﻿130 Dr. F. A. Lindemann on the 



equal to kf(r). This hypothesis, though not explicitly stated 

 in the ordinary electron theory, is accepted in its main 



outlines, £01* if: an electron were attracted with a force -3, 



3R 



the small kinetic energy attributed to it, ~^~ T, could never 



enable it to dissociate from the ion. The hypothesis seems 



to be rendered fairly plausible by the experiments on the 



reflexion of electrons by atoms described by Franck and 



Hertz *. 



2. The number of electrons per cm. 3 , N, the dielectric 



constant of the ions D and the constant k of the repulsive 



■force kf(r) are such that <£(N, /j)—^(N, D). The functions 



xj> and t/t will be defined later on. The equation probably 



N 

 reduces to I/2 3 2 = const., or if D is constant, to N~ ^/k. 



This hypothesis is introduced to account for Wiedemami- 

 Franz's law. 



We need only consider crystals for the time being, as all 

 metals consist of an agglomeration of, often microscopic, 

 crystals. A metal crystal would consist of two interleaved 

 space-lattices, one consisting of atoms or ions, one of 

 electrons. 



To work out the exact mathematical consequences oE this 

 conception will be a matter of great difficulty. This paper 

 will be confined to a general review of the various phenomena 

 and an outline of the way this hypothesis might explain 

 them. 



Electric conduction. — If a metal crystal is brought into an 

 electric field the electron space-lattice will shift in respect to 

 the atoms until the attraction of the more distant ions 

 counterbalances the force exerted by the field. If a source 

 of electrons is brought into contact with the one end and if 

 they can flow out at the other, e. g. if the crystal is connected 

 to the two poles of a battery, the attraction of the more 

 distant ions will be counterbalanced by the repulsion of the 

 inflowing electrons, and the electron space-lattice will move 

 continuously through the atomic space-lattice. In other 

 words, the electron space-lattice or crystal may be said to 

 melt at the one end and fresh layers may be said to freeze on 

 at the other end when a current flows. If the distance to 

 which the repulsive force of the ions extends, r , is less than 



- , half the distance between the centres of the atoms, the 



z 



* Verh. d. d. Phys. Ges. xv. p. 929 (1913) ; Phys. ZS. xiv. p. 1115 

 <1913). 



