656 SCIENCE PROGRESS 



equations, together with the four which determine the system of coordinates, 

 fourteen in all. But the existence of an invariant such as ds will have the effect, 

 as Hilbert has pointed out. of reducing the number which are independent by four, 

 so that there remain ten equations to determine the tent's. Moreover, Silberstein 

 has shown {R.A.S. M.N. 77, p. 366) that the element of length, and hence the 

 values of the ^'s at the origin, remain invariant to infinity in the absence of a 

 gravitational field, so that there are no outstanding constants, or arbitrary functions, 

 for determination, and therefore the ^'s, and consequently the gravitational field 

 specified by them, are completely determined throughout the time-space. Einstein 

 appears, as Silberstein suggests, to have overlooked this, and has attempted to 

 evade the determination of boundary conditions by a modification of his theory in 

 which he assumes that our physical space is of constant positive curvature, and 

 therefore finite, involving some extremely bizarre results, as Silberstein expresses 

 it, besides further complicating his equations. 



The introduction of an electromagnetic field gives four more equations, with 

 four parameters to be determined, and the resultant field is completely determined 

 by them's and these parameters. 



We see that Einstein's representation of gravitation does not present it as a 

 force or offer any physical account of its origin, but as a condition modifying the 

 metrical properties even of the time-space forming the ultimate system of reference 

 for all physical phenomena, and consequently the metrical properties of our physical 

 space, which therefore ceases to be Euclidian and varies in curvature from point 

 to point and moment to moment. Gravitation would, therefore, on this theory > 

 influence all physical phenomena. For example, at the surface of the sun, where 

 gravitation has about twenty-seven times its value at the earth's surface, the path 

 of a light ray would be bent to a measurable extent, and the unit of time would be 

 increased by an amount which would cause a measurable displacement of solar 

 spectroscopic lines towards the red. 



The first favourable opportunity of observationally testing the former conclusion 

 will occur during the coming total solar eclipse of May 29, when it will be sought 

 for. The latter effect has been sought for in a long-continued series of observa- 

 tions by St. John at the Mount Wilson Observatory with an absolutely negative 

 result, confirmed by later observations by Evershed at the Kodaikanal Observatory. 



It would appear then that Einstein's equivalence -brinciple must be rejected as 

 untenable. 



Now, in 1898, Gerber (see the writer's Treatise on Electrical Theory, p. 597), 

 on the assumption that gravitational potential is something propagated from the 

 attracting to the attracted mass with a velocity, v, which is very great compared 

 with the relative velocity of the two masses, obtained an expression for the 

 anomaly in the motion of Mercury's perihelion in terms of v, which, when v is 

 made equal to c = 300,000 kilometres per sec, becomes identical with that of 

 Einstein, giving 43*1 sees, per century, the observed value of the anomaly being 

 42*9. Taking as the gravitational potential the velocity potential of the ether in 

 any form of the gravitation theory in which the electrons are regarded as sources 

 or sinks of ether flow {ibid. pp. 601 -1 6), the anomaly is, therefore, fully accounted 

 for. Gravitation, in this theory, is assumed to act only on the hydrodynamic mass 

 of the electron nucleus, the inertia of which, if my argument was correct, is 

 negligible relatively to the electromagnetic inertia. Under these conditions an 

 agreement, to the order required to account for the anomaly, of Einstein's formula 

 with Gerber's would be expected. 



It should be noted that Einstein's mathematical definition of simultaneity 



