DOC.
1
MANUSCRIPT ON SPECIAL RELATIVITY
11
p
=
-
div
pg
£
pg =
-div
p.
Furthermore,
if,
for the sake of
brevity,
we
denote the total
density
of the conduction
electricity
E
pl
by p,
then
our
equation
becomes
div e
=
-div
p +
p, [p.
8]
or-in
accordance
with
the
definitional
equation given
for
d–
div
&
=
p,
where, however,
p
denotes the
density
of
the conduction
electricity
alone.
Let
us now
turn to
the first of
equations
(I).
The latter remains
valid,
but with the
difference that
we
have
to
put
the
sum
E
ngpg
+
E
nlpl
in
Place
of
nP.
But
according
to
our
definitional
equation
for
p
f
|(BS
pj
-
SX
p,
The last
equation
is
correct because
only
the
time derivative of
the
displacements
ng',
but
not
the time derivative
of
the
pg,
appears
to
be
multiplied by
finite
factors,
and
because,
obviously,
ng'
must
be
replaced by
ng.
If,
in
addition,
we
set
nlpl equal
to the total conduction
current i,
then the first
of
equations
(I) assumes
the form
curl
tf
-
{£
+ p +
I}.
c
or
also
curl
tf =
-
{&+!}
c
The
assumption
of
the existence of
polarization electricity
has
no
influence
on
the
form of the third and fourth
of
equations
(I).
Now
we
have
to
fit
equations
(I)
to
the
case
where
magnetically polarizable
bodies
are
present.
H. A.
Lorentz does this
by conceiving
of certain electricities
as
being
endowed with
cyclical motions;[23]
from the
standpoint
of the
pure
electron
theory
this
is
also the
only way
that
is
justified.
But for the sake
of
simplicity, we
will
base ourselves here
on
the
knowledge
that,
as
regards spatio-temporal
interrelations,
the
magnetic polarization
is
a
state
wholly analogous
to
the
polarization
of dielectrics.
Thus,
we
permit
ourselves
to
conceive of
magnetically polarizable
bodies
as being
endowed with bound
magnetic
volume densities. In
addition,
one
has
to
take into
account
the fact that
a magnetic phenomenon
that would
correspond
to
electrical conduction does
not
exist. For that
reason,
if
we
denote the
vector
of
magnetic polarization by m,
we
must
supplement
the last
two
of
equations (I) by
the
terms
-
1/c
m
and
-div
m,
respectively. Hence,
in
place
of
(I), we
obtain
finally
the