However, we obtain a new result of fundamental importance when we carry out the analogous consideration for a ray of light.  With respect to the Galileian reference-body K, such a ray of light is transmitted rectilinearly with the velocity c.  It can easily be shown that the path of the same ray of light is no longer a straight line when we consider it with reference to the accelerated chest (reference-body K1).  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.[2]*

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 unlinlited domain of validity ; its results hold only so long as we are able to disregard the influences of gravitational fields on the phenomena (e.g. of light).

Since it has often been contended by opponents of the theory of relativity that the special theory of relativity is overthrown by the general theory of relativity, it is perhaps advisable to make the facts of the case clearer by means of an appropriate comparison.  Before the development of electrodynamics the laws of electrostatics were looked upon as the laws of electricity.  At the present time we know that electric fields can be derived correctly from electrostatic considerations only for the case, which is never strictly