246 DOC.

4

KINETIC THEORY LECTURE NOTES

the editorial

note,

"Einstein

on

Brownian

Motion," pp.

206-222. The

treatment

given

here

differs

from earlier

ones by

Einstein and

is

instead

quite

similar

to

Langevin's approach

in

Langevin

1908.

In the

expression

below,

p

and

p0

denote the

mass-density

of the

particle

and of

the

liquid,

and

V is

the

particle's

volume.

[80]In 1908

and

1909

Perrin had

published a

series

of

papers reporting

measurements

of the

vertical

distribution of

suspended particles

under the influence of

gravity. See

Perrin

1912

and

1914b

for

reviews.

The

granules

of resin

employed

by

Perrin

were commonly

used

in

experi-

ments

on

Brownian

motion;

see, e.g.,

Nye 1972, pp.

102-103.

[81]Einstein

uses

Stokes's

law

(F

=

6nrjvP,

with F the

force

on

the

particle,

P

its radius,

and

n

the

viscosity

of the

fluid).

[82]The

Brownian motion of

rotating particles is

discussed

on

[p. 45].

[83]For

a

numerical

example, see,

e.g., Langevin

1905, pp.

120-121,

where

a

is

found

to

be of

the

order of

1/100

for

oxygen

at

0°C and

a

magnetic

field of

10,000

Gauss.

[84]See

Weiss 1907.

A

German version of

his

theory is

given

in Weiss 1908.

[85]See

Weiss

1907, 1908.

[86]See

Weiss

1908,

pp.

366-367.

[87]In the

original,

the words "scheinbar

unmagnetisierten"

have been inserted

by

interlinea-

tion;

the

word "nicht"

is

once

more

interlineated

in

a

second revision.

[88]For

a

discussion of this

point,

see

Weiss

1908, pp.

364-365. The M referred

to in

the

previous

sentence

denotes the molecular

magnetic

moment

rather than the molecular

weight.

[89]Einstein's

first treatment

of Brownian motion of

rotating particles

is in

Einstein

1906b

(Vol.

2,

Doc.

32).

The

treatment

given

here

differs

from the earlier

one

and instead

follows

the

approach

taken above

on

[pp.

41-42].

For

experimental investigations

on

rotational Brownian

motion,

see

Perrin

1909.

[90]This

formula

is

the

analog

of Stokes's

law

for

rotating spheres.

In Einstein

1906b

(Vol.

2,

Doc.

32), p.

379, Kirchhoff

1897 is

given

as

a source

for this

expression.

[91]The

same

notation

is

used

in

Einstein

1903

(Vol.

2,

Doc.

4), §6,

and Einstein

1910d

(Doc.

9),§1.

[92]The

square

brackets

are

in

the

original.

[93]The

notes

below

refer to

the electron

theory

of metals

as

set

forth

in

Drude

1900a, 1900b,

and

in

which thermal and electrical

phenomena were

accounted for

through

the

postulated

existence

in

metals of

freely

moving

electrical

charge

carriers.

See

Kaiser

1987

for

a

historical

review.

For

a

discussion of Einstein's

early

interest

in

the electron

theory

of metals

and

further

references, see

Vol.

1,

the editorial

note,

"Einstein

on

Thermal, Electrical,

and Radiation Phe-

nomena,"

pp.

235-237.

[94]Thermoelectric

effects

were

among

the main research interests of

Weber,

Einstein's

teacher,

and Einstein

may

have done

experimental investigations concerning

the

Thomson

effect in

Weber's

laboratory.

For further

details,

see

Vol.

1,

the

editorial

note,

"Einstein

on

Thermal, Electrical,

and Radiation

Phenomena,"

pp.

235-237.

[95]The

illustration of

irreversibility

alluded

to

here

is

related

to

an

argument

Einstein

gave

in

Einstein

et

al. 1914 (Doc.

27),

the discussion

following his

1911 Solvay

lecture,

on

pp.

356-

357.

The

same

argument

was

outlined

in

Einstein

to

Michele

Besso,

second half

of

August 1911,

and

in

Einstein

to

Michele

Besso, 11 September

1911.

[96]The

preceding

and

following page

of the

original

notebook

are

omitted. The former

contains calculations

that

seem

to be

related

to

the

quantization

of the motion of

a

rigid

rotator,

and the

latter,

a

fragment

of unrelated calculations.

[97]The

calculation

on

[p.

52]

should

presumably

be

seen

in

connection with the derivation

of the

pressure

of convection

in

an

ideal

gas using

the

virial theorem;

see [flyleaf]

and

[p.

1].

The virials of intermolecular

forces

are

discussed

in Boltzmann

1898, §§52-56,

where

a

general

intermolecular

repulsive

force

as a

function of radial distance

r

is

denoted

by f(r).

[98]The

square

brackets

are

in

the

original.

[99]The

square

brackets

are

in

the

original.

[100]The

material

on [pp.

53-54]

is

on

both sides of

a

loose sheet inserted

at

the end of the