DOC.
544 MAY 1918 563
must
be
taken.
The
boxed
equation produces
a
transcendental relation
between
u0
and
r0.
This
relation
is
formulated
most
elegantly
in
the
following
way.[5]
If
r
= a*
is
the
value for which
(64)
1/h2
vanishes,
and
one
sets
h2
1
+
2/xq
1
-
x
X
(.X2
+
x
+
j),
p
=
37
2
+
7a:-3
’
then
x
=
r0/a*
satisfies
the
equation[6]
p
+
1/hf1xhdp
=
x3;
given
r(0
7
1),
it
always
has
one
and
only
one
solution
x.
For
an
infinitely
thin
mass
zone,
an
infinitely large
mass
density
u0 results,[7] so
the total
mass
contained in
the
zone assumes a specific
finite value
#0;
if
I
have not miscalcu-
lated:
4V3
•
1/kVA,
whereas
the
mass,
in
the
case
that the
space
is filled
uniformly
at
density
A,
comes
to:
n.1/2kVA.[8]
This
result,
that the
mass
contained in
the
zone
does not
drop
to
0
even
when its thickness
approaches
0,
ought
to
meet
with
your
approval.[9]
Regarding
the
“point mass
solution”
(65), a
zonal horizon of
mass can
also
be constructed;[10]
asymmetric
around
equator
void
instead
of
equator
void void
point mass
point mass
For
the
[spherical]
mass
cap
(A),
the
density
must be
u1
A,
so
that
the
pressure
p
is
positive
in
the
interior;
for
if
the
radius
=
1
is
inserted:
(pos.)
A
-
Hi
z
-
zi
A
+
2ßi
z\
(neg.)
(~+-~-
\~
/10
=
1