SMITHSONIAN MATHEMATICAL TABLES
HYPERBOLIC FUNCTIONS
PREPARED BY
GEORGE F. BECKER AND C. E. VAN ORSTRAND
No 1871
CITY OF WASHINGTON
PUBLISHED BY THE SMITHSONIAN INSTITUTION
1909
, if
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 have 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.
CONTENTS.
INTRODUCTION :
Definitions and formulas
Geometrical illustrations
Methods of interpolation
Description of tables
Historical note
TABLE I :
Five place values of log sinh u, log cosh u, log tanh u, and log
coth n
TABLE II :
Five place values of sinh u, cosh u, tanh u, and coth u
TABLE III :
Five place values of sin u, cos u, log sin u, and log cos u, ti being
expressed in radians and their angular equivalents ....
TABLE IV :
The ascending and descending exponential to seven significant
figures with log]0 <?M to seven places
Nine place values of the same with ten place logarithms from
u= i to u = 100
Auxiliary table of multiples of log,0 e for interpolation of Iog10 eu.
'ABLE V :
Five place values of natural logarithms
Interpolation coefficients for Derivative Formula
'ABLE VI :
The gudermannian of u to seven places in radians and to the same
order of accuracy in degrees, minutes, and seconds ....
'ABLE 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)
'ABLE VIII :
Table for conversion of radians into angular measure and vice
versa
Numerical constants .
PAOB
vii
xxviii
xxxiv
xliii
xlviii
173
225
259
261
263
273
275
309
320
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 w, sinh u for the hyperbolic
sine of #, 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
gimiir — j . gu 4- imi-n __ gu . J(u + 2mit)i _ . giu
The second of these equations has a single imaginary period, 2 /TT, and the
third a single real period, 2 IT. Hence every exponential eu 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 TT. 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.
"Comptes Rendus. Paris, vol. 83, 1876, p. 594.
vii
Vlii 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:
and these functions are related by the equation
U2n «= Un Vn.
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'y d <?y
If c = a1, this gives
-Be-*,
where A and B are arbitrary constants ; so that the integral expression in-
cludes sinh x, cosh x, and the sum or difference of these functions.
If c^-b\
{ cos x + Bl sin x.
'Am. Jour, of Math., vol. i, 1878, p. 184.
DEFINITIONS AND FORMULAS.
IX
The hyperbolic functions may also be de-
fined geometrically with reference to any
hyperbola. y
Let OA = a, OB = b be the semi-axes of
the hyperbola AP, and its conjugate BP'
referred to the rectangular axes ox and
oy. The argument or independent variable u
and its functions are then given by : l
sector OAP A OAP
u = „ . _ , sinn u =
etc.
cosh u
FIG. i.
The areas of the triangles OAB, OAP, and OPB are respectively \ ab,
i ay and \ bx, and the area of the sector OAP is found from the equation of
the hyperbola,
to be
x"
0 ab , , x . y .
5=_log(_+Z).
Hence, in accordance with the above definitions,
- — — 1 (— 4-^
sinh u = ~ = \ (eu — e~ u
, -^ i / „ i » \
cosh u = — = j (^M T *~* ) .
a
Similarly the argument and functions of circular trigonometry are :
a
arc
radius'
A comparison of the preceding equations shows that there exist between
the two sets of arguments and functions inapy interesting analogies and rela-
tions. The arguments are in each case the ratio of two areas, although the
argument of the circular functions may also be defined as a ratio of two lines;
1 For definitions which are independent of the position of the sectorial areas see Prof.
James McMahon's " Hyperbolic Functions " and a paper " On the Introduction of the
lotion of Hyperbolic Functions," by Prof. M. W. Haskell, Bull. Am. Math. Soc., vol. i,
1894-95-
DEFINITIONS AND FORMULAS.
the hyperbolic functions stand in the same relation to the equilateral hyper-
bola as the circular functions do to the circle; each set of functions may be
defined analytically as a particular branch of the theory of the exponential
function, and it is possible to pass from the one to the other by means of the
imaginary i = I/ - i. For example,
sinh u —
cosh u =
tanh u =
—i sin iu,
cos iu,
— i tan iu.
Furthermore, every rational function of the hyperbolic functions and their
inverts can be integrated by the help of corresponding known integrals of cir-
cular functions. Thus, to find j sech u du from
/sec u du = - log -
2 to i
i + sin u
sin u
log
*.
tan —
2
U
i — tan —
substitute iu for u and reduce to the form
~ i -f- i tanh —
I sech u du = - log
i — i tanh -
2
If in this equation tanh - is replaced by jy, the second member coincides in
form with the expression for 2 tan -ly given below.
Hence
sech u du = 2 tan ^(tanh — )
gdu.
Similarly, when a differential is encountered the integral of which is not to
be found in this collection, it is expedient to deduce the corresponding
expression in cyclic functions by f
substitution of ix for x, etc. , and
then to make a search for its
integral.
Most interesting is the relation c/
existing between the formulae 01
spherical trigonometry and the
formulae of Lobachevsky's imag-
inary geometry, hyperbolic ge-
ometry, or pseudo - spherical
geometry, as it is sometimes
called. Lobachevsky defines the
angle CPA as the angle of parallelism, the line PC being the limiting position
of PR when the distance A Bis infinite. In this geometry two parallels, PC
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 Lobachevsky 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 // (<z) = sin B tan 77 (£) = sin C tan 77 (c),
sin // (£) sin // 0) = sin 77 (a) —cos // (6) cos 77 (» sin 77 (a) cos A,
sin 77 (a) cos A = — cos # cos C sin 77 («) -f sin .# sin C,
and also proves that
sin 77 (u) = (cos /«) -1 = (cosh ft) ~*,
tan 77 («) = i (sin /«) ~a = (sinh «) -1,
cos 77 (u) = — / tan iu = tanh u.
Hence the preceding equations may be written
sin A sin B sin C
sinh a sinh b sinh £ '
cosh a = cosh £ cosh c — sinh b sinh c cos ^4,
cos ^4 = — 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 iat ib, if.
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. Lobachevsky 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 + oo , sinh u assumes successive values between o and
+ oo just as tan a does when a varies from o to 90°; cosh u assumes values
between i and + °° like sec /?, and tanh u assumes values between o and i
1H. 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, /?, 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 <J>.
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-
erties and applications will
be considered in the section
on geometrical illustra-
tions. It is called guder-
mannian u and is written
<$>=gd u.
The following list of form-
ulas involving the hyper-
bolic functions might be
greatly extended, but it
includes the most useful
relations.1
D
FIG. 3.
'Taken \\ith additions from Prof. B. O. Peirce s Short Table of Integrals, and Prof.
MrMahon's Hyperbolic Functions.
DEFINITIONS AND FORMULAS.
Xlll
A.— RELATIONS BETWEEN HYPERBOLIC AND CIRCULAR FUNCTIONS.
tu,
+ gd u) ] -r- sin
w),
i . sinh u = — i sin in — tan gd u.
2. cosh u = cos z« — sec gd u.
3. tanh 21 = — i tan iu = sin ^ #.
4. tanh i /^ — tan |^ u.
5. £M = ( i -f sin gd u) -f- cos ^ w,
= [ i — cos
= tan (1 IT
6. sinh iu = i sin #.
7. cosh z'z* = cos u.
8. tanh /?<: = i tan #.
9. sinh (u ± zv) — ±: i sin (z' q= zV),
= sinh u cos z> ± z cosh
10. cosh (ft ± zV) = cos (z> =F iu}t
= cosh ?^ cos v zt / sinh z^ sin #.
11. cosh (wzV) = cos m TT. (m is an integer.)
12. sinh (2 w + i) J zV = z sin (2 m -\- i) i TT. (w is an integer.)
sin v.
B. — RELATIONS AMONG THE HYPERBOLIC FUNCTIONS.
13. sinh u = £( eu — c~u )
= 2 tanh * 21 -.
14. cosh u = * (eu -}- e~u}
= ( i 4- tanh2 i
15. tanhz/=(£M — e~u) -=-
1 6. sech « =
17. csch u -
1 8. coth 7* =
19. cosh2 u
20. sinh \ 2<
2 1 . cosh $ a
22. tanh I ^
23. sinh 2u
24. cosh 2?*
25. tanh 2u
26. sinh 3«
27. cosh 3?*
28. tanh yt
= — sinh (—u) =(csch u) ,-1
( i — tanh2 J w) = tanh z/ -r- ( i — tanh1 u]
- cosh ( — «) = (sech u)~\
- (i — tanh2 * «) = i -T- (i -
tanh (— «),
= ( i — sech2 «
(coth z/)"1 = sinh « -r- cosh z
sech (— u} = (i — tanh2 u)
— csch (— u) = (coth2 u —
— coth (— 11} = (csch2 u -\-
- sinh2 u = i .
' V\ (cosh u — i).
- V i(cosh « + i).
= (cosh u — i) -r- sinh u,
- sinh u -r- (i + cosh u) =\/ (cosh u — i) -=- (cosh «
2 sinh u cosh « = 2 tanh w -4- (i — tanh2 «).
i)
— i ,
-i- (i — tanh1 «)
= cosh2 u -f- sinh2 u = 2 cosh2
= i -f- 2 sinh2 u = (i 4- tanh
= 2 tanh « -r- (i + tanh2 u).
— 3 sinh u -\- \ sinhs ?/.
= 4 cosh3 w — 3 cosh u.
= (3 tanh ?^ + tanhs u) -r- (i -f 3 tauh2'//).
DEFINITIONS AND FORMULAS.
29. sinh nu =
n cosh"-1 u sinh u + OK"— 1X^ — 2) cosh"-1 u sinh8 u + .
6
30. cosh nu — cosh" u + - — cosh n ~2 u sinh2 w +
31. sinh u 4 sinh v — 2 sinh £ (& -f- z/) cosh i (w — z>).
32. sinh w — sinh z; = 2 cosh £ (« + v) sinh i (# — v).
33. cosh w 4 cosh v = 2 cosh £ (# 4 z;) cosh \ (u — v).
34. cosh u — cosh v = 2 sinh J (z/ + v} sinh J (w — z/) .
35. sinh u 4- cosh « = (i -f- tanh $• w) -f- (i — tanh \ u).
36. (sinh u 4- cosh «)n = cosh #« 4- sinh nu.
37. tanh # 4- tanh z; = sinh (u + z/) -f- cosh & cosh z/.
38. tanh 21 — tanh z/ = sinh (u — v} -+- cosh u cosh z/.
39. coth u 4- coth z; = sinh (# + z;) -f- sinh u sinh z;.
40. coth u — coth z; = — sinh (u — v) -~ sinh u sinh z/.
41. sinh (u ±L v) — sinh w cosh z; =b cosh u sinh z;.
42. cosh (u ±v) = cosh u cosh z; ± sinh u sinh z/.
43. tanh (u ±v) = (tanh w ± tanh v) -f- (i ± tanh & tanh z;).
44. coth (w ± z;) = (coth w coth z/ ± i) -f- (coth z; ± coth w).
45. sinh (u + z/) 4- sinh (z/ — z/) = 2 sinh u cosh z>.
46. sinh (u + z;) — sinh (« — z;) = 2 cosh w sinh z;.
47. cosh (w 4- z;) 4- cosh (u — v) = 2 cosh w cosh v.
48. cosh (w -f v) — cosh (w — v} = 2 sinh w sinh v.
49. tanh J (u + v) = (sinh « + sinh z;) -4- (cosh « 4 cosh v).
50. tanh I (u — v) = (sinh u — sinh z;) -f- (cosh u + cosh z/).
51. coth \ (u 4- v) = (sinh ?/ — sinh z;) -f- (cosh w — cosh z/).
52. coth \ (u — v) — (sinh u + sinh z>) -r- (cosh w — cosh v).
tanh w + tanh v _ sinh (z/ 4- v)
tanh w — tanh v ~ sinh (w — v)'
coth 7^ 4 coth v _ sinh (a 4- v)
coth w — coth v ~ sinh (w — v)'
55. sinh (w 4 v) 4 cosh (a 4 z;) = (cosh 11+ sinh u) (cosh z/ -f sinh v).
56. sinh (M 4 v) sinh (w — z;) = sinh2 u — sinh2 v,
= cosh2 w — cosh2 v.
57. cosh (w 4 z>) cosh (a — z;) = cosh2 a 4 sinh2 z/,
= sinh2 u 4 cosh2 z/.
58. sinh (miir) = o. (m is an integer).
59. cosh (mi IT) = ( — i)m.
60. tanh (mi -IT} = o.
61. sinh (u 4 mi*) = (— i)m sinh u.
62. cosh (« 4 miir) = (— i)m cosh w.
63. sinh (2 w+ i) } /«•= ± j.
DEFINITIONS AND FORMULAS.
64. cosh (2 m + i) -J- / TT = o.
65. sinh f ~ zb U\ = i cosh K.
xv
66. cosh r-±«J = ±z sinh z*.
67. tanh (« -f- zV) = tanh u.
68.
69.
70.
71-
72.
73-
74-
75. cos~ : u = — i cosh"1 u = — i log (u + i V i — u1).
76.
C. — INVERSE HYPERBOLIC FUNCTIONS.
• l-i —i 4- /~2 — _i /"I — C du
~J (u* + i
cosh"1 u = log (it -\- \/uz — i) =
)*
du
(V —
/* du
tanh"1 u — -1 log (i + «) — £ log ( i — u}=\ 2-
C du
coth-1 u = Hog ( i -f &) — Hog O — i ) = I - — 5- =
«/ i
sech-1^ -log f — + V/-V — 0 =— f^
3 \ U * U2 ) J 2l(l-
du
cosh"1
-1 w = log ( — +\/-Ir+ T ) = — 1~ .j/^sinh-1— •
* \u * zf J Ju(u*+i)X u
sin"1 21 — — i sinn"1 iu = — / log (m + I7 i — w2) .
tan~ ! 7^ = — i tanh" T iu = — . log ( i + «0 -- : log ( i — iu).
cot"1 u = / coth"1 zw = — : log (/w — i) — — . log (iu -f i).
77-
78. sin"1 iu = i sinh -1 u = i log (w -f V i
79
cos"1 iu = — i cosh"1 iu = -- i log (u -f- V i + «")•
tan"1 /w = i tanh"1 u = — log ( i -h «) -- log ( i — w) .
80.
81.
82. cosh-
cot
« = — i coth"1 u = --- log (« -f i) H --- log (u — i).
1 | (* + -M=sinlr1 £ (w -- -W
2 \ i^ / - V z/ /
tanl
?/'— i
w'4- i
i u — i
= 2 tann"1 = log u.
83. tanh~l tan u = \gd 2 u.
84. tan"1 tanh u = \gd~^2 u.
85. cosh"1 esc 2 u = — sinh-1 cot 2 u = — tanh~ T cos 2 // = log tan w.
XVI DEFINITIONS AND FORMULAS.
86. tanh"1 tan2 (-J- TT -f % u} = | log esc u.
87. tanh"1 tan2 1 u = % log sec 21.
88. cosh"1 ft ± cosh"1 ^ = cosh~1 [uv ± V (if i ) ( z»2 i )] .
89. sinh"1 u ± sinh"1 z; = sinh"1 \ii V i + z>2 ± z; I/ i -f- w2].
D. — SERIES.
90. £w = i + w + — |- + — j- H — - + . . . (V < oo . )
_ I xaj.1/ \3
92. log « = ^-^- + -i- (-^iy+ — ^±^1^*+ . . . (*>*.)
93. log ^ = 2 r ?' ~ j + — (^^i)3+— f^T1 )5+ . . .~i(w>°-)
L » -h j 3 \ w -f i / 5 V « -f i / J
94. log(I4-^^)=^^ LM»4-J_ ^3 L w* + . . . (w2 <i.)
234
> \ i—u J ~ 2 [_U "3" 5 J 7
/ >,,, L_ - v r—
96. loj
97. sinh u = u+ —
7/ 2/ 7/
98. COsh U = I + -^j- + — ,- -f ~6-y H- . . • (X <«o .)
/ . 4 7^2\
-v+V)
99. tanhw = «-~ W2 + — ^5 — -^-7-w7+ . . . («*<!"•'.)
100. 7^ coth »/ = i + ~ «* -- - u4 + — «6 — • • . («a < TS.)
3 45 945
101. sech if = i - L *» + JL ««_ .5L «•+... (w» < i^.)
102. 7^ csch u — i -- z/1 H — -? — u* -- - - if 4- . (it* <!«•*.)
6 360 15120
103. ^/ » = <#> = w — -i- u* -f — w5 -- — u( + . . . (w small.)
6 '24 5040
v i sech1 u T -; seclr' //
= -- sech u — - ... (u large.)
2 232 4 5
DEFINITIONS AND FORMULAS. xvii
104. « =**-' + =* + - *°
106.
107. tanh-!«=w +
v5
,08.
. . . .
i 2 I wf I 3 ** 1 3 5 "6
IOQ. sech"1 21 = cosh — = log --- • .
U U 22 244 246 6
i i ii i 3 i J 3 5 i
no. csch- « = anh- _«_-7_r + -_sr----5^?
U 22 244 2
B. — DERIVATIVES.
df
in. — j— = ^ .
du
"3- -==
ii4- -7— — w" (r + log« *)•
afo
af sinh u
115. - — = cosh u.
du
d cosh u
1 1 6. - = sinh u.
du
d tanh u
117. - - = seclr u.
du
d coth u
118. - - = — csch2 u.
du
d sech u ,
no. - -= — sech u. tanh?/.
du
d csch u
120. - -= — csch u. coth u.
du
d sinh-'1 u i
121.
! ir -f- I
122
I23.
DEFINITIONS AND FORMULAS.
d cosh ~ l u _ i
du
d tanh ~l u
du i —
d coth - l u i
I24' ' ~~du~ ~~T
d sech — l u
125-
126.
127.
du
d csch — l u
du
d gd u
du
128.
du
F. — INTEGRALS. (INTEGRATION CONSTANTS ARE OMITTED.)
129. I sinh u du = cosh u.
130. J cosh u du = sinh u.
131. J tanh udu = log cosh w.
132. j coth u du = log sinh u.
J33- ) sech 2t du = 2 tan — T ^M = gd u.
134. J csch u du = log tanh — .
135
. J sinhn# ^w = - — sinh"-1 u. cosh w — - -J sinhn~2 w du,
— sinh n + l u cosh ^ -- • — I sinh n + - u du.
n -\- i w -j- i J
136. I cosh" u du = — sinh u. coshn-1 u + — ^ — I cosh"— 2n du
J n n J
sinh u cosh"^1 u -f n + 2 ]co&
n + i J
n -}- i
I37- j H sinh u du — u cosh ?^ — sinh z^.
138. j u cosh udu =u sinh ?^ — cosh w.
J39- J «' sinh w rf u = (u? -4- 2) cosh 11 — 221 sinh w.
140. j -w" sinh 7^ ^ = un cosh ?^ — nun — i sinh ?/
-f w (n — i)J ww-2 sinh udu.
DEFINITIONS AND FORMULAS.
141. J sinh2 u du =^ (sinh u cosh u — &).
142. J sinh u. cosh u du = ^ cosh (2 ?*).
143. j cosh2 u du = % (sinh u cosh w -f u).
144. I tanh2 & du = u — tanh u.
145. 1 coth2 w du = u — coth u.
146. I sech2 ?/ du = tanh «.
147. J sech3 w afo = £ sech & tanh # -f £ gd w.
148. j csch2 u du = - coth w.
149. j sinh"1 « du = u sinh"1 u — (i + u2)^.
150. j cosh — 1 & </ft = u cosh"1 u — (u2 — i)H.
151. J tanh"1 u du = u tanh-1 u + \ log (i — u*).
152. J ft sinh — 1 udu =i (2 «2 + i) sinh"1 7^ — w (i 4- w2)^ 1.
I53- \u cosh"1 u dii=\ (2 u* — i) cosh—1 u — u ( w2 — i)^ .
154. j (cosh a -f- cosh u) -1 du = 2 csch «. tanh"1 (tanh £ w. tanh ^ a),
= csch « log cosh \ (u -J- a) — log cosh £ (u — a) •
X55- J (cos # ~*~ c08^ u)~l du = 2 esc a. tan"1 (tanh £ w. tan J a).
156. J (i + cos a. cosh u)~l du = 2 esc a. tanh-1 (tanh J ?/. tan £ a).
157. J sinh w cos ?^ ^ = % (cosh z*. cos ?^ -f sinh u. sin ?*).
158. j cosh w. cos udu = % (sinh #. cos ?^ + cosh u. sin w).
159. j sinh u. sin udu = ^ (cosh u. sin u — sinh 7^. cos «).
160. J cosh u. sin & afo = \ (sinh w. sin ?/ — cosh u. cos w).
161. J sinh (;««) sinh (?iu) du
= 2 2 I «« sinh (;//<) cosh (w«) — w cosh (;/«) sinh (mu) •
XIX
XX DEFINITIONS AND FORMULAS.
162. J cosh (mu} sinh (nu} du
= — 2 m sinh (nu) sinh (mu) — n cosh (nu) cosh (mu) -
163. J cosh (mu) cosh (nu) du
= — 2 w sinh (mu) cosh (w&) — w sinh (nu) cosh (w#) •
m — n L J
1 64. I sinh « tanh u du — sinh u — gd u.
/u
cosh u coth u du = cosh w + log tanh —
166. j sec & </# = gd~ l u.
167. I sec3 fj> d <f> = I (i -f- tan2 <^>)^ d/tan </> = -J- sec <^> tan <^> -j- 4- gd 1 <^>>
= -J- tan <£ ( i -4- tan2 <£)^ -f J sinh — l (tan <£ ) . Here <f> = gd u.
C du . u C du u
l68- I ~7~T~1 — ^T — sinh"1 — . I —i 2TT7-— sin~
•/ (w -f- a) ™ a *J (a — u ) T* a
C du ,u C —du u
l®9' i ~7~2 2Ti^ = cosn — • —7-* ^ri7— cos~
*J (u — flj/2 a j (a* — u*) /a a '
C du i . u C du i u
170. I — — r- = — tanh-1 — . — = — = — tan —
•^ \a — u )u<a a a *s a -\- u a a '
17 , . r - .<* ___ = ± coth- , i. r_ -^ = -L cot - , JL
•^ (w — « )«>n ^ # •/ a -f- M a a '
— du i . u C du i . w
— -^17= — sech"1 — . — — - = — sec- — .
« (a2 — u)% a a J u(u2 — a)/* a a
C — du i u C — du i . u
i/3- I — T~FT~^^V — — csch- — . —7-= ^ = — csc~ — .
j u (a -\- u'-y-i a a J u (UL — a) a a
C du i au + ^
174. -/ — 5— : — ; — : — ^ — ,= sinh~ a positive, ac >0 ;
J (au2+2bu+c)X y a (ac — Pj*
i —1 au H- b . . .,
L au + b
— — = cos"1 — ~i — ' a negative.
C du i au + b
175* i ~, — r~i 1 — ; — r — -7 ^TT/ tan— ac> b\
J (au1 -\-2bu-\- c) (ac — by* (ac — by*
— i au-\- b ac < £2,
= .„ — r^tanh" l-T75 rp, , .,, ,^
-i coth"1 tf?< "*" ^ ac<b\
DEFINITIONS AND FORMULAS.
ixi
I76- f (a-u)U(u-t,)y* =
tanh
~1
or- Hi- tan-1
\\u~~b >
A/£ — a
or - — ?——, coth-1 \\u~~b . (The real form is to be taken. )
(a — by* \ a — b
/du 2
(a-U)(b-uy^'- (b-ay
— u
or
— a
or — _^7tan-
. (The real form is to be taken.)
cosh-1 — .
178. f («2 - a^Y-dn = \u (w2 — a2)*- £ <*
*/
179. f(a2 - uz)X du = \ u (a2 - u^A -f J «2 sin-1 — .
»/ rt
1 80. j"^2 + (ty* du=\u (wf + a2)^ -f- 1. a2 sinh"1 -
/eau
eau du = - .
a
/eau
US" du = —j(au — i).
/^m ^OM ^ /*
7/m ^aM ^ ==- I ft"1"1 £«• dfw.
« a J
feandu _ _i __ F_ eau £ eau du ~|
84' J "IF" " m- i L lr^~ aJ ^^]
Jabu
abu du = -— : -- .
^lo«
186.
a" un na" un ~} n (n - i) a" un -* .
log a (log a)y (log a)3
n (n — i) (n — 2) . . 2. i a"
(loga)"*1
I87. J^*i = J?- [-- -^ - (^°2g}^_2 - ^.j1^^,-:
, (loga)*-1 r a« du n
(w — 2) (?/ — 3) ... 2.1 J u J*
L ("log «-8 ,
188.
Xxii DEFINITIONS AND FORMULAS.
r du eu
9' J i 4- e» = g i + eu'
u — log (a -\- be"
/
««-
/
(«
- log (I/a + &?mtt + I/
J«£u </# £M
(i + «72 "" i f« '
f eau\ogu i reaudu
194. J «- log « rf« = -^ - - - J -5— -
195. J log 21 du = u log u — u.
196. /«« lOg . A W.+ l [^- - -5^.] .
197. J (log «)n du = u (log *0n — w J (logtt)"-1 du.
Jum +1 HOP- u~}n n r»
um (log u}n du= -- -±-± ---- i jw» (log w)'1-
f Clog u)ndu (logz/)n + T
T99« J - — * W+I
Jdu u i r du
(log «)n = " (n — iXlogO71-1 " ' ii — i J (log//)
/WTO fifW Z/7U + ! 7;2 + I /• ?^M fl?
==; . I _
(log u)n (n — i) (log u)n ~ n — i ./ (log u)
/um du C e~y
i u = J —J- dy> where y = — (m+ i) log w.
f^tt
— = log (log u).
u log «
C du i
20^ - — _ - _ .
I/ W (log 7/,n (» - i) (Iog7^)n~l
206. J {a -f- du)m\og n du =
DEFINITIONS AND FORMULAS.
XX111
207. I u"1 1°S (« 4- £?0 du =
m -f-
L_rMm+Mog(a+*w)— b fu'n ^-1.
-h i L J a 4- ou J
208.
log (a -f-
/Mogmfa = i r iogj< r _^ -i
J (# 4~ ^j"* b (m — i) L (a 4~ buyn J u (a 4~ bu}m __ J.
210
Jlosr u du i . i /* loer (#
= — log & . log (a '
211. I (« -f ^M) log « <#' = ^-7 log u —
/log w ^
5 ==;
(« 4- buy*
20
~b [_(l°g w — 2) i/ (« 4- £wj -\- V a log ( i/xa 4- ^« 4- i a )
- V/X7 log (l/ a 4-£« — I/ «")"!, if « > o,
= -T- (logw — 2) I/ (a 4- ^«) 4- 2 ]/ — a tan"1 "J- , if <*<o.
^ L — a _J
/*x I/ "ir" I
213- I ^-°2"2 rf« =
Jo
2I4.
20, 2 a
x»» I 'n I^ r^~
u 2 n e ~ au2 du = — -*/
»/o 2 " <Z * d
215
216. I ^-«2-
217
218
219
> o.
r J I —
e—nu |/ w ^ — . / ^r
2 ;/ X n '
C e ~mi - l~*
Jo si
> o.
sinh (nu)
220.
o sinh
XXIV DEFINITIONS AND FORMULAS.
/•in- S*iir
221. sinh (mu) . sinh (nu) dii = I cosh (mu) . cosh (nu) du
»/0 «/0
= o, if m is different from n.
222 ( '"cosh2 (w«) du = — j " sinti* (mu~) du = l^L.
Jo Jo 2
X-f iTT
sinh (#*&) du = o.
-tir
/•» TT
224. cosh (w«) du = o.
Jo
Xin
sinh (w^^) cosh (nu) du = o.
- i IT
f*i n
226. I sinh (mil) cosh (wz^) du = o.
«/o
X1 log U 7T2
-2 - du = -- — .
i —u 6
rl log u 7T2
228. I - du = -- .
Jo I + U 12
X1 log U
— s_ du =
i — u1
f l ,
23°- Jo l0
7T2
8
I + U \ dU
X1 lOg W fl?M 7T
0^1^= -T1^2'
(Mp —u*)du p + i
~
233. (log u)n du = (— i)n . n\.
234.
=
237. «- log </« ==
DEFINITIONS AND FORMULAS.
XXV
G. — FORMULAS FOR THE SOLUTION OF PSEUDO-SPHERICAL TRIANGLES.
a. — Right Triangles.
cot // (a) sinh a
sin A =
cos A =
cot /7 (c) sinh c
cos 77 (b) _ tanh b
cos II (c) ~ ~ tanh c
sin #
cos A = - rrr-r- = sm /? cosh a.
cot A =
cos
sin 77 (a)
cot /7 (£) _ sinh b
cos 77 (a) tanh a '
_ cos 77 (g) _ tanh a
cos 77 (c) tanh c '
cos j =
sin A
sin"// £
= sin A cosh £.
_ cot 77 (£) _ _ sinh b
cot // (c) sinh ^
_ cot // (a) sinh &
= cos 11 d == *
sin
tan J. tan B = sin 77 (V) = sin // (a) sin 77 (£).
= sech c = sech # sech b.
b . — Obliqiie Tria ngles .
The general relations are :
cosh a = cosh b cosh c — sinh b sinh c cos A.
sin ^ sinh b = sin j9 sinh a.
coth a sinh <$ = cosh b cos C 4- sin C cot ^4.
cos A = — cos B cos C 4- sin B sin C cosh a.
Forti solves the six typical cases in the following manner:
CASE i. — Given a, b, c. Put 2p = a -f- b + c. Then,
tan
= J sinh (
*
(p — b) .sinh (p —
sinh p sinh (/» — a)
The conditions are a < b + c ; b <_a + c; and c< a + b.
CASE 2. — Given a, b, A. Draw the geodetic line CD perpendicular to AB.
^A, ~r. sinh b sin .7
Then a > Q9/ r-r < i ; cot £ O o ; and tanh \ c > o.
XXVI DEFINITIONS AND FORMULAS.
sinh b sin A
sin B =
1 r_
sinh #
tan (A —
sinh $ (a — b}
_
sin %(A—B)
CASE 3.— Given a, bt C. 2 A = TT — (A + B + 6").
, , / sin A sin (A + C)
tanh 4- £ = A/ -: — -
« * Olfl f /
sin (A + A) sin (A + B)
CASE 4.— Given A, B, c. A + B <ji and DBC <DBG. The angle
is the angle between the geodetic DB drawn perpendicular to AC and the
geodetic BG drawn parallel to AC.
cos \ (A — B~]
tanh % (a -f b) = tanh \ c -
. - sn -
tanh •-*- tanh ,—.
r_./sinh(/» — a)sinh(/-
*- — \ ~ • ; 7 ; ; 7~r~ r
sinh j^> sinn (p — c)
-b}
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 AB.
CASE 6.— Given A, B, C. A + B + C< *.
I sin A sin (A -I- A}
tanh -i- # = V -
* ' 01<
sin (A + B) sin (A -f C)
H. — FORMULAS FOR THE SOLUTION OF THE Cusic1.
If a cubic equation is given in the form
*" + az* + bz + c = o,
it can be reduced by the substitution z = x to the simpler form
o
*? + px + q = o.
'Taken from Des Ingeuieurs Taschenbuch der Hiitte, Berlin, iSth edition.
DEFINITIONS AND FORMULAS. XXvii
CASE i . — When x* -\- px ± q = o; p and q positive. Compute the auxiliary
variable u from sinh u = — ^—TT^A then the roots are
\P (\P)A
xl = =F 2 V \p sinh \ u.
x2 = ± V \ p sinh \ u -f i }/ p cosh \ u.
x3 = ± V \p sinh \ u - i i/ p cosh \ u.
CASE 2. — When *3 — px ± q = o; p and ^ positive. (£ />)* < (^- ^)'. Com-
>ute ?^ from cosh u =— ^. .N1/; then the roots are
^ = -f- 2 I/' |/> COsh I W.
x2 = ± I/ 4 /> cosh J /> -f- z I/ /> sinh
^r3 = ± V \p cosh \ u — i V p sinh \ u.
CASE 3. — When x* — px ± q = o; p and q positive. (£ /)3 >(£ $r)*. Com
>ute the angle « from cos u = -• l7; then the roots are
xl = =F 2 V i/ cos ^ z^.
^2 = =p 2 I/ 7 COS (|/+ 120°).
*3 = + 2 l / cos M
CASE 4. — When x* — px ±g = o; p and q positive. (-J- /)3 =
For applications of hyperbolic and circular functions to the solution of the
ibic whose coefficients are general (i. e., real or complex), see a brief paper
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,
I/I —
sn
in which k is the modulus and </> the amplitude, reduces to u = gd~l <j> 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 V 2,
— =u — 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 uc the arc of this circle from the positive x axis to the point xcyc
Then, of course, the circle may be repre-
sented by the two equations
xc = cos uc ; yc = sin uc .
Now, the area of the circular sector, whose
2.UC.I
yc
chord is 2yCy is
= «C) so that xc and
FIG. 4.
yc may be regarded as the cosine and sine of
a sector uc. The ellipse may be derived
from the unit circle by multiplying the or-
dinates yc by b. Hence, in the ellipse, the
area of the sector subtended by the chord
2 ye is, say, ue and ue = buc.
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 :
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 0, the new equation represents a prolate or a curtate cycloid, or better
the syncycloid. Thus the syntractrix may be considered as a syncycloid with an infinite
-I.
xxviii
Thus
GEOMETRICAL ILLUSTRATIONS.
xe = cos nc = cos -T-»
XXIX
ye . ue
= sm uc = ~- = sin — >
so that for the ellipse,
xc = xe = cos -r- ;
, . e
= 0 sin -7-*
6>
The equation
^presents an equilateral hyperbola, and if u is the area of the hyperbolic
:tor whose chord is 2y, then there can be no objection to writing
x = cosh u ; y = sinh u,
rhere cosh and sinh are functions whose nature is still to be determined,
te most evident relation is
cosh2 u — sinh2 u = i .
low if i = V — i, the hyperbola may be written
*•+£=!,
•hich is an ellipse whose major axis is unity and whose minor axis is i.
>mparing this with the ellipse discussed above, it appears at once that
u
x = cosh u = cos — >
t
- i_ . . *
y = sinh u = t sm — »
-, in an equivalent form,
cosh u = cos iu ; sinh ft = — i sin zw,
cosh iu = cos ft ; sinh ?# = / sin u.
le investigation of cosh u and sinh ft can be completed in various ways :
>r example, by writing out the series for cos iu and — / sin iu and showing
tat their sum or difference is e ± ".
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,
Bull. Geol. Soc. Am., vol. 2, 1891, p. 49, and Am. Jour. Sci., vol. 46, 1893. p. 337.
XXX
GEOMETRICAL ILLUSTRATIONS.
the area a ft 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 «•; 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 Plt at which the hyperbola is tangent
to the ellipse, are
I a
and the coordinates of the point c at which the hyperbola is tangent to the
unit circle, are
FIG. 5.
If the hyperbola is conceived as generated by the point c in moving from
its original position to Pl (or as a " line of flow "), its radius vector sweeps
over an hyperbolic sector ocPr If this area is called — -, then by a well-
known formula,
du = x dy — y dx,
and because xy
GEOMETRICAL ILLUSTRATIONS.
. (dy dx\
dn = .', -
' V y x )
XXXI
Since no integration constant is required,
v
u = ^ log ^ - = ^ log a2 or a = e".
x\
The area u is the sector oPl cPti, where the coordinates of Pt are x^ = y^
id jy2 = xr It is noteworthy that two other areas, AP^ cPt D and CDPl
3a, have this same value, for evidently
Xj-, /».»/,
y dx = I x dy = log a = u.
'he length. of the chord Pl P2 is
id half of this, or /> a/ is the hyperbolic sine which may evidently be put
the form
cu_e-u
sinh u = — —
2
>ince the curve Pl cP2 is an hyperbola,
id therefore
oa* — aP* =i,
e u 4- ^
oa = V i — sinh2 u =
= cosh
The diameters connecting the points of intersection of the unit circle and
le ellipse, whose axes are a and a—1, may be called the isocyclic diameters
the ellipse, because the circle and the ellipse have the same area. These
imeters are not conjugate. If the ellipse is conceived as the section on
ic greatest and least axes ot an ellipsoid of unit volume, the isocyclic
iiameters are the traces of the circular sections of the ellipsoid. The coordi-
ites of one of the points of intersection, say E, are
x =
I/a2
I a1
id therefore the angle v, which the vector oE makes with the major axis of
te ellipse, is given by the relation
tan v = a~l =e~u,
id it follows that
tan f 2v\ =± (cot v — tan v) = sinh u.
lis angle ^ — - — 2vJ is gd uy 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 bobl 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 fhakgd 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 —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^ c pz is an arc of an hyperbola y* — x* = i. If the area
of the sector o p^ c /2 is called u, a pl = sinh u and oa = cosh u. Make
bc=pl a and draw the associated ellipse shown in the diagram. Then the
angle boc=gdu / bo = cosh u and
tan gd ^t = sinh u
sec gd u = cosh u
sin gd u = 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
1 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
If — = cosh ult and -=- = cosh «2>
the angle v which the circular section makes with the greatest axis is given by
b — 2 — a — 2 tanh #,
----
tan v= , tanh iv ,
i c - - b — sinh it.,
If ul = ut and -- = a this expression reduces to tan v = a -1, or to the case of the
ellipsoid.
GEOMETRICAL ILLUSTRATIONS. XXxiii
the angle 90° — gdu, its magnitude is 2 <•", and the equation of the ellipse is
x1 -\-4fXy tan gd u -\- y1 (4 tan'2 gd u -j- 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
be derived from the circle by distortion, the process is that generally
:nown as "shearing motion or scission."
If the points in the circle are sought which correspond to the points on the
\
V
\
\
\
FIG. 6.
lajor axis of the ellipsoid, it will be found that the angle between the two
iitions (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
inciding with the isocyclic diameter of the ellipse, the result would have
the discovery of a system of ellipses whose envelopes are x= ± i,
lilar 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 /'"interme-
diate between two tabulated values, /^ and J\, corresponding to a fractional
value of the argument or to n o>, where n is always less than unity, and
preferably less than one-half.
Let Fn be the value of the function to be determined ; let F— \ and F— 2 be
tabulated values of F immediately preceding F^ and let F^ F^ be values
immediately following JF0. Denote /^ — FQ by alt other first differences (A')
being similarly represented. If also a2 — a^ = 6lt b^ — bQ = clt etc. , the whole
system of functions and differences is shown in the following schedule i1
F
J'
A"
j'"
*
A*
Jvi
F-t
b"
d"
f"
a"
c"
c"
F-l
b'
d'
f
"•
a
>•
c
'•
e
/.
F,
«,
b\
o*
c,
d,
c,
/!
The most familiar formula of interpolation is due to Newton, and in the
above notation it may be written thus:
= na
, -f
n (n— i) (« — 2) (« — 3)
notation and general outline of treatment here presented closely follow Mr.
IK-rlxirt L. Rice's treatise, Theory and Practice of Interpolation, 1899. The Nichols
Press, Lynn, Massachusetts.
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 av £,, c.t, </„.... In systematic
interpolation, such as is involved in the construction of tables, it is usual to
iploy the more rapidly converging formulas of Stirling or Bessel; but when
computing machine and a table of products are available it is sometimes
>s laborious to compute an extra term of Newton's formula than to calcu-
ite 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
ilations between the several differences.
In Stirling's formula the mean of the first differences next preceding and
)llowing FQ is made use of instead of only the latter, as in Newton's formula.
'he third differences are similarly treated, so that a0, <r0, etc., being new
mantities, are defined by
= CQ, etc.
'hese mean values are used in conjunction with the even differences on the
ime horizontal line with FQ in the schedule, and Stirling's formula is
= na
M(K»— !)(»«-- .4) ^
D 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
>, d, etc. , are these means they are defined in terms of the scheduled differ-
ices, thus :
'hey are used in conjunction with the simple odd differences ap clt etc., and
the formula is
!)»(«— I) O— 2)(«— i)
When n = \, or for interpolation to the middle of an interval, the co-
efficient of ^ vanishes and Fn — F0is independent of third differences, which
clearly a great advantage. In general this method is very advantageous
-hen n approaches one-half, while Stirling's formula is preferred for small
dues of n.
XXXVI METHODS OF INTERPOLATION.
When Bessel's formula is used for backward interpolation, it may be
written
, ,
2 1 \ 2 / 3!
n being taken as positive.
A distinct method of interpolation is founded directly upon Taylor's
theorem. If F0' F0" ', etc., are the successive derivatives of FQ, and w is the
constant increment of the argument, this fundamental theorem may be
written
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.)
Hence, to compute the first derivative, say from Stirling's formula, when
the 6th differences and -^j- 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 (J-) of the mean of the corresponding third differences, and divide the
result by w.
Newton's formula gives for arguments near the beginning of the series of
tabular values :
METHODS OF INTERPOLATION.
XXXV11
f." : =-.«-«,+ • • •)
and for arguments near the end of the series of tabular values,
' ' " " "'
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, Fn" t Fn'" , ..... can be expressed in terms of the differences of Fn'.
Ao distinguish the differences of F' from those of Ft they may be denoted
>y Greek letters, and the notation is exhibited in the following scheme :
a y
ft.
A
a = 2 a
= 27o
Using Stirling's formulae, page xxxvi, the successive derivatives inclusive
>f fifth differences are now
md the interpolation formula may be written
vn = Fo + nu>F'-{- H w (a — £ y ) + H W (f.
2 ! 3 !
or, neglecting fifth differences,
;/^ i w"%
yo -f —S, ;
id for backward interpolation
n
—
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 w Fn
is not great enough to influence the result, and it is therefore sufficient to use
F =F -\-n&(F' -\- — <O
n — 0 -h n <i> (, o -f- 2 a J
<o ao being the mean first difference of <o F' corresponding to FQ. This formula
is rigorous when third differences are zero. In most cases ° can be found
mentally, and since w ( F0' -f -— ao J is here to be regarded as an interpolated
value of o) F0't no confusion can arise as to the sign of the correction. It thus
becomes almost as easy to include w ao 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 (n)
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 Iog10 sinh 0.00304. In this case
n = 0.4 and the table gives
^, = 7-47712 ; a>F0' = 1447,7 ; w S = ~ 48,3,
the last two quantities being expressed in units of the fifth decimal place.
Interpolating & F' linearly for one-half the interval,
T» f rv i n \
w Fn = u> (FJ H <O— J447>7 — 0.2 x 48,3 =
2
multiplying this value by n and adding the result to the tabular value of th<
function, there results
Fn = 1438,0 x 0.4 -f 7-477!2 = 7.48287.
The corresponding difference formula (BessePs) is
The derivative formula (b) with two terms has the advantage of being mucl
inon: convenient than the difference formula, while the accuracy of the two
'ive-eighths of a unit) when the derivatives are tabulated to the
METHODS OF INTERPOLATION.
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
irely advantageous, because as much time is often consumed in looking them
ip as is saved by employing them ; but some formulas applicable to hyper-
>lic functions are so simple that when once suggested they can hardly be
Forgotten. Thus, Taylor's theorem gives at once
>h (it -f- n <•>) — cosh u = n <>» sinh u
2!
cosh u -f-
sinh u -f . . . ,
md 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* to*
— cos u = — n to sin u — cos u
2\
sin u -f- . . . . ,
the series for the sine being similar.
So, too,
log« (u + «co) — loge u = loge f
"
<
Simplest of all is the exponential,
<?tt(+ o. oi n -\- 0.000,05 w2 + 0.000,000,167 w*
£"(-(- o. ooi n -f- 0.000,000,5 n* + • • •)•
• • .)i(w=o.oi)
O=o.ooi)
series in n w may be replaced by h, and this may have any finite value.
specially when a computing machine is available, this formula is easily ap-
)lied and is, of course, rigorous.
From time to time inverse interpolation by a method more accurate than
irst differences is called for ; indeed, whenever interpolation of a function
>y higher differences is needful, it is equally needful that the argument cor-
sponding to a given function should be ascertained by a like process. The
icthod ordinarily pursued in such cases is to estimate two values of the argu-
lent, one a little greater and the other a little less than that of the required
irgument, interpolate corresponding values of the function, and finally inter-
)late 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 n, say n', and with this
estimated value we interpolate linearly as before and find the value of w /v
9
corresponding to one-half of the estimated interval ( -- \ . Then the required
interval (n) is equal to the difference between the given value and the nearest
tabular of the function divided by w Fn> . This method is in fact simply the
~2~
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 log:o sinh u = 7.48287. We first compute
n, = 7.48287 - 7.47712 =
1448,0
then the value of <*> Fn> in terms of the last tabular unit is found as before
T
by linear interpolation to be 1438,0. Hence
7.48287 — 7.47712
- = 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 whicl
gives the required result by a direct and rigorous method. To find such
formula, divide Taylor's series (eq. a} by & FJ , and put
Fn-F^ . £/T. *'/?" f_ ^ F* "5 F;
wF0' '/2 2"^0"/3 6"/V 24 "/V ~ I200,/;"
then the interpolation formula may be written
Reversing this series in accordance with the relation,2
x = - - + ( ~ «») -f 4 ( — aQ a, +
o o
"
( — a* a* + 5 ^o «i «a — 5
o
^4 + 3 «02 («./ -i- 2alaa] — 2ia0 a,2 a2 -f 14 V),
1 Rice's Theory and Practice of Interpolation, section 83.
'Prof. James McMahon : " On the General Term in the Reversion of Series." Hull.
Am. Math. Soc., April, 1894.
METHODS OF INTERPOLATION.
which is the reversed series of
y = a0 x -f a, x2 -h a.2 x3 -f a., x' + at x>\
and rearranging the terms,1
n = nl + n, [— wt/a + 2 («,/2)2— 5 («i/a)8 + <4 ("i/»)4 -
+ »,* [»,/, (-1+5 (*,/,) - 21 (»,/,)' + . . )]
+ "i8 [HI/, (-1+6 »,/,) + 3 («i/3)2 + • • •]
+ < [-*!/,+ ...I-
[n the actual computation it is convenient to put
xli
/*"„'
len, when successive values of w ^n' are tabulated in units of the last decimal
lace, and Stirling's coefficients are used,
*i/, =rm (a0-iy0) »,/, = t r a, (ft — TV S0)
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-
:nt. It is particularly convenient when differences higher than the second
are neglected. The formula then becomes
n = n, + n, [— r o> ac + 2 (r o> a0)2 — 5 (r a> a0)s + 14 (r a> a0)*] .
Since rut a0 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 Iog10 sinh u = 7.48287. We compute
7.48287 — 7.47712
nl=J— -=0.40
1447,7
r —
0.40
= 0.0001 ;
2"/*0 2 X 1447,7
HI r & a0 = 0.40 x o.oooi x ( — 48,3) = o.oo.
Hence n = n^ = 0.40 and u = 0.00304, the same as obtained by the other
method.
When Fn — eu, it is easily shown, either by means of series (d) or by inde-
pendent methods, that
n=- -f nv — 0.005 ;/!2 +0.000,033 n? -f . . ., (at r=o.oi)
n=-\-nl — 0.0005 w,2 -f 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, =
= 0.44587.
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 FQ 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*
A'
J"
J'"
J"'
13
2197
547
14
2744
84
631
6
15
3375
9°
+ 2
721
8
16
4096
98
- 8
819
o
17
4915
98
+ 12
917
12
18
5832
110
- 8
1027
4
19
6859
114
4- 2
1141
6
20
8000
120
1261
21
9261
1
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,
-f 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
serk-s 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. r 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/V. 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 (u ± iv) = sinh u cos v±i cosh u sin v,
cosh (u ± iv) = cosh u cos v ± i sinh u sin vt
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 additi
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 n
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
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 Iogi0 eu , eu and e — u to 7 decimal places from
u = o.ooo to 3.000 and from 3.00 to 6.00. The values of cu and e~u 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 ± M = cosh u ± sinh u
while, on the other hand,
•f *-«
sinh u = — — ; cosh u =
,, U a M —
tanh u = ; gd u = 2 tan — l eu — .
eu + e~u 2
It is further evident that a table of e - u is a table of natural antilogarithms.
Formula e on page xli affords aft 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 <?M, since this is <?M, while the derivative e~u is
— e ~u. In general the interpolation or extrapolation of the function is
very easy. (See formula c, page xxxix). The logarithm of e ~ u is not given
because, being merely the arithmetical complement of the Iog10 eu, it can
be read off as fast as it can be written down.
In any table of Iog10 eu where the interval of u is % the difference of
successive logarithms is constant and equal to w Iog10<? or 0.4342 9448
If the logarithm of eu + n w is required, this will be
(« + '*«0 Iog10 e = Iog10 eu + nto log]0 e.
Hence it is practicable to prepare an extended table of proportional parts 01
a table of n Iog10 e which is applicable to any table of Iog10 eu 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
w is unity, this is merely a 5 -place table of Iog10 eu . If, on the other hand,
<» is o.ooi, as in the earlier part of Table IV, the auxiliary table gives th<
increments corresponding to n to 8 places of decimals. Thus, if Iog10 <?°-OJ
is required, Table IV gives Iog10 £°-088 = 0.0382179, the auxiliary table gives
for— = 0.245, n Iog10 e = 0.10640; and since w = o.ooi, w n Iog10 c =
0.00010640, which added to log,0 £°-088, gives Iog10 £°-088-45 = 0.0383243. In
the latter portion of Table IV ^ is only o.oi; so that, if the Iog10 d?3-00245 is
wanted, the main table gives log^-°°= 1.3028834, and & times n log e is
o 0010640; so that the required number is i 3039474.
DESCRIPTION OF TABLES.
When Iog10 cu is required for n > 6.00 the auxiliary table is insufficient to
give y-place values. Then the main table, IV, may be used as an auxiliary
table. Thus
lOg £".088246 = I0g e\\ + Jog ^088246
= 4-7772393 +0.0383243 = 4.8155636.
In the second part of Table IV values of e± u and the logarithms of eu are
iven, n varying from i to 100. The logarithms are given to 10 decimals ;
le other functions to 9 significant figures. Such high values are seldom
led, but are included here lest these tables might some times fail the
jmputer.
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
jciprocals of the arguments, and since loge f — J = — logejy, the logarithms
>f the derivatives are the tabulated logarithms taken negatively. The
ible thus gives, in addition to the logarithms of 1000 whole numbers, the
jgarithms of 1000 proper fractions lying between o.ooi and unity.
The interpolation of natural logarithms is much less simple than is that
>f common logarithms, and this is the main reason why the latter are pre-
ferred for computation. A few simple rules, however, facilitate the needful
ilculations. When the natural logarithm of a vulgar fraction is required
is best to look out the logarithm of both numerator and denominator and
ibtract. If the natural logarithm is required of a fractional number stated
lecimally and less than 21.000, no attempt should be made to interpolate it
lirectly, because the third differences of the table cannot be neglected for
lumbers so near the beginning of the table. If the number lies between
[o.ooo and 21.000, as, for example, 12.345, it should be written 123 45 / 10,
id the required logarithm will be nat log 123.45 — nat log 10. It is safe to
iterpolate the first of these between nat log 123 and nat log 124, using the
>rmula for second differences. If the number whose logarithm is to be
mnd lies between i and 10, as, for example, 8.2468, it should be written
524.68 / 100, so that the required quantity is nat log 824.68 — nat log 100.
le first of these logarithms can be found by using only the mean first
lifferences or the tabulated derivatives between the logarithms of 824 and
125. For values of the argument between 21 and 158 interpolation requires
ic use of second differences, while above 158 average first differences or
the first derivative is sufficiently accurate, inasmuch as the error involved is
ss 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
rould not be expedient, because these reciprocals are themselves rounded
rallies. If the natural logarithm of 0.0068352 is wanted as accurately as
xlvi
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 <?, 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 it = 3.000 and from u = 3.00 to u = 6.00. In this table u is
expressed in radians, and gd 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 u, 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 = loge tan ( h
2 \ 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 uy 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 log. tan
-+lgd*
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-
- ussion 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
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
le in every 27 entries, were compared with Gudermann's y-decimal place
ible of the antigudermannian in radian measure. In nearly all cases Inman' s
ist figure was confirmed, but in a few instances the last figure is incorrect
a unit. Inquiry into these cases showed that the maximum error detected
ras less than 0.006 of a minute. Thus the last figure is not absolutely trust -
>rthy, but is near enough to enable the computer to interpolate accurately
5 places. If 7 places of the antigudermannian are required, they can be
mnd by inverse interpolation in Table VI.
The earlier part of Table VII may be interpolated by first differences with-
it considerable error. At about 84°3o' one-eighth of the second difference
icomes 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
versa. A few numerical constants are appended.
HISTORICAL NOTE.
The first and most important application of the functions now known as
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 A. =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
m / TT A. \
- = log, tan (-+--)
and this Mercator must have tabulated. He published his map without
explanation, however, and it was left to Edward Wright in 1599 to stat
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, Bononiae, 1757). He adopted the notation Sh. <j>, Ch. <£, for th<
hyperbolic functions and Sc. <£, Cc. <£ for the circular ones. He proved th<
addition theorem geometically, and derived a construction for the solutioi
of a cubic equation. Soon after Daviet de Foncenex showed how to inter-
change circular and hyperbolic functions by the use of y'' - - i , and gave
the analogue of de Moivre's theorem, the work resting more on analog}7,
however, than on clear definition (Reflex, sur les quant, imag. , Miscel.
Turin Soc., Tom. i). Johann Heinrich Lambert systematized the subj<
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 tables1."
C. Gudermann published an important memoir on Potential or Cycli<
hyperbolic functions in 1830', followed by extended tables. In recogni-
1 James McMahon, Hyperbolic Functions, p. 71.
7 Cn-lle's Journal, vols. 6, 7, 8, and 9. These memoirs were afterwards reprinted in
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 I.t-hre
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-
re's table of log tan (--+--) to 12 decimals. The argument advances
\ 4 2 /
>y increments of 30 minutes, but five differences are tabulated to facilitate
iterpolation.3 Gudermann in 1831 published* a table of the same func-
ion, u<=ing centesimal degrees and advancing by hundredths of a degree
)o'32//.4) from o to an entire quadrant, the function being given to seven
lecimal places. This was later supplemented by a table advancing by hun-
Iredths of a degree from 88° to 100°, the function being given to eleven
lecimal places. Gudermann also gave a 9-place table of log cosh it, log
;inh u, and log tanh u, from u = 2.000 to u = 5.000, and a lo-place
ible of the same functions from u = 5.00 to u = 12.00.
In 1862 Z. F. W. Gronau* published a 5-place table of hyperbolic func-
ions, the argument being the gudermannian gd u in sexagesimal degrees
id minutes. He tabulated to this argument log cosh u, log sinh u, and the
Iriggs logarithm of ( — + — J instead of the natural logarithms of this
Function, following therein a suggestion of Lambert.
In 1890 W. Ligowski issued his Tafeln der Hyperbelfunctionen und der
jreisfunctionen, which is admirably accurate and much the most useful
Election of tables of the hyperbolic functions hitherto printed. He filled
gap left by Gudermann by computing log sinh //, log cosh u, and log
inh u from u =0.000 to 2.000. These he gives to only 5 places, but in
Idition he tabulates gd n in degrees, minutes, seconds, and decimals of a
:ond. These values are in all cases sufficiently accurate to enable the com-
mter to take out from an ordinary table of logarithms y-place values of the
>gaiithmsof cosh u, sinh u, and tanh u. The argument ranges from o.ooo
2.000 and from 2.00 to 6.00 for gdu, while log cosh n and log sinh u are
irried up to u = 9.00. Ligowski also gives the natural functions cosh u,
inh it, cos ?/, and sin u to 6 decimals for values of u in radians from o.ooto
.00, the cosh u and sinh u being continued to u = 8 oo. The only fault
can find with Ligowski's tables is that the increments of the argument
re sometimes inconveniently large.
1 Phil. Mag., vol. 24, p. 19.
2 Thus spelled in Cayley's paper.
'Exercises de Cal. Int., vol. 2, 1816.
*Neueste Schriften der Naturforscher-Gesellschaft in Danzig, vol. 6, 1862.
HISTORICAL NOTE.
In 1883 F. W. Newman published a 12 -place table1 of the descending ex-
ponential from 21 = 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 it, and log tanh u have been computed; the remaining values have been
taken from the tables of Gudermann or I^igowski. 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 e ~u are all taken from Newman's great
table. Those of e + u from o.ooo to o.ioo 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 /-place
table of en given in Hiilsse's edition of Vega is inaccurate and really
amounts to no more than a 5- place table. The logarithms of eu were com-
puted independently of the values of eu.
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 Ivigowski 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 differences
of the values as printed, but from more extended values, or are computed
idependently, and the error of the derivatives as well as of the functions is
than one-half of a unit in the next succeeding decimal place.
These tables were prepared in connection with the geophysical work of
te United States Geological Survey, and are published with the permission
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
log sinh u
W FO'
log cosh u
«FO'
log tanh u
w Fo'
log coth u
o.oooo
00
— 00
0.00000
0,0
00
+ 00
00
.0001
6.00000
43429,4
.00000
6. ooooo
43429,4
4.00000
.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
.OOOOO
.77815
7238,2
.22185
.0007
.84510
6204,2
.OOOOO
.84510
6204,2
.15490
.0008
.90309
5428,7
.00000
.90309
5428,7
.09691
.0009
.95424
4825,5
.OOOOO
.95424
4825,5
.04576
O.OOIO
7.00000
4342,9
O.OOOOO
0,0
7.00000
4342,9
3.00000
.OOII
.04139
3948,1
.OOOOO
.04139
3948,1
2.95861
.0012
.07918
3619,1
.OOOOO
.07918
3619,1
.92082
.0013
.11394
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
27U,3
.OOOOO
.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
.OOOOO
.32222
2068, 1
.67778
.0022
.34242
1974,1
.OOOOO
.34242
1974,1
.65758
.0023
.36173
1888,2
.00000
.36173
1888,2
.63827
.0024
.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
.OOOOO
.41497
1670,4
.58503
.0027
.43136
1608,5
.00000
.43136
1608,5
.56864
.0028
.44716
I55i,i
.OOOOO
.44716
1551,0
.55284
.0029
.46240
1497,6
.OOOOO
.46240
1497,6
.53760
0.0030
7.47712
1447,7
0.00000
0,0
7.47712
1447,6
2.52288
.0031
.49136
1401,0
.OOOOO
.49136
1400,9
.50864
.0032
.50515
1357,2
.OOOOO
.50515
1357,2
.49485
.0033
.51851
1316,0
.OOOOO
.51851
1316,0
.48149
.0034
.53148
1277,3
.00000
.53148
1277,3
.46852
0.0035
7.54407
1240,8
0.00000
0,0
7.54407
1240,8
2.45593
.0036
. 55630
1206,4
.OOOOO
.55630
1206,4
.44370
.0037
.56820
ii73,8
.OOOOO
.56820
1173,8
.43180
.0038
. 57978
1142,9
.OOOOO
.57978
1142,9
.42022
.0039
.59107
1113,6
.OOOOO
.59106
1113,6
.40894
0.0040
7.60206
1085,7
O.OOOOO
0,0
7.60206
1085,7
2.39794
.0041
.61279
1059,3
.OOOOO
.61278
1059,2
.38722
.0042
.62325
1034,0
.OOOOO
.62325
1034,0
.37675
.0043
.63347
IOIO,O
.OOOOO
.63347
IOIO,O
.36653
.0044
.64345
987,0
.00000
.64345
987,0
.35655
0.0045
7.65321
965,1
O.OOOOO
0,0
7.65321
965,1
2.34679
.0046
.66276
944,1
.OOOOO
.66275
944,1
.33725
.0047
.67210
924,0
.OOOOO
.67209
924,0
.32791
.0048
.68124
904,8
.00001
.68124
904,8
.31876
.0049
.69020
886,3
.00001
.69019
886,3
.30981
0.0050
7.69897
868,6
O.OOOOI
0,0
7.69897
868,6
2.30103
u
log tan gd u
c- 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
<o Fo'
log cosh u « F
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
.OOOOI
.70757
851,5
-'43
.0052
.71601
835,2
.00001
.71600
835,2
iOO
.0053
.72428
819,4
.OOOOI
.72427
819,4
.275
.0054
.73240
804,3
.OOOOI
.73239
804,2
0.0055
7.74036
789,6
O.OOOOI
0,0
7.74036
789,6
2.25964
.0056
.74819
775,5
.OOOOI
.74818
775,5
.25182
.0057
.75588
761,9
.OOOOI
.75587
•24413
.0058
.76343
748,8
.00001
.76342
748,8
.23658
.0059
.77085
736,1
.OOOOI
.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
.OOOOI
.79239
700,5
.20761
.0063
•79934
689,4
.OOOOI
.79933
689,3
.20067
.0064
.80618
678,6
.OOOOI
.80617
678,6
. 19383
0.0065
7.81292
668,1
O.OOOOI
0,0
7.81291
668,1
2.18709
.0066
.81955
658,0
.OOOOI
.81954
658,0
.18046
.0067
.82608
648,2
.OOOOI
.82607
648,2
. 17393
.0068
.83251
638,7
.OOOOI
.83250
638,6
. 16750
.0069
.83885
629,4
.OOOOI
.83884
629,4
.16116
0.0070
7.84510
620,4
O.OOOOI
0,0
7.84509
620,4
2.I549I
.0071
.85126
6n,7
.OOOOI
.85125
611,7
.14875
.0072
.85734
603,2
.OOOOI
.85732
603,2
.14268
.0073
.86333
594,9
.OOOOI
.86332
594,9
.13668
.0074
.86924
586,9
.OOOOI
.86922
586,9
.13078
0.0075
7.87507
579J
O.OOOOI
0,0
7.87505
579,0
2.12495
.0076
.88082
57i,4
.OOOOI
.88081
571,4
.11919
.0077
.88649
.OOOOI
.88648
564,0
.H352
.0078
.89210
556$
.OOOOI
.80209
556,8
. I079I
.0079
.89763
549,7
.OOOOI
.89762
549,7
. 10238
0.0080
7.90309
542,9
O.OOOOI
0,0
7.90308
542,8
2.00692
.0081
.90849
536,2
.OOOOI
.90848
536,1
.09152
.0082
.91382
529,6
.00001
.91380
529,6
.08620
.0083
.91908
523,2
.00001
.91907
523,2
.08093
.0084
.92428
5i7,o
.00002
.92427
517,0
.07573
0.0085
7.92942
510,9
O.OOOO2
0,0
7.92941
510,9
2.07059
.0080
•93450
505,0
.00002
•93449
505,0
.06551
.0087
•93952
499,2
.00002
.93951
499,2
.06049
.0088
.94449
493,5
.00002
.94447
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.-'
.04097
.0092
.96379
472,1
.00002
.96378
472,0
.03622
.0093
.96849
467,0
.00002
.96847
.Oil-
.0094
.97313
462,0
.00002
.97312
40J,0
.02688
0.0095
7-97773
457,2
O.OOOO2
0,0
7.97771
457. T
2.0.
.0096
.98228
452,4
.00002
.98226
.01774
.0097
.98678
447,7
.00002
.98676
447.7
.01324
.0098
.99123
443,2
.00002
.99121
443.1
.00879
.0099
• 995^4
438,7
.00002
.99562
438,7
.00.;. -
O.OIOO
8.00001
434,3
O.OOOO2
0,0
7.99999
434,3
2. OOOOI
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
w Fo'
log coth u
0.0100
8.0OOOI
434,3
0.00002
0,0
7.99999
434,3
2.OOOOI
.OIOI
.00433
430,0
.OOOO2
8.00431
430,0
1.99509
.0102
.00861
425,8
.OOOO2
.00859
425,7
•99141
.0103
.01284
421,7
.00002
.01282
421,6
.98718
.0104
.01704
417,6
.OO002
.01702
417,6
.98298
0.0105
8.O2I2O
413,6
O.OOOO2
0,0
8.02117
413,6
1.97883
.0106
.02531
409,7
.00002
.02529
409,7
•97471
.0107
.02939
405,9
.OOO02
.02937
405,9
.97063
.0108
•03343
402,1
.OOO03
•03341
402,1
.96659
.0109
•03744
398,5
.00003
•03741
398,4
.96259
O.OIIO
8.O4I40
394,8
0.00003
0,0
8.04138
394,8
1.95862
.OIII
.04533
39i,3
.00003
.04531
391,2
.95469
.OII2
.04923
387,8
.00003
.04920
387,7
.95080
.0113
.05309
384,4
.00003
.05306
384,3
.94694
.0114
.05691
381,0
.00003
.05689
380,9
.943H
0.0115
8.O007I
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
37i,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
361,9
0.00003
0,1
8.07916 '
36i,9
1.92084
.OI2I
.08280
358,9
.00003
.08276
358,9
.91724
.OI22
.08637
356,0
.00003
.08634
355,9
.91366
.0123
.08092
353,i
.00003
.08988
353,0
.9IOI2
.0124
.09343
350,3
.00003
.09340
350,2
.90660
O.OI25
8.09692
347,5
0.00003
0,1
8.09689
347,4
I.003H
.OI26
.10038
344,7
.00003
.10035
344,6
.89965
.0127
. 10382
342,0
.00004
. 10378
341,9
.89622
.0128
. 10722
339,3
.OOO04
.10719
339,3
.89281
.0129
.11060
336,7
.00004
.11057
336,6
.88943
O.OI3O
8.11396
334,1
0.00004
0,1
8.11392
334,0
I.886o8
.OI3I
.11728
331,5
.OOOO4
.11725
33L5
.88275
.0132
. 12059
320,0
.OOO04
. 12055
329,0
.87945
•0133
.12386
326,6
.OOOO4
.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
.OOOO4
.13669
317,0
.86331
.0138
.13989
314,7
.00004
.13985
3M,7
.86015
.0139
• 14303
312,5
.00004
.14299
312,4
.85701
O.OI4O
8.14614
310,2
O.OOO04
0,1
8.14610
310,2
1.85390
.OI4I
. 14923
308,0
.00004
. 14919
308,0
.85081
.0142
.15230
305,9
.00004
.15226
305,8
.84774
.0143
.15535
303,7
.00004
.15531
303,7
.84469
.0144
.15838
301,6
.00005
.15833
301,6
.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
O.OI5O
8.17611
289,6
0.00005
0,1
8.17606
289,5
1.82394
U
log tan gd u
«F0'
log sec gd u
<•> Fo'
log sin gd u
- F,/
log esc gd u
SMITHSONIAN TABLES
Logarithms of Hyperbolic Functions.
u
log sinh u
u> Fu'
log cosh u
«Fo'
log tanh u
log coth u
0.0150
8.17611
289,6
O.OOOO5
0,1
8.17606
289,5
1.82394
.0151
.17899
287,6
.00005
.17894
287,6
.82106
.0152
.18186
285,7
.00005
.I8l8l
285,7
.81819
.0153
.18471
283,9
.00005
.18466
283,8
.81534
.0154
.18754
282,0
.OOOO5
. 18749
282,0
.81251
0.0155
8.19035
280,2
O.OOO05
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,i
.79* .
0.0160
8.20414
271,5
0.00006
0,1
8.20408
271,4
1-7'.
.0101
.20684
269,8
.00006
.20679
269,7
•79321
.0162
.20953
268,1
.00006
.20048
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.OOOO6
0,1
8.21744
263,2
1.78256
.0166
.22013
261,6
.00006
.22007
261,6
•77993
.0167
.22274
260,1
.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
O.OOOO6
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
.OOOO7
.24051
249,5
•75949
0.0175
8.24306
248,2
0.00007
0,1
8.24209
248,1
I.7570I
.0176
.24554
246,8
.00007
.24547
246,7
•75453
.0177
.24800
245,4
.OOOOJ
•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
.20002
238,6
.73998
.0183
.26248
237,3
.00007
.26240
237,3
.73760
.0184
.26484
236,1
.00007
.20477
236,0
.73523
0.0185
8.26720
234,8
O.OOOO7
0,1
8.26712
234,7
i.73-'88
.0186
.26954
233,5
.00008
.26946
A 233,4
.73054
.0187
.27187
232,3
.00008
.27179
232,2
.72821
.0188
.27418
231,0
.00008
.27411
231,0
.7-'589
.0189
.27649
229,8
.00008
.27641
229,7
359
0.0190
8.27878
228,6
0.00008
0,1
8.27870
228,5
1.72130
.0191
.28106
227,4
.00008
.28098
227,3
.7I9W
.0192
.28333
226,2
.00008
.28325
226,1
.71675
.0193
.28558
225,1
.00008
.28550
225,0
.7M50
.0194
.28783
223,9
.00008
.28775
223,8
.71225
0.0195
8.29006
222,7
0.00008
0,1
8.28998
1.71002
.0196
. 29228
221,6
.00008
.2922O
221,5
.70780
.0197
.29449
220,5
.00008
220,4
.7057
.0198
.29669
219,4
.00009
.29661
210,3
.703
.0199
.29888
218,3
.00009
.39880
.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
«F0'
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
0.0200
8.30106
217,2
0.00009
O,I
8.30097
217,1
1.69903
.0201
.30323
216,1
.00009
•30314
2 1 6,O
.69686
.0202
.30538
215,0
.00009
.30529
214,9
.69471
.0203
•30753
214,0
.00009
.30744
213,9
.69256
.O2O4
.30966
212,9
.00009
.30957
212,8
.69043
O.O2O5
8.3H78
211,9
O.OOOO9
0,1
8.31169
211,8
1.68831
.02O6
.31390
210,9
.00009
.31381
210,8
.68619
.O2O7
.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
0.0210
8.32225
206,8
O.OOOIO
0,1
8.32216
206,7
1.67784
.O2II
.32431
205,9
.00010
.32422
205,8
.67578
.0212
.32637
204,9
.00010
.32627
204,8
.67373
.0213
.32841
203,9
.000 10
.32831
203,8
.67169
.0214
.33045
203,0
.00010
.33035
202,9
.66965
O.O2IS
8.33247
202,0
O.OOOIO
0,1
8.33237
201,9
1.66763
.O2l6
•33449
20 1, i
.00010
.33439
2OI,O
.66561
.O2I7
.33649
200,2
.00010
.33639
200,1
.66361
.0218
.33849
199,2
.00010
.33839
199,2
.66161
.O2I9
.34048
198,3
.00010
.34037
198,2
.65963
O.O22O
8.34246
197,4
O.OOOII
0,1
8.34235
197,3
1.65765
.O22I
•34443
196,5
.OOOII
.34432
196,4
.65568
.O222
.34639
195,7
.OOOII
.34628
195,6
.65372
.O223
.34834
194,8
.OOOII
.34823
194,7
.65177
.O224
.35028
193,9
.OOOII
.35018
193,8
.64982
0.0225
8.35222
I93J
O.OOOII
0,1
8.35211
193,0
1.64789
.O226
.35415
192,2
.OOOII
.35403
192,1
.64597
.0227
.35606
191,4
.OOOII
•35595
191,3
.64405
.0228
•35797
190,5
.OOOII
.35786
100,4
.64214
.0229
.35987
i89,7
.OOOII
.35976
189,6
.64024
0.0230
8.36177
188,9
O.OOOII
0,1
8.36165
188,8
1.63835
.0231
•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
8.37009
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
O.024O
8.38025
181,0
0.00013
0,1
8.38013
180,9
1.61087
.O24I
.38206
180,2
.00013
•38193
180,1
.61807
.0242
.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
.39008
176,6
.00013
.39085
176,5
.60915
.0247
.39274
175,9
.00013
.39261
175,8
.60739
.0248
•39450
175,2
.00013
.39436
I75,o
.60564
.0249
.39624
174,5
.00013
.39611
174,3
.60389
O.O25O
8-39799
173,8
0.00014
0.1
8,39785
173,6
1.60215
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
<o Fo'
log cosh u
»W
log tanh u
« F,/
log coth u
0.0250
8.39799
173,8
0.00014
0,1
8.39785
173,6
1.60215
.0251
.39972
I73,i
.00014
.39958
173,0
.60042
.0252
.40145
172,4
.00014
.40131
172,3
1869
.0253
.40317
I7i,7
.00014
•40303
171,6
•59697
.0254
.40488
171,0
.00014
•40474
170,9
526
0.0255
8.40659
170,3
0.00014
0,1
8.40645
170,2
1.59355
.0256
.40829
169,7
.00014
.40815
169,6
.591*
.0257
.40998
169,0
.00014
.40084
168,9
.59016
.0258
.41167
168,4
.00014
.4H52
168,3
.58848
.0259
.41335
167,7
.00015
.4U20
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
165,7
.58180
.0263
.42001
165,2
.00015
.41086
165,1
.58014
.0264
.42165
164,5
.00015
.42150
164,4
.57850
0.0265
8.42330
163,9
0.00015
o.i
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
0.00016
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
159,0
.56395
.0274
.43780
158,5
.00016
.43764
158,4
.56236
0.0275
8.43939
158,0
0.00016
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
.45167
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
151,9
.00018
• 45625
151,8
•54375
.0287
•45794
I5L4
.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
.0296
8.46989
.47136
I46\8
0.00019
.00019
0,1
8.46970
.47116
147. T
I46,6
1.53030
.52884
.0297
.47282
146,3
.00019
.47363
737
.0208
.47428
145,8
.00019
.47409
M5,7
• 5->59l
.0299
•47574
145,3
.00019
•47554
M5,2
.52446
0.0300
8.47719
144,8
O.OOO20
0,1
8.47699
144,7
I.5230I
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
a> Fo'
log cosh u
"F0'
log tanh u
w Fo'
log coth u
0.0300
8.47719
144,8
O.OO020
O,I
8.47699
144,7
I.5230I
.0301
•47863
144,3
.0002O
.47844
144,2
.52156
.0302
.48007
143,8
.00020
.47987
143,7
.52013
.0303
.48151
143,4
.OOO2O
.48131
143,2
.51869
.0304
.48294
142,9
.OO02O
.48274
142,8
.51726
0.0305
8.48437
142,4
O.OOO20
0,1
8.48417
142,3
I.5I583
.0306
.48579
142,0
.OO02O
.48559
141,8
.51441
.0307
.48721
I4i,5
.O002O
.48700
141,4
.51300
.0308
.48862
141,0
.OOO2I
.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
.OO02I
.49262
139,6
.50738
.0312
.49423
139,2
.OOO2I
.49401
i39,i
.50599
.0313
.49562
138,8
.OOO2I
.49540
138,7
.50460
.0314
.49700
138,4
.OOO2I
.49679
138,2
.50321
o.03'i5
8.49838
137,9
O.OO022
0,1
8.49817
137,8
1.50183
.0316
.49976
137,5
.00022
•49954
137,3
.50046
.0317
.50113
137,0
.OOO22
.50091
136,9
.49909
.0318
.50250
136,6
.OOO22
.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
.OOO22
.50636
135,2
.49364
.0322
.50793
134,9
.00023
.50771
134,8
.49229
•0323 1 .50928
134,5
.OOO23
•50905
134*4
.49095
.0324
.51062
134,1
.OOO23
.51039
133,9
.48961
0.0325
8.51196
133,7
O.OOO23
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
.OOO23
.51572
132,3
.48428
.0329
.51727
132,1
.00023
.51704
I3i,9
.48296
0.0330
8.51859
I3i,7
O.OOO24
0,1
8.51836
I3i,5
1.48164 1
•0331
•51991
I3i,3
.OOO24
.51967
I3U
.48033
.0332
.52122
130,9
.OOO24
.52098
130,7
•47902 1
• 0333
.52252
130,5
.00024
.52228
130,3
.47772 1
•0334
.52383
130,1
.00024
.52358
129,9
.47642 1
0.0335
8.52513
129,7
o 00024
0,1
8.52488
129,5
I.475I2 1
.0336
.52642
129,3
.00025
.52618
129,2
.47382 1
•0337 .52771
128,9
.00025
.52747
128,8
•47253 1
•0338
.52900
128,5
.00025
.52875
128,4
.47125
•0339
.53028
128,2
.OOO25
.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
•0344
.53664
126,3
.OOO26
.53639
126,1
.46361
0.0345
8.53791
125,9
0.00026
0,1
8.53765
125,8
1.46235 I
.0346
.53916
125,6
.OOO26
0,2
.53800
125,4
.46110 1
• 0347
. 54042
125,2
.OOO26
.54016
125,1
.45984
.0348
.54167
124,8
.OOO26
.54140
124,7
.45860
• 0349
.54291
124,5
.OO026
.54265
124,3
.45735
0.0350
8.S44I6
124,1
O.OOO27
0,2
8.54389
124,0
l.456n |
u
log tan ad u
« Fo'
log sec gd u
<- Fo'
log sin gd u
*» Fo'
log esc gd u 1
SMITHSONIAN TABLES
Logarithms of Hyperbolic Functions.
u
log sinh u
.0 F0'
log cosh u
• Fo'
log tanh u
«F0'
log coth u
0.0350
8.54416
124,1
O.OOO27
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
.547^0
123,1
.00027
•54759
122,9
.45241
.0354
.54909
122,7
.00027
.54882
122,6
.45"8
0.0355
8.55032
122,4
0.00027
0,2
8.55005
122,2
1.44995
.0350
.55154
1 22,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
I2O.9
• 445"
0.0360
8.55640
120,7
0.00028
0,2
8.556II
120,5
1.44389
.0361
•55700
120,4
.00028
.55732
1 20,2
.44268
.0362
.55880
120,0
.00028
.55852
119,9
.44148
.0363
.50000
119,7
.00029
.55972
H9,5
.44028
.0304
. 50120
1 19,4
.00029
.56091
119,2
.43909
0.0365
8.56239
119,0
0.00029
0,2
8.56210
118,9
1.43700
.0366
.56308
118,7
.00029
•56329
118,6
.43671
.0367
• 504/0
118,4
.00029
.56447
118,2
-43553
.0368
•50595
118,1
.00029
.5656.5
117,9
•43435
.0369
.56/12
117,7
.00030
.566$
117,6
.43317
0.0370
8.56830
H7,4
0.00030
0,2
8.56800
"7,3
1.43200
.03/1
.56947
117,1
.00030
.56917
117,0
.43083
.0372
.57004
116,8
.00030
.57034
116,6
.42966
.0373 1 .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
"5,7
1.42617
.0376
. 57529
ii5,0
.00031
.57408
"5,4
.42502 ,
• 0377
.57644
H5,3
.00031
.57614
"5,i
.42386
.0378
.57760
114,9
.00031
.57729
"4,8
.42271
.0379
.57874
114,6
.00031
.57843
"4,5
.42157
0.0380
8.57989
114,3
0.00031
0,2
8.57957
"4,2
1.42043 '
.0381
.58103
114,0
.00032
.58071
"3,9
.41929
.0382
.58217
H3,7
.00032
.58185
"3,6
.41815
.0383
.58330
H3,4
.00032
.58209
"3,3
.41/01
.0384
.58444
"3,2
.00032
.58412
"3,0
.41588
0.0385
8.58557
112,9
0.00032
0,2
8.58525
"2,7
I.4I475
.0386
08670
112,6
.00032
.58637
"2,4
.41363
.0387
08782
112,3
.00033
.58749
112,1
.41251
.0388
.58894
1 1 2,0
.00033
.58861
111,8
• 4"39
.0389
.59006
Hi,7
.00033
.58973
i",5
.41027
0.0300
8.59H7
111,4
0.00033
0,2
8.59084
111,2
1.40916
.0391
.59229
in, i
.00033
.59196
111,0
.40804
.0392
• 59340
110,8
.00033
.59306
"0,7
.40694
• 0393
•59450
110,6
.00034
.59417
110,4
.40583
•0394
.59561
110,3
.00034
.59527
110,1
.40473
0.0395
8.59671
1 1 0,0
0.00034
0,2
8.50637
109,8
1.40363
•0306 .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
108,5
I.398I7
u log tan gd u
« Fo'
log sec gd u
« Fo'
log sin gd u
«F0'
log esc gd u
SMITHSONIAN TABLES
Logarithms of Hyperbolic Functions.
•
leg sinh u
-Fo'
log cosh u
-Fo'
log tanh u
to FO'
log coth u
|| 0.0400 ' 8.6o2i*
108,6
0.00035
0,2
8.60183
108,
1.39817
.0401 !
108,4
.00035
.60291
108,2
.39709
' -^
.0402
108,
.00035
.00399
107,9
.39601
.0403
107,8
.00035
.60507
107,6
• 39493
.0404
.60650
107,6
.00035
.60615
107,4
.39385
1 0.0405
8.'
107,3
0.00036
0,2
8.60722
107,1
I . 39278
.0406
.60865
107,0
.00036
.60829
106,9
.39171
.0407
.60971
106,8
.00035
.60935
106,6
.39065
.0408
.6lO/8
106,5
.00036
.61042
106,3
•38958
.0409
.6"i 184
106,2
.00036
.61148
106,1
.38852
I 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
.38450
.0414
.61712
105,0
.00037
.61675
104,8
•38325
I 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
.0418
.0419
.62026
.62*30
.62234
104,2
1.04,0
103,7
.00038
.00038
.00038
.61988
.62092
.62196
104,0
103,8
103,5
.38012
.37908
.37804
1 0.0420 8.62338
.0421 .62441
.0422 .62544
x* x-
103,5
103,2
103,0
0.00038
.00038
.00039
0,2
8.62299
.62403
.62505
103,3
103,0
102,8
I.3770I
•37597
• 37495 1
.0423
.0424
.02047
.62750
102,7
102,5
.00039
.00039
.62608
.62711
102,5
102,3
• 3.7392
•37289
.0427
.0428
.0429
8.62852
.62954
.63056
.63158
.63259
102,2
IO2,O
101,8
101,5
101,3
0.00039
.00039
.00040
.00040
.00040
0,2
8.62813
.62915
.63016
.63118
.63219
102,1
101,8
101,6
101,3
101,1
I.37I87
.37085
.36984
.36882 |
.36781 1
1 0.0430
.0431
.0432
.0433
.0434
8.63360
.63461
.63562
.63662
•63763
IOI.I
100,8
100,6
100,4
100,1
0.00040
.00040
.00041
.00041
.00041
O,2
'8.63320
.63421
.63521
.63622
.63722
100,9
100,6
100,4
100,2
99,9
1.36680
.36579
.36479
.36378
.36278 |
1 ° '
.0437
< • s
8.63863
.63062
.64062
99,9
99,7
99,4
0.00041
.00041
.00041
0,2
8.63822
.63921
.64020
99,7
99,5
99,3
1.36178
•30079 I
.3598o 1
• u^jo
.0439
164260
99,2
99,0
.00042
.00042
.64120
.64219
99,o
98,8
.35880
.35781
|| 0.0440
•«44«
!o444
8.6.
.64458
.64556
.64655
.64753
98,8
98,5
ftl
97,9
0.00042
.00042
.00042
.00043
•00043
0,2
8.64317
.64416
.64514
.64612
.64710
98,6
98,4
98,1
97,9
97,7
1.35683 1
.35584
.35486
.35388
•35290 |
H$
.0447
.0449
8.64850
.64948
.65045
.65142
.65239
97,7
97,0
ftfl
0.00043
.00043
.00043
.00044
.00044
0,2
8.64807
.64905
.65002
.65099
•65195
97,5
97,2
97,o
96,8
96,6
I-35I93 1
.35095 1
.34998 1
•34901
.34805 |
;
8.65336
96,6
0.00044
0,2
8.65292
06,4
I.34708 1
u
•tUnodu
,
•Fo'
==
0 sec gd u
-Fo'
— —
og sin gd u
- 1
og esc gd u 1
• MITMCONIAM TA«LC«
Logarithms of Hyperbolic Functions.
tl
log sinh u
O.FO'
log cosh u
«F0'
log tanh u
-Fo'
log coth u
I 0.0450
8.65336
96,6
0.00044
0,2
8.65292
964
I.3i,
.0451
.65432
96,4
.00044
06,2
.34
.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
.34.
1 0.0455
8.65816
95,5
0.00045
0,2
8.6|
95,3
1.3,
.0456
.65912
95,3
.00045
.65866
95,1
.34134
• 0457
.66007
95,1
.00045
.65961
94,9
• 34" 9
.0458
.66IO2
94,9
.00046
.66056
94,7
.35'- -
• 0459
.66197
94,7
.00046
.66151
94,5
.33849
1 0.0460
8.66291
94,5
0.00046
0,2
8.66245
94,3
1.3.;.
.0461
.66385
94,3
.00046
.66339
94,1
.33661
.0462
.66480
94,1
.06046
.66433
93,9
•335<>7
.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
•3-','
0.0470
8.67226
92,5
0.00048
O,2
8.67178
92,3
1-3-
.04/1 .67318
92,3
.00048
.67270
92,1
.32730
.0472
.67410
92,1
.00048
.67362
91,9
.32-038
• 0473
.67502
91,9
.00049
.67454
91,7
.325 ;
• 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
.0470
.67777
9i,3
.00049
.67728
91,1
.32272
.0477
.67868
9U
.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
O,2
8.68091
90,3
1.31909
.0481
.68231
90,4
.00050
.68181
90,2
.31819
.0482
.68322
90,2
.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
89,4
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
88,9
• 3H 2
.0489
.68948
88,9
.00052
.6^896
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
.30S 1
v0493
.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
8.60425
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
II 0.0500
8.69915
86,9
0.00054
0,2
8.69861
86,7
I.30I39
u log tan gd u
» Fo'
log sec gd u
«F0'
log sin gd u
• IV
log esc gd u
SMITHSONIAN TABLES
II
Logarithms of Hyperbolic Functions.
•
loo sinh u
» F0'
log cosh u
-IV
log tanh u
« Fo'
log coth u
0.0500
8.60915
86,9
0.00054
0,2
8.69861
86,7
I.30I39
.0501
.70002
86,8
.00054
.09947
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
O,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
.05ii
.70861
85,1
.00057
.70804
84,8
.29196
.0512
.70946
84,9
.00057
.70889
84,7
.29111 1
•0513
.71031
84,7
.00057
.70974
84,5
.29026 1
• 0514
.71115
84,6
.00057
.71058
84,3
.28942 1
0.0515
8.71200
84,4
0.00058
0,2
8.71142
84,2
1.28858 1
.0516
.71284
84,2
.00058
.71226
84,0
•28774 1
•0517
.71368
84,1
.00058
.71310
83,9
.28690 1
.0518
•7M52
83,9
.00058
•71394
83,7
.28606 1
.0519
.71536
83,8
.00058
.71478
83,5
.28522 1
0.0520
8.71620
83,6
0.00059
0,2
8.71561
83,4
1.28439 1
.0521
.71703
83,4
.00059
.71644
83,2
.28356 1
.71787
83,3
.00059
.71728
83,0
.28272 1
•0523
.71870
83,1
.00059
.71811
82,9
.28189 1
.0524
•71953
83,0
.00060
.71893
82,7
.28107 I
0.0525
8.72036
82,8
0.00060
0,2
8.71976
82,6
1.28024 1
.0526
.72119
82,6
.00060
•72059
82,4
.27941 1
•0527
.72201
.72284
82,5
82,3
.00060
.00061
.72141
. 72223
82,3
82,1
.27859 I
.72366
82,2
.00061
.72305
81,9
.27695 1
0530
8.72448
82,0
0.00061
0,2
8.72387
81,8
1.27613 1
• 0531
•0532
• 7-' 530
.72612
81,9
81,7
.00061
.00061
.72469
. 72550
81,6
81,5
.27531 1
.27450 1
.0533
1693
81,6
.00062
. 72632
81,3
.27368
•0534
775
81,4
.00062
.72713
81,2
.27287 1
0.0535
•0536
•0537
.0538
.0539
8.72856
•72937
,018
.73009
.73i8o
81,3
81,1
81,0
8p,8
80,7
0.00062
.00062
.00063
.00063
.00063
0,2
8.72794
.72875
.72956
.73036
.73H7
81,0
80,9
80,7
80,6
80,4
1.27206 I
•27125 1
.27044 1
.26964 1
.26883 1
0.0540
.0541
•0542
.0544
8.73260
•73341
.73501
•73581
80,5
80,4
80,2
80, i
79,9
0.00063
.00064
.00064
.00064
.00064
0,2
8.73197
•73277
•73357
.73436
.73517
80,3
80,1
80,0
79,8
79,7
1.26803 1
.26723 1
.26643 1
.26564 1
.26483 1
0.0545
.0547
.0548
.0549
8.73661
.73741
.73830
.73000
•73979
79,8
79,5
79,3
79,2
0.00064
.00065
.00065
.00065
.00065
0,2
8-73597
.73676
•73755
.73835
•73914
79,5
79,4
79,2
79,1
78,9
1.26403 1
.26324 1
•26245 1
.26165 I
.26086 I
0.0550
8.74058
feO
0.00066
0,2
8.73993
78,8
1.26007 1
ogttntdu
og iec gd u
=====—-—
- F,,'
• - ' i
log sin gd u
w Fo'
og esc gd u 1
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,o
O.OOO66
0,2
8.73993
78,8
1.26007
.0551
.74137
.00066
.74071
78,7
.25929
• 0552
.74216
78,8
.00066
.74150
78,5
.25850
.0553
.74295
78,6
.00066
.74*28
78,4
772
.0554
•74373
78,5
.00067
•74307
.25693
0.0555
8.7445-:
78,3
0.00067
0,2
8.74385
78,1
1.25615
• 0550
.74530
78,2
.00067
.74463<
77,9
.25537
• 0557
.74^08
78,0
.00067
•74541
77,8
•25459
.0558
.74686
77,9
.00068
.74618
77,7
.25382
.0559
.74764
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
.25M9
.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
.OO07O
•75312
76,4
.246^8
.75458
76,5
.O0070
.75388
76,3
.24612
.0569
•75535
76,4
.OO07O
• 7546^
76,2
•24536
0.05/0
8.75611
76,3
O.OOO7I
0,2
8.75540
76,0
1.24460
• 0571
.75687
76,1
.000/1
.75616
75,9
.24384
• 0572
.75763
76,o
.00071
•75692
75,8
.24308
.0573
.75839
75,9
.00071
.75768
75,6
.24232
.0574
.75915
75,7
.OOO72
.75844
75,5
.24156
0.0575
8.7599T
75,6
O.OOO72
0,2
8.75919
75,4
1.24081
• 05/0
.76066
75,5
.00072
0,2
.75994
75,2
.2400-')
• 0577
.76142
75,4
.OO072
0,3
.76069
75,i
.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
0,3
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
745
.00074
.76592
74,2
.23408
0.0585
8.76740
74,3
0.00074
0,3
8.76666
74J
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
8.77HO
73,7
0.00076
0,3
8-77035
73,4
1.22965
.0591
.77184
73,6
.00076
.77108
73,3
.22S 2
.0592
.77258
73,4
.00076
.77181
7&2
.22819
.0593
•77331
73,3
.00076
•77255
73J
.-'2745
.0594
.77404
73,2
.00077
.77328
72,9
0.0595
8.77477
73,1
0.00077
0,3
8.77400
i .22600
.0596
•77550
73,o
.00077
•77473
.2»527
.0597
.77623
72,8
.00077
.77546
.0598
.77606
72,7
.00078
.77618
.0599
.77769
72,6
.00078
.77691
72,3
. 22309
0.0600
8.77841
72,5
0.00078
0,3
8.77763
72,2
1.22237
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.
•
log sinh u
- Fo'
log cosh u
«Fo'
log tanh u
» Fo'
log coth u
0.0600
8.77841
72,5
0.00078
o,3
8.77763
72,2
1 . 22237
.779M
72,3
.00078
.77835
72,1
.22165
.0002
.77986
72,2
.00079
.77907
72,0
• .22093
.0003
.78058
72,1
.00079
.77979
7i,8
.22021
.0604
.78130
72,0
.00079
.78051
7i,7
.21949
0.0605
8.78202
71,9
0.00079
o,3
8.78123
71,6
I.2I877
.0006
7i,8
.00080
.78194
7i,5
.21806
.0607
71,0
.00080
.78266
7i,4
.21734
.0608
.7«*I7
71,5
.00080
.78337
7i,3
.21663
.0009
.78489
71,4
.00086
.78408
7i,i
.21592
0.0610
8.78560
71,3
0.00081
o,3
8.78479
7i,o
1.21521
.0611
.78631
71*2
.00081
.78550
70,9
.2-1450
.0612
.78702
7i,i
.00081
.78621
70,8
.21379
.0613
.78773
70,9
.00082
.78692
70,7
.21308
.0614
.78844
70,8
.00082
.78762
70,6
.21238
0.0615
8.78915
70,7
0.00082
o,3
8.78833
70,4
1.21167
.0616
.78986
70,6
.00082
.78903.
70,3
.21097
.0617
.79056
70,5
.00083
.78973
70,2
.21027
.0618
.79127
70,4
.00083
.79044
7o,i
.20956
.0619
.79197
70,3
.00083
.79114
7o,o
.20886
0.0620
8.79267
70,1
0.00083
o,3
8.79184
69,9
I. 20816
.0621
•79337
70,o
.00084
•79253
69,8
.20747
.0622
.79407
69,9
.00084
.79323
69,6
.20677
.0623
.79477
69,8
.00084
•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
.20309
.0627
.0628
•79755
.79825
69,4
69,2
.00085
.00086
.79670
« 79739
69,1
69,0
.20330
.20261
.0629
.79894
69,1
.00086
.79808
68,9
.20192
0.0630
.0631
.0632
.0633
8.79963
.80032
.80101
.80169
69,0
68,9
68,8
68,7
0.00086
.00086
.00087
.00087
0,3
8.79877
•79945
.80014
.80082
68,8
68,6
68,5
68,4
1.20123
.20055
.19986
. 19918
.0634
.80238
68,6
.00087
.80151
68,3
.19849
0.0635
.0696
.o6»
.0638
,0639
8.80307
.80375
.80443
.80512
.80580
68,5
68,4
68,3
68*
68,1
0.00088
.00088
.00088
.00088
.00089
o,3
8.80219
.80287
.80355
.80423
.80491
68,2
68,1
68,0
67,9
67,8
I . 19781
. 19713
.19645
. 19577
.19509
0.0640
,0641
• " ;-•
.0643
• " ;;
8.80648
.80716
.80783
.80851
.80919
68,0
67,8
67,7
<>7."
67,5
0.00089
.00089
.00089
.00090
.00090
0,3
8.80559
.80626
.80694
.80761
.80829
67,7
67,6
67,5
67,4
67,3
1.19441
. 19374
.19306
. 19239
.19171
0.0645
,0646
."•;;•
.0648
.</.,•;
8.80986
.61053
.81121
.81188
•81255
67,4
67,3
6>,0
0.00090
.00091
.00091
.00091
.00091
0,3
8.80896
.80963
.81030
.81097
.81164
67,1
67,0
66,9
66,8
66,7
1.19104
.19037
.18970
.18003
.18836
0.06fK>
8.81322
66,9
0.00002
0,3
8.81230
66,6
I . 18770
•
logt.nodu
- Fo'
=^^^-^—
oo tec ad u
- Fo'
ogsingd u
-IV
og esc gd u
__.
SM.TM.ON..H TA.LC* —————— ——J
Logarithms of Hyperbolic Functions.
u
log sinh u
- Fo'
log cosh u
«F0'
log tanh u
« Fo'
log coth u
0.0650
8.81322
66,9
0.00092
0,3
8.81230
66,6
I . 18770
. of>5 1
,8l3$>
663
.00092
.81297
66,5
. 18703
.0652
.81456
66,7
.00092
.81363
66,4
.18637
.81522
66,6
.00093
.81430
66,3
.18570
.0654
.81589
66,5
.00093
.81496
.I.V
0.0655
8.81655
66,4
0.00093
0,3
8.81562-
66,1
E.I84
.0656
.81722
<*u
.00093
.81628
66,0
. 18372
.81788
66,2
.00094
.81694
65,9
•
.81854
66,1
.00094
.81760
65,8
.18240
.0659
.81920
66,0
.00094
.81826
65,7
.181/4
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
.1;
.0663
.82183
65,6
.00095
.82088
65,3
•I7>
.0664
.82249
65,5
.00096
.82153
65,2
.17847
0.0665
8.82314
65,4
0.00096
0,3
8.82218
65,1
1.17782
.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
.1752-2
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
.17-' -
.0674
.82899
64,5
.00099
.82800
64,2
.17200
0.0675
8.82963
6-U4
0.00099
0,3
8.82864
64,1
1.1/136
.0676
.83028
64,3
.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
I. 16816
.0681
.83348
63,9
.OOIOI
.83248
63,6
.16752
.0682
.83412
63,8
.OOIOI
.833H
63,5
.16689
.0683
.83476
63,7
.00101
.83375
63,4
.16625
.0684
.83539
63,6
.00102
.83438
63,3
. 16562
0.0685
8.83603
63,5
O.OOIO2
0,3
8.83501
63,2
I . 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
0.0600
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
.84064
62,5
.15996
.0694
.84171
62,7
.00105
.84066
62,4
. I 5934
0.0695
8.84233
62,6
0.00105
o,3
8.84129
62,3
1.15871
.0696
.84296
62,5
.00105
.84191
62,2
.15809
.0697
.84358
62,4
.00105
.84-'53
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
log tan gd u
« Fo'
log sec gd u
*F0'
log sin gd u
« Fo'
log esc gd u
SMITHSONIAN TABLES
Logarithms of Hyperbolic Functions.
u
log sinh u
« Fo'
log cosh u
»*v
log tanh u
« Fo'
log coth u
0.0700
8.84545
62,1
O.OOIO6
0,3
8.84439
61,8
I.I556I
.0701
.84607
(>_', I
.OOIO7
.84501
61,8
•15499
.0702
.84669
62,0
.00107
.84562
6i,7
.15438
.0703
61,9
.00107
.84624
61,6
.153/6
.0704
.84793
61,8
.00108
.84686
6i,5
.15314
0.0705
8.84855
6i,7
O.OOloS
o,3
8.84747
61,4
I.I5253
.0700
61,6
.00108
.84808
6i,3
.15192
.0707
.*4';-8
61,5
.00108
.84870
61,2
.15130
.0708
.85040
6l,4
.00109
.8493'l
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
61,2
.OOIIO
.85114
60,9
.14886
.0712
.85285
61,1
.OOIIO
.85175
60,8
.14825
.0713
.85346
61,0
.OOIIO
.85235
60,7
. 14765
.0714
.85407
60,9
.OOIII
.85296
60,6
. 14704
0.0715
8.85468
60,8
O. OOIII
0,3
8.85357
60,5
I . 14643
.85528
60,8
.OOIII
.85417
60,4
.14583
.0717
.85589
60,7
.OOII2
.85478
60,4
. 14522
.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
.85831
60,3
.00113
.85718
60,0
.14282
.85891
60,3
.00113
.85778
59,9
. 14222
.85952
60,2
.00113
.85838
59,9
.14162
.86012
60,1
.00114
.85898
59,8
. 14102
0.0725
8.86072
60,0
O.OOII4
0,3
8.85958
59,7
I . 14042
.86132
59,9
.OOII4
.86017
59,6
•13983
.86192
.86251
59,8
59,8
.OOII5
.OOII5
.86077
.86137
59,5
59,5
.13923
.13863
.0729
.86311
59,7
.00115
.86196
59,4
.13804
0.0730
.0731
.0732
8.86371
.86430
.86490
59,6
59,5
59,4
O.OOII6
.OOII6
.OOIl6
0,3
8.86255
.86314
.86374
59,3
59,2
59,1
I • 13745
.13686
. 13626
.0733
.0734
.86549
.86609
59,4
59,3
.OOII7
.OOII7
.86433
.86492
59,0
59,0
. 13567
.13508
0.0735
.0736
.0737
.0738
.0739
8.86668
.86727
.786
.86845
.86904
59,2
59^0
59,0
58,9
O.OOII7
.OOIlS
.OOIlS
.OOIlS
.OOIlS
0,3
8.86551
.86609
.86668
.86727
.86785
58,9
58,8
58,7
58,6
58,6
I.I3449
. T339I
. 13332
. 13273
.13215
0.0740
.0743
•0744
8.86963
.87022
.87080
•H7I39
.87197
58,8
5K.7
58,5
O.OOII9
.OOII9
.00119
.00120
.00120
0,3
8.86844
.86002
.86961
.87019
.87077
58,5
58,4
58,3
58,2
58,2
I.I3I56
.13098
• 13039
.12981
.12923
0.0745
.0747
-
8.87256
.87314
.87372
58,4
58,2
O.OOI2O
.OOI2I
.OOI2I
,0,3
8.87135
.87193
.87251
58,i
58,o
57,9
I . 12865
.12807
• 12749
' v/*f°
.0749
'.874«9
e&i
.OOI2I
.00122
.87309
.87367
57,8
57,8
.12691
. 12633
0.07SO
8.87547
58,0
0.00122
0,3
8.87425
57,7
I. 12575
I
ogt.ntdu
^^===
_
og sec od u
«F0'
log sin gd u
*> Fo'
log esc gd u
ftM.TM.ON.AN TABLE* "
^^^••••••••^•^•^•^••M
16
Logarithms of Hyperbolic Functions.
u
log sinh u
«- Fo'
log cosh u
»FV
log tanh u
•Fo'
log coth u
0.0750
8.87547
58,0
O.OOI22
0,3
8.87425
57,7
I. 12575
.0751
.87605
57,9
.OOI22
.87482
57,6
.12518
.0752
.87663
57,9
.00123
.87540
57,5
. U4'xj
.0753
.87721
57,8
.00123
.87598
57,5
.12402
.0754
.87778
57,7
.00123
.87655
57,4
.12345
0.0755
8.87836
57,6
O.OOI24
o,3
8.87712
57,3
I.I2288
.0756
.87894
57,6
.00124
.87770
57,2
.12230
.0757
.87951
57,5
.00124
.87827
57,2
.12173
.0758
.88009
57,4
.00125
.87884
57,1
.I2Il6
.0759
.88066
57,3
.00125
.87941
57,0
.12059
0.0760
8.88123
57,3
O.OOI25
0,3
8.87998
56,9
I.I2OO2
.0761
.88180
57,2
.00126
.88055
56,8
•II945
.0762
.88238
57,1
.00126
.88112
56,8
.11888
.0763
.88295
57,o
.00126
.88168
56,7
. 1 1832
.0764
.88352
57,o
.OOI27
.88225
56,6
.H775
0.0765
8.88408
56,9
O.OOI27
0,3
8.88282
56,5
I.II7I8
.0766
.88465
56,8
.00127
.88338
56,5
.11662
.0767
.88522
56,7
.00128
.88394
56,4
.11006
.0768
.88579
56,7
.00128
.88451
56,3
•II549
.0769
.88635
56,6
.00128
.88507
56,3
•II493
0.0770
8.88692
56,5
O.OOI29
0,3
8.88563
56,2
I. I 1437
•0771
.88748
56,4
.00129
.88620
56,i
.11380
.0772
.88805
56,4
.00129
.88676
56,0
.11324
• 0773
.88861
56,3
.00130
.88732
56,0
.11268
.0774
.88917
56,2
.00130
.88787
55,9
.11213
0.0775
8.88974
56,2
0.00130
0,3
8.88843
55,8
1.11157
.0776
.89030
56,i
.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
0.00134
0,3
8.89398
55,1
I. 10002
.0786
.89587
55,4
.00134
.89453
55,o
.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
55,1
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
54o
.10109
0.0795
8.90082
54,7
0.00137
o,3
8.89945
54,4
i. 10055
.0796
.90137
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
«F0'
log sin gd u
« Fo'
log esc gd u
SMITHSONIAN TABLES
Logarithms of Hyperbolic Functions.
u
loo sinh u
<•» Fo'
loo cosh u
wF0'
loo 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,o
.09729
.0802
.90464
54,3
.00140
.90324
53,9
.09676
.0803
.90518
54,2
.00140
.00380
53,9
.09620
.0804
.90572
54,1
.00140
.90432
53,8
.09568
0.0805
8.90626
54,1
0.00141
0,3
8.90486
53,7
I.095I4
.0806
.00681
54,0
.00141
0,3
.00540
53,6
.09460
.0807
.90734
53,9
.00141
o,3
.90593
53,6
.09407
.0608
.00783
53,9
.00142
0,4
.90647
53,5
.09353
.0809
.90842
53,8
.00142
0,4
.00700
53,4
.09300
0.0810
8.00896
53,7
0.00142
0,4
8.90754
53,4
1.09246
.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
8.91020
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,o
.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
.91005
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
.0834
.92115
.92167
52,3
52,2
.00151
.00151
.91964
.92016
51,9
.08036
.07984
0.0835
8.92219
52,1
O.OOI5I
0,4
8.92068
5i,8
1.07932
.06136
.92271
52,1
.00152
.92120
5i,7
.07880
.0837
.92323
52,0
.00152
.92171
5i,6
.07829
,0838
5i,9
.00152
.92223
5i,6
•07777
,ofap
5i,9
.00153
.92274
5i,5
.07726
0.0840
8.0
51,8
0.00153
0,4
8.92326
5i,5
1.07674
.0842
."••.
.0844
.92634
,9rf86
51,8
5i,7
51,6
51,6
.00153
.00154
.00154
.00154
.92377
.92429
.92480
.92531
5i,4
51,3
5i,3
.07623
.07571
.07520
.07469
0.0845
.
Q sv%*v
51,5
51,5
O.OOI55
.00155
0,4
8.92582
•92634
51,2
1.07418
.07366
••••-'
s
51,4
51,3
51,3
.00156
.00156
.00156
.92685
.92736
.92787
5i!o
50^9
.07315
.07264
.07213
8.92994
51,2
0.00157
0,4
8.92837
50,8
1.07163
•
loo sec gd u
— _
loo sin od u
•••^•^•••M
« Fo'
m^mmtmmmmm^
log esc gd u
^•^•^^••iHH
18
Logarithms of Hyperbolic Functions.
u
log sinh u
- F:
log cosh u
-Fo'
loo tanh u
«F0'
log coth u
0.0850
8.92094
51,2
0.00157
0,4
8.9
50,8
1.07163
.0851
.93045
51,-'
.00157
.92888
50,8
.07112
.0852
.9300
5I.I
.00157
.92939
50,7
.07061
.0853
.93148
51,0
.00158
.<;-"/ *)
50,7
.07010
.0854
•93199
51,0
.00158
.93040
50,0
.06960
0.0855
8.93250
50,9
0.00159
0,4
8.93091
50,5
1.06909
.0850
•93300
50,9
.00159
.93Mi
50,5
.06859
.0857
•93351
50,8
.00159
.93192
50,4
.06808
.0858
•93402
50,7
.00160
.93242
50,4
.06758
.0859
•93453
50,7
.00160
.93293
50,3
.06707
0.0860
8.93503
50,6
O.OOIOO
0,4
8.93343
50,3
1.06657
.0861
.93554
50,6
.00161
•93393
50,2
.06607
.0862
.93604
50,5
.00161
•93443
50,i
.06557
.0863
.93655
50,4
.00162
•93493
5o,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
.93806
50,3
.00163
.93643
49,9
•OJ357
.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
50,0
0.00164
0,4
8.93843
49,7
1.06157
.0871
•94057
50,o
.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
.94041
49,4
.05959
0.0875
8.94256
49,8
0.00166
0,4
8.04090
49,4
1.05910
.0876
.94306
49,7
.00166
.94140
49,3
.05860
.0877
.94356
49,6
.00167
.94189
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,o
.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
O.OOI72
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
4&4
.05030
.0894
.95192
48,7
.00173
.95018
48,3
.04982
0.0895
8.95240
48,7
0.00174
o,4
8.95067
48.3
1-04933
.0896
.95289
48,6
.00174
-95II5
.04885
.0897
•95337
48,5
.00174
.95163
•04837
.0898
•95386
48,5
.00175
•952II
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
<- Fo'
log sin gd u
« Fo'
log esc gd u
SMITHSONIAN TABLES
Logarithms of Hyperbolic Functions.
B
.
log sinh u - Fo'
=
log cosh u
"
—
log tanh u
••^^•^••MMH
« Fo'
••MHHiiiiiiMMH^^
log coth u
1 0.0900
.MA'I
8.95483 !
•9;
48,4
48,3
48,3
0.00176
.00176
.00176
0,4
8.95307
.95355
.95403
48,0
47,9
47,9
1.04693
.04645
•04597
.OQ03
.95628
48,2
.00177
•95451
47,8
.04549
* X/3^'»J
.0904
.95676
48,2
.00177
•95499
47,8
.04501
1 0.0905
8.95724
48,1
48,1
0.00178
.00178
0,4
8.95547
•95594
47,7
47,7
1.04453
.04406
!oQO7
• y«?/ / m
^S20
48,0
.00178
.95642
47,6
.04358
[0908
.95808
48,0
.00179
.95689
47,6
.04311
.0909
•95916
47,9
.00179
•95737
47,5
.04263
| 0.0910
.0911
8.95964
.90012
47,9
47,8
O.OOlSo
.00180
0,4
8.95784
.95832
47,5
47,4
1.04216
.04168
.96060
47,8
.00180
.95879
47,4
.04121
.0913
.96107
47,7
.00181
.95927
47,3
-04073
.0914
.96155
47,6
.OOlSl
•95974
47,3
.04026
I 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
.06345
47,4
.00183
.96163
47,0
.03837
.0919
.96393
47,4
.00183
.96210
47,o
.03790
1 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
.96535
47,2
.00184
.96350
46,8
.03650
.0923
.96582
47,2
.00185
.96397
46,8
.03603
.0924
.06629
47,1
.00185
.96444
46,7
.03556
|| 0.0925
8.06676
47,1
O.OOI86
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
.0909
.96864
46,9
.00187
.96677
46,5
.03323
1 0.0930
8.06911
46,8
0.00188
0,4
8.96723
46,4
1.03277
•0931
•958
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
I 0>09?f
8.97144
46,6
O.OOIOO
0,4
8.96955
46,2
1.03045
.0*6
46,5
.OOIOO
.97001
46,1
.02999
46,5
.00190
.97047
46,1
•02953
464
.OOIQI
.97093
46,0
.02907
.0939
.97330
46,4
.00191
.97139
46,0
.02861
|| 0.0940
8.97377
46,3
0.00192
0,4
8.97185
45,9
1.02815
.0941
46,3
.00192
.97231
45,9
.02769
,094*
46,2
.00192
.97277
45,8
.02723
4M3
.97516
•97562
46,2
.00193
.00193
.97323
.97368
45,8
45,7
.02677
.02632
' "'
8.97608
46,1
0.00194
0,4
8.97414
45,7
1.02586
.0^654
46,0
.00194
.07460
45,6
.02540
.",;:
•97700
46,0
.00194
.97505
45,6
.02495
;jg
.00195
•97551
45,5
.02449
.ojTOd
45,9
.00195
.97597
45,5
.02403
I „ ,,, ()
8.97838
45,9
0.00106
0,4
8.97642
45,4
1.02358
1 "
log Un 8d u
-w
log sec gd u
«F0'
log sin gd u
« Fo'
log esc gd u
• MITMSONIAN
20
Logarithms of Hyperbolic Functions.
u
log sinh u
- Fo'
log cosh u
• F0'
log tanh u
- « Fo'
log coth u
0.0950
8.97838
45,9
0.00196
0,4
8.9;
45,4
1.02358
.0951
.9/883
45,«
.00196
45,4
.02313
.0952
.97929
45,8
.00197
•97733
45,3
.02267
• 0953
•97975
45,7
.00197
.97778
45,3
.O2222
.0954
.98021
45,7
.00197
.97823
45,2
.02177
0.0955
8.98066
45,6
0.00198
0,4
8.97869
45,2
I.02I3I
.0950
.98112
45,6
.00198
.97914
45,2
.02086
.0957
•98157
45,5
.00199
•97959
45,i
.02041
.0958
.08203
45,5
.00199
.98004
45,1
.01996
.0959
.98248
45,4
.00199
.98049
45,0
.01951
0.0060
8.98294
45,4
^.002OO
0,4
8.98094
45,0
1.01906
.0961
.98339
45,3
.OO2OO
•98139
44,9
.Ol86l
.0962
.98384
45,3
.00201
.98184
44,9
.Ol8l6
.0963
.98430
45,2
.O020I
.98229
44,8
.01771
.0064
.98475
45,2
.OO20I
.98273
44,8
.01727
0.0965
8.98520
45,1
O.OO202
0,4
8.98318
44,7
I.OI682
.0966
•98565
45,i
.OO2O2
.98363
44,7
.01637
.0967
.98610
45J
.00203
.98408
44,6
.01592
.0068
.98655
45,0
.00203
.98452
44,6
.01548
.0969
.98700
45,0
.00204
.98497
44,5
.01503
0.0970
8.98745
44,9
O.00204
0,4
8.98541
44,5
I. 01459
.0971
.98790
44,9
.00204
.98586
44,5
.OI4H
.0972
.08835
44,8
.002O5
.98630
44,4
.01370
.0973
.98880
44,8
.00205
.98675
44,4
.01325
.0974
.98925
44,7
.00206
.98719
44,3
.OI28l
0.0975
8.98969
44,7
O.O0206
0,4
8.98763
44,3
I.OI237
.0976
.99014
44,6
.00207
.98807
44,2
.01193
• 0977
•99059
44,6
.00207
.98852
44,2
.01148
.0978
.99103
44,5
.00207
.98896
44,1
.OIIO4
.0979
.99M8
44,5
.OO2O8
.98940
44,1
.OIOOO
0.0980
8.99192
44,5
O.OO2O8
0,4
8.98984
44,0
I.OIOI6
.0981
.99237
44,4
.00209
.99028
44,0
.00972
.0982
.99281
44,4
.OO2O9
.99072
43,9
.00928
.0983
.99325
44,3
.002O9
.99116
43,9
.00884
.0984
.99370
44,3
.O02IO
.99160
43,9
.00840
0.0985
8.994H
44,2
0.00210
0,4
8.09203
43,8
1.00797
.0086
.99458
44,2
.OO2I I
.99247
43,8
.00753
.0987
.99502
44,2
.00211
.99291
43,7
.00709
.0988
.99546
44J
.00212
•99335
43,7
.006(35
.0989
.99590
44,1
.OO2I2
•99378
43,6
.00622
0.0990
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
8.90639
43,4
1.00361
.0996
.99898
43,7
.00215
•99683
43,3
.00317
.0997
.99941
43,7
.00215
.99726
43,3
.00274
.0998
•99985
43,7
.002l6
•99769
46f2
.00231
.0999
9.00029
43,6
.OO2l6
.99812
43,-'
.00188
O.IOOO
9.00072
43,6
O.OO2I7
0,4
8.99856
43,1
1.00144
u
log tan gd u
« Fn'
log sec gd u
« Fo'
log sin gd u
« Fo'
log esc gd u
SMITHSONIAN TABLES
21
Logarithms of Hyperbolic Functions.
.
log sinh u
•-•V
log cosh u
.«
log tanh u
« Fo'
log coth u
I o.ioo
9.00072
435,7
0.00217
4,3
8.99856
431,4
1.00144
.101
.00506
431,5
.00221
4,4
9.00285
427,1
0.99715
.102
.00935
4-7,3
.O0226
4,4
.OO7IO
422,8
.99290
.103
4-3, 1
.0023O
4,5
.01131
4l8,7
.98869
.104
.01782
419,1
.00234
4,5
.01547
414,6
.98453
o. 105
9.02199
415,1
O.OO239
4,5
9.01960
410,6
0.98040
.100
.02612
411,2
.00244
4,6
.02368
406,7
.97632
.03021
407,4
.00248
4,6
.02773
402,8
.97227
.03427
403,7
•00253
4,7
.03174
399,o
.96826
.109
.03829
400,0
.00257
4,7
.03571
395,3
.96429
O.I 10
9.(
396,4
O.OO262
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 1
•H3
.05400
386,0
.00277
4,9
.05124
381,1
.94876
.114
.05785
382,6
.OO282
4,9
.05503
377,7
,.94497 1
i 0.115
9.06165
379,3
O.OO287
5,0
9.05879
374,3
0.94121
.06543
376,1
.OO292
5,o
.06252
.93748
.117
.06918
372,9
.00297
.06621
367!8
•93379 1
.118
.07289
369,8
.00302
5,1
.06987
364,7
•93013 1
.119
.07657
366,7
.00307
5,i
.07350
36i,5
.92650 I
; 0.120
9.08022
363,6
O.OO3I2
5,2
9.07710
358,5
0.92290 1
.121
.08384
360,7
.00317
5,2
.08067
355,4
•91933 I
.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
0.125
9.09804
349,2
0.00338
5,4
9.09466
343,8
0.90534 1
.126
.10152
346,5
.00344
5,4
.09808
34i,i
.90192 1
.127
5h
• 10497
343,8
.00349
5,5
. 10148
338,3
.89852 1
.128
.10840
341,1
.00355
5,5
. 10485
335,6
•89515
.11179
338,5
.00360
5,6
. 10819
333,0
.89181
0.130
9.II5I7
336,0
0.00366
5,6
9.HI5I
330,3
0.88849 1
.131
.11851
333,4
.00372
5,7
.11480
327,8
.88520
•132
.12183
330,9
•00377
5,7
.11806
325,2
.88194
.133
•134
.12513
.12840
328,5
326.0
.00383
.00389
5,7
5,8
.12130
• 12452
322,7
320,3
.87870
.87548
9.I3I65
323,7
0.00395
5,8
9.12771
317,8
0.87229 1
.138
•139
.13488
.13808
.14126
.14441
321,3
319,0
3l6,7
.00400
.00406
.00412
.00418
5,9
5,9
6,0
6,0
.13087
.13402
.13713
. 14023
315,4
313,1
310,7
308,5
.86913
.86598 1
.86287 1
.85977 I
0.140
.141
•M3
9.M
.15066
•15375
.15682
.15986
312,2
310,0
305,8
303,7
0.00424
.00430
.00436
.00443
.00449
6,0
6,1
6,1
6,2
6,2
9.14330
• M635
.14938
.15239
.15538
306,2
304,0
30i,8
209,6
297,5
0.85670 1
.85365 1
.85062 1
•84761
.84462 1
.149
9.16289
.17185
.17479
301,6
395,6
293,6
0.00455
.00461
.00468
.00474
.00480
6,3
6,3
6,3
6,4
6,4
9.15834
.16128
. 16420
.16711
.16999
295,4
293,3
291,2
289,2
287,2
0.84166 1
.83872
•83580
.83289
.83001
0.150
9.17772
291,7
0.00487
6,5
9.17285
285,2
0.82715 I
u
ofltingd u
og sec gd u
=====
« Fo'
-_
og sin gd u
—
« Fo'
ogcscgdu 1
Logarithms of Hyperbolic Functions.
u
log sinh u
« Fo'
log cosh u
-FO'
log tanh u
- Fo'
log coth u
0.150
9.17772
291,7
0.00487
6,5
9. 17^85
285,2
0.82715
.151
.18063
289,8
.00493
6,5
.17569
283,3
.82431
.152
.18351
287,9
.00500
6,6
.17852
.82148
.153
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
. 194^8
280,6
.00526
6,7
.18962
273,9
.81038
•157
. 197(18
278,9
.00533
6,8
. 19235
272, i
.80.
.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
0.7-
.101
.20870
272,1
.00560
6,9
.20310
265,1
.79690
.162
.21 141
270,4
.00567
7,o
•20574
263,4
.79426
.163
.21411
268,8
.00574
7,o
.20837
261,8
.79163
.I04
.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
.00596
7,i
.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
.235H
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
.733i8
.188
.27671
233,7
.00763
8,1
.26908
225,7
.73092
.189
.27004
232,5
.00771
8,1
.27133
224,4
.72867
0.190
9.28136
231,3
0.00779
8,2
9.27357
223,2
0.72
.191
.28367
230,1
.00787
8,2
.27580
221,9
.72420
.192
.28597
229,0
.00796
8,2
.27801
220,7
.193
.28825
227,8
.00804
8,3
.28021
219,5
.71979
.194
.29052
226,7
.00812
8,3
.28240
218,3
.71760
0.195
9.29278
225,5
0.00821
8,4
9.28458
217,2
0.715-;-'
.196
.29503
224,4
.00829
8,4
.28674
216,0
.71326
.197
.29727
223,3
.00837
8,4
.28890
214,9
.71110
.198
.29950
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
2H,5
0.70471
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.
