of any Functions of Multinomials. 51 
and by comparing the coefficients, of the different powers of 
x, with those in equation ( 1 ) , there will be found, 
B = c B 
11 1 it 
2 c B -f c B 
2 
w 1 11 1 11 
3cB + 2cB + cB 
, "-(«-0 , "•■(»— 2 ) / 1, ,, 1 
g — - n c B+(w— 1) c B+(« — 2) c B + .... + 2 ^ B -f c B 
1 2 « — 2 n — s 
72 — * ■ ■ ■ ■ ■ r, 
n 
( 2 )- 
1 1 
But B — / (c), B —f (rj, whence all the rest are known. I 
represent by strokes over the f the fluxional coefficients of 
f (c); the number of strokes marking the order. 
Though this is a complete solution of the problem, it affords 
by no means an easy way of calculating the coefficients ; on 
which account I shall not trouble the reader with examples. 
It will be shewn presently, that the method of derivation in 
M. Arbogasi's first section is easily obtained from this. 
3. Second Method. I here, as in the former case, consider 
/ 11 III 
the quantity c c x -f- c sc* c x 3 -[- to be a binomial, and 
take the fluxional coefficient of the function with respect to c ; 
but multiply by the partial fluxion r x, instead oi c x 2 c x x 
-j-, &c. ; we find, by this way of proceeding, for the 
sum of all those terms in ^ that are multiplied by the powers 
