Chemical Combination of Gases* 239 



tion of the molecules to remain approximately constant during 

 the time t, the number of molecules formed in the time x 

 bears to the number formed in. the time t the ratio of x to t ; 

 but the number formed in t is m, so that the number formed 

 in x is mx/t But the number of molecules dissociated in the 

 time St is the same as the number formed in the interval St, 

 t seconds ago, so that the number of molecules split up in 

 the time St is mSt/t In exactly the same way we see that the 

 number of pairs of atoms which combine in the time St= 

 nSt/T=n 2 St/r; so that if Sm be the increase in the number of 

 molecules in the time St, we have 



~ n 2 St m«. 



dra = — . — bt 



r t 



or y (1) 



dm t? m 

 ~dt~~r~~~~i 

 Similarly we may prove that 



dn 2m 2n 2 

 dt = ~T~~T r ' 



When things have got into a stationary state -^ and -^ both 

 vanish, so that 



7=? ^ 



Since n-{-2m = N, we have 



n + -n 2 = N (3) 



This equation will always determine n ; if the dissociation is 

 slight, so that the number of atoms is small compared with 

 the number of molecules, we have 



or 



T 



2lN 



From this equation we see that if r and t are independent of 

 N, which will be the case if the process is a reversible one, 

 and the dissociation produced by the action of light or elec- 

 tricity, then the ratio of the atoms actually free to the whole 

 number of atoms in the gas is inversely proportional to the 

 square root of the density, the temperature being supposed to 



l = \/: 



