244 Prof. W. M." Thornton on the Cause of Loweret 

 The field at which this occurs is 



b 2 



Fi = 



4c(l-e- a 



(5) 



and if time is given for infcerattraction to be complete 



When the applied field is alternating let F = F sinp£ ;. 

 then 



b 2 



^ sill ^ = 4c (l- 6 - tt ^ .... (6> 



where pt x is the phase at which failure occurs. Since 

 p — 27r/T, where T is the period, and a is always much 

 less than T, take t 1 = q/u, q being a small fraction. Then 



*.i* 



n(f)' + -}= 



V 



4c(l-€-«). 



"When — is small, 



I> 



b">* 



icq(l 



') 



(7> 



(8> 



This is constant, so that if breakdown occurs, as it always 

 does, in an early stage of the maximum possible polarization 

 (that is, the maximum which would be reached in a steady 

 field if the structure did not breakdown), ¥ p is constant, 

 and the breakdown voltage is inversely proportional to the 

 frequency. 



3. Polarization at a voltage well below that of breakdown 

 takes many hours to reach its final value of equilibrium in 

 the field, and this value is independent of the external field *. 

 The influence of time of application of the field on break- 

 down strength is very largely controlled by the rate at which 

 interattraction is established. 



A full experimental examination of the influence of time 

 of application on breakdown voltage has been made recently 

 by Mr. F. W. Peek, Jr. f. He has arrived at the empirical 

 formula i 



F^A + BT 4 , 



where Fi is the breakdown gradient and T the time of its 



* Phil. Mag. he. cit. 1910, p. 398. 

 t Loc. cit. p. 178. 



