DOC.

11

ARGUMENTS

FOR MOLECULAR

AGITATION

285

Published

in

Annalen der

Physik

40

(1913):

551-560. Dated

Zurich,

December

1912,

received

5 January 1913, published

20

March

1913.

[1]For

a

brief

account

of Einstein's collaboration with Otto

Stern,

see

the editorial

note,

"Einstein

and

Stern

on

Zero-Point

Energy,"

pp.

271-272.

[2]For

Planck's "second

theory,"

see

Planck

1911a,

1911b,

1912,

and

1914a. For

a

historical

discussion of

this

theory,

see

Kuhn

1978, chap. 10,

and Needell

1980,

chap.

4.

[3]See

Nernst

1911,

p.

270,

and

Nernst and Lindemann

1911,

p.

825.

For Einstein's earlier

criticism of Nernst's

approach,

see

Einstein 1914a

(Vol.

3,

Doc.

26), pp.

350-351.

[4]For

Einstein's earlier work

on

the

specific

heat of

solid bodies,

see

Einstein 1907a

(Vol.

2,

Doc.

38).

[5]Einstein

had earlier raised

this

question

in his

lecture

to

the

first

Solvay Congress

(see

Einstein 1914a

[Vol.

3,

Doc.

26],

p.

339).

[6]This

formula

was

earlier derived

in

Einstein 1914a

(Vol. 3,

Doc.

26), §4.

[7]See

Landolt and Börnstein

1912,

table

58,

for values of molecular diameters from

gas

theory.

[8]Eucken 1912.

[9]"-1"

in

the first

equality

should

be

"+1."

[10]See

Eucken

1912,

p.

149.

[11]For

alternative

interpretations

of Eucken's

results,

see

Ehrenfest

1913

and Holm 1913.

For

a

historical review of Holm's

work, see

Needell

1980, pp.

260-262;

for

a

contemporary

review,

see

Eucken

1914,

in

particular

p.

374.

[12]A

factor

2kp/h

is

missing

in

front of the second

integral. "-1"

in

the

last term

on

the

right-hand

side should

be

"-1/4."

[13]See Sackur

1912,

p.

414.

[14]Equation

(6)

is

used

in

the calculation of

the entropy, not equation

(5).

[15]Einstein

and

Hopf

1910b

(Vol.

3,

Doc.

8).

[16]Einstein

and

Stern did

not immediately accept

the

result that

a zero-point energy

of

hv

was

needed

to

derive Planck's

law. See the

editorial

note,

"Einstein and Stern

on

Zero-Point

Energy,"

p.

272.

[17]Planck

1913.

[18]A

factor

v

is

missing

on

the left-hand

side

of this

equation.

[19]See Curie

1895,

pp.

396-397.