ME. W. SPOTTISWOODE ON THE CALCULUS OF SYMBOLS. 
113 
by 
\iz. 
The conditions 
+ ^2(^y + )’*■ + 4'o(^), 
= n •^7)2 = 2 y^p = 7n ^0 = 2 I ^..,“1 / ? 
^m = 0 ^p = 0 ^3 = OT/nU72'5 _pj ( 
TT 
.m+p — q 
^> = 2, §-=0 give (PoT* 
j) = 2, Q=1 
p=2, (1=2 
^=1, 5=0 |2,),,(|)' +4'.(|)}-’ 
i=x {2^,(1)' 
i>=l, 2=2 
i> = 0, 2=0 
^ = 0, q=l 
2>=0, 2=2 
Hence taking the sum of all the terms, the coefficients of -r®, 
final remainder is 
'tt' vanish, and the 
These results may be compared with the actual dmsion, 
vl/,7r" + T , TT + \J/o ^ ^ .TT ‘ + <p,y + ?27J'" + ^i’r + ?>o(^^7r^ + ^7r-l-^ 
MDCCCLXIJ. 
Q 
