DOC.

19

LECTURE

ON

FLUCTUATIONS

455

sion for the

energy density

p

of

black-body

radiation

and

derives

from this

expression its

entropy density

s

(and

hence the

entropy

S),

using

the relation

dp/T

=

ds

(T

being

the

tempera-

ture).

In the first

approach,

which

he deleted, he

chose the

temperature

T

as

the

integration

variable, while in

a

second

approach, starting

at

the bottom of

[p. 2]

and carried

through

to

the

end of the

calculation, he

chose

p

as

the

integration

variable. In the second

approach

the

temperature is

expressed

by

the relation

hv/kT

=

lg(1

+

f/p),

where

h is

Planck's

constant,

K

Boltzmann's

constant,

v

the

frequency,

and

f

an

abbreviation for

8nhv3-c3,

c

being

the

speed

of

light.

[7]Einstein

discussed the

subject

of thermal fluctuations of

a

body

immersed

in

radiation with

H. A.

Lorentz after the lecture and

in

a

letter

to

Lorentz

some days

later;

see

Einstein

to H.

A.

Lorentz,

15 February

1911.

He

presented

a

detailed

account at

the

Solvay Congress; see

Einstein

1914

(Doc.

26),

pp.

342-348. For

his

earlier

analysis

of

a

mirror

moving

in

a

radiation

field,

see

Einstein

1909b

(Vol.

2,

Doc.

56),

pp.

189-190.