L OGAR I TH M I C TAB L E S P R GE OR E W I LL I A M ON E S OF. G J ELL VE TY CORN UNI RSI . FOURTH E I TI N D O . To romote the detection of errors i n the tab es one do lar i be ai d p l , l w ll p for the first notice of ever suc error. Address rof Jones at I thaca y h P . l flllhflll MA C M I L L A N A N D CO. Y m am a , N . GE G E OR E . W JON S . 18 93 . N N C O T E T S . Pa s -a . EXPLANATI ON OF THE TABLES I F R - LA E LOGARI TII MS 2- 14 . OU P C 1 s A four lace ta e of o ari thms of the na tural . num ers 1 2 i t a ta e of ro p bl l g b , , w h bl p orti ona differences in the mar i n and of the o ari t ms of the s uares c bes s uare - roots p l g , l g h q , u , q , - c be roots and reci rocals of the n m ers 1 2 99 . u p u b , , . - I I . U PLA E T I G N ME T I FUN TI NS FO R C R O O R C C O , A four- lace ta b e of o a ri t ms of the six rinci a tri onome tric functions i t differences for p l l g h p p l g , w h mi n tes and of the en t s of area i n radia ns. u , l g h I I I . LOGAR I TII MS NUM BERS OF , - m r - i A six ace ta e of o arit s of fo fi ure n mbers th a tab e of differe nces. pl bl l g h u g u , w l NSTANTS OF MATHEMATI S AND NA — W I GHTS AND MEASU ES CO C OF TURE E R , A ta e of useful consta nts with the o arithms of t ose in common use . bl , l g h ADDI TI N - SUBT A TI N LOGARI THMS O R C O , A six - ace ta b e of o ari thms so re ate d t a t their use the lo arithm of the sum a nd of the pl l l g l h , by , g ‘ diiterence of two numbers may be found from their logari thms wi thout ta king out the numbers SI NES AND TANGENTS SMA ANGLES OF LL , ” ” ° ° A tab e of the ra tios si n A :A ta n A :A for an e s 0 - b ere the o ari t mic si nes and l , gl , wh by l g h tan ents e sma are m actl t an Tab e I I g of th se ll angles found ore ex y h by l V . TRI GON MET I UNCTI NS O R C F O , A nve - lace ta b e of na tura sine s cosines tan ents a nd cota n enta of an es to p l l , , g , g gl ’ minutes and a six - lace ta e of t eir lo arithms i t diderences of o arithms for seconds ex , p bl h g , w h l g ressed in units of the si th decima lace p x l p . VI I NAT RAL A I THMS 105 - 111 I . U OG L R , - A six ace ta ble of na tura o arit ms of the decima num ers . 01 . 02 . (B of the na tura pl l l g h l b , , , , l n mbers 1 2 8 1218 and of the rime num ers et een 1218 and 10000. u , , , . , p b b w I ME AND M OSI TE NUMBERS 118 - 187 PR CO P , A ta e of ri me and com osite num e rs from 1 to 20000 with the ihctors of the com osite bl p p b , p - num ers t at are not di vi si e 2 or b and ten lace o ari t ms of the rimes. b h bl by , p l g h p S UARES 188- 180 Q , A ta e of the s ares of the na t ra 1 2 . 222. bl qu u l 1 , 1 - 1 140- 141 ounce, o ; 1 2 8 A tab e of the cubes of the decima numiee r . l l , , , S AR E- ROOTS 142- 145 QU , - m rs 1 2 and of A ta e of the s uare roots to fo r decimal laces of the na tural nu e . 299 bl q , u p , b , , , m rs 2 the decima nu e . 1 . l b , , XI I I UBE - R TS 148 - 15 1 . C OO , - im aces of e na t ra num rs 1 2 929 of the A ta e of the cu e roots to fo r dec a th e . bl b , u l pl , u l b , , , a 01 02 os m m s . m . decimals 1 2 s and of the deci . , . , . , . l , , , XI V RE I R ALS 152- 158 . C P OC , A ta e of the reci rocals of the decimal n m e rs . 01 . 02 . 08 bl p u b , , , — UA TE - S UARES 15 1 151 Q R R Q , - A tab e of the a r r ar s of the na t ra numbers 1 2 8 2000. te s u e . l qu q u l , , , BESSEL’ S E I I ENTS CO FF C , ’ A ta e of Besse s coemcients for second t ird fourt and fift differences for i nte r ola tion. bl l , h , h , h , p XVI I BI N MI A OEFFI I ENTS . O L C C , A e of inomia ooefi cients for second t ird fourth and fi ft differences for inter ola tion. tabl b l , h , , h , p I E R S OF BSE VATI N XVI I . R OR O R O , A ta e of ordina te s of the ro a i lit - curve val es of ro abi it i nte ra s and ot er va ues. bl p b b y , u p b l y g l , h l o ri t l SQ Geor e Wi iam Jones. C py gh , , by g ll ’ 2 “ H f /7" EXPLANATI ON or TH E TAB LES. N COMMO LOGARITH MS. F L I T FORM O A OGAR HK. Tns mus eu m:of a number is the exponent of that power to whi ch another num er se s r s s e . h , the ba , mu t be ai ed to give the number fir t nam d s c on use o is 10 as s s a re incom The ba e omm ly d in computati n , and mo t number mea surable o s of 10 s s s .of a n e p wer , a common logarithm, in general, con i t int ger, r s c and ss c a ss . the cha acteri ti , an endle de imal, the m nti a I f so n s of one is o of 10 a number be re lved i to two factor , which an integer p wer li s 1 and 10 of 10 is c c and the other e between , then the integer exponent the hara f ss teristi c a o is . a c e r s c is , and the log rithm of the other act r the manti a The char t i ti s u u and n a if s l man po itive if the n mber be larger than nity, eg tive it be ma ler the ss is s os c ac s c is ca e s n a v . ti a alway p itive. A negative har teri ti indi t d by the ig bo e it . fi 7770 10 and 7770 g , X log 0 77 z:10" 0 . 777 7 X and log . The logarithms of all numbers expressed by the same figures in the same order have different characteristics but the same mantissa for since all such numbers may f s m 10 be got one rom another by multiplying or dividing by o e integer power of , ms ff e their logarith di er by integ rs. i : c s a s of a u e In part cular if the de imal point tand fter the fir t figure n mb r, f s is 0 af e u s is 1 a counting rom the left, the characteri tic if t r two fig re , it if fter e fi s is 2 and so . So if l o s e fo s si thre gure , it , on , the decima p int tand b re the fir t g nifi nt u c c s i is 1 if z l a 2 ca c is . fig re, the hara teri t c one ero fol ow the de im l point, it 0 : E . 03 4 9 .