310
THE
RELATIVITY PRINCIPLE
[103]
We
thus obtain
i
+
4
cl
and
*
dX*
[pw(
+
~w\
1
+
iL
d!f
dlt
W
~
~K
etc
(31b)
dl*
dr
dY*
dZ*
w

w
etc (32b)
These equations
too
have
the
same
form
as
the
corresponding equations
of
the nonaccelerated
or
gravitationfree
space;
however,
c
is here
replaced
by
the value
=
c
$
1 +
JCL
[104]
[105]
From
this it follows that those
light
rays
that
do
not
propagate along
the
£axis
are
bent
by
the
gravitational
field;
it
can
easily
be
seen
that the
change
of
direction
amounts to
y/c2
sin
ip
per
cm
light
path,
where
p
denotes
the
angle
between
the direction
of gravity and
that of the light
ray.
With
the
help
of these
equations
and
the
equations
relating the field
strength
and
the electric
current
of
one
point, which
are
known
from
the
optics of bodies
at rest,
we can
calculate the effect
of
the
gravitational
field
on
optical
phenomena
in bodies
at rest.
One
has to
bear in
mind,
however,
that the
abovementioned equations from
the optics
of
bodies
at rest
hold for the local time
a.
Unfortunately,
the effect
of
the terrestrial
gravitational field is
so
small
according
to
our
theory
(because
of the
smallness
of
yx/c2
that there is
no
prospect
of
a
comparison
of
the
results
of
the
theory
with
experience.
If
we
successively
multiply equations
(31a)
and
(32a)
by
X*/4n
.....
N*/4n
and integrate
over
infinite
space,
we
obtain,
using
our
earlier notation,
[106]
1 +
^(w^+
urj^+
u^)du
+ 1 + +
Y2
N2)du

0
[107]
+ ur/ + u is the
energy
i)^
supplied
to
the
matter
per
unit
volume and
unit local
time
a
if this
energy
is
measured
by
measuring
tools
situated
at
the
corresponding
location.
Hence, according
to
(30),