ME. W. SPOTTISWOODE ON THE CAECTJEHS OE SYMBOLS. 
103 
And likewise in general the quotient of will be 
represented by a square table giving for the coefficient of 
i 1 . V 
-r 
+ '>^0 
•^1 
0 
(i-l)0-2) 
1.2 
1 * ^ t' 
+ 1 Vo 
r I 
'^0 
0 
( 8 .) 
■‘’+^ 45 "* 
■■ 
§ 2. External division of the Tr-arrangement hy a linear factor. 
I next investigate the condition that 4'i(f)7r+'v//o(f) may be an external factor of 
Performing the actual divisions, we have in the case of w=l, 
or, as the remainder may be more conveniently written, 
(1.) 
Again, in the case of w=2, 
+ <Pi'^+Po(j^‘^ + — <p'2 + 
<p2^' + -4'i (Ij) 7r + -4.o ^ 
|<Pi— 
or, transforming the remainder as in the former case, and continuing the division, 
{<Pl-<p2 + 92'*'-^--}^ + <Po 
■T+'vl/, 
[ 
ji 
^Pl <P2 + <P2 J 
[] 
