286
THE
RELATIVITY
PRINCIPLE
moving
with
it,1
and
the translational velocity
q
of the
system,
and
we
obtain
From
this it follows that
dE
1
W0
=
1 cl
E
=
1
E0
+
p(q)
,
a*
1
~
h
cz
[62]
where
p(q)
is
a
function
of
q
that is
unknown
for the time
being.
The
case
that
E0
equals 0,
i.e.,
that the
energy
of
the
moving
system
is
a
function
of
the velocity
q
alone,
has already been examined
in
§§
8
and
9.
From equation (14)
it follows
immediately
that
we
have to put
Thus
we
obtain
p(q)
=
\iC
+
const.
i
-
gcz
E
=
TP
1
-
hCL
(16a)
where
the
integration
constant
has been
omitted.
A
comparison
of this
expression
for
E
with
the
expression
for the kinetic
energy
of the material
point
contained
in
equation
(14) shows
that the
two
expressions have
the
same
form;
with
regard
to
the
dependence
of
the
energy
on
the translational velo-
city, the
physical
system
under
consideration
behaves
like
a
material
point
of
mass
M,
where
M
depends
on
the
system's
energy
content
E0
according to
the formula
'
-
P
+

(17)
This result is
of extraordinary
theoretical
importance
because the
inertial
mass
and
the
energy
of
a
physical
system appear
in it
as
things of
1Here, as
well
as
in the
following,
we
use
a
symbol
with the subscript
"0" to
indicate that the
quantity
in
question
refers
to
a
reference
system
that is
at
rest
relative
to
the
physical
system
considered. Since the
system
considered
is
at rest
relative
to S'
,
we can
replace
E'
by
E0
here.
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