84 
Mr. Knight on the Expansion 
1,0, 0,0,0, &c. > change generally Olfl ,‘ li&c .into 0>(<+I f and take 
the Jluent. 
...r 
2 >dly. Any terms , in , in which the units under 1 > 0 , 0 > o ; 0 ,&c. an d 
01000 &c ’ if ^ ie y are amon gA the factors , are the only figures in 
the first and second left hand places, will require a still further 
process. Take the fiuxional coefficient with respect to 0 , 0 ,i,S,o,&c.i 
and of this take the fluxion with respect to all the quantities except 
1,0,0, 0,0, 4 c. and o,., 0,0,0, &c. >' change generally 0 , 0 ,J„ f , kc . into 
o, 0,^1,. ,„ue. and take the fluent. 
The rule will proceed in this manner, till it contains n parts if 
the multinomial he of the nth order. The terms arising from all 
these parts must he added, and the same terms kepi only once. 
24. In treating multinomials of higher kinds, I have given 
rules by which certain terms are frequently found more than 
once : this was done for the sake of simplicity, and that the 
precepts might be easily retained in the memory ; but was by 
no means a matter of necessity ; for rules might without diffi- 
culty have been formed (as from equations (1/) and (|) for a 
double multinomial) by which no superfluous terms would have 
been found. 
25. It will not be an improper termination of this paper, to 
state what are the peculiar advantages of the method pursued 
in it. 
To many, I have no doubt, its brevity will be a recommend- 
ation ; and that it requires no notation different from that in 
common use. 
For though I have represented some of the fiuxional coeffi- 
