102 
ME. W. SPOTTISWOODE ON THE CAECITLirS OE SYMBOLS. 
1 
<P. 
' 
^’i 
0 
1 
'!r 
1 
1 
( 0 .) 
For the case of a cubic function of tt, 
^ +^.lE±2Mi±|=W^ 
y.x-+2^.|x-+p.|:x+p.|;xH2^.|^x+y .^ 
4^1 
TT+i^Po — pS 
( 
The quotient of which may be written 
<P^ (P2 ‘Pa 
0 0 
0 1 
1 
1 
(2’4^i+'4^o) 
2'4^'i+'4'o '4'i 
'4^1 + 2 2 
TT^ 
TT 
1 
( 6 .) 
Similarly, if the division be performed in the case of the quartic function, we shall 
find for the quotient of ((P47^^+?’3‘^*^■?’2‘^"4■<Pl‘^+?’o)('*^l'^+'4'o)^^ 
4'i 
X <p, 
0 
0 
0 
0 
0 
0 
1 
T' 
1 -^(4^i + ^o) ^2 
2'4'i + "^0 '^1 
' 4 ^ 1 + 2-^0 '<P\ + '^o 
T! 
3-iP\ + '^'o '^i 
3 ^: + 3^1 2•4.1+^j.„ 
s^/'i + '4'o ^ 
s-v^'i' +3'4/o 2-4/i+'4^o "4^1 
