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Xibrari!

of tbe

ntverstts of Wlisconstn

SCIENTIFIC MEMOIRS

EDITED BY

J. S. AMES, Ph.D.

PBOFB880R OF PHYSICS IN JOHNS HOPKINS UNIVERSITY

XIV

THE EXPANSION OF GASES BY HEAT

THE EXPANSION OF GASES

BY HEAT

MEMOIRS BY DALTON, GAY-LUSSAC, REGNAULT

AND CHAPPUIS

TRANSLATED AND EDITED BY

WYATT W. RANDALL, Ph.D.

HEADMASTER OF THE MACKENZIE SCHOOL, DOBBS FERRY, N. Y.

KEW YORK •:• CINCINNATI •:♦ CHICAGO

AMERICAN BOOK COMPANY

Copyright, 1902, bt
AMERICAN BOOK COMPANY.

Entered at Stationers^ HaJl, LancUm.

Expansion of Oases.
W. P. I

L3222H

bcr' l;5 1909

LH

'9Sca

y\

li

PREFATORY NOTE.

In preparing a volume to contain the classical memoirs
which treat of the law of the expansion of gases by heat, a
choice which will be satisfactory from all points of view can
scarcely be expected. The memoirs of Dalton, Gay-Lussac and
Regnault ai*e of course given in full; were it not for the very
comprehensive abstract given in Begnault's first paper, the
memoirs of Budberg would certainly have been included. It
has seemed best to the editor not to print in full any other
than the memoirs mentioned ; all others of sufficient import-
ance are referred to in the historical Introduction. An excep-
tion has been made, however, in the case of Chappuis's research,
for the proper comprehension of which a fuller abstract was
needed than could readily be included in the Introduction.
This abstract is therefore given separately.

The Bibliography contains, along with a few others closely
connected, a list of the memoirs printed in full or discussed in
the Introduction.

DoBBS Ferry, New York.

GENERAL CONTENTS.

Page.
Prefatory Note ....... v

Introduction ....... 3

On the Expansion of Gases by Heat. By John Dalton 17

Extract from ** A New System of Chemical Philosophy."

By John Dalton .,..,. 22
Biographical Sketch of Dalton , . , , , 22

Besearches upon the Rate of Expansion of Gases and

Vapors. By L. J. Gay-Lussac . .25

Biographical Sketch of Gay-Lussac .... 48

The Determination of the Rate of Expansion of Gases by
Heat. An extract from the " Traits de Physique "
of J. B. Biot ...... 61

Researches upon the Rate of Expansion of Gases. First

Memoir. By H. V. Regnault . . .63

Biographical Sketch of Regnault .... 120

^^^^itesearches upon the Rate of Expansion of Gases. Second

Memoir. By H. V. Regnault . .121

Researches upon the Gas Thermometer, and the Compari-
son of the Ga43 Thermometer with the Mercury Ther-
mometer. By P. Chappuis. Abstract . . 151
Bibliography ....... 159

Index ........ 161

vn

INTRODUCTION.

CONTENTS.

Dalton

Gay-Lussac

Dulong and Petit

Flaugergues

Rudberg

Magnus

Regnault

Balfour Stewart

Recknagel .

V, Jolly

Amagat

Mendeleeff and Kajander

Andrews

CalleJidar and Griffiths

Ohappuis and Harher

Wiebe and Bottcher

Kuenen and Randall

Melander . . .

Baly and Ramsay

PAGE

3
3
4
5

O

6

7

9

9

'9

10

11

12

13

13

13

14

14

15

INTRODUCTION.

The Law of the Expansiou of Oases by Heat^ yarionsly
called the Law of Charles, Dalton^ and Oay-Lussac^ seems to
have been for the first time definitely made known to the
scientific world by the English chemist. As Roscoe says^
** This law of equal expansion of all gases for equal increments
of temperature has been generally known on the Continent as
* Oay-Lussac's ' or * Charles's law,' but ought to be called * Dal-
ton's law of expansion/ as he first announced it and gave experi-
mental evidence of its truth, and the claims of the Manchester
philosopher are generally now allowed/' (John Dalton, and the
Rise of Modern Chemistry, page 96.)

The experimental basis upon which Dalton founded his
generalization was, however, meagre and, from a modern stand-
point, quite inaccurate — as was the case also with the evidence
uJ)on the strength of which he put forth his Law of Multiple
Proportions and the original Atomic Hypothesis. The work
done upon this subject by Dalton and Gay-Lussac — and es-
pecially by the latter, — the results of which were published in
1802, forms an epoch in the history of the careful study of the
properties of gases, if for no other reason than because of the
recognition of the necessity for the thorough removal of water
vapor from the gas examined, before concurrent results could

be expected.

Of the investigations carried out prior to the beginning of
the Nineteenth Century, Oay-Lussac gives a sufficient account
in his first memoir. During the year 1801 Dalton read a series
of papers before the Manchester Society, one of which treated
of the rate of expansion of air and other gases and records, as
its author states, experiments undertaken to test the results of
the research of Ouyton de Morveau and Duvernois. On
account of its bearing upon certain theories which he held
upon the nature of heat, Dalton's attention was especially
drawn to the increase in the rate of expansion with rise of

8

MEMOIRS ON

temperature^ and he does not seem to have calculated an aver-
age coefficient of expansion on the basis of the volume of the
gas at the melting-point of ice, from the results of these experi-
ments. After the publication of Gay-Lussac's research, how-
ever, he apparently repeated his experiments with greater cai*e,
using 32 ^'F. as one limit of the temperature-range, and calcu-
lated from the results thus obtained the coefficient which in his
"New System'* he states was the same as that announced by
Gay-Lussac. This matter is discussed in a footnote on page
72. Dalton's first paper was published before that of the
French savant, but in all probability not until the latter's ex-
perimental work had been completed.

It is singular that Gay-Lussac's later and, apparently in his
opinion, more accurate investigation, — an account of which is
given in the form of an extract from Biotas Traite de Physique
— should have been made known to the world only through
this means.

The results of the profound researches of Dulong and Petit
upon the absolute expansion of mercury and the relation be-
tween the mercury and gas scales of temperature, were to a
certain extent vitiated through their apparent acceptance of
the Gay-Lussac coefficient 0.00375 for the expansion of aire
One at least of their own experiments pointed to a figure much
nearer that now accepted as correct, but such evidence as now
exists indicates the use of the higher value in their computa-
tions. Their method involved the use of an open air-ther-
mometer whose tip was sealed after it had been heated to some
definite temperature; after the apparatus had been allowed to
cool again to 0°, the tip of the thermometer tube was again
opened under mercury and from the amount of mercury
drawn in the expansion of the air at the previous high temper-
ature was calculatedo Practically the same method was after-
wards employed by Rudberg and by Regnault in their researches
upon the rate of expansion of gases. Assuming the coefficient
0.00375 for air and calculating on this basis the true tempera-
tures registered by their air thermometers, Dulong and Petit
naturally found greater deviation from the air standard on the
part of mercury than the more accurate work of Regnault and
others has since proved to exist. Since the coefficient of ex-

4

EXPANSION OF GASES

pansion of mercury found by them has been shown by more
recent investigations to be very nearly exact, it remains but to
substitute the correct value for the coefficient of expansion of
air to determine, with only slight error, the actual deviation of
the mercury scale from the air scale of temperature.

In Gehler^s Physikalisches Worterbuch (1825) an account is
given of two researches upon the rate of expansion of air by
H. Flaugergues, published in the Journal de Pharmaeie,
Using a glass flask similar to that employed by Gay-Lussac in
his earlier experiments, he found 0.371168 for the amount of
the expansion of unit volume of air between 0° and 80° K. If
allowance must be made for the expansion of the flask, this
fraction becomes 0.375671 — nearly the same as Gay-Lussac*s.
It is not clear from the context that Flaugergues took the
expansion of the flask into account ; nevertheless it is likely,
and the coefficient first given, 0.00371, is probably his corrected
resulto The fact of the expansion of the containing vessel was
at that time well known and generally allowed for ; besides, in
the experiments described in the second paper the author
made use of a method intended to eliminate this factor : the
gas was contained in a cylindrical glass vessel in which was a
smaller leaden cylinder ; the gi'eater rate of expansion of the
lead was to bring about a decrease of the vesseFs capacity for
gas exactly compensating for the increase in the size of the
glass envelope. These experiments led to the figure 0.37174"
for the amount of the expansion" between 0^ and 80° E. —
practically identical with the former result. An experiment
with moist air yielded as a result 0.411.

The determinations of Flaugergues seem to have attracted
little attention, and, althongh they had pointed out the possi-
bility of error in Gay-Lussac's coefficient, it was not until the
publication of the very noteworthy memoirs of Eudberg that
the matter received due consideration.

In the course of an investigation which had for its object the
accurate determination of the melting points of the nietals
lead, tin and antimony on the scale of the air thermometer,
Eudberg had found that, assuming Gay-Lussac's coefficient
0.00375 to be correct, he was led to conclude that the coefficient
of expansion of glass was far greater at high temperatures than

5

MEMOIKS ON

its behavior at ordinary temperatures would appear to promise.
He accordingly undertook tiie re-determination of the air
coefficient, employing, first, a method in which both volume
and pressure varied, and, second, one in which the volume
remained constant. The original memoirs are not given in
the form of translation in this volume, as a sufficient abstract
of them is given by Kegnault in his first paper.

It will be well, in passing, to call attention to the fact that the
first method of experiment employed by Eudberg was that
which had been used previously by Dulong and Petit, but that
the second seems to have been original with him ; except for
comparatively slight modifications intended to secure greater
accuracy, the constant-volume air thermometer of to-day is the
invention of Rudberg.

Both methods of determination led to the same result : Gay-
Lussac's coefficient is too high by about one part in thirty-seven ;
the figure adopted by Rudberg as the probable coefficient of
expansion of air is *' between 0.00364 and 0.00365.'' It had
been his intention to investigate other gases as well, but his
death occurred shortly after the publication of the results
obtained for air.

The great importance of the question involved was generally
recognized and, consequently, within about four years the
results of two careful, quite independent, investigations, one
by Magnus in Berlin, the other by Regnault in Paris, made
their appearance. While neither of them was led to a figure
for the air coefficient quite so low as that adopted by Rudberg,
both were able to support the latter's contention that the
coefficient found by Gay-Lussac was far too high. It is interest-
ing to note, however, that just as the more accurate work of
Magnus and Regnault showed that Rudberg's coefficient was too
low, exactly the same fate has befallen the coefficient adopted
by Magnus and Regnault, through the investigations carried
out since 1860.

Magnus — as did also Regnault — endeavored to repeat the
later experiments of Gay-Lussac with air at constant pressure,
but found it impossible to secure uniform results, evidently
because the short mercury piston failed to close completely the
bore of the thermometer tube : air leaked in or out according

6

EXPANSION OF GASES

to the direction of movement of the mercury index and the
relative tension within and without the tube. Turning to
Budberg's second method : that by which the increase of
pressure within a gas reservoir of constant volume was measured
instead of the increase in the volume of a gas kept at constant
pressure : Magnus obtained eight values for a ranging from
0.00365032 to 0.00367899 with a mean of 0.00366508— at a
barometric pressure of 28 inches ; at 760 mm. pressure this
mean value becomes 0.0036678. At 28 inches pressure the
mean coefficient found for hydrogen was 0.00365659 ; for car-
bon dioxide, 0.00369087 ; for sulphur dioxide, 0.00385618^
While the mean value for air found by Magnus, after recalcula-
tion for a pressure of 760 mm., is nearer than is the mean
value found by Regnault by his four different methods, to the
coefficient for constant volume now accepted, this fact cannot
be interpreted as a prpof of greater accuracy of experimental
work on the part of the German physicist. Regnault's lowest
result was 0.0036549, and highest 0.0036747— a range of
0.0000198 in fifty determinations carried out by four distinct
methods ; for any one method the range amounted to but two
thirds of this amount, at the most. On the other hand,
Magnus's results, all by one method and only eight in number,
ranged 0.00002867. For hydrogen the range from highest to
lowest was 0.0000029 in four determinations ; for carbon dioxide,
0.00002228 in four ; for sulphur dioxide, 0.00006552 in three
determinations.

Magnus suggests as a possible explanation of the difference
between the results of Gay-Lussac and those of Rudberg and
himself, among other things, the fact that the former's gas
reservoir was actually in the boiling water of the bath instead
of in its vapor.

Regnault's two memoirs on the expansion of gases are given
in full in the form of a translation. It is to be noted that he
employed with success five different forms of apparatus to
determine this expansion between 0° and 100° : in the first of
these both volume and pressure varied to a considerable degree ;
in the second the volume remained more nearly constant ; in the
third and fourth the volume changed only to the extent of the
expansion of the glass envelope ; while in the fifth the increase

7

MEMOIRS ON

of volume was directly determined under constant pressure.
The last mentioned method established the fact that for most
gases the coefficient of expansion at constant pressure is slightly
greater than that at constant volume^ because such gases do
not exactly conform to Boyle's Law, but contract more rapidly
in proportion than the pressure upon them increases. Thus
the mean value found for air at constant volume is stated by
Regnault to be 0.003665, and that for constant pressure,
0.0036706,— at about atmospheric pressure. The latter coeffi-
cient increases as the pressure is increased : at about 3^ atmos-
pheres it is between 0.00369 and 0.00370.

Both Magnus and Regnault then proceeded independently to
re-determine the variation between the mercury scale and the
air scale of temperature. Since the data showing the dimen-
sions of the apparatus of Dulong and Petit were unknown, it
was impossible with certainty to re-calculate their results with
the aid of a more nearly correct coefficient of expansion for air.
Gay-Lussac had declared that air and mercury expand pro-
portionally even at comparatively high temperatures ; Dulong
and Petit found in their research that soon after passing 100°
mercury began to expand more rapidly, and that at about 300®
the temperature by the mercury scale was over 7° higher than
that calculated from the readings of their air thermometer.

Here, again, the superiority of the experimental work of
Regnault cannot be questioned. It established the fact that
the air thermometers and the mercury thermometers agree up to
about 250° ; above this point mercury expands more rapidly in
proportion than air, and at 350° (by the air thermometer) the
mercury thermometer stands about 3 ° higher.

Magnus's work, on the other hand, led to the practical con-
firmation of the results of Dulong and Petit. As Magnus had
used the coefficient 0.003665 (at 28 inches ; 0.0036678 at 760
mm.) in calculating his air thermometer temperatures, he was
led to believe that Dulong and Petit had not after all made use
of Gay-Lussac's coefficient, but that, having in a single inde-
pendent determination — as was known — found the coefficient
0.00365, they had employed the latter instead. This sup-
position Regnault, in criticizing Magnus's results, considered
extremely unlikely, on the ground that a study of Dulong Aud

8

EXPANSIOX OF GASES

Petit's results does not seem at all to confirm it, and that the
latter would hardly have depended upon a single determination
of so important a factor, especially when so at variance with
the generally accepted figure of Gay-Lussac. Into the
criticisms passed upon one-another's apparatus there is no need
here to go.

An investigation of the behavior of gas thermometers at
about — 88® led Eegnault to the conclusion that the coefficients
of expansion for air and hydrogen preserve closely the ratio
shown at higher temperatures.

In his comparison of the various gas thermometers in the
Memoires of the Academy of Sciences, Eegnault speaks of using
a coefficient for hydrogen smaller than he records in any of his
experiments. Lord Kelvin has called attention to the fact that
this statement is probably in error (See EncyclopcBdia Britau'
nicay article *^Heat^').

Mention may be made here, finally, of the study by Eegnault
of the coefficient of expansion of gases under high pressures,
the resiflts of which are contained in a later volume of the
Memoires,

The accuracy of the results of Eegnault for air at constant
volume was put to the test by Eecknagel and, still more rigor-
ously, by Balfour Stewart ; the results of the former confirmed
those of Magnus, so far as the value of the coefficient is con-
cerned, Eecknagel's mean value being 0.0036681. Stewart, like
Eecknagel, used the method employed successfully by Eudberg,
Magnus and Eegnault to find the coefficient of expansion from
the rise of tension in a gas kept at constant volume while its
temperature rises, but, using even greater care than did any of
his predecessors to secure pure dry air for his apparatus, and
employing every known refinement in the measurement of the
pressure changes, he obtained the figure 0.0036728 as the
av«*age of four results, the highest of which was 0.0036739 and
the lowest, 0.0036716.

The results recorded in the memoir of v. Jolly, although
scarcely to be compared as regards accuracy with those of
Stewart, are interesting because of the author's success in
simplifying the constant-volume gas thermometer. The differ-
ences between his highest and lowest results were, how-
B 9

MEMOIES ON

ever, not bo great as those between the corresponding figures
in the several series of Kegnault's determinations. He was also
successful in determining the coefficient of expansion of oxygen,
which Eegnault had failed to do. For air, v. Jolly found in 20
experiments: highest, 0.0036724; lowest, 0.003665; mean,
0.00366957. For oxygen (18 experiments) the highest was
0.003680 ; lowest, 0.0036683 ; mean, 0.0036743. For hydrogen,
the highest of 4 results was 0.0036600 ; lowest, 0.0036530 ;
mean, 0.0036562. For nitrogen, the highest of 4 results was
0.0036717 ; lowest, 0.0036655 ; mean, 0.0(/36677. For carbon
dioxide, the highest of 17 results was 0.0037144 ; lowest,
0.0036962 ; mean, 0.0037060.

Of tlie extensive and important researches of Amagat one
memoir and part of another have appeared in the form of a
translation in an earlier volume of this series — **The Laws of
Gases : Memoirs by Boyle and Amagat.'* Earlier than either
of these is a study (1873) of the variation of the coefficient of
expansion of gases with rise of temperature ; a constant-vol-
ume method based upon that of Eudberg was employed.
Assuming that for air the mean value of a = 0.00367 between
0° and 100°, he finds the mean values of a for sulphur dioxide
and carbon dioxide steadily decrease as the temperature rises.
Thus, for the former gas it is 0.003904 between 10** and 60°,
but 0.003798 between 10° and 250°; between 0° and 10° it is
0.00413, at 25° 0.00394, at 100° 0.003757, at 250^ 0.003685.
For carbon dioxide the mean value of a between 0° and 50°,
is 0.003714; between ° and 250° , 0.0037028; at °it is 0.003724;
at 50°, 0.003704; at 100°, 0.003695; at 250°, 0.003682.

From the memoir of 1881, the following may be quoted with
regard to the behavior of gases under high pressures:

**1. The coefficient of expansion of gases -(referred to unit
volume) increases with the pressure up to a maximum value,
beyond which it decreases indefinitely.

** 2. The maximum occurs at a pressure for which the pro-
duct jor is a minimum; consequently at this point the gas acci'
dentally obeys Mariotte's law.

*^ 3. For continually rising temperatures this maximum be-
comes less and less distinct and, finally, disappears.**

Hydrogen even at very low pressures seems already to have

10

EXPANSION OF GASES

passed the point where j^t; is a minimum; hence its coefficient
constantly decreases as pressure rises and as temperature rises.
The pressures employed in these experiments ranged from 40
to 320 metres of mercury.

In a later memoir (1893) are recorded results obtained
through a still greater range of pressures. Amagat says, ** An
inspection of Table 21 shows that at the outset the coefficient
of expansion increases with the pressure, as Begnault had
already found for pressures of a few atmospheres ; it then
passes through a maximum which occurs at a pressure rising
regularly with the temperature. During my first researches
on this subject these maxima seemed to coincide with those
pressures for which the product pv is a mimimum; but the
more extended data of the present memoir show this law to be
only approximate." With rise of pressure from 1000 to 3000
atmospheres, the coefficient of expansion of oxygen between 0®
and 16** steadily decreased from 0.00236 to 0.00134, that of
hydrogen from 0.00200 to 0.00128, that of nitrogen from
0.00193 to 0.00098, and that of air from 0.00206 to 0.00110.
Another series of experiments showed that with rise of pressure
from 200 to 1000 atmospheres a similar fall in the value of the
coefficient was to be noted. The coefficient in the case of car-
bon dioxide rises to a maximum and decreases; this maximum
occurs at higher and higher pressures as the temperature rises:
thus, at 137''— 198% a is 0.00369 (of the volume at 137° con-
sidered as unity) when the pressure is 75 atmospheres; 0.00798
(maximum value) at 200 atmospheres, 0.00386 at 500, and
0.00223 at 900 atmospheres. The coefficient of carbon dioxide
for constant pressure rises at first with the temperature, passes
a maximum, and then decreases as temperature rises; as the
pressure is higher, the maximum occurs at higher and higher
temperatures.

The elaborate investigations of Mendel6eff upon the proper-
ties of gases are to a large extent a terra ignota for those who
cannot read Russian ; only a few papers, usually meagre ab-
stracts, contained in journals published in Western Europe, are
available as sources of information. In papers published in
conjunction with Kajander, he discussed the disadvantages of
Eegnault's constant-pressure method, among others that only

11

MEMOIRS ON

about two thirds of the gas contained in the apparatus was at
the temperature of the water vapor. In fact, in his Princi-
ples of Chemistry (2nd Edition, Volume 1, page 133, note),
he goes so far as to state *^ Regnault, however, did not directly
determine the change of volume between 0° and 100°, but
measured the variation of tension with the change of tempera-
ture; but since gases do not entirely follow Mariotte^s law, the
change of volume cannot be directly judged by the variation
of tension." Nine results obtained with an apparatus in which
the entire volume of gas was surrounded with water vapor, and
various devices were employed to increase the accuracy .of the
readings, ranged from 0.0036814 to 0.0036876, with a mean of
0.0036843. This is the coefficient of expansion of air at a con-
stant pressure of about 760 mm.; the probable error of the
mean value is estimated by Mendeleeff to be 0.0000005.

In his Principles of Chemistry Mendeleeff gives the results
obtained at constant volume: for air, 0.00368; for hydrogen,
0.00367; for carbon dioxide, 0.00373; for hydrobromic acid
gas, 0.00386. At 3^ atmospheres pressure a becomes 0.00371
in the case of air. The coefficient of expansion of carbon
dioxide rises with pressure as follows : at 1 atmosphere, 0.00373;
at 3, 0.00389; at 8 atmospheres, 0.00413. In the case of hydro-
gen which is, on the other hand, less compressible than Boyle's
Law would lead one to expect, the rise of the coefficient with
increase of pressure is slower: at one atmosphere it is 0.00367;
at eight atmospheres, 0.00369.

In one paper Mendeleeff recalculates the results of Magnus,
Regnault and v. Jolly for air at constant volume, reducing the
barometric readings to 45 ° latitude. He gives the following
table:

Determinations As given by author Corrected value.

Majs^nus 8 0.0036651 0.0a36700

liegnault 15 0.003665 0.0036694

V. Jolly 20 0.0036696 0.0036702

Mean, 0.003670

The coefficient for constant pressure, as found by himself
with Kajander, is recalculated in the same way and given as
0.003681.

The investigations of Andrews upon the critical state,

12

EXPANSION OF OASES

among other points, led to a study of the coefficient of expan-
sion of carbon dioxide at higher pressures. He gives the
following figures for a (constant pressure) atO° — 7.5° :

Ttmos^'pherisi ^^ 16.25 20.01 24.8 27.7 81.1 34.5

Coefficient 0.00462 0.00520 0.00607 0.00700 0.00782 0.00895 0.01097.

The value of a (64° -100°) increases with increasing pressure
up to 0.01822 at 145.5 atmospheres; then decreases: at 223
atmospheres, a = 0.0084.

The coefficient for constant volume rises from 0.003526 at
21-24 atmospheres to 0.007018 at 94-118 atmospheres.

Several researches conducted during the past fifteen years
have shown extraordinary improvement in the accuracy of
measurement of pressure changes in gas thermometers. The
researches of Callendar upon the platinum thermometer and its
standardization by means of the gas thermometer, have led to
the improvement of the latter as an instrument for exact
determinations. The work of Chappuis is so striking an
example of the kind of accuracy referred to, that a much more
detailed abstract of his memoir is given in the body of the
book (page 153). The coefficients for hydrogen as found, by
him are : constant volume, 0.0036624 ; constant pressure,
0.0036600. If these are reduced to their limitary values which
refer to zero pressure, they become 0.0036624 and 0.0036625
respectively, giving as ^* absolute zero "on the centigrade scale
—273.04°. The mean coefficient of expansion found by him for
nitrogen, at constant volume, between 0° and 100° is
0.00367466. The figure found for air by Callendar and Grif-
fiths is almost identical, 0.0036749. The latter was, however,
the result of but a single determination. Wiebe and Bottcher
found an average value of 0.0036706 for air, in a series of figures
ranging from 0.0036694 to 0.0036713. Finally, Harker and
Chappuis, in a recent memoir, find as the coefficient of expan-
sion of nitrogen at constant volume (in glass) the figure
0.00367180 for an initial pressure of 793.5 mm. of mercury, and
0.0036683 for an initial pressure of 530.8 mm. of mercury. In
the limit, then, at zero pressure, it would be 0.0036613. The
limiting value for the coefficient at constant pressure is
0.0036612. These results indicate the limit of accuracy
attained np to this time.

13

MEMOIRS ON

In 1895 Kuenen and Randall examined the rate of expansion
of argon and helium through a considerable range of tem-
perature ; the fact tliat the coefficient remained almost constant
showed the absence of dissociation in the gases examined and
was taken as proof of their simple molecular condition.

Before closing, reference should be made to work done in
the study of the behavior of gases at very low pressures. The
results of the research of Melander are summarized in the
following table, where jo = initial pressure, y = final pressure,
a=a coefficient of expansion at the pressure j!?' ; the probable
error as calculated by Melander, is given for the first and last
values of a only, these being the limiting values.

I — Air.

p

P'

a

Error

752

1027.7

0.0a36660

0.0000005

376

513.7

6624

260

355.2

6606

170

232.2

6594

100

136.6

6630

78

106.6

6657

51.8

70.8

6717

29.1

38.8

6853

13.2

18.1

7172

6,6

9.1

7627

0.0000021

II-

—Air.

749

1023.4

0.0036642

0.0000004

254

346.9

6580

•

101

138.0

6634

75

102.5

6645

18.6

25.5

6895

5.8

7.98

7666

0.0000021

III — Carbon Dioxide.

