MR. S. H. BURBURY" ON THE COLLISION OF ELASTIC BODIES. 
419 
that is, 
(ii M \ 7 
N ^V) ^ + D)=e- 7iMU2 {l - ADMIT" + terms in D 3 }. 
(It will appear that terms in D 3 , &c., are not required.) 
Similarly /becomes 
n ^~ rn -^j (1 -f- df e - /m “ 2 (i — dhmu 3 + dd &c.). 
We will further suppose that the disturbance is introduced without changing the 
total energy. That gives the relation 
N. 
2h a + D) n 2h (1 + D) 2 k 
or 
N 
+ 
1 + D 1 1 + cl 
= N 4- n. 
15. The disturbance will subside by collisions between M and m. And we will 
treat of the case in which it subsides in such manner that the above values of F and f 
apply at every instant with the values that D and d at that instant have. Such a 
mode of subsidence is possible, at all events if our equations lead (as they do) to 
a relation of the form (1/K) ( dK/dt) = constant. 
Let us then form the function 
H = fT r. F (log F - 1) IP sin a da d/3 dV, 
J 0 J 0 J 0 
where U, a, and (3 are usual spherical coordinates, 
r CO /*7T c 2 tt 
+ /(log/— l) u 2 sin a da d/3 du, 
JO j 0J 0 
where F and /have the values above given. 
That is 
H = | log (1 + D)j]jF.U 3 sin « da d(3 dXJ 
+ f l°g (1 + d) \\\fu* sin a da d/3 du 
+ terms independent of D and d, 
H = N | log (1 + D) + n flog (1 + d), 
-j- terms independent of D and d, 
FIT 3 sin a da d/3 c/ U = N 
\i~ sin a da d/3 du = n. 
3 ii 2 
or 
because 
