406 Mr. W. M. Hicks on some Effects of Dissociation 



velocity r relative to m Y 



2W - — 



= — =r— sin 6 1 h6u 2 e P 2 $u, 



V 7T/3 3 



where 



u 2 + v 2 + 2uv cos # x = r 2 . 



For the same value of u when r becomes r + o> 7 #x becomes 

 6 l + c6 ly where 



sin ^18^1 = Sr, 



uv 



and the above number becomes 



2Wu _«% R 

 e /s 2 ow ror. 



Vtt/3 3 v 



To find the number of molecules impinging on m x with rela- 

 tive velocity between r and r + hr, this must be multiplied 

 by 7rs 2 r and integrated with respect to u over all possible 



^ yf ij z 



values of u, i. e. for such that ~ lies between ±1, or 



zav 



u-\-v>r, 



u~v< r. 



The number required is therefore 



2n/7t"NVV% f'+« ^ . 



= -o or 1 ue~P 2 au 



J>v J r _ v 



c /2 

 The proportion of those impinging with a blow > c is 1 j. 



Hence the whole number of impacts of the second system on 

 m 1 with a blow > c is 



—^ I (r'-c' 2 ){e P -e P }dr; 



and the whole number of blows > c between molecules of the 

 first and second kinds per unit of time is 



4NNV /^ cc /"» co (r-»)2 (r+»)2 _„2 



3 /q~ 1 I (^ 2 — c /2 ){e z 32 — e J9 }w «*dvdr. 



* 6 p 

 This may be put in the form 



~Sir~1 ^ ~c /2 > °?+Pdr\ { e y* -e v 2 }vdv, 



