36 OUTLINES OF NATURAL PHILOSOPHY. 



75. If A overtake B, the velocity lost by A is 



B(a b) .. , AB(a b) 



r r-~ ; and the motion lost hy it is - ^ ; 



xV -J- JL> A + J3 



the velocity gained by B is . ,~ > -^, and the 



> 



motion gained by it is -~ =~ , the same that 



.A. -j- Jj 



was lost by A. 



When B meets A, b becomes negative, and so 



the velocities gained or lost, are A X> 9 



A. ~p -t* 



A (a + 



76. If the two bodies before collision move in 

 lines making a given angle with one another, their 

 path after collision may be found, on the principle, 

 that there is no change made in the total quantity 

 of the motion of bodies by their action on one ano- 

 ther, in whatever direction their motion be estima- 

 ted. 



If AC (fig. 4.) represent the velocity and direction of 

 the motion of A, BC the velocity and direction of 

 the motion of B, before collision ; CG their joint 

 path, and their velocity after collision: Let BD 

 and GF be perpendicular to AC; then, because 

 the quantity of motion in the direction AC re- 



mains 



