DOC.
42
SPECIAL AND GENERAL RELATIVITY
357
Solution
of
Gravitation 113
gravitational
field
on measuring-rods,
clocks and
freely-
moving
material
points
continues
to
take
place according to
the
same
laws,
even
in
the
case
where
the
prevailing gravita-
tional field is not
derivable from
the
Galileian
special case,
simply by
means
of
a
transformation
of
co-ordinates.
The
next step
is
to investigate
the
space-time
behaviour of
the
gravitational
field
G,
which
was
derived from the Galileian
special
case
simply by
transformation of the co-ordinates.
This
behaviour
is
formulated in
a law,
which
is
always
valid,
no
matter
how
the
reference-body (mollusc)
used in the
descrip-
tion
may
be chosen.
This
law is
not yet
the
general
law
of the
gravitational
field,
since
the
gravitational
field
under
consideration
is
of
a
special
kind. In order
to
find
out
the
general
law-of-field
of
gravitation
we
still
require
to
obtain
a generalisation
of
the
law
as
found
above.
This
can
be obtained without
caprice,
however,
by
taking
into consideration
the
following
demands:
(a)
The
required generalisation must
likewise
satisfy
the
general postulate
of
relativity.
(b)
If there
is
any matter
in
the domain
under
consider-
ation,
only
its
inertial
mass,
and thus
according
to
Section
15
only
its
energy
is
of
importance
for
its effect in
exciting a
field.
(c)
Gravitational field and
matter
together
must
satisfy
the
law
of
the conservation
of
energy
(and
of
impulse).
Finally,
the
general principle
of
relativity permits
us
to
de-
termine
the
influence
of the
gravitational
field
on
the
course
of
all
those
processes
which take
place
according to
known
laws
when
a
gravitational
field
is absent,
i.e.
which have
al-