DOC.
377
MARCH
1912 277
Time
in field defined
by
the
postulate
that the
vel.
of
light c
depends,
indeed,
on
the
location,
but
not
on
the
direction.
c(xyz)
completely
determines the
gravitational
field.
By
definition,
c
is
determined
only
up
to
a
numerical
factor. All
equations
must be
constructed
accordingly.
Equation
of motion of
the
material
point
/
d_
dt
\
\
N
11
dc
dx
X
+
a
/
N1
_
q
m
dx
x
=
.
If
c
=
const.,
this
equation
becomes the
eq.
of motion of
the
ordinary theory
dt
of
relativity.
Righthand side, 1st
term
=
force
m
of
the
gravitational
field
on
the
point.
Second
term righthand
side
=
sum
of the
rest
of
the forces.
Force defined
by
force
dc
path[3]
=
energy
increment. The
force
on
the material
point
at rest is
m
.
You
can
cbe
see
that the dimension
of the force
is
different
from the
usual
one. Missing
is
a
factor
c,
which in
the
customary
theory,
where
c
is
constant,
can,
of
course,
also be
put
into the
denominator.
Every
force
or
energy
of
a
structure
(e.g.,
a
stretched
spring)
is
proportional
to
c,
and
thus
changes
from
place to
place.
Energy
of
the
point
mc
N
1
V
The
fit with
the
customary theory
of
relativity
is
staggering.
(For
example, one can
conclude from
these
eqs.
of
mot.
that the
gravitational mass
of
a
system
depends
on
the
kinetic
energy
of the relative motions of
its
parts
in
the
same manner as
the
system's
inertial
mass.)
The
electromag. equations
are
thus:
ae
tp
+
dt
=
curl
(c))
dt
0
=
div)


curl
(c@)
p
=
divS.
@
is
the field
strength,
defined
by a
transportable
spring
balance
provided
with
a
charge.
These
equations
are
deduced
from
the
equivalence
principle,
just
like
the
eqs.
of
mot.
of
the
material
point.
From them
follows
the
gravitation
of the
electromagnetic
energy,