DOC.
1
MANUSCRIPT ON SPECIAL RELATIVITY
19
principle
of
duality.
One
has
only
to
bear in mind that there is
no
magnetic analog
to
the electrical conduction
current.
Accordingly,
the field
equations
read
c
curl
1) -
C
=
(ji
-
curl
[q,p]
+ (i +
Hp)
div
e
=
-
div
p
+
p
c
curl
C
+
1)
=
-
(ttt
-
curl
[Hw])
div
f)
=
~
div
m
(Ib)
The form
of
these
equations
tempts one
to introduce
the
vectors h +
-
e
+
p,
c
1
[nm], h + m
as
field
vectors
and,
in this
way,
to
simplify
the
equations
considerably.
In this
way
one
obtains Minkowski's form of the field
equations,
which
agrees
with the form of the field
equations
for bodies
at
rest,
up
to
the
term
np.[32]
But
we
do
not
do
this,
for the
vectors
that
are
to
be introduced in this
way possess
no
simple physical
meaning.
What
one
gains
in the
simplicity
of the fundamental
equations through
their
introduction,
one
loses
again through
the fact that the
equations
that
give
the
connection between the
states
of the bodies and the field
vectors
become
more complicated. Taking
into
account
that the force
acting
on a
moving
unit of
electricity according
to
§2
is
equal
to e
+
1/c
[n,h] ("electromotive
force")
and that the force
acting on
the
moving magnetic charge
unit[33]
is
equal
to
h
-
1/c
[ne] ("magnetomotive
force"),[34] one
obtains, analogously
to
equations (8'),
p
=
(e
-
1)
(c
+
I
ft,!)])
c
m
=
(|i
-
1)
(1)
-
-
ft,C])
c
i
=
A(C
+
1
ft,ft)
c
(12)
Considered from
the
standpoint
of
the
relativity theory,
which will be
developed later,
[p.
15]
these
equations
can
hold
only
to
a
first
degree
of
approximation, i.e., only
if
one
neglects
those
terms
in the
equations
that
are multiplied by
n/c
to
the second
or
even
higher
power.[35]
Since such
terms
possess practical meaning only
in
a
very
few
cases,
because the velocities
occurring
in
practice
are
almost
always very
small in
comparison
with
c,
one
can
base one's
calculations
on
these Lorentz
equations
in
almost all of the
cases
that
correspond
to
observable
phenomena.
From them and
equations
(12),
for
example,
one can
easily provide
the
theory
for the
previously
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Extracted Text (may have errors)


DOC.
1
MANUSCRIPT ON SPECIAL RELATIVITY
19
principle
of
duality.
One
has
only
to
bear in mind that there is
no
magnetic analog
to
the electrical conduction
current.
Accordingly,
the field
equations
read
c
curl
1) -
C
=
(ji
-
curl
[q,p]
+ (i +
Hp)
div
e
=
-
div
p
+
p
c
curl
C
+
1)
=
-
(ttt
-
curl
[Hw])
div
f)
=
~
div
m
(Ib)
The form
of
these
equations
tempts one
to introduce
the
vectors h +
-
e
+
p,
c
1
[nm], h + m
as
field
vectors
and,
in this
way,
to
simplify
the
equations
considerably.
In this
way
one
obtains Minkowski's form of the field
equations,
which
agrees
with the form of the field
equations
for bodies
at
rest,
up
to
the
term
np.[32]
But
we
do
not
do
this,
for the
vectors
that
are
to
be introduced in this
way possess
no
simple physical
meaning.
What
one
gains
in the
simplicity
of the fundamental
equations through
their
introduction,
one
loses
again through
the fact that the
equations
that
give
the
connection between the
states
of the bodies and the field
vectors
become
more complicated. Taking
into
account
that the force
acting
on a
moving
unit of
electricity according
to
§2
is
equal
to e
+
1/c
[n,h] ("electromotive
force")
and that the force
acting on
the
moving magnetic charge
unit[33]
is
equal
to
h
-
1/c
[ne] ("magnetomotive
force"),[34] one
obtains, analogously
to
equations (8'),
p
=
(e
-
1)
(c
+
I
ft,!)])
c
m
=
(|i
-
1)
(1)
-
-
ft,C])
c
i
=
A(C
+
1
ft,ft)
c
(12)
Considered from
the
standpoint
of
the
relativity theory,
which will be
developed later,
[p.
15]
these
equations
can
hold
only
to
a
first
degree
of
approximation, i.e., only
if
one
neglects
those
terms
in the
equations
that
are multiplied by
n/c
to
the second
or
even
higher
power.[35]
Since such
terms
possess practical meaning only
in
a
very
few
cases,
because the velocities
occurring
in
practice
are
almost
always very
small in
comparison
with
c,
one
can
base one's
calculations
on
these Lorentz
equations
in
almost all of the
cases
that
correspond
to
observable
phenomena.
From them and
equations
(12),
for
example,
one can
easily provide
the
theory
for the
previously

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