DOC.
23 167
as a
basis, the
electrodynamic
foundation
of
Lorentz's
theory
of the electro-
dynamics
of
moving
bodies
agrees
with the
principle of
relativity.
Let
me
also
briefly
add
that
the
following important
proposition
can
easily be deduced
from the
equations
we
have
derived:
If
an
electrically
charged
body moves
arbitrarily
in
space
without
change
of
its
charge,
observed
from
a
coordinate
system
moving
with the
body,
then its
charge
will
also
remain
constant when
observed
from
the
system
"at
rest"
K.
~10.
Dynamics
of
the
(slowly
accelerated)
electron
In
an
electromagnetic
field let
a
pointlike
particle
endowed
with
an
electric
charge
e
(called "electron" in
what
follows) be
in
motion;
about
its
law of motion
we assume
only
the
following:
If the electron is
at rest
during
a
particular
epoch,
its
motion
in the
next
element of
time
will
occur
according
to
the
equations
.
d2x
»17*
"
ei'Y
=
El',
d2z
ß
IT1
"
eZ,
where
x,
y, z
denote the coordinates of
the electron
and
\i
its
mass,
as
long
as
the electron
moves
slowly.
Further,
let
the
electron's
velocity
in
some
given
time
epoch
be
v.
We
seek
to
find the
law
by
which
the electron is
moving
in
the
next
element
of
time.
Without
affecting
the
generality
of the consideration,
we can
and
will
assume
that
at
the
moment when
we
focus
on
it, the
electron is
at
the
coordinate
origin,
and
is
moving
with
velocity
v
along
the X-axis
of
the
coordinate
system K.
It is then obvious that
at
the instant indicated [38]
(t
=
0),
the electron
is
at rest
relative
to
the
coordinate
system
k
that
moves
with
constant
velocity
v
parallel
to the X-axis.
[37]