Viscosity of Mixed Gases, 423 



layer at x. Of course the average effect of the collision is 

 largely to destroy the two small relative velocities Lx/T) and 

 — Ix/D, and to convert the energy associated with them into 

 energy of agitation. This is easily proved in the theory of 

 viscosity, and then it is assumed that on the average a single 

 collision suffices to bring a pair of colliding molecules both 

 into the permanent state characteristic of the layer in which 

 they collide. But, as will be shown below, a single collision 

 does not on the average suffice to bring about this state ; and 

 the difficulty of defining in a simple manner the state of the 

 molecules in any layer at any instant, makes the relation 

 between viscosity and the constants of the molecules not so 

 definitely specifiable as in the numerical relations hitherto 

 given. What appears to me a better statement of the motions 

 of the molecules in each layer will be given below, though 

 the matter is really of slight importance in the case of a 

 single gas ; but when it comes to a question of a mixed gas, 

 then a correct specification of the state of each layer becomes 

 the essence of the problem. 



In the theory of the viscosity of a single gas, then, it is 

 customary to regard only those molecules which collide in a 

 layer as being characteristic of that layer, those molecules 

 which are passing through it without collision being taken 

 account of in some other layer where they do collide. An 

 approximate expression for the viscosity of a single gas can 

 be very easily established ; for if X is the mean free path, 

 then, as the mean paths have their directions evenly distri- 

 buted in space, the mean projection of the free paths on the 

 axis of x is the mean distance of a hemispherical surface of 

 radius X from the diametral plane, which is X/2. Thus all 

 the molecules which cross our plane at x may be said on the 

 average to have experienced their last encounter at distances 

 X/2 and — X/2 from it, so that each molecule that crosses from 

 a distance greater than x carries on the average momentum 

 of amount rmv\/2Y). If there are n molecules in unit volume 

 with average velocity v, then in unit time nv/6 may be taken 

 as the number of molecules crossing unit area ; so that the 

 positive momentum carried in unit time across unit area in 

 our plane from distances greater than x is nvmw\/12J), and 

 the same amount of negative momentum is carried in the 

 opposite direction across unit area, so that the total effect is 

 wramoX/GD, in which nmvX/6 is the viscosity 77. 



The constant 1/6 is not exact because of the rough and 

 ready approximations ; but, for the purpose in hand, it may 

 be regarded as not very different from the more accurate 

 •064, which takes its place as the result of the elaborate 



