ENERGY ACCELERATIONS, A STUDY IN ENERGY, &c! 287 



Tliis condition is a necessary conséquence of tlie otlier two (3) if 

 tliere is no exfernal Jlelil of force, for in tins case 



(h\ dx.^ \dx^y \jlx.iJ 



d^r _ d'^V _ d^F 

 dx^dx.^ dxj^ dx^ 



Hence it follows that in tlie case of binary eucounters in one dimen- 

 sion betvveen molécules in the absence of an external iield of force 

 MaxwelFs Law of Partition of Energy liolds good and there is no cor- 

 relation of velocity. 



Let us now investigate tlie gênerai conditions of energy equilibrium 

 wlieu the field of external force does not vanish. Tor tliis ]jurpose write 

 A',, A'o for the forces on the particles due to the Iield R, for their mutual 

 reaction, so that 



dl\ dV^ r/r, 2 , ^/Tio 



"*-i — — ~jr ^2= — -T~ '^= y— = + 



dx^^ dj:^ dxi d. 



also let 



dxi dxi"' ■" dx2 dxo"^' dx^^ dx^.^ dx\dx^ 



Tlien we obtain 

 f/2 ri 



1 ■>■ 



o d^" 



é 



dl 



= [{X, - un - m, [.\] [?2 +P] + ^"■i bh ^'J [P] 



— b\ "2] h"'-i [?i + p] -r »h [?2 + p]) 



