MR. S. PI. BURBURY ON THE COLLISION OF BLASTIC BODIES. 
421 
Therefore 
F/- F’f = N n (^y (1 + D) : ’ (l + df € -*{(M + ».)v»+i^P*} 
7T / \ 7T 
2 \ ) 
{D/Oi(U' 3 - U 3 ) + dhm (u 2 -tr) 
Now, if 9' be what 6 becomes after collision, 
U' 3 - U 3 = 2Yp . —(cos - cos 0) 
r M + m v 
" — u~ 
- 2Y p 
M 
]\I + m 
(cos O’ — cos 0) 
Also by the relation 
N , n , T , 
Hd + rr^ - N + ,i 
D = - 
nd 
N + (N + n) d ’ 
and making; these substitutions 
F'f - Ff = Nn (~J M (1 + D)» (1 + dfe~ k f + 
p 5 
hJ^-2 . V p. 
N + a 
Also 
M + m ' r ’ N + (N + ft) 
N + » 
(cos 0' — cos 6) d). 
. py 7 Mm , T 
°§’ py = ^ M + m P N + (N + n) d 
(cos 9 — cos 6') d. 
In forming (F'f' — Ff) log (Ff/F'f) we see that the last factor is squared, and so 
the product contains the factor d 2 . We may, therefore, now write 1 for (1 + D) 1 and 
(1 + d) ’, and also write (N + n)/N for (N + ??)/{N -j- (N -f~ n)d], otherwise we 
should have terms in d 3 . 
Therefore 
(F f - W) l»g §’=- N» (ff (t Y «" * 
] (M + m) . . - ,, . 
<- M + m 3 
) V* + 
Mill o ) 
p~ r 
a 3 y 3 
Jm 
M + m 
ITT.) O (N “P ^0 / /!/ 
4v~p~ — ^. 2 (cos 9 — cos u)\ 
Again, dK/dt contains the factor i fj denoting the frequency of collision. Now the 
number of collisions given V and p in unit of volume and time is proportional to 
7 rs 3 p, where s is the sum of the radii of M and m. Also all directions of p before 
collision are equally probable, and given the direction before collision, all directions 
after collision are equally probable. Therefore, given Y and p, the number in unit of 
