356, 357] Maxwells Theory of Diffusion 299 



We can use this equation to determine the value of the coefficient of diffusion. 

 There must be two kinds of gas, which we shall denote by suffixes 1, 2, and 

 which we shall suppose to be diffusing into one another in a direction 

 parallel to that of the axis of x. Equation (720) will of course apply only to 

 one kind of gas, let us say the first, but there will be an exactly similar 

 equation for the other kind of gas. 



In this equation we put Q =u, so that Q =(u ) l , the mass velocity of the 

 first gas. "We assume the motion of diffusion to be so slow that the devia- 

 tions from Maxwell's law and squares of mass velocities may be neglected to 

 a first approximation. 



Then ^q = ^ = ~^Pi > 



Pi 

 where p 1 is the partial pressure due to the first gas. 



The equation accordingly becomes 



d (u \ . , 9 , . . x 9 / PI\ v l v 



" -ar = > a* - & ("' ft) + ii x > + Aft 



or, simplifying by the neglect of (w )i 2 , and multiplying throughout by m 1} 



( = - d + Vl X 1 + mM^ (721). 



The value of A(w 1 ) is of course not zero, because collisions with molecules 

 of the second kind change the momentum of the first gas. In equation (690) 

 we obtained the value of A(w) 1 in the form 



A (u\ = ra 2 V! i/ 2 A/ - - A i ((t/ok- Oo)i ) 



V 7/c-j ~T" v/t-2 



If the motion of the gas has become "steady motion," the left-hand 



member of equation (721), namely m^v l -j- (u \, must vanish, so that the 



dt 



equation becomes 



= Vl Xj. + mjmi VM A / 



vOC V 





oac V m!+m 2 



Similarly, of course 



- m 1 m 2 v 1 v. 2 A/ - 



V 772-1 





- "2-^2 ""1 ""a"! "2 A / 



ox V m, + w., 



By addition we obtain 



L (pi 



the hydrostatic equation of equilibrium. 



