DOC.

4

KINETIC THEORY LECTURE NOTES

243

[14]In

Boltzmann

1896,

p. 18,

the

term

"Moleküle

hervorgehobener

Art" denotes those mole-

cules

whose

velocity components

are

inside

an

infinitesimal volume element around

a

certain

value.

Einstein

apparently refers to

those molecules whose

velocities

are

inside the solid

angle

dK.

[15]The lack of

dependence

of the heat

conductivity

(as

well

as

the

viscosity) on

the

density

was

experimentally

established

by

Stefan,

and

by

Kundt and

Warburg

(see Stefan

1872a, 1876,

and Kundt and

Warburg 1875a,

1875b).

The friction

coefficient

turned

out to be

slightly depen-

dent

on

the

pressure (see Warburg

and

Babo

1882).

[16]It

is

not

clear

what

source was

used

for the numerical values cited here.

They are compati-

ble,

though

not

identical,

with the values listed

in

Landolt

and

Börnstein

1905,

1912

(with

the

exception

of the

viscosity

coefficient

9?

for

oxygen,

which these tables

give as

2.060

x

10-4

at

room temperature).

[17]See

note

15.

[18]For

a

discussion of

this

point, see

Stefan

1872b

and

Boltzmann

1896,

p.

85.

[19]Einstein's

treatment

of diffusion

follows Boltzmann

1896,

§13.

Note that there

are

also

related formulas

in his

Scratch Notebook

(Appendix

A),

[pp. 24-25].

In the

following

calcula-

tion Einstein

temporarily changes

the notation

for

the

polar angle

from $

to

(p.

He

returns to

the former notation

on [pp.

9-10].

[20]For

the numerical calculation of

D

Einstein

uses

c

=

5x

104 cm/sec

(valid

for

nitrogen

or

oxygen

at

room temperature)

and

A

=

10-5

cm,

which

is

the value for

oxygen; see

[p.

8].

[21]Landolt

and

Börnstein

1905,

p.

375,

give

D

=

0.171

for the diffusion of

oxygen

into nitro-

gen

at 760

mm Hg

and

0°C. See

also

note

16.

[22]The

following

calculation

goes

back

to Loschmidt 1865

and

is

discussed

in Boltzmann

1896,

§12,

and

in

Meyer, O.

E.

1899, part

1, §69.

The determination of molecular dimensions

was

also the

subject

of Einstein's doctoral

thesis;

see

Vol.

2,

the editorial

note,

"Einstein's Disserta-

tion

on

the Determination of Molecular

Dimensions,"

pp.

170-182.

Although

in

this

case

"wahre Grösse der Moleküle"

refers to

the actual

size

of

molecules,

on

other occasions Ein-

stein

used

the

same

expression (or alternatively,

"Grösse der

Moleküle")

as a

synonym

for

Avogadro's

number,

just

as

he

used the word "Molekül"

to

denote

a

mole.

See,

e.g.,

Einstein

1904

(Vol. 2,

Doc.

5),

pp.

358-359,

Einstein

to

Jean

Perrin,

11

November

1909,

and Einstein

1979, pp. 38, 44.

[23]See

Perrin

1914a

for

a

survey

of methods for

determining Avogadro's

number,

including

a

list of the various numerical values obtained.

[24]The

square

brackets

are

in

the

original.

[25]There

is

a

minus

sign

missing

in

front

of

the

right-hand

sides

of the last

two

equations.

Some of the minus

signs

in

the

preceding equations

are

corrected from

plus signs. Perhaps

Einstein started the calculation

anew on

the next

page

because of

this

sign

problem.

See

also

[p. 53],

which

is

part

of

a

loose sheet inserted

at

the end of the

notebook,

for

a

related

calculation.

[26]See

Kundt and

Warburg 1875a, 1875b,

and

Smoluchowski 1898.

In Einstein

1922,

p.

823,

this

experimental

verification

is

given importance

because it

was

the

first

time

that

a new

effect

had

been

predicted

by

the kinetic

theory.

For further

details,

see

Brush

1976, §13.8.

[27]In the formulas

below,

cos

(p

should be

cos

9

and T should

read F.

[28]See

note 26.

[29]Knudsen's

investigations

on

the

properties

of rarefied

gases were

reported

in

a

number

of

articles,

published mainly

in

the

Annalen

der

Physik

between

1909

and

1911

(see, e.g.,

Knudsen

1909a, 1909b, 1910a, 1910b, 1910c,

1911).

A

comprehensive report

on

his work

was

given

at

the

1911

Solvay Congress (Knudsen 1912).

For Einstein's remarks

on

Knudsen's

lecture,

see

Doc.

25.

For

a

general

overview of Knudsen's

investigations, see

also

Knudsen 1934.

[30]In

the

expression

below

(which is

Poiseuille's

law), A

denotes the

pressure

difference

along

the

tube,

and

R is its

radius.

See

[p.

54],

which

is part

of

a

loose sheet inserted at the end of

the

notebook,

for

a

derivation. The factor

n/4

should

be

n/8.

"Querschnitt"

should

probably

be

"Weglänge."

[31]Einstein

assumes

that

the

mean

thermal

velocity

c

of the molecules has

a

nonvanishing