Volume 2: The Swiss Years: Writings, 1900-1909 Page 169 (205 of 692)

DOC.
14
HEURISTIC
VIEW OF
LIGHT
169
include
Hughes
1912 and
Richardson and
Compton
1912.
Although
the
equation was
gen-
erally accepted
after
Millikan's
work,
the
light
quantum concept was
not
accepted
until the mid-
1920s.
[45]
For
Lenard's
studies
of
cathode lumines-
cence,
see
Lenard
1903.
[46]
"PE"
should be
"IIE".
[47]
Lenard
1903.
[48]
For
previous
studies, see, e.g.,
Lenard
1900a and
1900c;
Stark
1902,
pp.
74-79; and
Stark
1909b,
pp.
614-616.
[49]
Lenard
1900a,
p.
495.
[50]
Stark
1902.
[51]
This
expression
is
equivalent
to the law
of
photochemical
equivalence,
established in Ein-
stein
1912a.
This section
may
be viewed
as
ini-
tiating
the field
of
quantum photochemistry.

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Extracted Text (may have errors)

DOC.
14
HEURISTIC
VIEW OF
LIGHT
169
include
Hughes
1912 and
Richardson and
Compton
1912.
Although
the
equation was
gen-
erally accepted
after
Millikan's
work,
the
light
quantum concept was
not
accepted
until the mid-
1920s.
[45]
For
Lenard's
studies
of
cathode lumines-
cence,
see
Lenard
1903.
[46]
"PE"
should be
"IIE".
[47]
Lenard
1903.
[48]
For
previous
studies, see, e.g.,
Lenard
1900a and
1900c;
Stark
1902,
pp.
74-79; and
Stark
1909b,
pp.
614-616.
[49]
Lenard
1900a,
p.
495.
[50]
Stark
1902.
[51]
This
expression
is
equivalent
to the law
of
photochemical
equivalence,
established in Ein-
stein
1912a.
This section
may
be viewed
as
ini-
tiating
the field
of
quantum photochemistry.

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EINSTEIN'S
DISSERTATION
ON THE DETERMINATION OF
MOLECULAR DIMENSIONS
I
Einstein
submitted
a
dissertation to the
University
of
Zurich in
1901,
about
a
year
after
graduation
from the
ETH,
but withdrew it
early
in 1902.[1]
In
a
successful
second
attempt
three
years later,
he combined the
techniques
of
classical
hydrodynamics
with
those of
the
theory
of diffusion to create
a new
method for the determination
of molecular
sizes and
of
Avogadro's
number, a
method he
applied
to solute
sugar
molecules.[2] The
dissertation
was
completed on
30
April
1905 and submitted to the
University
of
Zurich
on
20
July.[3]
On 19
August
1905, shortly
after the thesis
was accepted,
the Annalen
der
Physik
received
a
slightly
different version for
publication.[4]
Einstein 1906c
(Doc. 33), published
half
a year
later
as a supplement
to
Einstein
1906a,
utilizes
experimental
data not
previously
available to recalculate the size
of
sugar
mole-
cules. In
1911,
after
Jacques
Bancelin found
a discrepancy
between the results
of
his
experiments
and
Einstein's
predictions, a
calculational
error
in
Einstein
1905j (Doc.
15)
was
discovered. Traces
of
an
unsuccessful
attempt by
Einstein to locate the
error,
pre-
served
as marginalia
and interlineations in
an offprint
of
the
paper, are
discussed
in the
annotations to Doc. 15.
A
correction
of
the
error,
which
was
found
by
Ludwig
Hopf,
then
a
collaborator of
Einstein, is
published
in Einstein 1911d. The
correction
was
reiterated
in
Einstein
1920 and
integrated
into the
republication
of Einstein's
dissertation in
Einstein
1922.
[5]
II
By
1905 several methods
for
the
experimental
determination
of molecular dimensions
were
available.[6]
Although
estimates
of
upper
bounds for the sizes
of
microscopic
con-
stituents
of
matter
had been discussed for
a long
time,
the first reliable methods for deter-
mining
molecular sizes
were developed
in the second
half
of
the
nineteenth
century,
based
[1]
For evidence
of Einstein's
submission
of
the dissertation,
see
the
Receipt
for the Return
of
Doctoral
Fees,
1
February
1902
(Vol. 1,
Doc.
132).
[2]
See
Einstein
1905j (Doc. 15).
For
a study
of Einstein's
dissertation, see
Pais
1982,
chap.
2,
§5.
[3]
See Einstein
to
Rudolf
Martin,
20
July
1905.
[4]
The thesis
was
unanimously accepted
by
the
Mathematics and
Physics Faculty on
27
July
1905
(see
Protokollbuch der
Konferenz,
Abtei-
lung
VI A, SzZE Bibliothek,
Hs
1079:2).
For
the
changes
that Einstein made in the Annalen
version,
Einstein
1906a,
see
the notes
to
Ein-
stein
1905j (Doc.
15).
[5]
For
an English
translation of Einstein
1922,
see
Einstein
1926. For the
history
of
Einstein
1922,
edited
by
Reinhold Fürth,
see
the editorial
note,
"Einstein
on
Brownian Motion,"
§
I,
p.
206. Some
of Fürth's
annotations
for the
1922
edition
(see
Fürth
1922)
have been utilized in
these editorial notes.
[6]
For
a survey
of
the
development
of
meth-
ods
for
the determination of molecular dimen-
sions,
see
Brush
1976,
pp.
75-78.
For
a
contem-
porary
survey,
see
Meyer,
O. E.
1899,
chap.
10.

