176 DISSERTATION ON

MOLECULAR

DIMENSIONS

tion, acknowledged

that Einstein had chosen the

topic

himself and

pointed

out that

"the

arguments

and calculations

to be carried out

are

among

the most difficult in

hydrodynam-

ics"

("die

Ueberlegungen

und

Rechnungen,

die durchzuführen

sind,

gehören zu

den

schwierigsten

der

Hydrodynamik").

The other

reviewer,

Heinrich Burkhardt,

Professor

of

Mathematics at the

University

of

Zurich,

added:

"the

mode

of

treatment

demonstrates

fundamental

mastery

of

the

relevant mathematical methods"

("die

Art der

Behandlung

zeugt von

gründlicher Beherrschung

der

in Frage

kommenden mathematischen Metho-

den").[52] Although

Burkhardt checked

Einstein's

calculations,

he overlooked

a signifi-

cant

error

in

them.[53]

The

only

reported

criticism

of Einstein's

dissertation

was

for

being

too

short.[54]

Compared

to the other

topics

of

his research at the

time,

his

hydrodynamical

method

for

determining

molecular dimensions

was a

dissertation

topic uniquely

suited to the

em-

pirically

oriented Zurich academic environment.

In

contrast to

the

Brownian motion work,

for which the

experimental

techniques

needed to extract information from

observations

were

not

yet

available,

Einstein's

hydrodynamical

method for

determining

the

dimensions

of

solute molecules

enabled him

to

derive

new empirical

results from data in standard

tables.

IV

Like

Loschmidt's

method based

on

the kinetic

theory

of

gases,

Einstein's method

depends

on

two

equations

for two

unknowns, Avogadro's

number N and the

molecular

radius

P.[55]

The first

of Einstein's

equations

(the

second

equation on p.

21

of Einstein

1905j [Doc.

15])

follows from

a

relation between the coefficients

of

viscosity

of

a liquid

with and

without

suspended

molecules

(k*

and

k,

respectively),[56]

k*

=

k(l

+

9)

,

(l)[57]

where

(p

is

the fraction

of

the volume

occupied by

the solute molecules. This

equation,

in

turn, is

derived from

a study

of

the

dissipation

of

energy

in

the fluid.

[52]

Both

quotations

are

from

the Gutachten

über

das

Promotionsgesuch

des Hrn.

Einstein,

20-24

July

1905

(SzZSa,

U 110

e 9).

[53]

For

a

discussion

of

the

discovery

of

this

error

and

its

correction,

see

§

V.

[54] Seelig 1960,

p.

112, reports:

"Einstein

later

laughingly

recounted that his dissertation

was

at

first returned to him

by

Kleiner with

the

comment that it

was

too

short. After he had

added

a

single

sentence,

it

was

accepted

without

further comment") ("Lachend

hat Einstein

spä-

ter

erzählt,

daß ihm seine Dissertation zuerst

von

Kleiner mit der

Bemerkung zurückgeschickt

wurde,

sie sei

zu

kurz. Nachdem

er

noch

einen

einzigen

Satz

eingeschaltet hatte,

sei sie still-

schweigend angenommen

worden").

[55]

See Loschmidt 1865. In Einstein

1905j

(Doc. 15),

p.

5,

the kinetic

theory

of

gases

is

mentioned

as

the oldest

source

for the determi-

nation

of

molecular dimensions.

Loschmidt's

method

is

discussed in Einstein

1915a,

p.

258.

[56]

See

§

1

and

§

2

of

Einstein

1905j

(Doc.

15).

[57]

This

equation was

later

corrected;

the

error

and the

correct

equation are

discussed in

§

V.

For

later

comments

on

the limitations

of

this

equation,

see

Einstein

to

Hans Albert

Einstein,

before 13

December

1940;

see

also

Pais

1982,

p.

92.