of any Functions of Multinomials. 
79 
where, in every successive fluxional coefficient, certain terms 
are to be omitted, according to the usual rule. 
Perhaps the simplest way of using this equation, although 
we shall frequently get the same combinations more than once, 
is by the following 
Kule. 
To find B take the fluxion of B with respect to all the 
m,n ;n + i, n— i 
quantities , excepting c, c , c, & c. ; change every where , c into 
0,1 0,2 ^’ v 
^ T c „_l_ i and take the fluent with respect to this last. The same 
terms must he kept only once. 
B was found in article 17, from which we have, by this rule ; 
30 
B = ?W 2,2 + M [ 0,1 X 2,1 + 1,0 X 1,2 + 0,2 * 2,0 “f ^ } 
2,2 2 J 
2 . 
+ no { Ok x + kk x n } + ? (o Ik/ 
2 
Suppose that, beginning with B , we had calculated in this 
6,0 
manner B , B , B ; from these may be found, with the greatest 
sn 3’3 
ease, and without any more direct derivation, the twenty-eight first 
terms. For from B , B we find B , B merely by changing, in 
5,1 4,2 1,5 2,4 
the former, the numbers that are on the right hand of the 
commas (under the c's) to the left hand, and the reverse. All 
the other terms are found, by inverse derivation, from the 
equation B = 
m — /a, n—v 
1 
