DOCS.

283,

284

SEPTEMBER

1911

205

Now to

entropy

and

probability.

You

write

very amusingly:

"The

case

with

the

particle

...

is

really very

instructive,

but

evidently

I

have

not

yet

quite

understood what

the

point

is"(!)[11]

In the

case

of

a

particle,

the

point is

to know

the

probability

for

a

volume

element dr

at height

z.

If dr

is

realized

by means

of

a rigid

screened

box,

the

osmotic forces do

not do

any

work

when

the

box

is

raised

infinitely slowly.

If the

entropy

and

probability are

referred

to

this

area r,

which

is

always

of

the

same

size,

Boltzmann's

equation

holds

exactly.

The

same

is true

if

r

is

a

function of

z.

Only

one

must

then

take

into account

the

osmotic work

when

one

determines

S.

We

see

that

the strict

application

of the

principle is

possible only

if

the

state

region

can

be

realized

physically

and

changed

oo

slowly.

But

in

the

case

of

an isochorically

heated

subsystem, one

does

not

have the

means,

in

each

and

every

state,

for

preventing

this

subsystem from leaving a

certain

energy

interval 8E.

But the

exact values

of

S

and W would have to

refer

to such

an

interval,

in such

a

way

that

they

depend

not

only on

E,

but

also

on

8E.

Of

course,

the

region

to which

one

refers

S

and

W

can

also be

unbounded

(in

the

direction of smaller

entropy

values);

such

a

choice

is

sometimes

even

advantageous (osmotic pressure),

but

it

is

not,

in

principle,

essential.-

Think about

metals!

Something

sensible

must

be found

there. The

current

state

of

affairs

is

unbearable.[12]

Many

thanks

to

Anna

and

Vero

for

their

friendly

note.

Best

regards

to all

three of

you

from

your

Albert

Enclosed

is

a

note

from

my wife.[13]

284. From

Willem Julius

[Utrecht]

17 September

[191l][1]

I hope

that

you

will

not

take

it amiss

that

a

letter

in the

name

of

our

faculty

is

being

sent to

you

in

spite

of

your

response to

my

preliminary

inquiry.[2]

It

was

simply

unthinkable

not to

mention

your name

at

the

meeting,

and

people

were

generally

of the

view that

the

reason

you

had

given

for

your

refusal

was

not

of

such

a

fundamental

nature

that

it would be

pushy or even impermissible

on our

part to

make

one more

attempt

to

win

you over.

To

all

appearances,

mathematical

physics can

thrive in

the

Netherlands;

our faculty

wishes

to

work

actively

at creating

the conditions

that

would

most

favor such

a

development,

and

is

therefore

turning

to

you.-

I have

now

studied

at

a more

leisurely pace your

noteworthy paper,

the

proofs

of

which

I

had

returned,

unfortunately,

in

too

great

a

hurry.[3]

I would

not

presume

to

make

any

objection to

the theoretical

analysis.

I would

only

like to ask

whether

it

might

be

possible

that the relative

change

of

frequency

expected

for

the sun-earth

system

is

no