 .030 942 
 
 .248 0810 
 
 1.345 
 
 0.584 1261 
 
 3.838 187 
 
 0.260 5397 
 
 1.395 
 
 0.605 8408 
 
 4.034 975 
 
 0.247 8330 
 
 .346 
 
 .584 5604 
 
 .842 027 
 
 .260 2793 
 
 .396 
 
 .606 2751 
 
 .039 012 
 
 .247 5853 
 
 .347 
 
 .584 9947 
 
 .845 871 
 
 .260 0191 
 
 397 
 
 .606 7094 
 
 .043 053 
 
 .247 3379 
 
 .348 
 
 .585 4290 
 
 .849 718 
 
 .259 7593 
 
 .398 
 
 .607 1437 
 
 .047 098 
 
 .247 0907 
 
 349 
 
 .585 8633 
 
 853 570 
 
 .259 4996 
 
 399 
 
 .607 578o 
 
 .051 147 
 
 .246 8437 
 
 1-350 
 
 0.586 2976 
 
 3.857 426 
 
 0.259 2403 
 
 1.400 
 
 0.608 0123 
 
 4.055 200 
 
 0.246 5970 
 
 lo fle (e u ) 
 
 logio(e n ) 
 
 e u 
 
 e~ u 
 
 Io 0e (e u ) 
 
 looio(e u ) 
 
 e u 
 
 e~ u 
 
 SMITHSONIAN TABLES 
 
 239 
 
The Exponential. 
 
 u 
 
 loflio(e u ) 
 
 e u 
 
 .- 
 
 u 
 
 looio(e n ) 
 
 e u 
 
 e~ u 
 
 1.400 
 .401 
 .402 
 .403 
 .404 
 
 0.608 0123 
 .608 4466 
 .608 8809 
 .609 3152 
 .609 7495 
 
 4.O55 2OO 
 
 059 257 
 .063 318 
 .067 384 
 .071 453- 
 
 0.246 5970 
 .246 3505 
 .246 1043 
 .245 8583 
 .245 6125 
 
 1.450 
 451 
 452 
 
 453 
 .454 
 
 0.629 7270 
 .630 1613 
 630 5956 
 .631 0299 
 .631 4642 
 
 4-263 115 
 .267 380 
 .271 649 
 275 923 
 .280 201 
 
 0.234 5703 
 .234 3358 
 .234 1016 
 .233 8676 
 233 6339 
 
 1.405 
 
 .406 
 
 .407 
 
 .408 
 
 .409 
 
 0.610 1837 
 .610 6180 
 .611 0523 
 .611 4866 
 .611 9209 
 
 4.075 527 
 .079 604 
 .083 686 
 .087 772 
 .091 861 
 
 0.245 36/1 
 .245 1218 
 .244 8768 
 .244 6321 
 .244 3875 
 
 1-455 
 .456 
 457 
 458 
 459 
 
 0.631 8985 
 .632 3328 
 .632 7671 
 .633 2014 
 .633 6356 
 
 4.284 483 
 .288 770 
 .293 06 1 
 .297 356 
 .301 656 
 
 0.233 4004 
 .233 1671 
 .232 9340 
 .232 7012 
 .232 4686 
 
 1.410 
 
 .411 
 .412 
 .413 
 .414 
 
 0.612 3552 
 .612 7895 
 .613 2238 
 .613 6581 
 .614 0924 
 
 4.095 955 
 
 . 100 053 
 
 .104 156 
 .108 262 
 
 .112 372 
 
 0.244 1433 
 .243 8993 
 .243 6555 
 .243 4120 
 .243 1687 
 
 1.460 
 .461 
 .462 
 463 
 464 
 
 0.634 0609 
 .634 5042 
 634 9385 
 .635 3728 
 635 8071 
 
 4.305 960 
 .310 268 
 .314 580 
 .318 897 
 .323 218 
 
 0.232 2363 
 .232 0042 
 .231 7723 
 .231 5406 
 .231 3092 
 
 1.415 
 .416 
 
 .417 
 .418 
 .419 
 
 0.614 5267 
 .614 9610 
 615 3953 
 .615 8296 
 .616 2639 
 
 4.116 486 
 
 .120 605 
 
 .124 728 
 . 128 854 
 . 132 985 
 
 0.242 9256 
 .242 6828 
 .242 4402 
 .242 1979 
 .241 9559 
 
 1.465 
 .466 
 467 
 .468 
 469 
 
 0.636 2414 
 .636 6757 
 .637 i zoo 
 .637 5443 
 .637 9786 
 
 4.327 543 
 331 873 
 .336 207 
 340 545 
 .344 888 
 
 0.231 0780 
 .230 8470 
 .230 6163 
 .230 3858 
 .230 1555 
 
 1.420 
 
 .421 
 .422 
 .423 
 .424 
 
 0.616 6982 
 .617 1325 
 .617 5668 
 .618 ooio 
 .618 4353 
 
 4-137 120 
 .141 260 
 
 .145 403 
 .149 550 
 .153 702 
 
 0.241 7140 
 .241 4724 
 .241 2311 
 .240 9900 
 .240 7491 
 
 1.470 
 .471 
 472 
 473 
 .474 
 
 0.638 4129 
 638 8472 
 .639 2815 
 639 7158 
 .640 1501 
 
 4-349 235 
 353 587 
 .357 942 
 .362 302 
 .366667 
 
 0.229 9255 
 .229 6957 
 .229 4661 
 .229 2367 
 .229 0076 
 
 1.425 
 .426 
 
 .427 
 .428 
 
 .429 
 
 0.618 8696 
 .619 3039 
 .619 7382 
 .620 1725 
 .620 6068 
 
 4-157 858 
 .162 018 
 .166 182 
 .170 350 
 .174 523 
 
 0.240 5085 
 .240 2681 
 .240 0279 
 .239 788o 
 .239 5484 
 
 1.475 
 .476 
 477 
 .478 
 479 
 
 0.640 5844 
 .641 0187 
 .641 4529 
 .641 8872 
 .642 3215 
 
 4-371 036 
 .375 409 
 379 787 
 .384 169 
 .388 555 
 
 0.2!28 7787 
 
 .228 5501 
 .228 3216 
 .228 0934 
 .227 8654 
 
 1.430 
 .431 
 .432 
 .433 
 
 .434 
 
 0.621 0411 
 .621 4754 
 .621 0097 
 .622 3440 
 .622 7783 
 
 4.178 609 
 .182 880 
 .187 065 
 .191 254 
 .195 447 
 
 0.239 3089 
 .239 0697 
 .238 8308 
 .238 5921 
 .238 3536 
 
 1.480 
 .481 
 .482 
 .483 
 .484 
 
 0.642 7558 
 .643 1901 
 .643 6244 
 .644 0587 
 .644 4930 
 
 4.392 946 
 397 34i 
 .401 740 
 .406 144 
 .410 553 
 
 0.227 6377 
 .227 4102 
 .227 1829 
 .226 9558 
 .226 7290 
 
 1.435 
 .436 
 437 
 .438 
 439 
 
 0.623 2126 
 .623 6469 
 .624 0812 
 .624 5155 
 .624 9498 
 
 4.199 645 
 .203 847 
 .208 053 
 
 .212 263 
 
 .216 477 
 
 0.238 1154 
 .237 8774 
 .237 6396 
 .237 4021 
 .237 1648 
 
 1.485 
 .486 
 .487 
 .488 
 .489 
 
 0.644 92-73 
 .645 3616 
 045 7959 
 .646 2302 
 .646 6645 
 
 4.414 965 
 .419 383 
 .423 804 
 .428 230 
 .432 661 
 
 0.226 5023 
 .226 2760 
 .226 0498 
 .225 8239 
 
 .225 5981 
 
 1.440 
 441 
 .442 
 443 
 444 
 
 0.625 3841 
 .625 8183 
 .626 2526 
 .626 6869 
 
 .627 1212 
 
 4.220 696 
 .224 919 
 .229 146 
 .233 377 
 .237 612 
 
 0.236 9278 
 .236 6909 
 .236 4544 
 .236 2180 
 .235 98i9 
 
 1.490 
 .491 
 .492 
 493 
 494 
 
 0.647 0088 
 647 5331 
 .647 9674 
 .648 4017 
 .648 8360 
 
 4.437 096 
 
 441 535 
 445 979 
 .450 427 
 454 879 
 
 0.225 3727 
 .225 1474 
 .224 9224 
 .224 6976 
 
 .224 4730 
 
 1.445 
 .446 
 447 
 448 
 449 
 
 0.627 5555 
 
 .628 4241 
 .6288584 
 .629 2927 
 
 4.241 852 
 .246 096 
 .250 344 
 .254 597 
 .258 854 
 
 0.235 7461 
 .235 5104 
 .235 2751 
 .235 0399 
 .234 8050 
 
 1.495 
 .496 
 .497 
 .498 
 .499 
 
 0.649 2703 
 .649 7045 
 .650 1388 
 .650 5731 
 .651 0074 
 
 4.459 337 
 .463 798 
 .468 J :>4 
 .472 735 
 .477 210 
 
 0.224 2486 
 .224 0245 
 .223 8006 
 .223 5769 
 -'-'3 3534 
 
 1.450 
 
 0.629 7270 
 
 4.263 US 
 
 0.234 5703 
 
 1.500 
 
 0.651 4417 
 
 4.481 689 
 
 0.223 1302 
 
 looete") 
 
 M 
 
 e 
 
 .- 
 
 loo( u ) 
 
 loguXe ) 
 
 '" 
 
 e~ n 
 
 SMITHSONIAN TABLES 
 
 240 
 
The Exponential. 
 
 u 
 
 loflio(e") 
 
 e u 
 
 e u 
 
 u 
 
 looio(e n ) 
 
 e u 
 
 e~ u 
 
 1.500 
 
 0.651 4417 
 
 4.481 689 
 
 0.223 1302 
 
 1.550 
 
 0.673 1564 
 
 4.7H 470 
 
 O.2I2 2480 
 
 .501 
 
 .651 8760 
 
 486 173 
 
 .222 9O7I 
 
 551 
 
 .673 5907 
 
 .716 184 
 
 .212 0358 
 
 .502 
 
 .652 3103 
 
 .490 661 
 
 .222 6843 
 
 552 
 
 .674 0250 
 
 .720 903 
 
 .211 8239 
 
 .503 
 
 .652 7446 
 
 495 154 
 
 .222 4618 
 
 553 
 
 .674 4593 
 
 .725 626 
 
 .211 6l22 
 
 .504 
 
 .653 1789 
 
 .499 652 
 
 .222 2394 
 
 554 
 
 .674 8936 
 
 .730 354 
 
 .211 4007 
 
 1.505 
 
 0.653 6132 
 
 4.504 154 
 
 O.222 OI73 
 
 1.555 
 
 0.675 3279 
 
 4-735 087 
 
 O.2II 1894 
 
 .506 
 
 .654 0475 
 
 .508 660 
 
 .221 7954 
 
 .556 
 
 .675 7622 
 
 .739 824 
 
 .210 9783 
 
 .507 
 
 .654 48i8 
 
 .513 I7i 
 
 .221 5737 
 
 .557 
 
 .676 1905 
 
 .744 566 
 
 .210 7674 
 
 .508 
 
 .654 9161 
 
 .517686 
 
 .221 3522 
 
 .558 
 
 .676 6308 
 
 749 313 
 
 .210 5568 
 
 .509 
 
 .655 3504 
 
 .522 206 
 
 .221 I3IO 
 
 .559 
 
 .677 0651 
 
 754 065 
 
 .210 3463 
 
 1.510 
 
 0.655 7847 
 
 4.526 731 
 
 0.220 9100 
 
 1.560 
 
 0.677 4994 
 
 4.758 821 
 
 O.2IO 1361 
 
 .511 
 
 .656 2190 
 
 .531 260 
 
 .220 6892 
 
 .561 
 
 .677 9337 
 
 .763 582 
 
 .209 926O 
 
 .512 
 
 656 6533 
 
 535 793' 
 
 .220 4686 
 
 .562 
 
 .678 3680 
 
 .768 348 
 
 .2O9 7l62 
 
 .513 
 
 .657 0876 
 
 540 33i 
 
 .220 2482 
 
 .563 
 
 .678 8023 
 
 773 H9 
 
 .209 5066 
 
 .514 
 
 .657 5218 
 
 .544 874 
 
 .220 O28l 
 
 .564 
 
 .679 2366 
 
 .777 895 
 
 .209 2972 
 
 1.515 
 
 0.657 9561 
 
 4.549 421 
 
 O.2I9 8082 
 
 1.565 
 
 0.679 6709 
 
 4-782 675 
 
 O.2O9 0880 
 
 .516 
 
 .658 3904 
 
 .553 973 
 
 .219 5885 
 
 .566 
 
 .680 1052 
 
 .787 460 
 
 .208 8790 
 
 .517 
 
 .658 8247 
 
 .558 529 
 
 .219 3690 
 
 .567 
 
 .680 5395 
 
 .792 250 
 
 .2O8 6703 
 
 .518 
 
 .659 2590 
 
 .563 090 
 
 .219 1497 
 
 .568 
 
 .680 9737 
 
 797 045 
 
 .208 4617 
 
 .519 
 
 .659 6933 
 
 .567 655 
 
 .218 9307 
 
 .569 
 
 .681 4080 
 
 .801 844 
 
 .208 2533 
 
 1.520 
 
 o.65o 1276 
 
 4.572 225 
 
 0.218 7119 
 
 1.570 
 
 0.681 8423 
 
 4.806 648 
 
 O.2O8 O452 
 
 .521 
 
 .660 5619 
 
 .576 8bo 
 
 .218 4933 
 
 571 
 
 .682 2766 
 
 .811 457 
 
 .207 8372 
 
 .522 
 
 .660 9962 
 
 .581 379 
 
 .218 2749 
 
 572 
 
 .682 7109 
 
 .816 271 
 
 .207 6295 
 
 .523 
 
 .661 4305 
 
 .585 962 
 
 .218 0567 
 
 573 
 
 .683 1452 
 
 .821 090 
 
 .207 4220 
 
 .524 
 
 .661 8648 
 
 .590 551 
 
 .217 8388 
 
 574 
 
 .683 5795 
 
 .825 913 
 
 .207 2147 
 
 1.525 
 
 0.662 2991 
 
 4.595 144 
 
 0.217 6211 
 
 1-575 
 
 0.684 0138 
 
 4.830 742 
 
 0.207 0076 
 
 .526 
 
 .662 7334 
 
 .599 741 
 
 .217 4035 
 
 .576 
 
 .684 4481 
 
 .835 575 
 
 .206 8006 
 
 .527 
 
 .663 1677 
 
 .604 343 
 
 .217 1862 
 
 577 
 
 .684 8824 
 
 .840 413 
 
 .206 5940 
 
 .528 
 
 .663 6020 
 
 .608 950 
 
 .216 9692 
 
 .578 
 
 .685 3167 
 
 .845 256 
 
 .206 3875 
 
 .529 
 
 .664 0363 
 
 .613 561 
 
 .216 7523 
 
 579 
 
 .685 75io 
 
 .850 103 
 
 .206 1812 
 
 1.530 
 
 0.664 4706 
 
 4.618 177 
 
 0.216 5357 
 
 1.580 
 
 0.686 1853 
 
 4.854 956 
 
 0.205 9751 
 
 .531 
 
 .664 9049 
 
 .622 797 
 
 .216 3192 
 
 .581 
 
 .686 6196 
 
 .859 813 
 
 .205 7692 
 
 .532 
 
 .665 3391 
 
 .627 422 
 
 .216 1030 
 
 .582 
 
 .687 0539 
 
 .864 675 
 
 .205 5636 
 
 533 
 
 .665 7734 
 
 .632 052 
 
 .215 8870 
 
 .583 
 
 .687 4882 
 
 .869 543 
 
 .205 358i 
 
 534 
 
 .666 2077 
 
 .636 687 
 
 .215 6713 
 
 .584 
 
 .687 9225 
 
 .874 415 
 
 .205 1528 
 
 1.535 
 
 0.666 6420 
 
 4.641 326 
 
 0.215 4557 
 
 1.585 
 
 0.688 3568 
 
 4.879 291 
 
 0.204 9478 
 
 .536 
 
 .667 0763 
 
 .645 969 
 
 .215 2403 
 
 .586 
 
 .688 7910 
 
 .884 173 
 
 .204 7429 
 
 537 
 
 .667 5106 
 
 .650 617 
 
 .215 02.52 
 
 .587 
 
 .689 2253 
 
 .889 060 
 
 .204 5383 
 
 .538 
 
 .667 9449 
 
 .655 270 
 
 .214 8103 
 
 .588 
 
 .689 6596 
 
 .893 951 
 
 .204 3339 
 
 .539 
 
 .668 3792 
 
 .659 928 
 
 .214 5956 
 
 .589 
 
 .690 0939 
 
 .898 848 
 
 .204 1296 
 
 1.540 
 
 0.668 8135 
 
 4.664 590 
 
 0.214 3811 
 
 1.590 
 
 0.690 5282 
 
 4.903 749 
 
 0.203 9256 
 
 541 
 
 .669 2478 
 
 .669 257 
 
 .214 1668 
 
 591 
 
 .690 9625 
 
 .908655 
 
 .203 7218 
 
 .542 
 
 .669 6821 
 
 .673 929 
 
 .213 9528 
 
 .592 
 
 .691 3968 
 
 .913 566 
 
 .203 5182 
 
 .543 
 
 .670 1164 
 
 .678 605 
 
 .213 7389 
 
 .593 
 
 .691 8311 
 
 .918 482 
 
 .203 3148 
 
 .544 
 
 .670 5507 
 
 .683 286 
 
 213 S253 
 
 594 
 
 .692 2654 
 
 .923 403 
 
 .203 1115 
 
 1-545 
 
 0.670 9850 
 
 4.687 972 
 
 0.213 3119 
 
 1-595 
 
 0.692 6997 
 
 4.928 329 
 
 O.2O2 9085 
 
 .546 
 
 .671 4193 
 
 .692 662 
 
 .213 0987 
 
 596 
 
 .693 1340 
 
 .933 260 
 
 .202 7057 
 
 .547 
 
 .671 8536 
 
 .697 357 
 
 .212 8857 
 
 597 
 
 .693 5683 
 
 .938 196 
 
 .202 5031 
 
 .548 
 
 .672 2879 
 
 .702 057 
 
 .212 6729 
 
 .598 
 
 .694 0026 
 
 943 136 
 
 .202 3007 
 
 .549 
 
 .672 7222 
 
 .706 761 
 
 .212 4603 
 
 599 
 
 .694 4369 
 
 .948 082 
 
 .202 0985 
 
 1-550 
 
 0.673 1564 
 
 4.711 470 
 
 O.2I2 2480 
 
 1. 600 
 
 0.694 8712 
 
 4-953 032 
 
 0.201 8965 
 
 log e (e n ) 
 
 looio(e n ) 
 
 e u 
 
 e~ u 
 
 looe(e u ) 
 
 looio(e u ) 
 
 e u 
 
 e~ u 
 
 SMITHSONIAN TABLES 
 
 241 
 
The Exponential. 
 
 u 
 
 Ioo 10 (e u ) 
 
 e u 
 
 e~ u 
 
 u 
 
 looio(e u ) 
 
 e u 
 
 e~ u 
 
 1. 600 
 
 0.694 8712 
 
 4-953 032 
 
 0.201 8965 
 
 1.650 
 
 0.716 5859 
 
 5.206 980 
 
 0. 192 0499 
 
 .601 
 
 .695 3055 
 
 957 988 
 
 .201 6947 
 
 .651 
 
 .717 O202 
 
 .212 189 
 
 .191 8580 
 
 .602 
 
 .695 7398 
 
 .962 948 
 
 .201 4931 
 
 .652 
 
 .717 4545 
 
 .217 404 
 
 .191 6662 
 
 .603 
 
 .696 1741 
 
 .967 9U 
 
 .201 2917 
 
 .653 
 
 .717 8888 
 
 .222 624 
 
 .191 4746 
 
 .604 
 
 .6966083 
 
 .972 884 
 
 .2OI O9O5 
 
 .654 
 
 .718 3231 
 
 .227 849 
 
 .191 2832 
 
 1.605 
 
 0,697 0426 
 
 4.977 860 
 
 0.200 8896 
 
 1.655 
 
 0.718 7574 
 
 5.233 080 
 
 0.191 0921 
 
 .606 
 
 .097 4769 
 
 .982 840 
 
 .200 6888 
 
 .656 
 
 .719 1917 
 
 .238 3l6 
 
 .190 9011 
 
 .607 
 
 .697 9H2 
 
 .987 825 
 
 .200 4882 
 
 .657 
 
 .719 6260 
 
 243 557 
 
 .190 7103 
 
 .608 
 
 .698 3455 
 
 .992 816 
 
 .200 2878 
 
 .658 
 
 .720 0603 
 
 .248 803 
 
 .190 5196 
 
 .609 
 
 .698 7798 
 
 .997 811 
 
 .200 0876 
 
 .659 
 
 .720 4945 
 
 254 054 
 
 .190 3292 
 
 1.610 
 
 0.699 2141 
 
 5.002 811 
 
 o. 109 8876 
 
 1.660 
 
 0.720 9288 
 
 5-259 3ii 
 
 0.190 1300 
 
 .611 
 
 .6996484 
 
 .007 817 
 
 . 199 6878 
 
 .661 
 
 .721 3631 
 
 .264 573 
 
 .1899489 
 
 .612 
 
 .700 0827 
 
 .012 827 
 
 . 199 4882 
 
 .662 
 
 .721 7974 
 
 .269 840 
 
 .189 7591 
 
 .613 
 
 .700 5170 
 
 .017 842 
 
 .199 2888 
 
 .663 
 
 .722 2317 
 
 .275 112 
 
 .189 5694 
 
 .614 
 
 700 9513 
 
 .022 863 
 
 .199 0897 
 
 .664 
 
 .722 6660 
 
 .280 39O 
 
 .189 3799 
 
 1.615 
 
 0.701 3856 
 
 5.027 888 
 
 0.198 8907 
 
 1.665 
 
 0.723 1003 
 
 5.285 673 
 
 0.189 1907 
 
 .616 
 
 .701 8199 
 
 .032 918 
 
 .198 6919 
 
 .666 
 
 .723 5346 
 
 .290 962 
 
 .189 0016 
 
 .617 
 
 .702 2542 
 
 .037 954 
 
 .198 4933 
 
 .667 
 
 .723 9689 
 
 .296 255 
 
 .188 8127 
 
 .618 
 
 .702 6885 
 
 .042 994 
 
 .198 2949 
 
 .668 
 
 .724 4032 
 
 .301 554 
 
 . 188 6239 
 
 .619 
 
 .703 1228 
 
 .048 040 
 
 .198 0967 
 
 .669 
 
 .724 8375 
 
 .306858 
 
 .1884354 
 
 1.620 
 
 0.703 5571 
 
 5.053 090 
 
 0.197 8987 
 
 1.670 
 
 0.725 2718 
 
 5.312 168 
 
 o. 188 2471 
 
 .621 
 
 .703 9914 
 
 .058 146 
 
 .197 7009 
 
 .671 
 
 .725 7061 
 
 .317 483 
 
 .188 0589 
 
 .622 
 
 .704 4256 
 
 .063 207 
 
 .197 5033 
 
 .672 
 
 .726 1404 
 
 .322 803 
 
 . 187 8709 
 
 .623 
 
 .704 8599 
 
 .068 272 
 
 .197 3059 
 
 .673 
 
 .726 5747 
 
 .328 128 
 
 . 187 6832 
 
 .624 
 
 .705 2942 
 
 .073 343 
 
 .197 1087 
 
 .674 
 
 .727 0090 
 
 333 459 
 
 . 187 4956 
 
 1.625 
 
 0.705 7285 
 
 5.078 419 
 
 0.196 9117 
 
 1.675 
 
 0.727 4433 
 
 5.338 795 
 
 0.187 3082 
 
 .626 
 
 .706 1628 
 
 .083 500 
 
 .196 7149 
 
 .676 
 
 .727 8776 
 
 344 137 
 
 .187 12 IO 
 
 .627 
 
 .706 5971 
 
 .088 586 
 
 .196 5182 
 
 .677 
 
 .728 3118 
 
 .349 483 
 
 . 186 9339 
 
 .628 
 
 .707 0314 
 
 .093 677 
 
 .196 3218 
 
 .678 
 
 .728 7461 
 
 .354 836 
 
 . 186 7471 
 
 .629 
 
 .707 4657 
 
 .098 773 
 
 .196 1256 
 
 .679 
 
 .729 1804 
 
 .360 193 
 
 .186 5604 
 
 1.630 
 
 0.707 9000 
 
 5.103 875 
 
 0.195 9296 
 
 1.680 
 
 0.729 6147 
 
 5.365 556 
 
 0.186 3740 
 
 .631 
 
 70S 3343 
 
 .108 981 
 
 195 7337 
 
 .681 
 
 .730 0490 
 
 .370 924 
 
 .186 1877 
 
 .632 
 
 .708 7686 
 
 .114 093 
 
 .195 538i 
 
 .682 
 
 730 4833 
 
 .376298 
 
 .186 0016 
 
 .633 
 
 .709 2029 
 
 .119 209 
 
 .195 3427 
 
 .683 
 
 .730 9176 
 
 .381 677 
 
 .185 8157 
 
 .634 
 
 .709 6372 
 
 .124 331 
 
 .195 1474 
 
 .684 
 
 .731 3519 
 
 .387 061 
 
 .185 6300 
 
 1.635 
 
 0.710 0715 
 
 5.129 458 
 
 0.194 9524 
 
 1.685 
 
 0.731 7862 
 
 5.392 451 
 
 0.185 4444 
 
 .636 
 
 .710 5058 
 
 .134 590 
 
 .194 7575 
 
 .686 
 
 .732 2205 
 
 .397 846 
 
 .185 2591 
 
 .637 
 
 .710 9401 
 
 .139 727 
 
 .194 5629 
 
 .687 
 
 .732 6548 
 
 .403 247 
 
 185 0739 
 
 .638 
 
 .711 3744 
 
 .144869 
 
 . 194 3684 
 
 .688 
 
 733 0891 
 
 .408 653 
 
 .1848889 
 
 .639 
 
 .711 8087 
 
 .150 017 
 
 .194 1741 
 
 .689 
 
 733 5234 
 
 .414 064 
 
 .184 7041 
 
 1.640 
 
 0.712 2430 
 
 S.IS5 170 
 
 0.193 9800 
 
 1.690 
 
 0.733 9577 
 
 5.419 48i 
 
 0.184 5195 
 
 .641 
 
 .712 6772 
 
 .100 327 
 
 .193 7802 
 
 .691 
 
 734 3920 
 
 424 903 
 
 184 3351 
 
 .642 
 
 .713 IH5 
 
 .165 490 
 
 193 5925 
 
 .692 
 
 .734 8263 
 
 430 331 
 
 .184 1509 
 
 .643 
 
 .713 5458 
 
 .170 658 
 
 .193 3990 
 
 .693 
 
 .735 2606 
 
 435 764 
 
 .183 9668 
 
 .644 
 
 .713 9801 
 
 .175 831 
 
 .193 2057 
 
 .694 
 
 735 6949 
 
 .441 202 
 
 .183 7829 
 
 i '645 
 
 0.714 4144 
 
 5.181 oio 
 
 0.193 0126 
 
 1.695 
 
 0.736 1291 
 
 5.446 646 
 
 0.183 5992 
 
 .646 
 
 .714 8487 
 
 .186 194 
 
 . 192 8196 
 
 .(*/> 
 
 73<> 5".>l 
 
 45^ 095 
 
 .183 4157 
 
 .647 
 
 .715 2830 
 
 .191 382 
 
 .192 6269 
 
 .697 
 
 .736 9977 
 
 457 550 
 
 .183 -'3-'4 
 
 .648 
 
 .715 7173 
 
 .106 576 
 
 .192 4344 
 
 .698 
 
 .737 4320 
 
 .463 oio 
 
 . 18;, 
 
 .649 
 
 .716 1516 
 
 .201 775 
 
 .192 2421 
 
 .699 
 
 737 8663 
 
 .468 476 
 
 . 182 8663 
 
 1.650 
 
 0.716 5859 
 
 5.206 980 
 
 0.192 0499 
 
 1.700 
 
 0.738 3006 
 
 5-473 947 
 
 0.182 6835 
 
 loo,(e u ) 
 
 loQicXe") 
 
 e" 
 
 e~ u 
 
 looo(e u ) 
 
 loo,,Xe u ) 
 
 e tt 
 
 e~ u 
 
 SMITHSONIAN TABLES 
 
 242 
 
The Exponential. 
 
 u 
 
 looio(e u ) 
 
 e u 
 
 e~ u 
 
 u 
 
 looio(e u ) 
 
 e u 
 
 e~ u 
 
 1.700 
 
 0.738 3006 
 
 5-473 947 
 
 0.182 6835 
 
 1-750 
 
 0.760 0153 
 
 5.754 603 
 
 0.173 7739 
 
 .701 
 
 .738 7349 
 
 .479 424 
 
 .182 5009 
 
 751 
 
 .760 4496 
 
 .760 360 
 
 .173 6003 
 
 .702 
 
 .739 1692 
 
 .484 906 
 
 .182 3185 
 
 752 
 
 .760 8839 
 
 .766 123 
 
 .173 4267 
 
 .703 
 
 .739 6o35 
 
 490 394 
 
 .182 1363 
 
 753 
 
 .761 3182 
 
 .771 892 
 
 .173 2534 
 
 .704 
 
 .740 0378 
 
 -495 887 
 
 .181 9542 
 
 754 
 
 .761 7525 
 
 .777 667 
 
 .173 0802 
 
 1.705 
 
 0.740 4721 
 
 5.501 386 
 
 0.181 7724 
 
 1.755 
 
 0.762 1868 
 
 5.783 448 
 
 0.172 9072 
 
 .706 
 
 .740 9064 
 
 .506 890 
 
 .181 5907 
 
 .756 
 
 .762 6211 
 
 .789 234 
 
 .172 7344 
 
 .707 
 
 .741 3407 
 
 .512 399 
 
 .181 4092 
 
 757 
 
 .763 0554 
 
 .795 026 
 
 .172 5618 
 
 .708 
 
 .741 7750 
 
 .517 915 
 
 .181 2279 
 
 .758 
 
 .763 4897 
 
 .800 824 
 
 .172 3893 
 
 .709 
 
 .742 2093 
 
 .523 435 
 
 .181 0467 
 
 759 
 
 .763 9240 
 
 .806 628 
 
 .172 2170 
 
 I.7IO 
 
 0.742 6436 
 
 5.528 961 
 
 0.180 8658 
 
 1.760 
 
 0.764 3583 
 
 5.812 437 
 
 0.172 0449 
 
 .711 
 
 743 0779 
 
 .534 493 
 
 . 180 6850 
 
 .761 
 
 .764 7926 
 
 .818 253 
 
 .171 8729 
 
 .712 
 
 .743 5122 
 
 .540 030 
 
 .180 5044 
 
 .762 
 
 .765 2269 
 
 .824 074 
 
 .171 7011 
 
 .713 
 
 743 9464 
 
 545 573 
 
 .180 3240 
 
 .763 
 
 .765 6612 
 
 .829 901 
 
 .171 5295 
 
 .714 
 
 .744 3807 
 
 55 1 I22 
 
 .180 1438 
 
 .764 
 
 .766 0955 
 
 .835 734 
 
 .171 358i 
 
 I.7I5 
 
 0.744 8150 
 
 5.556 676 
 
 0.179 9637 
 
 1.765 
 
 0.766 5298 
 
 5.841 572 
 
 0.171 1868 
 
 .7J6 
 
 .745 2493 
 
 .562 235 
 
 .179 7838 
 
 .766 
 
 .766 9641 
 
 .847 417 
 
 .171 0157 
 
 .717 
 
 745 6836 
 
 .567 800 
 
 .179 6042 
 
 .767 
 
 .767 3983 
 
 .853 267 
 
 .170 8448 
 
 .718 
 
 .746 1179 
 
 573 371 
 
 . 179 4246 
 
 .768 
 
 .767 8326 
 
 .859 123 
 
 .170 6740 
 
 .719 
 
 .746 5522 
 
 .578 947 
 
 . 179 2453 
 
 .769 
 
 .768 2669 
 
 .864 985 
 
 .170 5034 
 
 1.720 
 
 0.746 9865 
 
 5.584 528 
 
 0.179 0661 
 
 1.770 
 
 0.768 7012 
 
 5-870 853 
 
 0.170 3330 
 
 .721 
 
 .747 4208 
 
 .590 116 
 
 . 178 8872 
 
 .771 
 
 .769 1355 
 
 .876 727 
 
 .170 1627 
 
 .722 
 
 .747 8551 
 
 595 709 
 
 . 178 7084 
 
 .772 
 
 .769 5698 
 
 .882 607 
 
 . 169 0927 
 
 .723 
 
 .748 2894 
 
 .601 307 
 
 .178 5298 
 
 773 
 
 .770 0041 
 
 .888 492 
 
 . 169 8228 
 
 .724 
 
 .748 7237 
 
 .606 911 
 
 .178 3513 
 
 .774 
 
 .770 43^4 
 
 .894 384 
 
 .169 6530 
 
 1.725 
 
 0.749 1580 
 
 5.612 521 
 
 0.178 1731 
 
 1.775 
 
 0.770 8727 
 
 5.900 281 
 
 0.169 4834 
 
 .726 
 
 .749 5923 
 
 .618 136 
 
 .177 9950 
 
 776 
 
 771 3070 
 
 .906 184 
 
 .169 3HI 
 
 .727 
 
 .750 0266 
 
 .623 757 
 
 .177 8171 
 
 777 
 
 .771 7413 
 
 .912 094 
 
 .169 1448 
 
 .728 
 
 .750 4609 
 
 .629 384 
 
 . 177 6393 
 
 .778 
 
 .772 1756 
 
 .918 009 
 
 . 168 9758 
 
 .729 
 
 750 8952 
 
 .635 016 
 
 . 177 4618 
 
 779 
 
 .772 6099 
 
 .923 930 
 
 .168 8069 
 
 1.730 
 
 0.751 3295 
 
 5.640 654 
 
 o. 177 2844 
 
 1.780 
 
 0.773 0442 
 
 5.929 856 
 
 o. 168 6381 
 
 731 
 
 .751 7637 
 
 .646 297 
 
 .177 1072 
 
 .781 
 
 773 4785 
 
 935 789 
 
 .168 4696 
 
 732' 
 
 .752 1980 
 
 .651 947 
 
 .176 9302 
 
 .782 
 
 .773 9128 
 
 .941 728 
 
 .168 3012 
 
 733 
 
 .752 6323 
 
 .657 601 
 
 .176 7534 
 
 .783 
 
 774 3471 
 
 947 673 
 
 .168 1330 
 
 734 
 
 .753 0666 
 
 .663 262 
 
 .176 5767 
 
 .784 
 
 .774 7814 
 
 953 623 
 
 . 167 9649 
 
 I 735 
 
 0-753 5009 
 
 5,668 928 
 
 0.176 4002 
 
 1.785 
 
 0.775 2157 
 
 5.959 580 
 
 0.167 797i 
 
 .736 
 
 753 9352 
 
 .674 600 
 
 .176 2239 
 
 .786 
 
 .775 6499 
 
 .965 543 
 
 .107 6293 
 
 .737 
 
 754 3695 
 
 .680 277 
 
 .176 0478 
 
 .787 
 
 .776 0842 
 
 971 5ii 
 
 .167 4618 
 
 .738 
 
 .754 8038 
 
 .685 060 
 
 .175 8718 
 
 .788 
 
 .776 5185 
 
 .977 486 
 
 .167 2944 
 
 .739 
 
 .755 2381 
 
 .691 649 
 
 .175 6960 
 
 .789 
 
 .776 9528 
 
 .983466 
 
 .167 1272 
 
 1.740 
 
 0.755 6724 
 
 5.697 343 
 
 0.175 5204 
 
 1.790 
 
 0.777 3871 
 
 5.989 452 
 
 0.166 9602 
 
 .741 
 
 .756 1067 
 
 .703 044 
 
 .175 3450 
 
 .791 
 
 .777 8214 
 
 995 445 
 
 .166 7933 
 
 .742 
 
 .756 5410 
 
 .708 750 
 
 .175 1697 
 
 .792 
 
 .778 2557 
 
 6.001 443 
 
 . 166 6266 
 
 743 
 
 .756 9753 
 
 .714 461 
 
 .174 9946 
 
 .793 
 
 .778 6900 
 
 .007 448 
 
 .166 4600 
 
 744 
 
 .757 4096 
 
 .720 178 
 
 .174 8197 
 
 794 
 
 .779 1243 
 
 .013 458 
 
 . 166 2937 
 
 1.745 
 
 0.757 8439 
 
 5.725 901 
 
 o. 174 6450 
 
 1.795 
 
 0.779 5586 
 
 6.019 475 
 
 0.166 1275 
 
 .746 
 
 .758 2782 
 
 731 630 
 
 .174 4704 
 
 .796 
 
 779 9929 
 
 .025 497 
 
 .165 9614 
 
 * -747 
 
 .758 7125 
 
 737 365 
 
 .174 2960 
 
 797 
 
 .780 4272 
 
 .031 526 
 
 .165 7955 
 
 ^ .748 
 
 .759 1468 
 
 743 105 
 
 .174 1218 
 
 .798 
 
 .780 8615 
 
 .037 56o 
 
 .165 6298 
 
 .749 
 
 759 58io 
 
 .748 851 
 
 173 9478 
 
 799 
 
 .781 2958 
 
 .043 601 
 
 .165 4643 
 
 1-750 
 
 0.760 0153 
 
 5.754 603 
 
 0.173 7739 
 
 1.800 
 
 0.781 7301 
 
 6.049 647 
 
 0.165 2989 
 
 log e (e u ) 
 
 looio(e u ) 
 
 e u 
 
 e~ u 
 
 looe(e u ) 
 
 logio(e u ) 
 
 e u 
 
 e~ u 
 
 SMITHSONIAN TABLES 
 
 243 
 
The Exponential. 
 
 u 
 
 looio(e u ) 
 
 e" 
 
 e 
 
 u 
 
 Iog 10 (e a ) 
 
 e 
 
 e~ u 
 
 1.800 
 
 0.781 7301 
 
 6.049 647 
 
 0.165 2989 
 
 1.850 
 
 0.803 4448 
 
 6.359 820 
 
 0.157 2372 
 
 .801 
 
 .782 1644 
 
 .055 700 
 
 .165 1337 
 
 ' .851 
 
 .803 8791 
 
 .366 183 
 
 .157 0800 
 
 .802 
 
 .782 5587 
 
 .061 759 
 
 .164 9686 
 
 .852 
 
 .804 3134 
 
 372 552 
 
 .156 9230 
 
 .803 
 
 .783 0330 
 
 .067 824 
 
 . 164 8037 
 
 .853 
 
 .804 7477 
 
 .378 928 
 
 .156 7662 
 
 .804 
 
 .783 4672 
 
 .073 895 
 
 . 164 6390 
 
 .854 
 
 .805 1820 
 
 -385 310 
 
 .156 6095 
 
 1.805 
 
 0.783 9015 
 
 6.079 971 
 
 0. 164 4745 
 
 1.855 
 
 0.805 6163 
 
 6.391 698 
 
 0.156 4529 
 
 .806 
 
 .784 3358 
 
 .086 054 
 
 .164 3101 
 
 .856 
 
 .806 0506 
 
 .398 093 
 
 .156 2966 
 
 .807 
 
 .784 7701 
 
 .092 144 
 
 .164 1458 
 
 .857 
 
 .806 4849 
 
 .404 494 
 
 .156 1403 
 
 .808 
 
 .785 2044 
 
 .098 239 
 
 .163 9818 
 
 .858 
 
 .806 9191 
 
 .410 902 
 
 .155 9843 
 
 .809 
 
 .785 6387 
 
 .104 340 
 
 .163 8179 
 
 .859 
 
 .807 3534 
 
 .417 316 
 
 .155 8284 
 
 1.810 
 
 0.786 0730 
 
 6. I 10 447 
 
 0.163 6541 
 
 1.860 
 
 0.807 7877 
 
 6.423 737 
 
 0.155 6726 
 
 .811 
 
 .786 5073 
 
 .116 561 
 
 .163 4906 
 
 .861 
 
 .808 2220 
 
 .430 164 
 
 .155 5170 
 
 .812 
 
 .786 9416 
 
 .122 68l 
 
 .163 3272 
 
 .862 
 
 .808 6563 
 
 .436 597 
 
 .155 3616 
 
 .813 
 
 .787 3759 
 
 .128 806 
 
 .163 1639 
 
 .863 
 
 .809 0906 
 
 443 037 
 
 .155 2063 
 
 .814 
 
 .787 8102 
 
 .134 938 
 
 .163 0008 
 
 .864 
 
 .809 5249 
 
 .449 483 
 
 .155 0512 
 
 1.815 
 
 0.788 2445 
 
 6.141 076 
 
 0.162 8379 
 
 1.865 
 
 0.809 9592 
 
 6.455 936 
 
 0.154 8962 
 
 .816 
 
 .788 6788 
 
 .147 220 
 
 .162 6752 
 
 .866 
 
 .810 3935 
 
 462 395 
 
 .154 7414 
 
 .817 
 
 .789 H3I 
 
 153 371 
 
 .162 5126 
 
 .867 
 
 .810 8278 
 
 .468 861 
 
 . 154 5867 
 
 .818 
 
 .789 5474 
 
 .159 527 
 
 .162 3501 
 
 .868 
 
 .811 2621 
 
 475 333 
 
 . 154 4322 
 
 .819 
 
 .789 98i7 
 
 .165 690 
 
 .162 1879 
 
 .869 
 
 .811 6964 
 
 .481 811 
 
 . 154 2779 
 
 1.820 
 
 0.790 4160 
 
 6.171 858 
 
 0.162 0258 
 
 1.870 
 
 0.812 1307 
 
 6.488 296 
 
 0.154 1237 
 
 .821 
 
 .790 8503 
 
 . 178 033 
 
 .161 8638 
 
 ..871 
 
 .812 5650 
 
 .494 788 
 
 153 9696 
 
 .822 
 
 .791 2845 
 
 .184 215 
 
 .161 7020 
 
 .872 
 
 .812 9093 
 
 .501 286 
 
 .153 8157 
 
 .823 
 
 .791 7188 
 
 .190 402 
 
 .161 5404 
 
 .873 
 
 813 4336 
 
 .507 791 
 
 .153 6620 
 
 .824 
 
 792 1531 
 
 .196 595 
 
 .161 3789 
 
 .874 
 
 .813 8679 
 
 .514 302 
 
 .153 5084 
 
 1.825 
 
 0.792 5874 
 
 6. 202 795 
 
 0.161 2176 
 
 1.875 
 
 0.814 3022 
 
 6.520 819 
 
 0.153 3550 
 
 .826 
 
 .793 0217 
 
 .209 ooi 
 
 .161 0565 
 
 .876 
 
 .814 7364 
 
 .527 343 
 
 .153 2017 
 
 .827 
 
 793 4500 
 
 .215 213 
 
 . 160 8955 
 
 .877 
 
 .815 1707 
 
 533 874 
 
 .153 0486 
 
 .828 
 
 .793 8903 
 
 .221 431 
 
 .160 7347 
 
 .878 
 
 .815 6050 
 
 .540 411 
 
 .152 8956 
 
 .829 
 
 .794 3246 
 
 .227 656 
 
 .160 5741 
 
 .879 
 
 .816 0393 
 
 .546 955 
 
 .152 7428 
 
 1.830 
 
 0.794 7589 
 
 6.233 887 
 
 0.160 4136 
 
 1.880 
 
 0.816 4736 
 
 6.553 505 
 
 0.152 5901 
 
 .831 
 
 795 1932 
 
 .240 124 
 
 .160 2532 
 
 .881 
 
 .816 9079 
 
 .560 062 
 
 152 4376 
 
 .832 
 
 .795 6275 
 
 .246 367 
 
 .160 0931 
 
 .882 
 
 .817 3422 
 
 .566 625 
 
 .152 2852 
 
 .833 
 
 .796 0618 
 
 .252 616 
 
 . 159 9330 
 
 .883 
 
 .817 7765 
 
 573 195 
 
 .152 1330 
 
 .834 
 
 .796 4961 
 
 .258 872 
 
 .159 7732 
 
 .884 
 
 .818 2108 
 
 579 771 
 
 .151 9810 
 
 1.835 
 
 0.796 9304 
 
 6.265 134 
 
 o. 159 6135 
 
 1.885 
 
 0.818 6451 
 
 6.586 354 
 
 0.151 8291 
 
 .836 
 
 797 3647 
 
 .271 402 
 
 .159 4540 
 
 .886 
 
 .819 0794 
 
 .592 944 
 
 .151 677J 
 
 .837 
 
 797 7990 
 
 .277 677 
 
 .159 2946 
 
 .887 
 
 .819 5137 
 
 599 540 
 
 151 5257 
 
 .838 
 
 .798 2333 
 
 .283 958 
 
 .159 1354 
 
 .888 
 
 .819 9480 
 
 .606 143 
 
 .151 3743 
 
 .839 
 
 .798 6676 
 
 .290 245 
 
 .158 9763 
 
 .889 
 
 .820 3823 
 
 .612 753 
 
 .151 2230 
 
 1.840 
 
 0.799 1018 
 
 6.296 538 
 
 0.158 8174 
 
 1.890 
 
 0.820 8166 
 
 6.619 369 
 
 0.151 0718 
 
 .841 
 
 799 536i 
 
 .302 838 
 
 .158 6587 
 
 .891 
 
 .821 2509 
 
 .625 991 
 
 .150 9208 
 
 .842 
 
 799 9704 
 
 .309 M4 
 
 .158 5001 
 
 .892 
 
 .821 6852 
 
 .632 621 
 
 . 150 7700 
 
 .843 
 
 .800 J047 
 
 .315 456 
 
 .158 3417 
 
 .893 
 
 .822 1195 
 
 .639 257 
 
 .150 6193 
 
 .844 
 
 .800 8390 
 
 .321 775 
 
 .158 1834 
 
 .894 
 
 .822 5537 
 
 .645 899 
 
 . 150 4687 
 
 1.845 
 
 0.801 2733 
 
 6.328 loo 
 
 0.158 0253 
 
 1.895 
 
 0.822 9880 
 
 6.652 548 
 
 0.150 3183 
 
 .846 
 
 .801 7076 
 
 334 43i 
 
 .157 8'>74 
 
 .896 
 
 .823 4223 
 
 .659 204 
 
 .150 1681 
 
 .847 
 
 .802 1419 
 
 340 769 
 
 .157 7096 
 
 .897 
 
 .823 8566 
 
 .665 867 
 
 .150 0180 
 
 .848 
 
 .802 5762 
 
 347 H3 
 
 .157 5520 
 
 .898 
 
 .824 2909 
 
 .672 536 
 
 . 149 8681 
 
 .849 
 
 .803 0105 
 
 353 463 
 
 .157 3945 
 
 .899 
 
 .824 7252 
 
 .679 212 
 
 .149 7183 
 
 1.850 
 
 0.803 4448 
 
 6.359 820 
 
 0.157 2372 
 
 1.900 
 
 0.825 1595 
 
 6.685 804 
 
 0.149 5686 
 
 log.V) 
 
 looir/e ) 
 
 6 
 
 e- n 
 
 IOQe(e U ) 
 
 KxMe") 
 
 e u 
 
 e~ u 
 
 SMITHSONIAN TABLES 
 
 244 
 
The Exponential. 
 
 u 
 
 looio(e n ) 
 
 e u 
 
 e~ u 
 
 u 
 
 loaio(e) 
 
 e n 
 
 e~ u 
 
 1.900 
 
 0.825 1595 
 
 6.685 894 
 
 0.149 5686 
 
 1.950 
 
 0.846 8742 
 
 7.028688 
 
 0.142 2741 
 
 .001 
 
 825 5938 
 
 .692 584 
 
 . 149 4191 
 
 951 
 
 .847 3085 
 
 .035 720 
 
 .142 1319 
 
 .902 
 
 .826 0281 
 
 .699 280 
 
 .149 2698 
 
 952 
 
 .847 7428 
 
 .042 759 
 
 .141 9898 
 
 .003 
 
 .826 4624 
 
 .705 082 
 
 .149 1206 
 
 .953 
 
 .848 1771 
 
 .049 805 
 
 .141 8479 
 
 .004 
 
 .826 8967 
 
 .712 692 
 
 .148 9715 
 
 954 
 
 .848 6114 
 
 .056 859 
 
 .141 7061 
 
 1.905 
 
 0.827 3310' 
 
 6.719 408 
 
 0.148 8226 
 
 1.955 
 
 0.849 0457 
 
 7.063 919 
 
 0.141 5645 
 
 .906 
 
 .827 7653 
 
 .726 130 
 
 . 148 6739 
 
 .956 
 
 .849 4800 
 
 .070 986 
 
 .141 4230 
 
 .907 
 
 .828 1096 
 
 .732 860 
 
 . 148 5253 
 
 .957 
 
 .849 9143 
 
 .078 061 
 
 .141 2816 
 
 .908 
 
 .828 6339 
 
 739 596 
 
 148 3768 
 
 958 
 
 .850 3486 
 
 .085 143 
 
 .141 1404 
 
 .909 
 
 .829 0682 
 
 .746 339 
 
 .148 2285 
 
 959 
 
 .850 7829 
 
 .092 231 
 
 .140 9993 
 
 I.9IO 
 
 0.829 5025 
 
 6.753 089 
 
 0.148 0804 
 
 1.960 
 
 0.851 2172 
 
 7.099 327 
 
 0.140 8584 
 
 .911 
 
 .829 9368 
 
 759 845 
 
 .147 9324 
 
 .961 
 
 .851 6515 
 
 .106 430 
 
 .140 7176 
 
 .912 
 
 .830 3710 
 
 .766 608 
 
 .147 7845 
 
 .962 
 
 .852 0858 
 
 .113 540 
 
 .140 5770 
 
 .913 
 
 .830 8053 
 
 .773 378 
 
 . 147 6368 
 
 .963 
 
 .852 5201 
 
 .120 657 
 
 . 140 4365 
 
 .914 
 
 .831 2396 
 
 .780 155 
 
 .147 4892 
 
 .964 
 
 .852 9544 
 
 .127 781 
 
 .140 2961 
 
 I.9I5 
 
 0.831 6739 
 
 6.786 939 
 
 0.147 34l8 
 
 1.965 
 
 0.853 3887 
 
 7.I349I3 
 
 0.140 1559 
 
 .916 
 
 .832 1082 
 
 793 729 
 
 .147 1946 
 
 .966 
 
 .853 8230 
 
 .142 051 
 
 .140 0158 
 
 .917 
 
 .832 5425 
 
 .800 526 
 
 .147 0474 
 
 .967 
 
 .854 2572 
 
 .149 197 
 
 .139 8759 
 
 .918 
 
 .832 9768 
 
 .807 330 
 
 .146 0005 
 
 .968 
 
 .854 6915 
 
 .156 349 
 
 .139 7300 
 
 .919 
 
 .833 4IH 
 
 .814 141 
 
 .146 7536 
 
 .969 
 
 .855 1258 
 
 .163 509 
 
 .139 596"4 
 
 1.920 
 
 0.833 8454 
 
 6.820 958 
 
 0.146 6070 
 
 1.970 
 
 0.855 5601 
 
 7.170 676 
 
 0.139 4569 
 
 .921 
 
 .834 2797 
 
 .827 783 
 
 .146 4604 
 
 .971 
 
 .855 9944 
 
 177 851 
 
 .139 3175 
 
 .922 
 
 .834 7140 
 
 .834 614 
 
 .146 3140 
 
 .972 
 
 .856 4287 
 
 .185 032 
 
 .139 1782 
 
 923 
 
 .835 1483 
 
 .841 452 
 
 .146 1678 
 
 973 
 
 .856 8630 
 
 . 192 221 
 
 . 139 0391 
 
 .924 
 
 .835 5826 
 
 .848 297 
 
 .146 0217 
 
 974 
 
 .857 2973 
 
 .199 417 
 
 .138 9001 
 
 1.925 
 
 0.836 0169 
 
 6.855 149 
 
 0.145 8758 
 
 1.975 
 
 0.857 73l6 
 
 7.206 620 
 
 0.138 7613 
 
 .926 
 
 .836 4512 
 
 .862 007 
 
 .145 7300 
 
 976 
 
 .858 1659 
 
 .213 830 
 
 . 138 6226 
 
 .927 
 
 .836 8855 
 
 .868 873 
 
 .145 5843 
 
 977 
 
 .858 6002 
 
 .221 O47 
 
 . 138 4841 
 
 .928 
 
 .837 3198 
 
 .875 745 
 
 .145 4388 
 
 .978 
 
 .859 0345 
 
 .228 272 
 
 . 138 3457 
 
 .929 
 
 837 7541 
 
 .882 624 
 
 .145 2934 
 
 979 
 
 .859 4688 
 
 .235 504 
 
 .138 2074 
 
 1.930 
 
 0.838 1884 
 
 6.889 5io 
 
 0.145 1482 
 
 1.980 
 
 0.859 9031 
 
 7.242 743 
 
 0. 138 0692 
 
 931 
 
 .838 6226 
 
 .896 403 
 
 .145 0031 
 
 .981 
 
 .860 3374 
 
 .249 989 
 
 .137 9312 
 
 932 
 
 .839 0569 
 
 .903 303 
 
 . 144 8582 
 
 .982 
 
 .860 7717 
 
 .257 243 
 
 .137 7934 
 
 933 
 
 .839 4912 
 
 .9IO 2IO 
 
 .144 7134 
 
 .983 
 
 .861 2060 
 
 .264 504 
 
 .137 6557 
 
 934 
 
 839 9255 
 
 .917 123 
 
 .144 5688 
 
 .984 
 
 .861 6403 
 
 .271 772 
 
 .137 5i8i 
 
 1-935 
 
 0.840 3598 
 
 6.924 044 
 
 0. 144 4243 
 
 1.985 
 
 0.862 0745 
 
 7.279 047 
 
 0.137 3806 
 
 .936 
 
 .840 7941 
 
 .930 972 
 
 .144 2799 
 
 .986 
 
 .862 5088 
 
 .286 330 
 
 137 2433 
 
 937 
 
 .841 2284 
 
 .937 90-5 
 
 .144 1357 
 
 .987 
 
 .862 9431 
 
 .293 620 
 
 .137 1061 
 
 .938 
 
 .841 6627 
 
 .944 847 
 
 .143 99i6 
 
 .988 
 
 863 3774 
 
 .300 917 
 
 .136 0691 
 
 939 
 
 .842 0970 
 
 .951 796 
 
 .143 8477 
 
 .989 
 
 .863 8117 
 
 .308 222 
 
 . 136 8322 
 
 1.940 
 
 0.842 5313 
 
 6.958 751 
 
 0.143 7039 
 
 1.990 
 
 0.864 2460 
 
 7.315 534 
 
 0.136 6954 
 
 .941 
 
 .842 9656 
 
 .965 713 
 
 .143 5603 
 
 .991 
 
 .864 6803 
 
 .322 853 
 
 .136 5588 
 
 .942 
 
 .843 3999 
 
 .972 682 
 
 .143 4168 
 
 992 
 
 .865 1146 
 
 330 179 
 
 . 136 4223 
 
 943 
 
 .843 8342 
 
 979 659 
 
 .143 2735 
 
 993 
 
 .865 5489 
 
 337 513 
 
 .136 2860 
 
 .944 
 
 .844 2685 
 
 .986 642 
 
 .143 1303 
 
 .994 
 
 .865 9832 
 
 .344 854 
 
 .136 1497 
 
 1.945 
 
 0.844 7028 
 
 6.993 632 
 
 0.142 0872 
 
 1.995 
 
 0.866 4175 
 
 7.352 203 
 
 0.136 0137 
 
 .946 
 
 .845 I37 1 
 
 7.000 629 
 
 .142 8443 
 
 .996 
 
 .866 8518 
 
 359 559 
 
 .135 8777 
 
 947 
 
 .845 5714 
 
 .007 633 
 
 .142 7015 
 
 997 
 
 .867 2861 
 
 .366 922 
 
 .135 7419 
 
 .948 
 
 .846 0057 
 
 .014 644 
 
 .142 5589 
 
 .998 
 
 .867 7204 
 
 374 293 
 
 .135 6062 
 
 .949 
 
 .846 4399 
 
 .021 662 
 
 .142 4164 
 
 .999 
 
 .868 1547 
 
 .381 671 
 
 .135 4707 
 
 1.950 
 
 0.846 8742 
 
 7.028 688 
 
 0.142 2741 
 
 2.OOO 
 
 0.868 5890 
 
 7.389 056 
 
 O.I3S 3353 
 
 log e (e u ) 
 
 looio(e u ) 
 
 e u 
 
 e~ u 
 
 lo fle (e u ) 
 
 looio(e u ) 
 
 e u 
 
 e~ u 
 
 SMITHSONIAN TABLES 
 
 245 
 
The Exponential. 
 
 u 
 
 looio(e u ) 
 
 e u 
 
 e- u 
 
 u 
 
 looio(e u ) 
 
 e u 
 
 e~ u 
 
 2.OOO 
 
 0.868 5890 
 
 7.389 056 
 
 0.135 3353 
 
 2.050 
 
 0.890 3037 
 
 7.767 901 
 
 0.128 7349 
 
 .OOI 
 
 .869 0233 
 
 .396 449 
 
 .135 2000 
 
 .051 
 
 .890 738a 
 
 775 673 
 
 .128 6062 
 
 .OO2 
 
 .003 
 
 .869 4576 
 .8698918 
 
 .403 849 
 .411 257 
 
 .135 0649 
 .134 9299 
 
 .052 
 053 
 
 891 1723 
 .891 6066 
 
 783 452 
 .791 240 
 
 . 128 4777 
 .128 3493 
 
 .004 
 
 .870 3261 
 
 .418 672 
 
 134 7950 
 
 054 
 
 .892 0409 
 
 799 035 
 
 .128 22 10 
 
 2.005 
 
 0.870 7604 
 
 7.426 094 
 
 o. 134 6603 
 
 2.055 
 
 0.892 4752 
 
 7.806 838 
 
 0.128 0928 
 
 .006 
 
 .871 1947 
 
 433 524 
 
 .134 5257 
 
 .056 
 
 .892 9095 
 
 .814 649 
 
 .127 9648 
 
 .007 
 
 .871 6290 
 
 .440 961 
 
 .134 3912 
 
 057 
 
 893 3437 
 
 .822 467 
 
 .127 8369 
 
 .008 
 
 .872 0633 
 
 .448 406 
 
 .134 2569 
 
 .058 
 
 .893 778o 
 
 .830 294 
 
 .127 7091 
 
 .009 
 
 .872 4976 
 
 .455 858 
 
 .134 1227 
 
 .059 
 
 .894 2123 
 
 .838 128 
 
 .127 5815 
 
 2.OIO 
 .Oil 
 
 0.872 9319 
 .873 3662 
 
 7.463 317 
 .470 784 
 
 0.133 9887 
 .133 8548 
 
 2.060 
 .061 
 
 0.894 6466 
 .895 0809 
 
 7.845 970 
 .853 820 
 
 0.127 4540 
 .127 3266 
 
 .OI2 
 
 .873 8005 
 
 .478 259 
 
 .133 7210 
 
 .062 
 
 .895 5152 
 
 .861 677 
 
 .127 1993 
 
 .013 
 
 .874 2348 
 
 .485 74i 
 
 .133 5873 
 
 .063 
 
 895 9495 
 
 .869 543 
 
 .127 0722 
 
 .014 
 
 .874 6691 
 
 .493 230 
 
 .133 4538 
 
 .064 
 
 .896 3838 
 
 .877 417 
 
 . 126 9452 
 
 2.015 
 
 0.875 1034 
 
 7.500 727 
 
 0.133 3204 
 
 2.065 
 
 0.896 8181 
 
 7.885 298 
 
 0.126 8183 
 
 .016 
 
 .875 5377 
 
 .508 232 
 
 .133 1871 
 
 .066 
 
 .897 2524 
 
 .893 187 
 
 .126 6915 
 
 .017 
 
 .875 9720 
 
 .515 744 
 
 .133 0540 
 
 .067 
 
 .897 6867 
 
 .901 084 
 
 .126 5649 
 
 .018 
 
 .876 4063 
 
 .523 263 
 
 .132 9210 
 
 .068 
 
 .898 1210 
 
 .908 989 
 
 .126 4384 
 
 .OIp 
 
 .876 8406 
 
 530 790 
 
 .132 7882 
 
 .069 
 
 ' .898 5553 
 
 .916 902 
 
 .126 3120 
 
 2.020 
 
 0.877 2749 
 
 7.538 325 
 
 o. 132 6555 
 
 2.070 
 
 0.898 9896 
 
 7.924 823 
 
 0.126 1858 
 
 .021 
 
 .877 7091 
 
 .545 867 
 
 .132 5229 
 
 .071 
 
 .899 4239 
 
 932 752 
 
 .126 0597 
 
 .022 
 
 .878 1434 
 
 553 417 
 
 .132 3904 
 
 .072 
 
 .899 8582 
 
 .940 689 
 
 .125 9337 
 
 .023 
 
 .878 5777 
 
 .560 974 
 
 .132 2581 
 
 073 
 
 .900 2925 
 
 948 633 
 
 .125 8078 
 
 .024 
 
 .879 0120 
 
 .568 539 
 
 .132 1259 
 
 .074 
 
 .900 7268 
 
 .956 586 
 
 .125 6820 
 
 2.O25 
 
 0.879 4463 
 
 7.576 III 
 
 0.131 9938 
 
 2.075 
 
 0.901 1610 
 
 7.964 546 
 
 0.125 5564 
 
 .026 .879 8806 
 
 .583 691 
 
 .131 8619 
 
 .076 
 
 .901 5953 
 
 972 515 
 
 .125 4309 
 
 .027 | .880 3M9 
 
 .591 278 
 
 .131 73oi 
 
 077 
 
 .902 0296 
 
 .980 491 
 
 .125 3056 
 
 .028 .880 7492 
 
 .598 873 
 
 .131 5985 
 
 .078 
 
 .902 4639 
 
 .988476 
 
 .125 1803 
 
 .029 
 
 .881 1835 
 
 .606 476 
 
 .131 4669 
 
 .079 
 
 .902 8982 
 
 .996468 
 
 .125 0552 
 
 2.030 
 
 0.881 6178 
 
 7.614 086 
 
 0.131 3355 
 
 2.080 
 
 0.903 3325 
 
 8.004 469 
 
 0. 124 9302 
 
 .031 
 
 .882 0521 
 
 .621 704 
 
 .131 2043 
 
 .081 
 
 .903 7668 
 
 .012 477 
 
 . 124 8053 
 
 .032 
 
 .882 4864 
 
 .629 330 
 
 .131 0731 
 
 .082 
 
 .904 201 1 .020 494 
 
 .124 6806 
 
 033 
 
 .882 9207 
 
 .636 963 
 
 .130 9421 
 
 .083 
 
 .904 6354 
 
 .028 518 
 
 .124 5560 
 
 034 
 
 .883 3550 
 
 .644 604 
 
 .130 8112 
 
 .084 
 
 .905 0697 
 
 .036 551 
 
 .124 4315 
 
 2.035 
 
 0.883 7893 
 
 7.652 252 
 
 0.130 6805 
 
 2.085 
 
 0.905 5040 
 
 8.044 591 
 
 0.124 3071 
 
 .036 
 
 .884 2236 
 
 .659 9o8 
 
 . 130 5499 
 
 .086 
 
 .905 9383 
 
 .052 640 
 
 .124 1829 
 
 037 
 
 .884 6579 
 
 .667 572 
 
 .130 4194 
 
 .087 
 
 .906 3726 
 
 .060 697 
 
 . 124 0588 
 
 .038 
 
 .885 0922 
 
 .675 243 
 
 .130 2890 
 
 .088 
 
 .906 8069 
 
 .068 761 
 
 . 123 9348 
 
 039 
 
 .885 5264 
 
 .682 922 
 
 .130 1588 
 
 .089 
 
 .907 2412 
 
 .076 834 
 
 .123 8109 
 
 2.040 
 
 0.885 96o7 
 
 7.690 609 
 
 0.130 0287 
 
 2.090 
 
 0.907 6755 
 
 8.084 915 
 
 0.123 6871 
 
 .041 
 
 .886 3950 
 
 .698 304 
 
 .1298987 
 
 .091 
 
 .908 1098 
 
 .093 004 
 
 .123 5635 
 
 .042 
 
 .8868293 
 
 .706 006 
 
 .129 7689 
 
 .092 
 
 .908 5441 
 
 .IOI IOI 
 
 .123 4400 
 
 043 
 
 .887 2636 
 
 .713 7i6 
 
 .129 6392 
 
 .093 
 
 .908 9784 
 
 .109 206 
 
 .123 3166 
 
 .044 
 
 .887 6979 
 
 .721 433 
 
 .129 5096 
 
 .094 
 
 .909 4126 
 
 .117 320 
 
 .123 1934 
 
 2.045 
 
 0.888 1322 
 
 7.729 159 
 
 0.129 3802 
 
 2.095 
 
 0.909 8469 
 
 8.125 441 
 
 0.123 0702 
 
 .046 
 
 .888 5665 
 
 .736 892 
 
 . 129 2509 
 
 .096 
 
 .910 2812 
 
 133 570 
 
 . 122 9472 
 
 .047 
 
 .889 0008 
 
 .744 632 
 
 .129 1217 
 
 .097 
 
 .910 7155 
 
 .141 708 
 
 . 122 8243 
 
 .048 
 
 889 4351 
 
 752 381 
 
 .128 9926 
 
 .098 
 
 .911 1498 
 
 . 149 854 
 
 .122 7016 
 
 .049 
 
 .8898694 
 
 .760 137 
 
 .1288637 
 
 .099 
 
 .911 5841 
 
 .158 008 
 
 .122 5789 
 
 2.050 
 
 0.890 3037 
 
 7.767 901 
 
 0.128 7349 
 
 2.100 
 
 0.912 0184 
 
 8.166 170 
 
 0.122 4564 
 
 loo,-(e u ) 
 
 loo,,Xe a ) 
 
 6 
 
 a"" 
 
 log,fe") 
 
 looio(e u ) 
 
 e tt 
 
 e~ u 
 
 SMITHSONIAN TABLES 
 
The Exponential. 
 
 u 
 
 looio(e u ) 
 
 e u 
 
 e 
 
 u 
 
 loflio(e u ) 
 
 e u 
 
 e- a 
 
 2.IOO 
 
 0.912 0184 
 
 8.166 170 
 
 0.122 4564 
 
 2.150 
 
 0.933 7331 
 
 8.584 858 
 
 0.116 4842 
 
 .IOI 
 
 .912 4527 
 
 .174 340 
 
 .122 3340 
 
 .151 
 
 .934 1674 
 
 593 448 
 
 .116 3677 
 
 .IO2 
 
 .912 8870 
 
 .182 519 
 
 .122 2Il8 
 
 .152 
 
 .934 6017 
 
 .602 045 
 
 .116 2514 
 
 .103 
 
 .913 3213 
 
 .190 705 
 
 .122 0896 
 
 .153 
 
 .935 0360 
 
 .610 652 
 
 .116 1352 
 
 .104 
 
 .913 7SS6 
 
 .198 900 
 
 .121 9676 
 
 .154 
 
 935 4703 
 
 .619 267 
 
 .116 0192 
 
 2.105 
 
 0.914 1899 
 
 8.207 103 
 
 O.I2I 8457 
 
 2.155 
 
 0.935 9046 
 
 8.627 890 
 
 0.115 9032 
 
 .106 
 
 .914 6242 
 
 .215 314 
 
 .121 7239 
 
 .156 
 
 .936 3389 
 
 .636 522 
 
 .115 7873 
 
 .107 
 
 .915 0585 
 
 .223 534 
 
 .121 6O22 
 
 157 
 
 .936 7732 
 
 .645 163 
 
 .115 6716 
 
 .108 
 
 .915 4928 
 
 .231 761 
 
 .121 4807 
 
 .158 
 
 937 2075 
 
 .653 813 
 
 .115 556o 
 
 .109 
 
 .915 9271 
 
 .239 997 
 
 .121 3593 
 
 .159 
 
 .937 6418 
 
 .662 471 
 
 .115 4405 
 
 2. IIO 
 
 0.916 3614 
 
 8.248 241 
 
 O.I2I 2380 
 
 2.160 
 
 0.938 0761 
 
 8.671 138 
 
 0.115 3251 
 
 .III 
 
 .916 7957 
 
 .256 494 
 
 .121 1168 
 
 .161 
 
 .938 5104 
 
 .679 813 
 
 .115 2099 
 
 .112 
 
 .917 2299 
 
 .264 754 
 
 . 120 9957 
 
 .162 
 
 .938 9447 
 
 .688497 
 
 .115 0947 
 
 .113 
 
 .917 6642 
 
 .273 023 
 
 . 120 8748 
 
 .163 
 
 939 3790 
 
 .697 190 
 
 .114 9797 
 
 .114 
 
 .918 0985 
 
 .281 300 
 
 .120 7540 
 
 .164 
 
 939 8133 
 
 .705 892 
 
 .114 8647 
 
 2.II5 
 
 0.918 5328 
 
 8.289 586 
 
 0.120 6333 
 
 2.165 
 
 0.940 2476 
 
 8.714 602 
 
 0.114 7499 
 
 .116 
 
 .918 9671 
 
 .297 879 
 
 .120 5127 
 
 .166 
 
 .940 6818 
 
 .723 321 
 
 .114 6352 
 
 .117 
 
 .919 4014 
 
 .306 182 
 
 .120 3923 
 
 .167 
 
 .941 1161 
 
 .732 049 
 
 .114 5207 
 
 .118 
 
 .919 8357 
 
 .314 492 
 
 .120 2719 
 
 .168 
 
 .941 5504 
 
 .740 785 
 
 .114 4062 
 
 .119 
 
 .920 2700 
 
 .322 811 
 
 .120 1517 
 
 .169 
 
 .941 9847 
 
 749 530 
 
 .114 2919 
 
 2.I2O 
 
 0.920 7043 
 
 8.331 137 
 
 0.120 03l6 
 
 2.170 
 
 0.942 4190 
 
 8.758 284 
 
 0.114 1776 
 
 .121 
 
 .921 1386 
 
 339 473 
 
 .119 9H7 
 
 .171 
 
 .942 8533 
 
 .767 047 
 
 .114 0635 
 
 .122 
 
 .921 5729 
 
 .347 816 
 
 .119 79l8 
 
 .172 
 
 .943 2876 
 
 .775 818 
 
 .H3 9495 
 
 .123 
 
 .922 0072 
 
 .356 168 
 
 .119 6721 
 
 .173 
 
 .943 7219 
 
 .784 598 
 
 .113 8356 
 
 .124 
 
 .922 4415 
 
 .364 529 
 
 .119 5525 
 
 174 
 
 .944 1562 
 
 .793 387 
 
 .113 7218 
 
 2.125 
 
 0.922 8758 
 
 8.372 897 
 
 0.119 4330 
 
 2.175 
 
 0.944 5905 
 
 8.802 185 
 
 0.113 6082 
 
 .126 
 
 .923 3101 
 
 .381 275 
 
 .119 3U6 
 
 .176 
 
 .945 0248 
 
 .810 992 
 
 .113 4046 
 
 .127 
 
 .923 7444 
 
 .389 660 
 
 .119 1943 
 
 .177 
 
 945 4591 
 
 .819 807 
 
 .113 3812 
 
 .128 
 
 .924 1787 
 
 .398 054 
 
 .119 0752 
 
 .178 
 
 .945 8934 
 
 .828 631 
 
 .113 2678 
 
 .129 
 
 .924 6130 
 
 .406 456 
 
 .118 9562 
 
 .179 
 
 .946 3277 
 
 .837 464 
 
 .113 1546 
 
 2.130 
 
 0.925 0472 
 
 8.414 867 
 
 0.118 8373 
 
 2.180 
 
 0.946 7620 
 
 8.846 306 
 
 0.113 0415 
 
 .131 
 
 .925 4815 
 
 .423 286 
 
 .118 7185 
 
 .181 
 
 .947 1963 
 
 .855 157 
 
 .112 9285 
 
 .132 
 
 .925 9158 
 
 431 713 
 
 .118 5999 
 
 .182 
 
 .947 6306 
 
 .864 017 
 
 .112 8l57 
 
 .133 
 
 .926 3501 
 
 .440 149 
 
 .118 4813 
 
 .183 
 
 .948 0649 
 
 .872 885 
 
 .112 7029 
 
 .134 
 
 .926 7844 
 
 .448 594 
 
 .118 3629 
 
 .184 
 
 .948 4991 
 
 .881 762 
 
 .112 5903 
 
 2.135 
 
 0.927 2187 
 
 8.457 047 
 
 0.118 2446 
 
 2.185 
 
 0.948 9334 
 
 8.890 649 
 
 0.112 4777 
 
 .136 
 
 .927 6530 
 
 .465 508 
 
 .118 1264 
 
 .186 
 
 949 3677 
 
 .899 544 
 
 .112 3653 
 
 137 
 
 .928 0873 
 
 473 978 
 
 .118 0083 
 
 .187 
 
 .949 8020 
 
 .908 448 
 
 .112 253O 
 
 .138 
 
 .928 5216 
 
 .482 456 
 
 .117 8904 
 
 .188 
 
 .950 2363 
 
 .917 361 
 
 .112 1408 
 
 .139 
 
 .928 9559 
 
 .490 942 
 
 .117 7726 
 
 .189 
 
 .950 6706 
 
 .926 282 
 
 .112 O287 
 
 2.140 
 
 0.929 3902 
 
 8.499 438 
 
 0.117 6548 
 
 2.190 
 
 0.951 1049 
 
 8.935 213 
 
 o.i u 9167 
 
 .141 
 
 .929 8245 
 
 .507 941 
 
 .117 5372 
 
 .191 
 
 951 5392 
 
 944 153 
 
 .III 8049 
 
 .142 
 
 .930 2588 
 
 .5i6 454 
 
 .117 4198 
 
 .192 
 
 951 9735 
 
 953 ioi 
 
 .III 6931 
 
 143 
 
 930 0931 
 
 .524 974 
 
 .117 3024 
 
 193 
 
 .952 4078 
 
 .962 059 
 
 .III 5815 
 
 .144 
 
 .93-1 1274 
 
 533 503 
 
 .117 1852 
 
 .194 
 
 .952 8421 
 
 .971 026 
 
 .III 4700 
 
 2.145 
 
 0.931 S6i7 
 
 8.542 041 
 
 0.117 0680 
 
 2.195 
 
 0.953 2764 
 
 8.080 ooi 
 
 o.in 3586 
 
 .146 
 
 .931 9960 
 
 .550 588 
 
 .116 9510 
 
 .196 
 
 953 7107 
 
 .988 986 
 
 III 2473 
 
 .147 
 
 932 4303 
 
 559 142 
 
 .116 8341 
 
 .197 
 
 954 1450 
 
 .997 979 
 
 .III 1361 
 
 .148 
 
 .932 8645 
 
 .567 706 
 
 .116 7174 
 
 .198 
 
 954 5793 
 
 9.006 982 
 
 .III O25O 
 
 .149 
 
 .933 2988 
 
 .576 278 
 
 .116 6007 
 
 .199 
 
 955 0136 
 
 .015 993 
 
 .no 9140 
 
 2.150 
 
 0.933 7331 
 
 8.584 858 
 
 0.116 4842 
 
 2. 2OO 
 
 0.955 4479 
 
 9.025 013 
 
 o.i 10 8032 
 
 log e (e u ) 
 
 looioCe 11 ) 
 
 e u 
 
 e- u 
 
 log e (e u ) 
 
 Iogi (e u ) 
 
 e n 
 
 e~ u 
 
 SMITHSONIAN TABLES 
 
 247 
 
The Exponential. 
 
 u 
 
 logio(e u ) 
 
 e u 
 
 e~ u 
 
 u 
 
 looio(e n ) 
 
 e u 
 
 e- tt 
 
 2.2OO 
 
 0.955 4479 
 
 9.025 013 
 
 o.i 10 8032 
 
 2.250 
 
 0.977 1626 
 
 9.487 736 
 
 0.105 3992 
 
 .2OI 
 
 .955 8822 
 
 .034 043 
 
 .no 6924 
 
 .251 
 
 977 5969 
 
 .497 228 
 
 105 2939 
 
 .202 
 
 .956 3164 
 
 .043 082 
 
 .110 5818 
 
 .252 
 
 .978 0312 
 
 .506 730 
 
 .105 1886 
 
 .203 
 
 .956 7507 
 
 .052 129 
 
 .no 4712 
 
 .253 
 
 .978 4655 
 
 .516 242 
 
 .105 0835 
 
 .204 
 
 957 1850 
 
 .061 186 
 
 .no 3608 
 
 .254 
 
 .9788998 
 
 .525 763 
 
 .104 9785 
 
 2.2O5 
 
 0.957 6193 
 
 9.070 252 
 
 o.i 10 2505 
 
 2.255 
 
 0.979 3341 
 
 9-535 293 
 
 o. 104 8735 
 
 .206 
 
 .958 0536 
 
 .079 326 
 
 .no 1403 
 
 .256 
 
 .979 7684 
 
 .544 833 
 
 .104 7687 
 
 .207 
 
 .958 4879 
 
 .088 410 
 
 . 1 10 0302 
 
 257 
 
 .980 2026 
 
 554 383 
 
 .104 6640 
 
 .208 
 
 .958 9222 
 
 .097 503 
 
 .109 9203 
 
 258 
 
 .980 6369 
 
 .563 942 
 
 .104 5594 
 
 .209 
 
 959 3565 
 
 .106 605 
 
 .109 8104 
 
 259 
 
 .981 0712 
 
 573 5ii 
 
 .104 4549 
 
 2.2IO 
 
 0.959 7908 
 
 9.H5 7i6 
 
 0.109 7006 
 
 2.260 
 
 0.081 5055 
 
 9-583 089 
 
 0.104 3505 
 
 .211 
 
 .960 2251 
 
 . 124 837 
 
 .109 5910 
 
 .261 
 
 981 9398 
 
 .592 677 
 
 .104 2462 
 
 .212 
 .213 
 
 .960 6594 
 .961 0937 
 
 .133 966 
 .143 105 
 
 .109 4815 
 . 109 3720 
 
 .262 
 .263 
 
 .982 3741 
 .982 8084 
 
 .602 275 
 .611 882 
 
 .104 1420 
 . 104 0379 
 
 .214 
 
 .961 5280 
 
 .152 252 
 
 .109 2627 
 
 .264 
 
 .983 2427 
 
 .621 498 
 
 .103 9339 
 
 2.215 
 
 0.961 9623 
 
 9.161 409 
 
 0.109 1535 
 
 2.265 
 
 0.983 6770 
 
 9.631 125 
 
 0.103 8300 
 
 .216 
 
 .962 3966 
 
 .170 575 
 
 .109 0444 
 
 .266 
 
 .984 III3 
 
 .640 761 
 
 .103 7263 
 
 .217 
 
 .962 8309 
 
 . 179 750 
 
 . 108 9354 
 
 .267 
 
 984 5456 
 
 .650 406 
 
 .103 6226 
 
 .218 
 
 .963 2652 
 
 .188 935 
 
 . 108 8265 
 
 .268 
 
 984 9799 
 
 .660 061 
 
 .103 5190 
 
 .219 
 
 .963 6995 
 
 .198 128 
 
 .108 7178 
 
 .269 
 
 .985 4142 
 
 .669 726 
 
 .103 4155 
 
 2.22O 
 
 0.964 1337 
 
 9.207 331 
 
 o.loS 6091 
 
 2.270 
 
 0.985 8485 
 
 9.679 401 
 
 0.103 3122 
 
 .221 
 
 .964 5680 
 
 .216 543 
 
 .108 5006 
 
 .271 
 
 .986 2828 
 
 .689085 
 
 .103 2089 
 
 .222 
 
 .965 0023 
 
 .225 764 
 
 .108 3921 
 
 .272 
 
 .986 7171 
 
 .698 779 
 
 .103 1058 
 
 .223 
 
 .965 4366 
 
 .234 994 
 
 .108 2838 
 
 .273 
 
 .987 1514 
 
 .708 483 
 
 .103 0027 
 
 .224 
 
 .965 8709 
 
 .244 234 
 
 .108 1755 
 
 .274 
 
 .987 5857 
 
 .718 106 
 
 .102 8998 
 
 2.225 
 
 0.966 3052 
 
 9.253 483 
 
 0.108 0674 
 
 2.275 
 
 0.988 0199 
 
 9.727 919 
 
 0.102 7969 
 
 .226 
 
 965 7395 
 
 .262 741 
 
 .107 9594 
 
 .276 
 
 .988 4542 
 
 737 652 
 
 .102 6942 
 
 .227 
 
 .957 1738 
 
 .272 008 
 
 .107 8515 
 
 .277 
 
 .988 8885 
 
 747 394 
 
 .102 5915 
 
 .228 
 
 .967 6081 
 
 .281 285 
 
 .107 7437 
 
 .278 
 
 .989 3228 
 
 .757 147 
 
 .IO2 4890 
 
 .229 
 
 .968 0424 
 
 .290 571 
 
 .107 6360 
 
 .279 
 
 989 757i 
 
 .766 909 
 
 .102 3865 
 
 2.23O 
 
 0.968 4767 
 
 9.299 866 
 
 0.107 5284 
 
 2.280 
 
 0.990 1914 
 
 9.776 680 
 
 0.102 2842 
 
 .231 
 
 .968 9110 
 
 .309 I7i 
 
 .107 4210 
 
 .281 
 
 .990 6257 
 
 .786 462 
 
 .IO2 l82O 
 
 .232 
 
 969 3453 
 
 ^ ^ *JT*J\J 
 
 .318 484 
 
 .107 3136 
 
 .282 
 
 .991 0600 
 
 .796 253 
 
 . 102 0798 
 
 233 
 
 .969 7796 
 
 .327 808 
 
 .107 2063 
 
 283 
 
 .991 4943 
 
 .806 054 
 
 .101 9778 
 
 .234 
 
 .970 2139 
 
 337 UO 
 
 .107 0992 
 
 .284 
 
 .991 9286 
 
 .815 865 
 
 .101 8759 
 
 2.235 
 
 O.970 6482 
 
 9.346 482 
 
 0.106 9921 
 
 2.285 
 
 0.992 3629 
 
 9.825 686 
 
 o.ioi 7741 
 
 
 
 .236 
 
 .971 0825 
 
 355 833 
 
 . 106 8852 
 
 .286 
 
 .992 7972 
 
 835 517 
 
 .101 6723 
 
 237 
 
 .971 5l68 
 
 365 194 
 
 .106 7784 
 
 .287 
 
 993 2315 
 
 845 357 
 
 .101 5707 
 
 .238 
 
 .971 9511 
 
 374 563 
 
 .106 6716 
 
 .288 
 
 .993 6658 
 
 .855 208 
 
 .101 4692 
 
 239 
 
 972 3853 
 
 383 943 
 
 .106 5650 
 
 .289 
 
 .994 looi 
 
 .865 068 
 
 .101 3678 
 
 2.240 
 
 0.972 8l96 
 
 9-393 331 
 
 0.106 4585 
 
 2.290 
 
 0.994 5344 
 
 9.874 938 
 
 o.ioi 2665 
 
 .241 
 
 973 2539 
 
 .402 729 
 
 .106 3521 
 
 .291 
 
 .994 9687 
 
 .884 818 
 
 .101 1652 
 
 .242 
 
 .973 6882 
 
 .412 137 
 
 .106 2458 
 
 .292 
 
 995 4030 
 
 .894 707 
 
 .101 0641 
 
 .243 
 
 .974 1225 
 
 .421 554 
 
 .106 1396 
 
 .293 
 
 995 8372 
 
 .904 607 
 
 .100 9631 
 
 .244 
 
 .974 5568 
 
 .430 980 
 
 . 106 0335 
 
 .294 
 
 .996 2715 
 
 914 517 
 
 . IOO 8622 
 
 2.245 
 
 0.974 9911 
 
 9.440 416 
 
 0.105 9275 
 
 2.295 
 
 0.996 7058 
 
 9.924 436 
 
 o.ioo 7614 
 
 .246 
 
 .975 4254 
 
 .449 861 
 
 .105 8217 
 
 .296 
 
 .097 1401 
 
 934 365 
 
 .100 6607 
 
 247 
 
 .975 8597 
 
 459 315 
 
 .105 7159 
 
 .297 
 
 997 5744 
 
 .944 305 
 
 .106 5601 
 
 .248 
 
 .976 2940 
 
 .468 779 
 
 .105 6102 
 
 .298 
 
 .9980087 
 
 954 -'54 
 
 .100 4596 
 
 .249 
 
 .976 7283 
 
 .478 253 
 
 .105 5047 
 
 299 
 
 .098 4430 
 
 .964 213 
 
 . loo 3592 
 
 2.250 
 
 0.977 1626 
 
 9.487 73<5 
 
 0.105 3992 
 
 2.300 
 
 0.098 8773 
 
 9.974 182 
 
 o.ioo 2588 
 
 Io0c(e) 
 
 looi.Xe) 
 
 e u 
 
 e- u 
 
 lo flc (e u ) 
 
 looio(e a ) 
 
 e u 
 
 -" 
 
 SMITHSONIAN TABLES 
 
 248 
 
The Exponential. 
 
 u 
 
 looio(e u ) 
 
 e u 
 
 e~ u 
 
 u 
 
 logio(e n ) 
 
 e u 
 
 e~ u 
 
 2.300 
 
 0.098 8773 
 
 9.974 182 
 
 o.ioo 2588 
 
 2.350 
 
 I.O20 592O 
 
 10.485 570 
 
 0.095 3692 
 
 .301 
 
 .999 3116 
 
 .984 162 
 
 .100 1586 
 
 .351 
 
 .O2I 0263 
 
 .496 061 
 
 .095 2738 
 
 .302 
 
 999 7459 
 
 .994 151 
 
 .100 0585 
 
 .352 
 
 .O2I 4606 
 
 .506 562 
 
 .095 1786 
 
 .303 
 
 i.ooo 1802 
 
 10.004 150 
 
 .099 9585 
 
 353 
 
 .O2I 8949 
 
 .517 074 
 
 .095 0835 
 
 .304 
 
 .coo 6145 
 
 .014 159 
 
 .0998586 
 
 354 
 
 .022 3292 
 
 .527 596 
 
 .094 9884 
 
 2.305 
 
 i.ooi 0488 
 
 10.024 178 
 
 0.099 7588 
 
 2.355 
 
 1.022 7635 
 
 10.538 129 
 
 0.094 8935 
 
 .306 
 
 .001 4831 
 
 .034 207 
 
 .099 6591 
 
 .356 
 
 .023 1978 
 
 .548 672 
 
 .094 7987 
 
 .307 
 
 .001 9174 
 
 .044 247 
 
 .099 5595 
 
 357 
 
 .023 6321 
 
 .559 226 
 
 .094 7039 
 
 .308 
 
 .002 3517 
 
 .054 296 
 
 .099 4600 
 
 358 
 
 .024 0664 
 
 .569 791 
 
 .094 6093 
 
 .309 
 
 .002 7860 
 
 .064 355 
 
 .099 3606 
 
 359 
 
 .024 50O7 
 
 .580366 
 
 .094 5147 
 
 2.310 
 
 1.003 2203 
 
 10.074 425 
 
 0.099 2613 
 
 2.360 
 
 1.024 9350 
 
 10.590 95i 
 
 0.094 4202 
 
 .311 
 
 .003 6545 
 
 .084 504 
 
 .099 1620 
 
 .361 
 
 .025 3693 
 
 .601 548 
 
 .094 3259 
 
 .312 
 
 .004 0888 
 
 .094 594 
 
 .099 0629 
 
 .362 
 
 .025 8036 
 
 .612 155 
 
 .094 2316 
 
 .313 
 
 .004 5231 
 
 . 104 693 
 
 .098 9639 
 
 .363 
 
 .026 2379 
 
 .622 772 
 
 .094 1374 
 
 .314 
 
 .004 9574 
 
 .114 803 
 
 .098 8650 
 
 .364 
 
 .026 6722 
 
 .633 400 
 
 .094 0433 
 
 2.315 
 
 1.005 3917 
 
 10.124 923 
 
 0.098 7662 
 
 2.365 
 
 1.027 1064 
 
 10.644 039 
 
 0.093 9493 
 
 .316 
 
 .005 8260 
 
 .135 053 
 
 .0986675 
 
 .366 
 
 .027 5407 
 
 .654 688 
 
 .093 8554 
 
 .317 
 
 .006 2603 
 
 .145 193 
 
 .098 5688 
 
 .367 
 
 .027 9750 
 
 .665 348 
 
 .093 7616 
 
 .318 
 
 .006 6946 
 
 155 343 
 
 .098 4703 
 
 .368 
 
 .028 4093 
 
 .676 019 
 
 .093 6679 
 
 .319 
 
 .007 1289 
 
 .165 504 
 
 .098 3719 
 
 .369 
 
 .028 8436 
 
 .686 700 
 
 .093 5743 
 
 2.320 
 
 1.007 5632 
 
 10.175 674 
 
 0.098 2736 
 
 2.370 
 
 1.029 2779 
 
 10.697 392 
 
 0.093 4807 
 
 .321 
 
 .007 9975 
 
 .I&5 855 
 
 .098 1754 
 
 .371 
 
 .029 7122 
 
 .708 095 
 
 .093 3873 
 
 .322 
 
 .008 4318 
 
 .196 046 
 
 .098 0772 
 
 372 
 
 .030 1465 
 
 .718 808 
 
 .093 2940 
 
 .323 
 
 .0088661 
 
 .206 247 
 
 .097 9792 
 
 373 
 
 .030 5808 
 
 .729 533 
 
 .093 2007 
 
 .324 
 
 .009 3004 
 
 .216 459 
 
 .097 8813 
 
 374 
 
 .031 0151 
 
 .740 268 
 
 .093 1076 
 
 2.325 
 
 1.009 7347 
 
 10.226 680 
 
 0.097 7834 
 
 2.375 
 
 1.031 4494 
 
 10.751 013 
 
 0.093 0145 
 
 .326 
 
 .010 1690 
 
 .236 912 
 
 .097 6857 
 
 .376 
 
 .031 8837 
 
 .761 770 
 
 .092 9215 
 
 .327 
 
 .010 6033 
 
 .247 154 
 
 .097 5881 
 
 377 
 
 .032 3180 
 
 772 537 
 
 .092 8286 
 
 .328 
 
 .011 0376 
 
 .257 406 
 
 .097 4905 
 
 .378 
 
 .032 7523 
 
 783 315 
 
 092 7359 
 
 .329 
 
 .011 4718 
 
 .267669 
 
 .097 3931 
 
 379 
 
 .033 1866 
 
 .794 103 
 
 .092 6432 
 
 2.330 
 .331 
 
 i. on 9061 
 
 .012 3404 
 
 10.277 942 
 .288 225 
 
 0.097 2957 
 .097 1985 
 
 2.380 
 .381 
 
 1.033 6209 
 .034 0552 
 
 10.804 903 
 .815 713 
 
 0.092 5506 
 .092 4581 
 
 .332 
 
 .012 7747 
 
 .298 518 
 
 .097 1014 
 
 .382 
 
 .034 4895 
 
 .826 534 
 
 .092 3657 
 
 .333 
 
 .013 2090 
 
 .308 822 
 
 .097 0043 
 
 .383 
 
 .034 9238 
 
 .837 366 
 
 .092 2733 
 
 .334 
 
 .013 6433 
 
 .319 136 
 
 .096 9073 
 
 .384 
 
 .035 358o 
 
 .848 209 
 
 .092 1811 
 
 2.335 
 
 1.014 0776 
 
 10.329 460 
 
 0.096 8105 
 
 2.385 
 
 1.035 7923 
 
 10.859 063 
 
 0.092 0890 
 
 .336 
 
 .014 5119 
 
 339 795 
 
 .096 7137 
 
 .386 
 
 .036 2266 
 
 .869927 
 
 .091 9969 
 
 .337 
 
 .014 9462 
 
 .350 140 
 
 .096 6171 
 
 .387 
 
 .036 6609 
 
 .880 803 
 
 .091 0050 
 
 .338 
 
 .015 3805 
 
 .360 495 
 
 .096 5205 
 
 .388 
 
 .037 0952 
 
 .991 689 
 
 .091 8131 
 
 339 
 
 .015 8148 
 
 .370861 
 
 .096 4240 
 
 .389 
 
 .037 5295 
 
 .902 586 
 
 .091 7214 
 
 2.340 
 
 1.016 2491 
 
 10.381 237 
 
 0.096 3276 
 
 2.390 
 
 1.037 9638 
 
 10.913 494 
 
 0.091 6297 
 
 341 
 
 . .016 6834 
 
 391 623 
 
 .096 2314 
 
 391 
 
 .038 3981 
 
 .924 413 
 
 .091 538i 
 
 342 
 
 .017 ii77 
 
 .402 020 
 
 .096 1352 
 
 .392 
 
 .038 8324 
 
 935 343 
 
 .091 4466 
 
 343 
 
 .017 5520 
 
 .412 427 
 
 .096 0391 
 
 393 
 
 .039 2667 
 
 .946 284 
 
 .091 3552 
 
 344 
 
 .017 9863 
 
 .422 845 
 
 095 9431 
 
 394 
 
 .039 7010 
 
 957 235 
 
 .091 2639 
 
 2.345 
 
 1.018 4206 
 
 10.433 273 
 
 0.095 8472 
 
 2.395 
 
 1.040 1353 
 
 10.968 198 
 
 0.091 1727 
 
 346 
 
 .018 8549 
 
 .443 7ii 
 
 .095 7514 
 
 .396 
 
 .040 5696 
 
 .979 172 
 
 .091 0816 
 
 347 
 
 .019 2891 
 
 .454 160 
 
 .095 6557 
 
 397 
 
 .041 0039 
 
 .990 156 
 
 .090 9905 
 
 .348 
 
 .019 7234 
 
 .464 620 
 
 .095 5601 
 
 .398 
 
 .041 4382 
 
 II. 001 152 
 
 .090 8996 
 
 349 
 
 .020 1577 
 
 .475 089 
 
 .095 4646 
 
 399 
 
 .041 8725 
 
 .012 159 
 
 .090 8087 
 
 2-350 
 
 1.020 5920 
 
 10.485 570 
 
 0.095 3692 
 
 2.400 
 
 1.042 3068 
 
 11.023 176 
 
 0.090 7180 
 
 log e (e u ) 
 
 logio(e u ) 
 
 e u 
 
 e~ u 
 
 log e (e u ) 
 
 lo fll o(e u ) 
 
 e u 
 
 e~~ u 
 
 SMITHSONIAN TABLES 
 
 249 
 
The Exponential. 
 
 u 
 
 looio(e n ) 
 
 e u 
 
 e~ u 
 
 u 
 
 looio(e u ) 
 
 e n 
 
 e u 
 
 2.400 
 
 1.042 3068 
 
 11.023 176 
 
 0.090 7180 
 
 2.450 
 
 1.064 0215 
 
 11.588 347 
 
 0.086 2936 
 
 .401 
 
 .042 7411 
 
 .034 205 
 
 .090 6273 
 
 451 
 
 .064 4558 
 
 .599 941 
 
 .086 2073 
 
 .402 
 
 043 1753 
 
 045 245 
 
 .090 5367 
 
 452 
 
 .064 8001 
 
 .611 547 
 
 .086 1212 
 
 .403 
 
 .043 6006 
 
 .056 296 
 
 .090 4462 
 
 453 
 
 .065 3244 
 
 .623 164 
 
 .086 0351 
 
 .404 
 
 .044 0439 
 
 067 357 
 
 .090 3558 
 
 .454 
 
 .065 7587 
 
 634 793 
 
 .085 9491 
 
 2.405 
 
 1.044 4782 
 
 11.078 430 
 
 o.ooo 2655 
 
 2.455 
 
 I. 066 1930 
 
 11.646 434 
 
 0.085 8632 
 
 .406 
 
 .044 9125 
 
 .089 514 
 
 000 1753 
 
 .456 
 
 .066 6272 
 
 .658 086 
 
 .085 7774 
 
 .407 
 
 .045 3468 
 
 .100 609 
 
 .000 0851 
 
 457 
 
 .067 0615 
 
 .669 750 
 
 .085 6916 
 
 .408 
 
 .045 78ii 
 
 .in 715 
 
 .089 9951 
 
 458 
 
 .067 4958 
 
 .681 425 
 
 .085 6060 
 
 .409 
 
 .046 2154 
 
 .122 833 
 
 .089 9052 
 
 459 
 
 .067 9301 
 
 .693 113 
 
 .085 5204 
 
 2.410 
 
 1.046 6497 
 
 11.133 96l 
 
 0.089 8153 
 
 2.460 
 
 I. 068 3644 
 
 11.704 812 
 
 0.085 4350 
 
 .411 
 
 .047 0840 
 
 .145 101 
 
 .089 7255 
 
 .461 
 
 .068 7987 
 
 .716 522 
 
 .085 3496 
 
 .412 
 
 .047 5183 
 
 .156 251 
 
 .089 6358 
 
 .462 
 
 .069 2330 
 
 .728 245 
 
 .085 2643 
 
 .413 
 .414 
 
 .047 9526 
 .048 3869 
 
 .167 413 
 .178 586 
 
 .089 5463 
 .089 4568 
 
 .463 
 .464 
 
 .069 66731 
 .070 1016 
 
 .739 979 
 751 725 
 
 .085 1790 
 .085 0939 
 
 2.415 
 
 1.048 8212 
 
 II.I89 770 
 
 0.089 3673 
 
 2.465 
 
 1.070 5359 
 
 11.763 482 
 
 0.085 0088 
 
 .416 
 
 049 2555 
 
 .2OO 966 
 
 .089 2780 
 
 .466 
 
 .070 9702 
 
 .775 252 
 
 .084 9239 
 
 .417 
 
 .049 6898 
 
 .212 172 
 
 .089 1888 
 
 .467 
 
 .071 4045 
 
 .787 033 
 
 .084 8390 
 
 .418 
 
 .050 1241 
 
 .223 390 
 
 .089 0006 
 
 .468 
 
 .071 8388 
 
 .708 826 
 
 .084 7542 
 
 .419 
 
 .050 5584 
 
 .234 619 
 
 .089 0106 
 
 .469 
 
 .072 2731 
 
 .810 630 
 
 .0846695 
 
 2.420 
 
 1.050 9926 
 
 11.245 859 
 
 0.088 9216 
 
 2.470 
 
 1.072 7074 
 
 11.822 447 
 
 0.084 5849 
 
 .421 
 
 .051 4269 
 
 .257 III 
 
 .088 8327 
 
 .471 
 
 .073 1417 
 
 .834 275 
 
 .084 5003 
 
 .422 
 
 .051 8612 
 
 .268 374 
 
 .088 7440 
 
 .472 
 
 .073 576o 
 
 .846 115 
 
 .084 4159 
 
 .423 
 
 .052 2955 
 
 .279 648 
 
 .088 6553 
 
 .473 
 
 .074 0103 
 
 .857 967 
 
 .084 3315 
 
 .424 
 
 .052 7298 
 
 .290 933 
 
 .088 5666 
 
 474 
 
 .074 4445 
 
 .869831 
 
 .084 2472 
 
 2.425 
 
 1.053 1641 
 
 11.302 229 
 
 0.088 4781 
 
 2.475 
 
 1.074 8788 
 
 11.881 707 
 
 0.084 1630 
 
 .426 
 
 .053 5984 
 
 .313 537 
 
 .0883897 
 
 476 
 
 .075 3i3i 
 
 .893 595 
 
 .084 0789 
 
 .427 
 
 .054 0327 
 
 .324 857 
 
 .088 3013 
 
 .477 
 
 .075 7474 
 
 .905 494 
 
 .083 9948 
 
 .428 
 
 .054 4670 
 
 .336 187 
 
 .088 2131 
 
 478 
 
 .076 1817 
 
 .917 406 
 
 .083 9109 
 
 .429 
 
 .054 9013 
 
 347 529 
 
 .088 1249 
 
 479 
 
 .076 6160 
 
 .929 329 
 
 .083 8270 
 
 2.430 
 
 1.055 3356 
 
 11.358 882 
 
 0.088 0368 
 
 2.480 
 
 1.077 0503 
 
 11.941 264 
 
 0.083 7432 
 
 .431 
 
 .055 7699 
 
 370 247 
 
 .087 9488 
 
 .481 
 
 .077 4846 
 
 .953 212 
 
 .083 6595 
 
 .432 
 
 .056 2042 
 
 .381 623 
 
 .087 8609 
 
 .482 
 
 .077 9189 
 
 .965 171 
 
 .083 5759 
 
 433 
 
 .056 6385 
 
 .393 oio 
 
 .087 7731 
 
 .483 
 
 078 3532 
 
 977 H2 
 
 .083 4924 
 
 434 
 
 .057 0728 
 
 .404 409 
 
 .087 6854 
 
 .484 
 
 .078 7875 
 
 .089 125 
 
 .083 4089 
 
 2.435 
 
 1.057 5071 
 
 11.415 819 
 
 0.087 5977 
 
 2.485 
 
 1.079 2218 
 
 12.001 120 
 
 0.083 3256 
 
 .436 
 
 .057 9414 
 
 .427 240 
 
 .087 5102 
 
 .486 
 
 .079 6561 
 
 .013 127 
 
 .083 2423 
 
 437 
 
 .058 3757 
 
 .438 673 
 
 .087 4227 
 
 .487 
 
 .080 0004 
 
 .025 147 
 
 .083 1591 
 
 .438 
 
 .0588099 
 
 .450 118 
 
 .087 3353 
 
 .488 
 
 .080 5247 
 
 .037 178 
 
 .083 0760 
 
 439 
 
 .059 2442 
 
 461 573 
 
 .087 2481 
 
 .489 
 
 .080 9590 
 
 .049 221 
 
 .082 9929 
 
 2.440 
 
 1.059 6785 
 
 11.473 041 
 
 0.087 1609 
 
 2.490 
 
 1.081 3933 
 
 12.061 276 
 
 0.082 9100 
 
 .441 
 
 .060 1128 
 
 .484 520 
 
 .087 0737 
 
 .491 
 
 .081 8276 
 
 .073 343 
 
 .082 8271 
 
 442 
 
 .060 5471 
 
 .496 oio 
 
 .086 9867 
 
 .492 
 
 .082 2618 
 
 .085 423 
 
 .082 7443 
 
 443 
 
 .060 9814 
 
 507 512 
 
 .086 8998 
 
 493 
 
 .082 6961 
 
 .097 5U 
 
 .082 6616 
 
 .444 
 
 .061 4157 
 
 .519 025 
 
 .086 8129 
 
 .494 
 
 .083 1304 
 
 .109 618 
 
 .082 5790 
 
 2.445 
 
 1.061 8500 
 
 11.530 550 
 
 0.086 7261 
 
 2.495 
 
 1.083 5647 
 
 12. 121 734 
 
 0.082 4065 
 
 .446 . 
 
 .062 2843 
 
 .542 086 
 
 .086 6395 
 
 .496 
 
 .083 9990 
 
 .133861 
 
 .082 4140 
 
 447 
 
 .062 7186 
 
 553 634 
 
 .086 5529 
 
 497 
 
 .084 4333 
 
 .146 ooi 
 
 .082 3316 
 
 .448 
 
 .063 1529 
 
 .565 193 
 
 .0864663 
 
 .498 
 
 .084 8676 
 
 .158 153 
 
 .082 j.j;.* 
 
 449 
 
 .063 5872 
 
 .576 764 
 
 .086 3799 
 
 499 
 
 .085 3019 
 
 .170 318 
 
 .082 1671 
 
 2.450 
 
 1.064 0215 
 
 n.588 347 
 
 0.086 2936 
 
 2.500 
 
 1.085 7302 
 
 12.182 494 
 
 0.082 0850 
 
 I0fle(e) 
 
 loouXe") 
 
 e u 
 
 e~ u 
 
 IOQe(e D ) 
 
 lo fllo (e u ) 
 
 e" 
 
 e-" 
 
 SMITHSONIAN TABLES 
 
 250 
 
The Exponential. 
 
 u 
 
 loflio(e u ) 
 
 e u 
 
 e 
 
 u 
 
 Ioflio(e") 
 
 e u 
 
 e- n 
 
 2.500 
 
 1.085 7362 
 
 12.182 494 
 
 0.082 0850 
 
 2.550 
 
 I. 107 4509 
 
 12.807 IO4 
 
 0.078 0817 
 
 .501 
 
 .086 1705 
 
 .194 683 
 
 .082 0030 
 
 551 
 
 .107 8852 
 
 .819 917 
 
 .078 0036 
 
 .502 
 
 .086 6048 
 
 .206 883 
 
 .081 9210 
 
 552 
 
 .108 3195 
 
 .832 744 
 
 .077 9257 
 
 .503 
 
 .087 0391 
 
 .219 096 
 
 .081 8391 
 
 553 
 
 .108 7538 
 
 .845 583 
 
 .077 8478 
 
 .504 
 
 .087 4734 
 
 .231 322 
 
 .081 7573 
 
 554 
 
 .109 1881 
 
 .858 435 
 
 .077 7700 
 
 2.505 
 
 1.087 9077 
 
 12.243 559 
 
 0.081 6756 
 
 2.555 
 
 1.109 6224 
 
 12.871 300 
 
 0.077 6922 
 
 .506 
 
 .088 3420 
 
 .255 809 
 
 .081 5940 
 
 .556 
 
 .no 0567 
 
 .884 177 
 
 .077 6146 
 
 .507 
 
 .088 7763 
 
 .268 071 
 
 .081 5124 
 
 .557 
 
 .no 4910 
 
 .897 068 
 
 .077 5370 
 
 .508 
 
 .089 2106 
 
 .280 345 
 
 .081 4309 
 
 .558 
 
 .110 9253 
 
 .909 972* 
 
 .077 4595 
 
 .509 
 
 .089 6449 
 
 .292 631 
 
 .081 3495 
 
 559 
 
 .III 3596 
 
 .922 888 
 
 .077 3821 
 
 2.510 
 
 1.090 0791 
 
 12.304 930 
 
 0.081 2682 
 
 2.560 
 
 i. in 7939 
 
 12.935 817 
 
 0.077 3047 
 
 .511 
 
 .090 5U4 
 
 .317 241 
 
 .081 1870 
 
 .561 
 
 .112 2282 
 
 .948 760. 
 
