110 PROFESSOR CAYLEY ON POLYZOMAL CURVES. 



IU+ mV+ nW = which have a node), and the result arrived at is that for the 

 curve A 



Order = 3 (r - 1) (3r - 2) , 



Class = G (r - l) 2 , 



Nodes = f (r - 1) (27r 3 - 63r 2 + 22r + 16) , 



Cusps = 3 (r - 1) (Ir - 8) , 



Double tangents = § (r— 1) (12r 3 - 36r 2 + 19r + 16) , 



Inflexions = 12 (r - 1) (r - 2) ; 



so that, finally, the number of the cuspidal curves Jjjj + J^y + j n jy ={) 

 is = 3 (r — 1) (Ir — 8), and the number of the binodal curves of the same form 

 is = f (r - 1) (27r 3 - G3r 2 + 22r + 16). When the given curves are conies, or 

 for r - 2, these numbers are = 18 and 36 respectively ; but the formula? are 

 not applicable to the case where the conies have a point or points of intersection 

 in common ; nor, consequently, to the case of the three circles. 



