350
DOC.
361 JULY
1917
361.
From Hans
Thirring[1]
[Vienna,
11-17
July
1917]
As Prof.
Frank[2]
may
have told
you,
the
young
Viennese school
is
examining
the
theory
of
gravitation
closely. My
friend Flamm had
a
little
notice
appear
in
the
fall in
the
Phys. Zeitschr.,
is
presently
working on
a new
publication,[3]
and
I
likewise have been
doing
a
few
calculations in
the
short leisure hours left to
me
beside
my
technical duties in
the
military.[4]
Before
publishing
my results,
I
would like to send
you
a
little
report
in the
hope
of perhaps
receiving
another
stimulus
directly
from
you-we
have
been
orphaned
here in
Vienna,
as
you know,
ever
since Hasenöhrl’s
death
and
must
help
ourselves
as
best
we
can.[5]
I
am
primarily occupied
with the
relativity of
rotational
motion-a
problem
that
naturally must
be
regarded
as
solved
by your theory.
For
ex.,
the
fact
that
for
an
observer
positioned
on
the
Earth’s surface
the
same
laws of
motion
are
valid
both
in
system
(I):
rotating
Earth,
fixed-star
sky
at
rest,
and
in
system (II):
Earth
at
rest, rotating
fixed-star
sky,
is
guaranteed,
of
course,
by
the
general
invariance
of
the
field
and
motion
equations.[6]
The matter
thus
actually
should be
settled.
But there
are
many physicists
(particularly
experimentalists)
for whom
this result
is
too
mathematically
abstract
and who would
like to have
proven by
a
concrete
example
that
according
to
your theory
the
rotational
motion of distant
masses
is
capable
of
causing
a
kind of force
like
centrifugal
force
on a
mass-point
at rest.
In order
to
show
this,
I
proceeded
as
follows: I
imagine
an oo
thin
hollow
sphere
of radius
a
(the
fixed-star
sphere)
at
L
velocity
w
rotating
around the
Z-axis,[7]
and calculate
the
field at
the
origin
x
=
b;
y
=
z
=
0;
b
a, according
to
the
method
of
approximative
integration of
the
field
equations
(Berl.
Ber.
1916,
p.
688).[8]
Excepting
the
higher-order
terms
in
b/a,
I
obtain;[9]
g44
-
-
1
+
Air
a
1
+
u2a2 +
10
a2
M
is
the
mass
of the hollow
sphere.
The
significant
term
(all
the
rest
are
obviously
constant) is:
kM1/4na10 .
w2b2.
Through
differentiation
d2x/dt2
=
const.
w2b
results
for
the
acceleration.[10]
This
completely corresponds
to
the
centrifugal
force,
by
which
the
equivalency
of
systems
I and
II
from before
are
thus
proven
with
a
simple example. Now,
the
force
on a
point
outside
of
the
equatorial
plane
was
of
further interest
to
me.
For
the
test point
with the
polar
coordinates
r
and
d,
(p
=
0):[11]
k
M
g44
-
-1 + ---\
1
+
u) a
47T a
2
"2