774 Prof. J. H. Jeans on the 



assigned to them by Maxwell's law *. At a temperature T 



given by RT = ^y , the law of distribution of velocities is 



ly'^rM^^^^. . . . (1) 



It an electric force X is brought into play parallel to Ox, 

 this distribution will immediately be altered. Each electron 

 will acquire momentum parallel to Ox at a rate X<?, but this 

 gain in momentum will be held in check by a perpetual 

 transfer of momentum between each electron and all the 

 molecules by which it is influenced at any instant. 



Under law (1), the average value of it is zero. Under the 

 new law, the average of u will have some value a , different 

 from zero. Corresponding to any value of u , there is a 

 current i x parallel to Ox of amount 



i x ^ Neu Q (2) 



3. A brief calculation will show that for all values of X 

 with which we shall be concerned, uq is small in comparison 

 with the average numerical values of u. We may perfectly 

 legitimately neglect squares of n , and, in particular, in calcu- 

 lating any quantity which has ultimately to be multiplied by 

 u 0i we may assume formula (1) to give the distribution of 

 velocities. 



4. We proceed now to calculate an expression for the 

 transfer of momentum between electrons and molecules. 

 We shall do this first, for simplicity, upon the supposition 

 that the motion consists of free paths and collisions. After- 

 wards we shall find a perfectly general expression. 



Consider an electron approaching a molecule with a velocity 

 of components u, v, w. It will describe a curved orbit having 

 its free path before collision and its free path after collision 

 as asymptotes. Its loss of momentum at collision will depend 

 on u, v, w, on the orientation of the molecule, and on the 

 position in which the free path before collision meets a 

 perpendicular plane through the centre of the molecule. 



We know that all positions are equally likely for this latter 

 point, and if the solid is isotropic all orientations are equally 

 likely for the molecule. On averaging, w T e can find the 

 probable loss of momentum at collision. Clearly this average 



* It is important to remember that Maxwell's law gives the partition 

 of velocities for particles in collision or acted on by an}' field of force, as 

 well as when on a free-path. The existence of a field of force alters the 

 distribution of denshVy, but not of velocities (cf. the author's ' Dynamical 

 Theory of Gases,' p. 78). 





