DOC.

14

89

the radiation

may

be

considered

as

the

most

disordered

process

imaginable.2

He

found

~Ev

=

SvPv

[14]

Ev

is here the

mean energy

of

a

resonator

with the

proper

frequency

v

(per

oscillation

component),

L

the

velocity

of light,

v

the

frequency,

and

pvdv

the

energy

per

unit

volume

of that

part

of the radiation

whose frequency

lies

between

v

and

v +

dv.

If,

on

the

whole,

the radiation

energy

of

frequency

v

does not

con-

tinually decrease

or

increase,

we

must

have

f1

-1

=

\

•

R

8lfV2

m K

=

If

~W

1

•

[15]

2This

assumption

can

be

formulated

as

follows.

We

expand

the

Z-component

of

[12]

the electrical force

(Z)

at

an

arbitrary

point

of the

space

considered in

a

time interval

between

t

=

0

and t

=

T (where

T

shall denote

a

time

period

that is

very

large

relative

to

all

pertinent oscillation

periods)

in

a

Fourier series

V=oo

Z

= ^

ky

sin(2jz/

j

+

ay)

,

v-\

where

Av

0

and

0

av

2t.

If

one

imagines

that

at

the

same

point

in

space

such

an

expansion

is

made

arbitrarily

often

at

randomly

chosen

initial

points

of

time, then

one

will

obtain different

sets

of values for the

quantities

Av

and

av.

For

the

frequency of

occurrence

of

the various

combinations of values

of

the quantities

Av

and

av,

there will exist, then,

(statistical) probabilities

dV

of the

form

dW

=

f(A1A2...o1o2...)dA1dA2...da1da2...

The

radiation is in the

most

disordered

state

imaginable when

f(A1,A2...a1,a2...)

=

A1(A1)F2(A2)...f1(a1).f2(a2)...

,

i.e.,

when

the

probability of

a

specific value

of

one

of the quantities

A

or

a

is

independent

of the values taken

by

the other

quantities

A

and

a,

re-

spectively.

Hence,

the

more

closely

fulfilled the condition that

the individ-

ual pairs of quantities

Av

and

av

depend

on

the emission

and

absorption

processes

of

particular

groups

of

resonators,

the closer

to

a

"most

disordered

state

imaginable"

the radiation is

to be viewed

in

our case.

[13]