of any Functions of Multinomials. 83 
Rule. 
Take the fluxion of the latter with respect to all the quantities 
except c , 0 ^ >v , Q f n , &c that have nothing on the left hand of 
the first comma ; change generally ^ f p> &c . into ^ h &c< and 
take the fluent with respect to this last. The same terms must be 
kept only once. 
The extension of this to any number of multinomials is ex- 
actly the same as the similar extension, for double multino- 
mials, in the last article. 
Second General Problem. 
23. It is required , in the case of the last problem , to find 
B without a knowledge of any other coefficient. 
Vty My Ty Sy ty ScC « (Jr 
"-(r- 1) 
This will be accomplished if we can find T which multiplies 
1 ) "...r r 
(p (r) from \U which multiplies <p{c). 
Rule. 
”... r 
1 st. Take the fluxional coefficient of \J/ with respect to x ® 0?&Ce , 
and of this fluxional coefficient take the fluxion with respect to all 
the quantities ; change generally ^ f &c> into ® ^ &c> and take 
the fluent with respect to this last. 
”...r 
vdly. If there be any terms in in which the unit under 
i,o,o,o,o,Scc.> if it one of the factors, is the only left hand figure , 
they will require a further process. 
Take the fluxional coefficient with respect to 0}1}0 f 0} &Cs , and of 
this take the fluxion with respect to all the quantities, except 
M 2 
