FOUNDATIONS OF THE KINETIC THEORY OF GASES. 1033 



Refer the motion to the centre, 0, of one of the encountering particles. Let A be 

 the point midway between the particles at encounter, B that of impact, the encountering 

 particle coming parallel to CO. Let OA = a/2, OB (as before) = s/2. Let 6, <j> be the 



angles of incidence and refraction at encounter, \jj that of incidence at impact, u and w 

 the relative speeds before and after the encounter. Then 



u sin 6 = w sin ; 



and, if Pc 2 represent double the work done in the encounter by the molecular forces, 



u 2 cos 2 6 + c 2 = w 2 cos 2 <p 

 so that 



U 2 + C 2 = W 2 . 



Also it is obvious from the diagram that 



au 



s sin i|r = a sin <p = — sin 6 



w 



Hence the encounter will not be followed by an impact if 



sm0> 



au 



§ 60. We must next find the average value of an encounter, and also of an impact ; 

 in the latter case taking account of all the encounters whether or not they involve an 

 impact. 



The numerical value of the encouDter-impulse in the above figure is evidently 



~P(w cos <p — u cos 0)/2 , 



which must be doubled to include the repetition on separation ; and the average value, 

 when the relative speed is u, is 



2P / sin 6 cos 6(w cos <j> — u cos 6)d0 



= S( (c2+u2)f_c3_u3 ) (3) - 



