1908-9.] On Energy Accelerations and Partition of Energy. 369 
If 
^1^2 
good. 
d$j jm> 2 
?Jx 1 dx 2 . 
is negative, Maxwell’s Law cannot possibly hold 
In the special case when ju 2 — — ju v Maxwell’s Law cannot possibly hold 
good if 
0dy 2 
_dx 1 dx 2 _i 
cannot hold good if 
is positive; and in the case when the Law 
m 1 m 2 
— - -v -‘ 1 is negative. 
-OX 1 ox 2 J 
In considering the question of stability in the case when Maxwell’s Law 
rp)2y- 
liolds good, we obtained a condition that 3 
ds 2 J 
+ 
d 2 f 2 df 
7> ' ~ 
should be 
positive ; this becomes a condition that 
condition is satisfied. 
-02 y 
L ds 2 J 
dr 2 r dr_ 
should be positive ; and this 
The Law of the Direct Distance. 
(17) Let the law of force between the particles be supposed now to be 
that of the direct distance. 
Let f(r) = b\r 2 . Then 
We obtain at once 
df d 2 f . 1 ( df\ 2 0 „ 
-4-= A > = and ( -f- ) = A2 ^ 2 
rdr dr 1 \drJ 
whence 
0V\ 2 ' 
ds) 
- [q 2 + r 2 ] 
'02V' 
0^ 
-X[^ + 2 2] = o 
Also we must have 
A 2 [r 2 ] + ? 
'N 
u> [ ec 
co 
1 _1 
9“ 
M | A + 
~0 2 V~ 
1 
La* 2 J 
0 2 ] = 
~(dV\ 
\dxj 
2 ~ 
ifh + ™ 2 ) 
a 2 v 
_dx 2 _ 
These equations may be written in the forms 
[x- 2 ] = 
and 
I 1 1 
©)■] 
+ A2 
a$j a$ 2 
_a.x ] ax 2 _ 
+ w 2 ) 
a 2 ^ 
_a^ 2 _ 
[ < 1 2 + r 2 ] = 
'04>A 2 
At W(S 
m i l 1 2 
~d$> x a<h 2 ~ 
dx x dx 2 _ 
m i m 2 i x + m 2/h 
m x + m 2 1 m l + m 2 
fdxf _ 
} m 
24 
VOL. XXIX. 
