[ 4o: ] 

 fum of this feries will exprefs the logarithm of the ratio of 



.V— 2!2- r , . ^ AT 4-2 2 



v. J. I X 1 •^' — I or of .V + I . .v — I X - 



''^ ^ x + z] X—2 



If two prodiifls of any dimenfions whatever, differ in their 

 lowefl terms only, and the ftcond terms of all the factors in each 

 prodnd be equally multiplied ; the produds of the fadlors fo 

 changed will ftiU differ in their lowefl terms only, but the differ- 

 ence in this cafe will be the difference of the original produds mul- 

 tiplied into the common multiplier of the fecond terms of the 

 factors raifed to the fame dimenfion with the higheft term of 

 either produd. For the terms of the original produds, beginning 

 with the highefl term in each, are refpcdively multiplied by 

 the terms of a geometrical progrefTion, whofe firft term is unity, 

 and fecond the common multiplier; fo that the terms of the 

 latter produds, which are correfpondent to terms that were equal 

 in the firft produds, will be equal to each other ; and the terms 

 of the latter, correfpondent to thofe which differed in the iirfl 

 produds, will have a difference equal to the difference of the 

 terms in the firft produds, multiplied by the correfpondent term 

 of the geometrical progrefTion above-mentioned. 



Let t?i denote the common multiplier, and n the index of the 

 higheft term in the produdls ; the geometrical progrefTion will 

 ftand thus, i,m, ?n', m\ &c. , wz". Let the latter produds be 



both 