749

102S.1

0.0037264

0.0000005

347

474.9

6856

267

365.2

6803

169.5

231.7

6701

101.5

138.7

6657

55.8

70.2

6641

18.1

24.7

6753

0.0000015

IV — Hydrogen.

764.5

1043.6

0.0036504

0.0000002

351.7

480.1

6518

191.0

260.8

6547

111.7

152.5

6548

48.4

66.2

6595

20.1

27.4

6721

9.3

12.8

7002
14

0.0000022

EXPANSION OF GASES

It will be noted that with decrease of pressure the value of a
falls until a minimum is reached and then rises again ; with
hydrogen, on the one hand, the minimum seems to have been
reached at about atmospheric pressure ; with air the minimum
occurs at about 300 mm. pressure^ and with carbon dioxide at
about 100 mm.

The accuracy of the results obtained by other experimenters
at very low pressures, has been challenged by Baly and Rum-
say, who point out the difficulty of the removal of all gas from
a glass vessel and the likelihood of the presence in the gas
examined of carbon dioxide and water vapor given off from
the walls of the vessel after the pressure has been lowered. The
shrinkage of the vessel under atmospheric pressure after the
removal of most of the gas contained in it, is another source of
serious error. Of course these difficulties become important
only at very low pressures. The following table contains the
figures found for tlie coefficients of expansion of hydrogen,
oxygen and nitrogen at pressures below 5.5 mm. :

I — Hydrogen.
Pressure in mm. 4.7 3.47 0.25 0.096 0.077

.003656 0.003653 0.003623 0.003366 0.003327

Coefficient

( 0.003€

II — Oxygen.
Pressure in mm. 5.1 5.3 4.0 2.5 1.4 0.083 0.07

rnpffipiPiVf -3 ^^T ^^ ^^^ ^^^ 53V.T iriiT ^1? ??V.7

^"^"^^*^"*' (0.003831 0.003846 0.003817 0.003984 0.003998 0.004292 0.004098 0.004161

III — ^Nitrogen.

Pressure in mm. 5.3 4.97 3.0 1.1 0.8

Coefficient -f ^^* "sihs Wrrs ^i? ^Jt

(0.003290 0.003238 0003315 0.003290 0.003021

Pressure in mm. 0.6 0.6 0.6 0.6

^^oemcieuc -j^jjoogsi? 0.002911 0.002653 o.oc3096 0.0033220.003058 0.002095 0.002915

Mean of eight results at 0.6 mm. — ^J.3^ [—0.002919].

Baly and Eamsay give their results in common fractions ; the

corresponding decimal fractions have been introduced for the

15

EXPANSION OF GASES

sake of comparison with the results of others. The authors
sum up their results as follows :

" 1. The coefficient of expansion of hydrogen with tem-
perature decreases as pressure la lowered. It is normal down
to a pressure of 0.1 mm.

** 2, The coefficient of expansion of oxygen is greater than the
normal one, being ^Jg instead of ^^ ; it increases with decrease
of pressure to ^J^ at 1.4 mm. ; at 0.7 mm. of pressure it is
erratic ; but at lower pressures it again becomes more constant,
still showing, however, a tendency to increase as the pressure is
decreased.

" 3. With nitrogen the coefficient of expansion is lower than
th6 normal (^i?) at pressures between 5 and 1 mm. ; at lower
pressures, like that of hydrogen, its coefficient of expansion
decreases ; that is, the gas becomes more elastic.

'^4. So far as it was possible to experiment with carbon
dioxide, its behavior appears to resemble that of hydrogen and
nitrogen, but owing to the tendency which it has to condense
and cling to the gauge, trustworthy measurements were im-
possible to attain. These results confirm those of Mendel6eff ^
and Siljestrom,^ although they are deduced from thermal ex-
pansion, while theirs were deduced from the compressibility
of the gas. And Bohr's results' as regards the abnormality
of oxygen were also confirmed, although likewise by a diflferent
method.^'

1 Annalea de Chimie et de Physique, [5] 9, 111-116 (1876).

2 Bihnng till K. Svenaka Vet. Akad. Handlinc/ar,, % 1 (1873) ; Pog-
gendorff's A^naleriy 151, 462-482, 573-6a3 (1874).

> Wiedei iiiauu's Annalerif fM7, 459-479 (1886).

16

EXPERIMENTAL ESSAYS

On the Constitution of Mixed Oases; On the Force of Steam
or Vapor from Water and other liquids in different tempera-
tures, both in a Torricellian Vacuum and in Air; On Evapora-
tion; and on the Expansion of Gases by Heat

By John Dalton

From the Memoirs of the Literary and Philosophical Society

of Manchester y volume 5, part 2, pages 695-602 (1802)
Translated into German: Oilhert^s Annalen, volume Vl^ pages

310-318 (1802)

17

CONTENTS.

Object ......

Necessity of drying gases experimented with

Apparatus used; tnanipulation

Results .....

Comparative expansion in lower and upper parts of
meter scale ....

Experiments with gases other than air
Conclusions .....

Biographical Sketch ....

PAGE

a a

19

• •

19

19,

20

20,

21

thermo-

• •

21

• •

21

• •

21

• •

23

18

»\

ON THE EXPANSION OP GASES BY HEAT.

By Johk Dalton.

The principal occasion of this essay is another on the same
subject by Messrs. de Morveau and du Vernois in the first vol-
ume of the Annales de Chimie, It appearing to them that the
results of the experiments of De Luc, Col. Koi, de Saussure,
Priestley, Vandermoude, BerthoUet and Monge did not suffi-
ciently accord with one another; and that it would be of
importance to determine not only the whole expansion of each
gas from two distant points, such as the freezing and boiling,
but likewise whether that expansion be uniform in every part
of the scale, they instituted a series of experiments expressly
for those purposes. The result of which was that betwixt the
temperatures of 32° and 212°, the whole expansion of one gas
differs much from that of another, it being in one case about
-^ of the original, and in others more than 12 times that expan-
sion; and that the expansion is much more for a given number
of degrees in the higher than in the lower part of the scale.
These conclusions were so extremely discordant with and even
contradictory to those of others, that I could not but suspect
some great fallacy in them, and found it in reality to be the
fact: I have no doubt it arose from the want of due care to
keep the apparatus and materials free from moisture.

My method of experimenting on this subject is simple, and
therefore less liable to error. A straight manometer tube, such
as has been mentioned, is duly divided into equal portions of
capacity; it is then dried by a wire and thread, and the open
end inserted through a cork into a phial containing sulphuric
acid, in order that the aqueous vapour may be drawn out of
the tube; this is essential if we operate in temperatures
lower than that of the atmosphere, otherwise not. For want
of this attention, Col. Roi, in his valuable paper in the Phih
Trans, vol. 67, has been led into some erroneous conclusions.
— A small column of dry mercury is then let down to a proper

19

MEMOIBS ON

point in the manometer, and it is ready for experiment with
common air.

It requires some address to fill the manometer with any other
gas. — I succeeded best as follows: filled the tube with dry
mercury; then pushed down a wire and thready so that when
the wire was got to the end of the tube, a thick covering of
thread just entered the open end, and held the mercury like a
cork, so that the tube could be inverted without losing the con-
tents; then having a glass funnel with a perforated cork over
the water apparatus, containing the gas, I slipped the mano-
meter through the hole in the cork, and putting my hand into
the water under the funnel, drew the wire out of the mano-
meter, and with it the mercury; upon which the gas entered
the manometer. For carbonic acid gas, I opened the sealed
end of the manometer, drew it out to a capillary bore, and
forced a stream of the gas through the tube; then putting my
finger on the other end, sealed it again by a blowpipe, and let
down a small column of mercury to the proper point.

When the manometer was to be exposed to a heat of 212°, I
used a Florence flask with a long glass tube corked into it, in
such sort that as much of the manometer as was necessary to
be exposed to the temperature might be in the tube; then
water at the bottom of the flask was made to boil violently, so
that a constant stream of vapour issued out of the top of the
glass tube, which was found to raise the thermometer to 212®.
Small specks of white paint were put upon the divisions of the
manometer together with numbers which were discernible
through the containing tube. For lower temperatures a deep
tin vessel containing hot water was used in which the mano-
meter was immersed, the water being well agitated previously
to each observation.

From a great many experiments made in this way on com-
mon air, and likewise upon hydrogenous gas, oxygenous and
nitrous gases, and carbonic acid gas, I can assert that the con-
clusions of DeLnc, Eoi, Saussure, Berthollet, etc., are nearly
accurate throughout, and that those of de Morveau and du Ver-
nois are extremely inaccurate in the higher temperatures.

I have repeatedly found that 1000 parts of common air of
the temperature 55 ° and common pressure, expand to 1321

20

EXPANSION OP GASES ^ ,,

)

parts in the manometer; to which adding 4 parts for the cor-
responding expansion of glass^ we have 325 parts increase upon
1000 from 66® to 212*^; or for 167® of the thermometric scale.
As for the expansion in the intermediate degrees, which Col.
Boi's experiments show to be a slowly diminishing one above
the temperature of 67®, but which de Morveau^s on the con-
trary show to be a rapidly increasing one in the higher part of
the scale; I am obliged to allow that Col. Boi is right, though
it makes in some degree against an hypothesis I have formed
relative to the subject; he has certainly however made the
diminution too great from 72® downwards, owing to his not
perceiving that he actually destroyed a portion of the elastic
fluid he was operating upon (aqueous vapour) in reducing its
temperature so low; if his air had been previously dried by sul-
phuric acid, etc., he would not have found so remarkable
diminution below 72 ®. My experiments give for 77i® above 56 ®,
167 parts; for the next 77 J*^ only 158 parts: and the expansion
in every part of the scale seems to be a gradually diminishing
one in ascending.

The results of several experiments made upon hydrogenous
gas, oxygenous gas, carbonic acid gas and nitrous gas, which
were all the kinds I tried, agreed with those on common air
not only in total expansion, but in the gradual diminution of
it in ascending : the small differences observed never exceeded
6 or 8 parts on the whole 325 ; and differences to this amount
will take place in common air when not freed from aqueous
vapour which was the situation of all my factitious gases.

Upon the whole therefore I see no suflBcient reason why we
may not conclude, that all elastic fluids under the samepressure
expand equally by heat — and that /or any given expansion of
mercury y the corresponding expansion of air is proportionally
something less, the higher the temperature.

This remarkable fact that all elastic fluids expand the same
quantity in the same circumstances, plainly shows that the ex-
pansion in solid and liquid bodies seems to depend upon an ad-
justment of the two opposite forces of heat and chemical af-
finity, the one a constant force in the same temperature, the
other a variable one, according to the nature of the body ;
hence the unequal expansion of such bodies. It seems there-

21

7^

MEMOIES ON

fore that general laws respecting the absolute quantity and the
nature of heat, are more likely to be derived from elastic fluids
than from other substances.^

Dalton, in his New System of Chemical Philosophy (London:
1808), page 19, in discussing a proposed new method of denot-
ing temperature, says in reference to the expansion of gases:
'^The volume at 32° is taken 1000, and at 212% 1376 accord-
to Gay-Lussac's and my own experiments. As for the expan-
sion at intermediate degrees, Gen. Boy makes the temperature
at midway of total expansion, 116^ old scale ; from the re-
sults of my former experiments {Manch. Mem. Vol. 5, Part 2,
page 599), the temperature may be estimated at 119^; but I
had not then an opportunity of having air at 32°. By my
more recent experiments I am convinced that dry air at 32°
will expand the same quantity from that to 117° or 118° of
common scale, as from the last term to 212°. According to
the theory in the above Table it appears, that air of 117° will
be 1188, or have acquired one half its total expansion. Now
if the theory accord so well with experiment in the middle of
the interval, we cannot expect it to do otherwise in the inter-
mediate points. '^

Biographical Sketch.

John Dalton was born in Cumberland, England, in the year
1766. He was to a large extent self-taught and, when grown,
was able to support himself by teaching school while, through
the kindness of a friend, who helped him by lending him books
on scientific subjects, he studied hard to acquire a knowledge
of natural philosophy. His papers on meteorological subjects
drew attention to him and in 1793 he was appointed to the pro-
fessorship of mathematics and natural philosophy in the Man-
chester New College. Simultaneous observations made in Cum-

1 Note by Translator: The paper concludes with an exposition of
Dalton*8 theory that the absolute temperature increased at the same rate
as the cube root of the volume in the case of f^ases, by which he finds the
temperature of absolute cold to be 1515° below 0° F.

22

EXPANSION OF GASES

berland and at Manchester enabled him to calculate the height
of the aurora from the earth^s surface. The fact that water
vapor exists mixed, and not combined, in the air was announced
by him at this time. In 1794 he called attention to the ex-
istence of color blindness or ** Daltonism/* as it was sometimes
called, having discovered that it was a feature of his own vision.
Continuing his meteorological studies, he was led to giving a
definition of the ** dew-point.*' In 1800 he noted the rise of
temperature which takes place in gases when compressed. Of
the four important papers read before the Manchester Society
in 1801, the fourth is the one quoted in full. In the first he
brings out ** Dalton's law of mixed gases," assuming that gas
particles are elastic only towards particles of the same kind.
In the second paper, ** On the force of steam,*' he describes
the dew-point hygrometer and predicts the liquifaction of gases
by cold and pressure. In the third paper he shows that evap-
oration is proportional to the temperature, whether in air or i7i
vacuo. That four such contributions to science should have been
presented at one time is striking proof of the extraordinary
powers of their author.

The data upon which the Law of Multiple Proportions is
based were next brought forward and, soon after, in 1803-5, the
Atomic Hypothesis and the announcement of the atomic
weights of some of the elements. Following the promulgation
of his views in Thomson's System of Chemistry (1807), Dalton
published in 1808 his New System of Cliemistry, In this he an-
ticipated in a way Dulong and Petit*s Law, for he seemed to 'as-
sume for the atoms of all elements equal capacity for heat.

In 182.5, on the establishment of the Eoyal Society Prize, it
was first bestowed upon Dalton in recognition of his contribu-
tions to the advancement of chemistry.

Dalton lived until 1844, but his classical memoirs practically
all belong to the period before 1815.

23

KESEARCHES UPON THE RATE OP EXP AN-
SION OP GASES AND VAPORS.

By L. J. Gay-Lussac.

Fromthe Annales de Chimie^ series 1, volume 43, pages 137 —
175 (1802). Translated into Oerman, Gilbert's Annalen, vol-
ume 12, pages 257—291 (1802).

25

CONTENTS.

PAGE

Object of the investigation 27

Effect of the presence of moisture upon the expansion of

gases 29

Earlier investigations :

Amontons 30

Nuguet 31

Lahire 31

Stancari , . . . . . , . .32

Colonel Roy 33

Saussure 33

Priestley 33

Mo7ige, Berthollet and Vaiidermonde . . .34

Guyton de Morveau and Duvernois . . . .35

Charles 37

Apparatus and manipulation :

First Method 38

Same, simplified 40

Results with air 42

Results with other gases ♦ 43

Method employed for gases soluble in water . . .44

Results 45

Experiments upon ether vapor 47

Conclusions 48

Biographical Sketch 48

26

RESEARCHES UPON THE RATE OP EXP AN-
SION OP GASES AND VAPORS.

By L. J. Gay-Lussac.

Part I.
Object of this Memoir,

Fob a long time physicists have busied themselves with [the
problem of] the expansion of gases; but their researches pre-
sent such great discrepancies in the results that, instead of
establishing their views, they call, on the contrary, for a more
rigorous investigation.

The expansion of vapors has attracted the attention of physi-
cists to a less extent. Although for a long time the extraordi-
nary properties of steam have been recognized and the most
beneficent applications of them have been brought about,
Ziegler and Bettancourt are the only ones, to my knowledge,
who have endeavored accurately to determine them. Their
experiments cannot however lead to a knowledge of the actual
expansion of this vapor; since, having always some water in
their apparatus, there was, for each new degree of heat, an
expansion of the vapor produced by former increments of heat
and an increase of volume due to the formation of new vapor —
two causes which combined evidently to push up the mercury
in their manometer.^

1 The apparatus of Bettancourt consists of a boiler of copper with
a cover of the same metal, through which three tubes pass. The first
serves to introduce water into the boiler; throu«:h the second is inserted
the stem of a thermometer intended to show the temperature of the
vapor, and to the third is attached a suitably shaped barometer tube to
measure the tension of this same vapor. A vacuum is produced in the
boiler with the aid of a pneumatic pump, which is connected by means
of a tube provided with a stop cock. The apparatus of Ziegler differs
but little from that of Bettancourt; but Ziegler not having produced, as
Bettancourt did, a vacuum in his boiler, there results a great difference
in their experimental data. (Architecture hydraulique de Prony, Tome
11).

27

MEMOIRS ON

N The thermometer, as it exists to-day, cannot serve to show
with accuracy relative amounts of heat, because we do not yet
know what relation exists between the degrees of the ther-
mometer and the quantities of heat which they can indicate.
We believe, it is true, in general, equal divisions of its scale
correspond to equal increments of caloric; but this view is
supported by no very positive fact.
] It must therefore be admitted that we are far from having
exact knowledge of the expansion of gases and vapors and of
the movements of the thermometer; and in the meantime
there is every day a call, in physics and in chemistry, to reduce
a given volume of gas at one temperature to another; to meas-
ure the heat given off or absorbed in the change of constitution
of substances, that given off or absorbed by the same body in
passing from one temperature to another; in the arts, in calcu-
lating the efficiency of steam engines, in ascertaining the rate
of expansion of many substances; in meteorology, in deter-
mining the quantity of water held in solution in the air — a
quantity which varies with its temperature and its density and
follows a law as yet unknown. Finally, in the preparation of
tables of refraction by astronomers and in the application of the
barometer to the measurement of altitudes, it becomes indis-
pensable to know with accuracy the temperature of the air and
the law of its expansion.

Although these facts have made it very desirable to engage
in a work of such general application, the difficulty of the
investigations which it demands would have prevented my de-
voting myself to it, had I not been on the other hand strongly
urged by Citizen Bertliollet, whose pupil I have the honor to be.
To him I owe the means necessary for the prosecution of this
research, during which I have often been assisted by his advice
and by that of Citizen Laplace: men whose reputation will add
to the confidence my work would inspire.

The researches I have undertaken upon the law of the ex-
pansion of gases and vapors, and upon the movements of the
thermometer, not being yet complete, I have for ray object in
this memoir only to investigate the expansion of gases and
vapors for one definite rise of temperature and to make it clear
that this is the same for all these fiuids; but before giving an

28

EXPANSION OF GASES

account of my experiments, I think I ought to give an histori-
cal survey of what has been done upon this subject. And as
I add at the same time some comments upon the means whicli
have been employed, I intend to preface them with a discus-
sion of one of the chief causes for uncertainty which can
enter into this class of investigations. Although it is very
important and although it seems to have been unknown to
the majority of the physicists who have studied the expansion
of gases, it will be enough for me merely to state it to make
its influence felt. What I say of atmospheric air will apply to
other gases.

This cause of uncertainty is due to the presence of water in
the apparatus. As a matter of fact if a few drops of this fluid
are left in a vessel filled with air whose temperature is then
raised to that of boiling water, this water, on passing into the
form of a vapor, will occupy about 1800 times as great a volume
as at first, and by this means will drive out a very large part of
the air originally enclosed in the vessel. It necessarily follows
that when this vapor is condensed — and therefore occupies a
space 1800 times as small — we should ascribe to the air remain-
ing in the vessel an expansion far too great; for it would be
assumed that it was this air which at the temperature of boiling
water filled all the space in the vessel. If we do not carry the
temperature up to this point, the same source of inaccuracy
will nevertheless exist, and its extent will be proportional to
the temperature at which we stop: for in this case the water
will not all evaporate, but the air will dissolve more and more as
the temperature rises and will consequently assume a greater and
greater volume over and above that which it owes to the heat;
so that when we pass to a lower temperature the volume of air
which fills all the space in the vessel will decrease from two
causes: (1) through the loss of its caloric, (2) through that of
the water which it holds in solution. Too great an expansion
would thus be assumed for the air.

Speaking generally, whenever there is enclosed with gases
any liquid, or even any solid which like sal ammoniac, for
example, can be dissolved or become vaporized at the tempera-
ture to which it is to be raised, errors must of necessity result
in the determination of the expansion of these gases.

29

MEMOIKS ON

Part II.

Historical Sketch of what has been done upon the

Expansion of Gases,

The expansion of atmospheric air by heat was well known
before the time of Amontons, but this physicist is apparently
the first to seek to determine its amount for a given rise of
temperature. To attain this result he enclosed some air with
the aid of mercury in a flask connected with one of the arms
of a reversed siphon^ and placed this apparatus in a bath of hot
water.^ The air expanded by the heat presses upon the mer-
cury and forces it into the other branch of the siphon; so that
he judged, by the height of the mercury compared with its
level in the flask, the tension the air had reached.

From various experiments made upon different volumes of
air, he concludes {Mem. de Vacad.y 1699, 1702): (1) ^'That the
heat of boiling water has limits which it does not pass; (2)
that various volumes of air increase their tensions at the same
rate for equal degrees of heat, and vice versd; (3) that the heat
of boiling water increases the tension only until it is capable
of sustaining about the weight of a column of mercury of ten
inches' height.^'

It appears then that, however compressed a volume of air
may be, the heat of boiling water always increases its tension
one third; that is to say, a volume of air compressed, for
example, under a column of 60 inches of mercury, including
the weight of the atmosphere, will support, at the temperature
of boiling water, a column of mercury of about 80 inches. He
therefore concludes '^that the same degree of heat, small as it
may be, will always increase the tension of the air more and
more as this air is supporting a greater and greater weight.'*

If Amontons had started from a degree of heat more clearly
defined than what he calls an average, — which would have been
at that time scarcely possible — it would have been possible to
calculate from his experiments with sufficient approximation

iThe air enclosed in the flask, not being able to escape when the
mercury is poured in, is a little more compressed than it would be
naturally; but if no other pressure than that of the atmosphere is de-
sired, it would be very easy to avoid this slight inconvenience.

30

EXPANSION OF GASES

the expansion of atmospheric air; yet^ since he conducted his
comparisons wifch volumes of gas of very unequal density^ one
may conclude from them that, however dense a volume of air
may be, the increase of elasticity which this air acquires for the
same degree of heat always bears the sams relation to that which
it had prior to the experiment.

Nuguet, in seeking to verify the results of Amontons^ ob-
tained others entirely unlike them. In one of his experiments,
the volume of the air expanded by the heat of boiling water
and the original volume were to one another as 2 to 1, and in
two other experiments as 16 to 1. His apparatus consisted of a
flask inverted and sunk in a water bath whose temperature he
raised to that of boiling water. It is evident that this appara-
tus was extremely defective, since the air in it was always in
contact with water; and Nuguet had in addition let some
water into his flask. It is not surprising, therefore, that he
obtianed results so discordant and, so to speak, so extraordin-
ary. (Mem, de Vacad,, 1708. Lahire.)

This great difference between the results of Amontons and
those of Nuguet upon the rate of expansion of atmospheric
air, and the realization that it had been subjected to experi-
ment under conditions which were not usual, led Lahire to ap-
ply himself to the same problem. The apparatus of which he
made use was identical with that of Amontons, except that the
bulb carried a small tube which he sealed after having intro-
duced the mercury. By this means, the mercury being at the
same level in the bulb and in the syphon, the air which he sub-
jected to experiment was no more compressed than the sur-
rounding air. With this apparatus Lahire found, first, in one
experiment that the air expanded from an average temperature
up to that of boiling water, could not sustain a column of mer-
cury of one third of the weight of the atmosphere; later, he
found in another, the thermometer being lower and the barom-
eter higher than in the former experiment, that the air, ex-
panded by the heat of boiling water, could not support a col-
umn of mercury so high as the former one. These two results
are evidently contradictory; but Lahire suspected no error and
drew the conclusion from them that we are bound to admit
that we do not yet know the nature of the air.

31

MEMOIKS ON

In order to explaiu the great difference which existed be-
tween his results and those of Naguet, a difference far too
great not to be due to some outside influence, Lahire noticed
that Nuguet had let a little water into his apparatus; and from
this fact he concluded that it might be this water which^ on be-
ing converted into vapor and expelling a large part of the air
enclosed in the flask^ had produced so great an expansion. He
was thoroughly confirmed in his opinion by the result of an ex-
periment carried out after Nuguet's method, in which he let a
little water into the flask; for he found that the volume of the
air expanded from the average temperature up to that of boil-
ing water, and the original volumes were to one another as 35^
is to 1. {Meni. de VcLcad.y 1708.)

At the same time M. Stancari of Bologna showed that water
increases to a considerable degree the volume of air at a tem-
perature but slightly raised. We therefore owe to these two
physicists the important discovery of the influence of water up-
on the expansion of atmospheric air; yet although they have
by their experiments given the matter prominence, it has since
been generally overlooked. To the slight attention paid to
this influence must be ascribed the great divergencies found in
the results of physicists upon the expansibility of gases.

It is known that the altitudes to which one ascends in the
atmosphere are given by the logarithms of the corresponding
heights of the barometric column. If the density of the air were
always the same, it would be easy thus to calculate the alti-
tude of one place above another stated place, by observing the
barometer there. It would therefore be important to distin-
guish the causes that affect the density of the air, in order to
make the necessary corrections in the heights given by the ba-
rometer.

Deluc, who has inaugurated a new era in this department of
physics, recognized in heat one of these causes. In order
clearly to identify its effect, he began by endeavoring to fix the
temperature at which the logarithms indicate directly the cor-
rect altitudes, and found, on comparing numerous observations
made at places whose altitudes he had determined with accur-
acy, that this was the case at the temperature of 16f ° of the
thermometer graduated in 80 divisions, and this he calls tmi-

32

EXPANSION OF GASES

perature fixe. Therefore to make correctioii for the effects of
heat above and below this fixed pointy he again compared the
altitudes found from the logarithms with those he had meas-
ured, attributing to heat the variations of the first from the
second^ and drew the conclusion that '^in the neighborhood of
the fixed temperature^ the correction for one degree of the
thermometer would be to the altitude of the place as 1 is to
215.'^ (RecheVy sur les modif. de rat, IV Fart, Ch. HI.)

