204
DOC.
15
MOLECULAR DIMENSIONS
" +
5/6 p3
Ae/p3"
is added
to
the
right-hand
side
of
this
equation.
After the last
terms
of
the second
and
third
equations,
series of dots
are
added.
These interlineations
are presumably
related to
the
marginal
calculations
indicated in note
14.
[24]
In
Einstein's
reprint
(see
note
14),
the
term
" +
5/6
P3
AE/p3"
is
added to the
right-hand
side of
this
equation.
This interlineation
is
presumably
related to the
marginal
calculations indicated in
note
14.
[25]
In
Einstein's
reprint
(see
note
14),
the
term
" -
5/3
kP3A
(1/p3
-
9
E/p5)"
is
added
to
the
right-
hand side
of
this
equation.
This addition
is
pre-
sumably
related
to the
marginal
calculations
re-
ferred to
in
note 14.
[26]
This
equation
and the
subsequent one are
incorrect.
Apart
from minor
errors, they
contain
a
calculational
error bearing on
the numerical
factors. In Einstein
1906a,
" +
25" in front
of
the last term in the
equation
for
X{
is
changed
to
"-25".
In
Einstein's
reprint
(see
note
14),
the
factor
"£2"
in the last
term
on
the
right-hand
side
of this
equation
is
corrected to "EE", and
the factor
"n2" in front of the
parenthesis
in the
last term
on
the
right-hand
side
of
the
equation
for
Xn
is corrected
to
£n.
The calculational
error
that is
also contained in these
equations,
and
some
of its
consequences, are
corrected in Ein-
stein 1911d. The corrections
are integrated
into
the
text
of
the
reprint
of
this
paper
in Einstein
1922. For
an
account
of the
discovery
of
this
er-
ror
and
of
its
correction,
see
the editorial note,
"Einstein's
Dissertation
on
the Determination
of
Molecular
Dimensions,"
§
V, pp.
179-182.
The correct
equations are:
X7)
=
+
5
kP3
(A
+ B)^j]
-
25kP3
+
BV2
+
C£2)
P7
Xi =
+
5
kP3
(A
+ C)tt
-
25kP3
tt{Ai;2
+
BV2
+
CI2)
P7
[27] "-10"
should be
replaced by
"-5,"
and
"25"
by
"20"
(see previous note).
[28]
The third
"+"
sign
should be
replaced
by
"="
as
corrected in Einstein 1922.
"-10"
should
be
replaced by
"-5,"
and
"20"
by
"15"
(see
note
26).
[29]
In
Einstein's
reprint (see
note
14),
the
fac-
tor
"4/15"
was
changed
to
"8/15"
and
then
changed
back to
"4/15".
[30]
"4/15"
should be
replaced by
"8/15"
as
corrected in
Einstein's
reprint
(see
note
14).
[31]
This
equation
should be
(see
note
26):
W
=
8/3
tt
R3
k
82
+
4/3
it
P3
k
82
=
2b2k(V
+
l/2).
[32]
"8"
should be
"82".
This correction
is
made in
Einstein's
reprint (see
note
14).
[33]
It follows from the correction to
eq. (7)
that the
dissipated energy
is
actually
increased
by
half
this amount. The statement in the text
is
only partially
corrected in Einstein
1922;
the
amount
is
correctly given
but still
described
as a
diminution. The final sentence
of
this
paragraph,
which
no longer applies
to the corrected calcu-
lation,
is
omitted
from
Einstein 1922.
[34]
The
point
should be denoted
by xv, yv,
zv,
as
corrected in Einstein 1906a.
[35]
The second denominator should be
Pv3
as
corrected in Einstein 1906a.
[36]
The heat
production
per
unit time
is
actu-
ally
increased
by 82
k
f.
The correct
equations
are
thus
(see
note
26):
W
=
2
h2
k +
nh2
k&,
and W
=
2
S2
k
(1
+
cp/2).
[37]
The
following
two sentences
are
revised in
Einstein 1922:
"In
order to calculate from
equa-
tion
(7b)
the coefficient
of
friction
of
an
inhomo-
geneous
mixture
of
fluid and
suspended spheres
(in
the
following
called
"mixture"
for
short)
which
we
are
examining,
we
must further take
into consideration that
A, B,
C
are
not
values
of
the
primary
dilations
of
the motion
of
fluid
rep-
resented in
equation
(8);
we
want to
designate
the
primary
dilations
of
the mixture
as
A*, B*,
C*"
("Um
aus
Gleichung (7b)
den
Reibungs-
koeffizienten
der
von uns
betrachteten in-
homogenen
Mischung
von
Flüssigkeit
und
sus-
pendierten Kugeln
(im
Folgenden
kurz
"Mischung"
genannt) zu
berechnen,
müssen
wir noch
berücksichtigen,
daß
A, B,
C nicht die
Werte der
Hauptdilatationen
der
in
Gleichungen
(8)
dargestellten Flüssigkeitsbewegung
sind;
wir
wollen die
Hauptdilatationen
der
Mischung A*,
B*,
C*
nennen").
[38]
In this and the
following
two
equations,
the
sign
after "="
should be
"+."
The third
equation
should have "zv" instead
of
"x"
in the
numerator;
the latter correction
is made in Ein-
stein 1906a.