108 DOC.

5

GENERAL MOLECULAR

THEORY OF HEAT

of

a

distribution

of

microstates

over a hypersur-

face

of

constant

energy.

[14]

It

is

not clear

just

what Einstein

meant

by

the

term

"kinetische Atomtheorie"

("kinetic

theory

of

atoms").

The term

suggests a

kinetic

theory,

like the kinetic

theory

of

gases,

but

ap-

plicable

to

any system

with

an

atomistic

struc-

ture,

that

is,

possessing

a

finite

number

of

de-

grees

of freedom. See the editorial

note,

"Einstein

on

the Foundations

of

Statistical

Physics,"

note

59.

[15]

See Boltzmann 1898a,

§

42.

What

was

"geläufig" ("customary")

was

Boltzmann's

proof

of

the

equipartition

theorem

(see

Einstein

1902b

[Doc. 3],

note

22);

Boltzmann did

not

go

on

to

estimate the value

of

K

(or,

equivalently,

the Boltzmann

constant,

k-see

Einstein 1902b

[Doc.

3], note 25),

as

Einstein did below.

[16]

Einstein 1903

(Doc. 4).

The

incompressi-

bility

condition,

E(d(pv/dpdv) =

0, is

not stated

explicitly

in

the cited

paper;

this

is

Einstein's

first

mention

of

it

in

print.

See Einstein 1903

(Doc.

4), note

7.

[17]

The first

exponent

in

both the

numerator

and the denominator

on

this

line

should be

-O(x1

...

xn)/2KT0; a

minus

sign

should be

added to the

exponent

inside the

integrals

in both

the

numerator

and the denominator

on

this line

and the

next.

The factor

preceding

the left-hand

side

of

the next line should be 3/2.

[18]

Boltzmann 1898a.

[19]

This

is

the

same

value

of

R given

in

Planck

1901b,

p.

564,

which

is

probably

Einstein's

source (see

note 5).

[20]

Nowhere in

Meyer,

O. E.

1877, 1895,

or

1899 does

one

find the value

of

N

given

here.

However,

exactly

this value

is

given

in

Planck

1901b,

p.

566,

where Planck cited

Meyer,

O. E.

1899,

p.

337.

At

the

time

of

this

paper,

there

was

considerable

uncertainty regarding

the

value

of

Avogadro's number,

N. For

a

discus-

sion

of

the

problems

involved in its determina-

tion, see

the editorial

note,

"Einstein's

Disser-

tation

on

the Determination

of

Molecular

Dimensions,"

pp.

179-182.

[21]

Einstein's

value for

K

yields a

value of

1.30

x 10-16,

for Boltzmann's

constant. Planck

calculated

the value 1.346

x 10-16

with the

help

of

his

formula for the

energy spectrum

of

black–

body

radiation

(see,

e.g.,

Planck

1901b,

p.

565).

The

agreement

between the two values

is

surprising,

given

the

uncertainty

in the value

of

N

(see note 20).

[22]

In this and in three

of

the

following

four

equations,

wE should be

w(E).

[23]

In the bracketed

expression,

E2

should

be

E2.

[24]

The first term

on

the

right-hand

side

should be

E2.

[25]

The first term

on

the left-hand side should

be

E2.

[26]

The term

on

the

right-hand

side should be

E2.

[27]

See

Stefan

1879 and Boltzmann 1884.

[28]

Einstein's

value for

c

is

the

same as

that

given

in

Planck

1901a,

p.

562, which, in turn,

cites Kurlbaum

1898, p.

759. For

K,

Einstein

used the value 6.5

x 10-17

calculated above

on p.

359.

[29]

The

equation xmT

=

constant, a special

case

of Wien's

displacement

law

(see

Wien

1893),

had been derived earlier

by

Einstein's

ETH

physics professor,

H. F.

Weber,

from his

semi-empirical

radiation law

(see Weber,

H. F.

1888;

for the

early history

of

the

displacement

law,

see

Kangro 1976,

chap.

3).

The value of

the

constant

used here

appears

to

be the

average

of

the value

(0.294) given

in Lummer

and

Pringsheim 1899,

p.

218,

and the value

(0.292)

given

in

Paschen

1901b,

p.

657. See

Paschen

1901b for

a summary

of

the

controversy over

the

value

of

this

constant.

[30]

In

a

letter

to

Conrad Habicht

of

15

April

1904,

Einstein

wrote

about

this result:

"I

have

now

found

in the

simplest way

the relation be-

tween

the

magnitude

of

the

elementary quanta

of

matter

and the

wave lengths

of radiation"

("Die

Beziehung

zwischen der Größe der Elementar-

quanta

der Materie und den

Strahlungswellen-

längen

habe ich

nun

in höchst

simpler

Weise

ge-

funden").