Colonel Boy has found a far greater rate of expansion for
air. According to him, in the neighborhood of 15° on a ther-
mometer graduated in 80 divisions, air expands j}^ of its vol-
ume for each degree. He also found that moist air expands
much more than dry air; but Saussure noted that in carrying
out his experiments, Col. Roy had admitted into his manome-
ter either water in a liquid state or water vapor and had con-
fused two things which should be distinguished, namely, the
conversion of water into an elastic fluid, and the expansibility
of air mixed with this vapor. (Philos. transact., 1777, p. 704.)

Saussure determined the rate of expansion of air in the neigh-
borhood of 6° to be ^i^ of its volume for each degree. His ex-
periments were performed with a large flask in which were
enclosed a thermometer and a barometer to indicate the varia-
tions of the temperature of the air and the corresponding ten-
sion acquired. In order to study the effect of water upon the
expansion of air, he enclosed in his flask air of varying degrees
of dryness, avoiding the formation anew of vapor, and, far from
finding this air more expansive than very dry air, he thought he
had discovered, on the contrary, that very dry air was even a
little more expansive than air which was very moist, but was
holding its moisture all the time entirely uncondensed. (Bs-
sat sur Vhygrometrie, page 1 08.)

Up to this time physicists had limited themselves to the ex-
pansion of atmospheric air, and the first to occupy himself with
that of other gases is the celebrated Priestley. He proceeded
as follows :

After having filled a flask, over mercury, with the gas he
wished to test, he fitted to it a bent tube, one of whose arms was
nearly horizontal, and left a little mercury in the neck of the
fiask so that the expansion of the gas could push it into the

33

MEMOIKS ON

tube. This doue^ he put his apparatus in a small woodeu box^
introduced a thermometer^ and carried it into rooms at differ-
ent temperatures : the expanded air caused the mercury to
move a greater or less distance along the tube^ and it was by
this distance measured in inches that Priestley determined the
expansibility of different gases. As all the experiments were
made with the same flask and the same tube^ which he probably
inclined always in the same way, they give a ratio among the
expansibilities of different gases, but not the actual expansion ;
for it would be necessary to know for that purpose the volume
of that part of the tube traversed by the mercury in compari-
son with that of the flask, and to know, in addition, the exact
inclination of the tube, of which Priestley makes no mention.
I shall not pause longer to discuss these experiments ; all the
more as Priestley himself did not put much confidence in them
and wished to repeat them under better conditions. Assuming
the volumes of the different gases equal, the expansion measured
in inches along the tube, for 4.44° of the thermometer gradu-
ated in 80 divisions, ^ would be :

Ordinary air 1.32 inches

Hydrogen gas 2.05 "

Nitrous gas 2.02 "

Carbonic acid gas .... 2.20 "

Muriatic acid gas .... 1.33 **

Oxygen gas 2.21 "

Nitrogen gas 1.65

Sulphurous acid gas .... 2.37

Fluoric acid gas 2.83 "

Ammoniacal gas 4.75 *^

{Experiments and Ohservations, etc, Book Vlly Section VI.)

In a memoir printed among those of the Academy for the
year 1786, Citizens Monge, Berthollot and Vandermonde have
concluded from an experiment that, for one degree atmospheric
air expands ts-^.s-s ^^ ^^^ volume, and hydrogen gas rffl.iy^.

Lastly, Citizen Guyton, realizing how little accord there was
on [the subject of] the rate of expansion of atmospheric air,

1 Note by Translator: On an 80-degree thermometer scale (e. g,
Reaumur's) 4.44° is the equivalent to 10° Fahrenheit. The latter was
evidently the temperature interval employed by Priestley.

34

tt

EXPANSION OP GASES

and that there were still no direct experiments on record which
determined the expansion of gases for slightly elevated degrees
of heat and for successive degrees near together, undertook^
with Citizen Davernois^ to throw some light upon this matter.
As their work is the most recent, I shall pause a moment to
endeavor to show what the causes are which were able to affect
their result.

Their apparatus consisted of a flask fitted with a bent tube
by means of which the air expelled from the flask by heat was
caught in a receiver in the mercury trough. The flask, full of
the gas they wished to subject to experiment, was immersed in
a bath at the temperature of melting ice and was held there
by an iron cover. They heated the bath to 20% 40% 60% 80%
successively, and caught in different receivers the gas forced
out by expansion through each of these intervals; they finally
determined the volumes of air escaping from the fiask by
measuring them in their respective receivers after having
reduced them to the temperature of melting ice, and thus
found the volume of that remaining in the fiask.^ But apart
from the fact that their apparatus made it necessary for them
to determine many constants — which must interfere with the
accuracy of their results — I note that, after the sinking of the
bent tube in the mercury, not having introduced some more
air into the fiask to replace the mercury which was pushed into
the tube as a result of the pressure of the mercury of the bath,
several degrees of heat would be needed before a single bubble
of air escaped from the fiask; so that, if they had made use of
lesser intervals, as, [for example] of 5*^ each, they would have
found that, starting from zero, the first degrees of heat would
have shown no expansion in the different gases. Indeed they
have observed an expansion for the first 20 degrees which, for
the majority of the gases, is far too small.

This source of error, although serious, would not have car-
ried the results of Citizens Guyton and Duvernois so wide of
the truth, had there not been others still more serious. Thus
I suspect that their fiask had not been properly dried and that
a little water may have got in during the introduction of the

1 Annalea de Chimiet Vol, I,

35

MEMOIKS ON

gases. Had a decigram of water remained^ it would have
served to alfect their results in a marked way^ especially towards
the higher degrees, where, in changing into an elastic fluid, it
would have forced a large part of the air out of the flask.

In this way can be explained the noticeably increasing pro-
gression which they have determined for all the gases, whereas
they ought to have found a decreasing one, on lowering to the
temperature of melting ice the amount forced out by each
expansion. I note in connection with this point, that Citizen
Guyton expresses himself as regards the expansion of hydrogen
gas as follows:^ ^^ The four [volumes] resulting from the expan-
sion were caught this time in a receiver which had been sur-
rounded with vessels filled with ice. In spite of this, the
mercury of the little trough showed upon the thermometer [a
temperature] 2, 3, 4, 6 degrees above zero, while the water of
the bath was at the same moment at 20, 40, 60, and 80 degrees
— a thing which could produce some inaccuracy in the deter-
mination of each of these quantities, but which cannot be of
much consequence, the expansion being very slight through
these first degrees.**

From this one may conclude that these physicists gave no
more care to reducing the volumes of the other gases to zero;
and, if this be the case, there results another source of uncer-
tainty in their experiments.

In comparing the volumes of gas left in the flask with those
that had been driven out by heat. Citizens Guyton and Duver-
nois have found that the gases oxygen, hydrogen, carbonic acid
and atmospheric air had shown a contraction and have given
as its cause combinations which had taken place during the
time of the experiments. Employing mercury which was very
pure and free from oxide, I have been unable to detect any
noticeable action between the metal and these gases from the
temperature of melting ice up to that of boiling water.

Below is a table of the results of Citizens Guyton and
Duvernois ; they have enclosed between parentheses those in
which they have little confidence.

^Annales de Chimie, T. I, page 284.

36

EXPANSION OF GASES

1

FromO*'
to 20°

Prom 20 °
to 40°

Prom 40°
to 60°

From 60°

to 80°

FromO

to 80°

Ordinary air
expands

Vital air

Nitrogen gas
Hydrogen gas

Nitrous gas

Carbonic
acid gas

Ammoniacal
gas

T^^.ffT

y.ir

skv

(TT.iT)

T.ivj

Wti

?.%!f

'f.V^

(3 + T.V^)

4 + iriir

^15^.?T

y.lr

t.Vt

5 + yi^.5r

^+T.iff!r

jivT

t.Vt

G.Vt)

(s-i.-s-s)

ir.Vy

W.TS

ifhj^

"s.iwff

(ff.V?)

T.Vy

Tf.i^V

j.iw

t.Vt

G.Vv)

l+TTjt.7

"sh^

T.Vy

1+riy

(3+:f.V^)

^-H:.f?¥

Before going further, I ought to say that, although I had
noted a great many times that the gases oxygen, nitrogen,
hydrogen, carbonic acid and atmospheric air expand to the
same extent from O*' to SO*', Citizen Charles had, fifteen years
before, discovered the same property in those gases ; but, never
having published his results, it was by the greatest chance that
I learned of them. He had also endeavored to determine the
rate of expansion of gases soluble in water and had found for
each a characteristic rate of expansion different from that of
the other gases. In respect to this my conclusions differ much
from his.

Citizen Charles employed as his apparatus a barometer the
chamber of which was of a large size. The gas which he wished
to submit to experiment was enclosed in the reservoir of the
barometer at the temperature 0° and under a pressure of 28
inches of mercury. When this barometer was submerged in
boiling water, the mercury rose in the tube and the excess of
the entire column over that of 28 inches indicates the tension
the gas had acquired ; but Citizen Charles having been kind
enough to show me the apparatus, I saw that the tube of the
barometer was very large in proportion to the capacity of the
reservoir ; so that the rise of the mercury above 28 inches did
not show all the tension the gas had acquired, since for that it
would be necessary that its volume in the reservoir had
remained constant. It therefore seems to me that the true

37

MEMOIRS ON

rate of expausion of gases cannot be deduced from these ex-
periments.

Part III.

Description of Apparatus.

A flask B {Fig. 1) is provided with an iron tap to which a
bent tube ID (See Fig. 2) can be fitted. The key of the tap
carries a lever LL pierced at its two ends to receive two cords
by which one can open and close the tap under water.

FIG. 1

To introduce gases into the flask, I made use of a glass bell
jar M {Fig. 1), to which are fitted a tap and a bent tube T,
and sunk in a vessel QS. On pouring water into the vessel
and opening the tap, the gas compressed in the bell jar escaped
by the tube and filled the flask B placed mouth-downward in
the mercury bath PO, When the flask is full, I close the tap,
adjust the tube ID {Fig, 2) and fix it in a cylindrical iron cage
EFOH, which I then place in a copper vessel AD^ full of
water. In order that there might be no communication between
the outside air and the gas enclosed in the flask when the tap
is opened, I lowered the end of the tube ID one or two
millimeters into the small mercury bath KX. This done, I
heat the bath and at intervals of lO*', let us say, open the tap
and immediately close it again. The gas, tending to expand

38

EXPANSION OF GASES

on account of the heat^ escapes rapidly from the flask and has
soon driven out the atmospheric air which filled the tube ;
from 40 "^ on the tap can with safety be left open until the end
of the operation : I prefer however alternately to open it and
close it, as I find that [under these circumstances] the gas in
the flask comes more rapidly to the temperature, of the bath.
After 15 or 20 minutes of boiling — a sufficient time for every-

HORIZONTAL SECTION
ON YZ

FIG. 2.

thing to come to the same temperature — I remove the end of
the tube ID from the mercury, in order to secure equilibrium
between the outside air and the gas in the flask, and then close
the tap. After having cooled the bath with ice or water, I
remove the apparatus, disconnect the flask from which I
remove the tube ID and also the lever LL and submerge it
completely in a bath of known temperature where I leave it
long enough for it to come perfectly to that temperature.

Now, on opening the tap, there enters the flask a volume of
water which is exactly equal, when equilibrium is restored, to
that of the gas which has been driven out by the heat. The tap

39

MEMOIRS ON

being closed, I remove the flask, carefully dry its surface and
weigh it in this condition ; afterwards I weigh it full of water
and empty, recording the results of each weighing. These
being known, I find the volume of the flask by subtracting the
weight of the empty flask from that of the flask filled with
water, and the volume of the water which represents the volume
of air driven out of the flask by the heat, by subtracting, again,
the weight of the empty flask from that of the flask when it
contained this water. It will thus be very easy to determine
the relationship between the original volume and the volume
when expanded.

This method has the advantage of possessing great accuracy ;

for, as the volumes are found from the weights, the error

which can be made in this determination must be very small,

even when use is made of balances of no great sensibility.

The apparatus I have described is simple enough in itself,

yet, as it calls for the use of ce-
ments and of a tap which must
bo of iron by reason of the mer-
cury, its manipulation is some-
what difficult. It will not there-
fore be out of place to describe
another apparatus also which I
have used and which, along with
great simplicity and easy manipu-
lation, possesses at least nearly
all the advantages of the former one.
It is a simple flask D {Fig, I, Plate II)
[See Fig, 3] whose neck must be at least
a decimeter long. After having filled it
with the gas I wish to subject to experi-
ment, in the way already described, I in-
troduce its neck about two centimeters
into the mercury contained in an ordinary
vessel OM^ and fasten it in an iron frame
as in the case of the former apparatus.
If I immerse it in this condition in a bath of hot water, the gas
expanded by the heat, in order to escape, will have to overcome,
not only the pressure of the mercury in the vessel, but that of

40

FIG. 3.

EXPANSION OF GASES

the water of the bath as well. To do away with this incon-
venience^ I introduce into the neck of the flask the end of a
very narrow bent tube B, taking care to keep the end closed
until it has been lowered into some mercury. To support the
tube, I fasten to the middle of it a cord on the end of which I
hang a weight and pass it over a support^ in such a way that
the weight by its action tends to lift the tube. The apparatus
being thus arranged^ I place it in a glass tank where there is a
depth of water equal to that which should be in the bath, I
open for a moment the end of the tube in order to establish
equilibrium with the pressure of the outside air, and close it
again at once. As there is a scale whose divisions are very
small upon the neck of the flask, I read the exact level of the
mercury ac inside the neck of the flask and record it, since it
is to this level that the volume of the flask extends. The end
of the tube B must be raised above the level ac, for otherwise
the mercury will enter the tube and offer a resistance to the
escape of the gas expanded by the heat. After all these ma-
nipulations — which take longer to describe than to carry out-^
I place the apparatus in a bath of hot water and open the end
of the tube Grafter having put it in a small mercury bath, as
in the former apparatus. When the flask has come to the tem-
perature of the boiling water, I remove the tube B (whose end
must have been previously withdrawn from the mercury), and
cool the bath. The mercury then rises in the flask ; but it will
be easy to put water in its place, when everything is at a lower
temperature. The volume of the flask and the volume of the
water which has taken the place of that part of the gas driven
out by the heat, are found in the way I have already described ;
only it is necessary in this calculation to add to the weight of
the empty flask that of the cylinder of water extending from
the level ac on the one hand to the end of the neck of the
flask on the other.

I should be able to give still further details, but I withhold
them in order not to be too diffuse : those a little practiced in
manipulation will readily supply them. However, as it is a mat-
ter of importance, after what I have said about the effects of
moisture, to remove it entirely from the apparatus, I will de-
scribe how I have been successful in doing so.
D 41

MEMOIES ON

If the flask is evidently wet, 1 begin by drying it with filter
paper ; then I heat it so as to evaporate a part of the moisture
which it still may contain, and, with the aid of a bellows to
which I have attached a glass tube, I carry into its interior a
current of air to drive out the vapor. These last operations
being repeated many times with the flask and the tube, both
become perfectly dry. With regard to the mercury which I
have used in my experiments,^ I have invariably used what was
very dry and pure.

In all the experiments the results of which I am about to
give, I have always brought back to the temperature of melting
ice the gases whose rate of expansion I have been able to de^
termine with the apparatus I have described ; and for this pur-
pose I had a bath where I kept the ice and in which the flask
was completely covered after having been taken from the bath
in which it had been subjected to experiment, and here I left ,
it for about half an hour, during which time I constantly stirred
the bath. The other fixed temperature which I resolved upon
for the same gases, is that of boiling water.

I have made some experiments at other temperatures ; but
they will have to be repeated, and moreover they will become
part of a treatise which I have begun upon the law of the ex-
pansibility of gases and vapors ; I shall confine myself there-
fore, as I have said, to a consideration of the rate of expansion
of gases for a definite rise of temperature — which will be that
comprised between the degree for melting ice and that for boil-
ing water. With respect to vapors, I shall compare their rate
of expansion with that of gases.

Part IV.

Experiments and RestiUs.

Making use of the two [forms of] apparatus I have de-
scribed — but more often the second than the first — and avoid-
ing all the sources of inaccuracy which I could foresee, I have
found from six experiments upon atmospheric air, the six fol-
lowing results : ^

^ My fiask held about 350 grams of water.

42

EXPANSION OF OASES

Starting from the temperature of melting ice, at that of
boiling water equal volumes of atmospheric air represented by
100 had become, respectively : —

137.40 ; 137.61 ; 137.44 ; 137.55 ; 137.48 ; 137.57 ;
the mean of which is nearly 137.50.^

If the total increase of volume be divided by the number of
degrees which produce^J it, or by 80, we find, making the
volume at 0° temperature equal to unity, that the increase of
volume for each degree is ijxi^^, or on the other hand, r^i^^^
for each degree of the centigrade thermometer.

Deluc having found ^^ for the coefficient, it would appear
at first sight tfiat our results are the same ; but if it be noted
that he starts from a temperature of 16|°, while I start from
a temperature of 0°, it will be seen that our results are quite
different. ^ I shall later consider this difference and show
that the coefficients of expansion vary with the temperature
from which we set out.

Hydrogen gas produced from iron by weak sulphuric acid
was submitted to two experiments : in one, through an eleva-
tion of temperature from that of melting ice to that of boiling
water, 100 parts [by volume] became 137.49 ; and in the other,
through the same rise of temperature 100 parts became 137.56.
The average of these two results is 137.52 — wliich differs only
slightly from the average result found for the expansion of
atmospheric air.

Oxygen gas given off from the oxygenated muriate of
potash [i. e., potassium chlorate] was tested three times and
gave the following results : 100 parts became

1 Although the differences among the results are not very consi-
derable, I believe I could have made them very small had I been able to
note the state of the barometer during the boiling of the water. How-
ever, I have always taken care to note its temperature at the moment
of boiling and I confess I have never noticed any marked variations.
As a matter of fact it requires a change of an inch in the barometer to
produce one of a degree in the boiling point of water,— which must
occur but rarely. However that may be, the mean result, 137.50, must
be very close.

2 Note by Translator: — In the memoir the second temperature stated
is ** 0®^ ; " it seems evident that this is a typographical eiTor.

43

MEMOIKS ON

137.47 ; 137.54 ; 137.46 ;
the mean of which is 137.48,

Nitrogen gas obtaiued tlirough the decomposifcion of am-
monia by oxygenated muriatic acid [i, e. clilorine] gave the fol-
lowing live results : 100 parts became

137.42 ; 137.56 ; 137.50 ; 137.46 ; 137.55 ;
the mean of which is 137.49.

Oq bringing together the preceding results and comparing
the expansion of the gases oxygen, hydrogen and nitrogen with
that of atmospheric air, there results a table like this —

Between the temperature of
melting ice and that of boil-
ing water, 100 parts of

Suffer an
increase of

Differences

Atmospheric air
Hydrogen gas
Oxygen gas
Nitrogen gas

37.50 parts
37.52
37.48
37.49

-f 0.02

— 0.02

— 0.01

The slight differences observable in the above results may
arise from the fact that it is impossible to make the conditions
rigorously identical in every experiment, and as they amount to
only two ten-thousandths of the original volume, we may safely
conclude that atmospheric air and the gases oxygen, hydrogen
and nitrogen expand to the same extent between the tempera-
ture of melting ice and that of boiling water.

In order to determine the rate of expansion of gases soluble
in water, I made a change in the apparatus. I used two tubes
TT{Fig, 2, Plate 11) [See^/^. 4] calibrated at the same time
over the same mercury bath AOy by means of a very small
measure.

Each time that I made use of this apparatus, I took care
that the quantity of mercury should be the same as when the
tubes were calibrated. I ought to say that, if the basin which
held the mercury suffered any injury, it was necessary to re-
calibrate the tubes for another bath ; indeed it would be well to
cut them from the same cylinder of glass and to give them the
same height, in order to have all the conditions as much the
same as possible.

Into one of these tubes I admitted atmospheric air down to

44

EXPANSIOK OF GASES

- T

— T

the lOOtli division^ for example^ and into the other the gas
whose mte of expansion I wished to determine^ also as far as the
100th division. I thus subject to test 100 equal measures of
each of two gases. I then place the apparatus in a heater
whose temperature I can control and watch the progress of the
expansion of the gases. However great tlie care I have taken to
observe closely, I haye never
perceived any difference and
have always noticed that the
same divisions were passed at
the same time in the two tubes.

The gases I have thus ex-
amined have never been intro-
duced directly into the tubes; I
have kept them for some time
before in an intermediate vessel
in which I put some drying-
agent, — for example, muriate of
lime, [i. e. calcium chloride] —
and made them pass thence into
the tubes by compressing them
with the aid of mercury which I
introduced by means of a safety
tube fitted to the intermediate
flask. If these precautions are neglected, there will almost
always result far too great an expansion ; we must therefore
avoid the contamination of unabsorbed moisture or of any
other substance capable readily of assuming the gaseous state.

100 measures of carbonic acid gas obtained from marble
with the aid of sulphuric acid were compared with 100 measures
of atmospheric air. From the fifth degree up to the 90th de-
gree the expansions were the same in the two tubes.

100 measures of muriatic acid gas produced with the aid of
concentrated sulphuric acid from muriate of soda [i, e, com-
mon salt] thoroughly dried by heat, having been compared
with 100 measures of atmospheric air from the 3d degree up to
the 86th, the expansions of the two gases were absolutely the
same. This experiment, as well as the preceding one, was re-
peated many times, and always gave the same result,

45

Fia. 4.

MEMOIBS OK

Sulphurous acid gas and nitrous gas, again^ showed under
the influence of heat the same expansion as atmospheric
air.

Dr. Priestley and Citizens Gujton and Duvernoia have found
very great expansibility in the case of ammonia gas. With the
idea of discovering the cause which was capable of vitiating
the results of their experiments, I introduced directly into one
of the tubes some ammonia gas produced by the decomposition of
muriate of ammonia by means of ordinary lime, and into the
other a suitable volume of atmospheric air. As the tempera-
ture rose, the ammonia gas expanded proportionally more than
the atmospheric air, in fact to such a degree as soon to become
twice as great; yet on examining the mercury surface and the
walls of the tube, after lowering the temperature, I noticed a
trace of liquid and some crystalline needles which could be
only muriate or carbonate of ammonia, and the whole disap-
peared on raising the temperature to a sufficient degree. How-
ever that may be, I began the experiment again by allowing
the ammonia gas to stand some time in an intermediate flask
where there was some caustic potash, and then, from 0° up to
95°, its expansion followed exactly that of atmospheric air. I
again examined the surface of the mercury and the walls of the
tube, when the temperature had returned to 0°, but this time
I noticed neither liquid nor crystalline needles. This experi-
ment, repeated many times, always met with the same suc-
cess.

It is thus evident, from what I have said, that not only a liq-
uid, but any other substance capable of assuming the gaseous
state can easily lead to error; it is necessary therefore to avoid
such things with the most scrupulous care.

The experiments of which I have given an account and all of
which were made with great care, prove without a doubt that
atmospheric air and the gases oxygen, hydrogen, nitrogen, nit-
rous gas, ammonia, muriatic acid, sulphurous acid and car-
bonic acid gases expand to the same extent for the same de-
grees of heat; and that consequently their greater or less dens-
ity under the same pressure and at the same temperature, their
greater or less solubility in water, and their individual charac-
ter, have no influence upon their expansibility.

46

EXPANSION OP GASES

In oonsideration of this fact I conclude that all gases^ speak-
ii^ geuerally, expand to the same extent through equal ranges
of heat; provided ail are subject to the same couditions.

These researches upon the rate of expansion of gases nat-
urally led me to investigate that of vapors; but expecting, from
the result of the above determinations, that they would expand
like gases, I decided to experiment upon only one vapor, and
chose that of sulphuric ether as being very easy to work with.

In order then to determine the rate of expansion of ether vapor
I made use of the two tubes of which I have already spoken,
atmospheric air serving throughout as a means of comparison.
This apparatus having been kept for some time in a heater
whose temperature was about 60°, I admitted ether vapor into
one of the tubes and atmospheric air into the other, in such a
way that each was filled to the same point. I then raised the
temperature of the heater from 60° to 100°, and had the satis-
faction of seeing that, whether rising or falling, the ether va-
por and the atmospheric air always stood at the same division
at the same moment. This experiment, which Citizen Berth-
ollet has witnessed, was repeated many times and I have never
been able to note any difference in its rate of expansion as com-
pared with that of atmospheric air. I would however empha-
size the fact that a few degrees above the boiling point of ether,
its contraction was a little more rapid than that of atmospheric
air. This phenomenon goes with one which many substances
exhibit in passing from the liquid to the solid state, but which
is no longer noticeable a few degrees above that at which the
change is made.

This experiment, by showing that ether vapor and gases ex-
pand at the same rate, makes it evident that this property is in
no way dependent upon the peculiar nature of the gases and
the vapors but solely upon their elastic character, and conse-
quently leads us to the conclusion that all gases and all vapors
expand to the same extent for the same degrees of heat.

Since all gases are expanded to the same extent by heat and
are equally compressible, and since these two properties are
mutually dependent, as I shall show elsewhere, vapors — which
are expansible to the same degree as gases — must also be
equally compressible: yet I emphasize the fact that this latter

47

MEMOIRS ON

coDclusiou can be true only so long as the compressed vapor re-
mains completely in its elastic state^ and this demands that its
temperature shall be high enough to overcome the pressure
which would tend to make it assume the liquid state.

I have quoted Saussure — and my experiments confirm his
view — to the effect that very dry air and air holding in solution
more or less moisture expand at the same rate; I am therefore
in a position to draw from all I have said the following con-
clusions: —

I. All gases, whatever their density or the quantity of water
which they hold in solution, and all vapors expand to the same
exteut for the same degree of heat.

II. In the case of the permanent gases, the increase of vol-
ume which each of them suffers between the degree of melting
ice and that of boiling water, amounts to ^t^^^ of the original
volume, for a thermometer divided in 80 parts, or ^^.J^ of the
same volume, for a centigrade thermometer.

In order to complete this research, it remains for me to de-
termine the law of the expansion of gases and vapors, with the
object of finding with its aid the coefficient of expansion for
any given degree of heat, and of establishing the true move-
ment of the thermometer. I am at work upon this new re-
search and, as soon as it is concluded, I shall have the honor of
laying an account of it before the Institute.

BlOGRAPHIOAL SKETCH.

