DOC.

10

MAY 1914

19

If

you develop only

the data

on

the

energy

line instead of

on

the

q,

p

plane

this

is not

so

clearly

obvious!!

£

=

a2/2p2

+

B2/2q2

+

cq2

+.....)

has likewise worked with such

a G(q,

p,

a).[11]

(4)

Whether the introduction

of

such

an a

in the

a

priori

G's contradicts the

spirit

of

Boltzmann,

since

the

system

does

of

its

own

accord.........

Please, please, dear,

dear

Einstein, delay

this

question

for

a

little bit

longer.-

I believe

myself entirely equal

to

this comment

as

well-but

communicating

this

in

writing

to

you

is

much

too

hard

a

task.-

So

simply accept provisionally my

statement of the

problem,

which bases itself

on

the introduction

of

such

a

G(q,

p,

a).

Then in

any

case

the

question remains,

of

course:

(5)

For

which

G(q,

p,

a)

is

the relation

udQ

=

dlgW

satisfied?

And

now

I

could

prove

the

following

statement:[12]

Let

i(q,

p, a)

be

the

2r-dimensional

volume

enclosed in

the

2r-dimensional

(molecule)

phase space

of

that

e(q,

p,

a)

=

const.

plane

which

goes

through

the

molecule

phase

point

q1....pr.

[For

Planck

resonators

i(q, p,

a, ß)

=

1/2(a2q2+ß2p2)/(aB/2n)

And let

G(q, p,

a)

be

any pure

function

of

i(q,

p,

a)

[such

as,

e.g.,

=

i2 or

lg

i

but

not iq

or

ai

+

i2

or

(a

+

q)i][13]

G(q,

p, a)

=

r(i).

For

every

such

G(q,

p,

a)

=

r(i(q,

p, a)),

the

accompanying

“most

probable”

distributions

f =

e

(i(q,P,a))

ƒ dTe~^£V(i)