Electrons concerned in Metallic Conduction. 249 



The current is N«/ =«i, 



or i 1 = a{A + ipB)e- i i«, .... (11) 



where 



*/0 



But tin's is not the whole current. In the first place there 

 is a polarization current, partly sethereal and partly material, 

 to be added to that of conduction. If K is the dielectric 

 capacity of the medium, and C the velocity of light in vacuo, 

 the polarization current is 



i 2 =-{KIA7rC 2 )ipae-y jt (13) 



Electrons belonging to the atoms, although not free to move 

 through a free path, will also contribute to the current by 

 their vibrations. In so far as they may be paired off with 

 elements of positive electricity into doublets in mean positions, 

 the effect of their vibrations will appear in the material 

 polarization current. This relates to their vibrations within 

 the atom, relatively to one another. We shall suppose that 

 each free electron in the metal necessitates the existence of 

 an unsaturated atom (perhaps, however, shared by several 

 free electrons) with a superabundance of positive electricity 

 equal to the charge on an electron. These extra charges 

 will contribute a current by their vibration, partly within 

 the atom and partly with the atom in its own vibrations as a 

 whole, but since their number is equal to that of the free 

 electrons, the magnitude of their contribution to the current 

 will bear a ratio to the previous conduction current which 

 must be small. For its magnitude cannot exceed that of the 

 ratio of atomic amplitude of vibration io mean free path of 

 an electron. The neglect of this current, in the absence 

 of sympathetic vibrations of the whole unsaturated atom, is 

 therefore valid. But if such vibrations are present this 

 argument fails, and the current thus concerned can be im- 

 portant. Similar considerations apply to the current contri- 

 bution from bodily convection of the saturated portion of an 

 atom. This must be a true current in an analogous way to 

 the effect, pointed out by Larmor, of translation of a finite 

 part of a moving material system. 



But if sympathetic vibrations are present to a certain 

 extent, increasing the atomic amplitude, the uncompensated 

 positive charges may contribute a current 



t^afC' + iDp)*-* 1 , .... (14) 

 where (C, D) are of like form with (A. B), C being un- 

 important in comparison with D/?, and both being positive 



