533] 
FACTORIALS, AND DERIVATIONS. 
473 
C. VIII. 
60 
but the object of the rule is to obtain this last-mentioned result directly, and under 
standing “ operate in regard to a letter ” to mean differentiate with regard to this 
letter and integrate with respect to the next succeeding letter, then the coefficients 
of the successive powers of x are all obtained from the first coefficient by operating 
thereon according to the rule of the last and the last but one; thus <£a, operating 
on a gives (f>'a. b; this operating in regard to b gives cf)'a. c, and in regard to a gives 
the term fra.c is to be operated upon in regard to c only, and it gives 
b 2 
(f)'a. d ; the other term fi'a. ^ operated on in regard to b gives <f>"a. be, and in regard 
b 3 
to a it gives (j)"'a. ^ ; and so on. But attending only to the literal parts, the terms, 
for instance b 2 , be, bd, &c., which present themselves in the formula, are the homogeneous 
c 2 
terms derived from b 2 , by the rule, as originally stated, with a view to the derivation 
of such terms.