1908-9.] On Energy Accelerations and Partition of Energy. 367 
This requires two complicated conditions, namely, that 
6T f 
+ 
1 
and 
M 
- 3T 
5 2T 
3 X 2 
W 
W 1 
f 
{fT s 
ry*L 
J l fi rp 
\ 4 If 
- 6T, 
- 12Tj 
rl 
o*2 
+ 
M 
4_ 
M 
W' 
. 0s 2 _ 
~d£ 
rdr 
1 
M 
'<v_ 
rdr 
]} 
1 
- 12T, 
1 
+ — 
~0 2 Y 
+1 
4/' 
7*2 
1 
7*2 
M 
_ 0S 2 _ 
M 
_dr 2 
rdr_ 
should be positive. 
(15) Having now obtained the general equations of energy equilibrium, 
let us proceed to apply the results to certain special cases. 
Let us consider first the case of two oppositely electrified equal masses. 
If we put /jlo = — /oq — — /a and = — the following simplifications 
appear : — 
70<V 2 ~ 
dx 1 / _j 
\dx, 
— / -I 
r a 2 $ 1 
0 2 $ 2 
1 
1 
r 0 2 vi 
_ 0 ^ 7 _. 
_ 0^’ 2 2 _ 
’2[x 
_ 0(£ 2 _ 
fJL _ 
-02y 
0S 2 
0vy _ 
ox) 
O 9 
= 
/a^v 
Ada?! 
'0$ 1 0$ 2 
_dx, dx e 
and 
The equations of energy equilibrium are 
2 - 1 
)H 
= A i 
/04>j\ 2 
+ 
0<^ 
0$7 
/ 
1 i 
- ' s i 2 - 
_0Zj 
0a? 2 _ 
_\0.r 1 y 
) 2 _ 0£, S* 2 - 
0aq 0^2 
2 m 
0^ T 
_0iC| 2 _ 
r 2 < 
4 
m 
d£ 
dr 
- - M 
m 
'ddf 
dr 2 
m 
fe 2 ] 
d£ 
rdr 
— lL [r 2 ] 
m 
02$! 
+ 2 4 
i/3£ 1 y + a$i » 2 " 
_0^] 2 _ 
m A 
_\0.r 1 / 0aq 0x 2 _ 
— — [ 2 2 ] 
0 2 3> T 
CU f 
:L 
1 
1 
v + 3 _5i ™s] 
- - [<f\ 
df 
1 
!N 
7 
ro 
1 
m 2 
_ \0.r 1 / 0aq dx 2 _ 
m L J 
_rdr 
(25). 
The condition for equipartition, according to Maxwell’s Law, becomes 
04 >, 
0r o 
0 2 3q 
= fX 
/0<£>A 2 0^ 0<3> 2 
-dy^zdf- 
_ 
_dx) 2 _ 
_ \0x 1 / 0aq 0£ 2 _ 
_dr 2 r dr _ 
(26). 
