DOC.
15
MOLECULAR DIMENSIONS
205
[39]
The
factor
in front
of
the second term in
the
first
equation
is
5/2
(see
Einstein
1906a).
In
deriving
the second
equation,
Einstein
used
the
equations
at
the bottom
of
p.
12
and the fact that
A
+
B
+
C
=
0.
[40]
In Einstein's
reprint
(see
note 14),
"
=
A2
+
B2 +
S2
(1

2Q)"
is added
to
the
righthand
side
of
this
equation
and then crossed
out.
[41]
The
correct
equation
is
(see
note
26):
W*
=
2
S2
k
(1
+
Q/2).
[42]
The correct
equation is (see note 26):
k*
=
k(1 +
2.5
Q).
[43]
The fraction
is
actually
2.5
times the total
volume
of
the
suspended spheres
(see
note
26).
[44]
The title
of
this
paragraph
in Einstein
1906a
is:
"On
the Volume
of
a
Dissolved Sub
stance
with
a
Molecular Volume Which
is
Large
in
Comparison to
the
Solvent"
("Uber das
Vo
lumen
einer
gelösten
Substanz
von
im
Vergleich
zum Lösungsmittel großem
Molekularvolu
men").
[45]
The
correct
equation
is
(see
note
26):
k*/k
= 1
+
2.5
Q.
[46]
See Landolt
and
Börnstein
1894,
p.
294.
In Einstein 1906c
(Doc. 33),
Einstein
uses more
recent
experimental
data.
[47]
The correct value
is
0.98
cm3 (see
note
26).
The
following
sentence
is
omitted in Ein
stein 1906a.
[48]
See
Landolt and
Börnstein
1894,
p.
231.
[49]
The
viscosity
is
actually one
and
onehalf
times
greater
(see note 26).
[50]
The
quantity
of
water
bound
to
a sugar
molecule has
a
volume that
is
actually
onehalf
that
of
the
sugar
molecule
(see note 26).
The
ex
istence
of
molecular
aggregates
in combination
with water
("Hydrathüllen")
was
debated
at
that
time
(see
the editorial
note,
"Einstein's
Disser
tation
on
the Determination
of
Molecular Di
mensions,"
§
II and
IV,
pp.
170173,
176
179).
[51]
The volume of
the
sphere is actually
0.98.342/N
cm3 (see note 26).
[52] Kirchhoff
1897, p.
380. The formula
was
first derived in Stokes 1845. For
a
discussion
of
its
applicability
to
objects
of
microscopic
di
mensions,
see
Fürth
1922,
pp.
5860, fn. 6.
[53]
The connection between diffusion and
os
motic
pressure was
first
explained
in Nernst
1888
(see
also
Nernst
1898,
p. 157;
Ostwald
1891,
p. 697).
[54]
This
equation was
first derived in Van 't
Hoff
1887;
it
is
also mentioned in
Einstein 1905i
(Doc. 14), p.
142.
[55]
The first denominator should be
6
it
k,
as
corrected in Einstein 1906a. This
equation was
independently
obtained in
Sutherland
1905
by a
similar
argument.
The idea to
use
this formula
for
a
determination
of
molecular dimension
may
have occurred to Einstein
as early as 1903; see
Einstein
to
Michele
Besso, 17
March
1903,
and
the discussion
of
this formula in the
editorial
note,
"Einstein's
Dissertation
on
the
Determi
nation
of Molecular
Dimensions,"
§
IV,
pp.
176179.
[56]
Einstein
1905k
(Doc.
16),
§
3. This
note
was presumably
added after the dissertation
was
submitted.
[57]
The correct
equation
is
(see
note
26):
k*/k
= 1
+
2.5
Q = 1
+
2.5
n
4/3
it
P3.
[58]
The
correct
equation
has
an
additional fac
tor 2/5
on
the
righthand
side
(see note 26).
[59]
For the
experimental
data,
see p.
17.
The
correct
value
is
80
(see note 26).
[60]
The value
given by
Einstein
is
interpolated
from the data in
Landolt and
Börnstein
1894,
p.
306. In Einstein 1906c
(Doc. 33),
Einstein
uses
more
recent
experimental
data.
[61]
The value
given by
Einstein
is
an interpo
lation from the data in Landolt
and
Börnstein
1894,
p.
288.
[62]
The values obtained
by using
the
correct
equations (see
Einstein
1922)
are:
P
=
6.2
108
cm;
and
N
=
3.3
1023 (per
mole).
[63]
For values
of
N obtained
by
other meth
ods,
see,
for
example,
Planck
1901b.