SMITHSONIAN MATHEMATICAL TABLES
HYPERBOLIC FUNCTIONS
PREPARED BY
GEORGE P. BECKER AND C. E. VAN ORSTRAND
FOURTH REPRINT
No. 1871
CITY OP WASHINGTON"
PUBLISHED BY THE SMITHSONIAN INSTITUTION
1931
ADVERTISEMENT.
Among the early publications of the Smithsonian Institution was a very
important volume of meteorological tables by Dr. Arnold Guyot. They were
so widely used by geographers and physicists as well as by meteorologists
that when the fourth edition was exhausted it was decided to recast the
, entire work and publish three separate volumes, Meteorological Tables,
^Geographical Tables, and Physical Tables, each of which has now passed
;= through several editions.
..!. In the application of the data of these volumes to the study of natural
'' phenomena certain mathematical tables beside those included in ordinary
tables of logarithms are urgently needed in order to save recurrent computa-
tion on the part of observers and investigators. It was therefore^ decided
to publish the present volume of Mathematical Tables, on Hyperbolic Func-
tions.
Hyperbolic Functions are extremely useful in every branch of pure physics
and in the applications of physics whether to observational and experimental
sciences or to technology. Thus whenever an entity (such as light, velocity,
i electricity, or radioactivity) is subject to gradual extinction or absorption,
1 the decay is represented by some form of Hyperbolic Functions. Mercator's
i> 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 arc in charge of the physical work
of the United States Geological Survey, have been led to prepare this volume.
;<! ' CHARUCS D. WALCOTT, Secretary.
'j WASHINGTON, D, C., April, 1909-
k~ In this first reprint of the Hyperbolic Functions a few misprints of trifling import-
v ancc have been corrected and four values of the exponential have been changed by a
{Limit in the eighth significant place. r D W
J April, ion.
In the second reprint of these Tables, several additional minor corrections have been
made, usually in the last decimal place. r D W
November, 1920.
in
IV ADVKHTIHICMICNT.
In the third reprint, a number of minor CIIDIK Imvo lirm runcrinl, ;i liiii <>i
publications containing hyperbolic and oxiuincnti.il fmirtiiw'; li,i:i ITII a.ldi-il i
historical note on page li, and the liililes of cirmlar ftint;ii(iii:i ,IIM! tin- r\|Huiniii.il
been extended to meet recent {lemands.
May, Kj2<\.
In tin's fourth reprint no need fur corriutionH IM:, linen
September, 1931.
I'AUII
CONTKNTS.
INTRODUCTION ;
i "i i 1 * * Y* rftitii
DdmiUoiiM and formulas v jj
(Urotnelricid illustrations . , . vvi.iii
A A. VI I I
Methods of interpolation xxxiv
Description of tables x |jjj
Historical mile X | V UI
TAHU( I :
I'ivo plan: values of log sinh //, log cosh , log liinh K, and log
eolh if
TAIH.IC n :
Kivi! place values of sinh , cosh , tanh //, and ooth it , , , 87
TAHI.K HI :
1'lvo pliuT vHluoHof .sin it, COM //, log ,iin u, and log eo.t w, being
expressed in radians and their angular equivalents .... 173
TAIU.I.; IV:
1 he uwiMiding and dt'soending exponential to seven s
(ignreN with log, r" lo nevt'ti ptiuvH
place vnliu-H of the .muiie with ten place logarithms from
i to n 100 a - ( .
Auxiliary table of multiples of log^-for interpolation of Iog w <f". afii
i.W V :
ve place values of natural logarithms aCn
olalion eouHieients for tlerivtilive formula 273
TAIII.K VI :
Tlie Kudormannian of n lo seven places In radians and to the name
order of aeouraey in degrees, niiuutys, and seconds .... 275
TAllUt VII;
The anti-'gndermannian to huiulrcdllm of a minute in ten us of
the KUilernwnnian expressed in degrees and minutcn from o" o'
lo My'* SO*. C'flito tiil'ie IH otherwlHe known as i\ tahle of me-
ridional parts for n wpherieal globe) .,..,.,.. 309
TAitut VIII:
Table for convention of ratUaim Into angular measure and vice
veisa - 30
Numerical constants , V WI
DEKINITIONS AND FORMULAS.
The hyperbolic functions are named the hyperbolic sine, cosine, tangent,
cotangent, secant, ami cosecant from their dose analogy to the circular I'une-
titin.s. the tangent being the ratio of the hyperbolic sine to the cosine uwl
the other three functions being reciprocals of these, a,s in circular trigonom-
etry, They are usimlly denoted by adding h Lo the symhols of the circtilur
funclioiiM, as cosh it for the hy|)erbolie cosine of it, siul) w for the hyperbolic
.sine of //, etc. 1
Historically speaking, the hyperbolic functions were evolved from studies
of the hyperbola, They might Imvo been deveiojwd from the Rooinolry of
the ellipse or the cutennry or that of other curves. Those functions, how-
ever, may be considered independently of any ueometrlcnl interpretation and
can be derived from very fundamental functional theorems.
At least two methods have been devised of dufiniiiK circular and hyper-
bolic functions analytically. One of these is due to Mr. Yvon Villureeau/
mid in MO extremely brief that it ciin be given here in a somewhat modified
form.
It bus long been known that
The second of these citations has u single imaginary jicriod, a /V, mid the
third (i (jingle real period, aw. Hence every exponential/' in which it is real
1ms a single imaginary period, 2 ITT, and every exponential with the munu Imso,
lull, with an liniiginary exponent, hasu real period, a jr. Now, all rout purely
drcnliir functions may bu expressed in terms of constmUs und'exponenUalH
with purely imaginary oxponenlH, and all real hyperbolic functions may
be expressed in terms of constants and exponentials with exclusively real
exponent.
IfvMice hyperbolic functloii.i may lie defined an the singly periodic expo-
itttiulul funetions with real exponents. The circular functions are I hen the
Hlngly periodic exponential functions with imaginary exponents.
It remains to be eonmdered how, from this point of view, the hyperbolic
functions of complex variables nut to be regarded. The question almost
answers itself ; for
1 Metre iMunpetitlloiiH it ml convwwwl, liul Itiwn UHiuil, In the iiotnlloii employed by It. ilc
cnant, itlh //, coli n, tiih u.
'Coaiptcs KoiuliiH. PdrlM, vol. H^, iHyfi, p. 59,1,
vli
vi n DKi'iNtTiONS AND
which is evidently the product or two function.'; one eiirnhir, Mir <,i
hyperbolic. vSuch functions have a real pniod andan imar.in.'ii v one,
since they tire single-valued they aie not elliptic i'liiiciion-i.
The circular and hyperbolic functions IK-MIK defined as al>,.v.', it j., ,,.,
as a matter of convenience Hint a few of Ihc simpler contliiimtioori <>i ,.*
uentials receive special names, us sine, cosine, etc.
The other analytical method of ^m-nili/.inj; the twu rlu-i<<rs n| t'nndi.
is due to Kclwnrd I^ucas, 1 and is too IOIIK to ! r.ivcn h.-n- in full, lm
method may be indicated. If a and fi ar<- Ihc iwu looi-i of MM- c. ( m
where /'and Q are positive or iu:;miv whole mimbnx ihn, tw.
may be defined as follows:
TJ a" --/>" ,,
f/ <,-.*'' ""' ^
and these functions arc related by the ei|imLimi
Lucas develops and studies these functions, |i mil | MJI 11( r , (!i| ,., w| , ti|i ,
tive number,,. He finds that all the theorem, n^UIn,. | |1(1I1 ( hi, ,,,i.lv
. 1
convened into those of ordinary trigonometry when // j, IVI .| m ,,| ,,.. ,
and Fby , cos . He infers that between tl, limiu , t j tttimi \ ;
be replaced by any real value, ami shows thai the i| M ,.n,,, n ,lr,li,, r
.,,,
and Kwhen translated into tri.ononuH.ic for.nuh, on thi, ,, ,
be verified. B y substitulin^ for n an imuf-inary m.-umrnl h,
functions also are found to be eo.np.hended I
If c = a\ this gives
?'
where A and B are arbit
KJ', or -,
COM .v
1 An.Jo l ,r.ofMnth.,vol,i (1 V H ( p ll H, ) .
tt AND I-'DKMIIJ.AH.
Tin: hyperbolic functions may also bo de-
fined. Kuonititrically with reference- to uny
hyperbola.
I,0t (),'t <---> ft, (>J> eca b 1)0 lllC M(!llli-RXi:S Of
llu* hyperbola Al\ and its cinijuj-uU: /V/ 1 '
referred to Liu; K-I: In uvular HN.UH o.v und
oy, The lU'tfiunenl or independent variable //
and its funclioiiH iirt: Uu-n Kivtin by ; '
A(J.-/A'
.
A (>,-//,''
A ( /'//
A 0,U
The urwiH of tlio U'innKk-H C^-///, O/// 1 , and 01 '/I rc mspeclivuly i /',
J j' and j Ar, und Uic nvc-n of tlu: Mticlor ^)//y IH found from ihu equation of
Ibo
to In;
lluncc, In uctiordttiico with UK; uhovu
fllnh 11 , 3 (>" -f "),
/ "
cosh // iw ' L 4 0"'h<" '").
*/. v /
rly the argument and finuHioiin of circular trlnouonietry lire :
0m 2 '^'M ftl>< '
' radius 1
v
Hill I-"*' ' Wi '- - 4 / (/"' "-" A 1 *""'*),
/'
../ ),
A aimpurlHon of lliu preceding cqunltoim Hlunvw Dint there extol bclwccn
tltc two HtitM of ui'KiiinenlM and fiiiiclloiiH many hileraiinjf nimloglcH nnd rcln-
lloim. The nrKint*nt arc in cneli cane tin* ratio of two nrcitH, iiHhough the
nrginnent of Uio circular functions may also 1>u defined u a mlio of two HIKJH;
'I'orrteflulUoiiH wliluh urn IndepDiuli'tiLof Hie |ittHliloii of LhoKcctorlul nreus HUC I'rof.
Jnm MoMnliun'H " HyiwrlxtHc I'luttttlriiw " nml tt jwiper "On Uie Introduction of the
Notion of HyparlKtllc 1'imctloiw," Iiy I'rof. M. W. Ilnnkell, Hull, Am. MiUli. SOB., vol. i,
189-1-93,
X
])IC KIN IT IONS AND KOKMIM.A)!.
the hyperbolic functions stand in the same ivlatimi lo llu- f t /uilitd-ntt hyj
bola as the circular functions do to the circle; ciieli M-l of I'nm'limi'. nm\
defined analytically as a particular branch of the theory o! ilu- rspiuicii
function, and it is possible to pass from thy one, lo the olhci hy iiirmi:i ol
imaginary /' = I/ - 1. For example,
sinh // ~-~ i sin /'//,
cosh // --> cos in,
tanh // - - / tiin/V/.
Furthermore, every rational function of the liypnbolir fund ion:, ,UH| M,
inverts can be integrated by the help of correspimditij; known inlr>;nilr t u| n
cular functions. Thus, to find \ sw:h // dn from
/.'
sin it
i I tun
sec it {fit -" - lo
*\
substitute tutor u and reduce to the form
H'/lunh
I sech n
i -/ tanh
If in this equation tanh is replaced hy.r, the annul mrmlmr ciur|.| M
form with the expression for a tan > jfivt-n below.
Hence
,
Jscch
" '
Similarly, when a differential i.s cnconntcrrd liu- inlr^nd of whirl, i,
be found in this collection, it is
expression in cyclic functions hy
substitution of ix for .r, ete,, aiul
then to make a search for its
integral.
Most interesting is the relation
existing between the formula: of
spherical trigonometry and the
formulae of I^obachevsky'.s imag-
inary geometry, hyperbolic g u .
ometry, or pseudo - .spherical
geometry, as it is sometimes
called. Lobachevsky defines the
to dnlun- thr r
DEFINITIONS AND FORMULAS. xl
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 II (/>)
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 t 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 t 6 t c and angles A, B, C to be drawn. He establishes as fundamental rela-
tions between the sides and angles of this triangle 1
sin A tan // (a) = sin B tan 11 () = sin C tan 11 (0.
sin 11 () sin 77 0) = sin 77 ( cos 77 () cos 77 (V) sin 77 () cos A t
sin 77 (a) cos A = cos B cos C sin 77 (a) -f sin B sin C,
and also proves that
sin U (?<;) = (cos z) ~ l = (cosh ?;) ~ ! ,
tan 77 () i (sin iu~) -1 = (sinh n) ~',
cos 77 () = -i tan iu = tanla n,
Hence the preceding equations may be written
sin A __ sin B __ sin C
sinh ~~ sinh b ~~ sinh c '
cosh a = cosh b cosh c siuh b sinh ^r cos yf,
cos A = cos B cos C -f sin .# siu C* cosh a.
These formulas are, in fact, precisely those of spherical trigonometry, In
which the real sides a, b, c have been replaced by the imaginaries ia t ib> ic.
If the triangle on the boundary surface is Infinitesimal, the above equations
reduce to the well-known relations between the sides and angles of a triangle
on the Euclidean plane. The theorems of non-Euclidean geometry may not
therefore be inconsistent with experience, for the largest triangle which we
can measure is infinitesimal in comparison with a triangle on the boundary
surface. I^obachevsky pointed out that a triangle on a boundary surface
would correspond to a triangle connecting three stars in distant parts of the
universe, aud 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 n assumes successive
values between o and + oo , siuh u assumes successive values between o and
+ oo just as tan a does when a varies from o to 90; cosh n assumes values
between i and + w like sec & and tanh u assumes values between o and i
'H. P. Manning's Noii-Buclidean Geometry, p, 60,
Xll
DKl'INITIONS AND 1*'<WMUI,AS.
hi the same way as sin y. The variation of the hyper! lolir 1'iMieliims thriiii};
out the entire plane and their similarity lo theeirenlar fund ions lietween I
limits <i" mid ifW j.-i .-ilnn
111 Ilk' dill)'.tiiin, ,'-ii i in r.t
of (lu- I'uiu'tiini'i j;j .sjiijj
periodic, time nill-,1 |ir
-'iiitj;li- value of u, ft, y n
r<'S|ioii(finj; in a |t;ulii'ul,
D
PIG. 3.
'Taken with
McMahon'8 Hyperbolic Pi, U cUoi, S . '
H will IK- found hy i.iif
Htitulinn in the (ii;<itioutr|
ric foniHihi' llnii n < * ft
~~ </', mid the rri|iiiici| i.'lil
lions an- Iheu-fuie
The aii^le / which leiidet*
it ptwiihl,- to evalllfllr- tin;
I l|l|t it'ni'i hy
means of the eitvnhu tune-
>i iiuif urciu Impoiuitet*
pinv and applied niathe,
Some til' i(r, pmp
erlis and nppliciiiinns will
bo considered in l\\<- fn-etiun
on Kt'nim-Uinil illu-.tu,,
liona. It |M called ^Utln
iimnniiin // mid in written
nlut involving Hie hypei-.
hoik 1 functiitn.'i might | Hr
Rrt-nlly extended, hut it
, ,!
rolatioim. 1
rcc'n Kborl Taltlu of 1
DEFINITIONS AND FORMULAS.
A. RELATIONS BETWEEN HYPERBOLIC AND CIRCULAR FUNCTIONS.
r . sinh = i siu iu = tan gd n,
2. cosh n = cos iu = sec gd u.
3. tauh n i tan iu = siu gd u,
4. tanh % u tan \gdit.
5. e" (r 4- sin g-^ K) -+-cosgd u,
= [ i cos (i TT +-rf z^) ] -^- siu (i TT + #rf ),
== tail (i-v-f \gdit}.
6. sinh z = z siii .
7. cosh in cos .
8. tanh in = i tan n.
g. sinh ( HI) = z sin ( =p *'),
= sinh u cos w dz ' cosh ?.; sin w.
10. cosh (?; iv) = cos (v + t),
= cosh 7^ cos v dr siuh ?t siu w.
n. cosh (V) = cos 7Wr. (w is an integer.)
12. sinh (2m + i) JV= j'sln (2?w-f- i) 5 TT. (? is an integer.)
B. RELATIONS AMONG THE HYPERBOLIC FUNCTIONS.
13- siuh u J( V c ") =* sinh ( ) = (csch)r 1
= 2 tanh i 7* -h (i - tauh 3 u} *= tanh 74 -4- (i tanh 1
14. coshw = J (f" + tf-") = cosh ( ) = (sech )-\
= (i -f- tanh 1 l-i- (i - tanh' J ) = i +- (i ~tanh 1 w).
15. tanh?^==:(^ fl )- f .( c -f- tf -) =__ tauh (-),
= (coth 7,!)" 1 siuh ?< -f- cosh = (i
16. sech == sech (--) = (r tauh 3 u)%,
17. csch u = csch ( ) ra (coth a u I)* 3 .
18. coth = - coth ( ) = (csch 1 + i)^.
19. cosh 5 ?^ sinh" u i.
20. siuh \u-\/\ (cosh i).
21. cosh \ u a (/ j(cosh ?i + i ) .
22. tanh I # = (cosh u i) -f- siuh u,
= siuh -H (i + cosh w) = i/ (cosh 7^ i) ~h (cosh w + i),
23. siuh 2?; = 2 sinh cosh w = 2 tanh ?t ~- (i tauh 1 .?<;)
24. cosh 2?^ = cosh 3 ?*; -f- sinh 8 n = 2 cosh" ?* i,
= 1+2 sinh 3 74 = (i -h tanh a ) -H (i - tauh 1 w),
25. tanh zu = 2 tanh w H- (i + tsuli* ) ,
26. siuh 3?^ = 3 sinh u -f 4 sinh 8 w.
27. cosh 3 = 4 cosh" 3 cosh ,
28. tanh 374 = (3 tanh it -f tanh 8 w) -t- (i -f .3 tanh 1 ).
XIV DEFINITIONS AND FORMULAS.
29. sinh nu
( n \( n i)(n 2)
n cosh"-' u sinh u 4 ^-^ 7^ cosh"" 1 w sinh' 4
30. cosh nn = cosh" n -I cosh " ~ 2 u sitih* u 4
2
31. sinh u 4 siuh # = 2 sinh J (7* 40 cosh j (74 0).
32. sinh 7; sinh w= 2 cosh J (71! 4 v) siuh i (7^ v).
33 . cosh ^; 4 cosh 2 2 cosh (u 4 ) cosh J ( ~- v) .
34. coshw cosh?; 2 sinh i(w 4 v) sinh (?! w).
35. siuh 4 cosh (i + tanh i K) -*- (i tanh i ).
36. (sinh 7/ 4 cosh 7*)" = cosh nn 4 sinh nu.
37. tanh 4 tauh v sinh (7^ 4 v ) -+ cosh ?<! cosh v.
38. tanh u tanh y = sinh (n 11} -r- cosh 7* cosh v.
39- coth n 4 coth = sinh ( 4 v) -s- siuh 7c sinh v.
40. coth u coth v= sinh (w )+- sinh n siuh v.
41. siuh (u y) sinh cosh v cosh n sinh v.
42. cosh ( v) = cosh n cosh w sinh u sinh w.
43- tauh ( i/) = (tauh u tanh v) -{- (i tanh ?^ tanh v).
44. coth ( ) = (coth u coth w x) * (coth v coth w).
45- sinh ( 4 v) 4 siuh ( w) = a sinh ?< cosh w.
46. sinh ( 4 ) siuh (7* w ) 2 cos h w gjuh Wi
47- cosh ( 4 w) 4 cosh ( - v ) = 2 cosh 7^ cosh w.
48. cosh ( 4 K) - cosh ( - ) = 2 sinh 7^ sinh w.
49. tanh I ( 4 ) - (sinh 7^ 4 sinh v) 4- (cosh 4 cosh v),
50. tanh i ( - V ) = (siuh - sinh ) s- (cosh 4 cosh v)
51. coth t ( 4 v) - (sinh - siuh p) -s- (cosh - cosh ).
52. coth i ( - ) (siuh 4 sinh V ) - (cosh - cosh ).
tanh u 4 tanh t; __ sinh (n 4 z)
tanh u tanh w ~ sinh ( )'
coth 7^ 4 coth p ^ ^ sinh ( 4 p)
' coth 7^ - coth v sinh(w- w ) 1
55- nh ( 4 ) 4 cosh ( + ) (cosh w+ sinh a) (cosh p + sinh ^
56. sinh ( 4 ) sinh ( ) siuh 3 7; - sinh 3 v
= cosh 5 u cosh 5 w.
57- cosh ( 4 ) cosh ( - ) = cosh = + sinh . P(
= sinh 1 7*4 cosh 3 w!
58. siuh (?z>) = . (mis an integer).
59. cosh (wzV) = ( i)-\
60. tanh(7;'ir) = o.
62. cosh ( + ,) (- i)
63-
DEFINITIONS AND FORMULAS. XV
64. cosh (2 m -f- i ) -3- i if = o.
65. sinh f n ) = i cosh n.
66. cosh ( u 1 = i sluh zi.
\ 2 /
67. tanli ( -h /JT) = tanh ?/,
C. INVERSE HYPERBOLIC FUNCTIONS.
68. siuh- 1 =
69. cosh" 1 ?/ log (?< + !/* 1) = sinh" 1 i
J (V I.)'*
/y/5/
- _.
I - ?
71. coth^w^UogCi+w) Hog (i)=
1-1 I ( I I / r ' \ / rf , , I
72. seen ' = log f -h \-~a- rj j f a y^= cosh" 1
,_! . /Jt_ I A /J_ i \ C fal _;._,_! I
74. sin"" 1 u s= 7' sinh" 1 M/ = /' log (in + j ^ 7^7^)7
75. cos" ! w = / cosh" 1 ?^ = i log ( -j- 2 i/ 1
, . - T , 1 J
2 t 2
77. cot" 1 7< = z'coth- 1 iw = j log (tw~z) ^log (ra-fi).
2 t 2
78. sin" 1 iwzsinh 1 " 1 7^ = * log (it + i/i +W 1 ).
79. cos" 1 iu ~ a cosh" 1 iu = * log (?f -f- l/i H-/* 1 ).
80. tan" 1 in = i tanh- 1 u = log ( i + ) -log ( i ) .
81. cot" 1 iu~~~ i coth- 1 n = iog ( -f i) + log(w i).
82.
i 1 i j U \ "" I " **-*-* "I
\ It- / \ 11 / $1* |- ^
= 2 tanh" 1 ; = log?;.
u -(- i **
83. taiih" 1 tan w = ^gd 2 u.
84. tau~ ! tanh n = ^gd~ l '2 n,
85. cosh" 1 esc 2 M = sinh- ] cot 2 u = tanh- 1 cos a = log tan K.
' IWI'INITIONM AND l-t HtMHl,A:i.
86. tanlr 1 tan 1 ( \ w (- f, it) ,i | ((} ; ot. ; //.
87. tanlr 1 tanM i< -. .} I< K - ,sa.: it.
38, COSlr 1 //;!;COsh ' V n.,'ih ' (//; t , { , ( - ,
89. siulr 1 siulr' w; ;K ii
90. ^^i + w + .f'.-!. " j. " ...
2! 3! l
92.
93-
; c,.;) <;(:, ;)<,., j
97- siuli^ w ^ , , w 1
3' Si"'" 7!
99. tauli M _.?, .,,.. , ...... 17
3 r 5 315" '' ' '
ioo. wcothw^j -f .J. w <_.i , , 3 ,
' 4S 9.15" ..... " ' ' '
'or. seoli w ^ r _J, , , 5 , fii
2 ' "" r< '
"--aechw--.. .ciw i ,1 Nt't'hS, i
5 """* ' (H lr|
DEFINITIONS AND KOKMULAS. xvit
1
24 5040
105. siuU-'=_J-j + JLA^_JL^_L!
23^245 2 4 6 7
_
2 21? 24 4 * 2 4 6
,06.
107.
j 5
108. -'-
109.
2 2 2
__
44 246 6 ( ? ><'j.)
no. cscli-^^^sinh- 1 = - -J 4. J.A J __ r 3 5 i
2 3' 2 4 5 6 246 ^
+ . . .(*>!.)
=, ]og A4.^^1_JLA^ + _LA_A^ m . . . CB . <10
U 22 244^2466 ^ ^ ;
E. DERIVATIVES.
rftf u
in. == (? u
(/fC
II2 . rfl^ll^i.
au u
d a" dv
IT 3- ~j~ a
du
rfw"
rf sinh
115. - ...... , - cosh u,
du
, d cosh 11
no.
au
d taiili n , ,
1 17, - , = sech 3 u.
du
_ rf coth . .
1 1 8. - -= -- csch 1 u.
au
d sech u
sech u.
, ,
an.
d csch it
I20t - - - = csch u. coth it.
an
d sinh~ l u i
121.
du |/ w i 4.
XVlJl DEFINITIONS AND FORMULAS.
d cosli ~ l n
122.
F. INTEGRA^. (INTEGRATION CONSTANTS ARK OMITTED.)
129. J siuh </ = cosh n.
130- J cosh rf = sinli 74.
131- J tanh rf?/ = log cosh u.
132. J coth ^ ^ log siiili n,
J33- I secli u dn = 2 tau ~ l />" o-H
,/ * i-" t. git .
134- I cscli ?^ rfw =log tauli .
1 o
2
135
= VTT siuh " + ' * cosh *
= - slnh . cosh-i +
137. J sinh ?; rftt = cosh n - sinli .
138. J n cosh H du = sinh ?i - cosh w.
139- J tf sinh rf = ( n a 4. 2)
140. J *' sinh u du =, u cosh
+ ( - r)J "
__ 2
_!
DEFINITIONS AND FORMULAS. XJX
141. J siiih 2 u dn ^ (siiih u cosli u it),
142. J sitih . cosh u du = cosh (2 w).
143. J cosh 2 n du = I (siuh ?^ cosh -f- ).
144. j tanh 2 K ^ =^ u tanli .
145. j coth 2 fl'tt u coth 7*.
146. j sech 2 ?c (/ = tanh ?^.
147. J sech" w rfw := i sec h t auh n + ^ gd /(.
148. J csch 1 ?^ ^ = coth n.
149. J sinh- 1 ?< rf? = sinh- 1 ?^ {i + u')>^.
150. J cosh~ l ^ = u cosli" 1 ( a - j)H,
151. J tanh- 1 u du ~ n tanh" 1 n + -|- log (j ),
152.
153-
154- J cosia coaw- 1 ^ = acsclirt. tanh -1 ( tanh . tanh | ),
csch rt [log; cosh -^ (u + ) - log cosh ^ ( - )1 .
155- J (cos + cosh )-' rf = 2 esc . tan- 1 (tanh ^ . tan -^).
156- J (i + cos a, cosh )- l dit = 2 c.sc . tanh-' (tanh -J. . tan | ).
157- J siuh cos rf M =1 (cosh . cos -h sinh u. sin ).
158. J cosh . cos tf = -I (sinh . cos + cosh . sin ).
159- J sinh 7^. sin udn = (cosh . siia u - sinh . cos ?t).
r6o. J cosh . sin rf = | (sillh , Hin _ cosh u CQs w)<
161. J sinh (;) sinh (?i) flT M
= ?1?^? L w sinh ^ M ") cosh C) - cosh {) sinh f ) "1 .
XX UBITNITIONS AND I'OUMIM.AH.
162. \ cosh (mu) sinh (nit) tin
- -I /v/sinh (tut) .sinh (titu) n cosh (nit) co.'ih ( ///)
wr w'L
163. I cosh (/) cosh (nu) du
~ -y j, w/ .sinh (;////) cosli (////) H sinh (w) cmli ('//) I
w n L |
164. j sinh tunh // </ - .shili ,/;</ //,
165. j cosh n cotli w f/// :. . cosh ;/ -( iir tunh "
./ a
166. J sec rt'w ~: gd~'' it.
/* ,-1
= I tan </. (i 4- tail" '/i)'^ -| ,J sinh > (Inn ./. ). J l,-,r /. v
,9. /* ,... r -'
- 1 (') ,; i,,. .)!,
* ra . i. ,..,,", r A
)< ./ ' ,
C ~~dU I /, y'
' J "w^ J ";;>v./ - : Hedi ' .
1 w c w 1 )^ rt /, ,;
I
ml '
, r_ ^
v ^7Z a -I- O /i
I7<1 " J (a^.C^'^'^.^u '"'''. Hhlll'"'
un
mONH AND KORM1M,A8,
/tin
. (<* )<*- /.'/ u
or
' roUr "
/* ''" 2 //
7- .1 (-// )^..//)'u - (/, ...^'^nnli- ' V *""'",
(' 1T ~" rt
' " / }
'" (a Wi ll >" ' V '. " (The renl form la to he taken.)
B. I Cw'-'ff 1 )'^" !"("' ') w - i'cosh>".
i i 1 1
Hill "" '
a
:>
.
. J (/('(tt'/Crf//- 1 Cff'.|.rt)J*.|. iflisi
/" 4"""
, f <" tfU t : .
<' (f
'* *
f ''""'' . 1 [" r"" /V-^-1
' " M /w I I," """- '"'"J ,..-i J'
"(" -Of" a) . , a.jrt"
1 " 1 '
- log M + IOK + fe^^ fl )' + i!LSi ! i
w f
DEFINITIONS AND FORMULAS.
C fa . e "
g. I - . - - Jog - - - -.
J I + e" I + "
- I TT-^T ~ - * w log ( ~f <k n '")
J <* + &"" a* L J
I f ^ _ * tall -
i ' J ae be-' "" , *X tan
/
(
- log ( | + /^'^ 4.
/7" ^ _ e"
(i + / ~~ M^ '
f-ui ^ tf au log?^ I ftf^rfw
IQi. f i? u " log 7^ rftt = & - .
^ a a J n
195. I Jog 7^ (/ = U log ?^ 7<!.
196. fMogrfw = 7* m +
5
197- J (log")" dto=tt (log 70"
199>
-f- 1
20 i
< 1.
. f d - _ = __ .. .._!_ r *'
j (io g ) o-i)(io g )-' ^ _rJ (tegiip
202 , - _ , WI rf
)" - c - 1) (log ) - i + IT=
r 7^ m ^ /^ e-v
2 3 ' J lo ^ J ~T
log ^ ~JT > were ^ = - ( + i) log .
204>
205-
2o6, J (a -f bu} m log K du =
l>Kl''tNlTH>NB AND KOKMUI.AS,
207. j //'" loft (a -|- /nt} titt
XX1U
ao8. /
(' //"' I ' ////. ~~\
.
(/ I- bit J
am;.
,
(a
<>< -1
' I -'-* 1
./ tt(,i'\*fin) m ~' l _}.
91
r Ititf // <//<
'i
/
213- I <
t'n
</
H '("( M) I a I ' lun
I TT I
, if
y/-
if <o.
3 i. f .
t)
217, | < "" ('// ,///
2iH.
219
rf ^ *
W > O.
. ("' d " ; Tr
*/ Hinh ()itt) a//.
/ ../ fi,. i
. I " lfli . "
*/y Hinh (ntt) t \,n'
DUFINITIONS AND l-'UUMfl.A 1 ;.
/li: /''"
221. I shih (mit) . sinh (nit) tin | rush (nm i . > ..-.h , utn ./
o, if W is ililtch-iil tnmi ,*;,
222. ( ' 'cash 1 (/) *///:: ( ' ' ;;inli'(w ) <///
Jo '"
/'I- i -r
223. I tiinh (///) //// : -- o.
./ i i:
/iir
224. I cosh (/////) da :- o.
./I)
/'I IT
225. I sinh (;//) cosli (ww) //// o,
i/f tr
/'fir
22f>. I Slllll (w/) COSll (//) (/ : II.
i/
/'' IflffW
227, ----- ........
Jo i it
f lo . ff "
1 I ......
t'l) I ~\- It
da-
(lit ..:--"
\- It 1 1>
229.
. y
230,
/I -f W \ ,/// TT
OK .......... - ..... . ... ,
" \ i . J if ( j
X 1 loff ?c. dtt TT
- l _,, ! r 3 '%"
- lf
2 33-
237.
J/
DIC1MNIT1ONH AND 1>'OHMUI,A,H. XXV
O. FOKMUI.AH I'OK TIIK SOLUTION OK I'mtUno-MJMIlCRICAI. TltlANOI.ltH.
rt...-.AYi,'/// Triangles.
rot // (a) sinh ti
Kin A , ,, . .
cot // (f) sum r
cos // (7') tunh l>
cos // .. t ...
cos // (c) limit c
i - SUI " /. i
oos A - . ., , , HIM // cosh a.
SIM // (it)
. . w>L//(M Hinh /'
col A , . \ .
COM // (<0 taiih
., cos//'*/) Until (/
aw A: . .. . . , .
cos// (c) Utnlt /
wlti // , , , ,
COM A= , ,,, r;:i n // COHll 0.
Hill // /O
Hill It .. C()l// <*>
Hill /I ' . II , , \ '
I'tll// (f) Hlltll ('
, (!0t // f") Mlltl
col /> ,, , /
OOH// ((>) tanh /'
tnn ^'1 Inn // : sin // (/:) sin // (<?) sin // (A).
; ndi /; well stu-h /'.
b.' Oblique Triangles*
The Koneriil rtiliiUunn nru:
coHh cosh // coHh r sinh (^ Hinli c COH //.
nin // Hitih /' Hin // sinh a,
eolli sinh /> uiosh /> cos cr-l* nin ("cot//.
COH // "" COH y/ COH 6' 4- sin // nin C'conh ,
I'Vtrtl HolvtiH llR! nix typical CUHOH in the followinj? manner:
CAHH J. Given , <5, <r. Put 2/ 4- 6 -I- f'. Then,
/v /O.Hinh (/^ r) i(
Hinh / mull (/> </)
The condlltoim r rt < // 4- c / <i < H- </ and r< -I- 6,
CABU 3. Given , (5, A, Draw tlit; K^dctic line CD perpendicular to Aff.
Then > C/> , -'-"I -'p -- < i ; cot J- C,' l> o ; and innh ^ ^ > o.
n
/n
XXVI DEFINITIONS AND !''OKMIM,AK.
Kinll b Mill //
a
. ,, tan !(// ..... //) .sink ,',(" -I /')
cosj C ~- , , ,\
z Kink i (a /')
t . , tank ! (a- /') sin A (,/ | /')
tank | c--- - V , ' , ',,; '
2 sin ^(A- />')
CASU 3. Given a, b, C, ?.&: '.-r (,-/ ) />' (-T).
. i / j , /,\ , ,,,oosh A ((C /')
-. _
Hill (A- 1-//) Hill (A I /,')
CASJS 4. Given A, tt t t. // .-[- /,' ,.; ff ft iul /V/f ' - 7 W/. Thr HIIK!'' /
is the angle between the geodetic DH driuvn pcriu'iMlit'iilar m ,/r'uiul
geodetic Z?^ drawn parallel to AC.
sinh/ sink (/. .,}
CASTS 5. Given //, #, a. , CJ) , in ,| ../ ,,.. // . K
CASH 6,-Given A t Ji t C, A
sin(A [. /,')!,, (A ,j- f) '
H.-FoilMUr,A KOH THM S()MITION UV TM1C C
If a cubic equation is given in the form
it can be reduced by the substitution ,., .v - ... lo , llo HilU|llc| .
1 I "
Era IdgMlouI1 ^ ac ,,
S AND FORMULAS.
CASK i . When a" + p x - q = 0; p and g positive. Compute the auxiliary
variable n from sinh ^ _ If . then the roota are
nr/ 7 t.iv/'J
~F 2 V' fp sillh I .
,v ( i/ .1. p sinn ]- H- / i/T" cos h I .
,V H = d= i/ -1.^6 s i n h | w - / i/7~cosh -I it.
CASK 2. When .v" -^: ? ^ ; p and ? positive. (-^) 3 < (| ? )'. Com-
pute u from cosh K = T ~X^_ ; then the roots are
=F a J/ -" cosh H.
,Y,, ~ -b i/ ^p cosh I w - / 1/7" si
.
CASK 3. When ;v" px q ^o; / and ^y positive. Q-/;) 3 >(^ y ). Com-
pute the angle H from cos u = - - .'^f AV> ; then the roots are
'
1 cO7.
A', = T 2 l/'j^COS (-1 7i + 120).
A- n q: 2 I/ -J./ cos (-J- 4- 240).
CASK 4. When A J /A- =b tf = O ; p and ,? positive.
For iipplicntions of hyperbolic and circular functions to the solution of the
cubic whose coefficients are general (/, e,, real or complex), see a brief paper
by Mr. W. D, I/aiubert 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 maybe shown that the elliptic integral of the first kind,
C
J
sn
in which k is the modulus and < the amplitude, reduces to u ~gd~^ </ when
fc i. The elliptic functions thus degenerate into the hyperbolic functions
when the modulus is equal to unity. A case in point is the elasticn, the
equation of which takes the form of an elliptic integral, excepting when the
modulus is unity. It then reduces to the two equations
= _ 2 tanh u; 2~ = -
a a cosh u
which is a syntractrix described by the free end of a rod whose middle point
traces out the tractory. 1
I,igowski gives the following easy geometrical method of demonstrating
the relations between the hyperbolic and circular functions. I,et the equation
of the circle of unit radius be
and call c the arc of this circle from the positive x axis to the point x 6 y
Then, of course, the circle may be repre-
sented by the two equations
x 6 cos c ; y = giu n ,
Now, the area of the circular sector, whose
chord is 2^, is e = _ ( ao that x e and
y c may be regarded as the cosine aud sine of
a sector . The ellipse may be derived
from the unit circle by multiplying the or-
. ., dinates ^ b y *. Hence, in the ellipse, the
FIG. 4. area of the sector subtended by the chord
2 j> e is, say, a and u t = du c .
1 If in these equations m is substituted for 2 they represent any syntractrix The two
equations, with this substitution, can be combined to the following;
(an xY y" 1
n by a P Inton a circle of * whose center i s in
ixviii
GEOMETRICAL ILLUSTRATIONS. XXlX
Thus
x c cos u e = cos
j/ c = sin ?<: c = ~ sin -^
^ b b
so that for the ellipse,
-v'
#' + J-= r
, . a
^ c Jtr e z^=: COS ; J' e = b Sill -jr- 1
^ ^
The equation
fl ,,.! T
X y 1
represents an equilateral hyperbola, and if u is the area of the hyperbolic
sector whose chord is 2j>, then there can be no objection to writing
x cosh u ; y sinh ,
where cosh and sinh are functions whose nature is still to be determined.
The most evident relation is
cosh 2 n sinh 1 n i.
Now if i V i) the hyperbola may be written
which is an ellipse whose major axis is unity and whose minor axis is i.
Comparing this with the ellipse discussed above, it appears at once that
i.
x = cosh it cos r*
z
. , . .
y = siuh u t sin -r-
^ *
or, in an equivalent form,
cosh u = cos z ; sinh ?c i sin w,
cosh iu = cos 7<t , sinh w = z sin .
The investigation of cosh n and sinh ?<i can be completed in various ways ;
for example, by writing out the series for cos iu and z sin iu and showing
that their sum or difference is e* u ,
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.
XXX
GEOMETRICAL IIJ.USTKA'flONS.
the area a /J may be chosen as the unit area, so that the equation of tlio
curve becomes
By varying the value of a. in this equation a family of ellipsis 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 tin; hyperbola
xy |, and this may be conceived as generated by the motion of n single
point. The coordinates of the point />,, at which the hyperbola is tangent
to the ellipse, are
V 2 a |/ 2
and the coordinates of the point c at which the hyperbola is tangent to the
unit circle, are
('hOMKTKICAr, lUUHTKATlONH. XXxl
and hi-aiust' .1 r .',,
iiiai no iiiLiwaliim mnsiiml is required,
'"' '"'^ " ' ll' vlnr .i/', ,</;, wluM- t! lli eoiirdi.n.te,, of r. HIV ,-::,.
and ,', .,.. U ,, not ( -worli, y t!,n( two oil,,-,' uruas, ,//', ,-/', n and \ '/>
ft ^ Mav HUM same value, for evidently '
1 / l( /j
J' " ' } .1' I/I' ' . loj'' It : .- l( f
'ill
The lentil) tit' the i-hunl /' /' i H
\ J
1 O -.f 1
f'" ' /' "
c (Mirvc /', (/!, i,s an liyperliolu,
I'" 11 If/','' 1 : I,
,. ),,.- -,
t'ti.sh it.
t
Ir.N r.mnnMnur U. point,, or iuU-.^-linn of tlu, unit drolc and
; <- Hl.| t ,uv M n, ,r , IIIlly , w Wlllw | lho iw ||(! (li
' " ' tll
. iv u- nunu! are,..
it m IIKIIUI - n MIB rfn iM
lll ,
o K caK,,l and ],,,4 ux,s ,,l an Hlip..ii ( | ol' imil volimu,, socw-
. met, nrv t h, trur,, of ih, rli,,,!,,,. f ,dinn, of lh, ,,11^1 Th oO < -
f on,' of lh,
dud H f(ilLw lliat
tan
his ,, K ] t i a ,, JM rfrf ,, ( or lhe
KH(Utrmn)niinn ()f W( s
xxxii GJCOMICTUICAI, IU.U.STUATION;;,
ellipse whatever the angle made by any line parallel tnnne fonryrllr <!iiuni'l<!
with a perpendicular on the other isocj-elk; diameter is the ^iitlri'intintiiuii nf tin
natural logarithm of the .semi-major axis, thisltciiu; exjiii's-u'd in letiii'iu!' tin
isocyclic radius, which in the general case is the ;;i|iiare runt, u| r tin- piml
net of the semiaxcs, 1 In the diagram the gndeimuniimn A-/-, i:< Nhmvit n\
bisected by the axis of the hyperbola, and il i.s worth rental kini; that il tin
ellipse were to be distorted into a circle by compiv.siiiiin the IIHIJIU uxifi ati(
elongating the minor axis, the line <>/> would he brought intu rninndenrt
with o& tt so that gd wean be defined as the angle thmnnh whitli an i.-iurvrlit
diameter has swept when the ellipse has been derived fnun si rin-le by inn
tational plane strain,
The angle 45 H- -which occurs in the formula fur niei Minimi \\\\\\\
f
is the angle made by cither Isocydic diametor of the dlipw with tin- uiinni
axis, and the tangent of this tingle is the semi-nnijiM axis .
The twofold relations of the hyperbolic fiim;l.imis tn the livpetlinlit ami
the ellipse arc illustrated in a somewhat different mumier in li^nte ft,
Here the curve/, c fa is an arc of an hyperbola y ' i. If tin- un?ti
of the sector ofa c fa is called //, a fa: sinh // and wt ni.-tli u, Mukts
bcp^a and draw the associated ellipse shown in the, fliu^ituii. Tlien tltd
angle boc~gdu< fo^cosh n ami
Ian pf/tt : s\\\\i u
KQQfj'd ir.-i t:osh it
Hin,i,'v/// tftiihw,
The ellipse has corresponding properties. Shift* the K"'l<'nmiMnin H tlm
angle between either isocyclic diameter ami a line |*r|H!ii<lii-ithir l. the ntliiM-
the line ob maybe regarded as coinciding with one ism'yelic.lm.MH,..' uml thr
axis of abscissas with the other. The major IIX!H of the Hliii^ tht-u IM-UVI-
'The locycli n fll fl i,.clcr iwcrt ia thin illiiHlr,iilu,i ,,f hypnlmH, hnu-UHM" llrn (M
drcutnr S eo Uon of n al.oar oUI|M lW . B ,lllp Hl) i (l | B w lleh h, WMn V I, (
proportional boUvec,, the Kre(l , BHl ,,,, ,, 1(Ht ,^ ^ *
If -BBcoah ;/ mid ^ R> conli
the BH K te , which the circular Heellu.. m,.k M will, u K .l.l ,xl I, K | VM( by
tun > .',. tniih iV
GEOMETRICAL ILLUSTRATIONS. XXX1H
the angle 90 ~gdn, its magnitude is 2 e\ and the equation of the ellipse is
x* +4xy tan gdn -f-y (4 tan'.gtf n -(- i) = i.
By varying the value of tan get n (or sinh w) a system of ellipses is obtained
whose envelopes are y = i, so that if any one of the ellipses is supposed
to be derived from the circle by distortion, the process is that generally
known as "shearing motion or scission."
If the points in the circle are sought which correspond to the points on the
major axis of the ellipsoid, it will be found that the angle between the two
positions (the angle of rotation) is equal to the gudennaimian '
If instead of the horizontal, the vertical line in figure 6 had been taken as
coinciding with the isoeyclic diameter of the ellipse, the result would have
been the discovery of a system of ellipses whose envelopes are x
similar in all respects excepting orientation to that discussed.
1 love's TreaLise on the Theory of Elasticity, vol. i, p. 43.
: I
METHODS OF INTERPOLATION.
It is not easy to describe the use of the tables which follow without t.
notes on the methods of interpolation with reference to which the}
arranged. In all of them the argument advances by equal increments, <
equal, say, to o. It is required to find a value of the function
diate between two tabulated values, F and F v corresponding' to a
value of the argument or toww, where?/ is always less than unity,
preferably less than one-half.
Let F n be the value of the function to be determined ; let 7C_ i and F-.
tabulated values of F immediately preceding F , and let F lt F A be va
immediately following F . Denote F, F by a lt other first differences
being similarly represented. If also rt a 1 = <5 I> ^ *V ^n etc '< t' 10 w:
system of functions aud differences is shown in the following schedule ;
F
A'
J"
A'"
+
*,
b"
d"
a"
c"
^-i
b'
d'
a'
*
c'
<
f.
,
*,
c,
<k
The most familiar formula of interpolation is due to Newton, and
above notation it may be written thus:
~
'The notation and general outline of treatment here presented closely follow ]
Herbert I,. RlC e's treatise, Theory and Practice of Interpolation, l8 gg The
Press, 1/yuu, Massachusetts,
XXXIV
OK JNTI'UL'Dl.ATlON. XXXV
Tin; eoullidi'iilH are llmsc of the Imimiiml theorem. Tills formula is appli-
cable Lo UK- first ink-rvals of u writ's, which j> t U nL the- eu.se with nny other
mode of inU'rpolalioii. ll may also ] mbipl.-d to the lust inlorvrd't by -mb-
sliLulhiK -"lor, Mind*', //,,:", rf". . . , for ,,,. /*,, ,-, ,/, ..... In systematic
interpolation, Mirh MM is involved in UK- construction of tublus, it is usiml to
employ Hie nioiv rapidly rnnviTKinn fornuiliiM of Stirling or ltos.^1; but when
n nmipuliii);' nim-him' mid u tal.K: of prmJiu-U mv avniluhU- it is soim:(iim-s
kiwi Ittborinus Ui ruinputc nn cxlrn UTIU of Kiuvlon 1 .-! formula limn to nilm--
lutrand itpply tlu- iiu-iui diliVn-na:s ndU'd for | v [lie- oilier nu ; (1i (l ds. Holh
HtirliiiK'.s and Hrsiu-I'M i'unnuliiM run IK- <U-rivc<l froin Newton's by knoxvii
ivltitiomi hi'lwtA'ti Mu; si'vrral diU'i-rtiiu-i-M,
In Stirlinjv'M foniuilu tin- moan of UK- firnl dilfurciUTH next pnx-odhitf niul
/;, is Hindi? M.wnl' iustiMid of only the latter, UM in Nnwlon'H fonimla,
third (Uirt'ivna-M mv .similarly Irciitwl, HO Unit , c ot ctt;., hcin^ m,'\v
titioH, arc dcfmt'il by
Thojit' nx-iin vahioM nr used in roujniuMmn with tin; ovun di(lVn.'iiWH on the
rnuno Imrlximlnl lint; wilb /;, in tlu: Huluidiiu?, and Kililin^'H foninilu IN
To interpolate Imekwiml it is only nt'nlful to MiihMtitnto - for w.
Tn HosMc-1'ji formulii u;t in niutlo of nu-mi ilitot-iKMtM of tlu; ovi-n onlcra, uiul
if fi.f/, etc.. arc tlu-no inuium ihcy naMlcfined In Uirnui of th scheduled elifTtM--
IMKX'H, tlUltl :
^V:*, rf '-'- rf ', rf(CU ,
*" jj
They imr ust:d inconjuni-lhin with ihu simple odd diffcirt-nccH </,, r,, etc., mid
llu- formula in
f -I \)tt(n i) (//--.a) (;/>-.',)
' (.', -I- ....
Whim w r ^ ,, r f nr inierpoluiion to tlu; middle of tut interval, tlio co-
idenloCc, vimiMhoHnnd /;.- -V^iH Intlciwiidont of third differojiccs, which
is clearly u (.;mU ndvanlii^, In general this method Jn very ndvaiitnKcoiiH
when H approntihuH on-hulf. while Htlrling' forinubi in preferred for twmll
values of ;/,
XXXVI METHODS OF INTERPOLATION.
When Bessel' s formula is used for backward interpolation, it may bo
written
/? -F - no! 4- " ( ""' r)
/_ / na -t
?^ being taken as positive.
A distinct method of interpolation is founded directly upon Taylor's
theorem. If F a ' FJ' t etc., are the successive derivatives of F ot and u is the
constant increment of the argument, this fundamental theorem may be
written
21 7 ! A !
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 StirlinR
according to ascending powers of and comparing coefficients,
(Bessel.) (Stirling.)
-5 (*i -) = ~
Hence, to compute the first derivative, say from Stirling's formula, when
the 6th differences and ^ of the mean of the corresponding third differences
are negligible, it is only needful to take the mean of the first differences pre-
ceding and following the tabular value of the function, subtract from it one-
sixth () of the mean of the corresponding third differences, and divide the
result by w,
Newton's formula gives for arguments near the beginning of the series of
tabular values ;
MICTIIODS 0V INTERPOLATION. XXXvii
and for nrtfittneiHs near the end of the KoricH of tabular values,
The dllTci'uncuH of the derlvntivoH nmy of course lie found and
in the sninc nmuncr na tluwe of uny otlicr funoLion, and th higher dorJvu-,
tives, /'Ii", /;,'", ..... cun be (ixpreHswl In icrmH of tlicdifforcnccs f /'N\
To distiiiKiiiHh the differences of ,/'" from those of /', they may lie rteiiolcd
by Greek letters, nnd the notation is exhibited in the following scheme :
/' '
* o
y, y,
A
UftiiiB Stirling's formukic, page xxxvl, ihc swcccsalvc dcrlvutivea Inchmive
of fifth differences are now
nnd the intcrnolatiou forunilii mny be written
A, /; + - /; + ^ ? K - S %) + "" 7 (A - ,V t) + "' ",'
' \t ' 4 '
or, neglecting fifth dlffer
flH...[^+
niul for backward interpolation
XXXviii * METHODS OF INTERPOLATION.
In the tables which follow, the first derivatives multiplied by are tabu-
lated iu 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 tbat the ^ part of the second difference of i/v'
is not great enough to influence the result, and it is therefore sufficient to use
co a g being the mean first difference of 01 F 1 corresponding to F . This formula
is rigorous when third differences are zero. In most cases -- can be found
2
/ ft \
, mentally, and since to ^ o ' -| -- oj is here to be regarded as an interpolated
value of a FJ, uo confusion can arise as to the sign of the correction. It thus
becomes almost as easy to include e>a o in the computation as to omit it. A
convenient rule is : Find by linear interpolation the value to /<"' for one-half
the interval \~y, multiply this interpolated value by the entire interval ()
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 log, sinh 0.00304. In this case
= 0.4 and the table gives
^ = 7-477"; "A' =M47,7; w <*<,= - 48, 3,
the last two quantities being expressed in units of the fifth decimal place.
Interpolating a F 1 linearly for one-half the interval,
, a F'^== (a (F^ -f-a )= 1447,7 -0.2 x 48,3 = 1438,0;
multiplying this value by and adding the result to the tabular value of the
function, there results
F n 1438,0 X 0.4 + 7.47712 7.48287.
The corresponding difference formula (Bessel's) is
The derivative formula (*) with two terms has the advantage of being much
more convenient than the difference formula, while the accuracy of the two
is the same (five-eighths of a unit) when the derivatives are tabulated to the
MKTHODS OP INTERPOLATION. XXXIX
same order of decimal as the function. lu 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 iu the next succeeding decimal place.
The accuracy of the two formulas is the same when the next succeeding
decimal of the derivative is tabulated. The error of the derivative formula
is then simply the error of the tabular value, while the error of the difference
formula may be =, > or < than that of the tabular value, but is never greater
than one-half of a unit.
Interpolation formulas which are applicable only to a single function are
rarely advantageous, because as much time is often consumed iu looking them
up as is saved by employing them ; but some formulas applicable to hyper-
bolic functions are so simple that when ouce suggested they can hardly be
forgotten. Thus, Taylor's theorem gives at once
1 / -, 1 -i . a <*> a , , n 3 * 3 . ,
cosh (u 4- n w) cosh u = n to siuh u ~\ -- y- cosh u 4- r - smh u 4- . . . ,
and the form for the sine is of course similar. Again, when, as here, the
cosine is tabulated with an argument in terms 'of radians,
, . , n 3 to 1 , u s cu 8 ,
cos ( 4- w ) cos n n o> sin u -- r- cos u -\ --- sin it- -j- . . . . ,
'2\ 3!
the series for the sine being similar.
So, too,
log B ( + w) log fl n == logo ( I + -~
n <
,3 ,..9
n
Simplest of all is the exponential,
= (4-o. OIH H- 0.000,05 ?/. 2 + 0.000,000,167 s + .), ("'=0.01)
= *(4-o.ooi 4- 0.000,000,5 ' 4- . , .) (=o.ooi)
The series in w may be replaced by //, and this may have any finite value,
Especially when a computing machine is available, this formula is easily ap-
plied and is, of course, rigorous.
From time to time inverse interpolation by a method more accurate than
first differences is called for ; indeed, whenever interpolation of a function
by higher differences is needful, it is equally needful that the argument cor-
responding to a given function should be ascertained by a like process. The
method ordinarily pursued in such cases is to estimate two values of the argu-
ment, one a little greater and the other a little less than that of the required
argument, interpolate corresponding values of the function, and finally inter-
polate linearly over the reduced interval for a final value of the argument-
xl METHODS OF INTERPOLATION.
Another method consists in interpolating values of the function and its deriv-
atives for an approximate value of the required interval nticl then computing
a correction to this approximate value by means of n reversed Taylor's .series. '
If second differences only are to be taken into account, the usual method
of procedure is to estimate an approximate value of w, say ', and with this
estimated value we interpolate linearly as before and find the value of /v
V
/ u r \
corresponding to one-half of the estimated interval f ). Then the required
X 2 /
interval (n) is equal to the difference between the given value and the nearest
tabular of the function divided by m ./v . This method is in fact simply the
'3
reverse of the one for direct interpolation. A recomputation is of cotir.se
necessary if the values of n and ' are not practically the same. As an illus-
tration, find it when log, sinh = 7.48^87. We first compute
, 7.48287 7.47712
H ^ ~ : '-Li = a A
1448,0 ' 4j
then the value of < TV in terms of the last tabular unit is found as Iwforo
s
by linear interpolation to be 1438,0. Hence
7.48287 7.477:2
_
Ol4 alld "
Since the estimated and computed values of the interval agree, there is no
need of a recomputatiou.
The methods which are based upon an estimated value of the argument
are unsystematic and clumsy. It is much better to use a formula which
gives the required result by a direct and rigorous method. To Hud such a
formula, divide Taylor's series (eq. a) by w/tf, and put
then the interpolation formula may be written
, = + /, J + /. 3 + / 4 ^ + /,
Reversing this series in accordance with the relation, 3
^r V 3 + 5 o i , 5 i a
J 5
+ ^ ( < , + 3 < (, + 2 rt[ ^ _ 2 ,
Rice's Theory and Practice of Inter potation, section "fi^
MitTHons OF irmciiror.A'rioN, xll
which is the reversed series of
and rearranging the terms, 1
- , 4 , [- ,/, 4 2 (,/,)' 5 (,/ 3 ) n -I- <* (wt/,) 1 4- . . .]
4 < [,/. (- i 4 5 (,/,) - si (,/,) + . . )]
-H ,' [/, C- i 4 6 ,/,) H- 3 <,/i ' 4 - - ]
4 <[-,/; 4 . . .] .......
In the actual computation it is convenient to put
then, when successive values of wj? n ' are tabulated in units of the last decimal
place, and Stirling's coefficients are used,
n f r^!T r ot (a V v ^ w /" !? CD fj8 1 - S ^
The formula is rigorous inclusive of fifth differences, and docs not require
the computation of an approximate value of H. It is applicable to any func-
tion or series of tabulated values whose successive derivatives become evanes-
cent. It is particularly convenient when differences higher than the second
are neglected. The formula then becomes
n ^ ?/, -|- , [ rm u -f 2 (rw a,)" 5 (''" "<,)' -f 14 0'<" )']
Since rw a is a very small quantity, the higher powers are .seldom needed, and,
should they be required, arc easily taken into account. A.s an example, lot
it be required to find when log w sinh = 7.48287. We compute
1447,7
0.40
--"- -?-!/ I /
and
, rta OH = 0.40 X O.OOOI X ( 48,3) - = O.OO.
Hence w7/,:o.4O and ~- 0.00304, the same as obtained by the other
method.
When y-; -.-/.'", it is easily shown, either by means of series (ft) or by inde-
pendent methods, that
s= -h ! 0.005 i 3 H- 0.000,033 / H" . . ., ( i-j o.oi )
= 4- , 0.0005 , + (w^ 0.001)
These formula afford an easy means of finding the natural logarithm of a
1 Sec, Blso, Inverse Interpolation by Meaiin of a Reversed Scrlca," Phil. Mng., May, 1908,
xlif
MUTirons OF INTKKPUI.ATION.
number from the tabular values of f. ' ", 'riias, Lo lind the natural
of 0.9642102, we compute
Substituting in the Inst of (he above ^illations
-.--o./|457 ---O.UOD.S X (n..|.s) v ".-l-l.'i'/V.
hence nat log" of 0.0642102 = ; o,o;$6.|. (<,?{,
One of the most important applications of diil'rieiuv, i-< the drlrrtion of
errors in values tabuhUed at equal intervals of Itir arj-utiu-nt. It nuiy hr
shown by substitution in the schedule of ditt'eirmvn (pa^r \sxiv) tlmi an
error, + e, in 1\ produces errors in UK- .successive ditlViviuvs ..f utiv tinier
which are multiples of c, the law of distribution of tin- multiplr-i IHMMK Unit
of the corresponding coefficients of tint binomial tliniirm, and (lie .'ii>;it!inf
the errors being alternately positive and nuKiilivr. Since MIIUC tntlrrdf dif.
fereuces of every continuous function must vanish, Ijn- ptrsnio- i.f uii ciiur
in a tabular value must ultimately result in producing mirn:.iivr diliriniri-s
of a certain order which alternate in sit;n. A comparison til' Ib.-:,,- .Ittlnriici'M
with the corresponding binomial coellicitMits enables om- lu rsliniiilr tb
uitude of the error. Thus in tin: series which follows :
X
,-
J'
.1"
13
2197
5'17
14
2744
S,j
"3 1
d
15
3375
on
1- 2
721
a
if)
'!<></>
98
M |
819
i >
17
1915
ij
H,'
yi7
i ;!
IS
5832
1(0
li
io;!7
1
19
6859
114
I- 2
11-1 1
'' 1
20
Hooo
120
1
1261
2 f
J2(il
i
the alternation in sigll O m,r in the fonrth-onlcr ,lilf,.,, ;lll r ; ,, ,uul Ih, ,-
-^ un SfT " 1C em ?r ita " f ('' 'I' *>' "- il-r, i" , f
Mum bin the value,,, -
ue,,,,,,,. The eun-ecUon.v 3| .|-8, .,,.,, . ....
d to tte fourth ain.e,,,, ccs amm t , lem l() vn , ,. J ^ ; -
..
es and in ostlmnling their i..n K i.ii.lcs.
rmrH in
DESCRIPTION OF TABLKvS.
Table I Is devoted to s-place values of the logarithmic hyperbolic nine,
vasine, tangent, and cotangent of n expressed in radians. The argument
n advances by ten-thousandths from o to o, i, by thousandths from o.i to
3,0, and by hundrcdtlm from 3,0 to 6.0. In this UK in nil the tables (except
Table VII), instead of the first differences, the first derivative's of the func-
tions multiplied by the tubular interval O) are tubulated in units of the hist
decimal place, under the heading ">/'J,'. As noted tibove, 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 ' " are given, from which in cftwe of need the hyper-
bolic functions can be found.
In Table II the natural values of the hyperbolic functions are tubulated
for the same arguments us in Table I. In .sonic instance.'! the value* lire
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 n -- - i siiih (it. and cos n = cosh t'n with their loga-
rithms to 5 decimal places, the argument if being expressed in radians.
The tabulation extends from ; - o.oooo to o. 1000, and from ft = o. 100 to
i. Goo, because yo - 1,570 70(13 radiniiH; so that, this value of "> hdug
A
borne in mind, the table affords the means of finding the sine or cosine of finy
arc expressed in mdiuus.
Independently of hyperbolic functions, this table is of ton convenient. It
also facilitates the computation of the principal hyperbolic functions of
complex variables. Thus
sinh ( :h /') ::-.! sinh n cos v H / cosh // sin v,
COHh ( :h h') ' COSh It COS V -I: / Hlllll W Sill V,
and to compute either of these functions it is only needful to take out two
tabulated logarithms from Table III, two from Table I, miikc two ntlditioiiH,
and look out two untilogarithms. It is of course conceivable that all the
four quantities involved .should be tabulated once for all ; but even if // and
v advanced only by lumdredtlis, such a table would occupy 200 pages. To
find from it functions corresponding to n and v expressed in tlioiiHniultliH
would require three interpolationsa process quite as laborious us the IIKO
of the tables here given.
Space which would otherwise be vacant IM utilized to give the angular
values of the radian arguments, or a table of conversion of radians from
xliH
JWSCKH'TION 01'' TAHI.I'M
o.oooo to o.iooo and from o.ioo to i.uoo into decrees, minute;!, Jieconds,
and hundred ths of a second.
Table IV gives the values of log,,,*'" , ?" ami ''""' l<> 7 decimal plmrs fn>m
u = o.ooo to 3.000 and from 3,00 to 6.00. Tlie values of <" mid / " enter
into a vast number of equation;) representing imlunil phenomena, especially
those (as Cournot remarked) which can he classed tinder lln- KCIU'I '*' <tenom~
inatioii of phenomena of absorption or gradual extinction. Tin* ascending
and descending exponentials may be regarded at will t'itlit'i 1 us hyperbolic
functions or as independent components of hyperhnlk 1 functions, since.
a*" -:- cosh it :'.T sinh
while, on the other hand,
e" --/--" . /" -I- f "'
-I cosh ;-.-
2
tanh n ~~- -'- - ,- ; }fd // a liiu
""
It is further evident tlmt a table of t" 1 -" is a lubk: of uutimil
Formulae on page xli affords an easy nuiaus of oliliiiniiif. UH- nuhuitl
rithm of a number from the tabular values of /' ' ". It is of roiinu' nm
sary to give the derivative of t 1 ", since this is <", while Ihr iJi-iivalivo < " in
<?~", In general the interpolation or extrapolation of ilit- I'um-iion is
veryeasy. (See formula c, page xxxix). The loj;aiilhtu of * i " is not f.;ivrn
because, being merely the arithmetical complement of tho loj'.,, r", it run
be read off as fast as it can be written down.
In any table of log )0 c" where the interval of h i, ilm dillViviico of
successive logarithms is constant and equal lo < ln)f w f or o,,|,vt,! <),|.|K <-..
If the logarithm of t'"-!-""' is required, this will In:
(u -|- ) log lu a -. . log,,, ,;" 1 i., log l( , ,-.
Hence it is practicable to prepare an exleiulod Uihlo of piopurtiiuiul parlH or
a table of log lo tf which is ajiplicnhle to any Kilih; of lo^,,, r" when lh*- tab-
ulated values are multiplied by w. Hudi nil auxiliary talilr IN niveu at ilui
close of Table IV, in which the argument " varies from n.inwt to u..vn.. If
w is unity, this is merely a 5-place table of log |(( ,-" . If. on ih<< oth.-i hand,
< is 0.001, as in the earlier part of Table IV, the auxiliary table K ivrs the
increments corresponding to n to 8 places of dednmK Thus, if \\\y^r ...... *-'
is required, Table IV gives log, ^--o.o^ai'/y, tin; imxiliiiry mW.: tfves
. w 1
tor-- = 0.245, w lojf w tf ^0.10640; and since M , u.tMii. . IOK,., '' -
CXOOOI0640, which added to log lo <?w\ gives lo^^^- Ol0 VM-J.n ''>
the latter portion of Table IV w is only 0,01; .so that, if UH? hV^ r 1 '"- 1 -- Is
wanted, the main table gives loj? *: -.: i.^oaHK.n. and w tints' M 1,. K HM
0.0010640; so that the required number is r, 3030.47*1'
DESCRIPTION OV 'JfABUtS.
When log,,, C H is required for u > 6.00 the auxiliary table is insufficient to
give 7-place values. Then tlie main table, IV, may be used a an auxiliary
table. Thus
n.oBH2Hi) : ^ L g tf n _|_ log
= 4, 7772393 -f 0.0383243 = 4*8155636-
In the second part of Table IV values of c 1 ;t; " and the logarithms of " arc
given, n varying from i to 100. The logarithms arc given to 10 decimals;
the other functions to 9 significant figures. Such high values are seldom
needed, but are included here lest these tables might some limes fail the
computer.
Table V gives the natural logarithms of numbers from i to 1000, with
their derivatives to 5 places of decimals. These derivatives are merely the
reciprocals of the arguments, and since log fl f j^~- logj', the logarithms
of the derivatives are the tabulated logarithms taken negatively. The
table thus gives, in addition to the logarithms of 1000 whole numbers, the
logarithms of 1000 proper fractions lying between o.oor and unity.
The interpolation of natural logarithms is much less .simple than is that
of common logarithms, and this IK the main reason why the latter arc pre-
ferred for computation. A few simple rules, however, facilitate the needful
calculations. When the natural logarithm of a vulgar fraction is required
it is best to look out the logarithm of both numerator and denominator and
subtract. If the natural logarithm is required of a fractional number .stated
decimally and less than 21.000, no attempt should be made to interpolate it
directly, because the third differences of the table cannot be neglected for
numbers so near the beginning of the table. If the number UGH between
10.000 and 21. ooo, ns, Cor example, 12.345, it should be written 123,45/10,
and the required logarithm will be unt log 123.45 nat log 10. It is safe to
interpolate the first of the.se between nat log 123 and nat log 124, using the
formula for second differences. If the number whose logarithm is to be
found lies between i and 10, as, for example, 8.2468, it should be written
824,68/100, so that the required quantity is tint log 824.68 nat log 100,
The first of these logarithms can be found by using only the mean first
differences or the tabulated derivatives between the logarithms of 824 and
825. For values of the argument between 21 and 158 interpolation requires
the use of second differences, while above 158 average first differences or
the first derivative in sufficiently accurate, inasmuch as the error involved is
less tlmn 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, front the reciprocal of 159 on to
the end of the table, or for numbers between 0,00628 and o.ooioo but thin
would uot be expedient, because these reciprocals are themselves rounded
values. If the natural logarithm of 0.0068352 is wanted as accurately aa
xlvi DESCRIPTION OF
the tables will give it, it is best to find the logarithm of 683.52 and to sub-
tract from it the logarithm of 100,000. (See also formula e t 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 nunilun-
may be written 246.90 / 20, and the natural logarithm of the numerator found
by help of the derivative, less uat log 20, is the required value.
The awkwardness of a table of natural logarithms is inherent and cannot
oe overcome by any device. It depends on the fact that e and the ba.se 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 Ix-i-n
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 S-p ace table of all numbers from t to 10,000, i,s only a Httlc mor,
zrr T th ? he : e offered) aud with * to0 * * * *> ^^ -
rl In b ? " faCt r SUch that the P roduct approaches 10,000.
Table VI gl ves the values of the gudermannian of n to 7 places from
v - 0.000 to = 3.000 and from = 3.00 to n = 6.00. In t hi table n
*** both i
> o u raa " s >* * ^ -- i*
tlieoretical work the gudermannian in radians is usually the more convenient
but for use ni finding hyperbolic functions it must be reduced o u ang e
, cosh = sec ^rf
= tam^, = log. too
., -* -. - - b. . .,, ,
Table VII is substantially a reversion o
S and
= 3437-7468 " = 3437.7468 log. t,n
Meridional Parts for a Sp he ^Q tobe Ith" '" lEttt0ni " a tobU! of
cussion of physical quest L ls a' "
Merca tor e hart , In the more
IHCSCKll'TION OK TAHI.KS. xlvll
elliptirily of Uur nuiridinn is nlhiwod for in i-ninpiitln^ Ublus of inuridioiml
pans, niiil ronsrqm-iilly IhiM tiililo will prolmlity IIUVIT In; a-produoiMl in ii
nvi)'nlor. Knr this iviison it t.s hurt* prrsiiivrd for computers who arc not
t'iit;u>',t'<l in imvif'.iition.
To U'SL this tiililr, \vliich is borrowed from Tiimmi, soo of tin; vitlui's, or
inn 1 in t:VLM-y ay rnlrk-M, \vrn- conii>iirwl with (.ndcmmmi's y-iUiuinml pliic'c
tuhlfiif Uu: mili|',ii(U'riii[inuiiui in nulimi inrnsnn-. tn iii'iirly all oiiHt'sIiunnn'M
lusl lir.urc was mul'mni'd, 1ml in u fi-vv iu.sLain'cs Hit; ln;;L ilnua: is ini'orrwt
liy it n nil. Inquiry into them* t-iist'M lilmwt'd Unit ihr niaxininin error dulct:tcd
win; Irs:; thiin ti.ittifi o!' u miimlr. Tliuti tin- lust Jitviin- is not nUHoInlt-ly Irusl-
worthy, tint i:i IRMII- i-nuiijvli to cnulth- the roin|)iUcr lo interpolate urciintti'ly
to /i plaei'.'i. If / plnrt'.'t of tin: tintif'.uik'niiimiium urn i t qiiin-d, they oan lw
found by invert' intorpnlutioii in Tablt* VI.
TluM'iirlu.-r purl of 'PnhU- VII niuy lu; inU'rpoliili'd liy firHt diffurcnrcM witli-
onl ciHmiilrrulili! iriTor. M itliont H.| n .V'' ono-dfrlilh of Liu: scrond <lifl'cu;nu;
In-i-onnv; iqiproximuldy half unit in lh lust tuhulatod placu, iiml beyond
this point wjooiid dilTcrriiri'H should IxTlnkuii into awount.
Talilc VIIT IM u liiltU* for ronvnlin^ mdlaim into angular niviiHitrc and
via vetsa. A. (Vw iiunutriail anwtnntH un: p|uinlcd.
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 \ =gd where \ is the latitude
CL
mthe "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
tan
(-1+ A)
and this _ Mercator must have tabulated. He published his map without
explanation, however, and it was left to Edward Wright in i TO9 to state
the formula for m,
.r'J^ aCUlal iUVent r f the h yP erbolic trigonometry," says Professor
McMahon "was Vincenzo Riccati, S. J. (Opuseuia ad res Phys. et Math
pertmens, Bononiae, 1757)- He adopted the notation Sk. *, a, A t for the
hyperbolic functions and fife 0, Co. for the circular ones. He proved the
additmu theorem geometically, aud derived a construction for the solution
of a cubic equation. Soon after Daviet de Fonoenex showed how to inter-
Ca '" Uder
C. Guderaann published an important memoir ou Potential or Cvclio
James McMahon, Hyperbolic Functions, p. 71
1II8TOWICAT,- NO'l'K.
tion of his eoniributioiw to the .subject, Ciiylcy, in iHfta,' proposed the
immo Kudernmnniun 1 for the angle which I,ambert culled transcendent.
and which hml been variously designated by others. Among oilier more
recent works on hyperbolic functions nre Sicgimiml Oiintlier'H U'hre
von den TTyperhelfunc.tioneu, ii, and Mr. James MoMuhou's Hyper-
bolic Function.-!, 4th edition, 1006.
The first lartfc tnhle of hyperbolic functions we have met with is r,ef?eu-
tlre'stnbieof ] ( , K tan ( '' -f M to 12 dcciinnls. The nr K uuiont advances
f ~t r
f>y increments of 30 minutes, but five differences are tabulated to facilitate
Interpolation." Oudmuann in 1831 puhlishod a table of the same func-
tion, uiug centesimal degrees and advancing by hundredths of u decree
(o"o'32".,|.) from o to an entire quadrant, the function being given to .seven
decimal places. This was Inter .supplemented by a table advancing by hun-
<lrcdtlwof a decree from HH to 100, the function hcMnj? K ivcn to eleven
decimal places. (Uidermatm also ^nvc a y-plnce table of log eosh it, lo
Hinli it, and lo^ tanh w, from it ; : 2 , l)()0 l() w ,. .. i(j-()00( (||ul , . p | ncc
tnhle of Liu: same functions from u : . ^.no to H =- ; 13.00.
In 1862 X. l'\ W. Oroimu 1 publinlied a 5-place table of hyperbolic funo-
tions, the nrKnmtmt beiiiR' the j,ni(k:nnanniin gj it. in .iexa).;uMiiiiul deKreuH
and minutes. Ho tabulated to this nrtfitment lo K - oosti //, lo^siuh //, dud the
InKftrltlim of ( * -|- '^'^ instead of the natural logarithms of this
function, following therein a Hn^t-'Mtlou of I ( ainl)ert,
In iyo W. r,i K o\vHkl issued IUH Tnfeln der Ilyperbelfmictlonen mid der
Kruisfunctionen, which in admirably accurate and much the most iwwfnl
collection of tables of the hyperbolic functions hitherto prhUod. lie Hllnl
the K ni> left by (Vudermann by computing ]o: mull u, lo w - cosh it, and lo^
tanh it from u ; ; o.ooo to 2.000. Thci.se ho j^vea to only 5 placcH, but in
addition he tubulates ^ lt i n dufireeH, minntcs, Hccouds, and decimals of u
.second. These values are in all cases sufficiently accurnle to enable the- com-
puter to talce out from an ordinary Uble of loKfirillmrs y-jtlacc values of the
logarithms of (:oH h , siuh n t and tanh w. The arjftnnunt ratios from o.ooo
to 2.(K.o and from 3.ex> to 6.00 farf><t w, while loj>- citHh // und log sinli are
enrriwl up to :<).,),>, I,i W owHki al.so gives the nnlural fuuclioiiM oo.sli it,
Minh w, cos w, and sin to 6 declmnls for vfilnenof u in radians from o.on to
a.oo, the cosh u and Inli ?t being continued to w = .: H.oo. The only fault
\ve can find with I^owrtld'H tables is that the Increments of the
Homctlnics inconveuieutly Inrgo.
1 1'lili, MK,, vol. a,|, p, 19.
'* Tlum Hpellutl In Oiylcy'n pnpur.
3 Rxcrclnufl tie Cfll. Int., vol. a, 1816,
4 Ncituflto Hchrlfluii dor NalurfonKtlier-GcacllBclmft In Dnn/.!^, vol. 6,
HISTORICAL NOTH.
Iii 1883 F. W. Newman published a 12 -place table 1 of the descending ex-
ponential from u o.ooo tow 15.349, and a i4-place table of the same fmie-
tiou 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. T,.
Glaisher's tables of the ascending and descending exponential to nine sig-
nificant figures, with lo-place logarithm a. 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 gudermamrian is tabulated in degrees, minutcH,
seconds, and tenths of a second, and the logarithms of the arguments nro
given to seven places.
In the volume here presented the first thousand values of log sinh u, log
cosh , and log tanli it 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 nnd of
the tangents for arguments > 2.0 have been computed; the remaining values
have been taken from the tables of Forti and Ugowski. A recoinpiiUtloii
of a great number of the borrowed values was made in order to obtain the
required accuracy. The values of coth and log coth n 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 Hiilssc'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 s~ lt are all taken from Newman's groat
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 e" given in Hiilsse's edition of Vega is inaccurate and really
amounts to no more than a 5-place table. The logarithms of e a were com-
puted independently of the values of c v ,
Tables V and VIII are borrowed.
The values of gd u in Table VI in terms of angle are taken from I,igow-
ski, excepting the thousand values between n = 2,000 and 3.000. These
were interpolated from Ligowski's values (2,00 to 3.00) with due cheeks 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 =a o.-joo to
u = 3.000 in order to secure accuracy in the seventh significant figure.
The remaining values were derived from Ugowski by converting angles
'Cambridge Phil. Soc., Trans,, vol. 13, 1883.
11IHTOKICAI, NO'IMC. 1J
into radians. A considerable number of his valm-K, however, were tented
by independent compulation.
Table VII is borrowed from the. Nntitieal table.s of James Finnan, rc'viwd
by James W. Tnumn, I,ondon, 1867, with a few small corrections.
Hiimlly, it may be re mar Iced LlmL the derivatives K tfiven in n u . su table*
have been computed for them. They urn not derived from the differences
of Ihe valuta as printed, but from more extended values, or an- computed
independently, and the error of the derivatives as well aw of the functions is
ICSH than one-half of a unit in the next sue.ceediiitf (lucimal place.
These table.s wore prepared in connection with the Keopliysiral work of
the United vStalefi Geological Survey, and are published with the ponnissiou
of the Director.
OKOUGI-; K Ili.;ctci.
C. K. VAN OUSTHANU,
WASHINGTON, I). C., January, i()o8,
lMiI!mviii W ari!Hi)im: rrfi-roncoH to rmnil piibJioniioiiH fonlaininr IIVIKT-
bolu: and oxpnneiiliat finn:l:ions:
IVruot, K, K. AbridKt:.! Tuhlus of HypcHjolic 1'iinrlin,,,. llnivrrsily of
( iiiiforma I'libfiraiionH in MiUhemntk-s. Vol. (, N<. ?, r.p. iiv 16., l> ( .b
16, 1915. ' '
Seven place vuluos of lo Rlll ^l.". im ,l | Kin <-,>s]. // a,v RIVC-M al i.ilorvals
of o.<M5 from o.ooo to 6,000 K^Llicr willi lirnl <lerivalivrs and the mean
of rhrir lii'Ht
Van Orstrand.C. K. Tablcn of Uu- Kxponcntial Kmiciion nml of
Jl^'vlw?^^*^ 110 ' 01 *'""^ NalinnnlAra.lrniynf.
Vol. XIV, lifth Memoir, pp. i 79. WashiiiKlon, ^i.
Values of ^, (.-'=, e ' r , sin , and cos ;/ nnt Riven al various i
of arRumcnl ranniiiK from I x in lo i. The nrj-nmenl for sonu-of (he la-
IJIUH cxUmds [o roo. TJm tabular values nmlain from 33 lo toM decimal-, or
'
Ilayashi Kciichi. I'nnfslelliKcTafehuh-r Kr.-is- und Ilyperbclfiinkliom-n
sowiodc-r iMinklioihmo'M.nd c " miuk-n NnlflrlH-ln-n Xablcn al Arumm-nl
l3 pai^cs. Berlin tmd I.tiipxi^, 1921,
Values of sin n, con tt, Ian //, niuh w, conh 11, lauh w, and e" are Inhnlaicd
It) 5, and <; -'' to 7 places nf decimals at inlorvals of 0,0001 from 0,0000 to
o.iooo; al intorvaiH of o.oor from o.ioo (o 3.0(10; m ink-rvals of O.CM from
3.(Ki lo 6.30; and at: intervals of o.i from 6.3 (< 10,0, Angular <!(|iiivHlrn(H
of -
s ai-Kuni(MH r<! Kivun to o.oi of a woond. IvxKMidecl values of ei 1 " are
tahnlatx'd at decimal intervals from o.ooor to i and at intervals of i from
I (O !()(>.
Hi HISTORICAL NOT1',
Kennelly, A. 1C. Tables of Sines, Cosines, Taiwnls, ( 'n^'caiils,
and Cotangent*) of Real and Complex 1 lypcrbolic Aiu',le:i, pp, i
printed 1111912 by Harvard [engineering . Journal Ollicc, Harvard Ih
Cambridge, Mass., from Harvard Knj.;mecriiig Juiinial, Y'nl. II, N... .:. iM;iv,
1903, and Vol. X, No. 4, January, nji-.
Values of tlio six hyporbolic fiuictinns an- lalmlatnl nl iiiln \-als | n.ui
from o.oo to 2.49 and aC intervals of o.i frmii :?.,"i to '/..s. Sinh n .nul ^ .> .h
are given to fi decimals from o.oo ID 2.00; to fl iln-inial.-. iVmu ,!,ot in i;.nn;
and to 4 decimals from 5.1 to 7.5. Tanli 11 is i;ivrn (n $ .Irriin.il-i, ami tin-
remaining functions art: given lo cither 3, .(. m' , [ i decimals.
Kcnnelly, A. 1C. Tables of Contplrx Hyperbolic ami Circular Kiiiiciitni;;,
240 pages. Harvard University Press, Cauibridj;c, Ma'.s. Sin mi I revived
edition, 1921.
The preceding table is incliuled in (his volume, and in addition values n|
e" o"
and log| are tabulnted rcspeclivcly to ,\ and y place:, u| dt-citnalti
at intervals of o.oi from 4.00 to 10.00.
('. I-'.. VAN t)si KA
WASHINGTON, D, C., May, n;.?,/.
TABLE I
LOGARITHMS OF HYPERBOLIC FUNCTIONS
Logarithms of Hyperbolic Function!).
Logarithms of Hyperbolic Functions.
11
loo slnli u
co Fi)'
loo cosh u
.w
loo tnnh u
t> FO'
loo colli u
O.OO5O
7.69897
868,6
O.OOOOI
0,0
7.69897
868,6
2.30103
.0051
.70757
851*6
.OOOOI
.70757
851,5
.29243
.0052
.71601
835,2
.OOOOI
.71600
835,2
,28400
.0053
. 72428
819,4
.OOQOI
.72427
819,4
.27573
.0054
.73240
804,3
.OOOOI
. 73239
804,2
,-j67i
0.0055
7.74036
789,6
O.OOOOI
0,0
7 - 74036
789,6
2.25064
.0056
.74819
775,5
.OOOOI
.74818
775,5
.25182
.0057
-75588
761,9
.OOOOI
.75587
761,9
.24413
.0058
.76343
7^8,8
.OOOOI
. 76342
748,8
.23658
.0059
.77085
736,1
.OOOOI
.77085
736,1
.22015
o.ooob
7.77815
723,8
O.OOOOI
0,0
7.77815
723,8
2,22185
.0061
.78533
712,0
.00001
. 78532
,21408
.0062
.79239
700,5
.0000 1
79239
700,5
.20761
.0063
.79934
689,4
.OOOOI
. 70933
680,3
. am 67
.0064
.80618
678,6
,00001
.80617
678,6
- 19383
0.0065
7.81292
668,1
O.OOOOI
0,0
7.81291
668,1
2 . !K70<)
.0066
.81955
658,0
.OOOOI
.81054
658,0
".'18046
.0067
.82608
648,2
.oooor
.82607
648,2
'73^3
.0068
83251
638,7
OOOOE
.83250
638,6
. 16750
.0069
.83885
629,4
.00001
.83884
620,4
.161 i(i
0.0070
7.845IO
620,4.
O.OOOOI
0,0
7.84509
620,4
3.I.M9I
.0071
.85126
611,7
.OOOOI
.85125
611,7
. 14875
.0072
85734
603,2
.OOQOI
.85732
603,2
. 14368
.0073
.86333
594,9
.00001
.8(1332
594 ,0
. i,i<yK
.0074
.86924
586,9
.OOOOI
.86922
. 13078
0.0075
7.87507
579,1
O.OOOOI
0,0
7.87505
579,0
2. 1 3495
. 0076
.88082
' 571,4
.OOOOI
.88081
571,4
, IKJI9
.0077
.88649
564,0
.OOOOI
.88648
504,0
.11352
.0078
.89210
556,8
.OOOOI
.80-209
556,8
. I07OI
,0079
.89763
549,7
.00001
.89762
54D.7
. IOJ38
0.0080
7.90309
542.9
O.OOOOT
0,0
7,90308
542,8
2,CV)f)2
,0081
.90849
536,2
.OOOOI
.90848
536,!
,W)\\2
.0082
.91382
529,6
.OOOOI
.91380
529,6
.l>S(i:!0
.0083
.91908
523,2
.OOOOI
.91907
523,2
,oKo<>3
.0084
.92428
517,0
.00002
.92427
517,0
07573
0.0085
7.92942
510,9
O.OOOO2
0,0
7.92941
510,9
3,07059
,0086
93450
505,0
.00002
.1)3449
505,0
.06551
,0087
93952
499,2
.00002
.03051
499,3
.0088
94449
493,5
.00002
-94447
403,5
.05553
.0089
.94940
488,0
.00002
- 94038
487,9
0.0090
7"-95425
482,6
0. 00002
0,0
7-95423
482,5
2.04577
.0091
.95905
477.3
.00002
95903
477)2
.<).|(X)7
.0092
.96379
472,1
.00002
,96378
472,0
.o.yija
.0093
.96849
467,0
.00002
.06847
467,0
.O.H53
.0094
.97313
462,0
,00002
,07312
462,0
,cuW
0.0095
7-97773
457.2
O. 00002
0,0
7.97771
457,1
2,02229
.0096
.98228
452,4
.00002
.98226
453.4
.0177-1
.0097
.98678
447,7
.00002
.98676
447,7
.0132.1
.0098
.09123
443,2
.00002
.99121
44.1,1
.CKXS7*>
.0099
.99564
438,7
.00002
.99562
438,7
.00438
O.OIOO
S. ooooi
434.3
0. 00002
0,0
7.99999
434,3
2. OOOOI
II
log Ian oJ u
IV
lopseoQil u
Fo'
IOQ sin ad 11
V
log oso oil u
SMITHSONIAN TABLES
LognritlmiH of Ilypcrholir Finn
O.OIOO
,0101
.0102
.0103
.0104
lOfl Blllll
0.0105
.010(1
.0107
.0108
,01 Of)
0.0115
,0116
.0117
.0118
.0119
0,0120
0,0125
.0127
,01,10
01,15
.0136
.01.17
.0138
.0130
0.0140
,OI;(3
.oi.M
O.OH5
8.0001
.01 &
.0170.
.025,)
.0-153
.05.10*
8.0(107
.oofbi
.0755'
8.07011
.oifcHi
.08637
8.(MX"J.i
. 10038
. I0,l8,i
. lo?jj
,1IO(X)
8. 1 !.1f/i
.11 7^8
13355
M303
.15^.10
'55.15
.15838
8. 16138
.
.1'iH.i
,111.7
317,0
,11-1,7
log coiii u
OL(0 .l(,|37
.or.|7
0.0150
. 16733
. 170.18
Wo
8. 170'] i
11 lot) Inn ad u
Pi.'
, { * k x >,.'
.(K "'I.,'
.IHMKI)
.(HHK'.J
.(XHXt]
.IHHHI.'i
loo tec flit II
SMITHIIONIAN TABUS
.U"ft' 1 iJ
,H(|(,7
Logarithms of Hyperbolic Functions.
II
log sinh u
" FO'
[op cosfi u
u FO'
Ion land u
* Fo'
log cotli u
0.0150
8.17611
289,6
0,00005
0,1
8,17606
289,5
1.82394.
.0151
.17899
287,6
.00005
.17894
287,6
.82106
.0152
.18186
285,7
.00005
.:8:8r
285,7
.81819
.0153
.18471
283,9
.00005
. 18466
283,8
.81534
.0154
.18754
282,0
.00005
. 18749
282,0
.81251
0.0155
8.19035
280,2
0.00005
O,T
8.19030
280,1
1.80970
.0156
. I93M
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
.20:36
273,1
.79864
0,0160
8.20414
271*5
0.00006
O,I
8.20408
271,4
I-79S92
.0161
.20684
269,8
.00006
.20679
269,7
.79321
.0162
.20953
268, r
.oooof)
.20948
268,0
.79052
.0163
.2:221
266,5
.00006
.21215
266,4
.78785
.0164
.21486
264,8
.00006
.21480
264,8
.78520
0.0165
8.21750
263,2
o.oooofi
0,1
8.2:744
263,2
1.78256
.0166
.220:3
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
0.00006
0,1
8.23641
255,4
1.7^959
.0171
.23302
254.0
.00006
.23295
253,9
.76705
.0172
.23555
252,5
.00006
.23540
252,4
.76451
.0173
.23807
251,1
.00006
. 23800
251,0
,76200
.0174
.24057
249,6
.00007
.24051
249,5
'75949
0.0175
8.24306
248,2
0,00007
0,1
8.24299
248,1
I. 75701
.0176
24554
246,8
,00007
-24547
246,7
75453
.0177
.24800
245,4
.00007
24793
245,3
.75207
.0178
.25044
2-14.0
.00007
- 25037
243,9
-7403
.0179
.25288
242,0
,60007
.2528:
242,6
.74719
0.0180
8.25530
241,3
0.00007
0,1
8.25523
241,2
1.74477
.0181
.25770
240,0
.00007
. 25763
239,9
.74237
.0182
.26010
238,6
.00007
,26002
238,6
.73998
.0183
.26248
237,3
.00007
. 26240
237,3
.737*50
,0184
.26484
236,1
.00007
26477
236,0
.73523
0,0185
8.26720
234.8
0.00007
o,:
8.26712
234.7
1.73288
.0186
.26954
233,5
.00008
. 26946
233,4
.73054
.0187
.27187
232,3
.00008
.27:70
232,2
.72821
.0188
.27418
231.0
.00008
.37411
231,0
.725Bo
.0189
.27649
229,8
.00008
.27641
220,7
72359
0,0190
8.27878
228,6
0.00008
0,1
8.27870
228,5
1.72130
.0191
.28106
227,4
,00008
.28098
227,3
.71002
.0192
.28333
226,2
.00008
.28325
226,1
.71675
.0193
.28558
225,1
.00008
.28550
225,0
,71450
.0194
.28783
223,9
.00008
.28775
223,8
.71225
0.0195
8,29006
222,7
0.00008
0,1
8.28998
222,7
1.71002
.0196
.29228
22I t 6
.00008
.29220
221,5
.70780
.0197
.29449
220,5
.00008
.29441
220,4
.70559
.0198
.29669
219,4
.00009
.29661
219,3
.70339
.0199
.29888
218,3
.00009
.29880
2l8,2
. 70120
O.O200
8.30106
217,2
O.OOOOQ
0,1
8.30097
217,1
1. 69903-
U
oa tan gd u
M Fo'
Qfl sea ad u
Fo'
DO sin oil u
* F(/
Icaciagd u
SMITHSONIAN TABLES
Logarithms of Hyperbolic Functions.
0.00009
.00009
.00009
.00009
.00009
8.311
313
-3159
.3I80
.3200
211,8
210,8
209,7
208,7
207,7
0. 00001)
,00009
.00009
.00009
.00009
8.32225
.32431
.32637
.32841
33045
8.322
.324:.
.3262
.3283
3303
200,7
205,8
204,8
203,8
202,0
8.33247
.33449
.33649
.33849
.34048
202,0
201,1
200,2
199,2
198,3
8.3323
-3343
.3363
3383
-3403
201,9
201,0
200, 1
199,2
108,2
8.34246
34443
34639
34834
.35028
197,4
195,5
195,7
194,8
193,9
8.3423
3443
-3462,
3482.
.35018
8.35222
35415
35606
35797
35087
0225
.0226
.0227
.0228
.0229
8.3521
35403
35595
357ST
35076
1.04780
64597
.64405
.6421.
.64024
192,2
191,4
190,5
189,7
8.36177
36365
.36553
36740
.36926
188,9
188,0
187,2
186,4
185,6
0230
0231
0232
0233
0234
8.36165
36353
-3654:
,36728
.3691,
63835
.63647
63459
.6327;
.63086
8.37111
37295
37479
.37662
.37844
0.0235
.0236
0237
.0238
.0239
184,8
184,1
183,3
182,5
181,7
8.37099
37283
37467
.37649
37832
I. 0200 I
.62717
62533
62351
.62168
8.38025
.38206
.38386
.38565
38743
0.0240
.0241
.0242
.0243
.0244
181,0
180,2
179,5
178,8
178,0
0.00013
.00013
.00013
.00013
.00013
8.38013
38193
38373
38552
38730
180,9
i8o,r
J7EM
178,7
177,9
i.oroH;
.61807
.61627
.61448
.61270
8.38921
.30098
.39274
.39450
.39624
0.0245
.0246
.0247
.0248
.0249
0,00013
00013
00013
00013
00013
8.38908
39085
.39261
39436
39611
1.61092
.60015
60739
60564
.60389
177,2
176,5
175,8
175,0
174,3
I73;S i 0.00014
IOQ sac nd u
8^39785
QQ sin ad u
SMITHSONIAN TABLES
of HypcrbriHc FunctionH.
lou alnli u
i.l.'i.H
1-H.H
loglait u<lu i *< IV
lua cosh u
O.IHHH.I
.01X11.)
1.1
.DtHll.
.IKHII.
II.IHHU ;
.(HKII.'i
Km.'J
IIJKMM 1
. m n 1 1 ,'
. HI H 1 | ;|
.IKHtl'l
OIXIl'l
.IHklMl
U.IHHMIl
. I M M 1 1 '/
I H N 1 1 '/
I.'i-Vt
1,'iit.H
i-1'i.H
MH!M
O.IMMIlIi
.(MHItM
.IHHII'J
II.IMMl'J
oo ana oil u
ll><] Illllll II
1,1'",'!
loo aln oil u
Kxi.,!
Pi/
DOlll II
..'I'Jl.
.51x111
,M Hi/ft
..; n 'x
S.H-l.'il
..'i-'.'i'Jl
SAM''
loootooiiii
BMiTMttOMiAM TABLKB
Logarithms of Hyperbolic Function?!.
8.49838
49976
.50113
.50250
.50386
0.0315
.0316
.0317
0318
.0319
137,9 I o.ooo.!
137.5 .OOOJ,!
137,0 .(MX12.!
136.6 [ .(xxx!.!
0.0320
0321
0322
0323
032,]
135,8
135,3
'34,9
13-1,5
13-1.1
50793
.50928
.51062
0.0325
.0326
.0327
.0328
.0329
133.7
133,3
"32,9
132,5
0.0330
0331
03,12
0333
033.1
8.53513
S2(M2
52771
529tH)
.53028
0.0335
033ft
0337
-0338
0339
8.5315(1
53284
534 n
5353.8
.53%
0.0340
0341
0342
0343
03-14
0.00025
.000,15
.fXX)25
8-53701
.53916
.54042
541(17
.54291
0.0345
.0346
0347
0348
03<I9
'25,9
125,0"
125,2
T24.8
1*1,5
o.oooafi
.(X)02(i
.(XX)2()
Logarithms of Hyperbolic Functions.
u
Ion siiili u
.H
IOQ cosh u
.w
Ion (anli u
to F '
IoD colh 11
0.0350
8.54416
124,1
0.00027
0,2
8.S43&0
124,0
I.456H
.0351
.54540
123,8
. 00027
-54513
123,6
,45487
.0352
.54663
123,4
.00027
123,3
,453<>4
.0353
.54786
123,1
.00027
54750
122,9
.0354
.54909
122,7
.00027
122,(>
45H8
0.0355
8.55032
122,4
0.00027
0,3
8.55005
122,2
1-44995
.0356
55154
1 22,O
.00028
*55ia7
121,9
.44873
0357
.552.76
121,7
. 1x1028
121,5
.4.1752
.0358
.55398
121,4
,00028
- 55370
121,2
..14630
.0359
55519
121,0
. 00028
.55491
120,9
..14500
0,0360
8.55640
120,7
0.00028
0,2
8.50: T
120,5
I.4-1T80.
.0361
55700
120,4
.00028
55732
1 20,2
.,-|J26K
.0362
.55880
1 20,0
.00028
.55852
H0.9
.44148
.0363
. 56000
i "9,7
.000 20
-55972
1 19,5
.4402-8
0364
.56120
1 19,4
.00029
< 56001
119,2
.43<Jf><>
0.0365
8.56239
119,0
0.00029
0,3
8.56210
nSu
I-4379O
.0366
.56358
118,7
.00020
56329
nftifi
.0367
.56476
118,4
.00029
.56447
118,2
-4355,1
.03(18
.S651>5
118,1
.00029
.56565
1 1 7.9
.4.1435
,03(19
.56712
117,7
.00030
.56683
117,6
43317
0.0370
8,56830
1 17,4
0.00030
0,2
8.56800
H7,3
1.43200
.0371
56947
117,1
.00030
56917
117,0
,43083
.0372
.57064
1 16,8
.00030
570,14
1 1 6,6
.0373
57iHi
1 16,5
,01x130
.57151
1 16,3
..12840
.0374
57- l U7
116,2
.00030
. 572()7
1 1 6,0
4-733
0.0375
8.57413
115,9
0.00031
0,3
B. 57383
"5.7
1.42617
.0370
57529
if5.fi
.00031
574 ( )H
1 15.4
.42502
-0377
.57644
' (5,3
,00031
. 57f>i4
.43386
.0378
.577(10
* 14,9
.00031
. 57720
] i.'|l
.42271
.0379
.57874
1 14,6
,011031
5784,1
H4.5
-13157
0.0380
8.579H9
H4,3
0.00031
0,2
8.57957
1 14, fl
1. 42ft |3
.0381
.58103
114,0
,00032
.58071
r "3,0
.41029
.0382
.58217
"3.7
.00032
.58185
1 13,6
4i"5
0383
.58330
" 13.4
.00032
. 58290
n.1,3
,41701
0384
.58444
113,2
.00032
-58412
1 13,0
.41588
0.0385
8-58557
112,9
0.00032
0,2
8.58525
113,7
i.4'475
.0386
.58670
1 1 2,6
.00032
. 58637
112,4
.41363
0387
.58782
112,3
.00033
.58740
112,1
.41251
.0388
.58894
112,0
00033
.58861
rn,H
.411,10
.0389
.59006
111,7
.00033
.58973
in,5
.41027
0.0390
8.59H7
in,4
0.00033
O,3
8.59084
111,2
1.40016
.0301
59229
iii.i
.00033
soryt)
I II ,0
. 40804
0392
.59340
n 0,8
.00033
.59300'
110,7
.40(10.1
0393
.59450
i ro,6
.00034
59-1 ' 7
1 10,4
.4n53
.0394
.50561
110,3
.00034
5P527
110,1
.40473
0.0305
8.59671
rio.o
0.00034
0,2
8.50637
I00,
1.40363
.0396
.59781
109,7
,00034
! 59747
roo/i
40353
0397
.59800
109,5
.00034
iao.,1
.40144
0398
.60000
roo,a
. 00034
> 50065
100,0
.40035
.0390
.60109
108,9
.00035
,60074
108,7
S&jrt
0,0400
8.60218
108,6
0.00035
O,3
8.60183
108,5
.1.30817
u
OQ tan ad u
W FO'
og aoo o<t u
w IV
loo aln D<! u
Hfif
loo oso gtl u
SMITHSONIAN TABUS
Logarithm!) of Hyperbolic i
SHITHBONIAN TABLKB
of Hyperbolic Functioim.
0.0,150
.iM5 1
'MS- 1
0.0.155
.0-1 S7
0.0.1/15
O.o-l/O
.0.1/1
.<M07
0.0500
u
si nh u
.Uno.t
H. (/.!;!(
*a Inn ml u
96,6
95.5
tM.'J
y-i.s
y-i..i
!.)-!. 5
KH,5
HH!O
"7,5
Hrt,!)
lou ooili ii
o.ooo/i/i
0.000,15
,000. 1 5
O.(XXK|(>
O.IHK),|7
.ooo.|H
, OIK My
.(IHO-(')
.UO050
.001150
o. 01x150
.00050
,110051
.IKXJ5I
-OfXI.S.1
o .0005.1
.0005,1
.0005.1
,(XH>5^|
0.0005.1
loa 100 till u
0..1
0,3
0,3
0,3
0,3
w Fo'
loa ttinli u
.05581)
.051X11
.670H5
.(17.15-1
,(17811)
R.OMooi
.08710
8.00-125
tou iln ad u
W5.1
ui.y
M.,1
y-vy
y i iU
yi.s
!)','
w
fth-l
88,1
87,0
87,8
R7.fi
87,1
8?;f
log co tli u
1 . ^'HJJ
.,1-7,10
, ill l<M
1.31015
.,10.11,1
Ion 010 get u
Logarithms of Hyperbolic Function:!.
11
ion sinli 11
w FIJ'
laO UOsli U
*/
Ion limit ii
... ('
Inu uotli u
o.osoo
8 . 690 1 5
86,.)
0.0005.
O..!
S.io'lMi
!!M,^
l..tH.i.
-osoi
. 70002
86,8
.0111)54
.( (/
''>' '. .'.
-i l| o. ! i.i
.0502
. 7<x)ft)
8o,<
.00055
/"".I
f!.'i..|
.- p 'X/l(i
.0503
.70175
>,.
.OO055
.; p ui.:i)
: -< ,-;
.-i^'v'x)
oso-l
.70261
86,2
.00055
. /( 1 .'t C I
fid, )
.,'U/0|
0.0505
8.70348
86,1
0.1x1055
1 1, .:
U.;'o,'<.'
:;.)
I.- '.)>! VS
.QSOf)
.70434
85,9
.(Mxi5d
.yu.ij'S
'Vi./'
./ui>.!.)
.0507
.70519
85.7
.1x105*1
yoi<>
S>. : ;
-''J.i.tO
.0508
. 70605
85,0
.00115(1
7", L i f >
">,
'"'M.'i
.0509
.70601
85,4
.00050
O'nti,
.,,
. .*>.('"
0.0510
8.70776
85,2
0,00050
n.j
./'n>-Hj
:;.>
t,,'>i-:Mi
.0511
. 7086
85,1
, Oi M 157
,/nMn
S | ,S
. -|,)H)(j
.0512
. 701)40
8.1,')
OOO57
. >' t W* i
,'* ;.;
. ,''ji i i
.0513
.71031
8-1,7
,00057
. 7 * >/ 1
;f i.. 1 '
. .:<*i.' i
.0514
.71115.
8.1,0
.00057
./Hi.-fi
!..!
..,'^il.j
0.0515
8.71200
8,
0.00058
0,2
K.7M-1.!
H|.,!
1 . .'.M,'i;;?l
.0516
.71*8,1
8.|,2
.OIK 158
.7i.M(.
N|.ii
. ,'S;'/,
.0517
.71368
84,
.011058
,/'i,iiii
!',(.'>
, ,'H'i.jo
.0518
7'452
83,')
.01 1058
J'l.i'H
f ',*,;'
, r 'HfMf)
0519
.71536
83,8
.dOo.sH
./'4/ fi
.l.:i
./M.'i.V
0,0520
8,71620
Hi 6
0,00051)
O,.!
H.ytr,"!
' J.I. 1
1 . -'H 1 (>
.0521
.71703
8,V
.01x151)
,/MM (
, ,', v t |<id
.0522
.71787
H3.3
.00051)
S i.ii
. .'*/'',:
.0523
.71870
8.1,
.1 MX 15')
.71811
Jt'vj
.ASllVj
.0524
71053
83,0
.(KllMX*
./l'),l
,'./
..MHI/
0.0525
8.7^036
82,8
O,,!
ff. ;!.,;'"
f (,',!,
1 -}t,IM
.0526
.72119
HJ|O
.OOO'iO
.J'.'u.vj
fl',1
,-V'Jll
.0527
.72201
8-',5
.ooirfm
/'" I 1
M,r, ( ..''.'i"i)
,osu8
, 72284
82, ')
.OOO'H
.".'.',' !
,M /'( "/.'.'!.,
.0529
. 72366
82,2
.0000 1
';-.' ; ."i'V'i
Jlli-)
,.'','< "ft
0.0530
8.72,148
K.!,0
0,(HXl6l
O,.
M,j-j(/
Hi.t;
1 . ,'7(1 [ t
.0.131
.72530
81,0
.OINllH
'.',' ..'['-'>
KI!I
'/'-,
.0532
.72612
81,7
.00o6l
,;'.;',!;u
H l , ->',
"''iqi
.0533
. 72693
81,0
.0(X)6,|
, "/'H,'
!',,l
' ''' i(iH
0534
7.5775
8...
.0006.!
I'.f/i.t
. ,7. '.'{;'
0.0535
8.72856
1,3
0. 000(1.!
o.,:
;.
Mm
.0530'
.729.17
Hl,i
.OOOfi.!
''"'{;
.'i i u
.... ;?
0537
.73018
8 1,0
.01 Kll' I
'''ll'-f'l
w '
. - / 1 .j ;
0538
-73WJ9
80,8
.(XKtfi'l
. '! Ct 1' i
'" i'(
-'/"I t
0539
.73180
80,7
.(HXAl
' / ll ', \
iJ!i
.'/fSl 1 !.'
0,0540
8.73260
805
O.IKH)6,{
0,1
H.7tlT
K,.
.'ti
.0541
733.11
Ho,4
.(XXXi,|
.73,:;-;'
(it* i
[ ,-' ' i
.0542
7.1421
80, n
,0(K)6,|
.. '
- 1 '/ .1
.0543
73501
80,1
,OOO(Vl
' "i tift
.^''!'
,,:( t\j
0544
73581
79,9
.0(Hl(l|
.'^.Si/
,I--
^:'1|!{'1
0.0545
8,73661
79,8
0.000fi,|
(,-;
- r, -
.0540
73-741
79.<>
.(KNIO'I
"p*i
''/\i'"i
f," j ''
1 . ,;f' (d.(
0547
.73820
79,5
.IXX'lOi;
' ,''<,'
'*'* '
'' !> ,1'' 1
.0548
73<joo
79..!
.00005
''' A'l'r
!''"'
..r'-.'lji
0549
73970
.0006,1)
'^i'/i'i
"/>, i
! SSl
0.0550
8.7405fl
79.0
O-lXXXVl
0,;i
K.?W
y.4*H
I ,.$'**)?
u 1
a Inn ail u
W ft)'
DO too ail u
-W
ou iln gil u
M f',,'
fiUCtl) Utl II
SMITHSONIAN TABUCS ""'''' " - ; ; -'---- : ' : --'
Logarithm)! of Hyperbolic Functions,
.tl.'i.W
O.dfjfHI
.0.171
or.y.t
.ofiy.|
0.0305
lou nlnli 11
.755.15
.Xfi.ll/
./'"SIX
-XX-'SH
-77,1.1"
.77-10-1
R.XX-IXX
ou Inn ml u
7S.S
7.1,?
7.1, <
xin
r,/
loo oouli u
O , I X K)! i/
. i x u K i/
. ( N II )( \'J
. < II H W >H
, IH)l)fx)
. in M>(" j
, ( K X I/ ( >
, < X X )/'( )
, t ll II 1/1 t
((.(HKl/l
, IK K Vj I
.000/1
.(XHI/'-l
-III XIX. 1 )
.oituys
. i M )/;;
.(xioX5
.(MKJ/7
(I,<HHIX7
IflDino ail ii
0..1
I (Hi limit u
K. 7.1'JO.!
75J.15
M.755-10
!7!iXf>H
xci/
.76518
.77iHi
77J5S
- 775 l<>
R. 777^.1
log sin ad u
w F,,'
7X,K
77.5
7X.-I
fX,.i
77,1
7*1.7
7'',o
75,0
75,' '
75,5
75,1
75 .J
7-1 ,X
7-1,6
7-1-5
7-1..1
7-1, J
7.I.H
7,1,7,
7.1,6
7.1.-I
7.1 ..I
wit
7-M>
log oo Mi u
I .;
--i.S5.17
100010 Oil U
BMITHOONIAH TAHLKV
Logarithms of Hyperbolic Functions,
J
log slnli u
.w
loa cash u
w
loa tnnli u
w F/
" ' i
loa ootli u
0.0600
8.77841
72,5
0.00078
0,3
8.77763
72,2
I . 2.!-!.'17
.0601
-77914
72,3
.00078
.77835
7A"
.22165
.0602
.77986
72,2
.00079
-77907
7~'.
.2..'O<J.1
.0603
-78058
72,1
.00079
-77979
7i,iH
. 22(12 I
.0504
.78130
72,0
.00079
.78051
7J.7
.2IO.|9
0.0605
8.78202
7i,9
0,00079
o,3
8.78123
71,6
I.2I77
.0606
.78274
71,8
.00080
.78194
71.5
,21806
.0607
.78346
71,6
.ooa So
.78206
71,,.
.21734
.0608
78417
71,5
.00080
.78337
71,3
,21663
.0609
.78489
.00080
.78408
7','
.21592
0.0610
8.78560
71,3
0.00081
o,3
8.78479
71,0
i 21521
.0611
.7S63I
71,2
.0008 r
.78550
-"1450
.0612
. 78702
71,1
.00081
.78621
TO!
21370
.0613
.78773
70,9
.00082
. 78692
70,7
21308
.0614
.78844
70,8
,00082
.78762
70,6
1-1238
0.0615
8.789F5
70,7
0.00082
0,3
8.78833
70,4
1.21167
.0616
.78986
70,6
.00082
78003.
70,3
.2101)7
.0617
.79056
70,5
.00083
70,2
.0618
.79127
70,,
.00083
.79044
. 20(>56
.0619
.79197
?o,3
.00083
,70114
70,0
.yo8ft
0.0620
8.79267
70,1
0.00083
0,3
8.79184
69-9
i. 208 1 (i
.0621
79337
70,0
.00084
.79253
69,8
.207.17
.0622
.79407
69,9
.00084
.70323
6<.>,6
.20(177
.0623
79477
69,8
.00084
70393
60,5
.20607
.0624
79547
69,7
.00084
69,.
.a>53K
0.0625
8.79616
69,6
0.00085
0,3
8.70532
69,3
l.20|6H
.0626
.79686
69,'5
.00085
.70601
! 20 lOO
.0627
.0628
70755
.70825
69,4
69,2
.00085
.00086
.79670
.79719
69,1
60,0
*ST.'
.0629
.79894
69,1
.00086
. .79808
68,9
! 20 192
0,0630
.0631
8.79963
.80032
69,0
68,9
0.00086
.00086
o,3
8.70877
.70945
fiUlti
1.2012,1
.0632
.Soroi
68,8
,00087
,80014
68, 5
' too&i
.0633
.80160
68,7
.00087
.80082
68,4
' lOlllH
.0634
.80238
68,6
.00087
.80151
68,3
iyKiy
0.0635
.0636
.0637
.0638
8.80307
80375
.80443
.80512
68,5
68,4
68,3
68,2
0.00088
.00088
.00088
.00088
o,3
8.80219
.80287
80355
.80-121
68,2
68,1
I . ip7i
''/MS
.0639
.80580
68,1
.00089
.u<j.|i,OF
.80491
6>,'K
.'ii)5oj
0,0640
.0641
.0642
.0643
.0644
8.806^8
.80716
.80783
.80851
.80919
68,0
67,8
67,7
67,6
67,5
0.00089
.00089
.00089
.00090
.00090
o,3
8.80559
.80626
.80694
.80761
.80829
67,7
67,6
f)74
C'7,3
- 19374
">A10
.19171
.0646
'.06$
.0649
8.80986
.81053
.81121
.SnSS
.81255
67,4
67,3
67,2
67,1
67,0
o.ooogo
.oooyi
.00091
.00091
.00091
o,3
8.80896
.&>963
.8l03O
.81097
.Sufi*
67,1
67,0
66,i)
66,8
66,7
. iHiJA'
0.0650
8.81322
66,9
0,00092
0.3
8.81230
66,6
i . 18770
u ,
a Ian ail u
la FO
DO sec od u
- Fo',.
loo sin oil u
w F '
loocsogdu I
14
Logarithms of Hyperbolic Functions.
11
log slnh u
-IV
too cosh it
HfJ
lop innli u
IV
|0<J COtll 11
0.0650
8.81322
W',9
C).(XXX)3
0,3
8.81230
fA6
.1 . 18770
.0651
.81389
Wi,8
.(MJ092
,81297
66,*;
18703
.O()53
.81450
66,7
. 0(X>J)2
.81363
6f>,4
.18637
of '53
.8l"i22
fi6,(j
.(MXMJ.1
.81430
6(>3
. 1 8570
.065-1
.H'580
W>,5
.tXK'93
,81496
a>,2
. 18504
0.0655
8.81655
(W.4
o. 001193
0,,l
8.8i5(u
6{i,i
1.18438
.OO56
.8l7J2
W>, ')
.CXXW),}
. 8 i 628
6f> o
.18172
Of>57
.81788
66,.!
.tXHHJ-l
.81694
6s!y
* *'ll/ **
,18306
. 0658
.81854
66,1
.OIKKJ.I
,8i7(x>
65,8
. 18240
.of 159
.81920
!,(
,CK.H)94
.81836
65,7
.18174.
O,o6fio
.0661
8.81986
8
O.O0095
.(xx 195
0,3
8.81801
65,6
I.jflM!)
.0662
.821*18
(is!?
.00095
! 82022
6sl4
! wS
,ofrfi,1
.82[8,1i
65,6
.00095
.82088
65,3
.17912
,0664
.82249
65,5
.OOOfXi
^82153
65,2
.I7|7
0.0665
8.82314
r>5,.i
o.oowXi
0,3
8.83218
6_5i
I 17782
,0666
,82380
65,3
.O009fi
.82283
.17717
,0667
.0(368
.0669
.82510
8^575
65,'i
65,0
.(X)o<)7
,(XXK)7
,00097
.82348
8-241,1
.82.378
fi^ls
6-1,7
. 17652
175^7
. 17522
0,0670
8.826.10
64,9
0.00097
0,3
8.82543
6,|,6
I . 17457
.0671
, 8J7O5
64,8
.(MH)tj8
.82(107
6. 1,5
.0(J72
.0673
.8277"
.83834
64,7
.oooj j8
.001198
.82672
.82736
61,4
6-1,3
' 17328
. 17X1.1
.0(174
.82891)
fills
.00099
.82800
64,2
. 17300
o , 0675
.0(17(1
.0677
,0678
.0679
! 83028
.8,1003
.83156
.83220
64I3
fttla
o.oooyy
,(HKX;9
.oo(XJ9
.00100
,<X)100
0,3
8.82864
. 82929
82904
.83056
.83120
64, 1
64, 1
6-1,0
6,w>
63,8
I. 17136
, 17071
, 17006
. 16044
.16880
0.0680
8.83384.
64,0
o, (xii no
0,3
8,83184
r ?3,7
i.ifiRifi
.0681
8;}348
63,')
.(X)ior
.83248
. 16752
. 0082
.83412
6,1,8
.00101
.83311
63,5
. 0683
.83476
63,7
.OOIOI
83375
6".1,4
, 16625
.ofH|
83539
63,6
.00102
.83^138
63,3
. 16562
0,0685
8.83603
6.1,5
O.OO1O2
0,3
8.81 soi
63,2.
1 . 1 6 iij<)
.ofiHf)
.83(1(16
.(K)1O2
18356.1
63,1
.1643(1
. of #7
.of 188
.0689
.83730
.83793
.83856
63,3
63,1
.00102
. oo 1 03
.00103
.83627
,83690
.83753
63,0
63,9
62,8
. 16373
.16310
. 16247
0,0690
8.83919
63,0
0,00103
0,3
8.83816
62,7
1.16184
.0691
.83982'
63,0
.00104
83879
62,7
.16121
.0692
of 193
!aiio8
62,9
62,8
.00104
.00104
839-11
62,6
62,5
,i6o5o_
0()94
.8.1171
62,7
.00105
.84060
62,4
rS(l
0,0/195
8.84233
62,6
0,00105
0,3
8.84129
62,3
1.15871
,ofx.Xi
.84206
62,5
.00105
.8419*
62,2
.15809
,<)(k)7
.8.1358
* 62,4.
.00105
84253
6a,i
15717
,ofx)8
,84421
62,3
.00106
8-13 1 5
62,0
.0699
.84-183
62,2
,00106
&1377
61,9
.15623
0.0700
8.84545
62,1
0.00106
u
oa inn ad u
u P '
OQ 8<
SMITHBONIAN TABLES
Logarithms of Hyperbolic Functions.
log sinEi u
<> fa
IOQ cash u
F '
loa tanh u
Fo'
loo colh u
O.O7QO
8.84545
62,1
Q.OOio5
o,3
8.84439
6l,3
i. 1556 r
.07OI
.84607
62,1
.00107
.84501
6i,
154I#
.0702
.84669
62,0
.00107
.84562
61,7
1543S
.0703
.84731
6i,9
.00107
.84624
61,6
'5376
.0/04
.84793
61,8
.00108
.84686
6i,5
153H
o . 0705
8.8.1855
61,7
O.OQIOS
o,3
8,84747
CM
'15253
.0706
.84917
61,6
.OQIOS
.84808
61.3
15192
.0707
.84978
6i,5
,OOI08
.84870
61,2
-15130
.0708
, 85040
61,4
.OOT09
.84931
61,1
.15069
.0709
.85101
61,4
.OOI09
.84992
61,0
.15008
0.0710
8.85162
6r,3
o.ooroy
o,3
8.85053
61,0
1.14947
.0711
.85224
61,2
.001 ro
.85114
6o,l>
.14886
.0712
-85285
61,1
.oorio
-8ST75
60,8
14825
.0713
.85346
6 r,o
.00110
.85235
60,7-
- 147<">5
.0714
.85407
60,9
.OOIII
.85205
60,6
14704
0.0715
8,85468
60,8
O.OOIII
0,3
8.85357
6o,5'
I.M643
.0716
.85528
60,8
.OOIII
.85417
60,4
'45S3
.0717
.85589
60,7
.OOII2
.85478
60,4
. 14522
.0718
.85650
60,6
,OO I 12
.85538
60,3
. 14462
.0719
.85710
6o.5
.00112
.85598
60,2
. 14402
0.0720
S.S577r
60,4
O.OOII2
o,3
8.85658
60, i
1 . 14345
.0721
.85831
60,3
.00113
.85718
60,0
. 14282
.0722
.85801
6o,j
.00113
.85778
59,9
.I.|322
.0723
.85952
60,2
.00113
.85838
59,9
.1.1162
.0724
,8Goi2
6o>i
.00114
.85898
59,8
.I4i02
0.0725
8. 86072
60,0
O. DOT 14
o,3
8.85958
59,7
1. 1 40-1 3
.0726
.85:32
59,9
,00114
.86017
S9/>
I3SS3
.0727
.86102
59,8
.00115
.86077
59,5
139.13
.0728
.86251
59,8
.00ri5
.86137
59,5
.13863
.0729
.86311
59,7
.00115
,86196
59,4
. 13804
0.0730
8.86371
59,6
o. 00116
0,3
8.86255
59,3
- 1-13745
.0731
.86430
5ft 5
.00116
,86314
59,2
. 13686
.0732
.85490
5<J,-4
.00116
.86374
59,1
. I3f6
.0733
.86549
59,4
.00117
.86433
59,0
- 13567
-0734
.86609
59,3
.00117
,86492
59,0
.13508
0.0735
8,86668
59,2
0.00117
0,3
8.86551
58,9
1 , 134-19
.0736
.86727
59,1
.00118
.86609
58,8
.13391
.0737
.86786
59,0
.00118
.86668
53,7
. T33J2
.0738
.86845
59,0
.00118
.86727
58,6
- 13273
.0739
,86904
58,9
.00118
.86785
58,6
.13215
0.0740
8.86963
58,8
0.00119
0,3
8.85844
58,5
I . 13156
.0741
.87022
58,7
.00119
,86yoa
58,4
.13098
.0742
.87080
58,6
.00119
.86961
58,3
. 13039
.0743
.87139
58,6
.00120
.87019
58,2
.12981
.0744
.87197
58,5
.00120
.87077
58,2
. 12923
0.0745
8.87256
58,1
O.OOI20
o,3
8.87135
53,1
I . 12865
.0746
.87314
58,3
.OOI2I
.87193'
58,0
.12807
.0747
.87372
58,2
OOT2I
.87251
S7,9
. 12749
.0748
87431
58,2
OOI21
.87309
57,S
.12(19!
.0749
.87489
58, t
.OOI22
.87367
57,8
. 12633
0.0750
8.87547
58,0
O.OOT22
o,3
8.87425
57,7
I. M57S
ii
loo tan ad u
Fo'
loo sec od u
u Fa'
IOQ sin ad u
10 FQ'
log cso frill
SMITUBCINIAN TABLES
16
Logarithms of Hyperbolic Functions.
u
IQQ sinh u
w Fu'
log oasli u
wfV
lOQ IClllll U
w Fo'
log colh 11
0.0750
8.87547
58,0
O.OOIiW
o,,l
8.S7-I35
57,7
r. 1^575
.0751
.87(105
57,9
.OOl^J
. 7 .l8a
57,6
.12518
.075-3
. 87(163
57,9
.lK)l-'3
. 875.I"
57,5
. 12460
."753
.87721
57.K
. ffl)i-'3
-7508
57,5
.T240J
75-l
.87778
57,7
.00123
7055
57,4
U.145
0.0755
8.87836
57,f>
CI.(X)1A|
0,3
8.87712
57,3
1 . 12288
-075<
.87894
57.<>
,ooii|
.87770
57.--'
. I223O
<V57
.795i
57,5
,001 -'4
.K7K27
57,-'
- i-'i73
-0758
.88009
57,4
.00125
.87884
57,1
.12116
.0759
.88066
57, .1
,ooj as
.87941
57,"
,12059
0.0760
8.88123
57,3
0.001:25
0,3
8.87998
5'>.9
1, U(X)2
.0701
.88180
57,3
.oou6
.88055
5(' f 8
. i >I5
.0702
.88238
57,'
.00126
.HHna
5<V
.nHHK
.0763
.88295
57,0
.0012(1
.88168
56,7
. l 1832
.076.1
.88,15^
57,o
.00127
.88225
50, (}
-H775
0.0765
8.88408
sc>,y
0.00127
0,3
8.88282
56.5
i .11718
.0766
. 88465
5<i,K
.011127
.88338
So',5
, i i66a
.0767
.88<;22
5^7
.00128
.8H.VX
5^,4
. n(io6
,o;f>S
.88579
5fi,7
.00128
.88451
56", 3
.11549
,0769
.88635
50,6
.00128
.88507
5<U
.11493
0.0770
8.88602
5C-.S
o. TOT ay
0,3
8.88563
5(i,a
T . 1 1437
77i
.887,18
S&<\
.00129
.88620
5^,i
. 11380
.>77J
.8881)5
56,4
.00 lay
,88676
5<M
.113^4
.0773'
.888CiT
SfttS
.00130
.88732
5^,0
.IIH68
.077-1
.88917
56,2
.00130
.88787
55,9
. 11213
0.0775
8.88074
5\a
0.00130
0,3
8.888.13
55,
I. HI57
.c>77(>
. 89030
5(',J
.00131
.88891)
55,7
, 1IIOI
.0777
.8<jo86
56,0
.00131
.88955
55,7
. i ia|5
.0778
.89142
5s.y
.00131
.ftjoio
55,6
. lOI^JO
.0770
.89198
5S,y
.ooi3H
.Syofifi
55,5
. io<>34
0.0780
8. 80253
S5.B
0.00132
o,3
8.8fJI22
55.5
i . 10878
.0781
89,309
55,7
.00132
.89177
55-1
. 1 08^3
.o;8j
893(>5
55/i
.00133
.80232
55,3
. 10768
. 0783
.89421
SS,
.00133
.KfjaSB
5.S,a
,10712
.078.1
.89.176
55,5
.00133
-8b3
55,2
. 10(157
o . 0785
8. 8953*2
55,4
0.00134
0,3
8.8ij3y8
55,1
r , 10602
.078(1
.89587
55i'1
.00134
89-15,1
55,"
- 10547
.0787
.itjXMa
55,3
,0013-1
.89508
55,o
. 10.193
.OJ-KS
,80698
55,2
.001.15
.89563
54,9
. 10437
.0789
.89753
55,2
.00135
.Srjfliii
M,
. 10382
0.0700
a.ftjRoB
55,1
0.00135
0,3
8.80672
54,7
i . io;ji}R
.0701
.89863
55.0
.00136
.J727
54i7
- 10273
,0702
.89918
54,y
,00136
.H<J782
54/i
. 10218
.070,1
.89973
5*1,9
.00136
.ft^jrt
54,5
. mi6,|
.079-1
.00028
5-I.H
.00137
.89891
54,5
, 10109
0.0795
' 8.00082
5'l,7
O. DOT 3-7
o,3
8.R9945
54i4
i , 10055
0796
.00137
5-1,7
.00137
.yoooo
5*1 13
, I 0000
.0707
.90192
S'l,6
.OOI38
.00054
54,3
.of)y.|0
. 0708
.00246"
S-1,5
.00138
.(XiioR
54,
,OOK03
.0799
.00301
54,5
.00138
.00162
54.1
,09838
0.0800
8.00355
54,4
O.OOT39
0,3
S.ooaifi
54. 1
1.0978-1
u
oa Inn atl u
w Fo'
OD sac oil u
w F,/
lag iln oil u
w Fo'
IOQ oia gd u
TABLKB
Logarithms of Hyperbolic Kunctimui.
u
log alnli i
ui Hi/
lou couli u
" fa
toil liiiili i,
,.,,:.-
>I>U COtll 1,
0.0800
8.9035
5.
(MKIM.
(..1
.'.' f ..' 1'
; M.'
i . i )/-. i i i
.0801
5.
.("H.I
, It 1 ' " i
.'' !>'
.'"/.:<(
.0802
.9046.
54
.OOt.H
.','M '1
i - ; -'' *
.i'.y./(.
.0803
9051
5. 1
.Dill. 1
,<J >,(.%!
'''.
.i-y./n
.0804
.!XI57
54
,(XH. I
.'*n.\-'
,-.i^
.i-l.'iUS
0.0805
8.906.'
s-i
(MKll.il
,.(
.'(.M 1 (Jf't
v-.t.; 1
I..KJ4 .
.0806
. yofxS
54
.IKII41
..I
.<J",'i-itl
.','.*
,,) |lK,
.0807
,91173.
53
,1X1141
.1
.'jn.-'l.t
.'.I.' 1
.lJ]ll/
.0808
0078.
53
,IKII, .'.
.(.ni'i;,'
,'',!> ."*
-fM i 1
.0801)
.yo8.|J
53
.inn. .:
..^.;',-.
;-.(. i
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0,0810
8.9089!
53
(MNH.l.
(VI
M, .,,;;;,..
M. I
, , M . ,,
.0811
!X)95<
53
.(Mil. ,1
,< f ^'-'
."inn
,0812
91003
5.1
00143
, i ji k'if . i
'! 1, i
,<"J|, U
.0813
91057
53.
,(NH.|3
.'.'"ll 1
','(!/
.0814
.91110
S3,
.00144
.,,,*y,v
;'(. i
'"M.l.l
0.0815
8.91164
53,
O.OOI.|.
It,,
H.-MM.M
SI, I
l.i^Vlci
.0816
,91217
53,
.om.|.j
,UH.7,l
!, | ( , ,
i Oil, '''
.0817
.91271
5,1,
.OOLJ.S
.'II l,''i
,V'j
. ih'^)V' 1
,0818
.91324
53,
.00145
.IJI \'-<>
t;,'''
. i " " ', , \
. iv't, 1 !.! [
.0819
91377
53,
.001. IS
.I>I.MI
','.'.
0,0820
8.9M30
53,
O.OOI,|0
0,1
M .ji -MI
, S-
.0821
91483
.(Xll.l'l
Jii't'r
\ '
''^' '
.0822
-OI5/J
53,<
.00147
,*>i.i't
>' ^ >
'..'{', hi
.0833
91589
5-V
.00147
.'ii. 1 1,?
J . i
* ,j,, : ..
.0824
. 91(142
5-),N
.001. 1/
,*> -'.,'
!,-Si;u,'i
0.0835
8. y 1605
5-',8
O.OOI4M
o,.
){ oi'ir
a . . <
.0826
.91747
5'!,7
.OOI4N
' l'n'< 1 '/)
.''.-i
' 4 *,'''''
.0827
.91800
12,6
.oni.iM
Dili'
'.-".'"
, i h i |n
. .'; i .*!
.0828
.91853''
5~',(
,om,(ij
'<(("'' I
:''," !
,i"-Vl.|i(
.0829
01905
52,5
.00149
!nry.7i !
;i"'!i'
.','JI].., :
0.0830
8.91958
52,
0.(X)I.|tj
'*,
Hltjt , u , {
'i -':, 1
1 ."Si,
. 083 f
.1)2010
^3,i
, (Mil 'ill
I 1 ]/ 1
'
.0832
.y2062
M 1
iooi'io
J /
,'>>'l" 1
,l*.U.|(l
* l q i
.0833
.0834
9.3115
.92(67
5^3
52,2
.00151
?i
F'ii
, I Irf 1, lil. 1 -
.
,' '>
'"/'^'l
0.0835
.0836
8. 92219
52,1
0.00151
.M
.,)..,*
M,H
I ,*'/') |,1
.0837
92323
52,0
.'(WHSJ
''''!''!','
.'it.'/
Hj'^t
.0838
.03375
51,9
,(M)lflj
''i /.
'. '
,,, j ;l,r<j
,0839
.92427
.<Hn;i3
i'lii^i
;||;'.'
"o*t */,('
0.6840
.-(An
8.92479
.92531
51.8
SI,M
-;;;;w
".1
..I. M ,I,
s.,^
'Wl
.084*
92583-
51,7,
ilMnVl
OAt?/
!>'.!
.< *>"'''?.(
0843 .
.0844
92634
.92686
.00154
''''' 'ii' J f
M!:!
!n/15.'i
'
' '',>,)'
,'*'.
"/ij'^J
3.0845
.084(1
1, 927,17
03789
Si.5
51,5
O.OOI.S.I
0,4
' i
S1.J
' ..o/aiH
!As
.92892
51,4
51,3
,0015(1
:?S:
,*;(.**
:!^U5
.929.13
5I..1
O.CK)I,17
w FM' Ion aln oil M
'SMITH80NPAN TflOLCB
MM
tt)
ll'U lltlBlt 11
',' 1.1
,l*l|(l.!
, l ll'l :
V,f
tllfj tlUlll 11
*'M' '|.l
'>.('*M
lo u (In a<! 11
,lH,ft
u F,,'
.nlwi.'i.'t
. I >f M K ")
logcinuil u
Logarithms of Hyperbolic
II
log si nl) u
u Fu'
[au coali u
- F,,'
lot) lilllll II
' r,,'
o.oyoo
8.9548.
48,
O.IXH70
o,
K.l.v(0>
-I'v
i..M<
.090
9553
48,,
.1x117(1
.'*:'. (:'.'
-I/. 1 '
.(i \(
.0902
.95581
48,3
.001/0
0>|".
4/,"
"1!
.oyo.
.95028
48,
.00177
O.vl.'i'
4;',''
"I!
.090.
.95<>7<
.|8,~
.00177
WVf
i ;','*
"15
0.0905
8.957-^'
9577-
48,1
48.1
0.00178
.00178
o,,
^\'>Mn\
-i; 1 .; 1
\'/.7
'"11
"II
.0907
.95H-1
.011178
,U;il'|.
4/."
."11
.ogot
.958(18
48,1
.OOI7U
.o, ! ;<'f
4;'."
."1,1
.0909
959 If
47,9
-OOl/tJ
.o.v'.O
-I/-;'.
.('M
0.0910
8.9501
,,;,,)
0.001811
0,4
S.057NI
l/.-'i
!."!.!
.0911
,9(1012
47,^
.ooiSo
.O.iM.l-,
i; p .-i
.Oil
.Oyi.3
.(jfkXJo
<l7i^
.(XllNo
.'J.'vi; 1 ';
i/'.-t
."It
.0913
.9(1107
.17,7
.Olll8l
.0;.'J,7
47.. 1
J'|"
.0914
.96155
47,6
.00181
'>;io74
-!/..(
.M|0
0.0915
8.96203
'17,6
o.ixiiflj
0,4
K../.o,M
.)/',.(
'-".(')
.09I()
.0250
47,5
.(xn8j
. i X tM ",'i
4i'. l
.'M'l
.0917
.0298
47,5
.00182
.i/il l.'i
1".'
.0918
.0345
47,4
.ooiH.i
,')\li.\
I/'."
, M (f[
,09iy
0393
47,4
.<H.ll8,t
, i / >,! 1
11',"
M;''
O.O92O
8.0440
47,3
o.ooiH|
0,4
H. </',!'< .
4'V,
,_,..
,0921
.047
47,3
.1x1184
-'/'.I'M
4".'"
,,,',(,
.0922
.0535
'17,-'
.00181
4 ''!'(
,0|l>
.0923
.0582
-17,-'
.00 185
.X'W
,|ii's
.nV
.0924
,96620
47,1
.(XH8.H
'/'111
i".;'
".15,
0.0925
8. 06?6
47,'
o.ootKfi
0.4
H.D.SIDI
I".;-'
i -".I, 'it
.0926
.967^3
47,0
,<xilWi
.'X> ! i(7
'i''! fl '
'",(]'
.0927
.0770
47,o
.(xn8(i
!i/i'.Mi
4''!''
",11
.09-'8
.0817
4(1,0
.1x1187
,if<ii\n
'i"!'i
.o,(.l|
.0929
.086.1
4(1,1)
,00187
.'Cif.;-;-
4''!.',
0.0930
8.09(1
4(1,8
0.00188
o.-l
.iX.-V(
I'M
I (Ml*
.0931
96958
4(1,8
.ooiHH
,l>'l7/il
I'M
!nV''
0932
.97004
46,7
.ixnHM
,i/*Stfi
..<ii
0933
.97051
46,7
,(ioiH()
,'X^,,!
l'i I
".U 1 '
0934
.97098
.(Kii8<j
.I/.^M,
4'C:
0.0935
8. 97 I'M
46,6
O.OIIIOO
0,4
K. <>/';
,('*,,!
,
.0936
.97191
4* >.S
,(XI1I>)
.'ij"i'i't
4'M
' 1 ^ J
-0937
. 97237
40,5
.(11111,10
.U"H|"
,i'i, 1
'll"lll
0038
.97~ J 8[
46,4
,00191
!'J;IM
T ( <
-I'M'
.n-fi/;
.0939
97330
46,4
.00191
.<>'/\.i>t
0.0940
8-97377
<|6,3
(K(X)HJ,!
<>,,|
H.MXUlS
i .ri,-M)
.0941
.974A1
46, i
.(XIH},!
t , ; .. , I'l
V' r 'j
.0942
. 974 f x)
46,^
.tXlHJJ
,,;'-'"
''-',.
i, ' i
.0943
975(6
46,2
.(X)IIJ.i
', JO ",','.
'i ;;!.'!
.".,, i
, ( In'' lj
.0944
.97562
46,1
OOKJ3
.'j;-,V"Ji
.It.'flJ
0.0945
.0946
8.97608
.97654
46,1
<|6,o
0.00)9,1
.(HH9,|
C,|
H.;;;.IM
i;.7
1 1 ' 'i t
,0947
-97700
46,0
.(Hili/l
"tt'Tur'
.'',
.0948
977'|6
'15,9
.(X)Kf5
't/'ftjil
*!)''f
'!!" t
two
.97792
'15,9
.<H)I(J5
aiL'j!
iuj'o
0.0950
R.97H38
45,!J
0,0010
0,4
.07l'M,j
.|n.-l
Iltll , lt ,
u
a tan ad u
w FQ'
oo sac ail u
F,'
OB ilri oil u
r,'
lug cio ad
SMITHSONIAN TABUS
Logarithms of Hyperbolic Functions,
u
log si nli n
Fo'
loo cosh u
w Fu'
loo til nli u
w Fo f
log oolh u
0.0950
8 97838
45,0
o.ooroli
0.-S
8.07642
45.4
1,02358
.0951
.97883
45,8
.00106
- Uy'< 187
45,4
.02313
.07920
45,8
.00 H)7
0773.1
45,3
,02267
- 0953
.07975
45,7
.00107
077X8
45,3
.O2222
0954
.98021
45,7
.00107
078^-3
45,2
.02177
0.0955
8.98066
45,'''
o.ooiyK
0,4
8.078(K)
45.2
1,02131
.0956
.98112
45><>
.00108
-070i.|
45,2
.02086
-0957
98157
45,5
ouiyy:
.07O50
45,1
. 0204 1
.0958
.98203
45.5
.ootyy
,<)H(K)4
45,1
.01096
.0959
.98*48
45,4
.ooiyy
-yHn.io
45,0
,01951
0.0960
8,98294
45.4
O.OOSjXl
0,4
8 . (>S<>()4
45,0
I. 01006
.0961
.98339
45,3
.ooaio
, y8 1 ,i<)
' 4>o
.Ol86l
. 0962
.9838.1
45,3
.00201
, yH i 84
t 4.0
.01816
.0963
. 08430
45,2
.00201
,()H.!20
-4,8
.01771
.0964
.98475
45,2
.00201
08-73
-4.8
.01727
0.0965
8.98520
45,i
0. 00202
0,4
8,yH.U
4<,7
I ,01682
.0966
08565
45,'
.OO.JO.J
fj^.t'y
' 'i7
.01637
.0967
,98610
45.1
.ou.30.1
.0841)8
* t .ft
,01592
.Q9(&
.98655
45,o
,<X)203
, 1)8,15 2
<i,6
.01548
.0969
.98700
45,0
.0020,|
,ij8.|,07
",5
,01503
0.0970
8.98745
44,0
O.O0204
0,4
8. 1^51 1
-..5
I. 01459
.0971
<j87yo
44,o
.O02O4
.fjNsWi
" ,5
.01414
0972
.98835
4-1,8
.OOJ05
.<j8f>30
. - ,4
.01370
0973
.98880
44,8
,(X>2f5
.1^175
-.,4
.01325
0974
.98925
44,7
.OOJOfi
yH^iy
;,3
.01281
0.0975
8.98969
44,7
o.ooaoli
0,4
8,ijH7<h
"i3
I. 01237
.0976
.00<> M
44,6
.00207
ijHHo?
.,,2
,01103
.0977
09059
44,6
. OOJ07
. ijM8,S2
. ! ,3
.01148
.0978
99101
44,5
. 00^07
. yHHi )l >
' ' ,1
.01104
.0970
.99148
44,5
.00208
-yHy.io
.*.!
.01060
0.0980
8.99192
44,5
0.00208
(VI
ft-gKcAl
,,,0
1.01016
.0981
.99337
44,4
,00209
,ytX)jK
it ,0
.OQ07 2
.0982
.99281
44,4
.ooaoy
.(>()( 17^
43,9
.00928
.0983
09325
44,3
.O020O
W i''
43,0
.00884
.0984
.90370
44,3
,00210
!.>*> I f)
43,0
.00840
0.0985
8.904-14
44,2
0.00210
0,4
R-W503
'43,8
1.00797
.0986
.99458
44,3
.00211
y*>~i7
43,8
.00753
.0987
.99502
44,2
.00211
jji>jr>l
43,7
.00709
.0988
- 99546
44,'
,CX)2I2
UJM35
43,7
,0066^5
.0989
-99500
44,1
.00212
W3?W
43,6
.O06~22
0.0090
8.09634
44,0
0.002T2
0,4
R, W|ii3
43,6
I .00578
,0991
.09678
44,0
.0031,1
.otj.i6ti
43,5
,00534
.0992
,99722
43,0
. ma 13
.( )*)$()<)
43,5
,00491
.0093
.99766
43,9
,0021-1
.JWS33
43,4
,00447
.0904
.99810
43,8
,0021-1
.yjjaX
43,4
, .00404
0.0995
8.09854
43,8
0,00215
0,4
8.0JX>39
43,4
1.00361
ooyrt
.00808
43,7
.00215
OfX>H,1
43,3
.00317
.0997
.99941
43,7
.00215
,\Kt?s(t
43,3
.00274
.0998
43,7
.00210
f WKJ
43,2
.00231
.099!)
9,00029
43,0
.002 10"
.998 1 !a
43,2
.00188
O.IOQO
o . 00072
43.fi
0,00217
0,4
fi.WjKfirt
43,1
1,00144
u
log tnnucl ji
Ftf
log 800 g<l u
.w
log tin ail u
6) Ft)'
log OBO gd u
SMITHSONIAN
Logarithms of Hyperbolic Functions.
u log slnli u u Fo
IOQ cosh u
w R
log tnnli it
0.100 | 9.00072 43
0.00217
8.90856
.101 .00506 43
.00221
9.00285
.102 .00935 427
.00226
f
.00710
.103 ,01360 423
.0023O
4
.01131
.104 .01782 419
.00234
i
01547
0.105 9.02199 415
0.00239
J
0.01960
.106 ,02612 41.
.00244
i
.0236.'-
.107 .03021 407,.
.00248
.02773
.loS .03427 403
.00253
t\
.03174
.109 .03829 400
.00257
i\
03S7I
O.I TO 9.04227 396
O.00262
4
o.o^Xis
.111 .04621 392,1
.00267
4
.('435.'
.112 .05013 389,;
.00272
4
.04741
.113 .05400 386
"4 .05785 382
.00277
.00282
4
4
.0512.
05503
0.115 9.06165 379
0,00287
5
9.05879
.116 .06543 376
.0029-'
5,
.117 .06918 372,
.002(J7
5,
,06621
-nS .07280 369,
.OO3O2
5,
.060X7
no .07657 366,
.00307
5,
07350
0.120 9.08022 363,
O.O03I2
5,
0-07710
.121 .08384 360,
.00317
5,
.080(17
. 122 .08744 357,
.OO322
5,
.08421
.123 .09100 354,
.00328
S,
.0877:3
124 -09453 352,
00333
5,
.09120
0.125 9.09804 349,2
.126 .10152 346,
0.00338
.00344
5,.
5,.
O.og.|66
.09808
127 . 10497 343,8
.00349
5,5
. 101.18
.128 ,10840 341,1
00355
5,.
- 10485
129 .ni7!> 338,5
.00360
5/>
.10819
0.130 9-11517 336,0
0,00366
5,6
9-11151
'3' -11851 333,4
.132 .12183 330,9
.00372
.00377
5,7
5,7
. r 1480
.11806
133 .12513 328,5
-134 .12840 326,0
.00383
.00389
5,7
5,8
.12130
. 12453
0.135 9-13165 323,7
0.00395
5,8
9.12771
137 .13808 319^0
138 .14126 316,7
.00400
.00406
.00412
5,9
5,9
6,0
. 13087
. 13402
13713
139 .14441 314,5
.00418
6,0
. 14023
0.140 9-14755 312,2
'41 .15066 310,0
0.00424
.00430
<M
9.14330
I 42 .15375 307,9
143 .15682 305,8
144 .15986 303,7
.00436
.00443
.00449
6,1
6,2
6,2
. 14938
- 15239
.15538
0.145 9.16289 301,6
.146 .16589 299,6
-147 . 16888 297,6
MS .17185 295,6
.149 .17479 293,6
0.00455
.00461
.00468
.00474
.00480
<5,3
6,4
6,4
.1(1138
. 16420
.16711
.16999
.150 1 9.17772 291,7
0.00487
6,5
o. 17285
u Ion Ian ail u u FO'
sec od u
u Fo'
OD sin ail u *.
377
358,
355,
352,
349,
343,8
34',
338,3
335,'
333,0
330,3
327,8
325, '-
322,7
320,3
3(3,1
310,7
308,5
306,2
304,0
301,8
29>i5
295,4
293,3
280,3
287,2
285,2
SMITHSONIAN TABLES
0.88849
H75-IH
o.8s(i7()
^53f'5
. 850(1 J
.847*11
.83001
0.82715
oo oia git u
Logarithms of Hyperbolic Fxinctions.
11
loo slnli u
F/
loo oosli u
"IV
log tiinh u
u F/
log co 111 u
o. 150
0-17772
391,7
0.00487
6,5
0.l7-'85
385,3
0,82715
151
. 18063
i."8o,8
-00403
() '5
- 175*>!>
283,3
,82431
.152
- 1835 I
287,0
. 00500
. I7<S<)2
- f 8'[,4
.82148
.15,1
. 18(138
28(1,1
. 00506
6/1
.18132
2-70,5
.818(18
.154
. 18024
1-84,2
.00513
6,6
.18411
277/i
.81581)
.i55
0- 1 *>207
,1-82,4
0.00520
67
y. 18(187
i!75,8
0.81313
.15''
. 10488
280,6
.00520'
(i?
. i8()(u
^73.0
.81038
I.S7
- I07d8
278,0
.00533
6,8
10A15
2X-!,t
.80765
. 1 58
,-'(104(1
277,1
. 011540
6,8
. 1 050(1
270,3
.8o.;o4
. 150
.20323
275,4
.00547
6,8
. I07?6
3(18/1
.8:uj,
o. 1 60
0. 20507
273,7
0,00554
6,0
0.20044
366,0
o.7f)i>5fi
.!()[
,208711
27~',r
.005(10
6,0
.at 13 10
"('5i'
. 7lX X i
. Id.!
. 2 1 1.] I
27",4
. 00567
7,o
. 3t)574
2(13.4
. 70426
. if >3
.2141 I
2(18,8
.00574
7,o
-208,17
yd 1,8
70 1 ' >3
. 164
-'id?!)
3(17,3
.00581-
7,1
^Xl.I
7HXM
O, 165
0-21045
265,6
0.00581)
7,'
9.2.1357
258,5
0,786.13
. ]()(!
. DiJ2 1
264,0
. 0050(1
7.1
.2I()I.|
i! 5(1,0
.7<S,(rt()
.3(17
.2.1473
26-', 5
.1X1603
7,2
.21871
355*3
.78120
.168
.2.735
260,0
.011(110
7,2
. 32 1 25
253,7
.77H75
. ifxj
-22005
250,4
.00(il7
7,3
,X!3?8
252,2
. 77622
o. 170
o. 2325-1
257,0
0,00625
7,3
""fi-.'0
250,6
0.77371
.171
235 1 1
256,4
,110(133
7,4
' .2:!87i>
2.10,1
.77121
.i/..'
.-'3767
255,0
.00630
7>'l
.331 -'8
247,6
.7687J
'73
,;I.]OJI
253,5
.00(1,17
7,4
- 23374
2.1U,I
.7d6-'(i
.'74
.2.127-1
35* r
.00654
7,5
34-1.6
.7(i3*i
0.175
0.3-1525
250,7
0.00662
7,5
0.23864
243,1!
0.7(113(1
.176
-24775
2-10,3
.oofifio
7,6
,i!.|30fi
241,7
. 75804
177
.2502.1
2.47,0
.00677
7,6
.24347'
340.3
.178
.25271
2-i6,5
oof 184
'fS-IU
. 1 70
-25517
2.15,2
.00602
7,7
! 34825
33M
o. 180
0,2-5762
2-13,!)
0.00700
7,7
0.25062
236, 1
0.74038
.181
.2(MX)5
2-12,5
. 0071x8
7,8
.25207
234 ,8
7'lXO.i
.18.:
. 26247
2,| 1,3
-00715
7,8
.25531
233,4
.744(10
- '83
. ;!f>487
a, |o,o
.00723
7,0
.25764
.74236'
.181
.30737
338,7
.00731
7,i)
. 35900
230>
.7400,1
o. 18^
. 26065
237,4
0.00730
7,!)
9.26226
220,5
0.73?>.|
.18(1
. 37-Ki i
.00747
H,o
.2(>.|<i4
228,2
-735.16
, 187
.27437
23'M)
.00755
8,0
.96/182
2.16,0
.733iK
.188
.27671
233,7
.00763
a, i
. yftjdH
225,7
.73002
.180
. 2700. [
232,5
.00771
8,1
.2.7133
.728(17
O, ttjf)
'o.3Ht3fi
231,3
0.00770
R.3
0.27357
233, a
0.72643
.10'
' .28367
230,1
.00787
8,2
.27580
22 1 ,0
.7-M30
. MJ2
. 28507
220,0
,00706
8,2
.37801
3J0.7
7-J 1 W
I !'3
. jH8;J5
227,8
.00804
8,3
,302I
210,5
.71070
I'M
. 20/152
226,7
.00813
8,3
.JA|0
2 [8,3
.71760
0. 105
0.20178
225,5
0,00821
8,4
9.28458
217,2
0,71542
. )()(>
20503
224,4
,00820
8,4
. 2Hf)7,|
2rd,o
.107
,i!<;727
333,3
.00837
8,4
.28800
*t<W
.71110
.108
, ;>005Q
222, a
.00846
8,5
.2O104
213,7
, yoHt/i
IW
.30173
221,1
,00854
8,5
3i)3t7
212,0'
. 70683
(j.aoo
0.303U3
220,0
0,00863
8,6
0.205^9
311.5
0.70471
u
log tun (id it
w FO'
00 100 0(1 11
J1*L
loo tin at) u
1.1 FO'
lOOCHJUll U
8MITHBONIAN
Logarithms of Hyperbolic Functions.
u
loo slnh u
- Fo'
log cosh u
"Fo'
log tanh u
Fo'
log colh u
0.20O
9.30392
220,
0.00863
8,
9.2952
211,
0.70471
.201
.30612
219,
.00871
8,
2974
2IO,<
.70260
.202
,30830
217,
.00880
8,
.2995
209,;
. 70050
.203
31047
216,
.00889
8,
3015
208,
.69841
.204
.31264
2i5*b
.00897
8,
.30366
2O7,
.69634
0.205
9.31479
214,1
0.00906
8,
9.30573
2O6,O
0,69427
.206
.3*693
2I3,i
.00915
8,8
.30778
205,0
.(19222
.207
3'907
2 1 2,1
.00924
8,<
30983
203,9
.69017
.203
.32119
211,1
.00033
8,9
.31186
202,9
.6881,
.209
.32330
210,8
.00942
8,9
-31389
201,9
.68611
0.21O
9.3254r
209,8
0.00951
9,0
9-3I590
20O,
0.68410
.211
.32750
208,9
.00960
9,o
.31790
199,8
.68210
.212
-3295S
207,9
.00969
9,
.31990
198,8
.68010
.213
.33166
207,0
.00978
9,i
.32188
197,9
.67812
.314
33372
206,O
.00987
' 9,2
-32385
196,9
.67615
0.215
9.33578
205,1
0.00996
9,2
9.32582
195,9
0.67418
.2l6
33783
2O4,2
.01005
9,2
.32777
194,9
.67223
.217
.33986
203,3
.01015
9,3
-32972
194,0
.67028
,2l8
.34189
202,4
.01024
9,3
33165
193,0
.66835
.219
34391
201,5
.01033
9,4
.33358
192,1
.66642
O.220
0-34592
200,6
0.01043
9,4
9-33549
101,2
0.66451
.221
347P2
199,7
.01052
9,4
33740
190,3
.662(10
.222
.34091
198,8
,01062
9,5
-33930
I89,3
.66070
.223
35100
198,0
.01071
9,5
.34119
188,4
.65881
.224
.35387
197,1
.01081
9,6
.34307
187,5
.65693
0.225
.226
9.35584
.35780
10,3
195,4
0.01090
.01100
9,6
9,7
9-34494
.34680
186.7
185,8
0.65506
.65320
.227
.228
.229
35975
.36169
.36362
194,6
193,8
193,0
.01109
.01119
.01129
9,7
9,7
9,8
.34865
.35050
.35234
184,9
184,0
183,2
6si35
.64950
.64766
0.230
.231
.232
.233
234
0.36555
.36747
36938
.37128
37317
192,1
191,3
190,5
180,8
189,0
0.01139
.01149
.01158
.01168
.01178
9,8
9,9
9,9
9,9
10,0
9.35416
.35598
35779
35959
36139
J82.3
181,5
180,6
179,8
179,0
0.64584
.64402
.64231
.64047
.63861
0.235
.236
237
.238
2,39
9>375o6
-37694
.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
IO,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
.24:
.242
-243
.244
9.38437
.38621
.38805
.38087
.39169
184,4
i83,7
183,0
182,2
181,5
0.01239
.01249
.01259
.01270
.01280
10,2
10,3
io,3
10,4
10,4
9.37198
37372
37545
-377I7
.37889
174,2
173,4
172,6
171,9
171,1
0.62802
.62628
.62455
.62283
.62111
0.245
.246
.247
.248
249
9-39350
.39531
39710
.35889
.40068
180,8
180,1
179,4
178,7
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
6r<l33
,61265
0.250
9.40245
177,3
0.01343
10,6
9.38002
166,7
0.61098
u
Joo tan ad u
Fo'
a sea ad u
?<!
og sin ad u
Fo'
og etc ad u
24
Logarithms of Hyperbolic Functions.
LL.
log alnli u
U P(|'
Ion cash u
wF</
IOQ tfinli u
" Ft/
loo oolh u
0.350
y. 40J.|5
J77..1
0.01^43
10,6
().38t)03
166,7
o,6uxj8
,351
.40.123
I7<i,0
.01354
10,7
..t'JolMj
[(>(),()
.(XMJ3I
,25.2
4"599
176,0
.oijhS
10,7
3U-M4
K>5.3
.(x)7<>6
253
-4'>7M
175,3
.01375
io,H
39390
KM, 5
.(K)(HJ1
.JS-I
.40049
17-1,0
.0138(1
10,8
.39563
163,8
.60437
0.255
0.41124
174,0
0.01397
10,8
y. 39727
163,1
o.(b373
-'56
.41297
I73i3
.oi.joS
10,1;
, 3<>Sijn
102,5
.60110
.357
..11.170
173.7
.in.|i9
10,9
.. 10053
l(l,
-59948
.a58
.4KM3
172,0
.OI.-IJO
I 1,0
.40313
idr.L
597H7
.-259
..|[Hi 4
I7I.4
.01. HI
11,0
.4037-1
160,4
.596^6
0.260
y.'iiy^fi
170,8
0. Of. |53
n,o
0.405,1-!
159,7
0.594(}f)
.301
,.|ais()
170,3
.01463
i U'
4<-'li<>3
159,1
.59307
.ao'j
..|33^()
K>9,5
.Ol.|74
ti.i
..10852
158,4
.50,148
.263
.42<|OS
i()8,y
.or.|Ks
11,2
4101O
157,8
. <j8iw)
.a(x|
,.^(,(M
168,3
.OI.|06
n,j
.-in<>8
157,1
.58832
o.arts
y.. 13833
167,7
0.01507
11,2
9.41324
156,5
o.s8*7fi
.ai
"layyy
167, l
.oisiy
11,3
..|I.|0
1 55,8
.58530
.aft?
,<i3r(>(i
K)0, 5
.01530
11,3
.416.16
155,2
.58364
.3(18
.'13333
165.0
.01541
M,.|
4T70C
154,5
.58^09
.yoy
,<U.|(j8
165,3
.01553
I VI
.41945
153,9
.58055
0.370
9-1.^3
164,7
0.0156.1
I VI
9.42009
153,3
0,57001
.371
.-IJ37
1 6.], 3
.01576
n,5
.-12353
I5-J.7
5774
hi! 7.!
.'I30UI
i6,i,(i
.01587
11,5
..) -'40,|
152,1
-57SIX'
.273
.<|.|I5'1
163,0
.en soy
n,6
.4255(1
151,4
57444
.27.1
M3I7
I6- V |
.Ol(>[()
n .6
.43707
150,8
.57^93
0.375
i>.-i.i.i7y
ifii.y
o.oi6^j
n,7
9.42857
150,2
0,57143
.376
,,i.i().i i
161,3
.01634
rr.7
.43007
149,0
, 56<W3
.J77
.-M8oa
i(io,K
.01(1(5
11,7
.43157
I4'J,0
.56843
.378
,.|.|<X^'
160,2
.01657
n,8
.43305
148,5
.56(95
.J79
4SI2J
159,7
.oi66y
n,8
43454
147,9
.56.>|6
o. sNu
y.-iSaHa
150,1
O.oi(8i
11,9
9.43601;
147,3
0,56399
.381
.<l5.|-ir
I5.C>
,0lfi03
n,<)
.43748
146,7
.50*52
. ya
"155!W
I5H.I
.01704
1 1. 9
43H95
I'|6,t
.56105
.-'H.i
.-1S7S7
157,5
.01716
13,0
.4.104"
145,6"
55<Xb
.3*1
"isyi^i
157,0
.01728
1 3,0
,44i8(i
145,0
.55814
0.385
y.it(k)7r
156,5
0.01740
13,1
9-44330
144.4
0,55670
.jK
,<K47
156,0
.OI75U
13,1
44475
143,9
.55535
.387
.-Ki33
155,5
.01765
rj,i
.44618
14.1,3
.5538-'
.288
..|653
I54,y
.01777
13,^
4-l76t
142,8
.553.19
.389
.4<tfV3
154,4
.OI?8y
13,3
.44904
143,3
.55096
O. 300
y.4ftl7
iS.VJ
o.oiHot
13,3
9.45046
14 r.7
0.54954
.31)1
.-17001
153,4
.01813
13,3
.45i7
i-jr.r
.5481,1
. 3(J,3
47IS4
152.9
.oiKafi
13,3
.45338
140,6
.54672
3<>3
, i i73or )
IS2.4
,01838
12,.\
.45468
140,1
54532
.aw
47459
15-J.o
.01851
12,4
.45608
139,5
.5439-5
0.3JM
y. 47^10
TSI.5
0.01863
13,5
9-45747
139,0
0.54253
.206
,.17763
iS'.o
.01875
12,5
..(5886
1,18,5
.54114
307
-179' 2
150,5
.01888
13,5
,4<X)2.|
138.0
.53976
.308
,4ftoft3
150,0
.OHjOO
I3,()
.46162
137,5
.53838
. '-HJQ
,48312
149,6
.oryij
12,6
-4<J209
136,9
53701
0,300
9-4^2
149,1
0.01026
12,7
9.4&13<3
136,4
0.53564
u
lou titn oil u
wFo'
loo too ail u
Fo'
Ionian ail u
H Fo'
lOflOSDOll U
SMITHSONIAN T A nuns
Logarithms of Ilynerholii: l-'imetioiiH.
II
log slnli u
10 IV
Inu cosli u
1- [>,'
IDU inn'i u
,.,'
o.,ioo
0.483!'-'
140.
o.OHMt
i ..;
'),!<' |.i"
U".
"-,'i.l.MM
.301
.4M510
148,
.(iM).(, 1
''./
4".;,' |
!,i;,.'>
.'-.I I-''
. 302
.48(150
148,
,(Jl'l;'i
i.-',/
..(f'^i'S
i.C-l
;i. *'>.:
303
,,|HHo7
147-
,OIM<>
i ,',H
..((.I 1.
l.lt.'i
Ji,U i/
304
.48954
1-17,
.0107;
I.-.H
. |i.j;-S
I.U.I
..S.10-!.!
0.305
9-49'oi
T4<>.
O.UMjM.
1 ,',,'i
...,i;'i .-
i.U."
",.i;.'. h w:i
.306
..|9_ l .|8
i.|(),
.(l.itlfl,
l.'.i)
-\'/-'\:<
l.l.i.
:i-V'Si
.307
4'M9. 1
M.'i, 1
.U.INI;
1 -',0
\'i.\';->
M.i."
O-'O.M
.308
,49540
1-15.
,(i,:o.;J
1,1."
-I -' > [ '
'.I. 1 ...
!1 '.)H">
.309
.49<>K5
M5.i
.UJ().|I
1.1,"
..i;-"i
l.l-V
-.'"',.' ('
0.310
9.40830
'44,'
n.o.!ii5
M."
M777.'l
UV,
. ';,;,' .si;
.3"
49974
144,
,o.;nd;'
M,
I/ 1 " 1 '/'
l.i'.ti
, i,,-, M ,'i
.312
.50118
143,7
,0.,'nSi
'.I,'
i' ; '',<;'
!.(".''
;,i'Xi'i
-313
SOJdi
14,1..
. 1 1.:< i 1 1
1,1,,!
,.|,'i|i..'!
' .(' ', '
, j; if (3,1
.314
.50.104
142,iS
.(Ml 1 17
1.1,.!
,.|!t,Mt
I. <!.<>
'.'i'/'IJ
0.315
9.50547
M-V
o.i).!l.;i)
l.U
M..|I.:;'
t. "),.'
11 '.'-I .'17.1
-3'0
.51X189
I4-M
.O.M3.I
M.,1
.,[.'i;i;,'i
i .''.;
.;,[.] |,|
317
5083 1
141,1
,o.ri.|H
M,,l
,.|.''V^{ j
i -.'(, ,-
. M (III
.318
.5972
141,1
,o.!iO(i
M.4
,,|M,'!|,:
i ,',',S
.jii'ifW
3"9
51113
1-10,7
.0..-I7.1
l.l.l
. |J!-j|u
i -*.-'., i
..'itirfsi
0.320
9.51254
!40,,1
n.OJi7
l.l.l
,,,.,,,,;..
i.f..-j
H.MI.,,,
.321
-51391
1,19,9
.().!,!l)il
'.I.;*
..|ui'M
i ..( i, i
.t;nf(Iifi
.322
.515.14
130,5
,().!-!l.|
1,1.;.
I 1 ',!''"
i.-, ...I
. i;i i' ..'i i
-32,1
.5107,1
1,19, 1
.H.!.!,!/'
1,1."
49 1 I 1
i ':,-.<
. M'vi.|
.3^1
.51813
1 3^,7
.o.;.i,|i
'.I.''
I'). 1 */!
1 ,'..,, I
.M'h''J
0-325
0.51050
138,3
O.O.f.t'il
M.II
<J..|-/-X>
I .?.),;
M. ',u in i
.326
.520SK
137,9
.O.MfiS
',1,7
..I'^t.M
1 -' L -
,> .i 1 i
-327
.53J3O
M7.5
.O.M.S.!
