276 



DEVELOPMENT of a certain 



r = (I + e'") P'", 



P"'=(l + f'^)p'^ 



&c. &c. 



N 



N"' + 



P* 



'f^'fmS^'", 





&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'', P'' ; 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+OP' 



&c. 



1 



N<! 



\=e 



,0+0 



js'+!p- 



-—fin 2^', 





- e'/e'" ( t+00+0('+^"') 

 2.2. 



-Z-iH ,2.2 ""■i-'t' 



1.2.2. 2 . 1 . •» »** Vf' 



&c. 



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

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

 the produ(5l of an infinite number of invariable fadlors, and 

 by the limit to which the feries of fl[uents F, P*, P"', &c. con- 

 ftantly tends ; and the latter by another infinite produdl, and 

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



the 



