CONSTITUTED OF SPHERICALLY SYMMETRICAL MOLECULES. 



477 



As we shall see, independent values of the radii of molecules may be obtained from 

 the coefficient of diffusion, which we proceed to consider. 



21. The Coefficient of Diffusion. 



As the coefficient of diffusion of a gas into itself can be expressed much more 

 simply than that of one gas into another, we will discuss it first, though it cannot be 

 measured experimentally. 



The expression obtained in Part I. was 



i/a . 1 



Since v is proportional to the pressure, it follows that D n varies inversely as the 

 pressure, the other factors being functions of the temperature alone. If we substitute 

 for P' a from equations (45), (48), and (52), and eliminate the molecular constants by 

 means of the expressions found in the preceding section for the corresponding values 

 of n, we get the following results : 



DU = -jj- - (rigid elastic spheres), 



P 



D n = , , \'(3 ) - (centres of force 



X (n) \ nl/ p 



G 



(attracting spheres), 



where in the last case C is the constant in SUTHERLAND'S law of viscosity. All these 

 formulae agree in showing that D u is a numerical multiple of /x//, the factor generally 

 being a function of the temperature, though with the first two hypotheses above, the 

 factor is a constant. When, in the case of the second hypothesis, we take n = 5 (as 

 MAXWELL did, the force being repulsive), the formula becomes 



D n = 1-543^ 

 P 



(MAXWELL'S fifth-power law), 



using the values already given for A, and A 3 . The extension to general values of n 



I 2 \ 



is interesting, if only for the unobvious character of the factor I 3 ). 



\ n I/ 



The best value of the numerical factor hitherto obtained, on the hypothesis that 

 the molecules are elastic spheres, is due to JEANS (see his treatise, p. 273). After 

 allowing for persistence of velocities, he deduces that 1'34 is its approximate value; 

 this is in very fair agreement with g, the result of the present theory. 



