352 DOC. 71 PRINCETON LECTURES
THE GENERAL THEORY
Ax2,
Ax3,
corresponding
to
the
ends of
a
unit
measuring
rod,
oriented
in
any
way,
shall
always satisfy
the relation
Ax12
+
Ax22
+
Ax32
=
1.
In
this
sense space
is
not
Euclid-
ean,
but “curved.” It
follows from
the
second of
the
relations above that
the
interval
between
two
beats of
the
unit
clock (dT
=
1)
corresponds to
the
“time”
1
+
k/8x
f
adV0/r
in
the unit
used in
our
system
of
co-ordinates. The
rate
[109]
of
a
clock
is
accordingly
slower the
greater is
the
mass
of
the
ponderable matter
in its
neighbourhood.
We
there-
fore
conclude that
spectral
lines
which
are
produced
on
the
sun’s surface will be
displaced
towards the
red,
com-
pared to
the
corresponding
lines
produced
on
the
earth,
by
about
2
.
10-6 of
their
wave-lengths.
At
first,
this
important consequence
of
the
theory appeared to
conflict
with
experiment;
but
results
obtained
during
the
past
years seem
to
make the
existence of this effect
more
and
more
probable,
and
it
can
hardly
be
doubted that
this
conse-
quence
of the
theory
will be
confirmed within the
next
years.
Another
important consequence
of
the
theory,
which
can
be
tested
experimentally,
has
to
do
with
the
path
of
rays
of
light.
In
the
general
theory
of
relativity
also
the
velocity
of
light
is
everywhere
the
same, relatively to
a
local
inertial
system.
This
velocity
is unity
in
our
natural
measure
of time.
The
law of
the
propagation
of
light
in
general
co-ordinates
is therefore, according
to
the
general
theory
of
relativity,
characterized,
by
the
equation
ds2
=
0.
To within the
approximation
which
we are
using,
and
in
the
system
of
co-ordinates which
we
have
selected,
the
[92]
[110]