 .077 2275 
 
 .512 
 
 .090 9477 
 
 .329 565 
 
 .081 IOS9 
 
 .562 
 
 .112 6625 
 
 .961 715 
 
 077 1503 
 
 .513 
 
 .091 3820 
 
 .341 900 
 
 .081 0248 
 
 .563 
 
 .113 0968 
 
 .974 683 
 
 .077 0732 
 
 .514 
 
 .091 8163 
 
 354 248 
 
 .080 9438 
 
 .564 
 
 .113 5311 
 
 .987664 
 
 .076 9961 
 
 2.515 
 
 1.092 2506 
 
 12.366 609 
 
 d 080 8629 
 
 2.565 
 
 I. 113 9653 
 
 13.000 658 
 
 0.076 9192 
 
 .516 
 
 .092 6849 
 
 .378 982 
 
 .c8o 7821 
 
 .566 
 
 .114 3996 
 
 .013 666 
 
 .076 8423 
 
 .517 
 
 .093 1192 
 
 391 307 
 
 .080 7013 
 
 .567 
 
 .114 8339 
 
 .026 686 
 
 .076 7655 
 
 .518 
 
 .093 5535 
 
 .403 764 
 
 .080 6207 
 
 .568 
 
 .115 2682 
 
 .039 719 
 
 .076 6888 
 
 .519 
 
 .093 9878 
 
 .416 174 
 
 .080 5401 
 
 .569 
 
 .115 7025 
 
 .052 765 
 
 .076 6121 
 
 2.520 
 
 1.094 4221 
 
 12.428 597 
 
 0.080 4596 
 
 2.570 
 
 1.116 1368 
 
 13.065 824 
 
 0.076 5355 
 
 .521 
 
 .094 8564 
 
 .441 032 
 
 .080 3792 
 
 571 
 
 .116 5711 
 
 .078 897 
 
 .076 4590 
 
 .522 
 
 .095 2907 
 
 453 479 
 
 .ofr- 2988 
 
 572 
 
 .117 0054 
 
 .091 982 
 
 .076 3826 
 
 .523 
 
 .095 7250 
 
 .465 958 
 
 .080 2186 
 
 .573 
 
 .117 4397 
 
 .105 081 
 
 .076 3063 
 
 .524 
 
 .096 1593 
 
 .478 411 
 
 .080 1384 
 
 574 
 
 .117 8740 
 
 .118 192 
 
 .076 2300 
 
 2.525 
 
 1.096 5936 
 
 12.490 895 
 
 0.080 0583 
 
 2.575 
 
 1.118 3083 
 
 13-131 317 
 
 0.076 1538 
 
 .526 
 
 .097 0279 
 
 .503 392 
 
 .079 9783 
 
 .576 
 
 .118 7426 
 
 144 455 
 
 .076 0777 
 
 .527 
 
 .097 4622 
 
 .515 902 
 
 .079 8984 
 
 577 
 
 .119 1769 
 
 .157 606 
 
 .076 0017 
 
 .528 
 
 .097 8965 
 
 .528 424 
 
 .079 8185 
 
 .578 
 
 .119 6112 
 
 .170 770 
 
 .075 9257 
 
 .529 
 
 .098 3307 
 
 540 959 
 
 .079 7387 
 
 579 
 
 . 120 0455 
 
 .183 948 
 
 .075 8498 
 
 2.530 
 
 1.098 7650 
 
 12.553 5o6 
 
 0.079 6590 
 
 2.580 
 
 I . 120 4798 
 
 13.197 138 
 
 0.075 7740 
 
 .531 
 
 .099 1993 
 
 .566 066 
 
 079 5794 
 
 .581 
 
 .120 9141 
 
 .210 342 
 
 .075 6983 
 
 .532 
 
 .099 6336 
 
 .578 638 
 
 .079 4999r 
 
 .582 
 
 .121 3484 
 
 .223 559 
 
 .075 6226 
 
 533 
 
 .100 0679 
 
 591 223 
 
 .079 4204 
 
 .583 
 
 .121 7826 
 
 .236 789 
 
 .075 5470 
 
 534 
 
 .100 5022 
 
 .603 821 
 
 .079 3410 
 
 .584 
 
 .122 2l69 
 
 .250 032 
 
 075 4715 
 
 2.535 
 
 i . 100 9365 
 
 12.616 431 
 
 0.079 2617 
 
 2.585 
 
 I. 122 6512 
 
 13.263 289 
 
 0.075 396i 
 
 .536 
 
 .101 3708 
 
 .629 054 
 
 .079 1825 
 
 .586 
 
 .123 0855 
 
 .276 559 
 
 .075 3207 
 
 537 
 
 .101 8051 
 
 .641 689 
 
 .079 1034 
 
 .587 
 
 .123 5198 
 
 .289 842 
 
 .075 2454 
 
 .538 
 
 .102 2394 
 
 .654 337 
 
 .079 0243 
 
 .588 
 
 .123 9541 
 
 303 139 
 
 .075 1702 
 
 .539 
 
 .102 6737 
 
 .666998 
 
 .078 9453 
 
 .589 
 
 .124 3884 
 
 .316 449 
 
 075 0951 
 
 2.540 
 
 1.103 1080 
 
 12.679 671 
 
 0.078 8664 
 
 2.590 
 
 I.I24 8227 
 
 13.329 772 
 
 O.075 O20O 
 
 541 
 
 .103 5423 
 
 .692 357 
 
 .078 7876 
 
 591 
 
 .125 2570 
 
 343 108 
 
 .074 9451 
 
 542 
 
 .103 9766 
 
 .705 056 
 
 .078 7088 
 
 .592 
 
 .125 6913 
 
 .356 458 
 
 .074 8701 
 
 543 
 
 .104 4109 
 
 .717 767 
 
 .078 6302 
 
 593 
 
 .126 1256 
 
 .369821 
 
 .074 7953 
 
 544 
 
 . 104 8452 
 
 .730 491 
 
 .078 5516 
 
 594 
 
 .126 5599 
 
 .383 198 
 
 .074 7206 
 
 2.545 
 
 i. 105 2795 
 
 12.743 228 
 
 0.078 4731 
 
 2.595 
 
 1.126 9942 
 
 13.396 587 
 
 0.074 6459 
 
 .546 
 
 .105 7138 
 
 755 978 
 
 .078 3946 
 
 .596 
 
 .127 4285 
 
 .409 991 
 
 .074 5713 
 
 547 
 
 .106 1480 
 
 .768 740 
 
 .078 3163 
 
 597 
 
 . 127 8628 
 
 .423 407 
 
 .074 4967 
 
 .548 
 
 .106 5823 
 
 .781 515 
 
 .078 2380 
 
 .598 
 
 .128 2971 
 
 .436 838 
 
 .074 4223 
 
 549 
 
 .107 0166 
 
 794 30J 
 
 .078 1598 
 
 599 
 
 .128 7314 
 
 .450 281 
 
 .074 3479 
 
 2-550 
 
 i. 107 4509 
 
 12.807 104 
 
 0.078 0817 
 
 2.600 
 
 1.129 1657 
 
 13.463 738 
 
 0.074 2736 
 
 Iofl e (e u ) 
 
 looio(e u ) 
 
 e u 
 
 e~ u 
 
 looe(e u ) 
 
 loflio(e n ) 
 
 e u 
 
 e _ n 
 
 SMITHSONIAN TABLES 
 
 251 
 
The Exponential. 
 
 u 
 
 looio(e u ) 
 
 e u 
 
 e- 
 
 u 
 
 Iog 10 (e u ) 
 
 e u 
 
 e u 
 
 2.600 
 
 1.129 1657 
 
 13.463 738 
 
 0.074 2736 
 
 2.650 
 
 I.I50 8804 
 
 14.154 039 
 
 0.070 6512 
 
 .601 
 
 .129 5999 
 
 .477 208 
 
 .074 1993 
 
 .651 
 
 .151 3147 
 
 .168 200 
 
 .070 5806 
 
 .602 
 
 . 130 0342 
 
 .490 692 
 
 .074 1252 
 
 .652 
 
 .151 7490 
 
 .182 375 
 
 .070 5101 
 
 .603 
 
 . 130 4685 
 
 .504 190 
 
 .074 0511 
 
 653 
 
 .152 1833 
 
 .196 565 
 
 .070 4396 
 
 .604 
 
 .130 9028 
 
 .517 701 
 
 .073 9771 
 
 .654 
 
 .152 6176 
 
 .210 768 
 
 .070 3692 
 
 2.605 
 
 I.I3I 3371 
 
 13.531 225 
 
 0.073 9031 
 
 2.655 
 
 I. 153 0518 
 
 14.224 986 
 
 0.070 2988 
 
 .606 
 
 .131 7714 
 
 544 763 
 
 .073 8293 
 
 .656 
 
 .153 4861 
 
 .239 218 
 
 .070 2286 
 
 .607 
 
 .132 2057 
 
 .558 315 
 
 .073 7555 
 
 657 
 
 .153 9204 
 
 .253 464 
 
 .070 1584 
 
 .608 
 
 .132 6400 
 
 .571 880 
 
 .073 6818 
 
 .658 
 
 154 3547 
 
 .267 725 
 
 .070 0883 
 
 .609 
 
 . 133 0743 
 
 .585 459 
 
 .073 6081 
 
 .659 
 
 . 154 7890 
 
 .282 ooo 
 
 .070 0182 
 
 2.610 
 
 1.133 5086 
 
 13.599 051 
 
 0.073 5345 
 
 2.660 
 
 I. 155 2233 
 
 14.296 289 
 
 0.069 9482 
 
 .611 
 
 .133 9429 
 
 .612 657 
 
 .073 4610 
 
 .661 
 
 155 6576 
 
 310 593 
 
 .069 8783 
 
 .612 
 
 . 134 3772 
 
 .626 276 
 
 .073 3876 
 
 .662 
 
 .156 0919 
 
 .324 910 
 
 .069 8085 
 
 .613 
 
 .1348115 
 
 .639 909 
 
 .073 3143 
 
 .663 
 
 .156 5262 
 
 .339 242 
 
 .069 7387 
 
 .614 
 
 .135 2458 
 
 .653 556 
 
 .073 2410 
 
 .664 
 
 . 156 9605 
 
 .353 589 
 
 .069 6690 
 
 2.615 
 
 1.135 6801 
 
 13.667 216 
 
 0.073 1678 
 
 2.665 
 
 I. 157 3948 
 
 14.367 950 
 
 0.069 5994 
 
 .616 
 
 .136 1144 
 
 .680 890 
 
 .073 0947 
 
 .666 
 
 . 157 8291 
 
 .382 325 
 
 .069 5298 
 
 .617 
 
 .136 5487 
 
 .694 578 
 
 .073 0216 
 
 .667 
 
 .158 2634 
 
 .396 714 
 
 .069 4603 
 
 .618 
 
 .136 9830 
 
 .708 280 
 
 .072 9486 
 
 .668 
 
 .158 6977 
 
 .411 118 
 
 .069 3909 
 
 .619 
 
 .137 4172 
 
 721 995 
 
 .072 8757 
 
 .669 
 
 .159 1320 
 
 425 536 
 
 .069 3215 
 
 2.620 
 
 I. 137 8515 
 
 13-735 724 
 
 0.072 8029 
 
 2.670 
 
 I. 159 5663 
 
 14.439 969 
 
 0.069 2522 
 
 .621 
 
 .138 2858 
 
 .749 466 
 
 .072 7301 
 
 .671 
 
 .160 0006 
 
 .454 416 
 
 .069 1830 
 
 .622 
 
 .138 7201 
 
 .763 222 
 
 .072 6574 
 
 .672 
 
 .160 4349 
 
 .468 878 
 
 .069 1139 
 
 .623 
 
 .139 1544 
 
 .776 993 
 
 .072 5848 
 
 .673 
 
 .160 8692 
 
 .483 354 
 
 .069 0448 
 
 .624 
 
 .139 5887 
 
 .790 776 
 
 .072 5122 
 
 .674 
 
 .161 3034 
 
 497 845 
 
 .0689758 
 
 2.625 
 
 I . 140 0230 
 
 13-804 574 
 
 0.072 4398 
 
 2.675 
 
 1.161 7377 
 
 14.512 350 
 
 0.068 0068 
 
 .626 
 
 . 140 4572 
 
 .818 386 
 
 .072 3674 
 
 .676 
 
 .162 1720 
 
 .526 869 
 
 .068 8380 
 
 .627 
 
 . 140 8916 
 
 .832 211 
 
 .072 2950 
 
 .677 
 
 .162 6063 
 
 .541 404 
 
 .068 7692 
 
 .628 
 
 .141 3259 
 
 .846 050 
 
 .072 2228 
 
 .678 
 
 .163 0406 
 
 .555 952 
 
 .068 7004 
 
 .629 
 
 .141 7602 
 
 .859 903 
 
 .072 1506 
 
 .679 
 
 . 163 4749 
 
 570 515 
 
 .068 6318 
 
 2.630 
 
 1.142 I94S 
 
 13.873 770 
 
 0.072 0785 
 
 2.680 
 
 1.163 9092 
 
 14.585 093 
 
 0.068 5632 
 
 .631 
 
 .142 6288 
 
 .887 651 
 
 .072 0064 
 
 .681 
 
 . 164 3435 
 
 .599686 
 
 .068 4946 
 
 .632 
 
 .143 0631 
 
 .001 545 
 
 .071 9344 
 
 .682 
 
 .164 7778 
 
 .614 293 
 
 .068 4262 
 
 .633 
 
 .143 4974 
 
 .915 454 
 
 .071 8626 
 
 .683 
 
 .165 2121 
 
 .628 914 
 
 .068 3578 
 
 .634 
 
 .143 9317 
 
 .929 376 
 
 .071 7907 
 
 .684 
 
 .165 6464 
 
 .643 550 
 
 .068 2894 
 
 2.635 
 
 1.144 3660 
 
 13-943 312 
 
 0.071 7190 
 
 2.685 
 
 1.166 0807 
 
 14.658 201 
 
 0.068 2212 
 
 .636 
 
 .144 8003 
 
 .957 263 
 
 .071 6473 
 
 .686 
 
 .166 5150 
 
 .672 867 
 
 .068 1530 
 
 .637 
 
 .145 2345 
 
 .971 227 
 
 .071 5757 
 
 .687 
 
 . 166 9493 
 
 .687 547 
 
 .068 0849 
 
 .638 
 
 .145 6688 
 
 .985 205 
 
 .071 5041 
 
 .688 
 
 .167 3836 
 
 .702 242 
 
 .068 0168 
 
 .639 
 
 .146 1031 
 
 999 197 
 
 .071 4327 
 
 .689 
 
 .167 8179 
 
 .716 952 
 
 .067 9489 
 
 2.640 
 
 1.146 5374 
 
 14.013 204 
 
 0.071 3613 
 
 2.690 
 
 1.168 2522 
 
 14.731 676 
 
 0.067 8809 
 
 .641 
 
 .146 9717 
 
 .027 224 
 
 .071 2899 
 
 .691 
 
 .168 6865 
 
 .746 415 
 
 .067 8l3I 
 
 .642 
 
 .147 4060 
 
 .041 258 
 
 .071 2187 
 
 .692 
 
 .169 1207 
 
 .761 169 
 
 .067 7453 
 
 .643 
 
 . 147 8403 
 
 .055 306 
 
 .071 1475 
 
 .693 
 
 .169 5550 
 
 775 937 
 
 .067 6776 
 
 .644 
 
 .148 2746 
 
 .069 369 
 
 .071 0764 
 
 .694 
 
 .169 9893 
 
 .790 721 
 
 .067 6100 
 
 2.645 
 
 1.148 7089 
 
 14.083 445 
 
 0.071 0054 
 
 2.695 
 
 1.170 4236 
 
 14.805 519 
 
 0.067 5424 
 
 .646 
 
 .149 1432 
 
 .097 536 
 
 .070 9344 
 
 .696 
 
 . 170 8579 
 
 .820 332 
 
 .067 4749 
 
 .647 
 
 .149 5775 
 
 .in 640 
 
 .070 8635 
 
 .697 
 
 .171 2922 
 
 .835 159 
 
 .067 4074 
 
 .648 
 
 .150 01 18 
 
 .125 759 
 
 .070 7927 
 
 
 .171 7265 
 
 .850 002 
 
 .067 3401 
 
 .649 
 
 .150 4461 
 
 . 139 892 
 
 .070 7219 
 
 .699 
 
 .172 1608 
 
 .864 859 
 
 .067 2728 
 
 2.650 
 
 1.150 8804 
 
 14.154 039 
 
 0.070 6512 
 
 2.700 
 
 I.I72 5951 
 
 14.879 732 
 
 0.067 2055 
 
 looe(e) 
 
 looicXe") 
 
 e n 
 
 e~ u 
 
 looe(e u ) 
 
 |* 
 
 e u 
 
 .- 
 
 SMITHSONIAN TABLES 
 
 252 
 
The Exponential. 
 
 u 
 
 logio(e n ) 
 
 e u 
 
 e- tt 
 
 u 
 
 log w (e u ) 
 
 e u 
 
 e- u 
 
 2.700 
 
 1.172 5951 
 
 14-879 732 
 
 0.067 2055 
 
 2.750 
 
 1.194 3098 
 
 15.642 632 
 
 0.063 9279 
 
 .701 
 
 .173 0294 
 
 .894 619 
 
 .067 1383 
 
 751 
 
 .194 7441 
 
 .658 282' 
 
 .063 8640 
 
 .702 
 
 .173 4637 
 
 .909 52i 
 
 .067 0712 
 
 752 
 
 .195 1784 
 
 .673 948 
 
 .063 8001 
 
 .703 
 
 .173 8980 
 
 .924 438 
 
 .067 0042 
 
 753 
 
 .195 6127 
 
 .689 630 
 
 .063 7364 
 
 .704 
 
 174 3323 
 
 .939 370 
 
 .066 9372 
 
 754 
 
 .196 0470 
 
 .705 328 
 
 .063 6727 
 
 2.705 
 
 1.174 7666 
 
 14-954 317 
 
 0.066 8703 
 
 2.755 
 
 1.196 4813 
 
 15.721 041 
 
 0.063 6090 
 
 .706 
 
 .175 2009 
 
 .969278 
 
 .066 8035 
 
 .756 
 
 .196 9156 
 
 .736 770 
 
 .063 5454 
 
 .707 
 
 175 6352 
 
 .984 255 
 
 .066 7367 
 
 757 
 
 .197 3499 
 
 752 514 
 
 .063 4819 
 
 .708 
 
 . 176 0695 
 
 .999 247 
 
 .066 6700 
 
 .758 
 
 .197 7842 
 
 .768 275 
 
 .063 4185 
 
 .709 
 
 176 5038 
 
 15.014 254 
 
 .066 6039 
 
 .759 
 
 .198 2185 
 
 .784 051 
 
 .063 3551 
 
 2.710 
 
 1.176 9380 
 
 15.029 275 
 
 0.066 5368 
 
 2.760 
 
 1.198 6528 
 
 15.799 843 
 
 0.063 2918 
 
 .711 
 
 .177 3723 
 
 .044 312 
 
 .066 4/03 
 
 .761 
 
 .199 0871 
 
 .815 651 
 
 .063 2285 
 
 .712 
 
 .1778066 
 
 059 364 
 
 .066 4039 
 
 .762 
 
 .199 5214 
 
 .831 474 
 
 .063 1653 
 
 .713 
 
 .178 2409 
 
 .074 431 
 
 .066 3375 
 
 .763 
 
 . 199 9557 
 
 .847 3H 
 
 .063 1022 
 
 .714 
 
 .178 6752 
 
 .089 513 
 
 .066 2712 
 
 764 
 
 .200 3899 
 
 .863 169 
 
 .063 O39I 
 
 2.715 
 
 1.179 1095 
 
 15.104 610 
 
 0.066 2050 
 
 2.765 
 
 1.200 8242 
 
 15.879 040 
 
 0.062 976l 
 
 .716 
 
 . .179 5438 
 
 .119 722 
 
 .066 1388 
 
 .766 
 
 .201 2585 
 
 .894 927 
 
 .062 9132 
 
 .717 
 
 . 179 978i 
 
 .134 850 
 
 .066 0727 
 
 .767 
 
 .201 6928 
 
 .910 830 
 
 .062 8503 
 
 .718 
 
 .180 4124 
 
 .149 992 1 
 
 .066 0066 
 
 .768 
 
 .202 1271 
 
 .926 749 
 
 .062 7875 
 
 .719 
 
 . 180 8467 
 
 .165 149 
 
 .065 9407 
 
 .769 
 
 .202 5614 
 
 .942 683 
 
 .062 7247 
 
 2.720 
 
 1.181 2810 
 
 15.180 322 
 
 0.065 8748 
 
 2.770 
 
 1.202 9957 
 
 15.958 634 
 
 O.O62 662O 
 
 .721 
 
 .181 7153 
 
 .195 5io 
 
 .065 8089 
 
 .771 
 
 .203 4300 
 
 .974 601 
 
 .062 5994 
 
 .722 
 
 .182 1496 
 
 .210 713 
 
 .065 7431 
 
 .772 
 
 .203 8643 
 
 990 583 
 
 .062 5368 
 
 .723 
 
 .182 5839 
 
 .225 932 
 
 .065 6774 
 
 773 
 
 .204 2986 
 
 16.006 582 
 
 .062 4743 
 
 .724 
 
 . 183 0182 
 
 .241 165 
 
 .065 6118 
 
 774 
 
 .204 7329 
 
 .022 596 
 
 .062 4119 
 
 2.725 
 
 1.183 4525 
 
 15.256 414 
 
 0.065 5462 
 
 2.775 
 
 1.205 1672 
 
 16.038 627 
 
 0.062 3495 
 
 .726 
 
 .183 8868 
 
 .271 678 
 
 .065 4807 
 
 .776 
 
 .205 6015 
 
 .054 674 
 
 .062 2872 
 
 .727 
 
 .184 3211 
 
 .286 957 
 
 .065 4152 
 
 777 
 
 .206 0358 
 
 .070 736 
 
 .062 2249 
 
 .728 
 
 .184 7553 
 
 .302 252 
 
 065 3499 
 
 .778 
 
 .206 4701 
 
 .086 815 
 
 .062 1627 
 
 .729 
 
 .185 1896 
 
 .317 562 
 
 .065 2845 
 
 .779 
 
 ,206 9044 
 
 .102 910 
 
 .062 1006 
 
 2.730 
 
 1.185 6239 
 
 15.332 887 
 
 0.065 2193 
 
 2.780 
 
 1.207 3387 
 
 I6.II9 O2I 
 
 0.062 0385 
 
 .731 
 
 . 186 0582 
 
 .348 228 
 
 .065 1541 
 
 .781 
 
 .207 7730 
 
 .135 148 
 
 .061 9765 
 
 .732 
 
 .186 4925 
 
 363 583 
 
 .065 0890 
 
 .782 
 
 .208 2072 
 
 .151 291 
 
 .061 9146 
 
 .733 
 
 . 186 9268 
 
 .378 955 
 
 .065 0239 
 
 .783 
 
 .208 6415 
 
 .167 451 
 
 .061 8527 
 
 .734 
 
 .187 3611 
 
 394 34i 
 
 .064 9589 
 
 .784 
 
 .209 0758 
 
 .183 626 
 
 .061 7908 
 
 2.735 
 
 1.187 7954 
 
 15.409 743 
 
 0.064 8940 
 
 2.785 
 
 1.209 5101 
 
 16.199 818 
 
 0.061 7291 
 
 .736 
 
 .188 2297 
 
 .425 161 
 
 .064 8291 
 
 .786 
 
 .209 9444 
 
 .216 026 
 
 .061 6674 
 
 .737 
 
 . 188 6640 
 
 .440 594 
 
 .064 7643 
 
 .787 
 
 .210 3787 
 
 .232 250 
 
 .061 6058 
 
 .738 
 
 .189 0983 
 
 .456 042 
 
 .064 6006 
 
 
 .210 8130 
 
 .248 490 
 
 .061 5442 
 
 .739 
 
 .189 5326 
 
 .471 5o6 
 
 .064 6349 
 
 '.& 
 
 .211 2473 
 
 .264 747 
 
 .061 4827 
 
 2.740 
 
 1.189 9669 
 
 15.486 985 
 
 0.064 5703 
 
 2.790 
 
 I. 211 68l6 
 
 16.281 020 
 
 0.061 4212 
 
 .741 
 
 .190 4012 
 
 .502 480 
 
 .064 5058 
 
 .791 
 
 .212 1159 
 
 .297 309 
 
 .061 3598 
 
 .742 
 
 .190 8355 
 
 .517 990 
 
 .064 4413 
 
 .792 
 
 .212 5502 
 
 .313 614 
 
 .061 2985 
 
 .743 
 
 .191 2698 
 
 .533 5i6 
 
 .064 3769 
 
 .793 
 
 .212 9845 
 
 329 936 
 
 .061 2372 
 
 .744 
 
 .191 7041 
 
 549 057 
 
 .064 3126 
 
 794 
 
 .213 4188 
 
 .346 274 
 
 .061 1760 
 
 2.745 
 
 1.192 1384 
 
 15.564 614 
 
 0.064 2483 
 
 2.795 
 
 I.2I3 8531 
 
 16.362 629 
 
 0.061 1149 
 
 .746 
 
 .192 5726 
 
 .580 186 
 
 .064 1841 
 
 .796 
 
 .214 2874 
 
 .379 ooo 
 
 .061 0538 
 
 .747 
 
 .193 0069 
 
 595 774 
 
 .064 1199 
 
 .797 
 
 .214 7217 
 
 395 387 
 
 .060 9928 
 
 .748 
 
 .193 4412 
 
 .611 378 
 
 .064 0558 
 
 .798 
 
 .215 1560 
 
 .411 790 
 
 .060 9318 
 
 .749 
 
 .193 8755 
 
 .626 997 
 
 .063 9918 
 
 .799 
 
 215 5903 
 
 .428 2IO 
 
 .060 8709 
 
 2.750 
 
 1.194 3098 
 
 15.642 632 
 
 0.063 9279 
 
 2.800 
 
 1.216 0245 
 
 16.444 647 
 
 0.060 8101 
 
 log e (e u ) 
 
 looio(e n ) 
 
 e u 
 
 e~~ u 
 
 looe(e u ) 
 
 looio(e n ) 
 
 e u 
 
 e~ u 
 
 SMITHSONIAN TABLES 
 
 253 
 
The Exponential. 
 
 u 
 
 logio(e u ) 
 
 e n 
 
 e u 
 
 u 
 
 looio(e n ) 
 
 e u 
 
 e~ u 
 
 2.800 
 
 I. 216 0245 
 
 16.444 647 
 
 0.060 8101 
 
 2.850 
 
 1-237 7393 
 
 17.287 782 
 
 0.057 8443 
 
 .801 
 
 .216 4588 
 
 .461 loo .060 7493 
 
 .851 
 
 .238 1736 
 
 .305 078 
 
 .057 7865 
 
 .802 
 
 .216 8931 
 
 .477 569 -060 6886 
 
 .852 
 
 .238 6079 
 
 .322 392 
 
 .057 7287 
 
 .803 
 
 .217 3274 
 
 .494 055 .060 6279 
 
 .853 
 
 .239 0422 
 
 339 723 
 
 .057 6710 
 
 .804 
 
 .217 7617 
 
 510 557 
 
 .060 5673 
 
 854 
 
 .239 4765 
 
 357 071 
 
 .057 6134 
 
 2.805 
 
 1.218 1960 
 
 16.527 076 
 
 0.060 5068 
 
 2.855 
 
 1.239 9107 
 
 17.374 437 
 
 0.057 5558 
 
 .806 
 
 .218 6303 
 
 543 611 
 
 .060 4463 
 
 .856 
 
 .240 3450 
 
 .391 820 
 
 .057 4083 
 
 .807 
 
 .219 0646 
 
 .560 163 
 
 .060 3859 
 
 857 
 
 .240 7793 
 
 .409 221 
 
 .057 4408 
 
 .808 
 
 .219 4989 
 
 .576 732 
 
 .060 3255 
 
 .858 
 
 .241 2136 
 
 .426 639 
 
 057 3834 
 
 .809 
 
 .219 9332 
 
 593 317 
 
 .060 2652 
 
 .859 
 
 .241 6479 
 
 .444 074 
 
 .057 3261 
 
 2.810 
 
 1.220 3675 
 
 16.609 9i8 
 
 0.060 2050 
 
 2.860 
 
 1.242 0822 
 
 17.461 527 
 
 0.057 2688 
 
 .811 
 
 .220 8018 
 
 .626 536 
 
 .060 1448 
 
 .861 
 
 .242 5165 
 
 .478 997 
 
 .057 2115 
 
 .812 
 
 .221 2361 
 
 .643 I7i 
 
 .060 0847 
 
 .862 
 
 .242 9508 
 
 .496 485 
 
 057 1543 
 
 .813 
 
 .221 6704 
 
 .659 823 
 
 .060 0246 
 
 .863 
 
 .243 3851 
 
 .513 990 
 
 .057 0972 
 
 .814 
 
 .222 1047 
 
 .676 491 
 
 .059 9047 
 
 .864 
 
 .243 8194 
 
 .531 513 
 
 .057 0401 
 
 2.815 
 
 1.222 5390 
 
 16.693 176 
 
 0.059 9047 
 
 2.865 
 
 1.244 2537 
 
 17.549 053 
 
 0.056 9831 
 
 .816 
 
 .222 9733 
 
 .709 877 
 
 .059 8448 
 
 .866 
 
 .244 6880 
 
 .566 611 
 
 .056 9262 
 
 .817 
 
 .223 4076 
 
 .726 596 
 
 .059 7850 
 
 .85 7 
 
 .245 1223 
 
 .584 186 
 
 .056 8693 
 
 .818 
 
 .223 8418 
 
 743 331 
 
 .059 7253 
 
 .868 
 
 .245 5566 
 
 .601 779 
 
 .056 8124 
 
 .819 
 
 .224 2761 
 
 .760 082 
 
 .059 6656 
 
 .869 
 
 .245 9909 
 
 .619 390 
 
 056 7557 
 
 2.820 
 
 1.224 7104 
 
 16.776 851 
 
 0.059 6059 
 
 2.870 
 
 1.246 4252 
 
 17.637 018 
 
 0.056 6989 
 
 .821 
 
 .225 1447 
 
 .793 636 
 
 059 5464 
 
 .871 
 
 .246 8595 
 
 .654 664 
 
 .056 6423 
 
 .822 
 
 .225 5790 
 
 .810 438 
 
 .059 4868 
 
 .872 
 
 .247 2938 
 
 .672 328 
 
 056 5856 
 
 .823 
 
 .824 
 
 .226 0133 
 .226 4476 
 
 .827 257 
 .844 692 
 
 .059 4274 
 .059 3680 
 
 .873 
 .874 
 
 .247 7280 
 .248 1623 
 
 .690 009 
 
 .707 708 
 
 .056 5291 
 .056 4726 
 
 2.825 
 
 1.226 8819 
 
 16.860 945 
 
 0.059 3087 
 
 2.875 
 
 1.248 5966 
 
 17.725 424 
 
 0.056 4161 
 
 .826 
 
 .227 3162 
 
 .877 814 
 
 .059 2494 
 
 .876 
 
 .249 0309 
 
 743 158 
 
 .056 3598 
 
 .827 
 
 .227 7505 
 
 .894 70i 
 
 .059 1902 
 
 .877 
 
 .249 4652 
 
 .760 910 
 
 .056 3034 
 
 .828 
 
 .228 1848 
 
 .911 604 
 
 .059 1310 
 
 .878 
 
 .249 8995 
 
 .778 680 
 
 .056 2471 
 
 .829 
 
 .228 6191 
 
 .928 524 
 
 .059 0719 
 
 .879 
 
 250 3338 
 
 .796468 
 
 .056 1909 
 
 2.830 
 
 1.229 0534 
 
 16.945 461 
 
 0.059 0129 
 
 2.880 
 
 1.250 7681 
 
 17.814 273 
 
 0.056 1348 
 
 .831 
 
 .229 4877 
 
 .962 415 
 
 .058 9539 
 
 .881 
 
 .251 2024 
 
 .832 096 
 
 .056 0787 
 
 .832 
 
 .229 9220 
 
 .979 386 
 
 .058 8949 
 
 .882 
 
 .251 6367 
 
 849 937 
 
 .056 0226 
 
 .833 
 
 .230 3563 
 
 .996 374 
 
 .058 8361 
 
 .883 
 
 .252 0710 
 
 .867 795 
 
 .055 9666 
 
 .834 
 
 .230 7906 
 
 17-013 378 
 
 058 7773 
 
 .884 
 
 .252 5053 
 
 .885 673 
 
 .055 9107 
 
 2.835 
 
 1.231 2249 
 
 17.030 400 
 
 0.058 7185 
 
 2.885 
 
 1.252 9396 
 
 17.903 568 
 
 0.055 8548 
 
 .836 
 
 .231 6592 
 
 .047 439 
 
 .058 6598 
 
 .886 
 
 .253 3739 
 
 .921 480 
 
 .055 7990 
 
 .837 
 
 .232 0934 
 
 .064 495 
 
 .058 6012 
 
 .887 
 
 .253 8082 
 
 939 411 
 
 055 7432 
 
 .838 
 
 .232 5277 
 
 .081 568 
 
 .058 5426 
 
 .888 
 
 .254 2425 
 
 .957 359 
 
 .055 6875 
 
 .839 
 
 .232 9620 
 
 .098658 
 
 .058 4841 
 
 .889 
 
 .254 6768 
 
 975 325 
 
 .055 6318 
 
 2.840 
 
 1.233 3963 
 
 17.115 766 
 
 0.058 4257 
 
 2.890 
 
 1.255 TIII 
 
 17-993 310 
 
 0.055 5762 
 
 .841 
 
 .233 8306 
 
 .132 890 
 
 058 3673 
 
 .891 
 
 .255 5453 
 
 18.011 312 
 
 .055 5207 
 
 .842 
 
 .234 2649 
 
 .150 031 
 
 .058 3089 
 
 .892 
 
 .255 9796 
 
 .029 332 
 
 .055 4652 
 
 .843 
 
 .234 6992 
 
 .167 190 
 
 .058 2507 
 
 .893 
 
 .256 4139 
 
 .047 371 
 
 .055 4097 
 
 .844 
 
 235 1335 
 
 .184 366 
 
 .058 1924 
 
 .894 
 
 .256 8482 
 
 .065 4^7 
 
 .055 3544 
 
 2.845 
 
 1.235 5678 
 
 17.201 559 
 
 0.058 1343 
 
 2.895 
 
 1.257 2825 
 
 18.083 SOT 
 
 0.055 2990 
 
 .846 
 
 .236 0021 
 
 .218 769 
 
 .058 0762 
 
 .896 
 
 .257 7i68 
 
 .101 594 
 
 .055 8438 
 
 .847 
 
 .236 4364 
 
 .235 996 
 
 .058 0181 
 
 .*,; 
 
 .258 1511 
 
 .119 705 
 
 .055 1885 
 
 .848 
 
 .236 8707 
 
 .253 241 
 
 .057 0601 
 
 .898 
 
 .258 5854 
 
 . 137 833 
 
 .055 U34 
 
 .849 
 
 .237 3050 
 
 .270 503 
 
 .057 9022 
 
 .899 
 
 .259 0197 
 
 .155 98o 
 
 055 0783 
 
 2.850 
 
 1.237 7393 
 
 17.287 782 
 
 0.057 8443 
 
 2.900 
 
 1.259 4540 
 
 18.174 MS 
 
 0.055 0232 
 
 lofe(e n ) 
 
 Iog 10 (e ) 
 
 e" 
 
 a 
 
 1ooc(e u ) 
 
 lo 0l ,Xe a ) 
 
 a" 
 
 e- 
 
 SMITHSONIAN TABLES 
 
 254 
 
The Exponential. 
 
 1 
 u 
 
 log w (e u ) 
 
 e u 
 
 e~ u 
 
 u 
 
 logio(e n ) 
 
 e n 
 
 e~ u 
 
 2.900 
 
 1.259 4540 
 
 18.174 145 
 
 0.055 0232 
 
 2.950 
 
 1.281 1687 
 
 19-105 954 
 
 0.052 3397 
 
 .501 
 
 .259 8883 
 
 .192 329 
 
 .054 9682 
 
 951 
 
 .281 6030 
 
 .125 069 
 
 .052 2874 
 
 .902 
 
 .260 3226 
 
 .210 530 
 
 .054 9133 
 
 952 
 
 .282 0373 
 
 .144 204 
 
 .052 2351 
 
 .903 
 
 .260 7569 
 
 .228 750 
 
 .054 8584 
 
 953 
 
 .282 4716 
 
 163 358 
 
 .052 1829 
 
 .904 
 
 .261 1912 
 
 .246 988 
 
 .054 8036 
 
 954 
 
 .282 9059 
 
 .182 531 
 
 .052 1308 
 
 2.905 
 
 1.261 6255 
 
 18.265 244 
 
 0.054 7488 
 
 2.955 
 
 1.283 3402 
 
 19.201 723 
 
 0.052 0787 
 
 .906 
 
 .262 0598 
 
 .283 5l8 
 
 .054 6941 
 
 .956 
 
 .283 7745 
 
 .220 934 
 
 .052 0266 
 
 .907 
 
 .262 4941 
 
 .301 811 
 
 .054 6304 
 
 957 
 
 .284 2088 
 
 .240 165 
 
 .051 9746 
 
 .908 
 
 .262 9284 
 
 .320 122 
 
 .054 5848 
 
 .958 
 
 .284 6431 
 
 .259 414 
 
 .051 9227 
 
 .909 
 
 .263 3626 
 
 .338 451 
 
 .051 5302 
 
 959 
 
 .285 0774 
 
 .278 683 
 
 .051 8708 
 
 2.910 
 
 1.263 7969 
 
 18.356" 799 
 
 0.054 4757 
 
 2.060 
 
 1.285 5H7 
 
 19.297 972 
 
 0.051 8189 
 
 .911 
 
 .264 2312 
 
 375 165 
 
 .054 4213 
 
 .961 
 
 .285 9460 
 
 .317 279 
 
 .051 7671 
 
 .912 
 
 .264 6655 
 
 393 549 
 
 .054 3669 
 
 .962 
 
 .286 3803 
 
 .336 606 
 
 .051 7154 
 
 .913 
 
 .265 0998 
 
 .411 952 
 
 .054 3125 
 
 .963 
 
 .286 8145 
 
 355 953 
 
 .051 6637 
 
 .914 
 
 .265 5341 
 
 430 373 
 
 .054 2583 
 
 .964 
 
 .287 2488 
 
 .375 3i8 
 
 .051 6121 
 
 2.915 
 
 1.265 9684 
 
 18.448 812 
 
 0.054 2040 
 
 2.965 
 
 1.287 6831 
 
 19.394 703 
 
 0.051 5605 
 
 .916 
 
 .266 4027 
 
 .467 270 
 
 .054 1499 
 
 .966 
 
 .288 1174 
 
 .414 108 
 
 .051 5089 
 
 .917 
 
 ' .266 8370 
 
 .485 747 
 
 .054 0957 
 
 .967 
 
 .288 5517 
 
 433 53i 
 
 .051 4575 
 
 .918 
 
 .267 2713 
 
 .504 242 
 
 .054 0417 
 
 .968 
 
 .2889860 
 
 452 975 
 
 .051 4060 
 
 .919 
 
 .267 7056 
 
 .522 755 
 
 .053 9876 
 
 .969 
 
 .289 4203 
 
 472 437 
 
 .051 3546 
 
 2.920 
 
 1.268 1399 
 
 18.541 287 
 
 0.053 9337 
 
 2.970 
 
 1.289 8546 
 
 19.491 920 
 
 0.051 3033 
 
 .921 
 
 .268 5742 
 
 559 838 
 
 .053 8758 
 
 971 
 
 .290 2889 
 
 .511 421 
 
 .051 2520 
 
 .922 
 
 .269 0085 
 
 .578 407 
 
 .053 8259 
 
 .972 
 
 .290 7232 
 
 .530 942 
 
 .051 2008 
 
 .923 
 
 .269 4428 
 
 .596 995 
 
 .053 7721 
 
 973 
 
 .291 1575 
 
 550 483 
 
 .051 1496 
 
 .924 
 
 .269 8771 
 
 .615 601 
 
 .053 7184 
 
 974 
 
 .291 5918 
 
 .570 043 
 
 .051 0985 
 
 2.925 
 
 1.270 3114 
 
 18.634 226 
 
 0.053 6647 
 
 2.975 
 
 1.292 0261 
 
 19.589 623 
 
 0.051 0474 
 
 .926 
 
 .270 7457 
 
 .652 870 
 
 .053 6111 
 
 .976 
 
 .292 4604 
 
 .609 223 
 
 .050 9964 
 
 .927 
 
 .271 1799 
 
 .671 532 
 
 053 5575 
 
 977 
 
 .292 8947 
 
 .628 842 
 
 .050 9454 
 
 .928 
 
 .271 6142 
 
 .690 213 
 
 .053 5039 
 
 .978 
 
 .293 3290 
 
 .648 480 
 
 .050 8045 
 
 .929 
 
 .272 0485 
 
 .708 912 
 
 .053 4505 
 
 979 
 
 .293 7633 
 
 .668 139 
 
 .050 8437 
 
 2.930 
 
 1.272 4828 
 
 18.727 631 
 
 0.053 3970 
 
 2.980 
 
 1.294 1976 
 
 19.687 817 
 
 0.050 7928 
 
 .931 
 
 .272 9171 
 
 .746 368 
 
 .053 3437 
 
 .981 
 
 .294 6319 
 
 .707 5U 
 
 .050 7421 
 
 .932 
 
 .273 3514 
 
 .765 123 
 
 .053 2904 
 
 .982 
 
 .295 0661 
 
 .727 232 
 
 .050 6913 
 
 933 
 
 273 7857 
 
 .783 898 
 
 .053 2371 
 
 .983 
 
 .295 5004 
 
 .746 969 
 
 .050 6407 
 
 934 
 
 .274 22OO 
 
 .802 691 
 
 .053 1839 
 
 .984 
 
 .295 9347 
 
 .766 726 
 
 .050 5901 
 
 2.935 
 
 1.274 6543 
 
 18.821 505 
 
 0.053 1307 
 
 2.985 
 
 1.296 3690 
 
 19.786 502 
 
 0.050 5395 
 
 .936 
 
 .275 0886 
 
 .840 334 
 
 .053 0776 
 
 .986 
 
 .296 8033 
 
 .806 299 
 
 .050 4890 
 
 937 
 
 .275 5229 
 
 .859 184 
 
 .053 0246 
 
 .987 
 
 .297 2376 
 
 .826 115 
 
 .050 4385 
 
 .938 
 
 .275 9572 
 
 .878 052 
 
 .052 9716 
 
 .988 
 
 .297 6719 
 
 .845 951 
 
 .050 3881 
 
 939 
 
 .276 3915 
 
 .896 940 
 
 .052 9186 
 
 .989 
 
 .298 1062 
 
 .865 807 
 
 .050 3377 
 
 2.940 
 
 1.276 8258 
 
 18.915 846 
 
 0.052 8657 
 
 2.990 
 
 1.298 5405 
 
 19.885 682 
 
 0.050 2874 
 
 .941 
 
 .277 2601 
 
 934 772 
 
 .052 8129 
 
 .991 
 
 .298 9748 
 
 .905 578 
 
 .050 2372 
 
 .942 
 
 .277 6944 
 
 953 7i6 
 
 .052 7601 
 
 .992 
 
 .299 4091 
 
 .925 494 
 
 .050 1870 
 
 943 
 
 .278 1287 
 
 .972 679 
 
 .052 7074 
 
 993 
 
 .299 8434 
 
 .945 429 
 
 .050 1368 
 
 944 
 
 .278 5630 
 
 .991 661 
 
 .052 6547 
 
 .994 
 
 .300 2777 
 
 .965 385 
 
 .050 0867 
 
 2.945 
 
 1.278 9972 
 
 19.010 662 
 
 0.052 6021 
 
 2.995 
 
 1.300 7120 
 
 19.985 360 
 
 0.050 0366 
 
 .946 
 
 .279 4315 
 
 .029 683 
 
 .052 5495 
 
 .996 
 
 .301 1463 
 
 20.005 355 
 
 .049 9866 
 
 947 
 
 .279 8658 
 
 .048 722 
 
 .052 4970 
 
 997 
 
 .301 5806 
 
 .025 371 
 
 .049 9367 
 
 .948 
 
 .280 3001 
 
 .067 780 
 
 .052 4445 
 
 .998 
 
 .302 0149 
 
 .045 406 
 
 .049 8867 
 
 949 
 
 .280 7344 
 
 .086857 
 
 .052 3921 
 
 999 
 
 .302 4492 
 
 .065 461 
 
 .049 8369 
 
 2.950 
 
 1.281 1687 
 
 19-105 954 
 
 0.052 3397 
 
 3.000 
 
 1.302 8834 
 
 20.085 537 
 
 0.049 7871 
 
 looe(e u ) 
 
 logio(e u ) 
 
 e u 
 
 e~ u 
 
 lo fle (e u ) 
 
 logio(e u ) 
 
 e u 
 
 e- u 
 
 SMITHSONIAN TABLES 
 
 255 
 
The Exponential. 
 
 u 
 
 looio(e u ) 
 
 e n 
 
 e u 
 
 u 
 
 logioCe") 
 
 e u 
 
 - 
 
 3.00 
 
 .01 
 
 .02 
 
 .03 
 .04 
 
 1.302 8834 
 .307 2264 
 311 5693 
 .315 9123 
 .320 2552 
 
 20.085 537 
 .287 400 
 .491 292 
 .697 233 
 .905 243 
 
 0.049 7871 
 .049 2917 
 .048 8012 
 .048 3156 
 .047 8349 
 
 3-50 
 
 51 
 
 52 
 .53 
 54 
 
 1.520 0307 
 .524 3736 
 .528 7166 
 .533 0595 
 537 4025 
 
 33-115 452 
 .448 268 
 .784 429 
 34.123 968 
 .466 919 
 
 0.030 1974 
 .029 8969 
 .029 5994 
 .029 3049 
 .029 0133 
 
 3-05 
 .06 
 .07 
 .08 
 .09 
 
 1.324 5982 
 .328 9411 
 .333 2841 
 .337 6270 
 .341 9699 
 
 2I.H5 344 
 .327 557 
 .541 903 
 .758 402 
 .977 078 
 
 0.047 3589 
 .046 8877 
 .046 4212 
 .045 9593 
 .045 5020 
 
 S :S 
 
 :i 
 
 59 
 
 1.541 7454 
 .546 0884 
 550 4313 
 554 7742 
 559 H72 
 
 34.813 318 
 35.163 197 
 .5i6 593 
 .873 541 
 36.234 076 
 
 0.028 7246 
 .028 4388 
 .028 1559 
 .027 8757 
 027 5983 
 
 3-10 
 .11 
 
 .12 
 
 .13 
 .14 
 
 1.346 3129 
 350 6558 
 .354 9988 
 359 3417 
 .363 6847 
 
 22.197 951 
 .421 044 
 .646 380 
 .873 080 
 23.103 867 
 
 0.045 0492 
 .044 6010 
 .044 1572 
 .043 7178 
 .043 2828 
 
 3.60 
 
 .6l 
 .62 
 .63 
 
 .64 
 
 1.563 4601 
 .567 8031 
 .572 1460 
 .576 4890 
 .580 8319 
 
 36.598 234 
 .966 053 
 37.337 568 
 .712 817 
 38.091 837 
 
 0.027 3237 
 .027 0518 
 .026 7827 
 .026 5162 
 .026 2523 
 
 3.15 
 .16 
 
 is 
 
 .19 
 
 1.368 0276 
 372 3706 
 .376 7U5 
 .381 0565 
 .385 3994 
 
 23.336 065 
 .570 596 
 .807 484 
 24.046 754 
 .288 427 
 
 0.042 8521 
 .042 4257 
 .042 0036 
 .041 5857 
 .041 1719 
 
 3.65 
 
 .66 
 .67 
 .68 
 .69 
 
 1.585 1749 
 089 5178 
 593 8607 
 .598 2037 
 .602 5466 
 
 38.474 666 
 .861 343 
 39.251 906 
 .646 394 
 40.044 847 
 
 0.025 9911 
 .025 7325 
 .025 4765 
 .025 2230 
 .024 9720 
 
 3.20 
 
 .21 
 .22 
 .23 
 .24 
 
 1.389 7423 
 .394 0853 
 .398 4282 
 .402 7712 
 .407 1141 
 
 24.532 530 
 .779086 
 
 25.O28 I2O 
 .279 657 
 
 533 722 
 
 0.040 7622 
 .040 3566 
 .039 9551 
 .039 5575 
 .039 1639 
 
 3.70 
 
 .71 
 72 
 
 73 
 74 
 
 I .606 8896 
 .611 2325 
 .615 5755 
 .619 9184 
 .624 2614 
 
 40.447 304 
 .853 807 
 41.264 394 
 .679 108 
 42.097 990 
 
 0.024 7235 
 .024 4775 
 .024 2340 
 .023 9928 
 .023 7541 
 
 3.25 
 .26 
 
 3 
 
 .29 
 
 1.411 4571 
 .415 8000 
 .420 1430 
 .424 4859 
 
 25.790 340 
 26.049 537 
 .3H 339 
 575 773 
 .842 864 
 
 0.038 7742 
 .038 3884 
 .038 0064 
 .037 6283 
 .037 2538 
 
 3 :^ 
 
 .77 
 78 
 .79 
 
 1.628 6043 
 632 9473 
 .637 2902 
 .641 6331 
 .645 9761 
 
 42.521 082 
 .948 426 
 43.380 065 
 .816 042 
 44.256 400 
 
 0.023 5177 
 .023 2837 
 .023 0521 
 .022 8227 
 .022 5956 
 
 3.30 
 .31 
 32 
 33 
 
 34 
 
 1.433 1718 
 437 5147 
 .441 8577 
 .446 2006 
 .450 5436 
 
 27.112 639 
 .385 125 
 .660 351 
 .938 342- 
 28.219 127 
 
 0.036 8832 
 .036 5162 
 .036 1528 
 .035 7931 
 .035 4370 
 
 3.8o 
 .81 
 .82 
 .83 
 .84 
 
 1.650 3190 
 .654 6620 
 .659 0049 
 .663 3479 
 .667 6908 
 
 44.701 184 
 
 45.150 439 
 .604 208 
 46.062 538 
 .525 474 
 
 0.022 3708 
 .022 1482 
 .O2I 9278 
 .O2I 7096 
 .O2I 4936 
 
 ':S 
 
 3 
 
 .39 
 
 1.454 8865 
 .459 2295 
 .463 5724 
 .467 9153 
 .472 2583 
 
 28.502 734 
 .789 191 
 29.078 527 
 .370 771 
 .665 952 
 
 0.035 0844 
 034 7353 
 .034 3896 
 .034 0475 
 .033 7087 
 
 ':!! 
 
 :! 
 
 .89 
 
 1.672 0338 
 .676 3767 
 .680 7196 
 .685 0626 
 .689 4055 
 
 46.093 063 
 47.465 351 
 942 386 
 48.424 215 
 .910 887 
 
 O.02I 2797 
 .021 0680 
 .020 8584 
 .020 6508 
 
 .020 4453 
 
 3.40 
 
 .41 
 
 .42 
 
 43 
 44 
 
 1.476 6012 
 .480 9442 
 .485 2871 
 .489 6301 
 .493 9730 
 
 29.964 100 
 30.265 244 
 .569 415 
 .876 643 
 31.186 958 
 
 0.033 3733 
 .033 0412 
 .032 7124 
 .032 3869 
 .032 0647 
 
 3-90 
 .91 
 .92 
 93 
 .94 
 
 1.693 7485 
 .698 0914 
 .702 4344 
 .706 7773 
 .711 1203 
 
 49.402 449 
 .898952 
 50.400 445 
 .906 978 
 51.418 601 
 
 0.020 2419 
 .020 O405 
 .OI9 8411 
 .019 6437 
 .OI9 4482 
 
 3-45 
 .46 
 47 
 .48 
 .49 
 
 1.498 3160 
 .502 6589 
 .507 0019 
 .511 3448 
 .515 6877 
 
 31.500 392 
 .816 977 
 32.136 743 
 .459 722 
 .785 948 
 
 0.031 7456 
 .031 4298 
 .031 1170 
 .030 8074 
 .030 5009 
 
 3 '?J 
 .96 
 
 .99 
 
 1.715 4632 
 .719 8061 
 .724 1491 
 .728 4920 
 732 8350 
 
 51.935 367 
 52.457 326 
 .984 53i 
 53.517 034 
 54.054 889 
 
 0.019 2547 
 .019 0631 
 .018 8734 
 .018 6856 
 .018 4997 
 
 3.50 
 
 1.520 0307 
 
 33-II5 452 
 
 0.030 1974 
 
 4.00 
 
 1.737 1779 
 
 54.598 150 
 
 0.018 3156 
 
 loflc(e) 
 
 looicXe") 
 
 e n 
 
 e~ u 
 
 looc(e n ) 
 
 loouXe") 
 
 '" 
 
 e~ u 
 
 SMITHSONIAN TABLCS 
 
 256 
 
The Exponential. 
 
 1 
 u 
 
 logio(e u ) 
 
 e u 
 
 e~ u 
 
 u 
 
 loflio(e n ) 
 
 e u 
 
 e 
 
 4.00 
 
 1-737 1779 
 
 54.598 150 
 
 0.018 3156 
 
 4.50 
 
 1.954 3252 
 
 90.017 131 
 
 o.on .1090 
 
 .01 
 
 .741 5209 
 
 55.146 871 
 
 .018 1334 
 
 .51 
 
 .958 6681 
 
 .921 819 
 
 .010 9985 
 
 .02 
 
 745 8638 
 
 .701 106 
 
 .017 9530 
 
 .52 
 
 .963 oni 
 
 91.835 598 
 
 .010 8890 
 
 03 
 
 .750 2068 
 
 56.260 911 
 
 .017 7743 
 
 53 
 
 .967 3540 
 
 92.758 561 
 
 .010 7807 
 
 .04 
 
 754 5497 
 
 .826 343 
 
 .017 5975 
 
 54 
 
 .971 6969 
 
 93.690 800 
 
 .010 6734 
 
 4-05 
 
 1.758 8927 
 
 57-397 457 
 
 0.017 4224 
 
 4-55 
 
 1.976 0399 
 
 94.632 408 
 
 o.oio 5672 
 
 .06 
 
 .763 2356 
 
 .974 3ii 
 
 .017 2490 
 
 .56 
 
 .980 3828 
 
 95.583 480 
 
 .010 4621 
 
 .07 
 
 .767 5785 
 
 58.556 963 
 
 .017 0774 
 
 57 
 
 .984 7258 
 
 96.544 no 
 
 .010 3580 
 
 .08 
 
 .771 9215 
 
 59.145 470 
 
 .016 9075 
 
 .58 
 
 .9890687 
 
 97.514 394 
 
 .010 2549 
 
 .09 
 
 .776 2644 
 
 .739 892 
 
 .016 7392 
 
 .59 
 
 993 4H7 
 
 98.494 430 
 
 .oio 1529 
 
 4.10 
 
 1.780 6074 
 
 60.340 288 
 
 0.016 5727 
 
 4.60 
 
 1.997 7546 
 
 99.484 3i6 
 
 o.oio 0518 
 
 .11 
 
 .784 9503 
 
 .946 718 
 
 .016 4078 
 
 .61 
 
 2.002 0976 
 
 100.484 150 
 
 .009 9518 
 
 .12 
 
 .789 2933 
 
 6i.559 242 
 
 .016 2445 
 
 .62 
 
 .006 4405 
 
 101.494 032 
 
 .009 8528 
 
 13 
 
 .793 6362 
 
 62.177 923 
 
 .016 0829 
 
 .63 
 
 .010 7835 
 
 102.514 064 
 
 .000 7548 
 
 .14 
 
 797 9792 
 
 .802 821 
 
 .015 9229 
 
 .64 
 
 .015 1264 
 
 103.544 348 
 
 .009 6577 
 
 4-15 
 
 1.802 3221 
 
 63.434 ooo 
 
 0.015 7644 
 
 4.65 
 
 2.019 4693 
 
 104.584 986 
 
 0.009 5616 
 
 .16 
 
 .806 6650 
 
 64.071 523 
 
 .015 6076 
 
 .66 
 
 .023 8123 
 
 105.636 082 
 
 .009 4665 
 
 17 
 
 .811 0080 
 
 .715 452 
 
 .015 4523 
 
 .67 
 
 .028 1552 
 
 106.697 743 
 
 .009 3723 
 
 .18 
 
 .815 3509 
 
 65.365 853 
 
 .015 2085 
 
 .68 
 
 .032 4082 
 
 107.770 073 
 
 .009 2790 
 
 .19 
 
 .819 6939 
 
 66.022 791 
 
 .015 1463 
 
 .69 
 
 .036 8411 
 
 108.853 180 
 
 .009 1867 
 
 4.20 
 
 1.824 0368 
 
 66.686 331 
 
 0.014 9956 
 
 4.70 
 
 2.041 1841 
 
 109.947 172 
 
 0.009 0953 
 
 .21 
 
 .828 3798 
 
 67-356 540 
 
 .014 8464 
 
 .71 
 
 .045 5270 
 
 111.052 160 
 
 .009 0048 
 
 .22 
 
 .832 7227 
 
 68.033 484 
 
 .014 6986 
 
 .72 
 
 .049 8700 
 
 112.168 253 
 
 .008 9152 
 
 23 
 
 .837 0657 
 
 .717 232 
 
 .014 5524 
 
 73. 
 
 .054 2129 
 
 113.295 563 
 
 .008 8265 
 
 .24 
 
 .841 4086 
 
 69.407 852 
 
 .014 4076 
 
 74 
 
 .058 5558 
 
 114.434 20 J 
 
 .008 7386 
 
 4-25 
 
 1.845 7515 
 
 70.105 412 
 
 0.014 2642 
 
 4.75 
 
 2.062 8o83 
 
 115.584 285 
 
 0.008 6=517 
 
 .26 
 
 .850 0945 
 
 .809983 
 
 .014 1223 
 
 76 
 
 .067 2417 
 
 II6.745 926 
 
 .008 5656 
 
 .27 
 
 .854 4374 
 
 71.521 636 
 
 .013 9818 
 
 77 
 
 .071 5847 
 
 II7.9I9 242 
 
 .008 4804 
 
 .28 
 
 .858 7804 
 
 72.240 440 
 
 .013 8427 
 
 . .78 
 
 .075 9276 
 
 II9.I04 351 
 
 .008 3960 
 
 .29 
 
 .863 1233 
 
 .966 468 
 
 .013 7049 
 
 .79 
 
 .080 2706 
 
 120.301 369 
 
 .008 3125 
 
 4.30 
 
 1.867 4663 
 
 73.699 794 
 
 0.013 5686 
 
 4.80 
 
 2.084 6135 
 
 I2I.5IO 418 
 
 0.008 2297 
 
 31 
 
 .871 8092 
 
 74.440 489 
 
 .013 4335 
 
 .81 
 
 .088 9565 
 
 122.731 61 8 
 
 .008 1479 
 
 32 
 
 .876 1522 
 
 75.188 628 
 
 .013 2999 
 
 .82 
 
 " .093 2994 
 
 123.965 091 
 
 .008 0668 
 
 33 
 
 .880 4951 
 
 .944 287 
 
 .013 1675 
 
 .83 
 
 .097 6423 
 
 125.210 961 
 
 .007 9865 
 
 34 
 
 .884 8381 
 
 76.707 539 
 
 .013 0365 
 
 .84 
 
 .101 9853 
 
 126.469 352 
 
 .007 9071 
 
 4-35 
 
 1.889 1810 
 
 77.478 463 
 
 0.012 9068 
 
 4.85 
 
 2.106 3282 
 
 127.740 390 
 
 0.007 8284 
 
 .36 
 
 .893 5239 
 
 78.257 134 
 
 .012 7784 
 
 .86 
 
 .no 6712 
 
 129.024 203 
 
 .007 7505 
 
 37 
 
 .897 8669 
 
 79.043 632 
 
 .012 6512 
 
 .87 
 
 .115 0141 
 
 130.320 918 
 
 .007 6734 
 
 .38 
 
 .902 2058 
 
 .838 033 
 
 .012 5254 
 
 .88 
 
 .119 357i 
 
 131.630 665 
 
 .007 5970 
 
 39 
 
 .906 5528 
 
 80.640 419 
 
 .012 4007 
 
 .89 
 
 .123 7000 
 
 132.953 575 
 
 .007 5214 
 
 4.40 
 
 1.910 8957 
 
 81.450 869 
 
 O.OI2 2773 
 
 4.90 
 
 2.128 0430 
 
 134.289 780 
 
 0.007 4466 
 
 .41 
 
 .915 2387 
 
 82.269 464 
 
 .012 1552 
 
 .91 
 
 .132 3859 
 
 135.639 415 
 
 .007 3725 
 
 .42 
 
 .919 5816 
 
 83.096 285 
 
 .012 0342 
 
 .92 
 
 . 136 7289 
 
 137.002 613 
 
 .007 2991 
 
 43 
 
 .923 9246 
 
 .931 417 
 
 .Oil 9U5 
 
 93 
 
 .141 0718 
 
 138.379 513 
 
 .007 2265 
 
 .44 
 
 .928 2675 
 
 84.774 942 
 
 .011 7959 
 
 .94 
 
 .145 4147 
 
 139.770 250 
 
 .007 1546 
 
 4-45 
 
 1.932 6104 
 
 85.626 944 
 
 o.on 6786 
 
 4.95 
 
 2.149 7577 
 
 141.174 964 
 
 0.007 0834 
 
 .46 
 
 .936 9534 
 
 86.487 509 
 
 .on 5624 
 
 .96 
 
 .154 1006 
 
 142.593 796 
 
 .007 0129 
 
 47 
 
 .941 2963 
 
 87.356 723 
 
 oil 4473 
 
 97 
 
 .158 4436 
 
 144.026 888 
 
 .006 9431 
 
 .48 
 
 945 6393 
 
 88.234 673 
 
 .oil 3334 
 
 .98 
 
 .162 7865 
 
 145.474 382 
 
 .006 8741 
 
 49 
 
 .949 9822 
 
 89.121 446 
 
 .on 2206 
 
 99 
 
 .167 1295 
 
 146.936 424 
 
 .006 8057 
 
 4-50 
 
 1.954 3252 
 
 90.017 131 
 
 ,0.011 1090 
 
 5.00 
 
 2.171 4724 
 
 148.413 159 
 
 0.006 7379 
 
 log e (e u ) 
 
 looio(e n ) 
 
 e u 
 
 e~ u 
 
 log e (e u ) 
 
 lodio(e u ) 
 
 e u 
 
 e~ u 
 
 SMITHSONIAN TABLES 
 
 257 
 
The Exponential. 
 
 u 
 
 looio(e u ) 
 
 e u 
 
 e~ u 
 
 u 
 
 looio(e u ) 
 
 e u 
 
 e 
 
 5.00 
 
 2.171 4724 
 
 148.413 159 
 
 0.006 7379 
 
 5.50 
 
 2.388 6197 
 
 244.691 932 
 
 0.004 0868 
 
 .01 
 
 .175 8154 
 
 149.904 736 
 
 .006 6709 
 
 51 
 
 .392 9626 
 
 247.151 127 
 
 .004 0461 
 
 .02 
 
 .180 1583 
 
 151.411 304 
 
 .006 6045 
 
 52 
 
 397 3055 
 
 249.635 037 
 
 .004 0058 
 
 .03 
 
 .184 5012 
 
 152.933 013 
 
 .006 5388 
 
 53 
 
 .401 6485 
 
 252.143 911 
 
 .003 9660 
 
 .04 
 
 .188 8442 
 
 154.470 015 
 
 .006 4737 
 
 54 
 
 .405 9914 
 
 254.677 999 
 
 .003 9265 
 
 5-05 
 
 2.193 18/1 
 
 156.022 464 
 
 0.006 4093 
 
 5-55 
 
 2.410 3344 
 
 257.237 556 
 
 0.003 8875 
 
 .06 
 
 .197 5301 
 
 157.590 516 
 
 .006 3456 
 
 .56 
 
 .414 6773 
 
 259.822 836 
 
 .003 8488 
 
 .07 
 
 .201 8730 
 
 159.174 327 
 
 .006 2824 
 
 57 
 
 .419 0203 
 
 262.434 099 
 
 .003 8105 
 
 .08 
 
 .206 2l6o 
 
 160.774 056 
 
 .006 2109 
 
 58 
 
 .423 3632 
 
 265.071 606 
 
 .003 7726 
 
 .09 
 
 .210 5589 
 
 162.389 862 
 
 .006 1580 
 
 59 
 
 .427 7062 
 
 267.735 620 
 
 .003 7350 
 
 5-10 
 
 2.214 9OI9 
 
 164.021 907 
 
 0.006 0967 
 
 5.6o 
 
 2.432 0491 
 
 270.426 407 
 
 0.003 6979 
 
 .11 
 
 .219 2448 
 
 165.670 355 
 
 .006 0361 
 
 .61 
 
 .436 3920 
 
 273.144 238 
 
 .003 6611 
 
 .12 
 
 .223 5877 
 
 167.335 369 
 
 .005 9760 
 
 .62 
 
 440 7350 
 
 275.889 383 
 
 .003 6246 
 
 13 
 
 .227 9307 
 
 169.017 118 
 
 .005 9166 
 
 .63 
 
 .445 0779 
 
 278.662 117 
 
 .'003 5886 
 
 .14 
 
 .232 2736 
 
 170.715 768 
 
 005 8577 
 
 .64 
 
 .449 4209 
 
 281.462 718 
 
 .003 5529 
 
 5.15 
 
 2.236 6l66 
 
 172.431 490 
 
 0.005 7994 
 
 5.65 
 
 2.453 7638 
 
 284.291 466 
 
 0.003 5175 
 
 .16 
 
 .240 9595 
 
 174.164 455 
 
 .005 7417 
 
 .66 
 
 .458 1068 
 
 287.148 642 
 
 .003 4825 
 
 .17 
 
 .245 3025 
 
 175-914 837 
 
 .005 6846 
 
 .67 
 
 .462 4497 
 
 200.034 534 
 
 .003 4479 
 
 .18 
 
 .249 6454 
 
 177.682 811 
 
 .005 6280 
 
 .68 
 
 .466 7927 
 
 292.949 430 
 
 .003 4136 
 
 .19 
 
 .253 9884 
 
 179.468 553 
 
 .005 5720 
 
 .69 
 
 .471 1356 
 
 295.893 620 
 
 .003 3796 
 
 5-20 
 
 2.258 3313 
 
 181.272 242 
 
 0.005 5166 
 
 5-70 
 
 2.475 4785 
 
 298.867 401 
 
 0.003 346o 
 
 .21 
 
 .262 6743 
 
 183.094 058 
 
 .005 4617 
 
 .71 
 
 .479 8215 
 
 301.871 068 
 
 .003 3127 
 
 .22 
 
 .267 0172 
 
 184.934 184 
 
 .005 4073 
 
 .72 
 
 .484 1644 
 
 304.904 923 
 
 .003 2797 
 
 23 
 
 .271 3601 
 
 186.792 804 
 
 005 3535 
 
 73 
 
 488 5074 
 
 307.069 268 
 
 .003 2471 
 
 .24 
 
 275 7031 
 
 188.670 103 
 
 .005 3003 
 
 74 
 
 492 8503 
 
 311.064 411 
 
 .003 2148 
 
 5-25 
 
 2.280 0460 
 
 190.566 269 
 
 0.005 2475 
 
 5-75 
 
 2.497 1933 
 
 314.190 660 
 
 0.003 1828 
 
 .26 
 
 .284 3890 
 
 192.481 491 
 
 .005 1953 
 
 .76 
 
 .501 5362 
 
 317.348 329 
 
 . .003 1511 
 
 .27 
 
 .288 7319 
 
 194.415 963 
 
 .005 1436 
 
 77 
 
 505 8792 
 
 320.537 733 
 
 .003 1198 
 
 .28 
 
 .293 0749 
 
 196.369 875 
 
 .005 0924 
 
 .78 
 
 .5IO 2221 
 
 323.759 190 
 
 .003 0887 
 
 .29 
 
 .297 4178 
 
 198.343 426 
 
 .005 0418 
 
 79 
 
 .514 5651 
 
 327.013 024 
 
 .003 0580 
 
 5.30 
 
 2.301 7608 
 
 200.336 8 10 
 
 0.004 9916" 
 
 5.8o 
 
 2.518 9080 
 
 330.299 560 
 
 0.003 0276 
 
 .31 
 
 .306 1037 
 
 202.350 228 
 
 .004 9419 
 
 .81 
 
 .523 2509 
 
 333.619 126 
 
 .002 9974 
 
 .32 
 
 .310 4466 
 
 204.383 882 
 
 /OO4 8928 
 
 .82 
 
 .527 5939 
 
 336.972 054 
 
 .002 9676 
 
 33 
 
 .314 7896 
 
 206.437 974 
 
 .004 8441 
 
 .83 
 
 531 9368 
 
 340.358 679 
 
 .002 9381 
 
 34 
 
 .319 1325 
 
 208.512 710 
 
 .004 7959 
 
 .84 
 
 .536 2798 
 
 343-779 341 
 
 .002 9088 
 
 5-35 
 
 2.323 4755 
 
 210.608 298 
 
 0.004 7482 
 
 5.85 
 
 2.540 6227 
 
 347.234 381 
 
 O.OO2 8799 
 
 .36 
 
 .327 8184 
 
 212.724 946 
 
 .004 7009 
 
 .86 
 
 .544 9657 
 
 350.724 144 
 
 .OO2 8512 
 
 37 
 
 .332 1614 
 
 214.862 868 
 
 .004 6541 
 
 .87 
 
 .549 3086 
 
 354-248 980 
 
 .002 8229 
 
 .38 
 
 .336 5043 
 
 217.022 275 
 
 .004 6078 
 
 .88 
 
 553 6516 
 
 357.809 242 
 
 .002 7948 
 
 39 
 
 .340 8473 
 
 219.203 386 
 
 .004 5620 
 
 .89 
 
 557 9945 
 
 361.405 284 
 
 .002 7670 
 
 5.40 
 
 2.345 1902 
 
 221.406 416 
 
 0.004 5i66 
 
 5-90 
 
 2.562 3374 
 
 365.037 468 
 
 0.002 7394 
 
 .41 
 
 349 5331 
 
 223.631 588 
 
 .004 4716 
 
 .91 
 
 .5666804 
 
 368.706 156 
 
 .002 7122 
 
 .42 
 
 .353 8761 
 
 225.879 122 
 
 .004 4271 
 
 .92 
 
 571 0233 
 
 372.411 714 
 
 .002 6852 
 
 43 
 
 .358 2190 
 
 228.149 245 
 
 .004 3831 
 
 93 
 
 .575 3663 
 
 376.154 5M 
 
 .002 6585 
 
 44 
 
 .362 5620 
 
 230.442 183 
 
 004 3395 
 
 94 
 
 579 7092 
 
 379-934 930 
 
 .002 6320 
 
 5-45 
 
 2.366 9049 
 
 232.758 166 
 
 0.004 2963 
 
 5-95 
 
 2.584 0522 
 
 383.753 339 
 
 O.OO2 6058 
 
 .46 
 
 .371 2479 
 
 235.097 424 
 
 .004 2536 
 
 .96 
 
 688 3951 
 
 387.610 124 
 
 .002 5799 
 
 47 
 
 .375 59o8 
 
 237.460 193 
 
 .004 21 12 
 
 97 
 
 592 738i 
 
 39L505 671 
 
 .002 5542 
 
 .48 
 
 .379 9338 
 
 239.846 707 
 
 .004 1093 
 
 , -98 
 
 .597 0810 
 
 395.440 368 
 
 .002 5288 
 
 .49 
 
 384 2767 
 
 242.257 207 
 
 .004 1278 
 
 99 
 
 .601 4239 
 
 399.414 610 
 
 .002 5037 
 
 5.50 
 
 2.388 6197 
 
 244.691 932 
 
 0.004 0868 
 
 6.00 
 
 2.605 7669 
 
 403.4^8 793 
 
 0.002 4788 
 
 log,(e u ) 
 
 100,0(6") 
 
 e" 
 
 e~ u 
 
 UMk(e) 
 
 looi<Xe u ) 
 
 e u 
 
 e~ a 
 
 SMITHSONIAN TABLES 
 
 258 
 
The Exponential. 
 
 u 
 
 looioCe") 
 
 e u 
 
 e- 
 
 I 
 
 .43429 44819 
 
 2.71 828 183 
 
 
 0.367 879 441 
 
 2 
 
 .86858 89638 
 
 7.38 905 610 
 
 
 0.135 335 283 
 
 3 
 
 1.30288 34457 
 
 20.0 855 369 
 
 
 (I) 497870684 
 
 4 
 
 I.737I7 79276 
 
 54-5 98i 500 
 
 
 (I) 183 156 389 
 
 5 
 
 2.17147 24095 
 
 148. 413 159 
 
 
 (2) 673 794 700 
 
 6 
 
 2.60576 68914 
 
 403. 428 793 
 
 
 (2) 247 875 218 
 
 7 
 
 3.04006 13733 
 
 109 6.63 316 
 
 
 (3) 911 88 i 966 
 
 8 
 
 3.47435 58552 
 
 298" 0.95 799 
 
 
 (3) 335 462 628 
 
 9 
 
 3.90865 03371 
 
 810 3.08 393 
 
 
 (3) 123 409 804 
 
 10 
 
 4.34294 48190 
 
 220 26.4 658 
 
 
 (4) 453 999 298 
 
 ii 
 
 4.77723 93009 
 
 598 74-1 417 
 
 
 (4) 167 017 008 
 
 12 
 
 5-2II53 37828 
 
 162 754. 791 
 
 
 (5) 614 421 235 
 
 13 
 
 5.64582 82647 
 
 442 413. 392 
 
 
 (5) 226 032 941 
 
 14 
 
 6.08012 27466 
 
 I2O 260 4.28 
 
 
 (6) 831 528 719 
 
 15 
 
 6.51441 72285 
 
 326 001 7-37 
 
 
 (6) 305 902 321 
 
 16 
 
 6.94871 I7I05 
 
 888 611 0.52 
 
 
 (6) 112 535 175 
 
 17 
 
 7.38300 61924 
 
 241 549 52.8 
 
 
 (7) 413 993 772 
 
 18 
 
 7.81730 06743 
 
 656 599 69.1 
 
 
 (7) 152 299 797 
 
 19 
 
 8.25159 51562 
 
 178 482 301 . 
 
 
 (8) 560 279 644 
 
 20 
 
 8.68588 96381 
 
 485 165 195. 
 
 
 (8) 206 115 362 
 
 21 
 
 9.12018 41200 
 
 131 881 573 
 
 '.I. 
 
 
 (9) 758 256 043 
 
 22 
 
 9.55447 86019 
 
 358 49i 285 
 
 X 
 
 
 (9) 278 946 809 
 
 23 
 
 9.98877 30838 
 
 974 480 345 
 
 ', 
 
 
 (9) 102 618 796 
 
 24 
 
 10.42306 75657 
 
 264 891 221 
 
 ~2\ 
 
 
 (10) 377 513 454 
 
 25 
 
 10.85736 20476 
 
 720 048 993 
 
 2 
 
 
 (10) 138 879 439 
 
 26 
 
 11.29165 65295 
 
 195 729 609 
 
 \3'. 
 
 
 (ii) 510908903 
 
 27 
 
 H.72595 10114 
 
 532 048 241 
 
 .3. 
 
 
 (ii) 187 952 882 
 
 28 
 
 12.16024 54933 
 
 144 625 707 
 
 A 
 
 
 (12) 691 440 Oil 
 
 29 
 
 12.59453 99752 
 
 393 133 430 
 
 
 
 (12) 254 366 565 
 
 30 
 
 13.02883 44571 
 
 106 864 746 
 
 [5. 
 
 
 (13) 935 762 297 
 
 31 
 
 13.46312 89390 
 
 290 488 497 
 
 '.5. 
 
 
 (13) 344247711 
 
 32 
 
 13.89742 34209 
 
 789 629 602 
 
 ''. 
 
 
 (13) 126 641 656 
 
 33 
 
 14.33171 79028 
 
 214 643 58o 
 
 6: 
 
 
 (14) 465 888 615 
 
 34 
 
 14.76601 23847 
 
 583 461 743 
 
 6; 
 
 
 (14) 171 390 843 
 
 35 
 
 15.20030 68666 
 
 158 601 345 
 
 '7. 
 
 
 (15) 630 511 676 
 
 36 
 
 15.63460 13485 
 
 431 123 155 
 
 7] 
 
 
 (15) 231 952 283 
 
 37 
 
 16.06889 58304 
 
 117 191 424 
 
 8] 
 
 
 (16) 853 304 763 
 
 38 
 
 16.50319 03123 
 
 3i8 559 3i8 [ 
 
 8] 
 
 
 (16) 313 9i3 279 
 
 39 
 
 16.93748 47942 
 
 865 934 004 [8; 
 
 
 (16) 115 482 242 
 
 40 
 
 17.37177 92761 
 
 235 385 267 [9] 
 
 
 (17) 424 835 426 
 
 41 
 
 17.80607 37580 
 
 639 843 493 I 
 
 
 
 (17) 156 288 219 
 
 42 
 
 18.24036 82399 
 
 173 927 494 [10: 
 
 
 (18) 574 952 227 
 
 43 
 
 18.67466 27218 
 
 472 783 947 [10: 
 
 
 (18) 211 513 104 
 
 44 
 
 19.10895 72037 
 
 128 516 ooi [ii] 
 
 (19) 778 113 22J. 
 
 45 
 
 19.54325 16856 
 
 349 342 711 [ii; 
 
 
 (19) 286 251 858 
 
 46 
 
 19.97754 61675 
 
 949 611 942 [n; 
 
 
 (19) 105 306 174 
 
 47 
 
 20.41184 06495 
 
 258 131 289 [12; 
 
 
 (20) 387 399 763 
 
 48 
 
 20.84613 51314 
 
 701 673 59i [12] 
 
 
 (20) 142 516 408 
 
 49 
 
 21.28042 96133 
 
 190 734 657 [i 
 
 
 
 (21) 524 288 566 
 
 50 
 
 21.71472 40952 
 
 518 470 553 [13] 
 
 
 (21) 192 874 985 
 
 The numbers in square brackets denote the numbers of figures between the 
 
 last figure given and the decimal point ; for example, the first nine figures of e 50 
 
 are 518470553, and there are 13 additional figures before the decimal point is 
 
 reached. The numbers in parentheses denote the numbers of ciphers between 
 
 the decimal point and the first significant figure ; 
 
 for example, in e 5 there 'are 
 
 21 ciphers between the decimal point and the figures 192874985. 
 
 TABLES 
 
 259 
 
The Exponential. 
 
 u 
 
 logio(e u ) 
 
 eu 
 
 e-u 
 
 51 
 
 22.14001 85771 
 
 140 934 90S [14] 
 
 (22) 709 547 416 
 
 52 
 
 22.58331 3^590 
 
 383 loo 800 [14] 
 
 (22) 261 027 907 
 
 53 
 
 23.01700 75409 
 
 104 137 594 [15] 
 
 (23) 960 268 005 
 
 54 
 
 23.45190 20228 
 
 283 075 330 [15] 
 
 (23) 353 262 857 
 
 55 
 
 23.88619 65047 
 
 769 4/8 527 [15] 
 
 (23) 129 958 143 
 
 56 
 
 24.32049 09866 
 
 209 165 950 [16] 
 
 (24) 478 089 288 
 
 57 
 
 24.75478 54685 
 
 568 572 ooo 16] 
 
 (24) 175 879 220 
 
 58 
 
 25.18907 99504 
 
 154 553 894 [17] 
 
 (25) 647 023 493 
 
 59 
 
 25-62337 44323 
 
 420 121 040 [17] 
 
 (25) 238 026 641 
 
 60 
 
 26.05766 89142 
 
 114 200 739 [18] 
 
 (26) 875 651 076 
 
 61 
 62 
 
 26.49196 33961 
 26.92625 78780 
 
 310 429 794 [18] 
 843 835 667 [18] 
 
 (26) 322 134 029 
 (26) 118 506 487 
 
 63 
 
 27-36055 23599 
 
 229 378 316 [19] 
 
 (27) 435 961 ooo 
 
 64 
 
 27.79484 68418 
 
 623 514 908 [19] 
 
 (27) 160 381 089 
 
 65 
 
 28.22914 13237 
 
 169 488 924 [20] 
 
 (28) 590 009 054 
 
 66 
 
 28.66343 58056 
 
 460 718 663 [20 
 
 
 (28) 217 O52 2OI 
 
 67 
 
 29.09773 02875 
 
 125 236 317 [21. 
 
 
 (29) 798 490 425 
 
 68 
 
 29.53202 47694 
 
 340 427 605 [21 
 
 
 (29) 293 748 211 
 
 69 
 
 29.96631 92513 
 
 925 378 172 [21. 
 
 
 (29) 108 063 928 
 
 70 
 
 30.40061 37332 
 
 251 543 867 [22^ 
 
 
 (30) 397 544 974 
 
 7i 
 
 30.83490 82151 
 
 683 767 123 [22] 
 
 (30) 146 248 623 
 
 72 
 
 31.26920 26970 
 
 185 867 175 [23] 
 
 (3i) 538 018 616 
 
 73 
 
 31.70349 71789 
 
 505 239 363 [23] 
 
 (3-1) 197 925 988 
 
 74 
 
 32.13779 16608 
 
 137 338 298 [24; 
 
 
 (32) 728 129 018 
 
 75 
 
 32.57208 61427 
 
 373 324 200 [24; 
 
 
 (32) 267 863 696 
 
 76 
 
 33.00638 06246 
 
 101 480 039 [25" 
 
 
 (33) 985 415 469 
 
 77 
 
 33.44067 51066 
 
 275 851 346 [25; 
 
 
 (33) 362 514 092 
 
 78 
 
 33.87496 95885 
 
 749 841 700 [25; 
 
 
 (33) 133 36i 482 
 
 79 
 
 34.30926 40704 
 
 203 828 107 [26] 
 
 (34) 490 609 473 
 
 80 
 
 34-74355 85523 
 
 554 062 238 [26] 
 
 (34) 180 485 139 
 
 81 
 
 35.17785 30342 
 
 150 609 731 [27] 
 
 (35) 663 967 720 
 
 82 
 
 35.61214-75161 
 
 409 399 696 [27] 
 
 (35) 244 260 074 
 
 83 
 
 36.04644 19980 
 
 in 286 376 [28] 
 
 (36) 898 582 594 
 
 84 
 
 36.48073 64799 
 
 302 507 732 [28] 
 
 (36) 330 570 063 . 
 
 85 
 
 36.91503 09618 
 
 822 301 271 [28 
 
 
 (36) 121 609 930 
 
 86 
 
 37-34932 54437 
 
 223 524 660 [29; 
 
 
 (37) 447 377 931 
 
 87 
 
 37.78361 99256 
 
 607 603 023 [29; 
 
 
 (37) 164 58i 143 
 
 88 
 
 38.21791 44075 
 
 165 163 626 [30" 
 
 
 (38) 605 460 189 
 
 89 
 
 38.65220 88894 
 
 448 961 282 [30 
 
 
 (38) 222 736 356 
 
 90 
 
 39.08650 33713 
 
 122 040 329 [31! 
 
 
 (39) 819 401 262 
 
 9i 
 
 39.52079 78532 
 
 331 740 oio [31] 
 
 (39) 301 440 879 
 
 92 
 
 39.95509 2335 1 
 
 ooi 762 841 [31] 
 
 (39) no 893 902 
 
 93 
 
 40.38938 68170 
 
 245 124 554 [32] 
 
 (40) 407 955 867 
 
 94 
 
 40.82368 12989 
 
 666 317 622 [32] 
 
 (40) 150 078 576 
 
 95 
 
 41.25797 578o8 
 
 181 123 908 [33] 
 
 (41) 552 108 228 
 
 96 
 
 41.69227 02627 
 
 492 345 829 [33] 
 
 (41) 203 109 266 
 
 97 
 
 42.12656 47446 
 
 133 833 472 [34] 
 
 (42) 747 197 234 
 
 98 
 
 42.56085 92265 
 
 363 797 095 [34] 
 
 (42) 274 878 501 
 
 99 
 
 42.99515 37084 
 
 088 903 032 [34] 
 
 (42) IOI 122 149 
 
 100 
 
 43.42944 81903 
 
 268 811 714 [35] 
 
 (43) 372 007 598 
 
 The numbers in square brackets denote the numbers of figures between the 
 
 last figure given and the decimal point ; for example, the first nine figures of e 1 * 
 
 are 518470553, and there are 13 additional figures before the decimal point is 
 
 reached. The numbers in parentheses denote the numbers of ciphers between 
 
 the decimal point and the first significant figure ; for example, in e~ M there are 
 
 2i ciphers between the decimal point and the figures 192874985. 
 
 SMITHSONIAN TABLES 
 
Auxiliary laoie ror interpolation 01 
 (p = n X 43429 44819 . . .) 
 
 n 
 
 P 
 
 n 
 
 p 
 
 n 
 
 P 
 
 n 
 
 p 
 
 n 
 
 p 
 
 o.ooo 
 
 OOO 
 
 O.050 
 
 2171 
 
 O.IOO 
 
 4343 
 
 O.I5O 
 
 6514 
 
 0.200 
 
 8686 
 
 .001 
 
 043 
 
 .051 
 
 2215 
 
 .IOI 
 
 4386 
 
 .151 
 
 6558 
 
 .2OI 
 
 8729 
 
 .002 
 
 087 
 
 .052 
 
 2258 
 
 .IO2 
 
 4430 
 
 .152 
 
 6601 
 
 .202 
 
 8773 
 
 .003 
 
 130 
 
 .053 
 
 2302 
 
 .103 
 
 4473 
 
 .153 
 
 6645 
 
 .203 
 
 8816 
 
 .004 
 
 174 
 
 .054 
 
 2345 
 
 .104 
 
 4517 
 
 .154 
 
 6668 
 
 .204 
 
 8860 
 
 0.005 
 
 217 
 
 0.055 
 
 2389 
 
 0.105 
 
 4500 
 
 0.155 
 
 6732 
 
 0.205 
 
 8903 
 
 .006 
 
 26l 
 
 .056 
 
 2432 
 
 .106 
 
 4604 
 
 .156 
 
 6775 
 
 .206 
 
 8946 
 
 .007 
 
 304 
 
 .057 
 
 2475 
 
 .107 
 
 4647 
 
 .157 
 
 6818 
 
 .207 
 
 8990 
 
 .008 
 
 347 
 
 .058 
 
 2519 
 
 .108 
 
 4690 
 
 .r 5 8 
 
 6862 
 
 .208 
 
 9033 
 
 .009 
 
 391 
 
 .059 
 
 2562 
 
 .109 
 
 4734 
 
 .159 
 
 6905 
 
 .209 
 
 9077 
 
 O.OIO 
 
 434 
 
 O.o6o 
 
 2606 
 
 O.I 10 
 
 4777 
 
 0.160 
 
 6949 
 
 O.2IO 
 
 9120 
 
 .on 
 
 478 
 
 .061 
 
 2649 
 
 .III 
 
 4821 
 
 .161 
 
 6992 
 
 .211 
 
 9164 
 
 .012 
 
 521 
 
 .062 
 
 2693 
 
 .112 
 
 4864 
 
 .162 
 
 7036 
 
 .212 
 
 9207 
 
 .013 
 
 565 
 
 .063 
 
 2736 
 
 113 
 
 4908 
 
 .163 
 
 7079 
 
 .213 
 
 9250 
 
 .014 
 
 608 
 
 .064 
 
 2779 
 
 .114 
 
 4951 
 
 .164 
 
 7122 
 
 .214 
 
 9294 
 
 0.015 
 
 651 
 
 0.065 
 
 2823 
 
 O.II5 
 
 4994 
 
 0.165 
 
 7166 
 
 0.215 
 
 9337 
 
 .016 
 
 695 
 
 .066 
 
 2866 
 
 .116 
 
 5038 
 
 .166 
 
 7209 
 
 .216 
 
 938i 
 
 .017 
 
 738 
 
 .067 
 
 2910 
 
 .117. 
 
 5081 
 
 .167 
 
 7253 
 
 .217 
 
 9424 
 
 .018 
 
 782 
 
 .068 
 
 2953 
 
 .118 
 
 5125 
 
 .168 
 
 7296 
 
 .218 
 
 9468 
 
 .019 
 
 825 
 
 .069 
 
 2997 
 
 .119 
 
 5i68 
 
 .169 
 
 7340 
 
 .219 
 
 95ii 
 
 0.020 
 
 869 
 
 0.070 
 
 3040 
 
 O.I2O 
 
 5212 
 
 0.170 
 
 7383 
 
 O.22O 
 
 9554 
 
 .O2I 
 
 912 
 
 .071 
 
 3083 
 
 .121 
 
 5255 
 
 .171 
 
 7426 
 
 .221 
 
 9598 
 
 .022 
 
 955 
 
 .072 
 
 3127 
 
 .122 
 
 5298 
 
 .172 
 
 7470 
 
 .222 
 
 
 .023 
 
 999 
 
 .073 
 
 3170 
 
 .123 
 
 5342 
 
 .173 
 
 7513 
 
 .223 
 
 9685 
 
 .024 
 
 1042 
 
 .074 
 
 3214 
 
 .124 
 
 5385 
 
 .174 
 
 7557 
 
 .224 
 
 9728 
 
 0.025 
 
 1086 
 
 0.075 
 
 3257 
 
 0.125 
 
 5429 
 
 0.175 
 
 7600 
 
 0.225 
 
 9772 
 
 .026 
 
 1129 
 
 .076 
 
 3301 
 
 .126 
 
 5472 
 
 .176 
 
 7644 
 
 .226 
 
 9815 
 
 .027 
 
 1 173 
 
 .077 
 
 3344 
 
 .127 
 
 55i6 
 
 .177 
 
 7687 
 
 .227 
 
 9858 
 
 .028 
 
 1216 
 
 .078 
 
 3387 
 
 .128 
 
 5559 
 
 .178 
 
 7730 
 
 .228 
 
 9902 
 
 .029 
 
 1259 
 
 079 
 
 3431 
 
 .129 
 
 5602 
 
 .179 
 
 7774 
 
 .229 
 
 9945 
 
 0.030 
 
 1303 
 
 0.080 
 
 3474 
 
 O.I30 
 
 5646 
 
 0.180 
 
 7817 
 
 O.230 
 
 9989 
 
 .031 
 
 1346 
 
 .081 
 
 35i8 
 
 .131 
 
 5689 
 
 .181 
 
 7861 
 
 .231 
 
 10032 
 
 .032 
 
 1390 
 
 .082 
 
 356i 
 
 .132 
 
 5733 
 
 .182 
 
 7904 
 
 .232 
 
 10076 
 
 033 
 
 1433 
 
 .083 
 
 3605 
 
 .133 
 
 5776 
 
 .183 
 
 7948 
 
 .233 
 
 10119 
 
 .034 
 
 1477 
 
 .084 
 
 3648 
 
 .134 
 
 5820 
 
 .184 
 
 7991 
 
 .234 
 
 10162 
 
 0.035 
 
 1520 
 
 0.085 
 
 3692 
 
 0.135 
 
 5863 
 
 0.185 
 
 8034 
 
 0.235 
 
 10206 
 
 .036 
 
 1563 
 
 .086 
 
 3735 
 
 . 136 
 
 59o6 
 
 .186 
 
 8078 
 
 .236 
 
 10249 
 
 .037 
 
 1607 
 
 .087 
 
 3778 
 
 .137 
 
 5950 
 
 .187 
 
 8121 
 
 .237 
 
 10293 
 
 .038 
 
 1650 
 
 .088 
 
 3822 
 
 .138 
 
 5993 
 
 .188 
 
 8165 
 
 .238 
 
 10336 
 
 .039 
 
 1694 
 
 .089 
 
 3865 
 
 .139 
 
 6037 
 
 .189 
 
 8208 
 
 .239 
 
 10380 
 
 0.040 
 
 1737 
 
 0.000 
 
 3909 
 
 0.140 
 
 6080 
 
 0.190 
 
 8252 
 
 0.240 
 
 10423 
 
 .041 
 
 1781 
 
 .091 
 
 3952 
 
 .141 
 
 6124 
 
 .191 
 
 8295 
 
 .241 
 
 10466 
 
 .042 
 
 1824 
 
 .092 
 
 3996 
 
 .142 
 
 6167 
 
 .192 
 
 8338 
 
 .242 
 
 10510 
 
 .043 
 
 1867 
 
 .093 
 
 4039 
 
 143 
 
 6210 
 
 .193 
 
 8382 
 
 .243 
 
 10553 
 
 .044 
 
 1911 
 
 .094 
 
 4082 
 
 .144 
 
 6254 
 
 .194 
 
 8425 
 
 244 
 
 10597 
 
 0.045 
 
 1954 
 
 0.095 
 
 4126 
 
 0.145 
 
 6297 
 
 0.195 
 
 8469 
 
 0.245 
 
 10640 
 
 .046 
 
 1998 
 
 .096 
 
 2169 
 
 .146 
 
 6341 
 
 .196 
 
 8512 
 
 .246 
 
 10684 
 
 .047 
 
 2041 
 
 .097 
 
 4213 
 
 .147 
 
 6384 
 
 .197 
 
 8556 
 
 .247 
 
 10727 
 
 .048 
 
 2085 
 
 .098 
 
 4256 
 
 .148 
 
 6428 
 
 .198 
 
 8599 
 
 .248 
 
 10771 
 
 .049 
 
 2128 
 
 .099 
 
 4300 
 
 .149 
 
 6471 
 
 .199 
 
 8642 
 
 .249 
 
 10814 
 
 0.050 
 
 2171 
 
 O.IOO 
 
 4343 
 
 0.150 
 
 6514 
 
 O.2OO 
 
 8686 
 
 0.250 
 
 10857 
 
 n 
 
 p 
 
 n 
 
 p 
 
 n 
 
 P 
 
 n 
 
 P 
 
 n 
 
 p 
 
 SMITHSONIAN TABLES 
 
 26l 
 
Auxiliary laoie tor interpolation of 
 (p = n X 43429 44819 . . . ) 
 
 n 
 
 p 
 
 n 
 
 p 
 
 n 
 
 p 
 
 n 
 
 p 
 
 n 
 
 P 
 
 0.250 
 
 10857 
 
 0.300 
 
 13029 
 
 0.350 
 
 I52OO 
 
 0.400 
 
 17372 
 
 0.450 
 
 19543 
 
 .251 
 
 IOOOI 
 
 .301 
 
 13072 
 
 351 
 
 15244 
 
 .401 
 
 I74I5 
 
 451 
 
 19587 
 
 .252 
 
 10944 
 
 302 
 
 I3"6 
 
 352 
 
 15287 
 
 .402 
 
 17459 
 
 452 
 
 19630 
 
 253 
 
 10988 
 
 303 
 
 I3I59 
 
 353 
 
 I533I 
 
 403 
 
 17502 
 
 -453 
 
 19674 
 
 254 
 
 II03I 
 
 .304 
 
 13203 
 
 354 
 
 15374 
 
 .404 
 
 17545 
 
 454 
 
 I97I7 
 
 0.255 
 
 1 1075 
 
 0.305 
 
 13246 
 
 0.355 
 
 I54I7 
 
 0.405 
 
 17589 
 
 0.455 
 
 -T+J+J 
 
 19760 
 
 .256 
 
 11118 
 
 .306 
 
 13289 
 
 .356 
 
 15461 
 
 .406 
 
 17632 
 
 .456 
 
 19804 
 
 .257 
 
 11161 
 
 .307 
 
 13333 
 
 .357 
 
 15504 
 
 .407 
 
 17676 
 
 457 
 
 19847 
 
 .258 
 
 11205 
 
 .308 
 
 13376 
 
 .358 
 
 15548 
 
 .408 
 
 17719 
 
 .458 
 
 19891 
 
 259 
 
 11248 
 
 .309 
 
 13420 
 
 359 
 
 I559I 
 
 .409 
 
 17763 
 
 459 
 
 19934 
 
 0.260 
 
 11292 
 
 0.310 
 
 13463 
 
 0.360 
 
 15635 
 
 0.410 
 
 17806 
 
 0.460 
 
 19978 
 
 .261 
 
 1 1335 
 
 .3" 
 
 13507 
 
 .361 
 
 15678 
 
 .4" 
 
 17850 
 
 .461 
 
 2O02I 
 
 .262 
 
 "379 
 
 .312 
 
 13550 
 
 .362 
 
 I572I 
 
 .412 
 
 17893 
 
 .462 
 
 20064 
 
 .263 
 
 11422 
 
 .313 
 
 13593 
 
 .363 
 
 I'5765 
 
 .413 
 
 17936 
 
 463 
 
 20108 
 
 .264 
 
 "465 
 
 .314 
 
 13637 
 
 .364 
 
 15808 
 
 .414 
 
 17980 
 
 .464 
 
 20I5I 
 
 0.265 
 
 n-509 
 
 0.315 
 
 13680 
 
 0.365 
 
 15852 
 
 0.415 
 
 18023 
 
 0.465 
 
 20195 
 
 .266 
 
 "552 
 
 .316 
 
 13724 
 
 .366 
 
 15895 
 
 .416 
 
 18067 
 
 .466 20238 
 
 .267 
 
 11596 
 
 .317 
 
 13767 
 
 .367 
 
 15939 
 
 .417 
 
 18110 
 
 .467 20282 
 
 .268 
 
 11639 
 
 .318 
 
 I38II 
 
 .368 
 
 15982 
 
 .418 
 
 18154 
 
 .468 20325 
 
 .269 
 
 11683 
 
 .319 
 
 13854 
 
 .369 
 
 16025 
 
 .419 
 
 18197 
 
 .469 
 
 20368 
 
 0.270 
 
 11726 
 
 0.320 
 
 13897 
 
 0.370 
 
 16069 
 
 0.420 
 
 18240 
 
 0.470 
 
 20412 
 
 .271 
 
 11769 
 
 .321 
 
 I394I 
 
 371 
 
 l6lI2 
 
 .421 
 
 18284 
 
 471 
 
 20455 
 
 .272 
 
 "813 
 
 .322 
 
 13984 
 
 .372 
 
 16156 
 
 .422 
 
 18327 
 
 .472 
 
 20499 
 
 .273 
 
 "856 
 
 .323 
 
 14028 
 
 373 
 
 16199 
 
 .423 
 
 18371 
 
 473 
 
 20542 
 
 .274 
 
 11900 
 
 .324 
 
 I407I 
 
 374 
 
 16243 
 
 .424 
 
 18414 
 
 .474 
 
 20586 
 
 0.275 
 
 "943 
 
 0.325 
 
 I4"5 
 
 0.375 
 
 16286 
 
 0.425 
 
 18458 
 
 0.475 
 
 20629 
 
 .276 
 
 11987 
 
 .326 
 
 14158 
 
 .376 
 
 16329 
 
 .426 
 
 18501 
 
 .476 
 
 20672 
 
 .277 
 
 12030 
 
 .327 
 
 14201 
 
 377 
 
 16373 
 
 .427 
 
 18544 
 
 .477 
 
 20716 
 
 .278 
 
 12073 
 
 .328 
 
 14245 
 
 .378 
 
 16416 
 
 .428 
 
 18588 
 
 .478 
 
 20759 
 
 .279 
 
 12117 
 
 .329 
 
 14288 
 
 .379 
 
 16460 
 
 .429 
 
 18631 
 
 .479 
 
 20803 
 
 0.280 
 
 12160 
 
 0.330 
 
 14332 
 
 0.380 
 
 16503 
 
 0.430 
 
 18675 
 
 0.480 
 
 20846 
 
 .281 
 
 12204 
 
 331 
 
 H375 
 
 .381 
 
 16547 
 
 431 
 
 18718 
 
 .481 
 
 20890 
 
 .282 
 
 12247 
 
 .332 
 
 14419 
 
 .382 
 
 16500 
 
 432 
 
 18762 
 
 .482 
 
 20933 
 
 .283 
 
 12291 
 
 333 
 
 14462 
 
 .383 
 
 16633 
 
 433 
 
 18805 
 
 .483 
 
 20976 
 
 .284 
 
 12334 
 
 334 
 
 14505 
 
 .384 
 
 16677 
 
 434 
 
 18848 
 
 .484 
 
 2IO2O 
 
 0.285 
 
 12377 
 
 0.335 
 
 14549 
 
 0.385 
 
 16720 
 
 0.435 
 
 18892 
 
 0.485 
 
 2IO63 
 
 .286 
 
 12421 
 
 .336 
 
 H592 
 
 .386 
 
 16764 
 
 .436 
 
 18935 
 
 .486 
 
 2IIO7 
 
 .287 
 
 12464 
 
 .337 
 
 14636 
 
 .387 
 
 16807 
 
 437 
 
 18979 
 
 .487 
 
 2II5O 
 
 .288 
 
 12508 
 
 .338 
 
 14679 
 
 .388 
 
 16851 
 
 .438 
 
 19022 
 
 .488 
 
 2II94 
 
 .289 
 
 I255I 
 
 339 
 
 14723 
 
 .389 
 
 16894 
 
 439 
 
 19066 
 
 .489 
 
 21237 
 
 0.290 
 
 12595 
 
 0.340 
 
 14766 
 
 0.390 
 
 16937 
 
 0.440 
 
 19109 
 
 0.490 
 
 21280 
 
 .291 
 
 12638 
 
 341 
 
 14809 
 
 391 
 
 16981 
 
 441 
 
 19152 
 
 .491 
 
 21324 
 
 .292 
 
 12681 
 
 .342 
 
 14853 
 
 392 
 
 17024 
 
 .442 
 
 19196 
 
 493 
 
 21367 
 
 .293 
 .294 
 
 12725 
 12768 
 
 .343 
 344 
 
 14896 
 14940 
 
 393 
 394 
 
 17068 
 I7III 
 
 443 
 444 
 
 19239 
 19283 
 
 493 
 494 
 
 21411 
 
 ^1454 
 
 0.295 
 
 12812 
 
 0.345 
 
 14983 
 
 0.395 
 
 I7I55 
 
 0.445 
 
 19326 
 
 0.495 
 
 21498 
 
 .296 
 
 12855 
 
 .346 
 
 15027 
 
 .396 
 
 I7I98 
 
 .446 
 
 19370 
 
 .496 
 
 21541 
 
 .297 
 
 12899 
 
 347 
 
 15070 
 
 397 
 
 17241 
 
 .447 
 
 I94I3 
 
 497 
 
 21584 
 
 .298 
 
 12942 
 
 .348 
 
 I5"3 
 
 .398 
 
 17285 
 
 .448 
 
 19456 
 
 .498 
 
 21628 
 
 .299 
 
 12985 
 
 349 
 
 I5I57 
 
 .399 
 
 17328 
 
 .449 
 
 19500 
 
 .499 
 
 21671 
 
 0.300 
 
 13029 
 
 0.350 
 
 15200 
 
 0.400 
 
 17372 
 
 0.450 
 
 19543 
 
 0.500 
 
 21715 
 
 n 
 
 p 
 
 n 
 
 P 
 
 n 
 
 p 
 
 n 
 
 p 
 
 n 
 
 p 
 
 SMITHSONIAN TABLE* 
 
 262 
 
TABLE V 
 
 NATURAL LOGARITHMS 
 
 NOTE. In Table V, for u greater than 158, linear interpolation of 
 log e w suffices to give a value whose error is not greater than one unit in 
 the last place. 
 
 263 
 
Natural Logarithms. 
 
 u 
 
 lOQeU 
 
 U.FO' 
 
 u 
 
 lOQ.U 
 
 IV 
 
 u 
 
 loo. u 
 
 *v 
 
 u 
 
 iog.u 
 
 <oF ' 
 
 o 
 
 CO 
 
 00 
 
 50 
 
 3.91202 
 
 2OOO 
 
 IOO 
 
 4.60517 
 
 IOOO 
 
 150 
 
 5.01064 
 
 667 
 
 I 
 
 o.ooooo 
 
 IOOOOO 
 
 
 3.93183 
 
 I96l 
 
 101 
 
 4.6I5I2 
 
 990 
 
 151 
 
 5.01728 
 
 662 
 
 2 
 
 0.69315 
 
 50000 
 
 52 
 
 3.95124 
 
 1923 
 
 IO2 
 
 4.62497 
 
 080 
 
 152 
 
 5.02388 
 
 658 
 
 3 
 
 1.09861 
 
 33333 
 
 53 
 
 3.97029 
 
 1887 
 
 103 
 
 4.63473 
 
 971 
 
 153 
 
 5.03044 
 
 654 
 
 4 
 
 1.38629 
 
 25000 
 
 54 
 
 3.98898 
 
 1852 
 
 104 
 
 4.64439 
 
 962 
 
 154 
 
 5.03695 . 
 
