242
ON
THE
INERTIA
OF
ENERGY
Thus,
if the limits for
r
in
the
above integral
expression
for
AE
were
independent
of
£,n,(,
we
would have ±E
=
0.
However,
this is
not
the
case,
for
from
the transformation
equation
t
=
ß
v
t + ji
it
it follows
immediately
that the time limits in the
moving
system
are
t
A
V
S-
_
..
.1
t
T
-
-
ji
i
and
T
~
~
JT
t
'
We imagine
that the
integral in
the
expression
for
AE
is
decomposed
into
three parts.
The
first part shall
comprise
the times
r
between
the
second
part
between
and
the third
between
"jf ~
ji
£
and
and
,
and
-
yz
t
The
second
part vanishes because its time limits
are
independent
of
£,n,(.
The
first
and
third
parts have
a
definite value
only
if the
assumption
is
made
that the forces
acting
on
the
body are
independent
of
time close
to
the times
t
=
t0
and t
=
t1,
such
that
the
electric force
X'
is inde-
pendent
of
time
for all
points
of the rigid
body
between
the
times
7
~ 7^
~
Y1
%
and
7.
~
and between
11
_
t
7
~
and
~ ~ Y1
^
,
respectively.
If the
X'
present
during
these
two
time intervals
are
called
X'1
and
X'2,
respectively,
one
obtains