Viscosity of Mixed Gases. 427 



from distances A/2 parallel to the axis of % on opposite sides 

 of the place of collision with velocities w\/2D an( i — w\/2D 

 relative to the layer at x which moves with its permanent 

 velocity aw/J), Now the total number of encounters occurring 

 in unit time in unit volume of the layer is nv/2, of which half 

 will occur between the molecules of the two sets, and the 

 other half between the members of each set amongst them- 

 selves. The average value of the momentum communicated 

 to one another by the molecules colliding with opposite velo- 

 cities a and a is 2(a + u)mm/3(m + m), so that while a mole- 

 cule brings in momentum ma to the layer, it loses on the 

 average at the first collision only 2ma/3 ; thus, after one 

 collision between each pair of molecules the distribution of 

 velocities may be represented by evenly distributed radii of a 

 sphere to represent the evenly distributed average velocities v, 

 then with half of these velocities taken at random compound 

 a velocity w\/QD in the direction of w, and with the other 

 half at random compound a velocity — w\/6D, so that the 

 original spherical surface is resolved into two having their 

 centres displaced in opposite directions by a distance repre- 

 senting itfA,/6D. According to the usual method of presenting 

 the theory of the viscosity of a gas, this distribution is 

 assumed to be identical with that represented by the undis- 

 placed sphere, and the assumption is plausible when it is 

 remembered that the small variations introduced by com- 

 pounding the small velocities w\/12D and — i^X/12D with 

 the average velocity v may be merged in the much larger 

 variations represented by Maxwell's law of the velocities 

 which we have ignored in considering only average velocities. 

 And yet an assumption which makes the effect of an 

 encounter practically independent of the amount of momentum 

 communicated by the colliding molecules to one another must 

 be erroneous, and must affect the usual expressions for 

 viscosity with an error appearing in the value of the numerical 

 coefficient. As each collision is only two thirds as effective 

 in communicating momentum as it is assumed to be in the 

 ordinary theory, we ought, in the usual expressions for the 

 viscosity, to introduce an additional numerical factor 2/3, 

 which would cause the value of the mean free path of a gas 

 as calculated from its experimental viscosity to be 3/2 of the 

 value usually given. 



With this principle, that the effective value of a collision is 

 proportional to the momentum exchanged by the colliding 

 molecules, we can adapt our equation (9) to the general case 

 of mixed gases by replacing i^/i^i hy (iv 2 /i v i) (l/ViAh) > where 

 t/Lti and i/j, 2 are the average momenta exchanged when 1 



