Modified Theory of Gravitation. 93 



accordance with (35) ; the supposition being that K is small 

 enough for a null result to be obtained in the test suggested 

 in § 24, but not with any great margin to spare. It might 

 be that the test referred to would give a positive result, and 

 in any case a much more sensitive disposition could easily be 

 devised. But since no such positive result has yet been re- 

 corded, we cannot on this score assign any lower limit to the 

 value of K, nor is our choice of something near the highest 

 of seemingly admissible values made necessary by the quan- 

 tities given in the table. The experimental determination of 

 the motional constant K, or of an upper limit to its value, 

 would be interesting quite apart from its bearing on this 

 theory ; the question involved being, essentially, whether or 

 not the total of setherial substance comprised in any given 

 volume is modified by the presence of atomic matter within 

 that volume. 



35. The values assumed for p and E (the density and the 

 constitutive energy per unit volume of the aether) are those 

 lately suggested by Sir 0. Lodge *, who has given very 

 convincingly his reasons for supposing that, in order of 

 magnitude, the true values may not be very different from 

 these estimates. Incidentally it may be remarked that 

 Lodge's estimate of the constitutive energy per unit volume 

 of the oether is about 6 times the electrostatic energy per 

 unit volume, close to the surface of a negative electron, cal- 

 culated on the usual assumptions that practically the whole 

 inertia of the electron is electromagnetic, and that the 

 ordinary linear relations of the electromagnetic field hold 

 good right up to the surface of the electron. 



36. For the wave-length of the primary disturbance, we 

 must assume a value so great that, even at distances of at 

 least several astronomical units, the inverse square law of 

 gravitational attraction is sensibly accurate. By putting 

 X=10 4 astronomical units, this condition seemed to be amply 

 fulfilled, since for distances small compared with X, the 

 deviations from the inverse-square law would be only of the 

 second order (§ 19). The chief consideration against assign- 

 ing a very much greater value to X is that J must be kept 

 small to preserve linearity of relations, and also, I imagine, 

 for general plausibility. 



37. The same consideration (keeping f small) leads us to 

 assign a fairly high value to fju (defined in § 28). It is diffi- 

 cult to see what sort of value fi should be expected to have : 

 whether the proportional increase of setherial compressi- 

 bility due to a space being " filled " with water instead of 



* Phil. Mag. vol. xiii., 1907 ; Nature, lxxv. p. 519, 1907. 



