Kinetic Theory of Dissociation in Gases. 19 



will be reached when the number of molecules decomposed 

 during any period of time is equal to the number formed 

 during the same period. As shown in previous theories*, 

 this equality is expressed by the equation 



^=N„ (0) 



and hence (C) expresses the condition of equilibrium. Here 

 fit) is a function of the temperature whose form has never 

 been successfully determined, so far as I am aware, either by 

 kinetic or thermodynamic methods. From (1) and (0) we 

 have further 



P~ 6f(t)Ki> ~ 6f(t)q* > • • • • W 



q denoting the dissociation ratio ~. If d is the density 



of the partly dissociated gas, corresponding to the state q, and 

 S the density of the completely dissociated body, then if the 

 formula (1) holds good, we have 



d_ N 1 + 2T$ 2 ( , 



8~ N X + IV •••••• W 



whence, substituting in (2), 



__ $(d-8) _ 2\t 



p ~- a (28-d) 2; a ~3f(ty • ' • V W 



which, for shortness, I shall call " Gibbs's Equation/'' 



§ 2. Gibbs's equation has been verified by various experi- 

 ments ; among others by those on nitrous acidj. Since we 

 leave the function a at present undetermined, we can prove 

 the formula by calculating the values of the expression 

 p(2$ — d) 2 /(d — 8) = a8, which should be constant for each 

 isotherm. From our data it is clearly seen that the 

 value of a does not considerably alter along any isotherm. 

 The constancy is of course still more perfect if we calculate 

 (for the isotherms E ; F, H, J, loc. cit.) the expression 



* To the kinetic or partly kinetic theories belong those of van der 

 Waals, Verslagen en Mededeelingen d. kon. Ak. d. Wet. [2] xv. p. 199 (1880) ; 

 Boltzmann, Wied. Ann. xxii. p. 39 (1884) ; and J. J . Thomson, Phil. 

 Mag. [5] xviii. p. 233 (1884). It is impossible to enter upon these theories 

 here ; I only remark that certain conclusions to which I have been led in 

 § 3 have already been indicated by Thomson. As for the rest I cannot 

 agree with Thomson's calculations. 



t E. and L. Natanson, Wied. Ann. xxiv. p. 454 (1885), and xxvii. 

 p. 606(1886). 



02 



