of any Functions of Multinomials. 
57 
values of B , B , &c. given by (4), and it will become 
n — 2 n — 3 
c* + , (9), 
where we must neglect, in the second term, every thing that 
/ 1 11 
contains c ; in the third term every thing that contains c or c ; 
and so on. 
If we did not do this, we should have the same combina- 
tions of letters, frequently, more than once. We may, how- 
ever, instead of proceeding according to the above given 
direction, omit the superfluous terms at last; and then the 
rule will be as follows : 
B b 1 n 
To find n , take the fluxion of n _ l with respect to c, c, c, &c. and 
"...m "...(m+0 
after changing, every where, c • into c take the fiu :nt with 
respect to this last ; observing to keep only once the same combina- 
tion of letters. 
But now iet us consider, whether we cannot, by omitting to 
make certain of the letters vary, prevent the same combina- 
tions from oeing repeated. 
m) \n l"...r\q "...(r — m) 
First, if, in the term P x ( c I x \ c I , we make c 
vary, according to the rule just now given, there results the 
combination P x { c ) x c x \ c ) ....(a); but 
the same duxional coefficient of f (c) that is multiplied by 
/"...(r— m)\n l".-r\q ("...(r—m)\n — i 
Pxl c ) xl c ) will be also multiplied by Px l c ) 
MDCCCXI. I 
