296 Prof. 0. W. Richardson on 



average electric transportation. In the presence of an 

 electric field the axes of the doublets tend to be pulled into 

 alignment with the field, so that on the average more 

 electrons travel in this direction than in others, and this 

 gives rise to an electric current. At low temperatures the 

 tendency to alignment is enormously enhanced by the mutual 

 action of the neighbouring doublets, and this state of affairs 

 causes phenomena closely resembling the super-conductive 

 state discovered by Kamerlingh Onnes. Evidently one 

 sharply marked difference between this form and the more 

 usual forms of electron theory is that the conductivity is due 

 to the effect of the electric field on the atoms from which 

 the electrons are ejected, and not to its effect on the motion 

 of electrons in the interval between collisions. At tempera- 

 tures sufficiently high for the specific heats of metals to 

 have become normal, this theory leads to the following ex- 

 pression for the electrical conductivity c at temperature t° K, 

 namely : — 



c= 3-ir-' 0) 



where N = the number of doublets in unit volume, 

 e = the electronic charge, 

 p = the number of times an atom emits an electron 



per second, 

 d = the distance between the centres of adjacent 



atoms, 

 M = the moment of a doublet, 

 and & = Boltzmann's constant. 



It is clearly of considerable importance to determine the 

 values of the quantities entering into equation (1). An 

 estimate of the moment M of the doublets may be obtained 

 by considering the emission of electrons from the surface of 

 the hot metal. 



Since the electrons only pass from an atom to its nearest 

 neighbours, the number of electrons crossing unit area in 

 the positive direction in the interior of the substance in unit 

 time will be %Npd in the absence of an electric field. The 

 number which escape from unit area of the surface per 

 second will be less than this on account of the work which 

 an electron has to do against the attraction of the metal for 

 it. To calculate this number it is necessary to know the 

 velocity of the electrons. Thomson * has shown that in 



* ' Corpuscular Theory of Matter,' he. cit. 