 649 
 
 5 
 
 1.60944 
 
 2OOOO 
 
 55 
 
 4-00733 
 
 1818 
 
 105 
 
 4.65396 
 
 952 
 
 155 
 
 5-04343 
 
 645 
 
 6 
 
 1.79176 
 
 16667 
 
 56 
 
 4.02535 
 
 1786 
 
 106 
 
 4.66344 
 
 943 
 
 156 
 
 5-04086 
 
 6 4 I 
 
 7 
 
 1.94591 
 
 14286 
 
 57 
 
 4.04305 
 
 1754 
 
 107 
 
 4.67283 
 
 935 
 
 157 
 
 5-05625 
 
 637 
 
 8 
 
 2.07944 
 
 12500 
 
 58 
 
 4.06044 
 
 1724 
 
 108 
 
 4.68213 
 
 926 
 
 158 
 
 5.06260 
 
 633 
 
 9 
 
 2.19722 
 
 mil 
 
 59 
 
 4.07754 
 
 1695 
 
 109 
 
 4.69135 
 
 917 
 
 159 
 
 5.06890 
 
 629 
 
 10 
 
 2.30259 
 
 IOOOO 
 
 60 
 
 4-09434 
 
 1667 
 
 1 10 
 
 4.70048 
 
 009 
 
 160 
 
 5.07517 
 
 625 
 
 ii 
 
 2-39790 
 
 9091 
 
 61 
 
 4.II087 
 
 1639 
 
 III 
 
 4.70953 
 
 901 
 
 161 
 
 5.08140 
 
 621 
 
 12 
 
 2.48491 
 
 8333 
 
 62 
 
 4.I27I3 
 
 1613 
 
 112 
 
 4.71850 
 
 893 
 
 162 
 
 5.08760 
 
 617 
 
 13 
 
 2.56495 
 
 7692 
 
 63 
 
 4.I43I3 
 
 1587 
 
 113 
 
 4.72739 
 
 885 
 
 163 
 
 5-09375 
 
 6l 3 
 
 14 
 
 2.63906 
 
 7143 
 
 64 
 
 4.15888 
 
 1562 
 
 114 
 
 4.73620 
 
 877 
 
 164 
 
 5.09987 
 
 610 
 
 15 
 
 2.70805 
 
 6667 
 
 6s 
 
 4.17439 
 
 1538 
 
 115 
 
 4-74493 
 
 870 
 
 165 
 
 5.10595 
 
 606 
 
 16 
 
 2.77259 
 
 6250 
 
 66 
 
 4.18965 
 
 1515 
 
 116 
 
 4.75359 
 
 862 
 
 166 
 
 5.III99 
 
 602 
 
 17 
 
 2.83321 
 
 5882 
 
 67 
 
 4.20469 
 
 1493 
 
 117 
 
 4.76217 
 
 855 
 
 167 
 
 5.H799 
 
 599 
 
 18 
 
 2.89037 
 
 5556 
 
 68 
 
 4.2I95I 
 
 1471 
 
 118 
 
 4.77068 
 
 847 
 
 168 
 
 5.12396 
 
 595 
 
 19 
 
 2.94444 
 
 5263 
 
 69 
 
 4.234H 
 
 1449 
 
 119 
 
 4.77912 
 
 840 
 
 169 
 
 5.12990 
 
 592 
 
 20 
 
 2.99573 
 
 5000 
 
 70 
 
 4.24850 
 
 1429 
 
 1 20 
 
 4.78749 
 
 833 
 
 170 
 
 5.13580 
 
 588 
 
 21 
 
 3.04452 
 
 4762 
 
 
 4.26268 
 
 1408 
 
 121 
 
 4-79579 
 
 826 
 
 171 
 
 5.14166 
 
 585 
 
 22 
 
 3.09104 
 
 4545 
 
 72 
 
 4.27667 
 
 1389 
 
 122 
 
 4.80402 
 
 820 
 
 172 
 
 5-14749 
 
 58i 
 
 23 
 
 3.13549 
 
 4348 
 
 73 
 
 4.20046 
 
 1370 
 
 123 
 
 4.81218 
 
 813 
 
 173 
 
 5.15329 
 
 578 
 
 24 
 
 3.17805 
 
 4167 
 
 74 
 
 4.30407 
 
 1351 
 
 124 
 
 4.82028 
 
 806 
 
 174 
 
 5.15906 
 
 575 
 
 25 
 
 3.21888 
 
 4000 
 
 75 
 
 4.31749 
 
 1333 
 
 125 
 
 4.82831 
 
 800 
 
 175 
 
 5.16479 
 
 571 
 
 26 
 
 3.25810 
 
 3846 
 
 76 
 
 4.33073 
 
 1316 
 
 126 
 
 4.83628 
 
 794 
 
 176 
 
 5.17048 
 
 568 
 
 27 
 
 3 . 29584 
 
 3704 
 
 77 
 
 4.34381 
 
 1299 
 
 127 
 
 4.84419 
 
 787 
 
 177 
 
 5.I76I5 
 
 565 
 
 28 
 
 3.33220 
 
 357i 
 
 78 
 
 4.35671 
 
 1282 
 
 128 
 
 4.85203 
 
 78i 
 
 178 
 
 5.I8I78 
 
 562 
 
 29 
 
 3.36730 
 
 3448 
 
 79 
 
 4.36945 
 
 1266 
 
 129 
 
 4.85981 
 
 775 
 
 179 
 
 5.18739 
 
 559 
 
 30 
 
 3.40120 
 
 3333 
 
 80 
 
 4.38203 
 
 1250 
 
 130 
 
 4.86753 
 
 769 
 
 180 
 
 5.19296 
 
 556 
 
 31 
 
 3-43399 
 
 3226 
 
 81 
 
 4-39445 
 
 1235 
 
 131 
 
 4.87520 
 
 763 
 
 181 
 
 5.19850 
 
 552 
 
 32 
 
 3.46574 
 
 3125 
 
 82 
 
 4.40672 
 
 1 220 
 
 132 
 
 4.88280 
 
 758 
 
 182 
 
 5 . 20401 
 
 549 
 
 33 
 34 
 
 3.49651 
 3-52636 
 
 3030 
 2941 
 
 83 
 84 
 
 4.41884 
 4.43082 
 
 1205 
 iigo 
 
 133 
 134 
 
 4.89035 
 4.89784 
 
 752 
 746 
 
 183 
 184 
 
 5.20949 
 5.21494 
 
 546 
 
 543 
 
 35 
 
 3.55535 
 
 2857 
 
 85 
 
 4.44265 
 
 1176 
 
 135 
 
 4.90527 
 
 741 
 
 185 
 
 5.22036 
 
 541 
 
 36 
 
 3.58352 
 
 2778 
 
 86 
 
 4-45435 
 
 1163 
 
 136 
 
 4.91265 
 
 735 
 
 186 
 
 5.22575 
 
 538 
 
 37 
 
 3.61092 
 
 2703 
 
 87 
 
 4.46591 
 
 1149 
 
 137 
 
 4.91998 
 
 730 
 
 187 
 
 5-23111 
 
 535 
 
 38 
 
 3.63759 
 
 2632 
 
 88 
 
 4-47734 
 
 1136 
 
 138 
 
 4.92725 
 
 725 
 
 188 
 
 5-23644 
 
 532 
 
 39 
 
 3.66356 
 
 2564 
 
 89 
 
 4.48864 
 
 1124 
 
 139 
 
 4.93447 
 
 719 
 
 189 
 
 5.24175 
 
 529 
 
 40 
 
 3.68888 
 
 2500 
 
 90 
 
 4.49981 
 
 mi 
 
 140 
 
 4.94164 
 
 714 
 
 190 
 
 5.24702 
 
 526 
 
 41 
 
 3.71357 
 
 2439 
 
 
 4.51086 
 
 1099 
 
 141 
 
 4.94876 
 
 709 
 
 191 
 
 5.25227 
 
 5-'4 
 
 42 
 43 
 44 
 
 3.73767 
 3.76120 
 3-78419 
 
 2381 
 2326 
 2273 
 
 92 
 93 
 94 
 
 4.52179 
 4.53200 
 4.54329 
 
 1087 
 1075 
 1064 
 
 142 
 
 143 
 144 
 
 4.95583 
 4.96284 
 4.96981 
 
 704 
 699 
 694 
 
 192 
 193 
 
 194 
 
 5.25750 
 5.26269 
 5.26786 
 
 521 
 5i8 
 515 
 
 45 
 
 3.80666 
 
 2222 
 
 95 
 
 4.55388 
 
 1053 
 
 145 
 
 4.97673 
 
 690 
 
 195 
 
 5.27300 
 
 513 
 
 46 
 
 3.82864 
 
 2174 
 
 96 
 
 T */*W 
 
 4.56435 
 
 1042 
 
 146 
 
 4.98361 
 
 
 196 
 
 5.27811 
 
 510 
 
 47 
 48 
 
 3.85015 
 3-87120 
 
 2128 
 2083 
 
 97 
 98 
 
 4.57471 
 4.58497 
 
 1031 
 
 IO2O 
 
 147 
 148 
 
 4.99043 
 4-99721 
 
 sn 
 680 
 
 676 
 
 197 
 198 
 
 5.28320 
 5.28827 
 
 508 
 505 
 
 49 
 
 3.89182 
 
 2041 
 
 99 
 
 4.59512 
 
 IOIO 
 
 149 
 
 5-00395 
 
 671 
 
 199 
 
 5.29330 
 
 503 
 
 50 
 
 3.91202 
 
 2000 
 
 TOO 
 
 4.60517 
 
 1000 
 
 ISO 
 
 5.01064 
 
 66 7 
 
 200 
 
 5.29832 
 
 500 
 
 e x 
 
 X 
 
 .- 
 
 e x 
 
 X 
 
 e~ x 
 
 e x 
 
 X 
 
 rj 
 
 e x 
 
 X 
 
 e~ x 
 
 SMITHSONIAN TABLES 
 
 264 
 
Natural Logarithms. 
 
 u 
 
 lOOell 
 
 Fo' 
 
 u 
 
 log.u 
 
 F O ' 
 
 u 
 
 log e u 
 
 F ' 
 
 u 
 
 lOflell 
 
 F O ' 
 
 200 
 
 5.20832 
 
 500 
 
 250 
 
 5.52146 
 
 400 
 
 300 
 
 5.70378 
 
 333 
 
 350 
 
 5.85793 
 
 286 
 
 201 
 
 5.30330 
 
 498 
 
 251 
 
 5.52545 
 
 398 
 
 301 
 
 5.707II 
 
 332 
 
 351 
 
 5.86079 
 
 285 
 
 202 
 
 5.30827 
 
 495 
 
 252 
 
 5.52943 
 
 397 
 
 302 
 
 5.71043 
 
 331 
 
 352 
 
 5.86363 
 
 284 
 
 203 
 
 5.3I32I 
 
 493 
 
 253 
 
 5-53339 
 
 395 
 
 303 
 
 5.71373 
 
 330 
 
 353 
 
 5.86647 
 
 283 
 
 2O4 
 
 5.3I8I2 
 
 490 
 
 254 
 
 5-53733 
 
 394 
 
 304 
 
 5.71703 
 
 329 
 
 354 
 
 5.86930 
 
 282 
 
 205 
 
 5.32301 
 
 488 
 
 255 
 
 5.54126 
 
 392 
 
 305 
 
 5.72031 
 
 328 
 
 355 
 
 5.87212 
 
 282 
 
 206 
 
 5.32788 
 
 485 
 
 256 
 
 5.54518 
 
 39i 
 
 306 
 
 5.72359 
 
 327 
 
 356 
 
 5.87493 
 
 281 
 
 207 
 
 5.33272 
 
 483 
 
 257 
 
 5-54908 
 
 389 
 
 307 
 
 5.72685 
 
 326 
 
 357 
 
 5.87774 
 
 280 
 
 208 
 
 5-33754 
 
 481 
 
 258 
 
 5.55206 
 
 388 
 
 308 
 
 5.73010 
 
 325 
 
 358 
 
 5.88053 
 
 279 
 
 209 
 
 5.34233 
 
 478 
 
 259 
 
 5.55683 
 
 386 
 
 309 
 
 5-73334 
 
 324 
 
 359 
 
 5.88332 
 
 279 
 
 2IO 
 
 5-347II 
 
 476 
 
 260 
 
 5.56068 
 
 385 
 
 310 
 
 5.73657 
 
 323 
 
 360 
 
 5.88610 
 
 278 
 
 211 
 
 5.35186 
 
 474 
 
 261 
 
 5.56452 
 
 383 
 
 3ii 
 
 5-73979 
 
 322 
 
 361 
 
 5.88888 
 
 277 
 
 212 
 
 5.35659 
 
 472 
 
 262 
 
 5.56834 
 
 382 
 
 312 
 
 5.74300 
 
 321 
 
 362 
 
 5.89164 
 
 276 
 
 213 
 
 5.36129 
 
 469 
 
 263 
 
 5.57215 
 
 380 
 
 313 
 
 5.74620 
 
 319 
 
 363 
 
 5.89440 
 
 275 
 
 214 
 
 5.36598 
 
 467 
 
 264 
 
 5-57595 
 
 379 
 
 314 
 
 5-74939 
 
 3l8 
 
 364 
 
 5.89715 
 
 275 
 
 215 
 
 5.37064 
 
 465 
 
 265 
 
 5.57973 
 
 377 
 
 315 
 
 5.75257 
 
 317 
 
 365 
 
 5.89990 
 
 274 
 
 216 
 
 5.37528 
 
 463 
 
 266 
 
 5.58350 
 
 376 
 
 316 
 
 5-75574 
 
 3i6 
 
 366 
 
 5-90263 
 
 273 
 
 217 
 
 5:37990" 
 
 461 
 
 267 
 
 5.58725 
 
 375 
 
 317 
 
 5.75890 
 
 315 
 
 367 
 
 5.90536 
 
 272 
 
 218 
 
 5.38450 
 
 459 
 
 268 
 
 5.59099 
 
 373 
 
 3i8 
 
 5.76205 
 
 314 
 
 368 
 
 5.90808 
 
 272 
 
 219 
 
 5-38007 
 
 457 
 
 269 
 
 5.59471 
 
 372 
 
 319 
 
 5-76519 
 
 313 
 
 369 
 
 5.91080 
 
 271 
 
 22O 
 
 5.39363 
 
 455 
 
 270 
 
 5.59842 
 
 370 
 
 320 
 
 5.76832 
 
 312 
 
 370 
 
 5.91350 
 
 270 
 
 221 
 
 5.398i6 
 
 452 
 
 271 
 
 5.60212 
 
 309 
 
 321 
 
 5.77144 
 
 312 
 
 37i 
 
 5.91620 
 
 270 
 
 222 
 
 5.40268 
 
 450 
 
 272 
 
 5.60580 
 
 368 
 
 322 
 
 5-77455 
 
 311 
 
 372 
 
 5.91889 
 
 269 
 
 223 
 
 5.40717 
 
 448 
 
 273 
 
 5.60947 
 
 366 
 
 323 
 
 5.77765 
 
 310 
 
 373 
 
 5.92158 
 
 268 
 
 224 
 
 5-41165 
 
 446 
 
 274 
 
 5.6I3I3 
 
 365 
 
 324 
 
 5.78074 
 
 309 
 
 374 
 
 5.92426 
 
 267 
 
 225 
 
 5.41610 
 
 444 
 
 275 
 
 5.6l677 
 
 364 
 
 325 
 
 5.78383 
 
 308 
 
 375 
 
 5.92693 
 
 267 
 
 226 
 
 5.42053 
 
 442 
 
 276 
 
 5.62040 
 
 362 
 
 326 
 
 5.78690 
 
 307 
 
 376 
 
 5.92959 
 
 266 
 
 227 
 
 5.42495 
 
 441 
 
 277 
 
 5.62402 
 
 361 
 
 327 
 
 5-78996 
 
 306 
 
 377 
 
 5.93225 
 
 265 
 
 228 
 
 5.42935 
 
 439 
 
 278 
 
 5.62762 
 
 360 
 
 328 
 
 5-79301 
 
 305 
 
 378 
 
 5.93489 
 
 265 
 
 229 
 
 5.43372 
 
 437 
 
 279 
 
 5.63I2I 
 
 358 
 
 329 
 
 5.79606 
 
 304 
 
 379 
 
 5-93754 
 
 264 
 
 230 
 
 5.438o8 
 
 435 
 
 280 
 
 5.63479 
 
 357 
 
 330 
 
 5.79909 
 
 303 
 
 380 
 
 5.94017 
 
 263 
 
 231 
 
 5.44242 
 
 433 
 
 281 
 
 5.63835 
 
 356 
 
 331 
 
 5.80212 
 
 302 
 
 381 
 
 5.94280 
 
 262 
 
 232 
 
 5.44674 
 
 431 
 
 282 
 
 5'.64I9I 
 
 355 
 
 332 
 
 5.80513 
 
 301 
 
 382 
 
 5.94542 
 
 262 
 
 233 
 
 5.45104 
 
 429 
 
 283 
 
 5.64545 
 
 353 
 
 333 
 
 5.80814 
 
 300 
 
 383 
 
 5.94803 
 
 261 
 
 234 
 
 5-45532 
 
 427 
 
 284 
 
 5.64897 
 
 352 
 
 334 
 
 5-81114 
 
 299 
 
 384 
 
 5-95064 
 
 260 
 
 235 
 
 5-45959 
 
 426 
 
 285 
 
 5.65249 
 
 351 
 
 335 
 
 5.8I4I3 
 
 299 
 
 385 
 
 5.95324 
 
 260 
 
 2 3 6 
 
 5.46383 
 
 424 
 
 286 
 
 5.65599 
 
 350 
 
 336 
 
 5-81711 
 
 298 
 
 386 
 
 5.95584 
 
 259 
 
 237 
 
 5.46806 
 
 422 
 
 287 
 
 5.65948 
 
 348 
 
 337 
 
 5.82008 
 
 297 
 
 387 
 
 5.95842 
 
 258 
 
 2 3 8 
 
 5.47227 
 
 420 
 
 288 
 
 5.66296 
 
 347 
 
 338 
 
 5-82305 
 
 296 
 
 388 
 
 5.96101 
 
 258 
 
 239 
 
 5.47646 
 
 418 
 
 289 
 
 5.66643 
 
 346 
 
 339 
 
 5.82600 
 
 295 
 
 389 
 
 5.96358 
 
 257 
 
 240 
 
 5-48064 
 
 417 
 
 290 
 
 5.66988 
 
 345 
 
 340 
 
 5.82895 
 
 294 
 
 390 
 
 5.96615 
 
 256 
 
 241 
 
 5.48480 
 
 415 
 
 291 
 
 5.67332 
 
 344 
 
 341 
 
 5.83188 
 
 293 
 
 391 
 
 5.96871 
 
 256 
 
 242 
 
 5.48894 
 
 413 
 
 292 
 
 5.67675 
 
 342 
 
 342 
 
 5.83481 
 
 292 
 
 392 
 
 5.97126 
 
 255 
 
 243 
 
 5.49306 
 
 412 
 
 293 
 
 5.68017 
 
 341 
 
 343 
 
 5.83773 
 
 292 
 
 393 
 
 5.9738i 
 
 254 
 
 244 
 
 5.49717 
 
 410 
 
 294 
 
 5.68358 
 
 340 
 
 344 
 
 5-84064 
 
 291 
 
 394 
 
 5.97635 
 
 254 
 
 245 
 
 5.50126 
 
 408 
 
 295 
 
 5.68698 
 
 339 
 
 345 
 
 5.84354 
 
 290 
 
 395 
 
 5.97889 
 
 253 
 
 2 4 6 
 
 5.50533 
 
 407 
 
 296 
 
 5.69036 
 
 338 
 
 346 
 
 5.84644 
 
 289 
 
 396 
 
 5.98141 
 
 253 
 
 247 
 
 5.50939 
 
 405 
 
 297 
 
 5.69373 
 
 337 
 
 347 
 
 5.84932 
 
 288 
 
 397 
 
 5.98394 
 
 252 
 
 2 4 8 
 
 5.51343 
 
 403 
 
 298 
 
 5.69709 
 
 336 
 
 348 
 
 5.85220 
 
 287 
 
 398 
 
 5-98645 
 
 251 
 
 249 
 
 5.51745 
 
 402 
 
 299 
 
 5.70044 
 
 334 
 
 349 
 
 5.85507 
 
 287 
 
 399 
 
 5.98896 
 
 251 
 
 250 
 
 5.52146 
 
 400 
 
 300 
 
 5.70378 
 
 333 
 
 350 
 
 5.85793 
 
 286 
 
 400 
 
 5.99146 
 
 250 
 
 e x 
 
 X 
 
 e- x 
 
 e* 
 
 X 
 
 e~x 
 
 e x 
 
 X 
 
 e x 
 
 e x 
 
 X 
 
 e x 
 
 SMITHSONIAN TABLES 
 
 265 
 
Natural Logarithms. 
 
 u 
 
 ^ 
 
 F ' 
 
 u 
 
 lOOeU 
 
 F O ' 
 
 U 
 
 (OQeU 
 
 F ' 
 
 u 
 
 log e u 
 
 F ' 
 
 400 
 
 5.99146 
 
 250 
 
 450 
 
 6.10925 
 
 222 
 
 500 
 
 6.2I46I 
 
 2OO 
 
 550 
 
 6.30992 
 
 182 
 
 40 1 
 
 5.99396 
 
 249 
 
 451 
 
 6. 1 1 147 
 
 222 
 
 501 
 
 6. 21661 
 
 200 
 
 55i 
 
 6.31173 
 
 181 
 
 402 
 
 5.99645 
 
 249 
 
 452 
 
 6.11368 
 
 221 
 
 502 
 
 6.21860 
 
 109 
 
 552 
 
 6.31355 
 
 181 
 
 403 
 
 5.99894 
 
 248 
 
 453 
 
 6.11589 
 
 221 
 
 503 
 
 6.22059 
 
 199 
 
 553 
 
 6.31536 
 
 181 
 
 404 
 
 6.00141 
 
 248 
 
 454 
 
 6. 11810 
 
 22O 
 
 504 
 
 6.22258 
 
 198 
 
 554 
 
 6.31716 
 
 181 
 
 405 
 
 6.00389 
 
 247 
 
 455 
 
 6. 12030 
 
 22O 
 
 505 
 
 6.22456 
 
 198 
 
 555 
 
 6.31897 
 
 180 
 
 406 
 
 6.00635 
 
 2 4 6 
 
 456 
 
 6.12249 
 
 219 
 
 506 
 
 6.22654 
 
 198 
 
 556 
 
 6.32077 
 
 180 
 
 407 
 
 6.00881 
 
 2 4 6 
 
 457 
 
 6.12468 
 
 219 
 
 507 
 
 6.22851 
 
 197 
 
 557 
 
 6.32257 
 
 180 
 
 408 
 
 6.01127 
 
 245 
 
 458 
 
 6.12687 
 
 218 
 
 508 
 
 6.23048 
 
 197 
 
 558 
 
 6.32436 
 
 179 
 
 409 
 
 6.01372 
 
 244 
 
 459 
 
 6. 12905 
 
 218 
 
 509 
 
 6.23245 
 
 196 
 
 559 
 
 6.32615 
 
 179 
 
 410 
 
 6.01616 
 
 244 
 
 460 
 
 6.13123 
 
 217 
 
 5io 
 
 6.23441 
 
 196 
 
 560 
 
 6.32794 
 
 179 
 
 411 
 
 6.01859 
 
 243 
 
 461 
 
 6.13340 
 
 217 
 
 511 
 
 6.23637 
 
 196 
 
 56i 
 
 6.32972 
 
 178 
 
 412 
 
 6.O2IO2 
 
 243 
 
 462 
 
 6.13556 
 
 216 
 
 512 
 
 6.23832 
 
 195 
 
 562 
 
 6.33150 
 
 178 
 
 413 
 
 6.O2345 
 
 242 
 
 463 
 
 6.13773 
 
 216 
 
 
 6.24028 
 
 195 
 
 563 
 
 6.33328 
 
 178 
 
 414 
 
 6.02587 
 
 242 
 
 464 
 
 6.13988 
 
 216 
 
 5i4 
 
 6.24222 
 
 195 
 
 564 
 
 6.33505 
 
 177 
 
 415 
 
 6.02828 
 
 241 
 
 465 
 
 6.14204 
 
 215 
 
 5i5 
 
 6.24417 
 
 194 
 
 565 
 
 6.33683 
 
 177 
 
 416 
 
 6.03069 
 
 240 
 
 466 
 
 6.14419 
 
 215 
 
 5i6 
 
 6.24611 
 
 194 
 
 566 
 
 6.33859 
 
 177 
 
 417 
 
 6.03309 
 
 240 
 
 467 
 
 6.14633 
 
 214 
 
 5i7 
 
 6.24804 
 
 193 
 
 567 
 
 6.34036 
 
 176 
 
 418 
 
 6.03548 
 
 239 
 
 468 
 
 6.14847 
 
 214 
 
 5i8 
 
 6.24998 
 
 193 
 
 568 
 
 6.34212 
 
 176 
 
 419 
 
 6.03787 
 
 239 
 
 469 
 
 6.15060 
 
 213 
 
 519 
 
 6.25190 
 
 193 
 
 569 
 
 6.34388 
 
 176 
 
 420 
 
 6.O4O25 
 
 238 
 
 470 
 
 6.15273 
 
 213 
 
 520 
 
 6.25383 
 
 192 
 
 570 
 
 6.34564 
 
 175 
 
 421 
 
 6.04263 
 
 238 
 
 47i 
 
 6.15486 
 
 212 
 
 521 
 
 6.25575 
 
 192 
 
 571 
 
 6.34739 
 
 175 
 
 422 
 
 6.O45OI 
 
 237 
 
 472 
 
 6.15698 
 
 212 
 
 522 
 
 6.25767 
 
 192 
 
 572 
 
 6.34914 
 
 175 
 
 423 
 
 6.04737 
 
 236 
 
 473 
 
 6.15910 
 
 211 
 
 523 
 
 6.25958 
 
 191 
 
 573 
 
 6.35089 
 
 175 
 
 424 
 
 6.04973 
 
 236 
 
 474 
 
 6.16121 
 
 211 
 
 524 
 
 6.26149 
 
 191 
 
 574 
 
 6.35263 
 
 174 
 
 425 
 
 6.05209 
 
 235 
 
 475 
 
 6.16331 
 
 211 
 
 525 
 
 6.26340 
 
 190 
 
 575 
 
 6.35437 
 
 174 
 
 426 
 
 6.05444 
 
 235 
 
 476 
 
 6.16542 
 
 210 
 
 526 
 
 6.26530 
 
 190 
 
 576 
 
 6.35611 
 
 174 
 
 427 
 
 6.05678 
 
 234 
 
 477 
 
 6. 16752 
 
 210 
 
 527 
 
 6.26720 
 
 190 
 
 577 
 
 6.35784 
 
 173 
 
 428 
 
 6.05912 
 
 234 
 
 478 
 
 6.16961 
 
 209 
 
 528 
 
 6.26910 
 
 189 
 
 578 
 
 6.35957 
 
 173 
 
 429 
 
 6.06146 
 
 233 
 
 479 
 
 6.17170 
 
 209 
 
 529 
 
 6.27099 
 
 189 
 
 579 
 
 6.36130 
 
 173 
 
 430 
 
 6.06379 
 
 233 
 
 480 
 
 6.17379 
 
 208 
 
 530 
 
 6.27288 
 
 189 
 
 58o 
 
 6.36303 
 
 172 
 
 431 
 
 6.06611 
 
 232 
 
 481 
 
 6.17587 
 
 208 
 
 531 
 
 6.27476 
 
 188 
 
 58i 
 
 6.30475 
 
 172 
 
 432 
 
 6.06843 
 
 231 
 
 482 
 
 6.17794 
 
 207 
 
 532 
 
 6.27664 
 
 188 
 
 582 
 
 6.36647 
 
 172 
 
 433 
 
 6.07074 
 
 231 
 
 483 
 
 6.18002 
 
 207 
 
 533 
 
 6.27852 
 
 188 
 
 583 
 
 6.36819 
 
 172 
 
 434 
 
 6.07304 
 
 230 
 
 484 
 
 6.18208 
 
 207 
 
 534 
 
 6.28040 
 
 187 
 
 584 
 
 6.36990 
 
 171 
 
 435 
 
 6.07535 
 
 230 
 
 485 
 
 6.18415 
 
 206 
 
 535 
 
 6.28227 
 
 187 
 
 585 
 
 6.37161 
 
 171 
 
 436 
 
 6.07764 
 
 229 
 
 486 
 
 6.18621 
 
 206 
 
 536 
 
 6.28413 
 
 187 
 
 586 
 
 6.37332 
 
 171 
 
 437 
 
 6.07993 
 
 229 
 
 487 
 
 6.18826 
 
 205 
 
 537 
 
 6.28600 
 
 186 
 
 587 
 
 6.37502 
 
 170 
 
 438 
 
 6.08222 
 
 228 
 
 488 
 
 6.19032 
 
 205 
 
 538 
 
 6.28786 
 
 186 
 
 588 
 
 6.37673 
 
 170 
 
 439 
 
 6.08450 
 
 228 
 
 489 
 
 6.19236 
 
 204 
 
 539 
 
 6.28972 
 
 186 
 
 589 
 
 6.37843 
 
 170 
 
 440 
 
 6.08677 
 
 227 
 
 490 
 
 6.19441 
 
 204 
 
 540 
 
 6.29157 
 
 185 
 
 590 
 
 6.38012 
 
 169 
 
 441 
 
 6.08904 
 
 227 
 
 491 
 
 6.19644 
 
 204 
 
 54i 
 
 6.2934-' 
 
 185 
 
 591 
 
 6.38182 
 
 169 
 
 442 
 
 6.09131 
 
 226 
 
 492 
 
 6.19848 
 
 203 
 
 542 
 
 6.29527 
 
 185 
 
 592 
 
 6.38351 
 
 169 
 
 443 
 
 6.09357 
 
 226 
 
 493 
 
 6.20051 
 
 203 
 
 543 
 
 6.29711 
 
 184 
 
 593 
 
 6.38519 
 
 169 
 
 444 
 
 6.09582 
 
 225 
 
 494 
 
 6.20254 
 
 202 
 
 544 
 
 6.29895 
 
 184 
 
 594 
 
 (,-.38088 
 
 168 
 
 445 
 
 6.09807 
 
 225 
 
 495 
 
 6.20456 
 
 2O2 
 
 545 
 
 6.30079 
 
 183 
 
 595 
 
 6.38856 
 
 168 
 
 446 
 
 6.10032 
 
 224 
 
 496 
 
 6.20658 
 
 2O2 
 
 546 
 
 6.30262 
 
 183 
 
 596 
 
 6.39024 
 
 168 
 
 447 
 
 6.10256 
 
 224 
 
 497 
 
 6.20859 
 
 201 
 
 547 
 
 6.30445 
 
 183 
 
 597 
 
 6.39192 
 
 168 
 
 448 
 
 6. 10479 
 
 223 
 
 498 
 
 6.21060 
 
 201 
 
 548 
 
 6.30628 
 
 182 
 
 598 
 
 6.39359 
 
 167 
 
 449 
 
 6.10702 
 
 223 
 
 499 
 
 6.21261 
 
 200 
 
 549 
 
 6.30810 
 
 182 
 
 599 
 
 6.395-*> 
 
 167 
 
 450 
 
 6.10925 
 
 222 
 
 500 
 
 6.21461 
 
 2OO 
 
 550 
 
 6.30992 
 
 182 
 
 600 
 
 6.39693 
 
 167 
 
 e x 
 
 x 
 
 e~ x 
 
 e* 
 
 X 
 
 .- 
 
 e x 
 
 x 
 
 e~ x 
 
 e x 
 
 x 
 
 e- x 
 
 SMITHSONIAN TABLES 
 
 266 
 
Natural Logarithms. 
 
 u 
 
 lOOell 
 
 F O ' 
 
 u 
 
 lOOeU 
 
 F O ' 
 
 u 
 
 lOOell 
 
 o>Fo' 
 
 u 
 
 lOQeU 
 
 F ' 
 
 600 
 
 6.39693 
 
 167 
 
 650 
 
 6.47097 
 
 154 
 
 700 
 
 6.55108 
 
 143 
 
 750 
 
 6.62007 
 
 133 
 
 601 
 
 6.39859 
 
 166 
 
 651 
 
 6.47851 
 
 154 
 
 701 
 
 6.55251 
 
 H3 
 
 75i 
 
 6.62141 
 
 133 
 
 602 
 
 6.40O26 
 
 166 
 
 652 
 
 6.48004 
 
 153 
 
 702 
 
 6.55393 
 
 142 
 
 752 
 
 6.62274 
 
 133 
 
 603 
 
 6.4OI92 
 
 166 
 
 653 
 
 6.48158 
 
 153 
 
 703 
 
 6.55536 
 
 142 
 
 753 
 
 6.62407 
 
 133 
 
 604 
 
 6.40357 
 
 166 
 
 654 
 
 6.483H 
 
 153 
 
 704 
 
 6.55678 
 
 142 
 
 754 
 
 6.62539 
 
 133 
 
 605 
 606 
 
 6.40523 
 6.40688 
 
 165 
 165 
 
 655 
 656 
 
 6.48464 
 6.48616 
 
 153 
 152 
 
 705 
 
 706 
 
 6.55820 
 6.55062 
 
 142 
 
 142 
 
 755 
 756 
 
 6.62672 
 6.62804 
 
 132 
 132 
 
 607 
 
 6.40853 
 
 165 
 
 657 
 
 6.48768 
 
 152 
 
 707 
 
 6.56103 
 
 141 
 
 757 
 
 6.62936 
 
 132 
 
 608 
 
 6.4IOI7 
 
 164 
 
 658 
 
 6.48920 
 
 152 
 
 708 
 
 6 . 56244 
 
 141 
 
 758 
 
 6.63068 
 
 132 
 
 609 
 
 6.4II82 
 
 164 
 
 659 
 
 6.49072 
 
 152 
 
 709 
 
 6.56386 
 
 141 
 
 759 
 
 6.63200 
 
 132 
 
 610 
 
 6.41346 
 
 164 
 
 660 
 
 6.49224 
 
 152 
 
 710 
 
 6.56526 
 
 141 
 
 760 
 
 6.63332 
 
 132 
 
 611 
 
 6.4I5IO 
 
 164 
 
 661 
 
 6.49375 
 
 151 
 
 711 
 
 6.56667 
 
 141 
 
 761 
 
 6.63463 
 
 131 
 
 612 
 
 6.41673 
 
 163 
 
 662 
 
 6.49527 
 
 151 
 
 712 
 
 6.56808 
 
 140 
 
 762 
 
 6.63595 
 
 131 
 
 613 
 
 6.41836 
 
 163 
 
 663 
 
 6.49677 
 
 151 
 
 7i3 
 
 6.56948 
 
 140 
 
 763 
 
 6.63726 
 
 131 
 
 614 
 
 6.41999 
 
 163 
 
 664 
 
 6.40828 
 
 151 
 
 7H 
 
 6.57088 
 
 140 
 
 764 
 
 6.63857 
 
 131 
 
 615 
 
 6.42162 
 
 163 
 
 665 
 
 6.49979 
 
 150 
 
 715 
 
 6.57228 
 
 140 
 
 765 
 
 6.63988 
 
 131 
 
 616 
 
 6.42325 
 
 162 
 
 666 
 
 6.50129 
 
 150 
 
 716 
 
 6.57368 
 
 140 
 
 766 
 
 6.64118 
 
 131 
 
 617 
 
 6.42487 
 
 162 
 
 667 
 
 6.50279 
 
 150 
 
 717 
 
 6.57508 
 
 139 
 
 767 
 
 6.64249 
 
 130 
 
 618 
 
 6.42649 
 
 162 
 
 668 
 
 6.50429 
 
 150 
 
 7i8 
 
 6.57647 
 
 139 
 
 768 
 
 6.64379 
 
 130 
 
 619 
 
 6.428II 
 
 162 
 
 669 
 
 6.50578 
 
 149 
 
 719 
 
 6.57786 
 
 139 
 
 769 
 
 6.64509 
 
 130 
 
 620 
 
 6.42972 
 
 161 
 
 670 
 
 6.50728 
 
 149 
 
 720 
 
 6.57925 
 
 139 
 
 770 
 
 6.64639 
 
 130 
 
 621 
 
 6.43133 
 
 161 
 
 671 
 
 6.50877 
 
 149 
 
 721 
 
 6.58064 
 
 139 
 
 771 
 
 6.64769 
 
 130 
 
 622 
 
 6.43294 
 
 161 
 
 672 
 
 6.51026 
 
 149 
 
 722 
 
 6.58203 
 
 
 772 
 
 6.64898 
 
 130 
 
 623 
 
 6.43455 
 
 161 
 
 673 
 
 6.5H75 
 
 149 
 
 723 
 
 6.58341 
 
 138 
 
 773 
 
 6.65028 
 
 129 
 
 624 
 
 6.43615 
 
 160 
 
 674 
 
 6.51323 
 
 148 
 
 724 
 
 6.58479 
 
 138 
 
 774' 
 
 6.65157 
 
 129 
 
 625 
 
 6.43775 
 
 160 
 
 675 
 
 6.5I47I 
 
 148 
 
 725 
 
 6.58617 
 
 138 
 
 775 
 
 6.65286 
 
 129 
 
 626 
 
 6-43935 
 
 160 
 
 676 
 
 6.51619 
 
 148 
 
 726 
 
 6.58755 
 
 138 
 
 776 
 
 6.65415 
 
 129 
 
 627 
 
 6.44095 
 
 159 
 
 677 
 
 6.51767 
 
 148 
 
 727 
 
 6.58893 
 
 138 
 
 777 
 
 6.65544 
 
 129 
 
 628 
 
 6.44254 
 
 159 
 
 678 
 
 6.5I9I5 
 
 147 
 
 728 
 
 6.59030 
 
 137 
 
 778 
 
 6.65673 
 
 129 
 
 629 
 
 6.44413 
 
 159 
 
 679 
 
 6.52062 
 
 147 
 
 729 
 
 6.59167 
 
 137 
 
 779 
 
 6.65801 
 
 128 
 
 630 
 
 6.44572 
 
 159 
 
 680 
 
 6.52209 
 
 147 
 
 730 
 
 6.59304 
 
 137 
 
 780 
 
 6.65929 
 
 128 
 
 631 
 
 6.44731 
 
 158 
 
 681 
 
 6.52356 
 
 H7 
 
 731 
 
 6.59441 
 
 137 
 
 78i 
 
 6.66058 
 
 128 
 
 632 
 
 6.44889 
 
 158 
 
 682 
 
 6.52503 
 
 147 
 
 732 
 
 6.59578 
 
 137 
 
 782 
 
 6.66185 
 
 128 
 
 633 
 
 6.45047 
 
 158 
 
 683 
 
 6.52649 
 
 146 
 
 733 
 
 6.59715 
 
 136 
 
 783 
 
 6.66313 
 
 128 
 
 634 
 
 6.45205 
 
 158 
 
 684 
 
 6.52796 
 
 146 
 
 734 
 
 6.59851 
 
 136 
 
 784 
 
 6.66441 
 
 128 
 
 635 
 
 6.45362 
 
 157 
 
 685 
 
 6.52942 
 
 146 
 
 735 
 
 6.59987 
 
 136 
 
 785 
 
 6.66568 
 
 127 
 
 636 
 
 6.45520 
 
 157 
 
 686 
 
 6.53088 
 
 146 
 
 736 
 
 6.60123 
 
 136 
 
 786 
 
 6.66696 
 
 127 
 
 637 
 
 6.45677 
 
 157 
 
 687 
 
 6.53233 
 
 146 
 
 737 
 
 6.60259 
 
 136 
 
 787 
 
 6.66823 
 
 127 
 
 638 
 
 6.45834 
 
 157 
 
 688 
 
 6.53379 
 
 145 
 
 738 
 
 6.60394 
 
 136 
 
 788 
 
 6.66950 
 
 127 
 
 639 
 
 6.45990 
 
 156 
 
 689 
 
 6.53524 
 
 US 
 
 739 
 
 6.60530 
 
 135 
 
 789 
 
 6.67077 
 
 127 
 
 
 
 
 
 i 
 
 
 
 
 
 
 
 
 640 
 
 6.46147 
 
 156 
 
 690 
 
 6.53669 
 
 145 
 
 740 
 
 6.60665 
 
 135 
 
 790 
 
 6.67203 
 
 127 
 
 641 
 
 6.46303 
 
 156 
 
 691 
 
 6.53814 
 
 H5 
 
 74i 
 
 6.60800 
 
 135 
 
 791 
 
 6.67330 
 
 126 
 
 642 
 
 6.46459 
 
 156 
 
 692 
 
 6.53959 
 
 H5 
 
 742 
 
 6.60935 
 
 135 
 
 792 
 
 6.67456 
 
 126 
 
 643 
 
 6.46614 
 
 156 
 
 693 
 
 6.54103 
 
 144 
 
 743 
 
 6.61070 
 
 135 
 
 793 
 
 6.67582 
 
 126 
 
 644 
 
 6.46770 
 
 155 
 
 694 
 
 6.54247 
 
 144 
 
 744 
 
 6.61204 
 
 134 
 
 794 
 
 6.67708 
 
 126 
 
 645 
 
 6.40925 
 
 155 
 
 695 
 
 6.54391 
 
 144 
 
 745 
 
 6.61338 
 
 134 
 
 795 
 
 6.67834 
 
 126 
 
 646 
 
 6.47O8O 
 
 155 
 
 696 
 
 6.54535 
 
 144 
 
 746 
 
 6.61473 
 
 134 
 
 796 
 
 6.67960 
 
 126 
 
 647 
 
 6.47235 
 
 155 
 
 697 
 
 6.54679 
 
 143 
 
 747 
 
 6.61607 
 
 134 
 
 797 
 
 6.68085 
 
 125 
 
 648 
 
 6.473'89 
 
 154 
 
 698 
 
 6.54822 
 
 143 
 
 748 
 
 6.61740 
 
 134 
 
 798 
 
 6.68211 
 
 125 
 
 649 
 
 6.47543 
 
 154 
 
 699 
 
 6.54965 
 
 143 
 
 749 
 
 6.61874 
 
 134 
 
 799 
 
 6.68336 
 
 125 
 
 650 
 
 6.47697 
 
 154 
 
 700 
 
 6.55108 
 
 143 
 
 750 
 
 6.62007 
 
 133 
 
 800 
 
 6.68461 
 
 125 
 
 e x 
 
 X 
 
 e- x 
 
 e* 
 
 x 
 
 e~ x 
 
 e x 
 
 X 
 
 e x 
 
 e x 
 
 x 
 
 e x 
 
 SMITHSONIAN TABLES 
 
 267 
 
Natural Logarithms. 
 
 u 
 
 lOfleU 
 
 F' 
 
 u 
 
 lOfleU 
 
 F 
 
 u 
 
 lOQ.U 
 
 F O ' 
 
 u 
 
 loo-u 
 
 F O ' 
 
 800 
 
 6.68461 
 
 125 
 
 850 
 
 6.74524 
 
 118 
 
 900 
 
 6.80239 
 
 in 
 
 950 
 
 6.85646 
 
 105 
 
 801 
 
 6.68586 
 
 125 
 
 851 
 
 6.74641 
 
 118 
 
 001 
 
 6.80351 
 
 in 
 
 95i 
 
 6.85751 
 
 105 
 
 802 
 
 6.68711 
 
 125 
 
 852 
 
 6.74759 
 
 117 
 
 002 
 
 6.80461 
 
 in 
 
 952 
 
 6.85857 
 
 105 
 
 803 
 
 6.68835 
 
 125 
 
 853 
 
 6.74876 
 
 117 
 
 903 
 
 6.80572 
 
 in 
 
 953 
 
 6.85961 
 
 105 
 
 804 
 
 6.68960 
 
 124 
 
 854 
 
 6.74993 
 
 117 
 
 904 
 
 6.80683 
 
 in 
 
 954 
 
 6.86066 
 
 105 
 
 805 
 
 6.69084 
 
 124 
 
 855 
 
 6.75110 
 
 117 
 
 905 
 
 6.80793 
 
 no 
 
 955 
 
 6.86I7I 
 
 105 
 
 806 
 
 6.69208 
 
 124 
 
 856 
 
 6.75227 
 
 117 
 
 906 
 
 6.80904 
 
 1 10 
 
 956 
 
 6.86276 
 
 105 
 
 807 
 
 6.69332 
 
 124 
 
 857 
 
 6.75344 
 
 117 
 
 907 
 
 6.8IOI4 
 
 1 10 
 
 957 
 
 6.86380 
 
 104 
 
 808 
 
 6.69456 
 
 124 
 
 858 
 
 6.7546o 
 
 117 
 
 908 
 
 6.8II24 
 
 no 
 
 958 
 
 6.86485 
 
 104 
 
 809 
 
 6.69580 
 
 124 
 
 859 
 
 6.75577 
 
 116 
 
 909 
 
 ,6.81235 
 
 no 
 
 959 
 
 6.86589 
 
 104 
 
 810 
 
 6.69703 
 
 123 
 
 860 
 
 6.75693 
 
 116 
 
 910 
 
 6.81344 
 
 no 
 
 960 
 
 6.86693 
 
 104 
 
 811 
 
 6.69827 
 
 123 
 
 86 1 
 
 6.75809 
 
 116 
 
 911 
 
 6.81454 
 
 1 10 
 
 961 
 
 6.86797 
 
 104 
 
 812 
 
 6.69950 
 
 123 
 
 862 
 
 6.75926 
 
 116 
 
 912 
 
 6.81564 
 
 IIO 
 
 962 
 
 6.86901 
 
 104 
 
 813 
 
 6.70073 
 
 123 
 
 8& 
 
 6.76041 
 
 116 
 
 913 
 
 6.81674 
 
 1 10 
 
 963 
 
 6.87005 
 
 104 
 
 814 
 
 6.70196 
 
 123 
 
 864 
 
 6.76157 
 
 116 
 
 914 
 
 6.81783 
 
 109 
 
 964 
 
 6.87109 
 
 104 
 
 815 
 
 6.70319 
 
 123 
 
 865 
 
 6.76273 
 
 116 
 
 915 
 
 6.8l892 
 
 109 
 
 965 
 
 6.87213 
 
 104 
 
 816 
 
 6.70441 
 
 123 
 
 866 
 
 6.76388 
 
 115 
 
 916 
 
 6.82002 
 
 109 
 
 966 
 
 6.87316 
 
 104 
 
 817 
 
 6.70564 
 
 122 
 
 867 
 
 6.76504 
 
 H5 
 
 917 
 
 6.82III 
 
 109 
 
 967 
 
 6.87420 
 
 103 
 
 818 
 
 6.70686 
 
 122 
 
 868 
 
 6.76619 
 
 115 
 
 918 
 
 6.8222O 
 
 109 
 
 968 
 
 6.87523 
 
 103 
 
 819 
 
 6.70808 
 
 122 
 
 869 
 
 6.76734 
 
 ii5 
 
 919 
 
 6.82329 
 
 109 
 
 969 
 
 6.87626 
 
 103 
 
 820 
 
 6.70930 
 
 122 
 
 870 
 
 6.76849 
 
 US 
 
 920 
 
 6.82437 
 
 109 
 
 970 
 
 6.87730 
 
 103 
 
 821 
 
 6.71052 
 
 122 
 
 871 
 
 6.76964 
 
 n5 
 
 921 
 
 6.82546 
 
 109 
 
 971 
 
 6.87833 
 
 103 
 
 822 
 
 6.71174 
 
 122 
 
 872 
 
 6.77079 
 
 H5 
 
 922 
 
 6.82655 
 
 108 
 
 972 
 
 6.87936 
 
 103 
 
 823 
 
 6.71296 
 
 122 
 
 873 
 
 6.77194 
 
 US 
 
 923 
 
 6.82763 
 
 108 
 
 973 
 
 6.88038 
 
 103 
 
 824 
 
 6.71417 
 
 121 
 
 874 
 
 6.77308 
 
 114 
 
 924 
 
 6.82871 
 
 108 
 
 974 
 
 6.88I4I 
 
 103 
 
 825 
 
 6.71538 
 
 121 
 
 875 
 
 6.77422 
 
 114 
 
 925 
 
 6.82979 
 
 108 
 
 975 
 
 6.88244 
 
 103 
 
 826 
 
 6.71659 
 
 121 
 
 876 
 
 6.77537 
 
 114 
 
 926 
 
 6.83087 
 
 108 
 
 976 
 
 6.88346 
 
 102 
 
 827 
 
 6.71780 
 
 121 
 
 877 
 
 6.77651 
 
 114 
 
 927 
 
 6.83195 
 
 108 
 
 977 6.88449 
 
 IO2 
 
 828 
 
 6.71901 
 
 121 
 
 878 
 
 6.77765 
 
 114 
 
 928 
 
 6.83303 
 
 108 
 
 978 6.88551 
 
 102 
 
 829 
 
 6.72022 
 
 121 
 
 879 
 
 6.77878 
 
 114 
 
 929 
 
 6.834H 
 
 108 
 
 979 
 
 6.88653 
 
 102 
 
 830 
 
 6.72143 
 
 1 2O 
 
 880 
 
 6.77992 
 
 114 
 
 930 
 
 6.83518 
 
 108 
 
 980 
 
 6.88755 
 
 IO2 
 
 831 
 
 6.72263 
 
 1 2O 
 
 881 
 
 6.78106 
 
 114 
 
 931 
 
 6.83626 
 
 107 
 
 98i 
 
 6.88857 
 
 102 
 
 832 
 
 6.72383 
 
 I2O 
 
 882 
 
 6.78219 
 
 113 
 
 932 
 
 6.83733 
 
 107 
 
 982 
 
 6.88959 
 
 IO2 
 
 833 
 
 6.72503 
 
 I2O 
 
 883 
 
 6.78333 
 
 113 
 
 933 
 
 6.83841 
 
 107 
 
 983 
 
 6.89061 
 
 102 
 
 834 
 
 6.72623 
 
 I2O 
 
 884 
 
 6.78446 
 
 113 
 
 934 
 
 6.83948 
 
 107 
 
 984 
 
 6.89163 
 
 IO2 
 
 835 
 
 6.72743 
 
 I2O 
 
 885 
 
 6.78559 
 
 113 
 
 935 
 
 6.84055 
 
 107 
 
 985 
 
 6.89264 
 
 102 
 
 8 3 5 
 
 6.72863 
 
 1 2O 
 
 886 
 
 6.78672 
 
 113 
 
 936 
 
 6.84162 
 
 107 
 
 986 
 
 6.89366 
 
 IOI 
 
 837 
 
 6.72982 
 
 119 
 
 887 
 
 6.78784 
 
 113 
 
 937 
 
 6.84268 
 
 107 
 
 987 
 
 6.89467 
 
 IOI 
 
 838 
 
 6.73102 
 
 119 
 
 888 
 
 6.78897 
 
 113 
 
 938 
 
 6.84375 
 
 107 
 
 988 
 
 6.89568 
 
 IOI 
 
 839 
 
 6.73221 
 
 119 
 
 889 
 
 6.79010 
 
 112 
 
 939 
 
 6.84482 
 
 106 
 
 989 
 
 6.89669 
 
 IOI 
 
 840 
 
 6.73340 
 
 119 
 
 890 
 
 6.79122 
 
 112 
 
 940 
 
 6.84588 
 
 106 
 
 990 
 
 6.89770 
 
 IOI 
 
 841 
 
 6.73459 
 
 119 
 
 891 
 
 6.79234 
 
 112 
 
 941 
 
 6.84094 
 
 106 
 
 991 
 
 6.89871 
 
 IOI 
 
 842 
 
 6.73578 
 
 119 
 
 892 
 
 6.79347 
 
 112 
 
 942 
 
 6.84801 
 
 106 
 
 992 
 
 6.89972 
 
 IOI 
 
 843 
 
 6.73697 
 
 119 
 
 893 
 
 6-79459 
 
 112 
 
 943 
 
 6.84907 
 
 106 
 
 993 
 
 6.90073 
 
 IOI 
 
 844 
 
 6.73815 
 
 118 
 
 894 
 
 6.79571 
 
 112 
 
 944 
 
 6.85013 
 
 106 
 
 994 
 
 6.90174 
 
 IOI 
 
 845 
 
 6.73934 
 
 118 
 
 895 
 
 6.79682 
 
 112 
 
 945 
 
 6.85II8 
 
 106 
 
 995 
 
 6.90274 
 
 IOI 
 
 846 
 
 6.74052 
 
 118 
 
 896 
 
 6.79794 
 
 112 
 
 946 
 
 6.85224 
 
 106 
 
 
 6.90375 
 
 100 
 
 847 
 
 6.74170 
 
 118 
 
 897 
 
 6.79906 
 
 III 
 
 947 
 
 6.85330 
 
 106 
 
 907 
 
 6.90475 
 
 100 
 
 848 
 
 6.74288 
 
 118 
 
 898 
 
 6.80017 
 
 III 
 
 948 
 
 6.85435 
 
 105 
 
 998 
 
 6.90575 
 
 IOO 
 
 849 
 
 6.74406 
 
 118 
 
 to 
 
 6.80128 
 
 III 
 
 949 
 
 6.85541 
 
 105 
 
 999 
 
 6.90675 
 
 IOO 
 
 850 
 
 6.74524 
 
 118 
 
 900 
 
 6.80239 
 
 III 
 
 950 
 
 6.85646 
 
 105 
 
 1000 
 
 6.90776 
 
 IOO 
 
 e* 
 
 X 
 
 ~ x 
 
 e x 
 
 X 
 
 e~ x 
 
 e x 
 
 X 
 
 e~ x 
 
 e x 
 
 X 
 
 e~ x 
 
 SMITHSONIAN TABLES 
 
 268 
 
Natural Logarithms. 
 
 u 
 
 Log e u 
 
 u 
 
 Log,u 
 
 u 
 
 LOfleU 
 
 u 
 
 lOOeU 
 
 u 
 
 LOOeU 
 
 IOOO 
 
 6.90776 
 
 1361 
 
 7.21598 
 
 1721 
 
 7.45066 
 
 2III 
 
 7.65492 
 
 2503 
 
 7.82525 
 
 1009 
 
 6.91672 
 
 1367 
 
 7-22037 
 
 1723 
 
 7.45182 
 
 2113 
 
 7.65586 
 
 2521 
 
 7.83241 
 
 1013 
 
 6.92067 
 
 1373 
 
 7.22475 
 
 1733 
 
 7.45761 
 
 .2129 
 
 7.66341 
 
 2531 
 
 7.83637 
 
 1019 
 
 6.92658 
 
 1381 
 
 7.23056 
 
 1741 
 
 7.46221 
 
 21311 
 
 7.66435 
 
 2539 
 
 7.83953 
 
 102 1 
 
 6.92854 
 
 1399 
 
 7.24351 
 
 1747 
 
 7.46566 
 
 2137 
 
 7.66716 
 
 2543 
 
 7.84110 
 
 1031 
 
 6.93828 
 
 1409 
 
 7.25004 
 
 1753 
 
 7.46908 
 
 2141 
 
 7.66903 
 
 2549 
 
 7.84346 
 
 1033 
 
 6.94022 
 
 1423 
 
 7.26052 
 
 1759 
 
 7.47250 
 
 2143 
 
 7.66996 
 
 2551 
 
 7.84424 
 
 1039 
 
 6.9460*1 
 
 1427 
 
 7.26333 
 
 1777 
 
 7.48268 
 
 2153 
 
 7.67462 
 
 2557 
 
 7.84659 
 
 IO49 
 
 6-95559 
 
 1429 
 
 7.26473 
 
 1783 
 
 7.48605 
 
 2161 
 
 7.67833 
 
 2579 
 
 7.85516 
 
 1051 
 
 6.95750 
 
 1433 
 
 7.26753 
 
 1787 
 
 7.48829 
 
 2179 
 
 7.68662 
 
 2591 
 
 7.85980 
 
 1061 
 
 6.96697 
 
 1439 
 
 7.27170 
 
 1789 
 
 7.48941 
 
 2203 
 
 7.69758 
 
 2593 
 
 7.86057 
 
 1063 
 
 6.96885 
 
 1447 
 
 7.27725 
 
 1801 
 
 7.49610 
 
 2207 
 
 7.69939 
 
 2609 
 
 7.86672 
 
 1069 
 
 6.97448 
 
 I45H 
 
 7.28001 
 
 1811 
 
 7.50163 
 
 2213 
 
 7.702110 
 
 2617 
 
 7.86978 
 
 1087 
 
 6.99118 
 
 1453 
 
 7.28139 
 
 1823 
 
 7.50824 
 
 2221 
 
 7.70571 
 
 2621 
 
 7.8713-1 
 
 1091 
 
 6.99485 
 
 1459 
 
 7.28551 
 
 1831 
 
 7.51262 
 
 2237 
 
 7.71289 
 
 2633 
 
 7.87588 
 
 1093 
 
 6.99568 
 
 1471 
 
 7.29370 
 
 1847 
 
 7.52132 
 
 2239 
 
 7.71378 
 
 2647 
 
 7.88118 
 
 1097 
 
 7.00033 
 
 1481 
 
 7.30047 
 
 1861 
 
 7.5-2887 
 
 2243 
 
 7.71-557 
 
 2657 
 
 7.88495 
 
 1103 
 
 7.00579 
 
 1483 
 
 7.30182 
 
 1867 
 
 7.53209 
 
 2251 
 
 7.71913 
 
 2659 
 
 7.88571 
 
 1109 
 
 7.01121 
 
 1487 
 
 7.30452 
 
 1871 
 
 7.53423 
 
 2267 
 
 7.72621 
 
 2663 
 
 7.887.21 
 
 1117 
 
 7.01840 
 
 1489 
 
 7.30586 
 
 1873 
 
 7.53530 
 
 2269 
 
 7.72709 
 
 2671 
 
 7.89021 
 
 1123 
 
 7-02376 
 
 1493 
 
 7.30854 
 
 1877 
 
 7.53743 
 
 2273 
 
 7.72886 
 
 2677 
 
 7.89245 
 
 1129 
 
 7.02909 
 
 1499 
 
 7.31255 
 
 1879 
 
 7.53849 
 
 228l 
 
 7.73237 
 
 2683 
 
 7.89469 
 
 1151 
 
 7.04839 
 
 I5H 
 
 7.32053 
 
 1889 
 
 7.54380 
 
 (2287 
 
 7.73500 
 
 2687 
 
 7.89618 
 
 H53 
 
 7.05012 
 
 1523 
 
 7.32844 
 
 1901 
 
 7.551014 
 
 2293 
 
 7.73762 
 
 2689 
 
 7.89692 
 
 1163 
 
 7.05876 
 
 1531 
 
 7.33368 
 
 1907 
 
 7.55329 
 
 2297 
 
 7.73936 
 
 2693 
 
 7.89841 
 
 1171 
 
 7.06561 
 
 1543 
 
 7.34148 
 
 1913 
 
 7.55643 
 
 2309 
 
 7.74457 
 
 2699 
 
 7.90064 
 
 1181 
 
 7.0741-2 
 
 1649 
 
 7.34536 
 
 I93i 
 
 7.56579 
 
 2311 
 
 7.74544 
 
 2707 
 
 7.90360 
 
 1187 
 
 7.07918 
 
 1553 
 
 7.34794 
 
 1933 
 
 7.56683 
 
 2333 
 
 7.75491 
 
 2711 
 
 7.90507 
 
 H93 
 
 7.08423 
 
 T559 
 
 7.35180 
 
 1949 
 
 7.57507 
 
 2339 
 
 7.75748 
 
 2713 
 
 7.90581 
 
 I2OI 
 
 7.09091 
 
 1567 
 
 7.35692 
 
 1951 
 
 7.57610 
 
 2341 
 
 7.75833 
 
 2719 
 
 7.90802 
 
 1213 
 
 7.10085 
 
 1571 
 
 7-35947 
 
 1973 
 
 7.58731 
 
 2347 
 
 7.76089 
 
 2729 
 
 7.91^169 
 
 1217 
 
 7.10414 
 
 1579 
 
 7.36455 
 
 1979 
 
 7.59035 
 
 2351 
 
 7.76260 
 
 2731 
 
 7.91242 
 
 1223 
 
 7.10906 
 
 1583 
 
 7.36708 
 
 1987 
 
 7.59438 
 
 2357 
 
 7.76514 
 
 2741 
 
 7.91608 
 
 I22p 
 
 7.11396 
 
 1597 
 
 7.37588 
 
 1993 
 
 7.59740 
 
 2371 
 
 7.77107 
 
 2749 
 
 7.91899 
 
 1231 
 
 7.II558 
 
 1601 
 
 7.37838 
 
 1997 
 
 7.59940 
 
 2377 
 
 7.77359 
 
 2753 
 
 7.92045 
 
 1237 
 
 7.12044 
 
 1607 
 
 7.38212 
 
 1909 
 
 7.60040 
 
 2381 
 
 7.77528 
 
 2767 
 
 7.92552 
 
 1249 
 
 7.13010 
 
 1609 
 
 7.38337 
 
 2003 
 
 7.60240 
 
 2383 
 
 7.77612 
 
 (2777 
 
 7.92913 
 
 1259 
 
 7.13807 
 
 1613 
 
 7.38585 
 
 2OII 
 
 7.60639 
 
 2389 
 
 7.77863 
 
 2789 
 
 7-93344 
 
 1277 
 
 7.15227 
 
 1619 
 
 7.38956 
 
 2017 
 
 7.60937 
 
 * ^*Jf 
 
 2393 
 
 7.78030 
 
 2791 
 
 7.93416 
 
 1279 
 
 7.15383 
 
 1621 
 
 7.39080 
 
 2027 
 
 7.61431 
 
 2399 
 
 7.78281 
 
 2797 
 
 7.93630 
 
 1283 
 
 7-15696 
 
 1627 
 
 7-39449 
 
 2029 
 
 7.61530 
 
 2411 
 
 7.78780 
 
 2801 
 
 7-93773 
 
 1289 
 
 7.16162 
 
 1637 
 
 7.40062 
 
 2039 
 
 7.62021 
 
 2417 
 
 7.79028 
 
 2803 
 
 7.93845 
 
 1291 
 
 7.16317 
 
 1657 
 
 7.41276 
 
 2053 
 
 7.62706 
 
 2423 
 
 7.79276 
 
 2819 
 
 7.94414 
 
 1297 
 
 7.16781 
 
 1663 
 
 7.41638 
 
 2063 
 
 7.63192 
 
 2437 
 
 7.79852 
 
 2833 
 
 7.94909 
 
 1301 
 
 7.17089 
 
 1667 
 
 7.41878 
 
 2069 
 
 7.63482 
 
 2441 
 
 7.80016 
 
 2837 
 
 7.95050 
 
 1303 
 
 7.17242 
 
 1669 
 
 7.41998 
 
 2081 
 
 7.64060 
 
 2447 
 
 7.80262 
 
 2843 
 
 7.95262 
 
 1307 
 
 7-17549 
 
 1693 
 
 7.43426 
 
 2083 
 
 7.64156 
 
 2459 
 
 7.80751 
 
 2851 
 
 7-95543 
 
 1319 
 
 7- '18463 
 
 1697 
 
 7.43662 
 
 2087 
 
 7.64348 
 
 . > 
 
 2467 
 
 7.81076 
 
 2857 
 
 7-95753 
 
 1321 
 
 7.18614 
 
 1699 
 
 7.43780 
 
 2089 
 
 7.64444 
 
 <2473 
 
 7.81319 
 
 2861 
 
 7.95893 
 
 1327 
 
 7.19068 
 
 1709 
 
 7-44'366 
 
 2099 
 
 7.64922 
 
 2477 
 
 7.81480 
 
 2879 
 
 7.96520 
 
 e* 
 
 X 
 
 e x 
 
 x 
 
 e x 
 
 X 
 
 e x 
 
 X 
 
 e x 
 
 X 
 
 SMITHSONIAN TABLES 
 
 269 
 
Natural Logarithms. 
 
 u 
 
 LofleU 
 
 u 
 
 LOQ.U 
 
 u 
 
 LoOeU 
 
 U 
 
 Log,u 
 
 u 
 
 LOQeU 
 
 2887 
 
 7.96797 
 
 3323 
 
 8.10862 
 
 3709 
 
 8.21852 
 
 4129 
 
 8.32579 
 
 4561 
 
 8.42530 
 
 2897 
 
 7.97M3 
 
 3329 
 
 8. i 1043 
 
 3719 
 
 8.22I2I 
 
 4133 
 
 8.32676 
 
 4567 
 
 8.42661 
 
 2903 
 
 7-97350 
 
 3331 
 
 8. 11-103 
 
 3727 
 
 8.22336 
 
 4139 
 
 8.32821 
 
 4583 
 
 8.430II 
 
 2909 
 
 7.97556 
 
 3343 
 
 8.11462 
 
 3733 
 
 8.22497 
 
 41-53 
 
 8.33159 
 
 4591 
 
 8.43185 
 
 2917 
 
 7.97831 
 
 3347 
 
 8.11582 
 
 3739 
 
 8.22657 
 
 4157 
 
 8.33255 
 
 4597 
 
 8.43310 
 
 2927 
 
 7.98173 
 
 3359 
 
 8.11940 
 
 3761 
 
 8.23244 
 
 4159 
 
 8.33303 
 
 4603 
 
 8.43446 
 
 2959 
 
 7.98582 
 
 336i 
 
 8.11099 
 
 3767 
 
 8.23403 
 
 4177 
 
 8.33735 
 
 4621 
 
 8.43837 
 
 2953 
 
 7-99058 
 
 3371 
 
 8.12296 
 
 3769 
 
 8.23456 
 
 4201 
 
 8.34308 
 
 4637 
 
 8.44182 
 
 2957 
 
 7.99193 
 
 3373 
 
 8.12356 
 
 3779 
 
 8.23721 
 
 4211 
 
 8.34546 
 
 4639 
 
 8.44225 
 
 2963 
 
 7.99396 
 
 3389 
 
 8.12829 
 
 3793 
 
 8.24091 
 
 4217 
 
 8.34688 
 
 4043 
 
 8.44312 
 
 2969 
 
 7.99598 
 
 3391 
 
 8.12888 
 
 3797 
 
 8.24197 
 
 4219 
 
 8.34735 
 
 4649 
 
 8.44441 
 
 2971 
 
 7.99665 
 
 3407 
 
 8. 13359 
 
 3803 
 
 8.24355 
 
 4229 
 
 8.34972 
 
 4651 
 
 8.44484 
 
 2999 
 
 8.00603 
 
 3413 
 
 8.13535 
 
 3821 
 
 8.24827 
 
 4231 
 
 8.35019 
 
 4657 
 
 6.44613 
 
 3001 
 
 8.00670 
 
 3433 
 
 8.14119 
 
 3823 
 
 8.24879 
 
 4241 
 
 8.35255 
 
 4663 
 
 8-4474T 
 
 301 1 
 
 8.01003 
 
 3449 
 
 8.14584 
 
 3833 
 
 8.25II4O 
 
 4243 
 
 8.35303 
 
 4673 
 
 8.44956 
 
 3019 
 
 8.01268 
 
 3457 
 
 8.14816 
 
 3847 
 
 8.25505 
 
 4253 
 
 8.35538 
 
 4679 
 
 8.45084 
 
 3023 
 
 8.01400 
 
 346i 
 
 8.14931 
 
 3851 
 
 8.25609 
 
 4259 
 
 8.35679 
 
 4691 
 
 8-45340 
 
 3037 
 
 8.01863 
 
 3463 
 
 8.14989 
 
 3^53 
 
 8.25661 
 
 4261 
 
 8.35726 
 
 4703 
 
 8.45596 
 
 3041 
 
 8.01994 
 
 3467 
 
 8.15104 
 
 386 3 
 
 8.25920 
 
 4271 
 
 8.35960 
 
 4721 
 
 8.4597* 
 
 3049 
 
 8.02257 
 
 3469 
 
 8.15162 
 
 3777 
 
 8.26282 
 
 4273 
 
 8.36007 
 
 4723 
 
 8.46020 
 
 3061 
 
 8.O265O 
 
 3491 
 
 8.15794 
 
 3881 
 
 8.26385 
 
 4283 
 
 8.36241 
 
 4729 
 
 8.46147 
 
 3067 
 
 8.02846 
 
 3499 
 
 8.16023 
 
 3889 
 
 8.26591 
 
 4289 
 
 8.36381 
 
 4733 
 
 8.46231 
 
 3079 
 
 8.03236 
 
 35ii 
 
 8.16366 
 
 3907 
 
 8.27053 
 
 4297 
 
 8.36567 
 
 4751 
 
 8.466II 
 
 3083 
 
 8.03366 
 
 3517 
 
 8. 16536 
 
 39ii 
 
 8.27155 
 
 4327 
 
 8.37263 
 
 4759 
 
 8.46779 
 
 3089 
 
 8.03560 
 
 3527 
 
 8.168.20 
 
 3917 
 
 8.27308 
 
 4337 
 
 8.37494 
 
 4783 
 
 8.47282 
 
 3109 
 
 8.04206 
 
 3529 
 
 8.16877 
 
 '3919 
 
 8.27359 
 
 4339 
 
 8.37540 
 
 4787 
 
 8.47366 
 
 3H9 
 
 8.04527 
 
 3533 
 
 8.16990 
 
 3923 
 
 8.27461 
 
 4349 
 
 8-37770 
 
 4789 
 
 8.47408 
 
 3121 
 
 8.04591 
 
 3539 
 
 8.17160 
 
 3929 
 
 8.27614 
 
 4357 
 
 8.37954 
 
 4793 
 
 8.47491 
 
 3137 
 
 8.05IO2 
 
 3541 
 
 8.17216 
 
 3931 
 
 8.27665 
 
 4363 
 
 8.38092 
 
 4799 
 
 8.476l6 
 
 3163 
 
 8.05928 
 
 3547 
 
 8.17386 
 
 3943 
 
 8.27970 
 
 4373 
 
 8.38320 
 
 4801 
 
 8.47653 
 
 3167 
 
 8.06054 
 
 3557 
 
 8.117667 
 
 3947 
 
 8.280?I 
 
 4391 
 
 8.38731 
 
 4813 
 
 8.47908 
 
 3169 
 
 8.06II7 
 
 3559 
 
 8. 17723 
 
 3967 
 
 8.28577 
 
 4397 
 
 8.38868 
 
 4817 
 
 8.47991 
 
 3181 
 
 8.00495 
 
 3571 
 
 8.18060 
 
 3989 
 
 8.29130 
 
 4409 
 
 8.39140 
 
 4831 
 
 8.48281 
 
 3187 
 
 8.06684 
 
 358i 
 
 8.18340 
 
 4001 
 
 8.29430 
 
 4421 
 
 8.39412 
 
 4861 
 
 8.48900 
 
 3191 
 
 8.06809 
 
 3583 
 
 8. 18396 
 
 4003 
 
 8.29480 
 
 4423 
 
 8.39457 
 
 4871 
 
 8.49105 
 
 3203 
 
 8.07I&4 
 
 3593 
 
 8.18674 
 
 4007 
 
 8.29580 
 
 4441 
 
 8.39863 
 
 4877 
 
 8.40229 
 
 3209 
 
 8.07371 
 
 3607 
 
 8.19063 
 
 4013 
 
 8.29729 
 
 4447 
 
 8.39998 
 
 4889 
 
 8.49474 
 
 3217 
 
 8.O762O 
 
 3613 
 
 8. 19229 
 
 4019 
 
 8.29879 
 
 4451 
 
 8.40088 
 
 4903 
 
 8.49760 
 
 3221 
 
 8.07745 
 
 3617 
 
 8. 19340 
 
 4021 
 
 8.29929 
 
 4457 
 
 8.40223 
 
 4909 
 
 8.49883 
 
 3229 
 
 8.07993 
 
 3023 
 
 8.19506 
 
 4027 
 
 8.30078 
 
 4463 
 
 8.40358 
 
 4919 
 
 8.50086 
 
 3251 
 
 8.08672 
 
 3631 
 
 8. 19726 
 
 4049 
 
 8.30623 
 
 448i 
 
 8.40760 
 
 4931 
 
 8.50330 
 
 3253 
 
 8.08733 
 
 3637 
 
 8.19891 
 
 4051 
 
 8.30672 
 
 4483 
 
 8.40805 
 
 4933 
 
 8.50370 
 
 3257 
 
 8.08856 
 
 3643 
 
 8.20056 
 
 4057 
 
 8.30820 
 
 4493 
 
 8.41028 
 
 4937 
 
 8.50451 
 
 3259 
 
 8.08918 
 
 3659 
 
 8.20495 
 
 4073 
 
 8.3I0I4 
 
 4507 
 
 8.41339 
 
 4943 
 
 8.50573 
 
 3271 
 
 8.09285 
 
 3671 
 
 8.20822 
 
 4079 
 
 8.3I36I 
 
 4513 
 
 8.41472 
 
 4951 
 
 8.50734 
 
 3^99 
 
 8. 10137 
 
 3673 
 
 8.20876 
 
 4091 
 
 8.31654 
 
 4517 
 
 8.41560 
 
 4957 
 
 8.50856 
 
 3301 
 
 8.10198 
 
 3677 
 
 8.20985 
 
 4093 
 
 8.31703 
 
 4519 
 
 8.41605 
 
 4967 
 
 8.51057 
 
 3307 
 
 8.10380 
 
 3691 
 
 8.21365 
 
 4099 
 
 8.31850 
 
 4523 
 
 8.41693 
 
 4969 
 
 8.51097 
 
 3313 
 
 8. 10561 
 
 3097 
 
 8.21528 
 
 4111 
 
 8.32142 
 
 4547 
 
 8.42222 
 
 4973 
 
 8.51178 
 
 3319 
 
 8.10742 
 
 3701 
 
 8.21636 
 
 4127 
 
 8.3253'I 
 
 4549 
 
 8.42266 
 
 4987 
 
 6.51459 
 
 e* 
 
 X 
 
 x 
 
 X 
 
 e>< 
 
 X 
 
 e x 
 
 X 
 
 e x 
 
 X 
 
 SMITHSONIAN TABLES 
 
 270 
 
Natural Logarithms. 
 
 u 
 
 LOQell 
 
 u 
 
 LoOeU 
 
 u 
 
 LOOeU 
 
 u 
 
 Logu 
 
 u 
 
 LOfleU 
 
 4993 
 
 8.51579 
 
 5437 
 
 8.60098 
 
 5849 
 
 8.67403 
 
 6287 
 
 8.746241 
 
 6733 
 
 "8.81478 
 
 4999 
 
 8.51099 
 
 5441 
 
 8.60172 
 
 5851 
 
 8.67437 
 
 6299 
 
 8.74815 
 
 6737 
 
 8.81537 
 
 5003 
 
 8.51779 
 
 5443 
 
 8.60209 
 
 5857 
 
 8.67539 
 
 6301 
 
 8.74846 
 
 6761 
 
 8.31893 
 
 5009 
 
 8. 51899 
 
 5449 
 
 8.60319 
 
 5861 
 
 8.67608 
 
 6311 
 
 8.75005 
 
 , 6763 
 
 8.81922 
 
 SOU 
 
 8.51939 
 
 5471 
 
 8.60722 
 
 5867 
 
 8.67710 
 
 6317 
 
 8.75100 
 
 6779 
 
 8.82158 
 
 '5021 
 
 8.52138 
 
 5477 
 
 8.60831 
 
 5869 
 
 8.67744 
 
 6323 
 
 8.75195 
 
 6781 
 
 8.82188 
 
 5023. 
 
 8.52178 
 
 5479 
 
 8.60868 
 
 5879 
 
 8.67914 
 
 6329 
 
 8.75290 
 
 6791 
 
 8.82335 
 
 5039 
 
 8.52496 
 
 5483 
 
 8.60941 
 
 588)1 
 
 8.67948 
 
 6337 
 
 8.75416 
 
 6793 
 
 8.82365 
 
 5051 
 
 8.52734 
 
 5501 
 
 8.61269, 
 
 5897 
 
 8.68220 
 
 6343 
 
 8.755ri 
 
 6803 
 
 8.82512 
 
 5059 
 
 8.52892 
 
 5503 
 
 8.6I3O5 
 
 5903 
 
 8.68322 
 
 6353 
 
 8.75668 
 
 6823 
 
 8.82805 
 
 5077 
 
 8.53248 
 
 5507 
 
 8.61378 
 
 5923 
 
 8.68660 
 
 6359 
 
 8.75763 
 
 6827 
 
 8.82864 
 
 5081 
 
 8.53326 
 
 5519 
 
 8.61595 
 
 5927 
 
 8.68727 
 
 6361 
 
 8.75794 
 
 6829 
 
 8.82893 
 
 5087 
 
 8.53444 
 
 5521 
 
 8.6l63I 
 
 5939 
 
 8.68930 
 
 6367 
 
 8.75888 
 
 6833 
 
 8.82952 
 
 5099 
 
 8.53680 
 
 5527 
 
 8.61740 
 
 '5953 
 
 8.69165 
 
 6373 
 
 8.75983 
 
 6841 
 
 8.83069 
 
 5101 
 
 8.53719 
 
 5531 
 
 8. 61812 
 
 5931 
 
 8.69634 
 
 6379 
 
 8.76077 
 
 6857 
 
 8.83303 
 
 5107 
 
 8.53837 
 
 5557 
 
 8.62281 
 
 5987 
 
 8.69735 
 
 6389 
 
 8.76233 
 
 6863 
 
 8.83390 
 
 5H3 
 
 8.53954 
 
 5563 
 
 8.62389 
 
 6007 
 
 8.70068 
 
 6397 
 
 8.76358 
 
 6869 
 
 8.83477 
 
 5H9 
 
 8.54071 
 
 5569 
 
 8.62497 
 
 6011 
 
 8.70135 
 
 6421 
 
 8.76733 
 
 6871 
 
 8.83506 
 
 5147 
 
 8.54617 
 
 5573 
 
 8.62569 
 
 6029 
 
 8.70434 
 
 6427 
 
 8.76826 
 
 6883 
 
 8.83681 
 
 5153 
 
 8.54733 
 
 558i 
 
 8.62/712 
 
 6037 
 
 8.70566 
 
 6449 
 
 8.77168 
 
 6889 
 
 8.83768 
 
 5167 
 
 8.55005 
 
 5591 
 
 8.62891 
 
 6043 
 
 8.70666 
 
 6451 
 
 8.77199 
 
 6907 
 
 8.84029 
 
 5171 
 
 8.55082 
 
 5623 
 
 8.63462 
 
 6047 
 
 8.70732 
 
 6469 
 
 8.77478 
 
 6911 
 
 8.84087 
 
 5179 
 
 8.55237 
 
 5639 
 
 8.63746 
 
 6053 
 
 8.70831 
 
 6473 
 
 8.77539 
 
 6917 
 
 8.84174 
 
 5189 
 
 8.55430 
 
 5641 
 
 8.63782 
 
 6067 
 
 8.71062 
 
 6481 
 
 8.77663 
 
 6947 
 
 8.84607 
 
 5197 
 
 8.55584 
 
 5647 
 
 8.63888 
 
 6073 
 
 8.71161 
 
 6491 
 
 8.77817 
 
 6949 
 
 8.8463S 
 
 5209 
 
 8.55814 
 
 5651 
 
 8.63959 
 
 6079 
 
 8.71260 
 
 6521 
 
 8.78278 
 
 6959 
 
 8.84779 
 
 5227 
 
 8.56159 
 
 5653 
 
 8.63994 
 
 6089 
 
 8.71424 
 
 6529 
 
 8.78401 
 
 6961 
 
 8.84808 
 
 5231 
 
 8.56236 
 
 5657 
 
 8.64065 
 
 6091 
 
 8.71457 
 
 6547 
 
 8.78676 
 
 6967 
 
 8.84894 
 
 S'23'3 
 
 8.56274 
 
 5659 
 
 8.64100 
 
 6101 
 
 8.71621 
 
 >- 
 
 6551 
 
 8.78737 
 
 6971 
 
 8.84951 
 
 5237 
 
 8.56350 
 
 5669 
 
 8.64277 
 
 6113 
 
 8.71817 
 
 6553 
 
 8.78768 
 
 6977 
 
 8.85037 
 
 5261 
 5273 
 
 8.56808 
 8.57035 
 
 5683 
 5689 
 
 8.64523 
 8.64629 
 
 6121 
 6131 
 
 8.71948 
 
 8.72111 
 
 6563 
 6569 
 
 8.78920 
 8.79012 
 
 6983 
 
 6991 
 
 8.85123 
 8.85238 
 
 5279 
 
 8.57149 
 
 5693 
 
 8.64699 
 
 6133 
 
 8.72144 
 
 6571 
 
 8.79042 
 
 6997 
 
 8.85324 
 
 5281 
 
 8.57187 
 
 5701 
 
 8.64840 
 
 6i43 
 
 8.72307 
 
 6577 
 
 8.79133 
 
 7001 
 
 8.85381 
 
 5297 
 
 8.57490 
 
 57i i 
 
 8.65015 
 
 6151 
 
 8.72437 
 
 6581 
 
 8.79194 
 
 7013 
 
 8.85552 
 
 5303 
 
 8.57603 
 
 5717 
 
 8.65120 
 
 6163 
 
 8.72632 
 
 6599 
 
 8.79467 
 
 7019 
 
 8.85638 
 
 5309 
 
 8.57716 
 
 5737 
 
 8.65469 
 
 6173 
 
 8.72794 
 
 6607 
 
 8.79588 
 
 7027 
 
 8.85752 
 
 5323 
 
 8.57979 
 
 5741 
 
 8.65539 
 
 6i97 
 
 8.73182 
 
 6619 
 
 8.79770 
 
 7039 
 
 8.85922 
 
 5333 
 
 8.58167 
 
 5743 
 
 8.65574 
 
 6199 
 
 8.73214 
 
 6637 
 
 8.80042 
 
 7043 
 
 8.85979 
 
 5347 
 
 8.58429 
 
 5749 
 
 8.65678 
 
 6203 
 
 8.73279 
 
 6653 
 
 8.80282 
 
 7057 
 
 8.86178 
 
 5351 
 
 8.58504 
 
 5779 
 
 8.66199 
 
 6211 
 
 8.73408 
 
 6659 
 
 8.80372 
 
 7069 
 
 8.86347 
 
 538i 
 
 8.59063 
 
 5783 
 
 8.66268 
 
 6217 
 
 8.73504 
 
 6661 
 
 8.80402 
 
 7079 
 
 8.86489 
 
 5387 
 
 8.59174 
 
 5791 
 
 8.66406 
 
 6221 
 
 8.73569 
 
 6673 
 
 8.80582 
 
 7103 
 
 8.86827 
 
 5393 
 
 8.59286 
 
 5801 
 
 8.66579 
 
 6229 
 
 8.73697 
 
 6679 
 
 8.80672 
 
 7109 
 
 8.86912 
 
 5399 
 
 8-59397 
 
 5807 
 
 8.66682 
 
 6247 
 
 8.73986 
 
 6689 
 
 8.80822 
 
 7121 
 
 8.87080 
 
 5407 
 
 8.59545 
 
 58i3 
 
 8.66785 
 
 6257 
 
 8.74146 
 
 6691 
 
 8.80852 
 
 7127 
 
 8.87165 
 
 5413 
 
 8.59656 
 
 5821 
 
 8.66923 
 
 6263 
 
 8.74241 
 
 6701 
 
 8.81001 
 
 7129 
 
 8.87193 
 
 5417 
 
 8.59730 
 
 5827 
 
 8.67026 
 
 6269 
 
 8.74337 
 
 6703 
 
 8.81031 
 
 7151 
 
 8.87501 
 
 5419 
 
 8.50767 
 
 5839 
 
 8.67231 
 
 6271 
 
 8.74369 
 
 6709 
 
 8.81121 
 
 7159 
 
 8.87613 
 
 5421 
 
 8.59988 
 
 5843 
 
 8.67300 
 
 6277 
 
 8.74465 
 
 6719 
 
 8.81269 
 
 7177 
 
 8.87864 
 
 e* 
 
 X 
 
 e x 
 
 X 
 
 e* 
 
 X 
 
 e x 
 
 X 
 
 6* 
 
 X 
 
 SMITHSONIAN TABLES 
 
 271 
 
Natural Logarithms. 
 
 u 
 
 LofleU 
 
 u 
 
 LOdeU 
 
 u 
 
 LOOe" 
 
 u Loo e u 
 
 u 
 
 Udell 
 
 7187 
 
 8.88003 
 
 7621 
 
 8.93866 
 
 8093 
 
 8.99875 
 
 8573 
 
 9.05637 
 
 9001 
 
 9.10509 
 
 7193 
 
 8.88086 
 
 7639 
 
 8.94102 
 
 8101 
 
 8.99974 
 
 8581 
 
 9.05731 
 
 9007 
 
 9.10576 
 
 7207 
 
 8.88281 
 
 7643 
 
 8.94155 
 
 8111 
 
 9.00008 
 
 8597 
 
 9.05917 
 
 9011 
 
 9.I062O 
 
 7211 
 
 8.88336 
 
 7649 
 
 8.94233 
 
 8117 
 
 9.OOI72 
 
 8599 
 
 9.05940 
 
 0013 
 
 9. 10642 
 
 7213 
 
 8.88364 
 
 7669 
 
 8.94494 
 
 8123 
 
 9.00245 
 
 8609 
 
 9.06056 
 
 9029 
 
 9.IO820 
 
 7219 
 
 8.88447 
 
 7673 
 
 8.94546 
 
 8i47 
 
 9.00541 
 
 8623 
 
 9.06219 
 
 0041 
 
 9.10953 
 
 7229 
 
 8.88586 
 
 7681 
 
 8.946511 
 
 8161 
 
 9.00712 
 
 8627 
 
 9.06265 
 
 9043 
 
 9.10975 
 
 7237 
 
 8.88696 
 
 7687 
 
 8.947^9 
 
 8167 
 
 9.00786 
 
 8629 9.06288 
 
 9049 
 
 9. IIO4I 
 
 7243 
 
 8.88779 
 
 7691 
 
 8.94781 
 
 8171 
 
 9.00835 
 
 8641 
 
 9. 06427 
 
 9059 
 
 9.IH5I 
 
 7247 
 
 8.88834 
 
 7699 
 
 8.94885 
 
 8179 
 
 9-00933 
 
 8647 
 
 9.06497 
 
 9067 
 
 9.11240 
 
 7253 
 
 8.88917 
 
 7703 
 
 8.94937 
 
 8191 
 
 9.01079 
 
 8663 
 
 9.06682 
 
 9091 
 
 9.11504 
 
 7283 
 
 8.89330 
 
 7717 
 
 8.95118 
 
 8209 
 
 9.01299 
 
 8669 
 
 9-06731 
 
 9103 
 
 9.11636 
 
 7297 
 
 8.89522 
 
 7723 
 
 8.95196 
 
 8219 
 
 9.OI42O 
 
 8677 
 
 9-06843 
 
 9109 
 
 9.11702 
 
 7307 
 
 8.89659 
 
 7727 
 
 8.95248 
 
 8221 
 
 9.01445 
 
 8681 
 
 9.06889 
 
 9127 
 
 9.11899 
 
 7309 
 
 8.89686 
 
 7741 
 
 8.95429 
 
 8231 
 
 9.01566 
 
 8689 
 
 9.06981 
 
 9133 
 
 9.11965 
 
 7321 
 
 8.89850 
 
 7753 
 
 8.95584 
 
 8233 
 
 9.01591 
 
 8693 
 
 9.07027 
 
 9137 
 
 9.12009 
 
 7331 
 
 8.89987 
 
 7757 
 
 8.95635 
 
 8237 
 
 9.0II639 
 
 8699 
 
 9.07096 
 
 9151 
 
 9.12162 
 
 7333 
 
 8.9OOI4 
 
 7759 
 
 8.95661 
 
 8243 
 
 9.0I7I2 
 
 8707 
 
 9.07188 
 
 9157 
 
 9.12227 
 
 7349 
 
 8.00232 
 
 7789 
 
 8.96047 
 
 8263 
 
 9.01954 
 
 8713 
 
 9.07257 
 
 9161 
 
 9.12271 
 
 7351 
 
 8.90259 
 
 7793 
 
 8.96098 
 
 8269 
 
 9.02O27 
 
 8719 
 
 9.07326 
 
 9173 
 
 9.12402 
 
 7369 
 
 8.90504 
 
 78i7 
 
 8.96406 
 
 8273 
 
 9.02075 
 
 8731 
 
 9.07464 
 
 9181 
 
 9. 12489 
 
 7393 
 
 8.90829 
 
 7823 
 
 8.96482 
 
 8287 
 
 Q.02244 
 
 8737 
 
 9.07532 
 
 9187 
 
 9.12554 
 
 7411 
 
 8.9IO72 
 
 7829 
 
 8.96559 
 
 8291 
 
 9.02293 
 
 8741 
 
 9.07578 
 
 9199 
 
 9.12685 
 
 7417 
 
 8.9H53 
 
 7841 
 
 8.96712 
 
 8293 
 
 9.02317 
 
 8747 
 
 9.07647 
 
 9203 
 
 9.12728 
 
 7433 
 
 8.91368 
 
 7853 
 
 8.96765 
 
 8297 
 
 9-02365 
 
 8753 
 
 9.07715 
 
 9209 
 
 9.12794 
 
 7451 
 
 8.9l6lO 
 
 7867 
 
 8.97043 
 
 8311 
 
 9.02634 
 
 8761 
 
 9.07807 
 
 9221 
 
 9.12924 
 
 7457 
 
 8.9II69I 
 
 7873 
 
 8.97119 
 
 8317 
 
 9.02606 
 
 8779 
 
 9.08012 
 
 9227 
 
 9.12989 
 
 7459 
 
 8.9I7I8 
 
 7877 
 
 8.97170 
 
 8329 
 
 9.02750 
 
 8783 
 
 9.08057 
 
 9239 
 
 9.13119 
 
 7477 
 
 8.91959 
 
 7879 
 
 8.97196 
 
 8353 
 
 9.03038 
 
 8803 
 
 9.08285 
 
 9241 
 
 9.1314'! 
 
 748i 
 
 8.92OI2 
 
 7883 
 
 8.97246 
 
 8363 
 
 9.03157 
 
 8807 
 
 9.08330 
 
 9257 
 
 9.13314 
 
 7487 
 
 8.92O92 
 
 7901 
 
 8.97474 
 
 8369 
 
 9.03'229 
 
 8819 
 
 9.08466 
 
 9277 
 
 9.13529 
 
 7489 
 
 8.92119 
 
 7907 
 
 8.97550 
 
 8377 
 
 9.03325 
 
 8821 
 
 9.08489 
 
 9281 
 
 9.13572 
 
 7499 
 
 8.92252 
 
 7919 
 
 8.97702 
 
 8387 
 
 9.03444 
 
 8831 
 
 9.08602 
 
 9283 
 
 9- 13594 
 
 7507 
 
 8.92359 
 
 7927 
 
 8.97803 
 
 8389 
 
 9.03468 
 
 8837 
 
 9.08670 
 
 9293 
 
 9.13702 
 
 7517 
 
 8.92492 
 
 7933 
 
 8.97879 
 
 8419 
 
 9.03825 
 
 8839 
 
 9.08693 
 
 9311 
 
 9.13895 
 
 7523 
 
 8.92572 
 
 7937 
 
 8.97929 
 
 8423 
 
 9.03872 
 
 8849 
 
 9.08806 
 
 9319 
 
 9.13981 
 
 7529 
 
 8.92652 
 
 7949 
 
 8.98080 
 
 8429 
 
 9-03943 
 
 8861 
 
 9.08941 
 
 9323 
 
 9.14024 
 
 7537 
 
 8.92758 
 
 7951 
 
 8.08105 
 
 8431 
 
 9.03967 
 
 8863 
 
 9.08064 
 
 9337 
 
 9.14174 
 
 7541 
 
 8.928II 
 
 7963 
 
 8.08256 
 
 8443 
 
 9.04109 
 
 8867 
 
 9.09009 
 
 9341 
 
 9.14217 
 
 7547 
 
 8.92891 
 
 7993 
 
 8.98632 
 
 8447 
 
 9.04157 
 
 8887 
 
 9.09234 
 
 9343 
 
 9-14238 
 
 7549 
 
 8.92917 
 
 8009 
 
 8.98832 
 
 8461 
 
 9.04322 
 
 8893 
 
 9.09302 
 
 9349 
 
 9- 14302 
 
 7559 
 
 8.93049 
 
 8011 
 
 8.98857 
 
 8467 
 
 9-04393 
 
 8923 
 
 9.09639 
 
 9371 
 
 9- U538 
 
 756i 
 
 8.93076 
 
 8017 
 
 8.98932 
 
 8501 
 
 9.04794 
 
 8929 
 
 9.09706 
 
 9377 
 
 9. 14602 
 
 7573 
 
 8.93234 
 
 8039 
 
 8.99206 
 
 8513 
 
 9-04935 
 
 8933 
 
 9.09751 
 
 9391 
 
 9.I475I 
 
 7577 
 
 8.93287 
 
 8053 
 
 8.99380 
 
 8521 
 
 9.05029 
 
 8941 
 
 9.09840 
 
 9397 
 
 9.14815 
 
 7583 
 
 8.93366 
 
 8059 
 
 8.99454 
 
 8527 
 
 9.05099 
 
 8951 
 
 9.09952 
 
 9403 
 
 9.14878 
 
 7589 
 
 8.93446 
 
 8069 
 
 8.99578 
 
 8537 
 
 9.05216 
 
 8963 
 
 9.10086 
 
 9413 
 
 9.14985 
 
 7591 
 
 8.93472 
 
 8081 
 
 8.99727 
 
 8539 
 
 9.05240 
 
 8969 
 
 9-IOI53 
 
 94-19 
 
 9.15048 
 
 7603 
 
 8.93630 
 
 8087 
 
 8.99801 
 
 8543 
 
 9.05287 
 
 8971 
 
 9-JOT75 
 
 9421 
 
 9.15070 
 
 7607 
 
 8.93682 
 
 8089 
 
 8.99826 
 
 8563 
 
 9.055-2U 
 
 8999 
 
 9.10487 
 
 9431 
 
 9.15176 
 
 e* 
 
 X 
 
 e x 
 
 X 
 
 e x 
 
 * 
 
 e* 
 
 X 
 
 e x 
 
 X 
 
 SMITHSONIAN TABLES 
 
 272 
 
Natural Logarithms. 
 
 u 
 
 Log e u 
 
 u 
 
 Log e U 
 
 U 
 
 Log,u 
 
 u 
 
 Logu 
 
 u 
 
 Loot-u 
 
 9433 
 
 9.I5I97 
 
 9551 
 
 9.16440 
 
 9719 
 
 9.18184 
 
 9833 
 
 9. 19350 
 
 9967 
 
 9.20703 
 
 9437 
 
 9- 15239 
 
 9587 
 
 9.l68l6 
 
 97-21 
 
 9. 18204 
 
 9839 
 
 9.19411 
 
 9973 
 
 9.20764 
 
 9439 
 
 9.15261 
 
 9601 
 
 9.16962 
 
 9733 
 
 9.18328 
 
 9851 
 
 9-19533 
 
 10000 
 
 9.21034 
 
 9461 
 
 9- 15493 
 
 9613 
 
 9.17087 
 
 9739 
 
 9-18389 
 
 9857 
 
 9.19594 
 
 100000 
 
 II.5I293 
 
 9463 
 
 9.I55I4 
 
 9619 
 
 9.I7I50 
 
 9743 
 
 9.18430 
 
 9859 
 
 9.19614 
 
 
 
 9467 
 
 9.15557 
 
 9623 
 
 9.I7I9I 
 
 9749 
 
 9- 18492 
 
 9871 
 
 9.19736 
 
 
 
 9473 
 
 9.15620 
 
 9629 
 
 9.17253 
 
 9767 
 
 9. 18676 
 
 9883 
 
 9.19857 
 
 
 
 9479 
 
 9.15683 
 
 9631 
 
 9.17274 
 
 9769 
 
 9.18697 
 
 9887 
 
 9.19898 
 
 
 
 9491 
 
 9.15810 
 
 9643 
 
 9-17399 
 
 978i 
 
 9. 18820 
 
 9901 
 
 9.20039 
 
 
 
 9497 
 
 9.15873 
 
 9649 
 
 9.I746I 
 
 9787 
 
 9.I888I 
 
 9907 
 
 9.20100 
 
 
 
 9511 
 
 9.16020 
 
 9661 
 
 9.17585 
 
 9791 
 
 9. 18922 
 
 9923 
 
 9.20261 
 
 
 
 9521 
 
 9.16126 
 
 9677 
 
 9. I775I 
 
 9803 
 
 9.19044 
 
 9929 
 
 9.20322 
 
 
 
 9533 
 
 9.16251 
 
 9679 
 
 9.17771 
 
 9811 
 
 9.19126 
 
 9931 
 
 9-20342 
 
 
 
 9539 
 
 9.^6314 
 
 9689 
 
 9. 17875 
 
 9817 
 
 9.I9I87 
 
 9941 
 
 9.20442 
 
 
 
 9547 
 
 9.16398 
 
 9697 
 
 9.17957 
 
 9829 
 
 9.19309 
 
 9949 
 
 9.20523 
 
 
 
 e x 
 
 X 
 
 e x 
 
 X 
 
 e* 
 
 X 
 
 e x 
 
 X 
 
 e x 
 
 X 
 
 Coefficients for Computing, 
 
 F^F.in-lV.* | % + 5- /J i (!L - i) yo ] . 
 
 n 
 
 n 2 
 
 Diff. 
 
 *-(-} 
 
 Diff. 
 
 n 
 
 n 2 
 
 Diff. 
 
 ("~-\\ 
 
 Diff. 
 