I'.'M 1
1 . , ;{
(iij)i'(i
.328
. 5230.1
1,17.1
.0/,!'l.<;
1,1,''
.';; tN .'>)l
1 -M. 1
!,i'cj'ij
-320
.5S500
I3<>,7
.O.'.lOiJ
i.l.H
.,';-.i,i
U.Vl
.,|.j!^j
0.330
9.52637
l.J<U
O.O.M-M
l.l.H
.;;,,,,,
i.'.',;
u l'/'!iO
331
5^773
13(1,0
o.M.l/-'
i,1,'(
!MM.I'I
i v, t
!.'iu;,f>.|
- 332
52909
l,15,o
.0,13,'U
M.'J
, l '", 1 i;>' 1
i -'!.;
<4''l U
333
530.14
'35."
.O/.l'i;;
i I,M
,'\< ';')
I.M.I '
.-I'l.t-M
-334
53179
UI.8
O.M79
i,|,"
.i;m'i,.i
i -<>,:;
0.335
9.S33r.|
"34,5
O.O.I.1U!
M,n
.) *,!, -|
i <> i
337
53-M8
-535H2
133!?
iiwS
14!'
i.|,i
, ;',!!> (1
.,11 I'll
. . i , i
i, '.'.'i
1 1 ->,'. |
"$k'l
339
53715
-53^19
'33,3
'33,o
;!S:K
14.1
!s!.pl'p
1 1'),,-
::lkE
0.340
9.5398[
M.;,f>
o.tui^
14..!
(i-msiK
I.*.! !
t) M !ij
-341
-5.|H.|
'3 -',3
,{)j,\yH
V !(,.[,
I'M
"Jij 1
.3.1-'
.54240
'31,9
,O.!.|i).!
' I-.1
' '' i "';
'.,'!' i
' >''! ?
343
-5-1378
13I>5
.u,;<ioii
.'it:t : -'' i
1 1 7, .r
".iji'ljj
-3/1-1
,5,1509
131,2
.o.iii.to
iii'i
i "
1 !(...'(
i^Mi
0.345
o.5.|fi.'|0
1.10,8
o.o.t.s.n
1.1,4
,. ,
nr.
"M, r
>3'|o
-S-'I771
"30, 5
,()_,;;.(',
, ''i,' J.' |
i u
"*'" ''
347
348
-54901
-55031
MO, i
ilSlil
l.|i*i
"'.'-.X
l//'/9
'349
55101
lajls
o.ijig,!
l.|,<<
i<i!t;,(!s
iiji'j
-!;'.'i^
0-350
9.55290
121), 1
euurty
M,"
1)pf ., (vS ,
n f
o. r,iM
u 1
ai) Inn ud u
"i IV
u too oil u
F,/
IDU ln (|<1 u
M IV
loo <:i<} git it
Logarithms of Hyperbolic Functions,
II
100 Blllll II
w F u '
loo cash u
-w
IOQ tanh u
w FJJ'
IOD ootli u
0.350
.351
55410
. 555-17
I2<),I
IJH.8
o . o^(k)7
,02637
14,7
9.52682
.52797
52911
"4,5
114,1
"3,7
0.47318
.47203
.47089
.354
55804
l:^
!oS
14.7
.53024
.53137
"3,4
"3,o
.46976
.46863
0-355
'1 C/ k
9-55931
1.7,4
o.f)^(.8i
14,8
P.53250
112,6
0,46750
35 f '
. sj'osy
i J7, i
ojoyd
14,8
* 53.163
112,3
.46637
357
35K
359
.56312
.50438
!:?
.02711
.02740
14,9
1-1,9
- 53475
- 53586
.53698
111,0
"1,5
m,2
46525
.46414
.46302
0.360
tl\-l
9.56564
.5661 jo
i-isls
0.0-755
.0-770
15,0
15,0
9.53809
. 5.1919
110,8
"0,5
0,46191
.46081
* iV '"
*e t
i .*, U
0-786
15,1
. 54030
I IO, I
.45970
* *r M
. 57005
I-'.|,H
:l!i.6
Isi!
.54140
54249
109,7
109,4
.45860
.45751
' 366
. 307
H-./.O
0.57'
5731.1
.57-137
124 2
0.02831
!oa86i
isla
15,3
9.54358
. 54576
IOQ.O
108,7
108,3
0.45642
455.13
45424
..lOn
-5750I
123,3
.02877
15,3
.54684
1 08,0
45316
.3()
576K-I
l 23,0
.0280J
15,3
54792
107,7
.45208
0.370
9- 578()7
I3J.7
o.oacjo;
15.4
9.54899
107,3
0.45101
371
37-3
..173
5704)
.58051
.58173
S
:il
15,4
is!s
. 55006
55II3
. 552^0
107,0
106,6
44994
.44887
.44780
374
.58205
121,5
.020f)0
15,5
1 06,0
.44674
0..175
. 376
377
.378
.S537
.58658
.58770
m,.;
1 ;!(),(>
!.;<),()
0.0^3
,03000
.03016
,03031
15,6
"5,6
15,6
'5,7
9-55432
-55537
. 55747
105,6
105,3
105,0
104,6
0.44568
.44463
.44358
.44253
-.179
.58899
I20,O
.03047
15,7
. 55852
104,3
.44148
. 380
9 , 5f r<)
1 1<),7
0.0.1063
15,8
9.55956
104,0
0.44044
.381
. 59 i 38
1 10,5
.03079
5,8
56059
103,7
4,1941
.,l8j
59^57
1 >!),.!
.03095
15,8
- 56163
103,3
.43837
. 383
.59377
I lK,o
.03110
15,9
.56266
103,0
43734
34
50495 "
1 18,0
,03121')
15,9
.56369
102,7
.43631
0.385
.380
'^sSil
IIK!<>
0.03142
.03158
16,0
9.56472
.56574
102,4
0.43528
.43426
.387
.59850
117,8
.0,1174
16,0
.56676
ior.8
43324
.388
.59067
1 17, 5
0,1 100
10,1
.56777
10 r ,4
43223
.381)
.(10085
117,2
.03206
16,1
.56879
ior,i
43I2I
0.390
o.fjomi
1 1 6,9
0.03222
16,1
9.56080
100,8
0.43020
-3!Ji
f 10319
1 1(1,7
,032.18
16,13
. 57080
100,5
.42920
< 3 ( W
,('K),|35
1 16,4
,03255
16,2
.S7i8l
100,2
.42819
303
.60551
1 1 0, 1
.03271
1 6, 2
.57281
90,0
42719
3<J4
.(io(>68
1 1 5,9
.03287
16,3
57380
99,6
.42620
0.305
9.60783
115,6
0.03303
16,3
9.57480
99,3
o. 425 20
* 306
,(>o8ij0
i '5(3
.03320
16,4
S7570
99.0
.42421
307
.61014
H5,l
.03336
if VI
.57678
oH,7
.42322
308
t 61129
I h|,8
- 03353
i6',4
.57776
98,4
.4222.4
3W
,6lJ44
i h|,6
.03,1(19
i6,S
.57875
98,1
,42125
0.400
9-61358
"4,3
0.03385
16,5
0-57973
97,8
0.42027
u
ou Inn nil u
u To'
a BOO ad u
w P '
IOQ aln ad u
Fc,'
loo oso ad u
SMITHSONIAN
Logarithms of Hyperbolic Functions.
1
u
lop sinh u
Fo'
Ion cosh u
t Fo'
loo tnnli u
u Fo'
log ooth u
0.400
9.61358
H4,3
o .03385
16,5
9-57973
97,8
0.42027
.401
.61472
114,0
.03402
16,5
58070
97,5
.41930
.402
.61586
H3,8
.03419
16.6
.58168
97,2
41832
.403
.6l/00
113,5
.03435
16.6
.58265
96,9
41735
404
.61813
- 113,3
.03452
16,6
.58361
<X>,6
.41639
0.405
9.61926
H3,o
0.03468
16,7
9.58458
96,3
0.41542
.406
.62039
112,8
.03485
16,7
-58554
96,1
.41446
-407
.62152
112,5
.03502
16,8
.58650
95,8
.4M50
.408
. 62264
112,3
.03519
16,8
.58746
95,5
.41254
.409
. 62376
112,0
.03535
16,8
.58841
95,2
-41159
0.410
9.62488
111,8
0.03552
16,9
9-58936
94,9
0.41064
.411
.62600
111,6
.03569
1 6,9
-59031
94,6
.40969
.412
.62711
ni,3
.03586
1 6,9
.59125
94,4
.40875
.413
.62823
iii.i
.03603
17.0
. 59220
94,1
.40780
.414
.62934
no,8
.03620
17,0
-593H
93,8
.40686
0.415
9.63044
110,6
0.03637
17,1
9.59407
93,5
0.40593
.416
.<J3I55
110,4
.03654
I7,i
-59501
93,3
-40499
-417
.63265
110,1
.03671
17,1
-59594
93,0
.40.-|o6
.418
.63375
109,9
.03688
17,2
.59687
92,7
.40313
.419
.63485
109,6
.03706
17,2
59779
92,4
.40221
0.420
9-63594
icx>,4
0.03723
17,2
9.59871
92,2
0,40129
.421
.63704
109,2
.03740
17,3
.59963
91,9
.40037
.422
.63813
109,0
.03757
17,3
.60055
91,6
309-1 S
.423
.63922
108,7
-03775
17,3
.60147
91,4
.39853
.424
.64030
108,5
. 03792
17,4
.60238
91,1
.39762
0.423
9-64139
108,3
0.03810
17,4
9.60329
00,8
0,3967 1
.426
.64247
108,0
. 03827
17,5
.60420
90,6
-395HO
.427
.64355
107,8
.03844
17,5
.60510
90,3
-39490
.428
.64462
107,6
. 03862
17,5
.60600
go, r
.39.100
.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
.64734
106,9
.03915
17,6
.60869
89,3
-39I3I
-432
.64891
106,7
.03932
17,7
-60959
89,0
3!X>4i
433
.64997
106,5
.03950
i7,7
.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
IQS.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
0.3833X
.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
.444
.66156
104,2
.04M7
18,1
.62009
86,1
3799C
0-445
9,66260
104,0
0.04165
18,1
9-62095
85,8
0.37905
.446
.66364
103,7
.04183
18,2
.62180
85,6
.37820
-447
.66468
IQ3. S
.04202
18,2
.62266
85,3
- 37734
.448
.66571
103,3
.04220
18,3
.62351
85,1
.37649
.449
.66674
103,1
.04238
18,3
.62436
84,9
.37564
0.450
9.66777
102,9
0.04256
18,3
9.62521
84,6
0-37479
u
00 Ian ad u
Fo'
oo sec D<J u
w Fo'
OQ sin ail u
Fo'
OQ 090 ad u
SMITHSONIAN TABLES
28
of Hyperbolic Puncllona.
J . .(
. -J'M
< * - .Jf'.'i
- -If'' 1
. -If')'
-li'M
.(It,
0. .
log iluli ti
no Inn at) u
Hll.n
I ( K >,< I
Ml<U
1 1 K i,i I
'.X',1
loii mull u
too son u<>
w FII' luu (nnli u
n w
I -j.il
!'),.'!
.(It'l
' 150
loo iltt mt u
tv
ux
Hi.H
H|,h
7.1.1
7=1.7
7.|!j
7-1,1
7,1.0
w ft/
luu colh ii
J/l-U
-,15V U
JOT
Tl-i ISOMIftH
Logarithms of Hyperbolic Functions.
u
loo slnh u
Fo'
log cosh u
-w
loo tanh u
Fo'
log co Hi u
0.500
9.71692
94,0
0.05217
20,1
9.66475
73,9
0.33525
.501
.71786
93,8
.05237
20,:
.66549
73,7
3345 1
.502
.71870
93,7
.05257
20,:
.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
.3323r
0.505
0.72l6o
93,2
0.05317
20,2
9.66842
72,9
0.33I5S
.506
72253
93,o
, .05338
20,3
.66915
72,8
.33085
.507
.72346
92,9
.05358
20,3
.66988
72,6
33012
.508
.72438
92,7
.05378
20,3
.67060
72,4
.32940
.509
.72531
92,6
.05399
20,4
.67133
72,2
.32867
0.510
9.72624
02,4
0.05419
20,4
9-67205
72,0
0.32795
.511
.72716
92,3
.05439
2O,4
.67277
.32723
.512
.72808
92,1
.05460
20,5
.67348
71,6
32652
.513
.72000
92,o
,05480
20,5
.67420
71,5
.32580
.514
.72992
91,8
.05501
20,5
.67491
.32500-
0.515
9.73084
91,7
0.05521
20,6
9.67562
7i,i
0.32438
.516
.73175
91,5
.05542
20,6
.67633
70,9
. 32367
.517
.73267
91,4
.05563
20,6
.67704
70,7
.32256
.518
.73358
91,2
.05583
20,7
.67775
70,5
.32225
.519
73449
91,1
.05604
20,7
-67845
70,3
.32:55
0.520
9-73540
90,9
0.05625
20,7
9.679:6
70,2
0.32084
.521
.73631
90,8
.05645
20,8
.67986
70,0
320:4
.522
.73722
go,6
.05666
20,8
.68056
69,8
.523
.73812
90,5
.05687
20,8
.68:25
69,6
.31875
.524
73903
90,3
.05708
20,9
68:95
69,5
.31805
0.525
9-73993
90,2
0.05729
20,9
9.68264
69,3
0.31736
.526
.74083
90,0
.05750
20,9
.68333
69,1
.31667
.527
.74173
89,9
.05771
21,0
.68402
68,9
.31598
.528
.74263
89,8
.05792
21,0
.6847:
68,7
.31529
.529
74353
89,6
.05813
21,0
.68540
68,6
.31460
0.530
9-74442
89,5
0.05834
21,1
9. '68608
68,4
0.31392
.531
74532
89,3
.05855
21,1
.68677
68,2
.31323
.532
.74621
89>2
.05876
2:,I
.68745
68,0
.31255
533
.74710
89,1
.05897
21,2
.68813
67,9
.31187
534
74795
88,9
.05918
21,2
.68880
67,7
.31120
0-535
9.74888
88,8
0.05940
21,2
9.68948
67,5
0.31052
.536
-74976
88,6
.05961
21,3
.69016
67,4
.30984
.537
.75065
. 88,5
.05982
21,3
.69083
67,2
.30917
.538
75^53
88,4
.06004
21,3
.69:50
67,0
.30850
539
.75242
88,2
.06025
21,4
.69217
66,9
-30783
0.540
9-75330
88,1
0.06046
21,4
9.69284
66,7
0.307:6
541
.75418
8S,o
.06068
21,4
.69350
66,5
.30650
542
.75506
87,8
.06089
21,5
.69417
66,3
.30583
543
75594
87,7
.06111
21,5
.69483
66,2
.305:7
544
.75681
87,6
.06132
31,5
.69540
66,0
.30451
0.545
9.75769
87,4
0.06154
21,6
9-69615
65,9
o . 30385
.546
.75856
87,3
.06175
21,6
.69681
65,7
303:9
547
-548
549
7S943
.76030
.76117
87,2
87,0
86,9
.06197
.06219
.06240
21,6
21,7
21,7
.69746
.69812
' .69877
65,5
65,4
65,2
.30254
.30188
.30123
0.550
9.76204
86,8
0.06262
21,7
9,69942
65,0
0.30058
u
on tan otf u
w Fo'
oo sec ad u
* Fo'
loo *ln ad u
* Fo'
lOO C90 (id U
SMITHSONIAN TABLES
Logarithms of Hyperbolic Functions.
u
on alnli u
-Fu'
op cosh u
to F q '
oo tanli LI
<> Fo'
OQ doth u
U.jjiy,
<).76.!0,|
8fi,8
o , 06262
21,7
9.69042
65,0
0.30058
S5I
7<>j(.)l
H(),6
.06284
. 71x307
64,9
20993
'.'i.S-!
,7*1377
86,5
,o(>3o(i
21 ',8
.70072 \
64,7
.29928
, 5^3
,764(14
8t> J
.ot>3^7
2f,8
.7013?
64,5
.29863
.!s<;4
7''550
8fi| 3
,o<349
21,9
,70201
64.4
.39799
(..c;,.^
9.76616
86 i
O . 0637 I
21,9
9.70265
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0.29735
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.06393
21,9
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64,1
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557
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29543
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.06459
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63,6
,29479
,#*>
0.770(15
85,5
0.06481
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9.70584
63,4
0.29416
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' .77151
8^4
.06503
22,1
. 70648
63,3
.29352
. S< M
.7723(1
8'"5 i*
.0(1525
22,1
.70711
63,1
.29289
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85,1
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22,2
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63,O
.29226
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.7740(1
H5,o
.06570
22,2
. 70837
62,8
.29163
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i>. 77491
84,9
0,06592
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62,7
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84,4
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62,2
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0.570
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0.06703
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61,9
61,7
0.28789
. 28727
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.(16748
22,4
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61,6
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0.06816
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22,5
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61,1
6 1,0
60,8
60,7
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0.28481
. 28420
-28359
.28290
.28238
u . 580
581
1 ski
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t&
82,9
82,7
82,6
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. 07020
22,7
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. 71883
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. 72(503
. 72063
6o,4
60,2
60, i
60,0
0.28178
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.27907
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ct. jMji
0-7<J'6s
82,5
0.07043
22,9
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59,7
0.27877
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22,9
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59,5
59,4
59.3
59,1
i 27758
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. 27640
Ot fJtJO
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8a,o
0.07157
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0.27581
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81,8
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23,0
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7
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slls 1
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23,1
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58*5
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507
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.80309
81,4
a 1,3
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81,1
8 1,0
0.07273
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23,2
23.2
23,2
23.J
9.72712
. 72770
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58,2
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58,0
57.8
57,7
0.27288
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.27172
.27114
.27056
O.<*00
9.80300
80,9
0.07389
23.3
9,73001
57,5
0,26999
u
loff inn pil u
M Ffl'
loo see IK! u
(0 FO'
Loo *ln a*i u
w FO'
looosoodu
Logarithms of Hyperbolic Functions.
u
loo sinli u
uFo'
IOD cosh u
.
log tanh u
Fo'
loo ootli u
0.600
9.80390
80,9
0.07389
23,3
9.73001
57,5
0.26999
.60
-8047
80,8
.07412
23.;
-73059
57,'
. 269.5 1
,602
.80552
80,7
.07436
23,4
73II6
57,3
.268&1
.603
.80632
80.5
-07459
23,4
73173
57,1
.26827
.604
.80713
80,4
.07482
23,<
73231
57,0
.26769
0.605
9.80793
80,3
0.07506
23,5
9.73287
56,9
0.26713
.606
.80874
80,2
.07529
23,5
733-14
56,7
.26650
.607
-80954
So, r
.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
g. 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
7379-1
55,7
. 26206
0.615
9-81591
79,3
0.07742
23,8
9-73849
55,5
0.26151
.616
.81671
79,2
.07766
23,8
73905
55,4
.26095
.617
.81750
79,1
.07790
23,8
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55,3
. 26040
.618
.81829
79,0
.07814
23,9
.74015
55,i
25985
.619
.81908
78,9
.07838
23,9
.74070
55,0
.25930
0.620
9.8rg87
78,8
0.07861
23,9
9.74125
54,9
0.25875
.621
.82065
78,7
.07885
24,0
.74180
54,7
.258^0
.622
.82144
78,6
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24,0
-74235
54,6
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78,5
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24,0
. 74 2 89
54,5
.257"
.624
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78,4
-07957
24,1
74344
54,3
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0.625
. 9-82380
78,3
0.07982
24,1
9-74398
54,2
0.25602
.626
.82458
78,2
.08006
24,1
74452
54,i
.25548
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.82536
78,1
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24,1
.74506
54,0
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.628
.82614
78,0
.08054
2-1,2
.74560
53,8
.25440
.629
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77,9
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24,2
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53,7
0.630
.631
632
9.82770
.82848
-82925
77,8
77,7
77,6
0.08102
.08126
.08151
24,2
24,3
24,3
9.74667
.74721
74774
53,6
53,5
53,3
0.25333
.25279
-633
-634
.83003
.83080
77,5
77,4
.08175
.08200
24,3
24,4
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.74881
53,2
53,1
.25172
.25119
0.635
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639
9-83158
83235
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.83466
77,3
77,3
77,2
7?io
0.08224
.08248
.08273
,08297
.08322
24,4
24,4
24,4
24,5
24,5
9-74934
.74987
.75092
.75145
53,0
52,8
52,7
52,6
52,5
0.25066
.25013
.24060
. 24008
.24855
0.640
.641
.642
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644
9-83543
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76,9
76,8
76,7
76,6
76>5
0.08346
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08395
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24,5
24,6
24,6
24,6
24,7
9.75197
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-75302
75354
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52,3
52,2
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51,9
0.24803
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. 24645
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0.645
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-647
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649
9.8393?
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76,4
76,3
76,2
76,i
76,1
0.08469
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24,7
24,7
24,7
24,8
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9.75457
75509
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75612
75663
51,7
51,6
5T,5
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51,3
0.24543
.24491
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24337
0.650
9.8.1308
76,0
0.08593
24,8
9-75715
5M
0.24285
u
ian ad u
.Fo'
oQsec ad u
.Fo'
OQ sin od u
*
ODC9Q Otl U
Logarithms of Hyperbolic Function;).
II
100 iltlll II
IV
Ing coali u
u F|i'
loo tnnli u
**f
lOQ Oolll II
0.050
9.84.108
; <,,0
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0-055
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0.08718
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9.75000
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7"OH.)
5",4
. -39'i I
617
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as.-l
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:Si
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laii'is
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9.87640
72 J
. (H)739
26,1
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26,1
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(u i'7
72 I
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20,2
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. 22(X>7
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72,0
71,9
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^
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45,7
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.21916
I 0.700
((.88000
71,9
0.09870
20,2
0.78130
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0.21870
u
loatnn uil it
w F</
too *oo a<l u
i.) Fu'
log sin fld u
" FO'
Inocioflilu
6MITHOHIAN
33
Logarithms of Hyperbolic Functions,
u loo slrh u
u Fu'
IOQ cosh u
-IV
Ion tanli u
Fo'
loa coth u
0.7OO 9.88000
71,9
0.09870
26,2
9.78130
45,6
0.21870
.701 .88072
71.8
,oy8<Xi
26,3
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45,5
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.702 .88l4/
71,7
.09923
26,3
. 7822 1
45,4
.21779
.703 .88216
71,6
.09949
26,3
,78266
45,3
.2173.
.704 -88287
71,6
09975
26,4
.78312
45,2
.21688
0.705 9.88359
71,5
O.IOOO2
26,4
9-78357
45,1
o. 21643
.706 .88430
71.4
. 10028
26,4
.78402
45,0
.21508
.707 .88502
71.3
1005 5
26,4
.78447
44,9
.2155,1
.708 .88573
71,3
.10081
26,5
.78492
44,8
.2150^
.709 .88644
71,2
.10108
26,5
.78536
.21464
0-710 9-88715
71,1
0.10134
26,5
9.78581
44,6
0.21419
.711 .88786
71*0
.10161
26,5
[78626
44,5
.21374
.712 .88857
71,0
.10187
26,6
.78670
44.'
.21330
.713 -88928
70,9
.10214
26,6
.78714
44,3
.2I2ttt>
.714 -88999
70,8
. 10240
26,6
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44,2
.21241
0.715 9.89070
70,8
o. 10267
26,7
9.78803
44 1 1
0.21197
.716 .89141
70,7
. 10294
26,7
78847
44,0
.21153
.717 .89211
.718 .89282
70,6
70,5
. 10320
. 10347
26,7
26,7
.78891
.78935
43,9
43,8
.21109
. 21035
719 .89352
70,5
10374
26,8
.78978
43,7
.21022
0.720 9-89423
.721 .89493
-722 .89563
.723 .89634
.724 .89704
70,4
70,3
70,3
70,2
70,1
0.1040.1
. 10427
10454
. 1048 1
,10508
26,8
26,8
26,8
26,9
26,9
9-79022
.79066
.79109
79IS3
.79196
43,6
43,5
43,4
43,3
43,2
0.20978
.20934
.20891
. 20847
. 2080.1
0.725 9.89774
.726 .89844
.727 -89914
.728 .89984
729 .90054
70,0
70,0
69,0
69,8
69,8
0.10535
. 10562
.10589
.10616
.10643
26,9
27,0
27,0
27,0
27,0
9-79239
.79282
.79325
.79368
794II
43,1
43,o
42,9
42,8
42,7
0.20761
.20718
20675
. 20632
. 20581;
0.730 9-90123
731 .90193
732 .90263
733 .90332
734 .90402
69,7
69,6
69,6
69,5
69,4
0.10670
. idfip?
.10724
.10751
.10778
27,1
27,1
27,1
27,1
27,2
9-79453
.79496
.79538
.79581
.79623
42,6
42,5
42,5
42,4
42,3
0,20547
.2050.1
. 20462
.204*9
.20377
0.735 9-00471
.736 .90540
737 .90610
.738 .90670
739 .90748
69,4
69,3
69,2
69,2
69,1
o . io8o5
10833
.10860
.10887
. 10915
27,2
27,2
27,2
27,3
27,3
0.79665
.79708
.79750
.79791
.79833
42,2
42,1
42,o
4i|8
0.20335
, 20292
.20250
.20209
.20167
0.740 9.90817
741 .90886
.742 .Q0955
743 .91024
-744 .91092
69,0
69,0
68,9
68,8
68,8
0.10942
.10969
-IOP97
.11024
.11051
27,3
27,3
27,4
27,4
27,4
9.79875
.79917
79958
.80000
.80041
41,7
41.6
4i,S
4M
41,3
0.20125
. 20083
. 20042
.20000
.19959
0-745 9.<m6r
746 .91230
747 .91298
748 .91367
749 -91436
68,7
68,6
68,6
68,5
68,4
0.11079
. ii ro6
.11134
.infir
.11189
27,5
27,5
27,5
27,5
27,6
9.80082
.80124
.80165
.80206
.80247
41,2
41,2
41,1
41,0
40,9
0,19918
.19876
. 19835
10794
19753
0-750 1 9.91504
68,4
0.11216
27,6
9.80288
40,8
0,19712
u loo tan ad u
oo seo ail u
Fo'
IOD aln gd u
w Fo'
loo oo gd u
SMITHSONIAN TABLES
34
Logarithms of Hyperbolic Functions.
11
Ina slnh u
w Fo'
log ooali u
<-Fo'
IOQ lanh u
Fo'
loo oo Ih u
0.750
<.M)I50.1
6H |4
0.11216
27,6
9.80288
40,8
0,10712
.751
.91572
08,3
. 1 1244
27.6
.80328
40,7
. 10072
.752
.91(141
68,2
.11272
27,6
,803.60
40,6
. IlXUl
7S.1
.91700
f.H,2
. I 1290
27,7
.80410
40,5
. losyo
754
.91777
68,1
."327
27,7
.80450
40,4
* 10550
0.755
9.91845
68,1
0.11355
27,7
9.80490
40,3
o. 10510
.756
91913
f>8,o
.11382
^7,7
.80531
40,3
. 10469
757
.91981
67,9
.1 1.|1O
27,8
.80571
40,2
. 10429
-758
9-3049
67,0
.11438
27,8
.80611
40,1
. 19389
759
.02117
67,8
, 1 1466
27,8
.80651
40,0
. 39349
0.760
9.92185
67,7
0.11493
27,8
0.80691
39,9
o. 10309
.761
.92252
67,7
.1.1521
27,9
.80731
39,8
, 19269
.762
.02,320
67,6
.11540
27,9
.80771
39,7
. 10229
7f'3
.02387
07.6
.11577
27,9
.80810
39.6
. IOIQO
.764
.02455
67,5
.11605
27,9
.80850
39,0
. JI50
0.765
9.92522
67,4
0.11633
28,0
9.80880
39,5
O.IOMI
.766
.02500
67,4
.!!()( I
28,0
.80020
39,4
* 19071
.767
.02657
67,3
. 1 1680
2H.O
.80968
39,3
- 19032
.768
.92724
67,3
.11717
28,0
.81007
39,2
.IM0M
.760
.92792
67,2
,.117-15
28,1
.81047
30, 1
. I&J53
0,770
9.92859
67,1
o.i 1773
28,1
9.81086
39,0
0.18914
.77E
.02026
67,1
.11801
2,I
.81125
39,0
.18875
.772
9^993
67,0
.11820
28,1
.81164
38,9
. i83fl
773
.93060
67,0
.n5
28,2
.81202
38,8
. 18798
774
.93127
66,0
.11886
28,2
.81241
38,7
18759
0-775
9.93IO.J
66,8
0.1191,1
28.2
i). 81280
38,6
o. 18720
.77<>
.93261
66,8
.11942
2S,2
.81^18
38,5
.18682
.777
.93327
66,7
. i 1970
28,3
.81357
38,4
.lf43
.778
93394
66,7
i 1990
28,3
.81395
3^,4
. 18605
779
93-101
66,6
,12037
28,3
.81434
3B,3
.18566
o.7fio
9.93527
66,5
0. 12055
28,3
9.81472
38,2
o. 78528
.7*1
93594
66,5
. 12084
28,4
,8lS10
38,1
. 18400
.78,1
.03600
66,4
.12112
28,4
.81548
38,0
. 18452
-783
.93737
66,4
. 12!<1I
28,4
.81586
37,9
.18414
.784
93793
66,3
.I2l6(>
28,4
.81624
37,9
.18376
o.75
9.93859
66,2
O.I2I97
28.5
9.81663
37,8
o. 18338 1
.786
93925
66,2
,12226
2,5
.81699
37,7
. 18301
7^7
93992
66,1
.12254
2,5
.8(737
37,6
. 18263
,788
.94058
66,1
.12283
28,5
.81775
37,5
.iteas
,789
.94124
66,0
.12312
28,6
.81812
37,4
.18188
0.700
9.94190
66,0
0.1234O
28, (i
p. 81850
37,4
0.18150
791
.94256
65.9
,12360
28,6
.81887
37,3
.18113
793
.94321
65,8
. 12397
28,6
.81024
37,3
.1807(1
793
.94387
65,8
,12426
28,7
.81061
37.1
. 18039
.794
94453
6S.7
, 12455
28,7
.81998
37.0
.18002
0.7<J5
9.04519
65,7
0.12-183
28,7
9-82035
37,o
o.i7</i5
. 7<X>
.045&I
65,6
.12512
28,7
,82072
36,P
. 17928
.797
.04650
65,6
.12541
28,8
.82109
36,8
. 17891
.70S
,94716
65,5
, 12570
28,8
.82140
36,7
T7854
-799
.94781
65,5
,12598
28.B
.82183
36,6
.17817
0.800
9.P4846
.-_ 6Sl ''
0.12627
28,8
0.82219
36,6
0,17781
u
log Inn flilu
H Fo'
lOfl SflO fltl U
Fo'
loo sin ad u
w Fo'
loaosoodu
BMITHHDNIAN TABLES
35
LognriUims of Ilypcrlmlu; Kitmrti
o.8oo
.Hoi
.Hi).!
.803
.8o.|
0.805
,8o()
.807
.8oS
,809
o.8n
.811
.'813
.81.:
.Hid
.817
.818
.819
o.8.>o
.8*1
0.835
.8i'l)
.8..?
,8-8
0,8,10
-3'
.83-'
8.13
.834
0.835
Xi7
o,8.[o
.84-1
o.8.|5
,8.|6
.847
,8. ( 8
lou sinli i
9-94H4
949'
1)497
.9504
95 1"
<;.95i 7
95A1
953^
934,1,
9-9S498
950J7
.9569-
95757
9.958.!
95951
.y6oi. c
<X'5<J3
.067,21
9.!/>78.|
.96976
y .
.97167
.97230
.97-f03
97357
0,850
975-17
.976' TO
97(173
979-'5
.97988
9.!>8o5i
IDQ Inn ml u
65,
6-5,
oil!'
M.5
6,1,1
loo coili it
i). i :(>.!/
135.1.1
135''.!
o. 1,11151
.i.i/ii
1377"
o. i.tKoo
.138,10
O. l,|fHJt)
D o (l ii
IdU
log tin uil u
Ing co DI) u
SMITHDOMIAN TAHLKB
I,<n;aHtlimn of Hyperbolic Kuiiclionti.
(),}'( HI
fl.f'J-wi
I(IU (lull II
.(KI'iHt)
,<IO;MI
ri.nn.ix
Ing Inn ad u
('i,,l
(>M
(kt,H
(io,X
too coili u
.15 H) I
. I J1-W5
Pi/
.l",o
jo,H
.11,0
.11.0
.11.0
,'iu
.11,1
lou Innli u
ij.Hji.it i
.S.M.IO
too tin gtl u
Fo'
.1',''
.11,5
.1".S
loo oolli u
I). lfK|H
. KHlIJi
. I. "it 55
t.SIJS
0.1.'Hf>|
0.1.MOI
TAB UK*
Logarithms of Hyperbolic Kiiiirlioiin.
11
log slnh u
F,;
loD CO ill u
-r;
IdO l^lili 11
^ r,, 1
!<>(] liotli u
o.ooc
0.0113?
6o,<
U. I5(>2>*
,U."
M.8,.,,V-
<'..'.
". 1. ||<)l
.9"
.ONI)?
no,<
. is6;;N
31.1
"u' 1 ' 1 ' 1 !!
-'"' '
- 1.14(11
.902
OU'.sf
60,5
. 15680
31."
',''''"'';
-''. !
1413-t
9".
.0131,^
60,5
,15;'.!!
,U..!
.}';., MM
''''.,
, i,|.|uj
.90.
.01379
(11,5
157.1-!
31.-'
.,'.'>'.,'/
-'''..
- "-M73
0.005
0,0143*
(*>
0.15783
3',-!
o.Jiyv.1
/u. .
"."134
,<jo(
,015011
00,.
, 15814
3'..'
,H.it '!{;',
.''(,'
-14.115
.907
.0151x1
60,,
. 1581(1
.U..1
.8;t/':'
,-' I.
, i4.:M<j
.(jot
.01621
60,3
15877
3 1.3
.;> n
.''/,ll
, i.l.'.'ifi
.909
.01681
60,.
.I59tt8
3'.3
M.V/.I
-''. '
,i.\jjy
0.910
0.01741
/kl,:
O.I5U3M
3".3
,>.iwl
/Ji.M
i.i.|n
.911
.01801
60, ..
. 15071
.11,3
.)i;i!{_tu
,'N.;;
.i.|i/ii
912
.018(11
60, 1
. tUXU
.U.I
.H.V 1 !;!')
,-H.H
.14141
.013
.01921
6o,l
. I'-'.U
.U.I
.Jl'iftfiJi
-'8,;'
.ill!.-
SKI
.oioHi
6o,l
' " lfX '' ;
31. 1
.Myjix
' M '''
, ).|i>8.t
0,915
0.02041
60,0
O.H-O.X.
31.4
'J,M;,.,|.'i
,-M.f,
o. i-lc.S.S
.916
.02101
60,0
.Ifil.jH
.U.I
.H;;.)/,!
-''v :
. l.|(l.!0
917
.(12161
5<J,0
. 16151)
.Ui.'i
. .S( KM.!
*' !',.''*
, i ,cM
.918
.02221
59.9
. IlitUl
.u.r.
.Nf>o(t
v''l,.|
'3'X*J
919
.02281
5'J.o
. 16.!,!.]
31,5
ft ""'^
.-", 1
'!('; n
0,920
0,02341
5'),H
o, 16',;*;4
,u,;i
..),;;< ,;w
-!*.. 1
n. M')U
.921
, 0240 1
SO. 8
. 16,185
31,5
,i<di it.
/.' i, .
, l.lfl'li
-922
,02.|6l
50,8
16317
.U/i
.Jl'tl H
,-*.-<
i iMi'fi
y
.02520
50.7
. 16.148
3'.''
.M'ii;',<
=-f!v I
- 1 |H,;H
,924
.02580
59.7
"'.I*'
.11. '
,M'.,'.-.
,rH.i
.IJMiHI
0.9J5
0.02640
50,6'
0, l'i,|ll
.U,''
IJ.W..!.'Jt
,'M.u
. i t/XJ
.926
,02fXJO
50,6
. "6-1 13
3l/i
.Jifijyt
7.u
M/44
.<W7
o-75 ( )
50/i
"M75
,U>/
,8'i,:M(
,.>_,,
'3/1''
.928
.02819
59.5
. 1 651X1
!u./
,,'!(,(l j
-I 1 /. 1 !
.9^9
.02878
50,5
.10538
31,7
.M(.; tt ii
.'A!f
.'i>'o
0.930
o.()2()37
KM
o. Hi. r i7ii
.U,/'
i).!V. ( l
_, .,
M, t fl (J
931
02997
50,4
. 16MI,!
.u.;'
,M//;ij'i
A/
I'l'^ 1 }
932
.03056
59,4
l'rf'33
,11,
Jv/i'i."')
." f'l
, n'iXX
.033
.03116
59..1
.lONi.i;
,11,8
..^.I'i.'l
-'iV,
.934
.03175
50,3
. 166<)X
,U.H
,)i.|>'H
';vi
.uiiJJ
0-935
0.03234
59,3
0.16721)
3I.H
,,..;,,;;;;
''A 1
*. i.ii'j;;
.036
03^93
50,2
. 16761
!u.9
Hdjij'i
t.t-lfX
937
.9,1H
.113353
.0,1413
59. J
59.1
.1671).!
,U,'J
;^i;j;;
ii
.1341"
'3I<3
930
.03471
5'J.t
. idNtfi
3 LW
.twij
.' >'.'.l
0.940
0.03530
59,1
0. iM&l
U.'J
. ;('/,u
"
n 1 II 1 H
94T
.942
.9-13
! 03648
.03707
50.0
. I6*)5ij
. l6()H |
,1'Mt
3 A"
,W
:K!IJ;!
.O'. t
.13331
.1,1304
9-14
.0376(1
5H,9
, 1701(1
^yji't
it''w
i '3^5"
0-945
0.03825
189
0, l?o,|H
I'O
,. H'i"*y
('.
,946
.03884
58io
. 17080
ll''o
'MdKiM
'-/M
' 1 Ml/
947
.9-18
.039.1,1
.04001
.04060
58,8
58,8
.1711.1
.1714-1
.17176
ii
;lf^
"7v*
,I3!70
.1.11-1.1
0.950
0.04119
58,7
o,iy,'oH
;).', i
ij.M'-dti
j'in
M M'M)
u
oo Inn nil ii
W Fu'
Ufl IOC Qlt K
: F /'
lou tin ml u
w Fd*
lot) cio 0tl u
of Hyperbolic 'KuncliouH.
u log alnli u
.'XM
tX 'I
1, 000
u
.n.SIIJ
.littJIO
0.of.|.W
O.U70II
log Inn il u
,<i8,o
57,')
57.'J
57.7
57.7
S7>*'
57.5
57.5
57.5
57..1
5W
57.J
57.-1
57.a
57.a
57,1
57.1
57,1
S7.0
M P w '
log co sli u
o, 17/08
.17.1'',!
.17757
1705,1
iH I?''
log sao
iHHoii
ifl.W
Oil II
.1J.7
3'l,7
33,0
3.1,"
33."
3.1.0
3.1. r
3.1.1
Fu'
lOQ Illtlll II
,871.11
.8/1.17
."7533
.87708
.8773.1
.877.18
.8778.1
0,87807
. 878.1 J
.878.17
.87881
.87006'
.87055
,H8oo.i
.HHojH
.8Hm
.Krti.|
log tin oil u
.'(,,1
a 5.0
J5.8
J5.7.
asls
35.5
js!!i
25.1
2.|,5
a.1.3
a.i,a
log oolli u
.1^53
0.1.^.7
. ufiyi
.U50.I
.133*'7
0.12,117
.131,13
.iwtH
.l-MUI
.11876
. 1 1853
o.nH.-a
SMITHSONIAN
Logarithms of Hyperbolic Functions.
u
log sinh u
.*
log cosh u
a Fo'
loo tanh u
Fa'
lou ooth n
1. 000
0.0701
57,o
0.18839
33,
9.88[72
23,9
0.11828
.001
.07068
57,o
. 18872
33,
.88i9f
23,9
. 1 180.1
.002
.0712
57,o
. 18905
33,1
.88220
23.8
.11780
.003
.0718
56,9
- 18938
33,1
.8824,
23,
.11756
.004
.07239
.18971
33,1
.88268
23,8
.11732
1.005
0.07296
56,9
0.19004
33,2
9.88291
23,7
0.11709
.006
07353
56,8
.19038
33,2
.88315
23,7
.11685
.007
.07410
56,8
.19071
33,2
.88339
23, <~
. t tOfii
.008
.07466
56,8
. 19104
33,2
.88362
23,f
.11638
.009
.07523
56,7
- I8I37
33,2
.88386
23,5
.11614
1. 010
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
. 1 1407
1.015
0.07863
56,6
0.19337
33,3
9.88526
23,2
0.11474
.016
.0792C
56,5
. 19370
33,4
.88549
23,2
.11451
.017
.07976
56,5
. 19404
33,4
.88572
23, T
. 1 1428
.018
.08033
56,5
. 19437
33,4
-88595
23,1
. 1 1405
.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
- I957I
33,5
.88687
22,9
JI 3 r 3
.023
.08315
56,3
.19604
33,5
.88710
22,8
. t 1290
.024
.08371
56,3
.10638
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
.H109
.028
.08596
56,2
. 19772
33,6
.88824
22,6
.11176
.029
.08652
56,1
.19806
33,6
.88846
22,6
.11154
1.030
0.08708
56,i
o. 19839
33,6
9.88869
22,5
O.TII3I
.031
.08764
56,1
. 19873
33,6
.88891
22,5
.032
.08820
56,1
.19906
33,6
.88914
22,4
! 1 1086
-033
.08876
56,0
. 19940
33,7
.88936
22,4
.11064
-034
.08932
56,0
.19974
-33,7
.88959
22,3
.11041
1-035
0.08988
56,0
0,20007
33,7
9.88981
22,3
o.noiy
.036
.09044
55,9
.20041
33,7
.89003
22,2
, 10997
037
.038
.09100
.09156
55,9
55,9
.20075
.20109
33,7
33,7
.89025
.89048
22,2
22,1
. 10975
10952
.039
.09312
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
,ioS8f)
.042
043
09379
.09435
55,8
55,7
.20244
.20278
33,8
33,8
.89136
.89158
22,0
21,9
. 10864
. 10842
.044
.09491
55,7
.20311
33,9
.89180
21,9
.10820
1.045
.046
.047
.048
.049
0.09547
.09602
.09658
' .09714
.09769
55,7
55,7
55,6
55,6
55,6
0.20345
.20379
.20413
.20447
.20481
33,9
33,9
33,9
33,9
33,9
9.89201
.89223
.89245
.89267
.89288
21,8
21,8
21,7
21,7
21,6
0.10799
. 10777
. 10755
. 10733
. 10712
1.050
0.09825
55,6
0.20515
34,o
9.89310
21,6
0.10690
U
oo tan gd u
W
SBC Qti U
* Fu'
DO sin oil u
IV
og ota git u
SMITHSONIAN TABLES """*
40
Logarithms of Hyperbolic Functions.
u
loo sinli tt
(u Fu'
loa cosh u
"F '
loa tiinh u
"V
[OP GOtll II
1 .050
0.00825
55,6
0.20515
34.0
9.893IO
21,6
o.iofxjo
.051
.00880
55,5
.20540
34,0
89331
21,6
. loto)
052
09936
55,5
.20583
34,0
89353
21,5
. 10647
053
.00991
55,5
.20617
34,0
89375
21,5
. 10625
"54
.10047
55,4
.20651
34,o
.89396
21,4
. io4
i .055
056
O. IOI02
.10158
55,4
55,4
o . 20685
.20710
34,0
34,1
9.89417
.89439
21,4
21,3
0,10583
. 10561
'058
. I02I3
. 10268
55,4
55,3
.20753
.20787
34,1
34,1
. 894fio
.89481
21,3
21,2
- 105.10
-10519
-059
. 10324
55,3
. 2082 i
34,1
.89502
21,2
, 10498
1 .060
.Of it
. 062
.063
.064
0.10370
10434
. 10489
10545
.10600
55.3
55,3
55,2
55.2
55,2
0.20855
.20880
. 20924
.20958
,20992
34,1
34,1
34,2
34,2
34,2
0-89524
89545
.89566
.89587
.89608
21,2
21,1
21,1
2I.O
2I,O
0.10476
-10455
. 10434
* 104 13
, 10392
1.065
.066
0.10655
.10710
55, 1
55,1
0.21026
.21060
34,2
34,2
9.80620
. 89650
2O,0
20,9
0.10371
. 10350
.067
.068
. 10765
. 10820
55,1
55>i
.21094
.21129
34,2
34,3
.89671
.89692
20,9
20,8
10329
. 10308
-069
. 10875
55,0
.21163
34,3
.89712
20,8
. 10288
1.070
o. 10930
55,0
0.21197
34,3
9.89733
2O,7
0.10267
.071
. 10985
55,o
.21232
34,3
.80754
2O,7
. 10246
.072
. i 1040
55,0
.21266
34,3
2O.6
. 10226
-073
.11095
54,9
.21300
34,3
.89705
20,6
. 10205
.074
.11150
54,9
.21335
34,4
,89816
20,6
. 10184
1.075
, 076
0,11205
.11260
54,9
54,9
0.21369
.21403
34,4
34,4
9-89836
.89857
20,5
20,5
0.10164
-10143
077
.078
H3I5
i 1370
54,8
54,8
.21438
.21472
34,4
34,4
.80877
.80898
20,4
20,4
.1012,1
.10102
.079
. i 1424
54,8
.21507
34,4
.89918
20,3
. 10082
r.o8o
o.i 1479
54,8
0.21541
34,4
9.80938
20,1
O. tOOf>2
.081
.082
.083
,084
.11534
.11589
. i 1643
. i 1698
54,7
54,7
54,7
54,7
21575
.21(110
.21644
.21679
34,5
34,5
34,5
34,5
.89959
.89970
89990
.90019
20,3
20,2
2O,2
2O,1
. IOO.(I
,10021
. 1000 1
.09981
1.085
.086
-087
O.H753
. i 1807
. 1 1862
sl',6
54,6
0.21713
.21748
.21782
34,5
34,5
34."
9-900J9
.00059
.90079
2O, I
2O,1
20,0
o.oo<Xii
. 0994 1
.01)021
* 088
..11916
54,5
.21817
3 -'1,6
. cjoow
2O.O
.OOOOl
.089
.11971
54,5
.21852
34,6
.90119
19,9
.09881
T ,O(JO
o. 12025
54,5
0.21886
34,6
0.00139
19,9
0.09861
, 09 1
. 12080
54,5
.21921
34,6
.90159
19,9
.00841
092
.12134
54,4
.21955
34,6
.90179
19,8
.01)821
-093
. 12189
54,4
.21990
34,7
.90199
10,8
.09801
094
. 12243
54,4
. 22025
34,7
.90218
19,7
.09782
1.095
o. 12298
54,4
0.22059
34,7
9,90238
19,7
0.09762
. 096
. 12352
54,4
. 22094
34,7
.90258
10.6
.09742
-"97
.098
. 12406
. 12461
54,3
5-1,3
,22129
.22164
34,7
34,7
.00277
.90207
19.6
.09723
.09703
099
.12515
54,3
.22198
34,7
-90317
I&5
.09683
1 . 100
o. 12569
54,3
0.22233
34.H
9-003.16
19,5
0.09664
11
an Inn nil u
<> Fo'
on sec ad u
"Fo'
oa sin gd 11
Fo'
oa cso 0(1 u
SMITHSONIAN
Logarithms of Ilypcrliolii: K
u
Ion si nil u
W
I . I Oil
o.iusft)
5-1
,101
J^r'jj
5-1
. 103
JJ73H
M
. 10,|
.1-786
5-1
1. 105
O.UR-IO
5-1
. I(JO'
, i JiSij-i
5-1
.107
.UiO-ltS
5-1
.108
. i;f(M)-!
5-1
. my
. 13050
5-1
I , 1 1C.
0,1,1111
5-1.
.in
'3 '''5
5-1.
. MJ
. 13218
M,
.113
.13-7^
53.
.11-1
-KM- 1 ''
53,
1.115
(M;tfr>
53.
.116
- 13-13-1
53.
!n8
.'35-I- 1
53!
.ny
M5i,X>
53,
1,120
o, 136-11)
53,
, 121
.13703
<M,
,\2
. 13757
53,
,12,1
. 1386.]
53,
1 . 125
0.13018
53.
. 126
'3!)7-!
53,'
.127
MO25
53, (
,12K
- 1. 1079
53,'
.129
i.| ".13
53,'
1 . 130
o. i.|iH()
53,
.131
,i.|a,|o
53,.
.1,12
M-U1
53,.
-1,13
- r-13.17
53,.
I3'1
.i.Uoo
53..
I 135
o. i,|,|5.i
53,
, I, 16
.1-1507
53,.
.1,17
i>| 560
53,.
-138
.i.|6[.|
53,.
.130
l -W>?
53,;
i , r.io
0.14720
53,.'
.ij|i
.I.I77-I
53J
, i.|3
. i.[Mj7
.U.I
1-13
. i.|8f)
53.3
. 1.1-1
- M93-I
53,-
I.MS
o. 14087
53,-
. i.|6
.150.10
53,-
.1-17
- ISOM3
53,-
,L|K
.I5i.|6
. IAV
.1J2(X)
M! I
1.150
0.15253
5,1,1
u
OB tan ml ii
w Fo'
Ion coih ii
.-'3353
-MJi.lt'
,,M'iO!
DO inu uil u
lull tnnli u
.n,s
.1 I.K
3 I,' 1
,t5..|
.15,5
r,'
,'JHrfi/
IUD iln o'l ti
."'13.1
. ">.-:*.!
F,' I OSJ CM) (Hi M
SMITHHOHIAN TAHLKU
Logarilhmt) of Hyperbolic Functions.
II
lotl Slllll U
w Fu'
lau oosli u
wF '
loo tnnh u
a F u '
lOQ COlll U
1 . 150
(>. 1535,1
5.1.1
().33'J*)
35,5
(>,c>l;j()2
17,6
0.08738
. 1,11
. 1530"
53. 1
,a.|u*!0'
35,5
,<Jlj8n
17,6
.08720
. t, 1 ;.!
1535!)
5.1. i
.a,|0l
35.5
9'2()7
17,5
.08703
- 1.13
.IMU
5.W*
.a-HW
35,6
-'.)I315
17,5
.08(185
- 15-1
. 15,1(15
53.0
3<|I3.1
35,6
-9133- 1
17,5
.08668
1 l.'iS
o. 155 iH
5.1,0
o.a.|i(i
.15,6
<>!)! 350
17,4
o, 08(150
. ISO
.15571
53,0
.a-iaai
35,6
UI367
i?>-l
.086,13
.'57
, 15(14. i
5.1,0
.3.| AW
35,6
.<)i,l8s
i?,3
.08615
. i.<i8
- I5(>77
5-VJ
..!.|i!75
35,6
.(>i.|oa
17,3
.08508
. i.iu
- 157,30
5-VJ
.3.1311
36,6
.)i-IM)
17,3
.08581
I . IfXt
o. 15783
5-',<>
o.2.|3-|6
35,7
t).t)i.|36
17.2
0.08564
. Kit
. 1583(1
5-!,i)
.2-I.1H3
35,7
UM5-I
i?,^
.08546
. 10.!
. 15888
5-J.*)
.i!.MiK
35,7
.91-171
17,2
.08539
. ld,1
WM
5AH
a.1'153
35,7
.yi.-|8
I7,i
.08512
, KM
15994
.W.8
.3.|.|8i)
35,7
91505
17,1
.08495
I . 165
O, 16047
.W,K
0.2,|SZS
35,7
9-91522
I7,i
0.08478
,100
. KilOO
5'A8
.3,| 5(W
35,7
-9'S.W
17,0
.08461
.107
. I(!I52
52,7
.a.|S!)ti
35,
.91556'
17,0
.oH.|.|.|
. io8
. I (1.305
5A7
.2,|(3
35.H
-9I573
17,0
.08427
, Hv)
. 16258
Sa,7
.a^ifW
35,H
.yisyo
16,9
.08410
I, 170
o* (6311
5^,7
0.3.170J
35,
9.91607
I'M)
0.08303
.171
. 1(1,1(13
52,7
.3.17,1!)
35,"
.fjK'i.M
I'M)
.08376"
.172
. i6.| K)
S^,(i
.3.1775
35,8
.916-1 r
16,8
.08359
17.1
. I(I,|(K>
53,6
,2.1811
3S.
-91658
16,8
.08342
.17,1
. rdSJi
S2,(i
.2.1847
35,<J
.9167,1
16,8
.08326
I '"75
0. HI57-I
52.6
o.J.iHW.1
35.U
f>.()ifji
16,7
0,08300
. 17(1
. Krfijfj
52,6
.a-wii)
35,!>
.01708
16,7
.oHay'a
.177
. I(rfi7(>
53.5
.a.|yM
35,9
.91724
16,7
.08276
.178
. i(>7,ir
5-'.5
.a-iy^i
3S,0
.91741
!(),()
.08559
.17!)
. K.7H-I
53,5
. 2502(1
35,0
OI75N
1(1,6
.082,1 a
1.180
o. i6H,Ki
58,5
o.^sofu
35,9
9'9177-t
16,6
0.08226
.iHi
. i()HKy
53,5
. 251.11 j8
35,<;
.91791
if',5
.08209
.lj
. I<H),| I
52,.|
.35134
36,0
,(jiHo7
16,5
.08103
.IH.1
. ltH)t).\
SM
.25170
3(1,0
,(ji834
16,4
.08176'
.m.|
. 170.16
Sa,.|
.agaofi
3(1,0
. 01840
l(',4
.08160
1 . 1S
0. !70<J<)
53,4
0.253-12
36,0
{).9iH57
I'M
0.08143
.180
.17151
S3,.l
.25278
3(1,0
- 9^73
16,3
.08127
.187
. 1 7^0,1
S3.3
.2531-1
36.0
.OiHKij
16,3
.08111
.inn
. ijasf*
5^,3
.25350
36,0
.9i!X)6
16,3
.08004
.IJ
.1730H
5.3
-253M
3^1
.91932
if), 3
.08078
i . i<ja
o. i7,lfV)
53.3
0,25422
30,1
U-9MJ3B
16,2
0.08062
,iiji
-I7-H3
53,3
3S.|5
3f',l
.9I9M
I(),2
,o8tt|6
, MM
- I7'I''S
53,3
35,|(>|
36, 1
9197"
ifi,a
.08030
MJ3
- 17517
5^,3
.35530
36', I
.9M)87
i(i,t
.08013
MM
. i75Ciy
5i!,3
.3556?
3f>,l
.92003
1 6, i
.07907
1 lOS
0.176^1
52,2
0,25003
36,1
o.i^mo
16,1
0.07081
. uX>
, 17074
53,^
.25639
36,3
.92035
lfi,0
.07905
.197
. 17726
5^,3
.25675
3(1,3
.93051
lf),0
.07949
,108
. 17778
53,1
.25711
36,2
.93007
1 6,0
07933
.199
. 17830
52, t
.357-17
36,2
,92083
15.9
.07917
t.iicx)
0.17883
52,1
0.25784
3(i.3
p. 92099
15,9
0,07001
u
loo Inn ml u
W Po'
lOO 100 Ql! U
w fV
log itn gd u
w F</
loDotogdu
43
Logarithms of Hyperbolic Functions.
u
loo slnh u
10 FO
Ion cosh
u Fu'
Ion tnnh u
IU CO III U
I.20C
0.1788,
5-
0.257
3V
O.O.MKJ*
1 . ! i.f
U.O/i.d
.20
- 1793-
52
.258
,if
.|).tl .
1;
.o; 1 . 1 ^
I
,20;
1 7o8<
5-
.258
.if
.<).;i, Ii
1-
.o;'8/ t
1
.20,1
.' 1803*
52
.25*11
3f
,M.M.|(
l.'ii'
"/''\ ; i.
.20.
,18090
52
.259-
31
.9.!id~
'
.M7H.IM
1.205
o. 18142
52
o.asyf
3<
9.i).ri7i L
';.
",n;'8, ; ..
.206
.18194
5-3
.lifXK
3'
.1)2 I'M
';>
.11^17
.207
. i824(
53
.2(10.
.1'
.().!.!(>;
' '
II//IM
,20$
. 18298
51
. 2(>07,
3'
.1)2.!. !5
l.'i
n /77 t ;
.209
. 18350
51
.2611
36
.!WJ4
i;i
.n;7i^'i
1,210
0.18402
51
0,2(114
,1"
I). 1 ).'.!;
l.'i
""/'/' II
.211
- IS454
51
.2018
.<).',.'/
l. ! )
I
.212
. 18506
5r,
,2621
36,'
.<i,;.:8
l.'i
"''/'[{
[
.213
.18558
51,
.2625
36,.
,(),!(!
.uvtnj>{
.21.]
. 18610
5i
. 2629
iwin
l. f i
.M/l^,,
I.2I5
o. 18662
51,
0.2632
3'
),<).! u
l.'i.
n.tvirf."
.216
.187.3
51,
,2636
36,.
'' ! 34
l.'i.
.ilVdiii
.217
. 18765
5^i
.2640
id,.
,i).Mfi,
,d''iVi
.218
.18817
.2643
,Vv
.92.17'
l.'i.,
1 ,/.,,",,
.219
. 18869
51,
36,
.n;-.'^i
1.220
0.18920
sr,
0.20511
36,
<).i)J,|[
i;i.
o . i;'.-;i f i
.221
. 18972
51,
.26547
3'V
1 i.
.222
, 19024
51,7
.26583
36,
.gJ-44'
1 i.
jc'ii/n't
.223
- 19075
51,7
.26621
36,
.0.145'
1 i.
n /';i'!4
.224
.19127
51,7
. 2(>65(
3'',
!)-!- 17
l.'i.
1 . 225
0.19179
5 1/
0.26(M)3
at\j
)j.tj..|(
u ii-.'i
.226
. 19230
51,6
.2(172!
3 ( >i,
.g,!;in[
l.'i.
' t y/l, r \
.227
. 10282
51,6
. 267(16
16 (
I ; s i
',,',.
.228
- 19334
S',6
.26802
'.(,'(,
*O '''' 1 1
' ', ,
. 229
19385
51,6
.26831)
36/1
iiwsV*
liiiu
-''; ; i /i
1.230
0.194,17
51,5
0.2687(1
3'','i
o.ost'i
1(|
.231
, 19488
Si.5
.2(x)ij
{d (>
.'o"'i"'(
i M
' .' 'I
1
.232
- 19540
5i,5
.26940
j|(,}i
iiJJ'iiM
t'n
"i ' ' i
2,13
10591
51,5
.26985
36,6
!o!'fy
III
, i,^ |i 9
-234
- 19643
51,5
.'WU2
,)6,6
!|jJf.M
M>i
'''/S!
1-235
0.19694
51,5
0.27059
I' 1 7
.
t ,
,2,l6
. 19746
51,-
. J7(M)~,
V>V
'o''ii"ii
If ^J
O i MV {'Mi
.237
.238
- '9797
.10848
51,.
51,4
.'#!&!
36.7
.(),!' 1(1 Ji
li"'
14,;-
1 I f '
' '/ ,1 'i^ ^
-23')
.19900
51,4
.-7205
!vs?
!!!l ; (-)i
i ;.,
i4,J'
-0X3'!'
1.240
O.I995I
5M
0,272,12
3' >,7
(),iW(kj
1 1 V
. 2.| I
.20003
5',4
. 27279
l6 7
'o"" ,
HI/
' '"'"
.242
243
.244
.20054
.20105
,2015?
51.3
51,3
.-'7,1 1 <J
27353
.27389
36,7
36,8
B5
M!O
.M/r'7'l
.U/,^l,!
245
. 246
0.20208
. 20259
51,3
51,3
0.27426
36,8
!) ';;-:?'i
I4,li
n.,,7,,8
.247
.248
.20,110
. 20362
51,2
51,2
.2749!)
;|!]HM
14.5
"/'''?! 1
.249
.20413
51,2
2757.1
ii'Jn
.'ijl'840
'1.4
llrii'o ;
1.250
0.20464
51,2
0.27(5 10
3'',8
f ^
~-.. ,...-._.,
*" i-'f
1 H 1I L I
u,o7i>|'i
m
u loo tan oil ii 1 w FO' I
"-"" " "" -*
so 800 gel ii
~" "
F'
aln ud ii
... r,, (
a oia ail u
SMITHSONIAN TAHI. """"""' ' ' ' ' ' ''" ' i n^.,.,,,..,,,,,;,*
of Hyperbolic Functions.
-7X
.-7*
. -70
..(My
..:HM
.JN.(
t ,,;<jo
I. JOS
...MX,
- -107
I., 100
loo slnli u
. -< iji i ,'i
..rniiiH
too Inn ad u
.'i'..
.SL-
Si, n
,'iO.li
ijo!, 1 )
MS
5"rl
Ing ooili u
0. .!/'<)/')
..(Stiifi
loo tea ail 11
F u '
.17..1
,17,.l
.17..!
,17,.l
.17..!
.17.1
-17..I
"IV
Ion Unit u
M-M5
.'MSN
(MW5.17
a aln ad u
1,1,7
1.1.5
1.1.5
1.1.5
".1,5
1.1,0
IV
log oolh u
-('71. i
.0711
.0710
0.0707.
.uyofx
.uyuj<
,070.1.
.1X1851
.1*755
.0(1701
O.lrfrfj'il
0.1X1,163
no 010 oil u
SMITHDONIAN TAHLEH
Logarithms of Hyperbolic Kuuctioim.
.25505
ino Inn oil u
SMITHSONIAN TAIIUO
! of Hyperbolic Functions.
,(*;
.en
log nlnh it
,;< ft
J7.WS
0. ,!/,(,)
-I'J.
l(i[) onili 11
..1,11-17
u log (an ml u w F, log mo ad tl u tj m u ii n gd u
lu Innli it
,lH,l
ilKi
-1H..1
W5.W
-W-I.W4
11.
II,
II,
It,
11, (
11,5
11,5
".5
11,.
M,,
"
n,.
"?
11,3
n 1.1
11, -J
11,2
11,1
11,1
11,1
11,1
11,0
11,0
11,0
11,0
11,0
KMJ
HMJ
10,8
IO!K
10,8
10.7
10,7
10.7
10,7
i o/i
10,6
IV
loo oolli ii
0.05788
.i>S77<
.115705
'57M
-05/-.I- 1
.05707
051150
0.05(110'
.05(105
055'J-I
.('5571
0.055(10
.055.18
05,^7
,05516'
0.05505
.05.10,1
.05,18,1
.05.1(11
0.05.150
054,1'J
.05,1 ~>H
.05-117
.0537.1
.05.1*1,1
.05331
.05,1 no
.05,110
0.051-88
Ofl CIO (til U
9MITIIOONI*N T^HLKfl
Logarithms of Hyperbolic Functions.
u
loo slnh u
- F '
-
IOQ cosh u
to F(
loa tnnh
10 Fo'
loo coth
1,40:
0.2797^
49,
o.332f
38
9-947
IO
o.ogjB
.40
.2802..
49,c
33300
38
-947
K
.oga?
.402
.2807;
49,c
3333
38
9-I7,
K
,(>52<
I
-403
.28121
49,c
3337
38
947-
K
.0535
.404
.28170
49.C
-3341
38
9-175
10
.053.
1.405
0.28219
49,0
0.3345
38
9-947<
TO
0.05-M
.406
.28268
49,0
.3349
38
-9477
10
.ogj-
.407
-28317
49,0
-3353
38
-9478
IO
. us-' i
.408
.28366
49,o
-3357
38
9179
IO,.
.OS JO.
.409
.28415
48,9
.3360
38
.9480
IO,.
-0519
1.410
0.28464
48,9
0.3364
38
9.9481
IO,.
0.0518
.411
.28512
48,9
-3368
38
.9482
IO,.
.11517.
.412
.28561
48,9
3372
38
.9483
io,;
.0510;
-413
.28610
48,9
.3376
38
.9484
10
.414
.28659
48,9
.338o
38
10,
,ogi.'
1.415
0.28708
48,9
0.33840
38,
9-94868
10,
0.051,1
.416
.28757
48,9
.33878
38,
.9487
10,
.ogu
.417
.28806
48.9
-33917
38,
.94889
10,
.051 1
.418
-28855
48,8
33956
38,
.94899
10,
.05 10
.419
.28503
48,8
.3399-
38,
-94909
10,
05001
1.420
0.28952
48,8
0-34033
38,6
9.949I9
10,
o,o*ioHi
.421
.29001
48,8
-34071
38.C
.94930
IO,
.()57<
.422
.29050
48,8
34110
38,
94940
10,
.ogfK>
423
.29099
48,8
.34149
38,7
94950
10,
-'
05050
.424
.29147
48,8
.34187
38,7
.94960
10,
.(55040
.427
.428
.429
0.29196
.29245
,29294
-29342
.29391
48,8
48,8
48,7
48,7
48,7
0.34226
-34265
.34304
34342
.34381
38,7
38,7
38,7
38,7
38,7
9.94970
.94980
-94990
95000
95010
10,1
TO, I
IO,O
1 0,0
10,0
0.050,10
.051 wo
.05010
,0500x1
1.430
-431
-432
433
-434
0.29440
.29489
-29537
.29586
-29635
48,7
48,7
48.7
48,7
48,7
0.34420
34458
34497
34536
-34575
38,7
38,7
38.7
38,8
38,8
9-95020
.95030
.95040
.95050
.95060
10,0
1 0,0
9,9
9,9
9,9
0.04080
.0-197,0
.04950
.04940
1-435
-436
437
43
-439
0.29683
-29732
.29781
.29829
.29878
48,7
48,6
48,6
48,6
48,6
0.34613
-34652
3469:
34730
34769
38,8
38,8
38,8
38,8
38,8
9.95070
.95080
.95090
.95099
.95109
9,9
9.9
Q,H
0.04030
. 049,10
.04910
.U.| WO I
.04 Ho i
1.440
-441
.442
443
.444
0.29926
.29975
.30024
.30072
.30121
48,6
48,6
48,6
48,6
48,6
0.34807
.34846
-34885
.34924
.34963
38,8
38,8
38,8
38,8
38,8
.95139
.95M8
95158
9,8
9,7
9,7
9,7
o.a|8Hi
.04871
,o.|H6r
.04853
.04843
1.445
.446
447
-448
.449
0.30169
.30218
.30266
30315
-30363
48,5
48,5
48,5
48,5
48,5
0.35002
35040
35079
-35II8
35157
38,9
38,9
38,9
38,9
38,9
9.95T68
-95177
.95187
-95197
.95206
9,7
9,7
9/J
9,6
0.04832 1
. 04823 1
04813 f
,04803
.04704
1-450
' 304 12
48,5
0.35196
38,9
9.95216
or
On i **Q i
^^^^^^m*tmm
o tan gdii
.
*
Fo' 1
- . 1
^"^~mm^m
)Q SBO Oil U
'
i
"Fo'
w iS
" - ~ .
Bin ad u
ji. . 1_
ji
.04/04
010 ad u 1
Logarithms of Hyperbolic Functions.
11
loo sliili u
W Fo'
log cosh 11
w
IOQ la nil u
.F U '
Ion cotlv u
1.450
0.30412
48,5
0.35106
18, y
9-95236
0,6
0.04784
-151
. 3046t
48,5
- 35235
3-i;
.953J5
9/i
('4775
45 -3
.30509
48,5
.35274
38,9
.95235
9,5
.047(15
453
-30557
48,5
.35313
.18,9
95245
9,5
.04755
-454
,3oOo(
48,4
35352
38,9
9525-
9,5
.04746
1.455
0.30654
48,4
0.35391
38,9
9-95264
9,5
0.04736
456
.30703
4,<
.35429
39,o
.95273
9.5
.047-7
457
.30751
48,4
354<>8
39,o
.95283
9,5
.04717
.458
30799
48,,
.35507.
39,o
.95292
9..
.04708
459
.308-18
48,4
355-1''
39,o
-953" 8
04(Hjo
1.460
0.30896
48,,
0.35585
39,o
9-953II
<V
o,04<>8(.)
.461
.30945
48,4
35624
39,0
95320
9,4
.04(180
. 462
30003
48,,
.35663
,19,0
95330
9,4
.04670
463
.31041
48,3
35702
39,o
95339
9,3
.ai6(ii
-464
.31000
4,3
35741
39.O
9534
,04652
1.465
.466
.467
0.31138
.31186
-31235
48,3
48,3
48,3
IS
39 ,o
39,0
39,0
9.95358
.95367
-95.V6
9.3
9,3
9,3
0.04642
.04633
.468
.31283
48,3
. 35897
39, f
.95385
9,2
.04615
469
-31331
48,3
.35937
39, t
-95395
9,2
.04(105
1.470
471
.472
0.31379
.31428
.31476
48,3
48,3
48,3
0.35976
.36054
39,1
39,1
39,1
9-95-104
.95413
-95422
9,2
0,2
0,0451X1
.04587
473
474
31524
.31572
48,2
48,2
36093
.36132
39,1
39.1
* 954 3 i
95441
9,2
9,1
04 569
.04559
1.475
-476
.477
479
0,31621
31669
-3I7I7
.31765
.31814
48,2
48,2
48,2
0.36171
.36210
36249
.36388
,36328
39.1
39,1
3ft i
3ft i
9-95450
95459
-95477
.05486
9,r
9.1
9,1
9,1
9,0
0.04550
,04541
.04332
-04523
,04514
1.480
.481
.482
483
.484
0.31862
.31910
31958
.32006
32054
48,2
'18,2
<l8,2
48,1
48,1
o. 36367
.3f>4o6
.36484
.36523
39,2
39, a
39,2
39,2
39,3
9-95495
.95504
-955M
.95522
95531
9,f>
9.0
0.04505
t>4496
.0.(478
'04469
1.485
.486
.487
.488
489
0.32102
32151
.32199
.32247
32295
48,1
48,1
48,1
48,1
48,1
0.36563
. 36(102
,36641
.36680
36719
39,2
39,2
39,2
39,2
39.3
95540
95549
.95558
.95567
95576
8,9
8,9
8,9
8,9
.04451
.04442
-0-1433
.04,124
1.490
491
492
493
494
0.32343
32391
32439
.32487
32535
48,1
48,1
48,1
48,0
48,0
0.36759
.36798
.36837
36876
.36916
39.2
39,2
39.2
39,3
39,3
' -95593
.95602
.95620
8,8
8,8
8,8
8^8
0.04416
.04407
04389
.04380
1.495
.496
-497
.498
.499
0.32583
.32631
.32679
.32727
.32775
48,0
4H,o
48,0
48,0
48,0
0.36955
-3699-1
37033
.37073
,37112
39.3
39,3
39,3
39,3
39,3
9.95628
.95637
.95646
.95655
.95663
8,8
8,7
8,7
8,7
8,7
0.04373
.04363
04354
04345
.04337
1.500
0.32833
48,0
0.37I5I
39,3
9.05672
8,7
0.04328
u 1
oo Ian pit u
" Fo'
oo eo ad u
w Fo'
lovdnodi.'
W Fo*
ICflCIO Oil U
Logarithms of Ilyperliolu: Fimrliniiii.
SMITHflONIflN TflOLKO
Logarithms o Hyperbolic Functions.
u
loo slnh U
w Fo'
log cosli u
<" Fo'
lop liinh u
w Fo'
tOC GOlll U
i. 550
0.352H
47,5
O-39 1 .>()
39,7
9.1X1084
__
o. 03910
-551
.35258
47,5
.39166
39.7
.ofioyj
7,K
O39OM
SS2
.35306
47,5
. 39206
39,7
.96100
7,"
.0,3900
-55,1
.35353
47,5
.30243
39,7
.yfiioS
7,K
,ojH(V
-554
35401
47.5
.30^5
39,7
.96116
7,B
.038H4
r. 555
0.35448
'17,5
0.39325
39.7
9.1X1123
7,8
0.03877
556
.3540
47,5
.39365
39,7
.96131
7,7
.03869
-557
35543
47,5
.39404
39,7
.lX"39
7,7
.o;)86l
-558
35591
47,5
39444
39.7
96147
7,7
03853
559
.35038
47,5
.3948.1
39.7
.96154
7,7
.03846
1.560
0.35A86
47,<l
0.30524
39,8
9.96162
7,7
0.03838
.561
35733
47,'l
395(>3
39.H
.9(1170
7,7
.03830
.562
35780
47.-I
, 39603
39.H
96177
7,7
,OJ|8J3
.563
35828
47,4
. t VJ<M3
39,H
.96185
7,<>
.03815
-5f)4
.35875
47,'l
39683
3<>,H
96193
7,<>
,03807
I.56S
'0.35923
47.-I
0.30733
3ft
9.06200
7,6
0,03800
.566
35970
47,4
.39762
39,H
,96208
7,6
.03792
.567
.36017
47,4
. 3ySo2
3U.H
.96215
7,6
,03785
-568
.36065
47,4
.398.J2
3'j,n
9622,1
' 7,6
.03777
.5fi9
,36112
47,4
.30882
39,8
'(X3i
7,5
<W6y
1-570
0.36160
'17,<l
0,39921
39.B
9.*X>338
7,5
0,03762
-571
.36207
47,4
391)61
3tt
.96246
7,5
03754
572
.36254
47,3
.40001
39.H
.fX'253
7.5
03747
573
.36302
47,3
.4004:
30.8
.(/iafii
7.5
03730
574
.36349
47,3
,4aoHr
mo
.1X)268
7,5
.03732
r-575
0,36396
47,3
0.40121
30.0
Q.vCayG
7,5
0.03724
-576
.36444
47.3
.40161
39,9
.OT>23
7.4
.03717
-577
.36491
47,3
.40200
39,0
.X>29'
7,4
.03700
.578
.36538
47,3
.40240
30,9
.96298
7,4
.0,170*
5.79
.36585
47,3
.40280
30.9
.<Xi305
7,4
03fi!>5
1,580
0.36633
47,3
0.40320
39,U
9.<j63i3
7,4
0,03687
-S8i
.36680
47,3
.40360
39.U
.96320
7,4
.O3(>Ko
.582
.36727
47,3
.40,100
39,9
.fXW37
7,4
.03673
-58,1
.36775
-17,3
.40440
30,9
!X>3,3,1
7,3
.03665
.584
.36823
47,2
.40480
39,0
.06343
7,3
.03658
1.585
0,36869
47,2
0,40520
39,0
9- {X*34
7,3
0.03651
.586
.36916
47,2
.40560
30,0
tXi357
7,3
.0.5643
.587
.36064
47,2
.40599
30.9
t/i364
7,3
.03636
.588
37011
47,a
,40639
39,0
lXi37 1
7,3
.03^29
.589
.37058
47,3
.40679
40,0
.96379
7,3
.03621
I.S90
0.37105
47,2
0,40719
,(0,0
9.96386
7,2
0.0.1614
S9I
.37152
47,3
.40759
40,0
06303
7,'-3
.03607
592
.37200
47,2
.40799
40,0
.96400
7.2
.03fJOO
593
.37247
47,3
.40839
40,0
.96407
7,2
.03593
594
37204
47,2
.40879
.10,0
0415
7,2
0355
1-595
0. 373-1 1
47,3
o. 40910
'10,0
0,06422
7,2
0.03578
.596
.37388
47,2
.40959
40,0
.96429
7,2
03571
597
37435
'17, t
.40999
40,0
.96436
7,1
.03564
SUB
.37482
47,t
.41039
40,0
96-143
7,1
.03557
5P9
37530
47,1
.41070
40,0
.96450
7,1
.03550
i. 600
0.37577
47,i
o,4mo
40,0
9.96457
7,1
0.03543
u
log tan ad u
w Fo*
loo o ail u
H IV
lop tin oil u
IV
loo aio ait u
SMITHSONIAN TAB LEU
Logarithms of Hyperbolic Kimclioim,
1.600
.601
.602
.603
.604
1. 005
.606
.607
.608
.600
0.38048
.38095
.381.12
. .38189
.38236
0.38283
.38330
.38377
.38-124
.38.171
1.020
.621
.622
.623
,62,1
0.38518
.38565
.38612
1.623
.626
.627
.628
.620
.38846
.38893
.380-10
1.630
-631
.(132
633
.634
0.38987
300,14
.39081
.39128
39175
'OSS
.636
637
.638
.639
39315
.39362
.39.100
1.640
.641
.643
.643
.644
0.3WS6
39502
39540
30506
1.645
.646
.647
.648
.649
0.30690
.39736
.39783
39830
39877
SMITHtONIAN TftMLM
Logarithms of Hyperbolic Functions.
ii
loo el nh u
<o Fo <
log oosli u
*Fo'
loo tnnh LI
-FO'
Ion ootli ii
1.650
0.39923
46,8
0,43120
40,3
9.96795
6,
0.03205
.651
.39970
46,7
.43169
.06801
03199
.652
.40017
43209
40,.
.96808
.03192
.653
.40064
43250
.96814
.03186
.654
.40110
.43290
,</)820
.03180
1-655
0.40157
A<\7
0.43330
40,4
9.96827
6,,
0.03173
.656
.40204
43371
.96833
6,3
.03167
.657
.40251
4341 1
.96840
,03160
.658
.40297
43451
.9(1846
03"54
.659
.40344
43492
.96852
.03148
1. 660
0,40391
46,7
0-43532
40,,
9 96858
6,3
0.03142
.661
.662
40437
.40484
43573
.43613
196865
.96871
03135
.03120-
663
40531
.43653
.9687?
.03123
.664
40577
43694
.96883
6,2
.03117
1.665
.666
0.40624
.40671
46,7
46,6
0-43734
.43775
40,
9-96890
.96896
6,2
0.03110
.03104
.667
.668
.40717
.40764
438r5
.43856
. 96902
.96008
03099
.669
.40811
.43896
40,5
96915
03085
1.670
0.40857
46,6
0.43037
40,5
9-96921
6,2
0-03079
.671
.40904
43977
.96927
.03073
.672
.673
.40950
.40097
.44017
.44058
-96933
969.19
0,1
.03067
.03061
.674
.41044
.44099
.96945
.03055
1.675
/-_/-
0,41090
46,6
0.44139
40,5
9.96951
6,1
0.03049
.676
677
.678
679
-4II37
.41183
. .41230
.41277
.44179
.44:220
.44260
44301
.96957
.96964
.96970
.96976
.03043
. 03036
-03030
.03024
1.680
.681
.682
.683
0.41323
.41370
.41416
.41463
46,6
46,5
0.44341
.44383
.44422
.44463
40,5
9.96982
.96988
-96994
.97000
6,0
0.03018
.030:2
.03006
.03000
.684
.41509
.44503
.97006
.0299?}
1.685
.686
.687
.688
.689
0.41556
.41602
.41649
.41695
.41742
46,5
0.44544
.44585
.44625
.44666
-4-1706
40,5
40,6
9-97012
.97018
.97024
.97030
,97036
6,0
5,9
0.02988
.02982
.02976"
.02970
.02964
1.690
.691
.692
693
.694
0.41788
41835
-41881
.41928
.41974
0.44747
. .44787
.44828
.44869
.44P09
-
9-97o.|2
.97047
97053
97059
,97065
5,9
0.02958
02953
.02947
.02941
02935
1.695
.696
.697
.698
.699
0.42021
.42067
.42114
.42160
.42207
46,5
4(5,4
0-44950
.44900
45031
.45072
.45112
40,6
9.97071
.97077
.97083
.97089
.97094
5,9
S3
0.02920
.02923
.02917
.02911
.02906
1.700
0-42353
46,4
0-45153
40,6
9.97100
S3
o.oapoo
"
oo (an ail u
Fo'
oo aao ad u
IV
oo tin ad u
w Fo'
op 010 ad u
S3
Logarithms of Hyperbolic Function;).
0,43 i ft
-432-7
.4.127,1
43319
4335
Logarithms of Hyperbolic Functions.
II
loo a lull u
lt)(J OOlll LI
.w
loa Innli u
w IV
loa co Hi 11
1 . 7<io
0.44507
40,i
0.47191
10,9
9.97176
r > 1
o o'dM
75"
4401.1
-1 7 -M"
-97.l8a
sla
.0^)18
75.1
.'t'S
47.H3
.97.187
, 97,J9J
.02613
. 754
-I47M
47.154
-07397
!oa6i)3
1.755
.1.44707
4'M
0.47395
4"iO
9.9740J
5,3
0,02598
/,*''
44"-l'l
.1743"
.O7.|(>8
_()JR(IJ
;$
44 ( )3'>
-17477
974M
iojJH;
.75"
-1408.!
47550
'.ww
.02577
1.7(10
701
45074
4'M
O.47(HK)
.47(14 1
40,9
' -974.1.)
3,1
0.0:1572
,OJ5"7
,/iu
"15 '-'0
.4768.1
07-1.19
. 02 ij() I
763
,45i(>0
477~'-'
97444
.ojljijii
7(>4
.45-HJ
4776.1
4 ".o
97449
.02551
1.70.1
0.45J58
46, 1
o..|7Htt|
H,o
9-074S4
5,1
o.<u54(i
, "7(7
.7(18
45350
46,0
:: '^i:
97459
974' "4
.02541
I"**
4544-!
47-/HS
.97474
!o^526
1.770
0.45488
46,0
(>.48(Xty
41,0
9-9747'J
3,0
O.OJ^I
.771
455.14
,r|KO,'il)
.97481
.02516
77J
4Si>Ho
-I^HJI
.074^
.0:1511
77.1
.450.17
.4813^
.07404
.(WSOfi
774
1567,1
4^t?.l
97499
,0250 1
1.77.1
0-45719
46,0
0.4JI4
41,0
9.97S04
5.0
0.02406
1 / /
" *1 ft/"*)
i *l****i};l
uyjoo
.02401
777
.45810
.48^x1
.07514
77*1
.45856
4H.W7
io-MHi
. 779
4 590^
.48.178
.975^1
.02476
I. >','<.>
0.45948
46,0
0.48419
41,0
0.975^1)
4,9
0.02471
!7J
:?H4
.4^1040
,4(>oK(i
..[84(1(1
.4HJ01
.4858,)
075.14
97539
07544
07540
.02461
. 02456
.02451
1.78.1
"::S
45,9
0.48(124
.4HWK1
41,1
0.9755-1
97S50
4,0
0.02446
.02441
,787
,40^70
.4871)7
07564
.788
'4'i,l^'
.48748
,975(iH
,02433
1?HM
.4'^
, 48789
97573
.02437
I-7'J"
0.4(1408
45.9
0,4^830
41,1
9.07578
.1,8
O.OZJ32
-701
45454
.48871
075^3
.02417
7'W
,,\(}5M
.4891.)
.975HH
,02413
70.1
4^54^'
14895,)
07593
.0.1407
791
4059-i
4^W1
.97507
.0240,1
1-705
o , 46637
45.9
0.490.1S
41,1
9, 9760 J
4,H
OP 0,1398
7<Xi
, 46fiH3
.41x76
,97(ki7
.02393
<797
. 467,39
49' '7
.976 i a
0*188
-79H
4('775
-49 '50
-07617
.02,183
799
.(t(Hil
..IOWXI
-976JI
.02379
I. Boo
O..i6.%7
45.9
0.49^41
41.1
9.97(^6'
4,8
0,04374
u
oa tun ml u
MFfl'
OQ BOO Oil U
*> N
og iln od it
w To'
foooiaqdu
55
Lognrithmfi of Hyperbolic iMii.ctin.m.
0.4700/
.4)714-
.47'KH
472.14
47^79
I.Sl
.81
.81
.81
.81
15.8 (>,.|<XW
0-4755-1
.47600
.47646
1.8.10
.831
.832
8.13
.8.14
1-835
.836
.8.17
.838
.8.30
.48515
.48561
.48606
.48652
1.845
.846
.847
.848
.849
SMITHSONIAN
Logarithms of Hyperbolic Kuncliomi.
.K
-H5-
I.H55
i57
i.Mo
.Htii
.Hfu
l.H(>5
.'HI 17
.H/ft
.H77
i.HHn
.Mil
.HHy
.MHH
.Hiji
l.i/K)
log ttlnli u
I'WXS
-5'M.IO
. !i(tM jo
.,11 ofi;
O..SM.VI
on Inn u<l u
F,,'
15,'
45,5
45.5
15.S
-15.5
45,5
45,4
F u '
lug oosli u
ii.5i.VU
5MI.1
-Sl'l.'f'
.5>074
'5171(1
51757
.5.!"! 15
. 5-HI-I7
o.SJ.1.17
ci.5J5.l4
0.5 .17.11
.5.7'i.i
.52K.il
.5,1000
M|3
. 5.1 a 1 ; t
0.5.U7-I
OU 160 fl(I U
41,4
41.5
41,5
41,5
loa tnnli u
.07040
.070*11
0.07077
.07*^5
.97'/>.1
.fjHoo5
.f>tH,l
0.1,^057
oo tin oil u
*> Po'
4,1
4.1
loy colli ii
.ojnH
.(W1IC
O.IWI05
.0*1076
.0,1072
o.ojoa.i
.oaoiy
.(won
.0^007
,OI*WI
.01071
.01959
.01955
.01051
.oiy.|7
OD 010 ail u
SMITHNOHIAH
Logarithms of Hyperbolic Function;!.
of Hyperbolic KiiiicUons.
1 ,'A'i
.'At
''1,1
J.fHlO
U
lou nlnli u
..'i.'il.U
- SMS7
5577,1
0.5JW53
OB tan gd u
IS'
.1.1.1
IS. I
15.0
Inu 001 li u
SS'J.'i.S
5^75
.."I7t7
0-57335
57.177
57-1 "J
S750J
0.37511
no Rao oil u
" r,/
ir,K
H.B
w F,/
lou tanli ii
lOQBlllfllill
to {-V
.1,5
.1,5
3.-I
3.3
3.3
,1,2
3.2
3.3
w F,,'
Ion catli u
0.01758
.017,17
.017,1.1
.017.11
.01727
0.0173-1
.01 7 jo
.01717
.0171.1
.(11710
0.01706
0170,1
.01700
.01096
,01679
.0167(1
0.0167,1
.01659
0,01656
.0165.1
.OIO,|6'
.01617
.01(113
.01610
0.01607
.oidoi
01597
.0159,1
Inootoailti
8MITHHONIAH TftULCR
59
Logiti'ithm.4 of IlypcrholU: l-'uncli
0.5685;)
.50898
.56043
.56088
57033
loo Inn ail 11
SMITHSONIAN TABI.M
Logarithms of Hyperbolic Functions.
u
loa slnli u
0) FO'
IOQ cash u
u FO'
loo Ianh u
Fo'
lag coth u
2.05
0.58202
44,<
. ">0f>4 1
42,0
9.98560
2,9
0.01440
-05
.58246
.5JXJ83
98561
01437
.052
.5829
.59725
.yH"j6f
.01434
.053
58336
.59767
.<j8"jfiQ
,01431
-054
.5838
.59809
.98572
.01428
2.055
0.5842^"
44,9
0.59851
42,0
9.98575
2,9
0.01425
05f
.58471
.59893
OK57J-
-2,8
.01422
.057
.058
059
.585 if
.58561
,5S6of
-59935
59977
r 600 19
.98580
08583
.08586
.01420
.01417
.01414
2.060
.061
.062
.063
0.58650
.58695
-58740
.58785
.58830
44.9
0.60061
.60104
.6014^
,60188
. 60230
42,0
42,1
0-08589
.98592
.98595
98597
.98600
2,8
0.01411
.01408
,01405
.01403
.01400
2.065
.066
.067
.068
-069
0.58875
.58920
.59009
.59054
44,8
0.60272
.60314
.60356
.60308
.60440
42,1
g . 98603
.98606
,98609
.08611
.98614
2,8
0.01307
,01304
.01301
.01380
.01386
2.070
0.59099
44,8
0.60482
42,1
0.08617
2,8
0,01383
.071
.072
073
.59189
.59233
.59278
.60524
.60566
.60608
,60650
. 08620
. 08622
.98625
,08628
2,7
,01380
.01378
01375
.01372
2.075
.076
0.59323
.59368
44,8
0,60692
.60734
42,1
g. 0863 i
.08633
2,7
0,01360
,01367
.077
.078
.59413
59457
.60777
.60819
.98636
.01364,
079
-59502
.60861
.08642
01358
2.080
.081
.082
-083
.084
0-59547
59592
5037
.59681
.59726
44,8
0.60903
.60945
.60987
.61029
.61071
42,1
9.08644
.98647
.98650
.08652
. .98655
2,7
0.01356
.01353
.01350
.01348
01345
2.085
.086
.087
.088
.089
0.59771
.59816
.59861
59005
59950
44,8
0,61113
.61155
.61198
.61240
.61282
42, r
9.08658
.98660
.98663
.98(166
.98668
2,7
0,01342
,01340
01337
.01,134
.01332
2.090
.091
.092
093
.094
0-59995
.60040
.60085
.60129
.60174
44,8
0.61324
.61366
.61408
.61450
.61492
42,1
0.08671
.98674
.98676
.98679
.98682
2,7
2,6
O.OI.129
.01326
.01324
.01321
.01318
2.095
.096
.097
.098
.099
0.60219
.60261
.60308
.60353
,60398
44,8
0.61535
.61577
.61619
,6i66r
.61703
9.98684
.98687
.08600
.08692
08695
2,6
0.01316
-01313
.01310
.01308
.01303
2. .100
0.60443
44,8
0.61745
42,;'
0.08697
2,6
0.01303
U
Ian gd u
u FO'
sac gtl u
F u '
oa sin ad u
.V
op oso tnl 11
SMITHSONIAN TABLES
61
LognrithniH of Hyperbolic Functions.
u
|OQ Slllll 11
u Fo'
loo ciisli ii
" \\f
lull liinli u
. t ; .,'
1U COlll U
2. ICK
O.6044;
44,*
0.01741;
4-M
<). ( ^'J7
-'/'
11,111,10,1
.10
,101.
.(i048?
.0053-
44.7
.01787
.618,10
4A.I
']^''-!M
.(11,100
.103
.(10577
.(1187-
.1^4/11;,
.<l| ,'CJJi
.10.
.60622
.01914
.ift'itt
,UIJ)M
2.105
o.6o6Yif
44.7
O.OUJ50
,|.!.-!
OjjHym
.!/,
U.OU'-K)
.!()(
.6071 i
.011)98
,'X^'i.i
.01,187
.107
.6o;")C
,6.!040
,i>S; p l<>
,01 jH.(
.108
.60801
,6.!f)8,i
, i ly | fi
.tii.'Hj
,109
,60845
-6.M..'5
../!; -M
.<"J7y
2,110
0.60890
44,7
O.O.M07
4.:,.!
O.'A-'.f
.!,0
(>. 01.177
.III
.60935
,(..!'( 1O
.1 >*(/,:( t
-', .'i
.OU74
.112
.60979
,6.[.fS'
.^S^'.'H
.01 jyjt
.11.1
.61024
,(u ').!
'V/'.l I
.01. '{J
.114
.61069
.OJ.UO
"8; j ,n
.iiiJh?
2.II5
0.61114
44,7
O.f'J.tfH
.[.!,.)
i>.i>4i',((i
',;;
O.OI.'f,,|
.116
.61158
,Oj,|..'O
,().'i7,lH
,oi,(fij
.117
.'61203
.(U.|0',I
.'(8741
.Ol jr h ,j
.118
.61248
.Cupo.)
.'A' I.I
.ni,iji7
.119
.61292
.o.fMO
.o8;'4'.
01 .'ji,|
2.130
0.61337
44,7
0.6,158')
E ' '
I'n
o.o'iJM"
f.'i
M.OUijJ
.121
.61382
.(WO.U
.'A'.'il
,oij|9
.122
.61427
.6.107,1
.'A'fi.l
.01^17
.12,1
.61471
6J7'.'>
,1^17;;*!
.124
,61516
.(U7.H7
.ijft/.lM
,01^44
2.125
0.61561
44,7
0.0.-8(xi
,!,..
J.'^'Ol
J..1
O.OI.M9
.126
,12?
.61605
,61650
.O.r8i.!
:i;|Ii!
imj'u
.128
.61695
,0.!().tO
,'^M;'uS
, ( ,r r ''|j
.120
6i73y
.OJ909
.A'71
-1HWJ
2.130
0.61784
4-1,7
n. 03011
4-!,'!
. )l ,^y.l
'J.'i
lt.M|JJ7
.131
.61829
0305,1
,i^;';'d
J.'l
.i)IJ^4
.132
.61873
0,1005
.^'7;'8
.01, UJ
. M3
.61918
('.11.17
.i>H;'M|
.OUItj
M'l
61963
.0,1180
..^;-H,l
.OUI7
2.1,15
o. (12007
44,7
0,(i,t,!J.!
4-V!
O.oK/8-i
J..I
ii.iiui'
. MO
.62053
'M.;0.|
,f>^i''' { H
iouij
137
.62097
0,1,100
.<A'j"
.OU10
.138
.62141
,(i,i.(49
. <)M/<H
139
.62186
'''.UOl
I'.l ',.
'X'/'^'i
.01 j tos
2.140
0,6^31
44.6
0.0,l.f,Vt
4J,y
l>ilf v{., 1>S
J..I
O.nuoj
.141
.6.3.375
.03475
. i>SMi w t
Ol *iK)
.142
.62320
.o.KiiH
.'A'vc
"iiiitjH
1.13
62365
.O.t.'iOd
4-'il
[i>*W(tij
'(II 101
. 144
.62409
.(),1(H>!
'.\Wtiy
!mioj
2.145
.146
0.62.154
.62498
44,6
(I.O,10.|4
.0.1(^7
M
'^Sl
^
"'""IS
.147
.148
! 62588
, 0,l7-!9
0,1771
'!jw!-
!oi i,%
.140
.62632
,l>*i,'ll9
.on Mi
2.150
0,62677
44,6'
0.^3856'
|i!,.1
O.f^Jl
a..,
0.01179
u
a Inn (i du
w fu'
00 ion d'f 11
W fif
1QO ,M^
W FJ/
Ing CIB Qd u
SMITHUONIAN TABLKH
Logarithms of Hyperbolic Functions.
u
loo si nh u
"> Fo'
IOQ cosh u
w Fo'
IOQ tanli a
u Fo'
loa cotli u
2.150
.151
0.62677
.62722
44,6
0.63856
.63898
42,3
9.08821
.9882,
2,4
0.01179
.152
-15-3
.154
.62766
.62811
.62855
.63940
.63982
.64025
.98826
.98828
.98831
2 >i
.01174
.01172
.01169
3.155
.156
.157
.158
.159
0.62900
.62945
.62989
63034
.63079
44,6
0.64067
.64109
.64152
.64194
.64.236
42,3
9.98833
.98835
.98838
.98840
.98842
2,3
0.01167
,01 165
.01162
.on6a
.01158
2.l6o
.161
.162
.163
.164
0.63123
.63168
.63212
.63257
.63302
44,6"
0,64278
.64321
.64363
-64405
.6,1448
42,3
0-98845
.98847
-98849
.98852
.98854
2,3
0.01155
.01153
.01151
.01148
.01146
2.165
,166
.167
.168
.169
0.63346
.63391
.63435
.63480
.63524
-1/1,6
0.64490
.64532
.64574
.64617
.64659
42,3
9.08856
.98859
.98861
.08863
.98865
2,3
0.01144
.01141
.01139
.01137
.01135
2.170
.171
.172
.173
.174
0.63569
.63614
.63658
.63703
.63747
44,6
0.64701
.64744
.64786
.64828
.64871
42,3
9.08868
.98870
.98872
.98874
.98877
2,3
2,2
0.01132
.01130
,01128
.01126
.01123
3.175
.176
.177
.178
.170
0.63792
.63836
.63881
.63926
.63970
44,6
0.64913
.64955
.64998
.65040
. 65082
42,3
0.98870
.98881
,98883
.98886
.98888
2,2
O.OU2I
.oiirg
,01117
,01114
.01112
2.180
.181
.182
.183
.184
0.64015
64059
.64104
.64148
.64193
44,6
44,5
0.65125
.65167
.65209
.65252
.65294
42,3
9.98890
.98892
.98894
.98897
.98899
2,3
O.OIIIO
.ono3
.01106
.01103
.or 10 i
2.185
.186
.187
.188
.189
0.64237
.64282
.64326
.6/1371
.64416
44,5
0.65336"
.65379
.65421
.65463
.65506
-12,3
42,4
D.9890I
.98903
.98905
.98908
.98910
2,2
0.01099
.01097
.01095
.01092
,01090
2.190
.191
.192
193
.194
0.64460
.64505
.64549
.64594
.64638
-14,5
0.65548
.65590
.65633
.65675
.65718
42,4
9.98912
.9891-]
,98916
.98910
.98921
2,2
0.01088
.01086
.01084
.oioBr
.01079
2.195
.196
.197
.198
.199
0.64683
.64727
.64772
.64816
.64861
44,5
0.65760
.65802
.65845
.65887
.65929
42,4
9.98923
98925
.98927
.98920
.98931
2,2
2,1
0.01077
.01075
.01073
,01071
.01069
2. 20O
0.64905
44,3
0.65972
42,4
9.98934
2,1
0,01066
U
a tan ad u
w Fo'
Ofl 860 ait U
Fo'
OD sin ad u
u F '
OD 090 pd u
SMITHSONIAN TABLES
Logarithms of Hyperbolic Kunctio.m.
u
Ion slnli 11
F/
loa oosli u
.*,
lou tiuili it
1(1(1 CIlllll 11
2.20O
.201
0.64005
.64950
.1-1,5
":S:j
- l ' M
.O'i'l.l'l
.'i'''),lM
.M
Ultrfi,)
, ( 1 1 < K i j
.202
64094
* .)
11 .'. .
, ( ......
.203
65039
.(lOOOI.)
' '! ]i '
' Lj
.204
.6SO3
.(if.l-ll
'""
.)'
2.205
.206
0,65128
,14,5
0.(X>l8.|
.111 .!.!(!
I-M
":::; | : i
J, t
1 1 . 1 1 1 M.'jl 1
.Illll5,|
.207
,2oy
.65217
.65261
,65306
.(;>.;( 18
.6(131 1
.6:'353
;S;?;
.'MlljiU
.imi.]7
2.210
0.65350
1-1,5
0.6'u'jO
4 -VI
<>.'>^:i!i
-'. l
11.0104;;
J 12
.653U5
.65-130
.6(14,18
;!^!!!u
.01041
.21,1
.654*1
.65528
:!Ss
:ul!j;i
.oio.(7
2.215
0.65573
I'l.S
n.dfificiH
.|.M
"'f'!':':
J, 1
o.on.,15
.210
.05017
JJJ*!
!Iv!^
.uiu.n
.217
.218
.65706
.65751
.''('735
'* 1' ^// /
:^!/.l
,010.7
2.220
0.65795
-14,5
o ' if tS '(]
4A4
J.O^/.'i
.*,"
u.iilnj.-i
.231
,6 S Kio
.(rfv'Ki.l
,i)S'';-
.11111^3
. 222
,6588.1
.()!Hj(i;i
'"'iMi'!
.HlHJl
:S!
:65973
;lIl:Jli*
:!^Vi
.moid
2.2.!=;
0.66017
4-1,5
O.'l/O.l,!
l-'.l
i..w.
.!,' '
il.lMol,)
,22()
,6(i()!)J
670/1
,ij. k ).M!t
.11101.)
.227
,6M06
'ir!* 1
p !iv*'
.moio
'.S;
.66105
if!/.!! 1 .,!
>,M
.UllH/l
2 . 230
0.66J40
4-1,4
(I. (>-. U
4A4
.i.'i^i'X'
A"
u,m<xi,|
23r
. (16.184
,d7..'8''i
,r),'v/>!l
.OHKI,!
.(if 1328
.073.,'';
,I/J*HNI
, ( 1 1 HI XI
.233
66373
.''737'
,'CJil'l.;
,iifii,*jM
.66,|!7
.'71M
.'.j-JoiH
.IHJ...XI
2.2,15
0.6646.1
'H,4
0.' '7456
I-M
*),trf**i
j.n
H.,,K |M
. 236
,66506
,M7.|(|'|
,*fii*M
.li'ij'J.!
-37
.66551
.''7>1'
,],;,;;
,,jHI
.IMJI;i>t
.2*lK
.66595
,'17583
,<?j"i.:
,(NI*)Hrt
.239
.66640
.676J'.
.<f)"i 1
..XhjM
2.2,]0
0.66684
4-1,4
O.d^rf^
I.I..1
i).'^(" il'i
.','
lt.mi.Al
.241
.66728
.6/711
,i j"^ ilH
,(HHjH,!
.242
.66773
' I 77, | i3
,1/jtH'l
.(NH^Sl
.24.1
.66817
"77',.''
,^>l,)l
.I'rtMJ/iJ
.66862
.''/'H.iH
.WU,t
.IH.07X
2.245
0.66006
<H,4
o.67fWi
M.-i
I>.'^M<;
1,0
tt.tXftfS
. 246
66050
'79.!.]
,<i,V
.fH/M
.247
.66905
,^P>n"j
.(>"*7I
.248
67030
,6H4H>S
,'r 1 ",)!
,(*ii*X*j
.249
.67084
,6Hn5i
'^M,l
.(HK/tf
3.250
0.67128
.14,1
o.fiH.HM
-1 .(..'I
O...I.MS
1,0
H.mv.';
u
log tnn ad n
.w"
loo 100 gd u
w F,,'
lOUtlnuif il
w F,i'
llt(J C0 (l 11
SMITHSONIAN TABLIB
r, 4
Logarithms ,of Hyperbolic Functions.
11
loo sinli u
Fo'
IOQ cosh u
<oF '
loo tanh u
w Fo'
Ion coth u
2.250
0.67128
44,4
0.68093
42,5
9-09035
1,9
0.00965
.251
6717.3
.68136
.9503?
.00963
.25-*
.67217
.68178
.99039
.00961
.253
.67261
.68220
.99041
.00959
.254
.67306
.68263
.99043
.00957
2.255
0.67350
44,4
0.68305
42,5
9.09045
1,0
0.00955
.256
67394
.683-18
.99047
00953
.257
.67439
.68390
.99048
.00952
.258
-f'7483
.68433
.09050
,00950
.259
.67528
.68475
.99052
.00948
2/260
0.67572
44,4
0.68518
42,5
9.09054
1.0
0.00946
.261
.67616
.68560
.99056
.00944
.262
.67661
.68603
.09058
.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
.09069
.00931
.269
.67971
.68300
99071
.00929
2.270
0.68016
44,4
0.68943
42,5'
9.09073
1,9
0.00927
.271
.68060
.68985
.99075
.00925
.272
.68105
.69028
.99077
1,8
.009.23
.27.1
.68 [49
.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
.692-11
.99086
.00914
.278
.68371
.69283
.99088
.00912
.279
.68415
44,3
.69326
.99089
.oogii
2.280
0.68459
44,3
0.69368
42,5
9.99091
1,8
0.00909
.-281
.68504
.69411
.99093
,00907
.282
.68548
.69453
09005
.00905
.283
.68592
.6940
,
99007
,00903
.284
.68637
.69538
.99098
.00902
2.285
0.68681
-14,3
0.69581
42,5
9.99100
1,8
0.00900
.286
.68725
,60623
.99102
.00898
.287
.68770
.69666
.99104
.00896
.288
.68814
.69708
.99106
.00894
.289
.68858
.69751
.99107
.00893
2.290
0.68903
44,3
0.6979;!
42,5
9.99100
1,8
0.00891
.291
.68947
.69836
.99HI
.00889
.292
.68991
.69879
42,6
99"3
.00887
.293
.69036
.69921
.GDI'S
.00885
.294
.69080
.69964
.99116
.00884
2,295
0.69124
44,3
0.70006
42,6
9.99118
T,8
0.00882
.296
.69169
,70049
.99120
.00880
297
.69213
.70091
.99123
.00878
.298
.69257
.70134
.99123
.00877
.299
.69303
.70177
.Q9I25
1,7
00875
2.300
0.69346
44,3
0.70219
42,6
9.99127
1,7
0.00873
u
loo tan fltl u
Fo'
log seo gd u
Fo'
loo sin ad u
Fo'
lag oao Dd u
SMITHSONIAN TABLCB
Logarithms of Hypcrbolk: Function:).
2,y
.31
-3t
y
>y
2.30
-30
.30
-30
.30t
-3'
31
3 '
-31
317
310
32<
3^1
323
2-3^5
.3^6
..W
32)
2.330
.33'
-33-'
333
33-1
2-335
-336
-337
2,340
3-1 1
3-13
-3-14
a. 34 5
347
Ion fllnli u
.60471;
0.6^568
69656
,607(X>
0.70010
-70055
.70143
.70.76
-70365
.70409
.7054 *
.7058(1
.70(1.10
.70719
-70763
-71073
0.71117
.71161
-71250
71204
.350
.7 [4:17
.71471
.71515
0.71559
loo Ian oil u
IDQ oosli u
.3
14..1
.705(10
,7o(>o.)
0,71071
-71113
.7115(1
-71-151
7 K'.!,S
.71(1(17
.7^307
lOQ 111)0 Oil 11
lll(] lilhll 11
,1/11. 'Ill
.'/Jl'h't
.'/JHj.t
Kl sin oil u M [-.,'
1 1 , i * iU 1 7
.,-vM,
,mHl.j
.,MK>|,.,
, I K >H ( I
M, IX )({_([
.(H)Sl(J
...(Mi;
,(*.*!( K 1
M.Ut/l/)
toti Giogd u
SMiTHBONiflN TABLES
Logarithms of Hyperbolic Functions.
11
loo slnh u
u Fo'
IOQ cosh u
"Fo'
log tanh u
Fo'
log noth u
2.350
0.7E559
44,2
0.72349
42,6
g. 99210
1,6
0.00790
-351
.71604
.72302
,99212
.00788
.352
.71648
.72435
.99213
.00787
.353
.71602
.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
.9!>2I9
.00781
-357
.71869
.7264*!
.99221
.00779
.358
.7KJI3
.72691
.99223
.00777
359
.71957
.72733
.99224
.00776
2.360
0.72002
. 44,2
0.72776
42,7
9.99226
i,5
0.00774
.361
,72046
.72819
,99227
.00773
.362
.72090
.72861
.09229
.00771
3f>3
.72134
.72904-
.09230
.00770
-364
.7^178
.72947
.09232
.00768
2.365
0.72223
44,2
0.72989
42,7
9-99233
1,5
0.00767
.366
, 72267
.73032
.99235
.00765
.,<'7
723H
.73075
.99236
.00764
.368
7235S
.73117
.99238
.00762
.3<J9
.72399
.73160
.99239
.00761
2,370
0.72444
44,2
0.73203
42,7
0.99241
i,5
0.00759
371
.72488
.73245
.99242
,00758
372
.72532
.73288
.99244
.00756
373
.72576
.73331
.99245
.00755
374
. 72620
.73373
*99247
.00753
2.375
0.72665
44,2
0.73416
42,7
9.99249
i,5
0.00751
.376
.72709
73459
.99250
.00750
.377
.72753
73501
.99252
.00748
37
.72797
.73544
99253
.00747
379
.72841
.73587
.99254
.00746
2.380
0.72885
44,2
0,73630
42,7
9.99256
1,5
0,00744
.381
.72930
.73672
.99257
.00743
.382
-72974
.73715
.99259
.007.41
.383
.384
.73018
.73062
.73758
.73800
.90,260
.99262
.00740
.00738
2.385
0.73106
44,2
0.738-13
42,7
9-99263
l>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
0.7405<J
42,7
9.99271
i.S
0.00729
-391
73371
740Q9
.99272
.00728
-392
.73416
. 74U2
.99274
.00726
393
.73460
.74185
.99275
1,4
.00725
394
.73504
. 74227
.99277
.00723
2.395
0.73348
44.2
0.74270
4^,7
9.99278
1,4
0.00722
.396
73592
.74313
.99279
.00721
397
398
399
.73636
.73680
.73725
.74355
.74398
74441
,99281
.99282
.99284
.00719
.00718
.00716
2.400
0.73769
44,2
0.74484
42,7
9-99285
1,4
0.00715
u
lea Ian ad u
Fo'
loo see od u
<o Fo'
log Bin gd u
U Fo'
loo aid od u
SMITHSONIAN TABUS
6 7
Logarithms of Hyperbolic Functions.
u
loa slnh u
oj FO'
loa casli u
.w
loa to nh 11
co Fo'
loo oath u
2.400
0.73769
44,
0.74484
42,7
9.9928,
I,-
0.01)715
,401
.7381^
44,
.74526
.99287
.0071:
.402
.73857
.74569
.99288
.00712
403
73901
.74612
.99281
.00711
.404
-73945
74655
.99291
.(.10709
2.405
0.73990
44,
0.74697
42,7
9.99292
I.'
0.0070!:
.406
74034
M740
.9929,
.00706
.407
.74078
-74783
99295
.OO7OS
.408
.74122
.74825
.99297
o7!l
.409
.74166
.74868
.99298
.00702
2,410
0.74210
44,1
0.749"
4^,7
9-99299
1.4
0.00701
.411
74254
74954
99301
.oofiof
.412
.74298
.74996
99302
.0060}
-413
74343
.75039
.99304
,00696
.414
74387
.75082
99305
.00695
2.415
.416
0.74431
74475
44,1
0.75125
.75167
42,7
9.99306
.99308
1,4
0.00694
.00692
.417
.418
.419
74519
-74563
.74607
-75210
.75253
-75296
-99309
99310
99312
.00691
.00690
.00688
2.420
0.74652
44J
0.75338
42,7
9.99313
1,4
0.00687
.421
.74696
7538 1
.99315
.oof MS
.422
.423
.424
74740
.74784
.74828
.75424
-75467
.75509
42,8
99316
.99317
.99319
.oofj&i
.00683
.00681
2.425
.426
.427
.428
.429
0.74872
.74916
.74960
.75004
.75049
44,1
0.75552
-75595
-75638
.75680
.75723
42,8
9-99320
.99321
-99323
.99324
.99325
i,4
1,3
0.00680
,00679
.00677
.00676
.00675
2.430
.431
.432
0.75093
-75I37-
44,1
0-75X66
.75809
.75851
42,8
9.99327
.99328
-99329
1,3
0.00673
,00672
.oof 17 1
-433
434
.75225
-75269
75937
99331
99332
.00660
.00668
2.435
.436
437
.438
439
0.75313
75357
.75401
.75445
-75490
44J
0,75080
.76022
.76065
.76108
.76151
42,8
9-99333
-99335
.99336
-99337
99339
1,3
0.00667
.00665
,00664
. 1x1663
.00661
2.440
.441
.442
443
.444
0.75534
75578
. 75622
.75666
-75710
44,i
0,76194
.76236
.76279
.76322
.76305
42,8
9-99340
99341
99343
99344
-99345
i,3
0.00660
.00659
.00657
.oof 156
.00655
2-445
.446
447
.448
.449
0.75754
.75798
.75842
-75&B6
-75930
44,1
0.76407
76450
.76403
.76536
.76579
42,8
9-99347
.99348
.99349
99351
-99352
1,3
0.00653
,00652
.00651
,00649
.00648
2-450
0-75975
44,1
0.76621
42,8
9-99353
1.3
O.OoTx|7
u
og tan od u
.Fo'
o BOO ad u
Fo'
OD*lnod u
Fo'
oaoiogd u
68
Logarithms of Hyperbolic Functions.
u
Ion slnh u
w Fo'
lag cash u
iV
loo tanli u
U) Fo'
IOQ coth u
2.450
0.75975
44,1
0.76621
42,8
9-99353
1,3
o.oo!)47
-451
.76019
.76664
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
.456
. 76239
.76878
.99361
.00639
457
.76283
.76921
993<>2
. 00638
4S8
-76327
.76964
99363
. 00637
-459
.76371
. 77006
.993^5
.00635
2.460
0.76415
44,1
0.77049
42,8
9.99366
i>3
0,00634
.461
.76459
770CJ2
.99367
.00633
.462
.76503
-771,15
.99369
.00631
.463
.76547
.77178
99370
.00630
.464
.76592
.77220
99371
.00629
2.465
0.76636
44,i
0,77263
42,8
9-99372
1,3
0,00628
.466
.76680
.77306
99374
.00626
.467
.76724
-77349
99375
.00625
.468
.76768
77392
-99376
1,3
. 00624
.469
.76812
-77435
99377
.00623
2.470
0,76856
44J
0.77477
42,8
9-99379
1,2
0.00621
.471
.76900
.77520
.99380
.00620
.472
' .76944
.77563
.9938i
,00619
473
.76988
.77606
.99382
.00618
-474
.77032
.77649
.99384
.00616
2-475
0.77076
44,0
0.77691
42,8
9.993S5
1,2
0.00615
.476
,77120
77734
.99386
.00614
477
.77164
77777
.99387
.00613
478
. 77208
. 77820
.99388
.00612
479
.77252
77863
99390
.00610
2.480
o , 77296
44.o
o.779of)
42,8
9-99391
1,2
0.00609
.481
.77340
.77948
99392
.00608
.482
.77384
77991
99393
.00607
-483
.77429
.78034
99394
.00606
4&4
-77473
.78077
.90396
,00604
2.485
0.77517
44,0
0.78120
42,8
9-99397
1,2
0,00603
.486
.7756i
.78163
99398
.00602
.487
.77605
.78205
. 99399
.00601
.488
.77649
.78248
.99401
.00599
.489
.77693
.78292
.99402
.00598
2,450
0-77737
44,0
0,78334
42,8
9.99403
1,2
0.00597 1
.491
.77781
.78377
99404
.00596
.492
.77825
.78420
.99405
.00595
493
.7786g
.78462
.99406
.00594
,494
.77913
78505
.99408
.00592
2.495
0.77957
44,0
0.78548
42,8
9.99409
1,2
0.00591
40
.78001
.78591
.99410
,00590
497
-78045
78634
.99411
.00589
.498
.78089
.78677
-99412
.00588
499
.78133
.78719
.99414
.00586
2.500
0.78177
44,0
0.78762
42,8
9.994IS
1,2
0-00585
u
log Ian ad u
Fo'
loo tec od u
Fo'
loa sin ad u
F</
loo osogt) u
SMITHSONIAN TABLES
6 9
Logarithms of Hyperbolic Functions.
u
loa slnh u
w Fo'
IOQ cosh u
"F,/
log tanh u
Fo'
loo ootli u
2.500
0.78177
44,0
o, 78762
42,8
9.994I5
1,2
0.00585
.501
.78221
.78805
.99416
.00584
.502
.78265
.78848
42,9
99417
.00583
.503
78309
.78891
.99418
.00582
.504
78353
.78934
.99419
.00581
2.505
0.78397
44,0
0.78977
42,9
9-9942!
1,2
0.00579
.506
.78441
.79019
.99422
.00578
.507
.78485
.79062
.99423
.00577
.508
78529
.79105
.99424
.509
.78573
.79148
.99425
1,1
.00575
1' a-sro
0.78617
4-1,o
0.79191
42,9
9.99426
1,1
0,00574
.511
.78661
.79234
.99427
.00573
.512
.78705
.79277
.99429
.00571
.513
.78749
.79319
99430
.00570
.5M
78793
.79363
99431
.00569
2.515
0.78837
44,o
0.79405
42,9
9-99432
1,1
0.0056!:
-516
.78881
.79448
-99433
.00567
517
.78925
.79491
-99434
. 00566
.518
.78969
.79534
-99435
. 00565
519
79013
79577
99437
.0056;
2.520
0.79057
44,o
0.79619
42,9
9.99438
1,1
0.00562
.521
.79101
.79662
99439
.00561
.522
523
-79145
.79189
.79705
.79748
.09440
.99441
.00560
.00559
.524
79233
79791
.99442
.00558
B-525
.526
0.79277
79321
44,0
0.79834
.79877
42,9
9-99443
.99444
1,1
0.00557
.00556
.527
.528
.529
.79365
.79409
79453
.79920
.70962
.80005
99446
99447
.99448
.00554
00553
.00552
2.530
531
532
533
534
o. 79497
79541
.79585
.79629
.7<X>73
44,0
0.80048
.80091
.80134
.80177
.80220
42,9
9.99449
.99450
99451
.99452
99453
1,1
0.00551
.00550
.00549
.00548
.00547
2.535
.536
537
.538
539
0.79717
.79805
. 79849
79893
440
0.80263
.80306
.80348
.80391
.80434
42,9
9-99454
99455
99456
99458
9045Q
1,1
0,00546
.00545
.00544
.00542
.00541
2,540
541
542
543
-544
0-79937
799Sr
.80025
.80069
.80113
44,o
0.80477
.80520
80563
.80606
.80649
42,9
9.99460
.99461
.99462
.90463
90464
1,1
0.00540
.00539
00538
.00537
.00536
2.545
.546
547
548
549
0.80157
.80201
.80245
.80289
.80333
0.80692
.80734
.80777
.80820
.80863
42,9
99466
.99467
.99468
.90469
1,1
0.00535
.00534
.00533
.00532
00531
2-550
0.80377
44-0
0.80506
42,9
9-99470
1,1
0.00530
u 1
OB tan od u
10 F/
oo SBC gd u
u Fp'
DO sin gd u
-V
1 00 010 0(1 U
70
Logarithms of Hyperbolic Functions.
55.1
5M
557
55*
. ,'jfl I
5' i.l
.;;(,[
'Sf'5
5' 17
J.S70
..'i7i
57-1
57,1
.17-1
-t.575
57''
577
57H
..KNl
.5*9
501
5'J.l
3.5'J.I
Ion ulnli u
,Ho.|fv|
o.Ho^tjf
.HuiHi)
.Ki 1.1,1
o. Hi 2,50'
.Hl3i|3
0. Hi. 175
.Hi'Si<;
H 1 5(1.1
! 8 165 1
o.Ras73
oo tnn u<i u
rv
I.VJ
Po'
OOBll U
.8io7K
o.8rui
.81378
.81431
0.81550
0,817(1.1
.8JOJJ
.HJ.I
.
.83010
oo 100 ail u
-I-VJ
.(2,0
13,0
-l.l.o
F/
loo tnnli u
.*W-I7'
W.17,1
W-I7-I
-W-17S
WIU7
WWW
-W.107
.!W5i8
lop iln oil u
IV
1,1
I.O
1,0
1,0
1,0
1,0
1,0
1,0
1,0
1,0
lau DO Hi u
u FV
.00535
o,(X>5^(
.1x15 j.i
,00521
.00518
.005 17
.00515
0.0051. |
().(X)SO)J
.1x1500
.00503
.00501
,00500
.oo.|<X
O.OO.|O.J
.00.11) ,3
.IXM9I
.IKMIXJ
.00-187
.0048?
.oo,]8i
.oo,| 80
0.00,179
l OB 010 u<i u
BMITHSONIAN TAm.cn
Logarithms of Hyperbolic Functions.
11
loo si nli u
- F/
Lop cosh u
F '
loo tanh u
10 Fo'
lop 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
1 .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
-13.9
0.83482
43,0
9-99530
0,9
0.00470
.611
.83056
.83525
99531
.00469
.612
.83100
.83568
99532
.00468
.613
.83144
.83611
99533
.00467
.614
.83188
.83654
99534
.00466
2.615
.616
0.83232
.83276
43,9
0.83^97
.83740
43,0
9-99535
.99536
0,9
0.00465
.00464
,617
.83320
.83783
99537
.00463
.618
.83364
.83826
.99538
.00462
.619
.83407
.83869
99539
.00461
2.620
0.83451
43,9
0.83912
43,0
9-99540
0,9
0.00460
.621
.83495
.83955
99541
.00459
.622
83539
.83998
99541
.00459
.623
.83583
,8404:
.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
.620
.83846
.84200
.99548
.00452
2.630
0.83890
43,9
0.84341
43,0
9-99549
0,9
o.oo-i 51
.631
.83934
.84384
-99550
.00450
.632
.83978
.84427
99551
.00449
-633
.84022
.84470
99551
.00449
.634
.84066
.84513
99552
.00448
2.635
0.84110
43,9
0.84556
43,0
9-99553
0,9
O.OO447
.636
.84154
.84599
99554
.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
.6;| 2
.84417
.84857
99559
.00441
.643
.84461
. 84900
.99560
.00440
.644
.84505
.84943
.99561
.00439
2.645
0.84548
43,9
0.84986
43,0
9.99562
0,9
0.00438
.646
.84592
. 85029
1 .99563
.00437
.647
.84636
' .85072
.99564
.00436
.648
.84680
-85IT5
99565
004,15
.649
.84724
.85158
.99566
.00434
2.650
0.84768
43,9
0,85201
43,0
9-99566
0,9
0.00/134
u
log Ian fid u
*> FQ'
looseo gd u
Ttf
loo sin ad u
W Fo'
log 010 ad u
SMITHSONIAN TABLES
Logarithms of Hyperbolic Functions.
u
log slnh u
tv
loo cosh u
"Fo'
loo lanh u
w Fo'
log coth u
2.650
0.84768
43,9
0.85201
43,0
9.99566
0,9
0.00434
.651
.652
653
.84812
.84855
-84899
.85244
.85287
.85330
.99567
.99568
.99569
-00433
,00432
.00431
.654
.84943
85373
99570
.00430
2.655
.656
.657
.658
.659
0,84987
.85031
.85075
.85119
.85162
43,9
0,85416
85459
85502
.85545
.85588
43.0
9-99571
99572
9957^
-99573
99574
0,0
0.00429
.00428
.00428
.00427
.00426
2.660
.661
.662
.663
.664
0,85206
.85250
.85294
.85338
.85382
43,9
0.85631
.85674
85717
.85760
-85803
43,0
9-99575
99576
99577
-99578
-99578
0,8
0,00425,
.00424
,00423
.00422
,00422
2.665
.666
0.85426
.85469
43,9
0.85846
.85889
43,0
9-99579
-99580
0,8
0.00421
.00420
.667
.668
.669
-855I3
85557
.85601
43,8
.85932
.85975 .
.86018
.99581
.09582
.99583
.00419
,00418
.00417
2.670
.671
0.85645
.85689
43,8
0.86o6l
.86104
43,0
9.99583
.99584
0,8
0.00417
.00416
.672
.85733
.86147
-99585
.00415
673
.85776
.86190
.09586
.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
.OO4I2
.677
.85952
.86363
99589
.0041 1
.678
. 85996
.8640^
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
09594
,00406
.684
.86259
.86664
-99595
.00405
3.68s
0.86302
43,8
0.86707
43,o
9-99596
0,8
0,00404
.686
.86346
,86750
09597
.00403
.687
.86390
.86793
99597
,00403
.688
.86434
.86836
09598
,00402
.689
.86478
.86879
99599
,00401
2.690
0.86522
43,8
0,86922
43,0
9,99600
o,S
0,O0400
.691
.86565
,86965
09601
.00399
692
.86609
,87008
.99601
.00399
.693
-86653
.8705:
.09602
.00398
.694
.86697
.87094
.09503
.00397
2.695
0,86741
43,8
0.87137
43,0
9.09604
0,8
0,00396
.696
,8678^
.87180
,09605
.00395
.697
.86828
.87223
.99605
.00395
.698
.86872
.87266
,Qo6o6
.00394
699
.86916
.87309
.09607
.00393
2.700
0.86960
43,8
0.87352
43,0
9.09608
0,8
0.00392
u
log tan 0d u
Fo'
lop aeo Qil u
Fo'
log sin gd u
.Fo'
Icpcso gd u
SMITHSONIAN TABLEB
Logarithms of Hyperbolic K
11
loa slnli ti
..V
IfiU cosh n
W K,,' t(l|] Illllll II '" 1'..'
Illll DOtll U
a. ?oo
0.%***
43,
u.H/.l.S.:
1,1,'
<j, <."/>.';
'.it
".".<>.!
.701
.8700.
8/,i<J;i
,,^X.K l i
'"M'j.l
.702
.8704
8/4, 1' 1
-'"'"*'
'-M'JI
.703
.8709
.S/.iNi
, 1 n / 1| i
"",1'JO
.704
8713
.KXV
, < c X 1 1 1
.nniSg
2.705
0.87171
43,8
o.8/.'i('/
u<
M,'^.'-'
,,;t
u.uu.KW
.706
,87^,
. 8;'( ,m
-iv,''l .:
.11*1,1X8
,707
871 is |
.VVH.i
.u ,,1^7
.708
. 87 1 1 1
. 871 )/
.l,'/'!.]
,i>i,.(8(,
700
.8735-
.8/;'.in
. < / X > I ;i
<x',!<\'i
2.710
o.87iof
.. (il ,s
o,8;7S.i
1.1."
'.-^Pl,,
M..S
ii.CKMHs
.711
.8744-
.878,:!)
.iy</iHi
.(Hi.ifi
,712
,8748?
,8>',^K)
. ' .' f i /
,IH]_(M_.
713
.87 r }V
.8/.JI.!
jj-/n,'i
'"M8.!
,714
.87573
.8yg;;;i
'"''""
.IMI^Ml
2.715
0.876 17
I3.H
o,8jv)H
4.1.1
J.U-/>1.(
u. !i
(I.IHI(8|
,716
.87(1(11
.8,'to,|i
.'>/<'>
.HMHi)
.717
.87705
,88ofi|
.'f^'-'t
"M7 1 .
.718
.87749
.881.!;-
,,/X'.'.'
7i*>
.87702
,K8i;u
..J./..-J 1
|N| .l/8
2.720
0.8783(1
43,8
n.8Mji.i
4.1."
U.'^X'.'.l I'.'*
u, ( KI,|7X
.721
.87880
,8M.!;,(,
,1^/1,' 1
.m 1,17(1
.722
723
.'87068
.88,:t)<j
;;;j;;;-j
i',;'
Ifll 3/'.'i
.72-1
.88011
, HH^Hj;
.
.""Mx'l
2.725
0,8805.1
1,1,8
O.lH|.'!i
4.1.1
.t.|Xl
' ,7M()
.KHoyy
.88171
.'/X'.rH
,l*M/-'
.727
.88l. | )
88;i 1 ,^
,1/^1 ,.;i
.(Hi'iy '
.728
.88187
.WfjiflH
.i/^.,'.,
iui'ivi
.720
.88330
.HHJKH
.IJ-XM-I
it"M7<>
2.730
731
0.88274
.88118
4.1,8
;S;y
.1.1.1
";;-;;
n.tm.ff'nj
732
.Wtf'a
,887,^1
'rXif,! iMi'lU'i
733
.88,106
.K^/7,1
!jij<'Vi 'im'i/iv
-734
.88.140
,8.'ii,
-'^XMJ
..h; )( ,7
2.735
0.88.101
I.1.K
o.8Hf<S'J
.1.1, 1
J'/XMI ti-
l> IMif^l
.7.10
.885.17
.H^X),;
i'/x-Vi "
'ni'i'ii'
737
,88581
;S5
' '
:-;!!;:!
2.740
O.'HSX*
13,8
o.'iir.
,),'(, |
.//*.,
.<-M|M
7<|i
! 8875<"i
.Kyii/
' ./.I
''
u.m.j ,
742
. 8K8oo
,8<;i(i[
' ( . ( ' (
,,
-743
.88844
.H<).;i>:\
'(cX,'ii
" .1 "
7-14
.88887
.Hj.,'.|>'
!-//''!!
^M,W
2-745
o.SKoir
4,1,8
O.Kiwijit
ill.l
<
.746"
88075
>8<).i,i,i
,,. *
' y ( ,
'"
"''* ,:, l u
747
.748
.8gofu
.80,170
.W||H|
'/X'l.t
^'"'3J7
.749
.80106
.Kjjjft,!
'//MI
i"M,'i''
2.750
0,80150
.118
,. q, ,,.,.
---._, ,
Mi
u.i _/,j*^i
4,1.1
'J' ' /X* 1.^ ^ "*/'
t J . t * * { n H
u 1
on Inn ail n
w
D seo flil u
'. w' '
i
og iln oil u I M i'/
tnqcmxitl u
SMITHBONIAN TAULKB ""*"" ' " ''*' "' ' """""" '"""'
Logarithms of Hyperbolic Functions.
u
Ion slnh u
IV
lo a cosh u
"F '
IOQ lanli EI
w Fo'
log coih u
2.750
0.89150
43,8
0.89505
43,1
9.90645
0,7
0.00355
.751
.89194
.89548
.99646
00354
.752
.89238
.89591
.99646
-00354
753
.89281
.89634
.09647
' -00353
754
.89325
.89677
.99648
.00352
2.755
0.89369
43,8
0.89720
43,1
9.99649
o,7
0.00351
.756
.89413'
.89764
.90649
.00351
757
.89457
.89807
.90630
.00350
758
.89500
.89850
99651
.00349
759
.89544
-89893
.99651
.00349
2.760
0.89588
43,8
0.89936
43,1
9.99652
0,7
0.00348
.761
.89632
.89979
.99653
.00347
.762
.89676
.90022
99^53
.00347
.763
.89719
.90065
,99654
.00346
.764
.89763
.OOloS
.99<5S5
00345
2.765
0.89807
43,8
0.90151
43,1
9.99656
o,7
0.00344
.766
.89851
.90194
.99656
.00344
.767
.89894
90237
.99657
-00343
.768
.89938
.90281
.99658
.00342
.769
.89982
.90324
.99558
.00342
2.770
0.90O26
43,8
0.90367
43,1
9-99659
0,7
0.00341
.771
.90069
.90410
.99660
.00340
.772
.90113
.90453
.99660
.00340
in
90157
.90496
.99661
.00339
-774
O020I
COS39
.99662
.00338
2-775
0.90245
43,8
0.90582
43,1
9.99662
o,7
0.00338
.776
.90288
.90625
.99663
.00337
777
.00332
.90668
.99664
.00336
.778
.90376
.90712
.99664
.00336
-779
.90420
90755
.99665
.00335
2.780
0.90463
43,8
0.90798
43,1
9.99666
o,7
0.00334
.781
.90507
.9084!'
,99666
.00334
.782
-9055I
.90884
.09667
.00333
.783
90595
.90927
.99668
.00332
-784
.90638
.90970
.99668
.00332
2.785
0.90682
43,8
0.91013
43,1
9.99669
0,7
0.00331
.786
.90726
.91056
.99670
.00330
-787
.90770
.91099
.99670
.00330
.788
.00813
.91142
.90671
.00329
.789
.90857
.91186
.99672
.00328
2.790
0.9O90I
43,8
0.91229
43,1
9,99672
0,7
0.00328
.791
.90945
.91272
.99673
,00327
.792
.90989
.91315
.99674
.00326
793
.91032
.91358
.09674
.00326
794
.91076
.91401
90675
.00325
2.795
0,91120
43,8
0.91444
43,1
9.99676
0,6
0.00324
.796
.91164
.91487
.09676
.00324
797
.91207
.91530
99677
.00323
.798
.91251
.91574
.09678
.00322
799
.91295
.91617
.90678
,00322
2,800
0.91339
43,8
0.91660
43,1
9.99579
0,6
O.OO32I
u
log tan od u
Fo'
log sec od u
F</
IOQ Gin od u
w Fo'
log esc gd u
SMITHSONIAN TABLES
Logarithms of Hyperbolic
u
IOQ einli u
-
!HOI
!yi38j
.Ho.:
.l)[.|.!O
.803
yi-i7<>
.804
-yi.ii-1
2.805
o.yis.v-
.8(Xi
,y[<x>[
.8117
.yi<M3
.8ntt
.yiOSy
.800
-yi73-i
2.810
0.01770'
.811
.yiS-'o
.8].!
,y 18(14
.813
.i)i(jo7
.81.1
. y i 05 ]
~.'8io
o.yHjtjjJ
.817
,y.!08j
.818
.()Ji j/i
.8iy
.yjiTo
a. 830
o,y,.M3
!H">
.ijj.ioi
-8J3
9-3. 1 5
.S-M
''"'^
!tf
:S
.8_'H
:i!S
"Xl'i
o.yj(i5l
. y. 1(105
.832
.<).!738
H3.1
.11^78^
.834
.yj8j(i
a. 8.15
O.<JJ8(K)
.836
.y.if)i.l
.'838
.y3(H)i
.830
.y,io.|.|
o . 93088
iiii
93 i 3-
.5)3170
93iy
2.8.I.S
[1.93307
.9335o
;& ( y
s
2.850
0.935*5
u
op tnn ad u
w |
'13,7
13,7
13,7
13,7_
-.!
lug cosh u
O.tJIl'fc'Hl
00 BOO U(l tl
.13.<
P,/
lou Inuli u
. < f t' *<{ i
. i )i X ^ 1
. > I- )' J 1
< t . i P i' ) I
.'/'"M
J, !/
.Iff*!*)
lo ilti IK! it
llIU Clllll 11
0,fi
n.no.jifi
. ' M 1 7
.""317
.i'i,(id
""3','i
1 1 , i i.i 1 5
"".!'.!
.(nl.li> 1 !
.'"i-'Uf,
Hi) II
SMITHSONIAN TABUS
Logarithms of Hyperbolic lAmclions.
.8.1*'
.857
.8(12
.86.1
.H()7
.HliH
.Wiy
^.870
.871
,872
-H7.1
.7-l
.87*'
.877
,878
70
).88n
!ltttj
!nn'i
.HKft
-BHg
3-ffyo
.Hoi
inlii
./!
IU slnli u
.051.1,1
F,.'
1.1.7
1.1.7
1.1.7
1.3,7
u tog Inn oil u * P,,' log noo oil u > F.'
IDU onsh u
o I.I'M
0.15.1U
-05-11,1
.!)5,|'
.!tS7'. r i
0-0507.1
.1,1,-:
lou tn nil u
007 i a
W7I-I
-007'!)
0-007-!"
007.!'
-IW7.il
O.W7.P
W73J
u Fu'
0,6
0,5
0,5
0,5
u F,/
log ootli u
o.oojyi
,0028(J
.00*^7
.00287
.OOJH.-I
.00280
.00278
.00278
0.1x1276
.00276
, 0027,1
0,00274
.00^72
,(K)37()
.(Xt.?7o
.1x1267
.1x1267
,(X)26Y)
0.00266
.00265
.0026.1
.0026,1
0.0026,1
lOOOIOQlIU
SMITHOOHIAH
77
Logarithms of Ilyperbolii: l''um:lioiiii.
2, (XX)
2.005
,yo()
.1)07
-90S
.yoy
2.910
2.915
yio
9'9
2. 9 JO
.921
.92J
3.925
.0J6
>.!7
.92
939
9,11
93.1
.934
3.035
9,l6
9,17
939
a.9-10
.941
.942
9-13
9-14
2.9.15
3. 050
Ion slnh u
0.95711
-9575-1
.95^5
.9.197.1
,yfjio.|
.X759
0.970.11
97'iXi
0.972-10
.97-'H.1
97,1-7
97.171
.97414
.975113
.97.1.15
-97589
97*>33
0,97670'
. 97720
977'M
.97807
0.07895
on Inn u<t u
F u '
.13,7
-13,7
<I3.7
43,7
43,7
I3.7
|CIO GOill U
.C.XHJ.M
O.O/-'")
.07,15.1
-97'ii"'
i). 074^.1
.J7.S.-M
.9757"
(i, 077" I
0774 1
.07787
4.1.
' F,,'
tl)(| lllllll II
.10;.!''
ij. '/)>'!"
."'I'M
ll'l) ODlll II
,1 **,)() I
.txM,)!
.IX), ',1(1
SMITHSONIAN TAPLKO
Logarithms of Hyperbolic Functions.
Ion ilnli ti
ID Fl|'
lou coali u
IOQ tnnh.ii
IV
loo coth u
1J5-I
OS 7
.1X1,!
<X7
<X>!>
.071
OH?
2,000
W3
W-l
.999
3.000
u
.IWI17
W6I
WSM
000-17
.00090
1.00034
1,1,7
13,7
1,1-7
'I3/'
W47.1
005 I S
-WJ7/.I
looUn oil
Fo'
I .00077
.00120
.OOlfi.)
,0020fi
,00350
1 .002(),1
too 100 pit u
.13,2
13.3
13,2
-13,3
W766
W77,t
-W77.1
MW5
W777
W777
<m>
0-W7HO
997R.I
loo *ln ad u
o,S
o,5
0,5
.ooj;j6
.00230
.OOJ.tO
,002,10
.00227
0.(X)326
.00226
.00225
0.00224
.00224
0.00223
.00321
.00221
.00221
.00220
0.00220
.002 If)
.00210
.OO2T8
.002(8
0.00217
.OOJI7
.00217
.00216
0,00215
loo 010 ail
TAB no
Logarithms of Hyperbolic
II
loo slnli u
w Fo'
log cosh u
M F,,'
Ntu (tuili u
liu oolh u
3-00
r .00078
436,5
I.IX1JIJ.1
-l.l-M
"""i;!- ;
1.3
O..O.MS
.or
.00514
436,4
.0072;;
43-!.-!
.i/)/.")
1..'
.00 ji i
.02
.<xii)50
436,4
.01 157
43-'-.'
.'/".(
4,1
.110,107
.03
.01387
43'',3
.olfiS*)
43-J.3
.<>>)','>/
I.'
.IHKJO.l
.0.1
.01823
436,3
.020.!.!
4.1-U
,<K-HM
4,u
.UIHW
3.05
1.02250
43(i,.i
I.O.!.|5I
43-M
<>.<><:'.'<>,
'!'
u.onio;;
.06
.02(19(1
43' W
.o.f8.v.
.13-'. 1
.'/) H)
3.- 1
.OOIl)I
*>7
.03132
43",-)
.033'"
43-M
.'J'l-'il.i
3.7
. ! K ) 1 87
,oWi8
436,i
.0375'
43''.. ! '
,*f frit',*
3n'
.OOIil.)
.oy
,04<K)4
4.16,1
.04181
4 3 -YS
.i>jH.:(i
.(,'
.txiifio
3,10
I .04440
43'','
l.O.l'HO
4 3.J.S
.^>V|
3,,'i
M.OOI76
, u
.04876
436.O
.o*io|i)
43-M 1
.ip ft,'.','
3.1
.""'73
.12
.05312
436,0
,o>|Hi
43-M-
.ic^'.u
3.1
,(HI|()
1.1
.05748
436,0
."5"'4
.13-',"
.<)<^3 t
3,3
.IMH(/I
.I.|
.oo'iKj
435,9
"63,17
I.I.!./
.oo 1 !.!/'
3.3
.innh.l
3.15
i.oATiao
435,9
1,0^770
43-',7
O.i/jKl'
,1,,!
i.mi.'i'j
' .if)
.07056
435,1)
.07.!'..'
4 3 -!.7
.'j-f^i 1
3,'
.00156
'7
.07.192
4 l'i.8
.076.15
43'\' !
./>! 17
3.'
,ihii;i3
07027
435.H
,t tor/A
43 '.''
.ix^yi
3."
.iKti;itt
.10
08363
435,
,"H;-,IO
43 .',
'/>^3
-Vl
,ihn.|7
3.20
i .oKTyi)
435,7
1 .O8o.|3
43.!."
u.-j.,;^,
-VJ
u. 1x1144
. ji
.003-J5
435.7
."'M7' 1
13-'."
.'.CjM.'t"
f 1 .'^
.mt.]!
, 22
.01X170
435,7
,O()8OO
4,1.'."
.iflM'ii
I-.',* '
,tKll3(J
."'i
, lotofi
435,7
. in.: ).!
I3-'|N
.i/f.'l'.l
"'.i'
.11113(1
.all
.1054 a
435,6
Ml> 7*
433."
, i/ >.'!'.;
-f.7
""l.U
3-25
I , ifflj77
435/>
I. lioS
433."
ij.if>'fr-j
,','
u. 001,11
.art
.11413
435,6
. 15 |i
133."
,'fj"/.-!
'.''
, i M H ,;M
,27
. i i 849
435,6
. HJ/4
433."
.t** 1 '/;;
-'. i
. 1 M 1 1 ,!Ji
.28
,ia2ft|
435.5
. .1407
433.1
.<^>M^7
fVi
.O<ll.!3
.20
.12720
435,5
. 2M.|0
433,1
.i-);''j
-'.1
-tltUJI
3,1"
1.13155
435,5
1. 3.173
433.'
'(,^^1,!
-', 1
MJHHtH
,H
.13591
435,5
37"''
433.'
. 1 f >!t'i I
i3
.<xil 16
.3-!
. 14026
435,4
. I i.l"
433.-;
J/jJiK't
-*,.t
4
,13
.1446')
435.4
4S73
433.-'
.i/jW!')
.',,-
.ml ll
34
. 14*97
435,4
. i(ri
433.-'
./>;v;i
,!,,!
.IMIIO')
3,15
1.1 <ma
435i4
1.15439
4 33. -i
'I.'XJ^M
.' 1
II,'K)1O7
,16
. 15768
435.3
. 1587,!
433,-t
.'/>"' >! i i
-'..
.liHO.'i
,17
. 16203
435,3
.16306
433.3
.i^iJii;*
'.1
.1 HI III,)
3
. 16638
435,3
. 1673"
433.3
,\rf^f\
A*
.mint
39
.1707.1
435.3
.1717-'
433.3
w"
rf.u
.thHhW
3.40
1.17501)
435,3
1 , I7(ki;i
13,1.3
I.'/^M
I."
H.".(.X(7
,41
.17944
435,-'
. iNo.ti)
433,3
.'J'j'f", 1 .
l.'l
.fHlX),<j
,42
,18171)
435,-!
. tM|7-!
,' ' t, |
,1^x^17
l.'l
.IHUHJ'I
.43
.18814
435,.:
. lNi)0'i
.133,1
.'^//"j
.MKH/1
44
, 10250
435,-!
. '"33"
43.1.1
,(wi i
I,M
.IK* l. 1 ^
3-45
i . 10685
43.V
l . 1.J77-!
433.1
J.'^H,T
I.H
1 1 , ( K M >MM
.46
.,20120
435,-'
.,f(l.!()ft
433.4
.'^CH I
I./
,|XV>. V 'J|
47
.-'('555
435,1
..i'if'3'i
433.H
.'ffflli
t.J'
, In H |
.48
. 20O!X>
435, '
...'i"73
433.,'i
,<fi>t\H
I. 1 '
.IWWhM,!
49
,3t.ias
435,1
.JlfiOfl
433,5
.'ffti'l
I.' 1
.1HHIKI
3-5"
T, aiRTfl
435.1
I, JIM!"
433.5
WUSl
I/'
n.tKK^
u
og Inn ml n
w F n '
00flO(Hl U
GM P '
ro
'i
Ino ain ml u 1
r,f
Itig *;i(! Qtt u
SMITHSONIAN TAIU.EO
Ro
Logarithms of Hyperbolic FimcLiona,
J.5
Si
3-55
57
50
3-fiS
3-75
77
!?0
3 ."0
.m
M
Ho
3-00
.01
.()*'
.04
.07
,08
W
IOH slnli u
,.!,[<JO()
-W7''
I..1-V.1.1
353-I-'
35777
.3(1311
37515
.'It W.I
i.. i, V>oo
135, "
135."
-I35.0
13-1,7
I3'l.7
'13-1.7
'13-1,7
<13-l.fi
Ion GDBll U
.J.I 5-1 1
.71-1,1
H757<>
.'.!07.15
3017')
-33* MO
.3-1.1 1 7
.353^1
35KiH
3755-1
I. .|i. 15!)
133.5
-133.K
133,0
133,')
13-1,0
lou Intili u
- .<)004-l
O-WW-17
VW55
.1^)057
00'X>3
Fy'
1,3
T,J
1,1
1,0
o,H
o,7
o,7
o,C,
ion ootli u
O.(XK>7()
,00078
.1)0070
.w 107,1
o.ooo7J
.(KM I70
.000(11
O.OOO.'jl)
.00035
.(K)OS.|
.(KIOSO
O.IXXM3
.000,|,1
,(KK),|0
.(MX 1,10
.00033
,fXX)3l
,00030
Ina lan atl u
lopflooaif u w Fu'
M IV
too 010 otl u
BMITHBONIAN
8l
Logarithms of Hyperbolic Function!
.0
.02
4.0'
.of
-07
.oS
.(H
.1-1
4. 15
.16
.17
.18
,|.J5
.2(1
~7
.X)
31
33
4.35
.37
30
4 .40
.41
.43
"14
4-45
"17
-4!)
4-50
u
loo slnli i
l.4,1(i<x
-4-I03
.475"
1.479.1*
.43Ht
1.50118
.5055,1
i.Saaji
.527-15
5.1100
535IM
5-104)
1.54-l'M
.50201
r .
.57070
57505
.570,10
.50242
.(K1II1
r ,
.(11414
.(iiftio
.62^,1
.62718
.C).|03I
-<M'I5S
D tnn ad II
- Fu'
434.
1.1-t.S
I'll.. 1 !
I.TM
4.1.1,'!
toa cosh u
.-I7ICU
4/5.C
[ .501411
.JiJ.llli
5 --7- 1.1
ii.V'M
5-l'M7
D ma ad
loo innli u
I. ')>]/!
fifty-
t)U lift oil u
lou cHi u
. i x x i,;M
.oui.,7
.'Nil,! I
.{KHI.fl
, 1 11 n 1 1 ;i
.11 tin, 1 !
, I M 1 1 '/
: I X II I I )'
, I X H 1 1 1 1
.(Nttfl
.IHMIlfi
,IXII,)
. 1 K K 1 1 .[
.twittU
fiifl BIO gtl u
SMITHOONIAN TABL<Q
Logarithms of Hyperbolic Functions.
u
log slnh u
10 Fo'
IQQ cosh u
<oF '
loo tanh u
<a Fo'
loo coth u
4-50
1.65324
434,4
I .65335
434,2
9,99989
O,2
O.OOO1I
Si
65759
.65769
.99989
.00011
-52
.66193
.66203
.99990
-OOOIO
53
.66627
.66637
99990
.00010
-54
.67062
.67072
.99990
.OOOIO
4-55
1.67496
434,4
1.67506
434,2
9-99990
0,2
O. OOOIO
.56
.67931
.67940
.99990
.OOOIO
. -57
.68365
68374
.90991
.00009
58
.68799
.68808
99991
.00009
-59
.69234
.60243
.90991
.00009
4.60
1.69668
434,4
1.69677
434,2
9.99991
O,2
0.00009
.61
.70102
.70111
99991
.00009
.62
70537
.70545
.99992
.00008
.63
.70971
.70979
.99992
.00008
.64
.71406
.71414
.99992
.00008
4-65
1.71840
434,4
1.71848
434,2
9.90992
O,2
0.00008
.66
.72274
.72282
.90992
.00008
.67
.72709
.72716
-99992
,00008
.68
.73143
73151
99993
0,1
.00007
.69
73577
.73585
.99993
.00007
4.70
1.74012
434,4
I.740I9
434,2
0-99993
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
o,r
0.00007
.76
.76618
.76624
99994
.00006
77
.77052
.77059
.99994
.00006
-73
.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
o . 00005
.86
.80962
.80967
,99995
.00005
-87
.81396
.81401
99995
.00005
.88
.81830
.81835
-99995
.00005
.89
.82265
.82269
-99995
.00005
4.90
1.82699
434,3
1.82704
434,2
9-99995
0,1
0,00005
91
.83133
.8 3 J3S
99995
.00005
.92
.83568
.83572
99995
.00005
-93
.84002
.84006
99995
.00005
-94
.84436
.8444(
434,3
.99996
,00004
4-95
1.8.1871
434,3
1.84875
434,3
9.99996
0,1
0.00004
.96
.85305
.85309
-99990
.00004
97
85739
.85743
. 09996
.00004
.98
.86174
.86178
.99996
.00004
-99
.86608
.86612
.99996
.00004
5.00
I .87042
434,3
1.87046
434,3
9.99996
0,1
0.00004
u
log tan ad u
Fo'
loosed gtf u
wF(/
lOQsIn fld u
w Fo'
lOflCSOQd U
SMITHSONIAN TABLES
Logarithms of Hyperbolic KuncUoim.
11
I oil ainti u
w Fu'
IOQ cnBli u
*> Fu'
lou Innli u
... t-,, 1
1l)U Olllll I]
5.oo
1.87042
-13-ti
i ,8704'
1,14.
\>.wt>
0.1
O.fXXKM
.0
.87477
,87481
.tPHtlli
.IHMH1.)
.0
. 8?< ) 1 1
. 871 1 1 <"
.'i*/j ( />
. 1 H II N >4
.0
.K834S
-883.!'
,<jjt^)"
, Ul h K l,|
.0.
,88780
8878.
.i^jjiX>
, IMiiHl.j
5-0
1.89214
43>l.
l.Hc).M>
I.M..
9.XMX>
IM
n, ,-,,,.!
.89648
,H<Xi>
.i^)*/i;'
. t ; < K K ).l
.0
. yooH.i
.ijooW
.'J-J 1 ^!/
. 1 H N H l,|
.01
.90SI7
.<;n;;.:t
..'j<j'j>'
.1 '111 11.1
.09
yoysi
.'KKJjiS
.t>ny
.til IX 1,(
5-10
1.91.186
434,,
l.9U8g
4.M.,
tt.WHV
".1
I ' . 1 II M M 1.)
.11
.01820
,iji8.;.i
.<!>?><>,'
.UHHI.l
.12
.02254
9--W
,tfH')','
. IX H H 1,1
1,1
,92681)
,<(.jfK),!
.w ftty
.I'llNI, 1
.!,
.931^3
.IMUfi
,*w>y
.UKHI.I
5,15
1-03557
134,.
1 ,935111
4,n..
').<// n't'
0,1
1 1 . t H H 1,1
.If
u.iyy-s
.<).!< JU|
.<fff>'/
. ( *i K 1,1
.'7
i)-\-\~(>
.<)] |--9
.iff-fty
.HiMJ
.18
,tj4Hfio
. y (8' '3
,ifW f '
.t'IHHl.1
19
.952(J4
.95.^7
MW)7
. 1 H H H t.l
5-20
I "5729
43.1,3
I -957,11
4.1 1..1
n.twff
n,t
tl, MXX^l
.21
, 06 I 63
, < )' 1 1 ( i( i
.tfffi'f
, H i| * ) 1
.22
<X>5<>7
.(XrfKNt
.i/Mj-V
, -ix/l
2,1
.97(132
97034
.IfUffl
u,n
. si,!
.24
. 974(/i
.|J74 ( J
.iff i 1 ft
. N**U
5.25
I.97<)00
4.14,3
1 .97<)<>.1
4,l!,.l
iJ.tppPtH
O.M
I'.lhMXIJ
,26
.#335
.i|8.1.'17
,ifP}jK
.11,1,1,1,1
.27
,987<X)
.i;8 i /7i
.tpjipjH
,l*Nl-!
.28
,<j()i'(>l
.<)<). ;itfi
,l^|i l i
(MUNI '
.29
.99(138
.Ift^i-lO
,iffjifH
. 1 K t- H !'
5-30
2.00072
434.3
...HK.74
4.14,3
tl.iffit^
11.11
M.CHMhIJ
33
,00041
ilMt'l-M
,i^^,S
JX^l!'
-33
.01375
.01. '177
,iji/((>M
t*i fit '
34
.01809
niHl I
.t>^>l
.'UK*)]
5.11
2.022.|4
434,3
, , lj(|
,i 1 1.1
, .(
-.17
.02678
.0,3112
.11.111.)
I.V)i,i
,i/^M
" : ;;;;;i
.38
354 7
,i/>i/>H
"ifl-itj
39
.03981
.0^3
.f^/jll). 1 )
!IM'W)J
5.40
2.04415
434.3
2.0-MI7
43 I..1
U.ij-^jf*
(t.tl
M.IKHItU
,41
. (),'|8.|()
.{i,lH|ii
.'/> l f
(,( 1,1,1 J
.42
.o<;^8.|
,d i i,!8';
, 1[
'_
4.1
.05718
.(I'tJ-F^O
[lyJ-JI.M
' '
44
.06152
.06154
j>mH
!<^x>j
5-45
.46
2 . 0^587
434,3
3 :!$S
I.M..1
IJ.I/^J'J.M
.'//?>^
l',*t
";:;:;"
47
.48
.07455
.07890
.07JS7
:i^l]
49
.08324
.oM,iL'5
i>J>W
ilJilll
5-50
2.08758
434 ,.1
3.()7ft)
4/11,3
tl.WK/W
(Ml
IMJTHNM
u
a Inn oil u
W FU
fl a (to uiF u
,;
00 iln B<! 11
t |
,,.,-/
Logarithms of Hyperbolic Functions.
u
lop sinh u
u Fo'
IOQ cosh u
ia Fo'
loo tanli u
u Fo'
loo coth u
5.50
2.08758
434,3
2.08760
434,3
9-99999
0,0
0.00001
.51
.52
-S3
.09193
.09627
.10061
.09194
,09628
.10063
-99999
99999
-99999
.00001
.OOOOI
.00001
-54
10495
. 10497
99999
.00001
S-S5
2.109.10
434.3
2.10931
434,3
9-99999
0,0
0. OOOOI
.56
.11364
.11365
99999
.00001
57
. 1 1708
.11800
.99999
.OOOOI
.58
12233
12234
.99999
.00001
59
.12667
.12668
.99999
.OOOOI
5.6o
2.13101
434,3
2.13103
434,3
9-99999
0,0
0. OOOOI
.61
.13536
. 13537
99999
.00001
.62
. 13970
.13971
99999
.00001
.63
. 14404
. 14405
99999
.00001
.64
14839
. 14840
99999
.00001
5-65
2,15273
434,3
2.15274
434,3
9-99999
0,0
0. OOOOI
.65
. 15707
.15708
99999
,00001
-67
,16141
.16142
.99099
.OOOOI
.68
. 16576
. 16577
.99999
.00001
.69
.I7OIO
.17011
-99999
.00001
5-70
2.17444
434,3
2.17445
434,3
9.99999
0,0
0. OOOOI
71
.17879
.17880
.99999
.00001
.72
.18313
.18314
.99999
.00001
73
. 18747
.18748
.99999
.OOOOI
74
.19182
. 19182
99999
.00001
5-75
2.IQ6l6
434,3
2.19617
434,3
9-99999
0,0
0. OOOOI
-76
.2O050
.20051
99999
.00001
77
.20484
.20485
-99999
.OOOOI
.78
.20919
.20920
.99999
,00001
79
-21353
.21354
99999
.00001
5. Ho
2.21787
434,3
2.21788
434,3
9-95999
0,0
0. OOOOI
.Si
,22222
.22222
.99999
.00001
.82
.22656
.22657
.99999
.OOOOI
.83
.23090
230QI
99999
.00001
.84
.23525
.23525
99999
.00001
5.85
2,23959
434,3
2.23960
434,3
9-99999
0,0
0.00001
.86
.24393
.24394
,99999
.OOOOI
-87
.24828
.24828
99999
.00001
88
. 25262
.25262
,99999
,00001
.89
.25696
.25697
.99999
.00001
5-90
2.26I3O
434,3
2,26l3I
434,3
9-99999
0,0
0,00001
.91
.26565
.26565
.99999
.00001
.92
.26999
,27000
99999
.OOOOI
-93
-27433
27434
99999
.OOOOI
-94
.27868
.27868
-99999
.00001
5-95
2.28302
434,3
2.28303
434,3
9-99999
0,0
0. OOOOI
.96
. 28736
.28737
-99999
.00001
-97
.29171
.29171
-99999
.00001
.98
.29605
.29605
.99999
,00001
-99
-30039
.30040
-99999
.00001
6. GO
2-30473
434,3
2.30474
434,3
9-99999
0,0
0,00001
u
loo Ian oil u
w Fo'
loo sec ad u
F '
loo sin ad u
Fo'
loo DID ad u
SMITHSONIAN TABLES
TABLE II
NATURAL HYPERBOLIC FUNCTIONS
Natural Hyperbolic Functions.
u
slnli u
'> F.,'
GOSll II
, Fo'
til nli u
" F,,'
Clltll II
- F,,'
o.ooo
0,00000
10,1
I. (XXXX
0,(
(1 .( X X X X 1
!(!,(
./
.000
.00010
.(XKXX
.(XX)KI
KXHUI.inl
t<l1MXKK),ll
.000
.O002(
.(XXXX
.(XM).!O
,',t x m . i N >
.!.'i<KiXM)
.000,
.(X)03(
.OIXXX
,IXXM
3. 13,1-, 1. 1
111111,1
.000.
.00040
.IXXXX
.(xxvjn
'''""'""
fi.!r, lMM ,
o.ooo.
0.00050
I0,(
1 .(XXXX
(1,(
(l.lXXI.'id
IU.<
.;.XKI.^I
.liXKXi.n
,OOO(
,O(X)(X
.IMXXX
. ( x X )U I
lU^i.d/
'/7i7.H
.0007
,(XXt7(
.(XXXX
.(Nioyo
l,|.;H. ;('/
j(r|oM ( j
.OOOi 1
,0008l
,(XKHK
. < X X W )
I, !.'!<>. IM
I.M '.;;;,(>
.0000
.oocxx
.(XKXX
.O.KKXI
1 1 1 1 . 1 1
'AM:;,/
0.0010
O.OOIOO
10,(
1 ,00000
0,0
n.(Xii(xi
11 1,11
MXI,(XI
HKHX,0
.0011
.OO1U
.(XXXKI
.1X11 IO
Jlt'J.il'J
H. !().(,;;
.oou
,OOI2(
.(XMJIX)
.(n.;o
'133.33
'"J'l'tl'l
.(X)I3
.00130
.()()()
.(XI [30
/' ( "'>"'3
.'i'J'7,.
.OOI,|
.00140
,<HXXX)
.1x114(1
/I.I.V'J
;,io.;,u
0.0015
0.00150
.001(10
10,0
I.(XXXX)
.O(XXX)
(>,(!
( t . i x ) i /;o
KM i
d 'Ji.oii
-M-H.-I
.0017
,01118
.00170
.(X)i8u
,<HK1(X)
.(XXX10
. ( M 1 1 '/{ 1
.1X11)^1
w: ;i<l
.t-1'1','
.ooiy
.00 MX)
.(XXXH)
.(K)HJ<)
?,;!(... Vt
Jwii
0.0020
0.00200
10,0
I.(XHXX)
(),('
U.IXI.MKI
IO,U
;;i n i . i x i
.1'iiHI.O
. 002 1
.OOJ1O
.(XX XXI
.UN, Ma
l/'l'. t'l
;',' ,v f.
,0022
.OO.320
.(XKXK)
. ( X \,!.',l }
1,'i-l .'>;>
.'./>' 1,1
.0024
.O0.i,10
. 1XI2-IO
.llfXXXI
.(N)^.(O
,| ld.fi/
1.^/1,4
1 >'.('', 1
0.0025
o.otwso
10,0
I.(XXXH)
(),()
(I.IHI,!.:;o
1 ( M i
.l(hl,(Mt
1'HMI.II
. 0026
,OO.rfio
.(X)Oilll
.(>,:i)
3 ; '| .f'.l
1 I/'J 1
.0027
.0028
:3!
,<HXX)fl
.IXXXXI
'III'-S!
It. 1 ;;* -M
!',??
.0020
.(X)2<X)
.(XUMH)
.INWI
.(!!..(
nH'j/i
:S
1.00300
.1x1310
10,0
[.(l(X)Otl
.(KXXNI
(,('
"'X
1(1,0
'i;!:!:i!
itn, i
IM |U,fl
.0033
.1x13 jo
.(XXX)I
.(xt'j.H)
',!./>,
'>/''/>
.003,1
,(X>33o
.(KXHII
,0113311
3*M.ni
tjlH, i
00,1.1
.1x1340
.OIHXII
.1x13 )(l
/u'l.tj
I'/.;;/!
0.0035
.(X)3f)
1.00,150
,(X>3(x>
10,0
.(XIOI1I
.(I1KXI1
0,0
.(MI3I)I>
II Ml
^^
Mid.,]
.0037
.(HI370
.ooiini
.(liMVD
,'"ll *'
"tll'l 1
.0038
.003!)
.00381)
. 003^0
.(HXX)I
.OIHXH
IN 13811
'f,t. If'
Ej/i
0.00.|0
.0041
.00-1 2
0.00400
.oo.| 1 1)
.011430
10,0
.(XXXII
.(XXXII
.(XXN)I
11,11
).<K>1<K>
,(KI| IU
,<m\.',n
10,11
j;;u.ixi
S'/t.y
.004,1
.0044
,(X>43O
,(K)-140
.(XX)OI
, (XXX II
.(l\,\
'.l-f., ! i''
ii
0.0045
0.00450
10,0
.(KHXII
0,0
).<KI,(.'i(l !
!<>,<
, , ,
1018
.0046
.00460
.I1IXXH
.(Xi4<K)
, , ,,
'(''' *
.0047
.0048
.0049
.00470
.00480
.00400
.(XXXM
.IXK101
.00001
,iMl|)'(i
.oa|Ko
.1x141x1
21
.111,0
-1 1",. 1 !
