44 z Mr. Vince’s new Method of, &c. 
The general refolution of the given fluxion into a feries of 
fluxions of the fame kind, where the index of the unknown 
quantity without the vinculum keeps decreafing or increafing 
either by the index under or by half the index, has not, that 
I know of, before been given ; which furnifhes us at once not 
only with a very eafy method of continuing fluents, but alfo 
points out a very Ample method of inveftigating the fluent of 
the given fluxion without continuation. For if f A —p + b f B 
Hh c/C + d fD + &c.fB~p' + c'fC + d'fi) + &c./c — 
+ + &c. &c. then if for f B, f C, &c. &c. we 
fubftitute their refpe&ive values, we fliall get a general feries 
for/ A without continuation. The extent of any new method 
is, at fkft, feldom obvious •, and how far that which is here 
propofed may be fuccefsfully employed in other cafes will belt 
appear from its application. Different methods will always be 
found to have their ufes in particular cafes; for where one be- 
comes impracticable another will often be found to fucceed; 
and I hope that which is here offered will contribute fome- 
thing towards facilitating the inveftigation of fluents. 
