434 Wbolard — Generalised- Relativity and Gravitation. 



literature. One remarkable result is that these final 

 equations show that the gravitation field is created not 

 only by the matU r which is present, but also by the 

 stresses, momenta, and energy. 



Just as in Newtonian mechanics the field is determined 

 by one equation, viz., Poisson's 



V s V=-4wp (15) 



so in the new theory, the field is determined by a set of 

 ten equations. (July six of these are mutually independ- 

 ent, however, so that the g . :J and the field are not com- 

 pletely determined by them : for once all the //.. are known, 

 all the properties of the space as well as of the field are 

 known (since the g 9 determine both), i. e., the reference 

 system of coordinates is known ; the postulate of general 

 relativity requires that the reference frame be arbitrary, 

 so that these ten equations, describing as they do all the 

 phenomena of the system (since they depend upon the 

 matter, motions, electromagnetic fields, energy, etc., of 

 the system), must not also fix the reference system; four 

 additional conditions must be introduced before we can 

 derive the equations for any specific system of co- 

 ordinates. 



14. We shall now briefly consider the only three phe- 

 nomena indicated by the general relativity theory which 

 are of sufficient magnitude to render their observational 

 detection and verification a possibility at the present time. 



A fundamental assumption of the "older" relativity 

 was that the velocity of light in free space is constant. 

 In the general theory it is found that g 44 , which is approx- 

 imately the Newtonian potential, is, in a fairly homo- 

 geneous gravitation field, equal to the square of the 

 velocity of light in that system; i. e., the velocity of light 

 plays the role of a gravitation potential, and varies with 

 the gravitation-field; evidently, only in a homogeneous 

 gravitation field, or in the absence of gravitation, is the 

 velocity of light constant; only in these cases is the 

 "older" relativity valid, it becoming a special case under 

 the general theory. If the gravitation field is not homo- 

 geneous, i. e., if it varies in strength from point to point, 

 as actual fields do as the distance from the attracting 

 bodv varies, then a rav of light traversing free space is 

 continuallv changing its velocity; but if this happens, 

 the wave-fronts must also change 1heir direction. We 