 
 6 
 
 
 \2\2 ) 
 
 
 
 6 
 
 
 12 \2 / 
 
 
 o.oo 
 
 +0.0000 
 
 
 o.oooo 
 
 
 0.25 
 
 +O.OIO4 
 
 
 0.0202 
 
 
 .01 
 
 .0000 
 
 O 
 
 .0008 
 
 
 .26 
 
 -OII3 
 
 9 
 
 .O2O9 
 
 7 
 
 .02 
 
 .0001 
 
 I 
 
 .0017 
 
 9 
 
 8 
 
 .27 
 
 .OI22 
 
 9 
 
 .O2I7 
 
 7 
 
 .03 
 
 .0002 
 
 I 
 
 .0025 
 
 8 
 
 .28 
 
 .0131 
 
 y 
 
 9 
 
 .O224 
 
 8 
 
 .04 
 
 .0003 
 
 I 
 
 .0033 
 
 9 
 
 .29 
 
 .0140 
 
 10 
 
 .0232 
 
 7 
 
 0.05 
 
 +O.OOO4 
 
 
 0.0042 
 
 
 0.30 
 
 +0.0150 
 
 
 0.0239 
 
 
 .06 
 
 .0006 
 
 2 
 
 .0050 
 
 
 .31 
 
 .Ol6o 
 
 10 
 
 .0246 
 
 
 .07 
 
 .0008 
 
 2 
 
 .0058 
 
 
 .32 
 
 .0171 
 
 1 1 
 
 .0253 
 
 7 
 
 .08 
 
 .OOII 
 
 3 
 
 .0066 
 
 
 33 
 
 .0182 
 
 1 1 
 
 .O2Ob 
 
 
 .09 
 
 .0014 
 
 3 
 3 
 
 .0075 
 
 8 
 
 34 
 
 .0193 
 
 ii 
 ii 
 
 .0267 
 
 7 
 7 
 
 O.IO 
 
 +0.0017 
 
 
 0.0083 
 
 
 0.35 
 
 +O.02O4 
 
 
 O.O274 
 
 
 .11 
 
 .0020 
 
 3 
 
 .0091 
 
 
 .36 
 
 .O2l6 
 
 12 
 
 .0281 
 
 7 
 
 .12 
 
 .0024 
 
 4 
 
 .0099 
 
 
 37 
 
 .0228 
 
 12 
 
 .0287 
 
 
 
 -13 
 
 .0028 
 
 4 
 
 .0107 
 
 
 .38 
 
 .0241 
 
 13 
 
 .0294 
 
 I 
 
 .14 
 
 .0033 
 
 5 
 
 .0116 
 
 8 
 
 39 
 
 .0254 
 
 13 
 
 13 
 
 .0300 
 
 u 
 
 7 
 
 0.15 
 
 +0.0038 
 
 
 0.0124 
 
 
 0.40 
 
 +0.0267 
 
 
 0.03O7 
 
 
 .16 
 
 .0043 
 
 
 .0132 
 
 
 .41 
 
 .0280 
 
 13 
 
 .0313 
 
 
 17 
 
 .0048 
 
 5 
 
 .0140 
 
 
 .42 
 
 .0294 
 
 14 
 
 .0319 
 
 
 .18 
 
 .0054 
 
 
 .0148 
 
 
 43 
 
 .0308 
 
 14 
 
 .0325 
 
 
 .19 
 
 .0060 
 
 7 
 
 .0155 
 
 I 
 
 44 
 
 .0323 
 
 15 
 IS 
 
 .0331 
 
 6 
 
 O.2O 
 
 +0.0067 
 
 
 0.0163 
 
 
 0.45 
 
 +0.0338 
 
 
 -0.0337 
 
 
 .21 
 
 .0074 
 
 7 
 
 .0171 
 
 
 .46 
 
 .0353 
 
 15 
 
 .0343 
 
 t 
 
 .22 
 
 .0081 
 
 7 
 
 .0179 
 
 
 47 
 
 .0368 
 
 15 
 
 .0348 
 
 i 
 
 23 
 
 .0088 
 
 7 
 
 .0187 
 
 
 48 
 
 .0384 
 
 f* 
 
 0354 
 
 U 
 
 c 
 
 .24 
 
 .0096 
 
 8 
 
 .0194 
 
 8 
 
 49 
 
 .0400 
 
 17 
 
 .0359 
 
 1 
 
 0.25 
 
 +0.0104 
 
 
 O.O2O2 
 
 
 0.50 
 
 +0.0417 
 
 
 0.0365 
 
 
 SMITHSONIAN TABLES 
 
 273 
 
TABLE VI 
 
 THE fiUDERMANNIAN 
 
 275 
 
The Gudermannian. 
 
 u 
 
 gdu 
 
 U.FO' 
 
 gd u 
 
 u>F ' 
 
 u 
 
 gdu 
 
 F ' 
 
 gdu 
 
 F ' 
 
 
 
 
 o / // 
 
 tt 
 
 
 
 
 / // 
 
 ~ 
 
 o.ooo 
 
 O.OOO OOOO 
 
 oooo 
 
 OO 00. OO 
 
 206.26 
 
 O.O50 
 
 0.049 9792 
 
 9988 
 
 2 51 48.95 
 
 206.OI 
 
 .001 
 
 .001 oooo 
 
 oooo 
 
 o 03 26.26 
 
 206.26 
 
 .051 
 
 .050 9779 
 
 9987 
 
 2 55 14-95 
 
 2o6.0O 
 
 .002 
 
 .002 oooo 
 
 oooo 
 
 o 06 52.53 
 
 206.26 
 
 .052 
 
 .051 9766 
 
 9986 
 
 2 58 40.94 
 
 205.99 
 
 .003 
 
 .003 oooo 
 
 oooo 
 
 o 10 18.79 
 
 206.26 
 
 .053 
 
 .052 9752 
 
 9986 
 
 3 02 06.92 
 
 205.98 
 
 .004 
 
 .004 oooo 
 
 oooo 
 
 o 13 45-06 
 
 206.26 
 
 .054 
 
 053 9738 
 
 9985 
 
 3 05 32.89 
 
 205.96 
 
 0.005 
 
 0.005 oooo 
 
 oooo 
 
 o 17 11.32 
 
 206.26 
 
 0.055 
 
 0.054 9723 
 
 9985 
 
 3 08 58.85 
 
 205.95 
 
 .006 
 
 .006 oooo 
 
 oooo 
 
 20 37.58 
 
 206.26 
 
 .056 
 
 .055 9708 
 
 9984 
 
 3 12 24.80 
 
 205.94 
 
 .007 
 
 .006 0999 
 
 oooo 
 
 o 24 03.84 
 
 206.26 
 
 057 
 
 .056 9692 
 
 9984 
 
 3 15 50-73 
 
 205.93 
 
 .008 
 
 .007 9999 
 
 oooo 
 
 o 27 30.10 
 
 206.26 
 
 .058 
 
 .057 9^75 
 
 9983 
 
 3 19 16.66 
 
 205.02 
 
 .009 
 
 .008 9999 
 
 oooo 
 
 o 30 56.36 
 
 206.26 
 
 .059 
 
 .058 9658 
 
 9983 
 
 3 22 42.57 
 
 205.91 
 
 O.OIO 
 
 0.009 9998 
 
 9999 
 
 o 34 22. 61 
 
 206.25 
 
 0.060 
 
 0.059 9640 
 
 9982 
 
 3 26 08.47 
 
 205.89 
 
 .on 
 
 .010 9998 
 
 9999 
 
 o 37 48.87 
 
 206.25 
 
 .061 
 
 .060 9622 
 
 998i 
 
 3 29 34-36 
 
 205.88 
 
 .012 
 
 .oil 9997 
 
 9999 
 
 o 41 15.12 
 
 206.25 
 
 .062 
 
 .061 9603 
 
 9981 
 
 3 33 00.23 
 
 205.87 
 
 .013 
 
 .012 9996 
 
 9999 
 
 o 44 41.37 
 
 206.25 
 
 .063 
 
 .062 9584 
 
 9980 
 
 3 36 26.10 
 
 205.86 
 
 .014 
 
 .013 9995 
 
 9999 
 
 o 48 07.61 
 
 206.24 
 
 .064 
 
 .063 9564 
 
 9980 
 
 3 39 51-94 
 
 205.84 
 
 0.015 
 
 0.014 9994 
 
 9999 
 
 o 51 33-86 
 
 206.24 
 
 0.065 
 
 0.064 9543 
 
 9979 
 
 3 43 17.78 
 
 205.83 
 
 .016 
 
 015 9993 
 
 9999 
 
 o 55 00.10 
 
 206.24 
 
 .066 
 
 .065 9521 
 
 9978 
 
 3 46 43-60 
 
 205.82 
 
 .017 
 
 .016 9992 
 
 9999 
 
 o 58 26.33 
 
 206.23 
 
 .067 
 
 .066 9499 
 
 0978 
 
 3 50 09.41 
 
 205.8o 
 
 .018 
 
 .017 9990 
 
 9998 
 
 I 01 52-57 
 
 206.23 
 
 .068 
 
 .067 9477 
 
 9977 
 
 3 53 35-21 
 
 205-79 
 
 .019 
 
 .018 9989 
 
 9998 
 
 i 05.18.80 
 
 206.23 
 
 .069 
 
 .068 9453 
 
 9976 
 
 3 57 00.99 
 
 205.77 
 
 0.020 
 
 0.019 9987 
 
 9908 
 
 i 08 45.02 
 
 2O5.22 
 
 0.070 
 
 0.069 9429 
 
 9976 
 
 4 oo 26.76 
 
 205.76 
 
 .O2I 
 
 .020 9985 
 
 9998 
 
 I 12 11.24 
 
 206.22 
 
 .071 
 
 .070 9404 
 
 9975 
 
 4 03 52.51 
 
 205.75 
 
 .022 
 
 .021 9982 
 
 9998 
 
 I 15 37.46 
 
 2O5.2I 
 
 .072 
 
 .071 9379 
 
 9974 
 
 4 07 18.25 
 
 205-73 
 
 .023 
 
 .022 0980 
 
 9997 
 
 I 19 03.67 
 
 206.21 
 
 073 
 
 .072 9352 
 
 9973 
 
 4 10 43.08 
 
 205.72 
 
 .024 
 
 .023 9977 
 
 9997 
 
 I 22 29.88 
 
 206.21 
 
 074 
 
 .073 9326 
 
 9973 
 
 4 14 09.68 
 
 205.70 
 
 O.O25 
 
 0.024 9974 
 
 9997 
 
 I 25 56.08 
 
 2O6.2O 
 
 0.075 
 
 0.074 9298 
 
 9972 
 
 4 17 35.38 
 
 205.69 
 
 .026 
 
 .025 9971 
 
 9997 
 
 I 29 22.28 
 
 206.2O 
 
 .076 
 
 .075 9269 
 
 9971 
 
 4 21 01.06 
 
 205.67 
 
 .027 
 
 .026 9967 
 
 9996 
 
 I 32 48.47 
 
 2O6.I9 
 
 .077 
 
 .076 9240 
 
 9970 
 
 4 24 26.72 
 
 205.65 
 
 .028 
 
 .027 0963 
 
 9996 
 
 I 36 14.66 
 
 206.18 
 
 .078 
 
 .077 9210 
 
 9970 
 
 4 27 52.37 
 
 205.64 
 
 .029 
 
 .028 9959 
 
 9996 
 
 I 39 40.84 
 
 206.18 
 
 .079 
 
 .078 9180 
 
 9969 
 
 4 31 18.00 
 
 205.62 
 
 0.030 
 
 0.029 9955 
 
 9995 
 
 I 43 07.02 
 
 2O6.I7 
 
 0.080 
 
 0.079 9148 
 
 9968 
 
 4 34 43.61 
 
 2O5.6l 
 
 .031 
 
 .030 9950 
 
 9995 
 
 I 46 33.19 
 
 2O6.I7 
 
 .081 
 
 .080 9116 
 
 9967 
 
 4 38 09.21 
 
 205.59 
 
 .032 
 
 .031 9945 
 
 9995 
 
 i 49 59-35 
 
 2O6.l6 
 
 .082 
 
 .081 9083 
 
 9966 
 
 4 41 34.79 
 
 205.57 
 
 033 
 
 .032 0940 
 
 9995 
 
 i 53 25.50 
 
 206.15 
 
 .083 
 
 .082 0049 
 
 9966 
 
 4 45 00.36 
 
 205.56 
 
 .034 
 
 .033 9935 
 
 9994 
 
 I 56 51-65 
 
 2O6.I5 
 
 .084 
 
 .083 9014 
 
 9965 
 
 4 48 25.90 
 
 205.54 
 
 0.035 
 
 0.034 0929 
 
 9994 
 
 2 00 17.79 
 
 206.14 
 
 0.085 
 
 0.084 8978 
 
 9964 
 
 4 51 51.44 
 
 205.52 
 
 .036 
 
 .035 9922 
 
 9994 
 
 2 03 43-93 
 
 206.13 
 
 .086 
 
 .085 8942 
 
 9963 
 
 4 55 16.95 
 
 205.50 
 
 037 
 
 .036 9916 
 
 9993 
 
 2 O7 10. 06 
 
 206.12 
 
 .087 
 
 .086 8905 
 
 9962 
 
 4 58 42.44 
 
 205.49 
 
 .038 
 
 .037 9909 
 
 9993 
 
 2 IO 36.18 
 
 206.12 
 
 .088 
 
 .087 8866 
 
 9061 
 
 5 02 07.92 
 
 205-47 
 
 .039 
 
 .038 9901 
 
 9992 
 
 2 14 O2.29 
 
 206. II 
 
 .089 
 
 .088 8827 
 
 9961 
 
 5 05 33.38 
 
 *>5 -45 
 
 0.040 
 
 0.039 9893 
 
 9992 
 
 2 17 28.39 
 
 2O6.IO 
 
 0.000 
 
 0.089 8787 
 
 9960 
 
 5 08 58.82 
 
 205.43 
 
 .041 
 
 .040 9885 
 
 9992 
 
 2 20 54.49 
 
 206.09 
 
 .091 
 
 .090 8747 
 
 9959 
 
 5 12 24.25 
 
 205.41 
 
 .042 
 
 .041 9877 
 
 9991 
 
 2 24 2O.58 
 
 206.08 
 
 .092 
 
 .091 8705 
 
 9958 
 
 5 15 49.65 
 
 205.39 
 
 .043 
 
 .042 9868 
 
 9991 
 
 2 27 46.65 
 
 2O6.O7 
 
 093 
 
 .092 8662 
 
 9957 
 
 5 19 15.03 
 
 205.38 
 
 .044 
 
 .043 9858 
 
 9990 
 
 2 31 12.72 
 
 206.07 
 
 .094 
 
 .093 8619 
 
 9956 
 
 5 22 40.40 
 
 205.36 
 
 0.045 
 
 0.044 9848 
 
 9990 
 
 2 34 38.79 
 
 2O6.O6 
 
 0.095 
 
 0.094 8574 
 
 9955 
 
 5 26 05.75 
 
 205.34 
 
 .046 
 
 .045 9838 
 
 9989 
 
 2 38 04.84 
 
 206.05 
 
 .096 
 
 .095 8529 
 
 9954 
 
 5 29 31.08 
 
 205.32 
 
 .047 
 
 .046 9827 
 
 9989 
 
 2 41 30.88 
 
 206.04 
 
 .097 
 
 .096 8482 
 
 9953 
 
 5 32 56.38 
 
 205.30 
 
 .048 
 
 .047 9816 
 
 9988 
 
 2 44 56.91 
 
 2O6.O3 
 
 .098 
 
 .097 8435 
 
 9952 
 
 5 36 21.67 
 
 205.28 
 
 .049 
 
 .048 9804 
 
 9988 
 
 2 48 22.93 
 
 206.02 
 
 .099 
 
 .098 8387 
 
 0051 
 
 5 39 46.94 
 
 205.26 
 
 0.050 
 
 0.049 9792 
 
 9988 
 
 2 51 48.95 
 
 206.0I 
 
 O.IOO 
 
 0.099 8337 
 
 9950 
 
 5 43 12.19 
 
 205.24 
 
 u 
 
 2 tan-He")- * 
 
 > s ch u 
 
 2 tan-He" )-90 
 
 wsech u 
 
 u 
 
 2tan-'(e)-? 
 
 wsechu 
 
 2tan-'(e)-9(r ) 
 
 M sech u 
 
 IMITHSONIAN TABLES 
 
 276 
 
The Gudermannian. 
 
 II 
 
 gd u 
 
 Fo' 
 
 gdu 
 
 F ' 
 
 u 
 
 gd u 
 
 F ' 
 
 gdu 
 
 <-F ' 
 
 
 
 
 o / // 
 
 o 
 
 
 
 
 O / // 
 
 H 
 
 O.IOO 
 
 0.099 8337 
 
 9950 
 
 5 43 12.19 
 
 205.24 
 
 0.150 
 
 0.149 4406 
 
 9889 
 
 8 33 44-35 
 
 203.97 
 
 .101 
 
 .100 8287 
 
 9949 
 
 5 46 37-42 
 
 205.22 
 
 .151 
 
 . 150 4294 
 
 9887 
 
 8 37 08.30 
 
 203.94 
 
 .102 
 
 .101 8236 
 
 9948 
 
 5 50 02.62 
 
 205.20 
 
 .152 
 
 .151 4181 
 
 9886 
 
 8 40 32.22 
 
 203.90 
 
 .103 
 
 .102 8184 
 
 9947 
 
 5 53 27.81 
 
 205.18 
 
 .153 
 
 .152 4065 
 
 9884 
 
 8 43 56.11 
 
 203.87 
 
 .104 
 
 .103 8130 
 
 9946 
 
 5 56 52.97 
 
 205.15 
 
 154 
 
 153 3949 
 
 9883 
 
 8 47 19-96 
 
 203.84 
 
 0.105 
 
 0.104 8076 
 
 9945 
 
 6 oo 18.12 
 
 205.13 
 
 0.155 
 
 0.154 3831 
 
 9881 
 
 8 50 43-79 
 
 203.81 
 
 .106 
 
 .105 8021 
 
 9944 
 
 6 03 43.24 
 
 205.11 
 
 .156 
 
 .155 37ii 
 
 9880 
 
 8 54 07.59 
 
 203.78 
 
 .107 
 
 .106 7964 
 
 9943 
 
 6 07 08.34 
 
 205.09 
 
 .157 
 
 156 3590 
 
 9878 
 
 8 57 31.35 
 
 203.75 
 
 .108 
 
 .107 7907 
 
 9942 
 
 6 10 33.42 
 
 205.07 
 
 .158 
 
 .157 3467 
 
 9876 
 
 9 oo 55.o8 
 
 203.72 
 
 .109 
 
 .108 7848 
 
 9941 
 
 6 13 58.48 
 
 205.05 
 
 .159 
 
 .158 3343 
 
 9875 
 
 9 04 18.78 
 
 203.68 
 
 O.IIO 
 
 0.109 7788 
 
 9940 
 
 6 17 23.51 
 
 205.02 
 
 0.160 
 
 0.159 3217 
 
 9873 
 
 9 07 42.45 
 
 203.65 
 
 .III 
 
 .no 7728 
 
 9939 
 
 6 20 48.52 
 
 205.00 
 
 .161 
 
 .160 3089 
 
 9872 
 
 9 ii 06.09 
 
 203.62 
 
 .112 
 
 .in 7666 
 
 9938 
 
 6 24 13.51 
 
 204.98 
 
 .162 
 
 .161 2960 
 
 9870 
 
 9 14 29.69 
 
 203.59 
 
 113 
 
 .112 7603 
 
 9936 
 
 6 27 38.48 
 
 204.95 
 
 .163 
 
 .162 2830 
 
 9869 
 
 9 17 53-26 
 
 203.55 
 
 .114 
 
 113 7539 
 
 9935 
 
 6 31 03.42 
 
 204.93 
 
 .164 
 
 .163 2697 
 
 9867 
 
 9 21 16.80 
 
 203.52 
 
 O.II5 
 
 0.114 7474 
 
 9934 
 
 6 34 28.34 
 
 204.91 
 
 0.165 
 
 0.164 2564 
 
 9865 
 
 9 24 40.31 
 
 203.49 
 
 .116 
 
 .115 7407 
 
 9933 
 
 6 37 53.24 
 
 204.88 
 
 .166 
 
 .165 2428 
 
 9864 
 
 9 28 03.78 
 
 203.46 
 
 .117 
 
 .116 7340 
 
 9932 
 
 6 41 i8.ii 
 
 204.86 
 
 .167 
 
 .166 2291 
 
 9862 
 
 9 31 27.22 
 
 203.42 
 
 .118 
 
 .117 7271 
 
 9931 
 
 6 44 42.96 
 
 204.84 
 
 .168 
 
 .167 2153 
 
 9861 
 
 9 34 50.62 
 
 203.39 
 
 .119 
 
 .118 7201 
 
 9930 
 
 6 48 07.78 
 
 204.81 
 
 .169 
 
 .168 2OI2 
 
 9859 
 
 9 38 13-99 
 
 203-35 
 
 O.I2O 
 
 0.119 7130 
 
 9928 
 
 6 51 32.59 
 
 204.79 
 
 0.170 
 
 O.l69 l87O 
 
 9857 
 
 9 41 37.33 
 
 203.32 
 
 .121 
 
 .120 7058 
 
 9927 
 
 6 54 57.36 
 
 204.76 
 
 .171 
 
 .170 1727 
 
 9856 
 
 9 45 00.63 
 
 203.29 
 
 .122 
 
 .121 6985 
 
 9926 
 
 6 58 22.11 
 
 204-74 
 
 .172 
 
 .171 1581 
 
 9854 
 
 9 48 23.00 
 
 203.25 
 
 123 
 
 .122 6910 
 
 9925 
 
 7 01 46.84 
 
 204.71 
 
 .173 
 
 .172 1434 
 
 9852 
 
 9 51 47-14 
 
 203.22 
 
 .124 
 
 .123 6834 
 
 9924 
 
 70S 11.54 
 
 204.69 
 
 .174 
 
 .173 1286 
 
 9851 
 
 9 55 10.33 
 
 203.18 
 
 0.125 
 
 0.124 6757 
 
 9922 
 
 7 08 36.22 
 
 204.66 
 
 0.175 
 
 0.174 1136 
 
 9849 
 
 9.58 33.50 
 
 203.15 
 
 .126 
 
 .125 6679 
 
 9921 
 
 7 12 00.87 
 
 204.64 
 
 .176 
 
 .175 0083 
 
 9847 
 
 10 01 56.63 
 
 203.11 
 
 .127 
 
 .126 66OO 
 
 9920 
 
 7 15 25.49 
 
 204.61 
 
 .177 
 
 . 176 0830 
 
 9845 
 
 10 05 19.72 
 
 203.08 
 
 .128 
 
 .127 6519 
 
 9919 
 
 7 18 50.09 
 
 204.59 
 
 .178 
 
 . 177 0674 
 
 9844 
 
 10 08 42.78 
 
 203.04 
 
 .129 
 
 .128 6437 
 
 9917 
 
 7 22 14.67 
 
 204.56 
 
 .179 
 
 . 178 0517 
 
 9842 
 
 10 12 05.80 
 
 203.00 
 
 0.130 
 
 0.129 6354 
 
 9916 
 
 7 25 39.22 
 
 204-53 
 
 0.180 
 
 0.179 0358 
 
 9840 
 
 10 15 28.78 
 
 202.97 
 
 .131 
 
 .I3O 6269 
 
 9915 
 
 7 29 03.74 
 
 204.51 
 
 .181 
 
 .180 0197 
 
 9838 
 
 10 18 51.73 
 
 202.93 
 
 .132 
 
 .131 6183 
 
 9913 
 
 7 32 28.23 
 
 204.48 
 
 .182 
 
 .181 0035 
 
 9837 
 
 IO 22 14.65 
 
 202.00 
 
 .133 
 
 .132 6096 
 
 9912 
 
 7 35 52.70 
 
 204.45 
 
 .183 
 
 .181 9871 
 
 9835 
 
 10 25 37.52 
 
 202.86 
 
 .134 
 
 .133 6008 
 
 9911 
 
 7 39 I7.I4 
 
 204.43 
 
 .184 
 
 .182 9705 
 
 9833 
 
 10 29 00.36 
 
 202.82 
 
 0.135 
 
 0.134 59l8 
 
 9910 
 
 7 42 41.55 
 
 204.40 
 
 0.185 
 
 0.183 9537 
 
 9831 
 
 10 32 23.17 
 
 2O2 . 78 
 
 .136 
 
 135 5827 
 
 9908 
 
 7 46 05.94 
 
 204-37 
 
 .186 
 
 . 184 9367 
 
 9829 
 
 10 35 45-93 
 
 202.75 
 
 .137 
 
 136 5734 
 
 9907 
 
 7 49 30.29 
 
 204.34 
 
 .187 
 
 .185 9196 
 
 9828 
 
 10 39 08.66 
 
 202.71 
 
 .138 
 
 .137 5641 
 
 9906 
 
 7 52 54.62 
 
 204.32 
 
 .188 
 
 .186 9022 
 
 9826 
 
 10 42 3L35 
 
 202.67 
 
 .139 
 
 .138 5545 
 
 9904 
 
 7 56 18.93 
 
 204.29 
 
 .189 
 
 .187 8847 
 
 9824 
 
 10 45 54.01 
 
 2O2.63 
 
 0.140 
 
 0.139 5449 
 
 9903 
 
 7 59 43.20 
 
 204.26 
 
 0.190 
 
 o. 188 8670 
 
 9822 
 
 10 49 16.62 
 
 2O2.6O 
 
 .141 
 
 .140 5351 
 
 9901 
 
 8 03 07-45 
 
 204.23 
 
 .191 
 
 . 189 8492 
 
 5820 
 
 10 52 39.20 
 
 2O2.56 
 
 .142 
 
 .141 5252 
 
 9900 
 
 8 06 31.66 
 
 204.20 
 
 .192 
 
 .190 8311 
 
 9818 
 
 10 56 01.74 
 
 2O2.52 
 
 .143 
 
 .142 5151 
 
 9899 
 
 8 09 55.85 
 
 204.17 
 
 .193 
 
 .191 8129 
 
 9817 
 
 10 59 24.24 
 
 2O2.48 
 
 .144 
 
 .143 5049 
 
 9897 
 
 8 13 20. 01 
 
 204.14 
 
 .194 
 
 .192 7944 
 
 9815 
 
 ii 02 46.71 
 
 202.44 
 
 0.145 
 
 0.144 4946 
 
 9896 
 
 8 16 44.14 
 
 204.12 
 
 0.195 
 
 0.193 7758 
 
 0813 
 
 ii 06 09.13 
 
 2O2.4O 
 
 .146 
 
 .145 4841 
 
 9894 
 
 8 20 08.24 
 
 204.09 
 
 .196 
 
 .194 7570 
 
 9811 
 
 ii 09 31-51 
 
 202.37 
 
 .147 
 
 . 146 4734 
 
 9893 
 
 8 23 32.31 
 
 204.06 
 
 .197 
 
 .195 738o 
 
 9809 
 
 II 12 53.86 
 
 202.33 
 
 .148 
 
 .147 4626 
 
 9891 
 
 8 26 56.35 
 
 204.03 
 
 .198 
 
 .196 7188 
 
 9807 
 
 ii 16 16.17 
 
 202.29 
 
 .149 
 
 148 4517 
 
 9890 
 
 8 30 20.36 
 
 204.00 
 
 .199 
 
 .197 6994 
 
 9805 
 
 ii 19 38.43 
 
 202.2-5 
 
 0.150 
 
 0.149 4406 
 
 9889 
 
 8 33 44-35 
 
 203.97 
 
 0.200 
 
 0.198 6798 
 
 9803 
 
 ii 23 00.66 
 
 2O2.2I 
 
 u 
 
 2tan-'(e)- 
 
 <s:chu 
 
 2tan-He)-0 
 
 wsechu 
 
 U 
 
 2 tan-He")-^ 
 
 wsechu 
 
 atan-Keuy-SO 
 
 wsech u 
 
 SMITHSONIAN TABLES 
 
 277 
 
The Gudermannian. 
 
 u 
 
 gd u 
 
 F ' 
 
 gdu 
 
 U.FO" 
 
 u 
 
 gd u 
 
 <oFo' 
 
 gdu 
 
 Fo' 
 
 
 
 
 o / // 
 
 II 
 
 
 
 
 o / // 
 
 // 
 
 0.200 
 
 o. 198 6798 
 
 9803 
 
 II 23 00.66 
 
 202.21 
 
 0.250 
 
 0.247 4358 
 
 9695 
 
 H 10 37-30 
 
 199^98 
 
 .201 
 
 .199 66oi 
 
 9801 
 
 II 26 22.85 
 
 202.17 
 
 .251 
 
 .248 4052 
 
 9693 
 
 14 13 57.26 
 
 199.93 
 
 .202 
 
 .200 6401 
 
 9799 
 
 II 29 44.99 
 
 202.13 
 
 .252 
 
 .249 3744 
 
 9691 
 
 14 17 17.16 
 
 199-88 
 
 .203 
 
 .2OI 6200 
 
 9797 
 
 u 33 07.10 
 
 202.09 
 
 253 
 
 250 3434 
 
 9688 
 
 14 20 37.02 
 
 199.84 
 
 .204 
 
 .202 5996 
 
 9795 
 
 II 36 29.17 
 
 202.05 
 
 .254 
 
 .251 3121 
 
 9686 
 
 14 23 56.83 
 
 199.79 
 
 0.205 
 
 0.203 5790 
 
 9794 
 
 u 39 51.19 
 
 202.01 
 
 0.255 
 
 0.252 2805 
 
 9683 
 
 14 27 16.59 
 
 199-74 
 
 .206 
 
 .204 5583 
 
 9792 
 
 ii 43 13.18 
 
 2OI.96 
 
 .256 
 
 .253 2488 
 
 9681 
 
 14 30 36.31 
 
 199-69 
 
 .207 
 
 205 5374 
 
 9790 
 
 II 46 35.12 
 
 201.92 
 
 257 
 
 .254 2167 
 
 9679 
 
 14 33 55-97 
 
 199.64 
 
 .208 
 
 .206 5162 
 
 9788 
 
 u 49 57-02 
 
 201.88 
 
 .258 
 
 .255 1845 
 
 9676 
 
 14 37 15.58 
 
 199-59 
 
 .209 
 
 .207 4949 
 
 9786 
 
 II 53 18.89 
 
 201.84 
 
 .259 
 
 .256 1520 
 
 9674 
 
 14 40 35.14 
 
 199-53 
 
 0.210 
 
 0.208 4733 
 
 9783 
 
 II 56 40.71 
 
 201.80 
 
 0.260 
 
 0.257 H92 
 
 9671 
 
 14 43 54.65 
 
 199.48 
 
 .211 
 
 .209 4515 
 
 978i 
 
 12 oo 02.48 
 
 201.76 
 
 .261 
 
 .258 0862 
 
 9669 
 
 14 47 14.10 
 
 199-43 
 
 .212 
 
 .210 4296 
 
 9779 
 
 12 03 24.22 
 
 201.71 
 
 .262 
 
 .259 0530 
 
 9666 
 
 14 50 33.51 
 
 199.38 
 
 .213 
 
 .211 4074 
 
 9777 
 
 12 06 45.91 
 
 201.67 
 
 .263 
 
 .260 0195 
 
 9664 
 
 14 53 52.87 
 
 199-33 
 
 .214 
 
 .212 3851 
 
 9775 
 
 12 IO 07.56 
 
 201.63 
 
 .264 
 
 .260 9857 
 
 9661 
 
 14 57 12. 18 
 
 199.29 
 
 0.215 
 .2l6 
 
 0.213 3625 
 
 .214 3397 
 
 9773 
 9771 
 
 12 13 29.17 
 
 12 16 50.74 
 
 201.59 
 201.54 
 
 0.265 
 .266 
 
 0.261 9518 
 .262 9175 
 
 % 
 
 9656 
 
 15 00 31.43 
 15 03 50.63 
 
 199-24 
 199.19 
 
 .217 
 
 .215 3167 
 
 9769 
 
 12 20 12.26 
 
 201.50 
 
 .267 
 
 .263 8830 
 
 9654 
 
 15 07 09.78 
 
 199.13 
 
 .218 
 
 .216 2935 
 
 9767 
 
 12 23 33.74 
 
 201.46 
 
 .268 
 
 .264 8483 
 
 9651 
 
 15 10 28.88 
 
 199.08 
 
 .219 
 
 .217 2701 
 
 9765 
 
 12 26 55.18 
 
 201.42 
 
 .269 
 
 .265 8133 
 
 9649 
 
 15 13 47-93 
 
 199.03 
 
 O.22O 
 
 0.218 2465 
 
 9763 
 
 12 30 16.57 
 
 201.37 
 
 0.270 
 
 0.266 7781 
 
 9646 
 
 15 17 06.92 
 
 198.98 
 
 .221 
 
 .219 2227 
 
 9761 
 
 12 33 37-92 
 
 201.33 
 
 .271 
 
 .267 7425 
 
 9644 
 
 15 20 25.86 
 
 198.93 
 
 .222 
 
 .220 1986 
 
 9759 
 
 12 36 59-23 
 
 201.28 
 
 .272 
 
 .268 7068 
 
 9641 
 
 15 23 44-75 
 
 198.87 
 
 .223 
 
 .221 1744 
 
 9756 
 
 12 4O 2O.49 
 
 201.24 
 
 .273 
 
 .269 6708 
 
 9639 
 
 15 27 03.59 
 
 198.82 
 
 .224 
 
 .222 1499 
 
 9754 
 
 12 43 41-71 
 
 2OI.2O 
 
 .274 
 
 .270 6345 
 
 9636 
 
 15 30 22.37 
 
 198.77 
 
 0.225 
 
 0.223 1252 
 
 9752 
 
 12 47 02.88 
 
 201.15 
 
 0.275 
 
 0.271 5980 
 
 9633 
 
 15 33 41.10 
 
 108.71 
 
 .226 
 
 .224 1003 
 
 9750 
 
 12 5O 24.OI 
 
 2OI.II 
 
 .276 
 
 .272 5612 
 
 9631 
 
 15 36 59-78 
 
 198.66 
 
 .227 
 
 .225 0752 
 
 9748 
 
 12 53 45-10 
 
 2OI.06 
 
 .277 
 
 .273 5242 
 
 9628 
 
 15 40 18.41 
 
 198.61 
 
 .228 
 
 .226 0409 
 
 9746 
 
 12 57 06.14 
 
 201.02 
 
 .278 
 
 .274 4868 
 
 9626 
 
 15 43 36.98 
 
 198.55 
 
 .229 
 
 .227 0243 
 
 9743 
 
 13 oo 27.13 
 
 200.97 
 
 .279 
 
 .275 4493 
 
 9623 
 
 15 46 55-49 
 
 198.50 
 
 0.230 
 .231 
 
 0.227 9986 
 .228 9726 
 
 9741 
 9739 
 
 13 03 48.08 
 13 07 08.99 
 
 200.93 
 200.88 
 
 0.280 
 .281 
 
 0.276 4114 
 .277 3734 
 
 9620 
 
 9618 
 
 15 50 13.95 
 15 53 32.36 
 
 198-45 
 198.38 
 
 .232 
 
 .229 9464 
 
 9737 
 
 13 10 29.85 
 
 200.84 
 
 .282 
 
 .278 3350 
 
 96I-S 
 
 15 56 50.72 
 
 198.33 
 
 233 
 
 .230 9199 
 
 9735 
 
 13 13 50.66 
 
 200.79 
 
 .283 
 
 .279 2964 
 
 9612 
 
 16 oo 09.02 
 
 198.27 
 
 -234 
 
 .231 8933 
 
 9732 
 
 13 17 11.42 
 
 200.74 
 
 .284 
 
 .280 2575 
 
 9610 
 
 16 03 27.26 
 
 198.22 
 
 O.235 
 
 0.232 8664 
 
 9730 
 
 13 20 32.15 
 
 200.70 
 
 0.285 
 
 0.281 2184 
 
 9607 
 
 16 06 45-45 
 
 198.16 
 
 .236 
 
 233 8393 
 
 9728 
 
 13 23 52.82 
 
 200.65 
 
 .286 
 
 .282 1789 
 
 9604 
 
 16 10 03.58 
 
 198.11 
 
 .237 
 
 .234 8120 
 
 9726 
 
 13 27 13.45 
 
 200.60 
 
 .287 
 
 .283 1393 
 
 9602 
 
 16 13 21.66 
 
 198.05 
 
 .238 
 
 .235 7844 
 
 9723 
 
 13 30 34-03 
 
 200.56 
 
 .288 
 
 284 0993 
 
 9599 
 
 16 16 39.69 
 
 198.00 
 
 .239 
 
 .236 7566 
 
 9721 
 
 13 33 54.56 
 
 200.51 
 
 .289 
 
 .285 0591 
 
 9596 
 
 16 19 57.66 
 
 197-94 
 
 O.24O 
 
 0.237 7286 
 
 9719 
 
 13 37 15-05 
 
 200.46 
 
 0.290 
 
 0.286 0186 
 
 9594 
 
 16 23 15.57 
 
 197.89 
 
 .241 
 
 .238 7004 
 
 9716 
 
 13 40 35-49 
 
 200.42 
 
 .291 
 
 .286 9778 
 
 9591 
 
 16 26 33.43 
 
 197.83 
 
 .242 
 
 .239 6719 
 
 9714 
 
 13 43 55-88 
 
 200.37 
 
 .292 
 
 .287 9368 
 
 9588 
 
 16 29 51.23 
 
 197.77 
 
 243 
 
 .240 6432 
 
 9712 
 
 13 47 16.23 
 
 200.32 
 
 .293 
 
 .288 8955 
 
 9586 
 
 16 33 08.97 
 
 197.72 
 
 .244 
 
 .241 6143 
 
 97io 
 
 13 50 36.53 
 
 200.27 
 
 .294 
 
 .289 8539 
 
 9583 
 
 16 36 26.66 
 
 197.66 
 
 0.245 
 .246 
 
 0.242 5851 
 .243 5557 
 
 9707 
 9705 
 
 13 53 56.77 
 13 57 16.98 
 
 200.23 
 200.18 
 
 0.295 
 .296 
 
 0.200 8l2I 
 .291 7699 
 
 958o 
 9577 
 
 16 39 44.30 
 16 43 01.87 
 
 197-60 
 197.55 
 
 .247 
 
 .244 5261 
 
 9703 
 
 14 oo 37.13 
 
 200.13 
 
 .297 
 
 .292 7275 
 
 9575 
 
 16 46 19.39 
 
 197.49 
 
 .248 
 
 .245 4902 
 
 9700 
 
 14 03 57-23 
 
 200.08 
 
 .298 
 
 .293 6849 
 
 9572 
 
 16 49 36.85 
 
 197.43 
 
 249 
 
 .246 4661 
 
 9698 
 
 14 07 17-29 
 
 200.03 
 
 .299 
 
 .294 6419 
 
 9569 
 
 16 52 54.26 
 
 197.38 
 
 0.250 
 
 0.247 4358 
 
 9695 
 
 14 10 37.30 
 
 199.98 
 
 0.300 
 
 0.295 5987 
 
 9566 
 
 16 56 11.60 
 
 197.32 
 
 u 
 
 2 ton-He )-! 
 
 << sech u 
 
 2ton- 1 (e)-90 
 
 wsech u 
 
 u 
 
 2 ton-He") 
 
 wsechu 
 
 2tan-'(e)-90 
 
 tech u 
 
 SMITHSONIAN TABLES 
 
 278 
 
The Gudermannian. 
 
 u 
 
 gdu 
 
 tf 
 
 gdu 
 
 -w 
 
 u 
 
 gd u 
 
 F O ' 
 
 gdu 
 
 * 
 
 
 
 
 o y // 
 
 
 
 
 
 
 / // 
 
 m 
 
 0.300 
 
 0.295 5987 
 
 9566 
 
 16 56 11.60 
 
 197.32 
 
 0.350 
 
 0.343 0655 
 
 9417 
 
 19 39 22.34 
 
 194.25 
 
 .301 
 
 .296 5552 
 
 9563 
 
 16 59 28.89 
 
 197.26 
 
 351 
 
 .344 0071 
 
 9414 
 
 19 42 36.55 
 
 I94.I8 
 
 .302 
 
 .297 5114 
 
 956i 
 
 17 02 46.13 
 
 197.20 
 
 352 
 
 .344 0483 
 
 9411 
 
 19 45 50.70 
 
 194.11 
 
 .303 
 
 .298 4673 
 
 9558 
 
 17 06 03.30 
 
 197.15 
 
 .353 
 
 345 8893 
 
 9408 
 
 19 49 04.78 
 
 194.05 
 
 .304 
 
 .299 4229 
 
 9555 
 
 17 09 20.42 
 
 197.09 
 
 354 
 
 .346 8299 
 
 9405 
 
 19 52 18.80 
 
 193.98 
 
 0.305 
 
 0.300 3783 
 
 9552 
 
 17 12 37.48 
 
 197.03 
 
 0.355 
 
 0.347 7702 
 
 9401 
 
 19 55 32.75 
 
 193.92 
 
 .306 
 
 .301 3334 
 
 9549 
 
 17 15 54.48 
 
 196.97 
 
 .356 
 
 .348 7101 
 
 9398 
 
 19 58 46.63 
 
 193.85 
 
 .307 
 
 .302 2882 
 
 9547 
 
 17 19 11.42 
 
 196.91 
 
 .357 
 
 .349 6498 
 
 9395 
 
 20 02 00.45 
 
 193.78 
 
 .308 
 
 .303 2427 
 
 9544 
 
 17 22 28.30 
 
 196.85 
 
 3-58 
 
 350 5891 
 
 9392 
 
 20 05 14.20 
 
 193.72 
 
 .309 
 
 .304 1969 
 
 9541 
 
 17 25 45.12 
 
 196.79 
 
 359 
 
 .351 528i 
 
 9388 
 
 20 08 27.88 
 
 193.65 
 
 0.310 
 
 0.305 1509 
 
 9538 
 
 17 29 01.89 
 
 196.74 
 
 0.360 
 
 0.352 4668 
 
 9385 
 
 20 II 4L50 
 
 193.58 
 
 .311 
 
 .306 1045 
 
 9535 
 
 17 32 18.60 
 
 196.68 
 
 .361 
 
 353 4052 
 
 9382 
 
 20 14 55-05 
 
 193.52 
 
 .312 
 
 .307 0579 
 
 9532 
 
 17 35 35-24 
 
 196.62 
 
 .362 
 
 354 3432 
 
 9378 
 
 20 18 08.54 
 
 193.45 
 
 .313 
 
 .308 ono 
 
 9529 
 
 17 38 51.83 
 
 196.56 
 
 .363 
 
 355 2809 
 
 9375 
 
 2O 21 21.95 
 
 193.38 
 
 .314 
 
 .308 9638 
 
 9526 
 
 17 42 08.36 
 
 196.50 
 
 .364 
 
 .356 2183 
 
 9372 
 
 20 24 35.30 
 
 193.32 
 
 0.315 
 
 0.309 9163 
 
 9524 
 
 17 45 24.83 
 
 196.44 
 
 0.365 
 
 0.357 1554 
 
 9369 
 
 20 27 48.59 
 
 193.25 
 
 .316 
 
 .310 8685 
 
 9521 
 
 17 48 41.23 
 
 196.38 
 
 .366 
 
 .358 0921 
 
 9366 
 
 20 31 01.80 
 
 I93.I8 
 
 .317 
 
 .311 8204 
 
 95i8 
 
 17 51 57.58 
 
 196.32 
 
 .367 
 
 359 0285 
 
 9362 
 
 20 34 14.95 
 
 193.11 
 
 .318 
 
 .312 7721 
 
 9515 
 
 17 55 13-87 
 
 196.26 
 
 .368 
 
 .359 9646 
 
 9359 
 
 20 37 28.03 
 
 193.05 
 
 .319 
 
 .313 7234 
 
 9512 
 
 17 58 30.10 
 
 196.20 
 
 .369 
 
 .360 9003 
 
 9356 
 
 2O 4O 4I.O4 
 
 192.98 
 
 0.320 
 
 0.314 6744 
 
 9509 
 
 18 01 46.26 
 
 196.14 
 
 0.370 
 
 0.361 8358 
 
 9352 
 
 20 43 53.08 
 
 192.91 
 
 .321 
 
 .315 6252 
 
 9506 
 
 18 05 02.37 
 
 196.08 
 
 371 
 
 .362 7708 
 
 9349 
 
 20 47 06.86 
 
 192.84 
 
 .322 
 
 .316 5757 
 
 9503 
 
 18 08 18.42 
 
 196.01 
 
 372 
 
 363 7056 
 
 9346 
 
 20 50 19.66 
 
 192.77 
 
 .323 
 
 .317 5258 
 
 9500 
 
 18 u 34.40 
 
 195.95 
 
 373 
 
 .364 6400 
 
 9343 
 
 20 53 32.40 
 
 192 . 7O 
 
 .324 
 
 .318 4757 
 
 9497 
 
 18 14 50.32 
 
 195.89 
 
 374 
 
 .365 5741 
 
 9339 
 
 20 56 45-07 
 
 192.63 
 
 0.325 
 
 0.319 4252 
 
 9494 
 
 18 18 06. 19 
 
 195.83 
 
 0.375 
 
 0.366 5078 
 
 9336 
 
 20 59 57.67 
 
 192.57 
 
 .326 
 
 .320 3745 
 
 9491 
 
 18 21 21.99 
 
 195.77 
 
 .376 
 
 .367 4413 
 
 9332 
 
 21 O3 IO.20 
 
 192.50 
 
 .327 
 
 .321 3235 
 
 9488 
 
 18 24 37.72 
 
 195.71 
 
 377 
 
 .368 3743 
 
 9329 
 
 21 O6 22.66 
 
 192.43 
 
 .328 
 
 .322 2721 
 
 0485 
 
 18 27 53.40 
 
 195.65 
 
 .378 
 
 .369 3071 
 
 9326 
 
 21 09 35.05 
 
 192.36 
 
 .329 
 
 .323 2205 
 
 9482 
 
 18 31 09.02 
 
 195.58 
 
 .379 
 
 370 2395 
 
 9322 
 
 21 12 47.38 
 
 192.29 
 
 0.330 
 
 0.324 1686 
 
 9479 
 
 18 34 24.57 
 
 195.52 
 
 0.380 
 
 0.371 1716 
 
 9319 
 
 21 15 59.63 
 
 192.22 
 
 .331 
 
 .325 1163 
 
 9476 
 
 18 37 40.06 
 
 195.46 
 
 .381 
 
 .372 1033 
 
 9316 
 
 21 19 11.82 
 
 192.15 
 
 .332 
 
 .326 0638 
 
 9473 
 
 18 40 55-49 
 
 195.40 
 
 .382 
 
 373 0347 
 
 9312 
 
 21 22 23.93 
 
 192.08 
 
 .333 
 
 .327 ono 
 
 9470 
 
 18 44 10.85 
 
 195.33 
 
 .383 
 
 373 9658 
 
 9309 
 
 21 25 35.97 
 
 I92.OI 
 
 .334 
 
 .327 9578 
 
 9467 
 
 18 47 26.16 
 
 195.27 
 
 .384 
 
 374 8965 
 
 9305 
 
 21 28 47-95 
 
 191.94 
 
 0.335 
 
 0.328 9044 
 
 9464 
 
 18 50 41.40 
 
 195.21 
 
 0.385 
 
 0.375 8268 
 
 9302 
 
 21 31 59.85 
 
 191.87 
 
 .336 
 
 .329 8506 
 
 946i 
 
 18 53 56.57 
 
 195.15 
 
 .386 
 
 376 7569 
 
 9299 
 
 21 35 n.68 
 
 I9I.8O 
 
 337 
 
 330 7965 
 
 9458 
 
 18 57 11.69 
 
 195.08 
 
 .387 
 
 .3776866 
 
 9295 
 
 21 38 23.45 
 
 I9L73 
 
 338 
 
 .331 7422 
 
 9455 
 
 19 oo 26.74 
 
 195.02 
 
 .388 
 
 .378 6159 
 
 9292 
 
 21 41 35.14 
 
 191.66 
 
 339 
 
 .332 6875 
 
 9452 
 
 19 03 41.72 
 
 194.95 
 
 .389 
 
 379 5449 
 
 9288 
 
 21 44 46.76 
 
 I9L59 
 
 0.340 
 
 0.333 6325 
 
 9449 
 
 1-9 06 56.65 
 
 194.89 
 
 0.390 
 
 0.380 4736 
 
 9285 
 
 21 47 58.31 
 
 I9L5I 
 
 341 
 
 334 5772 
 
 9445 
 
 19 10 11.50 
 
 194.83 
 
 391 
 
 .381 4019 
 
 9281 
 
 21 51 09.79 
 
 191.44 
 
 342 
 
 335 52i6 
 
 9442 
 
 19 13 26.30 
 
 194.76 
 
 392 
 
 .382 3299 
 
 9278 
 
 21 54 21. 20 
 
 I9L37 
 
 343 
 
 .336 4657 
 
 9439 
 
 19 16 41.03 
 
 194.70 
 
 393 
 
 .383 2575 
 
 9275 
 
 21 57 32.53 
 
 I9L30 
 
 344 
 
 337 4095 
 
 9436 
 
 19 19 55.70 
 
 194.63 
 
 .394 
 
 .384 1848 
 
 9271 
 
 22 OO 43.80 
 
 I9L23 
 
 0.345 
 .346 
 
 0.338 3529 
 .339 2961 
 
 9433 
 9430 
 
 19 23 10.30 
 19 26 24.84 
 
 194.57 
 194.51 
 
 0.395 
 .396 
 
 0.385 i i 17 
 .386 0383 
 
 9268 
 9264 
 
 22 03 54.99 
 22 O7 O6. I I 
 
 I9I.I6 
 191.09 
 
 347 
 
 .340 2389 
 
 9427 
 
 19 29 39.31 
 
 194.44 
 
 397 
 
 .386 9645 
 
 9261 
 
 22 IO I7.l6 
 
 I9I.OI 
 
 -348 
 
 .341 1814 
 
 9424 
 
 19 32 53-72 
 
 194.38 
 
 .398 
 
 .387 8904 
 
 9257 
 
 22 13 28.14 
 
 190.94 
 
 349 
 
 .342 1236 
 
 9420 
 
 19 36 08.06 
 
 194.31 
 
 399 
 
 .388 8159 
 
 9254 
 
 22 l6 39.04 
 
 190.87 
 
 0.350 
 
 0.343 0655 
 
 9417 
 
 19 39 22.34 
 
 194.25 
 
 0.400 
 
 0.389 74ii 
 
 9250 
 
 22 19 49.88 
 
 190.80 
 
 u 
 
 2 tan-He*)-^ 
 
 w sech u 
 
 ">"-'< 
 
 <sechu 
 
 u 
 
 2t -I 
 
 <sechu 
 
 *,-*** 
 
 < sech u 
 
 SMITHSONIAN TABLES 
 
 279 
 
The Gudermannian. 
 
 u 
 
 gd u 
 
 F ' 
 
 gdu 
 
 F ' 
 
 u 
 
 gd u 
 
 <oF ' 
 
 gd u 
 
 Fo' 
 
 
 
 
 o / // 
 
 // 
 
 
 
 
 / // 
 
 // 
 
 0.400 
 
 0.389 74U 
 
 9250 
 
 22 19 49.88 
 
 I9O.80 
 
 0.450 
 
 0.435- 5388 
 
 9066 
 
 24 57 16.34 
 
 187.01 
 
 .401 
 
 .390 6660 
 
 9247 
 
 22 23 OO.64 
 
 190.72 
 
 451 
 
 .436 4453 
 
 9063 
 
 25 oo 23.31 
 
 186.93 
 
 .402 
 
 391 5904 
 
 9243 
 
 22 26 11.32 
 
 190.65 
 
 452 
 
 437 3514 
 
 9059 
 
 25 03 30.20 
 
 186.85 
 
 .403 
 
 .392 5146 
 
 9240 
 
 22 29 21.94 
 
 190.58 
 
 453 
 
 .438 2571 
 
 9055 
 
 25 06 37.01 
 
 186.77 
 
 .404 
 
 393 4383 
 
 9236 
 
 22 32 32.48 
 
 190.51 
 
 454 
 
 .439 1624 
 
 9051 
 
 25 09 43.74 
 
 186.69 
 
 0.405 
 
 0.394 36l8 
 
 9232 
 
 22 35 42.95 
 
 190.43 
 
 0.455 
 
 0.440 0673 
 
 9047 
 
 25* 12 50.39 
 
 186.61 
 
 .406 
 
 .395 2848 
 
 9229 
 
 22 38 53-35 
 
 190.36 
 
 .456 
 
 .440 9718 
 
 9043 
 
 25 15 56.96 
 
 186.53 
 
 .407 
 
 .396 2075 
 
 9225 
 
 22 42 03.67 
 
 190.29 
 
 457 
 
 .441 8759 
 
 9040 
 
 25 19 03.46 
 
 186.45 
 
 .408 
 
 .397 1299 
 
 9222 
 
 22 45 13.92 
 
 190.21 
 
 .458 
 
 442 7797 
 
 9036 
 
 25 22 09.87 
 
 186.37 
 
 .409 
 
 .398 0519 
 
 9218 
 
 22 48 24.09 
 
 190.14 
 
 459 
 
 443 6831 
 
 9032 
 
 25 25 16.20 
 
 186.29 
 
 0.410 
 
 0.398 9735 
 
 9215 
 
 22 51 34.19 
 
 190.06 
 
 0.460 
 
 0.444 586i 
 
 9028 
 
 25 28 22.46 
 
 186.21 
 
 .411 
 
 .399 8948 
 
 9211 
 
 22 54 44-22 
 
 189.99 
 
 .461 
 
 .445 4886 
 
 9024 
 
 25 31 28.63 
 
 186.13 
 
 .412 
 
 .400 8157 
 
 9207 
 
 22 57 54-lS 
 
 189.92 
 
 .462 
 
 .446 3909 
 
 9020 
 
 25 34 34.72 
 
 186.05 
 
 .413 
 
 .401 7363 
 
 9204 
 
 23 01 04.06 
 
 189.84 
 
 .463 
 
 .447 2927 
 
 9016 
 
 25 37 40.74 
 
 185.97 
 
 .414 
 
 .402 6565 
 
 9200 
 
 23 04 13.86 
 
 189.77 
 
 .464 
 
 .448 1941 
 
 9012 
 
 25 40 46.67 
 
 185.89 
 
 0.415 
 
 0.403 5763 
 
 9197 
 
 23 07 23.59 
 
 189.69 
 
 0.465 
 
 0.449 0951 
 
 9008 
 
 25 43 52.52 
 
 185.81 
 
 .416 
 
 .404 4958 
 
 9193 
 
 23 10 33-25 
 
 189.62 
 
 .466 
 
 .449 9958 
 
 9004 
 
 25 46 58.29 
 
 185-73 
 
 .417 
 
 .405 4M9 
 
 9189 
 
 23 13 42.83 
 
 189.54 
 
 .467 
 
 .450 8060 
 
 9001 
 
 25 50 03.98 
 
 185.65 
 
 .418 
 
 .406 3337 
 
 9186 
 
 23 16 52-. 34 
 
 189.47 
 
 .468 
 
 .451 7959 
 
 8997 
 
 25 53 09.59 
 
 185-57 
 
 .419 
 
 .407 2521 
 
 9182 
 
 23 20 01.77 
 
 189.39 
 
 .469 
 
 .452 0954 
 
 8993 
 
 25 56 15.12 
 
 185.49 
 
 0.420 
 
 0.408 1701 
 
 9178 
 
 23 23 11.13 
 
 189.32 
 
 0.470 
 
 0.453 5944 
 
 8989 
 
 25 59 20.57 
 
 185.41 
 
 .421 
 
 .409 0878 
 
 9175 
 
 23 26 20.41 
 
 189.24 
 
 .471 
 
 454 4931 
 
 8985 
 
 26 02 25.93 
 
 185.33 
 
 .422 
 
 .410 0051 
 
 9171 
 
 23 29 29.62 
 
 I89.I7 
 
 .472 
 
 .455 39M 
 
 8581 
 
 26 05 31.22 
 
 185.24 
 
 .423 
 
 .410 9220 
 
 9168 
 
 23 32 38.75 
 
 189.09 
 
 473 
 
 .456 2893 
 
 8977 
 
 26 08 36.42 
 
 185.16 
 
 .424 
 
 .411 8386 
 
 9164 
 
 23 35 47.8i 
 
 189.02 
 
 .474 
 
 .457 1868 
 
 8973 
 
 26 ii 41-54 
 
 185.08 
 
 0.425 
 
 0.412 7548 
 
 9160 
 
 23 38 56.79 
 
 188.04 
 
 0.475 
 
 0.458 0839 
 
 8969 
 
 26 14 46.58 
 
 185.00 
 
 .426 
 
 .413 6706 
 
 9157 
 
 23 42 05.69 
 
 188.87 
 
 .476 
 
 .4589806 
 
 8965 
 
 26 17 51-54 
 
 184.92 
 
 .427 
 
 .414 5861 
 
 9153 
 
 23 45 14.52 
 
 188.79 
 
 477 
 
 .459 8/69 
 
 8961 
 
 26 20 56.42 
 
 184.84 
 
 .428 
 
 .415 5012 
 
 9149 
 
 23 48 23.27 
 
 188.71 
 
 .478 
 
 .460 7728 
 
 8957 
 
 26 24 OI.2I 
 
 184.75 
 
 .429 
 
 .416 4159 
 
 ^9145 
 
 23 51 31-95 
 
 188.64 
 
 479 
 
 .461 6683 
 
 8953 
 
 26 27 05.93 
 
 184.67 
 
 0.430 
 
 0.417 3303 
 
 9142 
 
 23 54 40.55 
 
 188.56 
 
 0.480 
 
 0.462 5634 
 
 8949 
 
 26 3O IO.56 
 
 184.59 
 
 .431 
 
 .418 2443 
 
 9138 
 
 23 57 49-07 
 
 188.49 
 
 .481 
 
 .463 4581 
 
 8945 
 
 26 33 15.10 
 
 184.51 
 
 .432 
 
 .419 1579 
 
 9U4 
 
 24 oo 57-52, 188.41 
 
 .482 
 
 .464 3524 
 
 8941 
 
 26 36 19.57 
 
 184.42 
 
 433 
 
 .420 0711 
 
 9131 
 
 24 04 05.89 188.33 
 
 .483 
 
 .465 2464 
 
 8937 
 
 26 39 23.95 
 
 184.34 
 
 434 
 
 .420 9840 
 
 9127 
 
 24 07 14.18 
 
 188.26 
 
 .484 
 
 .466 1399 
 
 8933 
 
 26 42 28.25 
 
 184.26 
 
 0.435 
 
 0.421 8965 
 
 9123 
 
 24 10 22.40 
 
 188.18 
 
 0.485 
 
 0.467 0330 
 
 8929 
 
 26 45 32.47 
 
 184.18 
 
 .436 
 
 .422 8086 
 
 9119 
 
 24 13 30.54 188.10 
 
 .485 
 
 .467 9257 
 
 8925 
 
 26 48 36.60 
 
 184.09 
 
 437 
 
 .423 7204 
 
 9116 
 
 24 16 38.60 
 
 188.02 
 
 ' .487 
 
 .468 8180 
 
 8921 
 
 26 51 40.65 
 
 184.01 
 
 .438 
 
 .424 6318 
 
 9112 
 
 24 19 46.59 
 
 187.95 
 
 .488 
 
 .469 7099 
 
 8917 
 
 26 54 44-62 
 
 183.93 
 
 439 
 
 .425 5428 
 
 9108 
 
 24 22 54.50 
 
 187.87 
 
 .489 
 
 .470 6014 
 
 8913 
 
 26 57 48.50 
 
 183.84 
 
 0.440 
 
 0.426 4534 
 
 9104 
 
 24 26 02.33 
 
 187.79 
 
 0.400 
 
 0.471 4925 
 
 8909 
 
 27 oo 52.31 
 
 183.76 
 
 .441 
 
 .427 3636 
 
 9101 24 29 10.08 
 
 187.71 
 
 49' 
 
 472 3832 
 
 8905 
 
 27 03 56.02 
 
 183.68 
 
 .442 
 
 .428 2735 
 
 9097 24 32 17.75 
 
 187.64 
 
 .492 
 
 473 2735 
 
 8901 
 
 27 06 59.66 
 
 183.59 
 
 443 
 
 .429 1830 
 
 9093 24 35 25.35 
 
 187.56 
 
 493 
 
 474 1633 
 
 8897 
 
 27 10 03.21 
 
 183.51 
 
 .444 
 
 .430 0921 
 
 9089 
 
 24 38 32.87 
 
 187.48 
 
 .494 
 
 .475 0528 
 
 SX<J3 
 
 27 13 06.68 
 
 183.42 
 
 0.445 
 
 0.431 0009 
 
 9085 
 
 24 41 40.31 
 
 187.40 
 
 0.495 
 
 0.475 9419 
 
 8889 
 
 27 16 10.06 
 
 183.34 
 
 .446 
 
 .431 9092 
 
 9082 24 44 47.67 
 
 187.32 
 
 .496 
 
 .476 8305 
 
 8885 
 
 27 19 13.36 
 
 183.26 
 
 447 
 
 .432 8172 
 
 9078 24 47 54.96 
 
 187.24 
 
 497 
 
 477 7i88 
 
 8880 
 
 27 22 16.57 
 
 183.17 
 
 .433 7248 
 
 9074 24 51 02.16 
 
 187.17 
 
 .498 
 
 .478 6066 
 
 8876 
 
 27 25 19.70 
 
 183.09 
 
 449 
 
 .434 6320 
 
 9070 
 
 24 54 09.29 
 
 187.09 
 
 499 
 
 .479 4941 
 
 8872 
 
 27 28 22.75 
 
 183.00 
 
 0.450 
 
 0.435 5388 
 
 9066 
 
 24 57 16.34 
 
 187.01 
 
 0.500 
 
 0.480 3811 
 
 8868 
 
 27 31 25.71 
 
 182.92 
 
 u 
 
 2Um-'<e)-* 
 
 usechu 
 
 2 Un-'(e u )-90- 
 
 "techu 
 
 u 
 
 2tan-'(e)-J 
 
 <*>sechu 
 
 2tan-'(c)-90 
 
 <> sech u 
 
 SMITHSONIAN TABLES 
 
 280 
 
The Gudermannian. 
 
 u 
 
 gdu 
 
 Fo' 
 
 gdu 
 
 F ' 
 
 u 
 
 gd u 
 
 a.Fo' 
 
 gdu 
 
 F ' 
 
 
 
 
 o / // 
 
 // 
 
 
 
 
 o / // 
 
 // 
 
 0.500 
 
 0.480 3811 
 
 8868 
 
 27 31 25.71 
 
 182.92 
 
 0.550 
 
 0.524 1996 
 
 8657 
 
 30 02 03.92 
 
 178.57 
 
 .501 
 
 .481 2677 
 
 8864 
 
 27 34 28.59 
 
 182.83 
 
 551 
 
 .525 0651 
 
 8653 
 
 30 05 02.45 
 
 178.48 
 
 .502 
 
 .482 1539 
 
 8860 
 
 27 37 31.38 
 
 182.75 
 
 552 
 
 .525 9302 
 
 8649 
 
 30 08 00.88 
 
 178.39 
 
 .503 
 
 .483 0397 
 
 8856 
 
 27 40 34.09 
 
 182.67 
 
 553 
 
 .526 7948 
 
 8644 
 
 30 10 59.23 
 
 178.30 
 
 .504 
 
 483 9251 
 
 8852 
 
 27 43 36.71 
 
 182.58 
 
 554 
 
 .527 6590 
 
 8640 
 
 30 13 57.48 
 
 178.21 
 
 0.505 
 
 0.484 8100 
 
 8848 
 
 27 46 39.25 
 
 182.50 
 
 0.555 
 
 0.528 5228 
 
 8636 
 
 30 16 55.65 
 
 178.12 
 
 .506 
 
 .485 6946 
 
 8844 
 
 27 49 41.70 
 
 182.41 
 
 556 
 
 .529 386i 
 
 8631 
 
 30 19 53.72 
 
 178.03 
 
 .507 
 
 .486 5787 
 
 8839 
 
 27 52 44.07 
 
 182.33 
 
 .557 
 
 .530 2490 
 
 8627 
 
 30 22 51.71 
 
 177.94 
 
 .508 
 
 .487 4625 
 
 8835 
 
 27 55 46.35 
 
 182.24 
 
 .558 
 
 531 HIS 
 
 8622 
 
 30 25 49.60 
 
 177.85 
 
 .509 
 
 .488 3458 
 
 8831 
 
 27 58 48.55 
 
 182.15 
 
 559 
 
 531 9735 
 
 8618 
 
 30 28 47.41 
 
 177.76 
 
 0.510 
 
 0.489 2287 
 
 8827 
 
 28 oi 50.66 
 
 182.07 
 
 0.560 
 
 0.532 8351 
 
 8614 
 
 30 31 45-12 
 
 177.67 
 
 .511 
 
 .490 I I 12 
 
 8823 
 
 28 04 52.69 
 
 181.98 
 
 .561 
 
 .533 6962 
 
 8609 
 
 30 34 42.75 
 
 177.58 
 
 .512 
 
 .490 9933 
 
 8819 
 
 28 07 54.63 
 
 181.90 
 
 .562 
 
 534 5569 
 
 8605 
 
 30 37 40.28 
 
 177.49 
 
 .513 
 
 .491 8749 
 
 8814 
 
 28 10 56.48 
 
 181.81 
 
 563 
 
 535 4172 
 
 8601 
 
 30 40 37.73 
 
 177.40 
 
 .514 
 
 .492 7562 
 
 8810 
 
 28 13 58.25 
 
 181.73 
 
 .564 
 
 .536 2771 
 
 8596 
 
 30 43 35.08 
 
 177.31 
 
 0.515 
 
 0.493 6370 
 
 8806 
 
 28 16 59-94 
 
 181.64 
 
 0.565 
 
 0.537 1365 
 
 8592 
 
 30 46 32.35 
 
 177.22 
 
 .516 
 
 .494 5174 
 
 8802 
 
 28 20 01.53 
 
 i8i.55 
 
 .566 
 
 .537 9954 
 
 8587 
 
 30 49 29.52 
 
 177.13 
 
 .517 
 
 495 3974 
 
 8798 
 
 28 23 03.04 
 
 181.47 
 
 .567 
 
 .538 8539 
 
 8583 
 
 30 52 26.60 
 
 177.04 
 
 .518 
 
 .496 2769 
 
 8794 
 
 28 26 04.47 
 
 181.38 
 
 .568 
 
 .539 7120 
 
 8579 
 
 30 55 23.59 
 
 176.95 
 
 .519 
 
 .497 1561 
 
 8789 
 
 28 29 05.81 
 
 181.29 
 
 .569 
 
 .540 5696 
 
 8574 
 
 30 58 20.49 
 
 176.85 
 
 0.520 
 
 0.498 0348 
 
 8785 
 
 28 32 07.06 
 
 181.21 
 
 0.570 
 
 0.541 4268 
 
 8570 
 
 31 oi 17.30 
 
 176.76 
 
 .521 
 
 .498 9131 
 
 8781 
 
 28 35 08.22 
 
 181.12 
 
 571 
 
 .542 2836 
 
 8565 
 
 31 04 14.02 
 
 176.67 
 
 .522 
 
 .499 7910 
 
 8777 
 
 28 38 09.30 
 
 181.04 
 
 572 
 
 543 1399 
 
 8561 
 
 31 07 10.65 
 
 176.58 
 
 .523 
 
 .500 6685 
 
 8773 
 
 28 41 10.29 
 
 180.95 
 
 573 
 
 .543 9958 
 
 8556 
 
 31 10 07.18 
 
 176.49 
 
 .524 
 
 501 5456 
 
 8768 
 
 28 44 11.20 
 
 180.86 
 
 574 
 
 .544 8512 
 
 8552 
 
 31 13 03.63 
 
 176.40 
 
 0.525 
 
 0.502 4222 
 
 8764 
 
 28 47 12. oi 
 
 180.77 
 
 0.575 
 
 0.545 7062 
 
 8548 
 
 31 15 59.98 
 
 176.31 
 
 .526 
 
 .503 2984 
 
 8760 
 
 28 50 12.75 
 
 180.69 
 
 .576 
 
 .546 5607 
 
 8543 
 
 31 18 56.24 
 
 176.22 
 
 .527 
 
 .504 1742 
 
 8756 
 
 28 53 13.39 
 
 180.60 
 
 577 
 
 .547 4148 
 
 8539 
 
 31 21 52.41 
 
 176.12 
 
 .528 
 
 .505 0495 
 
 8752 
 
 28 56 13-95 
 
 180.51 
 
 .578 
 
 .548 2685 
 
 8534 
 
 31 24 48.49 
 
 176.03 
 
 .529 
 
 505 9245 
 
 8747 
 
 28 59 14.41 
 
 180.43 
 
 579 
 
 .549 1217 
 
 8530 
 
 31 27 44-47 
 
 175.94 
 
 0.530 
 
 0.506 7990 
 
 8743 
 
 29 02 14.80 
 
 180.34 
 
 0.580 
 
 0.549 9744 
 
 8525 
 
 31 30 40.37 
 
 175.85 
 
 .531 
 
 .507 6731 
 
 8739 
 
 29 05 15.09 
 
 180.25 
 
 .581 
 
 .550 8267 
 
 8521 
 
 31 33 36.17 
 
 175.76 
 
 .532 
 
 .508 5468 
 
 8735 
 
 29 08 15.30 
 
 180.16 
 
 .582 
 
 .551 6786 
 
 8516 
 
 31 36 31.88 
 
 175-66 
 
 533 
 
 .509 4200 
 
 8730 
 
 29 ii 15.42 
 
 180.07 
 
 .583 
 
 552 5300 
 
 8512 
 
 31 39 27.50 
 
 175.57 
 
 -534 
 
 .510 2928 
 
 8726 
 
 29 14 15.45 
 
 179.99 
 
 .584 
 
 553 3810 
 
 8508 
 
 31 42 23.03 
 
 175.48 
 
 0.535 
 
 0.511 1652 
 
 8722 
 
 29 17 15.39 
 
 179.90 
 
 0.585 
 
 0.554 2315 
 
 8503 
 
 3'i 45 18.46 
 
 175.39 
 
 .536 
 
 .512 0372 
 
 8717 
 
 29 20 15.24 
 
 179.81 
 
 .586 
 
 -555 0816 
 
 8499 
 
 31 48 13.80 
 
 175.30 
 
 537 
 
 .512 9087 
 
 8713 
 
 29 23 15.01 
 
 179.72 
 
 .587 
 
 555 9313 
 
 8494 
 
 31 51 09.05 
 
 175.20 
 
 .538 
 
 .513 7798 
 
 8709 
 
 29 26 14.69 
 
 179.63 
 
 .588 
 
 .556 7804 
 
 8490 
 
 31 54 04.21 
 
 I75.II 
 
 539 
 
 .514 6505 
 
 8705 
 
 29 29 14.28 
 
 179.55 
 
 .589 
 
 557 6292 
 
 8485 
 
 31 56 59.27 
 
 175.02 
 
 0.540 
 
 0.515 5207 
 
 8700 
 
 29 32 13-78 
 
 179.46 
 
 0.590 
 
 0.558 4775 
 
 8481 
 
 31 59 54.25 
 
 174.93 
 
 541 
 
 .516 3905 
 
 8696 
 
 29 35 13-20 
 
 179.37 
 
 591 
 
 559 3253 
 
 8476 
 
 32 02 49. 13 
 
 174.83 
 
 542 
 
 .517 2599 
 
 8692 
 
 29 38 12.52 
 
 179.28 
 
 .592 
 
 .560 1727 
 
 8472 
 
 32 05 43.91 
 
 174.74 
 
 .543 
 
 .518 1289 
 
 8687 
 
 29 41 11.76 
 
 179.19 
 
 593 
 
 .561 0196 
 
 8467 
 
 32 08 38.61 
 
 174.65 
 
 544 
 
 5i8 9974 
 
 8683 
 
 29 44 10.91 
 
 179. 10 
 
 .594 
 
 .561 8661 
 
 8463 
 
 32 ii 33.21 
 
 174-55 
 
 o>-545 
 
 0.519 8655 
 
 8679 
 
 29 47 09.96 
 
 179.01 
 
 0.595 
 
 0.562.7122 
 
 8458 
 
 32 14 27.71 
 
 174.46 
 
 .546 
 
 .520 7332 
 
 8675 
 
 29 50 08.93 
 
 178.93 
 
 .596 
 
 063 5577 
 
 8454 
 
 32 17 22.13 
 
 174.37 
 
 .547 
 
 .521 6004 
 
 8670 
 
 29 53 07.81 
 
 178.84 
 
 597 
 
 .564 4029 
 
 8449 
 
 32 20 16.45 
 
 174.27 
 
 .548 
 
 .522 4673 
 
 8666 
 
 29 56 06. 61 
 
 178.75 
 
 .598 
 
 .565 2476 
 
 8445 
 
 32 23 10.68 
 
 174-18 
 
 549 
 
 .523 3336 
 
 8662 
 
 29 59 05.31 
 
 178.66 
 
 599 
 
 .566 0918 
 
 8440 
 
 32 26 04.81 
 
 174.09 
 
 0.550 
 
 0.524 1996 
 
 8657 
 
 30 02 03.92 
 
 178.57 
 
 0.6oo 
 
 0.566 9356 
 
 8436 
 
 32 28 58.85 
 
 173.99 
 
 u 
 
 2tan-Ke)~ 
 
 <> sech u 
 
 2tan- 1 (e)-90 
 
 w sech u 
 
 u 
 
 2 tan-He")-^ 
 
 wsechu 
 
 Ztan-Keuh-SO 
 
 u> sech u 
 
 MITHSONIAN TABLES 
 
 28l 
 
The Gudermannian. 
 
 u 
 
 gd u 
 
 F ' 
 
 gd u 
 
 F ' 
 
 u 
 
 gdu 
 
 O.FO' 
 
 gdu 
 
 Fo' 
 
 
 
 
 / // 
 
 M 
 
 
 
 
 
 
 0.600 
 
 0.566 9356 
 
 8436 
 
 32 28 58.85 
 
 173.99 
 
 0.650 
 
 0.6o8 5398 
 
 8205 
 
 34 52 00.34 
 
 169.24 
 
 .601 
 
 .567 7789 
 
 8431 
 
 32 31 52.80 
 
 173.90 
 
 .651 
 
 .609 3600 
 
 8200 
 
 34 54 49.52 
 
 169.14 
 
 .002 
 
 .568 6218 
 
 8426 
 
 32 34 46.66 
 
 I73.8I 
 
 .652 
 
 .610 1708 
 
 8195 
 
 34 57 38.62 
 
 169.04 
 
 .003 
 
 .569 4642 
 
 8422 
 
 32 37 40.42 
 
 173.71 
 
 .653 
 
 .610 9991 
 
 8191 
 
 35 oo 27.61 
 
 168.95 
 
 .004 
 
 570 3061 
 
 8417 
 
 32 40 34.09 
 
 173.62 
 
 .654 
 
 .6ll 8179 
 
 8186 
 
 35 03 16.51 
 
 168.85 
 
 0.605 
 
 0.571 1476 
 
 8413 
 
 32 43 27.66 
 
 173.53 
 
 0.655 
 
 0.612 6363 
 
 8181 
 
 35 06 05.31 
 
 168.75 
 
 .606 
 
 .571 9887 
 
 8408 
 
 32 46 21.14 
 
 173-43 
 
 .656 
 
 .613 4542 
 
 8i77 
 
 35 08 54-01 
 
 168.66 
 
 .607 
 
 .572 8293 
 
 8404 
 
 32 49 14.52 
 
 173.34 
 
 .657 
 
 .614 2716 
 
 8172 
 
 35 u 42.62 
 
 168.56 
 
 .608 
 
 573 6694 
 
 8399 
 
 32 52 07.82 
 
 173.24 
 
 .658 
 
 .615 0886 
 
 8167 
 
 35 14 3LI3 
 
 168.46 
 
 .609 
 
 574 5091 
 
 8395 
 
 32 55 01.01 
 
 173.15 
 
 .659 
 
 .615 9051 
 
 8163 
 
 35 17 19-54 
 
 168.36 
 
 0.610 
 
 0.575 3484 
 
 8390 
 
 32 57 54.12 
 
 173.06 
 
 0.660 
 
 0.616 7211 
 
 8158 
 
 35 20 07.86 
 
 168.27 
 
 .611 
 
 .576 1871 
 
 8385 
 
 33 oo 47.13 
 
 172.96 
 
 .661 
 
 .617 5366 
 
 8i53 
 
 35 22 56.08 
 
 168.17 
 
 .612 
 
 577 0255 
 
 8381 
 
 33 03 40.04 
 
 172.87 
 
 .662 
 
 .618 3517 
 
 8148 
 
 35 25 44.20 
 
 168.07 
 
 .613 
 
 .577 8633 
 
 8376 
 
 33 06 32.86 
 
 172.77 
 
 .663 
 
 .619 1663 
 
 8144 
 
 35 28 32.22 
 
 167.97 
 
 .614 
 
 .578 7007 
 
 8372 
 
 33 09 25.59 
 
 172.68 
 
 .664 
 
 .619 9804 
 
 8i39 
 
 35 31 20.14 
 
 167.88 
 
 0.615 
 
 0.579 5377 
 
 8367 
 
 33 12 18.22 
 
 172.59 
 
 0.665 
 
 0.620 7041 
 
 8134 
 
 35 34 07.97 
 
 167.78 
 
 .616 
 
 .580 3741 
 
 8363 
 
 33 15 10.76 
 
 172.49 
 
 .666 
 
 .621 6073 
 
 8129 
 
 35 36 55.70 
 
 167.68 
 
 .617 
 
 .581 2IO2 
 
 8358 
 
 33 18 03.20 
 
 172.40 
 
 .667 
 
 .622 4200 
 
 8125 
 
 35 39 43-34 
 
 167.58 
 
 .618 
 
 .582 0457 
 
 8353 
 
 33 20 55.55 
 
 172.30 
 
 .668 
 
 .623 2322 
 
 8120 
 
 35 42 30.87 
 
 167.49 
 
 .619 
 
 .582 8809 
 
 8349 
 
 33 23 47.81 
 
 172.21 
 
 .669 
 
 .624 0440 
 
 8115 
 
 35 45 18.31 
 
 167.39 
 
 0.620 
 
 0.583 7155 
 
 8344 
 
 33 26 39.97 
 
 172.11 
 
 0.670 
 
 0.624 8553 
 
 8110 
 
 35 48 05.65 
 
 167.29 
 
 .621 
 
 .584 5497 
 
 8340 
 
 33 29 32.03 
 
 172.02 
 
 .671 
 
 .625 6661 
 
 8106 
 
 35 50 52.89 
 
 167.19 
 
 .622 
 
 085 3834 
 
 8335 
 
 33 32 24.00 
 
 171.92 
 
 .672 
 
 .626 4764 
 
 8101 
 
 35 53 40.03 
 
 167.09 
 
 .623 
 
 .586 2167 
 
 8330 
 
 33 35 J5-87 
 
 171.83 
 
 .673 
 
 .627 2863 
 
 8096 
 
 35 56 27.08 
 
 167.00 
 
 .624 
 
 087 0495 
 
 8326 
 
 33 38 07.65 
 
 I7L73 
 
 .674 
 
 .628 0956 
 
 8091 
 
 35 59 14.03 
 
 166.90 
 
 0.625 
 
 0.587 8819 
 
 8321 
 
 33 40 59-34 
 
 171.64 
 
 0.675 
 
 0.628 9046 
 
 8087 
 
 36 02 00.88 
 
 166.83 
 
 .626 
 
 .588 7137 
 
 8317 
 
 33 43 50.93 
 
 I7L54 
 
 .676 
 
 .629 7130 
 
 8082 
 
 36 04 47.63 
 
 166.70 
 
 .627 
 
 089 5452 
 
 8312 
 
 33 46 42.42 
 
 I7L45 
 
 .677 
 
 .630 5209 
 
 8077 
 
 36 07 34.28 
 
 166.60 
 
 .628 
 
 .500 3761 
 
 8307 
 
 33 49 33-82 
 
 I7L35 
 
 .678 
 
 .631 3284 
 
 8072 
 
 36 10 20.84 
 
 166.51 
 
 .629 
 
 .591 2066 
 
 8303 
 
 33 52 25.12 
 
 171.26 
 
 .679 
 
 632 1354 
 
 8068 
 
 36 13 07.29 
 
 166.41 
 
 0.630 
 
 0.592 0367 
 
 8298 
 
 33 55 16.33 
 
 171.16 
 
 0.680 
 
 0.632 9420 
 
 8063 
 
 36 15 53.65 
 
 166.31 
 
 .631 
 
 .592 8662 
 
 8293 
 
 33 58 07.44 
 
 171.06 
 
 .681 
 
 .633 748o 
 
 8058 
 
 36 18 39.91 
 
 166.21 
 
 .632 
 
 593 6954 
 
 8289 
 
 34 oo 58.46 
 
 170.97 
 
 .682 
 
 .634 5536 
 
 8053 
 
 36 21 26.07 
 
 166.11 
 
 .633 
 
 .594 5240 
 
 8284 
 
 34 03 49.38 
 
 170.87 
 
 .683 
 
 .635 3587 
 
 8049 
 
 36 24 12.14 
 
 166.01 
 
 634 
 
 595 3522 
 
 8280 
 
 34 06 40.20 
 
 170.78 
 
 .684 
 
 .636 1633 
 
 8044 
 
 36 26 58.10 
 
 165.92 
 
 0.635 
 
 0.596 1799 
 
 8275 
 
 34 09 30.93 
 
 170.68 
 
 0.685 
 
 0.636 9675 
 
 8039 
 
 36 29 43-97 
 
 165.82 
 
 .636 
 
 597 0072 
 
 8270 
 
 34 12 21.56 
 
 170.59 
 
 .686 
 
 637 77ii 
 
 8034 
 
 36 32 29.74 
 
 165.72 
 
 .637 
 
 597 8339 
 
 8266 
 
 34 15 12.10 
 
 170.49 
 
 .687 
 
 638 5743 
 
 8029 
 
 36 35 I5.4I 
 
 165.62 
 
 .638 
 
 .5986603 
 
 8261 
 
 34 18 02.54 
 
 170.39 
 
 .688 
 
 639 3770 
 
 8025 
 
 36 38 00.98 
 
 165.52 
 
 639 
 
 .599 486i 
 
 8256 
 
 34 20 52.89 
 
 170.30 
 
 .689 
 
 .640 1792 
 
 8020 
 
 36 40 46.45 
 
 165.42 
 
 0.640 
 
 0.600 3115 
 
 8252 
 
 34 23 43.14 
 
 I/0.2O 
 
 0.600 
 
 0.640 9810 
 
 8015 
 
 36 43 31.82 
 
 165.32 
 
 .641 
 
 .601 1364 
 
 8247 
 
 34 26 33.29 
 
 I/O. II 
 
 .691 
 
 .641 7823 
 
 8010 
 
 36 46 17-09 
 
 165.22 
 
 .642 
 
 .601 9609 
 
 8242 
 
 34 29 23.35 
 
 170.01 
 
 .692 
 
 .642 5830 
 
 8006 
 
 36 49 02.27 
 
 165.13 
 
 .643 
 
 .602 7849 
 
 8238 
 
 34 32 13.31 
 
 169.91 
 
 .693 
 
 .643 3834 
 
 8001 
 
 36 51 47.34 
 
 165.03 
 
 .644 
 
 .603 6084 
 
 8233 
 
 34 35 03.17 
 
 169.82 
 
 .694 
 
 .644 1832 
 
 7996 
 
 36 54 3-'- 32 
 
 164.93 
 
 0.645 
 
 0.604 4315 
 
 8228 
 
 34 37 52.04 
 
 169.72 
 
 0.695 
 
 0.644 9825 
 
 799i 
 
 36 57 17-20 
 
 164.83 
 
 .646 
 
 .605 2541 
 
 8224 
 
 34 40 42.61 
 
 169.62 
 
 .696 
 
 .645 7814 
 
 7986 
 
 37 oo 01.98 
 
 164.73 
 
 .647 
 
 .606 0762 
 
 8219 
 
 34 43 32.19 
 
 169.53 
 
 .697 
 
 .646 5798 
 
 798i 
 
 37 02 46.66 
 
 164.63 
 
 .648 
 
 .606 8979 
 
 8214 
 
 34 46 21.67 
 
 169.43 
 
 .698 
 
 647 3777 
 
 7977 
 
 37 05 31. -'4 
 
 164.53 
 
 .649 
 
 .607 7190 
 
 8210 
 
 34 49 H.05 
 
 169.33 
 
 .699 
 
 .648 1751 
 
 7972 
 
 37 08 15-7-' 
 
 164.43 
 
 0.650 
 
 0.608 5398 
 
 8205 
 
 34 52 00.34 
 
 169.24 
 
 0.700 
 
 0.648 9721 
 
 7967 
 
 37 u 00.10 
 
 164.33 
 
 u 
 
 2ton-'(e)~ 
 
 < sech u 
 
 Ztan-Keuh-SO 
 
 M sech u 
 
 u 
 
 2 ton-He")- g 
 
 -sechu 
 
 2tan-'(e)-9ff> 
 
 ' sech u 
 
 SMITHSONIAN TABLES 
 
 282 
 
The Gudermannian. 
 
 I 
 
 gd u 
 
 F ' 
 
 gdu 
 
 <>Fu' 
 
 u 
 
 gdu 
 
 "Fo' 
 
 gd u 
 
 F ' 
 
 
 
 
 / // 
 
 /7 
 
 
 
 
 o y // 
 
 // 
 
 0.700 
 
 0.648 9721 
 
 7967 
 
 37 ii 00.10 
 
 164.33 
 
 0.750 
 
 0.688 2014 
 
 7724 
 
 39 25 51.72 
 
 159.32 
 
 .701 
 
 .649 7685 
 
 7962 
 
 37 13 44.38 
 
 164.23 
 
 751 
 
 .688 9735 
 
 7719 
 
 39 28 30.98 
 
 159.22 
 
 .702 
 
 .650 5645 
 
 7957 
 
 37 16 28.57 
 
 164.13 
 
 752 
 
 .689 7451 
 
 7714 
 
 39 31 10.15 
 
 159.11 
 
 .703 
 
 .651 3600 
 
 7953 
 
 37 19 12.65 
 
 164.03 
 
 .753 
 
 .690 5163 
 
 7709 
 
 39 33 49-21 
 
 159.01 
 
 .704 
 
 .652 1550 
 
 7948 
 
 37 21 56.63 
 
 163.93 
 
 754 
 
 .691 2870 
 
 7704 
 
 39 36 28.18 
 
 158.91 
 
 0.705 
 
 0.652 9496 
 
 7943 
 
 37 24 40.52 
 
 163.84 
 
 0.755 
 
 0.692 0572 
 
 7699 
 
 39 39 07.04 
 
 158.81 
 
 .706 
 
 .653 7436 
 
 7938 
 
 37 27 24.31 
 
 163.74 
 
 .756 
 
 .692 8269 
 
 7694 
 
 39 41 45.80 
 
 158.71 
 
 .707 
 
 .654 5372 
 
 7933 
 
 37 30 07-99 
 
 163.64 
 
 757 
 
 693 596i 
 
 7690 
 
 39 44 24.46 
 
 158.61 
 
 .708 
 
 .655 3303 
 
 7928 
 
 37 32 51.58 
 
 163.54 
 
 .758 
 
 .694 3648 
 
 7685 
 
 39 47 03.01 
 
 158.51 
 
 .709 
 
 .656 1229 
 
 7924 
 
 37 35 35.o6 
 
 163.44 
 
 759 
 
 .695 1330 
 
 7680 
 
 39 49 41.47 
 
 158.40 
 
 0.710 
 
 0.656 9150 
 
 7919 
 
 37 38 18.45 
 
 163.34 
 
 0.760 
 
 0.695 9007 
 
 7675 
 
 39 52 19-82 
 
 158.30 
 
 .711 
 
 .657 7067 
 
 79U 
 
 37 41 01.74 
 
 163.24 
 
 .761 
 
 .6966679 
 
 7670 
 
 39 54 58.07 
 
 158.20 
 
 .712 
 
 .658 4978 
 
 7909 
 
 37 43 44.92 
 
 163 . 14 
 
 .762 
 
 .697 4347 
 
 7665 
 
 39 57 36.23 
 
 158.10 
 
 .713 
 
 .659 2885 
 
 7904 
 
 37 46 28.01 
 
 163.04 
 
 .763 
 
 .698 2009 
 
 7660 
 
 40 oo 14.28 
 
 158.00 
 
 .714 
 
 .660 0787 
 
 7899 
 
 37 49 11.00 
 
 162.94 
 
 .764 
 
 .6989667 
 
 7655 
 
 40 02 52.22 
 
 157.90 
 
 0.715 
 
 0.660 8684 
 
 7895 
 
 37 51 53.89 
 
 162.84 
 
 0.765 
 
 0.699 7319 
 
 7650 
 
 40 05 30.07 
 
 157.80 
 
 .716 
 
 .661 6576 
 
 7890 
 
 37 54 36.68 
 
 162.74 
 
 .766 
 
 .700 4967 
 
 7645 
 
 40 08 07.81 
 
 157.69 
 
 .717 
 
 .662 4463 
 
 7885 
 
 37 57 19.36 
 
 162.64 
 
 .767 
 
 .701 2610 
 
 7640 
 
 40 10 45.46 
 
 157.59 
 
 .718 
 
 .663 2346 
 
 7880 
 
 38 oo 01.95 
 
 162.54 
 
 .768 
 
 .702 0248 
 
 7635 
 
 40 13 23.00 
 
 157.49 
 
 .719 
 
 .664 0223 
 
 7875 
 
 38 02 44.44 
 
 162.44 
 
 .769 
 
 .702 7880 
 
 7630 
 
 40 16 00.44 
 
 157.39 
 
 0.720 
 
 0.664 8096 
 
 7870 
 
 38 05 26.83 
 
 162.34 
 
 0.770 
 
 0.703 5508 
 
 7625 
 
 40 18 37.78 
 
 157.29 
 
 .721 
 
 .665 5964 
 
 7865 
 
 38 08 09.11 
 
 162.24 
 
 .771 
 
 .704 3131 
 
 7620 40 21 15.01 
 
 157.19 
 
 .722 
 
 .666 3827 
 
 7861 
 
 38 10 51.30 
 
 162.14 
 
 772 
 
 70S 0750 
 
 76l6 
 
 40 23 52.15 
 
 157.08 
 
 .723 
 
 .667 1685 
 
 7856 
 
 38 13 33-39 
 
 162.04 
 
 773 
 
 .705 8363 
 
 76ll 
 
 40 26 29.18 
 
 156.08 
 
 .724 
 
 667 9539 
 
 7851 
 
 38 16 15.37 
 
 I6I.94 
 
 774 
 
 .706 5971 
 
 7606 
 
 40 29 06. i i 
 
 156.88 
 
 0.725 
 
 0.668 7387 
 
 7846 
 
 38 18 57.26 
 
 161.84 
 
 0.775 
 
 0.707 3574 
 
 76OI 
 
 40 31 42.94 
 
 156.78 
 
 .726 
 
 .669 5231 
 
 7841 
 
 38 21 39.05 
 
 161.74 
 
 .776 
 
 .708 1173 
 
 7596 
 
 40 34 19.67 
 
 156.68 
 
 .727 
 
 .670 3069 
 
 7836 
 
 38 24 20.73 
 
 161.64 
 
 .777 
 
 .708 8766 
 
 7591 
 
 40 36 56.29 
 
 156.57 
 
 .728 
 
 .671 0903 
 
 7831 
 
 38 27 02.32 
 
 I6I.54 
 
 .778 
 
 .709 6354 
 
 7586 
 
 40 39 32.82 
 
 156.47 
 
 .729 
 
 .671 8732 
 
 7827 
 
 38 29 43.80 
 
 I6I.43 
 
 .779 
 
 .710 3938 
 
 7581 
 
 40 42 09.24 
 
 156.37 
 
 0.730 
 
 0.672 6556 
 
 7822 
 
 38 32 25.19 
 
 161.33 
 
 0.780 
 
 0.711 1516 
 
 7576 
 
 40 44 45.56 
 
 156.27 
 
 .731 
 
 .673 4376 
 
 78i7 
 
 38 35 06.47 
 
 l6l.23 
 
 .781 
 
 .711 9090 
 
 7571 
 
 40 47 21.77 
 
 156.17 
 
 .732 
 
 .674 2190 
 
 7812 
 
 38 37 47.65 
 
 l6l.I3 
 
 .782 
 
 .712 6659 
 
 7566 
 
 40 49 57.89 
 
 156.06 
 
 733 
 
 .675 oooo 
 
 7807 
 
 38 40 28.74 
 
 161.03 
 
 .783 
 
 .713 4223 
 
 756i 
 
 40 52 33-90 
 
 155-96 
 
 734 
 
 .675 7804 
 
 7802 
 
 38 43 09.72 
 
 160.93 
 
 .784 
 
 .714 1781 
 
 7556 
 
 40 55 09.81 
 
 155.86 
 
 0.735 
 
 0.676 5604 
 
 7797 
 
 38 45 50.60 
 
 160.83 
 
 0.785 
 
 0.714 9335 
 
 7551 
 
 40 57 45.62 
 
 155.76 
 
 .736 
 
 .677 3399 
 
 7792 
 
 38 48 31.38 
 
 160.73 
 
 .786 
 
 .715 6884 
 
 7546 
 
 41 oo 21.33 
 
 155-66 
 
 .737 
 
 .678 1189 
 
 7788 
 
 38 51 12.06 
 
 160.63 
 
 .787 
 
 .716 4428 
 
 7541 
 
 41 02 56.94 
 
 155-55 
 
 .738 
 
 .678 8974 
 
 7783 
 
 38 53 52.64 
 
 160.53 
 
 .788 
 
 .717 1967 
 
 7537 
 
 41 05 32.44 
 
 155.45 
 
 739 
 
 .679 6754 
 
 7778 
 
 38 56 33-12 
 
 100.43 
 
 .789 
 
 .717 9501 
 
 7532 
 
 41 08 07.84 
 
 155.35 
 
 0.740 
 
 0.680 4530 
 
 7773 
 
 38 59 13.50 
 
 160.33 
 
 0.790 
 
 0.718 7030 
 
 7527 
 
 41 10 43.14 
 
 155.25 
 
 .741 
 
 .681 2300 
 
 7768 
 
 39 oi 53.77 
 
 160.23 
 
 791 
 
 .719 4554 
 
 7522 
 
 4i 13 18.33 
 
 155.15 
 
 .742 
 
 .682 0065 
 
 7763 
 
 39 04 33-95 
 
 160.13 
 
 792 
 
 .720 2073 
 
 7517 
 
 41 15 53-43 
 
 155.04 
 
 743 
 
 .682 7826 
 
 7758 
 
 39 07 14-02 
 
 l6o.O2 
 
 793 
 
 .720 9588 
 
 7512 
 
 41 18 28.42 
 
 154.94 
 
 744 
 
 .683 5582 
 
 7753 
 
 39 09 54.00 
 
 159.92 
 
 .794 
 
 .721 7097 
 
 7507 
 
 41 21 03.31 
 
 154.84 
 
 0.745 
 
 0.684 3333 
 
 7748 
 
 39 12 33.87 
 
 159.82 
 
 0.795 
 
 0.722 4601 
 
 7502 
 
 41 23 38.10 
 
 154.74 
 
 .746 
 
 .685 1079 
 
 7744 
 
 39 15 13.64 
 
 159.72 
 
 .796 
 
 .723 2101 
 
 7497 
 
 41 26 12.78 
 
 154.63 
 
 .747 
 
 .685 8820 
 
 7739 
 
 39 17 53.31 
 
 159.62 
 
 .797 
 
 .723 9595 
 
 7492 
 
 41 28 47.36 
 
 154.53 
 
 .748 
 
 .686 6556 
 
 7734 
 
 39 20 32.88 
 
 159.52 
 
 .798 
 
 .724 7084 
 
 7487 
 
 41 31 21.84 
 
 154.43 
 
 749 
 
 .687 4287 
 
 7729 
 
 39 23 12.35 
 
 159.42 
 
 799 
 
 .725 4569 
 
 7482 
 
 41 33 56.22 
 
 154.33 
 
 0.750 
 
 0.688 2014 
 
 7724 
 
 39 25 51.72 
 
 159.32 
 
 0.800 
 
 0.726 2048 
 
 7477 
 
 41 36 30.50 
 
 154-22 
 
 u 
 
 2tan-Ke)-| 
 
 cosechu 
 
 Zten-W-go 
 
 wsechu 
 
 u 
 
 2tan-'(e u )~ 
 
 wsechu 
 
 Ztan-Keuh-SO 
 
 w sech u 
 
 SMITHSONIAN TABLES 
 
 283 
 
The Gudermannian. 
 
 u 
 
 gdu 
 
 -FO' 
 
 gd u 
 
 .* 
 
 u 
 
 gdu 
 
 F O ' 
 
 gdu 
 
 F ' 
 
 
 
 
 / // 
 
 m 
 
 
 
 
 o / // 
 
 M 
 
 0.800 
 
 0.726 2048 
 
 7477 
 
 41 36 30.50 
 
 154-22 
 
 0.850 
 
 0.762 9677 
 
 7228 
 
 43 42 53.38 
 
 149.09 
 
 .801 
 
 .726 9523 
 
 7472 
 
 41 39 04.67 
 
 154.12 
 
 .851 
 
 .763 6902 
 
 7223 
 
 43 45 22.41 
 
 148.98 
 
 .802 
 
 .727 6992 
 
 7467 
 
 41 41 38.74 
 
 154.02 
 
 .852 
 
 .764 4122 
 
 7218 
 
 43 47 51-34 
 
 148.88 
 
 .803 
 
 .728 4457 
 
 7462 
 
 41 44 12.71 
 
 153.92 
 
 .853 
 
 .765 1338 
 
 7213 
 
 43 50 20.17 
 
 148.78 
 
 .804 
 
 .729 1916 
 
 7457 
 
 41 46 46.57 
 
 153.81 
 
 .854 
 
 .765 8548 
 
 7208 
 
 43 52 48.89 
 
 148.67 
 
 0.805 
 
 0.729 9371 
 
 7452 
 
 41 49 20.34 
 
 153.71 
 
 0.855 
 
 0.766 5754 
 
 7203 
 
 43 55 17.52 
 
 148.57 
 
 .806 
 
 .730 6821 
 
 7447 
 
 41 51 54-00 
 
 I53.6I 
 
 .856 
 
 767 2954 
 
 7198 
 
 43 57 46.04 
 
 148.47 
 
 .807 
 
 .731 4266 
 
 7442 
 
 41 54 27.56 
 
 153.51 
 
 .857 
 
 .768 0149 
 
 7193 
 
 44 oo 14.45 
 
 148.36 
 
 .808 
 
 732 1705 
 
 7437 
 
 41 57 01.01 
 
 153.40 
 
 .858 
 
 .768 7340 
 
 7188 
 
 44 02 42.76 
 
 148.26 
 
 .809 
 
 .732 9140 
 
 7432 
 
 41 59 34.36 
 
 153.30 
 
 .859 
 
 .769 4525 
 
 7183 
 
 44 05 10.97 
 
 148.16 
 
 0.810 
 
 0.733 6570 
 
 7427 
 
 42 02 07.62 
 
 153.20 
 
 0.860 
 
 0.770 1706 
 
 7178 
 
 44 07 39.o8 
 
 148.06 
 
 .811 
 
 .734 3995 
 
 7422 
 
 42 04 40.76 
 
 I53-IO 
 
 .861 
 
 .770 8881 
 
 7173 
 
 44 10 07.08 
 
 147.95 
 
 .812 
 
 .735 UU 
 
 7417 
 
 42 07 13.81 
 
 152.99 
 
 .862 
 
 .771 6051 7168 
 
 44 12 34.98 
 
 147.85 
 
 .813 
 
 .735 8829 
 
 7412 
 
 42 09 46.75 
 
 152.89 
 
 .863 
 
 .772 3217 7163 
 
 44 15 02.78 
 
 147-75 
 
 .814 
 
 .736 6239 
 
 7407 
 
 42 12 19.59 
 
 152.79 
 
 .864 
 
 .773 0377 
 
 7158 
 
 44 17 30.48 
 
 147-64 
 
 0.815 
 
 0.737 3644 
 
 7402 
 
 42 14 52.33 
 
 152.69 
 
 0.865 
 
 0.773 7533 
 
 7153 
 
 44 19 58.07 
 
 147-54 
 
 .816 
 
 .738 1044 
 
 7397 
 
 42 17 24.96 
 
 152.58 
 
 .866 
 
 .774 4683 
 
 7148 
 
 44 22 25.56 
 
 147-44 
 
 .817 
 
 .738 8439 
 
 7392 
 
 42 19 57.50 
 
 152.48 
 
 .867 
 
 775 1829 
 
 7143 
 
 44 24 52.94 
 
 147-33 
 
 .818 
 
 .739 5829 
 
 7387 
 
 42 22 29-93 
 
 152.38 
 
 .868 
 
 775 8969 
 
 7138 
 
 44 27 20.22 
 
 147.23 
 
 .819 
 
 .740 3214 
 
 7383 
 
 42 25 O2.25 
 
 152.28 
 
 .869 
 
 .776 6104 
 
 7133 
 
 44 29 47.40 
 
 147.13 
 
 0.820 
 
 0.741 0594 
 
 7378 
 
 42 27 34.48 
 
 152.. 17 
 
 0.870 
 
 0.777 3235 
 
 7128 
 
 44 32 14-48 
 
 147-02 
 
 .821 
 
 .741 7969 
 
 7373 
 
 42 30 O6.6O 
 
 152.07 
 
 .871 
 
 .778 0360 
 
 7123 
 
 44 34 41.45 
 
 146.92 
 
 .822 
 
 .742 5339 
 
 7368 
 
 42 32 38.62 
 
 151.97 
 
 .872 
 
 .778 7481 
 
 7118 
 
 44 37 08.32 
 
 146.82 
 
 .823 
 
 .743 2704 
 
 7363 
 
 42 35 10.53 
 
 151.86 
 
 .873 
 
 779 4596 
 
 7113 
 
 44 39 35.09 
 
 146.71 
 
 .824 
 
 .744 0064 
 
 7358 
 
 42 37 42.34 
 
 151.76 
 
 .874 
 
 .780 1707 
 
 7108 
 
 44 42 01.75 
 
 146.61 
 
 0.825 
 
 0.744 7420 
 
 7353 
 
 42 40 14.05 
 
 151.66 
 
 0.875 
 
 0.780 8812 
 
 7103 
 
 44 44 28.31 
 
 146.51 
 
 .826 
 
 745 4770 
 
 7348 
 
 42 42 45.66 
 
 I5L56 
 
 .876 
 
 .781 5912 
 
 7098 
 
 44 46 54-77 
 
 146.41 
 
 .827 
 
 .746 2115 
 
 7343 
 
 42 45 17.17 
 
 I5L45 
 
 .877 
 
 .782 3008 
 
 7093 
 
 44 49 21.12 
 
 146.30 
 
 .828 
 
 .746 9455 
 
 7338 
 
 42 47 48.57 
 
 I5L35 
 
 .878 
 
 .783 0008 
 
 7088 
 
 44 51 47.37 
 
 146.20 
 
 .829 
 
 .747 6790 
 
 7333 
 
 42 50 19.87 
 
 I5L25 
 
 .879 
 
 .783 7184 
 
 7083 
 
 44 54 13.52 
 
 146. 10 
 
 0.830 
 
 0.748 4120 
 
 7328 
 
 42 52 51.06 
 
 I5LI4 
 
 0.880 
 
 0.784 4264 
 
 7078 
 
 44 56 39.56 
 
 145.99 
 
 .831 
 
 .749 1446 
 
 7323 
 
 42 55 22.16 
 
 151.04 
 
 .881 
 
 .785 1340 
 
 7073 
 
 44 59 05.50 
 
 145.89 
 
 .832 
 
 749 8766 
 
 73i8 
 
 42 57 53-15 
 
 150.94 
 
 .882 
 
 .785 8410 
 
 7068 
 
 45 oi 31.34 
 
 145.79 
 
 .833 
 
 .750 6081 
 
 7313 
 
 43 oo 24.04 
 
 150.84 
 
 .883 
 
 .786 5476 
 
 7063 
 
 45 03 57.o8 
 
 145.68 
 
 .834 
 
 .751 3391 
 
 7308 
 
 43 02 54.82 
 
 150.73 
 
 .884 
 
 .787 2536 
 
 7058 
 
 45 06 22.71 
 
 145.58 
 
 0.835 
 
 0.752 0697 
 
 7303 
 
 43 05 25.50 
 
 150.63 
 
 0.885 
 
 0.787 9591 
 
 7053 
 
 45 08 48.24 
 
 145.48 
 
 .836 
 
 752 7997 
 
 7298 
 
 43 07 56.08 
 
 150.53 
 
 .886 
 
 .788 6642 
 
 7048 
 
 45 u 13-66 
 
 145.37 
 
 .837 
 
 .753 5292 
 
 7293 
 
 43 10 26.56 
 
 150.42 
 
 .887 
 
 .789 3687 
 
 7043 
 
 45 13 38.59 
 
 145.27 
 
 .838 
 
 754 2582 
 
 7288 
 
 43 12 56.93 
 
 150.32 
 
 .888 
 
 .790 0728 
 
 7038 
 
 45 16 04.21 
 
 145.17 
 
 1 .839 
 
 .7549868 
 
 7283 
 
 43 15 27.20 
 
 150.22 
 
 .889 
 
 .790 7763 
 
 7033 
 
 45 18 29.32 
 
 145.06 
 
 0.840 
 
 0.755 7148 
 
 7278 
 
 43 17 57.37 
 
 150.12 
 
 0.890 
 
 0.791 4794 
 
 7028 
 
 45 20 54-34 
 
 144.96 
 
 .841 
 
 .756 4423 
 
 
 43 20 27.43 
 
 150.01 
 
 .891 
 
 .792 1819 
 
 7023 
 
 45 23 19.25 
 
 144.86 
 
 .842 
 
 757 1694 
 
 7268 
 
 43 22 57.39 
 
 149.91 
 
 .892 
 
 .792 8839 
 
 7018 
 
 45 25 44.05 
 
 144.76 
 
 .843 
 
 .757 8959 
 
 7263 
 
 43 25 27.25 
 
 149.81 
 
 .893 
 
 .793 5855 
 
 7013 
 
 45 28 08.76 
 
 144.65 
 
 .844 
 
 .758 6219 
 
 7258 
 
 43 27 57.01 
 
 149.70 
 
 .894 
 
 .794 2865 
 
 7008 
 
 45 30 33.36 
 
 144.55 
 
 0.845 
 .846 
 
 0.759 3475 
 .760 0725 
 
 7248 
 
 43 30 26.66 
 43 32 56.21 
 
 149.60 
 149.50 
 
 0.895 
 .896 
 
 0.794 9871 
 .795 6871 
 
 7003 
 6998 
 
 45 32 57.85 
 45 35 22.25 
 
 144.45 
 
 144.34 
 
 .847 
 .848 
 
 .760 7970 
 .761 5211 
 
 7238 
 
 43 35 25.65 
 43 37 55.00 
 
 149.39 
 149.29 
 
 
 .796 3867 
 .797 0857 
 
 6993 
 6988 
 
 45 37 46.54 
 45 40 10.73 
 
 144.24 
 144.14 
 
 .849 
 
 .762 2446 
 
 7233 
 
 43 40 24.24 
 
 149.19 
 
 .899 
 
 797 7843 
 
 6983 
 
 45 42 34.81 
 
 144.03 
 
 0.850 
 
 0.762 9677 
 
 7228 
 
 43 42 53.38 
 
 149.09 
 
 0.900 
 
 0.798 4823 
 
 6978 
 
 45 44 58.80 
 
 143.93 
 
 - 
 
 2 tan-He") -j 
 
 wsechu 
 
 2tan-'(e)-90 2 
 
 <> sech u 
 
 u 
 
 2 *"-'<">-i 
 
 wsechu 
 
 2 tan-He" )-90 
 
 < sech u 
 
 SMITHSONIAN TABLES 
 
 284 
 
The Gude rmannian. 
 
