414 DOC.
13
ELASTIC BEHAVIOR AND
SPECIFIC
HEAT
Sutherland,
Madelung
had
published
a
detailed
study
of molecular
vibrations
and their rela-
tionship
to
optical wavelengths
in
the infrared
region
(see
Madelung
1909).
For
Einstein's later
comments
on Madelung's
work,
of
which
he
was
not
aware
at
the time of
the
present paper, see
Einstein
1911d
(Doc.
15).
[4]The distinction between the motions of
charged
and of
uncharged
atomic constituents
had
earlier
played a
role
in
Einstein's
theory
of the
specific
heats of
solids; see
Einstein
1907d
(Vol.
2,
Doc.
42).
[5]Sutherland
presented experimental
evidence for
his
idea,
which
is
based
on
optical
mea-
surements. He first calculated the elastic
wavelengths
of alkali
metals and
halogens
and
subse-
quently
determined the elastic
wavelengths
of the
corresponding
alkali halides
by
addition. He
then
compared
the
resulting wavelength
for each salt
to
the
optical
wavelength
of
the
same
salt
as
measured
by
Rubens and
Hollnagel, finding
that
the
two
wavelengths are
indeed
in
an
approximately
constant
ratio. Later
Einstein
himself took
an
interest
in
Rubens's
optical
mea-
surements;
see
Einstein
to
Heinrich
Zangger,
13-16 December
1911.
[6]Einstein
1907a
(Vol. 2,
Doc.
38).
[7]See
Einstein
1911a
(Doc.
12),
pp.
168-169.
[8]Einstein had shown that
an
atomistic
interpretation
of Eötvös's
law
on
capillarity requires
the
assumption
that the
range
of interaction
("Wirkungssphäre")
of
a
molecule
is
proportional
to
the distance of
neighboring molecules;
see
Einstein
1911a
(Doc.
12),
p. 167.
[9]The
e on
the
right-hand
side
of this
equation
should
be
c.
[10]N/v should
be
N/v.
[11]Analogous
formulas
(with
different numerical
factors)
had earlier been obtained
by
Madelung
(see
Madelung
1909, p. 103),
and Sutherland
(see
Sutherland
1910, p. 658).
[12]Grüneisen
1908.
The
reference is to
table
17
on p.
848.
The
table
lists measurements
by
four
observers, including Grüneisen,
of
the
cubic
compressibilities
(in cgs
units) at 18°C
for the
elements
listed
in
Einstein's table above. Similar tables
(for
different selections
of
substances)
are
found
in
Madelung
1909, p. 104,
Madelung
1910a, p. 55,
and
Sutherland
1910, p.
659.
In his
first
paper, Madelung compared
the
wavelengths
determined
on
the basis of values for the
elastic constants
as
measured
by
Voigt
and
Röntgen
with
approximate wavelengths
determined
by
Drude from the
electromagnetic theory
of
dispersion.
In
1910 both
Madelung
and
Suther-
land made
use
of the
recent
optical measurements by
Rubens
and collaborators.
[13]For
Einstein's derivation of
this
formula, see
Einstein
1907a
(Vol. 2,
Doc.
38), p. 186.
[14]K
should
be
k,
Boltzmann's
constant.
[15]Nernst
1910b.
Nernst's value of
a
for
silver
is
given on p.
29.