276 DEVELOPMENT of a certain 



p*= (i + /")p"; 



&c. &c. 



&C 



and thus we may proceed as far as we pleafe. If thefe equa- 

 tions be now combined with the equations fimilar to them 

 which we have already found (Art. 3. and 4.), and the quan- 

 tities N', P' ; N', Vfj N'", P ', &c. be gradually exterminated in 

 the fame way as in obtaining the equations of Art 4. we get the 

 following feries of equations : 



= (i + 0(i-f-^)P" 



= (1 + ')(! + '')(« + '"OF", 



&c. 



f — ?< (' + g/ ) m' 4. x P (l+O r 



\ e — — JN + 2 P ^fina^, 



2.2 ' (.2 ' 2.iJ 2.2 ll, - L *r 2.2.2. 2 " n 4^j 



2.2,2.2 ""H-Y 2.2.2.2 . 2.2 "«IO<p • 

 &C 



If we fuppofe thefe values of P and N to be continued in- 

 definitely, it is evident that the former will be expreffed by 

 the product of an infinite number of invariable factors, and 

 by the limit to which the feries of fluents P', F, P'", &c. con- 

 flantly tends ; and the latter by another infinite product, and 

 two infinite feries, which involve alfo P, and the limits to which 



the 





