Modified Theory of Gravitation. Ill 



71. Now the mass of aether " extruded " by the electron 

 is 4?rpCRi 3 an( i the expression (97) bears to this the ratio 

 % C, which may be very small provided C is small enough. 

 Moreover, in the table given above, the mass of aether 

 " extruded " by one gram of neutral matter is estimated at 

 2*9 X 10~ 4 gram; and it therefore seems possible that the 

 theory proposed may involve only a very minute non-electro- 

 magnetic term in the total inertia of a body. 



72. Alternatively let the aether be regarded (for present 

 purposes of illustration) as made up of thin coreless vortex- 

 filaments pervading a frictionless liquid * of density p ; the 

 sum total of the vacuous cores comprised in any considerable 

 volume of aether being so small a proportion of that volume 

 that p may sensibly be identified with the average density 

 of the aether. Let us further suppose, as in § 70, that the 

 constitution of an electron involves setherial displacements 

 expressible by {96), and that such differences of density as 

 exist from one volume-element of aether to another are due 

 solely to altered diameter of the vacuous cores, no alteration 

 in the total length of cores per unit volume being involved. 

 It then appears that what we have called the gravitational 

 part of the inertia of an electron, in addition to the quantity 

 (97) contains a term 



§ p x volume of electron x average value of j volume of vacua 

 per unit volume of aether x (-70°) l°g ~ j ; • (98) 



where r + 8r is the radius of a vacuous core at a distance R 

 from the centre of the electron, and r x is a length corre- 

 sponding in order of magnitude with the scale of structure of 

 the aether. In (98) " volume of electron " must be under- 

 stood as extending to all that region wherein dSrJdJi differs 

 sensibly from zero. The addition of the term (98) does not 

 disturb the conclusion that the gravitational part of the 

 inertia of an electron may be very small compared with the 

 mass of aether which the electron " extrudes." 



Appendix D. 

 ^L Kinetic Model of a Slightly Compressible Medium. 



73. The representation of the electromagnetic properties 

 even of free aether by means of a turbulently moving liquid 

 is beset by difficulties which may well prove to be insuper- 

 able ; but it is nevertheless interesting to remark that [a 

 * Of, Appendix D. 



