DOC.
1
MANUSCRIPT
ON SPECIAL RELATIVITY
17
force the
physically
intuitive
formula[29]
f
=
ep
+1
[i,
ffl
-
Igrad
(C
p)
+
(pv) c
+
I
[M]
c
2
c
-
i-grad
(J),
m)
+
(mVj
1)
-
-
[m,c]
2
c
(11a)
1
In this formula
only
the
terms
-1/2
grad (ep)
and
-grad(hm)
were
physically
opaque. They
owe
their
appearance
to
the
assumption,
which
we
introduced
above,
that
during
an
infinitesimally
small
displacement
of the
matter
the dielectric
constant
of
the material
particle always
remains
unchanged,
even
in the
case
where the
particle
changes
its volume in
the
course
of the
displacement.
Thus,
these
terms
correspond
[p.
13]
to
a
physically unjustified
assumption.
But
they are
also of subordinate interest
because
they
are
not
capable
of
producing
motion in
incompressible
substances,
but
only
changes
in
pressure.
§4.
Lorentz's
Equations
for
(Slowly)
Moving
Media
As in the
case
of bodies
at
rest,
we again
start out
from the
fundamental
equations
(I)
in
§1,
which, however,
for
reasons
analyzed
in
§2, we
must
modify by assuming
the
presence
of several
continua
of
electrical
density,
which
are
to
be viewed
partly
as
carriers of
polarization
and
partly
as
carriers of the electrical conduction
currents
and
corresponding charges.
In
addition,
the third and the fourth of
equations (I)
are
to
be
supplemented by adding
terms
corresponding
to
the
magnetic polarization
currents. But because of the
duality
of electric and
magnetic processes,
it suffices
to
set
up
the
first two
equations
for
our case.
They
read
curl
h=
=
1/
(C
+
£
(ijgpg
+
£
H/P/)
c
div
If,
for the sake of
brevity,
we
denote
the
sum
of
the
second and the third
term
within
the bracket
on
the left-hand side
by
a,
then
a is
the
vector
of the total
electrical
current
with
respect
to
an
observer
at rest.
Our task
is to
express
a
by
means
of the
vectors
n,
i
(conduction current
vector)
and
p
(polarization vector),
the last
two
of
which
can
be
sharply
defined
only
for bodies
at rest,
that
is,
in
our
case,
for
an
observer
moving
with the material element under consideration.
If
one
chooses
an
infinitesimally small, plane
surface element
o
at rest,
with
a
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Extracted Text (may have errors)


DOC.
1
MANUSCRIPT
ON SPECIAL RELATIVITY
17
force the
physically
intuitive
formula[29]
f
=
ep
+1
[i,
ffl
-
Igrad
(C
p)
+
(pv) c
+
I
[M]
c
2
c
-
i-grad
(J),
m)
+
(mVj
1)
-
-
[m,c]
2
c
(11a)
1
In this formula
only
the
terms
-1/2
grad (ep)
and
-grad(hm)
were
physically
opaque. They
owe
their
appearance
to
the
assumption,
which
we
introduced
above,
that
during
an
infinitesimally
small
displacement
of the
matter
the dielectric
constant
of
the material
particle always
remains
unchanged,
even
in the
case
where the
particle
changes
its volume in
the
course
of the
displacement.
Thus,
these
terms
correspond
[p.
13]
to
a
physically unjustified
assumption.
But
they are
also of subordinate interest
because
they
are
not
capable
of
producing
motion in
incompressible
substances,
but
only
changes
in
pressure.
§4.
Lorentz's
Equations
for
(Slowly)
Moving
Media
As in the
case
of bodies
at
rest,
we again
start out
from the
fundamental
equations
(I)
in
§1,
which, however,
for
reasons
analyzed
in
§2, we
must
modify by assuming
the
presence
of several
continua
of
electrical
density,
which
are
to
be viewed
partly
as
carriers of
polarization
and
partly
as
carriers of the electrical conduction
currents
and
corresponding charges.
In
addition,
the third and the fourth of
equations (I)
are
to
be
supplemented by adding
terms
corresponding
to
the
magnetic polarization
currents. But because of the
duality
of electric and
magnetic processes,
it suffices
to
set
up
the
first two
equations
for
our case.
They
read
curl
h=
=
1/
(C
+
£
(ijgpg
+
£
H/P/)
c
div
If,
for the sake of
brevity,
we
denote
the
sum
of
the
second and the third
term
within
the bracket
on
the left-hand side
by
a,
then
a is
the
vector
of the total
electrical
current
with
respect
to
an
observer
at rest.
Our task
is to
express
a
by
means
of the
vectors
n,
i
(conduction current
vector)
and
p
(polarization vector),
the last
two
of
which
can
be
sharply
defined
only
for bodies
at rest,
that
is,
in
our
case,
for
an
observer
moving
with the material element under consideration.
If
one
chooses
an
infinitesimally small, plane
surface element
o
at rest,
with
a

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