510 Displacement Currents [OH. xvn 



Let the charged body be supposed to be of mass m and to move with a 

 velocity v which is small compared with C, the velocity of light. The kinetic 

 energy of the motion of the mass is ^mv*. In addition to this, there is the 

 energy, which we have seen must be treated as kinetic, of the displacement- 

 currents in the ether. Since the current at any point is proportional to v, 

 the total energy of the whole system of currents will be proportional to v 2 , 

 say J Mv*, where M depends on the amount and distribution of the charge. 



The total kinetic energy of the moving system is now seen to be 



An analogy from hydrodynamics will illustrate the result at which we have arrived. 

 Suppose we have a balloon of mass m moving in air with a velocity v and displacing a 

 mass m' of air. If the velocity v is small compared with the velocity of propagation of 

 waves in air, the motion of the balloon will set up currents in the air surrounding it, such 

 that the velocity of these currents will be proportional to v at every point. The whole 

 kinetic energy of the motion will accordingly be 



the term \m& being contributed by the motion of the matter of the balloon itself, and the 

 term \ Mv 2 , by the air-currents outside the balloon. The value of M is comparable with m', 

 the mass of air displaced for instance if the balloon is spherical, the value of M is known 

 to be \vri (cf. Lamb, Hydrodynamics, 91). 



586. Remembering that the whole motion of a system can be determined 

 from a knowledge of its energy alone, we see that the charged body we have 

 considered will move (so long as its velocity is small compared with that of 

 light), as though it were an uncharged body of mass m + M. . Thus there is 

 an apparent increase of mass produced by the charge on the body. 



A numerical calculation will shew that even the most intense charge which 

 can be placed on a body by laboratory methods will result only in a quite 

 inappreciable apparent increase in mass. The case stands differently when 

 we consider the permanent charge of the electron. We have no accurate 

 knowledge of the size of the electron, but it can be shewn that if this is com- 

 parable with 10~ 13 cms., then the apparent increase in the mass of the electron 

 is comparable with the total mass. The smaller the electron is that is to 

 say, the more concentrated its charge is the greater is the proportion of its 

 apparent mass which must be attributed to its electrification. As we review 

 in imagination the different possible sizes of electrons, we must at last come to 

 electrons so small that the whole of their apparent mass arises solely from 

 their electrification. The kinetic energy of such an electron in motion will 

 consist entirely of the electromagnetic energy of displacement-currents set up 

 by the motion of the electric charge associated with the electron. 



Since it is conceivable, and even probable, that all matter is composed of 

 electrons, we see that the hypothesis that all kinetic energy is electro- 



