Page:Eddington A. Space Time and Gravitation. 1920.djvu/140

124 is perhaps more important, we need a planet with a sharp elliptical orbit, so that it is easy to observe how its apses move round. Both these conditions are fulfilled in the case of Mercury. It is the fastest of the planets, and the predicted advance of the orbit amounts to 43″ per century; further the eccentricity of its orbit is far greater than that of any of the other seven planets.

Now an unexplained advance of the orbit of Mercury had long been known. It had occupied the attention of Le Verrier, who, having successfully predicted the planet Neptune from the disturbances of Uranus, thought that the anomalous motion of Mercury might be due to an interior planet, which was called Vulcan in anticipation. But, though thoroughly sought for, Vulcan has never turned up. Shortly before Einstein arrived at his law of gravitation, the accepted figures were as follows. The actual observed advance of the orbit was 574″ per century; the calculated perturbations produced by all the known planets amounted to 532″ per century. The excess of 42″ per century remained to be explained. Although the amount could scarcely be relied on to a second of arc, it was at least thirty times as great as the probable accidental error.

The big discrepancy from the Newtonian gravitational theory is thus in agreement with Einstein's prediction of an advance of 43″ per century.

The derivation of this prediction from Einstein's law can only be followed by mathematical analysis; but it may be remarked that any slight deviation from the inverse square law is likely to cause an advance or recession of the apse of the orbit. That a particle, if it does not move in a circle, should oscillate between two extreme distances is natural enough; it could scarcely do anything else unless it had sufficient speed to break away altogether. But the interval between the two extremes will not in general be half a revolution. It is only under the exact adjustment of the inverse square law that this happens, so that the orbit closes up and the next revolution starts at the same point. I do not think that any "simple explanation" of this property of the inverse-square law has been given; and it seems fair to remind those, who complain of the difficulty of understanding Einstein's prediction of the advance of the perihelion,