THE KINETIC THEORY OF MATTER. 145 



gas parallel to the plane and in the given direction and an opposite force 

 on the upper gas. 



Let us consider a gas contained between two plane parallel boundary 

 walls AB, CD (Fig. 77) a distance d apart, the lower plane CD being 

 fixed and the upper plane AB moving with constant velocity v from left 

 to right. We shall assume that the layer of gas in contact with each 

 wall has no motion relative to that wall, and that the velocity increases 

 uniformly as we pass up from CD to AB, so that at a distance x from 



CD it is . Let the viscous tangential force of one layer on the next 

 d 



layer per square centimetre in the direction of motion be F. The motion 

 of each layer relative to the one below it being uniform, the force F is 

 the same on each layer and ultimately acts on each boundary. 



Direct experiments on the vibration of a plane disc close to another 

 plane disc fixed parallel to it show that for a given gas in a given con- 

 dition F is proportional to , and so tend to justify our assumptions. 



ct 



It may be mentioned, however, that when the pressure of the gas is 







FIG. 77. 



very much reduced we are no longer able to assume that the layers in 

 contact with the boundary planes are fixed relative to them. There is, 

 in fact, side slip. This, however, is inversely proportional to the pressure 

 of the gas, and is negligible at ordinary pressures. 



Let us now imagine a plane EF, 1 cm. square, parallel to the boundary 

 planes and consider the transfer of molecules across it. Let u be the 

 average velocity of the layer at EF from left to right. The molecules 

 moving down through EF will come from various distances and so carry 

 with them various amounts of momentum parallel to u. Let us suppose 

 that they carry on the average the momentum possessed by the mole- 

 cules in the plane indicated by the upper dotted line and distant from 

 EF by the M.F.P. = L say. According to Joule's method, the mass 



moving down through EF in one second is p . 



6 



The velocity parallel to u, at the distance L above EF, is u + ' 



d 



Hence the momentum parallel to u transferred across the plane in one 



second is p ( u -[ - ) 



6\ d J 