Louis Joseph Gay-Lussao was born in 1778. He received
his scientific education at the i^cole Polytechnique and the
Bcole des Fonts et Chauss6es, and in 1800 became assistant to
BerthoUet. The research upon the expansion of gases by heat
was one of his first. Like his contemporary, Dalton, he was
much interested in the study of the atmosphere and in 1804
made analyses of the air, securing specimens from various
places — one, at a height of over 6,000 meters, in a balloon
ascent. The analysis of Water was also made at this time. In
1807 he published papers upon terrestrial magnetism and the

48

EXPANSION OF GASES

results of bis classic investigation of the volume-relations of
gases undergoing chemical ciiange. Along with Tlienard, he
studied the properties of the metals of the alkalies and of
chlorine, advocating, with Davy, their elementary character.
In 1809 he became Professor of Pliysics in the Faculty des Sci-
ences and Professor of Chemistry in the ^ficole Polytechniqiie;
in the same year, working with Thenard, he was able to isolate
boron and, later, iodine. The latter is considered one of his
most brilliant investigations. During the next few years he
published important memoirs upon the relationships existing be-
tween etjiylene, alcohol and ether. In 1815 he discovered cyan-
ogen and prepared pure hydrocyanic acid. In 1815 he devised
the syphon barometer.

Gay-Lussac's ingenuity frequently made itself evident in the
construction of new forms of apparatus: in addition to the
syphon barometer, we owe to him a large number of useful in-
struments constantly employed in the laboratory. His death
occurred in 1850.

49

THE DETERMINATION OF THE RATE OF
EXPANSION OF GASES BY HEAT.

By J. B. BIOT,

Translated from Volume I, Chapter IX, of the Author's " Traite

de Physique."

51

CONTENTS.

PAGE.

TJiird Metliod of Oay-Lussac: Apparatus ... 53

Need of excluding moisture; method of drying apparatus 54

Manipulation 55

Coefficient of expansion of glass containing-vessel . , 56

Results and conclusions 59

52

EXTRACT FROM BIOT'S TREATISE ON

PHYSICS :

t

BEING CHAPTER IX OF VOLUME I.

The Determination of the Rate of Expansion of Gases hy Heat.

The experiments of MM. Lavoisier and Laplace upon the
expansion of solid substances have shown us that between the
limits of [the temperature of] melting ice and [that of] boil-
ing water, the expansion of solid metals is practically propor-
tional to that of mercury. The same relation, between these
limits, exists as well between the expansion of mercury and
that of dry gases. This important deduction has been com-
pletely established by the experiments which M. Qay-Lussac
has made with this object in view, upon the rate of expansion
of gases. This skilful physicist having been willing to make
known to me the details of his experiments, and to permit me
to sketch the apparatus which he has devised for the purpose,
I shall proceed to describe here the course which he followed
in his investigations and the results to which he whs led.

In order to measure with accuracy the rate of expansion of
gaseous substances, it is necessary, first of all, to introduce
them, in known quantity, into tubes accurately graduated into
divisions of equal volume, and terminating in a bulb whose
volume should be considerable as compared with that of the
tube. It is necessary, further, that they should be kept there
under a known pressure, exposed to different temperatures and
the amounts by which they expand or contract under the dif-
ferent conditions observed ; in a word, it is necessary to make
a veritable gas thermometer. Yet although the statement of
this operation may be very simple, it demands, in order to be
accurate, many essential precautions which we shall now
discuss.

The first is, that the tubes in which the gases are contained
must be perfectly dry ; for we have already stated that glass

53

MEMOIRS ON

tubes lying open and exposed to the atmosphere, become cov-
ered inside with a slight, imperceptible layer of water which
heat sets free by converting it into vapor. If one did not begin
by removing this thin layer of water, the vapor which it gives
off at different temperatures would mix with the gas introduced
into the tube and would increase its volume ; and, since the
amount of the vapor thus produced would increase with the
temperature until the slight layer of water had become com-
pletely removed, it is evident that this outside cause will con-
stantly increase the expansion proper of the gas, in proportion
as the temperature rises : such is the error into which many
physicists have fallen.

The only way to avoid this difficulty is to drive out this
slight film of moisture by heating the tube until it is changed
to vapor ; but in order that the air may not enter again, it is
necessary to fill the tube with mercury, which is made to boil

T T

^0=^

M

17G. 1.

there, as in a thermometer ; and — which is important to notice
— whether this boiling removes or not the whole of the film
adhering to the glass, at least it can no more give off vapor
when the tube is kept at any temperature less than that at
which mercury boils. This is the first precaution M. Gay-Lus-
«ac has taken.

Next, in order to introduce only air or dry gases into the
tube, he connects to its open end another, larger tube TT,
Fig, 66 [Fig, 1], which may be regarded as a kind of receiver
intended to hold the gas. This tube is partly filled with bits
of muriate of lime [i. e,, calcium chloride] or of any other salts
capable of absorbing moisture. It is even possible to produce
a vacuum in it in order to introduce the gas without admixture
of air. Then in order to let a definite quantity enter the tube,
M. Gay-Lussac makes use of a very fine iron wire previously
introduced into the bore. He inclines the tube or turns it up-
side down, and thus removes a large part of the mercury which
it contains, whose place is taken by a definite volume of gas
refpresented by GG, Fig, 67, [Fig. 2]. With care, it can be ar-
ranged to have only a short column of mercury i/" which acts

54

EXPANSION OF GASES

as a piston, and all the space OG, from this point to the bulb
of the tube is filled with the dry gas which has been intro-
duced. If he is employing atmospheric air, there is no need of
producing a vacuum in the receiver TT; the air should be
allowed to remain some time in contact with the salts, after
which it is introduced into the tube QT, as we have described.

FIG. 2.

The gas having been introduced, it remains only to try the
effect of various known temperatures successively upon it ; for
this M. Gay-Lussac made use of a metal vessel AB, Fig. 67 [Fig.
2] rectangular in shape, the bottom of which fits upon a fur-
nace of the same size. Water is put in this vessel and is heated
to different temperatures. A thermometer F, placed vertically
in this water and whose stem projects above the cover of the
vessel, serves to indicate its temperature approximately and to
show if it is necessary to increase or diminish the heat.

The tube Tff, however, which contains the gas, must not be

put in the water in this position; for we have already ahown

by experiment that the different horizontal layers of a liquid,

which is being heated from the bottom, are not at the same

degree of temperature. Thus, in order to know exactly that

[temperature] which is producing an effect upon the gas, the

tube which contains it must be fixed in a horizontal position,

as Fig^ 67 [Fig, 2] shows it; then its temperature may be

accurately determined by an excellent thermometer tt placed

opposite it in the same layer and likewise fixed in a horizontal

position.

55

MEMOIRS ON

But we have stated that the vessel was of metal; how then
observe through its walls the divisions of the thermometer tt
and tlie movable point of the graduated tube to which at
any moment the gas-volume extends ? The point G and the
stem t of the thermometer cannot be kept continually outside
the hot-water bath^ for then these parts respectively, being no
longer at the temperature of the bath, would introduce an
error into the determination. Yet one can, without iuconveni-
ence, draw out the tubes from time to time, during the short
interval required to observe them: this M. Gay-Lussac accom-
plished iu a very simple way. The openings OC/ through which
the tubes pass into the vessel are closed with corks pierced
along their axes with a hole through which the tube in either
case can slip with some friction. Is it desired to observe the
condition of the gas GGf The tube TG is drawn out until
the end M ol the short column of mercury comes into sight at
the opening 0. It can then be seen at what division of the
tube it stands, and the volume of the gas at this moment is
known. Is it desired to note the temperature at the same
time? The stem is similarly drawn out until the end t of the
mercury column appears at the opening t?', and then the divi-
sion of the thermometer to which this corresponds indicates
the temperature at the time of the horizontal layer in which
the gas has been placed.

Thus at each moment the temperature of the gas is known
in the most exact way. Putting water at 0° at first, therefore,
in the vessel, then raising the temperature by successive steps
to that of boiling; or, vice versa, returning from boiling to the
melting point of ice; the movement of the gas and that of the
thermometer can be compared with accuracy — that is to say, at
any time, by the divisions marked upon the tube, the apparent
volume of the mercury and the apparent volume of the gas
may be known; but to have the real volumes, it is still necessary
to take into account the expansion of the glass of which the
tubes are made.

To study this effect properly, let us start from some definite
temperature — for example, that of melting ice. Let us desig-
nate by V the number of divisions which the gas then occu-
pies in the glass vessel that encloses it, and let us make use of

56

EXPANSION OF GASES

this number to express its volume. On the temperature rising
t degrees^ the volume of the gas will increase and become
F(1+(J), designating by d its cubical expansion from 0® to t
degrees^ and this is the unknown quantity we are looking for.
Let V be the number of divisions it now occupies in the tube.
As the latter expands each of its divisions has in reality a differ-
ent value from that which it had at the initial temperature^
and if the cubical expansion of the material of the tnbe^ for one
degree of the thermometer, is represented by -ff, P divisions
at the temperature / will be equal to F (1+Kt) of the original
divisions. This will therefore be the actual expression of the
new volume of the gas stated in terms of the original divisions
— that is to say, we shall have

F(l+d) F (l+iTO,
from which we obtain

J ^ V'-V V'Kt

The first term, y is the cubical expansion for a volume

equal to unity, assuming the vessel did not expand; and the
second term, y , is the correction whicTi must be made in the

first result on account of the expansion of the vessel.

F is determined at the beginning of the experiment; it is
the number of divisions occupied by the gas at the initial
temperature; subsequently, at other temperatures, the reading
gives F', the number of divisions the gas occupies at any given
moment. Moreover K is found from the expansion of solids;
thus the whole second number of our equation is known and,
consequently, on substituting their values for F, F', Ky t, ihe
expansion 6 is found jnst as it would have been determined in
a vessel upon which [a change of] temperature produced no
effect.

It only remains to take account of . the pressure to which
the gas is subjected, for we have seen that the volumes which
a given gas will occupy, at a given temperature, are inversely
proportional to the pressures to which it is subjected. Here, dur-
ing the experiments, the receiver, TT, Fig. 67 [Fig,2] remains
always open; the pressure of the atmosphere thus acts freely
upon the short column of mercury, M, close to the gas OG,
E 57

MEMOIRS ON

If the tube TO were vertical or inclined to the horizon, the
weight of this short cohimn M would also act upon the gas;
but the tube being horizontal, this weight is entirely carried by
the glass tube. The short column M opposes no pressure, no
resistance to the motion of the gas — unless, perhaps, that re-
sulting from its friction against the inner walls of the glass
tube; and this force is so small, when the column is short, that
it may be neglected. The weight, then, of the atmosphere is
the only force which weighs upon the gas GGy and it is deter-
mined by observing the height of the barometer at the time
of taking the readings. If this pressure remains constant
throughout the experiment, the corresponding volumes of gas
and of mercury may be directly compared with one another;
but, if it varies, all the readings must be reduced to one pres-
sure — which is easy, making use of Mariotte's Law,

Thus, letji? be the atmospheric pressure observed at the
beginning of the experiment and at the initial temperature,
when the gas in the vessel occupies a number V of divisions.
Let us suppose that it is desired to reduce this volume to what it
would have been under the constant pressure of 0.76 m., to which
we refer all observations. Then, according to Mariotte's Law,
the volume Fmust be reduced inversely as tke pressures ; that

is to say, in place of F we have ^p^.

In the same way, if we assume the pressure of the atmos-
phere to bey, when the gas is at the temperature t, and that
it occupies in the vessel a number of divisions represented by
F, this number, under a pressure of 0.76 m., but at a tem-
perature t, will become ■^^^.
^ 0.76

Therefore to arrive at the expansions which would have re-
sulted if the pressure had remained constant and equal to 0.76,

we must substitute for Fand F in our formula, ^ and -j^;
then the value of cJ becomes

. p' V'-p V p' V'Kt

Use must be made of this formula in order to take account
of all the attending conditions. When the pressure is con-

58

EXPANSION OF GASES

sfcant throughout the experiment, we have jo »=ji?', and we fall
back upon the formula which we had found at first.

When 6 shall have been thus determined for an interval of t
degrees, the experiment is begun again or is continued for an
interval 2ty 3t, .... ; and by comparison of the values of 6 with
one another, it may be known whether the rate of expansion
is uniform or variable. For, if it is uniform, the successive
expansions, <5, 2(J, 3<J, ....,, will be proportional to the differ-
ences in temperature ; but if the rate of expansion is increas-
ing or decreasing, this proportionality will not obtain. Per-
forming the experiment in this way, with all the precautions
we have described, repeating it a great number of times, as
well with atmospheric air as with the different gases, M. Gay-
Lussac arrived at the following results :

All the permanent gases, subjected to equal [changes of]
temperature, under the same pressure, expand by exactly the
same amount.

The amount of their common expansion, from the tem-
perature of melting ice up to that of 100 degrees of the
centigrade thermometer, is equal to 0.375 of their original
volume at 0°, assuming pressure to be constant.

Between these two limits the expansion of a gas is exactly
proportional to the expansion of mercury ; whence it follows
that, for every degree of the centigrade thermometer, and
under a given pressure, all gases expand by an amount equal to
0.00375 of the volume which they occupy at the temperature
of melting ice.

These results had been obtained almost simultaneously by
Mr. Dalton, the brilliant physicist of Manchester ; but the
work of M. Gay-Lussac was completed in France before that of
the English physicist could have been known. Mr. Dalton
finds the actual expansion slightly different from that [found] by
M. Gay-Lussac. He makes it equal to 0.372, and finds that, for
a given expansion of mercury, that of atmospheric air is a little
less in proportion and that this difference increases as the
temperature rises. Yet however great the skill of this philos-
opher in experimental research, we believe that the result of
M. Gay-Lussac may be considered as still more accurate, as
much by reason of the endless precautions he has taken to

59

MEMOIRS ON

obtain it, as because it agrees very well with all the other
physical determinations in which there is need to use the figure
for the absolute rate of expansion of gases.

It would not be out of the way to note on the other hand
that the ratio 0.00375 is exactly the one that has been found
for atmospheric air by the distinguished astronomer Tobie
Mayer, who appears to have been as skilful in the art of
physical experiment as in that of making and coordinating
astronomical observations. M. Gay-Lussac has stated in his
memoir that our renowned physicist, M. Charles, had long
before discovered the equal rate of expansion of gases and had
made it apparent by an apparatus constructed for his splendid
museum; but he had made no attempt to measure accurately
the absolute rate of their expansion. Doubtless we have reason
to regret the many other results of observation and experiment
which M. Charles had intended for use only in his public
lectures and which have never been published.

M. Gay-Lussac is in the same way convinced that the gaseous
substances produced by the evaporation of liquids expand at
the same rate as gases, so long as they do not become con-
densed to liquid form. To prove this, he removed the drying-
salts from the receiver TTy introduced into the tube TG gases
which had not been dried and consequently were charged with
moisture which could there take the form of vapor : moisture
which the drying-salts would take up with increase of weight.
By this means the space GG becomes filled with a mixture of
gas and aqueous vapor ; and this mixture, raised to different
higher temperatures in succession, expands exactly as would an
equal volume of dry gas. But one must not look for the same
law on lowering the temperature below the point at which the
gas was introduced ; for we shall prove later on, that a definite
volume of gas at a given temperature can hold only a certain
limited amount of water in the form of vapor, whence it follows
that if it is thus saturated with aqueous vapor at a given degree
of the thermometer and the temperature is lowered, a portion
of this vapor will be condensed to the liquid state. That part
which becomes liquid, occupying a far smaller volume, will
decrease the total volume of gas, will diminish its tension and^

60

EXPANSION OF GASES

as a result of this double effect^ will cause an apparent yariation
in the laws of expansion.

M. Gay-Lussac has in the same way studied the rate of ex-
pansion of ether vapor ; he finds it the same as that of gases,
— which leads to the belief that the conclusion holds good for
all kinds of yapors, so long as they remain in the gaseous
state.

With the aid of the results we have just described, we can
answer with accuracy all physical questions which might be
asked concerning the volume of a given quantity of gas sub-
jected in turn to various pressures and to various temperatures.

61

RESEAKCHES UPON THE RATE OF EX-
PANSION OF GASES.

By Henri Victor Eegnault.

From the Annales de Chimie et de Physique, 3d Series, volume
4, pages 5 — 67 (1842). Translated into German, Poggendorff's
Annalen, volume 55, pages 391 — 414 and 557 — 584. Also con-
tained in somewhat altered form in the Memoir es de V Academie
des Sciences, volume 21, pages 15 — 120 (1847).

63

CONTENTS.

Discussion of Rudherg^s researches .

" Dalton's "

First Series of determinations :

Apparatus and manipulation

Calculation of results .

Sources of possible error

Results

Second Series of determinations :

Apparatus and manipulation

Calculation of results .

Results with the several bulbs
Tliird series of determinations Expansion with constant

volume^ I :

Apparatus and manipulation . , . .

Calculation of results

xcesucvs •• ••••••

Disadvantages of the method . . . .
Fourth Series of determinations : Fxpafision with constant

volume, II :

Apparatus and manipulation

Calculation of results ....

Use of apparatus at higher pressures
Attempt to use Gay-Lussacs method
Discussion of possible sources of error in results

(c) Expansion of glass

(I) Barometric readings

(c) Temperature determinations .
Coefficient of Expansion of gases other than Air:

Method

Results

Sources of gases

Application of Fourth Method to Carbon dioxide

'' * * ' * Sn Iphurous acid gas

Direct comparison of two gases by Fourth Method

Biographical Sketch

64

PAGE
65

71

74
79
80
81

82

86
87

89
92
93
95

96
99
100
101
103
103
104
106

107
109
110
113
113
116
120

RESEARCHES UPON THE RATE OF EXPAN-

SION OP GASES.

By Victob Eegnault.

Part I.

Upon the Rate of Expansion of Atmospheric Air.

There is no numerical quantity in physics which has been
submitted to a greater number of experimental determinations
than the coefficient of expansion of air, and yet we cannot say
that up to the present time this coefficient is known with suf-
ficient accuracy.

The experiments of the older physicists gave such diverse
numbers that it was impossible to draw a satisfactory conclusion ;
most of the conditions which affect the phenomenon [of gas ex-
pansion] were entirely unknown.

The brilliant experiments of M. Gay-Lussac upon the rate of
expansion of gases seemed bound to put an end forever to the
uncertainty of physicists, M. Gay-Lussac showed by a great
many experiments that the coefficient of expansion between 0°
and 100® was the same for all gases, and for vapors so long as
they are kept a little above their points of condensation, and
that its value was 0.375. This coefficient was adopted by all
physicists and used in computations, until within the last few
years a Swedish physicist, M. Eudberg, threw doubt upon its
accuracy. By a series of carefully conducted experiments Eud-
berg sought to show that the coefficient of M. Gay-Lussac was
too high and that its true value must be between 364 and 365.

As Eudberg^s work has never appeared in France, it would
seem as well to give an abstract of it here.

Eudberg has published two memoirs upon the coefficient
of expansion of air. In the earlier (Poggendorff's Annalen,
Volume XLI) he uses for its determination a species of air-
thermometer formed of a bulb of glass [capable of] enclosing
from 120 to 150 grams of mercury and fused to a capillary tube.
A beginning is made by filling this apparatus with dry air.

65

MEMOIRS ON

For this purpose the open [end of the] capillary is inserted in
a tube filled with bits of calcium chloride. The bulb is
thoroughly heated with an alcohol lamp, then is allowed to
cool. After repeating this operation fifty or sixty times there
is nothing but dry air in the bulb.

At other times he placed the chloride-tube in communication
with an air-pump and produced a vacuum in it fifty or sixty
times in succession^ allowing the air to return each time.
These two methods of drying were employed indifferently;
they never gave [results] that differed noticeably.

The bulb, full of dry air and always fitted with
its calcium-chloride tube, was placed in a vessel
AB in which water was boiling (Fig. 1), of such
size that the bulb and capillary tube were com-
pletely surrounded by the vapor. After the water
had boiled for three quarters of an hour or an
hour, the calcium-chloride tube was removed and,
ten minutes later, the drawn-out point of the
tube was sealed with a flame, and at the same
time the height of the barometer was read.

The bulb was weighed upon a very delicate
balance ; it was then fixed in the apparatus [shown
in] Fig. 2. The capillary tube passes through a hole in a metal
capsule abc fastened to the upright AB, The arm CD is
lowered until the point of the capillary tube dips deep enough
in the small mercury-bath EFOH, The point of the tube is
broken off and the mercury rises into the bulb. The latter is
surrounded with crushed ice placed in the capsule dbc; the water
formed by the melting of the ice flows off through the little tube
/. The bulb is thus kept at 0° for at least two hours, the ice
being renewed as fast as it melts. The end of the capillary
tube is then stopped by means of a little soft wax held in a small
iron spoon, and at the same time the height of the barometer
is recorded.

The snow is then removed and a measurement made of the
height of the raised [column of] mercury. Rudberg used for
this purpose the apparatus KML consisting of a vertical
standard supported by a tripod with levelliug-screws. Up and
down this stem travels an arm Imo carrying a cylindrical ring gn

66

Fio. 1.

EXPANSION OF GASES

whose lower edge is exactly horizontal. This ring la lowered
until its lower edge coincides with the level of the mercury in
the bulb. At the same time the screw-rod KS is lowered until
ita point reaches the level suriace of the mercury in the bath.
The apparstue KML is then removed and the distance from
the ring to the point is measured with the aid of a graduated
rule.

The bulb is weighed with the mercury which it contains,
after the little piece of wax has been removed.

The thormometer tube is bent by means of a lamp in such a
way that its open end can dip in a email dish full of mercury.
The whole apparatus is filled with mercury which is carefully

Fio. 2.

heated until it boils. After it baa cooled down again, the
bulb and tube are covered with crushed ice eo that they may
become completely filled with mercury at 0°. The bulb is
then removed, care being taken to catch in a small capsule the
mercury which escapes on account of expansion, and placed in
the boiler, the mercury which flows out being caught in the
same little capsule. This mercury ia carefully weighed, as is
also that which has remained in the bulb. We thus have the
total weight of mercury which filled the apparatus at 0", and
67

MEMOIRS ON

all the data necessary for calculating the coefficient of expan-
sion of the glass.^

The glass used for Sudberg's apparatus was a Swedish pot-
ash glass of fieymira make. Its coefficient of expansion be-
tween 0° and 100° was found to be 0.002285 as a mean of
twenty-four experiments, the extreme figures of which are
0.002256 and 0.002321.

The first three experiments to determine the coefficient of
expansion of air were made without bringing the air" to 0° ; the
bulb was merely placed in a cylinder full of water whose tem-
perature was taken with a thermometer. The three experi-
ments gave the following numbers:

0.8633

0.3617

0.3623

Mean »= 0.3624
Rudberg does not consider these experiments very accurate,
(1) because the temperature of the water surrounding the bulb
was never perfectly stationary, but varied to a noticeable ex-
tent during the experiment; (2) because the difference of tem-
perature was not 100° but only 90°. The experiments made
with cooling of the air to 0°, gave:

0.3643

0.3654

0.3644

0.3650

0.3653

0.3636

0.3651

0.3643

0.3645

Mean =■ 0.3646

These experiments were made under very diverse barometric
pressures ; in fact, the height of the barometer varied from
742.77 to 779.85. Consequently, the temperature to which the
air was heated varied from 99.89° to 100.73°. The height of

[1 Note by Translator.— Rudberg' s method and apparatus are similar,
in all essential points, to those of Dulong and Petit in their comparison
of the air thermometer and the mercury thermometer. See page 3.]

68

EXPANSION OP GASES

the mercury column drawn up into the apparatus varied from
35 mm. to 166.5 mm.

fiudberg then discusses the causes which could introduce
constant errors in his results. He states that capillarity could
not produce a noticeable effect in his apparatus because it was
acting in a surface of mercury of about two-thirds of an inch
diameter. The friction of the mercury against the walls of the
capillary tube produced no effect: otherwise differences would
have been noticed among the experiments where the height [of
the column] of the mercury drawn up varied from 35 mm. to
166 mm.

Rudberg made, further, two experiments with large glass
tubes of §-inch diameter and 8 inches length. These experi-
ments he did not consider as accurate as the earlier ones, since
he could not boil the mercury in this form of apparatus.
They gave the two figures

0.3646
0.3662

Mean » 0.3654

Two experiments made with air which had not been dried
gave 0.3840 and 0.3902, which gives an idea of the influence of
moisture upon the coefficient of expansion. The same appara-
tus, having been dried again with care and filled with dry gas,
gave 0.3652.

In his second memoir (PoggendorflPs Annalen, Volume
XLIV), Eudberg gives a series of experiments made by means
of a special apparatus having for its object the determination
of the tension which a given quantity of dry air exhibits at 0°
and at 100°; this quantity always occupying the same volume,
allowance being made each time for the expansion of the glass.

This apparatus is represented in Fig. 3. It consists of a
cylinder AB filled with dry air and communicating with a
second tube dC by means of a capillary tube Bbd. The tube
dC is cemented into the cover of a box containing a leather
pouch filled with mercury, the volume of which can be re-
duced, as in the case of barometers, by means of the screw M,
A barometer-tube about 50 centimeters high is cemented into

69

MEMOIRS ON

the same cover. By means of the screw the mercury is made
to rise in the tubes. Upon tlie vertical part of the tube id a
very fine scratch is made at o. The mercury is forced up to
this mark by means of the screw, (1) when the reservoir AB \^
cooled to 0® by the aid of ice ; (2) when it is heated to 100°.

o'

Fio. 8.

The volume of the air thus remains the same at the two
temperatures, if the expansion of the glass be left out of ac-
count. In order to measure the heights of the mercury in the
two tubes, there is placed directly behind these tubes a brass
rule EPRND, graduated in millimeters, the divisions of which
on the lower portion, from a to I, have been extended enough
to pass behind both of the tubes at one time. The difference
in height between a and the meniscus of the mercury in ED
can thus be easily determined.

The reservoir AB was thoroughly dried before cementing
the tubes into the box. To this end, the lower portion of the

70

EXPANSION OP GASES

tube dC was drawn out to a poinu and connected with a very
large tube filled with calcium chloride, which in turn was con-
nected with a pump. The air having been exhausted about
fifty times and replaced by dry air, the drawn-out tip is closed
by means of a lamp. The tube dO was fitted into the box
filled with dry mercury, and when this tube was firmly ce-
mented in place, its point was broken off below the surface of
the mercury.

The capillary depression at a was determined by a direct ex-
periment before the narrow tube Bhd had been fused to the
reservoir AB. This depression had been found to be 18.5 mm.

