﻿the Electron Theory of Solids. 673 



electron to pass over a distance 2 c is comparable with the 

 time of vibration of the atom, any diminution in the temper- 

 ature will produce an abnormally large increase in the 

 conductivity, and thus the metal would show the super-con- 

 ductivity discovered by Kammerlingh-Onnes. 



The numbers we have just obtained for sodium show that 

 at a temperature of 3° Ab. the time taken by a collision 

 would be greater than 2 X 10~ u , and this is very long com- 

 pared with the time of vibration of the sodium atoms, which 

 have a frequency of 3*96 X 10 1J . There would be very little 

 transference of energy at this or even considerably higher 

 temperatures, so that the conductivity would be very 

 great. 



We have associated the time taken by a chain to pass over 

 the distance 2c at any temperature with the time of vibra- 

 tion of the light of predominant energy at that temperature. 

 On the theories of the variation of specific heat with temper- 

 atures given by Nernst, Einstein, and Debye, this variation 

 is a function of the ratio of the time of vibration of this 

 light to the time of vibration of the atom. Thus on the view 

 that the average time of a collision is about that of the time 

 of vibration of this light, the variation of the specific heat 

 with temperature and the communication of energy from the 

 electron to the atom depend upon exactly the same quantity, 

 and thus the variation of the specific heat with temperature 

 ought to be closely connected with the super-electrical 

 conductivity. The product 6a of the temperature and the 

 electrical conductivity ought to change rapidly with the 

 temperature when the specific heat does so. The product 6a 

 will increase as the specific heat diminishes ; if, however, 

 we were to plot the reciprocal of 6a against the tempe- 

 rature, we should expect to get a graph very similar to the 

 one representing the connexion between specific heat and 

 temperature. 



That a connexion of this kind does exist between l/6a and 

 the specific heat is, I think, shown by Table II., which 

 contains the values of l\6a for lead and silver calculated 

 from the values of the resistances given by Kammerlingh- 

 Onnes (communications from the Physical Laboratory of 

 Leiden, cxix. 1911); the third column contains the values 

 of #/© when ® = /iv/R, where N is the time of vibration of 

 the atom ; the fourth column gives the value of the specific 

 heat calculated by Debye's theory (Jeans, ' Kinetic Theory 

 of Gases,' §§ 553) ; and the fifth column the ratio of \\6a to 

 the specific heat. 



Phil. Mag. S. 6. Vol. 44. No. 262. Oct. 1922. 2 X 



