DOC.
38
OCTOBER
1914 45
38. From Adolf Schmidt
(Potsdam)
cur[rently] Berlin,
31
October
1914
Highly
esteemed
Colleague,
You
can
get
over
having
once
in
passing on some
occasion
or
other
been
inspired
with
an
idea similar
to
one
others
had
already
had. When
a long
time
ago
I
once
discovered
an
interesting
and useful
important
principle
on
spherical
functions[1]
about
which
not
even
the
slightest
mention
was
made in
any
textbook,
it
was
much
more disheartening
for
me finally
to discover
that
Franz Neumann
had
already proven
it
almost
50
years
beforehand.
Besides, your
article
(with some
comments
to be
incorporated at
the
begin-
ning)
certainly
does
seem
to
me
very
much worth
publication.[2]
The characteristic
which,
as
mentioned,
is
closely
connected
to
the character
of the
correlation
is
not
new, as
you
know.[3]
The
observation
about I
(along
with
the
optical analogy)
also
is
not
new;
for
this
is
covered
by
the
function introduced
by
Schuster under
the
term
“periodo-
gram.”[4] (As
far
as
I
can
remember,
Schuster’s
paper appeared
about
10
years
ago
in the
Proceedings
or
Transactions
of
the
Royal Society.)[5]
But
to
my knowledge
what
is
new,
at least in the
literature, is
the correlation
between
the
two
that
you propose.
Although
this
does not
provide
any
advan-
tage
in
general
toward
the
practical (numerical)
execution
of
the
analysis,
it
is
nonetheless
interesting
theoretically
and
may certainly
also be
of practical
use
at
one
time
in
special cases.
If
I
may
make
a
comment[6]
[By
the
way:
Does
the
final formula I(x)
=
4-n/
'k(A) cos(xA)dA
not follow
directly
from
2T(A)
= f0°°
I(x)
cos(xA)dx
ac-
cording
to
Fourier’s
integral
law?]
on
the
representation,
I would
think that the
introduction
of
x(oo)
could
present problems
to
some
readers.
It
is not
quite
clear
to
me,
at
least,
how it results
uniquely
and
clearly
from
the
general
definition of
x(A).
Would it not be
simpler
to
indicate
the
constant
in
(3a)
directly,
which
ap-
parently
comes
to
A20/2,
and
to set p(A)
=
x(A)-1/4A20?[7] A0
is
all too well-known
as
the
mean
value of
F.
Of
course,
x(oo)
=
1/4A20
could also be made
plausible;
but
I
have
not
succeeded in
achieving
this in
a
convincing, simple
manner.
However,
perhaps I
am
overlooking
the
nearest at hand!
What
you say
about the
planimeter,
the
description
of which
I
sent
you,
thor-
oughly
applies.[8]
It
just
yields
ƒydx.
But
you
have also
understood
me
quite
correctly
with
regard
to
my
suggestion
of
a
mechanical calculation of
ƒy1y2dx.
Unfortunately,
I
have
no more
descriptions
left
that
I
could have sent
you
of
a