1
log tinh u
« Fo'
log cosh u
• Fo'
log tanh u
« Fo'
log coth u
0.200
9.30392
22O.O
0.00863
8,6
9.29529
211,5
0.70471
.201
.30012
219,0
.00871
8,6
.29740
210,4
.70260
.202
.30830
217,9
.00880
8,7
.29950
209,3
.70050
.203
.31047
216,9
.00889
8,7
.30159
208,2
.69841
.204
.31264
215,8
.00897
8,7
.30366
207,1
.69634
0.205
9.3M79
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
• 3-2II9
211,8
.00933
8,9
.31186
202,9
.68814
.209
•32330
210,8
.00942
8,9
.31389
201,9
.68611
0.210
9.32541
209,8
0.00951
9,o
9.31590
200,8
0.68410
.211
• 3-750
208,9
.00960
9,o
.31790
199,8
.68210
.32958
207,9
.00969
9,i
.31900
198,8
.68010
•«3
.33166
207,0
.00978
9,i
.32188
197,9
.67812
.214
•33372
206,0
.00987
9,2
.32385
196,9
.67615
0.215
9.33578
205,1
0.00996
9,2
9.32582
195,9
0.67418
.33783
204,2
.01005
9,2
.32777
194,9
.67223
'2ll
.33086
203,3
.01015
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
0.220
9-34592
200,6
0.01043
9,4
9-33549
191,2
0.66451
•34792
199,7
.01052
9,4
•33740
190,3
.66260
• 34991
198,8
.01062
9,5
•33930
189,3
.66070
.35190
198,0
.01071
9,5
.34H9
188,4
.65881
.224
.35387
197,1
.01081
9,6
.34307
i87,5
•65693
0.225
.226
9.35584
.35780
196,3
195,4
0.01090
.01100
9,6
9,7
9.34494
.34680
186,7
185,8
0.65506
.65320
•35975
.36169
194,6
193,8
.01109
.01119
9,7
9,7
.34865
.35050
184,9
184,0
.65135
.64950
.229
.36362
193,0
.01129
9,8
.35234
183,2
.64766
O.23O
9.36555
192,1
0.01139
9,8
9.35416
182,3
0.64584
•231
.36747
I9i,3
.01149
9,9
.35598
181,5
.64402
.233
•234
.36938
.37128
.37317
ioo,5
189,8
189,0
.01158
.01168
.01178
9,9
9,9
10,0
•35779
•35959
.36139
180,6
179,8
179,0
.64221
.64047
.63861
0.235
• 239
9.37506
•37604
.37881
.38067
.38252
188,2
187,4
186,7
185,9
185,2
0.01188
.01198
.01208
.01219
.01229
10,0
10,1
10,1
10,1
10,2
9.36317
.36495
.36672
.36848
.37024
178,2
177,4
176,6
175,8
175,0
0.63683
.63505
.63328
.63152
.62976
0.240
.241
.242
•243
9.38437
.38621
.38805
.38987
.39109
184,4
i«3,7
i«3.o
182,2
i«i,5
0.01239
.01249
.01259
.01270
.01280
10,2
10,3
10,3
10,4
10,4
9.37108
.37372
•37545
•37717
.37889
174,2
173,4
172,6
i7i,9
171,1
0.62802
.62628
.62455
.62283
.62111
0.245
:•
..-.,
9-39350
•39531
•39710
.39889
.40068
180,8
1X0,1
178,0
0.01291
.01301
.01312
.01322
•01333
10,4
10,5
10,5
10,6
10,6
9.38060
.38230
.38309
.38567
.38735
170,4
169,6
168,9
168,1
167,4
0.61940
.61770
.61601
.61433
.61265
0.250
9.40245
177,3
0.01343
10,6
9.38002
166,7
0.61098
•
.
log tin Od u
«F,'
!!-
log tec gd u
-FO'
log sin gd u
<•> Fo'
log esc gd u
BH.TM.ON..H TA.LI. ' 1
24
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
9.38002
KA7
0.61098
.251
.404J2
176,6
.01354
10,7
.39069
.60931
.-'5-'
.40599
176,0
.01365
10,7
.39234
165,3
.60766
.253
.40774
175,3
.01375
10,8
.39399
.00001
• -'54
.40949
174,6
.01385
10,8
.39563
163,8
.00437
0.255
9.4II24
174,0
0.01397
10,8
9.39727
163,1
0.60273
.250
.41297
173,3
.01408
10,9
.39890
162,5
.00110
.-'57
.414/0
172,7
.01419
10,9
.40052
.59948
.258
.41643
172,0
.01430
II,O
.40213
161,1
-787
• -'59
.41814
171,4
.01441
11,0
•40374
160,4
• 59
0.260
9.41986
170,8
0.01452
11,0
9.40534
159,7
0.59466
•42TS6
170,2
.01463
n, i
.40693
I59,i
.59307
.262
.43326
169,5
.01474
11,1
.40852
158,4
.591-48
.263
.42495
168,9
.01485
11,2
.41010
157,8
08990
.264
.42664
168,3
.01496
11,2
.41168
I57,i
.5*
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
.38520
.267
•43166
166,5
.01530
ii,3
.41636
155,2
08364
.268
•43332
i65,9
.01541
11,4
.41791
154,5
.58209
.269
.43498
l65,3
.01553
11,4
•41945
153,9
08055
0.270
9.43663
164,7
0.01564
n,4
9.42099
153,3
0.57901
.271
.43827
164,2
.01576
n,5
.42252
152,7
.57/48
.272
.43991
163,6
.01587
n,5
.42404
152,1
.57;
• 273
.44154
163,0
.01599
11,6
.42556
151,4
.57444
.274
.44317
162,4
.Ol6lO
11,6
.42707
150,8
.572
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
.56093
.277
.44802
160,8
.01645
n,7
.43157
I49,o
.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
-'52
.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
M5,o
.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
M3,9
.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
14-',-'
.55096
O.20O
9.46847
153,9
0.01801
12,3
9.45046
MI.7
0.54054
.291
.47001
153,4
.01813
12,3
•45187
141,1
.54813
.292
.47154
152,9
.01826
12,3
.45328
140.0
.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
9.4/610
I5i,5
0.01863
12,5
9-45747
139.0
0.54253
.290
.47702
151,0
.01875
12,5
.45886
.54114
.297
.47912
150,5
.01888
12,5
.46024
138.0
.53976
.298
.48063
150,0
.01900
12,6
.46162
137,5
.53838
.299
.48212
149,0
.01913
12,6
.46299
1 36", 9
.53701
0.300
9.48362
I49J
0.01926
12,7
9.46436
136,4
0.53564
u
log tan gd u
« Fo'
log sec gd u
• IV
log sin gd u
•> Fo'
log esc gd u
SMITHSONIAN TABLES
Logarithms of Hyperbolic Functions.
u
log sinh u
««> FO'
log cosh u
«F0'
log tanh u
« Fo'
log coth u
0.300
9-48362
149,1
0.01926
12,7
9.46436
136,4
0.53564
.301
.48510
148,6
.01938
12,7
.46572
135,9
.53428
.302
.48659
148,-'
.01951
12,7
.46708
135,4
.53292
.303
.48807
.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
9.47H2
133,9
0.52888
.306
.49248
146,3
.02002
12,9
.47245
133,4
•52755
.307
.49394
145,9
.02015
12,9
•47379
133,0
.52621
.308
•49540
145,4
.O2028
13,0
•475II
132,5
•52489
.309
•49685
145,0
.O204I
13,0
.47644
132,0
•52356
0.310
9.49830
144,6
O.O2O54
13,0
9-47775
131,5
0.52225
.311
•49974
I44,i
.O206/
13,1
•47907
131,0
•52093
.312
.50118
143,7
.O2080
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
0.02120
13,2
9.48427
129,2
0.51573
.316
.50689
142,0
•02133
13,3
.48556
128,7
.51444
.317
.50831
141,6
.O2I46
13,3
.48684
128,2
.5UI6
.318
.50972
141,1
.02160
13,4
.48812
127,8
.51188
.319
•5III3
140,7
.02173
13,4
.48940
127,3
.51060
0.320'
9.51254
140,3
0.02187
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
0.02254
13,6
9.49696
124,7
0.50304
.326
.52088
137,9
.02268
13,7
.49820
124,2
.50180
•327
. 52226
137,5
.02282
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
0.02323
13,8
9.50314
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
I2O.8
.49200
0.335
9.53314
134,5
0.02393
14,0
9.50921
120,4
0.49079
.336
.53448
I34,i
.02407
14,1
.51041
1 2O,0
.48959
• 337
.53582
133,7
.O242I
14,1
.51161
119,6
.48839
.338
.53715
133,3
.02435
14,1
.51281
119,2
.48719
.339
.53849
133,0
.02449
14,2
.51400
118,8
.48600
0.340
9.53981
132,6
0.02463
14,2
9.5I5I8
118,4
0.48482
• 341
•54II4
132,3
.02478
14,3
.51636
118,0
.48364
• 342
04246
I3I,9
.02492
14,3
.51754
117,6
.48246
• 343
.54378
131,5
.02506
.51872
117,2
.48128
•344
•54509
131,2
.02520
14,4
.51989
116,8
.48011
0.345
•» jA
9.54640
130,8
0.02535
14,4
9.52105
116,4
0.47895
•340
•54771
130,5
•02549
14,5
.52221
116,0
•47779
• 347
.348
•54901
.55031
130,1
129,8
.02564
.02578
14,5
14,5
•52337
• 52453
H5,7
.47663
•47547
.55161
129,5
.02593
14,6
.52568
114^9
•47432
0.350
9.55200
129,1
0.02607
14,6
9.52682
H4,5
0.47318
u
log tan Od u
log sec gd u
« Fo'
log sin gd u
« Fa'
log esc gd u
SMITHSONIAN TABLE*
26
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
i_>X,,S
.02622
14,0
•52797
114,1
.47203
.352
•55547
I2&4
.02637
M,7
.529H
113,7
.47089
.353
.55676
128,1
.00651
M,7
.53024
I 13,4
• 354
.55804
1.27,8
.O9666
14,8
.53137
113,0
0.355
9.55931
127,4
0.02681
14,8
9.53250
112,6
0.46750
• 350
.56059
127,1
.02696
M,8
.53363
H2.3
"37
• 357
.56185
126,8
.02711
M,9
•53475
1 11,9
.46525
• 358
.50312
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
0.53809
no.8
0.46191
.361
.56690
125,5
.02770
I5,o
.53919
110,5
.46081
.362
.56815
125,2
.02786
I5,i
.54030
110,1
•45970
.363
.56940
124,8
.02801
i5,i
•54140
109,7
.45860
.364
.57065
124,5
.02816
i5,i
.54249
109,4
.45751
0.365
9.57189
124,2
0.02831
15,2
9.54358
109,0
0.45642
.366
.57313
123,9
.0284:)
15,2
04467
108,7
•45533
.367
•57437
123,6
.02861
15,3
•54576
108,3
.45424
.368
.57561
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
0.02007
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
.55113
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
1 2O,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
.44M8
0.380
9.59019
H9,7
0.03063
15,8
9.55956
104,0
0.44044
.381
.59138
ii9,5
.03079
15,8
.56059
103,7
.43941
.382
.59257
119,2
•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
1 1 8,0
.03158
16,0
.56574
IO2.I
.43426
.387
•59850
117,8
.03174
16,0
.56676
101,8
.43324
.388
.50967
H7,5
.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
9.57480
99,3
0.42520
.396
.60899
H5,3
.03320
16,4
•57579
09,0
.42421
• 397
.61014
H5,i
.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
iM,3
0.03385
16,5
9-57973
97,8
0.42027
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
«F0'
log tanh u
« Fo'
log coth u
0.400
9.61358
114,3
0.03385
16,5
9-57973
97,8
0.42027
.401
.61472
114,0
.03402
16,5
08070
97,5
.41930
.402
.61586
ii3,8
.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
H3,0
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
1 1 2,0
.03535
16,8
.58841
95,2
•4II59
0.410
9.62488
111,8
0.03552
16,9
9.58936
94,9
0.41064
.411
.62600
111,6
.03569
16,9
.59031
94,6
.40969
.412
.62711
iii,3
.03586
16,9
.59125
94,4
•40875
.413
.62823
in, i
.03603
17,0
.59220
94,i
.40780
.414
.62934
110,8
.03620
17,0
.59314
93,8
.40686
0.415
9.63044
1 1 0,6
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,o
. 40406
.418
.63375
109,9
.03688
17,2
.59587
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
9i,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
0.39671
.426
.64247
108,0
.03827
17,5
.60420
90,6
.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
0.03986
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
1 8,0
.61836
86,5
.38164
•443
.66052
104,4
.04129
18,1
.61923
86,3
.38077
.66156
104,2
.04147
18,1
.62009
86,1
•37991
0.445
9.66260
.66364
104,0
103,7
0.04165
.04183
18,1
18,2
9.62095
.62180
85,8
85,6
0.37905
.37820
.66468
103,5
. 04202
18,2
.62266
85,3
•37734
• MB
.66571
.66674
103,3
103,1
.04220
.04238
18,3
18,3
•62351
.62436
85,1
84,9
.37649
.3/504
0.450
9.66777
102,9
0.04256
18,3
9.62521
84,6
0.37479
u loo tan <jd u
« Fo'
og sec gd u
« Fo'
og sin gd u
w Fo'
log esc gd u
SMITHSONIAN TABLES
28
Logarithms of Hyperbolic Functions.
u
log sinh u
o> Fo'
log cosh u
«- Fo' 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
-'OO5
84,4
•37395
.452
.66983
102,5
.04293
18,4
.62690
84,1
•37310
• 453
.(>7085
102,3
.04312
18,4
.62774
.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
.0438 >
18,6
.63107
83,0
.36883
.458
.^7594
101,4
.04404
18,6
.63100
82,8
.36810
• 459
.67696
IOI,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
.0459-2
19,0
.64007
80,5
.35993
.409
.68698
99,3
.04611
19,0
.64087
80,3
.35913
0.470
9.68797
99,1
0.04630
19,0
9.64167
80, i
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
.0470^
19,2
.64486
79,2
.35514
0.475
9.69290
98,2
0.04726
19,2
9.64565
79,o
0.35435
: -476
.69388
98,0
•04745
19,2
.64644
78,8
.35356
• 477
.69486
97,8
.04764
19,3
.64722
78,6
.35278
.4/8
.69584
97,7
.04783
19,3
.64801
78,4
•35199
• 479
.69682
97,5
.04803
19,3
•64879
78,2
-35I2I
0.480
9.09779
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
.65113
77,5
.34887
.483
.70070
96,8
.04880
19,5
.65190
77,3
.34810
; .484
.70167
06,6
.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,i
.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
.7H25
95,0
.05097
19,9
.66028
75,i
•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'
log esc gd u
SMITHSONIAN TABLES
Logarithms of Hyperbolic Functions.
u
log sinh u
<- Fo7
log cosh u
«F0'
log tanh u
co Fo'
log coth u
0.500
9.71692
94,0
0.05217
20,1
9.66475
73,9
0.33525
.501
.71785
93,8
.05237
20,1
.66549
73,7
•33451
.502
.71879
93,7
.05257
2O, I
.66623
73,5
•33377
.503
.71973
93,5
.05277
20,2
.66696
73,3
•33304
.504
.72066
93,3
.05297
20,2
.66769
73,i
•33231
0.505
9.72160
93,2
0.05317
20,2
9.66842
72,9
0.33158
-505
.72253
93,o
.05338
20,3
.66915
72,8
•33085
• 507
.72346
92,9
.05358
20,3
.66988
72,6
.33012
.508
.7-M38
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,o
0.32795 1
•511
.72716
92,3
•05439
20,4
.67277
7i,8
.32723
•512
.72808
92,1
.05460
20,5
.67348
7i,6
• 32652
.513
.72000
92,0
.05480
20,5
.67420
7i,5
.32580
oM
.72992
91,8
.05501
20,5
.67491
71,3
.32509 1
0.515
9.73084
91,7
0.05521
20,6
9.67562
7U
0.32438 1
.516
.73175
91,5
•05542
20,6
.67633
70,9
.32367 1
• 517
.73267
91,4
•05563
20,6
.67704
70,7
.32296
.518
.73358
91,2
.05583
20,7
.67775
70,5
. 32225
.519
.73449
91,1
.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,o
•32014 1
• 522
.73722
90,6
.05666
20,8
.68056
69,8
.31944 1
.523
.73812
90,5
.05687
20,8
.68125
69,6
.31875 1
•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 1
.526
.74083
90,0
.05750
20,9
.68333
69,1
.31667
•527
.74173
£9'§
.05771
2I,O
.68402
68,9
.31598
.528
•74263
89,8
.05792
21,0
.68471
68,7
.31529
•529
•74353
89,6
.05813
2I,O
.68540
68,6
.31460 1
0.530
9-74442
89,5
0.05834
21,1
9.68608
68,4
0.31392 1
•531
•74532
89,3
•05855
21,1
.68677
68,2
.31323 1
• 532
.74621
89,2
.05876
21,1
.68745
68,0
.31255 1
•533
•74710
89,1
•05897
21,2
.68813
67,9
•31187 1
•534
•74799
88,9
.05918
21,2
.68880
67,7
.31120
0.535
.536
9.74888
.74976
88,8
88,6
0.05940
.05961
21,2
21,3
9.68948
.69016
67,5
67,4
0.31052 1
.30984 1
•537
.75065
88,5
.05982
21,3
.69083
67,2
.30917 1
.538
•75153
88,4
.06004
21,3
.69150
67,0
•30850 1
• 539
•75242
88,2
.06025
21,4
.69217
66,9
.30783
0.540
• 541
.542
•543
•544
9-75330
•75418
•75506
•75594
.75681
88,1
88,0
87,8
87,7
87,6
0.06046
.06068
.06089
.06111
.06132
21,4
21,4
21,5
21,5
21,5
9.69284
.69350
.09417
.69483
.69549
66,7
66,5
66,3
66,2
66,0
0.30716
.30650
.30583
•30517 |
.30451
0.545
• 546
•547
.548
9.75769
.75856
•75943
.76030
.76117
87,4
87,3
87,2
87,0
86,9
0.06154
.06175
.06197
.06219
.06240
21,6
21,6
21,6
21,7
21,7
9.69615
.69681
.69746
.69812
.69877
65,9
65,7
65,5
65,4
65,2
0.30385
.30319
.30254 1
.30188
•30123 1
0.550
9.76204
86,8
0.06262
21,7
9.69942
65,0
0.30058
u
oo tan Od u
• FO'
og sec gd u
« Fo'
log sin gd u
« Fo'
log esc gd u 1
SMITHSONIAN T*«n«
Logarithms of Hyperbolic Functions.
u
loo sinh u
« Fo'
log cosh u
«F0'
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
1
.55.2
.76377
86,5
.06306
21,8
.70072
.2992
• 553
86,4
.06327
21,8
.70137
>53
• 554
.70550
86,3
.06349
21,9
.7O2OI
04,4
0.555
9-76636
86,1
0.06371
21,9
9-70265
64,2
0.2ft
.556
.76722
86,0
.06393
21,9
.70329
.29' -71
• 557
.76808
85,9
.06415
22,0
.70393
63,9
• 558
.76894
85,7
.06437
22,0
•70457
63,7
543
• 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
0.29410
.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
.509
.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
.28-. .
.574
.78250
83,8
.06793
22,5
.71457
61,3
.28543
0.575
9.78334
83,7
0.06816
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
9-7875I
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
.00974
22,8
.71943
00,1
.28057
.583
.79000
82,7
.06997
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
.2,-SiS
.587
•79330
82,3
.07088
22,9
.72242
59,4
.27758
.588
•794T2
82,2
.07111
23,0
.72301
59,2
.27699
.589
•79494
82,1
.07134
23,0
.72360
59,1
.27640
0.590
9.79576
82,0
0.07157
23,0
9.72419
58,9
0.27581
• 591
.79658
81,8
.07180
23,0
.72478
58,8
• -'7522
• 5<>2
•79740
81,7
.07203
23,1
.72537
58,7
.27463
• 593
.79822
81,6
.07226
23,1
.72595
58,5
.27405
•594
•79903
8i,5
.07-M9
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
•07342
33,3
.7-'886
57,8
.27114
• 599
.80309
81,0
.07366
23,3
.72944
57,7
.27056
0.600
9-80300
80,9
0.07389
23,3
9-73001
57,5
0.26099
u
log tan gd u
<- Fo'
log sec gd u w Fo'
log sin gd u
« Fo'
log esc gd u
SMITHSONIAN TABLES
Logarithms of Hyperbolic Functions.
u
log sinh u
«F0'
log cosh u
«F0'
log tanh u
« Fo'
log coth u
0.000
9.80390
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
.73H6
57,3
.26884
.603
.80632
80,5
.07459
23,4
.73173
57,i
.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
.80874
80,2
.07529
23,5
•73344
56,7
.26656
.607
.80954
80, 1
•07553
23,5
•73401
56,6
.26599
.608
.81034
80,0
.07576
23,6
•73457
56,5
.26543
.609
.81114
79,9
.07600
23,6
.73514
56,3
.26486
0.610
9.81194
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,i
.07790
23,8
.73960
55,3
.26040
.618
.81829
79,o
.07814
23,9
.74015
55,i
.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
.25711
.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
54,1
.25548
.627
.82536
78,i
.08030
24,1
.74506
54,o
•25494
.628
.82614
78,o
.08054
24,2
.74560
53,8
.25440
.629
.82692
77,9
.08078
24,2
.74614
53,7
.25386
0.630
9.82770
77,8
0.08102
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
•74774
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
•?33i2
77,2
.08273
24,4
.75040
52,7
.24960
.638
.83389
77,i
.08297
24,5
.75092
52,6
.24908
•639
.83466
77,0
.08322
24,5
•75145
52,5
.24855
0.640
.644
9.83543
.83620
.83697
.83774
.83850
76,9
76,8
76,7
76,6
76,5
0.08346
.08371
•0&395
.08420
.08445
24,5
24,6
24,6
24,6
24,7
9.75197
.75249
• 75302
.75354
.75406
52,3
52,2
52,i
52,o
5i,9
0.24803
.24751
.24698
.24646
.24594
?
9.83927
.84003
.84079
.84155
.84232
76,4
76,3
76,2
76,i
76,1
0.08469
.08494
.08519
•08543
.08568
24,7
24,7
24,7
24,8
24,8
9-75457
.75509
.75561
.75612
.75663
5i,7
5i,6
5i,5
5i,4
51,3
0.24543
.24491
.24439
•24388
.24337
0.650
9.84308
76,o
0.08593
24,8
9.75715
Sltl
0.24285
u
log tan ad u
« Fo'
log sec gd u
« Fo'
log sin gd u
• For
log esc gd u
Logarithms of Hyperbolic Functions.
u
log sinh u
«F0'
log cosh u
• FO'
log tanh u
• Fo'
log coth u
0.650
9.84308
76,0
0.08593
24,8
9.75715
$1,1
0.24285
.651
.84383
75,9
.O86l8
24,9
.75766
51,0
A34
.652
.84459
75,8
.08643
24,9
50,9
.24183
.653
.84535
75,7
.08668
24,9
.75867
50,8
•-'41 33
.654
.84011
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
.70019
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
50,0
0.23780
.661
-85138
75,0
.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
0.665
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
742
.09121
25,4
.76763
48,7
.23237
.672
.85958
74,1
.09146
25,5
.76812
48,6
.23188
.673
.86032
74,0
.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
.86621
73,3
.09377
25,7
.77245
47,6
•22755
.682
.86694
73,3
.09402
25,7
.77292
47,5
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,o
0.09480
25,8
9.77434
47,2
0.22566
.686
.86987
72,9
.09505
25,9
.77481
47,1
.22519
.687
.87060
72,9
•09531
25,9
.77528
47,0
.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
0.22099
.696
.87712
72,2
.09765
26,1
.77947
46,0
.22053
.697
•87784
72,i
.09792
26,2
.77993
45,9
.22007
.608
.87856
72,o
.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
« Fo'
log esc gd u
SMITHSONIAN TABLES
33
Logarithms of Hyperbolic Functions.
u
log sinh u
U, Fo'
log cosh u
«F0'
log tanh u
« Fo'
log coth u
0.700
.701
9.88000
.88072
71,9
71,8
0.09870
.0989)
26,2
26,3
9.78130
.78176
45,6
45,5
0.21870
.21824
.702
.88144
.09923
26,3
.78221
45,4
•21779
• j\J*»
.701
.88216
71 6
.09949
26,3
.78266
45,3
.21734
• /V'O
.704
.88287
7MS
.09975
26,4
.78312
45,2
.21688
0.705
.706
9.88359
.88430
7i,5
7i,4
O.IOOO2
. 10028
26,4
26,4
9.78357
.78402
45,1
45,0
0.21643
.21598
.707
.88502
.10055
26,4
.78447
44,9
.21553
• / v/
.708
.88573
7^3
.I008l
26,5
.78492
44,8
.21508
.709
.88644
71^2
.IOIO8
26,5
.78536
44,7
.21464
0.710
9.88715
71,1
O.IOI34
26,5
9.78581
44,6
0.21419
.711
.88786
71,0
.I0l6l
26,5
.78626
44,5
.21374
.712
.88857
71,0
. IOl87
26,6
.78670
44,4
.21330
.88928
70,9
.10214
26,6
.78714
44,3
.21286
.714
.88999
70,8
. IO24O
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
•21153
.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
0.10401
26,8
9.79022
43,6
O.2O978
.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
70,1
.10508
26,9
.79196
43,2
.20804
0.725
9.89774
70,0
0.10535
26,9
9.79239
43,1
0.20761
.726
.89844
70,0
. 10562
27,O
.79282
43,0
.20718
.727
.89914
69,9
.10589
27,0
.79325
42,9
.20675
.728
•89984
69,8
.10616
27,0
.79368
42,8
.20632
.729
.00054
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
.10697
27,1
.79496
42,5
.20504
• 732
.90263
69,6
. 10724
27,1
.79538
42,5
. 20462
• 733
.00332
69,5
.10751
27,1
.79581
42,4
.20419
• 734
.90402
69,4
. 10778
27,2
.79623
42,3
.20377
0.735
9.90471
69,4
0.10806
27,2
9.79665
42,2
0.20335
.736
.90540
69,3
. 10833
27,2
.79708
42,1
. 20292
• 737
.90610
69,2
.10860
27,2
.79750
42,0
. 20250
.738
.90679
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
41,7
0.20125
.741
,90886
69,0
.10969
27,3
.79917
41,6
.20083
.90955
68,9
.10997
27,4
.79958
41,5
.20042
.743
68,8
. i 1024
27,4
.80000
' 41,4
.20000
.91092
68,8
.11051
27,4
.80041
41,3
. • 19959
0.745
9.911'.!
68,7
0.11079
27,5
9.80082
41,2
0.19918
.91230
68,6
.11106
27,5
.80124
41,2
.19876
.91208
.11134
27,5
.80165
41,1
•19835
68^5
.11161
27,5
.80206
41,0
• 19794
68*4
.11189
27,6
.80247
40,9
. 19753
0.750
9.91504
68,4
0.11216
27,6
9.80288
40,8
0.19712
a
log tin gd u
"F°'
log sec gd u
»F0'
log sin gd u
«- Fo'
log esc gd u
SMITHSONIAN TABLES
34
Logarithms of Hyperbolic Functions.
u
log sinh u
« Fo'
log cosh u
-Fo'
log tanh u
-Fo'
log coth u
0.750
9.91504
68,4
O.H2I6
27,6
9.80288
40,8
O.I',
.751
.91572
68,3
.11244
27,6
.80328
40,7
.10672
• 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
O.I95IO
.756
.91913
68,0
.11382
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
•II549
27,9
.80771
39,7
.19229
.763
.92387
67,6
•II577
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
O.I9III
.766
.92590
67,4
.11661
28,0
.80929
39,4
.19071
.767
.92657
67,3
.11689
28,0
.80968
39,3
.10032
.768
.92724
67,3
.11717
28,0
.81007
39,2
.18993
.769
.92792
67,2
•II745
28,1
.81047
39,1
.18953
0.770
9.92859
67,1
O.II773
28,1
9.81086
39,0
0.18914
.771
.92926
67,1
.11801
28,1
.81125
39,0
.18875
.772
.92993
67,0
. i 1829
28,1
.81164
38,9
.18836
• 773
.93060
67,0
.11858
28,2
.81202
38,8
.18798
• 774
.93127
66,9
.11886
28,2
.81241
38,7
• 18759
0./75
9.93194
66,8
0.11914
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
.11999
28,3
.81395
38,4
.18605
• 779
.93461
66,6
. 12027
28,3
.81434
38,3
.18566
0.780
9.93527
66,5
o. 12055
28,3
9.81472
38,2
0.18528
.781
.93594
66,5
.12084
28,4
.81510
38,1
.18400
.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
.12109
28,4
.81624
37,9
.18376
0.785
9.93859
66,2
O.I2I97
28,5
9.81662
37,8
o. 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
.12309
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
37,1
.18039
• 794
. -94453
65,7
.12455
28,7
.81908
37,0
.18002
0.795
9.94519
65,7
0. 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
.9478i
65,5
.12598
28,8
.82183
36,6
.17817
0.800
9-94846
65,4
0.12627
28,8
9.82219
36,6
0.17781
u
log tan gd u
w Fo'
log sec gd u
« Fo'
log sin gd u
« Fo'
log esc gd u
SMITHSONIAN TABLES
35
Logarithms of Hyperbolic Functions.
u
log sinh u
u, Fo'
log cosh u
«F0'
log tanh u
w 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
. 17/08
.803
.95042
65,2
.12714
28,9
.82329
36,3
.17671
*•*
.804
.95108
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
65,0
. 12859
29,0
.82509
35,9
. 17491
.809
•95433
64,9
.12888
29,I
.82545
35,9
• 17455
0.810
9.95498
64,9
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
0.13209
29,3
9.82935
35,o
0.17065
.821
.96208
64,3
.13238
29,3
.82970
34,9
. 17030
.822
.96272
64,2
.13268
29,4
.83005
34,9
.10995
.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
o. 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
34,1
. 16650
.833
.96976
63,7
. 13592
29,6
.83384
34,0
.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
'$1
.97230
63,5
.13711
29,7
.83519
33,8
. 16481
.838
.97293
63,4
. 13740
29,7
.83553
33,7
. 16447
.839
•97357
63,4
. 13770
29,8
.83587
33,6
.16413
0.840
9.97420
63,3
0.13800
29,8
9.83620
33,5
0.16380
.841
.97484
63,3
.13830
29,8
.83654
33,5
. 16346
.842
.843
•97547
.97610
63,2
63,2
.13860
.13889
29,8
29,9
.83687
.83721
33,4
33,3
.16313
. 16279
• 844
.97673
63,1
. 13919
29,9
.83754
33,3
. 16246
0.845
9.97736
63,1
0.13949
29,9
9.83787
33,2
0.16213
.846
63,0
. 13979
29,9
.83820
33,1
.16180
.847
, ,
63,0
.14009
29,9
•83853
33,0
.16147
.97988
62,9
62,9
. 14039
.14069
30,0
30,0
.83886
.83919
33,0
32,9
.16114
.16081
0.850
9.98051
62,8
0.14099
30,0
9.83952
32,8
0.16048
I
log tan gd U
- Fo'
log sec gd u
« Fu'
loo sin gd u
» Fo'
log esc gd u
SMITHSONIAN TABLCS
Logarithms of Hyperbolic Functions.
u
log sinh u
« F,/
log cosh u
-F,/
log tanh u
« Fo'
log coth u
0.850
9.98051
62,8
o. 14099
30,0
9.83952
32,8
0.16048
.851
|8lI4
<>j,X
.14129
30,0
.839«5
'Ji5
.852
.98177
62,7
.14159
30,1
.84018
.15982
.853
.08239
62,7
.14189
30,1
.84050
•50
.854
.98302
62,7
.14219
30,1
.84083
3-V>
.15917
0.855
9.08365
62,6
0.14249
30,1
9.84115
32,5
0.15885
.856
.98427
62,6
. 14279
30,1
.84M8
32,4
.15852
.857
.08490
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
•08739
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
. 14521
30,3
.84405
31,9
.15595
0.865
9.98988
62,1
0.14552
30,3
9.84437
31,8
0.15563
.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
3i,6
.15468
.869
.99237
62,0
. 14673
30,4
.84563
3i,5
•15437
0.870
9.99299
61,9
0.14704
30,5
9.84595
3i,5
0.15405
.871
.99361
61,9
. 14734
30,5
.84626
3i,4
. 15374
.872
.99422
61,8
. 14765
30,5
.84658
3i,3
.15342
.873
.99484
61,8
. 14795
30,5
.84689
3i,3
.I53H
.874
.99546
6i,7
. 14826
30,5
.84720
3i,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
3i,i
.15217
.877
.99731
61,6
. 14917
30,6
.84814
3i,o
.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
9.84906
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
6i,3
.15101
30,7
.84998
30,6
.15002
.884
.00161
6i,3
.15132
30,8
.85029
30,5
• M97I
0.885
O.O0222
6i,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
.883
.00406
61,1
.15255
30,9
.85151
30,3
. 14849
.889
.00467
61,1
.15286
30,9
.85181
30,2
. 14819
0.850
O.O0528
61,0
0.15317
30,9
9.852II
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
.14609
• 894
.00772
60,9
.15441
3i,o
.85331
29,9
.14669
0.895
0.00833
60,8
o. 15472
31,0
9.85361
29,8
o. 14639
.896
.00894
60,8
.15503
3i,o
.85391
29,8
.14609
.897
.00955
60,8
.15534
31,0
.85421
29,7
. M579
.898
.01015
60,7
. 15565
3i,i
.85450
29,6
. M550
.899
.01076
60,7
.15596
3IJ
.85480
29,6
.14520
O.QOO
0.01137
60,6
o. 15627
3i,i
9.85509
29,5
o. 14491
U
log tan gd u
« 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
«F0'
log tanh u
« Fo'
log coth u
0.900
O.OII37
60,6
0.15627
31,1
9.85509
29,5
0.14491
.901
.01197
60,6
.15658
31,1
.85539
29,5
.14461
.902
.01258
60,5
.15689
31,2
.85568
29,4
.14432
.903
.01318
60,5
.15721
31,2
.85598
29,3
. 14402
.904
.01379
60,5
.15752
31,2
.85627
29,3
. M373
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
.Ol68l
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
.Ol8oi
00,2
. I597I
31,3
.85830
28,8
. 14170
.912
.01861
60, 1
.16002
31,4
.85859
28,8
.14141
.913
.01921
GO, I
.16033
31,4
.85888
28,7
.14112
.914
.01981
6O, I
.16065
31,4
.85917
28,7
.14083
0.915
O.O2O4I
00,0
0.16096
31,4
9.85945
28,6
0.14055
.916
.02101
60,0
. 16128
31,4
.85974
28,5
. 14026
.917
,O2l6l
59,9
.16159
31,5
.86002
28,5
.13998
.918
.O222I
59,9
.16191
31,5
.86031
28,4
.13069
.919
.O228l
59,9
. 16222
31,5
.86059
28,4
.13941
0.920
0.02341
59,8
0.16254
31,5
9.86088
28,3
0.13912
.921
.O24OI
59,8
. 16285
31,5
.86116
28,2
.13884
.922
.02461
59,8
. 16317
3i,6
.86144
28,2
. 13856
.923
.O252O
59,7
. 16348
3i,6
.86172
28,1
. 13828
.924
.O2580
59,7
. 16380
3i,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
.O28l9
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
o. 16570
3i,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
.86450
27,5
. 13550
•934
.03175
59,3
.16697
31,8
.86478
27,5
. 13522
0.935
0.03234
59,3
o . 16729
31,8
9-86505
27,4
0.13495
.03293
59,2
. 16761
31,9
.86533
27,4
. 13467
.03353
59,2
. 16792
31,9
.86560
27,3
.13440
.938
.03412
59,1
. 16824
31,9
.86587
27,3
. I34I3
•939
.03471
59,1
.16856
31,9
.86615
27,2
. 13385
0.940
0.03530
59,1
0.16888
31,9
9.86642
27,1
o. 13358
•03589
59,0
.16920
32,0
.86669
27,1
.13331
.03648
59,0
.16952
32,0
.86696
27,0
. 13304
•'Ml
.03707
.03766
59,0
58,9
.16984
. 17016
32,0
32,0
.86723
.86750
27,0
26,9
. 13277
. 13250
0.03825
.03884
58,9
58,9
0.17048
.17080
32,0
32,0
9.86777
.86804
26,9
26,8
0.13223
.13196
it
.03943
58,8
. 17112
32,1
.86830
26,7
.13170
.04001
.04060
58,8
58,7
.17144
.17176
32,1
32,1
.86857
.86884
26,7
26,6
.I3U3
.13116
0-950
0.04119
5*£
0.17208
32,1
9.86910
26,6
o. 13090
u
log tin gd u
log sec gd u
.w
log sin gd u
w Fo'
log esc gd u
SMITHSONIAN TABLED
Logarithms of Hyperbolic Functions.
u
log sinh u
a, Fo'
log cosh u
«F0'
log tanh u
«FO'
log coth u
0.950
0.041 I<;
58,7
0.17208
32,1
9.86910
26,6
0.13090
.951
.04178
58,7
.17241
3-M
.86937
26,5
.13063
.952
.04236
58,6
. 17273
32,2
.86Q63
26,5
.13037
•953
.04295
58,6
.17305
3-V
.86990
26,4
.13010
•954
•04353
58,6
.17337
3-7,-'
.87016
26,4
.12984
0.955
0.04412
58,5
o. 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
. i 2905
.958
.04587
58,4
.17466
32,3
.87121
26,1
. i 2879
• 959
.04646
58,4
.17498
32,3
.87M7
26,1
.12853
0.960
0.04704
58,4
o.i753i
32,3
9.87173
26,0
0.12827
.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
.127.';
.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
o. 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
o. 12569
.971
.05344
58,0
.17887
32,5
.87456
25,4
.12544
.972
.05402
57,9
.17920
32,6
.87482
25,4
.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
.12021
• 993
.06611
57,2
.18608
32,9
.88003
24,3
.11997
•994
.06669
57,2
.18641
33,o
.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
33,0
.88076
24.1
.11924
•997
.06840
57,i
. 18740
33,0
.88100
24,1
.II9OO
.998
.06897
57,i
.18773
33,o
.88124
24,0
. 1 1876
.999
.06954
57,1
.18806
33,i
.88148
24,0
.11852
1. 000
0.07011
57,o
0.18839
33,1
9.88172
23,9
O.II828
u
log tan gd u
co Fo'
log sec gd u
«0 Fu'
log sin gd u
*> F/
log esc gd u
SMITHSONIAN TABLES
39
Logarithms of Hyperbolic Functions.
u
log sinh u
« Fo'
log cosh u
«Fo'
log tanh u
« Fo'
log coth u
I.OOO
O.070II
57,o
0.18839
33J
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
0.10004
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
I.OIO
0.07580
56,7
0.19171
33,3
9.88409
23,5
0.11591
.on
.07637
56,7
. 19204
33,3
.88433
23,4
.11567
.012
.07693
56,7
.19237
33,3
.88456
23,4
.11544
.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.I 1474
.016
.0792O
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
.19471
33,4
.88619
23,0
.11381
i. 020
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
1.025
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
I.O3O
0.08708
56,1
0.19839
33,6
9.88869
22,5
0.11131
.031
.08764
56,i
.10873
33,6
.88891
22,5
.11109
.032
.08820
56,i
.19906
33,6
.88914
22,4
.11086
• 033
.08876
56,o
.19940
33,7
.88936
22,4
.11064
• 034
.08932
56,o
.19974
33,7
.88959
22,3
.11041
1.035
0.08988
56,o
0.20007
33,7
9.88981
22,3
0.11019
.036
.00044
55,9
.20041
33,7
.89003
22,2
.10597
.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
.89070
22,1
. 10930
1.040
0.09268
55,8
0.20176
33,8
9.89092
22,0
0.10908
.041
.09324
55,8
.20210
33,8
.89114
22,O
.10886
.042
.09379
55,8
.20244
33,8
.89136
22,O
.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
o. 10709
.09602
55,7
.20379
33,9
.89223
21,8
. 10777
.047
.09658
55,<>
.20413
33,9
.89245
21,7
. 10755
.048
55,6
.20447
33,9
.89267
21,7
. 10733
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
•
loo tan gd u
-Fo'
log sec gd u
- F,,'
log sin gd u
« Fo'
log esc gd u
SMITHSONIAN TAULKS
Logarithms of Hyperbolic Functions.
u
log sinh u
« Fu'
log cosh u
«Fo'
log tanh u
- Fo'
log coth u
1.050
0.00825
55,6
0.20515
34,0
9.89310
21,6
0.10690
.051
.09880
55,5
• 20549
34,o
1331
21,6
.10669
.052
.09936
55,5
.20583
34,o
.89353
21,5
.10647
• 053
.09991
55,5
.20617
34,o
.89375
21,5
.10625
• 054
.10047
55,4
.20651
34,0
.89396
21,4
.10604
1.055
O.IOIO2
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
.89400
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
34,1
.89545
21,1
. 10455
.062
.10489
55,2
.20924
34,2
.89566
21,1
• 10434
.063
• 10545
55,2
.20958
34,2
.89587
2I,O
.10413
.064
.10600
55,2
.20992
34,2
.89608
21,0
. 10392
1.065
0.10655
55,i
0.21026
34,2
9.89629
20,9
0.10371
.066
.I07IO
55,i
.21060
34,2
.89650
20,9
. 10350
.067
. 10765
55,i
.21094
34,2
.89671
20,9
.10329
.068
.IO82O
55,i
.21129
34,3
.89692
20,8
.10308
.069
.10875
55,0
.21163
34,3
.89712
20,8
.10288
1.070
o. 10930
55,o
0.21197
34,3
9.89733
20,7
0.10267
.071
.10985
55,o
.21232
34,3
.89754
20,7
. 10246
.072
. 1 1040
55,o
.21266
34,3
.89774
20,6
.10226
.073
.11095
54,9
.21300
34,3
.89795
20,6
. 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
.IOIO2
.079
.11424
54,8
.21507
34,4
.89918
20,3
.10082
1.080
O.I 1479
54,8
0.21541
34,4
9.89938
20,3
O.IO062
.081
.11534
54,7
.21575
34,5
.89959
20,3
.IOO4I
.082
.11589
54,7
.21610
34,5
.89979
20,2
.IOO2 I
.083
.11643
54,7
.21644
34,5
.89999
20,2
.IOOOI
.084
.11698
54,7
.21679
34,5
.90019
20,1
.09981
1.085
0.11753
54,6
0.21713
34,5
9.90039
20,1
0.09961
.086
.11807
54,6
.21748
34,5
.90059
20,1
.09941
.087
.11862
54,6
.21782
34,6
.90079
20,0
.09921
.088
.11916
54,5
.21817
34,6
.90009
2O,O
.09901
.089
.11971
54,5
.21852
34,6
.90119
19,9
.09881
1.090
0.12025
54,5
0.21886
34,6
9.90139
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
0.09762
.096
. 12352
54,4
.22094
34,7
.90258
19,6
.09742
.097
.12406
54,3
.22129
34,7
.00277
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
»F0'
log sin gd u
« Fo'
log esc gd u
SMITHSONIAN TABLES
Logarithms of Hyperbolic Functions.
u
log sinh u
«F0'
log cosh u
«F0'
log tanh u
« Fo'
log coth u
I.IOO
.101
0.12569
.12623
54,3
54,2
0.22233
.22268
34,8
34,8
9.90336
.90356
19,5
19,4
0.09664
.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
1. 105
0.12840
54,i
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
.90510
19,1
.09490
[.IIC
O.I3III
540
0.22582
34,9
9.90529
I9,i
0.09471
.III
.13165
54,o
.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
I. US
0.13380
53,9
0.22756
35,0
9.90624
18,9
0.09376
.116
• 13434
53,9
.22791
35,o
.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,i
.90699
18,7
.09301
I. 120
o. 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,i
.90755
18,6
.09245
.123
.i38u
53,7
.23037
35,i
.00774
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
18,5
0.09189
.125
. 13972
53,6
.23142
35,2
.90830
18,5
.09170
.127
. 14025
53,6
.23177
35,2
.90848
18,4
.09152
.128
• U079
53,6
.23213
35,2
.90866
18,4
.09134
.129
.14133
53,6
.23248
35,2
.90885
18,4
.09115
I.I3O
0.14186
53,5
0.23283
35,2
9.90903
18,3
0.09097
.131
. 14240
53,5
.23318
35,2
.90921
18,3
.09079
.132
.M293
53,5
.23353
35,3
.90940
18,3
.09060
•133
. U347
53,5
.23389
35,3
.00958
18,2
.05042
•134
.14400
53,5
.23424
35,3
.90976
18,2
.09024
I.I35
0.14454
53,4
0.23459
35,3
9.90994
18,1
0.09006
.136
.14507
53,4
.23495
35.3
.9IOI2
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
I.I40
0.14720
53,3
0.23636
35,4
9.91085
18,0
0.08915
.141
. M774
53,3
.23671
35,4
.9IIO2
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
• M934
53,2
.23778
35,4
.91156
17,8
.08844
1
0. 14987
.15040
53,2
53,2
0.23813
.23848
35,4
35,5
9.9H74
.91192
17,8
17,7
0.08826
.08808
• 147
.15093
53,2
.23884
35,5
.91209
17,7
.08791
.148
.15146
53,2
.23919
35,5
.91227
17,7
.08773
.15200
53,1
•23955
35,5
.91245
17,6
.08755
1.150
0.15253
53,1
0.23990
35,5
9.91262
17,6
0.08738
u
log tan get u
« Fo'
log sec gd u
«- Fo'
log sin gd u
» Fo'
log esc gd u
SMITHSONIAN TA«LC«
Logarithms of Hyperbolic Functions.
u
log sinh u
» Fo'
log cosh u
• Fo'
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
53,1
. 24026
35,5
.91280
17,6
.08720
.152
•15359
53,1
.2.1'
35,5
.91297
17,5
.08703
.153
.15412
53,0
.24097
35,6
.91315
17,5
.08685
•154
.15465
53,0
.-'4133
35,6
.91332
17,5
.08668
1. 155
O.I55I8
53,o
O.24I68
35,6
9.91350
17,4
0.08650
.150
.15571
53,o
.24204
35,6
.91367
17,4
.08633
• 157
.15624
53,0
.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
9.9U36
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
.15941
52,8
.24453
35,7
.91488
I7,i
.08512
.164
•15994
52,8
.24489
35,7
.91505
I7,i
.08495
1.165
0.16047
52,8
0.24525
35,7
9.91522
I7,i
0.08478
.166
.16100
52,8
.2456C
35,7
.91539
I7,o
.08461
.167
.16152
52,7
.24596
35,8
.91556
I7,o
.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
.O8l93
.183
.16994
52,4
.25170
36,0
.91824
16,4
.08176
.184
. 17046
52,4
.252O6
36,0
.91840
16,4
.08160
1.185
0.17099
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
.25314
36,0
.91889
16,3
.O8lll
.188
. 17256
52,3
•25350
36,0
.91906
16,3
.08094
.189
.17308
52,3
.25386
36,1
.91922
16,2
.08078
1.190
o. 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
O.I762I
52,2
O.256O3
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
.25711
36,2
.92067
16,0
.07933
.199
. 17830
52,1
•25747
36,2
.92083
15,9
.07917
i. 200
0.17882
52,1
0.25784
36,2
9.92099
15,9
0.07901
u
tog tan gd u
« Fo'
log sec gd u
«F0'
log sin gd u
*• Fo'
log esc gd u
SMITHSONIAN TABLFS
43
Logarithms of Hyperbolic Functions.
r=7=
==
log sinh u
— ^=
•— r^—.^^—
log cosh u
____—n»E-
«F0'
•^••^•••••••••B
log tanh u
»•— —r— —
««> Fo'
•^•MM^^MMMM^H
log coth u
1.200
.201
.202
.203
.204
0.17882
.17934
.17985
. 18038
.18090
52,1
52,i
52,1
52,0
52,0
0.25784
.25820
.25856
.25892
.25929
36,2
36,2
36,2
36,2
36,3
9.92099
.92114
.92130
.92146
.92162
15,9
15,9
15,8
15,8
15,8
O.079OI
.07886
.0/870
.07854
.07838
1.205
.206
0.18142
. 18194
52,0
52,0
0.25965
.26001
36,3
36,3
9.92178
.92193
15,7
15,7
0.07822
.07807
.207
. 18246
52,0
.26037
36,3
.92209
15,7
.07791
.208
.18298
51,9
.26074
36,3
.92225
15,6
•07775
.209
. 18350
51,9
.26110
36,3
.92240
15,6
.07700
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
51,9
.26219
36,4
.92287
15,5
.07713
.213
.214
.18558
.18610
51,9
51,8
.26255
.26292
36,4
36,4
.92302
.92318
15,5
15,4
.07698
.07682
I.2I5
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
.26474
36,5
.92395
15,3
.07605
1.220
0.18920
5i,7
0.26510
36,5
9.92410
15,3
0.07500
.221
.18972
5i,7
.26547
36,5
.92425
15,2
•07575
.222
.19024
.26583
36,5
•92440
15,2
.07560
.223
.19075
SI»7
.26620
36,5
.92456
15,2
.07544
.224
.19127
5i,7
.26656
36,5
.92471
I5,i
.07529
1.225
O.I9I79
5i,6
0.26693
36,5
9.92486
15,1
0.075H
.226
. 19230
5i!6
.26729
36,5
.92501
15,1
.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
.26949
36,6
.92591
14,9
.07409
.233
. I959I
5i,5
.26985
36,6
.92606
14,9
.07394
.234
.19643
. 27022
36,6
.92621
14,8
.07379
1.235
0.10694
5i,5
0.27059
36,7
9.92635
14,8
0.07365
.236
• 19746
5i,4
.27095
36,7
.92650
14,8
.07350
.237
. 19797
5i,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
.2OOO3
51,4
.27279
36,7
.92724
14,6
.07276
.242
.20054
5i,3
.27316
36,7
.92738
14,6
.07262
.243
.20IO5
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
.20310
.20362
51,2
5i,2
.27499
.27536
36,8
36,8
.92811
.92825
14,4
14,4
.07189
.07175
.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
w Fo'
log esc gd u
SMITHSONIAN TABLES
44
Logarithms of Hyperbolic Functions.
u
log sinh u
«- Fo'
log cosh u
-Fo'
log tanh u
-Fo'
log coth u
1.250
0.204(4
51,2
0.27610
36,8
I4t4
0.07146
.251
.20515
51,2
.27
.92868
M,3
.07132
. o->
.20566
Si**
.27^1
36,9
.<;->883
M,3
.07H7
• 253
.20618
5i,i
.277-' i
36,9
.92897
14,3
.07103
.254
.20669
5i,i
•27757
36,9
.92911
143
.07089
1.255
0.20720
5i,i
0.27794
36,9
9.92926
14,2
0.07074
.20771
$1,1
.27831
36,9
.92940
I4,j
.07060
.^57
.20822
5i,i
.27868
36,9
.92954
14,2
.07046
.258
.20873
5i,i
.27905
36,9
.92968
14,1
.07032
• -'59
.20924
5i,o
.27942
36,9
.92982
M,i
.07018
1.260
0.20975
5i,o
0.27979
37,o
9.92996
M,i
0.07004
.26]
.21026
•51,0
.28016
37,o
.93010
14,0
.06990
.262
.21077
5i,o
.28053
37,o
.93024
14,0
.06976
.263
.21128
5i,o
.28090
37,0
.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,o
.93080
13,9
.06920
.267
.21332
50,9
.28238
37,o
.93094
13,9
.06906
.268
.21383
50,9
.28275
37J
.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
37J
.93U9
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
.22308
50,6
.29018
37,3
•93379
13,3
.06621
.289
.22448
50,6
.29056
37,3
•93392
13,3
.06608
i. 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
U.-'
.06568
.293
.22650
50,5
.2920.5
37,3
•93445
13,2
.06555
.294
.22701
50,5
.29242
37,4
.93458
U,i
.06542
1.295
0.22751
50,5
0.29280
37,4
9-9347-'
13,1
0.06528
.296
.22802
50,5
.29317
37,4
.93485
I3,i
.06515
.297
.22852
50,4
•29355
37,4
.93498
13,1
.06502
.298
.22003
50,4
.29392
37-4
•935II
13.0
.06489
.299
•22953
50,4
.29429
37,4
.93524
13,0
.06476
1.300
0.23004
50,4
0.29467
37,4
9-93537
13,0
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
«F0'
log cosh u
«F0'
log tanh u
w 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
.23908
50,i
.30142
37,6
.93766
12,5
.06234
.319
.23958
5o,i
.30180
37,6
•93779
12,5
.06221
1.320
0.24009
50,i
0.30217
37,6
9.93791
12,5
0.06209
.321
.24059
50,i
.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
5o,o
.30481
37,7
.93878
12,3
.06122
.328
.24409
50,0
.30519
37,7
.93890
12,3
.06110
.329
.24459
50,o
.30557
37,7
•93902
12,2
.06098
1.330
0.24509
50,0
0.30594
37,8
9.93914
12,2
0.06086
.331
.24559
49,9
.30632
37,8
.93927
12,2
.06073
.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
1 2,O
.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
..U-'
.25107
49,8
.31048
37,9
.94059
11,9
.05941
.343
.25157
49,8
.31086
37,9
.94071
11,9
.05929
.25207
49,8
.31124
37,9
.94083
11,9
.05917
'
0.25257
.25306
49,8
49,7
0.31162
.31200
37,9
37,9
9.94095
.94107
11,8
11,8
0.05005
.05893
3
.25356
.25406
49,7
49,7
.31238
.31276
37,9
37,9
.94H9
.94130
n,8
11,8
.05881
.05870
.25456
49,7
.31314
37,9
.94142
11,8
.05858
1.350
0.25505
49,7
0.31352
38,0
9-94154
n,7
0.05846
u
loo tan gd u
• Fo'
log sec gd u
« Fo'
log sin gd u
" Fo'
log esc gd u
(MlTMtONUN TABLE*
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
9.04154
n,7
0.05846
.351
• -'5555
49,7
.31390
38,0
.94166
n,7
.05834
.352
.25605
49,7
.3M28
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
11,6
•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
u,5
•05753
• 359
.25952
49,6
.31604
38,1
.94258
n,5
•05742
1.360
0.20002
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
n,4
.05707
.363
.26I5O
49,5
.31846
38,1
.94304
11,4
.05696
.364
.262OO
49,5
.31884
38,1
.94316
11,4
.05684
1.365
0.26249
49,5
0.31922
38,1
9.94327
n,4
0.05673
.366
.26299
49,5
.31960
38,1
.94338
1 1*4
.05662
• 307
.26348
49,5
.31998
38,1
•94350
n,3
.05650
.368
.26398
49,5
.32036
38,1
.94361
u,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
• 375
.26793
49,3
.32342
38,2
•94451
II, I
•05549
• 377
.26842
49,3
.32380
38,2
.94462
II, I
• 05
.373
.26891
49,3
.32418
38,-2
•94473
II, I
•05527
• 379
.26941
49,3
.32457
38,2
.94484
II, I
.05516
1.380
0.26990
49,3
0.32495
38,3
9-94495
II,O
0.05505
.381
.27039
49,3
.32533
38,3
-94506
II,O
•05494
.382'
.27089
49,3
•325/1
38,3
-945T7
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
.385
.27286
49,2
.32725
38,3
.94561
10,9
•05439
.387
•27335
49,2
.32763
38,3
•94572
10,9
• 05
.388
.27384
49,2
.32801
38,3
.94583
1 0,9
•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
o . 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
• 33M7
38,4
.94680
10,7
•05320
.398
.27875
49,1
.33185
38,4
.94690
10,6
-05310
•399
.27925
49,1
.332*1
38,4
.94701
10,6
.05299
1.400
0.27974
49J
0.33262
38,5
9.94712
10,6
0.05288
u tog tan gd u
<«> FO'
log sec gd u
w Fo'
log sin gd u
« Fo'
log esc gd u
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
io,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
.28415
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
.04858
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
IO,2
0.05081
.421
.29001
48,8
.34071
38,6
.94930
10,2
•05070
.422
.29050
48,8
•34110
38,7
•94940
10,1
.05060
.423
.29009
48,8
.34149
38,7
•94950
10,1
.05050
.424
.29147
48,8
.34187
38,7
.94960
10,1
.05040
1.425
0.29196
48,8
0.34226
38,7
9.94970
10,1
0.05030
.426
.29245
48,8
•34265
38,7
.94980
IO,I
.05020
.427
.29294
48,7
•34304
38,7
•94990
IO,O
.05010
.428
.29342
48,7
•34342
38,7
.95000
10,0
.05000
.429
.29391
48,7
.3438i
38,7
.95010
IO,0
.04990
1.430
o . 29440
48,7
0.34420
38,7
9-95020
10,0
0.04980
.431
.29489
48,7
.34458
38,7
.95030
10,0
.04970
.432
.29537
48,7
•34497
38,7
.95040
9,9
.04960
•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
.43^
.29829
48,6
•34730
38,8
.95099
9,8
.04901
•439
.29878
48,6
.34709
38,8
.95109
9,8
.04891
1.440*
0.29926
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
.446
0.30169
.30218
48,5
48,5
0.35002
.35040
38,9
38,9
9.95168
.95177
9,7
9,7
0.04832
•04823
•447
.448
.449
.30266
.30315
.30363
48,5
4«o
48,5
.35079
.35n8
.35157
38,9
38,9
38,9
-95187
.95197
.95206
9,6
9,6
9,6
.04813
.04803
.04794
1.450
0.30412
48,5
0.35196
38,9
9.95216
9,6
0.04784
•
loo tan gd u
« Fo'
log sec gd u
« Fo'
log sin gd u
« Fo'
log esc gd u
SMITHSONIAN TABLE*
48
Logarithms of Hyperbolic Functions.
u
tog sinh u
« Fo'
log cosh u
-Fo'
log tanh u
W Fo'
log coth u
1.450
0.30412
48,5
0.35196
38,9
9.95-'i<>
9,6
0.04784
.451
.30460
48,5
.35235
3«,9
.95225
9,6
.04775
• 45-'
.30509
48,5
.35274
38,9
.95235
9,5
•04765
• 453
.30557
4«,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
• 45<>
.30703
48,4
• 354-">
39,o
•95273
9,5
.04727
• 457
.30751
48,4
•35468
39,0
•95283
9,5
.04717
.458
.30709
48,4
.35507
39,0
•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,o
.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
0.3II38
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
.4/1
.31428
48,3
•36015
39,1
.95413
9,2
.04587
.472
.3M76
48,3
.36054
39,1
•95422
9,2
.04578
• 473
.31524
48,2
.36093
39,1
.95431
9,2
.04569
• 474
.31572
48,2
.36132
39,1
.95441
9,1
•04559
1-475
O.3I62I
48,2
0.36171
39,1
9-95450
9J
0.04550
.476
.31669
48,2
.36210
39,1
•95459
9,1
.04541
• 477
•3I7I7
48,2
.36249
39,1
.95468
9,1
.04532
.478
.31765
48,2
.36288
39,1
•95477
9,i
.04523
• 479
.3T8i4
48,2
.36328
39,1
.95486
9,0
.045H
1.480
0.31862
48,2
0.36367
39,2
9-95495
9,0
0.04505
.481
.31910
48,2
.36406
39,2
•95504
9,0
.04496
.482
.31958
48,2
.36445
39,2
.95513
9,0
.04487
.483
.32006
48,1
.36484
39,2
•95522
9,0
.04478
.484
.32054
48,1
.36523
39,2
•95531
9,o
.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
.95611
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
log tan gd u
« Fo'
log sec gd u
-Fo'
log sin gd u
« Fo'
log esc gd u
SMITHSONIAN TABLES
49
Logarithms of Hyperbolic Functions.
u
log sinh u
u>Fo'
log cosh u
«F0'
log tanh u
«- Fo'
log coth u
1.500
.501
.502
.503
0.32823
.32871
.32919
.32967
48,0
48,0
48,0
48,0
0.37I5I
.3/191
.37230
.37269
39,3
39,3
39,3
39,3
9.95672
.95681
.95689
.95698
8,7
8,7
8,6
8,6
0.04328
.04319
.04311
.04302
.504
.33015
47,9
.37309
39,3
•95707
8,6
.04293
1.505
.506
0.33063
•33III
47,9
47,9
0.37348
.37387
39,3
39,4
9.95715
.95724
8,6
8,6
0.04285
.04276
.507
.33159
47,9
.37427
39,4
•95732
o'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
O.33542
47,8
0.37742
39,4
9.95800
8,4
0.04200
.516
.33590
47,8
.37781
39,4
.95808
8,4
.041921
.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
o!o4i 17
.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
•342II
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
.9598i
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
9.96005
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
on
.34925
47,6
.38888
39,6
.96037
7,9
.03963
0.34073
47,6
0.38928
39,6
9-96045
7,9
0.03955
47,6
.38968
39,7
•96053
7,9
.03947
47,6
.39007
39,7
.96061
7,9
•03939
47,5
•39047
39,7
.96069
7,9
.03931
.540
47,5
.39087
39,7
.96077
7,9
.03923
I.S50
0.35211
47,5
0.39126
39,7
9.96084
7,8
0.03916
•
log tan od u
«F0'
log sec gd u
- F0'
log sin gd u
«- Fo'
log esc gd u
SMITHSONIAN TABLES
Logarithms of Hyperbolic Functions.
u
log sinh u
« Fo'
log cosh u
• F0'
log tanh u
« Fo'
loo coth u
1.550
0.352H
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
.3f2o6
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
•35591
47,5
.39444
39,7
.96147
7,7
.03853
.559
.35638
47,5
.39484
39,7
.96154
7,7
.03846
1.560
0.35686
47,4
0.39524
39,8
9.96162
7,7
0.03838
.561
•35733
47,4
.39563
39,8
.96170
7,7
.03830
.562
35780
47,4
•39603
39,8
.96177
7,7
.03823
.563
35828
47,4
.39643
39,8
.96185
7,6
.03815
.564
.35875
47,4
.39683
39,8
.96193
7,6
.03807
1.565
0.35923
47,4
0.39722
39,8
9.96200
7,6
0.03800
.566
•35970
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
0.03/62
• 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
0.03/24
.576
.36444
47,3
.40161
39,9
.96283
7,4
.03717
• 577
.36491
47,3
.40200
39,9
.96291
7,4
.03/09
.578
.36538
47,3
.40240
39,9
.96298
7,4
.03/02
•579
.36585
47,3
.40280
39,9
.96305
7,4
.03 '95
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
.03^73
.583
.36775
47,3
.40440
39,9
.96335
7,3
• 03
.584
.36822
47,2
.40480
39,9
.96342
7,3
.03 5 3
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
.36064
47,2
•40599
39,9
.96364
7,3
.03030
.588
.37011
47,2
.40639
39,9
.96371
7,3
.03
.589
.37058
47,2
.40679
40,0
.96379
7,3
.03621
1.500
0.37105
47,2
0.40719
40,0
9.96385
7,2
0.03
.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-'
• 035' '3
• 594
.37294
47.2
.40879
40,0
.96415
7,2
.035
1-595
0.37341
47,2
0.40919
40,0
9.96422
7,2
0.03578
.596
.37388
47,2
.40959
40,0
.96429
7,2
.03571
:3
•37435
.37482
47J
47,1
.40999
.41039
40,0
40,0
.96436
.96443
7,1
7,i
.03564
•03557
.599
•37530
47,1
.41079
40,0
.96450
7,1
.03550
i. 600
0.37577
47,1
0.4HI9
40,0
9.96457
7,1
0.03543
u log tan gd u
a. Fo'
log sec gd u
<- Fo'
log sin gd u *> F '
log esc gd u
SMITHSONIAN TABLES
Logarithms of Hyperbolic Functions.
u
oo sinh u
« Fo'
loo cosh u
«FO'
loo tanh u
« Fo'
loo coth u
1. 600
0-37577
47,1
0.41119
40,0
9.96457
7,1
0.03543
.601
.37624
.41159
.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,o
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
.96535
6,9
•03465
.612
.38142
.41600
.96542
.03458
.613
.38189
.41640
.96548
.03452
.614
.38236
.41680
.96555
•03445
1.615
0.38283
47,o
0.41720
40,1
9.96562
6,9
0.03438
.616
.38330
.41761
.96569
•03431
.617
.38377
.41801
.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
.96750
.03250
•644
.39643
.42887
.96756
.03244
1.645
0.39600
46,8
0.42927
40,3
9.96763
6,5
0.03237
.646
.39736
.42967
.96769
.03231
.39783
.43008
.96776
.03224
.648
.30830
.43048
.96782
6,4
.03218
.649
•39877
.43088
.96788
.03212
1.650
0.30923
46,8
0.43129
40,3
9.96795
6,4
0.03205
u
log tan »d u
« Fo'
loo sec od u
« Fo'
loo sin od u
<- Fo'
loo esc od u
SMITHSONIAN TABLES
Logarithms of Hyperbolic Functions.
u
log sinh u
w Fo'
log cosh u
«F,'
log tanh u
log coin u
1.650
0.39923
46,8
0.43129
40,3
9-96795
<U
0.03205
.651
.399/0
46,7
.43109
.96801
.03199
.652
.40017
.43209
40,4
.96808
.03192
.653
.40064
.43250
.96814
.03186
.654
.40110
.43290
.96820
.03180
1.655
0.40157
46,7
0.43330
40,4
9.96827
6,4
0.03173
.6s<)
.40204
.43371
•96833
6,3
.03167
.657
.40251
.434H
.96840
.03160
.658
.40297
.43451
.96846
.03154
.659
.40344
•43492
.96852
.03148
I.66o
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
.06883
6,2
.03117
1.665
0.40624
46,7
0-43734
40,4
9.06890
6,2
0.03IIO
.666
.40671
46,6
•43775
.96896
.03104
.667
.40717
.43815
.96902
.03098
.668
.40764
.43856
.96908
.03092
.669
.40811
.43896
40,5
.06915
.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
•96933
6,1
.03067
•673
.40097
.44058
•96939
.03061
•674
.41044
.44098
•96945
.03055
1.675
O.4IO9O
46,6
0.44139
40,5
9.06951
6,1
0.03049
.676
.41137
.44179
•96957
.03043
.677
.41183
.44220
.96964
.03036
.678
. .41230
.44260
.90970
.03030
.679
.41277
.44301
.96976
.03024
i. 680
0.41323
46,6
0.44341
40,5
9.96982
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
.02<, .
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
O.4202I
46,5
0.44950
40,6
9.97071
5,9
O.O2929
.696
.42067
.44990
.97077
.02923
.697
.42114
46,4
.45031
.97083
5,8
.OJQi;
.698
.42160
.45072
.97089
.O29II
•699
.42207
.45H2
.97094
.02906
1.700
0.42253
46,4
0.45153
40,6
9.97100
5,8
0.02900
u
log tan gd u
« Fo'
log sec gd u
« Fo'
log sin gd u
*. Fo'
log esc gd u
SMITHSONIAN TABLES
53
Logarithms of Hyperbolic Functions.
=— ^=?
u
= ==
log sinh u
^•^^•^•••i
« Fo'
••••^••^•••^
log cosh u
^••••^
«F0'
•^^^•^^••••i
log tanh u
••••••••••••••
« Fo'
••mMBDHHHB^H
log coth u
1.700
.701
0.42253
.42299
46,4
0.45153
.45193
40,6
9.97100
.97106
5,8
0.02900
.02894
.702
.703
.704
.42346
.42392
•42439
.45234
.45275
.45315
.97112
.97118
.97123
.02888
.02882
.02877
1.705
.706
0.42485
.42531
46,4
0.45356
.45397
40,7
9.97129
.97135
5,7
0.02871
.02865 j
.707
.708
.42578
.42624
•45437
.45478
.97141
.97146
. 02859
.02854
.709
.42671
•45519
.97152
.02848
1. 710
.711
.712
0.42717
.42763
.42810
46,4
0.45559
.45600
.45641
40,7
9.97158
.97163
.97169
5,7
0.02842
.02837
.02831
•713
.714
.42856
.42902
46,3
.45681
•45722
.97175
.97180
5,6
.02825
.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
.45920
.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
9.97296
5,4
0.02704
.736
.43920
.46619
.97302
.02698
• 737
•43067
.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
.44198
.46864
•97334
.02666
.743
.44244
.46905
•97339
.02661
.44200
.46945
40,9
.97345
.02U55
1-745
0.44336
46,2
0.46986
40,9
9.97350
5,3
0.02650
.44382
.47027
.97355
.02645
• 747
.44428
.47068
.97360
.02640
.748
46,1
.47109
.97366
.02634
• 749
.44521
.47150
•97371
.02629
I.7SO
0.44567
46,1
0.47I9I
40,9
9.97376
5,3
0.02624
•
log tan od u
« Fo'
log sec gd u
<- Fo'
log sin gd u
» Fo'
log esc gd u
SMITHSONIAN TABLIC
54
Logarithms of Hyperbolic Functions.
u
log sinh u
« Fo'
log cosh u
«FO'
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
• 75<>
.44844
.47436
.97408
.0-
• 757
.44890
•47477
•97413
.0258;
.758
•44936
.47518
.97418
.02: a
• 759
.44982
.47559
.97423
.02577
1.760
0.45028
46,1
0.47600
40,9
9.97428
5,1
0.0-
.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
.47885
.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,o
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
.45002
.48378
.97524
.02476
1.780
0.45948
46,0
0.48419
41,0
9.97529
4,9
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
41,1
9-97554
4,9
0.02446
.786
.46224
.48666
•97559
.02441
.787
.46270
.48707
.97504
.02436
.788
.46316
.48748
.97568
•02432
.789
.46362
.48789
•97573
.02427
1.790
0.46408
45,9
0.48830
41,1
9.97578
4,8
0.02422
.791
.46454
.48871
.97583
.02417
.792
.46500
.4891-'
.97588
.02412
• 793
.46546
.48953
•97593
.02407
• 794
.46592
.48994
•97597
.02403
1-795
0.46637
45,9
0.40035
41,1
9.97602
4,8
0.02398
.796
.46683
.49076
.97607
.02393
• 797
.46729
.49117
.97612
.02388
.798
.46775
.49159
.97617
.02383
• 799
.46821
.49200
.97621
.02379
1.800
0.46867
45,9
0.49241
41*1
9.97626
4,8
0.02374
u
log tan gd u
« Fo'
log sec gd u
« Fo'
log sin gd u
« Fo'
log esc gd u
SMITHSONIAN TABLES
55
Logarithms of Hyperbolic Functions.
u
log sinh u
« Fo'
log cosh u
«F0'
log tanh u
«•» Fo'
log coth u
1.800
0.46867
45,9
0.49241
4U
9.97626
4,8
0.02374
.801
.46913
.49282
.97631
4,7
.02369
.802
.46959
.49323
.97636
.02364
.803
.47004
.49364
.97640
.02360
.804
.4/050
45,8
.49405
.97645
•02355
1.805
0.47096
45,8
0.49446
41,1
9.97650
47
0.02350
.806
.47M-7
.49483
.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
0.40858
41,2
9-97696
4,6
0.02304
.816
.47600
.49899
•97701
.02299
.817
.47646
•49940
.97705
.02295
.818
.47692
.40982
•97710
.02290
.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
.824
•47921
.47966
.50188
.50229
•97733
•97737
.02267
.02263
1.825
.826
.827
.828
.820
0.48012
.48058
.48104
.48149
•48195
45,7
0.50270
.50311
.50353
.50394
.50435
41,2
9.97742
.97746
•97751
•97755
.97760
45
0.02258
.02254
.02249
•02245
.02240
1.830
.831
.832
.833
.834
0.48241
.48286
.48332
.48378
.48424
45,7
0.50476
.50518
.50559
.50600
.50641
41,3
9.97764
.97769
•97773
•97778
.97782
4,5
4,4
0.02236
.02231
.02227
.02222
.02218
1.835
.836
.837
.838
Jfe
0.48469
.48515
.48561
.48606
.48652
45,7
0.50683
.50724
.50765
.50806
.50848
41,3
9.97787
•97791
•97796
.97800
.97804
44
0.02213
.02209
.02204
.02200
.02196
1.840
o ,
0.48698
.48743
.48789
OO -
45,7
0.50889
.50930
.50972
41,3
9.97809
•97813
.97817
4,4
0.02191
.£»l87
.0218;,
••43
o
.48835
.51013
.97822
.02178
•94 \
.48880
.51054
.97826
4,3
.02174
0.48926
•48972
.49017
•40063
.49109
45,7
45,6
0.51096
.51137
.5H78
.51219
.51261
41,3
9.97831
.97835
.97839
.97843
.97848
4,3
0.02169
.02K>5
.02161
.02157
.02152
1.850
0.49154
45,6
0.51302
41,3
9.97852
4,3
0.02148
u
__
log Ian gd u
;=S HHi
. -^ «•» .
« Fo'
iii=
og sec gd u
« Fo'
•~
og sin gd u
••••••••••••••i
« Fo'
MNBMBIMMB
log esc gd u
•••••••••••••
Logarithms of Hyperbolic Functions.
u
log sinh u
a> Fo'
log cosh u
• Fo'
log tanh u
- Fo'
log coth u
1.850
0.49154
45,6
0.51302
41,3
9.97852
4,3
0.02148
.851
.49200
.51343
.97856
.02144
.852
.49246
.51385
.97861
.02139
.853
.49291
• 51-;-' >
.97865
.02135
.854
•49337
.51468
41,4
.97869
.02J31
1.855
0.49382
45,6
0.51509
4M
9.97873
4,3
0.02127
.850
.49428
.51550
.97878
4,2
.O2I22
.857
•49474
.51592
.97882
.02118
• .858
.49519
.51633
.97886
.02114
.859
.49565
•51674
.97890
.O2I 10
1.860
0.49610
45,6
0.51716
41,4
9.97895
4,2
0.02105
.861
.49656
.51757
.97899
.02IOI
.862
.49702
.51708
.97903
.02097
.863
•49747
.51840
.97907
02003
.854
•49793
.51881
•97911
.02089
1.865
0.49838
45,6
0.51023
41,4
9.97916
4,2
O.O2O84
.866
.49884
.51964
.97920
.0208O
.867
.49929
.52005
.97924
.02076
.868
•49975
.52047
.97928
4,1
.02072
.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
.97981
.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
9.97907
4,0
0.02003
.886
•50794
.52793
.98001
.01099
.887
.50840
.52834
.98005
.OIQ95
.888
•50885
.52876
.08009
.01991
.889
.50931
.52917
.98013
.01987
1.890
0.50976
45,5
0.52959
41,5
9.98017
4,0
o.o:
.891
.51021
.53000
.98021
.OT' ?
.892
.51067
45,4
.53042
.08025
.01
.893
.51112
•53083
.98029
3,9
.01071
.894
• SUSS
.53125
•98033
.01967
1.895
0.51203
45,4
0.53166
41,5
9.98037
3,9
0.01963
.896
.51249
.53208
.98041
.01959
.897
.51294
.53249
.98045
.01955
.898
.51340
.53291
.08049
.01951
.899
.51385
.53332
.98053
.01947
1.900
0.51430
45,4
0.53374
4T,5
9.98057
3,9
0.01943
I
log tan ad u
« Fo'
log sec gd u
« Fo'
log sin gd u
« F0'
log esc gd u
SMITHSONIAN TABLES
57
Logarithms of Hyperbolic Functions.
u
log sinh u
« Fo'
log cosh u
«F0'
log tanh u
<- Fo'
log coth u
1.900
0.5M30
45.4
0.53374
41,5
9.98057
3,9
0.01943
.901
.902 1
** ^*"^ ,
.51476
•5I52I
.53415
•53457
.98060
.98064
.01940
.01936
.903
.904
.51567
.51612
.53498
•53540
.98068
.98072
.01932 !
.01928
1.005
0.51657
45,4
o.5358i
41,5
9.98076
3,8
0.01924
.906
•5I7O3
.53623
41,6
.98080
.01920
.907
.51748
.53665
.98084
.01916
.908 .51794
.53706
.98087
.01913
.909
.51839
.53748
.98091
.01909
I.9IO
0.51884
45,4
0.53789
41,6
9.98095
3,8
O.OIQ05
.911
.51930
.53831
.98099
.OIQOI
.912
.51975
.53872
.08103
.01897
•9U
. 52020
.53914
.08106
.01894
.914
.52066
.53956
.98110
.01890
I.QIS
O.52III
45,4
0.53997
41,6
9.98114
3,8
o.oi885
.916
.52157
. 54039
.98118
.01882
.917
. 52202
45,3
.54080
.08122
.01878
.918
.52247
.54122
.98125
.01875
.919
.52293
.54164
.98129
3,7
.01871
1.920
0.52338
45,3
0.54205
41,6
9.o8l33
3,7
0.01867
.921
.52383
.54247
.98137
.01863
.922
• 52429
.54288
.98140
.01860
.923
.52474
.54330
.08144'
.01856
.924
.52519
•54372
.98148
.01852
1.925
0.52565
45,3
0.54413
41,6
9-98151
3,7
0.01849
.926
.52610
.54455
.O8i55
.01845
.927
.52655
.54496
.98159
.01841
.928
.52700
.54538
.98162
.01838
.929
.52746
.54580
.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
.08177
3,6
.01823
•933
.52927
.54746
.08181
.01819
• 934
.52972
.54783
4i,7
.98184
.01816
1-935
0.53018
45,3
0.54830
41,7
9.08188
3,6
0.01812
.936
.53063
.54871
.08192
.01808
.937
.53108
.54913
.98195
.01805
.938
.53153
.54955
.98199
.01801
•939
.53109
.54996
.98202
.01798
1.940
0.53244
45,3
0.55038
4i,7
9.98206
3,6
0.01794
.041
.53289
.55080
.98210
.01790
.942
.53334
•55I2I
.98213
.01787
.043
.53380
45,2
.55163
.98217
.01783
.944
.53425
•55205
.98220
.01780
1.945
0-53470
45,2
0.55246
4i,7
9.98224
3,6
0.01776
.946
.53515
.55288
.98227
3,5
.01773
•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 gd u
- F,,'
log sec gd u
« Fo'
log sin gd u
-FO'
log esc gd u
SMITHSONIAN TABLES
Logarithms of Hyperbolic Functions.
u
log sink u
«F0'
log cosh u
•Fo'
log tanh u
* Fo'
log coth u
1.950
0.53696
45,2
0-55455
41,7
9.r>
3,5
0.01758
.951
• 5374-2
•55 •
.98245
.01755
• 952
.53787
.55538
<J49
.01751
• 953
.53832
.55.
.98252
.Oi;
• 954
.53877
.55622
.98256
.017
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
.98273
.01727
1.960
0.54148
45,2
0.55872
41,7
9.98276
3,4
0.01724
.961
.54194
.55914
.98280
.01720
.962
.54239
.55955
.98283
.01717
.963
.54284
•55997
.98287
.01713
.954
.54329
•56039
41,8
.98290
.01710
1.065
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
9-98311
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
.5496i
.56624
.98337
.01663
• 979
.55006
.56666
.98341
.01659
1.980
0.55051
45,1
0.56707
41,8
9.98344
3,3
0.01656
.981
.55097
.56749
.98347
.01653
.982
•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
•98364
.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
41,9
9.98393
3,2
0.01607
.996
.55773
•57377
.98396
.01604
•997
•55818
.57419
.98399
.01601
.998
.55863
.5746o
.98403
•01597
•999
.55908
•57502
.98406
•01594
2.OOO
0.55953
45,o
0-57544
4i,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.
1
log sinh u
u. Fo'
log cosh u
«F0'
log tanh u
W FO'
log coth u
2.OOO
0.55953
45,o
0.57544
41,9
9.98409
3,2
O.OI59I
.OOI
.55098
.98412
.01588
.OO2
.56043
.'57628
.98415
.01585
.OO3
.56088
.57670
.98418
.01582
.004
.56133
.57712
.98422
.01578
2.005
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
2.010
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
2.015
0.56628
45,o
0.58172
41,9
9.98456
3,1
0.01544
.016
.56673
.58214
.98459
.01541
.017
.56718
.58256
.98462
.01538
.018
.56723
.58298
.98465
.01535
.019
.56808
.58340
.98468
.01532
2. 02O
0.56853
45,0
0.58382
41,9
9.98471
3,1
0.01529
.021
.56898
.58424
.98474
.01526
.022
.56943
.58466
.98477
3,0
.01523
.023
.56988
.58508
.98480
.01520
.024
•5703^
.58550
.98484
.01516
2.025
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
0.57303
45,0
0.58802
42,0
9.98502
3,0
0.01498
.031
.57348
.58843
.98505
.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
.08543
.01457
0.57977
44,9
0.59431
42,0
9.98546
2,9
0.01454
• 59473
.98549
.01451
.047 I
.59515
•59557
.98552
.98555
.01448
.01445
•049 , .58157
•59599
.98558
.01442
2.050 0.58202
44,9
0.59641
42,0
9-98560
2,9
0.01440
" loo tin od u
log tec gd u
« Fo'
log sin gd u
w Fo'
log esc gd u
SMITHSONIAN TA*LC«
60
Logarithms of Hyperbolic Functions.
u
loo sinh u
« Fo'
log cosh u
-F,/
log tanh u
« Fo'
log coth u
2.050
0.58202
44,9
0.59641
42,0
9-98560
2,9
o.o;
.051
.58246
.59683
.98563
.01437
.052
.58291
.597 -'5
.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
.98595
.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
2.090
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
.008
.60353
.61661
.98692
.01308
.099
.60398
.61703
.98695
.01305
2.IOO
0.60443
44,8
0.61745
42,1
9.98697
2,6
0.01303
U
log tan gd u
« Fo'
log sec gd u
« Fo'
log sin gd u
-FO'
log esc gd u
SMITHSONIAN TABLES
61
Logarithms of Hyperbolic Functions.
u
log sinh u
« Fo'
log cosh u
-Fo'
log tanh u
« Fo'
log coth u
2.IOO
0.00443
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
.IO3
.00577
.61872
.98705
.01295
.104
.60622
.61914
.98708
.01292
2. IO5
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. HO
0.6o8oo
44,7
0.62167
42,2
9.98723
2,6
0.01277
.III
.60935
.62209
.98726
2,5
.01274
.112
.60979
.62251
.98728
.01272
•113
.61024
.62293
.98731
.01269
.114
.61069
.62336
.98733
.01267
2.II5
O.6III4
44,7
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
.119
.61292
.62546
.98746
.01254
2.120
0.61337
44,7
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
44,7
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
.129
.61739
.62969
•98771
.01229
2.130
0.61784
44,7
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
2.135
O.62OO7
44,7
0.63222
42,2
9.98785
2,4
0.01215
.136
.62052
.63264
.98788
.01212
.137
.62097
.63306
.98790
.OI2IO
.138
.6214]
.63349
.98793
.OI2O7
.139
.62186
.63391
.98795
.OI2O5
3.140
0.62231
44,6
0.63433
42,2
9.98798
2,4
O.OI2O2
.141
.62275
.63475
.98800
.OI200
,143
.62320
.63518
.98802
.OIIOjS
.143
.63560
42,3
.98805
.01195
•144
.62409
.63602
.98807
.01193
2.145
0.62454
44,6
0.63644
42,3
9.98810
2,4
O.OII9O
.63687
.98812
.01188
.147
.62543
.63729
.98814
.01186
.63771
.98817
.01183
.62632
.63813
.98819
.OIlSl
2.150
0/».
44,6
0.63856
42,3
9.98821
2,4
O.OII79
•
log tan gd u
-FO'
log sec gd u
-Fo'
log sin gd u
« Fo'
loo esc gd u
SMITMOONIAN TABLES
62
Logarithms of Hyperbolic Functions.
u
log sinh u
- F0'
log cosh u
• Fo'
log tanh u
- Fo'
log coth u
2.150
0.62677
44,6
0.63856
42,3
9.08821
2,4
O.OII79
.151
.62722
.63898
.98824
.01170
.152
.62766
.63940
.98826
2,3
.01174
.153
.62811
.63982
.98828
.01172
.154
.62855
.64025
.98831
.01109
2.155
0.62900
44,6
0.64067
42,3
9.98333
2,3
O.OIl67
.156
.62945
.62989
.64109
.6415-'
.98835
.98838
.01165
.01162
. 158
.63034
.64194
.98840
.01160
.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
•OII53
.162
.63212
.64363
.98849
.OII5I
.163
.63257
.64405
.98852
.01148
.164
.63302
.64448
•98854
.01146
2.165
0.63346
44,6
0.64490
42,3
9.98856
2,3
O.OII44
.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
O.OII32
.171
.63614
.64744
.98870
.01130
.172
.63658
.64786
.98872
.OII28
.173
.63703
.64828
.98874
.OII26
• 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
.01117
.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
.OIIO6
183
.64148
.65252
.98897
.01103
.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
0.64905
44,5
0.65972
42,4
9.98934
2,1
0.01066
U
log tan gd u
« Fo'
log sec gd u
«F0'
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
2.2OO
0.64905
44,5
0.65972
42,4
9.98934
2,1
O.OIO66
.201
.64950
.66014
.98936
.01064
.202
.64994
.66056
.98938
.01062
.203
.65039
.66099
.98940
.01060
.204
.65083
.66141
.98942
.01058
2.205
0.65128
44,5
0.66184
42,4
9.98944
2,1
0.01056
.20J
.6517^
.66226
.98946
.01054
.207
.65217
.66268
.98948
.01052
.208
.65261
.66311
.98950
.01050
.209
.65306
.66353
.98953
.01047
2.210
0.65350
44,5
0.66396
42,4
9.98955
2,1
0.01045
.211
.65395
.66438
.98957
.01043
.212
.66480
.98959
.01041
.213
.65484
.66523
.98961
.01039
.214
.65528
.66565
.98963
.01037
2.215
0.65573
44,5
0.66608
42,4
9.98965
2,1
0.01035
.216
.65617
.66650
.08967
.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
.01021
.223
.65928
.66947
.98982
.01018
.224
.65973
.66989
.98984
.OIOI6
2.225
O.66OI7
44,5
0.67032
42,4
9.98086
2,0
O.OIOI4
.225
.66062
.67074
.98988
.OIOI2
.227
.66106
.67117
.98990
.OIOIO
.228
.66151
44,4
.67159
.98092
.OIOO8
.220
.66195
.67202
.98094
.01006
2.230
0.66240
44,4
0.67244
42,4
9.98996
2,O
O.OIOO4
.231
.66284
.67286
.98098
.OIOO2
.66328
.67329
.90000
.OIOOO
•233
.66373
.67371
.90002
.00908
•234
.66417
.674U
.99004
.00996
2.235
0.66462
44,4
0.67456
42,4
9.99006
2,0
0.00994
.236
.66506
.67499
.00008
.00992
•237
.66551
.67541
42,5
.00010
.00900
.238
.66595
.67583
.09012
.00988
.239
.66640
.67626
.99014
.00986
2.240
0.66684
44,4
0.67668
42,5
9.99016
2,0
0.00084
.241
.66728
.67711
.99018
.00982
•66773
.67753
.99019
.00981
• 243
.66817
.67796
.00021
.00979
.244
.66862
.67838
.09023
.00977
2.245
.247
.248
0.66906
.66950
.66995
.67039
.67084
44,4
0.67881
.67923
.67966
.68008
.68051
42,5
9.99025
.99027
.90029
.90031
.90033
1,9
0.00975
.00973
.00971
.00969
.00967
2.250
0.67128
44,4
0.68093
42,5
9.99035
i,9
0.00965
u
loo tin od u
« Fo'
log sec gd u
«- Fo'
log sin gd u
» Fo'
log esc gd u
SMITHSONIAN TABLE*
Logarithms of Hyperbolic Functions.
u
log sinh u
« Fo'
log cosh u
«F0'
log tanh u
« Fo'
log coth u
2.250
0.67128
44,4
0.68093
42,5
9.99035
1,9
0.0:
• -'51
•"7173
:i3'->
.99037
.00963
.-'5->
.67217
.68178
.99039
.OO96l
.253
.67261
.68->->o
.99041
.00959
• -'54
.6/306
.08263
.99043
•00957
2.255
0.67350
44,4
0.68305
42,5
9.99045
1,9
0.00955
.256
•(>7394
.68348
.99047
.00953
.257
• <>7439
.68390
.99048
.00952
.258
.67483
.68433
.99050
.00950
.259
.67528
.68475
.99052
.00948
2.260
0.67572
44,4
0.68518
42,5
9.99054
i,9
0.00946
.261
.67616
.68560
.99056
.00944
.262
.67661
.68603
.99058
.00942
.263
.67705
.68645
.99060
.00940
.264
.67750
.68688
.99062
.00938
2.265
0.67794
44,4
0.68730
42,5
9.99064
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
44,4
0.68943
42,5
9.99073
1,9
0.00927
.271
.68060
.68985
.99075
.00925
.272
.68105
.69028
.99077
1,8
.00923
.273
.68149
.69070
.99078
.00922
.274
.68193
.69113
.99080
.00920
2.275
0.68238
44,4
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
4^,5
9.99TOO
1,8
0.00000
.286
.68725
.69623
.99102
.00898
.287
.68770
.69666
.99104
.00896
.288
.68814
.69708
.09106
.00894
.289
.68858
.69751
.99107
.00893
2.200
0.68003
44,3
0.69794
42,5
9.99109
1,8
0.00891
.291
.68947
.69836
.99HI
.00889
.292
.68091
.69879
42,6
.99H3
.00887
• 293
.69036
.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
1,7
.00875
2.300
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 csc gd u
N TABLES
Logarithms of Hyperbolic Functions.
u
log sinh u
» Fo'
log cosh u
«F0'
log tanh u
« Fo'
log coth u
2.300
0.69346
44,3
0.70219
42,6
9.99127
1,7
0.00873
.301
.09390
.70262
.99129
.00871
.302
.69435
• 70304
.99130
.00870
• 303
•69479
.70347
.09132
.00868
.304
.09523
.70389
.99134
.00866
2.305
0.69568
44,3
0.70432
42,6
9.99136
i,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
44,3
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
-'.315
O.70OIO
44,3
0.70858
42,6
9.99153
1,7
0.00847
.316
.70055
.70900
•99154
.00846
.317
.70099
•70943
.99156
.00844
.318
.70143
.70986
.09158
.00842
.319
.70188
.71028
.99159
.00841
2 . 320
0.70232
44,3
0.71071
42,6
9.99l6l
i,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
i,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
44,3
0.71497
42,6
9.99178
1,6
0.00822
•331
.70719
•71539
.09179
.00821
•332
.70763
.71582
.99181
.00819
-333
.70807
.71625
.99183
.00817
• 334
.70852
.71667
.99184
.00816
2-335
0.70896
44,3
0.71710
42,6
9.99186
1,6
0.00814
.336
.70940
44,2
•71753
.09188
.00812
•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
.71066
.99106
.00804
• 342
.71206
.72008
.99197
.00803
• 343
.71250
.72051
.99199
.00801
• 344
.71294
.72094
.99200
.00800
2.345
0.7U3K
44*2
0.72136
42,6
9.09202
1,6
0.00798
.72179
.99204
.00796
•347
.71427
.72221
.99205
.00795
.348
.7M7I
.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 Un gd u
• IV
log sec gd u
<o Fo'
log sin gd u
« Fo'
log esc gd u
SMITHSONIAN TABLES
66
Logarithms of Hyperbolic Functions.
u
log sinh u
« Fu'
log cosh u
«F0'
log tanh u
-Fo'
loo coth u
2.350
0.71559
44,2
0.72349
42,6
9.99210
1,6
O.OO79O
.351
.71604
• 72
.99212
.00788
-352
•71
.72435
.99213
.CX
.353
•7'
.72477
42,7
•99215
.00785
• 354
.71736
.72520
.99216
.00784
2.355
0.71781
44,2
0.72563
42,7
9.99218
1,6
0.00782
• 356
.71825
.72605
.99319
.00781
• 357
.71869
.72648
.99221
.00
.358
.71913
.72691
.99223
.00777
• 359
.71957
.72733
.90224
.00770
2 . 3'tO
O.72OO2
44,2
0.72776
42,7
9.99226
1,5
0.00774 :
.361
. 72046
.72819
.99227
.oc
.362
.72090
.72861
.99229
.00771
.72134
.72904
.99230
.00; . i
.364
.72178
.72947
.99232
.00768
2.365
0.72223
. 44,2
0.72989
42,7
9.99233
i,5
o.o;
.72267
.73032
.99235
.007 is
.367
.723H
.73075
.99236
.00764
.368
.72355
.73117
.99238
.007 2
.369
.72399
.73160
.99239
.OO76l
2.370
0.72444
44,2
0.73203
42,7
9.99241
1,5
0.00759 :
.371
.72488
•73245
.99242
.005
• 37-
.72532
.73288
.99244
.00756
• 373
.72576
.73331
.99245
.00755
• 374
.72620
•73373
•99247
.0075o
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
.00
-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
i,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
9.09285
1,4
0.00715
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.
I
log sinh u
» Fo'
log cosh u
«F0'
log tanh u
w Fo'
log coth u
2.400
0.73769
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
.74034
•74740
.99294
.00/06
.407
.74078
.74783
.99295
.00705
.408
.74122
.74825
.99297
.00703
.409
.74166
.74868
.99298
.00702
2.410
0.74210
44*1
0.749H
42,7
9.99299
1,4
0.00701
.411
.74254
.74954
.99301
.00699
.412
.74298
.74996
.99302
.00608
.413
•74343
.75039
.09304
.00696
.414
.74387
.75082
.99305
.00695
2.415
0.74431
41,1
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
i,4
0.00680
.426
.74916
.75595
.99321
.00679
.427
.74060
.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
0.7598o
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
0.76194
42,8
9.99340
i,3
0.00660
.441
.442
• 443
•75578
.75622
.75666
.76236
.76279
.76322
.99341
•99343
•99344
.00659
.00657
.00656
.444
•75710
.76365
.99345
.00655
2-415
• 447
0-75754
.75708
.75842
44,1
0.76407
.76450
.76493
42,8
9-99347
.99348
.99349
i,3
0.00653
.00652
.00651
.448
.75886
.76536
•99351
.00649
•75930
.76579
.99352
.00648
2-450
0.75975
44,1
0.766*21
42,8
9-99353
1,3
0.00647
u
log tan gd u
-Fo'
log sec gd u
- Fo'
log sin gd u
« Fo'
log esc gd u
SMITHSONIAN TABLES
68
Logarithms of Hyperbolic Functions.
u
log sinh u
w Fo'
log cosh u
»FV
log tanh u « Fo'
log coth u
2.450
0.75975
44,1
0.76621
42,8
9-99353
1,3
0.0
.451
019
"64
•99354
.00646
.452
.76063
.76707
•09356
.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
• 45"
.76239
.76878
.99361
.00 |
.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
.401
.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
44ti
0.77477
42,8
9.99379
1,2
0.00621
.471
.76900
•77520
.99380
.00620
.472
.76044
.77563
.99381
.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
.oo5i3
• 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
•99394
.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
.00002
.487
• 77605
.78205
•99399
.00001
.488
.77649
.78248
.99401
.00509
.489
.77693
.78292
.99402
.00598
2.490
0.77737
44,0
0.78334
42,8
9.99403
1,2
0.00597
.491
.77781
.78377
.09404
.00596
.492
.77825
.78420
.09405
.00595
• 493
•77869
.78462
.09406
.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
.99410
.00500
• 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
»F0'
log sin gd u
« Fo'
log esc gd u
SMITHSONIAN TABLES
69
Logarithms of Hyperbolic Functions.
==
u
•
og sinh u
=
« Fo'
"
log cosh u
— »«•—
«FO'
m^^mmmm^mmmtm
log tanh u
CBOMHBBBHKMBI
«- Fo'
•^••^•^•MMH
log coth u
— • *
2.500
.501
.502
.503
.504
0.78177
.78221
.78265
.78309
.78353
44,0
0.78762
.78805
.78848
.78891
.78934
42,8
42,9
9.99415
.99416
.99417
.99418
.99419
1,2
0.00585
.00584
.00583
.00582
.00581
2.505
.506
0.78397
.78441
44,0
0.78977
.79019
42,9
9.99421
.99422
1,2
0.00579
.00578
.507
.508
.509
.78485
.78529
.78573
.79062
.79105
.79148
.99423
.99424
.99425
1,1
.00577
.00576
.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
.514
.78749
.78793
•79319
.79362
.99430
•99431
.00570
.00569
2.515
0.78837
.78881
44,0
0.79405
. 79448
42,9
9-99432
.99433
1,1
0.00568
.00567
517
.78925
.79491
.99434
.00566
:5i8
.519
.78969
.79013
.79534
.79577
•99435
•99437
.00565
-00563
2.520
.521
0.79057
.79101
44,0
0.79619
.79662
42,9
9.99438
•99439
1,1
0.00562
.00561
.522
.79145
.79705
•99440
.00560
.523
.79189
.79748
.99441
-00559
— -O
.524
.79233
•79791
.99442
.00558
2.525
.526
0.79277
•79321
44,0
0.79834
.79877
42,9
9.99443
•99444
1,1
0.00557
.00556
.527
.79365
.79920
.99446
.00554
.528
.79409
.79062
.99447
•00553
.529
•79453
.80005
.99448
.00552
2.530
0.79497
44,0
0.80048
42,9
9.99449
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
.79849
.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
.80520
.99461
.00539
.542
[&02S
.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
.80201
.80734
.99466
.00534
.80245
,80389
.80777
.80820
.99467
.99468
.00533
.00532
.549
.80333
.80863
.99469
.00531
2-550
0.80377
44,0
0.80006
42,9
9.99470
1,1
0.00530
u
log tan gd u
<- F,/
log sec gd u
<•> Fo'
log sin gd u
-V
log esc gd u
SMITHSONIAN TABLES
Logarithms of Hyperbolic Functions.
u
log sinh u
<- Fo'
log cosh u
«F0'
log tanh u
«F0'
log coth u
2.550
0.80377
44,0
0.80906
42,9
9.99470
i,i
0.00530
.551
.80420
.80949
.99471
.00529
.552
.80464
.80992
•99473
.00527
• 553
.80508
.81035
•99474
.00526
• 554
.80552
.81078
•99475
.00525
2.555
0.80506
44,0
o. 81121
42,9
9.99476
1,0
0.00524
• 55<J
.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
1,0
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
.81209
.81807
.99492
.00: I
• 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
.581
0.81695
.81739
43,9
0.82194
.82237
42,9
9.99501
.99502
1,0
0.00499
.00498
.582
.81783
.82279
.99503
.00497
.583
.81827
.82322
.99504
.00496
.584
.81871
.82365
.99505
.or
2.585
0.81915
43,9
0.82408
42,9
9.99506
1,0
0.00494
.586
.81958
.82451
.99507
.004 3
.587
.82002
.82494
.99508
.00492
.588
.82046
.82537
.99509
.00491
.589
.82090
.82580
.99510
.00490
2.500
• 591
0.82134
.82178
43,9
0.82623
.82666
42,9
9.99511
.99512
1,0
0.00480
.00488
• 592
.82222
.82700
.99513
.OO
•593
.82266
.8275-'
• 995M
.00,;-
• 594
.82310
.82795
.99515
.00485
2.595
.596
• 597
.598
• 599
0.82354
.82398
.82442
.82485
.82529
43,9
0.82838
.82881
.82924
.82967
.83010
42,9
43,0
9.99516
.99517
.99518
.99519
.90520
1,0
0.00484
.00483
.00482
.00481
.00480
2.600
0.82573
43,9
0.83052
43,o
9.99521
1,0
O.OO479
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
u, Fo'
log cosh u
«F0'
log tanh u
« Fo'
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
0,9
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
o,9
0.00470
.611
.83056
.83525
.99531
.00469
.612
.83100
.83568
•99532
.00468
.613
.83144
.83611
•99533
.00467
.614
.83188
.83654
•99534
.00466
2.6l5
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,o
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
.627
.83759
.84213
.99546
.00454
.628
.83802
.84256
•99547
•00453
.629
.83846
.84299
• 99548
•00452
2.630
0.83890
43,9
0.84341
43,0
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
.636
0.84110
.84154
43,9
0.84556
.84599
43,0
9-99553
•99554
0,9
0.00447
.00446
•637
.84197
.84642
•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
.642
.84417
.84857
•99559
.00441
.84461
.84000
.9956o
.00440
.84505
•84943
.99561
.00439
0.84548
43,9
0.84986
43,0
9.99562
0,9
0.00438
1
.84592
.84636
.84680
.84724
.85029
.85072
.85115
.85158
.99563
.99564
.99565
.99566
•00437
.00436
.00435
.00434
2.650
0.84768
43,9
0.85201
43,0
9.99566
0,9
0.00434
u
i
A
log tan gd u
^5=
=
log sec gd u
,
«F0'
•«••••••••
log sin gd u
•••••^^•••••••l
« Fo'
••^••I^^MBI
log esc gd u
•••^^•^^MMI
72
Logarithms of Hyperbolic Functions.
u
log sinh u
W Fu'
log cosh u
-FO'
log tanh u
«F0'
log coth u
2.650
0.84768
43,9
0.85201
43,0
9.99566
0,9
0.00434
.651
.84812
.85244
•09567
•00433
.652
.84855
.85287
.99568
.00432
653
.84899
•«5330
.99569
.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
.00;. .
.664
.85382
.85803
•99578
.00422
2.665
0.85426
43,9
0.85846
43,0
9-99579
0,8
0.00421
.666
•85469
.85889
.99580
.00420
.667
.85513
.85932
.99581
.00419
.668
.85557
43,8
.85975
.99582
.00418
.669
.85601
.86018
.99583
.00417
2.670
0.85645
43,8
0.86o6l
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
.86664
•99595
.00405
2.685
0.86302
43,8
0.86707
43,0
9.99596
0,8
0.00404 ,
.686
.86346
.86750
•99597
.00403
.687
.86390
.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
.86965
.00601
.00399
.692
.86609
.87008
.09601
.00399
.693
.86653
.87051
.99602
.00308
.694
.86697
.87094
.99603
.00397
2.695
0.86741
43,8
0.87137
43,0
9.99604
0,8
0.00306
.696
.86785
.87180
.09605
• 00395
-697
.86828
.87223
.99605
•00395
.698
.86872
.87266
.99606
.00304
.699
.86916
.87309
.99607
.00393
2.700
0.86o6o
43,8
0.87352
43,0
9.09608
0,8
0.00392
u
log tan gd u
« Fo'
log sec gd u
« Fo'
log sin gd u
« Fo'
log esc gd u
SMITHSONIAN TABLES
73
Logarithms of Hyperbolic Functions.
u log sinh u
•^•^^•^•^
« Fo'
—
log cosh u
^==
• Fo'
••^•i^^HH^MH
log tanh u
^^•••^^•M
«- Fo'
••••••^M^M^KH
log coth u
2.700
.701
.702
.703
.704
0.86960
.87004
.87048
.87091
.87135
43,8
0.87352
.87395
.87438
.87481
.87524
43,0
9.99608
.99608
.99609
.99610
.99611
0,8
0.00392
.00392
.00391
.00390
.00389
2.705
.706
.707
.708
.709
0.87179
.87223
.87267
.87310
.87354
43,8
0.87567
.87610
.87654
.87697
.87740
43,0
9.90612
.99612
.99613
.99614
.99615
0,8
0.00388
.00388
.00387
.00386
.00385
2.710
.711
.712
.713
.714
0.87398
.87442
.87486
.87530
.87573
43,8
0.87783
.87826
.87869
.87912
.87955
43,o
9.99615
.99616
•99617
• .99618
.99619
0,8
0.00385
.00384
.00383
.00382
.00381
2.715
.716
0.87617
.87661
43,8
0.87998
.88041
43,1
9.99619
.99620
0,8
0.00381
.00380
.717
.718
.719
.87705
.87749
.87792
.88084
.88127
.88170
.99621
.99622
.99622
.00379
.00378
.00378
2.720
.721
0.87836
.87880
43,8
0.88213
.88256
43,1
9.99623
.99624
0,8
0.00377
.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
43J
9.99627
o,7
0.00373
.726
.88099
.88471
.99628
.00372
.727
.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
0.88493
43,8
0.88859
43,1
9.99634
o,7
0.00366
.736
.88537
.88962
.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
•99639
.00361
.742
.88800
.89161
•99639
.00361
• 743
.88844
.89204
.99640
.00360
•744
,88887
.89247
.99641
.00359
2.745
0.88931
.88975
43,8
0.89290
.89333
43,1
9.99641
.99642
0,7
0.00359
.00358
•747
.89019
.89376
•99643
.00357
,89063
.89419
.99644
.00356
.89106
.89462
.99644
.00356
2.750
0.89150
43,8
0.89505
43J
9-09645
o,7
0.00355
u
log tan gd u
-FO'
log sec gd u
« Fo'
log sin gd u
« Fo'
log esc gd u
SMITHSONIAN TABLC*
74
Logarithms of Hyperbolic Functions.
u
log sinh u
« Fg'
log cosh u
«F0'
log tanh u
« Fo'
loo eoth 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
.750
.89413
.Spjfo
.99649
.00351
.757
.89457
.89807
.99650
.00350
• 758
.89500
.89850
.90651
.00349
• 759
.89544
.85893
.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
.754
.89763
.90108
.99655
.00345
2.765
0.89807
43,8
0.9015-
43,1
9.99656
o,7
0.00344
.766
.89851
.99656
•00344
.767
.89894
.99657
.00343
.768
.89938
.•^
.99658
.00342
.769
.89982
•503-^
.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
.00496
.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
0.00463
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
0.00682
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
x-
.99672
.00328
2.700
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
.9MOI
.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
• 7<>8
.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
«o F,/
log esc gd u
SMITHSONIAN TABLES
75
Logarithms of Hyperbolic Functions.
u loo sinh u
« Fo'
loo cosh u
• Fo'
loo tanh u
W Fo'
log coth u
2.800
0.91339
43,8
0.91660
43,1
9.99679
O,6
0.00321
.801
.91382
.91/03
.59679
.00321
.802
.91426
.91746
.99580
.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
.8oj
.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
9.99585
0,6
0.00315
.811
.91820
.92134
.99686
.00314
.812
.91864
.92177
.99686
.00314
.813
.91907
.92220
.99687
.00313
.814
.91951
.92263
.99588
.00312
2.815
0.91995
43,7
0.92306
43,1
9.99688
0,6
0.00312
.816
.92039
•92350
.99689
.00311
.817
.92082
.92393
.99690
.00310
.818
.92126
.92436
.99690
.00310
.819
.92170
.92479
.99691
.00309
2.820
0.92213
43,7
0.92522
43J
9.99691
0,6
0.00309
.821
.92257
.92565
.99692
.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
.99696
.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
.99608
.00302
.832
.92738
•93040
.99699
.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
0.00299
.836
.92913
.93212
.99701
.00299
.837
.92957
.93255
.99702
.00298
.838
.93001
.93298
.99702
.00298
.839
.93044
•93341
•99703
.00297
2.840
0.93088
43,7
0.93385
43,1
9.99704
0,6
0.00296
,84]
.93132
.93428
.09704
.00296
.842
.93176
•93471
•99705
.00295
.843
.844
.93219
.93263
.935M
•93557
.99705
.99706
.00295
.00294
2.845
Q /i
0.93307
43,7
0.93600
43,1
9.99706
0,6
0.00294
,846
o »
.93350
.93643
•99707
.00293
.847
•93394
.93687
.99708
.00292
• '^ l^
.93438
•93730
.99708
.00292
>84p
.93482
.93773
.99709
.00291
2.850
0.93525
43,7
0.93816
43,1
9.99709
0,6
0.00291
u
loo tan od u
• FO'
loo tec od u
« Fo'
loo sin od u
« Fo'
log esc gd u
SMITHSONIAN TABLE*
Logarithms of Hyperbolic Functions.
u
log sinh u
« Fo'
log cosh u
• Ft/
log tanh u
« Fo'
log coth u
0.93525
43,7
0.93816
43,i
9.99709
0,6
0.00291
.851
.93569
.93859
.99710
.00290
.85-'
.93613
.93902
.99711
.00- - ,
.853
.93657
.93945
.99711
.OO289
.854
.93700
.93Q89
.99712
.00288
2.855
0.93744
43,7
0.94032
43,1
9.99712
0,0
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
O.OO285
.85i
.94006
.94291
.99716
.00284
.862
.94050
•94334
.99716
.O0284
.863
.94094
.94377
•99717
.OO283
.8.4
.94137
•94420
.99717
.OO283
2.8 >'
0.94181
43,7
0.94463
43,1
9.99718
0,6
O.OOJ82
.8 >'>
.94225
.94506
.99719
.OO28l
.8 ,7
.94269
•94549
.99719
.O028l
.858
.94312
•94593
.99720
.00280
.859
.94356
.94636
43,2
.99720
.O028O
2.870
0.94400
43,7
0.94679
43,2
9.99721
0,6
O.002/9
.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
0.0
.876
.94662
.94938
.99724
.0027
.8/7
.94706
.94981
.99725
.00275
.878
.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
2.88s
0-95055
43,7
0.95326
43,2
9.99729
o,5
0.00271
.886
•95099
.95309
.99730
.00270
.887
.95143
.95413
.99730
.00270
.888
.95185
.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
.9536i
.05628
•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. COO
0.957H
43,7
0-95974
43.2
9-99737
0,5
0.00263
U
log tan gd u
« Fo'
log sec gd u
*
w Fo' log sin gd u
« Fo'
log esc gd u
SMITHSONIAN TABLES
77
Logarithms of Hyperbolic Functions.
u
log sinh u
o>Fo'
log cosh u
«F0'
log tanh u
» Fo'
log coth u
2.900
0.957II
43,7
0-95974
43,2
9-99737
0,5
0.00263
.901
•95754
.96017
•99738
.00262
.902
.95798
.96060
•99738
.00262
.903
.95842
.06103
•99739
.00261
.904
.95885
.96146
•99739
.00261
2.905
0.95929
43,7
0.96190
43,2
9.09740
o,5
O.0020O
.906
•95973
.06233
.99740
.00260
.907
.96017
.56276
.99741
.00259
.908
.96060
.96319
•99741
.00259
.909
.96104
.96362
.99742
.00258
2.910
0.96148
43,7
0.96405
43,2
9.99742
0,5
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
.09746
.00254
.919
.96541
.96794
•99747
.00253
2.920
0.96584
43,7
0.968.??
43,2
9-99747
o,5
0.00253
.921
.96628
.96880
.99748
.00252
.922
.96672
.96923
.09748
.00252
.923
.96716
.96967
.99749
.00251
.924
.96759
.970IO
.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
.936
0.97240
.97283
43,7
0.97485
.97528
43,2
9-99755
•99755
o,5
0.00245
.00245
•937
.97327
.97571
.99756
.00244
•938
•97371
.97614
-09756
.00244
•939
.97414
.97658
•99757
.00243
0.97458
43,7
0.97701
43,2
9-99757
o,5
0.00243
•97502
•97744
.99758
.00242
•97545
.97787
•99758
.00242
.97589
.97830
•99759
.00241
•<v44
.97633
.97874
•99759
.00241
2.945
0.97676
43,7
0.97917
43,2
9.99760
o,5
0.00240
.<>v>
.97720
.97960
.99760
.00240
.<;;;
.97764
.98003
.99761
.00239
.97807
.98046
.99761
.00239
,949
.97851
.98089
.99762
.00238
2.Q50
0.97895
43,7
0.98133
43,2
9.99762
o,5
0.00238
u
log tin 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
2.950
0.9/895
43,7
0.98133
43,2
9.99762
o,5
O.CK
.951
.97938
.98170
•99763
.00- /
.95-'
.97982
.gBsig
•99763
.00237
• 953
.98026
-<>j
•09763
.00
• 954
.98069
• <>S305
.99764
.00236
2.955
0.98113
43,7
0.98349
43,2
9-99764
o,5
0.00236
.956
.98157
.98392
.99765
.00235
• 957
.98200
^98435
•99765
.00235
.958
.98244
.08478
.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
•99767
.00233
.962
.98419
.98651
.99768
.00232
.963
.98462
.98694
.99768
.00232
.964
.98506
.98737
.99709
.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
.00-'-
• 977
.99074
.99299
•99775
.00225
.978
.99117
•9934^
•99775
0,4
.00225
•979
.99161
.99385
•99775
.00225
2.980
0.99205
43,7
0.99429
43,2
9.99776
0,4
O.O0224
.981
.99248
.99472
.99776
.OO224
.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
0.00222
.986
.99466
.99688
•99779
.00221
.987
.99510
•99731
•99779
.00221
.988
•99554
•99774
•99779
.00221
.989
•99597
.99818
.99780
.00220
2.990
0.99641
43,6
0.99861
43,2
9.9978o
0,4
0.00220
.991
•99685
.99904
.99781
.00219
• 992
.99728
•99947
.99781
.00219
•993
.99772
.99990
.09782
.00218
.994
.99816
1.00034
.99782
.00218
2.995
0.99859
43,6
1.00077
43,2
9.99783
0,4
0.002T7
.996
.99903
.00120
.99783
.00217
• 997
•99947
.00163
.99783
.00217
.998
.99090
.00206
.99784
.OOJ
.999
1.00034
.00250
.99784
.00216
3-ooo
1.00078
43,6
1.00293
43,2
9-99785
0,4
0.00215
u
log tan gd u
<- Fo'
log sec gd u
«F0'
log sin gd u
« Fo'
.log esc gd u
SMITHSONIAN TABLES
79
Logarithms of Hyperbolic Functions.
u
log sinh u
« Fo'
log cosh u
«Fo'
log tanh u
« Fo'
log coth u
3-oo
1.00078
436,5
1.00293
432,1
9.99785
4,3
O.002I5
.01
.00514
436,4
.00725
432,2
.99789
4,2
.00211
.02
.00950
436,4
.01157
432,2
•99793
4,1
.00207
.03
.01387
43'>,3
.01589
432,3
.99797
4,1
.00203
.04
.01823
436,3
.02022
432,3
.99801
4,0
.00199
3.05
1.02259
436,2
1.02454
432,4
9.99805
3,9
O.OOI95
.06
.02696
430,2
.02880
432,4
.99809
3,8
.00191
.07
.03132
436,2
•03319
432,4
.90813
3,7
.00187
.08
.03568
436,1
.03/51
432,5
.99817
3,7
.00183
.09
.04004
436,1
.04184
432,5
.99820
3,6
.00180
3.10
1.04440
436,1
1.04616
432,5
9.99824
3,5
O.OOI76
.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
.00163
3-15
1.06620
435,9
1.06779
432,7
9.99841
3,2
O.OOI59
.16
.07056
435,9
.07212
432,7
.99844
3,1
.00156
.17
.07492
435,8
.07645
432,8
.99847
3,1
.00153
.18
.07927
435,8
.08078
432,8
.90850
3,o
.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
0.00144
.21
.09235
435,7
.09376
432,9
.99859
2,8
.00141
.22
.09670
435,7
.00809
432,9
.90861
2,8
.00139
•23
.10106
435,7
. 10242
432,9
.99864
2,7
.00136
.24
. 10542
435,6
.10675
433,0
.99867
2,7
.00133
3.25
i . 10977
435,6
1.11108
433,0
9.99869
2,6
0.00131
.26
.11413
435,6
.11541
433,0
.09872
2,6
.00128
.27
.11849
435,6
.11974
433,0
.99875
2,5
.00125
.28
. 12284
435,5
. 12407
433J
.99877
2,5
.00123
.29
.12720
435,5
. 12840
433,1
.99879
2,4
.OOI2I
3.30
I.I3I55
435,5
i . 13273
433J
9.99882
2,4
O.OOIlS
•31
.13591
435,5
.13706
433,1
.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
.00109
3.35
i • 15332
43Sv4
i. i 5439
433,2
9-99893
2,1
O.OOT07
.36
.15768
435,3
.15872
433,2
•09895
2,1
.OOIO5
•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
. 18379
435,2
.18472
.99907
1,9
.00093
• 43
.18814
435,2
.18906
433.4
.09909
1,8
.00091
.44
. 19250
435,2
• 19339
433,4
.99911
1,8
.00089
3-45
1.19685
435,2
I.I9772
433,4
9.99912
1,8
0.00088
.46
.20120
435,2
.20206
433,4
.99914
!,7
.00086
•47
.20555
435,1
.20639
433,5
.99916
1,7
.00084
.48
.20900
435,1
.21073
433,5
.99918
1,6
.00082
.21425
435,1
.21506
433,5
.99919
1,6
.00081
3-50
1.21
435,1
1.21940
433,5
9.99921
1,6
0.00079
u
log tan gd u
-Fo'
log sec gd u
«- Fo'
log sin gd u
.F0'
log esc gd u
SMITHSONIAN TABLES
80
Logarithms of Hyperbolic Functions.
u
log sinh u
<- Fo'
log cosh u
«F0'
log tanh u
log coth u
3.50
I. 21860
435,1
1.21940
433,5
9.99921
1,6
O.OOO79
.51
.22373
.99922
.00078
.52
.22731
.22807
.99924
i,5
.00076
.53
.23166
435,0
.23240
•99925
.00075
• 54
.23601
.23674
433,6
.99927
.00073
3o5
1 . 24036
435,0
1.24107
433,6
9.99928
1,4
0.00072
.56
.24471
.24541
.99930
.00070
.57
.24906
.24975
.99931
.00069
.53
.25341
.25408
•99933
1,3
.00067
• 59
.25776
.25842
•99934
.00066
3.6o
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
1,1
.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
• 71
.30994
.31046
.99948
1,0
.00052
.72
.3M29
.3M8o
•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
3.80
1.34907
434,7
I.3495I
433,9
9-99957
0,9
0.00043
.81
•35342
.35384
.99957
.00043
.82
•35777
.358i8
.99958
0,8
.00042
.83
.36211
.36252
•99959
.00041
.84
.36646
.36686
.99960
.00040
3.85
i.37o8i
4347
I.37I20
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
3-00
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
.01
.40558
.40501
>o66
.00034
•94
.40993
.41025
.99967
.00033
3-05
1.41427
434,6
I.4I4S9
434,0
9.99968
0,6
O.OOCK2
.96
.41862
.41893
.99968
.00032
•97
.42296
•42327
.99969
.00031
.08
.42731
.42761
.99970
.00030
.99
.43166
.43195
•99970
.OO03O
4.00
1.43600
434,6
1.43629
434-0
9.00971
0,6
O.00029
u
log tan gd u
« Fo'
tog sec gd u
*> Fo'
log sin gd u
« Fo'
log esc gd u
SMITHSONIAN TABLES
81
Logarithms of Hyperbolic Functions.
u
log sinh u
.v
log cosh u
«F0'
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
.09971
.00029
.02
.44409
.44497
.99972
.00028
•03
.44904
.44931
•99973
o,5
.OO027
.04
.45339
.45365
.99973
.00027
4-05
1.45773
4346
1.45799
4340
9-99974
0,5
0.00026
.06
.46208
.46233
•99974
.00026
.07
.46642
4345
.46668
.99975
.00025
.08
.47077
.47102
.99975
.00025
.09
•475II
.47536
434,1
.99976
.00024
4.10
1.47946
4345
1.47970
4341
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
.00022
4.15
1.50118
4345
1.50140
434,1
9.99978
0,4
O.OOO22
.16
.50553
.50574
•99979
.OOO2I
• 17
.50987
.51008
.99979
.OOO2I
.18
.51422
.51442
.99980
.OO020
.19
.51856
.51876
.99980
.OOO20
4.20
1.52291
434,5
1.52310
434,1
9.9998o
0,4
O.OOO2O
.21
.52725
•52745
.90081
.00019
.22
.53i6o
.53179
.99981
.OOOI9
.23
•53594
.53613
.99982
.OOOlS
.24
.54029
.54047
.99982
.OOOlS
4.25
1.54463
4345
i.5448i
434,1
9.99982
0,4
O.OOOlS
.26
.54898
.54915
.99983
o,3
.00017
.27
.55332
•55349
.99983
.00017
.28
.55767
.55783
.99983
.OOOI7
.29
.56201
.56217
.99984
.00016
4.30
1.56636
434,5
1.56652
434,1
9.99984
o,3
O.OOOl6
.31
.57070
.57086
.99984
.00016
•32
•57505
434,4
•57520
.99985
.OOOI5
•33
.57939
•57954
.99985
.OOOlS
•34
.58373
.58388
.99985
.OOOI5
4-35
1.58808
434,4
1.58822
434,1
9.99986
0,3
O.OOOI4
.36
.59242
.59256
434,2
.99986
.00014
•37
.38
.59677
.60111
.59691
.60125
.99986
.99986
.OOOI4
.OOOI4
• 39
.60546
.60559
.99987
.00013
4.40
.41
.42
•43
.44
1.60980
.61414
.61849
.62283
.62718
4344
1.60993
.61427
.61861
.62296
.62730
4342
9.90087
.99087
.99987
.99988
.99988
0,3
0,2
O.OOOI3
.00013
.00013
.OOOI2
.OOOI2
4-45
1.63152
•63587
4344
1.63164
.63598
434,2
9.99988
.99988
0,2
O.OOOI2
.OOOI2
t»
.64032
.99989
.OOOII
,48
.64467
.99989
.OOOII
,64890
.64901
.99989
.OOOII
4-So
5324
434,4
1.65335
434,2
9.99989
0,2
O. OOOII
u
log tan od u
•»jj
log sec gd u
« Fo'
log sin gd u
W FO'
log csc gd u
IMITHBONIAN TABLES
82
Logarithms of Hyperbolic Functions.
u
log sinh u
« Fu'
log cosh u
«F0'
log tanh u
«F0'
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
.00010
• 54
.67062
.67072
.99990
.00010
4-55
1.67496
434,4
1.67506
434,2
9.99990
0,2
O.OOOIO
• 50
.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
9.99091
0,2
0.00009
.61
.70IO2
.70111
.99991
.00009
.62
.70537
.70545
.99992
.00008
.63
.70971
•70979
.99992
.00008
•64
.71406
.7I4U
.99992
.00008
4-65
1.71840
434,4
1.71848
434,2
9.90992
0,2
0.00008
.66
.722/4
.72282
.99992
.00008
.67
.72709
.72716
.99992
.00008
.•68
.73143
.73151
•99993
0,1
.00007
.69
.73577
.73585
.99993
.00007
4.70
i . 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
.80062
.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
9.00096
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
4343
1.8/046
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.
