1918] on Gravitation and the Principle of Relativity 225 



effect can be detected. Mercury moves at 30 miles a second ; Venus 

 at 22 ; the Earth at 18J. But there is a difficulty about Venus and 

 the Earth. Their orbits are nearly circular, and you cannot tell in 

 which direction a circle is pointing. Mercury combines the favour- 

 able conditions of a high speed and a satisfactorily elongated orbit 

 ^\hose direction at any time can be measured with considerable 

 precision. It is found by observation that the orbit of Mercury is 

 advancing at the rate of 574 seconds of arc a century. This is in 

 great measure due to the attraction of the other planets, which are 

 pulling the orbit out of shape and changing its position. The 

 amount of this influence can be calculated very accurately, and 

 amounts to 532 seconds per century. There is thus a difference of 

 42 seconds a century unaccounted for ; and this has for long been 

 known as one of the most celebrated discordances between observa- 

 tion and gravitational theory in astronomy. It is thirty times 

 greater than the probable error which we should expect from 

 uncertainties in the observations and theory. There are other 

 puzzling discordances, especially in connection with the motion of 

 the moon ; but the conditions in that case are more complicated, 

 and I scarcely think they offer so direct a challenge to gravitational 

 theory. Now Einstein's theory predicts that there will be a rotation 

 of the orbit of Mercury additional to that produced by the action of 

 the planets ; and it predicts the exact amount — namely, that in one 

 revolution of the planet the orbit will advance by a fraction of a 

 revolution equal to three times the square of the ratio of the velocity 

 of the planet to the velocity of light. We can work that out, and 

 we find that the advance should be 43 seconds a century — just 

 about the amount required. Thus whilst the Newtonian law leaves 

 a discordance of over 40 seconds, Einstein's law agrees with observa- 

 tion to within a second or so. 



Of course this superiority would be discounted if we could fiud 

 some other application where the old Newtonian law liad proved the 

 better. But that has not happened. In all other cases the two laws 

 agree so nearly that it has not been possible to discriminate between 

 them by observation. The new law corrects the old where the old 

 failed, and refrains from spoiling any agreement that already exists. 

 The next best chance of applying the new theory is in the advance of 

 the orbit of Mars ; here Einstein's new law "gilds refined gold " by 

 slightly improving an agreement which was already sufficiently good 

 — a " wasteful and ridiculous excess " which is at any rate not un- 

 favourable to the new theory. 



There is another possibility of testing Einstein's theory, which it 

 is hoped to carry out at the first opportunity. This relates to the 

 action of gravitation on a ray of light. It is now known that electro- 

 magnetic energy possesses the property of inertia or mass, and probably 

 the whole of the mass of ordinary matter is due to the electromagnetic 

 energy which it contains. Light is a form of electromagnetic energy, 



