130 



Prof. W. M. Thornton on the 



4. The cause of this Law. 



In the failure of hard steel under mechanical tension 

 there is very small permanent strain, and the material breaks 

 with extreme suddenness. There is a definite intensity of 

 stress at which it fails, independent of the length of the 

 specimen, unless this is short. The work done on unit volume 

 is here the same for all lengths. The electrical case differs 

 from this in that though the displacement is also proportional 

 to the intensity of the stress, the latter depends not on area 

 but on length between the end plates. The effect of this is 

 that in the latter (also simple elastic) case it is the total work 

 done in breakdown that is independent of the thickness. 

 The work done on unit volume is proportional to the square 

 of the intensity of the field in it, which, as experiment shows, 

 is not the same at all thicknesses of breakdown. That the 

 same relation should be found to hold with equal accuracy 

 in absorbing media is somewhat remarkable, and it is 

 necessary to consider the nature of the internal forces. A 

 non-crystalline medium may be assumed to have a space- 

 lattice of equilateral triangles. Around a line of centres 

 forming a chain through it, other centres are grouped in 

 pentagonal rings alternately upright and inverted. In the 

 rings beyond this there are 10 centres and so on. Consider 

 these as a system of elements polarized under the influence 

 of an applied field. 



Fiar. 1. 



+ ~f 



>fc 



F 



\r / 



\ / 



A^Z_d___. 



¥■ 



?F^ 





^ 



+ -f- 



+ v Ja'- 



-i 



<i / 







A 



& 



The total forces on any one are : — 



(1) Repulsions of similar charges which are in equilibrium 



everywhere, and do not affect the displacement. 



(2) Attractions of the next in line on one side of the 



centre, causing an increase of displacement. 



(3) Attractions on the other side giving a restoring force. 



(4) Similar forces inclined to the line of the field from 



the surrounding rings. 



