in the Kinetic Theory of Gases. 311 



left, and lose velocity in direction x by encounters. Here 



And we assume 



F = N(^)V*» 2 (1 + X<M<» 8 )), 



where </>(w 2 ) is an nndetermined function. The disturbance 

 is of the first order. 



16. Viscosity of a single gas. — A gas on either side of the 

 plane of xz is uniform throughout as regards temperature 

 and density. On the negative side of the plane y = — a the 

 gas has, and is constrained to maintain, a constant velocity, 

 v, of simple translation in direction x. And on the positive 

 side of the plane y=+a, a constant velocity —v of simple 

 translation in that direction. The problem is to find the 

 quantity of x momentum which under those circumstances is 

 carried across unit area of the plane of xz per unit of time in 

 the positive direction by molecules crossing that plane. 

 Take any two planes parallel to xz and distant Sy from each 

 other. Suppose for a moment that on the negative side of 

 the negative plane the gas has a velocity, v, of simple transla- 

 tion in direction x. Then the number of the class 



\ fjuv (o 2 day dS 

 per unit of volume is 



N( J ^fe- k " 2 <0*dG>d8{l + 2\kcov\. 



The number of this class which cross the negative plane in 

 the positive direction per unit of area and time is 



N(^ye- k » 2 (o 3 dcodS{(jL + 2\/xka>v\. 



The number of the same class that cross the positive plane in 

 the positive direction per unit of area and of time is 



N^Ve-^ 2 a)VZ^S ^fi + 2\fikeo(v+By~\\. 



And, but for encounters, the class within the layer between 

 the planes would gain in number per unit of volume and time 

 by the quantity 



~ N (^f e- k " 2 o> 3 dco dS . V • 2*© ~. 



In steady motion the number of the class in question is 

 diminished by encounters by the same quantity. 



