110 
ME. W. SPOTTISWOODE ON THE CALCULUS OE SYMBOLS. 
4^2 j ^0 — ^^ (^04^3 +^14^0 + ^24^0) 
and the terms independent of 7r = 
^0 + ' + 
<p2 4^2 4^1+ +2 
<p3 0 4/i 
cp, 0 0 
both of which may be comprised under the single formula 
’T <Po 4^0 +0 +0 
1 <Pi + +++1 2+0 ++1 
0 <P2 4^2 4^1+ +2 ++2+1+ +2' 
0 <p3 0 4^2 + + 2+2 
0 (p4 0 0 + 
§ 4. To divide externally hj 
The first term in the quotient will be 
“Pn _N-M 
u ’ 
+ + 2 + 1 + +2 
4^1 + 2+2 
4^2. 
(m-p) 
N-M+p 
M+p , 
(1.) 
( 2 .) 
(3.) 
(4.) 
the product of this into the divisor 
and the remainder 
^n=N- n = M > ■^p = mr_^^ /'Pn \ ^ '^+N- 
2n=0 ^TO=0 Ym+=0 \j^t ^ 
the first term of which is 
{<?»-, M-1] 
Let (Pn = ^o> Q'lid let the coefficient of above written =Oi ; then the next term in 
$ 
the quotient will be and the product of this into the divisor will take the 
same form as (2.), writing only O, for O#, or (p^. The remainder will be the same as 
(3.), with the addition of the term 
(5.) 
and the first term of the entire remainder will be 
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