136
REVIEW OF MATHIAS
under the totally
unexplained assumption
that
(dQ/dv)T
has
finite values
at
[2]
infinitesimally small values
of
T.
Doc. 19
Review
of
M.
E.
MATHIAS,
"The
Constant
a
of
Rectilinear Diameters
and
the
Laws
of
Corresponding
States"
("La
constante
a
des
diametres rectilignes
et
les lois
des etats
correspondents
(2e memoire),"
Journal
de
Physique
theorique
et
appliquee
4
(Series
4)
(1905):
77-91)
[Beiblätter
zu
den
Annalen
der
Physik 29
(1905):
634]
[1]
[2]
If
y
denotes
a
function
of
the
density
of
a
liquid
and
its saturated
vapor
that
depends
linearly
on
the
temperature,
which has
already been
examined
by
the author in
previous
articles (J.
de
Phys.
(3) 8
(1899): 407,
[3] and
ibid.
(3)
2
(1893):
5), then the relation
y =
A(1
+
a[1
+
m])
holds, where
A
denotes
the
critical
density,
m
the
temperature,
with the critical
temp-
erature
taken
as
the unit,
and
a a
constant.
If
the
law
of
corresponding
[4]
states
were
strictly fulfilled,
a
would
have to be
a
universal
constant.
Based
on
experimental
data
on
37
substances it is
shown
that this is
not
the
case.
While
for the
majority
of the
examined
substances
a
deviates
only
little
from unity,
this
quantity has
considerably
smaller values for
gases
difficult
to liquefy,
the value for
hydrogen being
0.236.
The
author finds
now
that
even
though
the
quantity
b
=
a/(O (0
=
absolute critical
temper-
ature)
is
not
a
universal
constant
either, it
has
nevertheless almost the
same
value for substances
of
similar
chemical
constitution;
he
proposes
that
substances
be
divided into "series"
(substances
with almost
equal
b)
and
"groups"
(substances
with
approximately equal
a).