﻿the Electron Theory of Solids. 679 



The ratio of K to cr, the electrical conductivity, is given 

 by the equation 



K _ 1_ e we 

 a ~ 12 g e 2 ' 



The right-hand side of this equation does not involve any 

 quantity peculiar to the metal ; hence the ratio of the thermal 

 to the electrical conductivity should at the same temperature 

 be the same for all metals, and at different temperatures 

 should be proportional to the absolute temperature. This is 

 the well-known law of Wiedemann and Franz, which is obeyed 

 with fair accuracy by many metals. 



Summary. 



This paper contains a calculation of the compressibility of 

 a divalent element, calcium, and also that of the diamond by 

 the method given in my paper on the Electron Theory of 

 Solids (Phil. Mag. April 1921). The results obtained are 

 in good agreement with those found by experiment. The 

 same theory is then applied to the consideration of metallic 

 conduction, electrical and thermal. It follows from the 

 theory that when an individual electron is displaced relatively 

 to its neighbours, the frequency of the vibration is that cor- 

 responding to the visible or ultra-violet part of the spectrum ; 

 these vibrations would not, unless at extremely high temper- 

 atures, absorb an appreciable amount of energy. When, 

 however, instead of a single electron being displaced, a chain 

 of electrons lying along one of the lines of the lattice is 

 displaced as a rigid body relatively to the neighbouring- 

 atoms and electrons, the time of vibration of this chain may 

 be very long, so long that even at very low temperatures the 

 chain may acquire the full quantum of kinetic energy cor- 

 responding to one degree of freedom at its temperature. 

 Thus chains of electrons moving like rigid bodies may travel 

 along the lines of the lattices, and carry electricity and energy 

 from one part of the metal to another. The theory that 

 electric and thermal conductivity is due to the movement of 

 these chains is worked out, and is shown to account for the 

 variation of electrical resistance with temperature, for the 

 super-conductivity of metals at very low temperatures dis- 

 covered by Kammerlingh-Onnes, and for Wiedemann and 

 Franz's law of the proportion between electrical and thermal 

 conductivity. 



