﻿664 Sir J. J. Thomson : Further Studies on 



equilibrium is stable for this mode of displacement. A 

 negative term will occur in the expression for p 2 if the 

 electrons along one line of the lattice are displaced relatively 

 to those on adjacei t lines, even though the displacements 

 are not equal and opposite. The view I wish to put forward 

 is that in metals the frequency of this type of vibration is so 

 low that the equilibrium for such a displacement is practically 

 neutral, and therefore that a system vibrating in this way 

 can absorb at any temperature the full amount of energy 

 which at that temperature corresponds to each degree of 

 freedom. 



It may be desirable to illustrate the argument by a 

 particular case (fig. 1). Let us take that where the electrons 



Fig. 1. 



ISNNN 



^ T^r^j 



A A' A" A'" 



are arranged in a simple cubical space lattice with the atoms 

 at the centres of the cubes. Then, if an electron were dis- 

 placed independently of the others, the frequency of its 

 vibration would be very great and it would absorb very 

 little energy ; while if a chain of electrons along a lattice 

 like AA' A"A n/ were displaced along the line of the lattice, 

 the time of vibration of the chain might be comparatively 

 infinite, so that the chain would absorb the full amount of 

 energy corresponding to one degree of freedom. However 

 many electrons there may be in the chain, it has only one 

 degree of freedom, for the nature of the displacement 

 supposes that they move as a rigid body along a definite 

 line. To sum up, the study of the frequencies of vibrations 

 of the lattice of electrons shows that while at ordinary 

 temperatures little energy could go into vibrations corre- 

 sponding to the motion of an electron as a separate individual, 

 yet groups of electrons along a lattice forming a rigid chain 

 and moving in the direction of the length of the chain might 

 absorb a full quantum of energy. 



Thus in a solid with the constitution we have sketched, 

 chains of electrons lying along a line of a lattice may be 

 travelling along that line carrying energy and electricity 

 from one part of the solid to another; the frequency of 



