If two independent stars are seen in the same line of vision within about 1″, one being a great distance behind the other, the conditions seem at first more favourable. I do not know if any such pairs exist. It would seem that we ought to see the more distant star not only by the direct ray, which would be practically undisturbed, but also by a ray passing round the other side of the nearer star and bent by it to the necessary extent. The second image would, of course, be indistinguishable from that of the nearer star; but it would give it additional brightness, which would disappear in time when the two stars receded. But consider a pencil of light coming past the nearer star; the inner edge will be bent more than the outer edge, so that the divergence is increased. The increase is very small; but then the whole divergence of a pencil from a source some hundred billion miles away is very minute. It is easily calculated that the increased divergence would so weaken the light as to make it impossible to detect it when it reached us[1].
If two unconnected stars approached the line of sight still more closely, so that one almost occulted the other, observable effects might be perceived. When the proximity was such that the direct ray from the more distant star passed within about 100 million kilometres of the nearer star, it would begin to fade appreciably. The course of the ray would not yet be appreciably deflected, but the divergence of the pencil would be rapidly increased, and less light from the star would enter our telescopes. The test is scarcely likely to be an important one, since a sufficiently close approach is not likely to occur; and in any case it would be difficult to feel confident that the fading was not due to a nebulous atmosphere around the nearer star.
The theory gives small corrections to the motion of the moon which have been investigated by de Sitter. Both the axis of the orbit and its line of intersection with the ecliptic should advance about 2″ per century more than the Newtonian theory indicates. Neither observation nor Newtonian theory are as yet pushed to sufficient accuracy to test this; but a comparatively small increase in accuracy would make a comparison possible.
Since certain stars are perhaps ten times more massive than the sun, without the radius being unduly increased, they should show a greater shift of the spectral lines and might be more
- ↑ Appendix, Note 12.
