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In the first place, we see from this expression that two clocks of
identical construction will go at different rates when situated at
different distances from the centre of the disc. This result is also
valid from the standpoint of an observer who is rotating with the disc.
Now, as judged from the disc, the latter is in a gravitational field of
potential , hence the result we have obtained will hold quite
generally for gravitational fields. Furthermore, we can regard an atom
which is emitting spectral lines as a clock, so that the following
statement will hold:
_An atom absorbs or emits light of a frequency which is dependent on
the potential of the gravitational field in which it is situated._
The frequency of an atom situated on the surface of a heavenly body
will be somewhat less than the frequency of an atom of the same element
which is situated in free space (or on the surface of a smaller
celestial body).
Now = _K (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
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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_ are known.
It is an open question whether or not this effect exists, and at the
present time (1920) astronomers are working with great zeal towards the
solution. Owing to the smallness of the effect in the case of the sun,
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