1
log sinh u
-IV
log cosh u
-Fo'
log tanh u
a. Fo'
log coth u
S.oo
.OI
1.87042
.87477
434,3
1.87046
.87480
434,3
9.99996
.99996
0,1
O.OOOO4
.00004
.02
.87911
.87915
.99996
.00004
.03
.04
.88345
.88780
.88349
.88783
.99996
.99996
.00004
.00004
5-O5
1.89214
434,3
1.89217
434,3
9.99996
0,1
0.00004
.06
.89648
.89652
.99997
.00003
.07
.90083
.90086
.99997
.00003
.08
.90517
.90520
.99997
.00003
.09
.90951
.90955
.99997
.00003
5.10
I.9I386
434,3
I.9I389
434,3
9.99997
0,1
O.OOOO3
.11
.91820
.91823
.99997
.00003
.12
.92254
.92257
.99997
.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
O.OOOO3
.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
.97469
.99998
.00002
5.25
1.97900
434,3
1.97903
434,3
9.99998
0,0
O.OOOO2
.26
.08335
.98337
-99998
.00002
•27
.08769
.08771
.99998
.OOOO2
.28-
.99203
.09206
.99998
.OOOO2
.29
.99638
.99640
.99998
.OOOO2
5-30
2.OOO72
434,3
. 2.00074
434,3
9.99998
0,0
O.OOOO2
•31
.00506
.00508
•99998
.O0002
•32
.00941
.00943
.99998
.OOOO2
• 33
•01375
.01377
.99998
.00002
• 34
.01809
.01811
.99998
.OOOO2
5-35
2.02244
434,3
2.02246
434,3
9.99998
0,0
0.00002
.36
.02678
.02680
•99998
.00002
•37
.03112
.03114
.99998
.OOO02
.38
•03547
•
.03548
.90998
.OOO02
• 39
.03981
.03983
.99998
.OOOO2
5.40
.41
, 2.04415
.04849
434,3
2.04417
.04851
434,3
9.99998
•99998
0,0
O.OOOO2
.00002
.42
.05284
•05285
.99098
.OOOO2
•43
.057T8
.05720
.90998
.00002
•44
.06152
.06154
.99998
.00002
5-45
2.06587
434,3
2.06588
434,3
9.99998
0,0
O.OOOO2
.O7O2I
.07023
.99098
.OOOO2
.47
.07455
•07457
.99098
.OOOO2
.48
.07800
.07891
.90998
.OOOO2
• 49
.08324
.08325
•99999
.OOOOI
5-50
2.08758
434,3
2.08760
434,3
9.90009
0,0
O.OOOOI
u
log tan gd u
«F0'
log sec gd u
« Fo'
log sin gd u
<- Fo'
log esc gd u
SMITHSONIAN TABLES
84
Logarithms of Hyperbolic Functions.
u
log sinh u
« Fo'
log cosh u
™
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
.00627
.09628
.99999
.00001
• 53
.IOO6l
.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
.13971
-99999
.00001
-63
.14404
. U405
•99999
.00001
.64
. 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
.23000
.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
.24393
• -'4394
-99999
.00001
• 87
.24828
.24828
-99999
.00001
.88
.25262
.25262
-99999
.00001
.89
.25696
.25697
-99999
.00001
5-90
2.26130
434,3
2.26131
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
.29T7I
.29171 .
.90099
.00001
• 98
.29605
.29605
•99999
.00001
.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
co F,,'
log sin gd u
o> F/
log csc gd u
SMITHSONIAN TABLES
TABLE II
NATURAL HYPERBOLIC FUNCTIONS
87
Natural Hyperbolic Functions.
• u
sinh u
<-F0'
cosh u
«F0'
tanh u
«- F0'
coth u
<•> Fo'
0.0000
O.OOOOO
IO,O
1. 00000
0,0
O.OOOOO
10,0
Oo'
GO
.0001
.OOOIO
.00000
.OOOIO
IOOOO.OO
1000000,0
.0002
.OOO2O
.00000
.00020
5000.00
250000,0
.0003
.OO03O
.00000
.00030
3333.33
niiii, i
.0004
.OO04O
.00000
.00040
2500.00
62500,0
0.0005
O.OOO5O
10,0
I.OOOOO
0,0
0.00050
IO,O
2000.00
40000,0
.0006
.00060
.00000
.00060
1666.67
27777,8
.O007
.00070
.00000
.00070
1428.57
20408,2
.0008
.00080
.00000
.00080
1250.00
15625,0
.OO09
.00090
.00000
.00090
IIII. II
12345,7
O.OOIO
O.OOIOO
1 0,0
I.OOOOO
0,0
O.OOIOO
10,0
IOOO.OO
10000,0
.0011
.OOIIO
.00000
.OOIIO
909.09
8264,5
.0012
.OOI2O
.00000
.00120
833.33
6944,4
.0013
.00130
.00000
.00130
769.23
5917,2
.0014
.OOI40
.00000
.00140
714.29
5102,0
0.0015
O.OOI5O
1 0,0
I.OOOOO
0,0
0.00150
IO,0
666.67
4444,4
.0016
.OOl6o
.00000
.00160
625.00
3906,2
.0017
.OOI70
.00000
.00170
588.24
3460,2
.0018
.OOlSo
.00000
.00180
555.56
3086,4
.0019
.00190
.00000
.00190
526.32
2770,1
O.OO2O
O.O020O
IO,O
I.OOOOO
0,0
0.002OO
10,0
500.00
2500,0
.O02I .002IO
.00000
.00210
476.19
2267,6
.0022 .00220
.00000
.00220
454.55
2066, 1
.0023 .00230
.00000
.00230
434.78
1890,4
.O024
.00240
.00000
.00240
416.67
1736,1
0.0025
0.00250
IO>O
I.OOOOO
0,0
0.00250
10,0
400.00
1 600,0
.0026 .00260
.00000
.00260
384.62
1479,3
.O027
.00270
.00000
.00270
370.37
1371,7
.0028
.00280
.00000
.00280
357.14
1275,5
.OO29
.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 .00310
.00000
.00310
322.58
1040,6
.0032
.00320
.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
10,0
I.OOOOI
0,0
0.00350
IO,O
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
.00390
256.41
657,5
0.0040
0.00400
10,0
I.OOOOI
0,0
0.00400
1 0,0
250.00
625,0
.OO4I
.00410
.00001
.00410
243.90
594,9
.0042
.00420
.OOOOI
.00420
238.10
566,9
.0043
.00001
.00430
232.56
540,8
.0044
.00440
.OOOOI
.00440
227.27
516,5
0.0045
.0046
0.00450
IO,O
I.OOOOI
.00001
0,0
0.00450
.00460
IO,O
222 . 22
217.39
493,8
472,6
.0047
.0048
.00470
.00001
.00001
.00470
.00480
212.77
208.33
452,7
434,0
.0049
.00490
.00001
.00490
204.08
416,5
0.0050
0.00500
10,0
I.OOOOI
0,1
0.00500
10,0
200.00
400,0
u
tin gd u
•Fo'
tec gd u
«F0'
sin gd u
«- Fo'
csc gd u
- Fo'
SMITHSONIAN TABLE*
88
Natural Hyperbolic Functions.
u
sinli u
• Fo'
COSh u
-Fo'
tanh u
« Fo'
coth u
-F,/
0.0050
O.OO5OO
10,0
I.OOOOI
0,1
0.00500
10,0
200.00
400,0
.0051
.00510
.00001
.00510
196.08
384,5 i
.0052
.00520
.00001
.OO52O
309,8 i
.0053
.00530
.00001
.00530
35to
.0054
.00540
.00001
.00540
185.19
342,9
0.0055
O.OO55O
IO,O
I.OOO02
0,1
0.00550
10,0
181.82
330,6
.0050
.00560
.00002
.00500
178.57
3iH,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
O.OO6OO
IO,O
I.OOOO2
0,1
O.OO6OO
IO,O
166.67
277,8
.0061
.006IO
.00002
.OO6IO
163.94
208,7 !
.0062
.00620
.00002
.00620
l6l.29
200,1
.0063
.O053O
.00002
.00630
158.73
.0064
.00640
.00002
.00640
156.25
244,1
0.0065
O.O065O
10,0
I.OOO02
0,1
0.00650
IO,O
153.85
236,7
.0066
.0066O
.OO002
.00660
I5L52
229,6
.0067
.00670
.00002
.00670
149.26
222,8
.00^8
.oo58o
.OOO02
.00680
147.06
216,3
.0069
.00690
.OOOO2
.00690
144-93
2IO.O
0.0070
0.00700
IO,O
I.OO002
0,1
0.00700
10,0
142.86
204,1
.0071
.00710
.00003
.00710
140.85
198,4
.0072
.00720
.00003
.00720
138.89
192,9
.0073
.00730
.00003
.00730
136.99
187/5
.0074
.00740
.00003
.00740
135.14
182,6
0.0075
0.00750
10,0
1.00003
O,I
O.O075O
10,0
133-34
177,8
.0076
.00760
.00003
.00760
131.58
I73,i
.0077
.00770
.00003
.00770
129.87
168,7
.0078
.00780
.00003
.00780
128.21
164,4
.0079
.00790
.00003
.00790
126.58
160,2
o.ooSo
0.00800
IO,O
I.OOOO3
01,
O.OOSOO
10,0
I25.OO
156,2
.0081
.00810
.O0003
.00810
123.46
i5-',4
.0082
.00820
.OOOO3
.00820
121.95
148,7
.0083
.00830
.OOOO3
.00830
120.48
145,2
.0084
.00840
.00004
.00840
119.05
ML/
0.0085
0.00850
IO,O
I.OOOO4
0,1
O.0085O
IO,O
117.65
138,4
.0086
.00860
.OO004
.00860
II6.28
135,2
.0087
.00870
.OO004
.00870
114-95
132,1
.0088
.00880
.OOOO4
.00880
113.64
129,1
.0089
.00890
.00004
.00890
112.36
126,2
0.0090
0.00900
10,0
1.00004
0,1
o.ooooo
10,0
III. II
123,5
.0091
.00910
.00004
.00910
109.89
120,8
.0092
.00920
.00004
.00920
IO8.7O
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
1 0,0
105.27
no,8
.0096
.00960
.00005
.00960
104.17
108,5
.0097
.00970
.00005
.00970
103.10
106,3
.0098
.00980
.00005
.00980
IO2.O4
104,1
.0099
.00090
.00005
.00900
IOI.OI
102,0
O.OIOO
O.OIOOO
IO,O
1.00005
0,1
O.OIOOO
IO,O
IOO.OO
100,0
u
tan gd u
«- Fo'
sec gd u
w Fo'
sin gd u
« Fo'
csc gd u
-Fo'
SMITHSONIAN TABLES
89
Natural Hyperbolic Functions.
u
sinh U
«F0'
cosh u
• Fo'
tanh u
« Fo'
coth u
- Fo'
O.OIOO
0.01000
IO.O
1.00005
0,1
0.01000
IO,O
100.003
1000,0
.OIOI
.01010
.00005
.01010
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
IO,O
1.00006
0,1
0.01050
10,0
95.242
907,0
.0106
.01060
.00006
.01060
94.343
890,0
.0107
.01070
.00006
.01070
93.462
873,4
.0108
.01080
.00006
.01080
92.596
857,3
.0109
.01090
.00006
.01090
91.747
841,6
O.OIIO
O.OIIOO
IO,O
1.00006
0,1
O.OIIOO
IO,O
90.913
826,4
.0111
.01110
.00006
.OHIO
90.094
811,6
.OII2
.OII2O
.00006
.01120
89.289
797,2
.0113
.01130
.00006
.01130
88.499
783,1
.0114
.01140
.00006
.01140
87.723
769,4
0.0115
0.01150
10,0
1.00007
0,1
0.01150
IO,0
86.960
756,i
.0116
.01160
.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
0.01200
10,0
83.337
694,4
.OI2I
.OI2IO
.00007
.OI2IO
82.649
683,0
.OI22
.OI22O
.00007
.OI22O
81.971
671,8
• 0123
.01230
.00008
.01230
81.305
660,9
.OI24
.01240
.00008
.OI24O
80.649
650,3
0.0125
O.OI25O
10,0
1.00008
O,I
0.01250
10,0
80.004
- 640,0
.OI26
.OI26O
.00008
.01260
79.369
629,8
.0127
.OI270
.00008
.01270
78.744
620,0
.0128
.01280
.00008
.01280
78.129
610,3
.OI2Q
.01200
.00008
.OI20O
77.524
600,9
O.OI3O
0.01300
10,0
1.00008
0,1
O.OI30O
10,0
76.927
591,7
.OI3I
.OI3IO
.00009
.01310
76.340
582,7
.0132
.01320
.00009
.01320
75.762
573,9
•0133
.01330
.00009
-OI330
75.192
565,3
.0134
.01340
.00009
.01340
74.631
556,9
0.0135
0.01350
1 0,0
1.00009
0,1
0.01350
IO,O
74.079
548,7
.0136
.01300
.00009
.01300
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
0.0140
O.OI4OO
IO,O
I.OOOIO
O,I
O.OI4OO
10,0
71.433
510,2
.0141
.OI4IO
.00010
.OI4IO
70.927
503,0
.0142
.01420
.00010
.OI42O
70.427
495,9
•0143
.01430
.00010
.OI43O
69.935
489,0
.01440
.00010
.OI44O
69.449
482,2
0.0145
0.01450
.01460
10,0
i.ooori
.00011
0,1
0.01450
.01460
1 0,0
68.970
68.498
475,6
469,1
•0147
.01470
.01480
.OOOII
.OOOII
.01470
.01480
68.032
67.573
462,7
456,5
.0149
.OI49O
.00011
.01490
67.119
450,4
0.0150
0.01500
10,0
I. OOOII
0,2
0.01500
10,0
66.672
444»4
•
tin gd u
« Fo'
sec gd u
« Fo'
sin gd u
« Fo'
csc gd u
- Fo'
SMITHSONIAN TABLES
Natural Hyperbolic Functions.
u
sinh u
• Fo'
cosh u
«F0'
tanh u
«- P./
coth u
• F«'
0.0150
O.OI5OO
I O,O
I.OOOII
0,2
0.01500
10,0
66.672
444,4
.0151
.OI5IO
.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
421,0 :
0.0155
O.OI55O
10,0
I.OOOI2
0,2
O.OI550
10,0
64.521
416,2
.oi5<>
.01500
.00012
.01560
64.108
410,9
• 0157
.01570
.00012
.01570
63.699
405,7
. .0158
.01580
.00012
.01580
63.296
400,5
.0159
.01590
.00013
.01590
62.898
395,5
0.0160
O.OIOOO
10,0
1.00013
0,2
O.OIOOO
10,0
62.505
390,6
, .0161
.Ol6lO
.00013
.Ol6lO
62.117
385,8
.0162
.Ol62O
.00013
.01620
61.734
381,0
: .0163
.01630
.00013
.01630
61.355
376,3
'; .0164
.01640
.00013
.01640
60.081
371,8
0.0165
O.OI65O
IO,O
1.00014
0,2
0.01650
IO,O
60.612
367,3
: .0166
.Ol66o
.00014
.01660
60.247 362,9
; .0167
.01670
.00014
.01670
59.886
358,5
1 .0168
.01680
.00014
.01680
59.529
354,3
t .0169
.01690
.00014
.01690
59. 177
350,1
1 0.0170
O.OI7OO
IO,O
1.00014
0,2
0.01700
IO,O
58.829
346,0
1 .0171
.OI7IO
.00015
.01710
58.485
342.0
! .0172
.OI72O
.00015
.01720
58.U5
338,0
I .0173
.01730
.00015
.01730
57.809
334,1
! .0174
.01740
.00015
.01740
57-477
330,3
1 0.0175
O.OI75O
1 0,0
1.00015
0,2
O.OI75O
IO,O
57.149
326,5
.0176
.01760
.00015
.01760
56.824
322,8
.0177
.01770
.00016
.01770
56.503
319,2
! .0178
.OI78O
.00016
.01780
56.186
315,6
1 .0179
.01790
.00016
.01700
55.872
312,1
1 0.0180
O.OlSoO
IO,O
1.00016
0,2
O.OlSoo
10,0
55o62
308,6
.0181 .01810
.00016
.OlSlO
55-255
305,2
! .0182
.Ol82O
.00017
.01820
54-951
301,9
; .0183
.01830
.00017
.01830
54-651
208,6
| .0184
.01840
.00017
.01840
54-354
295,3
|| 0.0185
O.OI85O
10,0
1.00017
0,2
0.01850
IO,O
54.060
292,2
\ .0186
.01860
.00017
.01860
53-770
289,0
! .0187
.01870
.00017
.01870
53-482
285,9
.0188
.01880
.00018
.01880
53.198
282,9
j .0189
.OlSoO
.00018
.OlSQO
52.916
279,9
1 0.0190
O.OIOOO
10,0
1.00018
0,2
O.OIOOO
IO,O
52.638
277,0
.0191
.01910
.00018
.01910
52.362
274,1
I .0192
.OI92O
.00018
.01920
52.000
j; -i. j
! .0193
.OI93O
.00019
.01930
51.820
268,4
1 .0194
.01940
.00019
.01940
51.553
265,7
1 0.0195
O.OI95O
10,0
1.00019
0,2
0.01950
IO,O
51--^)
263,0
.0196
.01960
.00019
.01960
5I.OJ7
260,3
1 .0197
.OI97O
.00019
.01970
50.768
257,6
.0198
.01980
.00020
.01980
50.512
255,0
1 -0199
.01000
.00020
.01900
50.258
252,5
1 O.O2OO
O.02OOO
10,0
I.OOQ2O
0,2
O.O2OOO
IO,O
50.007
250,0
\ U
tan gd u
a. Fo'
sec gd u
« Fo'
sin gd u
•» Fo'
esc gd u •• Fo'
SMITHSONIAN TABLES
Natural Hyperbolic Functions.
I
sinh u
«F</
cosh u
«Fo'
tanh u
» F0'
coth u
« Fo'
O.O2OO
O.O2OOO
1 0,O
1.00020
0,2
0.02000
1 0,O
50.007
250,0
.O20I
.02010
.00020
.O2OIO
49.758
247,5
.O2O2
.O2O2O
.00020
.02020
49.512
245,0
• 0203
.02030
.00021
.02030
49.268
242,6
.O2O4
.02040
.00021
.02O4O
49.O26
240,3
O.O2O5
0.02050
IO,O
I. 00021
0,2
0.02050
IO,O
48.787
237,9
.O2O6
.O2050
.00021
.O2O50
48.551
235,6
.O2O7
.020/0
.00021
.02O70
48.316
233,3
.0208
.O2O80
.O0022
.O2O80
48.084
231,1
.O2O9
.02000
.00022
.02090
47.854
228,9
O.O2IO
O.02IOO
10,0
I.OO022
0,2
O.O2IOO
10,0
47.626
226,7
.0211
.O2IIO
.00022
.02110
47.400
224,6
.O2I2
.02120
.00022
.O2I2O
47.177
222,5
• 0213
.02130
.00023
.02130
46.955
220,4
.O2I4
.02140
.00023
.02I4O
46.736
218,3
O.O2I5
O.02I5O
10,0
I.O0023
0,2
0.02150
10,0
46.519
216,3
.0216
.02l60
.00023
.O2l6o
46.303
214,3
.0217
.02I7O
.00024
.02I7O
46.090
212,3
.0218
.O2I8O
.00024
.O2l8o
45.879
210,4
.O2I9
.02190
.00024
.02190
45-669
208,5
O.O22O
O.O22OO
IO,O
I.OO024
0,2
O.O220O
IO,O
45.462
206,6
.O22I
.O22IO
.00024
.022IO
45.256
204,7
.O222
.O2220
.00025
.02220
45-052
202,9
.O223
.02230
.00025
.02230
44.850
2O I, I
.0224
.O2240
.00025
.02240
44.650
199,3
0.0225
O.O2250
IO,O
1.00025
0,2
0.02250
IO,O
44.452
197,5
.0226
.0226O
.OOO26
.O226O
44.255
195,7
.O227
.O2270
.OOO26
.02270
44.060
I94,O
.0228
.O2280
.00026
•
.02280
43.867
192,3
.0229
.02290
.00026
.02290
43.676
190,7
O.O23O
O.O23OO
IO,O
I.OOO26
0,2
O.O23OO
10,0
43.486
189,0
.0231
.O23IO
.00027
.02310
43.298
187,4
.0232
.O232O
.OO027
.02320
43-111
185,8
.0233
.02330
.00027
.02330
42.926
184,2
.0234
.02340
.00027
.O234O
42.743
182,6
0.0235
.O236
0.02350
.02360
IO,O
1.00028
.00028
0,2
O.O235O
.02360
IO,O
42.561
42.381
181,1
i79,5
.0237
.0238
•02370
.02380
.00028
.OO028
.02370
.02380
42.2O2
42.025
178,0
176,5
.0239
.023yO
.OOO29
.02390
41.849
i75,o
0.0240
O.O24OO
10,0
1.00029
0,2
O.02400
10,0
41.675
173,6
.0241
.O24IO
.00029
.024IO
41.502
172,1
.0242
.O2420
.00029
.02420
4L330
170,7
.0243
.02430
.00030
.02430
4I.I6O
169,3
.0244
.02440
.00030
.02440
40.992
167,9
0.0245
.0246
0.02450
10,0
I.O003O
.OOO3O
0,2
O.O245O
.02460
10,0
40 . 824
40.659
166,6
165,2
.02470
.02480
.00031
.00031
.02469
.02479
40.494
40-331
^3,9
162,6
.02490
.OOO3I
.02489
40.169
161,3
0.0250
0.02500
10,0
I.OOO3I
0,3
O.02499
IO,O
40.008
1 60,0
I
==
tan od u
^==
• IV
IHM^^HBMI
sec ad u
=ii=
« Fo'
^••••^^^
sin gd u
•••^•••••^H
" Fo'
••••^^•••H
csc gd u
mmmtmfft^mmffm
« Fo'
••MlBi^^^HBBB
92
Natural Hyperbolic Functions.
I
sinh u
«FO'
cosh u
«F0'
tanh u
• Fo'
COth u
- Fo'
0.0250
0.02500'
IO,O
1.00031
0,3
0.02499
IO,O
4O.OO8
1 6o,O *
.0251
.02510
.00032
.02509
39.849
158,7 *
.0252
.O252O
.00032
.02519
39.691
157,4 !
.0253
.0254
.02530
.02540
.00032
.00032
.02529
•02539
39-534
39-379
155,0
0.0255
0.02550
IO,O
1.00033
0,3
0.02549
10,0
39.224
153,8
.0256
.02560
.00033
.02559
•
39.071
152,0
.0257
.025/0
.00033
.02569
38.919
151,4
.0258
.02580
.00033
•02579
38.768
150,2
.0259
.02590
.00034
.02589
38.619
149,0
0.0260
O.O26OO
IO,O
1.00034
o,3
0.02509
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
.0204
.02640
.00035
.02639
37-888
143,4 i
0.0265
O.O265O
IO,O
1.00035
0,3
0.02649
10,0
37-745
142,4
.0266
.02660
.00035
.02659
37.603
141,3
.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.027OO
IO,O
1.00036
0,3
0.02609
10,0
37.046
137,1
.0271
.02710
.00037
.02709
36.909
136,1
.0272
.0272O
.00037
.02719
36.774
135,1
.0273
.02730
.00037
.02729
36.639
I34J
.0274
.02740
.00038
.02739
36.505
133,2
0.0275
0.02750
IO,O
1.00038
0,3
0.02749
IO,O
36.373
132,2
.0276
.02760
.00038
.02759
36.241
131,2 i
.0277
.02770
.00038
.02769
36.110
130,3
.0278
.02780
.00039
.02779
35.o8o
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
.02820
.00040
.02819
35-4/0
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
o,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 I
.0289
.02890
.00042
.02889
34-6 J2
119,7
O.O20O
0.02900
IO,O
1.00042
0,3
0.02899
10,0
34.492
Ii8,9
.0291
.O292
.029IO
.O2920
.00042
.00043
.02909
.02919
34-374
34.256
118,1 ;
117,2 i
.0293
.02930
.00043
.02929
34.139
116,4
.0294
.02940
.00043
.02939
34.023
H5,7
O.O295
O.0295O
IO,O
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
O.O3OO
O.O3OOO
IO,O
1.00045
o,3
0.02999
10,0
33-343
in, i
u
tan gd u
<•> Fo' sec gd u
« Fo'
sin gd u
« Fo'
esc gd u
<- Fo'
SMITHSONIAN TABLES
93
Natural Hyperbolic Functions.
u
sinhu
«F0'
cosh u
»F0'
tanh u
« Fo'
coth u
« Fo'
0.0300
0.03000
10,0
1.00045
0,3
0.02999
IO,O
33.343
111,1
.0301
.O3OIO
.00045
.03009
33.233
110,3
.0302
.O3O2O
.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
10,0
1.00047
0,3
0.03049
10,0
32.797
107,5
.0306
.03060
.00047
.03059
32.690
106,8
.0307
.03070
.00047
.03069
32.584
106,1
.0308
.03080
.00047
.03079
32.478
105,4
.0309
.03090
.00048
.03089
32.373
104,7
0.0310
0.03100
IO,O
1.00048
0,3
0.03099
10,0
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
IO2,O
.0314
.03141
.00049
.03139
31.858
101,4
0.0315
0.03I5I
IO,O
1.00050
0,3
0.03149
IO,O
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
10,0
31.261
97,6
.0321
.03211
.00052
.03209
31.163
97,0
.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
.0326
0.03251
.03261
IO,O
1.00053
.00053
0,3
0.03249
.03259
IO,O
30.780
30.686
94,6
94,1
.0327
.0328
.03271
.03281
.00053
.00054
.03269
.03279
30.592
30.499
93,5
92,9
.0329
.03291
.00054
.03289
30.406
92,4
0.0330
0.03301
10,0
1.00054
0,3
0.03299
10,0
30.314
91,8
.0331
.033H
.00055
.03309
30.223
91,2
.0332
.03321
.00055
.03319
30. 132
9O,7
•0333
.03331
.00055
.03329
30.041
90,1
•0334
.03341
.00056
•03339
29.951
89,6
0.0335
.0336
0.03351
.03361
10,0
1.00056
.00056
o,3
0-03349
•03359
IO,O
29.862
29.773
89,1
88,5
.0337
.0338
.03371
.03381
.00057
.00057
.03369
•03379
29.685
29.597
88,0
87,5
•0339
.03391
.00057
.03389
29.510
87,0
0.0340
.0341
.0342
• 0343
0.03401
.03411
.03421
•03431
10,0
1.00058
.00058
.00058
.00059
0,3
0.03399
.03409
.03419
•03429
IO,O
29.423
29.337
29.251
29.166
86,6
86,0
85,5
85,0
-O344
.03441
.00059
•03439
29.081
84,5
0.0345
.0346
•0347
.0348
.0349
0.03451
.03461
•03471
.03481
.03491
10,0
1.00060
.00060
.00060
.00061
.00061
o,3
0.03449
•03459
.03469
.03479
•03489
IO,O
28.997
28.913
28.830
28.747
28.665
84,0
83,5
83,0
82,5
82,1
0.0350
O.O35OI
10,0
i. 00061
0,4
0.03499
IO,O
28.583
81,6
u
tan gd u
• F0'
•ec gd u
« Fo'
sin gd u
« Fo'
csc gd u
- Fo'
SMITHSONIAN TABLES
— _
_
— __
— _
—
;
94
Natural Hyperbolic Functions.
I
sinh u
-Fa'
cosh u
«Fo*
tanh u
« F,/
COth u
- Fo'
0.0350
0.03501
10,0
I. OOo6l
0,4
0.03409
10,0
28.583
81,6
.0351
.03511
.OOO62
.03509
28.502
81,1
.0352
.03521
.OO062
.03519
28.4-'!
80,7
.0353
.03531
.00062
•03529
28.340
80,2
.0354
.03541
.00063
.03539
28.
79,8
0.0355
0.03551
10,0
1.00063
0,4
0.03549
10,0
28.l8l
79,3
*****5
.0356
.03561
.00063
.03558
28.102
78,9
.0357
.03571
.00064
.03568
28.023
78,4
.0358
.03581
.00064
.03578
27-945
78,0
.0359
•03591
.00064
.03588
27.867
77,6
0.0360
0.036OI
10,0
I.OOO65
0,4
0.03598
10,0
27.790
77,1
.0361
.O36ll
.00065
.03608
27.713
76,7
.0362
.03621
.OOO66
.03618
27.636
76,3
.0363
.03631
.00066
.03628
27.500
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,o
.0366
.03661
.00067
.03658
27-335
74,6
.0367
.03671
.00067
.03668
27.260
74.-;
.0368
.03681
.00068
.03678
27.186
73,8 I
.0369
.03691
.00068
.03688
27.H3
73,4
0.0370
0.03701
10,0
1.00068
0,4
0.03698
IO,O
27.039
73,o
• 0371
.03711
.00069
.03708
26.967
72,6
.0372
.03721
.00069
.03718
26.894
72,2
.0373
.03731
.OOO7O
.03728
26.822
7i,8
.0374
•03741
.00070
.03738
26.750
7i,5
0.0375
0.03751
I O,0
1.00070
0,4
0.03748
IO,O
26.679
7i,i
.0376
.03761
.OO07I
.03758
26.608
70,7
.0377
.03771
.00071
.03768
26.538
70,3
.0378
.03781
.OO07I
.03778
26.468
70,0
.0379
.03791
.OOO72
.03788
26.398
69,6
0.0380
0.03801
IO,O
I.O0072
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
IO,O
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
0.03901
IO,O
1.00076
0,4
0.03898
10,0
25.654
65,7
.0391
.03911
.00076
.03908
25.588
65,4
.0392
.0393
.03921
.03931
.00077
.00077
.03918
.03928
25.523
25.458
64,0
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
.0396
.03961
.00078
.03958
25.266
63,7
• 0397
.03971
.00079
.03968
25.202
63,4
.0398
.03981
.00079
.039/8
25.139
63,1
.0399
.03991
.00080
.03988
25.076
62,8
0.0400
0.04001
10,0
1.00080
0,4
0.03098
10,0
25.013
62,5
u
tan ad u «•> F0'
sec ad u j •» F '
sin gd u
« Fo'
esc gd u
« Fo'
i
SMITHSONIAN TABLES
95
Natural Hyperbolic Functions.
1
sinh u
U.FO'
cosh u
"Fo'
tanh u
« Fo'
coth u
« Fo'
0.0400
.0401
.0402
.0403
.0404
O.0400I
.O40I I
.04021
.04031
.04041
10,0
1.00080
.00080
.00081
.00081
.00082
0,4
0.03998
.04008
.04018
.O4O28
.04038
10,0
25.013
24.951
24.889
24.827
24.766
62,5
62,2
61,8
61,5
61,2
0.0405
.0406
.0407
.0408
.0409
0.04051
.04061
.04071
.04081
.04091
IO,O
1.00082
.00082
.00083
.00083
.00084
0,4
0.04048
.04058
.04068
.04078
.04088
10,0
24.705
24.644
24.584
24.523
24.464
60,8
60,6
60,3
60,0
59,7
0.0410
0.04IOI
IO,O
1.00084
0,4
0.04098
IO,O
24.404
59,5
.0411
.0412
.0413
.0414
.04111
.04121
.04131
.04141
.00084
.00085
.00085
.ooo85
.04108
.O4Il8
.04128
.04138
24.345
24.286
24.227
24.168
59,2
58,9
58,7
58,3
0.0415
.0416
0.04I5I
.04l6l
IO,O
1.00086
.00087
0,4
0.04148
.04158
IO,O
24.110
24.052
58,o
57,8
.0417
.04171
.00087
.04168
23.995
57,5
.0418
.04l8l
.00087
.04178
23.937
57,2
.0419
.04191
.00088
.04188
23.880
56,9
0.0420
.0421
O.O42OI
.04211
IO,O
1.00088
.00089
0,4
0.04198
.04208
10,0
23.824
23.767
56,7
56,4
.0422
.04221
.00089
.04217
23.711
56,1
.0423
.04231
.00089
.04227
23.655
55,9
.0424
.04241
.00090
.04237
23.599
55,6
0.0425
O.0425I
IO,O
1.00090
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
O.0430I
IO,O
1.00092
0,4
0.04297
IO,O
23.270
54,0
.0431
.04311
.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,i
0.0435
0.04351
10,0
1.00095
0,4
0.04347
IO,O
23.003
52,8
»0«6
.04361
.00095
.04357
22.950
52,6
• 0437
.04371
.00095
.04367
22.858
52,3
.0438
.04381
.00096
•04377
22.846
52,1
.0439
.04391
.00096
•04387
22.794
51,9
0.0440
O.O44OI
IO,0
1.00097
0,4
0.04397
IO,O
22.742
5i,6
.0441
.04411
.00097
.04407
22.690
5i,4
.0442
.04421
.00098
.04417
22.639
51,2
.04431
.00098
.04427
22.588
50.0
.0444
.04441
-
.00099
.04437
22.537
50,7
0.0445
0.04451
10,0
1.00099
0,4
0.04447
10,0
22.487
50,5
.0446
.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
10,0
I.OOIOI
0,5
0.04497
1 0,0
22.237
49,3
u
tin gd u
«F0'
sec gd u
« Fo'
sin gd u «- F,'
csc gd u <•» Fo'
SMITHSONIAN TABLES
96
Natural Hyperbolic Functions.
u
sinh u
,w
cosh u
-Fo'
tanh u
•* Fo'
coth u
- Fo'
0.0450
O.O45O2
10,0
I.OOIOI
o,5
0.04497
10,0
22.237
49,3
.0451
.04512
.OOIO2
.04507
22.188
49,1
.0452
.04522
.00102
•04517
22.139
48,9
.0453
•04532
.OOIO3
•04527
22.090
48,7
.0454
.04542
.OOIO3
•04537
22.042
48,5
0.0455
0.04552
IO,O
I. 00104
o,5
0.04547
IO,O
21.993
48,3
.0456
.04502
.OOIO4
•04557
21-945
48,1
.0457
•04572
.OOIO4
.04567
21.897
47,8
.0458
.04582
.00105
•04577
21.849
47,6
.0459
.04592
.OOIO5
.04587
21.802
47,4
0.0460
0.04602
IO,O
1.00106
0,5
0.04597
IO,O
21-754
47,2
.0461
.04612
.OOIO6
.04607
21.707
47,0
.0462
.04622
.OOIO7
.04617
21.660
46,8
.0463
.04632
.OOI07
.04627
21.614
46,6
.0464
.04642
.OOIOS
•04637
21.567
46,4
0.0465
0.04652
10,0
I.OOIO8
o,5
0.04647
10,0
21.521
46,2
.0466
.04662
.OOIO9
.04657
21.475
46,0
.0467
.04672
.00109
.04667
21.429
45,8
.0468
.04682
.00110
.04677
21.383
45,6
.0469
.04692
.OOIIO
.04687
21.338
454
0.0470
O.O47O2
IO,O
I.OOIIO
0,5
0.04697
10,0
21.292
45,2
.0471
.04712
.OOIII
•04707
21.247
45,0
.0472
.04722
.OOIII
.04716
21. 2O2
44,9
.0473
.04732
.OOII2
.04726
21.157
44.7 i
.0474
.04742
.00112
.04736
21.113
44,5
0.0475
0.04752
10,0
I. OOII3
o,5
0.04746
10,0
21.068
44,3
.0476
.04762
.00113
.04756
2I.O24
44 ,i
.0477
.04772
.00114
.04766
2O.98O
43,9
.0478
.04782
.00114
.04776
20.936
43,7
.0479
.04792
.00115
.04786
20.893
43,6
0.0480
0.04802
10,0
I. 001 15
o,5
0.04796
10,0
2O.849
43,4
.0481
.04812
.00116
.04806
20.806
43,2
.0482
.04822
.00116
.04816
20.763
43,0
.0483
.04832
.00117
.04826
2O.72O
42,8
.0484
.04842
.00117
.04836
20.677
42,7
0.0485
0.04852
10,0
1.00118
o,5
0.04846
IO,O
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
20.424
41,6
.0491
.04912
.00121
.04906
20.383
41,4 !
.0492
.04922
.00121
.04916
20.342
41,3
.0493
.04932
.OOI22
.04926
20-300
41,1
• 0494
.04942
.OOI22
.04936
20.259
40,9
0.0495
0.04952
10,0
I.OOI23
0,5
0.04946
10,0
20.2TQ
40,8
.0496
.04062
.00123
.04956
20.178
40,6
.0497
.04972
.00124
.04966
20.137
40,5
.0498
.04082
.OOI24
.04976
20.097
40,3
.0499
.04992
.00125
.04986
20.057
40,1
0.0500
O.O5OO2
IO,O
I.OOI25
0,5
0.04906
10,0
20.017
40,0
u
tan gd u
« Fo'
sec gd u
« Fo'
sin gd u
« Fo'
esc gd u
M F
SMITHSONIAN TABLES
97
Natural Hyperbolic Functions.
u
• inh u
«F0'
cosh u
«FO'
tanh u
« Fo'
coth u
« Fo'
0.0500
.0501
.0502
.0503
.0504
0.05002
.05OI2
.05022
.05032
.05042
10,0
1.00125
.00126
.00126
.00127
.00127
o,5
0.04996
.05006
.05016
.05026
.05036
IO,O
2O.OI7
19.977
19.937
19.897
19.858
40,0
39,8
39,6
39,5
39,3
0.0505
.0506
0.05052
.05062
10,0
1.00128
.00128
o,5
0.05046
.05056
10,0
19.819
19.780
39,2
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
O.05IO2
10,0
1.00130
0,5
0.05096
IO,O
19.625
38,4
.0511
.05112
.00131
.05106
19.587
38,3
.0512
.05122
.00131
.05116
19.548
38,1
.0513
.05132
.00132
.05126
19.510
38,0
.0514
.05142
.00132
.05135
19.472
37,8
0.0515
0.05152
10,0
1.00133
o,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
o,5
0.05195
IO,O
19.248
36,9
.0521
.05212
.00136
.05205
19.211
36,8
.0522
.05222
.00136
.05215
19.174
36,7
.0523
.05232
.00137
.05225
19.138
36,5
.0524
.05242
.00137
.05235
19.101
36,4
0.0525
0.05252
10,0
1.00138
o,5
0.05245
IO,O
19.065
36,2
.0526
.05262
.00138
.05255
I9.O29
36,1
.0527
.05272
.00139
.05265
18.993
36,0
.0528
.05282
.00139
.05275
18.957
35,8
.0529
.05292
.00140
.05285
I8.92I
35,7
0.0530
O.05302
IO,O
1.00140
o,5
0.05295
10,0
18.886
35,6
.0531
.05312
.00141
.05305
18.850
35,4
.0532
.05323
.00142
.05315
I8.8I5
35,3
• 0533
•05333
.00142
.05325
18.779
35,2
•0534
.05343
.00143
•05335
18.744
35:0
0.0535
0.05353
10,0
1.00143
0,5
0.05345
10,0
l8.709
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
.05433
.00147
.05425
18.434
33,9
.0544
•05443
.00148
•05435
18.400
33,8
0.0545
0.05453
10,0
1.00149
0,5
0.05445
IO,O
18.367
33,6
.0546
.05463
.00149
.05455
18.333
33,5
•0547
.05473
.00150
.05465
l8.300
33,4
.05483
.00150
.05475
18.266
33,3
.0549
•05493
.00151
.05484
18.233
33,1
p.0550
0.05503
10,0
1.00151
0,6
0.05494
10,0
18.200
33,0
•
tan gd u
• Fo'
tec gd u
• Fo'
sin gd u
«•> Fo'
esc gd u
« Fo'
SMITHSONIAN TABLES
Natural Hyperbolic Functions.
u
•inh u
«F0'
COSh u
«Fu'
tanh u
- Fo'
coth u
- Fo'
0.0550
0.05503
IO,O
I.OOI5I
0,6
0.05494
10,0
18.200
33,0
.0551
.05513
.OOI52
.05504
18.167
32,9
.0552
.05523
.OOI52
.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
I. 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
17.008
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
31,7
.0562
.05623
.00158
.05614
I7.8I2
3i,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
10,0
17.718
31,3
.0566
.05663
.00160
.05654
I7.687
31,2
.0567
•05673
.00161
.05664
17.656
3M
.0568
.05683
.00161
.05674
17.625
3i,o
.0569
•05693
.00162
.05684
17-594
30,9
0.0570
0.05703
1 0,0
1.00162
0,6
0.05694
10,0
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
17.200
29,8
0.0580
0.05803
IO,0
1.00168
0,6
0.05794
IO,O
I7.26l
29,7
.0581
.05813
.00169
.05803
17.231
29,6
.0582
.05823
.00169
.05813
I7.2O2
29o
.0583
.05833
.00170
.05823
17.172
29,4
.0584
•05843
.00171
.05833
I7.M3
29,3
0.0585
0.05853
IO,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
16.908
28,8
0.0500
0.05003
IO,0
1.00174
0,6
0.05893
10,0
16.069
28,7
.0591
•05913
.00175
.05903
16.940
28,6
.0592
•05923
.00175
•05913
l6.9T2
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
10,0
16.827
28,2
.0596
.05964
.00178
.05953
16.798
38,1
.0597
.05974
.00178
.05963
16.770
28,0
.0598
• 0599
.05084
.05994
.00179
.00179
.05973
.05983
16.742
I6.7I4
27,9
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'
esc gd u
« Fo'
SMITHSONIAN TABLES.
99
Natural Hyperbolic Functions.
u
sinh u
«FO'
cosh u
-Fo'
tanh u
« Fo'
coth u
« Fo'
0.0600
0.060O4
10,0
1.00180
0,6
0.05993
IO,O
16.687
27,7
.0601
.06014
.00181
.06003
16.659
27,7
.0602
.06024
.00181
.06013
16.631
27,6
.0603
.00034
.00182
.06023
16.604
27,5
.OJ04
.06044
.00182
.06033
16.576
27,4
0.0605
0.06054
10,0
1.00183
0,6
0.06043
10,0
16.549
27,3
.0606
.06064
.00184
.06053
16.522
27,2
.OXDJ
.06074
.00184
.06063
16.495
27,1
.0608
.06084
.00185
.06073
16.468
27.0
.o5o9
.06094
.00185
.06082
16.441
26,9
o.o5io
O.o6l04
IO,O
1.00186
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
O.o6l54
IO,O
1.00189
0,6
0.06142
IO,O
16.281
26,4
.0616
.06164
.00190
.06152
16.254
26,3
.0617
.06174
.00190
.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
1.00192
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
1.00195
0,6
0.06242
IO,O
16.021
25,6
.0626
.06264
.00106
.06252
15.995
25,5
.0627
.06274
.00197
.06262
15.970
25,4
.0628
.06284
.00197
.06272
15.944
25,3
.0629
.06294
.00198
.06282
15.919
25,2
0.0630
0.06304
IO,O
1.00199
0,6
0.06292
10,0
15.894
25,2
.0631
.06314
.00199
.06302
15.869
25,1
.0632
.06324
.00200
.06312
15.844
25,O
.0633
•06334
.00200
.06322
15.819
24,9
.0634
.06344
.00201
.06332
15.794
24,8
0.0635
0.06354
10,0
1.00202
0,6
0.06342
IO,O
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
.OO2O4
.06381
15.671
24,5
0.0640
0.06404
IO,O
1.00205
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
.OO207
.06421
15.574
24,2
.06444
.O0207
.06431
15.549
241
0.0645
0.06454
IO,0
1.00208
0,6
0.06441
10,0
15.525
24,0
.0646
.06464
.00209
.06451
15.501
23,9
.06475
•06485
.OO2O9
.OO2IO
.06461
.06471
15.478
15-454
81
.0649
.06495
.00211
.06481
15.430
23,7
0.0650
0.06505
10,0
I.OO2II
o,7
0.06491
10,0
15.406
23,6
u
tin gd u
« Fo'
sec gd u
<o Fo'
sin gd u
« Fo'
csc gd u
w Fo'
SMITHSONIAN TABLE*
100
Natural Hyperbolic Functions.
u
sinh u
»F</
cosh u
• Po'
tanh u «•> F
coth u
- F./
0.0650
0.06505
IO,O
I.O02II
0,7
0.06491
10,0
15.406
23,6
.0651
.06515
.OO2I2
.06501
15.383
23,6
.0652
.06525
.O02I3
.06511
15.359
23,5
.0653
.06535
.OO2I3
.06521
15.336
23,4
.0654
.00545
.00214
.06531
15.312
23,3
0.0655
0.06555
10,0
I.OO2I5
0,7
0.06541
10,0
15.289
23,3
.0656
.06565
.00215
.06551
15.266
23,2
.0657
.06575
.00216
.06561
15.243
23,1
.0658
.06585
.00217
.06571
15.219
23,1
.0659
.06595
.00217
.06580
15.196
23,0
0.0660
0.06605
1 0,0
I.002I8
o,7
0.06590
10,0
15.174
22,9
.0661
.06615
.00219
.06600
15.151
22,9
.0662
.06625
.O02I9
.06610
15.128
22,8
.0663
.06635
.OO22O
.06620
15.105
22,7
.0664
.06645
.OO22I
.06630
15.082
22,6
0.0665
0.06655
IO,0
I.O022I
o,7
0.06640
IO,O
I5.060
22,6
.0666
.06665
.OO222
.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
10,0
14.948
22,2
.0671
.06715
.00225
.06700
I4.9a5
22,2
.0672
.06725
.00226
.06710
14.003
22,1
.0673
.06735
.O0227
.06720
I4.88I
22,0
.0674
•06745
.OO227
.06730
14.859
22,O
0.0675
0.06755
IO,O
1.00228
o,7
0.06/40
IO,O
14.837
21,9
.0676
.06765
.OO229
.06750
14.815
21,8
.0677
.06775
.OO229
.06760
14-794
21,8
.0678
.06785
.00230
.06770
14.772
21,7
.0679
.06795
.00231
.06780
14.750
21,7
0.0680
0.06805
10,0
I.0023I
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
IO,O
1.00235
o,7
0.06839
10,0
14.621
21,3
.0686
.06865
.00235
.06849
I4.600
21,2
.0687
.06875
.00236
.06859
U-579
21,2
.0688
.06885
.00237
.06869
I4o58
21,1
.0689
.06895
.00237
.06879
14-537
21,0
0.0600
0.06905
IO,O
1.00238
o,7
0.06889
10,0
14.516
21,0
.0691
.06916
.00239
,068»
14.495
20,9
.0692
.06926
.0024O
.06909
14-474
20,8
.0693
.06936
.0024O
.06019
14-453
20,8
.0694
.06946
.OO24I
.06929
M.432
20,7
0.0695
0.06956
IO,O
I.OO242
o,7
0.06939
10,0
14.412
20,7
.0696
.06966
.00242
.06949
14.391
20,6
.0697
.06976
.00243
.06959
14.3/0
20,6
.0698
.06986
.00244
.06069
14.350
20,5
.0699
.06996
.00244
.00979
14.329
20,4
0.0700
0.07006
1 0,0
1.00245
o,7
0.06989
10,0
14.309
20,4
u
tan gd u
««> FO' sec fld u «* Fo'
sin od u
« Fo'
esc ad u
« Fo'
SMITHSONIAN TABLES
101
Natural Hyperbolic Functions.
u
• inh u «•> FO'
cosh u
»F»
tanh u
« Fo'
coth u
- Fo'
0.0700
0.07006
10,0
1.00245
0,7
0.06989
10,0
14.309
20,4
.0701
.07016
.00246
.06999
14.289
20,3
.0702
.07026
.00247
.07008
14.268
20,3
.0703
.07036
.00247
.07018
14-248
20,2
.0704
.07046
.00248
.07028
14.228
2O, I
0.0705
0.07056
IO,O
1.00249
0,7
0.07038
10,0
14.208
20,1
.0/OJ
.07056
.00249
.07048
14.188
2O,0
.0707
.07076
.00250
.07058
14.168
20,O
.0708
.07086
.00251
.07068
14.148
19,9
.0709
.07096
.00251
.07078
9,9
14.128
19,9
0.0710
O.07I06
10,0
I . 00252
0,7
0.07088
9,9
14.108
19,8
.0711
.07116
.00253
.07098
14.088
19,7
.0712
.O7I26
.00254
.07108
14.069
19,7
.0713
.07136
.00254
.07118
14.049
19,6
.0714
.07146
.00255
.07128
14.029
19,6
0.0715
O.07I56
IO,O
1.00256
o,7
0.07138
9,9
I4.OIO
19,5
.0716
.07166
.00256
.07148
13.990
19,5
.0717
.07176
.00257
.07158
13.971
19,4
.0718
.07185
.00258
.07168
13.952
19,4
.0719
.07196
.00259
.07178
13.932
19,3
0.0720
0.07205
IO,O
1.00259
o,7
0.07188
9,9
13.913
19,3
.0721
.07216
.00260
.07198
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
10,0
1.00263
o,7
0.07237
9*9
I3.8I7
19,0
.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
.07295
.00266
.07277
13.742
18,8
0.0730
0.07306
IO,O
1.00267
o,7
0.07287
9,9
13.723
18,7
.0731
.07317
.00267
.07297
13.704
1*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
1 0,0
1.00270
o,7
0.07337
9,9
13-630
18,5
.0736
.07367
.00271
•07347
I3.6ll
18,4
•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
1 0,0
1.00274
o,7
0.07387
9,9
13.538
18,2
.0741 .07417
.00275
.07396
13.520
18,2
.0742
.07427
.00275
.07406
13.502
18,1
•07437
.00276
.07416
13-484
18,1
•0744
•07447
.00277
.07426
13.466
18,0
0.07457
10^0
1.00278
o,7
0.07436
9,9
13.448
18,0
.00278
.07446
13.430
17,9
•0747
.0748
•07477
•07487
.00279
.00280
.07456
.07466
13.412
13 • 394
17,9
[7,8
.0749
.07497
.00281
.07476
I3.37<3
17,8
0.0750
7507
10,0
I.002>Sl
0,8
o. 07486
9,9
13.358
17,7
u . tan gd u u, F '
sec gd u
« Fo'
sin gd u
<- Fo'
esc gd u
«- Fo'
SMITHSONIAN TABLES
102
Natural Hyperbolic Functions.
u
sinh u
«F0'
cosh u
<-Fo'
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
.O0282
.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
13.2^8
17,6
0.0755
0.07557
IO,O
I.O0285
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
I.OO289
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
.O029I
.07615
13.132
I7,i
.0764
.07647
.OO292
.07625
13.114
17,1
0.0765
0.07657
IO,O
1.00293
0,8
0.07635
9,9
13.097
I7J
.0766
.07667
.00294
.07645
13.080
I7,o
.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
•07/05
12.979
16,7
• 0773
.07/38
.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
.077/8
.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
1 6,0
•0791
.07918
.00313
.07894
12.669
15,9
.0792
.07928
.00314
.07903
12.653
15,9
• 0793
•07938
.00315
.07913
12.637
15,9
.0794
• .07948
.00315
.07923
12.621
0.0795
O.079S8
IO,O
1.00316
0,8
0.07933
9,9
12.605
IS*
.0796
.07968
.00317
.07943
15,7
.0797
.07978
.00318
.07953
12.574
15,7
.0798
.07988
.00319
.07963
W.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
<- Fo'
sec gd u
• Fo'
sin gd u
« Fo'
esc gd u
• Fo'
SMITHSONIAN TABLES
103
Natural Hyperbolic Functions.
1
sinh u
«FO'
cosh u
»F0'
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
0.08059
10,0
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.o8lO9
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
I5,o
.0816
.08169
.00333
.08142
12.282
I5,o
.0817
.O8l79
.00334
.08152
12.267
14,9
.0818
.08189
•00335
.08162
12.252
14,9
.0819
.O8l99
.00336
.08172
12.237
14,9
0.0820
O.o82O9
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
I2.IQ3
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
I2.IO5
14,6
.0829
.08299
.00344
.08271
I2.O9O
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
.0833
.0834
.08330
.08340
.08350
•00346
.00347
.00348
.08301
.08311
.08321
12.047
12.033
12.018
14,4
14,4
14,3
0.0835
.0836
.0837
.0838
.0839
0.08360
.08370
.08380
.08390
.08400
IO,O
1.00349
.00350
.00350
.00351
.00352
0,8
0.08331
.08341
.08351
.08360
.08370
9,9
12.004
11.990
u.975
11.961
11.947
14,3
14,3
14,2
14,2
14,2
0.0840
.0841
.0842
.0844
0.08410
.08420
.08430
.08440
.08450
1 0,0
1.00353
•00354
.00355
.00356
.00356
0,8
0.08380
.08390
.08400
.08410
.08420
9,9
n.933
11.919
11.905
11.890
11.876
14,1
14,1
14,1
14,0
14,0
0.0845
.0846
.0847
.0849
0.08460
.08470
.08480
.064QO
.08500
10,0
1-00357
.00358
.00359
.00360
.00361
0,8
0,9
0.08430
.08440
.08450
.08460
.08470
9,9
11.862
11.849
n.835
11.821
11.807
14,0
13,9
13,9
13,9
13,8
0.0850
O.OSSIO
10,0
1.00361
0,9
0.08480
9,9
11-793
13,8
u
tan gd u
»*'
•ec gd u
« Fo'
sin gd u
« Fo'
esc gd u
« Fo'
SMITHSONIAN TABLE*
104
Natural Hyperbolic Functions.
u
sinh u
-Fo'
cosh u
<* F,,'
tanh u
- Fo'
coth u
« Fo'
0.0850
0.08510
IO,0
1.00361
0,9
0.08480
9,9
H.793
13,8
.0851
.08520
.00362
.08490
11.779
13,8
.0852
.08530
.00363
.08499
11.795
13,7
.0853
.08540
.00364
.08509
11.752
13,7
.0854
.08550
.00365
.08519
n.738
13,7
0.0855
0.08560
IO,0
I.OO366
0,9
0.08529
9,9
11.724
13,6
.0850
.08570
.00367
.08539
11.711
13,6
.0857
.08580
.00367
.08549
11.697
13,6
.0858
.08591
.00368
.08559
11.684
13,6
.0859
.08001
.00369
.08569
11.670
13,5
0.0860
o. 08611
IO,O
I.O037O
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
10,0
1.00374
o,9
0.08628
9,9
11.590
13,3
.0866
.08671
.00375
.08638
11.576
13,3
.0867
.08681
.00376
.08648
11-563
13,3
.0868
.08691
.00377
.08558
11.550
13,2
.0869
.O87OI
.00378
.08668
n.536
13,2
0.0870
0.087II
10,0
1.00379
0,9
0.08678
9,9
11.523
13,2
.0871
.08721
.00380
.08688
11.510
I3,i
.0872
.08731
.00380
.08698
n.497
I3,i
.0873
.08741
.00381
.08708
11.484
I3,i
.0874
.08/51
.00382
.08718
11.471
13,1
0.0875
0.08761
IO,O
1.00383
0,9
0.08728
9,9
11.458
I3,o
.0876
.08771
.00384
.08738
11-445
I3,o
.0877
.08781
.00385
.08748
n.432
I3,o
.0878
.08791
.00386
.08758
11.419
12,9
.0879
.08801
.00387
.08767
11.406
12,9
0.0880
o. 08811
IO,O
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
11-354
12,8
.0884
.08852
.00391
.08817
11.342
12,8
0.0885
0.08862
IO,O
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
IO,O
1.00396
0,9
0.08877
9,9
11.266
.0891
.08922
.00397
.08886
n.253
.0892
.08932
.00398
.08896
11.240
12,5
.0893
.08942
.00399
.08006
11.228
1 2.5
.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
I -'.4
.0897
.08982
.00403
.08046
11.178
12,4 .
.0898
.08992
.00403
.08956
11.166
12.4
.0899
.09002
.00404
.08966
H.I53
12,3
0.0900
0.09012
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
105
Natural Hyperbolic Functions.
u
sinh u
«F0'
cosh u
"F0'
tanh u
« Fo'
coth u
« Fo'
0.0900
0.09012
10,0
1.00405
0,9
'0.08976
9,9
II.I4I
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
II.O92
12,2
0.0905
0.09062
I O,O
1.00410
0,9
0.09025
9,9
II.oSo
12,2
.0906
.090/2
.00411
.09035
II.068
12,1
.0907
.09082
.00412
.09045
11.056
12,1
.0908
.09092
.00413
.09055
11.043
12,1
.0909
.09103
.00413
.09065
11.031
12,1
0.0910
O.O9II3
IO,O
1.00414
0,9
0.09075
9,9
11.019
I2,O
.0911
.09123
.00415
.09085
11.007
1 2,O
.0912
.09133
.00416
.09095
10.995
1 2,O
.0913
.09143
.00417
.09105
10.983
12,0
.0914
.09153
.00418
.09115
10.971
11,9
0.0915
0.09163
10,0
1.00419
0,9
0.09125
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
11,8
.0919
.09203
.00423
.09164
10.912
n,8
0.0920
0.09213
IO,O
1.00423
0,9
0.09174
9,9
10.900
n,8
.0921
.09223
.00424
.09184
10.888
11,8
.0922
.09233
.00425
.09194
10.877
n,7
.0923
.09243
.00426
.09204
10.865
ii,7
.0924
•09253
.00427
.09214
10.853
n,7
0.0925
0.09263
10,0
1.00428
0,9
0.09224
9,9
10.842
ii,7
.0926
.09273
.00429
.09234
10.830
n,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
ii,5
•0934
.09354
.00436
•09313
10.738
n,4
0.0935
0.09364
IO,O
1.00437
0,9
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
n,3
0.0940
0.00414
IO,0
1.00442
0,9
0.09372
9,9
10.670
n,3
.0941
.09424
.00443
.09382
10.658
H,3
.0942
.09434
.00444
.09392
10.647
11,2
•0943
.09444
.00445
.09402
10.636
11,2
.0944
.09454
.00446
.09412
10.625
11,2
0.0945
0.09464
10,0
1.00447
0,9
0.09422
9,9
10.613
11,2
.09474
.00448
.09432
10.602
U, I
.09484
.00449
.09442
10.591
II, I
.09404
.00450
0,9
.09452
10.580
11,1
.0949
.09504
.00451
1,0
.09462
10.569
II, I
0.0950
0.09514
10,0
1.00452
1,0
0.09472
9,9
10.558
11,0
u
tin gd u
-Fo'
sec gd u
« Fo'
sin gd u
« Fo'
esc gd u
« Fo'
iMITHSON'AN TABLES
106
Natural Hyperbolic Functions.
u
Sinn u
«F0'
cosh u
-Fo'
tanh u
•» Fo'
coth u
« Fo'
0.0950 I 0.09514
I O,0
1.00452 1,0
0.09472
9,9
10.558
11,0
.oj5i
.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
.0^511
10.514
11,0 :
0.0955
0.09565
IO,O
1.00456
1,0
0.09521
9,9
10.503
I0£
.0950
.09575
.00457
.09531
10.492
10,9 !
.0957
•0^585
.00458
.09541
10.481
10,9
.0958
.09595
.00459
.09551
10.470
10,9
.0959
.oc>x)5
.004^0
.09501
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
.00404
.00600
10.416
10,7 i
.0964
.09655
.00465
.09610
10.406
10,7
0.0965
0.09665
10,0
1.00466
1,0
0.09620
9,9
10.395
10,7
.0966
.09:^75
.00407
.09630
10.384
io,7 1
.0967
.09685
.004^8
.09640
10.373
10,7
.0968
.09695
.00469
.09650
10.363
10,6
.0969
.09705
.00470
.09660
10.352
1 0,6
0.0970
0.09715
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
10,5
.0974
.09755
•00475
.09709
10.299
10,5
0.0975
0.09765
IO,0
1.00476
1,0
0.09719
9,9
10.289
10,5 :
.0976 .09770
•00477
.09729
10.278
10,5 !
.0977 .o»;7c$)
.00478
•09739
10.268
10,4
.0978
.09795
.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 i
.0987
.09886
.00487 |
.09838
10.165
10,2
.0988
.09896
.00488
.09848
10.154
10,2
.0989
.09906
.00489
.09858
10. 144
10,2
0.0090
0.09916
IO,O
1.00490
1,0
0.05868
9,9
10.134
10,2
.0091
.09926
.00491
.09978
10.124
10,1 !
.0992
.09936
.00492
.09888
10.114
10,1
•0993
.09946
.00493
.00897
10. 104
10. 1
.0994
.09956
.00494
.09907
10.093
10,1
0.0995
0.09966
10,0
1.00495
1,0
0.00917
9,9
10.083
10,1
.0906
.09976
.00496
.09927
10.073
IO,0
.0997
.09987
.00497
•09937
10.063
IO,O
.0998
.09997
.00498
.09947
10.053
IO,O
.0999
.10007
.00499
.09957
10.043
IO,O
O.IOOO
0.10017
10,1
1.00500
1,0
0.09967
9,9
10.033
10,0
u tan gd u
«F0'
sec gd u
«FO'
sin gd u
« Fo'
esc gd u
a, Fo'
SMITHSONIAN TABLES
107
Natural Hyperbolic Functions.
u
sinh u
-F.'
cosh u
«F0'
tanh u
« Fo'
coth u
» Fo'
0 . 100
O.IOOI7
100,5
1.00500
10,0
0,00967
99,o
10.0333
996,7
.101
.10117
100,5
.00510
10,1
.10066
99,0
9.9346
977,0
.102
.10218
100,5
.00521
10,2
. 10165
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
O.I05I9
1 00,6
1.00552
10,5
o. 10462
98,9
9.5588
903,7
.106
.10620
100,6
.00562
1 0,6
.10560
98,9
.4093
886,7
.107
. 10720
1 00,6
.00573
10,7
. 10659
98,9
.3814
870,1
.108
.10821
100,6
.00584
10,8
. 10758
98,8
.2952
854,0
.109
.IO922
100,6
•00595
10,9
.10857
98,8
.2106
838,4
O.I 10
O.I 1022
100,6
1.00606
11,0
o. 10956
98,8
9-1275
823,1
.III
.11123
100,6
.00617
n, i
.11055
98,8
.0460
808,3
.112
.11223
100,6
.00628
11,2
•III53
98,8
8.9659
793,9
.113
. I 1324
100,6
.00639
11,3
.11252
98,7
.8872
779,8
.114
.11425
100,7
.00651
11,4
.11351
98,7
.8099
766,1
O.II5
O.II525
100,7
1.00662
H5
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
H,8
.11746
98,6
.5139
.119
. i 1928
100,7
.00709
11,9
.11844
98,6
•4430
702,8
O.I2O
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
0.125
0.12533
100,8
1.00782
12,5
0.12435
98,5
8.0416
636,7
.126
. 12633
ioo,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
100,8
.00820
12,8
.12731
98,4
.8551
607,0
.129
.12936
100,8
.00833
12,9
. 12829
98,4
• 7949
597,6
0.130
o. 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
5/o,6
.133
. 13339
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
0.13541
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
5U,3
0.140
0.14046
IOI,O
1.00982
14,0
0.13909
98,1
7.1895
506,9
.141
.14147
101,0
.00996
14,1
.14007
98,0
• 1391
459,7
.I4J
. 14248
IOI,O
.OIOIO
14,2
. 14105
98,0
.0895
492,6
.143
. 14349
IOI,O
.01024
14,3
. 14203
98,0
.0406
485,7
.144
.14450
IOI,O
.01039
14,4
.14301
98,0
6.9924
478,9
0.145
0.14551
101,1
I. 01053
14,6
0.14399
97,9
6.9448
472,3
.146
IOI,I
.01068
14,7
• T4497
97,9
.8979
465,8
.147
. 14753
IOI,I
.01082
14,8
• 14595
97,9
.8517
459,5
.148
IOI,I
.01097
T4,9
. 14693
97,8
.8060
453,2
101,1
.OIII2
15,0
.14791
97,8
.7610
447.1
0.150
0.15056
101,1
I. 01 127
15,1
0.14889
97,8
6.7166
44i,i
u
tin gd u
« Fo'
sec gd u
« Fo'
sin gd u
« Fo'
esc gd u
-Fo' .
IMITHSONIAN TABLES
108
Natural Hyperbolic Functions.
u
•inh u
»Fo'
cosh u
»Fo'
tanh u
«- F,/
coth u
Fo'
0.150
o. 15056
IOI,I
I. 01 127
I5,i
0.14889
97,8
6.7166
441,1
.151
.15157
IOI,I
.01142
15,2
.14985
97,8
435,3
.152
.15259
101,2
.01157
15,3
.15084
97,7
.6295
429,5
.153
.154
.15360
.15461
IOI.2
101,2
.01173
.01188
15,4
15,5
.15182
.15279
97,7
97,7
.5869
.5448
423,9
418,3
0.155
0.15562
IOI,2
I. OI2O4
15,6
0.15377
97,6
6.5032
412,9
.156
.15663
IOI,2
.01219
15,7
.15475
97,6
.4622
407,6
.157
.15765
IOI,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
373,1
.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.I7082
101,4
1.01448
i7,i
0.16838
97,2
5.9389
342,7
.171
.17183
ioi,5
.01466
17,2
.16935
97,i
.9048
338,7
.172
.17285
101,5
.01483
17,3
.17032
97,i
.8712
334,7
.173
.17386
101,5
.01500
17,4
.17129
97,i
.8379
330,8
.174
.17488
ioi,5
.01518
17,5
. 17226
97,0
.8050
327,0
0.175
0.17589
ioi,5
i. 01535
17,6
0.17324
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
5.6i54
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
.4960
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
.4008
282,7
.188
.18911
101,8
.01772
18,9
. 18582
96,5
.3817
279,6
.189
.19013
101,8
.01791
19,0
.18678
06,5
• 3339
276,6
0.190
O.I9II5
101,8
i. 01810
19,1
0.18775
96,5
5.3263
273-7
.191
.19216
101,8
.01830
19,2
.18871
96,4
.2091
270,8
.192
.19318
101,8
.01849
19,3
.18967
96,4
.2-722
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
o. 19624
101,9
1.01907
19,6
o. 19257
96,3
S.I930
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 i
• 199
.2OO32
102,0
.01987
20,0
.19641
96,i
.0913
249,2
O.2OO
O.2OI34
102,0
1.02007
20,1
o. 19738
96,1
5.0665
246,7
U
tan gd u
» Fo'
sec gd u
u Fo'
sin gd u
« Fo'
esc gd u
W FO'
SMITHSONIAN TABLES
109
Natural Hyperbolic Functions.
u
sinhu
«Fo'
cash u
«Fo'
tanh u
w FO'
coth u
• <0 FO'
O.20O
0.20134
102,0
1.02007
20,1
o. 19738
96,1
5-0665
246,7
.2OI
.20236
IO2,O
.02027
20,2
.19834
96,1
.0419
244,2
.202
.20338
IO2,O
.02047
20,3
.19930
06,0
.0176
241,8
.203
.20440
IO2,I
.02068
20,4
.2OO26
96,0
4.9936
239,4
.204
.20542
IO2,I
.02088
20,5
.20122
96,0
.9698
237,0
0.205
0.20644
102,1
1.02109
20,6
0.20218
95,9
4.9462
234,6
.206
.20746
IO2,I
.02129
20,7
.20313
95,9
.9228
232,3
.207
.20848
IO2,2
.02150
20,8
.20409
95,8
.8997
230,1
.208
.20950
IO2,2
.02171
21,0
.20505
95,8
.8768
227,8
.209
.21052
102,2
.02192
21,1
.2O60I
95,8
.8542
225,6
0.210
0.2II55
IO2,2
1.02213
21,2
O.2O097
95,7
4.8317
223,5
.211
.21257
IO2,2
.02234
21,3
.2O792
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
.2IO79
95,6
.7440
215,1
O.2I5
0.21666
102,3
1.02320
21,7
0.21175
95,5
4.7226
213,0
.216
.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
.02385
22,0
.21461
95,4
.6596
207,1
.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
20 1, 4
.222
.22383
102,5
.02474
22,4
.21842
95,2
.5783
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
0.225
0.22600
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
1 02,6
.02588
22,9
.22318
95,0
.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
0.230
0.23203
102,7
1.02657
23,2
0.22603
9d.O
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
1.77,8
.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
.02943
24,4
.23738
94,4
.2126
i67,5
.243
103,0
.02067
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
.24849
103,0
.03041
24,8
.24115
94,2
.1467
162,0
•24Z
,24953
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
0.24492
94,0
4.0830
156,7
u tin gd u
<•> P./ sec ad u
« Fo'
sin gd u
« Fo'
esc gd u
0> FO'
SMITHSONIAN TABLES
1 10
Natural Hyperbolic Functions.
u
•inh u
»Fo'
cosh u
-Fo'
tanh u
« Fo'
coth u
<- Fo'
0.250
0.25261
103,1
1.03141
25,3
0.24492
94,0
4.0830
156,7
.251
.25364
103,2
.03167
25,4
.34586
94,0
.0674
155,4 :
.252
.25468
IO3,2
.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
.0616
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
.0037
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
0.268II
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
93J
.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
131,9
• 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
.7M7
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
103,9
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
.29096
104,1
.04147
29,1
.27937
92,2
• 5795
118,1
.288
.29200
104,2
.04176
29,2
.28029
92,1
.5677
117,3 !
.289
.29304
104,2
.04205
29,3
.28121
92,1
.5560
116,5
0.200
0.29408
104,2
1.04235
29,4
0.28213
92,0
3.5444
H5,6
.291
.29512
104,3
.04264
29,5
.28305
92,0
.5329
114,8
.292
.29617
104,3
.04294
29,6
.28397
91,9
.5214
114,0
.293
.29721
104,3
.04323
29,7
.28489
91,9
.5101
113.-' [
.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
9i,8
3-;
in,6
.296
.30034
104,4
.04413
30,0
.28765
9L7
•47<>5
110,9 ;
.297
.30139
104,4
.04443
30,1
.28856
9i,7
.4654
110,1
.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 j
! 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
« Fo'
esc gd u
« Fo'
SMITHSONIAN TABLES
III
Natural Hyperbolic Functions.
u
sinh u
-Fo'
cosh u
«Fo'
tanh u
<*> FO'
coth u
- Fo'
0.300
0.30452
104,5
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
.29314
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
.31185
104,7
.04750
31,2
.29771
91,1
• 3590
102,8
.308
.31289
104,8
.04/81
3i,3
.29862
91,1
.3488
IO2,I
.309
.31394
104,8
.04812
3i,4
.29953
91,0
.3386
101,5
0.310
0.31499
104,8
1.04844
3i,S
0.30044
91,0
• 3.3285
100,8
.311
.31604
104,9
.04875
3i,6
.30135
90,9
• 3184
100,1
.312
.31709
104,9
.04907
3i,7
.30226
90,9
.3085
99,5
.313
.31814
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
1.05002
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
.05099
32,3
.30770
90,5
.2499
95,6
.319
.32444
105,1
.05131
32,4
.30860
90,5
.2404
95,0
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
.2029
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
.05596
33,9
.32121
89,7
.1132
86,9
•334
.34024
105,6
.05630
34,o
.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
.32390
89,5
.0874
85,3
• 337
.34342
105,7
•05732
34,3
.32480
89,5
.0789
84,8
.338
•339
•34447
•34553
105,8
105,8
.05767
.05801
34,4
34,6
.32569
.32658
89,4
89,3
.0704
.0620
84,3
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
35,1
•33104
89,0
.0207
81,2
0.345
0.35188
106,0
1.06011
35,2
0.33193
89,0
3.0126
80,8
.35295
106,0
.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
.334OO
88,8
.9886
79,3
• 349
106,2
.06152
35,6
•33549
88,7
.9807
78,8
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'
IITHCONIAN TABLES
112
Natural Hyperbolic Functions.
u
sinh u
»F0'
cosh u
«-Fo'
tanh u
w F,/
coth u
* Fo'
0.350
0.35719
106,2
I. 06188
35,7
0.33638
88,7
2.9729
7a4
.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
.0496
77,0
• 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,i
.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
37,0
.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
7i,8
.366
.37423
106,8
.06773
37,4
.35049
87,7
.8532
7L4
.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
.06961
38,0
.35487
87,4
.8180
60,4
• 372
.38064
107,0
.06999
38,1
•35574
87,3
.8110
• 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
.38/07
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
38,9
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
39J
.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
39i5
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
.39781
107,6
.07622
39,8
.36963
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
•37394
86,0
.6742
61,5
• 394
.40427
107,9
.07863
40,4
.37480
86,0
.6681
61,2
0.395
0.40535
107,9
1.07003
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
.07084
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
»F0'
sec gd u
« Fo'
sin gd u
» Fo'
esc gd u
« Fo'
SMITHSONIAN TABLES.
"3
Natural Hyperbolic Functions.
0
sinh u
«F0'
cosh u
• Fo'
tanh u
« Fo'
coth u
« Fo'
0.400
.401
.402
.403
0.41075
.41183
.41292
.41400
108,1
108,1
108,2
108,2
I.o8l07
.08148
.08190
.08231
4LI
41,2
41,3
41,4
0.37995
.38080
.38166
.38251
85,6
85,5
85,4
85,4
2.6319
.6260
.6201
•6i43
59,3
59,o
58,7
58,3
.404
.41508
108,3
.08272
4L5
.38337
85,3
.6085
58,o
0.405
.406
0.41616
.41725
108,3
108,4
1.08314
.08356
41,6
41,7
0.38422
.38507
85,2
85,2
2.6027
.5969
57,7
57,4
.407
.408
.409
.41833
.41941
.42050
108,4
108,4
108,5
.08397
.08439
.08481
41,8
4i,9
42,0
.38592
.38677
.38762
85,1
85,0
85,0
.5912
.5855
.5798
57,1
56,8
56,6
0.410
.411
0.42158
.42267
108,5
108,6
1.08523
.08566
42,2
42,3
0.38847
.38932
84,9
84,8
2.5742
.5686
56,3
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
"•t ..;
.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,o
.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
.00037
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
.40699
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,i
.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
110,0
.09974
45,8
•41613
82,7
.4031
47,7
-444
.45873
1 10,0
.10020
45,9
.41695
82,6
.3983
47,5
0.445
.446
0.45983
.46093
110,1
110,1
i. 10066
.10112
46,0
46,1
0.41778
.41861
82,5
82,5
2:3J36
47,3
47,i
•447
.46204
110,2
.10158
46,2
.41943
82,4
'3842
46,8
.448
.463x4
IIO,2
.IO2O4
46,3
.42025
82,3
• 3795
46,6
• 449
.46424
no,3
.10251
46,4
.42108
82,3
•3749
46,4
| 0.450
110,3
1 . 10297
46,5
0.42190
82,2
2.3702
46,2
1
tan gd u
«F0'
sec gd u
« Fo'
sin gd u
«- Fo'
esc gd u
« F0'
SMITHSONIAN TABLES
114
Natural Hyperbolic Functions.
I
sinh u
»Fo'
cosh u
»Fo*
tanh u
« Fo'
coth u
- Fo'
0.450
0.46534
110,3
I . 10297
46,5
0.42190
82,2
2.3702
46,2
.451
.46645
no,3
.10344
46,6
.42273
82,1
.3656
46,0
.452
.46755
110,4
.10390
46,8
•42354
82,1
.3610
45,7
• 453
.46865
110,4
. 10437
46,9
.42436
82,0
.3565
45,5
• 454
.40970
110,5
.10484
47,0
.42518
81,9
.3519
45,3
0.455
0.47086
110,5
1.10531
47,1
0.42600
81,9
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
81,7
.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
81,5
2.3251
44,1
.461
•47750
110,8
.10816
47,8
.43090
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
81,3
.3120
43,5
.464
.48083
III,O
.10959
48,1
•43334
81,2
.3077
43,3
0.465
0.48194
111,0
i . i 1007
48,2
0.43415
81,2
2.3033
43,1
.466
.48305
in, i
.11056
48,3
.43496
81,1
.2091
42,9
.467
.48410
in, i
.11104
48,4
.43577
81,0
.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
0.4/0
0.48750
111,2
I.II250
48,7
0.43820
80,8
2.2821
42,1
.4/1
.48861
in,3
.11299
48,9
•43901
80,7
• 2779
41,9
.472
.48972
in,3
.11348
49,0
.43981
80,7
.2737
4L7
• 473
.490S4
111,4
.11397
49,i
.44062
80,6
.2695
41,5
•474
•49195
111,4
.11446
49,2
.44M3
80,5
.2654
41,3
0.475
0.49306
ill,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
.49641
111,6
.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
111,7
I- i 1743
49,9
0.44624
80, i
2.2409
40,2
.481
.4997:)
111,8
.11793
50,0
•44704
80,0
.2369
40,0
.482
.50088
111,8
.11843
50,i
.44784
79,9
.2329
39,9
.483
. 50200
111,9
.11893
50,2
•44864
79,9
.2289
39,7
.484
.50312
111,9
•II943
50,3
.44944
79,8
.2250
39,5
0.485
0.50424
1 1 2,0
I.II994
50,4
0.45024
79,7
2.22IO
39,3
.486
.50536
112,0
.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
0.50984
112,2
1.12247
5i,o
0.45422
79,4
2.2016
38,5
• 491
•51097
112,3
.12298
5i,i
•45501
79,3
.1978
38,3
.49-'
.51209
112,3
. 12349
5i,2
.45580
79,2
.1939
38,1
.493
•5I32I
112,4
. 12401
51.3
.45659
79,2
.1001
38,0
•494
•5M34
112,5
. 12452
51,4
•45739
79,1
.1863
37,8
0.495
0.51546
112,5
1.12503
51,5
0.45818
79,0
2.1826
37,6
.496
.51659
112,6
.12555
51,7
.45897
78,9
.1788
37,5
• 497
.51771
112,6
. i 2607
5i,8
•45975
78,9
.1751
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
0.52IIO
112,8
i . 12763
52,i
0.46212
78,6
2.1640
36,8
tan gd u
a. Fo'
sec gd u
« Fo'
sin gd u
»w
esc gd u
« Fo'
SMITHSONIAN TABLES
Natural Hyperbolic Functions.
u
sinh u
.W
cosh u
»Fo*
tanh u
w 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
.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
113,0
I . 13025
52,7
0.46604
78,3
2.1457
36,0
.506
.52787
113,1
. 13077
52,8
.46682
78,2
.1421
35,9
.507
.52000
113,1
.13130
52,9
.46760
78,1
.1386
35,7
.508
.53013
113,2
.13183
53,o
.46839
78,i
.1350
35,6
•509
.53127
113,2
.13236
53,i
.46917
78,o
.1314
35,4
0.510
0.53240
113,3
I . 13289
53,2
0.46995
77,9
2.1279
35,3
.511
•53353
ii3,3
. 13343
53,4
.47072
77,9
.1244
35,1
.512
.53466
H3,4
•13396
53,5
.47150
77,8
.1209
35,o I
.513
.53580
H3,4
.13450
53,6
.47228
77,7
.1174
34,8!
.514
.53093
H3,5
.13503
53,7
.47306
77,6
•II39
34,7
0.515
0.53807
113,6
I. 13557
53,8
0.47383
77,5
2.IIO5
34,5
.516
.53920
n 3,6
.13611
53,9
.47461
77,5
.1070
34,4
.517
•54034
H3,7
.13665
54,0
.47538
77,4
.1036
34,3
.518
.54148
.13719
54,1
.47615
77,3
.1002
34,1
.519
.54262
113,8
. 13773
54,3
•47693
77,3
.0968
34,0
0.520
0.54375
113,8
1.13827
54,4
0.47770
77,2
2.0934
33,8
.521
.54489
H3,9
.13882
54,5
.47847
77,1
.0900
337
.522
.54603
. 13936
54,6
.47924
77,o
.0866
33,5
.523
.54717
1 14,0
.13991
54,7
.48001
77,o
.0833
33,4
.524
.54831
114,0
. 14046
54,8
.48078
76,9
.0799
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
"4,4
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
H4,7
I . 14656
56,1
0.48919
76,i
2.0442
3i,8
.536
.56204
ii4,7
.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
• 539
.56548
114,9
.14881
56,5
.49223
75,8
.0316
3i,3
0.540
0.56663
114,9
I.I4938
56,7
0.49299
75,7
2.0284
3i,i
.541
• 56778
115,0
.14994
56,8
•49374
75,6
• 0253
31.0
.542
.56893
115,1
.15051
56,9
•49450
75,5
.0222
30,9
• 543
.57008
115,1
.15108
57,o
.49526
75,5
.OI92
30,8
• 544
.57123
"5,2
.15165
57,1
.49601
75,4
.Ol6l
30,6
0.545
0.57238
"5,2
I.I5223
57,2
0.49676
75,3
2.0130
30,5
•57354
1 1 5,3
.15280
57,4
•49752
75,2
.OIOO
30,4
.547
•57469
115,3
•15337
57,5
.49827
75,2
.O07O
30,3
.548
.57584
H5,4
.15395
57,6
.49902
75,i
.0039
30,2
• 549
•57700
"5,5
.15452
57,7
•49977
75,0
.0009
30,0
0.550
0.57815
"5,5
I.I55IO
57,8
0.50052
74,9
1.9979
29,9
u
tan gd u
- Fo'
sec gd u
« Fo'
sin gd u
« Fo'
esc gd u
« Fo'
SMITHSONIAN TABLCS
116
Natural Hyperbolic Functions.
u
sinh u
«F0'
cosh u
»FO'
tanh u
« F/
coth u
-Fo'
0.550
0.57815
H5,5
I.I55IO
57,8
0.50052
74,9
1.9979
29,9
.551
.57931
H5,6
.15568
57,9
.50127
74,9
.9949
29,8
.552
.58046
H5,6
.15626
58,o
. 50202
74,8
.0920
20,7
• 553
.58162
H5,7
.15684
58,2
•50277
74,7
.9890
29,6
• 554
.58278
115,7
.15742
58,3
.50351
746
.9860
29,4
0.555
0.58393
115,8
1.15801
58,4
0.50426
74,6
1.9831
2Q.3
.556
.58509
H5,9
.15859
58,5
.50500
74,5
.9802
29,2
• 557
.58625
n5,9
.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
.10035
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
.16212
59,2
.50946
74,o
.9629
2*,5
.563
.59322
116,3
. 16272
59,3
.51020
74,0
.9600
28,4
.564
.59438
116,3
.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
•50904
116,6
. 16570
59,9
.51389
73,6
.9459
27,9
.569
.60020
116,6
.16630
60,0
.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
73J
1.9267
27,1
.576
.60838
117,1
.17053
60,8
.51975
73,o
.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
1.17297
61,3
0.52267
72,7
I.9I33
26,6
.581
.61424
H7,4
.1/358
61,4
.52339
72,6
.9106
26,5
.582
.61542
H7,4
. 17420
• 61,5
.52412
72,5
.9080
26,4
083
.61659
"7.5
.17481
61,7
02484
72,5
.9053
26,3
.584
.61777
ii7,5
. 17543
61,8
.52557
72,4
.9027
25,2
0.585
0.61894
117,6
1.17605
6i,9
0.52629
72,3
1.9001
26,1
.586
.62012
H7,7
.17667
62,0
.52701
72,2
.8975
26,0
.587
.62130
H7,7
. 17729
62,1
•52773
72,2
.8949
25,9
.588
.62247
117,8
. I779I
62,2
.52846
72,1
.8923
2>8
.589
.62305
H7,9
.17853
62,4
.52918
72,0
.8897
-'5-7
0.590
0.62483
H7,9
1.17916
62,5
0.52900
71,9
1.8872
25,6
• 591
.62001
118,0
.17978
62,6
.53051
7i,8
.8846
• 592
.62719
118,0
.18041
62,7
.53133
7i,8
.8821
25.4 i
.593
.62837
118,1
. 18104
62,8
.53205
7i,7
.8795
-'5.3 ,
• 594
.62955
118,2
.18167
63,0
.532/7
7i,6
.87/0
0.595
0.63073
1 1 8,2
i . 18230
63,1
0.53348
7i,5
1.8745
25J :
.596
.63192
118,3
.18293
63,2
•53420
7i,5
.8720
25,0
• 597
.63310
118,4
. i«356
63,3
.53491
7i,4
• 8695
24,9
.598
.63428
118,4
.18419
63,4
.53562
7i,3
.8670
-'4,9
• 599
.63547
118,5
.18483
63,5
.53634
71,2
.8645
24.8
0.600
0.63665
n8,5
I.I8547
63,7
0.53705
71,2
1.8620
24,7
u
tan gd u
w Fo'
sec gd u
«F0'
sin gd u
« Fo'
esc gd u
u, Fo'
SMITHSONIAN TABLES
117
Natural Hyperbolic Functions.
u
sinh u
a>Fo'
cosh u
"Fo'
tanh u
«- Fo'
coth u
« Fo'
0.600
0.63665
"8,5
I . 18547
63,7
0.53705
71,2
1.8620
24,7
.601
.63784
118,6
.18610
63,8
.53776
71,1
.8596
24,6
.002
.63903
"8,7
.18674
63,9
.53847
71,0
.8571
24,5
.003
.64021
"8,7
.18738
64,0
.53918
70,9
.8547
24,4
.604
.64140
118,8
.18802
64,1
.53989
70,9
.8522
243
0.005
0.64259
118,9
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
64,5
•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
119,2
1.19189
649
0.54413
70,4
1.8378
23,8
.611
.64973
"9,3
. 19254
65,0
.54483
70,3
.8354
23,7
.612
.65093
<*t ^r\J
"9,3
.19319
65,1
.54553
70,2
.8331
23,6
.613
.65212
"9,4
• 19384
65,2
•54624
70,2
.8307
23,5
.614
.65331
"9,4
.19449
65,3
.54694
70,i
.8284
23,4
0.615
0.65451
"9,5
I.I95I5
65,5
0.54764
70,o
1.8260
23,3
.616
.65570
"9,6
.19580
65,6
.54834
69,9
.8237
23,3
.617
.65690
"9,6
.19646
65,7
.54004
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
I . 19844
66,0
o.55"3
69,6
I.8I45
22,9
.621
.66169
"9,9
.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
120,1
.20109
66,5
.55391
69,3
.8054
22,6
0.625
0.66649
120,2
I.20I75
66,6
0.55460
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
.67OIO
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
1.7919
22,1
.631
.67371
120,6
.20577
67,4
.55874
68,8
.7897
22,O
.632
.67492
120,6
.20645
67,5
•55943
68,7
.7875
22,O
.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
o . 56149
68,5
I . 7810
21,7
.636
.67975
120,9
.20916
68,0
.56217
68,4
.7788
21,6
.637
.68096
I2I,O
.20984
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
.68581
121,3
.21257
68,6
.50558
68,0
.7681
21,3 !
.642
121,3
.21326
68,7
.56626
67,9
.7660
2\,2
.68823
121,4
•21395
68,8
.56694
67,9
.7639
21,1
,6fe45
121,5
.21463
68,9
.56762
67,8
.7618
21,0
0.69066
121,5
I.2I532
69,1
0.56829
67,7
1.7597
21,0
!_'!,'»
.2IOO2
<><j,-'
.56897
67,6
.7576
20,9
.649
.69431
121,7
121,7
121,8
.21671
.21740
.2l8lO
69,3
69,4
69,6
.56965
.57032
.57100
67,6
67,5
67,4
.7555
• 7534
.7513
20,8
20,7
20,7
0.650
0.69675
121,9
I.2I879
69,7
0.57167
67,3
1-7493
20,6
u
tan ad u
« Fu'
sec gd u
<- Fo'
sin od u
u> Fo'
esc gd u
« Fo'
SMITHSONIAN TABLES
118
Natural Hyperbolic Functions.
u
sinh u
• Fo'
cosh u
«F,/
tanh u
«- F0'
coth u
• H
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
70,0
.57369
67,1
• 7431
20,4 '
.654
.70163
122,2
.22159
70,2
.57436
67,0
.7411
20,3
0.655
0.70285
122,2
I . 22229
70,3
0.57503
66,9
I-739I
20,2
.656
.70407
122,3
.22300
70,4
.57570
66,9
.7370
20,2
.657
.70530
122,4
.22370
70,5
.57636
66,8
.7350
20,1
.658
.70652
122,4
.22441
70,7
•57703
66,7
•7330
2O,O
.659
•70775
122,5
.22511
70,8
•57770
66,6
•7310
20,0
0.660
0.70897
122,6
1.22582
70,9
0.57836
66,5
1.7290
19,9
.661
.71020
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
7i,3
.58036
66,3
.7231
19,7
.664
.71388
122,9
.22867
7i,4
.58102
66,2
.7211
19,6
0.665
0.7I5H
122,9
1.22938
7i,5
0.58168
66,2
1.7192
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
i9,i !
.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
.72991
123,8
.23805
73,0
.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
.594H
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,i
•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
.7448-'
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
i7,9
.692
•74857
124,9
.24914
74,9
.59927
64,1
.6687
17,8
• 693
.74982
125,0
.24989
75,0
•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
.60240
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
«F0'
sec gd u
« Fo'
sin gd u
« Fo'
esc gd u
« Fo'
SMITHSONIAN TABLES
119
Natural Hyperbolic Functions.
u
sinh u
<-Fo'
cosh u
«F0'
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,i
.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
I7,i
0.705
0.76487
125,9
1.25898
76,5
0.60753
63,1
1.6460
I7,i
.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
.76855
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,i
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
.6325
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,o
.61505
62,2
.6259
16,4
.718
.78130
126,9
.26903
78,1
.61567
62,1
.6242
16,4
.719
.78257
127,0
.26981
78,3
.61629-
62,0
.6226
16,3
0.720
0.78384
127,1
1.27059
78,4
0.61691
61,9
I.62IO
16,3
.721
.78511
127,1
.27138
78,5
.6x753
61,9
.6194
16,2
.722
.78338
127,2
.27216
78,6
.61815
61,8
.6177
16,2
.723
.78766
127,3
.27295
78,8
.61876
6i,7
.6161
16,1
.724
.78893
127,4
.27374
78,9
.61938
61,6
.6145
16,1
0.725
0.79020
127,5
1.27453
I9,o
O.62OOO
61,6
1.6129
16,0
.726
.79M8
127,5
.27532
79,1
.62061
6i,5
.6113
1 6,0
.727
.792/5
127,6
.27611
79,3
.62123
61,4
.0097
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
.5987
15,6
0.735
0.80209
128,2
I . 28249
80,3
0.62611
60,8
I • 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
.81199
128,8
.28815
81,2
.63035
60,3
.5864
15,2
•743
.81327
128,9
.28896
81,3
•63095
60,2
.5849
I5,i
•744
129,0
.28977
81,5
.63156
60, i
.5834
I5,i
0.745
0.81585
129,1
1.29059
81,6
0.63216
60,0
1.5819
I5,o
.81714
!-">,!
.29140
8i,7
.63276
60,0
• 5804
I5,o
• 747
.81844
129,2
.29222
81,8
.63336
59,9
.5789
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
tin get u
« Fo'
sec fld u
«-Fo'
sin gd u
«- Fo'
esc gd u
w Fo'
SMITHSONIAN TABLES
120
Natural Hyperbolic Functions.
u
sinh u
*>Fo'
cosh u
u>Fo'
tanh u
-Fo'
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
M,7 i
.752
.82491
129,6
.29633
82,5
.63634
59,5
• 5/15
14,7
• 753
.82620
129,7
.29716
82,6
.63' n\
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
.2<-
83,0
.63871
59,2
0656
U,5
• 757
.83140
130,0
.30047
83,1
•63931
59,1
.5642
M,5
• 758
.83270
130,1
.30130
83,3
.63990
59,1
.5628
1 4,4
• 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
0084
14,3
.762
.83791
130,5
.30464
83,8
.64225
58,8
• 5570
M,-J
.763
.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
I.3O7I6
84,2
0.64401
58,5
1.5528
14,1
.766
.84314
130,8
.3080I
84,3
.64460
58,4
.5514
14,1
.767
.84445
130,9
.30885
84,4
.64518
58,4
.5500
M,0 ,
.768
.84576
131,0
.30970
84,6
.64576
58,3
.5486
14,0
.769
.84707
I3U
.31054
84,7
.64635
58,2
• 5472
13,9
0.770
0.84838
I3IJ
I.3H39
848
0.64693
58,1
1.5458
13,9
.771
.84969
131,2
.31224
85,0
.64751
58,1
• 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
131,7
.31650
85,6
.65040
57,7
.5375
13,6
• 777
.85758
131,7
.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
I.3I994
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,i
.5267
13,3
0.785
0.86814
132,4
1.32426
85,8
0.65557
57,0
1.5254
13,3
.786
.86947
K32,5
.32513
86,9
.65614
56,9
.5241
13,2
-787
.87079
132,6
.32600
87,1
.65671
56,9
.5228
13,2
.788
.87212
132,7
.32687
87,2
.65727
56,8
.5214
13,1
.789
•87345
132,8
.32775
87,3
.65784
56,7
.5201
13,1
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
133,0
.33037
87,7
.65954
56,5
.5162
13,0
• 793
.87877
133,1
.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
56,1
.5098
12,8
.798
.88543
133,6
.33566
88,5
.66292
56,1
.5085
12,8
• 799
.88677
133,7
.33655
88,7
.66348
56,0
.5072
12,7
0.800
0.888II
133,7
1.33743
88,8
0.66404
55,9
1.5059
12,7
u
tan gd u
« Fo'
sec gd u
u> Fo'
sin gd u
« Fo'
esc gd u
« Fo'
SMITHSONIAN TABLES
121
Natural Hyperbolic Functions.
u
sinh u
«F0'
cosh u
-Fo'
tanh u
" 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
.89078
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
.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
.66849
55,3
•4959
12,4
.809
.90018
134,5
.34548
90,0
.66904
55,2
•4947
12,3
0.810
0.90152
134,6
1.34638
90,2
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
.8!4
.90692
135,0
•35000
90,7
.67179
54,9
.4886
12,2
0.815
0.90827
I35,i
I.3509I
90,8
0.67234
54,8
1.4873
12,1
.816
.90962
135,2
.35182
91,0
.67289
54,7
.4861
12,1
.817
.91097
135,3
.35273
91,1
.67343
54,6
.4849
12,0
.818
.91232
135,4
.35364
91,2
.67398
546
.4837
12,0
.819
.91368
135,5
•35455
9i,4
.67453
54,5
.4825
I2,O
0.820
0.91503
135,5
1-35547
9i,5
0.67507
544
1.4813
H,9
.821
.91639
135,6
.35638
91,6
.67561
544
.4801
11,9
.822
.91775
135,7
.35730
9i,8
.67616
543
.4789
11,9
.823
.91910
135,8
.35822
9i,9
.67670
542
.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
n,7
.828
.92591
136,3
.36283
92,6
.67940
53,8
.4719
.829
.92727
136,4
.36376
92,7
•67994
53,8
• 4707
11,6
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
93,1
.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
53,4
.4649
o.«35
0-93547
136,9
1.36934
93,5
0.68315
53,3
1.4638
11,4
.836
.93684
i37,o
.37028
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
94,0
-68475
53,i
.4604
n,3
.839
.94095
137,3
•37310
941
.68528
53,0
• 4593
n,3
0.840
0.04233
137,4
1.37404
94,2
0.68581
53,0
1.4581
n,3
.841
.94370
137,5
.37498
94,4
.68634
52,9
.4570
11,2
.842
.94508
137,6
•37593
94,5
.68687
52,8
• 4559
11,2
.843
.94045
137,7
•37687
94,6
.68739
52,7
.4548
11,2
.844
•947«3
137,8
•37/8-'
94,8
.68792
52,7
•4537
II, I
0.845
0.94921
137,9
1.37877
94,9
0.68845
52,6
1.4525
11,1
.846
.95059
138,0
.37972
95,1
.68897
52,5
•45U
II, I
.95W
.38067
95,2
.68950
52,5
.4503
II,O
.848
138,2
.38162
95,3
.69002
52,4
.4492
II O
•95473
138,3
.38258
95,5
.69055
52,3
.4481
iiio
0.850
0.95612
138,4
1.38353
95,6
0.69107
52,2
1.4470
10,9
u
tin gd u
-Fo'
sec gd u
-Fo'
sin gd u
- Fo'
esc gd u
« Fo'
ITHSONIAN TABLE*
122
Natural Hyperbolic Functions.
u
sinh u
«F,/
cosh u
• ft"
tanh u
a>Fu'
coth u
»F0'
0.850
0.950IJ
138,4
1.38353
95,6
0.69107
52,2
1.4470
10,9
.851
•95750
l.vNI
95,7
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
g -._'
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
<A4
.69419
5i,8
.4405
10,8
.857
139,0
.39026
96,6
5i,7
• 4395
10,7
.858
.96721
I39J
.39122
96,7
.09523
51,7
.4384
10,7
.859
.9(3861
139,2
.39219
9' >,9
•69574
5i,6
•4373
10,7
0.860
0.97000
139,3
I.393I6
97,o
0.69626
5i,5
1.4362
10,6
.85i
•97139
139,4
.39413
97J
.69677
5i,5
.4352
10,6
.862
•97279
139,5
•39510
97,3
.69729
5i,4
•4341
10,6
.863
.97418
139,6
.30608
97,4
.69780
5i,3
.4331
10,5
.864
.97558
139,7
•39705
97,6
.69831
51,2
.4320
10,5
0.865
0.97698
139,8
1.39803
97,7
0.69882
51,2
I.43IO
10,5
.856
.97838
139,9
.39901
97,8
•69934
5i,i
.4299
10,4 i
.867
.97978
140,0
•39999
98,0
.69985
5i,o
.4289
10,4
.868
.98ll8
140,1
.4O097
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./OI37
50,8
1.4258
10,3
.871
.98538
140,4
.40392
9^,5
.70188
50,7
•4-M7
10,3
.872
.98679
140,5
.40490
98,7
.70239
50,7
•4-'37
10,3
.873
.98819
140,6
98,8
.70290
50,6
.4227
10,2
.874
.98960
140,7
.40688
99,0
.70340
50,5
.4217
10,2
0.875
0.99101
140,8
1.40787
99,i
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
.417')
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
5o,i
I.4I56
IO,O
.881
•99947
Ui,4
.41384
99,9
.70692
50,0
.4140
1 0,0
.882
1.00089
i4i,5
.41484
100,1
.70742
50,0
.4136
1 0,0
.883
.00230
141,6
.41584
100,2
.70792
49,9
.4120
IO,O
.884
.00372
Ui,7
.41684
100,4
.70842
49,8
.4110
9,9
0.885
1.00514
141,8
I.4I785
100,5
0.70892
49,7
1.4106
9,9
.885
.00655
141,9
.41886
100,7
.70941
49,7
.4096
9,9
.887
.00797
142,0
.41086
100,8
.70991
49,6
.4086
.888
.00939
142,1
.42087
100,9
.71040
49,5
.4076
9,8
.889
.01081
142,2
.42188
101,1
.71000
49,5
.4067
9,8
0.890
1.01224
142,3
1.42289
IOI,2
0.7H39
49,4
1.4057
9,8
.s,.
.01366
142,4
.42391
101,4
.71189
49,3
.4047
9,7
.01508
142,5
.42492
JtOI,5
.71238
49,3
.4037
9,7 '
.893
.01651
T4-',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
•7M34
49,0
• 3999
9,6
.897
.O2222
M3,o
.43001
102,2
.7M83
48,9
.3089
9,6
.898
.02363
I43,i
.43104
T02.4
.71532
48,8
.3980
9,5
.899
.02508
143,2
.43206
102,5
.71581
48,8
•3970
9,<5
0.900
1.02652
M3,3
1.43309
102,7
0.71630
48,7
l.396i
9,5
u
tan gd u
«F0'
sec gd u
CO F '
s'n ad u
«F0'
esc gd u
<- F,'
SMITHSONIAN TABLES
123
Natural Hyperbolic Functions.
u
sinh u
»Fo'
cosh u
»Fo'
tanh u
w FO'
coth u
<oFo'
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
.435U
103
.71727
48,6
• 3942
9,4
.903
.03082
144
.43617
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
.04608
145
.44700
105
.72305
47,7
.3830
9,1
0.915
1.04813
145
1.44865
105
0.72352
47,7
I.382I
9,1
.916
.04958
145
.44569
105
.72400
47,6
• 3812
9J
.917
.05103
145
.45075
105
.72448
47,5
• 3803
9,1
.918
.05248
145
.45180
105
.72495
47,4
• 3794
9,o
.919
.05393
145
.45285
105
•72542
47,4
.3785
9,0
0.920
1.05539
145
1-45390
106
0.72500
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,o
I-373I
8,9
.926
.06413
146
.46026
106
.72872
46,9
• 3723
8,8
.927
.06559
146
.46133
107
.72919
46,8
• 3714
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
T.0773I
147
1.46900
108
0.73292
46,3
1.3644
8,6
.936
.07878
M7
.47098
108
•73338
46,2
.3636
8,6
•937
.08026
M7
.47206
108
.73384
46,1
.3627
8,6
.938
.08173
M7
.47314
108
•73430
46,1
.3618
8,5
•939
.08320
M7
.47422
108
•734/6
46,0
.3610
8,5
0.040
1.08468
148
1-47530
icS
0.73522
45,9
1.3601
8,5
.08615
148
.47639
109
.73568
45,9
• 3593
8,5
.042
.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
148
.48184
109
•73797
45,5
• 3551
8,4
•947
148
• l*-"J3
TTO
•73842
45,5
• 3542
8,3
.948
148
.48403
no
•73888
454
• 3534
8,3
.09800
149
.48513
no
•73933
45,3
.3526
8,3
0.950
1.09948
149
1.48623
no
0.73978
45,3
I.35I7
8,3
u
tin od u
«F0'
sec gd u
«FO'
sin od u
»Fo'
esc gd u
a, F/
SMITHSONIAN TABLES
124
Natural Hyperbolic Functions.
u
sinh u
.*/
cosh u
.IV
tanhu
«Fo'
cothu
-FO'
0.950
1.09948
149
1.48623
no
0.73978
45,3
I.35I7
8,3
.951
.10097
149
.48733
IIO
.74024
45,2
• 3509
8,2
.952
. 10246
149
.48843
no
.74069
45,1
• 3501
8,2
.953
•10395
149
.48953
IIO
.74114
45,1
•3493
8,2
.954
.10544
149
.49064
in
•74159
45,o
• 3485
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
.3460
8,1
.958
. i i 141
150
.49507
in
.74338
44,7
• 3452
8,1
• 959
.11291
150
.49618
in
.74383
44,7
• 3444
8,1
0.960
i . 1 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
1.50289
112
0.74650
44,3
1.3396
7,9
.966
.12341
ISO
.50401
112
•74694
44,2
.3388
7,9
.967
.12491
.50513
112
.74738
44,1
.3380
7,9
.968
. 12642
151
.50626
H3
.74702
44,1
•3372
7,9
.969
. 12792
151
.50739
.74826
44,0
.3364
7,9
0.970
I . 12943
151
1.50851
113
0.74870
43,9
1.3356
7,8
.971
.13094
151
.50064
113
.74914
43,9
•3349
7,8'
.972
.13245
151
.51078
113
.74958
43,8
•3341
7,8;
.973
.13396
151
.51191
113
•75002
43,7
• 3333
7,8
• 974
• 13547
151
.51304
H4
.75046
43,7
• 3325
7,8
0.975
1.13699
151
I.5I4I8
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
. M305
152
•51874
114
.75263
43,4
.3287
7,7
0.980
i . 14457
152
1.51088
144
0.75307
43,3
1.3279
7,6
.981
.14609
152
.52103
US
•75350
43,2
.3271
7,6
.982
.14761
152
.52218
115
•75393
43,2
.3264
7,6
.983
• I49H
152
.52332
US
.75436
43,1
•3256
7,6
• 984
.15066
152
.52447
H5
•75479
43,0
.3249
7,6
0.985
1.15219
153
1.52563
H5
0.75522
43,0
I.324I
7,5
.986
.15371
153
.52678
US
42,9
.3234
7,5
.987
.15524
153
.52793
116
.75608
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
0.990
1.15983
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
4*3
I.3I67
7,3
.996
.16004
154
.53839
117
.75991
.3159
7,3
• 997
.17058
154
.53956
117
.76033
4-?.J
7,3
.998
•999
.17212
.17366
154
154
.54073
.54191
117
117
.76075
.76117
4-M
42,1
.3MS
.3138
7,3
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
«F0'
sin gd u
«- F '
esc gd u *> FO'
SMITHSONIAN TABLES
125
Natural Hyperbolic Functions.
u
sinh u
*Fo'
cosh u
.IV
tanh u
«FO'
coth u
..V
I.OOO I.I752O
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
.3116
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
I . 18293
155
1.54898
118
0.76369
41,7
1.3094
7,1
.006
.18448
155
.55016
118
.76410
41,6
.3087
7,i
.007
.18603
155
.55134
119
.76452
41,6
.3080
7,1
.008
.18758
155
.55253
119
.76493
41,5
.3073
.009
.18914
155
•55372
119
.76535
41,4
.3066
7,i
I.OIO
I.I9009
155
I.5549I
119
0.76576
41,4
1.3059
7,1
.Oil
. 19225
156
.556io
119
.76618
41,3
.3052
7^o
.012
.19380
156
.55729
119
.76659
41,2
.3045
7,o
.013
• 19536
156
120
.76700
41,2
.3038
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
.2O004
156
.56208
120
.76823
41,0
.3017
6,9
.017
.20l6o
156
.56328
120
.76864
40,9
.3OIO
6,9
.018
.20317
156
.56449
120
.76005
40,9
.3003
6,9
.019
.20473
157
.56569
120
.76946
40,8
.2996
6,9
I.O20
1.20630
157
1.56689
121
0.76987
40,7
1.2989
6,9
.021
.20787
157
.56810
121
. 77027
40,7
.2982
6,9
.022
.20944
157
^56931
121
.77068
40,6
.2976
6,8!
.023
.2IIOI
157
.57052
121
.77109
40,5
.2069
6,8
.024
.21258
157
.57173
121
.77149
40,5
.2962
6,8
1.025
.O26
I.2I4I5
.21572
157
157
1.57295
.57416
121
122
0.77190
.77230
40,4
40,4
1-2955
.2948
6,8 !
6,8 |
.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
1.22203
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
.775H
39,9
.2901
6,6
.034
.22836
158
.58394
123
•77551
39,9
.2895
6,6
1.035
1.22994
159
I.585I7
123
0.77591
39,8
1.2888
6,6
.036
.23153
159
.58640
123
.77630
39,7
.2882
6,6
.037
.23311
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
159
.59257
124
.77828
39,4
.2849
6,5
.042
•043
.24107
.24266
159
160
.59381
.59506
124
124
.77858
• 77W
39,4
39,3
.2842
.2836
.044
.24426
160
• 5030
124
.77946
39,2
.2829
6J
1.24585
160
1-59755
125
0.77985
39,2
1.2823
6,4
160
.59879
125
.78025
39,1
.2816
6,4
.047
.048
.25065
160
.60004
.60129
125
125
.78064
.78103
39,1
39,0
.2810
.2804
6,4
6,4
.25225
160
.60254
125
.78142
38,9
.2797
6,4
1.050
[.25305
160
1.60379
125
0.78181
38,9
1.2791
6,4
u tan gd u
«F0'
sec gd u
-F.'
sin gd u
U.FU'
esc gd u
• Fo'
SMITHSONIAN TABLE*
126
Natural Hyperbolic Functions.
u
sinh u
• F<f
cosh u
u> r;
tanhu
-P.'
cothu
-Fo'
1.050
1.25386
160
1.60379
125
0.78181
33,9
I.279I
6\4
.051
.25546
161
.60505
126
.78219
38,8
•2785
6,3
.052
.25707
161
.60631
i_>>
.78258
38,8
.2778
6,3
.053
.25867
161
.6075''
126
.78297
38,7
.2772
6,3
• 054
.26028
161
.60882
126
.78336
38,6
.2766
6,3
1.055
I.26l89
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
.6l2,')[
127
.78451
38,4
•2747
6,2
.058
.26673
161
.61388
127
.78490
38,4
.2741
6,2
• 059
.26834
162
.61514
127
.78528
38,3
.2734
6,2
i. 060
I . 26996
162
1.61641
127
0.78566
38,3
1.2728
6,2 i
.061
• -'7157
162
.61768
127
.78605
38,2
.2722
.062
.27319
162
.61896
127
.78643
38,2
.2716
6,2
.063
.27481
162
.62023
127
.78681
38,1
.2710
6,2
.064
.27643
162
.62151
128
.78719
38,0
•2-703
6,1
1.065
1.27806
162
1.62278
128
0.78757
38,0
1.2697
6,1
.27968
162
.62406
128
.7879=;
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
.78908
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
.2643
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
37,0
.2601
5,9 |
.082
•30583
164
.64475
131
•79394
37,0
.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
.64998
131
•79541
36,7
.2572
5,8
.087
.3M07
165
.65130
131
.79578
36,7
.2566
5.8
.088
.31572
165
.65261
132
.79615
36,6
.2560
.089
•31737
165
.65393
132
.79551
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
.092
.32234
166
.65789
132
.79761
36,4
.2538
5,7 '
•093
.32400
166
.65921
132
•79797
36,3
5.7
.094
.32566
166
.66053
133
.79833
36,3
5,7
1.095
1.32732
166
1.66186
133
0.79870
36,2
1.2520
5,7
.096
.32898
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
1. 100
1.33565
167
1.66852
134
0.80050
35,9
1.2492
5,6
u
tan gd u
«F</
sec gd u
-FO'
sin gd u
W Fo'
esc gd u
• Ft'
SMITHSONIAN TABLES
127
Natural Hyperbolic Functions.
u
sinh u
«Fo'
cosh u
• Fo'
tanh u
«F0*
cothu
"Fo'
1. 100
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
.34736
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. 1 10
1.35240
168
1.68196
135
o. 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 i
•113
•35745
169
.68602
136
.80512
35,2
.2421
5,4
.114
•35914
169
.68738
136
.80547
35,1
.2415
5,4
J.II5
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,o
.2399
5,4
.118
.36590
169
.69283
137
.80687
34,9
•2394
5,4 !
.IIQ
.36759
169
.69420
137
.80722
34,8
.2388
5,3
*.I20
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
.37008
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
.126
.37949
170
.70381
138
.80065
34,4
•2351
5,3
.127
.38119
171
.70519
138
.80999
34,4
.2346
5,2
.128
.38290
171
• 70658
138
.81033
34,3
•2341
5,2
.129
.38460
171
.70796
138
.81068
34,3
•2335
- 5,2
I.I30
1.38631
171
1.70934
139
0.81102
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
-39I45
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
.30659
172
.71769
140
.81306
33,9
.2299
5,1
•'37
.35831
172
.71909
140
.81340
33,8
.2294
5,
.138
.40003
172
•72049
140
.81374
33,8
.2289
5,
• 139
•40175
172
.72189
140
.81408
33,7
.2284
5,
1.140
1-40347
172
1.72329
140
0.81441
33,7
1.2279
5,
.141
.40520
172
.72470
141
.81475
33,6
.2274
5,
.142
173
.72610
141
.81509
33,6
.2269
5,
•143
.40865
173
•72751
141
.81542
33,5
.2264
5,o
.141
.41038
173
.72892
141
.81576
33,5
.2259
5,o
1.41211
173
1-73033
141
0.81609
33,4
1.2254
5,o
.Lf6
.41384
173
•73175
141
.81642
33,3
.2249
5,o
•M7
.41557
173
.73316
142
.81676
33,3
.2244
5,o
.41731
173
•73458
142
.81709
33,2
.2239
5,o
.41904
174
•73599
142
.81742
33,2
.2234
5,0
1.42078
174
i -7374 I
142
0.81775
33,1
1.2229
5,o
u
tan gd u
• Fo'
sec gd u
• IV
singd u
-Fo'
esc gd u
»F0'
ItTMSONIAN TABLES
T28
Natural Hyperbolic Functions.
u
sinh u
«F</
cosh u
"F,;
tanhu
«F0'
cothu
1.150
I.42O78
174
I.7374I
142
0.81775
33J
1.2229
5,0
.151
,42*52
174
.73884
142
.81809
33.1
4,9
.152
.41426
174
.74026
142
.81842
33,0
.22IQ
4,9
.153
. 42f*>0
174
.74168
143
.81875
33,0
.2214
4,9
• 154
.42774
174
•743II
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
M3
.82006
32,8
.2194
4,9
.158
.43472
175
.74884
U3
.82039
32,7
.2189
4,9
• 159
.43547
175
.75027
144
.82071
32,6
.2185
4,8
1.160
1.43822
175
I.75I7I
144
0.82104
32,6
I. 2l8o
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
.448/6
176
.76037
145
.82299
32,3
.2151
4,8
.167
.45052
176
.76182
145
.82331
32,2
.2146
4,8
.168
.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
.76909
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
I.2I08
4.7
.176
.46644
177
.77495
147
.82619
3i,7
.2104
4,7
.177
.46821
178
.77641
147
.82650
3i,7
.2099
4,6
.178
.46999
178
.77788
M7
.82682
3i,6
.2095
4,6
.179
.47177
178
•77935
M7
.82714
3i,6
.2090
4,6
1.180
1.47355
178
1.78083
147
0.82745
3i,5
1.2085
4,6
.181
•47533
178
.78230
148
.82777
3i,5
.2081
4,6
.182
.47711
178
.783/8
148
.82808
3i,4
.2076
4.6
.183
.47890
179
.78525
148
.82840
3i,4
.2072
4/>
.184
.48068
179
.78673
148
.82871
3L3
.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
.79119
M9
.82965
31,2
.2053
4,5
.188
.48784
179
.79267
149
.82996
3U
.2049
4,5
.189
.48964
179
.79416
M9
.83027
3U
.2044
4o
1.190
I.49H3
180
1.79565
149
0.83058
31,0
1.2040
4,5
.191
.49323
180
.797U
149
.83089
3i,o
• 2035
4,5
.192
-49502
180
.79864
ISO
.83120
30,9
.2031
4,5 •
.103
.49682
180
.80013
ISO
.83151
30,9
.2026
4,5
.194
.49862
180
.80163
150
.83182
30,8
. 2022
4,5
I.I95
i . 50043
180
1.80313
150
0.83212
30,8
I.2OI7
4,4 '
.196
. 50223
180
.80463
ISO
.83243
30,7
.2013
4,4 ;
• i<7
.50404
181
.80614
150
.83274
30,7
.2009
4,4 ;
.198
• 50584
181
.80764
I5i
.83304
30,6
.2OO4
4,4
.199
.50765
181
.80915
151
.83335
30,6
.2OOO
4,4
I.2OO
1.50946
181
i. 81066
151
0.83365
30,5
1. 1995
4,4
U
tan gd u
• Fo'
sec gd u
-Fo'
sin gd u
»Fo'
esc gd u
«F0'
SMITHSONIAN TABLES
Natural Hyperbolic Functions.
u
sinh u
-Fu'
cosh u
«FO'
tanh u
«F0'
coth u
«Fo'
I.2OO
1.50946
181
1. 81066
151
0.83365
30,5
I. 1995
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
• 5U50
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
1. 210
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
1. 215
1.53679
183
1.83350
154
0.83817
29,7
1.1931
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
.83906
29,6
.1918
4,2
.219
.54414
184
.83966
154
.83936
29,5
.1914
4,2
1.220
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
.56076
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
06633
186
.85833
157
.84287
29,0
.1864
4,1
.232
.56819
186
.85089
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
1-57377
186
1.86461
157
0.84402
28,8
i . 1848
4,0
.57564
187
.86618
158
.84431
28,7
.1844
4,0
.237
•57750
187
.86776
158
.84460
28,7
.1840
4,o
.238
•57937
187
•86934
158
.84488
28,6
.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
.58686
188
.87567
159
.84602
28,4
.1820
4,0
.243
.58874
188
.87726
159
.84631
28,4
.1816
4,0
.244
.5^062
188
.87885
159
•84659
28,3
.1812
4,0
i . 5<;2so
188
1.88044
159
0.84688
28,3
i. 1808
3,9
188
.88203
159
.84716
28,2
.1804
3,9
188
.88363
160
.84744
28,2
.1800
3,9
189
.88522
160
.84772
28,1
.1796
3,9
.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
tin od u
«F0'
sec gd u
«F0'
sin gd u
«F0'
esc gd u
«Fo'
SMITHSONIAN TABLES
I30
Natural Hyperbolic Functions.
u
sinh u
• Fe'
cosh u
-Fo'
tanhu
«F0'
coth u
»F»'
1.250
I.60I92
189
1.88842
160
0.84828
28,0
1.1789
3,9
.251
.60381
189
.89003
100
.84856
28,0
.1785
3,9
.252
.60570
189
.89163
161
.84884
27,9
.1781
3,9
.253
.60759
I8g
.89324
161
.84912
27,9
.1777
3,9
.254
.00949
189
.89485
161
.84940
27,9
.1773
3,9
1.255
I.6II38
190
1.89646
161
0.84968
27,8
1.1769
3,9
.256
.61328
190
.89807
161
.84996
27,8
.1765
33
• 257
.61518
190
.&g68
162
.85023
27,7
.1761
3,8
.258
.61708
190
.90130
162
.85051
27,7
.1758
3,8
.259
.61898
100
.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
191
.90616
162
•85134
27,5
.1746
3,8
.262
.62470
191
.90778
162
.85161
27,5
.1742
3,8
.263
.62661
191
.00941
163
.85189
27,4
.1739
3,8
.264
.62851
191
.91104
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
I.64OOI
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
.647/1
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
I.6600I
195
1.94566
167
0.85781
26,4
i . 1658
3,6
.286
.67096
195
•94733
167
.85808
26,4
.1654
3,6
.287
.67290
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
.69051
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
I.9709I
170
0.86172
25,7
1.1005
3,5
u
tan gd u
«FO'
sec gd u
• FO'
sin gd u
«F0'
esc gd u
«F0'
SMITHSONIAN TABLES
Natural Hyperbolic Functions.
u
sinh u
«F0'
cosh u
«F0'
tanh u
«FO'
coth u
• Fo'
1.300
1.69838
197
1.97091
170
0.86172
25,7
1.1605
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
.1591
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
171
.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
I.I570
3,4
.311
.72017
199
.08972
172
.86453
25,3
• 1567
3,4
.312
.72216
199
.09144
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
200
2.00007
173
.86604
25,0
.1547
3,3
.318
•73414
200
.00181
173
.86629
25,0
•1544
3,3
.319
.73614
200
•00354
174
.86653
24,9
.1540
3,3
1.320
I.738I4
20 1
2.00528
174
0.86678
24,9
i. 1537
3,3
.321
.74015
20 1
.00702
174
.86703
24,8
.1534
3,3
.322
.74216
20 1
.00876
174
.86728
24,8
.1530
3,3
.323
.74417
20 1
.01050
174
.86753
24,7
.1527
3,3
.324
.74618
20 1
.01225
175
.86778
24,7
.1524
3,3
1.325
I.748I9
2OI
2.01309
175
0.86802
24,7
1.1520
3,3
.326
.75021
2O2
.01574
175
.86827
24,6
.1517
3,3
.327
•75222
2O2
.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
202
2.02276
176
0.86925
24,4
1.1504
3,2
.331
.76031
202
.02452
176
.86949
24,4
.1501
3,2
.332
.76233
203
.02628
176
.86974
24,4
.1408
3,2
.333
.76436
203
.02804
175
.86998
24,3
.1495
3.2
.334
.76639
203
.02981
177
.87022
24,3
.1491
3,2
1.335
1.76842
203
2.03158
i/7
0.87047
24,2
1.1488
3,2
.336
.77045
203
•03335
177
.87071
24,2
.1485
3,2
• 337
.77249
204
.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 . 1472
3,2
• 341
.78064
2O4
.04222
1/8
.87191
24,0
.1469
3,2
•31-'
.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 . 1456
3,1
.79087
205
.05115
179
.87311
23,8
• 1453
3,1
• 317
•79293
205
.05294
179
.87334
23,7
.1450
3J
.348
205
•05474
179
.87358
23,7
•U47
3J
•79704
206
•05653
180
.87382
23,6
.1444
3,1
1-350
1.79909
206
2.05833
180
0.87405
23,6
1.1441
3,1
u
tin od u
••
•Fo'
- -
•ec gd u
•
• FO'
^—^m^^m
sin gd u
ma^mmmmmm^m
• Fo'
^^••^••H
esc od u
i
• FO'
^•^••••••^H
33JBAT MAIWO8HTIM2
Natural Hyperbolic Functions.
u
sinh u
w P./ coih u
«F0'
tanh u
«Fo'
cothu
• ft'
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
.8745-'
23,5
.1435
3,1
• 353
.80528
206
.06374
181
.87470
23,5
.1432
3,1
• 354
•80734
207
.06555
181
.87499
23,4
.1429
3,1
1-355
I.8094I
207
2.06735
181
0.87523
23,4
1.1426
3,1
• 350
.81148
207
.06916
181
.87546
23,4
. 1423
3,0
• 357
.81355
207
.07098
181
.8/570
23,3
.1419
3,0
.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,o
.362
.82392
208
.08007
182
.87686
23,1
.1404
3,o
.363
.82000
208
.08190
183
•87709
23,1
.1401
3,o
.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
..1392
3,0
.367
.83435
209
.08922
183
.87801
22,9
.1389
3,0
.368
•83644
209
.09105
184
.87824
22,9
.1386
3,o
.369
.83853
209
.09289
184
.87846
22,8
•1384
3,o
1.370
1.84062
209
2.09473
184
0.87869
22,8
1.1381
3,o
• 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
.10211
185
.87960
22,6
.1369
2,0
1.375
I.85II2
2IO
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
.IO766
186
.88028
22,5
.1360
2,9
• 3/8
.85744
211
.10952
186
.88050
22,5
• 1357
2.9
.379
.85955
211
.11138
186
.88073
22,4
.1354
2.9
1.380
1. 86166
211
2.II324
186
0.88095
22,4
I.I35I
2,9
.381
.85378
212
.11510
i85
.88117
22,4
.1348
2,9
.382
.86589
212
.11097
187
.88140
22,3
• U46
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
I. 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
213
.12820
188
.88273
22,1
.1328
2,8
.389
.88076
213
.13008
188
.88295
22,0
.1326
1.390
1.88280
213
2.13196
188
0.88317
22,0
i.iaaa
2,8
• 391
.88502
213
.13385
189
.88339
22,0
.1320
2,8
• 392
.88716
2T4
.13573
189
.88361
21,9
.1317
2,8
• 393
.88929
214
.13762
189
.88383
21,9
.1314
2,8
•394
.89143
214
•I395I
189
.88405
21,8
.1312
2,8
1.395
1. 80357
214
2.14140
189
0.88427
21,8
1.1309
2*
.396
.89571
214
• M330
190
.884J8
21,8
.1306
2,8
• 397
.80786
215
. T4520
TOO
.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
1.90430
215
2.15090
190
0.88535
21,6
1.1295
2,8
u
tan gd u
«F0'
sec gd u
• IV
sin gd u
• ft'
esc gd u
O.FO'
SMITHSONIAN TABLCS
#33
MAIMO3HTIM3
Natural Hyperbolic Functions.