 
 
 gd u 
 
 F ' 
 
 gdu 
 
 oF ' 
 
 u 
 
 gdu 
 
 ->F O ' 
 
 gdu 
 
 Fo' 
 
 0.900 
 
 0.798 4823 
 
 6978 
 
 o / // 
 
 45 44 58.8o 
 
 143-93 
 
 * 
 
 0.950 
 
 0.832 7479 
 
 6728 
 
 47 42 46.58 
 
 I 38*78 
 
 .901 
 
 799 1798 
 
 0973 
 
 45 47 22.67 
 
 143.83 
 
 .951 
 
 .833 4205 
 
 6723 
 
 47 45 05.31 
 
 138. 68 
 
 .902 
 
 799 8769 
 
 6968 
 
 45 49 46.45 
 
 143.72 
 
 .952 
 
 .834 0926 
 
 6719 
 
 47 47 23.94 
 
 138.58 
 
 .903 
 
 .800 5734 
 
 6963 
 
 45 52 10.12 
 
 143.62 
 
 .953 
 
 .834 7642 
 
 6714 
 
 47 49 42.47 
 
 138.48 
 
 .904 
 
 .801 2695 
 
 6958 
 
 45 54 33.69 
 
 143.52 
 
 .954 
 
 .835 4353 
 
 6709 
 
 47 52 00.89 
 
 138.37 
 
 0.905 
 
 0.801 9650 
 
 6953 
 
 45 56 57.16 
 
 143.42 
 
 0.955 
 
 0.836 1059 
 
 6704 
 
 47 54 19.22 
 
 138.27 
 
 .906 
 
 .802 6601 
 
 6948 
 
 45 59 20.52 
 
 143.31 
 
 .956 
 
 .836 7700 
 
 6699 
 
 47 56 37.44 
 
 138.17 
 
 .907 
 
 803 3546 
 
 6943 
 
 46 01 43.78 
 
 143.21 
 
 957 
 
 .837 4456 
 
 6694 
 
 47 58 55-55 
 
 138.07 
 
 .908 
 
 .804 0487 
 
 6938 
 
 46 04 06.94 
 
 143 . I I 
 
 .958 
 
 .838 1147 
 
 6689 
 
 48 01 13.57 
 
 137.96 
 
 .909 
 
 .804 7422 
 
 6933 
 
 46 06 30.00 
 
 143-00 
 
 959 
 
 .838 7833 
 
 6684 
 
 48 03 31.48 
 
 137.86 
 
 0.910 
 
 0.805 4353 
 
 6928 
 
 46 08 52.95 
 
 142.90 
 
 0.960 
 
 0.839 4514 
 
 6679 
 
 48 05 49.29 
 
 137.76 
 
 .911 
 
 .806 1278 
 
 6923 
 
 46 ii 15.79 
 
 142.80 
 
 .961 
 
 .840 1191 
 
 6674 
 
 48 08 07.00 
 
 137.66 
 
 .912 
 
 .806 8198 
 
 6918 
 
 46 13 38.54 
 
 142.69 
 
 .962 
 
 .840 7862 
 
 6669 
 
 48 10 24.60 
 
 U7.55 
 
 .913 
 
 .807 5H4 
 
 6913 
 
 46 16 01.18 
 
 142.59 
 
 .963 
 
 .841 4528 
 
 6664 
 
 48 12 42.IO 
 
 137.45 
 
 .914 
 
 .808 2024 
 
 6908 
 
 46 18 23.72 
 
 142.49 
 
 .964 
 
 .842 1190 
 
 6659 
 
 48 14 59-50 
 
 137.35 
 
 0.915 
 
 0.808 8930 
 
 6903 
 
 46 20 46.16 
 
 142.38 
 
 0.965 
 
 0.842 7846 
 
 6654 
 
 48 17 16.80 
 
 137.25 
 
 .916 
 
 809 5830 
 
 6898 
 
 46 23 08.49 
 
 142.28 
 
 .966 
 
 .843 4497 
 
 6649 
 
 48 19 33-99 
 
 137.14 
 
 .917 
 
 .810 2726 
 
 6893 
 
 46 25 30.72 
 
 142.18 
 
 .967 
 
 .844 1144 
 
 6644 
 
 48 21 51.09 
 
 137.04 
 
 .918 
 
 .810 9616 
 
 6888 
 
 46 27 52.85 
 
 142.08 
 
 .968 
 
 .844 7785 
 
 6639 
 
 48 24 08.08 
 
 136.04 
 
 .919 
 
 .811 6502 
 
 6883 
 
 46 30 14.87 
 
 141.97 
 
 .969 
 
 .845 4422 
 
 6634 
 
 48 26 24.96 
 
 136.84 
 
 0.920 
 
 0.812 3383 
 
 6878 
 
 46 32 36.79 
 
 141.87 
 
 0.970 
 
 0.846 1053 
 
 6629 
 
 48 28 41.75 
 
 136.73 
 
 .921 
 
 .813 0258 
 
 6873 
 
 46 34 58.6i 
 
 141.77 
 
 .971 
 
 .846 7680 
 
 6624 
 
 48 30 58.43 
 
 136.63 
 
 .922 
 
 .813 7129 
 
 6868 
 
 46 37 20.33 
 
 141.66 
 
 .972 
 
 .847 4301 
 
 6619 
 
 48 33 I5.oi 
 
 136.53 
 
 .923 
 
 .814 3994 
 
 6863 
 
 46 39 41.94 
 
 141.56 
 
 973 
 
 .848 0918 
 
 6614 
 
 48 35 3L49 
 
 136.43 
 
 .924 
 
 .815 0855 
 
 6858 
 
 46 42 03.45 
 
 141.46 
 
 974 
 
 .848 7530 
 
 6609 
 
 48 37 47.87 
 
 136.32 
 
 0.925 
 
 0.815 7710 
 
 6853 
 
 46 44 24.85 
 
 I4L35 
 
 0.975 
 
 0.849 4136 
 
 6604 
 
 48 40 04.14 
 
 136.22 
 
 .926 
 
 .816 4561 
 
 6848 
 
 46 46 46.16 
 
 141.25 
 
 .976 
 
 .850 0738 
 
 6599 
 
 48 42 20.31 
 
 136.12 
 
 .927 
 
 .817 1406 
 
 6843 
 
 46 49 07.36 
 
 I4LI5 
 
 977 
 
 .850 7335 
 
 6594 
 
 48 44 36.38 
 
 136.02 
 
 .928 
 
 .817 8247 
 
 6838 
 
 46 51 28.45 
 
 141-05 
 
 .978 
 
 .851 3927 
 
 6589 
 
 48 46 52.34 
 
 135.92 
 
 .929 
 
 .818 5083 
 
 6833 
 
 46 53 49-45 
 
 140.94 
 
 979 
 
 .852 0514 
 
 6584 
 
 48 49 08.21 
 
 I35.8I 
 
 0.930 
 
 0.819 1913 
 
 6828 
 
 46 56 10.34 
 
 140.84 
 
 0.980 
 
 0.852 7096 
 
 6579 
 
 48 51 23.97 
 
 135.71 
 
 .931 
 
 .819 8739 
 
 6823 
 
 46 58 31.13 
 
 140.74 
 
 .981 
 
 .853 3673 
 
 6574 
 
 48 53 39.63 
 
 I35.6I 
 
 .932 
 
 .820 5560 
 
 6818 
 
 47 oo 51.81 
 
 140.63 
 
 .982 
 
 .854 0245 
 
 6570 
 
 48 55 55.19 
 
 135.51 
 
 933 
 
 .821 2375 
 
 6813 
 
 47 03 12.40 
 
 140.53 
 
 .983 
 
 .854 6812 
 
 6565 
 
 48 58 10.64 
 
 135.40 
 
 934 
 
 .821 9186 
 
 6808 
 
 47 05 32.88 
 
 140.43 
 
 .984 
 
 .855 3374 
 
 6560 
 
 49 oo 26.00 
 
 135.30 
 
 0.935 
 
 0.822 5092 
 
 6803 
 
 47 07 53.25 
 
 140.33 
 
 0.985 
 
 0.855 9931 
 
 6555 
 
 49 02 41.25 
 
 135.20 
 
 .936 
 
 .823 2792 
 
 6798 
 
 47 10 13.53 
 
 140.22 
 
 .986 
 
 .856 6483 
 
 6550 
 
 49 04 56.40 
 
 135.10 
 
 937 
 
 .823 9588 
 
 6793 
 
 47 12 33.70 
 
 140. 12 
 
 .987 
 
 .857 3030 
 
 545 
 
 49 07 11.44 
 
 135-00 
 
 .938 
 
 .824 6379 
 
 6788 
 
 47 14 53.77 
 
 I4O.O2 
 
 .988 
 
 .857 9573 
 
 6540 
 
 49 09 26.39 
 
 134.89 
 
 939 
 
 .825 3164 
 
 6783 
 
 47 17 13-74 
 
 139.91 
 
 .989 
 
 .858 6110 
 
 6535 
 
 49 II 41.23 
 
 134.79 
 
 0.040 
 
 0.825 9945 
 
 6778 
 
 47 19 33.6o 
 
 I39.8I 
 
 0.990 
 
 0.859 2642 
 
 6530 
 
 49 13 55-97 
 
 134.69 
 
 .941 
 
 .826 6721 
 
 6773 
 
 47 21 53.36 
 
 139.71 
 
 .991 
 
 .859 9170 
 
 6525 
 
 49 16 10. 61 
 
 134.59 
 
 .942 
 
 .827 3492 
 
 6768 
 
 47 24 13-02 
 
 I39.6I 
 
 .992 
 
 .860 5692 
 
 6520 
 
 49 1825.15 
 
 134.49 
 
 943 
 
 .828 0257 
 
 6763 
 
 47 26 32.57 
 
 139.50 
 
 .993 
 
 .86l 22IO 
 
 6515 
 
 49 20 39.58 
 
 134.38 
 
 .944 
 
 .828 7018 
 
 6758 
 
 47 28 52.02 
 
 139.40 
 
 .994 
 
 .851 8723 
 
 6510 
 
 49 22 53.92 
 
 134-28 
 
 0.945 
 
 0.829 3774 
 
 6753 
 
 47 31 n.37 
 
 139.30 
 
 0.995 
 
 0.862 5230 
 
 6505 
 
 49 25 08. 15 
 
 I34.I8 
 
 .946 
 
 .830 0525 
 
 6748 
 
 47 33 30.62 
 
 139.20 
 
 .996 
 
 .863 1733 
 
 6500 
 
 49 27 22.28 
 
 135.08 
 
 947 
 
 .830 7271 
 
 6743 
 
 47 35 49.76 
 
 139.09 
 
 997 
 
 .863 8231 
 
 6495 
 
 49 29 36.30 
 
 133.98 
 
 .948 
 
 .831 4012 
 
 6738 
 
 47 38 08.80 
 
 138.99 
 
 .998 
 
 .864 4724 
 
 6490 
 
 49 31 50.23 
 
 133.87 
 
 .949 
 
 .832 0748 
 
 6733 
 
 47 40 27.74 
 
 138.89 
 
 .999 
 
 .865 I i 12 
 
 6485 
 
 49 34 04.05 
 
 133.77 
 
 0.950 
 
 0.832 7479 
 
 6728 
 
 47 42 46.58 
 
 138.78 
 
 I.OOO 
 
 0.865 7695 
 
 6481 
 
 49 36 17.77 
 
 133.67 
 
 u 
 
 2 tan-He*) 
 
 <> sech u 
 
 2lan-(e)-90 
 
 < sech u 
 
 u 
 
 2tan-Ke)- 
 
 < sech u 
 
 Ztan-Ke^-SO 
 
 co sech u 
 
 SMITHSONIAN TABLES 
 
 285 
 
The Gudermannian. 
 
 u 
 
 gdu 
 
 F O ' 
 
 gdu 
 
 F ' 
 
 u 
 
 gdu 
 
 <oF ' 
 
 gdu 
 
 F ' 
 
 1. 000 
 
 0.865 7695 
 
 6481 
 
 49 < V 17-77 
 
 133*67 
 
 1.050 
 
 0.897 5576 
 
 6235 
 
 ox// 
 
 51 25 34.55 
 
 i28?6i 
 
 .001 
 
 .866 4173 
 
 6476 
 
 49 38 31-39 
 
 133.57 
 
 .051 
 
 .808 1809 
 
 6230 
 
 51 27 43.11 
 
 128.51 
 
 .002 
 
 .867 0646 
 
 6471 
 
 49 40 44.91 
 
 133.47 
 
 .052 
 
 .8988037 
 
 6225 
 
 51 29 51.57 
 
 128.41 
 
 .003 
 
 .867 7H4 6466 
 
 49 42 58.33 
 
 133.37 
 
 053 
 
 .899 4260 
 
 6221 
 
 51 31 59.92 
 
 128.31 
 
 .004 
 
 .858 35/8 
 
 6461 
 
 49 45 11.64 
 
 133.26 
 
 054 
 
 .900 0478 
 
 6216 
 
 51 34 08. 18 
 
 128.21 
 
 1.005 
 
 0.869 0036 
 
 6456 
 
 49 47 24.86 
 
 I33.I6 
 
 1.055 
 
 0.900 6691 
 
 6211 
 
 51 36 16.34 
 
 128.11 
 
 .006 
 
 .879 6489 
 
 6451 
 
 49 49 37.97 
 
 133.06 
 
 .056 
 
 .901 2900 
 
 6206 
 
 51 38 24.40 
 
 128.01 
 
 .007 
 
 .870 2938 
 
 6446 
 
 49 5i 50.98 
 
 132.06 
 
 .057 
 
 .901 9103 
 
 62OI 
 
 51 40 32.36 
 
 127.91 
 
 .008 
 
 .870 9381 
 
 6441 
 
 49 54 03.89 
 
 132.86 
 
 .058 
 
 .802 5302 
 
 6196 
 
 51 42 40.21 
 
 127.81 
 
 .009 
 
 .871 5820 
 
 6436 
 
 49 56 16.69 
 
 132.76 
 
 .059 
 
 .903 1496 
 
 6191 
 
 51 44 47-97 
 
 127.71 
 
 I.OIO 
 
 0.872 2254 
 
 6431 
 
 49 58 29.40 
 
 132.65 
 
 i. 060 
 
 0.903 7685 
 
 6187 
 
 51 46 55.63 
 
 127.61 
 
 .Oil 
 
 .872 8682 
 
 6426 
 
 50 oo 42.00 
 
 132.55 
 
 .061 
 
 .904 3869 
 
 6l82 
 
 51 49 03.18 
 
 127.51 
 
 .012 
 
 .873 5io6 
 
 6421 
 
 50 02 54.50 
 
 132.45 
 
 .052 
 
 .905 0048 
 
 6177 
 
 51 51 10.64 
 
 127.41 
 
 .013 
 
 .874 1525 
 
 6416 
 
 50 05 06.90 
 
 132.35 
 
 .063 
 
 .905 6222 
 
 6172 
 
 51 53 18.00 
 
 127.31 
 
 .014 
 
 874 7939 
 
 6412 
 
 50 07 19.20 
 
 I32.25 
 
 .064 
 
 .906 2392 
 
 6167 
 
 51 55 25.25 
 
 127.21 
 
 1.015 
 
 0.875 4348 
 
 6407 
 
 50 09 31.40 
 
 132.15 
 
 1.065 
 
 0.906 8557 
 
 6162 
 
 51 57 32.41 
 
 127.11 
 
 .016 
 
 .876 0752 i 6402 
 
 50 ii 43.49 
 
 132.04 
 
 .066 
 
 907 47i6 
 
 6157 
 
 51 59 39.46 
 
 127.01 
 
 .017 
 
 .876 7152 1 6397 
 
 50 13 55-49 
 
 I3L94 
 
 .o5 7 
 
 .908 0871 
 
 6153 
 
 52 oi 46.42 
 
 126.91 
 
 .018 
 
 .877 3546 
 
 6392 
 
 50 16 07.38 
 
 131.84 
 
 .o58 
 
 .908 7022 
 
 6148 
 
 52 03 53-27 
 
 126.81 
 
 .019 
 
 .877 9936 
 
 6387 
 
 50 18 19.17 
 
 131.74 
 
 .069 
 
 .909 3167 
 
 6143 
 
 52 06 00.03 
 
 126.71 
 
 I.O2O 
 
 0.878 6320 
 
 6382 
 
 50 20 30.86 
 
 131.64 
 
 1.070 
 
 0.909 9307 
 
 6138 
 
 52 08 06.68 
 
 126.61 
 
 .021 
 
 .879 2700 
 
 6377 
 
 50 22 42.45 
 
 I3L54 
 
 .071 
 
 .910 5443 
 
 6133 
 
 52 10 13.24 
 
 126.51 
 
 .022 
 
 .879 9074 
 
 6372 
 
 50 24 53-94 
 
 131.44 
 
 .072 
 
 .911 1574 
 
 6128 
 
 52 12 19.70 
 
 126.41 
 
 .023 
 
 .880 5444 
 
 6367 
 
 50 27 05.32 
 
 I3L34 
 
 .073 
 
 .911 7699 
 
 6123 
 
 52 14 26.05 
 
 126.31 
 
 .024 
 
 .881 1809 
 
 6362 
 
 50 29 16.61 
 
 I3L23 
 
 .074 
 
 .912 3821 
 
 6118 
 
 52 16 32.31 
 
 126.21 
 
 1.025 
 
 0.881 8169 
 
 6357 
 
 50 31 27.79 
 
 I3LI3 
 
 1.075 
 
 0.912 9937 
 
 6114 
 
 52 18 38.46 
 
 126.11 
 
 .026 
 
 .882 4524 
 
 6353 
 
 50 33 38.87 
 
 I3L03 
 
 .076 
 
 .913 6048 
 
 6109 
 
 52 20 44-52 
 
 126.01 
 
 .027 
 
 .883 0874 
 
 6348 
 
 50 35 49.85 
 
 130.93 
 
 .077 
 
 .914 2155 
 
 6104 
 
 52 22 50.48 
 
 125.91 
 
 .028 
 
 .883 7219 
 
 6343 
 
 50 38 00.73 
 
 130.83 
 
 .078 
 
 .914 8256 
 
 6009 
 
 52 24 56.33 
 
 125.81 
 
 .029 
 
 .8843560 
 
 6338 
 
 50 40 11.51 
 
 130.73 
 
 .079 
 
 .915 4353 
 
 6094 
 
 52 27 02.09 
 
 125.71' 
 
 1.030 
 
 0.884 9895 
 
 6333 
 
 50 42 22 . 19 
 
 130.63 
 
 1.080 
 
 0.916 0445 
 
 6090 
 
 52 29 07.75 
 
 125.61 
 
 .031 
 
 .885 6226 
 
 6328 
 
 50 44 32.76 
 
 130.53 
 
 .081 
 
 .916 6532 
 
 6085 
 
 52 31 13.30 
 
 125-51 
 
 .032 
 
 .886 2551 
 
 6323 
 
 50 46 43-24 
 
 130.42 
 
 .082 
 
 .917 2615 
 
 6080 
 
 52 33 18.76 
 
 125.41 
 
 .033 
 
 .886 8872 
 
 6318 
 
 50 48 53.6i 
 
 130.32 
 
 .083 
 
 .917 8692 
 
 6075 
 
 52 35 24.12 
 
 125.31 
 
 .034 
 
 .887 5188 
 
 6313 
 
 50 51 03.89 
 
 130.22 
 
 .084 
 
 .918 4765 
 
 6070 
 
 52 37 29.38 
 
 125.21 
 
 1.035 
 
 0.888 1499 
 
 6308 
 
 50 53 14.06 
 
 I3O.I2 
 
 1.085 
 
 0.919 0833 
 
 6065 
 
 52 39 34-54 
 
 125.11 
 
 .036 
 
 .888 7805 
 
 6304 
 
 50 55 24.13 
 
 I3O.02 
 
 .086 
 
 .919 6896 
 
 6061 
 
 52 41 39-60 
 
 125.01 
 
 .037 
 
 .889 4106 
 
 6299 
 
 50 57 34-10 
 
 129.92 
 
 .087 
 
 .920 2954 
 
 6056 
 
 52 43 44.56 
 
 124.91 
 
 .038 
 
 .890 0402 
 
 
 50 59 43-97 
 
 129.82 
 
 .088 
 
 .920 9008 
 
 6051 
 
 52 45 49-42 
 
 124.81 
 
 039 
 
 .8906693 
 
 6289 
 
 51 oi 53-74 
 
 129.72 
 
 .089 
 
 .921 5056 
 
 6046 
 
 52 47 54-18 
 
 124.71 
 
 1.040 
 
 0.891 2980 
 
 6284 
 
 51 04 03.41 
 
 129.62 
 
 1.090 
 
 0.922 iioo 
 
 6041 
 
 52 49 58.85 
 
 124.61 
 
 .041 
 
 .891 9262 6279 
 
 51 06 12.98 
 
 129.52 
 
 .091 
 
 .922 7139 
 
 6037 
 
 52 52 03.41 
 
 124.51 
 
 .042 
 
 .892 5538 6274 
 
 51 08 22.44 
 
 129.42 
 
 .092 
 
 .923 3173 
 
 6032 
 
 52 54 07.87 
 
 124.41 
 
 043 
 
 .893 1810 
 
 6269 
 
 51 10 31.81 
 
 129.32 
 
 .093 
 
 .923 9203 
 
 6027 
 
 52 56 12.24 
 
 I _\; . 
 
 .044 
 
 .893 8077 
 
 6264 
 
 51 12 41.07 
 
 129.21 
 
 .094 
 
 .924 5227 
 
 6022 
 
 52 58 16.50 
 
 124.22 
 
 1.045 
 
 0.804 4339 
 
 6260 
 
 51 14 50.24 
 
 I29.II 
 
 1.095 
 
 0.925 1247 
 
 6017 
 
 53 00 20.67 
 
 124.12 
 
 .046 
 
 .895 0596 
 
 6255 
 
 51 16 59.30 
 
 129.01 
 
 .006 
 
 .925 7262 
 
 6013 
 
 53 02 24.74 
 
 124.02 
 
 .047 
 
 .895 6848 
 
 6250 
 
 51 19 08.26 
 
 128.91 
 
 .097 
 
 .926 3272 
 
 6008 
 
 53 04 28.70 
 
 123.92 
 
 .048 
 
 .8963096 
 
 6245 
 
 51 21 17.12 
 
 I28.8I 
 
 .098 
 
 .926 9278 
 
 6003 
 
 53 06 32.57 
 
 123.82 
 
 .049 
 
 .896 9338 
 
 6240 
 
 51 23 25.88 
 
 128.71 
 
 .099 
 
 .927 5278 
 
 5998 
 
 53 08 36.34 
 
 U3*M 
 
 1.050 
 
 0.897 5576 
 
 6235 
 
 5i 25 34-55 
 
 I28.6I 
 
 1. 100 
 
 0.928 1274 
 
 5993 
 
 53 10 40.01 
 
 123.62 
 
 u 
 
 2tan-'(e)~ 
 
 < sech u 
 
 2tan- 1 (e)-90 
 
 usech u 
 
 u 
 
 2tan- 1 (e)~ 
 
 wsechu 
 
 2 tan-He") -90 
 
 < sech u 
 
 SMITHSONIAN TABLES 
 
 286 
 
The Gudermannian. 
 
 u 
 
 gdu 
 
 o>Fo' 
 
 gdu 
 
 F</ ' 
 
 u 
 
 gdu 
 
 Fo' 
 
 gdu 
 
 F < 
 
 
 
 
 / // 
 
 // 
 
 
 
 
 o / // 
 
 // 
 
 I. TOO 
 
 0.928 1274 
 
 5993 
 
 53 10 40.01 
 
 123.62 
 
 I.I50 
 
 0.957 498o 
 
 5756 
 
 54 51 38.15 
 
 118.72 
 
 .IOI 
 
 .928 7265 
 
 5989 
 
 53 12 43.59 
 
 123.52 
 
 151 
 
 .958 0734 
 
 5751 
 
 54 53 36.82 
 
 118.62 
 
 .IO2 
 
 .929 3251 
 
 5984 
 
 53 14 47.06 
 
 123.42 
 
 .152 
 
 .958 6482 
 
 5746 
 
 54 55 35-39 
 
 118.53 
 
 .103 
 
 .929 9232 
 
 5979 
 
 53 16 50.43 
 
 123.32 
 
 .153 
 
 .559 2226 
 
 5742 
 
 54 57 33.87 
 
 118.43 
 
 .104 
 
 .930 5209 
 
 5974 
 
 53 18 53-71 
 
 123.23 
 
 154 
 
 959 7965 
 
 5737 
 
 54 59 32.25 
 
 118.33 
 
 1. 105 
 
 0.931 1181 
 
 59^9 
 
 53 20 56.89 
 
 123.13 
 
 1. 155 
 
 0.960 3700 
 
 5732 
 
 55 oi 30.53 
 
 II8.23 
 
 .106 
 
 .931 7148 
 
 5965 
 
 53 22 59.96 
 
 123.03 
 
 .156 
 
 .960 9430 
 
 5727 
 
 55 03 28.72 
 
 118.14 
 
 .107 
 
 .932 3110 
 
 5960 
 
 53 25 02.94 
 
 122.93 
 
 .157 
 
 961 5155 
 
 5723 
 
 55 05 26.81 
 
 118.04 
 
 .108 
 
 .932 9067 
 
 5955 
 
 53 27 05.82 
 
 122.83 
 
 .158 
 
 .962 0875 
 
 57i8 
 
 55 07 24.80 
 
 117.94 
 
 .109 
 
 .933 5020 
 
 5950 
 
 53 29 08.60 
 
 122.73 
 
 .159 
 
 .962 6591 
 
 5713 
 
 55 09 22.69 
 
 H7.85 
 
 I. IIO 
 
 0.934 0968 
 
 5945 
 
 53 31 11.29 
 
 122.63 
 
 1.160 
 
 0.963 2302 
 
 5709 
 
 55 ii 20.49 
 
 117-75 
 
 .in 
 
 .934 6911 
 
 5941 
 
 53 33 13.87 
 
 122.54 
 
 .161 
 
 .963 8008 
 
 5704 
 
 55 13 18.19 
 
 117.65 
 
 .112 
 
 .935 2849 
 
 5936 
 
 53 35 16.36 
 
 122.44 
 
 .162 
 
 .064 37io 
 
 5699 
 
 55 15 I5.8o 
 
 117.56 
 
 .113 
 
 .935 8782 
 
 5931 
 
 53 37 18.75 
 
 122.34 
 
 .163 
 
 .964 9407 
 
 5695 
 
 55 17 13.31 
 
 117.46 
 
 .114 
 
 .936 4711 
 
 5926 
 
 53 39 21.03 
 
 122.24 
 
 .164 
 
 .965 5099 
 
 5690 
 
 55 19 10.72 
 
 117.36 
 
 1. 115 
 
 0.937 0635 
 
 5922 
 
 53 41 23.22 
 
 122.14 
 
 1.165 
 
 0.066 0787 
 
 5685 
 
 55 21 08.04 
 
 117.27 
 
 .116 
 
 937 6554 
 
 5917 
 
 53 43 25.32 
 
 I22.O4 
 
 .166 
 
 .966 6470 
 
 5681 
 
 55 23 05.26 
 
 117.17 
 
 .117 
 
 .938 2469 
 
 5912 
 
 53 45 27.31 
 
 122.94 
 
 .167 
 
 .967 2148 
 
 5676 
 
 55 25 02.38 
 
 117.07 
 
 .118 
 
 .938' 8378 
 
 5907 
 
 53 47 29.21 
 
 121.85 
 
 .168 
 
 .967 7822 
 
 5671 
 
 55 26 59.41 
 
 116.58 
 
 .119 
 
 .939 4283 
 
 5902 
 
 53 49 31.00 
 
 121.75 
 
 .169 
 
 .968 3491 
 
 5667 
 
 55 28 56.34 
 
 116.88 
 
 1. 120 
 
 0.940 0183 
 
 5898 
 
 53 51 32.70 
 
 121.65 
 
 1.170 
 
 0.068 9155 
 
 5662 
 
 55 30 53.17 
 
 116.79 
 
 .121 
 
 .940 6079 
 
 5893 
 
 53 53 34.30 
 
 121.55 
 
 .171 
 
 .969 4815 
 
 5657 
 
 55 32 49-91 
 
 116.69 
 
 .122 
 
 .941 1069 
 
 5888 
 
 53 55 35.8o 
 
 121.45 
 
 .172 
 
 .970 0470 
 
 5653 
 
 55 34 46.55 
 
 116.59 
 
 .123 
 
 .941 7855 
 
 5883 
 
 53 57 37.21 
 
 121.35 
 
 173 
 
 .970 6120 
 
 5648 
 
 55 36 43-10 
 
 116.50 
 
 .124 
 
 942 3736 
 
 5879 
 
 53 59 38.51 
 
 121.26 
 
 .174 
 
 .971 1766 
 
 5643 
 
 55 38 39-54 
 
 116.40 
 
 1. 125 
 
 0.942 9613 
 
 5874 
 
 54 oi 39-72 
 
 121.16 
 
 1. 175 
 
 0.971 7407 
 
 5639 
 
 55 40 35-90 
 
 116.31 
 
 .126 
 
 .943 5484 
 
 5869 
 
 54 03 40.83 
 
 121.06 
 
 .1,76 
 
 972 3043 
 
 5634 
 
 55 42 32.16 
 
 116.21 
 
 .127 
 
 .944 1351 
 
 5864 
 
 54 05 41.84 
 
 120.96 
 
 .177 
 
 .972 8675 
 
 5629 
 
 55 44 28.32 
 
 n6.ii 
 
 .128 
 
 .944 7213 
 
 5860 
 
 54 07 42.76 
 
 120.86 
 
 .178 
 
 973 4301 
 
 5625 
 
 55 46 24.38 
 
 116.02 
 
 .129 
 
 945 3070 
 
 5855 
 
 54 09 43.57 
 
 120.77 
 
 .179 
 
 .973 9924 
 
 5620 
 
 55 48 20.35 
 
 115-92 
 
 1.130 
 
 0.945 8923 
 
 5850 
 
 54 u 44.29 
 
 120.67 
 
 1.180 
 
 0.974 5542 
 
 5615 
 
 55 50 16.22 
 
 115.83 
 
 .131 
 
 .946 4771 
 
 5845 
 
 54 13 44.91 
 
 120.57 
 
 .181 
 
 .975 1155 
 
 5611 
 
 55 52 12.00 
 
 H5.73 
 
 .132 
 
 .947 0614 
 
 5841 
 
 54 15 45.43 
 
 120.47 
 
 .182 
 
 .975 6763 
 
 5606 
 
 55 54 07.68 
 
 115-63 
 
 .133 
 
 .947 6452 
 
 5836 
 
 54 17 45-86 
 
 120.38 
 
 .183 
 
 .976 2367 
 
 5601 
 
 55 56 03.27 
 
 115-54 
 
 .134 
 
 .948 2286 
 
 5831 
 
 54 19 46.18 
 
 120.28 
 
 .184 
 
 .976 7966 
 
 5597 
 
 55 57 58.76 
 
 115.44 
 
 1. 135 
 
 0.948 8115 
 
 5826 
 
 54 21 46.41 
 
 120.18 
 
 1.185 
 
 0.977 356o 
 
 5592 
 
 55 59 54.15 
 
 115-35 
 
 .136 
 
 .949 3939 
 
 5822 
 
 54 23 46.54 
 
 120.08 
 
 .186 
 
 977 9150 
 
 5588 
 
 56 oi 49-45 
 
 115.25 
 
 .137 
 
 .949 9758 
 
 5817 
 
 54 25 46.58 
 
 119.98 
 
 ..187 
 
 .978 4735 
 
 5583 
 
 56 03 44-66 
 
 115.16 
 
 .138 
 
 950 5573 
 
 5812 
 
 54 27 46.51 
 
 119.89 
 
 .188 
 
 .979 0316 
 
 5578 
 
 56 05 39.76 
 
 115.06 
 
 .139 
 
 951 1383 
 
 5807 
 
 54 29 46.35 
 
 H9.79 
 
 .189 
 
 .979 5892 
 
 5574 
 
 56 07 34.78 
 
 114.96 
 
 1.140 
 
 0.951 7188 
 
 5803 
 
 54 31 46.09 
 
 119.69 
 
 1.190 
 
 0.080 1463 
 
 5569 
 
 56 09 29.69 
 
 114.87 
 
 .141 
 
 .952 2588. 
 
 5798 
 
 54 33 45-74 
 
 119.59 
 
 .191 
 
 .980 7030 
 
 5564 
 
 56 ii 24.51 
 
 114.77 
 
 .142 
 
 .952 8784 
 
 5793 
 
 54 35 45.28 
 
 119.50 
 
 .192 
 
 .981 2592 
 
 556o 
 
 56 13 19.24 
 
 114.68 
 
 .143 
 
 .953 4575 
 
 5789 
 
 54 37 44-73 
 
 119.40 
 
 .193 
 
 .981 8149 
 
 5555 
 
 56 15 13-87 
 
 114.58 
 
 .144 
 
 954 0361 
 
 57&4 
 
 54 39 44.08 
 
 119-30 
 
 .194 
 
 .982 3702 
 
 5551 
 
 56 17 08.41 
 
 114.49 
 
 1. 145 
 
 0.954 6143 
 
 5779 
 
 54 4i 43-34 
 
 119.21 
 
 1. 195 
 
 0.982 9251 
 
 5546 
 
 56 19 02.85 
 
 114-39 
 
 .146 
 
 .955 1920 
 
 5775 
 
 54 43 42.49 
 
 119.11 
 
 .196 
 
 .983 4794 
 
 5541 
 
 56 20 57.19 
 
 114.30 
 
 .147 
 
 .955 7692 
 
 5770 
 
 54 45 41.55 
 
 119.01 
 
 .197 
 
 .984 0333 
 
 5537 
 
 56 22 51.44 
 
 114.20 
 
 .148 
 
 .956 3460 
 
 5765 
 
 54 47 40.51 
 
 118.91 
 
 .198 
 
 .984 5868 
 
 5532 
 
 56 24 45.00 
 
 114.11 
 
 .149 
 
 .956 9222 
 
 5760 
 
 54 49 39.38 
 
 118.82 
 
 .199 
 
 .985 1397 
 
 5527 
 
 56 26 39.66 
 
 114.01 
 
 1.150 
 
 0.957 498o 
 
 5756 
 
 54 51 38.15 
 
 118.72 
 
 1. 200 
 
 0.985 6922 
 
 5523 
 
 56 28 33.62 
 
 113-92 
 
 u 
 
 2tan-'(e*)-^ 
 
 < sech u 
 
 2tan~ 1 (e)-90 
 
 <*> sech u 
 
 u 
 
 atan-W- 
 
 <> sech u 
 
 2tan- 1 (e*)-90 
 
 eu sech u 
 
 SMITHSONIAN TABLES 
 
 287 
 
The Gude rmannian. 
 
 u 
 
 gdu 
 
 F ' 
 
 gdu 
 
 F> 
 
 u 
 
 gdu 
 
 * 
 
 gdu 
 
 ^ 
 
 I.2OO 
 
 0.985 6922 
 
 5523 
 
 56 28 33.62 
 
 113*92 
 
 1.250 
 
 I. 012 7356 
 
 5295 
 
 / // 
 
 58 oi 31.72 
 
 109/23 
 
 .2OI 
 
 .986 2443 
 
 5518 
 
 56 30 27.49 
 
 113.82 
 
 .251 
 
 .OI3 2649 
 
 5291 
 
 58 03 20.89 
 
 109.13 
 
 .202 
 
 .986 7959 
 
 5514 
 
 56 32 21.26 
 
 H3.73 
 
 .252 
 
 .013 7938 
 
 5286 
 
 58 05 09.08 
 
 109.04 
 
 .203 
 
 .987 3470 
 
 5509 
 
 56 34 14.94 
 
 113.63 
 
 .253 
 
 .014 3222 
 
 5282 
 
 58 06 58.98 
 
 108.95 
 
 .204 
 
 .987 8977 
 
 5504 
 
 56 36 08.53 
 
 113-54 
 
 254 
 
 .014 85O2 
 
 5277 
 
 58 08 47-88 
 
 108.86 
 
 1.205 
 
 0.988 4479 
 
 5500 
 
 56 38 02.02 
 
 113.44 
 
 1.255 
 
 i. 015 3777 
 
 5273 
 
 58 10 36.69 
 
 108.76 
 
 .206 
 
 .988 9977 
 
 5495 
 
 56 39 55.42 
 
 113-35 
 
 .256 
 
 .015 9048 
 
 5269 
 
 58 12 25.40 
 
 108.67 
 
 .207 
 
 .989 5470 
 
 5491 
 
 56 41 48.72 
 
 H3.25 
 
 257 
 
 .016 4314 
 
 5264 
 
 58 14 14.03 
 
 io8'.s8 
 
 .208 
 
 .090 0958 
 
 5486 
 
 56 43 41 .92 
 
 II3.I6 
 
 .258 
 
 .016 9576 
 
 5260 
 
 58 16 02.56 
 
 108.49 
 
 .209 
 
 .990 6442 
 
 5482 
 
 56 45 35.03 
 
 II3.06 
 
 259 
 
 .017 4833 
 
 5255 
 
 58 17 51.00 
 
 108.39 
 
 I.2IO 
 
 0.991 1921 
 
 5477 
 
 56 47 28.05 
 
 112.97 
 
 1.260 
 
 1.018 0086 
 
 5251 
 
 58 19 39-35 
 
 108.30 
 
 .211 
 
 .991 7396 
 
 5472 
 
 56 49 20.97 
 
 112.88 
 
 .261 
 
 .018 5335 
 
 5246 58 21 27.6l 
 
 108.21 
 
 .212 
 
 .992 2866 
 
 5468 
 
 56 51 13.80 
 
 112.78 
 
 .262 
 
 .019 0578 
 
 5242 
 
 58 23 15.77 
 
 108.12 
 
 .213 
 
 992 8331 
 
 5463 
 
 56 53 06.54 
 
 112.69 
 
 .263 
 
 .019 5818 
 
 5237 
 
 58 25 03. 84 
 
 108.03 
 
 .214 
 
 993 3792 
 
 5459 
 
 56 54 59- 17 
 
 112.59 
 
 .264 
 
 .020 1053 
 
 5233 
 
 58 26 51.82 
 
 107.93 
 
 1. 215 
 
 0.993 9249 
 
 5454 
 
 56 56 51.72 
 
 112.50 
 
 1.265 
 
 1.020 6283 
 
 5228 
 
 58 28 39-71 
 
 107.84 
 
 .2l6 
 
 .994 4700 
 
 5449 
 
 56 58 44.17 
 
 112.40 
 
 .266 
 
 .021 1510 
 
 5224 
 
 58 30 27.50 
 
 107.75 
 
 .217 
 
 .995 0148 
 
 5445 
 
 57 oo 36.53 
 
 112.31 
 
 .267 
 
 .021 6731 
 
 5219 
 
 58 32 15.21 
 
 107.66 
 
 .218 
 
 995 5590 
 
 5440 
 
 57 02 28.79 
 
 112.22 
 
 .268 
 
 .022 1948 
 
 5215 
 
 58 34 02.82 
 
 107-57 
 
 .219 
 
 .996 1028 
 
 5436 
 
 57 04 20.96 
 
 112. 12 
 
 .269 
 
 .022 7l6l 
 
 5210 
 
 58 35 50.34 
 
 107.47 
 
 1.220 
 
 0.996 6462 
 
 5431 
 
 57 06 13.03 
 
 112.03 
 
 1.270 
 
 1.023 2369 
 
 5206 
 
 58 37 37.77 
 
 107.38 
 
 .221 
 
 .997 1891 
 
 5427 
 
 57 08 05.01 
 
 111.93 
 
 .271 
 
 .023 7573 
 
 52O2 
 
 58 39 25.10 
 
 107.29 
 
 .222 
 
 .997 7315 
 
 5422 
 
 57 09 56.90 
 
 111.84 
 
 .272 
 
 .024 2772 
 
 5197 
 
 58 41 12.35 
 
 107.20 
 
 .223 
 
 .998 2735 
 
 54i8 
 
 57 ii 48.69 
 
 111.74 
 
 .273 
 
 .024 7967 
 
 5193 
 
 58 42 59-50 
 
 107 . i i 
 
 .224 
 
 .998 8150 
 
 54U 
 
 57 13 40.39 
 
 111.65 
 
 .274 
 
 .025 3158 
 
 5188 
 
 58 44 46.56 
 
 107.02 
 
 1.225 
 
 0.999 356i 
 
 5408 
 
 57 15 31.99 
 
 111.56 
 
 1.275 
 
 1.025 8344 
 
 5184 
 
 58 46 33-53 
 
 106.92 
 
 .226 
 
 .999 8967 
 
 5404 
 
 57 17 23.50 
 
 111.46 
 
 .276 
 
 .026 3526 
 
 5179 
 
 58 48 20.41 
 
 106.83 
 
 .227 
 
 i. ooo 4369 
 
 5399 
 
 57 19 14.92 
 
 IH.37 
 
 .277 
 
 .026 8703 
 
 5175 
 
 58 50 07.20 
 
 106.74 
 
 .228 
 
 .000 9766 
 
 5395 
 
 57 21 06.24 
 
 111.28 
 
 .278 
 
 .027 3876 
 
 5171 
 
 58 51 53-90 
 
 106.65 
 
 .229 
 
 .001 5158 
 
 5390 
 
 57 22 57.47 
 
 III.I8 
 
 .279 
 
 .027 9044 
 
 5166 
 
 58 53 40-50 
 
 106.56 
 
 1.230 
 
 I.OO2 0546 
 
 5386 
 
 57 24 48.60 
 
 111.09 
 
 1.280 
 
 1.028 4208 
 
 5162 
 
 58 55 27.02 
 
 106.47 
 
 .231 
 
 .002 5930 
 
 538i 
 
 57 26 39.64 
 
 110.99 
 
 .281 
 
 .028 9367 
 
 5157 
 
 58 57 13.44 
 
 106.38 
 
 .232 
 
 .003 1309 
 
 5377 
 
 57 28 30.59 
 
 110.90 
 
 .282 
 
 .029 4523 
 
 5153 
 
 58 58 59-77 
 
 106.29 
 
 .233 
 
 .003 6683 
 
 5372 
 
 57 30 21.45 
 
 110.81 
 
 .283 
 
 .029 0673 
 
 5H8 
 
 59 oo 46.01 
 
 106.19 
 
 .234 
 
 .004 2053 
 
 5368 
 
 57 32 12.21 
 
 110.71 
 
 .284 
 
 .030 4819 
 
 5144 
 
 59 02 32.16 
 
 106.10 
 
 1.235 
 
 1.004 7418 
 
 5363 
 
 57 34 02.88 
 
 110.62 
 
 1.285 
 
 1.030 9961 
 
 5UO 
 
 59 04 18.22 
 
 106.01 
 
 .236 
 
 .005 2779 
 
 5359 
 
 57 35 53-45 
 
 no.53 
 
 .286 
 
 .031 5099 
 
 5135 
 
 59 06 04.19 
 
 105.92 
 
 .237 
 
 .005 8135 
 
 5354 
 
 57 37 43.93 
 
 110.43 
 
 .287 
 
 .032 0232 
 
 5131 
 
 59 07 50.o6 
 
 105.83 
 
 .238 
 
 .006 3487 
 
 5349 
 
 57 39 34.32 
 
 110.34 
 
 .288 
 
 .032 5360 
 
 5126 
 
 59 09 35.85 
 
 ios-74 
 
 .239 
 
 .006 8834 
 
 5345 
 
 57 41 24.61 
 
 110.25 
 
 .289 
 
 .033 0485 
 
 5122 
 
 59 u 21.54 
 
 105.65 
 
 1.240 
 
 1.007 4177 
 
 5340 
 
 57 43 14.82 
 
 110.15 
 
 1.290 
 
 1.033 5605 
 
 5Il8 
 
 59 13 07.15 
 
 105.56 
 
 .241 
 
 .007 9515 
 
 5336 
 
 57 45 04.92 
 
 no. 06 
 
 .291 
 
 .034 0720 
 
 5H3 
 
 59 14 52.66 
 
 105.47 
 
 .242 
 
 .0084840 
 
 5331 
 
 57 46 54-94 
 
 109.97 
 
 .292 
 
 .034 5831 
 
 5109 
 
 59 16 38.08 
 
 105.38 
 
 .243 
 
 .009 0178 
 
 5327 
 
 57 48 44.86 
 
 109.88 
 
 .293 
 
 .035 0938 
 
 5104 
 
 59 18 23.41 
 
 105.29 
 
 .244 
 
 .009 5503 
 
 5322 
 
 57 50 34.69 
 
 109.78 
 
 .294 
 
 .035 6040 
 
 5100 
 
 59 20 08.66 
 
 105.20 
 
 1.245 
 
 i.oio 0823 
 
 53i8 
 
 57 52 24.43 
 
 109.69 
 
 1.295 
 
 1.036 1138 
 
 5096 
 
 59 21 53.8i 
 
 105 . i i 
 
 .246 
 
 .010 6139 
 
 5313 
 
 57 54 14.07 
 
 109.60 
 
 .296 
 
 .036 6231 
 
 5091 
 
 59 23 38.87 
 
 105.02 
 
 .247 
 
 .on 1450 
 
 5309 
 
 57 56 03.62 
 
 109.50 
 
 .297 
 
 .037 1320 
 
 5087 
 
 59 25 23.84 
 
 104.93 
 
 .248 
 
 .on 6756 
 
 5304 
 
 57 57 53.o8 
 
 109.41 
 
 .298 
 
 .037 6405 
 
 5083 
 
 59 27 08.72 
 
 104.83 
 
 .249 
 
 .012 2058 
 
 5300 
 
 57 59 42.44 
 
 109.32 
 
 .299 
 
 .038 1485 
 
 5078 
 
 59 28 53-51 
 
 104-74 
 
 1.250 
 
 I. 012 7356 
 
 5295 
 
 58 oi 31.72 
 
 109.23 
 
 1.300 
 
 1.038 6561 
 
 5074 
 
 59 30 38.21 
 
 104.65 
 
 u 
 
 *"-<">-l 
 
 < sech u 
 
 2tan- 1 (e u )-90 
 
 wsechu 
 
 u 
 
 2 tan-He")-- 
 
 < sech u 
 
 2tan-Ue")-90 c 
 
 <sechu 
 
 SMITHSONIAN TABLES 
 
 288 
 
The Gudermannian. 
 
 u 
 
 Odu 
 
 Fo' 
 
 gdu 
 
 <oF ' 
 
 u 
 
 ad u 
 
 F ' 
 
 gdu 
 
 "Fo' 
 
 
 
 
 / // 
 
 // 
 
 
 
 
 o / // 
 
 // 
 
 1.300 
 
 1.038 6561 
 
 5074 
 
 59 30 38.21 
 
 104.65 
 
 1.350 
 
 1.063 4837 
 
 4858 
 
 60 55 59.27 
 
 IOO.2I 
 
 .301 
 
 .039 1633 
 
 5069 
 
 59 32 22.82 
 
 104.56 
 
 .351 
 
 .063 9694 
 
 4854 
 
 60 57 39-43 
 
 100.12 
 
 .302 
 
 .039 6700 
 
 5065 
 
 59 34 07-34 
 
 104.47 
 
 352 
 
 .064 4546 
 
 4850 
 
 60 59 19.51 
 
 100.03 
 
 .303 
 
 .040 1763 
 
 5061 
 
 59 35 51.77 
 
 104.38 
 
 353 
 
 .064 9393 
 
 4846 
 
 61 oo 59.50 
 
 99.95 
 
 .304 
 
 .040 6822 
 
 5056 
 
 59 37 36.10 
 
 104.29 
 
 354 
 
 .065 4237 
 
 4841 
 
 61 02 39.41 
 
 99.86 
 
 1.305 
 
 1.041 1876 
 
 5052 
 
 59 39 20.35 
 
 104.29 
 
 1.355 
 
 1.065 9076 
 
 4837 
 
 61 04 19.22 
 
 99.77 
 
 .306 
 
 .041 6926 
 
 5048 
 
 59 41 04.51 
 
 104.11 
 
 356 
 
 .066 3911 
 
 4833 
 
 61 05 58.95 
 
 99.69 
 
 .307 
 
 .042 1971 
 
 5043 
 
 59 42 48.58 
 
 104.02 
 
 357 
 
 .066 8742 
 
 4829 
 
 61 07 38.59 
 
 99.60 
 
 .308 
 
 .042 7012 
 
 5039 
 
 59 44 32.56 
 
 103.93 
 
 358 
 
 .067 3568 
 
 4824 
 
 61 09 18.15 
 
 99.51 
 
 .309 
 
 .043 2049 
 
 5035 
 
 59 46 16.45 
 
 103.84 
 
 359 
 
 .067 8390 
 
 4820 
 
 61 10 57.61 
 
 99.42 
 
 i.3'0 
 
 1.043 7o8i 
 
 5030 
 
 59 48 00.25 
 
 103.76 
 
 1.360 
 
 i. 068 3209 
 
 4816 
 
 61 12 36.99 
 
 99-34 
 
 .311 
 
 .044 2109 
 
 5026 
 
 59 49 43.96 
 
 103.67 
 
 .361 
 
 .068 8022 
 
 4812 
 
 61 14 16.29 
 
 99.25 
 
 .312 
 
 .044 7133 
 
 5O2I 
 
 59 51 27.58 
 
 103.58 
 
 .362 
 
 .069 2832 
 
 4808 
 
 61 15 55-49 
 
 99-16 
 
 .313 
 
 .045 2152 
 
 5017 
 
 59 53 11. ii 
 
 103.49 
 
 .363 
 
 .069 7637 
 
 4803 
 
 61 17 34.61 
 
 99.08 
 
 .314 
 
 .045 7i67 
 
 5013 
 
 59 54 54.55 
 
 103.40 
 
 .304 
 
 .070 2439 
 
 4799 
 
 61 19 13.64 
 
 98.99 
 
 I.3I5 
 
 1.046 2178 
 
 5008 
 
 59 56 37.91 
 
 103.31 
 
 1.365 
 
 1.070 7236 
 
 4795 
 
 61 20 52.59 
 
 98.90 
 
 .316 
 
 .046 7184 
 
 5004 
 
 59 58 21.17 
 
 103.22 
 
 .366 
 
 .071 2028 
 
 4791 
 
 61 22 31.45 
 
 98.82 
 
 .317 
 
 .047 2186 
 
 5000 
 
 60 oo 04.34 
 
 103.13 
 
 .367 
 
 .071 6817 
 
 4786 
 
 6l 24 IO.22 
 
 98.73 
 
 .318 
 
 .047 7184 
 
 4995 
 
 60 01 47.43 
 
 103.04 
 
 .368 
 
 .072 1601 
 
 4782 
 
 61 25 48.90 
 
 98.64 
 
 .319 
 
 .048 2177 
 
 4991 
 
 60 03 30.42 
 
 102.95 
 
 .369 
 
 .072 6382 
 
 4778 
 
 61 27 27.50 
 
 98.56 
 
 1.320 
 
 1.048 7166 
 
 4987 
 
 60 05 13.33 
 
 102.86 
 
 1.370 
 
 1.073 1158 
 
 4774 
 
 61 29 06. 01 
 
 98.47 
 
 .321 
 
 .049 2151 
 
 4983 
 
 60 06 56.14 
 
 102.77 
 
 371 
 
 .073 5929 
 
 4770 
 
 61 30 44-44 
 
 98.38 
 
 .322 
 
 .049 7131 
 
 4978 
 
 60 08 38.87 
 
 102.68 
 
 .372 
 
 .074 0697 
 
 4766 
 
 61 32 22.78 
 
 98.30 
 
 .323 
 
 .050 2107 
 
 4974 
 
 60 10 21.51 
 
 102.59 
 
 373 
 
 .074 546o 
 
 476l 
 
 61 34 01.03 
 
 98.21 
 
 324 
 
 .050 7079 
 
 4970 
 
 60 12 04.06 
 
 102.50 
 
 374 
 
 .075 O220 
 
 4757 
 
 61 35 39-20 
 
 98.12 
 
 1.325 
 
 1.051 2046 
 
 4965 
 
 60 13 46.52 
 
 102.42 
 
 1.375 
 
 1.075 4975 
 
 4753 
 
 61 37 17.26 
 
 98.04 
 
 .326 
 
 .051 7009 
 
 496i 
 
 60 15 28.89 
 
 102.33 
 
 .376 
 
 .075 9725 
 
 4749 
 
 61 38 55.27 
 
 97-95 
 
 .327 
 
 .052 1968 
 
 4957 
 
 60 17 11.17 
 
 102.24 
 
 .377 
 
 .076 4472 
 
 4745 
 
 61 40 33.18 
 
 97.86 
 
 .328 
 
 .052 6923 
 
 4952 
 
 60 18 53-37 
 
 102.15 
 
 .378 
 
 .076 9215 
 
 4740 
 
 61 42 ii.oo 
 
 97.78 
 
 .329 
 
 .053 1873 
 
 4948 
 
 60 20 35-47 
 
 102.06 
 
 379 
 
 .077 3953 
 
 4736 
 
 61 43 48.73 
 
 97.69 
 
 1-330 
 
 1.053 6819 
 
 4944 
 
 6O 22 17.49 
 
 101.97 
 
 1.380 
 
 1.077 8687 
 
 4732 
 
 61 45 26.38 
 
 97.6i 
 
 331 
 
 .054 1760 
 
 4939 
 
 60 23 59.41 
 
 101.88 
 
 .381 
 
 .078 3417 
 
 4728 
 
 61 47 03.94 
 
 97.52 
 
 332 
 
 .0546698 
 
 4935 
 
 60 25 4L25 
 
 101.79 
 
 .382 
 
 .078 8143 
 
 4724 
 
 61 48 41.42 
 
 97.43 
 
 333 
 
 .055 1631 
 
 4931 
 
 60 27 23.0O 
 
 101.71 
 
 .383 
 
 .079 2865 
 
 4720 
 
 61 50 18.81 
 
 97.35 
 
 334 
 
 055 6559 
 
 4927 
 
 60 29 04.67 
 
 101.62 
 
 .384 
 
 .079 7582 
 
 4715 
 
 61 51 56.12 
 
 97.26 
 
 1.335 
 
 1.056 1484 
 
 4922 
 
 00 30 46.24 
 
 101.53 
 
 1.385 
 
 1.080 2295 
 
 4711 
 
 61 53 33.34 
 
 97.18 
 
 .336 
 
 .056 6404 
 
 4918 
 
 60 32 27.72 
 
 101.44 
 
 .386 
 
 .080 7005 
 
 4707 
 
 61 55 10.47 
 
 97.09 
 
 .337 
 
 .057 1320 
 
 4914 
 
 60 34 09. 12 
 
 101.35 
 
 .387 
 
 .081 1710 
 
 4703 
 
 61 56 47.52 
 
 97.01 
 
 .338 
 
 .057 6231 
 
 4909 
 
 60 35 50.43 
 
 101.26 
 
 .388 
 
 .081 6411 
 
 4699 
 
 61 58 24.48 
 
 96.92 
 
 .339 
 
 .058 1139 
 
 4905 
 
 60 37 31.65 
 
 101.18 
 
 .389 
 
 .082 1107 
 
 4695 
 
 62 oo 01.36 
 
 96.83 
 
 1.340 
 
 1.058 6042 
 
 4001 
 
 60 39 12.78 
 
 101.09 
 
 1.390 
 
 1.082 5800 
 
 4691 
 
 62 01 38.15 
 
 96.75 
 
 341 
 
 .059 0940 
 
 4897 
 
 60 40 53.83 
 
 101.00 
 
 391 
 
 .083 0488 
 
 4686 
 
 62 03 14.86 
 
 96.66 
 
 .342 
 
 .059 5835 
 
 4892 
 
 60 42 34.78 
 
 100.91 
 
 .392 
 
 083 5173 
 
 4682 
 
 62 04 51.48 
 
 96.58 
 
 .343 
 
 .060 0725 
 
 4888 
 
 60 44 15.65 
 
 100.82 
 
 .393 
 
 .083 9853 
 
 4678 
 
 62 06 28.01 
 
 96.49 
 
 344 
 
 .060 5611 
 
 4884 
 
 60 45 56.43 
 
 100.74 
 
 394 
 
 .084 4529 
 
 4674 
 
 62 08 04.46 
 
 96.41 
 
 1.345 
 
 1.061 0493 
 
 4880 
 
 60 47 37.12 
 
 100.65 
 
 1.395 
 
 1.084 9201 
 
 4670 
 
 62 09 40.83 
 
 96.32 
 
 .346 
 
 .061 5370 
 
 4875 
 
 60 49 17.73 
 
 100.56 
 
 396 
 
 .085 3868 
 
 4666 
 
 62 II 17.11 
 
 96.24 
 
 .347 
 
 .062 0243 
 
 4871 
 
 60 50 58.24 
 
 100.47 
 
 397 
 
 .085 8532 
 
 4662 
 
 62 12 53.30 
 
 96.15 
 
 .348 
 
 .062 5112 
 
 4867 
 
 60 52 38.67 
 
 100.38 
 
 .398 
 
 .086 3192 
 
 4657 
 
 62 14 29.41 
 
 96.017 
 
 .349 
 
 .062 9977 
 
 4863 
 
 60 54 19.01 
 
 100.30 
 
 399 
 
 .086 7847 
 
 4653 
 
 62 16 05.44 
 
 95.98 
 
 1-350 
 
 1.063 4837 
 
 4858 
 
 60 55 59.27 
 
 100.21 
 
 1.400 
 
 1.087 2498 
 
 4649 
 
 62 17 41-37 
 
 95.90 
 
 u 
 
 2 tan-He")- jj 
 
 wsechu 
 
 2tan- 1 (e)-90 
 
 w sech u 
 
 u 
 
 2tan-Ke)- 
 
 wsechu 
 
 2tan- 1 (e)-90 
 
 < sech u 
 
 SMITHSONIAN TABLES 
 
 289 
 
The Gudermannian. 
 
 u 
 
 gdu 
 
 Fo' 
 
 gdu 
 
 Fo' 
 
 u 
 
 gd u 
 
 F O ' 
 
 gd u 
 
 <-F ' 
 
 1.400 
 
 1.087 2498 
 
 4649 
 
 o / // 
 
 62 17 41.37 
 
 95-90 
 
 1.450 
 
 1.109 9869 
 
 4447 
 
 633S' Si'W 
 
 91.72 
 
 .401 
 
 .087 7145 
 
 4645 
 
 62 19 17.23 
 
 95.81 
 
 .451 
 
 .110 4314 
 
 4443 
 
 63 37 22.92 
 
 91.64 
 
 .402 
 
 .088 1788 
 
 4641 
 
 62 20 53.00 
 
 95-73 
 
 452 
 
 .1108755 
 
 4439 
 
 63 38 54-52 
 
 91.56 
 
 .403 
 
 .088 6427 
 
 4637 
 
 62 22 28.68 
 
 95.64 
 
 453 
 
 .iii 3192 
 
 4435 
 
 63 40 26.03 
 
 91.47 
 
 .404 
 
 .089 1062 
 
 4633 
 
 62 24 04.28 
 
 95.56 
 
 454 
 
 .in 7624 
 
 4431 
 
 63 41 57.46 
 
 91-39 
 
 1.405 
 
 1.089 5093 
 
 4629 
 
 62 25 39.80 
 
 95-47 
 
 1.455 
 
 I. I 12 2O53 
 
 4427 
 
 63 43 28.82 
 
 91.31 
 
 .406 
 
 .090 0320 
 
 4625 
 
 62 27 15.23 
 
 95-39 
 
 .456 
 
 .112 6478 
 
 4423 
 
 63 45 00.08 
 
 91.23 
 
 .407 
 
 .090 4942 
 
 4620 
 
 62 28 50.58 
 
 95.30 
 
 457 
 
 .113 0899 
 
 4419 
 
 63 46 31.27 
 
 91.15 
 
 .406 
 
 .090 9561 
 
 4616 
 
 62 3O 25.84 
 
 95-22 
 
 .458 
 
 .113 5316 
 
 4415 
 
 63 48 02.38 
 
 91.07 
 
 .409 
 
 .091 4175 
 
 4612 
 
 62 32 01.02 
 
 95.14 
 
 459 
 
 .113 9729 
 
 4411 
 
 63 49 33-40 
 
 90.98 
 
 1.410 
 
 1.091 8/85 
 
 4608 
 
 62 33 36.11 
 
 95.05 
 
 1.460 
 
 I. I 14 4138 
 
 4407 
 
 63 51 04.35 
 
 90.90 
 
 .411 
 
 .092 3391 
 
 4604 
 
 62 35 II. 12 
 
 94.97 
 
 .461 
 
 .114 8543 
 
 4403 
 
 63 52 35-21 
 
 90.82 
 
 .412 
 
 .092 7993 
 
 4600 
 
 62 36 46.04 
 
 94.88 
 
 .462 
 
 .115 2944 
 
 4399 
 
 63 54 05.99 
 
 90.74 
 
 .413 
 
 .093 2591 
 
 4596 
 
 62 38 20.88 
 
 94-80 
 
 .463 
 
 .115 7341 
 
 4395 
 
 63 55 36.68 
 
 90.66 
 
 .414 
 
 093 7l85 
 
 4592 
 
 62 39 55.64 
 
 94.71 
 
 .464 
 
 .116 1734 
 
 4391 
 
 63 57 07.30 
 
 90.58 
 
 1.415 
 
 1.094 1775 
 
 4588 
 
 62 41 30.31 
 
 94-63 
 
 1.465 
 
 1.116 6124 
 
 4387 
 
 63 58 37.83 
 
 90.49 
 
 .416 
 
 .094 6361 
 
 4584 
 
 62 43 04.90 
 
 94-55 
 
 .466 
 
 .117 0509 
 
 4383 
 
 64 oo 08.29 
 
 90.41 
 
 .417 
 
 .095 0942 
 
 4580 
 
 62 44 39.40 
 
 94.46 
 
 .467 
 
 .117 4890 
 
 4379 
 
 64 oi 38.66 
 
 90.33 
 
 .418 
 
 095 5520 
 
 4576 
 
 62 46 13.82 
 
 94-38 
 
 .468 
 
 .117 9268 
 
 4375 
 
 64 03 08.95 
 
 90.25 
 
 .419 
 
 .096 0094 
 
 4571 
 
 62 47 48.16 
 
 94.29 
 
 .469 
 
 .118 3641 
 
 4372 
 
 64 04 39.16 
 
 90.17 
 
 1.420 
 
 1.096 4663 
 
 4567 
 
 62 49 22.41 
 
 94.21 
 
 1.470 
 
 1.118 Son 
 
 4368 
 
 64 06 09.29 
 
 90.09 
 
 .421 
 
 .096 9228 
 
 4563 
 
 62 50 56.58 
 
 94.13 
 
 .471 
 
 .119 2377 
 
 4364 
 
 64 07 39-34 
 
 90.01 
 
 .422 
 
 .097 3790 
 
 4559 
 
 62 52 30.66 
 
 94.04 
 
 .472 
 
 .119 6738 
 
 4360 
 
 64 09 09.31 
 
 89.93 
 
 .423 
 
 .097 8347 
 
 4555 
 
 62 54 04.66 
 
 93.96 
 
 473 
 
 .120 1096 
 
 4356 
 
 64 10 39.19 
 
 89.85 
 
 .424 
 
 .098 2900 
 
 4551 
 
 62 55 38.58 
 
 93.88 
 
 .474 
 
 .120 5450 
 
 4352 
 
 64 12 O9.OO 
 
 89.76 
 
 1.425 
 
 1.098 7449 
 
 4547 
 
 62 57 12.41 
 
 93-79 
 
 1.475 
 
 I. 120 0800 
 
 4348 
 
 64 13 38.72 
 
 89.68 
 
 .426 
 
 .099 1994 
 
 4543 
 
 62 58 46.16 
 
 93-71 
 
 \476 
 
 .121 4146 
 
 4344 
 
 64 15 08.37 
 
 89-60 
 
 .427 
 
 .099 6536 
 
 4539 
 
 63 oo 19.83 
 
 93-62 
 
 477 
 
 .121 8488 
 
 4340 
 
 64 16 37-93 
 
 89-52 
 
 .428 
 
 .100 1073 
 
 4535 
 
 63 01 53-41 
 
 93-54 
 
 .4178 
 
 .122 2826 
 
 4336 
 
 64 18 07.41 
 
 89.44 
 
 .429 
 
 .100 5606 
 
 4531 
 
 63 03 26.91 
 
 93.46 
 
 479 
 
 .122 7l6l 
 
 4332 
 
 64 19 36.81 
 
 89.36 
 
 1.430 
 
 i.ioi 0134 
 
 4527 
 
 63 05 00.33 
 
 93-37 
 
 1.480 
 
 I. 123 1491 
 
 4328 
 
 64 21 O6.I3 
 
 89.28 
 
 .431 
 
 .101 4659 
 
 4523 
 
 63 06 33.66 
 
 93.29 
 
 .481 
 
 .123 5818 
 
 4325 
 
 64 22 35-37 
 
 89.20 
 
 .432 
 
 .101 9180 
 
 4519 
 
 63 08 06.91 
 
 93.21 
 
 .482 
 
 .124 OI4O 
 
 4321 
 
 64 24 04.53 
 
 89.12 
 
 433 
 
 .102 3697 
 
 4515 
 
 63 09 40.08 
 
 93-13 
 
 .483 
 
 .124 4459 
 
 4317 
 
 64 25 33.61 
 
 89-04 
 
 434 
 
 .102 8210 
 
 4511 
 
 63 ii 13.16 
 
 93-04 
 
 .484 
 
 .1248774 
 
 4313 
 
 64 27 02. 61 
 
 88.96 
 
 1-435 
 
 1.103 2719 
 
 4507 
 
 63 12 46.16 
 
 92.96 
 
 1.485 
 
 1.125 3085 
 
 4309 
 
 64 28 31.53 
 
 88.88 
 
 .436 
 
 .103 7223 
 
 4503 
 
 63 14 19.08 
 
 92.88 
 
 .486 
 
 .125 7392 
 
 4305 
 
 64 30 00.37 
 
 88.80 
 
 437 
 
 .104 1724 
 
 4499 
 
 63 15 5i.9i 
 
 92.79 
 
 .487 
 
 .126 1695 
 
 4301 
 
 64 31 29.13 
 
 88.72 
 
 .438 
 
 .104 6221 
 
 4495 
 
 63 17 24.66 
 
 92.71 
 
 .488 
 
 .126 5994 
 
 4297 
 
 64 32 57.81 
 
 88.64 
 
 439 
 
 .105 0714 
 
 4491 
 
 63 18 57-33 
 
 92.63 
 
 .489 
 
 .127 0289 
 
 4293 
 
 64 34 26.41 
 
 88.56 
 
 1.440 
 
 i. 105 5202 
 
 4487 
 
 63 20 29.92 
 
 92.54 
 
 1.490 
 
 I. 127 458i 
 
 4290 
 
 64 35 54-93 
 
 88.48 
 
 .441 
 
 .105 9687 
 
 4483 
 
 63 22 O2.42 
 
 92.46 
 
 491 
 
 .127 8869 
 
 4286 
 
 64 37 23.37 
 
 88.40 
 
 442 
 
 .106 4168 
 
 4479 
 
 63 23 34.84 
 
 92.38 
 
 .492 
 
 .128 3152 
 
 4282 
 
 64 38 51.72 
 
 88.32 
 
 443 
 
 .106 8644 
 
 4475 
 
 63 25 07.18 
 
 92.30 
 
 493 
 
 .128 7432 
 
 4278 
 
 64 40 20.00 
 
 8S.-24 
 
 444 
 
 .107 3H7 
 
 4471 
 
 63 26 39-44 
 
 92.21 
 
 .494 
 
 .129 1708 
 
 4274 
 
 64 41 48.20 
 
 88.16 
 
 1-445 
 
 i. 107 7586 
 
 4467 
 
 63 28 ii. 61 
 
 92.13 
 
 1.495 
 
 1.129 598o 
 
 4270 
 
 <>4 43 16.32 
 
 88.08 
 
 .446 
 
 . 108 2050 
 
 4463 
 
 63 29 43-70 
 
 92.05 
 
 .496 
 
 . 130 0249 
 
 4266 
 
 64 44 44.36 
 
 88.00 
 
 447 
 
 .108 6511 
 
 4459 
 
 63 31 15.71 
 
 91.97 
 
 497 
 
 .130 4513 
 
 4263 
 
 64 46 12.32 
 
 87.92 
 
 .448 
 
 .109 0968 
 
 4455 
 
 63 32 47.63 
 
 91.88 
 
 .498 
 
 .1308774 
 
 4259 
 
 64 47 40.20 
 
 87.84 
 
 449 
 
 .109 5421 
 
 4451 
 
 63 34 19.48 
 
 91.80 
 
 .499 
 
 .131 3031 
 
 4255 
 
 04 49 08.01 
 
 87.76 
 
 1.450 
 
 1.109 9869 
 
 4447 
 
 63 35 51.24 
 
 91.72 
 
 1.500 
 
 1.131 7283 
 
 4251 
 
 64 50 35-73 
 
 87.68 
 
 u 
 
 2 tan-He")- J 
 
 < sech u 
 
 2tan->(e)-90 
 
 wsech u 
 
 u 
 
 2tan-'(e)-^ 
 
 wsechu 
 
 2tan-Ke)-90 
 
 sech u 
 
 SMITHSONIAN TABLES 
 
 290 
 
The Gudermannian. 
 
 u 
 
 gd u 
 
 <-Fo' 
 
 gd u 
 
 F ' 
 
 u 
 
 gdu 
 
 F ' 
 
 gd u 
 
 F ' 
 
 1.500 
 
 I.I3I 7283 
 
 4251 
 
 64 50 35-73 
 
 87^68 
 
 1.550 
 
 1.152 5078 
 
 4062 
 
 / // 
 
 66 02 01.81 
 
 83*78 
 
 .501 
 
 .132 1532 
 
 4247 
 
 64 52 03.37 
 
 87.60 
 
 .551 
 
 152 9139 
 
 4058 
 
 66 03 25.55 
 
 83.71 
 
 .502 
 
 .132 5778 
 
 4243 
 
 64 53 30.93 
 
 87.52 
 
 .552 
 
 .153 3195 
 
 4055 
 
 66 04 49.22 
 
 83.63 
 
 .503 
 
 .133 0019 
 
 4239 
 
 64 54 58.42 
 
 87.44 
 
 553 
 
 .153 7248 
 
 4051 
 
 66 06 12. 81 
 
 83.55 
 
 .504 
 
 .133 4257 
 
 4236 
 
 64 56 25.82 
 
 87.37 
 
 .554 
 
 .154 1297 
 
 4047 
 
 66 07 36.33 
 
 83.48 
 
 1.505 
 
 I. 133 8490 
 
 4232 
 
 64 57 53.15 
 
 87.29 
 
 1.555 
 
 1. 154 5342 
 
 4043 
 
 66 08 59.77 
 
 83.40 
 
 .506 
 
 .134 2720 
 
 4228 
 
 64 59 20.40 
 
 87.21 
 
 .556 
 
 .154 9384 
 
 4040 
 
 66 10 23.14 
 
 83.33 
 
 .507 
 
 . 134 6946 
 
 4224 
 
 65 oo 47.56 
 
 87.13 
 
 557 
 
 .155 342i 
 
 4036 
 
 66 ii 46.42 
 
 83-25 
 
 .508 
 
 .135 n68 
 
 422O 
 
 65 02 14.65 
 
 87.05 
 
 .558 
 
 .155 7456 
 
 4032 
 
 66 13 09.63 
 
 83.17 
 
 .509 
 
 135 5387 
 
 4216 
 
 65 03 41.66 
 
 86.97 
 
 .'559 
 
 .156 1486 
 
 4029 
 
 66 14 32.77 
 
 83.10 
 
 1.510 
 
 1.135 9601 
 
 4213 
 
 65 05 08.59 
 
 86.89 
 
 1.560 
 
 1.156 5513 
 
 4025 
 
 66 15 55-83 
 
 83.02 
 
 .511 
 
 .136 3812 
 
 4209 
 
 65 06 35.44 
 
 86.81 
 
 .561 
 
 . 156 9536 
 
 4021 
 
 66 17 18.81 
 
 82.95 
 
 .512 
 
 . 136 8019 
 
 4205 
 
 65 O8 02.22 
 
 86.73 
 
 .562 
 
 157 3556 
 
 4018 
 
 66 18 41.72 
 
 82.87 
 
 .513 
 
 .137 2222 
 
 42OI 
 
 65 09 28.91 
 
 86.66 
 
 .563 
 
 .157 7571 
 
 4014 
 
 66 20 04 . 55 
 
 82.79 
 
 .514 
 
 .137 6421 
 
 4197 
 
 65 10 55-53 
 
 86.58 
 
 .564 
 
 .158 1583 
 
 4010 
 
 66 21 27.31 
 
 82.72 
 
 1.515 
 
 I.I38 O6l7 
 
 4194 
 
 65 12 22.07 
 
 86.50 
 
 1.565 
 
 1.158 5592 
 
 4007 
 
 66 22 49-99 
 
 82.64 
 
 .516 
 
 . 138 4808 
 
 4100 
 
 65 13 48.52 
 
 86.42 
 
 .566 
 
 . 158 9597 
 
 4003 
 
 66 24 12.59 
 
 82.57 
 
 .517 
 
 .1388006 
 
 4186 
 
 65 15 14.91 
 
 86.34 
 
 .567 
 
 159 3598 
 
 3999 
 
 66 25 35.12 
 
 82.49 
 
 .518 
 
 .139 3180 
 
 4182 
 
 65 16 41.21 
 
 86.26 
 
 .568 
 
 159 7595 
 
 3996 
 
 66 26 57.57 
 
 82.42 
 
 .519 
 
 . 139 7300 
 
 4178 
 
 65 18 07.43 
 
 86.18 
 
 .569 
 
 .160 1589 
 
 3992 
 
 66 28 19.95 
 
 82.34 
 
 1.520 
 
 1.140 1537 
 
 4175 
 
 65 1933.58 
 
 86.11 
 
 1.570 
 
 1.160 5579 
 
 3988 
 
 66 29 42.25 
 
 82.26 
 
 .521 
 
 .140 5709 
 
 4171 
 
 65 20 59-64 
 
 86.03 
 
 571 
 
 . 160 9566 
 
 3985 
 
 66 31 04.48 
 
 82.19 
 
 .522 
 
 .140 9878 
 
 4167 
 
 65 22 25.63 
 
 85.95 
 
 .572 
 
 .161 3548 
 
 398i 
 
 66 32 26.63 
 
 82.11 
 
 .523 
 
 .141 4043 
 
 4163 
 
 65 23 51.54 
 
 85.87 
 
 573 
 
 .161 7527 
 
 3977 
 
 66 33 48.71 
 
 82.04 
 
 .524 
 
 .141 8205 
 
 4159 
 
 65 25 17.38 
 
 85.79 
 
 574 
 
 .162 1503 
 
 3974 
 
 66 35 10.71 
 
 8l.o6 
 
 1.525 
 
 1.142 2362 
 
 4156 
 
 65 26 43.13 
 
 85.72 
 
 1-575 
 
 1.162 5475 
 
 3970 
 
 66 36 32.63 
 
 81.89 
 
 .526 
 
 .142 6516 
 
 4152 
 
 65 28 08. 81 
 
 85-64 
 
 .576 
 
 . 162 9443 
 
 3966 
 
 66 37 54.48 
 
 81.81 
 
 .527 
 
 .143 0666 
 
 4148 
 
 65 29 34.41 
 
 85.56 
 
 577 
 
 .163 3408 
 
 3963 
 
 66 39 16.26 
 
 8i.74 
 
 .528 
 
 .143 4812 
 
 4144 
 
 65 30 59-93 
 
 85.48 
 
 578 
 
 .163 7369 
 
 3959 
 
 66 40 37.96 
 
 81.66 
 
 .529 
 
 .143 8954 
 
 4141 
 
 65 32 25.37 
 
 85.40 
 
 579 
 
 .164 1326 
 
 3955 
 
 66 41 59.58 
 
 8i.59 
 
 1.530 
 
 1.144 3093 
 
 4137 
 
 65 33 50.74 
 
 85.33 
 
 1.580 
 
 1.164 5279 
 
 3952 
 
 66 43 21.13 
 
 81.51 
 
 .531 
 
 . 144 7228 
 
 4133 
 
 65 35 16.02 
 
 85.25 
 
 .581 
 
 . 164 9230 
 
 3948 
 
 66 44 42.61 
 
 81.44 
 
 .532 
 
 145 1359 
 
 4129 
 
 65 36 41-23 
 
 85.17 
 
 .582 
 
 .165 3176 
 
 3945 
 
 66 46 04.01 
 
 81.36 
 
 533 
 
 .145 5486 
 
 4125 
 
 65 38 06.37 
 
 85.09 
 
 .583 
 
 .165 7119 
 
 3941 
 
 66 47 25.33 
 
 81.29 
 
 .534 
 
 .145 9610 
 
 4122 
 
 65 39 31.42 
 
 85.02 
 
 .584 
 
 .166 1058 
 
 3937 
 
 66 48 46.58 
 
 Si. 21 
 
 1.535 
 
 1.146 3730 
 
 4Il8 
 
 65 40 56.40 
 
 84.94 
 
 1.585 
 
 i . 166 4993 
 
 3934 
 
 66 50 07.76 
 
 8I.I4 
 
 536 
 
 . 146 7846 
 
 4II4 
 
 65 42 21.30 
 
 84.86 
 
 .586 
 
 . 166 8925 
 
 3930 
 
 66 51 28.86 
 
 8!.o6 
 
 .537 
 
 .147 1958 
 
 4110 
 
 65 43 46.12 
 
 84.78 
 
 .587 
 
 . 167 2854 
 
 3926 
 
 66 52 49.89 
 
 80.99 
 
 .538 
 
 .147 6067 
 
 4107 
 
 65 45 10.87 
 
 84.71 
 
 .588 
 
 . 167 6778 
 
 3923 
 
 66 54 10.84 
 
 80.92 
 
 539 
 
 . 148 0172 
 
 4103 
 
 65 46 35-54 
 
 84.63 
 
 .589 
 
 .168 0699 
 
 3919 
 
 66 55 31.72 
 
 80.84 
 
 1.540 
 
 1.1484273 
 
 4099 
 
 65 48 00.13 
 
 84.55 
 
 1-590 
 
 1.168 4617 
 
 39i6 
 
 66 56 52.52 
 
 80.77 
 
 541 
 
 . 148 8370 
 
 4095 
 
 65 49 24.64 
 
 84.48 
 
 .591 
 
 .168 8531 
 
 3912 
 
 66 58 13.25 
 
 80.69 
 
 542 
 
 . 149 2464 
 
 4092 
 
 65 50 49.08 
 
 84.40 
 
 592 
 
 .169 2441 
 
 3908 
 
 66 59 33-91 
 
 80.62 
 
 .543 
 
 . 149 6554 
 
 4088 
 
 65 52 13.44 
 
 84.32 
 
 .593' 
 
 .169 6348 
 
 3905 
 
 67 oo 54.49 
 
 80.54 
 
 544 
 
 .150 0640 
 
 4084 
 
 65 53 37-72 
 
 84.25 
 
 594 
 
 .170 0251 
 
 3901 
 
 67 02 15.00 
 
 80.47 
 
 1.545 
 .546 
 
 1.150 4722 
 .150 8801 
 
 408l 
 
 4077 
 
 65 '55 01.93 
 65 56 26.06 
 
 84.17 
 84.09 
 
 I<S ?J 
 .596 
 
 1.170 4150 
 . 170 8046 
 
 3898 
 3894 
 
 67 03 35.43: 
 67 04 55.79 
 
 80.40 
 80.32 
 
 547 
 
 .151 2876 
 
 4073 
 
 65 57 SO.ii 
 
 84.01 
 
 597 
 
 .171 1938 
 
 3891 
 
 67 06 16.07 
 
 80.25 
 
 .548 
 
 .151 6947 
 
 4069 
 
 65 59 14.08 
 
 83.94 
 
 .598 
 
 .171 5827 
 
 3887 
 
 67 07 36.28 
 
 80.17 
 
 549 
 
 .152 1015 
 
 4066 
 
 66 oo 37.98 
 
 83.86 
 
 599 
 
 .171 9712' 
 
 3883 
 
 67 08 56.42 
 
 80.10 
 
 1-550 
 
 1.152 5078 
 
 4062 
 
 66 02 01.81 
 
 83.78 
 
 I.obo 
 
 1.1723594 
 
 3880 
 
 67 10 16.48 
 
 80.03 
 
 u 
 
 atan-Heu)-! 
 
 wsechu 
 
 2lan-Ke)-90 
 
 wsechu 
 
 u 
 
 2tan- J (e")- 
 
 wsechu 
 
 2tan- 1 (e u )-90 
 
 ( sech u 
 
 SMITHSONIAN TABLES 
 
 2QI 
 
The Gudermannian. 
 
 u 
 
 gdu 
 
 F ' 
 
 gdu 
 
 U.FO" 
 
 u 
 
 gdu 
 
 * 
 
 gd u 
 
 ^ 
 
 1. 600 
 
 1.172 3594 
 
 3880 
 
 o / // 
 
 67 10 16.48 
 
 So'os 
 
 1.650 
 
 I.I9I 3170 
 
 3704 
 
 68 1 5' 26^76 
 
 76.41 
 
 .601 
 
 .172 7472 
 
 3876 
 
 67 II 36.47 
 
 79-95 
 
 .651 
 
 .191 6872 
 
 3701 
 
 68 16 43.13 
 
 76.34 
 
 .602 
 
 .173 1346 
 
 3873 
 
 67 12 56.39 
 
 79-88 
 
 .652 
 
 .192 0571 
 
 3097 
 
 68 17 59-44 
 
 76.27 
 
 .603 
 
 .173 5217 
 
 3869 
 
 67 14 16.23 
 
 79.81 
 
 .653 
 
 .192 4267 
 
 3694 
 
 68 19 15.67 
 
 76.20 
 
 .604 
 
 .173 90&4 
 
 3865 
 
 67 15 36.0O 
 
 79-73 
 
 .654 
 
 .192 7960 
 
 3691 
 
 68 20 31.83 
 
 76.12 
 
 1.605 
 
 I. 174 2048 
 
 3862 
 
 67 16 55-69 
 
 79.66 
 
 1.655 
 
 I.I93 1648 
 
 3687 
 
 68 21 47.92 
 
 76.05 
 
 .606 
 
 .174 6808 
 
 3858 
 
 67 18 15.31 
 
 79-58 
 
 .656 
 
 193 5334 
 
 3684 
 
 68 23 03.93 
 
 75.98 
 
 .607 
 
 .175 0665 
 
 3855 
 
 67 19 34.86 
 
 79-51 
 
 .657 
 
 .193 9016 
 
 3680 
 
 68 24 19.88 
 
 75.91 
 
 .608 
 
 .175 4518 
 
 3851 
 
 67 20 54-34 
 
 79-44 
 
 .658 
 
 .194 2695 
 
 3677 
 
 68 25 35.76 
 
 75.84 
 
 .609 
 
 .175 8367 
 
 3848 
 
 67 22 13.74 
 
 79.36 
 
 .659 
 
 . 194 6370 
 
 3674 
 
 6826 51.57 
 
 75-77 
 
 1.610 
 
 1.176 2213 
 
 3844 
 
 67 23 33.07 
 
 79.29 
 
 1.660 
 
 I.I95 0042 
 
 3670 
 
 68 28 07.30 
 
 75-70 
 
 .611 
 
 . 176 6056 
 
 3841 
 
 67 24 52.32 
 
 79.22 
 
 .661 
 
 .195 3710 
 
 3667 
 
 68 29 22.97 
 
 75.63 
 
 .612 
 
 . 176 9895 
 
 3837 
 
 67 26 II.5O 
 
 79-15 
 
 .662 
 
 195 7375 
 
 3663 
 
 68 30 38.56 
 
 75.56 
 
 .613 
 
 . 177 3730 
 
 3834 
 
 67 27 3O.6l 
 
 79-07 
 
 .663 
 
 .196 1037 
 
 3660 
 
 68 31 54-09 
 
 75.49 
 
 .614 
 
 .177 7562 
 
 3830 
 
 67 28 49.65 
 
 79.00 
 
 .664 
 
 . 196 4695 
 
 3656 
 
 68 33 09.54 
 
 75-43 
 
 1.615 
 
 1.178 1390 
 
 3826 
 
 67 30 08. 61 
 
 78.93 
 
 1.665 
 
 1.196 8349 
 
 3653 
 
 68 34 24.93 
 
 75.36 
 
 .616 
 
 .178 5215 
 
 3823 
 
 67 31 27.50 
 
 78.85 
 
 .666 
 
 .197 2OOI 
 
 3650 
 
 68 35 40.24 
 
 75.29 
 
 .617 
 
 . 178 9036 
 
 3819 
 
 67 32 46.32 
 
 78.78 
 
 .667 
 
 .197 5649 
 
 3646 
 
 68 36 55-49 
 
 75-22 
 
 .618 
 
 . 179 2853 
 
 38l6 
 
 67 34 05.06 
 
 78.71 
 
 .668 
 
 . 197 9293 
 
 3643 
 
 68 38 10.66 
 
 75.15 
 
 .619 
 
 .1796667 
 
 3812 
 
 67 35 23.73 
 
 78.63 
 
 .669 
 
 . 198 2935 
 
 3639 
 
 68 39 25.77 
 
 75.08 
 
 1.620 
 
 i . 180 0478 
 
 3809 
 
 67 36 42.33 
 
 78.56 
 
 1.670 
 
 I . 198 6572 
 
 3636 
 
 68 40 40.80 
 
 75-01 
 
 .621 
 
 .180 4285 
 
 3805 
 
 67 38 00.86 
 
 78-49 
 
 .671 
 
 . 199 0207 
 
 3633 
 
 68 41 55-77 
 
 74-94 
 
 .622 
 
 .180 8089 
 
 3802 
 
 67 39 19-31 
 
 78.42 
 
 .672 
 
 .1993838 
 
 3629 
 
 68 43 10.66 
 
 74-87 
 
 .623 
 
 .181 1889 
 
 3798 
 
 67 40 37.69 
 
 78.34 
 
 .673 
 
 .199 7465 
 
 3626 
 
 68 44 25.49 
 
 74.8o 
 
 .624 
 
 .181 5685 
 
 3795 
 
 67 41 56.00 
 
 78.27 
 
 .674 
 
 .200 1090 
 
 3623 
 
 68 45 40.24 
 
 74-72 
 
 1.625 
 
 1.181 9478 
 
 3791 
 
 67 43 H.24 
 
 78.20 
 
 1.675 
 
 I. 200 4711 
 
 3619 
 
 68 46 54-93 
 
 74.65 
 
 .626 
 
 .182 3268 
 
 3788 
 
 67 44 32.40 
 
 78.13 
 
 .676 
 
 .200 8328 
 
 3616 
 
 68 48 09.55 
 
 74-58 
 
 .627 
 
 . 182 7054 
 
 3784 
 
 67 45 50.49 
 
 78.06 
 
 .677 
 
 .2OI 1942 
 
 3612 
 
 68 49 24.09 
 
 74-51 
 
 .628 
 
 .183 0836 
 
 378i 
 
 67 47 08.51 
 
 77.98 
 
 .678 
 
 .201 5553 
 
 3609 
 
 68 50 38.57 
 
 74-44 
 
 .629 
 
 .183 4615 
 
 3777 
 
 67 48 26.46 
 
 77-91 
 
 .679 
 
 .201 9160 
 
 3606 
 
 68 51 52.98 
 
 74-37 
 
 1.630 
 
 1.183 8300 
 
 3774 
 
 67 49 44-33 
 
 77.84 
 
 1.680 
 
 i. 202 2764 
 
 3602 
 
 68 53 07.32 
 
 74.30 
 
 .631 
 
 .184 2162 
 
 3770 
 
 67 51 02.13 
 
 77-77 
 
 .681 
 
 .202 6365 
 
 3599 
 
 68 54 21.58 
 
 74-23 
 
 .632 
 
 .184 593i 
 
 3767 
 
 67 52 19.86 
 
 77.69 
 
 .682 
 
 .202 0962 
 
 3596 
 
 68 55 35-78 
 
 74-17 
 
 .633 
 
 .184 9696 
 
 3763 
 
 67 53 37.52 
 
 77.62 
 
 .683 
 
 .203 3556 
 
 3592 
 
 68 56 49.92 
 
 74.10 
 
 .634 
 
 .185 3457 
 
 376o 
 
 67 54 55.ii 
 
 77-55 
 
 .684 
 
 .203 7147 
 
 3589 
 
 68 58 03.98 
 
 74-03 
 
 1.635 
 
 1.185 7215 
 
 3756 
 
 67 56 12.62 
 
 77.48 
 
 1.685 
 
 1.204 0734 
 
 3586 
 
 68 59 17.97 
 
 73.o6 
 
 .636 
 
 .186 0970 
 
 3753 
 
 67 57 30.07 
 
 77-41 
 
 .686 
 
 .204 4318 
 
 3582 
 
 69 oo 31.89 
 
 73-89 
 
 .637 
 
 .186 4721 
 
 3749 
 
 67 58 47-44 
 
 77.34 
 
 .687 
 
 .204 7899 
 
 3579 
 
 69 oi 45-75 
 
 73.82 
 
 .638 
 
 .1868469 
 
 3746 
 
 68 oo 04.74 
 
 77-26 
 
 .688 
 
 .205 1476 
 
 3576 
 
 69 02 59.53 
 
 73-75 
 
 .639 
 
 .187 2213 
 
 3742 
 
 68 01 21.97 
 
 77.19 
 
 .689 
 
 .205 5050 
 
 3572 
 
 69 04 13.25 
 
 73-68 
 
 1.640 
 
 1.187 5953 
 
 3739 
 
 68 02 39.12 
 
 77.12 
 
 1.690 
 
 1.205 8620 
 
 3569 
 
 69 05 26.90 
 
 73.6i 
 
 .641 
 
 . 187 9691 
 
 3735 
 
 68 03 56.21 
 
 77-05 
 
 .691 
 
 .206 2187 
 
 3566 
 
 69 06 40.48 
 
 73-54 
 
 .642 
 
 . 188 3424 
 
 3732 
 
 68 05 13-22 
 
 76.98 
 
 .692 
 
 .206 5751 
 
 3562 
 
 69 07 53.99 
 
 73.48 
 
 .643 
 
 .188 7155 
 
 3729 
 
 68 06 30.16 
 
 76.91 
 
 .693 
 
 .206 9312 
 
 3559 
 
 69 09 07.43 
 
 73-41 
 
 .644 
 
 .189 0881 
 
 3725 
 
 68 07 47-03 
 
 76.83 
 
 .694 
 
 .207 2869 
 
 3556 
 
 69 10 20.80 
 
 73-34 
 
 1.645 
 
 I . 189 4605 
 
 3722 
 
 68 09 03.83 
 
 76.76 
 
 1.695 
 
 1.207 6423 
 
 3552 
 
 69 ii 34.11 
 
 73-27 
 
 .646 
 
 .1898325 
 
 37i8 
 
 68 10 20.56 
 
 76.69 
 
 .696 
 
 .207 9974 
 
 3549 
 
 69 12 47-34 
 
 73-20 
 
 -647 
 
 .190 2041 
 
 3715 
 
 68 ii 37.22 
 
 76.62 
 
 697 
 
 .208 3521 
 
 3546 
 
 69 14 OO.5I 
 
 73-13 
 
 .648 
 
 .190 5754 
 
 
 68 12 53.80 
 
 76.55 
 
 .698 
 
 .208 7065 
 
 3542 
 
 69 15 I3.6l 
 
 73-07 
 
 .649 
 
 . 190 9463 
 
 3708 
 
 68 14 10.32 
 
 76.48 
 
 .699 
 
 .209 0605 
 
 3539 
 
 69 16 26.64 
 
 73-00 
 
 1.650 
 
 I.I9I 3170 
 
 3704 
 
 68 15 26.76 
 
 76.41 
 
 1.700 
 
 1.209 4143 
 
 3536 
 
 69 17 39.6o 
 
 72.93 
 
 u 
 
 jf 
 
 wsechu 
 
 2tan-'(e)-90 
 
 < tech u 
 
 u 
 
 ""-'<">-i 
 
 usechu 
 
 ""-""^ 
 
 -sechu 
 
 SMITHSONIAN TABLES 
 
 292 
 
The Gudermannian. 
 
 u 
 
 QdU 
 
 F ' 
 
 gd u 
 
 o.Fo' 
 
 u 
 
 gdu 
 
 F O ' 
 
 gd u 
 
 <oF ' 
 
 
 
 
 / // 
 
 
 
 
 
 
 / // 
 
 // 
 
 1.700 
 
 1.209 4H3 
 
 3536 
 
 69 17 39.60 
 
 72.93 
 
 1.750 
 
 1.226 6847 
 
 3374 
 
 70 17 01.89 
 
 69.59 
 
 .701 
 
 .209 7677 
 
 3532 
 
 69 18 52.50 
 
 72.86 
 
 751 
 
 .227 0219 
 
 3370 
 
 70 18 11.44 
 
 69.52 
 
 .702 
 
 .210 1208 
 
 3529 
 
 69 20 05.32 
 
 72.79 
 
 .752 
 
 .227 3588 
 
 3367 
 
 70 19 20.93 
 
 69.45 
 
 .703 
 
 .210 4735 
 
 3526 
 
 69 21 18.08 
 
 72.72 
 
 753 
 
 .227 0954 
 
 3364 
 
 70 20 30.35 
 
 69.39 
 
 .704 
 
 .210 8259 
 
 3522 
 
 09 22 30.77 
 
 72.66 
 
 754 
 
 .228 03l6 
 
 2361 
 
 70 21 39.71 
 
 69.32 
 
 1.705 
 
 I. 211 1780 
 
 3519 
 
 69 23 43-39 
 
 72.59 
 
 1.755 
 
 1.228 3676 
 
 3358 
 
 70 22 49.00 
 
 69.26 
 
 .706 
 
 .211 5297 
 
 35l6 
 
 69 24 55-95 
 
 72.52 
 
 .756 
 
 .228 7032 
 
 3355 
 
 70 23 58.23 
 
 69.19 
 
 .707 
 
 .211 88l2 
 
 3513 
 
 69 26 08.43 
 
 72-45 
 
 757 
 
 .229 0385 
 
 3351 
 
 70 25 07-39 
 
 69.13 
 
 .708 
 
 .212 2323 
 
 3509 
 
 69 27 20.85 
 
 72.38 
 
 .758 
 
 .229 3735 
 
 3348 
 
 70 26 16.48 
 
 69.06 
 
 .709 
 
 .212 5830 
 
 5506 
 
 69 28 33.20 
 
 72.32 
 
 759 
 
 .229 7082 
 
 3345 
 
 70 27 25.51 
 
 69.00 
 
 1.710 
 
 I. 2 12 9335 
 
 3503 
 
 69 29 45.49 
 
 72.25 
 
 1.760 
 
 1.230 0425 
 
 3342 
 
 70 28 34-48 
 
 68.93 
 
 .711 
 
 .213 2836 
 
 3499 
 
 69 30 57.70 
 
 72.18 
 
 .761 
 
 .230 3765 
 
 3339 
 
 70 29 43.38 
 
 68.87 
 
 .712 
 
 .213 6334 
 
 3496 
 
 69 32 09.85 
 
 72.11 
 
 .762 
 
 .230 7103 
 
 3336 
 
 70 30 52.22 
 
 68.80 
 
 .713 
 
 .213 0828 
 
 3493 
 
 69 33 21.93 
 
 72.05 
 
 .763 
 
 .231 0437 
 
 3333 
 
 70 32 00.09 
 
 68.74 
 
 .714 
 
 .214 3319 
 
 3490 
 
 69 34 33-94 
 
 71.98 
 
 .764 
 
 .231 3768 
 
 3329 
 
 70 33 09.69 
 
 68.6> 
 
 1.715 
 
 1.214 6807 
 
 3486 
 
 69 35 45.89 
 
 71.91 
 
 1.765 
 
 1.231 7006 
 
 3326 
 
 70 34 18.33 
 
 68.61 
 
 .716 
 
 .215 0292 
 
 3483 
 
 69 36 57.76 
 
 71.84 
 
 .766 
 
 .232 0420 
 
 3323 
 
 70 35 26.91 
 
 68.54 
 
 .717 
 .718 
 
 .215 3774 
 .215 7252 
 
 348o 
 3477 
 
 69 38 09.57 
 69 39 21.32 
 
 71.78 
 71.71 
 
 .767 
 .768 
 
 .232 3742 
 .232 7060 
 
 3320 
 3317 
 
 70 36 35.42 
 70 37 43-87 
 
 68.48 
 68.42 
 
 .719 
 
 .216 0727 
 
 3473 
 
 69 40 32.99 
 
 71.64 
 
 .769 
 
 .233 0376 
 
 33M 
 
 70 38 52.25 
 
 68.35 
 
 1.720 
 
 I. 216 4198 
 
 3470 
 
 69 41 44.60 
 
 71.58 
 
 1.770 
 
 1.233 3688 
 
 3311 
 
 70 40 00.57 
 
 68.29 
 
 .721 
 
 .216 7667 
 
 3467 
 
 69 42 56. 14 
 
 7i.5i 
 
 771 
 
 .233 6997 
 
 3307 
 
 70 41 08.83 
 
 68.22 
 
 .722 
 
 .217 1132 
 
 3464 
 
 69 44 07.62 
 
 71.44 
 
 .772 
 
 .234 0303 
 
 3304 
 
 70 42 17.02 
 
 68.16 
 
 .723 
 
 .217 4594 
 
 3400 
 
 69 45 19.02 
 
 71.37 
 
 773 
 
 .234 3606 
 
 3301 
 
 70 43 25.14 
 
 68.09 
 
 .724 
 
 .217 8053 
 
 3457 
 
 69 46 30.37 
 
 7i.3i 
 
 774 
 
 .234 6905 
 
 3298 
 
 70 44 33.20 
 
 68.03 
 
 1.725 
 
 i. 218 1508 
 
 3454 
 
 69 47 41.64 
 
 71.23 
 
 1.775 
 
 1.235 O2O2 
 
 3295 
 
 7045 41.20 
 
 67-96 
 
 .726 
 
 .218 4060 
 
 3451 
 
 69 48 52.85 
 
 71.16 
 
 .776 
 
 235 3495 
 
 3292 
 
 70 46 49.13 
 
 67.90 
 
 .727 
 
 .218 8409 
 
 3447 
 
 69 50 03.99 
 
 71.10 
 
 777 
 
 .235 6786 
 
 3289 
 
 70 47 57-00 
 
 67.84 
 
 .728 
 
 .219 1855 
 
 3444 
 
 69 51 15.06 
 
 71.03 
 
 .778 
 
 .236 0073 
 
 3286 
 
 70 49 04.80 
 
 67.77 
 
 .729 
 
 .219 5297 
 
 3441 
 
 69 52 26.06 
 
 70.96 
 
 779 
 
 .236 3357 
 
 3283 
 
 70 50 12.54 
 
 67.71 
 
 1.730 
 
 I.2I98737 
 
 3438 
 
 69 53 37-90 
 
 70.00 
 
 1.780 
 
 1.236 6638 
 
 3279 
 
 70 51 20.22 
 
 67.64 
 
 .731 
 
 .220 2173 
 
 3434 
 
 69 54 47.88 
 
 70.83 
 
 .781 
 
 .236 9916 
 
 3276 
 
 70 52 27.83 
 
 67.58 
 
 .732 
 
 .220 5605 
 
 3431 
 
 69 55 58.68 
 
 70.76 
 
 .782 
 
 .237 3i9i 
 
 3273 
 
 70 53 35.38 
 
 67.52 
 
 .733 
 
 .220 0035 
 
 3428 
 
 69 57 09.42 
 
 70.70 
 
 .783 
 
 .237 6463 
 
 3270 
 
 70 54 42.87 
 
 67.45 
 
 734 
 
 .221 2461 
 
 3425 
 
 69 58 20. 10 
 
 70.63 
 
 .784 
 
 .237 9731 
 
 3267 
 
 70 55 50.29 
 
 67.39 
 
 1.735 
 
 I. 221 5885 
 
 3422 
 
 69 59 30.71 
 
 70.56 
 
 1.785 
 
 1.238 2097 
 
 3264 
 
 70 56 57.65 
 
 67.33 
 
 .736 
 
 .221 9304 
 
 3418 
 
 70 oo 41.25 
 
 70.50 
 
 .786 
 
 .238 6259 
 
 3261 
 
 70 58 04.94 
 
 67.26 
 
 737 
 
 .222 2721 
 
 3415 
 
 70 01 51.72 
 
 70.43 
 
 .787 
 
 .238 9519 
 
 3258 
 
 70 59 12.17 
 
 67.20 
 
 .738 
 
 .222 6135 
 
 3412 
 
 70 03 02.13 
 
 70.37 
 
 .788 
 
 .239 2775 
 
 3255 
 
 71 oo 19.34 
 
 67.13 
 
 739 
 
 .222 9545 
 
 3409 
 
 70 04 12.47 
 
 70.30 
 
 .789 
 
 .239 6028 
 
 3252 
 
 71 01 26.44 
 
 67.07 
 
 1.740 
 
 1.223 2952 
 
 3405 
 
 70 05 22.75 
 
 70.23 
 
 1.790 
 
 1.2399279 
 
 3249 
 
 71 02 33.48 
 
 67.01 
 
 .741 
 
 .223 6356 
 
 3402 
 
 70 06 32.96 
 
 70.18 
 
 .791 
 
 .240 2526 
 
 3246 
 
 71 03 40.46 
 
 66.94 
 
 742 
 
 .223 9757 
 
 3399 
 
 70 07 43.10 
 
 70.11 
 
 .792 
 
 .240 5770 
 
 3243' 
 
 71 04 47-37 
 
 66.88 
 
 743 
 
 .224 3154 
 
 3396 
 
 70 08 53-18 
 
 70.05 
 
 793 
 
 .240 9011 
 
 3239 
 
 71 05 54-22 
 
 66.82 
 
 744 
 
 .224 6548 
 
 3393 
 
 70 10 03.19 
 
 69.98 
 
 .794 
 
 .241 2249 
 
 3236 
 
 71 07 01.01 
 
 66.76 
 
 1.745 
 
 1.224 9940 
 
 3390 
 
 70 ii 13.14 
 
 69.91 
 
 1.795 
 
 1.241 5483 
 
 3233 
 
 71 08 07.73 
 
 66.69 
 
 .746 
 
 .225 3328 
 
 3386 
 
 70 12 23.02 
 
 69.85 
 
 .796 
 
 .241 8715 
 
 3230 
 
 71 09 14.39 
 
 66.63 
 
 747 
 
 .225 6712 
 
 3383 
 
 70 13 32.84 
 
 69.78 
 
 797 
 
 .242 1044 
 
 3227 
 
 71 10 20.99 
 
 66.57 
 
 .748 
 
 .226 0094 
 
 338o 
 
 70 14 42.59 
 
 69.72 
 
 .798 
 
 .242 5170 
 
 3224 
 
 71 II 27.52 
 
 66.50 
 
 749 
 
 .226 3472 
 
 3377 
 
 70 15 52.27 
 
 69.65 
 
 799 
 
 .242 8392 
 
 3221 
 
 71 12- 33-99 
 
 66.44 
 
 1.750 
 
 1.226 6847 
 
 3374 
 
 70 17 01.89 
 
 69.59 
 
 1.800 
 
 1.243 1612 
 
 3218 
 
 71 13 40.40 
 
 66.38 
 
 u 
 
 2 tan-He") 
 
 >sechu 
 
 atan-Keih-SO 
 
 w sech u 
 
 u 
 
 2tan-Ke)-!5 
 
 wsechu 
 
 Ztan-Keuh-eO 
 
 co sech u 
 
 SMITHSONIAN TABLES 
 
 293 
 
The Gudermannian. 
 
 u 
 
 gd u 
 
 O>FO' 
 
 gd u 
 
 O.FO' 
 
 U 
 
 gdu 
 
 F ' 
 
 odu 
 
 F</ 
 
 1. 800 
 
 1.243' 1612 
 
 3218 
 
 o / // 
 
 71 13 40.40 
 
 66? 3 8 
 
 1.850 
 
 1.258 8759 
 
 3069 
 
 72 07 41.78 
 
 
 
