836 Prof. H. A. Wilson on the Electron Theory 



Let u denote the velocity of a particular group due to an 

 electric force X acting parallel to the x axis and suppose 

 (vide infra) 



£ t (<mmu)=(mxe-(m/3u, 



where /3 is a function of V, m the mass, and e the charge of 

 an electron. If Nw = j itdN, u will be the average velocity 

 of all the N electrons in the x direction and 



j(Nmi* ) = NX*--j , #*rfN. 



Jeans*, in his very interesting and valuable investigation, 

 obtained the equation 



j (Nmw o ) = NX0— N7W0, 



so that J/gudN 



7 fudK 



Since u varies with the time, it follows that 7 is not in 

 general a constant. If, however, we take all the electrons to 

 have the same velocity of agitation, we get <y = ft. In Jeans' 

 investigation he took 7 to be independent ot the time, which 

 seems to be equivalent to ignoring the velocity distribution. 

 If this is not done, then it is necessary to find as a function 

 of V, which requires special assumptions to be made. 



Jeans obtained his equation on the assumption that the 

 time dt in it is large compared with the time of a collision. 

 If it is taken so large that during it a particular electron 

 will have successively many velocities, then the velocity of 

 all the electrons will be the same on the average over dt, and 

 so the equation will be true. I think this requires dt to be 

 large compared with the time between two collisions between 

 one electron and other electrons (not atoms, since collisions 

 with atoms do not alter the velocity much). If this is so, it 

 means that Jeans' equation will only be strictly correct for 

 vibrations of much smaller frequency than those in infra- 

 red radiation. At the same time, of course, it will be approxi- 

 mately correct even for rapid vibrations, because the assumption 

 that all the electrons have the same velocity of agitation 

 represents the facts fairly well in such problems. 



In view of these considerations, it seemed to be worth while 

 to work out the theory on the lines followed by Jeans, but 



* Phil. Mag. June 1902, and July 1909. 



