of/> things, and bccaufe the permutations of two things are two 

 without regard to order, when the order is fixed the whole 

 number of permutations muft be alfo divided by the number of 

 permutations in each order that is fixed, that is by'2 x 2 X 2 X &c.' 

 ffj z= 2V alfo becaufe gr a' are the fame, it muft be divided by 

 f X f — I X _ _ I. Whence the number of permutations or 

 the coefiicient of ai" bi is as above ftated, &c. &c. 



Example I. The 6"" fluxion of x" = 



«— 3 



m...m — IX -if 4J «* k' 



1—6 



_ «— 4 

 -3« + 



Example II. The 8"" fluxion of x^ when a — 0, and the 



1^ S''' 5'''> ^"^ y**"' °'' t'^^ fluxions of the uneven orders are alfo = is 



\ \ t f ? ■ 8. 7 



56 X iv + 70 x'. For in this cafe the coefF. of x «■ = ' x 2 = 



56, and the coefF. oix"- = 



%■ 7- «• 5 



X 2 = 70. 



4 3. 2. 1 1 X a. I 



Example lit. The coeff". of x' in the 7'"' fluxion of k^, when 

 the even fluxions are = is 



T t 2 7. 6 . 



