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
right-hand
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
one-half
times
greater
(see note 26).
[50]
The
quantity
of
water
bound
to
a sugar
molecule has
a
volume that
is
actually
one-half
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.
170-173,
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.
58-60, 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.
176-179.
[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
right-hand
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
10-8
cm;
and
N
=
3.3
1023 (per
mole).
[63]
For values
of
N obtained
by
other meth-
ods,
see,
for
example,
Planck
1901b.