The calculation of the experiment is extremely simple.
When the air is cooled to 0°, let

H' = the barometric pressure,
h' = tJie difference of level aa,
e = the capillary depression at «;
we then have for the tension of the air, H' + h' — e.

When the air is heated to the temperature Thy means of [the

vapor of] boiling water, we have for its tension, H" + A" — e.

Hence

H" 4- h" — e
1 + "r= fl> + ft--e <1 + '^^-

Twelve experiments made according to this method gave the
following figures :

0.3640 0.3643

0.3648 0.3648

0.3641 0.3653

0.3648 0.3640

0.3640 0.3664

. 0.3656 0.3645

Mean =0.36457.
This mean is the same as that found by the former method ;
Eudberg concludes that the expansion of air from 0° to 100°
must be between 0.364 and 0.365.

Eudberg closes his second memoir with an important state-
ment which had already been made by Gilbert in 1803 (Gilbert^s
Annalen, Volume XIV, page 267), but which has since been
completely forgotten, namely, that the experiments of Mr,
Dalton and M. Gay-Lussac which have been looked upon as

71

MEMOIRS ON

haying given almost identical results, on the contrary differ a
good deal. In fact, in Dalton's memoir^ taken from the
Memoirs of the Manchester Society (Gilbert's Annalen, Vol-
ume XII, page 313), it is stated, '* I found from many deter-
minations that 1000 parts of atmospheric air, under the ordin-
ary pressure of the atmosphere, expand between 65® P. and
212° P., so as to form a volume of 1321 ; which gives, after
adding 4 parts for the expansion of the glass, an expansion of
325 parts for a difference of temperature of 157° of the Fah-
renheit scale/'

It is evident that the volume of air which is here regarded as
unity is that which the air had at 55° F. or 12.78° 0. If on
the other hand we consider as unity the volume of the air at
0°, and if we denote by lOOo the expansion between 0° and 100®,
the results of Dalton give :

1 -f- 12.78a : 1 + 100 a :: 1000 : 1325 ; hence
100 a ^ 0.892.

This is therefore the real result of Dalton's experiments.*
Dalton does not, however, seem to have been aware of the error
which had crept into his calculations, for he says in his "New
System of Chemical Philosophy "• : " The volume of the air,
according to the experiments of M. Oay-Lussac and my own,
being 1000 at 32° F., becomes 1376 at 212° F." *

1 See pages 20-21.

a Note by Translator:— The figure 0.3912, as given by Rudberg and by
Magnus, is more nearly correct than 0^92.

B See page 22.

* Note by Translator:— If Dalton made use of the data given in his
memoir of 1801 (See p. 20-21) as a basis for the statement quoted by Reg-
nault above — as the latter evidently assumes — he was clearly in en*or.
It happens that the coefficient in accordance with which a volume of
1000 would become 1326 through a rise of temperature of 157° F., or
87.22° C— that is, for the number of degrees lying between the lowest
temperature he employed, 55 ° F., or 12.78° C, and the boiling-point of
water— is 0.00207 for each Fahrenheit, and 0.00373 for each Centigrade
degree. This coincides quite closely with that found by Gay-Lussac in
the case of gases when the volume atO° C. is compared with that at 100°
C. Yet it is clear that Dalton's 0.00373 represents the fraction of its
volume at 12.78 ° C by which the volume of a gas increases for each de-
gree between 12.78° and 100 °C.; while Gay-Lussac's 0.00376 represents

72

EXPANSION OP GASES

Thus, according to the experiments of Eudberg, the coefficient
of expansion of air accepted for a long time by physicists is
much too high. Should the figure 0.3646, which is the mean
result of his experiments, be adopted now in physical compu-
tations?

It seemed to me that new experiments were called for to re-
move all doubts in this direction, and I have not hesitated to
devote myself to the work, feeling that the determinations
would be of service to science, even if they merely confirmed
the results obtained by the skillful Swedish physicist.

I have carried out my experiments by four different meth-
ods.

the fraction of its volume at ° C. by which the volume of a gas increases
for each degree between 0° and 100° C. The two coefficients are not
"sensibly the same/' because they do not represent the same thing.
The words in quotation-marks are from 'Preston^ s Theory of Heat (p. 190,
footnote) where the author, following Hegnault, assumes that Dal ton cal-
culated his coefficient from the data of his memoir of 1801, but somehow
misunderstands Regnault's method of calculating the coefficient, and
claims (incorrectly) that the French savant had overlooked the fact that
Dalton's lowest temperature was 12.78° C. and not0°. Yet if we use
the coefficient 0.00373 in the way Gay-Lussac used his 0.00375, Dalton's
1000 volumes at 12.78° would have been reduced to 954.5 at 0°, and
would have expanded to 1312.4 at 100°, instead of the 1325 which he re-
cords. If, on the other hand, we make use of the coefficient 0.00392 cal-
culated by Regnault, Dalton's 1000 volumes at 12.78° would have been
reduced to 952.3 at 0°, and would have expanded to) 325.6 at 100°, —
which is what actually was found.

It would appear, however, that neither Rudberg, Regnault nor Pres-
ton has carefully read Dalton's statement in his ** New System," for in
it he says, ** The volume at 32° is taken 1000, and at 212° , 1376, accord-
ing to Gay-Lussac's and my own experiments. As for the expansion at
intermediate degrees, Gen. Roy makes the temperature at midway of
total expansion, 116^ old scale; from the results of my former experi-
ments (Manch. Mem. Vol. 5, Part 2, page 599) the temperature may be es-
timated at 119J; but I had not then an opportunity of having air at 32 °.
By my more recent experiments, lam convinced that dry air at 32°
will expand the same quantity from that to 117° or 118° of common
scale, as from the last term to 212°," etc.

A study of this passage apparently shows that, after the publication
of Gay-Lussac's memoir, Dal ton repeated his experiments with greater
care, using the freezing point of water as his lowest temperature, and

^ 73

/

MEMOIfiS ON

First Series of Experiments,

The determination was made by a method similar to that
used by Rudberg in his earlier research, and which is in other
respects that by the aid of which Dulong and Petit made the
comparison of the mercury thermometer with the air thermom-
eter. I replaced Rudberg*s small bulb, however, which held
but 150 to 200 grams of mercury, by cylindrical reservoirs of 25
to 30 mm. diameter and of about 110 mm. length, capable of
holding 800 to 1000 grams of mercury. I preferred the cylin-
drical to the spherical form, because the former does not pro-
duce the refraction effects of the latter, which are likely to in-
troduce considerable errors when the heights of the mercury
[columns] drawn up are read from a distance with the aid of a
glass. It also seemed advisable to me to increase the capacity
of the air reservoir.

The cylindrical reservoir AB {Fig. 4) ended in a capillary
tube A CD the bore of which varied in different cases between
i mm. and 2 mm. The capillary tube was drawn out to a point
and its end was bent at a right angle.

This apparatus was fixed by means of a cork E in the cover

obtaining results confirming closely those of his French contemporary.
These later figures are thns the ones referred to in the first part of the
passage quoted above. The fact that '* more recent experiments'* with
"dry air at 32° " were made by Dalton seems to have been entirely
overlooked by the authors referred to above.

Moreover, nowhere in his 1801 memoir does Dalton calculate the coef-
ficient of expansion between 0° and 100° of the gases with which he
experimented. He does not appear to have considered the question of
their volume at 32° F. at all ; his whole attention was directed to their
behavior above 55° F. Yet Biot, in his Treatise on Physica, praises
Dalton' s skill as an experimenter and states that the latter found
the expansion of gases between 0° and 100° to be 0.372. (See page 59.)
Biot must himself have calculated the figure 0.372 from Dalton's data
of 1801— for Dalton does not give it in either of the extracts quoted
above, — or else it is based upon later and more accurate determinations
made by the English philosopher after the publication of the work of
Gay-Lussac.

It seems much more reasonable to suppose that Dalton actually ob-
tained results —after 1801— justifying the claim he makes in his New
System and explaining the statement of Biot, than to suppose that both
Dalton and Biot were guilty of the same arithmetical blunder.

74

EXPANSION OF GASES

^J5P of a tin-plate vessel F in which water is boiled. The va-
por which is formed in the lower part of the vessel is obliged
to pass out by way of the annular space LU which is for the
purpose of preventing its cooling by reason of the contact of
the outside air, before escaping by the lateral pipe M, At N
there is a small tubulure and, in the inner wall and directly oppo-
site, a small round hole 0, In the neck is fitted by means of a
cork a bent glass tube F which acts as a manometer, and one
of the open ends of which passes through the hole and is
thus in direct communication with the interior of the vessel F.
The other end is open to the air. The water column contained

Fio. 4.

in the two vertical arms shows, by the difference of level,
whether the pressure is the same inside and out. The reser-
voir AB and the capillary tube attached to it are thus com-
pletely surrounded by the vapor of boiling water.

When the water is boiling vigorously, the tip of the capillary
tube is connected by means of a rubber tube with a drying
apparatus. This consists of U-shaped tubes O, O', each about

75

MEMOIRS ON

a meter long and 20 mm. in diameter. These tubes are filled
witli broken pnmice atone moiateiied with concentrated sulphu-
ric acid ; tliey are connected with one anotlier by rubber tubes,
and with a small baud pump P. By means of this pump a
vacunm is produced twenty-five or thirty times in the appara-
tus, and, eaeii time, the air is allowed to enter again very
slowly by opening the taps in tlie proper way. The taps are
left wide open the last time so that the air in the reservoir is in
direct communication with the atmosphere.

The apparatus is left in tliis condition for from a half-hour
to an hour ; the drying apparatus is then disconnected. As it
is conceivable that the
pumice stone might by
y chance become paclied

somewhere in the tubes GO'
and the enclosed acid pro-
duce a continual obstruc-
tion to the entrance of the
air, and as in consequence
an excess of pressure would
be needed to force it into
the reservoir, I have always
taken care to disconnect
first the rubber tube a;
it is evident that in this
way, even if the air of the
reservoir is under a slightly
lower pressure than that
of the atmosphere, it will
still be dried air, that con-
tained between a and D,
which will enter the res-
ervoir and produce equilib-
^^■^ rinm. In my experiments

this precaution was unneces-
sary, as the pumice atone was only soaked in sulphuric acid.
The rubber tube i? is tlien removed and the apparatus allowed
to stand several minutes in direct communication with the
atmosphere ; finally the drawn-ont tip of the capillary tube is
76

EXPANSION OF GASES

closed by means of a blowpipe, and at the same time the height
of the barometer is recorded. We thus have .the reservoir AB
filled with dry air at the temperature of the [water-] vapor and
under the pressure of the atmosphere.

The reservoir after being removed from the heater was
fastened in the support shown in perspective in Fig, 5. This
support consists of a circular plate HE' in the centre of which
is a short tube 0, and supported upon three vertical legs P, P',
P", joined for greater steadiness at their lower ends by a circle
of metal QQ', Three inclined metal rods are arranged sym-
metrically about the short tube Oj they terminate above in
small balls with screw adjustment. The air reservoir ^^ rests
upon these balls and tlie capillary stem is held by a cork fitted
into the short tube. Greater steadiness is given it by means of
the screw V working in the movable cross-bar JfiV.

Upon one of the vertical legs P' is mounted a cross-bar mn
which carries a movable piece shown on a mm{u\\m
larger scale in Fig, 6. It consists of a little Vt
iron spoon ^attached to an iron stem fg |
which can be raised or lowered at will in the
piece abed. This piece can be slid along |'
the horizontal arm mn, which in turn can
be fastened at any height to the leg P' by
means of the set screw v.

Upon another leg P is arranged a horizon-
tal arm st which is capable of adjustment
and can be held by a set screw; it carries a
screw rod ending at top and bottom in a
rounded point.

The reservoir is fixed in the apparatus in such a way that the
bent portion CD of the capillary tube is pointed directly
towards the leg P, and a mark is made upon the leg P/ at the
height at which the adjustable piece mn must be fastened in
order that the centre of the little spoon ^ shall be exactly at
the height and in the direction of the bent portion of CD,

This being arranged, the apparatus is placed above a small
bath of mercury, in such a way that the capillary tube dips in
the mercury at least 5-6 centimeters. A very fine file mark
has been previously made across the stem CD at the point

77

/

Fia. 6.

MEMOIES ON

where it is desired to break it off. The tip is then broken off
with a small pair of pincers; the mercury enters the capillary
tube and rises to a certain height in the reservoir; this is then
surrounded with snow or finely crushed ice, and the apparatus
is allowed to stand undisturbed for at least an hour or an hour
and a half, in order to let it come exactly to the temperature of
melting ice. Meantime the spoon has been carefully lowered
to the proper depth in the mercury. From time to time the
apparatus is gently jarred to overcome the resistance — should
there be any — which the mercury might meet with in its ascent
within the capillary tube.

The little spoon is. then pushed forward along its arm until
the opening of the capillary tube is buried in the wax, and at
the same time the exact height of the barometer is recorded.
The arm st is lowered along the leg P, and the point of the
screw is accurately adjusted to the level of the mercury surface
in the bath. The ice which enveloped the tube is completely
removed, and the drawn-up column of mercury is allowed to
come to the temperature of the surrounding air.

It now remains to measure the height of the drawn-up mer-
cury ; for this, I made use of a cathetometer of M. Gambey's
design, which gives directly, with its vernier, a reading within
a fiftieth of a millimeter. One sights with the horizontal tele-
scope at the level of the mercury^ in the tube AB, then the
glass is lowered and is sighted at the upper point of the screw;
adding to the difference of level thus found the distance be-
tween the two points of the screw — which has been previously
measured with the same instrument — one has the total height
of the drawn-up mercury. More commonly we sight directly
at the lower point of the screw, after having lowered the bath
T — which is easily done by removing the support S.

The reservoir AB with the mercury drawn up is then re-
moved. It is weighed, then completely filled with mercury

1 Care must be taken, when one sights with the glass at the upper
line of the meniscus, not to be led into error through reflection-phe-
nomena at the curved surface of the mercury. The procedure which
seems to me surest, consists in placing a candle in the line of the menis-
cus and behind it, in such a way that the shape of the meniscus is out-
lined in black against the flame of the candle.

78'

EXPANSION OF GASES

"which is thoroughly boiled to drive out air and moisture en-
tirely; finally it is buried in ice while the open end dips in a
dish full of mercury. After an hour and a half or two hours,
when one is certain that the mercury is perfectly stationary at
the opening in the tip, the ice is removed and the mercury
which flows out of the apparatus through expansion is caught
in a small capsule. The reservoir is next hung in the same
boiler which was used to expand the air ; the mercury which
escapes is caught in the little capsule. The barometer is read
while the boiling is in progress. The mercury caught in the
capsule is weighed, as well as the reservoir with the mercury
it still contains. The weight of the mercury at 0° which
exactly fills the reservoir at 0° is consequently known, and
one has given all that is necessary for calculating (1) the expan-
sion of the containing vessel; (2) the expansion of the air con-
tained.

Let H be the barometric pressure at the time when the
drawn-out tip of the tube was sealed with the blowpipe ;

^the boiling point of water under this pressure;

W the barometric pressure when the tip was closed with the
wax under the mercury ;

h the height of the drawn-up mercury ;

P the weight of the mercury drawn up ;

P' the weight of the mercury at 0° which fills the apparatus
atO^;

p the weight of the mercury forced out by expansion between
the temperature of melting ice and that {T\) of water boiling
under a barometric pressure H\ ;

100 6 the amount, finally, by which a volume 1 of glass ex-
pands between 0° and 100°;

And 100 a the amount by which a volume 1 of dry air expands
between the same limits.

The heights H, IT, h, are supposed, for greater simplicity,
to have been reduced to 0° by calculation. We shall have for
determining S the equation:

79

MEMOIES ON

whence

(P'-p) ri+_Zi.l-P'

, 5550

P'Ti

and for calculating a.

whence

(p, _ P) (1 + a D ^^'*= P' (1 + STU

^ {P' — P){H' — h)

In making my experiments in the way that has been de-
scribed I have not been slow to see a very serious source of
error. In breaking off the point of the capillary tube under
the mercury, I noticed that even when the stem dipped almost
a decimeter into the mercury, there was always a minute quan-
tity of air drawn in which added itself to the air in the reser-
voir. The mercury does not wet the glass, and there is a little
space, probably filled with air, between the glass tube and the
mercury. It is by way of this sheath that the outside air is
drawn in, by a process similar to that of a bugle, during the
ascending movement of the mercury. This phenomenon of
aspiration is sometimes noticed by the fact that whole bubbles
of a;r rise in the capillary tube after the manner of a piston.

I had much difficulty at first in preventing this result. By
placing upon the part of the tube under the mercury many
small discs of a substance wetted by mercury, like well cleaned
brass, I succeeded in preventing the entrance of the outside air.
In order to be completely out of reach of this source of error,
I combined this method witli another which consists in pour-
ing upon the mercury, before breaking off the point and after
having taken hold of the tip with the pincers, a layer of con-
centrated sulphuric acid. This layer of acid is removed when
the reservoir has been lowered to 0° by the ice ; the surface of
the bath of mercury is cleaned and then the arm Kn is lowered.

It is also important that the iron pincers with which the
point of the capillary tube is broken off, should always be at
some distance from the scratch of the file upon the stem by
which the break is brought about. Otherwise, if the opening
of the capillary tube touches the pincers, one may see rise in

80

EXPANSION OP GASES

the tube a little bubble of air which has its source in that which
remains adhering to the surface of the pincers.

I bring together in the following table the results obtained
in the fourteen experiments I made by this method.

Number

of

H

H'

h

P

Bxperi-

ment

mm.

mm.

mm.

gr.

1

760.08

760.57

111.02

856.145

2

759.67

755.72

98.67

770.465

8

730.40

749.81

99.8:2

805.75

4

744.61

744.78

100.60

800.27

5

747.99

'748.79

106.35

790.69

6

751.48

752.68

102 3if

913.48

7

763.27

763.27

97.45

855.24

8

766.34

765.00

102.50

854.86

9

764.14

763.92

102.87

805.14

10

763.84

763.62

102.17

854.79

11

754.55

752.34

1C5.80

790.49

12

750.29

750.57

68.48

853.82

13

751.94

751.72

74.91

769.452

14

764.62

764.50

122.31

853.447

f

T

^1

Tr

P

100 «

1+100 a

gr.

mm.

o

gr.

119.915

100.00

760.60

100.02

12.870

0.008714

1.36656

116.780

99.99

753.75

99.7V

11.665

0.002576

1.36626

122 60

99.&1

44

• 4

44

0.002650

1.36659

190.19

99.43

744.60

99.43

12.050

0.002601

1.36579

114.31

99.55

748.20

99.56

11.931

002592

1.36625

137.74

99.68

44

44

4«

0.002680

1.36549

136 318

100.13

763.30

100.13

13.015

0.002544

1.36673

180.60

100.20

765.30

100.20

13 025

0.002537

1.86634

122.79

100.16

764.10

100.16

12.225

0.002583

1.36689

131.10

100.13

763.51

100.14

13.005

0.002548

1.36610

113.364

99.80

754.50

99.80

11.942

0.002607

1.36671

163.794

99.64

44

t i

i(

0.002570

1.36591

141.710

99.70

750.86

99.66

11.633

0.002576

1.36041

108.417

100.18

768.63

100.32

13.008

0.002551

1.3667:3

Mean

Extremes.

{1:

19.1277 6

14

86689
36549

1.36623

The mean
difference bet

Greatest difference 0.00140

for the fourteen experiments is 1.36623. The

ween the two extreme figures 1.36689

and 1.36549

is 0.00140

that is, what amounts to, at most, -^-^ of the quantity to be
measured.

The figures given by the fourteen experiments are all much
higher than the mean 1.3646 which Rudberg obtained in the
experiments made by a quite similar method. I believe that
this difference can be ascribed to the fact of the sucking in, in
Riidberg's experiments, of the outside air ; it seems unlikely
that, working by his method, this source of error could have
been avoided : on the other hand it is clear that it escaped his
notice, if only because he does not mention it.

The errors introduced through this sucking-in are so much
the more noticeable as one works with a smaller volume of air.

I did not at first succeed in preventing this sucking-in ; I am

81

MEMOIES ON

convinced that in my earlier experiments it still had a notice-
able effect and rendered some of my figures too low. What con-
' firms me in this view is that, starting from the time when the
sucking-in was made impossible, I obtained no figure lower
than 1.3658.

Second Series of Experiments.

The experiments of this second series were made by a method
slightly different from that followed in the former series ; but
the apparatus was arranged so that the volume of air subjected
to experiment remained practically the same at the temperature
of melting ice and at that of boiling water, so that the whole
effect of the expansion by heat is changed to a variation of
tension.

A glass bulb of 350 to 400 cubic centimeters' capacity is
sealed to a capillary tube about 38 centimeters long ; on this
capillary tube, at a distance of 11 centimeters from the bulb,
is put a piece of very regular tubing about 50 mm. long and of
sufficiently great diameter to show only a very slight capillary
effect. The capillary tube at its end is drawn out to a point
and bent at a right angle.

The first thing to be done consists in calibrating this appara-
tus accurately and determining its coefficient of expansion.
For this it must be completely filled with mercury at the
temperature of 0*^. This is a delicate operation, as all physi-
cists will agree, for it is nothing else than constructing a
thermometer whose reservoir shall contain about 5 kilograms
of mercury.

To introduce the mercury, the bulb is connected, by means
of a rubber tube 2>, Fig, 7, with a bent tube DE fastened to a
support ; mercury is poured into this tube DE, If the bore
of the capillary tube is not very small, the bulb is easily filled
three-quarters full without any necessity for exhausting through
the tube E ; but to succeed in filling it, one may have to
exhaust several times by means of the tube E. The best way
is to connect this tube with the small pump of Pig, 4, page 75.
The bulb may thus be filled in a very short time.

It is then necessary to bring the mercury to boiling : to this

82

EXPANSION OF. GASES

end the bulb A is placed upon a hollow grating OG over a
small furnace F, Fig. 8, the capillary tube having an inclina-
tion of about 45 ° and its bent end CD being below the surface
in a dish full of very pure mercury. Some coals are then put
in the furnace, below the grating, then they are successively
placed upon the grating itself and upon the bulb^ and finally
E

?

K

FiQ. 7.

Fio. 8.

the latter is entirely covered with hot coals. When the mercury
in the bulb approaches the boiling temperature, the mercury in
the dish D is heated with an alcohol lamp, and with a second
alcohol lamp the capillary tube is cautiously heated throughout
its length. As soon as the mercury begins to boil in the bulb,
the operation must be watched with the greatest care ; for if this
boiling becomes too vigorous, if it drives out of the bulb too
large a volume of liquid mercury displaced by mercury vapor,
it is almost impossible to prevent the apparatus being broken
at the instant when, the boiling having stopped, the mercury
rushes back into the bulb ; this results in very violent hammer-
ing and return-shocks which ordinarily extend as far as the
bent part OD of the capillary tube.

Therefore as one sees the mercury boiling in the vessel, a
part of the coals must quickly be removed and the operation
be made as smooth as possible. The coals are taken away
entirely as soon as the moisture seems to have been completely

83

MEMOIRS ON

driven out, or even when the volume of mercury vapor has
become considerable. The mercury then returns into the
apparatus and, as it has been previously heated in the dish, it
does not break the capillary tube, as it would certainly do with-
out this. When the bulb is once more full, one looks to see if
a trace of moisture remains ; in case some still remains, the
boiling must be begun again. Speaking generally, it serves
better to bring it to the boiling point again and again, rather
than to continue the boiling for too long a time ; in this way
the breaking of the apparatus is more easily avoided.

When the vessel is completely full of mercury, it is allowed
to cool to the temperature of the air, then is surrounded with
a thick envelope of crushed ice. It requires* many hours for
the mass of mercury to arrive absolutely at the temperature of
0°. When it is certain that this point has been reached, the
dish full of mercury is removed and is replaced by a small
empty capsule. The ice having been got out of the way, the bulb
is warmed with the aid of hot coals placed at some distance
from it, so as to raise it to a temperature some degrees higher
than the surrounding one; then it is hung in a small bag in
the boiling apparatus of Fig. 4 [page 75], to which an exten-
sion has been fitted, so that the whole capillary tube is sur-
rounded by the steam, and the mercury is caught in the same
capsule. By weighing the mercury forced out and that re-
maining in the apparatus, it is evident we have the necessary
data for calculating the volume of the apparatus at 0° and
the extent to which it expands between and 100°.

To find the expansion of air, the bulb is hung in the boiler
after the mercury has been so completely removed that not the
smallest globule remains upon the walls or in the tube. The
bulb is connected with the drying apparatus, Fig, 4. In a
word, one goes to work exactly as has been described in the
account of the former series.

When the end of the capillary tube has been sealed with a
lamp, the apparatus is adjusted to a support shown in Fig. 9.
The expanded part B of the tube comes below the plate EE'.
By means of a cork on the stem at My a tin-plate tray is put in
place, in which crushed ice must be piled up, to keep the vol-
ume J5 at 0°. The capillary tube dips in a small bath of mer-

84

EXPANSION OF GASES

cury T. The tip of the bent part CD is broken off, all the
precautions being exactly followed which have been pointed
out in the first account, to prevent the entrance of air; finally
the vessel A is surrounded with ice after having put over it
from above a cylinder of tin-plate which is entirely filled with
crushed ice. In the same way the volume B and the part of
the capillary stem which is above the tray M are surrounded
with ice.

Upon one of the legs of the support P' is arranged a mov-
able arm mn carrying the small adjustable spoon of Fig, 6;
this is lowered into the mercury. A mark has previously been

■*i I

FIG. 9.

made upon the leg P" at the point where mn should be clamped
in order that the spoon JT may be at the level and in a line
with the tube CD,

The apparatus having been left in the ice for about an hour,
the tip D is sealed by pushing forward the spoon K, and at the
same time the barometer is read; finally, the point of the
screw t, which is arranged upon a small special apparatus R,
is made to coincide with the surface of the mercury in the
bath.

The ice which is in the tray M is then removed. At the
end of three-quarters of an hour or an hour, when it is certain
that the column of mercury drawn up is in temperature-equi-

85

MEMOIES ON

librium with the surrounding air^ the height of this column is
measured with the cathetometer. The dimensions of the tube
and the level at which the mercury bath is placed, are such that
the mercury comes to rest in the space B and fills it about
half full.

