[ 398 ] 



The ferics will then exhibit the logarithm of the ratio of 



■*■* — 2 . — -,, ^ .V+ I ; 



x+ I\ X — - . A'— I ,% or of "- j X X~2 '. X+ 2 ; of x+ {]' ; 



,, X + 2 , .V — I * 



AT— 1> X or of AT— 2 ■ " 1 X x—2 ; vvhcrc, the antecedents 



•^ - 2' • A" + I / 



being lefs than the confequents, if the logarithm of x + i/ or 

 of AT — 2 be required, the fum of the above feries is to be fub- 



^ _1_ 2 V _ T * 



traded from the logarithm of a:— i,' x or of i x a'^- 2, 



° ' X— 2 x-\- i\ 



refpedively. 



The fmiller the fador, by which any given number whofe 

 logarithm is fought, is denoted, the fafler will the feries con- 

 verge. 



For the abfolute value of each fador, and therefore the va- 

 lue of each produd, is by this means encreafed. — Then fince 

 the fum of the produds is increafed, their difference being un- 

 varied, the feries will converge faftcr. 



Though we have this advantage by making a fmaller fador 

 reprefent the number whofe logarithm is required, yet it may 

 be objeded, that this implies the neceffity of being previoufly 

 acquainted with the logarithms of greater numbers. But the 

 difnculty of this, will in the prefent cafe, be removed, if the 

 prime number whofe logarithm is required (that number being 



underftood 



