Page:Eddington A. Space Time and Gravitation. 1920.djvu/141

VIII] that the real trouble is that they have not yet succeeded in making clear to the uninitiated this recondite result of the Newtonian theory. The slight modifications introduced by Einstein's law of gravitation upset this fine adjustment, so that the oscillation between the extremes occupies slightly more than a revolution. A simple example of this effect of a small deviation from the inverse-square law was actually given by Newton.

It had already been recognised that the change of mass with velocity may cause an advance of perihelion; but owing to the ambiguity of Newton's law of gravitation the discussion was unsatisfactory. It was, however, clear that the effect was too small to account for the motion of perihelion of Mercury, the prediction being $$\tfrac{1}{2}v^2/C^2$$, or at most $$v^2/C^2$$. Einstein's theory is the only one which gives the full amount $$3v^2/C^2$$.

It was suggested by Lodge that, this variation of mass with velocity might account for the whole motion of the orbit of Mercury, if account were taken of the sun's unknown absolute motion through the aether, combining sometimes additively and sometimes negatively with the orbital motion. In a discussion between him and the writer, it appeared that, if the absolute motion were sufficient to produce this effect on Mercury, it must give observable effects for Venus and the Earth; and these do not exist. Indeed from the close accordance of Venus and the Earth with observation, it is possible to conclude that, either the sun's motion through the aether is improbably small, or gravitation must conform to relativity, in the sense of the restricted principle (p. 20), and conceal the effects of the increase of mass with speed so far as an additive uniform motion is concerned.

Unfortunately it is not possible to obtain any further test of Einstein's law of gravitation from the remaining planets. We have to pass over Venus and the Earth, whose orbits are too nearly circular to show the advance of the apses observationally. Coming next to Mars with a moderately eccentric orbit, the speed is very much smaller, and the predicted advance is only 1″.3 per century. Now the accepted figures show an observed advance (additional to that produced by known causes) of 5″ per century, so that Einstein's correction improves the accordance of observation with theory; but, since the result for Mars