A.— MATHEMATICAL AND PHYSICAL SCIENCES. 17 



affected by the presence of gravitating bodies. Assuming that matter is 

 electrical in its nature, it is inferred that matter will be attracted to places 

 of greater dielectric constant. It seems possible that something of this 

 sort was what FitzGerald had in mind. 



Let us now consider some of the consequences of Einstein's theory. 

 One of the first of them is that when a planet moves round a central 

 attracting body in a nearly circular orbit, the perihelion of the orbit 

 advances by (approximately) 6nv 2 / c i in each revolution, where v is the 

 planet's velocity and c is the velocity of light. This gives for the motion 

 of the perihelion of Mercury almost exactly the amount (42" per century) 

 which is found from observation. Another consequence is that light-rays 

 which pass near a massive body are deflected, the bending at the sun's 

 limb being l"-75. This was confirmed observationally by the British 

 expeditions to the eclipse of May 1919, and still more decisively by the 

 Lick Observatory expedition to the Australian eclipse of September 1922 : 

 the Lick observers found for the shift l"-72±0"-ll, which differs from 

 Einstein's predicted value by much less than its estimated probable 

 error. Yet another result of general relativity is that, by the Principle 

 of Equivalence, light which reaches us from a place of different gravita- 

 tional potential (such as the sun) must exhibit a kind of Doppler effect. 

 This ' gravitational shift of the solar spectral lines ' is now generally 

 admitted to be confirmed by comparisons of wave-lengths at the centre of 

 the sun's disc with wave-lengths from the arc in vacuo ; and in 1925 the 

 effect was observed, on a much larger scale, by W. S. Adams in the 

 spectrum of the companion of Sirius. 



Besides the effects which have been verified observationally there are 

 many consequences of Einstein's theory which are of interest as opening 

 up new fields or presenting new inter-relations of phenomena in astronomy 

 and physics. For instance, there is a contribution to the precession of 

 the equinoxes which, unlike ordinary precession, does not depend on the 

 oblateness of the earth. Again, the bending of the rays of light near a 

 gravitating body, which has been observed in the case of the sun and the 

 companion of Sirius, may, theoretically at any rate, be so pronounced 

 that the ray is permanently captured by the attracting body, and describes 

 for ever a track round and round it, which approaches spirally and 

 asymptotically to a circle whose centre is at the centre of gravitation. 

 Yet another deduction is that an electrified body, or a single electron, 

 which is at rest in a varying gravitational field, must emit radiation. 

 Indeed, now that a definite connection has been set up between electricity 

 and gravitation, the whole of electromagnetic theory must be rewritten. 



As a further illustration of the (as yet) unexplored possibilities of the 

 new physics, let us consider the well-known equations for the potential 

 of Newtonian gravitation, namely Laplace's equation 



8*y , s 2 v , s^v = 



in space where there, is no matter, and Poisson's equation 



8 2 V S 2 V S 2 V = _ 4 

 8z 2 + S^ 2 + 8z 2 " " np 



1927 C 



