DOC. 9 FORMAL FOUNDATION OF RELATIVITY
63
Electromagnetic equations
of
moving
bodies
for
the
case
considering
only
bodies
with
dielectric
constant
1
and
magnetic permeability 1.
Let
us
consider the electric
and
magnetic polarization
of bodies
only
insofar
as
they
cause
electric and
magnetic
%
charge
densities;
there shall be
no
electric
or
magnetic "polarization
currents."
Electric conduction
currents
along
conductors, however,
shall be considered. The
generalcovariant
field
equations
for this
case
are
found
by taking
into
account
(on
the
righthand
sides of the
equations)
the electric and
magnetic
convection currents
as
well
as
the electric conduction current
along
conductors.
Let
p
be the
charge density
of
polarization
electrons and conduction electrons
combined,
as
has been
previously
defined.
p«
dx
ds

is then the Vfourvector of the
convection
current, produced
jointly
by polarization
electrons
and conduction
electrons.
Let
p
be the
previously
defined
magnetic charge density
that
originates
from
the
(rigid) magnetic polarization.
P(m)
dx
ds
;
is then
the
Vfourvector
of
the
magnetic
convection current.
Another Vfourvector will
correspond
to the conduction
current,
and
we
shall
denote
by
it
(8M).
It is determined
by
the fact that in the "normal
system"
"1
,
.14
8
=
Ag
and,
on
the other
hand,
82
=

^ A^
24
«3
,
^34
8
A8
8=0
dxx
ds
=
0,
dx7
ds
=
0,
dx2
ds
=
0,
dxA
ds
=
1
{12}
These
conditions
are
met
by setting
aß
"S
The field
equations
then turn out
to
be
E
dfT.
v
dxv
P(e)
dx£
ds
+
8'
E
a?r
v
dxv
P
(M)
dx
ds
(55)
(56)
Field
equations
for
isotropic, electrically
and
magnetically polarizable moving
[p. 1065]
bodies.
We
modify
the
case
which
we
just considered,
and
now
also take into account
electric and
magnetic polarization
currents. It is assumed that
in
the comoved normal