582 DOC.
561
JUNE
1918
extended
over
the
region
of
integration
*4
We consider
specially[4]
A4
=
J
fd4dxidx2dx2dx4
=
J
Ja
dx4
-
Ja
Ax4
because
dj/dx4
=
0.
dx
4
One has
JU=-~-,...
z~x4
(2)
and the
question
arises,
from which
transformation
law does
this
quantity follow?
In
order to find
this,
I
assign
quantities
Ax1, Ax2,
Ax3
to
Ax4
so
that
(Ax1,
Ax2, Ax3,
Ax4)
form
a
four vector.
To
arrive
at
this,
I
take
Ax4
to be
large
against
the
system’s
spatial
dimensions,
which
can
be indicated
by
the
diagram.[5]
(x4)2
/
If
now (x1)1, (x2)1, (x3)1, (x4)1
is
a
point
within
the
system
at
time
(x4)1,
(x1)2, (x2)2, (x3)2, (x4)2
is
a
point
within
the
system
at
time
(x4)2,
then the
differences
Ax1
=
(x1)2
-
(x1)1
etc.