Page:Relativity (1931).djvu/178

element which is situated in free space (or on the surface of a smaller celestial body).

Now $\phi =-K{\frac {M}{r}}$, where $K$ is Newton’s constant of gravitation, and $M$ is the mass of the heavenly body. Thus a displacement towards the red ought to take place for spectral lines produced at the surface of stars as compared with the spectral lines of the same element produced at the surface of the earth, the amount of this displacement being

${\frac {\nu _{0}-\nu }{\nu _{0}}}={\frac {K}{c^{2}}}{\frac {M}{r}}$.

For the sun, the displacement towards the red predicted by theory amounts to about two millionths of the wave-length. A trustworthy calculation is not possible in the case of the stars, because in general neither the mass $M$ nor the radius $r$ is known.

It is an open question whether or not this effect exists, and at the present time astronomers are working with great zeal towards the solution. Owing to the smallness of the effect in the case of the sun, it is difficult to form an opinion as to its existence. Whereas Grebe and Bachem (Bonn), as a result of their own measurements and those of Evershed and Schwarzschild on the cyanogen bands, have placed the existence of the effect almost beyond doubt, other investigators, par-