which lies nearest the sun.  Since the time of Leverrier, it has been known that the ellipse corresponding to the orbit of Mercury, after it has been corrected for the influences mentioned above, is not stationary with respect to the fixed stars, but that it rotates exceedingly slowly in the plane of the orbit and in the sense of the orbital motion.  The value obtained for this rotary movement of the orbital ellipse was 43 seconds of arc per century, an amount ensured to be correct to within a few seconds of arc.  This effect can be explained by means of classical mechanics only on the assumption of hypotheses which have little probability, and which were devised solely for this purponse.

On the basis of the general theory of relativity, it is found that the ellipse of every planet round the sun must necessarily rotate in the manner indicated above ; that for all the planets, with the exception of Mercury, this rotation is too small to be detected with the delicacy of observation possible at the present time ; but that in the case of Mercury it must amount to 43 seconds of arc per century, a result which is strictly in agreement with observation.

Apart from this one, it has hitherto been possible to make only two deductions from the theory which admit of being tested by observation, to wit, the curvature of light rays by the gravitational field of the sun,*x and a displacement of the spectral lines of light reaching us from large stars, as compared with the corresponding lines for light produced in an analogous manner terrestrially (i.e. by the same kind of atom).** These two deductions from the theory have both been confirmed.

  Notes

*) First observed by Eddington and others in 1919. (Cf.  Appendix III, pp. 126-129).

**) Established by Adams in 1924. (Cf. p. 132)

PART III

CONSIDERATIONS ON THE UNIVERSE AS A WHOLE

COSMOLOGICAL DIFFICULTIES OF NEWTON’S THEORY

Part from the difficulty discussed in Section 21, there is a second fundamental difficulty attending classical celestial mechanics, which, to the best of my knowledge, was first discussed in detail by the astronomer Seeliger.  If we ponder over the question as to how the universe, considered as a whole, is to be regarded, the first answer that suggests itself to us is surely this:  As regards space (and time) the universe is infinite.  There are stars everywhere, so that the density of matter, although very variable in detail, is nevertheless on the average everywhere the same.  In other words:  However far we might travel through space, we should find everywhere an attenuated swarm of fixed stars of approrimately the same kind and density.

This view is not in harmony with the theory of Newton.  The latter theory rather requires that the universe should have a kind of centre in which the density of the stars is a maximum, and that as we proceed outwards from this centre the group-density of the stars should diminish, until finally, at great distances, it is succeeded by an infinite region of emptiness.  The stellar universe ought to be a finite island in the infinite ocean of space.*