I
sinh u
wF0'
cosh u
wF0'
tanh u
W FO'
coth u
• F0'
1.400
.401
.402
.403
.404
1.90430
.90645
.90861
.91076
.91292
215
215
215
216
216
2.15090
.15280
.15471
.15662
.15853
100
191
191
191
191
0.88535
.88557
.88578
.88600
.88621
21,6
21,6
21,5
21,5
21,5
I. 1295
.1292
.1289
.1287
.1284
2,8
2,8
2,7
2,7
2,7
1 .40=1
1.91508
216
2.16045
192
0.88643
21,4
I . 1281
2,7
M. .^JJ
.406
.407
.91724
.91940
216
216
. 16236
.16428
192
192
.88664
.88686
21,4
21,3
.1279
.1276
2,7
2,7
• '•fV/
.408
.92157
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
.93O25
217
. I739I
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
2I,O
i . 1254
2,7
.416
.9389$
218
. 18164
194
.88876
2I,O
.1252
2,7
.417
.418
.419
.94114
.94333
•94551
218
219
219
.18358
.18553
.18747
194
194
195
.88897
.88918
.88939
21,0
20,9
20,9
.1249
.1246
.1244
2,7
2,6
2,6
1.420
.421
.422
1.94770
.94989
.95209
219
219
219
2.18942
.19137
. 19332
195
195
195
0.88960
.88981
.89002
20,9
20,8
20,8
1.1241
.1238
.1236
2,6
2,6
2,6
.423
.95428
22O
. 19527
195
.89022
20,8
• 1233
2,6
.424
.95648
220
. 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
22O
.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
2.20000
197
0.89167
20,5
I.I2I5
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
.98298
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
.H95
2,5
•439
.98966
223
.22682
199
•89350
20,2
.1192
2,5
1.440
1.99188
223
2.22881
199
0.89370
20,1
1.1189
2,5
.441
.99411
223
.23080
199
.89390
20,1
.1187
2,5
.442
•99635
223
.23280
200
.89410
2O, I
.1184
2,5
• 443
,998$8
223
.23480
200
.89430
20,O
.1182
2,5
.444
2.00082
224
.23680
200
.89450
2O,O
.1179
2,5
1.445
2.00305
224
2.23880
200
0.89470
2O,O
I. 1177
2,5
.446
.00529
224
.24080
201
.89490
19,9
.1174
2,5
•447
.00753
224
.24281
201
.89510
19,9
.1172
2,5
. Mfl
.00978
224
.24482
201
.89530
19,8
.1169
2,5
>440
.01202
225
.24683
201
.89550
19,8
.1167
2,5
1-450
2.01427
225
2.24884
201
0.89569
19,8
1.1165
2,5
u
tan gd u
«FO'
sec gd u
«F0'
sin gd u
-Fo'
esc gd u
-FO'
SMITHSONIAN TABLES
134
Natural Hyperbolic Functions.
u
sinh u
«Fo'
cosh u
W Fu'
tanhu
«F0'
coth u
«F0'
1.450
2.01427
225
2.24884
2OI
0.89509
19,8
I . I 165
2,5
.451
.01052
225
.25080
2O2
.89589
19,7
.1162
2,5
.452
.01877
225
.25288
2O2
19,7
.1100
2,5
.453
.02103
225
.25490
2O2
.89628
19,7
.1157
2,4
• 454
.02328
226
.25692
2O2
.89648
19,6
.1155
2,4 i
1-455
2.02554
226
2.25894
203
0.80668
19,6
1.1152
2,4
.45<J
.02780
226
.20097
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
2A
1.460
2.03686
227
2.26910
204
0.89765
19,4
i . i 140
2A
.461
.03913
227
.27114
204
.89785
19,4
.1138
2,4
.462
.04140
227
.27318
204
.89804
19,4
.1135
2,4
.463
.04368
228
.27522
204
.89823
19,3
.1133
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
1.1128
2,4
.466
.05051
228
.28136
205
.89881
19,2
.1126
2,4
.467
.05280
228
.28341
205
.89000
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
23O
.29784
207
.00034
18,9
.IIO7
2,3
1.475
2.07113
230
2.29991
207
0.90053
18,9
I . I IO5
2,3
• 476
.07343
230
.30198
207
.00072
18,9
.IIO2
2.3
.477
•07573
230
.30405
208
.00000
18,8
.IIOO
2,3
.478
.07804
231
.30613
208
.90109
18,8
.1098
2,3
•479
.08034
231
.30821
208
.90128
18,8
.1095
2,3
1.480
2.08265
231
2.31029
208
0.90147
18,7
1. 1093
2,3
.481
.08497
231
.31238
208
.90166
18,7
.IO9I
2,3
.482
.08728
231
.3U46
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
I.I082
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
.IOI20
233
.32703
2IO
.90296
18,5
.1075
2,3
.489
. 10353
233
.32913
210
.90314
18,4
.10/2
2,3
1-450
2.10586
233
2.33123
211
0.90332
18,4
I . 1070
9,3
.491
.10819
233
•33334
211
.90351
18,4
.1068
2.2
.492
•11053
234
•33545
21 1
.90369
18,3
. io'j6
2.J
•493
.11286
234
.33756
211
.50388
18,3
.1063
2.2
• 494
.11520
234
.33968
212
.90406
18,3
.1061
2,2
1.495
2.II754
234
2.34179
212
0.0:0424
18,2
i . 1059
J.J
.496
.11989
234
•34391
212
•50442
18,2
.1057
2,2
• 497
. i 2223
235
.34603
212
.00460
18,2
• 1055
2,2
.493
.12458
235
.34816
212
•50479
18,1
. 1052
2.2
.499
.12693
23S
.35028
213
.90497
18,1
.1050
2,2
1-500
2.12928
235
2.35241
213
0.90515
18,1
1.1048
u
tan gd u
«F0'
sec gd u
• FO'
sin gd u
«F0'
esc gd u
»F0'
SMITHSONIAN TABLES
135
Natural Hyperbolic Functions.
u
sinh u
«F0'
cosh u
W FO'
tanh u
• IV
coth u
«F0'
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
236
.35667
213
.90551
18,0
.1044
2,2
.503
. 13635
236
.35881
214
.90569
18,0
.1041
2,2
.504
.13871
236
•36095
214
.90587
17,9
.1039
2,2
1.505
2.I4I07
236
2.36309
214
0.90605
17,9
i . 1037
2,2
.506
. M343
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.I529I
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
1.1015
2,1
.516
.16719
239
.38678
217
.90800
17,6
.1013
2,1
.517
.16958
239
.38895
217
.90817
17,5
.ion
2,1
.518
.17197
239
.39H2
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
1.1005
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
1.0994
2,1
.526
.19117
241
.40857
219
.90974
17,2
.•0992
2,1
.527
• 19358
241
.41076
219
.90091
17,2
.0990
2,1
.528
•19599
241
.41296
22O
.91008
17,2
.0988
2,1
.529
.19840
242
.41516
220
.91025
I7,i
.0986
2,1
1.530
2.2O082
242
2.41736
220
0.91042
I7,i
1.0984
2,1
.531
.20324
242
.41956
220
.91060
I7,i
.0582
2,1
.532
.20566
242
.42176
221
.91077
I7,i
.0980
2,1
•533
.20808
242
.42397
221
.91094
17,0
.0978
2,1
•534
.21051
243
.42618
221
.91111
17,0
.0976
2,O
1-535
2.21293
243
2.42839
221
0.91128
17,0
1.0974
2,0
.536
.21536
243
.43060
222
.91145
1 6,9
.0972
2,0
•537
.21780
243
.43282
222
.91161
16,9
.0970
2,0
.538
.22023
244
.43504
222
.91178
16,9
.0068
2,O
•539
.22267
244
.43726
222
.9H95
16,8
.0965
2,0
1.540
2.22510
244
2.43949
223
0.91212
16,8
1.0963
2,0
• 541
.22755
244
.44171
223
.91229
16,8
.0961
2,O
.542
.22099
244
•44394
223
.91246
16,7
.0959
2,O
• 543
.23243
245
.44617
223
.91262
16,7
•0957
2,0
•544..
.23488
245
.44841
223
.91279
16,7
.0955
2,O
2.23733
245
2.45064
224
0.91296
16,7
1.0953
2,O
.23978
245
.45288
224
.91312
16,6
.0951
2,0
.24224
.24469
246
246
•45512
.45736
224
224
.91329
.91345
16,6
16,6
.0949
.0947
2,0
2,0
•24715
246
.45961
225
.91362
16,5
.0945
2,O
I.SSO
2.24961
246
2.46186
225
0.91379
16,5
1.0943
2,O
u
tan gd u
«FO'
sec gd u
• FO'
sin gd u
«F0'
esc gd u
• Fo'
i>MITM80MIAN TABLE*
Natural Hyperbolic Functions.
u
sinh u
«Fu'
cosh u
«F«'
tanhu
-FO'
cothu
1.550
2.24961
246
2.46186
225
0.91379
16,5
1.0943
2,0
.551
.-'5207
240
.40411
225
.91395
1<>,5
.0942
2,0
.552
.25454
247
• 4"
225
.9I4H
.0940
2,0
• 553
.25701
247
.46!
226
.91428
16,4
.0938
2,0
• 554
.-'5948
247
.47088
226
.9M44
10,4
.0936
2,0
1-555
2.26195
247
2.47314
226
0.91461
16,3
1.0934
2,0
• 556
• -'''442
248
•47540
226
.91477
16,3
.0932
2,0
• 557
. _' ;:>9O
248
.477^7
227
.91493
16,3
.0930
1,9
• 558
938
248
•47993
227
.91510
16,3
.0928
1,9
• 559
.27180
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
.27083
249
•48b75
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
1,9
• 504
.28430
249
.49360
228
.91607
16,1
.0916
1,9
1.565
2.28379
250
2.49588
229
0.91623
16,1
1.0914
1,9
.566
.a693Q
250
.49817
229
.91639
1 6,0
.0912
1,9
.567
•23179
250
.50046
229
.91655
16,0
.0911
1,9
.568
• -'9429
250
.50275
229
.91671
1 6,0
.0909
1,9
.569
. 2(/o8o
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
.51195
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
1.590
2.34991
255
2.55384
235
0.92015
15,3
1.0868
1,8
• 591
.35247
256
.55619
235
.92030
15,3
.0856
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
I5,i
.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
15,1
1.0850
1,8
u
tan gd u
wF0'
sec gd u
«F0'
sin gd u
*
u> F '
esc gd u
co F '
SMITHSONIAN TABLES
137
Natural Hyperbolic Functions.
u
sinh u
*Fo'
cosh u
.IV
tanh u
.«
coth u
.«
1.600
2.37557
258
2.57746
238
0.92167
15,1
I.0850
1,8
.001
.37815
258
.57984
238
.92182
15,0
.0848
1,8
.602
.38073
258
.58222
238
.92197
i5,o
.0846
1,8
.603
.38331
258
.58460
238
.92212
I5,o
.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
J,7
.607
.39367
259
.59416
239
.92272
14,9
.0838
!,7
.608
.39626
260
.59655
240
.92286
14,8
.0836
1,7
.609
.39886
260
.59895
240
.92301
14,8
.0834
1,7
1.610
2.40146
260
2.60135
240
0.92316
14,8
1.0832
1,7
.611
.40406
260
.60375
240
.92331
14,8
.0831
1,7
.612
.40667
261
.60616
241
.92346
14,7
.0829
.613
.40928
261
.60857
241
.92360
14,7
.0827
1,7
.614
.41189
261
.61098
241
.92375
14,7
.0825
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
.618
.42235
262
.62064
242
.92433
14,6
.0819
1^7
.619
.42497
262
.62307
242
.92448
14,5
.O8l7
1,7
1.620
2.42760
263
2.62549
243
0.92462
14,5
I.08I5
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
.O8l0
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
.628
.44858
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
2.64990
245
0.92606
14,2
I.O7O8
1,7
.631
.45662
265
.65236
246
.92620
14,2
.0797
1,7
.632
.45928
265
.65482
246
.92635
14,2
.0795
.633
.46193
266
.65728
246
.92649
14,2
.0793
1,6
.634
.46459
266
.65974
246
.92663
14,1
.0792
1,6
1.635
2.46725
266
2.66221
247
0.92677
14,1
1.0790
1,6
.636
.46992
266
.66467
247
.92691
.0789
1,6
.637
.47258
267
.66715
247
.92705
1 4,' I
.0787
1,6
,638
.47525
267
.66962
248
.92719
14,0
.0785
1,6
•639
.47792
267
.67210
248
.92733
14,0
.0784
1,6
[.640
2.48059
.48327
267
268
2.67457
.67706
248
248
0.92747
.92761
14,0
I4,o
1.0782
.0780
1,6
1,6
•48595
268
268
.67954
.68203
249
249
.92775
.92789
13,9
13,9
.0779
.0777
1,6
1,6
.49131
268
.68452
249
.92803
13,9
.0776
1,6
2.49400
269
2.68701
249
0.92817
13,9
1.0774
1,6
s
•4Q&Q
269
.68951
250
.92831
13,8
.0772
1,6
.647
6L
•49938
269
.69200
250
.92844
13,8
.0771
1,6
48
.50207
269
.69451
250
.92858
13,8
.0769
1,6
.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 ad u
«FU'
sec gd u
*F0'
sin gd u
»Fo'
esc gd u
-W
ITM«ONIAN TABLES
138
Natural Hyperbolic Functions.
u
sinh u
«F«'
cosh u
»F,'
tanh u
»*'
cothu
-Fo'
1.650
2.50746
270
2.69951
251
0.92886
13,7
1.0766
1,6
.651
.51017
270
. 7O202
-J5i
.92809
13,7
1,6
.652
.51287
270
.70454
251
.92913
13,7
.070.5
1,6
.653
.5155"
271
.70705
252
.92927
13,6
.0761
1,6
.654
.51828
271
.70957
252
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
0.93022
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
,5
.663
.54277
273
.73234
254
.93062
13,4
.0746
,5
.664
•54551
273
.73489
255
.93075
13,4
• 0744
,5
1.665
2.54824
274
2.73743
255
0.93089
13,3
1.0742
,5
.666
.55098
274
•73998
255
•93102
13,3
.0741
,5
.667
•55372
274
.74253
255
.93U5
13,3
• 0739
,5
.668
.55647
275
.74509
256
.93129
13,3
.0738
,5
.669
.55921
275
.74765
256
.93M2
13,2
.0736
,5
1.670
2.56196
275
2.75021
256
,0.93155
13,2
1.0735
,5
.671
.56471
275
.75277
256
.93168
13,2
•0733
,5
.672
.56747
276
•75534
257
.93182
13,2
.0732
,5
.673
•57022
276
.75791
257
.93195
13,1
•0730
,5
• 674
.57298
276
.76048
257
.93208
13,1
.0729
,5
1.675
2-57574
276
2.76305
258
0.93221
13,1
1.0727
,5
.676
.57851
277
.76563
258
.93234
13,1
.0726
,5
.677
.58127
277
.76821
258
.93247
13,0
.0724
,5
.678
08404
277
.770F9
258
.93260
I3,o
.0723
,5
.679
.58682
277
.77338
259
.93273
13,0
.0721
,5
i. 680
2.58959
278
2.77596
259
0.93286
I3,o
1.0720
,5
.681
.59237
278
.77856
259
•93299
13,0
.0718
,5
.682
.59515
278
.78115
260
.93312
12,9
.0717
,5
.683
.59793
278
.78375
260
•93325
12,9
.0715
,5
.684
.60072
279
.78635
260
.93338
12,9
.0714
,5
1.685
2.60350
279
2.78895
260
0.93351
12,9
1.0712
,5
.686
.60629
279
.79155
261
.93364
12,8
.0711
,5
.687
.60000
279
.79416
261
.93376
12,8
.0709
,5
AS8
.61188
280
.79677
261
•93389
12,8
.0708
,5
.689
.61468
280
.79938
261
.93402
12,8
.0706
,5
1.690
2.61748
280
2.80200
262
0-934T5
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
.80987
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
.rxx>
.63434
2&2
.81776
263
.93491
12,6
.0696
M
.697
.63716
.82039
264
.93503
12,6
.0695
1,4
.6g8
.63908
282
.82303
264
.93516
12,5
.0693
1,4
.699
.64280
283
.82567
264
.93528
12,5
.0692
1,4
1.700
2.64563
283
2.82832
265
0.93541
12,5
1.0691
M
u
tan gd u
«F0'
sec gd u
o>F,/
sin gd u
o,F'
esc gd u
«F0'
SMITHSONIAN TABLE.S
139
Natural Hyperbolic Functions.
u
sinh u
»Fo'
cosh u
»Fo'
tanh u
«Fo
co'.h u
• Fo'
1. 700
2.64563
283
2.82832
265
0.93541
12,5
1.0691
1,4
.701
.64840
283
.83og6
2(35
•93553
12,5
.0689
1,4
.702
.65129
283
-83361
205
•935GJ
12,5
.0588
1,4
.703
.65413
284
.83627
265
.93578
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
.o582
1,4
.707
.66550
285
.84690
267
.93628
12,3
.0681
1,4
.708
.66834
285
.84957
267
.93640
12,3
.0679
1,4
.709
.67119
285
.85224
267
.93652
12,3
.0678
1,4
1.710
2.67405
285
2.85491
267
0.93665
12,3
1.0676
1,4
.711
.67690
285
.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
i,4
1.720
2.70273
288
2.88l8o
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
1 2,O
.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
200
.00079
272
.93870
11,9
.0653
,3
.728
.72587
290
.90351
273
.93882
11,9
.0652
,3
.729
.72878
291
.90624
273
.93894
11,8
.0650
,3
1.730
2.73168
291
2.90897
273
0-93905
11,8
1.0649
,3
.731
.73400
291
.91170
273
•93917
11,8
.0648
,3
.732
.73751
291
.91444
274
•93929
11,8
.0646
,3
• 733
.74042
292
.91718
274
•93941
11,8
.0645
i,3
.734
•74334
292
.91992
274
•93953
ii,7
.0644
1,3
1.735
2 . 74626
292
2.92266
275
0.93964
n,7
1.0642
,3
.736
.74919
293
.92541
275
.93976
n,7
.0641
,3
• 737
.75211
293
.92816
275
.93988
n,7
.0540
,3
.738
•75504
293
.93092
276
•93999
11,6
.0638
,3
• 739
.75798
293
.9336"7
276
.94011
n,6
.0637
,3
1.740
2.76091
294
2.93643
276
0.94023
11,6
1.0536
,3
• 741
.76385
294
.93919
276
•94034
11,6
.0634
,3
.742
.76679
294
.94196
277
.94046
11,6
.0533
,3
• 743
.76973
294
•94473
277
•94057
ii,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
.77858
295
•95305
278
.94092
n,5
.0628
,3
• 747
.78153
296
.95583
278
.94103
11,4
.0627
,3
.740
,78445
206
.95861
278
.94H5
11,4
.0625
,3
.78745
296
.96140
279
.94126
n,4
.0624
,3
1.750
2.70041
296
2.96419
279
0.94138
11,4
1.0623
1,3
u
tin gd u
«FO'
sec gd u
«FO'
sin gd u
w r,i'
esc gd u
• F«'
SMITHSONIAN TABLES
I4O
Natural Hyperbolic Functions.
u
sinh u
»fo'
cosh u
«Fu'
tanh u
CO F
cothu
~ F
! 1-750
2.79041
296
2. 964 IV
279
0.94138
11,4
I.c
1,3
' .751
.79338
297
.96698
279
.94149
11,4
.0621
1,3
.752
•79035
297
.96978
280
.94160
n,3
.0620
1,3
i .753
.79932
297
.97257
280
.94172
n,3
.0619
1,3
.754
.80229
298
•97537
280
.94183
n,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
.08379
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
11,1
.0669
1,3
.762
.82619
300
.99789
283
.94273
11,1
.0608
1,3
.763
.82919
300
3.00072
283
.94284
II, I
.0606
1,2
.764
.83219
300
.00355
283
.94295
II, I
.0605
1,2
1.765
2.83519
301
3-00638
284
0.94306
II, I
1.0604
1,2
.766
.83820
301
.00922
284
.94317
11,0
.0603
1,2
.767
.84121
301
.01206
284
.94328
11,0
.0601
1,2
.768
.84422
301
.01400
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
0.94416
10,9
1.0591
1,2
i .776
.86844
304
.03775
287
.94426
10,8
.0500
1,2
1 .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
i 1.785
2.89589
306
3-06369
290
0.94523
10,7
1.0579
1,2
. .786
.89896
307
.06659
290
.94534
1 0,6
.0578
1,2
: .787
.90202
307
.06049
290
•94544
10,6
.0577
1,2
: .788
.50510
307
.07239
291
•94555
10,6
.0576
1,2
; .789
.90817
308
.07530
291
•94565
10,6
.0575
1,2
' 1.790
2.9II25
308
3.07821
291
0.94576
10,6
i -0574
1,2
• 791
.9M33
308
.08112
291
.94587
10,5
• 057-'
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
10,5
.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
i -797
.gaa87
310
.00856
293
.94649
10.4
1,2
• 798
•935Q7
3TO
.10160
294
.94660
10,4
.0564
1,2
; .799
.93907
310
• 10453
294
•94670
10,4
.0563
1,2
1.800
2.94217
311
3.10747
294
0.94681
10,4
1.0562
1,2
u
tan ad u
«FO'
sec ad u
«F0'
sin gd u
«F0'
esc od u
• IV
SMITHSONIAN TABLES
141
Natural Hyperbolic Functions.
u
sinh u
U.FO'
cosh u
• Fo'
tanh u
»Fo'
coth u
<•> FU'
1.800
2.94217
311
3.10747
294
0.94681
10,4
1.0562
1,2
.801
.94528
311
. I 1042
295
.94691
10,3
.0561
1,2
.802
.(^4840
311'
.11336
295
•94/01
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.I3705
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
IO,I
.0548
1,1
.813
.98282
315
.14599
298
.94814
IO,I
• 0547
1,1
.814
.98597
3i5
.14897
299
.94824
10,1
.0546
1,1
1.815
2.98912
315
3.I5I96
299
0.94834
IO,I
1.0545
1,1
.816
.99227
315
.15495
299
.94844
IO,O
.0544
1,1
.817
•99543
316
.15794
300
.94854
IO,O
.0543
IJ
.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
10,0
.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
•17809
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
•94063
9,8
• .0530
I.I
.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
•94992
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
.21543
306
.95041
9,7
.0522
1,1
.837
.838
•05919
.06241
322
322
.21849
.22155
306
306
.95051
.95060
9,7
9,6
.0521
•0520
1,1
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
.07209
323
.23075
307
•95089
9,6
.0516
1,1
.842
•07532
323
.23382
308
.95099
9,6
• 0515
I»l
.843
.07856
324
.23690
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
1,0
.847
•09153
325
•24924
309
.95146
9,5
.0510
1,0
.XjX
.09478
325
•25233
309
.95T56
9,5
.OSOQ
1,0
.849
.09803
326
•25543
310
.95165
9,4
.0508
1.0
1.850
3.IOI2Q
326
3-25853
310
0.95175
9,4
1.0507
I,O
u
tan od u
«F0'
sec gd u
«FO'
sin gd u
»Fo'
csc gd u
<oF0'
SMITHSONIAN TABLCS
142
Natural Hyperbolic Functions.
u
sinh u
«FO'
cosh u
«Fo'
tanhu
«F0'
coth u
-F;
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
9A
.0505
i.o
.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
I.O5O2
1,0
.856
.12090
328
• -'7719
312
.95231
9,3
.O5OI
1,0
.857
.12418
3->8
. 2.S032
312
.95240
9,3
.O5OO
1,0
.858
. 12746
328
.28344
313
•95-M9
9,3
.0499
1,0
.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
3U
.95277
9,2
.0496
1,0
.862
.14062
330
.29598
3U
.95285
9,2
• 0495
1,0
• 853
. 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
0.953U
9,2
1.0492
1,0
.866
.15383
331
.30857
315
.95323
9,1
.0491
1,0
.867
.15/14
331
.31172
316
.95332
9,1
.0490
1,0
.868
.16045
331
.31488
316
.95341
9,1
.0489
1,0
.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
1,0
.872
.17374
333
.32755
317
.95378
9,o
.0485
1,0
.873
.17706
333
•33073
3l8
.95387
9,0
.0484
I,O
.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
.954U
9,0
.0481
1,0
• 877
.19041
334
.34346
319
.95422
8,9
.0480
1,0
.878
. 19376
335
.34665
319
.95431
8,9
.0479
1,0
.879
.19711
335
.34985
320
•95440
8,9
.0478
1,0
1.880
3.20046
335
3.35305
320
0.95449
8,9
1.0477
I,O
.881
.20381
336
.35625
320
.95458
8,9
.0476
I,O
.882
.20717
336
.35946
321
.95467
8,9
• 0475
1,0
.883
.21053
336
.36266
321
.95476
8,8
.0474
I,O
.884
.21390
337
.36588
321
.95485
8,8
.0473
1,0
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
I,O
.887
.888
.22401
.22738
338
338
•37553
.37876
322
323
•955II
.95520
8,8
8,8
.0470
.0469
1,0
1,0
.889
.23076
338
•38199
323
.95529
8,7
.0468
1,0
i. 800
3.23415
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
.398i8
325
.95572
8,7
.0463
0,9
1.895
3-25112
340
3.40M3
325
o.9558i
8,6
1.0462
0,9
.896
• 2545-'
340
.40469
325
.95589
8,6
.0461
0,9
.897
.25792
34i
.40794
326
.95598
8,6
.0460
0,9
.898
.26133
341
.41120
326
.95607
8,6
.04<K>
0,9
.899
.26475
341
• 4M47
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
«F0'
sec gd u
«F0'
sin gd u
«F0'
esc gd u
<o F '
SMITHSONIAN TABLES
Natural Hyperbolic Functions.
u
sinhu
CO Fo'
cosh u
-Fo'
tanh u
w FO'
cothu
™
1.900
3.26816
342
3.41773
327,
0.95624
8,6
1.0458
0,9
.901
.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
0,9
.909
.29906
345
.44728
330
•95700
8,4
.0449
0,9
1.910
3.30250
345
3.45058
330
0.95709
8,4
1.0448
0,9
.911
.30596
345
.45389
33i
•95717
8,4
.0447
0,9
.912
.30041
346
•45720
33i
•95725
8,4
.0447
0,9
.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
•35II4
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
o,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
338
.95881
8,1
.0430
o,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
3o3423
339
0.95914
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
0,9
.941
.41108
355
.55464
341
.95961
7,9
.0421
0,9
•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
0,9
__ f
3.42532
357
3.56831
343
0.95993
7,9
1.0417
o,9
.046
. (joQp
357
•57174
343
.96001
.0417
0,9
•947
.948
;_>47
•43604
358
358
.57517
.57860
343
344
.96009
.96016
7J
.0416
.0415
0,9
0,9
•949
.43962
358
.58204
344
.96024
73
.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
«F0'
sin gd u
«F0'
esc gd u
«FO'
TABLE*
144
Natural Hyperbolic Functions.
u
sinh u
« Fo'
cosh u
- Fo'
tanh u
" F
coth u
»K
1.950
3.14321
359
3.58548
344
0.96032
7,8
1.0413
0,8
.951
.44<>70
359
.58893
345
.96040
7,8
.0412
.952
.45038
359
• 5<J-}37
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
.6o52O
346
.96078
7,7
.0408
•957
.46839
261
.60967
347
.96086
7,7
.0407
.958
.47^00
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
.0308
.969
.51196
365
.65155
351
.96177
7,5
•0397
1.9/0
3.5I56I
366
3-65507
352
0.06185
7,5
1.0397
0,8
.971
.51927
366
•65858
352
.96192
7,5
.0396
.972
.52293
366
.66211
352
.96109
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
.96251
7,4
.0389
1.980
3-55234
369
3.69041
355
0.06259
7,3
1.0389
0,8
.981
.55603
369
.69396
356
.96266
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
.96302
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
74
.0382
1.990
308942
373
3-72611
359
0.06331
7.2
1.0381
0,8
.991
.59315
373
•72971
359
.96339
7,-'
.0380
.992
.59588
373
•73330
360
.96346
7.2
• 0379
•993
.60061
374
.73600
360
.96353
7,2
•0379
•994
•60435
374
•74050
360
.96360
7,1
• 0378
1-995
3.60809
374
3-744II
36i
0.96367
7J
1-0377
0,8;
.996
.61184
375
.74772
361
.95374
7,i
.0376
• 997
.61550
375
.75133
362
.95382
7,i
• 0375
.998
.61934
375
•754Q5
362
.96389
7-1
• 0375
•999
.62310
376
.75857
362
.96396
7-1
• 0374
2.000
3.62686
376
3 . 76220
363
0.96403
7.1
1-0373
0,8 I
u
tan gd u
«F0'
sec gd u
-FO'
sin gd u
"> F ' esc gd u <•> FO'
SMITHSONIAN TABLES
Natural Hyperbolic Functions.
u
sinh u
»F»'
cosh u
«FU'
tanh u
«Fo'
coth u
«F0'
2.000
3.62686
376
3.76220
363
0.96403
7,1
1.0373
0,8
.001
.63062
377
.76582
363
.96410
7,1
.0372
.002
.63439
377
.76946
363
.96417
7,o
.0372
.003
.63816
377
.77309
364
.96424
7,o
• 0371
.004
.64194
378
.77673
364
.95431
7,o
.0370
2.005
3.64572
378
3.78038
365
0.96438
7,o
1.0369
0,8
.006
.64950
378
.78402
365
.96445
7,o
.0369
0,8
.007
.65328
379
.78/68
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.OIO
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
.96500
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
.0535
6,8
• 0359
2.O20
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
.7M36
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
.857/8
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
.75690
389
.88771
376
•96635
6,6
.0348
2.035
3.76079
389
3.89147
376
0.96642
6,6
1.0347
o,7
.036
390
.89523
376
.96648
6,6
• 0347
.037
390
.89900
377
.0655
6,6
• 0346
.038
.77248
390
.90277
377
.96662
6,6
.0345
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
390
.91789
379
.96688
6,5
• 0343
•043
392
.92168
379
.96694
6,5
• 0342
393
.92547
380
.96701
6,5
.0341
1
393
3.92<)27
380
0.96707
6,5
1.0340
o,7
393
•93307
380
.96714
6,5
.0340
381
.96720
6,5
• 0339
394
38r
.96727
6,4
• 0338
394
•94450
382
.96733
6,4
.0338
2.050
3.81958
395
3-94832
382
0.96740
6,4
1-0337
o,7
u
tan od u
... F'
sec gd u
• FO'
sin gd u
e*F0'
esc gd u
«Fo'
IMITHCONIAN TABLE*
146
Natural Hyperbolic Functions.
u
sinh u
" F,/
cosh u
« F/
tanh u
• Pc
cothu
»p,'
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
•95597
383
•96752
6,4
.0336
.053
•83145
396
•95979
383
.96759
64
• 0335
.054
.83541
396
.96363
384
.96765
6,4
.0334
2.055
3.83937
397
3.95747
384
0.96771
6,4
1.0334
o,7
.050
.84334
397
.97131
384
.96778
6,3
.0333
.057
.84732
398
.97515
385
.96784
6,3
.0332
.058
.85139
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
.06822
6,3
.0328
.064
.87524
400
4.00218
388
.96828
6,2
.0328
2.065
3.87924
401
4.00606
388
0.96834
6,2
1.0327
o,7
.060
.88325
401
.00594
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
0,7
.071
.90335
403
.02941
390
.96872
6,2
.0323
.072
.90738
403
.03331
39i
.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
.96914
6,1
.0318
.079
.93571
406
.06076
394
.96920
6,1
.0318
2.080
3-93977
406
4.06470
394
0.96926
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
.90951
6,0
• 0315
2.085
3-96014
408
4.08445
396
0.06957
6,0
1.0314
0,6
.086
.96423
409
.08841
396
.06963
6,0
•0313
.087
.96832
409
•09238
397
.96969
6,0
.0313
.088
.97241
410
.09635
397
.90975
6,0
.0312
.089
.97651
410
.10032
398
.96980
5,9
.0311
2.000
3.98061
410
4-10430
398
0.96986
5,9
1.0311
0,6
.091
.98472
411
.10828
398
.96992
5,9
.0310
.092
.98883
411
. 11227
399
.90998
5,9
.0309
.093
.99294
412
.11626
399
.97004
5,9
.0309
.094
.99706
412
. 12026
400
.97OIO
5,9
.0308
2.095
4.00II9
412
4.12426
400
O.97OI6
5,9
1.0308
0,6
.096
.00531
413
.12826
401
.97022
5,9
.0307
.097
.00944
413
. 13227
401
.97028
5,9
.0306
.098
.01358
414
. 13628
401
•97034
5*
.0306
.099
•OI77I
4U
.14029
402
.97039
5,8
.0305
2. TOO
4.02186
4U
4.I443I
402
0.9/045
5,8
1.0304
0,6
U
tan ad u
<oF0'
sec gd u
-Fo'
sin gd u
o>F '
esc gd u
«FO'
SMITHSONIAN TABLES
147
Natural Hyperbolic Functions.
u
sinh u
•»Fo'
cosh u
U.FO'
tanh u
<•> FO' coth u
<•> F0'
2.100
4.O2I86
414
4.I443I
402
0.97045
5,8
1.0304
0,6
.101
.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
.10043
404
.97068
5,8
.0302
2.105
4.04263
416
4. 16447
404
0.97074
5,8
1.0301
0,6
. I<X>
.04680
417
.16852
405
.97080
5,8
.0301
.107
.05097
417
.1/257
405
.97086
5,7
.0300
.108
.055U
418
.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
.97114
5,7
.0297
•113
.07607
420
.19695
408
.97120
5,7
.0297
.114
.08027
420
.2OI03
408
.97126
5,7
.0296
2. 115
4.08448
421
4.2O5II
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
.09711
422
.21738
410
.97148
5,6
.0294
.119
. IOI33
422
.22148
410
.97154
5,6
.0293
2.I2O
4-10555
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
2.125
4.12673
425
4.24617
413
0.97187
5,5
1.0289
0,6
.126
.13008
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
4.10089
431
4.30855
419
0.97269
5,4
1.0281
0,6
.141
.19520
431
•31274
420
.97275
5,4
.0280
.i.jj
.19952
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
4-2i-M<;
433
4.32955
421
0.97296
5,3
1.0278
0,6
.2I6&J
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
.22984
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
«F0'
sec gd u
«F0'
sin gd u
-Fo'
esc od u
u> F./
SMITHSONIAN TABLE*
T.lR
Natural Hyperbolic Functions.
u
sinh u
"F,;
cosh u
U Fu'
tanh u
*Fo
cothu
" F '
2.150
4.23419
435
4.35067
423
0.97323
5,3
1.0275
0,6
.151
.23854
435
.35491
424
.97328
5,3
.o_>75
.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
.20037
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
0,5
2.160
4.27791
439
4.39323
428
0-97375
5,2
1.0270
o,5
.161
.28230
440
.39751
428
.9738o
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
4.4U68
430
0.97401
5,1
1.0267
o,5
.166
.30434
442
.41898
430
.97406
5,i
.0266
.167
.30876
442
.42328
431
.974H
5,i
.0266
.168
.31319
443
.42760
43i
.97416
5,i
.0265
.169
.31762
443
.43191
432
•97421
5,i
.0265
2.170
4.32205
444
4.43623
432
0.97426
5,i
1.0264
0,5
.171
.32649
444 1 .44056
433
•97431
5,i
.0264
.172
.33093
444
.44488
433
.97436
5J
.0263
•173 .33538
445
.44922
434
•97441
5,i
.0263
.174 i .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 i -35321
447 .46659
435
.97462
5,o
.0260
.178
.35768
447 .4/095
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
i .0259
o,5
.181
.37111
448 .48404
437
.97482
5,o
.0258
.182
.37560
44<j .48842
438
.97487
5,o
.0258
.183
.38009
449 i .49279
438
•97491
5,o
.0257
.184
.38459
450
.49718
438
.97496
4,9
• 0257
2.185
4.38009
450
4-50156
439
0.97501
4,9
1.0256
o,5
.186
•39359
451
.50595
439
.97506
4,9
.0256
.187
•3Q8TO
451
.51035
440
•975II
4,9
• 0255
.188
.40261
451
•514/5
440
.97516
4,9
• 0255
.189
.40713
452
.51916
441
•97521
4,9
.0254
2. TOO
4.4II65
452
4.52356
44i
0.97526
4,9
1.0254
o,5
.191
.41617
453
.52798
442
•97531
4,9
• 0253
.192
.42070
453
.53240
442
.97536
4-')
• 0253
•193
.42524
454
.53682
443
•97541
4,0
.0252
.194
.42978
454
.54125
443
•97545
4,8
.0252
2.195
4.43432
455
4.54568
443
0.97550
j.1^ 1.0251
o,5
.196
.43887
455
•55012
444
•97555
4,8 .0251
.197
.44342
455
• 55456
444
.97560
. 0250
.198
.44798
456
• 55900
445
.Q7565
4.S .0250
.199
•45254
456
.56345
445
.97570
4*
.0249
2.2OO
4.457H
457
4.56791
446
0.97574
4-*
1.0249
o,5
U
tan gd u
«Fo'
sec gd u
u> F
sin gd u
w F
esc gd u
• IV
SMITHSONIAN TABLES
149
Natural Hyperbolic Functions.
u
sinhu
»F,/
cosh u
«F0'
tanh u
«Fo'
coth u
«F0'
2.2OO
4-457II
457
4.56791
446
0.97574
4,8
1.0249
o,5
.2OI
.202
.46168
.46625
457
458
.57237
.57683
446
447
.97579
.97584
4,8
4,8
.0248
.0248
.203
.47083
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
•48459
459
•59473
448
.97603
4,7
.0246
.207
.48919
460
•59922
449
.97608
4,7
.0245
.208
•49379
460
.60371
449
.97612
4,7
.0245
.209
.-IC840
461
.60821
450
.97617
4,7
.0244
2.2IO
4.50301
461
4.61271
450
0.97622
4,7
1.0244
0,5
.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
2.215
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
o,5
.221
. 55402
466
.66252
455
.97673
4,6
.0238
.222
.55839
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
4-5727I
468
4.68078
457
0.97691
4,6
1.0236
o,5
.226
. 57730
409
.68535
458
.97696
4,6
.0236
.227
.58208
469
.68993
458
.97700
4,5
.0235
.228
08677
469
.69451
459
•97705
4,5
.0235
.229
.59M7
470
.69910
459
.97709
4,5
.0234
2.230
4o06i7
4/0
4.70370
460
0.977H
4,5
1.0234
0,5
.231
.60087
471
.70830
460
.97718
4,5
.0233
.232
.60559
47i
.71290
461
•97723
4,5
• 0233
•233
.61030
472
.71751
461
.Q7727
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
.6389
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
476
.75919
465
.97768
4,4
.0228
• 243
•''577 1
476
•76385
466
•97772
4,4
.0228
.244
477
.76851
466
.97776
4,4
.0227
2.245
4.66724
477
4.77317
467
o.977Sr
4,4
1.0227
o,5
.67202
478
.77784
467
.97785
4,4
.0227
.247
478
.78252
468
.97790
4,4
.0226
.248
479
.78719
468
•97794
4,4
.0226
• 249
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
- F '
sec gd u
« F,/
sin oil u
»FQ'
esc gd u
»F0'
iMITHSONIAN TABLES
Natural Hyperbolic Functions.
u
sinh u
«F,/
cosh u
<•» Fo'
tanh u
»*'
coth u
« F,'
2.250
4.69II7
480
4.79657
409
0.97803
4,3
1.0225
o,5
.251
.69597
480
.80126
470
.97807
4,3
.0224
.252
.70077
48l
.80506
470
.97811
4,3
.0224
.253
.70558
481
.81066
471
.978l6
4,3
.0223
.254
.71039
482
.81537
471
.97820
4,3
.0223
o,5
. 2.255
4.7I52I
482
4.82008
472
0.97824
4,3
1.0222
0,4
.256
.72003
482
.82480
472
.97829
4,3
.0222
.257
.72486
483
.82952
472
.97833
4,3
.0222
.258
.72069
483
.83425
473
.97837
4,3
.0221
.259
•73453
484
.83898
473
.97841
4,3
.0221
2.260
4-73937
484
4.84372
474
0.97846
4,3
1.0220
0,4
.261
•74422
485
.84846
474
.97850
4,3
.0220
.262
•74007
485
.85321
475
.97854
4,2
.0219
.263
•75392
486
•85796
475
.97858
4,2
.0219
.264
.75878
486
.86272
476
.97863
4,2
.0218
2.265
4.76365
487
4.86748
476
0.97867
4,2
1. 02l8
0,4
.266
.76852
487
.87224
477
.97871
4,2
.0218
.267
.77339
488
.87701
477
.97875
42
.O2I7
.268
.77827
488
.88179
478
.97879
4,2
.0217
.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
.0215
.272
.79784
490
.90094
480
.97896
4,2
.0215
.273
.80274
491
.00574
480
.97900
4,2
.0214
.274
.80765
491
.91055
481
•97905
4,1
.0214
2.275
4.81256
492
4.9I536
481
0.97909
4,1
I.02I4
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.02II
0,4
.281
.84214
494
.94432
484
.97933
4J
.O2II
.282
.84709
495
.94917
485
•97937
4,1
.O2I I
.283
.85204
495
.95402
485
•97942
4J
.O2IO
.284
.85699
496
.95887
486
.97946
4,1
.O2IO
2.285
4.86196
496
4.96373
486
0.97950
4,1
1.0209
0,4
.286
.86692
497
.96859
487
.97954
4,1
.0209
.287
.87189
497
.97346
487
.97958
4,0
.0208
.288
.87687
498
.97834
488
.97962
4,0
.0208
.289
.88185
498
.98322
488
.97966
4,o
.0208
2.200
4.88684
499
4.98810
489
0.97970
4,0
1.0207
0,4
.291
.89183
499
.99299
489
•97974
4,o
.0207
.292
.89682
500
.99789
490
.97978
4,0
.0206
.293
.90182
500
5-00279
490
.97982
4,0
.O2O6
.294
.90683
501
.00769
491
.97986
4,0
.0206
2.295
4.91184
50i
5.01260
491
0.97990
4,0
1.0205
0,4
.296
.91685
502
-OI75I
492
•97994
4,o
.0205
.297
.92187
502
.02243
492
.97998
4,0
.O2O4
.298
.92690
503
.02736
493
.98002
4.0
.O2O4
• 299
.93193
503
.03229
493
.98006
3,9
.0203
2.300
4.936oj6
504
5.03722
494
0.98010
3,9
I.02O3
0,4
• •
t=
tan gd u
«Fo'
sec gd u
-Fo'
sin gd u
«F0'
csc gd u
« F,/
SMITHSONIAN TABLES
Natural Hyperbolic Functions.
u
sinh u
" F,,'
cosh u
O.FO'
tanh u
O.FO'
coth u
«F0'
2.300
4.93696
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
.0202
.304
.95715
506
.05701
496
.98025
3,9
.0201
2.305
4.96221
506
5.06197
496
0.98029
3,9
I. 0201
0,4
.306
.96727
507
.06693
497
.98033
3,9
.0201
.307
.97234
507
.07190
497
.08037
3,9
.O20O
.308
•97742
508
.07688
408
.98041
3,9
.O2OO
.309
.98250
508
.08186
498
.98045
3,9
.0199
2.310
4.08758
509
5.08684
499
0.98049
3,9
I.OI99
0,4
31 1
.99267
509
.09183
499
.98053
3,9
.0199
.312
.313
•99777
5.00286
5io
.09683
. 10183
500
500
.98056
.08060
3,8
3,8
.0108
.0108
.314
.00797
5ii
.10683
501
.98064
3,8
•0197
2.315
5.01308
5ii
5.III84
50i
0.98068
3,8
I. 0197
0,4
.316
.01819
512
.11686
502
.98072
3,8
.0197
.317
.318
.02331
.02844
512
513
.12188
.12691
502
503
.98076
.98079
3,8
3,8
.0196
.0196
.319
.03357
513
.13194
503
.98083
3,8
.0195
2.320
5.03870
5H
5.13697
504
0.98087
3,8
I. 0195
0,4
.321
.04384
514
. 14202
504
.98091
3,8
.0195
.322
.04898
515
.14706
505
• 980.75
3,8
,0194
.323
•05413
515
.15211
505
.08098
3,8
.0194
.324
.05929
5i6
.15717
506
.98102
3,8
.0193
2.325
5.06445
5i6
5.16223
506
0.98106
3,8
I. 0193
0,4
.326
.06061
517
. 16730
507
.98110
3,7
.0193
.327
.07478
517
• 17237
507
.98113
3,7
.0192
.328
.07906
5i8
. 17745
508
.98117
3,7
.0192
.329
.08514
5i8
. 18253
509
.98121
3,7
.0192
2.330
5-00032
519
5.18762
50Q
0.08124
3,7
1.0191
0,4
.331
.09551
519
.19271
510
.98128
3,7
.0191
.332
.10071
520
. I978I
510
-98132
3,7
.0100
.333
.10591
520
. 20291
511
.98136
3,7
.0100
•334
.mil
521
.20802
5ii
.08139
3,7
.0190
2.335
5.11632
521
5.2I3U
512
0.98143
3,7
1.0189
0,4
.336
.12154
522
.21825
512
.O8l47
3,7
.0189
•337
. 12676
522
.22338
.98150
3,7
• .0188
.338
.13199
523
.22851
513
•98154
3,7
.0188
•339
.13722
523
.23364
.98158
3,7
.0188
2.340
5.14245
524
5-23878
5T4
0.98161
3,6
1.0187
0,4
•34'
. ^4770
524
.24393
515
.98165
3,6
.0187
•342
.15294
525
.24908
515
.< 8i\>;>
3,6
.0187
• 343
.15819
525
.25423
.98172
3,6
.0186
.344
• 16345
526
•25939
5i6
3,6
.0186
2.345
5.16871
526
5.26456
517
0.98179
3,6
1.0185
0,4
.17*8
527
.26973
517
.08183
3,6
.0185
• 347
• 17925
527
.27491
5i8
.08187
3,6
.0185
.348
528
.28009
5i8
.98100
3,6
.0184
• 349
-.18981
529
.28528
519
.08194
3,6
.0184
2.350
S.I95IO
529
5.29047
520
0.98197
3,6
1.0184
0,4
u tan gd u
«F0'
tec gd u
-Fo'
sin gd u
-FU-
csc gd u
<oF0'
SMITHSONIAN TABLCS
152
Natural Hyperbolic Functions.
u
sinh u
• Fo'
cosh u
-Fo'
tanhu
">F0'
coth u
• ft*
2.350
5.I95IO
529
5.20047
520
0.98197
3,6
I.OI84
0,4
.351
.20039
530
.a$>$67
5-?0
<2OI
3,6
.0183
.352
.20569
530
.30087
521
.98204
3,6
.0183
.353
.2IIOO
531
.30608
521
.98208
3,6
.0182
.354
.21630
531
.31129
522
.98212
3,5
.0182
2.355
5.22162
532
5.3I65I
522
0.98215
3,5
I.OI82
OA
.356
.22694
532
.32174
523
.98219
3,5
.Ol8l
• 357
• 2322(>
533
.32697
523
.98222
3,5
.0181
.358
•23759
533
•33220
524
.98226
3,5
.Ol8l
• 359
.24293
534
•33744
524
.98229
3,5
.0180
2.360
5.24827
534
5.34269
525
0.98233
3,5
I.OlSo
0,4
.361
.25361
535
•34794
525
.98236
3,5
.Ol8o
.362
.25896
535
.35319
526
.98240
3,5
.0179
.363
• -"'432
536
.35845
526
•98243
3,5
.0179
.364
.26968
536
.3637^ 527
.98247
3,5
.0178
2.365
5.27504
537
5.36899 528
0.98250
3,5
I.OI78
OA
.366
.28042
537
.37427 528
.98254
3,5
.0178
.367
.28579
538
•37955 529
.98257
3,5
.0177
.368
.-'9118
538
.38484 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
I.OI76
OA
• 371
.30735
540
.400/4 531
.98271
3,4
.0176
• 372
.31276
54i
.40605 531
.98274
3,4
.0176
• 373
.31817
54i
.4H37 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
i. 0175
0,4
.376
.33442
543
•42735 533
.98288
3,4
.0174
OA
•377
.33985
543
.43268 534
.98291
3,4
.0174
OA
•3/8
.34529
544
.43803 535
.98295
3,4
• 0173
0,3 ;
• 379
.35073
544
•44337 535
.98298
3,4
• 0173
o,3
2.380
5.356i8
545
5.44873 536
0.08301
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
•37*55
546
.46482
537
.g&il
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
o,3
.386
•38897
548
.48096
539
.98322
3,3
.0171
.387
.39445
549
• 4&J35 539
.98325
3,3
.0170
.388
•39994
549
•491/5 540
.<A^8
3,3
.0170
.389
•40543
550
.49715 541
.98331
3,3
.0170
2.390
5.41093
550
5.50256 541
0.98335
3,3
1.0169
o,3
• 391
.41644
55i
.50798 542
.98338
3,3
.0169
• 392
•42195
55i
.51339 54-'
.98341
3,3
.0169
•393
.42746
552
.51882 543
.98345
3,3
•394
.43299
55-?
.52425 543
•98348
3,3
.01 .8
2.395
5.43851
553
5.52969 544
0.98351
3,3
[.0166
0,3
.396
•44405
554
•53513 544
.98354
3,3
•397
.44958
554
.54057 545
.98358
3,3
.398
•45513
555
•54603 546
.98361
3,3
.0167
• 399
.46068
555
.55148 546
.98364
3,2
.0166
2.400
5.46623
556
5.55695 547
0.98367
3,2
I. 0166
o,3
u
tan gd u
<o Fo'
sec gd u «•» Fo'
sin gd u
F
csc gd u
u> F.'
SMITHSONIAN TABLES
153
Natural Hyperbolic Functions.
u
sinh u
• Fb'
cosh u
«F0'
tanh u
wF0'
cothu
«F0'
2.400
5.46623
556
5.55695
547
0.08367
3,2
I. Ol66
o,3
.401
.471/9
556
.56242
547
•98371
3,2
.0166
.402
•47735
557
06789
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
0.08384
3,2
1.0164
o,3
.406
.49967
559
.58984
550
•98387
3,2
.0164
.407
.50526
560
.59535
55i
.98390
3,2
.0164
.408
.51086
560
.6oo85
55i
.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
1.0163
o,3
.411
.52769
562
.61741
553
.98403
3,2
.0162
.412
.53331
562
.62294
553
.98406
3,2
.0162
.413
.53893
563
.62848
554
.08409
3,2
.0162
.414
.54456
563
.63402
554
.98412
3,2
.Ol6l
2.415
5.55020
564
5.63957
555
0.98415
3,1
1.0161
o,3
.416
.55584
565
.64512
556
.08418
3,1
.0161
.417
.418
.56149
.56715
565
566
.65068
.65624
556
557
.98422
•98425
3,1
3,1
.0160
.0160
.419
.57280
566
.66181
557
.98428
3,1
.0160
2.420
5.57847
567
5.66739
558
0.08431
3,1
1.0159
o,3
.421
.58414
567
.67297
558
.98434
3,1
.0159
.422
.58981
568
.67856
559
.98437
3,1
.0159
.423
•59550
568
.68415
56o
.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
0,3
.426
.61257
570
.70096
56i
.98450
3,1
.0157
.427
.61828
57i
.70658
562
.98453
3J
.0157
.428
.62309
571
.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
3,1
1.0156
0,3
.431 ; .64115
573
.72910
564
•98465
3,0
.0156
.432
.64688
573
•73474
565
.98468
3,o
.0156
•433
.65262
574
* 74039
565
.98471
3,0
.0155
• 434
.65836
575
.74605
566
•98474
3,0
.0155
2.435
• 436
5.66411
086
575
576
5.75I7I
•75738
566
567
0.98477
.98480
3,0
3,0
1.0155
• 0154
o,3
.437
.67563
576
•76305
568
•98483
3,0
• 0154
.438
.68139
577
.76873
568
.98486
3,0-
.0154
•439
.68716
577
•77441
569
.98489
3,o
.0153
2.440
5.69294
578
5.78010
569
0.08492
3,o
1.0153
0,3
• 441
.69872
579
•78580
570
.98495
3,o
• 0153
• 44-'
.70451
579
•79150
570
.98498
3,o
.0152
•443
.71031
580
.79721
57i
.98501
3,o
.0152
• 444
.71611
58o
.80292
572
.98504
3,0
.0152
2.445
5.72I9I
58i
5.80864
572
0.08507
3,0
1.0152
0,3
.72772
58i
.81436
573
.08510
3,0
.0151
•447
.448
•73354
.73936
582
583
.82009
.82583
573
574
.08513
.98516
3,0
2,9
.0151
.0151
.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,:
$ec od u
«F0'
sin od u
-Fo'
esc gd u
-FO'
ITHSONIAM T ABLCS
Natural Hyperbolic Functions.
u
sinh u
«Fu'
cosh u
«F,/
tanh u
«Fo*
cothu
-F •
2.450
5.75103
584
5.83732
575
0.98522
2,9
1.0150
0,3
.451
.75687
584
•84307
.9«525
2,9
.0150
.452
.76271
585
.84883
576
2,9
.0149
• 453
.76856
585
,85460
577
.98530
2,9
.0149
• 454
•7744-'
58'J
.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
.7<J7')'
588
.88352
58o
.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
1.0147
0,3
.461
.81559
590
.90094
582
.98554
2,9
.0147
.462
.82149
591
.90675
582
.98556
2,9
.0146
• 463
.82740
591
.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
.5«57I
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
0.98579
2,8
1.0144
0,3
.471
.87489
596
•95939
587
.98582
2,8
.0144
• 372
.88085
597
.96527
588
.98585
2,8
.0144
.473
.88682
597
.97115
589
.08588
2,8
.0143
•474
.89279
498
•97704
589
.98590
2,8
.0143
\
2.475
5.89877
598
5-98294
590
0.98593
2,8
1.0143
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
.08615
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
.08629
2,7
.0139
• 489
.98311
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
600
.98637
2,7
.0138
.402
6.00134
608
.08408
600
.98640
2,7
.0138
•493
.00743
609
.00009
601
.98643
2,7
.0138
•494
.01352
610
.09610
001
.98645
2,7
.0137
2-495
6.01962
610
6.IO2II
602
0.98648
2,7
I. 0137
o,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
0,3
u
tan gd u
«FO'
sec gd u
• FO'
sin gd u
• FQ'
csc gd u
«FO'
SMITHSONIAN TABLES
155
Natural Hyperbolic Functions.
u
sinh u
W FO'
cosh u
<oF0'
tanh u
« Fo'
coth u
« Fo'
2.500
6.05020
6l3
6.13229
605
0.58661
2,7
1.0136
0,3
.501
.05634
614
. 13834
600
.58664
2,7
.0135
.502
.OJ248
614
.14440
6o5
.58557
2,6
.0135
.503
.06863
615
• 15047
607
.98669
2,6
.0135
.504
.07478
616
.15654
607
.58672
2,6
.0135
2.505
6.08094
616
6.16262
608
0.58675
2,6
1.0134
0,3
.500
.08711
617
.16870
609
.98677
2,6
.0134
.507
.09328
617
. 17479
609
.98680
2,6
.0134
.508
.09946
618
.18089
610
58683
2,6
.0134
.509
. 10564
619
.18699
611
.58685
2,6
.0133
2.510
6.11183
619
6.19310
611
0.98688
2,6
I. 0133
0,3
•511
.11803
620
. 19921
612
.98550
2,6
.0133
.512
. 12423
621
.20534
612
.98593
2,6
.0132
.513
.13044
621
.21146
613
.98596
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
.58706
2,6
.0131
.518
.16157
624
.24219
616
.58708
2,6
.0131
.519
.16782
625
.24836
617
.58711
2,6
.0131
2.520
6. 17407
625
6.25453
617
0.98714
2,6
1.0130
0,3
.521
.18033
626
.26071
618
.58716
2,6
.0130
.522
. 18659
627
.26689
619
.98719
2,5
.0130
.523
.19286
627
.27308
619
.58721
2,5
.0130
.524
.19514
628
.27927
620
.98724
2,5
.0129
2.525
6.20542
629
6.28548
621
0.08726
2,5
1.0129
0,3
.526
.21171
629
.29169
621
.98729
2,5
.0129
.527
.21800
630
.29790
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
0.58739
2,5
1.0128
0,3
.531
•24324
632
.32282
624
.58741
2,5
.0127
.532
.24957
633
.32907
625
.58744
2,5
.0127
•533
.25590
634
•33532
626
.98746
2,5
.0127
•534
. 26224
634
.34158
626
.98749
2,5
.0127
2.535
6.26858
635
6.34785
627
0.98751
2,5
1.0126
0,3
.536
.27494
635
.35412
627
•58754
2,5
.0126
• 537
.28129
636
.36040
628
•98756
2,5
.0126
• 538
.28766
637
.36668
629
.58759
2,5
.0126
.539
.29403
637
•37297
629
.98761
2,5
.0125
2.540
6.30040
638
6.37927
630
0.98764
2,5
1.0125
0,3
.541
.30678
639
.38557
631
.98766
2,5
.0125
0,3
• 542
« 3 ' 3 1 7
639
.39188
631
.98769
2,4
.0125
0,3
•543
• 31957
640
.30820
632
.98771
2,4
.0124
0,3
•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
• 5-1' '
.33879
''l-
.41710
634
.98778
2,4
.0124
• 547
• 548
•549
.35164
.35807
643
644
.42353
•43623
635
635
636
.58781
.98783
.98786
2,4
2,4
2,4
.0123
.0123
.0123
2.550
6.36451
644
6.44259
636
0.98788
2,4
1.0123
CX2
u
tan gd u
• Fo'
sec gd u
"F"'
sin gd u
.Fo'
csc gd u
»F,'
SMITHSONIAN TABLES
156
Natural Hyperbolic Functions.
u
sinh u
»Fo'
cosh u
w f»
tanh u
«Fo'
coth u
-Fo'
2.550
6.36451
644
6.44259
636
0.98788
2,4
I.OI23
0,2
.551
.37096
645
.44896
637
.98790
2,4
.0122
.552
•37741
646
•45533
638
.98793
2,4
.OI22
• 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
O2
.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. 0120
0,2
.561
•43577
651
.51299
644
.08814
2,4
.0120
.562
.44228
652
644
.98817
2,4
.0120
.563
.44880
653
.52588
645
.98819
2,3
.0120
.564
•45533
653
.53233
646
.98821
2,3
.0119
2.565
6.46187
654
6.53879
646
0.98824
2,3
I. 01 19
0,2
.566
.46841
655
.54525
647
.08826
2,3
.0119
.567
.47496
655
.55173
647
.98828
2,3
.0119
.568
.48152
656
.55820
648
.98831
2,3
.0118
.569
.48808
656
.56469
649
.98833
2,3
.0118
2.570
6.49464
657
6.57n8
649
0.98835
2,3
I.OIlS
0,2
• 571
.50122
658
.57768
650
.98838
2,3
.0118
• 572
.50/80
658
.58418
651
.98840
2,3
.0117
-573
.51439
659
.50069
651
.98842
2,3
.0117
• 574
.52008
660
.59721
652
•98845
2,3
.0117
2.575
6.52758
660
6.60374
653
0.98847
2,3
I.OII7
0,2
.576
.53419
661
.61027
653
•98849
2,3
.0116
• 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
.0116
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
.OII5
.584
.58728
666
.66275
659
.98867
2,3
.0115
2.585
6.59395
667
6.66934
659
0.98870
2,2
I. OII4
0,2
.586
.60062
668
.67594
660
.98872
2,2
.OII4
.587
.60730
668
.68254
661
.98874
2,2
.OII4
.588
.61398
669
.68915
661
.98876
2,2
.OII4
.589
.62068
670
.69577
662
.98878
2,2
.OII3
2.500
6.62738
670
6.70240
663
0.98881
2,2
I. 0113
0,2
• 591
.63408
671
.70003
663
.Q8883
2,2
.OII3
• 592
.64079
672
.71566
664
.98885
2,2
• OII3
• 593
.64751
672
.72231
665
.98887
2,2
.0113
• 594
.65424
673
.72896
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
.0112
.597
.67446
675
.74895
667
.98896
2,2
.OTI2
.598
.68121
676
.75563
668
.98898
2,2
.0111
• 599
.68797
676
.76231
669
.98901
2,2
.OIII
2.600
6.69473
677
6.76901
669
0.98503
2.2
I.OIII
0,2
u
tan gd u
• Fo'
sec gd u
« R,'
sin gd u
• Ft'
csc gd u
• IV
SMITHSONIAN TABLES
Natural Hyperbolic Functions.
u
sinh u
-Fo'
cosh u
O>F;
tanh u
"F0'
cothu
"F0'
2.600
6.69473
677
6.76901
669
0.98903
2,2
I.OIII
0,2
.601
.70150
678
.77570
670
.98905
2,2
.OIII
.602
.70828
678
.78241
671
.98907
2,2
.OIIO
.603
.71507
679
.78912
67*
.98009
2,2
.OIIO
f
.604
.72186
680
.79584
672
.08911
2,2
.0110
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
.98931
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
.80390
688
.87699
680
.98937
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
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
2,0
.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
0.08977
2,0
1.0103
0,2
.636
.94281
701
.01446
694
.98979
2,0
.0103
.637
.94983
702
.02140
695
.98981
2,O
.0103
.638
.95685
703
.02835
696
.98983
2,O
.0103
.639
.96388
704
•03532
696
.98985
2,O
.0103
2.640
6.97092
704
7.04228
697
0.98987
2,0
I.OI02
0,2
.641
•97797
705
.04926
698
.98989
2,0
.0102
.98502
706
.05624
699
.98991
2,O
.0102
,99306
706
.06323
699
.98993
2,O
.0102
.(>\\
.99915
707
.07022
700
•98995
2,0
.0102
2.645
7.00622
708
7.07723
701
0.98997
2,O
I.OIOI
0,2
.646
.01330
708
.08423
701
.58999
2,0
.OIOI
.02039
709
.09125
702
.99001
2,0
.OIOI
.648
.02748
710
.09828
703
.09003
2,0
.OIOI
.649
.03458
711
•I053I
703
.99005
2,0
.OIOI
2.650
7.04169
711
7.H234
704
0.99007
2,0
I.OIOO
0,2
V
tan gd u
«F0'
sec gd u
-Fo'
sin gd u
wF0'
csc gd u
«oF0'
SMITHSONIAN TABLES
158
Natural Hyperbolic Functions.
u
sinh u
«F0'
cosh u
«FO'
tanh u
«F0'
coth u
-F '
2.650
7.04109
711
7-II234
704
0.99007
2,0
I.OIOO
0,2
.651
.0488]
712
. 1 1939
705
.99009
2,0
.0100
.652
•05593
713
.13044
706
.99011
2,0
.0100
.653
.00306
713
.13350
706
.00013
2,0
.0100
.654
.07020
714
. 14057
707
.99015
2,O
.0100
2.655
7.07734
715
7.14764
708
0.90016
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
.99023
1,9
.0009
.659
.10599
718
.17601
711
.09024
1,9
.0099
2.660
7.H3I7
718
7.18312
711
0.09026
,9
1.0098
0,2
.661
.12036
719
.19024
712
.99028
,9
.0098
.662
• 12755
720
. 19736
713
.99030
,9
.0098
.663
• 13475
720
.20449
713
.99032
,9
.0098
.664
.14196
721
.21163
714
.99034
,9
.0098
2.665
7.14918
722
7.21877
715
0.90036
,9
1.0097
0,2
.666
.15040
723
.22593
716
.99038
,9
.0097
.667
. 16363
723
.23309
716
.09040
,9
.0097
.668
.17086
724
.24025
717
.90042
,9
.0097
.669
.17811
725
.24743
718
.99044
,9
.0097
2.670
7.18536
725
7-25461
719
0.99045
,9
1.0096
0,2
.671
. 19262
726
.26180
719
.99047
,9
.0096
.672
.19988
727
.26900
720
.99049
,9
.0096
.673
.20715
728
.27620
721
.00051
,9
.0096
.674
•21443
728
.28341
721
.90053
,9
.0096
2.675
7.22172
729
7.29063
722
0.09055
,9
1.0095
0,2
.676
.22902
730
.29785
723
.99057
,9
.0095
.677
.23632
73i
.30509
724
•99059
,9
.0095
.678
.24363
73i
.31233
724
.90060
i,9
.0095
.679
.25094
732
.31957
725
.99062
,9
.0095
2.680
7.25827
733
7-32683
726
0.09064
i,9
1.0094
0,2
.681
.26560
733
•33409
727
.99066
i,9
.0094
.682
.27293
734
.34136
727
.99068
i,9
.0094
.683
.28028
735
.34864
728
.99070
1,9
.0094
.684
.28763
736
•35592
729
.99072
1,8
.0094
2.685
7.29499
736
7-36321
729
0.90073
1,8
1.0094
0,2
.686
.30236
737
.37051
730
.90075
1,8
.0093
.687
.30973
738
.37782
731
.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
74i
.40711
734
.99084
1,8
.0092
.692
•34671
74i
.41446
735
.99086
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
.90094
1,8
.0091
.697
.38388
745
.45128
738
.00095
1,8
.0091
.698
.39133
746
.45867
739
.90097
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
a. Fo'
sec gd u
«FO'
sin gd u
«F0'
esc gd u
« F '
SMITHSONIAN TABLES
159
Natural Hyperbolic Functions.
u
sinhu
»FO'
cosh u
*>Fo'
tanh u
«Fo'
coth u
«Fo'
2.700
7.40626
747
7-47347
741
0.99101
4
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
.99106
1,8
.0090
.704
.43622
750
.50315
744
.99108
1,8
.0000
2.705
7-44372
751
7.51059
744
0.09110
1,8
1.0090
0,2
.706
.45124
75^
.51804
745
.99111
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
.09117
1,8
.0089
2.710
7.48137
755
7.54791
748
0.99118
1,8
1.0089
0,2
.711
.48892
756
•55539
749
.99120
1,8
.0089
.712
.40648
756
.56288
750
.99122
i,7
.0089
• 713
• 50405
757
.57038
750
.99124
i,7
.0088
.714
.51162
758
.57789
75i
.99125
i,7
.0088
2.715
7.51920
759
7.58541
752
0.09127
1,7
1.0088
O,2
.716
.52679
759
.59293
753
.99129
i,7
.0088
.717
•53439
760
.60046
753
.99131
1,7
.0088
.718
.54199
76i
.60800
754
.99132
i,7
.0088
.719
.54960
762
.61555
755
•99134
1,7
.0087
2.720
7.55722
762
7.62310
756
0.99136
i,7
1.0087
0,2
.721
.56485
763
.63066
756
•99138
1,7
.0087
.722
.57249
764
.63823
757
•99139
i,7
.0087
.723
•58013
765
.64580
758
.99141
i,7
.0087
.724
.58778
765
.65339
759
•99143
i,7
.0086
2.725
7-59543
766
7.66058
760
0.99144
i,7
1.0086
0,2
.726
.60310
767
.66858
760
•09146
i,7
.0086
.727
.61077
768
.67619
76i
.99148
i,7
.0086
.728
.61845
768
.68380
762
.99150
i,7
.0086
.729
.62614
769
.69142
763
•99151
1,7
.0086
2.730
7.63383
770
7.69005
763
0.99153
1,7
1.0085
0,2
.731
•64154
77i
.70669
764
.99155
i,7
.0085
.732
.64925
77i
.71434
765
.99156
i,7
.0085
•733
.65697
772
.72199
766
.99158
i,7
.0085
• 734
.66469
773
.72965
766
,99160
1,7
.0085
2.735
7.67242
774
7-73732
767
0.99161
i,7
1.0085
0,2
.736
.68017
774
•74500
768
.90163
i,7
.0084
• 737
.68791
775
.75268
769
•99165
i,7
.0084
.738
.69567
776
.76037
770
.^9166
i,7
.0084
•739
.70344
777
.76807
770
.99168
i,7
.0084
2.740
7.71121
778
7.77578
77 1
0.99170
i,7
1.0084
O,2
• 741
.71809
778
.78349
772
.09171
i,7
.0084
.742
.72677
779
.79122
773
.99173
1,6
.0083
• 743
•73457
780
.70895
773
.99175
1,6
.0083
• 744
•74237
78i
.80668
774
.09176
1,6
.0083
2.745
7.75018
78i
7.81443
775
0.09178
1,6
1.0083
O,2
.75800
782
.82219
776
.99179
1,6
.0083
• 747
783
•82995
777
.99181
1,6
.0083
.748
784
.83772
777
.90183
1,6
.0082
•7*150
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
- F,;
sec gd u
*»F0'
sin gd u
«•> F,;
esc gd i!
<oFo'
SMITHSONIAN TABLES
lf:0
Natural Hyperbolic Functions.
u
sinh u
«F0'
cosh u
WF,;
tanh u
u, F;
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
1,6
.0081
2-755
7.82872
789
7-89232
783
0.99194
1,6
1.0081
0,2
.756
.83661
790
.90016
784
.99196
1,6
.0081
• 757
.84452
791
.90800
784
.99197
1,6
.0081
.758
.85243
792
.91585
785
.99199
1,6
.0081
• 759
.85035
792
.92370
786
.99200
1,6
.0081
2.760
7.85828
793
7.93157
787
0.99202
1,6
1.0080
0,2
.761
.87621
794
•93944
788
.99204
1,6
.0080
.762
.88415
795
•94732
788
.99205
1,6
.0080
.763
.89211
796
•95521
789
.99207
1,6
.0080
.764
.90006
796
.96310
790
.99208
1,6
.0080
2.765
7.90803
797
7.97IOI
791
0.99210
1,6
1.0080
0,2
.766
.91601
798
.97892
792
.09212
1,6
.0079
.767
.92399
799
.98684
792
.99213
1,6
•0079
.768
.93198
799
.99477
793
.99215
1,6
.0079
.769
.93998
800
8.00270
794
.99216
1,6
.0079
2.770
7-94799
801
8.01065
795
0.09218
1,6
1.0079
0,2
• 771
.95600
802
.01860
796
.99219
1,6
.0079
.772
.96402
803
.02656
756
.99221
1,6
.0079
• 773
.97205
803
.03453
797
.99222
i,5
.0078
• 774
.98009
804
.04250
798
.99224
i,5
.0078
2.775
7.98814
805
8.05049
799
0.99226
i,5
1.0078
0,2
.776
.99619
806
.05848
800
.09227
1,5
.0078
.777
8.00426
807
.06648
800
.99229
i,5
.0078
.778
.01233
807
.07449
801
.99230
i,5
.0078
• 779
.02O40
808
.08251
802
.99232
i,5
.0077
2.780
8.02849
809
8.00053
803
0.09233
i,5
1.0077
0,2
.781
.03659
810
.09856
804
.59235
i,5
.0077
.782
.04469
811
.10660
804
.99236
1,5
.0077
.783
.05280
811
.11465
805
.09238
1,5
.0077
.784
.06092
812
.12271
806
.99239
1,5
.0077
2.785
8.06004
813
8.13077
807
0.99241
i,5
1.0077
0,2
.786
.07718
814
.13885
808
.99242
i,5
.0076
.787
.08532
815
•14693
809
.99244
i,5
.0076
.788
•09347
816
. 15502
809
.99245
1,5
.0076
.789
. 10163
816
.16311
810
.99247
i,5
.0076
2.700
8.10080
817
8.17122
8xi
0.99248
i,5
1.0076
0,2
.791
.11797
818
• 17933
812
.99250
i,5
.0076
.792
.12616
819
. 18746
813
.90251
i,5
.0075
.793
. T 3435
820
• 19559
813
.99*53
TO
.0075
• 794
. M255
820
.20373
814
•59254
1,5
.0075
2.795
8.15076
821
8.21187
815
0.99256
i,5
1.0075
0,2
.796
.15897
822
.22003
816
•09257
i,5
• 0075
0,2
• 797
. 16720
823
.22819
817
-992Sg
i,5
.0075
0,2
.798
• 17543
824
.23636
818
.019260
i,5
.0075
0,2
.799
. 18367
824
.24454
818
.99262
i,5
.0074
0,1
2.800
8.19192
825
8.25273
819
0.09263
1,5
1.0074
0,1
u
tan gd u
»FO'
sec ad u
-FO'
sin gd u
«F0'
esc gd u
-IV
SMITHSONIAN TABLES
161
Natural Hyperbolic Functions.
u
sinhu
«F0'
cosh u
-Fo'
tanhu
»F0'
coth u
-IV
2.800
8.19192
825
8.25273
819
0.99263
,5
1.0074
0,1
.801
.20018
826
.26092
820
.99265
,5
.0074
.802
.20844
827
.26913
821
.99266
,5
.0074
.803
.21671
828
•27734
822
.99268
,5
.0074
.804
.22499
829
.28556
822
.99269
,5
.0074
2.805
8.23328
829
8.29379
823
0.99270
,5
1.0073
0,1
.806
.24158
830
.30203
824
.99272
,5
.0073
.807
.24989
831
.31027
825
.99273
.0073
.808
. 25820
832
.31853
826
.99275
!,4
.0073
.809
.26653
833
.32679
827
.99276
1,4
.0073
2.810
8.27486
834
8.33506
827
0.99278
1,4
1.0073
0,1
.811
. 28320
834
•34334
828
.99279
.0073
.812
.29154
835
.35163
829
.99281
M
.0072
.813
.29990
836
•35992
830
.99282
.0072
.814
.30826
837
.36823
831
.99283
1,4
.0072
2.815
8.31664
838
8.37654
832
0.99285
1,4
1.0072
0,1
.816
.32502
838
.38486
833
.99286
.0072
.817
.33341
839
•39319
833
.99288
M
.0072
.818
.34180
840
.40153
834
.99289
1,4
.0072
.819
•35021
841
.40987
835
.99291
.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
.0071
.823
.38391
844
•44334
838
.59296
!,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
01
.826
.40928
847
•46853
84I
•99300
1,4
.0070
.827
.41776
848
.47695
842
.09302
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
850
8.50224
844
0.99306
1,4
1.0070
0,1
.831
.45173
851
.51068
845
•99307
1,4
.0070
.832
.46025
852
•5I9I4
846
•99309
1,4
.0070
.833
.46877
853
.52760
847
•99310
1,4
.0069
.834
.47730
854
.53608
848
•993II
.0069
2.835
8.48584
854
8.54456
849
0.99313
i,4
1.0069
0,1
.836
•49439
855
.55305
849
•99314
J A
.0069
.837
.50295
856
.56155
850
.99316
T»4
.0069
.838
.5H5I
857
.57006
851
.99317
1,4
.0069
.839
.52009
858
.57857
852
.99318
1,4
.0069
2.840
.841
.842
8.52867
.53726
.54586
|9
860
8.58710
.59563
.60417
853
854
855
0.99320
.99321
. .99322
1,4
1,4
1.0069
.0068
.0068
0,1
.843
.844
•55447
.56309
86 1
862
.61272
.62128
855
856
.99324
.99325
1,3
1,3
.0068
.0068
1.845
.846
.848
.849
8.57I7I
,#035
,58899
.60630
863
864
865
866
866
8.62985
.63842
.64701
.65560
.66420
857
858
859
860
861
0.99326
.99328
.99329
•99330
•993'32
1,3
1,3
1,3
1,3
1,3
1.0068
.0068
.0068
.0067
.0067
0,1
2.850
867
8.67281
861
0.99333
1,3
1.0067
0,1
u
•SBB
e» -_ ..
tan ad u
-
«F0'
-'
sec gd u
— _
.
sin ad u
— __
a> F,'
•••MHMMH
esc ad u
^^mmmmimmmmfmm
coFo'
^•QVMMBBMIBB^^BMV
162
Natural Hyperbolic Functions.
u
sinh u
«F0'
cosh u
<« Fo'
tanh u
«- F,/ coth u
-Fo'
2.850
8.61497
867
8.67281
86 1
0.99333
1,3 1.0067
0,1
.851
.62365
868
.68143
862
•99334
1,3
.0067
.852
-63233
869
.69006
863
.99336
1,3
.0067
.853
.64103
870
.69870
864
1,3
.0067
.854
.64973
871
.70734
865
•99338
1,3
.0067
2.855
8.65844
872
8.71600
856
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
.85^
•69337
875
.75070
869
•99345
1,3
.0066
2.860
8.70213
876
8.75940
870
0.09346
1,3
1.0066
O,I
.861
.71089
877
.76810
871
.99348
1,3
.0066
.862
.71967
878
.77682
872
•99349
1,3
.0066
.863
.72843
879
.78554
873
•99350
1,3
.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
.86^
.75484
88 1
.81177
875
•99354
1,3
.0065
.867
-7 >3 <<>
882
.82053
876
•99355
i,3
.0065
.868
.77248
883
.82930
877
•99357
1,3
.0065
.869
.78132
884
.83807
878
•99358
i,3
.0065
2.870
8.79016
885
8.84686
879
0-99359
i,3
1.0065
0,1
.871
.79901
886
.85565
880
•99360
i,3
.0064
.872
.80787
885
.86446
881
•99362
i,3
.0064
-873
.81674
887
.87327
882
•99363
1,3
.0064
.874
.82562
888
.88209
883
•09364
i,3
.0064
2.875
8.83450
889
8.89092
883
0.99365
1,3
1.0064
0,1
.876
.84340
890
.89976
884
•99367
1,3
.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
i,3
1.0063
0,1
.881
.88801
894
.94409
889
•99373
i,3
.otxv;
.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
8.979/1
892
0.99378
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
.99382
1,2
.0062
.889
.95985
902
.01548
896
.99383
1,2
.0062
2.890
8.96887
902
9-02444
897
0.99384
1,2
1.0062
0,1
.891
.97790
903
.03342
898
•99385
1,2
.0062
.892
.98693
904
.04240
899
•99387
1,2
.0062
.893
.99598
905
.05139
900
•09388
1,2
.0062
.894
9-00504
906
.06039
901
•99389
1,2
.0061
2.895
9.01410
907
9.06940
901
0.99390
1,2
i. 0061
0,1
.896
.02318
908
.07842
902
•99391
I,-'
.0061
.897
.03226
909
.08745
903
• 99393
1,2
.0061
.898
•04135
910
.09648
904
•99394
1,2
.0061
.899
•05045
911
. 10553
005
•99395
1,2
.0061
2.900
9.05956
911
9.H458
906
0.99396
1,2
i. 0061
0,1
u
tan ad u
O.FO'
sec gd u
«FO'
sin gd u
» Fo' csc gd u
-FO'
SMITHSONIAN TABLES
Natural Hyperbolic Functions.
V
sinh u
»FV
cosh u
«F0'
tanh u
o> FO'
coth u
• Fo'
2.OOO
905956
911
9.H458
906
0.99396
1,2
I. 0061
0,1
.QOI
ofiS'yS
912
.12365
907
.99398
1,2
.0061
.002
.003
'.07781
.08695
913
914
. 13272
.14180
go8
909
•99399
.99400
1,2
1,2
.0060
.0060
.904
.09609
915
.15000
910
.99401
1,2
.0060
2.905
9.10525
9l6
9.16000
911
0.09402
1,2
I. 0060
0,1
.006
.11441
917
.16911
911
.09403
1,2
.0060
.007
•I2J59
9l8
.17823
912
•09405
1,2
.0060
.608
. 13277
919
.18735
913
.09406
1,2
.0060
.909
.14196
92O
.19649
914
.99407
1,2
.0060
2.910
9.I5II6
921
9.20564
915
0.99408
1,2
I. 0060
0,1
.911
.16037
921
.21479
916
.99409
1,2
.0059
.912
.16959
922
.22396
917
.99411
1,2
.0059
.913
.17882
9'23
.23313
918
.09412
1,2
.0059
.914
.18806
924
.24232
919
•99413
1,2
.0059
2.915
9- 19730
925
9.25I5I
920
0.09414
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
.90418
1,2
.0059
.919
.23438
929
.28837
923
.99419
1,2
.0058
2.920
9.24368
930
9.29761
924
0.09420
1,2
1.0058
0,1
.921
.25298
931
.30686
925
.09421
1,2
.0058
.922
.26229
932
.31612
926
.09422
1,2
.0058
.923
.27161
933
.32538
927
•99423
M
.0058
1 -924
• -
.28094
933
.33466
928
.99425
1,1
.0058
2.925
9.29028
934
9-34395
929
0.99426
1,1
1.0058
0,1
.926
.29963
935
.35324
930
.09427
1,1
.0058
.927 .30899
936
•36254
931
.09428
1,1
.0058
.928
•31835
937
.37186
932
.99429
1,1
.0057
•929
•32773
938
.38118
933
.99430
1,1
.0057
2.930
9.33712
939
9"3905l
934
0.99531
1,1
1.0057
0,1
•931
.34651
940
.39986
935
•99433
1,1
.0057
•932
.35592
941
.40921
936
•99434
1,1
.0057
•933
.36533
942
.41857
937
•99435
1,1
• 0057
•934
•37475
943
.42794
937
•99436
1,1
.0057
2.935
9.38419
944
9.43732
938
0.99437
1,1
1.0057
0,1
.936
.39363
945
.44671
939
.99438
1,1
.0057
.40308
946
.45610
940
.99439
1,1
.0056
.938
.4U54
947
.46551
941
.99440
1,1
.0056
.42201
947
•47493
942
.99441
1,1
.0056
9-43MG
948
9-48436
943
0-99443
1,1
1.0056
0,1
949
•49379
944
.99444
1,1
.0056
.45048
950
•50324
94'5
•99445
1,1
.0056
951
.51269
946
•99446
1,1
.0056
•46950
952
.52216
947
•99447
1,1
.0056
953
9.53163
948
0.99448
1,1
1.0055
0,1
954
.5-111-'
949
.99449
1,1
.0055
955
.55061
950
•99450
i,l
.0055
•948 ooA>7
990
.56011
951
•99451
1,1
.0055
.51723
957
.56963
952
•99453
1,1
.0055
3.950
E>.S*fc
M8
9.57915
953
0.99454
1,1
1.0055
0,1
•
t-nudu
• Fo'
sec gd u
• Fo'
sin gd u
«Fo'
CSC Qd U
" F,/
SMITHSONIAN TABLES
Natural Hyperbolic Functions.
u
sinh u
«F0'
cosh u
«F0'
tanh u
«F0'
coth u
• IV
2.950
9.52681
958
9.57915
953
0.99454
i
i. 0055
0,1
.951
.53639
959
.58868
954
.99455
i
.0055
.952
.54598
960
.59822
955
.994.56
i
.0055
•953
•55559
961
.00777
956
•99457
,
.0055
•954
.56520
962
.61733
957
.99458
•
.0055
2.955
9.57482
963
9.62690
957
0.99459
i
1.0054
0,1
.956
.58445
964
.63648
958
.99460
i
.0054
.957
.59410
965
.64607
959
.99461
i
.0054
.958
.60375
966
.65567
960
.99462
»
.0054
•959
.61341
967
.66528
96i
.99463
l
.0054
2.960
9.62308
967
9.67490
962
0.90464
i
1.0054
0,1
.961
.63276
968
.68452
963
.99465
i
.0054
.962
.64245
969
.69416
864
.99467
i
.0054
.963
.65214
970
.70381
965
.99468
i
.0054
.964
.66185
971
.71347
966
.99469
i
.0053
2.965
9.67157
972
9.72313
957
0-99470
1.0053
0,1
.966
.68130
973
.73281
968
.99471
i
.0053
.967
.69104
974
.74249
969
.99472
j
.0053
.968
.70078
975
.75219
970
•99473
j
.0053
.969
•71054
976
.76190
971
•99474
1,0
• 0053
2.970
9.72031
977
9.77l6l
972
0.00475
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
080
.80082
975
.99478
1,0
.0052
•974
•75947
981
.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
.99481
1,0
.0052
•977
.78895
984
.83989
979
.99482
1,0
.0052
.978
.79879
985
.84969
980
•99483
1,0
.0052
• 979
.8o855
986
.85949
58i
.99484
1,0
.0052
2.980
9.81851
987
9.86930
982
0.00485
1,0
1.0052
0,1
.981
.82839
988
.87913
983
.99486
1,0
.0052
.982
.83827
989
984
.99487
1,0
.0052
.983
.84816
000
.89880
985
.99488
1,0
.0051
.984
.85807
991
190866
986
.99489
I,O
.0051
2.985
9.86798
992
9.91852
987
0.99490
1,0
1.0051
0,1
.985
.87790
993
.92839
988
.99491
1,0
.0051
.987
.88784
994
.93828
989
•99492
1,0
.0051
.988
.89778
995
•94817
950
•99493
1,0
.0051
.989
.00773
996
.95807
991
• 99495
1,0
.0051
2.990
9.9T770
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
1,0
.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
IO.OI77O
997
0.99501
1,0
1.0050
0,1
.996
.97768
1003
.02767
9£8
.99502
1,0
.0050
• 997
.98772
1004
.03765
999
.99503
1,0
.0050
•998
.09776
1005
.04765
IOOO
.99504
1,0
.0050
.999
10.00781
1006
.05/65
IOOI
.99504
1,0
.0050
3.000
10.01787
1007
10.06766
1002
0.99505
1,0
1.0050
0,1
u
tan gd u
wF0'
sec gd u
• FO'
sin gd u
«FO'
esc gd u
«Fo'
SMITHSONIAN TABLES
165
Natural Hyperbolic Functions.
u
sinh u
»Fo'
cosh u
w FO'
tanh u
»F0'
coth u
<oF0'
3.00
IO.OI79
1007
10.0677
IOO2
0.99505
9,9
1.0050
1,0
.01
IO.II9I
1017
10.1683
1012
.99515
9,7
.0049
I,O
.02
10.2212
IO27
10.2700
IO22
.99525
9,5
.0048
I,O
• 03
10.3245
1037
10.3728
1032
•99534
9,3
.0047
0,9
.04
10.4287
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
1090
10.9022
1086
.99578
8,4
.0042
0,8
.09
10.9658
IIOI
11.0113
1097
.99587
8,2
.0041
0,8
3.10
11.0765
1 1 12
11.1215
1108
0.99595
8,1
1.0041
0,8
.11
II.I882
H23
I I . 2328
1119
.99603
7,9
.0040
0,8
. 12
II.3OII
H35
11.3453
1150
.90611
7,8
.0039
0,8
•13
II.4I5I
1146
11.4583
TT42
.09618
7,6
.0038
0,8
•U
H.5303
U57
11.5736
1 153
.99626
7,5
.0038
0,8
3-T5
11.6466
1169
11.6895
1165
0.99633
7,3
1.0037
o,7
.16
II.7O4I
1181
11.8065
1176
.99641
7,2
.0036
o,7
• 17
11.8827
1192
11.9247
Ti83
.59648
7,o
• 0035
o,7
.18
12.0026
1204
12.0442
I2OO
•95655
6,9
.0035
o,7
.19
12.1236
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
0.09700
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
I3M
.99712
5,8
.0029
0,6
.28
13.2691
1331
13-3067
1327
•99717
5,6
.0028
0,6
.29
13.4028
1344
13.4401
1340
.99723
5,5
.0028
0,6
3-30
13-5379
1357
13.5748
1354
0.99728
5,4
1.0027
o,5
•31
13.6743
i37i
13-7108
1367
.99734
5,3
.0027
o,5
•32
I3.8I2I
1385
13.8483
I38l
•09739
5,2
.0026
o,5
•33
13.9513
1399
13.9871
1395
•99744
5,i
.0026
o,5
•34
14.0918
1413
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 I47O
14.7024
1467
.99768
4,6
.0023
o,5
•39
I4.8l6l
1485
14.8498
1482
•99773
4,5
.0023
o,5
3-40
14.9654
1500
14.9987
1497
0.99777
4,4
I.O022
0,4
.41
IS.lKiI 1515
15.1491
1512
.99782
4A
.O022
0,4
.42
[5.2584 1530
15.3011
1527
.99786
4,3
.OO2I
o,4
•43
I5-4-'2T 1545
15-4545
1542
.99790
4,2
.0021
0,4
.44
I56l
15.6095
1558
.99795
4,1
.O02I
0,4
3-45
15-7343 1577
15.7661
1573
0.99799
4,0
I.OO20
0,4
.46
15.8928
1592
15.9242
1589
.99803
3,9
.OO2O
0,4
•47
16.0528
1608
16.0839
I605
.99807
3,9
.0019
0,4
.48
16.2145
1625
16.2453
l62I
.99810
3,8
.OOT9
0,4
16.3777
1641
16.4082
I638
.99814
3,7
.OOI9
0,4
3-50
16.5426
1657
16.5728
1654
0.99818
3,6
I.OOlS
0,4
u
tan gd u
«F0'
sec gd u
« F,/
sin gd u
u>F0'
csc gd u
<oF0'
SMITHSONIAN TABLCS
166
Natural Hyperbolic Functions.
u
sinh u
«F0'
cosh u
• Fo'
tanhu
«Fo'
coth u
3.50
16.5426
1657
16.5728
1654
0.998l8
3/5
I.OOlS
0,4
.51
16.7092
1674
16.7391
1671
.99821
3,6
.0018
OA
.52
16.8774
1691
16.9070
[688
.998aS
3,5
.0018
OA
.53
17.0473
1708
17.0766
1705
. <//S2<S
3,4
.OOI7
0,3
• 54
17.2190
i/-J5
17.2480
1722
.99833
3,4
.0017
0,3
3-55
l7.3<J-'3
1742
17.4210
1739
0.99835
3,3
I.OOI7
0,3
w wy
.#
170674
1760
I7-S
1757
.99838
3,2
.0016
0,3
• 57
17.744-'
1777
17-77-4
1/74
.99842
3,2
.0016
o,3
.58
17.9228
1795
I7.9507
1792
.99845
3.1
.O0l6
0,3
• 59
18. 1032
1813
18.1308
1810
.99848
3,o
.0015
o,3
3.6o
18.2855
1831
18.3128
1829
0.99851
3,0
I.OOI5
0,3
.61
18.4695
1850
18.4966
1847
.99854
2,9
.0015
o,3
.62
18.6554
1868
18.6822
1866
.99857
2,9
.0014
o,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
o,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
.OOI3
o,3
.67
19.6132
1964
19.6387
1961
.99870
2,6
.OOI3
o,3
.68
19.8106
1984
19.8358
1981
.09873
2,5
.OOI3
0,3 i
.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
• 7i
20.4147
2044 20.4391
2O4I
.99880
2,4
.OOI2
0,2
.72
20.6201
2064 20.6443
2052
.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
O,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
O,2
• 78
21.8966
2192
21.9194
2100
.99896
2,1
.0010
O,2
• 79
22.II69
2214
22.1395
2212
.99898
2,0
.0010
O,2
3.8o
22.3394
2236
22.3618
2234
0.99900
2,0
1. 0010
0,2
.81
22.5641
2259
22.5853
2256
.99902
2,0
.0010
0,2
.82
22.7911
2281
22.8131
2279
.99004
1,9
.0010
0,2
.83
23.O204
2304
23.0421
2302
.99906
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
0.09909
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
2420
.99915
1,7
.0009
0,2
.89
24.4452
2447
24.4657
2445
.99916
1,7
.0008
0.2
3-90
24.6911
2471
24.7113
2469
0.09918
1,6
1.0008
0.2
.91
24-9395
2496
24.9595
2494
.99920
1,6
.0008
0,2
.92
25.1903
2521
25.2101
2519
.99921
1,6
.0008
0,2 ;
•93
-'5-4437
2546
25.4633
-'544
.99923
i,5
.0008
0.2
•94
25.6g96
2572
25./K.,0
25/0
•99924
i,5
.0008
0.2
3-95
25.9581
2598
25-9773
2596
0.90926
1.5
1.0007
0,1
.96
26.2191
2624 j 26.2382
.99927
i,5"
.0007
0,1
•97
26.4828
2650
26.5017
2648
.90929
M
.0007
0,1
.98
26.7492
2677
26.7679
2675
.99930
1.4
.0007
0,1 !
• 99
27.OI82
2704
27.0367
2702
.99932
1,4
.0007
0,1 ,
4.00
27.2899
2731
27.3082
2729
0.99933
1,3
1.0007
o.i
u
tan gd u
«Fo'
sec gd u
«FO'
sin gd u
«F0'
csc gd u
«F0'
SMITHSONIAN TABLES
167
Natural Hyperbolic Functions.
u
sinh u
»Fo'
cosh u
O.FO'
tanh u
«- Fo'
coth u
wF0'
4.00
27.2899
2731
27.3082
2729
0.99933
1,3
1.0007
0,1
.01
27.5644
2758
27.5825
2756
.99934
,3
.0007
.02
27.8416
2786
27.8595
2784
.09936
,3
.0006
.03
28.1216
2814
28.1393
2812
.99937
,3
.0006
.04
28.4044
2842
28.4220
2840
.99938
,2
.0006
4-05
28.6000
2871
28.7074
2869
0.99939
,2
I. 0006
0,1
.06
28.9785
20OO
28.9958
2898
.99541
,2
.0006
.07
29.2699
2929
29.2870
2927
.99942
,2
.0006
.08
29.5643
2958
29.5812
2956
•99943
,1
.0006
.09
29.8616
2988
29.8783
2986
.99944
,1
.0006
4.10
30.l6l9
3018
30.1784
3016
0.99945
,1
1.0005
0,1
.11
30.4652
3048
30.4816
3047
.99946
,1
.0005
.12
30.7715
3079
30.7877
3077
.99947
,1
.0005
.13
31.0809
3110
31.0970
3108
.99948
1,0
.0005
.14
3L3934
3141
3L4094
3i39
•99949
1,0
.0005
4-15
3L709I
3172
31.7249
3171
0-99950
1,0
1.0005
0,1
.16
32.0280
3204
32.0436
3203
•99951
1,0
.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
•95954
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
0,9
.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
1.0004
0,1
.26
35-3979
3541
35.4121
3540
.99960
0,8
.0004
.27
35.7538
3577
35.7678
3575
.99961
0,8
.0004
.28
36.1133
3613
36. 1271
3611
.09962
0,8
.0004
.29
36.4764
3649
36.4901
3648
.99962
0,8
.0004
4-30
36.8431
3686
36.8567
3684
0.99963
o,7
1.0004
0,1
•31
37.2135
3723
37.2270
3721
.09964
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
0.99957
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
.59969
0,6
.0003
• 39
40.3140
4033
40.3264
4031
•59969
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
42.38l6
4239
42-3934
4238
.99972
0,6
.0003
4-45
42.8O76
4282
42.8193
4281
0-95973
o,5
1.0003
0,1
.46
43.2380
432*5
43.2495
4324
•99973
o,5
.0003
• 47
tf.6726
4368
43-6841
43r>7
o,5
.0003
.48
44- "17
4412
44.1230
4411
•99974
o,5
.0003
•49
44.5551
4457
44.5663
4456
•99975
o,5
.0003
4-50
45.0030
4501
45.0141
4500
0-99975
o,5
I.OOO2
0,0
u
tan ad u
«FO'
sec gd u
«FO'
sin gd u
«F,,'
csc gd u
<0 FO'
SMITHSONIAN TABLES
168
Natural Hyperbolic Functions.
u
sinh u
.w
cosh u
<- F0'
tanh u
.*•
cothu
-Fo'
4.50
45.0030
4501
45.0141
4500
0.99975
0,5
1.0002
0,0
.51
45-4554
4547
45.4664
4546
.99976
0,5
.0002
.52
45.9124
4592
45.9232
4591
.99976
0,5
.0002
• 53
46.3739
4638
46.3847
•99977
o,5
.0002
.54
46.8401
4685
46.8507
4684
•99977
0,5
.0002
4-55
47.3109
4732
47.3215
4731
0.99978
0,4
1.0002
0,0
.56
47.7865
478o
47.7970
4779
.99978
0,4
.0002
.57
48.2669
4828
48.2772
4827
•99979
0,4
.0002
.58 ! 48.7521
4876
48.7623
4875
•99979
0,4
.OOO2
• 59
49.2421
4925
49.2523
4924
•99979
0,4
.0002
4.60
49-7371
4975
49.7472
4974
0.99980
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
.90981
0,4
.OOQ2
.64
51.7673
5178
51.7770
5177
.99981
0,4
.0002
4-65
52.2877
5230
52.2073
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
.OO02
.68
53.8804
5389
53.8897
5388
•99983
0,3
.0002
.69
54-4220
5443
54.4312
5442
.99983
0,3
.0002
4-70
54.0690
5498
54.9781
5497
0.99983
0,3
1.0002
0,0
• 71
55.5216
5553
55.5306
5552
.99984
0,3
.OOO2
• 72
56.0797
5609
56.0886
5608
.90084
o,3
.OOO2
• 73
56.6434
5665
56.6522
5664
.99984
0,3
.0002
.74
57.2127
5722
57.2215
5721
•99985
0,3
.0002
4-75
57.7878
5780
57-7965
5779
0.09985
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
.0001
• 78
59.5480
5956
59.5564
5955
•99986
0,3
.0001
• 79
60. 1465
6015
60.1548
6015
.99986
0,3
.0001
4.80
6o.75H
6076
60.7593
6075
0.99986
0,3
I. OOOI
0,0
.81
61.3617
6137
61.3699
6136
.99987
0,3
.0001
.82
61.9785
6199
61.9866
6198
.99987
o,3
.0001
•83
62.6015
6261
62.6095
6260
.99987
o,3
.OOOI
• 84
63.2307
6324
63.2386
6323
.99987
0,3
.0001
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
4.00
67.1412
6715
67.1486
6714
0.99989
0,2
I. OOOI
0,0
.91
67.8160
6782
67-8234
6782
0,2
.0001
.92
68.4977
6850
68.5050
6850
.99989
0,2
.OOOI
•93
69.1861
6919
09.1934
6919
.90900
O,2
.OOOI
•94
69.8815
6989
69.8887
6988
.99990
0,2
.0001
4-95
70.5839
7059
70.5910
7058
0.90990
0,2
I. OOOI
0,0
.96
71.2934
7130
7L3004
7129
.99990
0,2
.0001
• 97
72.0100
7202
72.0169
7201
.99990
0,2
.OOOI
.98
72.7338
7274
72.7406
7273
.00991
0,2
.OOOI
•99
73-4648
7347
73.4716
7346
.99991
0,2
.0001
S.oo
74.2032
7421
74.3099
7420
0.99991
0,2
I. OOOI
0.0
u
tan gd u
«FO'
sec gd u
-Fo'
sin gd u
»•> F '
csc gd u
»F,'
SMITHSONIAN TABLES
169
Natural Hyperbolic Functions.
u
sinh u
wF0'
cosh u
"F0'
tanh u
"F0'
coth u
U>FO'
5.00
74.2032
7421
74-2099
7420
0.99991
0,2
I.OOOI
0,0
.01
74.94^0
7496
74-9557
7495
.99991
0,2
.0001
.02
75.7023
7571
75.7090
7570
.99991
0,2
.0001
•03
76.4632
7647
76.4608
7646
.99991
0,2
.0001
.04
77.2318
7724
77-2382
7723
.99992
0,2
.0001
5-05
78.0080
7801
78.0144
7801
0.99992
O,2
I.OOOI
0,0
.06
78.7921
7880
78.7984
7870
.99992
0,2
.0001
.07
79.5840
7959
79.5503
7958
.99992
0,2
.0001
.08
80.3839
8039
80.3901
8038
.99992
0,2
.0001
.09
81.1918
8120
81 . 1980
8119
.99992
O,2
.0001
5.10
82.0079
8201
82.0140
8201
0.09993
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.IS
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
8706
87.0603
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
9064
90.6389
9063
0.99994
0,1
I.OOOI
0,0
.21
9L5443
9155
91.5498
9154
.99994
O,I
.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
0.99994
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
IOO.I659
10017
100.1709
10017
0.09995
0,1
I.OOOO
0,0
.31
101. 1726
10118 101.1776
10117
•99995
0,1
.0000
•32
102.1895
IO2I9 102. T9^/|
10219
•99995
0,1
.0000
• 33
103.2166
IO322
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
I085I
108.5134
10851
.99996
0,1
.0000
• 39
109.5994
10960
109.6040
10960
.99996
0,1
.0000
5.40
110.7009
II07I
110.7055
11070
0.09996
0,1
I.OOOO
0,0
.41
111.8136
III82
in. 8180
11181
•99996
0,1
.0000
.42
112.9375
1 1 294
112.9418
11294
.99996
0,1
.0000
•43
114.0724
11408
114.0768
11407
.99996
0,1
.0000
• 44
II5.2I89
11522
115-2233
11522
•99996
0,1
.0000
5-45
116.3769
11638
116.3812
11638
0.99996
0,1
I.OOOO
0,0
IT7.5466
H755
117.5508
II755
.99996
0,1
.0000
•47
118.7280
11873
118.7322
11873
.99996
0,1
.0000
.48
T TQC)3
TT 0.9254
TTCQ2
•99997
0,1
.0000
.49
I2I.I265
12113
I2I.I3O7
I2II3
•99997
0,1
.0000
5-50
122.3439
12235
122.3480
12234
0.99997
0,1
I.OOOO
0,0
u
tan gd u
«F0'
sec gd u
»F0'
sin gd u
»Fo'
csc gd u
«F0'
SMITHSONIAN TABLES
170
Natural Hyperbolic Functions.
u
sinh u
«F
cosh u
0>Fo'
tanh u
«F;
coth u
«F0'
5.50
122.3439
12235
122.3480
12234
0.99997
0,1
I.OOOO
0,0
.51
123-5735
12358
123.5776
12357
.99997
0,1
.0000
• 52
124.8155
12482
124.8195
12482
•99997
o.r
.0000
.53
126.0700
12607
126.0739
12607
•99997
0,1
.0000
• 54
127.3370
12734
127.3410
12734
.99997
0,1
.0000
5.55
128.6168
12862
128.6207
12862
0.09997
0,1
I.OOOO
0,0
• 56
129.9095
12991
129.9133
12991
.99997
0,1
.0000
• 57
131.2151
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
I35-2IT4
13522
135.2150
13521
0.00997
0,1
I.OOOO
0,0
.61
136.5703
13657
136.5739
13657
•99997
0,1
.0000
.62
T37.9429
13795
137.9465
13794
.99997
0,1
.0000
.63
139.3293
13933
139.3329
13933
•99997
0,1
.0000
.64
140.7296
U073
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
I43.576I
M357
-99998
0,0
.0000
.67
U5.0I55
14502
145.0100
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
15710
157.0969
15709
0.99998
0,0
I.OOOO
0,0
.76
158.6726
15868
158.6757
15867
•99998
0,0
.0000
• 77
160.2673
16027
160.2704
16027
• .99998
0,0
.0000
.78
161.8781
16188
161.8811
16188
.99998
0,0
.0000
• 79
163.5050
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
I75.36o6
17536
175-3635
17536
.99998
0,0
.0000
.87
177.1231
I77I3
177.1259
17712
.99998
0,0
.0000
.88
178.0032
17891
178.9000
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
19381
193.8064
19380
.99999
0,0
.0000
•97
I95.75I6
19575
I95.754I
19575
•99999
0,0
.0000
• 98
I97.7I89
19772
197.7214
19772
.99999
0,0
.0000
•99
199.7061
I997I
199.7086
I997I
•99999
0,0
.0000
6.00
201.7132
20172
201.7156
20171
0.99999
0,0
I.OOOO
0,0
u
fan gd u
«F0'
sec gd u
wF0'
sin c: I u
" F '
csc gd u
«FO'
SMITHSONIAN TABLES
171
TABLE III
NATURAL AND LOGARITHMIC CIRCULAR FUNCTIONS
173
Circular Functions.
u
sin u
• Fo'
COS U
*> Fo' log sin u
• Fo'
log cos u
"Fo'
u
0.0000
0.00000
10,0
I.OOOOO
0,0
X
+ 00
o.ooooo
0,0
O OO 00.00
.OOOI ! .00010
.00000
6.00000
43429,4
.00000
o oo 20.63
.OOO2 .O002O
.00000
.30103
21714,7
.00000
o oo 41.25
.0003
.00030
.00000
.47712
14476,5
.00000
o oi 01.88 I
.OOO4
.00040
.00000
.60206
10857,4
.00000
o oi 22.51
O.OO05
0.00050
10,0
I.OOOOO
0,0
6.69897
8685,9
o.ooooo
0,0
o oi 43.13
.0006
.00060
.00000
.77815
7238,2
.00000
o 02 03.76
.OOO7
.00070
.00000
.84510
6204,2
.00000
0 02 24.35
.0008 | .OOOSO
.00000
.00309
5428,7
.00000
0 02 45.01
.0009
.00090
.00000
.95424
4825,5
.00000
o 03 05.64
O.OOIO
0.00100
IO,O
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
.11394
3340,7
.00000
o 04 28.14
.0014
.00140
.00000
. 14613
3102,1
.00000
o 04 48.77
0.0015
0.00150
10,0
I.OOOOO
0,0
7.17609
2895,3
o.ooooo
0,0
o 05 09.40
.0016 .00160
.00000
.20412
27H,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
O.O020O
10,0
I.OOOOO
0,0
7.30103
2171,5
o.ooooo
0,0
o 06 52.53
.OO2I .00210
.00000
.32222
2068,1
.00000
o 07 13.16
.0022 .00220
.00000
.34242
I074,i
.00000
o 07 33.78
.0023
.00230
.00000
.36173
1888,2
.00000
o 07 54-41
.OO24
.OO240
.00000
.38021
1809,6
.00000
o 08 15.04
O.OO25
O.OO25O
10,0
I.OOOOO
0,0
7.39794
1737,2
o.ooooo
0,0
o 08 35-66
.OO26
.OO260
.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
.OO2OO
.00000
.46240
1497,6
.00000
o 09 58.17
O.OO3O
0.00300
10,0
I.OOOOO
0,0
7.47712
1447,6
o.ooooo
0,0
o 10 18.79
.O03I
.00310
.00000
.49136
1400,9
.00000
o 10 39.42
.0032
.OO320
0.99999
.50515
1357,2
.00000
0 II 00.05
• 0033
.00330
.90099
.51851
1316,0
.00000
o ii 20.67
.0034
.00340
•99999
.53148
1277,3
.00000
o ii 41.30
0.0035
O.O035O
IO,O
0.09909
0,0
7.54407
1240,8
o.ooooo
0,0
O 12 OI.93
.0036 .00360
.99999
.55630
1206,4
.00000
0 12 22.55
•0037 .00370
.99999
.56820
ii73,8
.00000
0 12 43.18
.0038 .00380
.99999
.57978
1 142,9
.00000
o 13 03.81
.0039 .00390
.99999
.59106
1113,6
.00000
o 13 24.4.1
0.0040 0.00400
10,0
0.99999
0,0
7.60206
1085,7
0.00000
0,0
o 13 45.o6
.0041 .00410
.99999
.61278
1059,2
.00000
o 14 05.69
.0042 .00420
•99999
.62325
1034,0
.00000
o 14 26.31
.0043 -00430
.99599
.63347
1010,0
.00000
o 14 46.94
.0044
.00440
.99999
•64345
987,0
.00000
o 15 07.57
0.0045
0.00450
1 0,0
0.99999
0,0
7.65321
965,1
o.ooooo
0,0
o 15 28.19
.0046
.00460
.99999
.66276
944J
.00000
o 15 48.82
.0047
.00470
•99999
.67210
924,0
.00000
o 16 09.44
.0048
.00480
•99999
.68124
004,8
.00000
o 16 30.07
.0049
.00490
.99999
.69019
886,3
9-99999
o 16 50.70
O.OO5O
0.00500
10,0
0.99099
0,0
7.60897
868,6
9.09999
0,0
o 17 11.32
u
isinhiu
-Fo'
cosh iu
• FO'
sinh iu
"F0f
log cosh iu
«-F0'
u
loo .
SMITHSONIAN TABLES
174
Circular Functions.
u
sin u
«F0'
COS U
«F0'
log sin u
« Fo'
log cos u
«F0'
u
0.0050
O.O05OO
10,0
0.09999
0,0
7-69897
868,6
9.09999
0,0
o 17 11.32
.0051
.00510
•99999
0,1
.70757
851,6
.90999
o 17 31.95
.0052
.00520
.99999
.71600
835,2
.09999
o 17 52.58
.0053
.00530
.99999
.72427
819,4
.90999
o 18 13.20
.0054
.00540
.99999
.73239
804,2
.09099
o 18 33.83
0.0055
0.00550
IO,O
0.99998
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
761,9
.99999
o 19 35.71
.0058
.00580
.99998
.76343
748,8
.09990
o 19 56.34
.0059
.00590
.09998
.77085
736,1
.09999
0 20 16.96
0.0060
0.00600
10,0
0.99998
0,1
7.77815
723,8
9.99999
0,0
0 20 37-59
.0061
.00610
.99998
.78533
7H,9
.99999
o 20 58.22
.0062
.00620
.99998
•79239
700,5
•99999
0 21 18.84
.0063
.00630
.90908
.79934
689,3
.99999
0 21 39.47
.0064
.00640
.99998
.80618
678,6
•99999
O 22 00.09
0.0065
0.00650
10,0
0.99998
0,1
7.81291
668,1
9-99999
0,0
O 22 2O.72
.0066
.00660
.99998
.81954
658,0
.99999
0 22 41.35
.0067
.00670
.99998
.82607
648,2
•99999
o 23 01.97
.0068
.00680
.09998
.83251
638,7
.99999
O 23 22.00
.0069
.00690
.99998
.83885
629,4
.99999
o 23 43-23
0.0070
0.00700
10,0
0.99998
0,1
7.84509
620,4
9-99999
0,0
o 24 03.85
.0071
.00710
.99997
.85125
6n,7
.99999
o 24 24.48
.0072
.OO720
.99997
.85733
603,2
.99999
0 24 45.11
.0073
.00730
.99997
.86332
594,9
.99999
o 25 05.73
.0074
.00740
.99997
.86923
586,9
•99999
o 25 26.36
0.0075
0.00750
IO,O
0.99997
0,1
7.87506
579,0
9.99999
0,0
o 25 46.99
.0076
.00760
.99997
.88081
571,4
.99999
o 26 07.61
.0077
.00770
•99997
.88640
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
IO,0
0.99997
0,1
7.00309
542,9
9.99909
0,0
o 27 30.12
.0081
.00810
•99997
.90848
536,2
.99999
o 27 50.74
.0082
.00820
.99997
.91381
529,6
•99999
o 28 11.37
.0083
.00830
.99097
.91907
523,2
.99999
o 28 32.00
.0084
.00840
.99996
.92427
5i7,o
.99998
o 28 52.62
0.0085
0.00850
10,0
0.09996
0,1
7.92941
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
.99098
o 29 54.50
.0088
.00880
.99996
•94448
493,5
.09998
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
9.90998
0,0
o 30 56.38
.0091
.00910
.99996
•95904
477,2
.99998
o 31 17. oi
.0092
.00920
.99996
.96378
472,0
•99998
o 31 37.64
.0093
.00930
•99996
.96848
467,0
.90998
o 31 58.26
.0094
.00940
.99996
.97312
462,0
.99998
o 32 18.89
0.0095
0.00950
IO,O
0.99995
0,1
7-97772
457,1
9.99998
0,0
o 32 39.52
.0096
.00960
•99595
.98226
452,4
.99998
o 33 00.14
.0097
.00970
•99995
.98676
447,7
.99998
o 33 20.77
.0098
.00980
•99995
.99122
443J
.99998
o 33 41-40
.0099
.00990
•99995
.99563
438,7
.99998
0 34 02.02
O.OIOO
O.OIOOO
IO,O
0.99995
0,1
7.99999
434,3
9.90998
0,0
o 34 22.65
u
-isinhiu
wFo'
cosh iu
«FO'
, sinh iu
«F0'
log cosh iu
u> F '
u
log .
SMITHSONIAN TABLES
175
Circular Functions.
I
sin u
«Fo'
COS U
«F0'
log sin u
«- Fo'
log cos u
O.FO'
u
O.OIOO
O.OIOOO
10,0
0.99995
0,1
7.99999
434,3
9.99998
0,0
o°34' 22^65
.OIOI
.OIOIO
.99995
8.00431
430,0
.99998
0 34 43-27
.0102
.OIO2O
.99995
.00859
425,8
.99998
0 35 03.90
.0103
.01030
.99995
.01283
421,6
.99998
o 35 24.53
.0104
.OIO4O
•99995
.01703
417,6
.99998
o 35 45-15
0.0105
O.OIO5O
IO,O
0.99994
0,1
8.02II8
413,6
9.99998
0,0
o 36 05.78
.0106
.OI06O
•99994
.02530
409,7
.99998
o 36 26.41
.0107
.OIO7O
•99994
.02938
405,9
.99998
- j6 47-03
.0108
.01080
•99994
•03342
402,1
•99997
o 37 07.66
.0109
.01090
•99994
.03742
398,4
•99997
o 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
.0111
.OHIO
•99994
.04531
391,2
•99997
o 38 09.54
.0112
.OII2O
.99994
.04921
387,7
.99997
o 38 30.17
.0113
.01130
.99994
.05307
384,3
.99997
o 38 50.79
.0114
.01140
•99994
.05690
380,9
•99997
o 39 11.42
0.0115
0.01150
IO,O
0.99993
0,1
8.06069
377,6
9-99997
0,0
o 39 32.05
.0116
.01160
•99993
.06445
374,4
.99997
0,1
o 39 52.67
.0117
.01170
•99993
.06818
371,2
•99997
o 40 13.30
.0118
.01180
•99993
.07187
368,0
•99997
o 40 33-92
.0119
.01190
•99993
.07554
364,9
•99997
o 40 54-55
0.0120
O.OI2OO
IO,0
0.99993
0,1
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. o>
.OI24
.01240
•99992
•09341
350,2
•99997
o 42 37.68
0.0125
0.01250
10,0
0.99992
0,1
8.09690
347,4
9-99997
0,1
o 42 58.31
.0126
.01200
.99992
.10036
344,7
.99997
o 43 18.94
.OI27
.01270
•99992
• 10379
342,0
.99996
o 43 39.56
.0128
.OI28O
•99992
. 10720
339,3
•99996
o 44 00.19
.OI29
.OI29O
.99992
.11058
336,6
.99996
o 44 20.82
O.OI3O
O.OI3OO
IO,0
0.99992
0,1
8. i 1393
334,1
9.99996
0,1
0 44 41.44
.0131
.01310
.99991
.11726
331,5
•99996
0 45 02.07
.0132
.OI32O
.99991
. 12056
329,0
•99996
o 45 22.70
•0133
.01330
.99991
• 12384
326,5
.99996
o 45 43.32
.0134
.01340
.99991
.12709
324,1
.99996
o 46 03.95
0.0135
0.01350
IO,0
0.99991
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
3i7,o
•99996
o 47 05.83
.0138
.01380
.99090
• 13987
3H,7
.99996
o 47 26.45
.0139
.01390
•99950
.14300
312,4
.99996
o 47 47.o8
0.0140
0.01400
10,0
0.99090
0,1
8.14611
310,2
9.99996
0,1
o 48 07.71
.0141
.01410
.99990
. 14920
308,0
.99996
o 48 28.33
.0142
.OI42O
.99990
.15227
305,8
.99996
o 48 48.96
.0143
.01430
.99990
•15532
303,7
.99996
0 49 09.59
.0144
.01440
•99990
. 15835
301,6
•99995
O 49 30.21
0.0145
0.01450
1 0,0
0.99989
0,1
8.16135
209,5
9-99995
0,1
© 49 50.84
.0146
.01460
.99989
• 16434
297,4
.99995
o 50 11.47
.0147
.01470
.ggg8g
. 16730
295,4
•99995
o 50 32.09
.0148
.01480
.99989
.17025
293,4
•99995
o 50 52.72
.0149
.01490
.99989
.17317
291,5
• 99995
o 51 13-35
0.0150
0.01500
10,0
0.99989
0,1
8.17608
289,5
9-99995
0,1
o 51 33-97
u
-I tlnh lu
• ft
cosh iu
" F,,'
. sinh iu
*>Fo'
log cosh iu
-FO'
u
log .
