46 FOUNDATIONS OF

STATISTICAL PHYSICS

microcanonical

ensemble,

as

Boltzmann

proved

in the

Gastheorie,[40]

but also

for

a canon-

ical ensemble.[41]

Third and most

important,

Einstein

was working on a theory

of molecular

forces.[42]

The second

of

his two

papers on

this

subject,

Einstein 1902a

(Doc. 2),

rests

upon

what he

calls

a hypothetical

extension

of

the second law

of

thermodynamics

to

mixtures,

the indi-

vidual

components

of

which

are subject

to

arbitrary

external conservative

forces.[43]

At

issue

is

the

employment

in

thermodynamics

and kinetic

theory

of

idealized devices, such

as semipermeable

membranes,

which had been used

quite successfully

in

studies

of

dif-

fusion, dissociation,

and dilute

solutions,

in

spite

of

doubts about

even

the

approximate

feasibility

of

such

devices.[44]

Einstein

proposed

to

replace semipermeable

membranes

by

the

equally

idealized,

but

theoretically more

tractable,

device

of

arbitrary

external

conser-

vative forces.

A proof

of

the

validity

of

the second law when such forces

are

employed is

one

of

the

chief

results

of

his first

paper

on

statistical

physics.[45]

One additional

source may

have

impelled

Einstein to seek

a more general

foundation

for statistical

physics, independent

of

special assumptions

about the nature

of

the elemen-

tary

constituents

of

physical systems or

the interactions

among

them: his

reading

of

Ostwald and

Mach,

both

of

whom

were

well

known to

be

skeptical regarding hasty as-

sumptions concerning

the existence

of

molecules

or atoms.[46]

Given

Einstein's

firm

com-

mitment to the atomic

theory

(at

least in

the

form

of

the

assumption

that

mechanical

sys-

tems

possess only a

finite number

of

degrees

of

freedom)

and to

Boltzmann's

approach

to

statistical

physics,

the

skepticism

of

Ostwald and Mach could well have been

an

induce-

ment to free the foundations

of

statistical

physics

from

dependence upon

detailed and

debatable

hypotheses

about the constitution

of

the

systems

that

statistical

physics

aims to

describe.[47]

[40]

See Boltzmann

1898a,

p.

101.

[41]

See Einstein 1902b

(Doc. 3),

§

6. It

is

possible that,

in the doctoral dissertation that he

submitted in

1901,

Einstein's

interest in Boltz-

mann's

work

on

kinetic

theory

and in

Drude's

work

on

electron

theory may

have coalesced

with his work

on

molecular

forces;

for

a

discus-

sion

of

the

1901 dissertation,

see

the editorial

note,

"Einstein's

Dissertation

on

the Determi-

nation

of

Molecular

Dimensions,"

pp.

174-

175.

[42]

For discussions

of

this

work, see

Vol.

1,

the

editorial

note,

"Einstein

on

Molecular

Forces,"

pp.

264-266,

and,

in this volume, the

editorial

note,

"Einstein

on

the Nature

of

Mo-

lecular Forces,"

pp.

3-8.

[43]

See Einstein 1902a

(Doc. 2), p.

799.

[44]

For

a

review

of

this

topic, see

Planck

1891.

[45]

See Einstein 1902b

(Doc. 3),

p.

433.

[46]

See

especially

Ostwald

1893

and

Mach

1896. For evidence

that

Einstein read Ostwald

1893,

see

the

apparent

references to

it in

Ein-

stein

to

Mileva

Maric,

10

April 1901 (Vol.

1,

Doc.

97),

and in Einstein to

Wilhelm

Ostwald,

19

March

1901 (Vol.

1,

Doc.

92),

in which Ein-

stein claimed that his work

on capillarity

had

been

influenced

by

Ostwald. For evidence that

Einstein read

Mach, see

note

18 (for

an

early

expression

of Einstein's

high opinion

of

Mach,

see

Einstein

1916c).

[47]

Many years

later,

Einstein said about his

papers on

statistical

physics:

"My

principal

aim

in this

was

to

find facts that would

guarantee as

much

as possible

the existence

of

atoms

of

defi-

nite finite

size"

("Mein

Hauptziel

dabei

war

es,

Tatsachen

zu finden,

welche die Existenz

von

Atomen

von

bestimmter endlicher Grösse

mög-

lichst sicher stellten")

(Einstein 1979,

p.

44,

translation,

p.

45).

Einstein went

on

to

say

that

it

was

his work

on

Brownian

motion,

together

with

Planck's

determination

of

Avogadro's

con-

stant from the

Rayleigh-Jeans

radiation

law,

that

convinced the

"numerous

skeptics"

("zahl-

reichen

Skeptiker"),

including

Ostwald and

Mach,

of

the

reality

of

atoms

(Einstein 1979,