0.0050
,00500
10,0
.00001
0,1
l.(MK>
10.0
J(.H>
,!00,o
u
an ad u
F '
oo gd u
IV
tin qii u
F;
CIO fltl tl
- F u '
88
Natural Hyperbolic Functions.
u
slnli u
<1 Fo'
cosh LI
F U '
tanh u
-FO'
colh u
Fo'
0.0050
0.005OO
10,0
I. 0000 I
O,I
0.00500
IO,0
200.00
400,0
.0051
.00510
.00001
.00510
196.08
384,5
.0053
.O0520
.0000 I
.00520
192.31
369,8
.0053
.00530
.00001
.00530
188.68
356,0
.0054
.00540
.00001
.00540
185.19
342,9
0.0055
0.00550
IO,O
1.00002
O,I
0.00550
10,0
181.82
330,6
.0056
.00560
.00002
.00560
178.57
318,9
.0057
.00570
.00002
.00570
175.44
307,8
.0058
.00580
.00002
.00580
172.42
297,3
.0059
.O059O
.00002
.00590
169.49
287,3
o . 0060
0.00600
1 0,0
I.OOOO2
0,1
0.00600
10,0
166.67
277,8
.0061
.00610
.00002
.00610
163.94
268,7
.0062
.00620
.00002
.00620
161.29
260,1
.0063
.00630
.00002
.00630
158.73
251,9
.0064
.00640
.00002
.00640
156.25
244,1
O.OOfiS
0.00650
10,0
1.00003
o,r
0.00650
10,0
153.85
236,7
.0066
.00660
.00002
.00660
151.52
229,6
.00f)7
.00670
.00002
.00670
149.26
222,8
.oo!)8
.00680
.00002
.00680
147.06
216,3
.0069
.00690
,00002
.00690
144.93
210,0
0.0070
0.00700
10,0
I.OO003
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
187,6
.0074
.00740
.00003
.00740
135-14
182,6
0.0075
0.00750
10,0
1.00003
O,I
0.00750
10,0
133.34
177,8
.0076
.00760
.00003
.00760
131.58
173,1
.0077
.00770
.00003
.00770
129.87
168.7
.0078
.00780
.00003
.00780
128.21
164,4
.0079
.00750
.00003
.00790
126.58
1 60,2
0.0080
0.00800
10,0
1.00003
01,
0.00800
10,0
125.00
156,2
.0081
.00810
.00003
.00810
123.46
152,4
.0082
.00820
.00003
.00820
121.95
148,7
.0083
.00830
.00003
.00830
120.48
145,2
.0084
.00840
.00004
.00840
119.05
141,7
0.0085
0.00850
IO,O
1.00004
0,1
0.00850
IO,O
117.65
138,4
.0086
.00860
.00004
.00860
116.28
135,2
.0087
.00870
,00004
,00870
114.95
132,1
.0088
.00880
,00004
.00880
113.64
129,1
.0081)
.00890
.00004
,00890
112,36
126,2
0,OO90
0.00900
10,0
1,00004
0,1
O.OOQOO
10,0
III. II
123,5
.001; I
,00910
,00004
.00910
109.89
120,8
.0092
.00920
.00004
.00920
108.70
118,1
.0093
.00930
.00004
.00930
107.53
H5,6
.0094
.009-10
.00004
.00940
106.39
113,2
0,0095
0.00950
1 0,0
1.00005
0,1
0.00950
10,0
105.27
no,8
.0096
.00960
.00005
.00960
104.17
108,5
.0097
.00970
.00005
.00970
103.10
106,3
.0098
.00980
.00005
.00080
102.04
104,1
.0099
,00990
.00005
.00990
101.01
102,0
O.OTOO
O.OTOOO
10,0
1,00005
o,r
O.OIOOO
10,0
100. OO
100,0
U
tan od u
Fo'
SQO od u
Fo'
tin od u
<> Fo'
oao od u
* Fo'
SMITHSONIAN TABLES
8 9
Natural Hyperbolic Kuuctions.
II
slnli ii
"Fo
cosh ii
Fo'
In nli ii
F,/
(II) Ul II
~,v
O.OIOO
o.oioot
10,
l.(XXK)
0,1
O.OKHX
KM
I(X).OO,(
I(KX),0
.0101
.0101
.(XKX)
.OtOK
'J<).01,(
'ytn.,1
.0102
.010.;
,(K)1X)
.(tlO.H
<|M, 114,1
'Xi ,1
,0103
.0103
,(X!lKi;
.010, to
17-' )L
'J.l~',d
.0104
,010-1
.(XXX)
.O1O.|O
' /f J , 1 ^
'Ml.S
O.OI05
0,0105
10,(
I.(XXX
0,1
O.OIO.'iO
IO.I
O;;,.M.!
ijoX,(i
.OlOO' ,
.010(1
.(HHXX
.(IKKH)
"1-1 1.
H^,u
.0107
.01071
.OOlXrf
.(1 107*1
i),|..|d,j
'V. i-
.oioH
.oioKi
.(XXHX
.010)^)
'J.',.'iX>
HI;;.-, (
.oioy
.O10U(
.(XHXri
.010. Ml
'Ji.7 '/
'n.ii
O.OI10
O.OIIOf
10,(
l.!HXX)(
0,1
O.O1 KXI
10,1
Ml.Ol.l
HA,
.0111
.OUR
.OIHXX
.01 t 10
^I,("M
Kll!f
.0112
.om<
.(KXHtf
.01 l-'n
,'{,),. -Mr)
70" J
.0113
.oii.n
,(XXX)(
.01 1.10
M..|ljH|
/'M
.0114
.Oll.|(
.OOIXH"
.01 l,|0
/.;*.t.i
0.0115
O.OII.I*
10,0
l.(XIIX)7
0,1
o.oi i,<;o
10,1
Hll.lttH)
7.'i f ', I
.011(1
.01 ifx)
,1111007
,<M MX)
^-'i.,:!
M.I.I
.0117
.01170
.IXHK17
.01 17 '
H ; i,.l|,'l
.0118
.onHo
.(XMMI7
.01 1 Ho
H1.7V.
7iftl
.0110
.01100
.IHXX17
,OI I'M)
Wl.u.iH
0.0120
0.01 200
10,0
I.o(xxi7
0.1
(I.OI.IOO
lo,o
H.1-U7
'01,
.out
.oi.no
.(11)007
.01. MO
H.'.dj.j
(Jt.lil)
.OUJ
.012JO
.(MMX17
.01 J,!( 1
H I . i )'/
(>7i, M
.012,1
.012.10
.(xxx)S
.OI.MII
Ml ..(us
(/HI.IJ
.013^
.01J40
IXXXlfi
,OIJ,|0
ji i,i.,;,
f >,'i",.
0.0125
0.01250
10,0
.(XXX)N
0,1
0,(H.!,'i()
10,0
Mil.1H>|
OlOO
.Ot2(i
.01:: 60
.(XMKfH
.()!,!(*)
"o (';
o 'U'M
,011-7
.01270
,(XXK)H
.01, 170
y-'O-M
o'-o'o
.oiaH
.oi-'Ho
.(HX)OM
(lid 'I
.0129
.ouyo
.(XXXtf
.01 JX)
r/.;\j.
t**Vj
0.0130 (
1.01300
1 0,0
.CKXXXS
0,1
u.oi.im
10,0
"()..,'-
'yi 7
.0131
.01310
,<XXXX)
.01,11(1
;'d.,t|o
"iMj'y
.01.13
.01.1 M
.(XXMHJ
.(M.j.ro
.'v'.I.'J
.0133
.01330
.(XXXX)
.01.1,10
7,'i . l-j.
.oi.n
.013.10
.(X.XXHJ
.01,140
s.M'iy
0.01.15 C
01350
10,0
.(XKXM)
0,1
o.oi.iso
. tr .
M
-0136'
.013(10
,(XXXX>
;',(.<>,( i
(' ll(l
.0137
,01,170
.1KKKHJ
.01 17O
'' ' t 'j.
.0138
.01380
.(XXIIO
.ot.iHo
/.''iftM
'i ' '. 1
-0130
.01,11)0
.(XX) 10
.IM.I.X.
y'i'<*t\7
5 IX". 5
0,0140 o
.01400
10,0
1, OCX) 10
0,1
<).ii,|rti
1(1,1 1
"1
'11 J
.0141
.01410
.(XX)IO
.01410
''0 i)-'-
;! () '
.0142
.01,1.20
.01430
.(XX) 10
!!;!!
70.4.7
.Vj.n.'j
, .01*1
.01440
.(HX1IO
.(ll,|'|(l
t ).,{.&
|Hv,'j
o,oi,|5 o
.0146
.01450
.01i|f)O
10,0
.0001 1
0,1
0.01450
IO.II
Js'^J
.Wi
.0147
.0148
01470
01480
.(xxni
.(XX>II
.01470
;^<>!u
4'",'J
.0149
or. [oo
.00011
\n\Mi
*x!'no
I.W4
0.0150 o
01500
10,0
I.OOOII
0,2
o,oi5(vi
10,0
^I.rt 74
H-1,1
u 1 IB
n oil ii
Fo'
100 (111 U
F u '
ilri gd ii
w
010 pit U
V "
yo
Natural Hyperbolic Functions.
u
slnli u
Fo'
cosh u
<" F u '
tanh u
u Fo'
calh u
Fo'
0.0150
O.OISOO
10,0
1. 0001 1
0,2
0.01500
IO,O
66.672
444.4
.0151
.01510
.00011
.01510
66.230
438,5
.0152
.01520
.00012
.01520
65-795
432,8
.0153
.01530
.00012
-01530
65-365
427,2
.0154
.01540
.00012
.01540
64.940
421,6
0.0155
.0156
0.01550
.01560
:o,o
I.OOOI2
.00012
0,2
0.01550
.01560
IO,O
64.521
64.108
416,2
410,9
.0157
.0158
.01570
.01580
.00012
.00012
.01570
.01580
63.699
63.296
405,7
400,5
.0159
.01590
.00013
.01590
62.898
395,5
0.0160
O.0l6oo
10,0
1.00013
0,2
o. 01600 ,
10,0
62.505
390,6
.0161
,Ol6lO
.00013
.01610
62.117
385,8
.0162
.01620
.00013
.01620
61 . 734
381,0
.0163
.01630
,00013
.01630
61.355
376,3
.0164
.01640
.00013
.01640
60.981
371.8
0.0165
0.01650
10,0
1.00014
0,2
0.01650
10,0
60.612
367,3
.0166
.01660
.00014
.01660
60.247
362,9
,0167
.01670
.00014
.01670
59-886
358,5
.0168
.01680
.00014
.01680
59.529
354,3
.0169
.01690
.00014
.01690
59-177
350, r
0.0170
O.OI70O
10,0
1.00014
0,2
0.01700
10,0
58.829
346,o
.0171
,01710
.00015
.01710
58.485
342,0
.0172
.01720
. ,00015
.01720
58. 145
338,o
.0173
,01730
.00015
.01730
57-809
334,1
.0174
.01740
. .00015
.01740
57-477
330,3
0.0175
0.01750
10,0
1. 00015
0,2
0.01750
10,0
57-T49
326,5
.0176
,01760
.00015
.01760
56.824
322,8
.0177
.01770
.00016
.01770
56.503
319,2
.0178
.01780
.00016
.01780
56.186
315,6
.0179
.01790
.00016
.01790
55.872
312,1
0.0180
O.OI8OO
IO,O
I, 00016
0,2
0.01800
10,0
55.562
308,6
.0181
.OlSlO
.00016
.01810
55-255
305,2
.0182
,.01820
.00017
.01820
54-951
301,9
.0183
,01830
.00017
.01830
S4.65t
298,6
.0184
.01840
.00017
.01840
54-354
295.3
0.0185
O.OI85O
10,0
1.00017
0,2
0.01850
10,0
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
.0189
.01890
.00018
.01890
52.916
279,9
0.0190
0.01900
10,0
I. 00018
0,2
0.01900
10,0
' 52.638
277,0
.0101
.01910
.00018
,01910
52.362
274,1
,0192
.01920
.00018
.01920
52.090
271,2
.0193
.01930
.00019
. ,01930
51.820
268,4
. -0194
.01940
.00019
.01940
51-553
265,7
0.0195
0.01950
.10,0
1.00019
0,2
0.01950
10,0
51.289
263,0
,0196
.01960
.00019
.01960
51.027
260,3
.0197
.01970
.00019
.01970
S0.768
257,6
.0198
.01980
.00020
.01980
50.512
255,0
.0199
.01990
.00020
.01990
50.258
252,5
0,0200
O. 02000
IO,0
1,00020
0,2
0.02OOO
IO,O
50.007
250,0
u
tan ad u
Fo'
seo ail u
* Fo'
sin ail u
Fo'
oso ad u
Fo'
1
SMITH80NUN TABUS
Natural Hyperbolic Functions.
II
si nil U
,1V
cosh il
.w
Innli u
w F,'
Cdlll U
O.02OO
O.O200O
1 0,0
I. 000 2O
0,2
0. OJOOO
IO,O
50.007
.150,0
. 020 1
. JO 1
.(MX)JO
. ( )Jl Mil
.|'>.7.'!8
-:-IX,5
.O2O2
.02020
.OOOJO
. o.io.io
4u.;ii'!
-'4,'i.o
.020.1
.02030
.01X121
.02030
,|i)..r()8
.:.|.,',()
.020-1
.020-10
.0<X>21
.02010
,|i).oj i
j. 11 1,3
0.0205
0,02O5O
10,0
1. 001)21
0,2
0.02050
1 0,0
4.^.787
,!37,i)
.O2()6
.OJOfXJ
.00021
.O.JOiMI
18-riiif
-MS.' 1
.0207
,02070
,(XH)21
.().!( I/O
.18,31(1
-M3.3
.0208
.O2O8()
,0(X)22
,O.M)8.>
.|8.oS.|
MM
.020<J
.02001)
OOO22
.(tJIMX)
l/.-^.l
228,-)
O.O2IO
O.02EOO
10,0
l.(XM)JJ
O,2
D.O2IOO
10,0
.17.(i,-h
.:.'.(,,'/
.021 1
.O2I 1O
.{XX 122
.021 10
.17,4'"'
.:.;,|,(i
,O2I2
.O2I2O
.CXX)22
.(121-iO
47.1/7
''-', 5
.021,1
.02130
.(XX (23
.02130
4 (l ' l J;j. t )
.!.!0,,|
.0214
.02140
.(XX)23
,02140
4"-73<'
2.8,3
0.0215
0.02150
IO,O
I.OOOJ3
0,2
O.(t.!lf>0
10,0
.i*i.:.i'>
-!i 6,3
OJiO
.O2l6()
.O1X)23
.0,!l()i)
I''-3'M
"'K,i
.0217
.02170
,(XXU|
,02170
.((l.tHJO
21.!, 3
.0218
.O2l8()
.(XX)24
.(UlHo
4:1.870
210,.|
.0210
.021 go
.OOO2.|
.O2I (JO
.|.S.dfJ
208,5
O.O22O
O.O2200
10,0
1 ,(XX)24
0,2
O.O.!2lX)
10,0
.|S..|t'J
-ll^l.fi
.0221
.0221O
.txxui
.OJ.MO
i;> -.">''
-ID.], 7
,O222
.02220
.(XX)25
.1)2220
l.'i."5-'
,!U,!,(J
.022.1
.022.10
,(XX)25
.O.-'.t.lO
44.8i;u
.!Ol,I
.022-1
,022-10
,CXX)25
,02240
.|.|. "!io
>'MJ
0,0225
0.02250
1 0,0
i.(XX)J5
0,2
O.U2.J50
1 0,0
.M..IS.I
l'J7,5
,0226
,0226V)
.00026
.o.!.;/ HI
lO.'i.j-
,0227
.02270
,0(X>26
.O2.!>*0
4| ,ixxi
i'i|,o
.02.'8
.O2280
.000 ..'6
.!)2.!KO
.|3.fW>7
M).!,3
ojay
.022OO
,00021)
.OJJOO
43-"7"
lJf),7
0.0230
0.02300
10,0
I.OOOJ6'
0,.t
o. 0.1300
10,0
43.4W.
iHij.it
.0231
,02.110
.IXX127
.02310
. |3-~'i )U
tx!-i
. 0232
.023^0
,(XX)27
.(I.J320
.13.111
1 85,8
-0233
.O2330
.00027
. 0,1331 )
4,!. ),;()
iHl,,f
.0234
.02340
.00027
-O.M.IO
l.i.X-1.1
l82,f.
O.O235
0.02350
10,0
I,(XX)28
0,2
0.02330
I0,(l
,1.!.VU
l8l,[
.0236
.OJ,l6o
,00028
.(!.!3(H>
.u.'iMi
i/o.'i
.0237
.02370
.(XX 128
-0.137"
,|2.2(i.)
178,0
.0238
.02380
.(XX 128
.|,!.OJJi
IX' '.5
.023Q
.02390
.O002IJ
.0231x1
.|i.8|;
1 X5.<>
0.02-jO
0.02400
10,0
I .(XX) 20
0,2
0,0,1400
10,0
4 1. (>;;
i/.i,''
,0241
.02410
. IXX)2<)
.02410
41 ,. '!(',!
17.1,1
.O2.|2
.O2.|20
.(XX)20
.02,120
I I- 33"
170,7
.O2.|3
.02430
.(XX>30
.<>,!.) 30
41 . IfMI
.02,1:|
.O2.).|0
.(XX).IO
.O.!.|40
.(tl.iWJ
f'xIfJ
0,02.15
.0246
0.02450
.02460
10,0
I.(X'X\'|0
.(XX30
0,2
0.<)2.|,iVt
. 0.!4(K)
10,0
.|().6sij
ifrfi.fi
.0247
.02-170
.(XX)3T
,().'..\(X)
K). 101
id 'I (J
.0248
.02480
.OO03I
.02470
I". 331
'".)iV
.0249
,02400
.O003I
.OJ48.J
40. If*)
iftiia
0.0250
0.02500
10,0
1,00031
0,3
0.02.11)9
10,0
.(O.ooH
Ifkl.O
u
tan QI| u
w Fo'
BOO gtl u
w Fo'
iln ail 11
uf "'
CDC ad u
IV
SMITHDOKIAN TAD us
Natural Hyperbolic Functions.
u
ilnli u
coFo'
cosh u
td Fu'
lanh u
Fo'
cofh u
! N F '
0.0250
0.02500
10,0
1.00031
0,3
0.02499
IO,O
40.008
160,0
.0251
.02510
.00032
.02509
39-849
158,7
.0252
.02520
.00032
.02519
39.691
157,4
.0253
02530
.00032
.02520
39-534
156,2
.0254
.02540
.00032
. .02539
39-379
155,0
0.0255
.0256
0.02550
.02560
IO,0
I .00033
.00033
o,3
0.02549
.02559
IO,O
39-224
39-071
153,8
152,6
.0257
.0258
.02570
.02580
.00033
.00033
.02569
.02570
38.919
38.768
i5i,4
150,2
.0259
.02590
.00034
.02589
38.619
149,0
0.0260
.0261
.0262
.0263
.0264
0.02600
.02610
.02620
.02630
.02640
IO,O
1.00034
.00034
.00034
.00035
.00035
o,3
0.02509
.02609
.02619
.02629
02639
10,0
38.470
38.323
38.177
38.032
37-888
M7,9
146,8
145,7
144,5
143,4
0.0265
.0266
.0267
.0268
.0269
0.02650
.02660
.02670
.02680
.02690
10,0
1.00035
.00035
.00036
.00036
.00036
o,3
0.02649
.02659
.02669
.02679
.02689
IO,O
37-74S
37-603
37-462
37-322
37-184
142,4
141,3
140,2
139,2
138,2
0.0270
0.02700
IO.O
1.00036
o,3
0.02699
IO,O
37.046
137,1
.0271
.02710
.00037
.02700
36.909
136,1
.0272
.02720
.00037
.02719
36.774
135,1
.0273
.02730
.00037
.02729
36-630
134,1
.0274
. 02740
.00038
.02739
36.505
133,2
0.0275
.0276
0.02750
.02760
IO,O
i .00038
.00038
o,3
0,02749
.02759
IO,O
3(5-373
36.241
132,2
131,2
.0277
.02770
.00038
.02769
36.110
130,3
.0278
.02780
.00039
.02779
35-980
129,4
.0279
.02790
.00039
.02789
35.852
128,4
0.0280
0.02800
10,0
1.00039
o,3
0.02799
ro,o
35.724
127,5
.0281
.02810
.00039
.02809
35-597
126,6
.0282
.02820
.00040
.02819
35-470
125,7
.0283
.02830
.00040
.02829
35-345
124,8
.0284
,02&|O
.00040
.02839
35-221
124,0
0.0285
0,02850
10,0
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
.0289
.02890
.00042
.02889
34-612
119,7
0.0290
0.02900
IO,O
1.00042
0,3
0.02899
IO,O
34-49.2
118,9
.0291
.02910
.00042
.02909
34-374
. 118,1
.0292
.02920
.00043
.02919
34-256
117,2
.0203
.02930
.00043
.02929
34-139
116,4
.0294
.02940
.00043
.02939
34-023
ns,7
0.0205
0.02950
10,0
1.00044
0,3
0.02949
10,0
33-908
114,9
.0296
.02960
.00044
.02959
33-794
114,1
.0207
.02970
,00044
.02969
33-680
ii3,3
.0298
.02980
.00044
.02979
33.567
112,6
.0299
.02900
,00045
,02989
33-455
m,8
0.0300
0.03000
IO,O
1.00045
0,3
0.02999
10,0
33-343
iii.i
11
tan gd u
*> Fo'
aeo ad u
u Fo'
sin ad u
Fo'
080 Od U
w Fo'
SMITHSONIAN TABLES
93
Natural Hyperbolic I'unclioiiB.
11
sinli u
wFo'
cosli u
... FV
tnnli u
F,,'
CO 111 U
F u '
0.03OO
,O3Oi
.0302
.030,1
.0304
0.03000
.03010
.03020
.03030
.03040
10,0
1.000.15
.ooo.|5
.ooo.]6
.o<X)46
.000.16
0,3
.o.l( KM;
0,1O]9
.03O.!()
.o,J<M'J
1 0,0
33-313
33--M3
33-l-M
33.01,1
,!-!.!>),S
111,1
' 10,3
109,0
108,9
0.0305
0.03050
10,0
I. (xx). 17
o,3
(1.0,5011)
IO,O
3-J.>'<>7
1117,5
.0306
.03060
,(XK>4?
.O.IO^'J
'.!"!',. "if!
JV 1
.0307
.03070
.00047
.<M'H)
''",.v!
'
.0308
.0309
.03080
.03000
.(XX). 1 7
,000.18
.0.1079
3-!. 373
in,l,7
0.0310
0.03100
10,0
i ,(xx).i8
o,3
0.0.10W
[(),u
3 ;..:< M
lll-l.O
.0311
.03111
.(XX 148
.O3KXJ
,!" l( '.'i
'3.4
,0312
.03121
.00049
.031 19
,1J.(K..!
iu.!,7
-03M
.03131
.00049
-O.UJ9
'u 'H'^M
101,4
.0314
.03141
,(xx>49
03139
. ' .
0.0315
0.03ISI
10,0
I .00050
0,3
0.03140
10,0
31.757
100,7
.0316
.0,1l6l
.00050
.03159
3 ' ' '?' '
1 1 X ), 1
.0317
.03171
,<xx>5O
.1131(19
3'. Ji.'i' 1
W,5
.0318
.03181
.(xx>5i
0.1170
3' .-t.'jX
u '
.0310
,0,1iyi
,0005 I
.O.U.t9
3I-.IMJ
!K ,-!
0.0320
0.03201
10,0
1.01x151
o.3
o.o.U'JO
10,0
3 !..;( I
)7,'*
.0321:
.0321 1
.0005.!
O.l 21 V)
,11 - "'3
07,0
.0322
.0,1221
,0005.:
.0,1-! 1 9
,11 .irfix
'"''.''il
03-M
.03231
.(XX15-*
,0,1.'.!')
3O>'V '
9. L ii M
.032.1
.03~M I
.00052
-'MAW
3".' 1 /,'>
95.-!
0.0325
0,03251
10,0
I.o(xi53
o,3
o.<MJ.|<j
10,0
.10.780
).|,6
.0326
.03261
.00053
.<M.'i9
,jo,t8fi
'J.I.I
.0327
.03271
.00053
.I>,'1,!' "9
3o.;i'>-i
!J3i,'i
.0328
.03281
,00054
.03.) 70
,tO.,|</J
t),i,9
-0320
.03^91
.(x>054
.0,1 ,.'80
,10..|ilfi
!)'!-!
0.0330
0.0,1301
10,0
r.(x*)5.|
0,3
o.0.p>0
10,0
;v>..u.|
<)i,8
-33I
.03.311
.00055
. 0.1,11 xj
;tn, '.;,(
91,-'
.033-'
.03321
.00055
<M,iio
,K i . 1 .1 j
9O,7
.0,1,13
-03,131
,(XK)55
-O.l.W'J
3'i,O|i
'Xt.l
.0,134
.03341
.00056
-O.Ul'J
W.DSl
8*j,d
0.0335
0.03351
10,0
I .00056
0,3
0.033.1!)
10,0
W.Hf.j
8-j.i
0336
-03361
.00050
, ( t.i.i.Ho
^X73
Wt,5
.0337
.03371
,(XM57
O.l.Vc)
.m,'*8. ! i
88.0
-0.138
.03381
.o(Xi57
-0,1.179
^.. ( i<j>'
87.5
.0339
.03391
,<xx)57
-03,189
.'.').; Sio
87,0
0,03.10
0,o,l/|OI
10,0
1.00058
0,3
o.ii.uw
10,0
.:<).. 1-13
86,fi
.0341
.03411
.(X1058
,0,V|(X)
:<>-. 137
8(1,0
.0342
,03:|_>I
.1x1058
O.VIl'J
,!ij,-!.11
85,, 1
.03.1,1
.03431
.<xxi5<)
.03.1 J*j
,!tj. ttrfi
85,0
.0344
.03441
00050
.0.1439
.I'J.I^I
8.|,5
0,0345
0.03451
10,0
1.00060
0,3
0.0.1440
10,1)
j.w7
81.0
.0346
.03461
,(XXX"N)
.,145 ( J
jH.gi i
H.l.S
.0347
.03471
.00060
,03,169
.iK.H.ju
H.y>
.0348
.0,1481
.(XXX"il
0,147*J
;:8.x,|7
8.!,S
0349
.03491
.(xxXil
.(t,viHy
n 'H.(AS
8j,'i
0.0350
0.03501
10,0
i.oooO't
0,,|
o.o.n<x>
10,0
"'H. T 'iH.l
8i,r,
u
Inn oil u
w F u '
BOO Oil U
Fy'
In od u
-F,,'
Cto gil u
M Fg'
SMITHSONIAN TADUES
94
Natural Hyperbolic Functions.
u
sinh
in Fo'
cosh u
&>'
tanh u
"JV
colh u
F '
0.0350
0,03501
10,0
I. 00061
0.4
0.03499
IO,0
28.583
81,6
.0351
035II
.00062
03509
28.502
81,1
.0352
.03521
.00062
.03519
28.421
80,7
.0353
.03531
.00062
03529
28.340
80,2
.035-1
.03541
.00063
03539
28.260
79,8
0.0355
0.03551
IO,O
1.00063
0,4
0.03549
IO,O
28.181
79>3
.0356
.03561
.00063
.03558
28.102
78,9
.0357
.03571
,00064
.03568
28.023
78,4
.0353
03581
.00064
.03578
27.945
78,0
.0359
.03591
.00064
03588
27.867
77,6
0.0360
0.03601
10,0
1.00065
0,4
0.03598
10,0
27.790
77,i
.0361
.03611
.00065
.03608
27.713
76,7
.0362
.03621
.00066
.03618
27.636
76,3
.0363
.03631
.00066
.03628
27.560
75,9
.0364
.03641
.00066
03638
27.485
75,4
0.0365
0.03651
IO,O
1.00067
0,4
0.03648
IO,O
27.409
75,0
.0366
.03661
.00067
.03658
27.335
74.6
.0367
.03671
.00067
.03668
27.260
74,2
.0368
.03681
.00068
03678
27.186
73,8
.0369
.03691
.00068
.03688
27.113
. 73,4 ,
0.0370
0.03701
10,0
1.00068
0,4
0.03698
IO,O
27.039
73,o
.0371
.03711
.00069
.03708
26.967
72,6
.0372
.03721
.00069
.03718
26.894
72,2
0373
.03731
.00070
.03728
26.822
71,8
-0374
.03741
.00070
.03738
26.750
71,5
0.0375
0.03751
IO,0
1.00070
0,4
0.03748
10,0
26.679
71,1
.0376
.0376:
.00071
.03758
26.608
70,7 1
0377
.03771
.00071
.03768
26.538
70,3 1
.0378
.03781
.00071
.03778
26.468
70,0
0379
.03791
.00072
.03788
26.398
69,6
0.0380
0.03801
IO,O
1.00072
0,4
0.03798
10,0
26.328
69,2
.0381
.03811
,00073
.03808
26.259
68,9
.0382
.0382:
.00073
.03818
26.191
68,5
.0383
.03831
,00073
.03828
26. 122
68,1
.0384
.03841
.00074
.03838
26.054
67,8
0.0385
0.03851
10,0
1.00074
0,4
0.03848
10,0
25.987
67,4
.0386
,03861
.00075
.03858
25.920
67,1
.0387
.03871
.00075
.03868
25.853
66,7
.0388
.03881
.00075
.03878
25.786
66,4
0389
.03891
.00076
.03888
25 . 720
66,1
0.0390
0,03901
10,0
1.00076
0,4
0,03898
IO,O
25.654
65,7
.0391
.03911
. 01x576
.03908
25.588
65,4
.0392
.03921
.00077
.03918
25.523
64,0
-0393
.03931
.00077
.03928
25.458
64,7
0394
.03941
,00078
.03938
25.394
64,4
0.0395
0.03951
IO,0
1.00078
0,4
0.03948
10,0
25.330
64,1
.0396
.03961
.00078
.03958
25.266
63,7
0397
.03971
.00079
.03968
25.202 .
63.4
.0398
.03981
.00079
.03978
25.139
63,1
-0399
.03991
.00080
.03988
25.076
62,8
0.0400
0.04OOI
10,0
1.00080
0,4
0.03998
10,0
25.013
62,5
u
tan ad u
Fo'
nea ad u
w Fo'
sin ad u
Fo'
080 ad u
Fo'
SMITHSONIAN TABLES
95
Natural Hyperbolic Kimctlonn.
II
ilnli u
*
cosli u
.K
tnnh u
r,/
CO III 11
F u '
0.0400
,0401
.O.1O2
.0-103
0.04001
.0401 i
,040-21
.04031
1 0,0
l.oooHo
,00080
,(KXi8i
.00081
0,4
t).O3<X)8
.04008
.o|oi 8
10,0
J4.M.7
fi.;,j
61,8
'M.S
6l,2
.040-1
.04041
.01x18,;
,'
0.0405
.O.]0()
.0407
.0408
.0.109
o.0.|05i
,040(11
.04071
.o-ioHl
.04001
1 0,0
i ,(xx>8j
.01x18.:
.00083
.1x11x83
.ixx>84
0,4
0.040.18
. 040.18
,040:18
.04078
.04088
-'1 /".'
I)0,O
0.0410
0.04101
IO,O
1.01x184
0,4
0,040118
10,0
J.I. 40 1
JW.S
.0411
.0412
.04111
.04121
.ixxi84
,(xxxH5
Io[li8
Jl!'.':' ; ',
r!!j
.0413
.0414
.04131
.04141
.00085
.(XX)H()
.04138
i!:S
SH|.I
0.0415
.O.|l()
0.04151
.04101
10,0
I. OOO.H6
.00087
o,.|
0.04148
.041.18
10,0
;V|. 1 10
syl
.0417
,0418
.0410
.04171
.04181
.04101
.00087
.OCXtfW
.04178
.04188
ii:I
,'i7..'>
!i'',O
0.0420
0,04201
10,0
t .00088
0,4
0.04 M>8
10,0
-M.8.M
;|(',7
.0421
,04211
.01x189
.04^08
';\-'/' } '/
,'i fl ,4
.(XUJ
.04221
,ixxi8o
.04.117
.!,! ./M
.'i' 1 , i
.0423
.04231
.(XXjty)
.O4,!,!7
M.' 1 .'':!
!i.V>
.0424
.04241
.1X1000
.04.137
J.1..'W)
,'i,S,6
0.0425
0.04 1151
10,0
1. 0001X1
0,4
o.n4,.'.|7
to.o
.M-.'ill
SS..1
.0426
.042(11
.(MKM)l
<M.!!X
,13.488
Mi, '
.0427
.04^71
,<X)l)i)I
.O.|.!()7
*M.. i.i.i
H4.8
.0428
,04281
.OIMXV
.04.1/7
M-.^'o
M. ( >
.0420
.04291
.(X10.J.!
.04,187
-M..I-'I
S-l.,1
0.0430
0,04301
10,0
I.OOOJV
0,4
o.(i4,!i)X
10,0
.'.,{,. W*
S-l.<>
.0431
.04311
,(xx>93
.04307
,M.'"d
.'1,1.8
.043^
.04321
.(KXXJ.l
.04,HX
.'.1. ' (l .l
. r i,1.6
.04.1.1
.04331
.(KXXJ4
. 043.7
.'.I. Hl
S.I..J
.0434
.04341
. 00004
.01.1.17
J.I. n jit i
S.I. I
0.0435
0.04,151
10,0
r.ocws
0,4
0.04347
10,0
-M.'K'.l
SJ.8
.043(1
.04361
.fXXHJ.i;
'IM357
-f.t.OSn
5*',(
0437
.0437t
,(XX)05
.043(17
,M.8i|H
.U.I
.04.18
,04381
,1XX*.)6
.01.177
,; .; . 8 1' i
!i-, 1
.0-1,30
.04301
,0001X1
.04.187
,!.!.7')1
,'ii.M
0.0440
0.04401
10,0
1 (XXXJ?
O..1
0,04307
1 0,0
< . .. , ,
S I /'
.0441
.044 tr
.(K)(K,)7
, if ,
.04407
,!,!>/'
M.-l
.0442
.04421
'
.(MXHjH
.OIM7
M.('3'>
,'ii.J
.044,1
.04431
,<HX;8
.041J7
r,!,HNM
,'iO,f>
.0444
.04441
.(XX MX)
.('44.17
-M.5.1/
50,7
0.0445
0.04451
10,0
i .ooogo
0,4
0.01447
10,0
..'.!. 47
LJO.J;
.0446
.04461
.(XKXX)
('1457
.!,!.. U<
!i",,l
.0447
.04471
.(XHCX)
.04467
r!.!.,lK('l
50,0
.0448
.04481
.0011X1
.01477
,M.'l3'i
4').H
.0449
.04493
.00101
.04487
J,!.rfy
iy.fi
0.0450
0.04502
ro,o
I. 00101
0,5
0. 04497
10/1
.r.!..;.17
.19,1
u
Ian ad u
w Fo'
800 Ull 11
w Fo'
itn ait u
-w
cm od u
F</
SMITHBONIAN TAHUO
Natural Hyperbolic Functions.
11
Inli u
"< V,,'
oosli n
-Co'
In nli u
-Fy
00 111 U
* IV
o.o-15'i
0. 0.1502
10,0
l.(X)KH
o,S
o.o.|.|OX
10,0
.a.17
'1!J,3
.0.151
.0.151-'
.(xmi,:
.0.1507
22. lH8
19,1
.o.l5-i
.045-!-!
.(M1IO.!
-0.1517
22.1.19
'|8,9
o,( 5,1
.045.1-'
.(Mil O,l
-0-15-7
22.O1JO
4H,7
.0-15-1
.O.I5-I-*
.( 1010,1
o.|5,17
2J.O-U
-lH,5
0.0.155
0.0455-'
10,0
1 .(XtlO.j
0,5
0.045-17
10,0
ai.OW
4H.3
.0.150
.045''.!
,OOIO.|
.0.1557
-!'-!> 15
.|8, i
.o-l 5;
-o.rix-
.00104
.o,15'>7
2i.Mj7
47-N
.o.llH
.0.]5.!
.(K)l(>5
-0-15X7
2 [ , H.ll)
47,6
.0.150
.0,15').!
.(KH05
.045X7
2I.H02
4X,4
O.O,|6O
0. 0.|(.0.!
10,0
1 .OOKWl
0,5
0.04507
10,0
21-754
I7.u
.O,[0l
.o.|6l.i
.(HtH)f)
.O.((K)7
21.707
4X,
.O.|0.!
,O.|(l.!J
.<KHOX
.04617
21.660
,[6,8
,O.|0,1
.().|6,1.)
.001(17
,o.]6.:x
a (.61.)
,10,6
O lO'l
.().l(),],t
.ooioS
.0.16,17
21.567
i\Ci t i\
0.0.165
(1.0405.!
10,0
I .(x>l()8
0,5
o. (146,17
10,0
46,2
.(1,1'rii
,(),](K1J
.(HIKHJ
.0-1(157
21.4X5
46,0
.0.167
,0.167.!
.(K)IO(J
.0,1(167
21,.|2(>
45,8
O 1'i'i
|OS '
AMI 10
.0.1077
2 1 . 38,1
45,6
.o,]6<)
.o.|0<v
.(XII 10
.0.1687
21.3,18
45,4
0.0470
0.0.170.)
10,0
I .(XII 10
o,5
0,0.1697
10,0
ar.jya
45,3
.(MX'
.11,171.!
.(Xll 11
,0,1707
2I.2.|X
'I5,o
.0,172
,0-1 7 j
.(X)l II
.04716
2 1 , 202
44,0
'oi7 1
.O,17 1,!
.OOI 1.!
,o,|7.;6
21.157
44,7
.04X-I
.o.ix'i-i
.0011.!
.0,1X36
21,113
-14,5
0.0.1X5
0.0475.!
10,0
1 .001 I.I
o,5
0.0.17.16'
10,0
21.068
-1-1,3
.04X6
.0,170,!
.001 M
.0-175(1
21.024
1-1,1
0.1X7
,(101 1.)
.o.|X06
2().(}Ho
13,9
.0.178
,o,|7Hj
.(KM l,|
.04X7''
20.<j;i6
43,7.
.0470
.047').!
.(X)l 15
.0.1 XH(i
ai.K()3
43,6
0.o.|Hn
O.O-lHo,!
10,0
1 .001 15
0,5
o.o.lX'Xf
10,0
^'tt'ili
43,4
.<>|8.i
!o'.|H,!J
.(KM 1(1
!o!l8i6
20.763
13,0
p o,|Si
.0 |M,i.i
.(Hll 17
.0.1826
no . 7-0
'U ! >8
!o.|8'i
.(148.).!
.001 17
.048,16
20.677
-I -',7
0.0.185
,o,(HO.J
10,0
I.OOII8
.(XII lit
o,5
d.o.l8,iO
.0,1856
10,0
20.635
;!
:U!HX
,0]88
<M8o
.d.|Hx'
. < l.iHHj
,<l,|H'jJ
.00119
.(XII H)
!()4H76
2(). 5 5"
20 . SO.'!
Si
O.O.jOO
o.o.|;v
10,0
1 .00130
.O01.il
o,5
o.O-ifyXi
.o,|iX>6
10,0
aol-lSi
:!u
.010,.!
'.(MOJJ
.(XIU'I
.(),1<J 16
20.3,12
4i,3
.(),)* ),!'!
,0(112J
. ( >4o;;6
i!0.300
'ii,i
'Q.W
.010<N
. 00 1 .12
.04936
20.259
'10,9
0.0.105
0.04052
10,0
I .(X1I2.1
.0012.1
0,5
0.0,1946
.0.1956
IO,O
20. 2 1<)
20.178
40,8
-10,6
.0.107
.0.107-!
,o,|i.tH2
.(XH2.|
,0-lt/lll
.o.l'JXf")
20.01);
40^3
!<M(
,041^92
.(XHJf,
.(MUnG
20.057
'|0,I
O.OSfX)
0.0500J
10,0
r. 00125
0,5
0.0.1(//l
10,0
20.017
^0,0
u
Un oil u
-----
BdO Q(l U
U Fg'
tin ad u
IL^
OID ail u
-w
SMITHOONIAN
Natural Hyperbolic FunciicmH,
u
si iih ii
-w
QOSll II
' IV
Innli u
i; /
Qolll II
- .V "
0.0500
0.05002
ro,o
i. on 1:15
<>,5
o.o.|i)<X
KM
-'0,017
40,0
.050
.05012
.(XH-!(
,ti5<)(
10.077
30,8
.0502
.0502-
.O012(
.050 if
10-0,17
30,6
050;
.050,1-
.O0127
.0502*
M). 807
.10,5
.050-
. 050.1 i
,00127
.0503*
lO.Miif
.10.3
0.0505
0,0505-
10,0
I.OOIltf
0.5
0.0504'
I0,<
10,810
,10,2
050(
.05062
.0012):
O5(>5(
10.780
30,0
.0507
.05072
.001 JO
.05066
10.741
38,0
.0508
.0508;.
.00120
.0507(1
Ml./n.!
38,7
.0500
.05002
.00130
.0508(1
nM'6.1
38,0
0,0510
0.05102
10,0
1.00130
",5
0.(>50<X>
IO.O
10.*'.!;)
38,4
.0511
.05112
.00131
.05106
'!J-.'i87
38,3
.0512
.05122
. (K) 1 3 1
,05116
Hj, ;; |8
38,1
-0513
.05132
.OQI32
.o<iti!6
10-,'ini
38,0
0514
.05142
.OOI32
-05135
10.47.1
!/.
0.0515
0.05152
10,0
I.OOI33
0,5
0.05145
10,0
l<).43.<;
37.7
.0516
.05162
00133
-05155
10. 3>j7
37,5
.0517
.05172
.00134
.05165
IO.,i')O
.17,4
.0518
.05182
.0013.1
.05175
I0..1.U
.17.J
.0510
.05102
.00135
.05185
.17,1
0,0520
0.05302
10,0
1-00135
o,5
0.03105
10,0
nj.-MH
,t'',o
.0521
.05212
.00136
. 05.105
1 . -! 1 1
{68.
.0522
.05222
.00136
.05.: 15
10.174
&,7
0523
.05232
.00137
0fl.'-'S
nj.i.iM
36,5
,0524
.05242
.00137
-('5J35
10. 101
.16,4
0.0525
0.05252
10,0
1.00138
0,5
0.05J4S
10,0
lO.o'iji
K'.-J
.052(1
.05262
.00138
05.155
io.o,:o
3 (> !l
.0527
.05272
.00130
.05,.'! 15
1 M , i ji >\
3*1,0
.0528
.05282
.00130
.05.175
18,017
.0520
.05292
.00140
.05285
iH.OJi
3A7
0.0530
0.05302
10,0
1.00140
o,5
(1.05^)5
10,0
|8,JW6
,15. <>
053 1
.05312
.(10141
.05305
1 8 , 851 1
053 2
.05323
,(xi 143
.05315
1 8 , 8 1 ,s
aii.;i
-0533
.05,133
.1x1142
. 053.15
18.770
.0534
.05343
.00 1. 13
< '5,135
it? o
0.0535
0530"
0.05.153
.05363
10,0
1.00143
.00144
o.5
0.0534. 1 ;
10,0
in'
34.0
0537
.0538
-05373
.05383
.on i, M
.00145
53<>S
.05375
;|j;!fji|
3 1,6
31.5
.0539
05393
.00145
-o.^HS
iS-571
;)4.4
0.0540
0-05403
10,0
1,00146
0,5
".0530. 1 )
10,0
lH.'ii7
1-1.1
.0541
.05413
.00146
05405
iH,''i<u
ill. I
.0542
.0542,1
.00147
-05415
lH]'j| K V(
34,0
.054.1
.0543.1
.00147
.05435
it*!!i.vi
0544
05443
,00148
05435
lH.4IHt
.tiiK
0.0545
.05,16
0.05453
-05463
10,0
.00140
.(Xi 1 49
0,5
0-05445
05455
10,0
IH'HI
11. "i
.0547
.0548
.0549
05473
05483
05403
.00150
.00150
.00151
.05465
05475
.05484
lH.3(/t
ii.nj
.1.1.4
.1,1-1
,'1.1,1
0.0550
0.05503
10,0
,00151
0.6
0.05494
10,0
IR.2(
3,1,0
u
an Oil ii
ft'
eo gil u
w Fo'
In oil u
W Pi/
oo gif u
* Ho'
Natural Hyperbolic Functions.
u
si nli u
.w
cosh u
ta Fo'
tanh u
.IV
colh u
.Fo'
0.0550
0.05503
10,0
1.00151
0,6
0.05494
10,0
18.200
33,0
.0551
.05513
.00152
05504
18.167
32,9
.0552
.05523
.00152
05514
18.134
32,8
.0553
-05533
.00153
.05524
18.102
32,7
.0554
.05543
.00153
05534
18.069
32,5
0.0555
0.05553
10,0
I. 00154
0,6
0.05544
10,0
18.037
32,4
.0556
.05563
.00155
05554
18.004
32,3
.0557
.05573
.00155
.05564
17.972
32,2
.0558
.05583
.00156
05574
17.940
32,1
.0559
05593
.00156
17.908
32,0
0.0560
.0561
0.05603
.05613
IO,O
I. 00157
.00157
0,6
05594
v . 05604
10,0
17.876
17.844
31,9
31,7
.0562
.05623
.00158
.05614
17.812
31,6
.0563
.05633
.00159
.05624
17.781
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
17.687
31.2
.0567
05673
,00161
.05664
17.656
3M
.0568
.05683
.00161
.05674
17.625
31,0
.0569
.05693
.00162
.05684
17.594
30,9
0.0570
0.05703
10,0
1.00162
0,6
0.05694
IO,O
17.563
30,7
.0571
.05713
.00163
.05704
17.532
30,6
.0572
.05723
.00164
.05714
17.502
30,5
.0573
05733
.00164
.05724
17.471
30,4
.0574
.05743
,00165
.05734
17.441
30,3
0.0575
0.05753
10,0
1.00165
0,6
0-05744
10,0
17.410
30,2
.0576
.05763
.00166
.05754
17.380
30,1
.0577
.05773
.00167
.05764
17.350
30,0
.0578
.05783
.00167
.05774
17.320
29,9
.0579
.05793
,00168
.05784
17.290
29,8
0.0580
0.05803
10,0
I. 00168
0,6
0.05794
10,0
17.261
29,7
.0581
05813
.00169
.05803
17.231
29,6
.0582
.05823
.00169
05813
.17.202
29,5
.0583
-05833
.00170
.05823
17.172
29,4
.0584
.05843
.00171
.05833
17.143
29,3
0.0585
0.05853
10,0
1.00171
0,6
0.05843
IO,O
17.114
29,2
.0586
.05863
.00172
.05853
17.084
29,1
.0587
.05873
.00172
.05863
17.055
29,0
.0588
.05883
.00173
.05873
17.026
28,9
.0589
.05893
.00174
.05883
16.998
28,8
0,0590
0.05903
10,0
1.00174
0,6
0.05893
10,0
16.969
28,7
r\ f
.0591
.05913
.00175
.05903
16.940
28,6
.0592
.05923
.00175
.05913
16.912
28,5
.0593
.05933
.00176
.05923
16.883
28,4
.0594
05943
.00176
.05933
16.855
28,3
0.0595
0.05954
10,0
1.00177
0,6
0.05943
10,0
16.827
28,2
.0596
.0597
.05964
.05974
.00178
.00178
.05Q53
.05963
16,798
16.770
28,1
28,0
.0598
.05984
.00179
05973
16.742
27,9
.0599
.05994
.00179
05983
16.714
27,8
0.0600
0.06004
10,0
1.00180
0,6
0.05993
10,0
16.687
27,7
u
tan od u
-IV
tea ad u
u Fo'
sin ad u
<> F/
010 gd u
U Fo'
SMITHSONIAN
99
Natural Hyperbolic Funclions.
u
ilnh u
-W
cosli u
-a;
Innli n
-F U -
CDtll II
a ft,'
0.0600
0.0600.
10,0
I.ooi8(
(M
0.05W,
10,1
lO.OJty
'*73
.0601
.0601.
.0018
.ofxio,
H),0;i(J
'*'/>?
.0602
.060.;,
.0018
.ofmi.
III. (Ml
^7,0
.0603
.0603.
.0018-.
.(Xn)2.
lO.Oo)
-7,5
.o!ki
.0604-1
,0018-
.o(x),i,'
10,570
J7.4
o.orto;
0.0605.
10,0
1.0018,
o/
o.iX>.|,i
10,1
10.54.;
-7,3
,060!
,0606:
.<x)l8.
oU)5,'
10.52.!
27,2
.0607
,o(>07-
,(xn8,
.oOoii.l
lO.,|i;S
27,1
.0608
,o(ioS.
,(K)l8,'
.(X-o^i
16.4(18
27.0
.ofjoy
. 0(109.
.txil85
.I1U)8.!
10.. HI
o.ofiio
0.0610.
10,0
i,ooi8(
0,0
O.OlK'M).!
KM
10.414
26 8
,0611
,o6ih
.00187
,(Xno2
l('.,l'^'
20!
.0612
.0612.
.00187
.(lOl 12
10.300
-.'0,7
.0(113
.06134
.00188
.06122
Hi, 334
26,0
.0614
.06144
.(X)l89
.0:1132
10.31' 17
*'0.5
0.0615
0.06154
10,0
i.ootKu
0,0
o.n(n.|.!
IO.O
If 1.28 1
i!0,4
.0616
,o6i6.|
.01)190
,06152
lO.j'K
,;(l,3
,0617
.06174
.00190
,0<i in.!
|0..!A V 1
20,2
.0618
.06184
.00191
, of it 7.!
1(1. JO.!
.!') 1
.0619
.06194
.(X)192
.(XilHj
If). I/'O
,;(.ii
0.0620
0,06204
IO,0
1.0010,3
0,6
0.06102
10.0
IO.I.HO
20,0
.0621
.06214
.0(1HJ3
,n6.M2
10. i.;|
I.S.9
.Ofisa
.0622.1
.00194
.(X'2I.i
Ifl.O'^
.()()23
.06234
.00 KM
.0022.;
10.072
j'^y
,0624
.06244
.00195
.06232
|0.0|f>
J5,0
0.0625
0.0625,1
10,0
I.(X)MJ5
0,6
(1, 06242
10,0
10.021
Jl/i
. 0626
.1X1264
.ooiyft
.00232
l l i,t/)*i
J'i "j
.0627
.06274
.<x>l<)7
.oruhj
i 'i.tj/'o
jV'i
.0628
.0628.1
.00197
.06,17,?
IS.ij.l 4
*'iii.i
.0629
.0620.1
.(Xti98
.(K.282
15. oh;
0.0630
0.06304
10,0
1. 001 (JO
0,6
0.0().ii)2
10,0
1 Ji , H'J i
js,j
.0631-
.06314
.<X~H<j()
,O!>3O,!
1 <i . Kt ij
-J'B j
.0632
.06324
,<X>2()O
,00312
'S .8 14
J5,0
.0(133
.0(1334
.OO2I H)
,o(i3jj
lH.8l"J
.0634
.063,14
.00201
.0633.!
IJl./'M
a!i!
0.0635
0.06354
10,0
I. (X 1202
0,6
.(tf(i.u
10,0
1,1.7("J
j|8
,0(136
.06364
.IK).!02
.iXt'l^t
ai 7
.0637
.06374
,00203
.06301
I H '. "l'i P
j'.ifj
,0638
.06384
.00204
.06371
I'i.Oijf,
i"i "i
.0639
.06394
.OO20.1
.00381
I,'l.'o7i
-f.iiii
0,0640
.0641
0.06404
.06414
10,0
I .(X1205
0,6
o.oO.wi
,OfJ,|OI
10,0
t.'i.f'4'i
15,022
J: 1 ; 4
.0642
.064 34
.0(1206
. Oti 1 1 [
I 1 "<)8
. . '.
06.13
.06434
. 00207
.'oo,|.!l
ll! 174
.',1,2
.0644
.06444
,<X>207
.00431
i s .'MI;
->r t |-<
U.1,1
0,0645
0.06454
10,0
.00208
0,6
0,0(i|l I
1 0,0
11 U 1 '
.0646
,06.17
.0648
.0649
.06464
.06,175
.06485
.06495
.OO^X)
.00209
,00210
.0021 I
.0<M5I
.O(i4(ll
.00,171
15-4.1I
-!."l!'J
0.0650
0.06505
10,0
.0021 1
0,7
0.06491
.0,0
1S.-106
33,6
u
flu od u
Po'
oo a<i u
iV
llFt Dd U
_,
aio oil u '
'"">'
SMITHSONIAN
IOC)
Natural Hyperbolic Functions.
u
sinh u
<oF H '
cosh u
F '
tanh u
F '
colh u
Fo'
0,0650
0.06505
10,0
I.O02II
o,7
0.06491
10,0
15.406
23,6
.0651
.05515
,00212
.06501
15.383
23,6
.0652
.06525
,00213
.06511
15-359
23,5
.0653
.06535
.00213
.06521
15.336
23,4
.0654
.06545
.00214
06531
15-312
23.3
0,0655
0.06555
IO,0
I. 00215
o,7
0.06541
1 0,0
15-289
23,3
.0656
.06565
.00215
.06551
15.266
23i2
.0657
.06575
.00216
.06561
I5.243
23,1
.0658
.06585
.00217
.06571
15-219
23 ,1
.0659
.06595
.00217
.06580
15.196
23,0
0.0660
0.06605
10,0
1.00218
o,7
0.06590
10,0
15.174
22,9
.0661
.0661 5
.00219
,06600
15.151
22,9
.0662
.06625
.00219
.06610
15.128
22,8
.0663
.06635
.00220
.06620
15.105
22,7
.0664
.06645
,00221
.06630
15.082
22,6
0,0665
0.06655
IO,0
I.O022T
o,7
0.06640
ro h o
15.060
22,6
.0666
.06665
.O0222
.06650
15.037
22,5
.066;
.06675
.00223
.06660
15.015
22,4
.0668
.06685
.O0223
.06670
14.992
22,4
.0669
.06695
.O0224
.06680
14.970
22,3
0.0670
0.06705
10,0
I.O022S
o,7
0.06690
io h o
14.948
22,2
.0671
.06715
.00225
.06700
14.025
22,2
.0672
.06725
.O0226
.06710
14.903
22,1
.0673
.067.15
.00227
.06720
14.881
22,0
,0674
.06745
.O0227
.06730
14.859
22,O
0.0675
0.06755
1 0,0
1.00228
o,7
0.06740
10,0
14.837
21,9
.0676
.06765
.00229
.06750
14-815
21,8
.0677
.06775
.00229
.06760
14-794
21,8
.0678
.06785
.00230
.06770
14.772
21,7
.0(179
.06795
,00231
.06780
14,750
21,7
0.0680
0.06805
10,0
I.O023I
o,7
0.06790
10,0
14.729
21,6
.ofiHi
.06815
.00232
.06799
14.707
21,5
.0(182
.06825
.00233
.06809
14.685
21,5
.0683
.06835
.00233
.06819
14.664
21,4
.0684
,06845
,00234
.06829
14.643
21,3
0.0685
0.06855
10,0
1,00235
o,7
0.06839
1 0,0
14.621
21,3
.0686
.06865
.00235
.06849
14.600
21,2
.0687
.06875
.00236
.06859
14-579
2T,2
.0688
.06885
.00237
.06869
14.558
2T,T
.0689
,06895
.00237
,06879
14- 537
21,O
0.0690
0.06905
IO,0
1.00238
o,7
0.06889
IO.O
14.516
2T,O
.0691
.06916
.00239
.06899
14-495
20,9
.0692
.06926
.00240
.06900
14-474
20,8
.0693
.06936
.00240
.06919
14-453
20,8
.0694
,06946
,00241
.06929
14-432
20,7
0.0695
0.06956
10,0
1,00242
o,7
0.06939
IO,O
14.412
20,7
.0696
.06966
.00242
.06949
14.391
20,6
.0697
.06976
.00243
.06959
14.370
20,6
.0698
.06986
.00244
.06969
14.350
20,5
.0699
.06996
.00244
.06979
14.329
20,4
0.0700
0.07006
IO,0
1.00245
0,7
0.06989
ro,o
14.309
20,4
u
tan gd u
w Fo'
IBD gd u
Fo'
tin ad u
w Fo'
0*0 ad u
Fo'
SMITHSONIAN TABLES
101
Natural Hyperbolic FiinelUmH.
u
si nil u
W
cosli u
- F .;
Iniili u
<> F,,'
0.0700
0.07006
10,0
1.00245
0.7
O.<Xx)8<,)
,..
14. 3' JO
20,4
.0701
.0702
.0703
.07026
.07036
.00247
,00247
. ( >/'( K )8
,07018
14.2 lit
..!l),2
.0704
. 07046
.00248
'"'
I4.J.;,S
2O,1
0.0705
0.07056
10,0
1.00241)
o,7
o . I >7i 138
10,1)
14. 208
20,1
,0706
07Ofi6
.00240
.ii/n.|8
14. l 88
,'(>,( 1
.0707
.07076
.110250
.07058
14. iM
2I,U
.0708
.0700
.07086
,07006
.(10.351
.oo.!5i
.07078
0,0
!:!:!!!
10,0
10,0
0.0710
0.07106
10,0
1.00252
o,7
o.i 17088
0,0
14.108
10,8
.0711
.07116
.00253
,07(11)8
14.088
10,7
,0712
.07126
.00254
.07108
I.|.XHJ
10,7
.0713
.07136
.00254
.071 18
14-040
10,0
-0714
.07146
00255
.07128
14. u,:<j
10,6
0.0715
0,07156
10,0
1.00256
o,7
0.07138
0,>
14.010
10,5
.0716
.07166
.00256
.117148
13. w
19,5
.0717
.07176
.(X>257
.07158
13.071
10,4
.0718
.07186
.00258
,()7KkS
13.0*1.!
MM
.0710
.0710
.00250
.07178
13.03.:
19-3
0.0720
0.07206
10,0
1.00250
o.7
0.07188
<J,0
13-013
"J,3
.0721
,07216
,(X)26O
.0711)8
13.801
MM
.0722
.07226
.<X>26[
,07.x 17
13-874
U),J!
.0733
.07236
.00261
.07.!! 7
13-8;;;;
10, 1
.0724
.07246
.00262
.07227
13.8.10
10,0
0.0725
0.07256
ro,o
1. 00263
o,7
0.07237
0,0
13-817
10,0
.0726
.07266
.00264
.07247
1 .1 - Xo8
18.0
.0727
.07276
.00264
07257
1 ,( . 7J'g
l8,g
.0728
.07286
.<xi265
.07.!' '7
l.l./'fil
18,8
.0720
.07296
,<X12W)
.07277
M. /'42
!8,H
0,0730
0,07306
10,0
I. 00267
0,7
0.07287
<>.o
M.7-M
18,7
,0731
.07317
.00 -'67
,0/207
'3-/'"'l
18,7
.0732
.07327
.00268
.07307
l,(.(>K'i
i8,h
.0733
-07337
.00260
.07317
13. <-tt'/
l8,d
-0734
-07347
.imt'v)
0732;
I3.I'|H
lH.5 1
0.0735
0,07357
10,0
1,00270
o,7
0.07337
0,0
l.l.'M"
18,^5
.0736
.07367
,(XU7l
-07317
13.61 t
|,1
.0737
,07377
.00,37,?
-"7357
13.503
.0738
.07387
.00272
- 1 73 ( '7
1,1-^75
!<!
.0739
-073<J7
-00273
-07377
I3-, 'if/'
iH.,1
0.0740
0.07407
10,0
1.00274
0.7
0.07387
0,')
13.5.18
[8,.!
.0741
.07417
.00275
.0731X1
13,,'t,!O
(8,^
.07-12
.07427
.1x1275
.07,11 if i
M V '!
18, (
07-13
07-137
.w^o"
.0741(1
I3.48|
i8,r
07-14
,07447
.00277
.07420
13.4'""
18,0
0.0745
0.07457
10,0
i. (10278
o,7
0,07436
0,0
13.448
18,0
.0746
.07407
.(10278
.0741''
1.1. . 13't-
17,0
.0747
.07477
.OOJ70
07456
13.412
I7iO
.0748
.07487
.00280
,M74(Ki
17*8
.0740
-074<J7
.00281
.07476
i]\.'y/t>
17$
0.0750
0.07507
ro,o
1.00281
0,8
0.07486
w
I.1.,S
17-7
u
Inn oil ti
u Fo'
BOO Oil U
M Ft/
In nil u
Tw"
Old oil u
^Fo'
SMITHSONIAN TABUB
103
Natural Hyperbolic Fund ions.
II
ilnli u
JUL
ooali u
Fu'
tun h u
w Fu'
oo Mi u
w Fo'
0.0750
O.O7507
IO,O
1.00281
0,8
0,07.1 86
9,9
13.358
17.7
.075'
.07517
.00282
,0741X1
13.34I
17.7
.075-'
.07527
,(xu83
,07506
17,7
0753
-07537
.0028.1
. 07516
13.305
17,6
.075-1
.07547
.00.184
.0752(1
13.288
17,6
0.0755
0.07557
10,0
i.mjHfi
0,8
0.07536
9,9
13-270
"7,5
.0750
.07507
,<X).;8()
.075.16
13-253
'7,5
.0757
.0758
.07577
.07587
:!I!:;87
.0755(1
.07566
13-235
13.218
.0750
.07507
.(H1288
-07575
13-201
W\3
0.0760
.0761
.07617
IO,O
'ilS
0,8
0.07585
9,0
13-183
1 3. UK)
17,3
17,2
.0762
.076.1
.07627
.07637
.00200
.Ojriios
.07615
13.140
13.133
17,2
17,1
,07(i.|
-076-17
.OOJOU
.07625
13.11.1
17,1
0.0765
,0766
0.07657
.076(17
10,0
.(X1204
0,8
0.07(135
9,9
13-097
13.080
i?.i
17,0
.07(17
.07678
.O029.|
.07655
i 3.063
17,0
.07(18
.0769
.07<to8
;!3
.07665
.07675
73.046
13-030
l(t,9
I(),9
0.0770
0.077ti8
10,0
1,00207
0,8
0.07685
0,9
13.013
16,8
,0771
.0771^
.O0207
.07()95
168
.0772
,07728
.0029.S
.07705
12.979
16,7
-077.1
. 07738
.00209
,07715
12.0/12
16,7
.077.1
.077-18
.00300
.07725
12.916
16,7
0.0775
0.077.18
10,0
I . 00300
0,8
0.07735
0,0
12.929
1 6.6
.0776
.0776H
.(X 1.101
.077<M
12.912
16,6
.0777
.07778
.OtWU
.0775.1
la.Kt/i
165
.0778
.07788
-0030,1
.07764
12,879
io!s
.0770
.07708
,(X)30,|
.07774
12.8(13
0.0780
0.07808
1 0,0
I,0030,|
0,8
0.0778-1
0,9
12.817
1 6,4
,0781
.07818
.00305
,07704
12.830
16,4
.0782
.117828
.00,106
.0780.)
12.814
16,3
.0783
.07838
.00,107
,o?8i.|
12.707
16,3
.078.1
,07R|8
.00307
.0782.1
12.781
0.0785
(1.07858
10,0
1.00308
0,8
0.0783.1
0,0
12.765
16,2
.0786
.078(18
00309
.078,|.|
I a. 740
1 6,2
,0787
.07878
.00310
.0785.1
ia.733
i(i,r
.0788
.07888
.00311
. 07864
T2.717
16, 1
.0789
.07898
.00311'
.0787.1
12.701
i(i,o
0.07911
0.07008
ro,o
1, 00.1 12
0,8
0.07884
9,9
12,685
16,0
.0791
.07018
.00313
,07894
12.6fx)
15,9
.0792
.07028
.00314
.071x13
12.653
15,9
.079;)
.07038
.00.115
.07013
12.637
15,9
.0791
.079.18
.00315
.07923
12.621
1 5,H
0.0705
0,07058
10,0
1,00316
0,8
o , 07933
9,0
12.605
15,8
.0706
.07968
.00317
070;|3
'1 2. 58f>
15,7
.0707
,07'J7
.00318
.07053
12-57-1
15,7
.0708
.07088
.00310
07063
12.558
15,7
07P9
07999
.00319
07073
ra.s,|2
1 5,6
0,0800
^?L
10,0
1.00.120
0,8
0.07083
9,9
12.527
15,6-
u
tun Hil u
w Fu'
too ail u
u Co'
alfl Dll U
w F '
010 flll U
___
QMITHHONIAN TABUM
103
Natural Hyperbolic Functions.
u
tinh u
" Fo'
cosh u
u Fu'
tanh u
Ft,'
coth u
o,F Q '
0.0800
0.08009
10,0
1.00320
0,8
0.07983
9,9
12.527
15,6
.0801
.0802
.0803
.0804
.08019
.08029
.08039
.08049
.00321
.00322
.00323
.00323
.07993
.08003
.08013
.08023
12.511
12.496
12.480
12.465
15,6
15,5
15,5
15,4
0.0805
0.08059
10,0
1.00324
o,S
0.08033
o,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
0.08109
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
15,1
.0813
.08139
.00331
.08112
12.327
I5,i
.0814
.08149
.00331
.08122
12.312
15,1
0,0815
0.oSl59
10,0
I .00332
0,8
0.08132
9,9
I2.2Q7
15,0
.0816
.08169
.00333
.08142
12.282
15,0
.08:7
.08179
00334
.08152
12.267
14,9
.0818
.08189
.00335
.08162
12.252
14.9
.0819
.08109
.00336
.08172
12.237
14,9
0.0820
0,08209
10,0
1.00336
0,8
0.08182
9>9
12.222
14,8
.0821
.08219
.00337
.08192
12.208
14,8
.0822
.08229
.00338
.08202
12.193
14,8
.0823
.08239
.00339
.08211
12.178
14,7
.0824
.08249
.00340
.08221
I2.I63
14,7
0.0825
0.08259
10,0
1.00341
0,8
0.08231
9.9
12.149
H7
.0826
.08269
.00341
.08241
12.134
14,6
.0827
.08279
.00342
.08251
12.119
14,6
.0828
.08289
.00343
.08261
12.105
14,6
.0829
.08299
.00344
,08271
12.090
14,5
0.0830
0.08310
10,0
1.00345
0,8
0.08281
9.9
12.076
14,5
.0831
.08320
.00345
.08291
12.061
14.4
.0832
.08330
.00346
.08301
. '
I2.0.J7
14.4
.0833
.08340
.00347
.08311
12.033
14,4
.0834
.08350
.00348
.08321
13. 0:8.
14,3
0.0835
0,08360
10,0
I .00349
0,8
0.08331
0,9
I2.0O4
14,3
.0836
.08370
.00350
.083,11
II.99O
14,3
-0837
.08380
.00350
.08351
n.975
14,2
.0838
,08390
.00351
.08360
11.961
14,2
.0839
.08400
.00352
.08370
11.947.
14,2
0.0840
0.08410
10,0
i .00353
0,8
0.08380
9.9
H.933
14,1
.0841
.08420
00354
.08390
11.919
14,1
.0842
.08430
.0035$
.08400
11,905.
I4,i
.0843
.08440
.00356
.08410
:r.8oo
14,0
.0844
.08450
.00356
.08420
11.876.
14,0
0.0845
0.08460
10,0
1.00357
0,8
0.08430
9,9
ii.fifa
I4,o
.0846
.08470
-00358
.08440
11.849
13,9
.0847
.08480
-00359
.08450
11.835
13,9
.0848
.08490
.00360
.08460
11.821
13,9
.0849
.08500
.00361
0,9
.08470
11.807.
13,8
0.0850
0.08510
10,0
1.00361
0,9
o.oS.|8o
9,9
n.793
13,8
u
tan ad u
Fo'
sec gd u
u Fo'
sin gd u
Fo'
010 gd u
< Fo ;
SMITHSONIAN TABLES
104
Natural Hyperbolic Functions.
o.ihS-iS
l). Off II I
.0.41)1
.
,nHd,|
o.oH75
;oH77
,oH79
o.tiHHo
,oM,j
,0>Wl
.oMH.|
o.oHM.H
o,oK<x
.oHa
.oKof
.0*07
ulnli u
r '
I'll
O.O.V 1
o.oHHi I
.()HS.n
u Inn oil u
10,0
10,0
10,0
10,1
10,0
oonli u
, 1 M \\< if I
.oo.v/o
i .m.tf.1
.00.175
.011,170
.00.177
i .00.17')
.(H).lHo
.00,105
.00,10,1;
.0040*
1,OO,|OI
1.0040,
0,0
0,
w fV too oil u " IV il" 'l
Innh u
.085.11;
0.08777
.oKyK
9.9
9,'
ooih u
11-793
11-779
11.705
i i . 75^
H.7J-1
11.711
11. 'i97
I l .070
n .6,10
1 1 .61(1
M.5<X>
M. 5* '3
".550
"53'i
11.510
n.. 107
n-171
II.15H
"MS
1.351
H..10,
1I..IOI
n.aS.
M.J.K
1 1 . .!0.
n.iy
11.17
1 1 , i fit
n. is
i i.i.i
010 ail u
13,8
133
13,7
'3,7
13,7
13.''
13,0
13,5
13,5
13.5
i, VI
1 3.. I
13.3
13,3
13,3
13.H
13,2
13,1
1,1.1
1 3. 1
1.1,1
13,0
M,0
i -'.7
12,0
12,6
12,
i A
in.
12,
12,
SMITH&ONIAN
rog
Natural Hyperbolic Functions.
u
si nil 11
(U FU'
coali u
*,
tnnli u
F,,'
t!lllll U
0.0900
0.09012
10,0
1.00405
0,9
0.08976
U.'
1 1 . l.|l
1 '
.0901
.09022
, 00400
,089,%
1 1 . i.nj
I.f '(
.0902
.09032
.00407
.(xSi)<Xi
11.117
1 ' 'l
,0903
.09042
.00408
.(XXHrfl
11 . in|
1^,2
.0904
.09052
.00409
.09015
It .(11).!
U,2
0.0905
0.09062
10,0
1.00410
<M)
0.(KMI.'5
l),t
1 1 .0^1)
1.!,.!
.0906
.00073
,IH).|1 I
.090 is
11. (if ,8
l-M
.0907
.09082
.0041."
01)045
1 1 .05(1
.txjo8
.09092
.00413
U.i
.0909
.09103
.00413
.ojjofii;
t 1.0,11
0.0910
0.09113
10,0
1.0041.
0,9
o.OfxiXI
<),<
11 .Oil)
J.!,O
.0911
.09123
,00415
.(MXlS'"}
1 1 . i x 17
I .!,< )
.0912
.09133
.0041(1
.090O 5
iii,o
0913
09143
.00417
.09105
to ijH't
.0914
.09153
.00418
10.971
11,9
0.0915
0.09163
10,0
1.00419
0,9
o.wus
10 lien
1 1,(
,0916
.0917
.09173
.09183
.00420
.00421
.<XW|
111,048
11,0
.0918
.09193
.00422
.00154
io!ol
1 ','.
1 l,f
.0919
.09203
.00433
.09164
loio'u
11,8
0.0920
0.09213
10,0
1.00423
0,9
(>.<xjl74
9,9
KI.IXX)
I i.f 1
.0921
.0922
0923
.09223
.09233
.093-1.1
,0042.
.00425
.00426
.O9lS|
,<K)I()|
.OUi!0.|
10. WH
10.877
n,8
11,7
1 1 n
.0924
.09253
.00417
10.853
1 'i/
0.0925
.092(1
.0927
0.09263
09273
.09283
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102,5
.02452
22,3
.21/47
0,'i,3
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201,4
,222
.22383
102,5
.02474
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)<JO,6
.221
.22485
102,5
.02407
22,5
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"07,8
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.22588
102,5
.02510
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.J20.U
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^7
I'X',0
0.225
0,22690
102,5
1.02542
2.1,7
0.2.M28
<>.'!, I
4.;; lo,:
104,2
.220
,22703
1 02
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.227
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.220
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102,7
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.231
.2.1306
102,7
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184,1
. 232
.2.1400
102,7
.02703
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,22703
0|,8
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182,5
.2,13
.235 if
102,7
.02727
-Mi,'*
.22887
01,8
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1 80,0
.234
.23014
102,8
,02750
23.0
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04.7
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"79,3
0.235
0.23717
I0.!,8
1 .02774
-M.7
(.. 13077
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4-3331
t,77,M
.236
. 23820
102,8
.02708
M,8
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\ytt\J
.237
. 23022
102,8
.02822
2,1,0
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'7-1.7
.238
.24025
102,8
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.24I2tf
102,0
.02870
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0.240
0.24231
102,0
1.02804
24,2
0,23550
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^1334
I O2,0
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;! -li,t
.23* -44
01,4
. .:.','> |
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.242
~M-437
102,0
.02013
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O|, I
167,1
13
.24540
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2.1,5
"'38.1,1
1,3
, 1050
I66,i
.244
.24643
103,0
M&W
:i.|,(
.~M<M7
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"'1,7
0.24.5
.246
.24840
T 0,1,0
103,0
\ .03016
.03041
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0,240.! t
01.-!
01,..'
' ' I4''7
1 0.1,3
.247
.24052
1O3,I
.03066
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.242 10
0|, (
. i.iofi
lfK)()
.248
25055
io,i,r
.03001
25,1
.24304
. 1146
1 50 1
.249
.25158
103,1
.03116
uii.s
01,0
. i *$'/
ijtf)
0.250
0.2526-1
103,1
T. 03T.| I
3M
0.24402
01,0
,|.(i8.|o
Uifi,7
u
Ian ud u
"""'
800 Oil 11
" IV
aln oil u
' r r
UNO Utl II
SMITHOONIAN TABLES
1 10
Natural Hyperbolic Punclions.
.253
.25-1
o.^xS
,..76
.-77
o.aNo
O.i!00
. .10.1
tinli 11
.115571
o.. 15777
o.^HHH/
0.3045
tnn ad i
< ft'
KM, i
1 03,. i
10.1,.!
10,1,.!
HM.I
104)5
104,5
ooali
.0,1.405
.0,1751)
1.0,15.11
F,,'
7,1
7,.|
7.5
I'H.H
Inn Ii u
o.. 15.1.10
ASS-M
.^173.1
.-7105
0.277S3
0.^7.1
-'1XMO
M F (1 '
9.1,0
i>!i!
0.1,7
0,1,7
03,5
03,'l
93,3
93,3
93,0
93,0
9-M
9-M
9',0
01,8
9'.X
01,0
!JI,5
OOlll 11
.0519
.0.105
.0213
4.0062
.9Xi.l
.1.9.124
.ijlKo
.755
3-^115
.8067
3 '79.13
75.16
-7405
3-7-70'
XMX
.'1510
ATX)
.5795
.4054
.-IS-IS
155,4
15 1,7
J50.5
i!iV
14(1,0
143)5
M!>,f
137^0
135,9
13-1,9
133,9
1.11,0
30,9
134,3
123,-t
122,5
119,0
116)5
1 14,
114,0
11.1,;;
1 1 1,6
1 !0,0
110,1
109,3
109,6
107,8
w Pi,
800 Oil II
dill 0<l U
cio ail u
H Pfl'
III
Natural Hyperbolic Functions.
ll
si nli u
u Fn 1
cosh u
"' F, ( '
tn nli u
-1 F,,'
(HI til II
Fu'
0,300
0.30452
104,5
1.04534
30,5
t)..:i)i3i
'Ji.S
3 1,127
107,8
.301
.30557
104,6
.o.|5<>4
3O,0
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!>,5
,.|.i.:o
107,1
3<W
.30661
104,6
.0-1595
30,7
.20314
OI.-1
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lod,,)
303
.307(16
104,6
.n.|6j()
30,8
,i!lf.|"f'
Ul,|
,.|<x)7
K)5,()
-.104
,30870
104,7
.0465(1
30,9
29 197
9 1 -.1
.390-'
104,9
0.305
0.30975
104,7
1 .04* $7
3 1 ,o
o.JO.'iN
91,2
,1.37'V
I(X|,J
.306
.31080
i4.7
.0.1718
3M
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9i,.:
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i'M,5
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10.1,7
.04750
3',2
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.31289
10-1,8
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31394
104,8
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0.310
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104.8
1.04844
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.311
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104,9
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.312
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104,9
.0.1907
31.7
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.31.1
.31814
104,9
049.19
31.8
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. -:i^5
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.31-1
.31919
105,0
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3 1 ,9
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1)0.8
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0.315
0,320^4
105,0
1,0500.3
32,0
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97,5
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3'7
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33330
105,'
.05099
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.30770
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05/i
-319
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105,1
.05131
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95,0
0.320
0.32549
105,2
1.0516',)
3U.5
0.30951
'.XVI
3.a,((hj
94,4
.321
.32654
lo.'i.j
.0519!)
32,7
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90,4
.,!.!! 5
9.1.H
.322
32759
105,2
,o5-'J9
32,8
.3N31
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. .'. I ,.'.!
9.1,.!
.323
.32*65
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3-i,9
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'X',3
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92,6'
-32-1
.32970
105,3
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- '937
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0.325
0.33075
105,3
1.05328
33.1
0.3I.[0.!
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3-i"'l5
'JI.4
.326
33'*'
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.053'"
33.*
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9<t. 1
. 1/5-1
yii.8
327
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105,4
.05394
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. Krfi.l
'A3
.32H
33391
105,4
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.11,4
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"57.1
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.329
33497
105,5
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33.5
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0.330
0.33602
105,5
1.05495
33,o
0,3185.!
8.),,J
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8,'V'
331
3370K
105,5
.05,S.*K
33,7
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8.),H
1,107
HS,o
.332
33*13
105,0'
.05562
33.H
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89,7
. I.JIU
H7.5
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105,6
.05596
;i.i,9
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8o,>'
. 1 I.1J
H",'j
334
.3-1024
105.6
.05630
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H6.4
0-335
0,34130
105,7
1.0566.]
34, 1
o.3;t.iiH
H.,,6
;i.'-).'i9
Hi,
33f*
.34336
10.V
.05698
34,2
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.r^74
5.3
-337
34342
105,7
.05732
3-1.3
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H<).5
,(i/8l
H|,H
-33
34447
105,8
.05767
34-1
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. 1 \',H } 1
H-1.3
330
34553
105,8
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34.6
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H.l.H
0.340
0.346"59
105,8
1.05836"
34,7
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*^,.J
3.0.'i/i
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341
.34765
105,9
.05871
34.H
32H.17
89,-!
-"15.1
8-',y
342
34*71
105,9
05005
3-1.0
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8-).,!
<Ml''
N.f,j
343
34977
105,9
.05910
3!i.o
3.1" 15
H<J,I
.(i.:Jfcj
Mi, 7
.34-1
3502
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35,1
3.1IO,|
89,0
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MI..I
0.345
0.35 t88
iofi,o
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3.01;;*',
8(i,B
346
.35^9,1
1 <>(,(>
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35,3
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.tuM'i
8<),3
347
35401
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79,
.348
.35507
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.06117
35,5
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8.'i.H
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349
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100,3
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35,6
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78,8
0-350
0.35719
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35,7
0.3363M
HS,7
a.i)/ji>
7^1
u
Inn ml u
IV
900 Qll U
Fo'
ill) Ufl U
w F,.'
CIO l)il II
Fo'
SMITHSONIAN TADLKB
112
Natural Hyperbolic Functions.
tl
slnh u
"Pi/
CQBll U
-Fo'
In nli u
-IV
ootli u
w Fu'
0.350
0.35719
iofi.2
1.06188
35,7
0,33638
88,7
2.0731)
73,4
.351
.358-!,';
100,.!
.O0,!..'.|
35,
.3374(1
iSS,6
.9651
77,9
.354
35031
lof>,3
,O(>JjO
35,!>
338 1 5
SH/i
9573
77,5
.353
.3603^
Hrf).,l
.06.105
36,0
331X13
8H,5
,().((/)
7X,o
35-1
36l. 14
10(1,3
o< 133.!
36,1
330UJ
88,,)
.9-119
7<>,5
0.355
(>.3(i.J5o
to6,,|
I ,o6'3()8
3' ,,1
o.3.|oNo
88,. i
4-0343
76,1
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3' '3 57
[(Mi .1
.Od-lO.]
id ,
.'l.ll(M)
iJii i
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7=; 7
357
[(KM
.<)(),|.|(}
3'',5
l) 1 ' '
HK"I
.0101
/:>,/
75,^
-358
36570
10*1,5
0647?
3d,l>
.3-1.1-15
H8.2
.()!!(>
350
. 36(176
106,5
.06514
36,X
34433
rt.S \
iw-M
7-\>3
0.360
0.36783
i<>6,6
i .oC.^jio
36,8
0.34541
yo i
2.8<XxM
73.9
.301
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ind.d
.0(1587
30.U
,3.|<KXJ
HH!O
,8804
73,5
.3'i.;
3'n>0(>
iu(.,d
.o6(u|
3X.O
3461)7
JW,u
,8K2i
73,1
-3'M
.3710,!
106.7
.iilit^ii
37,t
.34785
87,0
i O/-JO
74,6
3'H
37400
106,7
.oWiyS
37,4
.34873
87,8
H(l7 *i
73,2
0.365
0.3731''
i <>6,7
i .116736
37,3
0.3,1061
87,8
2.8603
71,8
3' 1 * 1
-37443
HiO.H
.(16773
37,4
.350.10
87,7
.8534
7M
36/'
3X5-10
loh.K
,O(hSl(l
37,5
.35136
87,7
-8,|(k)
. 3' iH
37'M'i
lod.M
, < if iM |K
37,6
.35444
.83^1
70,6
-3^'
37743
106,1)
.(XtHWt
37,7
.35314
xis
,8310
70,2
0-370
0.37H.S(i
106,0
1 .0(W).i3
37.!)
0.35309
87,5
2.82,10
69,8
371
3/057
107,0
,0(J(H
38,0
35487
87,4
.SiKii
6y,.i
374
.38*1(1.)
107,0
.odojjij
38,1
35574
87,3
.Hi io
f),0
373
.38171
107,0
.07037
'l8,;>
356fi I
87,3
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68,6
374
.38478
107,1
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38,3
357-19
87,4
.7973
68,a
0.375
0.3838*;
107,1
1.0711.)
38,4
0.35836
87,4
2.70(15
^7,9
376
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KiX,4
.07154
,M5
- 35043
87,1
.7837
67,5
377
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107,.)
.0X101
38,6
.36010
97,11
77/'o
67,1
'378
3871 17
107,,;
.0x430
38,7
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87,0
7703
66,7
370
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0.380
0,381)..'!
107,3
1.0x307
38,9
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86,8
2.7570
66,0
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0x340
30,o
, 3(1358
K6.K
7505
65,7
3*4
3') 130
K>7,.|
' * 17385
30, '
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8(1,7
7-130
65,3
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107,4
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30. ^
.36531
86,7
7374
64, ()
38-1
3<J3<>'
107,5
.07-164
39,4
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K6,(>
fi-l.fi
0.38.1
0.30-158
H'7,5
1.07503
3 ( >,5
0.3670.]
8<t,5
3.7-Mi
6.|,2
.380
.305(16
107,5
.('75-13
30,6
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86,5
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63,0
> 38/
.30073
107,6
.07584
30,7
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-71I7
63,5
. 'iH?t
.30781
107,0
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30,8
361X13
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7051
6*3,2
3Hy
308%
107,7
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30,9
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Wi,3
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62,8
0.300
0.300^/1
107,7
1.0770;!
40,0
0.37136
fifi,a
2/KJJ8
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301
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107,7
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303
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86,0
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6 1, 5
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107,0
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86,0
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61,2
0.305
0.40535
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1.0700.1
10,5
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0.37566
376S4
5.0
85,8
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307
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108,0
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85,8
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(k),2
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ioH,o
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40,1)
378-'-i
85,7
('438
59.9
399
40<X>7
loH.i
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I 1,0
37909
85,6
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59,6
0.400
0.41075
108,1
1.08107
41,1
0.37095
85,6
2.6310
S9,3
u
Inn ad u
W Fu'
800 U<l II
wf v
ill) Oil II
w
DID ail ii
u Ft^
SMITHSONIAN
Natural Hyperbolic Funclions.
u
ainli u
.IV
cosh u
i., IV
tnnd u
.V
culli u
F (1 <
0.400
0.41075
TOS.T
I.o8l07
41,1
o.3/9<t5
K5,<>
2.6.119
59,3
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4 "83
108,1
.08148
41,2
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8.1,5
.(l.HM)
50,o
.402
.41292
108,2
.o8l(JO
|i.3
. ,18 1 ( it i
85.4
.(l.fOI
.'18,7
,403
108,2
.082.11
41.4
. 38.!5 1
8 ; ;,4
.(n,|.i
58.3
.40-1
.41508
108,3
.08272
41,5
.,(8,1.17
85,3
.(rfi5
58,o
0.405
0.41616
1081
1.118,114
41.0
0,38(22
85,2
2.(Xt27
.'17,7
.406
.41725
lofVi
.08350
41,7
.38507
85,2
.;;<>'>')
57,4
,407
.41833
ro8,4
.08,107
-H.8
.38502
85. i
..'I')!.!
.17,1
.408
.41941
108,4
.08430
I'.O
.38(177
85,0
:i f \'i. ! i
,'il 1.8
.409
.420511
108,5
.08481
4~M>
.38702
8;;,o
..'i/'j8
5' '.6
0.410
0.42158
108,5
r.oRut
4 A2
o.l88 17
8 1,<)
.!.;i74.-
56.3
.411
.422(17
108,6
.0856(1
4 -',3
-38.).!.!
84,8
,.'i()8(i
5'i,o
.412
.42370
1 08,6
.08(108
-12,4
3<X)17
84,8
-.'i'M"
55,7
.413
.42484
108,7
.08(150
42,5
.,1010.!
8 1,7
- 5574
55,4
.414
.43503
108,7
,0869.1
42,0
30186
84,'.
55'0
55, 1
0.415
0.42702
108,7
l .08736
4-' 7
0-3037'
8,|,0
J.S-l'M
54,8
.416
.42810
108,8
.08778
-12,8
.3035*'
84,5
-.'i 4<N)
M.o'
.417
.42919
108,8
.08821
42,0
3044"
8,1.4
. jijiji;
54,3
.418
.43028
108,9
.08864
43.0
30524
8 1,4
53"!
.419
.43137
108,0
.08907
43.1
-,1<X>09
8|,.l
!i-'47
53.7
0.420
0.43246
100,0
1.08950
13,2
0.3N60.1
84,2
.,'..'; n>.|
53,5
.421
43355
109,0
-o8<x),|
43,4
30777
>.'i'-|O
53,2
.422
.43464
109,0
-09037
43,5
.3<)8i>i
8|!'i
. . ! ;i 187
Ji-V)
.42.1
43573
109,1
,o*jo8i
43,0
3 ( X>|5
H|,o
( i'M |
'i-!.7
.424
.43082
ioy,i
,09124
43,7
..|0020
8,|,o
-4<> ; 1.i
52.4
0.425
0-43791
[09,2
t. 001 68
43.8
0.401 1,1
83,0
2. ,|).')
!i.!.*
.426
.43900
100,3
.Ol).!l J
43,0
.40107
83.8
.4877
51.0
427
44O09
109,3
.0925(1
44.o
..[0,;8i
8 1.8
.,|S.:(i
51.6
.428
.4.-! no
100,3
.00301)
44.1
.40,16;;
8.1,7
,4/71
Ji'.'l
.429
.44228
HH),3
09344
44-J
.40440
83,0
0.430
0.44337
'09,4
1.09388
44.3
0.4053.!
8l,6
.1.407-'
iVVt
.431
.44447
100,4
.09433
44,4
.4001(1
8x'i
Si ,( i
.432
4455C'
109.5
-09177
-14.6
.40(101)
K.1,1
.,|v'i
V> 4
.433
.44666
109,5
.095^2
44.7
4078.1
8,1,1
4v'i'
50,1
434
.44775
109,6
.<19567
44.H
.408(1(1
83,3
.44711
40,9
0.435
0.44885
109,6
[,0<>6[i
44.0
o..|Ot),jO
H.i,.!
2.44/1
-10.6
.436
44095
109.7
.0965')
45.0
,411)32
8 (,.!
437'
40.4
437
45104
109.7
,(X)7oi
45.1
.41115
8.M
43-M
40..!
-.138
,45214
100,7
.o<)747
45.-!
,.|l ii)i)
8 j.t i
48.1)
439
"1533.1
109,8
09792
-15.3
.41282
83.0
,.\,\.-.\
-|8,7
0.440
0-45434
109,8
1.00837
45,4
0.4136]
HJ.O
.!-4i7';
-!,4
.441
45543
109,9
-09883
45,5
41.117
8,!,8
.-1 1-7
-18,2
.442
45653
109.9
.099 .;8
45,7
.41530
8 8
48,0
443
.45763
1 10,0
ixx)74
45.8
.4161,1
8,1.7
-4"3i
47,7
.444
45873
1 10,0
. KX>20
45.9
.41695
8j,6
.o'lt
47,5
0-445
0-450^3
110,1
i . 10066
46,0
0.41778
8,!,;;
i!-3'M'i
47,3
.446
46093
110,1
. 101 12
46', l
.41861
8,!,.<i
. l8,'i<J
47.1
447
.46204
1 10,2
.10158
46,2
4IOU
.38),'
46,8
.448
.46314
1 10,2
. 10.104
<l''(3
8lt
37'J.'i
46.6'
449
.46424
1 10,3
.10251
46,4
.42108
82,3
3740
46,4
0.450
0.46534
no,3
I . I02<)7
46,5
0.4211/1
82,2
3..1?OJ
&*
u
tun nil u
w fV
BOD Oil H
Vif
iln oil u
-ft/
010 Qll U
.Fo'
SMITHSONIAN Tautea
114
il Hyperbolic Functions.
u
ilnli u
ooah u
In nh 11
oulli u
0.-150
.-151
.-l.'i.i
..15.1
t)..|55
..|57
-I5H
..|5!)
o.,|/oHo
..(UN
o.fioo
..[7/SU
..|7Mhl
!!|HoHj
..!.
Sl/71
.fiiKH-1
Inn oil u
l in,, |
1 io,.|
no,5
no, 5
in,7
m,H
1 1 1 ,H
1 1 i.o
I I 1.0
11.1,1 1
I U!,l
I I.!, I
II.!,.!
KM)] I
1 1 7-13
1 1 70.1
!,!< IX
ROD 0<l U
17.1
17.3
I7..I
17.5
.17,H
17,0
,|H.o
10,3
10,4
10,5
10.0
51 Ml
!i< >, I
fid,.!
51 .ft
51.7
si.o
SJM
w Fu'
.-I.(S77
M7H1
aln ail 11
Ht,H
Hi.7
Hl!(.
Hi. 5
Hij
HT.J
Hi, I
Hi,o
Ho,.!
H(i, i
70,7
70.7
70,5
7'.M
a. 3' 17-1
Jt. iKafi
.I7HK
.175'
.17.1-1
. lf)7'
010 Oil l>
45,7
. Ji!3
1.0
1.7
1,5
1,3
.|l,5
'M.3
|0,H
I"/'
40,,)
40.0
,10,' J
.10.7
30.-!
37.H
37.5
37i3
37,1
To'
SMITHSONIAN TA.HI.ICI)
Natural Hyperbolic Functions.
u
tinh u
<oF '
cosh ii
wFn'
tanii u
-Fo'
coin u
<u Fo'
0.500
0.52110
112,8
1 . 12763
52,1
0.46212
78,6
2.1640
36,8
.501
.52.222
112,8
.12815
52,2
.46290
78,6
.1603
36,7
.502
52J35
112,9
.12867
52,3
.46369
78,5
.1566
36,5
-503
.52448
H2,t)
.12919
52,4
.46447
78,4
.1530
36,4
.504
.525^1
113,0
. 12972
52,6
.46526
78,4
1493
36,2
0.505
0.52674
"3,0
1.13025
52,7
0.46604
78,3
2.1457
36,0
.506
.52787
113,1
.13077
52,8
.46682
78,2
.1421
35,9
-507
.52900
113,1
. 13130
52,9
.467(10
78,1
. 1386
35,7
.508
-53013
"3,2
.13183
53,0
.46839
78,1
1350
35,6
509
-53127
113,2
13236
53,1
.46917
78,0
.1314
35,4
0.510
0.53240
"3.3
1.13289
53,2
0.46995
77,9
2.1279
35,3
.511
-53353
"3.3
13343
53,4
.47072
77,9
.1244
35,1
.512
.534<>6
"3,4
T33Q6
53,5
.47150
77,8
.1209
35,0
-5U
.535So
"3,4
13450
53>6
.47228
77,7
.1174
34,8
-5M
.53693
"3,5
.13503
53,7
.47306
77,6
"39
34,7
0.515
0.53807
113,6
i "3557
53,8
0.47383
77,5
2. I 105
34,5
-5i6
-53020
"3,6
I3G"
53,9
.47461
77,5
.I07O
,34 rl
517
54034
"3,7
13665
54,0
.47538
77,4
. 1036
34,3
5iS
54 MS
"3>7
.13719
54.E
.4/615
77,3
.1002
34,1
.519
.54262
113,8
- 13773
54,3
.47693
77,3
.0968
34,0
0.520
0.5-1375
"3,8
I . 13827
54,4
0.47770
77,2
2.0934
33,8
.521
.54489
"3,9
.13882
54,5
.47847
77,i
.0900
33-7
.522
. 54603
"3,9
. 13936
54,6
47924
77,o
.0866
33,5
523
54717
114,0
.13091
54,7
.48001
77,0
.0833
33,4
.524
.54831
114,0
. 14046
54,8
.48078
76,9
.0799
33,3
Q-52.S
0.54945
"4,1
1.14101
54,9
0.48155
7f>,8
2.0766
33,1
. 526
5505D
114,2*
.14156
55,1
.48232
76,7
.0733
33,0
.527
.55173
114,2
.14211
55,2
.48308
76,7
.O7OO
32,9
.528
.55288
"4,3
. T426!)
55,3
48385
7(tf
.0668
32,7
.529
- 55402
"4,3
. I432T
55,4
.48463
76,5
.0635
32,6
0.530
0.55516
T I'M
1 , 14377
55,5
0.48538
;6,4
2.0603
32,4
-53'
55<>3i
1 14,4
. M432
55,6
.48615
76,4
.0570
32,3
532
55745
"4,5
. 14488
55,7
.48591
76,3
.0538
32,2
53,1
.55860
"4,5
T45-I4
55,9
-48767
76,2
.0506
32,0
534
- 55974
1 14,6
. 14600
56,0
,48843
76,1
.0474
31,9
0-535
o . 56089
"4,7
I . 14656
56,1
0.48919
76,1
2,0:|42
3r,8
.536
. 56204
"4>7
.14712
56,2
.48995
76,0
.0410
3', 7
537
-56318
114,8
.14768
56,3
.41,071
75,9
.0378
3i,5
.538
.56433
1 14,8
.14825
56,4
49147
75,8
0347
3i,4
539
.56548
114,9
,14881
56,5
49223
75,8
.0316
3i,3
0-540
o . 56663
"4,9
1.14938
56,7
0.49299
75,7
2.0284
3i>i
.541
.56778
"5iO
T4994
56,8
49374
75,6
.0253
3*>o
<542
.56803
"5,1
.15051
56,9
49450
75,5
.0222
30,9
543
.57008
"5,1
.15108
57,o
.49526
75,5
.0192
30,8
544
.57123
"5,2
.15165
57,1
,49601
75,4
,0l6l
30,6
0.545
0.57238
"5.2
1.15223
57,2
0.49676
75,3
2.OI30
30,5
.546
57354
"5,3
. i 5280
57,4
49752
7S,2
.0100
30,4
547
57469
"5.3
-15337
57,5
.49827
75,2
.OO70
30,3
.548
.57584
"5,4
-15395
57,6
-49902
75,i
0039
30,2
540
57700
"5,5
-15452
57,7
499;7
75,o
.OOOg
30,0
0.550
0.57815
"5,5
I.I55IO
57,8
0.50052
74,9
1.9979
29,9
u
tan ad u
Fo'
sec ad u
* Fo'
sin ad u
Fo'
csc gd u
u Fo'
SMITHSONIAN TABLES
116
Natural Hyperbolic Functions.
SMITHSONIAN TABi.ru
Natural Hyperbolic Functions.
u
ilnh u
coF '
cosh u
in Fo'
tanh u
u Fo'
coth u
" Fo'
0.600
o .63665
iiS.5
1.18547
63,7
0.53705
71,2
1.8620
24,7
.601
.63784
118,6
.18610
63,8
.53776
7i,i
.8596
24,6
.602
.63903
118,7
.18674
63,9
.53847
71,0
.8571
24,5
.603
.64021
n8,7
.18738
64,0
.53918
70,9
8547
24,4
.604
,64140
118,8
.18802
64,1
.53989
70,9
.8522
24,3
0,60.5
0.64259
118,9
1.18866
64,3
0.54060
70,8
1.8498
24,2
.606
6437S
118,9
.1893'
64,4
.54131
70,7
.8474
24,1
.607
.64407
119,0
.18995
64,5
-54201
70,6
.8450
24,0
.608
.64616
no,:
. igof)O
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
i . 19189
64,9
0.54413
70,4
1.8378
23,8
.611
.64973
ii9,3
. 19254
65,0
.54483
70,3
8354
23,7
.612
65093
H9.3
.19319
65J
54553
70,2
.8331
23,6
.613
.65212
119,4
. 19384
65,2
.54624
70,2
.8307
23,5
.614
65331
119,4
19449
65,3
.54694
70,1
.8284
23,4
0.615
0.6S45I
ii9,5
I.I95IS
65,5
0.54764
70,0
1.8260
23,3
.616
.65570
119,6
.19580
65,6
.54834
69,9
.8237
23,3
.617
.65690
119,6
. 19646
65,7
.54904
69,9
.8214
23,2
.618
.65810
119,7
.19712
65,8
54973
69,8
.8191
23,1
,619
.65929
119,8
. 19778
65,9
55043
69,7
.8168
23,0
0.620
0.66049
119,8
1.19844
66,0
0.55II3
69,6
I.8I45
22,9
,621
.66169
119,9
.iggio
66,2
.55182
69,5
.8122
22,8
.622
.66289
120,0
. 19976
66,3
.55252
69,5
.8009
22,8
.623
.66409
120,0
.20042
66,4
55321
69,4
.8076
22,7
.624
.66529
1 20, i
.20109
66,5
55391
69,3
.8054
22,6
0.625
0.66649
120,2
1.20175
66,6
0.55460
69,2
1.8031
22,5
.626
.66769
I2O,2
. 20242
66,8
55529
69,2
.8009
22,4
.627
.66800
120,3
. 20309
66,9
.55598
69,1
.7986
22,4
,628
.67010
120,4
.20376
67,0
.55667
69,0
.7964
22,3
.629
.67130
120,4
.20443
67,1
.55736
68,9
.7942
22,2
0.630
0.67251
120,5
I. 205 TO
C>7,3
0.55805
68,9
1.7919
22,1
.631
.67371
120,6
.20577
67,4
.55874
68,8
.7897
22,0
.632
674 02
120,6
.20645
67,5
55943
68,7
.7375
22,O
.633
.67613
1 20,7
.20712
67-6
.56011
68,6
.7853
21,9
634
.67734
120,8
.20780
67,7
.56080
68,6
.7832
21,8
0.635
0.67854
120,8
1.20848
67,9
0.56149
68,5
1.7810
21,7
.636
.67975
120,9
.20916
68,0
.56217
68,4
.7788
21,6
637
.68096
12 1,
, 20984
68,1
.56285
68,3
.7767
21,6
.638
.68217
i2i,r
.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
I2F.2
I.2II89
68,5
0.56490
68,r
1.7702
21,3
.641
.68581
121,3
.21257
68,6
.56558
68,0
.7681
2t,3
.642
.68702
121,3
.21326
68,7
. 56626
6?,9
.7660
21,2
.643
.68823
121,4
.21395
68,8
.56694
67,9
.7639
21,1
.644
.68945
121,5
.21463
68,9
.56762
67,8
.7618
21,0
0.645
0.69066
121,5
I.2I532
69,1
0.56829
67,7
1-7597
21,0
.646
.69188
131,6
.21602
69,2
.56897
67,6
7576
20,9
,647
.69309
121,7
.21671
69,3
.56965
67,6
7555
20,8
.648
.69431
I2f,7
.21740
69,4
.57032
67,5
7534
20,7
.640
.69553
121,8
.21810
69,6
.57100
67,4
-75I3
20,7
0.650
0.69675
121,9
1.21879
69,7
O.Syify
6>,3
1-7493
20,6
u
tan ad u
m Fo'
seo ad u
<> Fo'
sin od u
<o Fo'
oso od u
ui Fo'
SMITHSONIAN TABLES
118
Natural Hyperbolic Functions.
o.6i;o
.(>5i
.65.!
.65.1
.<>. ( ;.i
-<>5X
O.(rfX>
.0(1.!
.(I'M
o.(><>5
,d(>(i
.0(10
.67-1
0.075
O.fM)
((.(185
,<>8o
.(87
O.tHJO
'*>,!
0.700
u
slnli u
.70 KM
.711.1-!
-Xi-:"5
. X i ,iM
-X-I/M.'
X'l^.'ix
,74<jM..'
.75107
. 75,157
7S733
tnn oil u
coali u
i.J.J.7
i.i.;,X
1 .!.),
I..VI.H
l.!5,(l
,. !,!,}( X)
Fo'
.,!.,'.H1
. jjs I I
1.25517
HOC Oil U
<o Pi/
7(i,o
X'.o
XI, i
Xi,.l
Xi, -I
7'.5
7,1.4
7.1.5
75,1
75.1
75.5
7Si<>
75,7
tanli u
<>.57if>7
-5X-M-I
57,101
-5X.1' '0
-57.13''
5X5/0
-5X'M''
.57/03
-5XXXO
-5X'MM
0.581(18
.58/00
0.50I5-!
.50-.' 1 7
-505-11
<5<X'o, 1 i
. SW.l I
.(10055
o.doi 18
aln oil u
67,1
(.7,0
00,8
65,')
(i5,7
"5,5
65,5
"5,-!
65,-!
"4.D
"4.8
d-1,5
6.1,8
6,1.7
6;i,<>
63,6
COlll II
747-!
-745-!
-7-131
- x!l?o
X.150
.7^X0
-X-M'
'.7W
715,1
.X'3.1
Xl'.l
i . 7W5
.7056
!xo'iK
.('705
('XX7
.6X50
,('17.11
-('705
. (1(187
I . fit 134
.(1581
.6564
I .6546
DSO ()(1 U
Fa'
2O,f)
1:0,5
20,5
'0,7
iy,6
iy.5
if),o
10,0
18,8
18,8
18,7
18,3
18,1
18,0
18,0
J7.7
17.7.
17,6
17,6
'7,5
17.4
SMITHBOHIAM TARUM
"9
Natural Hyperbolic Functions.
u
si nh u
I*FO'
cosh u
F '
tanh u
fj
coth u
i" Fo'
0,700
0.75858
125,5
1.25517
75,9
0.60437
63,5
1.6546
17,4
.701
75084
135,6
.25593
76,0
.60500
63,4
.6529
17,3
.702
. 761 10
125,7
.25669
76,1
.60564
63,3
.6512
17,3
703
76-235
125,7
. 25M5
76,2
.60627
63,2
.6494
17,2
.704
7f">3G i
125,8
.25821
.76,4
.60690
63,2
.6477
17,1
0.705
o. 76487
125,9
1.25858
76,5
0.60753
63.1
i .6460
17,1
,706
.76(113
126,0
25974
76,6
.60816
63,0
.6443
17,0
.707
76739
126,1
.26051
7*5,7
.60879
62,9
.6426
17,0
.708
.76865
126,1
.26128
76,9
.60942
62,9
.6409
16,9
709
.76901
126,2
. 26205
77,0
.61005
62,8
6392
16,9
0.710
0.77117
126,3
i . 26282
77,i
o.6io58
62,7
1.6375
16,8
.711
. 77244
126,4
. 26359
77,2
.61130
62,6
/>353
16,8
712
. 77370
126,4
. 26436
774
.61193
62,6
.6342
16,7
7U
77497
126,5
.26514
77,5
.61255
62,5
.6325
1 6,7
.714
. 77623
126,6
26591
77,6
.61318
62,4
.6308
16,6
0.715
0.77750
126,7
I . 26669
77,7
0.61380
62,3
1.6292
16,5
.716
.77876
126,7
.26747
77,0
.61443
62,2
.6275
16,5
.717
.78003
126,8
.26825
78,0
.61505
62.2
.6259
16,4
.718
78'30
126,9
.26903
78,1
.61567
62,1
.6242
16,4
-719
78257
127,0
.26081
78,3
.61629
62,0
.6226
16,3
o . 7 JO
0.78384
127,1
1.27059
78,4
0.61691
61,9
1.6210
16,3
.721
7S5IT
127,1
.27138
78,5
61753
6 1,0
.6194
16,2
.722
.78-138
127,2
.27216
78,6
.firfirs
6 1,8
.6177
16,2
.7~'3
. 78766
127,3
.27295
78,8
.61876
fir, 7
.6161
16,1
.734
.78893
127,4
-27374
78,9
.61038
6r,6
.6145
16,1
0,725
0.7Q020
127.5
1.27453
79.o
0.62000
6r,6
1.6129
1 6,0
,726
70I4'S
127,5
27532
79.1
.62061
61,5
.6113
1 6,0
.727
. 79275
127,6
.27611
79.3
.62123
6i,4
.6007
15,9
.728
79403
127,7
.27650
79,4
.62184
6r, 3
,6o8r
15,0
-72CJ
79531
127,8
.27770
79,5
.62245
(u,3
.6065
15,8
0,730
0.70^59
127,8
1.27849
79,7
0.62307
61,2
1.6050
15,8
.731
,79785
127,9
.27929
79,8
.62368
GT.I
.6034
15,7
.733
. -799T4
1.28.0
. 28009
79,9
.62.129
6r,o
.6018
15,7
7,13
.80042
728,1
.28089
80,0
.62490
6r,o
.6003
15,6
7.1-1
.80171
128,2
.28169
80,2
.62551
60,9
. .5987
15,6
0-735
0.80299
128,2
1.28249
80,3
0.62611
60,8
1*5972
15,5
. 7$
.80427
128,3
.28330
80,4
.62672
60,7
.5956
rs,5
737
.S055S
128,4
.28410
80,6
.62733
60,6
5941
15,4
.738
.80684
128.5
.28401
80,7
.62794
60,6
.5925
15,4
739
.80812
128,6
.28572
80,8
.62854
60,5
.5910
15,3
0.740
0.80041
128,7
1.28652
80,9
0.62915
60,4
1.5895
15,3
MI
.81070
128,7
.28733
81,1
.62975
60,3
.5879
15,2
.743
.81199
128,8
.28815
81,2
.63035
60,3
.5864
15,2
743
.81327
128,0
.28896
81,3
.63095
60,2
.5849
I5,i
744
.81456
120,0
28977
Si.5
.63156
60, i
.5834
15,1
0.745
0.81585
120, r
I . 29059
Si t 6
0.63216
60,0
1.5819
15,0
. 746
.81714
129, r
.29140
8i >7
.63276
60,0
.5804
15,0
7-!7
.81844
129,2
, 29222
8i>8
.6333Q
59,9
.5789
14,9
.743
.81973
i ay, 3
.29304
82,0
.63395
59,8
5774
14,9
749
.83102
129,4
.29386
83,1
.63455
59,7
5759
M,8
0.750
0,82232
120,5
1.29468
82,2
0.63515
59,7
1.5744
14,8
a
tan gd u
w Fo'
sec gd u
w Fo'
sin ail u
Fo'
aso gd u
Fo'
SMITHSONIAN
1 2O
Natural Hyperbolic Functions.
0.750
751
75-i
753
75-1
0-755
757
.758
-759
0.760
.701
7<<J
0-775
776
.777
'm
0.780
0,785
0,790
.791
.70.!
.793
791
0.795
797
.798
79'J
0.8oo
ilnli u
o,8.!J3.
o.BjHHn
.83010
O.H35.10
.831 if 1 1
-8.1791
.8.131,1
.H.M.IS
.HIS?''
-81707
.85100
.85,131
0.85,10.1
,H!KUI
o.HKi.13
.88410
.88543
0.88HH
oil u
m F,,
1.10,0
131,0
131,1
1,11,1
131,,!
MM
1,11,5
1.11,7
l,(I,7
l,y,(>
M4l
1.13,0
13.1,7
Fo'
an ah u
Ji-ITW
.,13 US
1-33301
1.3374.1
mo oil u
8.1,5
8.1.1
N'U
HS! i
85,5
HS',<>
Wi!*5
87,1
87^3
87,5,
HH!O
88,8
In nli n
OA1515
.(1303-1
.63(10-1
.6.1753
.'',11)1)0
.0,157(1
.0.17.11
(). (1527 1
O.CI5.S57
.05(171
057^7
0,658,11
AW5-I
.OfHH I
,6ftKi7
tin oil u
59,7
59.0
59.-1
59, .1
58,0
57,9
57.H
S7.7.
57,6
57,5
57,5
57.-I
57-3
57,1
57,0
5f|,9
S0,o
5<j,<
so'io
55,9
00 III 11
1. 57-14
-5730
.5715
1.5(171
1 . 559!)
, 5570
.5556
. 55-ia
551-1
.SSffl)
is-17J
1.5-15*
- 5.1,10
-5416
i . 539
- 5.175
- 5.1'n
.53-lK
- 533.1
I . 532!
-53I'7
.5267
1 . 535-1
.52-11
.53JH
.521-1
.5^01
I.5I88
.513*'
1.51^3
.5085
507^
1.5059
oio gil ti
1-1,7
M,?
M!<>
1-1,5
1-1,5
14,4
M.3
1-1.3
i,(, r
l.|,0
h|,0
1.1.9
13,9
i.1,H
13,7
i3>7
13."
13,6"
13.5
13.5
13.'1
i!i!s
13,3
13.3
13,1
1 3. 1
13,0
13.0
13.0
ia,8
13,7
12,7
SHITHOONIAN
121
Natural Hyperbolic Functions.
u
linh u
uFt,'
cosh ii
u> Fo'
tanli u
F '
CO III U
u Fo'
0.800
o.SSSir
133,7
1-33743
88,8
0,66404
55,9
1.5059
12,7
.8or
.88944
133,8
-33832
88,9
.66460
55,8
5047
12,6
.802
.89078
"33,9
33921
8y,i
66515
55,8
.5034
12,6
.803
.80212
134,0
34011
89,2
.66571
55,7
.5022
12,6
.804
-89346
134,1
-34100
89,3
.66627
55,6
.5009
12,5
0.805
0.89480
134,2
I.34I89
89,5
0,66682
55,5
1.4996
12,5
.806
.89615
134,3
34279
89,6
.66738
55,5
.4984
12,5
.807
.80749
134,4
.34368
89,7
.66793
55,4
.4972
12,4
.808
.80883
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
o. 00152
134,6
1 .34638
90,2
0.66959
55,2
1-4935
12,3
,811
.90287
r34,7
34729
90,3
.67014
55,i
.4922
12,3
.812
.90422
T34.8
.34819
90,4
.67069
55,0
.4910
12,2
.813
.90557
T34.9
-34909
90,6
.67124
54,9
.4898
12,2
.814
.90692
135,0
35000
90,7
,67179
54,9
.4886
12,2
0.815
0.90827
135,1
I.3S09I
00,8
0.67234
54,8
1.4873
12,1
.Sifi
.90962
135,2
.35182
91,0
.67289
54,7
.4861
12,1
.817
,91097
'35,3
.35273
01,1
.67343
54,6
.4849
1 2,O
.818
.91232
135,4
.35364
91,2
.67398
54,6
.4837
12,0
.819
.91368
135,5
35455
9i,4
.67453
54,5
.4825
12,0
0.820
0.91503
135,5
1.35547
9i,5
0.67507
54,4
1.4813
n,9
.821
.91639
135,6
.35638
91,6
.67561
54,4
.4801
11,9
.822
.91775.
135,7
35730
91,8
.67616
54,3
.4789
11,9
.823
.91910
135,8
.35822
91,9
.67670
54,2
4778
n,8
.824
,92046
135,9
359T4
92,0
,67724
54,1
.4766
11,8
0.825
0.92182
136,0
1.36006
92,2
0.67778
54,1
1-4754
n,8
.826
.92318
136,1
.36098
92,3
.67832
54,0
,4742
11,7
.827
.92454
136,2
.36190
92,5
.67886
53,9
4731
n,7
.828
.92591
136,3
.36283
92,6
.67940
53,8
.4719
n,7
.829
.92727
136,4
.36376
92,7
.67994
53,8
.4707
n,6
0.830
0.92863
r36,5
1.36468
92,9
0.68048
53,7
1.4696
i r,6
.831
.93000
136,6
.36561
93,0
.68101
53,6
.4684
ir,6
.832
03137
136,7
.366S4
93,1
.68155
53,5
.4672
n,5
.833
.9,1273
136,7
.36748
93,3
.68208
53,5
.4661
ir,5
.834
.93410
U6,8
.36841
93,4
.68262
53,4
,4649
n,5
0.835
0.93547
136,9
1.36934
93,5
0.68315
53,3
1.4638
11,4
.836
.93684
137,0
.37028
93,7
.68368
53,3
.4627
11,4
.8,17
.93821
137,1
.37122
93,8
.68422
53,2
.46:5
11,4
.838
9395S
137,2
.37216
94.0
68475
53,1
.4604
11,3
-839
-9409S
137,3
-37310
04,1
.68528
53,0
4593
ii,3
0,840
0,94233
137,4
1.37404
94,2
0,68581
53,o
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
.94645
137,7
.37687
94,6
68739
52,7
.4548
11,2
.844
.94783
137,8
.37782
94,8
.68792
52,7
4537
11,1
0.845
0.94921
137,9
1.37877
94,9
0.68845
52,6
1-4S25
11,1
.840
95059
138,0
.37972
95,1
.68897
52,5
4514
11,1
.847
.95IQ7
138,1
.38067
95,2
.68950
52,5
4503
11,0
.848
95335
138,2
.38162
95,3
.69002
52,4
.4492
11,0
949
.05473
138,3
.38258
95,5
.60055
52,3
.4481
11,0
0,850
0.95612
138,4
I.3S353
95,6
0.69107
52,2
1-4470
10,9
u
tan ad u
<o Fo'
sec ad u .
u Fo'
sin gd u
" Fo'
080 Q[J U
<- Fo'
SMITHSONIAN TABLES
122
NtUurnl Hyperbolic Functions.
alnli u t" Fi' ocisli it i IV Innli u
O.WHM
1 .IKHlHl)
t nn ml u
M3.3
r. .1-707
seo nd u
11X1,1
KHi,.!
lIHl.t)
101,1
101,.!
MM, |
103,7
| U)
7M'\1
.715.1-!
715'Si
aln 0<E u
.HI, i
Jit,"
Jilt, 5
<i(t,5
.|H,y
(10 III II
I.. MTU
I..I.JSK
..].!. 17
..1-M7
1 ..[.!)(")
..(ixiy
-KM 7
ail u
Fa'
"VJ
"VJ
!(>!
10,8
10.8
10,7
io,7
10,7
10,5
10,5
10.5
IU.,1
10,0
10,0
10,0
10,0
<J,H
y.8
y.7
0,7
wlx
U/'
U.S
wFi/
Natural Hyperbolic Kvmctions.
o.yno
.001
0.905
.007
.<jnK
.you
0,910
.911
.y[J
9i;l
0.015
9>6
.917
-918
-9'9
0,0.20
.929
-931
93,1
-934
0,935
937
939
0.940
.941
-94.1
0-945
.9,1(1
9-17
949
0,950
alnli u
l. 0.265 j
-OJ795
1. 0.1:1/0
.0510.1
.05-MK
.05393
1.05539
,05(>8.|
.058:10
of 1705
.of (851
0714.1
.07.1,18
I.077.1I
.0817.1
i .09207
-09.155
.0950.1
1.09948
Inn ail u
'45
i -15
'45
145
145
1-15
145
1-17
1-17
147
1-17
147
"47
"47
"47
'-17
1-19
149
OOfill 11
..1.1411
.43514
.43' "7
i. 44,14 -^
.4444"
.44551
.-147(10
--I5I175
1.45.190
.4>10!>
.458l.|
l.459-!0
.405(10
.40775
.47.H
r. 475.10
.47"3'l
-477 iN
47^57
..|Kn75
..|8,!0.1
BOO a<l
105
105
H'5
105
105
105
K'5
10'i
loO
I IK' i
Hrfi
107
107
107
107
108
108
108
KM)
KM.)
KM)
KM)
10*)
10i)
no
no
no
no
w F,/
0.7,15.;.!
735'W
sin u'l u
CO 111 II
I .lO'l
..V'/'i
3 11 "!
,i". ! ;.i
1 ,.1'HII
-3}i'M
'.3;ii7
CSI) flll 11
'J,5
9,5
9.4
9,4
9,0
8,.)
8,8
8,8
8,8
8,8
8,h
8,5
8,5
8,5
MM
SMITHHONIAN TAPI.CB
124
Natural Hyperbolic Functions,
u
si nli u
a.F '
oosh u
<> Fu'
tanh u
u Fo'
oath u
uF<f
0.950
1.09948
149
1.48623
no
0.73978
45,3
I-35I7
8,3
.951
.10097
149
-4733
no
.74024
45,2
3509
8,2
.952
. 10246
149
.4*843
no
.740&P
45,1
3501
8,2
953
10395
149
4&>53
1 10
.74114
45,1
3493
8,2
954
. 10544
149
.49064
in
.74159
45,0
3483
8,2
0.955
1 . 10693
149
r-49174
in
0.74204
44,9
1.3476
8,2
.956
.10842
149
.49285
m
74249
44,9
.3468
8,1
-957
.10991
149
.49396
in
.74294
44,8
.3460
8,1
.958
.11141
t5o
.49507
in
74338
44,7
3452
8,1
-959
.11291
150
.49618
in
.74383
44,7
3444
8,1
0.960
1 . 1 1440
ISO
T .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
.7456i
44,4
.3412
8,0
.964
. 12040
150
.50176
112
.74606
44,3
-3404
8,0
0.965
I.I2IQQ
150
I . 50289
112
0.746SO
44,3
1.3396
7,9
.956
.12341
150
.50401
112
.74694
44,2
-3388
7,9
.967
. 12491
151
30513
112
74738
44,1
.3380
7,9
.968
.12642
151
. 50626
"3
-747M2
44,1
3372
7.9
.969
. 12702
151
50739
113
.74826
44,0
.3364
7,9
0.970
I.I2943
151
1.50851
H3
0.74870
43,9
1.3356
7,8
.971
.13094
151
.50964
113
.74914
43,9
3349
7,3
.972
.13245
151
.51078
H3
74958
43,8
334t
7,8
973
- I33iX>
IS!
.51191
"3
-75002
43,7
3333
7,8
.974
.13547
151
.5U04
114
.75046
43,7
.3325
7,8
0.975
1,13699
ISI
1.51418
114
0.75089
43,6
I-33I7
7,7
.976
.13850
152
.51532
114
-75I33
43,6
3310
7,7
.977
. 14002
IS2
.51646
114
75176
43,5
.3302
7,7
.978
.14154
152
.51760
114
7522O
43,4
3294
7,7
.979
. 14305
152
.51874
114
.75263
43,4
.3287
7,7
0.980
i . 14457
152
1.51988
144
0.75307
43,3
1.3279
7,6
.981
.14609
152
.52103
US
75350
43,2
.3271
7,6
.982
.14761
152
.52218
115
75393
43,2
.3264
7,6
.983
. 14914
IS2
.53332
US
.75436
43,1
.3256
7,6
-084
.15066
152
.52447
IIS
75479
43,o
3249
7,6
0.985
r. 15219
133
1.52563
115
0.75522
43,o
1.3241
7,5
.985
-I537I
153
.52678
H5
75565
42,9
3234
7,3
987
. 15524
153
.52793
. 116
.75608
42,8
.3226
7,5
.988
. 15677
153
.52909
nfi
.756sr
42,8
3219
7-5
.989
. 15830
153
.53025
116
75694
42,7
.3211
7,5
0.990
1.15983
153
I.S3MI
ii<5
0.75736
42,6
1.3204
7,4
.991
.16136
153
53257
116
73779
42,6
.3196
7,4
'992
. 16289
i S3
.53373
116
.75821
42,5
.3189
7,4
993
. 16443
153
.53489
116
.75864
42,4
.3182
7,4
.994
.16596
154
.33606
117
.75906
42,4
.3174
7,4
0.995
r. IG7SO
154
1.53722
117
0-75949
42,3
1.3167
7,3
.996
.16904
154
.53839
117
75991
42,3
3159
7,3
997
17058
154
.53956
117
.76033
42,2
.3152
7,3
.998
.17212
. 154
.54073
117
.76075
42,1
.3143
7,3
999
.17366
154
.34191
117
,76117
42,1
.3138
7,3
I.OOO
1.17520
154
I.S4308
118
0.76159
42,0
1.3130
7,2
u
tan od u
ti Ft'
sec gd u
u Fo'
sin od u
U! Fl)'
cso ad u
*>F '
SMITHSONIAN TABLE*
12-
Natural Hyperbolic Functions.
II
ainh u
01 F/
cash u
w Fo'
tftnh u
Fo'
coth u
-Fo'
1. 000
I . 17520
154
1.54308
iiS
0.76159
42,0
1.3130
7,2
,001
17674
154
.54426
118
.7620:
41,9
3123
7,2
,002
. 17829
155
54543
118
.76243
41.9
,3116
7,2
.003
. 17984
I5S
.54661
ir8
.76285
41,8
-3109
7,2
,OO.|
. 18:38
155
54779
118
.76327
41,7
.3102
7,2
1.005
1 , 1829.1
155
1.54898
118
0.76369
41,7
1.3094
7,1
.006
. 18448
155
.55016
118
.76410
41,6
.3087
7,1
.007
.18603
155
-55I34
119
.76452
41,6
.3080
7,1
.008
. 18758
155
55253
119
.76493
41,5
.3073
7,1
.009
. 18914
155
55372
119
.76535
41,4
.3066
7,i
1. 010
1.19069
155
I.5S49I
119
0.76576
41,4
1.3059
7,1
,011
. 19225
156
.55610
119
.76618
41.3
.3052
7,o
,012
.19380
156
55723
119
.76650
41,2
.3045
7,o
.013
19536
r 5 6
.55849
r 20
.76700
41,2
.3038
7,o
.014
.19692
156
.55<X59
120
.76741
41,1
.3031
7,o
1. 015
1 . 10848
156
1,56088
120
0.76782
41,0
I . 3024
7,o
.016
.20004
156
.56208
1 2O
-76823
41,0
3017
6,9
.017
.20160
156
.56328
1 2O
.76864
40,9
.3010
6,9
.018
.20317
156
56449
120
.76305
40,9
3003
6,9
,OI<>
.20473
157
.56560
I2O
. 76946
40,8
.2996
6,9
I.02O
1 . 20630
157
1.56689
121
0.76987
40,7
1 , 2989
6,9
,O2 1
,20787
157
.56810
121
.77027
40,7
. 2982
6,9
.022
.20944
T57
.56931
121
.77068
40,6
. 2976
- 6,8
-02,3
.2IIOI
157
.57052
121
.77109
40,5
.2969
6,8
.0-24
,21258
157
.57173
121
.77149
40,5
,2962
6,8
I ,O25
I.2J4I5
157
i. 57295
121
0.77r*)0
l,4
1.2955
6,8
,026
.21572
157
.57416
122
.77230
40,4
.2048
6,8
.027
.21730
i;8
57538
122
.77270
40,3
. 2942
6,7
,028
.21887
158
. 576(10
122
.77310
40,2
2935
6,7
.O2C)
. 22045
158
.57782
122
77351
40,2
. 2928
6,7
I.O30
I . 222O3
158
1.57904
122
0.77391
40,1
i . 2921
6,7
031
.22361
158
.58026
122
-77431
40,0
. 2915
0,7
.032
.22519
158
.58148
123
77471
40,0
.2908
6,7
.033
. 22677
158
.58271
123
775II
39,9
.2901
6,6
.034
. 22836
158
.58394
123
.77551
39,9
.2895
6,6
i .035
1.22994
150
1.58517
123
0-77S9I
39,8
1.2888
6,6
.036
.23153
159
,58640
123
.77630
30,7
.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
.030
.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
.O.| I
.23947
159
.59257
124
.77828
39,4
.2849
6,5
.042
.24107
159
.59381
124
-77868
39,4
.2842
6,5
0-13
, 2426(1
I6o
.59506
124
.77907
39,3
.2836
6,5
.044
,24426
160
.59630
124
-77946
39,2
.2829
6,5
1 .045
1-24585
160
1-59755
125
0.77985
39,2
i . 2823
C,4
.046
,24745
160
.59879
125
.78025
39,t
.2816
6,4
.047
,24005
1 60
.60004
125
.78064
39,1
.2810
6,4
.048
, 25065
160
.60129
125
.78103
39,0
. 2804
6,4
.049
.25225
160
.60254
125
.78142
38,9
-2797
6,4
1. 050
1.25386
160
1,60379
125
0,78181
38,9
i - 2791
6,4
it
Inn ail u
IV
sec od ii
"Fo'
sin nil u
0) Fo'
QSC fl(i 11
wF '
SMITHSONIAN TABLES
126
Natural Hyperbolic lAmctioim,
l.t'SS
.OS 7
lid. I
,Od|
l.i ids
.(id/
.ot)
.(Ml
<*).!
.<K)7
l. Itxi
u
a I nil ii
1.J5.1KO
..iS/t'7
Inn u<l
uonli ii
.017(18
.O.MSl
1 ,0,M7N
I.ddlKd
1,10
1,1(1
I,U
I,H
1,1'
I.V
w IV
tnnh u
Bill Ull II
t lH.()
,1X,7
.1X,.l
,ix,;i
.IX, -i
-1X.I
,1(1,0
.T',''
3*M
!v!!i
36,0
as.'j
00 III U
J7JJ
JXlO
.td.|,i
iidill
V
TABLKB
Natural Hyperbolic Functions.
11
sinh u
Fo'
cosh u
u Fu'
tanh u
FO'
coth u
Fo'
I. TOO
I' 335(JS
167
1.66852
134
0.80050
35,9
I . 2492
5,6
.101
33732
167
.66986
134
.SooS5
35.9
.2487
5l
.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
.67337
134
.80193
35.7
.2470
5,5
1.105
1.34401
168
1.67522
134
0.80229
35.6
1.2464
5,5
, 1 06
.34568
168
.67656
135
.80264
35,6
.2459
5.5
,107
.34736
168
.67791
135
.80300
35.5
2453
5,5
.108
349<>4
168
,67926
135
.80335
35,5
.2448
5,5
.iog
.35072
168
.68061
135
.80371
35.4
.2442
5,5
1 . 1 10
1,35240
168
I .68196
135
0.80406
35,3
E.2437
5,5
.in
.35408
168
.68331
135
.80442
35.3
.2431
5,5
. 112
.35577
168
.68467
136
.80477
35.2
.2426
5,4
.113
35745
169
.68502
136
.80512
35,2
.2421
5,4
,114
35014
169
.68738
136
.80547
35,1
.2415
5,4
I.H5
1.36083
169
1.68874
136
0.80582
35,1
1.2410
S.4
.116
.36252
169
.69010
136
.80617
35,0
.2404
5>4
H7
.36421
169
.69147
13"
,80652
35,0
2399
5,4
.118
.36590
169
.69283
137
.80687
34,9
.2394
5>4
.119
'.36759
169
.69420
137
.80722
34,8
.2388
5,3
T.I2O
1.36929
170
1.69557
137
0.80757
34,8
1.2383
5,3
.">.!
.37098
170
.69694
137
.80792
34.7
.2378
5,3
,122
.37268
170
.69831
137
,80826
34,7
.2372
5,3
.123
.T24
.37438
37<8
170
170
.69968
.70106
137
138
,80861
.80896
34.6
34.6
.2367
.2362
5,3
5.3
I-I25
1.37778
170
1.70243
138
0.80930
34,5
1.2356
5,3
.126
37949
170
.70381
138
80965
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
I 3 S
.81068
34,3
2335
5,2
1,130
1.38631
171
1.70934
139
o, 81102
34,2
I . 2330
5.2
-131
.38802
171
.71073
T39
,81136
34,2
.2325
5,2
.132
38973
171
.71212
139
.81170
34,1
.2320
5i2
133
-39145
171
.71351
139
.81204
. 34,1
.2315
5.2
.134
.39316
171
.71493
T39
.81238
34,o
.2309
5,2
I-I35
1-30488
172
1.71630
139
0.81272
33,9
1.2304
5,
.136
39639
172
.71769
140
,81306
33,9
.2299
S.
137
.3583'
172
.71509
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.
I, F40
1 .40347
172
1.72329
140
0.81/141
33,7
1.2279
5,1
.141
.40520
172
.72470
141
,81475
33,6
.2274
5,1
.142
,40692
173
.72610
141
.81509
33,6
.2269
S.I
.143
.40865
173
.72751
14:
.81542
33,5
.2264
5,o
.144
.41038
i?3
.72892
141
.81576
33,5
.2259
5,o
i.T45
1.41211
173
L73033
141
0.81609
33,4
1.2254
5,0
.146
.41384
173
73175
141
.81642
33,3
.2249
5.Q
.147
4IS57
173
733T6
142
.81676
33,3
.2244
S.o
.148
.41731
173
. 73458
142
.81709
33,2
.2239
5,o
.149
.41904
174
73599
142
,81742
33,2
.2234
S.o
] i.rso
1.42078
174
I.7374I
142
0.81775
33,1
1.2229
S,o
i
ttFtf
sec od u
wF '
sin ad u
u Fa'
osc ad u
wFo'
128
Natural Hyperbolic Functions.
II
ilnli u
10 fa'
CO Bll II
( fa
tntili u
-F.-
OOtll U
-F fl '
1 . 1 50
I .12078
174
1.73741
I.|U
0.81775
33,1
I . 2220
5,o
.15"
-I225.J
174
.7388.1
I.|J
.MlftK)
33,1
.222.)
4,9
.15-'
,12.1-6
174
. 7402(1
142
.818,12
33,0
.2211)
4,9
.153
.|2(HX>
174
.7.1168
M3
.81875
33,0
.221.1
4.9
.154
.1277.1
174
.7-1311
143
.81907
3^,9
.2209
4,9
1.155
1 .4^948
'74
1.74454
1-13
0.810.10
32,f>
I . 2204
4,9
. 156
..|3U3
"75
. 74597
143
.81117,1
32,8
3109
4.9
.157
' 43-97
175
.7.17.10
M3
.82(KXi
32,8
.219.]
4,9
.158
..1347-.'
'75
7.188.1
143
.82030
3^,7
.2180
4.9
.159
175
.75027
1-14
,8^071
32,()
.2185
4,8
I . (60
i..i;i8w
175
1.75171
i.|4
0.82104
32,6
I. 2180
4,8
.101
.43998
175
75315
144
821,17
32)5
.2175
4,8
, l()2
.44173
175
75459
1-14
,821(10
32,5
.2170
4,8
, l6l
17(1
.75(103
144
,82202
3-',4
.21(15
4,8
. 164
.-I45-J4
176
.75748
MS
,82J,vi
.a K
4.8
I 105
I.. 14700
176"
1.75802
145
0.822("rfi
32,3
1,2156
4,8
.100
.4487C
17(1
.7<i037
MS
. 82209
32,3
.2151
4,8
. 1(17
176
,7618*'
1-15
.82,1,11
32,2
.2146
4,8
, 1 08
.45228
.76327
M5
.82,1(1,1
.2141
4,7
. I'M)
.45405
176
7647-J
145
82395
32.1
.2137
4,7
I.l/O
i.4558i
177
1,76(118
14(1
0.82427
32,1
1.2132
4,7
.171
.45758
177
.7671-4
I.|(t
.82,151)
32,0
.217
4,7
.I7J
4 5935
177
.7(>909
Lid
.HJ.IIJI
.12,0
.2123
4,7
- 173
.401 U!
177
.7X050
146
8252.1
31,9
.2118
4,7
.40280
177
. 77202
i.i(i
.82555
31,8
.2113
4,7
1.175
l.(\ti\(Xt
177
i-773-lH
l.l()
0.82587
31,8
1.3108
4,7
. 17(1
, 4(164 4
177
774.95
M7
.82010
31,7
.210.1
4,7
.177
..((iMai
178
77<''4'
'47
.82050
31,7
.aooy
4,6
.178
,,\(#M)
1?8
.77788
147
.82(182
31,6
. 200.5
4.6
179
.47177
l?8
77U.15
147
.82714
31,6
.KXJO
4,()
1.180
1-47355
178
1.7808,1
147
11.82745
31,5
1 . 20vHs
4,6
.181
4X533
47711
178
.78^,10
.78378
148
.82777
31.5
3L4
. 2076
4,6
Ii8,i
179
.785^'!
l.|8
,828.1(1
3 1 ,4
.2072
4,6
,184
I^V/k^J
t iM>4n * i
179
.78(173
l.|8
.82871
31,3
.20(17
4,6"
I.i8s
1.. (824 7
179
i. 7882 J
148
0.82902
31,3
i. aorta
4,6
. 180
170
. yfyya
148
8293;}
3i.a
.2058
4,5
.187
,.lM()<)ii
791 iy
M9
.821/15
3 1, a
.3053
4,5
.188
,48784
'79
. 79207
M9
,820<X>
3M
.2049
4,5
.180
.48964
179
.7041(1
149
.83027
31,1
.20-14
4,5
t . 190
1.49143
iflo
1.70563
MO
0.8,1058
31.0
1.2040
4,5
191
493^3
iHo
,71)71.1
i,|(j
.83089
31,0
.2035
4,5
.4050,1
180
, 7J'j8f i.|
150
.83130
30,9
.2031
4,5
'93
,.19/i8,J
iKo
.80013
150
.8,1151
30,9
. 2026
4*5
.40862
180
.8016.)
ISO
.8318-}
30,8
.2022
4,5
1 . 105
i.WM.1
j8o
1,80313
ISO
o.8,uu
' 30,8
I. 201?
4,4
.19(1
! ""joa )')
180
,80463
150
.83^43
30,7
.201.1
4,4
. 197
, VMO'I
181
,8<XiM
150
.83274
30,7.
.aooy
4,4
.198
.5(1584
181
. 80764
151
.8.1304
30,6
.2004
4,4
. J99
5<>765
iHi
.Hoy i 5
15 '
8.1335
30,6
.2000
4,4
1.200
1. 5Q9,|f)
181
1.810(16
151
0.833^5
3Q.S
1. 1995
4,4
u
Ungtl u
w IV
IOQ ad u
wlV
(in ail u
u F,,'
OtO Q't II
- -
8MITHBONIAN
129
Natural Hyperbolic Functions.
11
sinh u
w Fo'
cosh 11
u Fo'
tanh u
ui Fj'
cotli u
o> Fo'
I.2OO
1.50946
181
I. 81066
151
0.83363
30,5
I. 1995
4,4
,2OI
-Si 127
181
.8l2!7
351
.83396
30,5
.1991
4,4
.202
.51309
181
.81368
ISI
.83426
30,4
1987
4,4
.203
.51490
182
.81519
151
.83457
30,3
.1982
4,4
.204
.51672
182
.81671
152
.83487
30,3
1978
4,3
1 . 2O5
1.51853
182
1.81823
152
0.83517
30,2
i 1974
4,3
.206
.52035
182
.81974
152
.83548
30,2
.1969
4,3
.207
.52217
182
.82127
152
.83578
30, 1
.1965
4,3
.208
.52400
182
.82279
152
.83608
30,1
,1961
4,3
,209
. 52582
182
.82431
153
.83638
30,0
.1956
4,3
I.2IO
1.52764
183
T .82584
153
0.83668
30,0
I.I953
4,3
.211
.53947
183
.82737
153
.83&g8
29,9
.1948
4,3
,212
.53130
183
.828QO
153
.83728
29,9
1943
4,3
.213
.53313
183
.83043
153
.83758
29,8
1939
4,3
.214
.53496
183
.83197
J53
.83788
29,8
1935
4,2
I.2I5
1.53679
183
1.83350
154
0.83817
29,7
1.1931
4,2
.2l6
.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
IS4
.83036
29,5
.1914
4,2
i. 220
I . 54598
184
I.84I2I
155
0.83965
29,5
1.1910
4,2
.221
. 54782
184
.84276
355
.83905
29,4
.1905
4,2
.222
.54966
184
.84430
155
.84024
29,4
.1001
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
.223
.56076
185
.85364
J56
.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
20,0
1.1868
4,1
.231
.56633
186
.85833
157
.84287
29,O
.1864
4,1
.232
.56819
186
.85989
157
.84316
28,9
.1860
4,1
233
.57005
186
.86146
157
84345
28,9
.1856
4,1
234
.57191
186
.86303
157
.84374
28,8
.1852
4,1
1-235
I 57377
186
1.86461
157
0.84402
28,8
1,1848
4,0
.236
.57564
187
.86618
I5S
.84431
28,7
.1844
4,0
.237
-.55750
187
.86776
158
.841160
28,7
,1840
4,0
.238
57937
187
.86934
158
.84488
28,6
.1836
4,0
.239
. 58:24
187
.87092
J58
84517
28,6
.1832
4,0
1.240
I . 5831 i
187
i .87250
IS8
0.84546
28,5
1.1828
4,0
.241
.58409
187
.87408
158
84574
28,5
.1824
4,0
.242
.58686
i8S
.87567
150
.84602
28,4
.1820
4,o
.243
58874
188
.87726
159
.84631
28,4
.1816
4,o
.244
.50062
IBS
.87885
159
.84659
28,3
.1812
4,0
1.245
i . 59250
188
1.88044
159
0.84688
28,3
I. 1808
3,9
.246
59438
188
.88203
159
.84716
28,2
.1804
3,9
.247
.59626
188
.88363
160
.84744
28,2
.1800
3,9
.248
.59Si5
189
.88522
160
.84772
28,1
.1796
3,9
.249
.60003
189
.88682
160
.84800
28,1
.1792
3,9
1.250
1.60192
189
1.88842
160
0.84828
28,0
1.1789
3,9
u
tan ad u
c-Fo'
sea git u
F '
sin gd u
wF '
oso oil u
*>Fo'
SMITHSONIAN TABLES
130
Natural Hyperbolic Functions.
II
si nh u
-ft'
cosh it
ul FO'
tflnh u
..V
oath u
-w
1.250
1,60192
189
1.88842
160
0.84828
28,0
1.1789
3,9
.251
.60381
189
.89003
160
.84856
28,0
.1785
3,9
.252
.60570
189
.89163
161
.84884
27,9
.1781
3,9
253
60759
189
.89324
161
.84912
27,9
.1777
3,9
.254
.60949
189
.89435
161
.84940
27.9
.1773
3,9
1.255
1.61138
190
1 .89646
161
0.84968
27,8
1.1760
3,9
.256
,61328
190
.89807
161
.84996
27,8
.1765
3,8
-257
.61518
190
.891/18
162
.85023
27,7
. 1761
3,8
.258
.61708
190
.90130
162
.85051
27,7
.1758
3,8
.259
.61898
190
.90292
162
,85079
27,6
.1754
3,3
i .260
1 .62088
190
1.90454
162
0.85106
27,6
I.I750
3,8
.261
.62279
191
.90616
162
.85134
27,5
.1746
3,8
.262
.62470
10 1
.90778
162
.85161
27,5
,1742
3,3
.263
.62661
lyi
.90941
163
.S5E89
27,4
.1739
3,8
. 264
.62851
191
.91104
163
.85216
27,4
- 1735
3,8
1.265
i .63043
791
1.91267
163
0.85244
27,3
I.I73I
3,8
.266
.63234
19 T
.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 .64001
192
I . 92084
164
0.85380
27,1
1.1712
3.7
.271
.64193
192
. 92248
164
.85407
27,1
.1709
3,7
.272
,6438(1
192
.92413
164
-85434
27,0
.1705
3,7
-273
.274
.64578
.64771
193
193
92577
.92742
165
165
.85461
.85488
27,0
26,9
.1701
.1698
3,7
3.7
1 .275
.276
.277
.278
.279
1.64964
.65157
.65350
.65543
.65736
193
193
103
194
1.92907
.93072
.93237
.93402
.93568
165
165
165
166
166
0.85515
.85542
.85568
.85595
,85622
26,9
26,8
26,8
26,7
26,7
1.1694
.1600
.1687
.1683
.1679
3,7
3,7
3,7
3,6
3,6
1.280
.281
.282
.283
.284
i . 65930
,66124
.66318
.66512
.(16706
194
194
194
194
194
1-93734
.93900
.94066
.94233
-94399
166
167
167
0.85648
.85675
.85702
,85728
.85755
26,6
26,6
26,6
26,5
26,5
1.1676
.1672
.1668
. 1 66s
.1661
3,6
3,6
3,6
3,6
3,6
1.285
.286
,287
.288
.289
i ,66901
.67096
.67200
.67485
.67680
195
195
195
195
195
1.94566
-94733
.94900
.950(18
.95235
167
167
167
167
168
0.85781
,8so8
.85834
.85860
.85886
26,4
26,4
26,3
26,3
26,2
I , 1658
. 1654
- 1650
. 1647
,1643
3,6
3,<5
3,<3
3,6
3,6
1.290
,21)1
.292
.293
1.67876
.68071
,68267
.68463
.68659
195
196
196
196
1 .95403
.05571
95739
-95907
.96076
168
168
168
io"fi
169
0.85913
85939
.85965
.85991
,86017
26,2
26,1
2(1,1
26,1
26,0
i . 1640
. 1636
. 1633
. 1629
.1626
3,5
3,5
3.5
3,5
3,5
I 295
i .68855
196
1.96245
169
0.86043
26,0
i . 1622
3,5
.2Qf)
.297
.298
.209
.69051
.69248
.69444
.69641
i()6
197
197
197
.96414
.96752
.96922
169
169
169
170
,86o6(j
.86095
.86121
.86147
25,9
25,9
25,8
25,8
.1619
.1615
.1612
.1608
3.5
3,5
3,5
3,5
1.300
1.69838
197
i .97091
170
0.86172
25,7
1.1605
3.5
u
lan titi u
H
see 0*1 u
*Fo'
sin od u
*>F fl '
esa ad u
F '
SMITHSONIAN TABLES
Natural Hyperbolic Functions.
u
sinh u
f<{
cash u
MFi.'
tanli u
ia Fo'
GOill U
<) Fo'
1.300
1.69838
197
1.97091
170
0.86172
25,7
I . l6o5
3,5
.30
70035
197
.97261
170
.86108
25,7
, 160;
3,5
-30
.70233
197
-97431
170
.86224
25,7
.1598
3,5
303
.70430
ro8
.97602
170
,8()24C
25,6
. 159-
3,4
.304
.7062^
198
97772
171
.86275
25,6
.1591
3,4
1.30.
1.70826
198
1-97943
171
0.86300
25,5
1.1587
3,4
.306
.71024
108
.98114
171
.86326
25,5
.1584
3,4
.307
.71222
198
.98285
171
.86351
25,4
.1581
3,4
-308
.71420
igf:
.98456
171
.86377
25,4
-1577
3,4
.309
.71619
199
.98628
172
.86402
25,3
.1574
3,4
1,310
1.71818
199
1,98800
I?2
0,86428
25,3
1 . 1570
3,4
.311
.72017
199
.98972
172
.86453
25,3
-1567
.312
.72216
199
.99144
172
.86478
25,2
.1564
3,'!
.313
.72415
:OQ
.99316
172
.86503
25,2
.1560
.314
.72614
199
.90489
173
.86528
25,1
-1557
3,4
I-3I5
r. 728 14
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
*3I9
73614
200
.00354
174
-86653
24,9
- 1540
3,3
1.320
1.73814
201
2.00528
174
0.86678
24,9
i. I 537
3,3
-321
.74015
201
.00702
174
.86703
24,8
.1534
3,3
.322
.74216
2O I
.00876
174
.86728
24,8
-1530
3,3
.323
744 17
2O I
.01050
174
-86753
24,7
.1527
3,3
.324
,74618
201
.01225
175
.86778
24,7
.1524
3,3
1.325
1.74819
201
2.01399
175
0,86802
24,7
I.I520
3,3
.326
,75021
2O2
.01574
175
.86827
24,6
.1517
3,3
327
. 75222
202
,01749
175
.86851
24,6
.1514
3,3
.328
75424
2O2
.01925
175
.86876
24,5
3,2
.329
.75626
202
.02100
176
,86900
24,5
.1507
3,2
1-330
1.75828
2O2
2.02276
176
0.86025
24,4
I.I504
3,2
331
.76031
202
.02452
176
.86949
24,4
.1501
3,2
-332
333
,76233
76436
203
203
.02628
.02804
176
176
,86974
.86998
24,4
24,3
.1498
1495
3,2
3,2
334
.76639
203
.02981
177
.87022
24,3
.1491
3,2
1-335
1.76842
203
2.03158
177
0.87047
24,2
I . 1488
3.2
.336
77045
203
.03335
177
.87071
24,2
. 1485
3,2
337
.338
339
.77249
77453
.77656
2O4
204
2O4
.03512
.03689
.03867
177
177
178
.87095
.87119
.87143
24,1
24,1
24,1
. 1482
.1479
1475
3,2
3.2
3,2
1.340
I . 77860
204
2.04044
178
0.87167
24,0
I . 1472
3.2
341
-342
.78064
.78268
204
204
,04223
.04401
178
178
.87191
.87215
24,0
23,9
. 1469
.1466
3,2
3,1
-343
.344
* 78473
.78677
205
205
04570
.04758
178
179
87239
.87263
23,9
23,9
1463
.1460
3.1
3,1
1-345
-346
1.78882
-70087
205
2.04036
.05115
T7Q
179
0.87287
.87311
23,8
23,8
I.I456
M53
3,1
3,1
347
-348
. 79293
.79498
205
205
.05204
05474
179
179
.87334
87358
23,7
23,7
- 14 SO
- 1447
3,1
.349
.79704
206
.05653
180
.87382
23,6
.1444
3,'i
1-350
.79909
206
2.05833
180
0.87405
23,6
1.1441
3,1
-=L=
an ad u
wFo'
eo ad u
.FO'
sin ad u
w Fo'
010 gd u
*F '
132
Natural Hyperbolic Functions,
..w-1
-ll'ii
I-.V'S
.;((>( i
1 .370
-,17i
(Illll II
.N,!tiOO
I.K.UH7
.K.U.KI
H.M.1S
.H.VI.M
,HH;if.
IV (loilt u
.UK)
.Mil
-.(Xi
JHI
,1111
.110
nut
,!l 1
Jt
JM
-SIS
U IAD fl(l U w IV 8 (tfl gtl 11
.(XJ 1(1,1
.lll.iK
J. 1 I,U|
. II^IO
r,.'
180
iM<>
181
iHi
iHi
[Hi
lKn
iWi
'5?
!y
ifl7
iHH
iftfl
iftl
I'X)
If XI
Innh u
.JWi.((t
O.SH.U7
0.H|J7
\wi\yn
iHHsi.i
0.885.1S
iln oil u
IV
JJ.-I
yr.H
31,8
31,7
31,7
ooth u
M ii>
'M 1.1
1.1410
.l.]07
. 1401
.MH.I
l.I.lfll
. i.i(k)
- 1.157
. M54
. 1.1-13
- 1,140
1 . 1.137
. 1.1.1-1
- M.1I
. 1.1 JH
I .
MM
.MU
010 ad u
.1,0
.1,0
.i.o
.1,0
.1.0
,1.0
.1.0
3.0
.1.0
a,t)
AW
AO
j.y
X 1 ,')
J|H
2,8
a,8
8MITHOHtAN
133
Natural Hyperbolic Functions.
u
slnh u
<o Fo'
cosh u
u) Fo'
tilnli u
u Fa'
COlll U
F'
1.400
.401
.402
.403
.404
1.90430
.90645
.90861
.91076
.91292
215
2J5
215
2 if)
216
2.15090
. 15280
- t547l
. 15662
. 15853
I9O
191
191
IQI
191
0.88535
- -885S7
.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
1.405
.406
.407
1.91508
.91724
.9I94O
216
216
216
2 . T6045
. 16236
. 16428
192
192
192
0.88643
.88664
.88686
21,4
21,4
21,3
1.1281
.1279
. 1276
2,7
2,7
2,7
.408
.92157
217
.l662O
192
.88707
21,3
1273
2,7
.409
-92374
217
.16812
192
.88728
21,3
.1270
2,7
1.410
.411
.412
-413
1.92591
.92808
.93025
-93242
217
217
217
218
2.1700.5
.17198
. I73QI
.T7584
193
1 93
193
193
0.88749
.88771
.88792
.88813
21,2
21,2
21,2
21,1
I . 1268
.1265
.1262
.1260
2,7
2,7
2,7
2,7
.414
.93460
218
.17777,
193
.88834
21,1
-1257
2,7
I.4IS
1 .93678
218
2.I797I
194
0.88855
21,0
I . 1254
2,7
.416
.93696
218
. 18164
194
.88876
2I,O
.1252
2,7
.41?
.94114
218
. 18358
194
.88897
21,0
. I2:|9
2,7
.418
94333
219
- 18553 '
194
.88918
20,9
, 1246
2,6
-410
94551
219
. 18747
195
.88939
2O,9
.1244
2,6
1 ,420
.421
.422
I .94770
.94930
-9520g
219
219
219
2.18942
- 19137
- 19332
195
195
T95
0.88060
.88981
.80002
20,9
20,8
20,8
I.T24I
.1238
. 1236
2,6
2,6
2,6
423
.424
.95428
.95648
2 2O
220
- 19527
. 19723
195
196
.89022
.89043
20,8
20,7
1233
.1231
2,6
,2,6
1 .425
1,95867
2 2O
2, 19918
196
0,89064
20,7
i , 1228
2,6
. 426
.96087
220
, 20 1 14
196
.89084
20,6
.1225
2,6
.427
.06308
220
.20310
196
.89105
20,6
1223
2,6
.428
.96528
221
. 20507
197
.89126
20,6
.1220
2,6
.429
.96749
221
.20704
197
.89146
20,5
.1218
2,6
1. 4V)
1,969-70
221
2.20OOO
197
0.89167
20,5
i.wig
2,6
431
.97191
221
.2IO97
197
.89187
20,5
.1212
2,6
.432
,97412
221
.21295
197
.89208
20,4
.1210
2,6
433
97^33
221
.21492
198
.89228
20,4
.1207
2,6
434
978S5
222
,2lCgO
198
.89248
20,3
.1205
2,6
1-435
1.98076
222
2.21888
IQS
0.89269
20,3
1 . 1202
2,5
436
.08298
222
.22086
198
.89289
20,3
.1200
2,5
437
,98521
222
.22285
199
.89309
20,2
."97
2,5
.438
98743
222
.22483
199
.89329
20,2
."95
2,5
-439
.98966
223
.22682
199
.89350
20,2
.1192
2,5
1.440
I.99IS8
223
2,2288l
199
0.89370
20,1
r . 1 189
2,5
441
.99411
223
,23080
199
.89390
20,1
.1187
2.5
442
.99635
223
.23280
200
.80410
20,1
.1184
2,5
443
.99858
223
.23480
200
.89430
20,0
.1182
2,5
.444
2.00082
224
.23680
20O
.89450
20,0
"79
2,5
1-445
2.00305
224
2.23880
2OO
0,89470
20,0
i. "77
2,5
.44(5
.00529
224
.24080
201
.89-190
19,9
- 1 174
2,5
.447
.00753
224
. 24281
201
.89510
19,9
.1172
2,5
-448
.00978
224
. 24482
2O I
-89530
19,8
,1169
2,5
-449
.OI202
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 gil u
wF '
SDO flll U
u Fo'
sin ad u
u Fo'
cso ad u
ta F '
SMITHSONIAN TABLES
134
Natural Hyperbolic Functions.
I ..|(.S
.|K)
' .-lO.'i
-I'X'
-toy
i .51x1
, HtHlu
lll(l Ult 11
.1"
co uli ii
i,v it i
,tHyr,.i
,.|.'|'J,1
. .L7tM
..t.Ul-1
aim gil u
Iniih u
.Htjfxit)
,'XiiHi
Kill (](l II
'> To'
IM.S
HAS
iH.y
18. 1
Qfltll U
I. nfis
.IHU
. 1I(X)
i'S5
. I ISO
. 1 1. |X
M-15
ii.M
- ' MS
.113:1
. n.n
UK)
i . 1 1 if')
.ni.i
,111.!
I. 1105
. I HI.!
. IHK)
- UHJ5
l-H)),i
. KXJI
! io8(i
. toH-t
i . loHj
. wytj
7S
. IOX-I
.1001
1 . 1050
. 1050
i.io,|H
cao uil u
BMITMBONIAH TAHLKB
135
Natural Hyperbolic Functlona.
It
tlnli u
-Fo'
cosh u
M Fu'
In nh u
r;
CO 111 tl
- F,,'
1.500
2. 12028
2.15
2.35341
313
0.00515
IH.I
i . iu,|H
2,2
.501
I3l6,1
235
-35454
313
003.1.1
1 8,0
, ni|(i
2,2
.503
13399
230
. 3 ")0t '7
313
9O.H5 1
1 8,0
. IO.).|
A3
.503
13035
336
.35881
21.)
.005(10
iH.o
. luii
2,2
.504
.13871
330
3<*>95
. JI -I
,yo587
17.0
. 10.10
3,2
1.505
2.14107
33<i
3 . 36300
Jl.(
IMXXKtt
17,0
i . 11137
i >
,506
- 1434,1
237
.36533
21. 1
,1)0(123
I/'.O
''MS
A3
.507
14580
337
, 36737
315
.OOO.ll
17.8
.1' M.I
A3
.508
.1481?
337
36053
215
.i)O(i, i ;8
17.8
. 1030
2,2
soy
.15054
3,17
.37167
315
.00076
!>',
. U'28
2 2
1.510
2.15391
3,17
3..17383
215
0.1XX)|
"7.7
1 . 102(1
2 2
.511
.15539
238
37597
Jilft
,<X>7I2
"7.7
, IO'.|
2,2
.512
.WOO'
338
.37813
216
.tjo7- p 'J
17.7
. 102.1
3,1
.513
, I(l00j|
238
. 38020
216
007. |7
17.''
. 1020
At
-514
. l()242
2,18
38345
aid
907115
17,0
.IOlH
Al
1.515
2.l648l
238
2.38461
216
< 1.1x178-1
I7/'
1. HH.'i
a, i
.16719
2.19
.38678
217
,i)08<xi
1 7,0
' llll.l
A!
Si?
.16058
339
38H95
217
.1/1817
17.'i
. lot i
i r
*>t *
.518
.17197
239
.,19113
217
.00835
W,'$
. KKX)
2 I
.519
.17436
239
.39339
217
.O08.S3
17.5
. IIMI/f
2,1
1.520
2.17676
2.|0
2.39547
218
0.1x1870
17.4
I.HHI/i
'1 1
**l *
.531
.17915
240
-.19765
218
j887
17,4
, II X !,(
A I
532
.18155
240
39983
2lN
OO<)O5
17.1
.1IN1I
A I
.533
240
,,|02OI
aiK
.Mf).!3
I7..1
.tn^jM
A I
.534
. I803<1
2,|0
.40419
310
.'-O'J.IO
'7,3
.IK^/I
Al
1.525
2,18876
2,|I
2., 10038
211)
<t. 00057
17.3
i .0004
2,1
536
.19117
24!
.40857
2H)
.iXn/7,1
17.3
.O^M
2,1
.537
19358
241
.41070
210
. "> *f) I
I '} !
,tnfm
A I
.528
19599
24 r
,-lui/i
ajn
,0'oo8
17.-!
.!),*
Al
.529
. 108,10
243
4i!)iO
3,10
.OIOJ5
'7.1
.ii-jtoi
1.530
2 , 20082
242
2.41736"
220
o. 01642
17.1
l.t>jM|
2 I
.531
.20324
24 j
.41950
2.!O
.Otodo
17,1
,(hjM,[
3,1
.532
.2056^1
2,|2
.42176
221
.01077
17,1
.iHjfiit
2,1
.533
.20808
2,|2
43,197
lUI
.OH")!
.tnj/'M
2,1
53-1
.21051
243
42618
221
.01(11
'7,0
.(fj/'f-
2,0
1.535
2.21203
24,1
2.42830
22 1
0,01 128
17.0
I.1NJ7.|
3,0
-S.lO
.21530
243
.. 130(10
%'JIJ!
.01 1. 15
.OiJ>2
AN
5,17
.21780
243
.43383
32J
,t)lt(H
lft.0
,IN)70
.538
. 2202.1
244
43PO.J
332
.01178
lf',0
.O-X-S
AO
.5.19
.22X17
344
43736
22J
01105
10,8
.<*/')
AO
1.540
2.22510
244
2-43949
333
O.OUU
10.8
i.(*X1
AO
541
.33755
244
.44171
323
.OU'J'J
l6.8
,(H/t|
AO
542
.32000
244
44,194
2>!,1
,01240
If',7
,tWi
AO
54.1
.23a.-j3
345
.44617
33.1
0120,1
10.7
,(,57
2,0
.544
.23488
245
.44841
323
.91270
AO
1.545
2.237,13
245
3,U<Vi(
22,1
o.oi^X.
if'. 7
l.(fl
20
.540
.23978
245.
.45388
iUJ
.OI.1U*
win
3.0
S47
.24224
2,|(i
..155IJ
32.)
.01330
l(..(i
548
,2.|.|00.
246
457.V'
^\
.91,1-15
K',0
,))). (7
20
549
.24715
246
4501
225
|0,,1
.WI5
A'O
1.550
2.2496-r
2.|6
2.4618/3
335
0.01370
10,5
I.tf*
3,0
u
Ian fltl u
JL5L
100 0(1 II
.w
sin oil u
.w
010 Oil u
' B 'F~
TANLH
Natural Hyperbolic Functions.
i.JtSo
551
. 55 ->
,553
554
I 55 H
-55(1
.557
1,500
S't i
50.!
.50.)
.#'5
.507
-573
. 57-1
57''
577
..178
. 570
1.580
.581
. .180
.5X7
.588
..'191
503
i.fioo
llllll U
i.ii.uX'n
.. 15.107
.-15948
.^(ifHX)
--IIHM8
,'8l8l
.J9I7 1 .]
,Jt).\M
J..UI-1')
Ml'',!
.3307J
-317.1''
., if fi 15
3.37357
Un Qd ii
.150
a 5. i
J5J
i.n-l
354
a.S 7
w f,'
Q0ll II
47540
-177' '7
48I.7S
.40817
5(1.175
.50505
a. 50735
,51(15(1
..'I*' I HJ
5J.15"
..W5HJ
53.SU
.. 1.17.1 S
. .15%!
.5/035
57J7J
5750!;
IQO <l u
JJO
a.i.1
3.1-1
a.15
a.15
a.17
a.17
338
W Pi,'
tnnli u
0.01379
OMi'i
.01.144
.91510
.91574
-0'50I
OH '55
yK'71
0.91703
0.9I78.J
-91813
.OH/HI
0.92167
iln oil 11
Ki.5
Ifi.l
KM
in, i
15,9
IS!H
"5,8
15,7
15,7
15,7
IS/'
15,'i
15.5
15,5
15,5
15.-1
15.4
15.4
15,4
15,3
15.3
15,3
1 5! I
OOlll 11
1-0934
.093-!
,0030
.CXJIO
1.091.1
.0907
1.0905
.0903
,(X,)01
.0809
1-0805
,o8ix)
.0888
1.0880"
.oSK|
!o88i
.1)879
1.0877
.0873
.0871
.0870
1.0868
.oWii
1.0850
.085?
.0855
,0852
1.0850
010 ad u
14 Pi)'
r,/
Natural Hyperbolic Functions,
u
si ah u
<oF,'
cosh u
Fo'
tanh u
*l Fo'
colfi u
10 FO'
1. 600
2-37557
258
2.57746
238
0.92167
i5,r
1.0850
1,8
.601
37^15
258
.57984
238
.92182
i5,o
.0848
1,8
.602
38073
258
.58222
238
92197
i5,o
.0846
1,8
.603
38331
258
.58460
238
.92212
15,0
-oats
1,8
.604
38590
259
.58639
239
.02227
14,9
.0843
1,8
1.605
2.38840
259
2.58037
239
0.92242
M.9
1.0841
1,8
.606
.39108
259
.59176
239
.92257
M,9
.0839
1,7
.607
39367
259
.59416
239
.92272
14,9
.0838
i,7
.608
.39626
260
.59655
240
.92286
14,8
.0836
i,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
i,7
.611
.40406
260
60375
240
.92331
14,8
.0831
i,7
,612
.40667
261
.60616
241
.92346
M,7
.0829
i,7
.613
.40928
261
.60857
241-
.92360
1-1,7
.0827
1,7
.614
.41189
261
.61098
241
.92375
14,7
.0825
1,7
1.615
2.4:450
261
2.61339
241
0.92390
14,6
1.0824
1,7
.616
.41711
262
.61581
242
.92404
14,6
.0822
i,7
.617
4T973
262
.61822
242
.92419
14,6
.0820
1,7
.618
.42235
262
.62064
242
.92433
14,6
.0819
1,7
.619
.42407
262
,62307
242
.92448
14,5
.0817
1,7
1.620
2.42760
263
2.62549
243
0.92462
t4,5
1.0815
i,7
.621
.43022
263
. 62702
243
.92477
H5
.0814
i,7
.622
.43285
263
63035
243
.92491
14,5
.OS [2
i,7
.623
..13548
263
.63279
244
.02506
14,4
.o8lO
i,7
,624
.43812
264
-63522
244
.92520
i<l,4
.0808
i,7
1.625
2-4407S
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
f)4255
245
.92563
14,3
.0803
"i7
.628
.44868
26.1
.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
1.0798
1,7
.631
. 45662
265
. 65236
246
.92620
14,2
.0797
1,7
.632
.45928
265
.65482
246
02635
14,2
-0705
1,7
.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
14,1
.0789
1,6
.637
.47258
267
-66715
247
.02705
14,1
.0787
1,6
.638
.47525
267
,66962
248
.92719
I.|,0
.075
1,6
-639
.47792
267
.67210
248
.92733
14,0
.0784
1,6
1.640
2..[8059
267
2.67457
248
0.02747
14,0
1.0782
1,6
,641
.48337
268
,67706
248
.92761
1 4,0
.0780
1,6
.642
.48595
268
.67054
249
-02775
13,9
0779
1,6
-643
,48863
268
.68203
249
.92789
12,9
.0777
1,6
.644
.49131
268
.68.-I52
249
.92803
13,9
.0776
1,6
1.645
2.494OO
269
2.68701
249
0,92817
13,0
1.0774
1,6
.6-16
.49669
269
.68951
250
.92831
-13,8
,0772
1,6
.647
.49938
269
.69200
250
.92844
13,8
.0771
1,6
.648
. 50207
269
.69451
250
.02858
13,8
.0769
1,6
.649
50477
270
.69701
250
.92872
13,7
.0768
i
1.650
2.50746
270
2.69951
251
0.92886
13,7
1.0766
, :,6
u'
Ian ad u
* FQ'
sac ad u
6* F(('
sin gel u
ia Fo'
oso ad u
"Fo'
SMITHSONIAN TABLES
138
Natural Hyperbolic Functions.
u
alnh u
,F,,'
ooali u
F -
tnnh u
Hi F '
CO 111 II
-Fo'
1.050
J.50740
axo
a.6tx.) S i
as I
o.U388(i
13,7
i.07(i(i
1,6
.('51
.51017
ifXo
XO30J
351
- 9-'8^J
1:3,7
.0764
1,6
. 1 >5- !
