398 Proceedings of the Royal Irish Academy. 



The pedal of the curve p = - ^) ' ( , or the locus of the feet of per- 



pendiculars from the origin on the tangent lines, is easily seen to be 

 given by 



_ dx dy 



df dcji dcf> df 

 dx ' dy dx ' dy 



or by 



^dx dy dy dx 

 This curve is in general of the degree 4 (?? - 1) 



yyd^dj, fdj, d_l_d4 df 



_ ' dx dy ' \dx ' dy dy ' dx 