 63.30 
 
 .801 
 
 .243 4828 
 
 3215 
 
 71 14 46.75 
 
 66.31 
 
 .851 
 
 .219 1826 
 
 3066 
 
 72 08 45.05 
 
 63.24 
 
 .802 
 
 .243 8042 
 
 3212 
 
 71 15 53.03 
 
 66.25 
 
 .852 
 
 .259 4890 
 
 3063 
 
 72 09 48.26 
 
 63:18 
 
 .803 
 
 .244 1252 
 
 3209 
 
 71 16 59.25 
 
 66.19 
 
 .853 
 
 .259 7952 
 
 3060 
 
 72 10 51.41 
 
 63.12 
 
 .804 
 
 .244 4460 
 
 3206 
 
 71 18 05.41 
 
 66.13 
 
 .854 
 
 .260 ion 
 
 3057 
 
 72 II 54.50 
 
 63.06 
 
 1.805 
 
 1.244 7664 
 
 3203 
 
 71 19 11.50 
 
 66.06 
 
 1.855 
 
 1.260 4066 
 
 3054 
 
 72 12 57.53 
 
 63.00 
 
 .806 
 
 .245 0865 
 
 3200 
 
 71 20 17.53 
 
 66.00 
 
 .856 
 
 .260 7119 
 
 3051 
 
 72 14 OO.5O 
 
 62.94 
 
 .807 
 
 .245 4064 
 
 3i97 
 
 71 21 23.50 
 
 65.94 
 
 .857 
 
 .261 0169 
 
 3048 
 
 72 15 03.41 
 
 62.88 
 
 .808 
 
 .245 7259 
 
 3i94 
 
 71 22 29.41 
 
 65.88 
 
 .858 
 
 .261 3216 
 
 3046 
 
 72 16 06.26 
 
 62.82 
 
 .809 
 
 .246 0451 
 
 3191 
 
 71 23 35.26 
 
 65.81 
 
 .859 
 
 .261 6260 
 
 3043 
 
 72 17 09.05 
 
 62.76 
 
 1.810 
 
 1.246 3640 
 
 3188 
 
 71 24 41.04 
 
 65.75 
 
 1.860 
 
 1.261 9302 
 
 3040 
 
 72 18 11.78 
 
 62.70 
 
 .811 
 
 .246 6827 
 
 3185 
 
 71 25 46.76 
 
 65.69 
 
 .861 
 
 .262 2340 
 
 3037 
 
 72 19 14.45 
 
 62.64 
 
 .812 
 
 .247 ooio 
 
 3182 
 
 71 26 52.42 
 
 65.63 
 
 .862 
 
 .262 5375 
 
 3034 
 
 72 20 17.06 
 
 62.58 
 
 .813 
 
 .247 3100 
 
 3i79 
 
 71 27 58.01 
 
 65.56 
 
 .863 
 
 .262 8408 
 
 3031 
 
 72 21 I9.6l 
 
 62.52 
 
 .814 
 
 .247 6367 
 
 3176 
 
 71 29 03.54 
 
 65.50 
 
 .864 
 
 .263 1438 
 
 3028 
 
 72 22 22. IO 
 
 62.46 
 
 1.815 
 
 1.247 9541 
 
 3i73 
 
 71 .30 09.02 
 
 65.44 
 
 1.865 
 
 1.263 4464 
 
 3025 
 
 72 23 24.54 
 
 62.40 
 
 .816 
 
 .248 2712 
 
 3170 
 
 71 31 14.42 
 
 65.38 
 
 .866 
 
 .263 7488 
 
 3022 
 
 72 24 26.91 
 
 62.34 
 
 .817 
 
 .248 5880 
 
 3167 
 
 71 32 19.77 
 
 65.32 
 
 .867 
 
 .264 0509 
 
 3020 
 
 72 25 29.22 
 
 62.28 
 
 .818 
 
 .248 9046 
 
 3164 
 
 71 33 25.06 
 
 65.25 
 
 .868 
 
 .264 3527 
 
 3017 
 
 72 26 31.47 
 
 62.22 
 
 .819 
 
 .249 2208 
 
 3161 
 
 71 34 30.28 
 
 65.19 
 
 .869 
 
 .264 6543 
 
 3014 
 
 72 27 33-67 
 
 62.16 
 
 1.820 
 
 1.249 5367 
 
 3158 
 
 7i 35 35-44 
 
 65.13 
 
 1.870 
 
 1.264 9555 
 
 3011 
 
 72 28 35.80 
 
 62.11 
 
 .821 
 
 .249 8523 
 
 3i55 
 
 71 36 40.54 
 
 65.07 
 
 .871 
 
 .265 2565 
 
 3008 
 
 72 29 37-88 
 
 62.05 
 
 .822 
 
 .250 1676 
 
 3152 
 
 71 37 45.58 
 
 65.01 
 
 .872 
 
 .265 5571 
 
 3005 
 
 72 30 39.90 
 
 61.99 
 
 .823 
 
 .250 4826 
 
 3i49 
 
 71 38 50.56 
 
 64.95 
 
 .873 
 
 .265 8575 
 
 3002 
 
 72 31 41-85 
 
 61.93 
 
 .824 
 
 .250 7973 
 
 3146 
 
 71 39 55-47 
 
 64.88 
 
 .874 
 
 .266 1576 
 
 2999 
 
 72 32 43-75 
 
 61.87 
 
 1.825 
 
 1.251 1118 
 
 3U3 
 
 71 41 00.32 
 
 64.82 
 
 1.875 
 
 1.266 4574 
 
 2997 
 
 72 33 45-59 
 
 61.81 
 
 .826 
 
 .251 4259 
 
 3140 
 
 71 42 05.11 
 
 64.76 
 
 .876 
 
 .266 7569 
 
 2994 
 
 72 34 47.37 
 
 6i.75 
 
 .827 
 
 .251 7397 
 
 3i37 
 
 71 43 09.84 
 
 64.70 
 
 .877 
 
 .267 0562 
 
 
 72 35 49-09 
 
 61.69 
 
 .828 
 
 .252 0532 
 
 3i34 
 
 71 44 14.51 
 
 64.64 
 
 .878 
 
 .267 3551 
 
 2988 
 
 72 36 50.75 
 
 61.63 
 
 .829 
 
 .252 3664 
 
 3131 
 
 71 45 19.12 
 
 64.58 
 
 .879 
 
 .267 6538 
 
 2985 
 
 72 37 52.36 
 
 6i.57 
 
 1.830 
 
 1.252 6794 
 
 3128 
 
 71 46 23.67 
 
 64.52 
 
 1.880 
 
 1.267 9521 
 
 2982 
 
 72 38 53-90 
 
 61.52 
 
 .831 
 
 .252 9920 
 
 3125 
 
 71 47 28.15 
 
 64.45 
 
 .881 
 
 .268 2502 
 
 2980 
 
 72 39 55-39 
 
 61.46 
 
 .832 
 
 .253 3043 
 
 3122 
 
 71 48 32.57 
 
 64.39 
 
 .882 
 
 .268 5480 
 
 2977 
 
 72 40 56.82 
 
 61.40 
 
 .833 
 
 .253 6164 
 
 3119 
 
 71 49 36.94 
 
 64.33 
 
 .883 
 
 .268 8456 
 
 2974 
 
 72 41 58.19 
 
 61.34 
 
 .834 
 
 .253 9281 
 
 3116 
 
 71 5041.24 
 
 64.27 
 
 .884 
 
 .269 1428 
 
 2971 
 
 72 42 59.50 
 
 61.28 
 
 1.835 
 
 1.254 2396 
 
 3113 
 
 71 51 45.48 
 
 64.21 
 
 1.885 
 
 1.269 4308 
 
 2068 
 
 72 44 00.75 
 
 61.22 
 
 .836 
 
 .254 5507 
 
 3110 
 
 71 52 49.66 
 
 64.15 
 
 .886 
 
 .269 7364 
 
 2965 
 
 72 45 01.94 
 
 61.16 
 
 .837 
 
 .254 8616 
 
 3107 
 
 71 53 53-77 
 
 64.09 
 
 .887 
 
 .270 0328 
 
 2962 
 
 72 46 03.08 
 
 6i.n 
 
 .838 
 
 .255 1721 
 
 3104 
 
 71 54 57.83 
 
 64.03 
 
 .888 
 
 .270 3289 
 
 2960 
 
 7247 04.15 
 
 61.05 
 
 .839 
 
 .255 4824 
 
 3101 
 
 71 56 01.83 
 
 63.97 
 
 .889 
 
 .270 6248 
 
 2957 
 
 72 48 05.17 
 
 60.99 
 
 1.840 
 
 1.255 7923 
 
 3098 
 
 71 57 05.76 
 
 63.91 
 
 1.890 
 
 1.270 9203 
 
 2954 
 
 72 49 06.13 
 
 60.93 
 
 .841 
 
 .256 IO2O 
 
 3095 
 
 71 58 09.64 
 
 63-84 
 
 .891 
 
 .271 2156 
 
 2951 
 
 72 50 07.03 
 
 60.87 
 
 .842 
 
 .256 4114 
 
 3092 
 
 71 59 13-45 
 
 63.78 
 
 .892 
 
 .271 5106 
 
 2948 
 
 72 51 07.88 
 
 60.81 
 
 .843 
 
 .256 7205 
 
 3089 
 
 72 oo 17.21 
 
 63.72 
 
 .893 
 
 .271 8053 
 
 2946 
 
 72 52 08.66 
 
 60.76 
 
 .844 
 
 .257 0293 
 
 3086 
 
 72 01 20.90 
 
 63.66 
 
 .894 
 
 .272 0997 
 
 2943 
 
 72 53 09.39 
 
 60.70 
 
 1.845 
 
 1.257 3378 
 
 3084 
 
 72 02 24.53 
 
 63.60 
 
 1.895 
 
 1.272 3938 
 
 2940 
 
 7*2 54 10.06 
 
 60.64 
 
 .846 
 
 .257 6460 
 
 3081 
 
 72 03 28.10 
 
 63.54 
 
 .896 
 
 .272 6877 
 
 2937 
 
 72 55 10.67 
 
 60.58 
 
 .847 
 
 .257 9539 
 
 3078 
 
 72 04 31.61 
 
 63.48 
 
 .897 
 
 .272 9812 
 
 2934 
 
 72 56 11.23 
 
 60.52 
 
 .848 
 
 .258 2615 
 
 3075 
 
 72 05 35.06 
 
 63.42 
 
 .898 
 
 .273 2745 
 
 2932 
 
 72 57 11.72 
 
 60.47 
 
 .849 
 
 .258 5688 
 
 3072 
 
 72 06 38.45 
 
 63-36 
 
 .899 
 
 .273 5675 
 
 2929 
 
 72 58 12. 16 
 
 60.41 
 
 1.850 
 
 1.2588759 
 
 3069 
 
 72 07 41.78 
 
 63.30 
 
 1.900 
 
 1.273 8603 
 
 2926 
 
 72 59 12.54 
 
 60.35 
 
 u 
 
 2tan- 1 (e)-~ 
 
 <> sech u 
 
 2tan- 1 (e)-90 
 
 wsechu 
 
 u 
 
 2tan-'(e)-2 
 
 o> sech u 
 
 2tan- J (e)-90 
 
 sech u 
 
 SMITHSONIAN TABLES 
 
 294 
 
The Gudermannian. 
 
 u 
 
 gdu 
 
 Fo' 
 
 gd u 
 
 F ' 
 
 u 
 
 gd u 
 
 
 
 gdu 
 
 " 
 
 
 
 
 / // 
 
 m 
 
 
 
 
 o / // 
 
 m 
 
 1.900 
 
 1.273 8603 
 
 2926 
 
 72 59 12.54 
 
 60.35 
 
 1-950 
 
 1.288 1451 
 
 2789 
 
 73 48 19.01 
 
 57-53 
 
 .901 
 
 .274 1527 
 
 2923 
 
 73 oo 12.86 
 
 60.29 
 
 .951 
 
 .288 4239 
 
 2786 
 
 73 49 16.51 
 
 57-47 
 
 .902 
 
 .274 4449 
 
 2920 
 
 73 oi 13.13 
 
 60.24 
 
 .952 
 
 .288 7024 
 
 2784 
 
 73 50 13-95 
 
 57.42 
 
 .903 
 
 .274 7368 
 
 2918 
 
 73 02 13.33 
 
 60. 18 
 
 953 
 
 .2889806 
 
 2781 
 
 73 51 11.34 
 
 57.36 
 
 .904 
 
 .275 0284 
 
 2915 
 
 73 03 13.48 
 
 60.12 
 
 954 
 
 .289 2586 
 
 2778 
 
 73 52 08.68 
 
 57.31 
 
 1.005 
 
 1.275 3197 
 
 2912 
 
 73 04 13.58 
 
 60.06 
 
 1.955 
 
 1.289 5363 
 
 2776 
 
 73 53 05.96 
 
 57.25 
 
 .906 
 
 .275 6108 
 
 2909 
 
 73 05 13.61 
 
 60. oi 
 
 .956 
 
 .289 8137 
 
 2773 
 
 73 5403.18 
 
 57.20 
 
 .907 
 
 .275 9016 
 
 2906 
 
 73 06 13.59 
 
 59-95 
 
 .957 
 
 .290 0009 
 
 2770 
 
 73 55 00.35 
 
 57.14 
 
 .908 
 
 .276 1921 
 
 2004 
 
 73 07 13-51 
 
 59.89 
 
 .958 
 
 .290 3678 
 
 2768 
 
 73 55 57.46 
 
 57.09 
 
 .909 
 
 .276 4823 
 
 2001 
 
 73 08 13-37 
 
 59.83 
 
 959 
 
 .290 6444 
 
 2765 
 
 73 56 54.52 
 
 57-03 
 
 1.910 
 
 1.276 7722 
 
 2898 
 
 73 09 13.18 
 
 59.78 
 
 1.960 
 
 1.290 9208 
 
 2762 
 
 73 57 51.53 
 
 56.98 
 
 .911 
 
 .277 0619 
 
 2895 
 
 73 10 12.92 
 
 59.72 
 
 .961 
 
 .291 1969 
 
 2760 
 
 73 58 48.48 
 
 56.92 
 
 .912 
 
 .277 3513 
 
 2893 
 
 73 II 12.62 
 
 59.66 
 
 .962 
 
 .291 4727 
 
 2757 
 
 73 59 45.38 
 
 56.87 
 
 .913 
 
 .277 6404 
 
 2890 
 
 73 12 12.25 
 
 59.6i 
 
 .963 
 
 .291 7483 
 
 2754 
 
 74 oo 42.22 
 
 56.81 
 
 .914 
 
 .277 9292 
 
 2887 
 
 73 13 11.83 
 
 59-55 
 
 .964 
 
 .292 0236 
 
 2752 
 
 74 Oi 39-00 
 
 56.76 
 
 I.9I5 
 .916 
 
 1.278 2178 
 .278 5061 
 
 2884 
 2881 
 
 73 14 n.35 
 73 15 10.81 
 
 59.49 
 59-43 
 
 'pjs 
 
 .966 
 
 1.292 2987 
 .292 5734 
 
 2749 
 2746 
 
 74 02 35.73 
 74 03 32.41 
 
 56.70 
 56.65 
 
 .917 
 
 .278 7941 
 
 2879 
 
 73 16 10.22 
 
 59.38 
 
 .967 
 
 .292 8480 
 
 2744 
 
 74 04 29.03 
 
 56.60 
 
 .918 
 
 .279 0818 
 
 2876 
 
 73 17 09.56 
 
 59-32 
 
 .968 
 
 .293 1222 
 
 2741 
 
 74 05 25.60 
 
 56.54 
 
 .919 
 
 .279 3693 
 
 2873 
 
 73 18 08.86 
 
 59.26 
 
 .969 
 
 .293 3962 
 
 2739 
 
 74 06 22.12 
 
 56.49 
 
 1.920 
 
 1.279 6565 
 
 2870 
 
 73 19 08.09 
 
 59-21 
 
 1.970 
 
 1.293 6699 
 
 2736 
 
 74 07 18.58 
 
 56.43 
 
 .921 
 
 .279 9434 
 
 2868 
 
 73 20 07.27 
 
 59.15 
 
 .971 
 
 .293 9434 
 
 2733 
 
 74 08 14.98 
 
 56.38 
 
 .922 
 
 .280 2300 
 
 2865 
 
 73 21 06.39 
 
 59-09 
 
 972 
 
 .294 2166 
 
 2731 
 
 74 09 11.33 
 
 56.32 
 
 .923 
 
 .280 5164 
 
 2862 
 
 73 22 05.46 
 
 59.04 
 
 .973 
 
 .294 4895 
 
 2728 
 
 74 10 07.63 
 
 56.27 
 
 .924 
 
 .280 8024 
 
 2859 
 
 73 23 04-47 
 
 58.98 
 
 .974 
 
 .294 7622 
 
 2725 
 
 74 II 03.87 
 
 56.22 
 
 1.925 
 
 1.281 0883 
 
 2857 
 
 73 24 03.42 
 
 58.92 
 
 1.975 
 
 1.295 0346 
 
 2723 
 
 74 12 00.06 
 
 56.16 
 
 .926 
 
 .281 3738 
 
 2854 
 
 73 25 02.32 
 
 58.87 
 
 .976 
 
 .295 3068 
 
 2720 
 
 74 12 56.20 
 
 56.11 
 
 .927 
 
 .281 6590 
 
 2851 
 
 73 26 01.16 
 
 58.81 
 
 977 
 
 .295 5786 
 
 2718 
 
 74 13 52.28 
 
 56.05 
 
 .928 
 
 .281 9440 
 
 2849 
 
 73 26 59-94 
 
 58.76 
 
 .978 
 
 .295 8503 
 
 2715 
 
 74 14 48.30 
 
 56.00 
 
 .929 
 
 .282 2288 
 
 2846 
 
 73 27 58.67 
 
 58.70 
 
 979 
 
 .296 1216 
 
 2712 
 
 74 15 44.28 
 
 55-95 
 
 1.930 
 
 1.282 5132 
 
 2843 
 
 73 28 57-34 
 
 58.64 
 
 1.980 
 
 1.296 3927 
 
 2710 
 
 74 16 40.20 
 
 55.89 
 
 931 
 
 .282 7974 
 
 2840 
 
 73 29 55.95 
 
 58.59 
 
 .981 
 
 .2966636 
 
 2707 
 
 74 17 36.06 
 
 55.84 
 
 932 
 
 .283 0813 
 
 2838 
 
 73 30 54.51 
 
 58.53 
 
 .982 
 
 .296 9342 
 
 2705 
 
 74 18 31.87 
 
 55.78 
 
 .933 
 934 
 
 .283 3649 
 .283 6482 
 
 2835 
 2832 
 
 73 3i 53.01 
 73 32 51.46 
 
 58.47 
 58.42 
 
 .983 
 
 .984 
 
 .297 2045 
 .297 4745 
 
 2702 
 2699 
 
 74 19 27.63 
 47 20 23.34 
 
 55.73 
 55.68 
 
 1-935 
 
 1.283 9313 
 
 2829 
 
 73 33 49.85 
 
 58.36 
 
 1.985 
 
 1.297 7443 
 
 2697 
 
 74 21 1^.99 
 
 55.62 
 
 .936 
 
 .284 2141 
 
 2827 
 
 73 34 48.18 
 
 58.31 
 
 .986 
 
 .298 0139 
 
 2694 
 
 74 22 14.58 
 
 55-57 
 
 .937 
 
 .284 4967 
 
 2824 
 
 73 35 46.46 
 
 58.25 
 
 .987 
 
 .298 2832 
 
 2692 
 
 74 23 10.13 
 
 55.52 
 
 .938 
 
 .284 7789 
 
 2821 
 
 73 36 44-68 
 
 58.19 
 
 .988 
 
 .298 5522 
 
 2689 
 
 74 24 05.62 
 
 55.46 
 
 .939 
 
 .285 0609 
 
 2819 
 
 73 37 42.85 
 
 58.14 
 
 .989 
 
 .298 8210 
 
 2686 
 
 74 25 01.05 
 
 55.41 
 
 1.040 
 
 1.285 3427 
 
 28l6 
 
 73 38 40.96 
 
 58.08 
 
 1.990 
 
 1.299 0895 
 
 2684 
 
 74 25 56.44 
 
 55.36 
 
 .941 
 
 .285 6241 
 
 2813 
 
 73 39 39.01 
 
 58.03 
 
 .991 
 
 .209 3577 
 
 2681 
 
 74 26 51.77 
 
 55-30 
 
 .942 
 
 .285 9053 
 
 28ll 
 
 73 40 37-01 
 
 57-97 
 
 .992 
 
 .299 6257 
 
 2679 
 
 74 27 47.04 
 
 55-25 
 
 943 
 
 .286 1862 
 
 2808 
 
 73 4i 34-95 
 
 57.92 
 
 993 
 
 .299 8934 
 
 2676 
 
 74 28 42.27 
 
 55-20 
 
 .944 
 
 .2864669 
 
 2805 
 
 73 42 32.84 
 
 57-86 
 
 .994 
 
 .300 1609 
 
 2673' 
 
 74 29 37.44 
 
 55.14 
 
 1.945 
 
 1.286 7473 
 
 2802 
 
 73 43 30.68 
 
 57.8o 
 
 1.995 
 
 1.300 4281 
 
 2671 
 
 74 30 32.55 
 
 55.09 
 
 .946 
 
 .287 0274 
 
 2800 
 
 73 44 28.45 
 
 57-75 
 
 .996 
 
 .300 6951 
 
 2668 
 
 74 31 27.62 
 
 55.04 
 
 947 
 
 .287 3072 
 
 2797 
 
 73 45 26.17 
 
 57.69 
 
 997 
 
 .300 9618 
 
 2666 
 
 74 32 22.63 
 
 54.98 
 
 .948 
 
 .287 5868 
 
 2794 
 
 73 46 23.84 
 
 57.64 
 
 .998 
 
 .301 2282 
 
 2663 
 
 74 33 17.59 
 
 
 949 
 
 .287 8661 
 
 2792 
 
 73 47 21.45 
 
 57.58 
 
 .999 
 
 .301 4944 
 
 2661 
 
 74 34 12.49 
 
 54.88 
 
 1.950 
 
 1.288 1451 
 
 2789 
 
 73 48 19.01 
 
 57-53 
 
 2.000 
 
 1.301 7603 
 
 2658 
 
 74 35 Q7.34 
 
 54.83 
 
 u 
 
 2ta "- 1(e >-i 
 
 co sech u 
 
 "^H* 
 
 w sech u 
 
 U 
 
 7T 
 
 CD sech u 
 
 * 
 
 w sech u 
 
 SMITHSONIAN TABLES 
 
 2Q5 
 
The Gudermannian. 
 
 u 
 
 Qdu 
 
 wF ' 
 
 gd u 
 
 wF ' 
 
 u 
 
 gd u 
 
 F ' 
 
 gdu 
 
 F O ' 
 
 2.000 
 
 1.301 7603 
 
 2658 
 
 74 35 07-34 
 
 54*83 
 
 2.050 
 
 1.314 7349 
 
 2533 
 
 o / // 
 
 75 19 43-53 
 
 a 
 
 52.24 
 
 .001 
 
 .302 0260 
 
 2655 
 
 74 36 02.14 
 
 54-77 
 
 .051 
 
 .314 988o 
 
 2530 
 
 75 20 35.75 
 
 52.19 
 
 .002 
 
 .302 2914 
 
 2653 
 
 74 36 56.89 
 
 54.72 
 
 .052 
 
 .315 2409 
 
 2528 
 
 75 21 27.91 
 
 52.14 
 
 .003 
 .004 
 
 .302 5566 
 .302 8215 
 
 2650 
 2648 
 
 74 37 51.58 
 74 38 46.22 
 
 54.67 
 54.61 
 
 .053 
 .054 
 
 .315 4936 
 .315 7400 
 
 2525 
 2523 
 
 75 22 20.03 
 75 23 12.09 
 
 52.09 
 52.04 
 
 2.005 
 
 1.303 0861 
 
 2645 
 
 74 39 40.81 
 
 54.56 
 
 2.055 
 
 I.3I5 0982 
 
 2520 
 
 75 24 04.11 
 
 51.99 
 
 .006 
 
 .007 
 
 .303 3505 
 .303 6147 
 
 2643 
 2640 
 
 74 40 35-35 
 74 41 29.83 
 
 54-51 
 54.46 
 
 .056 
 .057 
 
 .316 2501 
 .316 5018 
 
 2518 
 2516 
 
 75 24 56.07 
 75 25 47.98 
 
 51-94 
 
 51.89 
 
 .008 
 
 .303 8786 
 
 2638 
 
 74 42 24.26 
 
 54.40 
 
 .058 
 
 316 7532 
 
 2513 
 
 75 26 39.85 
 
 51.84 
 
 .009 
 
 .304 1422 
 
 2635 
 
 74 43 18.64 
 
 54-35 
 
 .059 
 
 .317 0044 
 
 2511 
 
 75 27 31.66 
 
 5L79 
 
 2.OIO 
 
 1.304 4056 
 
 2633 
 
 74 44 12.97 
 
 54-30 
 
 2.060 
 
 1.317 2554 
 
 2508 
 
 75 28 23.42 
 
 51.74 
 
 .Oil 
 
 .304 6687 
 
 2630 
 
 74 45 07.24 
 
 54.25 
 
 .061 
 
 .317 5o6i 
 
 2506 
 
 75 29 15.14 
 
 51.69 
 
 .012 
 
 .304 0316 
 
 2627 
 
 74 46 01.46 
 
 54.19 
 
 .062 
 
 .317 7566 
 
 2503 
 
 75 30 06.80 
 
 51.64 
 
 .013 
 
 .305 1942 
 
 2625 
 
 74 46 55.63 
 
 54.14 
 
 .063 
 
 .318 0068 
 
 2501 
 
 75 30 58.41 
 
 5L59 
 
 .014 
 
 .305 4566 
 
 2622 
 
 74 47 49-74 
 
 54.09 
 
 .064 
 
 .318 2568 
 
 2499 
 
 75 31 49.98 
 
 51.54 
 
 2.015 
 
 1-305 7187 
 
 2620 
 
 74 48 43.8i 
 
 54.04 
 
 2.065 
 
 1.318 5065 
 
 2496 
 
 75 32 41-49 
 
 51.49 
 
 .Ol6 
 
 .305 9805 
 
 2617 
 
 74 49 37.82 
 
 53-99 
 
 .066 
 
 .318 756o 
 
 2494 
 
 75 33 32.95 
 
 51.44 
 
 .017 
 
 .306 2421 
 
 2615 
 
 74 50 31-78 
 
 53-93 
 
 .067 
 
 .319 0053 
 
 2491 
 
 75 34 24.37 
 
 51-39 
 
 .018 
 
 .306 5035 
 
 2612 
 
 74 51 25.69 
 
 53-88 
 
 .068 
 
 .319 2543 
 
 2489 
 
 75 35 15.73 
 
 51.34 
 
 .OI9 
 
 .306 7646 
 
 26lO 
 
 74 52 19.54 
 
 53.83 
 
 .069 
 
 .319 5031 
 
 2487 
 
 75 36 07.04 
 
 51.29 
 
 2.O2O 
 
 1.307 0254 
 
 2007 
 
 74 53 13.35 
 
 53.78 
 
 2.070 
 
 L3I9 75i6 
 
 2484 
 
 75 36 58.31 
 
 51.24 
 
 .021 
 
 .307 2860 
 
 2605 
 
 74 54 07.10 
 
 53-73 
 
 .071 
 
 .319 9999 
 
 2482 
 
 75 37 49.52 
 
 51-19 
 
 .022 
 
 .307 5464 
 
 2OO2 
 
 74 55 00.80 
 
 53.67 
 
 .072 
 
 .320 2480 
 
 2479 
 
 75 38 40.69 
 
 5LI4 
 
 .023 
 
 .307 8065 
 
 2600 
 
 74 55 54-45 
 
 53.62 
 
 .073 
 
 .320 4958 
 
 2477 
 
 75 39 31-80 
 
 51.09 
 
 .024 
 
 .3080663 
 
 2597 
 
 74 56 48.05 
 
 53-57 
 
 .074 
 
 320 7433 
 
 2475 
 
 75 40 22.87 
 
 5L04 
 
 2.O25 
 
 1.308 3259 
 
 2595 
 
 74 57 41-59 
 
 53.52 
 
 2.075 
 
 1.3209907 
 
 2472 
 
 75 41 13.89 
 
 50-99 
 
 .026 
 
 308 5853 
 
 2592 
 
 74 58 35.o8 
 
 53-47 
 
 .076 
 
 .321 2378 
 
 2470 
 
 75 42 04.85 
 
 50-94 
 
 .027 
 
 .308 8443 
 
 2590 
 
 74 59 28.52 
 
 53.42 
 
 .077 
 
 .321 4846 
 
 2467 
 
 75 42 55-77 
 
 50.89 
 
 .028 
 
 .309 1032 
 
 2587 
 
 75 oo 21.91 
 
 53.36 
 
 .078 
 
 .321 7312 
 
 2465 
 
 75 43 46.64 
 
 50.84 
 
 .O29 
 
 .309 3618 
 
 2585 
 
 75 oi 15.25 
 
 53-31 
 
 .079 
 
 .321 9776 
 
 2463 
 
 75 44 37.46 
 
 50.79 
 
 2.030 
 
 1.309 6201 
 
 2582 
 
 75 02 08.54 
 
 53-26 
 
 2.080 
 
 1.322 2238 
 
 2460 
 
 75 45 28.23 
 
 50.75 
 
 .031 
 
 .309 8782 
 
 2580 
 
 75 03 01.78 
 
 53-21 
 
 .081 
 
 .322 4697 
 
 2458 
 
 75 46 18.95 
 
 50.70 
 
 .032 
 
 .310 1361 
 
 2577 
 
 75 03 54-96 
 
 53.i6 
 
 .082 
 
 .322 7153 
 
 2455 
 
 75 47 09.62 
 
 50.65 
 
 033 
 
 310 3936 
 
 2575 
 
 75 04 48.09 
 
 53.ii 
 
 .083 
 
 .322 9608 
 
 2453 
 
 75 48 00.24 
 
 50.60 
 
 .034 
 
 .310 6510 
 
 2572 
 
 75 05 41.17 
 
 53.06 
 
 .084 
 
 .323 2059 
 
 2451 
 
 75 48 50.82 
 
 50.55 
 
 2.035 
 
 I.3IO 9081 
 
 2570 
 
 75 06 34-20 
 
 53-00 
 
 2.085 
 
 1.323 4509 
 
 2448 
 
 75 49 41.34 
 
 50.50 
 
 .036 
 
 .311 1649 
 
 2567 
 
 75 07 27.18 
 
 52.95 
 
 .086 
 
 .323 6956 
 
 2446 
 
 75 50 31-82 
 
 50-45 
 
 .037 
 
 .3H 4215 
 
 2565 
 
 75 08 20. i i 
 
 52.90 
 
 .087 
 
 .323 9401 
 
 2444 
 
 75 51 22.25 
 
 50.40 
 
 .038 
 
 .311 6779 
 
 2562 
 
 75 09 12.99 
 
 52.85 
 
 .088 
 
 .324 1843 
 
 2441 
 
 75 52 12.62 
 
 50-35 
 
 .039 
 
 .311 9340 
 
 2560 
 
 75 10 05.81 
 
 52.80 
 
 .089 
 
 .324 4283 
 
 2439 
 
 75 53 02.95 
 
 50.30 
 
 2.040 
 
 1.312 1898 
 
 2557 
 
 75 10 58.59 
 
 52.75 
 
 2.090 
 
 1.324 6721 
 
 2436 
 
 75 53 53.23 
 
 5O.26 
 
 .041 
 
 .312 4455 
 
 2555 
 
 75 II 5L3I 
 
 52.70 
 
 .091 
 
 .324 9156 
 
 2434 
 
 75 54 43.46 
 
 5O.2I 
 
 .042 
 
 .312 7008 
 
 2552 
 
 75 12 43.98 
 
 52.65 
 
 .092 
 
 .325 1589 
 
 2432 
 
 75 55 33.65 
 
 50.16 
 
 .043 
 
 .312 9559 
 
 2550 
 
 75 13 36.60 
 
 52.60 
 
 .093 
 
 .325 4020 
 
 2429 
 
 75 56 23.78 
 
 50.11 
 
 .044 
 
 .313 2108 
 
 2547 
 
 75 1429.17 
 
 52.55 
 
 .094 
 
 .325 6448 
 
 2427 
 
 75 57 13-86 
 
 50.06 
 
 2.045 
 
 I.3I3 4654 
 
 2545 
 
 75 15 21.69 
 
 52.49 
 
 2.095 
 
 1.325 8874 
 
 2425 
 
 75 58 03.90 
 
 50.01 
 
 .046 
 
 .313 7198 
 
 2543 
 
 75 16 14.16 
 
 52.44 
 
 .096 
 
 .326 1297 
 
 2422 
 
 75 58 53-89 
 
 49.06 
 
 .047 
 
 .313 9739 
 
 2540 
 
 75 17 06.58 
 
 52.39 
 
 .097 
 
 .326 3718 
 
 2420 
 
 75 59 43.83 
 
 49.92 
 
 .048 
 
 .314 2278 
 
 2538 
 
 75 17 58.95 
 
 52.34 
 
 .098 
 
 .326 6137 
 
 2418 
 
 76 00 33-72 
 
 49-87 
 
 .049 
 
 .314 48i5 
 
 2535 
 
 75 18 51.27 
 
 52.29 
 
 .009 
 
 .326 8554 
 
 2415 
 
 76 oi 23.56 
 
 49-82 
 
 2.050 
 
 I.3U 7349 
 
 2533 
 
 75 19 43.53 
 
 52.24 
 
 2.100 
 
 1.327 0968 
 
 2413 
 
 76 02 13.36 
 
 49-77 
 
 u 
 
 2 tan-He")-;; 
 
 " sech u 
 
 2tan-'(e u >-90 
 
 "sechu 
 
 u 
 
 2 tan-He")- 2 
 
 <sechu 
 
 2tan- 1 (e)-90 
 
 sech u 
 
 SMITHSONIAN TABLES 
 
 296 
 
The Gudermannian. 
 
 u 
 
 gd u 
 
 F>' 
 
 gdu 
 
 F</ 
 
 u 
 
 gdu 
 
 "F</ 
 
 gdu 
 
 O.FO' 
 
 
 
 
 o / // 
 
 // 
 
 
 
 
 o / // 
 
 
 
 2.100 
 
 1.327 0968 
 
 2413 
 
 76 02 13.36 
 
 49-77 
 
 2.150 
 
 1.338 8732 
 
 2298 
 
 76 42 42.42 
 
 47.41 
 
 .101 
 
 .327 3380 
 
 2411 
 
 76 O3 O3 . I I 
 
 49-72 
 
 .151 
 
 339 1029 
 
 2296 
 
 76 43 29.81 
 
 47.36 
 
 .102 
 
 .327 5789 
 
 2408 
 
 76 03 52.80 
 
 49.67 
 
 .152 
 
 339 3325 
 
 2294 
 
 76 44 17.15 
 
 47-32 
 
 .103 
 
 .327 8196 
 
 2406 
 
 76 04 42.45 
 
 49.63 
 
 .153 
 
 339 56i7 
 
 2292 
 
 76 45 04.44 
 
 47-27 
 
 .104 
 
 .328 oooi 
 
 2404 
 
 76 05 32.06 
 
 49.58 
 
 .154 
 
 .339 7908 
 
 2290 
 
 76 45 51-69 
 
 47-23 
 
 2.105 
 
 1.328 3003 
 
 2401 
 
 76 06 21. 61 
 
 49-53 
 
 2.155 
 
 1.340 0197 
 
 2287 
 
 76 46 38.89 
 
 47.18 
 
 .106 
 
 .328 5403 
 
 2399 
 
 76 07 u. n 
 
 49.48 
 
 .156 
 
 .340 2483 
 
 2285 
 
 76 47 26.05 
 
 47.13 
 
 .107 
 
 .328 7801 
 
 2397 
 
 76 08 00.57 
 
 49-43' 
 
 .157 
 
 .340 4767 
 
 2283 
 
 76 48 13.16 
 
 47-09 
 
 .108 
 
 .329 0197 
 
 2394 
 
 76 08 49.08 
 
 49-39 
 
 .158 
 
 .340 7049 
 
 2281 
 
 76 49 00.23 
 
 47.04 
 
 .109 
 
 .329 2590 
 
 2392 
 
 76 09 39-34 
 
 49-34 
 
 .159 
 
 .340 9328 
 
 2278 
 
 76 49 47.25 
 
 47.00 
 
 2. IIO 
 
 1.329 4980 
 
 2390 
 
 76 10 28.66 
 
 49.29 
 
 2.160 
 
 1.341 1605 
 
 2276 
 
 76 50 34-22 
 
 46.95 
 
 .III 
 
 .329 7369 
 
 2387 
 
 76 n 17.92 
 
 49.24 
 
 .161 
 
 .341 388l 
 
 2274 
 
 76 51 21.15 
 
 46.90 
 
 .112 
 
 .329 9755 
 
 2385 
 
 76 12 07.14 
 
 49-19 
 
 .162 
 
 .341 6153 
 
 2272 
 
 76 52 08.03 
 
 46.86 
 
 113 
 
 .330 2139 
 
 2383 
 
 76 12 56.31 
 
 49-15 
 
 .163 
 
 .341 8424 
 
 2270 
 
 76 52 54.87 
 
 46.81 
 
 .114 
 
 330 4520 
 
 2380 
 
 76 13 45.43 
 
 49-10 
 
 .164 
 
 .342 0693 
 
 2267 
 
 76 53 41.66 
 
 46.77 
 
 2.IIS 
 
 1.330 6900 
 
 2378 
 
 76 14 34.51 
 
 49-05 
 
 2.165 
 
 1.342 2959 
 
 2265 
 
 76 54 28.40 
 
 46.72 
 
 .116 
 
 .330 9277 
 
 2376 
 
 76 15 23.54 
 
 49.00 
 
 .166 
 
 .342 5223 
 
 2263 
 
 76 55 iS.io 
 
 46.68 
 
 .117 
 
 .331 1651 
 
 2373 
 
 76 16 12.52 
 
 48.96 
 
 .167 
 
 .342 7485 
 
 2261 
 
 76 56 01.76 
 
 46.63 
 
 .118 
 
 .331 4023 
 
 2371 
 
 76 17 01.45 
 
 48.91 
 
 .168 
 
 .342 9744 
 
 2259 
 
 76 56 48.36 
 
 46.59 
 
 .119 
 
 331 6393 
 
 2369 
 
 76 17 50.33 
 
 48.86 
 
 .169 
 
 .343 2002 
 
 2256 
 
 76 57 34-93 
 
 46.54 
 
 2.I2O 
 
 I.33I 8761 
 
 2367 
 
 76 18 39-17 
 
 48.81 
 
 2.170 
 
 1.343 4257 
 
 2254 
 
 76 58 21.45 
 
 46.50 
 
 .121 
 
 .332 1127 
 
 2364 
 
 76 19 27.96 
 
 48.77 
 
 .171 
 
 343 6510 
 
 2252 
 
 76 59 07.92 
 
 46.45 
 
 .122 
 
 .332 3490 
 
 2362 
 
 76 20 16.70 
 
 48.72 
 
 .172 
 
 .343 8761 
 
 2250 
 
 76 59 54-35 
 
 46.41 
 
 .123 
 
 .332 5850 
 
 2360 
 
 76 21 05.40 
 
 48.67 
 
 .173 
 
 .344' 1010 
 
 2248 
 
 77 oo 40.73 
 
 46.36 
 
 .124 
 
 .332 8209 
 
 2357 
 
 76 21 54.04 
 
 48.62 
 
 .174 
 
 .344 3256 
 
 2245 
 
 77 oi 27.07 
 
 46.31 
 
 2.125 
 
 1.333 0565 
 
 2355 
 
 76 22 42.64 
 
 4858 
 
 2.175 
 
 1.344 5501 
 
 2243 
 
 77 02 13.36 
 
 46.27 
 
 .126 
 
 333 2919 
 
 2353 
 
 76 23 31.20 
 
 48.53 
 
 .176 
 
 .344 7743 
 
 2241 
 
 77 02 59.61 
 
 46.22 
 
 .127 
 
 333 5271 
 
 2350 
 
 76 24 19.70 
 
 48.48 
 
 .177 
 
 -344 9983 
 
 2239 
 
 77 03 45-8i 
 
 46.18 
 
 .128 
 
 333 7620 
 
 2348 
 
 76 25 08. 16 
 
 48.44 
 
 .178 
 
 .345 2220 
 
 2237 
 
 77 04 31.06 
 
 46.13 
 
 .129 
 
 333 9967 
 
 2346 
 
 76 25 56.57 
 
 48.39 
 
 .179 
 
 -345 4456 
 
 2234 
 
 77 05 18.08 
 
 46.09 
 
 2.I3O 
 
 1.334 2312 
 
 2344 
 
 76 26 44.94 
 
 48.34 
 
 2.180 
 
 1.345 6689 
 
 2232 
 
 77 06 04.14 
 
 46.04 
 
 .131 
 
 334 4054 
 
 2341 
 
 76 27 33.26 
 
 48.29 
 
 .181 
 
 -345 8921 
 
 2230 
 
 77 06 50.17 
 
 46.00 
 
 .132 
 
 334 6995 
 
 2339 
 
 70 28 21.53 
 
 48.25 
 
 ,.182 
 
 .346 1150 
 
 2228 
 
 77 07 36.14 
 
 45-95 
 
 133 
 
 334 9333 
 
 2337 
 
 76 29 09.75 
 
 48.20 
 
 .183 
 
 .346 3377 
 
 2226 
 
 77 08 22.08 
 
 45.91 
 
 134 
 
 .335 1668 
 
 2335 
 
 76 29 57-93 
 
 48.15 
 
 .184 
 
 .346 5601 
 
 2224 
 
 77 09 07.96 
 
 45.87 
 
 2.135 
 
 1.335 4002 
 
 2332 
 
 76 30 46.06 
 
 48.11 
 
 2.185 
 
 1.346 7824 
 
 2221 
 
 77 09 53.8i 
 
 45.82 
 
 .136 
 
 335 6333 
 
 2330 
 
 76 31 34. 14 
 
 48.06 
 
 .186 
 
 .347 0044 
 
 2219 
 
 77 10 39-60 
 
 45-78 
 
 .137 
 
 .335 8662 
 
 2328 
 
 76 32 22.18 
 
 48.01 
 
 .187 
 
 .347 2262 
 
 2217 
 
 77 n 25.36 
 
 45-73 
 
 .138 
 
 .336 0988 
 
 2325 
 
 75 33 10.17 
 
 47-97 
 
 .188 
 
 .347 4478 
 
 2215 
 
 77 12 11.07 
 
 45.69 
 
 139 
 
 .336 3313 
 
 2323 
 
 76 33 58.11 
 
 47.92 
 
 .189 
 
 .347 6692 
 
 2213 
 
 77 12 56.73 
 
 45.64 
 
 2.140 
 
 1.336 5635 
 
 2321 
 
 76 34 46.01 
 
 47.87 
 
 2.190 
 
 1.347 8904 
 
 221 1 
 
 77 13 42.35 
 
 45-6o 
 
 .141 
 
 .336 7955 
 
 2319 
 
 76 35 33.86 
 
 47.83 
 
 .191 
 
 .348 1114 
 
 2208 
 
 77 14 27.93 
 
 45-55 
 
 .142 
 
 .337 0272 
 
 2316 
 
 76 36 21.66 
 
 47-78 
 
 .192 
 
 .348 3321 
 
 22O6 
 
 77 15 13.46 
 
 45-51 
 
 143 
 
 .337 2588 
 
 2314 
 
 76 37 09.42 
 
 47-73 
 
 .193 
 
 .348 5526 
 
 22O4 
 
 77 15 58.95 
 
 45.46 
 
 .144 
 
 337 4901 
 
 2312 
 
 76 37 57.13 
 
 47.69 
 
 .194 
 
 .348 7729 
 
 22O2 
 
 77 16 44-39 
 
 45.42 
 
 2.145 
 
 1.337 7212 
 
 2310 
 
 76 38 44-79 
 
 47.64 
 
 2.195 
 
 1.348 9930 
 
 220O 
 
 77 17 29.79 
 
 45.38 
 
 .I 4 6 
 
 337 9520 
 
 2307 
 
 76 39 32.41 
 
 47-59 
 
 .196 
 
 .349 2129 
 
 2108 
 
 77 18 15.14 
 
 45-33 
 
 147 
 
 .338 1826 
 
 2305 
 
 76 40 19.98 
 
 47.55 
 
 .197 
 
 .349 4326 
 
 2ig6 
 
 77 19 00.45 
 
 45.29 
 
 .148 
 
 .338 4131 
 
 2303 
 
 76 41 07.51 
 
 47-50 
 
 .198 
 
 .349 6520 
 
 2193 
 
 77 19 45.72 
 
 45.24 
 
 .149 
 
 .338 6432 
 
 2301 
 
 76 41 54-99 
 
 47.46 
 
 .199 
 
 349 8713 
 
 2IQI 
 
 77 20 30.94 
 
 45.20 
 
 2.ISO 
 
 1.338 8732 
 
 2298 
 
 76 42 42.42 
 
 47-41 
 
 2. 2OO 
 
 1.3500903 
 
 2189 
 
 77 21 i6.ii 
 
 45.16 
 
 u 
 
 2tan-Ke")~ 
 
 wsechu 
 
 2tan-Ke)-90 
 
 w sech u 
 
 U 
 
 atan-Keu) 
 
 osechu 
 
 2tan~ 1 (e u )-90 
 
 <> sech u 
 
 SMITHSONIAN TABLES 
 
 297 
 
The Gude rmannian. 
 
 u 
 
 gdu 
 
 <oF ' 
 
 gd u 
 
 oF ' 
 
 u 
 
 odu 
 
 F ' 
 
 Odu 
 
 <oF ' 
 
 
 
 
 / // 
 
 // 
 
 
 
 
 O 4 // 
 
 // 
 
 2.2OO 
 
 I.3SO 0003 
 
 2189 
 
 77 21 16.11 
 
 45-l6 
 
 2.250 
 
 1.360 7733 
 
 2085 
 
 77 57 59-64 
 
 43-00 
 
 .201 
 
 350 3091 
 
 2187 
 
 77 22 01.25 
 
 45-11 
 
 .251 
 
 .360 9817 
 
 2083 
 
 77 58 42.62 
 
 42.96 
 
 .202 
 
 350 5277 
 
 2185 
 
 77 22 46.34 
 
 45-07 
 
 .252 
 
 .361 1809 
 
 2081 
 
 77 59 25.56 
 
 42.92 
 
 .203 
 
 .350 7461 
 
 2183 
 
 77 23 31.38 
 
 45.02 
 
 .253 
 
 .361 39/8 
 
 2079 
 
 78 oo 08.46 
 
 42.88 
 
 .204 
 
 350 9643 
 
 2181 
 
 77 24 16.38 
 
 44.98 
 
 254 
 
 .361 6056 
 
 2077 
 
 78 oo 51.32 
 
 42.83 
 
 2.2O5 
 
 1.351 1822 
 
 2179 
 
 77 25 01.34 
 
 44-94 
 
 2.255 
 
 1.361 8132 
 
 2075 
 
 78 01 34.13 
 
 42.79 
 
 .206 
 
 .351 4000 
 
 2176 
 
 77 25 46.25 
 
 44-89 
 
 .256 
 
 .362 0205 
 
 2073 
 
 78 02 16.00 
 
 42.75 
 
 .207 
 
 351 6175 
 
 2174 
 
 77 26 31-12 
 
 44.85 
 
 257 
 
 .362 2277 
 
 2071 
 
 78 02 59.63 
 
 42.71 
 
 .208 
 
 351 8348 
 
 2172 
 
 77 27 15.95 
 
 44-80 
 
 .258 
 
 .362 4347 
 
 2069 
 
 78 03 42.32 
 
 42.67 
 
 .209 
 
 352 0519 
 
 2170 
 
 77 28 00.73 
 
 44-76 
 
 259 
 
 .362 6414 
 
 2067 
 
 78 04 24.97 
 
 42.63 
 
 2.210 
 
 1.352 2688 
 
 2168 
 
 77 28 45-47 
 
 44.72 
 
 2.260 
 
 1.362 8480 
 
 2065 
 
 78 05 07.57 
 
 42.58 
 
 .211 
 
 352 4855 
 
 2166 
 
 77 29 30.16 
 
 44.67 
 
 .261 
 
 .363 0543 
 
 2063 
 
 78 05 50.13 
 
 42.54 
 
 .212 
 
 .352 7020 
 
 2164 
 
 77 30 14-82 
 
 44.63 
 
 .262 
 
 .363 2605 
 
 2060 
 
 78 06 32.66 
 
 42.50 
 
 .213 
 
 352 9183 
 
 2162 
 
 77 30 59-42 
 
 44-59 
 
 .263 
 
 .363 4664 
 
 2058 
 
 7807 15.14 
 
 42.46 
 
 .214 
 
 353 1343 
 
 2159 
 
 77 31 43-99 
 
 44.54 
 
 .264 
 
 .363 6722 
 
 2056 
 
 78 07 57-57 
 
 42.42 
 
 2.215 
 
 1.353 3502 
 
 2157 
 
 77 32 28.51 
 
 44-50 
 
 2.265 
 
 1.363 8777 
 
 2054 
 
 78 08 39.97 
 
 42.38 
 
 .216 
 
 353 5658 
 
 2155 
 
 77 33 12.99 
 
 44.46 
 
 .266 
 
 .364 0831 
 
 2052 
 
 78 09 22.33 
 
 42.33 
 
 .217 
 
 353 7812 
 
 2153 
 
 77 33 57-42 
 
 44-41 
 
 .267 
 
 .364 2882 
 
 2050 
 
 78 10 04.64 
 
 42.29 
 
 .218 
 
 353 0064 
 
 2151 
 
 77 34 41-81 
 
 44-37 
 
 .268 
 
 .364 4931 
 
 2048 
 
 78 10 46.91 
 
 42.25 
 
 .219 
 
 354 2114 
 
 2149 
 
 77 35 26.16 
 
 44-33 
 
 ' .269 
 
 .364 6979 
 
 2046 
 
 78 II 29.14 
 
 42.21 
 
 2.22O 
 
 1.354 4262 
 
 2147 
 
 77 36 10.46 
 
 44-28 
 
 2.270 
 
 1.364 9024 
 
 2044 
 
 78 12 11.33 
 
 42.17 
 
 .221 
 
 .354 6408 
 
 2145 
 
 77 36 54-72 
 
 44-24 
 
 .271 
 
 .365 1068 
 
 2042 
 
 78 12 53.48 
 
 42.13 
 
 .222 
 
 354 8552 
 
 2143 
 
 77 37 38.94 
 
 44.20 
 
 .272 
 
 .365 3109 
 
 2040 
 
 78 13 35.59 
 
 42.09 
 
 .223 
 
 .355 0693 
 
 2141 
 
 77 38 23.11 
 
 44-15 
 
 .273 
 
 .365 5149 
 
 2038 
 
 78 14 17.66 
 
 42.05 
 
 .224 
 
 355 2833 
 
 2138 
 
 77 39 07.24 
 
 44.11 
 
 .274 
 
 .365 7i86 
 
 2036 
 
 78 14 59-68 
 
 42.00 
 
 2.225 
 
 1.355 4970 
 
 2136 
 
 77 39 51.33 
 
 44-07 
 
 2.275 
 
 1.365 9221 
 
 2034 
 
 78 15 41.66 
 
 41-06 
 
 .226 
 
 355 71.06 
 
 2134 
 
 77 40 35.38 
 
 44.02 
 
 .276 
 
 .366 1255 
 
 2032 
 
 78 1 6 23.61 
 
 41.92 
 
 .227 
 
 355 9239 
 
 2132 
 
 77 41 19.38 
 
 43.98 
 
 .277 
 
 .366 3286 
 
 2030 
 
 78 17 05.51 
 
 41.88 
 
 .228 
 
 .356 1370 
 
 2130 
 
 77 42 03.34 
 
 43-94 
 
 .278 
 
 .366 5316 
 
 2028 
 
 78 17 47-37 
 
 41.84 
 
 .229 
 
 .356 3499 
 
 2128 
 
 77 42 47-25 
 
 43.89 
 
 .279 
 
 .366 7343 
 
 2026 
 
 78 18 29.19 
 
 41.80 
 
 2.230 
 
 I.356 5626 
 
 2126 
 
 77 43 3LI3 
 
 43.85 
 
 2.280 
 
 1.366 9369 
 
 2024 
 
 78 19 10.97 
 
 41.76 
 
 .231 
 
 .356 7751 
 
 2124 
 
 77 44 14.96 
 
 43.8i 
 
 .281 
 
 .367 1392 
 
 2023 
 
 78 19 52.71 
 
 41.72 
 
 .232 
 
 .356 9874 
 
 2122 
 
 77 44 58.74 
 
 43-77 
 
 .282 
 
 .367 34 U 
 
 2021 
 
 78 20 34-40 
 
 41.68 
 
 233 
 
 .357 2095 
 
 2I2O 
 
 77 45 42.49 
 
 43.72 
 
 .283 
 
 .367 5433 
 
 2OI9 
 
 78 21 16.06 
 
 41.64 
 
 234 
 
 357 4H4 
 
 2118 
 
 77 4626.19 
 
 43-68 
 
 .284 
 
 .367 7451 
 
 2017 
 
 78 21 57.68 
 
 41.60 
 
 2.235 
 
 1.357 6230 
 
 2116 
 
 77 47 09.85 
 
 43.64 
 
 2.285 
 
 1.367 9466 
 
 2015 
 
 78 22> 39.25 
 
 41.55 
 
 .236 
 
 357 8345 
 
 2114 
 
 77 47 53-47 
 
 43.6o 
 
 .286 
 
 .368 1480 
 
 2013 
 
 78 23 20.78 
 
 41.51 
 
 .237 
 
 .358 0457 
 
 2III 
 
 77 48 37-04 
 
 43-55 
 
 .287 
 
 .368 3492 
 
 2OII 
 
 78 24 02.28 
 
 41.47 
 
 .238 
 
 .358 2568 
 
 2IO9 
 
 77 49 20.57 
 
 43.51 
 
 .288 
 
 .368 5501 
 
 2OO9 
 
 78 24 43-73 
 
 4L43 
 
 239 
 
 358 4676 
 
 2107 
 
 77 50 04.06 
 
 43-47 
 
 .289 
 
 .368 7509 
 
 2007 
 
 78 25 25.14 
 
 41.39 
 
 2.24O 
 
 .241 
 
 1.3586783 
 .358 8887 
 
 2105 
 2103 
 
 77 50 47-51 
 77 51 30.91 
 
 43-43 
 43.38 
 
 2.290 
 
 .291 
 
 ..3689515 
 .369 1519 
 
 2005 
 2003 
 
 78 26 06.51 
 
 78 26 47-85 
 
 41-35 
 41.31 
 
 .242 
 
 .359 0989 
 
 2101 
 
 77 52 14.27 
 
 43-34 
 
 .292 
 
 .369 3521 
 
 ' 2OOI 
 
 78 27 29. 14 
 
 41.27 
 
 .243 
 
 .359 3089 
 
 2099 
 
 77 52 57-59 
 
 43.30 
 
 .293 
 
 .369 5520 
 
 1999 
 
 78 28 10.39 
 
 41.23 
 
 .244 
 
 359 5i87 
 
 2097 
 
 77 53 40.87 
 
 43-26 
 
 .294 
 
 .369 75i8 
 
 1997 
 
 78 28 51.60 
 
 41.19 
 
 2.245 
 
 1.359 7283 
 
 2095 
 
 77 54 24.10 
 
 43-21 
 
 2.295 
 
 1.369 95U 
 
 1995 
 
 78 29 32.77 
 
 4LI5 
 
 .246 
 
 359 9377 
 
 2093 
 
 77 55 07.29 
 
 43.17 
 
 .296 
 
 .370 1508 
 
 1993 
 
 78 30 13.89 
 
 41.11 
 
 .247 
 
 .360 1469 
 
 2091 
 
 77 55 50.44 
 
 43.13 
 
 .297 
 
 370 3500 
 
 1991 
 
 78 30 54.98 
 
 41.07 
 
 .248 
 
 .360 3559 
 
 2089 
 
 77 56 33-55 
 
 43-09 
 
 .298 
 
 .370 5490 
 
 1989 
 
 78 31 36.03 
 
 41.03 
 
 .249 
 
 .360 5647 
 
 2087 
 
 77 57 16.62 
 
 43-04 
 
 .299 
 
 370 7479 
 
 1987 
 
 78 32 17.04 
 
 40.99 
 
 2.25O 
 
 1.3607733 
 
 2085 
 
 77 57 59.64 
 
 43-00 
 
 2.300 
 
 1-370 9465 
 
 1985 
 
 78 32 58.01 
 
 40.95 
 
 U 
 
 2tan-'(e)- 
 
 usechu 
 
 Ztan-'Ce'O-SO 
 
 u sech u 
 
 u 
 
 2tan-'(e u )-J 
 
 wsechu 
 
 atan-He'O-SO 
 
 wsechu 
 
 SMITHSONIAN TABLES 
 
 298 
 
The Gudermannian. 
 
 u 
 
 gd u 
 
 Fu' 
 
 gd u 
 
 <oF ' 
 
 u 
 
 gd u 
 
 F ' 
 
 gdu 
 
 <-F ' 
 
 2.300 
 
 1.370 9465 
 
 1985 
 
 78 32' s8''oi 
 
 40-95 
 
 2.350 
 
 1.380 6331 
 
 1800 
 
 o / // 
 
 79 06 16.03 
 
 38^ 
 
 .301 
 
 .371 1449 
 
 1983 
 
 78 33 38.94 
 
 40.91 
 
 351 
 
 .380 8221 
 
 1888 
 
 79 06 55-00 
 
 38.9. 
 
 .302 
 
 371 3431 
 
 I98l 
 
 78 34 19-82 
 
 40.87 
 
 352 
 
 .381 0108 
 
 1886 
 
 79 07 33-93 
 
 38.9 
 
 .303 
 
 .371 5412 
 
 1979 
 
 78 35 00.67 
 
 40.83 
 
 353 
 
 .381 1994 
 
 1885 
 
 79 08 12. 82 
 
 38.8: 
 
 .304 
 
 371 7390 
 
 1977 
 
 78 35 41.48 
 
 40.79 
 
 354 
 
 .381 3877 
 
 1883 
 
 79 08 51-67 
 
 38. a 
 
 2.305 
 
 I-37I 9367 
 
 1975 
 
 78 36 22.25 
 
 40.75 
 
 2.355 
 
 1.381 5759 
 
 1881 
 
 79 09 30.49 
 
 38.8< 
 
 .306 
 
 .372 1341 
 
 1974 
 
 78 37 02.98 
 
 40.71 
 
 .356 
 
 .381 7639 
 
 1879 
 
 79 10 09.27 
 
 38.7< 
 
 .307 
 
 .372 3314 
 
 1972 
 
 78 37 43-66 
 
 40.66 
 
 357 
 
 381 9517 
 
 1877 
 
 79 IO 48.01 
 
 38.7 
 
 .308 
 
 .372 5284 
 
 1970 
 
 78 38 24.31 
 
 40.63 
 
 .358 
 
 .382 1394 
 
 1875 
 
 79 II 26.71 
 
 38.0J 
 
 .309 
 
 372 7253 
 
 1968 
 
 78 39 04.92 
 
 40.59 
 
 359 
 
 .382 3268 
 
 1874 
 
 79 12 05.37 
 
 38.6, 
 
 2.310 
 
 1.372 9220 
 
 1966 
 
 78 39 45-49 
 
 40.55 
 
 2.360 
 
 1.382 5141 
 
 1872 
 
 79 12 44.00 
 
 38.6 
 
 .311 
 
 .373 n85 
 
 1964 
 
 78 40 26.02 
 
 40.51 
 
 .361 
 
 .382 7012 
 
 1870 
 
 79 13 22.59 
 
 38.5, 
 
 .312 
 
 373 3148 
 
 1962 
 
 78 41 06.51 
 
 40.47 
 
 .362 
 
 .382 8881 
 
 1868 
 
 79 14 01.14 
 
 38.5 
 
 .313 
 
 373 5109 
 
 1960 
 
 78 41 46.96 
 
 40.43 
 
 .363 
 
 .383 0748 
 
 1866 
 
 79 14 39.65 
 
 38.4< 
 
 .314 
 
 .373 7068 
 
 1958 
 
 78 42 27.37 
 
 40.39 
 
 364 
 
 .383 2613 
 
 1864 
 
 79 15 18.12 
 
 38.4< 
 
 2.315 
 
 1-373 9025 
 
 1956 
 
 78 43 07.74 
 
 40.35 
 
 2.365 
 
 1.383 4476 
 
 1863 
 
 79 15 56.56 
 
 38.4: 
 
 .316 
 
 .3740980 
 
 1954 
 
 78 43 48.07 
 
 40.31 
 
 .366 
 
 .383 6338 
 
 1861 
 
 79 16 34.96 
 
 38.3^ 
 
 .317 
 
 374 2934 
 
 1952 
 
 78 44 28.36 
 
 40.27 
 
 .367 
 
 .383 8198 
 
 1859 
 
 79 17 13.32 
 
 38.3^ 
 
 .318 
 
 374 4885 
 
 1950 
 
 78 45 08. 6l 
 
 40.23 
 
 .368 
 
 .384 0056 
 
 1857 
 
 79 17 51-64 
 
 38. 3< 
 
 .319 
 
 374 6835 
 
 1949 
 
 78 45 48.82 
 
 40.19 
 
 .369 
 
 .384 1912 
 
 i855 
 
 79 18 29.93 
 
 38.2. 
 
 2.320 
 
 1.374 8782 
 
 1947 
 
 78 46 28.99 
 
 40.15 
 
 2.370 
 
 1.3843766 
 
 1853 
 
 79 19 08. 18 
 
 38.2, 
 
 .321 
 
 .375 0728 
 
 1945 
 
 78 47 09.13 
 
 40.11 
 
 -371 
 
 .384 5619 
 
 1852 
 
 79 19 46.39 
 
 38. K 
 
 .322 
 
 .375 2672 
 
 1943 
 
 78 47 49-22 
 
 40.07 
 
 372 
 
 .384 7470 
 
 1850 
 
 79 20 24.56 
 
 38.1 
 
 .323 
 
 .375 4614 
 
 1941 
 
 78 48 29.28 
 
 40.04 
 
 373 
 
 .384 93i8 
 
 1848 
 
 79 21 02.70 
 
 38. L 
 
 .324 
 
 375 6554 
 
 1939 
 
 78 49 09.29 
 
 40.OO 
 
 374 
 
 .385 1165 
 
 1846 
 
 79 21 40.80 
 
 38.0J 
 
 2.325 
 
 1.375 8492 
 
 1937 
 
 78 49 49.27 
 
 39.96 
 
 2.375 
 
 1.385 3011 
 
 1844 
 
 79 22 18.86 
 
 38.0, 
 
 1 .326 
 
 .376 0428 
 
 1935 
 
 78 50 29.21 
 
 39.92 
 
 .376 
 
 .385 4854 
 
 1843 
 
 79 22 56.88 
 
 38. a 
 
 .327 
 
 .376 2362 
 
 1933 
 
 78 51 09.10 
 
 39.88 
 
 .377 
 
 .385 6696 
 
 1841 
 
 79 23 34.87 
 
 37-9, 
 
 .328 
 
 .376 4295 
 
 1931 
 
 78 51 48.96 
 
 39.84 
 
 .378 
 
 .385 8536 
 
 1839 
 
 79 24 12. 81 
 
 37.9. 
 
 .329 
 
 .376 6225 
 
 1930 
 
 78 52 28.78 
 
 39.80 
 
 379 
 
 .386 0374 
 
 1837 
 
 79 24 50.73 
 
 37-8< 
 
 2.330 
 
 1.376 8154 
 
 1928 
 
 78 53 08.56 
 
 39.76 
 
 2.380 
 
 1.386 2210 
 
 1835 
 
 79 25 28.60 
 
 37.& 
 
 .331 
 
 .377 0081 
 
 1926 
 
 78 53 48.30 
 
 39.72 
 
 .381 
 
 .386 4044 
 
 1833 
 
 79 26 06.44 
 
 37-8: 
 
 .332 
 
 .377 2006 
 
 1924 
 
 78 54 28.01 
 
 39-68 
 
 .382 
 
 .386 5877 
 
 1832 
 
 79 26 44.24 
 
 37-7* 
 
 333 
 
 .377 3929 
 
 1922 
 
 78 55 07.67 
 
 39.64 
 
 .383 
 
 .386 7708 
 
 1830 
 
 79 27 22.00 
 
 37-7- 
 
 334 
 
 .377 5850 
 
 1920 
 
 78 55 47.29 
 
 39.6i 
 
 .384 
 
 .386 9537 
 
 1828 
 
 79 27 59-73 
 
 37-7 
 
 2.335 
 
 1.377 7709 
 
 1918 
 
 78 56 26.88 
 
 39.57 
 
 2.385 
 
 1.387 1364 
 
 1826 
 
 79 28 37.41 
 
 37.6; 
 
 .336 
 
 .377 9686 
 
 1916 
 
 78 57 06.43 
 
 39-53 
 
 .386 
 
 .387 3189 
 
 1824 
 
 79 29 15.07 
 
 37-6, 
 
 337 
 
 .378 1601 
 
 1914 
 
 78 57 45-94 
 
 39-49 
 
 .387 
 
 .387 5013 
 
 1823 
 
 79 29 52.68 
 
 37- 6( 
 
 .338 
 
 .378 35i5 
 
 1913 
 
 78 58 25.40 
 
 39-45 
 
 .388 
 
 .387 6834 
 
 1821 
 
 79 30 30.26 
 
 37- 5< 
 
 339 
 
 .378 5427 
 
 IQII 
 
 78 59 04.84 
 
 39.41 
 
 .389 
 
 387 8655 
 
 1819 
 
 79 31 07.80 
 
 37.5- 
 
 2.340 
 
 1.378 7336 
 
 1909 
 
 78 59 44.23 
 
 39.37 
 
 2.300 
 
 1.388 0473 
 
 1817 
 
 79 31 45-30 
 
 37-4< 
 
 341 
 
 .378 9244 
 
 1907 
 
 79 oo 23.58 
 
 39-33 
 
 391 
 
 .388 2289 
 
 1816 
 
 79 32 22.77 
 
 37-4! 
 
 342 
 
 379 H50 
 
 1905 
 
 79 01 02.89 
 
 39-30 
 
 392 
 
 .388 4104 
 
 1814 
 
 79 33 00.20 
 
 37.4] 
 
 1 -343 
 
 379 3054 
 
 1903 
 
 79 01 42.17 
 
 39.26 
 
 393 
 
 .388 5917 
 
 1812 
 
 79 33 37-59 
 
 37.3; 
 
 344 
 
 379 4957 
 
 1901 
 
 79 02 21.41 
 
 39.22 
 
 394 
 
 .388 7728 
 
 1810 
 
 79 34 14.95 
 
 37-3^ 
 
 2-345 
 
 1.3796857 
 
 1899 
 
 79 03 00.61 
 
 39.18 
 
 2.395 
 
 1.3889537 
 
 1808 
 
 79 34 52.27 
 
 37. 3< 
 
 .346 
 
 379 8756 
 
 1898 
 
 79 03 39-77 
 
 39.14 
 
 .396 
 
 389 1345 
 
 1807 
 
 79 35 29.55 
 
 37- 2( 
 
 ^348 
 
 .380 0652 
 .380 2547 
 
 1896 
 1894 
 
 79 04 18.89 
 79 04 57.97 
 
 39.10 
 39.06 
 
 .397 
 .398 
 
 .389 3150 
 .389 4954 
 
 1805 
 1803 
 
 79 36 06.80 
 79 36 44.01 
 
 37.2: 
 37- K 
 
 349 
 
 .380 4440 
 
 1892 
 
 79 05 37-02 
 
 39.03 
 
 399 
 
 .389 6757 
 
 1801 
 
 79 37 21.18 
 
 37. if 
 
 2-350 
 
 1.380 6331 
 
 1890 
 
 79 06 16.03 
 
 38.99 
 
 2.400 
 
 1.3898557 
 
 1800 
 
 79 37 58.32 
 
 37-1^ 
 
 u 
 
 2tan- 1 (e)- 
 
 ws'ch u 
 
 2 tan-Ke^-SO 
 
 <>sech u 
 
 u 
 
 2tan- J (eu)~ 
 
 wsechu 
 
 2tan-'(e)-90 
 
 > sech u 
 
 SMITHSONIAN TABLES 
 
 299 
 
The Gude rmannian. 
 
 u 
 
 gd u 
 
 Fo' 
 
 gd u 
 
 wF ' 
 
 u 
 
 gd u 
 
 Fo' 
 
 gdu 
 
 F ' 
 
 2.400 
 
 1.3898557 
 
 1800 
 
 79 37 58.32 
 
 37-12 
 
 2.450 
 
 1.3986356 
 
 1713 
 
 / // 
 
 80 08 09.31 
 
 35-34 
 
 .401 
 
 390 0356 
 
 1798 
 
 79 38 35-42 
 
 37.08 
 
 451 
 
 .398 8069 
 
 I7II 
 
 80 08 44.63 
 
 35.30 
 
 .402 
 .403 
 
 390 2153 
 390 3948 
 
 1796 
 1794 
 
 79 39 12.48 
 79 39 49.51 
 
 37.05 
 37-01 
 
 .452 
 .453 
 
 398 9779 
 .399 1488 
 
 I7IO 
 
 1708 
 
 80 09 19.91 
 
 80 09 55.i6 
 
 35.27 
 35.23 
 
 .404 
 
 390 5741 
 
 1792 
 
 79 40 26.50 
 
 36.97 
 
 454 
 
 .399 3195 
 
 1706 
 
 80 10 30.37 
 
 35-20 
 
 2.405 
 
 1-390 7533 
 
 1791 
 
 79 41 03.45 
 
 36.94 
 
 2.455 
 
 1.399 4901 
 
 1705 
 
 80 II 05.55 
 
 35.i6 
 
 .406 
 
 390 9323 
 
 1/89 
 
 79 41 40.37 
 
 36.90 
 
 .456 
 
 .3996605 
 
 1703 
 
 80 II 40.70 
 
 35.13 
 
 .407 
 
 .391 mi 
 
 1787 
 
 79 42 17-25 
 
 36.86 
 
 457 
 
 399 8307 
 
 1701 
 
 80 12 I5.8l 
 
 35-09 
 
 .408 
 
 .391 2897 
 
 1785 
 
 79 42 54.10 
 
 36.83 
 
 .458 
 
 .400 0007 
 
 1700 
 
 80 12 50.88 
 
 35.o6 
 
 .409 
 
 .391 4681 
 
 1784 
 
 79 43 30.91 
 
 36.79 
 
 459 
 
 .400 1706 
 
 1698 
 
 80 13 25.92 
 
 35-02 
 
 2.410 
 
 1.391 6464 
 
 1782 
 
 79 44 07.68 
 
 36.75 
 
 2.460 
 
 1.400 3403 
 
 1696 
 
 80 14 00.93 
 
 34.99 
 
 .411 
 
 .391 8245 
 
 1780 
 
 79 44 44.42 
 
 36.72 
 
 .461 
 
 .400 5099 
 
 1695 
 
 80 14 35-00 
 
 34-95 
 
 .412 
 
 .392 0025 
 
 1778 
 
 79 45 21.12 
 
 36.68 
 
 .462 
 
 .400 6793 
 
 1693 
 
 80 15 10.84 
 
 34.92 
 
 ^413 
 
 .392 1802 
 
 1777 
 
 79 45 57.78 
 
 36.65 
 
 463 
 
 .400 8485 
 
 1691 
 
 80 15 45-74 
 
 34.89 
 
 .414 
 
 392 3578 
 
 1775 
 
 79 46 34.41 
 
 36.61 
 
 .464 
 
 .401 0175 
 
 1690 
 
 80 16 20.61 
 
 34.85 
 
 2.415 
 
 1.392 5352 
 
 1773 
 
 79 47 11.00 
 
 36.57 
 
 2.465 
 
 1.401 1864 
 
 1688 
 
 80 16 55-45 
 
 34.82 
 
 .416 
 
 .392 7124 
 
 1771 
 
 79 47 47.56 
 
 36.54 
 
 .466 
 
 .401 3551 
 
 1686 
 
 80 17 30.25 
 
 34.78 
 
 .417 
 
 .392 8895 
 
 1770 
 
 79 48 24.08 
 
 36.50 
 
 .467 
 
 .401 5237 
 
 1685 
 
 80 18 05.01 
 
 34-75 
 
 .418 
 
 393 0664 
 
 1768 
 
 79 49 00.57 
 
 36.47 
 
 .468 
 
 .401 6921 
 
 1683 
 
 80 18 39.74 
 
 34.71 
 
 .419 
 
 393 2431 
 
 1766 
 
 79 49 37-02 
 
 36.43 
 
 .469 
 
 .401 8603 
 
 1681 
 
 80 19 14.44 
 
 34.68 
 
 2.420 
 
 1.393 4196 
 
 1764 
 
 79 50 13.43 
 
 36.39 
 
 2.470 
 
 1.402 0283 
 
 1680 
 
 80 19 49.10 
 
 34.65 
 
 .421 
 
 .393 596o 
 
 1763 
 
 79 50 49.8o 
 
 36.36 
 
 .471 
 
 .402 1962 
 
 1678 
 
 So 20 23.73 
 
 34.6i 
 
 .422 
 
 393 7722 
 
 1761 
 
 79 51 26.15 
 
 36.32 
 
 .472 
 
 .402 3639 
 
 1676 
 
 80 20 58.33 
 
 34.58 
 
 .423 
 
 393 9482 
 
 1759 
 
 79 52 02.45 
 
 36.29 
 
 473 
 
 .402 5315 
 
 1675 
 
 80 21 32.89 
 
 34-54 
 
 .424 
 
 .394 1240 
 
 1758 
 
 79 52 38.72 
 
 36.25 
 
 474 
 
 .402 6989 
 
 1673 
 
 80 22 07.41 
 
 34.51 
 
 2.425 
 
 1-394 2097 
 
 1756 
 
 79 53 14.96 
 
 36.22 
 
 2.475 
 
 1.402 8661 
 
 1672 
 
 80 22 41.91 
 
 34.48 
 
 .426 
 
 394 4752 
 
 1754 
 
 79 53 51.15 
 
 36.18 
 
 .476 
 
 .403 0332 
 
 1670 
 
 80 23 16.36 
 
 34-44 
 
 .427 
 
 394 6505 
 
 1752 
 
 79 54 27.32 
 
 36.14 
 
 477 
 
 .403 20OI 
 
 1668 
 
 80 23 50.79 
 
 34-41 
 
 .428 
 
 .394 8257 
 
 1751 
 
 79 55 03.44 
 
 36.11 
 
 .478 
 
 .403 3668 
 
 1666 
 
 80 24 25.18 
 
 34-37 
 
 .429 
 
 .395 0006 
 
 1749 
 
 79 55 39-54 
 
 36.07 
 
 479 
 
 .403 5334 
 
 1665 
 
 80 24 59-54 
 
 34-34 
 
 2.430 
 
 1.395 1754 
 
 1747 
 
 79 56 15.59 
 
 36.04 
 
 2.480 
 
 1.403 6098 
 
 1663 
 
 80 25 33.86 
 
 34-31 
 
 .431 
 
 .395 3501 
 
 1745 
 
 79 56 51.61 
 
 36.00 
 
 .481 
 
 .403 8660 
 
 1662 
 
 80 26 08.15 
 
 34-27 
 
 .432 
 
 395 5245 
 
 1744 
 
 79 57 27.60 
 
 35-97 
 
 .482 
 
 .404 0321 
 
 1660 
 
 80 26 42.40 
 
 34-24 
 
 433 
 
 395 6988 
 
 1742 
 
 79 58 03.55 
 
 35.93 
 
 .483 
 
 .404 1980 
 
 1658 
 
 8O 27 l6.O2 
 
 34-20 
 
 434 
 
 395 8729 
 
 1740 
 
 79 58 39.46 
 
 35.90 
 
 .484 
 
 .404 3637 
 
 1657 
 
 80 27 5O.8l 
 
 34-17 
 
 2-435 
 
 1.396 0469 
 
 1739 
 
 79 59 15.34 
 
 35-86 
 
 2.485 
 
 1.404 5293 
 
 1655 
 
 80 28 24.97 
 
 34.14 
 
 .436 
 
 .396 2207 
 
 1737 
 
 79 59 5LI9 
 
 35.83 
 
 .486 
 
 .404 6947 
 
 1653 
 
 80 28 59.09 
 
 34-10 
 
 437 
 
 .396 3943 
 
 1735 
 
 80 oo 26.99 
 
 35-79 
 
 .487 
 
 .404 8600 
 
 1652 
 
 80 29 33.17 
 
 34-07 
 
 .438 
 
 .396 5677 
 
 1733 
 
 80 01 02.77 
 
 35.76 
 
 .488 
 
 .405 0251 
 
 1650 
 
 80 30 07.23 
 
 34-04 
 
 439 
 
 .396 7410 
 
 1732 
 
 80 01 38.51 
 
 35.72 
 
 .489 
 
 .405 1900 
 
 1648 
 
 80 30 4L25 
 
 34-00 
 
 2.440 
 
 1.396 9141 
 
 1730 
 
 80 02 14.21 
 
 35.69 
 
 2.490 
 
 1.405 3548 
 
 1647 
 
 80 31 15.23 
 
 33-97 
 
 .441 
 
 .397 0870 
 
 1728 
 
 80 02 49.88 
 
 35.65 
 
 .491 
 
 .405 5194 
 
 1645 
 
 80 31 49-19 
 
 33.94 
 
 .442 
 
 397 2597 
 
 1727 
 
 80 03 25.51 
 
 35.62 
 
 .492 
 
 .405 6838 
 
 1644 
 
 8O 32 23.IO 
 
 33.90 
 
 443 
 
 .397 4323 
 
 1725 
 
 80 04 oi.n 
 
 35.58 
 
 493 
 
 .405 8481 
 
 1642 
 
 80 32 56.99 
 
 33-87 
 
 .444 
 
 397 6047 
 
 1723 
 
 80 04 36.67 
 
 35-54 
 
 494 
 
 .406 0122 
 
 1640 
 
 80 33 30.84 
 
 33.84 
 
 2-445 
 .446 
 
 1.397 7770 
 397 9490 
 
 1722 
 1720 
 
 8O 05 12. 2O 
 
 80 05 47.69 
 
 35.51 
 35.48 
 
 2.495 
 .496 
 
 I.4O5 1762 
 .406 3400 
 
 1639 
 1637 
 
 80 34 04.66 
 80 34 38.45 
 
 33-80 
 33-77 
 
 447 
 
 .308 1209 
 
 1718 
 
 80 06 23.15 
 
 35-44 
 
 .497 
 
 .406 5036 
 
 1636 
 
 80 35 12. 20 
 
 33-74 
 
 .448 
 
 .398 2927 
 
 1716 
 
 80 06 58.57 
 
 35.41 
 
 .408 
 
 .406 6671 
 
 1634 
 
 80 35 45-92 
 
 33.70 
 
 .449 
 
 .398 4642 
 
 1715 
 
 80 07 33.96 
 
 35-37 
 
 .499 
 
 .406 8304 
 
 1632 
 
 80 36 19.60 
 
 33-<>7 
 
 2.450 
 
 1.3086356 
 
 1713 
 
 80 08 09.31 
 
 35-34 
 
 2.500 
 
 1.4069936 
 
 1631 
 
 80 36 53-26 
 
 33.64 
 
 u 
 
 2 tan-He )-^ 
 
 <> sech u 
 
 2tan-He n )-90 
 
 u> sech u 
 
 u 
 
 2tan-'(e)- 
 
 w sech u 
 
 2tan- 1 (e u )-90 
 
 to sech u 
 
 SMITHSONIAN TABLES 
 
 300 
 
The Gude rmannian. 
 
 u 
 
 gd u 
 
 wF ' 
 
 gd u 
 
 Fo' 
 
 u 
 
 gdu 
 
 wF ' 
 
 fldu 
 
 F</ 
 
 2.500 
 
 1.406 9936 
 
 1631 
 
 o / // 
 
 80 36 53.26 
 
 33.64 
 
 2.550 
 
 1.414 9492 
 
 1552 
 
 o / // 
 
 81 04 14.22 
 
 // 
 32.02 
 
 .501 
 
 .407 1566 
 
 1629 
 
 80 37 26.88 
 
 33.60 
 
 551 
 
 .415 1043 
 
 1551 
 
 81 04 46.22 
 
 31-98 
 
 .502 
 
 .407 3194 
 
 1627 
 
 80 38 00.46 
 
 33.57 
 
 .552 
 
 . .415 2593 
 
 1549 
 
 81 05 18.19 
 
 3L95 
 
 .503 
 
 .407 4821 
 
 1626 
 
 80 38 34-01 
 
 33.54 
 
 .553 
 
 .415 4142 
 
 1548 
 
 81 05 50.13 
 
 31.92 
 
 .504 
 
 .407 6446 
 
 1624 
 
 80 39 07.54 
 
 33-50 
 
 .554 
 
 .415 5688 
 
 1546 
 
 81 06 22.03 
 
 31.89 
 
 2.505 
 
 1.407 8069 
 
 1623 
 
 80 39 41.02, 
 
 33-47 
 
 2.555 
 
 1.415 7234 
 
 1545 
 
 81 06 53.91 
 
 31-85 
 
 .506 
 
 .407 9691 
 
 l62I 
 
 80 40 14.47 
 
 33-44 
 
 .556 
 
 .415 8778 
 
 1543 
 
 81 07 25.75 
 
 31-83 
 
 .507 
 
 .408 1311 
 
 1619 
 
 80 40 47-90 
 
 33-40 
 
 557 
 
 .416 0320 
 
 1541 
 
 Si 07 57.56 
 
 31-80 
 
 .508 
 
 .408 2930 
 
 1618 
 
 80 41 21.28 
 
 33-37 
 
 .558 
 
 .416 1860 
 
 1540 
 
 81 08 29.34 
 
 31.76 
 
 .509 
 
 .408 4547 
 
 1616 
 
 80 41 54.64 
 
 33-34 
 
 -559 
 
 .416 3400 
 
 1538 
 
 81 09 01.09 
 
 31-73 
 
 2.510 
 
 1.408 6163 
 
 1615 
 
 80 42 27.96 
 
 33.31 
 
 2.560 
 
 1.416 4937 
 
 1537 
 
 81 09 32.80 
 
 31.70 
 
 .511 
 
 .408 7777 
 
 1613 
 
 80 43 01.25 
 
 33-27 
 
 .561 
 
 .416 6473 
 
 1535 
 
 81 10 04.49 
 
 31.67 
 
 .512 
 
 .408 9389 
 
 1612 
 
 80 43' 34.51 
 
 33-24 
 
 .562 
 
 .416 8008 
 
 1534 
 
 81 10 36.14 
 
 31.64 
 
 .513 
 
 .409 1000 
 
 1610 
 
 80 44 07-73 
 
 33-21 
 
 -563 
 
 .416 9541 
 
 1532 
 
 81 ii 07.77 
 
 31.61 
 
 .514 
 
 .409 2609 
 
 1608 
 
 80 44 40.92 
 
 33-17 
 
 -564 
 
 .417 1073 
 
 1531 
 
 81 ii 39.36 
 
 31.58 
 
 2.515 
 
 1.409 4216 
 
 1607 
 
 80 45 14.08 
 
 33.14 
 
 2.565 
 
 1.417 2603 
 
 1529 
 
 81 12 10.92 
 
 31-54 
 
 .516 
 
 .409 5822 
 
 1605 
 
 80 45 47-20 
 
 33-11 
 
 .566 
 
 .417 4131 
 
 1528 
 
 81 12 42.45 
 
 3I.5I 
 
 .517 
 
 .409 7427 
 
 1604 
 
 80 46 20.30 
 
 33-08 
 
 .567 
 
 .417 5659 
 
 1526 
 
 81 13 13.95 
 
 3L48 
 
 .518 
 
 .409 9029 
 
 1602 
 
 80 46 53.36 
 
 33-04 
 
 .568 
 
 .417 7184 
 
 1525 
 
 81 13 45.41 
 
 3L45 
 
 .519 
 
 .410 0631 
 
 1600 
 
 80 47 26.38 
 
 33.01 
 
 -569 
 
 .417 8708 
 
 1523 
 
 81 14 16.85 
 
 31.42 
 
 2.520 
 
 1.410 2230 
 
 1599 
 
 80 47 59.38 
 
 32.98 
 
 2.570 
 
 1.418 0231 
 
 1522 
 
 81 14 48.25 
 
 31-39 
 
 .521 
 
 .410 3828 
 
 1597 
 
 80 48 32.34 
 
 32.95 
 
 571 
 
 .418 1752 
 
 1520 
 
 81 15 19.63 
 
 3L36 
 
 .522 
 
 .410 5425 
 
 1596 
 
 80 49 05.27 
 
 32.91 
 
 572 
 
 .418 3271 
 
 1519 
 
 Si 15 50.97 
 
 3L33 
 
 .523 
 
 .410 7020 
 
 1594 
 
 80 49 38. 17 
 
 32.88 
 
 573 
 
 .418 4789 
 
 1517 
 
 81 16 22.28 
 
 31.30 
 
 .524 
 
 .410 8613 
 
 1593 
 
 80 50 11.03 
 
 32.85 
 
 574 
 
 .418 6306 
 
 1516 
 
 81 16 53.56 
 
 31.27 
 
 2.525 
 
 1.411 0205 
 
 1591 
 
 80 50 43-86 
 
 32.82 
 
 2.575 
 
 1.418 7821 
 
 I5H 
 
 81 17 24.81 
 
 31-23 
 
 .526 
 
 .411 1795 
 
 1589 
 
 80 51 16.66 
 
 32.78 
 
 .576 
 
 .418 9334 
 
 I5U 
 
 81 17 56.03 
 
 31.20 
 
 .527 
 
 .411 3384 
 
 1588 
 
 80 51 49-43 
 
 32.75 
 
 .577 
 
 .419 0847 
 
 I5H 
 
 81 18 27.22 
 
 3LI7 
 
 .528 
 
 .411 4971 
 
 1586 
 
 80 52 22.17 
 
 32.72 
 
 .578 
 
 .419 2357 
 
 1510 
 
 Si 18 58.38 
 
 3I.I4 
 
 .529 
 
 .411 6556 
 
 1585 
 
 80 52 54.87 
 
 32.69 
 
 579 
 
 .419 3866 
 
 1508 
 
 81 19 29.50 
 
 31.11 
 
 2.530 
 
 1.411 8140 
 
 1583 
 
 80 53 27.54 
 
 32.65 
 
 2.580 
 
 1.419 5374 
 
 1507 
 
 81 20 00.60 
 
 31-08 
 
 .531 
 
 .411 9722 
 
 1582 
 
 80 54 oo. 18 
 
 32.62 
 
 .581 
 
 .419 6880 
 
 1505 
 
 81 20 31.67 
 
 3i .05 
 
 .532 
 
 .412 1303 
 
 1580 
 
 80 54 32.78 
 
 32.59 
 
 .582 
 
 .419 8384 
 
 1504 
 
 Si 21 02.70 
 
 31.02 
 
 .533 
 
 .412 2882 
 
 1578 
 
 So 55 05.36 
 
 32-56 
 
 .583 
 
 .419 9888 
 
 1502 
 
 81 21 33.70 
 
 30.99 
 
 534 
 
 .412 4460 
 
 1577 
 
 80 55 37.90 
 
 32.53 
 
 .584 
 
 .420 1389 
 
 1501 
 
 8l 22 04.68 
 
 30.96 
 
 2.535 
 
 1.412 6036 
 
 1575 
 
 80 56 10.41 
 
 32.49 
 
 2.585 
 
 1.420 2889 
 
 1499 
 
 Si 22 35.62 
 
 30.93 
 
 .536 
 
 .412 7611 
 
 1574 
 
 80 56 42.89 
 
 32.46 
 
 .586 
 
 .420 4388 
 
 1498 
 
 81 23 06.53 
 
 30.90 
 
 537 
 
 .412 9184 
 
 1572 
 
 80 57 15-33 
 
 32.43 
 
 .587 
 
 .420 5885 
 
 1496 
 
 81 23 37.41 
 
 30.87 
 
 .538 
 
 .413 0755 
 
 1571 
 
 80 57 47-75 
 
 32.40 
 
 .588 
 
 .420 7381 
 
 1495 
 
 81 24 08.26 
 
 30.84 
 
 539 
 
 .413 2325 
 
 1569 
 
 80 58 20.13 
 
 32.37 
 
 .589 
 
 .420 8875 
 
 1493 
 
 81 24 39.09 
 
 30.81 
 
 2.540 
 
 1.413 3893 
 
 1568 
 
 80 58 52.48 
 
 32-33 
 
 2.590 
 
 1.421 0368 
 
 1492 
 
 81 25 09.88 
 
 30.77 
 
 541 
 
 .413 5460 
 
 1566 
 
 So 59 24.80 
 
 32.30 
 
 591 
 
 .421 1859 
 
 1491 
 
 81 25 40.63 
 
 30.74 
 
 542 
 
 .413 7025 
 
 1564 
 
 So 59 57.o8 
 
 32.27 
 
 592 
 
 .421 3349 
 
 1489 
 
 81 26 11.36 
 
 30.71 
 
 543 
 
 .413 8589 
 
 1563 
 
 81 oo 29.34 
 
 32.24 
 
 .593 
 
 .421 4837 
 
 1488 
 
 81 26 42.06 
 
 30.68 
 
 544 
 
 .414 0151 
 
 1561 
 
 81 01 01.56 
 
 32.21 
 
 594 
 
 .421 6324 
 
 1486 
 
 81 27 12.73 
 
 30.65 
 
 2.545 
 
 1.414 1712 
 
 1560 
 
 81 oi 33-75 
 
 32.17 
 
 2.595 
 
 1.421 7809 
 
 1485 
 
 81 27 43.37 
 
 30.62 
 
 .546 
 
 .414 3271 
 
 1558 
 
 81 02 05.91 
 
 32.14 
 
 .596 
 
 .421 9293 
 
 1483 
 
 81 28 13.98 
 
 30.59 
 
 547 
 
 .414 4829 
 
 1557 
 
 81 02 38.03 
 
 32.11 
 
 .597 
 
 .422 0776 
 
 1482 
 
 81 28 44-55 
 
 30.56 
 
 .548 
 
 .414 6385 
 
 1555 
 
 81 03 10.13 
 
 32.08 
 
 .598 
 
 .422 2257 
 
 1480 
 
 81 29 15.10 
 
 30.53 
 
 549 
 
 .414 7939 
 
 1554 
 
 81 03 42.19 
 
 32.05 
 
 .599 
 
 .422 3736 
 
 1479 
 
 81 29 45.62 
 
 30.50 
 
 2-550 
 
 1.414 9492 
 
 1552 
 
 81 04 14.22 
 
 32.02 
 
 2.600 
 
 1.422 5214 
 
 1477 
 
 81 30 i6.n 
 
 30.47 
 
 u 
 
 2tan-Ke)- 
 
 sech u 
 
 2tan- 1 (e")-90 
 
 o> sech u 
 
 u 
 
 2tan-Ke u )- 
 
 sech u 
 
 2tan- 1 (e")-90 
 
 u> sech u 
 
 SMITHSONIAN TABLES 
 
 301 
 
The Gudermannian. 
 
 u 
 
 gd u 
 
 .* 
 
 gd u 
 
 ^ 
 
 u 
 
 gd u 
 
 F ' 
 
 gd u 
 
 ~^T 
 
 2.600 
 
 1.422 5214 
 
 1477 
 
 / // 
 
 81 30 i6.n 
 
 30*47 
 
 2.650 
 
 1.429 7283 
 
 1406 
 
 / // 
 
 81 55 02.63 
 
 29.00 
 
 .601 
 
 .422 6691 
 
 1476 
 
 81 30 46.56 
 
 30.44 
 
 .651 
 
 .4298688 
 
 1405 
 
 81 55 31.62 
 
 28.97 
 
 .602 
 
 .422 8166 
 
 1474 
 
 81 31 16.99 
 
 30.41 
 
 .652 
 
 .430 0092 
 
 1403 
 
 81 56 00.58 
 
 28.94 
 
 .603 
 
 .422 9640 
 
 1473 
 
 81 31 47-39 
 
 30.38 
 
 .653 
 
 430 1495 
 
 1402 
 
 81 56 29.51 
 
 28.92 
 
 .604 
 
 .423 III2 
 
 1471 
 
 81 32 17.75 
 
 30.35 
 
 .654 
 
 .430 2896 
 
 1400 
 
 81 56 58.41 
 
 28.89 
 
 2.605 
 
 1.423 2583 
 
 1470 
 
 81 32 48.09 
 
 30.32 
 
 2.655 
 
 1.430 4296 
 
 1399 
 
 81 57 27.28 
 
 28.86 
 
 .606 
 
 .423 4052 
 
 1469 
 
 81 33 18.40 
 
 30.29 
 
 .656 
 
 430 5694 
 
 1^98 
 
 81 57 56.12 
 
 28.83 
 
 .607 
 
 .423 5520 
 
 1467 
 
 81 33 48.67 
 
 30.26 
 
 .657 
 
 430 7091 
 
 1396 
 
 81 58 24.94 
 
 28.80 
 
 .608 
 
 .4236986 
 
 1466 
 
 81 34 18.92 
 
 30.23 
 
 .658 
 
 .430 8487 
 
 1395 
 
 Si 58 53.72 
 
 28.77 
 
 .609 
 
 .423 8451 
 
 1464 
 
 81 34 49-iU 
 
 30.20 
 
 .659 
 
 .430 9881 
 
 1394 
 
 81 59 22.48 
 
 28.74 
 
 2.610 
 
 1.423 9915 
 
 1463 
 
 81 35 19.32 
 
 30.17 
 
 2.660 
 
 I.43I 1274 
 
 1392 
 
 81 59 51.21 
 
 28.72 
 
 .611 
 
 .424 1377 
 
 1461 
 
 81 35 49.48 
 
 30.14 
 
 .661 
 
 .431 2665 
 
 1391 
 
 82 oo 19.91 
 
 28.69 
 
 .612 
 
 .424 2837 
 
 1460 
 
 81 36 19.61 
 
 30.11 
 
 .662 
 
 431 4055 
 
 1389 
 
 82 oo 48.58 
 
 28.66 
 
 .613 
 
 .424 4297 
 
 1458 
 
 81 36 49-71 
 
 30.08 
 
 .663 
 
 .431 5444 
 
 1388 
 
 82 01 17.23 
 
 28.63 
 
 .614 
 
 424 5754 
 
 1457 
 
 81 37 19.77 
 
 30.05 
 
 .664 
 
 .431 6831 
 
 1387 
 
 82 01 45.84 
 
 28.60 
 
 2.615 
 
 1.424 7211 
 
 1456 
 
 81 37 49-8i 
 
 30.02 
 
 2.665 
 
 1.431 8217 
 
 1385 
 
 82 02 14.43 
 
 28.57 
 
 .6l6 
 
 .4248665 
 
 1454 
 
 81 38 19-82 
 
 29.99 
 
 .666 
 
 .431 9602 
 
 1384 
 
 82 O2 42.99 
 
 28.55 
 
 .617 
 
 .425 0119 
 
 1453 
 
 81 38 49.80 
 
 29.96 
 
 .667 
 
 .432 0985 
 
 1383 
 
 82 O3 11.52 
 
 28.52 
 
 .6l8 
 
 .425 1571 
 
 1451 
 
 81 39 19.75 
 
 29-93 
 
 .668 
 
 .432 2367 
 
 1381 
 
 82 O3 40.02 
 
 28.49 
 
 .619 
 
 .425 3021 
 
 1450 
 
 81 39 49.67 
 
 29.90 
 
 .669 
 
 432 3747 
 
 1380 
 
 82 O4 O8.5O 
 
 28.46 
 
 2.62O 
 
 1.425 4470 
 
 1448 
 
 81 40 19.56 
 
 29.87 
 
 2.670 
 
 1.432 5127 
 
 1378 
 
 82 04 36.95 
 
 28.43 
 
 .621 
 
 .425 5918 
 
 1447 
 
 81 40 49.42 
 
 29.85 
 
 .671 
 
 .432 6504 
 
 1377 
 
 82 05 05.36 
 
 28.40 
 
 .622 
 
 .425 7364 
 
 1446 
 
 81 41 19.25 
 
 29.82 
 
 .672 
 
 .432 7881 
 
 1376 
 
 82 05 33-75 
 
 28.38 
 
 .623 
 
 .425 8809 
 
 1444 
 
 81 41 49.05 
 
 29.79 
 
 .673 
 
 .432 9256 
 
 1374 
 
 82 06 O2. 12 
 
 28.35 
 
 .624 
 
 .426 0252 
 
 1443 
 
 81 42 18.82 
 
 29.76 
 
 .674 
 
 .433 0629 
 
 . 1373 
 
 82 06 3O.45 
 
 28.32 
 
 2.625 
 
 1.426 1694 
 
 144,1 
 
 81 42 48.56 
 
 29.73 
 
 2.675 
 
 1.433 2002 
 
 1372 
 
 82 06 58.76 
 
 28.29 
 
 .626 
 
 .426 3135 
 
 1440 
 
 81 43 18.28 
 
 29.70 
 
 .676 
 
 .433 3373 
 
 1370 
 
 82 07 27.03 
 
 28.26 
 
 .627 
 
 .426 4574 
 
 1438 
 
 81 43 47.96 
 
 29.67 
 
 .677 
 
 .433 4742 
 
 
 82 O7 55.28 
 
 28.24 
 
 .628 
 
 .426 6012 
 
 1437 
 
 81 44 17-61 
 
 29.64 
 
 .678 
 
 .433 6110 
 
 1368 
 
 82 08 23.51 
 
 28.21 
 
 .629 
 
 .426 7448 
 
 1436 
 
 81 44 47-24 
 
 29.61 
 
 .679 
 
 433 7477 
 
 1366 
 
 82 08 51.70 
 
 28.18 
 
 2.630 
 
 1.426 8883 
 
 1434 
 
 81 45 16.83 
 
 29.58 
 
 2.680 
 
 1.433 8843 
 
 1365 
 
 82 09 19-86 
 
 28.15 
 
 .631 
 
 .427 0316 
 
 1433 
 
 81 45 46.40 
 
 29.55 
 
 .681 
 
 .434 0207 
 
 1363 
 
 82 09 48.00 
 
 28.12 
 
 .632 
 
 .427 1748 
 
 
 81 46 15.94 
 
 29.52 
 
 .682 
 
 .434 1570 
 
 1362 
 
 82 10 16.11 
 
 28.10 
 
 .633 
 
 .427 3179 
 
 1430 
 
 81 46 45-44 
 
 29.49 
 
 .683 
 
 .434 2931 
 
 1361 
 
 82 10 44.20 
 
 28.07 
 
 .634 
 
 .427 4608 
 
 1428 
 
 81 47 14.92 
 
 29.46 
 
 .684 
 
 .434 4291 
 
 1359 
 
 82 ii 12.25 
 
 28.04 
 
 2.635 
 
 1.427 6036 
 
 1427 
 
 81 47 44-37 
 
 29-43 
 
 2.685 
 
 1.434 5650 
 
 1358 
 
 82 ii 40.28 
 
 28.01 
 
 .636 
 
 .427 7462 
 
 1426 
 
 81 48 13.79 
 
 29.41 
 
 .686 
 
 .434 7008 
 
 1357 
 
 82 12 08.28 
 
 27.99 
 
 .637 
 
 .427 8887 
 
 1424 
 
 81 4843.18 
 
 29.38 
 
 .687 
 
 .434 8364 
 
 1355 
 
 82 12 36.25 
 
 27.96 
 
 .638 
 
 .428 0310 
 
 1423 
 
 81 49 12.55 
 
 29.35 
 
 .688 
 
 .434 9719 
 
 1354 
 
 82 13 O4.I9 
 
 27.93 
 
 .639 
 
 .428 1732 
 
 1421 
 
 81 49 41.88 
 
 29.32 
 
 .689 
 
 .435 1072 
 
 1353 
 
 82 13 32.11 
 
 27.90 
 
 2.640 
 
 1.428 3153 
 
 1420 
 
 81 50 ii. 18 
 
 29.29 
 
 2.690 
 
 1.435 2424 
 
 1351 
 
 82 13 59-99 
 
 27.87 
 
 .641 
 
 .428 4572 
 
 1419 
 
 81 50 40.46 
 
 29.26 
 
 .691 
 
 435 3775 
 
 1350 
 
 82 14 27.86 
 
 27-85 
 
 .642 
 
 .428 5990 
 
 1417 
 
 81 51 09.70 
 
 29.23 
 
 .692 
 
 435 5124 
 
 1349 
 
 82 14 55.69 
 
 27.82 
 
 .643 
 
 .428 7407 
 
 1416 
 
 81 51 38.92 
 
 29.20 
 
 .693 
 
 .435 6472 
 
 1347 
 
 82 15 23.49 
 
 27.79 
 
 .644 
 
 .428 8822 
 
 1414 
 
 81 52 08.11 
 
 29.17 
 
 .694 
 
 435 78i9 
 
 1346 
 
 82 15 51.27 
 
 27.77 
 
 2.645 
 
 1.429 0236 
 
 1413 
 
 81 52 37-27 
 
 29.14 
 
 2.695 
 
 1.435 9164 
 
 1345 
 
 82 16 19.02 
 
 27.74 
 
 .646 
 
 .429 1648 
 
 1412 
 
 81 53 06.40 
 
 29.12 
 
 .696 
 
 .436 0508 
 
 1343 
 
 82 16 46.75 
 
 27.71 
 
 .647 
 
 .429 3059 
 
 1410 
 
 81 53 35-50 
 
 29.09 
 
 .697 
 
 .436 1851 
 
 1342 
 
 82 17 14.44 
 
 27.68 
 
 .648 
 
 .429 4468 
 
 1409 
 
 81 54 04.57 
 
 29.06 
 
 .698 
 
 .436 3192 
 
 
 82 17 42.11 
 
 27.65 
 
 .649 
 
 .429 5876 
 
 1407 
 
 81 54 33.62 
 
 29.03 
 
 .699 
 
 .436 4532 
 
 1339 
 
 82 18 09.75 
 
 27.63 
 
 2.650 
 
 1.429 7283 
 
 1406 
 
 81 55 02.63 
 
 29.00 
 
 2.700 
 
 1.436 5871 
 
 1338 
 
 82 18 37.36 
 
 27.60 
 
 U 
 
 7T 
 
 2 
 
 u sech u 
 
 ""-"^ 
 
 wsechu 
 
 u 
 
 2 tan-He")- jj 
 
 wsechu 
 
 2tan-'(e)-90 
 
 wsechu 
 
 SMITHSONIAN TABLES 
 
 302 
 
The Gudermannian. 
 
 . 
 
 gdu 
 
 * 
 
 gdu 
 
 , 
 
 u 
 
 gdu 
 
 -F ' 
 
 gd u 
 
 -w 
 
 2.700 
 
 1.436 5871 
 
 1338 
 
 82 18 37^36 
 
 27.60 
 
 2.750 
 
 1.443 "44 
 
 1273 
 
 o / // 
 
 82 41 03.70 
 
 26^26 
 
 .701 
 
 .436 7209 
 
 1337 
 
 82 19 04.95 
 
 27.57 
 
 751 
 
 .443' 2416 
 
 1272 
 
 82 41 29.95 
 
 26.24 
 
 .702 
 
 .436 8545 
 
 1335 
 
 82 19 32.51 
 
 27.54 
 
 752 
 
 .443 3688 
 
 1271 
 
 82 41 56. 18 
 
 26.21 
 
 .703 
 
 .436 9879 
 
 1334 
 
 82 20 00.04 
 
 27.52 
 
 753 
 
 .443 4958 
 
 1270 
 
 82 42 22.38 
 
 26.19 
 
 704 
 
 .437 1213 
 
 1333 
 
 82 20 27.54 
 
 27.49 
 
 .754 
 
 .443 6227 
 
 1268 
 
 82 42 48.55 
 
 26.16 
 
 2.705 
 
 1.437 2545 
 
 1331 
 
 82 2O 55.O2 
 
 27.46 
 
 2.755 
 
 1.443 7495 
 
 1267 
 
 82 43 14.70 
 
 26.14 
 
 .706 
 
 .437 3876 
 
 1330 
 
 82 21 22.47 
 
 27.44 
 
 .756 
 
 .443 8761 
 
 1266 
 
 82 43 40.82 
 
 26.11 
 
 .707 
 
 437 5205 
 
 1329 
 
 82 21 49.89 
 
 27.41 
 
 757 
 
 .444 0026 
 
 1265 
 
 82 44 06.02 
 
 26.08 
 
 .708 
 
 .437 6533 
 
 1327 
 
 82 22 17.29 
 
 27.38 
 
 .758 
 
 .444 1200 
 
 1263 
 
 82 44 32.99 
 
 26.06 
 
 .709 
 
 .437 7860 
 
 1326 
 
 82 22 44.66 
 
 27-35 
 
 759 
 
 .444 2553 
 
 1262 
 
 82 44 59.03 
 
 26.03 
 
 2.710 
 
 1.437 9i86 
 
 1325 
 
 82 23 12. OO 
 
 27-33 
 
 2.760 
 
 1.444 3814 
 
 1261 
 
 82 45 25.05 
 
 26.01 
 
 .7ii 
 
 .438 0510 
 
 1324 
 
 82 23 39.31 
 
 27.30 
 
 .761 
 
 .444 5074 
 
 1260 
 
 82 45 51.04 
 
 25.98 
 
 .712 
 
 .438 1833 
 
 1322 
 
 82 24 06.60 
 
 27.27 
 
 .762 
 
 .444 6333 
 
 1258 
 
 82 46 17.01 
 
 25.95 
 
 713 
 
 .438 3154 
 
 1321 
 
 82 24 33-85 
 
 27.25, 
 
 .763 
 
 .444 7591 
 
 1257 
 
 82 46 42.95 
 
 25.93 
 
 .714 
 
 .438 4475 
 
 1320 
 
 82 25 01.09 
 
 27.22 
 
 .764 
 
 .444 8847 
 
 1256 
 
 82 47 08.87 
 
 25.90 
 
 2.715 
 
 1.438 5794 
 
 1318 
 
 82 25 28.29 
 
 27.19 
 
 2.765 
 
 ri.445 0102 
 
 1255 
 
 82 47 34.76 
 
 25.88 
 
 .7i6 
 
 .438 7in 
 
 1317 
 
 82 25 55.47 
 
 27.17 
 
 .766 
 
 445 1356 
 
 1253 
 
 82 48 00.62 
 
 25.85 
 
 .717 
 
 .438 8428 
 
 1316 
 
 82 26 22.63 
 
 27.14 
 
 .767 
 
 .445 2609 
 
 1252 
 
 82 48 26.46 
 
 25-83 
 
 .718 
 
 .438 9743 
 
 1314 
 
 82 26 49.75 
 
 27.11 
 
 .768 
 
 .445 386o 
 
 1251 
 
 82 48 52.27 
 
 25.86 
 
 .719 
 
 439 1057 
 
 1313 
 
 82 27 16.85 
 
 27.08 
 
 .769 
 
 445 SHI 
 
 1250 
 
 82 49 18.06 
 
 25.77 
 
 2.720 
 
 1.439 2369 
 
 1312 
 
 82 27 43-92' 
 
 27.06 
 
 2.770 
 
 1.445 6360 
 
 1248 
 
 82 49 43.82 
 
 25.75 
 
 .721 
 
 439 3680 
 
 1310 
 
 82 28 10.96 
 
 27.03 
 
 .771 
 
 .445 7607 
 
 1247 
 
 82 50 09.56 
 
 25.72 
 
 .722 
 
 -439 4990 
 
 1309 
 
 82 28 37.98 
 
 27.00 
 
 772 
 
 .445 8854 
 
 1246 
 
 82 50 35.27 
 
 25.70 
 
 723 
 
 439 6299 
 
 1308 
 
 82 29 04.97 
 
 26.08 
 
 773 
 
 .446 0099 
 
 1245 
 
 82 51 00.95 
 
 25.67 
 
 .724 
 
 439 7606 
 
 1307 
 
 82 29 31.94 
 
 26.95 
 
 774 
 
 .446 1343 
 
 1243 
 
 82 51 26.61 
 
 25.65 
 
 2.725 
 
 1.4398912 
 
 1305 
 
 82 29 58.87 
 
 26.92 
 
 2.775 
 
 1.446 2586 
 
 1242 
 
 82 51 52.25 
 
 25.62 
 
 .726 
 
 .440 0216 
 
 1304 
 
 82 30 25.79 
 
 26.90 
 
 .776 
 
 .446 3827 
 
 1241 
 
 82 521 17.86 
 
 25.60 
 
 .727 
 
 .440 1520 
 
 1303 
 
 82 30 52.67 
 
 26.87 
 
 777 
 
 .446 5068 
 
 1240 
 
 82 52 43.44 
 
 25.57 
 
 .728 
 
 .440 2822 
 
 1301 
 
 82 31 19.53 
 
 26.84 
 
 .778 
 
 .446 6307 
 
 1238 
 
 82 53 09.00 
 
 25.55 
 
 .729 
 
 .440 4123 
 
 1300 
 
 82 31 46.36 
 
 26.82 
 
 .779 
 
 .446 7545 
 
 1237 
 
 82 53 34-53 
 
 25.52 
 
 2.730 
 
 1.440 5422 
 
 1299 
 
 82 32 13.16 
 
 26.79 
 
 2.780 
 
 1.446 8781 
 
 1236 
 
 82 54 00.04 
 
 25.49 
 
 731 
 
 .440 6720 
 
 1298 
 
 82 32 39.94 
 
 26.76 
 
 .781 
 
 .447 0017 
 
 1235 
 
 82 54 25.52 
 
 25.47 
 
 .732' 
 
 .440 8017 
 
 1296 
 
 82 33 06.69 
 
 26.74 
 
 .782 
 
 .447 1251 
 
 1234 
 
 82 54 50.98 
 
 25.44 
 
 733 
 
 .440 9313 
 
 1295 
 
 82 33 33.42 
 
 26.71 
 
 .783 
 
 .447 2484 
 
 1232 
 
 82 55 16.41 
 
 25.42 
 
 734 
 
 .441 0607 
 
 1294 
 
 82 34 oo.ii 
 
 26.68 
 
 .784 
 
 .447 37i6 
 
 1231 
 
 82 55 41.81 
 
 25-39 
 
 2.735 
 
 1.441 1900 
 
 1292 
 
 82 34 26.78 
 
 26.66 
 
 2.785 
 
 1.447 4946 
 
 1230 
 
 82 56 07.19 
 
 25.37 
 
 .736 
 
 .441 3192 
 
 1291 
 
 82 34 53.43 
 
 26.63 
 
 .786 
 
 447 6175 
 
 1229 
 
 82 56 32.55 
 
 25.34 
 
 .737 
 
 .441 4483 
 
 I2OO 
 
 82 35 20.05 
 
 26.61 
 
 .787 
 
 .447 7403 
 
 1227 
 
 82 56 57-88 
 
 25.32 
 
 .738 
 
 .441 5772 
 
 1289 
 
 82 35 46.64 
 
 26.58 
 
 .788 
 
 .447 8630 
 
 1226 
 
 82 57 23. 19 
 
 25.29 
 
 .739 
 
 .441 7060 
 
 1287 
 
 82 36 13.21 
 
 26.55 
 
 .789 
 
 .447 9856 
 
 1225 
 
 82 57 48.47 
 
 25.27 
 
 2.740 
 
 1.441.8347 
 
 1286 
 
 82 36 39-75 
 
 26.53 
 
 2.790 
 
 1.448 1080 
 
 1224 
 
 82 58 13.72 
 
 25.24 
 
 741 
 
 .441 9632 
 
 1285 
 
 82 37 06.26 
 
 26.50 
 
 791 
 
 .448 2303 
 
 1223 
 
 82 58 38.95 
 
 25.22 
 
 742 
 
 .442 0916 
 
 1283 
 
 82 37 32-75 
 
 26.47 
 
 .792 
 
 .448 3525 
 
 122 1 
 
 82 59 04.16 
 
 25.19 
 
 .743 
 
 .442 2199 
 
 1282 
 
 82 37 59.21 
 
 26.45 
 
 793 
 
 .448 4746 
 
 I22O 
 
 82 59 29.34 
 
 25.I7 
 
 .744 
 
 .442 3481 
 
 I28l 
 
 82 38 25.64 
 
 26.42 
 
 794 
 
 .4485966 
 
 1219 
 
 82 59 54.49 
 
 25.14 
 
 2.745 
 
 1.442 476l 
 
 1280 
 
 82 38 52.05 
 
 26.40 
 
 2.795 
 
 1.448 7184 
 
 1218 
 
 83 oo 19.62 
 
 25.12 
 
 .746. 
 