5 i -87
270
. 70.154
~5l
9"9 3 ,1
T3.7
.07(13
1,6
.653
51557
~]\
.70705
3S~
9-9-7
13.6
.07(11
1,6
.65-1
.51838
.'71
7"957
' 53
. 929. |o
1,1,6
.0760
1,6
1.655
3.530J)<)
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SMITIIOONIAN TAIIUC*
139
Natural Hyperbolic Functions.
f
u
slnh u
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10 Fo'
colli u
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2.64563
283
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0.93603
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284
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285
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2.67405
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286
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SMITHSONIAN
140
Natural Hyperbolic Functions.
11
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SMITMBOHIAH TAHi.ro
141
natural
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2.94217
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3-10747
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16995
. 301
.04894
10,0
05.lH
1,1
' .83-1
.01126
317
.17206
301
.0190.1
9,0
.0537
1,1
' -.823
.014.43
3(8
. T7S07
301
.94014
9,0
.05.1''
1,1
.;;^<<
.01761
318
.17899
303
.94924
9,0
.0535
I.I
Y.8u5
3.02079
3"8
3.18201
302
0.94933
!),0
1 .053 1
1,1
-.826
.02397
310
. 18503
30J
.91943
0,0
0<i,1.1
1,1
.827
.02716
3 M.)
. 18805
303
UI953
9,8
.o.'i3J
1,1
.828
.03035
319
.19108
303
.'M'Al
0,
,0530
1,1
.82()
.0335-1
310
.19411
303
.0-1973
<J,8
.05.10
1,1
1.830
3.03674
320
3- '9715
304
0.(J498.1
9.K
1.0528
1,1
.831
. 0309-1
320
.20010
304
.9 IWJ
0,8
.05. 17
1,1
.8.13
.04314
320
.20323
304
,(J5<K)-!
0,7
.0526
1,1
.833
.04034
32 r
. 20627
305
950U
0.7
.0525
I,
.834
.04955
321
,1-0932
35
,9502J
9.7
.0524
I,
1.835
3.05^76
321
3. 21 337
305
O.'W^f
0.7
I, O.M.I
1,
.836
.05507
322
.21543
306
.95041
9,7
.05,1,1
1,
.837
.05910
3M
.a l8.|9
306
.950.H1
<),7
.U.S.! I
1,
.838
.ofia.ji
122
,22155
306
.Oft***
9.6
.OS-I
1,1
.Say
.06503
322
.22461
307
.05070
9,(i
.0510
I.I
1.840
3.06886
323
3.33768
307
o.95ixSo
0,6"
I. O.iilH
1,1
.841
.07209
323
.23075
307
.05089
9,'i
.0510
1,1
.843
.07532
323
.23382
308
.05090
0,f'
-0.115
I.I
.843
.07856
324
.2361x1
308
95108
0,5
.0514
1,1
.an,
.08180
32.1
.23998
30K
95MH
9,5
.05 M
1,1
1.845
3,08504
3*1
3/24306
309
0,951-7
0,5
1,0,^12
1,1
.846
.08828
325
.24615
3W
.95(37
0,5
OJiU
1,0
.847
.0915.1
325
.24924
309
.05146
0.5
.0510
1.0
.848
,00478
325
.25233
309
.9Sl5(i
9,5
.0500
1.0
.849
.09803
320
35543
310
.ysifis
!>.!
.oso
1,0
1,850
3.10129
326
3-25853
310
0.95175
9,4
1,0507
1,0
u
Ian oil u
14 p Q '
mo ail u
nFo'
iln ad u
w F u '
010 gtl u
F,/
SMITHSONIAN TAB us
142
Natural Hyperbolic Functions.
1.850
iw
I.K55
!H57
!K5<>
l ,H<Ki
!<u
.8(13
,8fXl
.807
.808
1.870
.871
.87..'
H/3
.87(1
.877
.878
H79
l .880
.881
.88.!
.883
,H8|
1.885
.88fi
.887
.888
H8y
i.Myo
.yi
1.805
.Ht/i
r.yw
u
9 lull u
. I 1 ION
. 1 1.1.15
3.1(7(1.!
. I.JOIJO
.U.|'i8
.i..'74<
1.173-!
15700
-.'07 1 y
..1 1053
A17S3
J-I77J
fl.afiftlfl
Ion tjit u
330
3JO
.1.1"
.1.11
3,13
3,1.1
.133
3.1.)
3.M
ililS
.115,
33''
337
3.17
MO
M
.1-1 1
"fV
ooah N
.1.2585.1
J77M)
.,(1804
..HOJ7
|..1^X>
3755.1
.,!')! 7"
3..10I-J3
900 till II
.110
311
3I.J
J',1
313
31.1
314
315
.115
315
31(1
31 ft
.117
317
318
3lK
3l8
3'!)
3M)
.1"
3*5
335
337
Innli u
ysiy.1
O.W77
95350
0.05-105
.'J5.M.I
0.05-l-W
.W5-l7(i
O.IW-I'J.1
95511
955-JO
0.05537
.y.wif>
.'J5555
-955'U
95572
tin ad u
w Fg
!J,3
U.3
9,1
9,0
9,o
9,o
0,0
H.H
8,K
8,8
8,H
8,8
;?
B,7
8,7
8/i
8.5
8^0
8,6
aotli 11
1.0507
.osort
.0505
.050.1-
.050:1
i .0502
.050 1
.O.|(>)
-o.|(J5
.04M
l .0492
.0488
1.0.187
.o.|85
.0483
0.179
1.0,177
0475
0-173
i. 0172
0471
.0470
1.04(17
.0466
0-|fy)
.(^6.1
,0|fi3
.0460
1.0458
QIC flll U
T,O
1,0
1,0
1,0
1,0
1,0
1,0
1,0
M)
1,0
1,0
1,0
1,11
1,0
1,0
1,0
1,0
,1,0
1,0
1,0
1,0
JtO
o,'p
0,9
o.y
0,9
0,9
o,y
0,0
w fa'
SMITHSONIAN TAULIC*
143
Natural Hyperbolic Functions,
tl
si nli ti
11 Fu'
cosli ii
, , C '
u r,,
in nli u
Fa'
COlll U
Fo'
i. Ooo
3.26816
342
3-1 '77.1
327
0.95624
H/i
1.0458
">o
.go i
.27158
343
.4JKJO
327
.950,1*
H,5
('457
0,9
-902
27500
342
.42.|27
3&
-95641
8,5
0456
0,9
00.1
.a 78-1 3
343
.4-'75S
328
-95049
8,5
-0455
(>,<J
.904
.28186
343
.43083
328
-95658
8,5
.0454
0,9
I. DOS
3,28529
343
3.434"
329
0.05666
H.5
I. 04 S3
0,9
.906
.28873
344
.4374')
329
95675
8,5
.0452
0,9
.<jo;
.2921;
344
.440<)y
329
-!>568,T
8,4
0451
0,9
.908
.20561
344
44393
3.10
.<>56yJ
8,4
0450
0,9
.yog
. 40906
345
4472K
330
-95700
8,4
0449
0,9
1.910
3.30^50
345
3.45058
330
0.95709
8,4
1.0448
0,9
.911
. 3059()
345
.4538y
331
US7I7
8,4
.0447
0,9
.912
.30941
346
.45720
33 1
-95725
8,4
-0447
0,9
.013
.31287
346
4<i05 1
33'
95734
8,4
.0446
0,9
.914
.31633
346
.46382
332
-95742
8,3
-0445
0,9
1,915
3.31980
347
3.46>I4
332
0.95750
8,3
1.0444
o,9
.916
.323-2?
347
.47046
332
-95759
8,3
.0443
o,9
.917
.32(17,1
347
.47379
333
95767
8,3
.0442
o,9
.918
.33021
348
.477 '2
333
95775
8,3
.0441
0,9
.919
.33369
348
.48045
333
.95783
8,3
.0440
o,9
1,920
3.33718
348
3.48378
334
0.95702
8,2
i. a 139
0,<J
.921
.34066
349
.48712
334
,05800
8,2
.0438
0,9
.922
.34"=! tS
349
.49046
334
.05808
8,2
.0438
0,9
-923
.3'176'I
349
.49,^1
335
.95816
8,2
-0437
0,9
.924
.35114
350
,49716
335
.93825
8,2
.0436
0,9
1.925
3.35.<>4
350
3-50051
335
0.05833
H,j
1.0435
o,9
.926
.35814
35<i
.50387
.136
.95841
,!
0434
QM
.927
.36164
35"
.50723
336
.<J58.!0
8,1
."433
<w
.928
.36535
35'
51059
337
.95857
8,1
.0-133
0,0
,929
.36867
35"
.5139(1
337
.95865
8,f
.0.131
<VJ
1-930
3.37218
352
3.51733
337
0.95873
8,1
1.0430
<M>
-931
-37570
352
.52070
338
.05881
8,1
-0.130
0,0
932
.37922
352
.52408
3.i8
-95890
8.1
.04*9
o h o
933
.38275
353
,52746
33
.9581)8
8,0
.o,|28
0,0
934
.38628
353
.53085
330
.95906
8,0
.0427
0,0
1.935
3.389i
353
3.531-n
339
0.9S9I-1
1V>
1.0426
0,9
03f>
.39335
354
.53763
339
.05023
8,0
.0425
0,0
9.17
39"80
354
54102
,340
.05630
8,0
.0424
0,0
.938
.40043
354
.54-143
340
.95638
8,0
.0423
0,9
939
40397
355
.54783
340
95945
7,9
.0423
<VJ
1.940
3.40752
355
3-55123
341
0-95053
7,<>
1.0422
0,0
941
.4tro8
355
.55464
3-1 1
-05961
7,9
.0421
0,0
.(XI a
41-163
356
.55805
341
05961)
7,6
,0420
0,0
-043
.41811)
356
.56147
3-1 2
-95977
7,9
.0410
0.0
-944
.42176
356
.56-189
34 a
.95985
7,9
.0418
0,0
1-945
3.42.W2
357
3.56831
343
0,05993
7,9
1.0417
0,0
.9*16
.42889
357
.57174
,143
.06001
7.8
.041?
0,0
947
.43*17
358
.57517
3. 13
.<XGO
7,8
.0416
0,0
.9.18
.43604
35
.57860
3-14
.96016
7,8
.0415
0,0
.949
.43962
358
.58204
344
.96024
7,
,0414
0,0
1.950
3.44321
359
3.5S548
344
0.96032
7,8
1.0413
0,8
u
Inn ad ii
Fi>'
SQO ail u
w Fo'
eln gtl u
w Fo'
o>o att u
wFV
SMITHSONIAN TABLES
1/14
Natural Hyperbolic Functions.
II
111 [ill U
-,
coali n
" F "'. .
tnnlt u
Fb'
COtll U
FV
1. 95"
.951
.95,1
951
3- LI.!-' I
..l.'io.iH
,l'i
3'H)
-.'i^'M
344
3-15
3.15
3-15
, 9(1032
.1X1047
7,8
7,8
7,7
7,7
1.0413
.0412
.0412
.0411
0,8
. J >o()3
7,7
.0410
l.'J.'i.'i
''I; 1 .'*
.I'x*
3,()U.!74
3-|(i
0.1/107T
7*7
1.0409
0,8
' '' '. ,.
' I<)K til
\ ( j.
'(miriiy
uv
yf ioyS
7,7
.0408
Mii 1 ,'
..175(1,:
3(11
3< 1.!
.(.131.1
3-18
. 5/x>86
. yCk>tj4
.yfiioi
7>7
7,7
7,6
.0407
.0407
.0406
I.(jfX)
!(jfi..'
.<jf 13
,.IH().IJt
,(' ' 1
' .''-M.'i7
.(>,!/()()
-'J3",S5
:>!
o.</i i ay
.1X1134
7,6
7,6
7,6
T f.
1.0405
.0404
.0403
0,8
.9(14
.. 19.1/4
3<M
.()3,|u.|
iii!
ilX"H39
7,"
7,6
,0402
.0402
I <Xi'i
1 107 tfl
3(11
't.'M? 1 )!
350
O.llfi] -iv
n /",
n S
'iii
* /i'll.'l'l
*'' :>^ ' ^ <t/
/.a
I .0401
0,0
, .'
'! ! ,"
i
i '1 I'M
35<>
* '.X> 1 55
7,5
.0400
. v
o'M (M
!
Hi' 1 !
35 1J
iX n ( )^
7,5
.0399
,<X>'
li"".!'
,1* '!i
,(l,|O(l,|
35r
<)fi r 70
7,5
.0398
.<j(>g
..IMgli
,1< >;;
,()() )<)!)
351
y:ii77
7,5
.0397
1.07"
.1.5i5<ii
,1'rft
3,(j;i;io7
353
0.96(85
7,5
I .0397
o.S
.0/1
M'W/
3(^1
.(>Ii"Jin
35 J
. 96 1 yn
7,5
.0396
.97-!
5--O.1
ilfi*'
,frfl,!ll
3 5 a
^X' 1 1 yy
7,5
.0395
-07.1
..I-'' 1 . 1 !''
307
,()( 15(13
353
9fu(i7
7,4
0394
.974
.;i,in,!(i
,'l''7
,()(^i*i
353
.</ur.|
7,4
0393
l.')7,<;
3<!i.l.lu,l
,V'7
3.ri7j(iii
35.1
0.9T^3
7,4
1-0393
0,8
.<V<|
..'i.l/' 111
,l(i.M
, ( (/( 1,13
35-1
.<)(u^y
7,4
.0392
.')77
MI-'M
3()M
.'17077
35-1
.9(1237
7,4
,0391
.O/'M
ti-M'J 1 '
3'^
'18331,
35-1
.<Xu.i4
7,4
.0390
.07'J
, r, |!V. l i
.K")
.(iHti
355
.<X^5i
7,4
.0389
i.oKo
3..15.M-1
,l'"J
3.(H)".1I
35S
o.<X)259
7,3
1.0389
0,8
.ijMl
.'i!i ( ' fl .l
,1'")
''iJ.VJ'i
35* i
. ^i^/i
7,3
.0388
.t)H,!
.,'i.'i<J7.!
,17"
.'xj/'.'i-!
35' '
,<>(u73
7,3
.0387
( Ai
.Jid.M--!
37"
.7ti[()H
356
.(Xi^Ki
7,3
.0386
.<>K|
5''7I3
37"
.7i).K5
357
.<>b88
7,3
.0386
l.'jK.'i
.(..'i/'i'H.i
;i7>
3-7(tH,!i
357
o.yfiaos
7,3
1-0385
0,8
. >4( i
-itf-is-i
.17 1
.71 1/-'"
357
. 96303
7,3
-0384
. ( >^7
3j-,i
7i)i.i''
.96310
7,2
0383
.OHM
,j;H|ij7
37-!
./MM'Jl
35K
96317
7,2
.0382
OKo
.jiH.'if*.)
7J-J5.1
35<>
.963.24
7,2
.0382
1 .ij<X)
3, ;i)!if [.;
373
.1. /.it'll I
359
0.0f)33i
7,2
1.0381
o,S
.l)ijl
. '>') U 'i
373
-7-W
350
96339
7,2
.0380
.IJ'J.!
,,'iO'pHM
,17.1
, 73331 1
3('O
, 96346
7,2
.0379
.'JU1
(KH.Ifi
37-1
.73<''Vi
3fi<>
3fi<)
.96360
7,2
7,1
0379
0378
LOOK
3,(i<iH(li)
17-1
l.^lin
' 3'''
0.96367
7,i
1.0377
0,8
.<w
.6118]
37 'i
74/7-
.96374
7, 1
.0376
.<M7
.'il.'ifiU
375
751,1.1
3f>"
.96382
7,i
0375
,<)<)H
,(Hi)il
7 c t-|0 ( >
'\C)'
.96389
7,1
-0375
.'<<;
,(^;iH)
37<i
75H57
3tia
.96396
7J
0374
u.oon
;,.6,(Wi
flTfi
3.7'^"
363
0.96.103
7,i
1.0373
0,8
u
Inn oil ii
w Fi'
aeo gil u
w I't/
sin gd u
u FI/
cso ad 11
<oF '
SMITHSONIAN
145
Natural Hyperbolic Functions.
tt
slnli u
ufj
oasli u
lil FU'
tanli ti
ui Fu'
OOlll II
-*
2.000
3.62686
376
3.76220
363
0.0X1403
7,1
1.0373
0,8
.001
.63062
377
.7(1582
303
.'X'4IO
7,1
.037-1
.002
.('3430
377
.76946
3<|3
, 9641 7
7,o
.037.1
.003
.63816
377
77300
3 ( M
. 1X1424
7,o
.0371
.004
.64194
378
.77073
3<>4
9(1.131
7,o
-0370
2.005
3.64572
37H
3.78038
3<i5
0,96438
7.0
I.(M<>
0,8
.O()6
378
.78402
3'>5
.9/14.15
7.0
.03(1)
0,8
.00?
! 65328
370
.78768
365
.iX'452
7,o
. t .(( 18
o,7
.008
.65707
370
79M3
3'>6
.06450
7.o
' ',!' '7
.000
.(10087
379
.79499
36(1
,iX'4(rf'
0,9
,O3()d
2.OIO
3.66.166
iHo
3.7981^
l(>6
0.0647,1
o,9
I ,o,t6fi
o,7
.Oil
.66846
380
.80232
1(17
(1,0
.0305
.012
.67227
381
8o5*)9
3''7
.011487
(M)
.03(1.1
.013
.67608
381
, Hoof 16
368
.90403
(i.O
.0303
.014
.67989
381
.81.134
368
,96500
6,9
> 03(1,1
2.015
3.68370
382
3.81702
368
o.<X>5O7
6,0
1 .11362
0,7
.OK)
.68752
382
.82071
3(MJ
.9(1514
6,9
.0.101
.017
.69134
382
.82,140
3('K>
.<X>5Ji
6,8
.<UfiO
.018
.69517
383
.828110
370
.0(1528
6,8
.0,1' I"
.019
.69900
383
.83170
3?o
<X'<i35
6,H
.0350
2.020
3 . 70283
384
3.83540
370
0.96541
6.H
1.0.158
0,7
.021
. 70667
384
.83010
371
.1X1548
d,M
. ( ^1^8
,O22
.71051
384
.ft] 290
371
-'Xi,S55
(1,8
.0357
.023
.71436
385
,846(1;!
371
.(X'5''2
(i.K
.0,156
.024
.71821
35
.85033
37-'
-fXiii'xH
'',7
.'U55
2.025
3 . 72206
385
3.5405
37-J
o.'AW.
(i, x
1.035.1
o,7
.O2()
-72591
l8f)
, 85778
373
.<X'58.!
(',7
.0354
.027
.72977
386
.MI 50
373
.'X>58i>
0,7
,028
.73364
387
.86524
373
.'X'595
0,7
"3.1-1
.029
-73750
387
.86897
374
.(Xi(H)J
.03!i-'
2.030
3.74I3H
.187
3.87271
374
O.fXifKX)
6.7
,.(,,,;,
d,7
.031
.74525
388
.87645
375
ixt'iiji
<i,7
.O.VSO
.032
-74913
388
.88020
375
,(X>6-I2
(i.d
o,(5o
.033
75301
388
-88395
375
.<Xi<)20
(j,(i
-0340
034
.75090
380
.88771
37''
.Xtf'MS
f.,6
.0348
2.035
1.76079
389
3.89147
37'">
O.9'<('4r!
6,6
'0,117
o,7
.036
'.76468
3<X>
.805-33
37''
.'XtO.18
6,6
o!l47
.037
.76858
390
.89900
377
.1X^155
6,6
034(1
038
77^|8
3<)0
.90277
377
.<XV)iu
6,6
,11315
.030
.77638
301
90654
378
.(X 16(18
(',6
o.t45
2.040
3 . 78029
301
3.91032
378
<>.'X>675
<"i
i.o.l II
(>.7
.041
.784^0
391
.91410
378
. 9668 i
'Cl
0,143
,042
.78812
393
.01789
370
,(X>'i8M
6,5
o.li.l
043
.70204
392
.921(18
379
,9(/HJ4
''"i
.044
. 7059f>
303
02547
.9^701
(',5
.1)341
2.045
1.79o8o
393
3.0^7
380
o*.(Xi707
6,5
1.0340
o.7
,04(1
.80382
393
.93307
380
.1/171. -I
6,,'i
<Ml'
.0-17
.80776
304
,Ol68H
18 1
,1X172(1
'j.5
. < 1 1 i'i
.048
.81169
304
.940(10.
381
<Xi7^7
!oVi8
.049
.81564
304
-94450
3#3
!X'73.1
<M
.0338
2.050
3- 81958
395
3-04832
jto
o.</i740
6,4
i .0.137
0,7
u
Inn Bd u
.w
aao ail u
ui r ( ,'
In oil u
"""'
use gil u
...
SMITHBONIAN TAB no
Natural Hyperbolic Functions.
u
sinh u
la F u '
oosh u
la Frf
tanh u
IV
ooth u
<) F fl '
2.050
3.8KJ5S
395
3-94832
382
0.96740
6,4
1.033?
O,7
.051
.82353
395
.95214
382
.96746
6,4
.0336
.052
.82749
396
95597
383
.96752
6,4
.0336
.053
.83145
396
-95979
33
.96759
6,4
0335
.054
.83541
396
.96363
384
.96765
6,4
0334
2.055
3.83937
397
3-96747
384
0.96771
6,4
1.0334
o.7
.056
.84334
397
.97^31
34
.96778
6,3
.0333
.057
.84732
398
-97515
385
.96784
6,3
.0332
.058
.85129
398
.97900
385
.96790
6,3
.0332
.059
.85527
398
.98285
386
.96797
6,3
0331
2.060
3-85926
399
3.98671
386
0.96803
6,3
1.0330
0,7
.061
.86325
399
99057
386
.96809
6,3
.0330
.062
.86724
399
99444
387
.96816
6,3
.0329
.063
.87124
400
.09831
387
.96822
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
0,7
.066
.88325
401
.00994
388
.96841
6,2
.0326
.067
.88726
401
.01382
389
.96847
6,2
.0326
.068
.80128
402
.01771
389
.96853
6,2
.0325
.069
.89530
402
.02161
390
.96859
6,-2
.0324
2.070
3.89932
403
4-02550
390
0.96865
6,2
1 . 0324
o,7
.071
.90335
403
.02041
300
.96872
6,2
-0323
.072
.90738
403
.03331
39'
.96878
6,1
.0322
.073
.91141
404
. 03722
391
.96884
6,1
.0322
.074
.91545
404
.04113
392
.96890
6,1
.0321
2.075
3-9I950
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
.93t65
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
.06933
6,0
.0316
.082
.94791
407
.07259
395
.96939
6,0
-0316
083
95roS
408
.07654
395
.96945
6,0
.0315
.084
. 95606
408
, 08049
396
.96951
6,0
-0315
2.085
3-96014
408
4.08-145
396
0.96957
6,0
1.0314
0,6
.086
.96423
409
.08841
396
.96963
6,0
-0313
.087
.96832
409
.09338
397
.96969
6,0
.0313
.088
.97241
410
.09635
397
.96975
6,0
,0312
.089
.97651
410
.10032
398
.96980
5,9
.0311
2.090
3.98061
410
4 > 10430
308
0.96986
5,9
1.0311
0,6
.091
.08473
411
.10828
398
.96992
5,9
.0310
,092
.98883
411
.1122?
399
.96998
5,9
.0309
.093
.99294
412
.11626
399
.97004
5,9
.0309
.094
.90706
412
. 12026
400
.97010
5,9
.0308
2.095
4.00119
412
4.12426
400
0,97016
5,9
1.0308
0,6
.096
.00531
413
. 12826
401
.97022
5,9
.0307
.097
.00944
4U
. 13227
401
.97028
5,9
.0306
.098
.01358
414
. 13628
401
97034
S>8
.0306
.099
.01771
414
. I4O29
402
.97039
5,8
,0305
2,100
4.02186
414
4.14431
402
0.97045
5>8
1.0304
0,6
u
tan ad u
*>IV
sea ad u
wF '
sin ad u
<=> Fa'
osc gd u
"Fo'
SMITHSONIAN TABLES
147
Natural Hyperbolic Functions.
u
srnFi u
w Fo'
cash u
F '
tanh u
u Fo'
co Hi u
Fo'
2.100
4.02IS6
414
4- I443I
402
0.97045
5,8
1.0304
0,6
.IOI
.02600
415
14834
403
.97051
5,8
.0304
.102
.03015
415
15237
403
97057
5,8
0303
.103
.03431
416
. 15640
403
97063
5,8
0303
.104
03S47
416
.16043
404
. 97068
5,8
.0302
2.105
4 .04263
416
4.16447
404
0.97074
5,8
I. 0301
0,6
.106
,04680
417
. 16852
405
.97080
5,8
.0301
.107
.05097
417
17257
405
.97086
5,7
.0300
.108
.05514
418
.17662
406
.97091
5,7
.0300
.109
.05932
418
.18068
406
.97Q97
5,7
.0299
2. no
4.06350
418
4.18474
406
0.97103
5,7
1.0298
0,6
.in
.06769
419
.rSSSi
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
42O
.20103
408
.97126
5,7
,0296
2.115
4.08448
421
4.20511
408
0.97131
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
.10133
422
.22148
410
97154
5,6
.0293
2.120
4-10555
423
4.22558
4:1
0.97159
. 5,6
1.0292
0,6
.121
. 10978
423
.229(10
411
.97165
5,6
.0292
.122
.11401
423
23380
411
.97171
5,6
.0291
-123
. 1 1825
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
.13098
425
. 25029
413
97193
5,5
.0289
. 12?
-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
o,G
.I36
17369
429
.29182
417
.97248
5,4
.0283
-137
I779S
430
.29599
418
97253
5,4
.0282
.138
. 1822$
430
.30017
418
.97258
5,4
.0282
139
. 18658
430
30436
419
.97264
5,4
,0281
2. 140
4.19089
43 T
4-30855
419
0.97269
5,4
1.0281
0,6
.141
. 19520
431
-31274
420
97275
5,4
.0280
.142
. 19952
432
.31694
420
.97280
5,4
.0280
143
.20384
432
-32U4
420
.97285
5,4
.0279
,144
.20816
433
32534
421
.97291
5,3
.0278
2. MS
4-21249
433
4-32955
421
0.07296
5,3
i .0278
0,6
.146
.21682
433
33377
422
.97301
5,3
.0277
.147
.22115
434
33799
422
97307
5,3
.0277
.148
.22549
434
.34221
423
.97312
5,3
.0276
.149
.22984
435
.346-14
423
97317
5,3
.0276
2.150
4.23419
435
4-35067
423
0.97323
5,3
1.0275
Oj6
u
tan ad u
uF '
sea ad u
fc>F '
sin Q4 u
<o Fo'
oso od u
Fo"
SMITHSONIAN TABLES
148
NiiUinil Hyperbolic Functions,
11
aiiih u
uuali u
'" I ; u'
tn tilt u
< Fu'
aotli u
~ -Fo' "
.;. 150
I.J.VMO
1.15
.1-. 15<)6 ?
<U.1
O-P7.1-M
5,;i
1-0-75
O,6
. ifli
-M^S-l
1.15
15-101
-l-i-l
OX.l-K
5,!l
0-75
.15-'
..!,].!< )0
-1,1"
-.1501.H
l-'-l
.1)7,1,1.1
5..1
1 5.1
.J.[7Jft
I,!' 1
-,1'M.'10
l"5
<J7,1.1^
5..1
.0-7,1
I5.|
.J5IOJ
-1.17
;i''X<M
-l-i5
07.1-1-1
"--7,1
J.i 55
1 . J5500
-1,17
l.;l7i'J<)
.|j6
o. 07,l-|o
5.J
I.OJ7J
0,6
. 15''
..I'M i,l7
1.1^
-.IX' 1 15
.|JO
07,15.1
5,-i
.OJXJ
0,6
.157
.,!<M/. r ;
l.lH
.,lSo.|j
.).!(
07.150
5>-
.(W7i
",5
. l sM
. .:( x 1 1 ,1
l.lN
. ,itt |* vS
1-7
0/M' '5
5..J
.0-71
0,5
. 1 50
.JX.15-'
-U!)
.,1,S,^X'
1-7
U7.170
3.-'
.UJ70
o,5
2. H'io
-I.-7X01
I.1<J
1..1*>.U.1
.|.;S
0.07.175
5.a
1.0.70
0.5
,101
.JJ.1()
-1-10
'^X5i
.|j
.O7.tfj"
5.-'
,OJ(K)
. I'M
.JO I 1 1
LI i
!!|(Kx'i
'<\ii
07,100
5!!'
lljjjjrt
.I'M
.J055I
LI I
..|HMH
-1.10
OX.llX)
5,1
,02i\7
.:. ifts
.I.JOW1
Mi
,|..|l.|6H
1,10
O.OX.K"
5,i
i ,oj()7
o.S
. l<>o
,1 1 M,M
LI- 5
,.|lo<)tS
dl"
-O7.|o6
5.1
,OJ()0
"17
. ,v )iSx< i
,|.|.!
,.l.!,l.|H
I,U
OX-l'l
S.i
,0.!('rf)
. i US
.,11.110
l-l.'l
,.|.!7' )()
l.li
OX.| 16
5.1
,oj()5
.[(H,
.,!!>'*>.!
L1.1
"I,UOI
I.1J
.07-IJi
5,1
.oj(i5
J.I 711
-I-.MJOS
111
I "l.lft-M
'I.U
o.<)7.|.:6
5,1
I ,OJ6;|
o,S
.'/I
,,(,rl),|0
111
..|.|O,^6
l.t.l
07. |,1i
5,1
.().!( ).[
.17.1
-,U |M M
LLI
,.|,|.|MtS
111
>07.|,i'i
5,1
.O.!(>,1
-iX.l
..1.15.1N
Llii
..[.|0.!J
l.l-l
07.1-11
5.1
.o^(i;i
.17.1
,'UON.l
LI5
.I5;iss
1.1-1
.!)7.|-|6
5,0
,o:;(u
j.171
.|,,1.|.[,!0
-Lift
.l.-157'X)
l.l-l
0,07.15:!
5.o
1 .OJfi2
o,5
.170
.,1-1^7,1
.11''
.,|(i.!.J.(
1.15
.07.157
5,o
,().!() I
.177
,lfl,U!i
MX
..)(>( ISO
1.15
, OX. l<>-'
5.0
.OJ()0
.17-S
.,157'iM
LIX
.,(7(xjs
l.l'l
5,o
.oj(k)
. 170
..10JI5
,|.|H
.. 1 75,1 1
1.16
.07-1 7 ^
5.o
OJ50
j.iHo
|..10('A1
,|.|H
I- 1X067
1,17
0.07.177
S,o
1 .OJflJ
<>,5
.iKi
. 37 1 1 1
.|,lH
..|K|o,|
i;ix
,07.|iSj
5.o
,(Wi8
. ltf.1
.;175<H>
LIO
,,|fW,|.:
I.1H
07-|iS7
5.0
,o..'5H
. iK.l
, ;{H( H HJ
LI'J
..10.70
.1.1"
.07-101
5,o
-OJ57
. IK |
J'S.|50
i:;o
,.|07iH
l.1
.07-l'X'
1,0
.0.157
J.I S
.I..I-HOOO
150
.1,50156
1.10
0.07501
LO
I.OJ56
o,5
. I.S6
.10.1SO
IS i
.50505
1.10
,o75ofi
1,0
itujjfi
. 187
.,loNlO
151
..'iio.'i, 1 ;
.MO
.075M
.1.0
.(W55
.|HM
,.|O,!<H
151
ii'-ixs
LI"
.075 1''
1.0
('.!5S
. iKo
.. 1071.1
ISJ
.5I!H(
1-11
07.WI
1,0
OJS-I
,MOO
.|.,| lifts
.(5,-j
|.S-i,6
-LI'
0.075-!f'
1,0
I .03,1.1
o,5
. 101
, ,j 1(117
.15,1
S"XoH
LI"
.075.1 1
.1,0
Oii.'i.l
. 10.!
.,(.:( 170
15.1
5.1 -MO
,|,|.!
.075.1''
,1,0
-OJ^.I
. 10,1
.,) J.<i.!.l
1.1.1
-S.l'iiS,!
1-1.1
075.M
1,0
.OJ.I"
- 10.1
..I^MXH
IM
siu'S
LI.1
075-15
-I.H
.0233
H. 105
l-l.ll.V!
155
l-S-tsftH
1.1.1
0,07550
I.K
MUSI
0,5
,KJ<)
,.|,lAH/'
.155
.5501.1
LI'I
.07555
-l,
.(US'
.107
..|.|,M.!
155
55.15''
til
.07 5' >o
,|,H
.0^50
I iXoK
I5'|
550OO
LI5
OX5< '5
I.K
,0,!50
.100
.-l.'i.J.'i.l
I5'i
Sft.l 1 5
MS
07570
,|,K
,0~'.|!J
2 . 200
,|..|57t(
157
'1.56X0 1
MC.
0.07S7-I
4,
1. 03.10
o,5
II
tun ail u
wFi,'
BOO Oil 11
Fu'
tin ail u
<u f,'
oso gil u
-hf
SMITHHOHIAN TABUII
149
Natural Hyperbolic Functions.
u
si nh u
Pu'
oosli u
w fV
tnnli u
" Fu'
OOlll II
F '
2.200
4.457n
457
4.56791
446
0,97574
"l,8
1.0.140
0,5
.2OI
.46168
457
.57237
446
97570
4,8
.().!. |8
.202
.46625
. 5 7' "83
447
07584
4,8
.0.148
.203
.47083
458
.58130
447
.97589
4.8
.024?
.204
47541
459
5577
44H
-97593
4,8
.0,147
2.205
4,48000
459
4-59025
|.|
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4,7
l.o.!46
0.5
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, 48459
459
.59473
448
.97003
4.7
.024(1
.207
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4<io
.59922
449
.f)7(X)8
4,7
.0,145
.208
49379
460
.60371
440
.97012
4,7
-0245
,2oy
.49840
461
.60821
450
.97617
4,7
.0.144
2,210
4 - 5030 1
461
4.61271
450
0.07622
4.7
r. 0:144
0,5
.211
.50762
462
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451
. 07620
4.7
-0243
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462
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45'
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4.7
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463
626'" |
452
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1,7
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.52149
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45-!
.97040
4,7
.0242
2,215
4-52613
464
4.63528
453
0.07645
4,7
I.o-Mi
o.S
.216
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464
.<)398l
453
.07650
4.0
, 0,141
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53541
464
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454
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4,6
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.54005
.64888
454
.07659
4,6
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.219
54471
4(15
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454
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4,"
.0239
2.220
4.54936
466
4.65797
455
tt.tfftM
4,6
r .0239
0,5
,221
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466
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455
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4,6
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.222
46?
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45''
.07678
4.''
. ( 1.138
.223
.56336
46"?
.67164
45''
.07682
4,6
OJ37
.224
.56803
468
.67620
457
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0.137
2,225
4.57271
468
4.68078
457
0.0760.1
4,6
l.OJ.Tfi
o,S
,22f)
57739
469
.68535
158
. iJ7(i/)
4,6
,0,13(1
.227
.58208
.68993
458
.07700
4,,1
0,135
.228
.58677
409
.69451
459
-07705
4,, 1 !
o..'3<i
.229
-59147
470
.69910
459
97709
4,5
OJ.l'i
2.230
4.596I7
470
4'7'>370
460
0.07714
4,5
1 ,0,134
0,5
.231
.60087
47 1
. 70830
4'iO
,07718
4,5
0233
.232
.60559
471
,71290
461
077-S3
4,5
. 0,133
.233
.61030
472
.71751
461
97727
4,5
.0,133
.234
.615112
47-3
462
97733
4,5
.UJ.y
2.235
4, 61074
473
4.72674
462
0-07730
-t.5
I.OJ3J
o,5
. 236
.62447
473
.73130
46*!
.97741
.1.5
.0.1,11
.237
.62921
474
-73590
463
.97745
4.5
.0,131
,238
.63395
474
. 74062
46.1
97750
4,4
.OJ30
.239
,63869
475
745-'5
4(M
97754
4.4
.0230
2.240
4.64344
475
4.74989
464
0-97759
4,4
l.flJM)
o.S
.241
.64810
475
.75454
4 ''S
.97703
4,4
.OJ-HJ
.242
.65295
476
75919
465
. 077' >8
4.4
.MJ^H
.243
-0577'
476
7('35
4(Vi
-07772
4,4
.O-'JM
.244
.66247
477
,76851
466
.97776
4,4
.02.17
2.245
4.66724
477
4- 773 '7
467
0.07781
4,4
I .o,U7
o,5
. 246
,67203
478
.77784
467
-97785
l.-l
. < u jy
.247
.67680
478
.78252
.07790
,dj.;(i
.248
.68158
479
.78710
408
,0770,,l
4,4
,o^*j6
.249
.68637
479
.79188
469
97798
4,4
,o^s
2,250
4.69117
480
4.79657
469
0.9780.1
4,3
1 ,0,3,33
o,5
u
Inn nil u
wFo'
BOO Oil tl
FI,'
aln o*l u
w F u '
010 Oil U
.W
SMITHSONIAN
TgO
Natural Hyperbolic Fimctiong.
11
alnli u
Fi/
cosli u
tnnd u
"> Fo'
cotli u
.Fo'
2.250
4.69117
480
4.70657
460
0,97803
4,3
1 .0225
o,5
..-'51
.(*>507
-|8o
, Ho 126
470
.97807
4,3
.0224
.252
.70077
.'[Hi
,H[>ti<X>
470
.97811
.0224
253
.7<>558
.(81
.81066
.978 1 ()
4,3
.0223
.254
.71039
482
Hi537
47'
. 97820
4,3
.0223
o,5
2.255
4.71521
482
.l.H.!OoK
472
0.97824
4,3
1.0222
0,4
. 256
.72* KM
.|Hj
.8j.)8o
4?2
. 97829
4,3
.0222
57
.72486
483
.8^052
472
.97833
4,3
.0222
< 2^8
.721X19
|8 1
Hi 1 >( i
,i i
.0^21
.250
.73453
484
.3!)H
473
.97841
.|,.i
4,3
2.2(10
4-73037
,||
4- H 1372
474
0.978.16
-,3
1.0220
0,4
.2(1 1
.74.|2,!
485
,H.|H,|(i
474
. 97850
,3
.0220
.262
.741)07
485
.85321
475
.()78<v|
. ,.!
.0219
,2(M
7539- ;
486
857<X"i
475
,07858
i .2
,02 li)
.264
757H
.|H6
,80272
476'
97863
-,-'
.02IH
a. arts
4. 7<305
.|H7
4.867,18
47'"'
0.97867
^,2
1, 0218
0,4
. 2(i6
.70852
487
.8722.1
477
.97871
, ,2
,0218
.267
77339
488
.87/01
477
07875
i .2
,0217
, 268
.77827
.|H8
.KKiTO
.07870
. 2
,0217
. 269
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481)
.88(157
478
0788,1
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2.270
4.78801
48*)
4.8<.)i3(i
47')
0.97888
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1. 02 If)
0,4
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7''.!i)|
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470
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40O
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.978i/)
. ,2
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,Ho.!74
491
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480
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' .-!
,02f.\
.274
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.[91
-91055
481
97005
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a."'?, 1 !
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492
4,01530'
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0.97000
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I.OJI4
0,4
. 270
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492
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482
97'JI.I
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,82240
49-'
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.97917
',1
.O2I3
.278
.8.1733
403
,9J(>S.l
483
97921
,1
.0212
. 270
.8322(1
403
.93.1(15
M
97925
,1
.0212
2.280
[,8i7'0
404
4.0304H
484
0.97920
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1.0211
0,4
,281
.84214
494
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48 1
9793.1
,'
.0211
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4<>5
.94917
485
970.17
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,0211
. At
.85204
40t
.O^IO.!
iH^
.97942
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,0210
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, 85' xjo
4<Xi
-9.H887
486
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2.285
4,8fiii/i
4'Xi
4-'X)373
486'
0.97950
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1.0200
0,4
. 286
,86692
407
.<X^50
487
97954
,1
.0200
.287
.87189
407
97.146
487
07958
4,o
.0208
..:88
,87(187
498
.1)7834
488
.97962
.020H
uHy
.8818;;
I'jH
.1)8322
488
97<,X>6
4!"
,0208
a. auo
4.88f|
400
.(.(jMHio
480
0.97970
4,0
I .0207
0,4
.291
. 89 I 83
400
.992(19
489
.97974
4.0
,0207
. 20..'
.89' 182
5( X)
.99/89
400
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4,0
,02(>6
...'03
.()OlH2
500
5.00271)
4'X>
.97082
4,"
,0206
,<XX.)83
50 f
.007(>9
401
97086
4,o
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2.295
,|.f!ll8,|
501
5.di2(k
40 1
0.97090
4.0
1.0205
0,4
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.OKkSf)
502
'.01751
492
970-M
4,0
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.92187
SJ
. 02243
402
. 97<)oH
4,0
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503
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403
.(j8()03
4.0
.0204
,93103
503
.03229
403
,tj8(H)rt
3.y
.0203
2 . 'MX')
4-03oVXi
504
5,03723
494
o.oHtno
3.0
1,0203
0,4
U
inn ml u
Pi,'
ROD (111 LI
W F|)'
gin oil U
u |V
oao ad u
" W
SMITHAQNIAN TADUB
Natural Hyperbolic Functions.
u
si n.li
R/
cosh u
01 Fo'
tanh u
u> Fu'
oo Hi u
-F '
2.300
4-93^9(3
504
5.03X22
4D4
0.98010
3,9
1 . 0203
0>4
.301
.Q420O
504
.04216
494
.98014
3,9
.0203
.302
.9470S
505
.04710
495
.98018
3,9
.0202
.303
.95210
505
.05205
405
.98021
3,9
.0202
*3(>4
.95715
506
.05701
496
.98025
3,9
.02OI
2.305
4.96221
5Q<>
5-06197
496
0.98029
3,9
1.0201
0,4
.306
.56727
507
.06693
497
98033
3,9
.02OI
.307
97234
507
.07190
497
.98037
3,9
. 02OO
.308
.97742
508
.07688
498
.98041
3,9
.O200
309
.98250
508
.08186
498
.98045
3,9
.0199
2.310
4.98758
509
5.08684
409
0.98049
3,9
I.OI99
0,4
-3IT
.99267
509
.09183
499
98053
3,9
.OI<39
.312
99777
510
. 09683
500
.98056
3,8
.0198
3'3
5.00286
5"0
. 10183
500
.98060
3,8
.0198
.314
.00797
511
.10683
501
.98064
3,8
.0197
2.3IS
S-OIjoS
Sir
5-11184
501
0.98068
3,8
1.0197
0,4
.316
.01819
512
. i i685
502
.98072
3,8
.0197
.317
.02331
512
.12188
502
.98076
3,8
.0196
3fS
. 02844
513
. 12691
503
.98079
3,8
.0196
.3")
.03357
SI3
.13194
503
.98083
3,8
.0195
2.320
5.03870
514
5 13697
504
0.98087
3,8
1.0195
0,4
.321
.04384
514
. 14202
504
.98091
3,8
.0195
.322
.04898
515
.14706
505
.98005
3,
.0194
323
.054'3
' 515
.15211
505
.98008
3,8
.0194
.324
.05929
576
-I57I7
506
.98102
3,8
0193
2,325
5.06445
5>6
5-16223
506
0.98106
3,8
i. 0193
0,4
. 326
.06961
517
. 16730
507
.981 to
3,7
0193
327
.07478
517
. 17237
507
98113
3,7
.0192
-328
.07996
5 r8
- 17745
508
.98117
3,7
.0192
329
.08514
518
. 18253
509
.98121
3,7
.0192
2.330
5-09032
519
5.18762
509
0.98124
3,7
1.0191
0,4
331
.09551
519
. 19271
510
.98128
3,7
.019 1
-332
. 10071
520
. 19781
5io
.98132
3,7
.0190
333
. 10501
520
. 20291
5ii
.98136
3,7
.0190
334
.mil
521
.20802
SEI
98139
3,7
,0190
2.335
5.11632
521
5.21314
5*2
0.98143
3,7
1.0189
0,4
.336
.12154
522
.21825
572
.98M7
3,7
.0189
337
. i 2676
522
.22338
513
.98150
3,7
.oiHS
.338
I3I09
533
.22851
513
.98154
3,7
.0188
339
. 13722
523
,23364
514
-98158
3,7
.0188
2.340
5.14245
5^4
5.23878
SM
0*98161
3,6
1.0187
0,4
341
14770
524
24393
5rS
.98165
3,6
.0187
342
. 15294
525
.24908
5T5
.98169
3,6
.0187
-343
.15819
525
.25423
5i6
.98172
3,6
.0186
-344
- 16345
526
.25939
516
.98176
3,6
.0186
2-345
5-16871
526
5. 26.1 56
517
0.98179
3,6
1,0185
0,4
.346
.17398
527
-26973
5*7
98183
3,6
.0185
347
.17925
52?
.27491
518
.98187
3,6
.0185
.348
- 18453
528
.28009
SiS
.98100
3,6
.0184
-349
.18981
529
,28528
510
.98194
3,6
.0184
2.350
5.10510
529
5.29047
520
0.98197
3,6
1,0184
0,4
u
tan od u
*> Fa'
seootl u
Fo'
sin ail u
<o Fo'
esc gtt u
u F<j'
SMITHSONIAN TABLES
152
Natural Hyperbolic Functions.
II
gliili n
- f '
coali n
In nil LI
w F,'
nolli it
-F U '
a. 35"
5-10510
5-*o
5-'-!' )i>47
5~'o
O.()8h)7
3,6
1.0184
0,4
-351
..HHl.iO
;i.i'>
..!(J5"7
5.:o
,(j8.i(il
3,d
.0183
35-!
.,!I)5(XJ
53"
, 31 )i 187
5Ji
.i>S.;o4
'i,' 1
.01X1
353
,.;i KIU
53 1
. 3( rf hS
5. fi
,i)Sj{)8
3,d
,oij
. 3.'i4
. ~' t ( ),it 1
531
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5"'"
.y_'iJ
3,5
.oiHj
a. .155
5,,!,M(i.!
53 -i
5.31051
').!"'
O.i^JlS
3,5
i.nifc!
0,4
3;iO
1 'ill) 1
53"
3" '74
5 3
. ( >8 ' 1 1 1
3,3
.01*1
-357
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!i)L-'
3,5
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, ^H
-M/'.'iO
533
33-!-!O
5J4
J)*J.!d
3,5
.0181
. 350
..!.p)3
534
3374-1
5J-I
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3,5
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' VHI
f .|S7
534
S-34.:^)
5-5
(i.t)*-Ml
3.5
i.oiHn
0,4
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"5301
535
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5-! 5
,<>Sj3d
3,5
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. id,!
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535
-35310
5J'
.i>8j4(i
3.5
oi/o
'.(,.
,.rti.|,(.!
S3' 1
35*15
i> J (i
.<XS.!,I1
3.5
.0170
3" I
,.!h()d8
5.1*'
5-7
i<J*l ; 47
3.5
.0178
a. Vis
S * *"/^M
537
5-3<>8oo
SJfi
O.<)*.!50
3.5
1.0178
0,4
.30*1
IXI J 1 1
537
374-7
5.!*
.<j8.!54
3,5
.0178
- 3 f '7
. .iH;j/'0
538
37055
5'<)
.(j*J57
3,5
.0177
3 (l *
,..'i)i ;8
53*
3*4*1
5 JO
,0*Jdr
3,4
.0177
3''0
..!(>! 15(1
539
30" 14
53"
,yj04
3,4
"'77
,1.37"
5..KM.XI
;;,(()
5.30544
53"
0.0*.!(i7
,1.4
1.017(1
0,4
371
3"735
540
.4(1(174
531
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3,4
.017(1
37-!
.31. .'7' '
54'
,,|nlkt.s
531
<>8.!74
3,4
,0176
- 373
.31*17
511
.41137
53 '
,()H.!7tS
3,4
.0175
.3-Mii8
5-1 J
.,\\t'*XJ
53^
.yHjHr
3,4
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-'375
ti.3j.XK)
51-;
5. 4 ;!.'()[
533
0.1)8285
3.-I
1.0175
0,4
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331 1- !
543
' -U7.15
533
.(j*.:H*
3,4
."'74
0,4
377
33oM5
543
,.|3J(W
534
.()*.:<) i
3,4
.11174
0.4
- 37*
34. r '- ;
5-14
..(3803
535
. ' )8 j< J5
3,4
.0173
",3
. 370
35073
S.I-1
44337
535
.084)8
3-1
.0173
",3
,[.3*0
3.35(ilM
!i45
5-44*73
53d"
0.0*3"!
3,4
I."I73
0,3
. ,18 1
3 (l "'3
545
* -4S4OO
53d'
- 0831 15
3.4
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.'(* !
.;)d/nH
54'
-45045
537
.i)8,((l8
3.-I
,017.3
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37-!'i3
54''
,,,|d4*\!
537
.0831 1
3.3
.01 7-J
.37801
547
.470.10
53
.')*,H5
3,3
,0171
a. #5
5.38340
5-1*
5-I755H
53H
O.ij*il
3,3
1.0171
o,3
"ili-Sd
,38Kf)7
.,|(4(M)fl
530
.083.!.!
3,3
.0171
.3*7
3O44Ii
54')
4*' '35
530
083'.'5
3.3
.0170
.3*8
3<W1
540
40175
54"
. i>S3^'8
3.3
,0170
.389
40|i43
..iy?is
54 1
.08331
3,3
,0170
;!.300
5-41003
550
S.5o,!5(i
541
o.yH.MS
3,3
i.o Kjy
",3
.301
.41(14.1
55 1
51 '70*
54 '
.1)833^
3,3
.otdy
3<M
,,|jlt)ji
55'
.513,10
5-l-J
.08341
3.3
.01(19
-303
304
:;!S
55-3
isiS
343
543
'.1*345
0834^
3,3
3,3
ioKiti
2.305
30<>
.307
.41058
553
554
5S-1
555
!ii4"57
.,H4(t"3
544
544
543
0,<)*,151
.1)8354
.0*35^
3,3
3,3
3,3
3,3
i.oifiH
.01(17
.0167
.0167
o,3
.390
.,((Ktf>H
55S
5514*
5-K'
.1)83(14
3,2
.()!
2.400
5.406'.*
55ft
S-SSTxjS
5-17
".oH 3 (i7
3,3
i.oifi6
0,3
n
Inn nil u
auo ud il
WF "'
slu ail n
... F,,'
cso ail n
. :
SMITHUOHIAN TAULCH
153
Natural Hyperbolic Functiona.
11
slnli II
i* FD'
cosh it
(0 FU'
In nli u
w FU'
colli u
, Fo'
2.400
5.46023
ssf
5.55695
547
0.1^367
3.-
!, II|66
0,3
.401
.47179
55<
.5024-
547
.<>H.f7i
3.-
.OHrfl
.40-
-477.15
557
.56789
548
.98374
3,-
.(HOiJ
<|03
.4jyj
557
573.17
548
.98.177
3.--
OK>5
.40.
.48850
558
-57881
549
.yS,iH<
3.-
Old;;
2.40. c
5.49408
558
5-58435
5-19
.')S,i|
3,..'
I. ()]<>,
0,3
.406
49967
55!)
.5898.1
5 SO
9W
3,-!
.0104
.'1"7
.50520
5(x>
-59535
To I
<>8,i';o
,!.-'
.0104
.40!-
,51086
560
,(k)(X^6
55'
.'^3'J3
3.-!
016,1
409
,51646
56r
.60637
55-:
9-^3^'
3.-;
.010,1
2.410
5.52207
56-r
5.61 i8g
55-!
0.<j8.|oo
3.-.'
1.016.}
o.3
.411
.52769
5<>2
.(ii?4i
553
.'jH,|o.t
1,2
.Oil).!
.412
53331
tfw
.62294
553
.(>H4(t(i
3,-!
.(ll(t,!
.413
-5389,1
S<>3
.6_>8.|N
554
.<>^.UH)
3,-!
,ni6.!
.414
5'14'Sft
56.)
.(4tw
554
,>S4U
3...'
.otfu
2.415
5-55020
5('M
5.63957
555
o.<>84ij;
3.'
i.oKii
<',3
.416
.55584
565
,64512
55"
.<>S.|iH
3.1
.nidi
.417
.5(1149
565
,(i5o(i8
55<>
.<>H|jj
3.1
.(H(l
.418
.56715
5<>6
,656-1.1
557
.1)84.!.';
3,1
.OKx)
.'110
.57280
5<>6
-<)6l8l
557
. 984^8
3.1
,<H('MI
2.420
5.57847
56>
5-6f>739
558
0.98131
3."
1 .UI,iO
o,3
.421
.541 'I
567
.6?2i)y
558
-08(31
3.t
Ol.'iO
.422
.58981
SOU
.(i7H5(i
559
.<>N|,I7
3,1
.oi;i')
|23
5955"
568
.6KjiS
5<>o
-<j8|4(j
3,'
.oi.'iH
.424
.601 18
569
.68975
560
-<)8443
3.1
oi.';M
2 425
5,60688
570
5-6i)535
561
0.<^|.(fi
3,"
i.oi^H
o,3
4->6
.61257
570
7(HXi
561
.t^lSti
3.1
0157
4-7
.6iH,>8
571
.7(i5H
56.!
<)H|5.1
3.'
0157
4--8
. 6.331 jo
571
.71..' 20
S<ij
.<jS.|so
3,1
0157
420
.62070
572
.71783
5<M
*#<m
3,"
.OI.S7
2.4,30
5.63542
57-i
5.72346
564
o. 08462
3-1
i ,oi<i6
0,3
.'131
.64115
573
.7.!UH)
5("M
.'iN|ft5
3,o
.nriiCt
4.ia
.64688
573
7.M7.I
565
,(^|OM
3,0
.Ol.'ifi
-'1,13
,6526,?
57.1
-74(>39
565
-u8|/i
3.0
oi.'i.'i
"134
.65836
575
- 74<>5
5' -6
!>H|7.1
3,o
.Ol'i.'i
2-435
5.66411
575
s. 75171
566
.'jM|77
3.o
'.01,15
0,3
436
.66086
576
.75738
5(7
.<(H|8i)
3.o
-0154
-437
.6756,1
57f
.76305
568
.'>8|H. t
3.0
.lit, 14
438
.681,10
577
. X<873
568
,ijH.|Wi
3,0
.0154
430
.68716
577
-77.141
5<>9
.984.^
3.<>
oiji3
2.440
> 69294
578
5.780 io
5<**J
o.oM|(w
3,0
1.0153
, 0,3
.441
.69872
579
.78580
,'i7"
.98105
3,o
-0153
.442
-70451
579
Ttfl.W
.i7<t
.0*198
3,'>
.in.i.t
443
.71031
#n
797^1
571
.OH.sni
3.o
.01,').!
.444
.71611
580
.80292
57-'
.!>85<>4
3,0
,015.!
2.445
5.72191
581
S.RoJWi
.W
(1.98507
3,o
(.(KflJ
(>,.1
.446
.72772
581
.81436
573
.0-8;; HI
3,0
,0151
-H7
73354
$8J
.821HHJ
573
oM<>i.i
3,0
Ol.Sl
.448
73036
583
.258.1
57.1
.(jHSift
~,o
.OI5F
.440
7-1519
583
.B3IS7
575
(^519
a,tf
.orso
2.450
5.75103
584
5.83732
575
0.985^'
~',9
1,0150
0,3
11
tnn oil u
M pi,'
SOO l)ll 11
"IV
*ln oil u
Fi,'
ctood u
1 F,,'
SMITHSONIAN TAHLEB
154
Naturnl Hyperbolic KuncUons,
a. 4 50
.451
453
.454
a. 4 55
!.|S7
.458
.450
a..|rts
.4(16
..jfKJ
474
a 475
47<>
477
47K
470
.483
.484
403
40-1
2.405
.406
.409
a. BOO
slnli u
5.7510,1
, 7685(1
,7744^
.78(115
! 80380
.Hi5SO
5.8.UW4.
.851111
.H8oHs
.8K6HJ
5.92876
.(All i
.00743
.03183
.03705
.04408
6,05020
585
588
505
5',X>
507
507
(if) I
(K1S
finrt
607
(XHJ
(no
610
fin
Cm
613
613
w Pi/
.,|HiH
.05415
.06013
.06611
.(K/XX>
.II.H7
IflOfllt U
570
577
577
578
57!)
57!)
"Ai
5H5
Sfi
sw
504
505
ax
507
5l)
(ioo
(ifHl
fin i
(bi
605
In nli u
U857I
.'^574
<. '.^570
.08615
-oH(iiH
2,0
2rfJ
2,8
2,8
2,8
3,K
2,8
3.8
3,8
y!
a,7
a,7
a,7
a!7
2,7
a!?
2,7
2,7
3,7
2,7
w IV
oolh u
1.0150
.0150
Q14W
.0148
,0147
.0146
.0146
1.0146
.0145
.0145
.0145
.014,1
1. 0144
.0144
.014,1
.01.13
1.0143
,0142
,0142
.014 -a
.0143
1,0141
.0141
.0141
.01.10
.0140
1.0140
,0140
.0130
.0130
0130
1.0138
,0138
.0138
,0138
1.0137
.0137
.0136
.0136
.0136
1.0136
flio pd u
(>,3
0,3
0,3
0,3
0,3
0,3
0,3
0,3
0,3
o,3
BMITHOONIAN TAHUCS
'55
Natural Hyperbolic Functions.
II
el nil u
!> Fu'
coali u
<i FU
tnnli u
w F,/
Oil 111 11
" IV
2 . 500
6.050_>o
6i3
(i. I,VJ(J
(J05
0.(>Su>t
2 7
I .01,10
<>,3
.5l
.056,14
(H.(
.l.tfUl
(X)(
.(,\S[>(>,1
2.7
oi,(5
. 502
.of>j.|K
014
.14440
(X)0
,<)H(i(>7
.!,(!
01,15
5o;i
.of MM
015
.15047
(107
.oKfrt*)
J,0
<>I,15
50-1
.07.178
()IO
15654
6117
,>S(.7.!
~',<l
-'I35
2.505
6'. 08004
616
6.l6.!(L'
(i()8
o.<;8ii75
.!,(!
1. lll.il
0,3
..S<*'
.0871 1
(117
. KiS7()
(MM)
.<)8ii/7
,!,O
.01,14
5<>7
.OO.^S
017
.1747')
(MM)
.i>S(>K()
,.',( >
"i.M
. 5ott
.00046
(iiH
. (Hiirti)
(l[(>
.()S(iM.t
.!,fl
"Ml
5<>o
. 105(14
6iy
. iH6ytj
(HI
.i^iSs
.(,(
."i.U
2.510
(i. 1 118.1
(ny
6. nyio
(ill
o.))8uSH
.'.,(>
i. 013.1
,.)
-5H
, 11803
('<)
. [i^)21
(11.!
.(>}t']n
.!,(!
."1.1.1
51-'
.U-I.M
6ji
.jnsil
dl.:
.<)S(x)3
.!.(!
Ol.l,!
.513
.1.1044
0,11
.Jl l.(6
613
.((Kin/)
.!.(!
.01,1-!
Sl-l
.1,1605
(ujt
, jiy(k)
(il,|
,i^(H>S
J,(i
.01,1.!
2-5T5
6.14287
6-'j
6.2J.17-I
(114
0.08701
..',()
1 .OT.l.!
0,3
.51')
. 14910
(-23
.j.ijS8
615
.08/0.1
.!,()
.01.11
.517
. 1553.1
(>2,[
.3.1*11.1
(H()
.i^/ofi
2.O
01,11
5"8
.10157
(U|
.J.|JIO
did
. 0871 iH
-Mi
.01,11
Sm
. K>7HJ
(S
..-483')
(117
.<jH7M
,!.(!
01,11
2.520
6. 17407
fiJS
6.25453
617
0.1)871,1
.!,(>
1 .0130
0,3
.5^1
. 18033
(>J()
.J(M)7[
6iM
,oH/iO
.!.(
.01,10
522
. iHOW
6J7
..'(rf^g
(HO
.^'(/H)
AS
.01,1(1
52.1
. 10280'
(u?
..730M
(in)
.^7.M
A.'i
01,10
.52-1
.10014
(.;S
, --71)27
(MO
-JH/-M
AS
.l)t.!0
2.525
6.205-12
6-1;
6.js.|H
6.ri
o.(j.M/'.!d
AS
1 .Ol.'i)
<i,3
.526
.-'1171
(i.!()
,.\i)\(V)
().!!
.<jS>'.!iJ
A3
.oi.to
.5-'7
.JtNoo
630
..ji )/x)
6.;.:
.'^7.U
A.'i
.uu'N
.528
. 2-M.10
630
-30.|12
<>.!,!
.0873.1
A:i
.di.:
529
,2,10(11
<M'
3H>35
623
.'> l f/.l"
'i ;i
.iiuH
2-5.10
6". 2,VH)2
(>,1-'
('MiM
(1.14
0,087,11)
2,5
I.OI.IM
",3
5.11
. a.|.v.|
032
..l.!..'H.!
(i..|
.08741
>'i , ! i
.oi,,7
5.1 3
24057
<V13
..12^>7
6,!;i
.0^74-1
A. ! i
.01.17
5.1.1
!55<X>
'i,)4
3.1532
(>.!(!
..^746
'i. ! t
.di,7
534
.2fU2.|
'M4
.3.|158
(>.'.<>
.08740
A.'i
.01.7
2-5,15
<;.2rtH58
'MS
6'. 34785
fay
o-'^.^i
A.'i
1 .Ot/h
<',,!
536
"7.104
(i35
.354'2
fay
.o87M
AS
,(H,!tl
5,17
.aHuu
636
.360,10
(i.rH
,')H75"
AS
.OI,!'l
-538
.28760
6.17
..IdfViK
6.!.;
.',^759
AS
.oi-:6
539
.20.10,1
(>37
.372U7
<W
.'>876l
AS
.HI.!. 1 )
2.540
6.300,10
63!!
6,37027
6^0
n.ijH/(i,|
AS
1. 01. ,'5
",3
Mi
. 30678
<lw
.3855?
rt.H
.0871*6
AS
, o r ';;
"<.1
54-i
..11,117
630
..10I8H
631
.t&yt*)
.!,.!
Ol.!5
"-3
.543
31957
640
,3i)Sjo
6,1.!
.08771
3,,|
.ni.!(
<.3
544
.32597
640
.40452
633
.08773
2,4
,(H Jl
(),J
2.545
"'.33238
(ill
6,.|HiM5
<"'33
0.1^776
2.4
I.OI.M
(),J
546
33879
f.|2
.4'7'9
''34
.^77S
A I
.tllA(
547
-34521
<i|3
-12353
'MS
.087-81
A-t
.oi,;.)
.548
.35lfM
6.13
,.l3oKK
'MS
.'^783
.niiu
-54!)
.35807
6.|4
.43623
636'
.(jK;K(i
3 i
. r i
-OJJ.l
2-550
6.36451
AM
fi..|.|:>S9
6/t
o,.j87H8
A-l
I.ou'3
aa
u
Inn oil u
u Fo'
BOO fltl II
"Ft,'
alii oil u
"Po*
010 oil u
Fo'
SMITHDONIAN TAOLEB
Natural Hyperbolic Functions.
u
si nh u
i" Fu'
cosh 11
u, F lt '
tanh LI
u Fo'
colh u
> Fo'
2.550
.551
6.36451
.37096
644
645
6.^4350
.44896
636
637
0.98788
.98790
2,4
2,4
1.0123
.0122
0,2
.552
.37741
646
45533
638
98793
2,4
.0122
553
-38387
646
.46172
638
98795
2,4
.0122
554
39033
647
.46810
639
.98798
2,4
.0122
2.555
6.39680
647
6-47450
640
0.98800
2,4
I.OI2I
O,2
.556
.40328
648
.48090
640
.98802
2,4
.0121
.557
.40977
649
.48730
6 4 I
.9880=5
2,4
.O12I
. 558
.41626
649
49372
642
.98807
2,4
.OI2I
55S
.42275
650
.50014
642
.98810
2,4
.OI2O
2.560
6.42926
65t
6.50656
643
0.98812
2,4
I.OI2O
O,2
.561
43577
651
.51299
644
.98814
2,4
.OI2O
.562
.44228
652
.51943
644
.98817
2,4
.OI2O
. 5C'3
.44880
653
.52588
645
.98819
2,3
.OI2O
.564
45533
653
53233
646
.98821
2,3
.0119
2.565
6.46187
654
6.53879
646
0.98824
2,3
I.OITO,
O,2
.566
.46841
655
54525
647
.98826
2,3
.0119
.567
.47496
655
55173
647
.98828
2,3
.OII9
.568
.48152
656
.55820
648
.98831
2,3
.0118
.569
.48808
656
.56469
649
-08833
2,3
.0118
2.570
6.49464
657
6.57H8
649
0.98835
2,3
1.0118
O,2
571
.50122
658
.57768
6fjo
.08838
2,3
.0118
572
.50780
658
584r8
65i
.98840
2,3
.0117
573
.51430
(159
.59069
651
.98842
2,3
.0117
574
.52098
660
-59721
652
.98845
2,3
.0117
2.575
6.52758
660
6.60374
653
0.98847
2,3
1,0117
0,2
.5/6
.53419
6>i
.61027
653
.98849
2,3
.0116
577
.54080
662
.61680
654
.98851
2,3
.0116
578
.54742
662
62335
655
.98854
2.3
.0116
579
.55405
663
.62990
655
.98856
2,3
.0116
2.580
6.56068
664
6.63646
6s6
0.08858
2,3
I. 0115
0,2
.581
56732
664
.64302
657
.98860
2,3
.0115
.582
57397
665
.64959
657
.98863
2,3
,ori5
.583
. 58062
666
.65617
658
.98865
2,3
.ons
.584
.58728
666
.66275
6S9
.98867
2,3
.0115
2.585
6.59395
667
6.66934
659
0.98870
2,2
I.OTI4
O,2
-586
.60062
668
.67594
660
.98872
2,2
.OtI4
.587
.60730
668
.68254
66 1
.98874
2,2
.O1'I4
.588
61398
669
.68915
661
.08876
2,2
.0114
.589
.62068
670
.69577
662
.08878
2,2
.0113
2.590
6.62738
670
6.70240
663
0.98881
2,2
1.0II3
0,3
591
.63408
671
.70903
663
.98883
2,2
OII3
592
.64079
672
.71566
664
.08885
2,2
.01 rs
593
.64751
672
.72231
665
.98887
2,2
.0113
594
.65424
673
.,72896
665
.98800
2,2
.0112
2.595
6.6(1097
674
6,73562
666
0.98802
2,2
LOT 12
O,2
.596
.66771
674
.74228
667
.98804
2,2
.0112
597
.67446
675
74895
667
.08896
2,2
.0112
.598
.6S12T
676
.75563
668
.98898
2,2
.Ollt
599
.68797
(176
. 7623 i
669
.98501
2,2
.0111
2.600
6.69473
677
6.76901
669
0.98903
2,2
I.OIH
O,2
u
Ian cd u
* Fu'
sod odu
u Fo'
sin gd u
<" Fo'
csc ad u
wF a '
SMITHSONIAN TABLES
157
Natural Hyperbolic Functions,
u
sinli u
F(f
cash ti
i> Fo'
tanli u
"> Fg'
OOtll U
Ul Fu'
2.600
6.69473
677
6.76901
669
0,98903
2,2
I.OIII
0,2
.601
.70150
678
77570
670
.98905
2,2
.0111
.602
.70828
678
.78241
6 7 I
.08907
2,2
.OTIO
.603
.71507
679
.78912
672
.98009
2,2
.OIIO
.604
.72186
680
.79584
672
,98911
2,2
.0110
2.605
6.72866
680
6.80256
673
0.98914
2,2
I. 01 10
0,3
.606
73547
681
.80930
674
,98916
2,2
.oiro
.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
.S4983
678
.98929
2,1
.0108
.613
.78330
686
.85661
678
.98931
2,1
.0108
.614
.70016
686
,86340
670
98933
2,1
.0108
2.615
6-79702
687
6.87019
680
0.98935
2,r
i. 0108
0,3
.616
.80390
688
.87699
680
98937
2,1
.0107
.617
.81078
688
.88380
68r
.98939
2,r
.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
.QIIIO
684
.98948
2,1
.0106
.622
.84528
692
.91794
685
.($950
2,1
.0106
.623
.85220
692
.92479
685
.98952
2,1
.010(1
.624
.85913
693
.93164
686
.08954
2,1
.0106
2.625
6.86607
694
6.93851
687
0,98956
2,1
1.0106
0,3
.626
.87301
695
.94538
687
,98958
2,1
.0105
.627
.87096
695
-95225
688
.98960
2,1
.0105
.628
.88691
696
.95914
689
.98962
2,1
.0105
.629
,89388
097
.96603
680
.98964
2,1
.0105
2.630
6.00085
697
6.97292
690
0.98966
2,1
1.0104
0,2
-631
.90782
698
.97983
691
,08968
2,1
,0104
.633
.91481
699
.98674
691
.98970
2,O
.0104
633
,92180
699
.99366
692
.98972
2,0
.0104
.634
.92879
700
7.00058
693
.98974
2,O
.0104
2.635
6.935&0
701
7.00753
694
0.08977
2,0
1.0103
0,2
.636
. 94281
701
.01446
694
.98979
2,O
.0103
.637
.94983
702
.O2I40
695
.98981
2,0
.0103
.638
9S68S
703
.02835
696
.08983
2,O
.0103
.639
.96388
704
.03532
696
.98985
2,0
.0103
2.640
6.97092
704
7.O4228
697
0.98987
2,0
1,0102
0,2
.641
,97797
70S
, 04926
698
.98989
2,0-
.OI02
.642
.98502
7o6
.05624
690
.98991
2,0
.0102
.643
.99208
706
,06323
<J99
.98993
2,O
.OIO2
.644
.90915
707
. 07O22
700
.98995
2,0
,0102
2.645
7,00622
708
7.07723
701
0.08997
2,0
I.OIOI
0,2
.646
.01330
708
. 08423
701
.98999
2,O
.0101
.647
,03039
709
.09125
702
.99001
2,0
.010!
.648
.02748
710
,0f)828
703
.99003
2,0
,OIOI
.649
.03458
711
-IOS31
73
.99005
2,0
.oior
2.650
7.04169
711
7-II234
704
O.Q90Q7
2,O
I. 0100
0,2
u
Ian ad u
*Fo'
seogd u
*Fc/
singii u
w Fo'
cso ad u
, wFo'
SMITHSONIAN TABLES
Nntimtl Hyperbolic Functions.
.(15-!
.''5,1
<'.<>'l
i.liHo
.(.Hi
a. f5
alnli n
7-.lij.liJO
Inn flJ it
(U p,,'
XiX
718
7iH
7JJ
X-M
7-M
X-7
7!*
7.1.1
7,1.1
7,11
?M
7.V>
7>l I
M"
7-1 u
7-l.i
7-1-1
7-M
71.1
Ml.
7-17
M7
onali u
. 17(101
7- ~'<X >''.'!
geo yd u
Xii
71.:
XM
XL!
7'.|
7,'H
7.1"
7.1'
7.1-!
7,1.!
7.1-1
7.15
7.15
^'H
M
7.V)
7*1 1
tnnli u
.<)<)< iS.'l
In nil u
1,0
1,0
1,0
1,8
a fa'
colli u
I. 0100
.OKX)
.OKX)
.OKX)
,0100
oow
.I.HMJ7
.(KW/(
ixxjs
I .()0(J.|
,tXX>3
.(XXJ2
1,0093
,(K)()t
.001)1
1,0091
010 Qll II
p,,'
0,3
0,3
0,3
o,a
0M It HBO HI AN
159
Natural Hyperbolic Functions.
11
sinb u
ui F '
cosh u
IV
Unli ti
.oF,,'
ooth u
uF u '
2,700
7 . 40626
747
7.47347
74t
0.99101
i,S
1.0091
O,2
.701
.41374
748
.48088
74i
99103
r,8
.0091
.702
.42122
749
.48830
742
.59104
1,8
.ooyo
.703
. 42872
750
.49572
743
.99106
1,8
.O090
.704
.43622
750
.50315
744
.99108
1,8
.0090
2.705
7-44372
75i
7.51059
744
0.99110
1,8
1.0090
O,2
.706
45124
752
.51804
745
.00111
1,8
.0090
.707
.45S7f)
753
.52550
746
99U3
1,8
.009
.7o
. 46629
753
.53396
747
99' '5
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
O,2
.711
.48892
756
55539
749
.99120
1,8
.00^9
,712
.49648
756
.56288
750
.99122
i,7
.00&)
.713
50405
757
.57038
750
.99124
i,7
.0088
| -7M
.51162
758
.57789
751
99125
1,7
.0088
2.715
7,51920
759
7.58541
752
0.99127
1,7
1.0088
0,2
.71!)
.52679
759
-59293
753
-99129
T,7
.0088
.717
. 53439
760
.60046
753
99131
i,7
.0088
.718
.54199
761
.60800
754
.99132
i,7
.0088
.719
-5496o
762
.61555
755
99134
i,7
.0087
2.720
7-55722
762
7.62310
756
0.99136
r-7
1.0087
O,2
-721
.56485
763
.6306(1
756
.99138
T,7
.0087
.722
.57249
764
,63823
757
.99139
i,7
.0087
.723
- 58013
7^5
.64580
758
.99141
i,7
.DOS?
.724
.58778
765
.65339
759
.99143
i,7
.0086
2.725
7- 50543
766
7,66098
760
0.99144
i,7
I. 0086
O,2
,726
.60310
767
.66858
760
.99146
i,7
.0086
.727
.61077
768
,67619
761
.99148
1,7
.0086
.728
,61845
768
.68380
762
.99150
1,7
.0086
.729
.62614
769
.69142
7<J3
99I5I
1,7
.0086
2.730
7-63383
77Q
7 -(1990S
763
0.99153
1,7
I.OOSS
0,2
.733
.64154
771
.70669
764
-99155
t,7
.DOSS
.732
-64925
77i
-71434
765
99156
1.7
.DOSS
733
.65697
772
.72199
766
.99158
1,7
.0085
734
.66469
773
.72965
766
.99160
i,7
.0085
2.735
7.67242
774
7-73732
767
0.99161
i,7
I.OOSS
0,2
-736
.68017
774
74500
768
-99163
1,7
,0084
-737
.68791
775
.75268
769
.99165
i,7
.0084
.738
.69567
77f>
.76037
770
.99166
i,7
.0084
739
.70344
777
.76807
770
.99168
i,7
.O084
2.740
7.71121
778
7.77578
771
0.99170
1,7
I.008;|
0,2
741
.71899
778
.78349
772
.99171
i,7
.0084
.742
.72677
779
.79122
773
99173
r,6
.0083
-743
73457
780
.70895
773
99175
i,<5
.0083
744
.74237
781
.80668
774
.99176
1,6
.0083
2.745
7.75018
781
7.81443
775
0.99178
1,6
1.0083
O,2
.746
. 75800
782
.822.19
776
.99179
T,6
.0083
747
.76583
783
.82905
777
.99181
1,6
.0083
.748
.77366
784
.83772
777
.99183
1,6
,OO82
-749
.78150
785
.84549
778
.99:84
1,6
.0082
2.750
7.7S93S
7S5
7-85328
779
0.99186
1,6
I.OO82
O,2
u
tan Qd u
u FO'
sec ad u
F D '
sin gd u
ia fo
CSO 0(1 U
"F '
SMITHSONIAN TABLES
1 60
Ntiturnl Hyperbolic Inunctions.
(.775
77<>
777
77<J
.78.
.78.!
.78,1
.781
,787
.788
.701
702
70,1
-7<J.|
707
,7')8
799
a.Hoo
alnli u
.80507
.85 j.i.i
,88115
7. <) 17'JO
.<),' HI
ft,
.Lift Id
. I.1J.15
8.15
1 *i
.id'
7H1
tflngd it
7<X>
707
Hoi
Hi I.!
K< 15
Hod
KM;
Ko7
Ho8
Hio
Mil
811
Hid
8(8
HJO
w Ft'
OOHll U
.8l)io7
! 88, 1 50
'.8gj,i..'
.(JlKHi)
.o. r >;;.!i
, 1/1,1 10
H, 010(15
.10,111
-'0.17,1
H. 85273
IQQ gil u
7/0
785
70-1
705
709
800
u
80.1
8o(i
8117
8n
Hu
8r8
HiK
Iniili u
W-J-15
WJ2-17
0.^263
F,,'
,5
.5
,5
.5
.5
,5
i!5
00 III II
1 ,0(>vSj
-cx>8i
i.cxxSi
,tx)8i
i. 0080
.0080
I.CK)80
.0070
.0071)
.OOJfC)
.(XJ78
i .0078
.0078
.0078
.0078
1.0077
.cxi77
.(XJ77
.0077
-exi77
1.0077
.007(1
.007(1
.0076
1.0076
.0076
0075
-0075
i .0075
.0075
.0075
.0075
.007-1
1,0074
eso gJ u
O,i
0,2
0,2
0,2
0,2
0,3
0,2
0,2
0,2
0,2
0,1
0,1
wF u '
BMITHDOHIAN
161
Natural Hyperbolic Functions.
II
sinh u
"Fo'
oosli ti
ia Fa'
Innli u
<" Fo'
a olli u
id Fo'
2.800
8. 19192
825
8.25273
8 rr>
0.99263
r,5
r.0074
0,1
.801
.200 1
826
.26092
820
.99365
i,5
.0074
.802
.20844
827
. 26913
821
. 99266
r,5
.0074
,803
.21671
828
27734
822
. 99268
r,5
.0074
.804
.22499
829
.28556
822
. 0026y
1,5
.0074
2.805
8. 23328
829
8.29379
823
0.99270
i,5
1.0073
0,1
.806
.24158
830
. 30203
824
.99272
1,5
.0073
.807
.24989
831
.31027
825
09273
1,4
.0073
.808
. 25820
832
-31853
826
.99375
1.4
.0073
.809
.26653
833
. 32679
827
.99276
i,4
.0073
2.810
8. 27486
834
8.33506
827
o . 99278
1,4
1.0073
0,1
.811
. 28320
834
34334
828
.99279
1,4
.0073
.812
.29154
835
-35163
829
.99281
1,4
.0072
.813
.29990
836
35992
830
. 99283
1,4
.0072
.814
.30826
837
.36823
831
.09283
1,4
.0072
2.815
8.31664
838
8.37654
832
0.09285
1,4
1.0072
o,r
.816
.32502
838
.38486
833
. 99286
1,4
.0072
.817
3,1341
839
3S3I9
833
.99288
1,4
.0072
.818
.34180
840
40t53
834
.99289
1,4
.0073
.819
.35021
841
.40987
835
.09201
i,4
.0071
2.820
8.35862
842
8.41823
836
0.99292
1.4
1.0071
0,1
.821
.36704
843
.42659
837
.99293
1,4
.0071
.822
.37548
8-13
4344)6
838
0929S
1,4
.0071
.823
.38391
844
44334
838
ooayfl
1,4
.0071
.824
39236
845
45^73
839
.99298
1.4
.0071
2.825
8.40082
846
8.46013
840
0.99290.
1.4
1,0071
0,1
,826
.40928
847
.46853
841
.99300
1,4
,0070
.827
4*776
848
47605
8:j2
99302
1,4
.0070
.828
,42624
849
.48537
8.13
.99303
1-1
.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
'.4
.0070
.832
.46025
852
.5I9T4
846
D9309
M
.0070
-833
.46877
853
.52760
847
99310
1.4
,0069
.834
-'17730
854
.53fio8
848
99311
1.4
.0069
2.835
8.48584
854
8,54456
8-1.9
0.99313
M
r.oofx)
O,I
.836
.40439
855
55305
-19
.99314
r,4
.0069
-837
-50295
856
. 56155
50
.99316
1,4
.0069
.838
.5it5t
857
,57006
851
.99317
M
.0069
.830
.5200*)
858
.57857
852
.99318
r,4
.0069
2.840
8.52867
859
8.58710
853
0.99320
1,4
1.0069
O,I
.841
.53726
860
.59563
854
99321
M
.0068
.842
.54586
860
.60417
855
.99322
1,4
.0068
-843
55447
86 1
.61272
855
09324
1,3
.0068
.844
.S<5309
862
.62128
856
99325
1,3
,0068
2.845
.846
8.57T7I
58035
863
864
8.62985
.638-12
857
858
0,90326
.99328
1,3
1,3
i. 0068
.0068
0,1
.847
.58899
865
.64701
859
,99329
1,3
.0068
.848
.SQT&l
866
.65560
860
99330
1,3
.0067
.840
.60630
866
.66420
86r
DOM 2
1,3
,0067
2.850
8.61497
867
8,67281
86 r
0.99333
J,3
1,0067
0,1
u
tan ad u
wFo'
sec nil u
<ofV
sin gd u
" F(|'
080 ntf U
Id F '
SMITHBONJAN
Natural Hyperbolic Functions.
851
.857
.858
.Kfl.l
.HfM)
.8/8
87?
,8Hi
\VA~\
a.8Hs
'.887
,88H
.81X1
i8yH
BJllll 11
8.(ii.l*J7
.'"M.17
H.i/iH87
Inn ad u
87.;
8/.1
K-73
K/5
K/(i
K/S
KM I
H8(i
JWfi
H88
Hgo
Mij!
MCJJ
MOI
I.KHI
tjtn
um
U"
coali 11
. X. 1 !"?"
.'W75H
.O.W-M
.",11 *J
100 Oil U
w Pu'
HIM
HIM
.Hf.8
8711
8/1
N/M
8X5
H/S
8/0
8kl
KH.1
88s
8H
8>M
</*(>
i/tl
(XII
yen
t-Fg'
Innh n
'XW.17
was 5
ti'MS?
f W.I'M
W.17I
W377
wafts
WS/3W
tlntttl u
1.3
1.3
1.3
1.3
1.3
1.3
1,3
"i3
1.3
1.3
1.3
1,3
>,3
1,3
",3
1,3
1,3
1.3
1.3
1,3
1,3
1.3
1,3
",. I
1.3
1,3
1,1!
l J
r,a
1,2
r,a
rla
r,2
t.a
r,2
1,3
1,3
DO Ml LI
i .oofi?
.cxXifi
.(X5f)(i
.oofis
.01X15
1 .00(15
I . (xXi,3
. f.xX"t.i
. (XXl J
.CicXia
i.cxXia
l.ocXii
,OO(H
.ooTii
.ocXii
i.ocXJi
CJO (]4 U
Fo'
0,1
0,1
O.I
0,1
0,1
0,1
o,r
0,1
o,r
0,1
w Fo'
M1THHONIAN
163
Natural Hyperbolic Functions.
u
sJnh u
* Fo'
cosh u
.Fo'
tanh u
U) Fo'
oolh u
.Fo'
2.900
9-0595^"
911
9-11458
906
0.99306
1,2
I. O06l
0,1
9or
.06868
912
. 12365
907
99398
1,2
.0061
.902
.07781
913
- 13272
COS
-99399
1,2
.0060
-903
.08695
914
.14180
909
99400
1,2
.0060
.904
.09609
915
.15090
910
.99401
1,2
.0060
2.905
9-10525
916
9.16000
yn
0.99402
1,2
I. 0060
0,1
.906
.11441
917
.16911
gir
.99403
1,2
.0060
.907
12359
918
. 17823
912
99405
1,2
.0060
.908
. 13277
919
.18735
913
.9940^
1,2
.0060
-009
. 14196
920
.19649
914
99407
1,2
.0060
2.910
9. 15116
921
9.20564
9'5
0.99408
1,2
I. 0060
0,1
.91 1
. 16037
921
.21479
916
.99409
1,2
.0059
.912
. 16959
922
. 22396
917
99411
1,2
.0059
913
.17882
923
-23313
giS
.99412
1,2
.0059
.914
.18806
924
. 24232
919
-99413
1,2
.0059
2.915
9. 19730
925
9-25151
920
0.90414
1,2
I .0059
0,1
.916
.20656
926
.26071
921
99415
1,2
.0059
917
.21583
927
.26992
922
.99416
1,2
.0059
.918
.22510
928
.27914
923
.99418
1,2
.0059
.919
.23438
929
.28837
923
-99419
1,2
.0058
2.920
9.24368
930
9,29761
924
0.99420
1,2
1.0058
0,1
.921
.25298
931
.30686
925
.99421
1,2
.0058
.922
.26229
932
.31612
926
.99422
1,2
.0058
.923
.27161
933
.32538
927
90423
.0058
.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
.29063
935
. 35324
930
.99427
1,1
.0058
.927
.30899
936
36254
.99428
,0058
.928
.31835
937
.37186
932
.99429
1,1
.0057
.929
32773
938
.38118
933
.99430
1,1
-0057
2.930
9-33712
939
9.39051
934
0.99531
1,1
1.0057
0,1
931
.34651
940
.39386
935
-99433
I, I
.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
] i
.0057
-937
.40308
946
-45610
940
99439
',1
.0056
-93S
.41254
947
.46551
941
99440
1,1
.0056
939
.42201
947
.47493
942
.99441
1,1
,0056
2.940
9.43149
948
9-48436
P43
0.99443
i,r
1.0056
0,1
941
.44098
949
-49379
044
-99444
1,1
.0056
.942
.45048
950
50324
945
.99445
1,1
.0056
943
45999
95 r
.51269
046
99446
i.i
.0056
944
.46950
952
.52216
947
-99447
.0056
2-945
9-47903
953
9-53163
048
0.99448
1,1
1.0055
0,1
.946
.48857
954
.54112
949
99449
1,1
.0055
-947
.49811
955
-55061
050
.99450
i.i
0055
.948
,50767
956
.56011
951
-99451
1,1
.0055
949
,51723
957
.56962
952
-99453
i,i
.0055
2.950
9.52681
958
9-57915
953
0.99454
i,i
1.0055
0,1
u
tan ad u
wF '
sec fld u
.w
sin gd u
Fo<
cso ad u
.Fo'
SMITHSONIAN TABLES
164
Natural Hyperbolic Functions.
u
sinh u
*>F '
cosh u
F '
tanh u
ia f '
cotii u
"F '
2.950
9.52681
958
9.57915
953
0.994S4
1,1
1.0055
O,I
.951
.53639
959
.58868
954
994'55
1,1
0055
.952
.54598
960
.59822
955
9945<5
1,1
.0055
.953
. 55559
961
.60777
956
-99457
I.I
.0055
.954
. 56520
962
.61733
957
9945S
1,1
.0055
2.955
9.57-182
963
9.62690
957
0-99459
1,1
1.0054
0,1
.956
. 5&145
964
.63648
958
.99460
1,1
.0054
.057
59410
965
.64607
959
.99461
1,1
.0054
.058
.60375
966
.65567
gfw
.99462
1,1
.0054
959
.61341
967
.66528
961
.99463
1,1
.0054
2.960
9.62308
967
9.67490
962
0.99464
1,1
1.0054
o,r
.961
.63276
968
.68452
963
.99465
1,1
0054
.9!>2
.64245
969
.69416
9&4
.99467
II
.0054
.963
.65214
970
.70381
565
.99468
1,1
0054
.964
.66185
971
7*347
966
.99469
1,1
.0053
2.965
9 -C7r57
972
9.72313
957
0.99470
I.I
1.0053
0,1
.966
.68130
973
.73281
0G8
.99471
1,1
0053
.967
.69104
974
.74249
969
.99.[72
1,1
.0053
.968
.70078
975
.752I9
970
99473
1,1
0053
.969
.71054
976
.76190
971
.99474
1,0
0053
2.970
9.72031
977
9.77161
972
0.99475
I,O
1.0053
0,1
.971
- 73008
978
.78134
973
-99476
1,0
.0053
.972
.73987
979
-79107
974
99477
I,O
.0053
073
-74067
980
.80082
975
-99-178
1,0
.0052
.974
75947
981
.81057
976
99479
1,0
.0052
2.975
9.76929
982
9.82034
977
0.99480
I,O
1.0052
O,I
.976
779II
983
.8301 1
978
.99481
I,O
.0052
-977
.78895
984
83989
979
.99482
I,O
.0052
.978
79879
985
.84969
980
99483
1,0
.0052
079
.8oS55
986
.85949
pSi
.99484
I,O
.0052
2.980
9.81851
937
9-86930
982
0.99485
T,O
1.0052
0,1
.981
.82839
988
.879U
983
.99486
1,0
.0052
.982
.83827
989
.88896
984
99487
1,0
.0052
.983
.84816
990
.89880
985
.99488
r,o
.0051
.984
.85807
991
.90866
986
.99489
I,O
.0051
2.985
9.86798
992
9.91852
987
0.99490
iiO
1,0051
0,1
.985
.87790
993
.92839
988
-99491
1,0
.0051
.987
.88784
994
.93828
989
.99492
I,O
.005"
.988
.89778
995
.94817
990
99493
1,0
.0051
.989
-9Q773
996
-95807
991
.99495
1,0
.0051
2.990
9.91770
997
9.9679S
992
0.99406
1,0
1.0051
0,1
.991
.92767
998
.97791
993
99497
I,O
.0051
992
.93765
999
.98784
994
99498
1,0
.0051
993
.94765
IOQO
.99778
995
99499
I,O
.0050
994
.95765
TOO I
10.00774
996
-99500
1,0
.0050
2.995
9.96766
IOO2
10.01770
997
0.99501
I,O
1.0050
0,1
.996
.97768
1003
.02767
908
.99502
1,0
.0050
997
.98772
IOO4
.03765
999
99503
I,O
.0050
.998
.99776
1005
.04765
IOOO
.99504
1,0
.0050
-999
10.00781
IO06
.05765
IOOI
99504
1,0
.0050
3.000
io.. 01 787
1007
10.06766
IO02
0.99505
1,0
1.0050
O,I
u
tan fld u
*>F '
seo od u
Fo'
tin gd u
wFo'
cso gd u
" Fo'
SMITHSONIAN TABLES
165
Natural Hyperbolic Functions.
u
si.nh u
< Fo'
cosh u
-tf
tanli u
-F,-
coth u
^Fo'
..OI
.02
.03
.04
0.0179
0.1191
Q.22I2
0.3245
10.4287
1007
1017
1027
1037
1048
O.o677
0.1683
0,2700
0.3728
0.4765
1002
IOI2
1022
1032
1043
0.99505
.99515
-99525
.99534
-99543
9,9
9,7
9,5
1.0050
.0049
.0048
.0047
.0046
1,0
1,0
1,0
0,9
0,9
3-05
.06
.07
.08
.09
10.5340
10.6403
10.7477
to. 8562
10.9658
1058
1069
1079
1090
IIOI
0.5814
0.6872
0.79-12
a '.9022
ii. 0113
1053
1064
1075
1086
1097
0.99552
.99561
99570
.99578
.99587
8,9
8,8
8,6
8,4
8,2
i .0045
.0044
.0043
.0042
.0041
o,9
0,9
o,9
0,8
0,8
3-10
.11
.12
.13
.14
11.0765
11.1882
11.3011
11.4131
ir.5303
JII2
1123
1135
1146
"57
11.1215
11.2328-
11-3453
13.4588
H.5736
1108
1119
1130
1142
"S3
0.99595
.99603
.99611
,99618
,99626
8,1
7,9
7,8
7,6
7,5
1.0041
.0040
.0039
.0038.
.0038
oV
0,8
0,8 '
0,8
3.15
.16
.17
.18
.19
11.6466
11.7641
11.8827
12.0026
12.1236
1169
1181
1192
1204
1216
11.6895
11.8065
11.9247
12.0442
12.1648
1165
1176
1188
1200
1212
0.99633
.90641
.90648
.99655
.99662'
7,3
7,2
7,o
6,9
6,8
i .0037
.0036
.0035
.0035
.0034
o,7
o,7
o,7
o,7
o,7
3.20
.21
.22
.23
.24
12.2459
12.3694
12.4941
12.6200
12.7473
1229
1241
1253
1266
1279
12.2865
12.4097
12.5340
12.6595
12.7864
1225
1237
1249
1262
1275
0.99668
-99675
.99681
.99688
-99694
6,6
6,5
6,4
6,2
' 6,1
1.6033
.0033
.0032
.0031
.0031
0,7
0,7
0,6
0,6
0,6
3-25
.26
.27
.28
12.8758
13.0056
13-1367
13.2691
13.4028
1291
1304
1317
1331
1344
12.9146
13-0440
13.1747
13-3067
13-4401
1288
I30J
I3M
1327
1340
.99706
.99712
.99717
.99723
6,0
5,9
5,8
5,6
5,5
1.0030
.0030
.0025
,O02
,002f
,0,6
0,6
0,6-
0,6
1 0,6.
3-30
-32
33
34
13-5379
13.6743
13.8121
13.9513
14.0918
1357
1385
1399
1413
13-574^
13.7108
13-8483
13-9871
14.1273
1354
1367
1395
1409
0.99728
.99734
.99739
-99744
.99749
5,4
5,3
5,2
5io
I.G027
.OO27
.002(
(0026
.00^5
o,5
o,5
o,5
a,:
0,5
3-35
.36
-37
.38
14/2338
14.3772
14.5221
14.668,
"^427
1441
1456
1470
14.2689
14.4120
I4-5565
14.702.:
1423
1438
1452
1467
0,99754
-99759
.99764
.99768
4,9
4,8
4,7
4,6
1.0025
.OO3;
.OQ2,
.002;
, 0,5
0,5
o,5
P.5'
-39
14.8161
1485
14.8408
1482
99773
4.5
.OO2;
o,5
3-40
.d
14.9654
15,116
1500
ISIS
14.5987
1497
1512
0.99777
.99782
4,4
4,4
1.0022
.O022
0,4
0,4'
. -4
.42
15.2684
15-3011
1527
.99786
4,
,OO2
0,4
i .-(
..43
44
15-422
I5-577-
1545
15-4545
15-6095
1542
1558
.99790
9979
4,
4,
.002
.002
0,4
'0,4
3-4
. 15-734.
1577
rs.766i
1573
0.99799
- 4,
I.O020
0,4
.46
.A
15-892;
16.052.
1592
1608
15-9242
16.0839
1589
1605
.9980
998o
3,
3,
,OO20
.OOI
0,4
0,4
**
.A
16.214
. 1625
16.2453
162
.0981
3,
.001
,0,4
*t
.4
16.377
164
16.4082
1638
.0981
3,
.001
0,4
3-5
i6.542
1657
16 .-5728
1654
'0.9981
3,
I. OOI
0,4
u
Ian ad u
"> Fo
. see gtt u
u Fo'
sin ad u
.V
CSQ ad u
" Fo/ ',,.
SMITHSONIAN TABLES
166
Natural Hyperbolic Functions.
u
si nil u
"F,/
oosli u
(o Ft,
tnnli u
- Fo -
ootlt u
F.'
3 50
Hi.5.|.JO'
Ifi57
16.5728
1(')54
O.O(j8i8
3.6
I, 0018
0,4
5"
10.700.!
1074
1(1.7391
1(171
. (.1982 1
3,(>
.0018
o,4
5-
1(1.877.1
1(191
1(1.9070
K>88
99825
3.5
.0018
0,4
SI
'7.O-1 73
1708
17.07!*,')
1 705
. 9,\S28
3.4
.0017
o,3
54
17. 2 H.JO
!7-'5
i7-2.]8o
172^
99832
3.4
.0017
0,3
3-55
17.3023
1742
17.4210
'7.10
0.^835
3.3
1.0017
o,3
S ( >
17.5074^
17(10
1 7 . 51)58
1757
99838
,3,2
.0016
o,3
17.7-l-ia
1777
17.772-1
1774
.998.12
3,-'
.00 if)
0,3
S8
17,9228
1 705
17.95<'7
1792
9*j8.| 5
3,1
,ooi(i
o.3
59
18, KM-
1813
l8.i3ixS
1810
1/;8.|8
3,o
.0015
0,3
3.60
18.2855
1831
18.3128
1829
o . 0085 i
3,"
1.0015
0,3
' !()i
|8.4<>05
1850
i8.4()!)(j
I&17
-99854.
2,9
.0015
0,3
.0.1
18.055.1
i8()S
i8.(i8.;j
|8(J()
. <>(>S57
2.9
.0014
0,3
Al
i8.8,'i32 /
1887
i8.8(i()7
l88;|
.99^59
2,8
.0014
o,3
19.0328
iyo6
19.0590
1003
,oy8()2
2,8
.0014
o,3
V<'">
10.33,13
1025
io.aso.i
It)33
o.9o8()5
2,7
I. 00 14
o,3
' ,60'
19-4178
ID-I-1
19. 4435
iy.| 2
.yy8()8
2,(i
.0013
o,3
('7
19. (1132
nX>4
19- (M87
19(11
. 99870
2,0
.0013
0,3
.oH
"lo.MioO
1984
10.8358
1981
. (K;873
2,5
.0013
o,3
20,0099
2<K)3
20.03.19
200 1
99875
2,5
.0012
0,2
1-70
20.21 13
UOJ.|
20.2360
202 1
0.99878
2,4
1.0012
0,2
' -71
2O..1I47
:!<K|/|
20.439,1
2041
,t)(j88o
2,4
.OOI2
0,2
. 72
jfMi.ioi
i'0()4
20,().j,|3
2(K'l2
99883
2,3
.0012
0,2
73
2O.H270
2085
20.85H)
2083
99885
2,3
.0012
0,2
74
UK 0,171
jioii
21 .()(){>
2104
99H87
2,3
.OOII
0,2
3 . 75
;!i.2,|88
2127
21.2723
2125
0.1^)889
2,2
I, 001!
O,2
;M.40.!()
2140
21.4859
214(1
!)<^)2
2,2
.0011
0,2
77
Jl ,(1785
.; 1 70
21 //I lit)
2l('l8
9!j8(>(
2,1
.(XIII
0,2
.78
.ii .ftXiO'
.!! .9194
2190
W8iX>
2,1
,0010
0,2
70
22. i 169
2214
22.1305
2212
, 998<)8
2,0
,O010
0,2
3.80
:;.!. 330-1
2J3(i
2.i.3(ii8
2234
O.IJWXKJ
2,0
I. 0010
0,2
.81
2.!,SfMI
i!J59
.!2.,SK()3
225(1
. 991)02
2,0
,OOIO
0,2
.82
li.! [701 l
2^81
2,!. 8 13*1
2J70
.^XX'.'I
1,0
.0010
0,'2
-.83
JiioJO,!
2304
23.IM2I
23O2
.()< )()(>! i
1,0
,0009
0,2
33.35-11
3337
33.3735
3335
99!X)8
1,8
.0000
0,2
I.Hl
"3-4859.
3311
3 5072
-M- 19
'o,W>09
1,8
1.0009
0,2
% !8il
:l'i . 722 1
i!374
23.7432
-37-
.99911
r,8
.0009
0,2
.;,i < of'io8
jV)8
23.1)810
MIX'
y*w 1 3
1,7
.0009
0,2
!H8
.89
*\^M
2447
'i!:^
i!iS
yogis
1,7
i,7
.0000
.0008
0,2
0,2
* .91
io3
24.691 i
25. 1003
25 .(MX)
i?
24.7113
24-9505
U.S. 3 10 1
25.7190
2519
3S.M
999-"
1.5
1,5
r.oooft
.0008
,0008
.0008
,0008
0,2
0,2
0,2
p,2
0,2
3 05
a^.o-iKi
29>8
35.0773
359f>
0.99926
i,5
1.0007
0,1
.'X'
2(1.2491
i!(L!4
2*1.2382
2(123
.99927
J,5
,0007
o.i
07
.08
.yy
ifHffi
26', ^0
2()77
270.1
an' . 50 1 7
~'7-03n'7
2702
9W30
M
.0007
.0007
- .0007
0,1
0,1
0,1
4.00
aj-.aHw
2731
sy.ytito
272(J
0.99933
1,3
1.0007
0,1
u
Inn ml u
BOO (111 II
w Fo'
alii ail u
WlV
080 a<l u
.. UFO/
SMITHSONIAN TADUKB
167
Natural Hyperbolic Functions.
u
sinh u
ia Fo'
cosh it
" Fu'
tanh u
F '
colli u
H> Fo'
4.00
27.2899
2731
27.3082
2729
0.99933
1,3
1.0007
0,1
.01
27 . 5644
2758
27.5825
2756
99934
1,3
.0007
.02
27.8416
2786
27.8595
2784
.99936
1,3
.0006
.03
28.1216
28t4
28.1393
2812
99937
1,3
.0006
.04
28.4044
2842
28.4220
2840
.99938
1,2
.0006.
4.05
28.6900
2871
28.7074
2869
0.99939
1,2
I. 0006
0,1
f
.00
28.97S5
290O
28.9958
2898
.99941
1,2
.0006
.07
29.2699
2929
29.2870
2927
99942
1,2
.0006
.08
29.5643
2958
29.5812
2956
99943
1,1
.0006
.09
29.8616
2988
29.8783
2086
99944
1,1
.0006
4.10
30.1619
3 0:S
30.1784
3016
0-99945
1,1
1.0005
0,1
.11
30.4652
3048
30.4816
3047
-99946
1,1
.0005
.12
30.7715
30/9
30.7877
3077
-99947
I, I
.0005
13
31,0809
3HO
31.0970
3108
.99948
1,0
.0005
.14
31.3934
3141
31.4094
3139
99949
1,0
.0005
4.15
31.7091
3172
3L7249
3171
0.99950
I,O
1.0005
0,1
.16
32.0280
3204
32.0436
3203
-99951
I,O
.0005
.17
32.3500
3237
32.3655
3235
99952
1,0
.0005
.18
32.6753
3269
32.6906
3268
99953
0,9
.0005
.19
33.0038
3302
33.0100
3300
-59954
0,9
.0005
4.20
33-3357
3335
33.3507
3334
0-99955
0,9
1.0004
0,1
.21
33-67o8
3369
33-6857
3367
.99956
o,9
.0004
.22
34.0094
3402
34-024T
3401
-99957
0,9
.0004
.23
34.35>3
3437
34.3659
3435
.913958
0,8
.0004
.24
34-6967
3471
34.7"I
3470
.99958
0,8
.0004
4.25
35.0456
3506
35-0598
3505
o. 9^959
0,8
:.ooo4
0,1
.26
35-3979
3541
35-4121
3540
,99960
0,8
.0004
.27
35.753S
3577
35.7678
3575
.99961
0,8
.0004
.28
36.1133
3613
36.1271
3611
.99962
0,8
.0004
.29
36.4764
3649
36.4901
3648
.99962
0,8
.0004
4.30
36.8431
3686
36.8567
3684
0.99963
o,7
1.0004
0,1
31
37-2135
3723
37.2270
3721
.99964
o,7
.0004
32
37-5877
3760
37.6010
3759
-95965
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
3375
38.7457
3873
0.99967
o,7
1.0003
O,I
.36
39.1222
3913
39.1350
3912
.99967
o,7
.0003
37
39-5155
3953
39- 528l
3952
.99968
0,6
.0003
.38
39.9128
3993
39-9253
3991
-99969
0,6
.0003
39
40.3140
4033
40,3264
4031
.99969
0,6
.0003
4.40
40-7193
4073
40.7316"
4072
0.09970
0,6
1.0003
O,I
.41
41 . 1287
4114
41. 1408
4113
.99970
0,6
.0003
.42
41.5421
4155
41.5542
4154
.99971
0,6
.0003
*43
41-9508
4197
41.9717
4196
.99972
0,6
.1x103
.44
42.3816
4239
42-3934
4238
99972
0,6
.0003
4-45
42.8076
4282
42.8193
4281
0.95973
o,5
1.0003
0,1
,46
43.238o
4325
43.2495
4324
-99973
o,5
.0003
47
43,6726
4368
43-6841
4367
-09974
o,5
.0003
.48
44-"i7
4412
44-1230
4411
.99974
o,5
.OOOi
-49
44-5551
4457
44-5663
4456
-99975
o,5
.0003
4.SO
45-0030
4501
45.0141
4500
0.9P975
o,'5
I.O002
0,0
u
tan ad u
uF '
sea ad u
Fo'
sin ad u
61 Fo'
esc ad u
oFo'
SMITHBONIAN TAUIIS
168
Natural Hyperbolic Functions.
-1-50
.51
5-1
I .S3
57
59
ninli
.15-155.1
-I - 75
77
79
' '.Hi
'X
5. Of
11
l').737i
5.J.JH77
57.7'
67.141,1
<y,Hi(rf>
oH-4077
(n).iWn
7 ' -93 1
7,I.(HCHI
COHll 11
45.0141
ii"7S
5, US
SJH9
4500
(HIIS
*H,l7
.t75
5<i/- 1
SMS
5177
5J.il
5HJ7
S'JSS
1.5050
tnn ad 11
no oil u
Innli u
7 1 "9
7-73
.0')<J<Xt
O.i/XXJ"
Bin oil 11
o,5
o,5
o!s
o,5
o,3
0,3
0,3
o,3
0,3
0,3
o,3
0,3
o,3
o,3
0,3
0,3
0,'J
o,a
on Hi u
I.OOOi!
,(XXU
1,0002
.(XX).!
,(XKW
.txto^
i.mxw
.(XX)J
.(XX)-i
.(XX)-'
,(XX)J
.(XX)J
.(HXU
.(XX)J
I.CXXW
.(XX)J
.(XKi.:
.(XX)J
T.(XX)I
.(XK)I
.(XXI I
l.OOflt
.(HXII
.(XX) I
,<XK)I
.(XX) I
.(XX) I
T.OOOI
,(XM)I
I, (XX) I
.0(X)I
,(XX)I
,(KX)t
I .0001
080 ml ii
0,0
0,0
0,0
0,0
0,0
0,0
0,0
0,0
0,0
TALIUM
I fit)
Natural Hyperbolic Functions.
u
slnh u
w Fo'
oosli u
F '
tanh u
"Fo'
cadi u
^Fo'
S-oo
74-2032
7421
74.2099
7420
0.99991
O,2
i.ooor
0,0
.01
74-9490
7496
74.9557
7495
99991
O,2
.0001
.02
75.7023
7571
75.7090
7570
.90391
O,2
.0001
.03
76.4632
7647
76.4698
7646
.99991
0,2
.0001
.04
77.2318
7724
77.2382
7723
99992
O,2
,0001
S-05
78.0080
7801
78.0144
7801
0.99992
O,2
r.oooi
0,0
.06
78.7921
7880
78.7984
7879
99992
O,2
.0001
.07
79.5840
7959
79.5503
7958
-99992
0,2
.000:
.08
80.3839
8039
80,3901
8038
99992
0,2
.OOQI
.09
81.1918
8120
81.1980
8119
99992
O,2
,0001
5. 10
82.0079
8201
82.0140
8201
0.99993
0,1
I.OOOI
0,0
.n
82,8322
8284
82.8382
8283
99993
0,1
.0001
.12
83-6647
8367
83.6707
8366
-9!>993
0,1
.0001
13
84.5056
8451
84.5115
8451
-99993
O,I
OOOI
.14
85.3550
8536
85.3608
8535
-99993
O,I
.0001
5-lS
86.2128
8622
86.2186
8621
0-99993
o,r
I.OOOI
0,0
.16
87.0794
8709
87.0851
8708
99993
0,1
.OOOI
E7
87.9546
8 7
87.9603
8795
99994
0,1
.ooor
.18
88.8386
8884
88.8442
8884
99994
O,I
.0001
.19
89-7315
8974
89.7371
8973
99994
0,1
.OOOI
5-20
00.6334
9064
90.6389
9063
0.99904
0,1
I.OOOI
0,0
.21
91.5443
9155
91 . 5498
9154
99994
O,I
.OOOI
.22
02.4644
9247
92.4698
9246
99994
0,1
' .OOOI
.23
93-3937
9340
93.3991
9339
-9999-1
O,I
.OOOI
.24
94.3324
9434
94-3377
9433
99994
0,1
.OOOI
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
.OOOI
.27
97.2054-
9721
97.2106
9721
-93995
0,1
.OOOI
.28
98. 1824
9819
98.1875
9818
99995
0,1
.OOOI
.20
99.1692
9917
99.1742
9917
9G995
0,1
.OOOI
5-30
100.1659
10017
100.1709
10017
0.99995
0,1
I.OOOO
0,0
31
101.1726
10118
101 . 1776
10117
99995
0,1
. .0000
-32
102 . 1895
10219
102.1944
10219
-99995
0,1
.0000
33
IO3.2I66
10322
103.2274
10322
99995
0,1
.0000
-34
104.2540
10426
104.2588
10425
-99995
0,1
.0000
5.35
105.3018
10531
105.3065
10530
0-99995
0,1
I.OOOO
0,0
.36
106.3601
10636
106.3648
10636
.99996
0,1
.onoo
37
107,4291
10743
107.4338
10743
99996
0,1
.0000
.38
IOS.5088
10851
108.5134
10851
.90096
0,1
.0000
-39
109-5994
10960
109.6040
10960
.99996,
0,1
.0000
S-40
110.7009
11071
110.7055
II070
0.99996
0,1
I.OOOO
0,0
.41
III.8I36
11182
111.8180
inSi
.99996
0,1
.0000
,42
112-9375
I I2M
112.9418
11294
.9999*5
0,1
.0000
43
114.0724
11408
114.0768
11407
.99996
0,1
.0000
44
115.2189
11522
115.2233
11522
99006
0,1
.0000
5-45
116.3769
11638
116.3812
11638
0.99995
O,T
I.OOOO
0,0
.46
117.5466
1 1755
117.5508
n 755
.90996
O,I
.0000
47
118.7280
11873
118.7322
11873
.99996
0,1
.0000
.48
119.9213
"993
119.9254
11992
99997
o,r
.0000
.49
121 , 1265
I2II3
121 . 1307
12113
-99997
0,1
.0000
5-50
122.3439
12235
122,3480
12234
0.99997
0,1
I.OOOO
0,0
u
tan gd u
uFo'
sea ad u
Fo'
sin ad u
w Fo'
cso ad u
"Fo'
SMITHSONIAN TABLES
170
Natural Hyperbolic Functions.
u
slnli u
Fo'
cosh u
in FO'
tanh u
-Fo'
coth u
U) Fo'
5.50
22.3439
12235
22.3480
12234
0.99997
0,1
I.OOOO
0,0
.5'
23.S73-5
12358
123.5776
12357
99997
O.I
.0000
.52
24.8155
12482
124.8195
12482
-99997
O,I
.0000
S3
26.0700
12607
126.0739
12607
.99997
0,1
.0000
-54
127.3370
12734
127.3410
12734
99997
O,I
..oooo
5. 55
128.6168
12862
128.620?
12862
0-99997
O,I
I.OOOO
0,0
-56
129.9095
12991
129.9133
12991
-99997
O,I
.0000
.57
I3I.2I5I
13122
131.2190
13122
99997
0,1
.0000
58
132.5339
13254
132.5377
13253
-99997
O,I
.0000
59
133-8659
13387
133.8697
13387
-99997
O.I
.0000
5.60
I35.2H4
13522
135.2150
I352I
0.99997
O,I
I.OOOO
0,0
.61
136.5703
13657
136.5739
13657
99997
O,I
.0000
.62
137.9429
13795
I37-9465
13794
.99997
0,1
.0000
.63
M0.3293
13933
139.3329
13933
99997
0,1
.0000
.64
140.7296
14073
140.7331
14073
-99997
0,1
.0000
5-65
142 . 1440
I42I5
142.1475
14214
0.99998
0,0
I.OOOO
0,0
.66
M3-5726
14358
I43.576I
T4357
-99998
0,0
.0000
.67
145-0155
14502
145.0190
14502
.99998
0,0
.0000
.68
146.4730
14648
146.4764
14647
.99998
0,0
.0000
.69
M7-945I
14795
I47-9485
14795
.99998
0,0
.0000
5-70
149-4320
14944
149.4354
M943
0.99998
0,0
I.OOOO
0,0
7i
150-9339
15004
150.9372
15093
.99998
0,0
.0000
.72
152.4508
15245
152.454!
15245
99998
0,0 '
.0000
73
T53.9830
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
15857
.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
I65.-M83
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
170.180^
17018
.99998
0,0
,0000
.84
171.8882
17189
171.8911
17189
99998
0,0
.0000
5.85
173.6158
17362
173.6186
17362
0.99998
0,0
I.OOOO
0,0
.86
175.3606
17536
175.3635
17536
.99998
0,0
.0000
.87
T77-I23I
I77I3
177-1259
17712
.99998
0,0
.0000
.88
178.9032
17891
178.9060
17890
-99998
0,0
.0000
.89
180.7013
18070
180.7040
18070
.99998
0,0
,0000
5-90
I82.5I74
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
188.078T
18808
99999
0,0
,0000
94
183.966
18997
189.9688
18997
99999
0,0
.6000
\
5-95
191.875*
19188
191 .8780
19188
0.99999
-0,0
I.OOOO
0,0
^<-f,i
Ofi
193,803*
I938i
193.8064
19380
99999
0,0
.0000
-97
195.7516
19575
I95.754I
19575
99999
0,0
.0000
-98
197.7189
19772
I97-72M
19772
99999
0,0
.0000
99
199.706
19971
199.7086
I997I
-99999
0,0
.0000
6.00
201.7132
20:72
201.7156
20171
0-99999
0,0
I.OOOO
0,0
u
fen od u
u Fo'
see gd u
wF '
sin od u
* Fo'
csc ad u
*Fo'
SMITHSONIAN TABLES
171
TABLE III
NATURAL AND LOGARITHMIC CIRCULAR FUNCTIONS
173
Circular Functions.
tl
sin u
>F '
coa u
uFo'
log sin U
u Fo'
loo cos u
FO'
II
o.oooo
O. 00000
IO,O
I.OOOOO
0,0
OS
+
O. OOOOO
0,0
o oo oo.oo
.OOO!
.OOOIO
,00000
6.00000
43429,4
.OOOOO
o oo 20.63
.OOO2
.00020
.00000
.30103
21714,7
.OOOOO
o oo 41.25
.0003
.00030
.QOOQO
.47712
14476,5
.OOOOO
o 01 01.88
.OQO4
.00040
.OOOOO
.60206
I0857,4
.OOOOO
o oi 22.51
O.OOO5
o . 00050
10,0
I.OOOOO
0,0
6.69897
8685,9
O. OOOOO
0,0
01 43-13
,OOO6
.00060
.OOOOO
.7/815
7238,2
.OOOOO
o 02 03.76
.GOO?
. 00070
.OOOOO
.84510
6204,2
.OOOOO
02 24.39
.OOOB
.00080
.OOOOO
.90309
5428,7
.OOOOO
o 02 4'5.oi
.QOO9
.00090
.OOOOO
95424
4825,5
.OOOOO
o 03 05.64
O.OOIO
O.QOIOO
10,0
I.OOOOO
0,0
7.00000
4342,9
0. OOOOO
0,0
o 03 26.26
.OOII
.ooiro
.OOOOO
.04139
3948,1
.OOOOO
03 46.89
.0012
.00120
.OOOOO
.07918
3619, 1
.OOOOO
o 04 07.52
.0013
.00130
.OOOOO
.11394
3340,7
.OOOOO
o 04 28. 14
.0014
.00140
.OOOOO
. 14613
3102,1
.OOOOO
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
.OOOOO
.20412
27:4,3
.00000
o 05 30.02
.0017
.00170
.00000
.23045
2554,7
.OOOOO
o 05 50.65
.0018
.00180
.00000
.25527
2412,7
.OOOOO
o 06 11.28
.0010
. 00150
.OOOOO
.27875
2285,8
.00000
o 06 31.90
O.O020
O.OO2OO
10,0
I.OOOOO
0,0
7-30103
2I7T.S
0. OOOOO
0,0
o 06 52.53
.OO2I
.002 IQ
,00000
.32222
2O68, T
.OOOQO
o 07 13.16
.OO22
.00220
.OOOOO
.34-242
1974,1
,00000
o 07 33.78
.OO2 3
.00230
.00000
.36173
1888,2
.OOOOO
o 07 54-41
.0024
.00240
.00000
.38021
1809,6
.OOOOO
o 08 15.04
O.OO25
0.00250
IO,O
I.OOOOO
0,0
7 -39794
1737,2
0. OOOOO
0,0
08 35.66
.OO26
.00260
.OOOOO
.41497
1670,4
.OOOOO
o 08 56.29
.OO27
.00270
.OOOOO
.43-136
1608,5
.OOOOO
o 09 16.91
.OO28
.00280
.OOOOO
.44716
T55T,0
.OOOOO
09 37-54
.OO29
.00290
.OOOOO
.46240
1497,6
.OOOOO
o 09 58.17
O.OOIO
0.00300
IO,O
I.OOOOO
0,0
7.47712
1447.6
0. OOOOO
0,0
O TO T8.79
.0031
.00310
.OOOOO
.4913"
1400,9
.OOOOO
o 10 39.42
.0032
.00320
0.99909
.50515
1357,2
.OOOOO
II 00.05
.OO33
. 00330
.09999
SiSsi
1316,0
.OOOOO
o ii 20.67
.0034
.00340
.99999
.53M8
1277,3
.OOOOO
o ii 41.30
0.0035
0.00350
10,0
0.99999
0,0
7.S4407
1240,8
O, OOOOO
0,0
12 01.93
.0036
.00360
.09999
.55630
1206,4
.OOOOO
12 22/55
-0037
.00370
,99909
.56820
H73,8
.OOOOO
12 43.l8
.0038
.00380
.99999
57978
1142,9
.OOOOO
o 13 03.81
.0030
.00390
.99999
.59106
1113,6
.OOOOO
o 13 24. 43
0.0040
0.00400
IO,0
0.99999
0,0
7.60206
1085,7
0. OOOOO
0,0
o 13 45,06
.0041
.00410
00999
.61278
1059,2
.OOOOO
o 14 05.69
.0042
.00420
.99999
.62325
1034,0
.OOOOO
o 14 26.31
.0043
.00430
-99099
63347
IOIO,0
.OOOOO
o 14 46.94
..0044
.00440
.99999
.64345
987,0
.OOOOO
o 15 07.57
0.0045
0.00450
IO,0
0.99999
0,0
7.65321
965,1
0.00000
0,0
o 15 28.19
,0046
.00460
.99999
.66276
044,1
.OOQOO
o 15 48.82
.0047
.00470
99999
.67210
924,0
.OOOOO
o 1 6 00,44
.0048
.00480
.99999
.68124
904,8
.OOOOO
o 16 30.07
.0049
.00490
.99999
.69019
886,3
9.99999
o 16 50.70
0.0050
0.00500
IO,0
0.99999
0,0
7.65897
868,6
9.99999
0,0
o 17 11.32
u
-islnhiu
*>Fo'
cosh EII
uFo'
. sinh [u
100 ;
oF '
ooooshiu
wF '
u
SMITHSONIAN TAB LI 3
174
Circular Function a.
,
(l(rf)i)
(J077
I KM
IKrfW
EWKJl
a In u
, ( u i.'j 1 1
.Of ),';.!(
.(Xrf/M
.(Kl/'ffll
.IN HKHt
.IHKJIO
'.(IIOOO
I al nli In
1(1,0
10.0
HJ.O
10,0
ro.o
.'WIW
w.w/
(H)lll til
10 fo' Ion alii
0,1
0,1
0,1
0,1
0,1
O h I
7(175
.7 HUM
7-7^15
7H5.1.
.Kodi
-O.'lO.fl
-0|.|.|K
7.0.1-13.1
77.1,5
(>78.fi
57 ",.
-IW.1
MWiS
M7.7
'13-1.3
105 C03
<#JW<
OW09
WWW
'KWW
wxwf*
MX ft
uooalilu
u Fo'
0,0
O,0
0,O
0,0
0,0
0,0
0,0
0,0
0,0
0,0
<> 17 31. y.
o 17 52* 5)
o 18 13. a
o 18 33.8.
o iH 54.<|<
o ig 1-5.0)
o 10 35-7
o ig 'j;6..i<
o 20 16
o ao 37 .5!
O a) 58. 2~
o a i 3<M;
O 22 OO.01
O 2^ ao . 7,
o aa <| i . 3;
o 1:3 01.97
O i!3 ^2.60
o aj -13-2.1
o 24 03.85
o a. i .'(5. ir
(t g 05.7;
o a5 26. 3f
o as <|G.iX)
o afi 07.61
o 2l\ a8.2.-|
o 2ft ,.8.87
o a? 09.. W
o 27 ,to.T-a
o a? 50. 7-1
o a8 u.
o aH 3.2,00
o ay 13.25
o ag 3,].fW
o .1" "iS-'i.l
o 30 35- 7<)
o 30 56. 3
o 31 17.01
O 31 37. (i|
o 31 58, art
o 33 iW.H<>
o 3-i .iy., sa
i) 33 oct. i.|
33 20.77
o 33 41. '10
3.) 02.03
34 aa. (is
HONIAH
175
Circular Functions.
u
sin u
uF '
cos u
" Fo'
Ian sin u
u Fo'
loa cos u
Fo'
u
O.OIOO
O.O1OOO
IO,O
0.99995
0,1
7-99999
434,3
9.99998
0,0
o 34 sw'-'fis
OIOI
.01010
99595
8.00431
430,0
.99998
34 43-27
,0102
.01020
C9995
. 00859
425,8
99P98
35 03.90
.0103
.0104
.01030
.01040
90905
.99995
.01283
.01703
421,6
417,6
999D8
.99398
o 35 4.53
o 35 45.15
0,0105
,0106
0.01050
.oroGo
10,0
0-99994
-99994
0,1
8,02118
.02530
413,6
4.09,7
9-99998
.99998
O,0
o 36 05,78
o 36 26,41
,0107
.0*070
95994
. 02938
405,9
.9991)8
o ./) 47.03
.0108
.oroSo
99994
. 03342
402,1
99997
o 37 07.66
,0109
.oiogo
,99994
03742
398,4
99997
37 28.29
O.OIIO
0,01100
IO,O
0.99994
O,I
8.04138
394,8
9-99507
0,0
37 48-91
.OIII
.onio
.99904
04531
301,2
.99907
o 3^ 09.54
.0112
.01120
99094
.04921
3^7.7
99997
o 38 30.17
.0113
.01130
99994
.0.5307
3fM.3
99907
o 38 50.79
.0114
.01140
99994
.05690
380,9
93997
o 39 11.42
0.0115
0.01150
10,0
0-99993
0,1
8.06069
377,6
9-99997
0,0
o 39 32.05
.0116
.01160
9D993
.06445
374,4
99997
0,1
39 52.67
.0117
.01170
93993
,o58 18
37^,2
99907
o 40 13.30
.0118
.01180
CC9D3
,07187
3^8,0
-99997
o 40 33.02
.0119
.oiigo
99993
.07554
364,0
99997
o 40 54-55
Q.OI2O
O.OI2OO
ro,o
0.99993
0,1
8.07917
361,9
9-99997
0,1
o 41 15,18
.0121
.O12IO
99993
.08277
358,9
09997
o 41 35,80
.OI22
.OI22O
99993
. 08635
356,0
.90997
o 41 56,43
.0123
.OI23O
.90992
.08989
353,1
90997
o 42 17. of)
.OI24
.OI24O
.09992
.09341
350,2
99997
o 42 37-68
O.OI25
O.OI2SO
ro,o
O.C9992
0,1
8.09690
347,4
9-99997
0,1
o 42 58,31
.OI26
.OI260
,99992
. 10036
344,7
99997
o 43 iS.pJ
.0127
.0:270
.99992
. 10379
342.0
9090
o 43 39.50
.0128
.01280
,99992
. 10720
330,3
,9990
o ,|4 oo, rg
.0120
.01290
.99992
. 1 1058
33<V>
.99996
44 '20. &2
0.0130
O.OI3OO
10,0
0.99992
0,1
8. 1 1393
3*1.1
9-9990
0,1
o 44 41.44
.0131
.01310
.99991
.11726
331.5
999XJ
o 45 02,07
.0132
.01320
* 0999 i
. 12056
329,0
.99996
o 45 22.70
-0133
.01330
.99901
. 12384
32<J,5
.99996
o 45 43-32
.0134
.01340
,99991
. 12709
324,1
-9990
o 46 03-05
0.0135
0.01350
10,0
0,99991
0,1
8. 13032
321,7
9.9999t>
0,1
o 46 24.5?
.0136
.01360
.99991
. 13353
319.3
.99996
o 4<5 45 . 20
.0137
.01370
.99991
. 13671
317,0
.99996
47 05-83
.0138
,01380
. -99900
13087
3^1,7
.99996
a 47 2fi.4S
.0139
.01390
.99950
14300
312,4
9990
47 47.08
0.0140
0.01400
1 0,0
0,99990
0,1
8. 14611
310,2
9.99996
0,1
o 48 07.71
.0141
.OI4IO
.99990
. 14920
308,0
9990
o 48 28.3,1
.0142
.01420
9G990
. 15227
305,8
9D90
o 48 48.96
.0143
.01430
.99990
.15532
303,7
.99996
o 49 09.59
.0144
.OI44O
-99990
15835
301,6
99995
o 49 30.21
0.0145
0.01450
1 0,0
0,99989
0,1
8. 16135
299,5
0.99905
0,1
e 49 50.84
.0146
,01460
,99989
164311
297,4
-.99995
o 50 n-47
.0147
.01470
.99980
. 16730
205,4
-99995
o 50 32.09
.0148
.01480
.99989
. 17025
293,4
-99995
o 50 52.72
.0149
.0149O
.99389
.17317
2<Ji,5
-99995
51 13-35
O.OISo
O.OISOO
1 0,O
o.ppoSp
0,1
8.17608
289,5
9-99905
0,1
o 51 33-97
u
-Istnhiu
a>F '
oosh lu
u Fo'
. slnhlu
a Fo'
log cos ft lu
FQ'
u
IUH I
SMITHSONIAN TABLES
176
Circular Functions.
El
Bill II
<> r,,'
oos ii
<" V,,'
lOO Hill II
loo cos ii
-IV
II
150
0,0.500
10,0
o.oyufio
0,1
K. ix')H
.,& )t .
DCKMK
O,I
.0151
.(US.!
,01510
.015.10
.0<)o8<)
,ot<o88
0,J
'.\ml
ife?
:i!SS?
o 51 54- (
o 5^ 15.23
0153
.015-1
.01530
.01540
;<WM8
. 18x50
iSio
, <J9;)(>5
53 35.85
o 5J 50.48
0.0155
.015(1
.01 '17
.0158
0.015,10
,015<H
.01570
.01580
m,o
o.<)i)o88
0,.!
I'M u
-70,(
:<JJ!95
0,1
53 17.10
<> 53 37-7,1
o 53 58.36
54 18,08
.oi'50
.01500
. I*. 1087
, JO 138
-7,l! '"
.yyijys
o 54 39.61
O.OI(K)
.0101
O.llHKK)
.010EO
10,0
0,01)087
,00987
(V!
8 ::X!i?
171,4
(J :;25{1
0,1
o 55 00.24
o 55 20.86
.010.!
,oio,:o
.0^87
. Jt 11)50
.ifx^, i
y*wi
o 55 41.49
Olo.i
.01030
.000^7
.JIJE7
Jd(V|
,00004
56 02.12
.Ol(>4
,oi<MO
.w.tfy
.ji.|Hj
j(i|,K
.<J!W<>4
o 56 22.74
o,uiO;i
.oli-O
0.01050
.OlOOO
10,0
::!!5l!
0,J
H :"S;
W>
^IjJJJJl
0,t
o 56 43-17
o 57 04.00
.0107
,O1<>8
.01070
,01680
,oot;ft.i
:i"SJ
3!
<J'^W4
o 57 24., 62
o 57 45.25
,0160
.OKMJO
.W.M
.JJ7H;
-257,0
.yyyjxi
o 5805.88
0.0170
0,01700
10,0
O.DJoHti
0,.!
8..M0.13
-255,. i
9.9WI
0,1
o 58 26.50
.0171
.OIXIO
,OOO8.'i
..!,l.;ijK
^5,1,0
9!J9*M
o 58 47-13
.1117.)
,O17,!O
.0'J*j8ji
-M55i
'5"',5
.(jyy<;.|
o 5!J 07.75
.017,1
.01730
.i;008,'i
..! t l8tU
251,0
,<)ty.H).\
o sy 28.38
.017-1
.01740
.W<>X$
.J-in.W
~'-l9i''
.'mm
59 49.01
0.017;;
0.01750
1O.O
0,00085
(),'
8.J430J
_'.|8, i
9 W993
0,1
oo 00.63
.017(1
.01700
!J*Jo8s
... fc ,|540
-'-10,7
WW3
(H) 30.26
0177
.01X70
,<j<j<)84
.,,'4705
~'45,3
0<)i)<)l
oo 5Q.8i)
.0178
.01780
.Ot8,|
..tSo.li)
yjws
oi 11.51
.0170
,oi7ijo
.|JO> V M
,,!5.;8.i
J.|j,(i
-WJIJ3
01 32.14
< M >io
O.Ol8(H)
10,0
o.0<t<;8|
0"
K.JHWS
>\i-
(^K)l
0,1
01 52. 77
!oi8i
.01810
.WiH]
,;,lo,o
IW93
v. . ,!">//
.ill K2
.Ol8.!O
.<;^,H3
.JIKKIS
-38,6
-*^XJ03
02 1.1,02
.1118 1
,oi8.(u
.O'l'jH.i
. J(>.!,|3
~'37,,1
.0*XJ<).1
02 54,65
.0181
.01840
.00' ^'.1
..:'-479
WJ<)3
03 IS.37
0.0185
o.mH'jo
10,0
o.0()i^3
0,.!
8,j(i7i5
-Ml. 7
?.wni
0,1
03 35-90
.018(1
,oi8<>o
.i^joXt
..jfHHI)
-M.1.5
" 'W<J9-'
0.1 56.53
.0187
.018x0
,ij')<j8,t
,y?l8ii
-M.J,J
.yj'jjw
04 17-15
,oiMK
.01880
.OO'^.*
."741 3
jji,o
-yiw-
04 .17.78
.0180
.Ol8.,o
,0'J-JH,!
.J7h.|,|
^P,8
oiwiw
I 04 58.40
O.OKJO
o.oiooo
10,0
o.<^j8.i
0,,i
M.,.'7H73
^'8,5
y.yiji^j
0,1
i 05 19.03
.0101
.01010
.O'J'fMj
,8l(H
JJ7.|
> yy< )(w
i 05 30,66
,010-i
.OMJ.!0
,0*)jH.!
...'S,i_7
w/yiv
i 06 00.28
010,1
,O1U3O
. 0^)081
,,;8s ( il
"~5.o
.OfJ*Jt>iJ
i 06 20,91
,0101
,01040
.0^181
-477
-M3.8
.',)!J9'> 1
i 06' 41.54
0.0105
0.01050
10,0
n.t^-oHi
(I,J
8..!i;ooi
jjj,7
ii.yijijtjj
0,1
i 07 02.16
,011/1
.OlOfN!
.00081
, ;JO. J,!.l
jji,(i
- !^^W-
I 07 22.70
0107
,01070
.%'<jHl
-'0444
J^O,.|
,yijt)(j;i
i 07 ,13.43
.0108
, 1 1 ;8o
.ifj*;Ho
. Ji/t!i.|
-M0,,l
09' >yi
r 08 04.04
.0100,
.OM/jn
,<ji)i>So
,J()HJ
^18,^
iiiwyi
i 08 24.67
0,0^00
0.0,000
,0,0
0. !W ,ft)
0,.!
8,3;iKX)
217,1
0-lKWJi
0,1
i 08 45-30
u
I ilnlilu
-W
muli In
w Fo'
lB" n f^
in P,|'
DU nosh lu
.w
u
SMITHSONIAN TABUKH
177
Circular Functions.
u
sin u
<oF '
COS U
<a Fo'
lag sin u
ia FO'
log cos u
IU Fo'
u
O.O200
0.02000
10,0
0.99980
0,2
8.30100
217,1
9.99991
0,1
io8'4s"ao
.02OI
,02010
.99980
30317
216,0
99991
I 09 05.92
.02O2
. O202O
.99980
.30532
2I'5,0
.99991
i oo 26,55
.0203
.0204
.02O3O
.O204O
99979
.99979
30747
.30960
213,9
212,9
.99991
.99991
I 09 47.18
i 10 07.80
0.0205
.0206
O.O2O5O
,O205O
10,0
0.99979
99979
0,2
8.31172
.31384
211,8
210,8
9-99991
.99991
0,1
i 10 28.43
i 10 49.06
.0207
.O207O
99979
31594
209,8
.99991
I II 09.68
.0208
.02080
.99978
.31803
208,8
99991
I 11 30.31
.0209
,O209O
.99978
.32012
207,8
.99991
I II 50.9.3
Q.O2IO
0.02IOO
IO,O
0.99978
0,2
8.32219
306,8
9.99990
0,1
I 12 11.56
.0211
.O21IO
.99978
.32425
205,8
,99990
I 12 32.19
,0212
.O212O
.99978
.32630
204,8
.99990
I 12 52.8l
.0213
.O2I3O
99977
32835
203,9
.99990
I 13 13-44
.0214
.02I4O
.99977
.33038
202,9
,99990
I U 34-07
0.0215
O.O2I50
ro,o
0.99977
O,2
8.33241
202,0
9,99990
0,1
I 13 54.69
.02l6
,02l6o
99977
33442
201,0
-99990
i 14 15.32
.021?
.02I7O
99976
33643
200,1
.99990
I 14 35-95
.02l8
.O2I8O
.99976
33842
199,2
.99990
I 14 56.57
.O2I9
.02I9O
.99976
.34041
198,3
.99990
i 15 17-20
O.O22O
O.O2200
10,0
0.90976
O,2
8.34239
197,4
9.99989
0,1
i 15 37.83
.0221
.O22IO
99976
34436
196,5
.90989
I IS 58.45
.0222
.02220
99975
34632
105,6
.09989
i 16 19.08
.0223
.O223O
99975
.34827
194,7
.99989
i 16 39.71
.O224
.02240
99975
35021
193,8
.99989
I 17 00-33
0.0225
0.02250
10,0
0.99975
0,2
8.35215
I93,o
9-99989
0,1
I 17 20.96
.0226
.0226O
99974
.35407
192,1
.99989
i 17 41.58
,0227
.O2270
-99974
35509
191,3
.99989
I l8 02.21
.O228
,02280
.99974
35790
190,4
.99989
I l8 22.84
.O229
.02290
-99974
189,6
.99989
I 18 43.46
O.O230
0.0230O
10,0
0.99974
0,2
8.36169
188,8
9.99989
0,1
i 19 04.09
.0231
.02310
99973
.36357
188,0
.99988
i 19 '24 . 72
.O232
.O232O
59973
.36545
187,2
.99988
i 19 45-34
0233
.02330
99973
36732
186,4
99938
i 20 05.97
.0234
.02340
99973
.36918
185,6
.99988
I 20 26.60
0.0235
0.02350
10,0
0.99972
0,2
8.37103
184,8
9.99988
0,1
I 2O 47.22
.0236
.02360
.99972
.37287
184,0
.99988
I 21 07.85
.0237
.02370
99972
37471
183,2
.99088
r si 28.48
.0238
.02380
.99972
.37654
182,4
.90988
I 21 49-IO
.0239
.02390
-99971
.37836
181,7
.99988
I 22 09-73
0.0240
O.O240O
IO,O
0.99971
0,2
8.38017
180,9
9-99987
0,1
I 22 30.36
.0241
.02410
.99971
.38198
180,2
.99987
I 2'2 50.98
.0242
.O242O
-99971
.38377
179,4
.99987
I 23 II.6l
.0243
.02430
.99970
.38556
178,7
,99987
I 23 32.23
.0244
.02440
.99970
.38735
178,0
.99987
I 23 52.86
0.0245
O.O245O
10,0
0.99970
0,2
8.38912
177,2
9.99987
0,1
I 24 13.49
.0246
.02460
.99970
.39089
176,5
.99987
I -24 34.li
.0247
.0247O
.99969
.39265
175,8
.99987
I 24 54-74
.0248
.02480
.99969
.39441
i75,i
.99987
I 25 T5.37
.0249
.02490
.99969
39615
174,4
-99987
i 25 35-99
0.0250
O.O2500
IO,0
0,99969
0,2
8.39789
173,7
0.99986
0,1
i 25 56.02
u
-Islnhlu
-w
cosli iu
N
. slnhju
.*
log cash iu
.*
u
SMITHSONIAN TABLC*
Circular Functions.
u
sin u
luFo'
COS U
Fo'
IOQ sin u
w Fu'
log cos u
" Fo'
U
0.0250
0.02500
IO,O
0.99969
0,2
8.397SD
173,7
9.99986
O,I
I 25 '56.62
.0251
.02510
.99969
o,3
-39963
173,0
.99986
I 26 17,25
.0252
.02520
.99968
.40135
172.3
.99986
I 26 37.87
.0253
.02530
.99968
.40307
171,6
.99986
I 26 58.50
.0254
.02540
,99968
.40479
170,9
.99986
I 27 19.13
0.0255
0.02550
10,0
0.99967
0,3
8.40649
170,3
9.99986
0,1
I 2? 39-75
.0256-
.02560
.99967
.40819
169,6
.99086
I 28 00.38
.0257
.02570
.99967
.40989
168,0
.93986
I "28 21. Ql
.0258
.02580
.99967
4II57
168,3
.95986
I 28 41 . 63
.0259
.02590
.99966
.41325
167,6
.99985
I 29 O2.26
0.0260
0.02600
IO,O
0,99966
o,3
8.41492
167,0
9.99985
O,I
i 29 22.88
.0261
.02610
.99966
.41659
166,4.
.99985
I 29 43 -5t
.0262
,02620
.99966
.41825
165,7
.99985
I 30 04.14
.0263
.02630
.99965
.41991
165,1
99985
I 30 24.76
.0264
.02640
.99965
-42I55
164,5
.99985
I 30 45-39
0.0265
0.02650
10,0
0.99965
o,3
8.42320
163,8
9- 59<>S5
0,1
I 3: 06.02
.0266
.02660
.99965
.42.1S3
163,2
.99985
I 31 26.64
.0267
,02670
.99964
.42646
162,6
.99985
I 31 47-27
.0268
.02680
.99964
.42808
162,0
.99984
I 32 07.90
.0269
.02690
.99964
.42970
161,4
.99984
I 32 28,52
0.0270
0.02700
10,0
0.99964
o,3
8.43131
160,8
9.99984
0,1
I 32 49-15
,0271
.02710
.99963
.43292
160,2
99984
I 33 09.78
.0272
. 02720
.99963
4345'2
159,6
.99984
t 33 30.40
.0273
.02730
.99963
.436lT
I59,o
.99984
I 33 51-03
.0274
.02740
.99962
43770
158,5
99984
I 34 n. 66
0.0275
0.02750
IO,O
0.99962
0,3
8.43923
157.9
9.95984
O,I
I 34 32.28
.0276
.02760
.99962
.44085
157,3
,99983
I 34 52.01
.0277
.02770
.99962
.44242
156,7
99983
i 35 13-54
.0278
.02780
.99961
-14399
156,3
.09083
I 35 34-16
.0279
O27QO
.99961
44555
155,6
.95983
i 35 54-79
0.0280
0.02800
IO,O
0.99961
o,3
8.44710
155,1
9.99983
0,1
I 36 IS-4I
.0281
.02810
.99961
.44865
i'54,5
99983
I 36 36.04
.0282
.02820
,99960
-45019
I54,o
.99983
I 36 56.67
. 0283
.02830
999f>o
45173
153.4
.99983
I 37 17.29
.0284
.02840
.99960
.45326
152,9
.99982
i 37 37-92
0.0285
0,02850
10,0
0.99959
o,3
8.45479
152,3
9.99982
0,1
I 37 SS.55
.0286
.02860
99959
.45631
151,8
.99983
I 38 10.17
.0287
.02870
.00959
.45782
15 ',3
.99982
I 38 39.8o
.0288
.02880
99959
45933
150,8
.99982
I 39 00.43
,0289
.02800
.99958
.46084
150,2
.99982
I 39 21- OS
0.0290
0.02900
10,0
0.99958
0,3
8.46234
149.7
9.99982
0,1
I 39 41 . 68
.0291
.02910
.99058
.46383
149,2
.99982
I 40 02.31
.021)2
.02920
.99957
.46533
148,7
.99681
I 40 22.93
.0293
.02930
-99957
.46681
148,2
.09981
I 40 43 - 56
.0294
.02940
99957
.46828
147,7
.99981
1 41 04.19
O.O295
0.02950
10,0
0.99956
0,3
8.46976
147,2
9.99981
0,1
I 41 24.81
.0296
.02960
.9005(5
.47123
146,7
.99981
I 41 45-44
.0297
.02970
.99956
.47269
146,2
.99981
. I 42 06,06
.O2Q8
.02980
.99956
474T5
145,7
.99981
I 42 26.69-
-O209
.O2QOO
99955
.47561
145,2
.99981
I 42 47-32
0.0300
O.0300O
10,0
0.99955
0,3
8.47706
144.7
9.99980
O,I
I 43 07.04
U
-rlilnhlu
<oF</
cosh in
ta FQ'
, sinh tu
w FV
log cosh iii
"Fo*
11
ion
SMITHSONIAN TABLES
179
Circular Functions.
u
sin u
Fo'
COS U
to FU'
Ion sin u
Fo'
loo cos i
F '
u
0.0300
0.03000
IO,0
0-99955
0,3
8.47706
144,7
9.99980
O,I
i43'7?W
.0301
.03010
99955
-47850
144,2
.99980
I 43 28.57
.0302
.03020
99954
.47994
143-8
999SO
I 43 49-20
.0303
.03030
-99954
.481.38
143,3
.99580
I 44 09.82
.0304
.03040
99954
.48281
142,8
.99980
I 44 30.45
0.0305
0.03050
10,0
0.99953
o,3
8.48423
142,3
9.99980
0,1
I 44 5i-o8
.0306
.03060
99953
.4^565
141,9
.99980
i 45 n.?o
.0307
.03070
99953
.48707
141,4
.99980
i 45 32.33
.0308
.03080
99953
.48848
141,0
99979
r 45 52-96
.0309
.03090
99952
.48989
140,5
9997P
I 46 13.58
0.0310
0.03100
10,0
0.99952
0,3
8.49129
140,1
9-99979
0,1
I 46 34.21
.0311
.03109
.99952
.49269
139,6
99979
i 46 54.84
.0312
.03119
93951
.49408
139,2
.99979
i 47 15-46
.0313
.03120
99951
49547
138,7
99979
i 47 36.09
.0314
.03139
99951
.49686
138,3
.99979
i 47 56.71
0.0315
0.03149
10,0
0.99950
0,3
3.49824
137,8
9.99978
0,1
i 48 17-34
.03:6
' .03159
-99950
-4901
137.4
99978
i 43 37-97
-0317
.03169
99950
.50099
137,0
.99978
i 48 S8.59
.0318
.03179
99949
50235
136,5
.99978
i 49 19.22
.0319
.03189
99949
.50372
136,1
-99978
i 49 39-85
0.0320
0.03199
10,0
0.99949
0,3
8.50508
135,7
9.99978
0,1
i 50 00.47
.0321
.03209
.99948
.50643
135.2
99978
I 50 21.10
.0322
.03219
.59948
.50778
134,8
.99977
i 50 41-73
.0323
.03229
.99948
-50913
134,4
99977
I Si 02.35
.0324
.03239
.99948
-51047
134.0
99977
I 51 22.58
0.0325
0.03249
10,0
0.99947
o,3
8.51181
133,6
9-99977
0,1
I 51 43.6i
.0326
03259
99947
.51314
133,2
.99977
i 52 at. 23
.0327
.03269
99947
.51447
132,8
.99977
i 52 24.86
.0328
.03279
.99946
.51580
132,4
99977
i 52 45.49
.0320
.03289
.09946
.51712
132,0
99976
i 53 06. i I
0.0330
0.03299
10,0
0.99946
o,3
8.51844
131,6
9.99976
0,1
i 53 26.74
0331
.03309
99945
51975
131,2
-99976
i 53 47-37
.0332
.03319
99945
.52106
130,8
.99976
i 54 07.99
.0333
.03329
99945
.52236
130,4
.99976
i 54 28.62
0334
03339
,59944
.52367
130,0
.99976
i 54 49-24
0.0335
0.03349
IO,O
0.99944
o,3
8.52496
129,6
9.99976
0,t
i 55 09.87
.0336
-03359
-99944
. 52626
129,2
99975
I 55 30.50
-0337
.03369
99943
.52755
128,8
99975
i 55 51-12
.0338
.03379
99943
.52883
128,4
99975
I 56 11.75
.0339
.03389
99943
-53012
128,1
99975
i 56 32-38
0.0340
0.03399
10,0
0.99942
0,3
8.53MO
127,7
9-99975
0,1
i 56 53-00
.0341
.03409
.99942
.53267
127,3
-99975
i 57 U-63
.0342
.03419
99942
53394
126,9
-99975
I 57 34.26
.0343
.03429
-99941
53521
126,6
.99974
i 57 54.88
-0344
03439
.99941
53647
126,2
99974
i 58 I5-SI
0.0345
0.03449
10,0
0.99940
o,3
8-53773
125,8
9-99974
0,1
i 58 36.14
.0346
.03459
99940
.53899
125,5
99974
0,2
I 58 56.76
0347
.03469
99940
. 54024
125,1
-99974
i 59 17.39
.0348
-03479
99939
.54149
124,7
.99974
I 59 38.02
-0349
.03489
99939
.54274
124,4
-99974
I 59 58.64
0.0350
0.03499
10,0
0.99939
0,3
8.54398
124,0
9-59973
0,3
2 OO 19.27
u
Isinhlu
"Ft,'
cosh lu
uF '
si nil lu
<u Fo'
og cosh iu
IV
U
OD ,
SMITHSONIAN TABLES
180
Circular Functions.
O.O.I jit)
.0351
.035-!
0.0355
0357
.0358
.035*)
aln
03500
0.0354'J
0.0385
.038;,
'lilnltfu < T,
IV cnu u <,. t-Y lou nln n u F,/ Ion
.'))' Ml
O.WMo
.|J')0.!IJ
.<J* I').!/'
co nit lu
0,4
'F,,'
8.55621
.557.11
.55861
.,'17.77
5/5"<(
.577.1')
.57*5.1
. 5*5.15
/MX Ml
ll 8,q
H7,(i
H7..1
1 17,0
1 !(),]
115,4
I "5,1
1 1.1.5
11.1,7
IU.5
I 1 2,.!
i n,n
110,7
110,5
IIO.J
100,0'
HHJ.I
'.)-. W7.1
WJ7'
',J9?.X'7
loucoaliht
F u '
0,J
0,3
0,2
2 oo iy.27
2 CHI 3<j.Ki)
2 01 00.52
2 or 21.15
2 01 41.77
2 O2 02.4O
2 O2 23.03
2 02 43.65
2 03 04,28
2 03 24.*)!
2 03 45-53
2 04 4X-4
2 05 08.04
2 05 28.67
2 05 4y.2y
2 Of) (Jl).lJ2
2 o;i 30.54
2 06 51.17
2 (17 II.KO
2 O? 32.42
;i 07 53-05
2 OS 13.68
2 118 34.30
2 oR 54,93
a <x> 1 5 56
2 oy 36, 18
2 oy 56.81
2 10 17,44
2 IO 38.06
2 10 58. 6<J
2 12 00.57
2 13 21.20
2 12 4I.H2
J 13 02.4'5
J 13 ^3.7
-' 13 ,13-70
2 14 0.1.33
_' 14 2,|.y5
2 14 .15.5
2 15 0().21
2 15 26.83
2 15 47-1')
2 I(j 08. (XJ
2 I(j 28.71
2 1(1 4"-,1'l
2 1? 09.07
2 17 30.59
TAB LIE a
181
Circular Functions.
u
sin u
<a fit'
cos u
uFo'
log sin u
uj F u '
log cos n
F '
U
0.0400
0.03999
I O,O
0.99920
0,4
8.60194
108,5
9.99965
O,2
2i7'3o"so
.O4OI
.04009
.99920
.60303
108,2
.99965
2 17 51.22
.0402
.04019
.99919
,60411
108,0
.99965
2 IS 11.85
.0403
.04029
.99919
.60519
107,7
.99965
2 IS 32.47
.0404
.04039
.99918
.60626
107,4
.99965
2 18 53'- 10
0.0405
0,04049
I O,O
0.99918
0,4
8.60734
107,2
9.99964
O,2
2 19 I3.72
.0406
.04059
.99918
.60841
1 06,9
.99964
2 19 34-35
.0407
.04069
99917
.60947
106,6
.90964
2 19 54.98
.0408
.04079
99917
.61054
106,4
.99964
2 20 I5.6O
.0409
.04080
.99916
.61160
106, i
.99964
2 20 36.23
0.0410
0.04099
I O,O
0.99916
0.4
8.61266
105,9
9.99963
0,2
2 20 56.86
.0411
.04109
.99916
.6137^
105,6
.99963
2 21 17.48
.0412
.04119
99915
.61477
105,4
.99963
2 21 38.1!
.0413
,04129
.95915
.61583
'05,1
.99963
2 21 58.74
.0411
-04139
999B4
.61688
104,8
.99963
2 22 19.36
0.0415
0.04149
10,0
0.99914
0,4
8.61792
104,6
9.99963
0,2
2 22 39-99
.0416
.04159
.99913
.61897
104,3
.99962
2 23 O0.62
.0417
.04169
.99913
,62001
104,1
.99962
2 23 21.24
.0418
.04179
-999I3
.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,0
0.99912
0,4
8.62312
103,3
9.99962
0,2
2 24 23.12
.0421
.04209
.99911
.62415
103,1
.99962
2 24 43.75
.0422
.04219
.99911
.62518
102,9
.99961
2 25 04.37
.0423
.04229
.99911
.62621
102,6
.99961
2 25 25-00
.0424
.04239
.99910
.62724
102,4
.99961
2 25 45.63
o . 0425
0.04249
IO,0
0.99910
0,4
8.62826
102,1
9.99961
O,2
2 26 Ofi.2=j
.0426
.04259
.99909
.62928
ioi,y
.99961
2 26 26.8fi
.0427
.04269
.90309
.63030
101,6
.99960
2 26 47.51
.0428
.04279
.99908
.63131
101,4
.99960
2 27 08. 13
.0429
.04289
.99908
.63232
101,2
.99960
2 27 28.76
0.0430
0.04299
IO,O
0.99908
0,4
8.63333
100,9
9.99960
O,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 11.89
o.043'5
0.04349
IO,O
0.99905
0,4
8.63835
99,8
9-99959
O,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 J
99958
2 30 34.40
0439
.04389
.99904
64233
98,9
.99958
2 30 55-02
0.0440
0.04399
10,0
0.99903
0,4
8.64331
98,6
9.99958
0,2
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
.044^9
.99902
.64626
98,0
99957
2 32 17,53
.0444
04439
G990I
.64724
97,7
99957
2 32 38. 16
0,0445
0.04449
10,0
o.oggoi
0,4
8.64822
97,5
9-99957
O,2
2 32 58.78
.0446
.04459
.99901
.64919
97i3
99957
2 33 10.41
.0447
.04469
.99900
.65016
97 J
99957
2 33 40.04
.0448
04479
.59900
.651.13
96,9
99956
2 34 00.66
.0449
.04488
.99899
.65210
96,7
.99956
2 34 21.29
0.0450
0.04498
IO,O
0.99899
0,4
8.65307
06,4
9-90956
O,2
2 34 41.02
u
-Islnhiu
<o Fo'
cosh iu
Fo'
, slnli iu
to Fo'
oacoshlu
"Fo'
u
IOQ j
SMITHSONIAN TABLES
182
Circular Functions.
o.o.]5"
.n.|5"
.045-2
.0-157
O.II.SH
.0.159
O.O.](K)
.04/11
uln 11
.04538
nlnlilu
' r,,'
10,0
10,0
10,0
OOBll III
* F u '
".5
o,S
0,5
0,5
0,5
Inu Bin
('5.J03
('5505
.0507(1
9l,i'
00,8
H8,o
88,7
MH.a
H8.o
7.5
w Fu'
loo o8 ii
.yyyss
9995-
U.WW5.1-
.<Wio
99919
9-9WI9
WWW
.09917
louaoalilu
0,2
0,2
0,2
0,2
0,2
2 35 02.54
a 35 AM?
2 35 .13. Ho
2 30 04.42
2 36 25.05
2 $ 4'.<i.6S
2 37 0(1.30
2 37 art.;
-' 37 47.55
't iSl i\W
* v i'J IKi,
a 38 28.81
-' 38 4y.43
2 3<) 10. Of)
2 39 30.6
a 39 51.3
2 40 II. p
2 40 3^-57
2 41 iJ.'Sa
2 .[I 3.1.45
2 -|I 55,07
2 -12 15.70
2 .[2 56.95
2 -13 17.58
a .13 38.20
a -13 58-83
2 -14 19. -|6
2 44 40,08
2 45 00.71
a 45 2i-3.|
2 45 -1'.<J6
2 4<| O2.5tJ
a 46 aj.a:
246.13.84
2 -|7 04.47
2 -|7 25.10
2 47 -15- 7- 1
a 48 26. ()8
a 48 -i7.(k)
2 49 08,23
a -10 28.85
a 49 .|y.<i
2 50 10. II
2 go 30.73
i! 50 5 1 . 36
2 51 !!.<)(>
2 51 32.6l
2 51 53.24
SMITHSONIAN
183
Circular Functions.
1 II
a! n u
-w
coa ii
.*
IOQ sin u
... F,.'
log (HI a i
u
0.0500
O.O.HJOi
10,0
0,01/175
o,5
8,0^,
8(,,8
.i.W
0,.!
! 51 '53'.' ..'.|
O5oi
.05(X)! 1
W8?5
,/MJ<XI(J
N(*,h
-!^^ALH
.; 5.-' 1,1.87
.050.!
. (150 It-
. 01)874
.ytHJ^j
Mij,,]
,(py.) [ % [ ;
' .''-' 34--l*J
MLYl 1
() F(J 1<
1 tf l4'/ 1
*ji > i i^
Ui , i
* x w 1 1 "
r- . r- "
* {'3*' .'
'rA -/-I
t /\'\ 4 V^
' '
/ 1 1 r \ ,'i
" .'" .l.'l - 1
.O50.|
.05038
W l <7.1
-70-M5
8:,i
W/15
'' 53 15-75
0.0505
0.0504*
1 0,0
0.00873
o,5
8.70.11 1
8V)
U.'^,045
n,j
! 5.1 .(''1.37
.o.i*)f:
.0505}-
,iji),S7.f
. 70 \' >7
85,8
.<JC) | )4 |
'' r >\ '17 .(X)
.0507
.O5G(
.t^j.S^j
.7o.|.J
85.0
.0>"J.t4
.; 54 17- CM
.0508
,05078
.0^871
.705118
85,4
.'W4 |
-J 5I..18..I5
0500
.05088
.oi;87o
7<>5.1
85-1
.'^J44
- 54 58.88
0.0510
0.0509)-
10,0
o.^S^o
o.5
8.70738
5.i
0.')<><;|3
o,.:
,. 5.; MJ.IJI
.051 1
.O5ift l
,<;()8(io
.708. 13
84,0
.'J | J 1 >|3
-' 5.'i -I"- 1,1
.051-2
.051 1. 1
. <ji)8( K;
.7njoK
8|,7
'WU
-'. .'Id 00.7(1
-051.1
,051 -i*
.t;<ti%8
,701^)3
8|,d
.ijijijll
.' i\(, ,. l . ^
0514
-05138
.yoKTiK
-7 '077
84,1
.'^/)43
.! ;;(> .|*.oi
0.0515
0.05148
1 0,0
o.w8C>7
o,5
8.7i[(i.;
84,3
.'/) ).(J
(1,.!
.i 57 o.t.r.i
-0510
0-515' 1
W867
.7 1.^46
8 I.I
.WJ4,!
.! 57 -M-J()
-0517
. 05 1 of-
.<)<;8o(i
7M.10
81,0
.O'JO]"
-! .17 .1.1- 8g
.0518
.05178
.(XjfWi
.71414
83,8
. i f |( | | ,;
0510
.05 i8X
.<*)Hf>5
-7'4'J7
.!/;
,'^/<)4l
' 5 -'5 '14
0.05:10
0.0510!
10,0
o.<w%5
o,5
8.71581
83.4
O.*,j')4l
0,J
-! 58 45.77
.051-1
.0520f-
W^'i-l
.7lO(i|
83.3
.<W|I
.52a
.O^-ilf-
,i^>8()4
,717,17
8 1, i
'J 1 ) 1 ) 1 1
.! JiU J7.0.!
05.1.1
.05.,-^
.<^^i,l
7 ' 8.1' '
83.0
.ll). 1 1
! 50 47- <>5
.0524
. 05.138
yy8("w
-7I ( >'.1
8.!,8
,<)I^J4O
3 IHI 1)8. ..'8
0.0525
0.05^48
10,0
O , (^)N(i.!
o,5
8,7iij(Xi
8.1.0
'J.OO.)I<I
(I,.!
,1 oo ,:8,ijo
.05 -if)
.05J5N
, ^^("i j
.7..'o/ij
8^5
.<^;u|u
3 on 40.53
05*7
.O5J()8
,<>ii8rn
.7.1101
HJ..I
,(JV)|U
3 01 10. id
.05--8
.05-78
. Df>8(i i
-7->-'4,t
H.!,.!
.'J</)3')
3 01 30.78
.5 JJ>
.05-?88
,og8<k}
7J.TJ5
HJ,
.'J'/),f ( J
.1 "I 51.41
0.0530
>.05.!()8
10,0
o.tj()H.'io
o,5
8.7.!407
Hi <>
O-'^J.i'J
0,,'
,1 o.t 1.1,03
05,11
.05308
. ij<;85i)
81!;'
.'^^j!io
,i I),! ,\.'..(')t>
.05,1-'
.0531?
.f)<^5o
.7.1571
8 i.O
-^''J.IO
3 'I-' 53-~!>
.0533
05.U7
.WiH-iM
.7-''i5.!
81,4
.'"> | )38
,1 03 13.01
.05,14
.05.137
!W857
7-7.1.1
81,3
,i)i)<)38
.1 "3 .'1-1-54
0.0535
1.053-17
10,0
o.t)<jH57
0.5
8.7.!8i5
HI.I
().i^j';,(8
0,.!
3 <>3 55-17
05,10
-05357
!/)85(>
.7..'8ijo
Ho.o
-<j'/i!l8
3 <M 15.7*J
.1)5,17
.053(17
, (ji;85l i
7-!U77
80.8
W37
1 IM 1O..U
0538
.< '3.177
.<)<>855
80,0
'i ( C)37
3 "1 57- (l 5
.05,W
.05.187
.wAw
-7.li.l8
80,5
.',/J<M7
3 oil 17. (i?
0.0540
'.05307
10,0
0.^54
0,5
8.73.M8
Ho,;i
<).'^^37
0,.!
3 <itj 38.30
.0541
.05407
.^.'854
.7.1"'/ 1 *
8o,.i
.1/^(3(1
3 <i;i ,sH.y,i
.054J
05417
, <^.j853
.733711
80,0
'j'J'j,!''
3 (Ki '19.55
-"543
.054:7
0^>^53
73450
70.0
.'/Hjilf'
,1 <>i> 40. ]8
05-14
.05437
.1^)85^
- 735.18
70.8
.'V7J3"
.1 07 ix).8i
0.05-15
1.05447
10,0
o.<5,i
0.5
8.73(118
7" Mi
0.')<)>3, ; i
(W
3 "7 m -LI
.0540
.('5457
. 'X-85 1
.73<*>8
79,5
.'/I'M!"!
3 07 4.!,n(
05-17
05407
. ( '^5o
7,1777
70i3
,'CIOl'i
3 08 o.i.(W
.0548
-05-177
.(.)!JH50
.7.185(1
70,^!
<ri'jV r i
3 itf -'3..11
.05-10
.05487
WJ8-IM
. 7.5935
!W)!l5
0,0550
-05497
10,0
o.^jR^t)
o,5
8.74014
7H,>
'.).'mM
0,.
3.KMM-ST.
u
lalnlilu
u Fu'
onaliln
<> Fu'
loo"" 1 ; 1 "
Fu'
ounnslilu
V
ti
SMTHBONIAN
184
Circular Functions.
II
sin u
- IV
OOB 11
, F,,'
loa Bin u
10|] COB II
'" F/
U
0.0550
>. O5497
10,0
().()< )K|<)
o,5
8,74014
78,9
>9W34
0,2
3 oy 04.56
<>55i
.05'507
.<)(;8.|8
0,6
74003
7!7
99934
3 oy 25.19
.055-!
05-517
.<j<jS.|8
.74172
78,0
99934
3 oy 45.82
.0553
055.I7
.i)i;S.i7
7-1-50
78,5
W)34
3 io 06.44
i>S5'l
-05537
99847
7.134)
78,3
-99933
3 io 27.07
0.0555
o.o5'547
IO,O
0,1)9840'
0,("l
8.7.1407
78,2
>.yyy33
0,2
3 io 47-70
.0556
OS'5'57
( )')8.|5
74485
78,0
99!)33
3 II 08.32
.0557
.05567
' f )8 ] 5
.745('3
77.'J
'99933
3 u 28.95
.O5'. i ;8
.05577
.i)i)S.|.|
.74' '4 1
77,7
. <>()()3 1 2
3 u 49-58
.0559
.'15587
>W 8.|.|
74719
77,6
yyy.v
3 12 10,20
0.0560
o,o5597
10,0
o,,,, )8. l: .
