[ 392 ] 



and s t"hc fum of the numbers, as before ; and ^ the quote found 

 upon dividing, the logarithm of fome number according to that 

 fyftem, by Napier's logarithm of the fame number. 



It is evident, that the lefs d is in refped of s, the fafter the 

 •ferics will converge ; fo that the conftrudion of the logarithms 

 of prime numbers, W'ill be rendered more eafy and expeditious, 

 by finding two great produds, which fliall have a fmall difference ; 

 one of which produds, fhall be compofed entirely of fadors 

 whofe logarithms are already known, and the other, fhall have 

 in its compofition, the number whofe logarithm is fought, or fome 

 power of that number; and, if it have any other fadors, the lo- 

 garithms of ihefe fadors mufl be previoufly known. 



Having found fuch produds, we may, by the application of 

 the above-mentioned feries, find the logarithm of their ratio to 

 each other •, which is the fame with the logarithm of the ratio of 

 the firft produd (or that which is compofed entirely of fadors 

 whofe loe;arithms are kno'vn) divided by the fador or compound 

 of fadors whofe logarithms are known (if there be any fuch) 

 in the latter produd, to the prime number whofe logarithm is 

 fought, or feme power of that number. Then, from the loga- 

 rithm of the antecedent, and the logarithm of the ratio, we have, 

 fcy addition or fubtradion, the logarithm of the confcquent. 



I PROPOSE 



