_K _). From this we conclude, _that, in general, rays of light are
propagated curvilinearly in gravitational fields._ In two respects this
result is of great importance.
In the first place, it can be compared with the reality. Although a
detailed examination of the question shows that the curvature of light
rays required by the general theory of relativity is only exceedingly
small for the gravitational fields at our disposal in practice, its
estimated magnitude for light rays passing the sun at grazing incidence
is nevertheless 1.7 seconds of arc. This ought to manifest itself in
the following way. As seen from the earth, certain fixed stars appear
to be in the neighbourhood of the sun, and are thus capable of
observation during a total eclipse of the sun. At such times, these
stars ought to appear to be displaced outwards from the sun by an
amount indicated above, as compared with their apparent position in the
sky when the sun is situated at another part of the heavens. The
examination of the correctness or otherwise of this deduction is a
problem of the greatest importance, the early solution of which is to
be expected of astronomers.[16]
[16] By means of the star photographs of two expeditions equipped by a
Joint Committee of the Royal and Royal Astronomical Societies, the
existence of the deflection of light demanded by theory was first
confirmed during the solar eclipse of 29th May, 1919. (Cf. Appendix
III.)
In the second place our result shows that, according to the general
theory of relativity, the law of the constancy of the velocity of light
in vacuo, which constitutes one of the two fundamental assumptions in
the special theory of relativity and to which we have already
frequently referred, cannot claim any unlimited validity. A curvature
of rays of light can only take place when the velocity of propagation
of light varies with position. Now we might think that as a consequence
of this, the special theory of relativity and with it the whole theory
of relativity would be laid in the dust. But in reality this is not the
case. We can only conclude that the special theory of relativity cannot
claim an unlimited domain of validity; its results hold only so long as
we are able to disregard the influences of gravitational fields on the
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