0,6
8,74796
77,5
)-9W32
O,2
3 12 30.83
.05(11
.05*107
.<.)<)8,i,)
.74873
77,3
9W3-2
3 12 5i.4'>
.05''-!
.05017
.0984.!
- 74951
77.-!
, 9fj<j,i 1
3 13 12.08
o"6 1
.056.7
.(j*j8,|.!
. 75<-'2o
77, f
>'W.)3I
3 13 32.7'
.050.1
.9'.j8.|i
.75105
.09931
3 13 53-3-1
0.0565
0.056.17
10,0
0.09840
o,r
8.75182
76,8
9.yyy3i
0,2
3 14 I3.9<>
.056(1
.05057
9!J84O
75J5H
7(i,6
iJ!W30
3 "4 34-59
.05' '7
,05(107
.i,i)839
-75335
76,5
WJ93"
3 14 55-21
,05(1^7
<.;j8,10
75411
76,4
. W93O
3 15 15.84
.05' J
, 1 15*187
99838
7MK
70,2
. ytj< J3o
3 15 36.47
0.057"
.0571
0.05607
.05707
10,0
9<>S,i7
o,r,
-75'MO
70,'o
U :S{5J
0,2
3 15 57- 9
3 16 17,72
.05717
,i)i jjt,i( i
.75710
75,8
,91)929
3 16 38.35
.0573
,057-! 7
.'nV'
7570.)
7-5,7
9!J02()
3 16 5H.97
.057-1
.05737
, i)983'5
.75807
7-5,6
.yyyaK
3 17 MJ.60
,0570
o. 05747
-05757
10,0
o.iji^l,:;
'1983.1
o/i
7(>0[K
75,4
75,3
!J ;lw5
0,2
0,3
3 17 40.23
3 18 00.85
.0577
.0578
-0;>7'>7
.05777
.9*j8,V|
- ( J*Al3
.7(1093
.7<H(K)
75,-'
75.1
'.S
3 18 21.48
3 18 .]2. ll
0579
.05787
.9083--'
.7(12. 14
74.9
9y9^7
3 19 02.73
0.0580
.0581
.058,,'
0.05797
.05807
. 1 158 1 7
111,0
o-9'AlJ
i*J')K,li
9; (83 1
0,6
8.76318
76303
..7d.]6H
74.8
7^1,7
7-1,5
9 (MW
,91)926
0,3
3 19 23.36
3 19 43-99
3 20 04.61
M I' M ' 7
,1)1^30
, /(t'l-iJ
74,4
-f)91)2(i
3 20 25,24
.058' I
05837
.7(1617
74,3
.99926
3 20 45-86
05fU-
o u<;8|7
IO,0
O.'j(j8.i<>
0,6
8.70691
74,2
9-W926
0,3
3 21 06.49
.0587
.058K
0589
.05857
.05877
,<>()8j8
,')<>8,t7
, ij ^8j/
\7(x$>
74.o
73,9
73,8
73/>
:SS
3 21 27.12
3 ^1 47.7-1
3 22 08.37
3 22 29,00
0,0500
0,05897
10,0
"fijf;
0,6
H :?ym
73,5
73,4
9 :SSii
0,3
3 22 49.62
.0503
. 1 150 1 7
,05927
,(ji.;8j5
, 77.180
73,3
73.2
:<55i!
3 23 30.88
3 23 51.50
.0591
-05937
.ox;H.!.i
.77353
73,o
.99923
3 24 2. 3
0,05<J5
.051/1
.0597
.051)8
0.05946
-0507f
10,0
.(/.jHjt
0,0
77499
7757-!
^777'7
7^8
73.7
7-1.5
11
0,3
3 24 32.76
3 24 53.38
3 25 i-l.oi
3 25 34/>4
3 25 55. 2<3
O.o:*>o
.wfi
10,0
o.wto
o,G
8.7778!)
7^,3
9.m
0,3
3 26 15,89
r"'
Ultlhlll
a (V
cosh lu
wfV
loo"" 1 ;-"
-IV
lauaoBlili
to FO
u
SMITHSONIAN
Circular Functions.
11
sin u
-IV
COS U
-F.
IOQ sin
Id FO'
log cos
ia FO
U
o.oSo
0.05996
1 0,0
0.99820
0,6
8.7778
72,3
9-9992
o,3
326'i5'.'Sg
.060
.06006
.99819
.7786
72,-
9992
3 26 36.51
.060
.0601
.99819
7793
72,
9092
3 26 57- 14
.0603
.0602
.99818
.7800
71,9
9992
3 27 17.77
.060.
.0603
.99818
7807
71,8
9992
3 27 38.39
O.o6o 3
0.0604
IO,O
0.99817
0,6
8.7814
71,7
9-95920
o,3
3 27 59.02
,o6of
.0(105
.ogSif
.7822
.99920
3 28 19.65
.0607
.o6o6T
.9981^
7829
71,5
99920
3 28 40.27
.0608
. ofo?
.99815
-7836
71,;
.99920
3 29 oo.QO
.0609
.06086
99815
.7843
71,2
.99919
3 29 21.53
0.0610
0.0609
:o,o
0.99814
0,6
8.7850
7M
9.09919
0,3
3 29 42.15
.0611
.06106
.09813
.7857
71,0
.99919
3 30 02.78
.0612
.06116
.99813
.78648
70,9
.99919
3 30 23.4:
.061;
.ofiiaf
.99812
.78719
70,8
.99918
3 30 44-03
.061^
.06136
.99812
.78790
70,6
-999I8
3 31 04.66
0,0615
o.o6i4f
IO..O
0.99811
0,6
8.78860
70,5
9.99918
o,3
3 3 1 25.29
.o5 16
.o6i5t
.99810
.7893
70,4
99918
3 31 45-91
,0617
.o6i6f
.99810
.7900
70,3
.99917
3 32 06.54
.0618
.06176
.99809
.79071
70,2
.99917
3 32 27, :7
.0619
.o6i8f
.99808
.79141
70,1
.99917
3 32 47-79
0.0620
o.o6r9(
IO,O
0.99808
0,6
8.79211
70,0
9.99916
0,3
3 33 08.42
.0621
.06206
.99807
. 79281
69,8
.90916
3 33 29.04
.0622
.06216
.99807
79351
69,7
.99916
3 33 49-67
,0623
. 06226
.99806
79421
69,6
.99916
3 34 10.30
.0624
.06236
.99805
79490
69,5
99985
3 34 30.92
0.0625
0.06246
IO,O
0.99805
0,6
8.7956o
69,4
9.99915
0,3
3 34 51-55
.0626
.06256
.99804
.79629
69,3
99915
3 35 12. :8
.0627
.06266
.99804
.79698
69,2
99915
3 35 32.80
.0628
.06276
.99803
.79767
69,1
.999:4
3 35 53-4,1
.0629
.06286
.9980-2
79836
69,0
.999:4
3 36 14-06
0.0630
o. 06291:
IO,Q
0.99802
0,6
8.79905
68,8
9.99914
o,3
3 36 34-68
0631
.0630!:
.99801
.79974
68,7
999 T 3
3 ,36 55.31
.0632
.063:6
.99800
.80043
68,6
99913
3 37 *5 -9-1
0633
.06326
.99800
.80111
68,5
999T3
3 37 36.5^
.0634-
.06336
.99799
.80180
68,4
.99913
3 37 57-19
0.0635
0.06346
IO.O
0.99798
0,6
8.80248
68,3
9-99QI2
0,3
3 38 17.82
.0636
.06356
.99798
.80316
68,2
.59912
3 38 38.44
0637
.06366
.99797
.80385
68,1
,999:2
3 38 59.07
.0638
.06376
99797
.80453
68,0
99912
3 39 19.69
.0639
.06386
.99796
.80521
67,9
.99911
3 39 40.32
0.0640
.0641
.06396
.06406
IO,0
0.99795
99795
0,6
8.80588
67,8
67,7
9.999*1
999II
0,3
3 40 00.95
3 40 21.57
.0642
.06416
-99794
.80724
99D:o
3 40 42,20
.0643
.06426
99793
-80791
C74
.99910
3 4: 02.83
.0644
.06436
99793
.80859
67,3
.999:0
3 41 23.45
0.0645
,o6.{6
.0647
.0648
.0649
.06446
.06456
,06465
-06475
.06485
JO,O
0.99792
99791
.99791
.99790
.99789
0,6
8.80926
.80993
.Siofio
.81127
.81194
67,2
67,0
66,9
66,8
.99910
.99909
99309
.99909
.99908
0,3
3 41 44-oS
3 <42 04.71
3 42 25.33
3 42 45-oG
3 43 06.59
0.0650
.06495
IO,O
.99789
0,6
.81261
66,7
.99908
0,3
3 43 27.21
u
slnhfu
" F :
cosh iu
.Fo'
alnh iu
F '
gcoahfu
.N
u
00 ,
SMITHSONIAN TABLES
186
Circular Functions.
0.0050
.0(l*>l
.of* M
.(MM
0.0(1*15
. o* rf >( i
0.0(170
.(1071
.i)0/',!
.0(1/3
.01.7.1
.007*1
.0077
O.O(i<O
.Of H)l
.000,1
-IMHJI
o.oOoji
O.M7OO
nin II
.od."iM;i
. 1 )( rf H I
ialnhlu
10,0
o. on/Mi)
().*) )//<>
.007.0
loo ain
.8i
-S.Kn 1.1.1
" F,,'
(i5,7
''5,5
''5,4
6.|,o
04,8
loo cos u
9.0; )<)07
O.IW05"
0. 00000
.90800
louooalilu
Fu'
0..1
0,3
0.3
0,3
3 43 27.21
3 43 -17.84
3 44 08-47
3 44 29.09
3 44 40.72
3 45 10.34
3 45 30.07
3 45 5 [.on
3 46 3~'l 85
3 4'"' 53.48
3 47 14-10
3 47 34-73
3 47 55-3<>
3 ,|8 15.98
3 48 36. (n
3 ! 57.24
3 40 38.40
3 49 59-12
3 50 HJ-74
3 5" -10-37
3 5' o.'.W
3 5i ai.fe
3 51 42.25
3 52 02.87
3 52 iJ3-50
3 5'J 44-13
3 53 04-75
3 53 25.38
3 53 ifi.oi
3 54 0(1,63
3 54 27.26
3 54 47.89
3 55 08.;
3 55 29.
3 55 -10.77
3 56' 10. 3|J
3 5O 3^.(
3 56 5L<
3 57 12.27
3 57 32-JJO
3 57 53-52
3 58 14- 15
3 5 55-40
3 50 16-03
3 59 3^>-'
3 59 57-28
4 (K) 17.01
4 W 38.54
Circular Functions.
u
sin u
"Fo'
COS U
u FO'
log sin u
ta Fo'
log cos u
-Fo'
u
0.0700
0.06994
10,0
0.99755
o,7
8.84474
61,9
9.99894
0,3
4oo'38.'s4
.0701
.07004
99754
.84536
61,9
.99893
4 oo 59-i6
.0702
.07014
99754
.84598
61,8
.99893
4 01 19-79
.0703
.07024
99753
.84660
61,7
.99893
4 oi 40.42
.0704
-0703(
99752
.84721
61,6
.99892
4 02 01.04
0.0705
0.07044
1 0,0
0.99752
o,7
8.84783
61,5
9.99832
0,3
4 02 21.67
.0706
.07054
.99751
.84844
61,4
.99892
4 02 42.30
.0707
.07064
.99750
.84906
6 1, 3
.99831
4 03 02.92
.0708
.07074
99749
-84967
61,2
.90891
4 03 23-55
.0709
.07084
.99749
.85028
61,2
.99891
4 03 44. '7
0.0710
.0711
.0712
.0713
.0714
0.07094
.07104
.07114
.07124
.07134
10,0
0.99?48
99747
99747
.59746
.99745
o,7
8,85089
.85150
.85211
.85272
.85333
61,1
61,0
60,9
60,8
60,7
9,99890
,99850
.93890
.99890
.99889
o,3
4 04 04.80
4 04 25-43
4 04 46-05
4 05 06.68
4 05 27.31
0.0715
.0716
0.07144
.07154
1 0,0
0.99744
99744
o,7
8.85394
.85454
60,6
60,6
9.99889
.99889
0,3
4 05 47-93
4 06 08.56
.0717
.07164
99743
.85515
60,5
.99888
4 06 29.19
.0718
.07174
.59742
-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 31.07
.0721
.07204
.99740
.85756
60, i
.59887
4 07 51-69
.0722
.07214
.99739
.85816
60,0
.99887
4 08 12.32
.0723
.07224
-99739
.85876
60,0
.90885
4 08 32.95
.0724
.07234
99738
.85936
59,9
.59886
4 08 53-57
0.0725
0.07244
10,0
0.99737
0,7
8.85996
59,8
9.99886
0,3
4 09 14.20
.0726
07254
.99737
.86056
59,7
.99885
4 09 34.82
.0727
.07264
.99736
.86115
59,6
.99885
4 09 55-45
.0728
.07274
.99735
.86175
59,6
.95885
4 ro 16.08
.0729
.07284
-99734
.85234
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 u 17.96
.0732
.07313
.99732
.86412
59,2
.99884
4 n 38.58
.0733
.07323
99731
.86472
59,1
.99883
4 II 59-21
.0734
.07333
.99731
8&53I
59,1
.99883
4 12 19.84
0.0755
0.07343
10,0
0.99730
o,7
8.86590
59,0
9.99883
o,3
4 12 40.46
.0736
07353
.99729
.86649
58,9
.99882
4 13 01.09
.0737
.07363
.99729
.86707
58,8
..99882
4 13 21.72
.0738
.07373
.99728
.86766
58,7
.99882
4 13 42-34
.0739.
.07383
93727
.86825
58,7
.99881
4 14 02.97
0.0740
0.07393
10,0
0.09726
o,7
8.85834
58,6
9.99881
0,3
4 14 23.60
.0741
.07403
.99726
.86942
58,5
.99881
4 14 44-22
.0742
.07413'
.99725
.87001
58,4
.99880
4 15 04.85
.0743
.07423
.99724
87059
58,3
.99880
4 15 25.40
-0744
07433
.99723
.87117
58,3
.99880
4 15 46.10
0.0745
0.07443
10,0
0.99723
o,7
8.87175
58,2
9-99879
0,3
4 16 06.73
,0746
07453
,99722
.87234
58,1
.99879
4 16 27.35
.0747
.07463
.99721
.87292
58,o
-99879
4 16 47.98
.0748
.07473
.99720
-87350
58,0
.99878
4 17 08. 61
.0749
.07483
.99720
.87408
57,9
.99878
4 17 29.23
0.0750
0.07493
10,0
0.99719
0,7
8.87465
57,8
0.99878
0,3
4 17 49-86"
Y. C '
f
.sinh iu
m C'
u
-[ slnh lu
J Fo
cosh in
QJ FO
10D -
M ro
tOQ OOSn IU
U
SMITHSONIAN TABLES
188
Circular Functions.
u
Bill 11
<" IV
COS U
1 F 1
loo sin
uFu '
log coa
"> F u
U
0.0751
0.07.K)
10,!
o,(]()7i<
0,7
(iH
8.87.16
57,8
9.9087.
~
^ ' ( "
.075-
'<>75'!
'. 007 17
u,r
8/S'
57,7
.9987
4 18 10.49
.075.
"75"',
, (jo/ 1 7
!87;ii}
c^'J
-997
4 18 31.11
.075.
0753
90/i(
. 8769
5/is
9!J87
4 18 51-74
4 19 12.37
0,0755
.075!
.0757
.075'
0.0754
.075",
0758.
10,0
o,007ir
.ij<)7i.
.0071.:
.01)71,
0,8
8-8775
!H7r,
!75i
57,-
57,3
57,3
57,-'
57,1
997(
.9^87)
0,3
4 19 32.99
4 19 53.62
4 20 14.25
4 20 34,87
4 20 55-50
0.07(10
.07(11
.0711.;
0.0750.
, 1 I/I K ),
,07(ll;
10,1)
o.OO/n
.9071 1
,90710
0,8
8.88{),|(
.88iM)7
57,o
57,0
-9987,
0,3
4 21 16.13
4 21 3(1.75
.o/<M
.<)7(l.!,
"7<M,
90/o<;
:S
Sfiifi
56,7
9!)(S7.
, 9()8/;
0987;
4 21 57.38
4 22 (8.00
4 22 38.63
0.0765
0.076.1,
IO.O
o.ijij^oH
0,8
8 H8i>
,-
.07(1(1
.07('7
.0708
.0/1 )Ji t
. 07* it ).
.07(17.
.0070?
.007<>l>
88-137
5o|6
50,5
t?(\ ,
i
9!$7
99^7
o,3
4 22 59.26
4 23 10.88
4 23 40.51
.0769
.0708,
.'JO/o'l
'^i)'' q :
*i^','t
-9')87_
4 24 01 , I;
5 ,4
9!w
4 24 21,76
0.0770
."77'
.077.1
.077,1
.11770,
.0771.!
.077.!-!
10,O
0,OU/0,|
90/OJ
o,R
K.HWiof
.KS!>(, U
^88775
56',T
.9087
0,3
i 24 -12.39
4 25 03.02
4 25 23,64
'1 2 s , .'1.1,27
, o//.|
.077,1.!
,00701
56io
.99870
', *! !'. , */
4 26 04.90
OiO//;i
.077"
0777
.0778
.0779
0.0771.!
"775-!
.117/0,1
.0/77-!
.07/8,1
10,0
O.lfO/IK)
. o 1 >'">07
.8,4<),|;
,8Si)(jf
.M'xi, 1 !.!
.81 1 1 K
55,9
55,9
55.8
55,7
55,6
9.99861
. yoHfif,
. yflSf it;
. f^fif 1
0,3
4 26 25.52
4 2fi .16.15
4 27 06.7*
4 27 17.40
4 27 48.03
0.0780
.0781
. i t/H.i
.o/S, t
.o;'8.|
1,07/0.!
,0/80,!
.U/NI.J
.0/>t!.!
-0/8,1.!
10,0
o.ijo^x'i
.O'XiJ.H
.00t'),|
I|)*XMJ,|
0,8
8.81(165
55,6
55,5
55,4
55,4
55,3
.99867
.1)08(17
-W8!7
o,3
4 28 08.65
4 28 29.28
4 28 ,|9-9I
4 29 TO. 53
4 29 31.16
0.07X5
'"/'Ijl-j
10,0
O,IK)69.I
o,H
H.KDMJ
55.3
).09fifi
0,3
4 29 51-79
io/8/ 1
!f I/MM
lt','}i'f t
.'tO'ilJO
;S
55, i
55, 1
iSJSS
4 30 12,41
1 30 33-04
,0780
.n/,1/..
,0>'MS,!
.ijOf>8 ( )
!%'!'5
55.0
54,9
.99865
I 30 53-67
4 31 14.29
0,071))!
.0701
.O/iJO.!
IO,0
ti,<jiji>H8
0,8
8.81)718
54.9
54.8
'iwrnj
0,3
4 31 34-02
4 31 55.55
.0/0-!
.0/)l.!
,Ov6S/
,Hi;Mj/
5>l,7
. 91^6.1
1 33 16.17
0/91
.O/'tJ,!
0703.!
.fjotWg
.8i)0,l6
54,7
. <)<,v%3
4 32 36.80
4 32 57-13
.079(1
."707
.0/.J.|,!
o/'ij'i.!
.(/Of),!
10,0
;!Jxw!
0,8
t.8'>ti')l
,tnm.\5
.IjOIOl)
5-M
54..I
- W)8'i3
.yytSf'u
0,3
4 33 18.05
4 33 3.<i8
4 33 59-31
. 1 l/<j,S
.0/07-!
O'jM*!
.90154
54,3
, 00862
4 34 19-93
07',)!)
.o/thS.1
.<>J(i8l
.{XunH
S-I.J
,<>jH6l
4 34 40,56
0.0800
.0/001
10,0
|.|>.X'^)
0,8
K.ycwfij
H.a
,098:11
o,3
4 35 01.18
U
ilnliln
I'll'
DDlh III
w Pu*
1
w Fi)'
ou cos hlii
ia F u '
u
SMITHSONIAN
Circular Functions.
u
sin u
u Fo'
CDS U
<> Fo'
ICQ sin u
u Fo'
ICQ cos u
U) Fo'
u
0.0800
0.079QI
10,0
0.99680
0,8
8.90263
54,2
9.99861
0,3
43s'oi'.'i8
.0801
.08001
.99679
.90317
54,1
.99861
4 35 21. 81
.0802
.08011
.90679
.90371
54,0
.99860
4 35 42-44
.0803
.08021
.99678
.90425
54,0
.998(10
4 36 03.06
.0804
.08031
.99677
.90479
53.9
.99859
4 36 23.69
0.0805
0.08041
10,0
0.99676
0,8
8.90533
53,8
9.908S9
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
.09858
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
.90857
4 38 48.08
.0812
,08111
.99671
.90908
53,4
.99857
4 39 08.70
.0813
.08121
.90670
.90961
53,3
.99856
4 39 29.33
.0814
.08131
.99669
.91014
53,2
.99856
4 39 49.Q6
0.0815
0.08141
10,0
0.99668
0,8
8.91068
53,2
9.99856
0,4
4 40 10.58
.0816
.081-5:
.99667
.91121
53i*
.99855
4 40 31-21
.0817
.08161
.99666
.91174
53,0
.99855
4 40 51-83
.0818
.08171
.99666
.91227
53,o
.99855
4 41 I2,,|G
.0819
.08181
.99665
.91280
52,9
.99854
4 4i 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 14-34
.0822
.08211
.99662
.91438
52,7
.90853
4 42 34-97
.0823
.08221
.99662
.QI4PI
52,7
99853
4 42 55-59
.0824
.08231
.99661
.01544
52,6
.99852
4 43 16.22
0,0825
0.08241
10,0
0.99660
0,8
8.91596
52,5
9.99852
0,4
4 43 36.85
.0826
.08251
.99659
.91649
52,5
.99852
4 43 57-47
.0827
.08261
.99658
.91701
52,4
.99851
4 44 18.10
.0828
.08271
.99657
.91753
52,3
-99851
4 44 38.73
.0829
.0828:
-99657
.91806
52,3
.99851
4 44 59-35
0.0830
0.08290
IO,O
0.99656
0,8
8.91858
52,2
9.99850
0,4
4 45 I9-98
.0831
.08300
99655
.91910
52,1
99850
4 45 40.61
.0832
.08310
.99654
.91962
52,1
.99850
4 46 01.23
-0833
.08320
.99653
.92014
52,0
.09849
4 46 21.86
.0834
.08330
.99652
.92066
52,o
.99849
4 46 42.48
0.0835
0.08340
IO,O
0.99652
0,8
8.92118
51,9
9.99848
0,4
4 47 03.11
.0836
.083-50
.99651
.92170
51,8
.99848
4 47 23.74
.0837
.08360
.99650
.92222
5i,8
.99848
4 47 44-36
.0838
.08370
.99649
.92274
5i,X
-99847
4 48 04-99
.0839
.08380
.99648
.92325
51,6
90847
4 48 25.62
0.0840
0.08390
10,0
0.99647
0,8
8.92377
5T.6
9.99847
0,4
4 48 46.24
.0841
.08400
.99647
.92428
5i,5
.99846
4 49 06.87
.0842
.08410
.99646
.92480
Sr.S
.99846
4 49 27. 50
.0843
.08420
.99645
-92531
5M
.99846
4 49 48.12
.0844
.08430
.99644
.92583
51,3
.99845
4 50 o8.75
0.0845
0.08440
10,0
0.99643
0,8
8.92634
51,3
9.99845
0,4
4 SO 29.38
.0846
.08450
.99642
.92685
51,2
-99844
4 50 50.00
-0847
.08460
.99642
.92736
51,2
.90844
4 Si 10.63
.0848
.08470
.99641
.92788
51,1
-99844
4 51 31-26
.0849
.08480
.99640
.92839
51,0
.99843
4 Si 51-88
0.0850
0.08490
10,0
0.99639
0,8
8.92890
'5i,o
9-99S43
0,4
4 52 12.51
u
-islnhlu
Fo'
cash 111
F '
, slnli iu
u Fo'
oa cosh [u
<oFo'
u
lug .
SMITHSONIAN TABLES
190
.0-853
o854
0.0855
.08(17
0,0870
.0871
.087,!
0.087';
.087*1
.0*77
0,o8M'i
.oM.%
-oHS?
o.of-too
Circulnr Functions.
0.<KJ(K>
nln u
, ( VS;1I H )
,o8;;io
,oMji,!O
<" F,,'
.
.(iHfllKJ
.ijtXi.ro
.ij"Xn I
111,0
1 ilnlitu
R,'
OOBll III
o.K
o.O
.0,150
'MO-I
.'),!< J<J
,'J.|0.|(
,o.|0of
.
.0,^07(1
OU
slnli hi
50,7
So,6
50,6
50,5
50,4
50,3
50.3
5O,i
50,0
50.0
10,5
10,5
10,.
IH.7
Fti'
0-OOH.i.
.(Mi
o,
0,4
0.4
0,4
0,4
4 52 3;
4 5* 53-7
4 53 14.3
4 53 35.0
4 53 55. o"
4 54 16'.:
4 54 36.8*
4 54 57-5
4 55 18. i
4 55 38.7
4 55 59-4
4 56 20.0
4 56 40.6
4 57 oi.ai
4 57 21.9
A 57 4^.5
4 58 03. if
4 58 23. 7<
4 58 44.4:
4 59 05.0.
4 59 25. (if
4 59 -Ki. 2*
5 oo ofi.o
5 oo a7.s
5 oo 48.17
5 oi 08.80
5 oi 20. ,|;
5 ot 50.05
5 oa 10. 6>
5 02 31.30
5 03 '12.56
5 03 33.18
5 03 53.81
S r
5 <:
5 04 55.69
5 05 16.31
5 05 36". 04
5 05 5; -57
5 06 18. 19
06 38.82
ort 50-45
07 TO. 07
S 07 40.7
5 08 01.33
5 08 21.05
18 42.58
S 09 03.21
"i 09 23 .83
TAHLCB
10 1
Circular Functions.
LI
sin u
"Fo'
COS U
u Fo'
IOQ sin u
" Fo'
lOQ COS 11
"Fu'
u
O.0900
0.08988
10,0
0.99595
0,9
S.95366
48,1
9.99824
0,4
S 09' 23'.'83
.OQOI
.O902
.0903
.0904
.08998
.09008
.09018
.09028
-99594
99593
99593
99592
.95414
954<'2
95510
.95558
48,1
48,0
48,0
47,9
.99823
.99823
.99823
.99822
5 09 44-4'J
5 io 05.09
5 10 25.71
5 10 46.34
0,0905
.0906
.090?
0.09038
.09048
.09058
10,0
0.99591
.99590
.995&>
0,9
8.95606
.95653
95701
47,9
47,8
47,8
9.99822
.(jO322
.99821
0,4
5 il 06.96
5 ir 27.59
5 u 48.22
.OQ08
.0909
.09068
.09077
.995S8
.99587
95749
95797
47,7
47,6
.99821
.9982O
5 12 08.84
5 12 29.47
0.0910
0.09087
10,0
0.99586
0,9
S.95844
47,6
9.9982O
0,4
5 12 50.10
.091 1
.00097
.99585
.95892
47,5
.99820
5 13 10.72
,0912
.09107
.09584
95939
47,5
.99819
5 U 31-35
.0913
.09117
.99584
.95987
47,4
.99819
5 13 5I-98
.0914
.09127
.995S3
.96034
47,4
.998l8
5 14 12.60
0.0915
0.09137
IO,O
0.99582
0,9
8.96081
47,3
9.99818
0,4
5 M 33-23
.0916
.09147
99S8[
.96129
47,3
.99818
5 14 53- 86
.091;
.09157
.99580
.96176
47,2
.99817
5 15 14 "(8
,0918
.09167
99579
.96223
47,2
.99817
5 i5 35-11
.0919
.09177
.99578
.96270
47,1
.99816
5 15 55-74
0.0920
0.09187
10,0
0.99577
0,9
8.96317
47J
9.99816
0,4
5 16 16.36
.0921
,09197
.99576
96365
47,0
.99816
5.16 36.99
.0922
.09207
99575
,96412
47,0
.99815
5 rf> 57-f>2
.0923
.09217
99574
.96458
46,9
.99815
5 17 18.24
.0924
.09227
99573
.96505
46,9
.99814
5 17 38. 7
0.0925
0.09237
IO,O
0.09572
0,9
8.96552
46,8
9.59814
0,4
5 17 59-49
. O(J2(J
.09247
.9957^
. 9^99
46,8
yo8r4
5 18 20 , i 2
.0027
.09257
99571
.96646
46,7
99813
5 18 4<>-75
,0928
.09267
99570
.96692
46,7
.99813
5 19 01.37
.0929
.09277
.99569
.96739
46,6
.99812
5 ip 22.00
0,0930
0.09287
10,0
0.09568
o,9
8.96786
46,6
9.99812
0,4
5 to 42.63
.0931
.09297
.99567
.96832
46,5
.9<)Sl2
5 20 03.25
.0932
.00307
.99566
.06879
46,5
.<J98ii
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
IO,O
0.99563
o,9
8.97018
46,3
9.00810
0,4
5 21 25.76
.0936
.09346
.99562
.97064
46,3
.99809
5 21 46.39
.0937
.OD356
9956i
.97110
46,2
%'8o9
5 22 07. or
.0938
.03366
9956o
.97157
46,2
.99800
5 22 27.64
.0039
.09376
99559
.97203
46,1
.99808
5 22 48,27
0.0940
0.09386
10,0
0-99559
o,9
8.97249
46,1
9.99808
0,4
5 23 08. fit)
.09.11
.09396
.99558
97295
46,0
.09807
5 23 29.52
.0942
.09406
99557
57341
46,0
.99807
5 23 50.14
.0943
.09416
.99556
.97J87
45,9
.99807
5 2-| 10.77
0944
.09426
99555
97433
45,9
.99806
5 24 31,40
0,0945
0.09436
IO,O
0.99554
0,9
8.97479
45,8
9.95806
0,4
5 24 52.02
,0946
.09446
99553
.97524
45,8
.90805
5 25 12,65
.0947
.09456
99552
97570
45,7
99805
5 25 33-28
.0948
.09466
99551
.97616
45,7
.99805
5 25 53.90
.0949
.09476
99550
.97661
45,6
.99804
5 26 14.53
0,0950
0.09486
IO,O
o. 99549
0,9
8.97707
45,6
9.09804
o,4
5 26 35.16
u
-IsinhTu
<o Fo'
cosh lu
d Fo'
. slnli iu
*> Fo'
log cosh lu
wF '
u
log
SMITHSONIAN TABLES
192
Circular Functions.
o.oitfo
-095,1
o,oo,<;5
.00;;"
O.OUflO
.out 1 1
.((Ofrfi
.(H)'>o
0.0070
.oi)7l
.(H)/*.!
007,1
.01)7,1
O.IHlK'i
.onMH
.ooSij
.000.1
o.ixjujj
09< 19
0. 1000
II
sin u
.(HJ.'iU)
ll till III
WS-W
.09511
O.OO.'UO
cnali In
< F,,'
Ion aln u
.< 17707
1,0
< I
.98070
981 15
H. 00.7,1
'W7.S-I
45,5
45,5
45,4
45.-I
45,3
15..!
I5,J
45,-'
15.1
15, "
15,1
I4.H
4-1.7
14.7
1.1.0
13.0
1.1,7
43/j
Ul!s
1.1,5
13,5
\M
.13,3
43,3
w Fo'
lOQ COS 11
W7W
9-99797
9-W795
9U79-1
O.WT
W7H8
,997^'
0.097^5
0.99783
OQOOtlllU
0,4
0,4
0,4
CU
5 s(
5 ^
5 ^
S ^
5 28
5 28
5 ''<:)
5 "0
5 3d
5 30
5 30
5 31
5 -I'
5 .11
5 3~
5 .12
5 33
5 .1.1
5 3.1
5 34
5 34
5 34
5 35
5 35
5 35
5 ,1*)
5 36
5 .lf>
5 37
5 37
5 37
538
5 38
5 ;*H
5 .19
5 39
5 39
S '!f>
5 40
5 'If
5 -M
S 41
5 42
5 4"J
5 <|2
5 43
S 43
37.04
57-ftt
18,29
38. y*
59-54
-'O. I?
40.79
01.42
21.0$
<|2.67
4-1-55
05-iH
25.81
07.0(1
27. oy
08.94
29.57
50.19
10.82
31.45
12.70
3.1-32
53-95
I-I.58
35-20
55-8.1
16.46
37-08
57-71
18.34
38.90'
59-59
20.22
oi ! 4Xi
4a.7"2
0,1-35
23-97
44.60
05-23
as. 85
S -13 4fi.48
193
Circular Functions.
II
sin u
"F '
cos u
u, Fo'
log sin u
u Fo'
lOQ COS U
"F u '
u
o.loo
0.09983
99,5
0.90500
10,0
8.90928
432,8
9.99782
4,4
S^lsVMS
.101
. 10083
99,5
.99490
10,1
9.00358
428,5
.99778
4,4
5 47 12.75
.102
.10182
99.5
.99480
1 0,2
.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 31-54
O.IOS
,I06
o. 10481
.10580
09,4
99,4
o. 99449
99439
10,5
10,6
9-02039
.02449
412,1
408,2
9.09760
.99756
4,6
4,6
6 oo 57-80
6 04 24.07
.107
.108
.10680
10779
99,4
99,4
.99428
90417
1 0,7
10,8
.02855
.03258
40/1,3
400,6
.99751
.99746
4,7
4,7
6 07 50.33
6 ii 16.60
.109
.10878
99,4
.90407
10,9
.03657
396,9
.99741
4,8
6 14 42.86
O.IIO
0.10078
99,4
0.09396
11,0
9-04052
393,2
9.99737
4,8
6 18 09.13
.in
.11077
99,4
09385
n, i
.04-143
389,6
.99732
4,8
6 21 35-39
.112
.11177
99,4
99373
11,2
.04831
386,1
.99727
4,9
6 25 01 .66
.113
.11276
99,4
.09362
ii,3
.05215
382,7
.99722
4,9
6 28 27.92
.114
.H375
99,4
99351
11,4
.05596
379,3
.99717
5,o
6 31 54-19
O.II5
O.I 1475
99,3
0-99339
ii,5
9-05974
376,0
9.99712
5,o
6 35 20.45
.116
"574
99,3
.99328
11,6
.06348
372,7
.99707
5,1
6 38 46-7-'
.117
.11673
99,3
.99316
11,7
.06719
369,5
.99702
5,r
6 42 12.98
.118
."773
99,3
.99305
11,8
.07087
366,3
.99697
5,i
6 45 39-^5
.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 3t-78
.121
. 12070
99,3
.99269
12,1
.08173
357,2
.99681
5,3
6 55 58.04
.122
.12170
99,3
.99257
12,2
.08528
354,2
,99676
5,3
6 59 24.31
.123
.12269
99,2
.99245
12,3
.08881
351,3
.99671
5,4
7 02 50.57
.124
.12368
99,2
.99232
12,4
.09231
348,4
.99665'
5,4
7 06 16.84
0.125
0.12467
99,2
0.99220
12,5
9.09578
345,6
9.99660
5,5
7 09 43-10
.126
. 12567
99,2
.99207
12,6
.09922
342,9
.99654
5,5
7 13 09-37
.127
.12666
99,2
-09195
12,7
. 10264
340,1
.99649
5,5
7 16 35.63
.128
. 12765
99,2
.99182
12,8
.10602
337,4
99643-
5,6
7 20 or .90
.i2g
.12864
99,2
.99169
12,9
.10938
334,8
.99638
5,6
7 23 28.16
0.130
o, 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
. I 1603
329,6
.99626
5,7
7 30 20.69
.132
.13162
99,1
99130
13,2
."931
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
0.09000
13,5
9.12901
319,7
9-99603
5,9
7 44 05.75
.136
.13558
99,1
.99077
13,6
13220
317,4
99597
5,9
7 47 32.01
-137
13657
99,1
.99063
13,7
13536
315,0
99591
6,0
7 50 58.28
.138
I375C
99,0
.99049
13,8
13850
312,7
.99585
6,0
7 54 24-54
.139
-:38S5
99,0
.99036
13,9
. 14162
310,4
99579
6,1
7 57 5o.8l
0.140
0.13054
99,0
0.99022
14,0
9.14471
308,2
9-99573
6,1
8 01 17.07
.141
. 14053
99,0
.99008
14,1
. 14778
306,0
.99567
6,2
8 04 43.34.
.142
.14152
99,0
.98903
14,2
15083
303,8
.99561
6,2
8 08 09. 60
-143
.14251
99,0
.98979
14,3
15385
30 1, 6
-99554
6,3
8 ii 35.87
.144
M350
99,0
.98965
14,4
.15686
299,5
.99548
6,3
8 15 02.13
0.145
0.14449
09,0
0.989SI
14,4
9- 15985
297,4
9.99542
6,3
8 18 '28,40
.146
. 14548
08,0
.98936
14,5
, 16281
295,3
99535
6,4
8 21 54.66
.147
. 14647
98,9
.98921
14,6
i6575
293,3
.99529
6,4
8 25 20. 93
.148
. 14740
98,9
.98907
M,7
.16868
291,3
.99523
6,5
8 28 47.19
.149
. 14845
98,9
.98892
14,8
-I7IS8
289,3
.99516
6,5
8 32 13.46
0.150
0.14944
98,9
0.98877
14,9
9- 17446
28714
9.99510
6,6
S 35 39-72
u
-Islnhlu
wF '
cosh lu
Fo'
. alnh lu
ta Fo'
oo cosh lu
"F '
u
log j
SMITHSONIAN TABLES
IQ4
Circular Functions.
0.150
.15"
.15-
."53
154
0.155
.150
."57
.158
.150
,ldy
.IdH
o. 170
. 171
.17.!
'73
.174
o. 175
.170
.177
.178
.170
0. itt)
.180
.187
.188
. 180
0. 100
.101
. 194
0.105
.107
. l(jH
.100
Bin n
0.14044
."5<M3
.151-1.1
0.15438
.15537
. i 5734
. H..M.S
. I'M. r/
>. ld,|.!, r i
.Idd.M
! idM-io
.I7ni7
.17115
.17700
.17805
0.17003
, I Hoot
, iSioo
.iHttMtj
. 1008.1
. loiHo
. 10,70
- 10573
MJ071
. 10700
lalnhlu
> Ft '
98,0
JN,D
98,8
OH,,
08.3
At
1)8,0
onih In
10 IV
1?,!)
19.3
10.5
10.6
10,7
19,0
loo sin u
.20701
. 2IO.I6
57' '7
-'8507
y. 30813
. ilnh In
log <-
^74,3
272,0
-f'7,
J54.5
253,0
232,1
.'20, S
2275)
217/i
215,3
ai.j,2
lOQ CCS U
.09435
W413
.90399
09354
99339
99300
9-992H
99203
.99195
.99178
.99153
99134
9,99126
logooililu
Pi,'
6,6
6,6
6,7
6,7
6,7
6,8
6,8
6,9
6,9
7.'
7,1
7,2
7,3
7,3
7,5
7,5
7.5
7,f">
7,7
7,7
7,9
7,0
7,9
8,0
8,0
8,1
8,1
8,2
8,2
8,3
8,4
8,1
8,4
8,5
8,5
8,6
8,6
8,7
8,7
8,8
8,8
8 39 05.99
8 42 3^.25
8 45 58.52
8 49 24.78
8 S2 51.04
8 56 17.31
8 59 43-57
y 03 09.84
y ofi 36.10
9 10 02,37
y 13 28.1
16 54-00
y 20 21. i(i
9 23 47.43
9 27 13.69
9 30 39-!
y 34 06.22
37 32.49
y 40 58.75
944 25.02
9 47 51.28
9 51 17-55
9 54 43.8i
y 58 10.08
10 01 36.34.
10 05 02.61
10 08 28.87
10 n 55-14
10 15 21,40
10 18 47.67
10 22 13-93
10 25 40.19
10 29 06.46
10 32 32.72
10 35 58.09
10 30 25,25
10 42 51.52
10 4ft 17.78
If) 49 44.05
10 53 iq,.
10 56 36". 58
n oo 02.84
11 03 29- II
II 06 55.37
II TO 21.6,1
n 13 47-(jo
II 17 14.17
II 20 40.43
II 24 06.70
II 27 32.96
SMITHSONIAN TABU a
195
Circular Functions.
u
. sin u
uF '
cos u
u Fo*
log sin u
" Fo'
log cos
01 Fo'
U
0.2OO
0.19867
98,0
0.08007
19,9
9.20813
214,2
9.99126
8,8
II 27 32.96
.2OI
I996o
98,0
.97987
20,O
.30027
213,1
.99117
8,8
II 30 59-23
.202
,20063
98,0
97967
20,1
.30239
212,1
,99ioS
8,9
II 34 25-49
,2O^
.2016
97,9
-97947
20,2
.30451
211,0
99099
8,9
n 37 51.76
,2Oi
.20259
97,9
.97926
20,3
.30661
209,9
.99090
9,0
ii 41 18.02
0.2O5
0.2035?
97,9
0.97906
20,4
9,30871
2O8,C
9.99081
9,0
II 44 44.29
,2O(
-^0455
97,9
.97886
20,5
-3I079
207,8
.99072
9J
u 48 10.55
.207
.20552
97,9
-97S65
20,6
.31286
206,8
.95063
9,1
u 51 36.81
.208
. 20650
97,8
.97845
20,7
.31493
205,8
.99054
9,2
n 55 03.08
.209
.20748
97,8
.97824
20,7
.31698
204,8
.9904-
9,2
u 58 29,34
0.2IO
0.20846
97,8
0.97803
20,8
9-31902
203,8
9-99035
9,3
12 OI 55.6l
.211
.230-1;
97,8
.977S2
20,9
32IOf
203,8
.99026
9,3
12 05 21.87
.212
.21042
97,3
.977^1
2I,O
.32308
201,8
9COI7
9,3
12 08 .(8, 14
.213
.21139
97,7
,97740
21,1
.32509
200,8
.99007
9,4
12 12 14.40
.214
.21237
97,7
-97719
21*2
.32709
199,8
.98998
9,4
12 15 40.67
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
.21624
07,6
.97633
21,6
.33501
196,0
.98960
9,6
12 2Q 25.73
.219
.21725
97.6
.97612
21,7
.33697
195,1
.08950
9,7
12 32 51-99
0.22O
0.21823
97,6
0-97500
2T,S
9-33891
194,2
9.98940
9,7
12 36 lS.26
.2.21
.21921
97,6
-9756S
21,9
.34085
193,3
.98931
9,8
12 39 44-52
.222
. 22Olf
97,5
.97546
22,0
.34278
192,4
.98921
9,8
12 43 10.79
.223
,22Il6
97,5
97524
22, r
.34470
191,3
.98911
9,8
12 46 37.05
.224
.22212
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
T8g,8
9.98891
9,9
12 53 29.58
.226
.22408
97,5
97457
22,4
35041
188,9
,98881
10,0
12 56 55-85
.22?
. 22^05
97,4
-97435
22,5
35229
188,0
-98S7E
10,0
13 oo 22. M
,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 O? 14.64
0.230
0.227gS
97,4
0.97367
22,8
0.35789
i85,5
9.98841
10,2
13 10 40.91
.231
.22805
97,3
97344
22,9
-35974
184,7
-98831
IO,2
13 14 07,17
.232
.22992
97,3
97321
23,0
-36158
183,8
.98821
10,3
13 17 33-44
.233
.23090
97,3
.9729S
23,1
.36342
183,0
.98810
10,3
I.I 20 59.7O
-234
.23187
97,3
-97275
23,2
-36525
182,2
.98800
10,4
13 24 25.96
0.235
0.232S4
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
2357*5
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
10,6
13 41 37-29
0.240
0.23770
97,1
0,97134
23,8
9.37603
177,5
9-CS737
10,6
13 45 03.55
.241
.23867
97,1
,97110
23,9
.37780
176,7
.98720
10,7
13 48 29.82
,242
.23064
97,i
.97086
2.|,0
37957
175,9
,98716
10,7
13 51 56-08
, -2
.24062
97,i
.97062
24,1
.38132
175,2
.98705
10,8
13 55 22.35
.244
.24150
97,o
.97038
24,2
.38307
174,4
.98694
10,8
13 58 48.61
0.245
0.24256
97,o
0.97014
24,3
9.38i8i
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
-2-17
.24450
97,0
.969!>5
24,4
.38827
172,2
.98662
11,0
14 09 07.41
.348
24547
96,9
.96941
24,5
.38959
I7i,5
.98651
11,0
14 12 33,67
.249
.24643
56,9
,96916
24,6
.39170
170,8
.98640
11,0
14 15 59-94
0.250
0.24740
96,9
0,96891
24,7
9.39341
170,1
9-9S528
11,1
14 19 26.20
u
Isinhiu
<oFo'
cosh in
F O '
,sinn iu
<a F(j'
oo cosh in
w Fo'
u
log
SMITHSONIAN TABLES
196
Circular Functions.
II
sin u
-V
COS II
.*
log sin u
-V
log pos u
co FQ'
u
0.300
0.29552
95,5
0.95534
29,6
9-47059
140,4
.98016
13,4
7 ii 19-44
301
302
303
-304
.20648
-2Q743
.29838
.29934
95,5
95,5
95,4
95,4
.95504
-95474
-95445
.95415
29,6
2o'8
29,9
.47199
47339
.47478
.47616
139,9
139,4
138,9
138,4
.08002
.97989
97975
.97962
13,5
13,5
13,6
13,6
7 H 45.71
7 18 H.97
7 21 38.24
7 25 04.50
o . 305
0.30029
95,4
0.95385
30,0
9-47755
137,9
J. 97948
13,7
7 28 30-77
3(>
307
-308
.309
.30125
.30220.
.30315
,30411
95,4
95,3
95,3
95,3
95355
.95324
95294
.95264
30,1
30,2
30,3
30,4
.47892
. 48029
.48166
.48303
137,5
I37,o
136,5
136,0
-97934
.97920
97907
.97893
13,7
13,8
13,8
13,9
7 3i 57-03
7 35 23-30
7 38 49.56
7 42 15-83
0.310
-311
.312
313
0.30506
.30601
.30696
. 30791
95,2
95,2
95,2
95,1
0.95233
.95203
.95172
PS Mi
30,5
30,6
30,7
30,8
9.48438
.48574
.48709"
.48843
135,6
134,7
134,2
9.97879
.97865
.97851
.978.17
13,9
14,0
14,0
14,1
7 45 42.09
7 49 o8.35
7 52 34-62
7 56 oo. 83
-3C4
.30887
95,1
.9S"i
30,9
.48977
133,7
.97823
14, r
7 59 27-15
0.315
.316
.317
-3T8
.319
0.30982
. 31077
.31172
.31267
.31362
95,1
95,0
95,o
95,0
95,0
0.95080
.95049
.95017
,94986
-94955
31,0
31,2
31,3
31,4
.49244
-49376
.49508
.49640
133,3
132,8
132,4
131,9
131,5
9.97809
.97795
.97780'
.97766
97752
14,2
14,2
14*2
14-3
14,3
8 02 53-41
8 05 19-68
8 09 45-94
8 13 12.21
8 16 38.47
0.320
.321
.322
.323
.324
0.31457
.31552
.31646
.31741
.31836
94,9
94,9
94,9
94,8
94,8
0.94924
.94892
.94860
.94829
94797
31,5
31,6
31,6
31,7
31,8
9-49771
.49902
.50032
.50162
. 50292
130,6
130,2
129,7
9-97737
.97723
.97709
.97694
.97679
14,4
14,4
M,5
14,5
14,6
18 20 04-74
18 23 31-00
18 26,57-27
18 30 23.53
18 33 49-8o
0.325
. 326
.327
-328
.329
0.3I93I
. 32026
.32120
-32215
.32310
94,8
94,7
94,7
94,7
94,6
0.947G5
94733
-94701
.94669
.94637
31,9
32,0
32,1
32,2
32,3
9.50421
.50550-
.50678
.50806
. 50033
128,9
128,5
128,0
127,6
127,2
9.97665
.97650
.97635
.97621
.97606
14,6
14,7
M,7
14,8
143
18 37 16.06
18 40 42.33
18 44 08.59
18 47 34.86
18 51 01.12
0.330
.331
332
-333
334
0.32404
- 32499
.3-2593
.32688
.32782
94*6
94,6
94,5
94.5
94,5
0,94604
94572
-94539
94S07
.94474
32,4
32,5
32,6
32,7
32,8
9.51060
.51187
.51313
51439
.51564
126,8
126,4
126,0
125,6
125,2
9-97591
.97576
.97561
-9754C
97531
14,9
14,9
15,0
I5,o
18 54 27-39
18 57 53.6s
ig 01 19.92
19 04 46.18
19 08 12.45
0.335
0.32877
94,4
0.94441
32,9
9.51689
124,8
9-975iC
I5,i
19 ii 38.71
.336
.32971
94,4
.94408
33,o
.51814
124,4
.97501
15,2
19 IS '04-97
337
.33066
94,4
94375
33,1
.51938
124,0
, 9748f
15,2
19 18 31.24
.338
.33160
94,3
-9-1342
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
o. 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
343
- 33537
94,2
94,2
.94209
.94175
33,5
33,6
52553
.5267,
122,0
121,6
.97409
-97394
15,5
15,5
19 35 42.56!
19 39 08.8-3
.344
- 33726
94,1
.9.1141
33,7
.52796
121,2
.97378
I5 ' 6
19 42 35-09
0.345
346
0.33820
3391*
94,1
94,1
0.9410S
.94074
33,8
33,9
0.52917
.5303'
I2O,
120,5
9.9736
9734
15,6
15,7
19 46 01.36
19 49 27.62
_ - (Ir.
347
348
349
- 3400S
.34102
.34196
94,0
94,0
94,0
.94040
,94006
93972
34,0
34,1
34,2
.53I5S
-5327B
5339
120,1
119,7
119,3
.9733
9731
9730
15,7
15,8
15,8
19 52 53.89
19 $6 20. 15
19 59 46.42
0.350
0.34290
93.9
0.93937
34,3
0.5351C
119,0
9.9728
15,9
20 03 12. 6E
u
-Islnhhl
.
oosli iii
.
sinh i
uFo'
lOQCOSll
.w
u
00 '
SMITHSONIAN TABLES
Circular Functions,
0.350
0.355
,35"
.357
350
O..VJS
3<X>
nlii u
34<>"5
0,3(11(1.)
-3'MI"
0.3(1(1,7
1 slnh In
U.I'J'M
COlll III
PII' log Bin u
54310
54457
55 MX
.50,|i)l
,;;()( 10
lif '7 10
57M5
lo U
8ltlil
1 10,0
1 18,6
"17,5
117,2
1 16,1
"5,7
113,0
nalj
100,4
H)9,ll
"'7,5
105,7
HM|K
104,2
103,0
102,7
|0[| OU3 U
'17155
.07106
.1)7074
.#'7.1-1
.96716
Fo'
15,9
'5,9
1 6,0
16,0
1 6, i
16,1
ifo
16,5
i6,5
1 6,7
16,7
17,0
17,0
17,1
I?,'
IW
17,^
17.3
17,3
17.4
17,4
17,5
"7,5
17.6
"7,7
17,0
i!b
18,3
18,3
20 03 12.<)8
20 <>:> 38.95
jo 10 05. a i
20 13 31.48
20 16 57-74
20 20 24.0T
2O 23 50.27
20 27 16.54
20 30 42.80
20 34 09.07
*n 37 35-33
20 41 01. ()0
20 44 27. 86
20 47 54.12
20 51 20.39
20 54 46.65
20 58 12,92
21 01 30.l8
21 05 05-45
21 ()8 31.71
21 II 57.08
21 15 24.24
l8 50.51
22 r6,77
25 43,04
20 00.30
,13 35-57
3d 01.83
39 28.10
21 42 54.36
21 46 20,63
21 <|() .|6.89
21 53 13.16
21 56 39,42
22 00 05. (M)
17,6 122 03 31.05
22 <>6 58. 2i
22 JO 24,48
32 13 50.74
22 17 17.01
22 20 ,|3.27
22 24 09-54
22 27 35-80
^2 31 02.07
22 34 28.33
22 37 5-1-60
22 41 20.86
2ii 4!* 13-30
22 51 39.66
22 55 05.93
BMITHBOHIAH
Circular Functions,
11
sin u
ta F u '
COS 11
la Fo'
loo sin u
*> Ft/
log cos 11
<u F u '
11
0.400
o. 38942
92,1
0.92106
38,9
0-59042
102,7
9.96429
18,4
2255'o5''y2
.401
300.14
92,1
.92067
39,o
.59144
\O2,4
.96410
18,4
22 58 32-19
,402
.39126
92,0
.92028
39,1
- 59247
102,2
.96392
18,5
23 oi 58.45
.403
392 r8
92,0
.91089
39,2
59349
101,9
.963X4
18,5
23 05 24.72
.404
-39310
91,9
,91950
39,3
. 59450
ioi,6
.96355
18,6
23 OS 50.98
0.405
0,39402
91,9
0.91910
39,4
9 -59552
101,3
9.9t>336
18,6
23 12 17.25
. 40(1
. 39404
01,9
.91871
39.5
- 59653
101,0
.03iS
18,7
23 15 43-Si
407
.39586
91,8
.91831
39,6
- 59754
TOQ,7
.96299
18,7
23 19 09-78
.408
.39&T7
91,8
.91792
39,7
-50854
100,5
.96280
18,8
23 22 36.04
,409
.397&>
9i,8
.91752
39,8
5C955
100,2
.96262
18,8
23 26 02.31
0,410
o,39S5i
91,7
0.91712
39,9
9,60055
99,9
9.96243
iS.g
23 29 28.57
.411
39953
9',7
.91672
40,0
60155
99,6
,96224
1 8,y
23 32 54-84
.412
..10044
91,6
,91632
40,0
.60254
99,4
.96205
19,0
23 36 21.10
.413
,40136
91,6
.91592
40,1
.60353
99, r
.9:1186
19,0
23 39 47.36
.414
. 40227
91,6
.91552
40,2
.60.152
98,8
.96167
it), i
23 43 13-63
0,415
0.40310
91,5
0.91512
40,3
9.C055I
98,6
9.96148
IQ,I
23 46 39.89
,416
.40410
9L5
9I47I
40,4
.60649
98,3
.96128
19,2
23 50 00. 16
.417
,418
. 40502
-40593
91.4
9M
.91431
.91390
40,5
40,6
. 60748
.60845
9S,o
97,8
.96109
.96090
19,2
19.3
23 53 32.42
23 56 58.69
419
.40685
91,3
9USO
40,7
60943
97,5
,96071
19,3
24 00 24.95
0.420
o . 40776
91,3
0.91309
40,8
9.61041
97,3
9.96051
19,4
24 03 51-22
.421
.40867
0ii3
.91268
40,9
,61138
97,o
. 06032
19,4
24 07 17.48
.422
.40959
91,2
,91227
41,0
.61234
&5,7
.96012
19,5
24 10 43-75
4-'3
.41050
91,2
.91185
41,0
.6:331
9(i,S
95993
19,6
24 14 io. oi
f n
,424
.41141
91,1
.91M5
41,1
.61427
96,2
95973
19,6
24 17 36,28
0.425
0.4123-2
Oi.i
0,91104
41,2
9.61524
96,0
9-95954
lf>,7
24 21 02.54
.426
41323
91, i
. 91063
41,3
.61619
95,7
95934
19,7
24 24 28.81
.427
.41414
g 1,0
.91021
41,4
.61715
95,5
.95914
19,8
24 27 55.07
.428
41505
9r,o
.90980
41,5
.6lS TO
95,2
95894
T0,
24 31 21.34
.429
.41590
90,9
.90938
41,6
.61905
W,9
.95875
iy,9
24 34 47.60
0.430
0,41687
90,9
0.90897
41,7
g.62OOO
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
Co,8
.90813
4L9
.62189
94,2
.95815
20,0
24 45 06.40
433
.419(10
90,8
.90771
42,0
.622&3
94,0
.95795
20, i
24 48 32.66
"134
.42050
90,7
.90729
42,1
.62377
93,7
95775
20,1
24 Si 58.93
0.43S
0.42141
90,7
o. 90(187
42,1
9.62471
93,5
9.95755
20,2
24 55 25.19
.43(1
.42232
90,6
.90645
42,2
.62564
93,2
95734
20,2
24 58 5I-46
--I37
. 42,122
90,6
, yo(io3
42,3
.62657
93,0
-957M
20,3
25 02 17.72
.438
,42413
90,6
. 90560
42,4
.62750
92,8
.95694
20,3
25 05 43-99
439
.42503
90,5
,90518
42,5
,628-|2
92,5
.95673
20,4
25 oy 10.25
0.440
0.42594
90,5
0.90475
42,6
9.^2935
92,2
9,95653
20,4
25 12 36-51
441
. 42084
yo, 4
.90433
42,7
.63O27
92,0
.95632
20,5
25 16 02.78
.442
.42775
00,4
, 90390
42,8
.63119
9i,8
.95612
20,6
25 19 29.04
443
.438(15
90,3
.90347
42,9
.63310
91.5
-95591
20,6
25 22 55.31
44*
.42956
90,3
,90304
43,0
.63302
01,3
-95571
20,7
25 25 21.57!
0.445
0.43046
00,3
0,90261
43.0
0.63393
9M
9-95550
2O,7
25 29 47.84
r
44"
.43136
90,2
.90218
43,1
.63484
90,8
,95529
20,8
25 33 14.10
.447
,43226
00,2
.00175
43,2
v63'575
90,6
-95509
20,8
25 36 40.37
.448
.43316"
90,1
.90132
43,3
.63665
90,4
.65488
20,9
25 40 06,63
449
.43406
90,1
.90088
43,4
.63755
90,1
954(57
20,9
25 43 32.90
0.450
0.43497
9O,O
0.900.15
43,5
9.63845
89,9
9.95446
21,0
25 4^ 59 -16
u
-lilnhlu
w Fo'
oosh In
*iF '
. alnli ill
w Fo'
loaooah lu
*>Fo'
u
100 i
SMITHSOMAM TABLES
2OO
Circular Functions.
87.J
7,n
85,7
H5,5
H'l!7
8-1,4
H|,:J
8.1,0
8,1,8
Hi/
Hi,,
80.'
Ho,.
Ho.,
Mo,
70,
70,
71),
0[] CDS 11
05'1'l'i
542S
05310
.1)527''
05255
05-!'-!
051-17
-05050
05<>37
.04MI.1
-04071
.01010
.040.7
O-lH.17
.<H7iH)
04717
.04055
.04033
.0.1517
'M/1417
.0143.1
,1)4100
.0437<>
21,0
lOQCOSlllll
a 1, 5
a 1,7
2,0
25 50 25.43
35 53 5t.'*J
25 57 I7-0(>
2() oo 44.22
26 04 10-40
26 07 30-75
2() 1! O3.0-'
2(j 14 aj.28
2(1 17 55-55
2(1 21 31.81
2() 28 14.34
,1,1
J3.3
23,3
A3,4
26 35 Oli.H?
2(i 3^ 33-13
26 41 50-4"
2,'i 45 25. 66
20 48 5' -1)3
2(1 5J i8.nj
2( 55 4-1-40
26 50 10.72
^7 02 36. 09
27 o(i 03.25
27 oy ay. 52
^7 i^ 55.78
27 id 22,05
27 10 48.31
J7 -'3 14.58
27 !{') 40.81
.17 311 07. it
-!7 33 33-37
27 3 fl 50. ''4
27 43 siM?
27 47 18.4,1
J7 5" .t-l-70
27 54 10. y!>
27 57 37-23
28 oi 03.40
28 07 5<>.oa
AS n 22.28
28 14 4-55
28 iH 14.81
28 21 41.08
.;K J5 07-34
28 28 33/11
28 31 5!) "
28 35 af.M
28 38 52.40
OMITHVONIAN TADLKB
201
Circular Functions.
,
u
sin ii
" Fu '
COS II
01 FO'
loo sin u
<0 Fo'
lOO CDS II
F U '
u
0.500
0.47043
87,8
0.87758
47,9
9.68072
79,5
0-94329
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
.94281
23,8
28 45 44-93
503
.48206
87,6
.87614
48,2
.68310
7^9
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
24,0
28 56 03-73
.506
.48468
87,5
.87469
48,5
.68546
78,4
.94185
24,1
28 59 29.99
507
.48556
87,4
.87421
48,6
.68624
78,2
.94161
24,1
29 02 56.26
.508
.48643
87,4
.87372
48,6
.68702
78,0
94137
24,2
29 06 22.52
509
.48730
87,3
.87323
48,7
.68780
77,8
94II3
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
. 94O54
24,3
29 16 41-32
512
.48992
87,2
.87177
49,0
.69013
77,3
.94040
24,4
29 20 07.58
.513
.49079
87,1
.87128
49J
.69090
.94016
24,5
29 23 33.85
.514
,49166
87,1
.87078
49,2
.69167
76i9
93991
24,5
29 27 oo.ii
0.515
0.49253
87,0
0.87029
49,3
9.69244
767
9.93967
24,6
29 30 26.38
.516
.49340
87,0
.86980
49,3
.69320
76,6
93942
24,6
29 33 52.64
5'7
.49427
86,9
.86931
49,4
.69397
76,4
93917
24,7
29 37 18.90
.518
-49514
86,9
.86881
49,5
69473
76,2
93893
24,8
29 40 45-17
.519
.49601
86,8
.86832
49,6
.69549
76,0
.93868
24,8
29 44 11-43
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
9.70002
75,0
9.93718
25,2
30 04 49.02
.526
. 50208
86,5
.86482
50,2
.70077.
74,8
.93693
25,2
30 08 15.29
.527
-50294
86,4
.86432
50,3
.70152
74,6
.93667
25,3
30 it 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- 9359J
25,4
30 22 00.35
.531
.50640
86,2
.86230
50,6
.70449
74,o
.93566
25,5
30 25 26.61
532
.50726
86,2
.86179
50,7
.70523
73,8
93540
25,6
30 28 52.88
-533
.50812
86,1
,86129
50,8
.70597
73,6
.93515
.25,6
30 32 19.14
534
.50898
86,1
.86078
50,9
.70670
73,4
.93489
25,7
30 35 45-41
0.535
0.50984
86,0
0.86027
5i,o
9.70743
73,3
9.93463
25,7
30 39 11-67
.536
.51070
86,0
.85976
51, *
.70817
73,1
93438
25,8
30 42 37.941
S37
.51156
85,9
85925
51,2
.70890
72,9
.93412
25,9
30 46 04,20
.538
.51242
85.9
.85874
51,2
. 70963
72,8
.93386
25,9
30 49 30.47
539
51328
85,8
,85822
51,3
.71035
72,6
.93360
26,0
30 53 56-73
0.540
0.51414
85,8
0.85771
51,4
9.71108
72,5
9-93334
26,0
30 56 23.00
541
.51499
85,7
.85719
5i,S
.71180
72,3
.93308
26,1
30 59 49.26
.542
.51585
85,7
.85668
51,6
.71252
72,1
.93282
26,2
3T 03 15.52
543
.51671
85,6
.85616
51.7
.71324
72,0
93256
26,2
31 ofi 41-79
544
.51756
85,6
.85565
5i,8
.71396
71,8
.93229
26,3
31 10 08.05
0-545
0.51842
85,5
0.85513
5r,8
9.71468
71,6
9.93203
26,3
31 13 34-32
.546
.51927
85,5
.85461
5i,9
-71540
7i,5
.93177
26,4
3: 17 00,58
.547
52013
85,4
.85409
52,0
.71611
.93150
26,4
31 20 26.85
.548
.52098
85,4
.85357
52,1
.71682
71,2
.93124
26,5
31 23 53.11
549
.52183
85,3
.85305
52,2
-71753
71,0
.93097
26,6
31 27 19-38
0.550
0.52269
85,3
0,85252
52,3
9,71824
70,8
0.93071
26,6
31 30 45.64
u
1 slnh In
F'
003 h lit
<oF '
. ilnh In
.Fo'
QQOOShlU
"Fo'
u
luu -
SMITHSONIAN TABLES
2O2
Circular Functions.
u
sin u
Fo'
cos u
w Fo'
Ion sin u
w Fu'
log cos u
U) Fo'
u
0.550
0,52269
85,3
0.85252
52,3
9.71824
70,8
9.93071
26,6
31 "30' 45?04
.551
.52354
85,2
.85200
52,4
.71895
70,7
.93044
26,7
31 34 11.91
.552
52439
85,1
.85148
52,4
.71956
70,5
.93017
26,7
31 37 38.17
553
.52524
85, 1
.85095
52,5
.72036
70,4
.92991
26,8
31 41 04-44
554
.52609
85,0
85043
52,6
.72106
70,2
.92964
26,9
31 44 30.70
0-555
o . 52694
85,0
0.84990
52,7
9.72176
70,0
9.92937
26,9
31 47 56.97
.556
.52779
84,9
84937
52,8
.72246
69,9
.92910
27,0
31 51 23.23
557
.52864
84,9
.84884
52,9
.72316
69,7
.92883
27,0
31 54 49-50
-558
- 52949
84,8
.84832
52,9
72.386
69,6
.92856
27,1
31 58 15-76
-559
53034
84,8
.84779
53,o
.72455
69,4
.92829
27,2
32 01 42.03
0.560
0.53119
84,7
0.84726
53,1
9.72525
69,3
9.92801
27,2
32 05 08.29
-56i
.53203
84,7
.84672
53,2
72594
69.1
.92774
27,3
32 08 34-56
. 563
.53288
84,6
.84619
53,3
.72663
69,0
92747
27,3
32 12 00.82
.563
53373
84,6
.84566
53,4
.72732
68,8
.92719
27,4
32 15 27.09
.564
53457
84,5
.84512
53,5
.72801
68,7
.92692
27,5
32 18 53-35
0.565
0.53542
84,5
0.84459
53,5
9.72869
68.5
9-92665
27,5
32 22 19.62
.5(i(>
. .53^26
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
5<X)
.53879
84,3
.84244
53,9
73142
67,9
92554
27,8
32 36 04.67
0.570
0.53953
84,2
0.84190
54,0
9.73210
67,8
9.92526
27,8
32 39 30.94
-571
.54047
84,1
.84136
54,0
.73277
67,6
.92498
27,9
32 42 57.20
.572
.54131
84,1
.84082
54,1
73345
67,5
.92470
28,0
32 46 23-47
573
.54216
84,0
.84028
54,2
.73412
67,3
.92442
28,0
32 49 49-73
574
54300
84,0
.83974
54,3
.7348o
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
.57(1
54467
83,9
.83865
54,5
.736:4
66,9
92358
28,2
33 oo 08.53
-577
54551
83,8
.83810
54,6
.73680
66,7
.92330
28,3
33 03 34-79
.578
.54635
83,8
.83756
54,6
73747
66,6
.92301
28,3
33 07 01. 06
579
54719
83,7
,83701
54,7
.73814
66,4
-92273
28,4
33 10 27.32
0.580
0.54802
83,6
0.83646
54,8
9.73880
66,3
9-92245
28,5
33 13 53-59
SHi
.54886
83,6
.83591
54,9
.73946
66,2
.92216
28,5
33 17 I9-85
.582
.54970
83,5
.83536
55,0
.74012
66,0
.92188
28,6
33 20 46.12
.583
.55053
83,5
.83481
55, r
.74078
65,9
.92159
28,6
33 24 12.38
.584
55137
83,4
.83426
55,i
74144
65,7
.92130
28,7
33 2? 38.65
0.585
0.55220
83,4
0.83371
55,2
9.74210
65,6
9.92102
28,8
33 31 04.91
.1K6
55303
83,3
.83316
55,3
74275
65,4
.92073
28,8
33 34 31 18
-587
.55387
83,3
.83261
55,4
74340
65,3
.92044
28,9
33 37 57-44
.588
55470
83,2
.83205
S5.S
.74406
65,1
92015
29,0
33 41 23.71
-589
55553
83,1
.83150
55,6
.74471
65,0
.91986
29,0
33 44 49-97
0.590
0.55636
83,1
0.83094
55,6
9.74536
64,9
9.9I957
29,1
33 48 16,24
SOi
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
29,2
33 55 o8.77
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
0.5(1051
82,8
0.82815
S6,r
9.748S8
64,2
9.91811
29,4
34 05 27.56
.59f>
56134
82,8
.82759
56,i
.74922
64,0
.91781
29,5
34 08 53.82
597
.56216
82,7
.82703
5<>,2
.74986
63,9
.91752
29,5
34 12 20.09
.598
.56299
82,6
.82646
56,3
.75050
63,8
.91722
29,6
34 IS 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
9.75I77
63,5
9.91663
29,7
34 22 38.88
u
-Islnhlu
wFo'
cosh In
"Fo'
i, n !n.h.L
log j
Fa'
lagaoshl
ta FQ'
u
SMITHSONIAN TABLES
203
Circular Functions.
II
sin u
-W
DOB II
.*
loa sin u
P '
loo cou u
(''
u
o . (>oo
0.56464
82,5
0.82534
5* '.5
9.75177
03,5
y.ynfM
-=9.7
.M" J . ! < . I :.SH
.601
5' '5-1 7
U ,
,H2."|77
5'>,5
7 5 -'4 '
('3.3
.91033
20,8
3-1 J" 05.15
.6oj
, S6(i-'ij
82,4
,82420
50,( i
75301
63.-!
.Ol'l,|
2 1.8
,14 -!9 31.41
.603
,5(17 1 2
o 1 .
.81*364
56.7
7S3'>7
(M.I
-01574
20,9
,11 ,12 57.'8
.604
HJ.3
.82307
56,8
.75-130
049
yis.M
30,0
31 36 23-U-l
0.605
0.56876
8J,3
0.82250
5' ',9
9-75-I93
<.!,8
9.91514
30,0
3-1 30 50.21
.6o!>
. S6058
82,2
,82193
57."
75550
6J.7
.1)1484
30,1
34 43 16.47
.(107
57*1-1 1
U j .
.821311
57,0
./50i8
6J.5
9I-1.H4
30,2
3-1 46 42.74
,<ioH
57145
H2, I
.82079
57.1
./56Hi
64-4
.01441
311,2
.14 50 no. on
.6oj)
.57~'05
KJ,O
,82022
57,-!
757-13
('4-3
fJl.103
30,3
34 53 35 .-7
0,610
0.<J7287
8j,o
0.81965
57,3
9.75H05
(12,1
0-*M3'i3
30,4
34 57 01.53
.(ill
.571(19
8 1,0
, 8 1 (j< 17
57.4
.758117
(u,o
.0133-'
30,4
35 "0 27-80
57451
8 1,9
.81850
57,5
-750.I9
61,0
.01,10.!
,10.5
35 03 5.|.(Hi
!<>I3
.5753-!
8 1,8
.81793
57,5
.75' Xli
dl,7
.01-71
.10.5
35 07 20.33
.614
57' "4.
81,7
.81735
57,6
.76053
61,0
..JI241
30,6
35 "0 40.59
0.615
0.57(106
81,7
o. H 1(177
57,7
9.76114
6 1,5
O.OI2IO
30.7
35 I 1 12.86
.616
57778
.Hiliji)
57.S
,76170
6iM
.01 179
30,7
35 "7 ,(0.12
.617
.57859
Hi!(i
.Hi 5(1-'
57,9
7' '41 7
(n, J
.01 l.|9
30,8
35 -H 05.39
.618
579-1'
8 1,5
.HI 504
57.9
7'iji)8
61,1
.01 1 18
30,0
35 --'4 3'A'i
.610
. 58022
HIM
58,0
7' '359
61,0
.01087
3".0
3.'i -'/' r>7.!JJ
0.620
0.58104
HIM
0,81388
tf l
i;. 76,1^0
6o,H
9.0IO5(i
3i,o
35 31 24.18
.(121
.58185
81330
5H.2
.76481
(xi.7
.91025
.I','
35 34 .10.44
,6.:2
. ^82(16
HU
.Hu7i
58.3
7654-!
(10,0
.'JIHiOl
3".i
35 38 10,71
623
58347
8 1,2
.HUM
58,3
60, \
.'fii9'3
3',.!
.15 4" -I-'- 97
6 ' i
8l,:i
.HI 155
vA i
. /(i(/H
do i
'X'9 J I
.11,3
Ci 45 09.24
0,625
0.58510
Hi, I
o.HioiXi
5H.5
9.76/41
00, J
o.i;mj!K)
31,3
35 4H 35-50
. 626
.5851)!
Hi,o
.81038
58,* i
.76783
60, 1
,91)8(19
3M
35 5-' 01.77
,6'>7
-Ul'.pj ]
Hi,n
. 8tx 170
r8 "
7' iH 1 !
[(i 1 1
.1)0837
1 1 "
35 5:i 28. 03
'"/
.628
'" t )87<n
,8uo2i)
i;88
,7(K)Ol
VJ,8
. it )Ki )( i
lli ! i
35 58 54.30
'58834
Holy
JjHiH
-76963
50,7
.90774
3I.'
311 02 20.56
0,630
0.5H9I4
80,8
0.80803
58,0
9.770-!.!
50,0
0.00743
3'. 7
36 05 40,83
.631
. 5Htl95
80,7
.80744
50|O
.7/08,1
50,4
.00711
31,7
3 (l 09 13.09
.5007f)
8o,7
.801185
59, l
.7/141
50,3
.011(179
31.8
,1*' 12 39.36
Xu
59157
80,6
.8062(1
59, *!
./7.?oo
59, J
.0!I'>17
3 ' .9
36 |I< 05. (i.;
.63-1
.59417
8o,(i
.8056(1
50,4
7/.J59
50. l
. i H H 1 1 5
31.0
3 ( > 10 31.89
0.635
0.59318
80,5
0.80507
5'), 3
9-773'H
iH.o
9.90583
3.!,o
30 .!.! 58, 15
A-6
.59398
Ho,4
.80148
S9,4.
77377
S8.8
005,'il
3-M
.10 Jl. J.|,.|J
637
59-179
Ho,.|
. 80388
.10,5
7743 ; '
58.7
.')O,~)IO
32, 1
,(0 ,;o ;\o,o8
638
59559
Ho,3
. 803.10
59,"
77405
58,0
.1^0,187
12 .!
3" 33 I". 95
639
59639
80,3
.Ho.il 19
:i9,6
-77553
5H.S
yn-iss
343
30 30 43..!!
0.640
0.597-'(>
80,2
0.80210
59,7
0.776U
SH..1
9.90441
3-!, 3
30 40 09,48
.1.41
. 50800
80, 1
.80150
59,
.771.70
58,2
.90300
344
.(6 43 35.7-1
.642
.59880
Ho, I
.80090
50,9
. 77728
58,1
90358
.145
,10 47 oj.oi
.643
. 50')(io
80,0
.80030
60,0
.777-86
58,0
. 003.15
34-5
31 1 50 2H,^7
.644
,60040
Ho,o
79970
(io.o
778-M
57,H
.90293
346
3" ?3 S-l-5-1
0,645
o. (in 120
79,0
0.700TO
60, 1
9.7790.:
57,7
0.002U)
34"
36 57 20. Hii
.64(1
,60.200
79,8
.79850
do.j
77959
,|)tl227
32.7
.17 (Hi 47,06
.647
.60280
79,8
.70701-
60,3
,78017
57,5
,I.)OT05
37 04 13. .13
A|H
.(10350
79,7
.797-!')
00,(|
.78074
57M
.OOl'ij
34^9
37 07 39-. S')
.6.|9
60439
79,7
, 71/1(10
60M
7813-!
57.-
.IJOI2()
3-'.!t
37 II 05.8(1
0,650
o, (10519
Tftfi
0.70608
Co,5
9-7.H9
57,1
""'
33.'
37 M 3 J.I 2
u
-lalnlilu
-IV
oosh lu
.-V
, OB !!!>jU8
.W
lOBOOllllll
.w
u
BMITHOONIAN TAHLKS
204
Circular Functions.
-<>54
O.'J'M)
Jrfi.i
o.frfi.1
.(if 7
O.dKo
.081
O,d8,'i
(UnjO
.(MJI
.(if).!
sin n
.'10837
O , ( i( K 1 I (.
.(U7N5
.hi. So.*
.(1104.!
.'M.1.1S
IOQ sin u
7X50;i
o- 77-14 J
.7737'J
.7731.1
I ulnli In '< IV coh In " IV
lii.7
lii, H
f'.l.X
(1,|,n
r.4,1
.HOOI I
(>. 80II8
.80330
.Hi KM/.
iHiMHi
57,1
5'', 5
5' i, i
5(1,0
55,8
55.7.
55,0
55,5
55,0
54,5
5-I.-I
5-1.3
5-1, '
5.1.0
53,5
53,4
53,3
S3,-'
53,1
51,0
5 "I?
SI/'
Ion coa u
.1x11130
.HHHu
HHHjd
.HS755
Oflcoslilu <" F/
*> Fo'
3.1.0
3.1,1
33,4
33,4
33,5
,13,7
33,8
33,8
33.9
34,0
34,1
34, i
3- 1, '2
34,3
34,3
34,4
34,5
3.1,5
34,7
34,8
34.9
35,0
35,0
35,1
35,-'
35,3
35,3
35,4
35,5
35,(>
!is!7
35,9
3d',o
37 i? 58.39
37 24 50. i)a
37 -8 17.18
37 31 43-45
37 35 WJ.7I
37 38 35.t;8
37 42 02.24
37 45 2H.5I
37 48 54-77
37 52 21.04
37 55 47.30
37 59 '3-57
38 03 3y. 83
38 ofi 0(1 . iq
38 Of> 32.36
38 12 58.(>3
38 id 24. 8y
38 19 51.16
38 23 17.42
38 af> 43. (18
38 30 (X>.<J5
38 37 02.48'
38 40 1-8.74
3 43 55-01
38 47 a 1. 27
38 50 47-54
38 57 40.07
39 01 0(1.33
39 o.j 32,{}q
39 07 58.80'
39 U 25.13
3!) 14 51-39
39 18 17. (id*
39 21 43-92
39 i-'S 10. HJ
39 nH 3d. 45
39 3^ 02.72
39 38 55-25
3U 4a a i. 5 i
3945 47.78
39 49 14.04
39 53 .K'-.H
.19 5d Oil. 57
39 59 32.83
|o oj 50. ro
|o of) 25.;
TAIILKS
Circular Functions.
u
sin u
F</
cos u
in Fo'
loo sin u
Fo'
loo cos u
F '
u
0,700
.701
0.64422
.6-1498
76,5
76,4
0.76484
. 76420
64,4
64,5
9.80903
-80955
51,6
51,5
9.88357
.88321
36,6
36,7
40 06 25.36
40 09 5I.63
.702
703
.64575
.64651
76,4
7^,3
.76355
,76291
64,6
<>4,7
,81006
.81057
91.4
5i,2
.88284
.88247
36,7
36,8
40 13 17.89
40 16 44 - J 6
.704
.6472?
76,2
. 76226
64,7
.81109
Si.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
.76006
64,9
.81211
50,9
.88136
37,0
40 27 02.95
.707
- 64956
76,O
.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
So,6
.88025
37,3
40 37 21.75
0.710
0.65183
75,S
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
.713
-65335
-654'T
75,7
75.6
.75706
.75640
65,3
65,4
.81515
.81565
50,3
50,2
.87913
.87875
37,5
37,6
40 47 40-54
40 51 06. 81
.714
.65486
75,6
.75575
65,5
.81615
50,i
.87838
37,6
40 54 33.07
0.715
o. 65562
75,5
0.75509
65,6
9-81665
50,0
9.87800
37,7
40 57 59-34
.716
.65637
75,4
75444
65,6
.81715
49,9
.87762
37,8
41 01 25.60
.717
.65713
75,4
75378
65,7
.81765
49,8
.87724
37,9
41 04 5T.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
0.75i8r
65,9
9.81914
49,5
9.87611
38,t
41 15 10.65
.721
.66014
75,i
75"S
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
7S,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
o .66314
74,8
0.74850
66,3
9.82160
49,o
9.87419
38,5
4T 32 2I.Q8
.726
.66388
74,8
.74784
66,4
.82203
48,9
.8738:
38,6
41 35 48.25
.727
.66463
74,7
74717 .
66,5
.82258
48,8
.87342
38,6
41 39 14.51
.728
.729
.66538
,66612
74,7
74,6
.74651
.74584
66,5
66,6
.82307
.82356
48,7
48,6
.87303
.87265
38,7
38,8
41 42 40.78
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
39,0
41 56 25.84
-733
.66910
74,3
74317
66,9
.82549
48,2
.87109
39.1
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, T
9.82646
48,0
9-87030
39,3
42 06 44.63
.736
.6713-3
74,i
.74116
67,1
.82694
47,9
,86ogi
39,3
42 10 10.90
-737
.67207
74,o
.74049
67,2
.82741
47,9.
.86952
39,4
42 13 37-16
73S
.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
.742
.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
40,0
42 37 41.02
.0-745
o. 67797
73,5
0.73509
67,8
9.83121
47,i
9-86634
40,0
42 41 '07. 28
-746
.67871
73,4
73441
67,9
.83168
47-0
.86594
40,1
42 44 33.55
747
.67944
73,4
-73373
67,9
.832:5
46,9
.85554
40,2
42 47 '59-81
-748
.68017
73,3
73305
68,0
.83262
46,8
.86513
40,3
42 51 26.08
-749
,68091
73.2
.73237
68,1
.83309
46,7
.86473
40,4'
42 54 52.34
0.750
0.68164
73.2
0.73169
68,2
9.83355
46,6
9-86433
40,5
42 58 18.60
u
-Istnhlu
W
cosh ill
Fo'
| nn sinhl
ui Fo'
log cosh iu
wF</
j
ion- j
SMITHSONIAN TABLES
2O6
Circular Functions.
SMITHIONIAN
Circular Functions.
u
s\n u
.*
COS II
.*
. IOQ sin i
tu Fo'
lOQ COS 1
- W
u
O.SDO
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
.85616
42,1
.84260
4 4,8
45 53 3H.H
.802
.71875
69,5
.69527
71,9
.85658
42,0
.84215
44,9
45 57 04-37
.803
-7194^
69,5
60455
71,9
.85700
41,9
.84170
45,o
46 oo 30.64
.804
69,4
.69383
72,0
.85742
41,8
,84125
45,1
46 03 56.90
0.805
0,72083
69,3
0.69311
72,1
9.85783
4i,a
0.84080
45,2
46 07 23, 17
.SoG
.72152
69,2
.69239
72,2
.85825
41,7
.84035
45,3
46 10 40.4.1
.807
. 72222
69,2
.69167
72,2
.85867
41,6
.8,-jcjoo
45,3
46 14 15.70
.808
.72291
6y,i
.69095
72,3
.85908
41,5
839-14
45,4
t\ft 17 41 .06
.809
.72360
69,0
.69022
72,4
.85950
4M
.83899
45,5
46 21 08.23
0,810
0.7242^
6S,o
0.68950
72,4
9.859yi
41,3
9-83853
45,6
46 24 34-49
,811
.72498
68,9
.68877
72,5
,86032
4L3
.83808
45,7
46 28 00.76
.812
. 72566
68.8
,68805
72,6
.86074
41,2
.83762
45,
46 31 27.02
.813
72635
68,7
.68732
72,6
.86115
41,1
.83716
45,9
4" 34 53 -2<J
,814
.72704
68,7
.68660
72,7
.86156
41,0
,83670
46,0
-|fi 38 19-55
0.815
0.72773
68,6
0.68587
72,8
9.86197
40,9
9.83624
46,1
46 41 45.82
.816
.72841
68,5
.68514
72,8
,86238
40,8
.83578
46,2
46 45 12.08
.817
.72910
68,4
.68441
72,9
.86278
40,8
.83532
'|6,3
464838.35
.818
.72978
68,4
.68368
73,0
.86319
40,7
-83-185
46,4
46 52 04.61
.819
.73046
68,3
.68295
73,o
.86360
40,6
.83439
40,5
46 55 30.88
0,820
0,731115
68.2
0.68222
73,i
9.86400
40,5
9.83393
46,5
46 58 57.14
.821
.73183
68,1
.68149
73,2
.86441
40,4
.83346
4,6
47 02 33.41
.822
.73251
68,r
.68076
73,3
.86481
40,4
83299
46,7
47 05 4<;.<>7
.823
.73319
68,0
.68002
73,3
.86522
40,3
83252
46,8
47 oy 15*94
.824
.73387
67,9
.67929
73,4
.86562
40,3
. 83206
4.6,9
47 12 42.20
0.82.5
0.73455
67,9
0.67856
73,5
0. 8C602
40,1
9.83159
47,0
47 16 08.47
.826
73523
67,8
.67782
73,5
! 8664 a
40,0
,83112
47,1
47 19 34-73
.827
.73590
67,7
.67709
73,6
.86682
40,0
.83064
47,2
47 23 oo.oij
.828
.73658
67,6
-67635
73,7
.86722
39,9
.83017
47,3
-17 26 27.26
.829
.73726
67,6
.G75d
73,7
.86762
39,8
. 82970
47,4
47 29 53.52
0.830
0-73793
67,5
0,67488
73,8
986802
39,7
9.82022
47,5
47 33 19.79
.831
.73861
67,4
.67414
73-9
! 8684 i
39,6
.82875
47 30 46.05
.832
.73928
67,3
.67340
73,9
.86881
.82827
4?l7
47 40 12.32
.833
-73995
67,3
.67266
74,0
. 8*1920
39,5
.82779
47,8
47 43 38.58
-834
.74062
67,2
.67192
74,1
.86960
39,4
.82732
'17,9
47 47 04.85
0.835
0.74130
67,1
0.67118
74,1
986999
39,3
9,82684
48,0
47 50 31.11
.836
-837
.74197
.74264
67,0
67,0
.67044
.66969
74,2
74,3
.87038
.87078
39,2
39,2
-.82636
.82588
48,1
48,2
47 53 57.38
-17 57 23.64
.838
.839
-74331
.74398
66,9
66,8
.66895
.66821
74,3
74,4
.87117
.87156
39,1
39,0
.82539
.82491
48,3
<l8,4
48 oo 49.91
48 04 16.17
0.840
.841
.842
.843
0.74464
-74531
.74598
.74664
66,7
66,7
66,6
66,5
0.66746
.66672
.66597
.66523
74,5
74,5
74,6
74,7
9.87195
.87234
,87273
.8731'!
38,9
38,8
38,8
38,7
9.82443
.82394
.82346
. 82297
4.5
'|8,5
48,6
48,7
48 07 42.44
48 ii 08,70
48 14 34-97
48 18 01.23
844
74731
66,4
.66448
74,7
.87350
38,6
.82248
48,8
48 21 27.50
0.845
.846
.847
.848
.849
0.74797
-74863
74930
74Q96
.75062
66,4
66,3
66,2
66,t
66,1
0.66373
.66298
.66223
.66148
.66073
74,8
74,9
74,9
75,0
7S,i
9.87388
.87427
.87465
-87504
.87543
38,5
38,5
38,4
38,4
38,2
9.82199
.82150
.82101
.82052
.82003
48,9
49,0
49, 1
49,2
49,3
48 24 53.76
48 28 20.03
48 31 46.29
48 35 12. S^
48 38 38.82
0.850
0175128
66,0
0,65998
75,1
9-87580
38,2
9.81953
49,4
48 42 05.09
u
-Jslnhiu
F '
cosh IK
Fo'
.o -lop
to FO'
oaooslilu
wttf
u
SMITHSONIAN TABLES
208
Circular Functions.
u
sin u
F '
cos u
u FU'
log sin u
Fa'
too cos u
<" Fo'
u
0.850
.851
.852
.853
.854
0.75128
75194
.75260
. 75326
75391
66,0
65,9
65,8
65,8
65,7
0.65998
.65923
.65848
.65773
.65697
75,1
75,2
75,3
75,3
75,4
9-87580
.87618
-s?65<:
.87694
-87732
38,2
38,1
38,0
37,9
37,8
9.81953
.81904
.81854
.SrSos
Sr755
49,4
49iS
49,6
49,7
49.8
48 42 05.09
48 45 31-35
48 48 57-6i
48 52 23.88
48 55 50. 14
0.855
.856
.857
.858
.859
0.75457
75523
-755S8
75(154
.75719
65,6
65,5
65,5
654
65,3
0.65622
.65546
.65-171
.65395
.65310
75,5
75,5
75,6
75,7
75,7
9-87770
.87808
.87845
.87883
.87920
37,8
37,7
37,6
37,5
37,5
9.81705
.81655
.81605
.81555
.81504
49.9
5o,o
50,1
50,2
50,3
48 59 16.41
49 02 42.67
49 06 08.94
49 09 35.20
49 13 01.47
0.860
.861
.862
.863
.864
0.75784
.7S&!9
759rs
-75980
76045
65,2
65,2
65,1
65,0
64,9
0.65244
.65168
.65092
.65016
.64940
75,8
75,8
75,9
76,0
76,0
9.87958
87995
.88033
.88070
.88107
37,4
37,3
37,2
37,2
37,1
9.81454
81403
.81353
.81302
.81251
50.4
'50,5
50 f ?
50,8
50,9
49 t6 27.73
49 19 54-00
49 23 20.26
49 26 46.53
49 30 12.79
0.865
.866
.867
.868
.869
0.76110
. 76174
. 76239
. 76304
.76368
64,0
64,8
64,7
64,6
64,6
o. 64864
.64788
,64712
.64635
.645-59
-76,1
76,2
76,2
76,3
76.4
9.88144
.88181
.88218
.88255
,88201
37.0
36,9
36,9
36,8
36,7
9.81200
.81149
.81038
.81047
.80996
51,0
Sr.i
51,2
5t,3
51,4
49 33 39.06
49 37 05.32
49 40 31 59
4943 57-85
49 47 24-12
0.870
.871
0.76433
76497
64,5
64,4
0.64483
.64406
76.4
76,5
9.88328
.88365
36,6
36,6
9.80944
.80893
51,5
5i,6
49 50 50.38
49 54 16.65
.872
.76562
64,3
64330
76,6
.88401
36>5
.80841
51,7
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
7<i,S
9.88510
3*5,3
9.80686
52,o
50 08 01.71
.876
. 76818
64,0
.64023.
76,8
.88547
36,2
.80634
52, r
50 u 27.97
-877
.76882
63.9
.63946
76,9
.88583
36,1
.80581
52,2
50 14 54.24
.878
.76346
63,9
.63869
76,9
.885iQ
36,0
.80529
52,3
50 18 20.50
-879
.77010
63,8
.63792
77,o
.88555
36,0
.80477
52,4
50 21 46.76
0.880
0.77074
^3.7
0.63715
77,i
9.88691
55,9
0.80424
52,5
50 25 13-03
.881
-77138
63.6
.63638
77,i
.88727
35,8
.80372
52,6
50 28 39.29
.882
.77201
63,6
.63561
77,2
.88762
35,8
.80319
52,7
50 32 05 -56
.883
. 77265
63,5
.63484
77,3
.88708
3-5,7
.80266
52,9
50 35 3C.&3
.884
.77328
6j,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
77518
63,2
.63174
77,5
.88940
35,4
.80054
53,3
50 49 16.88
.888
.77581
63,1
.63096
77,6
.88976
35,3
.Sooor
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
35, r
.79840
53.7
51 03 01.94
.892
.77833
62,8
.62786
77,8
.89116
35,0
.79786
53,8
51 06 28.21
-893
.77896
62,7
.62708
77,9
.89151
35.o
.79732
53,9
51 09 54-47
.894
.77958
62,6
.62630
78,0
.89186
34,9
.70678
54,i
51 13 20.74
0.895
0.78021
62,6
0.62552
78,0
9.89221
34,8
9. 79624
54,2
51 16 47.00
.896
.78083
62,5
.62474
78,t
,89256
34,7
79570
54,3
51 20 13.27
.897
.78146
62,4
.62396
78,1
.89291
34,7
.79515
54,4
51 23 3P-53
.858
.78208
62,3
.62318
7S,2
89325
34,6
7946i
54,5
Si 27 05.80
.899
.78270
62,2
.62239
78,3
,89360
34,5
.79406
54,6
51 30 32.06
0,900
0.7S333'
62,2
0.62161
78,3
9.89394
34,5
9-79352
S4>7
51 33 58.33
u
Isinhlu
wF '
cosh iu
*F J
. slnh In
w FO'
OQ cosh lu
*>IV
u
100
SMITHSONIAN TABLES
Circular Functions.
u
sin u
~ F .<
COS U
61 Fo'
loo sin u
6. Fo'
lOQCOSU
"J Fo'
U
0,900
0.78333
62,2
0.62l6l
78,3
9.89394
34,5
9-79352
54,7
SiV 5^33
.901
78395
62,1
.62083
78,4
,89429
34,4
.79297
54,8
51 37 24.59
.002
. 78457
62,0
.62004
78,5
.89463
34,3
- 79242
55,0
51 40 50.86
.903
.78519
61,9
.61926
78,5
.89497
34,3
.79187
55,1
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
.907
.78704
.78766
6i,7
6r,6
,61690
78,7
78,8
,89600
.89634
34,0
34,0
.79021
.78966
55,4
55,5
51 54 35-91
51 58 02.18
.008
.78827
6i,5
.61532
78,8
.89668
33,9
.78910
55,6
52 OT 28.44
.909
.78889
6i,5
.61453
78,9
.89702
33,8
.78855
55,8
52 04 54.71
o.gio
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
79,0
.89769
33,7
.78743
56,0
52 II 47.24
.912
.79073
61,2
.61217
79,1
.89803
33,6
.78687
56,i
52 15 13-50
913
79134
61,1
.61137
79,1
.80836
33,6
.78631
56,2
52 18 39-77
.914
.79195
61,1
.61058
79,3
.89870
33,5
.78574
56,3
52 22 O6.03
0.915
.916
0.79256
.79317
61,0
60,9
0.60979
,60900
79-3
79,3
9-89903
.89937
. 33,4
33,3
9.78SI8
.78462
56,4
56,6
52 25 32.30
52 28 58.56
.917
79378
60,8
.60820
79,4
89970
33,3
.78405
56,7
52 32 34.83
.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>i
.78291
5<5,9
52 39 I7-36
0.920
0.79560
60,6
0.60582
70.6
9.90070
33,1
9.78234
S7,o
52 42 43.62
.921
.79621
60,5
.60502
79,6
.90103
33,0
.78177
57,2
52 46 09.89
.922
.79581
60,4
.60423
79,7
.90136
32,9
.78120
57,3
52 49 36.15
.923
79742
60,3
.60343
79,7
.90168
32,9
.78063
57,4
52 53 02.42
.924
.79802
60,3
.60263
79,8
.90201
32,8
.78005
57,5
52 56 28.68
0.925
0.79862
60,2
0.60183
79,9
9,90234
32,7
9.77948
57,6
52 59 54-95
.926
,79922
60, r
.60104
79,9
.90267
32,7
.77890
57,7
53 03 21.21
.927
.79982
60,0
.60024
80,0
.90299
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
So, I
.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
.80281
59,6
-59623
80,3
.93461
32,3
77541
58,5
53 23 58-80
933
.80341
59,5
.59543
80,3
00494
32,2
77483
58,6
53 27 25.06
934
.80400
59,5
- 59462
80,4
.90526
32,r
.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
773o6
59,o
53 37 43-86
937
.80579
59,2
.59221
80,6
.90622
31,9
.77247
59, i
53 41 10.12
.938
.80638
59,1
.59140
So,6
.90654
31,9
.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
50,o
0.58979
80,8
9.90717
31,7
9.77070
59,5
53 51 28.92
941
.80815
58,9
.58898
80,8
.90749-
31,7
. 77010
59,6
53 54 55.18
942
.80874
58,8
.58817
80,9
.90781
31,6
.76950
59,7
53 58 21,45
943
.80932
58,7
.58736
80,9
.90S 12
3i,5
.76891
59,8
54 or 47-71
,944
.80991
58,7
,'-58655
81,0
90844
31,5
.76831
60,0
54 05 13.98
0-945
0.81050
<JS,6
0.58574
81,0
9.90S75
3i,4
9.76771
60, 1
54 08 40.24
946
.81108
58,5
.58493
81,1
.90006
31,3
.76711
C0,2
54 12 06.51
947
.81167
58,4
.58412
81,2
.90938
31,3
.76650
60,3
54 15 32-77
.948
.81225
58,3
.58331
81,2
.90069
31,2
.76590
60,5
54 18 59.04
.949
.81283
58,2
. 58250
8i,3
.9IOOO
31,1
-76529
00,6
54 22 25.30
0-950
0.81342
58,2
0.58168
8l,3
9.9I03I
3M
9.76469
6o,7
54 25 51-57
u
-Islnhiu
u fa
cosh 1u
61 FO'
. a!nh lu
oi Fa 1
lOQCOshiu
,w
u
IOQ T
SMITHSONIAN TABLES
210
Circular Functions.
u
sin u
uFo'
cos u
.*'
log sin u
ID FO'
loo cos u
<*F '
U
0.950
0.81342
58,2
0.58168
Sl,3
9.91031
31,1
9.76469
60,7
5 4 V5i"57
.951
.81400
58,1
.58087
81,4
.91062
31,0
.76408
60,9
54 29 17-83
.952
.81458
58,0
.58006
8r,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
9"55
30,8
.76225
61,2
54 39 36.63
| 0.955
0.81631
57,8
0,57761
Si, 6
9.91186
30,7
9.76163
61,4
54 43 02.89
| -956
.81689
57,7
.57679
8i,7
,gr2i6
30,7
.76102
6i,5
54 46 29. 15
957
.81747
57,6
57597
81,7
.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
8 1,9
9-91339
30,4
9-75855
62,0
55 oo 14.21
.961
0.81976
57..1
.57270
82,0
.91369
30,3
75793
62,2
55 03 40.48
.962
.82034
57,2
-S7I88
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- or
.064
.82148
57,o
57024
82,1
.91460
30-1
.75606
62,6
55 13 59-27
0.965
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
7548t>
62,8
55 20 5'. So
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
20,9
75354
63,1
55 27 44.33
.969
.82432
56,6
. 56612
82,4
.91610
29,8
75291
63,2
55 31 10. 60
0.970
0.82489
56,5
0.56530
82,5
9.91639
29,8
9.75228
63,4
55 34 36.86
.971
.82545
56,4
.56447
82,5
.91669
29,7
-75164
.63,5
55 38 03.13
.972
,82601
56,4
.56365
82,6
.91699
29,6
75^01
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 4821.92
0-975
0.82770
56,1
0.56117
82,8
9.91787
29,4
9.74909
64,1
ss 51 48.19
.82826
56,0
- 56034
82,8
.91817
29,4
-74845
64,2
55 55 14-45
977
.82882
56,0
55951
82,9
.91846
29,3
.74781
64,3
55 58 40-72
.978
.82938
55,9
55868
82,9
91875
29,2
.74717
64,5
56 02 06.98
-979
.82994
55,8
.55785
83,0
.91905
29,2
-74652
64,6
56 05 33.25
0.980
0.83050
55,7
0.55702
83,0
9.91934
29,1
9.74587
64,8
56 08 59.51
.981
.83105
55,6
-556E9
83,1
.91963
29,1
-74522
64,9
56 12 25-77
.982
.83161
55,5
55536
83,2
.91992
29,0
74457
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
55,1
55120
83,4
.92136
28,7
-74I3I
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
o. 54869
83,6
9.92222
"28,5
9-73933
66,2
56 43 22.16
.991
83657
54,8
547S5
83,7
.92250
28,4
.73866
66,3
56 46 48.42
992.
.83712
54,7
54702
83,7
.92279
28,4
. 73800
66,5
56 50 14.69
.993
83767
54,6
.S46r8
83,8
.92307
28,3
73734
66,6
56 S3 40.95
994
.83821
54,5
54534
83,8
.92335
28,3
-73667
66,8
56 57 07.22
0-995
0.83876
54,5
0.54450
83,9
9-92364
28,2
9-73600
66,9
57 00 33.48
.996
.83930
54,4
.54366
83,9
.92392
28,1
73533
67,0
57 03 59-75
.997
-83985
54,3
.54282
84,0
.92420
28,1
.73466
67,2
57 07 26.01
.998
.84039
54,2
.54198
84,0
.92448
28,0
73399
67,3
57 10 52.28
.999
.84093
5/1,1
54U4
84,1
.92476
27,9
73331
67,5
57 14 i8.54
1. 000
0.84147
54,o
0.54030
84,1
9.92504
27,9
9.73264
67,6
57 17 44-8i
11
-islnhlu
. > Fo'
cosh lu
.Fo'
, slnh In
u Fo'
log cosh In
oFo'
u
ion ,
SMITHSONIAN TABLES
211
Circular Functions.
u
sin u
wFo'
cos a
<o Fo'
loo sin u
Fo'
lag cos i
fa Fo'
u
I. COO
0.84147
54,0
0.54030
84,1
9.92504
27,9
9.73264
67,6
57i7'44'.8i
.001
.84201
53.9
.53946
84,2
.92532
27,8
. 73K-X)
67,8
57 21 11.07
.002
.84255
53,9
.53862
84,3
.92560
27,8
.73128
67,9
57 24 37-34
.003
.84309
53,8
.53778
84,3
.92587
27,7
.73060
68,1
57 28 03.60
.004
.84363
53.7
.53693
84,4
.92615
27,6
.72992
68,2
57 31 29.87
1.005
0.84416
53,6
0.53609
84,4
9.92643
27.6
9.72924
68,4
57 34 56.13
.006
.84470
53,5
.53524
84,5
,92670
27,5
.72855
68,5
57 38 22.40
.007
.84523
53,4
.53440
84,5
9269S
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
.on
.84736
53,1
.53101
84,7
.92807
27,2
.725n
69,3'
57 55 33-72
.012
.84789
53,o
.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
1.0:5
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
.92042
26,9
.72162
70,1
58 12 45.04
.017
.85053
52,6
.52592
85,1
.92969
26,9
. 72002
70,2
58 16 11.31
.018
.85106
52,5
.52507
85,1
.92996
26,8
. 7-2022
70,4
58 19 37.57
.019
.85158
52,4
.52422
85,2
.93023
26,7
.71951
70,6
58 23 03.84
1.020
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
71,3
58 40 I5.i6
1.025
0.85471
51,9
0.51910
85,5
9.03182
26,4
9.71525
7i,5
58 43 4L43
.026
.85523
5i,8
.51824
85,5
.93208
26,3
-71453
7i,7
58 47 07.69
.027
.85575
51,7
.51739
85,6
.93235
26,3
-71382
7i,8
58 50 30-96
.028
.85627
51,7
.51653
85,6
.93261
26,2
.71310
72,0
58 54 00.22
.029
.85678
51,6
.51568
85,7
93287
26,1
.71238
72,2
58 57 26.49
1.030
0.85730
51,5
0.51482
85,7
9.93313
26,1
9.7H65
72,3
59 00 52.75
.031
.85781
5 M
.51396
85,8
.93339
26,0
.71093
72,5
59 04- 19.02
.032
-85833
Si,3
.51310
85,8
.93365
26,0
.71020
72,6
59 07 45-28
.033
.85884
5i,2
.51224
85,9
93391
25,9
.70948
72,8
59 ii n.54
-034
-85935
5I.I
51139
85,9
.93417
25,8
-70875
73,o
59 i'4 37- Si
1.035
0.85986
5i,i
0.51053
86,0
9-93443
25,8
9.70802
73, *
59 18 04.07
.036
.86037
5i,o
.50967
86,0
.93469
25,7
.70729
73,3
59 21 30.34
.037
.86088
50,9
.50881
86,1
93494
25,7
.70655
73,3
59 -24 56.60
.038
.86139
50,8
50794
86,1
.93520
25,6
.70582
73,6
59 28 22.87
.039
.86190
50,7
.50708
86,2
-93546
25,6
.70508
73,8
59 31 49-13
1.040
0.86240
50,6
0,50622
86,2
9-93571
25,5
9.70434
74,o
59 3S 15.40
.041
.86291
50,5
.50536
86,3
93597
25,4
.70360
74&
59 38 41-66
.042
.86341
50,4
.50449
8(5,3
.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
.046
.85543
50,1
.50104
86,5
.93723
25,1
.69987
75,0
59 55 52.99
.047
.86593
50,o
.50017
86,6
.93748
25,1
.69912
75,2
59 59 19.35
.048
.86643
49,9
.49930
86,6
-93773
25,0
69837
75,4
5o 02 45.52
.049
.86693
49,8
.49844
86,7
.93798
25,0
.69761
75,5
60 06 11.78
. 1.050
0.86742.
49,8
0.49757
86,7
9.93823
24,9
9.69686
75,7
60 09 38.05
u
Islnhlu
"F</
oosh iu
*Fo'
. sinh Iu
10 Fo'
oocoshlu
<oF '
u
log j
SMITHSONIAN TABLES
212
Circular Functions.
u
sin u
<o Fo'
cos a
F '
loosln u
Fo'
log cos u
"Fo'
u
1.050
.051
.052
053
0.85743
.86702
.86842
.86891
49,8
49,7
49,6
49,5
0-49757
.49670
49584
-49497
86,7
86,8
86,8
86,9
9-93S23
-93848
-93873
.93898
24,9
24,9
24,8
24,7
9.69686
.69670
.69534
69458
75,7
75,9
76,1
76,2
60 og'aS'.'os
Co 13 04.31
60 16 30.58
60 19 56.84
.054
.86941
49,4
.49410
86,9
93922
24,7
.69381
76,4
60 23 23. ii
1.055
.056
0.815990
.87039
49,3
49,2
0.49323
.49236
87,0
87,0
9-93947
93972
24,6
24,6
9-69305
.69228
76,6
76,8
60 26 49.37
60 30 15.64
.057
.058
.87088
.87138
49,1
49,1
49M9
.49062
87,1
87,1
93995
.94021
24,5
24-5
.69151
.69074
77,o
77, r
60 33 4I.90
60 37 08.17
.059
.87187
49,0
.48974
87,2
-94045
24,4
.68597
77,3
60 40 34-43
i. 060
.061
.062
.063
.064
0,87236
.87284
87333
.87382
87430
48,9
48,8
48,7
48,6
48,5
0.48887
.48800
48713
.48625
.48538
87,2
87,3
87,3
87,4
87,4
9.94069
.94094
.94118
.94142
.94166
24,3
24,3
24,2
24,2
24,1
9.68920
.68842
.68764
.68686
.68608
77,5
77,7
77,9
7S,o
78,2
60 44 00.69
60 47 26.96
60 50 53.22
60 54 19.49
60 57 45-75
1.065
0.87479
48,5
0.48450
87,5
9.94190
24,1
9-68530
7S.4
6l OI 12. O2
.066
.067
.87527
.87576
48,4
48,3
48363
.48275
87,5
87,6
.94214
.94238
24,0
23,9
.68451
.68373
78,6
?8,S
61 04 38.28
61 08 04.55
.068
.87624
48,2
.48188
87,6
.94262
33,9
.68294
79,o
61 ii 30.81
.069
.87672
48,1
.48100
87,7
.94'286
23,8
.68215
79,2
61 14 57.08
1.070
0.87720
48,0
0.48012
87,7
9-94310
23,8
9-68135
79,3
61 18 23.34
.071
.87768
47,9
.47925
87,8
94334
23,7
.68056
79,5
61 21 49.61
.072
.87816
47,8
.47837
87,8
943'57
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 34.6/
.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 i
94498
23,3
.67494
80,9
61 45 53.46
070
.88149
47,2
.47221
sali
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,o
.47045
88,2
.94568
23,2
.67251
8r,5
61 56 12.26
.082
.88290
47,0
.46956
88,3
.04591
23. i
.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 3-1.05
1.085
0.88430
46,7
0.46691
88,4
9.94660
22,9
9.66924
82,3
62 09 57,31
.086
-88477
46,6
.46603
88.5
.94683
22,9
.66841
82,5
62 13 23.58
.087
.88524
46,5
.46514
88,5
.94706
22,8
.66759
82,7
62 16 49.84
.088
.88570
46,4
. 46426
88,6
.94729
22,8
.66676
82,9
62 20 16.11
.089
.88616
46,3
.46337
88,6
-94751
22,7
-66593
83,1
62 23 42.37
i.ogo
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 34-9
.092
.88755
46,1
.46071
88,8
.94819
22,5
.66343
83,7
62 34 or. 17
.093
.88801
46,0
.45982
88,8
.94842
22,5
.66259
83.9
62 37 27-43
.094
.88847
45,9
.45894
QO Q
OQ,0
.94864
22,4
.66175
&[,!
62 40 53.70
1.095
0.88893
45,8
0.45805
88,9
9.94887
22,4
9.66091
84,3
62 44 19,96
.096
-88939
45,7
.45716
88,9
.94909
22,3
.66007
.84,5
62 47 46.23
.097
.88984
45,6
.45627
89,0
9493 1 !
22,3
,65922
84,7
62 51 12.49
.098
.80030
45,5
.45538
80,0
. 94954'
22,2
.65837
84,9
62 54 38.70
.099
.89075
45,4
.45449
89,r
.94976
22,2
.65752
85,1
62 58 05.02
I.IOO
0.89121
45,4
0.45360
89,1
9.94998
22, r
9.65667
85,3
63 oi 31.29
u
-Islnhlu
Fo'
cosh iu
Fo'
[nn ''"h In
log j
<> Fg'
og cosh lu
uF '
u
SMITHSONIAN TABLES
213
Circular Functions.
u
sin u
-Fo'
cos u
Fo'
loo sin a
-w
QQ coa u
-Fu'
u
1. 100
. 101
. 102
. 103
.104
O.S912I
.89166
.89211
.89256
.89301
45,4
45,3
45,2
45,1
45,0
0.45360
.45270
.45092
.45003
89,1
89,2
89,2
89,3
89,3
9.94998
.95020
.95054
.95086
22,1
22,O
22,O
21,9
2-1,9
.65667
,65581
.65496
.65410
.65324
85,3
85,5
85,8
86,0
86,2
3oi'3 I - 2 9
3 04 57-55
3 08 23.82
3 ir 50.08
3 '15 16.35
1. 105
. 106
,107
.108
.109
0.89346
.89391
.89436
.89481
.89525
44,9
44,8
44,7
44,6
44,6
0.44913
.44824
.44735
.44645
.44556
89,3
89,4
89,4
89,5
89,5
9.95108
.95151
95173
.95195
21,8
21,8
21,7
21,7
21,6
9.65238
.65151
.65064
.64977
.64890
86,4
86,6
86,8
87,0
87,3
3 18 42.61
3 22 08.88
3 25 35-14
3 29 01.41
13 32 27.67
I. 1 10
. Ill
.112
.113
.114
0.89570
.89614
.89559
.89703
.89747
44,5
44,4
44,3
44,2
44,1
0.44466
44377
-44287
-44197
.44108
89,6
89,6
89,7
89,7
89,7
9.95216
.95238
95259
95302
21,6
21,5
2'I,5
21,4
21,3
9.64803.
.64715
.64628
.64540
.64451
87,5
87,7
87,9
88,1
88,4
63 35 53-93
>3 39 20.20
J3 42 46.46
63 46 3.2.73
>3 49 38.99
i. US
.116
.117
.118
.119
0.89791
.89835
.89879
.89923
.89966
44,0
43,9
43.S
43,7
43,7
0.44018
.43928
.43838
.43748
.43658
89,8
89,8
89,9
89,9
9O,O
9-95323
95345
.95366
.95387
.95408
21,3
21,2
21,2
31,1
21,1
9.64363
.64274
.64185
.64096
.64007
88,6
88,8
89,0
89,3
89,5
63 53 05.26
63 56 31-52
>3 59 5-7-79
64 03 24.05
64 06 50.32
I. I2O
.121
0.90010
.90054
43,6
43,5
43,4
0.43568
.43478
.43388
9O,0
90,1
90,1
9.95429
95450
95471
2I,O
2I,O
2O,9
9.63917
.63827
.63737
89,7
90,0
90,2
64 10 16.58
64 13 42.85
64 17 09.11
.123
.124
.90140
.90184
43,3
43,2
.43298
.43208
9O,I
9O,2
95492
.95513
2O.9
20,8
-61647
.63556
90,4
90,6
64 20 35.38
64 24 01.64
I. 125
.126
.127
.128
. 129
0.90227
,90270
.90313
.90356
.00399
43,1
43,o
42,9
42,8
'12,8
0.43118
-43027
.42937
.42847
-42756
go, 2
9D.3
90,3
90,4
90,4
9-95534
95554
95575
.95596
956i6
20,8
20,7
:2O,6
2O,6
20,5
9-63466
.63375
.63^83
63192
.63100
90,9
91,1
91,3
91,6
01,8
64 27 27.91
64 30 54-17
64 34 20.44
64 37 46.70
64 41 I2 -97
1 . 130
.131
.132
.133
.134
0.90441
.90484
.90526
.90569
.90611
42,7
42,6
42,5
42,4
42,3
0.42666
.42576
.42485
-42394
.42304
90,4
90,5
90,5
9O,6
90,6
9.95637
.95657
.95678
.95698
.95718
20,5
20,4
2O,4
20,3
20,3
9.63008
.62916
.62824
.62731
.62638
92,1
92,3
92,5
92,8
93,0
64 44 39-23
64 48 05.50
64 51 31.76
64 54 58.03
64 58 24.29
I-I35
.136
.137
.138
.139
0.90653
,oo6VX:
-90738
.90780
.90822
42,2
42,1
42,0
4i',9
0.42213
-42123
.42032
,41941
-41850
90,7
90,7
90,8
90,8
9.95738
.95759
95779
95799
.95819
20,2
20,2
20,1
20, T
20,O
9.62545
.62451
.62358
.6226.'
.62170
93,3
93,5
93,8
94,0
94,2
65 01 50.56
65 05 16.82
65 08 43-08
65 12 09.35
65 15 35.6i
1.140
.141
.142
.143
.144
0.90863
.90905
.90947
.90988
.91030
41,8
41.7
41,6
41,5
41,4
0.41759
.41669
.41578
.47487
.41396
90,9
90,9
90,9
9i,o
91,0
9.95839
.95859
.95879
.95899
.95918
20,0
19,9
19,9
19,8
19,7
9,62075
.61981
.6i88f
.61791
.61695
94,5
94,7
95,o
95,2
95,5
65 10 01. &
65 22 28.1.
65 25 54-41
65 29 2O.67
65 32 46.94
I.I45
.146
.147
0.91071
.91112
41,3
41,2
41,1
0.41305
.41214
,41122
gr.I
91,1
91,2
9.95938
.95958
95977
19,7
19,6
19,6
9.61600
.6150^
.6140!
95,8
96,0
96,3
65 36 13-20
65 39 39-47
65 43 05.73
.148
,149
.91195
.91235
41,0
40,9
.41031
,40940
91,2
gi,2
95997
.96016
19,5
19,5
.6131
.6121
96,5
96,8
65 46 32.00
65 49 58.26
1 , 150
0.91276
40,8
0.40849
91,3
9.96036
10,4
p.flnt
97,o
65 53 24.53
u
-i sink In
.
cosh lu
.w
lnn alnh '
uFo'
loo cosh
Fo'
u
SMITHSONIAN TABLES
214
Circular Functions.
II
sin u
,Fo<
cos u
to Fo'
log sin u
- IV
[00 COS II
-P.-
u
1.200
.201
0,93204
.93240
36,2
36,1
0.36236
.36143
93,2
93,3
0.9694.1
.0(1900
1 6,9
16,8
y. 55914
111,7
iia,u
ft'jjis
.202
.203
.204
.93276
93348
36,0
36,0
35,9
.36049
.35956
.35863
93,3
93,3
93,3
<X' ( J77
.970) 1
Uiix
55577
55- KM
"~',7
08 aa 10.30
<! s 55 36.50
T.2O5
,206
.207
.208
0.9.1384
.93420
93455
93491
35,8
35,7
35,6
35,5
0,357*19
.35676
.35582
.35489
93,4
93,4
93,5
93,5
0.97027
.970.14
,07000
.j;/o77
1 0*6
16,5
16,5
y, 5535'
55-M7
.55' -'4
. 55001)
"3,4
"3.7
114,1
114,4
fJ 02 29,00
(x) 05 55, ft
(x.) u 4/,ftj
.209
-'*' I-*
.93526
35,4
.35395
93,5
-yX<>93
16,4
54H9S
n.|,8
6y i(i 14,15
1. 210
.211
.212
0,93562
93597
,936312
.15,3
35,2
35-1
0.35302
.35^08
35115
93,6
93,6
93,6
9.97110
.97126
.9714-!
16,4
'6,3
"0,3
U.5478o
.54^5
5454!)
nfi, i
"5,5
"5,8
fk) l() 40.42
fK> ^3 o!).(xS
.213
,93667
35-0
35021
93,7
.97159
l6,-2
54433
1 10, :'.
<*.) 21) S9,ai
.214
93702
34.9
.34927
93,7
.97175
i6,a
543 '7
"6,5
f"J 33 25,47
1. 215
0.93737-
.93772
34.8
34.7
0.34834
.34740
93,7
93,8
9,97101
.97207
16, i
16, i
9.54200
.54083
1 1(>,0
H7.J
f'*J 36 51,74
fxj 40 ]H,(X>
.217
.218
93806
.93841
34,6
34,6
34640"
34552
93,8
93,8
.9723^
1 6,0
16,0
'538.18
"7,0
1 18,0
<*> 43 44.2/
<*) 47 10.53
,219
.93876
34,5
.34458
93,9
.97255
I5.<>
.53730
"H,3
f> 5<i 3('.8o
1.220
0.93910
34,4'
0.34365
03,9
0.97271
IW>
y.SaTni
1 18,7
<'") S'l 0,1. o<j
.221
.93944
34,3
.34-271
93,9
.97^87
I5,
. 53492
"0,1
f> 57 29.33
.222
.93978
34,2
34177
94,0
.9730,1
'5,8
5337.1
"9,4
70 oo 55,59
223
.94013
34,1
.34083
94,0
O73'y
1 5.X
. 53253
1 10,8
70 o.| a i.Hfi
.224
.94047
34,0
.33989
U4,o
9733-1
IS.X
.53133
1JO.11
70 07 48. u
1.225
0.04081
33,9
0.33895
94,1
0.07,150
15,<">
y. 53013
120,5
70 ii 14.30
.226
,1)4,114
33,8
.33800
94,1
.973(10
IS/'
5~8fj;!
I ;!(),!)
7(1 I.I 40. ("5
.227
.94148
33,7
.33706
94,1
.07381
15,5
.52771
Ul,3
7*1 IK (16.IJ3
.228
33,6
,33612
94,2
.<>73<>7
15,5
.52050
121,7
70 21 33.18
.229
.94315
33,5
.33518
94,2
.97412
15,5
.52528
IJ2,I
70 a.| 59.,|4
1 . 230
0.94240
33,4
0.33424
94.2
9-9742H
15,4
y, 5,2406
122,5
70 28 25,71
.231
.94282
33,3
33330
94,3
9744.1
15.-I
.52283
1 *!!,<;
yti 31 51.1^
.232
33,2
.33235
94,3
9X45H
15,3
,5.1160
U3,J
7o 35 i8.*l
.2.13
94349
33,1
.33141
94,3
-97474
15,3
5 -'036
i ^3,6
70 ,1 4-I-5'
.234
.94382
33,o
.33047
94,4
.y74%
15,2
.51913
\2\
70 .|J 10.77
1.235
0.04415
33,0
0,32952
94,4
9.97504
15.2
0.51788
12,1 1
* *"!,'(
70 45 37,04
.236
.94448
32,9
.32858
9-1,4
.9X5 HJ
15. 1
.51(1(14
IAI.H
70 4<) 03..1<1
.237
.94481
32,8
.32763
!J4,5
9X534
15.1
51-539
ras.j
70 S3 29. S7
.238
.94513
32,7
.32669
Q4.5
.0X540
15,0
.5M13
125,6
7<> 55 55 -Hi
239
9454"'
32,6
.32574
94,5
.9X5f>4
15,0
.51287
126,1
70 59 aj.oy
1.240
0.94578
32,5
0.32480
04,6
9-97579
'4,9
0.51161
126,5
71 oa 48.3(1
.241
3-2,4
.32385
Wft
."7594
14,0
.51034
i 26,9
71 Of) 14 .&!
.242
04643
32,3
-32200
04,6
14. K
.5090?
U7.il
71 <xj <t-Hy
.243
.94675
.32196
94,7
9762J
. 50780
127,7
71 1307.15
,244
.94708
32,1
,32101
94,7
.9763B
14!;
. S0(52
71 Hi 33-43
1.245
0.94740
32,0.
o. 32006"
94.7
9.9765,1
M.7,
y. 50524
128,6
71 TO 50. (8
.246
.94772
31,9
.31912
94,8
.97668
.50395
U 1 *),"
Xi 23 35.95
247
.04803
3E.8
.31817
,97682
I4J6
. 5026(1
120,4
71 a<i ja.di
.248
9-18,15
31,7
.31722
943
.07607
14,5
.50136
129,8
71 30 18,48
.249
.94867
31,0
.31627
94,9
977"
14,5
CfWi/l
i JJVAJVAJ
130,3
71 30 44-74
1.250
0,94808
3i, 5
0.31532
94,9
9.97726
M.4
9.4y8X5
130.7
71 37 ir.oi
u
-Islnlilu
-w
coth In
.w
ijnhju
-W
lOQOoihlg
__
ii
SMITHSONIAN TADLK&
ai6
Circular Functions,
1.^50
.US"
. :?53
1.255
. J57
Xti
3<\7
.;68
1.370
.271
.27.*
1274
1.27.1
. 279
1.280
!3<3
1,290
-293
1-300
Bill U
0-05053
95oM(r
-95II7
05178
,95-MO
0.053(11
.95.151
.05MO
.OS5<>9
.95590
.95715
9574-1
95773
.i/lt 130'
i , i/ViH.|
.901 1 1
.111,5
J7,5
lilnhlu w Pi,' ooBhlu
,-yx/tj
0.301(15
.30010
.a? i 35
w Fu'
'l.S.o
95. i
05. '
05, i
95, 1
95,3
95,3
05,4
9sis
05,5
95/>
95/i
95!7
95.9
95,9
(X>,o
1/1,0
<Ai
<X>,2
(X>,a
loo sin u
!J77-|0
.97783
9-97797
.9785.1
- 979A1
.97937
97951
9.98005
.1)8032
.98045
.98058
,981 N
,98103
.98176
9.98202
9.98265
.98277
.98339
.98351
1-1,3
14,3
ivi,a
M.I
14,0
14,0
M.9
13.9
13,0
13,7
13,7
'3,7
13,6
13,5
13.5
13,4
'3,3
13.3
13,3
13.1
13,1
13,0
1.1,0
lalo
12,0
12,8
12,6
i a, 5
1 2, 5
12,4
12,3
12,3
12,2
loo ooa u
). 49875
19745
19349
.48950
9-48546
.48-111
.48002
9-l786 ; |
147588
-47449
47310
9.47170
9.46464
; 40 1 ?8
.45890
9.457.15
.45600
. 454'54
.45307
9.45013
.44865
447i6
-14567
-44417
9.44267
.44116
.43965
.43660
9-43507
-43353
9.42732
logooihlu w Fo'
130,7
131,1
131,6
132,5
'33,4
133,8
134.7
135,2
135,7
1 36, i
136,6
137.1
l'37,6
138,0
138,5
i,19,o
139,5
140,0
140,5
141,0
141,5
142,0
142,5
143,0
M3.5
144,1
145,1
145,6
146,2
146,7
M7.3
147,8
148,3
148,9
149,5
150,0
150,6
iSl.i
151,7
152,3
152,0
15.1.5
1'54/'
155,3
155,8
156,4
7\ 37 i I. oi
71 40 37-27
71 44 03-5-1
71 4X 29.80
71 50 56-07
71 54 22.33
71 57 48,60
72 oi 14,86
72 o.j 41.13
72 08 07,39
72 II 33.66
72 hi 59-92
72 18 26.19
72 21 S'2-45
72 25 18.72
72 28 44,98
72 32 11.24
72 35 37.51
72 39 03.77
72 42 30.04
72 45 56.30
72 49 22.57
72 52 48.83
72 56 15. m
72 59 41.36
73 03 07.63
73 06 33,89
73 10 oo. 16
73 13 26,42
73 16 52.6(j
73 20 18.95
73 23 45-22
73 -27 11.48
73 30 37-75
73 34 "4.01
73 37 ,10.28
73 40 56.54
73 44 '22,8l
73 47 49-07
73 51 15-34
73 '54 4i.6o
73 58 07.86
74 01 34-13
74 05 00,39
74 08 26,66"
74 n 52.92
74 15 19.19
74 18 45-45
74 22 11.72
74 25 37.98
74 29 at. a;
SMITHBOHIAN TA*U
217
Circular Functions.
11
sin u
a-Fo'
cos u
" F u '
lag sin u
Fu'
log cos u
F U '
u
1.30
0.96356
26,7
0.26750
96,4
9.98388
12,1
9.42732
156,4
742Q 04.25
.301
-<X>3^3
26,7
.26654
96,4
.98400
1 2,O
42575
i'57,o
74 32 30.51
*fZ >-O
30-3
.96409
26,6
26557
90,4
.08412
12,0
.42418
157-7
74 35 56.78
.303
-96436
26,5
.26461
56,4
.98424
n,9
.42260
158,3
74 3Q 23-04
.304
.96462
26,4
.26364
96,5
.9S436
n,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
.06515
26,2
.26171
00.5
.08459
n,8
.41782
160,2
74 49 41.84
.307
.96541
26,1
.26075
OG,5
.98471
n,7
.41622
160,8
74 53 08.10
.308
.96567
26,0
.25978
96,6
.9S4S3
n,7
.41461
161,4
74 56 34-37
309
.96593
25,9
.25882
96,6
.93494
n,6
.41299
162,1
75 oo 00.63
1.310
-3"
0.96618
.96644
25,8
25,7
0.25785
.25688
96,6
96,6
9.98506
.98518
11,6
11,5
9-4II37
.40974
162,7
163,4
75 03 26.90
75 06 53-16
.312
.96670
25,6
. 25592
96,7
08529
n,5
.40810
164,0
75 10 10.43
-3'3
.96695
25,5
25495
<X5,7
.98541
11,5
.40646
164,7
75 13 45.69
3H
.96721
25,4
-25398
05,7
.98552
11,4
.40481
165,4
75 17 11.9:1
I-3I5
0.96746
25,3
0.25302
96,7
9-08563
n,4
9.40315
166,1
75 20 38.22
.316
.96771
25,2
. 25205
96,8
.08575
u,3
.40148
166,7
75 24 04-49
.31?
.96797
25,1
.25108
96,8
.o353;>
n,3
.39981
167,4
75 27 30.75
.318
-3f9
.96822
.96847
25,0
24,9
.25011
. 24914
96,8
96,8
.98597
.98608
11,2
11,2
31>8i4
39645
168,1
168,8
75 30 57-01
75 34 23.28
1.320
0.96872
24,8
0.24818
06,9
9.98620
II, I
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
.323
,96921
.96946
24,6
24,5
. 24624
24527
06,9
96,9
.98642
-08653
n,o
n.o
.39135
.38964
170,9
i7r,7
75 44 42.07
75 48 08.34
.324
.96970
24,4
.24430
97,0
.98664
10,9
.38792
172,4
75 Si 34.6o
1.325
.326
.327
.328
.329
0.96994
.97019
.97043
,97067
.97091
24,3
24,2
24,1
24,0
23,9
0.24333
, 24236
.24139
.24042
.23945
97,0
97,o
97,0
07,1
97,1
0.98675
.08686
.98636
98707
.98718
10,9
10,8
10,8
10,8
10,7
9-38619
-38446
.38272
.38097
.37921
i73,r
i73,9
174,6
175,3
176,1
75 55 00.87
75 5S 27. 13
76 01 53-40
76 05 19.66
76 08 45-93
1-330
331
332
333
334
0.97H5
-97I39
.97162
.97186
.97209
23,8
23,8
23,7
23,6
'23,5
0.23848
.23750
.23653
.23556
.23459
97,1
97*1
97,2
07,2
07,2
9-98729
.98739
.98750
.98760
98771
10,7
10,6
10,6
10,5
10,5
9-37744
.37567
.37389
.37210
.37031
176,9
177,6
178,4
179,2
180,0
76 1-2 12.19
76 15 38.46
76 19 04.72
76 22 3O.O9
76 25 57-25
1-335
.336
337
.338
339
0-97333
.97256
.97279
97303
.97326
23,4
23,3
23,2
23,1
23,0
0.23362
.23264
.23167
.23070
.22973
97,2
97,3
97,3
97,3
97,3
9-98781
.98792
.98802
.98812
.98823
10,4
10,4
10,3
10,3
10,3
9-36851
.36669
.36487
.36305
.36121
1 80,8
181,6
182,4
183,2
184,0
76 29 23.52
76 3-2 49.78
76 36 16.05
76 39 42.31
76 43 08.58
40
41
42
343
,344
0.97348
97371
97394
97417
-97439
22,Q
22,8
22,7
22,6
22,5
0.22875
.22778
.22681
.32583
.22486
97,3
97,4
97,4
97.4
97.4
9-98833
.98843
.9S853
.98863
.98873
IO,2
IO,2
10,1
10,1
IO,O
9-35937
35751
.35565
.35373
-35I9I
184,8
i85,7
186,5
187,3
188,2
76 46 34-84
76 50 oi.n
76" 53 27.37
?6 56 53.63
77 oo 19.90
1. 345
.346
- -347
-348
349
0.97462
.97484
.97506
.97528
97550
22,4
22,3
22,2
22,1
22,0
0.22388
.22291
.22193
.22096
.21998
97,5
97,5
97,5
97,5
97>6
9-98883
.98893
.98903
.98913
.08923
IO.O
9,9
9,9
9,8
9,8
9-35002
.34813
.34622
.34431
34239
189,1
189,9
190,8
I9L7
192,6
77 03 46,16
77 07 12.43
77 10 38.63
77 U 04.96
77 17 31-22
1-350
0.97572
21,9
O.2IOOI
97,<5
9.98933
9,7
9.34046
193,5
77 20 57-40
u
-Islnhiu
*iFo'
cosh iu
oFo'
ir, n sinh '
"Fo'
loo cosh Iu
"F '
. u
iDfl j
SMITHSONIAN TABLES
218
Circular Functions.
u
sin u
*jFo'
COS U
"F '
log sin u
10 Fo'
log cos
" Fo'
u
1.350
351
352
353
354
0.97572
97594
.97616
97638
.97659
21,9
21,8
21,7
21,6
21,5
0.21901
.21803
.21705
.2:608
.21510
97,6
97,6
97,6
97,6
97,7
9.98933
.98942
.981)52
.98962
.98971
0,7
9,7
P.7
9,6
0,6
9.34046
.33852
33657
33461
.33264
193,5
194,4
195,3
196,2
197,2
772o'5/.'49
77 24 23.75
77 27 50.02
77 31 16.28
77 34 42-55
1-355
356
0.97681
.97702
21,4
21,3
0.21413
.21315
97,7
97,7
g.cSsSi
.98950
9,5
9,5
9.33067
.32868
198,1
109,1
77 38 08.81
77 41 35.o8
357
-O
.97723
2 1, '2
.21217
97,7
.9pooo
9,4
.32669
200,0
77 45 01.34
.358
-359
9774'
977C5
21,1
2I,O
.21119
. 21022
97,7
97,8
.99009
.99019
9,4
9,3
.32468
. 32267
201,0
202,0
77 48 27.61
77 51 53.87
1.360
.361
.362
-3f'3
364
0.97786
97807
.97828
.97849
.97869
20,9
20,8
20,7
20,6
20,5
O.20924
.20826
. 2O728
.20630
20533
97,8
97,8
97.8
97,8
97,9
9.99028
.99037
.99046
.99056
-99055
9,3
9,2
9,2
9,2
9,1
9-32064
.3rS6i
.31656
.31451
31244
203,0
204,O
205,0
2O6,O
207,0
77 55 20. 14
77 58 46.40
78 02 12.67
?S 05 38.93
78 09 05.20
1.365
0.97890
20,4
0.20-135
97,0
9.99074
9J
9-31037
208,0
?8 12 31.46
366
_/***
-97910
20,3
20337
97,9
-59083
9,0
.30828
209,1
78 15 57-73
367
9793-1
20,2
. 20239
97,9
.99092
9,0
30619
210,1
78 19 23.99
368
97951
20,1
.20141
98,0
.99101
8,9
. 30408
211,2
78 22 50.25
.369
.97971
20,O
. 20043
98,0
.99110
8,9
.30196
212,3
78 -26 16. 52
1.370
371
.372
0.97991
.98011
.98031
19,9
J,8
19,7
o. 19945
.19847
19749
98,0
98,0
f)8.o
9.99n9
.99127
99136
8,8
8,8
8,7
9.20983
.29769
.29554
213,4
214,5
2I'5,fi
78 20 42.78
7& 33 09.05
78 36 35-31
373
.98050
19,7
. 19^51
98,'
-99I45
8,7
.29338
2 1 6,7
78 40 01.58
374
.98070
19,6
19553
98,1
99154
8,7
.2pI2I
217,8
78 43 27,84
1-375
0.98089
19,5
0. I94'55
q8,l
9.99162
8,6
9-28903
219,0
78 46 54.11
376
.98109
19,4
19357
<l8,l
.99171
8,6
.28683
220,1
78 SO 20.37
377
.98128
19,3
19259
98,1
-99^79
. 8,5
.28462
221,3
78 53 46.64
.378
.98147
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
79 00 39. 17
1.380
0.98185
19,0
0.18964
98,2
9.99205
8,4
9.27793
224,9
79 04 05-43
381
.98204
18,9
.18866
98,2
.99213
8,3
,27568
226,1
79 07 31.70
382
.98223
18,8
. 18768
08,2
.99221
8,3
27341
227,3
79 10 57.36
.383
.98242
18,7
.18669
98,2
99230
8,3
.27113
228,5
79 14 24,23
-384
.98260
18,6
. 18571
98,3
.99238
8,2
.26884
229,8
79 17 50.49
1.385
0.98279
18,5
0.184.73
98,3
9.93246
8,2
9-26654
231,1
79 21 16.76
386
.98297
18,4
18375
98,3
.09254'
8,1
. 26422
232,3
79 24 43.O2
387
.98316
18,3
. 18276
98,3
,99262
8,1
.26189
233,6
79 28 09.29
388
.98334
18,2
.18178
98,3
.99270
8,0
25955
234,9
70 31 35.55
.389
.98352
18,1
.18080
98,4
.99278
8,0
.25719
236,3
79 35 01.82
1-390
0.98370
18,0
0.17981
98,4
9.99286
7,9
J. 25482
237,6
79 38 28.08
.391
.98388
17,9
.17883
58,4
.99294
7,9
.25244
238,9
70 41 54-35
.392
,9840(3
17,8
17785
98,4
.99302
7,8
.25004
240,3
79 45 20.61
393
.98424
17,7
. 17686
98,4
.99310
7,8
.24763
341,7
79 48 46-88
394
,9&!4'i
17,6
. 17588
8,4
.99318
7,8
.24521
243,1
79 52 13-14
1-395
0.98459
17,5
0.17489
98,5
9-993-25
7,7
9.24277
244,5
79 55 39.40
.396
.98476
17,4
- I739I
98,5
99333
7,7
.24032
245,9
79 59 05,67
397
.98494
17,3
, 17292
98,5
99341
7,6
23785
247,4
So 02 31.93
.398
.98511
17,2
I7I94
fi8,5
.99348
7,6
.23537
248,8
k) 05 58.20
399
.98528
I7,i
.17095
98,5
.09356
7,5
.23288
250,3
5o 09 24,46
1,400
0.98545
17,0
0.16997
98,5
9.09363
7,5
9,23036
251,8
SO 12 50.73
u
Islnhlu
u Fo'
oosh lu
"F '
alnh lu
" Fo'
oa oosh lu
F & '
U
00 |
SMITHSONIAN TABLES
219
Circular Functions.
u
sin u
FV
CDS U
<a Fo'
log sin u
Fo'
loo cos u
.*
u
1.400
.401
.402
.403
.404
0.98545
.98562
.98579
.98596
.98612
1 7,0
1 6,9
16,8
16,7
16,6
! 16898
.16800
.16701
.16602
98.5
98,6
98,6
98,6
98,6
.99371
.99378
.99386
99393
7,5
7,4
7,4
7,4
7,3
9-23036
.22784
. 22530
. 22274
.22017
251,8
253,3
254,8
256,4
258,0
to 16 16.99
Jo 19 43.26
to 23 09.52
80 26 35-79
1.405
.406
.407
.408
. 409
0.98629
.98645
.98662
.98678
.98694
16,5
16,4
16,3
16,2
16,1
0.16504
. 16405
. 16306
.l6lO9
e8,6
98,6
98,7
98,7
98,7
9.99400
.99408
-994I5
.99422
.99429
7,3
7,2
7,2
7, 1
9.21758
.21498
. 2 I 236
.2OQ72
,20707
259,5
261,1
2(J2,8
264,4
266,1
to 30 02.05
80 33 28.32
So 36 54-58
to 40 20.85
80 43 47.ii
1.410
.4"
.412
4T3
-414
0.98710
.98726
.98742
-98758
.98773
1 6,0
15,9
15,8
15,7
0.16010
.15912
.15813
.I57r4
. 15615
98,7
98,7
98,7
98,8
98,8
9.99436
99443
-99450
99457
.99464
7,0
7,0
7,o
6,9
6,9
9.2044O
.20172
.19901
.19629
- 19355
267,8
269,5
271,2
272,9
274,7
80 47 13.38
80 50 39-64
80 54 05-91
80 57 32.17
81 oo S8.44
I.4I5
.416
.417
. .418
.419
0.98789
.98804
.98820
-98835
.98850
15,5
15,4
15,3
15,2
O.I55I7
.15418
.15319
. 15220
.15121
98,8
98,8
es!s
98,9
9-99471
.99478
.99484
-99491
.99498
6,8
6,8
6,7
6,7
6,6
! 18802
.18523
. 18242
. 17959
276,5
278,3
28O,2
282,0
283,9
!i 04 24.70
81 07 50-97
Ji ii 17.23
81 14 43-50
81 18 09.76
1.4120
,421
.422
.42-3
-424
0.98865
.98880
.98895
.08910
.98924
15,0
14,9
14,8
14,7
14,6
0,15023
. 14924
. 14825
. 14726
. 14627
98,9
98,9
98,9
98,9
98,9
9.99504
.995"
.995^7
.99524
.99530
6,6
6,6
6,5
6,5
6,4
9.17674
.17388
.17099
.16808
.16515
285,8
287,8
289,7
291,7
293,7
ji 21 36.O2
8 I 25 02.20
81 28 28.55
Jj 31 54-82
81 35 21.08
1.425
.426
0.08939
M.5
0.1.4528
.14429
98,9
9-93537
99543
6,4
6,3
9. 16221
. 15924
295,8
297*8
81 38 47-35
ir 42 13. fit
. i^^u
.427
.428
!o8o68
.98982
14,2
. 14330
. 14231
99,0
99,0
90549
.99556
6,3
6,2
. 15625
. 15324
299.9
302,1
8 1 45 39-88
ir 49 06.14
.429
.98996
14,1
.14 13*2
99,0
.99562
6,2
.15021
304,2
81 52 32.41
K430
431
0.99010
.99024
14,0
13,9
0.14033
. 13934
99,0
99,0
9.99568
.99574
6,2
6,1
9. 14716
. 14408
306,4
308,6
Si 55 58.67
81 59 24.94
.432
433
.99038
.99052
U,7
. 13835
. 13736
99,0
99,1
.99586
6,1
6,0
! 13786
310,9
$2 02 5I.2O
82 06 17.47
4-34
.99066
13,6
. 13637
99,1
99592
6,0
- 13472
315,5
82 09 43-73
1-435
.436
.99079
.99093
13,5
13,4
o, 13538
. J3439
99,1
99,1
9.99598
.99604
5,9
5,9
9. 13155
. 12836
317,8
320,2
82 13 10. oo
82 16 36.26
437
.99:06
1-3.3
. 13340
99,1
.99610
5,8
.12515
322,7
82 20 02.53
.438
. -439
.99120
-99I33
13.2
.13241
99,1
99,1
.99616
.99622
5,8
5,8
.12191
.11865
325,1
327,6
82 23 28.70
82 26 55.06
1.440
0.99146
13,0
0.13042
99,1
9.99627
5,7
9.11536
330, t
82 30 21.32
.441
.99159
12,9
.12943
99,2
.99633
5,7
.1120.1
332,7
82 33 47.59
.442
.99172
12,8
. 12844
99,2
.9039
5,6
,10870
335,3
82 37 13.85
443
.99185
12,7
.12745
CJ9.2
.99644
5,6
. 10534
338,0
82 40 40.12
.444
.09197
12,6
. 112646
99,2
.99650
5,5
.10194
340,7
82 44 06,38
1.445
0.99210
12,5
0,12546
99,2
9.99655
5,5
9.09852
343,4
82 47 32,65
.446
.99222
12,4
- 12447
99,2
.99661
5,4
.09507
346,2
82 50 58.93
447
.99235
12,3
. T234S
,99666
5,4
.09160
349,0
82 54 25 . 17
.448
.99247
12,2
. 12249
99.2
.99672
5,4
.08809
351,9
82 57 51.44
-449
.99259
12,1
. I2I50
99,3
,99677
5,3
.08456
354,8
83 oi 17.70
1.450
0.59271
12,1
0.12050
99,3
9.93682
5,3
p.oSioo
357,8
83 04 43-97
u
-Islnhiu
.
cosli lu
<- Fo'
lnn slnh '
w Fo'
log oosh I
W
u
lug -
-SMITHSONIAN TABLES
220
Circular Functions.
u
sin u
. H
cot u
to Fo
loo sin i
* F '
log cos
J 11 Fo'
' ^^_^.
u
1.450
0.9927
12,1
o. 12050
99,
9.996&
5,3
a.oSioc
Ttf.S
8 ' "
.451
.452
-453
454
.9928
9929
9930
9931
12,0
11,9
11,8
11,7
. 1 1951
.11852
1 1752
.11653
99,3
99,3
99,3
99,3
!99588
99693
.90698
99703
5,2
5,2
5,1
5,1
0774C
.07378
.07013
.0664*
hji_r/ >*-
3<x>,8
363.9
367*0
370,1
83 oS 10.23
83 n 36.50
83 15 02.76
83 18 29,03
1-455
456
457
-458
459
0-9933
9934
9935
.0936
9937
11,6
114
11,2
o.i 1554
.11454
.11355
.11256
.11156
99,3
99,3
99^
99,4
99,4
9.99708
99713
.99718
.99723
.99728
5,1
5,o
5,0
4,9
4.9
9.06272
.05837
.05519
05137
04752
373,4
376,7
380,0
383,4
386,8
83 21 55.29
83 25 21.56
83 28 47.82
83 32 14.09
83 35 40.35
1.460
.461
.462
-463
.464
0.9938
9939
99409
.99420
-99430
11,1
11,0
10,9
10,8
1 0,7
o.i 1057
.10958
. 10858
. 10759
.-10659
99,4
99.4
99.4
99.4
99,4
9-99733
.99738
.99742
99747
99752
4,8
4.8
4>7
4,7
4,7
9.04364
.03971
03576
.03176
.02773
390,4
394,0
397,6
401,3
405,1
83 39 06.62
83 42 32.88
83 45 59- 15
83 49 25.41
83 52 51.68
1.465
.466
.467
.468
.469
0.9944
-9945
.99462
.99472
.99482
10,6
io,5
10,4
T0,3
10,2
0.10560
. 10460
. 10361
. 10262
. 10162
C9.4
69,5
99,5
99,5
99,5
9-99756
.99761
.99766
99770
-99775
4,6
4,6
4,5
4,5
4,4
9.02366
.01955
.01540
.01121
.00698
409,0
412,9
416,9
421,0
425,2
83 56 17.94
83 59 44-21
84 03 10.47
84 06 36.74
84 10 03.00
1.470
.471
.472
473
474
0.99492
-99502
99512
.99522
-99532
io,r
IO,O
0,9
9,8
9,7
0.10063
.09963
.09864
.09764
.09665
99,5
99,5
99,5
99,5
99,5
9-99779
.99783
.99788
99792
-99796
4,4
4,3
4,3
4,3
4,2
9.00271
8-9C839
99403
.98953
.98518
429,4
433,7
438,2
442,7
447,3
84 13 29,27
84 if) 55-53
84 20 21.79
84 23 48.06
84 27 14.32
M75
.476
477
-478
.479
0.99542
-9955 t
.99560
-99570
-99579
9,6
9,5
9,4
9,3
9,2
0.09565
.09465
.09366
.09266
.09167
99,5
99,6
99,6
99,6
99,6
9.99800
.99805
.99809
.99813
.99817
4,2
4,1
4,1
4,0
4,0
8.98068
.97614
97IS5
.96691
.96222
452,0
456,8
461,7
466,7
471,8
84 30 40-59
84 34 06.85
84 37 33-12
84 40 59.38
84 44 25-65
1.480
.481
.482
.483
484
0.99588
-99597
.99606
.99615
.99624
9,0
8,9
8,8
8,7
0.0906-7
.08968
,aS8f>8
,08768
.08669
99,6
99,6
99.6
99,6
99,6
9.90821
.99825
.99829
95832
.99836
4,0
3,9
3,9
3,8
3,8
S. 95747
.95267
.94782
94292
.0379(5
477,o
482,3
487,8
493,4
499,1
84 47 51.91
84 51 18.18
84 54 44.44
84 58 10,71
85 01 36.97
1-485
,486
.487
.488
.489
0.03632
.99641
-99649
99057
.99666
8,6
8,5
8,4
8,3
8,2
0.08569
.08469
.08370
.08270
.08171
99,6
09,6
99,6
09,7
99,7
9.99840
.99844
90847
.99851
99855
3,7
3,7
3,6
3,6
3,6
8.93294
,92786
.92272
.91751
.91235
504,9
510,9
517,1
523,3
529,8
85 05 03.24
85 08 29.50
85 ir 55.77
85 15 22,03
85 18 48.30
1.490
491
492
-493
0.99674
.99682
.99690
-99698
8,1
8,0
7,9
7,8
0.08071
.07971
.07871
,07772
99,7
99,7
99,7
99,7
99858
.99862
.99865
.99868
3,5
3,5
3,4
3,4
8.90692
.90152
.89606
.80052
536,3
543,1
55 7i i
35 22 14.56
35 25 40.83
35 29 07.09
*5 32 33.36
.494
.99705
7,7
.07672
99,7
,99872
3,3
.88491
564,4
85 35 59-62
r-495
0.99713
7,6
0.07572
99,7
-9&S75
3,3
8.87923
57r,9
35 39 25.89
.496
.99720
7,5
07473
99,7
.99878
3,3
579,6
$5 42 52.15
-497
.99728
7,4
.07373
99,7
.99882
3,2
! 35764
587,4
85 46 18.41
.498
99735
'7,3
.07273
99,7
.99885
3,2
.86173
595,5
55 49 44.68
499
.99742
7,2
.07173
99,7
.99888
3,1
S5573
603,9
85 53 10.94
1.500
0.99749
7,i
0,07074
99,7
.99891
3,1
3.84965
612,4
35 56 37,21
u
-1 slnhlu
IV
cosh iu
. w
inh lu
i 1
w Fo'
og cash Iu
. w
u
SMITHSONIAN TABUS
221
Circular Functions.
-^.^^-^g^^^^^^aaB^^^^^^
**
u
sin u
^Ft,'
DOS U
*>Fo'
log sin u
u, Fo'
00 COS It
,Fo'
u
1.500
.501
.502
.503
.504
3-99749
.99757
.99763
99770
.99777
7,i
7.o
6,9
6,8
6,7
.07074
.05974
.06874
.06774
.06675.
99,7
99,8
99,8
99,8
99,8
9.9989'
.09894
.59897
.99900
.99903
3,1
3,1
3,0
2,9
2,9
.8.1965
.84348
.83722
.83087
.82,143
612,4
62:, 2
630,3
639,6
649,2
556' 37-21
6 oo 03.47
f i 03 29-74
6 06 56.00
5 10 22.27
1.505
.506
.507
.508
.509
0.997S4
.90790
.99797
.99803
.99809
6,6
6,5
6,4
6,3
6,2
0.06575
.05475
.05375
.06276
.06176
99,8
99,8
tjo.8
99,8
99,8
9.95906
.09909
.OOP 13
.90914
.99917
2,9
2,8
2,8
2,7
2,7
.81789
.81125
.80450
.79765
.790&9
659,1
669,3
679,8
690,7
701,9
86 13 48.53
6 17 14-80
fi 20 41.06
86 24 07,33
86 -27 33-59
1.510
.511
.512
.513
514
0.00815
.09821
.99827
.99833
.9<j839
6,1
6,0
5,9
5,8
5,7
0.06076
.05976
.05876
.05776
.05677
99,8
99,
99,8
99,8
99,8
9.99920
.99922
.09925
.99927
.99930
2,6
2,6
2,6
2,5
2,5
.78361
.77642
.76910
.76166
.75409
713,5
725,4
737,8
750,6
763,8
86 30 59-^6
6 34 26.12
86 37 52-39
86 41 18.65
6 44 44.92
I.5I5
.516
Si;
.518
.519
0.09844
.99850
.99855
,99861
,99866
5,6
5,5
5,4
5,3
5,2
0.05577
.05477
.05377
.05277
.05177
99,8
99,8
99,9
99,9
99,9
9.99932
.99935
.99337
99939
99942
2,4
2,4
2,3
2,3
2,3
74638
.73853
73054
. 72240
.714^0
777,5
79i,8
806,5
821,8
837,7
86 48 11.18
6 5i 37-45
Sf> 55 03.71
6 58 29.98
87 oi 56.24
1-520
.521
.522
.523
.524
0.99871
.99876
.99881
.99886
.99891
5.1
5,0
4,9
4,8
4,7
0.05Q77
.0-1978
.04878
.04778
.04678
99,9
99,9
99,9
99,9
99,9
9-99944
.09946
.99948
.99950
.99952
2,2
2,2
2,1
2,1
2,O
8.70565
.69702
.68821
.67923
.67005
854,2
871,4
889,3
907.9
927,4
87 05 22.51
87 08 48.77
87 12 15.04
87 15 41.30
87 19 07.56
1-525
.526
527
.528
.529
0.99895
.99900
.99904
.09908
.99913
4,6
4,5
4.4
4,3
4,2
0.04578
.04478
.04378
.04278
.04178
99,9
99,9
99,9
99,9
99,9
9.99954
.99956
-9G958
.99960
.99962
2,0
1,9
1,9
1,9
1,8
8.66068
.65110
.64130
.63127
.62101
947,7
968,8
991.0
1014,2
1038,5
8? 22 33.83
{7 26 00.09
\7 29 26.36
87 32 52.62
87 36 18.89
1.530
531
.532
533
534
0.99917
.99921
.95925
.09929
.99932
4,1
4.o
3,9
3,8
3,7
0.04079
.03979
.03879
.03779
.03679
99,9
99,9
99,9
99,9
99,9
9.99964
.99966
-99967
.99969
.99971
1,8
i,7
1,7
1,6
1,6
8.61050
.59973
.S836S
57735
.5657
1064,0
1090,7
Iir8,9
1148,5
H79.7
87 39 45-15
87 43 n-4'2
87 4f> 37-68
^7 50 03-95
87 53 30.21
1-535
-536
-537
.538
539
0.99936
.99939
.99943
.99946
99949
3,6
3,5
3,4
3,3
3,2
Q.03579
.03479
.03379
.03279
.03179
99,9
99,9
99,9
99,9
99,9
9-99972
.99974
99975
.99977
.90978
1,6
i,5
i,5
r,4
1,4
8.55375
.5414.
.52879
.5157
. 50230
I2I'2,7
1247,6
1284,5
1323,7
1365,4
87 56 56.48
88 oo 22.74
88 03 49.01
88 07 15.27
88 10 41-54
1-540
.54*
.542
-543
^544
0.99953
.99956
-99959
.99961
.99964
3,1
3,0
2,9
2,8
2,7
0.03079
.02979
.02870
.02779
.02679
100,0
100,0
100,0
100,0
100,0
9-99D79
.9998
.9998
.9998
-9998
1,3
1,3
1,3
1,2
1,2
8.4884
47410
.4592
-4439
,4280
1409,8
1457,1
1507,7
1562,0
1620,3
88 14 07.80
88 I? 34-07
88 21 00.33
88 24 26.60
S8 27 52.86
1-545
.546
.547
.548
.549
0.99967
.99909
99972
99974
.99976
2,6
2*5
2,4
2.;
2,2
0,02579
.02479
.02379
.02279
.02179
100,0
100,0
100,0
100,0
100,0
9.f)0o8f
.9998
.99988.
.99989
.99930
I,T
1,1
1,0
1,0
0,9
S.4H5
.3943
.376:1
.3578
.3383
1683,2
1751,
1824,7
1904,8
1992,
88 31 19.13
88 34 45-39
88 38 IT. 66
88 41 37-f>2
884S 04.18
1-550
0.09978
2,
0.02079
100,0
9-9999
0,9
8.31796
2088,0
88 48 30-45
u
-] slnlilu
<> Fo
coshlu
<oF '
i nJ , sinh
w Fo'
loo cosh
u Fo
u
SMITHSONIAN TABLES
222
I.ODOU!
. ) |t n y n
I , I H K X II
I ,01 Mil K
I .OO: XX
. Of !i X K
,Oni H ir
.(NmiH
/HK)
UInlilii
Circular Functions.
iQQSIn
88
51 56.7
S S -'2 . (
i>
89 05 4' i. 7
oy 08.0
'-' 34-3'
, in 00.5
89 ly 2(1.8,
ftj 22 53,11
89 -'6 io.,i<
8ij 11.) 45. (i
.. 33 H.M<
89 36 38. K
|o 04.4
13 30. 61
89 46 56.9.
5O 23. 2~
53 -19
57 15.75
(X) 42.0
jo 04 08,2!
ID 07 34-5-
jo n oo.Hi
14 27.07
JO 17 53- 3J
jo 21 i().6c
Xi 24 45. 8f
>) 28 12.13
jo 31 3^.3'J
jo 35 04.66
jo 38 30.02
jo 41 57. TO
X> 45 23.45
jo 5J 15.98
o 55 42.25
5o 08.51
1 02 3.1,78
ort or. o.|
(xj 27.31
12 53-57
16 !<j.8|
19 46. 10
23 12.37
-'6 38, 63
i 30 04.00
i 33 31.1(1
i 36 57"13
OOSlllll
SMITHSONIAN TABLCB
Circular Functions.
irr^ i ^_j-^^^4-^^ ii
o.o 1
.1 1
.2
3
+-O.OOOOO OOOOO
.09983 34166
.19866 93308
.29552 02067
.38941 83423
+1,00000 ooooo
0.99500 41653
,98006 65778
-95533 64891
,92106 09940
CO
9.29813
9-47059
9.59042
0.00000
9-99782
9.99 126
9.98016
9-96429
CO OO OO.OOOOO 00 II
05 43 46.48062 47
ii 27 32.96124 94 1
17 ii 19-44187 4i II
22 55 05.92249 88 1
4
'.6
1
.0
+0.47942 55386
.56464 24734
,64421 76872
.71735 60909
.78332 69096
+0.87758 25619
.82533 56i49
.76484 21873
.69670 67093
.62160 99683
9.68072
9.75177
9.80503
9.85573
9-94329
9.91663
9.88357
9.84305
9-79352
28 38 52-40312 35 1
34 22 38.S8374 83
40 06 25.3643? 3 I
45 50 n.84499 77 II
Si 33 58-32562 24 1
'VI . - - i
tonnf\A
ey 17 44.80624 71 1
I.O
.1
.2
3
4
J -5
.6
.0
+0.84147 09848
.89120 73601
.93203 90860
.96355 81854
.98544 97300
+0-99749 49866
99957 36030
.99166 48105
.97384 76309
.94630 00877
+0.54030 23059
45359 61214
.36235 77545
.26749 88286
.16996 71429
+0.07073 72017
.02919 95223
.12884 44943
.22720 20947
.32328 95669
9.92504
9^98388
9.99891
9.999SJ
9-99636
9.98849
9-97 6 3
9^65667
9-55914
9.23036
8.84965
8.46538,,
9-iioo7 n
9.3S64I,,
9-50959,,
63 oi 3i.=86B 7 18 1
68 45 17-76749 f>5 II
74 29 04.24812 12 1
So 12 50,72874 59 II
85 56 37-20937 06 II
gi 40 23-6S999 54
97 24 10.17062 oi 1
103 07 56-65124 48
108 51 43-i3i86 95 It
-y
2.O
: .i
1 <d
+0.90929 74268
.86320 93666
.80849 64038
.74570 52122
.67546 31806
-0.41614 68365
.50484 61046
.58850 HI73
.66627 60213
-73739 37*55
9.95871
9.93612
9.90768
9.87257
9.82960
9.61925*
9.70316,,
9.76975 n
9-82365,,
114 35 29.61249 42 11
120 ig 16.09311 89 1
126 03 02.57374 36 II
131 46 49- 5436 83 1
13? 3 35-53499 3Q II
_ f _ .__ 1
t ^
fl OO'l?!
143 14 22.01561 77 II
2,5
1
+0.59847 21441
.51530 I37"
.A2717 ()88O2
0.80114 36i55
.85688 87534
,90407 21420
0.71223
9.63081
9.93292.,
9.95620,,
148 58 08.49624 24 1
154 4i 54.97686 11
160 25 4L45749 *<> I
:
' J r*jO/ J
.33498 81502
.23924 93292
.94222 2340?
,97095 81651
9'-37885
9.98720,,
166 09 27.93811 66 1
u
*
1
+ O.I4H2 OOOSl
+ .04158 06624
- .05837 41434
.15774 56941
-0.98999 24966
.99913 51503
.99829 47758
.98747 97699
.96679 81926
9-H959
8.61889
8.76622,,
9.40746,,
9.99563,.
9.99962
9.99453,1
9.98534,,
171 53 I4.f874 13
177 37 00.89936 60 1
183 20 47.37999 0? 11
189 04 33-86o6i 54 II
194 48 20.34124 01 II
,:
i
-0.35078 32277
,44252 04433
.52983 61409
,6ll85 78909
-0.93645 66873
.89675 84163
.84810 00317
.79096 77 IJ 9
,72593 23042
9-64593,,
9.72414,,
9.78665,,
9-83 744n
9-97M9
9,95268,,
9,9284.5,,
9.89816,,
9.86090,,
200 32 06.82186 48 1
206 15 53-30248 95 II
2ir 59 39-7H3" 43
217 43 26.26373 90 II
223 27 12.74436 37 1
.68776 61592
i ii
1
II -4
-0.75680 24953
.81827 7IIH
.87157 577H
.91616 59367
.95160 20739
0.65364 36209
.57482 39465
.49026 08213
.4,0079 91721
.30733 2S 7
9.87898,
9.91290,,
9.94031,
9,96197,,
9.97846,,
9-'/5953 n
9-69043,,
9-60293,,
9-48761,.
229 10 59.22498 84 1
234 54 45-70561 3J
240 38 32.18623 78
246 22 18.66686 25
252 06 05.14748 7 2 1
-0.97753 OIIJ7
.99369 10036
.99992 3257*
.99616 4608?
,98245 26126
-0.21079 57994
.11215 25269
- .01238 86635
+ ,08749 89834
.18651 23694
9-99 OI 3i
9.99997,
9-99 8 33
9.99231
9.o49 8l >
8.09302,,
8,94200
9.27071
257 49 5i.638n 19
263 33 38-10873 66
269 i? 24-58936 J4
275 oi 11.06998 61
280 4<l 57.55061 08
S.o
-0.95892 42747
+0.28366 21855
9.98178
9,45280 1 286 28 44-03123 55 II
Ir" ~" "l ~~" **" 1 1 alnll lit 1 1 it
SMITHBONIAM TABLES,
224
Circular Functions,
5-"
.1
0.5
!H
9
BtllU
88345 4 ( 's.sy
.H;)J3(> '/.|.|JJ
.77*76 44"7<>
o.u yo-l i 5408.1
.18316 ajjo-n
.1)8308 (j.jnjji
.01(181 3<)(in<j
(o.ai;;i i yijHfii
.40484 (}l).!l}(
-4041' 33SH
.S7'I3 9'/<'44
,i)(u,W\
.nnviy
"l.sy.M !f [
-o.,'(44O3 JiiOij
- 1 Hltih In
.y/5.s'> ^'/KS
'O.ijfioiy oisHfiy
,(]K.VJ(i K
.<)(,)'.')'') y
.'I'JijU.S H
.!.)(),) 18 ,]
.H(i().1<) 7400,1
.Hi 1,7 a ,siooi
'J'l.l.S'l 'I'.S.V/
3 0:1(119
()4*/73 l(H13l
o.H.iyoy 151
oath lu
log Bill U
.'/,( 0(JO,,
0.33 afiH
y.yfiaafi
o.JHiayr
y.yfiyoij
(j/n;;oa
9.2413(1,,
9-5<
log oofl n
9.45280
0-67073
9-74,^0
y. 80256
0.H(>6a
y.()ziS4-
y.iMyao
0-96730
9.90277
9.99850
9-90703
9- 87 73 a
9.78415
9.72105
9.64202
9,40012
'1-^8575
8-73204
9-53040,,
9-99330,,
9-9833.I,,
9.96868,,
9-94900,,
log ooali lu
286 28 44.03123 55
293 12 30.51186 02
297 56 16.99248 49
303 40 03.47310 96
309 aa 49-95373 43
315 07 36.43435 90
320 51 22,91498 37
326 35 09.39560 84
33 2 18 55.87623 32
338 02 42-35685 79
343 46 28.83748 26
349 30 15-31810 73
355 14 01.79873 20
360 57 48.27935 67
366 41 34.75998 14
372 25 21.24060 6t
378 09 07,72123 08
383 52 54-30185 55
389 36 40.68248 03
395 20 27.16310 50
401 04 13.64372 97
406 48 00.12435 44
412 31 46.60497 91
4^8 15 33.08560 38
423 59 19.56622 85
429 43 06,04685 32
435 26 52.52747 79
441 10 39.00810 26
446 54 25.48872 73
452 38 11.96935 21
458 21 58.44997 68
464 05 44.93060 15
469 49 31.41122 62
475 33 17-89185 09
4i 17 04.37247 56
487 oo 50.85310 03
492 44 37-33373 So
498 28 23.81434 97
504. is 10.29497 44
.W 55 56.77559 92
.^5 39 43-25622 39
521 23 29.73684. 86
527 oy 16.21747 33
532 51 02,69809 80
53 34 49i : /873 a?
