68 Proceedings of the Royal Irish Academy. 



If we refer to the equation for L in equation 6, we see that, 

 in the present case, it contains the factor u, so that L, M, and iV 

 are proportional to functions of the degree 



2m. - 2 + n - r, 



while Z, M, and JV, considered as functions of X and ju, are of 

 the degree 



when we reject the common factors, and consequently the degree 

 of A will he 



Hence, in general, a hicursul curve of the degree p has its 

 deficiency equal to (w - 1) where 2n is the degree of the quantic 

 under the radical. 



In our next paper we shall treat of a special class of bicursal 

 curves. 



