14 ELECTRIC INERTIA [CH. n. 



electrical inertia is proportional to the electrostatic 

 energy of the charge : that is to say, it is pro- 

 portional to the charge and its potential conjointly. 

 Call the charge e, and the radius of the sphere a, 

 the potential will be e/Ka (K being Faraday's 

 dialectric constant) ; and the appropriate inertia is 



where v is the velocity of light. (See Note at end 

 of chap, i.) 



Another way of putting it is to say that if a 

 real mass of this amount were moving with the 

 speed of light, its kinetic energy would be half as 

 great again as the potential energy of the electric 

 charge thus reckoned as mechanically equivalent 

 to it; 



for ~mv 2 = -e . = charge x potential 



4 2 KCI 2 



= potential energy. 



Now any appreciable quantity of matter, even a 

 milligramme, moving with the speed of light, must 

 have a prodigious amount of energy ; for, on the 

 ordinary assumption that mass is quite constant, 

 the energy of one milligramme rushing along with 

 the light-speed would amount to no less than 

 fifteen million foot-tons. Or as Sir William Crookes 

 has expressed it : a gramme, or fifteen grains, of 

 matter, moving with the speed of light, would have 

 energy enough to lift the British Navy to the top 

 of Ben Nevis. 



Consequently the inertia of any ordinary quantity 

 of electric charge must be exceedingly minute. 

 Notwithstanding this, it is quite doubtful whether 



