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.