1908-9.] On Energy Accelerations and Partition of Energy. 351 
The kinetic energy T 
= V\ 2 + y 2 + 
where 
= £( m i + m 2 )(^ 2 + y 2 + &) + ^"’ 2 + r 2 ^ 2 + 7 ’ 2 sin2 
1 2 
= + m 2 )(x 2 + ;?/ 2 + if 2 ) + ^M(r 2 + r 2 0 2 + r 2 sin 2 Oft 2 ) , 
M = 
m x + m 2 
The Force Function is specified as follows: — 
Let the interior force of the system be an attractive force between the 
masses, and let f(r) be the corresponding potential energy. 
The exterior forces are supposed due to the action of other molecules or 
to external disturbances ; if <F(£ f) be the potential of the field at any 
point (£, rj, £), we may suppose the potential energy due to this cause to be 
Vv Zj + pfifa, Vv %)• 
The whole potential energy Y is therefore equal to 
Vi, b) + /V%2> Vv z o) +A r ) • 
Forming Lagrange’s equations, we have 
(m 1 + m£)x — - 
/ , \- ov 
(?» 1 + m 2 ) y = - — 
/ , \- 0 v 
{m 1 + m 2 )z= - — 
M < r - r(0 2 + sin 2 0(f) 2 ) 
1 
MM - — (r 2 0) - r sin 6 cos 0</> 2 ) i 
r dt J 
M d 
/■ si n 0 dt 
(r 2 sin 2 0(f)) = - 
0V 
dx 
0Y 
av 
0Y 
or 
1 0Y 
r 00 
1 
0Y 
r sin 0 d<f> 
(1). 
(4) Let the assumption be made that for any given position of either of 
the particles all directions of translation of the molecule are equally probable. 
The actual motion is unknown, and we will apply the theory of pro- 
bability to the probable motion. 
Let us suppose that the probability that a particle is moving with a 
given velocity u x is equal to the probability that it is moving with the 
reverse velocity ; in other words, that the probability of u Y lying between 
u x and u 1 J r du 1 is equal to the probability of its lying between - -Uj and 
— u ± — dn Y in any direction. 
