186 



If for the powers of Q, R, S, &c. we substitute the powers 

 of the first, second, third, Sec. fluxions of .r, the above will be 



the formulae for the several orders effluxions of .r 7. For, the 

 fluxions of X are parts of the actual differences, no notice of 

 the remaining parts being necessary to be taken. And if, in 

 the formulae for the differences of the powers, we substitute 

 for the difference of the roots the fluxion of the root + the 

 rejected part of the actual difference of the root, the powers 

 of the fluxion of the root will be similar to those of the dif- 

 ferences of the root, with the same co-efiicients ; the remain- 

 ing powers of the fluxion of the root are not to be noticed, 

 as involving the members rejected in deriving the fluxion of x 

 from its actual differences. 



ESSAYS 



