172

DISSERTATION

ON

MOLECULAR

DIMENSIONS

or

ions

of

the

solute.[19]

Einstein's

dissertation contributed to the solution

of

this

prob-

lem.[20]

He recalled in 1909:

At the time

I

used the

viscosity

of

the solution to determine the volume

of

sugar

dissolved in water because in this

way

I

hoped

to take into account the volume

of

any

attached

water molecules.

Ich habe seinerzeit

zur Bestimmung

des Volumens des in Wasser

aufgelösten

Zuckers

deswegen

die

Viskosität

der

Lösung benutzt,

weil

ich

so

das Volumen

eventuel angelagerter Wassermoleküle mit

zu

berücksichtigen hoffte.[21]

The results obtained in his dissertation indicate that such

an

attachment does

occur.[22]

Einstein's

concerns

extended

beyond

this

particular question

to

more general

problems

of

the foundations

of

the

theory

of

radiation and the existence

of

atoms. He

later

empha-

sized:

A

precise

determination

of

the size

of

molecules

seems

to

me

of

the

highest

importance

because

Planck's

radiation formula

can

be tested

more

precisely

through

such

a

determination than

through

measurements

on

radiation.

Eine

präzise Bestimmung

der Grösse der Moleküle scheint mir deshalb

von

höchster

Wichtigkeit,

weil durch eine solche die

Strahlungsformel von

Planck

schärfer

geprüft

werden kann als durch

Strahlungsmessungen.[23]

The dissertation

also

marked

the first

major success

in

Einstein's

effort

to find

further

evidence

for

the atomic

hypothesis,

an

effort that culminated

in

his

explanation

of

Brown-

ian

motion.[24]

By

the end

of

1905 Einstein had

published

three

independent

methods

for

determining

molecular

dimensions,

and

in

the

following years

he found several

more.[25]

[19] Bousfield 1905b,

a study

of

the relation-

ship

between

the sizes

of

ions and the electrical

conductivity

of

electrolytes,

calls this the most

important open problem

of

the theory

of

aqueous

solutions

(p. 257).

For

contemporary

reviews

of

research

on hydrates, including a history

of

this

problem, see

Washburn 1908 and

1909,

and

Dhar

1914.

[20]

Einstein

1906a is cited in Washburn

1909,

p.

70,

and in

Herzfeld 1921,

p.

1025,

as provid-

ing

evidence

for the existence

of

an

association

between

a

solute molecule and molecules

of

the

solvent.

[21]

Einstein to

Jean

Perrin, 11

November

1909. The

importance

of

this

problem

for Ein-

stein is confirmed

by a

letter

that

Einstein wrote

to

Ludwig

Hopf

before 12

January 1911, em-

phasizing

the

significance

of

his

equation

for the

coefficient

of

viscosity,

"because

from

viscosity

one can

learn

something

about the volume

of

dissolved

molecules"

("weil

man aus

der Vis-

kosität

etwas

erfahren kann über das Volumen

gelöster Moleküle").

[22]

See Einstein

1905j (Doc. 15), p.

18.

[23]

Einstein

to

Jean

Perrin,

11

November

1909.

[24]

In his

Autobiographical Notes,

Einstein

stated that his work

on

statistical

mechanics,

which

preceded

his dissertation, aimed

at

find-

ing

"facts

...

that would

guarantee as

much

as

possible

the existence

of

atoms

of

definite finite

size"

("Tatsachen

...

welche die Existenz

von

Atomen

von

bestimmter endlicher

Grösse

mög-

lichst sicher stellten")

(Einstein 1979,

p.

44;

translation,

p. 45).

For further discussion

of

Ein-

stein's

interest in the

problem

of molecular

di-

mensions,

see

the editorial

notes,

"Einstein

on

the Foundations

of

Statistical

Physics,"

p.

46,

and

"Einstein

on

Brownian Motion,"

pp.

206-

222.

[25]

In addition to the method

published

in the

dissertation, other methods

for

the determina–