44
DOC.
37
OCTOBER
1914
Your
integrating apparatus
appeals
to
me
very
much.
Although,
as
it
is
described,
it
only
delivers
y
dx;
but
you
intended-if
I
have
understood
you
correctly-to turn it into
a
measuring
device for
J
y1y2dx
which
you
activate
through
engaging a
second
adjustable
friction clutch
so
that
the rotation of
the
planimeter
disk
is not
simply
proportional
to
dx,
but
propor-
tional
to
y2dx;
then,
of
course,
the
rotation of
the little
counter wheel becomes
proportional
to
y1y2dx.
Another
possibility
with which
you
could
manage
with
a
friction element
but
which would
require
two
integral operations
instead
would be
the
following:
You
have
an
instrument
in which
the
distance of
your
friction roll to
the
center
of
your
counter disk is
proportional
to
y2
(whether
this
is
easily realizable,
I
do not
know).
With
such
a
device
you
could
measure
f(y1+y2)2dx
and
ƒ(y1-y2)2dx,
thus
also
the
difference[6]
2/y1y2dx.
The construction
of
such
a
device
does
not
appear
to
me
to
be
particularly dif-
ficult.
When
we
meet
again,
we
could,
if
you
have
the
inclination
and the
time,
weigh
the
various
possibilities against one
another.
I
ask in advance for
your
forbearance, knowing
well
that
I
am a low-grade
dilettante
in such matters.
With
regards
from
your very
devoted
colleague,
A.
Einstein.