DOC.
71
PRINCETON LECTURES 347
THE GENERAL THEORY
We
must
now
note
that
equation
(96) is
valid
for
any
system
of
co-ordinates. We have
already
specialized
the
system
of co-ordinates in
that
we
have
chosen it
so
that
within the
region
considered the
guv
differ
infinitely
little
from
the
constant
values -duv. But this
condition remains
satisfied in
any
infinitesimal
change
of co-ordinates,
so
that
there
are
still four
conditions
to
which the
yuv
may
be
subjected, provided
these
conditions do
not
conflict
with
the conditions
for the
order
of
magnitude
of
the
yuv.
We
shall
now assume
that
the
system
of co-ordinates
is
so
chosen
that the
four
relations-
(100)
=
dy\,
=
dy^
_
dy"
dx, dx,
^
dx"
are
satisfied.
Then
(96a)
takes
the
form
(96b)
d2y",
dxj
2k
T*
[105]
These
equations may
be solved
by
the
method,
familiar
in
electrodynamics,
of
retarded
potentials;
we
get,
in
an
easily
understood
notation,
(101) y",
2L
[
T*(x«’
zo,
t
-
0
dV
27T
J
r
L
In
order
to
see
in
what
sense
this
theory
contains the
Newtonian
theory,
we
must
consider
in
greater
detail the
energy tensor
of
matter.
Considered
phenomenologically,
this
energy
tensor
is composed
of
that of
the
electromagnetic
field
and
of
matter
in
the
narrower
sense.
If
we
consider
the different
parts
of this
energy tensor
with
respect to
their order
of
magnitude,
it follows from
the
results of
the
special
theory
of
relativity
that the contribution of
the
electromagnetic
field
practically
vanishes in
comparison
[87]