DOC.
71
PRINCETON LECTURES 317
THE GENERAL
THEORY
after
this
numerical
equality is
reduced
to
an
equality
of
the real
nature
of
the
two concepts.
That
this
object
may
actually
be
attained
by
an
exten-
sion
of the
principle
of
relativity,
follows
from the
follow-
ing
consideration.
A
little reflection will
show
that the
law of the
equality
of
the inert and
the
gravitational
mass
is equivalent to
the
assertion that the
acceleration
imparted to
a
body by
a
gravitational
field
is independent
of the
nature
of the
body.
For
Newton’s
equation
of
motion
in
a
gravitational field,
written
out
in
full, is
(Inert
mass)
.
(Acceleration)
=
(Intensity
of the
gravitational field)
.
(Gravitational
mass).
[70]
It
is only
when there
is
numerical
equality
between the
inert and
gravitational
mass
that the acceleration
is
inde-
pendent
of the
nature
of
the
body.
Let
now
K be
an
inertial
system.
Masses
which
are
sufficiently
far
from
each other and
from
other
bodies
are
then,
with
respect
to
K,
free from
acceleration. We
shall also refer these
masses
to
a
system
of
co-ordinates
K', uniformly
acceler-
ated with
respect to K. Relatively to
K' all the
masses
have
equal
and
parallel
accelerations;
with
respect to
K'
they
behave
just
as
if
a
gravitational
field
were
present
and
K'
were
unaccelerated.
Overlooking
for
the
present
the
question
as
to
the “cause” of
such
a
gravitational field,
which
will
occupy
us
later,
there
is nothing
to prevent
our
conceiving
this
gravitational
field
as
real,
that
is,
the
conception
that K'
is
“at rest” and
a
gravitational
field
is
present
we
may
consider
as
equivalent to
the
concep-
tion that
only
K
is
an
“allowable”
system
of
co-ordinates
[71]
and
no
gravitational
field
is
present.
The
assumption
of
the
complete
physical
equivalence
of the
systems
of
coor-
[72]
dinates,
K
and
K',
we
call
the
“principle
of
equivalence;”
[57]