APPENDIX. 



429 



S S as an axis. We know indeed that one of the forces -^ 

 or -^- acting towards S or S , the locus of P is an ellipse ; 



but it would not follow that if both forces acted the same 

 curve would be the locus. That the force would be differ 

 ent is certain, because it would be as P c, and not as either 

 Pa or P a . But it may be said that the curve also would 

 be different. Let us,, however, suppose the case of the 

 curve, whatever it be, cutting the axis S S produced at 

 2: and 2 , points equally distant from S and S , so that 

 S^ = S *% ; also that the angle and the initial velocity of 

 projection from ^ and 2 is the same, and further that the 



