Electrolytic Theory of Dielectrics. 475 



For water and bisulphide of carbon . 1*8 x 10 -u , 

 For oxygen 1*2 x 10 -11 , 



numbers which are in satisfactory agreement with the ex- 

 pected result. It would be necessary to divide the M for 

 paired particles by 2, as it acts, as it were, on one side only 

 of each particle ; but the increased nearness of the particles 

 due to pairing probably increases M sufficiently to render this 

 unnecessary. 



Even in solids there must be some difference between the 

 electrical and mechanical elasticities. Pairing must have 

 taken place to a certain extent, or there would be no pyro- or 

 piezo-electricity. If, however, we may take the values of q 

 obtained from these two phenomena as an indication of the 

 amount of pairing actually achieved at ordinary temperatures 

 in unstrained solids, that amount is probably about a tenth of 

 what it might be, and may therefore be neglected for the 

 present purpose. 



It only remains now to consider the question of dielectric 

 strength. 



Divide the tenacity (T) of a substance, in any direction, by 

 the number of molecules in each sq. cm. of a plane at right 

 angles to that direction. The result is the greatest stress 

 which a single molecule can bear without being torn from its 

 neighbours. Hence, if M represent the mean value of Young's 

 Modulus up to this point, and A the corresponding displace- 

 ment of the molecule, we have, by (1) : — 



2M A = T 



n ' d n 



If now force be applied to each molecule by an electro- 

 static field, the disruptive discharge should occur at the point 

 where the molecules are subjected to this maximum possible 

 stress. In other words, by what has been said above, the 

 density of the fictive layer at the point of discharge will be 

 given by the equation 



qn A _ 



T ' d ~^x. 



Nowp=— - — . -T— , where -y- represents the slope of poten- 

 tial in the direction of the applied field (the surfaces at which 