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Extracted Text (may have errors)

EINSTEIN'S
DISSERTATION
ON THE DETERMINATION OF
MOLECULAR DIMENSIONS
I
Einstein
submitted
a
dissertation to the
University
of
Zurich in
1901,
about
a
year
after
graduation
from the
ETH,
but withdrew it
early
in 1902.[1]
In
a
successful
second
attempt
three
years later,
he combined the
techniques
of
classical
hydrodynamics
with
those of
the
theory
of diffusion to create
a new
method for the determination
of molecular
sizes and
of
Avogadro's
number, a
method he
applied
to solute
sugar
molecules.[2] The
dissertation
was
completed on
30
April
1905 and submitted to the
University
of
Zurich
on
20
July.[3]
On 19
August
1905, shortly
after the thesis
was accepted,
the Annalen
der
Physik
received
a
slightly
different version for
publication.[4]
Einstein 1906c
(Doc. 33), published
half
a year
later
as a supplement
to
Einstein
1906a,
utilizes
experimental
data not
previously
available to recalculate the size
of
sugar
mole-
cules. In
1911,
after
Jacques
Bancelin found
a discrepancy
between the results
of
his
experiments
and
Einstein's
predictions, a
calculational
error
in
Einstein
1905j (Doc.
15)
was
discovered. Traces
of
an
unsuccessful
attempt by
Einstein to locate the
error,
pre-
served
as marginalia
and interlineations in
an offprint
of
the
paper, are
discussed
in the
annotations to Doc. 15.
A
correction
of
the
error,
which
was
found
by
Ludwig
Hopf,
then
a
collaborator of
Einstein, is
published
in Einstein 1911d. The
correction
was
reiterated
in
Einstein
1920 and
integrated
into the
republication
of Einstein's
dissertation in
Einstein
1922.
[5]
II
By
1905 several methods
for
the
experimental
determination
of molecular dimensions
were
available.[6]
Although
estimates
of
upper
bounds for the sizes
of
microscopic
con-
stituents
of
matter
had been discussed for
a long
time,
the first reliable methods for deter-
mining
molecular sizes
were developed
in the second
half
of
the
nineteenth
century,
based
[1]
For evidence
of Einstein's
submission
of
the dissertation,
see
the
Receipt
for the Return
of
Doctoral
Fees,
1
February
1902
(Vol. 1,
Doc.
132).
[2]
See
Einstein
1905j (Doc. 15).
For
a study
of Einstein's
dissertation, see
Pais
1982,
chap.
2,
§5.
[3]
See Einstein
to
Rudolf
Martin,
20
July
1905.
[4]
The thesis
was
unanimously accepted
by
the
Mathematics and
Physics Faculty on
27
July
1905
(see
Protokollbuch der
Konferenz,
Abtei-
lung
VI A, SzZE Bibliothek,
Hs
1079:2).
For
the
changes
that Einstein made in the Annalen
version,
Einstein
1906a,
see
the notes
to
Ein-
stein
1905j (Doc.
15).
[5]
For
an English
translation of Einstein
1922,
see
Einstein
1926. For the
history
of
Einstein
1922,
edited
by
Reinhold Fürth,
see
the editorial
note,
"Einstein
on
Brownian Motion,"
§
I,
p.
206. Some
of Fürth's
annotations
for the
1922
edition
(see
Fürth
1922)
have been utilized in
these editorial notes.
[6]
For
a survey
of
the
development
of
meth-
ods
for
the determination of molecular dimen-
sions,
see
Brush
1976,
pp.
75-78.
For
a
contem-
porary
survey,
see
Meyer,
O. E.
1899,
chap.
10.

