DOC.
55
355
that
ro
vanishes
do
we
possess
definitions
on
which
(ideal)
measurements
of
these
quantities
could
be based, and
here
I have in
mind
those definitions
that
are
well
known
from
the
electrodynamics
of
bodies
at rest.
Therefore, if
upon
using
Minkowski's
equations
we
find that in
a
certain volume element of
the
body moving
with
velocity
rv
the field
vectors at
a
certain time
have
certain (vector) values
(E,
£,
S, ds, then
we
must
first
transform these
field
vectors to
a
reference
system
that is
at rest
with
respect
to
the
volume
element
in question.
Only
the
vectors
(£',
D', fj',
$3'
thus obtained
have
a
definite
physical
meaning
which
is
known
from
the
electrodynamics
of bodies
at
rest.
Thus,
Minkowski's
differential
equations
by
themselves
do
not have
any
content at
the points in
which
ro
^
0; however,they
do
so
when
taken
together
with
Minkowski's
transformation
equations and
with the stipulation that
for
the
case m
=
0
the
definitions
of
the
electrodynamics
of bodies
at
rest
must
be
valid for the field
vectors.
We
now
have
to
ask: Is Mirimanoff's
vector
£2
defined in
a
different
way
from
the
vector
we
have
denoted
by
#?
This is
not
the
case,
for the
following
reasons:
1. The
same
differential
equations and
transformation
equations
hold
for Mirimanoff's field
vectors
(E,
®,
£2, *8 as
for the
vectors
(E,
D,
Sj, *8
of
Minkowski's equations
(A).
2.
Mirimanoff's
vector
£2
as
well
as
the
vector ft
of
(A) are
defined
only
for the
case m
=
0.
However,
in that
case,
because of
Mirimanoff's
equation
£2
=
Sj

l^ßvo]
,
one
has
to put
£2
=
fj
=
field
strength; in exactly
the
same way,
in the
case
ro
=
0,
the
vector
S)
of
equations
(A)
is
equivalent
to
the field
strength in
the
sense
of the
electrodynamics
of bodies
at rest.
It follows
from
these
two
arguments
that Mirimanoff's
vector
£2
and
the
vector
io
of
(A) are
completely
equivalent.
4.
In order
to
compare
his
results
regarding
Wilson's
arrangement
with
those obtained
by
Mr. Laub
and
me,
the author
should
have
carried his consid
erations far
enough
to
arrive
at
relations
between
defined
quantities,
i.e.,
quantities accessible
to
observation
at
least in principle.
For
this
purpose
[4]