1908-9.] On Energy Accelerations and Partition of Energy. 861 
Again, using the equations (13) and (14), we have 
m 2 /q 
a 2 ^ 
— 7?q/x 2 
P 2 ^. 2 i 
m A m 2 
“0 2 V _ 
_0a? 1 2 _ 
_0a? o 2 _ 
711 j + 777 2 
0a? 2 _ 
0 2 V~ 
06' 2 
= (?>i 1 + m 2 ) 
when m 1 4= m 2 ; so that we have the important relation 
(17), 
-I 
“0 2 V~ 
(77?! + 777 9 ) 2 
“0 2 V~ 
L0a? 2 _ 
777 1 777 2 
_ 0S 2 _ 
Also, from the equations (9), 
0 2 V - 
d 2 f 
+ 
" 0 2 V~ 
_dr 2 _ 
_dr 2 _ 
_"0S 2 ~_ 
(18). 
(19). 
(11) The three equations of energy equilibrium finally take the forms 
[X s ] = 
m. 
m, 2 - ni 0 2 
. 2 
A^i 
Lwj/ J 
- /V 
7».W 
\dx 2 J _ 
J— 1 
a. 
_0a? 1 2 _ 
3 
r 2 9 
t 
( 777 2 + 777 2 \ 2 
1 
<M 
1 
to 
N 
y.1 
\ 777 1 7?7 2 / 
_\drj 
_ 2(m 1 + m 2 ) 
m^n 2 
_ 
J 
0cr 1 2 _ 
_m 1 + m 2 f /xyr/a^ 
777J - m 2 1 m 1 2 [\dx 1 
A 
rdr 
o 
_ wq + W2 2 
m l m 2 L dr 2 
M rw r 
m 2 2 L\0x 2 . 
(20) 
& 
' 2 0 2 <e 
2 Vj 
_ ??i 1 + m 2 
m l m 2 
AT 
rdr 
+ 
2 (m 1 + m 2 ) j /q‘ 
m T - 7/7 2 
?n. 
A) 
ye 
to 
1 
o 
_ Ah 
qa^V" 
_\0a? 1 J _ 
m 2 2 
_\0a? 2 / 
when the masses are unequal. 
They may also be written in the forms 
[a? 2 ] - - 
/h 
9_ 
dxj/ j 
+ / x 2 
0<t>! 0<t> 2 
0a; 2 0a?r 
3 
T 
(m 1 + 7?7 2 ) 
m 2 + m 2 
2 
.o0 2 $ 
m ] m 2 
dA 2 
ir/ 
'0 2 4> 2 
_ to:/ 2 _ 
_ 2(?^ + ??i 2 ) 
??2 1 m 2 
9 
df 
m 1 + vie 
Ah 
777-, 
0a?! 2 . 
/A | ( 7 77- j “t - 7?7 9 ) ] /q 
771! 
m 1 m 2 
7.^7. 
a^ 2 ' 
0a?! , 
7 77 2 777 2 
, 2 ^ 2 / 
/h 
7?7 2 
^r 2 J 
0$, 04>, I 
0a? 2 0a? 9 _ 
/h 
" 2 0^1 
77?! + 777 2 
777 x 
0a* 1 ‘ 2 _ 
777-, 777 2 
1 A 
r ^ yi 
Ah 
0$! 
0$ 2 
1 777! 
_\0a? 1 / _ 
m 0 
_0a?i 
0a- 2 _ 
2/X 1 (»W 1 + 777 9 ) ( /q 
777 2 777 9 I 777 x 
and these forms can be used in the case when the masses are equal. 
/ 
