L OGA RITH MIC A ND TRIGONOMETRIC TA BLES RE VISED EDITION PREPA RED UNDER THE DIRECTION OF EARLE RAYMO ND HEDRICK ENTIRELY RE-SET IN TYPE FAC E NEW YORK THE MACMILLAN COMPANY C O YRIGH T 19 13 A ND 1920 P , , B r T H E MA CMIL L A N COMPA NY. All rights reserved— no part of this book may be reprod uced in any formwithout mi i i ritin fr m h blish r per ss on n w g o t e pu e , except by a reviewer who wishes to quote brief passages in connection with a review written for inclusion in magazine or Dewspaper. e U and electrot d . Revis edition ublish A s 192 . Re rinte S t p ype ed p ed ugut , 0 p d A ril 1924 Ma Se tember D ecember 1925 A ril June 1926 January p , ; y , p , , ; p , , ; , l 2 mbe r 1 m m Juy, 19 7 ; March , D ece 928 ; Nove ber, 1929 October Nove ber 1930 ; , ; , , A ril October 19 1 F r ar 19 2 A r 3 a m r 1933 p , , 3 ; eb u y , 3 ; p il, 193 ; M y , 1933 ; Nove be , ; July, 1935. SET UP A ND EL E CT ROT YPE D BY TH E L NC ST ER RE S S INC . L NC STER PA A A P , , A A , . PRINTED IN T H E UNITED STATE S OF AMERICA H E F ERRIS RINT ING CO . NE W YORK BY T P , - 3 5 5 PREFACE The present edition of this book contains all of the tables in the r i u i i ns All have been reset in a new and ver re l ev o s e o . a p d t y dab e type . Great care has been exercised to preserve and to increase the great e r r li ili ha xiste in th revio e i i n d g ee Of e ab ty t t e d e p us d t o . For careful rea in Of the roo s either in the first roo s ma e romt or i h d g p f , p f d f ype n t e roo s m romcast lates I amin ebte to m u h r h p f ade f p , d d y da g te Elisabet n i h r L Mill r e r l a d h r h n Mr R c a . e t s ve a Of m e usba d, . d , o y own students, and to h llowin rien s in other institutions some ims wi h h t e fo g f d , t e t t e i r a h en s : Pro ess r . urrier B own ni rsi d Of t eir stu t o H . ve Pr d f C C , U ty ; o ess r i ni ersit f In iana Pro s r o H T . Dav s v O e o H . B ht f . , U y d ; f s . Dwig , M hue s Insti ute of Technolo Pr ess r B F ni assac s tt t o o . r gy ; f W. o d , U versi Of Mi hi an Pro essor A . ar in ni r i ty c g ; f M H d g, U ve s ty Of Arkansas ; Pr r Pomona olle Pr s r L h o ssor G . Jae e e o es o S n ni fe C . g , C g ; f . Jo ston, U r s r A K n ver i i Pr s s . J m s t o et o t o e o . e n r a A hin n y f D ; f p e d C . Hutc so , ni rsi f olora o Pro essor G Mullin r r ll U ve ty o C d ; f . W . s, Ba na d Co ege ol mi i r it Pr ess r L M P n h i u a n ve s o o . assa o M sa nst (C b U y) ; f , as c usetts I u h l r r t O T no o P o esso s H . L . Rietz Ros n F te f ec gy ; f , coe Woods, a d J. i w Pr ss r rs Reill ni t Of o a o e o E . E . s n I h y, U vers y I ; f Wat o , owa State Teac e ll r Falls r E . ilson mri n r o e e at e a D . a b e ass a d P o C g C d ; W W , C dg , M . ; fess r a hr n ant Athens olle e A hen Al am h Of o K t y Wy , C g , t s , ab a. Eac h s ns or rou s has rea th omlet r i h lin t e e perso g p d e c p e p oof . W t deep fee g, I may record also that the late Professor Louis Ingold of the University Of Miss uri rea the roo s u a 54 n h n m h l of o d p f p to p ge , a d ad se t e t e ast h within a wee Of his en ath n nu r 5 1 5. t ese pages k sudd de o Ja a y 2 , 93 ’ These careful readings render the possibility Of printers errors ex r ml m il h l l i n h r h an t e e y re ote . Wh e t e ca cuat o of t e p obability t at un iscovere err r exists is not simle a s ri t a un has en e t Of d d o p , t c cco t be k p each error found and of the total number not found by any one group Of rea ers so that a basis for a statistical calculation is nown : the result d , k ’ ing probability that even one undiscovered printers error exists is not mre h n one in man th usan o t a y o ds . I esire to ex ress here m than s ll tho ar ic larl those d p y k to a se , p t u y mentione abo e who hav assis e in h eff r t ma h s tables d v , e t d t e o t o ke t e e so ree romerrors and there ore s relia l now of no comarable f f f o b e . I k p me h f r rin hi li t od o secu g t s qua ty in a set Of tables . I repeat also my acknowledgment made in the original edition to man reviousl existin tabl s r i l rl h f an those y p y g e , pa t cua y t ose O Vega d of Houl urin th ro - rea in h h ha have e . D e o o w o a si te g p f d g, t se ve s s d comare these tables wi h a rea ari in a l in lu in p d t g t v ety Of exist g t b es, c d g several hi h- lace tables and h val h n r al la an g p , t e ues ave bee ec cu ted d chec e whenever a isa r mn h n o r k d d g ee e t as bee disc ve ed . Finall I i h mn n y, w s to e tio the excellent cooperation Of the editorial stafi Of the Macmillan oman un r h l ir i n r F C p y de t e ab e d ect o Of M . T . h Sutp en. E . R. HEDRICK CONTENTS EX PLANATION or THE TABLES TABLES PRINCIPALLY TO FIVE PLACES T LE MM N LO RITHMS or NUM ERS AB I. CO O GA B T LE AB Ia. T LE II A r THE TRI ONOMETRIC FUNCTIONS 21—44 AB . CT UAL VALUES o G T LE III or S AND T roa INTE RrOLATION AB a. VALUES T LE O L or TRI NOMETRIC F NC AB III. COMM N OGARrrHMS THE GO U TABLE REDUc rION or DE GREES TO RADIANS T L TRI N METRIC FUN TI NS r AN LES IN RADI NS 2- 3 AB E V. GO O C O o G A 9 9 T LE I r E REE S AB Va. REDUC T ON o RADIANS To D G TABLE 94- 111 T LE I 112- 114 AB VI . L r r l M TABLE VIII. MU TIPLES o M AND o / T LE IX ND L T M r HrrERBOLIC FUNCTI NS 116- 122 AB . VALUE S A OGARI H S o O T LE L ND R T MS r VE R NES 123—125 AB X . VA UES A LOGA I H o HA SI T LE F R LE— r PRIMES 120 - 127 AB X I. ACTO TAB LOGARITHMS o T LE X IIa AB . LE X IIb C M D TAB . O POUN DISCOUNT T LE X II AMOUNT or ANNUIT r AB c.