180

REVIEW OF BROWNIAN

MOTION

Doc. 32

ON

THE

THEORY OF BROWNIAN MOTION

by

A.

Einstein

[Annalen

der

Physik

19

(1906):

371-381]

Soon

after the

publication of

my

paper

on

the

motion

of

particles

[2] suspended

in

liquids

demanded

by

the molecular

theory

of heat,1

Mr. Siedentopf

[3] (Jena) informed

me

that

he and

other physicists-Prof.

Gouy

(Lyon)

probably

having

been

the first-had

become

convinced

by

direct observation that the

so-called

Brownian motion

is

caused

by

the

random

thermal

motion

of the

liquid's molecules.2

Not only

the qualitative

properties of

Brownian motion

but also the order of

magnitude

of

the

paths

traversed

by

the

particles

are

in

full

agreement

with the results of the

theory.

I

shall

not

compare

here the

meager

experimental

material available

to

me

with the results of the

theory,

but shall leave this

comparison

to

those

engaged

in

experimental investigation

[5]

of

this topic.

The

present

paper

shall

supplement

my

above-mentioned

paper

in

several

points.

We

will derive here

not only

the translatory, but

also the rotational

motion of

suspended

particles for the

simplest

special

case

when

the

particles

[6]

have

a

spherical

shape.

We

will also establish

the shortest observation times

for

which the result

given

in the

paper

is still

valid.

We

will

use

here

a more

general

method

of derivation,

partly

to

show

how

Brownian motion

relates

to

the

foundations of the molecular

theory

of heat,

and

partly to be

able

to

derive the

formulas for

the

translatory

and

for the

rotational

motion

by

a common

investigation.

Let

us assume

that

a

is

an

observable

parameter

of

a

physical

system

in

thermal

equilibrium and that

the

system

is

in so-called indifferent

equilibrium

at every

(possible) value of

a.

According

to

classical

thermodynamics,

which

makes

a

fundamental

distinction

between

heat

and

other kinds

of

energy,

spontaneous

changes

of

a

do not

take

place, but

according to

the molecular

theory

of heat

they

do. In

the follow-

ing

we

will

investigate

what

laws

these

changes

must obey according to

the

[1]

[4]

1A.

Einstein,

Ann.

d.

Phys.

17

(1905): 549.

2M. Gouy,

Jour.

de

Phys.

7,

No. 2

(1888):

561.