ARISING FROM INEQUALITIES OF TEMPERATURE. 711 



by Graham, is of an entirely different kind from the passage of gases through 

 capillary tubes, and is more nearly analogous to the flow of a gas through a 

 small hole in a thin plate. 



When the diameter of the hole and the thickness of the plate are both 

 small compared with the length of the free path of a molecule, then, as Sir 

 William Thomson has shown, any molecule which comes up to the hole on 

 either side will be in very little danger of encountering another molecule before 

 it has got fairly through to the other side. 



Hence the flow of gas in either direction through the hole will take place 

 very nearly in the same manner as if there had been a vacuum on the other 

 side of the hole, and this whether the gas on the other side of the hole is 

 of the same or of a different kind. 



If the gas on the two sides of the plate is of the same kind but at 

 different temperatures, a phenomenon will take place which we may call thermal 

 effusion. 



The velocity of the molecules is proportional to the square root of the 

 absolute temperature, and the quantity which passes out through the hole is 

 proportional to this velocity and to the density. Hence, on whichever side the 

 product of the density into the square root of the temperature is greatest, 

 more molecules will pass from that side than from the other through the 

 hole, and this will go on till this product is equal on both sides of the hole. 

 Hence the condition of equilibrium is that the density must be inversely as 

 the square root of the temperature, and since the pressure is as the product 

 of the density into the temperature, the pressure will be directly proportional 

 to the square root of the absolute temperature. 



The theory of thermal effusion through a small hole in a thin plate is 

 therefore a very simple one. It does not involve the theory of viscosity at all. 



The finer the pores of a porous plate, and the rarer the gas which effuses 

 through it, the more nearly does the passage of gas through the plate corre- 

 spond to what we have called effusion, and the less does it depend on the 

 viscosity of the gas. 



The coarser the pores of the plate and the denser the gas, the further 

 does the phenomenon depart from simple effusion, and the more nearly does it 

 approach to transpiration through a capillary tube, which depends altogether on 

 viscosity. 



