266 Mr. J. J. Thomson on the 



triplets of A do not exist, we have the following equations: — 



dm 2n 



dn m 2 

 dt ~~r x 



s 2m 2 mnq 

 + i~ Tx "" t 5 



+7-r - 



mnq 



7*5 



= -7- + 



dq _2r 



dt ~~ t 3 



dr^^q 2 

 dt ~~t 4 



ds mnq 

 dt ~" t 5 



s 2q 2 mnq 



t 5 



> 



(33) 



When things have got into a steady state, we have 



m 



t 5 = F 4 



f J 



(34) 



„2__ 





(35) 



a formula of exactly the same form as the one obtained on 

 the first hypothesis, so that the equilibrium state is the same 

 whichever hypothesis we adopt. 



If we take the third hypothesis, and use the same notation 

 as before, with the addition that 



— y~ — the time that elapses before a free atom of A 

 m 9 unites with two free atoms of A and an atom 

 of B simultaneously, 



this quantity is evidently inversely proportional to m 2 q, as 

 m?q is the number of groups, if m and q be large, which 

 can be formed of two A atoms and one B atom. If we sup- 

 pose that there are no triplets, and that the molecules of A 3 B 

 when decomposed split up into three atoms of A and one of 

 B, we have the following equations : — 



