336
DOC.
14
CORRECTION TO EINSTEIN 1906A
Doc.
14
Correction
to
My
Paper:
"A
New
Determination of Molecular
Dimensions"1
by
A.
Einstein
[Annalen
der
Physik
34
(1911): 591592]
Mr.
Bacelin,
who has
done
an
experimental
investigation
on
viscosities
of
suspensions
at
Mr.
Perrin's
instigation,
wrote
me a
few weeks
ago
that
according
to his
results the
coefficient
of
viscosity
of
suspensions
is considerably greater
than that
corresponding to
[2]
the formula
I
developed
in
§2
of
my
paper.
I
therefore
asked Mr.
Hopf
to check
my
[3]
calculations,
and
he
indeed found
a
mathematical
error
that
considerably
affects
the
result. In
what
follows,
I will correct this
error.
[4]
The
expressions
for the
pressure components
Xy
and
Xz
on p.
296
of the
paper
mentioned
above
are wrong
because of
an error
in
the differentiation
of the
velocity
components
u,
v,
w.
These
expressions
should read:
X
=

2kA
+
10
25kP3MI,
P5 P7
X
=
5kP3
(A + B)^r]

25kP3M^l,
y
P5 P7
X7
=
5kP3
(A
+0^

25kPiMH,7n
r
P5 P7
where
M
=
At1
+ Br\2 +
C
t2.
If
one
then
calculates
the
energy
transmitted
per
unit time
by
the
pressure
forces to
the
[5]
liquid
contained
in
the
sphere
of radius
R, one obtains,
instead of
equation
(7)
on
p.
296,
(7)
W
=
2Z2k(V +
'/2&).
Using
this
corrected
formula, one
obtains the
equation
[6]
k*
=
k(
1
+
2.5p).
instead of the
equation
k*
=
k(1
+
p), developed
in
§2.
Thus,
the
viscosity
coefficient
k*
of the
suspension is 2.5
times
more strongly
influenced
by
the total volume
q
of the
spheres suspended
in
a
unit volume
than
according
to
the formula found there.
[1]
1
A. Einstein. Ann.
d.
Phys.
19
(1906):
289
ff.