 .747 
 
 .442 6040 
 442 73i8 
 
 12.78 
 1277 
 
 82 39 18.43 
 
 82 39 44.79 
 
 20.37 
 26.34 
 
 .796 
 797 
 
 .448 8401 
 ,448 9617 
 
 1217 
 1215 
 
 83 oo 44.73 
 83 oi 09.81 
 
 25.09 
 25.07 
 
 .748 
 
 .442 8594 
 
 1276 
 
 82 40 I'l . 12 
 
 26.32 
 
 .798 
 
 .449 0832 
 
 1214 
 
 83 oi 34.86 
 
 25.04 
 
 749 
 
 .442 9870 
 
 1275 
 
 82 40 37.42 
 
 26.29 
 
 .799 
 
 .449 2045 
 
 1213 
 
 83 oi 59-50 
 
 25.02 
 
 2.750 
 
 1.443 H44 
 
 1273 
 
 82 41 03.70 
 
 26.26 
 
 2.800 
 
 1.449 3258 
 
 1212 
 
 83 02 24.90 
 
 24.99 
 
 u 
 
 JT 
 
 o sech u 
 
 2tan- 1 (e)-90 
 
 o> sech u 
 
 u 
 
 7T 
 
 to sech u 
 
 2tan- 1 (e")-90 
 
 w sech u 
 
 SMITHSONIAN TABLES 
 
 303 
 
The Gude rmannian. 
 
 u 
 
 gd u 
 
 *>' 
 
 gd u 
 
 F ' 
 
 u 
 
 gd u 
 
 F ' 
 
 gdu 
 
 F ' 
 
 2.800 
 
 1.449 3258 
 
 1212 
 
 83 02 24.90 
 
 24-99 
 
 2.850 
 
 1-455 2365 
 
 H53 
 
 o / // 
 83 22 44.07 
 
 23*78 
 
 .801 
 
 .449 4469 
 
 1211 
 
 83 02 49.88 
 
 24.97 
 
 .851 
 
 455 3517 H52 
 
 83 23 07.84 
 
 23.76 
 
 .802 
 
 .449 5679 
 
 1209 
 
 83 03 14.84 
 
 24.94 
 
 .852 
 
 .455 4668 1151 83 23 31.58 
 
 23.74 
 
 .803 
 
 .449 6888 
 
 I208 
 
 83 03 39-77 
 
 24.92 
 
 853 
 
 455 5819 1150 
 
 83 23 55.31 
 
 23.71 
 
 .804 
 
 .449 8095 
 
 1207 
 
 83 04 04.68 
 
 24.89 
 
 .854 
 
 .455 6968 1148 
 
 83 24 19.01 
 
 23.69 
 
 2.805 
 
 1.449 930i 
 
 I2O6 
 
 83 04 29.56 
 
 24.87 
 
 2.855 
 
 1.455 8115 H47 
 
 83 24 42.69 
 
 23.67! 
 
 .806 
 
 .450 0507 
 
 1205 
 
 83 04 54.42 
 
 24.85 
 
 .856 
 
 455 9262 1146 
 
 83 25 06.34 
 
 23.64 
 
 .807 
 
 .450 1710 
 
 1203 
 
 83 05 19.25 
 
 24.82 
 
 .857 
 
 .4560408, 1145 
 
 83 25 29.97 
 
 23.62 
 
 .808 
 
 .450 2913 
 
 I2O2i 
 
 83 05 44-06 
 
 24.80 
 
 .858 
 
 .456 1552 
 
 1144 
 
 83 25 53.58 
 
 23-59 
 
 .809 
 
 .450 4115 
 
 I2OI 
 
 83 06 08.84 
 
 24-77 
 
 .859 
 
 .456 2696 
 
 H43 
 
 83 26 17.16 
 
 23.57 
 
 ! 2.810 
 
 1-450 5315 
 
 I2OO 
 
 83 06 33.60 
 
 24.75 
 
 2.860 
 
 1.456 3838 
 
 1142 
 
 83 26 40.72 
 
 23.55 
 
 .8u 
 
 .450 6514 
 
 1199 
 
 83 06 58.33 
 
 24.72 
 
 .861 
 
 .456 4979 
 
 1140 
 
 83 27 04.25 
 
 23.52 
 
 .812 
 
 .450 7712 
 
 1198 
 
 83 07 23.04 
 
 24.70 
 
 .862 
 
 .456 6119 
 
 1139 
 
 83 27 27.77 
 
 23.50 
 
 .813 
 
 .450 8909 
 
 U96 
 
 83 07 47-73 
 
 24.67 
 
 .863 
 
 .456 7258 
 
 1138 
 
 83 27 51.26 
 
 23.48 
 
 .814 
 
 .451 0105 
 
 1 195 
 
 83 08 12.39 
 
 24.65 
 
 .864 
 
 .456 8395 
 
 H37 
 
 83 28 14.72 
 
 23.45 
 
 2.815 
 
 1.451 1299 
 
 1 194 
 
 83 08 37.03 
 
 24.62 
 
 2.865 
 
 1.456 9532 
 
 1136 
 
 83 28 38.16 
 
 23-43 
 
 .816 
 
 .451 2492 
 
 1 193 
 
 83 09 01.64 
 
 24.60 
 
 .866 
 
 .457 0667 
 
 1135 
 
 83 29 01.58 
 
 23.41 
 
 .817 
 
 451 3684 
 
 1191 
 
 83 09 26.23 
 
 24.58 
 
 .867 
 
 .457 1801 
 
 H34 
 
 83 29 24.98 
 
 23.38 
 
 .818 
 
 .451 4875 
 
 1190 
 
 83 09 50.79 
 
 24.55 
 
 .868 
 
 457 2935 
 
 1 133 
 
 83 29 48.35 
 
 23.36 
 
 .819 
 
 .451 6065 
 
 1189 
 
 83 10 15.33 
 
 24.53 
 
 .869 
 
 .457 4067 
 
 II3I 
 
 83 30 11.70 
 
 23.34 
 
 2.820 
 
 I-45I 7253 
 
 1188 
 
 83 10 39.84 
 
 24.50 
 
 2.870 
 
 1.457 5198 
 
 1130 
 
 83 30 35.03 
 
 23.32 
 
 .821 
 
 .451 8441 
 
 1187 
 
 83 ii 04.33 
 
 24.48 
 
 .871 
 
 .457 6327 
 
 1129 
 
 83 30 58.33 
 
 23.29 
 
 .822 
 
 .451 9627 
 
 1186 
 
 83 ii 28.80 
 
 24.45 
 
 .872 
 
 457 7456 
 
 1128 
 
 83 31 21. 61 
 
 23.27 
 
 .823 
 
 .452 0812 
 
 1184 
 
 83 ii 53.24 
 
 24-43 
 
 .873 
 
 .457 8584 
 
 1127 
 
 83 31 44.87 
 
 23.25 
 
 .824 
 
 .452 1995 
 
 1183 
 
 83 12 17.66 
 
 24.41 
 
 .874 
 
 457 9710 
 
 1126 
 
 83 32 08. II 
 
 23.22 
 
 2.825 
 
 1.452 3178 
 
 1182 
 
 83 12 42.O5 
 
 24.38 
 
 2.875 
 
 1.4580835 
 
 1 125 
 
 83 32 31.32 
 
 23.20 
 
 .826 
 
 452 4359 
 
 1181 
 
 83 13 06.42 
 
 24.36 
 
 .876 
 
 .458 1959 
 
 1124 
 
 83 32 54.50 
 
 23.18 
 
 .827 
 
 .452 5540 
 
 1180 
 
 83 13 30.76 
 
 24.33 
 
 .877 
 
 .458 3083 
 
 1123 
 
 83 33 17.67 
 
 23.15 
 
 .828 
 
 .452 6719 
 
 1178 
 
 83 13 55.08 
 
 24.31 
 
 .878 
 
 .458 4204 
 
 II2I 
 
 83 33 40.8i 
 
 23.13 
 
 .829 
 
 452 7897 
 
 1 177 
 
 83 14 19.38 
 
 24.28 
 
 .879 
 
 .458 5325 
 
 II2O 
 
 83 34 03.93 
 
 23.11 
 
 2.830 
 
 1.452 9073 
 
 1176 
 
 83 14 43.65 
 
 24.26 
 
 2.880 
 
 1.458 6445 
 
 III9 
 
 83 34 27.03 
 
 23.08 
 
 .831 
 
 .453 0249 
 
 1175 
 
 83 15 07.90 
 
 24.24 
 
 .881 
 
 .458 7564 
 
 1118 
 
 83 34 50.10 
 
 23.06 
 
 1 .832 
 
 453 1423 
 
 1 174 
 
 83 15 32.12 
 
 24.21 
 
 .882 
 
 .458 8681 
 
 III7 
 
 83 35 13.15 
 
 23.04 
 
 .833 
 
 453 2597 
 
 1 173 
 
 83 15 56.32 
 
 24.19 
 
 .883 
 
 .458 9798 
 
 1116 
 
 83 35 36.18 
 
 23.02 
 
 .834 
 
 453 3769 
 
 1171 
 
 83 16 20.50 
 
 24.16 
 
 .884 
 
 459 0913 
 
 IH5 
 
 83 35 59.18 
 
 22.99 
 
 2.835 
 
 1.453 4940 
 
 1170 
 
 83 16 44.65 
 
 24.14 
 
 2.885 
 
 1.459 2027 
 
 1114 
 
 83 36 22.16 
 
 22.97 
 
 .836 
 
 .453 6109 
 
 1169 
 
 83 17 08.78 
 
 24.12 
 
 .886 
 
 .459 3140 
 
 IM3 
 
 83 36 45-12 
 
 22.95 
 
 .837 
 
 .453 7278 
 
 1168 
 
 83 17 32.88 
 
 24.09 
 
 .887 
 
 .459 4252 
 
 mi 
 
 83 37 08.06 
 
 22.92 
 
 .838 
 
 .453 8445 
 
 1167 
 
 83 17 56.06 
 
 24.07 
 
 .888 
 
 .459 5363 
 
 I IIO 
 
 83 37 30.97 
 
 22.90 
 
 .839 
 
 .453 96i2 
 
 1166 
 
 83 18 2 i. 02 
 
 24.04 
 
 .889 
 
 .459 0473 
 
 1109 
 
 83 37 53-86 
 
 22.88 
 
 2.840 
 
 1.454 0777 
 
 1-165 
 
 83 18 45.05 
 
 24.02 
 
 2.890 
 
 1-459 758i 
 
 1108 
 
 83 38 16.73 
 
 22.86 
 
 .841 
 
 .454 1941 
 
 1163 
 
 83 19 09.06 
 
 24.00 
 
 .891 
 
 .4598689 
 
 1107 
 
 83 38 39.57 
 
 22.83 
 
 .842 
 
 .454 3104 
 
 1162 
 
 83 19 33.04 
 
 23-97 
 
 .892 
 
 459 9795 
 
 1106 
 
 83 39 02.40 
 
 22. 8l 
 
 .843 
 
 .454 4265 
 
 1161 
 
 83 19 57-01 
 
 23-95 
 
 .893 
 
 .460 0901 
 
 1105 
 
 83 39 25.19 
 
 22.79 
 
 .844 
 
 .454 5426 
 
 1160 
 
 83 20 20.94 
 
 23.93 
 
 .894 
 
 .460 2005 
 
 1104 
 
 83 39 47-97 
 
 22.77 
 
 2.845 
 
 1.454 6585 
 
 ii59 
 
 83 20 44-86 
 
 23.90 
 
 2.895 
 
 1.460 3108 
 
 1103 
 
 83 40 10.73 
 
 22.74 
 
 .846 
 
 454 7743 
 
 1158 
 
 83 21 08.74 
 
 23.88 
 
 .896 
 
 .460 4210 
 
 I IOI 
 
 83 40 33.46 
 
 
 .847 
 
 .454 8900 
 
 1156 
 
 83 21 32.6l 
 
 23.85 
 
 .897 
 
 .460 531 I 
 
 1 100 
 
 83 40 56.17 
 
 22.70 
 
 .848 
 
 455 0056 
 
 ii55 
 
 83 21 56.45 
 
 23-83 
 
 .898 
 
 .460 6411 
 
 1099 
 
 83 41 18.85 
 
 22.68 
 
 .849 
 
 .455 121 I 
 
 ii54 
 
 83 22 20.27 
 
 23.81 
 
 .899 
 
 .460 7510 
 
 1098 
 
 83 41 4L52 
 
 22.65 
 
 2.850 
 
 1.455 2365 
 
 1 153 
 
 83 22 44.07 
 
 23.78 
 
 2.000 
 
 1.460 8607 
 
 1097 
 
 83 42 04. 16 
 
 22.63 
 
 u 
 
 2tan-Ke)- 
 
 wsechu 
 
 2 tan-He" )-90 
 
 w sech u 
 
 u 
 
 2tan-Ke)- 
 
 wsechu 
 
 2 tan-He")- 90 
 
 u>sech u 
 
 SMITHSONIAN TABLES 
 
 304 
 
The Gudermannian. 
 
 u 
 
 gd u 
 
 iw 
 
 gd u 
 
 F</ 
 
 u 
 
 gd u 
 
 F O ' 
 
 gdu 
 
 o>F</ 
 
 2.900 
 
 1.460 8607 
 
 1097 
 
 o y // 
 
 83 42 04.16 
 
 22.63 
 
 2.950 
 
 1.466 21231 
 
 1044 
 
 o / // 
 
 84 oo 28.00 
 
 21.53 
 
 .901 
 
 .460 9704 
 
 1096 
 
 83 42 26.78 
 
 22. 6l 
 
 .951 
 
 .466 3167 
 
 1043 
 
 84 oo 49.53 
 
 21.51 
 
 .902 
 
 .461 0800 
 
 1095 
 
 83 42 49.37 
 
 22.59 
 
 952 
 
 .466 4209 
 
 1042 
 
 84 oi 11.03 
 
 21.49 
 
 .903 
 
 .461 1894 
 
 1094 
 
 83 43 H.95 
 
 22.56 
 
 953 
 
 .466 5251 
 
 1041 
 
 84 oi 32.51 
 
 21.47 
 
 .904 
 
 .461 2987 
 
 1093 
 
 83 43 34.50 
 
 22.54 
 
 954 
 
 .466 6291 
 
 1040 
 
 84 oi 53-97 
 
 21.45 
 
 2.005 
 
 1.461 4080 
 
 1092 
 
 83 43 57.03 
 
 22.52 
 
 2.955 
 
 1.466 7330 
 
 1039 
 
 84 02 15.40 
 
 21.43 
 
 .906 
 
 .461 5171 
 
 1091 
 
 83 44 19.54 
 
 22.50 
 
 .956 
 
 .466 8368 
 
 1038 
 
 84 02 36.82 
 
 21.40 
 
 .007 
 
 .461 6261 
 
 IOOO 
 
 83 44 42.02 
 
 22.47 
 
 957 
 
 .466 9406 
 
 1037 
 
 84 O2 58.21 
 
 21.38 
 
 .908 
 
 461 735O 
 
 1088 
 
 83 45 04.48 
 
 22.45 
 
 .958 
 
 .467 0442 
 
 1036 
 
 84 03 19.58 
 
 21.36 
 
 .909 
 
 .461 8438 
 
 1087 
 
 83 45 26.92' 
 
 22.43 
 
 959 
 
 .467 1477 
 
 1035 
 
 84 03 40.93 
 
 21.34 
 
 2.910 
 
 1.461 9525 
 
 1086 
 
 83 45 49-34 
 
 22.41 
 
 2.960 
 
 1.467 2511 
 
 1034 
 
 84 04 02.27 
 
 21.32 
 
 .911 
 
 .462 0610 
 
 1085 
 
 83 46 n.73 
 
 2-2.38 
 
 .961 
 
 .467 3544 
 
 1033 
 
 84 04 23.57 
 
 21.30 
 
 .912 
 
 .462 1695 
 
 1084 
 
 83 46 34.I-I 
 
 22.36 
 
 .062 
 
 .467 4576 
 
 1032 
 
 84 04 44.86 
 
 21.28 
 
 .913 
 
 .462 2779 
 
 1083 
 
 83 46 56.46 
 
 22.34 
 
 .963 
 
 .467 5607 
 
 1031 
 
 84 05 06. 13 
 
 21.26 
 
 .914 
 
 .462 3861 
 
 1082 
 
 83 47 18.79 
 
 22.32 
 
 .964 
 
 .467 6637 
 
 1029 
 
 84 05 27.37 
 
 21.23 
 
 2.915 
 
 1.462 4942 
 
 1081 
 
 83 47 41.09 
 
 22.30 
 
 2.065 
 
 1.467 7666 
 
 1028 
 
 84 05 48.60 
 
 21.21 
 
 .916 
 
 .462 6023 
 
 1080 
 
 83 48 03.38 
 
 22.27 
 
 .966 
 
 .467 8694 
 
 1027 
 
 84 06 09.80 
 
 21.19 
 
 .917 
 
 .462 7102 
 
 1079 
 
 83 48 25.64 
 
 22.25 
 
 .967 
 
 .467 9721 
 
 1026 
 
 84 06 30.98 
 
 21.17 
 
 .918 
 
 .462 8180 
 
 1078 
 
 83 48 47.88 
 
 22.23 
 
 .968 
 
 .468 0747 
 
 1025 
 
 84 06 52.14 
 
 21.15 
 
 .919 
 
 .462 9257 
 
 1077 
 
 83 49 10.10 
 
 22.21 
 
 .969 
 
 .468 1772 
 
 1024 
 
 84 07 13.29 
 
 21.13 
 
 2.920 
 
 1.463 0334 
 
 1076 
 
 83 49 32.29 
 
 22.18 
 
 2.970 
 
 1.468 2796 
 
 1023 
 
 84 07 34-40 
 
 21. II 
 
 .921 
 
 .463 1409 
 
 1074 
 
 83 49 54-47 
 
 22.16 
 
 .971 
 
 .468 3819 
 
 IO22 
 
 84 07 55.50 
 
 21.00 
 
 .922 
 
 .463 2483 
 
 1073 
 
 83 50 16.62 
 
 22.14 
 
 972 
 
 .468 4841 
 
 1021 
 
 84 08 16.58 
 
 21.07 
 
 923 
 
 .463 3555 
 
 1072 
 
 83 50 38.75 
 
 22.12 
 
 973 
 
 .468 5861 
 
 IO2O 
 
 84 08 37.64 
 
 21.05 
 
 .924 
 
 .463 4627 
 
 1071 
 
 83 5i 00.86 
 
 22. IO 
 
 974 
 
 .468 6881 
 
 1019 
 
 84 08 58.67 
 
 21.02 
 
 2.925 
 
 1.463 5698 
 
 1070 
 
 83 Si 22.04 
 
 22.O7 
 
 2.975 
 
 1.468 7000 
 
 1018 
 
 84 09 19.69 
 
 21. OO 
 
 .926 
 
 .463 6768 
 
 1069 
 
 83 51 45.00 
 
 22.05 
 
 .976 
 
 .468 8918 
 
 1017 
 
 84 09 40.68 
 
 20.08 
 
 .927 
 
 .463 7836 
 
 1068 
 
 83 52 07.05 
 
 22.03 
 
 977 
 
 .468 9935 
 
 1016 
 
 84 10 01.65 
 
 2O.06 
 
 .928 
 
 .463 8904 
 
 1067 
 
 83 52 29.07 
 
 22. OI 
 
 
 .469 0950 
 
 1015 
 
 84 10 22.60 
 
 20.04 
 
 .929 
 
 .463 9970 
 
 1066 
 
 83 52 51.06 
 
 21.99 
 
 979 
 
 .469 1965 
 
 1014 
 
 &4 10 43-53 
 
 20.02 
 
 2.930 
 
 1.464 1036 
 
 1065 
 
 83 53 13.04 
 
 21.97 
 
 2.980 
 
 1.469 2979 
 
 1013 
 
 84 II 04.44 
 
 20.00 
 
 931 
 932 
 
 .464 2100 
 .464 3163 
 
 1064 
 1063 
 
 83 53 34-99 
 83 53 56.93 
 
 21.94 
 21.92 
 
 ;^2 
 
 .469 3992 
 .469 5003 
 
 IOI2 
 IOII 
 
 84 II 25.33 
 
 84 II 46.20 
 
 20.88 
 20.86 
 
 933 
 
 .464 4226 
 
 1062 
 
 83 54 18.84 
 
 21.90 
 
 .983 
 
 .469 6014 
 
 1010 
 
 84 12 07.05 
 
 20.84 
 
 934 
 
 .464 5287 
 
 1061 
 
 83 54 40.73 
 
 21.88 
 
 .984 
 
 .469 7024 
 
 1009 
 
 84 12 27.88 
 
 20.82 
 
 2.935 
 
 1.464 6347 
 
 1060 
 
 83 55 02.59 
 
 21.86 
 
 2.985 
 
 1.469 8033 
 
 1008 
 
 84 12 48.68 
 
 20.80 
 
 .936 
 
 .464 7406 
 
 1059 
 
 83 55 24.44 
 
 21.83 
 
 .986 
 
 .469 9040 
 
 1007 
 
 84 13 09-47 
 
 20.78 
 
 .937 
 
 .464 8464 
 
 1058 
 
 83 55 46.26 
 
 21. 8l 
 
 .987 
 
 .470 0047 
 
 1006 
 
 84 13 30.23 
 
 20.75 
 
 .938 
 
 .464 9521 
 
 1056 
 
 83 56 08.07 
 
 21.79 
 
 .988 
 
 .470 1053 
 
 1005 
 
 84 13 50.98 
 
 20.73 
 
 939 
 
 .465 0577 
 
 1055 
 
 83 56 29.85 
 
 21.77 
 
 .989 
 
 .470 2057 
 
 1004 
 
 84 14 11.70 
 
 20.71 
 
 2.940 
 
 1.465 1632 
 
 1054 
 
 83 56 51.60 
 
 21.75 
 
 2.990 
 
 1.470 3061 
 
 1003 
 
 84 14 32.40 
 
 20.69 
 
 .941 
 
 .465 2686 
 
 1053 
 
 83 57 13.34 
 
 21.73 
 
 .991 
 
 .470 4064 
 
 IOO2 
 
 84 14 53.09 
 
 20.67 
 
 .942 
 
 .465 3739 
 
 1052 
 
 83 57 35.06 
 
 21.70 
 
 .992 
 
 .470 5065 
 
 IOOI 
 
 84 15 13.75 
 
 20.65 
 
 943 
 
 .465 4790 
 
 1051 
 
 83 57 56.75 
 
 21.68 
 
 .993 
 
 .470 6066 
 
 IOOO 
 
 84 15 34-39 
 
 20.63 
 
 .944 
 
 .465 5841 
 
 1050 
 
 83 58 18.42 
 
 21.66 
 
 .994 
 
 .470 7066 
 
 999 
 
 &4 15 55.01 
 
 20.61 
 
 2.045 
 
 1.465 6891 
 
 1049 
 
 83 58 40.07 
 
 21.64 
 
 2.995 
 
 1.470 8065 
 
 998 
 
 84 16 15.61 
 
 20.59 
 
 .946 
 
 .465 7939 
 
 1048 
 
 83 59 01.70 
 
 21.62 
 
 .996 
 
 .470 9062 
 
 997 
 
 84 16 36.19 
 
 20.57 
 
 947 
 
 .465 8987 
 
 1047 
 
 83 59 23.31 
 
 21.60 
 
 
 .471 0059 
 
 996 
 
 84 16 56.75 
 
 20.55 
 
 .948 
 
 .466 0033 
 
 1046 
 
 83 59 44.90 
 
 21.58 
 
 .998 
 
 .471 1055 
 
 995 
 
 84 17 17.29 
 
 20.53 
 
 .949 
 
 .466 1079 
 
 1045 
 
 84 oo 06.46 
 
 21.55 
 
 .999 
 
 .471 2050 
 
 994 
 
 84 17 37.8i 
 
 20.51 
 
 2.950 
 
 1.466 2123 
 
 1044 
 
 84 oo 28.00 
 
 21.53 
 
 3.000 
 
 I.47I 3043 
 
 993 
 
 84 17 58.30 
 
 20.49 
 
 u 
 
 7T 
 
 2 tan 1 (e u ) 
 2 
 
 co sech u 
 
 
 sech u 
 
 u 
 
 
 > sech u 
 
 2 tan~~ J ( u ) 90 
 
 w sech u 
 
 SMITHSONIAN TABLES 
 
 305 
 
The Gudermannian. 
 
 u 
 
 gd u 
 
 F ' 
 
 gd u 
 
 "Fo' 
 
 u 
 
 gd u 
 
 F ' 
 
 gdu 
 
 F ' 
 
 
 
 
 I II 
 
 // 
 
 
 
 
 O / // 
 
 // 
 
 3.00 
 
 I.47I 3043 
 
 9933 
 
 84 17 58.30 
 
 204.88 
 
 3-50 
 
 I.5I04I99 
 
 6034 
 
 86 32 26.47 
 
 124.46 
 
 .01 
 
 .472 2927 
 
 9835 
 
 84 21 22.17 
 
 202.8s 
 
 51 
 
 .511 0203 
 
 5974 
 
 86 34 30.31 
 
 123.22 
 
 .02 
 
 473 2713 
 
 9737 
 
 84 24 44.01 
 
 200.84 
 
 .52 
 
 .511 6147 
 
 5915 
 
 86 36 32.92 
 
 122. OO 
 
 03 
 
 .474 2401 
 
 9641 
 
 84 28 03.86 
 
 198.85 
 
 53 
 
 .512 2033 
 
 5856 
 
 86 38 34-31 
 
 120.79 
 
 .04 
 
 475 1994 
 
 9545 
 
 84 31 21.72 
 
 106.88 
 
 54 
 
 512 7859 
 
 5798 
 
 86 40 34.50 
 
 119-59 
 
 3.05 
 
 1.476 1492 
 
 9451 
 
 84 34 37.63 
 
 194.93 
 
 3-55 
 
 I.5I3 3628 
 
 5740 
 
 86 42 33.49 
 
 118.40 
 
 .06 
 
 .477 0896 
 
 9357 
 
 84 37 51.59 
 
 193-00 
 
 .56 
 
 .513 9340 
 
 5683 
 
 86 44 31.30 
 
 117.22 
 
 .07 
 
 .478 0206 
 
 9264 
 
 84 41 03.64 
 
 IQI.09 
 
 .57 
 
 .514 4995 
 
 5627 
 
 86 46 27.94 
 
 116.06 
 
 .08 
 
 .478 9425 
 
 9173 
 
 84 44 13.78 
 
 189.20 
 
 .58 
 
 .515 0594 
 
 5571 
 
 86 48 23.43 
 
 114.91 
 
 .09 
 
 479 8551 
 
 9082 
 
 84 47 22.04 
 
 187.32 
 
 .59 
 
 .515 6137 
 
 55i6 
 
 86 50 17.76 
 
 113.66 
 
 3.10 
 
 1.480 7588 
 
 8992 
 
 84 50 28.43 
 
 185.47 
 
 3.60 
 
 1.516 1625 
 
 546i 
 
 86 52 10.96 
 
 112.63 
 
 .11 
 
 .481 6535 
 
 9903 
 
 84 53 32.97 
 
 183.63 
 
 .6r 
 
 .516 7058 
 
 5406 
 
 86 54 03.03 
 
 i i i . 52 
 
 .12 
 
 .482 5393 
 
 8814 
 
 84 56 35.69 
 
 181.81 
 
 .62 
 
 .517 2438 
 
 5353 
 
 86 55 53-99 
 
 110.41 
 
 13 
 
 .483 4164 
 
 8727 
 
 84 59 36.59 
 
 180.00 
 
 .63 
 
 .517 7764 
 
 5300 
 
 86 57 43.85 
 
 109.31 
 
 , .14 
 
 .484 2847 
 
 8640 
 
 85 02 35.70 
 
 178.221 
 
 .64 
 
 .518 3037 
 
 5247 
 
 86 59 32.62 
 
 108.22 
 
 3-15 
 
 1.485 1445 
 
 8555 
 
 85 05 33-04 
 
 176.45 
 
 3.65 
 
 1.518 8258 
 
 5195 
 
 87 01 20.30 
 
 107.15 
 
 .16 
 
 .485 9957 
 
 8470 
 
 85 08 28.61 
 
 174.70 
 
 .66 
 
 .519 3427 
 
 5143 
 
 87 03 06.92 I 106.08 
 
 .17 
 
 .486 8385 
 
 8386 
 
 85 ii 22.45 
 
 172.97 
 
 .67 
 
 519 8544 
 
 5092 
 
 87 04 52.47 105.03 
 
 .18 
 
 .487 6729 
 
 8303 
 
 85 14 14.56 
 
 171.26 
 
 .68 
 
 .520 3611 
 
 5041 
 
 87 06 36.98 
 
 103.99 
 
 .19 
 
 ..488 4991 
 
 8221 
 
 85 17 04.97 
 
 169.56 
 
 .69 
 
 .520 8627 
 
 4991 
 
 87 08 20.45 
 
 102.95 
 
 3.20 
 
 1.489 3170 
 
 8i39 
 
 85 19 53.69 
 
 167.88 
 
 3.70 
 
 I.52I 3593 
 
 4942 
 
 87 10 02.89 
 
 101.93 
 
 .2*1 
 
 .490 1269 
 
 8058 
 
 85 22 40.73 
 
 166.21 
 
 71 
 
 .521 8511 
 
 4893 
 
 87 u 44.31 
 
 100.92 
 
 .22 
 
 .490 9287 
 
 7978 
 
 85 25 26.12 
 
 164.56 
 
 .72 
 
 .522 3379 
 
 4844 
 
 87 13 24.73 
 
 99.91 
 
 23 
 
 .491 7226 
 
 7899 
 
 85 28 09.86 
 
 162.93 
 
 73 
 
 .522 8i99 
 
 4796 
 
 87 IS 04.14 
 
 98.92 
 
 .24 
 
 .492 5085 
 
 7821 
 
 85 30 51.99 
 
 161.32 
 
 74 
 
 .523 2971 
 
 4748 
 
 87 16 42.57 
 
 97-94 
 
 3.25 
 
 1.493 2867 
 
 7743 
 
 85 33 32.50 
 
 I59.7I 
 
 3-75 
 
 1.523 7695 
 
 4701 
 
 87 l8 20.02 
 
 96.96 
 
 .26 
 
 .494 0572 
 
 7667 
 
 85 36 11.42 
 
 158.13 
 
 .76 
 
 .524 2373 
 
 4654 
 
 87 19 56.50 
 
 96.00 
 
 .27 
 
 .494 8200 
 
 7590 
 
 85 38 48.77 
 
 156.56 
 
 .77 
 
 .524 7004 
 
 4608 
 
 87 21 32.03 
 
 95-05 
 
 .28 
 
 495 5753 
 
 7515 
 
 85 41 24.55 
 
 155.01 
 
 .78 
 
 .525 1589 
 
 4562 
 
 87 23 O6.6b 
 
 04.10 
 
 .29 
 
 .496 3231 
 
 7441 
 
 85 43 58.79 
 
 153.47 
 
 79 
 
 .525 6128 
 
 4517 
 
 87 24 40.23 
 
 93-17 
 
 3-30 
 
 1.497 0634 
 
 7367 
 
 85 46 31.50 
 
 151.95 
 
 3.8o 
 
 1.526 0622 
 
 4472 
 
 87 26 12.93 
 
 02.24 
 
 31 
 
 .497 7964 
 
 7294 
 
 85 49 02.69 
 
 150.44 
 
 .81 
 
 .526 507^ 
 
 4428 
 
 87 27 44.71 
 
 91.32 
 
 32 
 
 .498 5221 
 
 7221 
 
 85 Si 32.38 
 
 148.95 
 
 .82 
 
 .526 9478 
 
 4384 
 
 87 29 15.58 
 
 00.42 
 
 33 
 
 .499 2407 
 
 7150 
 
 85 54 00.59 
 
 147.47 
 
 .83 
 
 .527 3839 
 
 4340 
 
 87 30 45.55 
 
 89.52 
 
 34 
 
 .499 9521 
 
 7079 
 
 85 56 27.32 
 
 146.00 
 
 .84 
 
 .527 8157 
 
 4297 
 
 87 32 14.62 
 
 88.63 
 
 3-35 
 
 1.500 6564 
 
 7008 
 
 85 58 52.60 
 
 144.56 
 
 3.8S 
 
 1.528 2433 
 
 4254 
 
 87 33 42.80 
 
 87.75 
 
 .36 
 
 501 3537 
 
 6939 
 
 86 01 16.44 
 
 143.12 
 
 .86 
 
 .528 6666 
 
 4212 
 
 87 35 10. II 
 
 86.87 
 
 37 
 
 .502 0441 
 
 6870 
 
 86 03 38.84 
 
 141.70 
 
 .87 
 
 .529 0856 
 
 4170 
 
 87 36 36.55 
 
 86.01 
 
 .38 
 
 .502 7277 
 
 6802 
 
 86 05 59.84 
 
 140.29 
 
 .88 
 
 .529 5005 
 
 4128 
 
 87 38 02.13 
 
 85.15 
 
 39 
 
 .503 4045 
 
 6734 
 
 86 08 19.44 
 
 138.90 
 
 .89 
 
 529 9113 
 
 4087 
 
 87 39 26.86 
 
 84.31 
 
 3-40 
 .41 
 
 1.504 0746 
 .504 7380 
 
 6667 
 6601 
 
 86 10 37.65 
 86 12 54.48 
 
 '37.52 
 136.16 
 
 3.90 
 .91 
 
 1.530 3180 
 .5307207 
 
 4047 
 4007 
 
 87 40 50.75 
 87 42 13.81 
 
 83.47 
 82.64 
 
 .42 
 
 505 3948 
 
 6536 
 
 86 15 09.96 
 
 134.80 
 
 .92 
 
 531 H93 
 
 3967 
 
 87 43 36.03 81.82 
 
 43 
 
 .506 0451 
 
 6471 
 
 86 17 24.10 
 
 133.47 
 
 93 
 
 .531 5140 
 
 3927 
 
 87 44 57-45 
 
 81.00 
 
 .44 
 
 .506 6889 
 
 6406 
 
 86 19 36.90 
 
 132.14 
 
 .94 
 
 .531 9048 
 
 3888 
 
 87 46 18.05 
 
 80.20 
 
 3-45 
 
 1.507 3264 
 
 6343 
 
 86 21 48.38 
 
 130.83 
 
 3-95 
 
 1.532 2917 
 
 3850 
 
 87 47 37.85 
 
 79-40 
 
 .46 
 
 .507 9575 
 
 6280 
 
 86 23 58.56 
 
 129.53 
 
 .96 
 
 .532 6747 
 
 3811 
 
 87 48 56.85 
 
 78.61 
 
 47 
 
 .508 5823 
 
 6217 
 
 8' 2 r ) 07.44 
 
 128.24 
 
 .97 
 
 533 0539 
 
 3773 
 
 87 50 15-07 
 
 77.83 
 
 .48 
 
 .509 2010 
 
 6156 
 
 86 28 15.05 
 
 126.97 
 
 .98 
 
 533 4294 
 
 3736 
 
 87 51 32.52 
 
 77.o6 
 
 .49 
 
 .509 8135 
 
 6095 
 
 86 30 21.39 
 
 125.71 
 
 99 
 
 .533 8011 
 
 3699 
 
 87 52 49.19 
 
 76.29 
 
 3.50 
 
 1.5104109 
 
 6034 
 
 86 32 26.47 
 
 124.46 
 
 4-OO 
 
 1.534 1691 
 
 3662 
 
 87 5405.10 
 
 75-53 
 
 u 
 
 2 tan-He")-^ 
 
 < sech u 
 
 2tan- 1 (eu)-90 |Wfcchu 
 
 u 
 
 2tan-'( u )-| 
 
 oosechu 
 
 2tan~ 1 (e)-90 
 
 sech u 
 
 SMITHSONIAN TABLES 
 
 306 
 
The Gudermannian. 
 
 u 
 
 gd u 
 
 ^ 
 
 gdu 
 
 
 
 
 u 
 
 gdu 
 
 * 
 
 gd u 
 
 Fo' 
 
 
 
 
 / // 
 
 
 
 
 
 
 / // 
 
 
 
 4.00 
 
 1.534 1691 
 
 3662 
 
 87 54 05.10 
 
 75.53 
 
 4-50 
 
 1.548 5792 
 
 2222 
 
 88 43 37-40 
 
 45.82 
 
 .01 
 
 534 5335 
 
 3626 
 
 87 55 20.26 
 
 74.78 
 
 51 
 
 .548 8003 
 
 2199 
 
 88 44 22.99 
 
 45.37 
 
 .02 
 
 534 8943 
 
 3590 
 
 87 56 34.67 
 
 74.04 
 
 .52 
 
 .549 0191 
 
 2178 
 
 88 45 08.13 
 
 44.92 
 
 03 
 
 .535 2514 
 
 3554 
 
 87 57 48.33 
 
 73.30 
 
 53 
 
 549 2358 
 
 2156 
 
 88 45 52.82 
 
 44.47 
 
 .04 
 
 535 6050 
 
 3Sl8 
 
 87 59 01.27 
 
 72.57 
 
 .54 
 
 549 4503 
 
 2134 
 
 88 46 37-07 
 
 44.03 
 
 4.05 
 
 .05 
 
 1.535 9551 
 .536 3017 
 
 3483 
 3449 
 
 88 oo 13.48 
 88 01 24.97 
 
 71.85 
 71.14 
 
 4-55 
 .56 
 
 1.549 6627 
 .549 8730 
 
 2113 
 2092 
 
 88 47 20.88 
 88 48 04.25 
 
 43.59 
 43.15 
 
 .07 
 
 .536 6449 
 
 3415 
 
 88 02 35.76 
 
 70.43 
 
 57 
 
 .550 0811 
 
 2O7I 
 
 88 48 47.19 
 
 42.73 
 
 .08 
 
 .536 9846 
 
 338i 
 
 88 03 45.83 
 
 69.73 
 
 .58 
 
 .550 2873 
 
 2051 
 
 88 49 29.70 
 
 42.30 
 
 .09 
 
 537 3210 
 
 3347 
 
 88 04 55.22 
 
 69.03 
 
 .59 
 
 550 4913 
 
 2030 
 
 88 50 11.79 
 
 41.88 
 
 4.10 
 
 1.537 6540 
 
 3314 
 
 88 06 03.91 
 
 68.35 
 
 4.60 
 
 1.550 6933 
 
 2O IO 
 
 88 50 53.46 
 
 41.46 
 
 .11 
 
 .537 9837 
 
 3281 
 
 88 07 11.91 
 
 67-67 
 
 .61 
 
 550 8933 
 
 1990 
 
 88 51 34.72 
 
 41.05 
 
 .12 
 
 .538 3102' 
 
 3248 
 
 88 08 19.25 
 
 67.00 
 
 .62 
 
 .551 0914 
 
 1970 
 
 88 52 15.56 
 
 40.64 
 
 13 
 
 .538 6333 
 
 3216 
 
 88 09 25.91 
 
 66.33 
 
 .63 
 
 .551 2874 
 
 1951 
 
 88 52 56.00 
 
 40.24 
 
 .14 
 
 .538 9533 
 
 3184 
 
 88 10 31.91 
 
 65.67 
 
 .64 
 
 .551 4815 
 
 1931 
 
 88 53 36.04 
 
 39.84 
 
 4.15 
 
 1.539 2701 
 
 3152 
 
 88 ii 37.25 
 
 65.02 
 
 4-65 
 
 i.55i 6737 
 
 1912 
 
 88 54 15.68 
 
 39.44 
 
 .16 
 
 539 5837 
 
 3121 
 
 88 12 41.94 
 
 64.37 
 
 .66 
 
 .551 8640 
 
 1893 
 
 88 54 54.92 
 
 39.05 
 
 17 
 
 .539 8943 
 
 3090 
 
 88 13 45.99 
 
 63.73 
 
 .67 
 
 .552 0523 
 
 1874 
 
 88 55 33.77 
 
 38.66 
 
 .18 
 
 .540 2017 
 
 3059 
 
 88 14 49.40 
 
 63.10 
 
 .68 
 
 .552 2388 
 
 1856 
 
 88 56 12.24 
 
 38.28 
 
 .19 
 
 .540 5061 
 
 3029 
 
 88 15 52.19 
 
 62.47 
 
 .69 
 
 552 4235 
 
 1837 
 
 88 56 50.33 
 
 37.89 
 
 4.20 
 
 1.540 8074 
 
 2998 
 
 88 16 54-34 
 
 61.85 
 
 4.70 
 
 1.552 6063 
 
 l8l9 
 
 88 57 28.03 
 
 37.52 
 
 .21 
 
 .541 1058 
 
 2969 
 
 88 17 55-88 
 
 61.23 
 
 71 
 
 552 7873 
 
 1801 
 
 88 58 05.36 
 
 37.14 
 
 .22 
 
 .541 4012 
 
 2939 
 
 88 18 56.81 
 
 60.62 
 
 72 
 
 .552 9664 
 
 1783 
 
 88 58 42.32 
 
 36.77 
 
 23 
 
 .541 6936 
 
 2910 
 
 88 19 57.13 
 
 60.02 
 
 .73 
 
 .'553 1438 
 
 1765 
 
 88 59 18.91 
 
 36.41 
 
 .24 
 
 .541 9831 
 
 2881 
 
 88 20 56.85 
 
 59.42 
 
 74 
 
 553 3195 
 
 1748 
 
 88 59 55.14 
 
 36.05 
 
 4.25 
 
 1.542 2698 
 
 2852 
 
 88 21 55.98' 
 
 'S8.8 3 
 
 4-75 
 
 1.553 4934 
 
 1730 
 
 89 oo 31.01 
 
 35.69 
 
 .26 
 
 542 5536 
 
 2824 
 
 88 22 54.52 
 
 58.2-5 
 
 .76 
 
 553 6655 
 
 1713 
 
 89 01 06.52 
 
 35-33 
 
 .27 
 
 .542 8346 
 
 2796 
 
 88 23 52.48 
 
 57.67 
 
 .77 
 
 553 8360 
 
 1696 
 
 89 oi 41.68 
 
 34.98 
 
 .28 
 
 .543 1128 
 
 2768 
 
 88 24 49.86 
 
 57-09 
 
 .78 
 
 .554 0047 
 
 1679 
 
 89 02 16.48 
 
 34.63 
 
 .29 
 
 .543 3882 
 
 2741 
 
 88 25 46.67 
 
 56.53 
 
 .79 
 
 554 1718 
 
 1662 
 
 89 02 50.94 
 
 34.29 
 
 4.30 
 
 1.543 6609 
 
 2713 
 
 88 26 42.91 
 
 55.96 
 
 4.80 
 
 1.554 3372 
 
 1646 
 
 89 03 25.06 
 
 33-95 
 
 .311 
 
 543 9308 
 
 2686 
 
 88 27 38.60 
 
 55.41 
 
 .81 
 
 .554 5010 
 
 1630 
 
 89 03 58.84 
 
 33.6i 
 
 .32 
 
 .544 1981 
 
 2660 
 
 80 28 33-73 
 
 54.86 
 
 .82 
 
 554 6631 
 
 1613 
 
 89 04 32.28 
 
 33.28 
 
 .33 
 
 .544 4628 
 
 2633 
 
 88 29 28.31 
 
 54.31 
 
 .83 
 
 554 8236 
 
 1597 
 
 89 05 05.39 
 
 32-94 
 
 .34 
 
 .544 7247 
 
 2607 
 
 88 30 22.35 
 
 53-77 
 
 .84 
 
 554 9825 
 
 1581 
 
 8905 38.17 
 
 32.62 
 
 4-35 
 
 1.544 9841 
 
 2581 
 
 88 31 15.85 
 
 53.24 
 
 4.85 
 
 1-555 1399 
 
 1566 
 
 89 06 10.63 
 
 32.29 
 
 .36 
 
 .545 2409 
 
 2555 
 
 88 32 08.82 
 
 52.71 
 
 .86 
 
 555 2957 
 
 1550 
 
 89 06 42.76 
 
 31.97 
 
 37 
 
 545 4952' 
 
 2530 
 
 88 33 01.27 
 
 52.18 
 
 .87 
 
 
 1535 
 
 89 07 14.57 
 
 31.65 
 
 .38 
 
 545 7469 
 
 2505 
 
 88 33 53.19 
 
 51.66 
 
 .88 
 
 .555 6026 
 
 1519 
 
 89 07 46.07 
 
 3L34 
 
 .39 
 
 545 996i 
 
 2480 
 
 88 34 44-59 
 
 51.15 
 
 .89 
 
 555 7538 
 
 1504 
 
 89 08 17.25 
 
 3L03 
 
 4.40 
 
 1.546 2429 
 
 2455 
 
 88 35 35-49 
 
 50.64 
 
 4.90 
 
 1.555 9034 
 
 1489 
 
 89 08 48. 12 
 
 30.72 
 
 .41 
 
 .546 4872 
 
 2431 
 
 88 36 25.88 
 
 50.14 
 
 .91 
 
 .556 0516 
 
 1474 
 
 89 09 18.69 
 
 30.41 
 
 .42 
 
 .546 7290 
 
 2407 
 
 88 37 i'S-76 
 
 49-64 
 
 .92 
 
 .556 1983 
 
 1460 
 
 89 09 48.95 
 
 30.11 
 
 .43 
 
 .546 9685 
 
 2383 
 
 88 38 05.15 
 
 49.14 
 
 93 
 
 .556 3436 
 
 1445 
 
 89 10 18.91 
 
 29.81 
 
 44 
 
 547 2055 
 
 2359 
 
 88 38 54.05 
 
 48.65 
 
 .94 
 
 .556 4874 
 
 1431 
 
 89 10 48.57 
 
 29.51 
 
 4-45 
 
 1.547 4403 
 
 2335 
 
 88 39 42.46 
 
 48.17 
 
 4-95 
 
 1.556 6297 
 
 1417 
 
 89 II 17.93 
 
 29.22 
 
 .46 
 
 .547 6726 
 
 2312 
 
 88 40 30.40 
 
 47.69 
 
 .96 
 
 .556 7707 
 
 1403 
 
 89 II 47.01 
 
 28.93 
 
 47 
 
 547 027 
 
 2289 
 
 88 41 17.85 
 
 47.22 
 
 97 
 
 556 9103 
 
 1389 
 
 89 12 15.79 
 
 28.64 
 
 .48 
 
 .548 1305 
 
 2266 
 
 88 42 04.83 
 
 46.75 
 
 .98 
 
 .557 0484 
 
 1375 
 
 89 12 44.29 
 
 28.36 
 
 .49 
 
 .548 356o 
 
 2244 
 
 88 42 51.35 
 
 46.28 
 
 99 
 
 557 1852 
 
 1361 
 
 89 13 12.51 
 
 28.07 
 
 4.50 
 
 1.548 5792 
 
 2222 
 
 88 43 37.40 
 
 45.82 
 
 5.00 
 
 1.557 3206 
 
 1348 
 
 89 13 40.44 
 
 27.79 
 
 U 
 
 2tan-Keu)-? 
 
 <o sech u 
 
 *rwr 
 
 co sech u 
 
 u 
 
 2 tan-He")-^ 
 
 co sech u 
 
 2tan- 1 (e)-90 
 
 <o sech u 
 
 SMITHSONIAN TABLES 
 
 307 
 
The Gudermannian. 
 
 H 
 
 gdu 
 
 Fo' 
 
 gd u 
 
 o>Fo' 
 
 u 
 
 gd u 
 
 -FO' 
 
 gdu 
 
 F ' 
 
 
 
 
 o / // 
 
 M 
 
 
 
 
 O / // 
 
 
 S.oo 
 
 1.557 3206 
 
 1348 
 
 89 13 40.44 
 
 27.79 
 
 5.50 
 
 1.562 6228 
 
 817 
 
 89 31 54-10 
 
 16^86 
 
 .01 
 
 557 4547 
 
 1334 
 
 89 14 08. io 
 
 27.52 
 
 SI 
 
 .562 7042 
 
 809 
 
 89 32 10.87 
 
 16.69 
 
 .02 
 
 557 5875 
 
 1321 
 
 89 U 35.48 
 
 27.24 
 
 52 
 
 .562 7847 
 
 801 
 
 89 32 27.48 
 
 16.53 
 
 03 
 
 .557 7189 
 
 1308 
 
 89 15 02.58 
 
 26.97 
 
 53 
 
 .562 8644 
 
 793 
 
 89 32 43.92 
 
 16.36 
 
 .04 
 
 557 8490 
 
 1295 
 
 89 15 29.42 
 
 26.71 
 
 54 
 
 .562 9433 
 
 785 
 
 89 33 00.20 
 
 16.20 
 
 5.05 
 
 1.557 9778 
 
 1282 
 
 89 15 56.00 
 
 26.44 
 
 5-55 
 
 1.563 0215 
 
 777 
 
 89 33 16.32 
 
 16.04 
 
 .06 
 
 .558 1054 
 
 1269 
 
 89 16 22.30 
 
 26.18 
 
 .56 
 
 .563 0988 
 
 770 
 
 89 33 32.27 
 
 15.88 
 
 .07 
 
 .558 2317 
 
 1256 
 
 89 16 48.35 
 
 25.92 
 
 57 
 
 .563 1754 
 
 762 
 
 89 33 48.07 
 
 15.72 
 
 .08 
 .09 
 
 .558 3567 
 .558 4804 
 
 1244 
 1232 
 
 89 17 14.14 
 89 17 39.67 
 
 25.66 
 25.40 
 
 .58 
 .59 
 
 .563 2512 
 .563 3263 
 
 755 
 747 
 
 89 34 03.71 
 89 34 19.20 
 
 15.56 
 15.41 
 
 S.io 
 
 1.558 6030 
 
 1219 
 
 89 18 04.94 
 
 25.15 
 
 5.6o 
 
 1.563 4006 
 
 740 
 
 89 34 34-53 
 
 15.25 
 
 .11 
 
 .558 7243 
 
 1207 
 
 89 18 29.97 
 
 24.90 
 
 .61 
 
 .563 4742 
 
 732' 
 
 89 34 49.71 
 
 15.10 
 
 .12 
 
 .558 8444 
 
 H95 
 
 89 18 54-74 
 
 24.65 
 
 .62 
 
 .563 5471 
 
 725 
 
 89 35 04-73 
 
 14.95 
 
 .13 
 
 .558 9633 
 
 Il83 
 
 89 19 19.27 
 
 24.41 
 
 .63 
 
 .563 6192- 
 
 7i8 
 
 89 35 I9.6i 
 
 14.80 
 
 .14 
 
 .559 0811 
 
 1172 
 
 89 19 43.56 
 
 24.16 
 
 .64 
 
 .563 6906 
 
 711 
 
 89 35 34-34 
 
 14.66 
 
 5-15 
 
 1.559 1976 
 
 1160 
 
 89 20 07.60 
 
 23.92 
 
 5.65 
 
 1.563 7613 
 
 703 
 
 89 35 48.93 
 
 14.51 
 
 .16 
 
 559 3131 
 
 1148 
 
 89 2O 3I.4O 
 
 23.69 
 
 .65 
 
 563 8313 
 
 697 
 
 89 36 03.36 
 
 14.37 
 
 17 
 
 559 4273 
 
 1 137 
 
 89 20 54-97 
 
 23.45 
 
 .67 
 
 .563 9006 
 
 690 
 
 89 36 17.66 
 
 14.22 
 
 .18 .559 5404 
 
 1126 
 
 89 21 I8.3I 
 
 23.22 
 
 .68 
 
 .563' 9692 
 
 683 
 
 89 36 31-81 
 
 14.08 
 
 .19 
 
 .559 6524 
 
 III4 
 
 89 21 41.41 
 
 22.99 
 
 .69 
 
 .564 0372 
 
 676 
 
 89 36 45. &2 
 
 13.94 
 
 5-20 
 
 1.559 7633 
 
 1103 
 
 89 22 04.28 
 
 22.76 
 
 5.70 
 
 1.564 1044 
 
 669 
 
 89 36 59-70 
 
 13.80 
 
 .21 
 
 559 8731 
 
 1092 
 
 89 22 26.92 
 
 22.53 
 
 71 
 
 .564 1710 
 
 663 
 
 89 37 13.43 
 
 13.67 
 
 .22 
 
 559 98i8 
 
 1081 
 
 89 22 49.34 
 
 22.31 
 
 .72 
 
 .564 2369 
 
 656 
 
 89 37 27.03 
 
 13.53 
 
 .23 
 
 .560 0894 
 
 1071 
 
 89 23 H.53 
 
 22.08 
 
 73 
 
 .564 3022 
 
 649 
 
 89 37 40.49 
 
 13.40 
 
 .24 
 
 .560 1959 
 
 1060 
 
 89 23 33.51 
 
 21.86 
 
 .74 
 
 .564 3668 
 
 643 
 
 89 37 53.82 
 
 13.26 
 
 5-25 
 
 1.560 3014 
 
 1049 
 
 89 23 55.26 
 
 21.65 
 
 5-75 
 
 1.564 4308 
 
 637 
 
 89 38 07.01 
 
 13.13 
 
 .26 
 
 .560 4058 
 
 1039 
 
 89 24 16.80 
 
 21.43 
 
 .76 
 
 .564 4941 
 
 630 
 
 89 38 20.08 
 
 13.00 
 
 .27 
 
 .560 5092 
 
 1029 
 
 89 24 38.13 
 
 21.22 
 
 77 
 
 .564 5568 
 
 624 
 
 89 38 33-01 
 
 12.87 
 
 .28 
 
 .560 6116 
 
 1018 
 
 89 24 59.24 
 
 21. OI 
 
 .78 
 
 .564 6189 
 
 618 
 
 89 38 45-82 
 
 12.74 
 
 .29 
 
 .560 7129 
 
 1008 
 
 89 25 2O.I4 
 
 20.80 
 
 79 
 
 .564 6804 
 
 612 
 
 89 38 58.50 
 
 12. 6l 
 
 5-30 
 
 1.560 8132 
 
 998 
 
 89 25 40.84 
 
 20.59 
 
 5.8o 
 
 1.564 7412 
 
 606 
 
 89 39 11.05 
 
 12.49 
 
 .31 
 
 .560 9126 
 
 988 
 
 89 26 OI.33 
 
 20.39 
 
 .81 
 
 .564 8015 
 
 599 
 
 89 39 23.48 
 
 12.37 
 
 32 
 
 .561 0109 
 
 979 
 
 89 26 21. 61 
 
 20. l8 
 
 .82 
 
 .564 8611 
 
 504 
 
 89 39 35.78 
 
 12.24 
 
 33 
 
 .561 1083 
 
 969 
 
 89 26 41.69 
 
 19.98 
 
 .83 
 
 .564 9202 
 
 588 
 
 89 39 47.96 
 
 12.12 
 
 34 
 
 .561 2047 
 
 959 
 
 89 27 01.58 
 
 19.78 
 
 .84 
 
 .564 9787 
 
 582 
 
 89 40 00.02 
 
 12.00 
 
 5-35 
 
 1.561 3001 
 
 950 
 
 89 27 21.26 
 
 19.59 
 
 5.85 
 
 1.565 0365 
 
 576 
 
 89 40 11.96 
 
 11.88 
 
 .36 
 
 .561 3946 
 
 940 
 
 89 27 40.75 
 
 19.39 
 
 .86 
 
 .565 0939 
 
 570 
 
 89 40 23.78 
 
 11.76 
 
 37 
 
 .561 4881 
 
 931 
 
 89 28 00.05 
 
 19.20 
 
 .87 
 
 .565 1506 
 
 565 
 
 89 40 35.48 
 
 11.65 
 
 .38 
 
 .561 5807 
 
 922 
 
 89 28 19.15 
 
 19.01 
 
 .88 
 
 .565 2068 
 
 559 
 
 89 40 47.07 
 
 "S3 
 
 39 
 
 .561 6724 
 
 912 
 
 89 28 38.06 
 
 18.82 
 
 .89 
 
 .565 2624 
 
 553 
 
 89 40 58.54 
 
 LI. 41 
 
 
 
 
 
 
 
 
 i 
 
 
 
 5.40 
 
 1.561 7632 
 
 903 
 
 89 28 56.79 
 
 18.63 
 
 S.oo 
 
 1.565 3175 
 
 548 
 
 89 41 09.90 
 
 11.30 
 
 .41 
 
 .561 8531 
 
 894 
 
 89 29 15.33 
 
 18.45 
 
 .91 
 
 .565 3720 
 
 542 
 
 89 41 21.15 
 
 11.19 
 
 .42 
 
 .561 9421 
 
 885 
 
 89 29 33.68 
 
 18.26 
 
 .92 
 
 .565 4259 
 
 537 
 
 89 41 32.28 
 
 II.08 
 
 43 
 
 .562 0302 
 
 877 
 
 89 29 31.85 
 
 18.08 
 
 93 
 
 .565 4794 
 
 532 
 
 89 41 43.30 
 
 10.97 
 
 .44 
 
 .562 1174 
 
 868 
 
 89 30 09.85 
 
 17.90 
 
 94 
 
 .565 5323 
 
 526 
 
 89 41 54-21 
 
 10.86 
 
 5-45 
 
 1.562 2038 
 
 859 
 
 89 30 27.66 
 
 17.72 
 
 5-95 
 
 1.565 5847 
 
 521 
 
 89 42 05.02 
 
 10.75 
 
 .46 
 
 .562 2893 
 
 851 
 
 89 30 45-29 
 
 17.55 
 
 .96 
 
 .565 6365 
 
 5i6 
 
 89 42 15.71 
 
 10.64 
 
 47 
 
 562 3739 
 
 842 
 
 89 31 02.75 
 
 17.37 
 
 .97 
 
 .565 6879 
 
 511 
 
 89 42 26.30 
 
 10.54 
 
 .48 
 
 .562 4577 
 
 834 
 
 89 31 20.04 
 
 17.20 
 
 .98 
 
 .565 7387 
 
 506 
 
 89 42 36.79 
 
 10.43 
 
 49 
 
 .562 5407 
 
 826 
 
 89 31 37.15 
 
 17-03 
 
 .99 
 
 .565 7890 
 
 Soi 
 
 89 42 47.17 
 
 10.33 
 
 5.50 
 
 1.562 6228 
 
 817 
 
 8931 54-10 
 
 16.86 
 
 6.00 
 
 1.565 8388 
 
 496 
 
 89 42 57-44 
 
 10.23 
 
 u 
 
 2tan-Ke)- 
 
 wsechu 
 
 2tan~ 1 (e)-90 
 
 > sech u 
 
 u 
 
 2 tan-Ken) 
 
 o>sechu 
 
 2tan~ 1 (e")-90 
 
 w sech u 
 
 SMITHSONIAN TABLES 
 
 308 
 
TABLE VII 
 
 THE ANMUDERMANNIAN 
 
 m expressed in minutes in terms of the Gudermannian, 
 
 gd u expressed in degrees and minutes. 
 
 i minute = o.ooo 2908 8821 radians, 
 
 o.ooo 2908 8821 m = log e tan f-L^-J- gd u) = u radians. 
 In this table the second decimal place is sometimes erroneous by a unit. 
 
 309 
 
The Anti-Gudermannian. 
 
 gdu 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 gdu 
 
 0' 
 
 o'.oo 
 
 60.00 
 
 120.02 
 
 180.08 
 
 240. ig 
 
 300.38 
 
 360.66 
 
 421.05 
 
 48i.57 
 
 542.23 
 
 603.07 
 
 0' 
 
 I 
 
 1. 00 
 
 61.00 
 
 121. 02 
 
 181.08 
 
 241.20 
 
 301.38 
 
 361.66 
 
 422.06 
 
 482.58 
 
 543.25 
 
 604.08 
 
 I 
 
 2 
 
 2.OO 
 
 62.00 
 
 I22.O3 
 
 182.08 
 
 242. 2O 
 
 302.39 
 
 362.67 
 
 423.06 
 
 483.59 
 
 544.26 
 
 605.10 
 
 2 
 
 3 
 
 3.00 
 
 63.00 
 
 123.03 
 
 183.09 
 
 243.20 
 
 303.39 
 
 363.67 
 
 424.07 
 
 484.60 
 
 545-217 
 
 606.12 
 
 3 
 
 4 
 
 4.00 
 
 64.00 
 
 124.03 
 
 184.09 
 
 244.20 
 
 304.40 
 
 364.68 
 
 425.08 
 
 485-61 
 
 546.28 
 
 607.13 
 
 4 
 
 5 
 
 5.00 
 
 65.00 
 
 125.03 
 
 185.09 
 
 245.31 
 
 3P5.40 
 
 365.69 
 
 426.09 
 
 486.62 
 
 547-30 
 
 608.15 
 
 5 
 
 6 
 
 6.00 
 
 66.00 
 
 I26.O3 
 
 186.09 
 
 246.21 
 
 306.40 
 
 366.69 
 
 427.09 
 
 487.63 
 
 548.31 
 
 609.16 
 
 6 
 
 7 
 
 7.00 
 
 67.00 
 
 127.03 
 
 187.09 
 
 247.21 
 
 307.41 
 
 367.70 
 
 428.10 
 
 488.64 
 
 549-32 
 
 610. 18 
 
 7 
 
 8 
 
 8.00 
 
 68.00 
 
 128.03 
 
 188.09 
 
 248.21 
 
 308.41 
 
 368.70 
 
 429.11 
 
 489.65 
 
 550.34 
 
 61 1 . 19 
 
 8 
 
 9 
 
 9.00 
 
 69.00 
 
 129.03 
 
 189.09 
 
 249-22' 
 
 309-42 
 
 369.71 
 
 430.12 
 
 490.66 
 
 55i. 36 
 
 612.21 
 
 9 
 
 IO 
 
 10. OO 
 
 70.00 
 
 130.03 
 
 190.10 
 
 250.212 
 
 310.42 
 
 370.72 
 
 43LI3 
 
 491.67 
 
 552.36 
 
 613.23 
 
 IO 
 
 ii 
 
 II. OO 
 
 71.00 
 
 I3L03 
 
 191.10 
 
 251.22 
 
 3H.42 
 
 371.72 
 
 432.13 
 
 492.68 
 
 553 -37 
 
 614.24 
 
 ii 
 
 12 
 
 12. OO 
 
 72.00 
 
 132.03 
 
 192.10 
 
 252.23 
 
 312.43 
 
 372.73 
 
 43-3.14 
 
 493.69 
 
 554.39 
 
 615.26 
 
 12 
 
 13' 
 
 IS. oo 
 
 73-00 
 
 IQG.03 
 
 I93.IO 
 
 253.23 
 
 313.43 
 
 373-74 
 
 434.15 
 
 494.70 
 
 555-40 
 
 616.27 
 
 13 
 
 14 
 
 14.00 
 
 74.01 
 
 1314. 03' 
 
 194.10 
 
 254-23 
 
 314.44 
 
 374-74 
 
 435.i6 
 
 495.71 
 
 356.41 
 
 617.29 
 
 U 
 
 IS 
 
 15.00 
 
 75.01 
 
 135.03 
 
 195.10 
 
 255.23 
 
 315.44 
 
 375-75 
 
 436.17 
 
 496.72 
 
 557-43 
 
 618.31 
 
 15 
 
 16 
 
 16.00 
 
 76.01 
 
 136.03 
 
 196.11 
 
 256.24 
 
 316.46 
 
 076.75 
 
 437.17 
 
 497-73 
 
 558.44 
 
 619.32 
 
 16 
 
 17 
 
 I/. OO 
 
 77.01 
 
 137-04 
 
 197.11 
 
 257.24 
 
 317-45 
 
 377.76 
 
 438. 18 
 
 498.74 
 
 559-45 
 
 620.34 
 
 17 
 
 18 
 
 18.00 
 
 78.01 
 
 138.04 
 
 198.11 
 
 258.24 
 
 318.45 
 
 378.76 
 
 439.19 
 
 499.75 
 
 560.47 
 
 621.36 
 
 18 
 
 19 
 
 19.00 
 
 79.01 
 
 139.04 
 
 199.11 
 
 259.25 
 
 319.46 
 
 379-77 
 
 440.20 
 
 500.76 
 
 561.48 
 
 622.37 
 
 19 
 
 20 
 
 20.00 
 
 So. 01 
 
 140.04 
 
 200. ii 
 
 200.25 
 
 320.46 
 
 380.78 
 
 441.21 
 
 501.77 
 
 562.49 
 
 623.39 
 
 20 
 
 21 
 
 21. OO 
 
 81.01 
 
 141.04 
 
 2OI.II 
 
 261.25 
 
 321.47 
 
 381.78 
 
 442.21 
 
 502.78 
 
 563.51 
 
 624.40 
 
 21 
 
 22 
 
 22'. OO 
 
 82.0)1 
 
 1412.04 
 
 2O2.I2 
 
 262.25 
 
 322.47 
 
 382.79 
 
 443-22 
 
 503-79 
 
 564.52 
 
 625.42 
 
 22 
 
 23 
 
 23.00 
 
 83.01 
 
 143-04 
 
 203-12 
 
 263.26 
 
 323.48 
 
 383.79 
 
 444.23 
 
 504.80 
 
 505.53 
 
 626.44 
 
 23 
 
 24' 
 
 24.00 
 
 84.01 
 
 144.04 
 
 204.12 
 
 264.26 
 
 324.48 
 
 384.80 
 
 445-24 
 
 505-81 
 
 566.55 
 
 627.45 
 
 24 
 
 25 
 
 2'5.00 
 
 85.01 
 
 145.04 
 
 205.12 
 
 265.26 
 
 325.48 
 
 385.81 
 
 446.25 
 
 506.83 
 
 567.56 
 
 628.47 
 
 25 
 
 26 
 
 26.00 
 
 86.01 
 
 146.04 
 
 206.12 
 
 266.27 
 
 326.49 
 
 386.81 
 
 447.26 
 
 507-8^ 
 
 568.57 
 
 629.49 
 
 26 
 
 27 
 
 27.00 
 
 87.01 
 
 147.04 
 
 207.13 
 
 267.27 
 
 327-49 
 
 387.82 
 
 448.26 
 
 508.85 
 
 569. '59 
 
 630.50 
 
 27 
 
 28 
 
 28.00 
 
 88.01 
 
 148.05 
 
 208.13 
 
 268.i2|7 
 
 328.50 
 
 388.83 
 
 449.27 
 
 509.86 
 
 570.00 
 
 631.52 
 
 28 
 
 29 
 
 29.00 
 
 89.01 
 
 149.05 
 
 209.13 
 
 269.27 
 
 329-50 
 
 389-83 
 
 450.28 
 
 910.87 
 
 571.62' 
 
 632.54 
 
 29 
 
 30 
 
 3O.OO 
 
 90.01 
 
 150.05 
 
 2IQ.I3' 
 
 270.28 
 
 330.51 
 
 390.84 
 
 451.29 
 
 511.88 
 
 572.63 
 
 633.56 
 
 30 
 
 31 
 
 31.00 
 
 91.01 
 
 151.05 
 
 211. 1(3 
 
 271.28 
 
 33'i.'5i 
 
 391.85 
 
 452.30 
 
 512.89 
 
 573.64 
 
 634.57 
 
 Si 
 
 32 
 
 32.00 
 
 92'. 01 
 
 152.015 
 
 212.13 
 
 272.28 
 
 332.52 
 
 392.85 
 
 453-31 
 
 513-90 
 
 574.66 
 
 635-59 
 
 32 
 
 33 
 
 33-00 
 
 93.01 
 
 153-05 
 
 213.14 
 
 273.29 
 
 333-52 
 
 393-86 
 
 454.32 
 
 514.91 
 
 575.67 
 
 636.61 
 
 33 
 
 (34 
 
 34.00 
 
 94.01 
 
 154-05 
 
 214.14 
 
 274.29 
 
 334-53 
 
 394-85 
 
 455-33 
 
 515.93 
 
 576.69 
 
 637.62 
 
 34 
 
 35 
 
 35-00 
 
 95-01 
 
 155-05 
 
 215.14 
 
 275-29' 
 
 335.53 
 
 395.87 
 
 456.33 
 
 516.94 
 
 577.70 
 
 638.64 
 
 35 
 
 36 
 
 36.00 
 
 96.01 
 
 156.05 
 
 216. 14 
 
 276.30 
 
 336.54 
 
 396.88 
 
 4157-34 
 
 517.95 
 
 578.71 
 
 639.66 
 
 36 
 
 37 
 
 37.oo 
 
 97-01 
 
 157-05 
 
 217.14 
 
 277-30 337-54 
 
 397-88 
 
 458.35 
 
 518.96 
 
 579-73 
 
 640.68 
 
 37 
 
 38 
 
 38.00 
 
 98.01 
 
 158.06 
 
 2I8.I5 
 
 278.30 
 
 338.55 
 
 398.89 
 
 459.36 
 
 519.97 
 
 580.74 
 
 641.69 
 
 38 
 
 39 
 
 39.00 
 
 99.01 
 
 i'59-o6 
 
 219.15 
 
 279-31 
 
 339-55 
 
 399-90 
 
 460.37 
 
 520.08 
 
 581.76 
 
 642.71 
 
 39 
 
 40 
 
 40.00 
 
 IOO.OI 
 
 160.06 
 
 22O.I5 
 
 280.31 
 
 340-56 
 
 400.91 
 
 461.38 
 
 521.99 
 
 582.77 
 
 043-73 
 
 40 
 
 41 
 
 41.00 
 
 101.01 
 
 161.06 
 
 221 . I& 
 
 281.31 
 
 341.56 
 
 401.91 
 
 462.39 
 
 523-01 
 
 583-79 
 
 644.75 
 
 41 
 
 42 
 
 42.00 
 
 IO2.OI 
 
 162.06 
 
 222.15 
 
 282.32 
 
 342.57 
 
 402.92 
 
 463-40 
 
 314.02 
 
 584.80 
 
 645.76 
 
 42 
 
 43 
 
 43.00 
 
 IO3.O2 
 
 163.06 
 
 2123.16 
 
 283.32 
 
 343-57 
 
 403-93 
 
 464. 4 1 
 
 525-03 
 
 585.81 
 
 646.78 
 
 43 
 
 44 
 
 44.00 
 
 104.02 
 
 164.06 
 
 .2i24.l6 
 
 284.32 
 
 344.58 
 
 404.93 
 
 465-41 
 
 526.04 
 
 586.83 
 
 647-80 
 
 44 
 
 45 
 
 45-00 
 
 105.02 
 
 165.06 
 
 22-5. 16 
 
 285. 33 
 
 34'5.58 
 
 405.94 
 
 466.42 
 
 527.05 
 
 587.84 
 
 648.821 
 
 415 
 
 46 
 
 46.00 
 
 IO6.O2 
 
 166.06 
 
 226.16 
 
 286.33 
 
 346.59 
 
 406.95 
 
 467.43 
 
 528.06 
 
 588.86 
 
 649.84 
 
 46 
 
 47 
 
 47.00 
 
 107.02 
 
 167.07 
 
 227.16 
 
 287.33 
 
 347-59 
 
 407.95 
 
 468.44 
 
 529.08 
 
 589.87 
 
 650.85 
 
 47 
 
 48 
 
 48.00 
 
 I08.O2 
 
 168.07 
 
 228.17 
 
 288.34 
 
 348.60 
 
 408.96 
 
 469.45 
 
 530.09 
 
 590.89 
 
 651.87 
 
 48 
 
 49 
 
 49.00 
 
 109.02 
 
 169.07 
 
 229.17 
 
 .289.34 
 
 349-60 
 
 409.97 
 
 470.46 
 
 531-10 
 
 591-90 
 
 652.89 
 
 49 
 
 50 
 
 50.00 
 
 110.02 
 
 170.07 
 
 230.17 
 
 200.34' 
 
 350.61 
 
 410.97 
 
 471.47 
 
 532HI 
 
 592.92 
 
 653-91 
 
 50 
 
 51 
 
 51.00 
 
 in. 02 
 
 171.07 
 
 231 . 17 
 
 291.35 
 
 35i.6i 
 
 4111.98 
 
 4172.48 
 
 533-12 
 
 593-93 
 
 654.93 
 
 51 
 
 52 
 
 52.00 
 
 112. 02 
 
 172.07 
 
 232.18 
 
 292.35 
 
 352.62 
 
 4112.99 
 
 473-49 
 
 534-14 
 
 594-95 
 
 S5S.94 
 
 52 
 
 53 
 
 53.OO 
 
 113.012 
 
 173-07 
 
 233-18 
 
 293.35 
 
 353.62 
 
 414.00 
 
 474.50 
 
 5315.15 
 
 595.96 
 
 6.56 
 
 53 
 
 54 
 
 54.00 
 
 114.02 
 
 174.07 
 
 234.18 
 
 294.36" 
 
 3154.63 
 
 415.00 
 
 475.51 
 
 536.16 
 
 596.98 
 
 657.98 
 
 54 
 
 55 
 
 55-00 
 
 115.02 
 
 175.07 
 
 235 .'18 
 
 295.36 
 
 355.63 
 
 416.01 
 
 476.52 
 
 537-17 
 
 597-99 
 
 659.00 
 
 55 
 
 56 
 
 56.00 
 
 116.02 
 
 176.08 
 
 236.18 
 
 296.37 
 
 3(56.64 
 
 417.02 
 
 4177.53 
 
 538.18 
 
 509.01 
 
 660.02 
 
 56 
 
 57 
 
 57.OO 
 
 117.02 
 
 177.08 
 
 237.19 
 
 297.37 
 
 357.64 
 
 418.03 
 
 478.54 
 
 539-20 
 
 600.02 
 
 661.04 
 
 57 
 
 58 
 
 -'/ 
 
 58.00 
 
 118.02 
 
 178.08 
 
 238.19 
 
 298.37 
 
 358.65 
 
 419.03 
 
 479.55 
 
 540.21 
 
 601.04 
 
 662.05 
 
 58 
 
 59 
 
 59.00 
 
 119.02 
 
 179-08 
 
 2-39.19 
 
 299.38 
 
 359.65 
 
 420.04 
 
 480.56 
 
 541.22 
 
 602.05 
 
 663.07 
 
 59 
 
 60 
 
 y* 
 60.00 
 
 120.02 
 
 180.08 
 
 2140.19 
 
 300.38 
 
 360.66 
 
 421.05 
 
 481.57 
 
 542.23 
 
 603.07 
 
 664.09 
 
 60 
 
 SMITHSONIAN TABLES 
 
 310 
 
The Anti-Gudermannian. 
 
 gd u 
 
 11 
 
 12 
 
 13 
 
 I4' 
 
 15 
 
 16 
 
 17 
 
 18 
 
 19 
 
 20 
 
 gd u 
 
 (/ 
 
 664/.09 
 
 725.32 
 
 786.78 
 
 848.49 
 
 910.46 
 
 972.73 
 
 1035.30 
 
 1098.22 
 
 1161.49 
 
 1225.14 
 
 <f 
 
 I 
 
 665.11 
 
 '726.34 
 
 787.81 
 
 849.52 
 
 911.50 
 
 973-77 
 
 1036.35 
 
 1099.27 
 
 1162.54 
 
 1226.20 
 
 I 
 
 2 
 
 666.13 
 
 727-37 
 
 788.83 
 
 850.55 
 
 912.53 
 
 974-81 
 
 1037.40 
 
 1100.32 
 
 1163.60 
 
 1227.27 
 
 2 
 
 3 
 
 667.15 
 
 728.39 
 
 789.86 
 
 851.58 
 
 913.57 
 
 975.85 
 
 1038.44 
 
 1101.37 
 
 1164.66 
 
 1228.33 
 
 3 
 
 4 
 
 668.17 
 
 729.41 
 
 790.89 
 
 852.61 
 
 914.60 
 
 976.89 
 
 1039.49 
 
 1102.42 
 
 1165.72 
 
 P2I29.4O 
 
 4 
 
 5 
 
 669.19 
 
 730.43 
 
 791.91 
 
 853.64 
 
 915.64 
 
 977-93 
 
 1040.53 
 
 1103.47 
 
 1166.78 
 
 1230.46 
 
 5 
 
 6 
 
 670.21 
 
 731.46 
 
 792.94 
 
 854-67 
 
 916.67 
 
 978.97 
 
 1041.58 
 
 1104.53 
 
 1167.83 
 
 1231.53' 
 
 6 
 
 7 
 
 671.212 
 
 732.48 
 
 793-97 
 
 855.70 
 
 917.71 
 
 980.01 
 
 1042.63 
 
 1105.58 
 
 1168.89 
 
 1232.59 
 
 7 
 
 8 
 
 672.24 
 
 733.50 
 
 794.99 
 
 856.73 
 
 918.75 
 
 981.05 
 
 1043.67 
 
 1106.63 
 
 1169.95 
 
 1233.66 
 
 8 
 
 9 
 
 673.26 
 
 734-53 
 
 796.02 
 
 857. 76 
 
 9119.78 
 
 982.09 
 
 1044-72 
 
 1107.68 
 
 1171.01 
 
 1234.72 
 
 9 
 
 10 
 
 674.28 
 
 735-55 
 
 797.04 
 
 858.80 
 
 920.82 
 
 983.13 
 
 1045.77 
 
 1108.74 
 
 1172.07 
 
 1235.79 
 
 10 
 
 ii 
 
 675.30 
 
 736.57 
 
 798.07 
 
 859.83 
 
 9(21.85 
 
 984.17 
 
 1046.81 
 
 1109.79 
 
 H73.I3 
 
 1236.85 
 
 II 
 
 112 
 
 676.32 
 
 737.59 
 
 799.10 
 
 860.86 
 
 922.89 
 
 985.22 
 
 1047.86 
 
 1110.84 
 
 1174.19 
 
 12.37.92 
 
 12 
 
 13 
 
 677.34 
 
 738.62 
 
 800.13 
 
 861.89 
 
 923.93 
 
 986.26 
 
 1048.91 
 
 1111.89 
 
 1175.24 
 
 1238.98 
 
 13 
 
 14 
 
 678.36 
 
 739.64 
 
 801 . 15 
 
 862.92 
 
 924.96 
 
 987.30 
 
 1049.95 
 
 1112,95 
 
 1176/30 
 
 1240.05 
 
 14 
 
 IS' 
 
 679.38 
 
 740.66 
 
 802.18 
 
 863.95 
 
 926.00 
 
 988.34 
 
 1051.00 
 
 1114.00 
 
 1177.36 
 
 1241.11 
 
 15 
 
 16 
 
 680.40 
 
 741.69 
 
 803.21 
 
 864.98 
 
 927.03 
 
 98^.38 
 
 1052.05 
 
 1115.05 
 
 1178.42' 
 
 1242, 18 
 
 16 
 
 17 
 
 681.42 
 
 742.71 
 
 804.24 
 
 866.02 
 
 928.07 
 
 990.42 
 
 1053.09 
 
 1116. n 
 
 1179.48 
 
 1243.25 
 
 17 
 
 18 
 
 682.44 
 
 743.73 
 
 805.216 
 
 867.05 
 
 929.11 
 
 99,1 -47 
 
 1054.14 
 
 1117.16 
 
 1180.54 
 
 1244.31 
 
 18 
 
 19 
 
 683.46 
 
 744.76 
 
 806.29 
 
 868.08 
 
 930.15 
 
 992.51 
 
 1055.19 
 
 1118.21 
 
 1181.60 
 
 1245.38 
 
 19 
 
 20 
 
 684.48 
 
 745.78 
 
 807.32 
 
 869.11 
 
 931.18 
 
 993-55 
 
 1056.24 
 
 1119.27 
 
 1182.66 
 
 1246.44 
 
 20 
 
 21 
 
 685.50 
 
 746.81 
 
 808. 3 '5 
 
 870.14 
 
 932.22 
 
 994-59 
 
 1057.28 
 
 1120.32 
 
 1183.72 
 
 11247.51 
 
 21 
 
 22 1 
 
 686.52 
 
 747.83 
 
 809.37 
 
 871.18 
 
 933.26 
 
 995.63 
 
 1058.33 
 
 11211.37 
 
 1184.78 
 
 1248.58 
 
 22 
 
 23 
 
 687.54 
 
 748.85 
 
 810.40 
 
 872.2.1 
 
 934.29 
 
 996.68 
 
 1059.38 
 
 1122,43 
 
 1185,84 
 
 1249.64 
 
 23 
 
 24 
 
 688.56 
 
 749.88 
 
 811.43 
 
 873.24 
 
 935.33 
 
 997.72 
 
 1060,43 
 
 11213.48 
 
 1186.90 
 
 1250.71 
 
 24 
 
 25 
 
 689.58 
 
 750.90 
 
 812.46 
 
 874-27 
 
 936.37 
 
 998.76 
 
 1061.48 
 
 1124.53 
 
 1187.96 
 
 1251.78 
 
 25 
 
 26 
 
 690.60 
 
 751.92 
 
 81/3.49 
 
 875.31 
 
 937.40 
 
 999.80 
 
 1062.512 
 
 1125.59 
 
 1189.02 
 
 1252.85 
 
 26 
 
 27 
 
 691.62 
 
 752.95 
 
 814.52 
 
 876.34 
 
 938.44 
 
 1000.85 
 
 1063.57 
 
 1126.64 
 
 1190.08' 
 
 12-53.91 
 
 27 
 
 28 
 
 692.64 
 
 753-97 
 
 815.54 
 
 877.37 
 
 939.48 
 
 1001.89 
 
 1064.62 
 
 1127.70 
 
 1191.14 
 
 1254.98 
 
 28 
 
 29 
 
 693.66 
 
 755.00 
 
 816.57 
 
 878.40 
 
 940.52 
 
 1002.93 
 
 1065.67 
 
 1128.75 
 
 1192.20 
 
 1256.05 
 
 29 
 
 30 
 
 694.68 
 
 756.02 
 
 817-60 
 
 879.44 
 
 94'i.56 
 
 1003.97 
 
 1066.72 
 
 1129.81 
 
 1193.26 
 
 1257.12 
 
 30 
 
 3>i 
 
 695.70 
 
 757.05 
 
 818.63 
 
 880.47 
 
 942.59 
 
 1005.02 
 
 1067.77 
 
 ri30.86 
 
 1194.32 
 
 1258.18 
 
 31 
 
 32 
 
 696.72 
 
 758.07 
 
 819.66 
 
 881.50 
 
 943.63 
 
 1006.06 
 
 1068.81 
 
 1131.92 
 
 1195.39 
 
 1259.25 
 
 32 
 
 33 
 
 697.74 
 
 759.09 
 
 820.69 
 
 882.54 
 
 944.67 
 
 1007.10 
 
 1069.86 
 
 H30.97 
 
 1196.45 
 
 1260.32 
 
 33 
 
 34 
 
 698.76 
 
 760.12 
 
 8211.71 
 
 883.57 
 
 945.71 
 
 1008. 16 
 
 1070.91 
 
 1134.03 
 
 H97.5I 
 
 1261.39 
 
 34 
 
 35 
 
 699.78 
 
 761.14 
 
 822.74 
 
 884.60 
 
 946.74 
 
 1009.19 
 
 1071.96 
 
 ii<35.o8 
 
 1198.57 
 
 1262.45 
 
 35 
 
 36 
 
 700.80 
 
 762.17 
 
 823.77 
 
 885.64. 
 
 947.78 
 
 1010.23 
 
 1073.01 
 
 1136.14 
 
 1199.63 
 
 1263.52 
 
 36 
 
 37 
 
 701.82 
 
 763.19 
 
 824.80 
 
 886.67 
 
 948.82 
 
 1011.28 
 
 1074.06 
 
 1137.19 
 
 1200.69 
 
 1264.59 
 
 37 
 
 38 
 
 702.85 
 
 764.212 
 
 825-83 
 
 887.70 
 
 049.86 
 
 1013.32 
 
 1075.11 
 
 1138.25 
 
 1201.75 
 
 1265.66 
 
 38 
 
 39 
 
 703.87 
 
 765.24 
 
 826.86 
 
 888.74 
 
 950.90 
 
 1013.36 
 
 1076.16 
 
 1139.30 
 
 1202.82' 
 
 1266.73 
 
 39 
 
 40 
 
 704.89 
 
 766.27 
 
 827.89 
 
 889.77 
 
 951-94 
 
 1014.4-1 
 
 1077.21 
 
 1140.36 
 
 1203.88 
 
 1267.80 
 
 40 
 
 4i 
 
 705-91 
 
 767.29 
 
 828.92 
 
 890.80 
 
 952.98 
 
 1015.45 
 
 1078.26 
 
 1141.41 
 
 1204.04 
 
 1268.87 
 
 41 
 
 42 
 
 706.93 
 
 768.32 
 
 829.95 
 
 891.84 
 
 954.01 
 
 1016.50 
 
 1079.31 
 
 1142.47 
 
 1206.00 
 
 11269.93 
 
 42 
 
 43 
 
 707.95 
 
 769.34 
 
 830.98 
 
 8921.87 
 
 955.05 
 
 1017.54 
 
 1080.36 
 
 1143.52 
 
 1207.06 
 
 1271.00 
 
 43 
 
 44 
 
 708.97 
 
 770-37 
 
 832.00 
 
 893.91 
 
 956.09 
 
 1018.58 
 
 1081.41 
 
 1 144'. 58 
 
 1208.13 
 
 1272.07 
 
 44 
 
 45 
 
 709.99 
 
 771.39 
 
 833.03 
 
 894.94 
 
 957.13 
 
 1019.63 
 
 1082-. 46 
 
 1145.64 
 
 1209.19 
 
 1273.14 
 
 45 
 
 46 
 
 711.02 
 
 772.42 
 
 834.06 
 
 895.97 
 
 958.17 
 
 1020.67 
 
 1083.51 
 
 1146.69 
 
 1210.25 
 
 1274.21 
 
 46 
 
 47 
 
 712.04 
 
 773-44 
 
 835.09 
 
 897-01 
 
 959.21 
 
 1021.72 
 
 1084.56 
 
 H47.75 
 
 1211.31 
 
 1275. ,28 
 
 47 
 
 48 
 
 713.06 
 
 774-47 
 
 836.12 
 
 898.04 
 
 960.25 
 
 1022.76 
 
 1085.61 
 
 1148.80 
 
 1212.38 
 
 1276.35 
 
 48 
 
 49 
 
 714.08 
 
 775-49 
 
 837.15 
 
 809.08 
 
 961.29 
 
 1023.81 
 
 1086.66 
 
 1149.86 
 
 1213.44 
 
 1277.42 
 
 49 
 
 50 
 
 7i5.io 
 
 776.52 
 
 838.18 
 
 goo. n 
 
 9612.33 
 
 1024,'. 85 
 
 1087.71 
 
 1150.92 
 
 1214.50 
 
 1278.49 
 
 50 
 
 51 
 
 7l6. 12 
 
 777-54 
 
 839.21 
 
 901.15 
 
 963.37 
 
 1025.90 
 
 1088.76 
 
 II5I.97 
 
 1215.57 
 
 1279.56 
 
 5i 
 
 'SB 
 
 717.15 
 
 778.57 
 
 840.24 
 
 902.18 
 
 964.41 
 
 1026.94 
 
 1089.81 
 
 1153.03 
 
 1216.63 
 
 1280.63 
 
 52 
 
 53 
 
 718.17 
 
 779-59 
 
 841.27 
 
 003.212 
 
 965.45 
 
 1027.99 
 
 1090.86 
 
 1154.09 
 
 1217.69 
 
 1281.70 
 
 53 
 
 54 
 
 719.19 
 
 7180.62 
 
 842'. 30 
 
 904.215 
 
 966.49 
 
 1029.03 
 
 1091.91 
 
 H55.I4 
 
 1218.76 
 
 1,282.77 
 
 54 
 
 5S 
 
 72O.2I 
 
 781.65 
 
 843.33 
 
 905.28 
 
 967.53 
 
 1030.08 
 
 1092.96 
 
 1156.20 
 
 1219.82 
 
 11283.84 
 
 55 
 
 56 
 
 7(21.23 
 
 782.67 
 
 844.36 
 
 906.32 
 
 968.57 
 
 1031.12 
 
 1094.01 
 
 1157.26 
 
 1220.88 
 
 1284.91 
 
 56 
 
 57 
 
 722.2^ 
 
 783.70 
 
 845.39 
 
 907.35 
 
 969.61 
 
 1032.17 
 
 1095.06 
 
 1158.32 
 
 1221.95 
 
 1285.98 
 
 57 
 
 58 
 
 723,28 
 
 784.73 
 
 846.42 
 
 908.39 
 
 970.6s 
 
 1033.21 
 
 1006. n 
 
 1159-37 
 
 1223.01 
 
 1287.05 
 
 58 
 
 59 
 
 724.30 
 
 785.75 
 
 847.45 
 
 909.43 
 
 971.69 
 
 1034.26 
 
 1097.16 
 
 1160.43 
 
 1224.07 
 
 1288. 13 
 
 59 
 
 60 
 
 725.312 
 
 786.78 
 
 848.49 
 
 910.46 
 
 972.73 
 
 1035.30 
 
 1098.22 1161.49 
 
 1225.14 
 
 1289.20 
 
 60 
 
 SMITHSONIAN TABLES 
 
The Anti-Gudermannian. 
 
 gdu 
 
 51 
 
 2t2 
 
 23 
 
 24 
 
 25 
 
 26 
 
 27 
 
 28 
 
 29 
 
 30 
 
 gdu 
 
 O' 
 
 12Z&.20 
 
 1353.69 
 
 1418.63 
 
 1484.06 
 
 1549.99 
 
 1616.47 
 
 1683.52 
 
 1751.16 
 
 1819.44 
 
 1888.38 
 
 0' 
 
 I 
 
 1200.27 
 
 1354.76 
 
 1419.72 
 
 1485.15 
 
 1551.10 
 
 1617.58 
 
 1684.64 
 
 1752.29 
 
 1820.58 
 
 1889.53 
 
 i 
 
 2 
 
 I29L34 
 
 I355.84 
 
 14120.80 
 
 1486.^5 
 
 1552.20 
 
 1618.70 
 
 1685,76 
 
 1753-43 
 
 18121.72 
 
 1890.69 
 
 2 
 
 3 
 
 1292.41 
 
 1356.92 
 
 1421.89 
 
 1487.34 
 
 1553.31 
 
 1619.81 
 
 1686.88 
 
 1754.56 
 
 1822.87 
 
 1891.84 
 
 3 
 
 4 
 
 1293.48 
 
 1358.00 
 
 1422.98 
 
 1488.44 
 
 1554.41 
 
 1620.92 
 
 1688.01 
 
 1755.69 
 
 1824.01 
 
 1893-03 
 
 4 
 
 5 
 
 I294-.55 
 
 1359.08 
 
 1424.06 
 
 1489.53 
 
 I5'55.5i 
 
 1622.04 
 
 1689.13 
 
 1756.83 
 
 18255.16 
 
 1894.15 
 
 5 
 
 6 
 
 1295.63 
 
 1360. 16 
 
 11425.15 
 
 1490.63 
 
 1556.62 
 
 1623.15 
 
 1690.25 
 
 1757.96 
 
 1826.30 
 
 1895.31 
 
 6 
 
 7 
 
 1296.70 
 
 1361.24 
 
 1426.24 
 
 1491.72 
 
 1557.72 
 
 1624.26 
 
 1691.38 
 
 1759.09 
 
 1827.44 
 
 1896.46 
 
 7 
 
 8 
 
 1297-77 
 
 1362.312 
 
 1427.32 
 
 1492.82 
 
 1558.83 
 
 16215.38 
 
 1692.50 
 
 1760.23 
 
 1828.59 
 
 1897.62 
 
 8 
 
 9 
 
 1298.84 
 
 1363.40 
 
 1428.41 
 
 1493.91 
 
 1559-93 
 
 1626.49 
 
 1693.62 
 
 1761.36 
 
 1829.73 
 
 1898.78 
 
 9 
 
 10 
 
 1299.91 
 
 1364-48 
 
 1429-50 
 
 1495.01 
 
 1561.04 
 
 1627.61 
 
 1694.75 
 
 1762.50 
 
 1830.88 
 
 1899-93 
 
 10 
 
 n 
 
 1300.99 
 
 1365.56 
 
 1430.59 
 
 1496.11 
 
 1562.14 
 
 1628.72 
 
 1695.87 
 
 1763.63 
 
 1832.02 
 
 1901.09 
 
 II 
 
 1-2 
 
 1302.06 
 
 1366.64 
 
 1431.68 
 
 1497.20 
 
 1563. <as 
 
 1629.84 
 
 1697.00 
 
 1764.77 
 
 1833.17 
 
 1902.25 
 
 12 
 
 IQ 
 
 1303.13 
 
 1367.72 
 
 1432.76 
 
 1498.30 
 
 r564.35 
 
 1630.95 
 
 1698.12 
 
 1765.90 
 
 1834.32 
 
 1903.40 
 
 13 
 
 14 
 
 1304.20 
 
 1368.80 
 
 1433.85 
 
 1499.40 
 
 1565.46 
 
 1632.06 
 
 1699.25 
 
 1767.04 
 
 1835.46 
 
 1904.56 
 
 14 
 
 15 
 
 1305.28 
 
 1369.88 
 
 1434.94 
 
 1500.49 
 
 1566.56 
 
 1633.18 
 
 1700.37 
 
 1768.17 
 
 1836.61 
 
 1905.72 
 
 15 
 
 16 
 
 1306.35 
 
 1370.96 
 
 1436.03 
 
 1-501 .59 
 
 1567.67 
 
 1634.29 
 
 1701.50 
 
 1769.31 
 
 1837.75' 
 
 1906.88 
 
 16 
 
 17 
 
 1307.42 
 
 1372.04 
 
 1437. 12 
 
 1502.69 
 
 1568.77 
 
 1635.41 
 
 1702.62 
 
 1770.44 
 
 1838.90 
 
 1908.03 
 
 17 
 
 18 
 
 ^1308.50 
 
 1373-12 
 
 1438.21 
 
 1503.78 
 
 1569.88 
 
 1636.512 
 
 1703.75 
 
 1771.58 
 
 1840.05 
 
 1909.19 
 
 18 
 
 19 
 
 1309.57 
 
 1374-20 
 
 1439.29 
 
 1504.88 
 
 1570.99 
 
 1637.64 
 
 1704.87 
 
 1772.71 
 
 1841.19 
 
 1910.35 
 
 19 
 
 20 
 
 1310.64 
 
 1375.28 
 
 1440.38 
 
 1505.98 
 
 1572.09 
 
 1638.76 
 
 1706.00 
 
 1773-85 
 
 1842.314 
 
 I9H.5I 
 
 20 
 
 21 
 
 1311.72 
 
 1376.36 
 
 1441.47 
 
 1507.08 
 
 1573-20 
 
 1639.87 
 
 1707. 12 
 
 1774.98 
 
 1843.49 
 
 1912.67 
 
 21 
 
 22 
 
 1312.79 
 
 1377.44 
 
 1442.56 
 
 1508.17 
 
 1574.31 
 
 1640.99 
 
 1708.25 
 
 1776.121 
 
 1844.64 
 
 1913.83 
 
 212 
 
 1213 
 
 1313.86 
 
 1378.52 
 
 1443.65 
 
 1509.27 
 
 1575.41 
 
 1642 . 10 
 
 1709.37 
 
 1777.26 
 
 1845.78 
 
 1914.98 
 
 23 
 
 24 
 
 1314.94 
 
 i379.6i 
 
 1444.74 
 
 1510.37 
 
 1576.52 
 
 16413.22 
 
 I7IO.5O 
 
 1778.39 
 
 1846.93 
 
 1916.14 
 
 24 
 
 25 
 
 1316.01 
 
 1380.69 
 
 1445.83 
 
 I5H.47 
 
 1577.63 
 
 1644.34 
 
 1711.63 
 
 1779.53 
 
 1848.08 
 
 1917.30 
 
 2>5 
 
 26 
 
 1317.08 
 
 i'38i.77 
 
 1446.92 
 
 I5H2.57 
 
 1578.73 
 
 1645. 4'S 
 
 1712.75 
 
 1780.67 
 
 1849. 23 
 
 1918.46 
 
 26 
 
 27 
 
 1318.16 
 
 1382.85 
 
 1448.01 
 
 1513-67 
 
 1579.84 
 
 1646.57 
 
 1713.88 
 
 1781.81 
 
 1850.37 
 
 1919.62 
 
 27 
 
 28 
 
 1319- 23 
 
 1383-93 
 
 1449.10 
 
 1514.76 
 
 1580.95 
 
 1647.69 
 
 1715-01 
 
 1782.94 
 
 1851.52 
 
 1920.78 
 
 28 
 
 29 
 
 1320.31 
 
 1385.02 
 
 I450'I9 
 
 1515.86 
 
 1582.06 
 
 1648.80 
 
 I7l6. 14 
 
 11784.08 
 
 1852.67 
 
 I92JI.94 
 
 29 
 
 30 
 
 1321.38 
 
 1386.10 
 
 1451.28 
 
 1516.96 
 
 1583.17 
 
 1649.92 
 
 1717.26 
 
 1785.22 
 
 1853.82 
 
 1923.10 
 
 30 
 
 31 
 
 132*2.45 
 
 1387.18 
 
 I45<2.37 
 
 1518.06 
 
 1584.27 
 
 1651.04 
 
 I7I8.39 
 
 1786.36 
 
 1854.97 
 
 1924.26 
 
 31 
 
 32 
 
 1323.53 
 
 1388.26 
 
 1453.46 
 
 1519.16 
 
 1585.38 
 
 1652.16 
 
 1719.52 
 
 1787.50 
 
 1856. Il 
 
 192(5.43' 
 
 32 
 
 33 
 
 1324.60 
 
 1389.35 
 
 1454.55 
 
 1520.26 
 
 1586.49 
 
 1653.^7 
 
 1720.65 
 
 1788.60 
 
 1857.27 
 
 1926.59 
 
 33 
 
 34 
 
 1325.68 
 
 11390.43 
 
 1455.64 
 
 1521.36 
 
 1587.60 
 
 1654.39 
 
 .1721.77 
 
 1789.77 
 
 1858.42 
 
 1927.75 
 
 34 
 
 315 
 
 1326.75 
 
 1391-51 
 
 1456.73 
 
 1522.46 
 
 1588.71 
 
 I655.5I 
 
 1722.90 
 
 1790.91 
 
 1859.57 
 
 1928.91 
 
 3*5 
 
 36 
 
 1327-83 
 
 1392.59 
 
 1457.83 
 
 1523.56 
 
 1589.82 
 
 1656.63 
 
 1724.03 
 
 1792.05 
 
 1860.72- 
 
 1930.07 
 
 36 
 
 37 
 
 1328.90 
 
 1393.68 
 
 1458.92 
 
 1524.66 
 
 1.590.92 
 
 1657.75 
 
 1725.16 
 
 1793.19 
 
 1861.87 
 
 1931.23 
 
 37 
 
 38 
 
 1329.98 
 
 1394.76 
 
 1460.01 
 
 1525.76 
 
 1592.03 
 
 1658.87 
 
 1726.29 
 
 1794.33 
 
 1863.02 
 
 1932.40 
 
 38 
 
 39 
 
 I33i.o6 
 
 1395.84 
 
 1461 . 10 
 
 1526.86 
 
 1593.14 
 
 1659-98 
 
 1727.42 
 
 1795-47 
 
 1864.17 
 
 1933.56 
 
 39 
 
 40 
 
 1332.13 
 
 1306.93 
 
 1462.19 
 
 1527.96 
 
 1594.25 
 
 1661 . 10 
 
 1728.54 
 
 1796.61 
 
 1865.32 
 
 1934.72 
 
 40 
 
 41 
 
 H333.2I 
 
 1398.01 
 
 1463.28 
 
 11529.06 
 
 1595.36 
 
 1662.22 
 
 1729.67 
 
 1797.75 
 
 1866.47 
 
 I935.8S 
 
 41 
 
 42> 
 
 1334.29 
 
 1399- 10 
 
 1464-38 
 
 1530. 16 
 
 1596.47 
 
 1663.34 
 
 1730.80 
 
 1798.89 
 
 1867.62- 
 
 1937.05 
 
 42 
 
 43 
 
 1335.37 
 
 1400. 18 
 
 1465.47 
 
 1531-26 
 
 r597-58 
 
 1664.46 
 
 1731.93 
 
 1800.03 
 
 1868.77 
 
 1938.21 
 
 43 
 
 44 
 
 1336.44 
 
 1401.26 
 
 1466.56 
 
 1532.36 
 
 1598.69 
 
 1665.58 
 
 1733.06 
 
 1801.17 
 
 1869.92 
 
 1939.37 
 
 44 
 
 4-5 
 
 1337.52 
 
 1402.35 
 
 1467.65 
 
 1533.46 
 
 1599.80 
 
 1666.70 
 
 ff734.I9 
 
 1802.31 
 
 1871.08 
 
 1940.54 
 
 45 
 
 46 
 
 13138.60 
 
 1403.43 
 
 1468.75 
 
 1534.56 
 
 1600.91 
 
 1667.82 
 
 1735.32 
 
 1803.45 
 
 1872.23 
 
 1941-70 
 
 46 
 
 47 
 
 1339.67 
 
 1404.52? 
 
 1469.84 
 
 1535-66 
 
 1602.02 
 
 1668.04 
 
 1736.45 
 
 1804.59 
 
 1873.38 
 
 1942.86 
 
 47 
 
 48 
 
 1340.75 
 
 1405.60 
 
 1470.93 
 
 1536.77 
 
 1603.13 
 
 1670.06 
 
 1737.58 
 
 1805.73 
 
 1874.53 
 
 1944.03 
 
 48 
 
 49 
 
 1341.83 
 
 1406.69 
 
 1472.02 
 
 1537.87 
 
 1604.24 
 
 1671.18 
 
 1738.71 
 
 1806.87 
 
 1875.69 
 
 1945.19 
 
 49 
 
 50 
 
 1342.91 
 
 1407.77 
 
 I473-I2 
 
 1538.97 
 
 1605.35 
 
 1672.30 
 
 1739.84 
 
 1808. 01 
 
 1876.84- 
 
 1946.36 
 
 50 
 
 Si 
 
 1343-98 
 
 1408.86 
 
 1474.21 
 
 1540.07 
 
 1606.46 
 
 1673-42 
 
 1740.98 
 
 1809.15 
 
 1877.99 
 
 1947.52 
 
 51 
 
 52 
 
 1345.06 
 
 1409.94 
 
 1475.30 
 
 I54LI7 
 
 1607.58 
 
 1674.54 
 
 1742.11 
 
 1810.30 
 
 1879. 14 
 
 1948.69 
 
 52 
 
 53 
 
 1346.14 
 
 1411.03 
 
 1476.40 
 
 154-2.27 
 
 1608.69 
 
 1675.66 
 
 r743.24 
 
 1811.44.' 
 
