2±& Dr. J. W. Nicholson on the Number of 



law of distribution of velocity is that of Maxwell, so that 

 d~N, the number of electrons whose velocity is between V, 

 V + dV, satisfies 



^N = 47rN(^/7r)"V 2 ^-^ a ^V, (4) 



where q is determined in the usual way in terms of the mean 

 velocity of agitation, then 



A>irea(q\\ f " cos (pt-o) e~^" 2 Y 2 dY /tCS 



If a is the conductivity, \a?a is the mean rate of produc- 

 tion of heat in the unit of volume on account of the electric 

 flow. This rate is also the mean value of N^u ^cos^, from 

 which may be deduced 



where <r is the steady conductivity. These are the important 

 results in the part of Wilson's paper with which we are 

 concerned. It is stated that this formula gives, by graphical 

 methods, values of K in most cases about twice as large as 

 those derived from the formula of Schuster and Jeans, 



<7/<7 = (l +J) ! mV/NV)->, .... (7) 



valid when all the electrons have the same velocity of 

 agitation. 



On the basis of the equal ion of motion of a group, which 

 is the essential feature of Wilson's investigation, differing in 

 its last term from that of Jeans, let us consider the optical 

 constants of a metal more minutely, on the simple lines 

 developed by Schuster. With an electric force ae~ ipt , for 

 which a real value may be inserted at the end, the equation 

 of motion of the group is 



md/dt (u dN) + mY {u dN) \l m = ea dN *-**, . . (8) 



whose solution is 



u dN = - - dN (ip-Yll m )- 1 e-&, 



or 



N eadK(ip + Y/lfn) ipf (q) 



and applying Maxwell's law, the mean velocity along the 

 direction of the force is 



„ 0= 1™/ l)*,* f^^ffl^; . (10) 



m \7r/ J p-+Yil m 2 