SMITHSONIAN TABLES
176
Circular Functions.
I
sin u
«FO'
COS U
• IV
log sin u
- F,/
log cos u
u
0.0150
0.01500
IO,O
0.99989
0,1
8.17608
289,5
9-99995
0,1
o°5i'33'-97
.0151
.01510
.90989
0,2
287,6
•99995
o 51 54.60
.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
O.OI55O
10,0
0.99988
0,2
8.I003I
280,2
9-99995
0,1
o 53 17-10
.0156
.01560
.99988
.I93H
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
.oi'59
.01590
.99987
.20138
273,1
•99995
0 54 39.61
0.0160
O.OIOOO
IO,O
0.99987
0,2
8.20410
271,4
9-99994
0,1
0 55 00.24
.0161
.Ol6lO
.99987
.20681
269,7
• 9999-*
o 55 20.86
.0162
.01620
.99987
.20950
268,1
•99994
o 55 41.49
.0163
.01630
.99987
.21217
266,4
•99994
o 56 02. 12
.0164
.01640
•99987
.21482
264,8
.99994
o 56 22.74
0.0165
0.01650
IO,O
0.90986
0,2
8.21746
263,2
9.99994
0,1
o 56 43-37;
.0166
.01660
.99986
.22009
261,6
•99994
o 57 04.00!
.0167
.01670
.99986
.22270
260,0
•99994
o 57 24.62
.0168
.01680
.99986
.22529
258,5
.99994
o 57 45.25
.0169
.01690
.99986
.22787
257,0
.99994
o 58 05.88
0.0170
O.OI70O
10,0
0.99986
0,2
8.23043
255,4
9-99994
0,1
o 58 26.50
.0171
.01710
.99985
.23298
253,9
•99994
o 58 47-13
.0172
.0173
.01720
.01730
.99985
.99985
.23551
.23802
252,5
251,0
.99994
•99994
o 59 07.75
o 59 28.38
.0174
.01740
.99985
.24053
249,6
•99993
o 59 49-01
0.0175
O.OI75O
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
.01790
.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
0.01850
10,0
0.99983
0,2
8.26715
234,7
9-99993
0,1
03 35.90'
.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
.01800
.99982
•27644
229,8
•99992
04 58.40
0.0190
0.01900
IO,O
0.09982
0,2
8.27873
228,5
9.99992
0,1
05 19-03
.0191
.OI9IO
.99982
.28101
227,4
.99992
05 39-66
.0192
.01920
.99982
.28327
226,2
.99992
06 00.28
.0193
.01930
.99981
.28553
225,0
•99992
06 20.91
.0194
.01940
.99981
.28777
223,8
.99992
06 41-54;
0.0195
O.OI950
IO,0
0.99981
0,2
8.29001
223,7
9.99992
0,1
07 02. 16
.0196
.01060
.99981
.29223
221,6
.99992
07 22.79
.0197
.OI97O
.99981
.29444
-2J0.4
.99992
07 43. 4-'
.0198
.01980
.99980
.29664
219,3
.99991
08 04.04
.0199
.01990
.99980
.29882
218,2
.99991
08 24.67
0.0200
O.O20OO
IO,O
0.99980
0,2
8.30100
217,1
9.99991
0,1
I 08 45-30
_• u •
01 F '
— rt*u ;.,
r '
sinh iu
««» F '
Inn /*ncKi in
M F '
u
i sinn lu
w ro
COSn IU
<•> ro
log .
*> PC
lOy cosn iu
*• TO
u
SMITHSONIAN TABLES
177
Circular Functions.
u
sin u
«F0'
COS U
«F0'
log sin u
« Fu'
log cos u
»FO'
u
O.O2OO
O.O2OOO
10,0
0.99980
0,2
8.30100
217,1
9.99991
0,1
°o8 45^30
.02OI
.O20IO
.99980
.30317
216,0
•99991
09 05.92
.O2O2
.O2020
.99980
.30532
215,0
.99991
09 26.55
.0203
.02030
.90979
.30747
213,9
•99991
09 47.i8
.0204
.O2O4O
.99979
.30960
212,9
.99991
10 07.80
O.02O5
O.O205O
IO,O
0.99979
0,2
8.31172
211,8
9.99991
0,1
10 28.43
.O206
.O2O6o
.99979
.3I3'84
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
O.O2IOO
IO,O
0.99978
0,2
8.32219
206,8
9.99990
0,1
12 11.56
.O2I I
.O2IIO
.99978
.32425
205,8
.99990
12 32.19
.O2I2
.O2I2O
.99978
.3^630
204,8
.99990
12 52.8l
.O2I3
.02130
.99977
.32835
203,9
.99990
13 13.44
.O2I4
.02140
. 99977
.33038
202,9
•99990
13 34.07
0.0215
O.O2I50
IO,O
0.99977
0,2
8.33241
202,0
9.99990
0,1
13 54-69
.0216
.02160
•99977
.33442
2OI,O
.99990
14 15.32
.O2I7
.02170
.99976
.33643
2OO,I
•99990
14 35-95
.0218
.02180
.99976
.33842
199,2
.99990
14 56.57
.0219
.02100
.99976
.34041
198,3
•99990
15 17-20
O.022O
O.022OO
IO,O
0.99976
0,2
8.34239
197,4
9.99989
0,1
15 37.83
.0221
.02210
.99976
.34436
196,5
.99989
15 58.45
.O222
.O2220
•99975
.34632
195,6
.99989
16 19.08
.0223
.02230
.99975
.34827
194,7
.99989
16 39-71
.O224
.O224O
•99975
•35021
193,8
.99989
17 00.33
O.O225
O.O225O
10,0
0.99975
0,2
8.35215
193,0
9.99989
0,1
17 20.96
.0226
.02200
.99974
•35407
192,1
•99989
17 4L58
.0227
.O2270
•99974
•35599
I9i,3
.99989
18 02. 21
.0228
.02280
•99974
.35790
190,4
.99989
18 22.84
.0229
.02290
•99974
.35980
189,6
.99989
18 43.46
O.O23O
0.02300
IO,O
0.99974
0,2
8.36169
r88,8
9.99989
0,1
i 19 04.09
.0231
.02310
•99973
.36357
.188,0
.99988
i 19 24.72
.O232
.02320
.99973
.36545
187,2
.99588
19 45-34
.0233
.02330
.99973
.36732
186,4
.99988
20 05-97
.0234
.02340
.99973
.36918
185,6
.99988
2O 26.6O
0.0235
0.02350
IO,O
0.99972
O,2
8.37103
184,8
9.99988
O,I
2O 47.22
.0236
.02300
•99972
-372'87
184,0
.99988
21 07.85
.0237
.02370
.99972
.37471
183,2
.99988
21 28.48
.0238
.02380
•99972
.37654
182,4
.99988
21 49.10
.0239
.02390
•99971
.37836
181,7
.99988
22 09.73
0.0240
0.02400
IO,O
0.99971
0,2
8.38017
180,9
9.99987
0,1
22 30.36
.0241
.02410
.99971
.38198
180,2
.99987
22 50.98
.0242
.O242O
.99971
.38377
179,4
.99987
23 ii. 61
.0243
.02430
.99970
.3<*556
178,7
.99987
23 32.23
.O244O
.99970
.38735
178,0
•99987
23 52.86
0.0245
0.02450
IO,O
0.99970
0,2
8.38912
177,2
9.90087
0,1
24 13.49
.0246
.024OO
.99970
.39089
176,5
.99987
24 34.11
.0247
.02470
.99969
.39265
175,8
.99087
24 54.74
.02480
.90969
.39441
i75,i
.99987
I 25 15.37
.02490
.99969
.39615
174,4
.99987
i 25 35-99
0.0250
0.02500
IO,O
0.09969
0,2
8.39789
173,7
9.99986
0,1
I 25 56.02
u
-i sinn iu
w c '
cosh iu
W Fn'
,_sinh iu
i » C '
f '
• 0
•» TO
loo ,
<» TO
log cosh iu
<«> TO
u
SMITHSONIAN TABLES
178
Circular Functions.
u
sin u
<-Fo'
cos u
• ft
log sin u
« F;
log cos u
-Fo'
u
0.0250
O.O25OO
10,0
0.99969
0,2
8.39789
173,7
9.99986
0,1
°25 -:
.0251
.02510
.99969
0,3
.39963
173,0
!fl9986
26 17.25
.0252
.02520
.99968
.40135
172,3
.99986
26 37.87
.0253
.02530
.99968
.40307
171,6
.99996
26 58.50
.0254
.02540
.99968
.40479
170,9
.99986
27 19.13 (
0.0255
0.02550
10,0
0.99967
0,3
8.40649
170,3
9.99986
0,1
27 39-75
.0256
.02500
.99967
.40819
169,6
.99986
28 00.38
.0257
.02570
,99967
.40989
168,9
.99986
28 21.01
.0258
.02580
.99967
.41157
168,3
.99986
28 41 -63
• 0259
.02590
.99966
•41325
167,6
.99985
29 O2.26
0.0260
0.02600
10,0
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
3i 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.O27OO
IO,O
0.99964
o,3
8.43I3I
160,8
9-99984
0,1
32 49-15
.0271
.O27IO
.99963
.43292
100,2
•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 n.66
0.0275
O.O275O
10,0
0.99962
0,3
8.43928
157,9
9.99984
0,1
34 32.28
.0276
.O270O
.99962
.44085
157,3
•99983
34 52.91
.0277
.02770
.99962
.44242
156,7
.99983
35 13-54
.0278
.02780
.99961
•44399
1-56,2
.99983
35 34-i6
.0279
.02790
.99961
•44555
155,6
.99983
35 54-79
0.0280
O.O2800
IO,O
0.99961
o,3
8.44710
I55,i
9-99983
0,1
36 15.41
.0281
.02810
.99961
.44865
*54,5
•99983
36 36.04
.0282
.02820
.99960
.45019
154,0
.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
IO,O
0.99959
0,3
8.45479
152,3
9.99982
0,1
37 58.55
.0286
.028tX>
•99959
.45631
I5i,8
•99982
38 19.17
.0287
.02870
•99959
.45782
I5i,3
.99982
38 39.80
.0288
.02880
•99959
•45933
150,8
.99982
39 00.43
.0289
.02890
•99958
.46084
150,2
.99982
39 21.05
O.020X)
0.02900
IO,O
0.99958
0,3
8.46234
149,7
9-99982
0,1
39 41.68
.0291
.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
O.O295
0.02950
IO,0
0.99956
o,3
8.46976
147,2
9-99981
0,1
41 24.81
.O296
.02960
.99956
.47123
146,7
.99981
41 45-44
.0297
.02970
•99956
.47269
146,2
.99981
42 06.06
.02Q8
.02980
•99956
•4/415
M5.7
.99981
42 26.69
.0259
.02990
•99955
.47561
145,2
.99981
4-' 47.32
0.0300
0.03000
10,0
0.99955
o,3
8.47706
144,7
9.9998o
0,1
I 43 07-94
r- ;
f r
sinh iu
P '
P /
U
-i sinh iu
w Fo
cosh iu
*> TO
loo ,
*» TO
loo cosh iu
*> TO
u
SMITHSONIAN TABLES
179
Circular Functions.
u
sin u
«F0'
COS U
-Fo'
log sin u
« Fo'
log cos u
"Fo'
U
0.0300
O.O3OOO
IO,0
0.99955
0,3
8.47706
144,7
9.99980
0,1
I 43 O7'.'o4
.0301
.03010
•99955
•47850
144,2
•99980
I 43 28.57
.0302
.03020
.99954
•47994
143.8
.999*0
43 49.20
.0303
.03030
.99954
•48138
143,3
.09980
44 09.82
.0304
.03040
•99954
.48281
142,8
.99980
44 30.45
0.0305
0.03050
10,0
0.99953
0,3
8.48423
142,3
9-99980
0,1
44 5i.o8
.0306
.03060
.99953
.48565
141,9
.99980
45 11.70
.0307
.030/0
.99953
•48707
141,4
.99980
45 32.33
.0308
.03080
•99953
.48848
141,0
•99979
i 45 52.96
.0309
.03000
•99952
.48989
140,5
.99979
I 46 13.58
0.0310
0.03IOO
10,0
0.09952
o,3
8.49129
140,1
9.9997"9
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
.90950
.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
IO,O
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
.99948
•50778
134,8
•99977
50 4L73
.0323
.03229
.09948
.50913
134,4
•99977
5i 02.35
.0324
.03239
.99948
.51047
134,0
•99977
51 22.98
0.0325
0.03249
10,0
0.99947
o,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
•99976
53 06. u
0.0330
0.03299
10,0
0.99946
o,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
IO,O
0-99944
o,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
1 0,0
0-99942
o,3
8.53'i40
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
.03429
.99941
.53521
126,6
.99974
57 54.88
•0344
•03439
•99941
.53647
126,2
•99974
58 15-51
0.0345
0.03449
10,0
0.90940
o,3
8.53773
125,8
9-99974
0,1
5836.14
.0346
•03459
.99940
.53899
125,5
•99974
0,2
58 56.76
.90940
•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
0.09939
o,3
8.54398
124,0
9-99973
0,2
2 oo 19.27
u
-itinhiu
<- Fo'
cosh iu
W fit'
.sinh iu
c '
. i C '
w • 0
tog ,
<«> l"o
og cosh iu
<«> ro
u
»MITH»ONIAN TABLES
1 80
Circular Functions.
u
sin u
wF0'
COS U
U>F,;
log sin u
- F '
log cos u
~Fo'
U
0.0350
0.03499
IO,0
0.99939
o,3
B.54398
124,0
9-99973
0,2
o / ./
2 OO 19.27
.0351
.03509
.99938
0,4
.545~>2
123,7
•WJ73
2 OO 39.89
.0352
.03519
.99938
.54645
123,3
.<//>73
2 OI OO.52
• 03'53
.03529
.99938
• 54768
123,0
•99973
2 OI 21.15
• 0354
•03539
•99937
•54891
122,6
•99973
2 01 4L77
0.0355
0.03549
IO.O
0.99937
0,4
8.55014
122,3
9-99973
0,2
2 O2 O2.40
.0356
•03559
.99937
.55136
121,9
•99972
2 02 23.03
• 0357
.03569
.99936
.55258
121,6
•99972
2 02 43.65
.0358
.03579
.99936
•55379
121,3
.99972
2 03 O4.28
• 0359
.03589
.99936
•55500
120,9
•99972
2 03 24.91
0.0360
0.03-509
IO,O
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 OS O8.O4
0.0365
0.03649
IO,O
0-99933
0,4
8.56220
118,9
9-99971
0,2
2 O5 -
.0366
• 03659
•99933
06338
118,6
•99971
2 05 ,
•0367
.03669
.99933
.56457
118,3
.99971
2 O6 09.92
.0368
.03679
•99932
.56575
118,0
•99971
2 06 30.54;
.0369
.03689
.99932
•56693
117,6
.99970
2 06 51.171
0.0370
0.03699
IO,O
0.99932
0,4
8.56810
H7,3
9-99970
0,2
2 O7 II.SOi
• 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
.57161
1 1 6,4
.99970
2 08 13.68
.0374
.03739
•99930
•57277
116,1
•99970
2 08 34-30
0.0375
0.03749
IO,O
0.99930
0,4
8.57393
115,8
9.99969
0,2
2 08 54-93 !
.0376
.03759
.99929
•57509
H5,4
•99969
2 09 1
• 0377
.03769
.99929
•57624
115,1
.99909
2 09 36.l8j
.0378
.03779
•99929
•57739
114,8
.99969
2 O9 56.8l i
.0379
.03789
.90928
•57854
ii4,5
.99969
2 10 17-44
0.0380
0.03799
10,0
0.99928
0,4
8.57968
114,2
9.99969
0,2
2 10 38.06
.0381
.03809
•99927
.58082
H3,9
.99968
2 10 58.69
.0382
.03819
•99927
.58106
113,6
.99968
2 II 19.32
.0383
.03829
.99927
•58309
H3,3
.99968
-' u 39-94!
.0384
.03839
.99926
.58422
113,0
.99968
2 12 00.57!
0.0385
0.03849
IO,O
0.99926
0,4
8.58535
112,7
9.99968
0,2
2 12 21.20
.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
in,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
ni,3
9.99967
0,2
2 14 04.33
.0391
.03909
•99924
.59207
III.O
.99967
2 M
.0392
.03919
•99923
.59317
110,7
.99967
2 I4
.0393
•03929
•99923
.59428
110,5
.99966
2 !=; <
• 0394
•03939
.99922
.59538
IIO,2
.99966
2 15 26.83
0.0395
0.03949
IO,O
0.99922
0,4
8.59648
109,9
9.99966
0,2
2 15 .
.0396
.03959
.99922
.59758
109,6
.99966
2 16 08.09
.0397
.03969
.99921
.59868
109,3
.99966
2 16 a
.0308
.03979
.99921
.59977
109,1
.99966
2 l6 49-341
• 0399
•03989
.99920
.60086
108,8
•99065
2 17 09.97!
0.0400
0.03999
1 0,0
0.99920
0,4
8.60194
108,5
9.99965
0,2
2 17 30.59
u
-isinhiu
<"F0'
cosh iu
«FO'
. sinh iu
«F0'
ogcoshiu
*> F '
u
log .
SMITHSONIAN TABLES
181
Circular Functions.
u
sin u
«Fo'
COS U
<» Fu' log sin u
« Fo'
log cos u
u» F,/ | u
0.0400
.0401
0.03999
.04009
10,0
0.99920
.99920
0,4
8.60194
.60303
108,5
108,2
9.99965
.99965
0,2
2 17 30-59
2 17 51.22
.0402
.04019
.99919
.60411
108,0
.99965
2 18 11.85
.0403
.04029
.99919
.60519
107,7
.90965
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
.60947
106,6
.99964
2 19 54-98
.0408
.04079
.99917
.61054
106,4
.90964
2 2O I5.6O
.0409
.04089
.99916
.61160
106,1
.99964
2 20 36.23
0.0410
0.04099
IO,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
.99963
2 21 58.74
.0411
.04139
.99914
.61688
104,8
.99963
2 22 19.36
0.0415
0.04149
IO,O
0.99914
0,4
8.61792
104,6
9.99963
O,2
2 22 39.99
.0416
.04159
.99913
.61897
104,3
.99962
2 23 00.62
.0417
.04169
.99913
.62001
104,1
.99962
2 23 21.24
.0418
.04179
.99913
.6210^5
103,8
.99962
2 23 41.87
.0419
.04189
.99912
.62209
103,6
.99962
2 24 02.50
0.0420
0.04199
IO,O
0.99912
0,4
8.62312
103,3
9.99962
O,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 25.00
.0424
.04239
.99910
.62724
102,4
.99961
2 25 45.63
0.0425
0.04249
IO,O
0.99910
0,4
8.62826
IO2,I
9.99961
0,2
2 26 O5.25
.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
IOI,2
.99960
2 27 28.76
0.0430
0.04299
10,0
0.99908
0,4
8.63333
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 11.80
0.043-5
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
0.04399
1 0,0
0.99903
0,4
8.64331
98,6
9.99958
O,2
2 31 15.65
.0441
.04409
.99903
.64430
98,4
.99958
2 31 36.28
.0442
.04419
.99902
.64528
98,2
.99958
2 31 56.90
.0443
.04429
.09902
.64626
98,0
•99957
2 32 17.53
.0444
.04439
.99901
.64724
97,7
•99957
2 32 38.16
0.0445
0.04449
IO,O
0.99901
0,4
8.64822
97,5
9-99957
O,2
2 32 58.78
.04459
.99901
.64919
97,3
•99957
2 33 19-41
.04409
.<//;oo
.65016
97,i
• 99957
2 33 40.04
.0448
.04475
.99900
•65113
96,9
•99956
2 34 00.66
.0449
.04488
.99899
.65210
96,7
.99956
2 34 21.29
0.0450
0.04498
10,0
0.95899
0,4
8.65307
96,4
9.99956
O,2
2 34 41-92
u
i.inhiu
• IV
cosh iu
«Fu'
. sinh iu
• F»'
log cosh iu
-FO'
u
loo ,
SMITHSONIAN TABLE*
182
Circular Functions.
u
sin u
«F0'
COS U
«Fo'
log sin u
- Fo'
log cos u
-Fo'
u
0.0450
0.04498
IO,O
0.99899
0,4
8.65307
96,4
9.99956
0,2
3*34' 41*92
.0451
.04508
.99898
o,5
.65403
96,2
.99956
2 35 02.54
.045-2
.04518
.99898
.65499
96,0
.99956
2 35 23.17
.0453
.04528
.99897
.65595
95,8
•99955
2 35 43-80,
.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 -
• 0457
.04568
.99896
.65976
95,o
• 99955
2 37 06.30
.0458
.04578
.90895
.66071
94,8
•99954
2 37 26.93
•0459
.04588
.9989-5
.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
IO,O
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
10,0
0.99890
o,5
8.67194
92,3
9-99952
0,2
2 41 34-45
.0471
.04708
.99889
.67286
92,r
•99952
2 41 55-07!
.0472
.04718
.99889
.67378
91,9
.99952
2 42 15.70
.0473
.04728
.99888
.67470
91,7
•99951
2 42 36.33
.0474
.04738
.99888
.67562
91*6
.99951
2 42 56.95
0.0475
.0476
0.04748
.04758
10,0
0.99887
.99887
o,5
8.67653
.67744
91,4
91,2
9-99951
.99951
0,2
2 43 17.58
2 43 38.20!
.0477
.04768
.99885
.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
10,0
0.99885
o,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
.00949
2 46 02.59
.0484
.04838
.99883
.68468
89,7
.09949
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./2
.0489
.04888
.99880
.68914
88,7
.99948
2 48 06.35
0.0490
0.04898
1 0,0
0.99880
o,5
8.60002
88,6
9.99948
0,2
2 48 26.98
.0491
.04908
•99879
.69091
88,4
.99948
2 48 47.6O
.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 5O IO.II
.0496
.04958
.99877
•69530
87,5
.99947
2 50 30.73!
.0497
.04968
.99877
.69618
87,3
•99946
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
10,0
0.99875
o,5
8.69879
86,8
9.99046
0,2
2 51 53-24
u
-i sinhiu
«F0'
cosh iu
-FO'
sinh iu
o> Fo' log cosh iu
«FO'
u
loo j
SMITHSONIAN TABLES
183
Circular Functions.
u
sin u
U.FO'
COS U
w Fo' loo sin u
<" Fo'
log cos u
<«> Fo'
u
0.0500
0.04998
10,0
0.99875
o,5
8.69879
86,8
9-99946
0,2
2 51 53724
.0501
.05008
.99875
.69966
86,6
•99945
2 52 I3-87
.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
1 0,0
0.99873
0,5
8.703H
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
.95870
.70653
85,2
•99944
2 54 58.88:
0.0510
0.05098
IO,O
0.99870
o,5
8.70738
85,1
9-99943
O,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
0.99867
o,5
8.71162
84,3
9.99942
O,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
0.05108
IO,O
0.99865
0,5
8.7I58I
83,4
9.99941
0,2
2 58 45-77
.0521
.05208
.99864
.71664-
83,3
•99941
2 59 06.40
.0522
.05218
.99864
•
.71747
83,1
.99941
2 59 27.02
.0523
.05228
.99863
.71830
83,0
•99941
2 59 47.65
.0524
.05238
.99863
.71913
82,8
•99940
3 oo 08.28
0.0525
0.05248
IO,O
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
1 0,0
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
10,0
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
• \377
.99855
.73057
80,6
•99937
3 04 57-05
• 0539
• 05387
.99855
.73138
80,5
•99937
3 05 17-67
','.0540
0.05397
10,0
0.99854
o,5
8.73218
80,3
9-99937
O,2
3 05 38.30
.0541
.05407
.99854
.73299
80,2
•99936
3 05 58.93
•05417
.99853
•73379
80,0
.99936
3 06 19.55
•05427
.99853
•73459
79,9
.99936
3 06 40.18
•0544
•05437
.99852
•73538
79,8
.99936
3 c/ 00.81
'•0545
0.05447
IO,O
0.99852
o,5
8.73618
79,6
9-99935
0,2
3 07 21.43
•05457
.99851
.73698
79,5
•99935
3 07 42.00
•05467
.99850
•73777
79,3
•99935
3 08 02.68
•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
u
-i tilth iu
«F,/
cosh iu
«F,/
sinh iu
• Ft'
log cosh iu
«F0'
u
log .
SM.TMBONIAN TABLES
184
Circular Functions.
u
sin u
«F0'
COS U
• ft'
loo sin u
« F,/
log cos u
«FU'
u
0.0-550
0.05497
I O,O
0.99849
o,5
8.74014
78,9
9.99934
0,2
3°09'o4.'56
.0551
.05507
.9^848
0,6
•74093
78,7
.99934
3 09 25.19
.05 5 ->
•05517
.99848
.74172
7<S/>
.99934
3 09 45-82
.0553
.05527
.99847
.74250
78,5
.99934
3 <o i-
.0554
.05537
.99847
.74329
78,3
•99933
3 10 27.07
0.0555
0.05547
10,0
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 n 28.95
• 0558
.05577
.99844
.74641
77,7
.99932
3 U 49.58
•0559
.05587
.99844
.74/19
77,6
.99932
3 12 IO.2O
0.0560
0.05597
10,0
0.99843
0,6
8.74796
77,5
9-99932
0,2
3 12 30.83
j .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 J
•99931
3 13 32.71
.0564
.05637
.99841
.75105
76,9
•99931
3 13 53-34
0.0565
0.05647
10,0
0.99840
0,6
8.75182
763
9-99931
0,2
3 U 13.96
.0566
.05657
.99840
.75258
76,6
•99930
3 14 34.59
.0567
.05667
.99839
•75335
76,5
.99930
3 U 55.21
.0568
.05677
.99839
•754II
76,4
•99930
3 15 15-84
.0569
.05687
.99838
.75488
76,2
.99930
3 15 36.47
0.0570
.0571
.0572
0.05697
.05707
.05717
IO.O
0.09838
.99837
.99836
0,6
8.75564
.75640
.75716
76,1
76,0
75,8
9.99929
.99929
.99929
0,2
3 15 57.09
3 16 17-72
3 16 38.35
.0573
.0574
.05727
.05737
.99836
.99835
•75792
.75867
75,7
75,6
.99929
.99928
3 16 58.97
3 17 19.60
0.0575
.0576
.0577
0.05747
.05757
.05767
10,0
0.99835
.99834
.99834
0,6
8.75943
.76018
•76093
75,4
75,3
75,2
9.99928
.90928
.99928
0,2
0,3
3 17 40.23
3 18 00.85
3 18 21.48
.0578
.05777
.99833
.76169
75J
.99927
3 18 42.11
.0579
.05787
.99832
.76244
74,9
.99927
3 19 02.73
0.0580
; .0581
.0582
.0583
.0584
0.05797
.05807
.05817
.05827
•05837
10,0
0.99832
.99831
.99831
.99830
.99830
0,6
8.76318
.76393
.76468
.76542
.76617
74,8
74,7
74,5
74,4
74,3
9.99927
.99927
.99926
.99926
.99926
0,3
3 19 23.36
3 19 43.99
3 20 04.61
3 20 25.24
3 20 45-86
i
0.0585
.0586
0.05847
.05857
10,0
0.99829
.99828
0,6
8.76691
• 76765
74,2
74,0
9.99926
.99925
0,3
3 21 06.49
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
9.00924
0,3
3 22 49.62'
.0591
.05007
.99825
.77133
73,4
.99924
3 23 10.25
« t. >
; .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
<>j^+j
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
.059/6
.99821
.77644
72,5
.09922
3 25 34-<>4
.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
0,3
3 26 15.89
u
-isinhiu
->Fo'
cosh iu
-F.' .og«inp
»Fo*
log cosh iu
«F0'
u
SMITHSONIAN TABLES
185
Circular Functions.
u
sin u
«F0'
COS U
« Fo' log sin u
<- Fo'
log cos u
«F0'
u
O.OJOO
0.05996
1 0,O
0.99820
0,6
8.77789
72,3
9.99922
0,3
3°26' is'.'8o.
.0601
.06006
.99819
.77861
72,2
.99922
3 26 36.51
.0602
.06016
.99819
•77933
72,1
.09921
3 26 57.14
.0603
.06026
.99818
.78005
71,9
.99921
3 27 17.77
.0604
.06036
.99818
.78077
7i,8
.99921
3 27 38.39
0.0605
0.06046
IO,0
0.99817
0,6
8.78149
7i,7
9-99920
o,3
3 27 59.02
.0606
.06056
.99816
.78221
7i,6
.99920
3 28 19.65
.0607
.06066
.90816
.78292
7i,5
.90920
3 28 40.27
.0608
.06076
.95815
.78364
7i,3
.99920
3 29 00.90
.0609
.06086
.99815
.78435
71,2
.99919
3 29 21.53
0.0610
0.06006
I O,O
0.99814
0,6
8.78506
7U
9.99919
0,3
3 29 42.15
.0611
.06106
.99813
.78577
71,0
.99919
3 30 02.78
.0512
.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
9.90918
0,3
3 31 25.29!
.0616
.06156
.99810
.78931
70,4
.99918
3 3i 45-91
.0617
.06166
.99810
.79001
70,3
.99917
3 32 06.54
.0618
.06176
.99809
.79071
70,2
.99917
3 32 27.17
.0619
.06186
.99808
.79141
70,i
.99917
3 32 47.79
0.0620
0.06106
IO,O
0.99808
0,6
8.79211
70,0
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
.09916
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
0,3
3 34 5L55
.0626
.06256
.99804
.79629
69,3
.99915
3 35 12. 18
.0627
.06266
.99804
.79698
69,2
.99915
3 35 32.8o
.0626
.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,O
0.99802
0,6
8.79905
68,8
9.09914
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
.90800
.80111
68,5
.90913
3 37 36.56
.0634
.06336
.99799
.80180
68,4
.99913
3 37 57-19
0.0635
0.06346
1 0,0
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 40.3-'
0.0640
0.06396
IO,O
o. 9979-5
0,6
8.80588
67,8
9.99911
o,3
3 40 00.95
.0641
.06406
.99795
.80656
67,7
.99911
3 40 21.57
.06416
•99794
.80724
67,6
.99910
3 40 42.20
.0643
.06426
• 99793
.80791
67,4
.09910
3 41 02.83
.06436
•99793
.80859
67,3
.99910
3 41 23.45
0."
0.06446
IO,O
0.99792
0,6
8.80926
67,2
9.99910
o,3
3 4i 44.o8
.0646
.06456
.99791
.80993
67,1
.09909
3 42 04.71
,06465
.99791
.81060
67,0
.99909
3 42 25.33
.06475
.99790
.81127
66,9
.99909
X3 42 45-96
.0649
.06485
.99789
.81194
66,8
.99908
3 43 06.59
0.0650
0.06495
10,0
0.09789
0,6
8.81261
66,7
9.90908
o,3
3 43 27.21
u
isinhiu
«F«'
cosh iu
-FO'
. sinh iu
«F0'
log cosh iu
«F0'
u
log ,
SMITMWONIAN TABLES
1 86
Circular Functions.
u
sin u
• Fo'
COS U
«F0*
log sin u
- F,/
log cos u
-F,-
u
0.0650
0.06495
IO,O
0.99789
0,6
8.81261
66,7
9.99908
O,3
0 , „
.0651
.06505
.997-S8
o,7
.81327
66,6
.99908
3 43 47.84
.0652
.0653
.06515
.06525
.99788
.99787
,8l3JM
.81460
66,5
66,4
•99008
.90907
3 44 08.47
3 44 29.09
.0654
•06535
.99786
.81527
66,3
.99907
3 44
0.0655
0.06545
10,0
0.99786
o,7
8.81593
66,2
9.99007
O,3
3 45 10.34
.0656
.06555
.99785
.81659
66,1
.09906
3 45 30.97
.0657
.06565
.99784
.81725
66,0
.99906
3 45 51.60
.0658
.06575
.99784
.81791
65*9
.09906
3 46 12.22
.0659
.06585
.99783
.81857
65,8
.90906
3 46 32.85
0.0660
0.06595
IO,O
0.99782
o,7
8.81923
65,7
9.09005
0,3
3 46 53.48
.0661
.06605
.99782
.81989
65,6
.99905
3 47 14.10
.0662
.0663
.06615
.06625
.99781
.99780
.82054
.82120
65,5
65,4
.99905
•09904
3 47 34-73
3 47 55- y>!
.0664
.06635
.09780
.82185
65,3
.99904
3 48 15-98
0.0665
0.06645
IO,O
0.99779
o,7
8.82250
65,2
9.99904
o,3
3 48 36.61
.0666
.06655
.99778
.82315
65,1
.99904
3 48 57.24
.0667
.06665
.99778
.82380
65,0
.90903
3 49 17-85
.0668
.06675
.99777
•82445
64,9
.09903
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
o,3
3 50 19-74
.0671
.06705
•99775
.82640
64,6
.99902
3 50 40.37
.0672
.06715
•99774
.82704
64,5
.90902
3 51 00.99
•0673
.06725
•99774
.82769
64,4
.99902
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
9.99901
0,3
3 52 02.87
.0676
.06755
•99772
.82962
64,1
.99001
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
.90770
.83154
63,9
.99900
3 53 25.38
0.0680
0.06795
IO,O
0.09769
o,7
8.83217
63,8
9.99900
o,3
3 53 46.01
.0681
.06805
.09768
.83281
63,7
.99899
3 54 06.63 1
.0682
.06815
.99768
.83345
63,6
.99899
3 54 27.26
.0683
.06825
.99767
.83408
63,5
.99899
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
o,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
0.0690
0.06895
IO,O
0.99762
o,7
8.83850
62,8
9.99897
o,3
3 57 12. -Y
.0691
.06905
.99761
.83913
62,8
.99896
3 57 32.90
.0692
.06914
.99761
.83976
62,7
.99806
3 57 53.52
.0693
.06924
.99760
.84039
62,6
.99896
3 58 14-15
.0694
.06934
.99759
.84101
62,5
.99895
3 58 3
0.0695
0.06944
IO,O
0.99759
o,7
8.84164
62,4
9-09895
o,3
3 58 55.40
.0696
.06954
.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
.09894
3 59 5
.0699
.06984
.99756
.84412
62,0
.09804
4 00 17-91
0.0700
0.06994
IO,0
0.99755
o,7
.84474
61,9
9-99894
o,3
4 oo 38.54
f t
. * C '
sinh iu
to F '
r t
u
- i sinh iu
w ro
cosh iu
w ro
og cosh iu
*» F0
u
SMITHSONIAN TABLES
187
Circular Functions.
u
sin u
w FO'
COS U
*>Fo'
log sin u
« Fo'
log cos u
«FO'
U
0.0700
0.06094
10,0
0.99755
o,7
8.84474
61,9
9.99894
0,3
4°oo' 38. '54
.0/01 ; .07004
•99754
.84536
6i,9
.99893
4 oo 59.i6
.0702 .07014
•99754
•84598
61,8
.99893
4 01 19.79
.0703 .07024
•99753
.84660
6i,7
.99893
4 01 40.42
.0704 .07031
•99752
.84721
61,6
.99892
4 02 01.04
0.0705 0.07044
IO,O
0.99752
o,7
8.84783
61,5
9.99892
0,3
4 02 21.67
.070:5 .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
IO,0
0.09748
o,7
8.85089
61,1
9.99890
o,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
IO,O
0.99744
o,7
8.85394
60,6
9.99889
0,3
4 05 47-93
.0716 .07154
.99744
•85454
60,6
.99889
4 06 08.56
.0717 .07164
-99743
.85515
60,5
.99838
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
10,0
0.99741
o,7
8.85696
60,2
9.99887
0,3
4 07 3L07
.0721 .07204
•99740
•85/56
60,1
.99887
4 07 51-69
.0/22 .07214
.99739
.85816
60,0
.99887
4 08 12.32
.0723 .0/224
•99739
.85876
60,0
.99886
4 08 32.95
.0724 .07234
.99738
.85936
59,9
.99886
4 08 53-57
0.0725
0.07244
1 0,0
0.99737
o,7
8.85996
59,8
9.99886
0,3
4 09 14-20
.0726 .O7254
•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 ii 38.58
.0733
.07323
•99731
.86472
59,1
.99883
4 ii 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,o
9-99883
o,3
4 12 40.46
.0736
•07353
.99729
.86649
58,9
.99882
4 U 01.09
.0737
.07363
.99729
.86707
58,8
.99882
4 13 21.72
.0738
.07373
.99728
.86766
58,7
.99882
4 U 42.34
•0739 -07383
•99727
.86825
58,7
.09881
4 H 02.97
0.0740 0.07393
IO,O
0.99726
o,7
8.86884
58,6
9.99881
o,3
4 14 23.60
.0741 .07403
.99726
.86942
58,5
.99881
4 14 44. 22 i
.0742 .07413
•99725
.87001
58,4
.99880
4 15 04.85
.0743 .07423
.997-24
•87059
58,3
.99880
4 15 25.48
.0744 -07433
.99723
.87117
58,3
.99880
4 15 46. 10
0.0745 0.07443
IO,0
0.09723
o,7
8.87175
58,2
9.99879
o,3
4 16 06.73
'•'> .07453
.0717 .07463
•99722
•99721
.87234
.87292
58,i
58,0
.99879
•99879
4 16 27-35
4 16 47- 1>8
S .07473
.99720
.87350
58,o
.99878
4 17 08. (>i
.0749
•07483
.99720
.87408
57,9
.99878
4 17 29.23
0.0750
0.07493
10,0
0.99719
o,7
8.87465
57,8
9.99878
0,3
4 i; 49.86
u
-i sinh iu
• H
cosh iu
«F0'
lOfl8^-"
-Fo'
ogcoshiu
«F,/
u
SMITHSONIAN TABLES
1 88
Circular Functions.
u
tin u
• ft
COS U
«Fo'
log sin u
« F,/
log cos u
u
0.0750
0.07493
IO,O
0.99719
o,7
8.87465
57,8
9.09878
0,3
4°i7'49'-'86
.0751
.07503
-718
0,8
.87523
57,7
.99877
4 i«S 10.49
.0/5-'
.07513
0717
.87581
57,6
.99577
4 18 31.11
• 0753
.07523
•717
.99877
4 18 51-74
• 0754
.07533
.99716
57,5
.93876
4 19 12.37
0.0755
0.07543
1 0,O
0.99715
0,8
8.87753
57,4
9.%876
0,3
4 19 32.99
.075(1
•07553
.99714
.87811
57,3
4 19 .
.0757
.07563
.99714
.87868
57,3
.99875
4 20
.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,o
9.99874
0,3
4 21 l6.I3
.07 )i
.07603
•997II
.88097
57,o
.99874
4 21 .
.07613
•99710
.88153
56,9
•99874
4 21 57.38
.0763
.07623
.99709
.S-L'io
.99873
4 22 iS.OO
.0764
.07633
.99/08
.88267
56,7
.%873
4 22 38.63
0.0765
0.07643
IO,O
0.99708
0,8
8.88324
56,7
9.99873
0,3
4 22 :
•07053
.99707
.88380
56,6
.99872
4 23 19.88
.99706
.88437
56,5
.99872
4 23 40.51
.07 8
.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
IO,O
0.99704
0,8
8.88606
56,3
9.99871
o,3
4 24 42-39
.0771
.07702
•99703
.88562
56,2
.99871
4 25 03.02
.0772
.07712
.99702
.88719
56,i
.99870
4 25 23. '>4!
• 0773
.07722
.99701
.88775
56,i
.99870
4 25 44-27
.0774
.07732
..99/01
.88831
56,0
.99870
4 26 04.90
0.0775
0.07742
10,0
0.99700
0,8
8.88887
55,9
9.99869
o,3
4 26 25.52
.0776
.07752
.99699
.88943
55,9
.99859
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
9.09868
o,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
55,1
.99866
4 30 12.41
.0787
.07862
.99690
.89553
55,i
.99865
4 30 33.04
.0788
.07872
.89608
55,o
.99865
4 30 53.67
.0789
.07882
•99689
.89663
54,9
.99865
4 31 M.29
0.0790
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
.<,<£ '4
4 32 16.17
• 0793
.07922
.99686
.89882
54,7
.99863
4 32 36.80
.0794
.07932
.99685
.89936
54,6
• 9i>803
4 32 57-43
0.0795
0.07942
IO,O
0.09684
0,8
8.89991
54,6
9.90863
0,3
4 33 18.05
.0796
.07952
.99683
.90045
54-4
.99862
4 33
.0797
.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 40.5^
0.0800
0.07991
10,0
0.99680
0,8
8.90263
54,2
9.90861
0,3
4 35 01.18
u
-isinhiu
»Fo'
cosh iu
-Fo'
lonSinh IU
•.FO'
logcosh iu
«>F '
u
loo .
SMITHSONIAN TABLES
189
Circular Functions.
u
sin u
«F0'
COS U
«Fo'
log sin u
« Fo'
log cos u
«FO'
u
O 4 H
0.0800
0.07991
10,0
0.99680
0,8
8.90263
54,2
9.99851
0,3
4 35 01. 18
.0801
.08001
.99679
.90317
54J
.99861
4 35 21. 81
.0802
.08011
.99679
.90371
54,0
.99860
4 35 42.44
.0803
.08021
.99678
.90425
54,0
.99860
4 36 03.06
********
.0804
.08031
.99677
•00479
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
.99570
.00961
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
.081-51
.99667
.91121
53,i
.99855
4 40 31-21
.0817
.08161
.99666
.9H74
53,o
.99855
4 40 51-83
.0818
.08171
.99666
.91227
53,o
.99855
4 41 12.46
.0819
.08181
.99665
.91280
52,9
.99854
4 41 33.09
0.0820
0.08191
10,0
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 U.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
10,0
0.09660
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
1 0,0
0.99556
0,8
8.91858
52,2
9.99850
0,4
4 45 19.98
.0831
.08300
.99655
.91910
52,i
.00850
4 45 40.61
.0832
.08310
.99654
.91962
52,1
.09850
4 46 01.23
.0833
.08320
.99653
.92014
52,0
.09849
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
.08350
.99651
.92170
5i,8
.99848
4 47 23.74
.0837
.08360
.99650
.92222
5i,8
.99848
4 47 44.36
.0838
.08370
.99649
.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
5i,5
.99846
4 49 06.87
.0842
.08410
.99646
.92480
5i,5
.99846
4 49 27.50
.0843
.08420
.99645
.92531
51,4
.99846
4 49 48.12
.0844
.08430
.99544
.92583
51,3
.99845
4 50 o8.75
0.0&4S
0.08440
1 0,0
0.99643
0,8
8.92634
5i,3
9.99845
0,4
4 50 29.38
.0846
.08450
.99642
.92685
5i,2
.99844
4 50 50.00
.08460
.99642
.92736
51,2
.99844
4 51 10.63
.0848
.08470
.99641
.92788
5i,i
.99844
4 51 3L26
.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
«F0'
cosh iu
«F,/
iog'infi-u
-Fo1
log cosh iu
«F,/
u
SMITHSONIAN TABLES
IQO
Circular Functions.
u
sin u
«F0'
COS U
-F'
log sin u
- Fo'
log cos u
-Fo'
u
0.0850
0.08490
10,0
0.99639
0,8
8.92800
51,0
9.09843
0,4
4°52'i2'.'5i
.0851
.08500
.09638
0,8
.92941
50,9
.99843
4 52 33-14
.0852
.08510
.00637
0,9
.'J-W
50,9
•99842
4 52- 53.76
.0853
.08520
.99636
.93042
50,8
.99843
4 53 U-39
.0854
.08530
.00636
•93093
50,7
.09841
4 53 35-01
0.0855
0.08540
I O,0
0.99635
0,9
8.93144
50,7
0.09841
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
0,9
8.93396
50,4
9.90839
0,4
4 55 38.77
.0861
.08509
.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
o,9
8.93647
50,i
9.09837
0,4
4 57 21.91
.0866
.08649
.99625
.93697
50,o
•99837
4 57 42.53
.0867
.08659
.99624
.94747
50,0
.99837
4 58 03 . 16
.0868
.08669
.99624
•93797
49,9
.99836
4 58 23.79
.0869
.08679
.09623
.93847
49,9
.99836
4 58 44-41
0.0870
0.08689
IO,O
0.09622
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 00 27.5*
0.0875
0.08739
IO,O
0.09617
0,9
8.94145
49,5
9-90834
0,4
5 oo 48.17
.0876
.08749
.99617
•94195
49,5
•99833
5 01 08.80
.0877
.08759
.996l6
.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
10,0
0.99613
0,9
8.94392
49,2
9.99832
0,4
5 02 31.30
.0881
.08799
.99512
•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 33-18
.0884
.08828
.99610
•94589
49,0
•99830
5 03 53-81
0.0885
0.08838
10,0
0.99609
o,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
.90607
•94735
48,8
.99829
5 04 55.69
.0888
.08868
.99606
•94784
48,8
.99829
5 05 16.31
.0889
.08878
.99605
•94833
48,7
.99828
5 05 36.94
0.0890
0.08888
1 0,0
0.99604
0,9
8.94882
48,7
9.09828
0,4
5 05 57.57
.0891
.08898
.99603
•94930
48,6
•99827
5 06 18.19
.0892
.08908
.99602
•94979
48,6
•99827
5 06 38.82
.0893
.08918
.90602
•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
0.09600
0,9
8.95124
48.4
9.09826
0,4
5 07 40.70
.0896
.08948
• 99599
.95173
48,3
.09825
5 08 01.33
.0897
.0898
.08958
.08968
•99597
•95221
.95269
48,3
48,2
.09825
•09825
5 08 21.95
5 08 42.58
.0899
.08978
.99596
.95317
48,2
.99824
5 09 03.21
0.0900
0.08088
IO,O
0.99595
0,9
8.95366
48,1
9-09824
0,4
5 09 23-83
u
-i sinh iu
«F0'
cosh iu
«FO'
sinh iu
«F0'
log cosh iu
«FO'
u
log .
SMITHSONIAN TABLES
Circular Functions.
u
sin u
«F0'
COS U
«F0'
log sin u
« Fo'
log cos u
«>Fo'
U
O / 44
0.0900
.0901
.0902
.0903
.0904
0.08988
.08998
.09008
.09018
.09028
IO,O
0.99595
.99594
.99593
•99593
.99592
o,9
8.95366
.954U
.95462
.95510
.95558
48,1
48,1
48,0
48,0
47,9
9.99824
.99823
.99823
.99823
.99822
0,4
5 09 23.83
5 09 44.46
5 10 05.09
5 10 25.71
5 10 46.34
0.0905
.0906
.0907
.0908
.0909
0.09038
.09048
.09058
.09068
.09077
1 0,O
0.99591
.99590
.99589
.99588
.99587
o,9
8.95606
.95653
.95701
.95749
.95797
47,9
47,8
47,8
47,7
47,6
9.99822
.99822
.99821
.99821
.99820
0,4
5 ii 06.96
5 ii 27.59
5 ii 48.22
5 12 08.84
5 12 29.47
0.0910
.0911
.0912
.0913
.0914
0.09087
.00097
.09107
.09117
.09127
I O,O
0.99586
.99585
.99584
.99584
.99583
o,9
8.95844
.95892
•95939
.95087
.96034
47,6
47,5
47,5
47,4
47,4
9.99820
.99820
.99819
.99819
.99818
0,4
5 12 50.10
5 13 10.72
5 13 31-35
5 13 5i.£'8
5 14 12.60
0.0915
.0916
.0917
0.09137
.09147
.09157
10,0
0.99582
.99581
.99580
0,9
8.96081
.96129
.96176
47,3
47,3
47,2
9.998l8
.99818
.90817
0,4
5 H 33-23
5 14 53-86
5 15 U.48
.0918
.0919
.09167
.09177
.99579
.99578
.96223
.96270
47,2
47,1
.09817
.99816
5 15 35.ii
5 15 55-74
0.0920
.0921
0.09187
.09197
IO,O
0.99577
.99576
o,9
8.96317
.96365
47,1
47,o
9.99816
.09816
0,4
5 16 16.36
5 16 36.99
.0922
.09207
•99575
.06412
47,o
.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
IO,O
0.99572
0,9
8.06552
46,8
9.99814
0,4
5 17 59-49
.0926
.09247
.99572
.96b99
46,8
.00814
5 18 20.12
.0927
.09257
.99571
.96646
46,7
.99813
5 18 40.75
.0928
.09267
.09570
.96692
46,7
.09813
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
9.99810
0,4
5 21 25.76
.0936
.09346
.99562
.97064
46,3
.99809
5 21 46.39
• 0937
.09356
.99561
.97110
46,2
.99809
5 22 07.OI
.0938
.09366
.09560
.97157
46,2
.99809
5 22 27.64
• 0939
.09376
.99559
.97203
46,1
.99808
5 22 48.27
0.0940
0.09386
1 0,0
0.99559
o,9
8.97249
46,1
9.99808
0,4
5 23 08.89
.09396
.99558
.97295
46,0
.99807
5 23 29.52
.09406
.99557
.57341
46,0
.99807
5 23 50.14
.0943
.09416
.99556
.97387
45,9
.99807
5 24 10.77
.0944
.09426
.99555
•97433
45,9
.99806
5 24 3L40
0.0945
0.00436
10,0
0.99554
0,9
8.97479
45,8
9.99806
0,4
5 24 52.02
.09446
.99553
.97524
45,8
.99805
5 25 12.65
.09456
•99552
•97570
45,7
.99805
5 25 33-28
.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'
I0n8inh j
»Fo'
log cosh i
«FO'
u
log ,
SMITHSONIAN TABLES
192
Circular Functions.
u
sin u
«F0'
COS U
«Fo'
log sin u
« F '
log cos u
»F«'
u
0.0950
0.09486
10,0
0.99549
0,9
8.97707
45,6
9.09804
0,4
o / //
5 26 35.16
.0951
.09496
.99548
0,9
•97753
45,5
.99803
5 26 55.78
.0952
.09506
•99547
1,0
.97798
45,5
.09803
.0953
.09516
.99546
.07844
45,4
.99802
7.04
.0954
.095^6
•99545
.97889
45,4
.99802
0.0955
0.09535
10,0
0.99544
I,O
8.97934
45,3
0.oo8tt
0,4
5 28 18.29
.0950
•09545
•99543
.97980
45,3
.99801
38.93
.0957
•09555
•99542
.98025
45,-'
.99801
59-54
.0958
• 09565
•99541
.98070
45,2
.99800
5 29 -
.0959
.09575
•99541
98II5
45,1
.99800
;o-79
0.0960
0.09585
10,0
0.99540
1,0
8.98160
45,1
9.99800
0,4
5 30 01.42
.0'/>I
•09595
•99539
.98205
45,1
•99799
5 30 22.05
.0952
.o>X)5
.99538
.98251
45,0
•99799
5 30 .
.0963
.09 >i5
•99537
.08295
45,0
•99798
5 3i 03.30
.0964
.09625
.99536
.98340
44,9
•99798
5 3i 23.93
0.0965
0.09635
IO,O
0.99535
1,0
8.98385
44,9
9.99797
0,4
5 31 44-55
.09%
.09645
•99534
.98430
44,8
•99797
5 32 05.18
.0967
.09655
•99533
.98475
44,8
.99797
5 32 25.81
.0968
.00665
•99532
.98520
44,7
•99796
5 32 46.43
.0959
.09675
•99531
.98564
44,7
•99796
5 33 07-06
O.O970
0.09685
IO,O
0.99530
1,0
8.98609
44,6
9-99795
0,4
5 33 -
.0971
.09695
.99529
.98654
44,6
.99795
5 33 -
.0972
.09705
.99528
.98698
44,5
.99795
5 34 08.94
•OQ73
.09715
.99527
.98743
44*5
•99794
5 34 29.57
• 097-i
.09725
.99526
.08787
44,4
•99794
5 34 50-19
0.0975
0.09735
10,0
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
.o<j77
.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
10,0
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--
.0983
.09814
.99517
.99185
44,0
.99790
5 37 55-^
.0984
.09824
.99516
.99229
44,0
•99789
5 38 16.,
0.0985
0.09834
IO,O
0.99515
1,0
8.99273
43,9
9.99/89
0,4
5 38 37.08
.0986
.09844
.99514
.99317
43,9
.99789
5 38 57-71
.0987
.-09854
.99513
.99361
43,9
.99788
5 39
.0988
.00864
.09512
-99405
43,8
.99788
5 39 38.96
.0989
.09874
•995II
•99449
43,8
.99787
5 39 59-5
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
.997
5 40 40.84
.09904
.99508
.99580
43,6
.99786
5 4i 01.47
.0993
.09914
.99507
.99624
43,6
.997
5 41 22.10
.0994
.09924
.99506
.99667
43,5
.99785
5 41 42.72
0.0995
0.09934
IO,O
0.99505
1,0
8.997H
43,5
9.99785 0,4
5 42 03.3=
.<>»••
.09944
.99504
•99754
43,5
.99784
5 42 23.97
.0997
.09953
•99503
.99798
43,4
.997&4
5 42 44.60
.0998
.09963
.99502
.99841
43,4
•997
5 43 05.2.:
.0999
.09973
.99501
.99884
43,3
•99/83
5 43 25. 85
O.IOOO
0.09983
10,0
0.99500
1,0
8.99928
43,3
9.99782
«4
5 43 46.48
u
isinhiu
->Fu'
cosh iu
»> FQ'
sinh iu
«-Fo'
log cosh iu u F ..'
u
log .
SMITHSONIAN TABLES
193
Circular Functions.
u
sin u
«F0'
cos u
«Fo'
log sin u
« Fo'
log cos u
-Fo'
u
O.IOO
0.09083
99,5
0.99500
10,0
8.99928
432,8
9.99782
4,4
5°43'46"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
.OI2O7
420,2
.99769
4,5
5 54 05.28
.104
. 10381
99,5
.99460
10,4
.01625
416,1
.99765
4,5
5 57 3L54
O.I05
o. 10481
99*4
0.99449
10,5
9-02039
412,1
9.99760
4,6
6 oo 57.8o
.106
.10580
99,4
.99439
10,6
.02449
408,2
.99756
4,6
6 04 24.07
.107
.I0680
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
o. 10978
99,4
0.99396
11,0
9.04052
393,2
9-99737
4,8
6 18 09.13
.in
.11077
99,4
.99385
n, i
•04443
389,6
.99732
48
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
n,3
.05215
382,7
.99722
4,9
6 28 27.92
.114
.11375
99,4
•99351
11,4
.05596
379,3
.99717
5,0
6 31 54-19
O.II5
O.I 1475
99,3
0.99339
n,5
9.05974
376,0
9.99712
5,o
6 35 20.45
.116
.H574
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
n,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
O.I2O
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
.9968!
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
35i,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
.096^9
5,5
7 16 35.63
.128
. 12765
99,2
.99182
12,8
.10602
337,4
5,6
7 20 01 .90
.129
.12864
99,2
.99169
12,9
.10938
334,8
.99638
5,6
7 23 28.16
0.130
0.12963
99,2
0.99156
13,0
9.11272
332,2
9.99632
5,7
7 26 54.42
.131
.13063
99,1
.99143
13,1
.11603
329,6
.99626
5,7
7 30 20.69
.132
.13162
99,1
.99130
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
.13360
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
3i5,o
•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
3io,4
.99579
6,1
7 57 5o.8i
0.140
0.13954
99,0
0.99022
14,0
9. 14471
308,2
9-99573
6,1
8 01 17.07
.141
• M053
99,0
.99008
14,1
• U778
306,0
.99567
6,2
8 04 43-34
.143
.14152
99,0
.98993
14,2
.15083
303,8
.9956i
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
.146
.147
,148
0.14449
.14548
.14647
. 14746
99,0
98,9
98,9
sfcg
98,9
0.98951
.98936
.98921
.98907
.98892
14,4
14,5
14,6
14,7
14,8
9.15985
. 16281
. 16575
.16868
.17158
297,4
295,3
293,3
291,3
289,3
9.99542
.99535
.99529
.99523
.99516
£3
6,4
6,4
6,5
6,5
8 18 28.40
8 21 54.66
8 25 20.93
8 28 47.19
8 32 13.46
0.150
0.14044
98,9
0.98877
14,9
9.1/446
287,4
9-99510
6,6
8 35 39-72
u
-isinhiu
*H
cosh iu
«FO'
sinh iu
• Fo'
og cosh iu
-FO'
u
iMITMSONIAN TABLES
104
Circular Functions.
u
sin u
»F0'
cos u
w F log sin u
" F :
log oos u
~ F u
0.150
0. 14944
98,9
0.98877
14,9
9.1/446
287,4
9.99510
6,6
8 35 39.72
.151
.15043
98,9
.98862
15,0
.17/33
285*
.99503
6,6
8 39 05.99
.152
.15142
98,8
.98847
JS,I
.18017
-'«3,5
.99496
6,7
« 42 32.25,
.153
.15240
98,8
.98832
15,2
.18300
281,6
.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
.15734
98,8
.98754
15,7
.19685
272,6
.99456
6,9
9 03 09.84
• 159
.15833
98,7
.98739
15,8
•19957
270,8
.99449
7,0
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
.16031
98,7
.98707
1 6,0
.20495
267,4
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
7,1
9 20 21. 16
.164
. 16327
98,7
.98658
16,3
.21290
202,4
.99413
7,2
9 23 47-43
0.165
o. 16425
98,6
0.98642
16,4
9.2I55I
260,8
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
9.99309
7,5
9 44 25.02
• i/i
.17017
98,5
.98542
i7,o
.23088
25i,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 43-8l
.174
.17312
98,5
.98490
17,3
.23836
247,1
•99339
7,6
9 58 10. 08
0.175
0.17411
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 n 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
O.IOO
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
.19082
98,2
.98162
19,1
.28063.
-'-'3-4
.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
n 06 55-37
0.195
0. 19377
98,1
0.98105
19,4
9.28728
219,9
9.99169
8,6
II TO 21.64
.196
. 19475
98,1
.98085
19,5
.28947
218,7
.99160
8,6
II 13 47.00
.197
. 19573
98,1
.98066
19,6
.29165
217,6
.99152
8,7
II 17 14.17
.198
.19671
98,0
.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. 19867
98,0
0.98007
19,9
9.29813
214.2
9.99126
8,8
II 27 32.96
U
-isinhiu
U.FO'
cosh iu
»F0'
sinh iu
« F,/
log cosh iu
«FO'
U
loo .
SMITHSONIAN TABLES
195
Circular Functions.
u
sin u
»F0'
cos u
«F0'
log sin u
« Fo'
log cos u
«F0'
u
O.2OO
0.19867
98,0
0.98007
19,9
9-29813
214,2
9.99126
8,8
1 1 °2/ 32 '96
.2OI
.19965
98,0
.97987
20,0
.30027
213,1
.99H7
8,8
ii 30 59-23
.2C2
.20063
98,0
.97967
20,1
.30239
212,1
.99108
8,9
n 34 25.49
.203
.20161
97,9
-97947
20,2
.30451
2II,O
.09099
8,9
ii 37 51.76
.204
.20259
97,9
.97926
20,3
.30661
209,9
.99090
9,0
II 41 18.02
0.205
0.20357
97,9
0.97906
20,4
9.30871
208,9
9.99081
9,o
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
20,6
.31286
206,8
•99063
9,1
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 55.61
.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
.09017
9,3
12 08 48.14
.213
.21139
97,7
.97740
21,1
•32509
200,8
.00007
9,4
12 12 14.40
.214
.21237
97,7
.97719
21,2
.32709
199,8
.98998
9,4
12 15 40.67
0.215
0.21335
97,7
0.97698
21,3
9.32909
198,9
9.98988
9,5
12 19 06.93
.216
.21432
97,7
.97676
21,4
•33107
197,9
.98979
9,5
12 22 33.20
.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
.08960
9,6
12 29 25.73
.219
.21725
97,6
.97612
21,7
.33697
i95,i
.98950
9,7
12 32 51.99
0.22O
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 50 03.32
0.225
0.22311
97,5
0.97479
22,3
9.34851
189,8
9.08891
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
.98851
10,1
13 07 14-64
0.230
0.22708
97,4
0.97367
22,8
9.35789
185,5
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
.08821
10,3
13 17 33-44
•233
.23000
97,3
.97298
23,1
.36342
183,0
.08810
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 11.02
.239
•23673
97,2
.97158
23,7
.37426
178,2
.98748
1 0,6
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
97,1
.97086
24,0
•37957
i75,9
.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
.97038
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
.06989
24,4
.38655
I73,o
.98672
10,9
14 05 41.14
•24450
97,0
.96965
24,4
.38827
172,2
.98662
11,0
14 09 07.41
.248
.24547
g60
.96941
24,5
.38099
I7i,5
•98651
11,0
14 12 33.67
.24643
96,9
.06916
24,6
.39170
170,8
.98640
II,O
14 15 59.94
0.250
0.24740
96,9
0.96891
24,7
9-39341
170,1
9.98628
n, i
14 19 26.20
u
-itinhiu
• IV
cosh iu
«F0'
. sinh iu
-Fo'
log cosh iu
«FO'
u
log ,
SMITHSONIAN TABLES
196
Circular Functions.
u
sin u
«FO'
cos u
- F '
log sin u
iu F
log cos u
o,F '
U
0.250
0.24740
96,9
0.96891
24,7
9.39341
170,1
9.08628
II, I
14 19 26.20
.251
.24837
96,9
.96866
24,8
•39510
.98617
II, I
14 22 52.47
.252
•24934
96,8
.96842
24,9
.39679
168,7
11,2
14 26 18.73
.253
.25031
96,8
.96817
25,0
.39848
168,0
.98595
11,2
14 29 45.00
.-'54
.25128
96,8
.96792
25,1
.40015
167,3
•98584
n,3
14 33 11.26
0.255
0.25225
96,8
0.96766
25,2
9.40182
166,6
9.98572
u,3
14 36 37.53
.256
.25321
96,7
.96741
25,3
•40349
165,9
.98561
n,4
14 40 03.79
.257
.25418
96,7
.96716
25,4
.40514
165,2
.98550
n,4
14 43 30.06
.258
.25515
96,7
.96690
25,5
.40679
164,6
.98538
",5
u 46 s
.259
.25611
96,7
.96665
25,6
.40843
163,9
.98527
ii,5
14 50 22.58
0.260
0.25708
96,6
0.06639
25,7
9.41007
163,3
9.98515
n,6
14 53 48.85
.261
.25805
96,6
.96613
25,8
.4H70
162,6
.98504
n,6
14 57 15.11
.262
.25901
96,6
.96587
25,9
.41332
162,0
.08492! 11,6
15 oo 41.38
.263
.25998
96,6
.96561
26,0
•41494
161,3
.984*0 1 1.7
15 04 07/14
.264
.26094
96,5
.96535
26,1
.41655
160,7
.98469 n,7
15 07 33-91
0.265
0.26191
96,5
0.96509
26,2
9.4I8I5
160,0
9.98457 11,8
15 ii 00.17
.266
.26287
96,5
.96483
26,3
.41975
159,4
.98445
11,8
15 14 20.44
.267
.26384
96,5
.96457
26,4
.42134
158,8
.98433
11,9
15 17 52.70
.268
.26480
96,4
.96430
26,5
.42292
158,2
.98421 J 11,9
15 21 18.97
.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 31 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
I55J
.98361
12,2
15 38 30.29
•2/4
.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
152,8
.98312 12,3
15 52 I5.35i
.278
•27443
96,2
.96161
27,4
.43844
152,2
.98300 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
9.44U7
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
.284
.27924
.28020
96,0
96,0
.06022
.95994
27,9
28,0
•44597
•44/46
LB8
•98237
.98225
12,6
12,7
16 12 52.94 i
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
U7,i
.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.29O
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
U5,o
.98135 13,0
16 40 23.06
.2Q2
.28787
95,8
.95767
28,8
.45919
M4.5
.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
M3,4
.98095
I3,i
16 50 41.85
0.295
0.29074
95,7
0.95680
29,1
9.46350
142,9
9.98082
13.2
H> 54 08. 12
.296
.29170
95,7
.95651
29,2
.46493
142.4
.98069
13,2
-U-38
.297
.29265
95,6
.95622
29,3
.46635
141.0
.98056
13,3
17 oi 00.65
.298
.29361
95,6
.95593
29,4
.46777
141,4
.98042
U.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
»F0'
cosh iu
„ Fo, | IOB!i"»LL»
• Fo'
log cosh iu
u> F '
u
SMITHSONIAN TABLES
197
Circular Functions.
u
sin u
«FO'
cos u
«F0'
log sin u
«- Fo'
log cos u
w FO'
u
0.300
0.29552
95,5
0.95534
29,6
9.47059
140,4
9.98016
13,4
17 Il'l9?44
.301
.29648
95,5
.95504
29,6
.47199
139,9
.98002
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
13,7
17 28 30.77
.306
.30125
95,4
.95355
30,1
.47892
137,5
.97934
13,7
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
.30411
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
135,1
.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
.95111
30,9
.48977
133,7
.97823
14,1
17 59 27.15
0.315
0.30982
95,i
0.95080
3i,o
9.49110
133,3
9.97809
14,2
18 02 53.41
.316
.31077
95,o
.95049
3i,i
.49244
132,8
•97795
14,2
18 06 19.68
.317
.31172
95,o
.95017
31,2
.49376
132,4
.97780'
14,2
18 09 45-94
.318
.31267
95,o
.94986
3i,3
.49508
I3i,9
.97766
14,3
l8 13 12.21
.319
.31362
95,o
•94955
3i,4
.49640
I3i,5
.97752
14,3
18 16 38.47
0.320
0.31457
94,9
0.94924
3i,5
9-49771
I3U
9-97737
14,4
18 20 04.74
.321
.31552
94,9
.94892
3i,6
.49902
130,6
.97723
14,4
18 23 31.00
.322
.31646
94,9
.94860
3i,6
.50032
130,2
.97709
14,5
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 49-80
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
M,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
01187
126,4
.97576
U,9
18 57 53.65
.332
.32593
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
0.94441
32,9
9-51689
124,8
9.97516
I5,i
19 ii 38.71
.336
.32971
94,4
.04408
33,0
.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
94J
0.94108
33,8
9.52917
120,8
9.97362
15,6
19 46 01.36
•33914
94,1
•94074
33,9
•53038
120,5
.97347
15,7
19 49 27.62
• 347
.34008
94,0
.94040
34,0
.53158
I2O,I
.97331
15,7
19 52 53-89
.348
•34102
94,0
.94006
34,1
.53278
H9,7
.97315
15,8
19 56 20.15
• 349
.34196
94,0
.93972
34,2
•53397
H9,3
.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
V
-Isinhiu
«F0'
cosh iu
«F,/
, sinh iu
-Fo'
log cosh iu
«FO'
u
log j
SMITHSONIAN TABLES
198
Circular Functions.
u
sin u
«oF,/
cos u
<o F ' log sin u
- F;
log cos u
co F U
0.350
0.34290
93,9
0.93937
34,3
9.53516
119,0
9.97284
15,9
20 03
.351
.34384
93,9
.93903
34,4
.53635
118,6
15,9
JO 0 i .
.352
.34478
93,9
.93869
34,5
•53754
118,2
20 10 05.21
! -353
•34571
93,8
.93834
34,6
.53872
H7,9
20 13 3L48 ;
i -354
.34665
93,8
•93799
34,7
.53989
H7,5
16,1
20 16
0.355
0-34759
93,8
0.93765
34,8
9.54107
117,2
9.97204
16,1
2O 2O 24.OI
.356
.34853
93,7
.93730
34,9
.54224
116,8
.971&H
20 23 50.27
.357
.34946
93,7
.93695
34,9
•54340
I I'M
.97172
16,2
20 27 16.54
.358
.35040
93,7
.93660
35,0
•54457
116,1
.97155
16,2
20 3O 42.8O
• 359
.35134
93,6
•93625
35,1
•54573
H5,7
•97139
1*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
i<M
20 41 01. '0
; .362
•354T5
93,5
•93519
35,4
.54918
H4,7
.97090
16,4
20 44 27.86
; .363
.35508
93,5
•93484
35,5
.55033
iM,3
.97074
16,5
20 47 54 . i 2
• .364
.35601
93,4
•93448
35,6
.55M7
114,0
.97057
16,5
20 51 2O-39
, 0.365
0.35095
93,4
0.93412
35,7
9.55261
H3,7
9.97040
16,6
20 54 4^.65
i .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
113,0
.97007
16,7 21 01 39.18
i .368.
.35975
93,3
•93305
36,0
.55600
112,6
.06950
16,7 21 05 05.45
! .369
.36068
93,3
.93269
36,1
•55713
112,3
.90974
16,8 21 08 31-71
' 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
.96923
16,9 21 18 50.51
.373
.36441
93,1
.93124
36,4
.56159
III,O
.96906
I/,O 21 22 16.77
• 374
.36534
93,1
.93087
36,5
.56270
110,7
.9^889
17,0 21 25 4^
0.375
0.36627
93,1
0.93051
36,6
9.56380
110,3
9.06872
17,1 21 2Q 09.30
.376
.36720
93,0
•93014
36,7
•56491
110,0
.93855
17,1 21 32 35.57
• 377
.36813
93,0
•92977
36,8
.56600
109,7
.96838
I/,2 21 36 01
.378
.36906
92,9
.92940
36,9
.56710
109,4
.96820
17,2 21 39 28,
• 379
.36999
92,9
•92904
37,o
.56819
109,0
.96803
17,3
21 42 54.06
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
17,4 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 00 05.69
0.385
0.37556
92,7
0.92680
37,6
9.57468
107,2
9.96699
17,6
22 03 31-95
.386
.37649
92,6
.92642
37,6
•57575
106,9
.96681
17,6 22 O6 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
1 06,0
.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
.96592
17,9
22 24 09-54
• 392
.38204
92,4
.92415
38,2
.58211
105,1
.96574
18,0 22 _>7 35-8o
•393
.38206
92,4
•92376
38,3
.58316
104.8
.96556
l8,0 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
.96502
22 41 20.86
•397
.38665
92,2
.92223
38,7
08732
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
-i sinh iii
»Fo'
cosh iu
«F0'
sinh iu
CO F,'
ogcosh iu
• FO'
U
log .
SMITHSONIAN TABLES
199
Circular Functions.
u
sin u
«F0'
cos u
wFo'
log sin u
« Fo'
loo cos u
"> FO'
u
0.400
0.38942
92,1
0.92106
38,9
9.59042
102,7
9.96429
18,4
22°55/05/./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
91,9
.91950
39,3
.59450
101,6
.96355
18,6
23 08 50.98
0.405
0.39402
91,9
0.91910
39,4
9.59552
101,3
9.96336
18,6
23 12 17.25
.406
•39494
91,9
.91871
39,5
.59653
101,0
.96318
18,7
23 15 43-51
.407
.39586
9i,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
9i,8
.91752
39,8
-59955
100,2
.96262
18,8
23 26 02.31
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
9i,6
.91632
40,0
.60254
99,4
.96205
19,0
23 36 21. IO
.413
.40136
91,6
.91592
40,1
.60353
99,1
.96186
19,0
23 39 47.36
.414
.40227
91,6
.91552
40,2
.60452
98,8
.96167
I9,i
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
9i,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
91,3
.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
9.96051
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
9U
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 28.81
.427
.41414
91,0
.91021
41,4
.61715
95,5
.959H
19,8
24 27 55.07
.428
.41505
9i,o
.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 47.6o
0.430
0.41687
90,9
0.90897
41,7
9.62000
94,7
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
.41060
90,8
.90771
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
.90603
42,3
.62657
93,o
.95714
20,3
25 02 17.72
.438
.42413
00,6
.90560
42,4
.62750
92,8
.95694
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
•44-'
.42775
90,4
.90390
42,8
.63119
9i,8
.95612
2O,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
91,3
•95571
20,7
25 216 21.57!
0.445
0.43046
90,3
0.90261
43,0
9.63393
91,1
9-95550
20,7
25 29 47-84
.43136
90,2
.90218
43,1
.63484
00,8
.95529
20,8
25 33 U.io
•447
.43M6
90,2
.90175
43,2
.63575
90,6
•95509
20,8
25 36 40.37
.448
.43316
90,1
.90132
43,3
.63665
00,4
.65488
20,9
25 40 06.63
•449
•43406
90,1
.90088
43,4
.63755
90,1
.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
• Fo'
cosh iu
• iv
sinh iu
• Fo'
log cosh iu
o>F0'
u
loo ,
SMITHSONIAN TABLES
2OO
Circular Functions.
u
sin u
«F0'
cos u
u* F ' log sin u
« F '
log cos u
-FO'
u
0.450
0-43407
00,0
0.90045
43,5
9.63845
89,9
9.95446
21,0
25°46/59''i6
.451
.43587
90,0
.C.OOO1
43,6
.63935
8Q,7
21,0
25 50 25.43:
• 45-
.43677
90,0
.89958
43-7
.64025
•95404
21,1
25 53 5
•453
.43766
89,9
.89914
43,8
.64114
89,2
31,1
25 57 17-96
• 454
•43^56
89,9
43,9
.64203
89,0
.95361
26 00 .;
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 3''- 75
• 4^7
.44126
89,7 ; .89738
44.1
.64469
88,3
21,4
26 u 03.02
.458
.44216
89,7 ! -89694
44,-'
.64557
88,1
.95276
21,4
_*) 14 29.28
• 459
.44305
89,6
.89650
44,3
.64645
87,9
•95255
21,5
26 17 5oo5
0.460
0-44395
89,6
0.89605
44,4
9.64733
87,7
9-95233
21,5
26 21 21. 8l
.461
•444*4
89,6
.89561
44.5
.64821
87,4
•95212
21,6
48.08
,462
•44574
890
.89516
44.6
.64908
87,2
• 95KO
21,6
26 28 14.34
.463
•44663
89,5
.89472
44,7
.64995
87,0
.95109
21,7
25 31 40.61
.464
•44753
89,4
.89427
44,8
.65082
86,8
.95M7
21,7
26 35 06.87
0.465
0.44842
89,4
0.89382
44,8
9.65169
85,6
9.95125
21,8
26 38 33-13
.466
•4493^
89,3
.89337
44,9
.65255
86,4
•95103
21,8
2(> 41 59.40
.467
•45021
89,3
.89292
45,0
.65341
86,1
.95081
21,9
25 45 25.60
.468
.45110
89,2
.89247
45,1
.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
9.9-5015
22,1
26 55 44-46
• 4/1
•45378
89,1
.89111
45,4
.65684
85,3
•94^93
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
-2.2
27 06 03.25
• 474
.45645
89,0
.88975
45,6
.65939
84,7
.94927
22,3
27 09 29.52
0-475
0.45734
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
.482
.46267
•46355
88,7
88,6
.88653
.88607
46,3
46,4
.66527
.66610
83,2
83.0
.94769
•94747
22,7
22,7
27 33 33-37
27 36 59.04
• 483
.46444
88,6
.88561
46,4
.66693
82,8
.94724
22.8
27 40 25.90
.484
•46532
88,5
.88514
46,5
.66/75
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
-Vv I
27 57 37-23
.489
•46974
88,3
.88280
47,o
.67186
81,6
.94586
23,1
28 oi 03.49
0.400
0.47063
88,2
0.88233
47,1
9.67268
81,4
9.94563
-V-'
28 04 29.76
.491
.47151 88,2
.88186
47,2
.67349
81,2
.94540
-'.>-'
28 07 56.02
.492
.47239 88,1
.88139
47,2
.67430
81,0
.94517
-'3-3
_-S u ;
• 493
.47327
88,1
.88092
47,3
.67511
80,8
.94493
2&3 28 14 48.55
•494
•47415
88,0
.88044
47,4
• 67592
80,6
.94470
-'3-4
28 18 14.81
0-495
0.47503
88,0
0.87997
47,5
9.67672
80,5
9-94447
-\3.4
28 21 41.08
.496
•47591
87,9
.87949
47,6
.67753
8oj
.94423
28 23 07.34
.497
• 476?>
87,9
.87902
47,7
.67833
80, i
.94400
33.61
.498
.47767
87,9
.87854
47,8
.67913
79,9
.94376
28 31 59-87
•499
.47855
87,8
.87806
47,9
.67993
79,7
•94352
28 35 26.14
0.500
0.47943
87,8
O_,__Q
0.0/7^0
47,9
9.68072
79,5
9.94329
28 38 52.40
u
-i sinh iu
•»Fo'
cosh iu
«F0'
.sinh i"
«Fo'
log cosh iu
«- F,/
u
log •
SMITHSONIAN TABLES
201
Circular Functions.
u
sin u
«F0'
cos u
«F0*
log sin u
« Fo'
log cos u
• Fo'
U
O / //
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 11.20
.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
240
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,o
•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,J
.94040
24,4
29 20 07.58
.513
.40079
87,1
.87128
49,1
.60050
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 52.04,
.517
.49427
86,9
.86931
49,4
.09397
76,4
.93917
24,7
29 37 18.50
.518
.495U
86,9
.86881
49,5
.69473
76,2
.93893
24,8
29 40 45-17
.519
.49601
86,8
.80832
49,6
.69549
76,0
.93868
24,8
29 44 H.43
0.520
0.49688
86,8
0.86782
49,7
9.69625
75,9
9.93843
24,9
29 47 37.70
.521
•49775
86,7
.86732
49,8
.69701
75,7
.93818
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
9.7OOO2
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 ii 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
30 22 00.35
.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
7353
9.93463
25,7
30 39 11.67
.536
.51070
86,0
.85976
5i,i
.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
.51328
85,8
.85822
5i,3
.71035
72,6
.93360
26,0
30 52 56.73
0.540
0.51414
85,8
0.85771
5i,4
9.71108
72,5
9-93334
26,0
30 56 23.00
• 541
.51499
85,7
.85719
5i,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
.51671
85,6
.85616
5i,7
./I324
72,0
.93256
26,2
31 06 41.79
•544
.51756
85,6
.85565
5i,8
.71396
7i,8
.93229
26,3
31 10 08.05
0.545
0.51842
85,5
0.85513
5i,8
9.7U68
7i,6
9.93203
26,3
31 13 34.32
.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
26,4
31 20 26.85
.548
.52098
85,4
.85357
52,1
.71682
71,2
.93124
26,5
31 23 53.11
.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
26,6
31 30 45.64
u
-1 sinh iu
w Fi.'
rosh iu
ID Fn'
.sinh iu
<i> P '
* V C '
*** ri)
cosn iu
•» TO
loo ,
<«> TO
log cosh iu
<«> ro
u
SMITHSONIAN TABLES
202
Circular Functions.
u
sin u
«F0'
cos u
u F ' log sin u
~ F'
log cos u
- F
u
0.550
0.52269
85,3
0.85252
52,3
9.71824
70,8
9.93071
20,6
31*30' 45?64
.551
.52354
85,2
.85200
52,4
,7l89S
70,7
•93044
26,7
31 34
• 55-'
.52439
85,1
.85148
52,4
,71966
70,5
.93017
26,7
31 37 38.J7
• 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
0.52694
85,0
0.84900
52,7
9.72176
70,0
9.92937
26,9
31 47 56.97
• 556
.52779
84,9
.84937
52,8
•7-J246
69,9
.92910
27,0
31 51 23.23
• 557
.52864
84,9
.84884
52,9
.72316
69,7
.92883
27,0
31 54 49.50
.558
.52949
84,8
.84832
52,9
.72386
69,6
.92856
27,1
31 58
• 559
.53034
84,8
.84779
53,0
.72455
69,4
.92829
27,2
32 oi 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
-'7.3
32 08 34.56
.562
.53288
84,6
.846-19
53,3
.72663
.92747
27,3
32 12 00.82
.563
.53373
84,6
.84566
53,4
.72732
688
.92719
27,4
32 15 27.09
.564
•53457
84,5
.84512
53,5
.72801
68j
.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
27,6
32 25 45.88
.567
•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
.509
.53879
84,2
.84244
53,9
.73U2
67,9
.92554
27,8
32 3J 04.07
0.570
0.53963
84,2
0.84190
54,o
9.73210
67,8
9.92526
27,8
32 39 30.94 '
o/i
•54047
84,1
.84136
54,o
.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 oi. 06
• 579
.54719
83,7
.83701
54,7
.738I4
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
•549/0
83,5
.83536
55,o
.74012
66,0
.92188
28,6
33 20 46.12
083
•55053
83,5
.83481
55,i
.74078
65,9
.92159
28,6
33 24 12.38
084
.55137
83,4
.83426
55,i
.74M4
65,7
.92130
28,7
33 27 38.65
0.585
0.55220
83,4
0.83371
55,2
9.74210
65,6
9.92IO2
28,8
33 31 04.91
.586
.55303
83,3
.83316
55,3
.74275
65,4
.92073
28,8
33 34 3i-i8(
087
.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
83,I
.83150
55,6
•74471
65,0
.91986
29,0
33 44 49.97
0.500
0.55636
83,I
0.83094
55,6
9.74536
64,9
9.91957
29,1
33 48 16.24
• 591
•55719
83,0
.83038
55,7
.74600
64,7
.91928
29,1
33 51 42.50
• 592
.55802
83,0
.82983
55,8
.74665
64,6
.91899
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
56,1
.74922
64,0
.91781
29o
34 08 53-82
•597
.56216
82,7
.82703
56,2
.74986
63,9
.91752
29,5
34 12 20.09
• 598
•56209
82,6
.82646
56,3
.75050
63,8
.91722
29,6
34 15 46.35
• 599
.56382
82,6
.82590
56,4
.75114
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
-isinhiu
" F,,'
cosh iu
u> F '
sinh iu
w Fo'
log cosh iu
• F,'
u
IOQ .
SMITHSONIAN TABLES
203
Circular Functions.
u
sin u
U.FO'
cos u
w Fo' loo sin u
- F,/
tog cos u
*>Fo'
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
.002
.56629
82,4
.82420
56,6
.75304
63,2
.91604
29,8
34 29 31.41
.003
.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
O.6O5
0.56876
82,3
0.82250
56,9
9-75493
62,8
9.91414
30,0
34 39 50.21
.606
.56958
82,2
.82193
57,o
.75556
62,7
.91484
30,1
34 43 16.47
.607
.57041
82,1
.82130
57,0
.756i8
62,5
.91454
30,2
34 46 42.74
.608
.57123
82,1
.82079
57,1
.75681
62,4
.91423
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
07369
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-o5
.613
.57532
81,8
.81793
57,5
.75991
6i,7
.91271
30,5
35 07 20.33
.614
.57514
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
_-_-Q
O///0
81,6
.81620
57,8
.76176
61,4
.9H79
30,7
35 17 39.12
.617
• 57859
81,6
.81562
57,9
.76237
61,2
.9H49
30,8
35 21 05-39
.618*
•57941
8i,5
.81504
57,9
.76298
61,1
.91118
30,9
35 24 31.05
.619
.58022
8i,4
.81446
58,o
.76359
61,0
.91087
30,9
35 27 57.Q2
0.620
0.58104
81,4
0.81388
58,1
9.76420
60,8
9.91056
3i,o
35 31 24.18
.621
.58l85
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
0.585IO
81,1
0.81096
58,5
9.76723
60,2
0.90900
3i,3
35 48 35-50
.626
.58591
81,0
.81038
58,6
.76783
60,1
.90869
3i,4
35 52 01.77
.627
.58672
8 1,0
.80979
58,7
.76843
59,9
•00837
3i,5
35 55 28.03
.628
.58753
80,9
58,8
.76903
59,8
.90806
3i,5
35 58 54-30
.629
.58834
80,9
.80862
58,8.
.76963
59,7
•90774
3i,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
.77HI
59,3
.90679
3i,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
.59800
80, i
.80150
59,8
.77670
58,2
.90390
32,4
36 43 35-74
80,1
.80000
59,9
.77728
58,1
•90358
32,5
36 47 02.01
80,0
.80030
60,0
•77786
58,0
.90325
32,5
36 50 2S.-
.60040
80,0
.79970
60,0
.77844
57,8
.90293
32,6
36 53 54-54
0.645
79,9
0.79910
60,1
9.77902
57,7
9.90260
32,7
36 57 20.80
79,8
.79850
60,2
•77959
'57,6
.00227
32,7
37 oo 47-06
79,8
.79790
60,3
.78017
57,5
.90195
32,8
37 04 13.33
79,7
.79729
60,4
•78074
574
.90162
32,9
37 07 39-59
•60439
79,7
.79669
60,4
.78132
57,2
.90129
32,9
37 ii 05.86
0.650
0.60519
79,6
0.79608
6o,5
9.78189
57,1
9.90096
33,0
37 14 32.12
u
-isinhiu
-Fo'
cosh iu
-FO'
. sinh iu
«F0'
log cosh iu
<-FO'
u
log ,
SMITHSONIAN TABLES
204
Circular Functions.
•
sin u
«F0'
cos u o> F ' log sin u
w f '
log cos u
-F '
u
0.650
0.60519
79,6
0.79608
60,5 9.78189
57,1
9.90006
33,0
O i 41
37 M 32.12
.651
.605^
79,5
• 7954-S
60,6
57,o
•90063
33,1
37 '7 58.39
.652
.60078
79,5
• 79487
60,7
.78303
56,9
.00030
33,2
37 -'i
.653
.60757
79,4
.79426
60,8
56,8
.80997
33,2
50.92
.654
.60837
79,4
.79366
60,8
.78416
56,7
.80963
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
• 7<;-'44
61,0
.78530
56,4
x< ,x< -
33,4
37 35 09.71
.61074
79,2
.79183
6x,i
.89863
33,5
37 3« 35-98
.658
.61154
79,1
.79122
61,2
.78642
.89850
33,6
• >-> . 24
.659
.61233
79,1
.79060
61,2
.78698
56,1
.89796
33,6
37 45 28.51
0.660
0.61312
79,0
0.78999
61,3
9.78754
56,0
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
.61785
78,6
.78630
61,8
.79088
55,3
.89559
34,1
38 09 32.36
.667
78,6
.78568
61,9
.79U3
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
.62020
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
0.62490
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 55.0i;
.6/7
.62646
77,9
.77946
62,6
.79689
54,o
.89179
34.9
38 47 21.27
.678
.62724
77,9
.77883
62,7
•79743
53,9
.89144
35,o
38 50
.679
.62802
77,8
.77820
62,8
.79797
53,8
.89109
35,o
38 54 13.80
0.680
0.62879
77,8
0.77757
62,9
9.79851
53,7
9.89074
35,i
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
.89004
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 U 51-39
.686
.63345
77,4
.77379
63,3
.80171
53,1
.88852
35,6
39 18 17.66!
.687
.63422
77,3
.77315
63,4
.80224
52,9
.88826
35,6
39 21 43-92J
.688
•63499
77,3
.77252
63,5
.80277
52,8
.88791
35,7
10.19;
.689
.63577
77,2
.77188
63,6
.80330
52,7
•88755
35,8
0.600
0.63654
77,i
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
77,0
.76997
63,8
.80487
52,4
.88647
36,0
39 38 5
.693
.63885
76,9
.76933
63,9
.80540
52,3
.88611
36,1
3<J 4-' 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
9.80' .44
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
5i,9
.884$?
36,4
39 56 <
.698
.64269
76,6
.76613
64,3
.80800
5i,8
.88430
36,4
39 59
.699
.04345
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
-i sinhiu
<•> Fo'
cosh iu
-IV
. sinh iu
u>F '
iogcosh iu
-FO'
u
log .
SMITHSONIAN TABLES
205
Circular Functions.
u
sin u
«F0'
cos u
»Fo'
log sin u
« Fo'
log cos u
• FO'
u
0.700
0.64422
76,5
0.76484
64,4
9-80903
5i,6
9.88357
36,6
0 / 41
40 06 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
5M
.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
9.81160
5i,o
9.88173
37,0
40 23 36.69
.706
.64880
76,1
.76096
64,9
.81211
50,9
.88136
37,0
40 27 02.95
.707
.64956
76,0
.76031
65,0
.81262
50,8
.88099
37,1
40 30 29.22
.708
.65032
76,0
.75966
65,0
.81312
50,7
.88062
37,2
40 33 55.48
.709
.65108
75,9
.75901
65,1
.81363
50,6
.88025
37,3
40 37 21.75
0.710
0.65183
75,8
0.75836
65,2
9.81414
50,5
9.87988
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,i
.87838
37,6
40 54 33-07
0.715
0.65562
75,5
0.75509
65,6
9-81665
5o,o
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,i
.75HS
66,0
.81963
49,4
.87572
38,2
41 18 36.93
.722
.66089
75,o
.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 14.51
.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
48,2
.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
.74116
67,1
.82694
47,9
.86991
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 20 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
• 74-'
.675/6
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
4O,o
42 37 41-02
0.745
0.67797
73,5
0.73509
67,8
9.83121
47,1
9.86634
40,0
42 41 07.28
.740
73,4
.73441
67,9
.83168
47,0
.86594
40,1
42 44 33.55
•717
73>4
•73373
67,9
.83215
46,9
.86554
40,2
42 47 59-8i
.;jX
.68017
73,3
.73305
68,0
.83262
46,8
.86513
40,3
42 51 26.08
,66091
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
u
-isinhiu
«F,/
cosh iu
nFo'
. sinh iu
-Fo'
oo cosh iu
-FO'
u
log .
SMITHSONIAN TABLES
2O6
Circular Functions.
u
sin u
«F0'
COS U
«Fo"
log sin u
«Fo'
log cos u
-Fo'
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
73J
.73101
68,2
.83402
46,5
.86392
40,5
43 01 44.87
.752
.68310
73,o
.73032
68,3
.83448
4' »,4
186352
43 05 11.13
• 753
.68383
73,o
.72964
68,4
.83495
46,3
40,7
43 08 37.40
• 754
.68456
72,9
.72896
68,5
.83541
46,2
.86270
40,8
43 u 03.66
0.755
0.68529
72,8
0.72827
68,5
9.83587
46,2
9.86229
40,9
43 15 29.93
.756
.68602
72,8
.72759
68,6
.83633
46,1
.86188
40,9
43 18 5
• 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
4L3
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
4M
43 39 33.78
.763
.69109
72,3
.72277
69,1
.83954
45,4
.85900
41,5
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
41,9
43 56 45.ii
.768
.69470
71,9
.71930
69,5
.84180
45,0
.85691
41,9
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 03.00
.771
.69685
7i,7
.71721
69,7
.84314
44,7
.85565
42,2
44 10 30.17
.772
•69757
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
70,0
9.84492
44,3
9.85395
42,5
44 24 15.22
• 776
.70043
7i,4
.71372
7o,o
.84536
44,3
.85353
42,6
44 27 41.49
• 777
.70114
7i,3
.71302
70,1
.84581
44,2
.85310
4*7
44 31 07-75
• 778
.70186
71,2
.71232
70,2
.84625
44,1
.85267
42,8
44 34 34.02
• 779
•70257
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 n.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
7i,o
.85104
43,1
.84792
43.7
45 12 22.93
0.790
0.71035
70,4
0.70385
7i,o
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 i5-4<>
.792
.71176
70,2
.70242
71,2
.85233
42,9
.84660
44,0
45 -- 41-73
• 793
.71246
70,2
.70171
71,2
.85276
42,8
.84616
44.1
45 26 07.99
• 794
.71316
70,i
.70100
7i,3
.85319
42,7
.84572
44-'
45 29 34.26
0.795
0.71386
70,0
o . 70028
7i,4
9.85362
42,6
44.3
45 33 00.52
.796
.7U56
70,0
.69957
7i,5
.85404
4 2,5
.84483
44,4
45 36 26.79
• 797
.71526
69,9
.69886
7i,5
4-', 4
.84439
44,4 45 39 53- O5
.798
.71596
<x),8
.69814
7i,6
.8S489
4*3
44.5
45 43
• 799
.71666
69,7
.69742
7i,7
.85531
42,3
.84350
44,0
45 46 45.58
0.800
0.71736
69,7
0.69671
7i,7
9.85573
442
9.84305
44,7
45 50 11.84
u
-isinhiu
CO F.,'
cosh iu
«- F.'
sinh iu
u. F
log cosh iu
«F'
;
loo ,
SMITHSONIAN TABLES
207
Circular Functions.
u
sin u
-Fo'
cos u
«Fo*
log sin u
a. Fo'
log cos u
<oF0'
u
O / 44
0.800
0.71736
69,7
0.69671
71,7
9.85573
42,2
9.84305
44,7
45 50 11.84
.801
.71805
69,6
.69599
7i,8
.85616
42,1
.84260
44,8
45 53 38.11
.802
.71875
09,5
.69527
7i,9
.85658
42,0
.84215
44,9
45 57 04-37
.803
.71944
69,5
.69455
7i,9
.85700
41,9
.84170
45,0
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
41,7
.84035
45,3
46 10 49-43
.807
. 72222
69,2
.69167
72,2
.85867
41,6
.83900
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
4i,3
9.83853
45,6
46 24 34.49
.811
.72498
68,9
.68877
72,5
.86032
4i,3
.83808
45,7
46 28 O0.76
.812
.725^6
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
.80238
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,o
.86360
40,6
.83439
46,5
46 55 30.88
0.820
o.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
39,8
.82970
47,4
47 29 53.52
0.830
0.73793
67,5
0.67488
73,8
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
74J
9.86999
39,3
9.82684
48,0
47 50 31.11
.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
.87117
39J
•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 4- -44
.841
•74531
66,7
.66672
74,5
.87234
38,8
.82394
48,5
48 II 08.70
.842
.74508
66,6
.66597
74,6
•87273
38,8
.82346
48,6
48 14 34-97
,843
.74664
66,5
.66523
74,7
.873H
38,7
.82297
48,7
48 18 01.23
.844
•74731
66,4
.66448
74,7
.87350
38,6
.82248
48,8
48 21 27.5O
0.845
0.74707
.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
.74810
66,2
.66223
74,9
.87465
38,4
.82101
49J
48 31
.74096
66,1
.66148
75,0
.87504
38,4
.82052
49,2
48 35 12.56
.849
.75062
66,1
.66073
75,1
.87542
38,2
.82003
49,3
48 38 38.82
0.850
0.75128
66,0
0.65998
75,i
9.87580
38,2
9.81953
49,4
48 42 05.09
u
-itinhiu
• u
cosh iu
«FO'
. sinh iu
«F0'
log cosh iu
-FO'
u
tog .
SMITHSONIAN TABLCS
208
Circular Functions.
! U
sin u
.«
COS U
.«
log sin u
-Fo'
log cos u
-Fo7
u
0.850
0.75128
66,0
0.65998
75,1
9.87580
38,2
9.81953
49,4
48 42 05' 09
.85!
•75194
65,9
.65923
75,2
.87618
38,1
.81904
49o
48 45 31.35
.75260
65,8
.65848
75,3
.87656
38,0
.81854
48 48
-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,«
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
•755^3
65,5
.65546
75,5
.87808
37,7
.81655
50,o
49 02 :
• 857
•75588
65,5
.65471
75,6
•87845
37,6
.81605
50,1
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 U 01.47
o.8fx>
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,i
9.88144
37,0
9.81200
5i,o
49 33 39.o6
.856
.76174
64,8
.64788
76,2
.88l8l
36,9
.81149
49 37 05.32
.857
.76239
64,7
.64712
76,2
.88218
36,9
.81098
51,2
49 40 31-59
.868
.76304
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
51,5
49 50 50.38
.871
.76497
64,4
.64406
76,5
.88365
36,6
.80893
5i,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
51,9
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 1 8 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
77J
9.88691
35,9
9.80424
52,5
50 25 13.03
.881
.77138
63,6
.63638
77,1
.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 0
.883
•77265
63,5
.63484
77,3
.88798
.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
53,1
50 42 24.35
.886
•77455
63,3
.63252
77,5
.88905
35,5 .80107
53,2
50 45 50.62 '
.887
•775T8
63,2
.63174
77,5
.88940
35,4 1 .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
0.890
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
35J
.75840
53,7
51 03 01.94
.892
.77833
62,8
.62786
77,8
.89116
35,o
.79786
53,8
51 06 2
.893
.77896
62,7
.62708
77,9
.89151
35,0
53,9
51 09 54-47
.894
.77958
62,6
.62630
78,0
.89185
34,9
.79678
54,1
51 13 20.74
0.895
0.78021
62,6
0.62552
78,0
9.89221
34,8
9-79624
54.-1
51 16 47.00
.896
.78083
62,5
.62474
78,1
.89256
34,7
•79570
54,3
51 Jo 13.27
.897
.78146
62,4
.62396
78,1
.89291
34,7
54.4
5i 23 39-53
.898
.78208
62,3
.62318
78,2
.89325
34,6
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
«> F ' log cosh iu
o> F '
u
loo .
SMITHSONIAN TABLES
20Q
Circular Functions.
I
sin u
«F0'
cos u
«F0*
log sin u
« Fo'
log cos u
«F0'
u
0.900
0.78333
62,2
0.62161
78,3
9.89394
345
9.79352
54,7
5i°33'58"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
61,9
.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
.906
.78704
6i,7
.61690
78,7
.89600
34,0
.79021
55,4
51 54 35.91
.907
.78766
61,6
.61611
78,8
•89634
34,0
.78966
55,5
51 58 02.18
.908
.78827
6i,5
.61532
78,8
.89668
33,9
.78910
55,6
52 01 28.44
.909
.78889
6i,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
.79012
61,3
.61296
79,o
.89769
33,7
.78743
56,o
52 ii 47.24
.912
.79073
61,2
.61217
79,i
.89803
33,6
.78687
56,1
52 15 13.50
.913
.79134
61,1
.61137
79,i
.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
.90003
33,2
.78348
56,8
52 35 51.09
.919
.79500
60,7
.60662
79,5
.90036
33>l
.78291
56,9
52 39 17.36
0.920
0.79560
60,6
0.60582
79,6
9.00070
33,1
9.78234
57,0
52 42 43.62
.921
.79621
60,5
.60502
79,6
.90103
33,o
.78177
57,2
52 46 09.89
.922
.79681
60,4
.60423
79,7
.00136
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, i
.60104
79,9
.90267
32,7
.77890
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
.00526
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
3i,9
.77247
59,1
53 41 10.12
.938
.80638
59,1
.59140
80,6
.90654
3i,9
.77188
59,2
53 44 36.39
•939
.80697
59,1
.59060
80,7
.90686
3i,8
.77129
59,3
53 48 02.65
0.940
0.80756
59,0
0.58079
80,8
9.00717
31,7
9.77070
59,5
53 51 28.92
.941
.80815
58,9
.58898
80,8
.90749
3i,7
.77010
59,6
53 54 55.i8
.942
.80874
58,8
.58817
80,9
.90781
3i,6
.76950
59,7
53 58 21.45
.943
.80932
58,7
.58736
80,9
.90812
3i,5
.76891
59,8
54 01 47-71
•944
.80991
58,7
.58655
81,0
.00844
3i,5
.76831
00,0
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
,8II08
58,5
.58493
81,1
.90906
3i,3
.76711
60,2
54 12 06.51
,81167
58,4
.58412
81,2
.90938
3i,3
.76650
60,3
54 15 32.77
,948
'%l22oS
58,3
•58331
81,2
.90069
31,2
.76590
60,5
54 18 59.04
.81283
58,2
.58250
81,3
.91000
3U
.76529
60,6
54 22 25.30
0.950
0.81342
58,2
0.58168
8i,3
9.9I03I
3i,i
9.76469
60,7
54 25 51.57
u
isinhiu
-F,/
cosh iu
«FO'
I0gsinh iu
»F0'
log cosh iu
-FO'
u
SMITHOONIAN TABLES
2IO
Circular Functions.
u
sin u
«Fo'
COS U
<-F,;
log sin u
« F '
log oos u
«F«'
u
0.950
0.81342
58,2
0.58168
81,3
9.9I03I
3U
9.76469
60,7
54°25'5i'.'57
.951
.81400
58,1
.58087
81,4
.91062
31,0
.76408
60,9
54 29 17.83
.952
.81458
58,0
.58006
81,5
.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
9.9II86
30,7
9.76l63
61,4
54 43 02.89
.956
.81689
57,7
.57679
8i,7
.9I2l6
30,7
.76102
61,5
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,i
.57106
82,1
.91429
30,2
.75668
62,4
55 10 33-01
.964
.82148
57,o
.57024
82,1
.91460
30,i
.75606
62,6
55 13 59.27
0.065
O.82205
56,9
0.56942
82,2
9.91490
30,1
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
.9l6lO
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
0.827/0
56,i
0.56117
82,8
9.91787
29,4
9.74909
64,1
55 51 48.19
.976
.82826
56,0
06034
82,8
.91817
29,4
.74845
64,2
55 55 U.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 18.30
.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
55J
.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,o
•54953
83,5
.92193
28,6
•73999
66,0
56 39 55.89
0.990
0.83603
54,9
0.54869
83,6
9.92222
28,5
9-73933
66,2
56 43 a
.991
.83657
54,8
.54785
83,7
.92250
28,4
.73866
66,3
56 46 4^-4-
.992
.83712
54,7
.54702
83,7
.92279
28,4
.73800
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 j
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
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 ;
.999
.84093
54,1
.54114
84,1
.92476
27,9
•73331
67,5
S7 U 18.54
1. 000
0.84U7
54,0
0.54030
84,1
9.92504
27,9
9.73264
67,6
57 17 44.8i
u
isinhiu
W Fo'
cosh iu
• ft
, sinh iu
log
u> F,'
'og cosh iu
w F,,'
u
SMITHSONIAN TABLES
211
Circular Functions.
u
sin u
»F0'
cos u
«F0'
log sin u
W FQ'
log cos u
<oF0'
u
I.OOO
0.84147
54,0
0.54030
84,1
9.92504
27,9
9.73264
67,6
57°i7/44/./8i
.OOI
.84201
53,9
. 53946
84,2
.92532
27,8
•73196
67,8
57 21 11.07
.OO2
.84255
.53862
84,3
.92560
27,8
.73128
67,9
57 24 37.34
.003
.84309
53,8
.53778
84,3
.92587
27,7
.73000
68,1
57 28 03.60
.004
.84363
53,7
.53693
84,4
.92615
27,6
.72992
68,2
57 3i 29.87
I.OO5
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 41 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
•72649
69,0
57 48 41.19
I.OIO
0.84683
53,2
0.53186
84,7
9.92780
27,3
9.72580
69,1
57 52 07.45
.Oil
.84736
53.1
.53101
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
.92861
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
.016
.85001
52,7
.52677
85,0
.92942
26,9
.72162
70,1
58 12 45.04
.017
.85053
52,6
.52592
85,I
.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
.019
.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
.021
.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
71,0
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
7i,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
5i,8
.51824
85,5
.93208
26,3
./I453
7i,7
58 47 07.69
.027
.85575
5i,7
.51739
85,6
.93235
26,3
.71382
7i,8
58 50 3-3.96
.028
.85627
5i,7
.51653
85,6
.93261
26,2
.71310
72,o
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
9.7II65
72,3
59 oo 52.75
.031
.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,O
.71020
72,6
59 07 45.28
•033
.85884
.51224
85,9
.93391
25,9
.70948
72,8
59 ii 11-54
.034
.85935
Siii
.51139
85,9
.93417
25,8
.70875
73,o
59 14 37-8i
I.OJ5
0.85986
5i,i
0.51053
86,0
9-93443
25,8
9.70802
73J
59 18 04.07
.036
.86037
5i!o
.50067
86,0
.93469
25,7
.70729
73,3
59 21 30.34
• 037
.86088
50,9
.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
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
86,3
•93597
25,4
.70360
74,-2
59 38 41.66
.042
.86341
50,4
.50449
86,3
.93622
25,4
.70286
74,3
59 42 07.93
.043
.86392
50,4
•50363
86,4
•93647
25,3
. 7021 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
50,i
.50104
86,5
.93723
25,1
.69987
75,0
59 55 52.99
.047
50,0
.50017
86,6
•93748
25,1
.69912
75,2
59 59 19.25
.048
49,9
.49930
86,6
•93773
25,0
.69837
75,4
60 02 45.52
•049
.86693
49,8
.49844
86,7
.93798
25,0
.69761
75,5
60 06 11.78
1.050
49,8
0.49757
86,7
9.93823
24,9
9.60686
75,7
60 09 38.05
u
-isinhiu
WF,;
cosh iu
WFO'
Ioo8ln-p
-To'
log cosh iu
-w
u
SMITHSONIAN TABLES
212
Circular Functions.
sin u
»w
CO* U
- FO*
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
6o°o9/ 38'.'o5
.051
.86792
49,7
.49670
86,8
.93848
.69610
60 13 04.31
.052
.86842
49,6
.49584
86,8
.93873
24,8
60 16 30.58
.053
.86891
49,5
.93898
24,7
•60458
76,2
60 19 56.84
.054
.86941
49,4
.49410
86,9
• 93922
24,7
.69381
60 23 23.11
1.055
0.86990
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 41.90
.058
.87138
49,1
.49062
87,1
.94021
24,5
.60074
77J
60 37 08.17
•059
.87187
49,0
.48974
87,2
.94045
244
.68997
77,3
60 40 34-43
1.060
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
.94H8
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
6l 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
.04262
33,9
.68294
79,o
61 ii 30.81
.069
.87672
4'8,i
.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
•4/925
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
.87911
47,7
.47661
87,9
.94405
23,6
.67816
80, i
61 32 08.40
1.075
0.87959
47,6
0.47573
88,0
9-94428
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, r
.94498
23,3
.67494
80,9
6 i 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
.94368
23,2
.67251
81,5
61 56 12.26
.082
.88290
47,o
.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
.465U
88,5
.94706
22,8
.66759
82,7
62 16 49.84
.088
.88570
46,4
.46426
88,6
•947-29
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
9.66510
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
.04819
22,5
.66343
83,7
62 34 01 . 17
• 093
.88801
46,0
.45982
88,8
.94842
22,5
.66259
83,9
62 37 27.43
.094
.88847
45,9
.45894
88,8
.94864
22,4
.66175
8U,i
62 40 53-70
1.095
0.88893
45,8
0.45805
88,9
9.94887
-'-'.4
9.66091
84,3
62 44 19.96
.096
.88939
45,7
.45716
88,9
.94909
22,3
.66007
84,5
(12 47 46.23
.097
.88984
45,6
•45627
89,0
•949JI
-'-'o
.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
.80075
45,4
•45449
89,1
.04976
22£
.65752
85,1
62 58 05.02
; I. 100
O.89I2I
45,4
0.45360
89,1
9.94908
22,1
9.65667
85,3
63 01 31.29
i u
-i sinhiu
• Fo'
cosh iu
-PC'
sinh iu
.Fo'
og cosh iu
• F0'
u
loo .
SMITHSONIAN TABLES
2I3
Circular Functions.
u
sin u
<-FO'
cos u
*>F0'
log sin u
« Fo'
log cos u
"Fo'
u
I. 100
0.89I2I
45,4
0.45360
89,1
9.94998
22,1
9.65667
85,3
63 oi'3i'.'29
.101
.89166
45,3
.45270
89,2
.95020
22,O
.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 ii 50.08
.104
.89301
45,0
.45003
89,3
.95086
2-1,9
.65324
86,2
63 15 i6.35
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 01.41
.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
9.648031
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 12.73
.114
.89747
44,1
.44108
89,7
-95302
21,3
.64451
88,4
63 49 38.99
I. US
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
'21,0
9.63917
89,7
64 10 16.58
.121
.00054
43,5
.43478
90,1
.95450
21,0
.63827
90,0
64 13 42.85
.122
.00097
43,4
.43388
90,1
.95471
2O,9
.63737
90,2
64 17 09.11
.123
.90140
43,3
.43298
00,1
.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
.90356
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
9i,8
64 41 12.97
I.I30
0.90441
42,7
0.42666
90,4
9.95637
20,5
9.63008
92,1
64 44 39.23
.131
.90484
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,o
64 58 24.29
1. 135
0.90653
42,2
0.42213
90,7
9.95738
20,2
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
4i,9
.41941
00,8
.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 35.61
1.140
0.00863
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
.00988
41,5
.41487
91,0
.95899
19,8
.61791
95,2
65 29 20.67
.144
.91030
41,4
.41396
91,0
.95918
19,7
.61695
95,5
65 32 46.94
1. 145
0.91071
41,3
0.41305
9i,i
9.95938
19,7
9.61600
95,8
65 36 13.20
.146
,91112
41,2
.41214
9i,i
.95958
19,6
.61504
96,0
65 39 39-47
.91153
.tu
.41122
91,2
•95977
19,6
.61408
96,3
65 43 05-73
.91195
41,0
.41031
91,2
•95997
19,5
.61311
96,5
65 46 32-00
.149
•91235
40,9
.40940
91,2
.96016
19,5
.61215
96,8
65 49 58.26
1.1-50
0.91276
40,8
0.40849
9i,3
9-96036
19,4
9.61118
97,0
65 53 24-53
u
-isinhiu
cosh iu
«Fo'
sinh iu
<"F0'
log cosh iu
<o F ,'
u
loo t
SMITHSONIAN TABLES
2I4
Circular Functions.
I
sin u
• Fo'
COS U
•Fo'
log sin u
* Fo'
log cos u
u
1.150
0.91276
40,8
0.40849
91,3
9.96036
19,4
9.61118
!,7,o
01 ,,
65 53 24.53;
.151
.91317
40,8
.40757
91,3
.96055
19,4
.61021
97,3
<>5 56 50./9
.152
.91358
40,7
.40666
91,4
.06075
19,3
97,6
66 oo 17.06
.153
.91399
40,6
.40575
91,4
.960M
19,3
to 03 43-32
.154
.9M39
40,5
.40483
91,4
.96113
19,2
.60726
98,1
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. §5
.156
.91520
40,3
.40300
91,5
.96152
19,1
.60531
<>') 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
.96100
19,0
.00333
99,2
66 20 54-65
.159
.91640
40,0
.40026
91,6
.96209
19,0
.60234
99,4
<yj ~>4 20.91
1.160
0.91680
39,9
0.39934
91,7
9.96228
18,9
9.60134
99,7
66 27 47.18
.161
.91720
39,8
.39842
91,7
.96246
18,9
.60034
1 00,0
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
101,1
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
.169
.92036
39J
.39107
92,O
.96396
18,5
.59226
102,2
66 584306
I. I/O
0.92075
39,o
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
.58918
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
08204
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
l
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 IO.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
9.57015
108,5
68 10 55.12
.191
.92874
37,1
.37073
92,9
.96789
17,3
.56906
108,8
oS 14 21.38
.192
.92911
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
1094
68 21 13.91
.194
.92985
36,8
.36794
93,0
.96841
17,2
.56578
109,8
08 -'4 40.18
I-I95
O.93O22
36,7
0.36701
93,0
9.96858
I7,i
9-56468
110,1
68 28 06.44
.196
.93058
36,6
.36608
93J
.96875
I7,i
.56358
110,4
68 31 38.71
.197
.93095
36,5
.36515
93,1
.96893
17,0
.56247
110,7
68 34 58.97
.198
.93131
36,4
.36422
93,1
.96910
I7,o
.56137
III.O
68 38 -
.199
.93168
36,3
.36329
93,2
.96927
16,9
.56025
111,4
68 41 51.50
1.200
0.93204
36,2
0.36236
93,2
9.96943
16,9
9.55914
in.7
68 45 17-77
u
-isinhiu
«-Fo'
cosh iu
• fg'
,sinh iu
^ F logcosh iu
«FO'
u
loo .
SMITHSONIAN TABLES
215
Circular Functions.
u
sin u
*>FO'
cos u
• Fo'
log sin u
*> Fo'
log cos u
"Fo'
u
1.200
0.93204
36,2
0.36236
93,2
9.96943
1 6,9
9-55914
111,7
68°45' I7"77
.2OI
.93240
36,1
.36143
93,2
.96960
16,8
.55802
II2,O
68 48 44.03
.202
.932/6
36,0
.36049
93,3
.96977
16,8
•55690
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
00464
H3,0
68 59 02.83
1.205
0.93384
35,8
0.35769
93,4
9.97027
16,6
9-55351
H3,4
69 02 29.09
.206
.93420
35,7
.35676
93,4
•9/044
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
H44
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
9.5478o
H5,i
69 19 40.42
.211
•93597
35,2
.35208
93,6
.97126
16,3
•54665
H5,5
69 23 06.68
.212
.93632
35,1
.35115
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
n6,5
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
.93806
34,6
.34646
93,8
.97223
16,0
.53965
117,6
69 43 44.27
.218
.93841
34,6
.34552
93,8
.97239
16,0
.53848
118,0
69 47 10. 53
.219
.93876
34,5
.34458
93,9
.97255
15,9
•53730
118,3
69 50 36.80
1.220
0.93910
34,4
0.34365
93,9
9.97271
15,9
9.536ii
118,7
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
119,4
70 oo 55-59
.223
.94013
34,1
.34083
94,0
.97319
15,7
.53253
119,8
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
9.973'50
15,6
9.53013
120,5
70 ii 14-39
.226
.94H4
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
.3361*2
94,2
• 97397
15,5
.52650
121,7
70 21 33-l8
.229
•94215
33,5
.33518
94,2
•97412
15,5
.52528
122,1
70 24 59.44
1.230
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
33J
.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
0.94415
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
1248
70 49 03.30
•237
.94481
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
149
9.51161
126,5
71 02 48.36
• -'ii
.9461/1
32,4
.32385
94,6
• 97594
149
•51034
126,9
71 06 14.62
.242
.94643
32,3
.32290
94,6
.97609
14,8
.50907
127,3
71 09 40.89
•-'43
.94675
32,12
.32196
94,7
.97624
148
•5078b
127,7
71 13 07.15
.94708
32,1
.32101
94,7
.97638
147
.50652
128,1
71 16 33.42
•-'17
0.94740
•94772
.94803
32,0
31,9
31,8
0.32006
.31912
.31817
94^8
94,8
9-97653'
.97668
.97682
147
14,6
14,6
9.50524
.50395
.50266
128,6
129,0
129,4
71 19 59.68
71 23 25.95
71 26 52.21
.248
31,7
.31722
94,8
.97697
145
.50136
129,8
71 30 18.48
•
•94867
31,6
.31627
94,9
.97711
145
.50006
130,3
71 33 44.74
1.250
0.94898
31,5
0.31532
949
9.97726
14,4
9.49875
130,7
71 37 ii. 01
u
-i iinh iu
• ft
cosh iu
«F,/
sinh iu
»Fo'
ogcoshiu
wFo'
u
log (
SMITHSONIAN TABLES
2l6
Circular Functions.
u
sin u
«F0'
cos u
»*'
log >in u
«« F '
loo cos u
1.250
0.94898
31,5
0.31532
94,9
9- '>;;-' -
M,4
9.49875
130,7
7i°37'ii'.'oi
.251
•94930
31,4
.31437
94,9
.97/40
14.4
131,1
71 40 37.27
.253
31,3
.31342
95,0
•97755
14^3
.49613
13*6
71 44 03.54
-253
•94993
3W
.31247
95,0
.97769
14,3
.49481
132,0
71 47 29.80
• -'54
.95024
3M
•31152
95,o
.97783
14,2
•49349
i3-',5
71 50 56.07
1.255
0.95055
31,1
0.31057
95,i
9-97797
14,2
9.40216
132,9
71 54 22.33
.256
.95086
3i,o
.30962
95,1
.97812
14,1 .49083
U3,4
71 57
.257
.95H7
30,9
.30867
95,i
.97826
14,1
.48950
133,8
72 01
.258
.95M8
30,8
.30772
95J
•97840
14.0
.48816
134,3
72 04 41-13
.259
.95178
30,7
.30677
95,2
.97854
M,0
.48681
134,7
72 08 07-39
1.260
0.95'209
30,6
0.30582
95,2
9.97868
13,9
9.48546
135,2
72 u 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
.97896
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
137,1
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
.366
.95391
30,0
.30010
95,4
.97951
13,7
.47726
138,0
72 32 11.24
.267
.95421
29,9
.20914
95,4
• 97</>4
13,6
.47588
138,5
72 35 37-51
.268
•95451
29,8
.29819
95,5
.97978
13,6
•47449
139,0
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
M0,5
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
141,5
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
M2,5
73 03 07-63
.276
.277
.95686
.95715
29,1
29,0
.29054
.28959
95,7
95,7
.98085
.98008
13,2
I3,i
.46321
.46178
143,0
M3o
73 06 33.89
73 10 00.16
.278
•95744
28,9
.28863
95,7
.98111
I3,i
•46034
I44.I
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
I3,o
9-45745
I45.I
73 20 18.95
.281
.95830
28,6
.28576
95,8
.98150
I3,o
.45600
M5,6
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
.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
9.450I3
147,8
73 37 30.28
.286
.95972
28,1
.28006
96,0
.98214
12,7
.44865
148,3
73 40 56.54
.287
.96000
28,0
.28000
96,0
.98227
12,7
.44716
M&9
73 44 22.81
.288
.96028
27,9
.27904
96,0
.98240
12,6
•44567
M9,5
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
96,1
9.98265
12,5
9.44267
150,6
73 54 4i.6o
.291
.96111
27,6
. 27616
96,1
.98277
12,5
.44116
I5i,i
73 58 07.86
.292
.96139
'27,5
.27520
96,i
.98290
12.4
.43965
I5i,7
74 01 34-13
• 293
.96166
27,4
.27424
96,2
.98302
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
•08339
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
.96302
26,9
.26943
96,3
.98364
12.2
.43044
155,2
74 22 11.72
.299
.96329
26,8
.2684.6
96,3
.983/6
12,1
.42888
155,8
74 25 37.98
1.300
0.96356
26,7
0.26750
96,4
9.98388
12,1
9-4-V3-'
156,4
74 29 04.25
u
-isinhiu
w F/
cosh iu
«FO'
sinh iu
-Fo'
loo cosh iu
»F,'
u
loo .
