170 L. Page — Relativity and tJie Ether. 



he particle considered : 



where V is the velocity of the particle considered ; and 



(-W (-Qvr--* 



and a similar expression for/*/ (3) 



(-?r ('-?*)* 



where f is the acceleration of the particle considered. 



To be in accordance with the Principle of Relativity, the 

 ether must have one of two possible characteristics : either (a) 

 it must be absolutely homogeneous, or (b) all non-homogenei- 

 ties must be moving in straight lines with the velocity of light. 

 For, since it would be impossible, ideally as well as actually, 

 to locate the same point in a homogeneous continuum at two 

 successive instants, it would be impossible to measure the 

 velocity of any material object relative to such a continuum. 

 Hence the existence of a perfectly homogeneous ether would 

 be in complete accord with the Principle of Relativity. 



To explain interactions between material particles, however, 

 it is necessary to assume the existence of non-homogeneities in 

 the ether. So we must make use of the second characteristic 

 which we may ascribe to the ether without contradicting the 

 Principle of Relativity: — the property of transmitting all non- 

 homogeneities in straight lines with the velocity of light. 

 Since this velocity is an invariant of the Lorentz-Einstein 

 transformation, the existence of non-homogeneities travelling 

 through the ether with the velocity of light would not provide 

 a means of measuring the velocity of a material particle rela- 

 tive to the ether. Consequently the Principle of Relativity 

 would be in no way violated by the assumption of the exist- 

 ence of such an ether. 



The character of these non-homogeneities, which, for brev- 

 ity, we may call strains,* will determine the state of the ether 

 at every point and instant. We will suppose that this strain 

 can be completely represented by a single- valued vector function 

 of position in space, E. This vector E must have the following 

 properties : (a) at any point the product of the volume element 

 dr and the divergence of E must be proportional to the charge 

 present in dr ; (b) the charge must be an invariant for the 



*The word " strain " is used in a perfectly general sense, and is not in- 

 tended to imply any relative displacement of discrete particles. 



