140 
MR. A. CAYLEY’S RESEARCHES ON THE PARTITION OF NUMBERS. 
and as before s extends from ^=1 to s=k. We have thus the actual value of the 
function 6x made use of in the memoir. 
A preceding formula gives 
= coefficient ^ in ^ 
which is a very simple expression for the non-circulating part of the fraction 
This is, in fact, Mr. Sylvester’s theorem above referred to. 
