244
ON
THE
INERTIA
OF
ENERGY
E
=
1
e
8j
(P+y
+
P
+
L'2
+ liP + N*)dxdydz
To
this
end
we use
the transformation
equations
contained in the
repeatedly
cited
paper,
and
transform the
above
expression
by
introducing
under
the
integral the quantities
that referred
to
a
coordinate
system
moving
with the
body.
We
then obtain
E
= w~
e
8
f
1
P
1
+
(f)^
I'2
+
(J"2
+
^'2) i(dfid(
.
1
-
(T)
It should
be
noted that the value of this
expression
depends
on
the orienta-
tion of the rigid
body
relative
to
the direction of
motion.
Hence,
if the
total kinetic
energy
of
the electrified
body
consisted
exclusively
of the
kinetic
energy
K0
of the
body
due to
its
ponderable
mass
and
of the
excess
of the
electromagnetic
energy
of
the
moving body
over
the electrostatic
energy
of the
body
when
at rest,
we
would
have
arrived
at
a
contradiction,
as
we
can
easily
see
from
the
following.
We
imagine
that the
body
under
consideration
rotates
infinitely
slowly
relative
to
the coordinate
system
moving
along
with
it,
with
no
external
influences
taking
place during
this
motion.
It is clear that this
motion
must
be possible
without
application
of
any
force, because
according to
the
principle
of
relativity
the
body's laws
of
motion
relative
to
the
system
moving
along
with it
are
the
same as
the
laws of motion
with
respect to
a
"stationary"
system.
We
now
observe the
uniformly
moving
and
infinitely
slowly
rotating
body
from
the
"stationary"
system.
Since the rotation is
supposed
to
be
infinitely
slow,
it
does not
contribute
anything
to
the kinetic
energy. The expression
for the kinetic
energy
in the
case
under
consideration
is therefore the
same as
it
would
be
if
no
rotation but
only
uniform parallel
translation
were
to
take
place.
However,
since in
the
course
of
the
motion
the
body
takes
up
different (arbitrary) positions,
and
the
energy
principle
must
hold
throughout
the
motion,
it is
clear that the kinetic
energy
of
an
electrified
body
in translational
motion cannot possibly
depend
on
its
orientation.