586
DOC.
564 JUNE
1918
restrict
myself
in
the
following
to
the
special theory
of
relativity,
the
drag
of
the
grav.
terms has
no
value).
Then
the
mean
value for
a
is
a
=
1
fGdT
Jo
adT,
G
a
phys.
sm[all]
world domain. If
one
applies
this
averaging process
to electro-
magn.
field
equations, upon
the
basis
of
a
model of matter
consisting
in
uncharged
molecules,
convective
charges &
conduction
current,
then the
resulting
equations
between
the
mean
values
are:
P0 =
electricity density
at rest
uu
=
dxu/ds
=
four-component velocity
[Vierergeschwindigkeit].
Fuv
=
dqu/dxv-dqv/dxu
(a)
dFuv/dxv-dMuv/dxv
=
Ju
(b)
dFuv/dxo+dFvo/dxu+dFou/dxv
=
0 (c)
Muv
=
p0/2(uvxu-uuxv)
(d)
An
essential
precondition
for
eq.
(d)
is that, for
the
phys.
small interval of
a
molecule,
ƒ pop^dr
=
0
applies.[2]
Derivation of
eq. (d)
&
of the
term
dMuv/dxv
in
(b)
is
but
a
transposition
of the
considerations
by
H. A.
Lorentz in
Encycl. d.
math.
Wiss. V
14,
N°
27
and
28
from
space
into
a
world.[3]
If
static
matter
Fuv
is identified
as {b,
e}
and
Muv
as {m,
p},
then
(b)
(c)
represent
Maxwell’s
eq.
&
eq.
(d) degenerates
into
the
familiar
expressions[4]
P
=
N
J2
ekx
k=1
n
j
&
m
=
NJ2
o]
k=i1
of
electron
theory. Qu
is
a
vector
&
scalar
pot.
To
determine the
force
density
K0,
I take
a
straightforward
course.
Let G
be
a convex
world
domain
that
intersects
arbitrarily
many
molecules. The force