The apparatus is detached and the mercury which has made
its way in is weighed.

The tubing of which the space B is made was chosen in suc-
cessive cases of different diameters; these dimensions were
never great enough for the capillarity to become nily but the
capillary depression is determined each time, by direct experi-
ment, in that part of the tube where the surface of th& mer-
cury comes to rest. For this purpose this tube is held vertical
with both ends open, and dipping in a bath of mercury. On
the slide which supports the glass of the cathetometer a hori-
zontal metallic rod is. fastened, to the end of which is fixed a
vertical pointer whose tip is adjusted for contact, successively
with the top of the meniscus in the tube and with the mercury
surface in the bath. The distance traversed by the zero of
the vernier of the instrument is the capillary depression.

We then have all the data necessary for calculating the ex-
pansion of the air. Using the same letters to designate simi-
lar things, as in the former method and, in addition, repre-
senting by c the capillary depression in the space By clearly we
have the equation

(1 -f cJ D £r = (i _ ^^[fl' - (A + c)] (1 + d D;
whence

Let us assume in all cases that the columns of mercury have
been reduced to 0° by calculation.

Three different vessels, A, B, 0, were used in these experi-
ments; to these were successively joined capillary tubes of
different bores.

I shall distinguish as many series of experiments as different
forms of apparatus.

86

J

EXPANSION OF GASES

4330.0 gr.
1.10 mm.

I. The results with this apparatus are as follows:

p.

c =

The coefficient of expansion of the glass could not be deter-
mined as the apparatus was broken during the boiling of the
mercury. For this one experiment made with vessel A the as-
sumption is made that 100s — 0.002306, as was found by ex-
periment with the vessel B.

The experiment upon the expansion of air gave

1-1- 100 a

1.36629

II. This apparatus was made with the vessel B; we have:

P= 4274.34 gr.,
p _ 65.708,
c= 1.10 mm.,
H «=- 749.37, whence Tl =— 99.60 ° .

We deduce from this

100^ = 0.002306.

H

JT

h + c

Z^

T

mm.

mm.

mm.

gr-

739.61

739.86

194.38

14,233

99.23°

H

ET

h + c

P'

T

1-flOOa

mm.
739.24
758.64

mm.
739.21
758.53

mm.
193.58
199.51

gr-
17,735

17,335

99.22°
99.95

1.36645
1.36593

2
3

III. Apparatus made with the vessel B, but using for the
space B on the capillary tube, a tubing of much greater diame-
ter.

For this apparatus it was found

P =4306.86 gr.,

p == 66.68,

c = 0.22 mm.,

ffl= 769.04, hence Ti = 100.34 ;

from which we find

100 (J = 0.002302.

With this apparatus I obtained the following figures :

4
6
6

7
8

H

H'

h + c

P'

mm.

mm.

mm.

gr.

764.70

764.31

198.78

36.095

767.24

767.19

199.98

34.825

768.10

767.40

199.62

34.845

770.57

770.70

200.86

34.490

771.07

770.26

199.53

41.780

T

1 + lOOa

100. IS**

1 .36610

100.27

1.36685

100.30

1.36590

100.40

1.36615

100.41

1.36691

87

MEM OIKS ON

IV. Apparatus made with the vessel 0,

P = 4878.60 gr.,

P =
c =

From ibis we deduce

9
10
11
12
13

74.795,
0.54 mm.,
749.32, bence Ti = 99.60®.
100 d = 0.002349.

H

H'

^ + c

P'

T

mm.

mm.

mm.

gr.

748.13

745.89

193.04

32.42

99.56°

754.10

751.51

194.73

30.64

99.78

740.14

744.53

196.86

32.305

99.26

746.91

74S. 13

196.23

31.355

99.51

747.54

747.28

194.69

31.486

99.53

1 + 100 a

1.36708
1.36695
1.36633
1.36708
1.36650

V. Apparatus made with the bulb C, but using for the space
B a tubing of a greater diameter and for capillary tubing one
of finer bore.

For this apparatus we have :

P = 4923.60 gr.,
c = 0.22 mm. ;
we bave assumed 100 <J = 0.002349.

14
15
16
17

H

H'

h + c

P'

T

mm.

mm.

mm.

gr.

746.69

747.16

191.98

58.551

99.50®

751.97

750.18

191.50

56.69

99.70

746.49

746.19

191.76

54.865

99.50

752.50

751.45

192. 17

61.30

99.72

1 + 100 a

1.36615
1.36594
1.36660
1.36666

VI. Apparatus constructed with the same bulb, substituting
for the finer capillary tube another of a larger bore.
The data for this apparatus are the following :

P = 4926.4 gr.,

c = 0.22 mm. ;
we bave assumed* 100 cJ = 0.002349.

This apparatus was used for but one experiment upon atmos-
pheric air ; it was intended for some experiments upon other
gases.

18

H

W

^ + c

P

T

mm.

mm.

mm.

gi*.

758.24

758.78

195.68

58.31

99.93 o

1 + 100 a

1.36614

Then bringing together all the figures obtained in this series
of experiments —

88

EXPANSIOM OF GASES

1.M629

1.36605

i.3ee4S

1.36638

1.36503

1.36T06

1.36610

1.36650

1.36585

LS6615

iMsaa

1.36501

1.36615

1.36660

1.36591

1.36666

1.86706

1.36614

hese experiments

is

The meaa of all th

1.SS633.

It does not practically differ from that obtained in the former
series.

Third Series op ExPERrMEirra.
This third series of experiments was made by meaos of an ap-

paratus copied from that described by Eiidberg in his second
memoir and which is represented in Fiff. 3 [page 70 ]. Theap-
paratus which I constructed is shown in Fiffs. 10, 11, 13.

MEMOIRS ON

A cylindrical glass reservoir AB, 35 millimeters in diameter
and 170 mm. long, is sealed to a capillary tube BODE, twice
bent at right angles. This tube terminates in a piece of tubing
EE of much larger size, which dips in a small mercury bath
MM\

This bath consists of a cylinder of heavy glass whose two
edges are tightly pressed against the two cast mountings J/,
M\ by means of the screw rods t, t\ t'\ The upper casting has
two tubulures T, T\ provided with screw threads on the outside.
These tubulures are closed by two copper screw caps bored
through the centre with holes to allow tubes to enter. The
lower casting carries a screw thread in which works a large
screw rod KL supporting a cast piston P inside the glass cylin-
der. This piston has a covering of linen greased with tallow :
at its centre is a small packing-box filled with oakum, through
which moves an iron rod//', 8 millimeters in diameter, which
screws up and down inside the large rod KLy and ends outside
with the knob/.

The small bath is fixed by means of set screws to a cast ver-
tical support NN\ but in such a way that it can be made to
move along the slots r r', — which is convenient for adjusting
the tubes. This bath is otherwise completely filled with
thoroughly dry mercury.

We begin by determining by a preliminary experiment the
capacity of the cylindrical reservoir AB and its coefficient of
expansion. We determine in the same way the volume of the
capillary tube from to Ey as well as that of the small portion
of the larger tube Ea down to a very fine mark scratched upon
this tube at «. We then dry the reservoir completely and fill
it with dry air : for this the drawn-out end of the tube is con-
nected with the drying apparatus. Fig, 4, page 75, and the whole
length of the reservoir and tube are warmed with hot coals.
A vacuum is produced a great many times and each time the
air is allowed to enter again. The hot coals are then removed,
there being free communication with the atmospheric air.
When the reservoir has cooled, it is placed in very cold water
or even in some ice ; finally, after some time, the tip of the
tube is closed by means of the blowpipe.

The cast upright NN' carries a cast bracket-arm FF'F"

90

EXPANSION OF GASES

fastened with screw bolts in the slots cut in the upright NN";
it can thus be adjusted at various heights. To this bracket-
arm is fastened permanently the copper cover 00' of a vessel
of the same metal OHH'O'. The cover is provided with two
tubulures /, /' ; in one the reservoir of air AB'\& fixed by means
of a cork ; in the other is placed a mercury weight- thermometer
A'B\ of exactly the same shape and dimensions as the air
reservoir. The two tubes rest upon a small cross piece A A'
fastened to the rod JJ\

The tube EF\^ introduced into the tubulure Tand, in order
to fasten it hermetically, is wrapped with a strip of linen
greased with tallow, which is then forced by means of the screw
cap E into the annular space formed in the tubulure. We thus
obtain an air-tight connection which will resist very great pres-
sure. The point of the tube EF\& then broken off by means
of an iron rod introduced through the second tubulure T\ and
in this second tubulure is fastened, in exactly the same way, a
piece of barometer tubing 00' ^ perfectly cylindrical through-
out its length and of exactly the same diameter as the end
tubing ^^ possesses below where it is drawn out. Besides it
was shown by direct experiment that there was no difference
between the capillary depressions in the two tubes.

To conduct the experiment, the two reservoirs ABy A' B' are
surrounded with melting ice which is put in a small bag and
hung from the copper cover 00' . By turning the rod KL the
piston is forced up until the mercury comes to rest at a in the
tube EF; the fine adjustment is made with the aid of the thin
rod ff'. A determination of the difference of level is then made
with the cathetometer, and at the same time the barometric
pressure is recorded.

The ice and the bag which contains it are then removed, the
vessel OHH'O' is fastened by means of screws to its cover 00',
and the water which it contains is then raised to boiling. By
pushing up the piston the mercury is maintained at the level a
in the tube EF, When it is certain that the air has come to
the temperature of the vapor, the mercury level is adjusted
exactly at a by means of the rods KL andjf' , and the difference
of level of the two columns of mercury is read with the cathe-
tometer, as well as the height of the barometer.

"91

MEMOIES ON

I made some experiments at firsts takings as Bndberg did^
the point a upon the capillary stem ; but I found that it was
very difficult by this raetliod to get accurate results. Thus,
although in one experiment the tube was of more than 1 mm.
diameter, the movement of the mercury in the tube was very,
irregular, by reason of the variation in the capillary action.
Sometimes the column in 00' would rise more than 1 mm.,
without the mercury at a being displaced to a visible extent ;
in the same way, on lowering the piston, the column'had often
fallen several millimeters in the tube 00\ while the meniscus
at a had only become flattened ; this sluggishness was not
entirely overcome by even quite sharp taps given the appara-
tus.

It became necessary to take the point a upon the larger tubing
EF. As this tubing was of exactly the same diameter as the
barometer tubing there was no correction to introduce for cap-
illarity; but it was necessary to take account of the small vol-
ume of air which was not heated.

Let P be the weight of mercury at 0° filling the reservoir AB
up to when it is at 0**;

p the weight of mercury which flows out at the temperature
of water boiling under the pressure If\ or at the tempera-
ture T^;

p' the weight of mercury which fills the capillary tube CDB
and the pari Ea of the larger tubing EF;

H the barometric pressure at the time when the reading is
made, the reservoirs being kept at 0** by melting ice;

h the difference of level of the two columns of mercury;

t the temperature of the surrounding air.
In the same way let us represent by

H' the barometric pressure when the reservoirs are heated by
boiling water;

T' the corresponding temperature of the vapor;

h" the difference of level of the two columns;

t' the temperature of the air.

Evidently we shall have the equation

hence

92*

EXPANSIOK OP GASES

i + .r ii^^^i^jH'^K'i ^

for, by reason of the small value of t^ we can always assume

that t — t.

I shall again here distinguish as many series of experiments
as special pieces of apparatus.

I. An experiment made to determine the volume of the air
reservoir and its coefficient of expansion, gave

P = 1975.862 gr.,
p = 29.852,
Hi =. 745.61 mm.,
Ti = 99.46°,
whence 100 J =» 0.002655.

By measurement, there was found for the weight of mercury
filling the capillary tube and the small piece of larger tubing
as far as the mark^

p « 9.740 gr.,

whence ? = 0.00493.

P

The tube being heated by the vapor of boiling water, two
readings made with a half-hour interval gave

H' 761.01 761.01

h* 296.70 296.70

t' 8.6° 8.8°

T 99.66' 99.66'

whence H'+h'=. 1047.71 1047.71

The reservoir being in melting ice, we have

H 749.98 749.88 749.78

h 20.63 20.59 20.63

t 8.5' 8.6' 8.6'

H+h 770.51 770.47 770.41

We shall take as an average

fl-^- A = 770.47.
Comparing this mean with the two determinations at the
boiling point of water, we have [the ratios]

1.36688, 1.36688.

A second series of experiments made with this apparatus
gave:
The tubes being in melting ice,

93

MEMOIRS ON

B 746.16 746.26 746.39 746.61 746.66

h 24.53 24.41 24.21 24.11 24.09

t 8.3* 8.3** 8.3*' 8.3*' 8.3»

H+K 770.69 770.67 770.60 770.72 770.75

Mean of H+ A = 770.69.

lu boiling water we have:

B' 740.79 741.01 741.14 743.20 743.26

h' 305.58 305.62 305.36 303.72 303.64

t' 9.00° 9.00O 9.00O 9.00«» 9.00*»

T 99.28° 99.29*' 99.29<» 99.37<» 99.37»

H' + h' 1146.37 1046.63 1046.50 1046.92 1046.90

On comparing each of the values of H' + h with the mean
770.69 of the determinations in melting ice, we have [the
ratios]:

1.36612
1.36643
1.36626
1.36651
1.36649

Mean - J:^1§L =1.36636.
o

II. With a second apparatus made with a reservoir cut from
the same piece of tubing as the former, we have

P= 1817.50 gr.;

assuming 100 d = 0.002555,

p' = 8.50 gr.,
-y- = 0.00468.

In melting ice we have:

H 752.60 752.60 752.65 752.67 752.40 752.25

h 19.58 19.58 19.76 19.66 19.74 20.24

t 11.0° 11.0° 11.0° ll.t)° 11.0° 11.0°

H + ;i.... 772.18 772.18 772.41 772.23 772.14 772.49

Mean ot H + h = 772.29.

In boiling water we have:

H' 751.15 751.13 751.13 751.08 751.05

h' 299.16 299.66 299.66 299.76 299.86

If 13.7°

JT+A'.... 1050.31 1050.79 1050.79 1050.84 1050.91

T 99.67°

94

EXPANSION OF GASES

The five values of H' + h'y compared with the mean of

H+ A, give [the ratios] :

1.36672

1.36714
1.36714
1.36730
1.36747

Mean == ^'^^'^ = 1.36715.

Thus the three series of experiments made by this method

gave the following mean values:

1.36688
1.36636
1.36715

General mean = ^-5 = 1.36679.

o

This average differs little from that found in the two former
series.

I do not think this method leads to the same accuracy as the
others which I have used. The tubes in which the columns of
mercury are measured, are not of large enough diameter to
make the capillary effect negligible; the capillary depression
amounts in these tubes to about 1 mm. This capillary depres-
sion, theoretically, does not enter into the calculation of the
constant, and, if it remains always the same, it exerts no* influ-
ence. Yet it is easy to show that this effect must vary between
rather wide limits, by measuring from time to time the heights
of the tops of the menisci ; we may thus realize that these
sometimes vary in the same experiment from a certain amount
to double that amount. As a matter of fact, here is a series of
measurements of the corresponding heights of the two menisci:

Tube EF Tube 00'

1.08 mm. 1.14 mm.

0.72 1.64

1.00 1.64

1.10 1.32

1.38 1.36

0.96 1.20

0.80 1.18

It is not possible that such marked variations in the heights

of the menisci do not involve very considerable changes in the

capillary depressions.

95

MEMOIES ON

Bndberg with his apparatus has fonnd lower figures than
miue. It is difficult with any certainty to determine the causes
of these differences. I have already stated above that I bad
never obtained good results when I fixed the mark a on the
capillary part BD of the tube; but I believe that still another
reason could be given which has led Kudberg to results that
are too low. This physicist has always in his calculations neg-
lected the little volume of air, not heated, which is contained
in the portion Ba of his capillary tube. This volume is very
small, nevertheless it is hardly probable that it can be entirely
neglected. Unfortunately, Eudberg has not given in his mem-
oir the dimensions of the different parts of his apparatus;
hence it is impossible to calculate now the correction this fact
would involve in his results.

Fourth Series of Experiments.
This series of experiments was made with an apparatus

FIG. 13.

96

FIG. 14.

EXPANSION OF GASES

which served the same end as that of the preceding series^
without possessing the same disadvantages. It consists of a
large bulb A (Figs. 13 and 14) of 800 to 1000 cubic centimet-
ers' capacity^ to which is sealed a capillary tube about 20 centi
meters in length. This bulb serves as the air-reservoir and
must be brought successively to 0® and to 100®; it is put in

» communication with a syphon tube full of mercury^ which

[ serves to measure the tension of the air.

I A tube e77of 16 to 17 mm. internal diameter^ perfectly cyl-

indrical^ is fastened by means of gum- mastic in an iron cast-
ing /ff provided with a tap JT. This carries a side tubulure H
in which is cemented a second tube HGFE of the same diame-
ter as the first throughout the length FO. This tube ends at
the top in a bent capillary tube FED, cut from the same capil-
lary tubing as the tube BC sealed to the bulb. The tube BC
fits close in a small copper three-way tube mno in which it is
firmly fastened with mastic. In the second arm o is cemented
a short piece of capillary tubing op which has been drawn out
at its end p.

The system of the two tubes IJ and EH is fastened to a
plank which is itself firmly secured, and in a perfectly vertical
position, to a cast-iron upright LL\

The bulb A is fastened once for all in a vessel of tin plate
MN, in which water can be boiled, or the bulb surrounded
with ice. This vessel rests upon an iron, tripod PQQ'P'. A
furnace upon a support 8 can be put below the vessel MN
and withdrawn at will.

This is now the way an experiment is made. The open end
of the tube op is connected with the drying apparatus {Fig. 4)
[page 75]; and in order to close the arm n of the copper
tube, a bit of tubing completely closed is attached to it with a
piece of rubber tubing. The water in the vessel MN is
brought to boiling, and a vacuum is produced a great many
times within the bulb, each time allowing the air to enter again
very slowly.

The tube HQFED had been dried at a high temperature in
the same way before being cemented in the tubulure H, and
very dry mercury is immediately poured into the tube //, so
as to fill completely the tube HOF up to the open end D. In

97

MEMOIRS ON

this way moisture is kept out of this tube. With the same idea
care is taken to keep the end of the tube D covered with a cap
of rubber.

The bulb A being filled with very dry air, the bit of stopped-
up tubing, which during the drying was over the tubulure w, is
removed, and the capillary tube DE is connected with this tu-
bulure by means of rubber; this tube fits closely in the copper
tubulure and comes butt-to-butt against the tube BCy so that
within the little copper three-way tube mno the only space
there is is the bore of the capillary tubes which meet there. At
other times the tube DEis fastened in the tubulure by means
of mastic.

The tap E is opened; the mercury which flows out is re-
placed in the tube EFO by air which has passed through the
drying apparatus. The mercury is run out until the level
stands in the tube FG at a mark a scratched on the glass. The
mercury stands at the same level in the two tubes, since on
both sides it is freely open to the air.

The drying apparatus is now disconnected and the tip p of
the tube op is closed by means of a lamp. At the same time
the height IT of the barometer is recorded.

The furnace which keeps the water boiling in the sheet-iron
vessel is removed. In order that the bulb A may become cool
more rapidly, the hot water is drawn off by opening the tap E;
the cover ahcdefgh is taken off and cold water is poured several
times into the vessel to cool the walls. Finally the bulb A is
completely covered with crushed ice, which is kept in place by
a cloth fastened to the edge cd of the vessel.

The air contracts on cooling, the mercury rises in the tube
OF; but it is maintained at the same level a by running out
some of the mercury through the tap K,

When it is certain that the air in the bulb A has come to
the temperature of melting ice, the barometric height H' is re-
corded, and the difference of level 0^ = 11' is measured by
means of the cathetometer. We thus have already all the
data necessary for determining the rate of expansion of
air; but we can get a second determination in the following
way:

The closed tip J9 is again connected with the drying appara-

98

EXPANSION OP GASES

tus; this apparatus is exhausted several times in succession^ to
make sure that it is full of dry air; then the tip jp is broken off.
The merciiry now falls in the tube FO, but it is brought back
to a by pouring mercury into the tube //.

After some time the tip^ is again closed by means of a lamp
and the height H" of the barometer is recorded. The ice is
then removed; the cover abed of the tin vessel is put back, and
the water poured into the vessel is brought to boiling once
more. By pouring mercury into the tube Z/the level is main-
tained at a in the tube FO, After the bulb has remained about
an hour in [the vapor of] the boiling water, [the height of] the
barometer H" is noted, and the difference of level ay^=h" of
the mercury in the two columns is measured.

In the calculation of the experiment it is necessary to take
account of the small volume of air that remains constantly at
the temperature of the surrounding air. For this we must
know the ratio of this volume to that of the bulb A. The
latter volume V had been determined by measurement with
distilled water, and the volume v of the air contained in the
capillary tubes BC^ DEFy op, as well as in the part Fa of the
larger tube, had been found by measurement with mercury.
We thus had:

Weight of mercury filling F= 9889.9 gr.,
ditto ditto v= 26.85;

hence p. = 0.002715.

I was not able directly to determine the coefficient of expan-
sion of the bulb A; it would have been necessary, for this, to
have boiled a mass of 9 to 10 kilograms of mercury in a bulb
of glass ending in a capillary tube, which seemed to me a prac-
tically impossible operation. I have assumed the figure 0.00233
for this coefficient, which is the mean of those found for the
two bulbs used in my Second Series of determinations. These
bulbs were the product of the same factory and were of the
same kind of glass.

The temperatures t, t\ f\ t''\ of the small volume of air v
were indicated by the small thermometer T' ; that of the col-
umns of mercury by the thermometer T whose cylindrical
reservoir had the same diameter as the tubes IJ and FO,

99

MEMOIES ON

The equation which serves for the first half of the experi-
ment is the following:

{i + ST)n

l + aT

H'-h'- -k

Vl + at

that which applies to the second half is

[H-^H' + h'^i

l+ar

//

(1 4- (J T") H'" ^h'"

H" - ^.

[H"' + h'" — if"]

Kl + a t'"

We have assumed in these equations

/«randr — T'.
We now have the figures obtained by this method:

First Half.

1
2
3

H

747.83
742.27
747.97

T

99.55»
99.34»
99.55'

t
14.0'
13.9
13.0

H'

747.43
744.25

748.52

197.49
198.56
198.76

I

t'
14.0'
13.5'
12.5'

14 100a
1.36592
1.36710
1.36662

Mean 1.36656

1
2
3

H"

r

H'"

rpm

h'"

V"

747.30

14.2'

746.45

99.50'

270.28

15.1'

744.59

13.1'

745.27

99.45'

267.59

15.6'

748.72

12.9'

749.19

99.59'

269.59

13.9'

1 + lOOa
1.36682
1.3G674
1.36580

Second Half,

2
Mean 1.36646

Thus the mean of the six determinations is 1.3665.

In the Fourth Method the expansion of the air is measured
under very different pressures : in fact, in the first half of each
experiment the air was under a pressure of only about 0.550 m.
when at 0®, and under the atmospheric pressure 0.760 m., when
heated to 100°. In the second half, the air at 0° is under the
atmospheric pressure 0.760 m., and the air heated to lOO*' is
under a pressure of about 1.040 m. As the experiments show no
difference in the numbers obtained in the two halves, it must
be concluded that, within these pressure limits, dry air shows
a practically constant coefficient of expansion.

It is very easy to arrange the apparatus so that it will serve
for the study of the expansion of air under greater pressures ;
in fact, it will suffice for this to give the tube BFGITsl con-
siderable capacity from a certain point 6 to IT, Fig. 15, sealing
the tipj9 at the time when the bulb as well as the tube EH as
far as H are full of dry air, then pouring mercury into the tube

100

EXPANSION OF GASES

U until the mercury-level coincides with a in the tube FaQ, the
bulb being snrrounded with melting ice; the mercury then
rises in the tube IJ a certain distance A, bo that the
volume of gas is then at 0° under a pressure H-\~h.
The bulb being raised to 100°, in order to keep the
level of the mercury at a in the tube PO, it is neces-
sary to pour a new lot of mercury into the tube JI,
which gives a difference of level A' and, consequently,
for the pressure upon the gas at 100°, if-j-A'. The
heights A and A' will be more considerable as the
volume of the tube iH is greater in proportion to
the volume of the bulb. Some experiments made by
the method thus modified will be discussed later.'

1 1 have also made some esperimentB to determine the
coefficient of expansion ot air by tlie method of M. Gay-
Lusaac. Tliis method consiatH, as is well known, in observ-
In^ the expausioLi suffered by dry air enclosed in an actual
til ermo meter, this air being separated from the outside air
by a tiny index of mercury.

The capillar; tube was measured, then graduated with
tbe ji^reatest care ; it was of 2.7 ram. boie and was marked
with 600 divisions in a length of 65S mm. Tiie experiment
was bejcun by filling this thermometer with mercury which
was again and again brought to boiling in the bulb and In Fio. is
tbe tube, then was entirely surrounded with ice; the point where the
mercury came to rest on the scale was noted. A portion of t1)e mercury
in the stem was made to Sow out and was weighed, then the ther-
mometer was once more put in the ice and tbe point noted where the
column came to rest This operation repeated three times iu different
parts of the scale, gave the following results :
Mercury at 0° l>etween 375.8 and 002.0 = 226.3 div.; 6.829 gr.
103.0 375.8 = 273.8 7.9W6

50.9 499.0 -- 448.1 13.128

From this we deduce for tbe weight of mercury at 0° occupying one
division ;

in the first interval 0.029306 gr.

in the second 0.029306

In the third 0.029297

Mean = "ftlSSjaaT^ 0.02S303.
The close agreement to be noticed in these figures proves satisfactorily
the accuracy of the graduation.

The mercury which at 0° filled the bulb and the stem as far as divi-
sion 50.9, weighed 27.916 gr.

101

MEMOIES ON

The four series of experiments which I have described in
detail have therefore given the following averages :

After the mercury has been completely removed from the apparatus,
it is connected by means of rubber tubing with a U-shaped tube con-
taining pumice stone moistened with sulphuric acid and is exhausted a
great many times while being warmed by means of hot coals. This
thermometer tube was fitted at the end with a bit of larger tubing in
which had been left a tiny drop of mercury to form the indent. The
apparatus being filled with dry air, the bulb is raised to such a tempera-
ture that the globule of mercury, when drawn into the capillary tube,
comes to rest at a convenient point when the thermometer is placed in
melting ice.