 1880.30 
 
 1949.85 
 
 53 
 
 54 
 
 1347.212 
 
 1412.11 
 
 1477.49 
 
 1543.38 
 
 1609.80 
 
 1676.79 
 
 I'744.37 
 
 1812.58 
 
 I88I.45 
 
 1951.02 
 
 54 
 
 55 
 
 1348.29 
 
 1413.20 
 
 1478.59 
 
 1544-48 
 
 1610.91 
 
 1677.91 
 
 1745-50 
 
 1813.72 
 
 1882.60 
 
 1952.18 
 
 55 
 
 56 
 
 1349-37 
 
 1414.28 
 
 1479.68 
 
 1545.58 
 
 1612.02 
 
 1670.03 
 
 1746.63 
 
 1814.86 
 
 1883.76 
 
 1953.35 
 
 56 
 
 57 
 
 1350.45 
 
 Hi'5.37 
 
 1480.77 
 
 1546.69 
 
 1613.13 
 
 1680.15 
 
 1747.76 
 
 1816.01 
 
 1884.91 
 
 I954.5I 
 
 57 
 
 58 
 
 1351.53 
 
 1416.46 
 
 1481.87 
 
 1547-79 
 
 1614.25 
 
 1681.27 
 
 1748.90 I8I7.I5 
 
 1886.07 
 
 1955.68 
 
 58 
 
 59 
 
 1352.61 
 
 1417-54 
 
 1482.96 
 
 1548.89 
 
 1615.36 
 
 1682.39 
 
 1750.03 l8l8.29 
 
 1887.32) 
 
 1056.85 
 
 59 
 
 60 
 
 U53.69 
 
 1418.63 
 
 1484.06 
 
 1549.99 
 
 1616.47 
 
 1683.52 
 
 1751. i6| 1819.44' 
 
 1888.38 
 
 1958.01 
 
 60 
 
 SMITHSONIAN TABLES 
 
 312 
 
The Anti-Gudermannian. 
 
 odu 
 
 31 
 
 32 
 
 33 
 
 34 
 
 35 
 
 36 
 
 37 
 
 38 
 
 39 
 
 40 
 
 gdu 
 
 0' 
 
 IQSS'.OI 
 
 2028.38 
 
 2099.53 
 
 2171.48 
 
 2244.29 
 
 2317.99 
 
 2392.63 
 
 2468.26 
 
 2544.93 
 
 2622.69 
 
 tf 
 
 i 
 
 1959.18 
 
 2029.56 
 
 2100.72 
 
 2172.69 
 
 2245.51 
 
 2319.22 
 
 2393-88 
 
 2469.53 
 
 2546.22 
 
 2624.00 
 
 I 
 
 2 
 
 1960.35 
 
 2030.74 
 
 2101.91 
 
 2173.89 
 
 212146.73 
 
 2320.46 
 
 2395.14 
 
 2470.80 
 
 2547-50 
 
 2625.30 
 
 2 
 
 3' 
 
 1961.51 
 
 2031.92 
 
 2103.10 
 
 2175.10 
 
 2247.95 
 
 2321.70 
 
 2396.39 
 
 2472.07 
 
 2548.79 
 
 12626.61 
 
 3 
 
 4 
 
 1962.68 
 
 2033.10 
 
 2104.30 
 
 2176.31 
 
 2249. 17 
 
 2322.93 
 
 2397.64 
 
 2473.34 
 
 2550.08 
 
 2627.91 
 
 4 
 
 5 
 
 1963.85 
 
 2034.28 
 
 2105.49 
 
 i2>!77. Si 
 
 2250.39 
 
 2324.17 
 
 2398.90 
 
 2474.61 
 
 2551.37 
 
 2629.22 
 
 5 
 
 6 
 
 1965.02 
 
 2035.46 
 
 2106.68 
 
 2178.72 
 
 2251.62 
 
 2325.41 
 
 2400.15 
 
 2475-88 
 
 2552.66 
 
 2630.53 
 
 6 
 
 7 
 
 1066.18 
 
 2036.64 
 
 2107.88 
 
 2179.93 
 
 2252.84 
 
 2*326.65 
 
 2401.40, 
 
 2477.15 
 
 2553-95 
 
 2631 .8^ 
 
 7 
 
 8 
 
 1967.35 
 
 2037.82 
 
 2109.07 
 
 .2181.14 
 
 2254.06 
 
 23.27. 8 
 
 2402.66 
 
 2478.42 
 
 2555.23 
 
 2633. 14 
 
 8 
 
 9 
 
 1968.52 
 
 2039.00 
 
 2110.27 
 
 2:182.35 
 
 2255.28 
 
 21329.12 
 
 2403.91 
 
 2479.69 
 
 2556.52 
 
 2634.45 
 
 9 
 
 10 
 
 1969.69 
 
 2040. 19 
 
 2111.46 
 
 2183.55 
 
 2256.51 
 
 2330.36 
 
 2405.17 
 
 2480.97 
 
 2557-81 
 
 2635.76 
 
 10 
 
 ii 
 
 1970.86 
 
 2041.37 
 
 2112.66 
 
 121184.76 
 
 2257.73 
 
 23131.60 
 
 2406.42 
 
 2482.024 
 
 2559. 10 
 
 2637.07 
 
 ii 
 
 12 
 
 1972.03 
 
 2042.55 
 
 2113.85 
 
 2185.97 
 
 2258.95 
 
 2332.84 
 
 2407.68 
 
 2483.51 
 
 2560.39 
 
 2638.38 
 
 12 
 
 13 
 
 1973.20 
 
 2043.. 73 
 
 2115.05 
 
 2187.18 
 
 2260.18 
 
 2*334.08 
 
 2408.93 
 
 2484.78 
 
 2561.68 
 
 2639.69 
 
 13 
 
 14 
 
 1974.37 
 
 2044.91 
 
 2116.24 
 
 0188.39 
 
 2261.40 
 
 2335.32 
 
 2410. 19 
 
 .21486.06 
 
 2562.97 
 
 2641.00 
 
 14 
 
 i'3 
 
 1975.54 
 
 2046.10 
 
 2117.44 
 
 2189.60 
 
 2262.63 
 
 2336.56 
 
 2411.44 
 
 2487.33 
 
 2564.27 
 
 2642.31 
 
 15 
 
 16 
 
 1976.71 
 
 2047.28 
 
 2118.63* 
 
 2190.81 
 
 2263.85 
 
 23137.80 
 
 24121.70 
 
 2488.60 
 
 2565.56 
 
 2643.62 
 
 16 
 
 17 
 
 1977.88 
 
 2048.46 
 
 2119.831 
 
 2192.02 
 
 2*265.08 
 
 2339.04 
 
 2413.96 
 
 2489.88 
 
 12566.85 
 
 2644.93 
 
 17 
 
 18 
 
 1979.05 
 
 2049.64 
 
 2121.03 
 
 2193.23 
 
 2266.30 
 
 2340.28 
 
 2415.21 
 
 2491.15 
 
 2568.14 
 
 2646.24 
 
 18 
 
 19 
 
 1980.22 
 
 2050.83 
 
 2122.22 
 
 21194.44 
 
 2267.53 
 
 2341.52 
 
 2416.47 
 
 2492.43 
 
 2569.413' 
 
 2647.55 
 
 19 
 
 20 
 
 1981.39 
 
 2052.01 
 
 2123.42 
 
 2195-65 
 
 2268.75 
 
 2342.76 
 
 .2417.73 
 
 2493.70 
 
 2570.73 
 
 2648.86 
 
 20 
 
 21 
 
 1982.56 
 
 2053.19 
 
 121124.62 
 
 2196.86 
 
 2269.98 
 
 2344.00 
 
 2418.99 
 
 2494.97 
 
 2572.02 
 
 2650. 17 
 
 21 
 
 22 
 
 1983.73 
 
 2054-38 
 
 21215.81 
 
 2198.07 
 
 2271.20 
 
 2345.25 
 
 2420.24 
 
 2496.25 
 
 2573.3I 
 
 2651.49 
 
 2J2 
 
 23' 
 
 1984.90 
 
 2055.56 
 
 2127.01 
 
 2199.29 
 
 227.2.43 
 
 2346.49 
 
 2421.50 
 
 2497.52 
 
 2574.61 
 
 2652.80 
 
 23 
 
 24 
 
 1986.07 
 
 2056.75 
 
 2128.21 
 
 22OO.'50 
 
 2273.66 
 
 2347.73 
 
 2422.76 
 
 2498.80 
 
 2575.90 
 
 2654.11 
 
 24 
 
 25 
 
 1987.24 
 
 2057.93 
 
 2129.41 
 
 2201.71 
 
 2274.88 
 
 2348.97 
 
 2424.02 
 
 2.5(00.08 
 
 2577.19 
 
 2655.43 
 
 25 
 
 26 
 
 1988.41 
 
 2059.11 
 
 2I3O.6I 
 
 2202.92 
 
 2276.11 
 
 2350.21 
 
 24215.28 
 
 2501.35 
 
 2578.49 
 
 2656.74 
 
 26 
 
 27 
 
 1989.59 
 
 2060.30 
 
 2I3iI.8b 
 
 2204.14 
 
 2277.34 
 
 2351.46 
 
 2426.54 
 
 2502.63 
 
 2579.78 
 
 2658.05 
 
 27 
 
 28 
 
 1990.76 
 
 12061 .49 
 
 2133-00 
 
 2205.35 
 
 2278.57 
 
 2352.70 
 
 2427.80 
 
 2503.91 
 
 2581.08 
 
 2659.37 
 
 28 
 
 29' 
 
 1991.93 
 
 2062.67 
 
 2134.20 
 
 2206.56 
 
 2279.79 
 
 2353.95 
 
 2429.06 
 
 2505.18 
 
 2582.37 
 
 2660.68 
 
 29 
 
 30 
 
 1993.10 
 
 2063.86 
 
 2135.40 
 
 2207.78 
 
 2281.02 
 
 2355.19 
 
 2430.32 
 
 2506.46 
 
 2583.67 
 
 2662.00 
 
 30 
 
 31 
 
 1994.28 
 
 2065.04 
 
 2136.60 
 
 12-208. 99 
 
 2282.25 
 
 2356.43 
 
 2431.58 
 
 2507.74 
 
 2584.07 
 
 2663.31 
 
 3i 
 
 32 
 
 1995.45 
 
 2066.231 
 
 2137.80 
 
 2210.20 
 
 2283.48 
 
 2357.68 
 
 2432.84 
 
 2509.02 
 
 2586.26 
 
 2664.63 
 
 32 
 
 33 
 
 1996.62 
 
 2057.41 
 
 2139.00 
 
 2211.42 
 
 2284.71 
 
 2358.92 
 
 24134.10 
 
 2510.30 
 
 .2587.56 
 
 2665.04 
 
 33 
 
 34 
 
 1997.80 
 
 2068.60 
 
 2140.20 
 
 2212.63 
 
 2285.94 
 
 2360.17 
 
 2435.36 
 
 2511.58 
 
 2588.86 
 
 
 34 
 
 3'5 
 
 1998.97 
 
 2069.79 
 
 2141.40 
 
 22113.84 
 
 2287.17 
 
 2361.41 
 
 2436.62 
 
 2512.86 
 
 2590.151 
 
 2668.58 
 
 3'5 
 
 36 
 
 2000.14 
 
 2070.97 
 
 2I42.6O 
 
 2215.06 
 
 2288.40 
 
 2*362.66 
 
 2437.89 
 
 2514-14 
 
 2591.45, 
 
 2669.89 
 
 36 
 
 37 
 
 2001.32 
 
 2072.16 
 
 2143.80 
 
 32l6.27 
 
 2289.63 
 
 2363.00 
 
 2439.15 
 
 2515.41 
 
 2592.75 
 
 2671.21 
 
 37 
 
 38 
 
 2002.49 
 
 2073-35 
 
 2145.00 
 
 2217.49 
 
 2200.86 
 
 2365.15 
 
 2440.41 
 
 2516.69 
 
 2594.05 
 
 2672.53 
 
 38 
 
 39 
 
 2003.67 
 
 2074.54 
 
 2I46.2O' 
 
 2218.70 
 
 12292.09 
 
 2366.40 
 
 2441.68 
 
 2517.97 
 
 2595.35 
 
 2673.85 
 
 39 
 
 40 
 
 2004.84 
 
 2075.72 
 
 2147.40 
 
 2219.92 
 
 2293.32 
 
 2367.64 
 
 2442.94 
 
 2519.25 
 
 2596.65 
 
 2675.16 
 
 40 
 
 41 
 
 2006.02 
 
 2076.91 
 
 2I48.6I 
 
 2221.14 
 
 2294.55 
 
 2368.89 
 
 2444.20 
 
 2520,54 
 
 2597.95 
 
 2676.48 
 
 41 
 
 42 
 
 2007.19 
 
 2078.10 
 
 2I49.8I 
 
 22212.36 
 
 2295.78 
 
 2370.14 
 
 2445'- 47 
 
 1252 1. 82 
 
 2599.24 
 
 2677.80 
 
 42 
 
 43 
 
 2008.37 
 
 2079.29 
 
 2ISLOI 
 
 2223.57 
 
 2297.01 
 
 2371.38 
 
 2446.73 
 
 2523. 10 
 
 2600.541 
 
 2679.12 
 
 43 
 
 44 
 
 2009.54 
 
 2080.48 
 
 2152.21! 
 
 2224.79 
 
 2298.24 
 
 2372.63 
 
 2447.99 
 
 21524.38 
 
 2601.84 
 
 2680.44 
 
 44 
 
 415 
 
 2010.72 
 
 2081.67 
 
 2153.41 
 
 2226.00 
 
 2299.48 
 
 2373.88 
 
 2449.26 
 
 25125.66 
 
 2603.14 
 
 2681.76 
 
 45 
 
 46 
 
 2011.90 
 
 2082.86 
 
 2154.62 
 
 22-27 22 
 
 2300.71 
 
 2375.13 
 
 2450.52 
 
 2526.95 
 
 2604.45 
 
 2683.08 
 
 46 
 
 47 
 
 2013.07 
 
 2084.04 
 
 2155.82 
 
 2228.44 
 
 2301.94 
 
 2376.38 
 
 2451.79 
 
 2528.213 
 
 2605.75 
 
 2684.40 
 
 47 
 
 48 
 
 2014.25 
 
 2085.23 
 
 2157.02 
 
 2229.66 
 
 2303.17 
 
 2377.63 
 
 2453-05 
 
 2529.51 
 
 2607.05 
 
 2685.72 
 
 48 
 
 49 
 
 2015.43 
 
 2086.42 
 
 2158.23 
 
 2230.87 
 
 2304.41 
 
 2378.87 
 
 2454.32 
 
 2530.79 
 
 2608.35 
 
 2687.04 
 
 49 
 
 SO 
 
 2016.60 
 
 2087.61 
 
 2159.43, 
 
 2032.O9 
 
 2305.64 
 
 2380.12 
 
 2455-58 
 
 2532.08 
 
 2609.65 
 
 2688.36 
 
 50 
 
 51 
 
 :2OI7.78 
 
 2088.80 
 
 2I60.63 
 
 2233.31 
 
 2306.88 
 
 2381.37 
 
 2456.85 
 
 2533-36 
 
 2610.95 
 
 2689.69 
 
 51 
 
 52 
 
 2018.96 
 
 2089.99 
 
 2I6I.84 
 
 2234.53 
 
 2308.11 
 
 2-382.62 
 
 2458.12 
 
 2534-65 
 
 2612.26 
 
 2691.01 
 
 52 
 
 S3 
 
 2020.13 
 
 2091.19 
 
 2163.04 
 
 2235.75 
 
 2309.34 
 
 2383.87 
 
 24'59.39 
 
 2535.93 
 
 2613.56 
 
 2692.33 
 
 53 
 
 54> 
 
 2021.31 
 
 (2092.38 
 
 2164.25 
 
 12036.97 
 
 213:10.58 
 
 2385.12 
 
 2460.65 
 
 2-537. 22 
 
 2614.86 
 
 2693.65 
 
 54 
 
 55 
 
 2022.49 
 
 2093.57 
 
 2165.45 
 
 2238.19 
 
 213,11.81 
 
 2386.37 
 
 2461.92 
 
 2538.50 
 
 2616.17 
 
 2694.98 
 
 55 
 
 56 
 
 2023.67 
 
 2094.76 
 
 2166.66 
 
 2239.41 
 
 121313 -05 
 
 2387.62 
 
 2463.19 
 
 2539-79 
 
 2617.47 
 
 2696.30 
 
 56 
 
 57 
 
 2024.85 
 
 2095.95 
 
 2167.86 
 
 2240.63 
 
 2314.28 
 
 2388.88 
 
 2464.46 
 
 2541.07 
 
 2618.78 
 
 2697-63 
 
 57 
 
 58 
 
 2026.03 
 
 2097-14 
 
 2169.07 
 
 2241.85 
 
 12315.52 
 
 2390.13 
 
 2465.72 
 
 2542.36 
 
 2620.08 
 
 2698.95 
 
 58 
 
 59 
 
 2027.20 
 
 2008.33 
 
 2I7O.28 
 
 2243.07 
 
 2316.75 
 
 2391-38 
 
 (2466.99 
 
 2543.64 
 
 2621.38 
 
 2700.27 
 
 59 
 
 60 
 
 2028.38 
 
 2099.53 
 
 2171.48 
 
 21244.29 
 
 2317.99 
 
 2392.63 
 
 2468.26 
 
 2544.93 
 
 2622.69 
 
 2701.60 
 
 60 
 
 SMITHSONIAN TABLES 
 
 313 
 
The Anti-Gudermannian. 
 
 od u 41 
 
 42 
 
 43 
 
 44 
 
 45 
 
 46 
 
 47 
 
 48 
 
 49 
 
 50 
 
 gdu 
 
 c/ 
 
 270 1 '.60 
 
 2781.71 
 
 2863.10 
 
 2945.81 
 
 3029.94 
 
 3H5.55 
 
 3202.71 
 
 329L53 
 
 3382.08 
 
 3474-47 
 
 tf 
 
 I 
 
 2702.92 
 
 2783.06 
 
 2864.46 
 
 2947.21 
 
 3031.35 
 
 3116.99 
 
 3204.18 
 
 3293.02 
 
 3383.61 
 
 3476.03 
 
 I 
 
 2 
 
 2704.25 
 
 2784.40 
 
 2865.83 
 
 2948.60 
 
 3032.77 
 
 3118.43 
 
 3205.65 
 
 3294.52 
 
 3385.13 
 
 3477-59 
 
 2 
 
 3 
 
 2705.57 
 
 2785.75 
 
 2667.20 
 
 2949.99 
 
 3034-18 
 
 3119.87 
 
 31207.12 
 
 3296.01 
 
 3386.66 
 
 3479- 14 
 
 3 
 
 4 
 
 2706.90 
 
 2787.09 
 
 2868.57 
 
 2951-38 
 
 3035.60 
 
 3121.31 
 
 3208.58 
 
 3297.51 
 
 3388.18 
 
 3480.70 
 
 4 
 
 5 
 
 2708.23 
 
 2788.44 
 
 2869.94 
 
 2952.77 
 
 3037.02 
 
 3122.75 
 
 3210.05 
 
 3299.01 
 
 3389.71 
 
 3482.26 
 
 5 
 
 6 
 
 2709.55 
 
 2789.79 
 
 2871.31 
 
 2954.16 
 
 3038.43 
 
 3124.19 
 
 3211.52 
 
 3300.51 
 
 3391.24 
 
 3483-82 
 
 6 
 
 7 
 
 2710.88 
 
 2791 . 14 
 
 2872.68 
 
 2955.56 
 
 3039.85 
 
 3125.63 
 
 3212.99 
 
 3302.00 
 
 3392.77 
 
 3485.38 
 
 7 
 
 8 
 
 2712.21 
 
 2792.49 
 
 2874-05 
 
 2956.95 
 
 3041.27 
 
 3127.08 
 
 3214.46 
 
 3303.50 
 
 3394.29 
 
 3486.94 
 
 8 
 
 9 
 
 2713.54 
 
 2793.84 
 
 2875-42 
 
 2958.34 
 
 3042.68 
 
 3128.52 
 
 3215.93 
 
 3305.00 
 
 3395.82 
 
 3488.50 
 
 9 
 
 10 
 
 2714.86 
 
 2795.19 
 
 2876.79 
 
 2959-74 
 
 3044.10 
 
 3129-96 
 
 3217.40 
 
 3306.50 
 
 3397-35 
 
 3490.06 
 
 10 
 
 ii 
 
 2716.19 
 
 2796.54 
 
 2878. 16 
 
 2961 . 13 
 
 3045.52 
 
 3131.41 
 
 3218.87 
 
 3308.00 
 
 3398.88 
 
 3491.62 
 
 ii 
 
 12 
 
 2717.52 
 
 2797.89 
 
 2879.53 
 
 2962.53 
 
 3046.94 
 
 3*132.85 
 
 3220.34 
 
 3309.50 
 
 3400.41 
 
 3493.18 
 
 12 
 
 13' 
 
 2718.85 
 
 2709.24 
 
 2880.90 
 
 2963.92 
 
 3048.36 
 
 3134.30 
 
 32211.82 
 
 3311.00 
 
 3401.04 
 
 3494.74 
 
 13 
 
 14 
 
 2720.18 
 
 2800.59 
 
 2882.28 
 
 2965.32 
 
 3049.78 
 
 3135.75 
 
 3223.29 
 
 3312.50 
 
 3403.47 
 
 3496.31 
 
 U 
 
 15 
 
 2721.51 
 
 2801.94 
 
 2883.65 
 
 2966.71 
 
 3051.20 
 
 3137.19 
 
 3224.76 
 
 3314.00 
 
 3405-00 
 
 3497.87 
 
 15 
 
 16 
 
 2722.84 
 
 2803.29 
 
 2885.02 
 
 2068. II 
 
 305-2.62 
 
 3138.64 
 
 3226.23 
 
 3315.50 
 
 3406.54 
 
 3499.43 
 
 16 
 
 17 
 
 2724.17 
 
 2804.64 
 
 2886.39 
 
 2969.50 
 
 3054.04 
 
 3140.08,3227.71 
 
 3-3-I7.00 
 
 3408.07 
 
 3501.00 
 
 17 
 
 18 
 
 2/25-50 
 
 2805.99 
 
 2887.77 
 
 2970.90 
 
 3055.46 
 
 3141.53 
 
 3229.18 
 
 33i8.5i 
 
 3409.60 
 
 3502.56 
 
 18 
 
 19 
 
 2726.83 
 
 2807.34 
 
 2889.14 
 
 2972.30 
 
 3056.88 
 
 3142.08 
 
 3230.66 
 
 3320.01 
 
 3411.14 
 
 3504.13 
 
 19 
 
 20 
 
 2728.17 
 
 2808.70 
 
 2890.52 
 
 2973.70 
 
 3058.31 
 
 3144.42 
 
 3232.13 
 
 3321.52 
 
 3412.67 
 
 3505.70 
 
 20 
 
 21 
 
 2729.50 
 
 2810.05 
 
 2891.89 
 
 2975.09 
 
 3059.73 
 
 3U5.87 
 
 3233.61 
 
 3323.02 
 
 3414.20 
 
 3507.26 
 
 21 
 
 22! 
 
 2730.83 
 
 2811.40 
 
 2893.27 
 
 2976.49 
 
 3061.15 
 
 3147.32 
 
 3235.08 
 
 3324.53 
 
 3415.74 
 
 3508.83 
 
 22 
 
 23 1 
 
 2732.16 
 
 2812.76 
 
 2894.64 
 
 2977.89 
 
 3062.58 
 
 31148.77 
 
 3236.56 
 
 3326.03 
 
 3417.28 
 
 3510.40 
 
 23 
 
 24 
 
 2733.50 
 
 2814.11 
 
 2896.02 
 
 2979.29 
 
 3064.00 
 
 3150.22 
 
 3238.04 
 
 3327.54 
 
 3418.81 
 
 35H.97 
 
 24 
 
 25 
 
 2734.83 
 
 2815.46 
 
 2897.40 
 
 2980.69 
 
 3065.42 
 
 3151.67 
 
 3239.52 
 
 3329.04 
 
 3420.35 
 
 3513.54 
 
 25 
 
 26 
 
 2736.16 
 
 2816.82 
 
 2898.77 
 
 2982.09 
 
 3066.85 
 
 3153.12 
 
 3240.09 
 
 3330.55 
 
 3421.89 
 
 35I5.IT 
 
 26 
 
 27 
 
 2/37.50 
 
 2818.17 
 
 2900.15 
 
 2983.49 
 
 3068.27 
 
 3154.57 
 
 3242.47 
 
 3332.06 
 
 3423-43 
 
 3516.68 
 
 27 
 
 28 
 
 2738.83 
 
 2819.53 
 
 2901.53 
 
 2984.89 
 
 3069.70 
 
 3156.03 
 
 3243.95 
 
 3333.56 
 
 3424.96 
 
 3518.25 
 
 28 
 
 29 
 
 2740.17 
 
 .2820.88 
 
 2902.91 
 
 2986.29 
 
 3071 . 13 
 
 3157.48 
 
 3245.43 
 
 3335.07 
 
 3426.50 
 
 3519.82 
 
 29 
 
 30 
 
 2741-50 
 
 2822.24 
 
 2904.28 
 
 2987.70 
 
 3072.55 
 
 3158.93 
 
 3246.91 
 
 3336.58 
 
 3428.04 
 
 3521.39 
 
 30 
 
 3i 
 
 2742.84 
 
 2823.60 
 
 2905.66 
 
 2989.10 
 
 3073.08 
 
 3160.38 
 
 3248.39 
 
 3338.09 
 
 3429.58 
 
 3522.96 
 
 3i 
 
 32 
 
 2744.17 
 
 2824.95 
 
 2907.04 
 
 2990.50 
 
 3075.41 
 
 3161.84 
 
 3249.87 
 
 3339.60 
 
 34-31.12 
 
 3524.54 
 
 32 
 
 33' 
 
 2745.51 
 
 2826.31 
 
 2908.42 
 
 2991.90 
 
 3076.84 
 
 3163.29 
 
 3251.35 
 
 334i.ii 
 
 3432.66 
 
 3526.li 
 
 33 
 
 34 
 
 2746.84 
 
 2827.67 
 
 2009.80 
 
 2993.31 
 
 3078.26 
 
 3164.74 
 
 3252.84 
 
 3342.62 
 
 3434.20 
 
 3527.68 
 
 34 
 
 35 
 
 2748.18 
 
 2829.03 
 
 2911.18 
 
 2994.71 
 
 3079.69 
 
 3166.20 
 
 3254-32 
 
 3344.14 
 
 3435-75 
 
 3529.26 
 
 35 
 
 36 
 
 2749.52 
 
 2830.39 
 
 2912.56 
 
 2906.12 
 
 3081.12 
 
 3167.65 
 
 3255.80 
 
 3345.65 
 
 3437-29 
 
 3530.83 
 
 36 
 
 37 
 
 2750.85 
 
 2831.74 
 
 2913.94 
 
 2997.52 
 
 3082.55 
 
 3169.11 
 
 3257.28 
 
 3347.16 
 
 3438.83 
 
 3532.41 
 
 37 
 
 38 
 
 2752.19 
 
 2833.10 
 
 2915.32 
 
 2998.93 
 
 3083.98 
 
 3170.57 
 
 3258.77 
 
 3348.67 
 
 3440.38 
 
 3533.99 
 
 38 
 
 39 
 
 2753.53 
 
 2834.46 
 
 2916.71 
 
 3000.33 
 
 3085.41 
 
 31172.02 
 
 31260.25 
 
 3350. 19 
 
 3441.92 
 
 3535.56 
 
 39 
 
 40 
 
 2754.87 
 
 2835.82 
 
 2918.09 
 
 3001.74 
 
 3086.84 
 
 3173.48 3261.74 
 
 3351.70 
 
 3443-47 
 
 3537.14 
 
 40 
 
 41 
 
 2756.21 
 
 2837.18 
 
 2919.47 
 
 3003.14 
 
 3088.27 
 
 3174.0413263.22 
 
 3-353.21 
 
 3445.01 
 
 3538.72 
 
 41 
 
 42 
 
 2757.55 
 
 2838.54 
 
 2920.85 
 
 3004.55 
 
 3089.70 
 
 3176.40 
 
 3264.71 
 
 3354-73 
 
 3446.56 
 
 3540.30 
 
 42 
 
 43 
 
 2758.89 
 
 2839.90 
 
 2922.24 
 
 3005.96 
 
 3091.14 
 
 3177.85 
 
 3266.19 
 
 3356.24 
 
 3448.10 
 
 3541.88 
 
 43 
 
 44 
 
 2760.23 
 
 2841.27 
 
 2923.62 
 
 3007.36 
 
 3092.57 
 
 3179.31 
 
 3267.68 
 
 3357.76 
 
 3449.65 
 
 3543-45 
 
 44 
 
 45 
 
 2761.57 
 
 2842.63 
 
 2925.01 
 
 3008.77 
 
 3094.00 
 
 3i8o.77 
 
 3269.17 
 
 3359.28 
 
 3451.20 
 
 3545.04 
 
 45 
 
 46 
 
 2762.91 
 
 2843.99 
 
 2926.39 
 
 3010.18 
 
 3095.43 
 
 3182.23 
 
 3270.65 
 
 3360.79 
 
 3452.75 
 
 3-546.62 
 
 46 
 
 47 
 
 2764.25 
 
 2845.35 
 
 2927.78 
 
 3011.59 
 
 3096.87 
 
 3183.69 3272.14 
 
 3362.31 
 
 3454.29 
 
 3548.20 
 
 47 
 
 48 
 
 2765.59 
 
 2846.71 
 
 2929.16 
 
 3013.00 
 
 3098.30 
 
 3185.15 3273.63 
 
 3363.83 
 
 3455.84 
 
 3549.78 
 
 48 
 
 49 
 
 2766.93 
 
 2848.08 
 
 2930.55 
 
 3014.41 
 
 3099.74 
 
 3l86.6l '3275. 12 
 
 3365.35 
 
 3457-39 
 
 3551.36 
 
 49 
 
 50 
 
 2768.27 
 
 2843.44 
 
 2931.93 
 
 3015.82 
 
 3101.17 
 
 3188.07 
 
 3276.61 
 
 3366.87 
 
 3458.94 
 
 3552.94 
 
 50 
 
 51 
 
 2769.62 
 
 2850.81 
 
 2933-32 
 
 3017.23 
 
 31102.60 
 
 3189.54 
 
 3278.10 
 
 3368.39 
 
 3460.49 
 
 3554-53 
 
 Si 
 
 52 
 
 2770.96 
 
 2852.17 
 
 2934-71 
 
 3018.64 
 
 3104.04 
 
 3191.00 3279.59 
 
 3369.91 
 
 3462.04 
 
 3556.li 
 
 52 
 
 53 
 
 2772.30 
 
 2853-53 
 
 2936.09 
 
 3020.05 
 
 3105.48 
 
 3-192.46 3281.08 
 
 337L43 
 
 3463.60 
 
 3557-70 
 
 53 
 
 54 
 
 2773.64 
 
 2854.90 
 
 2937.48 
 
 3021.46 
 
 3106.02 
 
 3193.92 3282.57 
 
 33712.95 
 
 3465.15 
 
 3559.28 
 
 54 
 
 55 
 
 2774.99 
 
 2856.26 
 
 2938.87 
 
 3022.87 
 
 3108.35 
 
 3195.39 
 
 3284.06 
 
 3374.47 
 
 3466.70 
 
 3560.87 
 
 55 
 
 56 
 
 2776.33 
 
 2857.63 
 
 2940.26 
 
 3024.29 
 
 3109.79 
 
 3196.85 
 
 3285.56 
 
 3375-99 
 
 3468.36 
 
 3562.45 
 
 56 
 
 57 
 
 2777.68 
 
 2858.99 
 
 2041.65 
 
 3025.70 
 
 3111.23 
 
 3198.32 
 
 3287.05 
 
 3377-51 
 
 34';.8i 
 
 3564.04 
 
 57 
 
 58 
 59 
 
 2779-02 
 2780.37 
 
 2860.36 
 2861.73 
 
 2043.04 
 2944.42 
 
 3027.11 
 3028.52 
 
 3112.67 
 3H4.IT 
 
 3199.7* 
 3201.25 
 
 3288,54 
 3290.04 
 
 3379-04 
 3380.56 
 
 3471.36 
 3472.02 
 
 3565.63 
 
 3567.22 
 
 58 
 59 
 
 60 
 
 2781.71 
 
 2863.10 
 
 2945.81 
 
 3029.94 
 
 3115.55 
 
 3202.71 
 
 3291.53 
 
 33&2.08 
 
 3474-47 
 
 3568.81 
 
 60 
 
 SMITHSONIAN TABLES 
 
The Anti-Gudermannian. 
 
 gdu 
 
 51 
 
 52 
 
 53 
 
 54 
 
 55 
 
 56 
 
 57 
 
 58 
 
 59 
 
 60 
 
 gdi 
 
 C/ 
 
 3568'.8i 
 
 3665.19 
 
 3763.76 
 
 3864.64 
 
 3967.97 
 
 4073.90 
 
 4182.62 
 
 4294.30 
 
 4409.14 
 
 4527.37 
 
 0' 
 
 I 
 
 3570.40 
 
 3666.82 
 
 3765.42 
 
 3866.34 
 
 3969.71 
 
 4075.69 
 
 4184.46 
 
 4296.19 
 
 4411.08 
 
 4529.37 
 
 I 
 
 2 
 
 3571-99 
 
 3668.44 
 
 3767.09 
 
 3868.04 
 
 397L46 
 
 4077-48 
 
 4186.29 
 
 4298.07 
 
 4413.03 
 
 453L37 
 
 2 
 
 3 
 
 3573.58 
 
 3670.07 
 
 3768.75 
 
 3869.74 
 
 3973.20 
 
 4079.27 
 
 4188.13 
 
 4299.96 
 
 4414.97 
 
 4533-37 
 
 3 
 
 4 
 
 3575-17 
 
 3671.70 
 
 3770.41 
 
 3871.45 
 
 3974-95 
 
 4081.06 
 
 41189.97 
 
 4301.85 
 
 4416.92 
 
 4535.38 
 
 4 
 
 5 
 
 3576.76 
 
 3673.32 
 
 3772.08 
 
 3873.15 
 
 3976.69 
 
 4082.86 
 
 4191.81 
 
 4303.74 
 
 4418.86 
 
 4537.38 
 
 5 
 
 6 
 
 3578.35 
 
 3674.95 
 
 3773.74 
 
 3874.86 
 
 3978.44 
 
 4084.65 
 
 4193.65 
 
 4305.64 
 
 4420.81 
 
 4539-39 
 
 6 
 
 7 
 
 3579-94 
 
 3676.58 
 
 3775.41 
 
 3876.56 
 
 3980. 19 
 
 4086.44 
 
 4195.49 
 
 4307.53 
 
 4422.76 
 
 4541.39 
 
 7 
 
 8 
 
 358i.54 
 
 3678.21 
 
 3777.08 
 
 3878.27 
 
 3981.94 
 
 4088.24 
 
 4197.33 
 
 4309. 4 
 
 4424.70 
 
 4543-40 
 
 g 
 
 9 
 
 3583.13 
 
 3679.84 
 
 3778.74 
 
 3879.98 
 
 3983.69 
 
 4000.03 
 
 4199.17 
 
 4311.32 
 
 4426.65 
 
 4545.41 
 
 9 
 
 10 
 
 3584.73 
 
 3681.47 
 
 3780.41 
 
 3881.68 
 
 3985.44 
 
 4091.83 
 
 4201 .02 
 
 4313.21 
 
 4428.60 
 
 4547.42 
 
 10 
 
 ii 
 
 3586.32 
 
 3683.10 
 
 3782.08' 
 
 3883.39 
 
 3987.19 
 
 4003.62 
 
 4202.87 
 
 43IS. II 
 
 4430.56 
 
 4549.43 
 
 ii 
 
 12 
 
 3587.92 
 
 3684.73 
 
 3783.75 
 
 3885.10 
 
 3988.94 
 
 4095.42 
 
 4204.71 
 
 4317.01 
 
 4432.51 
 
 4551.44' 
 
 12 
 
 13 
 
 3589.51 
 
 3686.36 
 
 3785.42 
 
 3886.81 
 
 3990.69 
 
 4097.22 
 
 4206.56 
 
 4318.91 
 
 4434.46 
 
 4553-45 
 
 13 
 
 14 
 
 359i.ii 
 
 3687.99 
 
 3787.09 
 
 3888.52 
 
 3992.45 
 
 4099.02 
 
 4208.41 
 
 4320.80 
 
 4436.42 
 
 4555.47 
 
 14 
 
 IS 
 
 3592.71 
 
 3689.63 
 
 3788.76 
 
 3890.23 
 
 3994 -0 
 
 4100.82 
 
 4210.26 
 
 4322.70 
 
 4438.37 
 
 4557.48 
 
 15 
 
 16 
 
 3594.30 
 
 3691.26 
 
 3790.43 
 
 3891.95 
 
 3995.96 
 
 4102.62 
 
 4212.10 
 
 4324-61 
 
 4440.33 
 
 4559.50 
 
 16 
 
 17 
 
 3595-90 
 
 3692.90 
 
 3792.10 
 
 3893.66 
 
 3997.71 
 
 4104.42 
 
 4213.95 
 
 4326.51 
 
 4442.29 
 
 4561.52 
 
 17 
 
 18 
 
 3597-50 
 
 3694.53 
 
 3793.78 
 
 3895.37 
 
 3999.47 
 
 4106.22 
 
 41215.80 
 
 4328.41 
 
 4444.24 
 
 4563.53 
 
 18 
 
 19 
 
 3599-10 
 
 3696.17 
 
 3795-45 
 
 3897.09 
 
 4001.22 
 
 4108.02 
 
 4217.66 
 
 4330.31 
 
 4446.20 
 
 4565.55 
 
 19 
 
 20 
 
 3600.70 
 
 3697.80 
 
 3797- 12 
 
 3898.80 
 
 4002.98 
 
 4109.82 
 
 4219.51 
 
 4332.22 
 
 4448.16 
 
 4567.57 
 
 20 
 
 21 
 
 3602.30 
 
 3699.44 
 
 3798.80 
 
 3900.52 
 
 4004.74 
 
 4111.63 
 
 4221.36 
 
 4334-12 
 
 4450. 12 
 
 4569.59 
 
 21 
 
 22 
 
 3603.90 
 
 3701.08 
 
 3800.47 
 
 3902.23 
 
 4006.50 
 
 4113.44 
 
 4223.22 
 
 4336.03 
 
 44512.09 
 
 4571.61 
 
 22 
 
 23 
 
 3605.50 
 
 3702.71 
 
 3802.15 
 
 3903. 95 
 
 4008.126 
 
 4115.24 
 
 4225.07 
 
 4337-94 
 
 4454.05 
 
 4573.64 
 
 23 
 
 24 
 
 3607.11 
 
 3704.35 
 
 3803.83 
 
 3905.67 
 
 4010.02 
 
 4117-05 
 
 4226.93 
 
 4339.84 
 
 4456.01 
 
 4575-66 
 
 24 
 
 25 
 
 3608.71 
 
 3705.99 
 
 3805.50 
 
 3907.38 
 
 4011.78 
 
 4118.85 
 
 4228.78 
 
 4341.75 
 
 4457.98 
 
 4577.69 
 
 25 
 
 26 
 
 3610.32 
 
 3707.63 
 
 3807.18 
 
 3909.10 
 
 4013.54 
 
 4120.66 
 
 4230.64 
 
 4343-66 
 
 4459.94 
 
 4579.71 
 
 26 
 
 27 
 
 3611.92 
 
 3709.27 
 
 3808.86 
 
 3910.82 
 
 4015.31 
 
 4122.47 
 
 4232.50 
 
 4345.57 
 
 4461.91 
 
 458i.74 
 
 .27 
 
 28 
 
 3613.52 
 
 3710.91 
 
 3810.54 
 
 3912.54 
 
 4017.07 
 
 4124.28 
 
 4234-36 
 
 4347.48 
 
 4463-88 
 
 4583.77 
 
 28 
 
 29 
 
 3615-13 
 
 3712.56 
 
 3812.22 
 
 3914.26 
 
 4018.84 
 
 4126.09 
 
 4236.22 
 
 4349.40 
 
 4465.85 
 
 4585.80 
 
 29 
 
 30 
 
 3616.74 
 
 3714.20 
 
 3813-90 
 
 39^5.99 
 
 4020.60 
 
 4127.90 
 
 4238.08 
 
 435L3I 
 
 4467-82 
 
 4587.83 
 
 30 
 
 3i 
 
 3618.34 
 
 3715.84 
 
 3815.58 
 
 3917.71 
 
 4022.37 
 
 4129.72 
 
 4239.04 
 
 4353.23 
 
 4469.79 
 
 4589.86 
 
 31 
 
 32 
 
 3619.95 
 
 3717.48 
 
 3817.27 
 
 3919.43 
 
 4024. 13 
 
 4I3H.53 
 
 4241.80 
 
 4355.14 
 
 4471.76 
 
 4591.89 
 
 32 
 
 33 
 
 3621.56 
 
 3719.13 
 
 3818.95 
 
 3921 . 16 
 
 4025.90 
 
 4133.34 
 
 4243.67 
 
 4357.06 
 
 4473-73 
 
 4593.92 
 
 33 
 
 34 
 
 3623.17 
 
 3720.77 
 
 3820.63 
 
 3922.88 
 
 4027.67 
 
 4i35.i6 
 
 4245.53 
 
 4358.97 
 
 4475.71 
 
 4595.96 
 
 34 
 
 35 
 
 3624.78 
 
 3722.42 
 
 3822.32 
 
 3924.61 
 
 4029.44 
 
 4136.97 
 
 4247.39 
 
 4360.89 
 
 4477.68 
 
 4598.00 
 
 35 
 
 36 
 
 3626.39 
 
 3724.06 
 
 3824.00 
 
 3926.33 
 
 4031.21 
 
 4138.79 
 
 4249.26 
 
 4362.81 
 
 4479-66 
 
 4600.03 
 
 36 
 
 37 
 
 3628.00 
 
 3725.71 
 
 3825.69 
 
 3928.06 
 
 4032.98 
 
 4140.61 
 
 4251.13 
 
 4364-73 
 
 4481.63 
 
 4602.07 
 
 37 
 
 38 
 
 3629.61 
 
 3727.36 
 
 3827.37 
 
 3929.79 
 
 4034.75 
 
 4142.42 
 
 4252.99 
 
 4366.65 
 
 4483.61 
 
 4604.11 
 
 38 
 
 39 
 
 3631.22 
 
 3729.01 
 
 3829.06 
 
 393L5I 
 
 4036.52 
 
 4144.24 
 
 4254.86 
 
 4368.57 
 
 4485.59 
 
 4606.15 
 
 39 
 
 40 
 
 3632.83 
 
 3730.66 
 
 3830.75 
 
 3933.24 
 
 4038.29 
 
 41146.06 
 
 4256.73 
 
 4370.50 
 
 4487.57 
 
 4608.19 
 
 40 
 
 4i 
 
 3634.44 
 
 373-2-30 
 
 3832.43 
 
 3934-97 
 
 4040.07 
 
 4147.88 
 
 4258.60 
 
 4372.42 
 
 4489.55 
 
 4610.23 
 
 41 
 
 42 
 
 3636.06 
 
 3733-95 
 
 3834.12 
 
 3936.70 
 
 4041.84 
 
 4149.70 
 
 4260.47 
 
 4374-34 
 
 4491.53 
 
 4612.27 
 
 42 
 
 43 
 
 3637.67 
 
 3735.6i 
 
 3835.81 
 
 3938.43 
 
 4043.61 
 
 4151.52 
 
 4262.34 
 
 4376.27 
 
 4493.51 
 
 4614.32 
 
 43 
 
 44' 
 
 3639.28 
 
 3737.26 
 
 3837.50 
 
 3040.16 
 
 4045.39 
 
 4153.35 
 
 4264.212 
 
 4378.20 
 
 4495 .'50 
 
 4616.36 
 
 44 
 
 45 
 
 3640.90 
 
 3738.91 
 
 3839. 19 
 
 3941.90 
 
 4047.17 
 
 4155.17 
 
 4266.09 
 
 4380. 12 
 
 4497.48 
 
 4618.41 
 
 45 
 
 46 
 
 3642.51 
 
 3740.56 
 
 3840.88 
 
 3943.63 
 
 4048.94 
 
 4157.00 
 
 4267.97 
 
 4382.05 
 
 4499-47 
 
 4620.45 
 
 46 
 
 47 
 
 3644.13 
 
 3742.21 
 
 3842.58 
 
 3945.36 
 
 4050.72 
 
 4158.82 
 
 4269.84 
 
 4383.98 
 
 4501.45 
 
 4622.50 
 
 47 
 
 48 
 
 3645.75 
 
 3743.87 
 
 3844.27 
 
 3947.10 
 
 4052.50 
 
 4160.65 
 
 4271.72 
 
 4385.91 
 
 4503.44 
 
 4624.55 
 
 48 
 
 49 
 
 3647.36 
 
 3745-52 
 
 3845.96 
 
 3948.83 
 
 4054.28 
 
 4162.47 
 
 4273.59 
 
 4387.84 
 
 4505.43 
 
 4626.60 
 
 49 
 
 50 
 
 3648.98 
 
 3747.18 
 
 3847.66 
 
 3950-57 
 
 4056.06 
 
 4164.30 
 
 4275.47 
 
 4389.77 
 
 4507.42 
 
 4628.65 
 
 50 
 
 51 
 
 3650.60 
 
 3748.83 
 
 3849.35 
 
 3952.31 
 
 4057.84 
 
 4166.13 
 
 4277.35 
 
 4391.70 
 
 4509.41 
 
 4630.71 
 
 5i 
 
 52 
 
 3652.22 
 
 3750.49 
 
 3851.05 
 
 3954.04 
 
 4059.62 
 
 4167.96 
 
 4279.23 
 
 4393.64 
 
 45'ii.40 
 
 4632.76 
 
 52 
 
 53 
 
 3653.84 
 
 3752.15 
 
 3852.75 
 
 3955.78 
 
 4061.41 
 
 4169.79 
 
 4281 . i i 
 
 4395.57 
 
 4513.39 
 
 4634-81 
 
 53 
 
 54 
 
 3655.46 
 
 3753.8o 
 
 3854.44 
 
 3957-52 
 
 4063.19 
 
 4171.62 
 
 4282.99 
 
 4397.51 
 
 4515.39 
 
 4636.87 
 
 54 
 
 55 
 
 3657.08 
 
 3755.46 
 
 3856. 14 
 
 3959.26 
 
 4064.97 
 
 4173.45 
 
 4284.87 
 
 4399.44 
 
 4517.38 
 
 4638.93 
 
 55 
 
 56 
 
 3658.70 
 
 3757-12 
 
 3857.84 
 
 3961.00 
 
 4066.76 
 
 4175.28 
 
 4286.76 
 
 4401.38 
 
 4519.38 
 
 4640.98 
 
 56 
 
 57 
 
 3660.32 
 
 3758.78 3859.54 
 
 3962.74 
 
 4068.54 
 
 4177.12 
 
 4288.64 
 
 4403.32 
 
 4521.37 
 
 4643.04 
 
 57 
 
 58 
 
 3661.95 
 
 3760.44 3861.24 
 
 3964.48 
 
 4070.33 
 
 41178.95 
 
 4290.53 
 
 4405-26 
 
 4523.37 
 
 4645.10 
 
 58 
 
 59 
 
 3663.57 
 
 3762.10 3862.94 
 
 3966.22 
 
 4072.12 
 
 4180.78 
 
 4292.41 
 
 4407.20 
 
 4525.37 
 
 4647.16 
 
 59 
 
 60 
 
 3665.19 
 
 3763.7613864.64 
 
 3967.97 
 
 4073.90 
 
 4182.62 
 
 4294.30 
 
 4409.14 
 
 4527.37 
 
 4649.23 
 
 60 
 
 SMITHSONIAN TABLES 
 
 315 
 
The Anti-Gudermannian. 
 
 gdu 
 
 61 
 
 62 
 
 63 
 
 64 
 
 65 
 
 66 67 
 
 68 
 
 69 
 
 70 
 
 gd u 
 
 o' 
 
 4649'-23 
 
 4774.98 4904.94 
 
 5039.42 
 
 5178.81 
 
 5323.5i| 5474.01 
 
 5630.82 
 
 5794.56 
 
 5965.92 
 
 Of 
 
 I 
 
 4651.29 
 
 4777. ii 4907. 14 
 
 3041.70 
 
 5181.18 
 
 5325.97!5476.57 
 
 5633.49 
 
 5797-35 
 
 5968.84 
 
 I 
 
 2 
 
 4653.35 
 
 4779. 251 4909. 35 
 
 5043.99 
 
 5183.54 
 
 5328.43 
 
 5479-13 
 
 5636.16 
 
 5800.14 
 
 5971.77 
 
 2 
 
 3 
 
 4655.42 
 
 4781.38 
 
 49H.55 
 
 5046.27 
 
 5185.91 
 
 5330.90 
 
 5481.69 
 
 5638.84 
 
 5802.94 
 
 5974.70 
 
 3 
 
 4 
 
 4657.49 
 
 4783.51 
 
 4913-76 5048.56 
 
 5188.29 
 
 5333.36 
 
 5484-26 
 
 5641-51 
 
 5805.74 
 
 5977.63 
 
 4 
 
 5 
 
 4659.55 
 
 4785.65 
 
 4915.97 
 
 5050.85 
 
 5190.66 
 
 5335.83 
 
 5486.83 
 
 5644.19 
 
 5808.54 5980.57 
 
 5 
 
 6 
 
 4661.62 
 
 4787.79 
 
 4918.18 
 
 5053.14 
 
 5193.03 
 
 5338.30 
 
 5489.40 
 
 5646.87 
 
 5811.34 
 
 5983.50 
 
 6 
 
 7 
 
 4663.69 
 
 4789.92 
 
 4920.39 
 
 5055.43 
 
 5I95.4I 
 
 5340.77 
 
 5491.97 
 
 5649.56 
 
 5814.15 
 
 5986.44 
 
 
 8 
 
 4665.76 
 
 4792.06 
 
 49212.60 
 
 5057.72 
 
 5197.79 
 
 5343.24 
 
 5494.54 
 
 5652.24 
 
 5816.95 
 
 5989.38 
 
 8 
 
 9 
 
 4667.83 
 
 4794-20 
 
 4924.81 
 
 5060.01 
 
 5200.17 
 
 5345.71 
 
 5497- ii 
 
 5654.93 
 
 5819.76 
 
 5992.33 
 
 9 
 
 10 
 
 4669.91 
 
 479^.34 
 
 4927.03 
 
 5062.30 
 
 5202.55 
 
 5348.18 
 
 5499.69 
 
 5657.61 
 
 5822.57 
 
 5995.27 
 
 10 
 
 ii 
 
 4671.98 
 
 4798.49 
 
 4929-24 
 
 5064.60 
 
 5204.93 
 
 5350.66 
 
 5502.27 
 
 5660.30 
 
 5825.39 
 
 5998.22 
 
 ii 
 
 12 
 
 4674-06 
 
 4800.63 
 
 4931.46 
 
 5066.90 
 
 5207.31 
 
 5353.14 
 
 5504.85 
 
 5663.00 
 
 5828.20 
 
 6001.17 
 
 V2 
 
 13 
 
 4676.13 
 
 4802.77 
 
 4933-68 
 
 5069.19 
 
 5209.70 
 
 5355.61 
 
 5507.43 
 
 5665.69 
 
 5831.02 
 
 6004.13 
 
 13 
 
 14 
 
 4678.21 
 
 4804.92 
 
 4935.90 
 
 5071.49 
 
 52112.08 
 
 5358.09 
 
 5510.01 
 
 5668.38 
 
 5833.84 
 
 6007.08 
 
 14 
 
 15 
 
 4680.29 
 
 4807.07 
 
 4938.12 
 
 5073.80 
 
 5214.47 
 
 5360.58 
 
 5512.60 
 
 5671 .08 
 
 5836.66 
 
 6010.04 
 
 15 
 
 16 
 
 4682.37 
 
 4809.21 
 
 4940-34 
 
 5076.10 
 
 5216.86 
 
 5363.06 
 
 55I5.I8 
 
 5673.78 
 
 5839.48 
 
 6013.00 
 
 16 
 
 17 
 
 4684.45 
 
 4811.36 
 
 4942.57 
 
 5078.40 
 
 5219.25 
 
 5365.55 
 
 5517.77 
 
 5676.48 
 
 5842.31 
 
 6015.96 
 
 17 
 
 18 
 
 4686.53 
 
 4813.51 
 
 4944-79 
 
 5080.71 
 
 5221.64 
 
 5368.03 
 
 5520.36 
 
 5679.19 
 
 5845.13 
 
 6018.93 
 
 18 
 
 19 
 
 4688.61 
 
 4815.67 
 
 4947.02 
 
 5083.01 
 
 5224.04 
 
 5370.52 
 
 5522.95 
 
 5681.89 
 
 5847.96 
 
 6021.90 
 
 19 
 
 20 
 
 4690.70 
 
 4817.82 
 
 4949-24 
 
 5085.32 
 
 52*26.43 
 
 5373.01 
 
 5525.55 
 
 5684.60 
 
 5850.79 
 
 6024.87 
 
 20 
 
 21 
 
 4692.78 
 
 4819.97 
 
 4951-47 
 
 5087.63 
 
 5228.83 
 
 5375-50 
 
 5528.14 
 
 5687.31 
 
 5853.63 
 
 6027.84 
 
 21 
 
 22 
 
 4694.87 
 
 4822.13 
 
 4953.70 
 
 5089.94 
 
 5231.23 
 
 5378.00 
 
 5530.74 
 
 5690.02 
 
 5856.47 
 
 6030.81 
 
 22 
 
 23 
 
 4696.96 
 
 4824.29 
 
 4955-94 
 
 5092.25 
 
 5233.63 
 
 5380.49 
 
 5533-34 
 
 5692.73 
 
 5859.31 
 
 6033.79 
 
 23 
 
 24 
 
 4699.05 
 
 4826.44 
 
 4958.17 
 
 5004.57 
 
 5236.03 
 
 5382.99 
 
 5535-94 
 
 5695.45 
 
 5862.15 
 
 6036.77 
 
 24 
 
 25 
 
 4701.14 
 
 4828.60 
 
 4960.40 
 
 5096.88 
 
 5238.43 
 
 5385.49 
 
 5538.55 
 
 5698.17 
 
 5864.99 
 
 6039.75 
 
 25 
 
 26 
 
 4703.23 
 
 4830.76 
 
 4962. 64 
 
 5099.20 
 
 5240.84 
 
 5387.99 
 
 5541.15 
 
 5700.89 
 
 5867.84 
 
 6042.74 
 
 26 
 
 27 
 
 4705.32 
 
 4832.93 
 
 4964.87 
 
 5101.52 
 
 5243-24 
 
 5390.49 
 
 5543.76 
 
 5703.6i 
 
 5870.69 
 
 6045.73 
 
 27 
 
 28 
 
 4707.41 
 
 4835.09 
 
 4967.11 
 
 5103.84 
 
 5245-65 
 
 5392.99 
 
 5546.37 
 
 5706.33 
 
 5873.54 
 
 6048.72 
 
 28 
 
 29 
 
 4709.51 
 
 4837.25 
 
 4969.35 
 
 5106.16 
 
 5248.06 
 
 5395.50 
 
 5548.98 
 
 5709-06 
 
 5876.39 
 
 6051.71 
 
 29 
 
 30 
 
 4711-60 
 
 4839.42 
 
 4971.59 
 
 5108.48 
 
 5250.47 
 
 5398.01 
 
 5551.59 
 
 57V. 78 
 
 5879.24 
 
 6054.70 
 
 30 
 
 31 
 
 4713.70 
 
 4841.58 
 
 4973.83 
 
 5110.80 
 
 5252.88 
 
 5400.52 
 
 5554.20 
 
 57I4.5I 
 
 5882.10 
 
 6057-70 
 
 31 
 
 32 4715.79 
 
 4843.75 
 
 4976.08 
 
 5113.13 
 
 5255.30 
 
 5403-03 
 
 5556.82 
 
 5717.25 
 
 5884.96 
 
 6060.70 
 
 32 
 
 33 4717.89 
 
 4845-92 
 
 4978.32 
 
 5H5.45 
 
 5257.71 
 
 5405.54 
 
 5559-44 
 
 5719-98 
 
 5887.82 
 
 6063.71 
 
 33 
 
 34 
 
 4719.99 
 
 4848.09 
 
 4980.57 
 
 5117.78 
 
 5260.13 
 
 5408.05 
 
 5562.06 5722.71 
 
 5890.68 
 
 6066.71 
 
 34 
 
 35 
 
 4722.09 
 
 4850.26 
 
 4982.82 
 
 5120.11 
 
 5262.55 
 
 5410.57 
 
 5564.68 
 
 5725.45 
 
 5893.55 
 
 6069.71 
 
 35 
 
 36 
 
 4724.19 
 
 4852.43 
 
 4985-06 
 
 5122.44 
 
 5264.97 
 
 54i3.o8 
 
 5567.30 
 
 5728.19 
 
 5896.41 
 
 6072.72 
 
 36 
 
 37 
 
 4726.30 
 
 4854.61 
 
 4987. 3* 
 
 5124.77 
 
 5267.39 
 
 5415.60 
 
 5569.93 
 
 5730.93 
 
 5899.28 
 
 6075.73 
 
 37 
 
 38 
 
 4728.40 
 
 4856.78 
 
 4989-56 
 
 5127.11 
 
 5269.81 
 
 5418.12 
 
 5572.55 
 
 5733.68 
 
 5902.15 
 
 6078.75 
 
 38 
 
 39 
 
 4730.51 
 
 4858.96 
 
 4991.82 
 
 5129.44 
 
 5272.23 
 
 5420.64 
 
 5575.18 
 
 5736.42 
 
 5905-03 
 
 6081.76 
 
 39 
 
 40 
 
 4732.61 
 
 4861.13 
 
 4994.07 
 
 3131.78 
 
 5274.66 
 
 5423.17 
 
 5577.8i 
 
 5739.17 
 
 5907.90 
 
 6084.78 
 
 40 
 
 41 
 
 4734.72 
 
 4863.31 
 
 4996.32 
 
 5i34.li 
 
 5277.09 
 
 5425.69 
 
 5580.44 
 
 5741.92 
 
 5910.78 
 
 6087.81 
 
 41 
 
 42 
 
 4736.83 
 
 4865.49 
 
 4998-58 
 
 5136.45 
 
 5279.52 
 
 5428.22 
 
 5583.08 
 
 5744.67 
 
 5913.67 
 
 6090.83 
 
 42 
 
 43 
 
 4738.94 
 
 4867.67 
 
 5000.84 
 
 5H38.79 
 
 5281.95 
 
 5430.75 
 
 5585.71 
 
 5747.43 
 
 5916.55 
 
 6093.86 
 
 43 
 
 44 
 
 4741.05 
 
 4869.86 
 
 5003.10 
 
 5141.14 
 
 5284.38 
 
 5433.28 
 
 5588.35 
 
 5750.18 
 
 5919.44 
 
 6096.89 
 
 44 
 
 45 
 
 4743.16 
 
 4872.04 
 
 5005.36 
 
 5143.48 
 
 5286.82 
 
 5435.8i 
 
 5590.09 
 
 5752.94 
 
 5922.32 
 
 6099.92 
 
 45 
 
 46 
 
 4745.28 
 
 4874-22 
 
 5007.62 
 
 5145.83 
 
 5289.25 
 
 5438.35 
 
 5593.64 
 
 5755-70 
 
 5925.22 
 
 6102.95 
 
 46 
 
 47 4747-39 
 
 4876.41 
 
 5009.88 
 
 5148.17 
 
 5291.69 
 
 5440.88 
 
 5596.28 
 
 5758.46 
 
 5928.11 
 
 6105.99 
 
 47 
 
 48 4749.51 
 
 4878.60 
 
 5012.15 
 
 5150.52 
 
 5294.13 
 
 5443.42 
 
 5598.93 
 
 5761.23 
 
 5931.00 
 
 6109.03 
 
 48 
 
 49 4751.63 
 
 4880.79 
 
 5014-41 
 
 5152.87 
 
 5296.57 
 
 5445.96 
 
 5601.57 
 
 5763.99 
 
 5933-90 
 
 6112.07 
 
 49 
 
 50 4753-74 
 
 4882.98 
 
 5016.68 
 
 5155.22 
 
 5299.01 
 
 5448.50 
 
 5604.22 
 
 5766.76 
 
 5936.80 
 
 6115.12 
 
 50 
 
 51 4755-86 
 
 4885.17 
 
 5018.94 
 
 5157.57 
 
 5301-45 
 
 5451.05 
 
 5606.87 
 
 5769.53 
 
 5939.70 
 
 6118.16 
 
 51 
 
 52 4757.98 
 
 4887.36 
 
 5021.21 
 
 5159.93 
 
 5303.90 
 
 5453.59 
 
 5609.53 
 
 5772.31 
 
 5942.61 
 
 6l2I. 21 
 
 52 
 
 53 4760.10 
 
 4889.55 
 
 5023.48 
 
 5162.28 
 
 5306.34 
 
 5456.14 
 
 5612.18 
 
 5775.08 
 
 5945.51 
 
 6124.26 
 
 53 
 
 54 4762.23 
 
 4891.75 
 
 5025.76 
 
 5164.64 
 
 5308.79 
 
 5458.68 
 
 5614.84 
 
 5777-86 
 
 5948.42 
 
 6127.32 
 
 54 
 
 55 4764.35 
 
 4893.94 
 
 5028.03 
 
 5167.00 
 
 53H.24 
 
 5461.23 
 
 5617-50 
 
 5780.64 
 
 5951.33 
 
 6130.38 
 
 55 
 
 56 4766.47 
 
 4896.14 
 
 5030.30 
 
 5169.36 
 
 5313.69 
 
 5463.78 
 
 5620.16 
 
 5783.42 
 
 5954.24 
 
 6133.44 
 
 56 
 
 57 4768.60 
 
 4898.34 
 
 5032.58 
 
 5171.72 
 
 53I6.I5 
 
 5466.34 
 
 5622.82 
 
 5786.20 
 
 5957.16 
 
 6136.50 
 
 57 
 
 58 4770.73 
 
 4900.54 
 
 5034.86 
 
 5174.08 
 
 53i8.6o 
 
 5468.89 
 
 5625.49 
 
 5788.98 
 
 so^o.oS 
 
 6139.56 
 
 58 
 
 59 4772.86 
 
 4902.74 5037.14 
 
 5176.44 
 
 5321.06 
 
 5471.45 
 
 5628. 15 
 
 579L77 
 
 5963.00 
 
 6142.63 
 
 59 
 
 60 14774.98 
 
 4004.9415039.42 
 
 5178.81 
 
 5323.51 5474.01 
 
 5630.82 
 
 5794-56 
 
 5965-92 
 
 6145.70 
 
 60 
 
 SMITHSONIAN TABLES 
 
 316 
 
The Anti-Gudermannian. 
 
 gdu 
 
 71 
 
 72 
 
 73 
 
 74 
 
 75 
 
 76 
 
 77 
 
 78 
 
 79 
 
 80 
 
 gdu| 
 
 C/ 
 
 6i45'-70 
 
 6334.84 
 
 6534.42 
 
 6745.74 
 
 6970.34 
 
 7210.07 
 
 7467.21 
 
 7744-57 
 
 8045.71 
 
 8375.20 
 
 0' 
 
 I 
 
 6148.77 
 
 6338.08 
 
 6537.85 
 
 6749.37 
 
 6974.20 
 
 7214.20 
 
 7471.66 
 
 7749.38 
 
 8050.95 
 
 8380.96 
 
 I 
 
 2 
 
 6151.85 
 
 6341.32 
 
 6541.27 
 
 6753.01 
 
 6978.07 
 
 7218.35 
 
 7476.11 
 
 7754-20 
 
 8056.20 
 
 8386.73 
 
 2 
 
 3 
 
 6154.93 
 
 6344-56 
 
 6544.70 
 
 6756.64 
 
 6981.95 
 
 7222.49 
 
 7480.57 
 
 7759-02 
 
 8061.46 
 
 8392.52 
 
 3 
 
 4 
 
 6158.01 
 
 6347.81 
 
 6548.13 
 
 6760.28 
 
 6985-83 
 
 7226.64 
 
 7485.03 
 
 7763.86 
 
 8066.73 
 
 8398.31 
 
 4 
 
 5 
 
 6161.09 
 
 6351.06 
 
 6551.57 
 
 6763.93 
 
 6989.71 
 
 7230.80 
 
 7489-50 
 
 7768.70 
 
 8072.01 
 
 8404.11 
 
 5 
 
 6 
 
 6164.18 
 
 6354.31 
 
 6555-01 
 
 6767.58 
 
 6993.60 
 
 7234.96 
 
 7493.98 
 
 7773-55 
 
 8077.29 
 
 8409.92 
 
 6 
 
 7 
 
 6167.27 
 
 6357.56 
 
 6558.45 
 
 6771.23 
 
 6997.49 
 
 7239-12 
 
 7498.46 
 
 7778.40 
 
 8082.58 
 
 8415.74 
 
 7 
 
 8 
 
 6170.36 
 
 6360.82 
 
 6561.89 
 
 6774.89 
 
 7001.38 
 
 7243.29 
 
 7502.95 
 
 7783.26 
 
 8087.88 
 
 8421.57 
 
 8 
 
 9 
 
 6i73.45 
 
 6364.08 
 
 6565.34 
 
 6778.55 
 
 7005.28 
 
 7247.47 
 
 7507.44 
 
 7788.12 
 
 8093-19 
 
 8427.42 
 
 9 
 
 10 
 
 6176.55 
 
 6367.35 
 
 6568.79 
 
 6782.21 
 
 7009.19 
 
 7251.65 
 
 7511.94 
 
 7793.00 
 
 8098.51 
 
 8433.27 
 
 10 
 
 II 
 
 6179.65 
 
 6370.61 
 
 6572.25 
 
 6785.88 
 
 7013.10 
 
 7255.83 
 
 7516.45 
 
 7797.88 
 
 8103.83 
 
 8439.13 
 
 ii 
 
 12 
 
 6182.75 
 
 6373.88 
 
 6575.70 
 
 6789.55 
 
 7017.01 
 
 7260.02 
 
 7520.96 
 
 7802.76 
 
 8109.17 
 
 8445.00 
 
 12 
 
 13 
 
 6185.85 
 
 6377-16 
 
 6579. 16 
 
 6793.22 
 
 7020.93 
 
 7264.22 
 
 7525.47 
 
 7807.66 
 
 8114.51 
 
 8450.88 
 
 13 
 
 14 
 
 6188.96 
 
 6380.43 
 
 6582.63 
 
 6796.90 
 
 7024.85 
 
 7268.42 
 
 7530.00 
 
 7812.56 
 
 8119.86 
 
 8456.77 
 
 14 
 
 15 
 
 6192.07 
 
 6383.71 
 
 6586.10 
 
 6800.58 
 
 7028.77 
 
 7272.62 
 
 7534.53 
 
 7817.46 
 
 8125.212 
 
 8462.67 
 
 15 
 
 16 
 
 6195 . 18 
 
 6386.99 
 
 6589.57 
 
 6804.27 
 
 7032.70 
 
 7276.83 
 
 7539.06 
 
 7822.38 
 
 8130.58 
 
 8468.58 
 
 16 
 
 17 
 
 6198.30 
 
 6390.28 
 
 6593.05 
 
 6807.96 
 
 7036.64 
 
 7281.05 
 
 7543.60 
 
 7827.30 
 
 8135.95 
 
 8474.50 
 
 17 
 
 18 
 
 6201.42 
 
 6393.57 
 
 6596.52 
 
 6811.65 
 
 7040.58 
 
 7285.27 
 
 7548. 15 
 
 7832.23 
 
 8141.33 
 
 8480.43 
 
 18 
 
 19 
 
 6204.54 
 
 6396.86 
 
 6600.01 
 
 6815.35 
 
 7044.52 
 
 7289.49 
 
 7552.70 
 
 7837.16 
 
 8146.72 
 
 8486.37 
 
 19 
 
 20 
 
 6207.66 
 
 6400.15 
 
 6603-49 
 
 6819.05 
 
 7048.47 
 
 7293.72 
 
 7557.26 
 
 7842.10 
 
 8152.12- 
 
 8492.32 
 
 20 
 
 121 
 
 6210.78 
 
 6403.44 
 
 6606.98 
 
 6822.75 
 
 7052.42 
 
 7297.96 
 
 7561.82 
 
 7847.05 
 
 8157.53 
 
 8498.28 
 
 21 
 
 22 
 
 6213.01 
 
 6406.74 
 
 6610.47 
 
 6826.46 
 
 7056.37 
 
 7302.20 
 
 7566.39 
 
 7852.01 
 
 8162.95 
 
 8504.25 
 
 22 
 
 23 
 
 6217.04 
 
 64110.05 
 
 6613.96 
 
 6830.18 
 
 7060.33 
 
 7306.44 
 
 7570.96 
 
 7856.97 
 
 8168.37 
 
 8510.23 
 
 23 
 
 24 
 
 6220. 1 8 
 
 6413-35 
 
 6617.46 
 
 6833-89 
 
 7064.30 
 
 7310.69 
 
 7575-54 
 
 7861.94 
 
 8173.80 
 
 8516.22 
 
 24 
 
 25 
 
 6223.31 
 
 6416.66 
 
 6620.97 
 
 6837.61 
 
 7068.27 
 
 7314.95 
 
 7580.13 
 
 7866.91 
 
 8179-24 
 
 8522.22 
 
 25 
 
 26 
 
 6226.45 
 
 6419.97 
 
 6624.47 
 
 6841.34 
 
 7072.24 
 
 7319.21 
 
 7584.72 
 
 7871.90 
 
 8184.69 
 
 8528.23 
 
 26 
 
 27 
 
 6229.59 
 
 6423.29 
 
 6627.98 
 
 6845.07 
 
 7076.22 
 
 7323.47 
 
 7589.^2 
 
 7876.89 
 
 8190.15 
 
 8534.26 
 
 27 
 
 28 
 
 6232.74 
 
 6426.61 
 
 6631.49 
 
 6848.80 
 
 7080.20 
 
 7327.74 
 
 7593.93 
 
 7881.89 
 
 8195.61 
 
 8540.29 
 
 28 
 
 29 
 
 6235-89 
 
 6429.93 
 
 6635.01 
 
 6852.53 
 
 7084.19 
 
 7332.02 
 
 7598.54 
 
 7886.89 
 
 8201.09 
 
 8546.33 
 
 129 
 
 30 
 
 6239.04 
 
 6433-25 
 
 6638.53 
 
 6856.27 
 
 7088.18 
 
 7336.30 
 
 7603.16 
 
 7891.91 
 
 8206.57 
 
 8552.38 
 
 30 
 
 31 
 
 6242.19 
 
 6436.58 
 
 6642.05 
 
 6860.02 
 
 7092.18 
 
 7340.55 
 
 7607-78 
 
 7896.93 
 
 8212.06 
 
 8558.45 
 
 31 
 
 32 
 
 6245.35 
 
 6439.91 
 
 6645.58 
 
 6863.77 
 
 7096.18 
 
 7344.88 
 
 7612.41 
 
 7901.95 
 
 8217.56 
 
 8564.52 
 
 32 
 
 33 
 
 6248.50 
 
 6443.24 
 
 6649.11 
 
 6867.52 
 
 7100.18 
 
 7349.18 
 
 7617.04 
 
 7906.98 
 
 8223.07 
 
 8570.61 
 
 33 
 
 34 
 
 6251.67 
 
 6446.58 
 
 6652.64 
 
 6871.27 
 
 7104.19 
 
 7353.48 
 
 7621.68 
 
 7912.03 
 
 8228.59 
 
 8576.70 
 
 34 
 
 35 
 
 6254-83 
 
 6449-92 
 
 6656.18 
 
 6875-03 
 
 7108.21 
 
 7357.79 
 
 7626.33 
 
 7917.08 
 
 8234.12 
 
 8582.81 
 
 35 
 
 36 
 
 6258.00 
 
 6453.26 
 
 6659.72 
 
 6878.80 
 
 7112.23 
 
 7362.10 
 
 7630.99 
 
 7922.13 
 
 8239.66 
 
 8588.93 
 
 36 
 
 37 
 
 6261.17 
 
 6456.61 
 
 6663.26 
 
 6882.56 
 
 7116.25 
 
 7366.42 
 
 7635.65 
 
 7927.19 
 
 8245.20 
 
 8595.06 
 
 37 
 
 38 
 
 6264.34 
 
 6459.95 
 
 6666.81 
 
 6886.34 
 
 7120.28 
 
 7370.74 
 
 7640.31 
 
 7932.26 
 
 8250.75 
 
 8601.20 
 
 38 
 
 39 
 
 6267.51 
 
 6463.31 
 
 6670.36 
 
 6890.11 
 
 7124.31 
 
 7375.07 
 
 7644.98 
 
 7937-34 
 
 8256.31 
 
 8607.35 
 
 39 
 
 40 
 
 6270.69 
 
 6466.66 
 
 6673.91 
 
 6893-89 
 
 7128.35 
 
 7379.40 
 
 7649.66 
 
 7942.43 
 
 8261.88 
 
 8613.51 
 
 40 
 
 41 
 
 6273.87 
 
 6470.02 
 
 6677.47 
 
 6897.68 
 
 7132.39 
 
 7383.74 
 
 7654.35 
 
 7947.52 
 
 8267.46 
 
 8619.68 
 
 4i 
 
 42 
 
 6277.05 
 
 6473.38 
 
 6681.03 
 
 6901.46 
 
 7136.43 
 
 7388.08 
 
 7659.04 
 
 7952.62 
 
 8273.05 
 
 8625.86 
 
 42 
 
 43 
 
 6280.24 
 
 6476.74 
 
 6684.59 
 
 6905.25 
 
 7140.48 
 
 7392.43 
 
 7663.74 
 
 7957.72 
 
 8278.65 
 
 8632.05 
 
 43 
 
 44 
 
 6283.43 
 
 6480.11 
 
 6688.16 
 
 6909.05 
 
 7144.54 
 
 7396.79 
 
 7668.44 
 
 7962.84 
 
 8284.25 
 
 8638.26 
 
 44 
 
 45 
 
 6286.62 
 
 6483.48 
 
 6691.73 
 
 6912.85 
 
 7148.60 
 
 7401.15 
 
 7673.15 
 
 7967.96 
 
 8289.87 
 
 8644-47 
 
 45 
 
 46 
 
 6289.82 
 
 6486.86 
 
 6695-31 
 
 6916.65 
 
 7152.67 
 
 7405.51 
 
 7677.87 
 
 7973.09 
 
 8295.49 
 
 8650.70 
 
 46 
 
 47 
 
 6293.01 
 
 6490.23 
 
 6698.89 
 
 6920.46 
 
 7156.74 
 
 7409.88 
 
 7682.59 
 
 7978.23 
 
 8301 . 12 
 
 8656.94 
 
 47 
 
 48 
 
 6296.21 
 
 6493.61 
 
 6702.47 
 
 6924.27 
 
 7160.81 
 
 7414. ,26 
 
 7687.32 
 
 7983.37 
 
 8306.77 
 
 8663.19 
 
 48 
 
 49 
 
 6299.42 
 
 6497.00 
 
 6706.06 
 
 6928.09 
 
 7164.89 
 
 7418.64 
 
 7692.05 
 
 7988.52 
 
 8312.42 
 
 8669.45 
 
 49 
 
 50 
 
 6302.62 
 
 6500.38 
 
 6709.65 
 
 6931-91 
 
 7168.97 
 
 7423.03 
 
 7696.79 
 
 7993.68 
 
 8318.08 
 
 8675.72 
 
 50 
 
 51 
 
 6305.83 
 
 6503.77 
 
 6713.24 
 
 6935.73 
 
 7173.05 
 
 7427.42 
 
 7701.54 
 
 7998.85 
 
 8323.75 
 
 8682.00 
 
 51 
 
 52 
 
 6309.04 
 
 6507.17 
 
 6716.84 
 
 6939.56 
 
 7177.15 
 
 7431.82 
 
 7706.30 
 
 8004.03 
 
 8329-43 
 
 8688.29 
 
 52 
 
 53 
 
 6312.26 
 
 6510.56 
 
 6720.44 
 
 6943.40 
 
 7181.25 
 
 7436.22 
 
 7711.06 
 
 8009.21 
 
 8335.12 
 
 8694.60 
 
 53 
 
 54 
 
 6315.48 
 
 6513.96 
 
 6724.04 
 
 6947.23 
 
 7185.35 
 
 7440.63 
 
 7715.63 
 
 8014.40 
 
 8340.82 
 
 8700.92 
 
 54 
 
 55 
 
 6318.70 
 
 6517.36 
 
 6727.65 
 
 6951.07 
 
 7189.46 
 
 7445-05 
 
 7720.60 
 
 8019,60 
 
 8346.52 
 
 8707.25 
 
 55 
 
 56 
 
 6321.92 
 
 6520.77 
 
 6731.26 
 
 6954.92 
 
 7193.57 
 
 7449.47 
 
 7725.38 
 
 8024. 81 
 
 8352.24 
 
 8713.59 
 
 56 
 
 57 
 
 6325.14 
 
 65124.18 
 
 6734.88 
 
 6958.77 
 
 7197.69 
 
 7453.89 
 
 7730.17 
 
 8030.02 
 
 8357.96 
 
 8719.94 
 
 57 
 
 58 
 
 6328.37 
 
 6527.59 
 
 6738.50 
 
 6962.62 
 
 7201.81 
 
 7458.33 
 
 7734.96 
 
 8035.24 
 
 8363-70 
 
 8726.30 
 
 58 
 
 59 
 
 6331.61 
 
 6531.01 
 
 6742.12 
 
 6066.48 
 
 7205.04 
 
 7462.76 
 
 7739.76 
 
 8040.47 
 
 8369.44 
 
 8732.68 
 
 59 
 
 60 
 
 6334.84 
 
 6534.42 
 
 6745.74 
 
 6970.34 
 
 7210.07 
 
 7467-21 
 
 7744-57 
 
 8045.71 
 
 8375.20 
 
 8739.06 
 
 60 
 
 SMITHSONIAN TABLES 
 
 317 
 
The Anti-Gudermaimian. 
 
 gd u 
 
 81 
 
 82 
 
 83 
 
 84 
 
 85 
 
 86 
 
 87 
 
 88 
 
 89 
 
 gd u 
 
 <y 
 
 8739'.o6 
 
 9145.46 
 
 9605.82 
 
 10136.89 
 
 10764.62 
 
 11532.52 
 
 12522.11 
 
 13916.43 
 
 16299.56 
 
 O' 
 
 I 
 
 8745-46 
 
 9152.65 
 
 9614.03 
 
 10146. 4^ 
 
 10776.11 
 
 11546.88 
 
 12541.27 
 
 13945.20 
 
 16357.34 
 
 I 
 
 2 
 
 8751.87 
 
 9159.86 
 
 9622.27 
 
 10156.07 
 
 10787.65 
 
 11561.31 
 
 12560.54 
 
 13974-22 
 
 16416.11 
 
 2 
 
 3 
 
 8758.29 
 
 9167.08 
 
 9630.52 
 
 10165.70 
 
 10799.22 
 
 11575.80 
 
 12579.91 
 
 14003.48 
 
 16475.90 
 
 3 
 
 4 
 
 8764.73 
 
 9174.32 
 
 9638.80 
 
 IOI75.37 
 
 10810.82 
 
 11590.34 
 
 12599.40 
 
 14033-00 
 
 16536.76 
 
 4 
 
 5 
 
 8771.17 
 
 9181.57 
 
 9647-09 
 
 10185.05 
 
 10822.47 
 
 11604.95 
 
 12619.00 
 
 14062.77 
 
 16598.69 
 
 5 
 
 6 
 
 8777.63 
 
 9188.84 
 
 9655.40 
 
 IOI94-77 
 
 10834. 16 
 
 11619.62 
 
 12638.70 
 
 14092.80 
 
 16661.78 
 
 6 
 
 7 
 
 8784.10 
 
 9196.13 
 
 0663.74 
 
 10204.51 
 
 10845.89 
 
 11634.36 
 
 12658.53 
 
 14123.09 
 
 16726.04 
 
 7 
 
 8 
 
 8790.58 
 
 9203.42 
 
 9672.09 
 
 10214.28 
 
 10857-65 
 
 11649.16 
 
 12678.46 
 
 14153.66 
 
 16791.53 
 
 8 
 
 9 
 
 8797.08 
 
 9210.74 
 
 9680.47 
 
 10224.08 
 
 10869.46 
 
 11664.02 
 
 12698.52 
 
 14184.49 
 
 16858.29 
 
 9 
 
 10 
 
 8803.58 
 
 9218.07 
 
 9688.86 
 
 10233.90 
 
 10881.31 
 
 11678.94 
 
 12718.69 
 
 14215.61 
 
 16926.36 
 
 10 
 
 ii 
 
 8810.10 
 
 9225.41 
 
 9697.28 
 
 10243.75 
 
 10893.20 
 
 11693.93 
 
 12738.98 
 
 14247.01 
 
 16995-81 
 
 ii 
 
 12 
 
 8816.63 
 
 9232.77 
 
 9705.71 
 
 10253.64 
 
 10905.13 
 
 11708.99 
 
 12759.39 
 
 14278.70 
 
 17066.70 
 
 12 
 
 13 
 
 8823.17 
 
 9240.15 
 
 97H.I7 
 
 10263.54 
 
 10917.10 
 
 11724.11 
 
 12779.92 
 
 14310.68 
 
 17139.09 
 
 13 
 
 H 
 
 8829.73 
 
 9247.54 
 
 9722.64 
 
 10273.48 
 
 10929.11 
 
 H739.30 
 
 12800.58 
 
 14342.97 
 
 17213-03 
 
 14 
 
 15 
 
 8836.30 
 
 9254.95 
 
 9731 . 14 
 
 10283.45 
 
 10941.17 
 
 H754.56 
 
 12821.36 
 
 14375.56 
 
 17288.57 
 
 15 
 
 16 
 
 8842.88 
 
 9262.37 
 
 9739-66 
 
 10293.45 
 
 10953-26 
 
 11769.88 
 
 12842.26 
 
 14408.46 
 
 17365.83 
 
 16 
 
 17 
 
 8849.47 
 
 9269.81 
 
 9748.20 
 
 10303.47 
 
 10965.40 
 
 11785.27 
 
 12863.30 
 
 14441.68 
 
 17444.87 
 
 17 
 
 18 
 
 8856.07 
 
 9277.27 
 
 9756.76 
 
 10313-53 
 
 T0977.59 
 
 11800.73 
 
 12884.46 
 
 H475.23 
 
 17525.77 
 
 18 
 
 19 
 
 8862.69 
 
 9284.74 
 
 9765.34 
 
 10323.61 
 
 10089.81 
 
 11816.26 
 
 12905.75 
 
 14509- 10 
 
 17608.63 
 
 19 
 
 20 
 
 8869.32 
 
 9292.23 
 
 9773-94 
 
 10333.72 
 
 [1002.08 
 
 11831.87 
 
 12927.18 
 
 I4543.3I 
 
 17693-49 
 
 20 
 
 21 
 
 8875-96 
 
 9299.73 
 
 9782.57 
 
 10343-85 
 
 11014.40 
 
 11847.54 
 
 12948.74 
 
 14577.87 
 
 17780.53 
 
 21 
 
 22 
 
 8882.62 
 
 9307.25 
 
 9791.21 
 
 10354-03 
 
 11026.75 
 
 11863.28 
 
 12970.44 
 
 14612.78 
 
 17869.83 
 
 22 
 
 23 
 
 8889.29 
 
 93I4.79 
 
 9799-88 
 
 10364.24 
 
 11039.15 
 
 11879.10 
 
 12092.27 
 
 14648.04 
 
 17961.51 
 
 23 
 
 24 
 
 8895.97 
 
 9322.34 
 
 9808.57 
 
 10374.47 
 
 11051.60 
 
 11894.99 
 
 13014-25 
 
 14683.67 
 
 18055.70 
 
 24 
 
 25 
 
 8902.66 
 
 9329.91 
 
 9817.28 
 
 10384-73 
 
 11064.09 
 
 11910.95 
 
 13036.36 
 
 14719.67 
 
 18152.55 
 
 25 
 
 26 
 
 8909.37 
 
 9337-49 
 
 9826.02 
 
 10395.03 
 
 11076.63 
 
 11926.09 
 
 13058.62 
 
 14756.05 
 
 18252.20 
 
 26 
 
 27 
 
 8916.09 
 
 9345-10 
 
 0834.77 
 
 10405.35 
 
 11089.21 
 
 11943.10 
 
 13081.02 
 
 14792.83 
 
 18354.83 
 
 27 
 
 28 
 
 8922.82 
 
 9352-72 
 
 0843.55 
 
 10415.71 
 
 11101.84 
 
 11959.29 
 
 13103.58 
 
 14830.00 
 
 18460.62 
 
 28 
 
 29 
 
 8929.57 
 
 9360.35 
 
 0852.35 
 
 10426.09 
 
 11114-52 
 
 H975.55 
 
 13126.27 
 
 14867.57 
 
 18569.76 
 
 29 
 
 30 
 
 8936.33 
 
 9368.00 
 
 9861.17 
 
 10436.51* 
 
 11127.24 
 
 11991.89 
 
 13149.12 
 
 14905-56 
 
 18682.49 
 
 30 
 
 31 
 
 8943.10 
 
 9375-67 
 
 9870.02 
 
 10446.96 
 
 11140.01 
 
 12008.31 
 
 13172.13 
 
 14943.08 
 
 18799.03 
 
 31 
 
 32 
 
 8949.88 
 
 93*83.36 
 
 9878.88 
 
 10457.44 
 
 11152.82 
 
 12024.81 
 
 13195.28 
 
 14982.83 
 
 18919.67 
 
 32 
 
 33 
 
 8956.68 
 
 9391.06 
 
 9887.77 
 
 10467.95 
 
 11165.69 
 
 12041.39 
 
 13218.60 
 
 15022.12 
 
 19044.69 
 
 33 
 
 3-1 
 
 8963.49 
 
 9398.79 
 
 9896.69 
 
 10478 . 50 
 
 11178.60 
 
 12058.05 
 
 13242.07 
 
 15061.87 
 
 19174.44 
 
 34 
 
 35 
 
 8970.32 
 
 9406.53 
 
 9005.63 
 
 10489.08 
 
 11191.56 
 
 12074.79 
 
 13265.70 
 
 15102.08 
 
 19309-27 
 
 35 
 
 36 
 
 8977.16 
 
 0414.28 
 
 9914.59 
 
 10409-69 
 
 11204.57 
 
 12091.60 
 
 13289.50 
 
 15142.77 
 
 19449.61 
 
 36 
 
 37 
 
 8984.01 
 
 9422.05 
 
 9923.57 
 
 10510.33 
 
 11217.63 
 
 12108.51 
 
 13313.47 
 
 15183.04 
 
 19595.92 
 
 37 
 
 38 
 
 8990.87 
 
 9429.84 
 
 9932.57 
 
 10521.01 
 
 11230.74 
 
 12125.49 
 
 13337.60 
 
 15225.62 
 
 19748.73 
 
 38 
 
 39 
 
 8097-75 
 
 9437.65 
 
 9941-60 
 
 10531-71 
 
 11243-90 
 
 12142.57 
 
 13361.90 
 
 15267.80 
 
 19908.66 
 
 39 
 
 40 
 
 9004.65 
 
 9445.48 
 
 9950.66 
 
 10542.45 
 
 11257.11 
 
 12159.72 
 
 13386.37 
 
 15310.51 
 
 20076.39 
 
 40 
 
 41 
 
 0011.55 
 
 9453.32 
 
 9959-73 
 
 10553.23 
 
 11270.37 
 
 12176.96 
 
 13411.02 
 
 15353.76 
 
 20252.72 
 
 41 
 
 42 
 
 9018.47 
 
 9461 . 18 
 
 9968.83 
 
 10564.04 
 
 11283.68 
 
 12194.29 
 
 13435.85 
 
 15397.56 
 
 .20438.59 
 
 42 
 
 43 
 
 0025.41 
 
 9469.06 
 
 9977.96 
 
 10574-88 
 
 11297.04 
 
 12211.71 
 
 13460.85 
 
 15441.92 
 
 20635.09 
 
 43 
 
 44 
 
 9032.36 
 
 9476.96 
 
 9987.11 
 
 10585.76 
 
 11310.46 
 
 12229.21 
 
 13486.05 
 
 15486.86 
 
 20843.50 
 
 44 
 
 45 
 
 9039.32 
 
 9484.87 
 
 9996.28 
 
 10596.67 
 
 11323-93 
 
 12246.81 
 
 I35H.43 
 
 15532.40 
 
 21065.37 
 
 45 
 
 46 
 
 9046.29 
 
 9492.81 
 
 10005.48 
 
 10607.62 
 
 11337.45 
 
 12264.49 
 
 13537-00 
 
 15578.55 
 
 21302.55 
 
 46 
 
 47 
 
 9053.28 
 
 9500.76 
 
 10014.70 
 
 10618.60 
 
 11351.02 
 
 12282.26 
 
 13562.75 
 
 15625.32 
 
 21557.31 
 
 47 
 
 48 
 
 9060.29 
 
 9508.73 
 
 10023.95 
 
 10629.61 
 
 11364.65 
 
 12300.13 
 
 13588.71 
 
 15672.75 
 
 21832.48 
 
 43 
 
 49 
 
 9067.31 
 
 95i6.7i 
 
 10033.22 
 
 10640.67 
 
 H378.33 
 
 12318.09 
 
 13614.85 
 
 15720.83 
 
 22131.60 
 
 49 
 
 50 
 
 9074.34 
 
 9524.72 
 
 10042.52 
 
 10651.75 
 
 11392.06 
 
 12336.15 
 
 13641.20 
 
 15769.59 
 
 22459.26 
 
 50 
 
 51 
 
 0081.39 
 
 9532.74 
 
 10051.84 
 
 10662.87 
 
 11405.85 
 
 12354.30 
 
 13667.75 
 
 15819.06 
 
 22821.46 
 
 51 
 
 52 
 
 9088.45 
 
 9540.79 
 
 10061.19 
 
 10674.03 
 
 11419.70 
 
 12372.54 
 
 13694.52 
 
 15869.25 
 
 23226.39 
 
 52 
 
 53 
 
 9095.52 
 
 9548.85 
 
 10070.56 
 
 10685.22 
 
 11433.60 
 
 12300.89 
 
 13721.48 
 
 15920.19 
 
 23685.42 
 
 53 
 
 54 
 
 9102.61 
 
 9556.93 
 
 10079.96 
 
 10696.46 
 
 11447.56 
 
 12409.33 
 
 13748.67 
 
 15971.89 
 
 24215-35 
 
 54 
 
 55 
 
 9109.72 
 
 9565.03 
 
 10080.38 
 
 10707.72 
 
 11461.58 
 
 12427.87 
 
 13776.07 
 
 16024.38 
 
 24842. 12 
 
 55 
 
 56 
 
 57 
 
 9116.84 
 9123.97 
 
 9573.15 
 9581.29 
 
 10008.83 
 10108.30 
 
 10719.03 
 10730.37 
 
 "475.65 
 11489.78 
 
 12446.51 
 12465.26 
 
 13803.68 
 13831.53 
 
 16077.68 
 16131.82 
 
 25609.23 
 26508.21 
 
 56 
 
 57 
 
 58 
 
 9131.12 
 
 9589.45 
 
 10117.81 
 
 I074L75 
 
 H503.97 
 
 12484.10 
 
 13859.60 
 
 16186.83 
 
 27992.10 
 
 58 
 
 59 
 
 9138.28 
 
 9597.62 
 
 10127.33 
 
 10753.17 
 
 11518.21 
 
 12503.05 
 
 13887.00 
 
 162.12.74 
 
 30374-96 
 
 59 
 
 to 
 
 9145.46 
 
 0605.82 
 
 10136.89 
 
 10764.62 
 
 11532.52 
 
 i 2522. i i 
 
 13916.43 
 
 16299.56 
 
 GO 
 
 60 
 
 SMITHSONIAN TABLES 
 
 From 84 30 7 onwards Interpolate by second differences. 
 
TABLE VIII 
 
 CONVERSION OF RADIANS INTO ANfiULAR MEASURE AND VICE VERSA 
 
 319 
 
Conversion of Angular Measure into Radians. 
 
 n 
 
 Radiant for n degrees 
 
 Radians for n minutes 
 
 Radians for n seconds 
 
 n 
 
 Radians for n degrees 
 
 I 
 
 0.01745 32925 2 
 
 0.00029 08882 I 
 
 o.ooooo 48481 4 
 
 61 
 
 1.06465 08437 2 
 
 2 
 
 .03490 65850 4 
 
 .00058 17764 2 
 
 .00000 96962 7 
 
 62 
 
 .08210 41362 4 
 
 3 
 
 .05235 98775 6 
 
 .00087 26646 3 
 
 .00001 45444 i 
 
 63 
 
 .09955 74287 6 
 
 4 
 
 .00981 31700 8 
 
 .OOIl6 35528 3 
 
 .ooooi 93925 5 
 
 64 
 
 .11701 07212 8 
 
 5 
 
 0.08726 64626 O 
 
 0.00145 44410 4 
 
 0.00002 42406 8 
 
 65 
 
 1.13446 40138 o 
 
 6 
 
 .10471 97551 2 
 
 00174 53292 5 
 
 .OOOO2 90888 2 
 
 66 
 
 .ISI9I 73063 2 
 
 7 
 
 .12217 30476 4 
 
 .00203 62174 6 
 
 .00003 39369 6 
 
 67 
 
 .16937 05988 4 
 
 8 
 
 . 13962 63401 6 
 
 .00232 71056 7 
 
 .00003 87850 9 
 
 68 
 
 .18682 38913 6 
 
 9 
 
 .15707 96326 8 
 
 .00261 79938 8 
 
 .00004 36332 3 
 
 69 
 
 .20427 71838 8 
 
 10 
 
 0.17453 29252 o 
 
 0.00290 88820 9 
 
 0.00004 84813 7 
 
 70 
 
 1.22173 04764 o 
 
 ii 
 
 . 19198 62177 2 
 
 .00319 97703 o 
 
 .00005 33295 o 
 
 7i 
 
 .23918 37689 2 
 
 12 
 
 .20943 95102 4 
 
 .00349 06585 o 
 
 .00005 81776 4 
 
 72 
 
 .25663 70614 4 
 
 13 
 
 .22689 28027 6 
 
 .00378 15467 i 
 
 .00006 30257 8 
 
 73 
 
 .27409 03539 6 
 
 14 
 
 .24434 60952 8 
 
 .00407 24349 2 
 
 .00006 78739 2 
 
 74 
 
 .29154 36464 8 
 
 15 
 
 0.26179 93878 o 
 
 0.00436 33231 3 
 
 0.00007 27220 5 
 
 75 
 
 1.30899 69390 o 
 
 16 
 
 : 27925 26803 2 
 
 .00465 42113 4 
 
 .00007 75701 9 
 
 76 
 
 .32645 02315 2 
 
 17 
 
 .29670 59728 4 
 
 .00494 50995 5 
 
 .00008 24183 3 
 
 77 
 
 .34390 35240 4 
 
 18 
 
 .31415 92653 6 
 
 .00523 59877 6 
 
 .00008 72664 6 
 
 7& 
 
 .36135 68165 6 
 
 19 
 
 .33i6i 25578 8 
 
 .00552 68759 6 
 
 .00009 21146 o 
 
 79 
 
 .37881 01090 8 
 
 20 
 
 0.34906 58504 o 
 
 0.00581 77641 7 
 
 0.00009 69627 4 
 
 80 
 
 1.39626 34016 o 
 
 21 
 
 .36651 91429 2 
 
 .00610 86523 8 
 
 .00010 18108 7 
 
 81 
 
 .41371 66941 2 
 
 22 
 
 .38397 24354 4 
 
 .00639 95405 9 
 
 .00010 66590 i 
 
 82 
 
 .43116 99866 4 
 
 23 
 
 .40142 57279 6 
 
 .00669 04288 o 
 
 .oooii 15071 5 
 
 83 
 
 .44862 32791 6 
 
 24 
 
 .41887 90204 8 
 
 .00698 13170 i 
 
 .oooii 63552 8 
 
 84 
 
 .46607 65716 8 
 
 25 
 
 0.43633 23130 o 
 
 0.00727 22052 2 
 
 O.OOOI2 I2O34 2 
 
 85 
 
 1.48352 98642 o 
 
 26 
 
 45378 56055 2 
 
 .00756 30934 3 
 
 .00012 60515 6 
 
 86 
 
 .50098 31567 2 
 
 27 
 
 .47123 88980 4 
 
 .00785 39816 3 
 
 .00013 08996 9 
 
 87 
 
 .51843 64492 4 
 
 28 
 
 .48869 21905 6 
 
 .00814 48698 4 
 
 .00013 57478 3 
 
 88 
 
 .53588 97417 6 
 
 29 
 
 .50614 54830 8 
 
 .00843 5758o 5 
 
 .00014 05959 7 
 
 89 
 
 55334 30342 7 
 
 30 
 
 0.52359 87756 o 
 
 0.00872 66462 6 
 
 0.00014 54441 o 
 
 90 
 
 1.57079 63267 9 
 
 31 
 
 .54105 2068l 2 
 
 .00901 75344 7 
 
 .00015 02922 4 
 
 9i 
 
 .58824 96193 i 
 
 32 
 
 .55850 53606 4 
 
 .00930 84226 8 
 
 .00015 5M03 8 
 
 92 
 
 .60570 29118 3 
 
 33 
 
 57595 86531 6 
 
 .00959 93io8 9 
 
 .00015 99885 i 
 
 93 
 
 .62315 62043 5 
 
 34 
 
 .59341 19456 8 
 
 .00989 01990 9 
 
 .00016 48366 5 
 
 94 
 
 .64060 94568 7 
 
 35 
 
 o.6io85 52382 o 
 
 0.01018 10873 
 
 0.00016 96847 9 
 
 95 
 
 1.65806 27893 9 
 
 36 
 
 .62831 85307 2 
 
 .01047 19755 i 
 
 .00017 45329 3 
 
 96 
 
 .67551 60819 i 
 
 37 
 
 .64577 18232 4 
 
 .01076 28637 2 
 
 .00017 93810 6 
 
 97 
 
 .69296 93744 3 
 
 38 
 
 .66322 5H57 6 
 
 .01105 37519 3 
 
 .00018 42292 o 
 
 98 
 
 .71042 26669 5 
 
 39 
 
 .68067 84082 8 
 
 .01134 46401 4 
 
 .00018 90773 4 
 
 99 
 
 .72787 59594 7 
 
 40 
 
 0.69813 17008 o 
 
 0.01163 55283 5 
 
 0.00019 39254 7 
 
 100 
 
 1.74532 92519 9 
 
 41 
 
 .71558 49933 2 
 
 .01192 64165 6 
 
 .00019 87736 i 
 
 no 
 
 .91986 21771 9 
 
 42 
 
 .73303 82858 4 
 
 .01 22 i 73047 6 
 
 .00020 36217 5 
 
 I2O 
 
 2.09439 51023 9 
 
 43 
 
 .75049 15783 6 
 
 .01250 81929 7 
 
 .00020 84698 8 
 
 130 
 
 .26892 80275 9 
 
 44 
 
 .76794 48708 8 
 
 .01279 90811 8 
 
 .00021 33180 2 
 
 140 
 
 .44346 09527 9 
 
 45 
 
 0.78539 81634 o 
 
 0.01308 99693 9 
 
 o. 00021 81661 6 
 
 ISO 
 
 2.61799 38779 9 
 
 46 
 
 .80285 14559 2 
 
 .01338 08576 o 
 
 .00022 30142 9 
 
 160 
 
 .79252 68031 9 
 
 47 
 
 .82030 47484 4 
 
 .01367 17458 i 
 
 .00022 78624 3 
 
 170 
 
 .96705 97283 9 
 
 48 
 
 .83775 80409 6 
 
 .01306 26340 2 
 
 .00023 27105 7 
 
 180 
 
 3.14159 26535 9 
 
 49 
 
 .85521 13334 8 
 
 .01425 35222 2 
 
 .00023 75587 o 
 
 190 
 
 .31612 55787 9 
 
 50 
 
 0.87266 46260 o 
 
 0.01454 44104 3 
 
 0.00024 24068 4 
 
 200 
 
 3.49065 85039 9 
 
 51 
 
 .89011 79185 2 
 
 .01483 52986 4 
 
 .00024 72549 8 
 
 2IO 
 
 .66519 14291 9 
 
 52 
 
 .90757 12 1 10 4 
 
 .01512 61868 5 
 
 .00025 21031 i 
 
 22O 
 
 .83972 43543 9 
 
 53 
 54 
 
 .92502 45035 6 
 .94247 77960 8 
 
 .01541 70750 6 
 .01570 79632 7 
 
 .00025 69512 5 
 .00026 17093 9 
 
 230 
 240 
 
 4.01425 72795 9 
 . 18879 02047 9 
 
 55 
 
 0.95993 10886 o 
 
 0.01599 88514 8 
 
 0.00026 66475 2 
 
 250 
 
 4-36332 31209 9 
 
 56 
 
 .97738 438l I 2 
 
 .01628 97396 9 
 
 .00027 14956 6 
 
 260 
 
 .53785 60551 9 
 
 57 
 
 .99483 76736 4 
 
 .01658 06278 9 
 
 .00027 63438 o 
 
 270 
 
 .71238 89803 8 
 
 58 
 
 1.01229 09661 6 
 
 .01687 15161 o 
 
 .00028 11919 4 
 
 300 
 
 5-23508 77559 8 
 
 59 
 
 .02974 42586 8 
 
 .01716 24043 i 
 
 .00028 60400 7 
 
 330 
 
 .75958 65315 8 
 
 60 
 
 1.04719 755120 
 
 0.01745 32925 2 
 
 0.00029 08882 i 
 
 36o 
 
 6.28318 53071 8 
 
 SMITHSONIAN TABLES 
 
 320 
 
Conversion of Radians into Angular Measure. 
 
 Radians 
 
 Angle 
 
 Radians 
 
 Angle 
 
 O.I 
 6.2 
 
 0.3 
 0.4 
 
 < // 
 
 05 43 46.48062 47 
 ii 27 32.96124 94 
 17 ii 19.44187 41 
 22 55 05.92249 88 
 
 0.006 
 .007 
 .008 
 .009 
 
 o 20 37-58883 75 
 24 03.85364 37 
 27 30.11845 oo 
 30 56.38325 62 
 
 0.5 
 0.6 
 0.7 
 0.8 
 0.9 
 
 28 38 52.40312 35 
 34 22 38.8837483 
 40 06 25.36437 30 
 45 50 n.84499 77 
 51 33 58.32562 24 
 
 O.OIOO 
 
 .0001 
 .0002 
 .0003 
 .0004 
 
 o 34 22.64806 25 
 oo 20.62648 06 
 oo 41.25296 12 
 
 01 01.87944 19 
 
 01 22.50592 25 
 
 I.OO 
 0.01 
 O.O2 
 0.03 
 O.O4 
 
 57 17 44.80624 71 
 oo 34 22.64806 25 
 01 08 45.29612 49 
 01 43 07.94418 74 
 02 17 30.59224 99 
 
 0.0005 
 .0006 
 .0007 
 
 .0008 
 .0009 
 
 o 01 43.13240 31 
 02 03.75888 37 
 02 24.38536 44 
 02 45.01184 50 
 03 05.63832 56 
 
 O.O5 
 O.06 
 
 0.07 
 0.08 
 0.09 
 
 02 51 53.24031 24 
 03 26 15.88837 48 
 04 oo 38.53643 73 
 04 35 01.18449 98 
 05 09 23.83256 22 
 
 O.OOIOO 
 
 .00001 
 .00002 
 .00003 
 .00004 
 
 o 03 26.26480 625 
 oo 02.06264 806 
 oo 04.12529 612 
 oo 06.18794 419 
 oo 08.25059 225 
 
 O.IOO 
 0.001 
 O.002 
 
 0.003 
 0.004 
 
 05 43 46.48062 47 
 oo 03 26.26480 62 
 oo 06 52.52961 25 
 oo 10 18.79441 87 
 oo 13 45.05922 50 
 
 0.00005 
 .00006 
 .00007 
 .00008 
 .00009 
 
 o oo 10.31324 031 
 oo 12.37588 837 
 oo 14.43853 644 
 oo 16.50118 450 
 oo 18.56383 256 
 
 0.005 
 
 00 17 11.32403 12 
 
 O.OOOIO 
 
 o oo 20.62648 062 
 
 SMITHSONIAN TABLES 
 
 Numerical Constants.' 
 
 Iog 10 2 = 0.30102 99956 63981 
 
 Iog e 2 = 0.69314 71805 59945 
 
 j 
 
 . 0.56418 95835 47756 
 
 log e io=2.30258 50929 94046 
 
 I 
 
 6=2.71828 18284 59045 
 
 Iog 10 = = 9.75142 50636 52933 
 
 ]/ IT 
 
 lo gio e = -43429 44819 03252 
 
 
 lo gio lo gio e = 9-63778 43i J 3 00537 
 
 J ^=1.25331 41373 15500 
 
 ir =3. 141 59 26535 89793 
 
 \ 2 
 
 Iog 10 ir = 0.49714 98726 94134 
 log e ir= 1.14472 98858 49400 
 
 / 2 =0.79788 45608 02865 
 
 \ IT 
 
 = 0.31830 98861 83791 
 
 IT 
 
 lo gio -J = 9-9 OI 94 00614 84924 
 
 ir 2 = 9. 86960 44010 89359 
 
 i radian = 206264.80624 70964 seconds 
 
 = 0.10132 11836 42338 
 
 = 3437-74677 07849 minutes 
 
 
 = 57.29577 95I3I degrees 
 
 I/ * =1.77245 38509 05516 
 
 Iog 10 206264.80625 = 5.31442 51332 
 
 SMITHSONIAN TABLES 
 
 3 2T 
 

YC 1 02296 
 
 *3' 
 <*^ 
 
 ASTRONOMY 
 
 II8RARY 
 UNIVERSITY OF CALIFORNIA LIBRARY