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
1931ADVERTISEMENT.
of the Smithsonian Institution was aAmong the early publications very
of tables Dr. Arnold wereimportant volume meteorological by Guyot. They
and as well as
so widely used by geographers physicists by meteorologists
edition was exhausted it was decided to recast the
that when the fourth
three Tables,
, entire work and publish separate volumes, Meteorological
each of which has now
Tables, and Physical Tables, passed^Geographical
several editions.
;= through
volumes to the of natural
..!. In the of the data of these study
application
''
beside those included in ordinary
certain mathematical tablesphenomena
needed in order to save recurrent computa-
tables of are urgently
logarithms
It was decided
tion on the of observers and investigators.
part therefore^
Mathematical on Func-
to the present volume of Tables, Hyperbolic
publish
tions.
useful in branch of physics
Functions are extremely every pureHyperbolic
of whether to observational and experimentaland in the applications physics
Thus whenever an as light, velocity,
sciences or to technology. entity (such
is to extinction or absorption,
i or radioactivity) subject gradual
electricity,
some form of Functions. Mercator's
1 the is represented by Hyperbolicdecay me-
Functions. Whenever
i> is likewise computed by Hyperbolic
projection
are most
to be measured they
chanical strains are regarded as great enough
de-
of Functions. Hence geological
in terms Hyperbolicsimply expressed
reason that
to such and it is for that
.formations invariably lead expression,
workwho arc in charge of the physicalMessrs. Becker and Van Orstrand,
this volume.have been led to prepare
of the United States Geological Survey,
'
CHARUCS D. WALCOTT, Secretary.
;i
publications containing and fmirtiiw'; li,i:i ITII a.ldi-il i
hyperbolic oxiuincnti.il
historical note on and the liililes of
page li, cirmlar ftint;ii(iii:i ,IIM! tin- r\|Huiniii.il
been extended to meet recent {lemands.
May, Kj2<\.
In tin's fourth no need fur corriutionH IM:, linen
reprint
September, 1931.CONTKNTS.
INTRODUCTION ;
rftitiiI'AUII
i "i i1 * * Y*
DdmiUoiiM and formulas vjj
(Urotnelricid illustrations . , . vvi.iiiA A. VI I I
Methods of interpolation xxxiv
of tables
Description x|jjj
Historical mile X |VUI
TAHU( I :
I'ivo plan: values of sinh
log //, log cosh , log liinh K, and
log
eolh if
n
TAIH.IC :
Kivi! place values of sinh cosh tanh
, , //, and ooth it , , ,
87
HI :TAHI.K
1'lvo
pliuT vHluoHof .sin it, COM ,iin and
//, log u, log eo.t w, being
expressed in radians and their angular equivalents ....
173
TAIU.I.; IV:
1 he uwiMiding and to
dt'soending exponential 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 of
multiples log^-for interpolation of Iog ,.v.', it j., ,,.,
as a matter of convenience Hint a few of Ihc
simpler contliiimtioori <>i ,.*
uentials receive us
special names, sine, cosine, etc.
The other method of
analytical ^m-nili/.inj; the twu rlu-i<"
TJ ,,
f/ ""' ^<,-.*''
and these
functions arc related theby ei|imLimi
Lucas and studies
develops these functions, |imil |
MJI 11( r, (!i| ,., w| , ti|i ,
tive number,,. He finds
that all the theorem, n^UIn,.. | |1(1I11 ( hi,
,,,i.lvconvened into those of
ordinary trigonometry when // j, .|m,,| ,,.. ,
IVIand , cos . HeFby infers that between tl, limiu , tj tttimi\ ;
be replaced realby any value, ami shows thai
the i|M,.n,,,.,,, n
,lr,li,,rand Kwhen translated
into tri.ononuH.ic for.nuh, on thi, ,,
,
be verified. By substitulin^ for n an
imuf-inary m.-umrnl
h,
functions also are found to be eo.np.hended I
or
KJ', -,
=
If c thisa\ gives
?'
whereA and B are arbit
COM .v
1An.Jol
,r.ofMnth.,vol,i H
(1 V ( pllH,) .