The greatest pains were taken to place the stem of the thermometer
in a perfectly horizontal position where the instrument was in ice or in
[the vapor of] boiling water, and it was given light taps to assist the
movement of the index.

I shall not describe in detail the numerous experiments made by this
method ; suffice it to say I was unable to get constant figures. The way
in which the thermometer tube was tapped, the points on the tube
where it was struck, produce a very marked effect upon the position of
the index. The movement of the index even seemed to depend upon
the more or less rapid changes of the temperature, which seems to show
that the mercury index does not close the tube perfectly, and that
would not be surprising after what we have seen above [page 80].
What confirms me in this opinion is that, in many experiments, the
index did not return to the same point, the thermometer being sur-
rounded with ice, when, in the interval, the apparatus had been heated
to the boiling point of water.

Thus, in one experiment, the index came to rest when the
thermometer was in ice, at 152.7 div.

In [the vapor of] boiling water at 534.5 div. ; the appara-
tus being again surrounded with ice, the index came to rest at. .154.5 div.
and meantime the barometer had not changed to any noticeable extent.

In another experiment the index came to rest in melting ice at 66.5
div. before the instrument had been put in [the vapor of] boiling water,
and at 66.0 div. after it had been heated. The barometer had changed
in a very marked way during the interval, but this change should have
produced a movement in the opposite direction.

However that may be, here are some of the figures I obtained by this

method : 1.3641

1.3626
1.3635
1.3647
1.3552

It is remarkable that all these figures are smaller than those yielded

by the other methods. This circumstance is probably the result of mere

chance.

102

EXPANSION OF GASES

First series 1.36623

Second series 1.36633

Third series 1.36679

Fourth series 1.36650

That is to say, about 1.3665.

I therefore propose to adopt for the coefficient of expansion
of dry air for each degree centigrade between the two fixed
points of the thermometer, 0.003665.*

We shall now proceed to take up in succession all the quan-
tities which enter into the calculation of the experiments, in
order to obtain an approximate value, at least, for the error
each of them may introduce.
The equation

^ "^ (P' — P) (H'—h) \

which applies to the first two series, comprises the weights P
and P' of mercury which can be determined with what may be

called absolute precision. Thus the factor _ cannot intro-
duce any noticeable error arising from its experimental deter-
mination.

The factor 1 -j-dT^ depends upon the expansion of the glass.
We have seen that this expansion was determined for each ap-
paratus by direct experiment and it must be admitted to be
rigorously exact; besides, since it is very small, a noteworthy
error in this coefficient would exert no appreciable effect upon
the value of the coefficient of expansion of air.

The coefficient of expansion of glass was determined as being
a function of the coefficient of expansion of mercury; I have
assumed for the latter coefficient the value y^.y = 0.01802,
found by Dulong and Petit. Unfortunately, some uncertainty
exists regarding the numerical value of this coefficient; in fact,
Dulong and Petit gave in their memoir only the following
values:

Expansion of mercury for each degree centigrade between

0° and 100% yyViy

ditto ditto 0^ and 200% y^y

ditto ditto O*" and 300% 53*55

^ M. Babinet has called my attention to the fact that, adopting for the
coefficient of expansion of air the figure 0.366666. . . , this coefficient
may be represented by the very simple fraction JJ, which is very easy to
use in calculations.

103

MEMOIRS ON

The temperatures are giyen here, as these distingnished phys-
icists explicitly state^ with reference to the air thermometer^
assuming for the coefficient of expansion 0.375; but if this co-
efficient is inaccurate and if the figure 0.3665 must be used^
then the intervals of temperature change appreciably and the
temperature 100® of Dulong becomes 102.7° , so that the coeffi-
cient yiJ.y should be about ^ greater, i

It is possible, however, that the coefficient of absolute expan-
sion of mercury between 0® and 100° given by Dulong and
Petit may be that which they found directly in their experi-
ments from [the temperature of] melting ice up to [that of]
boiling water, without deducing it from their interpolation-for-
mula. In this event it would not be affected by. the same
source of error as the values between 0° and 200° and between
0° and 300°. However that may be, new experiments alone
can decide the point.

What interests us at this moment is to see what difference
this could bring about in our coefficient of expansion of air.
Assuming the coefficient of absolute expansion of mercury be-
tween 0° and 100° too great by ^, the coefficieht of expansion
of glass would be too great by about ^. Thus, instead of the
figure 1.0026, we should have in the numerator the figure
1.0024, smaller than the former by xxy^Trxr* which would reduce
the figure 1.3665 by xv.iiyu* ^^^^^ is to say, would give 1.3662;
consequently this change would affect only the fourth decimal:
after all, it is a correction easily made in all my figures.

The factor gr^i which depends upon the barometric mea-
surements, is the one which is liable to the largest errors of ob-
servation. Physicists who have had occasion to make a large
number of barometric observations, know how difficult these
observations are when the attempt is made to reach the high-
est limit of accuracy. I do not believe I exaggerate when I
take it for granted that a barometric reading cannot be made
closer than -ji^ of a millimeter, however improved the measur-
ing apparatus may otherwise be. The difficulty lies in the fact
that the atmospheric pressure is constantly changing, but this

1 This point has already been made by M. Poggendorff, Poggendorff*8

Annalen^ Vol. XLI, page 467.

104

EXPANSION OF GASES

variation is at once shown by the barometer, yet as a rule,
only the changes in the form of the meniscus, and the varia-
tions in height do not take place in any regular way, but
rather by jerks. It is well, in order to avoid this trou-
ble, to tap the barometer to make the mercury column
move back and forth, before making a reading, yet it is
clear that the source of error is not completely done away with
by this means.

Each of the measurements H, H', h, is liable to the same er-
ror e. In order to determine the maximum deviation of indi-
vidual experiments, we shall suppose the errors made in H, H\ h,
to have such signs as will produce the greatest difference in
the final result. Thus, we will assume that instead of the

accurate factor „^__ . , observation has given us the factor

The error is then represented by

H + e H_

or

e(2g4 H'^h) ^
(H'—h) (H' — h-^e)'

or simply

by neglecting 2e in the denominator in comparison with H' — li.
As a result, the value of 1 + a2^ becomes

Assuming H ^ H' = 760 mm., h = 190 mm.; we shall have
for the last factor

760.00 mm. +£. J2??.
or 570 '

760.00 mm. + e X 3.67.

If e = 0.1 mm., then the total error resulting for 760.00 mm.
will be 0.367 mm., that is to say TTTi,%Tnr-

This gives for the total possible range of error in the experi-
ments, for this source of error alone, ttt^^xtxt.

It may thus be seen that if we assume it impossible to attain
H 105

MEMOIRS OK

an accuracy greater than ^^^ of a millimeter in barometric ob-
servations^ the determinations of the rate of expansion of air
will be liable, from this source of error alone, to show a maxi-
mum variation of about j^j^. It will be noticed that this is
close to the maximum variation to be observed in my results.

In order that the coefficient of expansion of air may be exact
up to the third decimal, the experiment which determines it
must not lead to an error of more than tAtt* The direct ex-
periment does not tell us, as a matter of fact, that 1000 parts
of air expand between 0® and 100° by 366 parts, which would
be an accuracy of only ^J^; but rather that 1000 parts of air
become 1366 in passing from 0° to 100°, which gives an accu-
racy of x^j.

The formulas which apply to the two later series of experi-
ments are evidently open to the same sources of error. The
possible error in the measurement of the heights of the col-
umns of mercury is probably even greater in the apparatus of
the Third Series, since the tubes are narrower and on this ac-
count show a greater variability in the capillary depression.

Yet there is in addition another source of uncertainty in
these two methods which did not enter into the two earlier
ones: it lies in the determination of the temperature of the vol-
ume of air which was not heated. The error resulting from
this might be quite large if this volume formed an appreciable
fraction of that which is brought to the fixed points: it is en-
tirely negligible in my experiments, since I took pains to carry
them out so that the volume of the air that was not heated
should never be but an extremely small fraction of the total
volume.

The temperature T of the vapor was calculated from the ob-
served barometric heights at the time of the boiling. I have
assumed in this calculation that a variation of 1° in the boiling-
point of the water corresponded to a difference of pressure of
26.7 mm. This figure is that given in the tables of the tensions
of water-vapor recently calculated by M. Biot. It seemed to
me better to adopt t'his figure, than to take the numbers found
by different physicists by determining with some one ther-
mometer the boiling point of water under various barometric
pressures.. These experiments could not result in great accu-

106

EXPANSION OF GASES

racy, for they were frequently carried out on days quite sepa-
rated from one another, and because the instrument had
probably already suffered some appreciable change in the inter-
val through the movement of the fixed points.

In order that these experiments should yield results that
could not be questioned, it must have been possible to take
note of the boiling point of water under various pressures, at
times close together, for example, in an apparatus where the
pressure could be varied at will, as in the apparatus of M.
Tabarie. A series of observations might even be made during
the ascent of a mountain and while care was being taken to
keep the thermometer constantly in [the vapor of] boiling
water during the ascent, in order to avoid as far as possible
movement of the fixed points.

However that may be, the figure I have assumed must be
very near the true one, and the error which could be produced
by it in the coefficient of expansion of air is entirely inappre-
ciable.

My barometric observations were made with a barometer with
a Fortin cistern, which had been carefully compared in a series
of measurements, with that of the Paris Observatory, corrected
for capillary depression, and all my observations were reduced
by calculation to [those of] the Observatory barometer.

After all, a small constant difference in the absolute values
of all the barometric heights would have liad no appreciable
effect upon the coefficient of expansion of air, since it would
have had to do only with the determination of the temperature
of the vapor, and its influence upon the other would be quite
inappreciable.

PAET II.

Upon the Rate of Expansion of certain other Oases.

The old coefficient adopted for the expansion of air being in-
accurate to the extent of ^, it is clear that it cannot be con-
sidered as proved that all gases have the same coefficient of

107

MEMOIRS ON

expansion; new determinations are necessary to decide whether
this law is strictly true or is only approximate.

I have made experiments upon nitrogen, hydrogen, oxide of
carhon [carbon monoxide], carbonic acid, sulphurous acid,
cyanogen, protoxide of nitrogen [nitrous oxide], hydrochloric
acid and ammonia. Most of these determinations were made
by Method II; some however were made by Method IV.

First, I shall describe in a few words how the experiment
was managed when Method II was employed. The bulb being
suspended in the steam vessel and connected with the drying-
apparatus, it was exhausted many times and the. air allowed to
re-enter slowly, in such a way as to dry the bulb thoroughly;
then to the second tubulure of the pump was attached the
apparatus in which the gas was produced. The bulb being
exhausted, as well as the gas-generating apparatus, the tap is
gradually opened so as to allow the gas to enter as fast as it is
formed : the progress of the operation is indicated by a safety
tube placed somewhere in the generating apparatus. When
the bulb was full of gas, it was exhausted, then allowed to be-
come full of gas once more, and so four or five times in succes-
sion. In other respects the experiment was conducted as has
been described [page 84].

In these determinations Bulb VI [page 88] was used, and
two new bulbs, VII and VIII, for which the following data
were obtained :

Bulb VII. Bulb VIII.

p =

4358.15 gr.

4250.70 gr.

p =

67.17

65.10

Hi =

753.62 mm.

752.68 mm.

Ti =

99.76°

99.73'*

Whence 100 6 =

0.002291

0.002385

c —

0.10 mm.

0.10 mm.

I have brought together in a single table the results obtained
by this method with different gases.

108

EXPANSION OF GASES

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109

MEMOIRS ON

I shall add a few words upon the way in which each gas was
prepared.

1. Nitrogen. — This gas was obtained by removing the oxygen
of the air by passing it through a glass tube filled with copper
turnings^ heated to redness. This tube was connected with
the tubulure of the pump. The bulb having been exhausted,
the tap is opened little by little; the air in passing over the hot
copper loses its oxygen and, later, gives up its moisture in the
drying tubes.

2. Oxygen, — I made many experiments upon oxygen gas, but
they yielded figures so various that it was impossible to reach
any decision from them. Mercury cannot be left in contact
with oxygen gas, even for a very short time, without absorbing
a small amount of the gas: its surface soon gives evidence of
mercury oxide and leaves a trail on the glass tube.

The same thing is noticed with mercury which is left in con-
tact with the air, but the change in this case is much slower,
requiring a period of several weeks to become appreciable.

The oxygen was prepared by heating potassium chlorate.'^

3. Hydrogen. — This gas was prepared by treating zinc with
dilute sulphuric acid ; before entering the pump and the dry-
ing apparatus, it was passed through two tubes, a meter long^
filled with pumice stone moistened with a solution of caustic
potash, and a third tube filled with pumice stone moistened
with a solution of silver sulphate. The gas was entirely with-
out odor. The introduction of the two tubes of pumice soaked
in a solution of potash is chiefly to hold back the small quan-
tity of odorous oily vapor which hydrogen gas always takes
with it and which is sufficient to change appreciably the expan-
sibility of the gas. In fact, in one experiment where the
hydrogen gas passed merely through a wash bottle containing
water, I found for its coefficient of expansion the figure 0.3686;

1 The copper turnings were first oxidized by heating in the pres-
ence of air, then reduced by a current of hydrogen gas.

2 Note by Translator : It seems likely that Regnault's oxygen was
not pure — possibly contained chlorine, or oxides of chlorine ; v. Jolly
states that oxygen carefully prepared from potassium chlorate, or elec-
trolytically, is entirely without action on mercury at the temperature of
the experiment.

110

EXPANSION OF GASES

a second determination in which the wash bottle contained pot-
ash-solution, gave the figure 0.3679.

4. Oxide of Carbon. — Prepared by decomposing oxalic acid
in the presence of concentrated sulphuric acid: the gas was
passed through a fiask containing a solution of caustic potash
to absorb the carbonic acid, then through a long tube filled
with pumice stone moistened with potash solution; from this it
passed into the drying apparatus.

5. Carbonic Acid. — Obtained by the decomposition of white
marble with dilute hydrochloric acid. The gas passed through
a wash bottle containing water and thence into the drying
apparatus.

6. Cyanogen, — This gas was prepared through the decompo-
sition by heat of cyanide of mercury contained in a small glass
retort; it passed through a flask provided with a safety tube
and filled with concentrated sulphuric acid, which serves to
regulate the flow of the gas.

7. Protoxide of Nitrogen, — The protoxide of nitrogen was
prepared by decomposing with the aid of heat ammonium
nitrate contained in a retort. The gas, before entering the
drying tubes, passed through a wash bottle containing a sola-
tion of protosulphate of iron [ferrous sulphate].

8. Sulphurous Acid, — This gas was prepared by heating mer-
cury with concentrated sulphuric acid. The gas passed through
a wash bottle containing concentrated sulphuric acid, then the
usual drying apparatus.

9. Hydrochloric Acid Gas, — Obtained by treating sea salt
with concentrated sulphuric acid; it was passed through a
flask containing concentrated sulphuric acid, then through
two tubes full of pumice stone soaked with sulphuric acid.

The experiments upon hydrochloric acid gas present nothing
out of the way. The mercury retained its brilliant surface. I
cannot have entire confidence, however, in the results obtained.
In fact, mercury is apparently not attacked by hydrochloric
acid gas by itself, but it is very quickly [attacked] as soon as
the gas is mixed with oxygen. It is conceivable that a few
thousandths of air, mixed with the hydrochloric acid gas
in the bulb, would serve to bring about a very perceptible

111

1

MEMOIRS ON

absorption of gas and in consequence to interfere with the
expansion.

10. Ammonia Gas. — Prepared by gently heating a concen-
trated aqueous solution of the gas. It passed through a
tube a meter long^ filled with caustic potash broken in small
pieces.

Ammonia gas yielded most various figures. The mercury
seemed to be greatly changed at the surface: it left a trail:
there had evidently been an absorption of gas; but it has been
impossible for me to determine the chemical reaction which
took place.

I found in succession the figures 0.370, 0.371, 0.373, accord-
ing as the gas had remained a longer or shorter time in contact
with the mercury.

It will be seen in the table above that nitrogen, hydrogen,
oxide of carbon have practically the same coefficient of
expansion as air, under the conditions when the determina-
tions were made, that is to say, the gases being under atmos-
pheric pressure when they are at the boiling point of water,
and under a pressure of about 550 millimeters when they are at
the melting point of ice.

Carbonic acid, protoxide of nitrogen and cyanogen, on the
contrary, show under the same circumstances a greater coeffi-
cient of expansion.

Sulphurous acid gas gave figures a little higher than those
obtained for the above gases; but the difference is so small
that one does not know whether it may not be due to the inev-
itable errors of experiment.

I do not discuss hydrochloric acid gas, since I look upon the
numbers obtained for this gas as doubtful.

My experiments therefore seem to show that gases do not
have, under the same conditions, exactly the same coefficient of
expansion. This coefficient varies for the gases I have exam-
ined, and with the conditions under which the determinations
were made, from 0.3665 to 0.3685.

This variation cannot be attributed to the fact that, at the
temperature of melting ice and under a pressure of 0.555 m.,
certain of these gases are close to their point of condensation;
for sulphurous acid is, of all these gases, the easiest to liquefy

112

EXPANSION OF GASES

and yet its coefficient of expansion is smaller than that of car-
bonic acid which at 0® is still removed by more than 90® from
its condensation point.

This modification^ which musfc be made in one of the most
beautiful laws of physics, seemed to me too important for me
not to endeavor to support it by other determinations.

I began by making several experiments with Method IV,
using exactly the same apparatus as had been used for air.

For carbonic acid gas I obtained the following results:

First Half.

1+lOOa

1.36831
1.36857

H

T

t

H'

h'

t'

1

756.52

99.870

13.40

755.47

200.58

13.0*

2

757.54

99.9P

12.90

758.02

202.55

11.7"

Mean ^ 1.36844

Second Half.

H"

t"

H'"

nvn

h'"

t'"

1 lOOo

1

758.47

11.8"

758.80

99.95°

275.67

14.8"

1.36846

2

758.47

11.8"

759.10

99.97"

275.51

14. l**

1.36866

Mean == 1.36856
These determinations give at least nearly the same figure as
that found by Method 11.

An experiment made with protoxide of nitrogen gave :
FiBST Half. ^ ^ . - -

H^ 747.03 mm.

r = 99.52 ®
t = 4.2°

H'== 748.08 mm.
A'= 198.39 mm
i'= 3.6°
1+100 a = 1.36701

Second Half.
H''= 747.72 mm.

r= 3.6°

H'"= 748.49 mm.
r"= 99.57®
/i '==,269.73 mm.
r '= 3.9 °
1+100 a _ 1.36797

Mean = 1.36749

The mean given by the determinations described above and
made by Method II, is 1.36763.

We have seen that Method II gave for the coefficient of expan-
sion of sulphurous acid a figure practically identical with that
found for air. I wished to find out whether this coefficient
would not become larger when working under greater pres-
sures.

An experiment made with sulphurous acid by Method IV,
gave :

113

MEMOIRS ON

FiBST Half. Second Hajlf.

H = 742.08 mm. W — 742.49 mm.

r— 99.33° r= 5.3°

t = 5.6 ° H' = 742.85 mm.

H'= 742.31 mm. r " = 99.36

^'= 196.64 mm. ^'" = 267.64 mm.

«'= 4.5° <"'= 6.6°

1-1-100 a = 1.36689 1 f-100 a = 1.36777

The figure obtained in the first half of the determination is
identical with that found in the experiments made by Method
II, whereas that given by the second half, that is, under
greater pressures, is notably greater.

A second trial was made by subjecting the sulphurous acid to
a little more than atmospheric pressure when the gas was at
0°. The bulb was surrounded with ice and the side tube put
in communication with the apparatus generating sulphurous
acid gas, when the mercury was run out by opening the tap,
so as to let the tube FH become entirely filled with sulphurous
acid gas. The tube^ was then sealed with a lamp. Mercury
was poured into the tube 0, so as to bring the level to a in the
tube FH, A difference of level h is then noted between
the two menisci. The ice was removed and the bulb raised to
the boiling point of water, as in the ordinary determinations.
We thus have :

B 743.59 mm.

t 5.6°^

h 28.69 mm.

H 743.92 mm.

T' 99.40°

h' 308.22 mm.

t 6.1°

l+lOOo 1.36907

Finally, a third determination was made subjecting the gas
to a much higher pressure still. For this the tube FH was
replaced by another, the lower part of which had a much
greater volume. This tube is shown in Fig, 15 [page 101].

Working exactly as in the second determination, we find :

114

EXPANSION OF GASES

fl""— 764.77 mm.

H' = 764.64 mm.

t— 5.9®

T — 100.17

h ~ 136.29 mm.

h' — 469.71 mm.

t'— 7.00®

* —.00836

whence

l+lOOa — 1.37413.

Thus for sulphurous acid the results are :

le gas at 0° under

At 100® under

a pressure of

a pressure of

545.67 mm.

742.08 mm.

1.36689

742.49

1010.49

1.36777

772.28

1052.14

1.36907

901.06

1234.35

1.37413

The coefficient of expansion of sulphurous acid therefore
increases in a very marked way in proportion as the pressure to
which the gas is subjected becomes greater. It is probable that
the same thing takes place in all compound gases for which the
law of volumes does not rigorously hold or which do not exactly
follow Mariotte's Law.

A similar variation is to be noticed in carbonic acid gas,
although in a much less decided way. We have seen that
Method IV, applied to this gas, gave :

Pressure at 0®

At 100®

554.89 mm.

756.52 mm.

1.36831

555.47

757.54

1.36857

758.47

1034.47

1.36846

759.10

1034.61

1.36866

The difference is not noteworthy. But an experiment made
with the modified apparatus which I have described, gave :

£r= 766.32 mm.

H^ = 766.14 mm.

t = 6.4®

T' = 100.23 ®

h = 134.77 mm.

AA

V = 6.4®

h' = 464.23 mm.

V

V

=

0.00336.

1 + lOC

)a

-s

1.36943.

115

MEMOIRS ON

Thaa, at 0° under a pressure of 901,09 mm. aud at 100°
nnder a pressure of 1230.37, the coefficient of expansion of car-
bonic acid gaa is distinctlj higher.

I have constructed an apparatus by means of which one may
at once detect unequal expansion in gases and wliich may serve
to measure this difference with accuracy. Tliia apparatus,
which is a kind of differential thermometer, consists of two
bulbs of equal capacity, complete with capillary tubes and
arranged exactly like the bulb of Method IV (Fig. 13), [page
96]. Each of these bulbs connects with a tube similar to the
tube FH of Figs. 13 and 14, cemented into a three-way tube
of iron provided with a tap, Fig. 16. The third branch, in the
middle, holds a piece of barometer tubing. The
two tubes FGR and F'G'H' were cut from the
same accurately cylindrical piece of tubing and
have exactly the same shape ; they are fixed as
alike as possible in the tubulures. One of the
bulbs is filled with dry air and the other with the
gas whose expansibility it is desired to compare
with that of air. Moreover, the bulbs are fast-
ened in the same tin vessel.

The bulbs being surrounded with melting ice,
and the mercury having been adjnsted to the
level of a mark scratched on one of the tubes,
the two Bide tubes op are closed with a lamp.
The mercury is then of necessity at the same level
in the two tubes FQH&nA F'O'H' and in the up-
right tube between them. The ice having been
removed and water put in the tin vessel, the
latter is brought to boiling while mercury is
poured into the intermediate tnbe to keep the
Via. its. level at the same point in the tube FGH. If
the two gases have the same coefficient of expansion, the two
menisci in the tubes FQS and F'G'H' will be at the same
level ; there will be a difference of level, on the other hand, if
the [rates of] expansion are unequal.

It would be very difficult to find two bulbs of exactly the
same capacity when they are sealed to their capillary tubes,
116

\

EXPANSION OF GASES

and also so to arrange the tubes FGH Q.nd F'O'H' that the vol-
ume of air contained in the upper part of these tubes should be
exactly equal when the mercury is at the same level and
adjusted to the mark made on one of them. Yet this is not

necessary ; it will, in fact, serve if the ratio -y^- is the same for

the two pieces of apparatus. It will do, indeed, for this to
take two bulbs of nearly the same volume and gauge them
carefully by means of distilled water, after they have been
attached to their capillary tubes. In the same way the tiny
volume in the part Fa of the tube FGH as far as the mark a,
is measured by means.of mercury; on the other tube F'G'H' are
made two marks, a' and a", and the volume up to of and that
between the two marks a and a", are calibrated by means of
mercury.

This done, we know the ratio ^ for the first bulb, and the
volume F' of the second bulb; then v' must be equal to

-^ P. It is easy to find the point on the tube G' H' which

corresponds to this volume v' ; its distance d from the mark a'
is then calculated.

The tube FGH being cemented in its tubulure and the
apparatus fastened to its vertical support, the tube FG'H' is
fixed in the place where it belongs. For this purpose, the level
of the mark a upon the tube FGHh found with the cathetom-
eter, and the glass is then turned towards the tube F'G'W.
If the latter tube is in the proper position, the crossing of the
threads of the glass should be aiming at the point which cor-
responds to the volume v^; consequently the mark af should be
at a distance d above or below ; by means of the instrument we
find whether this is in fact the case, that is, the glass is raised
or lowered by an amount d, and the tube F'G'H' is adjusted so
that the mark a' is hidden by the horizontal thread of the glass
in its new position ; then the tube is fastened in place with
mastic.

To make sure that the differential apparatus is properly
adjusted, an experiment is made, filling both bulbs with dry
air. The two side tubes op are closed when the bulbs are in
melting ice and the mercury has been brought to the level of a

117

MEMOIRS ON

in the tube FOH, The three columns of mercury are then at
the same level. Water is then put in the boiler and the level
of the mercury is kept at a; the mercury must be at exactly the
same height in PO'W if the apparatus is properly put together.

The results reached by this method are rendered still more
certain by performing a second experiment in which the gas
whose expansibility we wish to determine, is introduced into
the bulb which has hitherto held the air, while, on the other
hand, atmospheric air is put in the bulb which in the former
experiment contained the gas.

The equation which gives the expansibility of the gas in the
case of this apparatus is clearly

1 + a r =

{H"'-\-h!") (l + cJ r)

the symbols having the same meaning as on page 100.

