[ Z'^1 ] 

 Problems for finding Fluxions per Saltum. 



Pros. i. To find the «'* fluxion of «" when x does not flow 

 uniformly, and m denotes any whole, fradional or negative 

 number. 



Solution. Let a, 3, e, d - 



ift^ 2d^ 3d^ 4.th^ . 



fluxions of a. 



V. - - J', y, /3, « be the 

 - k"" - n— 4,H— 3,n— 2^»— I 



Then the n"' fluxion of ^v" 



mx X -\- n.a , 

 n. n — I 



I. 2 

 ti.n — I. n — 2 

 I. 2. 3 



&c. 



in 



Cy 



n. «— I. n— 2 



I. 2. I 



ab^ 



m,m—l X + n.n — l.n-—2 n— 3 

 &c. 



JB— 3 



ocim. OT— I. m — 2 >« +> &C. 



The following are the laws of this feries : 



I. The index of x diminishes in each term by unity, and is to 

 be continued till it becomes o or m — a. 



2. The coefiicient of a; is the produd of m.m — i. 

 nt — V — I, into the fum of quantities, with numeral cocfiicients 

 annexed, deduced from the different fluxions of x. 



3. These 



