[ 321 ] 



A METHOD of expreffing, isuhai pofible, the VALUE of ONE 

 VARIABLE QUANTI FY m INTEGRAL POWERS o/" ANO- 

 THER ^K^ CONSTANT QUANTITIES, having given EOIJK- 

 TIONS exprejfr^g the RELATION of thofe VARIABLE OJJAN- 

 TITIES. In which is contained the GENERAL DOCTRINE of 

 REVERSION e^SERIES, o/" APPROXIMATING to the ROOTS 

 of EQUATIONS, a7id of the SOLUTION of FLUXIONAL 

 EQUATJONS by SERIES. By the Rev. J. BRINKLEY, M. A 

 ANDREWS Prof ef or of AJironomy, and M. R. L A. 



X H E moft general and ufeful problem in analytics is, from a j^^^^ j^^^ ^^ 

 given relation between two variable quantities to exprefs one of ''^^ 

 thofe quantities in terms of the other and conftant quantities. 

 The cafes however in which this can be completely performed arc 

 few in comparifon of thofe in which it can be only partially done. 

 Among the partial folutions are thofe by feries not terminating. 

 When fuch feries converge they afford l^e folution required. Va- 

 rious methods have been given by authors for obtaining thefe 

 feries principally derived from thofe given by Sir I. Newton. Of 

 thefe the method of affuming a feries with coefficients to be de- 

 VoL. VII. S s termined 



