160 



MOTIONS OF FREE PARTICLES. 



[CHAP. ix. 



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

 altered, we have 



h + Sh h 



v + 8v v ' 



giving 



Fig. 45. 



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

 afterwards, we have 



, with A 2 = ^, 



^ 



giving SI = 21 approximately. 



Now I = a (1 e 2 ), and if e becomes e + Be, 

 - ZeaSe 



A 



- 



giving 



or 



a- = - a --- 



|_ /^ v J e v [_/*, aj 



1 - e 2 2Sv /I 1\ 



= *l*5 



e v \R aj 



Further the angle 6 which SP makes with the axis major is 

 given by the equation IjR = 1 + e cos 6 and it is clear that 



hence Sl/R = - f ^ - 1) + e sin 8r. 



e \-tt / 



