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HYPERBOLIC FUNCTIONS 1931

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387 pages
SMITHSONIAN MATHEMATICAL TABLESHYPERBOLIC FUNCTIONSPREPARED BYGEORGE P. BECKER AND C. E. VAN ORSTRANDFOURTH REPRINTNo. 1871CITY OP WASHINGTON"PUBLISHED BY THE SMITHSONIAN INSTITUTION1931ADVERTISEMENT.of the Smithsonian Institution was aAmong the early publications veryof tables Dr. Arnold wereimportant volume meteorological by Guyot. Theyand as well asso widely used by geographers physicists by meteorologistsedition was exhausted it was decided to recast thethat when the fourththree Tables,, entire work and publish separate volumes, Meteorologicaleach of which has nowTables, and Physical Tables, passed^Geographicalseveral editions.;= throughvolumes to the of natural..!. In the of the data of these studyapplication''beside those included in ordinarycertain mathematical tablesphenomenaneeded in order to save recurrent computa-tables of are urgentlylogarithmsIt was decidedtion on the of observers and investigators.part therefore^Mathematical on Func-to the present volume of Tables, Hyperbolicpublishtions.useful in branch of physicsFunctions are extremely every pureHyperbolicof whether to observational and experimentaland in the applications physicsThus whenever an as light, velocity,sciences or to technology. entity (suchis to extinction or absorption,i or radioactivity) subject gradualelectricity,some form of Functions. Mercator's1 the is represented by Hyperbolicdecay me-Functions. Wheneveri> is likewise computed by ...
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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. 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,) .