110 Dr. C. V. Burton on a 



Appendix C. 

 A Non-Electromagnetic Term in the Inertia of an Electron. 



69. It will readily be realised that, just as an electron 

 possesses mass or inertia o£ electromagnetic origin, so on our 

 theory the total effective mass o£ the electron comprises what 

 may be called a gravitational term. The amotions which are, 

 on this view, to be classed as of gravitational type are wholly 

 o£ the nature of irrotational bodily movements of the volume- 

 elements of aether. What has here been called the primary 

 disturbance is assumed to consist of compressional waves, 

 while the secondary disturbance — the supposed cause of gravi- 

 tation-stakes the form of a pulsatory movement whereof 

 every particle of matter may be regarded as a centre. 

 Finally, the motion of matter with respect to the aether 

 appears in general to involve (over and above electromagnetic 

 phenomena) an irrotational distribution of aetherial motion. 

 This necessarily implies the addition of a corresponding term 

 to the inertia of the matter in question ; but as will now 

 appear this term may, on our assumptions, be relatively 

 insignificant. By way of illustration, expressions for the 

 gravitational inertia of an electron, obtained on two further 

 alternative assumptions, will now be given. 



70. In the first place, let us suppose that the free aether is 

 a strictly continuous medium, and that the constitution of an 

 electron involves a modification of aetherial density expressible 

 as a continuous function of coordinates. Let the modifi- 

 cation of density be such as corresponds with a radial dis- 

 placement £R (measured outwards) of any element distant R 

 from the centre of the electron. It is understood, of course, 

 that the unmodified state of the aether, expressed by SR = 0, 

 is one of uniform density. In particular, let * 



SR = CR from R = to R = Rj ) '». 



8R=CR! 3 /R 2 from R=Ri to R = oo J ; " ^ b) 



then it can be shown that the corresponding term in the 

 inertia of the electron is 



f TpCFBJ, (97) 



where p as before is the density of the aether. 



* This distribution of SR suffers from the disadvantage that motion of 

 the electron through the aether involves impulsive changes of velocity of 

 those aether elements for which, instantaneously, R=R 1# A slight 

 modification of (96) would remove the objection, but at a great sacrifice 

 of that analytical simplicity which must always be a leading consideration 

 in the choice of purely illustrative examples. 



