108

DOC. 153 MAY 1909

One

could

argue

that the

conclusions

referring

to

black

radiation

in

the ether remain

valid

no

matter

how small

the material

mass

of

electrons, and

that

they

can

therefore

probably

also

be

applied

to

the

limiting

case

where

this

mass

is

zero.

However,

this

involves

a

rather

objectionable

passage

to

the

limit.

For that

reason

I

have

taken

up

the

question

again,

and

even

when

taking

into account the circumstance

pointed

out

by van

der

Waals,

I

succeeded

in

arriving

at

a

Gibbsian

ensemble

and at

my

earlier

conclusions

(Jeans's formula)

once

I

assumed that

it

is

permissible

to

neglect

the

terms with

q22,

q2q2[7]

and

q2q3

(in

this

case

the

above

equations serve

for

the determination of

the

coordinates

q2,

expressed

in

terms

of the

q1

and the

q3).

This

is

permitted

if

the

amplitude

of the

oscillations

of

the

electrons

(or

the radius of

curvature

of the

curved

parts

of their

trajectories) is

very

small

compared

with

the

wavelengths

under

consideration.

Thus,

basically

I

introduce

the

same

simplifying

assumption

that

is

often

used

to keep

the

equations

linear. To

be

sure,

the motions of

electrons

may

indeed

show

small

deviations

from

the formulas obtained

in this

way,

but,

when all

is

said

and

done,

one can

state

that

a

direct

and

simple

derivation of

the

radiation formulas

from the

electron

theory

in its

customary

form

is

very unlikely.

The

small

deviations

(related

to

the

magnitudes

of

second

order

with

respect to

the

q),

which

were

just

mentioned,

could

modify

a

radiation formula

a

little,

but

one can hardly expect

that

they

would

bring

about

a

complete change

in

the

form of the

formula

(from

Jeans's

to Planck's). Thus, just

like

you,[8]

I

come

to

the

conclusion

again

that

we

must resort to

considerations of the

kind

used

by

Planck.

For the

most

part,

I

completely

agree

with

your

discourse

on

this

matter

in

your

last

article,[9]

as,

for

example,

with

your

calculation

of the deviations

from the

mean

values

(most probable

values),

be

it

in the

energy

distribution

or

in

the radiation

pressure.

However,

I

would like

to

add

some

further remarks.

I perceive

it

as a

problem

in

Planck's

theory

that

the

state

of

the

radiation

in the

ether

turns out

differently

in it

depending

on

whether

the

energy

exchange

between

ponderable

matter

and

ether

is

mediated

by

"resonators"

or

"free electrons." With the

latter, whose

existence in

metals

can hardly

be

denied,

there

can

be

no

question

of

a

definite

frequency v,

and

thus

an

energy

element hv

also does

not

make

sense.

I

cannot arrive

at

any

conclusion

other than that

black

radiation

must correspond

to

Jeans's

equation

if

the

energy exchange

is

mediated

by

free

electrons. And

so we

would have the

peculiar

result that

if free

electrons

and Planck resonators

were

present

simultaneously,

the ether

would be

placed

into

one

state

by

the

energy

transmitters of

the

one

kind,

and

into

another,

different

state

by

the transmitters of the other

kind. This

does

not

seem very

plausible;

it

would also

contradict the

general thermodynamic law, according

to

which

the

equilibrium

between

two

phases A

and B

is independent

of the

nature

of

a

third

phase

that

we

interpose,

or

also

the notion that

the

expression

for

the

entropy

of

a

system

contains

(apart

from

the

universal

constants

like

the

gas

constant)

only

constants

related

to

the

properties

of the

system. According

to

this

latter

way

of

viewing

the

matter, it

is

unlikely

that

the h

that

appears

in the

entropy

of the ether

would