DOC.

1

PHENOMENA OF CAPILLARITY

21

the

molecular

force

was

much

greater

than the

molecular

radius.

However, by

the

end

of

the

nineteenth

century

there

were reasons

to ques-

tion this

assumption.

For

a

historical review of

this mean-field

approximation

in

capillary

the-

ory, see

Rowlinson

and

Widom

1982,

pp.

17-

21. See also note 7.

[9]

O

denotes the surface

area.

The

sign

of

the

last term in this

equation

should be

positive.

[10]

This

expression

for K'

is incorrect,

as

is

clear

even

from dimensional considerations.

Einstein

1911a, without

mentioning

the

present

paper, gives

the correct

expression

(see

the for-

mula

for

K2 on p.

167).

[11]

This

expression

is

actually

the surface

po-

tential

energy

per

unit

area.

[12]

See

Ostwald

1891,

pp.

528-530, for

Schiff's data

on

surface

tension;

pp.

376-385

list

values

for

the molar volumes

of

a large num-

ber

of

chemical

compounds

at

their

boiling

point.

[13]

Boltzmann 1898a,

pp.

59-60, calculates

an

expression

for

the heat

of

vaporization

of

a

liquid,

based

on

the intermolecular force

law, to

which

Einstein's

is

equivalent.

In

calculating

the

external work done

against atmospheric pres-

sure,

Einstein

neglected

the volume

of

the

liquid

in

comparison

with that

of

the

vapor.

[14]

Ostwald

1891,

pp.

354-356,

gives

values,

due to

Schiff,

for

the heat

of

vaporization

of

a

number of

compounds; pp.

376-385

lists molar

volumes

at

the

boiling point.

Einstein

uses

the

molar,

not the

molecular

values for both

D'm

and

v;

the external work is

put equal

to

RT

=

1.991

T

cal/mol

(see,

e.g.,

Nernst

1898,

p.

61).

[15]

Here

2,51

is the

average

of

the

quotients

given

in the

table,

and

4,17

.

107 is

the value of

the

mechanical

equivalent

of

heat used

by

Ein-

stein.

[16]

For the

meaning

of

"Wärmeinhalt,"

see

note 5.

[17]

Here,

K

and

a

denote the standard coeffi-

cients

of

isothermal

compressibility

and isobaric

thermal

expansion.

[18]

The

terms pK

and pa

should be

pvK

and

pva,

respectively.

[19]

The

right-hand

side

of this

equation

should

be

multiplied by v.

[20]

The

right-hand

side of

this

equation

should

be

multiplied by v.

[21]

P

here is the

potential energy

per

mole,

given

on

the last line

of

p.

518. This

expression

should be

multiplied by v.

[22]

The numerator

of

the left-hand side should

be

Ta.

[23]

See

Landolt and

Börnstein

1894,

pp.

107-

109. The

values

for

v

are

again

taken from Ost-

wald

1891, pp.

376-385

(Einstein

uses

the

mo-

lar,

not the molecular

volume).

[24]

The two results

are thermodynamically

equivalent, however.

If

the volume

of

the fluid

is neglected,

the

Clausius-Clapeyron equation

for

vaporization

is

m

\dT)v

Tv

with

v

the volume

of

the

vapor

and

Dm

the heat

of

vaporization. Neglecting

the

atmospheric

pressure,

as

did Einstein,

we may

set

Dm =

D'm.

The

identity

(dp/dT)v(dv/dp)T(dT/dv)p=-1

then gives

D'm

=

Tva/k

.

The existence

of

a

thermodynamic

relation be-

tween

Einstein's

two

results

is

suggested

in

a re-

view

of Einstein's

paper (Wiedeburg 1901).

[25]

See Ostwald

1891,

pp.

279,

398-399, for

a

discussion

of Mendeleev's

formula.

[26]

Possibly a

reference to

Ostwald's

use

of

Schiff's

data

to test

Eötvös's

law

(Ostwald

1891,

pp.

541-543).

[27]

See

note

6.

[28]

See

note

7.

[29]

See

note 8.