1908-9.] On Energy Accelerations and Partition of Energy. 363 
This is the condition, therefore, that Maxwell’s Law holds good in the 
general case. 
The occurrence of the term involving [q 4 ] makes it very difficult, if not 
practically impossible, to obtain another condition for equipartition of 
energy by this process. 
Now 
70Y y 
\9#/ 
_ (wj + m 2 )/x 1 
???, 
d<P 1 
dx. 
i / 
+ /x 2 
’0^ 0<E> 2 ~ 
_dxj dx 2 _ 
Therefore, since the square of a real quantity is necessarily positive, 
/V 
fSfiV 
L\ cxj J 
+ /q /q 
~0<J> 1 0<E> 2 " 
_ 0./q dx 2 __ 
is essentially positive ; so that, if Maxwell’s Law holds good, the condition 
for equipartition of energy which has been obtained shows that 
m 
_ \ drj 
2 _ 
2 /x | ji.) 
0<1> 1 0<l> 2 
_ 0Z‘] dx 0 _ 
(Pf 2 (If 
_ dr 2 r dr_ 
must be positive, in the case when the denominator does not vanish. 
(13) In the general case, when the masses are unequal and when 
Maxwell’s Law may or may not hold good, our investigations give at once 
certain simple inequalities. It does not matter which is the greater of the 
two masses ; let us suppose that m x > m 2 . 
It has been shown that 
and 
70YV 
A dx) 
0vy 
ds) 
m l + m 2 
m l - m 2 
9 ° 
TlX-y fXtT) 
Ml' 
_\0X 1 
q 2 ‘ 
9_ 
\0£C c 
m-^ — m^[_\dx 2 J 
0<L 
9 9 
wqqq- 
m , 
-• 
1 _ 1 
mpL\0^ 1 
This shows that, if our assumptions are justifiable, it is necessary that 
and 
9 9 
rn Pl l \ 
Now 
_\0X 1 / _ 
0$ i 
_V 0Xj 
> /q>“ 
/0^_y^ 
_ V dXn, 
<??q 2 /x 2 2 
70<EV 
A 0^9 
y^i 
70$ O \ 2 
AS^r 
= (Wj - ra 2 )jiq/x 2 
and ^4(i) 2 
A0-A / 
may be greater or less than m v a 2 
0^ 0$ 2 
. CUq 0^ 2 _ 
equations do not require that ^/m, 
necessarily negative. 
_ dx 1 dx 2 . 
dx 2 , 
; so that our 
should be necessarily positive or 
