348 DOC.
71
PRINCETON LECTURES
THE GENERAL THEORY
to
that
of
ponderable matter.
In
our
system
of
units,
the
energy
of
one
gram
of
matter
is equal to
1,
compared to
which the
energy
of the electric
fields
may
be
ignored,
and
also
the
energy
of deformation
of
matter,
and
even
the
chemical
energy.
We
get
an
approximation
that
is
fully
sufficient for
our
purpose
if
we
put
(102)
dx dx
=
0~
-
ds ds
ds2
=
g~dx~dx.
In
this,
a
is
the
density at rest,
that
is,
the
density
of the
ponderable matter,
in
the
ordinary
sense,
measured with
the aid
of
a
unit
measuring rod,
and referred
to
a
Galilean
system
of
co-ordinates
moving
with the
matter.
We
observe,
further,
that
in
the
co-ordinates
we
have
chosen,
we
shall make
only
a
relatively
small
error
if
we
replace
the
gur
by
-dur,
so
that
we
put
(102a) ds2
=
-
^
dx2.
The
previous developments
are
valid
however
rapidly
the
masses
which
generate
the
field
may
move
relatively
to
our
chosen
system
of
quasi-Galilean
co-ordinates.
But
in
astronomy
we
have
to
do with
masses
whose
velocities,
relatively to
the co-ordinate
system
employed,
are
always
small
compared to
the
velocity
of
light,
that
is,
small
compared to
1,
with
our
choice
of
the unit of time. We
therefore
get
an
approximation
which
is
sufficient for
nearly
all
practical purposes
if in
(101)
we
replace
the
retarded
potential
by
the
ordinary (non-retarded) potential,
and
if,
for
the
masses
which
generate
the
field,
we
put
dx
i
dxi
dx3
dxt
V
-
1
dl
(103a)
ds ds ds
°’
ds
dl
=
V-l.
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