390
DOC. 42 SPECIAL AND GENERAL RELATIVITY
150
Relativity
on
the surface of
a
smaller celestial
body).
Now
o
= -
KM/y,
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
ele-
ment
produced
at
the surface
of
the
earth,
the
amount
of this
displacement being
v0
-
v
KM
v0
=c2
y.
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
y 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,
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 Schwarz-
schild
on
the
cyanogen
bands,
have
placed
the existence of
the effect
almost
beyond
doubt,
other
investigators, particu-
larly
St.
John,
have
been
led
to
the
opposite opinion
in
con-
sequence
of their
measurements.
Mean
displacements
of
lines
towards the
less
refrangible
end
of the
spectrum are
certainly
revealed
by
statistical
investiga-
[96]
[97]
[98]
[99]