168
ELECTRODYNAMICS OF MOVING
BODIES
From
the
above assumption
combined
with the relativity
principle
it is
clear that,
viewed from
the
system
k,
the
electron will
move
during
the
immediately
following
time (for
small values
of
t) according
to
the
equations
d2
^
IPr
=
el',
eY
=
eZ',
where
the
symbols
?/,
(,
r,
X', Y',
Z'
refer
to
the
system
k.
If
we
also
stipulate that for
t
=
x
=
y
=
z
=
0
we
should
have
T =
(
=
ri
=
(
=
0,
then
the transformation
equations
of
§§3
and
6
will
be
valid,
so
that
we
get
T
-
ß
t
v
Jl
X"
(
=
ß(x
-
vt),
X'
=
X,
v =
y,
Y'
=
ß
(
=
z,
Z'
=
ß
[Z
+
j
M].
With
the
help
of these
equations
we
transform the
above
equations
of
[39]
motion from
system
k
to
system K
and
obtain
d2x
e 1
dt2
n
Jß
J,
(A)
6
1
ß
ß
y-
IN
d2z
IT1
e 1
ß
~ß
Z
+
I
M