180

DISSERTATION

ON

MOLECULAR

DIMENSIONS

from the

values Einstein obtained from his

hydrodynamical

method and

from Planck's

black-body

radiation

law.[80]

For

Einstein,

this

discrepancy was particularly significant

in

view

of

what he

regarded as

the

problematic

nature

of Planck's derivation of

the radiation

law.[81]

In 1909 Einstein drew

Perrin's

attention to his

hydrodynamical

method for

determining

the size

of

solute molecules. He

emphasized

that this method allows

one

to

take

into

ac-

count the volume

of

any

water

molecules attached to the solute molecules, and

suggested

its

application

to

the

suspensions

studied

by

Perrin.[82]

In the

following

year, an

experi-

mental

study

of Einstein's

formula for the

viscosity

coefficients

(eq.

[1]

above) was per-

formed in

Perrin's

laboratory by Jacques

Bancelin.[83]

Bancelin studied uniform

aqueous

emulsions

of

gamboge, prepared

with the

help

of Perrin's

method

of

fractional centrifu-

gation.

Bancelin confirmed that the increase

in

viscosity

does not

depend on

the size

of

the

suspended particles,

but

only on

the fraction

of

the total volume that

they

occupy.

However,

he found

a

value for the increased

viscosity

that differs

significantly

from

Einstein's

prediction.[84]

Bancelin sent

a report

of

his

experiments

to

Einstein,

apparently

citing

a

value

of

3.9 for the coefficient

of

p

in

eq.

(1),

instead

of

the

predicted

value

of

1.[85]

After

an

unsuccessful

attempt

to find

an error

in

his

calculations,[86]

Einstein

wrote to

his student and collaborator

Ludwig

Hopf:[87]

I

have checked

my previous

calculations and

arguments

and found

no error

in

them. You would

be

doing

a

great

service in this matter

if

you

would

carefully

recheck

my investigation.

Either there is

an

error in

the

work, or

the

volume of

[80]

For

Einstein's

derivation

of

Avogadro's

number from the law

of

black-body

radiation,

see

Einstein

1905i

(Doc. 14),

pp.

136-137.

[81]

See Einstein

to

Jean

Perrin,

11

November

1909, quoted

in

§

II.

For

a

discussion

of

Ein-

stein's

views

on

the foundations

of Planck's

the-

ory, see

the editorial

note,

"Einstein's

Early

Work

on

the

Quantum

Hypothesis,"

pp.

137-

138.

[82]

Einstein wrote:

"It

would

perhaps

not be

uninteresting

to

apply

to

your suspensions

the

method for

determining

the volume

of

the

sus-

pended

substance from the coefficients

of

vis-

cosity

and

to

make

a comparison

with the results

of

your

methods"

("Es wäre vielleicht nicht

un-

interessant, die Methode

zur Bestimmung

des

Volumens der

suspendierten

Substanz

aus

den

Reibungskoeffizienten

bei Ihren

Suspensionen

anzuwenden und

mit

den Resultaten

Ihrer

Me-

thoden

zu

vergleichen") (Einstein

to Jean

Per-

rin,

11

November

1909).

[83]

See Einstein

to

Jean

Perrin,

12

January

1911

and Bancelin 1911a

and

1911b.

[84]

For

Einstein's

value,

see

eq. (1).

[85]

On

12

January

1911,

Einstein wrote

to

Perrin:

"You will in

any case

be familiar

with

Bancelin's

report to me as

well

as

with

my

re-

ply" ("Der

Bericht

von

Herrn Bancelin

an

mich

sowie meine Antwort

an

ihn werden Ihnen

je-

denfalls bekannt sein"). This letter cites the

value

of 3.9

as

Bancelin's

result. In

a

letter

to

Hopf

written

shortly

before,

Einstein cited

a

value

of

3.8

(see

Einstein to

Ludwig

Hopf,

be-

fore

12

January

1911).

For further evidence

of

correspondence

between Einstein and

Bancelin,

see

also Bancelin 1911a,

p.

1383.

[86]

See Einstein

1905j (Doc. 15),

note

14,

for

evidence

of

this

attempt.

[87]

Ludwig

Hopf

was

Einstein's

student at the

University

of

Zurich. In the

summer

semester

of

1910 he

registered

for

Einstein's

lectures

on me-

chanics and kinetic

theory

of

heat,

and for his

physics

seminar

(Student

Files, SzZU,

Kassa-

Archiv).

In the

same year

he

published

two

joint

papers

with Einstein (Einstein

and

Hopf 1910a,

and

1910b).