DOC. 42 SPECIAL AND GENERAL
RELATIVITY 329
86
Relativity
other,
and
to
the
co-ordinate
system.
Should
we
be
justified
in
saying
that
for
this
reason
electrostatics is overthrown
by
the
field-equations
of
Maxwell
in
electrodynamics?
Not
in the
least. Electrostatics
is
contained in
electrodynamics
as a
lim-
iting case;
the
laws
of the latter lead
directly
to
those
of
the
former
for
the
case
in which the fields
are
invariable with
[45]
regard to
time. No fairer
destiny
could be allotted
to
any
physical theory,
than
that
it should
of
itself
point out
the
way
to
the
introduction of
a more
comprehensive theory,
in which
it lives
on as a
limiting
case.
In
the
example
of
the
transmission of
light
just
dealt
with,
we
have
seen
that
the
general theory
of
relativity
enables
us
to
derive
theoretically
the influence
of
a
gravitational
field
on
the
course
of natural
processes,
the
laws
of
which
are
already
known when
a
gravitational
field
is
absent. But the
most at-
tractive
problem, to
the solution
of
which the
general theory
of
relativity
supplies
the
key, concerns
the
investigation
of
the
laws
satisfied
by
the
gravitational
field itself.
Let
us
consider
this
for
a
moment.
We
are
acquainted
with
space-time
domains which
behave
(approximately)
in
a
"Galileian" fashion under suitable choice
of
reference-body, i.e.
domains in which
gravitational
fields
are
absent. If
we now
refer such
a
domain
to
a
reference-body
K'
possessing any
kind
of
motion,
then
relative
to
K' there exists
a
gravitational
field which
is
variable
with
respect
to
space
and
time.1
The
character
of
this
field will of
course
depend
on
the
motion chosen
for
K'.
According
to
the
general theory
of
rel-
1
This
follows
from
a
generalisation
of the discussion
in
Section
20.