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).