16 SCIENCE PROGRESS 



displacement of the order required by the relativity principle. 

 One feels reluctant to abandon Einstein's theory after its 

 success in explaining the discordance in the motion of the 

 perihelion of Mercury and yet it does not seem possible to doubt 

 the accuracy of the Mount Wilson measures. It is greatly 

 to be hoped that their result will be checked by Mr. Evershed 

 at the Kodaikanal Observatory. Meanwhile, it is to be re- 

 gretted that the present indications are that the splendid 

 opportunity provided by next year's total solar eclipse of 

 testing the third prediction of the theory will not be utilised. 

 If St. John's result is confirmed, Einstein's theory will probably 

 be one more to add to the long list of exploded gravitational 

 theories. 



W. de Sitter in the M.N., R.A.S., 78, 3, 191 7, has a third 

 paper dealing with the astronomical consequences of Einstein's 

 theory. In that theory, as originally advanced, there was a 

 difficulty in connection with the boundary conditions at infinity. 

 To overcome this the notion of a " curved " space was intro- 

 duced ; in this paper the consequences of that conception are 

 worked out. The ideas are very metaphysical and one cannot 

 but feel in reading the paper that physical conceptions have 

 been rather lost sight of, and that there is an artificiality in 

 the new extension. The matter has been more simply and 

 more generally treated by L. Silberstein in a paper on " Plane- 

 tary motion in space-time of any constant curvature accord- 

 ing to the generalised principle of relativity," which was read 

 before the Royal Astronomical Society at its March meeting. 

 (This paper has not appeared in print at the time of writing 

 these notes, but a summary appeared in The Observatory , 41, 

 162, 191 8.) In this paper, instead of treating of a space-time 

 with a preconceived curvature, the sign and amount of the 

 curvature is left entirely free and the equations of planetary 

 motion are developed in a purely relativistic manner. It is 

 shown that there are no reasons a priori for discarding a 

 Euclidean or hyperbolic world in favour of a spherical or an 

 elliptic one, and that the "world-curvature," if such exists, is 

 determinate. A method by which the order of magnitude of 

 this curvature can be assigned when the excess of Mercury's 

 perihelion motion is accurately known is indicated. 



A useful account in plain language of the nature of the 

 principle of relativity and of the meaning of gravitation on 



