340 Prof. 0. Reynolds on the Action of a Blast of 



therefore C will approach A with a velocity ~ — and in the same 



way, that the relative velocity of B and C will be -. 



Hence in this case the first effect of the impact will be to im- 

 press a velocity on the surface of each ball relative to its centre 

 equal to half the velocity of impact. If the bodies had been of 

 different materials, the results would have been somewhat dif- 

 ferent, although of the same character ; that is to say, these re- 

 lative velocities would not be equal. In such case these velocities 

 may be found in a manner which will be presently explained. 



Now, in order to impress this velocity on the surfaces, pres- 

 sure must exist between the bodies. This pressure will depend 

 on the velocities and on the natures of the bodies. To show this, 

 let 



v = surface-velocity at C towards A, in feet per second. 



X = the modulus of elasticity of A, 



d — the weight of 1 cubic foot, 



p = the intensity of pressure in pounds on the square foot. 



Then, for an elastic body, I shall 

 show that 



p: 



v \/ 



Xd 



9 ' 



Let be the initial position of C, 

 and x the initial distance of any point 

 P in OA from O, and a?-f-f its dis- 

 tance at the time /. 



Then for the equilibrium of a per- 

 pendicular lamina through P we have 



d d^__ dp 



g* df~~ dot? 



-_^. 



and from (1) and (2) we have 



dx ' 



dP d ' dx* 



(1) 



(2) 



(3) 



the solution of which is 



And at C, where <r = 0, 



M\/£<-*> 