544 18 35.65934 74
550 O2 32,13597 2(
555 46 08,62059 68
561 29 55.10132 15
567 13 41-58184 63
573 57 38.06347 10
TAHLEO,
224 a
Circular Functions.
u
stau
coan
log sin it
log DOS U
u
O 1 II
,
o.ooooo
OO OO OO. OOOOO OO
o
I
2
3
4
O.OOOOO OOOOO
+ .84147 09848
+ .90929 74268
+ .14112 00081
- .75680 24953
I, OOOOO OOOOO
+0.54030 23059
- .41614 68365
.98999 24966
- -65364 36209
9-92504
9.95871
9-14959
9.87898,,
9-73264
9-61925,1
9-90563,.
9.81534,,
57 17 44.80624 71
"4 35 29.61249 42
171 53 14.41874 13
229 10 59.22498 84
5
6
7
8
9
-0.95892 42747
- .27941 54982
+ .65698 65987
+ .98935 82466
+ .41211 84852
+0.28366 21855
+ .96017 02867
+ .75390 22543
- .1455 00338
.91113 02619
9.98178,,
9-446 2 5 n
9-81756
9.99535
9.61502
9.45280
9.98235
9.87732
9.16286,,
9-95958,,
286 28 44-3 I 23 55
343 46 28.83748 26
401 04 13-64372 97
458 21 58.44997 68
SIS 39 43-25622 39
10
ii
12
13
14
0,54402 11109
.99999 02066
- .53657 29180
+ .42016 70368
+ .99060 73557
-0.83907 15291
+ .00442 56980
+ -84385 39587
+ .90744 67815
+ -13673 72182
9-73562"
O. OOOOO n
9.72963,,
9.61342
9.99590
9-92380,,
7.64598
9.92627
9,95782
9-13589
572 57 28.06247 10
630 15 12.86871 81
687 32 57.67496 52
744 50 42.48121 23
802 08 27.28745 93
15
16
18
19
+0.65028 78402
- .28790 33167
- .96139 74919
- .75098 72468
+ .14987 72097
-0.75968. 79129
- .9S765 94803
- .27516 33381
+ .66031 67082
+ .98870 46182
9.81311
9-45925.,
9-17574
9.88064,,
9.98121,,
9-439 59,i
9.81975
9.99507
859 26 12.09370 64
916 43 56.89995 35
973 61 41.70620 06
1031 19 26.51244 77
1088 37 11.31869 48
20
21
22
23
+0.91294 52507
+ .83665 56385
- .00885 I 393
.84622 04042
+0.40808 20618
- .54772 92602
.99906 08264
-53283 30203
9.96044
9.92255
7.94701,,
9.92748,,
9.61075
9.73857,,
9.99998,,
9-72659,,
IMS 54 56-12494 19
1203 12 40.93118 90
1260 30 25.73743 61
1317 48 10.54368 32
24
- -90557 83620
+ .42417 90073
9.95693,1
9.62755
1375 05 55-3-1993 03
25
26
27
28
-0.13235 17501
+ .76255 84505
+ .95637 59284
+ .27090 57883
- .66363 38842
+0.99120 28119
+ .64691 93223
.29213 88087
.96260 58663
- .74805 75297
9.88227"
9.98063
9.43282
9-82 193n
9.99616
9,81085
9-46559
9-9834S.,
1432 23 40.15617 74
1489 41 24.96242 45
1546 59 09.76867 16
1604 16 54-57491 87
1661 34 39-38116 58
30
3 1
-0.98803 16241
- .40403 76453
+0.15425 14499
+ .91474 23578
9.99477,,
9.60642,,
9.18823
9.96130
1718 52 24,18741 29
1776 10 08.99366 oo
32
33
+ .55142 66812
+ .99991 18601
+ .83422 33605
- .01327 67472
9.74149
9.99996
9.92128
8.12309,,
1833 27 53-79990 71
1890 45 38.60615 42
34
+ .52908 26861
- .84857 02748
9.72352
9.92869,,
1948 03 23.41240 13
35
36
-0.42818 26695
- .99177 88534
0.90369 22051
.12796 36896
9 -63 1 63 n
9-99641.,
9.10709,,
2OO5 21 08.21864 84
2062 38 53-02489 55
37
- .64353 8l 334
+ .76541 40519
9.80857,,
9-88390
2119 56 37-83114 26
38
+ .29636 85787
+ '9550? 36440
! 9-47183
9.98004
2177 14 22.63738 97
39
+ .06379 53863
+ .26664 29324
9.98398
942593
2234 32 07.44363 68
40
+0.74511 31605
0.66693 80617
9.87222
9.8240911
2291 49 52.24988 39
41
- .15862 26688
- -9 8 733 92775
9.20037,,
9.9944?"
2349 7 37- 56i3 10
42
- .01652 15479
- -39998 5315
9-96214,,
9,60204,1
2406 25 21.86237 80
43
- .83177 47426
+ '555 11 33 OI 5
9-92001,,
9.74438
2463 43 06.66862 51
44
+ .01770 19251
+ .99984 33086
8.24802
9.99993
2521 oo 51.47487 22
45
+0.85090 35245
+0.52532 19888
9.92988
9.72043
2578 18 36.28111 93
46
+ .90178 83476
- .43217 79449
9-95510
9-63566,1
2635 36 21.08736 64
47
+ -12357 31227
- -99233 54692
9.09192
9.99666,1
2692 54 05.89361 35
48
- .76825 46613
- .64014 43393
9-8855i n
9.80628,1
2750 ii 50.69986 06
49
- -95375 26528
+ .30059 25437
9.97944i.
9,47798
2807 29 35.50610 77
So
-0.26237 48537
+0.96496 60285
9.41892,,
9.98451
2864 47 20,31235 48
u
istnhlu
cosh lu
. slnhiu
log cosh In
u
lOg j
SMITHSONIAN TABLES.
224 b
Circular Functions,
u
slnti
DOS U
log sin it
10 COS U
n
5o
Si
52
53
54
-0.26237 48537
+ .67022 91758
-j- ,98662 75Q2O
+ -39592 5IS02
- .55878 90489
4-0.96496 60285
4- .74215 41968
. 16299 07808
.91828 27862
.82930 98329
9.41892,,
9.82622
9.99415
9.5976i
9.74725
9-Q845I
9.87049
9.2I2l6,i
9,96298
9.91872*
2864 47 20.31235 48
2922 05 05.11860 ig
2979 22 49.92484 go
3036 40 34.73109 61
3093 58 19-53734 33
55
so
57
58
SO
-0.99975 SI734
- .52155 10021
+ .43616 47552
4- .91)287 26481
+ .63673 SOO?!
4-0.02212 67563
+ -85322 OlO??
4- ,89986 68270
+ .IlgiS 01354
.77108 O2230
9.99989-
9-7 1 730
9.63965
9.99689
9.80396
8.34492
9.93106
9.95418
9.07620
9.88710*
3.151 16 04.34359 03
3208 33 49-14983 74
3265 Si 33.956o8 45
3323 09 18.76233 16
3380 27 03.56857 87
60
6r
62
63
64
0.30481 06211
.96611 77700
.73918 06966
+ -i<>735 57003
-|- .92002 60382
0.95241 29804
.25810 16359
4- -67350 7 I(52 3
4- .98589 65816
4- -39185 72304
9.48403
9-9&503
9.86875,,
9-22364
9.96380
9-97883*
9-4II79j>
9.82834
9.99383
9.S93I3
3437 44 48.37482 58
3495 02 33.18107 29
3552 20 17,98732 oo
3609 38 02.79356 71
3666 55 47-5998i 42
6S
66
67
OS
69
-1-0.82682 86795
.02655 115:40
- - 8 555i 99790
~- .89792 76807
.11478 48138
-0,56245 38512
099 6 4 7456o
.51776 9799S
4- .44014 30225
4- -99339 03797
9.91742
8.42408
9-93223,,
9-95324"
9.05987"
9-75oog n
9-99985n
9.71414-1
9-04359
9.99712
3724 13 32,40606 13
3781 31 17.21230 84
3838 49 02.01855 55
3896 06 46,82480 26
3953 24 31.63104 97
70
7r
72
73
74
4-0.77389 06816
+ .OSioS 46533
+ - 2 538a 33628
.67677 19569
.98.514 62605
+0.63331 92031
~ ,30902 27282
.96725 05883
.73619 27182
+ .17171 73418
9.88868
9.97821
9-404S3
9-83044 n
9-99350*
9.80162
9,48999"
9.9S5S4n
9.86699,,
9.23481
4010 42 i6,4372(> 67
4068 oo 01.24354 38
4125 17 46.04979 09
4182 35 30.85603 So
4239 53 15-66228 51
75
76
77
78
79
-0.38778 16354
+ .56610 763(19
+ .99952 01586
+ .51397 84560
.44411 26687
4-0,92175 12697
4- .82433 1331 r
.397 50317
.85780 30932
.89597 09468
9-5S8sg n
9-75290
9-99979
9.71094
9-64749i
9.96461
9.91610
8.49101,,
9.93339i
9-952 sg n
4297 II 00,46853 22
4354 28 45-27477 93
4411 46 30.08102 64
4469 04 14.88727 35
4526 21 S9'69352 f>
80
81
82
83
84
-0.99388 86539
- .62988 70943
+ .31322 87824
4- .96836 44611
4- 733 I 9 03201
0,11038 72438
-4- .77668 59820
+ .94967 76979
-|- .24954 01180
.68002 34956
9.99734"
9.79926,,
9-495S6
9.98604
9.86522
9. 04292 n
9.89025
9.97758
9-39714
9.832520
4583 39 44.49976 77
4640 57 29.30601 48
4698 15 14.11226 it>
4755 3.2 58.91850 90
4812 50 43-72475 61
8S
86
8?
88
89
0.17607 56199
.92345 84470
.82181 78366
+ .03539 83027
4- .86006 94058
o.t>8437 66434
.38369 84449
+ .56p75 03343
+ -99937 32837
+ -51017 70449
9.24S70,,
9.96542,,
9.91478^
8.54898
9,t>3453
o.Q<>3*6n
g.5839pn
9.75568
9-99973
9.70772
4870 08 28.53100 32
4937 26 13-33725 3
4984 43 58.14349 74
5042 01 42.94974 45
5099 19 27-75599 16
go
9i
92
93
91
. +O.S9399 66636
4- .10598' 75118
.77946 60696
.94828 21413
- .24525 19855
0,44807 36161
.99436 74609
- .62644 44479
4- ,31742 87015
+ .96945 93667
9-9SI34
9.02525
- 9,89180,.
9.97694,,
. 9.38961,,
9-65i35
9-90755"
9.7968 8 rt
9.50165
9.98653
5156 37 12.56223 87
5213 54 57-36848 58
5271 12 42.17473 29
5328 30 26.98098 oo
5385 48 11,78722 71
95
9<3
97
98
99
4-0.68326 17147
4- ,98358 77454
4- ,37960 77390
-57338 18720
.99920 68342
+0.73017 35610
.18043 04493
-92514 75366
.81928 82453
+ .03982 08804
9-83459
0.99281
9-57934
9-75844"
9.999661!
9.86343
9.25631:,,
9.96621,,
o.9i344
8.6001 1
5443 05 56.59347 42
5500 23 4I-39972 13
5557 4i 26.20596 84
5614 59 n.01221 54
5672 16 55.81846 25
IQO,
0.50636 56411
+0,86231 88723
9.70446 r ,
9-93567
5729 34 40,62470 96
u
- 1 sink lu
ODSh lU
. slnhlu
log coai la
u
WB j
SMITHSONIAN TAB LES.
224C
TABLE IV
THE ASCENDING AND DESCENDINfi EXPONENTIAL AND
The Exponential.
u
loom*"")
o"
0""
u
IOQ10(0 H )
o u
-
O.OOO
.001
,003
.004
O.OOO (XXX)
.(xx) 434;i
,o(X) HdHo
.(X)i 30-'0
.001 737-'
I.(HX) (XX)
.(KM tlOl
,(xw 002
003 005
.004 008
I.OtX) OOOO
o.ow 0005
.()()7 0045
0.050
.051
.052
.053
054
0.021 7147
.022 I49O
.022 583.1
.023 0176
,023 4510
1.051 271
-052 .123
05.1 376
054 430
OS'S 485
0.951 2294
.950 2787
-949 3^89
.948 3800
947 4321
0.005
,(XX)
.007
.008
0.00,! 1715
.(H)3 (I.|OI
.003 4744
i .(X)5 013
.00(1 018
.(XhS 0,1.!
.IX.M 0180
.<W3 0-244
<A>2 0319
0.055
.056
057
.058
0.023 8862
.024 3205
.024 7548
.025 ifior
1.056 541
057 598
.058 656
059 7r5
0.946 4851
.945 5391
-944 5941
-94.1 6459
.000
,(X)3 <X>87
.OOf)U|I
.991 040.1
.059
.025 6234
.060 775
.942 7068
0.010
.01 1
,00.| ?/?'
I. 010 050
,011 tioi
o.poo o.j<>S
.yH(j 0003
0.060
.00!
0.026 0577
.026 4920
i. 06 i 837
.062 899
0-941 764S
.940 8232
.01.!
.013
.cms -'' i.S
.cxi.'i fi-15't
.1)1,* 1172
.013 08,1;
.(j8H 0717
.1)87 0841
,()((J
.001
.026 92(),1
fV'*7 lffl(\
,0f>3 <X)2
-939 8829
.014
.000' oMoi
.014 oyM
980" WJ75
. */ FJ
.064
\t*.f jJVUJll
.027 7948
.065 027
,066 092
-938 9,1,15
.938 0050
0.015
,010
o.ooli 514-1
.000' 0487
1.015 113
o.<)85 i no
.9811 1273
0.065
.ofifi
0,028 221)1
.028 (if)3,)
1.067 159
.068 227
0.937 0675
936 1309
.017
.018
.007 3830
.007 8173
.017 MS
.oiK 1(13
,<$ 1(110
;S
<02<) 5320
.069 295
,070 365
935 1952
.934 2605
.OMJ
.OOM -!5l(i
,oi<) 182
.yHi 1791
-0(HJ
.029 9663
.071 436
933 3267
0.020
0.008 MHO
I.OJO .!OI
o.oM 1987
0.070
0.030 aoo6
1.072 508
0-932 3938
.0.11
,<H) IJOJ
,<ui 22 j
-979 i!i(X>
.071
.030 8349
.073 581
931 4619
.<
.(X>9 5M. ( i
.(>,!.! .!4_4
,g?8 j.joj
.OX-J
.031 2602
.074 655
-930 5.109
.OJ3
.000 !)HMM
,o'3 -rf'7
,077 2(l!5
.073
.031 7035
.075 73'
.920 6008
,OJ.|
.010 4^31
,(>3.| 4JO
UX'i 2857
.074
032 1378
.076* 807
.928 6717
0.0-15
o.oio 8574
I. 025 315
0-975 3099
0.075
0.032 5721
1.077 884
0.927 743'5
.02/1
.on : j()i'/
>oj(i ,141
.07-1 .135'
.076
.033 006*4
.078 03
.926 8162
.0.7
.on 7yt
.0.17 .{(W
.073 31 "M
.077
.(133 4407
.080 042
.925 8899
,OJK
,oi;i Ut.j
.o:;8 31/1
.072 3884
.078
.0.13 8750
.081 123
.924 0644
.020
,OU! 5915
4) 4^5
971 4i'i5
079
.034 3093
.082 204
,924 0399
0.030
0.013 0,188
1.030 455
0.970 441'i
0.0>%
0.0.14 7436
r.o8.i 287
0.923 1163
.031
.013 .1(131
.031 ,|M
.'X) 47S'i
.081
.035 1779
084 371
.922 1037
.03 a
.013 8074
.o.iJ 518
,iX)H 5ofKi
.ote
.035 (inn
.085 456
.921 2720
.033
.01*1 3317
.033 55'
,1X17 5386
.083
.036' 0464
.086 542
.920 3Sn
.034
,01.) 7(100
.034 585
.!Xi(i .1715
.084
,036 4807
.087 629
9'9 43^3
0.035
O.OIJi '.JOO.l
1.035 fiJK)
0.(Xl5 6054
0.085
0.0.16 9150
1,088 717
0.918 5123
.03ft
.015 (1340
.03(1 (15(1
.1X14 r>,ib.i
.086
0,17 3403
.089806
.917 5942
.037
,oi(i ofMj
.037 'i<)3
.iX'M ("i7'1 1
.087
.037 7836
.000 8(>7
.910" 6771
-03H
.Old 50.1.1
.038 73'
.i/u 7120
.088
.0,18 2170
.nor o8K
.915 7609
.039
OKI 0375
.030 77"
I/il 7507
.oHu
.038 (1522
.003 08 i
.914 8450"
0,040
0.017 .'17 'H
1.040 Mir
O.ofifi 7ftj4
O.OIX)
0.0.19 o8T5
1.094 174
0.913 9312
.an
,017 Ho'ii
.041 HSJ
,i)SO ftao i
Of) I
.039 5208
.095 2tx)
.913 0177
.O.IJ
.OlH .140,1
,04^ HIJ,|
,(J5H H(V)8
.(KM
.0.19 9551
o(X> 365
.912 1051
.04,1
,oiK (1747
.043 038
957 PI'M
CKJ3
.0.10 3894
.097 462
911 1935
.010. 1000
.044 WH2
.05(1 9540
'094
0,|0 8237
.098 560
,910 2828
0.045
o.oio 5,1,13
I,0;|(i (UH
0.055 WJ75
0.095
0.041 2580
i .09?) 659
0.909 3729
.0|0
otg 0775
.IM7 i74
,055 (uao
,(xXi
.aii 6923
. 100 750
.908 4640
!o4
.04) 4IlH
.oao Rin'i
,0| IJJ
.040 171
.054 0874
;SX
.043 1266
,0.|2 5000
.101 860
. 102 963
.907 5560
,906 6489
.040
,041 3WX|
.050 320
lys'a lo'u
.099
.043 9952
.104 066
.905 7427
0,050
0.031 7M7
I.05I 371
0.95: 3204
O.IOO
0.043 42{M
I. 105 >7i
0.904 8374
<",
...*>
f
.-
~^r
10010(0")
e"
<T U
8MITHOmAN TABUS
226
The Exponential.
u
loaiota")
e u
e - u
U
,
e u
- ' '
O.IOO
0.043 4294
1. 105 171
0.904 8374
0.150
0.065 1442
1.161 834
0.860 ?0 go
,ior
,102
.043 8637
.044 2980
. 106 277
. 107 383
903 9330
.903 0296
.151
.152
.065 5785
.066 0128
. 162 997
.164 160
.859 8477
.103
.044 7323
. roS 491
.902 1270
.153
.066 4471
. 165 325
. 858 j 2 Q7
,104
.045 1666
. 109 600
.901 2253
154
.066 8814
. 166 491
857 27^0
0.105
0.045 6009
i. no 711
0.900 3245
0.155
0.067 3156
i . 167 658
o.SsS 4. ts3
.106
.046 0352
.in 822
.899 4246
-156
.067 7499
. 168 826
'855 5<n2
.107
.046 4695
.112 934
-898 5257
.157
.068 1842
.169 996
^54 >o4 r
.108
.046 9038
. 114 048
.897 6276
.158
.068 6185
.171 166
853 8 4 oS
.109
047 338i
.115 162
.896 7304
.159
.069 0528
.172 338
852 tx^
O.IIO
0.047 7724
1.116 278
0.895 8341
0.160
0.069 4871
I.I73 5ii
0.852 1438
.III
.048 2067
.117 395
.894 9387
.161
.069 9214
.174 685
.oSI 2<J2l
.112
.048 6410
n8 513
.894 0443
.162
.070 3557
.175 860
8oO ^^12
.113
049 0753
.119 632
.893 1507
.163
.070 7900
.17? 037
. 849 PQ T 2
.114
.049 5096
.120 752
.892 2580
.164
.071 2243
.178 214
'848 7420
0.115
0.049 9439
I . 121 873
0.891 3661
0.165
0.071 6586
I-I79 393
0.847 &t>37
.116
.050 3782
. 122 996
890 4752
.166
.072 0929
.180 573
847 0462
.117
.050 8125
.124 119
.889 5852
.167
!o72 5272
.181 754
846 1 996
.051 2467
.125 244
.888 6561
.168
.072 0615
.182 937
845 3538
.119
.051 6810
. 126 37O
.887 8078
.169
073 395S
.184 I2O
844 5089
O.I20
0.052 irsa
I . 127 497
0,886 9204
0.170
0.073 8301
I.I85 305
0.843 6648
.121
.052 5496
, . 128 625
.886 0340
,171
.074 2644'
. i85 491
.122
.052 9839
. 129 754
.885 1484
.172
.074 6987
. 187 678
.841 07921
.123
.053 4182
. 130 884
.884 2637
'73
.075 1329
.188 866
.841 1376
.124
.053 8525
. 132 016
-883 3798
174
.075 5672
,190 056
.840 2069
0.125
0.054 2868
i. 133 148
0.882 4969
0.175
0.076 0015
1.191 246
0.839 4570
.126
.054 7211
. 134 282
.881 6148
.176
.076 4358
.192 438
.838 GiSo
.127
.055 1554
T35 417
.880 7337
.177
.076 8701
.193 631
837 7708
.128
.055 5897
136 553
.879 8534
.178
.077 3044
. 194 825
.836 0-124
.129
.056 0240
.137 690
.878 9740
.179
.077 7387
.196 021
.836 1059
0.130
0.056 4583
1.138 828
0.878 0954
0.180
0.078 1730
I.I97 217
0,835 2702
.131
.056 8926
.139 968
.877 2178
.181
.078 6073
.198 415
.834 4354
.132
.057 3269
.141 108
.876 3410
.182
.079 0416
. 199 614
.833 6013
.133
.057 7612
.142 250
.875 4051
.183
079 4759
.200 814
.832 7682
.134
.058 J955
.143 393
.874 5901
.184
.079 9102
.202 Ol6
.831 0358
0.135
0.058 6298
i - 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 ;736
.137
.059 4983
. 146 828
.871 9702
.187
.081 213*
.205 627
.829 4437
.138
.059 9326
- M7 976
.871 0987
.188
.081 6474
.206 834
,828 614?
.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
0.190
0.082 5160
1.209 250
0.826 ffS&i
.141
.061 2355
.151 425
.868 4893
.191
.082 9502
.210 459
.826 1326
.142
.061 6698
.152 577
.857 6213
.192
-083 3845
.211 671
.825 3069
.143
.062 1041
153 730
.866 7541
193
.083 8188
.212 883
.824 4*530
.144
,o52 5384
.154884
.865 8877
.194
,084 2531
.214 O06
.823 6579
0.145
0.062- 9727
i . 156 040
0.865 0223
0.195
0.084 6874
I.2I5 311
0.823 S347
.146
.063 4070
.157 196
.864 1577
.195
".085 1217
.2l6 527
.822 OI22
.147
.063 8413
. 158 354
,863 2940
.197
.085 556o
.217 744
.821 l*XX>
.148
.064 2756
159 513
.862 4311
.198
.085 9903
.218 962
.820 3<5ox>
.149
.064 7099
. 160 673
.861 5691
.199
.086 4246
.220 l82
.819 54g>
0,150
0.065 1442
1.161 834
O.S6b 7080
O.20O
0.086 8589
1.221 4O3-
o.SiS 7303
,.,.,.-,
Ionise")
a"
Q ~u
,.(.",
looio(e u )
e u
a
SMITHSONIAN TABLES
227
The Exponential.
II
log 10(0")
e"
e- u
11
1ooio<e u )
e"
e-' 1
0.2OO
.2OI
.202
.203
.204
0.086 8589
.087 2932
.087 7275
.088 1618
.088 5961
I. 22 I 403
.222 625
.223 848
.225 0?2
.226 298
0.8:8 73o8
.817 9124
.817 0949
.816 2782
.815 4624
0.250
.251
.25-2
.253
.254
0.108 5736
.109 0079
. 109 4422
109 8765
.no 3108
I . 284 025
.285 310
.286 596
.287 883
,289 172
0.778 8008
.778 0224
.777 2447
.776 4679
.775 6918
0.205
,2O6
.207
.208
.2O9
0.089 0304
.089 4647
.089 8990
09 3333
.090 7675
1-227 525
.228 753
.229 983
.231 213
232 445
0.814 6473
.813 8331
.813 0196
.812 2070
-811 3952
0.255
.256
257
.258
259
o.no 7451
-III 1794
.III 6137
.112 0480
. 1 12 4823
1.290 462
291 753
-293 045
.294 339
.295 634
0.774 9165
774 1420
-773 3682
772 5952
.771 8230
0.2IO
.211
.212
.213
.214
0.091 2018
.091 6361
.092 0704
.092 5047
.092 9390
1.233 678
.234 9 '2
.236 148
237 385
,1238-623
0.810 5842
.809 7741
.808 9647
.808 1561
.807 3484
0.263
,261
.262
263
.264
O.I 12 9166
"3 3509
.113 7852
, 114 2194
H4 6537
1.296 030
.298228
.299 527
.300 827
.302 128
0.771 0516
.770 2809
.769 5110
.768 7419
-76? 9735
0.215
0.093 3733
1.239 862
0.806 5414
0.265
0.115 0880
1-303 43 T
0.767 2059
.2l6
.093 8076
.241 102
.805 7353
.266
.115 5223
304 735-
.766 4391
.217
.218
.094 2419
.094 6762
.242 344
-243 587
.804 9300
.804 1254
.267
.268
.115 9566
.116 3909
.306 040
307 347
. 765 6731
.764 0078
.219
,095 I IDS
-244 831
.803 3217
.269
,116 6252
-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 3^3
.801 7167
.271
.117 6938
3" 275
.762 6165
.222
.223
.096 4134
.096 &|77
.248 571
.249 821
.800 9154
.800 1148
.272
273
.118 1281
.118 5624
-312 587
,313 900
-76l 8543
.761 10928
.224
.097 2820
.251 071
799 3151
.274
.118 9967
315.215
-760 3321 |
0.225
0.097 7^3
1.252 323
0.798 5162
0.275
0.119 43 TO
I.3I6 531
0.759 572^
.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
75<5 5399
0.230
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
.I'23 0367
334 454
-755 0283
.232
.100 7563
,26l 120
.792 9461
.282
.122 4710
325 779
754 2737
-233
,ioi 1906
.262 381
-792 1536
283
. 122 9053
.327 105
753 5198
.234
.101 6249
.263 644
.791 3618
.284
.123 3396
328 433
.752 7666
0.235
O.IO2 O592
1.264 009
0.790 5708
0.285
0.123 7739
1.329 762
0.752 0143
.236
. 102 4935
.2(56 174
.789 7807
.286
.124 2082
.33* 092
.751 2626
-237
.102 9278
.267 441
.788 9913
.287
. 124 6425
332 424
. .750 5117
.238
.103 3621
.268 709
.788 203?
.288
.125 0768
333 757
,749 7616
-239
.103 7964
.269 979
.787 4H9
.289
.125 51 I I
335 092
.749 OI22
0.240
0.104 2307
1.271 249
0.786 6279
0.290
o, 125- 9454
1.336 427
0.748 2636
.241
.104 6650
,272 521
.785 8416
.291
.126 3797
337 70S
747 SI57
.242
.105 0993
-273 794
.785 0562
.292
.1-26 8140
.339 103
,746 7685
.243
.105 5336
.275 069
.784 2715
.293
.127 2483
340 443
.746 O22I
.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
r.343 126
O.744 53l6
.246
.106 8364
.278 900
.78t 9222
.296
.128 5512
.344 470
743 7S74
247
.107 2707
.280 179
.781 1407
.297
.128 9355
345 815
.743 0440
.248
.107 7050
.281 460
-780 3599
.298
.129 4108
347 162
.742 3013
.249
.108 1393
.282 742
.779 5800
.299
.129 8541
3'l8 510
-741 5594
0.250
0.108 5736
1,284 025
0.778 8008
0.300
0.130 2883
r-349 859
0.740 8182
,...(.-,
Ionise")
e"
.-
,.,.<.-,
,o,,.Ce',
o"
.-
SMITHSONIAN Taai.cs
228
The Exponential.
u
lop(e u )
e"
ft-"
11
,,<.-,
o"
. ^^
0.300
.301
. 1O2
0.130 2883
.130 7226
. I3r 1560
1.349 859
-351 209
35-* 561
0.740 8182
.740 0778
739 338i
0.350
-351
352
0.152 0031
- 152 4374
.152 8717
1,419 ofis
.420 487
.421 909
^ ^
. O*"*
33
.131 5912
353 9M
.738 5991
353
153 3060
.4^3 331
' ^ 2 S>^a
.304
.132 0255
.355 269
. 737 8609
354
.153 7402
.424 755
l7 l ^50
0.305
.306
0.132 4598
. 132 894 1
.357 982
0.737 1234
.7363866
0.355
.356
0.154 1745
. 154 6088
1.426 181
.427 608
3 , 7 Q I _
I ^ til
307
.308
.309
.133 3284
.133 7f>2?
- '3-1 T 97
359 341
.360 7CTI
.362 062
735 6506
734 9<53
.734 1808
357
358
359
-155 043^
155 4774
-155 9U7
.429 036
.430 466
.431 897
: |p;
0.310
3H
0.134 6313
.135 0656
1.363 425
364 789
0-733 4470
-732 71.19
0.360
.361
0,156 3460
.156 7803
1-433 329
434 7'>3
: > o?|
-312
313
3M
. 135 4999
.135 9342
.366 155
.367 523
.368 890
.731 9815
73" 2499
-730 5390
.362
.363
364
.157 2146
.157 <M8<)
.158 0832
.436 199
437 636
439 074
ill
0.315
0.136 8028
1.370 259
0.729 7889
0.365
0.158 5175
1.440 514
0.694 1Q07
.316
$8
.319
.137 2371
.137 6714
.138 1056
.138 5399
.371 630
.373 003
.374 376
375 751
.7 2 9 0595
.728 3308
.727 6028
.726 8755
.366
-367
.368
369
.158 9518
.150 38(11
.150 8204
.160 2547
441 955
443 3!>8
.444 8,| 2-
.446 288
^ ^"ijfcyj
692 1 *j2
& 1 43S-1
0,320
0.138 9742
1.377 128
0.726 1490
0-370
o . 160 6890
1-447 735
0.6QQ ?3U
.321
.139 4085
.378 5>
.725 4333
37'
.161 1233
449 183
,fxx> 0430
.322
.139 8428
.379 885
.724 (xj82
372
.161 5575
450 633
689 ;i5.|2
.323
.140 a??'
.381 265
.723 9739
373
.16 i 9918
.452 084
,68S GOj^
.324
.140 7114
.382 647
-723 2502
374
.162 4261
.453 537
68? 97<59
0.325
.326
.32?
.328
329
0.141 1457
.141 5800
.142 0143
.142 4486
.142 8829
1.384 031
.385 415
.386 801
.388 189
.389 578
0,722 5274
.721 8052
.721 0837
,720 3630
.710 6430
0-375
377
.378
379
0.162 8604
. 163 2947
.163 /jyo
.164 1633
.164 5976
1-454 991.
45fi 447
-457 904
-459 363
.460 823
0.687 2833
686 6033
.685 9161
.685 2305
684 SI 56
0.330
.331
.333
334
0.143 3172
.143 7515
.144 '858
.144 6201
.145 0544
1.390 968
.392 360
-393 753
.395 147
0.718 9237
,7.18 2052
7'7 473
.716 7702
.716 O538
0.380
.381
.382
i^'l
o. 165 0319
. 165 4662
. 165 9005
. 166 334K
.166 7691
1.462 285
.463 748
.465 212
.466 678
.468 145
0.683 8614
.683 1779
.682 4051
.681 8129
.681 1314
0.335
.336
337
.118
0.145 4887
.145 9229
.ri6 3572
1.397 940
399 339
.400 739
,402 141
0.715 338i
,714 6231
.713 (joHS
.7U 1953
0.385
.386
.387
.388
0.167 2034
167 6377
, 1 68 0720
.168 5063
1.469 614
.471 085
.472 556
474 030
0.680 4506
.679 09 1 1
,678 4123
* Oi) w
330
.147 2258
.403 543
. .712 4824
.389
.168 9406
.475 55
.67? 73 13
0.340
341
342
343
.344
0.147 6601
.148 0944
.148 5287
. 148 9630
.149 3973
1,404 948
.406 353
.407 760
.409 169
.410 579
.711 0589
.710 3482
.700 6382
.708 02&)
0.390
391
-392
393
394
0,169 3748
. l6y 809 T
.170 2434
.170 6777
.171 1120
1.476 p8 i
.478 459
-479 938
.481 418
.482 901
0,677 O5<J9
,676 3^ 3
675 7 ** 1
,675 02*5.7
,674 3S4I
0.345
.346
-347
0.149 8316
.150 2659
,150 7003
1.411 9QQ
.413 403
.414 817
0,708 2204
.707 5125
.706 8053
0-395
-397
O.I7I 54f>3
.171 9806
.172 4149
1.484 384
.485 860
.487 356
0.673 6S
.673 0007
,673 3jH
.348
151 1 14")
.416 232
.706 oxj8p
.398
.172 84<J2
.488 844
1(171 f ~ tfv .
.340
.151 5&S8
.417 649
.705 3931
399
.173 2835
.490 334
.670 py?
0.350
0,152 0031
1.419 068
0.704 6881
0.400
0.173 7178
I-49I 825
0.670 3200
laao(e ] )
logwte")
e"
a""
,.,rf,
,.rf>
e"
e~~
SMITHSONIAN
22Q
The Exponential.
u
1 no 10 Co")
e"
<r"
u
Ion iota")
a"
8-"
0.400
0.173 7178
1.491 823
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 8n
.668 9807
.452
.196 3011
571 452
636 3542
.403
.175 0207
.496 307
.668 3121
453
.196 7354
.573 024
.635 7l8l
.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
4S6
.198 0383
577 750
.633 8138
.407
.176 7579
.502 304
.663 6442
.457
.198 4726
579 329
. .633 l8f>3
.408
.177 1921
-503 807
.664 9789
.458
.198 9069
.580 009
.632 5475
.409
. 177 6264
.505 312
.664 3142
.459
-199 3412
.582 491
.631 9152
0.410
0.178 0607
1.506 818
0.663 6503
0.460
o. 199 7755
1.584 074
0.631 2836
.411
. 178 4950
.508 325-
.662 9869
.461
.200 2098
.58s 659
.630 6527
.412
.178 9293
.509 834
.662 3243
.462
.200 6441
587 245
,630 0223
.413'
. 179 3636
.511 345
.661 6623
.463
.201 0783
588833.
.629 3026
.414
.179 7979
.512 857
.661 ooio
464
.201 5126
.590 423
.628 7636
0.415
0.180 2323
1.514 37i
o.6Go 3403
0.465
0.201 9469
1.592 014
0.628 1351
.416
.180 6665
.515 886
.659 6803
.466
,2O2 3812
593 607
.627 5073
.417
,181 1008
517 403
.659 0209
.467
.202 8l55
.595 201
.625 8801
.4*18
.181 5351
.518 921
.658 3622
.468
.203 2408
. 596 797
.626 2535
.410
.181 9694
-.520 440
.657 7042
.469
.203 6841
598 395
.625 6276
0.420
o. 182 4037
1.521 962
0,657 0468
0.470
0.204 H84
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 Q870
.603 107
.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
.6o5 407
.622 5073
0.425
0.184 5752
1,529 590
0.653 7698
0-475
O.2O6 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
.534 186
.651 8114
.478
.207 5928
.612 845
.620 0222
.429
.186 3123
535 721
.651 1599
479
.208 0271
.614 459
.6l9 4 2 5
0.430
0.186 7466
1.537 258
0.650 5091
0,480
0.208 4614
i . 616 074
0.6:8 7834
431
,187 1809
.538 796
,649 8589
.481
.208 8956
.617 691
.618 1649
.432
.187 6152
540 335
.649 2094
,482
.209 3.299
.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 TOSS
.622 552
.616 3132
0-435
o. 188 9181
1-544 9<53
0.647 2647
0,485
0.210 6328
1.624 175
0.615 6972
43<5
. 189 3524
.546 509
.646 6177
.486
.211 0671
.625 800
.615 0818
437
. 189 7867
.548 056
.645 97H
.48?
.211 5014
.627 427
.614 4670
.438
. 190 23IO
.549 6o5
.645 3258
.488
.an 9357
.629 055
.613 8529
.439
. 190 -6553
.551 155
.644 6808
.489
,212 3700
.630685
.613 2393
0.440
O.I9I 0896
I.-5S2 707
0.644 O3<H
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
.44 2
.191 9582
-555 85
.642 7496
492
.213 6729
-635 584
,6n 4024
443
.192 392S
557 372
,642 ro7a
493
.214 1072
.637 221
.610 7913
.444
. 192 8267
558 930
.641 4654
494
.214 5415
.638 859
.610 1808
0.445
0.193 2610
1.560 490
0.640 824.1
0.495
0,214 9758
1.640 498
0.609 5709
.446
,103 6953
.562 051
.640 1838
.496
.315 4101
,642 140
.608 9616
-447
,194 1296
.563 614
.639 5439
497
,215 8444
.643 783
.608 3530
.448
.194 5<539
.565 179
.638 9047
.498
,216 2787
..645 427
.607 7449
.449
. 194 9982
.566 745
.638 2661
.499
,2l6 7129
-647 073
.607 1375
0.450
0.195.4325
1.568 312
0.637 6282
0.500
0,217 *47 3
1.646 721
0.6o6 5307
looote")
|onio(e u )
e u
e" u
looo(e")
iniwte")
e"
. U
e
SMITHSONIAN TABLKS
230
The Exponential,
u
IODlu(o")
o u
-
u
,,.<.>
o"
-"
0.500
0.217 1472
r.6:|8 721
0.606 5307
0.550
0,238 8620
1-733 253
o -576 949 1
-501
.217 5815
.650 371
.605 9244
551
.239 29(13
734 987
5?6 373
502
.218 0158
,652 022
.605 3188
55-i
259 71(>f)
.736 723
575 797
-503
.218 4501
.653 675
.604 7138
- 553
.2*10 i6.|8
.738 461
575 2_'H
-504
.218 88.J4
.655 329
.604 1004
-554
.240 5991
.740 200
-574 6.1ft
0.505
0.219 3187
1.656986
0.603 5056
0-555
0.241 0334
1.741 9-1 1
0-574 072;
5o6
219 7530
.658 643
.602 9024
556
.241 4(177
743 68.|
573 4<#:
507
.220 1873
.660 303
.602- 2998
-557
,241 9020
74'5 4~'8
572 035;
.508
.220 6216
.661 964
.601 6978
.558
,2.|2 3363
747 175
572 ft-H
.509
.221 0559
.663 627
.601 0964
559
.242 7706
748 923
571 7&X
0.510
O.22I 4QO2
1,665 291
0.600 4956
0.5(10
0.243 2049
1.750 673
0.571 *2ff)l
.511
.221 9245
.6:56 957
.599 8954
. <;(>'
.243 (>39J
.752 424
570 6.$]
.512
.222 3588
.668 625
-59?) 2958
-562
-244 0735
75-4 177
.570 cXtff
-5'3
.222 7931!
,670 295
5<j8 60.68
563
244 507W
755 932
5<x) ,|y&
.514
.2>3 2274
.671 966
.59^ 098-1
.564
.757 689
.S68*W8
0.515
0.223 6617
1.673 639
0.597 5006
0.565
0.2-15 376'4
1.759 448
0.568 3(ioi
5l6
.224 Og6o
.675 313
596 9034
.566
..245 8107
7(n 208
567 7y.j|
.517
224 5303
.(176 589
.59(1 3Q[)H
.567
.246 2450
7<>2 97"
-5l8
.224 9645
.678 667
595 7'o8
.568
246 6793
-764 734
.566 (\tft6
519
.225 3088
.680 346
.595 "54
569
.247 1136
.766 500
.566 oyu
0.520
0.225 8331
1.682028
0.594 5205
0.570
0.247 5479
1.768 267
0.565 5354
-521
,226 2674
.683 711
-593 9263
-571
.247 9821
.770 036
.522
,22f) 7OI7
.685 395
593 3327
572
.248 4164
,771 807
56.[ 3955
.523
.227 1360
.687 081
-592 7397
573
.2.|8 8507
.773 580
.563 kv-i
.524
.227 5703
.688 769
.592 r.|72
574
,2.(9 2850
775 354
0.525
0.3^8 0046
i ,6go 459
0-591 5554
0.575
0.240 7193
1.777 131
0,562 70-19
526
.228 43D
,692 150
SIX) 9f>4'
- 576
.250 1536
.778 <XHJ
.527
.228 873'2
-603 843
590 3734
577
.250 5879
.780 08K
.561 580!)
.528
229 3075
695 538
.589 7834
.578
.251 0222
.782 470
.5()l OEOJ
.529
.229 7418
.697 234
.589 1939
- 579
251 45<)5
.784 253
.5<N> 458S
0.530
0.230 1761
i .698 932
0.588 6050
0.580
0.251 8908
1.786 038
o.55> ft;8.(
-531
.230 6l04
,700 632
.58^ 0167
.581
.252 3251
-?H7 825
55<> 3.187
.532
.231 0-147
703 334
.587 4289
.582
.252 7594
.789 614
-558 77W7
.533
.231 4790
.704 037
. 58( 8418
583
25,3 1937
.791 405
558 2212
-534
231 9133
70S 742
S&i 2553
-S8.[
.253 6280
793 197
-557 <A32
0.535
0.232 3475
1.707 448
0.585 6693
0.585
0.254 0623
1.794 991
0.557 1059
.536
.232 7818
709 157
.585 0839
.586
254 .I0M
.796 787
-537
.233 2161
.710 867
.58-1 4991
-587
.254 9300
-798 585
is55 iwifl
.538
.233 6504
.712 573
.583 0T49
.588
255 3(i52
.81x1 384
-555 4370
.539
.234 0847
.714 202
.58,1 3313
.589
.255 7994
.802 185
-55-1 88m
0.540
0-234 5190
1.716 007
0.582 7483
0-590
0,256 2337
1.803 0H8
0.554 ,W3
541
234 9533
.717 724
.582 1658
591
.256 6680
805 793
553 7732
542
.235 3876
. 719 442
.581 5839
592
257 1023
..Ho7 (mo
553 2197
543
.235 8219
.721 163
,581 0026
593
-257 536(i
.809 409
.552 rtfiiM
.544
.236 2562
. 722 885
,580 4219
594
.257 9709
.811 219
552 IM4
0.545
.546
0,236 6905
.237 1248
1 . 724 608
72(5 334
0.579 8418
.579 2622
0-595
.596
0,258 4052
258 8395
1.813 031
814 8.|5
0.551 5'itfG
.551 in 13
-547
-237 5591
.728 061
.5786833
597
.259 2738
.816 66 i
,550 <i(>05
548
237 0934
.729 790
.578 1049
.598
.259 7081
.818 478
549 9101
-549
.238 4277
.731 S2I
.577 5270
-599
.260 1424
.820 .#$
.J19 3(107
0-550
0.238 8620
1.733 253
0.576 9498
0.600
0.260 5767
1.822 119
0,348 flnfl
IM < 8 ">
loamCe")
o u
e-"
lQQo(0 H )
_N<.",
o"
a-"
SMITHSONIAN TABVCS
231
The Exponential.
II
IOOlo(6 U )
e u
e-
u
,..(.-,
e"
8-"
o.6oo
.601
.602
.603
.604
0.260 5767
.261 ono
261 4453
.261 8796
.262 3139
1.822 119
.823 942
.825 767
-827 503
.829 422
0.348 8116
.548 263:
547 7i5i
-547 1677
.546 6208
0.650
.651
.652
.653
.654
0.282 2914
.282 7257
.283 i 600
283 5943
.284 0286
I.9I5 541
917 457
.919 376
.921 -296
.923 218
0,522 0458
521 32-40
.521 0027
. 520 4820
.519 96l8
0.605
,606
.607
.608
.609
0.262 7482
.263 1825
.263 6168
.264 0510
.264 4853
1.831 252
-833 084
.834 9^8
836 754
.838 592
0.546 0744
545 5286
544 9834
544 4387
543 8943
0.655
.656
.657
.658
.659
0.284 4629
.284 8972
285 3315
-285 7658
.286 2001
1.925 143
.927 069
.928 997
930 927
.932 859
0.519 4421
.518 0229
.5!8 4O42
.51? SS6r
.517 3<&4
0.610
.611
.612
0.264 9196
-265 3539
.265 7882
1,840 431
.842 273
.844 116
0-543 3509
.542 8078
542 2653
0.660
.65i
.662
0.285 6344
.287 0687
.287 5029
1-934 792
.936 728
.938 666
0.516 8513
5l6 3347
.515 8187
.613
.614
.266 2225
.266 6568
!847 808
541 7233
.541 1818
.663
.664
.287 937-2
.288 3715
.940 635
942 547
-515 3031
SI4 788l
0.615
0.267 0911
1.849 657
0,540 6409
0.665
0.288 8058
1-944 491
0.514 2735
.616
.617
267 5254
.267 9597
.851 507
.853 3&>
.540 1005
539 5607
.666
.667
.289 '2401
.289 6744
.946 436
.948 383
513 7595
.513 2460
.618
.619
.268 3940
.268 8283
.855 214
.857 070
.539 0214
.5384827
.668
.669
.290 1087
.290 5430
950 333
.952 284
512 7330
.512 2205
0.620
.621
0.269 2626
.269 6969
1.858 928
.860 788
0-537 9444
537 4068
0.670
.671
0.290 9773
.291 4116
1.954 237
.956 193
0,511 7086
.511 1971
.622
.270 1312
.862 650
.536 S6oO
.6712
.291 8459
.958 150
,510 6862
.623
270 5655
.864 513
.536 3330
.673
.292 2802
.960 109
^510 1738
.624
.270 9998
,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
7.964 033
0.509 1564
.626
.271 8683
.870 115
.334 7264
.676
,293 5831
.965 998
,508 6475
.627
.272 3026
.871 986
.534 1920
.677
.294 0174
.95? 065
.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 885o
.971 905
.507 1239
0.630
0.273 6035
1.877 611
0.532 59i8
0.680
0.295 3202
1-973 878
0.506 6170
.631
.274 0398
.879 489
-532 0593
.681
.295 7545
-975 853
..506 1106
.632
.274 4741
.881 370
531 5277
.682
.296 1888
.977 829
.505 6048
633
.274 90841
.883 252
530 9964
.683
.296 6231
.979 808
.505 0094
634
275 3427
.885 136
530 4657
.684
.297 0574
.981 789
504 5946
0.635
0.275 7770
1.887 023
0-529 9355
0.685
0.297 4917
1,983 772
0,504 OQ02
.636
.276 2113
,888 910
.529 4058
.686
.297 9260
.985 757
.503 5864
.637
.276 64:56
,890 800
.528 8767
.687
.258 3603
987 743
.503 0831
.638
.277 0799
.892 692
.528 3481
' .688
,298 7946
.989 732
,502 5802
.630
.277 3142
.894 585
.527 8200
.689
.299 2289
991 723
.502 0779
0.640
0.277 9485
1.896 481
0.527 2924
0.690
0.299 6632
1.993 7'6
0.501 5761
.641
.278 3828
.898378
.526 7654
.691
.300 0975
995 7io
.501 0747
.642
.278 8171
.900 278
.526 2389
.692
.300 5318
.997 707
500 5739
.643
.279 2514
.902 179
.525 7129
.693
.300 0661
999 ?o6
.500 0736
6.14
.279 6836
.904 082
.523 1875
694
.301 4004
2.OOI 706
-499 5X33
0.643
0.280 1199
1.905 087
0.524 6625
0,695
0.301 8347
2.O03 709
0.499 0744
.646
.280 5542
.907 894
.324 1381
.696
.302 2690
.005 7M
.498 5756
,6.17
.280 9883
.909 803
.523 61143
.697
.302 7033
.O07 721
.498 QX73
.648
.281 4228
.911 714
.523 0909
.698
.303 1375
.009 729
497 5X95
,649
.281 8371
.913 626
.522 5681
.699
.303 S7i8
.on 740
.497 0821
0.650
0,282 2914
1.015 541
0.522 0458
0,700
0.304 0061
2,013 753
0-495 5853
,.,(.>
Ionise")
e"
r"
,.,(.-,
,rf>
e u
8-
SMITHSONIAN TABUS
232
The Exponential.
u
loaiota")
B U
e- u
u
looio(e")
e"
e-
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
.015 767
.496 o8go
-751
.326 1552
. i 19 i 18
.471 8944
.702
304 8747
.017 784
495 5931
752
.326 5895
.121 238
.471 4-228
703
305 3090
.019 803
.495 0978
753
.327 0237
.123 36l
470 95i6
.704
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
,306 6119
.025 872
.493 6147
.756
.328 3266
, 129 740
.469 54o8
.707
.307 0462
.027 898
493 1213
757
.328 7609
.131 871
.469 0715
.708
.307 4805
.029 927
.492 6285
.7-58
.329 1952
. T34 004
.468 6027
.709
.307 9148
.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 4l6
-467 1990
.712
.309 2177
.038 063
.490 6619
.762
330 9324
.142 557
.466 7320
.713
.309 6520
.040 IO2
490 1715
763
-331 3667
. 144 701
.466 2655
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
3.148 994
0.4<>5 3339
.716
.310 9548
.046 232
.488 70312
.766
.332 6696
.151 144
.464 8688
.717
.3" 3891
.048 279
.488 2147
.767
.333 1039
153 297
.464 4042
.718
.311 8234
.050 328
.487 7267
.768
333 5382
.155 45 1
.463 9400
.719
.312 2577
.052 380
.487 2393
.769
333 9725
.157 608
-463 47^3
0.720
0.312 6920
2.054 433
0.486 7523
0.770
0.334 4o68
2.159 766
0.463 0131
.721
.313 1263
.056 489
.486 2657
.771
.334 8410
.161 927
.462 5503
.722
.313 5(5o6
.058 546
.485 7797
,773
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
33< 1439
. 168 423
,461 1647
0.?2S
0.314 8635
2.o54 731
0.484 3246
0.775
o,33<5 5782
2.170 592
0.460 7038
.726
.315 2978
,066-797
483 8405
v .776
337 0125
. 172 764
.460 2433
.727
.315 7321
.068865
.483 3569
777
.337 44<$
. 174 938
-450 7833
.728
.316 1664
070 935
.482 8738
778
.337 88n
.177 114
.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 oogo
0.780
0.338 7497
2,181 472
0.458 4060
-731
.317 4693
.077 157
.481 4273
.781
339 1840
.183655
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 0852
.784
,340 4869
. 100 2l6
.456 57^0
0-735
0.319 2064
2.085 482
0.479 5055
0.785
0,340 9212
2.192 407
0.456 H97
.736
-310 6407
.087 560
.479 0262
.786
.341 3555
.194 600
455 6638
737
.320 0750
.089 657
.478 5474
.787
341 7898
. 196 796
455 2084
.733
.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 2089
0,740
0.321 3779
2.095 936"
0.477 H39
0.790
0.343 0926
2,. 203 396
0-453 8448
741
.321 8122
.098 032
.470 6370
791
343 5269
.205 for
453 3912
.742
.322 2465
.loo 132
.476 1606
-792
.343 9612
.207 808
.452 938o
743
,322 6808
102 233
475 6847
793
344 3955
.210 017
-452 4853
744
.323 II5I
104 336
475 2093
-794
.344 8298
.212 22O
.452 0330
0.7415
0.323 5494
2.I06 441
0-474 7343
0-795
0.345 2641
2,214 44 1
0.451 5812
.746
-323 9837
.108 549
.474 2598
.795
.345 6984
,210 657
.451 1209
747
.324 4180
.no 659
.473 7858
-797
.346 1327
.218 874
.450 6790
.748
.324 8523
.112 770
473 31^2
-798
.346" 5670
.221 094
.450 2285
749
,325 2856
.114 884
472 8392
7C9
.347 0013
223 3l6
-449 7785
0.750
0.325 7209
2.117 ooo
0.472 3666
O.Soo
0-347 4356
2. 225 "541
0-449 2290
loDfl(e")
lodio(e u )
e u
e~ u
loooCe")
1 0010(8")
e u
a - a
SMITHSONIAN TABLIB
233
The Exponential.
II
,.(.-,
o 11
Q"
11
IOO(B B )
o"
"
o.8oo
'347 435*'
2.225 54'i
1-449 3200
0.850
0.369 1503
2.339 647
0.427 4149
.Hoi
.3.17 8(>09
.2-27 768
.448 8709
.851
.369 5846
.4-26 0877
.802
.348 3042
.229 096
.448 4312
.852
.370 0180
344 331
.426 5610
.803
348 7385
.232 228
-I47 9830
.853
370 4532
.346 676
,.|26 1346
.804
349 1728
.234 461
447 5352
.854
,370 8875
349 024
.425 7087
0.805
1-340 (id7i
2 . 236 fx>'i
0.4.17 0879
0.855
0.371 3218
2.351 374
0,4,25 283-2
.8of>
350 0414
.238 93,1
.44(1 041 1
.8=56
.371 7561
353 727
.424 8581
.807
35" 475d
,24'i 174
.44(1 10|f>
.857
.372 1004
.356 082
424 4335
.808
35" 'JO*) 1 )
.2.13 4 '.7
44'5 7487
.372 6247
35 439
,424 OOQ3
,80()
351 3142
-445 3031
'.859
373 0590
,360 79D
4^3 5855
0.810
>-35! 778, r )
2.247 <)o8
0.4, 14 858 1
o.8fio
0.373 4933
2.363 rfir
0.423 1621
,8M
.352 2128
.250 157
.444 4134
,85t
373 9275
365 525
.422 7391
.81 '
.352 (i.|7t
.252 408
.4. |3 </>i)2
,862
37-1 3618
.367 892
.422 3u!i6
.813
353 "8'4
.254 662
-443 5*55
.85-j
374 7*X'T
.370 2()[
,4-21 8945
353 5157
.255 1)1 8
.443 0822
.8fx'|
.375*2304
372 f>32
.421 4728
11.815
"353 95<X>
2.25.) 176
0-4412 6393
0.865
0.375 (KM7
2.375 006
0.421 0516
!8l(>
354 38(3
.201 436
442 H><'9
,8'i6
.376 0990
.377 38-!
,420 6307
.817
.35,1 8i8(i
,,'I'H 6<)0
4 If 75-19
.867
.376 5333
.370 761
.420 2103
355 -J5-1J
.265 Oftf
411 3'34
.868
.37(1 </)7f>
.382 142
.410 7003
!8i'i)
355 ('872
.268 230
440 8723
.869
377 4019
.384 5-25
.419 3707
0,8.!(l
0,356 1^15
2.270 500
0.440 4317
0.870
0.377 8362
2,386 on
0.418 9515
.821
.35<> 5558
.-37-J 77 1
439 90'4
.871
378 2705
389 209
.418 5328
8' '
J75 "45
430 5517
,872
.378 7048
.391 689
.418 1145
iJ3
357 4-M4
.277 322
.439 H23
873
379 I 30 i
394 082
.417 6966
357 8587
.279 ("xio
.438 6734
874
.379 5734
.396 478
.417 2791
0.835
0.358 2929
2.281 881
0.438 2350
0,875
0.380 0077
2.398 8?5
0,416 8620
K'O
.358 7.172
.281 l(i[
437 797"
.879
.380 4420
.401 275
.416 4454
Xy
.359 ''US
.-8fi -U'J
437 3504
.877
.380 8763
.403 678
.416 0291
350 5958
.288 737
.878
.381 3KXi
.406 083
.415 6l33
!!)
3<K) 0301
.291 027
-43'i 4K56
.879
.381 7448
.408 490
.415 1979
0.830
0.3(10 4644
2.293 319
0-136 0493
0,880
0.382 I?9I
2.410 900
0.414 7829
.831
.360 81)87
435 6135
,88i'
.382 f.134
413 312
.414 3683
3 ( i 333"
,:!97 910
435 178'
.882
.383 0,177
.415 726
.413 9542
'.833
.3(11 7(173
.300 ,-XX)
.434 7431
.88.1
.383 420
.418 143
.413 540-1
.834
,3f)2 2OI(
.302 S'o
.434 3080
,88-j
.383 9163
.420 563
.413 1271
0,835
(MO.J f>3W
2.304 814
0.433 745
0,885
0.38.1 35of)
2.422 084
0.412 7142
.830
.837
363 <'7*t2
.307 120
309 438
.433 4408
.433 ottffi
.885
.887
.384 7840
385 2192
425 409
.427 835
.412 3017
.411 88ol5
.838
3''3 f'388
.311 73'J
.888
385 f)W5
,430 264
411 4779
3'M- 373'
.314 052
.432 1424
.889
.385 0878
.432 6yo
,411 o656
0,840
0,364 8074
2.316 367
0.431 7105
O.&JO
0.3&> 522 I
2.435 130
0.410 6558
.'Wit; iir|il7
.318 08")
.431 2790
.891
.38(1 9564
437 566
410 2453
^^
.3(15 (17(10
.323 327
325 051
.430 8480
.430 4173
.892
.8jw
.894.
.387 3907
.387 8250
.388 2593
.440 005
.442 44''
.409 8353
.409 4256
,409 0164
o.8|5
.8,|0
0.366 (1788
2.327 978
.33'> 3 ( >7
0.429 5574
,.|2I) I28O
0.895
0.388 f*)36
.389 1279
2,447 336
.449 784
0.408 6076
.408 1993
*V>7 Hi 7 1
,.1'jH fXKJl
.8()7
.389 5622
452 235
.407 7012
!!?
\g(& -2817
.3(>8 7160
.334 072
337 3 () H
.428 27O!
!S99
-3&J 0964
390 4307
454 689
.457 145
.407 3836
.400 9704
0,850
0,369 1503
2. ,3-30 CM 7
0.4^7 4'49
o.yoo
0.390 8650
2-459 603
0.406 5^97
.*>
,.,*,
o"
.-
'-*'
10010(0")
e"
~ W
SMITHSONIAN TABUS
234
The Exponential,
u
,,<.",
e u
e - u
u
loo 10(0")
e"
e-
0.900
0.390 8650
2.459 603
0.406 5697
0-950
0.412 5708
2.585 7io
0.386 7470
.901
391 2993
.462 06,
.406 1633
951
.413 014
.588 297
.386 3545
.902
391 7336
.464 527
405 7573
952
.413 448.
-593 SSC
.385 9683
.903
392 1679
.466 993
.405 35i8
953
.413 8826
593 478
.385 5825
.904
.392 6022
.469 461
.404 9466
-954
.414 3169
595 073
.385 1971
0.905
0-393 0365
2,471 932
0.404 54 '9
0-955
0.414 7512
2.598 671
0.384 8121
.906
393 4708
474 405
.404 1375
.956
415 1855
.601 271
.384 4275
-907
39.3 9051
.476 88 I
.403 7336
957
.415 6198
.603 873
.384 0433
.908
394 3394
479 359
.403 3301
958
.476 0541
.606 478
.383 6594
.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
.97 1
395 6423
.486 808
.402 1219
95r
.417 3570
.614 309
.382 5102
.912
.396 0766
.489 296
.401 7200
.02
417 7913
.616 925
.382 1279
.913
396 5109
.491 787
.401 3185
.963
.418 2256
-679 543
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
O.g65
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 2220
.918
919
.398 6823
.399 1166
504 277
.506 782
-399 3169
.398 9178
.968
.969
.420 397T
.420 8314
.632 674
.635 308
.379 8420
379 4623
0.920
0-399 5509
2.509 290
0.398 5190
0.970
0.42: 2656
2.637 944
0.379 0830
.921
399 9852
.511 801
.398 1207
971
.421 6999
.640 584
37S 7041
.922
.400 4195
.514 .314
.397 7228
972
.422 1342
.643 226
.378 3256
.923
.924
.400 8538
.401 2881
.516 830
519 348
397 3253
.396 9281
973
974
.422 5685
.423 0028
.645 870
.648 517
377 9475
377 5097
0.925
0.401 7224
2.521 868
0.396 5314
0-975
0.423 4371
2.651 167
O-377 1924
.926
.402 1567
524 39i
396 I35i
976
.423 8774
.653 820
.376 8:53
-927
.40-2 59 10
.526 917
395 7391
977
424 3057
656 475
.376 4387
,928
-929
403 0253
.403 4596
529 445
531 976
395 3436
394 9485
978
979
.424 7400
.425 1743
.659 t33
.661 793
.376 0625
.375 6866
0.930
0.403 8939
2.534 509
0-394 5537
0.980
0.425 6086
2.664 456
O-375 3111
.931
.404 3282
537 045
394 1594
.981
.426 0429
.667 122
374 936o
-932
.404 7625
-539 583
393 7654
.982
.426 4772
.669 7OO
374 5612
-933
-934
.405 1968
.405 6310
.542 124
.544668
393 37i8
392 9786
983
984
.426 9115
.427 3458
,672 462
.675 135
-374 1869
373 8729
0-935
.936
0.406 0653
.406 4996
2.547 213
S49 762
0.392 5859
392 1935
0.985
.986
0.427 7801
.428 2144
2.677 812
.680 491
0-373 4392
373 0660
937
-938
939
.406 9339
.407 3682
.407 8025
552 313
554 867
557 423
391 8015
391 4099
391 0187
987
.988
989
.428 6487
,429 0829
.429 5172
683 173
685 857
.688 545
.372 6931
,372 3206
371 9485
0.940
0.408 2368
2.559 981
0.390 6278
0.990
0.4^9 9515
2.691 234
o.37r 57f>7
941
.942
-943
944
.408 6711
.409 1054
409 5397
409 9740
562 543
.565 107
567 673
.570 242
390 2374
.389 8474
.389 4577
.389 0684
991
992
993
-994
-430 3858
.430 8201
.431 2544
431 6887
.693 927
.696 622
.699 320
.702 02 i
371 2053
370 8343
370 4636
.370 0934
0-945
.946
947
-948
949
0.410 4083
.410 8426
.411 2769
.411 7112
.412 1455
2.572 813
575 387
577 964.
.580 543
.583 125
0.388 6796
.388 2911
.387 9030
387 5153
.387 1280
0.995
.996
-997
.998
0.432 1230
432 5573
432 9916
433 4259
433 8602
2.704 724
.707 430
.710 739
.7*2 851
.715 565
0,369 7234
369 3539
.368 9847
363 6lS9
.368 2475
0.950
0.412 5798
2.585 710
0.386 7410
1. 000
0-434 2945
2.718 282
0.367 8794
lunate")
loaioCe")
e"
e-
loiMe")
ia,*->
e"
e-'
SMITHSONIAN TABLES
235
The Exponential.
11
lotn. ( (o")
o"
o-
ti
IOQ ,0(0")
o"
o~
I.OOO
0.434 2945
2.718 282
0.367 8794
1.050
0.456 0002
2.857 651
0.340 9377
.001
-434 7-'88
,7JI 001
.3('7 5i'i7
.051
.456 4-135
.8(10 510
.3-10 5880
.(H12
-435 if Ml
.723 724
.367 1444
.052
.456 8778
.863 372
.349 2386
-O03
.435 597-1
.726 4'I0
.366 7775
053
457 3'2f
.866 237
.3-18 8895
.OO4
.436 (Mi?
.720 177
.366 4109
.054
457 74(>4
.869 105
343 5408
1.OO5
0.436 4660
3.731 W
o.<>6 and
1-055
0.458 1807
3.871 975
0.348 1924
.OOf)
.436 9<x>2
,734 641
.365 6788
.056
.458 6150
,874 840
.347 8444
-.(K)7
-137 3.145
737 377
-365 3133
-057
150 0493
.877 725
.347 4967
.008
.437 7688
74 I lc i
.364 9481
.058
-459 4836
,K8o 604
-3-17 1494
-OIXJ
.438 2031
742 857
3('4 5834
059
450 0179
.883 486
.346 8024
I. OIO
0.438 6374
2.745 6oi
0.364 2100
1.060
0.460 3522
2.886 371
0.346 4558
,()[ [
430 0717
748 348
.363 8549
.061
,460 78f)4
-88<> 259
.346 1095
.OIJ
43') SOU*
,751 (M>S
36,1 4013
.062
.461 2207
.802 150
345 7636
.oil
.430 '1403
.75.1 850
.363 1280
o ( M
.461 6550
805 043
,345 4180
.014
.440 3746
756 605
.362 7650
.064
.462 0893
.807 940
3-15 0728
1.015
o.4i|o 8o8()
2.750 36.1
0.362 4024
1.065
0.462 5236
2.000 839
0,344 7279
,()!()
.441 2432
7<IJ 12 |
.362 O.|03
.Of if)
403 9579
003 7-li
,344 3833
.OI7
-441 6775
.764 888
.361 (1783
.067
.463 3922
.906 646
344 0391
.018
.412 1118
.767 654
.361 3l60
,068
-163 8265
.909 555
343 6952
.010
44^ 54(>l
770 423
.360 9557
.069
.464 2608
.012 466
343 3517
1.02O
0.443 9804
2-773 105
0.360 5949
1.070
0.464 6951
2.015 379
0.343 OOSS
.0,11
443 4147
775 <)(K>
.360 2345
.071
.465 12^4.
.918 206
342 6657
,(!.!.!
.778 747
359 87-15
.072
.465 56;17
.021 2l6
.342 3232
.02.1
.444 2833
.781 5:7
.350 5148
073
.465 998o
924 1.19
,341 9810
.444 7'7S
.784 310
350 1554
.07-1
.466 4323
.927 064
.341 6392
I.O.M;
0.415 1518
2.787 095
0.358 70l">5
1.075
0.466 8666
2.929 903
0.341 2978
-OJli
445 58di
,781) 884
.358437H
.076
.467 3009
.932 924.
340 056(i
.027
.446 0,!U|
,79.i d75
.358 0706
.077
467 7352
035 859
340 (1158
.44'"' 4547
.705 460
357 7-! 17
.078
.468 1605
038 706
340 27.W
.020
,446 8800
.708 2()0
357 3f'4i
.079
.468 6037
9-M 736
-339 9353
r.o.io
0.417 3333
a.8or 066
0-357 0070
1.080
0,469 0360
2.944 680
0.339 5955
. 03 1
,801 8(hS
, T;(i (i^oi
.081
.469 4723
-9-17 626
339 2561
-03..'
iiriH I'jiO
.Hoo (174
.356 4)37
.082
.469 </oo6
-950 575
.338 0170
.033
.448 6262
,K<nj 482
-355 9375
.083
470 3-109
. .053 527
.338 5783
,,|i|<> 0605
,8l2 l!03
-355 58i8
.084
470 7752
.056 482
33S 2309
I 015
0.449 4948
3.KI5 lofi
0.355 226.1
1.085
0.471 2005
2.959 440
0.337 00i8
.03(1
^17 IJ2.1
354 8713
.086
.471 <M.l8
.062 401
337 5641
.017
45" 3*'34
'H'O XT'
354 Si/"'
.087
.472 0781
065 365
.337 2267
.03H
.039
.450 7077
45' -M-'O
'H?i *fy
! 353 8083
.088
.089
472 <M<>7
968 331
.971 301
.336 8806
.336 5529
1 .040
0.451 6(163
2.820 217
.832 048
0-353 '15-17
353 1014
I.00O
0,473 3810
.473 8153
2.974 274
.077 250
0.336 2165
-335 8804
!o'i'.i
.'153 5349
,834 881
352 7-l**5
.092
.474 2.]<X)
.080 220
335 5447
.043
. Oil. -I
.452 9(191
.837 717
.840 557
.352 3059
.352 0437
-003
.474 6839
.475 1182
.983 210
,986 195
335 2004
334 8743
-M'l
1.045
0.453 8377
2.843 390
0.351 6918
1.095
(M75 5525
a.080 183
0,334 5396
.454 2720
,846 243
<35 r 3403
.096
475 9868
.992 173
33-1 2052
.O.1 7
.84*) 001
.350 0801
.007
.476 4210
995 '67
333 8712
* v '' i /
.048
.049
-455 MO*'
455 5749
.KS'I 942
-854 795
350 6383
.350 2879
.01/8
.099
4X> 8553
.477 2896
.008 164
3.001 163
333 5375
.333 2041
1.050
0.456 0092
2,857 far
0-3-19 9377
I.IOO
0-477 7239
3,004 i 66
0.332 8711
loaiito")
,.-,-,
o"
a-
,.,(.",
IOHH/O")
o"
SMITHOONIAN TABUS
236
The Exponential.
u
loonj(e")
e u
e
u
looio(e")
e u
e -
I. 100
0.477 7239
3.004 166
0.332 8711
I.ISO
0.499 4387
3-T58 193
0.316 6368
.101
.478 158-
.007 172
-332 5384
!5 T
499 8729
161 353
.316 3203
.102
4?S 5925
.010 180
.332 2060
.152
-500 3072
.164 516
.316 0041
-103
,479 0268
.013 192
.331 8740
153
500 7415
. 167 682
.315 6883
.10,
479 46i
.016 207
-331 5423
.154
SOI 1758
170 851
.315 3728
1. 105
0.479 8954
3.OI9 22;
0.331 2109
1. 155
0.501 6101
3.174 023
0.315 0575
.106
.480 3297
.022 24;
.330 8798
.156
. 502 0444
-177 199
.314 7426
.107
.480 7640
.025 2-ljC
.330 5491
157
502 4787
. i So 378
.314 4281
.108
.481 1983
.028 2f,(
.330 2187
.158
.502 9130
- 183 5fo
.314 1138
. 109
.481 6326
.031 326
.329 8887
IS9
503 3473
- 186 745
-313 7998
i. no
0.482 o569
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
313 '729
. 112
482 9355
.040 433
.328 9205
.162
.504 6502
. 196 320
.312 8598
.113
.483 3698
043 475
328 5718
. 163
.505 0845
199 517
.312 5471
.114
.483 8041
.046 520
.328 2434
.164
.505 5iSS
..2O2 719
.312 2347
1. 115
0.484 2383
3.049 568
0.327 9153
i . 165
0-505 9531
3.205 923
0.311 9227
.116
.484 6726
.052 619
.327 5875
.166
.50!) 3874
.209 I3O
.311 6109
.117
.485 1069
.055 673
,327 2(501
.167
.506 8217
.212 341
.311 2994
.118
485 54 T2
-058 731
.326 9330
.168
.507 2560
215 555
.310 9883
.119
.485 9755
,o5i 791
.326 6062
.169
.507 6902
.218 773
-310 6775
I.I2O
0.486 4098
3-064 854
0.326 2798
1.170
0.508 1245
3.221 993
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.I25
0.488 5813
3.080 217
0.324 6525
I.I75
0.510 2960
3-238 143
0.308 8190
.126
.483 0156
.083 299
.324 3280
.176
510 7303
.241 383
308 5103
.127
.489 4499
.086 383
.324 0038
.177
.511 1646
.244 626
.308 2O2O
.128
.489 8842
.089 471
.323 6800
.178
SIT 5989
.247 872
-307 8t>39
.129
.490 3185
.092 562
-323 3565
.179
.512 0332
.251 121
.307 5ST>3
I.I30
0.490 7528
3-095 657
0.323 0333
T.I80
0.512 4675
3-254 374
0.307 2787
.131
.491 1871
.098 754
.322 7104
.181
.512 9018
.257 630
.306 9716
.132
.491 6214
.101 854
.322 3878
.182
.513 336i
. af 889
3o5 6648
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
1. 135
0.492 9242
3- in 174
0.321 4221
1.185
0.514 6390
3.270 687
0.305 7462
.136
493 3585
.114 286
.321 1009
.i85
S'S o?33
373 959
.305 4406
* -O
-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
1.140
0-495 0957
3 . 126 768
0.319 8190
1.190
0.516 8104
3.287 oSr
0.304 2213
.141
.142
-T43
.144
495 5300
495 9643
496 3986
-496 8329
. 129 897
. 133 028
-136 163
- 139 300
319 4994
.319 1800
.318 8610
-3i8 5423
.191
.192,
-193
.194
.517 2447
.517 6790
.518 1133
.518 5476
.290 370
.293 662
-296 957
300 256
.303 9172
.303 6134
.303 3100
.303 0068
I.MS
.146
.147
.148
,149
0.497 2672
497 7015
498 1358
.498 5701
-499 0044
3.142 441
. 145 585
-148 733
.151 883
155 036
0.318 2239
317 9059
.317 588i
-317 2707
.316 9536
1. 195
.196
.197
.198
.199
0.518 9819
.519 4162
-519 8505
.520 2848
.520 7191
3-303 558
-306 863
.310 .171
-313 483
.316 798
0.302 7040
.302 4014
.302 0992
.301 7972
-301 4956
I.I50
499 4387
.158 193
.316 6368
1. 200
0.521 1534
3.320 117
0.301 1942
loo e (e")
l.o,rf.>
e u
.-
Ioo (e u )
fOQio(e u )
a"
6-
SMITHSONIAN TABLES
237
The Exponential.
II
,,,,<o",
a"
<T"
ll
Ion 10(0")
e"
.,-"
1 .200
0.541 1534
3.320 117
0,301 1942
1.250
0.542 8681
3-490 3,13
0.286 5048
,-'01
.521 5877
-.123 439
,300 8932
251
543 324
49.1 8.15
.286 3184
,202
,54.! 044O
,3 jo 70. |
.3OO 5924
.254
543 7.167
-497 3,31
285 93-24
.203
.544 4503
3'3O OO.J
3<X1 29-20
253
.544 f?io
.500 830
.285 6466
.J4
.544 Kyuo
-3,13 424
.299 0918
254
-544 6053
.504 332
.285 3611
1 - 205
0,523 3-M9
3.336 759
0.2006030
1.255
0.545 030
3-507 838
0.285 0758
,;!l>6
523 759'
.340 ()()8
2<;9 3925
.250
5-15 4739
.5" ,148
.284 7909
.-07
.524 1034
343 '130
. 2ij() (x>32
.257
545 9082
.514 S()T
.284 503
. 4< >8
-524 6277
,340 78.]
.298 7943
. 258
546 3425
.518 378
.28-1 2219
..70!)
.545 0640
-350 '3,1
.308 4956
-259
.546 77(18
.521 8!>8
.283 9378
i ..no ,
0.5J5 403
3 -.153 .(85
o.2<)8 1973
i . 260
0.547 2110
3-5^5 421
0.283 6540
..Ml
-525 <)3<t
-350 8.|0
297 8994
.2(H
5-17 fM53
528 t>|o
283 3705
,.JI J
52(t 3<M')
.3(10 198
.297 (1015
. 4()4
. ^48 0796
532 479
,283 0873
.413
.520 7992
.303 500
.297 3040
- 263
-5.18 5139
.536 014
.282 8043
.4l.|
.527 2335
,3(1(1 945
.297 oof i0
26-1.
.548 0482
.539 551
.282 5217
1.215
0,547 6678
3.370 294
0.296 7100
1.265
0.5-19 3825
3-543 093
0.282 2393
.;!iO
,5jH IO.M
-373 (M
.20 -H35
,2fl(l
-549 8168
.546 638
.281 9572
..!I7
.5-!8 53'M
377 (Ml
.20 1772
. 267
.550 251:
.550 I8(i
-28r 6754
.418
.548 1^07
,380 420
,2<)5 8412
.268
.550 6854
553 738
.281 3938
- 1 "
.529 4050
.383 804
.295 5255
.269
551 H07
557 203
,281 1126
I.;!40
0.540, 8393
3.387 I 88
0.295 2302
1.270
0.551 5540
3.560 853
0.280 8316
,441
.530 473(1
' .390 577
-2<M 9351
.271
551 9883
-564 415
.280 5509
. 4.? J
,530 7070
-.193 9<i9
,2(M 6403
-552 4226
.567 <>Si
.280 2705
. 4 ..'3
531 I.|.!.!
3U7 3(15
.49.] 3458
273
552 8569
57t 55 r
.279 9904
.JJ|
53' 57(14.
..|()o 764
.294 0516
.274
553 2912
.575 124
.279 7105
I.44S
0.534 0107
3, ,|. | iM
0.2<3 7577
1.275
0.553 7255
3-578 701
0.279 4310
.44(1
5.12 4150
1 .407 572
.493 4(1.1 1
-554 1598
.582 282
.270 1517
. 447
-5.12 8703
i'93 17 {) 8
.277
554 594'
.585 Hfirt
,278 8727
. -!.;8
533 .V.V'
4'4 394
.4<;,J 8777
.478
555 0->83
.580 454
.278 5939
.441)
533 7479
,.|17 Km
.294 5850
279
555 4620
593 a|5
278 3155
I.JIO
ll.UI 1 844
3.441 230
0.292 2(jj6
1,280
0-555 809
3.50 640
0.278 0373
431
531 '"''5
..M4 (IS.!
.292 ooo-i
.281
556 3312
,.(ioo 238
277 7504
. 43.!
535 "508
.448 070
.491 7086
. 282
-556 7d55
.(k)3 8.|0
.477 4818
. 233
535 4M.sr
.431 5O<)
.291 4170
-283
557 1008
,(i07 :|.|0"
.277 2044
.234
535 9'94
-434 9-12
.291 1257
.48-1
-557 6341
.tin 055
276 9274
l.-'35
0.53(1 3537
3.438 379
0.290 83,18
1.285
0.558 08.|
3.614668
0,276 650(5
.2,5(1
.530' 7880
.2IJO 5441
. 486
.558 5047
.618 284
.276 3741
, <> 17 24.! 'I
..1 15 2O4
.200 2537
.287
.558 9370
,6'JI i/OI
.276 0078
!a3
-5.17 656(1
il|8 700
.488
-559 .17';i
.625 528
.275 82 rg
.538 0909
.454 [60
'.M.) 6737
.280
559 8056
629 156
.275 5462
1.440
0.5(8 S2S4
3-455 613
0.28") 38-13
1.290
0.560 2399
3-632 787
0.275 2708
. 24 1
.538 0595
,:!K*) 0<)50
.291
.560 6742
.636 421
274 0956
-539 3937
462 532
.488 8060
.561 1085
.640 059
.27} 7208
243
.465 00
.288 5174
293
.561 5428
.643 701
.274 4462
.MO 2623
,460 4(14
.294
.561 0771
.647 347
.274 1719
I.J4S
0.540 Ck/iCi
3-47-i 935
0,287 9409
.287 6531
1.295
, 20
0.562 4114
.562 8.156
3.650 90
.654 ('49
0.273 8979
-?73 624 t
'"17
!V|l So'^ii
"l79 888
.287 3656
.297
658 305
.273 3506
!a!|
249
54 ! ')*M)5
i]|8ft 854
,287 0784
.280 7914
.208
.299
.563 7M2
.564 I4SS
,66r 05
.665 629
. 2/3 0774
,272 8045
1.250
o.s-ia 868 r
3-400 343
0.286 5048
T.300
0.564 5828
3.659 297
0.272 5318
log u (e u )
logiotn 11 )
___
fl -u
tog,(e")
,.,<.>
u"
(T"
SMITHSONIAN
238
The Exponential.
u
looiota")
e u
e- u
U
looio(e u )
e u
o- u
1.300
0.564 5828
3.669 297
0.272 53l8
1-350
0.586 2976
3.857 426
0.259 2403
.301
.565 0171
.672 968
.272 2594
351
586 73i8
.861 285
.258 9811
.30.2
.565 4514
.676 643
271 y*73
352
.587 1661
.865 148
.258 7223
-303
.565 8857
.680 321
.271 7154
.353
.587 6004
.869 015
.258 4637
.304
.566 320O
.684 003
-271 4438
354
.588 0347
.872 886
.258 2054
1.305
0.566 7543
3.687 689
0.271 1725
1-355
0.588 4690
3-876 761
0.257 9473
.306
.567 1886
.691 379
.270 0015
.356
.588 9033
.880 640
.257 6895
307
.567 6229
.695 072
.2/0 6307
357
.589 3376
.884 522
-257 4319
.308
.568 0572
.698 769
.270 3602
-358
.589 7719
.888 409
257 1746
309
.568 4915
.702 469
.270 0900
359
.590 2062
.892 299
.256 9176
1.310
0-568 9258
3.706 174
0.269 8201
1.360
0.590 6405
3-896 193
0.256 6608
311
.569 3601
.709 882
.269 5504
.361
591 0748
.900 091
.256 4042
.312
.569 7944
713 593
.269 2810
.362
591 5091
.903 993
,256 1480
.313
.570 2287
.717 309
.269 oi 18
.363
-591 9434
.907 899
.255 8919
314
.570 6629
,721 028
.268 7429
-364
592 3777
.911 809
.255 6362
1.315
0.571 0972
3.724 75r
0.268 4743
1-365
0.592 8120
3.915 723
0.255 3807
.316
571 5315
.728 478
.268 2000
.366
593 2463
.919 641
255 1254
-317
571 9658
.732 208
.267 9379
.367
.593 6806
.923 562
.254 8704
.318
57-2 4001
735 942
.267 6701
.368
.594 H49
.927 488
254 6i57
.319
572 8344
739 680
.267 4026
.369
-594 5491
931 417
.254 3612
1.320
0.573 2687
3-743 421
0.267 1353
1.370
0-594 9834
3-935 351
0.254 1070
.321
573 7030
747 167
.266 8683
371
595 4^77
939 288
253 8530
.322
574 1373
750 916
,266 6016
372
.595 8520
943 229
-253 5993
.323
574 57i6
754 669
.266 3351
373
.596 2863
.947 174
-253 3458
.324
575 0059
.758 425
.266 0689
.374
.596 7206
951 124
.253 0926
1.325
0-575 4402
3-762 185
0.265 8030
1-375
0.597 1549
3-955 077
0.252 8396
.326
-575 8745
765 949
.265 5373
376
597 5892
-959 034
.252 5&>9
.327
576 3088
769 717
.265 2719
377
.598 0235
962 995
252 3344
.328
5/6 7431
773 489
.265 0067
-378
.598 4578
.966 960
.252 0822
.329
577 1774
.777 264
.264 7419
379
.598 8921
.970 920
-251 8303
1.330
0,577 6117
3.781 043
0.264 4773
1.380
0.599 3264
3.974 902
0.251 5786
331
.578 0460
.784 826
.264 2129
.381
599 7607
.978 879
-251 3271
332
.578 4802
.788 613
.263 9488
.382
.600 1950
.982 859
.251 0759
333
578 9145
.792 404
.263 6850
383
.600 6293
.986 844
.250 8249
334
-579 3488
.796 198
.263 4215
.384
.601 0636
990 833
.250 5742
1-335
0-579 7831
3-799 996
0.263 1582
1.385
0.601 4979
3-994 826
0.250 3238
336
337
-333
.580 2174
.580 6517
.581 0860
.803 798
.807 604
.811 413
.262 8951
.262 6324
.262 3699
.386
-387
.388
.601 9322
.602 3664
.602 8007
.998 823
4.002 824
.006 828
250 0736
.249 8237
,240, 5740
339
.581 5203
.815 226
.262 1076
.389
.603 2350
.OIO 837
249 3245
1.340
341
343
343
-344
0-581 954^
.582 3889
.582 8232
583 2575
.583 6918
3.819 044
.822 864
.826 689
.830 518
.834 350
0.261 8457
.261 5840
.261 3225
.261 0613
.260 8004
1.390
391
392
393
. -394
0.603 6693
.604 1036
604 5379
.604 9722
.605 4065
4.014 850
.018 867
.022 888
.026 913
030 942
0.249 0753
.248 8264
.248 5777
.248 3292
.348 0810
I- 345
.346
347
-343
349
0.584 1261
.584 5604
.584 9947
585 4290
.585 8633
3-838 187
.842 027
.845 871
.849 7r8
853 570
0.260 5397
.260 2793
.260 0191
259 7593
-259 4996
r.395
-396
397
-398
-399
0.605 8408
.606 2751
.606 7094
.607 1437
.607 5780
4-034 975
.039 OI2
.043 053
.047 098
.051 147
0.247 8330
247 553
247 3379
.247 0907
.246 8437
I- 350
0.586 2976
3.857 426
0.259 2403
1.400
0.608 0123
4.055 200
0.246 5970
loosta")
Id0io(a u )
e u
6~ U
IOQ (e u )
IODio(e u )
o"
(T"
SMITHSONIAN TABLES
239
The Exponential.
u
IOQIO(O U)
e"
B-
u
lQflio(e u >
e u
B - u
1.400
0.608 0123
4.055 200
0.246 5970
1.450
0.629 7270
4.263 US
0.234 5703
.401
.608 4466
059 257
.246 3505
451
.630 1613
.267 380
.234 3358
.402
.608 8809
.063 318
.246 1043
452
630 5956
.271 649
.234 1016
403
.609 3152
.067 384
-245 8583
453
.631 0299
275 923
.233 8676
.404
.609 7495
.071 453 1
.245 6125
454
.631 4642
.2SO 2OI
.233 6339
1.405
0.610 1837
4-075 527
0.245 3671
1-455
0.631 8985
4.2S4 483
0.233 4004
.406
,610 6180
.079 604
.245 1218
-456
.632 3328
.288 770
.233 1671
.407
.6n 0523
.083 686
.244 8768
457
.632 7671
.293 06 1
.232 9340
.408
.611 4866
.087 772
.244 6321
-458
.633 20 T4
.297 356
.232 7012
.409
.611 9209
.091 86r
244 3875
459
.633 6356
.301 656
.232 4686
1.410
0.612 3552
4-095 955
0.244 1433
1.460
0.634 0699
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 8O7I
.323 218
.231 3092
1.415
0.614 5267
4.II6 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 noo
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
. us 403
.241 2311
.472
.639 2815
357 942
.229 4661
.423
.Cii8 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.I578S8
0.240 5085
1-475
0.640 5844
4.371 036
0.228 7787
.426
.619 3039
.162 018
.240 2681
.641 0187
375 409
.228 5501
427
619 7382
.166 182
.240 0279
477
.641 4529
379 787
.228 3216
.428
,620 1725
i?o 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
4.178699
0,239 3089
1.480
0.642 7558
4.392 946
0.227 6377
.431
621 4754
.182 880
.239 0697
.481
643 1901
397 341
.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
.238 353^
-484
.644 4930
410 553
.226 7290
1.435
0.623 2126
4-199 645
0.238 I 154
1.485
0.644 92^3
4.414 965
0.226 5023
436
.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 0498
.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 598i
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
.442
.626 2526
.229 146
.236 4544
.492
.647 9674
445 979
.224 9224
443
.626 6869
233 377
.236 2l8o
-493
.648 4017
.450 427
.224 6976
444
.627 12 12
.237 612
.235 9819
-494
.648 8360
-454 879
.224 4730
1-445
0.627 5555
4.241 852
0.235 7461
1.495
0.649 2703
4-459 337
0.224 2486
.446
-447
.627 9898
.628 4241
.246 096
250 344
.235 5104
.235 2751
.496
-497
.649 7045
.650 1388
.463 798
.468 264
.224 0245
.223 8006
-448
.628 8584
.254 597
.235 0399
.408
650 5731
472 735
.223 5769
-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 3 3 2
log B (e u )
'*">
e u
.-
,.,*",
looiote")
"
e- u
SMITHSONIAN TASLCS
240
The Exponential.
If
InO 10(0")
e u
-"
u
log 10(6")
e"
e "
1.500
0.651 4417
4.481 689
0.223 1302
1-550
0.673 1564
4.711 470
O.2I2 2:[Sn
.501
.651 8760
486 173
.222 071
551
-673 5907
.716 l
.212 0358
502
.652 3103
.490 661
.222 684;
552
.674 0250
.720 90^
.211 8239
503
.652 7446
495 154
.222 46 if
553
674 4593
.725 626
,211 6l22
.504
.653 1789
.499 652
.222 239:
-554
674 8936
730 354
.211 4007
1.505
0.653 6132
4-504 154
0.222 OI73
t-555
0.675 3279
4-735 087
O.2II 1894
.506
654 0475
.508 660
.221 7954
556
.675 7622
.739 824
.210 9783
-507
.654 4818
-513 i7i
221 5737
-557
.676 1955
744 #56
.2IO 7674
-508
.654 9161
.517 686
.221 3522
.558
.676 630^
749 3 '3
.210 5568
-509
655 3504
.522 206
.221 1310
559
.677 0651
754 065
.210 3463
I-5IO
0.655 7847
4.526 731
O.22O 9100
1.560
0.677 4994
4.758 821
0.210 1361
-5"
.656 21 go
-531 260
.220 6892
.561
677 9337
763 582
.209 92(lO
-512
65<5 6533
535 793
.220 4686
562
.678 3680
.768 348
.209 7162
513
.657 0876
540 3.V
.220 2482
563
.678 8023
773 H9
.209 5066
oU
.657 5218
544 874
.220 O28l
.564
.679 2366
-777 895
.209 2972
I-5I5
0.657 9S6i
4-549 421
0.219 8082
1-565
0.679 6709
4-782 675
0.2O9 0880
.516
658 3904
553 973
219 5885
.566
.680 1052
.787 460
,208 8?(JO
sr?
.658 8247
558 529
.219 3690
-567
680 5395
792 250
.208 6703
-5i8
.659 2590
.563 090
.319 1497
.568
.680 9737
.797 045
.208 4617
-519
-659 6933
567 6 55
.218 9307
.569
.681 4080
.801 844
.208 2533
1.520
0.66o 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
-8n 457
.207 8372
.522
.660 9962
58i 379
.218 2749
-572
.682 7109
.816 271
.207 6295
523
.661 4305
585 962
.218 0567
573
-683 1452
.821 090
.207 422O
-534
.661 8648
590 551
.217 8388
574
-683 5795
-825 913
.207 2147
1.525
0.662 2991
4-595 M4
0.217 6211
1-575
0.684 0*38
4-830 742
0.207 OO76
.526
.662 7334
599 741
217 4035
57(3
.684 4481
835 575
.206 8006
.527
.663 1677
.604 343
.217 1862
-577
.684 8824
-840 413
.206 5940
.528
-.663 6020
.608 950
.216 9692
578
.685 3167
.845 256
206 3875
.529
.664 0363
.613 561
.216 7523
579
.685 75io
.850. 103
.206 1812
1.530
0,664 47o6 '
4.618 177
0.216 5357
I-SSo
0.686 1853
4.854 956
0.205 9751
531
.664 9049
,622 797
.216 3192
.581
.686 6i0
859 813
.205 7692
532
-655 3391
.627 422
.216 1030
.582
.687 0539
.864 675
-205 5636
533
.665 7734
.632 052
.215 8870
-583
.687 4882
.869 543
.205 358l
-534
.666 2077
.636 687
.215 6713
.584
.687 9225
.874 415
.205 1528
i 535
.536
53;
-538
539
0.666 6420
.667 0763
.667 5106
.667 9449
-668 3792
4.641 326
.645 969
.650.617
.655 270
.659 928
0-215 4557
.215. 2403
-215 0252
.214 8103
.214 5956
T.585
.586
.587
-588
.589
0.688 3568
.688 7910
.689 2253
.689 6596
.690 0939
4.879 291
.884 173
.889 060
893 951
.898 848
0.204 9478
.204 7429
-204 5383
-204 3339
,204 1296
1.540
.541
542
-543
544
0.668 8135
.669 2478
.669 6821
.670 1164
.670 5507
4.664 590
.669 257
.673 929
.678 605
.683 286
0.214 3Sir
.214 1668
.213 9528
.213 7389
-213 5253
1-590
-591
592
-593
-594
0.690 5282
-690 9625
-691 3968
.691 8311
.692 2654
4-003 749
908 655
.913 566
.918 482
-923 403
0.203 9256
.203 7218
.203 5182
,203 3148
-203 1115
1.545
-546
547
.548
549
0.670 9850
.671 4193
.671 8536
.672 2879
.672 7222
4-687 972
.692 662
-697 357
.702 057
.706 761
0.213 3119
.213 0987
.212 8857
.212 6729
.212 4603
1.595
.596
-597
-598
599
0.692 6997
.693 1340
-693 5683
.694 0026
694 4369
4.928 329
933 260
.938 196
943 i.l6
.948 082
0.202 9085
.202 7057
-202 5031
.202 3O07
.202 0985
1.550
-673 1564
4-711 470
0.212 2480
1. 600
0.694 8712
4-953 03.2
0.201 8965
looeCa")
IODi Q (e u )
e u
fl-"
Iog (e u )
log,o(e u >
6"
e- u
241
The Exponential.
11
Iodide")
o"
e-
it
loo 10(0")
o"
e-"
i.fioo
0,694 87 12
4-953 032
0.201 8965
1-650
0.716 5859
5.206 980
0.192 0499
.601
695 3055
957 988
.201 6047
-fiSi
.717 O202
.212 189
.191 8580
,602
.695 7398
.562 948
.201 493 r
.652
.717 4545
.217 404
. 191 6662
.603
.696 174:
.967 9T4
,2OT 2917
.653
.717 8888
..222 624
.191 4746
.604
.696 6083
.972 884
.201 OyOS
.654
.718 3231
.227 849
. 191 2832
1.605
0.697 0-126
4-977 8fio
0.200 88l)6
1 .655
0.718 7574
5-233 080
0.191 0921
.fofi
697 4?fi9
.982 840
.200 6888
.656
,719 HH7
.238 3'6
,190 9011
.(107
.697 0112
987 825
._>oo 4882
.657
.719 6260
.243 557
.190 7103
.608
.698 3-155
.992 816
.200 2878
.658
.720 0603
.248 803
,190 5T05
.609
.698 7798
.997 811
.200 0876
.659
.720 4945
.254 054
.190 3292
I.filO
0.699 2141
5.002 8ri
O.T99 8876
1. 660
0.720 9288
5-^59 31 i
o. 190 1390
.(in
.699 6484
.007 817
. 199 6878
.60i
.721 3631
264 573
. 189 9489
.612
.700 0827
.012 827
.199 4882
.662
.721 7974
.269 840
. 189 759i
.613
.700 5170
.017 8.]2
. 199 2888
.663
.722 2317
.275 112
. 189 5694
.614
.700 9513
.022 863
. 199 0897
.664
.722- 6660
.280 390
. 189 3799
I. <)T5
0.701 3856
5.027 888
o, 198 8c;o7
1,665
0.723 1003
5.285 673
0.189 1907
.616
.701 8199
.032 918
.198 6919
.666
723 534<>
.290 962
. 189 0016
.617
.702 2543
-037 954
198 4933
.667
.723 9689
.296 255
. 188 8127
.618
.702 6885
.0.12 994
. 198 2949
.6fiS
.72-1 4032
-301 554
. 188 6239
.6iy
.703 1228
.048 040
. 198 0967
.669
724 8375
.306 858
.1884354
1.620
0.703 557i
5'. 053 090
0.197 8987
1.670
0.725 2718
5.312 168
o. 188 2471
.62 1
.703 9914
.058 146
. 197 7009
.671
.725 7061
.317 483
. 188 0589
.(Y22
.704 4256
.063 207
-197 5033
,672
.726 1404
.322 803
. 187 8709
.623
704 8599
.068 272
. 197 3059
.673
.726 5747
.328 128
. 187 6832
.62.1
70S 2942
073 3-13
.197 1087
.674
.727 0090
-333 -159
. 187 4956
1.625
0.705 7285
5.078 419
0.196 9117
1.675
Q.727 4433
5.338 795
0.187 3082
.626
.70(1 Ki^S
.083 500
.196 7H9
.676
.727 8776
344 '37
.187 1210
.627
.706 5971
.088 56
.iy6 5182
.677
.728 3118
349 483
, 186 9339
.628
.707 0314
.01)3 677
. Kj6 3218
.678
.728 7461
354 83(>
,i8S 7471
.621)
.707 4657
-098 773
.196 125(1
.679
.729 1804
.# 193
.186 5604
1.630
0.707 9000
5-K 875
0.195 9296
i. 680
0.729 6147
5.365 556
0.186 3740
.631
70S 3313
.108 y8i
195 7337
.681
.730 0490
,370 924
.186 1877
.6$ 2
.708 7686
. 114 093
.195 53^1
.682
730 4833
,376 298
. 186 0016
fi33
.700 2029
. i 19 209
.195 3427
.683
73O 9176
.381 677
. 185 8157
.634
.709 6372
.124 33i
.195 1.174
.68:|
-731 3519
.387 06 1
.185 6300
1.635
0.710 0715
5-129 458
0.194 954
1.685
0.731 7862
5-392 451
0,185 4444
.636
.710 5058
.134 S!X)
.194 7575
.686
732 2205
.397 846
.185 2591
.<>37
.710 9-|Oi
. 139 727
.19-1 5629
.687
.732 6548
,403 247
. 185 0739
.638
7TT 37-14
. 144 860
. 194 3684
.688
733 0891
.408 653
.184 8889
639
.711 8087
-ISO 017
.194 1741
.689
-733 5334
.414 064
.184 7041
1.640
0.712 2430
S.I55 170
0.193 9800
1.690
0.733 9577
5.419 481
0.184 5195
.641
.712 077 J
.1(0 327
. 193 78;>4
,691
734 3920
.424 903
- i&t 3351
.(M2
.713 UTS
.I(J5 '190
.193 5025
.692
.734 8263
430 331
.184 1509
I'M 3
-713 5458
, 170 658
. 193 3990
-693
.735 2606
435 764
. 183 96(8
.6,)4
.7U i)80I
.175 831
. 193 2057
094'
-735 6949
.,|4I 202
.183 7829
i. 6.| s
0-7M 4*44
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 09S
.183 4157
.647
.715 2830
.tpl 382
. 192 6269
.697
.736 9977
457 550
.183 2324
,6.|8
7t5 ;t73
.196" 57^
.192 4344
,698
737 4320
.463 oio
. 183 0493
.649
.716 1516
,20t 775
,192 2421
.699
.737 8663
,468 476
. 182 8663
1.650
0,716 5859
5.206 080
0.192 0499
1.700
0.738 3006
5-473 9-17
0.182 6835
log B (e u )
toBwte")
o"
a""
loao(o u )
In Biota )
8 U
G-"
SMITHSONIAN TABLES
242
The Exponential.
u
,.,<.',
o"
<r u
u
loaiofo")
e u
e u
1.703
0.738 3006
5-473 947
0. 182 6835
1-750
0.760 0153
5-754 603
0.173 7739
.701
738 7349
.479 424
.182 5009
751
.760 4495
.760 360
.173 6003
.702
739 1692
.484 906
.182 3185
752
.760 8839
.766 123
.173 4267
.703
739 6035
490 394
.182 1363
753
.761 3182
.771 892
173 2534
.704
-740 0378
495 887
.181 9542
.754
-761 75-'S
777 667
.173 0802
1.705
0.740 4721
5-501 386
0.181 7724
1-755
0.762 iSfiS
5.783 448
0.172 9072
.706
.740 9064
.5oS 890
.181 5907
.756
.762 6211
-789 234
.172 7344
.707
.741 3407
512 399
. 181 4092
757
763 0554
-795 026
.172 5618
.708
.741 7750
Si? 915
.181 2279
.758
.763 4897
.800 824
. 772 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
5.8i2 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 358r
I.7IS
0.744 8150
5.556 676
o. 179 9637
1.765
0.766 5298
5-841 572
0.171 1868
.716
745 2493
.562 235
.1797838
.766
.766 9641
.847 417
.171 0157
.717
745 6836
.567 800
.179 6042
.767
767 3983
.853 267
. 170 8448
.7(8
-746 "79
573 371
. 179 4246
.768
.767 8326
.859 123
. 170 6740
.719
.746 5522
.578 947
-179 2453
.769
.768 2669
-864 985
.170 5034
1.720
0.746 9865
5.584 528
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 1627
.723
- 747 8551
595 709
.178 7084
772
-769 5698
.882 607
. 169 9027
.723
.748 2894
,6or 307
.178 5298
773
.770 0041
.888 492
. 169 8228
724
748 7237
.606 911
.178 3513
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
.726
749 5923
.618 136
- 177 9950
776
-771 3070
.906 184
.160 3141
.727
.750 0266
.623 757
.1778171
777
771 7413
.912 094
.169 1448
-723
.750 4609
629 384
- 177 6393
778
772 1756
.918 009
. 168 9758
729
.750 8952
.635 016
. 177 4618
779
.772 6099
.923 930
. 168 8069
1,730
0-751 3295
5.640 654
o. 177 2844
1.780
0.773 0442
5.929 856
0.168 6381
731
751 7637
,646 297
.177 1072
.781
.773 4785
935 78<J
. 168 4696
732
-752 1980
.651 947
.176 9302
.782
-773 9128
.941 728
.168 3012
733
752 6323
.657 601
- r?6 7534
.783
774 3471
-947 673
. 168 1330
734
-753 0666
.663 262
.176 5767
784
-774 7814
953 623
. 167 9649
r.735
.736
-737
-738
739
0-753 5009
753 9352
754 3695
754 8038
755 2381
5.668 928
.674 600
.680 277
.685 960
.691 649
0.176 4002
.176 2239
.176 0478
.175 8718
.175 6960
1.785
.786
.787
.788
.789
0-775 2157
775 6499
.776 0842
.776 5185
.776 9528
5.959 58o
-965 543
.971 5H
.977 486
.983 466
0.167 7971
. 167 6293
.167 4618
. 167 2944
.167 1272
1.740
0.755 6724
. . f ^
5-697 343
0.175 5204
1.790
0.777 3871
5.989 452
0,166 9602
741
.742
750 IOD7
7S6 54W
.703 044
-708 750
175 3450
.175 1697
.791
-792
777 8214
.778 2557
995 445
6.001 443
.166 7933
. 166 6266
.743
744
-756 9753
757 4056
.714 461
.720 178
174 9946
174 8197
793
-794
.778 6900
779 1243
.007 448
.013 458
. 166 4600
. 166 2937
1-745
.746
-747
.748
.749
Q-757 8439
.758 2782
758 7125
.759 1468
-759 58io
5-725 901
-731 630
-737 365
743 105
748 851
0. 174 6450
- 174 4704
.174 2960
.174 1218
173 9478
1-795
.796
797
.798
799
0-779 5586
-779 9929
.780 4272
.780 8615
.781 2958
6.019 475
,025 497
.031 526
.037 560
.043 601
0.166 1275
.165 9614
165 7955
. 165 6298
.165 4643
1-750
0.760 0153
5-754 603
0.173 7739
i.Soo
0.781 7301
6.049 647
0.165 2989
IODo(e")
Ionise")
e u
a-
Ioo (o u )
lotiio(e u )
e u
a-
SMITHSONIAN TABLES
243
The Exponential.
II
ioaio(o")
"
o-
. ii
loo ID (o")
"
o-
i.8oo
0.781 7301
).049 647
0.165 2980
1.850
0.803 4448
6.359 820
0.157 2372
.801
.782 1(144.
."55 7o
-165 1337
-851
.803 8701
.36(1 183
. 157 0800
.802
.78.! 5<]8?
.061 750
.164 0686
.852
804 3134
372 553
.156 9230
.803
.783 0330
.067 82.1
.164 80,17
.853
8o.| 7-177
.378 028
.156 7662
.8o.|
.783 467-3
.073 895
. 164 6390
.854
.805 1820
.385 3io
. 156 6095
1.805
),783 0015
6,070 07i
0.164 4745
T.855
0.805 6163
6.301 698
0.156 4529
.8ot)
.781 3358
.086 054
.164 3101
.856
.8o(i 0506
.398 093
.156 2066
.807
.784 7701
.002 144
.164 1458
-857
.806 48-10
,404 494
.156 1-103
.8118
.785 -MI
,0()8 230
.163 9818
.858
.806 (JTOT
.410 902
-155 9843
.800
.785 6387
.10-1 340
.163 8179
.859
.807 3534
.417 316
-155 8284
1.8111
0.786 0730
6,110 447
0.163 6541
i.afio
0.807 7877
6.423 737
0.155 6726
.811
.786 5073
.116 5(11
, 163 401)6
.861
.8()8 2220
.430 164
-155 5170
.812
.78(1 0416
.122 68[
.163 3272
.862
.808 6563
430 597
.155 3616
l8ia
.787 3759
.128 806
.163 1639
.863
.800 ooofi
443 037
.155 2063
.787 8102
.13-1 938
.163 0008
.864
.800 5249
-449 483
.155 0512
1.815
0.788 2445
6. i.] i 076
0.162 8379
i .865
0.809 9592
6-455 936
0.154 8962
.816
. 788 6788
.147 220
. l()2 6752
.8(16
.810 3035
.462 395
.1547414
.817
.78') 1131
.153 371
.162 5l-i6
.867
.810 8278
.468 86 1
.154 5867
.818
.780 S'1'74
. FS9 527
.162 3501
.868
,8l I 2621
.475 333
.154 4322
.Hiy
.789 0817
. 165 ogo
.162 1879
.8(>o
.811 6964
.481 811
.154 2779
1.820
0,790 4160
6,171 858
0.162 0258
1.870
0.812 1307
6.488 20f>
0.154 T237
.821
.700 8503
.178 033
.161 8638
.871
.812 5650
.494 788
153 0696
.82,!
.71}! 2845
.184 215
.161 7020
.872
.812 0093
.501 286
.153 8157
.823
.701 7188
. 100 40J
. 161 5404
-873
813 4336
507 791
,153 6620
79-! 1531
. iXi 505
.161 3789
.874
.813 8679
.514 302
153 5084
1.8";
0,79-3 5874
6.202 70S
0.161 2176
1.875
0.814 3022
6.520 819
0.153 3550
!njii
.703 0217
.161 0565
.876
.814 7364
.527 343
,153 2017
.827
703 45'W
,215 213
. 160 8o55
-877
.815 1707
. 533 874
.153 0486
11 . f
,703 8<.x>3
.221 431
.160 7347
.878
.815 (1050
.540 411
. 152 8056
1829
.227 656
.879
.816 0303
.546 955
.152 7428
1.8.10
8u
0.704 7S89
6.233 887
O.l6o 4136
.160 2532
1.880
.881
0.816" 4736
.816 0079
6.553 505
.560 062
0.152 5901
. 152 43 76
* ' \J l
, fs ^ J
70S 6J7S
.2,|6 367
,160 0931
.882
.817 3-133
.566 625
.152 2852
Hit
.796 0(il8
,252 <>i6
.159 9330
.883
.817 7765
573 195
.152 1330
Xii
.258 872
.159 773-i
.884
.818 2108
570 77i
.151 0810
1.835
0.796 9304
6.265 134
o, 150 6"l35
1.885
0.8l8 6451
6.586 354
O.I5I 8291
.816
.797 3''47
.271 402
.159 4540
.886
-819 0704
593 944
,151 677.?
.837
.838
.830
.797 7000
[7^8 6676
'''7*? ^1*7*7
l:i3 958
.200 345
ISO 2i*K
.150 135-1
.158 9763
.887
.888
.889
.819 5137
.819 9480
.820 3823
.500 540
.606 143
.612 753
.151 5257
.151 3743
,151 2230
:kii
,8.|2
.843
.8.14
0.709 Wi8
700 S3l
700 9704
.Hoo .1047
,800 8390
6.296 538
.3<" 838
315 45''
.321 775
0,158 8174
. 158 6587
.158 5001
.158 3417
.158 183-
1.890
.891
1893
0.820 8166
.821 2509
.821 6852
.822 1195
.822 5537
6.619 369
.625 001
.632 621
.639 257
.645 809
0,151 0718
, 150 9208
.150 7700
. ISO 6193
.150 4687
1.845
!ai8
.8.10
(),8o I 2733
.801 7076
.802 1419
.802 576' 2
.803 0105
6.328 100
334 43i
340 769
-347 M3
353 -!(>3
0,158 0253
.157 867-
.157 709*
.157 552(
. 157 3945
l8tXi
ls<jH
.890
0.822 9880
.823 422;
.823 8566
.824 2900
.824 7252
6,652 54^
,650 204
.665 867
.672 53^
.679 212
o.ISO 3183
.150 1681
. 150 0180
. 149 8(i8i
.149 7183
1.850
0.803 4448
6.359 820
0.157 2372
1.900
0.825 1595
6.685 89*
0.149 5686
lou(o")
looiiXu")
o"
-
,,(,,
,-**_
e u
<T U
SMITHBONIAN TABUS
The 'Exponential.
u
laiD<e u )
a"
e~ u
II
loaio(e u )
e u
6 "
1.900
0.825 1595
6.685 89;
0.149 5686
1.950
0.846 8742
7.028 688
O.I42 2741
.901
825 593S
-692 584
. 149 4191
.951
.847 3085
035 720
.142 1319
.002
.826 0281
.699 280
. 149 269}
952
.847 7428
-042 759
.T4I 9898
-903
.826 4624
-70S 982
.149 1206
953
.848 1771
.049 805
.141 8479
904
.826 8967
.712 692
. 148 9715
-954
.848 6114
.056 859
.141 7O6l
I -9O. [
0.827 3310
6.719 408
0.148 8226
T.955
0.849 0457
7-063 919
O.I4I 5645
.906
827 7653
.726 130
. 148 6739
.956
,849 4800
.070 985
MI 4230
.907
.828 1996
.732 860
. 148 5253
957
.849 9143
.078 06 i
.141 28l6
-90S
.828 6339
739 596"
.148 3768
958
.850 3486
-085 M3
.141 1404
.909
.829 0682
746 339
. 148 2285
959
.850 7829
.092 231
- MO 9993
I-9IO
0.829 5025
6.753 089
o. 148 0804
I. g6o
0.851 2172
7-009 327
0.140 8584
.QII
.829 9368
759 845
-147 9324
.961
.851 6515
.106 430
.140 717(1
.9:2
.830 3710
.766 608
-147 7845
.962
.852 0858
"3 540
.140 5770
913
830 8053
773 378
. 147 6368
.963
852 5201
. 120 657
. 140 4365
.914
.831 2396
-78o 155
. 147 4892
.964
852 9544
.127 78l
.140 2961
I.9I5
0.831 6739
6.786 939
0.147 34l8
1.965
0-853 38S7
7-134 9T3
0.140 1559
.916
.832 1082
.793 729
.147 1946
.966
.853 8230
.142 051
.140 0158
.917
.832 5425
.800 526
M7 0474
967
.854 2572
.149 197
T39 8759
9lS
.833 9768
807 330
,146 9005
.968
.854 6915
- 156 349
. 139 7360
.919
,833 4"!
.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
.071
.855 9944
.177 851
.139 3'75
.022
834 7140
.834 614
.146-3140
-972
.856 4287
.185 032
.139 1782
-923
S35 1483
-841 452
.146 1678
973
.856 8630
. 192 221
139 0391
.924
.835 5826
.848 207
.146 0217
974
.857 2973
.199 4i7
.138 9001
I.92S
0.836 0169
6.855 149
o. 145 8758
1.975
0.857 73i6
7.206 620
0.138 7613
.926
.836 4512
.862 007
145 7300
.970
.858 1659
.213 830
.138 6226
.927
9^8
.836 8855
.837 3198
.868 873
-875 745
145 5843
. 145 4388
-977
-978
.858 6002
.859 0345
.221 047
.228 272
. 138 4841
- 138 3457
.920
S37 7541
.882 624
.145 2934
-979
.859 4688
-235 504
.138 2074
1-930
0.838 1884
6.889 Sio
0.145 1482
1.980
O.SS9 9031
7.242 743
0.138 0692
931
.838 6226
.896 403
.145 0031
.98:
.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
083
.861 2060
.264 504
.137 6557
934
839 9255
.917 123
-144 56SS
.084
.861 6403
.271 772
.137 5i8i
1-935
936
937
.938
939
0.840 3598
.840 7941
.841 2284
.841 6627
.842 0970
6.924 044
-930 972
937 906
944 847
-951 796
0.144 4243
- 144 2799
-144 1357
-143 99i6
M3 8477
1.985
.986
987
.988
.989
0.862 0745
.862 5088
.862 9431
-863 3774
.863 8117
7.279 047
.286 330
.293 620
.300 917
.308 222
0.137 3806
-137 2433
.137 1061
.136 9691
. 136 8322
1.940
-941
942
-943
-9-44
0-842 5313
.842 9656
-843 3999
.843 8342
.844 2685
6.958 751
-965 713
.972 682
979 659
.986 642
0.143 7039
143 5603
-143 4i68
143 2735
-143 1303
1.990
.991
-992
993
994
0.864 2460
.864 6803
.865 1146
-865 5489
.865 9832
7-315 534
-322 853
-330 179
.337 513
-344 S$4
o. 136 6954
.136 5588
. 136 4223
.136 2860
.136 1497
1-945
'946
947
.948
-949
0.844 7028
.845 1371
845 57M
-846 0057
846 4399
6.993 632
7.000 629
.007 633
.014 644
.021 662
0.142 9872
.142 8443
.142 7015
.142 5589
.142 4164
1-995
.996
997
-998
-999
0.866 4175
.866 8518
.867 28<5r
.867 7204
.868 1547
7.352 203
-359 559
.366 922
374 293
.381 671
0.136 0137
- i35 8777
135 7419
.135 6062
. 135 4707
1.950
0.846 8742
7-028 688
.142 2741
2.000
0.868 5890
7.389 056
0.135 3353
loD C (e q >
Io0io(a u )
e"
fl -u
Io0o(e")
rodinfe")
B U '
e- u
SMITHSONIAN TABLES
245
The Exponential.
11
loaio(o">
o"
a-
11
loo(B u )
o"
o-
2.0OO
0,868 5890
7-38l) 056
0,135 3353
2.050
O.8f)0 3037
7.767 901
0. 128 7349
.001
8fx) 0233
3 ( -'!i -149
. 135 2OOO
.05"
890 7380
.775 673
. 128 6062
.OIU
.8(10 ,157(1
.403 841)
MS 0649
.052
.891 1723
.783 452
.128 4777
.(103
.869 8918
.411 257
. T34 9299
.053
.891 60(16
.791 240
.128 3493
.004
.870 32(11
.418 672
.134 795"
.054
.892 0409
-799 035
.128 2210
2.005
0,870 7604
7.426 094
0.134 6603
2.055
0.892 4752
7.806 838
O. 128 0928
. 1 )( }( )
.871 1047
.-133 5-'4
' 34 5257
.056
.892 (j95
,814 649
,127 9648
.007
.871 6.!<jo
.44(1 <)(>!
.'34 39'2
.057
-893 3437
.822 467
.127 8369
,008
.872 0(133
.448 406
.134 2561)
.058
.893 778o
.830 294
. 127 7091
,0119
.872 40/6
455 858
.134 122?
059
.894 2123
.838 128
. 127 5815
2. OH)
0.87.! 0319
7-4'il V7
0.133 9887
2.060
0.894 6466
7.845 970
0.127 4540
.01 1
.873 3<)62
.470 784
'33 8548
.Of) I
.895 oSoy
.853 820
.127 3266
.012
.873 Hi 105
.478 259
.1,1.1 7-no
,062
.895 5152
.861 677
-127 1993
.013
.874 ;.'3l8
.485 7-1"
.133 5873
.0(13
.8^5 9495
.869 543
.127 0722
.874 <><MH
-193 -'30
.'33 -1538
.06 1
.896 3838
.877 417
.126 9452
2,015
0.875 1034
7-500 727
0.1,13 3204
2.065
0.896 8181
7.885 298
0.126 8183
.016
.875 5,577
.508 232
,133 i87t
,a()6
.897 2^24
.893 187
.126 6915
.017
.875 07-!<>
.515 7-14
- '33 0540
,067
.897 6867
.901 084
.126 5649
.018
.87(1 40(13
C-l'l >t)-l
. 132 9210
.068
,8<)8 1210
.9118 989
. 126 4384
.010
.876 8|o(>
.530 700
.069
898 5553
.916 902
.126 3120
2. OJO
0,877 2749
7.538 325
0.132 (>555
2.070
0.898 9896
7-92-1 823
0.126 1858
.o.n
.877 7091
545 867
.132 5229
.071
.899 4239
932 752
. 126 0597
,oj.i
' .878 1434
553 .M7
i ,12 3<j04
.072
.891) 8582
.940 ()8y
.125 9337
.023
.878 5777
.5(10 974.
.132 2581
.073
.900 2935
.948 633
. 125 8078
.870 (1120
.568 539
.13-5 '259
.074.
.900 7268
,956 586
.125 6820
2,0.! 5
0.870 44<M
7.576 in
0.131 9938
2.075
0.901 1610
7.964 546
0.125 5564
.(12(1
,879 KHofi
-583 do i
. 131 8619
.07(1
.yoi 595,1
.97^ 515
.125 430f)
.0-7
.8811 3140
.591 278
.131 7301
.077
.902 0296
.080 491
.125 3056
.028
.880 749,!
.598 873
.131 59^,5
.078
.902 4639
.988 476
.125 1803
,OJ9
.KM i 1835
,(N)() 476
-Mi -|Wi9
.079
.902 8982
.996 468
. 125 055^
.ii.O.lO
0.881 6178
7,614 086
0.131 3355
2.080
0.903 3325
8.004 469
0,124 9302
.031
.88- 05-n
,6,11 704
.131 uo.13
.081
.903 7(168
.012 477
. 124 8053
.03.1
.882 4864
.620 330
.1,1' 11731
.082
, 904 20 1 1
,020 494
.124 6806
,033
!8a 0207
,6'rfi 9(11
.083
.904 6354
.028 518
. 124 556o
.034
.883 3550
,(144 604
.130 8112
.084
.905 0697
.036 55' i
.124 4315
3 . 035
o 881 7891
7.6S2 2^2
o. 130 6805
2,085
0.905 5040
8.044 591
o. 124 3071
036
.037
.038
.0,10
!H4 2236
!88l iWJt
.885 5264
.659 908
,6(17 572
.1,10 5499
.130 41 94
. 130 28yo
,130 1588
.086
.087
.088
.089
-90S 9383
,906 3726
.906 8069
.907 2412
.052 640
.afio 697
.068 761
.076 834
.124 1829
.124 0588
- 123 9348
,123 8109
2.040
.04 1
0.885 9607
.88(1 39SO
7/190 609
0.130 0287
2.090
.OIJ I
0.907 6755
,908 1098
8.084 915
,003 004
0.123 6871
. 123 5635
88(1 8201
.706 uo'i
. 120 7689
.01)2
.908 5441
.101 101
.123 4400
.044
!? 2<>tf>
.887 6970
713 7i6
.721 433
. 129 6393
. 129 5096
-093
.094
.908 9784
.909 4126
.109 206
.117 3^0
,123 3166
.123 1934
2.045
0.888 1.122
.888 5(165
7-720 159
.736 892
'l2(J -509
2.095
0,909 8469
.910 2812
8.125 44i
133 570
0.123 0702
. 122 9472
\n.\7
.048
.049
.889 (MK)8
l8By fe|
.129 1217.
! 128 8637
.097
.008
.099
.910 7" 55
.911 1498
.911 5841
.141 708
. '49 854
.158 008
.122 8243
.122 70l6
,122 5789
a. 050
0.890 3037
7.767 901
0.128 7349
2.100
0.912 0184
8.166 170
0. 122 4564
,<.,
,*",
o"
.-
~^~
loo 10(0")
o"
B -
SMITHSONIAN TAHUCH
24(1
The Exponential.
u
Ionise")
e"
<r u
u
loDio(e u )
e u
e~ u
2.100
0.912 0184
8.166 170
0.122 4564
2.150
0-933 7331
8.584 858
0.116 4842
.101
.912 4527
. 174 34
.122 3340
.151
.934 1674
593 448
. i 16 3677
.102
.912 8870
.182 519
.122 21 l8
.152
.934 6017
.602 045
.116 2514
.103
.913 3213
.190 705
, 122 0896
.153
935 0360
.610 652
.116 1352
.104
.913 7556
.198 QOO
.121 9676
-154
935 4703
.619 267
.116 0192
2.105
0.914 1899
8.207 103
O.I2I 8457
2.155
0.935 9046
8.627 890
0.115 9032
.106
.914 6242
.215 314
.121 7239
.156
.936 3389
.636 522
US 7873
.107
.915 0585
223 534
.121 6022
.157
.936 7732
.645 163
.115 6716
.roS
.915 4928
.231 761
.121 4807
.158
937 2075
653 813
US 556o
.109
.915 9271
.239 Q97
.121 3593
.159
.937 6418
.662 471
.115 4405
2. IIO
0.916 3614
8.248 241
O.I2I 2380
2.160
0.938 0761
8.671 138
o.iiS 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
.688 497
.115 0947
.113
.917 6643
.273 023
.120 8748
.163
.939 3790
.697 190
114 9797
.114
.918 0985
.281 300
.120 7540
.164
939 8133
-70S 892
. I 14 8647
2. IIS
0.918 5328
8.289 586
0.120 6333
2.165
0.940 2476
8.714 602
0.114 7499
.116
.918 9671
.297 879
,I2O 5127
.166
.940 68 r8
723 321
114 6352
.117
.919 4014
.306 182
.120 39 2 3
.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 Sn
.120 1517
.169
.941 9847
749 530
.114 2919
2. ISO
0.920 7043
8.331 137
0.120 0316
2.170
0.942 4190
8.758 284
0.114 1776
.121
.921 1386
339 473
.119 9117
.171
942 8533
. 767 047
.114 0635
.122
.921 5729
347 816
.119 79l8
.172
.943 2876
. 775 8r8
113 9495
.123
.922 0072
.356 168
.119 6721
.173
943 7219
.784598
.113 8356
.124
.922 4415
.364 529
-no 5525
.174
-944 1562
793 387
.113 7218
2.125
0.922 8758
8-372 897
0.119 4330
2.175
0.944 5905
8.802 185
o.i 13 6082
.126
.923 3101
.381 275
.119 3136
.176
.945 0248
.810 992
.113 4946
.127
-923 7444
.389 660
.119 1943
.177
-945 4591
.819 807
,ti3 3812
.128
.924 1787
.398 054
.119 0752
.178
945 8934
.828 631
.113 2678
.I2C)
.924 6130
.406 456
.118 9562
.179
946 3277
.837 464
,1.13 1546
2.130
0.925 0472
8.414 867
O.nS 8373
2.180
0.946 7620
8.846 306
0.113 0415
.131
.925 4815
.423 286
.118 7185
.181
947 1963
.855 157
.112 9285
.132
.925 9158
-431 713
.118 5999
.182
947 6306
.864 017
.IT2 Sl57
133
.926 350 1
.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.I3S
.136
0.927 2187
9 2 7 6530
8.457 047
.465 508
0.118 2446
.118 1264
2.185
.186
0.948 9334
949 3677
8.890 649
.899 544
o.i 12 4777
.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
9^7 36i
.112 T408
.139
.928 9559
.490 942
.117 7726
.189
.950 6706
,926 282
.112 0287
2.140
0.929 3902
8-499 438
0.117 6S48
2.190
0.951 1049
8-935 213
o.i u 9167
.141
.929 8245
507 94i
H7 5372
.191
951 5392
944 153
III 8049
,142
930 2588
5i6 454
.117 4198
.192
95T 9735
953 ior
.111 6931
.143
,,930 6931
-524 974
.117 3024
.193
.952 4078
.<X>2 059
.III 5815
.144
.931 1274
533 503
.117 1852
.194
.952 8421
.971 026
.III 4700
2.145
0.931 56i7
8.542 041
0.117 0680
2.195
0-953 2764
S.gSo ooi
0,111 3586
.146
.931 9960
550 S88
.no 9510
.196
953 7107
.088 986
.HI 2473
.147
.148
.149
932 4303
,932 8645
.933 2988
559 M2
.567 7o6
.576 278
.116 8341
.116 7174
.116 6007
197
.198
.199
054 1450
954 5793
955 0136
-997 979
9.006 982
015 993
.III I36l
.Til O2SO
. 110 9140
2.150
Q.933 7331
8.584 858
0.116 4842
2. 2OO
0.955 4479
9.025 013
o.no 8032
lofl c <e u )
looitite )
8
B - u
Ioo (e u )
logiote")
e u
o- 11
SMITHSONIAN TABLES
247
The Exponential.
11
lOQiute")
e u
e- n
u
loflio<e u )
o"
e "
2.2QQ
0-955 4479
9-025 013
o.no 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 3i<i4
.043 082
.no 5818
.252
.978 0312
>5o6 730
.105 1886
.203
.956 7507
.052 129
.no 4712
-253
-978 4655
.516 242
.105 0835
-2O4
-957 1850
.061 186
.no 3608
-254
9788908
.525 763
.104 9785
2,205
0.957 6i93
9.070 252
O.I TO 2505
2.255
0-979 3341
9-535 293
0.104 8735
,2O6
.958 0536
.079 326
.no 1403
.256
.979 7684
-544 833
.104 7687
.207
-958 4S70
.088 410
.110 0302
.257
.980 2026
554 333
.104 6640
.208
.958 9222
.097 503
.109 9203
-258
.980 6369
-5*>3 942
-104 5594
,2QQ
-959 3565
. 106 605
.109 8104
-259
.981 0712
573 5ii
. 104 4549
2.2TO
0-959 7908
9-H5 7i6
0.109 7006
2.260
0.981 5055
9.583 089
0. 104 3505
.211
.960 2251
. 124 837
.109 5910
.261
.981 9398
.592 677
.104 2462
.212
.060 6594
.'33 966
.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 I53S
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 5T90
.219
.963 6995
.198 128
.108 7178
.269
.985 4M2
.669 726
.103 4155
2.22O
0.964 13.17
9.207 33i
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
.965 002.1
.225 764
.108 3921
.272
.986 7171
.698 779
.103 1058
.223
.965 4366
.234 904
. 108 2838
-273
.987 1514
-70S 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
9-727 910
O.IO2 7969
.226
.966 7395
.262 741
. 107 9594
.276
.988 4542
737 652
.IO2 6942
.227
.967 1738
.272 008
.107 85:5
.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
2.23O
0.9^8 4767
9.299 866
0.107 5284
2.280
0.990 1914
9,776 680
O.IO2 2842
.231
.968 9110
.309 171
. 107 4210
.281
.990 6257
.786 462
.IO2 l82O
.232
-969 3453
.318 484
.107 3M<J
.282
.991 0600
.70 253
. IO2 0798
233
.969 7796
.327 808
. 107 2063
.283
-991 4943
.806 054
,ioi 9778
.234
.970 2139
337 MO
.107 0992
.284
.99: 9286
.815 865
.101 8759
2.235
0.970 6482
9.346 482
0.106 9921
2.285
0.992 3629
9.825 6S6
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
593 2315
845 357
.101 5707
.233
97* 95*1
.374 S63
. 106 6716
.288
993 6658
.855 208
.101 4692
-239
-972 3853
.383 943
. 106 5650
.289
.994 looi
.865 068
.101 3678
2,2 ; |0
0.972 8196
9-393 331
0.106 4585
2.290
0.904 5344
9.874 038
o.ioi 2665
.241
973 2539
.402 729
.106 3521
.291
.994 9687
.884 SiS
.101 1652
.242
.973 6882
.412 137
.106 2458
.292
995 4030
.894 707
.101 0641
-243
974 '225
.421 554
.106 1396
.293
995 8372
.904 607
.100 9631
.244
.974 5568
.430 980
.106 0335
.294
.996 2715
.914 Si?
.100 8622
2 . 245
0.974 9911
9.440 4"J
0.105 9275
2.295
0-996 7058
9.924 436
o.ioo 7614
.246
.975 4254
.449 861
.105 8217
.296
.997 I4QI
-934 365
.100 6607
,247
.975 8597
.459 3*5
.105 7159
.297
997 5744
-9-14 305
.100 5601
t *"*/
.248
.976 2940
.468 779
.105 6102
.298
.998 0087
-954 254
.100 4596
.24Q
.976 7283
4?S 253
-105 5047
-299
.998 4430
.964 213
.100 3592
2.250
0.977 1626
9.487 736
0.105 3P92
2.300
0.998 8773
9-974 182
o.ioo 2588
|OH D (Q">
lonio(e u )
o"
e- u
loads' 1 )
10Qio(e u )
e u
<r u
SMITHSONIAN TABLES
248
The Exponential.
1
U
u
logioCe")
o u
B-"
u
loo 10(0")
o"
2.300
.301
.302
0.998 8773
999 3H(>
999 7459
9.974 182
.984 162
994 151
o.ioo 2588
.100 1586
. TOO 0585
2-350
351
352
1.020 5920
.021 0263
,O2I 4606
10.485 570
..|<jo' 06 1
.506 502
0.095 3<592
.005 2738
.095 1786
-303
i.ooo 1802
10.004 ISO
.099 958S
353
.O2T Kg49
-517 "74
.095 "835
. J-.UO .
-304
.000 6:45
.014 159
.090 8586
354
.022 3292
.527 5<X>
.094 yti4
3.305
i. ooi 0488
10.024 178
O.CKJ9 7588
3.355
1.022 7635
10.538 T39
0.094 8935
.306
.001 4831
.034 207
.099 6591
.35<>
.023 1978
.548 (>72
.o.;)4 7987
-307
.001 9174
.044 247
.099 5595
.357
.023 6321
559 226
.OUI 7<>39
308
.002 3517
.054 206
.099 4600
-358
.024 0664
.569 70 i
.',). 1 6093
309
.002 7860
.064 355
.099 3606
-359
.024 5007
.580 3&>
.09-1 5147
2.310
1.003 2203
10.074 425
0.099 2613
2 . 360
1.034 9350
10.590 951
0.094 4202
.311
.003 f>S'15
.084 504
.099 1620
.301
025 3693
.(01 5.|H
094 1^59
.312
.004 o88S
.094 594
.ogy 0629
.3<iJ
.025 8036
,6 id 155
.094 2316
-313
.004 5231
. 104 693
.098 9f>39
3^3
.026 2379
.622 772
.094 1374
-314
.004 (J574
.114 803
.098 8650
.364
.026 (1722
.033 -|OQ
.094 0433
2.315
1.035 3917
10.124 923
0.098 7662
3.36S
1.027 1064
10.644 031.)
0.093 9.193
.316
.005 8260
.135 053
.098 6675
.366
.027 5407
.654 ("88
.093 8554
.317
,006 2603
MS '93
.098 5688
.3^7
.027 9750
.665 348
,093 7616
.318
.006 6946
-155 343
.098 4703
.3/>8
.028 4093
.676 oni
.01)3 (1679
-319
.007 1289
.165 504
.098 3719
.309
.028 8436
,68(i 700
."93 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
37T
.029 7122
.708 005
.093 3873
.322
.008 4318
,196 046
.098 0772
-37^
.030 1465
.718 8oH
"03 2940
-323
.008 866 r
.206 247
.097 9792
-373
.030 5808
.720 533
.093 2007
,324
.009 3004
.216 45Q
.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 OI.J5
.326
.010 1690
.236 912
.097 0857
37<>
.031 8837
.761 77"
,O(>2 1)2 IS
-327
.oto 6033
.247 154
.097 588r
' -377
.032 3180
773 537
.002 HaHti
.328
,011 0376
.257 4o6
.097 4905
-378
.032 752,1
.7^3 315
.01. W 735!)
-329
.ou 4718
.267 669
.097 3931
379
.033 1866
.79.} 103
.092 6432
2.330
i. on 9061
10.277 942
0.097 2957
2.380
1,033 0209
10.804 003
0.093 ssa'i
-331
.012 3404
.288 225
.097 1985
-3i
.034 0552
.8i5 7'3
.OO2 458]
332
.012 7747
.298 518
.097 1014
.382
.034 4895
H2fi SvM
.003 3057
333
.013 2090
.308 822
.097 0043
-.383
.034 9^
.837 36(>
.002 2733
334
.013 6433
.319 136
.096 9073
.384
.035 358o
,a-l8 209
.092 iHn
2.335
1.014 0776
10.329 460
0,096 8105
2.385
J-035 7923
10.859 063
0.092 0890
.336
.014 5119
339 795
.096 7137-
.380"
.036 22(16
.860 <)37
.001 99' >9
337
.014 9462
.330 140
.096 6171
.387
.036 (1609
.KHb Bt>3
.091 9050
-338
.015 3805
3&M95
.096 5205
.388
.037 0953
-8or 6K<>
.091 8131
-339
.015 8148
.370 861
.096 4240
.389
.037 5295
.902 5\%
.001 7214
2.340
1.016 2491
10.381 237
o.ooG 3276
2.390
1.037 </>38
10.913 491
(,.09T 6207
341
.016 6834
.391 623,
.096 2314
391
.038 398 [
,924 413
.091 5381
343
.017 1177
.402 020
.01)6 1352
393
.038 8324
935 343'
,<xji 4466
-343
.017 5520
.412 427
.096 0391
393
039 26(17
.946 284
.091 3552
344
.017 9863
.422 845
.095 9431
394
.039 7010
.057 235 1
.091 2(J39
2-345
1.018 4206
iQ-433 273
0.095 8472
2.395
1.040 1353
10.968 198
0.091 1727
346
.018 85.10
443 ?n
095 75M
.396
.040 5(196
.979 172
.091 0816
-347
.019 2891
.454 ifo
.095 "557
-397
,a|i 0039
.990 150
.090 9005
.348
.019 7234
.464 620
.095 '560 1
.398
.a|i 4382
n. ooi 152
.090 8906
349
.020 1577
.475 089
.095 4646
.399
,041 8725
.012 ISO
.000 8087
2.350
1.020 5920
10.485 570
0.095 3092
2.400
1.0,1 2 3068
11.023 I?C
0.090 7180
Iog {e u )
lo[no(e u )
a"
-
lOBoU")
logio(o")
e"
o-"
SMITHSONIAN TABLES
249
The Exponential,
11
,..(.-,
o"
er"
u
loaioCo")
Q"
e-
2 . 4<X)
1.042 30(18
11.023 176
o.oyo 7180
2.450
1.064 oars
11.588347
0.086 2936
.401
.042 741 i
"34 -O5
.090 6.>73
451
.064 4558
599 941
.086 2073
.40.!
O.|3 '753
045 245
.090 53(17
452
.064 8901
.fui 547
.086 12 12
.403
.043 (xwXf
.056 29(1
.(KX) 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.oyo 2655
2.455
1,066 1930
11.646 434
0.085 8f>32
.400
.044 01.15
.089 514
.090 1753
. 456
.066 6272
,658 086
.085 7774
.407
.045 34(18
, KX) (MX)
.otx) 0851
.457
.of>7 0615
6!>9 75t>
.085 6916
.408
<M5 /8M
in 715
,o8i> 9051
-458
.067 4958
,68 i 425
,085 (iofio
.409
.046 2154
.UJ 833
.o8y 9052
459
,0(17 9301
.693 113
.085 5204
2.410
1.04(1 6497
11.133 </>]
0,089 8153
2.460
1. 068 36.14
11,704 812
0.085 4350
.411
,o,(7 0840
.145 ioi
089 7^55
.461
.068 7987
.716 522
.085 340"
.,|U
047 5183
.156 251
.081) (1358
,O(M) 2330
.728 245
.085 2643
-1 13
o.|7 0526
.167 413
.089 5463
. 463
.069 6(173
739 979
.085 1790
.414
.048 38* it;
.178 58(1
.o8y 4S(>8
.464
.070 1016
751 725
.085 0939
2.415
1.048 Ha 1 2
1 1. 1 ft.) 770
o.o8() 3673
2.465
i.70 5359
11.763 482
0.085 0088
.41(1
049 2555
.200 ()(/>
,o8<j 2780
.466
.070 9702
775 252
,084 9239
..|I7
,040 (i8<>8
..!!.! 172
.(xSy 1888
.467
.071 4-l5
.787 033
,084 8390
. 4 1 8
.050 1241
.223 390
.o8(j (Kjofi
.408
.071 8388
.798 826
.084 7542
.419
050 5584
.234 <)[<)
.089 ourf)
.469
.072 2731
,8[Q 630
.084 6(195
3.420
1.050 9926
1 1. IMS 850
o.o8S 9216
2.470
1.072 7074
ti.823 447
0.084 5849
.421
.051 4J<>9
.257 III
.088 8327
471
073 1417
.834 275
.084 5003
..|jj
.O.HI 8!il.!
.208 374
.088 7440
.472
073 5760
.846 ITS
,084 4159
4 --3
.0-5.; :><)$$
.271) (.48
.088 6553
473
.074 0103
.857 9f>7
.084 3315
-I-M
,052 7.;<]8
,291) 933
.088 sOfirt
474
074 4-I45
.8(19 831
.084 2472
2.425
1.053 'O',|!
r 1.302 2.)
0.088 4781
2-475
1.074 8788
11.881 707
0.084 1630
.426
.053 5984.
.313 537
,088 3897
.476
.075 3131
93 595
.084 0789
4-!7
.0;J4 O3i!7
3-M 856
.088 3013
-477
"75 7474
.905 494
.083 9948
.4~;8
."54 4670
33" '87
,088 3131
,076 1817
.917 406
,083 9109
.054 9013
347 S-'9
,uK8 1249
479
.076 6160
,y2y 329
.083 8270
-i-430
1.055 335*'
1I.35H KH2
0.088 0368
2,480
t.077 0503
11.941 264
0.083 7432
-431
,055 7699
.370 247
.087 9488
.481
.077 48.16
.953 212
.083 6595
-43-'
,056 ,104,!
-381 (>.*3
.087 8(x)O.
.077 9189
.965 171
.083 S7S9
-133
-056 (138;;
3"3 on)
.087 7731
,48^
.078 3532
977 142
.083 4924.
.434
.057 07.18
,404 409
.087 (1854
.484
.078 775
.989 125
.083 4089
a- 135
1.057 507 t
11,415 8i<)
0.087 5Q77
2,485
1,079 2218
12.001 120
0,083 3256
.43"
.057 <MM
.427 240
.087 5102
.486
079 6561
.013 12?
.083 2423
137
.058 37S7
.438 o'73
,087 4227
,487
.0X0 0904
.025 147
.083 1591
43H
.058 80119
.450 l 18
.087 3353
.488
.080 5247
.037 178
.083 07(10
439
,059 2 142
-I"' 573
,087 2481
.489
.080 9590
,049 221
.082 9929
J..I40
1.059 6*785
11,473 041
0.087 1609
2.490
1.081 3933
I 2.o6l 276
0.082 9100
"111
,<}(K) 11-18
..lH| 5--0
,087 0737
.491
.081 8276
-073 '3-13
.082 8271
.44,1
i(H"H) ^171
,41)6 (HO
.086 98:17
492
.082 ::(ii8
.1185 '123
.082 7443
443
.(,;,() ( '},Si..|
.507 5'2
.086 8998
493
,082 (k/ii
.097 514
.082 66 16
.444
.061 4157
Sit) 045
,oHfi 8129
-194
.083 1304
. icy (118
.082 5790
3.-I4S
1 .()! 8500
11,530 550
0.086 7261
2.495
1,083 5647
12.121 734
0.082 4965
.440
.[).{ .;8.|3
.542 086
,(Wi 6395
.083 9090
.133 80 i
.082 4140
"147
.062 718(1
553 <'34
.086 5529
-497
' .084 4333
, 140 ix) i
.082 33i6
.448
.0(13 I5.ii)
5"'5 '03
.o8(i 4o'fii
.4<)H
.084 8076
.158 153
.082 2493
4'I9
,(Ki3 5872
.570' 7'M
.086 3799
.!<
.085 3019
,170 318
.082 1671
2.450
1,0640215
II.S883-I7
0.086 2936
2.500
1.085 7362
12.182 494
0,082 0850
km.< u >
Ingioto 11 )
o'-
.-
,.,.<.-
l(mio(Q u )
a"
o-
SMITHSONIAN TABLES
250
The Exponential.
u
lo Bn <.-)
fl "
e- u
u
loaio(e u )
8"
o u
2.500
.501
.502
.503
504
1.085 7362
.086 1/05
.086 6048
.087 0391
.087 4734
12.182 494
. 194 683
.206 883
.219 096
.231 322
0.082 0850
.082 0030
.081 9210
.081 8391
.081 7573
2.550
551
552
553
554
I. 107 4509
.107 8852
.108 3195
. 108 7538
.109 1881
12.807 104
.819 917
.832 744
.845 583
.858 435
0.078 0817
.078 0036
.077 9257
.077 8478
.077 7700
2.505
.506
.507
1.087 0077
.088 3420
.088 7/63
12.243 559
.255 Sop
.268 071
0.081 6756
.081 5940
.081 5124
2.555
.556
557
1.109 6224
.no 0567
.no 4910
12.871 300
.884 177
.897 068
0.077 6922
.077 6146
.077 5370
.508
.089 2106
. -089 6449
.280 345
.292 631
.081 4309
.081 3-19.5
.558
559
.110 9253
.in 3596
.909 972
.922 888
077 4595
.077 3821
2.510
.511
1.090 0791
.090 5134
12.304 930
.317 241
0.081 2fS2
,o8r 1870
2.560
.561
1. 1" 7939
.112 2282
12.935 817
.948 760
0.077 3047
.077 2275
.512
.090 9477
.329 565
.081 ioS9
.562
.112 6625
.(/)! 7'5
.077 1503
513
514
.091 3820
.091 8163
.341 900
354 248
.081 0248
.080 9438
.563
.564
.113 OC)68
.113 53 n
.974 683
.987 664
.077 0732
.076 9961
2.515
1.092 2506
12.366 609
o 080 8629
2.565
i. 113 9653
13.000 658
0.076 9192
.516
.092 6849
378 982
.c8o 7821
.566
. i 14 3996
.013 666
.076 8423
517
.093 1192
391 307
.080 7013
.567
.114 8339
.026 686
.076 7655
.518
.093 5535
403 764
.080 6207
.568
.115 2682
.039 719
.076 6888
519
.093 9878
.416 174
.080 5401
.569
US 7025
.052 765
,076 6121
2.520
1.094 4221
12.428 597
0.080 4596
2-570
1.116 1368
13.065 824
0.076 5355
.521
.094 8564
44T 032
.080 3792
571
.116 5711
.078 897
.076 4590
.522
.095 2907
453 479
.080 2988
.572
.117 0054
.091 982
.076 3826
.523
.095 7250
.465 938
.080 2186
573
117 4397
.105 08 i
,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 9733
.576
.118 7426
M4 455
.076 0777
527
.097 4622
.515 902
.079 8984
-577
.119 1769
.157 606
.0/6 0017
.528
.097 8965
.528 424
.079 8185
-573
.119 6112
.170 770
.075 9257
529
.098 3307
540 959
079 7387
579
120 0455
. 183 948
.075 8498
2-530
1.098 7650
12.553 506
0.079 6500
2.580
i. 120 4798
13.197 138
0.075 7740
.531
.099 1993
.566 066
079 5794
.58:
.120 9141
.210 342
.075 6983
532.
.099 6336
.578 638
.079 4999
.582
.121 3484
223 559
.075 6226
533
. 100 0679
.591 223
.079 4204
.583
.121 7826
.236 789
.075 5470
534
. 100 5022
.603 821
.079 3410
.584
.122 2169
.250 032
.075 4715
2.535
i . ioo 9365
12.616 431
0.079 2617
2.585
I. 122 6SI2
13.263 289
0.075 396i
.536
.101 3708
.629 054
.079 1825
.586
. 123 0855
.276 559
.075 3207
537
,ior 8051
.641 689
079 1034
.587
.123 5198
.289 842
.075 2454
.538
.102 2394
654 337
.079 0243
.588
123 9541
.303 139
.075 1702
539
.102 6737
.666998
.078 9453
.589
. I2 4 3884
.316 448
.075 0951
2.540
I. 103 1080
12.679 671
0.078 8664
2.590
I.I24 8227
13.329 772
O.075 O200
541
.103 5423
.692 357
.078 7876
591
.125 2570
343 108
.074 9451
542
. 103 9766
70S 056
.078 7088
592
. 125 6913
.356 458
.074 8701
543
.104 4109
.717 767
.078 6302
593
.126 1256
.369 821
074 7953
.544
. 104 8452
730 491
078 55l6
594
.126 5599
.383 '97
.074 7206
2.545
i. 105 2795
12.743 228
0.078 4731
2.595
1.126 9942
i3-39<> 587
0.074 6459
.546
.105 7138
755 978
.078 3946
.596
.127 4285
.409 991
.074 5713
547
.106 1480
.768 740
.078 3163
597
. 127 8628
423 407
.074 4967
.548
. 106 5823
.781 SIS
.078 2380
.598
.128 2971
.436 837
.074 4223
549
.107 0166
794 303
.078 1598
599
.128 73H
.450 281
-074 3479
2.550
I . 107 4509
12.807 104
0.078 0817
2.600
I. 129 i6S7
13-463 738
0.074 2.736
.oa D <e")
Io0io(e")
e u
.-
lon a (e u )
, Dl o<e)
e u
s-
SMITHSONIAN TABLES
251
The Exponential.
II
loo,(o")
o u
o"- u
u
I00iu(o")
o"
<r"
2,6(K>
I.I29 !657
13-163 738
0.074 2730
2.650
1.150 8804
14.154 039
0.070 6512
,(H)1
.1-'!) 5999
-'177 2QIJ
07-1 HJ93
.651
-151 3147
. l()8 200
.070 5806
.602
.130 03,12
..[(JO ()()J
.074 1252
.652
IS' 7490
. 183 375
.070 5101
.603
, 130 4685
.5O.| K.K>
.07.) O5II
.653
.152 7833
. H/> 565
.070 4396
.fio.i
. I3O (J02H
-517 70'
.073 9771
.654
.152 6176
.210 768
.070 3692
2,605
i.Ui 3371
T3-53T 225
0.073 9031
3.655
1.153 0518
14.224 986
0.070 2988
.60()
-K1I 771-1
.54-1 7''3
73 aya
.656
.153 4861
.239 218
.070 2286
.607
,i,U 20S7
55N 3'5
"73 7555
.657
.153 0204
-253 465
.070 1584
.608
. 13.3 6.|(H7
.571 KHr,
.073 6HrK
.658
154 3547
.267 725
.070 0883
.(i(Mj
133 "7-13
SMS '159
.073 6081
.659
.154 7&JO
.282 ooo>
.070 0182
2. 6 1(1
1.13,1 5086
13-5'W 051
0.073 5345
2.660
1.155 2233
14.296 289
0.069 9482
.(Ml
.'33 <M29
.61 a (157
.073 4610
.661
'55 6576
-3'o 593
.069 8783
.fiia
Ml 377-J
.<(> 1!7()
.073 3876
.6(>2
. 156 oyiy
-324 9'o
.069 8085
.('1,1
.134 Hi I.I
.630 yoy
."73 3143
,663
,156 5262
.339 242
.069 7387
.614
.135 -'458
f>53 556
.073 2410
.664
.156 <J6o5
353 589
.069 6690
2.615
1 . 135 (Wot
I3,6(i7 216
0.073 ^678
2.665
1.157 3948
14-367 950
0.069 5994
,oi<i
.136 1144
,(>H(i Hoo
.(173 oy.|7
.6fi6
.157 8291
.382 325
,069 5298
.(117
- 136 5487
CifM 57
,1173 0216
,tt\7
.158 2634
.396 714
.069 4603
.618
- 136 9830
.708 2
.072 0486
,668
.158 6977
.411 118
.069 3909
,619
,137 4'7-!
7ai W5
.072 8757
.660
.159 13^0
.425 536
.069 3215
2.(L'0
I.I37 8515
13-735 73-1
0.072 Roay
2,670
1. 1 59 5663
14.439 969
0.069 2522
,<UT
.138 ,1858
7-l<) 'l<i(>
.071! 730 1
.671
. 160 0006
.454 416
.069 1830
,6:13
. 138 7201
.763 a aj
.07-' 6574
.673
.160 4349
.468 878
.069 1139
.CiJ3
M<) i<J4'l
. 776 y?)3
.07J 58.18
.673
.160 8602
.483 354
.069 0448
.6~'4
- i 30 5887
. 7<xi 777
,0?J 5133
.674
.161 3034
497 8-15
.068 9753
2,625
I . T,(0 0230
I3,H().| 57.1
0.07J 4.V.J8
2. ()75
1.161 7377
14,512 350
0,068 9068
.(>.!<!
-l.|" -157.1
.KiH 3i
."7-i 3674
.676
.162 1720
.526 869
.068 8380
.627
. l.|() 8016
.832 *] i
.07^ >Jogo
.677
. 162 6063
541 404
.068 7(192
.628
.1-1 1 3-!5<>
,H.|6 050
.073 2a;i8
.678
.163 0406
555 952
.068 7004
.M
,I.|I 760.!
.HS<) ^'3
,072 1500'
-67'J
. 163 4749
570 515
.068 6318
2.630
1.1-13 10'|5
T3-873 77<>
0.073 0785
2.680
1,163 0093
I4.SS5 093
O.o68 5632
.631
. 14 J 6288
,HH7 651
.072 01X14
.681
.164 34.15
599 686
.068 4946
.632
. 143 0631
.Wi 5-15
.071 <>344
.682
.164 7778
.614 293
.068 4262
AW
M3 .|*)7-l
.M5 '15.1
,n7i 8f)^>6
63
.165 2I2T
,628 914.
.068 35?8
AM
.1-13 93'7
U2y 376
.071 7<J<7
.684
.165 6464
.643 55"i
,068 2894
2 /"MS
1.14,! 36<*>
I3>!)-I3 312
0.071 7i<)
2.685
1.166 0807
14.658 201
0.06S 2212
Avi
, l.|.| Kw.l
057 tf>3
.071 6473
,686
.166 5150
.672 867
.068 1530
Ai7
.1-15 23.15
.07' iia?
-07! 5757
.687
. 166 9493
.687 547
.068 0849
Al8
. r.|5 6688
<)H5 aos
.071 504'
,688
.167 3836
.702 242
.068 0168
AW
, 146 1031
twy 197
.071 <I337
,68y
.167 8l79
7'6 952
.067 9489
a,6.|o
1,146 5374
I,|.OI3 20.!
0.071 3613
a.o'go
1,168 2522
14.731 676
0,067 8809
,6,| f
,l.|6 9717
.0^7 33i
.071 aSyo
.<i<jr
. 168 6865
.746 4 '5
.067 8l3I
,6.|-!
,i.|7 .|rtio
.o.| I J5^
.071 2187
.692
.169 1207
.761 169
-067 7453
.6.1,1
, i,|7 H.|3
.055 3f
.071 i.|7S
('w
.169 555"
-775 937
.067 (1776
.6,1,1
. i.|H 27,1(1
.069 Z&j
.071 0764
,6y4
. 169 9893
790 721
,067 6100
a, 64^
i.i.jH 7o8<>
1-1.083 -145
0.07T 005-1
2.605
1,170 4236
14.805 519
0.067 5424
A|6
I.|0 1-133
o<J7 53<
.070 0344
,6(X)
.170 8579
.820 332
-067 4749
.6,17
MO 5775
. r i r (M(
.070 8635
.(i(J7
.171 2922
.835 159
.067 4074
' " | /
A|H
.CM!)
.150 onH
.150 -|.|6i
.125 75
. 139 &#
.070 7<jJ7
.070 7210
,("x)8
.699
.171 7265
,172 1608
.850 002
.864 859
.067 3401
,067 2728
2.650
1.150 8So.|
14.154 039
0.070 6512
2.700
I.I72 595 i
14.879 732
0.067 2055
IOfl.<D u >
IOio(8")
o u
o-"
loaod)")
looiirfo")
o"
(T"
SMITHSONIAN TABLES
252
The Exponential,
u
looioCe")
B"
6"
u
looioCa")
e"
e~ u
2.700
.701
.702
.703
.704
r-172 5951
.173 0294
.173 4637
.173 8980
- 174 3323
14-879 732
.894 619
.909 521
.924 438
939 370
0.067 2055
.067 1383
.067 0712
.067 0042
.066 9372
2.750
751
752
753
754
1.194 3098
. 194 744 1
.195 1784
.195 6127
. 196 0470
15.642 632
.658 282
673 948
.689 630
.705 328
0.063 9279
.063 8(>4O
.063 8001
.063 7364
.063 6727
2.705
.706
.707
.708
.709
I . 174 7666
.175 2009
*75 6352
.176 0695
. 176 5038
14-954 317
.969 278
.984 255
999 247
15.014 254
0.066 8703
,066 8035
.066 7367
.066 6700
.066 6039
2.755
.756
757
758
759
1.196 4813
.196 9156
. 197 3499
. 197 7842
.198 2185
15.721 041
.736 770
-752 514
. 768 275
.784 051
0.063 600
.063 5454
.063 4819
.063 4185
-063 355 T
2.710
.711
1.176 9380
.177 3723
15.029 276
.044 312
0.066 5368
.066 4703
2.760
.761
1.198 6528
.199 0871
15-799 843
.815 651
0.063 2918
.063 22.SS
,712
.177 806:3
059 364
.066 4039
.762
.199 5214
.831 474
.063 1653
.713
.714
. 178 2409
. 178 6752
.074 43 T
.089 513
.066 3375
.o56 2712
.763
.764
. 199 9557
.200 3899
.847 3t4
.863 169
.063 1022
.063 0391
2-715
1.179 1095
15.104 610
0.066 2050
2.765
1.200 8242
15.879 040
0.062 9761
.716
179 5438
,119 722
.066 1388
.766
.201 2585
.894 927
.062 9132
.717
.179 g;Sr
. 134 850
.066 0727
.767
.201 6928
.910 830
.062 850,1
.718
.180 4124
'49 99 2 '
.066 0066
.768
,202 1271
,926 749
.062 7875
.719
. 180 8467
.165 150
.065 9407
.769
.202 5614
942 683
.062 7247
2.720
i.iSr 2810
15.180 322
0.065 8748
2.770
T.202 9957
15.958 634
0,062 6620
,721
.181 7153
.195 5io
.065 So8o
771
.203 4300
.974 6oT
.062 5994
.722
.182 149:1.
.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 6n8
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 8S6S
.271 678
.065 4807
.776
.205 6015
.054 674
.062 287 j
.727
.184 32! I
.285 957
.065 4152
-777
.206 0358
.070 736
,062 2249
.728
184 7553
,302 252
.065 3499
778
.206 4701
.086 815
.062 1627
.185 1895
.317 562
.065 28-15
779
.206 9044
. 102 9IO
.062 1006
2.730
1.185 6239
15.332 887
0.065 2193
2.780
1.207 3387
l6.1I9 021
0.062 0385
.731
. 186 0582
.348 228
.065 1541
.?8[
.207 7730
.135 148
.Ofii 9765
.732
.186 4925
363 583
.065 0890
.782
.208 2072
.151 291
,061 9146
.733
. 186 9268
378 955
,065 0239
.783
.208 6415
.167 451
.061 8527
.734
.187 3611
394 34i
.064 9589
.784
.209 0758
. 183 626
.061 7908
2-735
1.187 7954
15.409 743
0.064 8940
2.785
1.209 5101
16.199 8t8
o.ofii 720 1
.736
.188 2297
.425 161
.064 8291
.786
.209 9444
.216 026
.061 667/1
737
.188 6640
.440 594
.064 7643
.787
,210 3787
,232 250
,061 6058
.738
. 189 0983
.456 042
.064 6996
.788
.210 8T30
.248 490
.ofii 5442
.739
. 189 5326
.471 506
.064 6349
.789
.211 2473
.264 7-17
.061 4827
2.740
1.189 9669
15-486 585
0.064 -5703
2.790
I. 21 I 68l6
l6.28l 020
0.061 4212
.741
.190 4012
.502 480
.064 5058
791
.212 1159
.297 309
.061 35(j8
.742
- 190 8355
.517 990
.064 4413
.793
' .212 5502
.313' 614
.061 2985
.743
.191 2698
533 5i6
.064 3769
793
.212 o&c;
.329 93<>
.061 2372
744
.191 7041
-549 057
.064 3126
.794
.213 4'88
.346 274
.061 1760
2-745
.746
1.192 1384
.192 5726
15.564 614
.580 186
0.064 2483
.064 1841
2.795
.796
1.213 8531
.214 2874
16.362 629
.379 ooo
0.061 H<t9
.061 0538
747
.748
.193 0069
. 193 4412
595 774
.61 r 378
.064 1199
.064 0558
.797
.798
.214 7217
.215 1560
.395 387
.411 790
.060 9928
.060 9318
749
-193 8755
.626 997
.063 9918
799
215 5903
,428 210
.060 8709
2.750
1.194 3098
15.642 632
0.063 9279
2.800
i. 216 0245
16.444 647
0.060 Sroi
looe(e n )
,.*">
e"
,(.,
lDio(e u )
e 11
e -
SMITHSONIAN TABLES
253
The Exponential.
u
loom(o")
o"
o~ u
u
loo luto")
u
.-
3.800
.216 0245
16.444 647
o.oilo 8101
2.850
.237 7393
17.287 782
0.057 8443
,801
.J1(1 4588
.461 100
.ofio 7403
.851
.238 1736
.305 078
.057 7865
.802
.3 If) 8031
177 5<>9
.060 6886
.852
.238 6079
.322 392
.057 7287
.803
.217 3274
-I9I "55
.of 10 6279
.853
.239 0422
339 723
.057 6710
.804
.217 7017
510 557
.060 5673
.854
.239 4765
357 071
.057 6134
2.805
i. 218 io(io
16.527 076
0,060 50(18
2.855
1.239 9107
17-374 437
0.057 5558
.81X1
.218 6303
5-13 (>"
.060 4463
.856
.240 3450
.391 820
.057 4983
.807
,.!io 0(146
.500 i 63
.060 3859
857
.240 7793
.409 221
.057 4408
.808
.219 4089
57(' 732
.060 3255
.241 2136
.426 630
.057 3834
,809
.219 933-i
593 3'" 7
.060 2652
iS59
.241 6479
.444 074
.057 3261
2.810
1 . 3.30 3675
16.600 018
0.060 2050
".8(ki
1.242 0822
17.461 527
0.057 2688
.811
.220 80I8
.626 536
.060 1448
.8(11
.242 5165
-178 997
.057 2115
.812
..321 236]
('-13 171
.o(ki 0847
.862
.242 9508
40 485
.057 1543
8 1 i
..;'! 6704
,651) 823
,o(io 034(1
.863
.243 3851
.513 pgo
.057 0972
!8L1
.232 1047
.676 491
059 9647
.86.|
.243 8194
531 513
.057 0401
3.81 i
I . 222 5390
16.693 !?('
0.059 9047
2,865
1.244 2537
17-549 053
0.056 9831
i8ii>
.-'.22 9733
.709 877
.059 8448
.866
.244 6880
.566 611
.056 0262
.817
,726 tyXi
050 7850
,8n>
.245 1223
.584 186
.056 8693
.818
!a:!3 8418
743 33*
.059 7253
.868
.245 5566
.601 779
.056 8124
.819
,J2.| 37(il
.760 082
.059 6656
.869
.245 9909
.619 350
.056 7557
a. 8 jo
1.23,| 7104
.225 1447
16.776 851
793 ('3(
0.059 6059
2.870
.871
1.246 4252
.246 8595
17.637 i8
.654 (-164
0.056 6989
.056 6433
'K" ,
..!25 5700
.810 438
'.059 4868
.872
.247 2038
.072 3^ 1
.056 5856
!S
.824
.226 0133
.827 257
,R|4 091
059 4 2 74
.059 3680
.873
874
.247 7280
.248 1623
,690 oof
.707 708
.056 5291
,056 4726
3.8.15
1.32(1 8810
r6.86o 945
.877 81.
0.059 3087
.059 2491
2.875
.876
1,248 5966
.249 0309
17.725 424
.743 158
0.056 4161
.056 3598
' M"'"
.227 7V) 1 )
.894 70
.059 1IJ02
.877
.249 4652
.760 910
.056 3034
18J8
..128 i8,|8
.()ll 60;
.050 1310
.878
.249 8995
.778 680
.056 2471
.228 6191
.928 S3.
.059 0719
.879
.250 3338
.796 468
.056 J09
3.830
1 . 220 053.]
16,945 46
-979 38*
0.059 0129
.058 9539
.058 8949
2.880
.88 r
.882
1.250 7681
.251 2024
,251 6367
17.814 273
.832 oyf
.849 937
0.056 1348
,056 0787
.056 0220
!33
.83-1
.230 35()3
996 37.
I7.013 378
.058 8361
.058 7773
,883
.884
.252 0710
.252 5053
.867 7'X
.885 673
.055 0666
.055 9107
3.835
-8i(
1.231 22.19
[7.030 400
.047 '!3 (
0.058 7185
.058 6598
3.885
1.252 0396
.253 3739
17.903 568
.921 480
0.055 8548
.055 79 ( jo
* \V
.8iv
"i'liJ WV\
,058 (bra
'.887
.253 8082
.939 4'
-055 7432
" * 'i I f
.838
.83'.
:$ 5!2
.081 56
,oy8 65'
.058 5426"
.058 48-11
,888
.88y
.254 2425
.254 67(18
.957 359
975 32
.055 6875
.055 6318
a. 840
Mil
t . 333 3</','
17- "5 76
0.058 4257
.058 3673
a ;gjj
1.255 ""
.255 5453
17.993 310
18,011 31
0,055 5762
.055 5207
,041
$13
,84.
