HGG Prof. Lynde P. Wheeler on the 



the present purpose to leave K indeterminate in the equa- 

 tions. The expressions which have been obtained for a, on 

 the other hand, contain but one un determined constant, and 

 consequently can be profitably used. 



The development of cr in terms of the frequency of the 

 current is best accomplished by the method due to Lorentz, 

 Jeans, and H. A. Wilson. It seems preferable to that of 

 Drude, in that the fractional term in the equation of motion 

 of the free electrons in the Litter's method receives a more 

 probable physical interpretation in the more recent method. 

 In this method the equation of motion of the electrons is 

 obtained from a consideration of the loss of momentum (in 

 the direction of the acting electric force) sustained by a 

 group of electrons having velocities lying between v and 

 v + dv. If we assume that the electric force is given by 

 E = E e -i -P', and that the law of the distribution of the 

 velocities among the groups is that of Maxwell, we obtain 

 from a consideration of the rate of production of heat per 

 unit volume, 



°=*A Stm"' • • (2) * 



where q is three-halves of the square of the average elec- 

 tronic velocity, <r is the electrical conductivity for steady 

 currents, and 



J 5 



,2 



0i = 



iWe 



(3) 



with e the charge, m the mass, and N the number of electrons 

 per unit volume. 



If we now expand (a/qv 2 + l)~ l in series and integrate 

 term by term, we get 



La\ ot, a- J 2i\' a \ 2a (laY J 



(T = (Tr 



1 1 " l l'.At (2*~1)(2i»-3) n m 



These integrations were first performed by Nicholson t- I am 



* II. A. Wilson, Phil. Mag. [6] xx. p. 835 (1910). Wilson there 

 assumes the electric force to be given by E — Eo cospt, and hence his 

 value for rr lacks the imaginary term of the above. 



t Nicholson, loc. cit. 



