504 
ON THE INTERSECTION OF CURVES. 
[868 
The two curves here intersect in the ab points (\ a = 0, 
mn — ab points 
"h-a > R'm—b > 
Uh ) &m—a> 
/jL b = 0), and in the 
say the {mn — h) points A are mn — ab — © of the last-mentioned points, and the S 
points B are the remaining © points together with the ab points. Here the general 
form of the curve of the order r passing through the mn — ab points, and therefore 
through the mn — 8 points A, is 
Ly—m—n+a+b > M r _ n > r—m 
'W > B ln _(j, U n _ b 
f^b > Bm—a j Vn—a 
= 0, 
where L r - m - n+a+h , M,._ n , N r _ m are arbitrary functions of the orders indicated by 
the respective suffixes. The theory in regard to the number of constants is of course 
altogether different from that which belongs to the case of the general functions 
P m , Q n \ and it is probable that much interesting theory would present itself in the 
consideration of particular cases. 
Cambridge, 22 March 1887.