354
COMMENT ON
MIRIMANOFF
Minkowski,
while
the
remaining
three
differential
equations
do not
contain
f)
and already
have
the
form of
the
corresponding
equations of Minkowski.
Indeed,
the author
says
himself that his
vectors
(£,
V,
Q,
and
93
transform
like the
vectors usually
denoted
by
(B,
®,
Jo,
93.
2. Similarly,
the
relations
between
the
vectors containing
material
constants
(e,
ß
and
a) do
not
differ
from Minkowski's
corresponding
relations.
I.e., the author
starts from
the postulate that for
a
coordinate
system
instantaneously at
rest
relative
to
the
system
point
under
consideration, the
equations
D
= eCE, Sj =
i
»,
3
=
r£
ß
should
hold;
if
one
bears
in
mind
that the (author's)
vector
fj
is identical
with the
vector
£2
for
ro
=
0,
and
that
£2
plays
exactly the
same
role
in
the author's differential
equations and
in his transformation
equations
as
m
does
in
Minkowski's
equations
(usually denoted
by
f), then
one
realizes that
these
equations, too,
agree
with
Minkowski's
corresponding
equations, except
that the notation
f)
is
replaced
by
the notation
£}.
3.
Thus,
it
has been
shown
that Mirimanoff's
quantity
£}
plays
the
same
role in all his
equations
as
the
quantity usually denoted
by
Jo
and
called
"magnetic
force"
or "magnetic
field
strength."
Nevertheless,
Mirimanoff's
equations would
have
a
different
content
than
those
of
Minkowski
if
by
definition
the quantity
£2
of Mirimanoff
would
have
a
different
physi-
cal
meaning
than the
quantity usually denoted
by
i.
In order
to
reach
a
conclusion in
that
matter,
we
first
ask
for
the
meaning
of the
vectors
(E,
D,
io,
93
i..
Minkowski's equations
curl
= h
If+1'
(A)
curl s
=
-
\ If
div
V
=
/?,
div
93
=
0
One
has
to
admit
that these
vectors have not
yet
been expressly
defined for
the
case
that the
velocity
rv
of matter
differs
from
zero;
only
for the
case