160 



MOTIONS OF FREE PARTICLES. 



[CHAP. ix. 



impulse, h + Bh afterwards, since the tangent to the path is un 

 altered, we have 



h + Bh _ h 



v + Bv v 



giving Bh = h . 



Fig. 45. 



Hence if I is the semi-latus rectum before the impulse, I + 

 afterwards, we have 



p (I + Bl) = h?(l + Y , with A 2 = id, 



c\ 



Bl = 21 approximately. 



Now Z = a (1 e*), and if e becomes e + Se, 



giving 





Further the angle ^ which /SP makes with the axis major is 

 given by the equation l/R = 1 + e cos and it is clear that 



hence 



