568 PROCEEDIXGS OF THE AMERICAN ACADEMY. 



It is deserving of notice that the properties stated above determine 

 the location of the poles of the elements of Yyr,(x), namely at the zeros 

 of I P{.r) I within the loop, the maximum order of the pole of any 

 element being precisely the order of the corresponding zero of | P(.r) |. 

 This is an immediate consequence of the relation. 



YM= ro(.r)P->(.r). 



H.^RVARD University, 

 Cambridge, Mass. 



