DOC.
15
MOLECULAR
DIMENSIONS 203
Published
by
K. J.
Wyss,
Bern. Dated
Bern,
30
April
1905.
[1]
For
Einstein's earlier
attempts
to obtain
a
doctorate,
see
the editorial
note,
"Einstein's
Dissertation
on
the Determination
of
Molecular
Dimensions,"
§
III,
pp.
173176.
[2]
The
dissertation
was formally
submitted
on
20
July
1905
(see
Einstein
to
Rudolf Martin
of
this
date).
[3]
Alfred Kleiner
was
Professor
of
Physics at
the
University
of Zurich. Einstein submitted the
dissertation
to
him. At
Kleiner's
request,
Hein
rich
Burkhardt,
Professor
of
Mathematics at the
University
of
Zurich,
checked the calculations in
Einstein's
dissertation
(see
the Gutachten über
das
Promotionsgesuch
des Hrn.
Einstein,
2024
July 1905,
SzZSa, U
110
e 9).
[4]
Einstein had stated
earlier
that he intended
to dedicate
his
dissertation to
Grossmann;
see
Einstein to
Mileva
Maric,
19
December
1901
(Vol. 1,
Doc.
130).
[5]
For
a
discussion
of
methods for determin
ing
molecular dimensions known
at
that
time,
see
the editorial
note,
"Einstein's
Dissertation
on
the Determination
of
Molecular Dimen
sions,"
§
II, pp.
170173.
[6]
Einstein's
argument closely
follows Kirch
hoff 1897,
Lecture
10, pp.
95108. For Ein
stein's
reading
of
Kirchhoff
1897, see
Einstein
to
Mileva
Maric,
29
July
1900 and
1
August
1900
(Vol.
1,
Docs. 68 and
69).
[7]
The
assumptions
made for the
liquid cor
respond
to those introduced in Kirchhoff 1897
on p.
374.
[8]
For
an argument
in which similar
boundary
conditions
for
the
hydrodynamical equations are
used, see Kirchhoff 1897,
pp.
378379.
[9]
The
following equations are
valid
if
the
ve
locities
are
assumed
to
be
infinitely
small,
and if
the motion
is
stationary (see
Kirchhoff 1897,
p.
374).
For
a
discussion
of
the NavierStokes
equations, see
Brush
1976,
book
2,
§
12.3,
pp.
432443.
[10] Kirchhoff 1897,
Lecture 26.
[11]
A
factor
k is missing
on
the
righthand
side
of
the last
equation
on
this
line;
this
error
is
cor
rected in Einstein 1906a.
[12]
Kirchhoff
1897,
pp.
378379.
The Kirch
hoff
text
begins:
"From
the
equations
9) [corre
sponding
to
(4)
in
Einstein's
text]
follows
Ap
=
0;
if
one assumes
p
according to
this condition
. .
."
("Aus den
Gleichungen
9)
folgt Ap
=
0;
hat
man
dieser
Bedingung gemäss
p
ange
nommen
. .
.")
and then continues
as quoted by
Einstein.
[13]
The denominator
on
the
righthand
side
should be
8£2;
this
error
is
corrected in Einstein
1906a.
[14]
The denominator
of
the first term
on
the
righthand
side should be
8£2;
this
error
is
cor
rected in
Einstein
1906a.
A
reprint
of
this article
in the Einstein Archive shows
marginalia
and
in
terlineations in
Einstein's
hand,
the first
of
which
refer to this
and the
following equation.
The term
"+g1/p"
was
added
to
the
righthand
side
of
the
equation
for
V
and then canceled.
These
marginalia
and interlineations
are pre
sumably part
of Einstein's
unsuccessful
attempt
to find
a
calculational
error; see
note
26
below,
and also the editorial
note,
"Einstein's
Disser
tation
on
the Determination
of
Molecular Di
mensions,"
§
V, pp.
179182.
On this
as
sumption, they
date from late 1910.
[15]
The
equation
for
u'
should be
(as
corrected
8r
in
Einstein
1906a):
u'
=
2c
S1/p/SE
.
In the
reprint
mentioned in
note 14,
the first derivative with
respect
to
£
was changed
to
a
second
derivative
and then
changed
back
to
a
first derivative.
At
the bottom
of
the
page,
the
following equations
are
written:
b
=
1/12
P5a
c
=
5/12
P3a
g
=
2/3 P3a.
[16]
The numerator
of
the last
term
in the
curly
parentheses
should be "82
(1/p)",
as
corrected
in
Einstein
1906a.
[17]
In
Einstein's
reprint
(see note 14),
a
factor
2/3
was
added
to
the first term
on
the
righthand
side
of
this
equation
and
then canceled.
[18] "Sn/SE"
should be
"Sp/SE"
as
corrected in
Einstein 1922.
[19]
The factor
preceding
the first
parenthesis
should
be,
as
corrected in Einstein 1906a:
P
3

5/2

P5
[20]
The
equations
should be:
u
=
U, v
=
V,
w
=
W.
[21]
Xe,
Xn, XI,
should
be
Xe,
etc.,
as cor
rected in
Einstein
1906a;
analogous
corrections
apply
to
the
subsequent
two
equations.
[22]
For the
following equations,
see
Kirchhoff
1897,
p.
369.
[23]
In Einstein's
reprint
(see
note
14),
the term