SMITHSONIAN TABLES
217
Circular Functions.
u
sin u
«-Fo'
cos u
«F0'
log sin u
« Fo'
log cos
» Fo' | u
1.300
0.96356
26,7
0.26750
96,4
9.98388
12,1
9.42732
156,4
74 29 04.25
.301
.96383
26,7
.26654
96,4
.98400
1 2,0
.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 U 45.69
.314
.96721
25,4
.25398
96,7
.98552
11,4
.40481
165,4
75 17 11.96
1.315
0.96746
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
1.320
0.06872
24,8
0.24818
96,9
9.08620
11,1
9.39476
169,5
75 37 49-54
.321
.96896
24,7
.24721
96,9
.98631
1 1,1
.39306
170,2
75 41 15.81
.322
.96921
24,6
.24624
96,9
.98642
11,0
.39135
170,9
75 44 42.07
•323
.06946
24,5
.24527
96,9
.98653
11,0
.38964
i7i,7
75 48 08.34
.324
.96970
24,4
.24430
97,o
.98664
10,9
.38792
172,4
75 5i 34-00
1.325
0.06094
24,3
0.24333
97,o
9.08675
10,9
9.38619
i73,i
75 55 00.87
.326
.97019
24,2
.241236
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,i
.98707
10,8
.38097
175,3
76 05 19.66
.329
.97091
23,9
.23945
97,1
.98718
10,7
•37921
I76,i
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
10,6
•37389
178,4
76 19 04.72
•333
.97186
23,6
.23556
97,2
.98760
10,5
•37210
179,2
76 22 30.09
•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
.231264
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 16.05
.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.ii
•342
22,7
.22681
97,4
.98853
10,1
• 35565
i86,<5
76 53 27.37
•343
.97417
22,6
.22583
97,4
.98863
IO,I
.35378
187,3
76 56 53-63
•344
•97439
22,5
.22486
97,4
.98873
IO,O
.35191
188,2
77 oo 19.90
1.345
0.07463
22,4
0.22388
97,5
9.98883
10,0
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
.348
.97506
22,2
22,1
.22193
.22096
97,5
97,5
•98003
.98913
9,9
9,8
.34622
•34431
190,8
i9i,7
77 10 38.69
77 14 04.96
•97550
.21998
97,6
.98923
9,8
•34239
192,6
77 17 31.22
1-350
21,9
0.21901
97,6
9.98933
9,7
9.34046
193,5
77 20 57-49
u
-isinhiu
«F,/
cosh iu
»F,/
. sinh iu
«F0'
OQ cosh iu
• Fo'
u
i
SMITHSONIAN TABLES
218
Circular Functions.
u
sin u
«Fo'
cos u
»K
log sin u
« F,'
log cos u
-Fo'
u
1.350
0-97572
21,9
0.21901
97,6
9.98933
9,7
9.34046
193,5
77°2o'57.49
.351
•97594
21,8
.21803
97,6
.08942
9,7
.3385-'
194,4
77 -'4
.352
.97616
21,7
.21705
97,6
.98952
9,7
•33' '57
77 27 50.02
.353
.97638
21,6
.21608
97,6
.98962
9,6
.33461
106,2
77 31 16.28
• 354
.97659
21,5
.21510
97,7
.98971
9,6
•33264
197,-'
77 34 42.55,
1-355
0.97681
21,4
0.21413
97,7
9.08581
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 35.08
.357
.97723
2 1, '2
.21217
97,7
.09000
9,4
.32669
2OO,O
77 45 01.34
.358
•97744
21,1
.21119
97,7
.09009
9,4
.32468
201,0
77 48 27.61
• 359
.97765
21,0
.21022
97,8
.99019
9,3
.32267
202,0
77 51 53.87
1.360
0.97786
20,9
0.20924
97,8
9.99028
9,3
9-32064
203,0
77 55 20.14
.361
.97807
20,8
.20826
97,8
.90037
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
.00056
9,2
.31451
2O6,O
78 05 38.93
.364
.97869
20,5
.20533
97,9
.99065
9,1
.31244
207,0
78 09 05.20
1.365
0.97800
20,4
0.20435
97,9
9.99074
9,1
9.31037
208,0
78 12 31.46
.366
.97910
20,3
•20337
97,9
.99083
9,0
.30828
209,1
78 15 57-73
.367
.97931
20,2
.20239
97,9
.99092
9,0
.30619
2IO,I
78 19 23.99
.368
.97951
20,1
.20141
98,0
.99101
8,9
.30408
211,2
78 22 50.25
.369
•97971
20,0
.20043
98,0
.99HO
8,9
.30196
212,3
78 26 16.52
1.370
0.97991
19,9
0.10945
98,0
9.99II9
8,8
9.20083
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
98.0
.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
•99154
8,7
.29121
217,8
78 43 27.84
1.375
0.98089
19,5
0. 194'55
98,1
9.99162
8,6
9.28903
219,0
78 46 54- I i
.376
.98109
19,4
. 19357
08,1
.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
.08147
19,2
.19160
98,1
.99188
8,5
.28240
222,5
78 57 12.90
• 379
.98166
19,1
.19062
98,2
.99196
8,4
.28017
223,7
7900 39.17
1.380
0.08185
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
.09213
8,3
.27568
226,1
79 07 31.70
.382
.98223
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
o. 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
.90262
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
0.17081
98,4
9.99286
7,9
9.25482
237,6
79 38 28.08
• 391
.98388
17,9
.17883
98,4
.99294
7,9
.25144
238,9
79 41 54-35
• 392
.98406
17,8
.17785
98,4
• 99302
7,8
.25004
-' 10.3
79 45 20.01
• 393
.98424
17,7
.17686
98,4
.99310
7,8
241.7
46.88
•394
•98441
17,6
.17588
98,4
•99318
7,8
.24521
243,1
79 5-' 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
1/4
. 17391
98,5
•99333
7,7
.24032
245^9
79 59 05.67
•397
.98494
17,3
.17292
98,5
•99341
7,6
.23783
247,4
80 02 31.93
.398
.98511
17,2
.17194
98,5
.99348
7,6
.23537
80 05 58.20
• 399
.98528
17,1
.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 u 50.73
u
-isinhiu |
«Fo'
cosh iu
w FY
, sinh iu
•.FO'
og cosh iu o» F ' u
log .
SMITHSONIAN TABLES
219
Circular Functions.
u
sin u
-Fo'
cos u
«F0'
log sin u
«o Fo'
log cos u
w Fo' 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
.400
.98645
16,4
. 16405
98,6
.99408
7,2
.21498
261,1 80 33 28.32
.407
.98662
16,3
. 16306
98,7
.09415
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 47-11
1.410
0.98710
1 6,0
o. 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,o
.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
98,8
.90491
6,7
.18242
282,0
81 14 43-50
.419
.98850
i'5, i
.15121
98,9
.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
149
. 14924
98,9
.99511
6,6
.17388
287,8
81 25 02.29
.422
.08895
14,8
.14825
98,9
.99517
6,5
.17099
289,7
81 28 28.55
•423
.08910
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
0.58939
14,5
0. 145&
98,9
9.99537
6,4
9.16221
295,8
81 38 47-35
.426
.98954
14,4
.14429
99,o
.99543
6,3
.15924
297,8 j8i 42 13.61
.427
.98968
H,3
. M330
99,0
• 99549
6,3
. 15625
299,9 81 45 39.88^
.428
.98982
14,2
. 14231
99,o
.99556
6,2
. 15324
302,1
81 49 06.14
.4129
.98996
14,1
. 14132
99,0
.99562
6,2
.I5O2I
304,2
81 52 32.41
1.430
O.990IO
14,0
0.14033
99,0
9.99568
6,2
9.I47I6
306,4
Si 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
.99580
6,1
. 14098
3io,9
82 02 51.20
•433
.99052
13,7
. 13736
99,1
.99586
6,0
.13786
313,2
82 06 17.47
•434
.99066
13,6
• 13637
99,1
•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
.09106
13,3
. 13340
99,1
.99610
5,8
.12515
322,7
82 20 02.53
.438
.99120
13,2
.13241
99,1
.96616
5,8
.I2IQI
325,1
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.H536
330,i
82 30 21.32
.441
.99159
12,9
.12943
99,2
.99633
5,7
.11204
332,7
82 33 47-59
.442
12,8
.12844
99,2
.99639
5,6
.IO87O
335,3
82 37 13.85
•443
.99185
12,7
• 12745
99,2
.99644
5,6
.10534
338,0
82 40 40.12
•444
.99197
12,5
. 12646
99,2
.90650
5,5
. 10194
340,7
82 44 06.38
1.445
O.992IO
12,5
0.12546
99,2
9.99655
5,5
9.00852
343,4
82 47 32.65
.446
.99222
12,4
.12447
99,2
.99661
5,4
.09507
346,2
82 50 58.91
.99235
I-'O
. 12348
99,2
.99666
5,4
.09160
349,0
82 54 25.17
.99247
12,2
. 12249
99,2
.99672
5,4
.08809
351,9
82 57 51.44
12,1
.12150
99,3
.99677
5,3
.08456
354,8
83 01 17.70
0.99271
12,1
0.12050
99,3
9.09682
5,3
9.08100
357,8
83 04 43-97
u
isinhiu
«F0'
cosh iu
«F0'
,0,-JShJL-
-Fo'
log cosh iu
c-F,,'
u
SMITHSONIAN TABLES
22O
Circular Functions.
u
sin u
.*
cos u
.«
log sin u
« Fo'
log cos u
-Fo'
u
1.450
0.99271
12,1
0.12050
99,3
9.99682
5,3
9-OSlOO
357,8
83V 4/97
.451
.99283
12,0
.11951
99,3
&
.07740
360,8
83 08 10.23
.452
.99295
n,9
. 1 1852
99,3
.99603
5,2
•07378
83 ii 36.50
.453
.99307
11,8
.11752
99,3
.99698
5,1
.07013
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
9.09708
5,1
9.06272
373-4
*3 21 55.29
.456
•99342
n,5
.H454
99,3
.99713
5,o
.05897
83 25 21.56
• 457
•99353
n,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
11,0
.10958
99,4
.99738
4,8
.03971
394,0
83 42 32.88
.462
.99409
10,9
.10858
99,4
•99743
4,7
.03576
83 45 59.15
.463
.99420
10,8
. 10759
99,4
.99747
4,7
•03176
401,3
83 49 2~5.4i
.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
425,2
84 10 03.00
1.470
0.99492
10,1
0.10063
99,5
9-99779
4,4
9.00271
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
0.09542
9,6
0.09565
99,5
9.09800
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
.99809
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
47i,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 51.91
.481
.99597
9,0
.08068
99,6
.99825
3,9
•95267
482,3
84 51 18.18
.482
.99606
8,9
. 088^)8
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
$4 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
.95844
3,7
.92786
510,9
3s 08 29.50
.487
.99649
8,4
.08370
99,6
.95847
3,6
.92272
517,1
85 ii 55.77
.488
.99657
8,3
.08270
99,7
.99851
3,6
.91751
52*3,3
85 15 22.03
.489
.99666
8,2
.08171
99,7
.99855
3,6
.9122-5
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
.99868.
3,4
.89052
557,1
33.36
•494
•99705
7,7
.07672
99,7
.99872
3,3
.88491
85 35 59.62
1-495
.496
0.99713
.99720
7,6
7,5
0.07572
.07473
99,7
99,7
9.99875
.99878
3,3
3,3
8.87923
.87348
571,9
579,6
85 39 25.89
^5 4-' 53.15
.497
.99728
7,4
.07373
99,7
.99882
3.2
.86764
587,4
85 46 18.41
.498
•99735
7,3
.07273
99,7
.99885
3.2
.86173
595,5
^5 40 44- < ~<8
.499
•99742
7,2
.07173
99,7
.99888
3,1
.85573
603,9
85 53 10.94
1.500
0.99749
7,1
0.07074
99,7
9.99891
3,1
8.84965
612,4
85 56 37-21
u
-isinhiu
»F0'
cosh iu
•w
sinh iu
« F '
OQ cosh iu
-p.-
u
log .
SMITHSONIAN TABLES
221
Circular Functions.
u
sin u
«FO'
COS U
«F0'
log sin u
« Fo'
log cos u
-F0'
u
1.500
0.99749
7,1
0.07074
99,7
9.99891
3,1
8.84065
612,4
85° 56' 37^2 1
.501
.99757
7,o
.06974
99,8
.99894
3,1
.84348
621,2
86 oo 03.47
.502
.99763
6,9
.06874
99,8
.99897
3,0
.83722
630,3
86 03 29.74
.503
.09770
6,8
.06774
99,8
.00000
2,9
.83087
639,6
86 06 56.00
.504
.99777
6,7
.06675
99,8
.99903
2,9
.82443
649,2
85 10 22.27
1.505
0.09784
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
.00914
2,7
.79765
600,7
86 24 07.33
.509
.99809
6,2
.06176
99,8
.99917
2,7
.79069
7oi,9
86 27 33.59
1.510
0.99815
6,1
0.06076
99,8
9.99920
2,6
8.78361
713,5
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
0.99844
5,6
0.05577
99,8
9.95932
2,4
8.74638
777,5
86 48 u. 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
0.09871
5,1
0.05077
99,9
9.09944
2,2
8.70565
854,2
87 05 22.51
.521
.99876
5,o
.04978
99,9
.00946
2,2
.69702
871,4
87 08 48.77
.522
.99881
4,9
.04878
99,9
.99948
2,1
.68821
889,3
87 12 15.04
.523
.99886
4,8
.04778
99,9
.00950
2,1
.67023
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
.90900
4,5
.04478
99,9
.99956
1,9
.65110
968,8
87 26 00.09
.527
.99904
4,4
•04378
99,9
•95958
1,9
.64130
091,0
87 29 26.36
.528
.09908
4,3
.04278
99,9
.99960
1,9
•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
9.09964
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 H.42
.532
.99925
3,9
.03879
99,9
.99967
i,7
.58868
1118,9
87 46 37-68
• 533
.90929
3,8
.03779
99,9
• 99069
1,6
. 57735
1148,5
87 50 03-95
• 534
•99932
3,7
.03679
99,9
.99971
1,6
•56571
H79,7
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
.90946
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
3J
0.03079
100,0
9.90079
i,3
8.48843
1409,8
88 14 07.80
• 541
.999S6
3,0
.02979
1 00,0
.09081
1,3
.47410
1457,1
88 17 34.07!
• 542
2,9
.02879
100,0
.99982
i,3
.45928
I50/,7
88 21 00.331
• 543
.99961
2,8
.02779
1 00,0
•95983
1,2
•44393
1562,0
88 24 26.60'
• 544
.99964
2,7
.02679
100,0
•99984
1,2
.42802
l620,3
88 27 52.86!
0.99967
2,6
0.02579
100,0
9.09086
1,1
8.41151
1683,2
88 31 19.13
.99969
2,5
.02479
100,0
.99987
1,1
•39434
1751,1
88 34 45-39
•547
.'//;/-'
2,4
•OJ379
100,0
.99988
1,0
•37647
l8_>47
88 38 11.66
2,3
.02279
1 00,0
•99989
1,0
• 35/83
1904,8
88 41 37-92
,99976
2,2
.02179
100,0
.99990
0,9
.33835
1592,2
88 45 04.18
1-550
2,1
0.02079
100,0
9.99991
0,9
8.31796
2088,0
88 48 30.45
u
-i tinti iu
-Fo'
cosh iu
»flo'
sinh iu
«F0'
ogcosh iu
»FO'
u
loo ,
SMITHSONIAN TABLES
222
Circular Functions.
u
sin u
«F0'
COS U
„*
log sin u
.w
log oos u
-FO'
u
1.550
0.99978
2,1
+0.02079
100,0
9.99991
0,9
8.31796
2088,0
88°48V:45
.551
.99980
2,O
.01980
.99991
0,9
.29056
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
1,7
.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 41-77
.556
.99989
1,5
.01480
.99995
0,6
.17014
2934,9
89 09 08.04
• 557
.99990
1,4
.01380
.99996
0,6
. 13975
3147,7
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
3681,4
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-IO
.561
•99995
1,0
.00980
.99998
0,4
7.99106
4433,1
89 26 19.36
•99996
0,9
.00880
.99998
0,4
•94430
4937,1
89 29 45.63
'563
.99997
0,8
.00780
.99999
o,3
5570,4
89 33 11-89
.564
.99998
o,7
.00680
.99999
o,3
^83227
6390,0
89 36 38.16
1.565
0.99998
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.OOOOO
0,2
.00180
.00000
0,1
.25438
24176,8
89 53 49.48
1.570
I.OOOOO
0,1
+0.00080
100,0
o.ooooo
0,0
6.90109
54537,4
89 57 15-75
.571
.00000
0,0
— .00020
.00000
0,0
6.3089411
213228,5 90 oo 42.01
.572
.00000
0,1
.00120
.00000
0,1
7.08051
36080,7
90 04 08.28
.573
.00000
0,2
.00220
.00000
0,1
.34315
19707,7
oo 07 34.54
.574
0.99999
0,3
.00320
.00000
0,1
.50565
90 ii 00.81
1-575
0.99999
0,4
—0.00420
100,0
o.ooooo
0,2
7.62363*1
10331,2
90 14 27.07
• 576
.99999
0,5
.00520
9.99999
0,2
.71631
8345,8
90 17 53-33
• 577
.99998
0,6
.00620
.99999
o,3
.79265
7000,5
9O 21 I9.OO
.578
•99997
o,7
.00720
.99999
0,3
.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
7.96396*
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
.OII20
•99997
o,5
.04935
3876,2
90 38 30.92
.583
•99993
1,2
.OI220
•99997
0,5
.08648
3558,5
90 41 57.19
084
.99991
1,3
.OI32O
.99996
0,6
.12068
3289,0
90 45 23.45
1.585
0.99990
1,4
—0.01420
100,0
9.99996
0,6
8.15239"
3057,4
90 48 49-72
.586
.99988
i,5
.01520
•99995
o,7
. 18193
2856,3
90 52 15-98
.587
.99987
1,6
.Ol62O
•99994
o,7
.20959
2680,0
90 55 42.25
.588
.99985
i 7
.01720
.99994
o,7
.23560
2524,2
90 59 08.51
.589
.99983
1,8
.OI82O
.99993
0,8
.26014
2385,5
91 02 34.78
1.590
0.99982
1,9
— O.OI92O
100,0
9.99992
0,8
8.28336,1
2261,2
91 06 01.04
.591
.99980
2,0
.O2O2O
.99991
0,9
.30540
2149,3
91 09 27.31
.592
.99978
2,1
.O2I2O
.99990
0,9
.32638
2047,9
91 12 53-57
• 593
•99975
2,2
.O2220
.99989
1,0
.34639
1955,6
91 16 ig.84
• 594
•99973
2,3
.O232O
.99988
1,0
.36552
1871,3
91 19 40.10
1-595
0.99971
2,4
— O.O242O
100,0
9.99987
1,1
8.383&4n
1794,0
91 23 12.37
.596
.99968
2,5
.O252O
.99986
1,1
.40142
1722,8
91 26 38.63
• 597
.99966
2,6
.0262O
•99985
1,1
.41831
1657,0
91 30 04.90
.598
.99963
2,7
.O2720
.99084
1.2
•43457
I596,i
91 33 3Li6
.599
.99960
2,8
.O282O
.99983
1,2
•450J5
1539,4
91 36 57-43
i. 600
0.99957
2,9
—0.02920
100,0
9.99981
1,3
8.46538,,
1486,7
91 40 23.69
u
-isinhiu
«F0'
cosh iu
wF0*
sinh iu
«F0'
log cosh iu
-Fo'
u
log .
SMITHSONIAN TABLES
223
TABLE IV
THE ASCENDING AND DESCENDING EXPONENTIAL AND
Log10(eu)
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.
•
looio(eu)
eu
e~u
u
looio(eu)
en
e u
o.ooo
o.ooo oooo
I. 000 000
I. 000 0000
0.050
O.O2I 7147
I.05I 271
0.951 2294
.001
.000 4343
.001 ooi
0.999 0005
.051
.022 1490
.052 323
.950 2787
.002
.000 8686
.OO2 OO2
.998 OO20
.052
.022 5833
•053 376
.949 3289
.003
.001 3029
.003 005
.997 0045
.053
.023 0176
.054 430
.948 3800
.004
.001 7372
.004 008
.996 0080
.054
.023 4519
.055 485
.947 43*21
0.005
O.O02 1715
1.005 013
0.995 0125
0.055
O.O23 8862
1.056 541
0.946 4851
.006
.OO2 6058
.006 018
.994 0180
.056
.024 3205
.057 598
•945 5391
.007
.OO3 O40I
.007 025
.993 0244
.057
.024 7548
.058 656
.944 5941
.008
.003 4744
.008 032
.992 0319
.058
.025 1891
•059 715
.943 6499
.009
.003 9087
.009 041
.991 0404
.059
.025 6234
.060 775
.942 7068
O.OIO
0.004 34^9
I. 010 050
0.990 0498
0.060
0.026 0577
1.061 837
0.941 7645
.Oil
.004 7772
.on 061
.989 0603
.061
.026 492O
.062 899
.940 8232
.012
.005 2115
.012 O72
.988 0717
.062
.O26 9263
.063 962
•939 8829
.013
•005 6458
.013 085
.087 0841
.063
.027 3606
.065 027
.938 9435
.014
.006 0801
.014 098
.986 0975
.064
.027 7948
.066 092
.938 0050
0.015
0.006 5144
1.015 113
0.985 IH9
0.065
0.028 2291
1.067 159
0.937 0675
.016
.006 9487
.016 129
.984 1273
.066
.028 6634
.068 227
.936 1309
.017
.007 3830
.017 145
.983 1437
.067
.029 0977
.069 295
.935 1952
.018
.007 8173
.018 163
.982 1610
.068
.029 5320
.070 365
.934 2605
.019
.008 2516
.019 182
.981 1794
.069
.029 9663
.071 436
•933 3267
O.O2O
0.008 6859
1.020 201
0.980 1987
0.070
0.030 4006
1.072 508
0.932 3938
.O2I
.009 I2O2
.O2I 222
.979 2190
.071
.030 8349
.073 58i
.931 4619
.022
.009 5545
.022 244
.978 2402
.072
.031 2692
.074 655
•930 5309
.023
.009 9888
.023 267
.977 2625
•073
•031 7035
.075 731
.929 6008
.024
.010 4231
.024 200
.976 2857
.074
.032 1378
.076 807
.928 6717
0.025
o.oio 8574
1.025 315
0.975 3099
0.075
0.032 5721
1.077 884
0.927 7435
.026
.on 2917
.026 341
•974 3351
.076
.033 0064
.078 963
.926 8162
.027
.on 7260
.027 368
.973 3612
.077
.033 4407
.080 042
.925 8899
.028
.012 1602
.028 396
•972 3884
.078
•033 8750
.081 123
.924 9644
.029
.012 5945
.029 425
•971 4165
.079
.034 3093
.082 204
.924 0399
O.030
0.013 0288
1.030 455
0.970 4455
0.080
0.034 7436
1.083 287
0.923 1163
.031
.013 4631
.031 486
.969 4756
.081
.035 1779
.084 37i
.922 1937
.032
.013 8974
.032 518
.968 5066
.082
.035 6121
.085 456
.921 2720
•033
.014 3317
•033 551
.967 5386
.083
.036 0464
.086 542
.920 3511
.034
.014 7660
•034 585
.966 5715
.084
.036 4807
.087 629
.919 4313
0.035
0.015 2003
1.035 620
0.065 6054
0.085
0.036 9150
i. 088 717
0.918 5123
.036
.015 6346
.036 656
.964 6403
.086
•037 3493
.089 806
.917 5942
.037
.016 0689
.037 693
.963 6761
.087
.037 7836
.090 897
.916 6771
.038
.016 5032
•038 73i
.962 7129
.088
.038 2179
.091 988
.915 7609
.039
.016 9375
.039 770
.961 7507
.089
.038 6522
.093 081
.914 8456
0.040
0.017 3718
1.040 811
0.960 7894
0.090
0.039 0865
1.094 174
0.913 9312
.041
.017 8061
.041 852
.959 8291
.091
.039 5208
.095 269
.913 0177
.042
.018 2404
.042 894
.958 8698
.092
.039 9551
.096 365
.912 1051
.043
.018 6747
.043 938
.957 9114
.093
.040 3894
.097 462
.911 1935
.044
.019 1090
.044 982
.956 9540
.094
.040 8237
.098 560
.910 2828
0.045
0.019 5433
1.046 028
0.955 9975
0.095
0.041 2580
1.099 659
0.909 3729
.019 0/75
.047 074
.955 0420
.096
.041 6923
.100 759
.908 4640
.047
.020 4118
.048 122
•954 0874
.097
.042 1266
.101 860
.907 556o
.048
.020 8461
.049 171
•953 1338
.098
.042 5609
.102 963
.906 6489
.049
.021 2804
.050 220
.952 1811
.099
.042 9952
.104 066
.90S 7427
0.050
0.021 7147
I.05I 271
0.951 2294
O.IOO
0.043 4294
1.105 171
0.904 8374
IOOe<«")
loo1(X«n)
en
e-
looe(eu)
logio(eu)
eu
e-n
SMITHSONIAN TABLES
The Exponential.
u
looiu(eu)
e"
e-
u
lofl,o(e°)
eu
e u
0.100
0.043 4-"M
I. 105 i/i
0.904 8374
0.150
0.065 1442
I.l6l 834
0.86o 7080
.101
.043 8637
.106 277
.903 9330
.151
.065 5785
8477
.102
.044 2980
.107 383
.903 0296
• 152
.066 0128
.858
.103
•044 7323
.IO8 4«;l
.902 1270
•153
.066 4471
3-'5
.858
.104
.045 1666
.IO9 OOO
.901 2253
.154
.0668814
491
.857 2720
0.105
0.045 6009
i. no 711
0.900 3245
0.155
0.067 3156
i . 167 658
0.856 4152
.106
.046 0352
.in 822
.899 4246
.150
.067 7499
3 826
.855 5592
.107
.046 4695
.112 934
.898 5257
• 157
.068 1842
; 906
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 0904
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
.851
.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 5006
. 120 752
.892 2580
.164
.071 2243
.178 214
.848 7420
O.II5
0.049 9439
i. 121 873
0.891 3661
0.165
0.071 6586
1. 179 393
0.847 8937
.110
.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
.888 6961
.168
.072 9615
.182 937
.845 3538
.119
.051 6810
.126 370
.887 8078
.169
.073 3958
.184 120
.844 5089
O.I2O
0.052 1153
I . 127 497
0.886 9204
0.170
0.073 8301
1.185 305
0.843 6648
.121
.052 5406
. 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
.188 866
.841 1376
.124
.053 8525
.132 016
.883 3798
.174
.075 5672
.190 056
.840 2969
O.I25
.126
0.054 2868
.054 72ii
i.i33 148
.134 282
0.882 4969
.881 6148
o.i75
.176
0.076 0015
.076 4358
1.191 246
.192 438
0.839 4570
.838 6180
.127
.055 1554
•135 417
.880 7337
.177
.076 8701
.193 631
.837
.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
O.I3O
0.056 4583
I . 138 828
0.878 0954
0.180
0.078 1730
I. 197 217
0.835 2702
.131
.056 8926
.139 968
.877 2178
.181
.078 6073
• 198 415
.834 4.o4
.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
•134
.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
1.150 274
0.869 3582
O.IOO
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
•M3
.062 1041
.153 730
.866 7541
.193
.083 8188
.212 883
.824 4820
.144
.062 5384
.865 8877
.194
.084 2531
.214 006
.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 556b
.217 744
.821 1906
.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
0.860 7080
O.2OO
0.086 8589
I. 221 403
0.818 7308
looe(eu)
looio(eu)
eu
e~u
lode(eu)
logiu(en)
en
e~u
SMITHSONIAN TABLES
227
The Exponential.
u
Ioo10(eu)
eu
e
"
looio(eu)
eu
e~u
0.200
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
.109 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
0.205
0.089 0304
1.227 525
0.814 6473
0.255
O.I 10 7451
1.290 462
0.774 9165
.206
.089 4647
.228 753
.813 8331
.256
.in 1794
.291 753
.774 1420
.207
.089 8990
.229 983
.813 0196
• 257
.in 6137
.293 045
.773 3682
.208
•090 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
0.8io 5842
0.260
O.II2 9166
1.296 930
0.771 0516
.211
.091 6361
.234 912
.809 7741
.261
.113 3509
.298228
.770 2809
.212
.092 0704
.236 148
.808 9647
.262
.113 7852
.299 527
.769 5110
.213
.092 5047
.237 385
.808 1561
.263
.1142194
.300 827
.768 7419
.214
.092 9390
.238-623
.807 3484
.264
.114 6537
.302 128
•767 9735
O.2I5
0.093 3733
1.239 862
0.806 5414
0.265
O.II5 0880
1.303 431
0.767 2059 1
.216
.093 8076
.241 IO2
.805 7353
.266
.115 5223
.304 735
.766 4391
.217
.094 2419
.242 344
.804 9300
.267
.115 9566
.306 040
.765 6731
.218
.094 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
.096 4U4
.248 571
.800 9154
.272
.118 1281
•312 587
.761 8543
.223
.096 8477
.249 821
.800 1148
.273
.118 5624
.313 Qoo
.761 0928
.224
.097 2820
.251 071
•799 3ISI
.274
.118 9967
.315 215
.760 3321
0.225
0.097 7163
1.252 323
0.798 5162
0.275
0.119 43io
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
.099 0191
.256 085
.796 1243
.278
.120 7339
.320 486
.757 2968
.229
.099 4534
•257 342
•795 3285
.279
.121 1682
.321 807
.756 5399
O.23O
0.099 8877
1.258 600
0.794 '5336
0.280
O.I2I 6025
1.323 130
0.755 7837
.231
.100 3220
.259 859
•793 7395
.281
.122 0367
.324 454
•755 0283
.232
.100 7563
.26l 120
.792 9461
.282
.122 47IO
.325 779
.754 2737
•233
.101 1906
.262 381
.792 1536
.283
. 122 9053
.327 105
•753 5io8
•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 2082
.331 092
.751 2626
.237
.102 9278
.267 441
.788 9913
.287
. 124 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 4149
.289
.125 5111
•335 092
.749 0122
O.24O
0.104 2307
1.271 249
0.786 6279
0.290
0.125 9454
1.336 427
0.748 2636
.241
.104 665O
.272 521
.785 8416
.291
.126 3797
•337 765
.747 5157
.242
.105 0993
.273 794
.785 0562
.292
.126 8140
•339 103
.746 7685
.243
.105 5336
.275 069
.784 2715
.293
.127 2483
•340 443
.746 022 i
.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
. 106 8364
.278 900
.781 9222
.296
.128 5512
•344 470
.743 7874
.107 2707
.280 179
.781 1407
.128 9855
•345 815
.743 0440
.107 7050
.281 460
.780 3599
.298
. 129 4198
.347 162
.742 3013
.249
.108 1393
.282 742
•779 5800
.299
. 129 8541
.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
log<Xeu)
looi(Xeu)
•tt
e~u
Io0e(eu)
looio(eu)
eu
e~u
SMITHSONIAN TABLES
228
The Exponential.
u
logio(eu)
eu
e~u
u
logto(eu)
e"
e °
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
.15-'
.420 487
.703
.302
.131 '.v->
•352 561
•739 338i
.352
.152 X,-i7
i 009
.703 2801
.303
.131 5912
•353 914
.738 5991
• 353
.153 3000
•423 331
.702
•304
. 132 0255
•355 269
•737 8609
•354
.153 7402
•424 755
.701 8750
0.305
0.132 4598
1.356 625
0.737 1234
0-355
0.154 1745
181
0.701 I7.U
.306
.132 8941
•357 982
.736 3866
.356
.154 6088
.427 608 .700 4726
• 307
.133 3284
•359 341
•735 6506
.357
• 155 0431
.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
.698 3744
0.310
0.134 6313
1.363 425
0.733 4470
0.360
o. 156 3460
1.433 329
0.697 6763
.311
.135 0656
.364 789
• 732 7U9
.361
. 156 7803
•434 7'\3
.696
.312
. 135 4999
.366 155
•731 98i5
.362
.157 2140
.436 199
.696 2824
.313
.135 9342
.367 522
.731 2499
.363
• 157 6489
•437 636
.695 5864
.314
.136 3685
.368 890
•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
0.604 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 I l~2 j
.319
•138 5399
•375 751
.726 8755
.369
. 160 2547
.446288
.691
0.320
0.138 9742
1.377 128
0.726 1490
0.370
0.160 6800
1.447 735
0.690 7343
.321
. 139 4085
.378 50' »
.725 4233
• 371
.161 1233,
.449 183
.600 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 '
• 324
.140 7H4
.382 647
.723 2-502
•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
.686 6023
.327
. 142 0143
.386 801
.721 0837
• 377
. i ,3 7290
.457 904
.685 9161
.328
. 142 4486
.388 189
.720 3630
.378
.164 1633
P 363
.68; .
.329
. 142 8829
.389 578
.719 6430
• 379
.164 5976
.460 823
.684 \
0.330
0.143 3172
1.390 968
0.718 9237
0.380
0.165 0319
1.462 285
0.683
.331
.143 7515
.392 360
.718 2052
.381
. 105 4662
•463 748
.683
.332
.144 1858
.393 753
•717 4873
.382
: 9005
.465 -'i-'
.682
•333
. 144 6201
.395 M7
.716 7702
.383
.1663348
• 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
0.167 2034
1.469 614
0.680 4506
• 336
.145 9229
•399 339
.714 <)_'3i
.38 i
.167 6377
•471 085
.679 7705
•337
• U6 3572
.400 739
.713 5088
.387
.168 0720
•472 556
.679
.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
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
0802 !
•342
. 148 5287
.407 76o
.710 3482
• 392
. 170 2434
•479 938
.675 7041
•343
. 148 9630
.409 169
.709 6382
.393
.170
.481 418
.675 '
•344
. U9 3973
.410 579
.7089289
. .394
.171 1 120
.482 901
.674 3541
0.345
0.149 8316
1.411 990
0.708 2204
0.395
O.I7I
1.484 -,84
<>8oo
•346
.150 2659
.413 403
.707 5125
.396
.171 0806
.485 869
oo^>7 !
•347
.150 7002
.414 817
.706 8053
• 397
.172 4M9
- 356
3340
.348
•151 U45
.416 232
.706 0989
.398
.172 8492
8 844
.671 (XJ20
• 349
.151 5688
.417 649
.705 3931
• 399
.173 2835
•490 334
•6/0 9907
0.350
0.152 0031
1.419 068
0.704 6881
0.400
0.173 7178
1.491 825
O.67O 32OO i
loge(ej)
logio(eu)
eu
e~u
loge(en)
logio(en)
eu
•- !
SMITHSONIAN TABLES
229
The Exponential.
u
lofllo(eu)
en
e-n
u
logio(eu)
eu
e~u
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 9908
.402
.174 5864
.494 811
.668 9807
.452
.196 3011
•571 452
.636 3542
.403
.175 O2O7
.496 307
.668 3121
•453
•196 7354
•573 024
.635 7181
.404
.175 4550
.497 804
.667 6441
• 454
.197 1697
•574 598
.635 0827
0.405
0.175 8893
1.499 303
0.666 9768
0.455
0.197 6040
1.576 173
0.634 4480
.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 IQ2I
.503 807
.664 9789
• 458
.198 9069
.580 909
•632 5475
.409
. 177 6264
.505 312
.664 3142
•459
.199 3412
.582 491
.631 9152
0.410
o. 178 0607
1.506 818
0.663 6503
0.460
0.199 7755
1.584 074
0.631 2836
.411
. 178 4950
.508 325
.6629869
.461
.200 2098
.585 659
.630 6527
.412
.178 9293
.509 834
.662 3243
.462
.•200 6441
.587 245
.630 0223
.413
.414
.179 3636
.179 7979
.511 345
•512 857
.661 6623
.661 ooio
.463
.464
.201 0783
.201 5126
.588 833
.590 423
.629 3926
.628 7636
0.415
o. 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 3812
•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 2498
.596 797
.626 2535
.419
.181 0694
.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 1184
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
.204 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
0.184 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 4025
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 5471
• 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 3132
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 9714
.487
.211 5014
.627 427
.614 4670
.438
.190 22-IO
.549 605
•645 3258
.488
.211 9357
.629 055
.613 8529
• 439
- 190 6553
.551 155
.644 6808
.489
.212 37OO
.630685
.613 2393
0.440
O.I9I 0896
I. '552 707
0.644 0364
0.490
O.2I2 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
0.445
O.I93 26lO
1.560 490
0.640 8243
0.495
0.214 9758
I.64O 498
0.609 5709
• ^3 6953
.562 051
.640 1838
.496
.215 4101
.642 I4O
.608 9616
•447
. i')4 1296
.5^3 614
.639 5439
.497
.215 8444
.643 783
.608 3530
..J-J.H
•194 5639
.565 179
.638 9047
.498
.216 2787
.645 427
.607 7449
.194 9982
.566 745
.638 2661
.499
.216 7129
.647 073
.607 1375
0.450
0.195 4325
1.568 312
0.637 6282
0.500
0.217 1472
1.648 721
0.606 5307
Ioo10(ea)
en
e~n
Io0e(eu)
lofllo(eu)
eu
e~u
SMITHSONIAN TABLES
230
The Exponential.
u
looio(eu)
eu
e~u
u
looio(en)
eu
e-n
0.500
.501
• 502
.503
.504
0.217 1472
•217 58i5
.218 0158
.218 4501
.218 8844
1.648 721
.650 371
.652 O22
.653 675
.655 329
0.606 5307
.605 9-M4
.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
•734 087
" 723
.738 4'' I
.740 200
0.576
•5/6 3731
•575 7971
• 575
.574 6466
0.505
.506
.507
.508
.509
0.219 3187
•219 7530
.220 1873
.220 62l6
.221 O559
1.656986
.658 643
.660 303
.661 964
.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
I.74I 941
•743 684
• 745 4-'S
•747 175
.748 923
0.574 0723
•573 4985
•5/2 9253
•572 3526
.571 78o6
0.510
.511
.512
.513
.514
O.22I 4902
.221 9245
.222 3588
.222 793-1
.223 2274
1.665 291
.666957
.668625
.670 295
.671 966
0.6oo 4956
•599 8954
.599 2958
.5986968
.598 0984
0.560
•561
.562
.563
.564
0.243 2049
•243 6392
.244 0735
.244 5078
•244 9421
1.750673
•752 424
•754 177
•755 932
•757 689
0.571 2091
.570 6381
.5/0 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
.675 313
.676 989
.678 667
.680 346
0.597 5006
.596 9034
.596 3068
•595 7io8
•595 i 154
0.565
.566
.567
.568
.569
0.245 3764
.245 8107
.246 2450
.246 6793
.247 1136
1.759448
.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 I3OO
.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 0046
.228 4389
.228 8732
.229 3075
.229 74l8
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
.780688
.782 470
•784 253
0.562 7049
.562 1424
.561 5806
.561 0193
.560 4585
0.530
.531
.532
•533
• 534
O.23O 1761
.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 8008
.252 3251
.252 7594
.253 1937
.253 6280
1.786 038
.787 825
.789 614
•791 405
•793 197
0.559 8^84
.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 9M9
.583 33U
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 3~'73
-553
• 553
.552 6668
• 552 H44
0.545
• 540
.547
.548
•549
0.236 6905
.237 1248
•237 5591
•237 9934
.238 4-V7
1.724 608
•726 334
.728 06 I
.729 790
.731 521
O-579 8418
.579 2622
.5786833
.578 1049
.577 52/0
0.595
.596
•5<)7
.598
• 599
0.258 4052
.258 8395
.250
.259 7081
.260 1424
1.813 031
.814
.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
0.260 5767
1.822 119
0.548 8116
looe(eu)
loflio(eu)
eu
e~u
looe(eu)
logio(en)
eu
e~u
SMITHSONIAN TABLES
231
The Exponential.
•
looio(en)
eu
e~u
u
loQio(eu)
ea
~^n
0.600
0.260 5767
1.822 119
0.548 8116
0.650
0.282 2914
1.915 541
0.522 0458
.601
.261 ono
.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 1677
.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 9i8
.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
0.66o
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 5029
.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
.290 1087
•950 333
.512 7330
.619
.268 8283
.857 070
.538 4827
.669
.290 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
.860 788
•537 4068
.671
.291 4116
.956 193
.511 1971
.622
.270 1312
.862 650
.5368696
.672
.291 8459
.958 150
.510 6862
.623
•270 5655
.864 513
.536 3330
.673
.292 2802
.960 109
.510 1758
.624
.270 0998
.865 379
•535 7970
.674
.292 7145
.962 070
.509 6658
0.625
0.271 4341
1.868-246
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
.971 905
.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
.298 3603
•987 743
.503 0831
.$38
.277 0709
.892 692
.528 3481
.688
.298 7946
.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
0.209 66312
1.993 7i6
0.501 5761
.278 3828
.898378
.526 7654
.691
.300 0975
.995 7io
.501 0747
.278 8171
.900 278
.526 2389
.692
.300 5318
.997 707
•500 5739 |
.643
.279 2514
.902 179
.525 7129
.693
.300 9661
•999 706
.500 0736
.644
.279 6856
.904 082
.525 1875
.694
.301 4004
2.001 706
.499 5738
0.648
0.280 1199
1.905 987
0.524 6625
0.695
0.301 8347
2.003 709
0.499 0744
.280 5542
.907 894
.524 1381
.696
.302 2690
.005 7U
.498 5756
.647
.280 9885
.009 803
•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
.on 740
.497 0821
0.650
0.282 2914
I.QI5 541
0.522 0458
0.700
0.304 0061
2.013 753
0.496 5853
logicAe")
eu
e-u
Io0e(eu)
logio(eu)
eu
e-u
SMITHSONIAN TABLES
232
The Exponential.
' U
loo,o(en)
eu
e u
u
loaio(e")
eu
e u
0.700
0.304 0061
2.013 753
0.496 5853
0.750
0.325 7209
2.117 ooo
0.472 3666
.701
.304 4404
.015 707
.496 0890
•751
.326 1552
. i 19 118
.471 8044
.702
.304 8747
.017 784
.495 5931
.75-'
.3* 5895
.121 238
.471 4228
• 703
.305 3000
.019 803
•495 0978
• 753
.327 0237
.123 361
•470 95l6
.70-4
.305 7433
.021 824
.494 6029
• 754
.327 4580
.125 485
.470 4809
0.705
0.306 1776
2.023 847
0.494 1086
0.755
0.327 8923
2.127 612
0.470 0106
.706
.30'-
.025 872
.493 6147
.756
.328 3266
9 740
.469 5408
• 707
.307 0462
.027 898
.493 1213
• 757
.328 7609
.131 871
.469 0715
.708
•307 4805
.029 927
.402 6285
.758
•329 1952
.134 004
.468 6027
.709
.307 9M8
.031 958
.492 1361
• 759
.329 6295
.136 139
.468 1343
0.710
0.308 3491
2.033 991
0.491 6442
0.760
0.330 0638
2. 138 276
0.467 6664
.711
.308 7834
.036 026
.491 1528
.761
•330 4981
.I4O 416
.467 1000
.712
.309 2177
.038 063
.490 6619
.762
.330 9324
•142 557
.466 7320
.713
.309 6520
.040 102
.490 1715
.763
.331 3667
•144 701
.466
.714
.310 0863
.042 144
.489 6815
.764
.331 8010
. 146 846
.465 7995
0.715
0.310 5206
2.O44 187
0.489 1921
0.765
0.332 2353
2.148 094
0.465 3339
.716
.310 9548
.046 232
.488 70312
.766
.3326696
.151 144
.464 8688
.717
.311 3891
.048 279
.488 2147
.767
.333 1039
.153 297
.464 4042 ;
.718
.311 8234
.050 328
.487 7267
.768
•333 5382
•155 451
.463 9400
.719
.312 2577
.052 380
.487 2393
.769
•333 9725
.157 608
.463 4763
0.720
0.312 6920
2.054 433
0.486 7523
0.7/0
0.334 4068
2.159 766
0.463 0131
.721
.313 1263
.056 489 .486 2657
• 771
•334 8410
.161 927
.462 5503
.722
.313 56o6
.058 546 .485 7797
.772
•335 2753
.164 090
.462 0880
-723
.313 9949
.060 606 .485 2942
.773
•335 7096
. 166 255
.461 6261
.724
.314 4292
.062 667
.484 8091
• 774
.336 1439
.168 423
.461 1647
o./»25
0.3U 8635
2.064 731
0.484 3246
0-775
0.336 5782
2.170 592
0.460 7038
.726
.315 2978
.066 797
.483 8405
.776
•337 0125
.172 764
.460 2433
.727
.315 7321
.068 865
.483 3569
• 777
.337 4468
.174 938
.459 7833
.728
.316 1664
•070 935
.482 8738
.778
•337 8811
.177 H4
•459 3237
.729
.316 6007
.073 007
.482 3911
• 779
.338 3154
.179 292
.458 8646
0.730
0.317 0350
2.075 081
0.481 9090
0.780
0.338 7497
2.181 472
0.458 4060
.731
.317 4693
.077 157
.481 4273
.781
.339 1840
.183 655
•457 9478
.732
.317 9036
.079 235
.480 9461
.782
•339 6183
.185 840
.457 4901
•733
•318 3379
.081 315
.480 4654
.783
.340 0526
.188 027
.457 0329
• 734
.318 7721
.083 398
.479 9852
.784
.3404869
.190 216
.456 5760
0.735
0.319 2064
2.085 482
0.479 5055
0.785
0.340 9212
2.192 407
0.456 1197
.736
.319 6407
.087 569
.479 0262
.785
•341 3555
.104 ooo
•455 6638 ;
• 737
.320 0750
.089657
.478 5474
.787
•341 78o8
.106 796
.455 2084 J
.738
.320 5093
.091 748
.478 0691
.788
.342 2241
.198 994
•454 7534 !
• 739
•320 9436
.093 841
.477 5913
.789
•342 6583
.201 194
.454 2989 :
0.740
0.321 3779
2.095 936
0.477 H39
0.700
0.343 0926
2.203 396
0.453 8448
.741
.321 8122
.098 032
.476 6370
.791
•343 5269
.205 601
•453 3912
• 742
.322 2465
.100 132
.476 1606
.792
.343 9612
.207 808
.452 9380
•743
.322 6808
.102 233
.475 6847
• 793
•344 3955
.210 017
• 45-1 4853
•744
•3->3 H5I
.104 336
.475 2093
,794
•344 8298
j 228
•452 0330
0.745
0.323 5494
2.106 441
0.474 7343
0.795
0.345 2641
2.214 441
0.451 58l2
.746
•323 9837
.108 549
.474 2598
.796
•345 6984
.216 657
.451 1299
•747
.324 4180
. i 10 659
.473 7858
• 797
.346 1327
.218 874
.450 6790
.748
.324 8523
.112 770
.473 3122
.798
.346 5670
.221 094
•450 2285
•749
.325 2866
.114 884
.472 8392
• 799
•347 0013
3 3i6
•449 7785
0.750
0.325 7209
2.117 ooo
0.472 3666
0.800
0.347 4356
2.225 541
0.449 3*290
IOQe(e")
!oou(eu)
eu
e~n
looe(e")
Iog10(eu)
e"
e~u
SMITHSONIAN TABLES
233
The Exponential.
u
looio(eu)
eu
e-
u
looio(eu)
eu
.- 1
0.800
0.347 4356
2.225 541
0.449 3200
0.850
0.369 1503
2-339 647
0.427 4149 1
.801
.347 8699
.227 768
.448 8799
.851
.369 5846
•341 988
.426 9877
.802
.348 3042
.229096
.448 4312
.852
.370 0189
•344 331
.426 5610 1
.803
.348 73&5
.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 9099
.243 417
•445 7487
.858
.372 6247
.358 439
.424 0093
.809
.351 3442
.245 661
•445 3031
.859
•373 0590
.360 799
.423 5855
0.810
0.351 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 5'255
.863
•374 796i
.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
.856
.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
.361 7673
.300 209
.434 7431
.883
.383 4820
.418 143
.413 5404
.834
.362 2016
.302 510
.434 3086
.884
•383 9163
.420 563
.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
.307 120
.433 4408
.886
.384 7849
.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 6535
.430 264
.411 4779
.839
•364 3731
.314 052
.432 1424
.889
.386 0878
.432 696
.411 0666
0.840
0.364 8074
2.316 367
0.431 7105
0.890
0.386 5221
2.435 130
0.410 6558 1
.365 24/17
.318 685
.431 2700
.891
.386 9564
•437 566
.410 2453
.842
• 3'>5 6760
.321 004
.430 8480
.892
.387 3907
.440 005
.409 8353
.843
.366 1 102
.323 327
.430 4173
.893
.387 8250
.442 446
.409 4256 1
•366 5445
.325 651
.429 9871
.894
.388 2593
.444 890
.409 0164
0.845
0.366 9788
2.327 978
0.429 5574
0.895
0.388 6936
2.447 336
0.408 6076 1
4131
8474
.368 2817
.368 7160
•330 307
•332 638
.334 972
•337 308
.429 1280
.428 6091
.428 2706
.427 8426
.896
.897
.898
• 899
.389 1279
.389 5622
.389 9964
•390 4307
.449 784
.452 235
.454 689
•457 145
.408 1092 1
.407 7912 II
.407 3836
.406 9764
0.850
0.369 1503
2.339 647
0.427 4149
0.900
0.390 8650
2.459 603
0.406 5697
— ^»^_ _^_^_
looi.Xe°)
^^^==
eu
—
e-°
loge(eu)
logio(eu)
eu
.- 1
SMITHSONIAN TABLES
The Exponential.
u
looio(eu)
eu
e-n
u
looio(e°)
en
e—
0.900
0.390 8650
2.459 603
0.406 5697
0.950
0.412 5798
2.585 710
0.386 7410
.901
•391 2093
a 064
.406 1633
•951
.413 0141
•5«* 297
.386 3545
.902
•391 7336
.464 527
.405 7573
•952
.413 4483
.590886
.385 -
.903
•392 1679
.466 993
.405 35i8
•953
.413 8826
•593 478
.385
.904
.392 <x>2J
.469 461
.404 9466
• 954
.4U 3169
.596 073
.380 il>7i
0.905
0.393 0365
2.471 932
0.404 5419
0.955
0.414 7512
2.598 671
0.384 8121
,go6
•393 4708
.474 405
.404 1375
.956
.415 1855
.601 271
.384 4275
.907
•393 9051
.476 881
.403 7336
•957
.415 6198
.603 873
.384 0433
.908
•394 3394
•479 359
.403 3301
.958
.416 0541
.606 478
.383 '
.909
•394 7737
.481 839
.402 9269
•959
.416 4884
.609 086
.383 2760
0.910
0.395 2080
2.484 323
0.402 5242
0.960
0.416 9227
2.611 696
0.382 8929
.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 1279
.913
.396 5109
.491 787
.401 3185
.963
.418 2256
.619 543
.381 7459
.914
.396 9452
.494 280
.400 9173
.964
.418 6599
.622 164
.381 3644
0.915
0.397 3795
2.496 775
0.400 5166
0.965
0.419 0942
2.624 788
0.380 9832
.916
•397 8137
.499 273
.400 1163
.966
.419 5285
.627 414
.380 6024
.917
.398 2480
•501 774
•399 7164
.967
.419 9628
.630 042
.380 222O
.918
.398 6823
.504 277
•399 3169
.968
.420 3971
.632 674
.379 8420
.919
.399 "66
.506 782
.398 9178
.969
.420 8314
.635 308
•379 4623
0.920
.921
0.399 5509
•399 9852
2.509 290
.511 801
0.398 5190
.398 1207
0.970
.971
0.421 2656
.421 6999
2.637 944
.640 584
0.379 0830
•378 7041
.922
.400 4195
.514 3H
.397 7228
.972
.422 1342
.643 226
.378 3256
• 923
.400 8538
.516 830
•397 3253
•973
.422 5685
.645 870
.377 9475
.924
.401 2881
.519 348
.396 9281
•974
.423 '0028
.648 517
•377 5697
0.925
0.401 7224
2.521 868
0.396 53U
0.975
0.423 4371
2.651 167
0.377 1924
.926
.402 1567
.524 391
.396 1351
.976
.423 8714
.653 820
.376 8153
.927
.402 5910
.526 917
•395 7391
• 977
.424 3057
.656 475
.376 4387
.928
.403 0253
.529 445
•395 3436
.978
.424 7400
.659 133
.376 0625
•929
.403 4596
•531 976
.394 9485
• 979
.425 1743
.661 793
.3756866
0.930
0.403 8939
2.534 509
0.394 5537
0.980
0.425 6086
2.664 456
0.375 3Hi
•931
.404 3'2&2
.537 045
.394 1594
.981
.426 0429
.667 122
.374 936o
.932
.404 7625
•539 583
•393 7654
.982
.426 4772
.669 790
.374 5612
• 933
.405 1968
.542 124
.393 37i8
.983
.426 9115
.672 462
.374 1869
.934
.405 6310
.544668
.392 9786
• 984
.427 3458
.675 135
•373 8129
0.935
0.406 0653
2.547 213
0-392 5859
0.985
0.427 7801
2.677 812
0.373 4392
.936
.406 4096
.549 762
•392 1935
.986
.428 2144
.680 491
.373 0660
• 937
.406 9339
•552 313
.391 8015
.987
.428 6487
.683 173
•372 6931
.938
.407 3682
•554 867
.391 4099
.988
.429 0829
.685 857
.372 3206
•939
.407 8025
.557 423
.391 0187
.989
.429 5172
.688 545
•371 9485
0.940
0.408 2368
2.559 98i
0.390 6278
0.990
0.429 9515
2.691 234
0.371 5767
.941
.408 6711
.562 543
•390 2374
.991
.430 3858
.693 9-V
•3/1 2053
.942
.409 1054
.565 107
.3898474
• 992
.430 8201
.606 OJ2
•370 S343
• 943
.409 5397
.567 673
•389 4577
• 993
.431 2544
.699 320
.370
•944
.409 9740
•570 242
.389 0684
>994
.431 6887
.702 02 i
.3/0 0934
0.945
0.410 4083
2.572 813
0.388 6796
0.995
0.432 1230
2.704 724
0.369 7-'34
.946
.410 8426
• 575 387 .388 2911
.996
•432 5573
.707 430
.369 3539
• 947
.411 2769
• 577 964 .387 9030
.997
.432 9916
.710 139
.368
.948
.411 7112
080 543
.387 5153
.998
.433 4-'59
.712 851
.368 6150
• 949
.41-' M55
.583 125
.387 1280
.999
.433 8602
.715 565
.368 2475
0.950
0.412 5798
2.585 710
0.386 7410
I.OOO
0.434 2945
2.718 282
0.367 8794
loge(eu)
looio(eu)
eu
e~u
lofle(eu)
log,0(eu) eu
e-1
SMITHSONIAN TABLES
235
The Exponential.
u
looio(eu)
eu
•-
u
loQio(eu)
en
e-n
1. 000
0.434 2945
2.718 282
0.367 8794
1.050
0.456 0092
2.857 651
0-349 9377
.001
.434 7288
.721 ooi
.367 5H7
.051
.456 4435
.860 510
•349 588o
.002
•435 1631
.723 724
.367 1444
.052
.456 8778
.863 372
•349 2386
.003
.004
.435 5974
.436 0317
.726 449
.729 177
.366 7775
.366 4109
.053
.054
.457 3121
•457 7464
.866237
.869 105
.3488895
.348 5408
1.005
0.436 4660
2.731 907
0.366 0446
1.055
0.458 1807
2.871 975
0.3148 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 US
.364 948i
.058
.459 4836
.880 604
.347 1494
.009
.438 2031
.742 857
.364 5834
.059
.459 9179
.883 486
.346 8024
I.OIO
0.438 6374
2.745 601
0.364 2190
i. 060
0.460 3522
2.886 371
0.346 4558
*-f—T -T «_/ «^
.Oil
.439 0717
.748 348
.363 8549
.061
.460 7864
.889 259
.346 1095
.012
•439 5o6o
.751 098
.363 4913
.062
.461 2207
.892 150
•345 7636
.013
.439 0403
•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 74i
•344 3833
.017
.441 6775
.764 888
.361 6783
.067
.463 3922
.906 646
.344 0391
.018
.442 1118
.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
1.020
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 9980
.924 139
.341 0810
.024
.444 7175
•784 3io
•359 1554
.074
.466 4323
.927 064
.341 6392
I.O25
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
.798266
•357 3641
.079
.468 6037
.941 736
•339 9363
1.030
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 90i8
.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
.336 8896
.039
.451 2320
.826389
•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 88 i
.352 7485
.092
.474 2496
.980 229
•335 5447
•043 .452 0691
.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
.454 2720
.846 243
•351 3403
.096
•475 9868
.992 173
•334 2052
.047
.454 7063
.849 091
•350 9891
.097
.476 4210
•995 167
•333 8712
.048
•455 1406
.851
•350 6383
.098
.476 8553
.998 164
.333 5375
•455 5749
.854 795
.350 2879
.099
.477 2896
3.001 163
•333 2041
1. 050
0.456 0002
2.857 651
0-349 9377
1. 100
0.477 7239
3.004 166
0.332 8711
1 loo^e";
lofl,,/en)
eu
e~u
looe(eu)
looiu(eu)
ett
e-u .
SMITHSONIAN TABLES
The Exponential.
u
Iodide")
eu
e-u
u
looio(eu)
e°
e n
1. 100
0.477 7239
3.004 166
0.332 8711
I.I50
0.499 4387
3.158 193
0.316 6368
.101
.478 I&2
.007 17-'
• 33-' 5384
.151
.499 8729
•i'»i 353
.316 3203
.IO2
.478 59-'5
.010 180
.332 2000
.152
.500 3072
. I" 4 5i<>
.316 0041
.103
.479 O268
.013 192
•331 8740
•153
.500 7415
,167 682
•315 6883
.104
.479 4611
.016 207
•331 5423
• 154
.501 1758
.170 851
.315 3728
1.105
0.479 8954
3-019 224
0.331 2109
1. 155
0.501 6101
3.174 023
0.315 0575
.106
.480 3297
.022 245
•330 8798
.156
.502 0444
.177 199
.314 7426
.107
.480 7640
.025 369
•330 5491
.157
.502 4787
.180 378
.314 4281
.108
.481 1083
.028 296
.330 2187
.158
.502 9130
.183 560
.3M 1138
.109
.481 6326
.031 326
.3298887
.159
.503 3473
.186 745
.313 7998
i. no
0.482 0669
3.034 358
0.329 5590
1.160
0.503 7816
3.189 933
0.313 4862
.in
.482 5012
.037 394
.329 2296
.161
.504 2159
•193 125
.3U
.112
.482 9355
.040 433
.328 0005
.162
.504 6502
.196 320
.312 8598
.113
.483 3698
.043 475
.328 57i8
.163
.505 0845
.199 517
.312 5471
.114
.483 8041
.046 520
.328 2434
.164
.505 5i88
,202 719
.312 2347
I. IIS
0.484 2383
3.049 568
0.327 9153
1.165
0.505 9531
3.205 923
0.311
.116
.484 6726
.052 619
.327 5875
.166
.506 3874
.209 130
.311 6109
.117
.485 1069
.055 673
.327 2601
.167
.506 8217
.212 341
.311 2994
.118
.485 5412
.058 731
.326 9330
.168
.507 2560
•215 555
.310 •
.119
.485 9755
.061 791
.326 6062
.169
.507 6902
.218 772
.310 •
I.I2O
0.486 4098
3.064 854
0.326 2798
1.170
0.508 1245
3.221 093
0.310 3669
.121
.486 8441
.067 921
.325 9537
.171
.508 5588
.225 216
.310 0567
.122
.487 2784
.070 990
.325 6279
.172
•508 9931
.228 443
.309 7468
.123
.487 7127
.074 063
.325 3024
• 173
.509 4274
.231 673
.309 4372
.124
.488 1470
.077 138
.324 9773
.174
.509 8617
.234 906
.309 1280
I. 125
0.488 5815
3.080 217
0.324 6525
1. 175
0.510 2960
3-238 143
0.308 8190
.126
.489 0156
.083 209
.324 3280
.176
• 510 7303
•241 383
.308 5103
.127
.489 4499
.086 383
.324 0038
.177
.511 1646
.244 626
.308 2020
.128
.489 8842
.089 471
.323 6800
.178
.511 5989
.247 872
.307 8939
.129
.490 3185
.092 562
•323 3565
.179
.512 0332
.251 121
.307 5862
I.I30
0.490 7528
3-095 657
0.323 0333
1.180
0.512 4675
3.254 374
0.307 2787
.131
.491 1871
.098 754
.322 7104
.181
.512 9018
.257 630
.306 97l6
.132
.491 6214
.101 854
.322 3878
.182
.513 336i
.260 889
.306 '
•133
.492 0556
. 104 957
.322 0656
.183
.513 7704
.264 152
.306 3583
•134
.492 4899
.108 064
•321 7437
.184
.514 2047
.267 418
.306 0521
I • 135
0.492 9242
3. I n 174
0.321 4221
1.185
0.514 6390
3.270 687
0.305 7462
.136
.493 3585
.114 286
.321 1009
.186
.515 0733
•273 959
.305 4406
•137
•493 7928
.117 402
.320 7799
.187
.515 5075
.277 235
.305 1353
.138
.494 2271
.120 521
.320 4593
.188
.515 9418
.280 514
.304 8303
•139
.494 6614
.123 643
.320 1390
.189
.516 3761
.283 796
.304 5256
I.I40
0-495 0957
3.126 768
0.319 8190
1.190
0.516 8104
3.287 081
0.304 2213
.141
•495 5300
.129 897
.319 4994
.191
.517 -'447
.290 370
.303
.142
•495 9643
.133 028
.319 1800
. 192;
.517 6790
.29.;
.303 6134
•143
.496 3986
.136 163
.318 8610
.193
.518 1133
.296 957
.303 3ioo
.144
.496 8329
.139 300
•318 5423
.194
•5l8 5476
.300 256
.303 0068
1. 145
0.497 2672
3.142 441
0.318 2239
1. 195
0.518 9819
3.3o;
0.302 7040
.146
•497 7015
• M5 585
.317 0059
.196
.519 4162
.306863
.302 4014
.147
.498 1358
.148 733
.317 588i
.197
.519 8505
.310 17-'
.302 0992
.148
.498 5701
.151 883
.317 2707
.198
.520 2848
.313 483
.301
.149
.499 0044
.155 036
.316 9536
.199
.520 7191
.316 798
.301 4956
I.I50
0.499 4387
3.158 193
0.316 6368
1.200
0-521 1534
3.320 117
0.301 1942
loge(eu)
looio(eu)
eu
e-u
IOQe(en)
looio(en) e"
e~*
SMITHSONIAN TABLES
237
The Exponential.
u
loaio(eu)
ea
e-n
u
looio(eu) eu
e~u
I.2OO
0.521 1534
3.320 117
0.301 1942
1.250
0.542 868l
3-490 343
0.286 5048
.2OI
.521 5877
.323 439
•300 8932
.251
.543 3024
.493 835
.286 2184
.202
.522 022O
.326 764
.300 5924
.252
•543 7367
•497 331
.285 9324
.203
.522 4563
• 330 092
.300 2920
.253
.544 1710
.500 830
.285 6466
.204
.522 8906
•333 424
.299 99i8
.254
.544 6053
.504 332
.285 3611
1.205
0.523 3249
3.336 759
0.299 6920
1.255
0.545 0396
3.507 838
0.285 0758
.206
.523 7591
.340 098
.299 3925
.256
•545 4739
•511 348
.284 7909
.207
.524 1934
•343 439
.299 0932
.257
•545 9082
.5U 861
.284 5063
.208
.524 6277
.346 784
.298 7943
.258
.546 3425
.518 378
.284 2219
.209
.525 O62O
.350 133
.298 4956
.259
.546 7768
.521 898
.283 9378
1. 210
0.525 4963
3-353 485
0.298 1973
1.260
O.547 21 IO
3.525 421
0.283 6540
.211
.525 9306
.356 840
.297 8992
.261
•547 6453
.528 949
.283 3705
.212
.526 3649
.360 108
.297 6015
.262
.548 0796
.532 479
.283 0873
.213
.526 7992
.363 500
.297 3040
.263
.548 5139
.536 014
.282 8043
.214
.527 2335
.366 925
.297 0069
.264
.548 9482
.539 55i
.282 5217
I.2I5
0.527 6678
3-370 294
0.296 7100
1.265
0.549 3825
3-543 093
0.282 2393
.216
.528 102 I
.373 666
.206 4135
.266
.549 8168
.546 638
.281 9572
.217
.528 53^4
.377 041
.296 1772
.267
•550 2511
.550 186
.281 6754
.218
.528 9707
.380 420
.295 8212
.268
•550 6854
.553 738
.281 3938
.219
.529 4050
.383 802
.295 5255
.269
• 551 H97
•557 293
.281 1126
I.22O
0.529 8393
3.387 188
0.295 2302
1.270
0.551 5540
3.56o 853
0.280 8316
.221
.530 2/36
•390 577
.294 9351
.271
.551 9883
.564 415
.280 5509
.222
.223
•530 7079
.531 1422
•393 969
•397 365
.294 6403
.294 3458
.272
• 273
.552 4226
•552 8569
.567 981
.571 551
.280 2705
.279 9904
.224
•531 5764
.400 764
.294 0516
.274
•553 2912
.575 124
.279 7105
1.225
0.532 0107
3.404 166
0.293 7577
1.275
0.553 7255
3.578 701
0.279 4310
.226
.532 4450
.407 572
.293 4641
.276
.554 1598
.582 282
.279 1517
.227
•532 8793
.410 981
.293 1708
.277
•554 5941
.585 866
.2788727
.228
• 533 3U6
.414 394
.292 8777
.278
.555 0283
.589 454
.278 5939
.229
•533 7479
.417 810
.292 5850
.279
•555 4626
.593 045
-278 3155
1.230
0.534 1822
3.421 230
0.292 2926
1.280
0.555 8969
3.506 640
0.278 0373
.231
.534 6165
.424 652
.292 0004
.281
.556 3312
.600 238
•277 7594
•-732
.535 0508
.428 079
.291 7086
.282
.556 7655
.603 840
.277 4818
.233
.535 4851
.431 509
.291 4170
.283
.557 1998
.607 446
.277 2044
.234
•535 9194
.434 942
.291 1257
.284
•557 6341
.611 055
.276 9274
1.235
0.536 3537
3.438 379
0.290 8348
1.285
0.558 0684
3.614 668
0.276 6506
.236
.536 7880
.441 819
.290 5441
.286
.558 5027
.618 284
.276 3741
•237
.537 2223
.445 262
.290 2537
.287
.558 9370
.621 905
.276 0978
.2.38
•537 6566
.448 709
.289 9636
.288
.559 3713
.625 528
.275 8219
•239
.538 0909
.452 160
.289 6737
.289
•559 8056
.629 156
.275 5462
1.240
0.538 5252
3.455 613
0.289 3842
1.290
0.560 2399
3.632 787
0.275 2708
• 53-x
•459 071
.289 0950
.291
.560 6742
.636 421
.274 9956
•539 3937
.462 532
.288 8060
292
.561 1085
.640 059
.27; 7208
.243
.539 8280
.465 996
.-'•Stf 5'74
293
.561 5428
.643 7oi
.274 4462
.540 2623
• 40y 4'H
.288 2290
.294
.561 9771
•647 347
• 474 i/i9
0.540
3.472 935
0.287 9409
1.295
0.562 4114
3.650 096
0.273 8979
•541 1309
.476 409
.-'87 6531
.296
.562 8456
.654 049
.273 6241
• 247
• 54'
-470888
.2X7 3656
• 297
.563 2799
.658 305
.273 3506
.248
.541 '//>5
.483 369
.287 0784
.298
.563 7142
.661 065
.27.3 0774
.486854
.286 79U
.299
.564 1485
.665 629
.272 8045
0.542 868l
3-490 343
0.286 5048
1.300
0.564 5828
3.669 297
0.272 5318 I
loo«(en)
•IM^^^^BMH^
Iog10(eu)
eu
e~u
IOQe(eU)
Io0lo(e")
e"
e~u
The Exponential.
u
looio(eu)
eu
e u
u
logio(eu)
e~°
1.300
.301
.302
.303
.304
0.564 5828
.505 0171
• 5<>5 45U
.565 8857
.566 3200
3-669 297
• 968
.676 643
.680 321
.684 003
0.272 5318
.272 2594
• 271 ^73
.271 7154
.271 4438
1-350
•351
•352
• 353
•354
0.586 2976
.586 7318
.587
.587 6004
.5880347
3.857 426
.861 285
.865 148
.869 015
- 885
2403
.258 9811
.258 ;
.258
.258 2054
1.305
.306
.307
.308
.309
0.566 7543
.567 1886
.567 6229
.568 0572
.568 4915
3-687689
.691 379
.695 072
.698 769
.702 469
0.271 1725
.270 9015
.270 6307
.270 3602
.270 0900
1.355
.356
• 357
• 358
• 359
0.588 4690
.588 9033
.589 3376
.589 7719
.590 2062
3.876 761
.880 640
.884 522
.888409
.892 299
0.257 9473
-257
4319
.257
.256 9176
I-H
Co Co Co Co Co
4^- Co Kj HI O
0.568 9258
• 5<>9 36oi
.569 7944
•570 2287
.570 6629
3.706 174
.709 882
.713 593
.717 309
.721 028
0.269 8201
.269 5504
.269 2810
.269 0118
.268 7429
1.360
.361
.362
.363
.364
0.590 6405
.591 0748
.591 5091
•591 9434
•592 3777
3.896 193
.900 091
.903 993
•9O7 899
.911 809
0.256 6608
.256 4042
.256 1480
.255 8919
• 255 '
I.3I5
.316
.317
.318
.319
0.571 0972
•571 5315
.571 9658
.572 4001
•5/2 8344
3.724 751
.728 478
.732 208
•735 942
.739680
0.268 4743
.268 2060
.267 9379
.267 6701
.267 4026
1.365
.366
.367
.368
.369
0.592 8120
.593 2463
.593 6806
.504 H49
•594 5491
3.915 723
.919 641
.923 562
.927 488
•931 417
0.255 3807
.255 1254
.254 8704
-254 6157
.254 3612
1.320
•321
•322
.323
.324
0.573 2687
•573 7030
•574 1373
•574 57i6
•575 0059
3-743 421
•747 167
•750 916
.754 669
.758 425
0.267 1353
.266 8683
.266 6016
.266 3351
.266 0689
1.370
• 371
• 372
• 373
.374
0.594 9834
•595 4177
•595 8520
.596 2863
.596 7206
3-935 351
.939 288
.943 229
•947 174
•951 124
0.254 1070
•253 8530
.253 5993
.253 3458
.253 0926
1.325
.326
.327
.328
.329
0.575 4402
•575 ^745
.576 3088
.576 743i
•577 1/74
3.762 185
.765 949
.769 717
.773 489
.777 264
0.265 8030
.265 5373
.265 2719
.265 0067
.264 7419
1.375
.376
• 377
.378
• 379
0.597 1549
•597 5892
.598 0235
.598 4578
.598 8921
3-955 077
•959 034
.962 995
.966 960
.970 929
0.252 8396
.252 5869
.252 3344
.252 0822
.251 8303
1-330
.331
•332
•333
•334
0.577 6117
.578 0460
.578 4802
.578 9M5
•579 3488
3.78i 043
.784 826
.788613
.792 404
.796 198
0.264 4773
.264 2129
.263 9488
.263 6850
.263 4215
1.380
.381
.382
.383
.384
0.599 3264
.599 7607
.600 1950
.600 6293
.601 0636
3.974 002
•978 879
2 859
.986844
-990 833
0.251 5785
•251 3271
.251 0759
.250 8249
-250 5742
1.335
.336
• 337
.338
.339
0-579 7831
.580 2174
.580 6517
.581 0860
.581 5203
3.799 996
.803 798
.807 604
.811 4I3
.815 226
0.263 1582
.262 8951
.262 6324
.262 3699
.262 1076
1.385
.386
.387
.388
.389
0.601 4979
.601 9322
.602 3664
.602 8007
.603 2350
3.994 826
-998 823
4.002 824
.006 828
.010 837
0.250 3238
.250 0736 i
.249
•24';
•249 3245
1-340
• 341
•342
•343
•344
0.581 9546
082 3889
.582 8232
083 2575
083 6918
3.819 044
.822 864
.830 518
•834 350
0.261 8457
.261 5840
.261 3225
.261 0613
.260 8004
1.350
• 391
.392
• 393
-.394
0.603 6693
.604 1036
•604 5379
.604
.605 4065
4.014 850
.01.^
.022 888
.026 913
.030 942
0.249 0753
.248
.248
.248 3292
.248 0810
1-345
•346
.347
.348
• 349
0.584 1261
.584 5604
.584 9947
.585 4290
.585 8633
3-838 187
.842 027
.845 «7i
.849 7i8
•853 570
0.260 5397
.200
.260 OI9I
.259 7593
.259 4996
1-395
.396
• 397
.398
.399
0.605 8408
2751
.606 7094
.607 U37
.607 578o
4-034 975
.039 012
.043 053
.047 008
.051 M7
0.247 8330
• 247
.247 3379
0907
.240 8437
1.350
0.586 2976
3.857 426
0.259 2403
1.400
0.6o8 0123 4-055 200
0.246 5970
looe(eu)
looio(eu) eu
e~u
loge(eu)
looio(eu) eu
e-u
SMITHSONIAN TABLES
239
The Exponential.
r~
logio(e")
eu
e-u
u
looio(eu)
eu
e~u i
1 400
0.6o8 0123
4.055 200
0.246 5970
1.450
0.629 7270
4.263 115
0.234 5703
•*• • *+s-/v'
1QI
.608 4466
.059 257
.246 3505
• 451
.630 1613
.267 380
.234 3358
•«|W *•
.402
.608 8809
.063 3l8
.246 1043
.452
.630 5956
.271 649
.234 1016
1Q}
.609 3152
.067 384
.245 8583
.453
.631 0299
•275 923
.233 8676
•fcr^-'O
•404
.609 7495
•071 453
.245 6125
• 454
.631 4642
.280 2OI
•233 6339
I.40S
0.610 1837
4-075 527
0.245 3671
1-455
0.631 8985
4.284 483
0.233 4004
.406
.610 6180
.079 604
.245 1218
.456
.632 3328
.288 770
.233 1671
4.O7
.611 0523
.083 686
.244 8768
.457
.632 7671
.293 061
.232 9340
••I*'/
.408
.611 4866
.087 772
.244 6321
• 458
.633 2014
.297 356
.232 7012
.409
.611 9209
.091 86 i
.244 3875
• 459
.633 6356
.301 656
.232 4686
1.410
0.612 3552
4-095 955
0.244 1433
1.460
0.634 0609
4.305 960
0.232 2363
.411
.612 7895
.100 053
.243 8993
.461
.634 5042
.310 268
.232 0042
.412
.613 2238
.104 156
.243 6555
.462
.634 9385
.314 580
.231 7723
.413
.613 6581
.108 262
.243 4120
.463
.635 3728
.318 897
.231 5406
.414
.614 0924
.112 372
.243 1687
.464
.635 8071
.323 218
.231 3092
1.415
0.614 5267
4.1l6 486
0.242 9256
1.465
0.636 2414
4.327 543
0.231 0780
.416
.614 9610
.I2O 605
.242 6828
.466
.636 6757
•331 873
.230 8470
.417
•615 3953
.124 728
.242 4402
• 467
.637 i ioo
.336 207
.230 6163
.418
.615 8296
. 128 854
.242 1979
.468
.637 5443
•340 545
.230 3858
.419
.616 2639
.132 985
.241 9559
.469
.637 9786
.344 888
.230 1555
1.420
0.616 6982
4.137 120
0.241 7140
1.470
0.638 4129
4-349 235
0.229 9255
.421
.617 1325
.141 260
.241 4724
.471
.638 8472
.353 587
.229 6957
.422
.617 5668
.145 403
.241 2311
.472
.639 2815
•357 942
.229 4661
.423
.618 ooio
.149 550
.240 9900
•473
•639 7158
.362 302
.229 2367
.424
.618 4353
.153 702
.240 7491
• 474
.640 1501
.366 667
.229 0076
1.425
0.618 8696
4.157 858
0.240 5085
1.475
0.640 5844
4.371 036
0.228 7787
.426
.619 3039
.162 018
.240 2681
• 476
.641 0187
•375 409
.228 5501
.427
.619 7382
.166 182
.240 0279
• 477
.641 4529
•379 787
.228 3216
.428
.620 1725
. 170 350
.239 7880
• 478
.641 8872
.384 169
.228 0934
.429
.620 6068
.174 523
.239 5484
• 479
.642 3215
.388 555
.227 8654
1.430
0.621 0411
0.178 699
0.239 3089
1.480
0.642 7558
4.392 946
0.227 6377
.431
.621 4754
.182 880
.239 0697
.481
.643 1901
•397 34i
.227 4102
•432
.621 9097
. 187 065
.238 8308
.482
.643 6244
.401 740
.227 1829
•433
.622 3440
.191 254
.238 5921
.483
.644 0587
.406 144
.226 9558
•434
.622 7783
.195 447
.238 3536
.484
.644 4930
.410 553
.226 /29O
1-435
0.623 2126
4.199 645
0.238 1154
1.485
0.644 92^3
4.414 065
0.226 5023
•430
.623 6469
.203 847
.237 8774
.486
.645 3616
.419 383 .226 2760
• 437
.624 0812
.208 053
.237 6396
.487
.645 7959
.423 804 .226 0458
.438
.624 5155
.212 263
.237 4021
.488
.646 2302
.428 230
.225 8239
• 439
.624 9498
.216 477
.237 1648
•489
.646 6645
.432 661
.225 5981
1.440
0.625 3841
4.220 696
0.236 9278
1.490
0.647 0988
4.437 096
0.225 3727
.441
.625 8183
.224 919
.236 6909
• 491
.647 5331
•441 535
.225 1474
.626 2526
.229 146
.236 4544
.492
.647 9674
•445 979
.224 9224
•443
.626 6869
•233 377
.236 2180
•493
.648 4017
.450 427
.224 6976
• 444
.627 1212
.237 612
.235 98i9
.494
.648 8360
.454 879
.224 4730
1-445
0.627 5555
4.241 852
0.235 746i
1-495
0.649 2703
4-459 337
O.224 2486
• 440
.627 9898
.246 096
•235 5104
.496
.649 7045
.463 798
.224 0245
.447
.628 4241
.250 344
.235 2751
.497
.650 1388
.468 2 14
.223 8006
.448
.628 8584
.235 0399
.498
•650 5731
.4/2 735
•223 5/69
.449
.629 2927
.258 854
.234 8050
• 499
.651 0074
.477 210
•223 3534
1-450
0.629 7270
4.263 115
0.234 5703
1.500
0.651 4417
4.481 689
0.223 1302
loo, re")
loojcKe")
eu
e~u
loge(eu)
looioCe")
eu
e~u
SMITHSONIAN TABLES
The Exponential.
u
looio(eu)
eu
e~u
u
log1(J(eu)
e°
e a
1.500
0.651 4417
4.481 689
0.223 1302
1.550
0.673 1564
4-71!
O.JI2 2480
.501
.051 8760
.486 173
9071
• 551
.673 5907
.716 184
.212 0358
.502
1 3103
.490 661
.222 6843
• 552
.674 0250
.720 903
.211
.503
.652 74-1''
•495 154
.222 4618
•553
.674 4593
.211
.504
•<>53 1789
.499 652
.222 2394
• 554
.674 8930
•730 354
.211 4007
1.505
0.653 6132
4.504 154
0.222 0173
1.555
0.675 3279
4-735 087
O.2II
.506
.654 0475
.508 660
.221 7954
.550
.675
.739 824
.210
.507
.654 4818
.513 I7i
.221 5737
• 557
.676
.744 566
.210
.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
O.22O 9IOO
1.560
0.677 4994
4.758 821
O.2IO U^I
.511
.656 2190
.531 260
.220 6892
.561
.677 9337
.209 •
.512
•656 6533
•535 793
.220 4686
.562
.678 3680
S 348
.209 7162
.513
.657 0876
•540 331
.220 2482
.563
.678 8023
.773 H9
.209 5066
.514
.657 52l8
.544 874
.220 O28l
.564
.679 2366
•777 895
.209
1.515
0.657 956l
4.549 421
O.2I9 8082
1.565
0.679 6709
4.782 675
0.209 0880
.516
.658 3904
•553 973
.219 5885
.566
.680 1052
.787 4'«
.208
.517
.658 8247
.558 529
.219 3690
.567
.680 5395
a 250
.208
.518
.659 2590
.563 ooo
.219 1497
.568
.680 9737
•797 045
.208
.519
.659 6933
.567 655
.218 9307
.569
.681 4080
.801 844
.208 2533
1.520
O.66o 1276
4.572 225
0.218 7119
1.570
0.681 8423
4.806 648
0.208 0452
.521
.660 5619
.576 800
.218 4933
.571
.682 2766
.811 457
.207
.522
.660 9962
.581 379
.218 2749
• 572
.682 7109
.816 271
.207
.523
.661 4305
.585 062
.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
.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
.533
.665 7734
.632 052
.215 8870
083
.687 4882
.869 543
.205 358i
•534
.666 2077
.636 687
.215 6713
084
.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 0252
.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
.908 655
.203 7218
• 542
.669 6821
.673 929
.213 9528
• 592
.691 3968
.913 506
.203 5182
• 543
.670 1164
.678 605
.213 7389
• 593
.691 8311
.918 482
.203 3148
•544
•670 5507
.683 286
.213 5253
'•594
.692 2654
3 403
.203 1115
1.545
0.670 9850
4.687 972
0.213 3119
1.595
0.692 6997
4.928 329
O.20J 9085
.546
.671 4193
.692 662
.213 0987
.596
.693 1340
3 260
.202
.547
.671 8536
.697 357
.212 8857
• 597
.693 5683
.938 106
.202 5031
• 548
• 549
.672 2879
.672 7222
.702 057
.706 761
.212 6729
.212 4603
.598
• 599
.694 0026
.694 4369
•943 136
.948 082
.202 3007
.202 O085
1-550
0.673 1564
4.711 470
0.212 2480
1.600
0.694 8712
4-953 032
0.201 8965
looe(eu)
looio(eu)
eu
e~u
looe(e°)
logio(eu)
eu
e-°
SMITHSONIAN TABLES
241
The Exponential.
I
looio(eu)
eu
e~u
u
looio(en)
eu
e~a
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 0947
.651
.717 0202
.212 189
.191 8580
.602
.695 7398
.962 948
.201 4931
.652
.717 4545
.217 404
.191 6662
.603
.696 1741
.967 914
.2OI 2917
.653
.717 8888
.•222 624
.191 4746
.604
.696 6083
.972 884
.2OI OOO5
.654
.718 3231
.227 849
.191 2832
1.605
0.697 0426
4.977 860
O.2OO 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
.092 816
.200 2878
.658
.720 0603
.248 803
.100 5196
.609
.698 7798
.997 811
.200 0876
.659
.720 4945
.254 054
. 190 3292
1.610
0.699 2141
5.002 811
0.199 8876
1.660
0.720 9288
5-259 3ii
0.190 1390
.611
.6996484
.007 817
. 199 6878
.661
.721 3631
.264 573
.189 9489
.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
.280 390
• 189 3799
1.615
0.701 3856
5.027 888
o. 198 8907
1.665
0.723 1003
5.285 673
0.189 1907
.616
.701 8199
.032 918
.198 6919
.666
.723 5346
.200 962
. 189 0016
.617
.702 2=142
•037 954
. 198 4933
.667
.723 0689
.296 255
. 188 8127
.618
.702 6885
.042 994
. 198 2949
.668
.724 4032
.301 554
. 188 6239
.619
.703 1228
.048 040
.1980967
.669
.724 8375
.306 858
.1884354
1.620
0.703 5571
5.053 090
0.197 8987
1.670
0.725 2718
5.312 168
0.188 2471
.621
.703 9914
.058 146
.197 7009
.671
.725 7o6i
.317 483
. 188 0589
.622
.704 4256
.063 207
.197 5033
.672
.726 1404
.322 803
. 187 8709
.623
.704 8509
.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
.376 298
.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
.710 9401
.139 727
.104 5629
.687
.732 6548
.403 247
.185 0739
.638
•711 3744
.144 869
.194 3684
.688
•733 0891
.408 653
.184 8889
.639
• 7H 8087
.150 017
.194 1741
.689
•733 5234
.414 064
. 184 7041
1.640
0.712 2430*
5.155 170
0.193 9800
1.690
0.733 9577
5.419 481
0.184 5195
.712 6772
.160 327
.193 7862
.691
.734 3920
.424 903
.184 3351
.713 1115
.165 490
.193 5925
.692
.734 8263
•430 331
.184 1509
.713 5458
.170 658
• 193 3990
.693
.735 2606
.435 764
.183 9668
.713 9801
•175 831
.'193 2057
.694
•735 6949
.441 202
.183 7829
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
.696
.736 5634
.452 095
.183 4'57
.715
.191 382
.192 6269
.697
.736 9977
•457 550
.183 2324
.648
7173
1516
.196 576
.201 775
.192 4344
.192 2421
.698
•699
•737 4320
•737 8663
.463 oio
.468 476
.183 0-103 j
. 182 8663
1.650
0.716 5859
5.206 980
0.192 0499
1.700
0.738 3006
5-473 947
0.182 6835
lofll(Xeu)
eu
e-"
logo(e")
loo,o(eu)
eu
e~u
• IONIAN TABLES
242
The Exponential.
u
looio(e")
eu
e-u
u
loo,o(eu)
S
e~u
1.700
0.738 3006
5-473 947
0.182 6835
1.750
0.760 0153
5-754 603
0.1/3 7739
.701
.738 7349
.479 4J4
.182 5009-
.751
.760
.760
.173 6003
.702
• 739
.4*4 906
.182 3185
• 752
.700 8839
• 123
.173
.703
•739 6035
•490 394
.182 1363
• 753
.761 3182
.7/1 892
.173 2534
.704
.740 0378
.495 887
.181 9542
• 754
.761 7525
.777
.173 0802
1.705
0.740 4721
5.501 386
o. 181 7724
1.755
0.762 1868
5.783 448
O. 172 9072
.706
.740 9064
.50* 800
.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
1.710
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
•551 122
.180 1438
.764
.766 0955
.835 734
.171 358i
1.715
0./44 8150
5.556 676
0.179 9637
1.765
0.766 5298
5.841 572
0.171 1868
.716
•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
.864985
.170 5034
1.720
0.746 0865
5.584 528
o. 179 0661
1.770
0.768 7012
5-870 853
o. 170 3330
.721
.747 4208
.590 116
. 178 8872
• 771
.769 1355
.876 727
.170 I '"127
.723
•747 8551
•595 709
.178 7084
.772
.7695698
.882 607
. 169 9927
.723
.748 2894
.601 307
.178 5298
• 773
.770 0041
.888 492
. 169 8228
.724
.748 7237
.606 911
.178 35U
• 774
•770 4384
.894 384
. 169 6530
1.725
0.749 1580
5.612 521
0.178 1731
1.775
0.770 8727
5.900 281
o. 169 4834
.720
.749 5923
.618 136
. 177 9950
.776
.7/1 3070
.906 184
.169 3141
.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
0.177 2844
1.780
0.773 0442
5.929 856
0.168 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
.7530666
.663 262
.176 5767
.784
•774 7814
•953 623
. 167 9649
1.735
0.753 5009
5,668 928
0.176 4002
1.785
0.775 2157
5-959 580
0.167 7971
.736
•753 9352
.674 600
.176 2239
.785
-775 6499
.965 543
0293
• 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 12-2
1.740
0.755 6724
5.697 343
0.175 5204
1.790
0.777 3871
54)89 452
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 4006
.720 178
.1/4 8i97
'•794
.779 1243
.013 458
. 166 2937
1-745
0.757 8439
5.725 901
0.174 6450
1.795
0.779 5586
6.019 475
0.166
• 746
.758 2782
•731 630
.174 4704
.796
•779 9929
•025 497
.165 9614
• 747
.758 7125
.737 365
.174 2960
• 797
.780 4-7-'
.031 526
.165
.748
.759 U68
•743 105
.174 1218
.798
.780 8615
.037
. 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
loge(eu)
looio(eu)
eu
a—
lofle(eu)
looio(eu)
eu e~u
SMITHSONIAN TABLES
243
The Exponential.
u
looio(eu)
eu
e-u
u
logio(eu)
eu
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
.365 183
.157 0800 1
.802
.782 5987
.061 759
.164 9686
.852
.804 3134
•372 552
. 156 9230 1
.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 3io
. 156 6095
1.805
0.783 0015
6.079 971
0.164 4745
1.855
0.805 6163
6.391 698
o. 156 4529
.806
./84 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
./85 6387
.104 340
.163 8i79
.859
.807 3534
.417 3i6
.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 68 I
.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 9817
.165 690
.162 1879
.869
.811 6964
.481 811
.154 2779
1.820
0.790 4160
6.I7I 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 9993
.501 286
.153 8157
.823
.791 7188
.IOO 4O2
.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 456o
.215 213
. 160 8955
.877
.815 1707
•533 874
.153 0486
.828
.829
.793 8903
.794 3246
.221 431
.227 656
.160 7347
.160 5741
.878
.879
.815 6050
.816 0393
.540 411
.546 955
.152 8956
.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 77i
.151 98io
1.835
0.796 9304
6.265 134
0.159 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 6773
.837
•797 7990
.277 677
.159 2946
.887
.819 5i37
•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
0.709 1018
6.296 538
0.158 8174
1.890
0.820 8166
6.619 369
•
0.151 0718
,799 536i
.302 838
.158 6587
.891
.821 2509
.625 991
.150 9208
.799 9704
.309 M4
.158 5001
.892
.821 6852
.632 621
.150 7700
4047
.315 45''
•158 3417
.893
.822 1195
.639 257
.150 6193
.844
.800 8390
.321 775
.158 1834
.894
.822 5537
.645 899
.1504687
0.801 2733
6.328 TOO
0.158 0253
1.895
0.822 9880
6.652 548
0.150 3183
.801 7076
•334 431
.157 8674
.896
.823 4223
.659 204
.150 1681
.802 1419
.340 769
.157 7096
• 897
.823 8566
.665 867
.150 0180
.802 5762
• 347 H3
.157 5520
.898
.824 2909
.672 536
.1498681
.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
6.685 894
0.149 5686
-•— ^MH^^M^H
looi<Xe°)
eu
e~u
loo«(eu)
looio(eu)
eu
.-
SMITHSONIAN TABLES
The Exponential.
u
looio(e°)
eu
e~u
u
log,0(e11)
eu
e~ u
1.900
0.825 1595
6.685 894
0.149 5686
1.950
0.846 8742
7.028688
0.142 2741
.901
.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
.903
.826 4624
.705 082
.149 1206
• 953
.848 1771
.049 805
.141 8479
.904
.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
.8494800
.070 986
.141 4230
.907
.828 1996
.732 860
. 148 5253
•957
.849 9143
.078 061
.141 2816
.908
.828 6339
•739 596
.148 3768
.958
.850 3486
.085 U3
.141 1404
.909
.829 0682
.746 339
.148 2285
•959
.850 7829
.092 231
.140 9993
1.910
0.829 5025
6.753 089
0.148 0804
1.960
0.851 2172
7.009 327
0.140 8584
.911
.829 9368
•759 845
. 147 9324
.961
.851 6515
.106 430
.140 7176
.912
.830 3710
.766608
.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
1.915
0.831 6739
6.786 939
0.147 34i8
1.965
0.853 3887
7.134 913
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 8/59
.918
.832 9768
.807 330
.146 9005
.968
.854 6915
.156 349
. 139 736o
.919
.833 4HI
.814 141
.146 7536
.969
.855 1258
.163 509
.139 5964
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 7MO
.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 7316
7.2O6 62O
0.138 7613
.926
.836 4512
.862 007
•145 7300
.970
.858 1659
.213 830
. 138 6226
.927
.836 8855
.868 873
.145 5843
•977
.858 6002
.221 047
.138 4*41
.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
6.889 510
0.145 1482
1.980
0.859 9031
7.242 743
o. 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
.910 210
• 144 7134
.983
.861 2060
.264 504
• U7 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
.937 906
•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 JJJ
.136
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 5003
.991
.864 6803
- 853
.1365588
.942
.843 3999
.972 682
. 143 4i68
•992
.865 1146
•330 179
. 136 4-'-'3
• 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 9872
1-995
0.866 4175
7-35-' 203
0.136 0137
.946
.845 1371
7.000 629
.142 8443
.996
.866 8518
•359 559
• US 8777
• 947
.&45 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
2.000
0.868 5890
7.389 056
0.135 3353
Io0e(eu)
looio(eu) eu
e~u
looe(eu)
logi.Xe")
eu
e~u
SMITHSONIAN TABLES
245
The Exponential.
u
logio(eu)
e
e-"
u
Iog10(eu)
eu
e u
2.000
.OOI
.002
.003
.004
0.868 5890
.869 0233
.869 4576
.8698918
.870 3261
7.389 056
.396 449
.403 849
.411 257
.418 672
0.135 3353
.135 2000
.135 0649
.134 9299
.134 7950
2.050
.051
.052
.053
•054
0.8oo 3037
.890 7380
.891 1723
.891 6066
.892 0409
7.767 901
•775 673
.783 452
.791 240
•799 035
0.128 7349
.128 6062
. 128 4777
.128 3493
.128 2210
2.005
.006
.007
.008
.009
0.870 7604
.871 1947
.871 6290
.872 0633
.872 4976
7.426 094
•433 524
.440 961
.448 406
.455 858
o. 134 6603
.134 5257
.134 3912
.134 2569
.134 1227
2.055
.056
.057
.058
.059
0.892 4752
.892 9095
.893 3437
.893 7780
.894 2123
7.806838
.814 649
.822 467
.830 294
.838 128
o. 128 0928
. 127 9648
. 127 8369
. 127 7091
.127 5815
2.010
.Oil
.012
.013
.014
0.872 9319
.873 3662
.873 8005
.874 2348
.874 6691
7.463 317
.470 784
.478 259
.485 741
•493 230
0.133 9887
.133 8548
.133 72io
.133 5873
.133 4538
2.060
.061
.062
.063
.064
0.894 6466
.895 0809
.895 5152
.895 9495
.896 3838
7.845 970
.853 820
.861 677
.869 543
.877 417
0.127 4540
.127 3266
.127 1993
.127 0722
. 126 9452
2.015
.016
.017
.018
.019
0.875 1034
.875 5377
.875 9720
.876 4063
.876 8406
7.500 727
.508 232
.515 744
.523 263
•530 790
0.133 3204
.133 1871
.133 0540
.132 9210
.132 7882
2.065
.066
.067
.068
.069
0.896 8181
.897 2524
.8976867
.898 1210
•898 5553
7-885 298
.893 187
.901 084
.908 989
.916 902
0.126 8183
.126 6915
.126 5649
.126 4384
.126 3120
2.02O
.021
.022
.023
.024
0.877 2749
.877 7091
.878 1434
.878 5777
.879 0120
7.538 325
•545 867
•553 417
.560 974
.568 539
0.132 6555
.132 5229
.132 3904
.132 2581
.132 1259
2.070
.071
.072
.073
.074
0.898 9896
.899 4239
.899 8582
.900 2925
.900 7268
7.924 823
.932 752
.940 689
.948 633
.956 586
0.126 1858
. 126 0597
. 125 9337
.125 8078
.125 6820
2.025
.026
.027
.028
.029
0.879 4463
.879 8806
.880 3H9
.880 7492
.881 1835
7.576 III
.583 691
.591 278
.598 873
.606 476
O.I3I 9938
.131 8619
.131 7301
.131 5985
.131 4669
2.075
.076
.077
.078
.079
0.901 1610
.901 5953
.902 0296
.902 4639
.902 8982
7.964 546
•972 515
.980 491
.988 476
.996 468
0.125 5564
.125 4309
.125 3056
.125 1803
.125 0552
2.030
.031
.032
.033
.034
0.881 6178
.882 0521
.882 4864
.882 92O7
.883 3550
7.614 086
.621 704
.629 330
.636 963
.644 604
0.131 3355
.131 2043
•131 0731
.130 9421
.130 8112
2.080
.081
.082
.083
.084
0.903 3325
.903 7668
.904 2OII
.904 6354
.905 0697
8.004 469
.012 477
.020 494
.028 518
.036 55'l
0.124 9302
. 124 8053
.124 6806
.124 5560
.124 4315
2.035
.036
.037
.038
.039
0.883 7893
.884 2236
.884 6579
.885 0922
.885 5264
7.652 252
.659908
.667 572
.675 243
.682 922
0.130 6805
•130 5499
.130 4194
.130 2800
.130 1588
2.085
.086
.087
.088
.089
0.905 5040
.905 9383
.906 3726
.906 8069
.907 2412
8.044 591
.052 640
.060 697
.068 761
.076 834
0.124 3071
.124 1829
. 124 0588
. 123 9348
.123 8109
2.040
.041
.043
.044
0.885 9607
.886 3950
.886 8293
.887 2636
.887 6979
7.690 609
.698 304
.706 006
.713 716
.721 433
0.130 0287
.1298987
.129 7689
. 129 6392
.129 5096
2.090
.091
.092
.093
.094
0.007 6755
.908 I008
.908 5441
.908 9784
.909 4126
8.084 915
.093 004
.101 101
.109 206
.117 320
0.123 6871
.123 5635
.123 4400
.123 3166
.123 1934
2.045
.046
• 047
.048
.049
0.888 1322
5665
.8890008
.889 4351
.8898694
7.729 159
.736 892
.744 632
•752 381
.760 137
0.129 3802
.129 2509
.129 1217
.128 9926
.128 8637
2.095
.096
.097
.098
•099
0.909 8469
.910 2812
.910 7155
.911 1498
•911 5841
8.125 441
.133 570
.141 708
.149 854
.158 008
0.123 0702
. 122 9472
. 122 8243
.122 7Ol6
.122 5789
2.050
0.890 3037
7.767 901
0.128 7349
2.100
0.912 Ol84
8.166 170
O.I22 4564
log '••>
log.Xe")
eu
e~u
loge(eu)
,0,,*°,
eu
r-
SMITHSONIAN TABLE*
246
The Exponential.
II
looio(eu)
eu
e-u
u
logio(ea)
en
e~a
2.IOO
0.912 0184
8.166 170
0.122 4564
2.150
0-933 7331
8.584858
0.116 4842
.101
.912 4527
.174 340
.122 3340
.151
.934 1674
-593 448
.116 3677
.IO2
.912 8870
.182 519
.122 21 l8
.152
.934 6017
.602 045
.116 2514
.IO3
.913 3213
.190 705
.122 0896
• 153
•935 0360
.610 652
.116 1352
.104
•913 7556
.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 3H
.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
.US 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 0047
•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
. I 14 8647
2.II5
0.918 5328
8.289 586
0.120 6333
2.165
0.040 2476
8.714 602
0.114 7499
.116
.918 9671
.297 879
.I2O 5127
.166
.940 6818
.723 321
. i 14 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
O.I2O O3l6
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
.113 9495
.123
.922 0072
.356 168
.119 6721
• 173
.943 7219
.784 598
.113 8356
.124
.922 4415
.364 529
.119 5525
.1/4
.944 1562
•793 387
.113 7218
2.125
0.922 8758
8.372 897
O.II9 4330
2. 175
0.944 5905
8.802 185
0.113 6082
.126
.923 3101
.381 275
.119 3136
.176
.945 0248
.810 992
.113 4946
.127
.923 7444
.389 660
.H9 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
. 1 18 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
.l8l
.947 1963
.855 157
. 1 12 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
8.800 649
o.i 12 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 2530
.138
.928 5216
.482 456
.117 8904
.188
.950 2363
.917 36l
.112 1408
.139
.928 9559
.490 942
.117 7726
.189
.950 6706
.926 282
.112 0287
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
.516 454
.117 4198
.192
•951 9735
.953 ioi
.III 6931
• 143
•930 6931
.524 974
.117 3024
.193
.952 4078
.962 059
•III 58l5
.144
.931 1274
•533 503
.117 1852
.194
.952 8421
.971 026
.III 4700
2.145
0.931 5617
8.542 041
0.117 0680
2.195
0.953 2764
8.980 ooi
o.in 3586
.146
.931 9960
.550 588
.116 9510
.196
.953 7107
.088 986
.ill 2473
• 147
.932 4303
• 559 14-'
.116 8341
.197
.954 1450
•997 979
.III 1301
.148
.932 8645
.567 706
.116 7174
.198
•954 5793
9.006 982
.III 0250
.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.no 8032
Iofle(eu)
Iog10(eu)
eu
e~~u
looe(eu)
looio(eu)
eu e-u
SMITHSONIAN TABLES
247
The Exponential.
I
looioCe")
eu
e-u
u
looio(en)
e"
e u
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
.110 3608
• 254
.9788098
.525 763
.104 9785
2.205
0.957 6193
9.070 252
o.i 10 2505
2.255
0-979 3341
9-535 293
0.104 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
o. 104 3505
.211
.960 2251
. 124 837
.109 5910
.261
.981 9398
.592 677
.104 2462
.212
.960 6594
.133 966
.109 4815
.262
.982 3741
.602 275
.104 1420
.213
.961 0937
.143 105
.109 3720
.263
.982 8084
.611 882
. 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
.2l6
.962 3966
.170 575
.109 0444
.266
.984 1113
.640 761
.103 7263
.217
.962 8309
.179 750
. 108 9354
.267
.984 5456
.650 406
.103 6226
.218
.963 2652
.188935
. 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
0.108 6091
2.270
0.985 8485
9.679 401
0.103 3122
.221
.964 5680
.216 543
.108 5006
.271
.986 2828
.689 085
.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
.718 196
. 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
.966 7395
.262 741
.107 9594
.276
.988 4542
.737 652
.102 6942
.227
.967 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 7571
.766 909
.102 3865
2.230
0.968 4767
9.299 866
0.107 5284
2.280
0.990 1914
9.776 680
O.I02 2842
.231
.968 9110
.309 171
.107 4210
.281
.090 6257
.786 462
.102 l82O
.232
.969 3453
.318 484
.107 3136
.282
.091 0600
.796 253
.IO2 0798
.233
.969 7796
.327 808
.107 2063
.283
.991 4943
.806 054
.101 9778
•234
•970 2139
.337 140
. 107 0992
.284
.991 9286
.815 865
.101 8759
2.235
0.970 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 5i7
.101 6723
•237
.971 5i68
•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
2.24O
0.972 8196
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
.9736882
.412 137
.106 2458
.292
•995 4030
.894 707
.10 I 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
.100 8622
2.245
0.074 9911
9.440 416
0.105 9275
2.295
0.096 7058
9.924 436
o.ioo 7614
•<J75 4254
.449 861
.105 8217
.296
.997 1401
•934 365
.100 6607
.247
•975 8597
•459 315
.105 7159
.297
•997 5744
•944 305
.100 5601
.248
.976 2940
.468 779
.105 6102
.298
.998 0087
• 954 -254
. 100 4596
.976 7283
.478 253
.105 5047
•299
.998 4430
.964 213
.100 3592
2.250
0.977 1626
9.487 736
0.105 3992
2.300
0.998 8773
9-974 182
o.ioo 2588
lofc<en)
Iodide0)
e°
e~u
looe(eu)
logio(en)
eu
e-u
SMITHSONIAN TABLES
248
The Exponential.
u
looio(eu)
eu
.-
u
looio(en)
eu
.-
2.300
0.998 8773
9.974 182
o.ioo 2588
2-350
1.020 5020
10.485 570
0.095 3692
.301
• 999 3H6
.984 162
.100 1586
.351
.O2I 0263
.491
.095 2738
.302
.999 7459
•994 151
. TOO 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
.000 6145
.014 159
.0998586
• 354
.022 3292
.527 596
.094 9884
2.305
i.ooi 0488
10.024 178
0.009 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
.054 206
.099 4600
.358
.024 0664
.569 791
.094 6093
.309
.002 7860
.064 355
.099 3606
• 359
.024 5007
.580366
.094 5M7
2.310
I.OO3 22O3
10.074 425
0.099 2613
2.360
1.024 9350
10.590 951
0.094 4202
.311
.003 6545
.084 504
.099 1620
.361
.025 3093
.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
.026 2379
.622 772
.094 1374
.314
.004 9574
.114 803
.098 8650
^
.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
.098 6675
.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 2040
.323
.008 8661
.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
• 3/8
.032 7523
.783 315
.092 7359
.329
.on 4718
.267 669
.097 3931
• 379
.033 1866
.794 103
.092 6432
2.330
i. on 9061
10.277 942
0.097 2957
2.380
1.033 6209
10.804 9O3
0.092 5506
.331
.012 3404
.288 225
.097 1985
.381
.034 0552
.815 7U
.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
.837366
.092 2733
.334
.013 6433
.319 136
.096 9073
.384
.035 358o
.848 209
.092 1811
2.335
1.014 0776
10.329 460
0.006 8105
2.385
1.035 7923
10.859 063
0.092 0890
.336
.014 5119
•339 795
.096 7U7
.386
.036 2266
.869927
.091 9969 i
• 337
.014 9462
.350 140
.096 6171
.387
.036 6609
.880 803
.091 9050
.338
.015 3805
.360 495
.096 5205
.388
.037 0952
.991 689
.091 8131
.339
.015 8148
.370 861
.096 4240
.389
.037 5295
.902 586
.091 7-^4
2.340
1.016 2491
10.381 237
0.096 3276
2.390
1.037 9638
I0.9U 494
0.091 6297
•341
.016 6834
.391 623
.096 2314
.391
.038 3981
.924 4U
.091 5381
.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 17-7
•346
.018 8549
.443 7ii
.095 75U
.396
.040 5696
.979 172
.091 0816
•347
.019 2891
.454 160
.095 6557
.397
.041 0039
.990 156
.000 9905
.348
.019 7234
.464 620
.095 56oi
.398
.041 4382
n.ooi 152
.090 8996
• 349
.020 1577
.475 089
.095 4646
.399
.041 8725
.012 159
.090 8087
2.350
i. 020 5920
10.485 570
0.095 3692
2.400
1.042 3068
11.023 176
0.090 7180
lofle(eu)
logio(eu)
•'
e~u
lOfleCe")
loa,o(en)
en
e-
SMITHSONIAN TABLES
249
The Exponential.
u
looio(eu)
eu
e~n
u
looio(eu)
en
e u
2.400
1.042 3068
11.023 176
O.ooo 7180
2.450
1.064 0215
n.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
• 45.2
.064 8901
.611 547
.086 1212
.403
.043 6096
.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 5H
•090 1753
.456
.066 6272
.658 086
.085 7774
.407
.045 3468
.100 609
.090 0851
.457
.067 0615
.669 750
.085 6916
.408
.045 78n
.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
.047 9526
.167 413
.089 5463
.463
.069 66731
.739 979
.085 1790
.414
.0483869
.178 586
.089 4568
.464
.070 1016
•751 725
.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
.200 966
.089 2780
.466
.070 9702
•775 252
.084 9^39
.417
.049 6898
. .212 172
.089 1888
.467
.071 4045
.787 033
.084 8390
.418
.050 1241
.223 390
.089 0996
.468
.071 8388
.708 826
.084 7542
.419
.050 5584
.234 619
.089 0106
.469
.072 2731
.810 630
.0846695
2.420
1.050 0926
11.245 859
0.088 9216
2.470
1.072 7074
11.822 447
0.084 5849
.421
.051 4269
.257 in
.088 8327
.471
.073 UI7
.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 i§i7
.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
.065 171
•083 5759
•433
.056 6385
•393 oio
.087 7731
.483
.078 3532
.977 142
.083 4924
•434
.057 0728
.404 409
.087 6854
.484
.078 7875
.989 125
.083 4089
2.435
1.057 5071
11.415 819
0.087 5977
2.485
1.079 2218
12.001 120
0.083 3256
• 43'>
.057 9414
.427 240
.087 5102
.486
.079 6561
.013 127
.083 2423
• 437
.058 3757
.438 673
.087 4227
.487
.080 0904
.025 147
.083 i59i
.438
.058 8099
.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
1.0596785
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
n.530 550
0.086 7261
2.495
1.083 5647
12. 12 i 734
0.082 4965
.446
.06-^
.542 086
.086 6395
.496
.083 9990
.133 86 i
.082 4140
.062 7186
.553 <>34
.086 5529
.497
.084 4333
.146 ooi
.082 3316
. i;.S
.063
.063 5872
.565 193
.576 764
.086 4663
.086 3799
.498
•499
.084 8676
.085 3019
.158 153
.170 318
.082 2493
.082 1671
2.450
1.064 0215
n.588 347
0.086 2936
2.500
1.085 7362
12.182 494
0.082 0850
I lo«e(eu)
loouXe0)
en
e~u
lofle(eu)
looio(eu)
eu
e~u
SMITHSONIAN TABLCS
250
The Exponential.
u
logio(eu)
eu
e~u
u
looio(eu)
eu
e "
2.500
1.085 7362
12.182 494
0.082 0850
2.550
I. 107 4509
12.807 104
0.078 0817
.501
.086 1705
.194683
.082 0030
.551
.107
.078 0036
.502
.503
.086 6048
.087 0391
.206 883
.219 096
.081 9210
.081 8391
•552
• 553
.108 3i<>5
. 108 7538
.83-
•845 5«3
.077 0257
.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
.507
.088 7763
.268 071
.081 5124
• 557
.no 4910
.897 068
.077 53/0
.508
.089 2106
.280 345
.081 4309
.558
.110 9253
.909 972
.077
.509
.089 6449
.292 631
.081 3495
.559
.in 3596
.922 888
.077 3821
2.510
I.OOO 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
.512
.090 9477
.329 565
.081 1059
.562
.112 6625
.961 715
•077 1503
.513
.091 3820
.341 900
.081 0248
.563
.113 0068
.974 683
.077 0732
.514
.091 8163
•354 248
.080 9438
• 504
.113 5311
.987664
.076 9961
2.515
1.092 2506
12.366 609
0 080 8629
2.565
I. H3 9653
13.000 658
0.076 9192
.516
.092 6849
.378 982
.c8o 7821
.566
.114 3996
.013 666
.076 8423
.517
.093 H92
.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 1/4
.080 5401
.569
.115 7025
.052 765
.076 6121
2.520
1.094 4221
12.428 597
0.080 4506
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 47<;
.08" 2988
.572
.117 0054
.091 082
.076 3826
.523
.095 7250
.465 938
.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 i
.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
1.008 7650
12.553 506
0.079 6500
2.580
I . 120 4798
13.197 138
0.075 7740
• 531
.099 1993
.566 066
.079 5794
.581
.120 9141
.210 342
.0/5 6083
• 532
.009 6336
.578 638
•079 4999
.582
.121 3484
• 223 559
.075 6226
• 533
.TOO 0679
.591 223
.079 4-'04
.583
.121 7826
.236 789
•075 5470 1
• 534
.100 5022
.603 821
.079 3410
.584
.122 2169
.250 032
.075 4715 ;
2.535
i . TOO 9365
12.616 431
0.079 2617
2.585
I. 122 6512
13.263 289
0.075 3961
.536
.101 3708
.629 054
.079 1825
.586
.123 0855
' 559
.075 3207
.537
.101 8051
.641 689
.079 1034
.587
.123 5108
.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
.1243884
.316 449
.075 0951
2.540
I. 103 I080
12.679 671
0.078 8664
2.590
I.I24 8227
13.329 772
O.075 O2OO
o4i
.103 5423
.692 357
.078 7876
.591
.125 2570
• 343 I08
.074 «M5i
• 542
.103 9766
.705 056
.078 7088
.592
.125 6913
• 35'
.074 8701
.543
.104 4109
.717 767
.078 6302
• 593
.126 1256
.Sfc
.074 7953
• 544
. 104 8452
.730 49i
.078 5516
.594
.126 5599
(3 198
.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 7U8
•755 978
.078 3946
.596
.127 4285
.409 99i
.074 5713
.547
.106 1480
.768 740
.078 3163
.1-7 8628
• 4-' 3 407
.074
.548
.106 5823
.781 515
.078 2380
• 598
.128 2971
.4:,
• 074
• 549
.107 0166
•794 303
.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
looe(eu)
logio(eu)
eu
e~u
looe(eu)
loflln(eu) eu
e~°
SMITHSONIAN TABLES
251
The Exponential.
u
looio(eu)
eu
e
u
log]0(eu)
eu
e
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
.400 692
.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
1.131 3371
13.531 225
0.073 9031
2.655
I.I53 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
.134 8115
.639 909
.073 3143
.663
.156 5262
.339 242
.009 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 7U
.069 4603
.618
.136 9830
.708 280
.072 0486
.668
. 158 6977
.411 118
.069 3909
.619
. 137 4172
.721 995
.072 8757
.669
.159 1320
.425 536
.069 3215
2.620
I.I37 8515
13.735 724
0.072 8029
2.670
1. 159 5663
14.439 969
0.069 2522
.621
.622
.138 2858
.138 7201
.749 466
.763 222
.072 7301
.072 6574
.671
.672
.160 0006
.160 4349
U68 878
.069 1830
.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
.068 9758
2.625
I . 140 0230
13.804 574
0.072 4398
2.675
1.161 7377
14.512 350
0.068 9068
.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 O50
.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 1945
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 2 12 I
.628 914
.068 3578
-634
•143 9317
.929 376
.071 7907
.684
.165 6464
.643 550
.068 2804
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 I53O
.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
. 147 4060
.041 258
.071 2187
.692
.169 1207
.761 169
.067 7453
.147 8403
.055 306
.071 1475
.693
.169 5550
•775 937
.067 677' >
.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
i . 170 4236
14.805 519
0.067 5424
.149 1432
.097 536
.070 9344
.696
. 170 8579
.820 332
.067 4749
• MM 5775
.ill 640
.070 8635
.697
.171 2922
.835 159
.067 40/4
.648
.150 01 18
.125 759
.070 7927
.698
.171 7265
.850 002
.067 3401
,640
.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
1.172 5951
14.879 732
0.067 2055
loo,(eu,
,ofll,e")
eu
,-«
Io0e(eu)
looio(eu)
eu
.-
SMITHSONIAN TABLES
252
The Exponential.
u
looio(eu)
eu
e~u
u
looio(eu)
eu
e~n
2.700
I.I72 5951
14.879 732
0.067 2055
2.750
I.I94 3098
15.642 632
0.063 9279
.701
• 173
.894 6l9
.067 1383
• 751
.194 7441
.658 282
.063
.702
.173 4637
.909 5-'i
.067 0712
• 752
.195 1784
.67.;
.063 8001
.703
. 173 8980
.924 438
.067 0042
• 753
.195 <"-'/
.689 630
.063
.704
•174 3323
•939 370
.066 9372
.754
.196 0470
.705 328
.063
2.705
1.174 7666
14.954 317
0.066 8703
2.755
1.196 4813
15.721 041
0.063 6090
.706
.707
.175 2009
•175 6352
.969278
•984 255
.066 8035
.066 7367
.756
• 757
.196
.197 3499
.736 770
•752 514
.063 5454
.063 4819
.708
. 176 0695
.999 247
.066 6700
.758
.197 7842
.768 275
.063 4185
.709
.I7<3 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
I . 198 6528
15.799 843
0.063 2918
.711
.177 3723
.044 312
.066 4703
.761
.199 0871
.815 051
.063
.712
.177 8066
.059 364
.066 4039
.762
.199 5214
.831 474
.063 1053
.713
.178 2409
.074 43i
.066 3375
.763
. 199 9557
.847 3M
.063 1022
.714
.178 6752
.089 513
.066 2712
.764
.200 3899
.863 169
.063 O39I
2.715
i. 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 9781
. 134 850
.066 0727
.767
.2OI 6928
.910 830
.062 8503
.718
.180 4124
.149 992
.066 0066
.768
.202 1271
.926 749
.062 7875
.719
.180 8467
.165 149
.065 9407
.769
.202 5614
.942 683
.062 /247
2.720
1.181 2810
15.180 322
0.065 8748
2.770
1.202 9957
15.958 634
0.062 6620
.721
.181 7153
.195 5io
.065 8089
.771
.203 4300
.974 601
.062 5904
.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 <>74
.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
.317 062
.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 021
0.062 0385
.731
.732
.186 0582
.186 4925
.348 228
.363 583
.065 1541
.065 0890
.781
.782
.207 7730
.208 2072
.135 M8
.151 291
.061 9765
.061 9146
.733
.186 9268
.378 955
.065 0239
.783
.208 6415
.167 451
.061 8527
.734
.187 3611
•394 341
.064 9589
.784
.209 0758
.183 626
.061 7908
2.735
1.187 7954
15.409 743
0.064 8940
2.785
1.209 5IOI
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 6996
.788
.210 8130
.248 490
-i -t^
.061 5442
.739
. 189 5326
.471 5o6
.064 6349
.789
.211 2473
.204 747
.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
.JU 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
.744
.191 7041
•549 057
.064 3126
• 794
.213 4188
.340 -'74
.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 38/
.060 9928
.748
.193 4412
.611 378
.064 0558
.798
.215 1500
.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
lOQeCe")
looio(eu)
eu
e~u
looe(en)
Iog10(en)
en
e-
SMITHSONIAN TABLES
253
The Exponential.
u lofllo(eu)
eu
e
u
looioCe")
eu
e~u
2.800
1.216 0245
16.444 647
0.060 8101
2.850
1.237 7393
17.287 782
0.057 8443
.801
.216 4588
.461 TOO
.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 4983
.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
.643 171
.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 5300
16.693 176
0.059 9047
2.865
1.244 2537
17-549 053
0.056 0831
.816
.222 9733
.709 877
.059 8448
.866
.244 6880
.566 611
.056 9262
.817
.223 4076
.726 596
.059 7850
.867
.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 6089
.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
.226 0133
.827 257
.059 4274
.873
.247 7280
.690 009
.056 5291
.824
.226 4476
.844 092
.059 3680
.874
.248 1623
.707 708
.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 7oi
.059 1902
.877
.249 4652
.760 910
•056 3034
.828
.228 1848
.911 604
.059 1310
.878
.249 8095
.778 680
.056 2471
.829
.228 6191
.928 524
.059 0719
.879
.250 3338
.796 468
.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 8049
.882
.251 6367
.849 937
.056 0226
.833
.230 3563
.996 374
.058 8361
.883
.252 0710
.867 796
.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
• -'31 6592
.047 439
.058 6598
.886
.253 3739
.921 480
.055 7990
•$3l
.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 mi
17-993 310
0.055 5762
.841
.233 8306
.132 890
•058 3673
.891
.255 5453
18.011 312
.055 5207
•ISO 031
.058 3089
.892
.255 9796
.029 332
.055 4652
.843
.234 6092
.167 190
.058 2507
.893
.256 4139
•047 37i
.055 4097
.844
•-'35 1335
. 184 3<>'>
.058 1924
•894
.256 8482
.065 427
•055 3544 !
2.845
1.235 5r>7*
.236 O02I
17.201 559
.218 769
•235 996
0.058 1343
.058 0762
.058 0181
2.895
.896
.897
1.257 282 q
.257 7168
.258 1511
18.083 501
.101 594
.119 705
0.055 2990
.055 2438 !
