68 



Journal of the Mitchell Society 



[December 



ing. In that case we would have found that y = + ~~7=^ • in cither 

 case, the final value of U would have been the same, namely 2ab. 



Method V 



By employing the parametric representation for an ellipse, we 



readily obtain a very elegant solution of the problem. Any point 



x'^ y2 

 on the ellipse — + -^ = 1 may be represented by 



X = a cos (|) 

 y = b sin (J) 



when <1> is the eccentric angle of the point on the ellipse, namely the 

 Hngle between the x - axis and the line joining the origin to the 

 point of intersection of the line y = o sin ^ with the circle x^ +y2 

 = a^ 



