76 PROCEEDINGS OF THE AMERICAN ACADEMY. 



assumptions, our only question here is whether (5) is necessarily true. 

 Examination shows that it involves the assumption, not explicitly 

 made thus far, that the free electrons in unequally heated metal tend 

 toward equality of gas-pressure, that the difference dp, between two 

 isothermal planes differing by dT, must be balanced, if we are to have 

 equilibrium, by the force /, applied to every free electron between 

 the planes. 



This assumption, which implies that the free electrons tend to the 

 condition 



n 1 R 1 T l = n 2 R 2 T 2 , (9) 



where the subscripts (1) and (2) refer to any two parts of the metal, 

 is by no means a matter of course when we are dealing with a gas 

 permeating narrow passages where differences of temperature exist. 



It is well known that, if a thin partition pierced only by a very small 

 hole separates two bodies of an ordinary gas, one at temperature T\, 

 the other at temperature To, the condition of equilibrium between the 

 two bodies of gas is not equality of pressure, but pvr-pz — Ti*S- T 2 * , 

 or, since p\\ p 2 : : n\T\\ n 2 T 2 , 



»i7\* = n 2 T 2 K 



That is, there is a certain tendency of the gas from the cold chamber 

 to the warm chamber, which must in the end be balanced by superior 

 pressure in the warm chamber. 15 



Going to the case of electrons, for which we assume R to be a varia- 

 ble, we have as the law of equilibrium under thermal effusion alone 



mWtf = n 2 (R 2 T 2 )K (90 16 



or, since p = nRT, p cc (RT)K 



15 Maxwell, toward the end of his memoir on Stresses in Rarefied Gases, says, 

 "The passage of gases through porous plates, as was shown 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 the 

 thin plate. 



"\Yhen 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. 



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

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

 spond to what we have called effusion." etc. 



16 For, another way of stating the condition of equilibrium in the case of 

 thermal effusion is, that the momentum of the particles per cu. cm. shall be the 

 same at one place as at another. If we take c as the "velocity of mean square," 

 this condition gives riiCi = 112C2, and we have already seen, in the footnote 

 on p. 69, that c<x(RT)h. 



