$6 Mr. Megh Nad Saha on the 



exterior to the electron, the first three terms involving 



(-7-;, -p, -j~\ can be reduced to a surface-integral. The 



bounding surface is taken to be at an infinite distance, 

 thereby the surface integrals are made to vanish. The 

 total force on the aether thus comes out in the form 



dM_l BM 



dl ~ Ic ~dt ' 



Now assuming that the force exerted by the aether on the 

 electron is equal and opposite to the force exerted by 

 the electron on the aether, the reaction of aether on the 



electron becomes equivalent to — j- ^— . In analogy with 



(iM\ 

 — ) a momentum. 



This is, in brief, the theory of Electromagnetic momentum 

 as developed by Abraham, Lorentz *, and others. We do 

 not enter into a discussion of the rival theories of Lorentz 

 and Abraham on the shape of the electron during motion. 

 The Electromagnetic mass is obtained from either of the 



relations m t = — , and mi = i-^r- , m t and im denoting 

 cv cqv 



respectively the transverse and longitudinal masses of the 

 electron. 



But several objections can be raised to this theory of 

 Electromagnetic momentum. In the first place, the in- 

 tegration is extended over the space of the observer, 

 whereas the Principle of Relativity requires that it should 

 be extended over the space perpendicular to the axis of 

 motion of the electron, and external to the volume occupied 

 by the electron. This is what I have done in the foregoing, 

 and I believe that this is quite in keeping with Minkowski's 

 ideas of equivalence of time and space. Secondly, the volume 

 of integration is supposed to be bounded by a sphere at an 

 infinite distance only, and no notice is taken of the internal 

 boundary which must coincide with the surface of the elec- 

 tron. In fact, it looks as if the surface-integrals had to go, 

 because the authors wanted to get rid of them. 



In the theory proposed by me, I have refrained from 

 putting any interpretation on the quantities (X^, X^ ...). 



* Lorentz, ' Theory of Electrons/ chap. 1, § 26 et seq. 



