﻿278 Electron Theory of Contact Electromotive Force. 



This argument does not apply if the electricity is present 

 in the conductor in the form of electrons. The smallest 

 quantity of electricity which can be removed at one step is 

 finite and equal to the charge of one electron. There is thus 

 always a part of the work done in removing an electron from 

 an uncharged conductor which is proportional to e 2 . This 

 difference between the potential energy of an electron inside 

 and outside the metal may be figured as the work done by 

 the electron against the attraction of its image in the con- 

 ductor. This is not infinite, as in the ordinary electrostatic 

 theory, because the volume density of the electrification in 

 the ultimate atoms of positive and negative electricity is 

 finite. Sir J. J. Thomson's view that the atoms are spheres 

 of uniformly distributed positive electricity occupied by 

 comparatively small negative electrons of charge <?, com- 

 parable in number with the atomic weight of the atom, and 

 having an equal total charge, leads to values of iv comparable 

 with those given by the results of experiments on the emission 

 of electrons from hot bodies. There is thus no necessity to 

 introduce electrical double layers to account for the existence 

 of the w's. 



This discussion brings out the necessity for using great 

 care in the employment of the terms electric force and electric 

 potential in problems of this character. To obtain the dif- 

 ference of potential between two points A and B it is not 

 sufficient to find the work done in taking an electron from 

 A to B, and to divide the result by the charge e. The 

 quantity thus obtained may differ not only in magnitude but 

 even in sign from the value corresponding to the limit when 

 e is made zero. 



The variation of w with 6 is a matter of considerable 

 practical interest. If one supposes that the positive electricity 

 in the conductor can be treated as though it were continuously 

 and uniformly distributed throughout its volume, then it 

 .appears that w is comparable with e 2 ;b, where b is the radius of 

 a sphere of the positive electricity which carries a charge e 

 equal to that of the negative electron. From this rough 

 view of the phenomena one would expect that w would 

 diminish with rising temperature, its temperature coefficient 

 being comparable with that of the linear expansion of the 

 material. The experimental data available are inadequate to 

 test this point satisfactorily. 



Some further applications of the method which has been 

 developed will be considered in a later paper. 



Palmer Physical Laboratory, 

 Princeton, N.J. 



