Viscosity of Mixed Gases. 425 



rest, the effect of collisions between the two sets of molecules 

 would be to keep m-^K 2 = m 2 /c 2 2 . If one of the solid planes is 

 set in motion with velocity w, then on the average a molecule 

 of 1 and a molecule of 2 coming from opposite sides of the 

 layer at x to collide in it will, in addition to the velocities of 

 agitation, have velocities (x + X 1 /2)iu/D and (x— \ 2 /2)w/D. 

 And the velocity of the centre of mass of the two molecules 

 is not ivx/D, characteristic of the layer at x; so that to assume 

 that a single collision between a 1 and a 2 suffices to bring 

 both to the state characteristic of the place where the collision 

 occurs is much less justifiable than in the case where 1 and 2 

 are identical. It is true that, corresponding to the pair we 

 have just considered, there is another pair whose relative 

 positions are the reverse, so that the velocity of the centre of 

 mass of the four molecules both before and after their col- 

 lisions is the wxjT) characteristic of the layer where they 

 collide ; but it is quite evident that there musfr be further 

 collisions before the four molecules can be treated as typical. 

 It simplifies the course of the work if for the moment we 

 ignore this difficulty and push on for an expression for the 

 viscosity of the mixture on the assumption that all collisions 

 are as effective as in a single gas : the result will be correct 

 for a mixture of gases of equal molecular masses, and will be 

 suitable for adaptation to the case where the molecular masses 

 are different. For the rest of the viscosity due to the mole- 

 cules of 2 we can write a similar expression to that just given, 

 and get 



_ n Y m^ n 2 m 2 v 2 2 _ 



v ~ (Ki^i + iM 6(21/2 + 2^1)' 



while for each ingredient of the mixture we have 

 ^m^ 2 n 2 m 2 v 2 



But m 1 v 2 — m 2 v 2 2 and m 1 /Ci 2 = m 2 K 2 2 , and the equations given 

 suffice for the elimination of everything but the ?7's ; 7ns, and 

 n's ; thus 



_ Vi 



-Wo. . . . . „ / rn . -4- rn.<>\% 



1 + 





V ^ {1Mv J,l im ^(^j (8) 



So far our equations have related to forceless smooth per- 

 fectly restitutional spherical molecules ; but as it has been 



