xxiv INTRODUCTION TO

VOLUME

3

William Sutherland

had been

working

for

some

time

on a

theory

of solids

composed

of

particles interacting

through

electrical

forces,

and Einstein built

on

Sutherland's

work. The

recent

work of Sutherland

on

the connection

be-

tween

optical

and elastic

properties

of

solids

was

made

possible by

Heinrich

Rubens's measurements

of

the

frequencies

of

the

residual

rays,

measurements

that

involved

techniques

for

working

further into the infrared

than

had

previ-

ously

been

possible.[39]

What

was new

and

unique

in Einstein's

approach

was

the

linking

of

specific

heats

to

the

optical

and elastic

properties,

a

linking

made

possible by

his

introduction of

quantum ideas.

In

fact,

despite

some

rather

rough

approximations

in his

calculations,

Einstein found

a

"truly

surprising"

agreement[40]

between

his

frequency

calculated from the

com-

pressibility

and

one

determined from Nernst's

specific

heat

data

for

silver,

the

one

substance

so

far for which

both

compressibility

and the

temperature

dependence

of

the

specific

heat had been measured.

Early

in

May 1911,

a

month

or so

after his

move

to

Prague,

Einstein

re-

ported

the results of further work

on

atomic vibrations in

solids.[41] Once

again

the incentive for his

investigation

had been Nernst's

experimental

find-

ings.

This

time, however,

the situation had become

more

complicated.

Nernst

and his coworkers had extended their

specific

heat

measurements

from

liquid

air

temperatures

down

to

the

temperature range

made available

by using

liquid hydrogen.

The results still confirmed Einstein's

theory qualitatively,

but

at

very

low

temperatures

the

experimental

curves

did

not fall off

so

quickly

with

decreasing

temperature

as

Einstein had

predicted

in

1907.[42]

In

his

new

paper

Einstein

argued

that

one

could not

really

treat

the

atoms

as oscillating

independently

of

one

another;

the oscillations of

an

atom

were

not

monochro-

matic and

were,

in

effect, subject

to

strong damping,

since

an

atom

within

one

cycle

could

exchange an appreciable

fraction of

its

energy

with

its

neighbors.

Einstein

offered

no

viable

way

of

dealing

with these

coupled

atomic

motions.

He did

provide

dimensional

arguments

in

support

of his work of

the

previous year

and also

in

support

of

still

another

method for

determining

the vibration

frequency,

a

method

given by

Nernst's student and collabo-

rator,

F.

A. Lindemann,

who related the

frequency

to

the solid's

melting

temperature.[43]

At the

same

time

that

Einstein

was

preparing

this

paper,

Nernst and

[39]See

the

notes

to

Einstein

1911b (Doc.

13);

see

also Einstein

1911d

(Doc.

15).

[40]"Diese

nahe

Übereinstimmung

ist wahrhaft überraschend." Einstein

1911b

(Doc.

13),

p.

174.

[41]Einstein

1911g

(Doc.

21).

[42]Nernst

1911c.

Nernst had

already pointed

out

this

discrepancy

in

1910. See

Nernst

1910b.

[43]Lindemann

1910.