Properties of a Molecule in a Substance. 115 



room for the molecules (M 3 — M 4 ). The value of x is given by 



N 3 + JS 4 N s + N 



M 5 r 3 -M 4 t' 4 , 



or 



_ /M 3 ^-M 4 r 4 \ 



The number of molecules 3 gained in the plane in question, 

 which is the diffusion £ 3 , is therefore 



n 3 l 3 dN 3 #N 3 



JSfs* <te N 3 + N 4 ' 



or 



and hence 



=i-^-R^^- M ^ 



N 3 r 3 fN 4 r 4 



/N 4 n 3 / 3 dN 3 1SW 4 olN_A 



In the case of a gas u 3 =v 4 and N 3 + N 4 = K a constant, which 

 reduces the foregoing equation to the well-known form re- 

 lating to a perfect gas. But in the case of a liquid v 3 is in 

 general not equal to v 4 . A case of special interest is obtained 

 when the concentrations of the two kinds of molecules in a 

 liquid mixture are the same. According to the distribution 

 of the molecules in space in such a case * we should expect 

 that v 3 is equal to v 4 . Some other properties of v 3 and r 4 

 may be noticed in this connexion f . 



The rate of diffusion of the molecules 4 in the opposite 

 direction to the molecules 3 is given by equation (7) on 

 interchanging the suffixes 3 and 4. It will be seen that the 

 equations giving the rates of diffusion in the two cases may 



be written S 3 = v 3 K and S 4 = i\K, and hence ^ = — • 



The quantities n 3 and w 4 are connected by the equation 

 7i 3 A + 7i 4 B = P n +^>, where P n is the intrinsic pressure and p 



the external pressure of the mixture, A = 2\53 x 10" . ▼ Tw 3 

 and B = 2*53x10~ 2( VTw 4 , An equation can be obtained 

 which does not contain these quantities on eliminating them 

 from the above equation and the diffusion equations. The 

 quantity P n can be obtained in terms of quantities that can 



be measured by means of the equation P n = ^-, which 



* Phil. Mag. April 1911, pp. 537-538, 

 t Loc. cit. pp. 54G-547. 

 12 



