DOC.
4
THEORY OF STATIC GRAVITATIONAL FIELD
111
§2.
Remarks about the Content
of the
Derived
Equations
At the
suggestion
of
P.
Ehrenfest,
I
will
refer
to
the
spring
balance that
I used
for the
intuitive
interpretation
of the field
vectors
in the last section
as
the
"pocket" spring
balance. In
general,
the
designation "pocket"
shall be used for
physical apparatus
that
[11]
is
thought
of
as being
taken
to
locations of different
gravitational potentials,
and the
indications of which
are
always
used
regardless
of the
magnitude
of
c
at
the location
at which
they
then
happen
to
be
found.2
Thus,
the clock that
gives
the
"light
time"
can
be
referred
to
as
the
"pocket
watch,"
the
spring
balance furnished with
a
unit of
electricity
at
the
point
of
contact
can
be referred
to
as
the
"pocket
field
meter," etc.
It follows from the earlier
paper
that the indication of
a
"pocket spring
balance"
[12]
does
not
measure directly
the force it
exerts. Instead,
this force has
to
be
set
equal
to
the indication of the
pocket spring
balance
multiplied
by c.
From this it follows
immediately
that the
ponderomotive
force exerted
on a
unit
of
electricity
at rest
in
K
is not to
be
set
equal
to
s
but
to
c
. s.
The
same applies
to the
field
vector s.
Since,
according
to
the
third of
equations
(1a),
rot(cs)
=
0 in
a
static electric
field,
and hence the
line
integral
of the
vector cs
vanishes
along
a
closed
curve,
we
see
that it
is
impossible
to
obtain work
indefinitely by carrying a quantity
of
electricity
over a
closed
path.
Now
we
formulate Coulomb's law for
a
space
of
constant
c.
It follows from the
last of
equations
(1a)
that the field of
a point charge e
is
given by
|s|
=
e/4tr2,
if
v
[13]
denotes the distance from the
point charge.
If
a
second electric
mass
e' is
present
in
this
case,
then the force
acting
on
it
is
equal
to
|s|
or cee'/atr2,
and
thus,
like
every
force of
an
arbitrary pocket system
in
a specific
state,
according
to
the earlier
paper,
proportional
to
c.
The
following
is
closely
connected with this result. We
bring
one
of the
two
exactly
identical condensers C and C' with
plates
a,b
and
a',
b',
respectively,
to
a place
of
gravitatonal potential c,
and the other
to
a
place
of
gravitational
potential
c'.
Let
a
be
conductively
connected with
a'
and b with b'. If
we
charge
the
condensers, then,
because of
rot(c@)
=
0,
the
charge
of the
two
condensers will
not
be the
same; instead,
=
c@'
and,
because of
p
=
div
S,
also
ce
=
c'e, if
e
and
e'
denote,
respectively,
the
charges
of the
two
condensers.
It follows
from the
expression
found for Coulomb's law that
it is not
1/2(@2
+
2), but
the
expression
c/2
(®2
+
$2) that
we
have
to set
equal
to
the
2The
designation "pocket"
shall indicate that these
things are
not used in
one
location
only
but
that, instead, they can
be
transported.