﻿Theory of the Metallic State. 131 



electron space-lattice can move unimpeded through the atom 

 space-lattice, as long as the atoms are at rest or as long as 



their vibrations do not extend to an amplitude — s— ^- This 



would correspond to the supra-conductive state described by 

 Kamerlingh-Onnes as occurring in pure metals at tempera- 

 tures below about #° *. If, however, the metal is not pure 

 this supra-conductive state can never be attained, for the 

 regularity of the original atomic space-lattice is destroyed by 

 the other atoms embedded in it, and the electron space-lattice 

 would always encounter a comparatively large resistance 

 which would be independent ot! the temperature. This 

 corresponds to the formula W = W +/(T) discovered by 

 JSTernst t, in which the resistance W is equal to the resist- 

 ance /(T) of the pure metal plus a constant W depending 

 upon the impurities. 



To return to the pure metal, as the temperature increases 

 the amplitude of the atomic vibrations increases and the 

 electron space-lattice can no longer pass without resistance. 



Every electron will have to pass through the spheres of 

 repulsion on its path and will transfer the kinetic energy 

 gained from the electric field to the atoms. The mean 

 velocity of the electron space-lattice v is obviously pro- 

 portional to the current as the number is constant ; the 



ex 

 m 

 where r is the time between two collisions with a repulsive 



sohere. t— - --, whilst the electron is in the immediate 

 v 



neighbourhood of an atom if v' is the atom's frequency. 



During the rest of the time t=-, where d is the distance 



during which the electron is further removed from the atom's 



centre than r + A, A being the atom's amplitude. Now, as 



we always have a very large number of electrons in any 



observable current, there are always a large number of 



electrons within the distance r + A of an atom,, consequently 



the time during which the entire electron space-lattice can 



move unimpeded is infinitesimal. It follows that Ohm's law 



holds good as the current a^-i — -.v. Further, it may be 



expected to hold for any current whose duration is of the 



. 1 

 order — , or greater. 



* Leiden Communications, 124 C, 



f Bed. Ber. ii. p. 23 (1911). 



K 2 



mean velocity imparted to one electron by the field is k— -t, 



