6

EINSTEIN'S

LECTURE NOTES

acceleration and

explains

basic elements of

vector

analysis.

In the later

lectures,

how-

ever,

he

does

not

systematically employ

a specific

vector

notation

(although

he

draws

an

occasional

vector

diagram

and

in

some

cases

uses a

script

character

to

represent

a

vector

and the

corresponding

roman

character

to

represent

its

magnitude).

In the

summer

semester 1910

Einstein

taught

a

sequel

to his

course

on

mechanics.

Student

notes

by

Walter

Dübi,

who audited the

course,

show

that

it

presented

an

exposition

of

hydrodynamics.

The

course

included

an

introductory

section

on

vector

analysis, beginning

with

a

presentation

of Stokes's and Gauss's theorems and

ending

with

a

derivation of Poisson's

equation

and Green's theorem. The

next part

of the

notes starts

with

a

treatment

of

the

dynamics

of

ideal fluids

and

a

derivation of Euler's

equations,

and

mainly

discusses various

types

of

flow in

liquids

and

gases.

The

notes

end with

a

discussion of

the

motion of

bodies in

viscous

fluids,

a

topic

that

had

played

an

important

part in

Einstein's earlier

research.[20]

III

The lecture

notes

on

kinetic

gas

theory

and statistical mechanics

presented

here

as

Doc.

4

were

written either for

a course on

the kinetic

theory

of heat

that

Einstein

gave

at

the

University

of Zurich in the

summer

semester 1910

or

for

a course on

the

same

topic given

in

Prague

in the

summer

semester

1912.[21] They

were

not

written before

1910,

since

they

include

a

particularly

detailed discussion of Knudsen's

investigations

on

the

properties

of rarefied

gases

which date from 1909-1910. Neither

were they

written after

1912,

as

becomes clear from

a

comparison

with lecture

notes

taken

by

students

attending

Einstein's

course on

molecular

theory

of heat

at

the ETH in the

summer

semester

1913.[22]

There

are

too

many

small

differences

in the

way

the

mate-

rial

is

presented

between the student

notes,

on

the

one

hand,

and Einstein's

own

notes,

on

the

other, to

make

it

likely

that

the

present

notes

were

written for that

particular

course.

In

addition,

the student

notes

include remarks

on

contemporary

research

problems

such

as

Eucken's

investigations

on

the

specific

heat of

hydrogen

at

low

temperatures,

that

are

not

touched

upon

in Einstein's

own

notes.[23]

Because

a

clear–

[20]See

Vol.

2,

the editorial

note,

"Einstein's Dissertation

on

the Determination of Molecular

Dimensions,"

pp.

170-182.

[21]Four

manuscript pages

(AD

5-164)

containing thermodynamic

calculations,

including

the

discussion of

an

equation

of

state

for extended

molecules,

can

be

dated

to

the

Prague period by

a slip

from

a

Prague

store

attached

to

them. These

pages

are

not

reproduced

here.

[22]The

students

were

Gustav

Eichelberg

and Walter Dällenbach.

Although

there

are many

small

differences in

presentation,

the student

notes

show

no

fundamental

conceptual

differences

with Einstein's notes.

[23]Eucken's results

(which were published

in Eucken

1912) are

discussed

in

the

notes

taken

by

Walter Dällenbach. In connection with the anomalous

behavior of the

specific

heat of

hydrogen at low temperatures,

Dällenbach

wrote

down that "not

a

soul knows

why or

according

to

which law"

("kein

Teufel weiss

warum

und nach

welchem

Gesetz").

For

more

on

Einstein's interest

in

the

problem

of

specific

heats,

see

the Introduction

to

this

volume,

pp.

xv-xxx.