DOC.
47
269
II.
ELECTRODYNAMIC PART
§7.
Transformation
of
the
Maxwell-Lorentz
equations
[35]
We
start from
the
equations3
In
these equations,
1
c
1
c
1
c
V
*dx
dN
dM
+
Tt
mmm
Sy
Tz
u rp
d¥
dL dN
+
Tt
Tz
-
fi
V
dz
dM
dL
+ si
U"'"
Sx
Sy
1
dL dY
dZ
c
Tt
= Tz
Sy
1 dM
dZ
dX
c
Si
-
Sx -
Tz
1
dN dX dY
c
Si
- Sy
Sx
(5)
(6)
(X,Y,Z)
is
the
vector
of electric field
strength,
(L,M,N)
is the
vector
of
magnetic
field
strength,
n
_
dX
M
ÖY
x
dz
p
-
fi
+
Ty
+
Tz
is the 4j-fold electric
density,
(ux,uy,uz)
is the
velocity vector of
electricity.
These
equations,
together
with the
assumption
that the electrical
masses
are
unchangeably
attached
to
small rigid bodies
(ions, electrons), form the
basis of Lorentz's
electrodynamics
and optics
of
moving
bodies.
If these
equations,
which
shall hold with
respect
to
the
system
S,
are
transformed
by
means
of the transformation
equations
(1) to
the
moving
system
S',
which
is
moving
relative
to S
as
in the
previous
considerations,
then
the
following equations
are
obtained: