212

REVIEW

OF

PLANCK'S

LECTURES

[6]

deductive

way,

only using

theoretical aids

adequately supported

empirically

[7]

-the author

uses a

hypothesis supported only

by

analogy-every impartial

reader will

find that

a

high

probability

attaches

to

the result obtained.

The

course

of

the

investigation

is

as

follows: First, the oscillation

equation

of

a

resonator of

small dimensions

and

small

damping,

located in

a

radiation field, is established

on

the basis

of Maxwell's equations.

Then

one

determines the

mean

energy

of

a

resonator

in

a

stationary

radiation field with

the aid of the oscillation

equation, and, using

the

second

law,

the

"temperature

of the resonator"

as

function

of

the

above

universal function.

[8]

This reduces the

problem

of

energy

distribution in the

normal

spectrum

to

the

task

of

determining

the

entropy

of

a

system

consisting

of

a

large

number

of

radiation

resonators

of the

same

frequency.

To

solve the latter

problem,

it is first

explained, based

on

Boltzmann's

[9]

works,

that

one

is led

to

a

correct

determination

of

the

entropy S

if

one

puts S

=

k

log

W,

where

k

denotes

a

(universal)

constant and

W

the

number

of "complexions." The

latter quantity represents the multiplicity of all

those

possible

distributions of the

elementary

variables that

belong

to

the

complex

of

observed

quantities to which

the

entropy

S

corresponds.

In

order

to

be

able

to

determine the

quantity

W

by

counting,

one

must

divide the

whole

available

region

of the

state

variables into discrete

elemen-

tary regions. In general,

the result

depends on

the absolute

magnitudes as

[10]

well

as on

the ratios

of

the

magnitudes

of

these

elementary regions. While

for

the determination

of

the

quantity

W

of

a

resonator

system one

chooses

the

magnitude

ratio

of

the

elementary

regions

as

in

a

sinusoidally

oscillating

structure

in the

theory of

gases,

one

chooses-in

contrast to

the

assumption

on

infinitesimally small

elementary

regions

generally used

until

now

in the

[11]

theory

of gases-the

elementary

regions to

be

of finite

magnitude

(=

hv),

where

v

denotes the

frequency

and

h

a

universal

constant;

hv

has

the

dimension of

energy. The

author

points repeatedly to

the

necessity of

introducing

this universal

constant

h

and

emphasizes

the

importance

of

a

physical

interpretation

(not

given

in

the

book)

of

the latter.

From

the

expression

for the

entropy

S,

obtained

in

the

way

indicated,

one

then derives the familiar Planck radiation

formula,

u

=

8ihv3

1

C3

hv/k-T