96 Dr. L. Silberstein on General Relativity 



that shift or the decrease of vibration frequency is directly 

 embodied in the tensor component g u , the coefficient of 

 c 2 dt 2 , produced by the gravitating centre, viz., in a first 

 approximation, 



_ 1 2M 



Another consequence of the theory, the bending of light 

 rays by a gravitating mass (represented by the above in 

 conjunction with other tensor components) still awaits its 

 verification. Hitherto there is not the slightest evidence 

 for the reality of such a phenomenon. It constitutes one of 

 the chief points of the programme for the 1919 Solar Eclipse 

 Expedition which seems particularly favourable for the pro- 

 posed observations, as was pointed out by Sir Frank Dyson. 

 Thus far the only positive and, one must confess, very 

 conspicuous and fascinating success of Einstein's theory 

 is the formula it gives without difficulty for the perihelion 

 motion, amounting for instance in the case of Mercury to 

 43" per century, the famous excess which has occupied the 

 attention of astronomers since the times of Le Verrier. But 

 it so happens that this remarkable result relating to the 

 secular motion of the perihelion is most vitally conditioned 

 by the same tensor component, g u *, which — to everybody's 

 true regret — has thus discredited itself at the Mount Wilson 

 Observatory. 



Such being the state of things, one is justified, if not in 

 condemning the equivalence hypothesis, at least in doubting 

 its validity and in not attributing to it anything like the im- 

 portance one cannot help ascribing to the general principle of 

 relativity. Whence the natural desire of the writer to draw 

 a sharp line between the two utterly heterogeneous elements 

 and, rejecting the former, to investigate some general physical 

 problems from the point of view of the latter alone. It may 

 be well to notice that the importance and utility of the 

 requirement of general covariance has been felt, and ex- 

 pressed with much force, by the mathematicians many years 

 ago and in a much wider field, viz. that of "the geometry" 

 of manifolds of any number of dimensions as represented 

 by quadratic differential forms, — of which the physicist's 

 " world " or space-time is but a particular example. Is not 



* The perihelion motion, as a delicate feature of planetary motion, is, 

 of course, given by // u in co-operation with the remaining coefficients. 

 To drop the variable part of g i4: itself, after the others have been 

 neglected, would make it impossible to get even the ordinary Keplerian 

 planetary motion. In short, the second term of gu is the chief term 

 involved in that motion. 