.234 2640
.ISO 03
.167 190
. 184 3(1
.058 3080
.058 2507
.058 192.
!ii:
.89.
.255 OTlX
.256 4 13'
.256 8482
.029 33
.047 37
,065 42
.055 4653
.055 4097
.055 35'!4
3.R|5
1.235 567^
17.201 55
0.058 1343
.058 0762
2.895
1.257 282;
.257 7i&
18.083 50
.101 59
0.055 3990
.055 2438
HI-
* -i if i 16
315 00
,058 0181
1!>7
.258 15"
."9 70
.055 1885
"MX
.Rl8
.236 8707
.253 24
.270 50
.057 0601
.057 0022
,8fj8
.899
.258 585*
.259 0197
. 137 83
. 155 080
.055 1334
.055 0783
2.850
J.237 7393
17- -'87 78
0.057 8443
2.000
1.250 4540
18.174 14
0.055 0232
',;;
lopiudi")
o"
'-"
,0,,< '<,
~^>
eU
o-"
SMITHSONIAN TABU*
254
The Exponential.
u
Io0io(e")
B U
a-"
u
log 10(0")
a"
a-
2.900
1.259 4540
18.174 145
0.055 0232
2.950
1.281 1687
19-105 954
' 0.052 3397
.90
.259 8883
.192 32
.054 9682
951
.281 6030
.125 o6c
.052 2874
.90
.260 3226
.210 53C
.054 9133
.952
.282 037;
.144 20.
.052 2351
.903
.260 7569
.228 75C
.054 8584
-953
.282 4716
.163 358
.052 1829
.904
.261 1912
.246 9SS
.054 8036
954
.282 9059
.182 531
.052 1308
2.900
1.261 6255
18.265 244
0.054 7488
2-955
1.283 3402
19.201 721
0.052 0787
.0of
.262 0598
.283 518
.054 G94I
.956
-283 7745
.220 934
.052 0260
907
.262 4941
.301 8n
.054 6394
957
.284 2088
.240 165
051 974<>
.90?
.262 9284
.320 T22
.054 5848
958
.284 6431
.259 4H
.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
2.960
1.285 5H7
19-297 972
0.051 8189
.911
.264 2312
375 165
.054 4213
.961
.285 9460
.317 279
051 7671
.912
.264 6655
-393 549
.054 3669
.962
.286 3803
.336 606
051 715-
.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 3T8
.051 6121
2.915
1.265 0684
18.448 812
0.054 2040
2.965
1.287 6831
19-394 703
0.051 5605
.916
.266 4027
.467 270
.054 T499
.966
.288 1174
.414 roS
051 5089
.917
.266 8370
485 747
-054 0957
.967
.288 5517
43'3 531
.051 4575
.918
.267 2713
-504 242
.054 0417
.968
.288 9860
-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
.924
.269 4428
.269 877:
SOS 995
.615 601
.053 7721
053 7184
973
-974
-291 1575
.291 5918
550 483
.570 043
.051 1496
.051 0985
2.925
.926
1.270 3114
.270 7457
18.634 226
.652 870
0.053 664?
.053 GUI
2.975
,976
1.292 0261
.292 4604
19.589 623
.609 223
0.051 0474
.050 9964
.927
.928
.271 1799
.271 6142
-671 532
.690 213
-053 5575
.053 5039
977
.978
.292 8947
-293 3290
.628 842
.648 480
.050 9454-
.050 8945
.929
.272 0485
.708 912
053 4505
979
-293 7633
.668 139
.050 8437
2.930
-931
932
933
-934
1,272 4828
.272 9171
273 3514
-273 7857
.274 2200
18.727 630
.746 36?
-765 123
.783898
.802 691
0.053 3970
053 3437
.053 2904
-053 2371
-053 1839
2.980
.981
.982
-9S3
.984
1.294 1976
.294 6319
.295 0661
.295 5004
.295 9347
19-687 817
707 514
.727 232
.746 969
.766 726
0.050 7928
.050 7421
.050 6913
.050 6407
-050 5901
2-935
-936
937
.938
939
1.274 6543
.275 0886
275 5229
275 9572
.276 3915
18.821 503
840 334
.859 184
.878 052
.896 940
0.053 1307
-053 0776
.053 0246
.052 9716
.052 9186
2.985
.986
.987
.988
-989
1.296 3690
296 8033
.297 2376
297 6719
.298 1062
19.786 502
.806 299
.826 115
845 951
.865 807
0.050 5395
.050 4890
050 4385
.050 3881
050 3377
2.940
.941
.942
943
-944
.276 8258
.277 26OI
.277 6944
.278 1287
.278 5630
18.915 846
-934 772
953 7'6
972 679
.991 661
0.052 8657
.052 8129
.052 7601
-052 7074
.052 6547
2.990
.991
.992
993
994
1.298 5405
.298 9748
.299 4091
299 8434
.300 2777
19.885 682
90S 578
-925 494
945 429
.965 385
0.050 2874
050 2372
.050 1870
.050 1368
,050 0867
2-945
.946
-947
-948
-949
.278 9972
-2/9 4315
.279 8658
.280 3001
.280 7344
I9.OIO 662
.029 683
.048 722
.067 780
.086857
0.052 6021
052 5495
-052 4970
.052 4445
.052 3921
2.995
996
997
998
999
1.300 7120
.301 1463
301 5806
.302 0149
.302 4492
19-085 360
20.005 355
025 371
.045 406
.065 461
0.050 0366
.049 9866
.049 9307
.049 8867 f
.049 8369
2.950
.281 1687
19.105 954
0.052 3397
3.000
1.302 8834
20.085 537
0.049 7871
loo a (e u )
NMhrf.")
e"
e-
Ingots")
.00,0(6")
e"
a""
255
The Exponential.
11
lopiu(o">
o"
u _ u
11
ion 10(0")
o"
e" u
3.00
.1)1
.<).!
.03
,04
1.302 8834
,307 JJ<M
..in 5<)<M
..US <>133
..V" 2552
JO. 085 5.17
,287 ,|(H)
..|')l _'().!
.607 -M3
.905 a.is
0.049 7871
.040 ~>0i7
.048 8012
.048 315(1
."-17 H.149
3-50
51
5.1
.54
1.520 0307
.524 373<>
.528 7166
533 0595
537 -1035
33.H5 453
.448 208
.784 428
34.13.1 yf>8
4* 919
0.030 1974
.029 8969
.029 5994
.029 3049
.029 0133
3 -OS
t. 3.1-1 5'^
2 1. 115 344
o,o.i7 3Sfi<)
3-55
I-54I 7454
34.813 31?
0.028 7246
.028 ,1.188
3-7 557
.541
.7.1H 40.:
977
.3.18 in 1 1
-.133 2
.337
3 1 1
1.3-
350
354
-35') 3417
3<>3 ''847
57"
807 484
754
288 427
34<
(). 0,19 537
33'
575 77.
86.
i. .133
.437 .1147
,441 KS77
,44(1 J
-15" 543<
fiou
.480 944
..|8S
(130
.493 973
100
30.265 3
IS
.046 .|J13
.045 0593
.045 50-H)
(1.045 0492
.044 (XHO
.044
.043
.0-13 -'-'
0.042 8521
.CM3 4^57
.042 0036
.041 ^857
.041 1719
0.040 7622
.040 3566
.039 0551
.039 5575
.039 1639
0.038 7743
.038 3884
,038 0(X>.|
.037 6283
.037 25.Vt
0.036; HH33
.036 5162
.036 1528
.035 7931
.035 4370
0.035 0844
.034 7353
.034 3*Wi
.034 0475
.033 7087
0.033 3733
.033 0-1 13
.033
.032 3
.032
0.031 7450"
.031 .|2y
.031 1170
.030 8074
.030 5009
0.030 1974
57
.58
59
3.60
.61
.62
At
3 As
Mi
.''7
M
.69
3.70
7'
72
73
74
3-75
7<
77
ITD
3.80
'.3
H.1
.84.
.86
.87
.88
91
D3
93
.94
3-95
.(/)
97
.98
.99
4.00
550 43M
554 7743
559 1172
1.563 4601
.567 8031
.576 48<x>
.580 8319
1.5^5 1749
.589 5178
.593 8607
.508 2037
.602 54*
1.60(1 8896
.fin 2325
.615 5755
,619 9184
.624 2614
1.628 6043
.632 9473
,(137 2902
.641 6331
.645 97o'i
1.650 3190
.654 (XiJO
.659 0049
.6(>3 3479
.(if 17 6908
1.672 0338
.676 37<>7
,(k8o 7196
.685 0626
,689 4055
5t6 593
.873 541
36.234 076
36.598 234
9(>6" 053
37.337 5 ( >8
,712 817
38.091 837
38.474 <>66
.861 343
39.251 90(1
.646 394
40.044 847
40.447 304
.853 807
41.2(14 394
.679 108
42.097 990
43.5.21 082
.948 4*
43.380 o(i
.8r6 04-'
44.256 400
44.701 184
45.1.50 439
.(Jo.i 208
46.062 538
525 474
46.993 0(13
47-4<>5 351
.942 3^>
48.424 215
.910 887
.028 1559
.027 8757
.027
0.037 3237
.027 0518
.02(1 7827
.026 5162
,026 2523
0.025 99"
.025 7325
.025 47C'5
.025 2230
.024 9720
0.024 7235
.024 4775
,024 2340
.023 9928
.023 7541
0.023 5177
.023 2837
.023 0521
.022 8227
.022 5956
0.022 3708
.022 1482
.021 03$
.021 7096
.021 4936
0.021 2797
.021 0680
,020 85^4
.020 650H
.020 4453
i/w 7485
49.402 449
0.020 2<
.698 0914
.898 9S^
.020 O;
702 4344
.?ofi 7773
.711 1203
50,400 445
,906 978
51.418 601
.019 8;
.019 0.
.019 4'
I.7I5 40.12
51.935 3f'7.
0.019 2,
.719 8061
,724 1491
52.457 326
.934 53i
.019 o(
.018 8;
n f\
.728 4920
.732 8350
S3-5I7 034.
54,054 889
,0l8 (K
.018 4<
1.737 1779
54.598 ISO
O.oiS 3
lDOld(c 11 )
o"
547
631
734
850
1997
6MITHBONIAN TANU8
250
The Exponential.
u
lomo(e u )
e"
e~ u
u
loaiote")
1 e-
4.00
1.737 1779
54.598 IS
0.018 3156
4-5
1.954 3252
90.017 131 o. on 1090
.01
.741 5209
55.146 87
.018 1334
5
.958 668r
.921 819 .010 9985
.02
745 8638
.701 io(
.017 9530
5
.963 on i
91.835 598 .010 8890
.03
750 2068
56.260 91
.017 7743
-S3
.067 3540
92.758 561 .010 7807
.04
754 5497
.826 34.
017 5975
.54
.971 6969
93.690 800 .010 6734
4.05
T.758 8927
57-397 45/
0.017 4224
4-55
1.976 0399
94.632 408 o.oio 5672
.06
763 2356
974 3n
.017 2490
.56
.980 3828
95.583 480 .010 4621
.07
767 5785
58.556 963
.017 0774
-57
.984 7258
96.544 no .010 3580
.08
771 9215
59-145 470
.016 9075
.58
.989 0687
97.514 394 .010 2549
.09
.776 2644
739 892
.016 7392
-59
.993 41 17
98.494 430 .010 1529
4.10
1.780 6074
60.340 288
o.o 16 5727
4.60
1-997 7546
99-484 316 o.oio 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
.62
.OOfi 4405
101.494 032 .009 8s^S
-13
793 6362
62.177 923
.016 0829
.63
.010 7835
102.514 064 .000 75^8
.14
.797 9792
.802 821
.015 9229
.64
.015 1204
103-544 348 .00<J 6577
4-15
I. 802 3221
63.434 ooo
0.015 7644
4.65
2.019 4693
104.584 986 o.ooo 56r6
.16
.806 6650
64-071 523
.015 6076
.66
.023 8123
105.636 082 .009 4661,
17
.811 0080
-715 452
-015 4523
-67
.028 1552
106.697 74 2 .009 3723
.18
.19
815 3509
.819 6939
65-365 853
66.022 791
.015 2985
.015 1463
. .68
.69
.032 4982
.036 8411
107.770 073 .000 2700
108.853 180 .009 i#()7
4.20
.21
1.824 0368
-828 3798
66.686 331
67.356 540
0,014 9956
.014 8464
4,70
2.041 1841
.045 5270
109.947 172 0.009 0953
111.052 i(io .009 OO4&
.22
.832 7227
68.033 484
.014 6986
.72
.049 700
112.168 253 -008 9152
.23
.24
.837 0657
.841 4086
.717 232
69.407 852
-014 5524
.014 4076
-73
74
.054 2129
.058 5558
113.295 562 .008 8265
114.434 20J .008 7386
4'. 25
.26
' .27
.28
,29
1-845 7515
-850 0945
854 4374
.858 7804
863 1233
70.105 412
.809 983
71.521 636
72,240 440
.966 468
0.014 2642
.014 1223
.013 9818
.013 8427
.013 7049
4-75
76
-77
78
-79
2.062 8988
.067 2417
.071 5847
.075 9276
.080 2706
115-584 285 0.008 6517
116.745 926 .008 5656
117.919 242 .008 4804
119.104 350 .008 3<j6o
120.301 369! ,008 3125
4-30
31
-32
33
34
1.867 4663
.871 8092
.876 1522
-880 4951
.884 8381
73.699 794
74-440 489
75.188628
.944 287
76.707 539
0.013 5686
-013 4335
.013 2999
013 1675
.013 0365
4.80
.81
.82
-83
.84
.084 6135
.088 9565
.093 2994
.097 6423
.101 9853
121.510 41?
122.731 618
123-965 091
125.210 961
126.469 352
O.OOS 22Q7
.008 1479
.008 oM8
.007 0865
.007 9071
' 4-35
-36
.37
.38
39
1.889 1810
-893 5239
.8978669
.902 2098
906 5528
77.478 463
78.257 134
79-043 632
o -838 033
80.640 419
0.012 9068
-012 7784
.012 6512.
012 5254
.012 4007
4.85
.86
.87
.88
.89
.106 3282
.no 6712
.115 0141
"9 3571
.123 7000
127.740390
129.024 202
130.320917
131,630 664
132-953 574
0.007 8284
.007 7505
.007 6734
007 5970
.007 5214
4.40
.41
.42
-43
-44
1.910 8957
.915 2387
.919 5816
.923 9246
.928 2675
81.450 869
82.269 464
83.096 285
-931 417
84.774 942
0.012 2773
012 1552
.OI2 O342
-on 9145
.on 7959
4-90
.91
.92
93
, -94
2.128 0430
.132 3859
. 136 7289
.141 0718
.145 4H7
134.289 780
135.639414
137.002 613
138.370 512
139-770 250
0.007 44<>6
.007 3725
.007 2991
.007 2265
.007 1546
4-45
.46
-47
.48
49
1.932 6104
.936 9534
.941 2963
945 6393
.949 9822
85.626 944
86.487 509
87.356 723
88.234 673
89.121 446
o.oii 6786
.011 5624
on 4473
oil 3334
.on 2206
4-95
.96
97
.98
.09
2.149 7577
.154 1006
158 4436
.162 7865
.167 1295
141.174064
142.593 796
144.026 887
M5.474382
146.936 423
0.007 0834
.007 0129
.006 9431
.006 8741
.006 8057
4-50
r-954 3252
90.017 131
o.oii 1090
5-00
2.171 4724
148.413 159
0.006 7379
lo..(a-)
lorf)
e u
e"""
o fc (.")
!Q,o<e>
e n
fl -u
SMITHSONIAN TABLES .. -
257
The Exponential.
II
loum(i) 11 )
"
0-
II
lofjiufo")
a"
e-"
fi.no
2.171 4724
48.413 159
0,006 7379
5.50
2.388 6197
244.691 932
0.00-1 0868
.01
.'75 8i54
40.004 73"
.006 6709
.51
.392 9626
247.151 127
.004. 0461
,O2
.180 1583
51 .41 1 304
,006 6045
52
397 3055
249.635 037
.004 0058
.03
. 184 finu
52.933 013
.006 5388
53
.401 6485
252.143 911
.003 9660
,04
,188 844.;
54-470 015
.006 ,1737
54
.405 9914
254.677 999
.003 9265
5.0S
.M93 1871
56.022 464
o.(X)6 4093
5-55
2.410 3344
257.237 55<>
0.003 8875
.<>6
.107 5301
57.590 51(1
.006 3456
56
.414 6773
259.822 836
.003 8488
.OX
.201 8730
50.174 327
.oofi 2824
.57
.419 0203
262.434 oi;<]
.003 8105
.08
,2<Xi 2I(K)
(m.774 056
.01)6 21$)
.58
423 3(>32
265.071 606
.003 7726
.09
.210 5589
(12.389 862
.oof) 15811
-59
.427 7062
267.735 620
.003 7350
fi.IO
2.214 OotO
l6,|.02l 907
O.OOT) <W)67
5.60
2,432 0491
270.426 407
0.003 6979
. 1 1
.210 2448
i"5, 670 355
,00fi 0361
.61
..136" 3920
273.144 238
,003 6611
.1.!
.J2.1 5877
107.335 3'/v
005 97(x>
,62
440 7350
275-889 383
.003 6246
, 13
,:i.!7 9307
i6(),<H7 118
,(H>5 9166
.63.
.445 0779
278/162 118
.003 5886
.14
,232 273(1
1/0.715 768
.005 8577
.64
449 4209
281.462 718
.003 5529
S.15
2,236 6166
172.431 490
0,005 7994
5.6-5
2-453 7638
284.291 .\6fi
0.003 5'75
' ,iit
240 9505
174.164 456
.005 74"7
,66
.458 1068
287.148643
.003 4825
.17
-M5 3025
175.014 837
.005 (i8.j6
.67
,462 4497
290.034 534
.003 4479
.18
-MO 6454
177.682 8(1
.005 6280
,466 7927
292.949 43
.003 4136
19
253 !>H8.|
I70-l<'8 553
.005 5720
\GQ
.471 1356
295-893 (MI
.003 37<X>
S.~'o
"-'58 33'3
181.272 242
0.005 SiM
5.70
2.475 4785
298.867 401
0.003 34(i
" .ji
..:<u <>743
183.094 ogfi
.""5 4(117
.71
.479 8215
301.871 068
.003 3127
1 2;!
,2(17 017.!
184.1)34 184
.005 4073
.484 1644
304.904 923
.003 2797
.23
,271 ,'i6oi
18(1.79;! 80.1
.005 3535
73
.488 5074
307. 969 268
.003 2471
.-'4
.375 7031
188.670 IDS
.005 3003
74
.402 8503
311.064 .|ii
,003 2148
5.25
2.280 0160
190. 566" 368
0.005 2475
5.7S
2.497 1933
314.190 660
0.003 1828
.2(1
!k| ,1800
192.481 /IT
.005 1953
76
.501 5362
317.348 329
.003 .1511
.27
.288 7310
194 -4 M <)f)3
."05 1436
77
.505 8792
320.537 733
.003 1198
.,'8
-03 "749
19/1.36*) 875
,(X>5 0924
.78
.510 2221
323.759 190
.003 0887
.29
.-'97 4178
198,343 425
.005 0418
.79
,5'4 5651
327.013 024
.003 0580
!i-3'
2.301 7(x>8
200.336 810
0,<xi.| 9916
5.8o
2,5l8 9080
330.299 5(io
0.003 0276
' -'.I'
.30(1 1037
202,350 228
004 <J4i9
,81
.523 2509
333.619 iaf
.003 9974
, V
.310 ,\.\(\t\
20,1, '181 882
.004. 8928
.82
.527 5939
330.972 054
.002 9676
33
.34
.314 7896
200.43*7 074
208. Si- 1 71"
.004 8441
.004 7959
.83
,84
!S3"' 2798
340.358 679
343.779 34i
.002 938l
.002 9088
5.3.1
3.3^3 4755
210.608 298
0.004 7482
s.8s
2 , 540 6227
347.234 3 8
0.002 8799
.'127 8184
212.724 946
.<x).|. 7009
.86
.544 9657
350.724 14.
.002 8512
'')/
.332 I'M.]
iii-t.HfiJ 868
.004 6541
.87
.549 3086
354-248 y&
.002 8229
ill*
>33 ( i 5043
217.0.12 275
.004 6078
.88
553 6516
357.809 242
.002 7948
34" 8.|73
.419,203 386
.004 5620
.89
.557 9945
361.405 28.
,002 7670
5.40
a. 345 loon
221.40(1 4l(
0.004 SlC6
5-90
2.562 337-1
365.037 46^
0.002 7394
4'
340 5,13'
,(X>,| 4716
91
.5666804
168. 706 il'
.002 7122
/O- ..
4.1
-353 8761
221.879 123
.004 4271
.92
.57^ 0233
372.411 71'
.002 6852
43
.338 a 190
228! 149 245
.004 3831
,93
.575 3663
37o' -154 5i<
,002 6585
41
,3(12 5620
330,442 183
.004 3395
94
-579 7002
379-934 93"
,002 6320
5-43
2.366 90-10
.371 2479
> 375 S0o8
.370 0338
232.758 166
23S."97 44
239.846 707
242.257 207
0.004 20/13
,iX)4 2536'
.(X14 2112
,{X>4 169,1
.oo.| 1278
5-95
.06
.07
9
2,584 0522
..588 3951
!597 "810
.601 4239
38,1.753 339
387.610 12;
391.505 67
395.440 368
399.414 610
0.002 1x158
.003 5799
,002 5542
.002 5288
.002 5037
S-50
3,388 6197
344.60, W
0.004 0868
G.oo
2.605 7&T>9
403.4-'8 793
0.002 4788
-__.
lOUHitfl")
o u
f
,o,,<o",
" ,.*>
o"
"."i.-lHi'.", 1 "'
TAULGB
258
The Exponential.
a
10.^)
8
e-u
II
,*,
o u
.-
6.00
.01
.02
2.605 7669
.610 1098
.614 4528
403.428 793
407.483 3 20
411.578 596
0.002 4788
.002 4541
.002 4297
6.50
51
.52
2.822 9141
.827 2571
.831 6000
665.141 633
671.826 418
678.578 385
o.ooi 5034
.001 4885
.001 4737
03
.04
618 7057
623 138?
415.715 029
419.803 35
.002 4055
.002 3816
53
.54
.835 9430
.840 2859
685.308 211
692.286 S? 8
.001 4590
Ooi 4445
6.05
.06
07
2.627 4816
.631 8246
.636 1675
424.113 030
428.375 437
432.680 682
0.002 3570
-002 3344
,002 3112
6.55
.56
-57
2.844 6289
.848 9718
.853 3H7
699,244 I?4
706.271 695
713.369 843
o.ooi 4301
.001 4159
.001 4018
.08
.09
.640 5104
.644 8534
437.029 195
441.421 411
.002 2882
-OO2 2654
-58
-59
-857 6577
,862 0006
720.530 3 2 9
727.780 870
.001 3878
.001 3740
6.10
2.649 ^63
445-857 77
O.OO2 2420
6.60
2.866 3436
735-095 189
o.ooi 3604
.11
-653 5393
450.338 715
-OO2 22O6
.61
.870 6865
742.483 oio
.001 3468
.12
.657 8822
454.864 694
.002 1985
.62
.875 0295
749.945 97
Ooi 3334
13
.662 2252
459.436 161
.002 1766
63
.870 3724
757.482 171
.001 3202
.14
.666 5681
464-053 57 1
.002 1540
.64
.883 7154
765.094 993
.001 3070
6.15
2.670 9111
468.717 387
0.002 1335
6.65
2.888 0583
772.784 326
o.ooi 2940
.16
675 2540
473.428 075
.003 1123
.66
.892 4012
780.550 937
.001 2811
-17
679 597
478.186 106
.OO2 OQI2
.67
.896 7442
788.395 604
.001 2684
.18
.683 9309
482.991 956
.002 0704
.68
.901 0871
706.319 112
.001 2538
.19
.688 2828
487.846 106
.OO2 0498
.69
0S 43 *
804.322 252
.001 2433
6.2O
2.692 6258
492.749 041
0.002 0204
6.70
2.909 773
812.403 825
o.ooi 2309
.21
.696 9687
497-7 01 251
.OO2 OO92
.71
.914 1160
820.570 630
.001 2187
.22
.701 3117
502.703 232
.001 9892
.72
.918 4589
828.817 5"
.001 2065
-23
.705 6546
507-755 483
.001 9695
73
.922 8019
837.147 266
.001 1945
.24
.709 9076
512.858 s
.001 0499
74
.927 1448
845.560 736
.001 1826
6.25
2.714 345
518.012 825
o.ooi 9305
6-75
2.931 4878
854-058 763
o.ooi 1709
.26
.718 6835
523.218 940
.001 9112
-76
-935 8307
862.642 196
.001 1592
.37
723 0264
528.477 3?8
.001 8922
77
04 1736
871.311 894
.001 1477
.28
727 3693
533.788 664
.001 8734
.78
.044 5i66
880.068 724
,001 1363
.29
731 7 I2 3
539- J S3 329
.001 8548
79
.948 8505
888.913 562
.001 1250
6.30
2-736 0552
544.571 910
o.ooi 8363
6.80
2.053 2025
897.847 292
o.ooi 1138
31
.740 3982
550.044 949
.001 8180
.81
-957 5454
906.870 807
,001 1027
-32
744 74"
555-572 992
.001 7099
.82
.961 8884
915.985 oio
.001 0917 .
33
.749 0841
561.156 594
.001 7820
.83
.966 2313
925.190 812
.001 0809
34
753 4270
566.796 311
.001 7643
.84
970 5743
934.489 135
.001 0701
6-35
2-757 77oo
572.492 709
o.ooi 7467
6.85
2.074 9172
943.880 907
o.ooi 0505
36
.762 1129
578.246 356
.001 7204
.86
.979 2601
953.367 067
.001 0489
37
.766 4558
584.057 829
.001 7122
.87
983 6031
962.948 566
,00 I 0385
38
.770 7988
580-927 ?o8
.001 6951
.88
.987 0460
972.626 360
.001 0281
39
.775 1417
595-856 58o
.001 6783
.89
.992 2890
982.401 417
,001 0170
6.40
2.779 4847
601.845 03$
o.ooi 6616
6.90
2.996 6310
992.274 716
o.ooi 0078
.41
.783 8276
607.893 681
.001 6450
.91
3.000 9749
1002.24 724
.000 9978
,43
.788 1706
614.003 114
.001 6287
.92
.005 3178
1012.31 009
.000 0878
43
792 5135
620.173 948
.001 6125
93
.009 6608
1022.49 398
,000 9780
44
.796 8565
626.406 800
.001 5964
.04
.014 0037
1032.77 021
.000 9683
6-45
2.801 1994
632.702 293
o.ooi 5805
6-95
3.018 3466
1043.14 073
o.ooo 9586
.46
.805 5424
639.061 057
.001 5648
.96
.022 6896
1053.63 356
.000 9491
47
.809 8853
645.483 727
.001 5492
97
027 0325
1064.22 275
.000 9397
.48
.814 2282
651.070 946
Ooi 5338
.98
031 3755
v 1074.91 837
.000 9303
49
.818 5712
658.523 3<>3
.001 5185
99
035 7184
1085.72 148
,000 9210
6.50
2.822 9141
665.141 633
0.001 5034
7.00
3.040 0614
1096.63 316
0,000 9119
u.*-
I***)
e.
e -u
..*.(
**,
e
6 -
SMITHSONIAN TABLES.
The Exponential.
11
,. B ,,,<0",
O 11
e-
11
ldgifl(o u )
o-
o-"
7-oo
3.040 0(114
iooft.fi, 3,6
o.ooo 9119
7-50
3,257 2086
1808.04 241
o.ooo 5531
.OI
.044 4043
1107.65 450
,000 9028
,261 5516
1826.21 354
.000 5476
.0:1
.048 7473
ii 18,78 662
.000 8938
.52
.265 ^945
1844.56 729
,000 5421
.03
.053 0901-
1130.03 061
.000 8849
53
.270 2374
1863.10 550
.000 5367
.04
057 '1332
1141,38 7(11
.000 8761
54
.274 5804
1881.83 3
.000 5314
'/.OS
3.061 7761
1152.85 874
o.ooo 8(174
7.55
3.278 9233
1900.74 273
o.ooo 5261
,06(1 tioo
1164.44 517
.000 8588
.56
.283 2663
1919.84 551
.000 5209
.07
.070 4d:!o
1 17(1,14 803
,000 8502
S7
.287 6092
1939.14 028
.000 5157
.08
.074 8049
1187.9(1 852
.000 8418
.58
.291 9522
1958.62 897
.000 5106
.01)
.079 1479
1 199.90 780
.000 8334
SO
.296 2951
1978.31 351
.000 5055
7.10
1.o8i 4008
1211.96 707
o.ooo 8251
7.60
3,300 6381
1998.19 590
o.ooo 5005
.1 [
.087 8338
1224.14 755
,000 8i(ii)
.61
.304 9810
2018.27 810
.000 4955
.12
,092 17(17
133(1.45 043
.000 8088
.62
.309 3 -MO
2038.56 213
.000 4905
.1,1
,096 5197
1248.87 697
.000 8007
.63
.313 66(19
2059.05 002
.000 4857
,I.|
.100 862(1
12(11.42 839
.aoo 7928
.64
.318 0098
2079.74 382
.000 4808
'" , TS
3.105 3055
1274.10 596
o.ooo 7849
7 As
3.322 3528
2100.64 559
O.OOD 4760
.1(1 '
.109 5485
128(1,01 003
.000 7771
.66
.326 (1957
2121.75 743
.000 4713
.113 8014
1 209.84 460
.000 7603
.67
331 0387
2143.08 145
.000 4666
a 8
.118 2344
1312. 90 826
.000 7617
.68
335 3816
2164.61 977
.000 4620
123 5773
1326.10 321
.000 7541
.fit)
339 7246
2186.37 456
.000 4574
7.20
3.136 9203
1339.43 076
o.ooo 7466
7.70
3-344 0675
2208.34 799
o.ooo 4528
.31
.131 3632
1353,80 227
.000 7392
.348 4105
2230.54 226
,060 4483
.131; 60(13
1366.48 906
.000 7318
,72
352 7534
2252.95 958
.000 4439
.23
.1 10 <M<)1
[180.22 250
,000 7245
7,1
-357 9<>3
2275.60 220
.000 4394.
.144 2920
1304-0') 397
.000 7173
74
361 4393
2298.47 238
.000 4351
7. HI
3,T/l8 "'.ISO
T4o8.ro 485
o.ooo 7102
7-7S
3.365 7822
2321.57 241
0,000 4307
!a(i
.152 9779
1433.35 654
.000 7031
.76
.370 1252
2344.90 461
.000 4265
,i.<J7 3200
1436.55 045
.000 6961
77
-374 4681
2368.47 129
,000 4222
!aH
,i(ti 6(M8
14 150.98 803
,000 6892
.78
.378 8111
2392,27 482
.000 4180
.39
,l(i(i 00(18
M<5.S7 070
.000 682,-:
79
383 IS40
2416,31 758
.000 4139
7 '40
3,170 3497
1480.29 90,1
0,000 675;
7.80
3,387 4970
2440.60 198
o.ooo 4097
-3 1
3.1
.174 (1027
.179 035(1
.183 3786
.187 7215
141)5.17 7H
.1510.20 397
1535-38 m
1540.71 3ii
,000 6681
.000 (1622
.000 fisjf
,000 6491
.81
.82
A|
SO* 8300
.396 1828
.400 5258
,404 8687
2465.13 044
2489,90 541
2514.92 937
2540.20 483
.000 4057
,000 4016
.000 3976
.000 3937
7-.1S
..V'
-.17
3.102 0(144
.19(1 4074
.BOO 75O3
1556.19 65;
1571,83 (>$(
1587.63 37^
1(103,38 977
O.OOO 64 2(
.000 6362
.000 (1291
,000 623!'
7-8S
.86
.87
.88
3.400 2117
413 SM6
,417 8976
.422 2405
2565.73 432
2591.52 038
3617.56 559
264.3.87 256
o.ooo 3898
.000 3859
.000 3820
.000 3782
30
.209 4362
1610.70 (in
.000 6r//
.89
.426 5835
2670.44 392
.000 3745
7.40
3-313 7793
.3l8 1221
1(152,42 63;
o.ooo fin;
,000 605
7-yo
3.430 9264
,4.35 2694
2697.28 233
2724.39 47
0,000 3707
,000 3671
44
.222 465f
.326 8080
.2,'jl IS09
:ifi6o,O3 35
1685.80 75'
1702.75 022
.000 59<J
.000 593
.000 5873
,92
.9.1
94
439 flI 23
143 9552
.448 2982
275I-77 i5
2779.42 680
2807.36 051
.000 3634
.000 3598
.000 3562
i
!ll6
47
49
3.335 '1030
.230 H,i6t
.a/|4 1708
,348 S a3 7
.353 8657
1719,86 31,
1737,14 8o(
1754,60 661
1773.24 078
1790.05 2Oi
o.ooo 581-
.000 575
.000 569
.000 564,
.000 558
7.05
.96
97
.98
99
3.453 6411
.456 9841
.461 3270
.465 (1700
.470 0129
2835.5? 495
2864.07 295
2892.85 73(
2921.93 106
2951.29 696
o.ooo 3527
.000 3492
.000 3457
.000 3422
.000 3388
7-SO
1,2^7 2081
1808.04 24
o.ooo 553
8.00
3-474 3S59
2980,95 799
o.ooo 3355
w
10Kn)(0 )
0"
-
"*<'
->
*
e-
SMITHflONIAN TABU8,
2 5 8b
The Exponential.
_
n
log^to")
O u
fl-U
H
Iog 10 (e)
0"
--"
8.00
3-474 3559
2980.95 799
o.ooo 3355
8.50
3.691 5031
4914.76 884
o.ooo 2035
.01
.478 6988
30IC.QI 711
.000 3321
.51
.695 8460
49(14.16 309
.000 2014
.02
.483 0417
3041.17 733
.000 3288
52
,700 i8t)o
5014.05 376
.000 1994
03
.487 3847
3071.74 167
.000 3255
-53
704 5319
5064.44 583
.000 1975
.04
.491 7276
3102.61 319
.000 3223
54
.708 8749
5II5-34 436
.000 1955
8.05
3.496 0706
3I33.79 497
o.ooo 3191
8.55
3,713 2178
5166.75 443
o.ooo 1935
.06
500 4135
3165.29 013
.000 3159
.56
.717 5608
5218.68 117
.000 1916
.07
504 7565
3197.10 183
.000 3128
57
.721 9037
5271.12 979
.000 1897
.08
.509 0904
3229.23 324
.000 3097
.58
.726 2467
5324.10 553
.000 1878
.09
SI3 4424
3261.68 757
.000 3066
59
.730 5896
5377.61 368
.000 1860
S.io
3-Si? 7853
3294.46 808
o.ooo 3035
8.60
3-734 Q325
5431.65 959
o.ooo 1841
.11
.522 1282
3327.57 803
.000 3005
.61
739 2755
5486.24 868
.000 1823
.12
.526 47 12
3361.02 075
.000 2975
.62
-743 6184
554T-38 639
.000 1805
.13
53 8141
3394-79 957
.000 2946
63
747 96i4
5597.07 825
.000 1787
.14
535 iS7i
3428.91 787
.000 2916
.64
752 3043
5653-32 982
.000 1769
8.15
3-539 SOQO
3463.37 907
o.ooo 2887
8.65
3.756 6473
5710.14 673
o.ooo 1751
.16
543 8430
3498.18 660
.000 2859
.66
.760 9902
5767.53 466
.000 1734
17
548 1859
3533-34 396
.000 2830
.67
765 3332
5825.49 935
,000 1717
.18
552 5289
3568.85 466
.000 2802
.68
.769 6761
5884.04 659
.000 1700
.19
.556 8718
3604.72 225
.000 2774
,69
-774 0190
5943.18 224
.000 1683
8.20
3.561 2148
3640.95 031
o.ooo 2747
8.70
3.778 3620
6002.91 222
o.ooo 1666
.21
565 5577
3677.54 247
.000 2719
?i
.782 7049
6063.24 249
,000 1649
.22
,569 9006
3714.50 238
.000 2692
.72
.787 0479
6124.17 909
.000 1633
23
.574 2436
375T.83 375
.000 2665
73
.791 3908
6185.72 Sir
.000 1617
.24
578 5863
3789.54 031
.000 2639
74
-795 7338
6247.89 5?I
,000 1601
8.25
.26
3-582 9295
.58? 2724
3827.62 582
3866.09 410
o.ooo 2613
.000 2587
8.75
.76
3.800 0767
.804 4197
6310.68 811
6374.11 158
o.ooo 1585
,000 1569
.27
.28
.29
591 6154
-595 9583
.600 3013
3904.94 899
3944.19 438
3983-83 419
.000 2561
.000 2535
.000 2510
77
.78
79
.808 7626
-813 1056
.817 4485
6438.17 246
6502.87 717
6568.23 218
-ooo 1553
.000 1538
.000 1522
8.30
31
32
33
-34
3.604 6442
.608 9871
.613 3301
.617 6730
.622 0160
4023.87 239
4064.31 298
4105.16 ooi
4146.41 755
4188.08 974
o.ooo 2485
.000 2460
.000 2436
.000 2412
.000 2388
8.80
.81
.82
83
.84
3.821 7914
.826 1344
830 4773
.834 8203
.839 1632
6634.24 401
6700.91 927
6768.26 463
6836,28 682
6904,99 264
o.ooo 1507
.000 1492
.000 1477
.000 1463
.000 1448
8-35
.36
37
38
39
3.626 3589
.630 7019
.635 0448
639 3878
643 7307
4230.18 074
4272.69 477
4315-63 606
4359-00 893
4402.81 769
o.ooo 2364
.000 2340
.000 2317
,000 2294
,000 2271
8.85
.86
.8?
.88
.89
3.843 5062
.84? 8491
.852 1921
-856 S35o
.860 8779
6974.38 897
7044.48 274
7115.28 097
7186.79 074
7259.01 918
o.ooo 1434
,000 1420
.000 1405
.000 1391
.000 1378
8.40
.41
.42
43
44
3.648 0736
.652 4166
656 7595
.661 1025
.665 4454
4447.06 675
4491.76 051
4536.90 346
4582.50 009
4628.55 498
O.OOQ 2249
,000 2226
,000 2204
.000 2182 .
.000 2161
8.90
.91
.92
93
94
3.865 2209
.869 5638
.873 9068
.878 2497
.882 5927
7331-97 354
7405.66 no
7480.08 923
7555.26 538
7631.19 706.
o.ooo 1364 1
.000 1350 J
.000 1337 1
.000 1324
.000 1310
8.45
.46
47
.48
49
3.669 7884
6?4 1313
.678 4743
.682 8172
.687 1602
4675.07 274
4722.05 800
4769.51 547
4817.44 990
4865.86 607
o.ooo 2139
.000 2118
.000 2097 1
.000 2076 1
.000 2055 1
8.95
.96
-97
.98
99
3-886 9356
.891 2786
.895 6215
.899 9644
.904 3074
7707.89 186
7785.35 746
7863.60 161
7942.63 212
8022.45 6pO
o.ooo 1297
,000 1284
.000 1272
,000 1259
.000 1247
8.50
3,691 5031
4914.76 884
o.ooo 2035
9.00
3-908 6503
8103,08 393
o.ooo 1234
Iff a (e u )
tofco(B)
U ,
e-u
ogo(e)
I<Ww(o u )
0"
6~
SMITHSONIAN TABLES. ' "' '" .mSi;
I" 1
2580
The Exponential.
11
,.
o u
Q-U I
11
**)
0"
-
O.otJ
3.908 6503
8103.08 393
o.ooo 1234 1
9-5
4.: 25 7976
13359-7 268
o.ooo 0749
,Q[
012 99,13
8184.52 127
.OOO 1222
Si
.130 1405
13493.9 943
.000 0741
,02
,917 33(12
82(16.77 78
.OOO I21O
,52
.1^4 48^5
13639,6 ::s
,000 0734
03
,921 67(12
8349-85 957
.OOO 1198
53
.138 8264
t37C'(>.5 QII
,000 0726
.04
.926 02 a i
8433,77 yf>
.OOO I I 86
-54
H3 l6l J4
13904.9 476
.000 0719
9' 5
3.9,1 3'Vn
8518.53 792
o.ooo 1:74.
Q-SS
4.T47 5123
14044.6 947
o.ooo 07:2
.934 7080
8604.15 0(15
.OOO i:62
56
-151 8552
14185.8 462
.000 0705
.07
0,19 0510
8690.62 381
.000 1151
57
.156 ig8a
14328.4 :63
.000 0698
.08
94,1 ,1030
8777.96 603
.000 1139
.:6o ij4[i
1,1472.4 KJ3
,000 0691
,09
.947 73 ( 'K
8866.18 605
.000 1128
59
.164 8841
14617.8 695
.000 0684
y.io
3.952 0798
81155.29 270
0.000 III'/
9.60
4.169 2270
14764.7 8:6
o.ooo 0677
,11
.956 4My
9045. 29 480
.OtlO IlOfi
'.6r
.'173 570
149:3.1 ?o:
.000 067:
,ta
.060 7657
1)136.20 162
.000 1095
.62
177 9^9
15063.0 499
.000 0664
it
,965 1086
9228.02 197
.000 1084
6l
.182 2559
152:44 361
.000 0657
''4
.969 45:6
9320.76 513
.000 1073
.64
.186 5988
I5367-3 437
.000 0651
y.i.S'
.1(1
,1-973 7045
978 1375
941,1.44 038
9500,05 708
o.ooo icfia
.000 1052
Ififi
4.190 94.18
-195 284?
15531.7 88:
15677.7 847
o.ooo 0644
,000 0638
,982 4804
(j6c)(].()2 469
.000 :04:
.67
.199 6276
15835-3 490
.000 0631
Ii8
.986 8233
0701.15 277
.000 1031
.68
.203 9706
1599'! -4 </>9
.000 0625
10
001 1(163
0798.65 098
.OOO IO2I
.69
208 3135
16155.2 443
.000 0619
9.20
1-095 ^092
9897. 12 906
0,000 10:0
9.70
i .212 6565
163:7.6 072
o.ooo 0613
.999 8522
0996.59 686
.000 1000
71
.2:6 9994
16481.6 0:9
.000 0607
lu'J
, ,oo.| 1951
:ooo7.o 643
.OOO O()()O
.73
.22: 3424
16647.2 447
.000 0601
iil
.008 '(381
10198.5 415
.000 0981
73
.225 6853
16814.5 523
.000 0595
,.!-!
.013 8810
. 10301.0 38(1
.000 0971
74
.230 0283
16983.5 414
.000 0589
.'.16
4,017 2240
.021 5(ifll)
10404..',' 657
10501).! 333
0,000 0961
.000 0952
9.75
4-2.14 3712
.238 7141
17:54.2 288
17326,6 3:7
o.ooo 0583
.000 0577
27
.'JH
,0;!5 9098
10(114.7 519
10721.4 319
,000 0942
.000 0933
77
.78
-243 057:
,247 4000
17500.7 672
17676.6 529
.000 057:
.000 0566
.034 5057
10829. i 841
.000 0923
79
251 7<13O
I78S<M 062
.000 0560
t\ 1O-
H K
:ooi8o 192
o.ooo 0914
9.80
4.256 0859
18033.7 449
o.ooo 0555
*J*iV
3'
33
34
.043 aHi(
,051 1)675
.05(1 3105
11047.9 <|8i
11158,9 8ii)
1137:. i 315
11.384.4 082
.000 0905
,000 0896
.000 0887
.000 0878
.8:
.Ha
.8,1
.84
.260 4289
.264 7718
.269 1:48
-273 4577
182:4.9 871
18398.0 50?
18582.9 542
18769.7 rfio
.000 0549
.000 0544
.000 0538
.000 0533
9-35
4,060 6534
1:408.8 334
11614.3 885
o.ooo 0870
.000 086:
'!S6
4,277 8006
.282 1436
18958.3 54
19:48.8 894
o.ooo 0527
.000 0522
37
.u(>9 3.103
11731.1 151
11849.0 148
.000 0852
.000 0844
.87
.88
.286 4865
.290 8295
19341-3 39
19535-7 227
,000 0517
.000 0512
39
!o7 025;!
1 1968.0 993
,000 0836
.89
.295 1724
19732.0 599
.000 0507
.41
,i 'i
.091 0540
T 2088.3 807
12209.8 710
o.ooo 0827
.000 08:9
.000 08: i
9.90
-92
4-299 5*54
.303 8583
.308 20:3
I993Q.3 74
20130.6 740
20332.9 90!
o.ooo 0502
.000 0497
,000 0492
./i j
.00!) H97Q
: 2456.5 a6y
12581.7 169
.000 0803
.000 0795
93
94
i ^l '? 5*1 *1 "
.3:6 8872
20537.3 <of
20743-7 443
.000 0487
.000 0482
y-45
.40
'17
49
4.104 0839
. to8 41.158
,112 V'lH'/
,117 III'/
.121 4546
12708,1 653
12835.8 84-
13964.8 872
13095.1 865
I333G.V 953
o.ooo o'/8y
.000 0779
.000 077:
.000 0764
.000 0756
0-9S
.96
97
,98
-y;
4.32: 2301
.3^5 5730
.329 9160
-3,14 2589
,338 60:9
20952.2 22,
21:62.7 95'
21375-4 85'
2:590,3 12,
2l807,2 98!
o.ooo 0477
.000 0473
,000 0468
,000 0463
.000 0459
0.50
4-135 797f>
I3J.W-7 **
o.ooo 0749
10.00
4.342 9448
22036-4 658
o.ooo 0454
lOftoO"
10K.<,(0")
B u
r-
.'
.,.(.>
O u
o-
SMITHSONIAN TADL.CB.
258 d
The Exponential.
.29
4.342 9448
.347 2878
351 6307
355 9737
.360 3166
4-364 6595
.369 0025
373 3454
377 6884
382 0313
4-3S6 3743
-390 7172
.395 0603
399 4031
.403 7460
4.408 0890
.412 4319
.416 7749
.421 1178
.425 4608
4.429 8037
434 146?
.438 4896
442 8325
447 i?55
4-45i 5184
-455 8614
.460 2043
464 5473
.468 8902
4-473 2332
477 5?6i
.481 9191
.486 2620
.490 6049
4-494 9479
.499 2908
503 6338
.507 9767
512 3197
4-516 6626
.521 0056
525 3485
.529 6914
-534 0344
4.538 3773
-542 7203
547 0632
551 4062
555 749i
22026.4 658
22247.8 355
22471.4 299
22697.2 715
22925.3 829
23155.7 868
23388.5 064
23623.5 648
23860.9 855
24100.7 924
24343.0 094
24587.6 607
24834.7 708
25084.3 644
25336-4 665
2559 1 -! 022
25848.2 971
26108.0 768
26370.4 673
26635.4 949
26903.1 861
27173.5 676
27446.6 665
27722.5 101
28001.: 259
28282.5 4^9
28566.7 862
28853.8 872
29143-8 736
39436.7 744
29732.6 189
30031.4 366
3Q333-2 576
30638.1 119
30946.0 300
31257.0 428
3I57LI 813
31888.4 770
32208.9 615
32532-6 669
32859.6 257
33189.8 704
335234 34i
33860.3 503
34200.6 534
34544-3 747
34891.5 514
35242.2 174
35596.4 075
35954-1 574
o.ooo 0454
.000 0449
.000 0445
.000 0441
.000 0436
o.ooo 0432
.000 0428
.000 0423
.000 0419
.000 0415
o.ooo 0411
.000 0407
.000 0403
.000 0399
.000 0395
o.ooo 0391
.000 0387
.000 0383
.000 0379
.000 0375
o.ooo 0372
.000 0368
.000 0364
.000 0361
.000 0357
o.ooo 0354
.000 0350
.000 0347
.000 0343
.000 0340
4.560 0921 36315.5 027
o.ooo 0336
.000 0333
.000 0330
.000 0326
.000 0323
o.ooo 0320
.000 0317
.000 0314
.000 0310
.000 0307
o.ooo 0304
.000 0301
.000 0298
.000 0295
.000 0293
O.OQO 0289
.000 0287
.000 0284
.000 0281
.000 0278
o.ooo 0275 I u, 00
4.560 0921
564 4,35
.568 7779
573 I2 9
577 4638
4.581 8068
.586 1497
.590 4027
504 8356
-599 1786
4.603 5215
.607 8645
.612 2074
.616 5503
,620 8933
4.625 2362
.629 5793
.633 9221
.638 2651
.642 6080
4/M(J 95 TO
.651 2939
.655 6368
.659 07QR
.664 3237
4.668 6657
.673 0086
.677 3516
.681 6945
686 0375
4-690 3804
694 7233
.699 0663
'703 4092
.707 7522
3 () 3.i5-S 027
36680.4 795
37049-1 2,|5
37421.4 7<M
37797-5 665
3^177.4 383
38561.1 279
3 H 948.6 737
39340-1 144
39735.4 8yi
40134.8 374
40538.1 993
40945.6 1,|Q
4I357.I 252
4r772.7 713
4^92-5 945
43616.6 372
430.I4-9 415
43477.5 504
43'JI4.5 070
44355-8 551
44801.6 389
45706.6 920
46166.0 519
o.ooo G~7$
.ODD O,'',',!
.000 njyo
.000 0^07
.000 o.'d.s
o.ooo
.000
.000
,000 0^5, \
.000
0,000 o;
.000
.GOO O!,) 3
4-712 0951
.716 4381
.720 7810
-725 1240
.729 4669
4-733 8099
.738 1528
742 4957
746 8387
751 1816
4-755 5246
759 8675
.764 2105
768 5534
.772 8964
4-777 2393
46630.0 285
47098.6 680
475V2.0 175
48050.1 242
48533.0 360
.'10020,8 OTT
49513.4 684
Soori.o 870
50513.7 068
51021,3. 780
51534.1 514
52052.0 782
52575.2 103
53103.5 999
53637.3 ooo
54176.3 638
54720,8 453
55270-7 989
55826.2 797
56387-3 431
56954-0 454
57526.4 430
58104.5 934
58688.5 543
59278.3 841
59874,1 417
o.ooo
.000
.000
.000
.000
o.ooo OM:
.000 (
.OOO Ol'JI
.000 cuiy
O.OOO (
.OOO OiilJ
.OOO OJKI
.000 c
.000 ocnli
o.ooo oao.|
.000 o
,OO() OSCO
.000 aiijH
.OOO OKJff
o.oao oil),]
.000 o.
.000 OHJO
.000 oi.SH
.000 a i
o.ooo 018,5
.000 oiH.j
.OOO QlKl
.000 0171)
.000 oiyy
o.ooo oryf.
.000 017,1
.000 017:1
.000 0170
OOO Olftl)
O.OOO OlCl'/
SMITHSONIAN TABLES.
258 e
The Exponential.
u
10|tm(0 U >
0"
o-
11
..,(.)
O 11
-
1 I.UO
4-777 -M')3
S08-M.I 4T7
o.ooo 01(17
11.50
4.904 3865
98715.7 710
O.OOO OIOI
,01
.781 $&>:<
60475.8 868
.000 0165
.51
.908 7295
90707.8 810
.OOO 01 OO
,n.i
785 O-'i.S'-!
(11083.6 7<}6
.000 0164
.53
5.003 0724
100 709.962
.000 0099
",1
.700 :!fi8i
61607.5 808
.OOO Ol() 2
5,1
.007 4154
TOI 722,114
.000 0098
.04
-79,| (nn
6-317.6 518
.000 01(10
*54
.on 7583
102 744.438
.000 0097
n.o.S
4.7<)8 (1540
12943.0 546
o.ooo 0150
".55
5.016 1013
103 777.037
o.ooo 0096
.lid
.803 uoyo
( '3.S7''-S 5")
.000 0157
S(i
.020 4442
104 820.013
.000 OOQ5
.07
,8oy (1300
64315.5 ofi8
.000 0156
57
.024 7872
105 873.472
.000 0094
,oS
.811 ()8:!<)
fit! oOGiO o "lil
.000 0154
.58
.029 1301
TOC 937.518
.000 0094
.00
.81(1 ,i2<jK
u ^ *\ 1 2 1 '/ flf) [
.000 0153
-59
.033 4730
108 012,258
.000 0093
1 1 . 1 O
4.8.10 668 y
(1(1171. i (ioa
0,000 0151
1 1. do
5.037 8ido
109 097.790
o.ooo 0092
.1 1
.825 01 iy
611836, i 1)14
.000 0150
.di
.042 1589
no 194.250
.000 0091
,i if
,Hai) 3546
(iy 507.0 0(13
.000 0148
.(12
.046 5010
in 301.721
.000 0090
'3
83,1 (>oyf>
(181X6.3 7- n
.oon 0147
.6l
.0^0 8448
ira 420.322
.000 0089
.14
.838 0405
688yi.fi 56,1
.000 0145
.64
-055 1878
113 550.165
.000 0088
ii.i';
4..|a l8is
69563.8 381
o.ooo 0144
ii.ds
5-0 W 5.10?
114 (191.303
o.ooo 0087
.16
.84 (i ya(ii|
yoafis.o 562
.000 0143
.(16
,0(13 8737
115 844.030
.000 0086
'7
,851 0(194
701)69.1 icifi
.000 0141
.fiy
.0(18 ai(if)
117 008,282
.000 008.1
,18
.855 4133
7i6rt2-3 631
.000 0140
.68
-072 5595
nH 184,235
,000 008,1
.H)
.8ii9 75,'tf
Va^oa.y 818
.000 0138
.69
.076 9025
TIC) 372.006
.000 oo8/|
1 1 . i'O
4,864 oi)8,i
731,10.4 418
O.OGO OT37
11.70
5.081 2454
120 571.7^5
o.ooo 0083
..!!
.868 4411
73865.4 150
.000 0135
.71
,085 5884
121 783.481
.000 0082
.;!.(
.Hya 7841
74607.7 748
.OfX) 01,1, (
1 ""*
.089 9313
123 007.425
.000 0081
M
.877 iayo
.000 0133
-73
.094 2743
124 243,670
.000 ooBo
.a.|
,881 4700
76114.9 518
.000 0131
74
.098 6172
125 493.340
.000 0080
i r.35
4.885 Riai
y68yo, t) f<)8
o.ooo 0130
"75
5.102 9602
126 753-559
o.ooo 0070
.;!()
.890 1551)
7 7 (is 11.5 758
.000 orai)
. .76
.toy 3031
128 027.453
.000 0078
.:/
.8114 408M
78,133.1) 07"
,000 0137
77
,iu (14(11
i2() 314.151
.000 0077
.,jK
,81)8 8.] iH
yoaat.a (no
,000 0126
.115 981)0
130 613.780
.000 0077
.30
.t)t.M 1847
8ooiy,4 488
.000 0125
79
.120 3319
131 926.470
,000 0076
1 1 .30
4.007 5376
ffoltat.fi 375
o.ooo oTa,|
11.80
5.124 (r/49
133 252.353
o.ooo 0075
.(]
.()ii 8/ofi
8i('i;-l3,(> 085
.con 0122
.81
.129 0178
1.14 591-5 01
,000 0074.
,\"
Ol6 2135
H24fvlsi 4""
.000 oiai
.83
.133 3608
135 94i|.22<)
.000 0074
-33
0-!<> S565
3;!H,i,Q 3 lilt
,000 0120
83
.1.17 70,17
t,17 310.491
.000 0073
3'l
.934 81104
8,|T:to.o 311
.000 OIK)
.84
.142 04(17
138 (190.485
.000 0072
IMS'
4.029 3.| i'i|
849(15,4 5'5
o.ooo 01 18
11.81
5.146 3896
140 084.347
o.ooo 0071
,3(1
0,'i.i SK'i
85811).! 6K"j
,000 0117
.86
.150 7326
14.1 492. 218
.000 007 1
37
.017 0-83
NfKiHi.K 675
,000 0115
.87
.155 0755
14.2 914-239
.000 0070
,y,|3 371 a
Hytci.O -j,| y
,000 0114
.88
-159 4i84
144 3 S- 55 1
.000 0069
il'J
,i),|6 6141
88433.9 574
.000 oir.i
.By
.163 7(114
145 80:. 298
.000 00(19
1 1.40
4,<)50 9571
8932 r. y 234
o.ooo on 2
11.90
5.i(>8 1043
147 afifi.fhs
o.ooo 00(18
OSS .1
OS9 6430
ijii'jfi.i 411)
,000 or ri
,000 0110
.92
.172 447.1
.176 7902
148 746,679
150 241.608
.000 00(17
.000 00(17
4 i
,9(13 9850
02O4l.d HA ft
.000 OIOI)
03
.181 1332
151 751,5(12
,000 oofrfi
44
,968 3:189
yayd'/.o iso
.000 OlOJi
-94
.185 4761
153 37(1.690
.000 0065
M'
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91901. 1 4(10
o.ooo 0106
11,95
5.189 8191
154 817.147
o.ooo 0065
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1)4845,0 703
,000 1005
,194 1620
156 373.085
,000 0064
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47
.48
.981 ,157V
98$ 7 OU 7
y57i)8,a 79 1
96761.0 678
.000 0104
.000 0103
-97
.08
.302 8479
157 944.6(10
159 sa 3 ' ^ 1
.000 0063
.000 0063
.40
,990 0,13(1
97 7.13-5 397
.OOO 0103
99
,207 KJOH
ifn 135-35-1
.000 006 a
11.50
4-9(M W$
97-5.'/ 7iO
o.ooo oroi
12.00
5- 211 5338
162 754.79"
o.oob oo&r
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-
SMITHSONIAN TAIIUP.
The Exponential.
ii, " i
u
**.>
a u
e-u
u
,.*,<..,
9 U
o-
12. CO
.OI
.02
03
.04
5-2II 5338
.215 8767
.220 2197
.224 5626
.228 9056
162 754-79 1
164 39-54
166 042.656
167 711.413
169 396.940
O.QOO Oo6l
.OOO Oo6l
.OOO O06O
.OOO 0060
.OOO O059
12.50
51
.52
.53
54
5.428 6810
433 0240
437 3669
44 1 7099
.446 0528
268 337.287
271 034.121
273 758.059
276 509-374
279 288.339
o.ooo 0037
.000 0037
.000 0037
.000 0036
.000 0036
I2.0=i
.Of)
.O?
.08
.09
5.233 2485
.23? 59 r 5
.241 9344
.246 2773
.250 6203
171 099.408
172 818.986
174 555.845
176 310.161
178 082.107
o.ooo 00 g 8
.000 0058
.000 0057
.000 0057
.000 0056
12.55
.56
57
58
59
5-4SO 3957
454 7387
.459 08:6
.463 4246
.46? 7675
282 095-233
284 930,338
287 793-935
290 686.312
293 607.758
o.ooo 0035
.000 0035
.000 0035
.000 0034
,000 0034
I2.IO
.11
.12
13
.14
5-254 9632
.259 3062
.263 6491
.267 9921
.272 3350
179 871.862
18: 679.605
183 505-515
185 349.776
187 2:2.572
o.ooo 0056
.000 0055
.000 0054
.000 0054
.000 0053
12.60
.6:
.62
.63
.64
5.472 1105
476 4534
.480 7964
.485 1393
.489 4823
296 558.565
299 539-028
302 549-446
305 590- n 8
308 661.350
o.ooo 0034
.000 0033
.000 0033
.000 0033
.000 0032
!i6
I?
.18
.19
5.276 6780
.281 0209
.285 3638
.289 7068
.294 0497
189 094.090
190 994-5 I 7
192 9:4.044
194 852.862
196 811.166
o.ooo 0053
,000 0052
.000 0052
.000 oogi
,000 0051
12.65
.66
6?
.68
.69
5493 8252
.498 :68i
.502 5111
.506 8540
.511 1970
311 763.448
314 896.723
318 061.488
321 258.059
324 486-756
o.ooo 0032
.000 0032
.000 0031
.000 0031
.000 0031
1 2. 2O
.21
,22
7 1
5.298 3927
302 73 5 6
.307 0786
,311 4215
198 789.:5i
200 7S7.or5
202 804.958
204 843. :82
o.ooo 0050
.000 0050
.000 0049
.000 0049
12.70
72
73
5-5I5 5399
.5:9 8829
.524 2258
.528 5688
327 747-902
331 041-823
334 368.849
337 729.311
o.ooo 0031
.000 0030
.000 0030
.000 0030
J
.24
.315 7645
206 901.890
.000 0048
74
-533 9 11 ?
341 123.547
,000 0029
12.25
.26
.2?
.28
.29
5.320 1074
324 453
328 7933
333 J 362
337 4792
208 981.289
211 081.586
213 202.991
215 345-7I7
217 509,977
o.ooo 0048
.000 0047
.000 0047
,000 0046
.000 0046
12.75
.76
77
78
79
5-537 2546
541 597 o
545 9405
-550 2835
554 6264
344 55I-S96
348 014.700
351 512.306
355 045.064
358 6:3.326
o.ooo 0029
,000 0029
,000 0028
.000 0028
.000 0028.
I2.3O
5.341 8221
219 695.989
o.ooo 0046
12.80
5.558 9694
362 217,450
o.ooo 0028
31
3'
33
34
.346 1651
.350 5080
-354 8510
350 1939
22: 903.970
224 134.142
226 386.728
228 661.952
.000 0045
.000 0045
.000 0044
.000 0044
.81
.82
.83
.84
-56? 6553
.571 9982
.576 3411
365 857.796
369 534.727
373 248.613
376, 999.824
.000 0027
.000 0027
.000 0027
.000 0027
12.35
36
37
5-363 5369
.367 8798
.372 2227
230 960.043
233 281.230
235 625.745
o.ooo 0043
.000 0043
.000 0042
12.85
.86
.87
5.580 6841
.585 0270
.589 3700
380 788.735
384 615.726
388 481-178
o.ooo 0026
.000 0026
.000 0026
18
3?6 5657
237 993-823
.000 0042
.88
-593 7129
392 385-479
.000 0025
\J
39
.380 9086
240 385.701.
,000 0042
.89
.598 0559
396 329.018
.000 0025
12.40
5.385 2516
242 801.6:7
o.ooo 0041
12.90
5.602 '3988
400 312.191
o.ooo 0025
.41
3 8 9 5945
245 241.8:4
.000 0041
.9:
.606 7418
404 335-396
.000 0025
.42
393 9375
247 706.536
.000 0040
.92
.611 0847
408 399.034
,000 0024
43
.398 2804
250 196.028
.000 0040
93
.615 4277
4" 503-5I3
.000 0024
44
.402 6234
252 710.539
.000 0040
94
.619 7706
416 649.24*
.000 0024
12.45
5.406 9663
255 250.323
0.000 0039
12.95
5.624 1135
420 836.636
o.ooo 0024
.46
.41: 3092
257 815.631
.000 0039
.96
.628 4565
435 066.115
,000 0024
47
.415 6522
260 406.721
.000 0038
97
.632 7994
429 338.100
.000 0023
.48
.419 9951
263 023.852
.000 0038
.98
.637 1424
433 653.020
.000 0023
49
.424 338i
265 667.286
.000 0038
99
.641 4853
438 011,305
.000 0023
12.50
5.428 6810
268 337- 2S 7
o.ooo 0037
13.00
5.645 8283
442 413-392
o.ooo 0023
log: B (fl u
log 1Q (e u )
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*
a-w
SMITHSONIAN TABLES.
258 g
The ISxponential.
74-! iSt.558
751 630.405
759 184.4:7
766 8:4.347
774 520.059
782 305.024
790 167.320
798 108.634.
8ofi 129.750
814 231,408
822 414.660
830 680.065
839 028.539
847 460.916
855 978-039
864 580.762
873 269.943
882 046.452
890 011.166
5.028 111)7
.1)32 4.626
.036 8056
.941 1485
94S
o.ooo ooiy
.OOO OOII)
.OOt) OOKJ
.OOO OOKJ
.000 ooiy
f)6,|.()O.S
534 yHK.aif.
O.OOO 001(1
.000 oo if
.000 oo if-
.000 ooiJ-
.OOO
O.OOO OOlf
..ooo ooty
.000 0017
.000 ooiy
.000 ooi'
O.OOO OOI'
.000 aoi
,000 oon
.000 00 1 (
.000 OOlf
908 008.765
O.OOO OOI 2
.OOO OOI 2
.OOO OOI 2
.OOO OOI 2
.OOO OOI 2
O.OOO OOI 2
.OOO 1 OOI 2
.OOO OOI 2
.OOO OOII
.OOO OOII
O.QOO OOII
.000 OOII
.OOO OOII
4632
2062
918 043.450
927 269.940
.OOO OOII
.QOO OOII
1/191
oif) 589.158
O.OQO OOII
5780
J20IJ
046 002.036
OSS 59-5T4
965 112.545
974 812.087
.000 OOII
,OOO OOIO
.OOO OOIO
.OOO OOIO
26^0
6068
9407
2927
984 609.111
994 504-597
100 4499-53
lot 4594-92
102 4791.77
O.OOO OOIO
.ODO OOIO
.OOO OOIO
.QOO OOIO
,OOO OOIO
9786
6645
0074
103 UOIJT.IO
104 5493-94
105 6001.33
106 6614.32
107 7333-97
O.OOO OOIO
.OOO OOIO
.000 0009
.000 0009
.000 0009
6933
0362
3792
7221
0651
108 8161.36
109 9097.56
in 0143.67
H2 1300.80
113. 2570.06
o.ooo 0009
,000 0009
.000 0009
.000 0009
.000 0009
4080
7510
0939
43<>0
7798
114 3952-58
H5 5449-5
116 7061.96
117 8791.12
119 0638.17
o.ooo 0009
.000 0009
.000 0009
.000 0008
,000 0008
1227
o( u >
120 2604.28
o.ooo 0008
-"
HMITH80NIAN TAHUKB
258 h
The Exponential.
Q
,.*,
a*
a-
w
,,,,
o u
.-
I4.OO
6.080 122
1 20 2604.2
o.ooo ooo
14.50
6.297 270
198 sl5Q.sC
o.ooo 0005
.O
.084 461'
121 4690.6
.000 ooo.
51
,301 6129
200 2686.3;;
.000 0005
.O
.oSS SoS
122 6898.5
.000 oooi
52
305 9559
202 2813. 6f
.000 0005
J
.093 151
123 9229.0
.000 ooo!
53
.310 298?
304 3143-27
.000 0005
.O.
.097 494
125 1683.5
.000 0008
54
.314 6418
206 3677.20
.000 0005
14.05
6.101 837
126 4263.1
o.ooo ooof
14-55
6.318 9847
208 4417.50
o.ooo 0005
.Of
.106 180.
127 6969.1.
.000 oooi
.56
323 3 2 77
210 5366.25
.000 0005
.07
.no 523,
128 9802.93
.000 ooof
57
.327 6706
212 6525.53
.000 0005
.08
.114 8663
130 2765.6
.000 ooof
58
.332 0135
214 789747
.000 0005
.09
.119 2092
131 5858.68
.000 ooof
59
.336 3565
216 9484.20
.000 0005
I4.IO
6.123 5522
133 9083.2!
o.ooo ooof
14.60
6,340 6994
2IQ 1287,88
o.ooo 0005
.11
.127 8951
134 2440.79
.000 0007
.61
.345 0424
221 3310.68
.000 0005
.12
.132 3381
135 5932-54
.000 0007
.62
349 3853
223 5554.83
.000 0004
.13
136 5810
136 9559-89
.000 0007
63
353 7283
225 8022.53
.000 0004
.14
.140 9240
138 3324.20
,000 0007
.64
.358 0712
228 0716.03
.000 0004
I4-I5
6.145 2669
139 7226.8,
o.ooo 0007
14.65
6.362 4142
230 3637.61
o.ooo 0004
.16
.149 6091
141 1269.20
.000 0007
.66
366 7571
232 6789.55
.000 0004
17
153 952*
142 5452.69
.000 0007
.67
.371 1000
235 0174.17
.000 0004
.18
.158 2958
143 9778.73
.000 0007
.68
375 4430
237 3793-82
.000 0004
.19
.162 6387
145 4248.75
.000 0007
.69
379 7859
239 7650,84
.000 0004
14.20
6.166 9816
146 8864.19
o.ooo 0007
14.70
6.384 1289
242 1747.63
o.ooo 0004
.21
.171 3246
148 3626.52
.000 0007
.71
.388 4718
244 6086.60
.OOO OOO,|
.22
.175 6675
149 8537.21
.000 0007
72
.392 8148
247 0670.18
.000 0004
-23
.180 0105
Z 5! 3597-?6
.000 0007
73
397 1577
249 5500.8,3
.000 0004
.24
184 3534
152 8809,67
.000 0007
74
.401 5007
252 0581.03
.000 0004
14.25
6.188 6964
154 4174.47
o.ooo 0006
14-75
6.405 8436
254 59I3-29
o.ooo 0004.
.26
193 0393
*S5 9693-68
.000 0006
.76
.410 1866
257 1500.14
.000 0004
.27
.197 3823
157 5368.86
.000 0006
77
.414 5295
259 7344.15
.000 0004
.28
.29
.201 7252
.206 0681
159 1201.58
160 7193-42
.000 0006
. .000 0006
.78
79
.418 8734
423 2154
363 3447-89
264 9813.98
.of jo 0004
.000 0004
14.30
32
33
34
6.210 4111
.214 7540
.219 0970
223 4399
.227 7829
162 3345-99
163 9660.88
165 6139.75
167 2784.23
168 9595.99
o.ooo 0006
.000 0006
.000 0006
,000 0006
.000 0006
14.80
.81
.82
83
.84
6.427 5583
431 9013
.436 2442
.440 5872
444 9301
267 6445.06
27 3343-78
273 0512.83
275 7954-94
278 5673.85
o.ooo 0004
.000 0004
.000 0004
.000 0004
,000 0004
14.35
-36
37
38
39
6.232 1258
.236 4688
.240 8117
.245 1546
.249 4976
170 6576.71
172 3728.09
174 1051.85
i75 8549.71
17? 6223.43
0,000 0006
.000 0006
.000 0006
.000 0006
.000 0006
14.83
.86
.87
.88
.89
6.449 2731
453 6'6o
457 9589
.462 3019
.466 6448
281 3^69.33
284 1947.17
287 0509.22
289 9358.32
29;, 8497.35
O.OOO OOO<|
.000 0004
.000 0003
.OOO OOO, 1 }
.000 0003
14.40
.41
.42
43
44
6.253 8405
258 1835
.262 5264
.266 8694
.271 2123
179 4074.77
181 2105.52
183 0317.49
184 8712.48
1 86 7292.35
o.ooo 0006
.000 0006
.000 0005
.000 0005
.000 0005
14.90
.91
.92
93
,94
6.470 9878
475 337
479 6737
.484 0166
488 3596
295 7929.24
298 7656.92
301 7683.37
304 8011.60
307 8644,62
o.ooo 0003
.000 0003
,000 0003
.000 0003
.000 0003
14-45
.46
47
.48
49
6-275 5553
.279 8982
.284 2412"
.288 5841
.292 9270
188 6058.95
190 5014.16
192 4159-87
194 3498.00
196 3030.48
o.ooo 0005
.000 0005
.000 0005
.000 0005
.000 0005
14-95
.96
97
.98
99
6,492 7025
497 0454
.501 3884
505 7313
510 0743
3io 9585.51
314 0837.37
317 2403.31
320 4286.49
323 6490.11
o.ooo 0003
.000 0003
.000 0003
,000 0003
.000 0003
14.50
6.297 2700
198 2759.26
o.ooo 0005
15.00
6.514 4172
326 9017.37
o.ooo 0003
*<,>
^
*
^
*.,.,
,*,<,.,
o u
o-
2581
The Exponential,
11
loou>(e' 1 )
e
e- u
I
.43429 44819
2.71 828 183
0.367 879 441
2
.86858 89638
7.38 905 610
0.135 335 283
3
1.30288 34457
20.0 855 369
(i) 407870684
4
I.737I7 79270
54.5 98r 500
(i) 183 156 389
5
2.17147 24095
148. 413 159
(2) 673 794 700
6
2.60576 68914
403. 428 793
(2) 247 875 218
7
3.04006 13733
109 6.63 316
(3) 911 88 i 956
8
3.47435 5^552
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 9C9 298
11
4-77723 03009
598 74-1 417
(4) 167 017 008
12
5.21153 37828
162 754- 791
(5) 614 421 235
-13
5.64582 82647
442 413- 392
(5) 226 032 941
14
6.08012 27466
120 260 4.28
(6) 831 528 719
IS
6.51441 72285
326 901 7-37
(6) 305 902 321
16
6.94871 17105
888 611 ' 0.52
(6) H2 535 175
17
7.38300 61924
241 549 52.8
(7) 4U 993 772
18
7.81730 06743
656 559 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
I3i 881 573 [i]
(9) 758 256 0^3
22
9-554-17 86019
358 491 285 [i]
(9) 278 946 809
2.3
9.98877 30838
974 480 345 [i]
(9) 102 618 796
24
10.42306 75657
264 891 221 [2]
(10) 377 513 454
25
10.85736 20476
720 048 993 [2]
(10) 138879439
26
11.29165 65295
195 729 609 [3l
(11) 510908903
27
11.72595 10114
532 048 241 [3]
(il) 187952 882
28
12.16024 54933
144 625 706 [4]
(12) 691 440 on
29
12.59-153 99752
393 133 430 E4]
(12) 254 366 565
30
13.02883 44S7I
106 864 746 [5]
(13) 935 762 297
31
13.46312 89390
290 488 497 IS]
(13) 3442477H
32
13.89742 34209
789 629 602 [5]
(13) 126 641 655
33
I4'33I7I 79028
214 643 580 [6]
(14) 465 888 615
34
14.76601 23847
583 461 743 [6]
(14) 171 390 843
35
15.20030 68666
158 601 345 [7]
(15) 630 511 676
36
15.63460 13485
43^ 123 155 [7]
(15) 231 952 283
37
16.06889 58304
117 191 424 [8]
(16) 853 304 763
38
16.50319 03123
3i8 559 3i8 [8]
(16) 313 913 279
39
16.93748 47942
865 934 004 [8]
(16) 115 482 242
40
17.37177 92761
235 385 267 f9]
(17) 424 835 426
41
17.80607 37S8o
639 843 494 [9]
(17) 156 288 219
42
18.2403(1 82399
173 927 493 [10]
(18) 574 952 226
43
18.67466 27218
472 783 947 [10]
(18) 211 513 104
-14
19.10895 72037
128 516 ooi [n]
(19) 778 113 22.L
45
19-54325 16856
349 342 711 [n]
(19) 286 251 858
. tf
J9. 9775-1 fiiftfS
9.(9 6n 942 [n]
(19) 105 306 174
47
20.41184 06495
258 131 289 [12]
(20) 387 399 7*53
48
20.84613 51314
701 673 59' [13]
(20) 142 516 408
49
21.280.12 96133
190 734 657 [T3l
(21) 524 288 S<S6
SO
21.71472 40952
5i8 470 553 [13]
(21) 192 874 98S
The numbers in square brackets denote the numbers of figures between the
last figure given and the decimal point; for example, the first nine figures of e
are $18470^3, and there arc 13 additional figures before the decimal point is
reached. The numbers in parentheses denote the numbers of ciphers between
Hie decimal point and the first significant figure; for example, m e there are
21 ciphers between the decimal point and the figures 192874985.
SMITHSONIAN TABLES
259
The Exponential.
It
lOQinfe")
e"
O-u
51
52
53
54
55
56
57
58
59
60
22.14901 85/71
22.58331 30590
23.01760 75409
23.45190 20228
23.88619 65047
24.32049 09866
24.75478 54685
25.18907 99504
25-62337 44323
26.05766 89142
140 934 COS [14]
383 100 800 [14]
104 137 594 [15]
283 075 330 [I5J
769 478 5-7 [I5J
209 165 950 -[10]
568 572 ooo [16]
154 553 894 d7]
420 121 040 [17]
114 200 739 [tSJ
(22) 709 547 4i6
(22) 26l 027 907
(23) 960 268 005
(23) 353 262 857
(23) 129 958 143
(24) 47H 089 288
(24) 175 879 220
(25) 647 023 493
(25) 238 026 641
(26) 875 651 076
61
62
26.49196 3396i
26.92625 78780
310 429 794 [18]
843 835 667 [18]
(26) 322 134 029
(26) 118 506486
63
64
27-36055 23599
27.70484 68418
229 378 316 [19]
623 514 908 [19]
(27) 435 96r ooo
(27) 160 381 089
65
28.22914 13237
169 488 924 [20]
(28) 590 009 054
66
28.66343 58056
460 718 663 [20]
(28) 217 052 201
67
29.09773 02875
125 236 317 [21]
(29) 798 490 425
68
29.53202 47694
340 427 605 [21]
(29) 203 7482H
69
29.96631 92513
925 378 173 [21]
(29) 108 063 928
70
30.40061 37332
30.83490 82151
251 543 867 [22]
683 767 123 [22]
(30) 397 544 974
(30) 146 248 023
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
O I U-T-- * 1 -r
32.13779 16508
137 338 298 [24]
(32) 728 129 018
75
32.57208 61427
373 324 200 [24]
(32) 267 863 696
76
33.00638 06246
101 480 039 [25]
(33) 985 415 469
77
33.44067 51066
275 851 345 [25]
(33) 362 514 092
78
33.87496 95885
749 841 700 [25]
(33) 133 3^r 482
79
34.30926 40704
203 828 107 [26]
(34) 490 609 47.3
So
34-74355 85523
554 062 238 [26]
(34) 180 485 139
Si
35.17785 30342
150 6o> 731 [27]
(35) 663 967 720
82
35.61214 75161
409 399 6t>T> [27]
(35) 244 260 074.
83
36.04644 19580
Hi 286 375 [28]
(36) 898 582 594-
84
36.48073 64799
302 507 732 [28]
(36) 330 570 oT>3
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) ">4 58r 143
88
38.21791 44075
165 163 625 [30]
(38) 605 460 190
89
38.65220 88894
448 961 282 [30]
(38) 222 736 356"
90
39.08650 33713
122 040 32() [31]
(39) 819 401 262
39-52079 78532
331 740 oio [31]
(39) 301 440 879
92
39.95509 23351
901 762 841 [31]
(39) no 893 (_X>2
93
40.38938 68170
245 124 554 [32]
(40) 407 955 867
94
40.82368 12989
666 317 622 f32]
(40) 150 078 576
95
41.25797 57808 .
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 TQ7 234
98
42.56085 92265
3<i3 797 095 [34]
(42) 274 878 501
99
42.99515 37084
088 303 032 [34]
(42) 101 122 140
100
43.4294481903
268 811 714 E35]
(43) 372 007 598
The numbers in square brackets denote the numbers of figures between the
last figure given and the decimal point; for example, the first nine figures of c w
are 5 I 847553, 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 c~ M there arc
21 ciphers between the decimal point and the figures 192874985.
SMITHSONIAN TABLES
260
AuxlHnry Table for Interpolation of Logio(e).
(p MI x ,u.|u(j 44819 . . .)
n
n
i.
11
11
li
n
it
n
t)
0,000
ooo
O.0.5O
2171
O.TOO
434.1
0.150
6514
O.2()O
8686
.(IOI
043
.051
2215
, IOI
-1380
.151
6558
,201
8729
.0(12
OH?
2258
. EO2
4-130
- 15-'
(JO/H
.202
8773
.(H),(
130
053
2302
. 10.1
1-17.1
5.1
fl()i| 5
.20,1
88 to
.(Kl|
174
.054
23-15
. 10,1
45I/
.154
fifiBS
.204
88(io
O.OOJj
217
O.Oitf
2189
0.105
45fio
0.155
67,12
O.205
890.1
2()l
.oii'i
-M.p
,10(1
4(10.1
. 15**
('775
.200
894C)
.007
3"4
.o'^y
-'IW
.107
I'M 7
- '57
(18 iH
.20?
8<)(jt)
.008
347
.05K
4690
. I'S^
(i8Ci2
,208
0(133
,O(K>
391
.059
2562
. 109
1731
. 159
6905
.209
977
O.OIO
1,1-1
o.ofio
i'6o(i
O.IIO
4777
o.ifio
6940
0.210
9120
.01 1
478
.OiH
.HMO
.III
4821
.161
6992
,211
9164
.(II J
,ofi.i
-!(^),l
,112
4804
.162
7036
.212
(J2O?
.01.1
Vl 1 !
,0(1.1
2X,"i<J
.113
4<1OS
- 1<>3
7070
.21.1
9250
,014
(Kl8
.oo.|
^77<J
.114
4051
. id)
7122
.214
02(M
0,015
.01(1
651
.(Mi6
1-83.1
. 1 1 5
, lih
>KM
50,58
o. 1*15
7166
7200
0.215
9337
938l
.017
7.18
,o(i7
20 HI
.117
5081
. 167
7253
.317
9.(24
.oiH
?Ha
.ooK
')53
.llH
512S
- "! 8
720t)
,2lK
y.'lo'S
.019
825
.ortO
2997
no
5I(>8
.169
7310
.279
95TI
0.0:10
86V)
0.070
3"40
O.I20
5312
o. 170
733
0.220
9554
,<).!!
01 J
.071
,'t* 183
. 121
5~55
.171
74"''
.221
osyH
'(,,.,;
.07.!
3127
.I2J
521 j8
. 172
747"
,222
1/M r
.024
104-1
.07.1
.07-1
3"70
.13.1
5.1-12
5385
.173
.174
75"3
7S57
:S!
9728
0,025
.02(1
.027
11 .JO
0.075
.077
3357
\\ay
.128
54X-1
553!*
0.175
. 17(1
.177
7(^7
7730
0.225
'.228
9773
9815
9858
!oju
1J.W
.079
3-1 3 J
.139
5603
.179
7774
.229
0945
o.o.to
1303
;[*f;
3-174
o. 130
.131
Sfufi
o.rHo
.181
7817
7861
0.230
9989
.0,12
1300
.OJJ2
35''"
'r!i
573.1
!i8l
79^
.233
toil!)
.O.J.]
M77
,oH,]
^('K
. 134
5820
!i4
7091
101 0'l!
0.035-
.037
-o.lK
.039
I 5 ( >3
liiox
|6<M
. ( h^( )
37.15
0. 1.15
M< ]
.137
5861
5*J<)'-
5<j,i;o
5W, 1
('037
o. 183
80,1*1
8078
8ui
8ifis
8208
0.333
.237
.2,18
.239
10293
10336
10380
0,040
17.17
O.CKJO
AW)
0.140
r^fe
O.IOO
8252
0.2,10
10423
IO;l(iO
(till
,0.|J
0|.l
is
y '
-loil'J
.143
6210
(125.
. HJ2
.191
8338
8382
. 2,|'|
10510
10553
10507
0.045
1954
0.09.1
4I2C
0. 1.15
6297
O.IOE
8469
:l'
10640
.047
,o.|H
soil.' 1
diatt
oyy
4300
]i47
638.
6428
<M7
.195
'i99
Sfiffl
8642
*w
!a(9
10727
1077 ^
10814
o.osc
2I7 r
O.IOO
43-13
O.tfiO
^
0,200
8C8T
0.250
J^-
11
P
n
it
n
n
n
P
n
V
TABUKB
Auxiliary Table for Interpolation of Logio(e").
(p = n X 43429 44819 . . .)
n
P
n
P
n
P
n
P
n
P
0.25
10857
0-300
13029
0.350
15200
0.400
17372
0.450
I9S43
-25
10901
-30
13072
-35
IS244
.40
174'S
45
19587
25;
10944
30
13116
352
15287
.402
17459
452
19630
25
10988
30
13159
353
I533I
.403
17502
453
19674
254
11031
.30
13203
-354
15374
-40-
17545
-45;
19717
0.25
II075
0.30
13246
0.355
I54I7
0.405
17589
0.455
19760
-256
irnS
.306
13289
.356
15461
.406
17632
-45f
19804
.257
11161
307
13333
357
15504
.407
17676
457
19847
.258
IT205
308
13376
.358
f=548
.408
17719
458
10891
.259
11248
309
13420
.359
I559I
.409
17763 1 -450
19934
0.260
11292
0.310
13463
0.360
15635
0.410
17806 | 0.460
19978
.261
"335
3H
13507
.361
15678
.4U
17850
.461
2O02I
.262
1 1 379
312
13550
.362
15721
.412
17893
.462
20064
.263
11422
-313
13593
363
r-5765
413
17936
.46,3
20108
.26.
11465
314
13637
.364
15808
.414
17980
.464
20I5I
0.265
11509
0.315
13680
0.365
15852
0.415
18023
0.465
20195
.266
II552
-316
13724
.366
15895
.416
18067
.466
20238
.267
11596
.317
13767
.367
15939
.417
18110
.467
20282
.268
11639
.318
13811
.368
15982
.418
18154
.468
2O325
.269
11683
.319
13854
-369
16025
.419
18197
.469
20368
0.270
11726
O.320
13897
0.370
16069
0.420
18240
0.470
2O4T2
.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
IIOOO
.324
14071
374
16243
.424
18414
.474
20586
0.275
.276
1 1943
11987
0.325
.326
I4II5
14158
0.375
.376
16286
16320
0.425
.426
18458
18501
0-475
476
20629
20672
.277
12030
.327
14201
377
16373
-427
18544
477
20716
.278
12073
.328
14245
.378
16416
.428
18588
.478
20759
279
12117
.329
14288
379
16460
.429
18631
.479
2O803
0.280
12160
0.330
T4332
0.380
16503
0.430
18675
0.480
20846
.281
fi
12204
331
14375
.381
16547
431
18718
.481
20S(jO
.282
-283
12247
12291
332
-333
14419
14462
382
.383
16590
16633
-432
433
18762
18805
.482
.483
201)33
20976
.284
12334
-334
14505
.384
16677
-434
18848
.484
21O20
0.285
.286
.287
.288
_.o n
12377
12421
12464
12508
0-335
.336
-337
338
14549
M592
14636
14679
0.385
.386
.387
.388
16720
16764
16807
16851
0.435
.436
437
.438
18892
18935
18979
19022
0.485
.486
.487
.488
21063
21107
21150
.289
12551
-339
4723
.389
16894
439
19066
.489
21237
0.290
.291
.292
293
.294
2595
2638
2681
2725
2768
0.340
-341
-342
343
344
4766
4809
4853
4896
4940
0.390
-391
-392
393
394
16937
16981
17024
17068
17111
0.440
.441
.442
443
-444
19109
19152
19196
19239
19283
0.490
491
493
493
-494
21280
21324
21367
21411
21454
0.295
.296
.297
.298
-299
2812
2855
2899
2942
2985
0.345
-346
.347
-348
-349
4983
5027
5070
5"3
5i'57
0-395
.396
397
.398
399
I7I55
17198
17241
17285
17328
0.445
.446
-447
448
.449
9326
9370
9413
9456
950Q
0.495
-496
497
.498
.499
21498
21541
21584
21628
21671
0.300
3029
0.3SO
5200
0,400
17372
0.450
9543
0,500
21715
n
P
n
p
n
p
n
R
n
p
262
TABLE V
NATURAL LOGARITHMS
K." -In Table V, for u greater than 158, linear interpolation of
!() mtlTieert to tfivc u value whose error in not greater than one unit in
the last iilacu.
263
Natural Logarithms.
u
IC DiU
w Fo'
u
,o fle u
O.FO'
u
lOUoll
Ul FO
u
lOQuU
-,rf
o
I
3
4
CO
o.ooooo
0.69315
1.09861
1.38629
w
IOOOOO
50000
33333
25000
50
51
52
53
54
3.91202
3.93:83
3-95124
3.97029
3.98898
2000
196:
1923
l887
:852
100
IOI
102
:o3
104
4.605:7
4.62497
4.63473
4.64439
:ooo
990
980
971
962
ISO
15*
152
:54
5.0IOf):|
5.0172?
5.02388
5- 0304.1
5.03695
667
663
640
5
6
7
S
9
1.60944
1.79176
i -9459 I
2.07944
2.19722
200OO
16667
14286
:25oo
inn
55
56
57
58
59
4.00733
4.02535
4.04305
4.06044
4.07754
1818
1786
1754
1724
:695
:os
106
107
108
109
4.66344
4.67283
4.68213
4.69U5
952
943
935
926
9:7
155.
157
158
5-043.13
5-04986
5.05625
f>45
641
637
621)
10
u
12
2.30259
2.39790
2.4849:
IOOOO
909:
8333
60
6:
62
4.09434
4.1:087
4.12713
1667
1639
:6:3
no
u:
:u
4.70048
4-70953
4.71850
909
90:
893
160
if) i
162
5.07517
5.08140
<)2l
("117
J3
2.56495
2.63906
7692
7M3
63
64
4.14313
4.15888
:587
1562
:i3
114
4.72739
4.73620
885
877
!u4
5.09375
(HO
15
2.70805
6667
65
4-:7439
:538
us
4-74493
870
165
5.10595
606
16
2.77259
6250
66
4.:8o55
1515
116
4-75359
862
if*)
5. moo
(X)3
*7
2.83321
5882
67
4.20469
:493
117
4.76217
855
167
5.ii7cj()
509
18
2.89037
5556
68
4.21951
1471
118
4 . 77068
8-47
ifxH
5. 1 330(1
595
19
2.94444
5263
69
4-234:1
1449
119
4.77912
840
169
S-iayyo
SO*
20
.2.99573
5000
70
4.24850
1429
120
4.78749
833
170
5.13580
588
21
3-04452
4762
71
4.26268
1408
12:
4-79579
826
171
5.l4i(i(i
385
22
3-09:04
4545
72
4.27667
:389
122
4.80402
820
17::
5-147.10
58:
23
3-:3549
4348
73
4.29046
1370
123
4.8:2:8
8:3
173
5-1532P
57
24
3-17805
4:67
74
4.30407
135:
124
4.82028
806
174
5-i5!X)<i
575
2-S
3.21888
4000
75
4.31749
:333
125
4.82831
800
175
5.:f>470
571
26
3-25810
3846
76
4.33073
13:6
126
4-83628
794
17(1
5-17048
Stft
27
3-29584
3704
77
4.3438I
1299
127
4-844:9
787
177
5.17015
565
28
3-33220
3571
78
4-3567I
1282
128
4-85203
78:
178
5.18:78
5<>.i
29
3.36730
3448
79
4-36945
1266
:29
4.8598:
775
170
5.18739
550
30
3.40120
3333
So
4.38203
1250
130
4.86753
769
:8o
5.:o2<X>
55f>
31
3-43399
3226
8:
4-39445
1235
131
4.87520
763
181
5.19850
552
35
3.46574
3:25
82
4.40672
1 220
132
4-88280
758
iH>
5.20401
519
33
3-4965:
3030
83
4.4:884
:205
133
4-80035
753
183
5.20949
546
34
3-52636
2941
84
4.43082
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200
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266
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6.52796
146
73'l
6.59851
136
784
6.66441
128
<M5
6,45362
157
685
6.52942
M6
7.15
6.5(X)87
136
785
6.66568
127
Ot6
0..|5So
157
(>86
6 . 53088
M'i
(U 10123
136
786
6.66(19(1
127
'M7
6..|5''77
'57
687
6.53233
1. 10
737
6.60259
136
787
6. (16823
127
0.45834
"57
688
6-53.V9
MS
7.18
6.6031).!
136
788
6.66950
127
'M9
0.45990
156
Mj
6-53524
MS
739
6.60530
135
789
6.67077
127
0)0
(i.. 16147
156
C>90
6.53669
145
740
6.60665
135
790
6.67203
127
(>,| I
''-I'M03
15(1
69 f
6.53814
'45
6.60800
135
79"
6-67.130
12(1
04.!
0.40459
156
(19J
6.5.1059
45
742
6.609,15
135
792
6,67456
126
643
0.4(161.)
156
('93
6.5,1103
44
74.1
6.61070
MS
793
6.67582
126
<M4
6,46770
155
09.1
6-5.12-17
14
744
6.61204
134
794
6.677-08
126
6-15
6.46025
I5 5
695
6.54301
4-1
745
6.61338
T34
795
6.67834
T26
(146
6,47080
155
O^Xi
6.54535
44
746
6.61473
134
796
6.679(10
(26
o.|7
(1.472,15
155
607
6.54679
13
747
6.61607
134.
797
6.68085
125
^ "173%
1 5-1
698
6.54822
-13
6.61740
134
798
6.68211
125
6-19
6. -175.13
154
6y9
6.541X15
-13
749
6,61874
134
799
6.68336
125
650
6.47697
154
700
6.55108
143
750
6.62007
133
800
6.68461
125
o*
X
r*
flX
x
^H
e*
X
7*"
~
X
^
SMITHBONIAN
Natural LognrithniB.
8oo
Hoi
804
8ns
8oti
807
808
8oy
810
811
8i.i
!:!
815
816
Ht8
8 fo
820
HJI
82(1
827
8.U
8.13
834
35
8,18
840
Ril
8.|2
843
R|6
849
850
.687ir
IfiSyfH
6.60208
6". (J07(>3
6 . 60827
6.6(J050
(i. 70073
6.70106
(i.703'0
fi. 70441
6.70564
6.70686
6.70808
6.700,30
6.71052
6.71174
6.71538
6.7165')
(1.71780
6.7HXM
6,72022
(..72263
(i. 7^3
,72503
6,72743
6.72863
1.721)82
6.73102
(). 73 22 1
('73340
6.73578
ft. 73607
6.73815
rt.73034
6.741)52
6.74288
6.74/106
6.74524
F u '
12.
12;
12'
12.
U.
i.;,
I
123
123
123
121
120
TI!J
ng
ny
no
118
118
118
118
118
118
118
e-x
8.if
85
853
s-
85*
857
Rfio
865
8Wi
800
871
874
75
876
877
880
881
88.!
i'|
885
886
M87
88.4
891
8'J7
XX)
lnu,,u
6.74871
6. 741 jo.
(1.75111
(>. 75,14-
6'. 75 577
''.75^)3
6,76157
6,76504
6.7<i6i()
6.76734
6.76(XJ|
6.77070
6.77104
6,77308
6. 774~'2
''-77537
6.7/051
<i. 777''5
6.77878
6.78uKi
6.78211,)
'7^333
6.78784
(|.?8H(;7
6,7,;{)IO
I-703.I7
' 71)15!)
'. 7')57I
1.80017
'). 80230
u
US
117
M 6
116
i Hi
I Hi
IK)
I Hi
115
115
115
"15
115
"5
115
US
114
114
114
in
015
(Hit
U35
03''
UI4
045
oso
0.8,rim,i
0.8.MII
('.8.1303
6.81055
6.8|^i,S
''.81.175
6.8501,1
.85118
-85330
.85435
-**55.|i
6.85646
u hS
108
loM
H'H
107
107
107
11.7
10')
rtxi
105
105
105
U.'i' 1 * i (i.fii iH'i
O,'iO
I/M)
'Ml
ft.!/'"74
101
1 101
Hll
Mil
Hll
ItMl
HHI
MX)
BMITHBONIAN TAHLEB
268
Natural Logarithms.
u
L o.,u
u
u
u
LDQ^U
u
LOQ C U
u
u,,
IOOO
6.90776
1361
7.21598
3721
7.45066
2iir
7.65492
2503
7.82525
1009
6.91672
1367
7.22037
1723
7.45182
2113
7.65586
2521
7.83241
'.1013
6.92067
1373
7.22475
1733
7.45761
i2I)2O.
7.66341
2531
7.83637
1019
6.92658
1381
7.23056
1741
7.46221
21311
7.66435
2539
7.83953
102 1
6.92854
1399
7.24351
1747
7.46566
2137
7.66716
2543
7.84110
1031
6.93828
1409
7.25064
1753
7.46908
2141
7.66003
2549
7,84.346
1033
6.94022
1423
7.26052
1759
7.47250
2143
7.66096
2551
7.84424
1039
6.94601
1427
7.26333
1777
7.48268
2153
7.67462
2557
7.84659
1049
6.95559
1429
7-26473
1783
7 48605
2161
7.67833
2579
7.85516
1051
6-95750
1433
7.26753
1787
7148829
2170
7.68662
2591
7.85980
1061
6.96697
1439
7.27170
1789
7.48941
2203
7.69758
2593
7.86057
1063
6.96885
1447
7.27725
1801
7.49610
2207
7.69939
2609
7/86672
1069
6.97448
I45i
7.28001
1811
7.50163
2213
7.70310
2617
7.86978
1087
6.99118
1453
7.28139
1823
7-50824
2221
7.70571
2621
7.8713.1
1091
6.99485
1459
7.28551
1831
7.51262
2237
7.71289
2633
7.87588
1093
6.99668
1471
7.29370
1847
7-52132
2239
7.71378
2647
7.88118
1097
7.00033
1481
7.30047
i8Gi
2243
7.71557
2657
7.88495
1103
7.00579
1483
7.30182
18^7
7-53209
2251
7.71913
2659
7.88571
1109
7.01121
1487
7.30452
1871
7 - 53423
2267
7.72621
2663
y.SS^Ji
1117
7.01840
1489
7.30586
1873
7-53530
2269
7.72709
2671
7.89021
1123
7.02376
1493
7.30854
1877
7-53X43
2273
7.72886
2677
7-89245
1129
7.02909
1499
7.31255
1879
7- 53S-!9
228T
7.73237
2683
7.89469
1151
7-04839
1511
7.32053
1889
7.54380
i2287
7.73500
2687
7.89&I8
IIS3
7.05012-
1533
7.32844
1901
7-55014
2293
7.73762
2689
7.89692
1163
7.05876
1531
7.33368
,1907
7.55329
2297 ,
7.73936
2693
7.898-11
1171
7.06561
1543
7.34148
1913
7.55643
2309
7.74457
2609
7.90064
1181
7.074"
1549
7.34536
103 1
7.56579
23n
7-74544
2707
7.90360
1187
7.07918
1553
7.34794
1933
7.56683
2333
7-75491
2711
7.90507
"93
7-08423
1559
7.35180
1949
7-57507
2339
7-75748
27:3
7-90581
120 1
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
7.9*1:69
1217
7.10414
1579
7.36455
1979
7 59035
2351
7.76260
2731
7.91242
1223
7.10906
1583
7.36708
1987
7.59438
2357
7.76514
2741
7.91608
1229
7.11306
1507
7.37588
1993
7-597-IO
2371
7.77107
2749
7.91890
1231
7- "558
1601.
7.37838
1997
7.59940
2377
7-77359
2753
7.92045
1237
7.12044
1607
7.^8212
1999
7.60040
2381
7.77528
2767
7.92552
1249
7.13010
1609
7.38337
2003
7.60240
2383
7.77612-
(2777
7.02913
T259
7-13807
1613
7.38585
201 1
7.60639
2389
7.7/863
2789
7-93344
1277
7-15227
1619
7.38956
2017
7-60937
2393
7.78030
2791
7.93416
1279
7.I53S3
1621
7.39080
2O27
7.6:431
2399
7.78281
2797
7.93630
1283
7.15696
1627
7-39449
2O29
7.6iS30
2411
7.78780
2801
7-93773
1289
7.16162
1637
7.40062
2039
7.62021
2417
7.79028
2803
7.93845
1291
7-16317
1657
7.41276
2053
7.62706"
2423
7.79276
2819
7.944:4
1297
7.16781
.1663
7.41638
2063
7.63192
2437
7-79852
2833
7.94909
1301
7.17089
1667
7.41878
2069
7.63482
2441
7.80016
2837
7.95050
1303
7.17242
1669
7.41998
2081
7.64060
2447
7.80262
2843
7.95262
1307
7-17549
1693
7.43426
2083
7.64156
2459
7.80751
2851
7.95543
7. .18463
1697
7.43662
2067
7.64348
2467
7.81076
2857
7-95753
1321
1327
7.18614
7,19068
1699
1709,
7.43780
7,441366
2089
2099
7-64444
7.64922-
12473
2477
7-SI339
7.81480
2861
2879
7-95893
7.96520
6*
X
6*
X
6*
X
e*
X
a*
X
SMITHSONIAN TABLES
269
Natural Logarithms.
u
LdOeU
u
LoOeU
u
LoQeLI
U
LOQ B U
11
Lofloii
2887
2897
7.96797
7-97143
3323
3329
8.10862
8.1104;
3709
3719
8.21852
8.2212
4:129
4133
8.32579
8. -32676
456l
4567
8.42530
8.42661
2503
7-97350
3331
8. i no;
3727
8.22336
4139
8.3283
4583
8.43011
2909
7-97S56
3343
8.11462
3733
8.22497
41-33
8.3-3159
4591
8.43185
2917
7.9/831
3347
8.11582
3739
8.22657
4157
8.33255
45Q7
8.43316
2927
7.98173
3359
8.11940
3761
8.23244
4159
8.33303
4603
3.43446
2959
7.98582
336r
S. 11999
3767
8.23403
4177
8.33735
4621
8.43837
2953
7.99058
3371
8. 12296
3769
8.23456
4201
8.34308
4637
8.44182
2957
7.99193
3373
8.12356
3779
8.23721
421 r
8.34546
4<J39
8.44225
2963
7-99396
3389
S. 12829
3793
8.24091
4217
8.34688
4643
8-44312
2969
7.9959S
3391
8.12888
3797
8.24197
41219
8-34735
4649
8.44441
2971
7.99665
3407
8.13359
3803
8.24355
4229
8.34972
4651
8.44484
2999
8.00603
3*13
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
8.01003.
3449
8. 14584
3833
8.25iI40
4243
S.35803
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
8.4650
3041
8.01994
3467
8.15104
3863
8.2592O
4271
8.35960
4721
8.45978
3049
8.02257
3469
8.15162
3777
8.26282
4*73
8,36007
4723
8.46020
3061
8.02650
3491
8. 15794
388r
8.26385
4283
8.36241
4729
8.46147
3067
8.02846
3499
8. 16023
3889
8.26591
4289
8.36381
4733
8.46231
30/9
8.03236
3511
8. 16366
3907
8.27053
4297
8.36567
4751
8.46611
3083
8.03366
3517
8. 16536
39"
S.27I55
4327
8.37263
4759
8.46779
3089
8.03560
3527
8.16820
3917
8.27308
4337
8.37494
4783
8.47282
3109
8.04206
3529
8.16877
3919
8.27339
4339
S.37540
478?
8.47366
3P
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
3931
8.27665
4363
8.38092
4790
8.47616
3163
8.05928
3547
8. 17386
3943
8.27970
4373
8.38320
4801
8.47658
3167
8.06054
3557
8.117667
3947
S.2807II
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
3.i8o6o
3989
8.29I3O
4409
3.39140
4831
8.48281
3187
8.06684
358r
8.18340
4001
8.29430
4421
8,39412
4861
8.48900
3191
8.06809
3583
8. 18396
4003
8.29480
4423
8.39457
47i
8.49105
3203
8.07184
3593
8.18674
4007
8.29580
4441
8.39863
4877
8,49229
3209
8.07371
3607
3. 19063
4013
8.29729
4447
8.30998
4889
8.49474
3217
8.07620
3613
3. 19229
4019
8.29879
4451
8.40088
4903
8.49760
3221
8.07745
3617
8. 19340
4021
8.29929
4457
3.40223'
490(3
8.49883
3229
8-07993
3623
8. 19506
4027
8.30078
4463
8.40358
4919
8.50086
3251
3253
3257
3259
3271
8.08672
8.08733
8.08856
S.oSgrS
8.09285
3631
3637
3643
3659
3671
8.19726
j. 19891
5. 20056
8.20495
8.20822
4049
4051
4057
4073
4079
8.30623
8.30672
8.30820
8.3II2H4
8.31361
4481
4483
4493
4507
4513
3.40760
3.40805
3.41028
8.4U39
8.41472
493't
4933
4937
4943
4951
8.50330
8.50370
8.50451
8.50573
8.50734
3299
3301
3307
33U
3319
8. 10137
8.10198
8.10380
8.10561
8,10742
3673
3677
3691
3697
3701
8.20876
8,20585
8.21365
J.2I528
8.21636
4091
4093
4099
4111
4127
S.3I654
8.31703
8.31850
3.32142
8.3253'I
4517
4519
4523
4547
4549
5.41560
4.41605
8.41693
i. 42222
8,42266
4957
4967
4969-
4973
4987
8.50856
8.51057
8.51097
8.5II7
8.5I4S9
a*
X
e*
X
e*
X
e*
X
B*
X
270
Natural Logarithms.
u
U,, u
a
L*.
u
LK-
u
u.
u
U De u
4993
4999
5003
SOQO.
SOU
8.51579
8.51639
8.51779
8.51899
8.51939
5437
54-13
5449
5471
8.60098
8.60172
8.60209
8.60319
8,60722
3849
5851
5857
5861
5867
8.67403
8.67437
8-67539
S.67608
S.677IO
6287
6299
6301
63 1' I
6317
8.746241
8.74SI5
8.74846
8.75005
8.75100
6733
6737
6761
6763
6779
8.81478
8.SI537
8.31893
8.81922
8.82158
'5021
5023
5039
5051
5059
8.52138
8.52178
8.52496
8.52734
8.52892
5477
5479
5483
5501
9503
8.6083,1
6.60S6S
8.6CK>4I
8.61269
8.61305
5869
5879
5897
5503
8.67744
8.67914
8.67948
8.68220
8.68322
63-23
6329
6337
6343
6353
8.75195
8.75200
8.75416
8.75511
8.7566S
6781
6791
6793
6803
6823
8.82188
8.82335
8.82365
8. 825:2
8.82805
5077
5081
8.53248
8.53326
5507
5519
8.61378
8.61595
5923
5927
S.6S660
8.6S727
6359
6361
8.75763
S-75794
6827
6829
8.82864
8..82S93
5087
5099
5101
8.53444
8.53680
8.53719
5521
5527
5531
8.6l63I
8.6I74O
S.6l8l2
5939
'5953
59811
8,68930
S.69I65
8.69634
6367
6373
6379
8,75S88
8.75983
8.76077
6833
6841
6857
8.82952
8.83069
8.83303
5107
5H3
5147
5153
8.53837
8.53954
8.54071
8.54617
8-54733
5557
5563
5569
5573
S58l
8.62281
8.62389
8.62497
8,62569
8.627(12
5987
6007
6oir
6029
6037
8.09735
8.70068
8.70E35
8.70434
8.70566
6389
6397
6421
6427
6449
8.76233
8.76358
8.76733
8.76826
S.77I68
6863
6869
6871
6883
6889
8.83300
8.83477
8.83506
8.83681
8.83768
5171
5179
5189
5197
8.55005
8.55082
8.55237
8.55430
8.55584
5591
5623
5639
5641
5647
8.62891
6.63462
8.63746
8.63782
8.63888
6043
6047
6053
6067
6073
8.70666
8.70732
8.70831
8.71062
8.71161
6451
6469
6473
6481
6491
8.77199
8.77478
S. 77539
8.77663
8.77817
6907
6911
6917
6947
6949
8.84029
8.84087
8.84174
8.84607
8.84635
5209
5227
5231
5'233
5237
8.55814
8.56159
8.56236
8.56274
8.56350
5651
5653
5657
5659
5669
8.63959
8.63994
8.64065
S.64IOO
8.64/277
6079
6089
6091
6101
6113
8.71260
8.71424
8.71457
8.71621
8.71817
6521
6529
6547
655 r
6553
8.78278
8.78401
8.78676
8.78737
8.78768
6959
6961
6967
6971
6977
8.84779
8.84808
8.84894
8,84951
8,85037
5273
5279
5281
8.56808
8-57035
8.57149
8.57187
5683
5689
5701
8.64523
8.64629
8.64699
8.64840
6121
6131
6i33
6i43
8.71948
8.72111
8.72144
8 . 72307
6563
6569
657i
6577
S. 78920
8.79012
8.70042
8.79133
6983
6991
6997
7001
8.85123
8.85238
8.85324
8.85381
-5297
8.57490
5711
8.6SOI5
6151
8.72437
6581
8.79194
7013
8.85552
5303
5309
8.57603
8.577'i6
5717
5737
8.65120
8.65469
6163
6173
8. 72632
8.72794
6599
6607
8.79467
8.79588
7019
7027
8.85638
8.85752
5323
5333
5347
8.57979
8.58167
8.58429
5741
5743
5749
8.65539
8.65-574
8.65678
6197
61190
6203
8.73182
8.73214
8.73279
6619
6637
6653
8.79770
8.80042
8.80282
7039
7043
7057
8.85922
8.85079
8.86178
5351
538i
8.58504
8.59063
577P
5783
8.66ro9
8.66268
6211
6217
8.73408
8.73504
6659
6661
8.80372
8.80402
7069
7079
8,86347
8.86489
5387
5393
5399
8.59174
8.59286
8.59397
5791
5801
5807
8.66406
8.66579
8.66682
6221
6229
6247
8.73569
8.73697
S.739S6
6673
6679
6689
8.80582
8.80672
8.80822
7103
7109
7121
8.86827
8.86012
8.87080
5407
5413
8,59545
8.59656
5813
5821
8,66785
8.66923
6257'
6263
8. 74146
8,74241
6691
6701
8.80852
8.81001
7127
7129
8.87165
8.87193
5417
5419
5421
8.59730
8.59767
8.59988
5827
5839
5843
8.67026
'8.67231
8.67300
6269
6271
6277
8.7-1337
8. 74369
8.74465
6703
6700
671.9
8.81031
8.81121
8.81269
7159
7177
8.87501
8.87613
8.87864
e*
X
flX
X
e*
y.
0*
X
*
X
SMITHSONIAN TABLES
271
Natural
7187
7 MM
7JU7
7JH
7^10
7-uo
7-M7
T-.M.I
7-M7
,
7^3
?.*ff
7307
733"
7.1 1<>
7351
7.1' W
7.| u
7.P7
7-157
7-150
71 77
7-|8i
7 ,|87
7-100
7507
751?
753,1
75-iO
7537
75-U
73-17
75-10
7550
7561
7573
757/
75*
7501
7(10;
S. 8828 i
\.$A$.i
i.8!<i 17
S.KHoi?
8. 80850
H.I 1050/1
H.(joH^)
8.0107.!
8-01153
H.oin'io
8.
K.
8,
8.0.H-K)
M.()Ji!.<iii
8.<M3.'iO
7717
7741'
77-1 1
775.1
7757
7750
7780
7703
7817
7873
70'0
7033
7037
705,1
71 A1
KIH?
HtMO
Hi I'M)
8087
8. 01 155
8,i7'M3
8.1)?] H)
8.WS/8
Kim
8111
8 1.|7
Midi
8170
8101
8.1H
8.U)
8^77
Rl'nJ
131
8501
KSi.1
85^1
8530
8S-I3
St>3
0"
LOU.II
0. 0-1.10.
Vl.0170
857.1
K/l'
8/53
8/ut
878,1
KKtg
KS.il
8M 1 1
1 , 1 K -
IJCHI/
i)cHI
t ,0 )1 J
tft;',<l
If II I/
'IHM
'(I'M)
UK/ 1 *
O--'"'
U-f-M
0,U' )
M;-I
o.ti'/
03') i
<t. 1 ll^'l'l
i. i l'X'5
J- 1
y. 151 7
flMITKBONIAN TAD UK
273
Natural Logarithms*
11
Lou ill
u
L*.
u
Loo u ll
II
LOU, u
LI
La GO u
(
o.i.'iio? 1
<1l
I). I('i,-l.|0
o/M)
iMRUtt
0833
y. rosso
0067
y, 20703
OI37
0. ,'i-MO
!>!i^7
y. KJSU't
07'- 1 ' 1
y.iW^M.
083!)
y.iy.|ii
0973
(J . 20764
Ol.iO
0. 1 1201
()'xU
u. i<itx>-i
0733
(>. 18328
1)851
y. 10533
IWXK)
y. '2 1 034
0|<>!
O. l,'i,|0,(
(X'n.j
i). ix<^7
073O
c>.lK;iH<)
!>^57
<J. i)504
100OOO
11.51293
II I'M
y.iSSM
tXiiy
y. I7iso
97.13
y,i8,|3O
08.VJ
y.iyCJi4
0,107
'M5.S57
(j(i.).l
0. IX'Ot
!*? I 1 .*
(>.iK.iy2
0871
o. 10736
047,1
o.i, "id.ro
^X'.!|J
<)- 17~53
0707
y. 18076
0883
y- 10857
l/<)
I). i;;dS;i
( Xi,ii
i). 17-7-1
MX'kj
t>. i8f.)7
<jH8?
y. Mj8<>S
Ol'H
o . i Ji8 i ( )
(X> |3
0. IX.VJ<)
^7^^
y. iftS:!(>
OfJ< JI
. (),2<X)3<)
0107
0- ISM/3
(/.. .)
y.i74*
97^7
y, iMWii
00"7
y.aoioo
US n
o.Kkwo
(jttii
o. C7.HH5
()7<ji
y.iHi).!.!
0923
(>.a02fii
O.S.-'l
'). I0l,!fi
1X177
0.17751
ijHo.1
<), njo.i'l
OEV9
y. 203 22
0533
0. l<Mf)I
( X'XO
o. EX77I
OHll
ij, iiji^Ci
OU3'
9.^0342
oiuo
0- 'O,U'|
(((KM*)
0, 17^75
13817
y, it)iKx
W'I'I
o.;r()442
O.TlX
y, l(i;)i>S
(XHJ7
!).i?P57
yR2o
0. 103"0
OP'IO
9.20523
0*
X
.
X
X
c*
X
O x
X
Coefficients for Computing,
-in [ u-~ %
-V- ( ll ' J -iV n l
6 ^ ia \ a / J'
n
tl
Dill.
\?\z "v
DHL
n
11
mil.
ii^)
Pill.
0.00
.01
| o.iKNK)
O
O.fHK'in
.unoM
K
H..15
t-O.OKM
OH3
o
O.0202
,02oy
r
1
it
'oj
MMHU
1
.IHH7
.(HIJ5
K
-7
0131
y
.032.-
S
.())
.01103
1
1
.00,1,1
.*>
.0140
10
.0232
7
O,U;i
I U.IKHM
.nuoC)
i!
.0050
R
u
:j;
.0100
JO
1 1
"";S3i
7
7
.OX
.08
.IK)
.IKHlM
?,
. 1 II J."iH
,0o(fi
.0075
o
S
.32
.3'
.0171
.0182
1 1
u
11
,02(17
7
7
7
0. U)
)(). 01117
o.onH.i
H
0.35
. |0.020.|
12
--0.0274
,()28E
7
. i.!
.IK1.K)
'.IMLtS
1
1
,01117
8
H
.37
..!
Si
12
13
.027
6
B
oi l(i
V
'!')
tO2 l J4
**
.03OO
. I'l
1M 33
f>
'
8
''
'3
o.i.S
Hi.wvtH
c
o.ol.il
R
0,411
-1-0.02(17
13
0.030?
6
.Hi
.17
J
-fHl-M
4f
s
fi
. 1 1 1 3 J
,UI,|O
.0155
R
8
7
K
-13
..11
.0323
IS
!S
.0319
.0325
.0331
6
6
ft
O..!0
i- : ;;^
"
.0171
K
8
o..ir.
[-0,0338
.035.-1
15
TS
-0.0337
."343
5
:;;;!
,0()8l
H
.OI7IJ
R
7
47
.48
"10
ilxki
,0.|00
1 6
irt
.0350
6
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,<HM.J(
H
'
8
i/
|-0. 010.1
'-0.0202
0.50
-1-0.0417
0.0365
WMITHSONIAH TABUC8
273
TABLE VI
THE GUDERMANNIAN
275
The Gudernwrmlnn,
o.oa
,00
.(X),
0.005
.oof
.00.
.cxxS
.fxx
O.OIO
.01
.01;
.013
0.015
.OK
.017
.018
.Oig
O.020
,0.31
.02;
.02,"
,02i\
O.OiJS
,Q2(
.027
.O2()
O.O30
.O3I
-033
.033
.O3.|
0.035
,036
037
-03
039
0.0. |0
.041
.042
-0-13
049
0,050
O.OOO (KXX
.OOI IX)O
.002 (KXX
,(X)3 (HO
.Ott| (XXX.
0.005 oooo
,CX)(j (XX J(
.O<l6 WM
,007 (j(X)<
.008 yu<)<
O.OOtJ
.010
on w<>;
.012 <XJ<)<
013 $j()i
015 yyw
.Olfi <J<XJ2
017 1
o.oip,
.022 cjyHo
0^3 W77
.(US o)7i
.032 (J0.|0
'"33 yy3fl
0.034 oy-y
.035 JJIJ23
O.lfi <Jf)l6
03** uyoi
1.030 0^03
o.[b 0885
.041
.043 <>S5K
.04-1 9&|8
(MS
.O.|7 (jSifi
,0/|S 980.1
.049 0792
u 2tun-'(6tt)"
wFo
r o
E (HKX
r OOH
I CXXH
I OOCX
I CHXX
I OfXX
I OfflX
T (XKK
OfXJ!
ixjys
WW-I
*jj
ijyiw
BGCll U
CXt 00.
o 03 -rit..r(
o (Ki 5. 5.
o 10 iH
o 17 11.3-
o wi 37. Sf
:\.\ 03. H
(l 117 30. n
30 fa. 3'
3.| J.!.(il
o 37 .|H.7
o ,|i i-i.
o .|4 -|i.37
o 48 07.'']
o 51 33 -Wj
o 55 rt>.n
5H ;.'(. 3.1
1 01 SJ.S7
1 OR .13, It.!
1 ! J 1 i..',|
I 15 3X.4<t
I M) "3.07
i i 1 .'; .i^.oS
ii f X" ) 1 7 /' )
2 "3 '13. !M
y 07 10. mi
;; in 3(1. iN
U 1. 1 OJ.Ji.J
;i 17 ^'H.,io
a a) 5,|.,iu
a 3-1 ;tH.;'!J
.3 3H IK|.R|
a .u 30. Hrt
a .14 sfi.oi
-|9.05
:<)(..
r(ii). M>
,'nCi. iH
..17
n/t. 17
i.rtt
0(1.117
'fyi.ofi
^i.ii.i
'CXi.Oi!
a BO Pi u
, (X !-
I.H.MU
>.fttjfl
gil ii
,>. h ll tjKfcS,) .
,tt!i,* ift [ij
(111 tl
,1 l,! ,r,|.Uv
.1 l.'i H'i.73
.1 MI Id.frf.
4 ,;i 01 ,trfi
4 -7 .'i-.'.,!?
I .(I lH,(i<i
I ! .11 l.l- (l "
>i .1*1 I I . r! I
"*!! -1 M M- II
rX'-'i .( 5 .|-'..|i
fl *'N .'.l-.V
Ji ( ,'iH.H,:
,'i u P '|. ,i,fi
;; ij* 4 ( '.*vi
!i 1*1 l.'i .<M
*fi:'.\ I S 4-J .(t,(
WM
-!";>. 4 ( '|
JiiS-lX
305.3*1
SMITHSONIAN
The Gudermannian.
II
ad u
-V
ail n
K.FO'
II
H<l U
.W
0(1 II
01 Fo'
O. IOO
<>.<>99 8337
9950
n i it
5 43 "2.19
205.24
0.150
0.149 4406
9889
1 II
8 33 44-35
203.97
. lot
, ](xi 8287
9949
5 46 37-42
205.22
-15'
.ISO 4294
0887
8 37 08,30
203.94
. 102
, KM 8,!3<i
9<)48
5 50 02.02
205 . 20
.152
.151 4l8l
9886
8 40 32.22
203.90
103
.102 8184
9947
5 53 27.81
205.18
T53
.152 4065
9884
8 43 56-11
203.87
. 104
.103 8130
994 <>
5 56 5-J.97
205.15
-154
153 3949
9883
8 47 19-06
203. 84
0.105
0.104 8076
9945
600 18.12
"'05.13
0-155
0.154 3831
9881
8 50 43-79
203.81
.106
.105 8o.n
W44
6 03 43.24
205 . 1 1
.156
155 37"
9880
8 54 07-59
203.78
. 107
.10(1 7064
9943
(i 07 08.34
205.00
.157
156 3500
9878
8 57 31-35
203-75
.108
.107 7007
0<>42
6 10 33,42
-'05.07
.158
157 3-lf>7
0876
9 oo 55.08
203.72
.io<)
.108 78,18
9D.ll
6 13 58.48
-'05.05
.159
158 3343
9875
9 04 18.78
203.68
o. no
0. 109 778H
9940
6 17 23.51
205.02
0.160
0.159 3217
9873
9 07 42.45
203.65
. i n
.11(1 7728
9939
6 20 48.52
205.00
.Kir
. 1 60 3089
9872
9 II 06.09
203.62
.11.!
,ni 7d<)(>
9038
6 24 13.51
204,98
.162
.161 2960
9870
9 14 29.69
203-59
.113
, 1 1.! 7603
99.V>
ft 27 38.48
204,95
. 103
. 162 2830
9869
9 17 53.26
203.55
.114
- 1 "3 753U
9935
6 3' 03.42
204 .93
. 164
.163 2697
9867
9 21 16.80
203.52
O.ITS
0.114 7474
9934
6 34 28.34
204.91
0.165
0.164 2^64.
9865
9 24 40.31
203.49
.11(1
.115 7407
9933
6 37 53-24
204.88
.166
. 165 2428
0864
9 28 03.78
203.46
.117
,116 7340
9932
(i .|I l8.1I
^04,86
.167
. 166 2291
9862
9 31 27.22
203.42
.118
.117 7^71
9931
6 44. 42.96
204.84
.168
, 167 2153
9861
9 34 50.62
203,31?
.119
.118 7201
9930
6 48 07.78
204.81
.169
. 168 2012
9859
9 38 13-99
203-35
0. 120
0.119 7130
0928
ft .Si 32.59
20.1.79
0.170
0.169 1870
9857
9 41 37-33
^03. 32
. 121
.120 7058
9927
6 54 57-30,
204 . 76
.171
.170 1727
9856
9 45 00.63
203.29
. 122
.121 6985.
9026
(i 58 22.11
204,74
. 172
.171 1581
9854
9 48 23.90
203.25
ii!;l
. 122 (kjro
9935
7 or 46. 84
204.71
.173
.172 1434
9852
9 Si 47-14
203.22
.124
.1 -'36834
99~'4
7 05 11-54
204 .69
.174
.173 1286
9851
9 55 10.33
203.18
*
o. 125
0.124 6757
9032
7 08 36.22
204.66
0.175
0.174 1136
98-19
9.58 33-50
203.15
,12(1
. i~*5 6679
O08J
7 12 00.87
204.64
.176
.175 0983
9847
10 01 56.63
203 . I I
.127
, 12(1 6(XX>
<)920
7 15 35.49
204-61
. I?7
. 176 0830
9845
10 05 19.72
203.08
.128
. 127 6519
9010
7 18 50. ex)
204.59
.178
. 177 0674
98:14
10 08 42.78
203.04
.129
.128 6.137
9917
7 22 14.67
204.56.
.179
.178 0517
9842
10 12 05.80
203.00
o. 130
0.129 '">354
9916
7 25 39.22
204-53
0.180
0.179 0358
9840
10 15 28.78
202.97
.131
.130 (i26()
9915
7 29 03-74
204,51
.181
.180 0197
9838
10 18 51.73
202.93
, 131 ("1183
9913
7 32 28.23
204.48
.182
.181 0035
9837
10 22 14.65
202,9O
. 13,1
, 132 6096
0912
7 35 53.70
204.45
-183
.181 9871
935
10 25 37.52
202.86
. 134
. 133 6008
91)11
7 39 17- M
204 -43
.184
.182 9705
9833
10 29 00.36
202.82
0.135
0.134 5018
9910
7 42 41.55
204.40
0.185
0.183 9537
9831
10 32 23.17
202.78
. 1 'l(>
135 3^27
7 46 05.94
204.37
.186
. 184 9367
9829
10 35 45-93
202.75
.137
136 ."1734
9907
7 49 3.i!9
204.34
.187
. 185 9196
9828
10 39 08.66
202.71
.'37 5<'4i
9<xj6
7 52 5.1.62
204-32
.188
. 186 9022
9826
10 42 3T.35
202.67
I J!>
.138 5545
9901
7 56 "18.93
204.29
-189
.187-8847
9824
1045 54-01
202,63
0.140
.141
0.139 '54-I9
.14" 5351
9903
7 59 43-20
8 03 07.45
204,26
204.23
0.190
.191
0.188 8670
. 189 84.92
9822
9820
10 49 16.62
10 52 39-20
203. 60
202.56
yfJOt)
8 oo' 31.66
204 . 20
,'192
.190 8311
9818
10 56 01.74
202.52
. M.I
.142 5151
( vv W)
8 09 55.85
204.17
.193
.IQI 8129
98(7
10 59 24.24
202.48
. 14!
> M3 50-19
9897
8 13 20.01
204.14
. 194
- 192 7944
98iS
II 02 46.71
202.44
o. 145
0,144 4940'
9896
8 if) 44 . 14
204.12
0.195
0.193 7758
9813
11 06 09.13
202.40
-MS '18-1 1
9894
8 20 08,24
204 .oy
,iof>
.194 7570
9811
II 09 31.51
202.37
.147
.149
. 146 -1734
. 147 402(1
.148 4517
9890
8 23 32.31
8 26 56.35
8 30 20.36
204.06
204 .03
204,00
.197
.108
.199
.195 738o
, 196 7188
- 197 699-1
9809
9807
9805
II 12 53.86
n 16 16.17
n 19 38.43
202.33
202.29
202.25
0, ISO
0.149 4406
9889
8 33 '14-35
203.97
0.2OO
o. 198 6798
9803
ii 23 00,66
202.21
u
lurw-j
...*
2lnrr'(a)-90
WHOOllU
U
2, M -.(0.,-1
usaohu
atar-ft-H*
uaeohu
SMITHSONIAN TABUCB
277
The Gudermannian.
u
od u
.*
od u
.
u
gd u
-IV
od u
-w
1 II
II
o / it
ft
0.20C
o. 198 6?of
98o.
ii 23 oo. &
5 2O2. 2
0,251
3 0.247 435*
J 969.
M 10 37. 3t
) 199. <>
,2O
.199 660
980
II 26 22.8
5 202.1;
.25
.248 405"
3 969,
14 13 57 -2(
1 199.9;
.20.
.200 64OI
979
) n 2944.0C
) 202.13
.25,
249 37-1'
969
M 17 17. ^
) 199.8
203
.201 620C
979/
n 33 07. K
) 202. OS
-25.
250 343-
ofifif
M 20 37.0;
199.8-.
.20.
.202 59oC
979:
n 36 29.1;
202. OJ
.254
-251 3-12
968C
14 23 56.81
99-79
0.205
0.203 5790
9794
n 39 Si- 1C
2O2.0I
0.255
0,252 280=
9683
14 27 I6.5C
199,7.
.204 5583
9792
n 43 I3.it:
201.96
.256
253 24&
9681
14 30 36.31
.207
-205 5374
9790
n 46 35-12
201.92
-257
.254 2167
9679
14 33 55-97
I yg. 6.
.208
.206 5162
9788
n 49 57-02
201.88
.258
-255 1845
967f
M 37 15-58
HJ9 . 50
.209
207 4949
9786
n 53 18.89
201.84
-259
-256 1520
9674
14 40 35 -M
199-5.1
0.210
0.208 4733
9783
ii 56 40.71
201.80
0.260
0.257 "92
9671
U 43 54.<>5
199. .j
.211
200 4515
978r
12 00 02.48
201.76
.261
.258 0862
9669
14 47 14-10
.212
.210 4296
9779
12 03 24.22
201.71
.262
259 0530
9666
M 50 33-51
TOO . $
.213
.211 4074
9777
12 06 45-91
201 .67
.263
.260 0195
9664
14 53 52-87
IO') V
.214
.212 3851
9775
12 10 07.56
201 .63
.264
.260 9857
9661
14 57 12. I
199^9
0.215
0.213 3625
9773
12 13 29.17
201 . 59
0.265
0,261 9518
0659
15 00 31-4
199.2,1
.2l6
.217
.218
214 3397
.215 3167
216 2935
9771
9769
9767
12 16 50.74
12 20 12.26
12 23 33.74
201.54
201.50
201.46
.266
. .267
,268
.262 917-;
.263 8830
.264 8483
9656
9654
9651
15 03 50.6;
15 07 09.7
15 10 28.88
ijw.is
199. i.i
199 . 08
219
.217 2701
9765
12 26 SS.lS
201.42
.269
.265 8133
9649
15 13 47-9
199*03
O.22O
.221
0.218 2465
.219 2227
9763
976i
12 30 16.57
12 33 37-92
201.37
201.33
0.270
.271
0.266 7781
. -267 7425
9646
15 17 06.0
15 20 25.86
njR.yR
.222
-223
.220 1986
.221 1744
9759
975
12 36 59-23
12 40 20.49
201,28
201.24
.272
-273
.268 7o58
.269 6708
064
9639
IS 23 44.7
15 27 03.5
I98.*K>
.224
.222 1499
975
>
12 43 41.71
201.20
-274
.270 6345
15 30 23.3
198! J7
0.225
.226
.227
.228
.229
0.223 1252
.224 1003
.225 0752
.226 0499
.227 0243
975
975
974
9746
9743
12 47 02.88
12 50 24.01
12 53 45.10
12 57 06.14
13 oo 27.13
201.15
201. I I
201.06
201.02
200.97
0.275
.276
-277
.278
.279
0.271 5980
,272 5612
.273 5242
.274 4868
275 -1493
963.
063
9628
0626
9623
15 33 41.10
15 3G 59-78
IS 40 18.41
'5 43 36.98
'5 46 55-49
198.71
198.66
198.61
198,35
198.50
0.230
.231
.232
-233
234
0.227 9986
.228 9726
.229 9464
-230 9199
231 8933
9741
9739
9737
9735
9732
13 03 48.08
13 07 08,99
13 10 29.85
13 13 50.66
13 17 11.42
200.93
200.88
200.84
2O0.79
200.74
0.280
.281
.282
.283
.284
0.276 4114
277 3734
-278 3350
.279 2964
-280 2575
9620
yfn8
gfli'S
0612
0610
15 50 13-95
IS 53 32.36
IS 50 50.72
16 oo 09.02
16 03 27.26
198.45
198.3*
itft! a?
198.22
Q.235
-236
237
-238
-239
0.232 8664
-233 8393
.234 8l20
235 7844
.236 7566
9730
9728
9726
9723
9721
13 20 32.15
13 23 52.82
T 3 27 13.45
13 30 34.03
13 33 54-56
200.70
200.65
2O0.60
200.56
200.51
0.285
.286
.287
.288
.289
0.281 2184
.282 1789
283 1393
.284 0993
-285 0591
9607
9604
9602
9590
16 06 45,45,
16 10 03. si
if) 13 21.66
16 16 39.69
16 iy 57.66
198.16
198 . 1 1
98.05
98.00
97-9-1
0.240
.241
.242
243
-244
0.237 7286
.238 7004
239 6719
.240 6432
.241 6143
9719
9716
9714
9712
9710
13 37 15-05
13 40 35-49
13 43 55-88
13 47 16.23
13 50 36.53
200.46
200.42 |
2O0.37
20O.32
200.27
0,290
.201
.292
293
-294
0.286 0186
-286 9778
-287 9368
288 8955
-289 8539
959-1
9591
9588
9586
9583
f6 23 15.57
'6 26 33,43
io 29 51.23
16 33 08.97
16" 36 26,66
97.8y
97.8,1
97-77
97-72
97-66
0.245
.246
.247
.248
-249
3.242 5851
243 5557
.244 5261
-245 4962
.246 4661
9707
9705
9703
97oo
9698
3 53 56.77
3 57 16.98
4 00 37.13
4 03 57.23
4 07 17.29 ,
200.23
200.l8
200.13
200.08
300.03
0.295
.206
-297
.298
209
3.290 8121
.291 7699
.292 7275
.293 6849
.294 6419
958o
9577
9575
9572
9569
6 39 44-30
6 43 01.87
6 46 19.39
6 49 36.85
6 52 54.26
9X.6o
97.55
97-<[<>
97-13
97..18
0.250
>-247 4358
9695
4 10 37,30
f99.pS
0-300 (
>'295 5987
0566
6 56 n. 60
97.32
u
sechu
- .
arr" J (fl u )-9Q &
seed u
Jseohu
u 2
tan-He")-!
Jseohu !
lan-'{a")-00
SMITHSONIAN TABLES - ' ITS
278
The Gudermannian.
II
Oil 11
,.,F'
firl M
UU II
II
ml 11
FU'
ad ii
F '
0.3IK)
.301
.302
0.205 /;<j87
.296 5552
.21)7 Hill
9563
11 / II
16 5(1 1 1. 60
16 59 28.80
n
197.32
0.350
0.343 0655
-344 0071
0-114
19 39 22.34
19 42 36-55
194.25
194-lS
. ", </ ti * * t
,,
/ u., .(i). i t j
97 -"
..152
-3'.|4 9483
94 1 1
M) 45 50,/o
104. n
.304
:$! :!!$
9555
17 of' 03.30
17 00 20.42
107.15
l 97 , 09
353
-354
345 8893
.346 8299
9408
9-105
19 49 04.78
19 52 18.80
194-05
193-08
0.305
0.300 3/83
955-i
17 U 37-48
197.03
0-355
0.347 7702
9401
19 55 32.75
193-03
.307
.308
-309
.302 2882
,303 24.7
..I'M 1069
054 l
!? '5 5-1 --|8
I? M) H.-12
17 22 -8.30
17 25 45.12
l (X) . y i
-357
-359
.348 7101
,349 6498
350 5891
-351 5281
9398
9395
9392
9388
19 58 46.63
20 02 00.45
20 05 14.20
20 08 27.88
193.85
193.78
193-72
193-6'S
0.310
0.305 1509
953H
17 29 oi .89
196.74
0,360
0.352 4668
9385
20 ir 41.50
193.58
.31.!
..U3
.,11-1
.307 0570
.308 01 to
3 ( >8 !X'.i8
95,15
17 32 l8. (K)
17 ,15 35-24
'7 38 51.83
19(1. (18
196,50
36 1
.362
iiVM
353 4052
-354 343-'
-355 2809
.356 2183
9382
9378
9375
937-*
20 14 55-05
20 18 08.54
20 21 21.95
20 24 35.30
193.52
193-45
193.38
193-32
0.315
..no
o,,i*xj 0'6i
,310 8685
052!
'7 45 24.83
lifts
0.365
0.357 1954
.358 09.31
9366
20 27 48.59
20 31 0(.8o
193-25
-.H7
.31 l 8204
051 8
'7 51 57-58
i'X>-32
.367
-359 0285
9362
20 34 14-95
uj3.ii
.,ll8
.,112 77- 11
9515
17 55 13-87
196.26
368
.359 5X146
9359
20 37 28.03
193.0.1
''"'
..U3 7-M4
95'.;
'7 58 30.10
196.20
30!)
.360 9003
9356
20 40 41,04
192,98
O..|.i
0.314 (i/,|4
0509
l8 01 46. Jh
106. l.|
0.370
0.361 8358
9352
20 43 53.08
192.91
-,t'!l
-.I'.'i '1252
950(1
18 05 02,37
nXt.oS
.371
.362 7708
9349
20 47 oo'.i%
192.84
,3.!.t
-,1iO ,'1757
95O.1
18 08 18. 42
106. or
372
.363 7056'
934<>
20 50 1 9. fit)
102.77
-3-3
-,1'7 Ii*'.'i8
05OO
18 it 34,40
105-05
373
.364 6400
9343
20 53 32.40
192.70
.)-' I
,l>8 -1757
9497
18 14 50.32
i95.8<)
-37-1
365 574'
9339
20 56 45-07
192.63
O.,1.!5
0..1IO .|,).'i.f
04<J4
18 18 06, 10
105-83
0.375
0.366 5078
9336
20 59 57.67
192.57
.326
.3-!" ,17-15
0401
18 21 ,il.<)9
105-77
-376
.Vi7 4-113
9332
2[ 03 10.20
192.50
.,M7
-.121 3-M5
O.|88
18 2,| 37.72
105-7'
377
-368 3743
9329
21 ()6 22. 66
192.43
.,i.;8
.,1.'.! 27-M
0)85
18 j? 53.40
105. d5
.378
.369 3071
9326
21 (KJ 35.05
192.36
..1-!0
.,123 2.105
0482
l8 ,jl <H>.O2
I95.5H
379
370 2.195
93- J 2
21 12 47.38
192.29
0..130
0.32,1 i08(>
9170
"K ,14 24.57
105.5.!
0.380
0.371 lyifi
93'9
21 15 59.63
192,22
-3.lt
3"'5 ' "'3
04/0
18 37 40. <X>
195.46
.381
.372 1033
9310
21 H> 11.82
192.15
.,1,1-!
,,).!() 0*138
0(73
18 40 55.40
195.40
.382
373 0.147
9312
21 22 23,93
192.08
-3,1,1
.3.17 oi 10
9470
18 44 10.85
195,33
.383
373 <X>58
9309
21 25 35-97
192.01
33!
.3-7 9578
9 1' '7
18 47 2(1. K)
195.27
-384
-374 8;X5
9305
21 28 47,95
KJ! -94
o.,V11
0.328 j044
04(14
18 50 41.40
195.21
0.385
0.375 8268
9302
21 31 59.85
191 .87
33'-
,\>V) 850(1
9l''l
iH 53 56-57
195- '5
.386
.376 75<>9
9209
21 35 11.68
191.80
-3.17
-.130 706-5
0-158
18 57 t l .60
| ( j c f ^
187
-377 6866
9295
21 38 23.45
'91 -73
3,|H
.,131 7,|.!2
Hj 00 26.74
105.0.!
.38*
.378 6159
21 41 35,!.'l
101.66
.,13')
.,11,! (1875
915-i
19 113 41.72
I91-9.S
.381)
-379 5-149
9288
21 44 46,76
HJI.S9
0.340
<>.,J33 6'3.!,<i
0440
M) Of) 56'. 65
104.89
0.390
0.380 4736
9285
21 47 58.31
191.51
,1.|i
3.1-1 .'177-i
944;;
19 lo 1 1.50
194.83
-391
.381 .|oiy
9281
21 51 09.79
191.44
1 1 '
i i K ( i ] ( |
044-!
If) 1,1 2fl.30
19.1.76
3')2
lH_> WiH)
9278
21 54 21.20
I9L37
34,1
>,1.1d 4 f '57
04.10
19 Id' 41.03
104.70
393
.383 2575
9275
21 57 32.53
191.30
.,1-14
3,17 4005
943"
10 19 55.70
U>4.d3
394
.384 1818
9271
22 OO 43.80
191.23
3-15
0,338 3520
9433
KJ 23 10.30
191.57
0.305
0.181 Hi?
9268
22 03 54-99
ryi . 16
>346
3.19 *i'X>'
91,10
10 ;!d 24.81
KM. 5'
39'>
.386 0383
926/1
22 07 Of). 1 1
191 -oj)
.]ii7
.340 2380
O.| 27
10 ;!0 39- .11
194.4-1
397
.386' 0645
9261
22 10 I7,l6
191.01
.').]H
,341 181.)
0424
10 32 53,72
I'M. 38
.387 8004
9257
22 13 28,14
100. 94
349
.342 123''
91^0
iy 36 08.06
194.31
399
.388 8159
9254
22 iG 39-04
190.87
n,i*.
0.34.! MSS
9H7
19 39 112.34
194.^5
0.400
0.389 74"
0250
32 19 49.88
190.80
11
w
1 Itlh (O ll )""n
(roll li
2 lim~'<ay-OG
OROOllU
it
JT
cisoaliii
a lM -, ( ,,-Bo.
u Bach u
8MITHBDHIAH TAI1I.CU
279
The Giulcrnmnninn.
0-430 0.417 3303
.418 2
-419 1579
.420 0711
.420 9840
24 10 22.40
24 13 ,10-54
16
i94rt.SU
22 51.50
-!'t .(M .((!.<* I
.!M ;;i ,
-* 5 1 -
.422 88f>
.423 7204
0.426 4534
.427
.428 2735
429 1830
-430 0921
0.440
.441
.442
-443
444
9104
yioi
0007
9093
29 10.08
24 32 r?.75
35 25-35
-M 38 32-87
-17,1 J7.15
474 "M,
0-445
.446
447
.448
449
0.431 0009
9092
-433 8172
433 7248
434 6320
24 41 40..1I
24 44 47. ')7
-M 47 54-!/>
24 5f 02.16
2.-| 54 09.29
!75 0410
!/(' H.iti
The Gudermannian,
11
uil u
-P.-
"""
- W
11
Oil U
c-Fo'
oil u
-Fu'
o,;;oo
0.480 3811
88d8
1 11
18/W
"550
0.524. 1996
8657
1 II
30 02 03.92
I7S : S7
.501
.481 .:077
88(14
~7 34 28.59
rSa.Ha
551
.525 0651
8653
30 05 02.45
17&.4&
. SMJ
,.|8j 1530
88(Mi
7 .17 31.38
182.75
552
.525 9302
8649
30 08 00.88
178.39
503
483 0397
885(1
J7 40 34.09
182.07
553
.526 7948
8644
30 io 59.23
178.30
.504
483 9251
HK5J
-27 43 ,'l0.7i
182.58
554
.527 6590
8640
30 13 57-48
178.21
o.soji
0..|H.| 8100
88.|
'-7 4<i 39, -!5
182.50
0-555
0.528 5228
8616
30 16 55-65
178.12
- ;i< "
.48") (M)-t')
88 14
J7 49 41.70
i8j..|i
550
.529 3861
8631
30 19 53-72
178-03
.507
..|80 5/87
8831)
J7 5-3 44-07
'82.33
-557
.530 2400
8627
30 22 ST. 71
177-94
il< )o
.487 4<>-!S
88 \*(
"7 5 1 ! 46. IS
18 > ' J i
-SR8
. CT r ] i [C
86 '2
1C\ J ) C lf\ {v~t
T T*7 He
.509
.488 3-158
883'!
.57 58 48.55
18.M5
1 i.iJ l '
.559
- *M l J ' * t>
S3' 9735
8618
o u ^s 4y >utj
30 28 47-41
1 // . 05
177.76
0.510
o.48() .jjH/
88.J7
J8 01 50.6(1
182.07
0.560
0-532 8351
8614
30 31 45.12
177.67
. ;> M
,,(90 1 1 l,!
88..M
.;8 o.|, ;i.j.(K>
181 ,(>S
561
533 6</)2
8609
30 34 42.75
177.58
.51.1
-4')0 W33
88ii(
,;8 07 54 ,03
181. (jo
. 5(1,3
53-1 5569
8605
30 37 40.28
177-49
. s M
491 8749
KHi.l
,;8 io 50.48
181.81
-56.1
535 4172
8fioi
30 40 37.73
177.40
514
49-! 75<
88m
)U Y .J I'V* rj H
181.73
.564
.536 2771
8596
30 43 35-08
177.31
O-.'il.'i
0-493 0'37o
88oO
.;8 irt 59.94
181.64
0.565
0-537 1365
8592
30 46 32-35
177.22
-lii'i
-494 5174
880.!
-'8 ;!() (11.53
181,55
-560
537 9954
8587
30 49 29.52
1/7-13
-5 [7
495 3U7-I
8708
28 23 03,04
i8,,,7
.567
.538 8539
8583
30 52 26.60
177-04
, 5 1 8
49ft ii?(>9
8704
.18 ;tO 04.47
181.38
-568
539 7'20
8579
30 55 23.59
176.95
-519
497 15'>1
8789
- K - !0 5.8l
iKi.ao
.569
-540 5696
8574
30 58 20.49
176.85
(t..WO
<>-4'j8 11348
8785
jH 33 07. of)
iHi.ai
0.570
0,541 4268
8570
31 01 17.30
176,76
5-!l
.498 91,11
8781
"8 'i'i 08 '''
181 . i;-.
171
.542 2836
8=;6<i
31 04. 14 ,02
17(),67
,4')0 79UI
8777
.'8 '(8 (Xj.'Ki
181 .04
572
-543 i 309
^J V '*J
8561
31 07 10.65
J/UtU/
176.58
5-M
.500 (1(185
8773
-;8 41 io.-!<)
180 .05
573
543 W58
8556
31 io 07.18
176.49
- 5J4
St'l 545''
8708
j8 44 u. ao
180.86
574
.5448512
8552
31 13 03.63
176.40
o,<i.!T
().,'!(),! 4J.U
8704
j8 47 KT.OI
180.77
0-575
0-545 7062
8548
31 15 50.98
176.31
-Ji.lO
,503 J08.|
87(10
~'8 511 u.75
i Ho . (19
576
.546 5607
8543
31 18 56.24
176.22
!W7
.504 1740
875(1
'8 53 13.39
180. do
577
547 4148
8539
31 21 52.41
176.12
, 5.18
-505 0495
8752
,:8 56 13,95
180.51
.578
.548 2685
8534
31 24 48.49
176.03
529
505 9-M5
8747
::8 59 14.41
180.43
.579
-549 1217
^ 8530
31 27 44.47
175.94
u.530
0,50(1 7990
H743
&) (u 14.80
180,34
0.580
0-5499744
8525
31 30 40.37
175.85
-531
,507 (1731
-9 05 15.09
180,25
.581
. 550 8267
8521
31 33 30. 17
175.76
53-1
.508 54(18
8735
~<) 08 15.30
iHo.Ki
.582
-551 6786
8516
31 36 31.88
175.66
S3.1
5O(J 4.!OO
8730
*!9 11 15..|2
180.07
583
.552 5300
8512
31 39 27-50
175.57
S3.I
.510 .19.18
87.10
a.) '-I IS-I5
179.99
.584
553 38m
8508
31 42 23.03
175.48
O..W5
0.511 ids-*
873.1
29 17 15-30
179.90
0.585
0.554 2315
8503
31 45 18,46
175.39
5,V'
. S'-i 0372
8717
^9 20 lfi.J.|
179.81
.586
555 081(1
8499
31 4B 13-80
175-30
5,(7
.fju 9087
8713
29 33 15.01
179.72
.587
555 9313
849-1
31 51 09-05
175.20
538
.513 7798
8709
29 20 l.|.(H>
179.63
58>S
.556 7804
8.190
31 54 04.21
175.11
5.W
.514 6505
8705
29 29 I.l.aJi
170.55
.589
557 6292
8485
31 50 59-27
175-02
0-540
o.$is TO
8700
20 33 13.78
170.46
0.590
0,558 4775
8481
31 59 54.25
174.93
.gio 3905
8696
ai> 35 M.ao
170.37
59 r
.559 3253
8476
32 02 49, 13
174.83
54.1
, C|7 Jl}<)9
80OJ
29 38 u.fia
1 79 . .'8
.592
.560 1727
8472
32 05 43.91
174.74
S-13
!'f)i8 1389
8(187
29 41 11.7(1
170.19
.593
.561 0106
8467
32 08 38.61
174.65
5i8 9974
8(183
jjj 44 10.91
I7U.10
59-1
.50 i 8061
8463
32 u 33,21
174.55
O.S-IS
<MIO 8655
8679
^9 47 09.96
179.01
0.595
0.562.7122
8458
32 14 27.71
174.46
540
/ejii 7<Vj
8071
29 50 08.93
178.93
50
.563 5577
8454
33 17 22,13
174.37
147
!ij]| 0004
867(1
29 S3 07,81
597
.564 4029
8449
32 20 16,45
174.27
5-|8
]'t-~,J ( l(>/)
800(>
29 5(1 ofi.Oi
178,75
598
.565 2476
8445
32 23 10.68
174.18
549
sS 3330
860.)
-V 59 05,31
178.66
.599
.566 0918
8440
32 26 04,81
174.09
0.550
0.5*1 nwfl
B657
30 02 03.92
178.57
o.Coo
0.566 9356
8436
32 28 58.85
173.90
u
^, K
wsooliu
.Un-K**-
u BOO (ill
u
7T
useohu
2tnn-^)-9Q*
u aooh u
8MITH90HIAN TAB 1-KB
The Gudermannian.
u
gd u
-W
gd u
.
u
ad u
.Ho'
ad u
"IV
0.600
.601
.602
.603
.604
o. 566 0356
.567 77S9
. 568 6218
. 569 4642
. 570 306I
8436
8431
8426
8422
8417
32 31 52.80
32 34 46.66
32 37 40.42
32 40 34.09
173.99
173.90
173-Sl
173.71
173-62
0.650
.65
.652
-653
-654
0.608 5398
.609 3600
.610 1708
.610 099
.6ll 8179
820
8200
819
819
/ II
34 52 00.3'
34 54 49-52
34 57 38.6-
35 oo 27.6
35 03 16.5
169.24
169.14
169.04
168.95
168.85
0.605
.606
.607
.608
.609
0-571 1476
.571 9887
-572 8293
.573 6604
.574 5091
8413
8408
8404
8399
8395
32 43 27.66
32 46 21.14
32 49 14.52
32 52 07,82
32 55 oi.Oi
173.53
173-43
173-34
173.24
173-15
0.655
.656
.657
.658
.659
0.612 6363
.613 4542
.614 2716
.615 o88f
.615 9051
818
8i77
8172
8167
8163
35 06 05.31
35 08 54.0
35 II 42. f)L
35 14 3LI3
35 17 19 .5-
I68.7S
168.66
168. $6
168.46
168.36
0.610
.611
0.575 3484
.576 1871
8390
8385
32 57 54.12
33 00 47.13
173.06
172.96
O.66o
.661
0.616 7211
-617 5366
8158
8153
35 20 07. 8C
35 22 56.08
168.27
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
,619 166;
8144
35 28 32,22
167.97
.614
.578 7007
8372
33 09 25,59
172,68
.664
.619 980,:
8139
35 31 20.14
167.88
0.615
0.579 5377
8367
33 T2 l8.22
172.59
0.665
0.620 7941
813;
35 34 07-97
167,78
.616
-580 3741
8363
33 IS 10.76
172.49
.666
.621 6073
8129
35 36 55-70
167.6*
.617
.581 2102
8358
33 18 03.20
172.40
.667
.622 4200
8125
35 30 43-34
167.5!-
.618
.582 0457
8353
33 20 55-55
172-30
.668
.623 2322
8T20
35 42 30.87
167.49
.619
.582 8809
8349
33 23 47-Si
172.21
.669
.624 0440
8115
35 45 18.31
167.30
0.620
0.583 7155
8344
33 26 39-97
172,11
0.670
0.624 8553
8110
35 48 05.65
167.2;)
.621
-584 5497
8340
33 29 32.03
172.02
.671
.625 6661
8106
35 50 52.89
167,10
.622
-385 3834
8335
33 32 24.00
I7L92
.672
.626 4764
8101
35 53 40.03
i67.o'j
.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
I7L73
.674
.628 0956
8091
35 59 14-03
l66,ijo
0.625
0.587 8819
8321
33 40 59-34
171.64
0.675
0.628 9046
8087
36 02 00.88
166,8:)
.626
.588 7137
8317
33 43 50.93
I7L54
.676
.629 7130
8082
Tfj 04 47.63
166.70
.627
.589 5452
8312
33 46 42.42
I7L45
.677
.630 5209
8077
36 07 34-28
i (rfi. 60
.628
590 376r
8307
33 49 33.82
I7L35
.678
.631 3284
8072
36 to 20.84
166.51
.629
.591 2066
8303
33 52 25.12
171.26
.679
.632 1354
8068
36 13 07.20
166.41
0.630
0.592 0367
8298
33 55 16.33
171.16
0.680
0.632 9420
8063
<> IS 53.65
166,31
.631
.592 8662
8293
33 58 07-44
171.06
.681
633 7480
8058
36 18 30.91
166.21
.632
593 6954
8289
34 oo 58.46
170.97
.682
-634 5536
8053
36 21 26.07
166, i i
.633
594 5240
8284
34 03 49.38
170.87
.683
<J35 3587
8049
<) 24 12. 14
166,01
.634
595 3522
8280
34 06 40.20
70.78
.684
.636 1633
8044
}6 26 58. 10
165.92
0.635
0.506 1799
8275
34 09 30.93
170.68
0.685
0.636 9675
8039
36 2') 43.07
165.82
.636
.597 0072
8270
34 12 21.56
70.59
.686
.637 7711
8034
36 32 ;;y.74
65.72
.637
507 8339
8266
34 15 I2.ro
70-49
.687
-638 5743
8029
36 35 15.41
165,62
.6.3.8
-598 6603
8261
34 18 02.54
70-39
.688
639 3770
8025
16 38 00.98
65.52
639
599 4861
8256
34 20 52.89
70-30
,689
.640 1792
8020
36 40 46.45
165.42
0.640
0.600 3115
8252
34 23 43.14
70.20
0.690
0.640 9810
8015
36 43 31.82
65.32
.641
.601 1364
8247
34 26 33.29
70.11
.691
.641 7823
8010
;6 46 17.09
65.22
.642
.601 9609
8242
34 29 23.35
70.01
.692
642 5830
8006
;6 49 02.27
65. 13
.643
.602 7849
8238
34 32 13.31
69.91
.693
.643 3834
8001
36 51 47.34
6,5-0}
.644
.603 6084
8233
34 35 03.17
69.82
.694
.044 1832
7996
3ft 54 3J-32
0.645
0.604 4315
8228
34 37 52.94
69.72
0.695
.644 9825
TWi
36 57 17.20
64,83
.646
-647
.648
.649
.605 2541
.606 0762
.606 8979
.607 7190
8224
8219
8214
8210
34 40 42.61
4 43 32.19
4 46 21.67
449 11.05
69.62
69.53
69.43
69.33
.696
.697
.698
.699
.645 7814
.646 5798
.647 3777
.648 1751
7986
7981
7977
7972
7 oo OT. 08
7 02 46, (A
7 05 31-24
7 08 15.72
i'",t
64.73
64-63
64.53
64.43
0.650
0.608 5398
8205
4 52 00.34
69.24
0.700
.648 9721
7967
7 II 00.10
64-33
u
atan-^
sechu
tan- l (e n )-90
sechu
u
tr<<.u>-|
seohu
tnn-'(o)-fJO
sachu
SMITHSONIAN TABLES
282
The Gudermannian.
II
Oil II
U.FH'
ail u
-W
u
Qtl 11
*Fo'
gd u
W
.> /
II
Oft/
ft
0.700
o.6,|8 0721
7<X>7
37 1 1 oo. to
164.33
0.750
0.688 2014
7724
39 25 51.72
'59.32
.701
.(140 V6H5
7' A:
37 13 44-38
l'>4.23
.751
.688 9735
7719
39 28 30.98
159-22
V( IC"7
17 10 2iH, $7
l6l 17
7c->
f$J\ 1 .1 C I
Trt A
-if\ i m r i-
1 *r. t r
7o;i
.651 3(MKI
7053
,!/ I ^ r **i ,, ^\f
37 10 12.65
1 1 1.\ , 1 ,)
/.I-
753
t"oy /4.T 1
.(>9O 5163
77 '4
7709
39 3 1 'O. 15
39 33 49-21
1 59 1 1
159-01
70-1
.052 1550
7948
37 -'I 56.03
I')3.93
754
.691 2870
7704
39 36 28.18
158.91
0.705
0.6S-! 0406
70.1.1
37 2.| 40.52
i63.R-|
0.755
0.603 0572
7609
39 39 07.04
158.81
-7"''
.''5.1 743''
70.lH
37 -7 j.i. 31
163.74
-756
.602 8269
7604
39 41 45.8o
158.71
.707
.654 537-'
70,13
37 30 07.90
1(13.64
757
.603 5(/n
7690
39 44 24.46
I58.6I
-7"8
.055 330,1
7U~'8
37 3^ 5L58
16.1.54
758
.604 3648
768")
39 47 03-or
158.51
7<>0
.050 l.'JO
7024
37 35 35-06
163.44
.759
.695 1330
7680
394941-47
158.40
0,710
0.656 9150
7010
37 38 i8-45
163.34
o . 760
0.695 9007
7675
39 53 19.82
158.30
.711
0,<;7 71167
7'.)l,|
37 4i 01.74
1(13.2-1
,761
,6y6 6(J79
7670
39 54 58.07
158.20
.71.!
.058 4078
7<JO9
37 43 44-02
163-14
.762
6(J7 4347
7665
39 57 36.23
I58,!0
.650 2HH|i
7<XM
37 46 -,'8.01
16.1.04
-763
.<V)8 2CKK>
7660
40 oo 14,28
158.00
^714
/t/u 1 1 I'?!!*!
k \ n n I \lf\if
7H<)9
37 49 n.OO
162.94
,764
.698 9667
7655
40 02 52.22
157-90
0.715
o.(rfk) 8684
7805
37 51 53-Bo
162, ai
0.765
0.609 7319
7650
40 05 30.07
157.80
.71''
.(rfn 0576
7800
37 54 30-08
16^74
. 766
.700 4967
7645
40 08 07.81
157.69
.717
.(KU .|4''3
XWHfj
37 57 10-36
-76?
.701 2610
7640
40 io 45.46
157-59
.718
.06.1 -1340
XHHo
3^ OO 01.05
162! s!|
.7(18
.702 oa.|8
7635
40 13 23,00
157.49
.664 (iJJ.1
775
38 02 44.4,1
162.44
.769
.703 7880
7630
40 16 00,44
157.39
0.7'!0
o.66,| Ho*/'
7H?o
38 1)5 26.83
162.34
0.770
0,703 5508
7625
40 18 37.78
157-20
.7.!!
,(rf)tj t <j(jo.|
7865
38 08 09. u
162.24
.77!
.704 3131
7620
40 21 15.01
157-19
.7,!.!
.iM 38.17
X<Hfi'i
38 10 51 .30
162. 14
.705 0750
7616
40 23 52.15
157.08
7-M
,(>f>7 1085
XK<;6
38 13 33-30
162.04
773
.705 8363
7611
40 26 29.18
156.08
7-M
'rf'7 0530
7HS1
38 Id 15.37
16 1 .94
774
706 5971
7606
40 29 oij.n
156.88
0.7-5
o.6OH 7387
78-1''
38 18 57.26
ifit.Ri
0.775
0.707 3574
7601
40 31 42-94
156.78
-7,!6
,tttx) j|,yi
7H.|l
!l8 21 30.05
161.74
.776
.708 1173
7596
40 34 19.67
IS6.6S
.7-7
.670 3060
7836
38 a.| .:o-73
777
.708 8766
7591
40 36 56.29
156.57
.671 <xx>3
7^3'
38 27 02.32
i6i.54
.778
. 709 6354
7586
40 39 32,82
156.47
. 7-!<>
.071 873.!
7HJ7
38 29 43.80
779
710 3938
7581
40 42 09.24
156.37
0.73"
0.672 65.16
7&U
3K .1 J 25 . 10
161.33
0.780
0.711 1516
7576
40 44 45.56
156.27
t'7,1 4370
7817
38 35 06.47
i(n .23
.781
,711 tjooo
7571
4047 21.77
156.17
73
,<i/,| ,MI)O
Xttu
38 ,17 47-65
161.13
.712 6659
7566
4049 57.89
156.06
7,13
,6/5 woo
7Ho7
38 40 28.74
161,03
;?ki
.713 4223
7561
40 52 33-90
155. 96
.731
.075 7H04
38 43 09,7.!
160.93
.714 1781
7556
40 55 09-81
,155-86
0.735
0.676 (5604
7707
38 45 50.6o
if k). 83
0.785
0.7M 9335
7551
40 57 45.62
155.76
73"
,677 3,i(,)i,j
770-!
38 48 31.38
100,73
.786
.715 6884
7546
41 oo 21.33
155.61")
737
.(17^ n H(>
.l 51 u,o6
KJ0.03
.787
.716 4428
7541
41 02 56.04
155-55
.(178 No74
773
38 53 5.!. 64
if io. 53
.717 1967
7537
41 05 32.44
155-45
.730
.''70 6751
38 56 33-'iJ
If *. 43
^789
.717 9501
7532
41 08 07.8-1
155-35
0.740
O.OKo 4530
7773
38 50 13.50
160.33
0,790
0.718 7030
7527
41 io 43.14
155-25
741
,(tHl J'llXI
77* iH
30 01 53-77
lC)0.23
>79"
.7M) 4554
7522
4' 13 '8.33
135-15
.74-!
7-13
!f*Kj xHJO
7703
30 04 33-95
160,02
793
.720 2073
.720 9588
75"7
7512
4' IS 53-43
41 18 28.42
155.04
154-94
-7-14
7753
3909 54^00
159-02
.794
,721 7097
7507
41 21 03.31
154.84
0-745
.746
747
7-10
:|S
7748
7744
7730
7734
7729
30 U 33.87
30 15 I3.6.|
30 17 53-31
30 20 3-3-88
,19 23 1 2. 35
159.82
159.72
159.02
150-52
150.42
0.795
7!Xi
.797
799
0.722 4601
.723 2 I 01
.723 9595
.724 7084
.725 4569
7502
7497
7492
7487
7482
41 23 38.10
41 26 12.78
41 2847.36
41 31 21.84
41 33 56.22
154.74
154-63!
154.53
154-43
154-33
0.750
0.688 2014
77*54
30 25 51.72
159.32
0.8oo
0.726 2048
7477
41 36* 30.50
154-22
II
IWHW-J
..!.
^^MC
wiechu
ii
ff
H .hH
8ta-(*HKP
usacliu
8MITHBONIAH TAIIUCO
283
The Giulci'iuniminn.
o.8r
!HI
0.81.
.HK
.81?
.818
.Bit
o.Sar
,8*3
,8.'.
0.825
.8*
.827
.828
0.8.10
Xl3
.'834
0.835
.836
37
.8,18
0.840
.841
0.845
,.|6
K.I7
.848
^50
0(1 U
0.726 20.
7-7 (*)i
-7-'K445
.7jy i
0.729 037
.733 i?o
.73- yi.|
0.733 f>57'
735 141.
.7.15 88.'<
0.737 3f>4-
.738 104.
.738 R|3<
730 582*
.740 331.
