68 
Mr. Knight on the 'Expansion 
where we must observe to neglect certain terms, according to 
the directions so often given : and if we apply here all that 
was said in article 6 , when we were considering a similar ex- 
pression for a function of one multinomial, we easily get the 
following 
Rule. 
To find Bfrom B , in the expansion of a function of any fun 
n n — i 
t n i n 
lions of the multinomials , c c x + c x and e -j- e x — e x * 
/ a 
4- and d -f- d x -f d a:*-}- and &c. 
ist. Consider only the c’s , and take thefiuxiGn of B , with re-* 
H — I 
sped to the last of them in each term ; and the last but one also, if 
it immediately precede the last in the number of its strokes : change , 
"...m "...(wi-fi) 
every where , c • into c *, and take the fluent of each term 
with respect to this last. 
t n ill 
idly. Neglect all terms in B which contain c, c, c, &c. and 
n— i 
proceed, with the remaining ones, in the same manner with respect 
to the e’s. 
i " in i n in 
§dly. Neglect all terms in B which contain c, c, c, &c. e, e, e, 
n — i 
&c. and proceed, with the remaining ones , in the same manner with 
respect to the d's. — And so on. 
Let it be required, in the case of two multinomials, to find 
B from B which is given in article 10. The first part of the 
4 3 
rule gives 
3 1 0 mi 2 >° i hi P 3>° c 2 ii 4 >° g 1,3 n n 2,3 p- u 1,1 in i 
$c-b<p{cc + T )+<p T c-\-(p — -{-<pce-\-<p-e-l r (pce 