168
DOC.
14
HEURISTIC VIEW OF LIGHT
Meyer,
O. E. 1899. For
a
discussion
of
Ein-
stein's
other methods for
determining
N, see
the
editorial
note,
"Einstein's
Dissertation
on
the
Determination of
Molecular Dimensions,"
§
IV, pp.176-179.
[22]
See Wien 1894.
[23]
See Wien
1896,
p.
667.
Wien's
formula
was originally expressed as
the
density
px
of
ra-
diation
of
wavelength
between
X
and
X
+
dX:
C
px
=
C/X5e x0
,
where
0 is
the
temperature,
C
is
a
constant, and
c
is
the
speed
of
light.
[24]
The best
contemporary experimental
tests
were reported
in Rubens
and
Kurlbaum
1901
and
Paschen
1901a. This
latter, p. 293,
states:
"For
larger
values
of
1/AT
than about 0.0003
(XT
about
3000)
the observations follow
the
Wien law within the
margin
of
error.
For
smaller
values
of
1/AT
than about
0.0003
(XT
about
3000)
deviations from the Wien law
appear
in all
curves" ("Für
grössere
Werte
von
1/XT
als
un-
gefähr
0,0003
(XT
3000
ungefähr) folgen
die
Beobachtungen
innerhalb
der
möglichen
Fehler
dem
Wien'schen
Gesetze. Für kleinere Werte
von
1/XT
als
ungefähr
0,0003
(XT
3000
unge-
fähr)
treten
in
allen Curven
Abweichungen
vom
Wien'schen
Gesetze
auf."
[25] S
refers to radiation with
frequencies
be-
tween
v
and
v
+ dv, and
E
=
pv
dv.
[26]
This
comparison
is further discussed in
§
5.
[27]
See Boltzmann 1877. The
name
"Boltz-
mannsches
Prinzip"
("Boltzmann's
princi-
ple"),
used
in
the next
section, is
Einstein's
ter-
minology.
[28]
For
a
discussion
of
Einstein's
definition
of
probability,
see
the editorial
note,
"Einstein
on
the Foundations
of Statistical
Physics,"
p.
52.
[29]
Klein
1974b,
p.
190, suggests
that the
ma-
terial Einstein
presented
in Einstein 1909b
(Doc.
56), p. 187,
is
a partial
fulfillment
of
this
prom-
ise.
[30]
See
also Einstein 1904
(Doc.
5),
pp.
355
and 359. C is
equivalent
to
Boltzmann's
con-
stant,
now
usually designated by
k.
[31]
The last term should be
multiplied
by T.
For the extension
of
the law
of
Boyle
and
Gay-
Lussac to dilute
solutions,
see
Van
't
Hoff
1887.
See also
Einstein
1905q
(Doc. 22),
§
1.
[32]
In Einstein 1906d
(Doc. 34),
p.
203,
Ein-
stein used
Planck's
equation
to
show that the
av-
erage energy
of
a
Wien oscillator
is
much
smaller than that
of
an energy quantum,
hv.
[33]
For
a contemporary
discussion
of Stokes's
rule,
see
Winkelmann
1906b,
"Fluoreszenz,"
pp.
785-798.
[34]
This conclusion
is
consistent with Knob-
lauch
1895,
p.
198,
which states that the inten-
sities
of
fluorescent and incident
light are pro-
portional,
"even
when the
intensity
of
the latter
is
varied in the ratio
1:6400"
("selbst
wenn
die
Intensität des letzteren im Verhältniss 1:6400
verändert wird").
[35]
For further discussion
of
such
exceptions,
set
Einstein
1909b
(Doc. 56),
p.
191.
[36]
For
a contemporary survey
of
the
photo-
electric effect, with
bibliography through
1904,
see
Schweidler 1904. In
1901
Einstein read Len-
ard
1900b,
which discusses the
photoelectric
ef-
fect
(see
Einstein to Mileva
Maric,
28
May
1901
[Vol. 1,
Doc.
111]).
[37]
Lenard
1902.
[38]
For
a
discussion
of the
relationship
be-
tween
the
photoelectric
effect
and the Volta ef-
fect,
see
Einstein 1906d
(Doc. 34), pp.
203-
206.
[39]
"Elektrische Masse"
("electric mass")
here refers to the
charge
of the electron.
[40]
Stark
1902, which
Einstein cites
on p.
148,
treats the ionization
of
a
neutral
gas
mole-
cule
by
ultraviolet
light as
"a
separation
of
the
negative
electron from
its
positive
remainder
atom"
("eine
Lostrennung
des
negativen
Elek-
trons
von
seinem
positiven
Restatom")
(p.
75).
Stark and
Steubing
1908,
pp.
490-491,
reports
a
"genetic"
relationship
between fluorescence
and the
photoelectric
effect. The former is
as-
sumed
to
be
a separation
of
an
electron from
a
molecule,
followed
by
the
"reattachment
of
the
electrons"
("Wiederanlagerung
der Elektro-
nen") with the emission
of
light;
the latter
is
treated
as
the
ejection
of
electrons from
a
metal.
[41] Using
the value
of
N obtained
on p.
137
and the value for the electric
charge
obtained in
Planck
1901b,
p.
566,
converted
from
esu
to
coul, the correct value
of E
is
9.6
x
104
coul.
Thus,
II
should be
multiplied by
10-7
to convert
erg/coul
to volts.
[42]
"II•
107" should be
"II•
10-7".
[43]
Lenard 1902.
Lenard's
values
ranged
be-
tween 1.5V to
3V, depending on
the material
studied. For
a
review
of Lenard's
work, see
Wheaton 1978b.
[44]
This and other
predictions
of Einstein's
equation
for IIE
were
confirmed
in
experiments
reported
in Millikan 1916a, 1916b.
Earlier tests

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Page 985. "On the General Molecular Theory of Heat" click to expand contents

Page 13113. Review of Arturo Giammarco, "A Case of Corresponding States in Thermodynamics" click to expand contents

Page 14914. "On a Heuristic Point of View Concerning the Production and Transformation of Light" click to expand contents

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Page 49650. "Elementary Theory of Brownian Motion" click to expand contents

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