585-587] Electromagnetic Mass 511 



magnetic, has in it nothing which is impossible or improbable. This 

 hypothesis is one which can be directly tested by experiment, so that we 

 pass at once to a discussion of the experimental evidence bearing on this 

 question. 



587. In our argument so far, we have considered the motion of a 

 charged body only when the velocity of motion is insignificant in comparison 

 with the velocity of light. The theory of the motion of charges moving 

 with a velocity comparable with that of light is beyond the scope of the 

 present book. From this theory, however, it appears, as might be expected, 

 that the kinetic energy of the displacement-currents set up by an electron 

 moving with a velocity v comparable with that of light ((7), is not simply 

 proportional to v 2 , but is a more or less complicated function of v and of v/C. 

 The exact form of this function cannot be determined: it depends upon the 

 hypotheses which are made as to the distribution of charge on the electron 

 and the behaviour of the electron when in rapid motion. 



Different hypotheses have been put forward by Bucherer, Lorentz, Einstein, 

 and Abraham, and the different hypotheses give rise to different formulae for 

 the kinetic energy of the motion. But on no hypothesis will this kinetic 

 energy be exactly proportional to v 2 except when v is small compared with G. 



In the motion of the cathode particles we have electrons moving with 

 velocities comparable with that of light. It is possible to determine experi- 

 mentally the momentum of these particles, and hence their energy, in terms 

 of their velocities. It is found that for velocities comparable with that of 

 light, the energy of motion is not proportional to v*. 



Now if we had an exact knowledge of the structure and behaviour of the 

 electron, we ought to find that the energy of motion could be treated as the 

 sum of two parts, a part J mv 2 representing the energy of motion of the mass 

 (if any), and a part, not proportional to v 2 , representing the energy of the dis- 

 placement-currents. By comparing the theoretically calculated values of the 

 energy with those observed, it would be possible to ascertain the value (if 

 any) of the quantity m, the material part of the electron. 



In point of fact none of the hypotheses which have so far been pub for- 

 ward are found to account in a perfectly satisfactory way for the observed 

 values of the energy. But two hypotheses, namely those of Bucherer and 

 Abraham, account for these values to within a very small error. If we ignore 

 this error, and examine what value has to be assigned to m, to get the best 

 agreement, we find that this value has to be very small, if not actually zero. 

 It is therefore probable that if the true hypothesis as to the structure of the 

 electron was known, it would lead to a value of m which would be absolutely 

 zero. We should find that the whole energy of motion arose from the dis- 

 placement-currents in the ether. But at present, until the true hypothesis 

 is found, this must be regarded only as conjecture. 



