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