[403] 



both c'ivided by m' ; the quotes wi'l have the fame ratio as tlie 

 latter produds, and the fame difTerence as the fifft produdls 

 have. Now the terms of the firft produds multipHed by the 

 correfpondent terms of this proerelfon, — , > . &:c. 



Ill 



m^' ni^'m^' ^ ^'' ^" ^'^^ terms of the preceding progrcfTion divided 

 by 771") gives the correfpondent terms of the quotes ; fo that if /« 

 be greater than r, the terms of the quotes will be lefs than the 

 terms of the firft produds refpeflivcly. — The contrary to this 

 happens, if ^2 be a proper fradion — In this laft cafe then, the 

 fum of the quotes being greater than that of the firft produds, 

 while the difference is the fame ; and the difference of the quotes 

 having the fame ratio to their fum, as the difference of the 

 latter produds to their fum, it appears that the difference of the 

 latter produds bears a lefs ratio to their fum, than the difference of 

 the firft produds bears to their fum ; fo that if the fecond terms 

 of the fadors of produds differing in their loweft terms only, 

 be all multiplied by the fame proper fradion, the feries exprefling 

 the logarithm of the ratio of the produds to each other will con- 

 verge fafter. 



'b^ 



I F the fecond terms of the fadors of produds differing 

 in their lovVeft terms only, be equally increafed by addition or 



3 E 2 diminifhed 



