Electrons concerned in Metallic Conduction. 251 



wave-length in vacuo. In the metal X is proportional to 

 the exponential of argument 



2llKZ . /27TVZ \ ,_„ 



so that v denotes the index of refraction, and k is a coefficient 

 of extinction, which we may call, after Schuster, the coefficient 

 of optical length. We have the relation 



47T 2 



U (^ 2 --* 2 + 2eVA:) = 47n> ( A-f ipB — ^K/IttC 2 ). 



Remembering thatp = 27rCy\, this leads to 



y/c = \CA, v 2 -/c 2 = K-47rBC 2 , . . . (21) 



where C is the velocity of light in vacuo, and A and B are 

 defined in (12). With p = in (11) the conductivity for a 

 steady current is 



so that 



(A B)-9a„ r (V. l«>)dVe-W 

 {A,lS)-.q<r ^ 1 + a/q y, -> • • (^3) 



where 



a = wptmWt ±N e A = 7r 3 /?i 2 o- u 2 C 2 /N 2 X-^, . . (24) 

 and with this value of a, 



= Vol T^T^ .... (25) 



xu -*"°J i + «A/V 



Jo l + aq\- 



(26) 



The first equation is of course identical with Wilson's 

 equation (5), which he derived from a consideration of heat 

 production. 



Wilson gives the second equation without proof, with 

 K=l, but has dropped a factor C 2 in the last term. A con- 

 sideration of the dimensions in time of the quantities concerned 

 will justify its presence. 



