His PROCEEDINGS OF THE AMERICAN ACADEMY. 



of a part of the initial charge, " binding " it, as it were, so that it can- 

 not take part in the discharge, and only becomes free gradually as 

 the polarization decays. A simple but crucial test as to which theory 

 in ust certainly be wrong is therefore to remove the armature plates of 

 a condenser immediately after an instantaneous discharge and test the 

 sign of their charges. This was done by Wullner, and the results con- 

 clusively disproved the older theory. 



Wullner observed the decreasing potential of charged condensers 

 made of the same kind of glass but of varying thicknesses, and 

 the results established a third law, which had been overlooked by 

 Kohlrausch : „ 



3. In condensers of the same dielectric but of different thicknesses and 

 shape the rate of fall of potential after equal times is the same. 



Still another law, of great importance, seems to have been first dis- 

 covered by Thomson, and may be stated thus : 



4. Residual charges come out of a condenser in the inverse order to 

 that in which they went in. Or, the rate of decay of residual charge 

 ihtring a long-continued short circuit is the same as its rate of forma- 

 tion duriny a long -continued charging. 



The second and third laws are ordinarily put together into a single 

 one, called the law of superposition. The first three may be general- 

 ized and briefly put into mathematical form : 



For condensers made of the same dielectric, the following equations 

 hold, provided we neglect losses to the air and those due to internal 

 conductivity : 



V, = V -f(t) Q t = Q -f(t) B t =Q - q t ; 



where V = charging potential, 



V, = potential t seconds after charging, 



Q = initial instantaneous charge, 



Q t = charge which may be drawn from condenser in an instan- 

 taneous short circuit after t seconds of insulation, 



lit = residual charge formed after t seconds of insulation. 

 Thus the function J\t) is one which is characteristic of any given 

 kind of dielectric, as paraffin or mica. 



Later researches have in general confirmed the law just given, but 

 have not added any others, unless we are willing to accept Hopkinson's 

 generalization of the law of superposition to include with instantaneous 

 forces forces acting at different times, and this has hardly been con- 

 clusively proved. 



The theories attempting to account for the cause of formation of 

 residual charges have in the main followed one of two fundamentally 



