330
EQUATIONS
FOR MOVING
BODIES
electric
current
by
s';
p'
shall denote
the
electric
density. For
the
reference
system
K'
there shall hold the
Maxwell-Hertz
equations:
(1)
curl' ft
=
4
IT"
+
5
(2)
curl1 (£'=--
i cm[
e
TT
'
(3)
div' D'
=
p
(4)
div'
»'
=
0
.
Let
us
consider
a
second
orthogonal
reference
system
K
whose
axes
are
permanently
parallel
to
those
of
K1.
Let
the
origin of
K'
move
in the
positive direction of the z-axis of
K
with
constant velocity
v.
As we
know, according
to
the
theory
of relativity the
following
transformation
equations1
will then hold for
every
point event,
provided
the starting time
point has been suitably
chosen:
x'
=
ß{x
-
vt)
y = y
z
t
I
_
t
_
Z
,
ß
V
t
-
JlX
ß
=
1
,
V1
1-
c*
where
x, y, z,
t
denote
the
space
and time
coordinates
in the
system K.
If
one
carries
out
the transformations,
one
obtains the
equations
(1a)
curl #
=
1
90
+ Jt + 5r
(2a)
curl
(S
=
-
1
c
TT
(3a)
div
V
=
p
,
[3]
1A.
Einstein,
Ann.
d.
Phys. 17
(1905):
902.