384
DOC.
23
PROPAGATION
OF LIGHT
[6]
(2a)
v, =
v
1
+

3
This
result
(valid
to
a
first
approximation according
to
our
derivation)
allows,
to
begin
with,
the
following application:
Let
v0
be
the
frequency
of
an
elementary
light source,
measured
by a
clock U
that
is
read
at
the
same
location. This
frequency is
then
independent
of the location
at which
both the
light
source
and
the
clock
are
set
up.
We
shall
imagine
that both
are
set
up
on
the
surface
of the
sun
(this
is
where
our system
S2
is located).
A
part
of the
light
there emitted reaches earth
(S1),
where
we measure
the
frequency
v
of the
arriving light by means
of
a
clock
U,
with
exactly
the
same
constitu
tion
as
the
clock
mentioned
above.
According
to
(2a), we
will
then
have
v
=
v 1 +

3
where $
is
the
(negative) gravitational potential
difference between the
solar surface
and
the earth.
Thus, according
to
our
conception,
the
spectral
lines
of
solar
light
must
be
shifted
somewhat
toward red
as
compared
with
the
corresponding spectral
lines
of
terrestrial
light sources,
which has
the relative
shift
amounting
to
v2

v
=
2
10"5.
[7]
If
the
conditions under
which
the solar
lines
are
generated
were
known
exactly,
this shift
would
be
accessible to
measurement.
However,
since
additional
factors
(pressure,
temperature)
influence the
position
of the
center
of
density
of
the
spectral lines,
it
is
difficult to establish
whether the influence of the
gravitational
potential
that
has
been
derived
above
really
exists.6
At
first
glance,
equations
(2)
and
(2a)
seem
to assert
something
absurd.
If the
transmission of
light
from
S2
to
S1
is continuous,
then
how
can
the number of
periods
arriving
per
second
at
S1
be
different from that emitted
at
S2?
But the
answer
is
simple.
We
cannot
simply
consider
v2
and
v1 as
frequencies (numbers
of
periods per
second)
because
we
have not
yet
defined
a
time in
the
system
K.
v2
denotes the
number of
periods
referred
to
the time unit of the
clock U at
S2,
and
v1
the
number
of
periods
referred
to
the time unit of the
identically
constituted
clock U at
S1.
There
[8]
[9]
6
L.
F. Jewell
(Journ.
de
phys.
6
[1897]: 84)
and
especially
Ch.
Fabry
and H. Boisson
(Compt.
rend.
148
[1909]:
688690)
did
actually
establish such shifts
of
fine
spectral
lines
toward the red end of
the
spectrum
of
the
order of
magnitude
calculated
above,
but
they
attributed them
to
an
effect
of
the
pressure
in the
absorbing
layer.