0.747 059-
741 7<Xi<
743 533!,
.743 270/1
.744 (Xjfl.i
0.744 7420
74S 4771
.746 2115
74'' 9455
.747 6700
,74# 4120
.749 14.(<>
.749 87(16
,750 0081
.75 i '339 i
75-i 7007
753 53JW
.75-1 358a
.754 oKM
755, 7MR
,750 4*123
.757
757 .
,75 ta
759 3475
760 0725
760 7070
7<i t 52 it
yCta 2446
762
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38.37
38.27
38.17
38.07
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37.76
37.66
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37-14
37-04
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136.84
136.73
136.63
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136.43
136.32
136.22
136.12
136.02
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133.87
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8MITHBQNIAN TAHLKB
285
The Gudermannian.
u
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gd u
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u
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0.865 769S
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u
128.61
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647
49 38 31-3
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623
51 27 43.1
128.51
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133-47
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622
51 29 51.5
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ay
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6466
49 42 58.3
133.37
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51 31 59-9
128.31
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646
49 45 11-64
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621
51 34 08.1
128.21
1.005
0.869 0036
645
49 47 24.86
I33.I6
1-055
0.900 6691
621
Si 36 16.3
I28.Ii
.006
.879 6489
645
49 49 37-9
I33.06
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.oor 2900
6206
51 38 24.4
128.01
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644
49 51 50.98
112.96
057
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620
51 40 32. i
127,01
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644
49 54 03.8
132.86
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6196
51 42 40.2
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127 8l
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643
49 56 16.69
132.76
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619
Si 44 47-9
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1. 010
0.872 2254
643
49 58 29.4
132.65
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0.903 7685
618
51 46 55.6
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50 oo 42.00
132.55
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618
51 49 03.1
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So 02 54-5
132.45
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.905 0048
617
51 51 10.6
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127.41
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641
50 05 06.90
132-35
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617
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127.11
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641
50 07 19.2
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616
5i 55 25.2
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127.21
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0.875 4348
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640
640
50 09 31-4
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132.15
132.04
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0.906 8557
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616
615
51 57 32.4
51 59 39-4
127.11
127.01
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639
639
638
50 13 55-4
50 16 07.3
50 18 19.1
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131.84
131.74
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615
6148
6143
52 oi 46.4
52 03 53.2
52 06 oo.o;
126.91
126.81
126.71
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0.878 6320
6 3 8
50 20 30.86
131.64
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0-909 9307
6138
52 0806.68
126,61
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637
50 22 42.45
I3L54
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910 5443
6i33
52 10 13.24
126.51
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6372
50 24 53.94
I3L44
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6128
52 12 10.70
126.41
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6367
6362
50 27 05.32
50 29 16.61
I3L34
131.23
073
.074
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.912 3821
612;
6118
52 14 26.05
52 16 32.31
126,31
126.21
1.025
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0.881 8169
.882 4524
.883 0874
.883 7219
.884 3560
6357
6353
6348
6343
6338
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50 33 38.87
50 35 49.85
o 38 00.73
o 40 11.51
131.13
I3L03
30.93
30.83
30.73
1.075
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0.912 9937
.913 6048
.914 2155
.914 8256
915 4353
6114
6ioc
6 10;
6099
6094
52 18 38.46
52 20 44.52
52 22 50.48
52 24 56.33
52 27 02.09
126.11
126.01
25.91
125.81
25.71
1.030
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0.884 9895
.885 6226
.886 2551
.8868872
.887 5188
6333
6328
6323
6318
6313
o 42 22.19
44 32.76
o 46 43-24
o 48 53-6r
o 51 03.80
30.63
30.53
30.42
30.32
30.22
1. 080
.081
.082
.083
.084
0.916 0445
.916 6532
.917 2615
.917 8692
.9i8 4765
6090
6085
6080
6075
6070
52 29 07.75
2 31 I3.30
2 33 18.76
2 35 24.12
2 37 29.38
25.61
25.51
25.41
25.31
25.21
1.035
.036
037
.038
039
0.8S8 1490
.8887805
.8894106
.890 0402
.8906693
630S
6304
6299
6294
6289
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o 55 24.13
57 34-10
o 59 43-97
i oi 53.74
30.12
30.02
29.92
29.82
29.72
1.085
.086
.087
.088
.089
0.919 0833
.919 6896
-920 2954
.920 9008
.921 5056
6065
6061
6056
6051
6546
2 39 34-54
2 41 39.6o
2 43 44.56
2 45 49.42
2 47 54.18
25.11
25.01
24,91
24.81
24.71
1.040
.041
.042
043
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0.891 2080
.891 9262
.892 5538
.893 1810
.893 8077
6284
6279
6274
6269
6264
i 04 03.41
i 06 12.98
i 08 22.44
i 10 31.81
I 12 41.07
2g.62
29.52
29.42
29.32
29.21
1.090
,ogi
.092
093
.094
0,922 I TOO
922 7139
923 3173
.923 9203
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6041
6037
6032
6027
6022
2 49 58.85
2 52 03.41
2 54 07.87
2 56 12.24
2 58 16.50
24,61
24.51
24.41
24.32
24.22
1.045
.046
047
.048
.049
0.894 4339
895 0596
.8956848
.8963096
896 9338
6260
6255
6250
6245
6240
I 14 50.24
i 16 59.30
I 19 08.26
I 21 17.12
i 23 25.88
29.11
29.01
28.91
28.81
28.71
1.095
.096
.097
.098
.099
0.92-5 1247
.925 7262
.926 3272
.926 9278
-927 5278
6017
6013
6008
6003
5998
3 00 20.6?
3 02 24.74
3 04 28,70
3 06 32,57
3 08 36.34
24.12
24.02
23.92
23.82
23.72
1.050
3.897 5576
6235
1 25 34-55
28.61
I. TOO
3.928 1274
5993
3 10 40.01
23.62
u 2
tan~ ! {fl u )-|
sechu
an-'feil-M
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u S
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1an- 1 (e")~8Q
sechu
286
The Glide rmannian.
11
ail u
10 Fu'
oilu
-w
II
ad u
*
fld U
T'
I.1OO
0.928 1274
5993
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53 10 40.01
II
123,62
1.150
0.957 4980
5756
O / 11
54 51 38.15
I lti"~2 ''
.101
.0_'8 72(15
5989
53 12 43-59
123.52
.151
.958 0734
5751
54 53 36.82
I \fi.*-2 .
, 1OJ
.929 3251
598.1
53 14 47.06
123.42
.152
.958 6482
5746
54 55 35-;
I 1 - . ' \
. 103
.929 9232
5979
53 10 50-43
123.32
. 153
.559 2226
5742
54 57 33.87
ii,-:. .; : - :
.104
.930 5209
5974
53 18 53-71
123,23
.15-1
-959 7965
5737
54 59 32-25
no..? 3 ,
1 . 105
0.931 1181
59&)
53 20 56. ft)
123 . 13
I 155
0.960 3700
5732
55 oi 30.53
nr<..*i.
.106
93' 7148
5965
53 22 59.96
123 .03
.156
.960 9430
5727
55 03 28.7-'
i j.v r
.107
.932 31 lo
506o
53 25 02.04
122.93
.157
.961 5155
5723
55 05 26.81
n ''- . i j s
.108
.932 9067
5055
53 27 05.83
122.83
.158
.0f>2 0875
55 07 24.80
i :".'*;
.109
.933 5020
5950
53 20 08. do
122.73
.159
.962 6591
5713
55 09 22.69
"7.83
i. no
0.034 0<X)8
59-15
53 31 11.29
122.63
1.160
0.963 2302
5709
55 u 20.49
1 17- 7?
.111
,9,14 (K)li
5941
53 33 13-87
122,54
.161
.963 8008
5704
55 13 18.19
I l?.t>-
,112
.035 2840
5936
53 35 16.36
122.44
.162
.oC).] 3710
5699
55 ^5 15.80
t <-'?*<
.113
.035 8782
593'
53 37 18.75
122.34
.163
.964. 9407
569S
55 17 13.31
117.46;
.114
.936 47"
5926
53 39 21.03
122.24
.164
9"5 5099
5690
55 19 10.7-3
nr.yi.
1. 115
0-937 0635
5922
53 41 23.22
122 . 14
1 . 165
0.06(1 0787
5685
55 21 08.04
nr._',-'
.116
.037 6554
5917
53 43 25.32
122.04
.166
.066 6470
5681
55 23 05. 26
1 17. 17
.117
,038 2469
5912
53 45 27.31
122.94
,167
.967 2148
5676
55 25 02.38
1I7>'7
,118
.938 8.-i7
590?
53 47 20.JI
121.85
,168
.967 7822
567 r
55 26 59.41
Tifi.i.s;
.119
.939 4283
5902
53 49 31-00
121,75
,169
.08 3491
5667
55 28 56.34
1 1*. to.
I.I2O
0.940 0183
5808
S3 51 32.70
121.65
1.170
0.968 9155
5662
55 30 53.r?
I H'. 7..,'
.121
,040 <x>79
5893
53 53 34.3"
121.55
.171
.y6y 4815
5657
55 32 49-01
.11 '>.'>
, 1 2..'
,0.| i Htfo
5888
53 55 35.8o
121.45
.172
970 0470
5653
55 34 46.55
I If !,'>;
.123
.(XIT 7855
5883
53 57 37-21
121.35
'73
.970 6120
5648
55 36 43-10
I H-. JO.
. 124
.94J 3736
5870
53 59 38'5i
121 .26
.174
.971 1766
5643
55 38 39-54
110.4.;}
1. 125
0.0,|2 y()E3
5R74
54 "I 39.72
121.16
1. 175
0.971 7407
5639
55 40 35-50
110,3!
,126
.943 54l
">S(x)
54 03 40.83
12 I. 06
. 1,76
.972 3043
5634
55 42 32.16
IlO.JE
.127
5864
54 05 .| l .84
120.06
.177
,972 8675
5629
55 44 28.32
no. it
.128
.014 7-*M
5860
54 07 42.76
120.86
.178
973 4301
5625
55 46 24.38
IHs.Oj
.120
945 3070
5855
54 09 43,57
120.77
.179
.073 992-1
5620
55 48 20.35
1 15 -9-'
1,130
0.945 By 33
S8so
54 " 44.29
120,67
1.180
0.974 5542
5615
55 50 16.22
1 T5 -8.5
13I
.946 4771
5845
54 13 44.01
120,57
.181
975 1155
561 1
55 52 12.00
115.7,*
.132
.947 ofiH
5811
54 15 45-43
120.47
,182
975 6763
5606
55 54 07.68
1 15 .6,
. 133
.947 6452
5836
54 17 45-86
120.38
.183
.976 2367
5601
55 56 03.27
n=i.".
. M4
,9.|8 23HC)
5831
54 19 46.18
120.28
.184
.976 7966
5597
55 57 58.76
115.4.
1 . 135
0.948 SITS
<i8"6
54 21 46.41
120. l8
1.185
0.977 356o
5592
55 59 54-15
1 15-3
. 136
.049 3!),19
5822
54 23 46.54
120,08
.186
977 0150
5588
56 oi 49.45
1 15-2.
.137
.949 0758
5817
54 25 46.58
119,98
.187
97K 4735
5583
56 03 44.66
115.1'--
.950 5573
5812
54 27 46.51
119.89
.188
,079 0316
5578
56 05 39.76
1 1 5.1/1
. 139
.951 1.1*43
5807
54 29 46.35
119.79
.189
.979 5892
5574
56 07 34.78
114.0
I . I.|0
0.951 7188
5803
54 31 46.09
119.69
1.190
0.980 1463
S56y
56 09 29.69
IM-&7'
.141
,952 2i;.S8
5798
54 33 45-74
119.59
.191
.980 7030
5564
56 II 24.51
II4-7"
.14-'
.052 87&|
5793
54 35 45.28
119.50
,192
.981 2592
556o
56 13 19-24
I !4-fS
. 143
.953 4575
54 3744-73
119,40
.193
.08 i 8149
5555
56 15 T3.S7
I U-?^
.144
.954 0361
5784
54 39 44.08
119.30
.19-1
.982 3702
5551
56 17 08.41
H4"I'>
i . 145
0.054 01-13
5779
54 41 43-34
110. 21
1. 195
0.982 9251
5546
56 19 02.85
I U-3'
.146
.955 I9W
5775
54 43 42.49
1 10 . 1 1
,196
.983 4791
5541
56 20 57-19
114-'
.147
.055 7f*>2
5770
54 45 41-55
110.01
.197
.98-4 0333
5537
56 22 51-44
II.'
. 149
.056 34(10
.956 9222
5765
5760
54 4740.51
54 49 39.38
118.91
118.82
,198
.199
.984 5868
.985 1397
5532
5527
56 24 45.6o
56 26 39.66
il
11
I.I50
0-957 498o
5756
54 51 38.15
118.72
1.200
0.985 6922
5523
56 28 33.62
"i
u
*""-<">-I
wjochg
2lan~'(Q")-BO
wBQCh u
U
t ,.-<-:
<> aoch u
2,a n -.<e*H**
" BKh
SMITHBONIAN TABLCB
287
The Giidcrmamrian.
II
till it
^
Ilil u
.W
u
adit
w
Oil 11
.^
o / //
If
" / //
ft
1.20
0.985 692
552
50' 28 33,6
113,0
1.25
r.oia 735
5 -'9
58 oi 31,7
109.23
.20
.986 244
551
56 30 27-4
II3-8
25
.013 "641
?.)
58 03 20. 8<
I0i>. 1,1
.20
.986 795
55 T
56 32 21.2
11,1.7
.-5
.013 ?03i l
5 -'8 1
58 oq (X).i^
101). 04
,20
.087 347
5501
56 34 14.9
II3.<i
.25,;
.014 3JJ
5-;8.
58 oii 58. i)>
108. i)5
.20.
.987 HU7
550
56 30 08,5
113-5
,25.
.014 850
5-77
58 uS 47.88
iH,H(i
1,20
0.988 447
5500
56 3tS oi.o
II.1.4
i. as
i. 015 3777
S3 7,
58 10 36. 6<
108.76
.20
.088 997
549
5*' 39 55-4
113-3
- as*
.015 904!
5~ iK
,'iN i.! j<i.4(
108,07
.2-07
.089 547
549
56 41 .(8-7
II3.2
.W/
.016 4.11.
5-:''.
58 14 14,0.
108.58
.20
090 095
^.[HC
56 43 41-9
113. 1'
-258
.(ii() <),17(
,HJU
58 Hi n.;.5<
108.40
.209
.(JOO 644
5482
SC> 45 35-0
1 13. of
.-'SO
-017 -|3.
5-'5r
,'l8 17 SUM
108.39
I.2K
0.991 H)2
5477
56 47 -'8.0
IIJ.CJ
1.260
i .018 (X)8f
5351
S' 1 * 10 39-35
1 08., 10
.21
.9! 739
547-
564U 20.9
iu.8,
.2(1
.018 5335
S"4 f
58 ,;[ 27. (i
108,21
.212
.992 286(
5468
5(i 51 13.8*
1 12.78
.26l
."it) 057, 1
S-4-
58 j.i 15-77
108. i >
.21,'
902 833
54<\
56 53 06.5.
[12. CM
.20.
.019 5818
5-M7
58 i!5 03.8.
n>S.o3
.21,
.993 379
5459
56 54 59-17
112.59
.26,
,020 105;
5^3.
Ii .16 51.8-
'07.03
1. 2 IS
0-993 9240
54 &
56" 5^ 51-7-
112.50
1.365
1.020 6.;8,
S.!.)M
5iH .:8 39,71
107.84
,21<
.(394 4700
5449
56 58 44-17
112.40
,26(
.(Ml 15 U
52J.
i|K ;'(O .17. 51
107,75
.217
.095 0148
5445
57 oo 36.53
n-i.31
.267
,OJI 67.11
pK 3~' 15- ill
.218
.905 SSfJO
5440
57 02 28. ;
ii,:, 22
.268
.033 I9.|f
5^1,'
58 3.| (U.K..
107.57
.219
.996 1028
543*
57 04 JO. IX
1 1,3. 12
.aft.
.02J 7 If) I
5J1
58 ,15 50.34
107-47
1.220
0,996 6462
5431
57 06 13.03
1 1 a. 03
T.J70
i.oj3 :M(>
5.!(Vi
#< .17 ,17-77
io7.;iS
.221
997 189
5427
57 08 05.01
1 1 I .U.
.271
-023 757.1
S^'O..'
107.29
.222-
.997 73t5
5422
57 09 56.91
in. 8.1
.1172
.oj.| 2772
5M>7
i8 41 12,35
107. jo
.22;
,(j()8 2735.
54 '
57 n 4H.60
111-7.1
.273
,().] 7(X7
.1' o.i
^ 4.! 59.50
107.11
.22,
.998 8150
5413
57 13 40-39
..'74
.UJS 3158
5188
58 .|4 40.56
107.02
1.225
0-999 35fil
5408
57 IS 31- W
ni. 56
i , 275
l.o.lji 8.M4
5il
iH 46' 33-53
10:1.93
.226
.909 &.X7
54t>4
J7 17 21 . "il!
ii 1,40
'76
'6 ~\^ '(>
iofi.8i
,227
i.ooo 4369
5390
57 iy 14-92
111.37
.277
.(>.!(> 8?()3
5175
1^ SO 07.^0
1011.74
.228
-ooo p76f
5395
57 21 ofi,j.|
1 1 . - v i u
...78
,nj7 387(1
S' 7 1
58 51 53,<X>
.229
.001 5158
53!Jt>
57 M 57-47
11.18
-J79
,OJ7 <XM4
iildl.
sH S.I -10.50
UK), 56
1 .230
1,002 0546
5386
57 2.| 48,60
1 1 .00
1.280
1.02H ,|208
51<ij
^8 55 .!7-OJ
106.47
.231
.002 5U30
538l
i7 2f 39.64
IO.99
.jSi
.OJ8 1)3(17
5157
iN 57 '3-41
.232
.003 1309
5377
S7 28 30.50
m.i;o
. 28 J
0.'9 4533
5IS.1
iH S8 S9-77
I Of). 2()
.233
.003 <X&3
5372
S7 30 21.45
ui.8l
.-(83
S"4
0(i. KJ
.234
.004 -'053
53<JB
57 32 12.21
10.71
.1-84
.030 .|.Shj
514-1
I't 0* JJ. Id
lOll. 10
1.235
.004 7418
S3<">3
7 34 02. aS
10.62
1.285
.030 9!/ii
;i'4"
W O.| IH.M
0(1.0 1
,236
,005 2779
5350
7 35 S3.45
10-53
.28(1
.031 s^><)
jiljt;
il.) "Kl ll], M)
.237
.005 8135
5354
7 .17 43-93
10,4.1
.287
,0.!.! OJ.U
SlVl
;o 07 so.o'i
05.83
,238
.006 3487
.006 8834
5349
5345
7 39 34-32
10,34
10,25
.'289
032 S,!6O
033 048s
W
S'l <) 3S.85
jw 11 -M.S.I
05-74
5.65
1.240
.241
.007 4177
.007 9515
,oo 4840
.009 0178
5340
5,136'
533 1
5327
7 45 04.93
7 4" S4-W
10.15
IO.OO
09.97
og.KK
.291
. 292
.293
033 MIO;;
.034 07^0
034 5831
035 0038
S1I3
5104
*> 13 07.15
y "4 SIM*)
<> in 38.08
OS.56'
05.47
05.38
OS. )
.&I4
009 5503
5323
7 50 34.60
09,78
.294
,035 <4O
5100
w jo OB!<X
I.AI5
.246
-oio 0823
,010 6139
5318
5313
7 52 2.1.43
754 14-07
09,69
09,60
1.295
.0.16 1138
.036 <iJ3i
32?
!w li 3^87
05.11
05.02
,2. 17
.248
.249
-on 1450
.on 6756
.012 2058
5309
5304
5300
7 56 03. (u
7 57 53- o
7 59 4 -'-41
09.50
09.41
00-33
.297
037 13^0
.(M7 CMOS
.038 1485
5087
5083
5078
y ^s 23. ai
U -7 "8-7-i
04.03
04.83
04.74
1,250
.012 7356
S29S
8 01 31.72
09.23
'300
.038 656 i
5074
30 3*i'2l
04.65
u
, M -v>-
800 ll 11
tortrtr*
*.
u
,-.(..)-;
ODOll II
lnir'(o)"flo u
Booh u
SMITHSONIAN TABLEB ' ' ' ' " "
288
The Guclc rmnnnian.
u
ud n
. W
Uil II
. w
11
ntlii
-IV
0(1 U
-W
1.300
-3"!
i ,038 6561
030 1033
ss
1 II
59 30 38.21
104.65
1-350
351
1-063 4837
.063 9694
4858
4854
60 55 59-27
60 57 39-43
n
100.21
100. 12
.30.!
.303
.304
.040 17(13
,(|l) I'M..!.!
il
59 34 07,34
59 35 51-77
59 37 30. 10
KM, 47
104.38
352
-353
354
064 4546
064 9393
.005 4.137
4850
4846
4841
60 59 19,51
61 ob 59.50
6l 02 39.41
IO0.03
99-95
99.86
1.305
1.041 1876
505.;
5U 30 a>. 35
104.2!)
1-355
1,065 0076
4837
61 04 19.22
99-77
..* .u
,i>4. lo/i
,'io.|3
50 41 04.51
59 4248.58
104. i i
-356
357
.066 3911
.066 8742
4833
4829
6 i 05 58.05
6 I 07 38.59
99.69
99.6o
. 31 lo
.04.! 701;!
5039
50 4-| 3-3.50
"03.03
.358
.067 3568
4824
fir 09 iB.is
9!)- 51
309
.o.|,] 2049
S035
59 <|0 16.45
103.84
359
.067 8390
4820
61 10 57.61
09-42
I.3IO
I ,013 7081
50,10
S9 48 00.25
103.76
1.360
1.068 3209
4816
61 12 36.99
99-34
..HI
,O.|4 -M0<)
5O.!()
59 49 43-<jO
103.07
,361
.068 8022
48:2
61 14 16.29
99-25
.31 J
.(Ml 7133
S*>.ii
59 SI 27.58
103,58
.362
,o(x) 2832
4808
61 15 55-49
09-l6
.31.1
.(MS isiSJ
5017
59 53 IT."
103-49
363
.060 7637
4803
61 17 34-61
OO.oS
.314
.015 7"'7
5013
59 54 54.55
103.40
.364
.070 2439
4799
Gi 19 13.64
98-99
!ai<>
1.04(1 .1178
.040 7184
;S!S
59 56' 37.91
59 58 21.17
103.31
103.22
1.365
366
1.070 7236
.071 2028
4795
4791
6 i 20 52.59
6l 22 31-45
08.90
98.82
.317
.(47 iiiKo
JiOOO
Oo oo o.|-34
103.13
.367
.071 6817
4786
6l 24' 10.22
98.73
.318
,(M7 7i8l
4 ( )95
OD oi 47,43
103.04
.368
.072 1601
4782
6 i 25 48.90
98.64
,310
,(j[H ,1177
4<f)l
Oo 03 30.42
102-95
-309
,072 6382
4778
61 27 27.50
98.56
1.3.:"
1,0 18 7idT>
.1987
00 05 13-33
102.86
1.370
1.073 "58
4774
6 i 29 06. oi
98.47
.3-1
,0.|<) :!l,'il
4983
Oo <x> 50.14
102.77
371
.073 5929
4770
61 3044.44
98.38
.3-!.!
.041) 7131
. [078
(k) 08 38.87
ioj.08
372
.074 0097
61 32 22.78
98.30
.3-M
,o;io ,MO?
I 1 '74
(XI 10 2(,S1
1 0.2. 59
373
-074 5460
4?6i
61 34 01.03
98.21
.3-'!
.050 7079
I97O
(>o ra 04.06
102,50
374
.075 0220
4757
61 35 39.20
98,12
I.3-!'i
1.051 -HMO'
l</>5
fx) 13 40.52
10.!., |2
1.375
1.075 '1975
4753
6l 37 17.28
98.04
.3"*'
.O-il /OIK)
4961
60 15 j,S.S*j
KU.33
370
.075 9725
4749
6 i 38 55-27
97-95
. ,17
.(i, 1 !.! igdM
1957
do 17 i i. 17
102.2.1
377
.076 4472
4M5
61 40 33-i8
97.86
.3.:8
,o<i,! (H>J.I
405 !
(>0 18 5,1-37
IOJ. IS
378
.076 9215
4740
61 42 ii.oo
97.78
.3~ l >
.0<i3 1873
49|8
(x) jo 35-17
loa.oti
379
.077 3953
4-736
Gi 43 48.73
07.69
1.3.10
1 .OS3 '"819
4911
(b 22 17,49
101.97
1.380
I .077 8687
4732
6l 45 26.38
97-6i
.3.11
.054 1700
4939
(HI 23 59.4.1
101.88
iHl
.078 3417
4728
61 47 03-94
97-52
-33-!
.054 (rfxjH
4U35
(N) .15 41,^5
101.79
.382
.078 8143
4724
61 48 41.42
97-43
33,1
OSS id.H
4931
do .'.'/ J3.00
101.71
.383
.079 2805
4720
61 50 18.81
97-35
-331
O;>fi djjft;
-19-7
do J 04.07
101.62
.384
.079 7582
4715
61 51 56.12
97-26
1.335
i .050 i,-|K|
,,<,,;!
no 30 46.24
IOI.53
1.385
I .080 2295
47"
Oi 53 33-34
97-18
.330
,050 0404
1918
Oo 32 27, 73
101,44
.386
.080 7005
4707
(il 55 M7
97-09
.337
.057 'iU'O
,jf)l,|
(k) 3-1 00,12
101.35
.387
.081 1710
4703
61 5647-52
97-01
.338
O.S7 '^31
.|i;ou
(> 35 50-13
101.20
.388
,081 6411
4609
61 58 24,48
96.92
.339
.058 n ,jy
I'jos
OS) 37 3i-<>5
101.18
.380
.082 1107
4^95
62 oo 01.36
96.83
K3-IO
1.058 (xx | a
4'XH
(b 39 [3.78
101.09
1.390
1,083 5800
4691
62 oi 38.15
96.75.
',11'
.<KiU OU.|O
4897
Oo 40 53.83
IOI.OO
.391
.083 0488
4686
62 03 14.86
96.66
.31-
.|8()2
60 42 34.78
100,91
.392
.083 5173
4682
62 a; 51.48
96.58
.3-13
,000 07.35
4888
do 44 iS.^S
100.82
393
.083 9853
4678
62 06 28.01
96.49
,000 SOl'l
4HH |
00 45 56.43
100.7-1
.3W
,084 4529
4674
62 08 04.46
96.41
1. 3-1 5
1,061 O.|93
4880
db 47 37. 12
100.65
1.395
1 .084 9201
4670
62 09 40.83
96.32
,odi 5370
-1875
00 49 17.73
100.56
.085 3868
4666
62 ir 17.11
96.24
.3-17
Oo 50 58.24
roo.47
-307
.085 8532
4662
62 12 53.30
96.15
,318
.3-19
tQOrf Jjy//
S
Oo 52 38.07
60 5-1 I9.0I
100.38
100.30
.398
.399
.086 3192
.086 78.17
'1657
4653
62 Id 29.41
62 16 05,44
96.07
95.98
1.350
T fi/ii ,iHi*7
i lUV'J *|"J/
.1858
60 55 50.27
100,31
1,100
1.087 2 498
4649
62 17 41.37
95.90
W
ttaHW-J
w sootl II
*-.<,)-*
w eooh u
u
2 tarr'(o)-g
wsoohu
ItaTH^p
wseoliu
TAB (.KB
289
The Gudermannian.
u
gel u
-w
gd u
-w
II
ad u
.w
ail u
<-Fo'
:.4oo
1.087 2498
4649
I II
62 17 41.37
95.90
1.450
1.109 9869
4447
1 II
63 35 51.24
91.72
.401
.087 7145
4645
62 19 17.23
95.81
-451
.no 4314
4443
63 37 22.92
91 .64
.402
.088 1788
4641
62 20 53.00
95-73
452
-no 8755
4439
63 38 54-52
91.56
.403
.088 6427
4637
62 22 28.68
95.64
-453
,m 3192
443S
63 40 26.03
91-47
,404
.089 IO02
4633
62 24 04,28
95.56
454
.IN 7624
4431
63 41 57.46
91.39
1.405
1.089 5693
4629
62 25 39,80
95-47
1.455
I.JI2 2053
4427
63 43 28.82
91.31
.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 oSw
44 19
63 46 31.27
9I-I5
.408
.090 9561
4616
62 30 25.84
95-22
458
.113 5316
4415
63 48 02.38
91.07
.409
.091 4175
4612
62 33 01.02
95. 14
.459
.113 97-29
4411
63 49 33-40
90.98
1.410
I.09I 8785
4608
62 33 36.11
95.05
1.460
1.114 4138
4407
63 51 04.35
90.90
.411
.092 3391
4604
62 35 n.ia
94-97
.461
.114 8543
4403
63 52 35-21
90.82
.412
.092 7993
4600
62 36 46.04
94-88
.462
.115 294-1
4399
63 54 05-99
90.74
.413
.093 2591
4596
62 38 20.88
94.80
.463
.115 734i
4395
63 55 36.68
90.66
.414
.093 7185
4592
62 39 55.64
94-71
.464
.116 1734
1391
63 57 07.30
90.58
1.415
1.094 1775
4588
62 41 30.31
94.63
1.465
1,116 6124
4387
63 58 37-83
90.49
.416
.094 6361
4584
62 43 04.90
94-55
.466
H7 0509
4383
64 oo 08.29
90.41
.417
.095 0942
4580
62 44 39.40
94-46
.467
.117 4890
4379
64 oi 38.66
90.33
.418
.095 5520
4576
62 46 13.82
94.38
.468
.117 9268
4375
64 03 08.95
90.25
.419
.096 0004
4571
62 47 48.16
94-29
.469
.118 3641
4372
64 04 39.16
90.17
1.420
1.096 4663
4567
62 49 22.41
94.21
1.470
1.118 Son
4368
64 06 09.29
90.09
.421
.096 9228
4563
62 50 56.58
94- 13
.471
.119 2377
'1364
04 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 B347
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 09.0O
89.76
1.425
1.098 7449
4547
62 57 12.41
93-79
1.475
I . I2O 0800
4348
64 13 38.72
89.68
.426
.099 *994
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 lf> 37.93
89-52
.428
.IOO 1073
4535
63 oi 53-41
93-54
.408
. 122 2826
4336
64 18 07.41
89.44
429
.loo 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.I3
89.28
.431
.101 4659
4523
63 06 33.66
93-29
.481
. 123 5818
4325
64. 22 35-37
89.20
.432
.roi 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
43^7
C>4 25 33.6i
80.0.1
.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
92.06
1.485
I. 125 3085
4309
64 28 31.^3
88.88
.436
,103 7223
4503
63 14 ig.oS
92.38
.486
.125 7392
4305
64 30 00.37
88.80
.437
.104 1724-
4499
63 is 51.91
92.79
,.487
,126 1695
4301
64 31 29.13
88.72
438
. 104 6221
4495
63 17 24-66
92.71
.488
. 126 59IJ4
4297
64 33 57-81
88.64
439
.105 0714
449 1
63 18 57-33
92.63
.489
.127 0289
4293
64 34 26.41
88.56
1.440
r. I 05 5202
4487
63 20 29.92
92.54
1.490
1,127 4581
4290
f>4 35 54-93
88.48
.441
.105 0687
4483
63 22 O2.42
92.46
.491
. 127 8869
4286
<M 37 23.37
88.40
.442.
.106 4168
4479
63 23 34.84
92.38
.492
. 128 3^52
4282
CM 38 51.72
88.32
443
. 106 8644
4475
63 25 07.18
92-30
493
. 128 7432
4278
64. 40 20.00
88 .'24
'444
.107 3117
4471
63 26 39-44
92.21
.494
4 129 I708
4274
64 41 48,20
88.16
1.445
i. 107 7586
4467
63 28 II. 6l
92.13
1.495
I . 129 SgBO
4270
64 43 16,32
88.08
.446
. i 08 2050
4463
63 29 43.70
92.05
.496
,130 0249
4366
64 44 44-36
88.00
447
.108 6511
4459
63 31 15.71
9L97
497
- 130 4513
4263
64 46 12.32
87.92
.448
,:o9 0968
4455
63 32 47.63
91.88
.498
. 130 8774
4259
64 47 40.20
87. 84
449
.109 5421
4451
63 34 I9.4S
91.80
,499
.131 3031
4255
64 49 08.01
87.76
1.450
i. 109 9869
4447
63 35 51.24
91.72
1.500
1.131 7283
4251
64 50 35-73
87-68
u
Tf
u sech u
2 fan- ! (e)-90
"SGOll U
u
2 Ian~ 1 (o 1 ')~
z
usoahu
2tan-V)-90
wSQCllll'
SMITHSONIAN TABLES
29O
The Gudcrmannian.
II
oil u
-p.-
Uil 11
-W
11
ml u
.H
Oil II
Fo'
1 .500
1. 1 .11 7-'3
'351
6-1 50 35.73
87'.'68
r-550
] . 152 5078
4062
/ II
06 02 01.81
83*78
,'iOl
. 13,1 153.;
' - ! 47
.'I'i]
. 1 '* OI f l<\
ytncrt
'\(\ r 1 "> c c c
Rt Tt
.5".!
.i.l.i 5778
. -M3
04 S3 30.03
87.52
552
* ' J>*- v 1 .);/
-153 3195
'I 1 -'.) 11
4055
"' o o -.13
66 04 49.22
"0 / '
83.63
.5<i3
. 133 omo
' .'30
d-l 54 58. 42
87.44'
-553
- 153 7248
4051
66 06 12.81
83.55
. 5o.|
.1.1.1 4-!S7
-130
04 50 -'5-8J
87.37
554
-154 1297
4047
66 07 36.33
83.48
1.505
1 .133 8.|ix>
. 2.12
64 57 53-15
87.29
1-555
1.IS4 5342
4043
66 08 59-77
83.40
-5od
. l,l.| .!7-!O
. .!~'8
d-l 50 .10.40
87. j i
-550
.'54 938-1
4040
66 io 23.14.
83.33
.507
.134 Oo-|d
. -!J.|
(>5 oil 47.50
87-1,1
557
-155 3421
4036
66 II 40.42
83.25
.508
. 135 1 id8
. ,!.!<>
dS 02 14.05
87.05
558
.155 7450
)6 13 09.63
83.17
. 509
.1.15 W87
..Md
05 03 -li.(>d
86.97
.'559
.156 1486
4029
66 14 3-2.77
83.10
i . 5 io
i .135 'X*oi
- 213
OS 05 08.50
86.89
r . 560
I.I56 55T3
4025
66 15 55.83
83.02
.511
.13(r 381 J
"OO
05 Od 35-44
80.81
-561
- i S6 9536
4021
06 17 18.81
82,95
.512
. 13(1 Hoio
. .!(>5
d5 08 02,2.!
86.73
-56.:
-'57 3556
40L8
66 18 41.72
82.87
5M
.1,17 .!.!,!.!
. 201
(iS oo L'8.01
80. dO
.563
157 757T
4014
66 20 04.55
82.79
-5'4
.137 <MJi
4 '97
65 io 55-53
86,58
-50-1.
.158 1583
4OK)
06 21 27.31
82,72
i. Sis
I, 138 0617
4194
65 ia 22.07
86.50
1.565
1-158 5592
4007
if) 22 49.99
82.64
,''ild
,138 4808
41911
0, ! i 13 48.52
8(1 . i\ j
.566
.158 9597
4003
60 24. 12.59
82.57
.517
.138 8006
4 186
d;; 15 14,01
86-34
-SO?
. '59 3598
3000
00 25 35.12
82.49
Jit 8
. 130 3180
418.!
(5 Id 41.-.JI
Wi.-jfi
-508
-159 7595
>6 26 57-57
82.42
.519
139 7360
4178
(iS 18 07-43
86. 18
.569
.160 1589
3993
66 28 19-95
82.34
1.520
I . I4*> 1-537
4175
65 I93.1.S8
86.ii
I.57<>
l.Tfio 5570
3988
66 29 42.25
82.26
.5.M
. 140 5709
4171
('5 20 So.d.j
80.03
-571
. 160 9566
3985
16 31 04,48
82.19
. 5-!.!
. 140 1)878
41(17
OS -!.! 25.03
85-95
57-!
idl 3548
(if) 32 26.63
82.11
.5.13
. 141 40-13
4'd3
(15 23 51 .54
85.87
573
. 161 7527
3977
(if) 33 48.7t
82,04
.5-'-!
.141 MJOS
4159
05 25 17.38
85-71)
574
.102 ISO.')
3974
66 35 10.71
81.96
I-5-!S
t . 14.! ,:.id,!
4156
65 3ft 43.1.1
8^.72
T-575
1.162 5475
3970
'i6 36 32.63
81.89
.;;.:()
. 14.; 0516
4 1 fW
dS ,18 08. 8 1
8s- <M
.570
. 162 9443
66 37 54-48
81.81
,;j,!7
, |,|3 (Xidd
4148
o.'i .:o ;i-|..|i
85.50
-577
.163 3408
3*X>3
66 39 16.26
81.74
5 .;8
.1-1.1 4812
4 '44
(15 30 50,03
8^.48
'63 7369
3050
06 40 37.96
81.66
.529
14.1 8954
.11-11
d5 il-i 25.37
85.4<>
579
.164 1326
3955
06 41 59-58
81.59
i . 53d
1.1-14 309.1
4137
65 .13 50-74
85-33
l . 580
1 . 164. 5279
3952
66 43 21.13
81.51
531
4133
OS 35 id.OJ
85.2S
-581
. I0..|, 9230
39-18
(>6 44 42.61
81.44
.".|.'i M.'iO
,|l.it)
d;; 30 41 ..!,i
85.17
5KJ
.165 3170
3945
60 4(1 04.01
81.36
. 53.1
.1.15 5480
4 l ;!5
os 38 06.37
85. oo
.583
.165 7119
3941
66 47 25.33
81.29
534
OS 39 31.42
85.02
.I(X) 1058
3937
66 48 46.58
81.21
1-535
l.Md 37.10
4118
djl 40 56,40
81.04
I.5H5
I , if/i 491,13
3034
66 50 07.76
81.14
.530
.14(1 78-|0
4 ' '4
d;; /).! 21.30
8-1 !80
.58(1
, i(Xi fy5
3930
66 51 28.86
81.06
537
.147 LO.SH
,| 1 10
(15 4,1 40. u
81.78
-!i^7
. 167 2854.
' 39~0
66 52 49.89
80.99
.538
.1-17 (10(17
4107
OS 45 "".87
8|.7I
.588
.167 677.^
3923
66 54 10.84
80.92
.148 OI7-!
4103
d5 4d 35-54
84.63
.589
. 168 0699
3919
66 55 31.72
80. 84
I . fi-IO
t.i,]8 4:173
4009
('15 48 oo. 13
8.1-55
1.500
1.168 4617
39l6
66 56 52.52
8o,77
54'
.1488370
4095
d<j At) y4,04
84,48
501
.1688531
39'2
(16 58 13-25
80. 69
409 j
dS 50 4O,ot J
84., 10
.'592
.160 2441
3908
(if) 50 ,13.9*
80.62
51.1
. 14') d!;<;[
.|< 188
lt5 ."W "3-41
8 1 . '12
593
. !(> 6348
3905
67 oo 5-1-49
80.54
544
.150 0(140
408 1
84.25
594
.170 0251
3001
67 02 15.00
80.47
1.545
1.150 ,|7.!ii
4081
65 '55 01.93
KM?
1.595
I.I70 4150
3898
67 03 35-43
80.40
54 (l
, ijiu 880 r
4077
OS 56 ^d.o(
84.09
,5<jd
.170 8(146
3804
0? 04 55-79
80.32
- 547
407,1
4009
OS 57 5". 1 1
84,01
8.1-91
.507
.171 1938
.171 58^7
3891
3887
(17 06 16,07
67 07 36-28
80.25
80.17
'.<i4<>
. ijiJ 1015
.food
df'i 00 37-"^
83.8(1
.509
.171 9712
3883
67 oS 56,42
80.10
1.55"
1-I5-! K'>78
.,,*,.
66 ( 01.81
83.78
i.Ooo
t.172 3594
3880
67 io 16.48
80.03
II
U.-W-J
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2lnn"'(o)-00
'OBOOllll
u
]
i
usooliu
2lnn~'Cc")-00
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The Guilci nmnnian.
i . 600
.6o,i
.60.]
1.605
.607
.fioS
.tox)
.<b;i
Xi<>
Aw
!rt!n
\(t.\,\
ad n
o.|/N
,187 UJl;
7". IS
100
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(Jtl U
;;;;.<>
-1"
('7 .|<) -l-l. .U
(17 ;>i o.:. 1,1
<jf{ 15 ^>.'/(i
m- Ho") Off 1
7 7- "I
77.77
77.'")
77 5,'i
77-lH
76. '
I.d.'iO
.(CM
.t&U
I.'XJCt
.^>S
-6j-j
,700
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. iDi <My.'.
, }>-'. '<><'
i . Hi. 1 ; im i-'
.i'j|i .1710
.i<>.'; 7.t7.^
, HX' 10.17
. H/i .!'":!
v'(VJ ,il,|;
m- '()- !
M -I'l '"J..'i;l
,i"l,M'' ; 1'f '!-'"<
.(Uo 1 '^ ;;' .(., >;7
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'*) UP ,|o.,|.'i
'" 1*7 !'.{.</>i
<*> III ,,'H.f?il
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mi Vi| (B ; 'l UCf'
7,1-.!*'
7.1- '.I
7.1 -'>7
7,j.ixi
10(1 11 11
BMITHBONIAN TAMUEB
The Gudcrmaniiian,
(1
ad ti
-w
ailu
wFo'
U
ad u
. w
ad u
- W
i.Too
.209 4143
3536
X) 17 39.60
72.93
1.750
.226 6847
3374
1 II
o 17 01.89
6o-59
.70'
.j(>9 7677
3533
9 18 52.50
72.86
751
.227 0219
3370
o 18 11.44
69.52
.70.!
.210 UOS
35"'<)
9 2O 05.32
72-79
752
.22? 3588
3367
o 19 20.93
69.45
.70.1
.210 4735
3S2(i
X) 21 18,08
72.72
753
.22? 6954
3364
20 30.35
69-39
-704
,;:io Husy
1'i"2
X> 22 30.77
72,66
754
.228 O3l6
2361
21 39.71
69.32
1. 70S
.211 1780
MI9
9 23 43.39
72.59
1-755
.228 3676
3358
TO 22 40 -OO
69.26
.?o<t
,21 I 5_!i>7
35i6
> 24 55.95
7.1.52
-756
,228 7032
3355
70 23 '58.23
69.19
.707
.ail 881.1
35 13
MJ 26 (l8.43
72-45
757
.229 0385
3351
o 25 07.30
69,13
.708
.212 2.V3
35<tO
*) 87 at). 85
72.38
-758
-229 3735
3348
o 26 16.48
69.06
709
.212 5830
3-506
it) 28 33.20
72.32
-759
.229 7082
3345
o 27 25,51
69.00
1,710
1.212 9335
3503
9 29 45-49
72.25
1.760
1.2300425
3343
70 28 34.48
68.93
.711
.,313 2830
3-199
>9 30 57-70
72.18
.761
.230 3765
3339
70 29 43.38
68.87
.713
.213 6334
34<X>
H) 32 09.85
72.11
.762
.230 7103
3336
70 30 52.22
68.80
.713
.21,1 ( >828
3493
> 33 21 .93
72.05
.763
-231 0437
3333
70 32 c,09
68.74
M 1 'I'HO
3490
y 34 33-9-1
71-98
.764
.231 3768
3329
70 33 09.69
68.67
r.7'5
1,214 6807
(> 35 45 -80
71-91
1.765
1.231 7096
3326
70 34 18.33
68.61
.716
.315 0293
343
xj 36 57.76
71.84
.766'
,232 0420
3323
70 35 26.91
68.54
-7i7
-J15 3774
348o
X) 38 09.57
71-78
.767
.232 3742
3320
70 36 35-42
68.48
.215 7.)i)2
3-177
)9 30 21.32
71.71
.768
,232 7060
3317
70 37 43.87
68.42
'719
.216 0737
3473
W 40 32.99
.X>9
-233 0376
3314
70 38 52.25
68-35
1,720
1,216 4198
3470
k> 41 44.60
71.58
1.770
1.233 3688
33"
70 40 00.57
68.29
,7-Ji
,,iid 7<rf>7
3-107
K> 43 56.14
71-51
.771
-233 6997
,130?
70 41 08,83
68.22
. ;!I7 i I3J
X) 44 07, (u
71.44
.772
-234 0303
3304
70 42 17.02
68.16
- 7-'3
.217 459-1
3460
69 45 10.02
71-37
-773
,234 3606
330 1
?o 43 25.14
68.09
7J-I
.217 H053
3-I57
19 -|6 30-37
7L3I
.774
.234 6905
3298
70 44 33,20
68.03
i.7J!i
l ..118 1508
345-1
(^ 47 41-64
71-23
1.775
I.23S 0202
3295
70 45 41-20
6?-o5
,7i!()
. ,!iH 49(10
3151
(MJ 48 52.85
71.16
.?7(>
-235 3495
3292
70 4649-13
67.90
'7J8
..!T8 RlOf)
3417
3-144
(x.) So 03-99
71.10
71.03
777
-778
.235 6786
,236 0073
3289
3286
70 47 57-00
70 49 04-80
67.84
67.77
.720
iai9 5207
6y 52 26. of
70.96
-779
.236 3357
3283
70 50 12,54
67.71
1-73"
i. an) 8737
.a jo 2173
3434
(HJ 53 37. <K
('*) 54 47-88
70.90
70-8,'
1.780
.781
1.236 6638
.236 9916
3279
3276
70 51 20.22
70 52 27.8;
67.64
67-58
-73.2
34,'U
(19 55 5H.6H
70. ?<
.782
-237 3101
3273
70 53 35-38
67-52
733
-7,14
.220 003,1
6<) 37 09-4?
(X.J 58 -to. 10
70.70
70,03
.783
.7&I
.237 6463
-237 9731
3270
3267
70 54 42.87
70 55 50.29
67-45
67-39
l 735
7.V
<w i*
1.221 5885
,231 0304
giy ;|7,il
3432
69 59 ,10-71
70 Od 41 -2b
70 oi 51-73
70 03 02.13
70.56
70.50
70-43
70-37
1.785
.yst
.787
.788
1,238 2997
.238 6259
-238 9519
-239 2775
3264
3261
3258
3255
70 56 57.65
70 58 04-9-1
70 59 12.17
71 oo 19.34
67.33
67.26
67.20
67-13
-739
la-JJ S>54J
3'ioy
70 04 13.47
70.30
.789
.239 6028
3252
71 oi 26.44
67.07
^741
.7-1 a
.7-1.1
74-
1.223 2052
-JJ3 635(
.^3 9757
.334 3'*
.22,| 0548
33'X:
33X
33<J3
70 05 22.75
70 06 32. Of
70 07 43. If
70 OK 53-'*
70 10 03.19
70.2;
70. Ti
70.11
70.0S
00,9
1.790
.791
.792
.793
.79-
1-239 9279
.240 2526
.240 5770
.240 oon
,241 2249
3249
3246
3243
3239
3236
71 02 33. 4f
71 03 40.46
71 04 47-37
71 05 54-22
71 07 01.01
67.01
66,94
66.88
66.82'
66.76
I-7*I5
7-K
.7-17
7-iH
.749
1 .334 004C
.225 6712
,2J6 009.
331X
1lH*
1 'iKf
3377
70 n 13.1*
70 12 83-02
70 13 32. &
70 M 42-59
70 IS 53.37
69-01
to.85
69.78
69.72
69.65
1.795
.796
-797
.798
.799
i. -24 1 5483
.241 8715
,342 194-
.242 5170
,242 8392
3233
3230
3227
322;
322
n 08 07.73
71 09 14-39
71 10 20.99
71 n 27.52
71 ia 33-99
66.69
66.63
66.57
66.50
66.44
1-750
1,3*66347
337'
70 1701.89
69.59
1.800
1.243 1612
3218
71 13 40.40
66.38
u
itochi
2 ,n-,,,-00.
wJOCll
u
ZlnrrKfl")-
usealiu
Zta-'tt-HW
ugeohu
BMITH80NIAN TANLKS
293
The Glide rmannian.
II
ad u
..v
flil u
wfi/
U
ad u
.
a (In
w
O 1 fl
a
' II
ft
i.Soo
1.243' 161
3218
71 13 40.40
66.38
1.850
1.258 8750
306*
72 07 41-78
63.30
.80
.243 482
321
71 14 46.7
66.3
.85
.210 [K2f
3o6C
72 08 45.0,
63.24
.80
321
71 is 53.03
66.25
.852
.259 4890
3063
72 09 48. 2f
63.18
.80
.244 125
3209
71 16 59.25
66. i<
85;
.259 7952
30(x
72 10 51.4
63.12
.8a
.244 4460
3206
71 18 05.4
66.13
8s
.260 101
3057
72 II 54-50
63.06
i. So.
1.244 766
320,
71 19 11.50
66.06
1.855
1.260 4o6f
305--
72 12 57-53
63.00
.806
.345 086
3200
7! 20 17.53
66.00
.856
.260 7119
3051
72 14 00.50
62.94
.807
.245 4064
3197
71 21 23.50
65-9;
.857
.261 oifx.
3048
72 IS 03,41
62.88
.808
.245 7259
3194
71 22 29.41
65.88
.858
.261 32 1(
30.1C
72 16 06. 2f
62.82
,809
.246 045
319
71 23 35.26
65.81
.859
,261 6260
3043
72 17 09.05
62,76
1.810
1.246 3640
3188
71 24 4I.O-
65.75
1, 860
1.261 9302
30.-IO
72 18 11.78
62.70
.811
.246 0827
3185
71 25 46.76
65.69
.86 r
.262 234(
3037
72 19 14-45
62.64
.812
.247 oon
3182
77 26 53.42
65-63
.862
.262 537^
3034
72 20 I?. Of
62.58
.813
.247 3190
3179
71 27 58.01
65.56
.863
.262 840*
3031
72 21 I9.6l
62.52
.814
.247 6367
3176
71 29 03.54
65.50
.86.
.263 1438
3028
72 2J 22.10
62.46
r.Srs
1.247 9541
3*73
71 ,30 09.02
65.44
i .8ft
1.263 446.1
3025
73 33 24.54
62.40
.816
.248 2712
3170
71 31 14.42
65-38
.866
.263 7488
3022
72 24 26. yi
62.3;
.817
.248 3880
3167
71 32 19-77
65.32
.867
.264 0509
3020
72 25 29,2;
62. 2fr
.818
.248 904f
3164
71 33 25.06
65.25
.868
-264 3527
3017
72 26 31.47
62.22
.819
.249 2208
3161
71 34 30. 28
65,19
.869
.264 6543
3014
72 27 33-67
62.16
1.820
1.249 5367
3158
71 35 35-44
65.13
1.870
1.264 9555
3011
72 28 35-80
62 . 1 1
.821
. 249 8523
3J55
71 36 40-54
65.07
.871
.265 2565
3008
72 29 37.88
62.05
.832
.250 1676
3152
71 3745.58
65.01
.872
.265 5571
3005
72 30 39-90
61.99
.823
.250 4826
3M9
71 38 50.56
64.95
.873
.265 8575
3003
72 31 41.85
61.93
.824
.250 7973
3146
71 39 55-47
64.88
.874
.266 1576
2990
72 32 43-75
61.87
I.S25
1.251 inf
3T43
71 41 00.32
64.82
1.875
1.2664574
2907
72 33 45-59
6i.8r
.826
2Sr 4259
3MO
71 42 05.11
64.76
.876
.266 75(19
2904
72 34 47-37
61.75
.827
.251 7397
3137
71 43 09,84
64.. 70
.877
.267 0562
2001
72 35 49.09
6l.(K)
.828
.252 0532
3134
71 44 14.51
64.64
,878
267 3551
2088
72 36 50.75
6 1 .63
.829
.252 3664
3"3i
71 45 19. 12
64.58
.879
.267 6538
2)85
72 37 52.36
61-57
I.83Q
i . 252 6794
3128
71 46 23.67
64 . 52
I.88o
1.267 952f
2082
7-2 38 53.90
61,52
.831
.252 9920
3125
71 47 28.15
64.45
.881
.208 250.*
2980
72 3<J 55-39
61.46
.832
253 30-13
3 C22
71 48 32.57
64.39
.882
.208 5480
2<J77
72 40 5(1.82
61.40
33
253 6164
3 1 TO
7" 49 36.94
f'4-33
.883
.268 8456
2974
72 41 58.19
61.34
.834
.253 9281
3H6
71 50 41.24
64.27
.884
.269 1.128
2971
72 42 S9-50
61.28
1-835
1.254 2396
3113
71 51 45.48
64 . 21
1.885
1,269 4308
2968
72 44 00.75
61.22
.836
-254 5507
3110
71 52 49. 06
64.15
.886
.269 7364
2965
72 <|S 01.94
61.16
.837
.254 8616
3107
71 53 53-77
64.09
.887
.270 0328
2962
72 46 03.08
6i.ii
.838
.255 1721
3104
71 54 57.83
64-03
.8R8
.270 3289
2960
7247 04.15
61.05
.839
,255 ,3824
3101
71 56 01.83
U3-97
.889
.270 6248
2957
7-i 48 05,17
60. yy
1,840
r.2-55 7923
3098
7i 57 05.76
63.91
1.890
1.270 9203
2QS4
72 49 06.13
60.93
.841
.256 1020
3095
71 58 09.64
63,84
.KOI
.271 2150
2951
72 50 07.03
60.87
.8-12
.256 4114
3092
71 59 13-45
63.78
.892
.271 5106
2948
72 51 07.88
60.81
843
.256 7205
3089
72 DO 17.21
63.72
fy>i
.271 8053
2946
72 52 08.66
60,76
844
.257 0293
3086
72 oi 20. go
63.66
.894
.272 0997
29-13
72 53 09-39
60,70
i.B-15
.257 3378
3084
72 02 2.-I.53
63.60
1,895
.272 3938
2940
7,2 54 to, 06
60.64
.846
.257 6460
3081
72 03 28.10
63.54
.272 6877
2937
2 55 10.67
60.58
.847
.&$
.849
.257 9539
.258 2615
.258 5688
3078
3075
3072
72 04 31.61
72 05 35.06
72 06 38.45
63.48
63.42
63.36
*97
.898
.899
.272 9812
-273 274 S
273 5675
2934
2932
2929
2 56 11.23
2 57 11.72
a 58 is, 16
60.52
60.47
60,41
1.850
.258 8?59
3069
2 O? 4L78
63.30
I.90O
.273 8603
2926
2 59 13.54
60.35
u
li-W-J
aeoii u
tair- ] e>-M
"""
u
^(,.,-i
SOON II
,-,,,-
uaocliu
SMITHSONIAN TABLES
294
The Glide rmannian.
11
oil u
.*
ad
.
u
ad u
.
Oil 11
-w
1 ,<XK)
I.. 73 K>3
-HWli
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n 59 12-54
60.35
' -950
.288 1451
2789
i //
3 48 19.01
n
57-53
,901
74 15-7
:;(].!,)
7,1 oo u.iSd
00. ^9
951
.288 4239
2786
3 49 16.51
57-47
-9".!
.-'74 4I!<>
:!().:<}
73 01 13.13
(k).24
-952
.288 7024
2784
3 50 13.95
57.42
MM
7-1 73* K
,!')lH
73 o.i 13.33
60.18
953
.288 9806
2781
3 Si 11.34
57.36
904
.-75 0.184
-1)15
73 03 13.48
oo. la
-954
.289 2586
2778
3 52 08.68
57-31
i.x>5
.-75 3'97
2.)!.!
73 o.| 13.58
60.06
t-955
.289 5363
2776
73 53 05.06
57.25
,<XX>
,-7;i Oio8
2909
73 05 13.61
60, 01
050
.-'8y 8137
2773
73 54 03.18
57-20
.IX>7
.-75 0116
.!IX)6
/3 oO 13.59
59-95
-957
.290 0909
2770
73 55 00.35
57-14
,<X>H
..170 IO.M
.!<XM
73 07 13.51
W.H*}
.058
.290 3678
2768
73 55 57-46
57.09
.909
.-'7< -iM.y
! ' x "
/3 oti 13-37
59.83
-959
.290 6444
2765
73 56 54-52
57-03
1 ,<)!()
[.,70 77-!-!
.!HgB
/3 ) 13.18
59-78
1.960
1.290 9208
2762
73 57 51-53
S6.o8
.<)! 1
,-77 (K)l()
'895
/3 i 12.92
59-7^
,(.X>i
.291 1969
2760
73 58 48.48
56.92
<)l '
77 3,'iM
.MM
73 1 1 i.i.i)j
59.66
(j/j-i
.-!<)! 4727
27^7
7T W /K.lS
16.87
.913
..77 0404
i:8<X>
59-61
i<X'3
.291 7483
/^v
2754
*) oy -ij.o tj
74 oo 42.22
i?u, W
56.81
-9"4
..77 <().!
,!SH7
/3 13 11-83
59-55
.<XJ4
.292 0236
2752
74 01 39-00
56.76
i.yis
r..!78 .5178
2884
73 M 11.35
59-49
i .965
1.21)2 2(j87
2749
74 02 35.73
56.70
.Old
.,178 :;o6i
ii8Hi
Ai '5 10.81
59-43
.966
292 5734
2746
74 03 32.41
56.65
.017
,.7H 7041
..'871)
/,! 10 10. 2J
50-38
.07
.292 &|Ho
2744
74 04. 29.03
56,60
.DIM
.,170 oHiH
;?H;6
/3 17 <).5<>
59.32
.968
.293 1222
2741
74 05 25.60
56.54
9'9
.-!79 3'>93
,^73
73 18 oS.Bfi
59. JO
(Xiy
.293 302
2739
74. 06 22.12
56.49
l .9.10
I..70 650;;
.;870
73 19 oH.09
59-21
1.970
1.293 6699
2736
74 07 18.58
56.43
.<).}[
.-70 9134
2H( >8
73 -H> 07.27
59-15
971
293 9434
2733
74 08 14.98
56.38
.((.!'
...'Ho .!,10O
..'Hos
73 -!l of). 39
59.09
.972
.294 2166
2731
7409 11.33
56.32
D.!3
,.:Ko 510,1
.tHf).!
73 '' O.i). 46
50.04
973
.294 .|8')S
2728
74 10 07.63
56.27
yj-i
..-Mo Ho.!.|
-'H59
73 23 04-47
58-y8
974
.294 7622
2725
74 " 03.87
56.22
1 ,0,!<i
l.:il OHH3
;!57
73 -M 03.4-'
58.92
1.975
i,2()5 0346
2723
74 12 00.06
56.16
,(j,:()
...!I 373H
-H.^l
73 as o.s.33
58.87
.976
.295 3068
2720
74 12 56.20
56.11
9-7
./HI o;;<xt
.^5'
7,1 ,!0 (11 . 10
5K.8i
977
.295 5786
2718
74 13 52.28
56.05
,;;Hl 0410
.;H.|()
73 .!<> 50.01
"18.70'
.978
.205 8503
2715
74 14 48.30
56.00
9-!9
,,:H,! iiJifa
1:846
73 27 58.67
58,70
979
.296 12l6
2712
74 IS 44.28
55-95
l.03<
i.Ai <ii3.!
;;H43
73 a8 57-34
58 6|
1.980
1.296 3927
2710
74 16 40,20
55-89
'Ml
, .'M.! 7<J74
,;H.|<]
73 -.f) 55-95
58-59
.981
,296 6636
2707
74 17 36.06
55.84
03J
,,;Hi i)Hl \
2H.(H
73 30 54-51
58, ">i
. 1)82
.296 9342
2705
74 1831.87
55.78
-033
, ,;H,l 30,|<i
-835
73 31 53-0!
58,. i7
.983
.297 2045
2702
74 19 27.63
55-73
.931
..>N.) 0,(M,!
283-!
73 32 5i|(
SH..|J
.984
.297 47-15
2699
47 20 23.34
55.68
1-93J)
i..:H3 <)3M
:;8;!9
73 33 -19.8;
58.36
1 .985
I- 297 74-13
2(io7
74 21 l8-99
55/>2
93'
.-'Hi .1141
.;H.7
73 34 '|H.uS
">H . 'i i
,oH(
.ayS 0139
2694
74 22 14.58
55-57
937
,;;H | 4<j07
.'H ' |
73 35 4'i. -|f
58.25
.987
.298 2832
2692
74 23 10.13
55-52
.93)-
.aHi 778*
28,: 1
73 3'' M'<#
58.19
.088
.298 5522
2689
74 24 05.62
55.46
930
..tH;j iXKtl)
-:Hi9
73 37 -l-i.85
58. 14
,989
,2<j8 8210
2686
74 25 01,05
55.41
I.OI
i.i'Ks 1127
aHif
73 38 40. (/
58.08
1-990
1.299 0895
2684
74 25 56-4'
55.36
'.Mil
!]HH oj.li
281-1
73 30 39.01
58.03
.299 3577
2681
742651-77
55-30
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, ,iSs <>o;v
.!8l'l
73 '|o 37-01
57-97
ty)~
.299 6257
2679
74 27 47 .0.
55.25
-"1.
,:Hif(-
73 -H 34-95
57-92
yjs
.299 8934
267?
74 28 42.27
55.20
.94-
,,:Ho 4(169
aHoS
n
73 -la 32.8
57-80
.994
.300 1609
2673
74 29 37.4,
55.14
1-01!
91*
917
9 U
94!
.,:H7 0.7*
iiiftx
73 43 30-68
73 -l-l aW-'lS
73 45 ao.l?
73 46 23.8.
73 -17 ai.^5
57-80
57-75
57 -o<
57-6-
57.58
1.99;
.997
.999
1,300 4281
.300 6951
.300 961*
.301 2282
.301 49-14
2671
2668
266C
2663
2661
74 30 32.55
74 31 27.62
74 32 22.63
74 33 17.59
74 34 12.49
55-09
55.04
54.98
54-93
54.88
1. 95*
i.iiHft M5I
a?H0
73 <|8 19-0
57-53
2.000
1.301 7003
2658
74 35 07-3'
54-83
"
.u^;
WflOQill
2 inn"'(o]- 00
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1
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SMITHSONIAN
295
The Gudormannian.
u
miu
oFo'
ad u
"IV
u
gd u
IV
ad u
<"F '
t 11
ii
a t ii
a
2.000
1.301 7603
2658
74 35 07-34
54-33
2.050
I.3I4 7349
2533
75 19 43-53
52.24
.001
.302 0260
2655
74 36 02.14
54-77
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.314 9880
2530
75 20 35-75
52.19
.002
.302 291,
2653
74 36 56.89
54-72
.052
.315 2409
2528
75 21 27.91
52.14
.003
.302 5566
2650
7437 51.58
54.67
.053
.315 4936
2525
75 22 20.03
52.09
.oa
.302 8215
2648
74 38 46.22
54.6i
.054
.315 7460
2523
75 2.1 12. CX)
52,04
2.005
1.303 0861
2645
74 39 40.8r
54.56
2.055
I.3I5 9982
2520
75 24 04. u
51-99
.oof
.303 3505
264:
74 40 35-35
54-51
.056
.316 2501
2518
75 24 56.07
51-94
.007
.303 6147
2641:
74 4 I 29,83
54.46
.057
.316 5018
2516
75 25 47.98
Sl.Sg
.008
.303 8786
2636
74 42 24.26
54.40
.058
3i6 7532
2513
75 26 39-85
51- 84
.009
.304 1422
2635
74 43 18.64
54-35
.059
.317 0044
2511
75 27 31-66
51-79
2.0IO
1,3044056
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
3 '7 Sodi
2506
75 29 15.14
51.69
.012
.304 9316
2627
74 46 01.46
54-19
.062
.317 7566
2503
75 3 06,80
51-64
.013
.,305 1042
2625
7446 55.63
54.14
,063
.318 0068
2501
75 30 58.41
51-59
,014
.305 4S66
2622
74 47 -19-74
54.09
.064
.318 2568
2499
75 31 49-98
51-54
2.015
1.305 7187
2620
744843-81
54.04
2.065
1.318 5065
2496
75 32 41-49
St. 49
.016
.305 9805
2617
74 49 37.82
53-99
.066
.318 756o
2494
75 33 32-95
51-44
.017
.306 2421
2615
74 50 31.78
53-93
.067
-3'9 0053
2401
75 34 2*1.37
51-39
.018
.306 5035
2612
74 51 25.69
53-88
.068
-319 2543
2489
75 35 15.73
51-34
.010
.306 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
I-3I9 7516
3,184
75 36 58.31
51.24
.021
.307 2860
2605
74 5407.10
53-73
.071
.319 9W9
2482
75 37 49.52
51.19
.022
.307 5464
2602
74 55 00.80
53.67
.072
.320 2480
2-179
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
.308 0663
2597
74 56 48.05
53.57
-074
.320 7433
2475
75 40 22.87
51.04
2.025
1.308 3259
2595
74 57 41-59
53-52
2.075
1.320 0007
2472
75 41 13-89
50.99
.026
.308 5853
2592
74 58 35-08
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
7S 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 3^:8
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 4<> 18.95
50.70
.032
.310 1361
2577
75 03 54-96
53-16
.082
.322 7153
2455
75 47 09.62
50.65
-033
.310 3936
2575
75 04 48.00
53-11
.083
.322 9608
2453
75 48 00.24
50,60
.034
.310 6510
2572
75 05 4:. 17
53.06
.084
-323 2059
2451
75 '18 50,82
50-55
2.035
1.310 9081
2570
75 06 34.20
53-00
2.085
1.323 4509
2448
75 4941.34
50.50
.036
.311 16.19
2567
75 07 27.18
52.05
.086
.323 6956
2446
75 5 31-82
50.45
.037
.3" 4215
2565
75 08 20.11
52.90
.087
.323 9401
2444
75 51 22.25
50.40
-.038
.3" 6779
2562
75 09 12.99
52.85
.088
.324 1843
2441
75 52 12.62
50.35
.039
3H 9340
2560
75 10 05.81
52.80
.089
,324 4283
2439
75 53 02.95
50.30
2.040
1.312 1898
2557
75 10 58.59
52-75
2.090
1,324 6721
2436
75 53 53.23
50.26
.041
312 4455
2555
75 n 5I.3I
52.70
,091
.324 9>56
2434
75 54 43.40'
50.21
.042
.312 7008
2552
75 1243.98
52.65
.092
.325 1589
2432
75 55 33.^5
50,16
043
312 9559
2550
75 13 3o.6o
52.60
.093
.325 4020
2,|29
75 56 23.78
SO.n
044
.313 2108
2547
75 14 29. 17
52-55
.094
.325 6448
2427
75 57 13.86
50,06
2.045
1.313 4^54
2545
75 IS 21.69
52-49
2.095
1.325 8874
2425
75 58 03.90
50.01
.046
.313 7198
2543
75 16 14.16
52.44
.096
,326 1297
2422
75 58 53.89
49-06
.047
-313 9739
2540
75 17 06.58
52.39
097
.326 37I
2. 1 20
75 59 43.S3
49.92
.048
.314 2278
2538
75 17 58.95
52-34
.098
.326 6137
24l8
76 00 33-72
49.87
.040
.314 4815
2535
75 18 51.27
52.29
.099
.326 8554
24 is
76 oi 23.56
49.82
2,050
I-3M 7349
2533
75 19 43-53
52.24
3.100
1 .327 0968
2413
76 02 13,36
49-77
u
tairHtfO-g
sechu
tan~ l t8)-90
" seoh u
U
2lan-'(a)-g
u sechu
Ztnn-'Ce'O-SO
wieohu
SMITHSONIAN TABLES
296
The Giidcrraamilan.
11
Ult 11
" iF "'
flll U
^'
u
ail u
-w
gtl u
- W
a. mo
1.3-7 ot/ift
a.U3
t 11
?6 02 13.36
49-77
2. ISO
1.338 8733
22OS
a J a
76 42 42-42
a
47-41
, 101
.10.!
liw 5780
J4<*
yl) 03 03 , 1 1
76 03 32,80
40.72
49.67
.IS'
.152
339 1029
-330 3325
3204-
76 43 29.81
7644 17.15
47.36
47-32
. 103
"^7 "', () '*
;?.]<)(>
7(1 04 42.4*5
40 -(>3
I S3
-339 5617
2292
7rt 45 04,44
47.27
.104
.328 (X l
240.1
70 05 32, oci
40.5
,154
339 7900
2200-
7645 51-69
47-23
3 . 105
1..1JH 3-003
-'401
76 oft a i. 6 1
40,53
2.155
1.340 01-07
2_>S?
76 46 38,89
47-T8
.ItXi
..1.& J)403
~M9U
70 07 1 1 . 1 1
49*4-8
.156
3.10 24#3
2285
76 47 26,05
47-13
.!<)/
.,t/H 78"!
J.W7
/( <xS 00.57
-10.43
.157
.3-10 4707
13283
76 48 13.16
47-09
. ii 18
.3.!') 0107
MO. |
76 08 49.98
49*39
.158
.3.10 7040
238l
76 49 00,23
47-04
.100
3- ( J -tfiJO
JJiM
76 oy 3U-34
49-34
.159
.340 9328
2278
76 49 47.2S
47-00
J, 1 [<)
1.320 ,ji)Ho
23JO
76 10 28.06
49.3*>
3,160
i 34: IC J05
2276
76 50 34-^2
46.95
,111
3--O 73<><t
2387
7(1 i i 17.0.:
40- 24
.101
-341 38i
X274
76 51 21,15
46.00
. IIJ
34> 97S5
-385
76 13 O7. l.|
49- '9
,iOi)
.341 0153
2272
76 52 08.03
46.86
. 11,1
..1,1" Ji.V)
-'3^3
yt\ u ;iO'.3i
40.IS
,163
341 843.1
227O
76 52 S4.87
46.81
.11.1
.3,11' -I. 1 ! JO
.5380
76 13 45- -13
49-10
,IC M
.342 0693
2267
76 S3 41.66
46.77
a. us
1-33" f *!*X)
~M/H
76 14 3-1.51
4'.).t>5
a.ifiS
t-342 2050
22(15
76 54 28.40
46.72
.IK)
-.13<> 9J77
3J7O
7(1 15 23.54
,|O.(M)
. 106
342 5323
2263
76" 55 IS. 10
46.68
.117
33" >5I
-M73
7() 1<> li!.J5J
4-H.llO'
.167
.34-a 745
230' 1
76 56 01.76
46.63
.liH
.,131 -IO-U
".17,1
7'' i? 01.45
48.(>I
,1-f'iR
342 <)744
2^59
76 56 48.36
46.59
. 1 19
3.1 1 0.19,1
J3'.J
70 17 311,33
48.86
. i6{>
.343 ^002
2256
76 57 34-93
46.54
j.iao
1,331 87(11
3307
76 l 39.17
4.Rr
2.170
t.343 4357
fl2S4
76 5821.45
46.50
,ui
.,1,1-' n J7
23* i i
76 i<) yty.tf*
48.77
.171
.313 0510
2^5^
70 59 07.02
46.45
.I3J
'.,1.U 3-l'JO
2362
76 .20 1(1,70
48.72
.t^j
343 8761
2250
70 59 54-35
46.41
. SU3
..1.1" JiH.'iu
.33(10
76 ji 05,40
48. (^
.173
.344' TOIO
2248
77 00 ,(0.73
46.36
.u.}
.33.! tfjOj)
3.157
70 ai 54,0-1
48. 6a
.174
3-M 3256
2245
77 01 27.07
46.31
a. 125
1.3.13 0,^15
.13. W
76 jj ,(3.6.|
48 58
2.175
f-344 5501
2243
77 02 13.36
46-27
333 0io
-MS3
7(1 ;!,| ,11. -jo
48.53
. i?o
344 7743
2241
77 02 59,61
46.22
.1.7
333 .'i--?'
MS"
7(1 .!4 lo-7<>
48.48
.177
3331)
7? 03 43 -i
46.18
..1.1.1 yta->
3348
76 35 08, 16
48.44
.178
,345 2220
2237
77 04 31 .96
46-13
.UJ
.,1,13 yyitf
a t -j.|0
70 35 50.57
48.39
.170
345 44S6
3334
77 05 18.08
46.09
2.130
1.334 J.l'*i
334-1
yd ^1 ,)4.)4
48 14
2.180
1-345 6689
2232
77 06 04 . 14
46.04
.1,11
.,(,14 4054
jj.ji
7*' -^7 33'-*'
48.^9
.181
.345 <>Ji
2230
77 06 50.17
46.00
.l.W
331= tWji
J33U
70 aS ;n. 53
48.2-1
,tHj
.340' 1150
2228
77 07 36.14
45-95
..HI U3J
3337
7(1 zf> (X-75
48.20
.183
-346 3377
2226
77 08 22.08
45-91
. 13-1
.3,15 HH-H
7<> ^ 57-93
irt.is
.18-1
.3-1< S6oi
2^24
77 09 07. y6
45.87
a.iVl
1.315 401)3
^13-)
7ft 30 ,i6.(X'
48.11
" r8~;
1.346 78.'. |
222 1
77 09 53-fil
45.82
.130
335 0,1,13
^33*'
7<i 31 3.1.1.1
4.ofi
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.3-17 ooi-l
221(>
77 10 39,60
45.78
MX
iM, r t K*i-!i;i
aji'H
yd 33 jj.itt
48.01
.187
.347 U2f)3
2217
77 n 25.36
45.73
,,13/t <Kj8H
a;!^
75 3.1 l"' 1 ?
47.07
.INK
.347 '1478
2315
77 r2 n.07
45<"9
'39
3,t ( ' 3.1 '3
3 1^3
7<i 33 38,11
17- 9^
.189
.347 W03
2213
77 12 5f'.73
45.64
3,140
l .3,16*5035
Jiai
76 34 46,01
47.87
a.njo
1.347 8004
22IT
77 T3 42.35
45.60
.3,1'* 70.S5
23 ii)
7< J 35 33 'Wi
47.3
.iyi
.348 "M
2208
77 14 27.03
45-55
. I, id
j li(i
7(1 3(1 31. Od
47.78
ma
.3-18 3321
2206
77 15 13.46
45.51
. 141
-337 -I58H
23 LI
?(i 37 OM2
47-73
.193
.348 5536
2204.
77 IS 58.95
45.46
."44
337 -iyt>l
j-ju
7i' 37 57-13
nj-l
.348 7729
2202
77 10 44-39
45-42
2,1, IS
1-317 7JIJ
W 10
76 3H -M-70
47-6.1
a . 105
i - 348 0930
2200
77 '7 29.79
45.33
337 OS3i>
^307
70 3!) 3-*.-l'i
47-59
. ifX' 1
-340 2U'()
2ioS
77 18 15.14
45-33
.1.17
.338 : j-ta<>
yjog
70 40 lo.yH
47.53
.IQ7
.349 43*>
2i<,;6
77 10 00.45
45.29
,148
il$ *U3'
3303
X' 41 o?.si
47-50
.n;8
.340 6520
2193
77 19 45-72
45-24
. 14')
'338 N3*
ajoi
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.W
.3.li? ^'3
2191
77 20 30.04
45-20
a. ISO
1.338 8732
3398
7 C ,13 ^-42
.(7-41
a. 200
1,3500903.
3180
77 2i 16.11
45-16
11
*-;
.H*.
!-.(*
waochu
u
7f
2lflll (0^)" - B*
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^-W-BO*
usechu
SMITHSONIAN
297
The Gwlcnmmninn.
2.^1O
..'II
.31,1
,.!17
,;nH
a. 3. 10
. ^-*t
.337
.338
a. -MS
':''!'
;i|8
Hdu
1.350 (X)03
-35" 5J77
35" ?.|0i
-350 <XM3
351 "'75
35H 0519
I , ^fi-! lHh\S
35J .1^55
1 . 353 350.!
-353 5<58
353 78U!
353 O'X'l
35-1 --'".I
i-35-l -I -to
35'l 855:!
.355 -'H.13
1-355 -lOJ'O
-355 7H'''
-355 0-MO
350' 1370
35'' 3.10')
1 . 35(> 5 ( '>~o'
35" 775'
-35" f)87'l
357 ^005
-357 -|H.|
-357 83.1;;
.358 0-157
.358 as/fl
.358 -'I070
i. 3580783
.358 HHy
35O oijHi)
-350 3oH<)
3!>!) 5187
1-350 7- l 8.1
350 IJ377
,#M> i,|f)
,,l(k) 3550
7733
2170
-T3-I
11(1 II
77 -M K>..l8
77 -'5 ni..i.|
77 -'5 .l<...'5
77 -*> 3 1. 1.;
77 J7 15-05
77 ;:S oo,73
77 .! .15-17
77 -!0 30. 10
77 3<> i.|.8.!
77 30 50.. I- 1
77 31 .13- '")
77 3'' io.,|d
77 30 5I-7-'
77 37 38-0.1
77 38 -M.II
77 ,10 07..!.]
77 'lo 35-!l8
77 -II I'l-.t^
77 .M <M..M
77 !! .17--J5
77 .|7 IHJ.HS
77 -17 53-17
77 -l8 37-o|
77 '!') 20.57
77 .W -17-51
77 M 30.1)1
77 5J I.M7
77 :<' 57-5'J
77 53 -10. M;
77 5-1 -M-io
77 55 07..:<j
77 55 !iO-|.|
77 P" 33.S. 1 !
77 57 KMu
77 57 5f).ftl
15.1"
-15-11
15-07
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M.5
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1.7-:
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1 51
1 50
1.1.85
1.1.81
1.1-77
.13.7-!
.1.1. (-8
,(.1. (xt
13-55
.13-51
-13-17
it! nh n
ti<i u
l-3''0 7733
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1,3"..! )-i.|H
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.11.1,1
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TAnt.cn
The Gwlcrmannian.
II
uil
"IV
,:,,
-IV
II
ml u
-w
0(1 U
w
a.;H.
-370 9-165
1985
ii / //
II
40.95
2.350
380 6331
1890
/ II
) 06 16.03
38.99
. ,'i' 1 1
3/1 '410
l ( ^3
/8 11 '18.04
40.01
-351
380 8221
1888
9 06 55.00
38.95
..to.!
37' 3-131
H)8l
/8 34 '19-82
40.87
.352
381 0108
i3S6
) 07 33.03
18.91
3 ll .l
3/1 !i-|M
1070
;8 35 00.67
40.83
.353
381 199.1
1885
9 08 12.82
38.87
. 30 1
.371 7.100
1077
/8 35 41.48
40.79
354
381 3877
1883
} 08 51.67
38.84
J. (0-,
.3/1 0167
i'>75
78 36 M.25
40,75
2.355
-3Hl 5750
1881
9 09 30-49
38.80
,30O
-37-! 1341
'0/4
/H 37 0.3. 08
40.7.1
.356
-381 7(139
1879
9 10 09.27
38.76
-.I 11 /
37"' 3.M-I
107,!
78 37 43-on
357
.381 9517
1877
9 10 48.01
38.72
, 31 ill
37-1 r i.!M.|
78 38 24.31
40.63
.358
.382 1394
18/5
9 II 26.71
38.08
-3<><;
37-1 "/JS3
iijOH
40.59
359
.382 3268
1874
9 12 05-37
38.64
.!.31"
,37,1 o.i.:o
MXfi
/8 3045-49
40.55
2.360
.382 5MI
1872
9 12 44.00
38.61
.3"
3/3 HN5
IOfi-1
/8 40 u(i.(u
40.51
,361
.;jHj 70 1 a
1870
9 13 22.59
38.57
.312
3/;> 3'48
K/U
40.47
.362
,382 8881
1868
9 14 01.14
38,53
.31.)
3/3 ,'i'oo
l</)
78 41 46.1)6
40-43
.363
.383 0748
1866
9 14 39-65
38.49
-373 7<>68
1958
78 43 27-37
40.39
.364'
-383 2613
1864
9 15 18.12
38.46
* i<>
. .1 1 /
37,1 "Xt.'ii
-37-1 0980
.,1/1 '"M4
lO.'i'i
78 43 07-7-1
/H 43 48.07
78 44 '8.36
40.35
40.31
40.27
,2.365
,366
.367
.383 44/6
-383 <)338
-383 8198
1863
r8fn
9 IS 56.56
9 16 34-96
9 17 13.32
38.42
38.38
38.34
.318
.,174 .1885
MM')
78 .15 oH.fn
78 .15 48.8.!
40.23
40.19
.368
-3f'9
.384 0056
.384 1912
185?
1855
9 17 51.6-1
9 18 29,93
38.30
38.27
o
- 1/.1 878.
1017
78 i\<\ '.:8.(>9
40.15
3.370
-384 3766
1853
79 19 08. i{
38.23
'\ji
'.V'' 1 ' oy/.l
/8 47 (KJ.I3
40.11
371
.384 5619
1852
79 19 46.39
38.19
'_'.,,_,
!'r' ( i '''>''
ion
/8 .17 49 -a-!
4.1.07
.372
-384 7470
1850
79 20 24,56
38.15
3 -'4
.375 4'"-
3/!i <W4
10| I
78 48 2).a8
78 40 o, -y
40,04
40.00
-373
374
.38.1 03i8
-385 1165
1848
1846
79 21 02.70
79 21 40.80.
38.12
38.08
'"!':;:
..17!i 8 JiM
, ,l/" (i|,t!i
i'M7
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30.0.!
2.375
37(1
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.385 .185-1
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79 22 18.86
70 22 56,88
38.04
38,00
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.376 ,|,:or>
-37'' (J.J.'i
1031
78 51 no. 10
78 51 48-')6
78 S~ -8.78
30.88
30.8)
39,80
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.378
.379
.38^ 6606
..185 8536
.38(1 0374
1841
1830
1837
79 23 34.87
70 24 12.8
79 24 50,73
37.97
37-93
37-89
.331
U.
,37'i Hi ,1 f |
.,(77 IM '8'
IO-i'4
78 53 o8.;;(i
78 Vl aHini
30-76
30.75
^38
1.386 2210
,386 404'
.386 5877
1835
183,
183
79 25 28.60
79 26 06. 4/
79 26 44-. 2,
37-86
37-82
37.78
.333
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.'.177 !i8.'i"
78 55 07.67
yH Ji. r i 47- -'0
30-64
30.61
'.38;
.38
.386 7708
.386 9537
183
182
79 27 22.00
79 27 59-7
37-74
37-71
t ii
1-377 776u
'9'8
Hjltt
78 56 26.88
78 57 06-.|'3
30-57
30-53
2.38
1.387 136
.387 3I&
182
182
79 28 37-4
79 29 15-0
37-^7
37.63
I.!'
337
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.378 i"oi
.378 35 ii
iiji-l
'O'.i
/8 57 4S-01
yH t;H ;!5.40
30-40
3')- 45
39-41
!a
.38.
.387 501
.387 683
.387 865
182
182
181
79 29 52,6
79 30 30.26
79 31 07.80
37.60
37.56
37.52
J.3-1
3t
34
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.31
i37 Wl
.379 nso
-370 30.H-1
1
,.0 ( . ,._ ',>
79 (xi a.i . fiH
70 01 42,17
79 (U Ji..|i
30-37
30-33
30-39
39.20
39.22
a. 390
.39
.39
.39
.39
1.388 O.|7
!tK8 410"
.388 501
.388 772
181
181
18 1
181
181
79 3t 45-3
79 32 22,7
79 33 00.2
79 33 37-5
79 34 14-9
37-49
37-45
37-41
37-37
37-34
J..H
3-1
.3-1
. 3^> 44 Jf
iw
180,
70 03 00-61
70 <>3 30-77
71) (MI i8.K<
70 0,1 57-07
79 05 37-o-
39.18
39.^4
30.10
30-o6
30-03
8.39;
.30
399
1-388 953
.389 134
-389 3'5
-380 495
.389 075
1808
180
180
180
180
79 34 52.2
79 35 29-5
79 36 06.80
79 36 44-o
7937 21. i
37.30
37.26
37.23
37-19
37-15
J..1S
1.381) 633
1X
79 of) l6.0,1
38.99
2.400
1.389 855
i8oc
79 37 58.3
37-12
|f
" waicli
2lnii"'(o l| V IK
' MIOCllI
11
2tim~'(a")-
wBOOll
2tnir% u )-0
usocliu
^
..I i i i *
; ;--."^i.
__"_*"*-.
.. i
^.HI^HVi^M
*PHH^W*J
8MIYHBUMIAM TABUB
299
The Gndcrmannian.
n
ail u
wIV
ail"
-w
It
Qll 11
-w
ail u
., F ,
Z>
1.389 8557
I&O
79 37 58.32
37<I Q
2.450
1.398 6356
1713
80 08 09.31
11
35.34
.401
.402
.403
.404
.31)0 0356
.390 2153
.390 3948
.390 574t
1796
179-1
1792
79 38 35-42
79 30 12.48
79 39 49-51
79 <|0 26.50
37.05
37. OT
36.97
-451
.452
.453
454
,,1<j8 80(19
.308 9779
.30!) 1488
.399 3195
1711
1710
1706
80 08 4.1.03
80 09 I9-9 1
8d tx) M, Hi
80 10 30.37
35.30
35.27
35.23
35-20
2.405
.406
.407
1.390 7533
390 9323
.391 mi
1787
79 41 03,45
79 41 40.37
79 42 17.25
36.94
36. < jo
36.86
2-455
-156
-457
1.300 4 ( X>1
399 6605
3ix') 8307
1705
1703
1701
Ho n 05.55
Ko ii 40.7"
Ho rj i.s-8i
35.16
3.1-13
.408
.409
.391 2897
.391 4681
IT^I
79 42 54-10
79 43 30.91
36.83
36.79
.458
459
..|(K> O1X17
..|oo 1706
I7<x>
1698
Ko u , r ;o,88
80 13 j.s.yj
3.'i-0<i
35-OJ
3.410
1.301 6464
1782
79 44 07.68
36.75
2.460
1.400 3-103
1696
ft) 14 <X).!>3
,14.99
.411
.391 8j,(5
1780
79 44 44-13
36 . 7-!
.461
.400 5099
l(i<J5
Ho l.| 35- l J<>
3-1-95
.412
'413
,392 0025
,392 1802
1778
1777
7945 21.12
79 45 57-78
36. 08
36.65
.462
.463
.400 67j,i
,.|<X> 8485
l6<M
Ho 15 10. 8 1
80 15 45. 7-1
n . i' hj * t
3.1 '.89
.414
.392 3578
1775
79 4<> 34-41
36.61
.46.1
-lot 0175
l6j>0
80 10 .10.01
;M.8s
2.415
,416
.417
.418
.419
1.39-2 5352
.392 7124
.393 0664
303 243*
"773
1771
T770
1768
176(1
70 .|7 n, oo
7947 47.56
79 48 24.08
79 <I9 00.57
79 49 37.02
36.57
36.54
30.50
36.47
36.43
\4&i
.4^7
.468
.469
I., 101 Irffy
.401 3551
.401 5237
..JO! (iO-'I
.,[01 8(iO3
1683
KiHi
ft) 16 35-15
80 17 3<>.2<i
80 iM 05.01
Ho 18 30-74
Ko 19 14.44
34-82
34-7H
34-75
31-68
2.420
.421
.422
1.393 419''
393 5</x>
.393 7722
1764
1763
1761
79 50 13-13
79 50 49.8o
79 51 20.15
36.39
36.32
3.470
471
-472
1.402 0283
.;|02 I<X-i
.402 36,19
1680
1(178
i6?(>
Ro 19 4'). 10
80 ,:o .,'3.73
Ho -M SH.3,1
34.01
34.58
4 '33
-303 9482
175')
71) S3 02.45
36.29
473
.4*12 5.1 '5
1075
4<> 21 3^.**^
34 54
.424
,.394 "40
1758
79 52 38.72
36.25
474
40-' 6989
1673
H< 2J 07.41
3-1* SI
.-126
,427
rtO
1.394 2907
.394 -1752
.394 6505
1756
1754
1753
79 53 14.<J6
79 53 SMS
79 54 27.32
36.22
36. 18
36.14
1/1 I 1
3.475
476
.477
1.402 8661
.403 033-!
,,|03 2001
1672
16711
80 3J 41-01
H<) .),! Ki.3'i
80 a,) ,'iO.Vo
80 .'i ,!<;.iK
34-|8
3-1-44
,14.41
,11,37
,42tt
439
.394 8257
.395 oouf)
1751
1749
79 55 03.44
79 55 39.54
JUl 1 1
36.07
.479
-|03 5331
Ififis'
8<i .!| 59-51
,11.34
2.430
.43!
1.395 1754
395 3501
^747
1745
79 56 15-59
79 5fi 5i.6i
36.04
36.00
iiii
i .403 6o | )H
.403 8660
&
Ho y(i oHi 15
.14-31
-432
.395 $'M$
'74-1
79 57 27.60
35-97
..|H<!
.40,1 03.: I
1660
Ho 26 .u-i
,14. -'4
.433
.395 6988
<743
70 58 03-55
35-93
.483
.404 1980
Ki58
H(t a7 io.d.i
3-l.ao
4>34
.395 8720
1740
79 58 39.46
35-<.X>
.48.1
,40-1 3<M7
K'.<i7
80 J7 50. Hi
.'14-17
2-435
.436
-437
.438
1.396 O.|f>9
.396 2207
.396 3943
3<X S677
1739
1737
1735
1733
79 59 15.34
79 59 51.19
Ho oo 26.99
80 or 02,77
35-86
35-83
35-79
35.76
2.485,
!47
,488
1.404 5293
.404 (>947
.40.1 H/kio
.405 0251
1655
K'53
1652
1650
Ro 28 24.97
Ko ;i,S 50. (f)
Hn *> .1,1-17
80 30 07. J3
3-1. M
31 . in
3-1-07
.11.0-1
439
.396 74">
1732
80 ot 38.51
35.72
.489
-105 1900
I6,l
8<> 30 .11,35
34.00
2.440
1.396 9MI
1730
80 02 14.21
35.69
3,490
i-|05 3548
1647
Ho 31 15. J3
;i3.97
441
397 0870
1728
80 02 49.88
35.65
.491
.405 5"/l
if MS
Hn 31 .\y.i\)
,1.1.94
.442
.397 2597
17^7
80 03 25.51
35,63
.-193
.405 (1838
"'14
H<1 .(.! -!,! 1"
,l.i>0^>
<443
397 4323
1725
80 04 oi, ft
35.58
.493
.405 8481
l^l-l
HO ,U f/KIXJ
,13.87
444
.397 00-17
1723
Ho o.| 36.67
35.54
49-1
,.|0(> 0122
1640
|> 3.) 30.81
3.1-8-1
2.445
1.397 7770
1723
Ro 05 12.20
.15.51
2.495
1.406 1762
i '"'39
Ho 3-1 oi.#'
,H.HO
44<:
397 9490
1720
80 05 47-69
35 > 48
.496
.406 3400
1637
8*> 34 ;i8,.|5
.U-77
447
.398 1209
1718
80 06 23.15
35-44
407
,,|tf> 5036
K'3'i
Ho 35 u. J<>
33-74
-448
.449
-398 2927
.398 4('43
1716
1715
80 06 58.57
80 07 33.00
35-41
35-37
.408
.499
.406 6671
.406 8304
163-1
1632
Ho 36 lij.OG
,1,1 TO
33-67
2,450
1.3986356
1713
80 08 09.31
35.3'f
2.500
i ,406 0936
1631
80 36 53.^6
, MifM
u
IT
wmxihu
"^
"IQCllU
u
|
i
wieahu
ll-HttM,
M chu
300
The Gwlcrmannian.
32.02
31-98
31-95
1551 -
1349 81 05 18.19
15.18 81 os 50.13
1545 81 06 53-91
15-13 81 07 25.7S
1341 8r 07 57-56
1540 81 08 20-31
1538 8 1 oy oi.o()
1537 81 09 32.80
1535 81 10 04.49
1534 81 10 3<i.i4
1332 81 ii 07,77
1531 8 1 n 39-36
31.70
31.67
.11.64
31.61
31.58
13 oi. US 33--!7| -5<>i
108 7777
It )H 0380
HXH)
100
4 40.92 33- 17 | -5<>-l
1529 Hi is 10.92
1528 Si 12 4^-45
1526 8t 13 13-95
IS 1.1.0*1 33.14
33-H
33-
1525 I 81 13 4S-4~I I ,11-45
132381 14 16.85 31.42
132281 14 48.25
1520 Hi 15 I9.<>3
1519 8l 15 50-97
1317 81 16 22.28
31-39
31. 3<
31-3
31.3
17 S9-38 33.98 | J. 570
It)0<i..i7 33.9,1
Sl-'.'i
/<),
410 H6i,t
1516 81 16 33.56 31-2
1514 i 17 24.81
1513 81 17 56.03
81 18 J7-22
81 18 58.38
1508 8 1 1929.50
782.
9334
08-17
^357
fil 40-43 32.7.1 | .577
31-08
31.05
31-02
30.09
30.06
1,507 8l 2000.60
1305 81 20 31.67
Hi 31 02.70
1503 81 21 33-70
1501 8t 22 04-68
537-1
im\
.4198.18.1
.419 <l88H
.420 1389
30.93
30.00
30-87
30.8-
' !'!"o 4388
-4-to 5885
.420
.420 887S
1496 Hi 23 37-41
1R7J Ho 57 15-33 '<- ! "'- i
1495 8 1 2408.26
R7 47-75 3J-to
iia^-13 ^-37
30.7
30-7
30-7
30.68
30-6
1491 8r 25 40.63
3349
421 48.17
421
,
S/M Ho s; 57.oH
30-6
30-5
30-5
30.5
30-5
1483 81 28 13.98
.431 9303
.422 0770
,432 2257
.422 3730
1479 81 2045.62
I t I i 1 * ' ' " '*' ""'* i*
1554 Bl 03 4J.ty 33.03
1477 Si 30 i6.n
The Gudermatmian.
u
ad u
. w
ad 11
.*
u
tFd u
.w
ad u
-w
2.600
1.422 5214
H77
81 30 16.11
u
30.47
2.650
1.429 7283
1406
1 II
8 1 55 02.63
29.00
.601
.422 6691
1476
81 30 46.56
30.44
.651
.4298688
1405
Si 55 31-62
28.97
.602
.422 8166
1474
81 31 16.99
30.41
.652
.430 0092
.1403
Si 56 00,58
28.94
.603
.422 9640
1473
Si 31 47-39
30.38
.653
.430 1495
1402
Si 56 29.51
28.92
.604
.423 11-12
1471
81 32 17-75
30-35
.654
.430 2896
1400
81 56 58.41
28.89
2,605
1.423 2583
1470
81 32 48.09
30-32
2.655
1.430 4296
1399
81 57 27.28
28.66
.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
1396
Si 58 24.94
28.80
.608
.423 6986
1466
Si 34 18.92
30.23
.658
,430 8487
1395
8t 58 53-72
28.77
.609
.423 8451
1464
Si 34 49-114
30.20
-659
.430 9881
1394
81 59 22.48
28.74
2.610
1.423 9915
1463
81 35 19-32
30.17
2.660
I.43I 1274
1392
8l 59 51.21
28.72
.61 1
.424 1377
1461
Si 35 49.48
30.14
.661
-431 2665
1391
82 oo 19.91
28.69
.612
.424 2837
1460
Si 36 19.61
30.11
.662
431 4055
1389
82 oo 48.58
28.66
.613
.424 4297
HS8
Si 36 49-71
30.08
.663
.431 5444
1388
82 oi 17.23
28.63
.614
.424 57S4
1457
81 37 19-77
30.05
.664
431 6831
1387
82 oi 45. 84
28,60
2.615
1.424 7211
1456
8l 37 49-8i
30.02
2.665
1,431 8217
1385
82 02 14.43
28.57
.616
.424 8665
1454
Si 38 19-82
29-99
.666
.431 9602
1384
82 02 42.99
28.55
.617
.425 0119
1453
Si 38 49-80
29.96
.667
.432 0985
1383
82 03 11.52
28.52
.618
.425 1571
Si 39 19-75
29-93
.668
.432 2367
1381
82 03 40,02
28.49
.619
.425 3021
1450
Si 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
i '147
8r 40 49.42
29.85
.671
.432 6504
1377
82 05 05.36
28.40
.622
.425 736-1
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 02. 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
1441
Si 42 48.56
29-73
2.675
1.433 2002
1372
82 06 58.76
28.29
.626
.426 3135
1440
Si 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
1437
81 44 17.61
29.64
.678
.433 6110
1368
82 08 23.51
28.21
.629
.426 7448
1436
81 44 47.24"
29,61
.679
-433 7477
1366
82 08 51.70
28.18
2.630
I .426 8883
1434
81 45 16.83
29.58
2.680
1-433 8843
I36S
82 09 19-86
28.15
.631
.437 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
1430
81 46 45-44
29.49
.683
.434 2931
1361
82 10 44.20
28,07
-634
.427 4608
1428
8 1 47 14-92
29.46
.684,
.434 4291
1359
82 ii 12.25
28.04
2-635
1.427 6036
1427
81 47 44-37
29-43
2.685
1-434 5650
1358
82 II 40.28
28.01
-636
.427 7462
1426
81 48 13-79
29.41
.686
.434 7008
1357
82 12 08.28
27.99
-637
.427 8887
1424
81 48 43.J8
29.38
.687
.434 8364
1355
S2 12 36.25
27.0
.638
.428 0310
1423
81 49 12.55
29-35
.688
434 9719
1354
82 13 04.19
27.93
.639
.428 1732
1421
81 49 41.88
29-32
.689
435 1072
1353
82 13 32.11
27.90
2.640
1.428 3153
1420
81 50 ii. 18
29.29
2.690
1-435 2424
1351
82 13 59-99
27.87
.641
.428 4572
1419
81 50 40.46
29.26
,691
435 3775
I3SO
82 14 27.86
27.85
.642
.428 5990
1417
81 51 09.70
29.23
.692-
435 5124
1349
82 14 55.69
27.82
.643
.428 7407
1416
8: 51 38.92
29.20
-693
-435 6472
1347
82 15 23.49
27.79
.644
.428 8822
1414
81 52 08. ii
29.17
.694
435 78i9
1346
82 15 51.27
27.77
2.645
1.429 0236
HI3
81 52 37-27
29,14
2.695
1.435 9104
1345
82 16 19.02
27.74
.646
.429 1648
1412
81 53 06.40
29.12
.696
.436 0508
1343
82 16 46.75
27.71
.647
429 3059
1410
81 53 35-50
29.09
.697
.436 1851
1342
82 17 14.44
27.68
.648
.429 4468
1409
Si 54 04*57
29.06
.698
.436 3192
1341
82 17 42,11
27.65
.649
.429 5876
1407
8l 54 33.62
29.03
.699
.430 4532
1339
82 18 09-75
27.63
2.650
1.429 7283
1406
81 55 02.63
29.00
2.700
1.436 5871
1338
82 18 37.36
27.60
u
IT
u sech u
2 ,-,..,- co .
useoliu
u
2tan- 1 (e)-~
., Hh .
2tan- 1 (e)-9Q
usechu
SMITHSONIAN TABLES
302
The Gude rmannian.
II
ad u
Ftf
ad u
<oF '
u
ad u
wFo'
ad u
FO'
2.700
.436 5871
1338
1 II
2 18 37.36
u
27.60
750
.443 H44
1273
a i it
2 41 03.70
//
26.26
.701
.436 7209
1337
2 ig 04.95
27-57
751
-443 2416
1272
2 41 29.95
26.24
.702
.436 8545
1335
2 19 32.51
27-54
752.
.443 3688
1271
2 41 56.18
26.21
.703
.436 9879
1334
2 2O 00.04
27.52
753
443 4958
1270
2 42 22.38
26.19
.704
.437 1213
1333
2 20 27.54
27-49
-754
.443 6227
1268
2 42 48.55
26.16
2.705
-437 2545
1331
2 2O 55.O2
27.46
-755
-443 7495
1267
?2 43 14.70
26.14
.706
-437 3876
1330
2 21 22.47
27.44,
.756
443 8761
1266
2 43 40.82
26.11
.707
-437 5205
1329
2 21 49.89
27.41
-757
.444 0026
1265
2 44 06.92
26.08
.708
-437 6533
1327
2 22' 17.29
27.38
.758
.444 1200
1263
i2 44 32.99
26.06
.709
.437 7860
1326
2 22 44.66
27-35
-759
444 2553
1262
2 44 59-03
26.03
2.710
.437 Ol86
1325
2 23 12. CO
27-33
.760
-444 3814
I26l
2 45 25.05
26.01
.7"
.438 0510
132-4
2 23 39-31
27,30
.761
-444 5074
1260
2 45 51.04
25-98
.712
.438 1833
1322
2 24 06.60
27.27
.762
444 6333
1258
2 46 I7.OI
25-95
-713
.438 3154
1321
2 24 33-86
27.25
.763
.444 7591
1257
}2 4642.95
25-93
7H
-438 4475
1320
2 25 OI.09
27.22
.764
-444 8847
1256
2 47 08.87
25.50
2.715
.438 5704
1318
2 25 28.29
27.19
2.765
.445 0102
1255
82 47 34-76
25.88
.716
-438 7"!
1317
& 25 55-47
27.17
.766
.445 1356
1253
.2 48 00.62
25-85
.717
.438 8428
1316
2 26 22.63
27.14
767
.445 2609
1252
'2 48 26.46
25-83
.718
.438 9743
I3U
2 26 49-75
27.11
.768
445 3860
1251
>2 48 52.27
25.80
.719
-439 1057
1313
2 27 16.85
27.08
.769
445 S"i
1250
82 49 18.06
25-77
2.720
439 2369
1312
2 27 43.92-
27.06
2.770
.445 6360
1248
fc 49 43.82
25-75
.721
.439 3680
1310
.2 28 10.96
27.03
.771
-445 760?
124?
i3 50 09.56
25.72
.722
-439 4900
1309
.2 28 37.98
27.00
-772
445 8854
1246
& 50 35.2?
25.70
-723
.724
.439 6299
.439 7606
1308
1307
\2 29 04-97
82 29 31 ,94
26.98
26.95
773
-774
.4460099
.446 1343
1245
1243
J2 51 00.95
82 51 26.61
25.67
25.65
2.725
.726
.439 S9I2
.440 0216
1305
1304
82 29 58.87
i2 30 25-79
26.92
26.90
2.775
.776
[.446 2586
.446 382?
1242
1241
\2 51 52.25
}2 52 17.86
25.62
25.60
.727
,728
.440 1520
.440 2822
1303
1301
}2 3O 52.67
82 31 19-53
26.87
26.84
777
77*
.446 5068
.446 6307
1240
1238
82 52 43-44
{2 53 oo.oo
25-57
25-55
.729
-440 4123
1300
82 31 46-36
26.82
.779
-446 7545
1237
82 53 34-53
25.52
2.730
-731
.732
-733
734
1.440 5422
.440 6720
.440 8017
.440 93U
.441 0607
1299
1298
1296
1295
1294
52 32 13-16
te 32 39-94
i2 33 06.69
J2 33 33-42'
82 34 oo.ii
26.79
26.76
26.74
26.71
26.68
2.780
.781
.782
.783
.784
1.446 8/Si
.447 0017
.447 1251
447 2484
447 3716
1236
1235
1234
1232
1231
J2 54 00.04
82 54 25-52
82 54 50-58
& 55 16.41
82 55 41-Sl
25-49
25-47
25-44
25-42
25-39
2.735
73f
.737
738
-739
1.441 1900
.441 3192
.441 4483
.441 5772
,441 7060
1292
1291
1290
1289
1287
?2 34 26.78
82 34 53-43
& 35 20.05
82 35 46-64
82 36 13-21
26.66
26.63
26.61
26.58
26.55
2.785
.786
787
.788
.789
I .447 4946
.447 6175
447 7403
.447 8630
447 98S6
1230
1229
1227
1226
1225
32 56 07.19
82 56 32-55
82 56 57-88
82 57 23- 1 9
82 57 48.47
25-37
25-34
25-32
25.29
25.27
2.740
.741
.742
74.
.7*
1.441 8347
.441 9632
,442 0916
.442 2IQ9
-442 348l
I2ST
1285
1283
1282
1281
82 36 39-75
82 37 06.26
82 37 32-75
82 37 59-21
82 38 2-5.64
26.53
26.50
26.47
26.45
26.42
2.790
.791
.792
793
794
1.448 1080
.448 2303
.448 3525
.448 4746
.448 5966
1224
122;
1221
T22O
1219
82 58 13.72
82 58 38.95
82 59 04.16
82 59 29.34
82 59 54-49
25.24
25.22
25-19
25.17
25.14
2.745
.746
-747
.7^8
74
1.442 476l
.442 6040
.442 73l8
.442 8594
.442 9870
1280
1278
1277
1276
127
82 38 52.05
82 39 i8-43
82 39 44-79
82 40 I'l . 12
82 40 37-42
26.40
26.37
26.34
26.32
26.29
2-795
.796
-797
.708
799
1.448 7184
,448 8401
.448 9617
.449 0832
-449 2045
I2lS
1217
1215
I2Ii
121;
83 00 19-62
83 00 44-73
83 oi 09.8
83 oi 34-86
83 oi 59-50
25.12
25.09
25-07
25.04
25.02
2.75
1.443 "44
127
82 41 03-70
26.26
2.800
1.449 3258
1212
83 02 24.00
24.99
u
2 lan-'te 11 )-
u secli
2 tnn-Ke'O-DO
useoh
u
Zten-He")-
UGBCtl
2tair*(ffO-P
usechu
SMITHSONIAN TABLES
303
The GuSermannian.
u
Dd u
-V
od u
*FV
u
Od
-IV
ail u
-IV
2.800
.801
.802
.803
.804
1.4493258
.449 4469
.449 5679
.449 6bSS
.449 8095
1212
I2II
1209
1208
120?
a i u
3 02 24.90
$3 02 49.68
to 03 14-84
to 03 39.77
83 04 04.68
u
24-99
24-97
24-94
24.92
24.89
2.850
.85-1
.852
.853
-854
1-455 2365
.455 35J7
.455 4668
.455 5819
.455 6968
"S3 1
"52
1150
1148
1 II
83 22 44.07
83 23 07.84
83 23 31.58
83 23 55.31
83 24 19.01
H
23.78
23.76
23-74
23.71
23.69
2.805
.806
.807
.808
.809
1.449 930i
-450 0507
.450 i?IO
450 2913
.450 4"S
1206
1205
1203
1203
1201
to 04 29.56
83 04 54-42
to 05 19-25
83 OS 44- of)
83 06 08.84
24.87
24-85
24-82
24.80
24.77
2.855
.856
.857
.858
.859
1.455 8115
455 9262
.456 0408
.456 I5S2
.456 2696
"47
1,146
H45
"44
"43'
to 24 42.69
83 25 06.34
83 25 29-97
83 25 53.58
83 26 17.16
23.67
23.6-1
23/)2
23-59
23-57
2.810
.81-1
.812
.813
.814
I.45053I5
.450 6514
.450 7712
.450 8goo
.451 0105
1200
"59
1198
11196
"95
to 06 33.60
to 06 58.33
83 07 23.04
83 07 47-73
83 08 12.39
24-75
24.72
24.70
24.67
24.65
2.860
.861
.862
.863
.864
1.456 3838
.456 4979
.4566119
.456 7258
.456 8395
1142
1140
1 139
1138
"37
to 26 40.72
83 27 04.25
83 27 27.77
to 27 51.26
83 28 14.72
23-55
23.52
23.50
23.48
23-45
2.8rs
.816
.817
.818
.819
1.451 1299
.451 2492
.451 3684
451 4875
.451 6065
"94
"93
1191
1190
1189
?3 08 37.03
to 09 01.64
to 09 26.23
to 09 50.79
83 10 15.33
24.62
24.60
24.58
24-55
24-53
2.865
.866
.867
.868
.869
1.456 9532
.457 0667
.457 1801
-457 2935
.457 4067
1136
"35
"34
"33
83 2838.16
83 29 01.58
83 29 24.98
83 *o 48.35
83 30 ".70
23-43
23.41
23.38
23.36
23-34
2.820
.821
.822
.823
.824
I.45I 7253
.451 8441
.451 9627
.452 0812
452 1995
riSS
1187
1186
1184
1183
83 10-39-84
83 u 04.33
83 " 28.80
83 " 53-24
83 12 17.66
24.50
24.48
24-45
24-43
24.41
2.870
.871
.872
-873
.874
1.457 5198
457 6327
.457 7456
457 8584
-457 9710
1130
1129
1128
1127
II26
83 30 35-03
83 30 58.33
33 31 21, 61
83 31 44-87
83 32 08. I i
23.32
23.29
23 . 27
23.25
23,22
2.825
.826
.827
.828
.829
1.4523178
.452 4359
-452 5540
.452 6719
.452 7897
1182
1181
1180
1178
"77
83 12 42.05
83 13 06.42
83 U 30.76
83 13 SS.oS
83 H 1 19.38
24.38
24.36
24-33
24,31
24.28
2.875
.876
.877
.878
.879
1.458 0835
.458 1959
.458 3083
.458 4204
.458 5325
1125
1124
"23
II2I
1120
83 32 31-32
83 32 54-50
83 33 17.67
83 33 40.81
83 34 03-93
23-20
23.18
23.15
23.13
23'."
2.830
.831
.832
.833
1-452 9073
.453 0249
453 1423
453 2597
1176
H75
"74
"73
83 14 43-US
83 '15 07.90
83 IS 32.12
83 IS 50-32
24.26
24.24
24.21
24.19
2.880
.881
.882
.883
1.4586445
.458 7504
.458 8681
.458 9798
lUi
1117
1116"
83 34 27.03
83 34 50. 10
83 35 13.15
83 35 36.18
23.08
23,06
23.04
23-02
-834
.453- 3769
1171
83 16 20,50
24.16
.884
459 0913
1115
83 35 59. 18
22.99
2.835
.836
1-4534940
.453 6109
1170
1169
83 16 44.65
83 17 08.78
24.14
24.12
2.885
.886
1.459 2027
.459 3140
1114
83 36 22.16
83 36 45-12
22.97
22.95
.837
453 727S
1168
83 17 32.88
24-09
.887
-459 4352
mi
83 37 08.06
22.92
.838
.839
.453 8445
.453 9612
1167
1166
83 i? 56.96
83 l8 21.02
24.07
24.04
,888
.889
.459 5303
459 6473
mo
1109
83 37 30.97
83 37 53.86
22.90
22.88
2,840
1.454 0777
ri6s
83 18 45.05
24,02
2.890
i. 459 7S8i
1108
83 38 16.73
22.86
.841
.454' 1941
116]
83 19 09.06
24.00
.891
.459 8689
no?
83 38 39-57
22.83
.842
.454 3104
1162
83 19 33-04
23.97
.892-
.459 9795
1106
83 39 02.40
22. 8l
.843
,454 426=
1161
83 19 57-01
23-95
.893
.460 0901
1105
83 392.5.19
22.79
.844
.454 5426
1160
83 20 20,94
23.93
.894
.460 2005
1104
83 39 47-97
22,77
2.845
i .454 6585
"59
83 20 44.86
23.90
2.895
1,460 3108
"03
85 40 10,73
22,74
.846
454 7743
1158
83 21 08.74
23.88
.896
.460 4210
no
83 40 33.46
22.72
.847
,4548900
1156
83 21 3a.6l
23.85
.897
.460 53"
IIOO
83 40 56.17
22.70
.848
.455 0056
"55
83 21 S6.45
23.83
.898
.460 6411
iooc
83 41 18.85
22.68
.849
.455 I2H
"54
83 22 20.27
23.81
.8gg
.460 75 10
109^
83 41 41.52
22.6S
2.850
1.455 2365
"53
83 22 44.07
23.78
2.900
1.460 8607
1097
83 42 04.16
221.63
u
., . IT
88 cH U
2tan- 1 (e u >-8CI
useohu
u
2tarrV)-;
w secli u
a tan -(*H
to sech u
SMITHSONIAN TABLES
34
The Gudermannian,
11
gd u
-F'
gd u
uF u '
u
ad u
uFo'
gd u
F/
2.000
.901
.902
503
.904
1 .460 8607
.460 9704
.461 0800
,461 1894
.461 2987
1097
1096
1095
1094
1093
D 4 II
33 42 O4.I6
83 42 26.78
83 42 49-37
83 43 n.Q5
83 43 34-50
u
22.63
22. 6l
22.59
22.56
22.54
2.950
.951
952
953
954
1.466 2123
466 3167
.466 4209
.466 5251
.466 6291
1044
1043
1042
1041
1040
,
84 oo 28.00
84 oo 49.53
84 oi 11.03
84 oi 32.51
84 oi 53.97
21. 53 1
21.51 i
21.49!
21.47,
21-45!
2.905
1.461 4080
1092
83 43 57.03
22.52
2-955
1.466 7330
. IO.SQ
84 02 15. .JO
21.43
.006
.461 5171
1091
83 44 19-54
22.50
.956
.466 8368
1038
8-t 02 36.82
21.40
.907
.461 6261
logo
83 44 42.02
22.47
957
.466 0406
10.17
8402 58.21
21.38
.90S
.909
.461 7350
.461 8438
1088
1087
83 45 04.48
83 45 26.92
22.45
22.43
958
959
.467 04-12
.467 M77
1036
1035
84 03 10.58
84 03 40.93
21.36
21.341
2.910
1,461 9325
1086
83 45 49-34
22.41
2.060
1.467 2511
1034
84 04 02.27
2I.32J
.911
.462 0610
1085
83 46 11.73
22.38
.961
.467 3544
1033
84 04 23-57
21.30!
.912
,462 1695
1084
83 46" 34- i'i
22.36
.962
.467 4576
1032
84 04 44-86
21.23,
9M
.462 2779
1083
83 46 56.46
22.34
-963
.467 5607
10.11
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 -op
22.30
2.965
1.467 7666
1028
84 05 48.60
21.21
.916
.462 6023
1080
83 48 03.38
22.27
.066
.467 8694
1027
84 06 09.80
21.19
.QI7
.462 7102
1079
83 48 25.64
22.25
.967
467 9721
10^6
S; 06 30.98
2r.I7J
.918
.462 8180
1078
83 48 47-88
22.23
.968
.468 0747
1025
84 06 52.14
2I.I5j
919
.462 9257
1077
83 49 10- 10
22.21
.969
.468 1772
102.1
8[ 07 13.29
21.13
2.92O
I .463 0334
1076
83 49 32.29
22.18
2.970
1.468 2796
1023
84 07 34-40
21. IIj
9-^1
.463 1409
1074
83 49 54-47
22.16
.971
.468 3819
IO22
84 07 55.50
21.O9J
,922
.463 2483
1073
83 50 16.62
22.14
972
.468 4841
102 1
8408 16.58
21.07
923
.463 3555
1072
83 So 38.75
22.12
973
.468 5861
IO2O
84 cS 37-64
21.05
.924
.463 4627
1071
83 51 00,86
22.10
974
.468 6881
10 10
84 08 58.67
21 ,02
2.925
1.463 5698
1070
83 Si 22.94
22.07
2.975
1.468 7900
10 IS
84 09 ig.ft)
21.00
.926
.463 6768
IQ(X>
83 51 45-00
22.05
9/6
.468 8918
1017
84 09 40. CS
20. OS
-027
.463 7836
1068
83 52 07.05
22.03
977
.468 9935
10 if)
84 10 01.65
20.96
.928
.463 8904
1067
83 52 29.07
22. OI
978
.469 0950
1015
84 10 22.60
20.94
.929
.463 9970
ro65
83 52 51-06
2I.Q9
979
.460 1965
1014
84 1043-53
20.92
2.930
1.464 1036
1065
83 53 13.04
2I.Q7
2.980
1.469 2979
1013
84 n 04-44
20.00
931
.464 2IOO
1064
83 53 34.
21.94
.981
.469 3992
1012
84 n 25-33
20.88
932
.464 3163
1063
83 53 56-93
21.92
.982
.469 5003
IOII
84 n 46.20
20.86
.933
.464 4226
1062
83 54 18-84
21. go
.983
.469 6014
1010
84 12 07. OT
20.84
934
.464 5287
1061
3 54 40.73
2I.8S
.984
.469 7024
loog
84 12 27.83
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
.4699040
1007
84 13 09-47
20.78
937
.464 8464.
1058
83 55 46.26
21. Si
.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
4<J5 0577
1055
83 56 29.85
21.7?
.989
.470 2057
1004
84 14 II-70
20.71
2.940
1.465 1632
1054
83 56 51.60
21.75
2.G90
1.470 3061
1003
84 14 32.40
20.69
.941
.465 2686
1053
83 57 13-34
21.73
991
.470 4064
1002
84 14 53-09
20.67
.942
465 3739
1052
83 57 35.o6
21.70
.992
470 5065
1001
84 15 13-75
20.65
943
.465 47QO
1051
83 57 56.75
21.68
993
.470 6066
IOOO
84- 15 34-39
20.63
-944
.465 5841
1050
83 58 18.42
21.66
.994
.470 7066
999
84 15 55-01
20.61
2.945
1.465 6891
1049
83 58 40-07
21.64
2-995
1.470 8065
998
84 16 I5.6l
20.59
,946
.465 7939
1048
83 59 01.70
21.62
.996
.470 9062
997
84 16 36.19
20.57
.947
.465 8987
1047
83 59 23.3I
21.60
.997
.471 0059
0o6
84 16 56.75
20.55
-'T*
.948
,466 0033
1046
83 59 44-90
21.58
.998
.471 1055
995
84 17 17-29
20.53
-949
.466 1079
1045
84 oo 06.46
21-55
.999
.471 2050
994
84 i? 37.31
20.51
2.950
1,466 2123
1044
84 oo 28.00
21.53
3.000
1.471 3043
993
84 17 58.30
20.49
u
2lan-'(e ll )-|
usechu
2 tan-'(fl u )-9Q Q
usechu
u
atan-Ke'0-|
usechu
2tan- ! (e)-9Q
tech u
SMITHSONIAN TABLES
305
The Gudermannian.
u
gd u
Fo'
ad u
v
u
gd u
*
gd u
^~
3.00
1.471 3043
9933
a i a
84 I? 58.30
204^88
3-50
I.5I04I99
6034
J6 32 26.47
^jT^T
.01
.02
-03
.04
.472 2927
473 2713
474 2401
475 1994
9835
9737
9641
9543
84 21 22.17
84 24 44-01
84 28 03.86
84 31 21.72
202.85
200.84
198.85
196.88
51
.52
-53
54.
.511 0203
.5" 6147
-512 2033
.512 7859
5974
5915
5856
5798
56 34 30.31
86 36 32.92
86 38 34.31
86 40 34-50
I2O . ^r^
3-05
.06
.07
1.476 1492
.477 0896
.478 0206
9451
9357
9264
84 34 37.63
8437 51.59
84 41 03.64
194.93
193.00
191.09
3-55
.56
57
I.SI3 3628
.513 9340
.514 4995
5740
5683
5627
86 42 33-49
86 44 31.30
36 46 27.94
113 "tO
.08
.09
.478 9425
-479 8551
9173
9082
8444 13.78
84 47 22,04
189.20
187.32
-S8
-59
.515 0594
-SIS 6137
5571
36 48 23.43
86 50 17.76
"4-01
3. TO
.11
1.480 7588
.481 6535
8592
9503
84 So 28.43
84 S3 32-97
185.47
183.63
3-6o
.6r
1.516 1625
.516 7058
5461
5406
$5 52 10.96
86 54 03-03
"?:fi
.12
13
.14
-482 3393
.483 4164
.484 2847
8814
8727
8640
84 56 35.69
84 59 36.59
8s 02 35.70
181.81
180.00
178.20
.62
.63
.64
.517 2438
.517 7764
.518 3037
5353
5300
3247
86 55 53-99
86 57 43-85
86 59 32.62
r Oj>-3T
3-15
1.485 1445
855S
85 05 33-04
176.45
3-65
1.518 8258
5195
?7 01 20.30
107, I S
.16
.485 9957
8470
85 08 28.61
174-70
.66
-319 342?
5M3
37 03 06.92
loG oJS
17
.486 8385
8386
85 II 22.45
172.97
.67
.519 8344
5092
87 04 52-47
105 . 03
.18
.487 6729
8303
85 14 I4-S6
171.26
.68
.520 3611
5041
$7 06 36.08
I0 3 - ?>0
.19
.488 4991
8221
85 17 04-97
169.56
.60
.520 8627
4991
87 08 20.45
IO2 . C>5
3'- 20
1.489 3170
8139
85 19 33.69
167.88
3-70
I.52I 3593
4942
87 10 02.89
T i-03
.31
.490 1269
8058
85 22 40.73
166.21
.71
.521 8511
4893'
87 II 44-31
lOO.Q^
.22
.490 9287
7978
83 2=5 26.12
164.56
.72
.522 3379
4844
87 13 24.73
9P -<3*
.23
.491 7226
7899
85 28 09.86
162.93
73
.322 8i99
4796
87 15 04.14
OB . <>;2
.24
.492 5085
7821
85 30 51-99
161.32
74
.523 2971
4748
87 16 42.57
97-t>4
3-25
1.493 2867
7743
8s 33 32-50
I59.7I
3-75
1.323 7<J95
4701
87 l8 20.02
96.<X>
.26
-494 0572
7667
8s 36 11-42
158.13
76
.524 2373
4654
8? 19 56.5O
96 . oo
.27
,494 8200
7590
85 38 48.77
156.56
77
.524 7004
4608
87 21 32.03
OS -05
.28
-495 5753
7515
85 41 24-55
155.01
.78
-525 1580
4562
87 23 06.60
94, TO
.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
7307
85 46 31.50
151.95
3.8o
I . 526 0622
4472
87 26 12.93
92.^4.
.31
-497 7964
7294
85 49 02.69
150.44
.81
.526 5072
4428
87 27 44.71
91 - 32
.32
.498 5*21
7221
85 51 32.38
148.95
.82
.526 9-|?8
438-1
87 29 15.58
90 . ^ =s
33
.499 2407
7150
85 3400.59
M7-47
-83
.327 3839
4340
87 30 45-55
89 . 5^
.34
.499 9521
7079
85 56 27.32
146.00
-84
.527 8157
4297
87 33 14.62
88.<33
3-35
1.5006564
7008
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. ox
.38
.502 7277
6802
86 05 39-84
140.29
.88
529 5005
4128
87 38 02.13
8s - IS
39
-503 4045
6734
86 08 19.44
138.90
.89
.529 9113
4087
87 39 26.86
84-3*
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 7380
6601
86 12 54-48
136. 16
.91
.530 7207
4007
87 42 13-81
82 . 04
.42
SOS 3948
6536
86 15 09.96
134.80
.92
531 1193
3967
87 43 3(>.03
81 . Sz
-43
.506 0451
6471
86 17 24.10
133-47
93
531 SMO
392?
87 44 57-45
Si .00
.44
.5066889
6406
86 19 36.90
132.14
.94
.331 9048
3888
87 46 18.05
80,20
3-45
.46
I .507 3264
SO? 9575
6343
6280
86 21 48.38
86 23 58.56
130-83
129.53
3-95
.96
1.532 2917
-532 6747
3850
38n
87 47 37.85
87 48 56.85
7P-40
78. ox
.47
.508 5823
6217
86 26 07.44
128.24
.97
533 0539
3773
87 50 15.07
77 .&3
.48
.509 2010
6156
86 28 15.05
126.97
.98
533 4294
3736
87 51 32.52
77 . oo
.49
-5098135
6095
86 30 21.39
125.71
.99
.533 Soil
3699
87 52 49-19
76.35?
3-50
I.5I04I99
6034
86 32 26,47
124.46
4.00
1.534 1691
3662
87 54 05.10
75-53
U
n
"seohu
,->-'
"sechu
u
2 Ian-He")--
osocliu
Itarw*
: seoH i
SMITHSONIAN TABLES
306
The Gudcrmnnnian.
. (XI
.01
,OJ
.0,1
.(.0.1
.<'>
.07
4-lo
.11
.ID
4.1.1
.10
ml u
K.M 1*113
.5.1S -i.ai
MS tio.'!|)
I-S.IS '1SS1
I-S37 fyi-
-MX
JIM !J'U
-Ml K>'<i
..Ml l''-' !l
lill >'-'IX
MX <,->,7
Qitu
I! I II
87540S.10
87 56 34.G7
MX 57 48.33
N/ ;;<> 01.17
M (X> 13.48
MU Oi iM.fiy
KH 07 u.j)i
MS oft 19.25
88 io 31,01
JW u 41.94
M 13 .15.99
HH 14 .19.40
HH iij 5i!.iu
M irt 5-1. .11
MU .HI
i snoK ti
MH ,'fi ,|.!,oi
H4 ,7 ,'iS.Oo
MM 31 ifi.tyi
MM !n 01.27
M j'l i-V-W
MK li'i iisltot
MM 3? i,'i.70
MS .lH (15.15
(W .tH 5.1.05
flH 30 43.4^
8jt 40 3<>.j|0
W* 4a 51.35
4J 37-10
XS-53
X.l- 78
X.I.G.I
X3-30
7J-57
71.1.1
7M3
67.00
CM -37
<M.X3
63. 10
'i i.Hs
(iO.03
(ill. (I.!
55-4,1
51-3I
S3- XX
5.!- "
51.15
50,64
48.17
47.32
SOIlll II
4-95
iiio
5.00
a tin
548 5793
.548 8003
.549 0191
-540 2358
549 4503
.549 6627
549 8730
.550 08 i i
5 SO 1-873
550 .
.550
-550
.551 0(>T4
5fil 1*874.
-SSI 4815
551 6737
552 0523
.552 3388
.553 42.15
,Sjj 6063
5S3 7873
.'553 M3
-S53 3195
553 M'55
553 83(10
551 0047
551 i?l8
554337-3
554 5010
.554 6031
554 8-'30'
.5549825
555 1399
55S 957
555 44W
555 7538
55'.'
556 0516
.556 ioS.1
.556 3436
.556 77^7
.550 9i*>3
557 aiK|
S57 1852
1.557 3206
2523
2199
2178
2156
2134
2092
2071
2051
2030
20I.O
1990
19X0
1951
1931
1912
193
1837
ifioi
1783
1765
1748
1X30
1713.
ififXi
166.2
1646
1630
15*17
1550
1535
15H)
1S04
1474
1445
1431
T389
1375
I34S
u BOG!) u
gdii
43 37.40
88 44 22.99
45 08.13
88 45 52.82
88 46 37.07
47 20.88
88 48 04.25
4847.19
49 29-70
50 11.79
50 5-3.46
88 51 34.7-2
H8 52 15.56
52 5(1,00
53 36.o,[
88 54 15.68
54 54-92
88 55 33-77
88 56 12.24
88 56 50-33
88 57 28.03
88 58 05.36
88 58 42.32
H8 59 18.91
HS 59 55.14
ft> oi 06.52
ft) oi 41.68
ft) 02 16.48
ft) 02 50.94
ft) 03 25.06
89 03 58-84
ftj o.-i 32.28
ft) 05 05.39
89 os 38.17
8f) 06 10.63
ft) 06 4^.76
ft) 07 14.57
89 07 46.07
ft) 08 17.25
8008 48.12.
ft; oo 18.69
ft) 09 ,[8.95
ft) io 18.91
89 to 48.57
ft) n 17-93
ft) n 47,01
ft) 12 13-79
ft) 12 44-29
ftj 13 I2.SI
89 13 40. -14
2tnn-'(B)-90
45.82
45-37
44-9*
44-47
44-03
43-59
43-15
42-73
43.30
41.88
41.46
41.05
40.64
40.24
39-84
30.44
39.05
38.66
38.28
37.89
37.52
37-14
36>l
36.05
35.69
35.33
34-98
34-63
34-20
33-95
33.01
33-28
32-94
32.62
32-29
31.97
31-34
SO. 72
30.41
30.11
29.51
29.22
28.93
28.6
28.3'
.4
.36
28.07
27.70
*> seeh u
The Gudermannian,
"""""''"'
iMII '*
F'
B^^BfH^nMUUUUUUll
j==
u
gd u
<oFo'
gdu
<oFo'
u
Qll 11
ad u
wFo'
5.oo
.01
.02
.03
.04
.557 3206
.557 4547
.557 5875
.557 7i89
557 8490
1348
1334
1321
1308
1295
1 II
39 U 40-44
3g 14 08. 10
89 14 35-48
3g 1502.58
9 15 20.42
u
27-79
27.52
27.24
26.97
26.71
5-50
.51
.52
.53
.54
562 6228
562 7042
.562 7847
. 562 8644
.562 9433
8l 7
8CK>
Sor
793
785
, II
J 31 54-10
So 32 10.87
) 32 27.4**
39 32 43.92
%> 33 00.20
16.86
16.69
16.53
16.36
16.20
5.05
.06
.07
.08
.09
.557 9778
.558 1054
.558 2317
,558 3567
.558 4804
1282
1269
1256
1244
1232
9 15 56.00
S9 16 22.30
89 16 48.35
89 17 I4.H
9 17 39.67
26.44
26.18
25.92
25.66
25.40
5-55
56
57
.58
.59
.563 0215
.563 0988
.563 1754
.563 2512
.563 3263
777
770
762
755
747
) 33 16.32
to 33 32.27
) 33 48-07
9 34 03-71
) 34 19-20
15$
15.72
15.56
15.41
1 5-10
.11
.12
.13
.14
.558 6030
.558 7243
.558 8444
.558 9633
.559 oSn
1219
1207
n<)5
1183
1172
9 18 04-94
89 18 29.97
18 54-74
9 19 19.27
89 19 43-56
25-isl
24.90!
24-65J
24-41
24.16
5.6o
.6!
.62
.63
.64
.363 4006
.563 4742
.563 5471
,563 6192'
.563 6506
740
73-2'
7^5
718
711
J 34 3-I-53
9 34 49-71
) 35 04-73
9 35 I0.6i
to 35 34-34
15.25
15.10
14.95
14.80
14.66
5.15
.16
.17
.18
.19
.559 1976
.559 313*
.559 *1273
.559 5404
559 6524
1160
1148
ri37
1126
1114
9 20 07.60
() 20 3I-40
89 20 54-97
9 21 18.31
89 21 41.41
23.92
23-69
23-45
23.22
22.99
5.65
.66
.67
.6H
.69
.563 ?6l3'
.563 8313
.563 9006
.563' 9692
.564 0372
73
697
690
683
6?6
89 35 48-93
9 36 03.36
9 36 17.66
1) <J ,1T.8l
89 36 45- Sa
14.51
14.37
14.22
14.118
13.94
5-20
.21
.22
-23
.24
.559 7633
.559 8731
.5599818
.560 0894
.560 1959
1103
1092
1081
1071
1060
9 22 04.28
22 26.92
Sg 22 49-34
89 23 n.53
89 23.33.91
22.76
22,53
22.31
22.08
21.86
S-70
.71
.72
73
74
.564 1041
.564 1710
.564 23<>9
.564 3022
.564 3668
660
663
656
6-19
<M3
89 36 59-70
89 37 13- '13
89 37 27.03
89 37 40-49
89 37 53.82
13.80
13.67
13.53
13.40
13.26
5-25
.26
27
.28
.20
1.560 301*
.560 4058
.560 5>2
.560 6iif
,560 7129
1049
1039
1029
lOlJ
I00<
89 23 55.26
So 24 16.80
19 24 38.13
89 24 59-24
89 25 20.14
21.65
21.43
21.22
21 .OI
20.8O
5-75
.76
-77
.78
79
1.564 4308
.564 494
.5CH 5568
.564 6189
, 564 6804
6 3 7
630
62.
618
6u
89 38 07.01
89 38 20. uS
80 38 33-01
89 3845-82
8y 38 5-50
13.13
13.0:1
12.87
12.74
12. 6l
5-30
-3
3
3
3
1.560 8132
.360 9126
.561 0109
,561 1083
.561 204
998
988
979
969
959
8y 25 40.84
& 26 01-33
3g 26 21.6
39 26 41.61
89 2701.58
' 20.59
20.39
20.18
19.98
19.78
j :r
.8
,8
.8
1.564 7412
.564 80 I
.564 Sii
.564 920
.564 978
6of
59
50
588
58
to 39 "-OS
89 39 23.4*!'
89 39 ,15.7
89 39 '17.96
89 40 00.02
12,49
12.37
12,24
12.12
12.00
5-3
-3
3
3
.3
1.561 300
.561 394
.561 488
.561 580
.561 672
95
94
93
92
91
89 27 21.2
89 27 40-7
89 28 oo.o
89 28 19- I
S3 28 38.06
19-59
19-39
19.20
19.01
:8.8a
5 : 8 86
.8
.88
.89
1.565 036
.565 093
.565 150
.565 2068
.565 262
57
57
56
S5
55
89 40 n.jX>
89 40 23.78
89 40 35.48
89 40 47-07
89 40 58-54
n.88
11.76
11.65
n-53
LI,, 11
5.40
4
-4
.43
4
1.561 763
.561 853
.561 942
.562 030
.562 117
90
89
88
87
868
89 28 56.7
89 29 15. 3J
89 29 33.68
89 29 51.6
89 30 09.8
18.63
18.45
18.26
18.08
17.90
5.90
9
9
9
9-
1.565 317
.565 372
.565 425
.5<J5 4794
.565 532
$4
54
53
53
52
89 41 09,90
8g 41 21.15
89 41 32. 2^
89 41 43-30
89 4.1 54-21
11.30
II. 10
11.08
10.97
10.86
5-4
4
,/
,t
,i
1,562 203
.562 289
.562 373
.562 457
.562 540
85
85
842
83
82
89 30 27.66
89 3045-2
89 31 02.7
89 31 20.0:
89 31 37-1
17.72
17-55
17.37
17.20
17.03
5-9
.96
9
9
,c
1.565 584
.565 636
.565 687
.565 738
.565 78QO
52
51
51
506
50
89 42' 05.02
8942 I5.7I
89 42 26.30
89 42 36.71,
8942/17.1?
10.75
10.64
10.54
10.43
10.33
5-5
1,562 622
81
8931 54-1
:6.86
6,oc
1.565 8388
. 4<#
89 42 57.44
10.23
u
2tan- l (fi u )-
uaech
2tair 1 (e)-9
useoltu
u
2 telVW-
wsech
2tair H (*')-9tf
3 useoliil
SMITHSONIAN TABLES
308
TABLE VII
THE ANTI-flUDERMANNIAN
in cximiHMwl in miiuilcs In Uiriua of the Gudermmnilati,
tfd \\ t!Xi>i'CHHt>d in degrees and minutes.
i inlnutu o.ooo ayc>8 KHai ractinns,
o.ouo atjoH HHai in JoK.Um f - 1 w-h ^gd u) u radians.
In thin Uiltlu tho, muoiiil decimal jtlacu in soinatlmes erroneous by a unit.
309
The Anti-Gudermannian.
Qd u
o"
i
2
3
4
5
6
7
go
9
10
Qihi
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
121. O2
181.08
1241.20
301.38
361.66
422.06
482,58
543-25
604.08
I
2
2.00
62.00
I22.O3
18^.08
242.120
302.39
362.67
423-06
483.59
544.26
605.10
a
3
3.00
63.00
123.03
183.09
243.20
303.39
363-67
4'24-o?
484.60
545.a;
606. 1 2'
3
4'
4.00
64.00
124.03
184.09
244.20
304-40
364.68
425.08
485.61
546,28
607.13
4
5
5-00
65.00
I2J.03'
185.09
245.24
305-40
365-69
4126.09
486.62
547-30
608. 15 :
5
6
6,00
66.00
126.03
186.09
246.21
306.40
366.69
427.09
467.63
548.31
609. 16
6
7
7.00
67.00
[27.03
187.09
247.21
307.41
367.70
428.10
488.64
5149.33
610, 18
7
8
8.00
68.00
128.03
188.09
248.21
308.41
368:70
4*9. i I
489.65
550.34
611. 19
8
9
o.oo
69.00
129-03
189.09
249.213'
309.42
369-71
4i30. 12
490.66
55L3I5
6 1 2. 2 1
9
10
10. OO
70.00
130.03
igo.io
25O.22 1
310.42
370.72
431-13
491.67
35^-36
6 1 -3. 23
10
II
11.00
71.00
I3I-03
191.10
251.22
311.42
371.72
432.13
492>.68
353-37
614.24
it
12
12. OO
72.00
I32-03
192.10
252.23
312-43
372.73
433-14
493-f>9
554-39
6115.316
12
13'
Ifl.OO
73-00
Iff3-03
193-1
253.23
313-43
373-74
434-15
494.70
555-40
616.27
13
14
14.00
74-or
1.314.03'
194.10
254-23'
314.44
374-74
435-16
495.7'
356.41
617.29
14
IS
15.00
75-01
135-03
195-10
255.23
3I5.44
375-75
436. 17
496.72
557-40
618.31
IS
16
16.00
76.01
136.03
10. II
256.24
316-145
S76-75
437-17
497-73
558.44
6.19.32'
16
i?
17.00
77-01
137-04
197- n
257.24
317-45
377.76
438-18
498.74
559-45
620. 34
17
18
18.00
78.01
1 38. at
198.11
258.24
318.45
378.76
439- 19
499.75
560,47
621.36
18
19
19.00
79-or
139-04
199- II
259-25
319.46"
379-77
440.20
500.76
561.48
622.37
19
20
20.00
80. 01
140.04
200.11
260.25
320.46
380.78
441.21
501.77
562.49
623.39
ao
21
2.1.00
81.01
1141.04
2OI . 1 1
261.25
321.47
381-78
442.21
502.78
563.51
624.40
21
22
22'. OO
82.01
142.04
2O2. 12
2612.25
322.47
382.79
443-22
503-79
564.52
625.42
22
23
23.00
83.01
143.04
203.12
263.26
323-48
383.79
444.23
504.80
505.53
626.44
23
24'
24.00
84.01
144-04
204. 12
264.26
324-48
384.80
445-24
505-81
566.55
627.45
24
25
25.00
85.01
145.04
.205- 12
265.26
325.48
385-81
446-25
506.83
567.56
626.47
35
26
26.00
86.01
146.04
206.12
266.27
326.49
386.81
447-26
507.84
5<.57
629.491
26
27
27.0O
87.01
T4'7-04
207.13
267.27
327.49
387-82
448.26
508.85
5d9.'59
630.50
27
28
28.00
88.01
148.05
208.13
263 .i2?
328.50
388.83
449-27
509-86
57o.6o
63 1 . 52
28
2g
20.00
89.01
149-05
209. 13
269.27
329.50
389-83
450.28
310.87
571.62
63.2.5.1
29
30
30.00
90.01
I50.0S
210. 1 3>
270.28
330.51
390.84
451.29
5H.88
572.63
633-56
30
3*
31.00
QI.OI
I5L05
an. 10
271.28
Stfi-Si
391.85
452.30
512.69
573.64.
634.57
fit
33
32.00
92.01
152.05
212.13
272.28
332-52
392.85
453-31
S'3-90
574-66
63'5.59
33
33
33-00
93-01
153-05
213-14
273.29
333-52
393.86
454-32
5M.9I
575.67
636.61
33
134
34-00
94-01
154-05
214,14
274.39
334-53
394-85
455-33
515-93
576.69
637.62'
34
35
35-00
95-01
135.05
215.14
275.29
335-53
395.87
456-33
516.94
577.70
638.64-
35
36
36.00
96,01
156.05
216. 14
276.30
336.54
396.88
457-34
517-95
S7fl.7i
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
218.15
278.30
338.55
398.89
459-36
5I9.97
580.74
641.69
38
39
39-00
99.01
l'59 -05
219.15
279-31
339-55
399.90
460.37
520.98
581,76
642.71
39
40
40.00
100. OI
160.06
320.15
280.31
340.56
400.91
461.38
521.99
582.77
643.73
40
41
41.00
IOI.OI
161.06
221 . 13.
281.31
341.56
401.91
462.39
523-01
53.79
6.14-75
41
42
42.00
IO2.OI
162.06
222.15
282.32
342-57
402.92
463.40
324. 02
584.80
64.5.76
42
43
43-00
IO3.O2'
163,06
323. 16
283- 3*
343-57
403.93
4641.41
525.03
585.81
6.46.78
43
44
44.00
IO4.O2
164,06
.224. 16
284.32
344.58
404.93
465.41
"j 26.04
586.83
647.80
44
45
45-00
105.02
165.06
225.16
285- 33
34>5-58
405-94
4166.42
S37.0S
587. 84
648.82'
45
46
46.00
106.02
166.06
2126.16
286.33
346-S9
406.95
467.43
528,06
588,86
649.84
46
47
47-00
107.02
167.07
227. 16
287-33
347-59
407.95
468.44
529.08
589.87
650.85
47
48
48.00
108.02
168.07
228. 17
288.34
348.60
408.96
469.45
5-30.09
590.89
651.87
&
40
49-00
109.031
169.07
229.17
1289.34'
349.6o
409-97
470.46
531 . 10
391-90
652.89
'19
50
50,00
110.02
170.07
230.17
290.341
350.6i
410.97
471-47
532.11
592.92
653 .fl"i
50
SI
51.00
in. 02
171.07
231 . 17
291-35
35i.6i
4111.98
4172.48
533-12
593-93
654.93
51
5<2
52.00
1 12. 02
172.07
332.18
292.35
352.62
4112.99
473-49
534- 14
594 .95
655-94
52
S3
53-00
113.03
17-3.07
233-18
293 -35
353.62
414.00
474.50
536.15
593.96
656.96
53
54
54-00
II4.O2
174.07
234'. 18
294.36
354-63
415.00
475-51
536. 16
506.98
657.98
54
55
55-00
115.02
175.07
235 .'18
295-36
355.63
416.01
476.52
537-17
597-99
659.00
55
56
56.00
116.02
176.08
236.18
296.37
356.64
417-02
477-53
538-18
599-01
660.02
56
57
57.00
117.02
177.08
237-19
297- '37
357-64
418.03
478.54
539-20
600.02
66 i ,04
57.
-s
58.00
118,02
178.08
238.19
208.37
358.65
419.03
479- 55
540.21
601.04
662.05
58
i
59-oo
119.02
179.08
239-19
299.38
359-65
420.04
480.56
541-22
602.05
663-07
59
1 'o.oo
I2O.O2
180.08
240.19
300.38
360.66
4M ,05
48i.57
542.33
603.07
664.09
60
IN TABLES
310
The Anti-Gudcrmannian.
mi
HI
.[!>
i/
51
H"
tf.17
>-j.iy
74-'-''i 7JS-M
670.3
(sH.!,|4
(M)l.(l.!
(;.!'
747- H
(rf,5(i 74'). H
7S5.'"
(Ktf.yo 757 -Of
1 f *
(H> I (.'/(| y(K). !.
/ui.Ko
XI,!. iM
77-'- -V
77.1-1
774-4
777-5
77H.fi
7-'5..V
13"
7<w. in
KM. 43
Km. 4!)
Hioisv
K.ii.71
H.w.7-1
8.M.77
WJ.J.KO
H?)lK!
WjK.ltt
.14
WtH.oH
Woy. 11
W74-7
W75. 3 1 1
K7!!l()
884. do
K<XJ . of
(XX) , Ii
()0l 15
IJOJ. l(
905- ^
910.4
15"
yil.50
9 l a. 53
013-57
yiH.5i
IJ24.(J(>
947.03
yjti.u?
921). 1 1
1)311 , 1 5
Uii.iW
y.M '-'!>
93". 37
<J.17.4<>
ij.Vi.5<J
<). 1 2 . "if
915-7"
050. i/j
DS-!.^
P57-1J
958.37
9fi3.3?
f/iS.4'5
(/>(), 6
971 X>
16"
17
18
19-
20
flii;
072.73
035.30
098.22
161.49
225.14
o'
970-77
036 . 35
1009.27
1612.54
226.20
1
<>74.8i
037.40
100.32
163.60
227 . 27
*
975.8.=;
038.44
101.37
16.1.66
228.33
J
y/(i . K(j
039 . 49
102.4:2
165.72
'229 4O
4
977-93
040.53
'103-47
166.78
230.46
5
078.97
041.58
104.. 53
167.83
231.53
6
otfo.oi
CX|i2 . 63
'105.58
168.89
3.32 . s<_)
7
981.05
043.67
1106.63
169.95
233-66
8
oSj.oo
044-7'- 1
107.68
171.01
234-7-'
V
983.13
045' -77
1108.74
172.07
235-79
IV
9&M7
046.81
1109.70
173.13
236.85
II
(j^5 . u J
047-86
nio. 8-1
174.19
2,37-92
I-'
ySo.itf)
048.91
1111,89
175.24
238.98
13
9X7.30
0.19-95
in 2. 95
176.30
240.05
34
y8S, 34
051.00
1114.00
177.36
241 . i i
35
980.38
05*2,05
I1I5-05
178.42'
242.. 18
I'i
<WO..'|i2
053-"!)
in 6. 1 1
179-48
243.25
17
i}0i.47
05-1 M
I IT?. l6
180.54
244-31
3,'?
i)i)j. 51
1055 - 19
1118,21
181.60
243.38
I't
993.55
056, 24
1119.27
182.66
246.44
20 ;
yiM". 1 )^
1057.2?
1120.3.2
1183.72
1247.51
21 '
W5.6, 1
058.3-,'
1 1 -31. 37
1184.78
1248.58
22.
<jij(),(
059.3S
1132.43
1185.84
1249-64
-'3
( .)!>7'7^
1060. 4v
11.33.48
n86.Qo
1250.71
-1
998.76
1061 ..it
11241,53
1187.96
1251.78
^5
Oi)o. So
1062 , 5'2
1125.59
ll8(>.O2
1252.85
2(1 -
i(XX.).Kf
iofy.57
1126.64
1190.08"
1253.91
~7
TiX)l .Ht,
i of 14. 62
11-27.70
1191.14
1254.98
j8
I(H>2 ,O. ;
1065.67
11-28.75
l ig?. 20
1256.05
2-.J .
1003-97
ioW'i.72
1129,81
1193.26
1257-12
o>0
1005.02
1067,77
M30.S6
1194.3^2
1258.18
31
lOOfi.OO"
1068 ,Bi
1131.92
1195.39
11259.25
3-
1007.10
io6g.86
113^.97
1196.45
1260. 3J
j.i
IDOH, I' 1
1070.91
1197-51
1261.39
.?"
looy.K
1071,96
it'jj.oa
1198.57
1262.45
35
ioro.2;
1073 .01
1 136. 14.
1199.63
1263.52
3*5
KIT I . 2t
in 74. of
1137.10
1200.69
1264.59
37
1OI3.32
to 75 i
1138.23
1201.75
1265.66
&>
IOI3.3'i
1076 . if
T I 39 -30
1202.82
1266.73
yj
10I4i. -I' 1
1077/2
1140.36
1203.88
1267.80
&
1015-45
I07fl.2f
TI4-I.4T
i20.| .04
1268.87
41
mi 6. 50
1079.3
1142.47
1206.00
11269.93
41*
1017.5.
If03 , 3f
114 3. -53
1207.06
1271 ,OO
-53
ioi8.5
1081,4
1144-. sS
1208.13
1272.07
4t
loiy.ti,
1082. .'if
n 45.64
1209,19
1273,14
45
1020.67
1083.5
1146.69
1210.25
1274 . 21
^5
1021 .7
I(>ft:| , 5f
114,7.75
1211.31
1275,^8
47
1022.?'
1085.6
1148.80
1212.38
1276.35
4*
102^-8
loHft.fif
II40.8C
1213.44
1277.42
40
iiwiji.B
1087.7
1150.9^
1214.50
1278.49
5
1035.90
ioRR.7
1131.97
1215.57
1279.56
Si
1089.8
1133-03
1216,63
1280.63
^ *
io_>7.iy
1090. 8C
ii'54.w
1.317.69
I3SI.70
53
lojjo * iy
IW>! .9
H5S- 1*
1218.76
L282.77
5-1
1030.0
1092. sX
1156.20
1219.82
IQ8-3.84
55
1031 . i
I00.1.O
11^7. 2f
1220.88
1284.91
35
1032 . i
lovS'.of
irsa.33
1221,95
1285.98
10313 < - v
1006.1
H5f>- 37
1323.01
1287.05
5S
1034 .aC
1097.1
1160.43
1224.07
1288. 13
W
1035-3
1098/2
1161.49
1225.14
1289.20
60
TAIILCB
311
The Anli-Gu<U:rmiumiiin,
ml
.1*
.13
.1-1
37
&
'HI
MW.57
1310. (>]
1 .11 1- 7-!
l.H-|-fM
1316.01
I.1J7.0H
i 3 <> 7B
133''. -M
W-<>7
1-1117.77
I.I7J.OJ
1.17-3.1.!
M7H..9J
l,|'/i. 1 1
1, 107--'"
ISM. -17
IM'I.?*'
1533-K'
iff |.07
ISVJ.-7
i. ( ;/y.('.i
I57-M-73
l(ii 16., (
ir.AS.7J
if.
Klttl . 10
ifif/i.yo
!'),!.'','
II H,/ ,(M I
t /'', ii'
l/nl .';n
171". M
Uil II
1-7^1.1*1
I/.t'l.t^l
11731.10
iy.t7.j-N
17.^.7"
"H'M-.l.'i
I/M7.^'
Uii't.jV
.U
37
-I"
.is
313
The Anti-Gudermamuan,
1 1 f <A . r i'i
Hi.'i | .1)11
MO/.H.S
M0').o/
:i 10. ','.'f
M I i ..](>
,1 !.('/
-'";;i-"l
.iH
.NHj").':!."
JKX'l.S't
i. Hi
J.I-M.TO
W5.JS
3393.63
!. 100.15
-1105.17
3468.26
2472.07
2473-3-I
2474.01
MUV-70
2494-97
1451 ..W
^455.'.^
'S'M'J
2505. 1
2507.7-1
3517.07
2520,54
.J5.il. 82
2537."
2538.50
2541.07
2C..J2, if)
2543 -fa
25--I4-93
2550.08
2553.95
2557.81
-'559- 10
2561 !J
2562.97
'5&1.27
2565.56
2568;'l4:
J 3 70. 73
7 3-;u
a.t.(u
75 . ()o
2577. 'i9
>-$-\<<)7.
2608.
2613.56
2614. Wi
2616,17
2617.47
2618.78
2621,38
afiaa.fxj
40
2622.69
2624.00
2(125.30
2627.91
2630.53
2631 .&|j
2633.14
2634-45
2635.76
2637.07
2638.38
2639.69
26,51.00
26.12,31
16.13.62
2647.55
2650. 17
2651.40.
2652,80
2654.11
2655.43
2656.74
2658.05
2(|(io.(i8
2663.31
2665.1x1.
>6fi7.26
2668.58
2071.21
2(172.53
L'673.85
2(/5 . 16
2676.48
2677.80
2679. 12
2681.76
2685.72
2/187.04
2688.36
2680. 6<j
26(JI ,01
26t>2.33'
2694.98
26(16.30
2^)97.63
2(x)8.()5
2700.27
2701,60
nil u
of
I
2
3
4
5
6
7
8
9
10
II
12
13
14
IS
16
17
18
20
21
23
24
25
26'
27
28
20
30
3T
33
33
34
35
36
37
39
40
41
4 a
43-
44
45
46
47
49
So
Si
52
53
54
55
56
S7 t
59
60
313
The Anli-Giitlcrnianninn.
ad u
.7o().ijo
3/08.33
ii/miKi'
J71-J.IM
2720 .SO
117,1.1.50
,3736.16
11737-50
-73*. K.I
27-10.17
-7-14.17
aT-lS.Si
'.17-10. 52
.750.85
2753-1 53
U754.H/
2756.21
^7!)7-5, l i
276/1.0.1
ii/6H.tJ.7
2760.62
.1773 .'M
3/76.3,1
-770.0.!
J7N1.71
.781,71
;.HH!,M
-!/OI.I.|
^8oi.!j.i
2063.10
JM7I-3I
.887.77
i!8(j8. 77
J*)0(), l,S
HXH.53
291 1 , ifi
20.13..13
,'031.7'
..-y.jH.H7
-usy.7-1
j'Xli. I.I
1)087.70
lioft), 10
300I-7'!
3003.1-1
300^.77
3(>l(t. l8
3013, (xi
31115. 8J
3017. M3
30^3.87
30.|.!.(i}i
305.|.Oj
3050-W
305H.3I
,1050-73
307.1. oft
.1075-11
307' i. 8 1
3078.. id
,ldH(i.8|
30<j<S.3*i
3101,17
.ll'M-01
31 1.3. (-7
3M,|.1I
BMITHftONIAN TftOLKO
The Anti-Gudermnnnian.
(Ill II
o'
I
I"
4'J
,(/<*>..!/
.t/lMJI
,171-!. !i<'
,1714.- :<>
5.1
,177,1-7-1
.1775.. M
,1'K >.'..
I047-17
4050.7-!
4<>flO.O()
4073. i a
*IOM.0o
|0<)5..|3
|<W)9.OJ
II 1.1. 44
4115.24
1117.05
1118.85
129,7.?
i.J' >5.i
133-34
,11,19,70
'1 155. >7
4I<>9.79
4175, '
57
.11189.07
4'iW-i?
4-'OI.OJ
4202.87
4213.95
4217.66
9-5i
4221.36
1225.07
-1 230.fi:)
.12.13.67
1-KHM7
4209,84
-1273.5!)
4277.35
4-79-23
4281 . 1 1
4292.41
4294.30
...58
4294.30
4296. 19
4^)8,07
4301.85
4303.74
4305.61,
4-.307.53
43IS.H
4317.01
4 3 JO. 80
4322.70
4324.6t
43.10-31
4.132.22
4336.03
43.17-04
4,143-66
4,145-57
4S17-48
4349-40
4351-31
435.1.23
4.155-14
-I.157.o6
4358.97
4360.80
4,162,81
436.1.. 73
4368,57
4370.50
4372-42
4374..14
4376.27
4380. 12
4,182,05
4387.84
4,189-77
4391-70
4393-64
4.195-57
4,197-51'
4.399-44
-1401.38
4403.32
4405.26
4407.20
4409. 14
._&!L_
4409.14
4411.08
4413.03
44'14.97
44i8!86
4422.76
4424,70
4426.65
4428, (b
4430.56
44.12.51
44.14.46
4438.37
4440.33
4442.29
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13916.43
16299, sf
CO
60
SMITHSONIAN TABLES * Prom 84. 3' onwnrda Interpolate by second dlfCcreuccu
318
TAULK VIII
CONVERSION OF RADIANS INTO ANGULAR MEASURE AND VICE VERSA
3'9
Conversion of Angular Measure into Radians.
n
adians lor n degrees
Radians (or n minutes
ailians for n seconds
II
mllnns lorn decrees
i
0.01745 32925 2
0.00029 08882 I
0.00000 48-181 4
61
1.06465 08437 2
2
3
4
.03490 65850 4
.05235 98775 6
.06981 31700 8
.00058 17764 2
.00087 26646 3
.00116 35528 3
.00000 9691x2 7
.ooooi 454-14 !
.00001 93925 5
63
64
loyyss 7-1287 6
.11701 07212 8
T^
5
6
8
9
0.08726 64626 O
.10471 97551 2
.12217 30476 4
.13962 63401 6
.15707 96326 8
0.00145 44410 4
.00174 53292 5
.00203 62174 6
.00232 71056 7
.00261 79938 8
0.00002 42406 8
.00002 90888 2
.00003 39369 6
.00003 87850 9
.00004 36332 3
65
66
67
68
69
I.I3-146 40138 o
.13191 73<*)3 2
. 16937 05988 4
. ittOH.3 38013 6
.204-7 7'838 8
_/* , ~.
10
II
12
13
14
O.I7453 1 29252 o
.19198 62177 2
.20943 95102 4
,22689 28027 6
.24434 60952 8
0,00290 88820 9
.00319 97703 o
.00349 06585 o
,00378 15467 i
.00407 24349 2
0.00004 84813 7
.00005 33295 o
.00005 81776 4
.00006 30257 8
.00006 78739 2
70
7 2
73
74
1,22173 04764 o
.23918 37689 2
.25663 70614. 4
.27409 03539 <>
.29154 36464 8
IS
16
17
18
19
0.26179 93878 o
.27925 26803 2
.29670 59728 4
.31415 92653 6
.33161 25578 8
0.00436 3323 1 3
.00465 42H3 4
.00494 50995 5
.00523 59877 6
.00552 68759 6
0.00007 27220 5
.00007 75701 9
.00008 24183 3
.00008 72664 6
.00009 21146
75
76
77
7-S
79
1 . 30&9<> 69390 o
.32045 02315 2
.3439" 35240 4
.36135 68165 6
.37881 01090 8
20
21
32
23
24
0.34906 58504 o
.36651 91429 *
.38397 24354 4
.40142 57279 6
.41887 90204 8
0.00581 77641 7
.00610 86523 8
.00639 95405 9
.00669 04288 o
.00698 13*7 i
0.00009 69627 4
.00010 18108 7
.00010 66590 i
.00011 15071 5
.00011 63552 8
80
81
82
83
84
1.39626 34016 o
.41371 66941 2
.43116 998(16 4
.44862 32791 6
.46607 65716 8
25
26
27
28
29
0.43633 23130 o
.45378 56055 2
.47123' 88980 4
.48869 21905 6
.50614 54830 8
0.00727 22052 2
.00756 30934 3
.00785 398i6 3
,00814 48698 4
.00843 57580 5
0.00012 12034' 2
.00012 60515 6
.00013 08996 9
.00013 57478 3
.00014 05959 7
85
86
87
88
89
1.48352 98642 o
.50098 3'iW 2
.51843 6-1492 4
.55334 30342 7
30
31
32
33
34
0.52359877560
.54105 20681 2
.55850 536o6 4
.57595 86531 6
.59341 19456 8
0.00872 66462 6
.00901 75344 7
.00930 84226 8
.00959 93io8 9
.00989 01990 9
0.00014 54441 o
.00015 02922 4
.00015 51403 8
.00015 99885 I
.00016 48366 5
go
92
93
9-1
I . 57079 63267 9
.58824 96i93 I
.60570 29118 3
.62315' 62043 5
.64060 9.1068 7
35
36
37
38
39
0.61086 52382 o
.62831 85307 2
.64577 18232 4
.66322 51157 6
.68067 ato82 8
0.01018 10873-
.01047 19755 i
.01076 28637 2
.01105 37519 3
.01134 46401 4
0.00016 96847 9
.00017 45329 3
.00017 93810 6
.00018 42292 a
.00018 90773 4
95
96
97
98
99
1.65806 27893 9
.67551 6btfi9 i
.(XJJ96 93744 3
.71042 26669 5
.72787 5959-1 7
40
41
42
43
44
0.69813 17008 o
.71558 49933 2
.73303 82858 4
.75049 15783 6
.76794 48708 8
0.01163 55283 5
.01192 64165 6
.01221 73047 6
.01250 81929 7
,01279 90811 8
0.00019 39254 7
.00019 87736 i
.00020 36217 5
.00020 84698 8
,00021 33180 2
100
no
120
I3O
140
1-74532 92519 9
.9iyW> 21771 9
2.09-139 51023 9
. 26892 '80275 9
.44346 09527 9
45
46
47
48
49
0.78539 81634 o
.80285 14559 2
.82030 47484 4
.83775 80409 6
.85521 13334 8
0.01308 99693 9
.01338 08576 o
.01367 17458 i
.01396 26340 2
.01425 35222 2
0.00021 81661 6
.00022 30J42 9
.00022 78624 3
.00023 27105 7
.00023 75587 o
tso
160
170
180
190
2.6r79!> 38779 9
.79252 68031 9
.96705 97283 9
3-H159 26535 9
.31612 55787 9
50
0.87266 46260 o
.89011 79185 2
0.01454 4-1104 3
.01483 52986 4
0.00024 24068 .1
.00024 72549 *
200
2IO
3.40065 85039 9
.6(1519 14291 9
e.
.90757 12110 4
.01512 61868 5
,00025 21031 I
220
.83972 43543 9
53
54
.92502 45035 6
.04247 77960 6
.01541 70750 6
.01570 79632 7
.00025' 69512- 5
.00026 17993 9
230
540
4.01425 72795 9
.18879 02047 9
55
56
57
0.95993 10886 o
.97738 438II 2
,99483 76736 4
0,01599 88514 8
.01628 97396 9
.01658 06278 9
O.OOO26 66475 2
.00027 14956 C
.00027 63438 o
250
2(X
27O
4.36332 31299 9
.53785 60551 9
,7i23H 89803
58
59
1.01229 09661 6
,02974 42586 8
,01687 15161 o
.01716 24043 I
.00028 11919 '
,00028 60400 7
300
330
5.235Q8 77559
.7595865315 8
60
1,04719 75512 o
0.01745 32925 2
0.00029 08883 I
360
6.28318 53071 8
SMITHSONIAN TABLES
320
Conversion of Radians into Angular Measure.
I liut Inn s
Anfllii
.i''.-|.SiK.! .17
.i.!.i*nj4 04
H)..|.|I7 .|l
i)-i.|).;.!4<) H8
Hail I [in a
O.OO(')
.007
Allfllo
o or 43,13:2.10 31
37
o 03 2(1,26.180 6'u5
00 OJ2. Of)26'4 806
(K.) 0:1. 125 JfJ 6l3
oo oS. 35059 '-'-5
o oo 10.31324 031
oo 12, 375^8 837
oo i-l.-l.l853 6.]4
oo 16. 50118 450
oo 18.56383 256
o oo
Numerical Ccmui
.fii'/v .t. U ".I
Kn.w ".'l ( l'/l>l V' 1 '/-'' '.H'.Vl
}?*' I.14.1V-! 0' m .1 H -I'M 1 * 1
,140111
8 9S8.15 47756
,,
V IT
J.25331 4T373 15500
02865
i riultan 206264. 80624 7o9 ri 4 seconds
= 3437 7'l fi 77 7 y 49 uiiimles
= 57-29577 95131 degrees
.l. 80625 S. 3^43 51332
8MlT)l6l)HIAM TAHI.K0
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