258 PROFESSOR TAIT ON THE 



value of the integral as a function of z before we can proceed with the further 

 details of the solution, and then the equation for Diffusion ceases to resemble 

 that of Fourier for Heat- Conduction. 



The difficulty, however, disappears entirely when we confine ourselves to 

 the study of the " steady state " (and is likewise much diminished in the study of 

 a variable state) in the special case when the mass of a particle is the same in 

 each of the two gaseous systems, whether the diameters be equal or no. For, 

 in that case, we have h x = h and oc x = x, so that the factor 1/(1 + z) can be taken 

 outside the integral sign. Thus, instead of x <& r , we have only to calculate C,. of 

 the previous section. 



XI. Pressure in a Mixture of Two Sets of Spheres. 



35. Suppose there be n x spheres of diameter s x and mass P l5 and n % with 

 s. 2) P 2 , per cubic unit. Let s = (s 1 + s 2 )/2. 



Then the average number of collisions of each P x with P x s is, per second, 



The impulse is, on the average (as in § 30), 



Similarly, each P x encounters, in each second (§ 23), the average number 



Mh t +h 2 ) g 



Z W h x i h s 



of P 2 s, and the average impact is 



p^py j h h 2 



Thus the average sum of impacts on a Pj is, per second, 



7T 



— 2P 1 ;-w l s 1 2 , due to PjS; and 



- 2 i(+p 2 ^7 7r ^ 2 ' duetoP ^- 



In the Virial expression <j2(Kr), {§ 30}, r must be taken as *, for the first of 

 these portions, and as s for the second. Hence we have 