.055 i^5
.848
1 8707
.253 241
.057 9601
.898
.258 5854
. U7 833
.055 1334
•-'37 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
18.174 145
0.055 0232
log,(eu)
lofll,Xeu)
eu
e~u
looe(eu)
logio(eu)
eu
e~u
SMITHSONIAN TABLES
254
The Exponential.
u
lofllo(eu)
eu
e u
u
looio(en)
en
e u
£.900
1.259 4540
18.174 145
0.055 0232
2.950
I.28l 1687
I9-I05 954'
0.052 3397
.501
.259 8883
. \')2 32<J
.054 </#2
.951
.281 6030
.125 069
.052
.902
.260
.210 530
•054 9133
• 952
.282 0373
.144 204
.052
.903
.260 75r*)
^ 750
.054 8584
•953
.282
3 358
.052 1829
.904
.261 1912
) 988
.054 8036
•954
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
.262 0598
,28,3
.054 6941
.956
1 7745
.220 934
.052 0266
.907
.262 4941
.301 811
.054
• 957
.284 2088
.240 165
.051 9746
.908
.262 9284
.320 122
.054 5848
.958
• -'Xj 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
.912
.264 6655
•393 549
.054 3669
.962
.286 3803
.336606
•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
•375 318
.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 M99
.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
.2880860
.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 8798
.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 3H4
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 8945
.929
.272 0485
.708 912
.053 4505
•979
.293 7633
.668 139
.050 8437
2.930
1.272 4828
18.727 631
0.053 39/0
2.980
1.294 1976
19.687 817
0.050 7928
.931
.272 9171
.746 368
.053 3437
.981
.294 6319
• 707 5M
.050 7421
.932
• 273 35U
•765 123
.053 2904
.982
.295 0661
•7-'7 *32
.050 6913
•933
.273 7857
.783 898
.053 2371
.983
•2<)5 5004
.746 969
.050 6407
•934
.274 22OO
.802 691
.053 1839
.984
.295 9347
.766726
.050 5901
2.935
1.274 6543
18.821 503
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
.82
•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
.091
.298 9748
.005 578
.050
.942
•277 6944
.953 7i6
.052 7601
•992
.299 4091
5 494
.050 1870
• 943
.278 1287
.972 679
.052 7074
•993
.299 8434
•94~
.050 1368
• 944
.278 5630
.991 661
.052 6547
•994
• 300 -777
.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 M"3
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
.086 857
.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")
looio(eu)
e"
e~u
lofle(eu)
looio(eu)
eu
e~u
SMITHSONIAN TABLES
255
The Exponential.
u
looio(en)
e"
e
u
looio(eu)
eu
e
3.00
1.302 8834
20.085 537
0.049 7871
3-50
1.520 0307
33.115 452
0.030 1974
.01
.307 2264
.287 400
.049 2917
• 51
.524 3736
.448 268
.029 8969
.02
.311 5693
.491 292
.048 8012
• 52
.528 7166
.784 429
.029 5994
•03
.315 9123
.697 233
.048 3156
.53
.533 0595
34.123 968
.029 3049
.04
.320 2552
•905 243
.047 8349
• 54
•537 4025
.466 919
.029 0133
3.05
1.324 5982
21.115 344
0.047 3589
3-55
1.541 7454
34.813 3l8
O.O28 7246
.06
.328 9411
.327 557
.046 8877
.56
.546 0884
35.163 197
.028 4388
.07
.333 2841
•541 903
.046 4212
• 57
•550 4313
.516 593
.028 1559
.08
.337 6270
.758 402
.045 9593
• 58
.554 7742
.873 54i
.027 8757
.09
.341 0699
.977 078
.045 5020
• 59
.559 1172
36.234 076
.027 5983
3-10
1.346 3129
22.197 951
0.045 0492
3-6o
1.563 4601
36.598 235
0.027 3237
.11
•350 6558
.421 044
.044 6010
.61
.567 8031
.966 053
.027 0518
.12
.354 9988
.646 380
.044 1572
.62
.572 1460
37-337 568
.026 7827
•13
•359 3417
.873 98o
.043 7178
.63
.576 4890
.712 817
.026 5162
.14
.363 6847
23.103 867
.043 2828
.64
.580 8319
38.091 837
.026 2523
3-15
1.368 0276
23.336 065
0.042 8521
3.65
1.585 1749
38.474 666
O.025 9911
.16
•3/2 3706
.570 596
.042 4257
.66
089 5178
•861 343
.025 7325
.17
.376 7U5
.807 484
.042 0036
.67
.593 8607
39.251 906
.025 4765
.18
.381 0565
24.046 754
.041 5857
.68
.598 2037
.646 394
.025 2230
• 19
.385 3994
.288 427
.041 1719
.69
.602 5466
40.044 847
.024 9720
3-20
1.389 7423
24.532 530
0.040 7622
3-70
I. 606 8896
40.447 304
0.024 7235
.21
•394 0853
. .779 086
.040 3566
• 71
.611 2325,
.853 807
.024 4775
.22
.398 4282
25.O28 I2O
.039 955i
.72
.615 5755
41.264 394
.024 2340
•23
.402 7712
.279 657
.039 5575
.73
.619 9184
.679 108
.023 9928
.24
.407 1141
•533 722
.039 1639
• 74
.624 2614
42.097 990
.023 7541
3-25
1.411 4571
25.790 340
0.038 7742
3-75
1.628 6043
42.521 082
0.023 5177
.26
.415 8000
26.049 537
.038 3884
.76
.632 9473
.948 426
.023 2837
.27
.420 1430
.311 339
.038 0064
.77
.637 2902
43.380 065
.023 0521
.28
.424 4859
•575 773
.037 6283
• 78
.641 6331
.816 042
.022 8227
,2Q
.428 8288
.842 864
.037 2538
• 79
.645 976i
44.256 400
.022 5956
3-30
1.433 I7l8
27.112 639
0.036 8832
3-80
1.650 3190
44-701 185
O.O22 3708
•31
• 437 5U7
•385 125
.036 5162
.81
.654 6620
45.150 439
.022 1482
•32
.441 8577
.660 351
.036 1528
.82
.659 0049
.604 208
.021 9278
•33
.446 2006
.938 34^
.035 7931
.83
.663 3479
46.062 538
.O2I 7096
.34
•450 5436
28.219 127
.035 4370
.84
.667 6908
.525 474
.021 4936
3-35
1.454 8865
28.502 734
0.035 0844
3-85
1.672 0338
46.993 063
O.02I 2797
.36
•459 2295
.789 191
•034 7353
.86
.676 3767
47.465 351
.021 0680
•37
.463 5724
29.078 5-V
.034 3&X)
.87
.680 7196
•942 386
.020 8584
.38
.467 9153
•370 771
.034 04/5
.88
.685 0626
48.424 215
.020 6508
•39
.472 2583
.665 952
.033 7087
.89
.689 4055
.910 887
.020 4453
3-40
1.4/6 6012
29.964 loo
0.033 3733
3.90
1.693 7485
49.402 449
O.O2O 2419
.41
.480
30.265 244
.033 0412
.91
.698 0914
.898952
.O2O 0405
•42
•4*5 2871
.569 415
.032 7124
.92
.702 4344
50.400 445
.OI9 8411
•43
.489 6301
•876 643
.032 3869
•93
.706 7773
.906 978
.019 6437
•44
•493 9730
31.186 958
.032 0647
.94
.711 1203
51.418 601
.019 4482
1.498 3160
31.500 392
0.031 7456
3-95
1.715 4632
5L935 367
0.019 -'547
.502 <>5<S9
.816 977
.031 4298
.96
.719 8061
52.457 326
.019 0631
.47
.507 0019
32.136 743
.031 1170
•97
.724 1491
.984 53i
.018 8734
.48
•SI'
•459 7^2
.030 8074
.98
.728 4920
53.517 034
.018 6856
.515 6877
.785 948
.030 5009
.99
.732 8350
54.054 889
.018 491)7
3.50
1-520 0307
33.H5 452
0.030 1974
4.00
1.737 1779
54.598 150
0.018 3156
loflc(e°)
loouXe")
eu
e~u
looe(eu)
loouAe")
eu
e~u
SMITHSONIAN TABLCS
256
The Exponen
Uiatj? '
u
logio(eu)
e"
e~°
/ u
looio(eu)
e°
e u
4.00
1-737 1779
54.598 150
o.oiS 3156^
4.50
1.954
90.017 131
O.OII IOOO
.01
• 741
55.14'' 871
.Ol8 ^K
• 51
i 819
.010
.02
.745
.701 K)'
.017 9jjO
• 52
.963 01 i i
91.835 598
.010
• 03
• 750 2068
56.260 911
.017 7743
.53
•967 3540
58 561
.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
j 408
O.OIO
.06
• 7''3 2356
•974 3ii
.017 2490
.5<>
.980 3828
95.583 480
.010
.07
.767 5785
58.556 963
.017 0774
• 57
.984 7258
,4 no
.010 3580
.08
.771 9215
59.145 4/0
.016 9075
.58
.989 0687
97.514 394
.010 2549
.09
.776 2f>44
•739 892
.016 7392
• 59
•993 4H7
98.494 430
.010 1529
4.10
1.780 6074
60.340 288
o.o 16 5727
4.60
1.997 7546
99.484 3i6
0.010 0518
.11
.784 9503
.946 718
.016 4078
.61
2. 002 0976
100.484 150
.009 9518
.12
.789 2933
61.559 242
.016 2445
.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 65/7
4.IS
1.802 3221
63.434 ooo
0.015 7644
4.65
2.019 4693
104.584 986
O.OOQ 5616
.16
.806 6650
64.071 523
.015 6076
.66
.023 8123
105.636 082
.009
.17
.811 0080
.715 452
.015 4523
.67
.028 1552
106.697 743
.009 3723
.18
.815 3509
65.365 853
.015 2985
.68
.032 4982
107.770 07}
.009 2790
.19
.819 6939
66.022 791
.015 1463
.69
.036 8411
108.853 180
.009 1867
4.2O
1 .825|. 0368
66.686 331
0.014 9956
4.70
2.041 1841
109-947 1/3
0.009 0953
.21
.828 3798
67.356 540
.014 8464
.71
.045 5270
111.052 160
<x>48
.22
.832 7227
68.033 484
.014 6986
.72
.049 8700
112.168 253
.008
•23
.837 0657
.717 232
.014 5524
• 73
.054 2129
113.295 5r\3
.008 8265
.24
.841 4086
69.407 852
.014 4076
• 74
.058 5558
114.434 202
.008 7386
4-25
1.845 7515
70.105 412
0.014 2642
4-75
2.062 8o83
115.584 285
o.coS 6=^17
.26
.850 0945
.809 983
.014 1223
.76
.067 2417
116.745 926
.008 5656
.27
.854 4374
71.521 636
.013 9818
• 77
.071 5847
117.919 242
.008 4804
.28
.858 7804
72.240 440
.013 8427
.78
.075 9276
119.104 351
.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
121.510 418
0.008 2297
•31
.871 8092
74.440 489
.013 4335
.81
.088 9565
1-2.731 618
.008 1479
•32
.876 1522
75-188 628
.013 2999
\g2
.093 2994
123.965 091
.008 0668
• 33
.880 4951
.944 287
.013 1675
!§3
.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
.OI2 6512
.87
.115 0141
130.320 918
.007 '
.38
.902 2098
.838 033
.012 5254
.88
.H9 357i
131.630 665
.007 5970
• 39
.906 5528
80.640 419
.OI2 4007
.89
.123 7000
132.953 575
.007 5214
4.40
1.910 8957
81.450 869
0.012 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 4.17 ••on 9145
-.93
.141 0718
138.379 5U
.007
•44
.928 2675
84.7/4 942
.on 7959
.94'
.145 4U7
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
.011 5024
.96
.154 1006
M2.593 796
.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
o.oii 1090
5.00
2. I/I 47-M
148.413 159
0.006 7379
I6fle(eu)
Iog10(eu)
eu
e~u
looe(eu)
loQio(en) eu
e~u
SMITHSONIAN TABLES
257
The Exponential.
u
lQQio(eu)
eu
e-n
u
looio(eu)
eu
e~u
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 1871
156.022 464
0.006 4093
5-55
2.410 3344
257.237 556
0.003 8875
.06
.197 5301
157-590 5i6
.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 2160
160.774 056
.006 2199
.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 9019
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
S.I5
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
290.034 534
.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
307.969 268
.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
.510 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
200.336 810
0.004 99i6
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
.004 8928
.82
.527 5939
336.972 054
.002 9676
•33
.3H 78o6
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 38l
O.OO2 8799
.36
.327 8184
212.724 946
.004 7009
.86
•544 9657
350.724 144
.002 8512
• 37
.332 1614
214.862 86a
.004 6541
.87
.549 3086
354.248 980
.OO2 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 5166
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 5H
.002 6585
• 44
.362 5620
230.442 183
.004 3395
.94
.579 7092
379-934 930
.002 6320
S.45
2.366 9049
232.758 166
0.004 2963
5-95
2.584 0522
383.753 339
O.OO2 6058
•371 2479
235.097 424
.004 2536
.96
•688 3951
387.610 124
.002 5799
• 47
.375 5908
237.460 193
.004 21 12
•97
.592 7381
391.505 671
.002 5542
> 9338
239.846 707
.004 1693
.98
.597 0810
395.440 368
.002 5288
.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
403.428 794
0.002 4788
log,(eu;
lofllo<en)
eB
e~u
loge(eu)
lofllo(eu)
eu
e~~u
SMITHSONIAN TABLCS
258
The Exponential.
u
logu,(eu)
e"
e-a
I
.43429 44819
2.71 828 183
0.367 879 441
2
.80858 89638
7-38 905 610
0.135 335
3
1.30288 34457
20.0 855 369
(I) 497870
4
I.73/I7 79-'7->
54-5 081 500
183 156 389
5
2.17147 24095
148. 413 159
700
6
2.60576 68914
403. 428 793
(2) 247 875 -'i.S
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 </,9 298
u
4.77723 93009
598 74-1 417
(4) id/ 017 008
12
5-2H53 37828
162 754. 791
(5) 614 421 235
13
5.64582 82647
442 413. 392
(5) 220 032 941
14
6.08012 27466
120 260 4.28
(6) 831 528 719
15
6.51441 72285
326 901 7.37
(6) 305 902 321
16
6.94871 17105
888 611 0.52
(6) 112 535 175
17
7.38300 61924
241 549 52.8
(7) 4U 993 77-»
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
[I]
(9) 278 946 809
23
9.98877 30838
974 480 345
[I]
(9) 102 618 796
24
10.42306 75657
264 891 221
[2]
do) 377 5U 454
25
10.85736 20476
720 048 993
[2]
(10) 138879439
26
11.29165 65295
195 729 609
[3]
(ii) 510 908 903
27
11.72595 10114
532 048 241
[3]
(ii) 187952882
28
12.16024 54933
144 625 707
u:
(12) 691 440 oil
29
12.59453 99752
393 133 430
[4
(12) 254 366 565
30
13.02883 4457 r
106 864 746
[5
d3) 935 762 297
31
13.46312 89390
290 488 497
[5.
(13) 344 247 711
32
13.89742 34209
789 629 602
[5
(13) 126 641 656
33
U.33I7I 79028
214 643 58o
[6;
(14) 465888615
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
43i 123 155
[7"
(15) 231 952 283
37
16.06889 58304
117 191 424
K
(16) 853 304 763
38
16.50319 03123
3i8 559 3i8
8:
(16) 3U 913 279
39
16.93748 47942
865 9?4 004
:8:
(16) 115 482 242
40
17.37177 92761
235 385 267
[9!
(17) 424 835 426
41
17.80607 3758o
639 843 493
[9:
(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
it;
(19) 778 113 224
45
19.54325 16856
349 342 711
ii]
(19) 286 251 858
46
19.97754 61675
949 611 942
ii]
(19) 105 306 174
47
20.41184 06495
258 131 289
12
(20) 387 399 763
48
20.84613 51314
701 673 591
12
(20) 142 516 408
49
21.28042 96133
190 734 657
13
(21) 524 288 566
50
21.71472 40952
518 470 553 [
13]
(21) 192 874 085
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 e80
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~w there are
21 ciphers between the decimal point and the figures 192874985.
SMITHSONIAN TABLES
25Q
The Exponential.
u
looio(e»)
eu
e— u
51
22.14901 85771
140 934 908 [14]
(22) 709 547 4i6
52
22.58331 30590
383 ioo 800 [14]
(22) 261 027 907
53
23.01/00 75409
104 137 594 [15]
(23) 960 268 005
54
23.45190 20228
283 075 330 [I5J
(23) 353 262 857
55
23.88619 65047
709 4/8 527 [15]
(23) 129 958 143
56
24.32049 09866
209 165 950 [16]
(24) 478 089 288
57
24.754/8 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
42O 121 O4O 17.
(25) 238 026 641
60
26.05766 89142
114 200 739 [18;
(26) 875 651 076
61
26.49196 33961
310 429 794 [18;
(26) 322 134 029
62
26.92625 78780
843 835 667 [18]
(26) 118 506 487
63
27.30055 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
109 488 924 [20]
(28) 590 009 054
66
28.66343 58056
460 7l8 663 [20.
(28) 217 052 201
67
29.09773 028/5
125 236 317 [2i;
(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
7i
30.40061 37332
30.83490 82151
251 543 867 [22;
683 767 123 [22;
(30) 397 544 974
(30) ^146 248 623
72
31.26920 26970
185 867 175 [23;
(31) 538 018 616
73
31.70349 71789
505 239 363 [23]
(31) 197 925 988
74
32.13779 16608
137 338 298 [24]
(32) 728 129 018
75
32.57208 61427
373 324 200 [24]
(32) 267 853 696
76
33.00638 06246
10 1 480 039 [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) 164 581 143
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 23351
GOT 762 841 [31]
(39) i 10 893 902
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
181 123 008 [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
988 003 032 [34
•(42) 101 122 149
100
43.42944 81903
268 811 714 [35
(43) 372 007 598
The numbers in square brackets denote the numbers of figures between the
la^t figure given and the decimal point; for example, the first nine figures of eM
Si847°:o3, and there are 13 additional figures before the decimal point is
lied. The numbers in parentheses denote the number? of ciphers between
the decimal point and the first significant figure; for example, in e"80 there are
2i ciphers between the decimal point and the figures 192874985.
SMITHSONIAN TABLES
260
Auxiliary Table for Interpolation of Logio(e").
(p = n X 43429 44819 • • •)
n
p
n
p
n
p
n
p
n p
o.ooo
OOO
O.050
2171
O.IOO
4343
0.150
6514
i
0.200 8686
.001
043
.051
2215
.101
4386
.151
6558
.201 8729
.002
087
.052
2258
.102
4430
.152
6601
.202 8773
.003
130
.053
2302
.103
4473
•153
6645
.203
8816
.004
174
.054
2345
.104
4517
.154
6688
.204
8860
0.005
217
0.055
2389
0.105
4560
0.155
6732
0.205
8903
.006
261
.056
2432
.106
4604
.150
.20'
.007
304
.057
2475
.107
4647
.157
6818
.207
.008
347
.058
2519
.108
4600
.158
6862
.208 (.033
.009
391
.059
2562
.109
4734
.159
6905
.209
9077
0.010
434
O.o6o
2606
O.IIO
4777
0.160
6949
O.2IO
9120
.Oil
478
.061
2649
.III
4821
.161
6992
.211 <,
.012
521
.062
2693
.112
4864
.162
7036
.212 92O7
.013
565
.063
2736
.113
4908
.163
7079
.213
.014
608
.064
2779
.114
4951
.164
7122
.214
93M
0.015
651
0.065
2823
O.II5
4994
0.165
7166
O.2I5
9337
.016
695
.066
2866
.116
5038
.166
7209
.2l6 938l
.017
.067
2910
.117
5081
.167
7253
.217 9424
.018
782
.068
2953
.118
5125
.168
7296
.218 9468
.019
825
.069
2997
.119
5168
.169
7340
.219
95ii
0.020
869
0.070
3040
0.120
5212
0.170
7383
O.22O
9554
.021
912
.071
3083
.121
5255
.171
7426
.221 9598
.022
955
.072
3127
.122
5208
.172
7470
.222 9641
.023
999
.073
3170
.123
5342
• 173
7513
.223 9685
.024
1042
.074
3214
.124
5385
.174
7557
.224
972*
0.025
1086
0.075
3257
0.125
5429
0.175
7600
0.225
9772
.026
1129
.076
3301
.126
5472
.176
7(>44
.226 j 9815
.027
H73
.077
3344
.127
55i6
.177
7687
.227 ! 9858
.028
1216
.078
3387
.128
5559
.178
7730
9902
.029
1259
.079
3431
.129
5602
.179
7774
.229
9945
0.030
1303
0.080
3474
0.130
5646
0.180
78i7
0.230
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
5006
.186
8078
.236
10249
• 037
1607
.087
3778
5950
.187
8121
.237
10293
.038
1650
.088
3822
. 138
5993
.188
Sio;
.238
10336
.039
1694
.089
3865
• 139
6037
.189
8208
.239
10380
0.040
1737
0.090
3909
0.140
6080
0.190
8252
0.240
10423
.041
1781
.091
3952
.141
o 1 24
.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
10^40
.046
1998
.096
2169
.146
6341
.196
8512
.24"
10684
.048
2041
2085
.097
.098
4-56
.147
.148
6384
6428
.197
.198
8556
8599
.247
.248
10727
I077I
.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
Auxiliary Table for Interpolation of Logio(e«).
(p = n X 43429 44819 . . .)
•
p
n p
n
p
n
P
n
p
0.250
10857
0.300
13029
0.350
15200
0.400
17372
0.450
19543
.251
10901
.301
13072
•351
15244
.401
I74I5
.451
19587
.252
10944
• 302
13116
•352
15287
.402
17459
.452
19630
.253
10988
.303
I3I59
.353
I533I
.403
17502
•453
19674
.254
11031
• 304
13203
• 354
15374
.404
17545
• 454
I97I7
0.255
1 1075
0.305
13246
0.355
I54I7
0.405
17589
0.455
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
I77I9
.458
19891
.259
11248
.309
13420
• 359
I559I
.409
17763
•459
19934
0.200
11292
0.310
13463
0.360
15635
O.4IO
17806
0.460
19978
.261
1 1335
.311
13507
.361
15678
.411
17850
.461
2OO2I
.262
H379
.312
13550
.362
15721
.412
17893
.462
20064
.263
11422
.313
13593
.363
15765
.413
17936
.463
2OIO8
.264
11465
.314
13637
.364
15808
.414
17980
.464
2OI5I
0.265
11509
0.315
13680
0.365
15852
0.415
18023
0.465
20195
.266
H552
.316
13724
.366
15895
.416
18067
.466
20238
.267
11596
.317
13767
.367
15939
.417
18110
.467
2O282
.268
11639
.318
13811
.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
16112
.421
18284
.471
20455
.272
11813
.322
13984
• 372
16156
.422
18327
• 472
20499
.273
11856
.323
14028
• 373
16199
.423
18371
• 473
20542
.274
11900
.324
14071
.374
16243
.424
18414
• 474
20586
0.275
H943
0.325
I4H5
0.375
16286
0.425
18458
0.475
20629
.276
11987
.326
14158
.376
16329
.426
18501
.476
20672
.277
12030
.327
I42OI
.377
16373
.427
i8544
• 477
2O7I6
.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
14375
.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
21020
0.285
12377
0.335
14549
0.385
16720
0.435
18892
0.485
21063
.2&'>
12421
.336
14592
.386
16764
.436
18935
.486
2IIO7
.287
12464
• 337
14636
.387
16807
•437
18979
.487
2II50
.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
12725
• 343
14896
• 393
17068
•443
19239
• 493
21411
•194
12768
.344
14940
.394
I7III
•444
19283
.494
21454
0.295
12812
0.345
14983
0.395
I7I55
0.445
19326
0.495
21498
,396
12855
.346
15027
.396
17198
.446
19370
.496
21541
.297
12899
• 347
15070
• 397
17241
• 447
I94I3
• 497
21584
.298
12942
.348
I5H3
• 398
17285
.448
19456
.498
21628
.299
12985
• 349
I5IS7
.399
17328
.449
19500
•499
21671
0.300
13029
0.350
15200
0.400
17372
0.450
19543
0.500
21715
i n
p
n
P
n
p
n
p
n
p
SMITHSONIAN TABLES
262
TABLE V
NATURAL LOGARITHMS
NOTE. — In Table V, for u greater than 158, linear interpolation of
logew suffices to give a value whose error is not greater than one unit in
the last place.
263
Natural Logarithms.
u
lOQeU
«Fo'
u
lOQeU
«FO'
u
!og,u
w FQ'
u
iog,u
<oF0'
o
— oo
oo
50
3.91202
2000
100
4.60517
1000
150
5.01064
667
I
o.ooooo
lOOOOO
51
3.93183
1961
101
4.6I5I2
990
151
5.01728
662
2
0.69315
50000
52
3.95124
1923
IO2
4.62497
980
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
20000
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
5.04986
641
1.94591
14286
57
4.04305
1754
107
4.67283
935
157
5.05625
637
3
2.07944
12500
58
4.06044
1724
108
4.68213
926
158
5.06260
633
9
2.19722
inn
59
4-07754
1695
109
4.69135
917
159
5.06800
629
10
2.30259
IOOOO
60
4.09434
1667
no
4.70048
909
160
5.07517
625
u
2.39790
9091
61
4.II087
1639
in
4-70953
901
161
5.08140
621
12
2.48491
8333
62
4.I27I3
1613
112
4.71850
893
162
5.08760
6l7
13
2.56495
7692
63
4.I43I3
1587
U3
4.72739
885
163
5.09375
6l3
14
2.63906
7U3
64
4.15888
1562
114
4.73620
877
164
5.09987
610
15
2.70805
6667
65
4-17439
1538
H5
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
4.2485O
1429
120
4.78749
833
170
5.13580
588
21
3-04452
4762
7i
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
4.29046
1370
123
4.81218
813
173
5.15329
578
24
3-17805
4i67
74
4.30407
i35i
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
3571
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
5.19206
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
3-49651
3030
83
4.41884
1205
133
4.80035
752
183
5.20949
546
34
3-52636
2941
84
4.43082
1190
134
4.89784
746
184
5-21494
543
35
3.55535
2857
8s
4.44265
1176
135
4.90527
74i
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
IIII
I4O
4.94164
714
190
5.24702
526
41
3.71357
2439
9i
4.51086
1099
141
4.94876
709
191
5.25227
524
42
3.73767
2381
92
4.52179
1087
142
4.95583
704
192
5.25750
521
43
3.76120
2326
93
4.53260
1075
143
4.96284
699
193
5.26269
518
44
3.78419
2273
94
4.54329
1064
144
4.96981
694
194
5.26786
515
45
3. 80666
2222
95
4.55388
1053
145
4.97673
690
195
5-27300
513
46
3-8-
2174
96
4.56435
1042
146
4.98361
685
196
5.27811
510
47
3.85015
2128
97
4-57471
1031
147
4.99043
680
197
5.28320
508
48
3-87120
2083
98
4.58497
IO2O
148
4.99721
676
198
5.28827
505
49
3.89182
2041
99
4-59512
IOIO
149
5.00395
671
199
5.29330
503
50
3.91202
2000
100
4.60517
1000
150
5.01064
667
200
5.29832
500
e*
X
e-x
ex
X
e~x
e*
X
e-x
e*
X
e-x
SMITHSONIAN TABLES
264
Natural Logarithms.
u
loo.u
«F0'
u
loo.u
mfj
u
log,u
»fV
u
loo.u
200
5.29832
500
250
0.52146
400
300
5.70378
333
350
v93
286
2OI
5.30330
498
251
5.52545
398
301
5.707H 332
35i
'079
285
2O2
5.30827
495
252
5.52943
397
302
5.71043 331
352
203
5.31321
493
253
5-53339
395
303
5.71373 330
353
"647
204
5.31812
490
254
5-53733
394
304
5.71/03
329
354
5-86930
205
5.32301
488
255
5.54I26
392
305
5./203I
328
355
S.87JU
282
206
5.32788
485
256
5.54518
391
306
5.72359
327
356
7403
281
207
5.33272
483
257
5.54908
389
307
5.7-?685
326
357
5.8/774
208
5.33754
481
258
5.55206
388
308
5-73010
325
358
5.88053
209
5.34233
478
259
5.55683
386
309
5-73334
324
359
0.88332
279
210
5.34711
476
260
5.56068
385
310
5.73657
323
3^0
5.88610
278
211
5.35186
474
261
5.56452
383
311
5-73979
322
361
5.88888
277
212
5.35659
472
262
506834
382
312
5 . 74300
321
362
5.89164
213
5.36129
469
263
5.57215
380
313
5-74620
319
363
5.89440
214
5.36598
467
264
5-57595
379
314
5-74939
3i8
364
5.89715
275
215
5.37064
465
265
5-57973
377
315
5.75257
317
365
5.89990
2/4
216
5.37528
463
266
5.58350
376
316
5-75574
3i6
366
5.90263
-J73
217
5- 37990
461
267
5.58725
375
317
5.75890
315
367
5.90536
218
5.38450
459
268
5.59099
373
318
5.76205
3U
368
5-90808
-V-'
219
5-38907
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
2/0
221
5.398i6
452
271
5.60212
309
321
5.7/144
312
371
5.91620
270
222
5.40268
450
272
5-60580
368
322
5.77455
3ii
372
5.91889
269
223
5.40717
448
273
5.60947
366
323
5.77765
310
373
5.92158
M i
224
5.4U65
446
2/4
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
5-63121
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
38i
5-94280
232
5.44674
431
282
5.64191
355
332
5-80513
301
382
5-9454-'
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
200
235
5.45959
426
285
5.65249
351
335
5.81413
299
385
5-95324
260
236
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
238
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
5.06615
256
24]
5.48480
415
291
5.67332
344
34i
5.83188 293
39i
5.06871
242
5.48894
413
292
5.67675
342
342
5.83481 i 292
392
5.9/126
243
5.49306
412
293
5.68017
341
343
5.83773 292
393
5.97381
244
5.49717
410
294
5.68358
340
344
5.84004
291
394
5.97635
254
245
5.50126
408
295
5.68698
339
345
5.84354
290
395
5.97889
253
246
5.50533
407
296
5-69036
338
346
5.84644 289
396
5.98141
-'53
247
5.50939
405
297
5.69373
337
347
5.84932 i 288
397
5.98394
248
5.51343
403
298
5.09709
336
348
5.85220 287
398
5.98645
251
249
5.51745
402
299
5.70044
334
349
5.85507
287
399
5.98806
251
250
5.52146
400
300
5.70378
333
350
5.85793
286
400
5.99U6
250 j
ex
X
e-*
ex
X
e-*
e*
X
e~*
e*
X
e— x
SMITHSONIAN TABLES
265
Natural Logarithms.
I
lOfleU
-FO'
u
lOQeU
»FO'
u
IOQ...U
O.FO'
u
logeu
«F0'
400
5.99146
250
450
6.10925
222
500
6.21461
200
550
6.30992
182
4UI
5.99396
249
45i
6. 1 1 147
222
501
6.21661
200
55i
6.3H73
181
402
5.99645
249
452
6.11368
221
502
6.21860
199
552
6.31355
181
403
5.99894
248
453
6.11589
221
503
6.22059
199
.553
6.31536
181
404
6.OOI4I
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
246
456
6.12249
219
506
6.22654
198
556
6.32077
180
407
6.0088l
246
457
6.12468
219
507
6.22851
197
557
6.32257
180
408
6.OII27
245
458
6.12687
218
508
6.23048
197
558
6.32436
i79
409
6.01372
244
459
6.12905
218
509
6.23245
196
559
6.32615
179
410
6.0l6l6
244
460
6.13123
217
510
6.23441
196
560
6.32/94
179
411
6.OI859
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
6.02345
242
463
6.13773
216
513
6.24028
195
563
6.33328
178
4U
6.02587
242
464
6,13988
216
514
6.24222
195
564
6.33505
177
415
6.02828
241
465
6.14204
215
515
6.24417
194
565
6.33683
177
416
6.03069
240
466
6.14419
215
516
6.24611
194
566
6.33859
177
417
6.03309
240
467
6.14633
214
517
6.24804
193
567
6.34036
176
418
6.03548
239
468
6.14847
214
518
6.24998
193
568
6.34212
176
419
6.03787
239
469
6.15060
213
519
6.25190
193
569
6.34388
176
420
6.04025
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
57i
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
43i
6.06611
232
481
6.17587
208
531
6.27476
188
58i
6.36475
172
432
6.06843
231
482
6.17704
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
I/O
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
44i
6.08904
227
491
6.19644
204
541
6.29342
185
59i
6.38182
169
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
6.38688
168
6.09807
225
495
6.20456
202
545
6.30079
183
595
6.38856
168
6. 10032
224
496
6.20658
2O2
546
6.30262
183
596
6.39024
168
1256
224
497
6.20859
201
547
6.30445
183
597
6.39192
168
6. 10479
223
498
6.21060
201
548
6.30628
182
598
6.39359
167
6.10702
223
499
6.21261
200
549
6.30810
182
599
6.39526
167
450
6.10925
222
500
6.21461
200
550
6.30992
182
600
6.39693
167
ex
X
e-x
6*
X
e-*
e*
X
e— x
e*
X
e~x
SMITHSONIAN TABLES
266
Natural Logarithms.
u
lOQeU
-FO'
u
lOQcU
o>Fo'
u
log u
•w
u log, u
-FO'
600
6.3Q693
167
650
6.47097
154
700
6.55108
M3
750
6.62007
133
601
6.39859
166
651
6.47851
154
701
:25I
M3
751 6.62141
133
602
6.40O26
166
652
6.48004
153
702
^393
142
6.62274
133
603
6.4OI92
166
653
-I5«
153
703
5530
14*
753
-4O7
133
604
6.40357
166
654
6.483II
153
704
0.55678
142
754
6.62539
133
605
6.40523
165
655
•U64
153
705
=820
142
y>72
132
606
6.40688
165
656
6.48616
152
706
6.55962
14 2
756
6.62804
132
607
6.40853
165
657
6.48768
152
707
'iO3
I4I
757
1930
132
608
6.4IOI7
164
658
6.48920
152
708
''244
141
758
132
609
6.4II82
164
659
6.49072
152
709
0.56386
141
759
6.63200
132
6 10
6.41346
164
660
6.49224
152
710
6.56526
141
760
6.63332
132
6n
6.4I5IO
164
661
6.49375
151
711
6667
MI
76i
6.63463
131
612
6.41673
163
662
6.49527
151
712
140
762
6.63595
131
613
(..41836
163
663
6.49677
151
7i3
6948
140
763
6.63726
131
614
6.41999
163
664
6.49828
151
7i4
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
7i6
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
ISO
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
723
6.58064
139
771
6.64769
130
622
6.43294
161
672
6.51026
M9
722
6.58203
139
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
6.51471
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
i59
677
6.51767
148
727
6.58893
138
777
6.65544
129
628
6.44254
159
678
6.5I9I5
147
728
6.59030
137
7/8
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
U7
730
6.59304
137
780
6.65929
128
631
6.44731
158
681
6.52356
147
731
6.59441
137
78i
6.66058
128
632
6.44889
158
682
6.5^503
U7
73-'
6.59578
137
782
6.66185
128
633
6.45047
158
683
6.52649
146
733
6.59715
136
783
6.66313
634
6.45205
158
684
6.52796
146
734
6.59851
I36
784
6.66441
635
6.45362
157
685
6.52942
146
735
6.59987
136
785
6.66568
636
6.45520
157
686
6.53088
146
•736
6.60123
136
786
"696
i -'7
637
6.45677
i57
687
6.53233
146
737
6.60259
136
787
6.6ff
127 ;
638
6.45834
i57
688
6.53379
U5
738
6.60394
136
788
6.66950
127
639
6.45990
156
689
6.535-'4
145
739
6.60530
135
789
W7
640
6.46147
156
690
6.53669
M5
740
6.60665
135
790
7-203
641
6.46303
156
691
6.53814
M5
74i
6.60800
135
791
6.<>7
04-'
0.46459
156
692
6.53959
U5
74-'
6.60935
135
792
6.07
643
6.46614
156
693
6.54103
144
743
6.61070
135
793
6.67
644
6.46770
155
694
6.54247
144
744
6.61204
134
794
6.6;
645
6.46925
155
695
6.54391
144
745
6.61338
134
795
#34
126
646
6.47080
155
696
6.54535
144
746
6.61473
134
796
7960
126
647
6.47235
155
697
6.54679
M3
747
6.61607
134
797
<o85
125
648
6.47389
154
698
6.54822
U3
748
6.61740
134
798
-u
649
6-47543
154
699
6.54965
143
749
6.61874
134
799
X336
125
650
6.47697
154
700
6.55108
1 43
750
6.62007
133
800
6.68461
125
ex
X
e~x
ex
x e~x
ex x
e~x
ex x
e~x
SMITHSONIAN TABLES
26-
Natural Logarithms.
u
IOQ,U
«F0'
u
log,u
w FQ
u
logeu
• Fo'
u
log, u
«FO'
800
6.68461
125
850
6.74524
118
900
6.80239
ill
950
6.85646
105
801
6.68586
125
851
6.74641
118
901
6.80351
in
95i
6.85751
105
802
6.687II
125
852
6.74759
117
902
6.80461
in
95^
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
806
6.60084
6.69208
124
124
855
856
6.75110
6.75227
117
117
905
906
6.80793
6.80904
no
no
955
956
6.86I7I
6.86276
105
105
807
808
6.69332
6.09456
124
124
857
858
6.75344
6.75460
117
117
907
908
6.81014
6.81124
1 10
1 10
957
958
6.86380
6.86485
104
104
809
6.69580
124
859
6.75577
116
909
6.81235
1 10
959
6.86589
104
810
6.69/03
123
860
6.75693
116
910
6.81344
no
960
6.86693
104
811
6.69827
123
85i
6.75809
116
911
6.81454
IIO
961
6.86797
104
812
6.69950
123
862
6.75926
116
912
6.81564
IIO
962
6.86901
104
813
6.70073
123
863
6.76041
116
913
6.81674
IIO
963
6.87005
104
8ii
6.70196
123
864
6.76157
116
914
6.81783
109
964
6.87109
104
815
6.70319
123
865
6.76273
116
915
6.81892
109
965
6.87213
104
816
6.70441
123
866
6.76388
H5
916
6.82002
109
966
6.87316
104
817
6.70564
122
867
6.76504
H5
917
6.82111
109
967
6.87420
103
818
6.70686
122
868
6.76619
H5
918
6.82220
109
968
6.87523
103
819
6.70808
122
869
6.76734
»S
919
6.82329
109
969
6.87626
103
820
6.70930
122
870
6.76849
115
920
6.82437
109
970
6.87730
103
821
6.71052
122
871
6.76964
H5
921
6.82546
109
971
6.87833
103
822
6.7II74
122
872
6.77079
H5
922
6.82655
108
972
6.87936
103
823
6.71206
122
873
6.77194
H5
923
6.82763
108
973
6.88038
103
824
6.7I4I7
121
874
6.77308
114
924
6.82871
108
974
6.88141
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
6.7I90I
121
878
6.77765
114
928
6.83303
108
978
6.88551
102
829
6.72O22
121
879
6.77878
114
929
6.83411
108
979
6.88653
102
830
6.72143
1 2O
880
6.77992
114
930
6.83518
108
980
6.88755
102
831
6.72263
1 2O
881
6.78106
114
93i
6.83626
107
981
6.88857
102
832
6.72383
I2O
882
6.78219
113
932
6.83733
107
982
6.88959
102
833
6.72503
120
883
6.78333
113
933
6.83841
107
983
6.89061
IO2
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
IO2
836
6.72863
1 2O
886
6.78672
ti3
936
6.84162
107
986
6.89366
101
837
6.72982
119
887
6.78784
H3
937
6.84268
107
987
6.89467
IOI
838
6.73IO2
IIQ
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
«4 1
6-73459
119
891
6.79234
112
941
6.84694
106
991
6.89871
IOI
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
6.00174
IOI
845
6.73934
1x8
895
6.79682
112
945
6.85118
106
995
6.90274
IOI
846
6.74052
118
896
6.79794
112
946
6.85224
106
996
6.90375
IOO
847
6.74170
118
897
6.79906
III
947
6.85330
106
997
6.90475
100
6.74288
118
898
6.80017
III
948
6.85435
105
998
6.90575
IOO
8«
6.74406
118
899
6.80128
III
949
6.85541
105
999
6.90675
IOO
850
6.74524
118
900
6.80239
III
950
6.85646
105
IOOO
6.90776
IOO
e*
X
e-*
ex
X
e~x
e*
X
e-x
e*
X
e-x
SMITHSONIAN TABLES
268
Natural Logarithms.
u
LoQcU
u
Log.u
u
Loovu
u
LOO.U
u Logcii
IOOO
6.90776
1361
7.21598
1721
7.45066
2III
7.65
2503
7-82525
1009
6.91072
1367
7-22037
1723
7-45J3J
2113
7.655^6
2521
-Ml
MO 1 3
6.9.2067
1373
7.22475
1733
7.45?'i
7-66341
2531
''37
1019
6.9-*>5<S
1381
7.23056
1741
7.46221
21311
2539
7.83953
102 1
6.92854
1399
7.24351
1747
7-46566
2137
2543
7.84110
1031
6.93828
1409
7.250d4
1753
7.46908
2141
7.66903
2549 7.84346
1033
6.94022
1423
7.20052
1759
7.47->50
2143
7.66996
2551
1039
6.94601
1427 7-2^333
1777
7.48268
7.67
|659
1049
6.95559
1429
7-2(>473
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
7.4»94'l
2203
7.60758
2593
7.86057
1063
1069
1087
1091
6.96885
6.97448
6.99118
6.99485
1447
1431
1453
M59
7.27725
7.28001
7-28139
7.28551
1801
1811
1823
1831
7.49610
7-50163
7.50824
7-51262
2207
2213
2221
2237
7.69939
7.702110
7.70571
7.71289
2609
2617
2633
7.86672
7.86978
7-87131 !
7.87588
1093
6.09668
1471
7.29370
1847
7.52132
2239
7.71378
2647
7.88118
1097
7-00033
1481
7.30047
1861
7. 5<2887
2243
7- 7i'557
2657
7.88495
1103
7.00579
1483
7.30182
1867
7-53209
2251
7.71913
2659
7.88571
1109
1117
7.01121
7.01840
1487
1489
7-30452
7.30586
1871
1873
7.53423
7.53530
2267
2269
7.72621
7.72709
2663
2671
7.887,21
7.89021
1123
7.02376
1493
7-30854
i877
7-53743
2273
7.72886
2677
7.89245
1129
7.02909
1499
7.31255
J^9
7.53849
228l
7.73237
2683
7-89409
1151
7.04839
I5II
7.32053
1889
7.5438o
12:287
7.73500
2687
7.80618
"53
1163
7.05012
7-05876
1523
1531
7.32844
7.33368
1901
,1907
7.55014
7.55329
2293
2297
7.73762
7.73936
2689
2693
7.89692
7-89841
1171
7.06561
1543
7.34148
I9U
7.55643
2309
7-74457
2699
7.90064
1181
7.07412
1-549
7.34536
I93i
7.56579
2311
7.74544
2707
7.90360
1187
7.07918
1553
7.34794
1933
7-56683
2333
7-75491
2711
7.00507
H93
7.08423
T559
7.35i8o
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
7.9W69
1217
1223
7.10414
7.10006
1579
1583
7.36455
7.36708
1979
1987
7.59035
7.59438
2351
2357
7.76260
7.765U
2731
2741
7-91242
7.91608
I22Q
1231
7.11396
7.H558
1597
1601
7.37588
7.37838
1993
1997
7.59740
7.59040
2371
2377
7.77107
7-77359
2749
2753
7.91899
7.92045
1237
7.12044
1607
7.38212
1999
7.60040
2381
7-77528
2767
7.90552
1249
1259
7.13010
7-13807
1609 7.3S337
1613 7.38585
2003
2OII
7.60240
7.60639
2383
2389
7.77612
7.77863
<2777
2789
7.92913
7-93344
1277
1279
7.15227
7.15383
1619
1621
7.33950
7.39080
2017
2027
7.60937
7.61431
2393
2399
7-78030
7.78281
2791
2797
7.93416
7.93630
1283
1289
7.15696
7.16162
1627
1637
7-39449
7.40062
2029
2039
7.61530
7.62021
2411
2417
7.78780
7.70028
2801
2803
7-93773
7-93
1291
1297
1301
7.16317
7.16781
7.17089
1657
.1663
1667
7.41276
7-41638
7.41878
2053
2063
2069
7.62706
7.63192
7.63482
24-M
2437
2441
7.79276
7.79852
7.80016
2819
2833
2837
7.944U
7.<U909
7.95050
1303
7.17242
1669
7.41998
2081
7.64060
2447
7.80262
2&43
7.95262
1307
1319
7.17549
7-18463
1693
1697
7.43426
7.43662
2083
2087
7.64156
7.64348
2459
2467
7.80751
7.81076
2851
2857
7-9:
7-95753
1321
7.18614
1699
7.43780
2089
7.64444
•2473
7.81319
2861
7.95893
132?
7.19068
1709
7.44366
2099
7.64922
2477
7.81480
2879
7.06520
ex
X
ex
X
ex
X
ex x
ex x
SMITHSONIAN TABLES
269
Natural Logarithms.
I
Logeu
u
LOQeU
u
LoOell
u
Logeu
u
Loflell
2887
7.96797
3323
8.10862
3709
8.21852
4129
8.32579
456i
8.42530
2897
7.97M3
3329
8.11043
3719
8.22I2I
4133
8.32676
4567
8.42661
2903
7-97350
3331
8.11-103
3727
8.22336
4139
8.32821
4583
8.43011
2909
7.97556
3343
8.11462
3733
8.22497
4i'5'3
8.33159
4591
8.43185
2917
7.97831
3347
8.11582
3739
8.2i2657
4157
8.33255
4597
8.43310
2927
7.98173
3359
8.11940
3761
8.23244
4159
8.33303
4603
8.43446
2959
7.985B2
336i
8.11999
3767
8.23403
4177
8.33735
4621
8.43837
2953
7.99058
3371
8.12296
3769
8.23456
4201
8.34'3o8
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
8.44613
3001
8.00670
3433
8.14119
3823
8.24879
4241
8.35255
4663
8.44741
3011
8.OIOO3
3449
8.14584
3833
8.251140
4243
8.3'5'303
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
3853
'8.25661
4261
8.35726
4703
8.45596
3041
8.01904
3467
8.15104
3^63
8.25920
4271
8.35960
4721
8.45978
3049
8.02257
3469
8.15162
3777
8.26282
4273
8.36007
4723
8.46020
3061
8.02650
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
3911
8.27155
4327
8.37263
4759
8.46779
3089
8.03500
3527
8.16820
3917
8.27308
4337
8.37494
4783
8.47282
3109
8.04206
3529
8.16877
3919
8.27359
4339
8.37540
4787
8.47366
3119
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
8.05102
3541
8.17216
393i
8.27665
4363
8.38092
4799
8.476l6
3163
8.05928
3547
8.17386
3943
8.27970
4373
8.38320
4801
8.47658
3167
8.06054
3557
8. a 7667
3947
8.2807*1
4391
8.38731
4813
8.47908
3169
8.06117
3559
8.17723
3967
8.28577
4397
8.38868
4817
8.47991
3181
8.06495
3571
8.18060
39®9
8.29130
4409
8.39HO
4831
' 8.48381
3187
8.06684
358i
8.18340
4001
8.29430
4421
8.39412
4861
8.48500
3191
8.06809
3583
8. 18396
4003
8.29480
4423
8.39457
48/1
8.49105
3203
8.07184
3593
8.18674
4007
8.29580
4441
8.39863
4877
8.49229
3209
8.07371
3607
8.19063
4013
8.29729
4447
8.39998
4889
8.49474
3217
8.07620
3613
8. 19229
4019
8.20879
4451
8.40088
4903
8.49/60
J2I71
8.07745
3617
8.19340
4021
8.20929
4457
8.40223
4909
8.49883
3229
8.07993
3623
8. 19506
4027
8.30078
4463
8.40358
4919
8.50086
3251
8.08672
3631
8. 19726
4049
8.30623
448i
8.40760
493'l
8.50330
3^53
8.08733
3637
8.19891
4051
8.30672
4483
8.40805
4933
8.50370
3->57
X.OS856
3643
8.20056
4057
8.30820
4493
8.41028
4937
8.50451
3259
-;i8
3659
8.20495
4073
8.3I.2U4
4507
8.41339
4943
8.50573
3271
8.09285
3671
8.20822
4079
8.31361
4513
8.41472
4951
8.50734
|999
8.10137
3673
8.20876
4091
8.31654
4517
8.41560
4957
8.50856
3301
oidB
3677
8.20985
4093
8.31703
4519
8.41605
4967
8.51057
3307
3691
8.21365
4099
8.31850
4523
8.41693
4969
8.51097
3.V3
8.10561
3697
8.21528
4111
8.32142
4547
8.42222
4973
8.51178
3319
8. 10742
3701
8.21636
4127
8.3253'!
4549
8.42266
4987
8.51459
e*
X
•*
X
ex
X
ex
X
ex
X
SMITHSONIAN TABLES
270
Natural Logarithms.
u
Log, u
u
LOQeU
u
Log,u
u
LOQ.U
u
Loo-u
4993
8.51579
5437
8.60008
5849
8.67403
6287
8.746241
6733
8.81478
4999
8.51699
5441
8.60172
5851
8.67437
6299
8.74815
6737
8.81537
5003
8.51779
5443
8.60209
5^7
8.67539
6301
8.74846
8.31893
5009
8.51899
5449
8.60319
5^'
8.67608
6311
8.75005
6763
8.81922
SOU
8.51939
5471
8.00722
5867
8.677IO
6317
8.75100
6779
8.82158
5021
8.52138
5477
8.6083'I
5869
8.67744
6323
8.75195
6781
.'i88
5023
8.52178
5<479
8.60868
5879
8.67914
6329
8.75200
6791
8.82335
5039
8.52496
5483
8.60941
589i
8.67948
6337
8.75416
6793
8.82365
5051
8.52734
5501
8.6X269
5897
8.68220
6343
•^•75 5"
6803
8.82512
5059
8.52892
5503
8.61305
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
636l
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
5IOI
8.53719
5531
8.61812
593U
8.69634
6379
8.76077
6857
8.83303
5107
8.53837
5557
8.62281
5987
8.09735
6389
8.76233
6863
8.83390
5U3
8.53954
5563
8.62389
6007
8.70068
6397
8.76358
6869
8.83477
5H9
8.54071
5569
8.62497
OOII
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
8.627112
6037
8.70566
6449
8.77168
6889
8.83768
5167
8.55005
5591
8.62891
6043
8.70666
645!
8.77199
6907
8.84029
5171
8.55082
5623
8.63462
6047
8.70/32
6469
8.77478
6911
8.84087
5179
8.55237
5639
8.63746
6053
8.70831
6473
8.77539
6917
8.84174
5i89
8.55430
5641
8.63782
6067
8.71062
6481
8.77663
6947
8.84607
5197
8.55584
5647
8.63888
6073
8.7II6I
6491
8.77817
6949
8.84635
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
5-73i
8.56236
5657
8.64065
6091
8.71457
6547
8.78676
6967
8.84894
5233
8.56274
5659
8.64100
6101
8.71621
6551
8.78737
6971
8.84951
5237
8.56350
5669
8.64277
6113
8.7I8I7
6553
8.78768
6977
8.85037
5261
8.56808
5683
8.64523
6121
8.71948
6563
8.78920
6983
8.85123
5273
8.57035
5689
8.64629
6131
8.72III
6569
8.79012
6991
8.85238
5279
8.57149
5693
8.64609
6133
8.72144
6571
8.79042
6997
8.85324
5281
8.57187
5701
8.64840
6143
8.72307
6577
8.79U3
7001
8.85381
5297
8.57490
57ii
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
5752
5323
8.57979
574i
8.65539
6197.
8.73182
6619
8.79770
7039
15922
5333
8.58167
5743
8.65574
6199
8.73-^M
6637
8.80042
7043
-)79
5347
8.58429
5749
8.65678
6203
8.73279
6653
8.80282
7057
T78
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
8.86489
5387
8.59174
5791
8.66406
6221
8.73569
6673
8.80582
7103
827
5393
8.59286
5801
8.66579
6229
8.73697
6679
8.80
7109
8.86912
5399
8.59397
5807
8.66682
6247
8.73986
6689
8.8
7121
8.87080
5407
8.59545
5813
8.66785
6257
8.74U6
6691
8.8,
7127
: 165
54U
8.59656
5821
8.66923
6263
8.74->4i
6701
8.81001
-193
5417
8-59730
5827
8.67026
6269
8.74337
6703
8.81031
7151
8.87501
5419
8.59767
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
ex
X
ex
X
e*
X
e*
X
e*
X
SMITHSONIAN TABLES
271
Natural Logarithms.
u
LflOeU
u
LOfleU
u
L™
u
LOQ,.U
u
Log,.u
7187
8.88003
7621
8.93866
8093
8.99875
8573
9.05637
9001
9.10509
7193
8.88086
7639
8.94IO2
8101
8.99974
8581
9-0573'!
9007
9.10576
7207
8.88281
7643
8.94155
8111
9.00098
8597
9.05917
9011
9. IO62O
7211
8.88336
7649
8.94233
8117
9.00172
8599
9.05940
9013
9. 10642
7213
8.88364
7669
8.94494
8123
9.00245
8609
9.06056
9029
9.I082O
7219
8.88447
7673
8.94546
8i47
9.00541
8623
9.06219
9041
9.10953
7229
8.88586
7681
8.94631
8161
9.00712
8627 9.06265
9043
9.10975
7237
8.88696
7687
8.94729
8167
9.00786
8629
9.06288
9049
9.II04I
7243
8.88779
7691
8.94781
8171
9-00835
8641
9.06427
9059
9-III5I
7247
8.88834
7699
8.94885
8179
9.00933
8647
9.06497
9067
9.IL240
7253
8.88917
7703
8.94937
8191
9.01079
8663
9.06682
9091
9.H504
7283
8.89330
7717
8.95118
8209
9.01299
8669
9-06731
9103
9.11636
7297
8.89522
7723
8.95196
8219
9.01420
8677
9-06843
9109
9.II702
7307
8.89659
7727
8.95248
8221
9.01445
8681
9.06889
9127
9.II899
7309
8.89686
7741
8.95429
8231
9.01566
8689
9.06981
9133
9.11965
7321
8.89850
7753
8.95584
8233
9.0I59I
8693
9.07027
9137
9.I20O9
73 3 1
8.89987
7757
8.95635
8237
9.01639
8699
9.07096
9151
9.I2I62
7333
8.90014
7759
8.95661
8243
9.01712
8707
9.07188
9157
9.12227
7349
8.90232
7789
8.96047
8263
9.01954
8713
9.07257
9161
9.12271
7351
8.90259
7793
8.96098
8269
9.02027
8719
9.07326
9173
7369
8.90504
7817
8.96406
8273
9.02075
8731
9.07464
9181
9. 12489
7393
8.90829
7823
8.96482
8287
9.02244
8737
9.07532
9187
9.12554
7411
8.91072
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
8.91610
7867
8.97043
8311
9-021534
8761
9.07807
9221
9. 12924
7457
8.911691
7873
8.97119
8317
9.02606
8779
9.08012
9227
9.12989
7450
8.91718
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.I3I4H
748i
8.92012
7883
8.97246
8363
9.03157
8807
9.08330
9257
9.I33I4
7487
8.92002
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
7400
8.92252
7919
8.97/02
8387
9.03444
8831
9.08602
9283
9- 13594
7507
8.92359
7027
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
8.92652
7949
8.98080
8429
9-03943
8861
9.08941
9323
9. 14024
7537
8.92758
7951
8.98105
8431
9.03967
8863
9.08964
9337
9.14174
754!
8.92811
7963
8.98256
8443
9.04109
8867
9.09009
9341
9.14217
7547
8.92891
7993
8.98632
8447
9.04157
8887
9.09234
9343
9.14238
8.92917
8009
8.98832
8461
9.04322
8893
9.09302
9349
9.14302
8.93049
8011
8.98857
8467
9-04393
8923
9.09639
9371
9.14538
-,076
8017
8.98932
8501
9-04794
8929
9.09706
9377
9.14602
1234
8039
8.99206
8513
9-04935
8933
9.09751
9391
9.I475I
7577
8.93287
8053
«• 003&)
8521
9.05029
8941
9.09840
9397
9-14815
8.93366
8059
6069
8-99454
8,99578
8527
8537
9.05099
9.05216
8951
8963
9.09952
9.10086
9403
9413
9.14878
9.14085
<U72
8081
8.99727
8539
9.05240
8969
9-10153
9419
9.15048
o&»
8089
8.99801
8.99826
8543
8563
9.05287
9-055211
8971
8999
9.10175
9.10487
9421
9431
9- 15070
9.15176
e*
X
ex
X
e*
X
e*
X
"
X
SMITHSONIAN TABLES
272
Natural Logarithms.
u
LofleU
u
LOO,,U
u
Looc.u
u
LOQ.U
U
Lofleu
9433
9.I5I97
9551
9.16440
9719
9.18184
9830
9. 19350
9967
9-20703
9437
9.15239
9587
9.l68l6
97 ji
9. 18204
9839
9.19411
9973
9.20764
9439
9.I526I
9601
9.16962
9733
9.1,^
9851
9- 19533
IOOOO
9.21034
9.15493
9613
9.17087
9739
9-18389
9857
IOOOOO
II-5I293
94' >3
9.I55I4
9619
9.I7I50
9743
9.18430
9859
9467
9-15557
9623
9.I7I9I
9749
9- 1&492
9871
9. 19736
1 9473
9.15620
9629
9.17"253
9767
9. 18676
9883
9479
9.15683
9631
9.17274
9769
9.18697
9887
9^19898
9491
9.I58IO
9643
9-17399
978i
9.18820
9901
9.20039
9497
9.15873
9649
9.I746I
9787
9.18881
9907
9.20100
95ii
9.16020
9661
9.17585
9791
9. 18922
9923
9.20261
9521
9.l6l26
9677
9. I775I
9803
9. 19044
9929
9.20322
9533
9.I625I
9679
9.I777I
9811
9.19126
9931
9-20342
9539
9.I63I4
9689
9.17875
9817
9.19187
994'i
9.20442
9547
9- 16398
9697
9.17957
9829
9. 19309
9949
9.20523
ex
X
ex
X
ex
X
ex
X
ex
X
Coefficients for Computing,
•
n2
6
Dili.
--(=!_,)
12\2 V
Difl.
n
n8
6
DHL
12\2 V
Diff.
o.oo
+O.OOOO
— o.oooo
0.25
+O.OIO4
— O.O2O2
M
.01
.0000
O
I
.0008
.26
.0113
9
.O2O9
i
.02
.0001
j
.0017
c
.27
.OI22
.0217
7
.03
.0002
j
.0025
O
Q
.28
.0131
.0224
/
8
.04
.0003
I
.0033
O
9
.29
.0140
10
.0232
7
0.05
+0.0004
+0.0042
0.30
+0.0150
—0.0239
.06
.0006
2
.0050
.31
.OIOO
.0246
.07
.0008
2
.0058
.32
.0171
.0253
7
.08
.0011
3
.0066
•33
.0182
.0260
.09
.0014
3
3
.0075
8
.34
.0193
I I
ii
.0267
7
7
O.IO
.11
.12
+0.0017
.0020
.0024
3
4
—0.0083
.0091
.0099
8
8
0-35
.36
• 37
+0.0204
.0216
.0228
12
IJ
—0.0274
.0281
.0287
6
.13
.0028
4
.0107
.38
.0241
13
.0294
A
.14
.0033
5
5
.0116
8
.39
.0254
13
13
.0300
\J
7
0.15
.16
+0.0038
.0043
5
^
—0.0124
.0132
8
8
0.40
• 41
+0.0267
.0280
13
—0.0307
.0313
6
6
.17
.18
.0048
.0054
6
.0140
.0148
8
.42
• 43
.0294
.0308
14
.0319
.0325
6
6
.19
.0060
7
.0155
8
.44
.0323
IS
.0331
6
O.20
+0.0067
—0.0163
Q
0.45
+0.0338
TC
—0.0337
6
.21
.22
.0074
.0081
7
.0171
.0179
O
8
•47
.0353
.0368
1 J
\6
.0343
.0348
.23
.0088
I
.0187
.48
.0384
.0354
.24
.0096
0
8
.0104
§
.49
.0400
if -0359
6
0.25
+0.0104
— O.O2O2
0.50
+0.0417
-0.0365
SMITHSONIAN TABLES
273
TABLE VI
THE GUDERMANNIAN
275
The Gudermannian.
u
gdu
<oFo'
gdu
"Fo'
u
gd u
«FO'
gdu
"F0'
o / //
a
o / //
a
o.ooo
O.OOO OOOO
I OOOO
0 OO OO.OO
206.26
O.O5O
0.049 9792
9988
2 51 48.95
206.OI
.001
.001 OOOO
I OOOO
o 03 26.26
206.26
.051
.050 9779
9987
2 55 H.95
206.0O
.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
0 20 37.58
206.26
.056
•055 9708
9984
3 12 24.80
205.94
.007
.006 9999
oooo
o 24 03.84
206.26
.057
.056 0692
9984
3 15 50.73
205-93
.008
.007 9999
I OOOO
o 27 30.10
206.26
.058
.057 o675
9983
3 19 16.66
205.92
.009
.008 9999
I OOOO
o 30 56.36
206.26
.059
.058 9658
9983
3 22 42.57
205.91
0.010
0.0099998
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
9981
3 29 34.36
205-88
.012
.on 9997
9999
o 41 15.12
2O6.25
.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
9978
3 50 09.41
205.80
.018
.017 9990
9998
I 01 52.57
206.23
.068
.067 9477
9977
3 53 35.21
205-79
.019
.018 9989
9>98
i 05 18.80
206.23
.069
.068 9453
9976
3 57 00.99
205-77
O.O20
0.019 9987
9998
i 08 45.02
2O5.22
0.070
0.069 9429
9976
4 oo 26.76
205.76
.021
.020 0985
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
2O6.2I
.072
.071 9379
9974
4 07 18.25
205-73
.023
.022 9080
9997
i 19 03.67
2O6.2I
.073
.072 9352
9973
4 10 43.08
205.72
.024
.023 9977
9997
I 22 29.88
2O6.2I
.074
.073 9326
9973
4 14 09.68
205.70
0.025
0.024 9974
9997
I 25 56.08
206.20
0.075
0.074 9298
9972
4 17 35.38
205.69
.026
.025 0971
9997
I 29 22.28
2O6.20
.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 9963
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
O.030
0.029 9955
9995
i 43 07.02
2O6.I7
0.080
0.079 9148
9968
4 34 43.61
205.61
.031
•030 9950
9995
i 46 33- J9
206.17
.081
.080 9116
9967
4 38 09.21
205.59
.032
•031 9945
9995
i 49 59-35
2O6.I6
.082
.081 9083
9966
4 41 34.79
205.57
.033
.032 9940
9995
i 53 25.50
206.15
.083
.082 9049
9966
4 45 00.36
205.56
• 034
•033 9935
9994
i 56 51-65
206.I5
.084
.083 9014
9965
4 48 25.90
205.54
0.035
0.034 0929
9994
2 oo 17.79
2O6.I4
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 i6.95
205.50
.037
.036 0916
9993
2 07 10.06
206.12
.087
.086 8905
9962
4 58 42.44
205-49
.038
.037 9909
9993
2 IO 36.18
2O6.I2
.088
.087 8866
996l
5 02 07.92
205.47
•039
.038 9901
9992
2 14 O2.29
2O6. 1 1
.089
.088 8827
9961
5 05 33.38
205.45
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
206.07
.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
•045 0838
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 0816
9088
2 44 56.91
206.03
.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-) -\
u; s Ch U
2tan-'(eu)-90°
wsechu
u
2tan-'(e«)~
wsechu
atan-Keuh-SO0
<» sech u
SMITHSONIAN TABLES
276
The Gudermannian.
u
gd u
•ft
gd u
•w
u
gdu
«F,/
gdu
«FO'
o / //
0
o / //
m
O.IOO
0.099 8337
9950
5 43 12.19
205.24
O.I5O
0.149 4406
9889
8 33 44-35
203.97
.101
.100 8287
9949
5 46 37-42
205.22
-I5I
.150 4294
989?
8 37 08.30
.IQ2
.IO I 8236
9948
5 50 02.62
205.20
•15-'
.151 4181
9886
8 40
203.90
.103
. 102 8184
9947
5 53 27.81
205.18
.153
.152 4065
9884
8 43
203.87
.104
.IO3 8l3O
9946
5 56 52.97
205.15
• 154
.153 3949
9883
8 47
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
<yv-s
8 57 31-35
203.75
.108
.107 7907
9942
6 10 33.42
205.07
.158
•157 3467
9876
9 oo 55.08
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
203.65
.in
.110 7728
9939
6 20 48.52
205.00
.161
.160 3089
9872
9 u 06.09
.112
.in 7666
9938
6 24 13.51
204.98
.162
.161 2960
9870
9 14 29.69
203.59
•113
.112 7003
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.IIS
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 7^71
9931
6 44 42.06
204.84
.168
. 167 2153
9861
9 34 50.62
203.39
.119
.118 7201
9930
6 48 07.78
204.81
.169
.168 2012
9859
9 38 13.99
203.35
O.I2O
0.119 7130
9928
6 51 32.59
204.79
0.170
0.109 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 I58l
9854
9 48 23.90
203.25
• 123
.122 O9IO
9925
7 01 46.84
204.71
.173
.172 1434
9852
9 51 47-U
203.22
.124
.123 6834
9924
7 05 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 H36
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
IO 12 O5.8O
203.00
0.130
0.129 6354
9916
7 25 39.22
204.53
0.180
0.179 0358
9&40
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 14.05
202.90
•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 5918
9910
7 42 41-55
204.40
0.185
0.183 9537
9831
10 32 23.17
202.78
.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
.!87
.185 9196
9828
10 39 08.66
202.71
.138
.137 5641
0906
7 52 54.62
204.32
.188
. 186 0022
9826
10 42 31-35
202.67
•139
.138 5545
9904
7 56 18.93
204.29
.189
.187 8847
9824
10 45 54-01
202.63
O.I40
0.139 5449
9903
7 59 43.20
204.26
O.IOO
o. 188 8670
9822
10 49 16.62
202.60
.141
•140 5351
9901
8 03 07.45
204.23
.191
. 189 8492
9820
10 52 39.20
202 . 56
.14-'
.141 5252
9000
8 06 31.66
204.20
.192
.190 8311
9818
10 56 01.74
•143
•142 5151
9899
8 09 55.85
204.17
.193
.191 8129
98i7
10 59 24.24
J02.48
.144
.143 5049
9897
8 13 20. 01
204.14
.194
. 192 7944
9815
u 02 46.71
202.44
0.145
0.144 4946
9896
8 16 44.14
204.12
0.195
0.193 7758
9813
ii 06 09.13
202.40
.146
.145 4841
9894
8 20 08.24
204.09
.196
.194 75/0
9811
ii 09 .
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
u 19 38.43
202 . 25
0.150
0.149 4406
0889
8 33 44-35
203.97
O.2OO
0.198 6798
0803
u 23 00.66
202.21
u
2tan-1(e»)-£
<•> sech u
2 tan-He")-*)0
w sech u
U
2tan-1(e«)~
<»sechu
2tan~1(e")-900
<» sech u
SMITHSONIAN TABLES
277
The Gude rmannian.
u
gd u
»F0'
gdu
«F</
u
gd u
«F0'
gd u
»IV
O / //
//
O / //
~
0.2OO
o. 108 6798
9803
ii 23 00.66
202.21
0.250
0.247 4358
9695
14 10 37.30
199.98
.2OI
.199 66oi
9801
u 26 22.85
202.17
.251
.248 4052
9693
14 13 57.26
199.93
.202
.200 6401
9799
u 29 44-99
2O2.I3
.252
.249 3744
9691
14 17 17.16
199.881
.203
.201 62OO
9797
u 33 07.10
2O2.O9
.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
2O2.OI
0.255
0.252 2805
9683
14 27 16.59
199.74
.206
.204 5583
9792
ii 43 13.18
201.96
.256
.253 2488
9681
14 30 36.31
199.69
.2O7
.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 1192
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
.210 420
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
.200 9857
9661
14 57 12. 18
199.29
0.215
0.213 3625
9773
12 13 29.17
201.59
0.265
0.261 95l8
9659
15 oo 31-43
199.24
.216
.214 3397
9771
12 l6 50.74
201.54
.266
.262 9175
9656
15 03 50.63
199.19
.217
.21-5 3167
9769
12 2O 12.20
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
109.08
.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 778l
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 4I.7I
201.20
.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
158.71
.226
.224 1003
9750
12 50 24.01
201. II
.276
.272 56l2
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 O499
9746
12 57 06.14
2OI.O2
.278
.274 4868
9626
15 43 36.08
198.55
.229
.227 0243
9743
13 oo 27.13
200.97
-279
.275 4493
9623
15 46 55-49
198.50
0.230
0.227 9986
9741
13 03 48.08
200.93
0.280
0.276 4114
9620
15 50 13-95
108.45
.231
.228 9726
9739
13 07 08.99
200.88
.281
.277 3734
9618
15 53 32.36
198.38
.232
.229 9464
9737
13 10 29.85
200.84
.282
.278 3350
9615
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
0.235
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 8l2O
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 0093
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
0.240
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
.239 6719
97U
13 43 55-88
200.37
.292
.287 9368
9588
16 29 51.23
197.77
.243
.240 0432
9712
13 47 16.23
200.32
.293
.288 8955
9586
16 33 08.97
197.72
.244
.241 6143
9710
13 50 36-53
200.27
.294
.289 8539
9583
16 36 26.66
197.66
0.245
0.242 5851
9707
13 53 56.77
200.23
0.295
0.290 8121
9580
16 39 44.30
197.60
.243 5557
9705
13 57 16.98
200.18
.296
.291 7699
9577
16 43 01.87
197.55
• -M7
.244 5261
9703
14 oo 37-13
200.13
.297
.292 7275
9575
16 46 19.39
197.49
.248
.245 4962
9700
H 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
9509
16 52 54.26
197.38
0.250
0.247 4358
9695
U 10 37.30
199.98
0.300
0.295 5987
9566
16 56 u. 60
197.32
u
2tan-»(e»)-l
<"$ech u
2tan-1(e»)-900
"tech u
u
2tan-'(e»0-j
wsechu
2tan-](e«)-900
wsech u
SMITHSONIAN TABLES
278
The Gudermannian.
u
gdu
*r
gdu
<H
u
gdu
*
gdu
.*<
0.300
0.295 5987
9566
o / //
16 56 1 1. 60
197.32
0.350
0-343 0655
9417
19 39
.301
.296 5552
9563
16 59 28.89
197.26
•351
•344 0071
94'4
36.SS
.302
95'"
17 02 46.13
197.20
• 352
•14!
194.11
.303
.298 4673
9558
17 06 03.30
197.15
.353
.345 8893
.304
.299 4229
9555
17 09 20.42
197.09
.354
.346 8299
9405
18.80
0.305
0.300 3783
9552
17 12 37.48
197-03
0.355
0-347 7702
0401
19 55
.306
•301 3334
9549
17 15 54.48
196.97
,356
.348 7101
.307
.302 2882
9547
17 19 11.42
196.91
•357
.349 6498
9395
20 02 00.45
.308
.303 2427
9544
17 22 28.30
196.85
.358
•350 5891
9392
20 05
.309
.304 1969
9541
17 25 45-12
196.79
• 359
.351 5281
9388
20 08 27.88
0.310
0.305 1509
9538
17 29 01.89
196.74
0.360
0.352 4668
9385
2O II 4I.5O
193.58
.311
.306 1045
9535
17 32 18.60
196.68
.361
•353 4052
9382
JO 14 55-05
.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
20 21 21.95
193.38
.314
.308 9638
9526
17 42 08.36
195.50
.364
.356 2183
9372
20 24 35.30
193.32
0.315
.316
0.309 9163
.310 8685
9524
9521
17 45 24.83
17 48 41-23
196.44
196.38
0.365
.365
0.357 1554
.358 0921
9309
9366
20 27 48.59
20 31 01.80
193.25
193.18
.317
.311 8204
95i8
17 51 57o8
196.32
.367
.359 0285
9362
20 34 14.95
.318
.312 7721
9515
17 55 13-87
196.26
.363
.359 9646
9359
20 37 28.03
193.05
.319
.313 7234
9512
17 58 30.10
I96.2O
.369
.360 9003
9356
20 40 41.04
0.320
0.314 6744
9509
18 01 46.26
196.14
0.3/0
0.361 8358
9352
20 43 53.98
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
I96.OI
• 37^
.363 7056
9346
20 50 19.66
.323
.317 5258
9500
18 u 34.40
195-95
• 373
.364 6400
9343
20 53 32.40
192.70 |
.324
.318 4757
9497
18 14 50.32
I95.89
•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 44U
9332
21 03 IO.2O
192.50
.327
.321 3235
9488
18 24 37.72
195.71
.377
.368 3743
9329
21 06 22.66
.328
.322 2721
9485
18 27 53.40
195.65
.378
.369 3071
9326
21 09 35-05
.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
IQ2.22
.331
.325 1163
9476
18 37 40.06
195.46
.381
•372 1033
9316
21 19 11.82
.332
.326 0638
9473
18 40 55-49
195.40
.382
•373 0347
9312
21 22 23.93
.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
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
9461
18 53 56.57
195.15
.386
.376 7569
9299
21 35 11.68
191.80
•337
•330 7965
9458
18 57 11.69
195.08
.387
.3776866
9295
21 38 23-45
igl .73
• 338
.331 7422
9455
19 oo 26.74
195.02
.388
.378 6159
21 41 35-14
•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
K) 06 56.65
194.89
0.390
0.380 4736
9285
21 47 58.31
191.51
•341
•334 5772
9445
19 10 11.50
194.83
.391
.381 4019
9_>Si
21 51 09.79
191.44
.342
•335 52i6
9442
19 13 26.30
194.76
.392
.382 3299
9278
21 54 _'i .JO
• 343
.336 4657
9439
19 16 41.03
194.70
• 393
.383 25/5
9275
21 57
191.30
•344
•337 4095
9436
19 19 55.70
194.63
• 394
.384 1848
9271
22 OO 43.80
191.23
0-345
0.338 3529
9433
19 23 10.30
194-57
0.395
0.385 III7
9268
22 03 54-99
I9I.I6
.346
•339 2961
9430
19 26 24.84
194.51
.396
.386 0383
9264
22 O7 O6. 1 1
191.09
•347
.340 2389
9427
19 29 39.31
194-44
• 397
.3869645
9261
22 IO 17.16
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.O4
190.87
0.350
0.343 0655
9417
19 39 22.34
194.25
0.400
0.389 741 1
9250
22 19 49.88
190.80
u
jr
<•> sech u
2tan~1(eu)-900
wsechu
u
2*n-(eu)-;
•osechu
t**WF
i» sech u
SMITHSONIAN TABLES
279
The Gudermannian.
u
gd u
-PC'
gd u
O.FO'
u
gd u
«F0'
gd u
"F0'
o / //
//
o / //
//
0.400
0.389 74"
9250
22 19 49.88
190.80
0.450
0.435- 5388
9066
24 57 i6.34
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
!86.85
.403
.392 5146
9240
22 29 21.04
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 3618
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 97i8
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 1209
9222
22 45 13.92
100.21
.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
IOO.O6
0.460
0.444 586l
0028
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 54.18
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
OOl6
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 4149
9189
23 13 42.83
189.54
.467
.450 8960
9OOI
25 50 03.08
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 6954
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
189.17
.472
• 455 39U
8981
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
I89.O2
•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
.4580806
8965
26 17 51.54
184.92
.427
.4U 586i
9153
23 45 14.52
188.79
• 477
•459 8769
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
9M5
23 Si 3L95
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
9134
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
.486
.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 7009
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 IO.O8
187.71
.491
.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
8893
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
•431 9092
goto
24 44 47.67
187.32
.496
.476 8305
8885
27 19 13.36
183.26
•117
.432 8172
9078
24 47 54.96
187.24
• 497
.477 7i88
8880
27 22 16.57
183.17
.448
•433 7248
9074
24 51 02.16
187.17
.498
.4786066
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 5368
9066
24 57 16.34
187.01
0.500
0.480 3811
8868
27 31 25.71
182.92
u
2t«n-'(e«)-2
«•» sech u
2tan-'(e«>-900
osech u
u
2 tan-He")—
w sech u
2tan-1(e")-90°
wsechu
SMITHSONIAN TABLES
280
The Gudermannian.
-
gd u
«F0'
gdu
•Fo'
u
gd u
gdu
-F '
o / //
//
Q 1 II
a
1 0.500
0.480 3811
8868
27 31 25.71
182.92-
0.550
0.524 1096
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 7048
8644
30 10
178.30
.504
.483 <J25i
8852
27 43 36.71
182.58
•554
.527 6590
8640
30 13 57.48
178.21
1 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
•550
.529 3861
8631
30 19 53-72
178-03
.507
.486 5787
8839
27 52 44.07
182.33
• 557
.530 2400
8627
30 22 5L7I
.508
.487 4625
8835
27 55 46.35
182.24
!S58
• 531 niS
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
1 0.510
0.489 2287
8827
28 01 50.66
182.07
0.560
0.532 8351
8614
30 31 45.12
177.67
.511
.490 1 1 12
8823
28 04 52.69
181.98
.561
•533 6962
8609
30 34 42.75
I77o8
.51-'
•490 9933
8819
28 07 54.63
181.00
.562
•534 5569
8605
30 37 40.28
177.49
.513
.491 8749
8814
28 10 56.48
181.81
063
•535 4172
8601
30 40 37-73
177.40
i oM
.492 7562
8810
28 13 58.25
181.73
.564
.536 2771
8596
30 43 35.08
I7/.3I i
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
1/7.04
.518
.406 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
.5^9
-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 01 17.30
176.76
- .521
.498 9131
8781
28 35 08.22
181.12
• 571
.542 2836
8565
31 04 14.02
! .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
I -524
•501 5456
8768
28 44 11.20
180.86
• 574
.544 8512
8552
31 13 03.63
1/6.40
0.525
0.502 4222
8764
28 47 12. 01
180.77
0-575
0.545 7062
8548
31 15 59.98
176.31
1 .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 4M8
8539
31 21 52.41
176.12
1 .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 7900
8743
29 02 14.80
180.34
0.580
0.549 9744
8525
31 30 40-37
175.85
I .53i
.507 6731
8739
29 05 15.09
180.25
.581
.550 8267
8521
31 33 36.17
175.76
1 -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
j -534
.510 2928
8726
29 14 15.45
179-99
.584
•553 3810
8508
31 42 23.03
175.48
0.53'5
0.511 1652
8722
29 17 15.39
179.00
0.585
0.554 2315
8503
31 45 18.46
175-39
i .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 93U 8404
31 51 09.05
175.20
! .538
.513 7798
8709
29 26 14.69
179.63
.588
.556 7804; 8490
31 54 04.21
175.11
! -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
•5i6 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 0106
8467
32 08 38.61
174.65
•544
•5i8 0974
8683
29 44 10.91
179.10
• 594
.561 8661
8403
32 u 33.21
I74o5
0-545
0.519 8655
8679
29 47 09.96
179-01
0.595
0.562.7122
8458
3-' 14 27.71
174.46
•54(3
•520 7332
8675
29 50 08.93
178.93
.596
.563 5577
8454
32 17 22.13
174.37
•547
.521 6004
8670
29 53 07.81
178.84
• 597
.564 4029
8449 32 20 10.45 174.27
.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
0.600
0.566 9356
8436
32 28 58.85
173.99
I u
2 tan-He")- £
wsechu
2tan-He«)-90°
«•» sech u
u
2tan-He")-£
<o sech u
atan-Keuh-SO0
<» sech u
SMITHSONIAN TABLES
28l
The Gudermannian.
u
gd u
™
gdu
*
u
gdu
»Fo'
gdu
.F,
0.600
0.566 9356
8436
32°28' 58.85
173.99
0.650
0.6o8 5398
8205
o / //
34 52 00.34
109.24
.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
,6lO 1798
8195
34 57 38.62
I69.O4
1 .603
.569 4642
8422
32 37 40.42
173.71
.653
.610 9991
8191
35 oo 27.61
I68.9T
.604
.570 3061
8417
32 40 34.09
173.62
.654
.6ll 8179
8l86
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
8177
35 08 54-01
168.66
.607
.572 8293
8404
32 49 14.52
173.34
.657
.614 2716
8172
35 II 42.62
168.56
.608
.573 6694
8399
32 52 07.82
173-24
.658
.615 0886
8167
35 14 31.13
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
8153
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
35 31 20.14
167.88
0.615
0.579 5377
8367
33 12 18.22
172.59
0.665
0.620 7941
8134
35 34 07.97
I67.7S
.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
I67.I9
.622
.585 3834
8335
33 32 24.00
171.92
.672
.626 4764
8101
35 53 40.03
167.09
.623
.586 2167
8330
33 35 15-87
171.83
.673
.627 2863
8096
35 56 27.08
167.00
.624
.587 0495
8326
33 38 07.65
171.73
.674
.628 0956
8091
35 59 14-03
I66.QO
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
8208
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 7480
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.IO
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
8339
8266
34 15 12.10
170.49
.687
.638 5743
8029
36 35 15.41
165.62
.638
.598 6603
8261
34 18 02.54
170.39
.688
•639 3770
8025
36 38 00.08
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
170.20
0.690
0.640 9810
8015
36 43 31-82
165.32
•'Ml
1 3^4
8247
34 26 33.29
170.11
.691
.641 7823
8010
36 46 17.09
165 . 22
.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
.603 6084
8233
34 35 03.17
169.82
.694
.644 1832
7996
36 54 32.32
164.93
0.604 4315
8228
34 37 52.94
169.72
0.695
0.644 9825
7991
36 57 17.20
164.83
.605 2541
8224
34 40 4a.0i
169.62
.696
.645 7814
7986
37 oo 01.98
164.73
.606 0762
8219
34 43 32.19
169.53
.697
.646 5798
798i
37 02 46.66
104. (>3
8214
34 46 21.67
169.43
.698
•647 3777
7977
37 05 31.24
164.53
.607 7190
8210
34 49 11.05
169.33
.699
.648 1751
7972
37 08 15.72
104-43
0.650
0.608 5398
8205
34 52 00.34
169.24
0.700
0.648 9721
7967
37 ii 00.10
164.33
u
2^-^-1
wsechu
"--'""-^
<•> sech u
u
2tan-'(e«)~
wsechu
2tan-He")-90°
wsech u
SMITHSONIAN TABLES
282
The Gudermannian.
u
gd u
*F,/
gdu
•IV
u
gdu
«F0'
gdu
o / //
tl
o /
//
0.700
0.648 9721
7967
37 u 00.10
164.33
0.750
0.688 2014
7724
39 25 5L72
159.32
.701
.649 7685
7962
37 13 44.38
164.23
.751
.688
7719
39 28 30.98
.702
.650 5645
7957
37 i'> 28.57
164.13
•75-'
.689 7451
7714
39 31 10.15
.703
.651 3OOO
7953
37 19 12.65
• 753
.690 5163
7709
39 33 49-21
.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
0.602 0572
7699
39 39 07.04
158.81
.706
.653 7436
7938
37 27 24.31
163-74
.756
.692 8269
7694
39 41 45.8o
158.71
.707
.654 5372
7933
37 30 07.99
163.64
• 757
.693 596i
7690
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
7914
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 .v
I58.IO
.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 H.OO
162.94
.764
.6989667
7655
40 02
i57-</>
0.715
0.660 8684
7895
37 51 53.89
162.84
0.765
0.699 7319
7650
40 05 30.07
I57.8o
.716
.661 6576
7800
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
7040 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
762O 4O 21 I5.OI
I57-I9
.-22
.666 3827
7861
38 10 51.30
162.14
.7/2
.705 0750
76l6 40 23 52.15
157.08
.723
.667 1685
7856
38 13 33.39
162.04
.773
.705 8363
76ll UO 26 29.l8
156.08
.724
•667 9539
7851
38 16 15.37
161.94
• 774
.706 5971
7006
40 29 06. i i
156.88
0.725
0.668 7387
7846
38 18 57.26
161.84
0.775
0.707 3574
7601
40 31 42.94
156.78
.726
.669 5231
7841
38 21 39.05
161.74
.776
.708 i 173
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 0003
7831
38 27 02.32
161.54
.778
.709 6354
7586:40 39 32.82
.729
.671 8732
7827
38 29 43.80
161.43
• 779
•710 3938
758i
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 45o6
•731
•673 4376
78i7
38 35 06.47
161.23
.781
.711 9000
7571 40 47 21.77
156.17
•732
.674 2100
7812
38 37 47.65
161.13
.782
.712 6659
7566 40 49 57.89
156.06
• 733
.675 oooo
7807
38 40 28.74
161 .03
.783
.713 4223
7561 40 52 33-90
155.96
•734
.675 7804
7802
38 43 09.72
160.93
.784
.714 1781
7556
4o 55 09.81
155.86
0./35
0.676 5604
7797
38 45 50.60
160.83
0.785
0.714 9335
7551
40 57
.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
.738
.678 8974
7783
38 53 52.64
160.53
.788
.717 1967
7537 4i 05 32-44
• 739
.679 6754
• 7778
38 56 33-12
160.43
.789
.717 9501
753-'
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
• 741
.681 2300
7768
39 oi 53.77
160.23
.791
.719 4554
7522 41 13 18-33
ISS.IS
•74-'
.682 0065
7763
39 04 33.95
160.13
.792
.720 2073
75'7 41 15 .:
155.04
•743
.682 7826
7758
39 07 14-02
160.02
• 793
.720 9588
75 u 41 18 _
•744
.683 5582
7753
39 09 54-00
159.92
.794
.721 7097
7507
41 Ji 03.31
154.84
0.745
0.684 3333
7748
39 12 33.87
159-82
0.795
0.722 4601
7502
41 jj? 38.10
154-74
.746
.685 1079
7744
39 15 13.64
159.72
.796
.723 2101
7497 41 26 i
•747
.685 8820
7739
39 17 53.31
• 797
9595
7492
41 28 47.30
.748
•749
.686 6556
.687 4287
7734
7729
39 20 32.88
39 23 12.35
[59.52
159.42
.798
• 799
.724 7084
.725 45<J9
7487
7482
41 3i
4i 33 56.22
154.43
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-Keu)-£
wsechu
2ten-Ke<1)-900
wsechu
u 2tan~'(eu)-2 *»sechu
2tan-1(eu)-9Q0
*» sech u
SMITHSONIAN TABLES
283
The Gudermannian.
u
gd u
•FO'
gd u
«Fo'
u
gd u
»F0'
gdu
«F0'
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
72l8
43 47 5L34
148.88
.803
.804
.728 4457
.729 1916
7462
7457
41 44 I2-7I
41 46 46.57
153-92
I53.8I
.853
.854
.765 1338
.765 8548
7213
7208
43 50 20.17
43 52 48.89
148.78
148.67
0.805
0.729 9371
7452
41 49 20.34
I53-/I
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
I48.47
.807
.731 4266
744-'
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
71/8
44 07 39.o8
148.06
.811
•734 3995
7422
42 04 40.76
153.10
.861
.770 8881
7173
44 10 07.08
147-95
.812
.735 1414
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
147.04
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
U7.33
.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 02.25
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 748i
7Il8
44 37 08.32
146.82
.823
.743 2704
7363
42 35 10.53
151.86
.873
•779 4596
7H3
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 0098
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
151.14
0.880
0.784 4264
7078
44 56 39.56
145.99
.831
.749 1446
7323
42 55 22.16
I5L04
.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 01 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 ii 13.66
145.37
.837
•753 5292
7293
43 10 26.56
150.42
.8&7
.789 3687
7043
45 13 38.59
145-27
.838
•754 2582
43 12 56.93
150.32
.888
.700 0728
7038
45 16 04.21
I45-I7
.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
I5O.I2
0.890
0.791 4794
7028
45 20 54.34
144.96
.756 4423
7273
43 20 27.43
I50.OI
.891
.792 1819
7023
45 23 19.25
144-86
•757 1694
7268
43 22 57.39
149.91
.892
.792 8839
7018
45 25 44.05
144.76
.757 8959
7263
43 25 27.25
I49.8I
.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
,848
.760 7970
• 7''i 5211
7243
7238
43 35 25.65
43 37 55.00
149-39
149.29
.897
.898
.796 3867
.797 0857
6993
6988
45 37 46.54
45 40 10.73
144.24
144.14
.762 2446
7233
43 40 24.24
149. 19
.899
•797 7843
0983
45 42 34.8i
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
u
2Un-Ke«)-2
<» tech u
2tan-1(e«)-900
wsechu
u
2tan-'(e«)~
wsechu
2tan-1(e")-90°
<» sech u
SMITHSONIAN TABLES
284
The Gude rmannian.
II
gd u
»Fo'
gdu
U>Fo'
u
odu
wF0'
gdu
•Fo'
o i ii
II
0.900
0.79^
6978
45 44 58.80
0.950
0.832 7479
6728
138^78
.901
.799 1798
6973
45 47
143.83
.951
.833 4205
47 45 05.31
138.68
.902
.799 8769
6968
45 49 46.45
143.72
.952
47 47
138.58
.903
.800 5734
6963
45 52 10.12
•953
47 49
.904
.801
6958
45 54 33- <V
143.53
•954
•835 4353
6709
00.89
0.905
0.801 9650
6953
45 56 57-^
M3- -12
0.955
0.836 1059
6704
47 54
138.27
.906
.802 6601
6948
45 59 20.52
143.31
.956
.836 7760
6699
37-44
.803 3546
46 01 43-78
143.21
•957
.837 4456
138.07
.908
.804 0487
6938
46 04 06.94
143-11
.958
.838 1147
48 oi
.909
.804 7422
6933
46 06 30.00
143.00
•959
.838 7833
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
.911
.806 1278
6923
46 ii 15.79
142.80
.961
.840 1191
6674
48 08 07.00
137-66
.912
. 8198
6918
46 13 38.54
142.69
.962
.840
6669
48 10 24.60
'
.913
.807 SIM
6913
46 16 01. 18
M2.59
.963
.841 45-78
48 12 42.10
.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
.809 5830
6898
46 23 08.49
142.28
.966
.843 4497
6649
48 19 33-99
137.14
.810 2726
6893
46 25 30.72
142.18
.844 1144
6644
48 21 51.09
137.04
.918
.810 9616
6888
46 27 52.85
142.08
.844 7785
6639
48 24 08.08
.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
136.73
.921
.813 0258
6873
46 34 58.61
141.77
.971
.846 7680
6624
48 30
136.63
.922
.813 7129
6868
46 37 20.33
141.66
.972
.847 4301
48 33 15.01
136.53
.923
.$14 3994
6863
46 39 41.94
141.56
•973
.848 0918
6614
48 35 31-49
136.43
.924
.815 0855
6858
46 42 03.45
141.46
• 974
.848 7530
6609
48 37 47.87
'
0.925
0.815 7710
6853
46 44 24.85
UI.35
0-975
0.849 4136
6604
48 40 04.14
136.22
.926
.816 4561
6848
46 46 46.16
I4L25
.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 7056
6579
48 51 23.97
.931
.819 8739
6823
46 58 31.13
140.74
.981
.853 3673
48 53 39.63
I35.6I
-93-'
.820 55'x)
6818
47 oo 51.81
140.63
.982
.854 0245
48 55
•933
.821 2375
6813
47 03 12.40
140.53
.983
.854 6812
6565
48 58
135.40
•934
.821 9186
6808
47 05 32.88
140.43
.984
.855 3374
6560
49 oo
135.30
0.935
0.822 5992
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
135-10
• 937
.823 9588
6793
47 12 33-70
140. 12
.987
-857 3030
6545
40 07 11.44
135.00
.938
.824 6379
6788
47 U 53-77
I4O.02
.988
.857 9573
6540
49 09 26.39
134.89
•939
.825 3164
6783
47 17 13-74
139.91
.989
.858 61 10
49 II 41.23
134.79
0.940
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
.942
.827 3492
6768
47 24 13.02
I39.6I
.992
.860 5692
6520
49 18 25.15
134.49
•943
.828 0257
6763
47 26 32.57
139.50
•993
.86l 22IO
6515
49 20 39o8
•944
.828 7018
6758
47 28 52.02
139.40
• 994
.851
6510
53.92
0.945
0.829 3774
6753
47 31 11.37
139.30
0.995
0.862 5230
08.15
I34.I8
.946
.830 0525
6748
47 33 30.62
139.20
.996
.863 1733
6500
I35.o8
•947
.830 7271
6743
47 35 49.76
139.09
•997
.863 8231
36.30
133.08
.948
.831 4012
6738
47 38 08.80
138.09
.998
.864 4724
6400
49 .u 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
1.000
0.865 7<595
6481
49 36 17.77
133.67
u
2tan-i(e»)-|
<•» sech u
2tan-He°)-900
<»sechu
u
2tan-'(e<0~
wsechu
2tan~1(e")-900
w sech u
SMITHSONIAN TABLES
285
The Gude rmannian.
u
gd u
wFo'
gdu
wF</
u
gd u
«F0'
gdu
o>F0'
o / //
//
O 4 //
//
I.OOO
0.865 7695
6481
49 36 17.77
133.67
1.050
0.897 5576
6235
Si 25 34-55
128.61
.001
.866 4173
6476
49 38 3L39
133.57
.051
.898 1809
6230
51 27 43.11
128.51
.002
.867 0646
6471
49 40 44.91
133-47
.052
.898 8037
6225
51 29 51.57
128.41
.003
.867 7H4
6466
49 42 58.33
133-37
.053
.809 4260
6221
51 3i 59.92
128.31
.004
.858 3578
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
I28.II
.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 51 50.98
132.96
.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
1. 010
0.872 2254
6431
49 58 29.40
132.65
i. 060
0.003 7685
6187
51 46 55.63
127.61
.Oil
.872 8682
6426
50 oo 42.00
132.55
.061
.904 3869
6182
51 49 03.18
127.51
.012
.873 5106
6421
50 02 54.50
132.45
.062
.005 0048
6177
51 51 10.64
127.41
.013
.874 1525
6416
50 05 06.90
132.35
.063
.005 6222
6172
51 53 18.00
127.31
.014
.874 7939
6412
50 07 19.20
132.25
.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
6l62
51 57 32.41
127.11
.016
.876 0752
6402
50 ii 43.49
132.04
.066
.907 47i6
6157
51 59 39.46
127.01
.017
.876 7152
6397
50 13 55-49
I3L94
.067
.908 0871
6153
52 01 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
I3L74
.069
.909 3167
6143
52 06 00.03
126.71
i. 020
0.878 6320
6382
50 20 30.86
131.64
1.070
0.009 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
6l23
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 0937
6114
52 18 38.46
I26.II
.026
.882 4524
6353
50 33 38.87
I3L03
.076
.913 6048
6109
52 20 44.52
I26.OI
.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
I25.8I
.029
.884 356o
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 H.o6
130.12
1.085
0.919 0833
6065
52 39 34-54
125.11
.888 7805
6304
50 55 24.13
130.02
.086
.919 6896
6061
52 41 39-6o
125.01
.889 4106
6209
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 01 53-74
129.72
.089
.921 5056
6046
52 47 54.i8
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
• 043
.892 5538
.893 1810
6274
6269
51 08 22.44
51 10 31.81
129.42
129.32
.092
•093
.923 3173
.923 9203
6032
6027
52 54 07.87
52 56 12.24
124.41
124.32
.044
.$93 8077
6264
51 12 41.07
129.21
.094
.924 5227
6022
52 58 16.50
124.22
1.045
; 4339
6260
51 14 50.24
129.11
1.095
0.925 1247
6017
53 oo 20.67
124.12
.895
6255
51 16 59.30
129.01
.006
.925 7262
6013
53 02 24.74
124.02
6250
51 19 08.26
U.S. 01
.097
.926 3272
6008
53 04 28.70
123.92
.048
.8963096
6245
51 21 17.12
128.81
.098
.926 9278
6003
53 06 32.57
123.82
.896 9338
6240
51 23 25.88
128.71
.099
.927 5278
5998
53 08 36.34
123.72
1.050
0.897 5576
6235
Si 25 34-55
128.61
1. 100
0.928 1274
5993
53 10 40.01
123.62
u
2tan-'(e«)-2
«> tech u
Ztan-UeuV-SO0
wsechu
u
2tan-'(ei>)-£
osechu
Ztan-Ke'O-GO0
o> sech u
SMITHSONIAN TABLES
286
The Gudermannian.
u
gd u
«F0'
gdu
«W
u
gdu
•Fo'
gdu
1. 100
0.928 1274
5993
o / //
53 10 40.01
//
123.62
I.I50
0.957 498o
5756
0 / //
54 51 38.15
Il8?72
.101
.928 7265
5989
53 12 43-59
123.52
• 151
.958 0734
5751
54 53 36.82
118.62
.102
.929 3251
5984
53 14 47.o6
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
n8.33
1.105
0.931 n8i
59^9
53 20 56.89
123.13
1. 155
0.060 3700
5732
55 01 30.53
118.23
.106
• 931 7M8
5965
53 22 59.96
123.03
.156
.060 9430
55 03
118.14
.107
.932 3HO
596o
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
' 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
117.85
I. IIO
0.934 0968
5945
53 31 11-29
122.63
1.160
0.963 2302
5709
55 u 20.49
H7.75
.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
.964 37io
5699
55 15 15-80
117.56
.113
•935 8782
5931
53 37 18.75
122.34
.163
.964 9407
5695
55 17 13.31
117.46
.114
.936 471 I
5926
53 39 21.03
122.24
.164
•965 5099
5090
55 19 10.72
117.36
I. H5
0.937 0635
5922
53 41 23.22
122.14
1.165
0.966 0787
5685
55 21 08.04
117.27
.116
•937 6554
5917
53 43 25.32
122.04
.166
.066 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
Il6.r.8
.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
0.968 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
116.50
.123
•941 7855
5883
53 57 37.21
121.35
.173
.970 6120
5648
55 36 43-10
116.50
.124
.94-' 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
.072 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
ii6.n
.128
.944 7213
5860
54 07 42.76
120.86
.178
•973 4301
5625
55 46 24.38
1 16.02
.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 ii 44.29
120.67
1.180
0.974 5542
56i5
55 50 16.22
115.83
.131
.946 4771
5845
54 13 44-91
120.57
.181
• 975 H55
5611
55 52 12.00
.132
.947 0614
5841
54 15 45-43
120.47
.182
.975 6763
5606
07.68
.133
.947 6452
5836
54 17 45-86
120.38
.183
.976 2367
5601
55 56 03.27
.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 3500
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
.137
.949 9758
5817
54 25 46.58
119.98
.187
.978 4735
5583
56 03 44.66
.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
0.980 1463
5569
56 09 29.69
114.87
.141
.952 2988
5798
54 33 45-74
119-59
.191
.980 7030
55<>4
56 II 24.51
114.77
.14-'
.952 8784
5793
54 35 45.28
119.50
.192
.981 2592
5560
56 13
.143
•953 4575
5789
54 37 44-73
119.40
.193
.981 8149
56 15
.144
•954 0361
5784
54 39 44.08
119.30
.194
.982 3702
5551
56 17 08.41
114.49
i. M5
0.954 6143
5779
54 41 43.34
119.21
1. 195
0.082 9251
56 19 02.85
114.39
.146
.955 1920
5775
54 43 42.49
119.11
.196
.083 4794
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
.9845868
5532
45.OO
114. II
.149
.956 9222
5700
54 49 39.38
118.82
.199
.985 1397
5527
39.66
114.01
1.150
0.957 498o
5756
54 51 38.15
118.72
1.200
0.085 6922
5523
56 28 33.62
113.92
u
2 tan-He0)-^
<o sech u
Ztan-'te^-SO0
wsech u
U
2tan-'(e")~
o> sech u
tan-Ke")-^)0
usechu
SMITHSONIAN TABLES
287
The Gudermannian.
u
odu
«F0'
gd u
<oF</
u
gdu
•IV
gdu
«IV
I.20O
0.985 0922
5523
0 / //
56 28 33.62
113*92
1.250
I. 012 7356
5295
o / //
5801 31.72
109.23
.2OI
.986 2443
5518
56 30 27.49
113.82
.251
.013 2649
5291
58 03 20.89
109.13
.202
.986 7959
55U
56 32 21.26
H3.73
.252
.013 7938
5286
58 05 09.98
109.04
.203
.987 3470
5509
56 34 14.94
113.63
.253
.014 3222
5282
58 06 58.98
108.95
.204
.087 8977
5504
56 36 o8.53
H3.54
.254
.014 8502
5277
58 08 47-88
108.86
I.2O5
0.988 4479
5500
56 38 02.02
II3-44
1.255
1.015 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
.2Oy
.989 54/0
5491
56 41 48.72
113.25
.257
.016 4314
5264
58 14 14.03
108.58
.208
.090 0958
5486
56 43 41.92
113.16
.258
.016 9576
5260
58 16 02.56
108.49
.209
.990 6442
5482
56 45 35.03
113.06
.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
I.2I5
0.993 9249
5454
56 56 51.72
I 12 . 5O
1.265
1.020 6283
5228
58 28 39-71
107.84
.216
.994 4700
5449
56 58 44.17
II2.4O
.266
.021 1510
5224
58 30 27.50
107.75
.217
.095 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
52IO
58 35 50.34
107.47
1.220
0.996 6462
5431
57 06 13.03
112.03
i. 270
1.023 2369
5206
58 37 37-77
107.38
.221
.997 1891
5427
57 08 05.01
111.93
.271
•023 7573
5202
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 u 48.69
in- 74
.273
.024 7967
5193
58 42 59.50
107 . I I
.224
.998 8150
5413
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
111.37
.277
.026 8703
5175 158 50 07.20
106.74
.228
.000 9766
5395
57 21 06.24
111.28
.278
.027 3876
5171
58 51 53.00
106.65
.229
.001 5158
5350
57 22 57-47
111.18
.279
.027 9044
5i66
58 53 40.50
106.56
I.23O
I.O02 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
.003 1309
5377
57 28 30.59
110.50
.282
.029 4523
5153
58 58 59.77
106.29
• 233
.003 6683
5372
57 30 21.45
110.81
.283
.029 9673
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
5140
59 04 18.22
106.01
.236
.005 2779
5359
57 35 53-45
H0.53
.286
.031 5099
5135
59 06 04.19
105.92
.237
.005 «i35
5354
57 37 43-93
110.43
.287
.032 0232
5131
59 07 50.06
105.83
.006 3487
5349
57 39 34.32
110.34
.288
.032 5360
5126
59 09 35.85
105.74
.239
.006 8834
5345
57 41 24.61
110.25
.289
.033 0485
5122
59 II 21.54
105.65
1.240
1.007 4177
5340
57 43 H.82
110.15
1.290
1.033 5605
5H8
59 13 07.15
105.56
.241
.007 95i5
5336
57 45 04.92
110.06
.291
.034 0720
5H3
59 14 52.66
105.47
.008 4840
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
.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 53.81
105.11
.010 6139
5313
57 54 14-07
109.60
.036 6231
5091
59 23 38.87
105.02
.oil 1450
5309
57 56 03.02
109.50
.297
.037 1320
5087
59 25 23.84
104.93
.248
.on 6756
.012 2058
5304
5300
57 57 53.o8
57 59 42.44
109.41
109.32
,296
.299
.037 6405
.038 1485
5083
5078
59 27 08.72
59 28 53oi
104.83
104.74
I.2SO
I. 012 7356
S29S
58 oi 31.72
109.23
1.300
1.038 6561
5074
59 30 38.21
104.65
u
2tan-'(e«)~
w tech u
2tan-'(e«)-900
wsechu
u
2 tan-He")-?
<o sech u
2 tan-He")-^
to sech u
SMITHSONIAN TABLES
288
The Gudermannian.
u
gd u
-Fo'
gdu
«F0'
u
gdu
•Fo'
gdu
«FO'
1.300
1.038 6561
5074
o / //
59 30 38.21
W65
1.350
1.063 4837
4858
0 / //
60 55 59.27
100.21
.301
.039 1633
59 32 22.82
104.5')
•351
.063 9694
30.43
IOO. 12
.302
.039 6700
5065
59 34 07.34
104.47
.352
4850 60 59 i
100.03
.303
.040 1763
5061
59 35 51.77
104.38
.353
.064 9393
4846 61 oo 59.50
.304
.040 0822
5056
59 37 36.10
104.29
• 354
•065 4->37
4841
61 02 39.41
99.86
1.305
1.041 1876
5052
59 39 20.35
104- 20
1.355
1.065 0076
6 i 04 19.22
.041 6926
5048
59 41 04.51
104. II
.356
.066 3911
05 58.95
.307
.042 1971
5043
59 42 48.58
104.02
• 357
.066 8742
4829 6 1 07 .
.308
.042 7012
5039
59 44 32.56
103.93
.358
.067 3568
4824 6r 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
1.310
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
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 ii. ii
103-49
.363
.069 7637
4803
61 17 34.61
99.08
.314
.045 7167
5013
59 54 54-55
103.40
.304
.070 2439
4799
61 19 13.64
98.99
1.315
1.046 2178
5008
59 56 37-91
103.31
1.365
1.070 7236
4795
61 20 52.59
08.90
.316
.046 7184
5004
59 58 21.17
103.22
.366
.071 2028
4791
6l 22 31.45
.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
47/8
6 i 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
.3-^1
.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
oi 3-
98.30
.323
.050 2107
4974
60 10 21.51
102.59
• 373
.074 546o
476i
61 34 01.03
98.21
.324
.050 7079
4970
OO 12 04.06
102.50
• 374
.075 0220
4757
61 35 39-20
98.12
1.325
1.051 2046
4965
00 13 46.52
102.42
1.375
1.075 4975
4753
61 37 17.28
98.04
.326
.051 7009
496i
60 15 28.89
102.33
.376
.075 9725
4749
61 38
97-95
.327
.052 1968
4957
60 17 11.17
102.24
• 377
•076 4472
4745
61 40 33.18
97.86
.3->8
.052 6923
4952
60 18 53-37
102.15
.378
.076 9215
4740
6 1 42 n.oo
97.78
.329
•053 1873
4948
60 20 35-47
102.06
• 379
•077 3953
4736
6 1 43 48.73
97.69
1.330
1.053 6819
4944
60 22 17.49
101.97
1.380
1.077 8687
4732
6l 45 26.38
97.6i
.331
.054 1760
4939
60 23 59.41
101.88
.381
.078 3417
4728
61 47 03.94
• 332
.0546698
4935
60 25 41.25
101.79
.382
.078 8143
47-U
61 48 41.42
97-43
• 333
.055 1631
4931
60 27 23.00
101.71
.383
.079 2865
47-'0
61 50
• 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
60 30 46.24
101.53
1.385
1.080 2295
471 1
61 53 33-34
9/.i8
.336
.056 6404
4918
60 32 27.72
101.44
.386
.080 7005
4/07
61 55 10.47
97-09
.337
.057 1320
4914
60 34 09. 12
101.35
.387
.081 1710
4703
61 56 47-52
.338
.057 6231
4909
60 35 50.43
101.26
.388
.081 6411
4609
6 i 58 24.48
.339
.058 1139
4905
60 37 31.65
101.18
.389
.082 1107
62 oo 01.36
96.83
1.340
1.058 6042
4901
60 39 12.78
101.09
1.390
1.082 5800
4691
62 oi 38.15
• 341
.059 0940
4897
60 40 53.83
IOI.OO
•391
.083 0488
4086
62 03 14.80
96.60
.342
.059 5835
4892
60 42 34./8
100.91
• 392
.083 5173
4682
02 04 51.48
96.58
.343
.060 0725
4888
60 44 15.65
100.82
.'393
.083 o853
62 06
96.49
• 344
.000 5611
4884
60 45 50-43
100.74
• 394
.084 4529
4674
62 OS 04.46
96.41
1.345
1.061 0493
4880
60 47 37.12
100.65
1.395
1.084 9201
62 09 40.83
96.32
.340
.061 5370
4875
60 49 17.73
100.56
• 396
.085 3868
02 II 17.11
.347
.062 0243
4871
60 50 58.24 100.47
• 397
.085
96.15
.348
.062 5112
4867
60 52 38.67 100.38
.398
.086 3192
02 14 29.41
96.07 j
.349
.062 9977
4863
60 54 19.01
100.30
•399
.080
02 10 05.44
95.98
1-350
1.063 4837
4858
60 55 59.27
IOO.2I
1.400
1.087 2498
4649
62 17 41.37
95.90
u
2 tan-He")-?
wsechu
2tan-1(e«)-900
« sech u
u
2 tan-He-)- £
<»sechu
2 tan-He")-*)0
•osech u
SMITHSONIAN TABLES
289
The Gudermannian.
u
gd u
•Fo'
gdu
wFo'
u
gd u
«>F(/
gd u
coFo'
1.400
1.087 2498
4649
0 / //
62 17 41.37
95.90
1.450
1.109 9869
4447
63°3s' 51*24
91 ''72
.401
.087 7145
4645
62 19 17.23
95.81
• 451
.110 43H
4443
63 37 22.92
91.64
.402
.088 1788
4641
62 20 53.00
95-73
• 452
.110 8755
4439
63 38 54o2
91.56
.403
.088 6427
4637
62 22 28.68
95.64
.453
.in 3192
4435
63 40 26.03
91.47
.404
.089 IOO2
4633
62 24 04.28
95.56
•454
.in 7624
4431
63 41 57.46
91-39
! I-405
1.089 5693
4629
62 25 39.80
95-47
1.455
I. I 12 2053
4427
63 43 28.82
9L3I
.406
.OOO 0320
4625
62 27 15.23
95-39
.456
.112 6478
4423
63 45 00.08
91.23
.407
.GOO 4942
4620
62 28 50.58
95-30
.457
.113 0809
4419
63 46 31.27
9LI5
.408
.000 9561
4616
62 30 25.84
95-22
.458
•113 53l6
4415
63 48 02.38
91.07
.409
.091 4175
4612
62 32 01. 02
95.14
.459
.113 9729
44"
63 49 33.40
90.98
1.410
1.091 8785
4608
62 33 36.11
95.05
1.460
I.II4 4138
4407
63 5i 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 7i85
4592
62 39 55.64
94.71
.464
.116 1734
4391
63 57 07.30
90.58
I.4I5
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
.095 094-'
458o
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.i6
90.17
1.420
1.096 4663
4567
62 49 22.41
94.21
1.470
1.118 8011
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 09.00
89.76
1.425
1.098 7449
4547
62 57 12.41
93-79
1.475
I.I2O 9800
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 oi 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.I23 1491
4328
64 21 06.13
89.28
•431
.101 4659
4523
63 06 33.66
93.29
.481
.123 58i8
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 33.6i
89.04
• 434
.102 82IO
4511
63 II 13.16
93.04
.484
. 124 8774
4313
64 27 02. 61
88.96
1.435
I.I03 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 51.91
92.79
.487
.126 1695
4301
64 31 29.13
88.72
.104 OJJI
4495
63 17 24.66
92.71
.488
.126 5994
4297
64 32 57.8i
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
1.127 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
8644
4475
63 25 07.18
92.30
•493
.128 7432
4278
64 40 20.00
88/24
.444
.107 3H7
4471
63 26 39.44
92.21
•494
.129 1708
4-74
04 41 48.20
88.16
1-445
i. 107 7586
4467
63 28 11.61
92.13
1.495
1.129 598o
4270
64 43 16.32
88.08
. i 08 2050
4463
63 29 43.70
92.05
.496
. 130 0249
4266
64 44 44.36
88.00
.ioX
4459
63 31 I5.7I
91.97
•497
.130 4513
4263
64 46 12.32
87.92
.109 0968
4455
63 32 47.63
91.88
.498
. 130 8774
4259
64 47 40.20
87.84
.440
.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
2tan-l(e«)-*
<•» tech u
2 tan-'(e«)-90°
<»sech u
u
2 tan-Kef)-^
wsech u
2tan-He«)-90°
wsech u
SMITHSONIAN TABLES
290
The Gudermannian.
u
gd u
•Fo'
gdu
•ft
u
gdu
«FO'
gdu
•Fo'
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
4058
66 03
.502
.132 5778
4-M3
64 53 30.93
87.52
• 552
.153
4055
.503
.133 0019
4239
64 54 58.42
87.44
• 553
4051
66 06
.504
• 133 4-J57
4-'3'J
64 56 25-82
87.37
.554
.154
4047
66 07 36.33
83.48
1.505
1. 133 8490
4232
64 57 53-15
87.29
1.555
i. 154 5342
4043
66 08 59.77
83.40
.506
.134 2720
4228
64 59 20.40
87.21
.550
.154 9384
4040
83-33
.507
.134 6046
4224
65 oo 47.56
87.13
.557
•155 3421
4036
66 ii
.508
.135 "68
4220
65 02 14- '>5
87-05
.558
.155 7456
4032
66 13 09.63
.509
.135 5387
4216
65 03 41.66
86.97
.'559
.156 1486
4029
83.10
1.510
I.I35 9601
4213
65 05 08.59
86.89
1.560
I.I56 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
•
.512
.136 8019
4205
65 08 02.22
86.73
.562
. 157 3556
4018
66 18 41.72
•513
.137 2222
4201
65 09 28.91
86.66
.563
•157 7571
4014
66 20 04 . 55
.514
.137 0421
4197
65 10 55-53
86.58
064
.158 1583
4010
66 21 27.31
1.515
1.1380617
4194
65 12 22.07
86.50
1.565
1.158 5592
4007
66 22 49-99
82.64
.516
. 138 4808
4190
65 13 43.52
86.42
.566
• 158 9597
4003
i 2 . 59
82.57
.517
.1388996
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
.519
. 139 7360
4178
65 18 07.43
86.18
• 569
.160 1589
3992
66 28 19-95
82.34
1.520
I.I40 1537
4175
65 19 33.58
86.11
1.570
1.160 5579
3988
66 29
82.26
.521
.140 5709
4171
65 20 59.64
86.03
.5/1
. 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
.523
.141 4043
4163
65 23 5L54
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
81.96
1.525
I.I42 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
81.74
.528
.143 48l2
4144
65 30 59.93
85.48
• 578
.163 7369
3959
66 40 37.96
81.66
.529
. M3 8954
4141
65 32 25.37
85.40
• 579
.164 1326
3955
66 41 59o8
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
4U3
65 35 16.02
85.25
.581
. 164 9230
3948
Oo 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 7"9
3941
66 47
81.29
• 534
.145 9610
4122
65 39 31.42
85.02
084
.166 1058
3937
6648
81.21
1-535
I • U6 3730
4118
65 40 56.40
84.94
1.585
i . 166 4993
3934
66 50 07.76
81.14
.536
.146 7846
4114
65 42 21.30
84.86
.586
.1668925
3930
66 51
81.06
• 537
.147 1958
4110
(35 43 46.12
84.78
.587
.167 2854
3926
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.:-'
80.84
1.540
1 . 148 4273
4099
65 48 00.13
84.55
1.590
i . 168 4617
3916
66 56
• 541
.14883/0
4095
65 49 24.64
84.48
• 591
.168 8531
80.69
.542
. 149 2464
4092
65 50 49.08
84.40
.592
.169 2441
3908
66 59 33-91
• 543
.149 <>554
4088
65 52 13.44
84-32
.593
.169 6348
3905
67 oo 54-49
80.54!
• 544
.150 0640
4084
<J5 53 37.72
84.25
• 594
.170 0251
3901
67 02 15.00
80.47
1.545
I.I50 4722
4081
65 55 01.93
84.17
1-595
1.170 4150
3898
67 03 35-43
80.40
.546
.150 8801
40/7
65 56 26.06
84.09
.596
.170 804* i
3894
67 04
80.32
•547
.151 2876
4073
65 57 50.li
84.01
• 597
.171 1938
3891
67 o(>
80.25
.548
.151 6947
4069
65 59 14.08
83-94
.598
.171 5827
3887
67 o;
80.17
.549
.152 1015
4066
66 oo 37.98
83.86
.599
.1/1
3883
67 08 50.42
80.10
1-550
1.152 5078
4062
66 02 01.81
83.78
I.obo
1.172 3594
3880
67 10 16.48
80.03
u
2tan-Kea)-|
wsechu
2tan~1(en>-90c
wsechu
u
2tan-Ke")-£
wsechu
2tan-](e")-900
<«> sech u
SMITHSONIAN TABLES
291
The Gudermannian.
u
gd u
u>Fo'
gdu
«F/
u
gdu
»Fo'
gdu
»Fo'
o / //
//
o / //
a
1. 600
I.I72 3594
3880
67 10 16.48
80.03
1.650
1.191 3170
3704
68 15 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
3697
68 17 59-44
76..27
.603
•173 5217
3869
67 14 16.23
79.81
.653
.192 4267
3604
68 19 15.67
76.20
.604
.173 9084
3865
67 15 36.00
79-73
.654
.192 7900
3691
68 20 31.83
76.12
1.605
1.174 2948
3862
67 16 55-69
79.66
1.655
1.193 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
75.08
.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
68 26 51.57
75.77
1.610
1.176 2213
3844
67 23 33.07
79.29
1.660
1.195 0042
3670'
68 28 07.30
75.70
.611
.176 6056
3841
67 24 52.32
79.22
.661
.195 37io
3667
68 29 22.97
75.63
.612
. 176 9895
3837
67 26 11.50
79.15
.662
.195 7375
3663
68 30 38.56
75.56
.613
• 1/7 3730
3834
67 27 30.6l
79-07
.663
.106 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 20OI
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
3816
67 34 05.06
78.71
.668
.197 9293
3643
68 38 10.66
75.15
.619
.179 6667
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 O207
3633
68 41 55-77
74.94
.622
.180 8089
3802
67 39 I9.3I
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
74.80
.624
.181 5685
3795
67 41 56.00
78.27
.674
.2OO lOpO
3623
68 45 40.24
74.72
1.625
1.181 9478
3791
67 43 14.24
78.20
1.675
I.2OO 4711
3619
68 46 54-93
74.65
.626
.182 3268
3788
67 44 32.40
78.13
.676
.200 8328
3616
684809.55
74o8
.627
. 182 7054
3/84
67 45 50.49
78.06
.677
.201 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
i . 183 8390
3774
67 49 44-33
77.84
1.680
1.202 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-^3
.632
.184 5931
3767
67 52 19.86
77-69
.682
.202 9962
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
<J7 54 55.ii
77-55
.684
.203 7M7
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
73.06
.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 01 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
1.187 5953
3739
68 02 39.12
77-12
i. 600
1.205 8620
3569
69 05 26.90
73.61
. iSy
3735
68 03 56.21
77-05
.691
.206 2187
3566
69 06 40.48
73-54
373^
68 05 13.22
76.08
.692
.206 575i
3562
69 07 53.99
73.48
7155
> 0881
3729
3725
<*S o> 30.16
68 07 47.03
76.91
76.83
.693
.694
.206 9312
.207 2869
3559
3556
69 09 07.43
69 10 20.80
73-41
73-34
1.180
3722
68 09 03.83
76.76
1.695
1.207 6423
3552
69 II 34.11
73.27
37i8
68 10 20.56
76.69
.696
.207 9974
3549
69 12 47-34
73- -'0
3715
68 ii 37.22
76.62
.697
.208 3521
3546
69 14 00.51
73.131
.648
37ii
68 12 53.80
76.55
.698
.208 7065
3542
69 15 I3.6l
73-07
.190
3708
68 14 10.32
76.48
.699
.209 0605
3539
69 16 26.64
73-00
1.650
1.191 3170
3704
68 15 26.76
76.41
1.700
1.209 4143
3536
69 17 39.60
72.93
u
2ten-Ke«)~
wsechu
2tan-'(e«)-900
wsechu
u
2tan-'(e»)-£
usechu
2tan-He«)-90°
w sech u
SMITHSONIAN TABLE*
292
The Gudermannian.
u
gd u
«Fi/
gdu
«Fo'
u
gdu
«F0'
Odu
o / //
„
O i tl
//
1.700
1.209 4143
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
33/0
70 18 11.44
69.52
.702
.210 I2O8
3529
69 20 05.32
72.79
• 752
3588
70 19 20.93
69.45
.703
.210 4735
3526
69 21 18.08
72.72
• 753
•227 6954
3364
70 20 30.35
69.39
.704
.210 8259
3522
09 22 30.77
72.66
• 754
.228 0316
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
7O 22 49.00
69.26
.706
.211 5297
35l6
09 24 55-95
72.52
.756
.228 7032
3355
70 23 58.23
69.19
.707
.211 8812
3513
69 26 08.43
72.45
• 757
.229 03-S5
3351
70 25
.708
.212 2}_>3
3509
69 27 20.85
72.38
.758
.229 3735
3348
70 26 16.48
69.06
.709
.212 5830
3506
09 28 33-20
72.32
• 759
.229 7082
3345
/o 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 37^5
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 9828
3493
69 33 21.93
72.05
.763
.231 0437
3333
70 32 00.09
68.74
.714
•214 3319
3490
60 34 33-94
7L98
.764
.231 3768
3329
70 33 09.69
68.67
1.715
T.2T4 6807
3486
69 35 45.89
71.91
1.765
1.231 7096
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
.719
• 215 377-1
.215 7252
.216 0727
3480
3477
3473
69 38 09-57
69 39 21.32
69 40 32.99
71.78
71.71
71.64
.767
.768
.769
.232 3742
.232 7060
.233 0376
3320
3317
33M
70 36 35.42
/o 37 43.87
70 38
68.48
68.42
68.35
1.720
i. 216 4198
3470
69 41 44.6b
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 0997
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
3460
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
70 45 41.20
67.06
.726
.218 4960
3451
69 48 52.85
71.16
.776
.235 3405 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 i
.728
.219 1855
3444
69 51 15.06
71.03
.778
.236 0073 3286
70 49 04.80
67.77 i
.729
.219 5297
3441
69 52 26.06
70.96
• 779
.236 3357
3283
70 50 12.54
67.71
1.730
1.219 8737
3438
69 53 37-90
70.90
1.780
1.236 6638
3279
70 51 20.22
67-64
.731
.220 2173
3434
69 54 47.88
70.83
.781
.236 0916
3276
70 52 27.83
67.58
.732
.220 5O05
3431
69 55 58.68
70.76
.782 .237 3191
3273
70 53 35.38
67-52!
