332
EQUATIONS
FOR MOVING
BODIES
To
obtain the
expressions
for the
primed
quantities
as
functions
of
the
unprimed ones,
one
has to interchange
the
primed
and
unprimed
quantities and
to replace
v by -v.
The equations
(la)
to
(4a), which
describe
the
electromagnetic processes
relative
to
the
system
K,
have
the
same
form
as
the
equations (1) to
(4).
We
will
therefore
use
the
same
terminology
for the quantities
£,
D,
ft,
35, p,
s
as
for
the
corresponding
quantities
relative
to the
system
K'.
Thus
£, D,
j,
95, p,
s are
the
electric force, the dielectric
displacement,
the
magnetic
force, the
magnetic induction,
the
electric
density, the
electric
current
with
respect
to
K.
For
vacuum
the transformation
equations (6) and (7)
reduce
to
the
equations
for electric
and
magnetic
forces
found
earlier.1
It is clear that
by
repeated
application of
transformations
of
the kind
that
we
have
just
performed
one
must always
arrive
at
equations of the
same
form
as
the
original
equations (1) to
(4),
and
that for
such
transformations
equations
(6)
to
(9) apply,
since
formally
the transformation did
not make
use
of the
fact
that
the
matter
was
at rest
relative
to
the
original
system
K'.
We
assume
that the transformed
equations
(1a)
to
(4a) are
also valid if
the
velocity
of
the
matter
is
spatially
and
temporally
variable,
which
will
be
[6]
correct in
the first
approximation.
It is remarkable that the
boundary
conditions for the
vectors S,
®,
f,
25
at
the
boundary
of
two
media
are
the
same as
for bodies
at
rest.
This
[7]
follows
directly
from equations
(1a)
to (4a).
Just like
equations
(1)
to
(4),
equations
(1a)
to
(4a)
hold quite
generally
for
inhomogeneous
and
anisotropic bodies.
They
do
not completely
determine the
electromagnetic processes,
however.
Rather, relations that
express
the
vectors
®,
5,
and
$ as
functions
of
£
and
o
need to
be
given
in addition.
We
will
now
give
such equations
for the
case
that the
matter is isotropic.
If
we
first consider the
case
when
all
matter
is
at
rest
relative
to
K', then the
following equations
hold with
respect
to
K':
1A.
Einstein, loc. cit.,
p.
909.