66 Proceedings of the Royal Irish Academy. 



We then show that 



BQ, + -in RQ is divisible by A, 

 when we obtain, on dividing by A, 



16II7? {B(4&D» + 2) + 12Q 2 AH\ + AQ: = 0, (14) 



where 



2 = ijj- _ yQAH - UAQ'D, + \AK* - 4A*QD lt , 



and 77" is the Hessian of 7-'. 



This equation gives us the eighteen inflexions of the curve and is expressed 

 in terms of the three quantics .7, Q, B and their invariants and co variants. 



