224 Professor A. S. Eddington [Feb. 1, 



ence, and for bodies moving with velocities much greater than those 

 of the planets, the difference would be considerable. 



This idea of the distortion of space as the modus operandi of 

 gravitation has led to a practical result — a new law of gra\'itation. 

 It is not brought in as a hypothetical explanation of gravitation ; if 

 Einstein's theory is true, it is simply of the nature of an experimental 

 fact. 



If we draw a circle on a sheet of paper and measure the ratio of 

 the circumference to the diameter, the result gives, if the experiment 

 is performed accurately enough, the well-known number -, which 

 has been calculated to 707 places of decimals. Now place a heavy 

 particle at or near the centre and repea,t the experiment ; the ratio 

 will be not exactly equal to tt, but a little more. The experiment has 

 not been performed, and is not likely to be performed, because the 

 difference to be looked for is so small ; but, if Einstein's theory is 

 correct, that must be the result. The space around the heavy particle 

 does not obey ordinary geometry ; it is non-Euclidean. The change 

 in its properties is not metaphysical, but something which with sufft- 

 cient care could be measured. You can keep to Euclidean space 

 if you like, and say that the measuring-rod has contracted or expanded 

 according as it is placed radially or transversely to the gravitational 

 force. That is all very well if the effect is small, but in a very 

 intense gravitational field it would lead to ridiculous results like those 

 we noticed in connection with the Michelson-Morley experiment — 

 everything expanding or contracting as it changed position, and no 

 one aware of any change going on. I think we have learnt our lesson 

 that it is better to be content with the space of experience, whether 

 it turns out to be Euclidean or not, and to leave to the mathematician 

 the transformation of the phenomena into a space with more ideal 

 properties. 



This consequence of the new law of gravitation, though theo- 

 retically observable, is not likely to be put to any practical test either 

 now or in the immediate future. But there are other consequences 

 which just come within the range of refined observation, and so give 

 an immediate practical importance to the new theory, which 

 has indeed scored one very striking success. If we could isolate 

 the sun and a single planet, then under the Newtonian law of 

 gravitation the planet would revolve in an ellipse, repeating the 

 same orbit indefinitely. Under the new law this is not quite true ; 

 the orbit is nearly an ellipse, but it does not exactly close up. and in 

 the next revolution the planet describes a ncAv ellipse in a slightly 

 advanced position. In other words, the elliptic orbit slowly turns 

 round in the same direction in which the planet is moving, so that 

 after the lapse of many centuries the orbit will point in a different 

 direction. The rate at which the orbit turns depends on the speed 

 of motion of the planet in its orbit, so we naturally turn to the 

 fastest moving planets, Mercury, Venus and the Earth, to see if the 



