DOC.

329

DECEMBER

1911 239

329.

From Fritz Haber

Dahlem

(Berlin), Königin

Luisestr.

14

19

December

1911

To

Prof. Dr.

Einstein,

Chair of Theoretical

Physics

at

the German

University, Prague

Highly

esteemed

Colleague:

It

is not

due

to

ungratefulness

but

to

ambition that

I

have not

written

to

you

earlier,

for

you

said

so

many

kind

things

in

your

letter[1]

that

I

felt

obliged

to

make

an

effort

to

justify

them.

You

will

read the

middling

result of

those efforts in

the

next

issue

of

the

Verhandlungen

der deutschen

physikalischen

Gesellschaft.[2]

The main

points

are

briefly

the

following:

A Coulomb

force

is

to be

introduced

in

the

equation

of

state

for solids.

The

value

for

the electrostatic

charge

of

the individual

electron

can

be

correctly

calculated

from the

compressibility

and the

atomic volume if

one assumes

that

this

Coulomb

force

opposes

the

compression.

The

solid

body

is

an

electronic

lattice in whose

meshes

the

positively

charged

particles

are

suspended.

The linear

oscillations of the

electrons

in this

lattice,

decomposed

in

two

cycles

of half

amplitude, produce

diamagnetism

in

the

presence

of

an

influence from

an

external

magnetic

field. With this

model,

one

obtains

exactly

the

right

order of

magnitude

and almost

the

right

magnitude

if

one

derives

the

susceptibility

from the

assumption

that

the maximum

amplitude is comparable to

the distance between

the

centers

of

two

atoms.

As in all of

these

arguments,

it

is

essential

for

the ratio of

the

maximum

amplitude

to

the

atomic

diameter

to

be

a

universal

quantity.

With

the

help

of the

same

model

one can

also

calculate the

paramagnetic

saturation from

the

frequency

of

the selective

photoelectric

ion

with

tolerable

accuracy.

This

picture

of the

electric solid

body

connects the

root

law with

your compressibility

law

and Lindemann's

formulas[3]

in

a

unified

way.

Apart

from

a

temperature-dependent

error,

the

quantity

hv

is

identical

with

the electrostatic

potential

of

the electron

in the

spatial

lattice of the

solid

multiplied

by

the

charge

of

the

electron.

Furthermore,

if the numerical values

are

correctly

chosen,

the

quantity

hv

agrees

to

within

3%

with

the heat of reaction

in all

of

the

examples

I calculated.

The

temperature

function

is

missing

in all

cases;

its

addition

would,

as

I believe,

completely

solve all difficulties.

From

a

theoretical

point

of

view,

I

regard

it

as a

great

lack

that

I do

not know

the

energy

equation

of

an

oscillator whose

frequency

depends

on

the

temperature.

This

is

characteristic of

the

majority

of natural

oscillators,

at

least of

the solid

ones.

It would be

of

the

greatest

value

to

know this

equation.

I

am

not

yet

finished with the

derivation of the thermal

effect

according

to

Richardson

from

the

same analyses,[4]

but

I

am

certain that

I will succeed in the

near