DOCS.
412,
413
JULY
1912 319
412.
From Pauline Einstein
[Heilbronn,] 2 July
1912
My
dear
children,
I
am
very
worried because of
your eyes,
dear
Albert;
be
so good
&
write
at
least
a
postcard.
When
does
the
vacation, in
fact,
start?
&
will
you
then
go
immediately to
Zurich?
I will
probably
be able
to
go
to Switzerland in
August;
will
you
already
be
there
at
that time?
Many greetings
to all
of
you
,
Mama
413. To Wilhelm
Wien
Prague,
10
July [1912]
Highly
esteemed
Colleague:
If
we assume
that the
inertial
mass
of
lead
is
smaller than the difference
(mass
of
uranium)
-
(mass
of
the helium
produced)
by an
amount that
corresponds
to
the
energy
of the uranium converted
to
the kinetic
energy
of the
a-rays,
but
that
an
exact
balance
exists for
the
gravitational
mass,
then the
relative
difference between the
oscillation
periods
of
a
uranium
pendulum
and
a
lead
pendulum
in
the
same
gravitational
field must be
about
2
·
10-4,
which
could
be
easily
proved
Tlead
=
Turanium
(1
+ 2
*10-4).
To
be
sure,
the
thing
would be
totally convincing only
if oscillation
experiments
of
such
accuracy
could also be
set up
for helium.
However,
if
it
could be
demonstrated that the
relative
difference
between the oscillation
periods
Turanium
and
Tlead
does
not
substantially
exceed
10-5,
then
the
proportionality
of
inertial and
gravitational
mass
would
be
adequately proved.
Don't
you
think that
it would be
possible
to achieve such
great
experimental
accuracy?
In
any
case,
this would be
of
great importance.
With
best
regards, your
A.
Einstein
Postscript. Subsequently
there occurred
to
me a
much
more
sensitive
method for
ascertaining
an
inexact
proportionality
between the inertial and
gravitational mass
of
uranium and
lead, if such exists.
For
in this
case
the
centrifugal
force
exerted
upon
bodies
on
account
of Earth's rotation
would not be
proportional
to
gravitation
for all bodies.
The
apparent plumb
directions of
a
uranium
plumb
and
a
lead
plumb
would have to
deviate
from
each
other.
Further,
a
torsion balance
with
a
piece
of uranium and
a
uranium
lead
piece
of
lead
placed on
its
beam
would have to
experience
a
torque
C *