358
DOC.
42
SPECIAL AND GENERAL
RELATIVITY
114
Relativity
ready
been
fitted into the frame of the
special
theory
of rel-
ativity.
In this connection
we proceed
in
principle according
to
the
method which
has
already
been
explained
for
measuring-
rods,
clocks and
freely-moving
material
points.
The
theory
of
gravitation
derived in this
way
from
the
gen-
eral
postulate
of
relativity
excels
not only
in
its
beauty;
nor
in
removing
the defect
attaching to
classical
mechanics which
was
brought to light
in Section
21;
nor
in
interpreting
the
empirical
law
of the
equality
of inertial and
gravitational
mass;
[58]
but
it
has also
already explained a
result of observation in
[59] astronomy, against
which
classical
mechanics
is powerless.
[60]
If
we
confine the
application
of the
theory to
the
case
where
the
gravitational
fields
can
be
regarded
as
being weak,
and in
which
all
masses move
with
respect to
the
co-ordinate
system
with velocities which
are
small
compared
with the
velocity
of
light,
we
then obtain
as
a
first
approximation
the
Newtonian
theory.
Thus
the latter
theory
is
obtained here without
any
particular assumption,
whereas Newton had
to
introduce
the
hypothesis
that the
force
of attraction between
mutually at-
tracting
material
points
is
inversely proportional to
the
square
of the distance between them.
If
we
increase
the
accuracy
of
the
calculation,
deviations from the
theory
of
Newton make
their
appearance, practically
all
of
which
must
nevertheless
escape
the
test
of
observation
owing
to
their smallness.
We
must
draw attention here
to
one
of these deviations.
According to
Newton's
theory,
a
planet
moves
round
the
sun
in
an
ellipse,
which would
permanently
maintain its
position
with
respect to
the fixed
stars,
if
we
could
disregard
the
mo-
tion of the fixed
stars
themselves and the action of the other