544

DOC.

26 THE

PROBLEM OF SPECIFIC HEATS

The document

printed

here

is

the

facsimile

of Einstein's

published

lecture for the first

Solvay

Congress

at

Brussels,

30

October-3

November

1911

(Einstein 1914;

the French translation

appeared as

Einstein

1912a).

The

printed text

shows

only

minor variations with

respect to

a

typescript

(in

BBU)

of

the

original

German

text

for the

lecture;

these variations

are

indicated

in

the

notes below.

[1]For

a

discussion of Einstein's contributions

to

this

field,

including

references

to

the second-

ary

literature,

see

Vol.

2,

the editorial

note,

"Einstein's

Early

Work

on

the

Quantum Hypothe-

sis," pp.

134-148.

[2]See

Weber 1875.

[3]Since

the

1870s,

optical dispersion

had

played

an

important

role

as one

of

the clues to

the

internal

properties

of

molecules

and

atoms;

for

a

historical

account, see,

e.g.,

Buchwald

1985,

in

particular, chaps.

27-29. In

1907

Einstein had

applied

his

theory

of

specific

heat to

show that

for normal

temperatures

no

contribution

to

the

specific

heat

is to be

expected

from the

elec-

tronic oscillations

which,

according

to

Drude

1904a

and

1904b,

account

for

dispersion

in

the

ultraviolet;

see

Einstein

1907a

(Vol.

2,

Doc.

38), p.

187.

[4]Planck

1906, §§104-166

rather than

pp.

104-166,

as correctly

stated

in

the German

type-

script

and the French translation.

[5]The following

formula

corresponds

to formula

(194)

in

§123

of Planck

1906.

The

following

argument is

a

summary

of

§1

of Einstein

1905i

(Vol. 2,

Doc.

14).

[6]The

following argument

summarizes Einstein's

theory

of

the

specific

heat of

solids

as given

in Einstein 1907a

(Vol.

2,

Doc.

38).

[7]Nernst

1911c,

p.

274.

In Nernst's

diagram

the

axes

bear the

designations

"absolute

temper-

ature"

("abs.

Temperatur")

and "atomic heat"

("Atomwärme"),

respectively.

In Einstein

1912a,

the

curves

are incorrectly

labeled

ß

rather than

ßv.

[8]Madelung

1909.

(The

German

typescript

reads

"Sieveking"

for

"Madelung"

in

the

text.)

In

this first

paper

on

the

subject, Madelung compared wavelengths

calculated

on

the basis of

elastic constants

with

wavelengths

determined

by

Drude from the

electromagnetic

theory

of

dispersion.

[9]Sutherland

1910.

[10]Madelung

1910b.

Already

in Madelung

1909, Madelung

had

attempted to

determine the

elastic vibrations of

a crystal,

but

his

attempt

was

based

on

an

incorrect

assumption; see

Madelung 1910a,

p.

43.

In

Madelung

1910a

and

1910b,

he

developed

a new

approach

and for

the first time

compared

his

results with the

optical measurements

on

"residual

rays" ("Rest-

strahlen") performed

by

Rubens and collaborators.

[11]Einstein

1911b

(Doc.

13).

The

page

number

120

should be

170.

[12]The

following

is

a

summary

of results first

published

in

Einstein

1911b

(Doc.

13).

For

further comments

by

Einstein

on Madelung's

work,

see

Einstein

1911d

(Doc.

15).

[13]Einstein had earlier

explored

the

application

of dimensional considerations

to

solid

state

properties

in

Einstein

1911g (Doc.

21).

[14]Lindemann

1910.

For

an

earlier discussion

by

Einstein of Lindemann's

work,

see

Einstein

1911g (Doc.

21),

§3.

[15]The

table is

given

in

Nernst

1911c,

p.

275.

[16]Nernst

and

Lindemann

1911a.

In their

paper,

Nernst and Lindemann

attempt an explana-

tion of their formula for

specific

heats

(quoted by

Einstein

as

formula

[4a]

on

this

page)

by

a

new

quantum hypothesis,

according

to which the

potential energy

of

an

oscillator is

subdivided

in

"half

quanta"

while

its kinetic

energy

is divided in "full

quanta."

The

following arguments

in

Einstein's

text

summarize his alternative

approach to

an

explanation

of

the

deviations between

his

original theory

and

experiment, as given

in

Einstein

1911g

(Doc.

21), §2,

and

the correction

in

proof

at

the end of this

paper.

For

Nernst's reaction to this

approach,

see, e.g.,

the

following

quotation

from Nernst and Lindemann: "It therefore

seems

quite impossible

that in

cases

such

as

KCl and the

like,

the failure of formula

(1)

[Einstein's

formula for

specific

heat] can be

explained

by

the

impurity

of

the

oscillations

or

by

a

strong damping,

which,

by

the

way,

would

have

to

be rather

extremely strong"

("Es

erscheint also wohl

ausgeschlossen,

in Fällen, wie

KCl

und

dergl.,

das

Versagen

der

Formel

(1)

mit Unreinheit der

Schwingungen

oder sehr starker