166
ELECTRODYNAMICS
OF MOVING BODIES
where
"
dX
A
dY
A
dZ
p
=
Tx
+
Ty
+
[36]
denotes
the
4r-fold
density
of electricity
and
(ux
,u ,u
)
the
electricity's
y
z
velocity
vector.
If
the electric
masses are
conceived
as
permanently
bound
to
small,
rigid bodies (ions, electrons), then these
equations
constitute the
electromagnetic
foundation
of
Lorentz's
electrodynamics
and optics
of
moving
bodies.
If,
using
the transformation
equations presented
in
§3
and
§6, we
transform these
equations,
which
should
be
valid
in
system
K,
to
system
k,
we
get
the
equations
1
+
dr
dN'
dM'
1
dl
dr
dZ'
V
u
f
+
w
Jrf
V
w
W'
1
^
dr
dL'
1
dM'
dZ'
dX
V
11
f
p
UFT
WWdN'
JW W
1
A
dZ'
dM
dL'
1
dN'
_
dX' dY'
V
u^p
IFF
W
dr)
'
J
dr
~dtj~
where
-
v
x
nJ
u t'
1
-
X
11
dr dr
.
dz'
0
I
+.
W
+
W
=
ß
i
-
X
=
UV
'
ß
1
-
V
u
z
=
U
c
/-
.
ß
1
-
Since-as follows
from
the addition
theorem
of velocities
(§5)-the
vector
{u,u,u,)
is
actually
the
velocity of
the electric
masses
measured
in the
system
k,
we
have
thus demonstrated that with
our
kinematic
principles
taken
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