.733
.220 9035
3428
69 57 09.42
70.70
.783 .237 ^463
3270
70 54 42.87
67.45 i
• 734
.221 2461
3425
69 58 20.10
70.63
.784
.237 9731
3267
/o 55 50.29
67.39
1-735
I. 221 5883
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
70 58 04.94
-737
.222 2721
3415
70 01 51.72
70.43
.787
•238 9519
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
• 741
.-'-'3 6356
3402
70 06 32.96
70.18
.791
.240 2526
3246
71 03 40.40
66.94
.742
.-'23 9757
3399
70 07 43.10
70.11
.79^
.240 57/0
3243
71 04 47-37
66.88
• 743
.224 3154
3396
70 08 53 . 18
70.05
• 793
.240 9011
3239
71 05
66.82
• 744
.224 6548
3393
70 10 03.19
69.98
.794
.241 2249
3230
71 07 01.01
66.76
1.745
1.224 9940
3390
70 II 13.14
69.91
1.795
1.241 5483
71 08 07.73
66.69
.746
.225 3328
3386
7O 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
.24-' KJ44
71 10 20.09
66.57;
.748
.226 0094
338o
70 14 42.59
69.72
.798
.242 5170
3224
-I II 27.52
66.50;
• 749
.226 3472
3377
TO 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 16" 12
3218
71 13 40.40
66.38
u
2 tan-He")—
usechu
2tan-1(eu)-900
« sech u
u
2tan-'(e»)-jj
usechu
Ztan-HeuJ-SO0
o> sech u
SMITHSONIAN TABLES
293
The Gudermannian.
u
gd u
-Fo<
gdu
*
u
gdu
„*
gdu
*
o / //
H
o / //
1.800
I.2431 1612
3218
71 13 40.40
66.38
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 00.50
62.94
.807
.245 4064
3197
7i 21 23.50
65.94
.857
.261 0169
3048
72 15 03.41
62.88
.808
.245 7259
3194
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 4L04
65.75
1.860
1.261 9302
3040
72 18 11.78
62.70
.811
.246 6827
3l85
71 25 46.76
65.69
.861
.262 2340
3037
72 19 14.45
62.64
.812
.247 ooio
3182
71 26 5^-42
65-63
.862
.262 5375
3034
72 20 I7.06
62.58
.813
.247 3190
3179
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
3173
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.QI
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 3L47
62.22
.819
.249 2208
3l6l
71 34 30.28
65.19
.869
.264 6543
3014
72 27 33.67
62.16
1.820
1.249 5367
3158
71 35 35-44
65.13
1.870
1.264 9555
3011
72 28 35.80
62.11
.821
•249 8523
3155
71 36 40.54
65.07
.871
.265 2565
3008
72 29 37-88
62.05
.822
.250 1676
3152
7i 37 45.58
65.01
.872
•265 5571
3005
72 30 39-90
61.99
.823
.250 4826
3149
7i 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
3143
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
* _ /
•251 7397
3137
71 43 09.84
64.70
.877
.267 0562
72 35 49.09
61.69
.828
.252 0532
3134
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
3H9
71 49 36.94
64.33
.883
.268 8456
2974
72 41 58.19
61.34
.834
.253 9281
3ll6
71 50 41.24
64.27
.884
.269 1428
2971
72 42 59.50
61.28
1.835
1.254 2396
3H3
71 51 45.48
64.21
1.885
1.269 4398
2968
72 44 00.75
61.22
.836
.254 5507
3HO
71 52 49-66
64.15
.886
.269 7364
2965
72 45 01.94
61.16
.837
.254 8616
3107
7i 53 53-77
64.09
.887
.270 0328
2962
72 46 03.08
61.11
.838
.255 1721
3104
7i 54 57.83
64.03
.888
.270 3289
2960
72 47 04.15
61.05
.839
.255 4824
3101
71 56 01.83
63.97
.889
.270 6248
2957
72 48 05.17
60.99
'
1.255 7923
.256 IO2O
3098
3095
71 57 05.76
71 58 09.64
63-91
63-84
1.890
.891
1.270 9203
.271 2156
2954
2951
72 49 06.13
72 50 07.03
60.93
60.87
.256 4114
3092
71 59 13.45
63.78
.892
.271 5106
2948
72 51 07.88
60. 81
7205
3089
72 oo 17.21
63.72
.893
.271 8053
2946
72 5-' 08.66
60.76
.844
.257 0293
3086
72 01 20.90
63.66
.894
.272 0997
2943
72 53 09-39
60.70
O £
1.257 3378
3084
72 02 24.53
63.60
1.895
1.272 3938
2940
72 54 10. 06
60.64
• 257
3081
72 03 28.10
63.54
.896
.272 6877
2937
72 55 10.67
60.58
O O
3078
72 04 31. ()I
63.48
.897
.272 9812
2934
72 56 11.23
60.52
.258 2615
3075
3072
72 05 35.06
72 06 38.45
63.42
63.36
.898
.899
•273 2745
.273 5675
2932
2929
72 57 11.72
72 58 12. 16
60.47
60.41
I.25887S9
3069
72 07 41.78
63.30
1.900
1.273 8603
2926
72 59 12.54
60.35
u
2tarr
«sechu
2tan-'(e»)-900
w sech u
u
7T
<•> sech u
2tan-](e«)-90°
«> sech u
TABLES
294
The Gudermannian.
u
OdU
«F0'
gdu
«Fo'
u
odu
«FO'
gdu
0 / //
//
o / //
//
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
2786
73 49
57-47 1
.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
.288 9806
2781
73 51 11-34
57.36
.904
.275 0284
2915
73 03 13.48
60.12
• 954
.-'89 2586
2778
73 52 08.68
57-31
1.905
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 54 03.18
57-20
.907
.275 90i6
2906
73 06 13.59
59-95
•957
.290 0909
2770
73 55 00.35
57-I41
.908
.276 1921
2904
73 07 13.51
59.89
.958
.290 3678
2768
73 55 57.46
57.09
.909
.276 4823
2901
73 08 13-37
59.83
•959
.2906444
2765
73 5<> 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
-'757
73 59 45.38
56.87
.913
.277 6404
2890
73 12 12.25
59-61
.963
.291 7483
2754
74 oo
56.81
.914
.277 929-'
2887
73 13 11.83
59-55
.964
.292 0236
2752
74 01 39.00
56.76
1.915
1.278 2178
2884
73 14 11.35
59.49
1.965
1.292 2987
2749
74 02 35.73
56.70
.916
.278 5061
2881
73 15 10.81
59-43
.966
.292" 5734
2746
74 03 32.41
56.65
.917
.278 7941
2879
73 16 10.22
59.38
.967
.292 8480
-'744
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 3093
2873
73 18 08.86
59.26
.969
.293 3062
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 oi. 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
I. 206 3927
2710
74 16 40.20
55.8Q
.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 1831.87
55.78
•933
.283 3649
2835
73 31 53.01
58-47
.983
.297 2045
2702
74 19 27.63
55.73
•934
.283 6482
2832
73 32 51.46
58.42
.984
.297 4745
2699
47 20 23.34
55-68
1-935
1.283 9313
2829
73 33 49.85
58.36
1.985
1.297 7443
2097
74 21 18.99
.936
.284 2141
2827
73 34 48.18
58.31
.986
.208 0139
2694
74 22 14.58
55-57
•937
.284 4967
2824
73 35 46.46
58.25
.987
.258 2832
2692
74 23 10.13
55.52:
.938
.2847789
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,
1.940
1.285 3427
2816
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
.299 3577
2681
74 20 51.77
55.30
• 942
.285 9053
2811
73 40 37.01
57-97
.992
.299 6257
2679
74 27 47.04
• 943
.286 1862
2808
73 41 34.95
57.92
•993
.299 8934
2676
74 28 42.27
55.20
•944
.286 4669
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
55.09
.946
.287 0274
2800
73 44 28.45
57-75
.996
.300 6951
2668
74 3i
55.04
.947
• -'87 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
57.04
.998
.301 2282
2663
74 33 17-59
•949
.287 8661
2792
73 47 -'1.45
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 07.34
54.83
u
2tan-'(e»)-£
<» sech u
2tan-Ke«)-90°
w sech u
u
atari-He")—
wsechu
Ztan-Keuh-SO0
CD sech u
SMITHSONIAN TABLES
295
The Gudermannian.
u
gd u
<-F0'
gdu
«F0'
u
gd u
«FO'
gdu
»Fo'
o / //
//
o / //
//
2.000
1.301 7603
2658
74 35 07.34
54.83
2.050
1.314 7349
2533
75 19 43-53
52.24
.001
.302 0260
2655
74 36 02.14
54-77
-051
.3H 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
.302 5566
2650
74 37 51.58
54.67
.053
.315 4936
2525
75 22 20.03
52-09
.004
.302 8215
2648
74 38 46.22
54.6i
.054
.315 746o
2523
75 23 12.09
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
.303 3505
2643
74 40 35-35
54-51
.056
.316 2501
2518
75 24 56.07
51-94
.007
.303 6147
2640
74 41 29.83
54.46
.057
.316 5018
2516
75 25 47.98
51-89
.008
.303 8786
2638
74 42 24.26
54-40
.058
-3i6 7532
2513
75 26 39.85
51.84
.009
.304 14^2
2635
74 43 18.64
54-35
.059
.317 0044
2511
75 27 31.66
51-79
2.OIO
1.304 4056
2633
74 44 12.97
54.30
2.060
I-3I7 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 93i6
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
51-59
.014
.305 4566
2622
74 47 49-74
54-09
.064
-318 2568
2499
75 3i 49-98
51-54
2.015
1.305 7i87
2620
74 48 43.8i
54-04
2.065
1.318 5065
2496
75 32 41-49
51.49
.016
.305 9805
2617
74 49 37.82
53-99
.066
.318 7560
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
.019
•3o5 7646
2610
74 52 19.54
53.83
.069
.319 5031
2487
75 36 07.04
51.29
2.020
1.307 0254
2607
74 53 13.35
53.78
2.070
1.319 7516
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
2602
74 55 00.80
53.67
.072
.320 2480
2479
75 38 40.69
51.14
• 023
.307 8065
2600
74 55 54-45
53-62
.073
.320 4958
2477
75 39 3i.8o
51.09
.024
.3080663
2597
74 56 48.05
53-57
.074
.320 7433
2475
75 40 22.87
51.04
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
.029
.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
1.310 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
.311 4215
2565
75 08 20. ii
52.90
.087
-323 940i
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
I.3I2 1898
2557
75 10 58.59
52.75
2.090
1.324 6721
2436
75 53 53.23
50.26
.312 4455
2555
75 u 51.31
52.70
.091
.324 9156
2434
75 54 43.46
5O.2I
.042
.312 7008
2552
75 12 43.08
52.65
.092
.325 1589
2432
75 55 33.65
50.16
.043
.312 9559
2550
75 13 30.60
52.60
.093
.325 4020
2429
75 56 23.78
50.11
.044
.313 2108
2547
75 14 29.17
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.OI
.31.-:
2543
75 16 14.16
52.44
.096
.326 1297
2422
75 58 53.89
49.96
.31.;
-'540
75 17 06.58
52-39
.097
.326 3718
2420
75 59 43.83
49.92
• 3I-;
2538
75 17 58.95
52.34
.098
.326 6137
2418
76 oo 33-72
49.87
.3M 4815
2535
75 18 51.27
52.29
.099
.326 8554
-'415
70 oi 23.56
49-82
2.050
I.3M 7349
2533
75 19 43-53
52.24
2.100
1.327 0968
2413
76 02 13.36
49-77
u
2tan->(e»)~2
«> tech u
2 lan-He«>-900
<••> sech u
U
2tan-Ke")-£
wsechu
2lan-1(eu)~900
wsechu
SMITHSONIAN TABLES
296
The Gudermannian.
u
gd u
»Fo'
Odu
-Fo'
u
gdu
«F0'
gdu
u,F'
2.100
1.327 0968
2413
o / //
76 02 13.36
49-77
2.150
1.3388732
2298
0 / M
76 42 42.42
.101
.327 3380
2411
T^ 03 03 . 1 1
49-72
.151
-339
2296
29.8l
47.36
.102
.327 5789
2408
76 03 52.80
49-67
-152
-339
2294
17.15
.103
.327
2406
76 04 42.45
-153
•33<>
2202
76 45 04.44
47-27
.104
.328 0601
2404
76 05 32.06
49o8
.154
-339 7908
229O
76 45 51-69
47-23 j
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 II. I I
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 49.98
49-39
.158
.340 7049
228l
76 49 00.23
47.04
.109
.329 2590
2392
76" 09 39.34
49-34
.159
-340 9328
76 49 47-25
47.00
2. no
1.329 4980
2390
76 10 28.66
49.29
2.160
1.341 1605
2276
76 50 34-22
.in
.329 7369
2387
76 II 17.92
49.24
.161
-341 3881
21.15
46.90
.112
.329 9755
2385
76 12 O7.I4
49.19
.162
-341 6153
76 52 08.03
.113
•330 2139
2383
76 12 56.31
49.15
.163
.341 8424
227O
76 52 54.87
46.81
.114
• 330 45 -'0
2380
76 13 45-43
49-10
.164
.342 0693
2267
76 53
46.77
2.115
1.330 6900
2378
76 14 34-51
49-05
2.165
1.342 2959
2265
76 54 28.40
.116
.330 9277
2376
76 15 23.54
49.00
.166
.342 5223
2263
76 55 15-10
46.68
.117
.331 1651
2373
76 16 12.52
48.96
.167
.342 7485
226l
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
2.120
1.331 8761
2367
76 18 39-17
48.81
2.170
1-343 4257
2254
76 58 21.45
46.50
.121
• 33-1 ii-'7
2364
76 19 27.96
48.77
.171
-343 6510
2252
76 59 07.92
.122
•332 3450
2362
76 20 16.70
48.72
.1-2
.343 8761
2250
76 59 54-35
.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
•333 2919
2353
76 23 31.20
48.53
.176
•344 7743
2241
77 02 59.61
.127
•333 5271
2350
76 24 19.70
48.48
.177
•344 0083
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
2.130
1.334 2312
2344
76 26 44-94
48.34
2.180
1.345 6689
2232
77 06 04.14
46.04 '
.131
.334 4654
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
77 07 36.14
•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
77 09 07-96
45-87
2.135
1.335 4002
2332
76 30 46.06
48.11
2.185
1.346 7824
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 ii 25.36
.138
.336 0988
2325
75 33 10.17
47-97
.188
-347 4478
11.07
45.69
•139
.336 3313
2323
76 33 58.11
47.92
.189
•347 6692
2213
77 12 56.73
2.140
1.336 5635
2321
76 34 46.01
47.87
2.190
1.347 8904
2JII
77 13
.141
.330 7955
2319
76 35 33-86
47.83
.191
.348 1114
2208
77 M
.142
.337 0272
2316
76 36 21.66
47.78
.192
.348 3321
2JOO
77 15 i3-4<>
•143
•337 2588
23H
76 37 09.42
47-73
.193
.348 5526
77 15 58-95
45.46
.144
•337 4901
2312
76 37 57.13
47-69
.194
.348
220J
44-39
45.42
2.145
1-337 7212
2310
76 38 44.79
47-64
2.195
1.348 9930
.146
•337 9520
2307
76 39 32.41
47-59
.196
-34<>
15-14
.147
.338 1826
2305
76 40 19.98
47-SS
.197
-34^
- 19 00.45
. .148
.338 4131
2303
76 41 07.51
47-50
-349
2193 77 19 A
•M9
.338 6432
2301
70 41 54-99
47.46
.199
-349 8713
2191
77 20 30.94
45-20
2.150
1.338 8732
2298
76 42 42.42
47.41
2. 2OO
1.3500003
2189
77 21 16.11
45-16
u
2tan-Ke«)-2
cosechu
atan-Keuh-eO0
w sech u
U
2tan-'(e«)-£
wsechu 2tan-1(e«)-»)0
w sech u
SMITHSONIAN TABLES
297
The Gudermannian.
u
gdu
-fo'
gdu
«Fo'
u
gd u
«FO'
gd u
"F0'
2.200
1.350 0003
2189
0 / //'
77 21 i6.n
45.16
2.250
1.360 7733
2085
O i //
77 57 59-64
//
43-00
.2OI
.350 3091
2187
77 22 01.25
45-11
.251
.360 9817
2083
77 58 42.62
42.06
.202
•350 5277
2185
77 22 46.34
45-07
.252
.361 1809
2081
77 59 25.56
42.92
.203
•350 746l
2183
77 23 31.38
45-02
•253
.361 3978
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
2.205
1.351 1822
2179
77 25 01.34
44-94
2.255
1.361 8132
2075
78 oi 34.13
42.79
.205
.351 4000
2176
77 25 46.25
44.89
.256
.362 0205
2073
78 02 16.00
42.75
.207
.208
•351 6l75
•351 8348
2174
2172
77 26 31.12
77 27 15-95
44.85
44-80
.257
.258
.362 2277
.362 4347
2071
2069
78 02 59.63
78 03 42.32
42.71
42.67
.209
•352 0519
2170
77 28 00.73
44.76
.259
.362 6414
2067
78 04 24.97
42.63
2.2IO
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
78 07 15-14
42.46
.214
•353 1343
2159
77 31 43-99
44-54
.264
.363 6722
2056
/8 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 9964
2151
77 34 4i.8i
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 0024
2044
78 12 11.33
42.17
.221
.354 6408
2145
77 36 54.72
44-24
.271
.365 1068
2042
/8 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.li
.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 7io6
2134
77 40 35.38
44.02
.276
.366 1255
2032
78 16 23.61
41.92
.227
•355 9239
2132
77 41 19.38
43.93
.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
2.23O
1.356 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 3414
202 1
78 20 34-40
41.68
•233
•357 2095
2I2O
77 45 42.49
43.72
.283
•367 5433
2019
78 21 16.06
41.64
•234
.357 4H4
2118
77 46 26.19
43.68
.284
•367 7451
2017
78 21 57.68
41.60
2.235
1.357 6230
21 16
77 47 09.85
43.64
2.285
1.367 9466
2015
78 22 39.25
4L55
.236
•357 8345
2114
77 47 53-47
43.6o
.286
.368 1480
2013
78 23 20.78
4I.5I
•237
.358 0457
2III
77 48 37.04
43.55
.287
.368 3492
2OII
78 24 02.28
41.47
.238
.358 2568
2109
77 49 20.57
43.51
.288
.368 5501
2O09
78 24 43.73
4L43
•239
•358 4676
2107
77 50 04.06
43-47
.289
.368 7509
2OO7
78 25 25.14
4L39
2.240
i.35<S 6783
2105
77 50 47-51
43-43
2.290
..3689515
2005
78 26 06.51
4L35
8887
2103
77 5i 30.91
43.38
.291
.369 1519
2003
78 26 47.85
4L3I
.242
•359 0989
2IOI
77 52 14.27
43-34
.292
.369 3521
2OOI
78 27 29.14
41.27
> 3089
2099
77 52 57-59
43-30
.293
.369 5520
1999
78 28 10.39
41.23
•359 5187
2097
77 53 40.87
43-26
.294
.369 75i8
1997
78 28 51.60
41.19
1-359 7283
2095
77 54 24.10
43-21
2.295
1.369 9514
1995
78 29 32.77
4LI5
2093
77 55 07.29
43.17
.370 1508
1993
78 30 13.89
41.11
2091
77 55 50.44
43-13
.297
•370 3500
IOQI
78 30 54.98
41.07
•360 3559
•360 5647
2089
2087
77 56 33-55
77 57 16.62
43.09
43-04
.298
.299
•370 5490
.370 7479
1989
1987
78 31 36.03
78 32 17.04
41-03
40.59
2 . 250
1-360 7733
2085
77 57 59.64
43-00
2.300
1-370 9465
1985
78 32 58.01
40-95
a
2Un-'(e»)-£
"sechu
2tan-1(e»)-90°
w sech u
u
2tan-'(eu)-^
oo sech u
2tan-1(e»)-90°
w sech u
SMITHSONIAN TABLES
298
The Gudermannian.
u
gd u
•Fo'
gd u
wF,/
u
gdu
gd u
2.300
1.370 9465
1985
0 / //
78 32 58.01
40*95
2.350
1.3806331
1890
0 / //
79 06 16.03
38'99
.301
.371 1449
1983
78 33 38.94
40.91
• 351
.380 8221
1888
79 06 55.00 38.95
.302
.303
•371 3431
•371 5412
1981
1979
78 34 19.82
78 35 00.67
40.87
40.83
• 352
.353
.381 OI08
.381 1994
1886
1885
79 07 33.0
79 08 12.82 38.87
.304
•371 7390
1977
78 35 41.48
40.79
• 354
.381 3877
1883
7908 J
38-84
2.305
I-37I 9367
1975
78 36 22.25
40.75
2.355
1.381 5759
1881
79 09 30.49
38.80
.306
.372 1341
1974
78 37 02.98
40.71
.356
.381
1879
79 10 09.27
38./6
.307
• 372 33U
1972
78 37 43-66
40.66
•357
•381 9517
1877
79 IO 48.01
38.72
.308
.372 5284
1970
78 38 24.31
40.63
• 358
.382 1304
1875
79 II 26.71
38.08
.309
•372 7253
1968
78 39 04.92
40.59
•359
.382 3268
1874
79 12 05-37
38.04
2.310
1.372 9220
1966
78 39 45-49
40.55
2.360
1.382 5141
1872
79 12 44.00
38.61
.311
• 373 n85
1964
78 40 26.02
40.51
.361
.382 7012
1870
79 13 22.59
38.57
.312
•373 3148
1962
78 41 06.51
40.47
.362
.382 8881
1868
79 14 oi . 14
38.53
.313
•373 5109
1960
78 41 46.06
40.43
.363
•383 0748
1866
79 U 39.65
38.49
.314
.373 7068
1958
78 42 27.37
40.39
.364
.383 2613
1864
79 15 18.12
38.46
2.315
1.373 9025
1956
78 43 07.74
40.35
2.365
1.383 4476
1863
79 15 56.56
38.42
.316
.374 0980
1954
78 43 48.07
40.31
.366
.383 6338
1861
79 16 34-96
38.38
.317
.374 2934
1952
78 44 28.36
40.27
.367
.383 8198
1859
79 17 13-32
38.34
.318
.374 4885
1950
78 45 08. 61
40.23
.368
.384 0056
1857
79 17 51.64
38.30
.319
•374 6835
1949
78 45 48.82
40.19
.369
.384 1912
1855
79 18 29.93
38.27
2.320
1.374 8782
1947
78 46 28.99
40.15
2.370
1.3843766
1853
79 19 08. 18
38.23
.321
.375 0728
1945
78 47 09. 13
40.11
.371
.384 5619
1852
79 19 46.39
38.19
.322
.375 2672
1943
78 47 49-22
40.07
•372
•384 7470
1850
79 20 24.56
38.15
.323
.375 4614
1941
78 48 29.28
40.04
.373
.384 93^8
1848
79 21 02.70
38.12
.324
•375 6554
1939
78 49 09.29
40.00
• 374
.385 1165
1846
79 21 40.80
38.08
2.325
1.375 8492
1937
78 49 49-27
39.96
2.375
1.385 3011
1844
79 22 18.86
38.04
.326
.376 0428
1935
78 50 29.21
39.92
.376
.385 4854
38.00
.327
.376 2362
1933
78 qi 09.10
39.88
• 377
.3856696
1841
79 23 34-87
37-97
.328
.376 4295
1931
78 51 48.96
39.84
.378
.385 8536
1839
79 24 12. 81
37-93
.329
.376 6225
1930
78 52 28.78
39-80
• 379
.386 0374
1837
79 24 50.73
37.89
2.330
1.376 8154
1928
78 53 08.56
39.76
2.380
1.386 2210
1835
79 25 28.60
37.86 ;
.331
.377 0081
1926
78 53 48.30
39.72
.381
.386 4044
1833
79 26 06.44
37-82!
.332
.377 2006
1924
78 54 28.01
39-68
.382
.386 5877
1832
79 26 44-24
37.78!
.333
.377 3929
1922
78 55 07.67
39.64
.383
.3<S6 7708
1830
79 27 22.00
37-74
•334
•377 5850
1920
78 55 47-29
39.61
.384
.386 9537
1828
79 27 59-73
37.71
2-335
1.377 7709
1918
78 56 26.88
39.57
2.385
1.387 1364
1826
79 28 37-41
37.67
.336
.3779686
1916
78 57 06.43
39-53
.386
.387 3i89
1824
79 29 15.07
37.63
•337
.378 1601
1914
78 57 45-94
39.49
.387
.387 5013
79 29 52.68
37.60
.338
.378 3515
1913
78 58 25.40
39-45
.388
.387 6834
1821
79 30 30.26
37.56
• 339
.378 5427
1911
78 59 04.84
39.41
.389
.387 8655
1819
79 31 07.80
37.52
2.340
1.378 7336
1909
78 59 44.23
39.37
2.390
1.388 0473
1817
79 3i 45-30
37.49
.341
.378 9244
1907
79 oo 23.58
39-33
• 391
.388 2289
1816
79 32 22.
37-45
•342
• 379 "SO
1905
79 01 02.89
39.30
.392
.388 4104
1814
79 33 00.20 37.41 j
•343
•379 3054
1003
79 01 42.17
39.26
.393
.388 5917
1812
79 33 37-
37.37
• 344
•379 4957
1901
79 02 21.41
39.22
• 394
.388 7728
1810
79 34 14.95
37-34
2.345
1.3796857
1899
79 03 oo. 61
39.18
2.395
1.3889537
1808
79 34 52.27
37.30
.346
•379 8756
1898
79 03 39-77
39.14
.396
.389 U45
• 347
.380 0(352
1896
79 04 18.89
39-10
.389 3150
1805
79 36 06.80 37.23
.348
.380 2547
1894
79 04 57-97
39.o6
.398
.389 4954
1803
793644-01 37.19
•349
.380 4440
1892
79 05 37-02
39-03
• 399
.389 6757
1801
79 37 21. 18
37.15
2.350
1.380 6331
1890
79 06 16.03
38.99
2.400
1.3898557
1800
79 37 58.32
37-12
u
2tan-»(e*)-|
ws ch u
2tan-1(e«)-90c
<«> sech u
u
2 tan-He")-^
<»sechu
2tan-1(e«)-9(r
<•> sech u
SMITHSONIAN TABLES
299
The Gudermannian.
u
gd u
«Fu'
gd u
.«
u
gd u
*n
gd u
*
O J //
a
0
a
2.400
1.3898557
I800
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.o8
.451
.398 8069
I7II 80 08 44.63
35-30
.402
.390 2153
1796
79 39 12.48
37.05
•452
.398 9779
1710 ! 80 09 19.91
35.27
.403
.390 3948
1794
79 39 49-51
37.01
.453
• 399 M88
1708
So 09 55 . 16
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
I.399490I
1705
80 II 05.55
35.i6
.406
•390 9323
1789
79 41 40.37
36.90
.456
• 399 6605
1703
80 II 40.70
35.13
.407
• 391 mi
1787
79 42 17.25
36.86
.457
•399 8307
1701
80 12 I5.8I
35-09
.408
.391 2897
1785
79 42 54.10
36.83
• 458
.400 0007
1700
So 12 50.88
35.o6
.409
.391 4681
1/84
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 35-90
34-95
.412
.392 0025
1778
79 45 21.12
36.68
.462
.400 6793
1693
So 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 ii.oo
36.57
2.465
1.401 1864
1688
So 16 55-45
34.82
.416
.392 7124
1771
79 47 47.56
36.54
.466
•401 3551
1686
So 17 30.25
34.78
.417
.392 8895
1770
79 48 24.08
36.50
•467
.401 5237
1685
So 18 05.01
34-75
.418
-393 0664
1768
79 49 00.57
36.47
.468
.401 6921
1683
So 18 39-74
34.71
.419
•393 2431
1766
79 49 37-02
36.43
.469
.401 8603
1681
So 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
I76l
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
SO 21 32.89
34-54
.424
.394 1240
1758
79 52 38.72
36.25
•474
.402 6989
1673
SO 22 07.41
34-51
2.425
1.394 2997
1756
79 53 14.96
36.22
2.475
1.402 8661
1672
8O 22 41.91
34-48
.426
•394 4752
1754
79 53 5LI5
36.18
.476
.403 0332
1670
80 23 16.36
34-44
.427
.394 6505
1752
79 54 27.32
36.14
•477
.403 200 I
1668
80 23 50.79
34-41
.428
.394 8257
1751
79 55 03.44
36.11
.478
.403 3668
1666
So 24 25.18
34-37
.429
.395 0006
1749
79 55 39-54
36.07
•479
.403 5334
1665
So 24 59-54
34-34
2.430
1-395 1754
1747
79 56 15.59
36.04
2.480
1.403 6908
1663
So 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
So 26 42.40
34-24
.433
.395 6988
1742
79 58 03.55
35-93
.483
.404 1980
1658
So 27 16.62
34-20
.434
•395 8729
1740
79 58 39.46
35-90
.484
.404 3637
1657
So 27 50.81
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
• 43r>
.396 2207
1737
79 59 5LI9
35-83
.486
.404 6947
1653
80 28 59.09
34.10
is
•396 3943
.396 5677
1735
1733
80 oo 26.99
80 01 02.77
35-79
35.76
.487
.488
.404 8600
.405 0251
1652
1650
So 29 33.17
So 30 07.23
34-07
34-04
.439
.396 74io
1732
80 01 38.51
35.72
.489
.405 1900
1648
80 30 41.25
34.00
2.440
1.396 9141
1730
80 02 14.21
35.69
2.490
1.405 3548
1647
So 31 15.23
33-97
.397 0870
1728
SO 02 49.88
35.65
.491
.405 5194
1645
So 31 49.19
33-94
•397 25';7
1727
80 03 25.51
35-62
.492
.405 6838
1644
80 32 23.10
33.90
•397 4323
1725
80 04 01. i i
35.58
•493
.405 8481
1642
80 32 56.99
33.87
•397 6047
1723
80 04 36.67
35-54
• 494
.406 OI22
1640
So 33 30.84
33.84
7770
1722
80 05 12.20
35.51
2.495
i.4o5 1762
1639
So 34 04.66
33.8o
•397 9490
1720
80 05 47.69
35.48
.496
.406 3400
1637
So 34 38.45
33.77
1209
1718
80 06
35-44
• 497
.406 5036
1636
So 35 12. 20
33-74
\~\<>
80 06 58.57
35.41
.498
.406 6671
1634
So 35 45.92
33.70
»&8
1715
80 07 33.96
35-37
.499
.406 8304
1632
80 36 19.60
33.67
2.450
1.3986356
1713
80 08 09.31
35-34
2.500
1.406 9936
1631
80 36 53.26
33.64
u
2
to sech u
2tan-1(e«V-90c
-osechu
u
2«>-i
t» sech ti
t*™*
<o sech u
SMITHSONIAN TABLES
300
The Gudermannian.
u
gdu
•IV
gdu
•w
u
otfu
*F«/
odn
-IV
o i u
a
O 1 II
u
2.500
1.406 9936
1631 80 36 53.26 33-64
2.550
1.414 0492
1552
8i 04 14.22
32.O2
.501
.407 1566
1629 80 37 26.88 3'3.6o
• 551
.415 1043
1551 81 04 46.22
31.08
.502
•407 3194
1627
80 38 00.46 33-57
•55-'
.415 2593
1549 81 05 18.19
31.95
.503
.407 4821
1626
80 38 34-01
33-54
• 553
.415 4142
1548 81 05 50.13
31.02
.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
I.4I5 7234
1545 81 06 53.91
31.86
.506
.407 9691
1621
So 40 M.47 33-44
.556
.415 8778 1543 81 07 25.75
31.83
.507
.408 I3H
1619
80 40 47.90 33.40
• 557
.4160320 1541 81 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
33.3i
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 looo
1610
80 44 07.73
33.21
.563
.416 9541
1532 81 u 07-77
3I.6l
.514
.409 2609
1608
80 44 40.92
33-17
.564
.417 1073
I53i 81 u 39.36
3L58
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.H
.566
.417 4131
1528 81 12 42.45
31.51
.517
.409 7427
1604
80 46 20.30
33.o8
.567
•417 5659
1526 81 13 13.95
31.48
.518
.409 9029
1602
80 46 53.36
33.04
• 568
.417 7184
1525 81 13 45.41
31-45
.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 31.36
.522
.410 5425
1596
80 49 05.27
32.91
.572
.418 3271
1519 81 15 50-97 31-33
.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
I59i
80 50 43-86
32.82
2.575
1.418 7821
1514 81 17 24.81
31.23
.526
.411 1795
1589
80 51 16.66
32.78
.576
.418 9334
1513 81 17 56.03
31.20
.527
.411 3384
1588
80 51 49-43
32.75
• 577
.419 0847
1511 81 18 27.22
3LI7
.528
.411 4971
1586
80 52 22.17
32.72
.5/8
• 4i«> 2357
1510 8 1 18 58.38
3I.M
.529
.411 6556
1585
80 52 54-87
32.69
• 579
.4193866
1508 81 19 29.50
31.11
2.530
1.411 8140
1583
80 53 27.54
32.65
2.580
I.4I9 5374
1.507 81 20 00.60
3I.o8
.531
.411 9722
1582
80 54 00.18
32.62
.581
.419 6880
1505 81 20 31.67
3L05
.532
.412 1303
1580
80 54 32.78
32.59
.582
.419 8384
1504 181 21 02.70
31.02
• 533
.412 2882
1578
80 55 05.36
32.56
.583
.4199888
1502 81 21 33.70
30.09
• 534
.412 4460
1377
80 55 37.90
32.53
• 584
.420 1389
1501
8 1 22 04.68
30.96
2.535
1.412 6036
1575
80 56 10.41
32.49
2.585
1.420 2889
1499
8 1 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
3-2-43
.587
.420 5885
1496 81 23 37.41
30.87
.538
.413 0755
I57i
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
30.8l
2.540
I.4I3 3893
1568
80 58 52.48
32-33
2.590
1.421 0368
1492
81 25 09.88
30.77
• 541
.413 5460
1566
80 59 24.80
32.30
.591
.421 1859
1491
81 25 40.63
30.74
• 542
.413 7025
1564
80 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 01 33-75
32.17
2.595
1.421 7809
1485
8 i 27 43-37
30.62
.546
.414 3271
1558
81 02 05.91
32.14
.596
.421 0293
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
1 479
81 29 45.02
30.50
2-550
1.414 9492
1552
81 04 14.22
32.02
2.6oo
1.422 5214
1477
81 30 16.11
30.47
u
2tan-He»)-£
<•» sech u
2 tan-He")-*)0
wsechu
u
2 tan-He")—
«sechu
2tan-He°>-90c
<»sechu
SMITHSONIAN TABLES
301
The Gudermannian.
H
gdu
U.FO'
gdu
*>F0'
u
gdu
«F0'
gdu
<oF0'
o / //
//
O / //
2.6OO
1.422 5214
1477
81 30 i6.n
30-47
2.650
1.429 7283
1406
81 55 02.63
29.00
.fol
.422 6691
1476
81 30 46.56
30.44
.651
.429 8688
1405
81 55 31.62
28.97
.602
.422 8166
U74
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
2.6O5
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
1398
81 57 56.12
28.83
.607
.423 5520
1467
81 33 48.67
30.26
.657
•430 7091
1306
81 58 24.94
28.80
.608
.423 6986
1466
3i 34 18.92
30.23
.658
.430 8487
1395
81 58 53.72
28.77
.609
•423 8451
1464
81 34 49-114
3O.2O
.659
.430 9881
1394
81 59 22.48
28.74
2.610
1.423 9915
1463
81 35 19.32
30.17
2.660
1.431 1274
1392
81 59 5I.2I
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
3i 36 19.61
3O.II
.662
.431 4055
I3'89
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 oi 45.84
28.00
2.615
1.424 7211
1456
81 37 49.8i
30.02
2.665
1.431 8217
1385
82 02 14.43
28.57
.616
.4248665
H54
81 38 19.82
29.99
.666
.431 9602
1384
82 02 42.99
28.55
.617
.425 0119
1453
81 38 49.8o
29.96
.667
.432 0985
1383
82 O3 11.52 28.52
.618
•425 1571
I4SI
81 39 19.75
29-93
.668
.432 2367
1381
82 O3 40.O2
28.49
.619
.425 3021
1450
81 39 49-67
29.90
.669
.432 3747
1380
82 04 08.50
28.46
2.620
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 30.45
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
1369
82 07 55.28
28.24
.628
.426 6012
M37
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
1431
81 46 15.94
29.52
.682
.434 1570
1362
82 10 16.11
28.10
.633
.427 3179
U30
81 46 45-44
29.49
.683
.434 2931
1361
82 10 44.20
28.07
•034
.427 4608
1428
81 47 14-92
29.46
.684
.434 4291
U59
82 ii 12.25
28.04
1.427 6036
1427
81 47 44.37
29-43
2.685
1.434 5650
1358
82 ii 40.28
28.01
.427
1426
81 48 13.79
29.41
.686
.434 7008
1357
82 12 08.28
27.99
.427 8887
1424
81 4843-18
29.38
.687
.434 8364
1355
82 12 36.25
27.96
.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 11.18
29.29
2.690
1.435 2424
1351
82 13 59-99
27.87
4572
1419
81 50 40.46
29.26
.691
•435 3775
1350
82 14 27.86
27-85
.642
5990
1417
81 51 09.70
29.23
.692
•435 5124 i 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. i i
29.17
.694
•435 7819
1346
82 15 51.27
27.77
1. 42- > 0236
1413
81 52 37.27
29.14
2.695
1-435 9164
1345
82 16 19.02
27.74
.4A» I ''4*
1412
81 53 06.40
2Q.I2
.696
.436 0508
1343
82 16 46.75
27.71
•4A> 3059
1410
81 53 35.50
29.09
.697
.436 1851
1342
82 17 14.44
27.68
.648
.429 44<>*
1409
81 54 04.57
29.06
.698
.436 3192
1341
82 17 42.11
27.65
> 5870
1407
81 54 33.62
29.03
.699
•436 4532
1339
82 18 09.75
27.63
1.429 7283
1406
81 55 02.63
29.00
2.700
1.436 5871
1338
82 18 37.36
27.60
u
2 *,.-(.»)--
<•» tech u
2Un-'(e»>-900
o>sechu
u
2tan-'(eu)~
«>sechu
2tan-1(e")-90°
<•> sech u
ITMSONIAN TABLC»
302
The Gudermannian.
u
gdu
<-Fo'
gdu
«FO'
u
gdu
«F0'
gdu
«F0'
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
1 27*
82 41
.702
.436 8545
1335
82 19 32.51 27.54
• 752
.443 3688
1271
82 41 56.1 -
.703
.436 0879
1334
82 20 00.04 27.52
• 753
•443
1270
82 42 22.38 26.19
.704
•437 1^13
1333
82 20 27.54
27.49
• 754
.443 6227
1268
18.55
26.16
2.705
1.437 2545
I33T
82 20 55.02
27.46
2.755
1.443 7495
1267
82 43 14.70
26.14
.706 .437 3876
U30
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 06.92
26.08
.708
.437 6533
1327
82 22 I?- -'9 27.38
.758
.444 1200
1263
82 44 32.09
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 12.00
27.33
2.760
1.444 3814
1261
8> 45 25.05
26.01
.711
.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 17.0
• 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
rl.445 OIO2
1255
£2 47 34.76
25.88
.716
.438 7HI
1317
82 25 55-47
27.17
.766
•445 1356
1253
Xj 48 00.02 25.85
.717
.438 8428
I3l6
82 26 22.63
27.14
.767
.445 2609
1252
824826.46 25-83
.718
.438 9743
1314
82 26 49-75
27.11
.768
.445 3860
1251
82 48 52.27 25.80
.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 368o
1310
82 28 10.06
27.03
.771
.445 7607
1247
82 50
.722
.439 4900
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
26.98
• 773
.446 0099 1245
82 51 oo. <>.-
.724
.439 7005
1307
82 29 31.94
26.95
.774
.446 1343
1243
82 51 26.61
25.65
2.725
1.439 8912
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
17.86
25.60
.727
•440 1520
U03
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
.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
S_> 54 25.52
25.47
• 732
.440 8017
1296
82 33 06.69
26.74
.782
-447 1251
1234
50.98
25.44!
• 733
•440 9313
1295
82 33 33.42
26.71
.783
.447 2484
1232
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
07.19
25.37
• 736
.441 3192
1291
82 34 53.43
26.63
.786
• 447 <'i75
1229
25-34
• 737
.441 4483
1290
82 35 20.05
26.61
.787
.447 7403
1237
57.88
25.32
.738
.441 5772
1289
82 35 46.64
26.58
.788
.447 8630
i 2J< >
82 57 23.19
25.29
• 739
.441 7060
1287
82 36 13.21
26.55
.789
-447 9856
122$
82 57 48.47
25.27
2.740
1.441 8347
1286
82 36 39-75
26.53
2.790
1.448 1080
[224
82 58 13.72
25.24
.741
.441 9632
1285
82 37 06.26
26.50
.791
.448 2303
i 223
38.95
.742
.442 0916
1283
82 37 32.75
26.47
• 792
.448 3525
1221
82 59 04.16
25-19!
•743
.442 2109
1282
82 37 59-21
26.45
• 793
.448 4746
82 59 29.34
--5.17,
• 744
.442 3481
1281
82 38 25-64
26. 42
.794
.448 5966
1219
82 59 54-49
25-14
2-745
1.442 4761
1280
82 38 52.05
26.40
2.795
1.448 7184
ui8
83 oo 19.62
25.12
.746
.442 6040
1278
82 39 18.43
26.37
.796
.448 8401
ui7
83 oo 44-73
25.09
• 747
.442 7318
1277
82 39 44.79
26.34
• 797
.448 9617
1215
83 or 09.81
25-07
• 748
.4428594
1276
82 40 II . 12
26.32
.798
.449 0832
1214
83 or 34.86
25.04
• 749
.4429870
1275
82 40 37.42
26.29
.799
.449 2045
1213
83 oi 59.90
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
2tan-Keu)-^
w sech u
atan-Ue^-SO0
usechu
u
2tan-'<e«)~
wsechu
2tan-He°)-900
»sechu
SMITHSONIAN TABLES
303
The Gudermannian.
I
gd u
«Fo'
gdu
»F0'
u
gdu
o>F0'
gdu
«Fo'
0 / //
u
0 / U
M
2.800
1.449 3253
1212
83 02 24.90
24.99
2.850
1-455 2365
1 153
83 22 44.07
23.78
.801
.449 4469
I2II
83 O2 49.88
24.97
.851
•455 3517
1152
83 23 07.84
23.76
.802
•449 5679
I2O9
83 03 14.84
24.94
.852
.455 4668 1151 83 23 31.58
23.74
.803
.449 6888
1208
83 03 39-77
24.92
•853
• 455 5819 "SO 83 23 55.31
23.71
.804
.4498095
1207
93 04 04.68
24.89
-854
-455 6968
1148
83 24 19.01
23.69
2.805
1.449 9301
I2O6
83 04 29.56
24.87
2.855
1.455 8115
1 147
83 24 42.69
23.67
.806
•450 0507
I2O5
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
.456 0408 i 1145
83 25 29.97
23.62
.808
•450 2913
I2O2'
83 05 44-o6
24.80
.858
.456 1552
1144
83 25 53.58
23.59
.809
• 450 4H5
I2OI
83 06 08.84
24.77
.859
.456 2696
H43
83 26 I7.I6
23.57
2.810
1-450 5315
I2OO
83 06 33.6o
24-75
2.860
1.456" 3838
1142
83 26 40.72
23-55
.811
.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
1,196
83 07 47-73
24.67
.863
.456 7258
1138
83 27 51.26
23.48
.814
.451 0105
H95
83 08 12.39
24.65
.864
.456 8395
H37
83 28 14.72
23.45
2.815
1.451 1299
"94
83 08 37-03
24.62
2.865
1.4569532
1136
83 28 38.16
23.43
.816
.451 2492
1193
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 487S
1190
83 09 50.79
24-55
.868
•457 2935
H33
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
1.451 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
.8-4
•452 1995
1183
83 12 17.66
24.41
.874
•457 9710
1126
83 32 08. u
23.22
2.825
1.452 3178
'1182
83 12 42.05
24.38
2.875
1.458 0835
1125
83 32 3L32
23.20
.826
.452 4359 Ti8i
83 13 06.42
24.36
.876
.458 1959
1124
83 32 54-50
23.18
.827
.452 5540 nSo
83 13 30.76
24.33
.877
-458 3083
1123
83 33 17.67
23.15
.828
.452 6719
1178
83 13 55.o8
24-31
.878
.458 4204
II2I
83 33 40.8i
23.13
.829
•452 7897
1177
83 14 19.38
24.28
.879
.458 5325
1120
83 34 03-93
23.11
2.830
1.452 9073
1176
83 M 43.65
24.26
2.880
1.458 6445
III9
83 34 27.03
23.08
.831
.453 0249
ii75
83 15 07.90
24.24
.881
.458 7564
1118
83 34 50.10
23.06
.832
•453 1423
1174
83 15 32.12
24.21
.882
.458 8681
1117
^3 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
1115
83 35 59.i8
22.99
2'§3I
I. 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
IU3 83 36 45-12
22.95
•S3Z
•453 7278
1168
83 17 32.88
24.09
.887
.459 4252
i ii i ! 83 37 08.06
22.92
.838
-453 8445
1167
83 17 56.96
24.07
.888
.459 5363
mo 83 37 30-97
22.90
.839
•453 96l2
1166
83 l8 2-1.02
24.04
.889
.459 6473
1 109 83 37 53-86
22.88
)
2.&40
1-454 0777
1-165
83 18 45.05
24.02
2.890
1.459 758l
1108 83 38 16.73
22.86
•*4' -454 1941
1163
83 19 09.06
24.00
.891
.4598689
Ii07!«3 38 39-57
22. S3
•*l-' -454 3104
1162
83 19 33-04
23-97
.892
•459 9795
110683 39 02.40
22.81 i
•«43 -454 4265
r MM
83 19 57-01
23-95
.893
.460 0901
1105 83 39 25.19
22.79
.&44
-454 5420
1160
83 20 20.94
23.93
.894
.460 2005
1104 83 39 47-97
22.77
2.845
1-454 '>5«5
1 150
83 20 44.86
23.90
2.895
1.460 3108
1103 83 40 10.73
22.74
•454 7743
rig
83 21 08.74
23.88
.896
.460 4210
i w ; S} 40 33.46
22 . 72
.to
.454 8900
1156
83 21 32.6l
23-85
• 897
.460 5311
i loo 83 40 56.17
22.70
.848
-455 0056
1155
83 21 56.45
23.83
.898
.460 6411
TOOO S.? 41 18.85
22.68
,849
-455 121 1
H54
83 22 20.27
23.81
.899
.460 7510
1098
83 41 4L52
22.65
2.850
'•455 2365
1153
83 22 44.07
23.78
2.900
1.460 8607
1097
83 42 04.16
22.63
•
2tan-'(e")-2
<*»sechu
atin-HeuJ-SO0
«•» sech u
u
2tar-Ke»)-~
usechu
2 tan-He")- 90°
co sech u
SMITHSONIAN TABLCB
304
The Gudermannian.
u
gdu
•Fo'
gdu
«F,/
•
gdu
«F0'
gdu
•IV
0 / //
a
O / U
u
2.900
1.460 8607
1097
83 42 04.16
22.63
2.950
1.466 2123
1044
84 oo 28.00
21.53
.901
.460 9/04
1096
83 42 26.78
22. 6l
.<;5i .466 3167
1043
84 oo 49.53
21.51
.902
.461 0800
1095
83 42 49-37
22.59
• 952 .466 4209
1042
84 01 1 1 .03
21.49
.903
.461 1894
1094
83 43 11-95
22.56
• 953 .466 5251
1041
84 01 32.51
21.47
.904
.461 2987
1093
83 43 34.50
22.54
•954
.466 6291
1040
84 oi 53.97
21.45
2.905
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
.907
.461 6261
IOOO
83 44 42.02
22.47
• 957
.466 0406
1037
84 02 58.21
21.38
.908
.461 7350
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
22.38
.961
.467 3544
1033
84 04 23.57
21.30
.912
.462 1695
1084
83 46 34- 1' i
22.36
.962
.467 4576
1032
840444.86
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
2.965
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
1022
84 07 55-50
2I.O9
.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 51 00.86
22.10
•974
.4686881
IOI9
84 08 58.67
21.02
2.925
1.463 5698
1070
83 Si 22.94
22.O7
2.975
1.468 7000
1018
84 09 19.69
21. OO
.926
.463 6768
1069
83 5i 45-00
22.05
.976
.468 8918
1017
84 09 40.68
20.98
.927
.463 7836
1068
83 52 07.05
22.03
.977
.468 9935
1016
84 10 01.65
20.96
.928
.463 8004
1067
83 52 29.07
22. OI
.978
.469 0950
1015
84 10 22.60
20.94
.929
.463 9970
1066
83 52 51.06
21.99
• 979
.469 1965
1014
84 10 43-53
20.92
2.930
1.464 1036
1065
83 53 13-04
21.97
2.980
1.469 2979
1013
84 II 04.44
20.90
.931
.464 2IOO
1064
83 53 34-99
21.94
.981
.469 3992
IOI2
84 II 25.33
20.88
i .932
.464 3163
1063
83 53 56.93
21.92
.982
.469 5003
IOII
84 II 46.20
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
21.68
.084
.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.O9
20.67
.942
.465 3739
1052
83 57 35.06
21.70
.992
.470 5065
1001 84 15 13.75
20.65
•943
.465 4790
1051
83 57 56.75
21.68
.993
.470 6066
IOOO 84. IS 34.39
20.63
•944
.465 5841
1050
83 58 18.42
21.66
.994
.470 7066
999
84 15 55.01
20.61
2-945
1.465 6891
1049
83 58 40.07
21.6*4
2.995
1.470 8065
90S
84 16 15.61
20.59
.946
.465 7939
1048
83 5901.70
21.62
.996
.470 0062
997
84 16 30.19
20.57
• 947
.465 8987
1047
83 59 23.31
21.60
•997
.471 0059
996
84 16 56.75
20.55
.948
.466 0033
1046
83 59 44.90
21.58
.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 37.81
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
atan-W-g
«> sech u
Ztan-Me")-*)0
wsech u
u
2tan-'(e°)-j[
wsechu
2tan-1(e°>-900
•xsechu
SMITHSONIAN TABLES
305
The Gudermannian.
u
gd u
«F0'
gdu
7
u
gd u
O.FO'
gdu
^
o / //
H
0 / //
~
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
202.85
•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
196.88
.54
•512 7859
5798
86 40 34-50
H9.59
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
191.09
• 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
84 53 32.97
183.63
.6r
.516 7058
5406
86 54 03.03 111.52
.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
178.22-
.64
.5l8 3037
5247
86 59 32.62
108.22
3.15
1.485 1445
8555
85 05 33-04
176.45
3.6s
1.518 8258
5195
87 oi 20.30
107.15
.16
.485 9957
8470
85 08 28.61
174.70
.66
.519 3427
5143
87 03 06.92
106.08
.17
.486 8385
8386
85 u 22.45
172.97
.67
.519 8544
5092
87 04 52.47
105.03
.18
.487 6729
8303
85 14 H.56
171.26
.68
.520 3611
5041
87 06 36.98
103.09
.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
8139
85 19 53.69
167.88
3.70
1.521 3593
4042
87 10 02.89
101.93
.2-1
.490 1269
8058
85 22 40.73
166.21
•71
.521 8511
4893
87 ii 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 8199
4796
87 15 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
159.71
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 06.60
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
I5L95
3.8o
1.526 0622
4472
87 26 12.93
92.24
•31
.497 7064
7294
85 49 02.69
150.44
.81
.526 5072-
4428
87 27 44.71
91.32
•32
.498 5221
7221
85 51 32.38
148.95
.82
.526 9478
4384
87 29 15.58
90.42
• 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
7OO8
85 58 52.60
144.56
3.85
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. I i
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 9"3
4087
87 39 26.86
84.31
3-40
1.504 0746
6667
86 10 37.65
137.52
3.90
1.530 3180
4047
87 40 50.75
83.47
• 41
.504 738o
6601
86 12 54.48
136. 16
.91
•530 7207
4007
87 42 13.81
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
•507 9575
6280
86 23 58.56
129.53
.96
.532 6747
3811
87 48 56.85
78.61
•47
.508 5823
6217
86 26 07.44
128.24
•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
77.06
•509 8135
6095
86 30 21.39
125.71
.99
.533 8011
3699
87 52 49- 19
76.29
3.50
I.5I04I99
6034
86 32 26.47
124.46
4.00
1.534 1691
3662
87 54 05.10
75.53
0
2
" tech u
2tan-Hei>-fl00
wsechu
u
7T
«>sechu
2tan-Ke«)-90°
«> sech u
SMITHSONIAN TABLES
306
The Gudermannian.
u
gdu
«F0'
Odu
«F.'
u
•it
u.F
Odu
•f
0 / //
//
Q i U
//
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
§7 55
74.78
• 51
8003
2199
22.99
45-37
.02
•534 8943
3590
87 56 34.67
74-04
• 52
•549 0191
2178
08.13
.03
.535 2514
3554
87 57 48.33
73.30
•53
' -'358
2156
44-47
.04
•535 6050
3518
87 59 01.27
72.57
•54
.549 4503
2134
8S 46 37-07
44-03
4-05
1.535 9551
3483
88 oo 13.48
71.85
4-55
1.549 6627
2113
88 47 20.88
4.1-59
.o:j
.536 3017
3449
88 01 24. <;/
/I.I4
.56
•549 8730
2092
88 48 04.25
43.15
.07
.536 6449
3415
88 02 35./6
70.43
• 57
• 550
2071
47. Ky 4~
.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
83 50 11.79
41.88
4.10
1.537 6540
3314
88 06 03.91
68.35
4.60
1.550 6933
2010
88 50 53.46
41.46
.u
•537 9837
3281
88 07 11.91
67.67
.61
.550 8933
1900
88 51 34-72
41.05
.12
.538 3102
3248
88 08 19.25
67.00
.62
•551 0914
1970
40.64
•13
.538 6333
3216
88 09 25. (,i
66.33
.63
•551 2874
1951
5'). oo
40.24 1
.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 u 37.25
65.02
4.65
I.55I 6737
IQI2
88 54
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 S3 55 33-77
38.66
.18
.540 2017
3059
8S 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
.21
1.540 8074
.541 1058
2098
2969
88 16 54-34
88 17 55.88
61.85
61.23
4.70
• 71
1.552- 6063
•552 7873
1819
1801
83 57 28.03
88 58 05.36
37.52!
37.U
.22
.541 4012
2939
88 18 56.81
60.62
.72
•552 9664
1783
88 58 42.32
36.77
•23
.541 69361 2910
8S 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
8S 59 55.M
36.05:
4-25
1.542 2698
2852
88 21 55.98
•58.83
4-75
1.553 4934
1730
89 oo 31.01
35.09
.26
.542 5536
2824
88 22 54.52
58.25
.76
•553 6655
1713
89 01 06.52
35-33
.27
.542 8346
2796
88 23 52.48
57.67
.77
•553 8360
1696
8-> 01 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 I7i8
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
.31
.543 9308
2686
88 27 38.60
55.41
.81
• .554 5010
1630
89 03 58.84
33.61!
.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
.«3
.554 8236
1597
80 05 05.39
•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
32.20
.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
•555 4499
1535
89 07 14-57
31.65'
.38
.545 7469
2505
8833 53.19
51.66
.88
.555 6026
1519
89 07 46.07
31-34
• 39
• 545 901
2480
88 34 44-59
5I-I5
.89
.555 7538
1504
89 08 17.25
31.03,
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 15.76
49.64
.92
.556 1083
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
29.8l
.44
•547 2055
2359
88 38 54.05
48.65
•94
.556 48/4
M3I
89 10 48.57
29-51
4-45
1.547 4403
2335
88 39 42-46
48.17
4-95
1.556 6207
1417
89 II 17.93
29.22
.46
.5476726
2312
88 40 30.40
47.69
.96
.556 7707
1403
8-j u 47.01
28.93
•47
.547 9027
88 41 17.85
47.22
•97
.556 9103
1389
15.79
28.04
.48
.548 1305
2266
88 42 04.83
46.75
.98
.557 04>U
1375
89 12
28.36
.49
.548 3560
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
S.oo
1.557 3206
1348
89 13 40-44
27.79
u
atan-He")"!
<» sech u
2tan-Ke")-900
<»sechu
u
2tan-'(e«)~
wsechu
Ztan-He^h-SO0
wsech u
SMITHSONIAN TABLES
307
The Gudermannian.
u
gdu
^~
gdu
.w
u
gd u
«*
gd u
»Fo'
5.00
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. 10
27.52
• 51
.562 7042
809
89 32 10.87
i6*.69
.02
.557 5875
1321
89 14 35.48
27.24
• 52
.562 7847
801
89 32 27.48
16.53
.03
.557 7189
1308
89 15 02.58
26.97
• S3
.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.O5
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
.558 3567
1244
89 17 M.I4
25.66
• 58
.563 2512
755
89 34 03.71
15.56
.09
.558 4804
1232
89 17 39.67
25.40
• 59
.563 3263
747
89 34 19.20
15.41
5.10
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
1195
89 18 54.74
24.65
.62
.563 5471
725
89 35 04-73
14.95
•13
.558 9633
1183
89 19 19-27
24.41
.63
.563 6192
7i8
89 35 I9.6i
14.80
.14
.559 oSii
1172
89 19 43.56
24.16
.64
.563 6906
711
89 35 34-34
14.66
S-i|
.16
1-559 19/6
.559 3i3'i
1160
1148
89 20 07.60
89 20 31.40
23.92
23.69
S:S
1.563 7613
.563 8313
703
697
89 35 48.93
89 36 03.36
14.51
14.37
.17
•559 4273
1 137
89 20 54-97
23.45
.67
.563 9006
690
89 36 17.66
14.22
.18
.19
•559 5404
•559 6524
1126
1114
89 21 I8.3I
89 21 41.41
23.22
22.99
.68
.69
• 563 0692
.564 0372
676
89 36 31.81
89 36 45.8*
14.08
13.04
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
80 37 13-43
13.67
.22
.5599818
1081
89 22 49.34
22.31
.72
.564 2369
656
89 37 27.03
13.53
.23
.560 0894
1071
89 23 11.53
22.08
•73
.564 3022
649
89 37 40.49
13.40
.24
.560 1959
1060
89 23 33.5ii
21.86
.74
.5643668
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
21.01
.78
.564 6189
618
89 38 45.82
12.74
.29
.560 7129
1008
89 25 20.14
20.80
• 79
.564 6804
612
89 38 58.50
12. 6l
5.30
1.560 8132
908
89 25 40.84
20.59
5.8o
1.564 7412
606
89 39 ".OS
12.49
•31
.560 9126
988
89 26 01.33
20.39
.81
.564 8015
599
89 39 23.48
12.37
.32
.561 0109
979
89 26 21.61
20. 18
.82
.564 8611
594
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 oi . 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
n.88
.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
I9.2O
.87
.565 1506
565
89 40 35.48
11.65
.38
.561 5807
922
89 28 19.15
I9.OI
.88
.565 2068
559
89 40 47.07
n.53
.39
.561 6724
912
89 28 38.06
18.82
.89
.565 2624
553
8940 58.54
LI. 41
5.40
1.561 7632
903
89 28 56.79
18.63
5.00
1.565 3i75
548
89 41 09.90
11.30
;' .501 8531
894
89 29 15.33
18.45
.91
.565 3720
542
99 41 21.15
II. 19
.561 9421
885
89 29 33.68
18.26
.92
.565 4259
537
89 41 32.28
11.08
.43
.502 0302
877
8929 51.85
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
§51
89 30 45.29
17-55
•96
.565 6365
89 42 15.71
10.64
.47
.562 3739
842
89 3i 02.75
17.37
•97
.5656879! 5li
89 42 26.30
10.54
..;8
.562 4577
834
89 31 20.04
17.20
.98
.565 7387
506
89 42 36.79
10.43
.49
.562 5407
826
89 3i 37-15
17.03
•99
.565 7890
50i
8942 47-17
10.33
5.50
1.562 6228
817
89 31 54-10
16.86
6.00
1.565 8388
496
89 42 57-44
10.23
u
2*n-Ke^2
«- tech u
.» ..«*-«.
«•» sech u
u
2 tan-He")-^
wsechu
Ztan-H.MK,
wsechu
ITHSONIAN TABLES
308
TABLE VII
THE ANTI=GUDERMANNIAN
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.tan f — 7r-f — gd u) = u radians.
In this table the second decimal place is sometimes erroneous by a unit.
309
The Anti-Gudermannian.
gdu
o°
~^~
2°
3°
4° 5° 6°
7°
8°
9°
10°
gdu
0'
o'.oo
60.00
120.02
180.08
240.19
300.38 360.66
421.05
481.57
542.23
603.07
o'
I
1. 00
61.00
I2T.02
181.08
241.20
301.38
361.66
422.06
482.58
543-25
604.08
I
2
2.00
62.00
122.03
182.08
24J.. 20 302.39
3'02 . 67
423-06
483.59
544.26 605.10
2
3
3.00
03.00
123.03
183.09
243.20 303.39
363.67
424.07
4<S4.w
545.2i7 606.12
3
4
4.00
(>4.00
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
245.21 305.40
365.69
426. 09
4^.62 547.30
608.15
5
6
6.00
66.00
126.03
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
611.19
8
9
9.00
69.00
129.03
189.09
249-212' 309.42
369.71
430.12
490.66
551.35
612.21
9
10
10. CO
70.00
130.03
190.10
250.212 310.42
370.72
43LI3
491.67
552.36
613.23
10
ii
II. OO
71.00
I3L03
191 . 10
251.22 311.42
371.72
432.13
492>.68
553-37
614.24
ii
12
12.00
72.00
132.03
192.10
252.23 312.43
372.73
433.14
493.69
554-39
615.26
12
13
13.00
73.00
IQ/3.03
193.10
253.23
313-43
373.74
434.15
494.70
555.40
616.27
13
14
14.00
74.01
I34J.O3
194.10
254.23
314.44
374.74
435.16
495.71
556.41
617.29
U
15
15.00
75-01
I35.03
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. ii
256.24.
316.46
076 - 75
437.17
497-73
558.44
619.32
16
17
17.00
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
80. 01
140.04
200. ii
260.25
320.46
380.78
441.21
501.77
562.49
623.39
20
21
21. OO
81.01
141.04
2OI.II
261.25
3121.47
381.78
442.21
502.78
563.51
624.40
21
22
22.00
82.011
142.04
2O2.I2
26(2.25
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
2O4.I2
264.26
324.48
384.80
445.24
505.81
566.55
627.45
24
25
25.00
85.01
I4'5.04
2O5. 12
265.26
325.48
385.81
446.25
506.83
567.56
628.47
26
26
26.00
86.01
146.04
206.12
266.27
326.49
386.81
447.26
507.84
568.57
629.49
26
27
27.00
87.01
147.04
207.13
267.27
327.49
387-82
448.26'
508-85
630.50
27 '
28
28.00
88.01
1418.05
208.13
268.. 217
328.50
388.83
449.27
509.86
570.00
631.52
28
29
29.00
89.01
149.05
209.13
269.271329.50
389.83
450.28
910.87 571.62-
632-54
29
30
30.00
90.01
150.05
210. 13
270.28 330.51
390-84
451.29
51 1. 88 | 572. 63
633.56
30
31
31.00
91.01
I5L05
2-11.1(3
271.2813311.51
391.85
452.30
512.891573.64
634.57
31 ;
32
32.00
92.01
152.05
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
04
34.00
94-01
154.05
214.14
274.29 334.53
394-85
4'55.33
515.93
576.691
637.62
34
35
35-00
95-01
IS5.05
215.14
275.29 335.53
395.87
456.33
516.94
577.70
638.64
35
36
36.00
96.01
156.05
2I6.I4
276.30 336.54
396.88
457-34
517.95
578:71
639.66
36
37
37-00
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
30
39.00
99-01
T'59-06
219.15
279.31
339-55
399.90
460.37
520.98
581.76
642.71
39
40
40.00
100.01
160.06
220.15
280.31
340.56
400.91
461.38
521.99
582.77
643-73
40
41
41.00
IOI.OI
161.06
221 . I&
281.31
34I.-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
924.02
584.80
645.76
43
43.00
103.02
163.06
223.16
283.32
343-57
403.93
4641.4*
525.03
585.81
6416.78
43 :
44
44.00
104.02
164.06
•2124.16
284.32
344.58
404.93
465.41
526.04
586.83
647.80
44
45
45-00
105.02
165.06
225 . 16
285.33
34'5.58
405.04
4166.42
527.05
587.84
648.82
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
48
47.00
48.00
107.02
I08.02
167.07
168.07
227.16
228.17
287.33
288.34
347-59
348.60
407.95
408.96
468.44
469.45
529.08
530.09
589.87
590.89
650.85
651.87
47
48
49
ICO. O2'
169.07
229.17
,289.34
349.60
409.97
470.46
53I.IO
591.90
652.89
49
50
50.00
110.02
170.07
230.17
290.34'
350.6i
410.97
471.47
532.ii
592.92
653.91
50
51
51.00
in. 02
171.07
231.17
291.35
35I.6I
4111.98
472.48
533-12
593-93
654.93
51
5*2
52.00
112. O2
172.07
232.18
292.35
352.62
4112.99
473.49
534- 14
594-95
655.94
52
53
53.oo
113.02,
173.07
233-18
293.35
353.62
414.00
474-50
535.15
595.96
656.96
53
54
54-00
114.02
174.07
234 . 18
294.36
354.63
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
176.08
236. 18
296.37
3156.64
417-02
477-53
538.18
509.01
660.02
56
57
57.00
117.02
177.08
237.19
297.37
357.64
418.03
478.54
539-20
600.02
661.04
58
58.00
118.02
178.08
238.19
298.37
358.65
419-03
479-55
540.21
601.04
662.05
58
5*>
179.08
2-39.19
299.38
359.65
420.04
480.56
541.22
602.05
663.07
59
<o
60.00
180.08
240.19
300.38
360.66
421 .05
481.57
542-23
603.07
664.09
60
SMITHSONIAN TABLE*
310
The Anti-Gudermannian.
gdu
11°
12°
13°
14'°
15°
;
18" 19°
20°
Qdu
(/
664'.09
725.32
7-%- 78
848.49
910.46
•J72-7J
1035.30
0'
I
665.11
726.34
787.81
849-5-'
<>n.5o
973-77
1036.35
1099.-,
1226.20
I
2
666.13
727.37
850.55
912.5.5
974-81
1037.40
1100.32 III
-•
3
7$£>.86
851.58
9i3o7
1038.44
1IOI.37 i:
4
668.17
790.89
1039.49
4
5
669.19
730-43
791.91
853.64
915.04
977-93
1040.53
1103.47 i;
1230.46
5
6
670.21
7JL46
792.04
854.67
916.67
978.97
1041.58
1104.53 1167.83
0
7
671 . 22
732.48
793- <J7
855.70
917.7'
980.01
1042.63
1105.
7
8
67^.24
733-50
794.99
850.73
918.75
981.05
1043.67
1106.63
1169.95
1233.00
8
9
673-26
734.53
796.02
g57.!76
919.78
982.09
1044.72
1107.68
1171.01
i -'34- 7-J
9
10
674.3«
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
921.85
984.17
1046.81
1109.79
1173.13
1236.85
II
12
676.32
737-59
799. 10
860.8(3
92-2.89
985.22
1047.86
1110.84 1174.19
12-37.92
12
13
677.34
738.62
800.13
861.89
923.93
966.26
1048.91
1111.8-; i
1238.98
13
14
678.36 739.64
801 . 15
tt>2.</2
924.96
087.30
1049.95
1112.95 117'.. 30
1240.05
U
15
679-38
740.66
802.18
863.95
925.00
988.34
1051.00
1114.00 1177.36
1241.11
16
680.40
741.69
803.21
864.98
927-03
989-38
1032.05
1115.05 1178.42
16
17
681.42
74.-'. 71
804.24
866.02
928.07
990.42
1053-09
1116. 1 1
1179.48
1243.25
17
18
(582.44
743-73
805.26
867.05
929.11
991.47
1054-14
I 117. 10
n&>.54
1244.31
18
19
683.46
744.76
806.29
868.08
930.15
992.51
1055-19
1118.21
[181.60
1245.38
19
20
684.48
745-/B
807.32
869.11
93I.I8
993-55
1050.24
1119.27
1246.44
-
21
685.50
746.81
8o8.3'5
870.14
932.22
994.59
1057.28
1120.32
1183.72
1247.51
_•
22
08:>.5_>
747.83
809.37
871 . 18
933-26
995.63
1058.33
1121.37
1184-78
22
33
687.54
748.85
810.40
8/2.2.1
934.29
996.68
1059.38
1122.43 1185.84
23
24
688.56
749.88
811.43
873.24
935-33
997.72
1060,43
1123.48 1186.90
1250.71
-.
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
999.8o
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
1253.91
J
28
692.64 753.97
815-54
877-37
939.48
1001.89
1064.62
1127.70 1191.14
1254.98
.
29
693.66! 755.00
816.57
878.40
940.52
1002.93
1065.67
1128.75 1192.20
1256.05
-
30
694.68
756.02
817.60
879-44
941-56
1003.97
1066.72
1129.81 1193.26
1257.12
30
3*1
695-70
757.05
818.63
880.47
942.59
1005.02
1067.77
1-130.86 1194.32
1258.18
31
32
696.72
758.07
819.66
881.50
943.63
1006.06
1068.81
1131.92 1195.39
32
33
697-74
759-09
820.69
882.54
944.67
1007.10
1069.86
1132.97 1196.45
1-260. 3-2
33
34
698.76
760.112
8)21.71
883.57
945.71
1008. 15
1070.91
11.34.03 1197.51
I26I.39
1
35
609.78
761.14
822.74
884.60
946.74
1009.19
1071.96
1135.08
1198.57
1262.45
35
36
700.80
762.17
823.77
S85-04
947.78
1010.23
1073.01
1136.14
1100.63
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
764.22
825-83
887.70
949-86
1012.3-2
1075.11
1138.25
1201.75
1265.66
38
39
703.87
765-24
826.86
888.74
950.00
1013.36
1076.16
1139.30
1202.8_>
1266.73
39
40
704.89
766.27
827.89
889.77
95L94
1014.41
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
I27I.OO
43
44
708.97
7/0.37
832.00
893.91
956.09
1018.58
1081.41
1144.58
1208.13
1272.07
.
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
/•
47
712.04
773-44
835.09
897.01
959-21
1021.72
1084.56
1147-75
1211.31
48
713-06
774-47
836. 12
898.04
960.25
1022.76
1085.61
1148.80
1276.35
48
49
714.08
775- '49
837.15
899.08
961.29
1023.81
1086.66
1149.86
1213.44
1277-42
4'J
50
715-10
776.52
838.18
900.11
962.33
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
1151.97
1215.57
1279.56
Si
•52
717.15
778.57
8L40.24
902.18
964.41
1026.04
1089-81
1153.03
1280.63
52
53
718.17
779-59
841.27
903.212
965.45
1090.86
1154.09
1217. u>
12^1.70
53
54
719.19
7180.62
842.30
904.25
966.49
1029.03
1091 .91
1155.14
I2I8.76
54
55
72O.2I
781.65
843.33
905.28
967-53
1030.08
1092.96
1156.20
I2I9.8l2
1283.84
SS
56
7!21.23
782.67
844.36
006.32
968.57
1031.12
1004.01
1220.88
1284.91
56
57
722.26
783.70
845.39
907.3S
969-61
1032.17
1095.06
1158.32
1221.95
1265.98
;-
58
723,28
784.73
846.42
908.39
970.65
1033.21
1096. ii
1159.37
1223.01
1-287.05
5
59
724.30
785.75
847.45
909.43
971.69
1034 . 26
1007.16
1160.43
1224.07
1288. 13
59
60
725.32
786.78
848.49
910.46
972-73
1035-30
1098. 22| Il6l.49
1225.14
1289.20
00
SMITHSONIAN TABLES
The Anti-Gudermannian.
gdu
21°
22°
23°
2-4°
2=5°
26°
27°
28°
29°
30°
gdu
o'
I289/.20
1353.69
1418.63
1484.06
1549-99
1616.47
1683.52
1751.16
1819.44
1888.38
cf
I
1290.27
1354.76
1419.72
1485.15
1551.10
1617.58
1684.64
1752.29
1820.58
1889.53
i
2
1291.34 1355.84
14120.80
1486. .25
1552.20
1618.70
1685.76
1753.43
1821.72
1890.69
2
3
1292.41 1356.92
1421.89
1487.34
1553.31
1619.81
1686.88
1754.56
18212.87
1891.84
3
4
1293.4)8 13=58.00
1422.98
1488.44
I554.4I
1620.92
1688.01
1755.69
1824.01
1893.00
4
5
I294-.55
1359.08
1424.06
1489.53
1555-51
1622.04
1689.13
1756.83
1825.16
1894.15
5
6
1295.63
1360. 16
It4t2(5.I5
1400.63
1556.62
1623.15
1600.25
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
1362.32
1427.32'
1492.82
1558.83
16215.38
1692.50
1760. 2$
1828.59
1897.62
8
9
1298.84
1363.40
1428.41
1493-91
1559-93
1626.49
1693.62
1761.36
18-29.73
1808.78
9
10
1299.91
1364.48
1429.50
1495.01
1561.04
1627.61
1694.75
1762.50
1830.88
1899.93
10
ii
1300.99
1365.56
1430.59
1496.11
1562.14
1628.72
1695.87
1763.63
1832.02
1901.09
II
!_>
1302.06
1366.641
1431.68
1497.20
1563. -215
1629.84
1697.00
1764.77
1833.17
1902.25
12
IB
1303.13
1367.72
1432.76
1498.30
F564.35
1^30.95
1698.12
1765.90
1834.32
1003.40
13
14
1304.20
1368.80
1433.85
1499.40
1565-46"
1632.06
1609.25
1767.04
1835.46
1904.56
14
15
1305.28
1-369.88
1434.04
1500.49
1566.56
1633.18
1700.37
1768.17
1836.61
1905.72
15
16
1306.35
1370-96
1436.03
1501.59
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
1 503. 78
1569.88
1636.50
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
14140.38
1505.98
1572.09
1638.76
1706.00
1773.85
1842.314
1911-51
20
21
I3H.72
1376.36
1441.47
1507.08
1573-20
1639.87
1707.12
I774.9S
1843.49
1912.67
21
22
1312.79
1377.44
1442.56
1508.17
1574.31
1640.99
1708.25
1776. 12
1844.64
1913.83
2(2
S3
1313.86
1378.52
1443.65
1509.27
I575.4I
1642.10
1709.37
1777.26
1845.78
1914.98
23
24
1314.94
1379.61
1444.74
1510.37
1*576.52
16413.22
1710.50
1778.39
I8U6.93
1916.14
24
25
1316.01
1380.69
1445.83
1511.47
1577.63
1044.34
1711.63
1779.53
1848.08
1917.30
2>5
! 26
1317-08
1381.77
1446.92
I5H2.57
1578.73
1645. 4'5
1712.75
1780.67
1849.^3
1918.46
26
27
1318.16
1-382.85
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
1450. 19
1515.86
1582.06
1648.86
1716. 14
11784.08
1852.67
19211.94
29
1321.38
1386.10
1451.28
1516.96
1583.17
1649.92
1717.26
1785.22
1853.82
1923.10
30
31
1322.45
1387.18
1452.37
1518.06
1584-27
1651.04
i'7i8.39
1786.36
1854.97
1924.26
31
32
1323.53
1388.26
1-453.46
1519-16
1585.38
1652 . 16
1719.52
1787.50
1856. 121
192(5.43'
33
1324.60
1389.35
1454.55
1520.26
1586.49
1653.27
1720.65
T788.60
1857.27
1926.59
33
34
1132-5.68
1390.43
1455.64-
1521.36
1587.60
1654-39
,1721.77
1789.77
1858.42
1927.75
34
35
1326.75
i39i.5i
1456.73
1522.46
1588.71
1722.90
1790.91
1859.57
1928.91
3*5
36
1327-83
1392.59
14-57.83
1523.56
1589.82
1656.63
1724.03
1792.05
1860.72-
1930.07
36
37
1328.90
1393.68
1458.92
1524.66
1590.92
1657-75
1725.16
1793.19
1861.87
1931-23
37
38
1329.98
1394.76
1460.01
152-5.76
1592.03
1658.87
1726.29
1794-33
1863.02
193^.40
38
I33i.o6
1395.84
1461 . 10
1526.86
i;593.i4
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
i'333.2i
1308.01
1463.28
11529.06
1595.36
1662.22
1729.67
1797.75
1866.47
1935-88
41
42
I334-29
1300.10
1464.38
1530. 16
1506.47
1663.34
1730.80
1708.89
1867.62
1937-05
42
40
1335-37
1400. 18
1465.47
1531.26
1597.58
1664.46
1731.93
I800.03
1868.77
1938.21
43
44
1336.44
1401.26
I466.-56
1532.36
1598.69
1665.58
1733-06
1801.17
1869.92
1939.37
44
1337.52
1402.35
1467-65
1533.46
1599.80
1666.70
1734. 19
1802.31
I87I.08
1940.54
45
1338.60
1403.43
1468.75
1534.56
1600.91
1667.82
1735.32
I803.45
1872.23
1041.70
46
1339.67
1404.52
1469.84
1535.66
1602.02
1668.94
1736.45
1873.38
1942.86
47
48
1340.75
1405.60
1470.93
1536.77
1603.13
1670.06
1737.58
I805.'73
1874.53
1944.03
4«
49
HO-V'x;
1472.02
1537.87
1604.24
1671.18
1738.71
1806.87
187=5.69
1945.19
49
50
1407.77
1473.12
1538.97
1605.35
1672.30
1739.84
iSoS.OI
1876.84
1946.36
50
Si
1343-98
1408.86
1474.21
1540.07
1606.46
1673.42
1740.08
1869.15
1877.99
1947-52
51
52
1345.06
1475.30
1541-17
1607.58
1674.54
1742.11
l8lO.3O
1879. 14
1948.69
52
53
'.M''- '•}
141 1 .03
1476.40
154-2.27
1608.69
1675.66
1743.24
1811.44'
1880.30
1949.85
53
54
[412.11
'477-40
1543.38
1609.80
1676.79
1744.37
1812.58
l88l.45 j I95I.O2
54
55
1348.29
1413.20
1478.59
1544.48
1610.91
1677.91
1745.50
1813.72
1882.60
1952.18
55
56
1 1 1 1 . _>X
1545.58
1612.02
1679.03
1746.63
1814.86
1883.76
T953-35
56
57
1350.45
'1*0.77
1546.69
1613.13
1680. 15
1747.76
1816.01
1884.91
1954.51
57
58
1351.53
i \\<>. \(>
i4«i.X7
1547-70
1614.25
1681.27
1748. oo ! 1817.15
1886.07
1955-68
58
60
1353.69
1418.63
1482.96
1484.06
1548.89
1549.99
1615.36
1616.47
1682.39
1683.52
1750.03 1818.29
1751.16 1819.44
1887.2121
1888.38
1956.85
1958.01
59
60
SMITHSONIAN TABLES
312
The Anti-Gudermannian.
gd u
31°
32°
33°
34°
35°
.'
37°
38'
»
40°
gdu
(/
i958'.oi
2028.38
2099-53
2171.48
2244.29
-'317.99
2392.63
2468.26
2622.69
*
I
1959- 18
2029.56
2100.72
2172.69
2245.51
2319.22
2393-88
246903
2024.00
i
2
KX*>-35
2030.74
2IOI .91
2173.89
2246.73
2320.46
2470.80
2025.30
2
3
1961.51
2031.92
2IO3.IO
2175.10
2247-95
2321.70
2472.07
2548.79
3
4
[962.68
2033. 10
2104.30
2176.31
2249.17
2550.08
4
5
1963.85
2034.28
2105.49
•21177.51
2250.39
2324.17
-'3'>8.90
2474.01
2551-37
2629.22
5
6
1965.02
2035.46
2106.68
2178.72
2251.62
2325.41
2400.15
2475.88
2630.53
6
7
K>X>.l8
2036.64
2107.88
2179.93
2252.84
2326.65
2401.40
2477.15
2553-95
7
8
1967-35
2037.82
2109.07
0181.14
2254.06
2327.89
2402.66
2478.42
-"'33-14
8
9
1968.52
2039.00
2IIO.27
2:182.35
2255.28
2329.12
2403.91
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
2331.60
2406.42
2482.124
2559. 10
2637.07
1 1
12
1972.03
2042.55
2113.85
2185.97
2258.95
2332.84
2407.68
2483.51
2560.30
2638.38
_•
13
1973.20
2043.73
2115.05
2187.18
2260.18
2334.08
2408.93
2484.78
2561.68
2639.69
U
14
1974.37
2044.91
2116.24
•2.188.39
2261.40
2335.32
2410.19
.2486.06
2562.97
2641.00
1
IS
1975.54
2046.10
2117.44
2189.60
2262.63
2336.56
2411.44
2487.33
2642.31
.
16
1976.71
2047.28
2118.6(3
2190.81
2263.85
23137.80
2412.70
2565.56
.".
17
1977.88
2048.46
2119.831
2192.02
2*265. 08
2339.04
2413.96
2489.88
12966.85
2644.93
17
18
1979.05
2049-64
2121.03
2193-23
2266.30
2340.28
2415-21
2568.14
2646.24
i,S
19
1980.22
2050.83
2L22.22
2194.44
2267.53
2341.52
2416.47
2492.43
2569.43
i<;
20
1581.39
2052.01
2123.42
2195-65
2268.75
2342.70
•-'4I/.73
2493.70
25/0.73
20
21
1982.56
2053.19
12124.62
2106.86
2269.98
2344.00
2418.09
2494.97
2572.02
2650.17
21
22
1983.73
2054.38
2125.81
2198.07
2271.20
2345.25
2420.24, 2496.25
-'573-31
2651.49
23
1984.90
2055-56
2I27.OI
2199.29
22712.43
2346.49
2421.50^2497.52
2652.80
-'3
24
1986.07
2056.75
2128.21
22OO.'50
2273.66
2347.73
2422.76 2498.80
2654.11
-'4
25
1587.24
2057.93
2129.41
2201.71
2274.88
2348.97
2424.02 2500.08
2577.19
2655.43
25
26
1988.41
2059.11
2I30.6I
22O2.92
2276.11
2350.21
2425.28 2501.35
2578.49
2656.74
26
27
1989.59
2060.30
2I3I.80
2204.14
2277.34
2351.46
2426.54 2502.63
2-579.78 2658.05
?7
28
1990.76
12061 .49
2133.00
2205.35
2278.57
2352.70
2427. So 2503.91 2581.08
29
1991.93
2062.67
2134.20
2206.56
2279.79
21353.95
2429.051 2505.IS _>=••
30
1993.10
2063.86
2135.40
2207.78
2281.02
23155.19
2430.312. 2506.46
30
31
1904.28
2065.04
2I36.6O
12208.09
2282.25
23156.43
2431.58 2507.74
2584-97
2663.31
31
S3
1995.45
2066.23
2137.80
22IO.2O
2283.48
2357.68
2432.84
2509.02 -
2664.63
3-
33
1996.62
2067.41
2139.00
2211.42
2284.71
2358.92
24134.10
2510..:
2665.04
33
34
1597.80
2068.60
2140.20
2212.63
2285.94
2360.17
2435-36
2511.58
2667.26
34
35
1998.97
2069.79
2141.40
2213.84
2287.17
2361.41
2436.62
2512.86
2500.15
2668.58
35
36
2000.14
2070.97
2142.60
2215.06
2288.40
2362.66
2437.8Q
2514.14
2501.45
->r/».S9
36
37
2001.32
2072 . 16
2143.80
32l6.27
2289.63
2363.90
2439.15
2515-41
37
38
2002.49
2073-35
2145.00
2217.49
2200.86
2365.15
2440.41
2594.05
^8
39
2003.67
2074.54
2146.20
2218.70
12-292.09
2366.40
2441.68
2517.97
2595.35
2673.85
39
40
2004.84
2075.72
2147.40
2219.92
2293. 3<2
2367.64
244&.9M
2519.25
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
2222.315
2295.78
2370. 14
2445.47
12521.82
2599.24
2677.80
42
43
2008.37
2079.29
2ISI-OI
2223.57
2297.01
2371.38
2446.73
2523-10
2679.12
43
44
2009.54
2080.48
2I52.2.I
2224.79
2208.24
2372.63
2447.90
2524.38
44
45
2010.72*
2081.67
2I5Q.4I
2226.00
2299.48
2373.88
2449.26
25125.66
2603.14
2681.76
45
46
2011.90
2082.86
2154.62
2227 . 22
2300.71
2375 -T3
24-50.52
2526.95
15
2683.08
-
47
2013.07
2084.04
2155.82
2228. 44
2301.04
2376.38
2451.79
2528.23
47
48
2OI4.25
2085.23
2157.0.2
2229.66
2303.17
2377.63
2453-05
12529. 5 i
2607.'
|S
49
2015.43
2086.412
2158.23
2230.87
2304.41
2378.87
2454-32
2530.79
2608.35 2687.04
49
50
2016.60
2087.61
2159.43
2232.09
2305.64
2380. 12
2455.'58
2532.08
2609.05 2688.36
50
51
20I7./8
2088.80
2160.63
2233.31
2306.88
3381.37
2456.85
2610.95 2689.69
51
52
2018.96
2089.99
2l6l.84
2234.53
2308.11
•2382.62
2458.12
2612.36 2-OI.OI
S«
53
2O2O.I3
2091.19
2163.04
2235.75
2309.34
2383.87
24'59.39
2535.93
•92.33
53
54
2021.31
2092.38
3164.25
121236.97
2310.58
2385.12
2460.65
2537.22
2014. 8/. 2093.65
54
55
2O22.49
2093.57
2165.45
2238.19
2311.81
0386.37
2461.92
2538.50
2694.98
55
56
2023.67
2094.76
2166.66
22139.41
•213113.05
2387.62
2463.19
2539.79
2617.47
2606.30
56
57
2024.85
2095.95
2167.86
2240.63
2314.28
2388.88
2464.46
2541-07
2618.78 2697.63
58
2026.03
2097.14
2109.07
2241.85
•21315.52
2390.13
2465.72
2542.36
2620.08
2698.95
58 '
59
2027.20
2098.33
2I7O.28
2243.07
2316.75
2391.38
£466.99
2543.64
2621.38
2700.27
59 i
60
2028.38
2099.53
2171.48
3244.29
2-317.99
2392.63
2468.26
2544-93
2622.09 2701.60
60
SMITHSONIAN TABLES
313
The Anti-Gudermannian.
gdu 41°
42°
43°
44°
45°
46°
47°
48°
49°
50°
gdu
cf 270 1 '.60
2781.71
2863.10
2945.81
3029.94
3H5.55
3202.71
3291.53
3382.08
3474-47
0'
I 2702.92
2783.06
2864.46
2947.21
3031.35
3Il6.99
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
-'705-57
2785.75
2%7 . 2O
2949.99
3034.18
3119.87
3207.12 3206.01
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
3I3L4I
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
2718.85
2799.24
2880.90
2963.92
3048.36
3134.30
3221.82
3311.00
3401.04
3404.74
13
14
2720.18
2800.59
2882.28
2965.32
3049.78
3135.75
3223.29
3312.50
3403.47
3496.31
14
IS
2721.51
2801.94
2883.65
2966.71
3051.20
3137.19
3224.76
33H.OO
3405.00
3497.87
IS
16
2722.84
2803.29
2885.02
2968.11
305-2.62
3138.64
3226.23
3315.50
3406.54
3499.43
16
2724.17
2804.64
2886.39
2069.50
3054.04
3'i40.o8
3227.71
3-3'i7.00
3408.07
3501.00
17
18
2725 . 50
2805.99
2887.77
2970.90
3055.46
3141.53
3229.18
3409-60
3502.56
18
19
2726.83
2807.34
2889.14
2972.30
3056.88
3142.98
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
3145.87
3233.61
3323.02
3414.20
3507.26
21
22
23
2730.83
2732.16
2811.40
2812.76
2893.27
2894-64
2976.49
2977.89
3061.15
3062.58
3147.32
31148.77
3235.08
3236.56
3324.53
3326.03
3415.74
3417.28
3508.83
3510.40
22
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
2808.77
2082.09
3066.85
3153.12
3240.09
3330. 55
3421.89
35I5.H
26
27
2737.50
2818.17
2900.15
2983-49
3068.27
3154.57
3242.47
3332.06
3423.43
3516.68
27
2738.83
2819.53
2901.53
2984.89
3069.70
3156.03
3243.95
3333.56
3424.^6
3518.25
28
2740. 17
•2820.88
2902.91
2986.29
3071 • 13
3157.48
3245.43
3335-07
3426.50
3519.82
'29
30
274L50
2822.24
2904.28
2987.70
3072.55
3158.93 3246.91
3428.04
3521.39
30
2742.84
2823.60
2905.66
2989.10
3073.98
3160.38
3248.39
3338.09
3429.58
3522.06
31
2744-17
2824.95
2907.04
2900.50
3075.41
3161.84
3249.87
3339.60
343LI2
3524.54
32
2745.51
2826.31
2908.42
2991.90
3076.84
3163.29
325L35
334i.li
3432.66
3526.11
33
34
2746.84
2827.67
2909.80
2993.31
3078.26
3164.74
3252.84
3342.62
3434-20
3527.68
34
35
2748.18
2829.03
291 1 . 18
2994.71
3079.69
3166.20
3254.32
3344-14
3435.75
3529.26
3'5
•2749.52
2830.39
2912.56
2996.12
308l . 12
3167.65
3255.8o
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
3083.08
3170.57
3258.77
3348.67
3440 . 38
3533-99
38
39
40
2753-53
2754.87
2834.46
2835.82
2916.71
2918.09
3000.33
3001.74
3085.41
3086.84
31172.02
3173.48
31260.25
3261.74
3350. 19
3351.70
3441.92
3443-47
3535-56
3537-14
39
40
41
2756.21
2837.18
2919.47
3003.14
3088.27
3174.94
3263.22
3353 -21
3445-01
3538.72
41
42
2758.89
2838.54
2839.90
2<>2O.85
2922.24
3004.55
3005.96
3089.70
3091.14
3176.40
3177.85
3264.71
3266.19
3354.73
3356.24
3446-56
3448. 10
3540.30
3541.88
42
43
44
2760.23
2841.27
2842.63
2923.62
2925.01
3007.36
3008.77
3092.57
3094-00
3179.31
3180.77
3267.68
3269.17
3357.76
3359.28
3449.65
345'i. 20
3543-45
3545-04
44
45
50
2.sk n • 90
3846.71
2X48.08
2849.44
2926.39
2927.78
2929.16
2930.55
2931.93
3010. 18
3011.59
3013.00
3014.41
3015.82
3095.43
3096.87
3098.30
3099.74
3101.17
3182.23
3183.69
3185.15
3186.61
3188.07
3270.65
3272.14
3273.63
3275.12
3276.61
3360.79
3362.31
3363.83
3365.35
3366.87
3452.75
3454.29
3455-84
3457-39
3458.94
3*546.62
3548.20
3549-78
3552.94
46
47
48
49
50
53
2769.62
2850.81
2852.17
2853-53
2856.26
2933.32
2934.71
2936.09
2937.48
2938.87
3017.23
3018.64
3020.05
3021.46
3022.87
31102.60
3104.04
3105.48
3106.92
3108.35
3 189. 54' 3278. TO
3191.00^279.59
3'IQ2. 46 3281.08
3 193. 92 13282. 57
3195.39 3284.06
3368.39
3369.91
3371.43
337-2.95
3374-47
3460.49
3462.04
3463.60
3465.15
3466.70
3554-53
3556.11
3557-70
3559-28
3560.87
51
52
53
54
55
2£ffl
2857.63
2940.26
3024.29
3109.79
3196.85
3285-56
3375-99
3468.26
3562.45
56
.0
2777.00
2*5X.99
2941.65
3025.70
3IH.23
3198.32
3287.05
3377.51
3469.81
3564-04
57
30
JTgo.tf
iU> i .
2943.04
2044.42
3027.11
3028.52
3112.67
3H4.II
3199.78
3201.25
3288.54
3290.04
3379-04
3380.56
3471.36
3472.02
3565.63
3567.22
58
59
%JU
-7i ' i • 7 '
2003.10
2945.61
3029.94
3H5.55
3202.71
3291.53
3382.08
3474-47
3568.81
60
1SONIAN TA
314
The Anti-Gudermannian.
gd u
5i°
5^°
53°
5^
57°
59°
6b°
</
3568'.8i
3665.19
37"3-7<>
I
3570.40
3666.82
3765.42
3866.34
3969.71
4075.69
4411.08
4529.37
i
2
3571-99
3668.44
3767.09
4077.48
4413.03
4531-37
2
3
3573.58
3670.07
3768.75
3869.74
4079.27
3
4
3575.^7
367 r. 70 3770.41
3871.45
3974-95
4081.06
41189.97
4535.38
4
5
3576.76
3673-0-'
37/2.08
3873.15
3976.69
4082.86
4191.81
4303.74
4418.86
4537.38
5
6
3578.35
36/4.05
3773.74
3874.86
3978.44
4084.65
4193.65
4305.64
4420.81
6
7
3579-94
3676.58
3775-41
3876.56
3980.19
4086.44
4195.49
4307-53
454L39
7
8
3581.54
3678.21
3777.08
3878.27
3981.94
4088.24
4197.33
4.543.40
8
9
3583.13
3679-84
3778.74
3879.98
4090.03
41199-17
4311.32
4545-41
9
10
3584.73
3681.47
3780.41
3881.68
39S5.44
4091.83
4201.02
4313.21
4428.60
4547-42
10
ii
3586.32
3683.10
3782.08
3883.39
3987.19
4093.62
4202.87
43IS.II
4430.56
4549-43
ii
12
3587.92
3684.73
37^3 • 75
3885.10
3988.94
4095.42
4204.71
4317.01
4432 • 5 i
4551.44
12
13
3589.51
3686.36
3785.42
3886.81
3990.69
4097.22
4206.56
43I8.9I
4434.46
4553.45
13
H
359i.ii
3687.99
3787-09
3888.52
3992-45
4099.02
4208.41
4320.80
4436.42
4555-47
14
15
3592.71
3689.63
3788.76
3800.23
3994-20
4100.82
4210.26
4322.70
4438.37
4557.48
IS
16
3594.30
3691.26
3790.43
3891.95
3995.96
4102.62
4212.10
4324.61
4440.33
4559-50
.
17
3595-90
3692.00
3792.10
3893.66
3997.71
4104.42
4213.95
4326.51
4442.29
4561.52
17
18
3597-50
3793.78
3895.37
3999-47
4106.22
41215. So
4328.41
4444.24
4563o3
18
19
3599- 10
3606.17
3795-45
3897-09
4001.22
4108.02
4217.66
4330.31
4446.20
4565.55
19
20
3600.70
3097.80
3797.12
3898.80
4002.98
4109.82
4219.51
4332.22
4448.16
4567.57
20
21
3602.30
3699.44
3708.80
3900.52
4004.74
4111.63
4221.36
4334-12
4450.12
4569.59
21
22
3603.90
3701.08
3800.47
3002.23
4006.50
4U3.44
4223.22
4336.03
44512.09
22
23
3605.50
3702.71
3802.15
3003. 95
4008.126
4115-24
4225.07
4337.94
4454.05
4573.64
23
-'4
3607.11
3/04.35
3803.83
3905.67
4010.02
4117.05
4226.93
4339.84
4456.01
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
-•••
27
3611.92
3709.27
3808.86
3910.82
4015.31
4122.47
4232.50
4345-57
4461.91
--:
28
3613.52
37lO.pl
3810.54
3912.54
4017.07
4124.28
4234.36
4347.43
4463-88
-••••
29
3615.13
3712.56
3812.22
3914.26
4018.84
4126.09
4236.22
4349.40
4465.85
2Q
30
3616.74
3714.20
3813-90
39^5.99
4020.60
4127.90
4238.08
435L3I
4467.82
30
31
3618.34
3715.84
3815.58
3917.71
4022.37
4129.72
4239.04
4353.23
4469.79
4589.86
3i
32
3619.95
3/17.48
3817.27
3919.43
4024. 13
4I3T.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
4T35.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
3*25.^9
3928.06
4032.98
4140.61
425LI3
4364.73
4481.63
4602.07
37
38
3629.61
3727.3<5
3827.37
3929.79
4034-75
4142.42
4252.09
4366.65
38
39
3631.22
3729.01
3829.06
393L5T
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
41
3634.44
3732.30
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
42
43
3637.67
3735.6i
3835.81
3938.43
4043.61
4I5L52
4262.34
4376.27
4403.51
43
44«
3639.28
3737.26
3837.50
3940.16
4045.39
4153.35
4264.22
4378.30
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
4501.45
47
48
3645.75
3743-87
3844.27
3947.10
4052.50
4160.65
4271 . 72
4385.01
4503.44
48
49
3647.36
3745-52
3845.06
3948.83
4054-28
4162.47
4505.43
4626.60
40
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
439T.70
4509.41
4630.71
5i
52
3652.22
3750.49
3851.05
3954.0414059.62
4167.96
4279.23
4393.64
4511.40
52
53
3653.84
3752.15
3852.75
3955-78 4061.41
4169.79
4281 . 1 1
4513-39
53
54
3655.46
3753.8o
3854.44
3957.52 4063.19
4171.62 4282.99
4397.51
4515.30
4656.87
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
4175.284286.76
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 4043-04
57
58 3661.95
3760.44 386 1.24
3964.48
4070.33
41178.95 4200.53
4405.26
4523.37
4645 • 10
58
59
3663.57
3762.10 3862.94
3066.22
4072.12
4180.78 4-
4407.20
4525.37
4647.16
59
60
3665.19
3763.7613864.64
3967.97
4073.90
4182.62 4204.30
4409.14
4527.37
4649.23
60
SMITHSONIAN TABLES
315
The Anti-Gudermannian.
fldu
61°
62°
63°
64°
65°
66° 67°
68°
69°
70°
odu
0'
4649'.23
4774. $
4904.94
5039.42
5178.81
5323.51 5474.01
5630.82
5794-56
5965.92
o'
I
4651.29
4777.11
4907.14
3041.70
5181.18
5325.97I5476.57
5633-49
5797-35
5968.84
I
2
4653.35
4779.25 4909.35
5043.09
5i83.54
5328.43
5479.13
5636.16
5800.14
5971.77
2
3
4655.42
4781.38 4911.55
50^6.27
5185.91
5330.00 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
4
5
4659.55
4/85.65 4915.97
5050.85
5190.66
5335.83 5486.83
5644.19
5808.54
5980.57
5
6
4661.62
4-87.79 4918.18 5053.14
5193.03
5338.30 5489.40
5646.87
5811.34
5983.50
6
7
4663.69
4789.9214920.39 5055.43
5I95.4I
5340.77 5491.97
5649.56
5814.15
5986.44
7
8 4665.76
4792. 06; 49 22. OO
5057.72
5197.79
5343.24 5494-54
5652.24
5816.95
5989.38
8
9 (4667.83
4704.20 4924.81
5060.01
5200. 17
5345-7i| 5497. n
5654.93
5819.76
5092.33
9
ID
4669.91
4796.34
1 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
4800.6314931.46
5066.90
5207.31
5353-14
5504.85
5663.00
5828.20
6001.17
12
13
4676.13
4802.77,4933.68
5069.19
5209.70
5355.6i
5507.43
5665.69
5831.02
6004.13
13
U
4678.21
4804.92
4935-00
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
6015.06
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
5226.43
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
5687.3-1
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 5094-57
5236.03
5382.991 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
4962.614
5099.20
5240.84
5387.09 554I-I5
5/00.89
5867.84
6042.74
26
27
4705.32
4832.93
4964.87
5101.52
5243-24
5390.49
5543.76
5703.61
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
32
4713.70
4715.79
4841.58.4973.83
4843.7514976.08
5110.80
5113.13
5252.88
5255.30
5400.52
5403.03
5554.20 57I4.5I
5556.82 5717.25
5882.10
5884.96
6057-70
6060.70
31
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
5800.68
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
5413.08
5567.30
5728.19
5896.41
6072.72
36
37
4726.30
4854.61
4987. 3'i
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
5005.03
6081.76
39
40
4732.6i
4861.13
4994.07
3131.78
5274.66
5423.17
5577.8i
5739- 17
5907.90
6084.78
40
41
4734.72
4863.31
4006.32
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
9138.79
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
5435.81
5590.09
5752.94
5922.32
6099.92
45
46
4745.28
4874.22
5007.62
6145.83
5289.25
5438.35
5593.64
5755.70
5925.22
6102.95
46
2
4747-39
4876.41 5009.88
O C\ S \
5148.17
5291.69
5440.88
5596.28
5758.46
5928.11
6105.99
47
40 4749.51
4878.60
5012. is
5150.52
5294.13
5443.42
5598.93
5761.23
5931.00
6109.03
48
49 I475I.63
4880.79
5014.4*
5-I52.87
5296.57
5445.96
5601.57
5763.09
5933.00
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
5r
4755-86
4885.17
t>t) f
5018.94
5157.57
5301.45
5451.05
5606.87
5769.53
5939.70
6118.16
Si
52
4757-98
4887.36
5021.21
5>I59.93
5303.00
5453.59
5609.53
5772.31
5042.61
6121.21
52
53
54
4760.10
4762.23
4680.55
4891.75
5023.48
5025.76
5162.28
5164.64
5^06.34
5308.79
5456.14
5458.68
5612.18
5614-84
5775.08
5777-86
5945.51
5048.42
6124.26
6127.32
53
54
55
4704.35
4893.04
5028.03
5167.00
5311.24
5461.23
5617.50
5780.64
595L33
6130.38
55
57 4768.60
4896.14
4898.34
5030.30
5032.58
5169.36
5171.72
5313.69
53I6.I5
5463-78
5466.34
5620.16
5622.82
5783.42
5786.20
5954-24
5957.16
6133-44
6136.50
56
57
58
4770-73
4900.54
5034.86
5174.08
53i8.6o
5468.89
5625.49
5788.08
5060.08
6139.56
58
£
4772.86
_r*
4002.74
5037.14
5176.44
5321.06
5471.45
5628. 15
5791.77
5963.00
6142.63
59
«> 4774.9» 4904.94
5039.42 5i7«.8i
5323.51 5474-01
5630.82
5704.56
5965.92
6145.70
00
316
The Anti-Gudermannian.
gdu
7i°
72°
73°
74°
75° 76°
77°
78°
79°
80°
gdu
Cf
6i45'./0
6334.84
6534.42
6745.74
6970.34 7210.07 74'
7744-57
8045.71
8375.20
oy
I
6148.77
6338.08
6537.85
6749.37
6974-20 7214.20 7471.66
7749.38
8050.95
8380.0
I
2
6151.85
6341.32
6541.27
6753.01 6978.07 7218.35
7754-20 8056.20 83--
2
3
6154.93
6344.56
6544-70
6756.64 6981.95 7->2->.49
7480.57
•;2.52
3
4
6158.01
6347.81
6548.13
6760.28
6985.83 7226.64
7485.03
-'>6.7.l 8.^08.31
4
5
6161.09
6351.06
655L57
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
7234.06
7493.08
7773-55
8077-29 8409.92
6
7
6167.27
6357.56
6558.45
677L23
6997-49
7239.12
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
6173.45
6364.08
6565.34
6778.55
7005 . 28
7247.47
7507.44
7788. 12
127.42
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
7520.0
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
H
6188.96
6380.43
6582.63
6796.90
7024.85,7268.42
7530.00
7812.56
8119.86
8456.77
15
6192.07
6383.71
6586.10
6800.58
7028.77
7272.62
7534-53
7817.46
8125.22
8462.67
15
16
6195.18
6386.90
6589-57
6804.27
7032.70
7276.83
7539-06
7822.38
8130.58
8468.58
16
17
6198.30
6390.28
6593.05
6807.0
7036.64
7281.05
7543.60
7827.30
8135.95 8474.50
17
18
6201.42
6393.57
6506.52
6811.65
7040.58
7285.27
7548.15
7832.23
8141.33 8480.43
18
19
6204.54
6306.86
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
21
6210.78
6403.44
6606.98
6822.75
7052.42 7297-96
7561.82
7847-05
8i57o3 8408.28
21
22
6213.91
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
7570.0
7856.97
8168.37 8510.23
23
24
6220.18
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
73H.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
7589.12
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
2X
29
6235-89
6429.93
6635.01
6852.53
7084.19 7332.02
7598.54
7886.89 8201.09 8546.33
29
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
780.93
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
7006.98
8223.07 8570.61
33
34
6251.67
6446.58
6652.64
6871.27
7104.19 7353.48
7621.68
7912.03
8228.59 ^:
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
7630.09
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
7644.08
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
41
42
6277.05
6473.38
6681.03
6901.46
7U6.43
7388.08
7659.04
7952.62 827;,. 05 8?>25.86
42
1 43
6280.24
6476.74
6684.59
6905.25
7140.48
7392.43
7663.7-}
7957-72
8632.05
43
44
6283.43
6480.11
6688.16
6009.05
7144.54
730-79
7668.44
702.8418284.25
8638.26
44
45
6286.62
6483.48
6691.73
6912,85
7148.60
7401.15
7673.I5
707.96 |8289.87
8644-47
45
46
6289.82
6486.86
6695.31
6916.65
7152.67
7405.51
7677.87
7973-09 8295.40
8650.70
46
47
6293.01
6490.23
6698.89
6920.46
7156.74
7409-88
7682.59
7978.23 8301.12
8656.04
47
48
6296.21
6493.61
6702.47
6924.27 ! 7160.81
7414.26
7687.32
7983.37j83o6.77
8663.19
48
49
6299.42
6497.00
6706.06
6928.09 7164.89
7418.64
7692.05
7988.52 8312.42
8660.45
49
50
6302.62
6500.38
6709.65
6931.91
7168.97
7423.03
760.79
7993.68 8318.08
8675.72
50
51
6305.83
6503.77
6713.24
6935.73
7173.06
7427.42
7701.54
7008.85 8323.75
8682.00
Si
52
6309.04
6507.17
6716.84
6939. s6! 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
8604.60
53 i
54
6315.48
6513.96
6724.04
6947. 23 '7185- 35
7440.63
7715.83
8014.40 8340.82
8700.92
54
55
6318.70
6517.36
6727.65
6951.07
7189.46
7445-05
77.20. 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
6524.18
6734.88
6958.77
7197.69
7453.89
7730.17
8030.02
8357-0
8719.04
57
58
6328.37
6527.59
6738.50
6962.62
7201 .81
7458.33
7734.0
8035.24
8363.70
8726.30
58
59
6331.61
6531.01
6742.12
6066.48
7205.04
7462.76
7739.76
8040.47
8.169.44
8732.68
59
6b
6334.84
6534.42
6745.74
6970.34
72IO.07
7467.21
7744.57
8045.71
8375.20
8739.06
60
SMITHSONIAN TABLES
317
The Anti-Gudermaunian.
gd u
81°
82°
83°
84°
85°
86°
87°
88°
89°
gd u
(/
8739/.o6
9U5.46
9605.82
10136.89
10764.62
11532.52
12522.11
13916.43
16299.56
0'
I
8745.46
9152.65
9614.03
10146. 4^
10776.11
11546.88
12541.27
13945.20
16357.34
I
2
S75I-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
10709.22
11575.80
12579.91
14003.48
16475-90
3
4
$764.73
9174.32
0638.80
10175.37
10810.82
11590.34
12509.40
14033.00
16536.76
4
5
877LI7
9l8l.57
9647.09
10185.05
10822.47
11604.95
12619.00
14062.77
16598.69
5
6
8777.63
9188.84
9655.40
10194-77
10834.16
11619.62
12638.70
14092.80
16661.78
6
7
8784.10
9196.13
9663.74
10204.51
10845.89
11634.36
12658.53
14123.09
16726.04
7
a
8790.58
9203.42
9672.09
10214.28
10857.65
11649.16
12678.46
14153.66
16791.53
8
9
8707.08
9210.74
9680.47
10224.08
10869.46
11664.02
12698.52
14184.49
16858.29
9
IO
8803.58
9218.07
9688.86
1023-3.00
10881.31
11678.94
12718.69
14215.61
16926.36
TO
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
10005.13
11708.99
12759-39
14278.70
17066.70
12
13
8823.17
9240.15
9714.17
10263.54
10917.10
11724.11
12779.92
14310.68
1/139.09
13
14
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
I094I.I7
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
10065.40
11785.27
12863.30
14441.68
17444.87
17
18
8856.07
9277.27
9756.76
10313.53
10977.59
11800.73
12884.46
14475.23
17525.77
18
19
8862.69
9284.74
9765.34
10323.61
10989.81
11816.26
12905.75
14509. 10
17608.63
19
20
8869.32
9292.23
9773-94
10333-72
11002.08
11831.87
12927.18
14543.31
17693-49
20
21
8875.96
9299.73
9782.57
10343-86
11014.40
11847.54
12948.74
T4577.87
17/80.53
21
22
8882.62
9307.25
9791.21
10354.03
11026.75
11863.28
12970.44
14612.78
17869.83
22
23
8889.29
93T4./9
9799.88
10364.24
II039.I5
i 1879. 10
12992.27
14648.04
17961.51
23
^4
8895.97
0322.34
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
3916.09
9345-10
9834.77
10405.35
11089.21
i 1943 • 10
13081.02
14792.83
18354.83
27
28
8922.82
9352./2
9843.55
10415.71
11101.84
11959.29
13103.58
14830.00
18460.62
28
29
8929.57
936o.35
9852.35
10426.09
11114.52
11975.55
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
8043.10
9375.67
9870.02
10446.96
11140.01
12008.31
13172.13
14943.98
18799-03
3i
32
8949-88
9383.36
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
1204.1.39
13218.60
15022.12
19044.69
33
34
8963.49
9398.79
0896.69
10478.50
11178.60
12058.05
13242.07
15061.87
19174.44
34
35
8970.32
9406.53
9905-63
10489.08
11191.56
12074.79
13265-70
15102.08
19309.27
35
8977.16
9414-28
9914.59
10409.69
11204.57
12091.60
13289.50
15142.77
19449.61
36
>84.oi
9422.05
9923.57
10510.33
11217.63
12108.51
I33U.47
15183.04
19595.92
37
38
J090.87
9429.84
9932.57
10521.01
11230.74
12125.49
i3337.6o
15225.62
19748.73
38
9
8997.75
M37-65
9941-60
I053L7I
11243.00
12142.57
13361.90
15267.80
19908.66
39
40
9004.65
9-145.48
9950.66
10542.45
11257-11
12159.72
13386.37
15310.51
20076.39
40
41
9011.55
J-153-32
9959-73
10553.23
11270.37
12176.96
13411.02
15353.76
20252.72
4i
42
joiH.47
*6i.i8
9968.83
10564.04
11283.68
12194.29
13435.85
15397.56
20438.59
42
43
9025.41
1469.06
9977.96
10574-88
11297.04
12211.71
13460.86
15441.92
20635.09
43
44
9032.36
9476.06
0987.11
10585.76
11310.46
12229.21
13486.05
15486.86
20843.50
44
45
J039-32
9484.87
9996.28
10506.67
"323.93
12246. Si
i35".43
15532.40
21065.37
45
46
0046.20
940-'.Xt
10005.48
10607.62
"337-45
12264.49
i3537.oo
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
I*
<>/J0.20
10023.95
10629.61
11364.65
12300.13
13588.71
15672.75
21832.48
48
40
106^.31
10033.22
10640.67
"378.33
12318.09
13614-85
15720.83
22131.60
49
So
9074.34
0524-72
10042.52
10651.75
11392.06
12336.15
13641.20
15769.59
22459.26
50
M
lOSl.JQ
10051.84
10662.87
11405.85
12354.30
13667.75
15819.06
22821.46
51
•
0088.45
9540.79
l(K>Ol . lo
10674-03
11419.70
12372.54
13694.52
15869.25
23226.39
52
S3
10070.56
10685.22
"433.60
12390.89
13721.48
15920.19
23685.42
53
M
10079.96
0696.46
11447.56
12409.33
13748.67
15971.89
24215.35
54
55
9100.72
10080.38
10707.72
11461.58
12427.87
13776.07
16024 . 38
24842. 12
55
56
0116.8}
0573.15
10008.83-
10719.03
11475.65
12446.51
13803.68
16077.68
25609.23
56
57
9581.20
ioi(>X. >o
10730.37
11489.78
12465.26
13831.53
16131.82
26598.21
57
5o
10117.81
ro; 1 1 . 75
11503.07
12484.10
13859.60
16186.83
27992.10
58
1
>\ »K.jX
10127.33
10753.17
II5I8.2I
12503.05
13887.90
16242.74
30374.06
50
••
K)I4S.46
•X-K.Xj
10130.80
10764.62111532.52
12522.11
13916.43
[<)_><)<>. -(>
00
(o
SMITHSONIAN TABLTS
•'>' onwards Interpolate by second differences.
318
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
.06981 31700 8
.00116 35528 3
.00001 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
.104/1 97551 2
•00174 53292 5
.00002 90888 2
66
.15191 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
.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 757OI 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
78
.36135 68165 6
19
.33161 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
86
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 66500 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
O.OO727 22O52 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 398i6 3
.00013 08906 9
87
.51843 64492 4
28
.48869 21005 6
.00814 48608 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
3i
.54105 20681 2
.00901 75344 7
.00015 02922 4
.58824 96193 i
32
•55850 53606 4
.00930 84226 8
.00015 51403 8
92
.60570 29118 3
33
.57595 86531 6
• 00959 93io8 9
.00015 09885 i
93
.62315 62043 5
34
•59341 19456 8
.00989 01900 9
.00016 48366 5
94
.64060 94968 7
35
0.61086 52382 o
0.01018 10873 o
0.00016 06847 9
95
1.65806 27893 9
36
.62831 853O7 2
.01047 19755 i
.00017 45329 3
96
.67551 60819 i
37
.64577 18232 4
.01076 28637 2
.00017 93810 6
.69206 93744 3
38
39
.66322 51157 6
.68067 84082 8
.01105 37519 3
.01134 46401 4
.00018 42292 o
.00018 90773 4
99
.71042 26669 5
•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
.01221 73047 6
.00020 36217 5
120
2.09439 51023 9
43
44
.75049 15783 6
.76794 48708 8
.01250 81929 7
.01279 90811 8
.00020 84698 8
.OOO2I 33180 2
130
140
.26892 80275 9
.44346 09527 9
s
0.78539 81634 o
.80285 14559 2
0.01308 99693 9
.01338 08576 o
0.00021 81661 6
.00022 30142 9
T
160
2.61709 387/9 9
.79252 68031 9
47
48
.82030 47484 4
.83775 80409 6
.01367 17458 i
.01396 26340 2
.00022 78624 3
.00023 27105 7
170
180
.06705 97283 9
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
i 7<>i8s 2
.01483 52986 4
.00024 72549 8
210
.66519 14291 9
52
.90757 121 10 4
.01512 61868 5
.00025 21031 I
220
.83972 43543 9
53
:'>35 6
.01541 70750 6
.00025 69512 5
230
4.01425 72795 9
54
17 7796o 8
.01570 79632 7
.00026 17993 9
24O
. 18879 02047 9
55
0.95993 10886 o
0.01509 88514 8
0.00026 66475 2
250
4.36332 3T299 9
57
,SlI 2
-736 4
.01628 97396 9
.01658 06278 9
.00027 14956 6
.00027 63438 o
200
270
.53785 60551 9
.71238 89803 8
58
t>f}\ 6
.01687 15161 o
.00028 11919 4
300
5.23508 77559 8
59
.02974 42586 3
.01716 24043 i
.00028 60400 7
330
.75958 65315 8
60
1.04719 75512 o
0.01745 32925 2
0.00029 oKSS2 i
360
6.28318 53071 8
SMITHSONIAN TABLCS
320
Conversion of Radians into Angular Measure.
Radians
Angle
Radians
Angle
O.I
0.2
0.3
0.4
05° 43 46.48062 47
II 27 32-96124 94
17 ii 19.44187 41
22 55 05.92249 88
O.OO6
.007
.008
.009
0 20 37.58883 75
; 37
27 30. 1 1845 oo
30 56.38325 62
0-5
0.6
0.7
0.8
0.9
28 38 52.40312 35
34 22 38.88374 83
40 06 25.36437 30
45 50 11.84499 77
51 33 58.32562 24
O.OIOO
.0001
.0002
.0003
.0004
0 34 22.64806 25
oo 20.62648 06
oo 41.25296 u
oi 01.87044 19
oi 22.50592 25
1. 00
O.OI
0.02
0.03
0.04
57 17 44.80624 /i
00 34 22.64806 25
01 08 45.29612 49
oi 43 07.94418 74
02 17 30.59224 99
0.0005
.0006
.0007
.0008
.0009
o oi 43.13240 31
02 03.75888 37
02 24.38536 44
02 45.01184 50
03 05.63832 56
0.05
0.06
0.07
0.08
0.09
02 51 53-24031 24
03 26 15.88837 48
04 oo 38.53643 73
04 35 01.1844998
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 06.18704 419
oo 08.25059
O.IOO
O.OOI
O.002
0.003
0.004
05 43 46.48062 47
oo 03 26.26480 62
oo 06 52.52961 25
OO TO 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
OO 17 II.324O3 12
0.00010
o oo 20.62648 062
SMITHSONIAN TABLES
Numerical Constants.
Iog102 = 0.30102 99956 63981
Ioge2 = 0.693 14 71805 59945
-— =0.56418 95835 47756
loge 10= 2.30258 50929 94046
I
6=2.71828 18284 59045
logio ~7^ = 9.75I42 50636 52933
Iogi0e = 0.43429 44819 03252
•n- = 3. 14 1 59 26535 89793
v tr
^^ = 1.25331 41373 15500
Iog10ir=r 0.497 14 98726 94134
logeir = i . 14472 98858 49400
J — = 0.79788 45608 02865
-1 = 0.31830 98861 83791
log,0 -/ — = 9.90194 00614 84924
IT1 = 9. 86960 44010 89359
i radian = 206264 . 80624 70964 seconds
—^ = 0.10132 11836 42338
= 3437.74677 07849 minutes
IT
= 57.29577 95I3I degrees
I/ IT = 1.77245 38509 05516
log,0 206264.80625 = 5.31442 51332
SMITHSONIAN TABLES
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