422 
MR. S. H. BURBURY ON THE COLLISION OF ELASTIC BODIES. 
volume and time of colliding pairs for which the angle between Y and p before 
collision is between 6 and 6 + clO is ^vs^p sin 6 cW, and the number for which after 
collision it lies between 6' and 6' + dO" is rs^p sin 6' dO'. Hence we have to 
multiply (cos O’ — cos 6f by ^vs°p sin 6 d6 sin 6' dd', and integrate in each case from 
7 t to 0. The result is §7 TS 2 p. 
And so we get 
dK 
dt 
= - f N n 
(N + nf 
N 3 
hW 
/ Mm Y 
\M + m) 
x rr r y 3 dv S m« da ^ \\/ P ^ 4 y y . 
Jo-'O-’O •'ri 
where V, a, /3 are usual spherical coordinates 
4 n 
v/ttN 
(N + w 3 ) 
-y/( M??l) 7 TS 3 „ 
(M + m)* \/h d ~ 
Also, as we have seen 
K = |^(N + n)d\ 
and therefore 
= - A-( N +»> Y 
K dt o^/ir ^ ' (M + wi) s s/h 
— — C suppose. 
And if K 0 , D 0 , d 0 be initial values, 
K = K 0 e -Ci , D = D 0 e -i<;i , d = d 0 e~ ict , 
the rate of subsidence is directly proportional to the density and to the square root of 
the absolute temperature.* 
* Since writing the above I find that this result has already been obtained for the case of elastic 
spheres by Professor Tait, by an independent method. 
