[ 432 ] 



6/ -rx. h , 6/ 6/ 

 = J-. 1 hen — ( = I + r-i 



12 + /' a 12 + /' 12+; 



12 + 6/+/^ .a 12 — 61 + 1^ T r ii L. 



= 72-6/ + /-^ '"^ ^^ = 7r;r67T7- ^"'"^ fyftemwhat- 



foever j ^ i ^^^ ^ 6^^+Z- ^^^ . ^ r.;^-- 6 ^L +Z'^ ^^^^^^ 



<? 12/)^— 6/Z+L^ ^ i2/*+6/)L+L* 



-if /-I = . ; then ^ = ?^J>P±^ and -J = lZ^±^. 



The fradlion — thrown into a feries will be i + /+ 



12 — 6/+/^ 



1 (- Y + &c. fo that the natural number cor- 



2 6 24 144 



refponding to Napier's logarithm / will be accurately expreffed 



thus ii^ "^ + _ + &c. Whence it appears that the 

 12 — 6/+/* 720 



fradion iAlL-__Z — will more accurately exprcfs the natural 

 12-6/+/= ^ ^ 



number of Napier's logarithm /, than the five firft terms (i + / + 



[ 1 ) of the original feries. Now in the application 



2 6 24 



of thefe terms to find the natural number of a logarithm, befides 

 reducing the given logarithm to Napier's fyftem if it be of any 

 other, three multiplications are neceflary, not to mention the 



divifions 



