1034 PROFESSOR TAIT ON THE 



The value of the subsequent impact is 



— Pio cos \/r , 

 and the average value 



2PWcos 6 sin /l - °J^ s i n *qm . 



When siv>au, the limits are and |, and the value is 



2 p s 2 ™ 2 /., / a 2 u*\f\ 



But when sw<jau, the limits are and sin -1 — , and the value is 



aw 



2-r, s 2 w 2 . , 



By (2) and (3) we find as the average value of the encounter, taking account of all 

 possible relative speeds, 



P 



+ 3' 



-«V' 



; h 2 1 udu ( (c 2 + U 2 )a —G Z -U Z J, 



or, if we write for simplicity, 



e 2 ±=Ac 2 /2, 



■«5»{ , *(»>/i-*^' , "* w »)- , ' /w -'v1} 



The expression obviously vanishes, as it ought to do, when e = 0. And it is always 

 positive, for its differential coefficient with respect to e is 



In a similar way (4) and (5) give, with (2), as the average impact per encounter, 



a/ci* -a* 



KC 



