﻿the Electron Theory of Solids. 665 



vibrations of these chains is so low that they readily absorb 

 energy even at low temperatures, so that the average energy 

 of the chains at the absolute temperature is kd, where 

 k represents the factor corresponding to one degree of 

 freedom. 



Thus, though the electrons in the solid are not free, and 

 xi re in a very different condition from those of an electron 

 gas diffused through the solid, yet like those in the gas they 

 can carry energy and electricity from one place to another. 

 In the gas, however, each electron is supposed to be moving 

 independently of its neighbour, and also to possess energy 

 'i\k0 corresponding to three degrees of freedom ; in our case 

 the agents which carry heat and electricity are not isolated 

 electrons, but chains of electrons moving as if the electrons 

 which compose them were rigidly connected together; thus, 

 however many electrons there may be in the chain, the 

 average energy of a chain will only be k0, i. e. one-third 

 of that of each electron on the gas theory. Thus on this 

 view the contributions of the electrons to the specific heat of 

 the solid will be a very small fraction of the contribution 

 of the same number of electrons on the gas theory. 



Professor Lindemann has given (Thil. Mag. xxix. p. 127, 

 1915) a theory of Metallic Conduction which, though on 

 quite different lines to the present one, agrees with it in 

 making the electrons which carry the current move along 

 the lines of the lattices, and in the view that the electrons 

 make no appreciable contribution to the specific heat. 



The existence of these chains requires that the frequency 

 of this vibration should be exceedingly small ; if the dimen- 

 sions and arrangements of the lattice are such that the 

 frequencies given by equation (2), are not less than 10 13 

 or so, the chains will not absorb energy at moderate tem- 

 peratures, and at these temperatures the solid will act as 

 an insulator. Thus it requires special conditions for the 

 lattices of electrons to give rise to conductivity, so that the 

 fact that neither boron nor the diamond is a conductor is 

 not inconsistent with the theory. The motion of the chains 

 need not necessarily be a reciprocating motion, for if the 

 amplitude of excursion of an electron in the chain exceeds 

 half the distance between two electrons, an electron such as 

 A' would shoot past another position of equilibrium; the 

 forces acting on it would change sign and would tend to 

 increase the distance still further; thus the chain would 

 continue to move on in one direction and would not oscillate 

 backwards and forwards. 



