80 Dr. C. V. Burton on a 



observable effects, some nice points o£ dynamics would seem 

 to be involved *. 



15. The primary effects of the hypothetical compressional 

 waves having been for the moment disposed of, the secondary 

 or gravitational effects may be considered. Every portion 

 of atomic matter, in so far as its presence implies altered com- 

 pressibility of* the setherial plenum (H^O), behaves as a centre 

 of pulsatory motion, or as an aggregation of such centres. 

 Thus the motion of the aether, to a second approximation, 

 is to be found by superposing on the wave-motion proper 

 a pulsatory motion due to a distribution of alternating source- 

 sink centres, to which should be added (except, as will 

 appear, when F = 0) a distribution of source-sink doublets 

 arising from the motion of atomic matter through the aether. 

 It will be assumed that the whole region of space under 

 consideration is so circumscribed that its greatest dimension 

 is very small compared with the shortest effective wave- 

 length of the compressional disturbance, so that, at any given 

 instant, the primary pressure-variation is sensibly in the 

 same phase throughout, while, to the same order of approxi- 

 mation, the source-sink centres just referred to may be 

 treated as if they existed in an incompressible medium. In 

 accordance with the assumptions explained in §§ 1, 11 above,, 

 the variations of normal (hydrostatic) pressure are taken to 

 outweigh in importance all other stresses evoked by varying 

 compression of the medium, and the whole motion to be 

 investigated is accordingly irrotational. 



16. Let a be the density of atomic matter at any point 

 (x, y, z) ; then the total compressibility of matter-encum- 

 bered aether contained in the volume-element dx dy dz exceeds 

 the total compressibility of a like volume of free aether by 



'B.adx dy dz, (8) 



in accordance with our definition of H (§ 8). Further, so 

 far as the primary disturbance is concerned, let the pressure 

 p be expressed by 



p=f+p;. ...... (9) 



the presence of atomic matter in the volume dx dy dz is thus 

 equivalent to a source of strength 



-K^adxdydz; (10) 



* Among the values which, in § 33 below, are tentatively assigned to 

 the various physical magnitudes involved, the variations of potential 

 energy of the sether are set down as so small in comparison with the 

 whole constitutive energy that the special difficulty above referred to 

 seems to be evaded. 



