vj? 



[ 333 ] 



a P y 



ofj',y, &.C. The coefficient of xj> z, &c. is readily deducible by the- 

 methods in the former problem, and is = 



«. « — I . « — "2 



« X « — r 



I x/3 X /3— I 



I X y X y 1 



I X, &C. 



Problem 3. To find the «'* fluxion of the fine of an arch x 

 taken m times when the arch does not flow uniformly^ 



Solution- Radius being unity. The n'^ fluxion of the fine 

 of mx 



w' J-, mx — , &c» 



The following are the laws of this feries : 



I. The quantities to which the produds of the fluxions and 

 their coefficients are affixed are fucceffively mcs, mx: m^ s, mx: w* 

 cs, mx: &d. The fign is + or — according as the number of pre- 

 ceding terms of cofines is even or odd. 



t. Tas 



