DOC.
1
MANUSCRIPT ON SPECIAL RELATIVITY
5
e
and
i
vanish. Rowland has shown that
a
rotating, electrically charged,
metal disk
generates a magnetic
field[8].
From
this
experiment one can
conclude that
an
electrically charged body moving
with
velocity
n
and
charge density
p
is
equivalent
to
a
current
distribution
of
current
density pij.
This
current,
which
is
called
a
convection
current,
has been introduced into the
theory
by
Maxwell[9]. Therefore,
if
one
aims for
an
equation
that
is
valid for
all
processes
in
vacuum,
one
will
replace
(1b)
with the
equation
curl
Jj =

(e
+
i
+ pq).
...(1c)
c
But
we can
write
this
equation
in
a simpler
form if
we
make
use
of
a
hypothesis
by
the
application
of which
H. A.
Lorentz has
tremendously
advanced
electrodynam
ics. The law of the conservation of the
quantities
of
electricity suggests
the
assumption
that
changes
of
location
are
the
only changes
that the
quantities
of
electricity
can
experience,
or
in other
words,
that electrical
currents
are
always
convection
currents.
According
to
this
assumption,
one
has
to
imagine
that
an [p.
3]
apparently chargefree
conductor contains
positively
and
negatively charged
corpuscles
the
sum
of whose
charges
is
zero;
in
that
case,
the electrical
current is
due
to
a
motion of the
positively charged corpuscles
with
respect
to
the
negatively
charged
ones.
On this
conception, equation
(1c)
reduces
to
curl
tf =

(e
+
p(\).
...(1d)
c
The
second
system
of
Maxwell's
equations
in the
absence
of
electrically
and
magnetically
polarizable media.
As
we
know,
Maxwell's second
system
of
equations
is
the
expression
of
Faraday's
law of
electromagnetic
induction for electric circuits
at rest
and for
infinitely
small
spaces,
if
one
also includes the
hypothesis
that the
magnetoelectrically
induced electromotive force
is
essentially
the
same as an
electrical field
strength.
For
slowly
changing magnetic
fields the law of induction
is
by
the
equation

e23
=
Jff"do,
...(3)
where the
integral
on
the left side is
to
be extended
over an
arbitrary
closed
curve,
and the
one on
the
right
over an
arbitrary
surface that has the above
curve as
its
boundary.
The orientation of the normal
in
the surface
integral
is
connected with the
direction in which the line
integral
is
taken
by
the
same
rule
as
above.
If
one
applies
the
equation
to
plane
surfaces of infinitesimal extension
in
both
dimensions,
one
obtains the
vector
equation
that
holds,
according
to Maxwell,
for
arbitrarily
fast
processes[10]
curl
@
if.
...(3a)
c