Centres of Percussion and Oscillation. 239 



363. If a body L, of any figure whatever, admitting only of Fi S- 173 - 

 a motion about a fixed point F, or about an axis passing through 

 F, which may in ether respects be situated as we choose, if, I 

 say, a body L be struck by a body JV, the motion of each after 

 collision may be determined by the principles above established. 



Thus, let u be the velocity of JV, before collision, accord- 

 ing to the perpendicular TH, and u' its velocity after collision ; 

 u u' will be the velocity, and N (u u'} the quantity of mo- 

 tion, lost by collision, and which will pass into the body L. This 290> 

 quantity of motion will cause in L a velocity of rotation, such 

 that the point 7 T , for example, will turn with a velocity 



-') X FH 354. 



v = v '' - X FT (i), 



jf m r 2 v /' 



F/f being drawn perpendicular to TH. Let the infinitely small 

 arc TT', described about the centre F, represent this velocity ; 

 the parallelogram TA T'C being formed upon the tangent TA 

 and the perpendicular TH, it will be seen, by substituting for 

 TT' the velocities TA, TC, that the velocity TA cannot affect 

 the velocity M'. which the body N must have ; but that the veloc- 

 ity TC would impair the velocity u' if it were smaller than u' ; 

 accordingly, since we suppose that u 1 is actually the velocity 

 which N preserves after collision, it is necessary that TC 

 should be equal to '. Now the similar triangles FHT, TCT. 

 give, 



FT i FH : TT or v : TC, 

 whence, 



and consequently 



u X FT 



V =-JIT' 



Substituting for u this value in the equation (i), we have 



vf_X_FT __ #(*-<) X FH 

 FH fmr* 



from which we deduce the value of u' ; thus* 



