DOC.

16

MOVEMENT OF SMALL PARTICLES 235

560

A.

Einstein.

Bewegung

etc.

Umgekehrt

läßt

sich die

gefundene

Beziehung

zur

Be-

stimmung von

N

benutzen.

Man

erhält:

v_

Rl-

V

'

Snkf*

Möge

es

bald einem

Forscher

gelingen,

die hier auf-

geworfene,

für die Theorie der Wärme

wichtige

Frage

zu

ent-

scheiden!

[23]

Bern,

Mai

1905.

(Eingegangen 11.

Mai

1905.)

Published in Annalen

der

Physik

17

(1905):

549-560.

Dated

Bern,

May

1905,

received

11

May

1905,

published

18

July

1905.

[1]

For

a

discussion

of Einstein's

familiarity

with

previous

work

on

Brownian

motion,

see

the

editorial

note,

"Einstein

on

Brownian Motion,"

§

IV,

pp.

210-214.

[2]

At this

time,

the kinetic

theory

of

heat

was

not

universally accepted.

For

a

brief

discussion,

see

the editorial

note,

"Einstein

on

Brownian

Motion,"

§

II,

pp.

207-208.

[3]

This

equation was

first derived in

Van

't

Hoff

1887;

it

is

used in Einstein

1905j (Doc.

15),

p.

19,

in

a

calculation

of

molecular dimensions.

[4]

The

concept

of

free

energy

is

used in the

treatment

of

the osmotic

pressure

in

Helmholtz

1903,

part

II,

§

2; see,

in

particular,

pp.

321-

326.

[5]

Einstein

1902b

(Doc. 3),

Einstein 1903

(Doc. 4).

[6]

For the

role

of

this condition in

Einstein's

statistical

physics, see

Einstein 1903

(Doc. 4),

note

7.

[7]

This

expression was

earlier derived in Ein-

stein 1902b

(Doc.

3),

p.

432.

[8]

For the derivation

of

this

expression, see

Einstein 1904

(Doc. 5),

§

3.

[9]

Einstein

1903 (Doc. 4); see, in particular,

S

3.

[10]

For

a

derivation

of

this

equation

based

on

Boltzmann's

principle,

see

Einstein 1905i

(Doc.

14),

§

5.

[11]

The main results

of

this section

are con-

tained in

Einstein

1905j

(Doc. 15),

§

4.

[12]

For

a

discussion

of

thermodynamic equi-

librium conditions

involving

the notion

of

free

energy, see, e.g.,

Nernst

1898,

pp.

28-30.

[13]

The first

equation easily

follows from

an

expression

for the

entropy as

the

one

derived in

Einstein

1905i

(Doc. 14),

p.

142,

fn.

1.

[14]

For

a

similar

argument involving a

diffu-

sion

process

and motion

of

ions under the

action

of

an

exterior

force,

see

Einstein 1902a

(Doc.

2).

[15]

Kirchhoff

1897, p.

380. The formula

was

first derived in Stokes 1845. For

a

discussion

of

its

applicability

to

objects

of

microscopic

di-

mensions,

see

Fürth

1922,

pp.

58-60,

fn.

6.

[16]

For

a more

detailed discussion

of

this

problem,

see

Einstein 1906b

(Doc. 32), §.5;

see

also

Fürth

1922,

pp.

60-61, fn.

8.

[17]

f

on

the

right-hand

side

is to

be taken

at

the

time

t.

[18]

This

equation was

first derived in

Fick

1855,

in which the

analogy

with heat conduction

is

used. For

a

brief

discussion

of

various deri-

vations,

see Herzfeld

1921,

§

22.

[19]

A similar

correspondence

between the

ran-

dom

error curve

and the Maxwell distribution

was

noted

by

Maxwell

(Maxwell 1860).

[20]

The value

given

for N

is

close to that in

Planck

1901b, but differs from those obtained in

Einstein

1905j

(Doc.

15)

and Einstein 1906c

(Doc. 33).