DOC. 56 THE RADIATION PROBLEM 551

Published in

Physikalische

Zeitschrift

10 (1909):

185-193.

Dated

Bern,

January

1909,

received

23

January

1909,

published

15

March 1909.

[1]

Lorentz 1908b.

[2]

Jeans

1908. See also

Jeans

1905c.

[3]

Ritz 1908b.

[4]

For

a

discussion

of

the works

cited,

see

the

editorial note,

"Einstein's

Early

Work

on

the

Quantum Hypothesis," pp.

144-146, and Kuhn

1978,

pp.

189-205.

All

of

the works cited

by

Einstein

refer

to

Lorentz 1908a,

to

which

Ein-

stein refers in the

slightly

revised version, Lo-

rentz

1909a

(see

Einstein

to

Hendrik

Lorentz, 13

April

1909).

[5]

See Ritz

1908b,

p.

904.

[6]

Ritz

1908b,

p.

904.

Beginning

with

"ohne,"

Ritz indicated

emphasis by using

spaced type

("Sperrdruck")

in the remainder

of

the

quotation.

[7]

Ritz offered

a

rebuttal to

Einstein's

argu-

ment

(see

Ritz

1909).

These and other

points

of

difference between Einstein and Ritz

are

noted

in Ritz

and

Einstein 1909

(Doc. 57).

[8]

Einstein and Hopf

disposed

of

this

doubt in

Einstein and

Hopf 1910a and 1910b.

[9]

Einstein

1905i

(Doc. 14).

[10] "Ev"

should be "Ev".

This

equation ap-

pears

in

Planck

1900e, p.

241.

[11]

Planck

1900a and 1906c.

[12]

Lorentz

1908a;

Jeans restated his law in

Jeans

1908, p.

853.

[13]

Planck

1906c.

[14]

For

a

discussion

of

the

nature

of

the

"Lücke"

("gap"),

see

the editorial

note,

"Ein-

stein

on

the Foundations

of

Statistical

Physics,"

pp.

48-50. The

references

to Gibbs

are

Gibbs

1902 and 1905.

[15]

The

disagreement

between the

"Jeans-Lo-

rentz"

law and

"all

radiation observations,"

as

well

as

the contradiction with

everyday experi-

ence,

were especially emphasized

in Lummer

and

Pringsheim 1908. Jeans

responded

in

Jeans

1908,

p.

853,

that

the

formula

does

agree

with

observations

of

long wavelength

thermal radia-

tion.

[16]

Planck

1906c, pp.

177-179.

[17]

Klein

1974b,

p.

190, suggests

that

the fol-

lowing

discussion

is

related

to

Einstein's

prom-

ise

to

show that statistical

probability

is

suffi-

cient

for the discussion

of

thermal

processes

(see

Einstein

1905i

[Doc. 14],

p.

140).

For

an

earlier

version

of

the

following

definition,

see

Einstein

1903

(Doc.

4),

pp.

171-172.

[18]

For further discussion

of

this

point, see

Einstein

1910c,

pp.

1276-1277.

[19]

See

Einstein

1906b

(Doc. 32),

pp.

372-

373,

where this

assumption

leads

to

an expres-

sion that

accounts

for Brownian motion. See

also the editorial

note,

"Einstein

on

Brownian

Motion,"

pp.

213-214.

[20]

The

bar

above

tv appears

to

be

a

printer's

error.

[21]

For

an

earlier derivation

of

this

formula,

see

Einstein

1903

(Doc. 4);

Einstein 1904

(Doc.

5), pp.

354-355; and Einstein 1905i

(Doc. 14),

pp.

140-141.

[22] See, e.g.,

Boltzmann

1877;

Planck

1900d,

pp.

242-243;

Planck

1906c, pp.

137-140.

[23]

Boltzmann 1877.

[24]

Boltzmann 1896.

[25]

See Einstein 1906d

(Doc. 34),

pp.

201-

202.

Planck

1906c,

pp.

178-179, discusses this

difficulty.

[26]

Einstein 1906d

(Doc. 34);

Einstein 1907a

(Doc. 38).

[27]

See Einstein 1905i

(Doc. 14),

pp.

132-

133,

and Einstein 1907h

(Doc. 45),

pp.

372-

373.

[28]

This is

Einstein's

first

use

of

h

to denote

what

is

now

called

"Planck's constant."

[29]

Einstein 1905i

(Doc. 14), especially pp.

139-144.

[30]

Wien's

formula

is

valid for

large

values

of

vlT.

[31]

H0

and

n0

are

the

equilibrium

values

of

H

and

n,

respectively.

[32]

For

an

earlier

version

of

this

argument, see

Einstein

1907b

(Doc. 39),

pp.

570-571.

[33]

In this

equation,

the absolute value

of

'cPJ\

should be

taken,

since this

quantity

is

negative

because

the

entropy

is

a

maximum.

[34]

In this

equation,

the absolute value

of

-rrr

should be

taken,

and in this and the fol-

lowing equation e2

should

be

e2.

This

expression

for

the

mean

square energy

fluctuation

is equiv-

alent

to

the

one given

in Einstein 1904

(Doc. 5),

p.

360.

fife-J

o

[35] Eq. (230) on p.

156

of

Planck

1906c is

an

expression

for the

entropy density

8

per

unit

vol-

ume

per

unit

frequency.

The

equivalent

expres-

sion for the

entropy

a,

defined

by

Einstein

above,

may

be written

8irkv2

f

a

=

cJp

3 H1

+

S^v3)108!1

+

8^v3)

c3p c3p

8uhv3^0^8irhv3

where

p

is

the

energy density per

unit

frequency.