66 
Mr. Knight on the Expansion 
11. To get methods of deriving any coefficient from the 
one immediately preceding it, we must substitute, in (£) and 
c e 
(s), the values of B and B given by the following equations, 
n—m n—m 
which are similar to those found before, in the case of one 
multinomial, and marked (4) and (5). 
B 
n— 1 
"...(m — 1) 
e 
n-~m 
, 772—1 . 
e- /ee....(m-z) 
; &C. ...(Q) 
2) n ~ m 
where, by any number of c’s or e’s placed under a quantity, 
I represent the depression of the fluxional coefficients of <p, 
contained in that quantity, so many orders, with respect to c 
or e. 
By combining equations (?j) and (£), we find 
"...(72-1) 
( 72“"“ 1 ^ C 
+ .... -j- 2 e [ ' ) 4 * e 
+ 
"...(77— l) 
+ » « ( C ( ‘„ — } + (»-») e 
+ &c. which in 
words is this ; To find B, take the fiuxion of B with respect to 
n-°i 
