124 Prof. W. M. Thornton on the 



then we see at once that 



~^(mv)a+?^ 2 (wV)s'], 



a, result which has already been obtained by another method, 

 and its bearing on the theory of the optical properties of 

 metals discussed at length. 



The general solution of the fundamental differential 

 equation of the theory, which has been obtained above, is 

 thus consistent with the results of particular cases of the 

 general problem which have been obtained independently 

 and occasionally by different methods, as of course it must 

 be. It is, moreover, deduced by an argument which implies 

 the minimum of hypotheses regarding the motion of the 

 -electrons and the dynamical nature of their collisions with 

 the atoms, so that the results deduced from it are probably 

 possessed of very great generality. 



The University, Sheffield, 

 December 7th, 1914. 



VIII. The Electric Strength of Solid Dielectrics. By W. M. 

 Thornton, D.Sc, D.Eng., Professor of Electrical Engi- 

 neering in Armstrong College, JYewcastle-ujJon-Tyne* . 



1. The icork of Electrical Breakdown is independent 

 of the thickness of the specimen. 



THE electric polarization of insulators has in general two 

 terms, an externally forced displacement and a sub- 

 sequent slower movement caused by interaction between 

 polarized elements f- Electric breakdown occurs when the 

 total displacement and energy stored exceed a certain limit, 

 •different for each material. 



In all cases of polarization in undirectional fields or at low 

 frequencies, less than 10,000 a second for example, inter- 

 attraction might be expected to have influence on the break- 

 down strength, for it will be shown that this force when it 

 occurs is in general greater than that of the applied field in 

 magnitude. 



* Communicated by the Author. 



t " The Polarization of Dielectrics in a Steady Field of Force," Proc. 

 Phys. Soc. Lond. vol. xxii. ; also Phil. Mag., March 1910. 



