Modified Theory of Gravitation. 75- 



tending to accelerate the motion of the electron simply 

 follows the gradient of diminishing pressure and is pro- 

 portional thereto. It further appears that the assumption 

 referred to might enable the elementary requirements of the 

 gravitation problem to be satisfied with the contribution of 

 only a very minute non-electromagnetic term to the total 

 effective inertia of an electron (Appendix D). 



7. Let F be a physical magnitude characteristic of all 

 electrically neutral (atomic) matter, and defined as follows : 

 if m is the mass of atomic matter included in any given 

 region, then Fmp is the defect of mass of setherial substance 

 contained within that region, as compared with the mass 

 included in an equal region tilled with free aether ; the 

 density of the aether being denoted by p. (As we shall 

 suppose the average density of retherial substance to be but 

 little different in a vacuum and in the densest atomic matter, 

 no more precise definition of p is needed in this connexion.) 

 Otherwise thus : if, within a region bounded by a fixed, ideal 

 surface and originally free from atomic matter, a mass m of 

 matter could be created, a volume F?rc of aether would flow 

 outward across the bounding surface. F may be called the 

 extrusion of aether per unit mass of matter. 



8. Consider further the application of a small additional 

 normal pressure hp to a surface bounding some definite 

 portion of the retherial medium, which is modified by the 

 presence of a mass m of atomic matter. A reduction of 

 volume will result, and we shall define another constant II 

 by the statement that the reduction of volume is greater by 

 Hr/i8/> than if the original volume had been wholly occupied 

 by free aether. Thus evidently 



n=-dY;j P (i) 



9. Let a particle of atomic matter be present where from 

 any cause there is a pressure-gradient in the aether. AVhen 

 the particle is displaced from one point to a second neigh- 

 bouring point, there is a flow of sether inward at the first 

 point, and a flow outward at the second point. If the 

 setherial normal pressure is greater at the first point than at 

 the second, work on the whole will be done by the pressure 

 during the displacement. 



Consider a particle m of matter at a point (#, y, z) where 

 the pressure is p, and let the particle be displaced to 

 {x + ox, y, z) where the pressure is p + 'dpj'b^' . hx. Also let 

 the particle be acted upon by such ideal forcive as may be 

 necessary to ensure that the displacement takes place very 

 slowly. There is work done by the pressure p at (#, y, z) 