If we differentiate with respect to a and 7^'", bearing in mind

» 1
that the factor ^ ^^ (Zr'" + A*" — ZT') is very small and may

be supposed contant and equal to ^, we have

\ (l4-(5r) dK

. . __ m

we can then write it simply

A « ^ h'"

a a=s .

That is, the difference in the coefficients of expansion of the
two gases is equal to the difference in the levels of the columns
of mercury in the two tubes FGHAud F'G'H, divided by the
barometric height at the time the two tubes were sealed when
the bulbs were in melting ice.

This result is not however altogether accurate, since we have

taken no account of the variation of the ratio -^ — which is

not the same at 100° as at 0® — for the gas which does not
expand at the same rate as air. But when the difference in the
ratio of expansion is very slight, the error introduced by this
omission is practically inappreciable. On the other hand, it is
easy to take it into account.

118

EXPANSION OF GASES

A test determination made by this method with carbonic acid
gas and atmospheric air^ gave

A h''' = 1.48 mm., H" = 757.20;
hence

1.48 mm. ^ ^^^ , , ^,
A a — ^^^^ = 0.002 (about);

that is^ the coefficient of expansion of carbonic acid gas is 0.002
higher than that of air — which gives 0.3685; and this, in fact,
is the figure which we found above [page 113J.

To prove the accuracy of the differential apparatus, I filled
both bulbs with dry air; I then found

A h"' = 0.08 mm.

This difference is probably due to the fact that the tubes
were not quite perfectly adjusted, but it is entirely inappreci-
able.

119

EXPANSION OF GASES

Biographical Sketch.

Henri Victor Regnault was born at Aix la Chapelle in the
year 1810, July 21. He was educated at the ficole Polytech-
nique and the ifecole des Mines. He became Gay-Lnssac's suc-
cessor as Professor of Chemistry in the former institution in
1840, and, the next year, Professor of Physics in the College de
France. Up to this time his researches were confined to
organic chemistry: an important paper on the ethers appeared
in 1835. From 1847 to 1854 he was Chief Engineer of Mines,
and subsequently became director of the famous porcelain
works at Sevres. From 1841, for over twenty years, he published
the results of research after research upon the physical con-
stants of gases, of liquids and of solids. In this extraordinary
series are to be foun4 investigations of the compressibility of
gases, liquids and solids; of their densities, and rates of expan-
sion; of the tension of vapors; of calorimetrical methods; of
the latent heat of substances; of their specific heat, etc., etc.
In addition, may be mentioned contributions to the mechanical
theory of heat and study of the velocity of sound. All the
records of his latest work were, to his great sorrow and to
the loss of the scientific world, destroyed during the Franco-
Prussian War. His scientific labors ended in 1872, but he
lived until Jan. 19, 1878. Regnault's great reputation rests
upon his extraordinary skill in devising and using apparatus.
It may be said that in whatever direction his researches led
him, he invariably succeeded in discovering sources of error in
the work of his predecessors and in eliminating it, at least in
large measure, from his own results.

120

EXPANSION OP GASES

only point to the fact that Mariotte's Law is not rigorously
true.

This objection does not seem to me to be justified^ for sev-
eral reasons. As a matter of fact Dulong and Arago did not in
their brilliant research discover any constant variation even at
pressures as high as 27 atmospheres, which in any case shows
that, between the limits of pressure of 1 and 27 atmospheres,
Mariotte's Law is practically exact ; hence we may conclude
that it would be rigorously accurate for differences of pressure
as small as those observed in our researches on any given gas,
at 0® and at 100°. It is clear that, were there a variation
which such small differences of pressure could render evident
in measurements of the rate of expansion, this variation would
certainly be revealed in a very marked degree by the great dif-
ferences of pressure in determinations made with as much care
as those of the distinguished physicists I have named.

I should state, too, that my experiments were carried out
under precisely those conditions which would be most favor-
able for exactness in Mariotte's Law, since it is the gas heated
to the temperature of 100° — consequently, at the very time
when it is farthest removed from its condensation point — ^that
it is subjected to the greatest pressure.

Finally, it should be noted that, in the parallel determina-
tions made upon the compressibility of different gases under
one and the same pressure, it was shown that the gases which
do not follow Mariotte's Law show a greater diminution of
volume than should take place according to the Law. There-
fore in my experiments, neglecting the changes occurring in the
molecular forces on account of the difference in temperature,
the volume of the gas at 100° ought to be smaller than what
exactly accords with Mariotte's Law ; so that the variation in
Mariotte's Law would tend to diminish the coeflBcient of expan-
sion with [increase of] the pressure, instead of increasing it as
we have found in our experiments.

After all, to avoid leaving any doubt upon this important
point in the dynamical theory of gases, I made a new series of
determinations by a method in which the increase in the vol-
ume of the gas is measured directly, while it remains under
practically the same pressure at 0° and at 100°. This method

J 137

MEMOIRS ON

is clearly the only one that can be used with gases which do
not follow Mariotte'a Law lor alight changes of pressure.

I shall describe briefly the apparatus I have used in these
determinations and which is based upon the same principle as
tiiat used by M. Pouillet in his air pyrometer. It is shown in
Mg.3.

A glass bulb sealed to a capillary tube is placed in a tin-plato
vessel MIf {Fig. 13, Volume IV) [page 96]. The tube is
cemented into the little three-way tube mno. In the side-
tubulure is cemented a short straight piece of capillary tub-
ing, or else a tube of the shape of abed, Fig. 1, Volume V [page
128], and containing some pellets of gum mastic, — according as
we must work under pressures lower or higher than that of the
atmosphere. Into the third tubiihire n is cemented the bent
capillary tube £'i^ connect] ng with the tube FH in which the
increase of volume of the air is measured. The latter is bo
chosen that the quantity of air which fills it to a when the bulb
138

EXPANSION OF GASES

is in melting ice, occupies, when the bulb is in [the vapor of]
boiling water, most of the space down to a mark ^ made upon
the narrower tube below. The tube FH is cemented with
mastic into the tubulure A of an iron support provided with
taps. Into the second tubulure B is cemented a glass tube BI,
a meter long in experiments made under atmospheric pressure.
This tube was replaced by one of 3 meters^ length when work-
ing with greater pressures.

The iron support lias two taps R and R\ The first tap R is
traversed by a single hole and serves to draw off a part of the
mercury contained in the apparatus. The second tap R'
is bored with two holes at right angles to each other, and
serves to connect the tube FH, according to the position given
it, with the barometric tube BI, or directly with the outside.
This arrangement is clearly seen in Fig^ 4 [page 138], which
represents a vertical section of the support and the two posi-
tions (a) and {h) of the tap R\ This support is fastened to a
cast tripod provided with levelling screws, upon which is fitted
a glass jacket filled with water for keeping the expansion reser-
voir at a known temperature. This jacket consists of a rect-
angular box two of whose opposite sides are made of glass.

The experiment is then made as follows :

The bulb being surrounded with melting ice, the tube op open
and connected with the apparatus which was used before to dry
the air, mercury is poured into the tube 5/until it reaches the
level of fl. The tap R being in position (a), the mercury of
course rises to the same level in the two communicating tubes.
The tube op is closed by means of a lamp, [the height of] the
barometer is recorded, as is also the temperature of the water
in the jacket, which has been carefully stirred from time to
time by means of the stirrer jf'^^' which is moved up and down
in a vertical plane so as to make it pass through all strata of
the liquid.

After removing the ice, the water in the vessel M is brought
to boiling. To keep the two columns of mercury at about the
same point, it becomes necessary to draw off mercury by open-
ing the tap R, A part of the air in the bulb thus passes into
the tube FH\ the two columns are brought approximately to
the same level ^, and the difference of height is determined

139

MEMOIRS ON

accurately by means of the oathetometer; ^ at the saxne time the
[height of the] barometer and the temperature of the jacket
are recorded. The water filling the jacket was continuously
stirred for at least a quarter of an hour before beginning the
observations, to give it a uniform temperature which would at
the same time be that of the air enclosed in the tube FH.

To be able from this experiment to calculate the coeflBcient
of expansion of air, we must know the capacity of the bulb, the
volume V from ^ to « of the air in the tube ^^ when the bulb
is in melting ice, and the volume v' from E io $ which is filled
by air when the bulb is in [the vapor of] boiling water. The
first is easily found by filling the bulb with mercury at 0^,
after having made it boil for a while in the apparatus, (See
volume IV, page 22 [page 82].)

The two volumes v and v' are determined in the following
way:

The drawn-out end of the tube op is broken off to allow com*
munication between the interior and the outside air,^ and mer-
cury is poured into the tube 5/ until this liquid entirely fills
the tube FH 9,^ far as 7 on the capillary tube. The tap R is
turned into the position (b). There is then no connection
between the tubes i^i^ and BI, but the mercury from FH flows
out by the opening 0\ This mercury is caught in a flask.
Mercury is allowed to run out until the meniscus comes exactly

i There was dan^r lest the jacket full of water would give rise, on
accouDt of refraotion, to deviations of the rays which come from the
menisci : a very simple test showed me there was no appreciable devia-
tion, at any rate in the places where the readings were made. The tub©
op being open, the mercury meniscus was adjusted at points all along
the tube FH in succession. It was seen, with the aid of the glass of the
cathetometer, that in all these positions the menisci were at the same
level in the two tubes FH and BL

a To prevent the entrance of moist air into the apparatus, care is
taken first to connect the tube op with the drying apparatus by means
of a rubber tube. In many experiments, chiefly those made upon gases
other than atmospheric air, the point of the tube op is not broken off.
The bulb being in the [vapor of] boiling water, mercury is poured into
the tube BI so that the liquid rises into the capillary part EF of the
tube FH\ the volumes v and v' are then calibrated as usuaL

140

EXPANSION OF GASES

to the position At a that it had in the first part of the experi-
ment: this is done with great precision with the aid of the glass
of the cathetometer.^ The mercury which has flowed out is
weighed^ aud from this the volume v is calculated.

The mercury is then run out until the meniscus coincides
with p. The weight* of mercury drawn off, added to that which
gave the volume v, will give us the volume u\ It is clear there
is a correction to be made on account of the temperature; if p
and J!?' represent the weights of mercury drawn off and i the
temperature of the water of the jacket at the time of the cali-
bration, the weights of mercury at 0° which will occupy the
volumes i; and t;', and which, consequently, actually represent

these volumes, are^ (1 + ^) and^' (1 + -^).

It is necessary to add to these volumes v and v the small
volume of the capillary tubing outside the vessel in which the
water is boiling. This volume was determined by a preliminary
calibration. On the other hand, since the temperature of the
air contained in these tubes is somewhat uncertain, it is desir-
able that this volume should be extremely small. In my appa-
ratus it never exceeded ^j^^^ of the capacity of the bulb.

In order to adapt the same apparatus for measuring the rate
of expansion of air under high pressures, the lateral tube op is
replaced by the twice-bent tube abed of Fig. 1 [page 128], and
dry air is forced into the bulb, while mercury is poured into the
tube BL When the desired pressure has been got in the bulb,
the gum mastic in the tube abed is melted so as to close the
apparatus hermetically ; the bulb is surrounded with melting
ice and the meniscus is adjusted to the mark a with the aid of
a cathetometer. The meniscus in the tube BI is brought in
line with a second cathetometer. In these measurements the
precautions noted on page 59 [page 129] are followed closely.

After removing the ice, the water in the vessel is raised to
boiling, and mercury is drawn off so as to make the level coin-
cide with P.

The height of the raised column of mercury is measured ; it

\ The flow of the mercury is made as slow as may be desired by turn-
ing the tap to the proper extent: it is easy to adjust the meniscus in
this way within about ^ of a millimeter.

141

MEMOIBS ON

•

is practically the same as that of the first part of the determi-
natiou.

If -ff and H' represent the barometric heights at the time of
the readings for [the temperatures of] melting ice and boiling
water, and A and h' the differences of level of the menisci in
the tubes of the apparatus, we evidently have the equation

hence

l+«r —

(ff+A)+ ^-^-^-^ «' ^'

The quantity a enters into the denominator of the second
member ; but as it affects the result only slightly, we make use
of the method of successive approximations, that is, an
approximate value is given a, from this the value of a in the
first member is calculated and this is then substituted in
the second member and yields the final value of 1 + aT,

In this method the greatest care must be exercised in the
determination of the volumes F, v and v, and, even more, in
the determination of the temperature t\ There is, finally,
another very important matter — the perfect drying of the tube
FH, This tube has a large capacity and, on account of the
arrangement of the apparatus, cannot be heated while it is
exhausted. In my experiments this tube was thoroughly dried
at a high temperature before being cemented into itstubulure,
and, when the apparatus was completely set up, a little mercury
was poured into the communicating tubes; the tap R was
turned to a position intermediate between (a) and (b), and the
apparatus exhausted, tlie bulb being surrounded by the vapor
of boiling water. By exhausting a great many times and then
allowing dry air to enter slowly, the moisture should not only
be completely removed from the bulb but also from the tube in
which the expansion is measured.

The table below contains the results obtained in the experi-
ments made by this method, at atmospheric pressure, upon air,
hydrogen, carbonic acid gas, protoxide of nitrogen, oxide of
carbon, sulphurous acid gas, and cyanogen.

The second part of the table contains [the results of] experi-

14?

EXPANSION OF GASES

I

+

ments made upon atmospheric air, hydrogen, and carbonic acid
gas under higher pressures.

SCO 95 '«* 00 01 o

£35 OS 1-^ iH •Tf 1-^

o 9 s CO 2

00 00 CO eo 03 v3

8iS

«o

i^ t- 5r & «^ -

CO 90 00 00 00 CO

O 00 ^

IS

ss

• •••••••••••••■ •■••••«

h«OQ0COa»Tf^0i9{QiHi-ii-liH0S«4*KCOQ0'^*Q-^

** l«» fr- t— c«- I- c- C» c- c- t- t- l>- t- f- t- f- W l>- t- l^ t-

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143

MEMOIES ON

Atmospheric air gives figures a little higher than the mean
of earlier determinations; yet the difference is inappreciable; it
may be attributed also to the fact that air does not conform
rigorously to Mariotte^s Law.

My earlier determinations gave for hydrogen the same
coefficient of expansion as for air. The new experiments
assign to hydrogen a coefficient slightly lower than that of air.
Hr. Magnus has already reached a similar result (Annales de
Chimie et de Physique, volume IV, page 334), but the differ-
ences are so small that it is difficult to decide the question; they
are within the limits of tiie errors of observation. As a matter
of fact, there are in Magnus' determinations with air many
figures which are still lower than those he has found for hydro-
gen; so that the question does not seem to me settled. It will
be seen later that the experiments made upon the rate of
expansion under higher pressures decide the matter in a very
clear way.

The hydrogen was prepared from very pure zinc; it was
passed through a wash bottle containing water, two tubes a
meter long full of pumice-stone soaked with a concentrated
solution of potash, a tube of equal length full of pumice stone
soaked with a solution of silver sulphate. Beyond the air
pump it traversed two tubes a meter long full of pumice stone
soaked with concentrated sulphuric acid, and a tube filled with
small bits of caustic potash. The latter was to hold back the
small quantity of sulphurous acid gas which might be formed
through the interaction of the hydrogen gas and the sulphuric
acid. This precaution had been neglected in the determina-
tions of the first memoir, yet I have never perceived any odor
from the presence of sulphurous acid in any of these experi-
ments.

Oxide of carbon gave the same figure as in the earlier
researches (volume IV, page 52 [page 109] ).

The coefficients of expansion of carbonic acid gas and pro-
toxide of nitrogen determined by this method are higher than
those obtained by the earlier methods (volume IV, pages 52, 56
and 57 [pages ]I09, 113, 115] ); this is unquestionably due to the
fact that these gases do not exactly conform to Mariotte's Law,
and that their volumes at 100°, under a pressure higher than

144

EXPANSION OP GASES

that to which they are subjected at this temperature in the
earlier methods, are smaller than they ought to be according
to this Law. We must expect to find similar results with all
gases more compressible than air.

The coefficients of expansion of sulphurous acid [gas] and
cyanogen are much higher than those of other gases. My
earlier researches (volume IV, pages 52 and 57 [pages 109 and
114] ) had, on the other hand, assigned them figures very little
higher than the /coefficient of expansion of atmospheric air.
The variations may be attributed to the fact that, sulphurous
[acid] gas and cyanogen being much more compressible than
air, their volume at 100°, calculated from the change of ten-
sion, is much too low and, consequently, gives too small a
coefficient of expansion. In an endeavor to verify this sup-
position by means of direct experiments, and after many trials,
I found that there had been a serious error in my former
determinations of sulphurous acid [gas] and cyanogen.

I have always had to face the difficulty of drying sulphurous
acid gas completely, the presence of a trace of moisture being
able, in the case of this very soluble gas, to cause much greater
variations than in other gases. My earliest experiments had
given for sulphurous acid [gas] figures much higher than those
to which I was led in my former research; but I discovered that
these figures became lower in proportion as the gas was more
slowly admitted into the bulb, — which I most naturally attrib-
uted to more perfect drying, — and it was only by having the
gas enter extremely slowly, compelling it to remain for a long
time in the tubes full of pumice stone soaked with concen-
trated sulphuric acid before introducing it into the bulb, that
I succeeded in securing constant figures. Working in this
Way, a source of error is introduced which then escaped me;
some dry air evidently entered the bulb along with the sulphur-
ous acid gas. The proportion of this air was greater, the
slower the introduction of the sulphurous acid gas. Now the
presence of a small amount of air is sufficient to lower appreci-
ably the coefficient of expansion of sulphurous acid [gas], since
the latter gas expands under these circumstances as if it were
under a very low pressure, and the coefficient of expansion of
sulphurous acid [gas] falls very rapidly with the pressure.

145

MEMOIES ON

I thought at that time that the entrance of air must be dne
to the fact that the apparatus (perhaps the taps of the pump
tlirough the action of the acid gas) had not remained gas-tight
during the long time the gas was making its way in. I am not
prepared to assert this was not the Case^ yet I can say that the
apparatus was always tested with great care each time before
commencing a series of experiments with any particular
gas.

Yet there is another source of error against which I was not
sufficiently on my guard in my earlier experiments. It lay in
the great difficulty met with in freeing the pumice stone and
sulphuric acid from air mechanically held or absorbed; thus, I
found, in the experiment§ with sulphurous acid [gas], that
after the apparatus had been exhausted three or four times in
succession, at least to 1 or 2 centimeters, and sulphurous acid
gas had been introduced each time, the gas in the bulb still
showed on testing an appreciable amount of air mixed in. In
the ordinary determinations with gases other than atmospheric
air, I was accustomed to exhaust at least ten or twelve times;
in the experiments with sulphurous acid gas I contented myself
with only three or four times, because of the very long time
required for each filling. In the experiments with cyanogen,
only two exhaustions were made, on account of the difficulty of
preparing a considerable quantity of this gas in a pure state.

Sulphurous acid gas in the recent determinations was pre-
pared by the action of mercury upon sulphuric acid; the gas
passed through a long inclined XT-tube full of concentrated sul-
phuric acid which the bubbles traversed very slowly; from this
it made its way to the bulb through a tube connecting with the
small air pump. This arrangement permitted the exhaustion,
not only of the receiving bulb, but also of the generating appa-
ratus. Besides, it was easy to prove, by means of the com-
municating tubes ^^and BI, that the apparatus was perfectly
gas tight.

The bulb had in this way been filled with perfectly pure sul-
phurous acid gas. I satisfied myself after the determinations
were over, by breaking off the tip of the tube op under mer-
cury and driving out part of the gas by pouring mercury into

146

EXPANSION OF GASES

the tube BL The gas was completely absorbed by a solution of
potash. 1

A similar arrangement was used in the work on cyanogen.
This gas was prepared by decomposing cyanide of mercury with
the aid of heat; it passed through a long column of concen-
trated sulphuric acid.

If we adopt the figures found for the coefficients of expansion
of the various gases by this last method, which is the only one
capable of giving comparable results when we wish to know the
rates of expansion of gases which do not follow Mariotte's Law,
it is apparent that the various gases show very different co-
efficients of expansion. We have found, as a matter of fact, for
these coefficients:

Hydrogen 0.36613

Atmospheric Air 0.36706

Oxide of Carbon 0.36688

Carbonic Acid Gas ^ 0.37099

Protoxide of Nitrogen 0.37195

Cyanogen 0.38767

Sulphurous Acid Gas 0.39028

I have already shown above that the coefficients of expansion
of carbonic acid gas and protoxide of nitrogen were higher
when determined by the last method than when calculated from
the clianges in tension. The variations are much greater for
the very compressible gases, such as cyanogen and sulphurous
acid gas, as may be understood from the following results,
which have been reached in the same series of determinations
as the figures given in the table above. As a matter of fact, in
order to obtain, with the apparatus of Fig, 3 [page 138], the
variations of tension in the gas occupying a constant volume,
when it is carried from the temperature of melting ice to that
of boiling water, it is only necessary to keep the level of the
mercury at a in the tube FH while the bulb is in [the vapor of]
boiling water, and to measure the difference of level between a

y It remains to be decided whether sulphurous acid gas is completely
dried by concentrated sulphuric acid, and whether it did not carry with
it a minute quantity of the latter acid. This point seemed to be hard
to decide by direct experiment; the coeflScient of expansion of the gas
is perhaps appreciably changed by the presence of an infinitesimal
quantity of [water] vapor.

147

MEMOIRS ON

and the meniscus of the mercury pushed up iu the tube BL
These determinations were made, in fact, in the three experi-
ments upon gaseous sulphurous acid and in the two experiments
upon cyanogen. With the values for U, t, h, v, and H-^h of
the table above [page 143] it is only necessary to combine the
following:

Sulphurous Acid Gas Cyanogen

I II III I II

H'..,. . .759.31 mm. 760.71 mm. 762.13 mm. 763.07 mm. 764.07 mm.

r 99.98° 100.03° IOO.O80 100.12° 100.15°

V 19.29° 19.88° 18.420 20.94° 19.16°

h' 288.62 mm. 286. 19 mm. 284.30 mm. 289.23 mm. 287.62 mm.

H' + ^'.1047.93 mm. 1046.90 mm. 1046.43 mm. 1052.80 mm. 1051.69 mm.

V 21.44 gr. 25.79^1'. 28.20 gr. 22.80 gr. 25.62gr.

1 + 100 a. 1.38439 1.38451 1.38470 1.38282 1.38298

Thus, we have found:

For Sulphurous Acid Gas:

By direct measurement of expansion. By calculation, from the change

of tension.

0.39094 0.38439

0.38987 0.38451

0.39004 0.38470

Mean 0.39028 0.38453^

For Cyanogen:

0.38766 , 0.38282

0.38768 0.38298

Mean 0.3876 7 0.38290

I have stated above that the coefficient of expansion of sul-
phurous acid gas rises quite rapidly with the pressure; this may
be observed in the following experiment, begun by filling the
bulb, while cooled with ice, and the expansion-tube FH down to
P, with sulphurous acid gas. The tube op was then sealed
with the lamp and, by pouring mercury into the tube BI, the
gas contained in the tube FHwsls forced back into the bulb.

1 This figure differs little from the mean assumed by Hr. Magnus, but
from three determinations which gave too divergent figures, viz.,
0.3897; 0.3839; 0.3832.

148

EXPANSION OP GASES

In other respects the determination is carried out as has
been described in volume IV, page 43 [page 99] ; we hare :

E = T61.33 mm. H' = 761.08 mm.

t = 18.83° r —100.04°

h •«■ 221.40 mm. r — 19. 10 °

V = 25.36 gr. ^'— 226-56 mm.

^-f. A — 082.73 mm. H' + A' «• 087.64 mm.

v' = 1780.44 gr.
1+. 00 a =1.39804.

Thus, for a change in pressure as slight as that from 760 mm.
to 980 mm., the coefficient of expansion of sulphurous acid
[gas] haa changed from 0.3902 to 0.3980, and the gas under
the pressure of 980 mm. is not even at 0® near its point of con-
densation.

It is likely, judging from this, that vapors have coefficients
of expansion very different from that of air at points slightly
removed from their points of condensation — consequently,
under the conditions where we usually meet them in our exper-
iments for determining their densities.

Let us now turn to the second part of the table [page 143]
which contains determinations made under a pressure of
2530 mm. (about 3.33 atmos.) with three gases, atmospheric air,
hydrogen, and carbonic acid gas. The very striking fact is
there apparent that hydrogen has maintained practically the
same coefficient of expansion as under atmospheric pressure ;
whereas air, and, above all, carbonic acid gas show a very
marked increase in their coefficients.

The variation in rates of expansion of atmospheric air and
carbonic acid gas is far more noteworthy in those experiments
where the pressure is the same at 0° and at 100°, than in those
where the rates of expansion were calculated from the change
of tension.

At the same time it is clear that in proportion as the pres-
sure under which the gases are studied is greater, so much the
more marked become the variations among their coefficients of
expansion. Hydrogen and atmospheric air, which have prac-
tically the same rate of expansion under ordinary barometric
pressure, show very marked differences when they are subjected
to pressures three or four times as great.

149

MEMOIRS ON EXPANSION OP GASES

Conclusions.

To sum up, my determinations do not confirm the two fun-
damental laws of the theory of gases, assumed up to the present
by all pliysicists to be exact, viz, : —

I. All gases expand to the same extent between the same
limits of temperature.

II, The rate of expansion of a given gas, between the same
limits of temperature, is independent of its original density.

Must these laws be banished from science for the future ? I
do not think so. I believe that these laws, along with all those
which have been discovered for gases, such as the Law of Vol-
umes, etc., are true at the limit, that is, that they come nearer
to conforming with the results of observation in proportion as
we use the gas in a more expanded condition.

These laws hold good for a perfect gaseous state, which the
gases that nature places before us, more or less approach, ac-
cording to their chemical characteristics ; according to the
temperature at which we study them and which may be, for
each in turn, more or less removed from the point where
change of state takes place ; finally and chiefly, according to
their condition of less or greater compression.

160

KESEAECHES upon the GAS THERMOMETER,

AND THE Comparison of the Gas Thermometer

WITH the Mercury Thermometer.

By p. Chappuis.

{Abstract)

Travaux et Mmnoires du Bureau International des Poidset
Mesures, volume 6 (1888); Archives des Sciences (Geneve), vol-
ume 20, pages 5—36, 153—179, 248—262 (1888).

151

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