﻿the Electron Theory of Solids. 675 



electrons in the chain move like a rigid body, each electron 

 has the same kinetic energy; we shall suppose that this 

 energy is the same as it' the whole of the chain were at the 

 temperature of its middle point, so that the kinetic energy 

 of the whole chain is that corresponding to one degree of 

 freedom at the temperature of the middle point of the 

 ch tin. 



Another important point is that the energy carried across 

 a plane by a chain of electrons passing right across it may, 

 when the temperature is not uniform, be much greater than 

 the actual kinetic energy in the chain when it first reaches 

 the plane. This is important because if it were not so the 

 transport of energy due to the motion of the chains would 

 not be great enough to account for the observed thermal 

 conductivity even if every disposable electron were utilized 

 to make up the chain. It must be remembered that on this 

 theory the number of disposable electrons in unit volume is 

 known; for example, in the alkali metals it is equal to the 

 number of atoms, and cannot be regarded as a quantity 

 which* can be adjusted so as to give the right value to the 

 thermal conductivi'y. 



To see how this additional transport of energy is brought 

 about, consider what happens when a chain of electrons 

 ABODE crosses the plane ZZ, moving past the atoms in 

 its neighbourhood and exchanging energy with them. If 

 2c be the distance between neighbouring electrons or atoms, 

 we shall define a collision between an atom and an electron 

 to be the passage of an electron past its shortest distance 

 from the atom. If we take the axis of x parallel to the 

 chain, then when the head A of the chain reaches ZZ 

 each of the electrons in the chain has ljn of the energy 

 corresponding to one degree of freedom at the temperature 



6 + y ~j~i where I is the length of the chain, n the number of 



its electrons, and 6 the temperature of the plane ZZ. When 

 A makes a collision with the atoms just to the left of: the 

 plane ZZ, it will momentarily lose an amount of energy 



•J 7 7/1 



proportional to -- — . This will lower its energy below that 



which must be possessed by every electron in a chain whose 

 middle point is now at a place where the temperature is 



04-J(Z — 2c) -j- ; this energy only differs from that before 



impact by ' , ; the electron has, however, since / is much 

 r J z/i ax 



2X2 



