DOC.
71
PRINCETON LECTURES 341
THE GENERAL THEORY
Both
terms
of
our
equation
of
motion
are
then
small
of
the
first
order. If
we
neglect
terms which,
relatively
to
these,
are
small of
the
first
order,
we
have
to put
ds2
=

dx2
=
dl2(1

q2)
Tub
=

Guv=
et
1/2
(DY2

DY

DY)
(93)
(94)
{3}
We
shall
now
introduce
an
approximation
of
a
second
kind. Let the
velocity
of
the material
particles
be
very
small
compared
to
that
of
light.
Then
ds
will be
the
same
as
the
time differential,
dl.
Further,
dx1/ds, dx2/ds,
dx3/ds
will
vanish
compared
to
dx4/ds.
We
shall
assume,
in
addi
tion,
that the
gravitational
field
varies
so
little with the
time that the derivatives of the
yuv
by
x4
may
be
neglected.
Then the
equation
of motion
(for u
=
1,
2,
3)
reduces
to
(90a)
dx2/dt2
=
d/dx2(y44/2)
This
equation is
identical with
Newton’s
equation
of
motion
for
a
material
particle
in
a
gravitational field,
if
we
identify
(y44/2)
with the
potential
of the
gravitational
field;
whether
or
not
this
is allowable, naturally depends
upon
the
field
equations
of
gravitation,
that
is,
it
depends
upon
whether
or
not
this
quantity satisfies,
to
a
first
approxi
mation,
the
same
laws of the field
as
the
gravitational poten
tial
in Newton’s
theory.
A
glance at
(90)
and
(90a)
shows
that the
Tuba
actually
do
play
the rôle of the
intensity
[98]
of
the
gravitational
field.
These
quantities
do
not
have
a
tensor
character.
Equations (90)
express
the influence of inertia and
gravitation upon
the material
particle.
The
unity
of
[81]