170
ELECTRODYNAMICS OF
MOVING
BODIES
It should
be
noted that these results
concerning
mass are
also valid for
ponderable
material
points,
since
a
ponderable
material
point
can
be made
into
an
electron (in
our
sense)
by
adding to
it
an
arbitrarily small electric
charge.
We
now
determine
the kinetic
energy
of
the electron. If
an
electron
starts out from
the
origin
of
the
system K
with
an
initial
velocity
0
and
is
moving
continually
along
the Xaxis
under
the influence of
an
electrostatic
force
X,
then it is clear that the
energy
drawn
from
the electrostatic field
has
the value
JeXdx.
Since the electron is
supposed
to
accelerate
slowly
and
will therefore
emit
no
energy
in the
form of
radiation,
the
energy
taken
from
the electrostatic field
must
be
equated
with the
energy
of motion
W
of
the
electron.
Bearing
in
mind
that the first
of
equations
(A)
holds
during
the
entire
process
of
motion considered,
we
obtain therefore
[43]
V
=
eXdx
v
0
ß3vdv
= ßV2
1
1
L

1
v
V
7
[44]
[45]
Thus,
W
becomes
infinitely
large
when
v
= V.
As
in
our
previous
results,
superluminary
velocities
have
no
possibility
of
existence.
This
expression
for kinetic
energy
too
must
be
valid for
ponderable
masses as
well
by
virtue
of
the
argument
presented
above.
Let
us
now
enumerate
those properties of the
motion
of the electron that
result
from
the
system
of
equations
(A)
and
are
accessible
to
experiment.
1.
It follows
from
the
second
equation
of the
system
of
equations
(A)
that
an
electric force
Y
and
a
magnetic
force
N
have
an
equally
strong
deflective effect
on an
electron
moving
with velocity
v
if
Y
=
N.v/V.
Thus
we
see
that
according
to
our
theory
we can
determine the
velocity
of the
electron for
any
arbitrary
velocity from
the ratio
of
the
magnetic
deflection
A
m
to
the electric
deflection
A
by
applying
the
law
e
_
v