680 RICE ART. L 



potentials and electron affinities is not a difficult matter, but 

 it requires the reader to be very clear on certain elementary 

 points in the theory of electricity. Thus the definition of elec- 

 tric potential at a point is given in the words "the work required 

 to bring unit positive change from infinity to the point," but 

 it is not always borne in mind that the transference of the 

 charge is assumed not to disturb the existing distribution of electric 

 charge in space. The neglect to take account of this proviso 

 will lead to paradox and perplexity in some cases. Thus 

 suppose we have an uncharged conductor far away from all 

 other conductors so that it is at zero potential. Now imagine 

 the test positive charge to approach the conductor from 

 infinity; as it gets near, a negative charge is iijduced on the 

 proximate face of the conductor and a positive on the re- 

 mote; an attraction is exerted on the test charge, which means 

 that work has been done on the charge in coming from infinity 

 to the conductor. Or, if a test charge be taken away from the 

 conductor, the disturbance of the distribution of charge which 

 existed in the conductor before the test charge was placed near it 

 will produce an attraction on the charge, and the unwary might 

 therefore infer that the uncharged conductor is at a negative 

 potential, the potential at infinity being taken to be zero as 

 usual; but of course that is an erroneous conclusion and due to 

 neglect of an essential feature of the definition of potential. 

 Another point to be borne in mind (but often overlooked) is 

 that there is no discontinuity of potential between a point in a 

 charged conductor and a point just outside it. The quantity 

 which is discontinuous is the intensity of electric force (which 

 is zero inside a statically charged conductor and equal to 4tk 

 just outside, where k is surface density of charge), and this 

 intensity is the gradient of the potential. A geometrical illus- 

 tration can be observed at a point on a graph where there is a 

 sharp break in the slope. There is no discontinuity in the 

 ordinate y, but one in the slope, i.e., ui the gradient of y, viz. 

 dy/dx. If there is a discontinuity in the potential at the sur- 

 face of a conductor, or at an interface between two conductors, 

 it can only arise owing to a "double layer" of opposite charges, 

 say a positive surface charge and, at a physically small distance 



