[ 4^3 ] 



The principal life of the faflors of the produ>ls of fix dimcn- 

 fions in the conflrudion of logarithms, will appear, when (by 

 reafon of the greatnefs of the produds which would arife) it be- 

 comes unneceflary to ufs a fingle term of the feries. 



Thus ; if it be fuliicient to have the logarithms of numbers 

 true to 7 places of decimals, the logarithms of numbers exceeding 

 lOO may be found by this method. Let the logarithm fought, be 

 that of loi, as before. 



;<— 8 = 86 Log. 1,93449 84512 The logarithm of the ratio of, 



X— 5=89 I, 949 -^.g 00066 • ^ — 



D ) > i'T-3'^y X- 8. .V- 5. A- — 3.x +-3. A"+ 5. 



x-3 = 9i 1,9590413923 ^^ ^p 



;<+3 = 97 1,9867717343 x + 8:^^*.x\A-4-7'=y'^'^- 



a:+5 = 99 J' 99563 51946 Therefore the logarithm of the 



^+8 = 103 2,0086001718 j-atio of, 



II' 83393 ^^9508 



x-8. x-s-x-z- «+3- *H- 5- «+8iJ 



5, 91696 84754 ^ — 7- ■^ 



: ^4-7 = £_ &c. J' being; taken 



\ ,/: „ 



equal to '- —L — i ; 



:>f-7 = 87 I, 93951 925261 y 



X =94 1,9731278536! 2.x'=^l\x\i^+^ 



, , I 4400 



3, 91264 71062 



^+7= loi Log. 2, 00432 13692-) , „ „ , 



( 94755 506, 845. So that the 

 true to the 8th decimal place. J 



i. e. in the prefent inftance 



that the 

 logarithm 



