570

DOCS.

550,

551 MAY

1918

result

is

that

a glowing body

has

an

outer

layer

of

electrons,

which has

a

“surface

pressure” (negative

surface

tension)

still

dependent

on

temperature.

On curved

surfaces,

a

“capillary pressure”

is

produced

entirely as

in

capillarity,

just of

the

opposite sign.

The

thermodynamics

of

this outer

layer

can

also be

developed

easily.[3]

With

cordial

regards, yours,

M.

von

Laue.

551.

To Hermann

Weyl

[Berlin,]

31

June

[May]

1918[1]

Dear

Colleague,

I

am glad

that

you

have

put

the

zone

affair in

order,

now.[2] The

result

of

your

calculation

now

corresponds completely

with

what had

to

be

expected.[3]

You

probably

already

sent

the

relevant correction to

Springer;

I

asked him to

wait

with the

printing

until

your

decision

arrived.[4]

Let’s

hope

the abominable

paper

shortage

does not

delay

the

appearance

of

your

book![5]

Now

to

the

question: spherical

or

elliptic.[6] I

do not

think that there

is

a

possi-

bility

of

really deciding

this

question

through

speculative

means.

A

vague feeling

leads

me

to

prefer

the

spherical one, though.

For

I

sense

that

those manifolds

are

the

simplest

in which

any

closed

curve can

be

contracted

continuously

to

one

point.

Other

people

must have

this

feeling

as well;

since otherwise

the

case

where

our

space

could be Euclidean and finite would

surely

also have been

taken

into

consideration

in

astronomy.

The two-dimensional Euclidean

space

would then

have

the

connectivity

properties

of

an

annulus.

It

is

a

Euclidean

plane,

on

which

every phenomenon

is

doubly periodic,

where

points

lying on

the

same

period

grid

are

identical. In

a

finite Euclidean

space

there

would be

three

kinds of closed

curves

not

continuously

reducible to

one

point. Analogously,

an

elliptic space,

in

contrast

to

the

spherical one, possesses

one

sort

that

cannot

be

contracted

continuously

to

one

point;

that

is

why

it

appeals

to

me

less

than the

spherical

one.

Can it be

proved

that the

elliptic space

is

the

only variety

of

the

spherical

space

that

can

be

obtained

through

the

addition

of

periodicity properties?

It

seems

to be

so.

Now

once again

to

your

Academy

paper.[7]

Could

one

really charge

the

Lord

with

inconsequence

for

not

seizing

the

opportunity

you

have found

to

harmonize

the

physical

world?[8] I

think

not. In

the

case

where

He

had

made

the

world

according

to

you, Weyl

II would have

come

along,

you

see,

to address Him

re-

proachfully thus:[9]