374 Note g: on electric leakage 



surface without passing through an electrified surface must be at the same 

 potential. Hence no finite portion of a surface can be free from charge, unless 

 the whole surface is free from charge. 



NOTE 9, ART. 124. 

 [On electric leakage.] 



The rate at which electricity passes from a conductor to the surrounding 

 air or from the surrounding air to a conductor was believed to be much greater 

 by Cavendish and his contemporaries than is consistent with modern experi- 

 ments. Judging from the statements of the electricians of each generation, it 

 would seem as if this rate had been diminishing steadily during the last hundred 

 years in exact correspondence with the improvements which have been made 

 in the construction of solid insulating supports for electrified conductors. 



Whenever the intensity of the electromotive force at the surface of a con- 

 ductor is sufficiently great, the air no doubt becomes charged*. This is the 

 case at a sharp point connected with the conductor even when the potential is 

 low, but when the curvature of the surface is continuous and gen tie, the conductor 

 must be raised to a high potential before any discharge to air begins to take place. 



Thus in Thomson's portable electrometer, in which there are two disks 

 placed parallel to each other at different potentials, the percentage loss of 

 electricity from day to day is very small, and seems to depend principally on 

 the solid insulators, for when the disks are placed very near each other, less 

 loss is observed than when they are further apart, though the intensity of the 

 force urging the electricity through the intervening stratum of air is greater 

 the nearer the disks are to each other. 



On the surface density of electricity near the vertex of a cone. 



Green has given in a note to his Essay, section (12), the following results of 

 an investigation which, so far as I am aware, he never published f. 



"Since this was written, I have obtained formulae serving to express, 

 generally, the law of the distribution of the electric fluid near the apex of 

 a cone, which forms part of a conducting surface of revolution having the same 

 axis. From these formulae it results that, when the apex of the cone is directed 

 inwards, the density of the fluid at any point p, near to it, is proportional 



* M. R. Nahrwold (Wiedemann's Annalen v. (1878), p. 440) finds that the dis- 

 charge from a sharp point communicates a charge to dusty air which can be 

 detected in the air for some time afterwards. This does not occur in air free from 

 dust. But the discharge from an incandescent platinum wire communicates a 

 lasting charge even to air free from dust. [Cf. the modern knowledge of leakage 

 as depending on the migrations of free electrons.] 



f [The results of Green were at length demonstrated by Prof. H. M. Macdonald, 

 Cambridge Phil. Trans, vol. xvm, 1900 (Stokes Memorial Volume), pp. 292-8.] 



